LMFDB - Embedded newform 98.2.g.b.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,2,Mod(9,98)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("98.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	98.g (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.2
Character	$\chi$	$=$	98.53
Dual form			98.2.g.b.37.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.826239 + 0.563320i) q^{2} +(0.0584109 + 0.0541974i) q^{3} +(0.365341 + 0.930874i) q^{4} +(-0.427005 + 0.131714i) q^{5} +(0.0177309 + 0.0776840i) q^{6} +(1.60505 + 2.10329i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.223716 - 2.98528i) q^{9} +O(q^{10})$	\(q+(0.826239 + 0.563320i) q^{2} +(0.0584109 + 0.0541974i) q^{3} +(0.365341 + 0.930874i) q^{4} +(-0.427005 + 0.131714i) q^{5} +(0.0177309 + 0.0776840i) q^{6} +(1.60505 + 2.10329i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.223716 - 2.98528i) q^{9} +(-0.427005 - 0.131714i) q^{10} +(0.349720 - 4.66669i) q^{11} +(-0.0291110 + 0.0741737i) q^{12} +(-6.27294 + 3.02089i) q^{13} +(0.141332 + 2.64197i) q^{14} +(-0.0320803 - 0.0154490i) q^{15} +(-0.733052 + 0.680173i) q^{16} +(1.31740 - 0.198566i) q^{17} +(1.49683 - 2.59258i) q^{18} +(-2.50434 - 4.33764i) q^{19} +(-0.278611 - 0.349367i) q^{20} +(-0.0202401 + 0.209844i) q^{21} +(2.91779 - 3.65879i) q^{22} +(3.25634 + 0.490814i) q^{23} +(-0.0658362 + 0.0448864i) q^{24} +(-3.96621 + 2.70412i) q^{25} +(-6.88467 - 1.03770i) q^{26} +(0.297769 - 0.373391i) q^{27} +(-1.37150 + 2.26252i) q^{28} +(3.44313 + 4.31754i) q^{29} +(-0.0178032 - 0.0308361i) q^{30} +(2.08698 - 3.61476i) q^{31} +(-0.988831 + 0.149042i) q^{32} +(0.273350 - 0.253632i) q^{33} +(1.20034 + 0.578055i) q^{34} +(-0.962396 - 0.686706i) q^{35} +(2.69719 - 1.29890i) q^{36} +(0.654285 - 1.66709i) q^{37} +(0.374299 - 4.99467i) q^{38} +(-0.530133 - 0.163524i) q^{39} +(-0.0333937 - 0.445608i) q^{40} +(-1.12713 + 4.93827i) q^{41} +(-0.134933 + 0.161980i) q^{42} +(1.75596 + 7.69334i) q^{43} +(4.47187 - 1.37939i) q^{44} +(0.488730 + 1.24526i) q^{45} +(2.41403 + 2.23989i) q^{46} +(4.41364 + 3.00917i) q^{47} -0.0796818 q^{48} +(-1.84762 + 6.75176i) q^{49} -4.80032 q^{50} +(0.0877122 + 0.0598012i) q^{51} +(-5.10383 - 4.73566i) q^{52} +(-3.28856 - 8.37913i) q^{53} +(0.456367 - 0.140771i) q^{54} +(0.465334 + 2.03876i) q^{55} +(-2.40771 + 1.09678i) q^{56} +(0.0888082 - 0.389094i) q^{57} +(0.412686 + 5.50691i) q^{58} +(9.60843 + 2.96381i) q^{59} +(0.00266087 - 0.0355069i) q^{60} +(-2.27134 + 5.78727i) q^{61} +(3.76061 - 1.81101i) q^{62} +(5.91982 - 5.26207i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(2.28068 - 2.11617i) q^{65} +(0.368728 - 0.0555768i) q^{66} +(-0.329108 + 0.570033i) q^{67} +(0.666140 + 1.15379i) q^{68} +(0.163605 + 0.205154i) q^{69} +(-0.408333 - 1.10952i) q^{70} +(0.158558 - 0.198826i) q^{71} +(2.96021 + 0.446181i) q^{72} +(-3.38108 + 2.30518i) q^{73} +(1.47970 - 1.00884i) q^{74} +(-0.378226 - 0.0570084i) q^{75} +(3.12286 - 3.91594i) q^{76} +(10.3767 - 6.75471i) q^{77} +(-0.345900 - 0.433744i) q^{78} +(-0.928280 - 1.60783i) q^{79} +(0.223429 - 0.386990i) q^{80} +(-8.84301 + 1.33287i) q^{81} +(-3.71310 + 3.44525i) q^{82} +(-14.1140 - 6.79694i) q^{83} +(-0.202733 + 0.0578238i) q^{84} +(-0.536382 + 0.258308i) q^{85} +(-2.88298 + 7.34570i) q^{86} +(-0.0328835 + 0.438800i) q^{87} +(4.47187 + 1.37939i) q^{88} +(-0.616956 - 8.23271i) q^{89} +(-0.297674 + 1.30420i) q^{90} +(-16.4222 - 8.34511i) q^{91} +(0.732787 + 3.21055i) q^{92} +(0.317813 - 0.0980323i) q^{93} +(1.95160 + 4.97259i) q^{94} +(1.64069 + 1.52234i) q^{95} +(-0.0658362 - 0.0448864i) q^{96} +16.8099 q^{97} +(-5.32998 + 4.53777i) q^{98} -14.0096 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9} - 11 q^{11} - 14 q^{13} + 9 q^{15} + 2 q^{16} - 7 q^{17} - 9 q^{18} - 14 q^{19} - 7 q^{20} - 7 q^{21} + q^{22} - 29 q^{23} - 8 q^{25} - 7 q^{26} - 7 q^{27} + 14 q^{28} + 13 q^{29} - 8 q^{30} - 28 q^{31} + 2 q^{32} - 14 q^{33} - 7 q^{34} - 35 q^{35} - 17 q^{36} + 20 q^{37} + 35 q^{38} + 56 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 6 q^{43} + 3 q^{44} + 7 q^{45} + 34 q^{46} + 42 q^{47} + 14 q^{48} + 28 q^{49} + 16 q^{50} + 32 q^{51} - 7 q^{52} - 60 q^{53} + 21 q^{54} - 14 q^{55} + 7 q^{56} + 23 q^{57} + 18 q^{58} + 49 q^{59} + 6 q^{60} - 14 q^{61} - 28 q^{63} - 4 q^{64} - 28 q^{65} + 21 q^{66} + 24 q^{67} - 14 q^{68} + 7 q^{69} - 28 q^{70} + 6 q^{71} - 2 q^{72} - 35 q^{73} - 15 q^{74} - 56 q^{75} + 49 q^{77} + 6 q^{79} - 14 q^{80} - 45 q^{81} - 14 q^{82} - 77 q^{83} - 21 q^{84} - 33 q^{85} - 38 q^{86} + 63 q^{87} + 3 q^{88} - 21 q^{90} - 21 q^{91} - 5 q^{92} - 38 q^{93} - 35 q^{94} + 86 q^{95} + 98 q^{97} + 28 q^{98} - 106 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9 - 11 * q^11 - 14 * q^13 + 9 * q^15 + 2 * q^16 - 7 * q^17 - 9 * q^18 - 14 * q^19 - 7 * q^20 - 7 * q^21 + q^22 - 29 * q^23 - 8 * q^25 - 7 * q^26 - 7 * q^27 + 14 * q^28 + 13 * q^29 - 8 * q^30 - 28 * q^31 + 2 * q^32 - 14 * q^33 - 7 * q^34 - 35 * q^35 - 17 * q^36 + 20 * q^37 + 35 * q^38 + 56 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 6 * q^43 + 3 * q^44 + 7 * q^45 + 34 * q^46 + 42 * q^47 + 14 * q^48 + 28 * q^49 + 16 * q^50 + 32 * q^51 - 7 * q^52 - 60 * q^53 + 21 * q^54 - 14 * q^55 + 7 * q^56 + 23 * q^57 + 18 * q^58 + 49 * q^59 + 6 * q^60 - 14 * q^61 - 28 * q^63 - 4 * q^64 - 28 * q^65 + 21 * q^66 + 24 * q^67 - 14 * q^68 + 7 * q^69 - 28 * q^70 + 6 * q^71 - 2 * q^72 - 35 * q^73 - 15 * q^74 - 56 * q^75 + 49 * q^77 + 6 * q^79 - 14 * q^80 - 45 * q^81 - 14 * q^82 - 77 * q^83 - 21 * q^84 - 33 * q^85 - 38 * q^86 + 63 * q^87 + 3 * q^88 - 21 * q^90 - 21 * q^91 - 5 * q^92 - 38 * q^93 - 35 * q^94 + 86 * q^95 + 98 * q^97 + 28 * q^98 - 106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{21}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.826239	+	0.563320i	0.584239	+	0.398327i
$2$	0.826239	+	0.563320i	0.584239	+	0.398327i
$3$	0.0584109	+	0.0541974i	0.0337236	+	0.0312909i	0.696855	−	0.717212i	$-0.254582\pi$
$3$	0.0584109	+	0.0541974i	0.0337236	+	0.0312909i	−0.663131	+	0.748503i	$0.730773\pi$
$4$	0.365341	+	0.930874i	0.182671	+	0.465437i
$5$	−0.427005	+	0.131714i	−0.190962	+	0.0589041i	−0.388761	−	0.921339i	$-0.627097\pi$
$5$	−0.427005	+	0.131714i	−0.190962	+	0.0589041i	0.197799	+	0.980243i	$0.436621\pi$
$6$	0.0177309	+	0.0776840i	0.00723860	+	0.0317144i
$7$	1.60505	+	2.10329i	0.606652	+	0.794967i
$7$	1.60505	+	2.10329i	0.606652	+	0.794967i
$8$	−0.222521	+	0.974928i	−0.0786730	+	0.344689i
$9$	−0.223716	−	2.98528i	−0.0745719	−	0.995093i
$10$	−0.427005	−	0.131714i	−0.135031	−	0.0416515i
$11$	0.349720	−	4.66669i	0.105445	−	1.40706i	−0.654003	−	0.756492i	$-0.726912\pi$
$11$	0.349720	−	4.66669i	0.105445	−	1.40706i	0.759448	−	0.650568i	$-0.225469\pi$
$12$	−0.0291110	+	0.0741737i	−0.00840363	+	0.0214121i
$13$	−6.27294	+	3.02089i	−1.73980	+	0.837844i	−0.756942	+	0.653482i	$0.773308\pi$
$13$	−6.27294	+	3.02089i	−1.73980	+	0.837844i	−0.982858	+	0.184362i	$0.940978\pi$
$14$	0.141332	+	2.64197i	0.0377727	+	0.706097i
$15$	−0.0320803	−	0.0154490i	−0.00828309	−	0.00398893i
$16$	−0.733052	+	0.680173i	−0.183263	+	0.170043i
$17$	1.31740	−	0.198566i	0.319516	−	0.0481593i	0.0126739	−	0.999920i	$-0.495966\pi$
$17$	1.31740	−	0.198566i	0.319516	−	0.0481593i	0.306842	+	0.951760i	$0.400728\pi$
$18$	1.49683	−	2.59258i	0.352805	−	0.611076i
$19$	−2.50434	−	4.33764i	−0.574535	−	0.995123i	−0.996092	−	0.0883215i	$-0.971850\pi$
$19$	−2.50434	−	4.33764i	−0.574535	−	0.995123i	0.421557	−	0.906802i	$-0.361484\pi$
$20$	−0.278611	−	0.349367i	−0.0622993	−	0.0781209i
$21$	−0.0202401	+	0.209844i	−0.00441676	+	0.0457918i
$22$	2.91779	−	3.65879i	0.622075	−	0.780058i
$23$	3.25634	+	0.490814i	0.678993	+	0.102342i	0.479479	−	0.877553i	$-0.340826\pi$
$23$	3.25634	+	0.490814i	0.678993	+	0.102342i	0.199514	+	0.979895i	$0.436064\pi$
$24$	−0.0658362	+	0.0448864i	−0.0134388	+	0.00916239i
$25$	−3.96621	+	2.70412i	−0.793242	+	0.540823i
$26$	−6.88467	−	1.03770i	−1.35020	−	0.203509i
$27$	0.297769	−	0.373391i	0.0573057	−	0.0718591i
$28$	−1.37150	+	2.26252i	−0.259190	+	0.427575i
$29$	3.44313	+	4.31754i	0.639373	+	0.801748i	0.990924	−	0.134421i	$-0.0429173\pi$
$29$	3.44313	+	4.31754i	0.639373	+	0.801748i	−0.351552	+	0.936168i	$0.614346\pi$
$30$	−0.0178032	−	0.0308361i	−0.00325041	−	0.00562987i
$31$	2.08698	−	3.61476i	0.374833	−	0.649230i	−0.615469	−	0.788161i	$-0.711033\pi$
$31$	2.08698	−	3.61476i	0.374833	−	0.649230i	0.990302	+	0.138931i	$0.0443667\pi$
$32$	−0.988831	+	0.149042i	−0.174802	+	0.0263472i
$33$	0.273350	−	0.253632i	0.0475841	−	0.0441516i
$34$	1.20034	+	0.578055i	0.205857	+	0.0991355i
$35$	−0.962396	−	0.686706i	−0.162675	−	0.116075i
$36$	2.69719	−	1.29890i	0.449531	−	0.216483i
$37$	0.654285	−	1.66709i	0.107564	−	0.274068i	−0.866950	−	0.498395i	$-0.833923\pi$
$37$	0.654285	−	1.66709i	0.107564	−	0.274068i	0.974514	+	0.224327i	$0.0720183\pi$
$38$	0.374299	−	4.99467i	0.0607193	−	0.810243i
$39$	−0.530133	−	0.163524i	−0.0848891	−	0.0261848i
$40$	−0.0333937	−	0.445608i	−0.00528001	−	0.0704568i
$41$	−1.12713	+	4.93827i	−0.176028	+	0.771228i	0.807411	+	0.589989i	$0.200868\pi$
$41$	−1.12713	+	4.93827i	−0.176028	+	0.771228i	−0.983439	+	0.181239i	$0.941989\pi$
$42$	−0.134933	+	0.161980i	−0.0208206	+	0.0249940i
$43$	1.75596	+	7.69334i	0.267781	+	1.17322i	0.912588	+	0.408879i	$0.134080\pi$
$43$	1.75596	+	7.69334i	0.267781	+	1.17322i	−0.644808	+	0.764345i	$0.723063\pi$
$44$	4.47187	−	1.37939i	0.674159	−	0.207951i
$45$	0.488730	+	1.24526i	0.0728555	+	0.185633i
$46$	2.41403	+	2.23989i	0.355929	+	0.330253i
$47$	4.41364	+	3.00917i	0.643796	+	0.438933i	0.840708	−	0.541488i	$-0.182139\pi$
$47$	4.41364	+	3.00917i	0.643796	+	0.438933i	−0.196912	+	0.980421i	$0.563091\pi$
$48$	−0.0796818			−0.0115011
$49$	−1.84762	+	6.75176i	−0.263946	+	0.964537i
$50$	−4.80032			−0.678868
$51$	0.0877122	+	0.0598012i	0.0122822	+	0.00837384i
$52$	−5.10383	−	4.73566i	−0.707774	−	0.656718i
$53$	−3.28856	−	8.37913i	−0.451719	−	1.15096i	−0.957534	−	0.288320i	$-0.906903\pi$
$53$	−3.28856	−	8.37913i	−0.451719	−	1.15096i	0.505815	−	0.862642i	$-0.331192\pi$
$54$	0.456367	−	0.140771i	0.0621037	−	0.0191565i
$55$	0.465334	+	2.03876i	0.0627456	+	0.274907i
$56$	−2.40771	+	1.09678i	−0.321744	+	0.146564i
$57$	0.0888082	−	0.389094i	0.0117629	−	0.0515368i
$58$	0.412686	+	5.50691i	0.0541883	+	0.723092i
$59$	9.60843	+	2.96381i	1.25091	+	0.385855i	0.848300	−	0.529516i	$-0.177626\pi$
$59$	9.60843	+	2.96381i	1.25091	+	0.385855i	0.402611	+	0.915371i	$0.368103\pi$
$60$	0.00266087	−	0.0355069i	0.000343517	−	0.00458392i
$61$	−2.27134	+	5.78727i	−0.290815	+	0.740985i	0.708561	+	0.705650i	$0.249345\pi$
$61$	−2.27134	+	5.78727i	−0.290815	+	0.740985i	−0.999376	+	0.0353346i	$0.988750\pi$
$62$	3.76061	−	1.81101i	0.477598	−	0.229999i
$63$	5.91982	−	5.26207i	0.745827	−	0.662958i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	2.28068	−	2.11617i	0.282884	−	0.262478i
$66$	0.368728	−	0.0555768i	0.0453873	−	0.00684103i
$67$	−0.329108	+	0.570033i	−0.0402070	+	0.0696406i	−0.885429	−	0.464775i	$-0.846135\pi$
$67$	−0.329108	+	0.570033i	−0.0402070	+	0.0696406i	0.845222	+	0.534416i	$0.179468\pi$
$68$	0.666140	+	1.15379i	0.0807813	+	0.139917i
$69$	0.163605	+	0.205154i	0.0196957	+	0.0246976i
$70$	−0.408333	−	1.10952i	−0.0488052	−	0.132613i
$71$	0.158558	−	0.198826i	0.0188174	−	0.0235963i	−0.772334	−	0.635217i	$-0.780911\pi$
$71$	0.158558	−	0.198826i	0.0188174	−	0.0235963i	0.791151	+	0.611621i	$0.209482\pi$
$72$	2.96021	+	0.446181i	0.348865	+	0.0525829i
$73$	−3.38108	+	2.30518i	−0.395726	+	0.269801i	−0.744792	−	0.667297i	$-0.767451\pi$
$73$	−3.38108	+	2.30518i	−0.395726	+	0.269801i	0.349066	+	0.937098i	$0.386499\pi$
$74$	1.47970	−	1.00884i	0.172012	−	0.117276i
$75$	−0.378226	−	0.0570084i	−0.0436738	−	0.00658276i
$76$	3.12286	−	3.91594i	0.358217	−	0.449189i
$77$	10.3767	−	6.75471i	1.18253	−	0.769771i
$78$	−0.345900	−	0.433744i	−0.0391654	−	0.0491119i
$79$	−0.928280	−	1.60783i	−0.104440	−	0.180895i	0.809069	−	0.587713i	$-0.199972\pi$
$79$	−0.928280	−	1.60783i	−0.104440	−	0.180895i	−0.913509	+	0.406818i	$0.866638\pi$
$80$	0.223429	−	0.386990i	0.0249801	−	0.0432668i
$81$	−8.84301	+	1.33287i	−0.982557	+	0.148097i
$82$	−3.71310	+	3.44525i	−0.410043	+	0.380465i
$83$	−14.1140	−	6.79694i	−1.54921	−	0.746061i	−0.553013	−	0.833172i	$-0.686522\pi$
$83$	−14.1140	−	6.79694i	−1.54921	−	0.746061i	−0.996199	+	0.0871112i	$0.972236\pi$
$84$	−0.202733	+	0.0578238i	−0.0221200	+	0.00630909i
$85$	−0.536382	+	0.258308i	−0.0581788	+	0.0280174i
$86$	−2.88298	+	7.34570i	−0.310879	+	0.792108i
$87$	−0.0328835	+	0.438800i	−0.00352548	+	0.0470443i
$88$	4.47187	+	1.37939i	0.476702	+	0.147043i
$89$	−0.616956	−	8.23271i	−0.0653972	−	0.872666i	−0.929375	−	0.369136i	$-0.879654\pi$
$89$	−0.616956	−	8.23271i	−0.0653972	−	0.872666i	0.863978	−	0.503529i	$-0.167965\pi$
$90$	−0.297674	+	1.30420i	−0.0313776	+	0.137474i
$91$	−16.4222	−	8.34511i	−1.72151	−	0.874805i
$92$	0.732787	+	3.21055i	0.0763984	+	0.334723i
$93$	0.317813	−	0.0980323i	0.0329557	−	0.0101655i
$94$	1.95160	+	4.97259i	0.201292	+	0.512883i
$95$	1.64069	+	1.52234i	0.168331	+	0.156189i
$96$	−0.0658362	−	0.0448864i	−0.00671938	−	0.00458120i
$97$	16.8099			1.70679			0.853393	−	0.521269i	$-0.174541\pi$
$97$	16.8099			1.70679			0.853393	+	0.521269i	$0.174541\pi$
$98$	−5.32998	+	4.53777i	−0.538409	+	0.458384i
$99$	−14.0096			−1.40802
$100$	−3.96621	−	2.70412i	−0.396621	−	0.270412i
$101$	−10.7213	−	9.94792i	−1.06681	−	0.989855i	−0.0668413	−	0.997764i	$-0.521292\pi$
$101$	−10.7213	−	9.94792i	−1.06681	−	0.989855i	−0.999969	+	0.00790853i	$0.997483\pi$
$102$	0.0387840	+	0.0988201i	0.00384019	+	0.00978465i
$103$	6.50170	−	2.00551i	0.640631	−	0.197609i	0.0426137	−	0.999092i	$-0.486432\pi$
$103$	6.50170	−	2.00551i	0.640631	−	0.197609i	0.598017	+	0.801483i	$0.295955\pi$
$104$	−1.54929	−	6.78788i	−0.151920	−	0.665606i
$105$	−0.0189967	−	0.0922705i	−0.00185389	−	0.00900468i
$106$	2.00299	−	8.77567i	0.194548	−	0.852369i
$107$	−0.120187	−	1.60379i	−0.0116190	−	0.155044i	−0.999995	−	0.00301816i	$-0.999039\pi$
$107$	−0.120187	−	1.60379i	−0.0116190	−	0.155044i	0.988376	−	0.152026i	$-0.0485798\pi$
$108$	0.456367	+	0.140771i	0.0439140	+	0.0135457i
$109$	−0.177976	+	2.37493i	−0.0170470	+	0.227477i	0.982173	+	0.187981i	$0.0601943\pi$
$109$	−0.177976	+	2.37493i	−0.0170470	+	0.227477i	−0.999220	+	0.0394960i	$0.987425\pi$
$110$	−0.763998	+	1.94664i	−0.0728444	+	0.185604i
$111$	0.128569	−	0.0619158i	0.0122033	−	0.00587678i
$112$	−2.60718	−	0.450106i	−0.246356	−	0.0425310i
$113$	−6.42208	−	3.09271i	−0.604139	−	0.290938i	0.106702	−	0.994291i	$-0.465971\pi$
$113$	−6.42208	−	3.09271i	−0.604139	−	0.290938i	−0.710840	+	0.703353i	$0.751685\pi$
$114$	0.292561	−	0.271457i	0.0274009	−	0.0254243i
$115$	−1.45512	+	0.219324i	−0.135690	+	0.0204520i
$116$	−2.76117	+	4.78249i	−0.256369	+	0.444043i
$117$	10.4216	+	18.0507i	0.963473	+	1.66878i
$118$	6.26929	+	7.86144i	0.577135	+	0.723704i
$119$	2.53213	+	2.45216i	0.232120	+	0.224789i
$120$	0.0222002	−	0.0278382i	0.00202660	−	0.00254127i
$121$	−10.7785	−	1.62460i	−0.979867	−	0.147691i
$122$	−5.13676	+	3.50218i	−0.465060	+	0.317073i
$123$	−0.333478	+	0.227361i	−0.0300687	+	0.0205005i
$124$	4.12734	+	0.622097i	0.370646	+	0.0558660i
$125$	2.73048	−	3.42391i	0.244221	−	0.306244i
$126$	7.85541	−	1.01297i	0.699816	−	0.0902424i
$127$	0.797487	+	1.00002i	0.0707655	+	0.0887371i	0.815954	−	0.578116i	$-0.196212\pi$
$127$	0.797487	+	1.00002i	0.0707655	+	0.0887371i	−0.745189	+	0.666854i	$0.767641\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−0.314392	+	0.544544i	−0.0276807	+	0.0479444i
$130$	3.07647	−	0.463703i	0.269824	−	0.0406695i
$131$	9.62518	−	8.93086i	0.840956	−	0.780293i	−0.136676	−	0.990616i	$-0.543642\pi$
$131$	9.62518	−	8.93086i	0.840956	−	0.780293i	0.977632	+	0.210323i	$0.0674514\pi$
$132$	0.335965	+	0.161792i	0.0292420	+	0.0140822i
$133$	5.10371	−	12.2295i	0.442548	−	1.06043i
$134$	−0.593033	+	0.285590i	−0.0512302	+	0.0246712i
$135$	−0.0779683	+	0.198660i	−0.00671045	+	0.0170979i
$136$	−0.0995614	+	1.32855i	−0.00853732	+	0.113923i
$137$	7.29079	+	2.24891i	0.622894	+	0.192137i	0.590107	−	0.807325i	$-0.299086\pi$
$137$	7.29079	+	2.24891i	0.622894	+	0.192137i	0.0327869	+	0.999462i	$0.489562\pi$
$138$	0.0196093	+	0.261668i	0.00166925	+	0.0222746i
$139$	1.24055	−	5.43520i	0.105222	−	0.461008i	−0.894676	−	0.446716i	$-0.852593\pi$
$139$	1.24055	−	5.43520i	0.105222	−	0.461008i	0.999898	−	0.0142920i	$-0.00454943\pi$
$140$	0.287634	−	1.14675i	0.0243095	−	0.0969182i
$141$	0.0947157	+	0.414976i	0.00797650	+	0.0349473i
$142$	0.243009	−	0.0749585i	0.0203929	−	0.00629038i
$143$	11.9038	+	30.3303i	0.995444	+	2.53635i
$144$	2.19450	+	2.03620i	0.182875	+	0.169683i
$145$	−2.03891	−	1.39011i	−0.169322	−	0.115442i
$146$	−4.09214			−0.338668
$147$	−0.473849	+	0.294240i	−0.0390824	+	0.0242685i
$148$	1.79089			0.147210
$149$	−0.628444	−	0.428466i	−0.0514841	−	0.0351013i	0.537305	−	0.843388i	$-0.319443\pi$
$149$	−0.628444	−	0.428466i	−0.0514841	−	0.0351013i	−0.588789	+	0.808287i	$0.700395\pi$
$150$	−0.280391	−	0.260165i	−0.0228938	−	0.0212424i
$151$	6.90648	+	17.5974i	0.562041	+	1.43206i	0.875856	+	0.482573i	$0.160298\pi$
$151$	6.90648	+	17.5974i	0.562041	+	1.43206i	−0.313815	+	0.949484i	$0.601607\pi$
$152$	4.78616	−	1.47633i	0.388208	−	0.119746i
$153$	−0.887498	−	3.88838i	−0.0717500	−	0.314357i
$154$	12.3787	+	0.264397i	0.997504	+	0.0213057i
$155$	−0.415039	+	1.81840i	−0.0333367	+	0.146058i
$156$	−0.0414587	−	0.553229i	−0.00331936	−	0.0442937i
$157$	6.73590	+	2.07775i	0.537583	+	0.165823i	0.551646	−	0.834079i	$-0.314000\pi$
$157$	6.73590	+	2.07775i	0.537583	+	0.165823i	−0.0140622	+	0.999901i	$0.504476\pi$
$158$	0.138741	−	1.85137i	0.0110376	−	0.147287i
$159$	0.262039	−	0.667664i	0.0207810	−	0.0529492i
$160$	0.402605	−	0.193884i	0.0318287	−	0.0153279i
$161$	4.19426	+	7.63678i	0.330554	+	0.601863i
$162$	−8.05727	−	3.88018i	−0.633039	−	0.304856i
$163$	−13.1752	+	12.2248i	−1.03196	+	0.957518i	−0.999120	−	0.0419429i	$-0.986645\pi$
$163$	−13.1752	+	12.2248i	−1.03196	+	0.957518i	−0.0328387	+	0.999461i	$0.510455\pi$
$164$	−5.00869	+	0.754938i	−0.391113	+	0.0589508i
$165$	−0.0833150	+	0.144306i	−0.00648607	+	0.0112342i
$166$	−7.83268	−	13.5666i	−0.607933	−	1.05297i
$167$	2.88240	+	3.61441i	0.223047	+	0.279692i	0.880746	−	0.473589i	$-0.157042\pi$
$167$	2.88240	+	3.61441i	0.223047	+	0.279692i	−0.657699	+	0.753280i	$0.728470\pi$
$168$	−0.200079	−	0.0664274i	−0.0154365	−	0.00512499i
$169$	22.1186	−	27.7359i	1.70143	−	2.13353i
$170$	−0.588690	−	0.0887307i	−0.0451505	−	0.00680534i
$171$	−12.3888	+	8.44655i	−0.947396	+	0.645924i
$172$	−6.52001	+	4.44527i	−0.497146	+	0.338948i
$173$	−5.54945	−	0.836445i	−0.421917	−	0.0635937i	−0.0653473	−	0.997863i	$-0.520816\pi$
$173$	−5.54945	−	0.836445i	−0.421917	−	0.0635937i	−0.356569	+	0.934269i	$0.616054\pi$
$174$	−0.274355	+	0.344030i	−0.0207988	+	0.0260808i
$175$	−12.0535	−	4.00183i	−0.911159	−	0.302510i
$176$	2.91779	+	3.65879i	0.219937	+	0.275792i
$177$	0.400607	+	0.693871i	0.0301114	+	0.0521545i
$178$	4.12790	−	7.14973i	0.309399	−	0.535895i
$179$	14.2861	−	2.15328i	1.06779	−	0.160943i	0.408444	−	0.912783i	$-0.366072\pi$
$179$	14.2861	−	2.15328i	1.06779	−	0.160943i	0.659346	+	0.751840i	$0.270833\pi$
$180$	−0.980630	+	0.909891i	−0.0730918	+	0.0678193i
$181$	12.2188	+	5.88427i	0.908217	+	0.437374i	0.828850	−	0.559471i	$-0.188996\pi$
$181$	12.2188	+	5.88427i	0.908217	+	0.437374i	0.0793670	+	0.996845i	$0.474710\pi$
$182$	−8.86768	−	16.1460i	−0.657316	−	1.19682i
$183$	−0.446326	+	0.214939i	−0.0329934	+	0.0158888i
$184$	−1.20311	+	3.06548i	−0.0886945	+	0.225990i
$185$	−0.0598044	+	0.798034i	−0.00439691	+	0.0586727i
$186$	0.317813	+	0.0980323i	0.0233032	+	0.00718808i
$187$	−0.465925	−	6.21733i	−0.0340718	−	0.454657i
$188$	−1.18867	+	5.20792i	−0.0866929	+	0.379827i
$189$	1.26328	+	0.0269825i	0.0918903	+	0.00196269i
$190$	0.498039	+	2.18205i	0.0361315	+	0.158303i
$191$	−19.5264	+	6.02311i	−1.41288	+	0.435817i	−0.904927	−	0.425567i	$-0.860075\pi$
$191$	−19.5264	+	6.02311i	−1.41288	+	0.435817i	−0.507956	+	0.861383i	$0.669599\pi$
$192$	−0.0291110	−	0.0741737i	−0.00210091	−	0.00535303i
$193$	8.80560	+	8.17040i	0.633841	+	0.588118i	0.930243	−	0.366945i	$-0.119596\pi$
$193$	8.80560	+	8.17040i	0.633841	+	0.588118i	−0.296402	+	0.955063i	$0.595787\pi$
$194$	13.8890	+	9.46934i	0.997170	+	0.679859i
$195$	0.247908			0.0177530
$196$	−6.96005	+	0.746793i	−0.497146	+	0.0533423i
$197$	−17.1323			−1.22063			−0.610314	−	0.792159i	$-0.708957\pi$
$197$	−17.1323			−1.22063			−0.610314	+	0.792159i	$0.708957\pi$
$198$	−11.5753	−	7.89189i	−0.822620	−	0.560853i
$199$	−16.4502	−	15.2636i	−1.16613	−	1.08201i	−0.995313	−	0.0967036i	$-0.969170\pi$
$199$	−16.4502	−	15.2636i	−1.16613	−	1.08201i	−0.170813	−	0.985303i	$-0.554639\pi$
$200$	−1.75375	−	4.46849i	−0.124009	−	0.315970i
$201$	−0.0501178	+	0.0154593i	−0.00353504	+	0.00109041i
$202$	−3.25450	−	14.2589i	−0.228986	−	1.00325i
$203$	−3.55464	+	14.1718i	−0.249487	+	0.994663i
$204$	−0.0236225	+	0.103497i	−0.00165390	+	0.00724623i
$205$	−0.169148	−	2.25712i	−0.0118138	−	0.157644i
$206$	6.50170	+	2.00551i	0.452995	+	0.139730i
$207$	0.736722	−	9.83087i	0.0512057	−	0.683293i
$208$	2.54366	−	6.48115i	0.176371	−	0.449387i
$209$	−21.1182	+	10.1700i	−1.46078	+	0.703474i
$210$	0.0362820	−	0.0869387i	0.00250370	−	0.00599934i
$211$	−12.4802	−	6.01014i	−0.859171	−	0.413755i	−0.0481974	−	0.998838i	$-0.515348\pi$
$211$	−12.4802	−	6.01014i	−0.859171	−	0.413755i	−0.810973	+	0.585083i	$0.801062\pi$
$212$	6.59846	−	6.12248i	0.453184	−	0.420493i
$213$	0.0200374	−	0.00302015i	0.00137294	−	0.000206937i
$214$	0.804143	−	1.39282i	0.0549701	−	0.0952110i
$215$	−1.76312	−	3.05381i	−0.120244	−	0.208268i
$216$	0.297769	+	0.373391i	0.0202606	+	0.0254060i
$217$	10.9526	−	1.41235i	0.743510	−	0.0958768i
$218$	−1.48489	+	1.86200i	−0.100570	+	0.126111i
$219$	−0.322427	−	0.0485980i	−0.0217876	−	0.00328395i
$220$	−1.72782	+	1.17801i	−0.116490	+	0.0794215i
$221$	−7.66412	+	5.22531i	−0.515545	+	0.351492i
$222$	0.141107	+	0.0212685i	0.00947051	+	0.00142745i
$223$	11.3851	−	14.2764i	0.762400	−	0.956019i	−0.237482	−	0.971392i	$-0.576322\pi$
$223$	11.3851	−	14.2764i	0.762400	−	0.956019i	0.999882	+	0.0153728i	$0.00489351\pi$
$224$	−1.90060	−	1.84057i	−0.126989	−	0.122978i
$225$	8.95985	+	11.2353i	0.597323	+	0.749019i
$226$	−3.56399	−	6.17300i	−0.237073	−	0.410622i
$227$	2.09787	−	3.63361i	0.139240	−	0.241171i	−0.787969	−	0.615715i	$-0.788867\pi$
$227$	2.09787	−	3.63361i	0.139240	−	0.241171i	0.927209	+	0.374544i	$0.122201\pi$
$228$	0.394643	−	0.0594828i	0.0261359	−	0.00393935i
$229$	−2.45056	+	2.27379i	−0.161938	+	0.150256i	−0.756980	−	0.653438i	$-0.773326\pi$
$229$	−2.45056	+	2.27379i	−0.161938	+	0.150256i	0.595042	+	0.803695i	$0.297135\pi$
$230$	−1.32582	−	0.638483i	−0.0874223	−	0.0421003i
$231$	0.972200	+	0.167841i	0.0639661	+	0.0110431i
$232$	−4.97546	+	2.39606i	−0.326655	+	0.157309i
$233$	8.22323	−	20.9524i	0.538722	−	1.37264i	−0.359519	−	0.933138i	$-0.617059\pi$
$233$	8.22323	−	20.9524i	0.538722	−	1.37264i	0.898241	−	0.439503i	$-0.144845\pi$
$234$	−1.55761	+	20.7848i	−0.101824	+	1.35875i
$235$	−2.28100	−	0.703594i	−0.148796	−	0.0458974i
$236$	0.751423	+	10.0270i	0.0489134	+	0.652705i
$237$	0.0329184	−	0.144225i	0.00213828	−	0.00936843i
$238$	0.710797	+	3.45247i	0.0460741	+	0.223790i
$239$	2.97591	+	13.0383i	0.192495	+	0.843377i	0.975260	+	0.221060i	$0.0709516\pi$
$239$	2.97591	+	13.0383i	0.192495	+	0.843377i	−0.782765	+	0.622318i	$0.786191\pi$
$240$	0.0340245	−	0.0104952i	0.00219627	−	0.000677461i
$241$	−3.87545	−	9.87448i	−0.249640	−	0.636071i	0.750040	−	0.661393i	$-0.230034\pi$
$241$	−3.87545	−	9.87448i	−0.249640	−	0.636071i	−0.999679	+	0.0253213i	$0.991939\pi$
$242$	−7.99048	−	7.41408i	−0.513647	−	0.476595i
$243$	−1.77256	−	1.20851i	−0.113710	−	0.0775262i
$244$	−6.21704			−0.398005
$245$	−0.100355	−	3.12639i	−0.00641145	−	0.199738i
$246$	−0.403609			−0.0257332
$247$	28.8131	+	19.6444i	1.83333	+	1.24995i
$248$	3.05973	+	2.83902i	0.194293	+	0.180278i
$249$	−0.456035	−	1.16196i	−0.0289000	−	0.0736360i
$250$	4.18478	−	1.29084i	0.264669	−	0.0816396i
$251$	−1.74996	−	7.66707i	−0.110456	−	0.483941i	−0.999651	−	0.0264122i	$-0.991592\pi$
$251$	−1.74996	−	7.66707i	−0.110456	−	0.483941i	0.889195	−	0.457529i	$-0.151265\pi$
$252$	7.06107	+	3.58816i	0.444806	+	0.226033i
$253$	3.42928	−	15.0247i	0.215597	−	0.944592i
$254$	0.0955849	+	1.27549i	0.00599753	+	0.0800315i
$255$	−0.0453302	−	0.0139825i	−0.00283869	−	0.000875619i
$256$	0.0747301	−	0.997204i	0.00467063	−	0.0623252i
$257$	−6.82645	+	17.3935i	−0.425822	+	1.08498i	0.543549	+	0.839377i	$0.317080\pi$
$257$	−6.82645	+	17.3935i	−0.425822	+	1.08498i	−0.969371	+	0.245600i	$0.921015\pi$
$258$	−0.566515	+	0.272819i	−0.0352697	+	0.0169850i
$259$	4.55653	−	1.29962i	0.283129	−	0.0807543i
$260$	2.80311	+	1.34991i	0.173842	+	0.0837177i
$261$	12.1188	−	11.2446i	0.750135	−	0.696023i
$262$	12.9836	−	1.95697i	0.802132	−	0.120902i
$263$	4.20012	−	7.27483i	0.258991	−	0.448585i	−0.706981	−	0.707232i	$-0.749943\pi$
$263$	4.20012	−	7.27483i	0.258991	−	0.448585i	0.965972	+	0.258647i	$0.0832768\pi$
$264$	0.186446	+	0.322935i	0.0114750	+	0.0198753i
$265$	2.50788	+	3.14478i	0.154058	+	0.193182i
$266$	11.1060	−	7.22945i	0.680952	−	0.443266i
$267$	0.410155	−	0.514318i	0.0251010	−	0.0314757i
$268$	−0.650865	−	0.0981021i	−0.0397579	−	0.00599254i
$269$	−10.9912	+	7.49367i	−0.670145	+	0.456897i	−0.849991	−	0.526798i	$-0.823392\pi$
$269$	−10.9912	+	7.49367i	−0.670145	+	0.456897i	0.179846	+	0.983695i	$0.442440\pi$
$270$	−0.176330	+	0.120220i	−0.0107311	+	0.00731633i
$271$	−1.25232	−	0.188757i	−0.0760729	−	0.0114661i	0.110896	−	0.993832i	$-0.464628\pi$
$271$	−1.25232	−	0.188757i	−0.0760729	−	0.0114661i	−0.186968	+	0.982366i	$0.559866\pi$
$272$	−0.830663	+	1.04162i	−0.0503663	+	0.0631574i
$273$	−0.506952	−	1.37748i	−0.0306821	−	0.0833692i
$274$	4.75707	+	5.96518i	0.287385	+	0.360370i
$275$	11.2322	+	19.4547i	0.677327	+	1.17317i
$276$	−0.131201	+	0.227246i	−0.00789736	+	0.0136786i
$277$	−17.9995	+	2.71299i	−1.08148	+	0.163008i	−0.665525	−	0.746375i	$-0.731792\pi$
$277$	−17.9995	+	2.71299i	−1.08148	+	0.163008i	−0.415960	+	0.909383i	$0.636554\pi$
$278$	4.08675	−	3.79195i	0.245107	−	0.227426i
$279$	−11.2580	−	5.42155i	−0.673996	−	0.324579i
$280$	0.883643	−	0.785460i	0.0528077	−	0.0469402i
$281$	12.7619	−	6.14583i	0.761314	−	0.366629i	−0.0125999	−	0.999921i	$-0.504011\pi$
$281$	12.7619	−	6.14583i	0.761314	−	0.366629i	0.773914	+	0.633291i	$0.218296\pi$
$282$	−0.155507	+	0.396225i	−0.00926030	+	0.0235948i
$283$	1.16594	−	15.5584i	0.0693081	−	0.924852i	−0.848849	−	0.528635i	$-0.822704\pi$
$283$	1.16594	−	15.5584i	0.0693081	−	0.924852i	0.918157	−	0.396217i	$-0.129677\pi$
$284$	0.243009	+	0.0749585i	0.0144200	+	0.00444797i
$285$	0.0133274	+	0.177842i	0.000789450	+	0.0105345i
$286$	−7.25032	+	31.7657i	−0.428720	+	1.87835i
$287$	−12.1957	+	5.55550i	−0.719888	+	0.327931i
$288$	0.666150	+	2.91859i	0.0392533	+	0.171980i
$289$	−14.5486	+	4.48766i	−0.855801	+	0.263980i
$290$	−0.901553	−	2.29712i	−0.0529410	−	0.134892i
$291$	0.981881	+	0.911052i	0.0575589	+	0.0534068i
$292$	−3.38108	−	2.30518i	−0.197863	−	0.134901i
$293$	23.7424			1.38705			0.693523	−	0.720434i	$-0.256057\pi$
$293$	23.7424			1.38705			0.693523	+	0.720434i	$0.256057\pi$
$294$	−0.557264	−	0.0238161i	−0.0325003	−	0.00138898i
$295$	−4.49322			−0.261606
$296$	1.47970	+	1.00884i	0.0860059	+	0.0586378i
$297$	−1.63836	−	1.52018i	−0.0950675	−	0.0882098i
$298$	−0.277881	−	0.708030i	−0.0160972	−	0.0410151i
$299$	−21.9095	+	6.75818i	−1.26706	+	0.390836i
$300$	−0.0851138	−	0.372908i	−0.00491405	−	0.0215299i
$301$	−13.3629	+	16.0415i	−0.770225	+	0.924616i
$302$	−4.20658	+	18.4302i	−0.242061	+	1.06054i
$303$	−0.0870899	−	1.16213i	−0.00500318	−	0.0667629i
$304$	4.78616	+	1.47633i	0.274505	+	0.0846735i
$305$	0.207610	−	2.77036i	0.0118877	−	0.158630i
$306$	1.45712	−	3.71268i	0.0832979	−	0.212240i
$307$	5.60332	−	2.69842i	0.319799	−	0.154007i	−0.267097	−	0.963670i	$-0.586064\pi$
$307$	5.60332	−	2.69842i	0.319799	−	0.154007i	0.586895	+	0.809663i	$0.300350\pi$
$308$	10.0788	+	7.19162i	0.574294	+	0.409781i
$309$	0.488463	+	0.235232i	0.0277877	+	0.0133819i
$310$	−1.36726	+	1.26864i	−0.0776554	+	0.0720537i
$311$	29.2857	−	4.41410i	1.66064	−	0.250301i	0.749380	−	0.662140i	$-0.230351\pi$
$311$	29.2857	−	4.41410i	1.66064	−	0.250301i	0.911257	+	0.411839i	$0.135113\pi$
$312$	0.277390	−	0.480453i	0.0157041	−	0.0272003i
$313$	−4.87410	−	8.44218i	−0.275500	−	0.477180i	0.694761	−	0.719241i	$-0.255510\pi$
$313$	−4.87410	−	8.44218i	−0.275500	−	0.477180i	−0.970261	+	0.242060i	$0.922177\pi$
$314$	4.39502	+	5.51119i	0.248026	+	0.311014i
$315$	−1.83471	+	3.02665i	−0.103374	+	0.170532i
$316$	1.15755	−	1.45152i	0.0651171	−	0.0816542i
$317$	7.37624	+	1.11179i	0.414291	+	0.0624443i	0.352881	−	0.935668i	$-0.385202\pi$
$317$	7.37624	+	1.11179i	0.414291	+	0.0624443i	0.0614101	+	0.998113i	$0.480440\pi$
$318$	0.592615	−	0.404038i	0.0332322	−	0.0226573i
$319$	21.3528	−	14.5581i	1.19553	−	0.815096i
$320$	0.441867	+	0.0666007i	0.0247011	+	0.00372309i
$321$	0.0799010	−	0.100193i	0.00445964	−	0.00559221i
$322$	−0.836491	+	8.67252i	−0.0466158	+	0.483301i
$323$	−4.16052	−	5.21713i	−0.231498	−	0.290289i
$324$	−4.47145	−	7.74478i	−0.248414	−	0.430265i
$325$	16.7110	−	28.9442i	0.926957	−	1.60554i
$326$	−17.7723	+	2.67874i	−0.984316	+	0.148362i
$327$	−0.139111	+	0.129076i	−0.00769284	+	0.00713791i
$328$	−4.56364	−	2.19774i	−0.251985	−	0.121350i
$329$	0.754976	+	14.1130i	0.0416232	+	0.778076i
$330$	−0.150128	+	0.0722981i	−0.00826430	+	0.00397988i
$331$	−0.667014	+	1.69952i	−0.0366624	+	0.0934143i	−0.948032	−	0.318174i	$-0.896930\pi$
$331$	−0.667014	+	1.69952i	−0.0366624	+	0.0934143i	0.911370	+	0.411588i	$0.135026\pi$
$332$	1.17067	−	15.6215i	0.0642490	−	0.857344i
$333$	−5.12311	−	1.58027i	−0.280745	−	0.0865982i
$334$	0.345478	+	4.61008i	0.0189037	+	0.252252i
$335$	0.0654499	−	0.286755i	0.00357591	−	0.0156671i
$336$	−0.127893	−	0.167594i	−0.00697716	−	0.00914298i
$337$	6.08808	+	26.6736i	0.331639	+	1.45301i	0.815956	+	0.578113i	$0.196211\pi$
$337$	6.08808	+	26.6736i	0.331639	+	1.45301i	−0.484317	+	0.874892i	$0.660932\pi$
$338$	33.8995	−	10.4566i	1.84389	−	0.568764i
$339$	−0.207503	−	0.528708i	−0.0112700	−	0.0287155i
$340$	−0.436415	−	0.404934i	−0.0236679	−	0.0219606i
$341$	−16.1391	−	11.0034i	−0.873981	−	0.595870i
$342$	−14.9942			−0.810795
$343$	−17.1664	+	6.95085i	−0.926899	+	0.375310i
$344$	−7.89119			−0.425465
$345$	−0.0968815	−	0.0660527i	−0.00521593	−	0.00355616i
$346$	−4.11398	−	3.81722i	−0.221169	−	0.205215i
$347$	−7.06061	−	17.9901i	−0.379033	−	0.965761i	−0.985351	−	0.170538i	$-0.945449\pi$
$347$	−7.06061	−	17.9901i	−0.379033	−	0.965761i	0.606318	−	0.795222i	$-0.292646\pi$
$348$	−0.420481	+	0.129701i	−0.0225402	+	0.00695272i
$349$	5.38975	+	23.6141i	0.288507	+	1.26403i	0.886575	+	0.462586i	$0.153078\pi$
$349$	5.38975	+	23.6141i	0.288507	+	1.26403i	−0.598068	+	0.801446i	$0.704065\pi$
$350$	−7.70476	−	10.0964i	−0.411837	−	0.539677i
$351$	−0.739917	+	3.24179i	−0.0394938	+	0.173034i
$352$	0.349720	+	4.66669i	0.0186401	+	0.248735i
$353$	−24.9079	−	7.68306i	−1.32571	−	0.408928i	−0.450547	−	0.892753i	$-0.648771\pi$
$353$	−24.9079	−	7.68306i	−1.32571	−	0.408928i	−0.875165	+	0.483825i	$0.839247\pi$
$354$	−0.0598747	+	0.798973i	−0.00318231	+	0.0424649i
$355$	−0.0415171	+	0.105784i	−0.00220350	+	0.00561442i
$356$	7.43821	−	3.58206i	0.394225	−	0.189849i
$357$	0.0150036	+	0.280468i	0.000794076	+	0.0148439i
$358$	13.0167	+	6.26850i	0.687953	+	0.331301i
$359$	2.40864	−	2.23489i	0.127123	−	0.117953i	−0.614049	−	0.789268i	$-0.710460\pi$
$359$	2.40864	−	2.23489i	0.127123	−	0.117953i	0.741173	+	0.671314i	$0.234270\pi$
$360$	−1.32279	+	0.199379i	−0.0697174	+	0.0105082i
$361$	−3.04342	+	5.27136i	−0.160180	+	0.277440i
$362$	6.78093	+	11.7449i	0.356398	+	0.617299i
$363$	−0.541535	−	0.679063i	−0.0284232	−	0.0356416i
$364$	1.76854	−	18.3358i	0.0926968	−	0.961056i
$365$	1.14011	−	1.42966i	0.0596763	−	0.0748318i
$366$	−0.489852	−	0.0738333i	−0.0256050	−	0.00385933i
$367$	2.20443	−	1.50296i	0.115071	−	0.0784537i	−0.504417	−	0.863460i	$-0.668293\pi$
$367$	2.20443	−	1.50296i	0.115071	−	0.0784537i	0.619488	+	0.785006i	$0.287340\pi$
$368$	−2.72090	+	1.85508i	−0.141837	+	0.0967027i
$369$	14.9943	+	2.26002i	0.780570	+	0.117652i
$370$	−0.498961	+	0.625678i	−0.0259398	+	0.0325274i
$371$	12.3454	−	20.3657i	0.640940	−	1.05734i
$372$	0.207366	+	0.260029i	0.0107514	+	0.0134819i
$373$	7.78275	+	13.4801i	0.402975	+	0.697974i	0.994084	−	0.108618i	$-0.0346427\pi$
$373$	7.78275	+	13.4801i	0.402975	+	0.697974i	−0.591108	+	0.806592i	$0.701309\pi$
$374$	3.11738	−	5.39947i	0.161196	−	0.279200i
$375$	0.345057	−	0.0520089i	0.0178187	−	0.00268573i
$376$	−3.91585	+	3.63338i	−0.201945	+	0.187377i
$377$	−34.6414	−	16.6824i	−1.78412	−	0.859187i
$378$	1.02857	+	0.733927i	0.0529041	+	0.0377491i
$379$	15.4105	−	7.42129i	0.791582	−	0.381206i	0.00601485	−	0.999982i	$-0.498085\pi$
$379$	15.4105	−	7.42129i	0.791582	−	0.381206i	0.785568	+	0.618776i	$0.212371\pi$
$380$	−0.817694	+	2.08345i	−0.0419468	+	0.106879i
$381$	−0.00761638	+	0.101634i	−0.000390199	+	0.00520685i
$382$	−19.5264	−	6.02311i	−0.999059	−	0.308169i
$383$	−0.542947	−	7.24512i	−0.0277433	−	0.370208i	−0.993745	−	0.111673i	$-0.964379\pi$
$383$	−0.542947	−	7.24512i	−0.0277433	−	0.370208i	0.966002	−	0.258536i	$-0.0832399\pi$
$384$	0.0177309	−	0.0776840i	0.000904825	−	0.00396430i
$385$	−3.54121	+	4.25105i	−0.180477	+	0.216653i
$386$	2.67298	+	11.7111i	0.136051	+	0.596078i
$387$	22.5740	−	6.96314i	1.14750	−	0.353956i
$388$	6.14134	+	15.6479i	0.311779	+	0.794401i
$389$	−14.6356	−	13.5798i	−0.742054	−	0.688525i	0.215589	−	0.976484i	$-0.430833\pi$
$389$	−14.6356	−	13.5798i	−0.742054	−	0.688525i	−0.957643	+	0.287959i	$0.907023\pi$
$390$	0.204831	+	0.139651i	0.0103720	+	0.00707152i
$391$	4.38735			0.221878
$392$	−6.17135	−	3.30371i	−0.311700	−	0.166862i
$393$	1.04625			0.0527761
$394$	−14.1554	−	9.65099i	−0.713139	−	0.486210i
$395$	0.608153	+	0.564284i	0.0305995	+	0.0283922i
$396$	−5.11829	−	13.0412i	−0.257204	−	0.655344i
$397$	−27.0859	+	8.35490i	−1.35940	+	0.419321i	−0.886881	−	0.461998i	$-0.847133\pi$
$397$	−27.0859	+	8.35490i	−1.35940	+	0.419321i	−0.472523	+	0.881318i	$0.656657\pi$
$398$	−4.99354	−	21.8781i	−0.250303	−	1.09665i
$399$	0.960918	−	0.437727i	0.0481061	−	0.0219138i
$400$	1.06817	−	4.67996i	0.0534086	−	0.233998i
$401$	−0.0699797	−	0.933814i	−0.00349462	−	0.0466325i	0.995184	−	0.0980259i	$-0.0312528\pi$
$401$	−0.0699797	−	0.933814i	−0.00349462	−	0.0466325i	−0.998678	+	0.0513934i	$0.983634\pi$
$402$	−0.0501178	−	0.0154593i	−0.00249965	−	0.000771040i
$403$	−2.17173	+	28.9797i	−0.108182	+	1.44358i
$404$	5.34332	−	13.6146i	0.265840	−	0.677350i
$405$	3.60045	−	1.73389i	0.178908	−	0.0861575i
$406$	−10.9202	+	9.70686i	−0.541961	+	0.481743i
$407$	−7.55098	−	3.63636i	−0.374288	−	0.180248i
$408$	−0.0778197	+	0.0722061i	−0.00385265	+	0.00357473i
$409$	−17.7366	+	2.67337i	−0.877019	+	0.132189i	−0.572095	−	0.820187i	$-0.693869\pi$
$409$	−17.7366	+	2.67337i	−0.877019	+	0.132189i	−0.304924	+	0.952377i	$0.598631\pi$
$410$	1.13173	−	1.96021i	0.0558919	−	0.0968077i
$411$	0.303976	+	0.526503i	0.0149941	+	0.0259705i
$412$	4.24221	+	5.31956i	0.208999	+	0.262076i
$413$	9.18829	+	24.9663i	0.452126	+	1.22851i
$414$	6.14664	−	7.70764i	0.302091	−	0.378810i
$415$	6.92199	+	1.04332i	0.339787	+	0.0512147i
$416$	5.75264	−	3.92208i	0.282046	−	0.192296i
$417$	0.367036	−	0.250241i	0.0179738	−	0.0122543i
$418$	−23.1777	−	3.49347i	−1.13366	−	0.170871i
$419$	−14.5842	+	18.2880i	−0.712486	+	0.893429i	−0.997887	−	0.0649791i	$-0.979302\pi$
$419$	−14.5842	+	18.2880i	−0.712486	+	0.893429i	0.285401	+	0.958408i	$0.407873\pi$
$420$	0.0789519	−	0.0513938i	0.00385246	−	0.00250776i
$421$	11.7547	+	14.7399i	0.572889	+	0.718380i	0.980882	−	0.194605i	$-0.0623426\pi$
$421$	11.7547	+	14.7399i	0.572889	+	0.718380i	−0.407993	+	0.912985i	$0.633771\pi$
$422$	−6.92598	−	11.9961i	−0.337151	−	0.583963i
$423$	7.99582	−	13.8492i	0.388770	−	0.673369i
$424$	8.90082	−	1.34158i	0.432262	−	0.0651530i
$425$	−4.68814	+	4.34995i	−0.227408	+	0.211004i
$426$	0.0182570	+	0.00879209i	0.000884553	+	0.000425978i
$427$	−15.8179	+	4.51160i	−0.765482	+	0.218332i
$428$	1.44902	−	0.697809i	0.0700408	−	0.0337299i
$429$	−0.948515	+	2.41678i	−0.0457947	+	0.116683i
$430$	0.263516	−	3.51638i	0.0127079	−	0.169575i
$431$	10.1771	+	3.13921i	0.490212	+	0.151211i	0.530000	−	0.847998i	$-0.322192\pi$
$431$	10.1771	+	3.13921i	0.490212	+	0.151211i	−0.0397876	+	0.999208i	$0.512668\pi$
$432$	0.0356900	+	0.476250i	0.00171713	+	0.0229136i
$433$	−1.59489	+	6.98767i	−0.0766456	+	0.335806i	−0.998684	−	0.0512930i	$-0.983666\pi$
$433$	−1.59489	+	6.98767i	−0.0766456	+	0.335806i	0.922038	+	0.387099i	$0.126523\pi$
$434$	9.84505	+	5.00287i	0.472578	+	0.240145i
$435$	−0.0437545	−	0.191701i	−0.00209787	−	0.00919136i
$436$	−2.27578	+	0.701985i	−0.108990	+	0.0336190i
$437$	−6.02599	−	15.3540i	−0.288262	−	0.734480i
$438$	−0.239025	−	0.221783i	−0.0114211	−	0.0105972i
$439$	−20.5292	−	13.9966i	−0.979806	−	0.668021i	−0.0362881	−	0.999341i	$-0.511553\pi$
$439$	−20.5292	−	13.9966i	−0.979806	−	0.668021i	−0.943518	+	0.331321i	$0.892506\pi$
$440$	−2.09119			−0.0996937
$441$	20.5692	+	4.00519i	0.979488	+	0.190723i
$442$	−9.27592			−0.441210
$443$	−14.6972	−	10.0204i	−0.698287	−	0.476084i	0.161411	−	0.986887i	$-0.448396\pi$
$443$	−14.6972	−	10.0204i	−0.698287	−	0.476084i	−0.859697	+	0.510804i	$0.829348\pi$
$444$	0.104607	+	0.0970615i	0.00496445	+	0.00460633i
$445$	1.34780	+	3.43415i	0.0638920	+	0.162794i
$446$	17.4490	−	5.38229i	0.826232	−	0.254859i
$447$	−0.0134862	−	0.0590871i	−0.000637877	−	0.00279472i
$448$	−0.533520	−	2.59140i	−0.0252064	−	0.122432i
$449$	5.31876	−	23.3030i	0.251008	−	1.09974i	−0.679560	−	0.733619i	$-0.737829\pi$
$449$	5.31876	−	23.3030i	0.251008	−	1.09974i	0.930568	−	0.366118i	$-0.119313\pi$
$450$	1.07391	+	14.3303i	0.0506245	+	0.675537i
$451$	22.6512	+	6.98696i	1.06660	+	0.329003i
$452$	0.532674	−	7.10804i	0.0250549	−	0.334334i
$453$	−0.550321	+	1.40219i	−0.0258563	+	0.0658808i
$454$	3.78023	−	1.82046i	0.177415	−	0.0854384i
$455$	8.11152	+	1.40038i	0.380274	+	0.0656507i
$456$	0.359577	+	0.173163i	0.0168387	+	0.00810911i
$457$	−6.77693	+	6.28807i	−0.317011	+	0.294144i	−0.822588	−	0.568638i	$-0.807470\pi$
$457$	−6.77693	+	6.28807i	−0.317011	+	0.294144i	0.505576	+	0.862782i	$0.331280\pi$
$458$	−3.30562	+	0.498243i	−0.154462	+	0.0232814i
$459$	0.318138	−	0.551032i	0.0148494	−	0.0257200i
$460$	−0.735777	−	1.27440i	−0.0343058	−	0.0594194i
$461$	11.9577	+	14.9945i	0.556925	+	0.698362i	0.977986	−	0.208670i	$-0.0669136\pi$
$461$	11.9577	+	14.9945i	0.556925	+	0.698362i	−0.421061	+	0.907032i	$0.638342\pi$
$462$	0.708721	+	0.686337i	0.0329727	+	0.0319313i
$463$	−3.44238	+	4.31660i	−0.159981	+	0.200610i	−0.855361	−	0.518033i	$-0.826665\pi$
$463$	−3.44238	+	4.31660i	−0.159981	+	0.200610i	0.695380	+	0.718642i	$0.255236\pi$
$464$	−5.46067	−	0.823063i	−0.253505	−	0.0382097i
$465$	−0.122796	+	0.0837206i	−0.00569451	+	0.00388245i
$466$	18.5973	−	12.6794i	0.861503	−	0.587363i
$467$	35.0712	+	5.28614i	1.62290	+	0.244613i	0.896626	−	0.442789i	$-0.146011\pi$
$467$	35.0712	+	5.28614i	1.62290	+	0.244613i	0.726277	+	0.687402i	$0.241249\pi$
$468$	−12.9955	+	16.2958i	−0.600716	+	0.753274i
$469$	−1.72718	+	0.222722i	−0.0797536	+	0.0102844i
$470$	−1.48830	−	1.86627i	−0.0686501	−	0.0860845i
$471$	0.280841	+	0.486432i	0.0129405	+	0.0224136i
$472$	−5.02758	+	8.70802i	−0.231413	+	0.400819i
$473$	36.5165	−	5.50398i	1.67903	−	0.253073i
$474$	0.108443	−	0.100621i	0.00498097	−	0.00462166i
$475$	21.6622	+	10.4320i	0.993931	+	0.478652i
$476$	−1.35756	+	3.25297i	−0.0622235	+	0.149100i
$477$	−24.2783	+	11.6918i	−1.11163	+	0.535332i
$478$	−4.88592	+	12.4491i	−0.223477	+	0.569410i
$479$	−1.98290	+	26.4599i	−0.0906009	+	1.20899i	0.747797	+	0.663927i	$0.231111\pi$
$479$	−1.98290	+	26.4599i	−0.0906009	+	1.20899i	−0.838398	+	0.545058i	$0.816508\pi$
$480$	0.0340245	+	0.0104952i	0.00155300	+	0.000479037i
$481$	0.931806	+	12.4341i	0.0424867	+	0.566946i
$482$	2.36045	−	10.3418i	0.107515	−	0.471056i
$483$	−0.168903	+	0.673390i	−0.00768536	+	0.0306403i
$484$	−2.42554	−	10.6270i	−0.110252	−	0.483045i
$485$	−7.17790	+	2.21409i	−0.325932	+	0.100537i
$486$	−0.783781	−	1.99704i	−0.0355530	−	0.0905877i
$487$	−14.0114	−	13.0007i	−0.634917	−	0.589117i	0.295624	−	0.955304i	$-0.404472\pi$
$487$	−14.0114	−	13.0007i	−0.634917	−	0.589117i	−0.930541	+	0.366188i	$0.880663\pi$
$488$	−5.13676	−	3.50218i	−0.232530	−	0.158536i
$489$	−1.43212			−0.0647629
$490$	1.67824	−	2.63968i	0.0758153	−	0.119249i
$491$	31.5030			1.42171			0.710855	−	0.703338i	$-0.248308\pi$
$491$	31.5030			1.42171			0.710855	+	0.703338i	$0.248308\pi$
$492$	−0.333478	−	0.227361i	−0.0150343	−	0.0102502i
$493$	5.39329	+	5.00424i	0.242902	+	0.225380i
$494$	12.7404	+	32.4620i	0.573217	+	1.46053i
$495$	5.98217	−	1.84526i	0.268879	−	0.0829381i
$496$	0.928794	+	4.06931i	0.0417041	+	0.182718i
$497$	0.672681	+	0.0143678i	0.0301739	+	0.000644484i
$498$	0.277760	−	1.21695i	0.0124467	−	0.0545327i
$499$	−1.62391	−	21.6696i	−0.0726963	−	0.970064i	−0.907646	−	0.419738i	$-0.862122\pi$
$499$	−1.62391	−	21.6696i	−0.0726963	−	0.970064i	0.834949	−	0.550327i	$-0.185497\pi$
$500$	4.18478	+	1.29084i	0.187149	+	0.0577279i
$501$	−0.0275283	+	0.367339i	−0.00122987	+	0.0164115i
$502$	2.87313	−	7.32062i	0.128234	−	0.326735i
$503$	−29.8959	+	14.3971i	−1.33299	+	0.641935i	−0.958446	−	0.285273i	$-0.907916\pi$
$503$	−29.8959	+	14.3971i	−1.33299	+	0.641935i	−0.374546	+	0.927208i	$0.622201\pi$
$504$	3.81285	+	6.94232i	0.169838	+	0.309235i
$505$	5.88833	+	2.83567i	0.262027	+	0.126186i
$506$	11.2971	−	10.4822i	0.502217	−	0.465989i
$507$	2.79518	−	0.421306i	0.124139	−	0.0187109i
$508$	−0.639535	+	1.10771i	−0.0283748	+	0.0491465i
$509$	2.35133	+	4.07262i	0.104221	+	0.180515i	0.913420	−	0.407019i	$-0.133432\pi$
$509$	2.35133	+	4.07262i	0.104221	+	0.180515i	−0.809199	+	0.587535i	$0.800099\pi$
$510$	−0.0295769	−	0.0370883i	−0.00130969	−	0.00164230i
$511$	−10.2753	−	3.41145i	−0.454551	−	0.150913i
$512$	0.623490	−	0.781831i	0.0275546	−	0.0345524i
$513$	−2.36535	−	0.356519i	−0.104433	−	0.0157407i
$514$	−15.4384	+	10.5257i	−0.680958	+	0.464269i
$515$	−2.51210	+	1.71272i	−0.110697	+	0.0754716i
$516$	−0.621762	−	0.0937155i	−0.0273715	−	0.00412559i
$517$	15.5864	−	19.5447i	0.685489	−	0.859576i
$518$	4.49688	+	1.49299i	0.197582	+	0.0655982i
$519$	−0.278815	−	0.349623i	−0.0122386	−	0.0153468i
$520$	1.55561	+	2.69439i	0.0682180	+	0.118157i
$521$	−17.3732	+	30.0913i	−0.761135	+	1.31832i	0.181131	+	0.983459i	$0.442024\pi$
$521$	−17.3732	+	30.0913i	−0.761135	+	1.31832i	−0.942266	+	0.334866i	$0.891309\pi$
$522$	16.3473	−	2.46396i	0.715503	−	0.107845i
$523$	4.63952	−	4.30484i	0.202872	−	0.188238i	−0.572193	−	0.820119i	$-0.693907\pi$
$523$	4.63952	−	4.30484i	0.202872	−	0.188238i	0.775065	+	0.631881i	$0.217717\pi$
$524$	11.8300	+	5.69702i	0.516795	+	0.248875i
$525$	−0.487167	−	0.887019i	−0.0212617	−	0.0387127i
$526$	7.56836	−	3.64473i	0.329996	−	0.158918i
$527$	2.03162	−	5.17648i	0.0884988	−	0.225491i
$528$	−0.0278663	+	0.371850i	−0.00121273	+	0.0161827i
$529$	−11.6154	−	3.58286i	−0.505015	−	0.155777i
$530$	0.300589	+	4.01108i	0.0130567	+	0.174230i
$531$	6.69824	−	29.3469i	0.290679	−	1.27355i
$532$	13.2487	+	0.282979i	0.574404	+	0.0122687i
$533$	−7.84755	−	34.3824i	−0.339915	−	1.48927i
$534$	0.628611	−	0.193901i	0.0272027	−	0.00839091i
$535$	0.262562	+	0.668996i	0.0113515	+	0.0289232i
$536$	−0.482507	−	0.447701i	−0.0208411	−	0.0193377i
$537$	0.951163	+	0.648492i	0.0410457	+	0.0279845i
$538$	−13.3027			−0.573519
$539$	30.8622	+	10.9835i	1.32933	+	0.473093i
$540$	−0.213412			−0.00918381
$541$	19.7357	+	13.4556i	0.848504	+	0.578501i	0.907640	−	0.419749i	$-0.137882\pi$
$541$	19.7357	+	13.4556i	0.848504	+	0.578501i	−0.0591356	+	0.998250i	$0.518834\pi$
$542$	−0.928383	−	0.861414i	−0.0398775	−	0.0370009i
$543$	0.394800	+	1.00593i	0.0169425	+	0.0431687i
$544$	−1.27309	+	0.392696i	−0.0545833	+	0.0168367i
$545$	−0.236813	−	1.03755i	−0.0101440	−	0.0444437i
$546$	0.357102	−	1.42371i	0.0152825	−	0.0609291i
$547$	−6.13147	+	26.8637i	−0.262163	+	1.14861i	0.656738	+	0.754119i	$0.271936\pi$
$547$	−6.13147	+	26.8637i	−0.262163	+	1.14861i	−0.918900	+	0.394490i	$0.870921\pi$
$548$	0.570172	+	7.60842i	0.0243566	+	0.325016i
$549$	17.7848	+	5.48587i	0.759035	+	0.234131i
$550$	−1.67877	+	22.4016i	−0.0715829	+	0.955207i
$551$	10.1052	−	25.7476i	0.430496	−	1.09689i
$552$	−0.236416	+	0.113852i	−0.0100625	+	0.00484585i
$553$	1.89179	−	4.53309i	0.0804469	−	0.192766i
$554$	−16.4002	−	7.89790i	−0.696776	−	0.335550i
$555$	−0.0467446	+	0.0433727i	−0.00198420	+	0.00184107i
$556$	5.51271	−	0.830908i	0.233791	−	0.0352383i
$557$	−4.84817	+	8.39728i	−0.205424	+	0.355804i	−0.950268	−	0.311434i	$-0.899191\pi$
$557$	−4.84817	+	8.39728i	−0.205424	+	0.355804i	0.744844	+	0.667239i	$0.232524\pi$
$558$	−6.24769	−	10.8213i	−0.264486	−	0.458103i
$559$	−34.2557	−	42.9554i	−1.44886	−	1.81682i
$560$	1.17257	−	0.151204i	0.0495499	−	0.00638954i
$561$	0.309748	−	0.388412i	0.0130776	−	0.0163988i
$562$	14.0065	+	2.11114i	0.590828	+	0.0890529i
$563$	−25.4499	+	17.3514i	−1.07258	+	0.731276i	−0.964823	−	0.262901i	$-0.915321\pi$
$563$	−25.4499	+	17.3514i	−1.07258	+	0.731276i	−0.107762	+	0.994177i	$0.534368\pi$
$564$	−0.351687	+	0.239776i	−0.0148087	+	0.0100964i
$565$	3.14961	+	0.474728i	0.132505	+	0.0199719i
$566$	9.72772	−	12.1982i	0.408886	−	0.512727i
$567$	−16.9969	−	16.4601i	−0.713802	−	0.691258i
$568$	0.158558	+	0.198826i	0.00665296	+	0.00834254i
$569$	−17.9741	−	31.1320i	−0.753512	−	1.30512i	−0.946111	−	0.323844i	$-0.895025\pi$
$569$	−17.9741	−	31.1320i	−0.753512	−	1.30512i	0.192599	−	0.981278i	$-0.438308\pi$
$570$	−0.0891705	+	0.154448i	−0.00373494	+	0.00646911i
$571$	11.9918	−	1.80748i	0.501842	−	0.0756406i	0.106757	−	0.994285i	$-0.465953\pi$
$571$	11.9918	−	1.80748i	0.501842	−	0.0756406i	0.395085	+	0.918645i	$0.370715\pi$
$572$	−23.8848	+	22.1618i	−0.998672	+	0.926633i
$573$	−1.46699	−	0.706467i	−0.0612845	−	0.0295131i
$574$	−13.2061	−	2.27990i	−0.551211	−	0.0951613i
$575$	−14.2425	+	6.85884i	−0.593954	+	0.286033i
$576$	−1.09370	+	2.78671i	−0.0455710	+	0.116113i
$577$	−0.896024	+	11.9566i	−0.0373020	+	0.497760i	0.946996	+	0.321245i	$0.104101\pi$
$577$	−0.896024	+	11.9566i	−0.0373020	+	0.497760i	−0.984298	+	0.176515i	$0.943518\pi$
$578$	−14.5486	−	4.48766i	−0.605143	−	0.186662i
$579$	0.0715285	+	0.954481i	0.00297262	+	0.0396669i
$580$	0.549116	−	2.40583i	0.0228008	−	0.0998967i
$581$	−8.35777	−	40.5952i	−0.346739	−	1.68417i
$582$	0.298054	+	1.30586i	0.0123547	+	0.0541296i
$583$	−40.2528	+	12.4164i	−1.66710	+	0.514233i
$584$	−1.49503	−	3.80926i	−0.0618646	−	0.157628i
$585$	−6.82757	−	6.33506i	−0.282285	−	0.261923i
$586$	19.6169	+	13.3746i	0.810367	+	0.552499i
$587$	22.2047			0.916486			0.458243	−	0.888827i	$-0.348479\pi$
$587$	22.2047			0.916486			0.458243	+	0.888827i	$0.348479\pi$
$588$	−0.447017	−	0.333596i	−0.0184347	−	0.0137573i
$589$	−20.9060			−0.861418
$590$	−3.71247	−	2.53112i	−0.152840	−	0.104205i
$591$	−1.00072	−	0.928528i	−0.0411639	−	0.0381946i
$592$	0.654285	+	1.66709i	0.0268909	+	0.0685170i
$593$	18.3799	−	5.66945i	0.754772	−	0.232816i	0.106591	−	0.994303i	$-0.466006\pi$
$593$	18.3799	−	5.66945i	0.754772	−	0.232816i	0.648181	+	0.761487i	$0.275530\pi$
$594$	−0.497332	−	2.17895i	−0.0204058	−	0.0894036i
$595$	−1.40422	−	0.713567i	−0.0575673	−	0.0292534i
$596$	0.169251	−	0.741538i	0.00693280	−	0.0303746i
$597$	−0.133626	−	1.78312i	−0.00546896	−	0.0729782i
$598$	−21.9095	−	6.75818i	−0.895946	−	0.276363i
$599$	−0.987589	+	13.1785i	−0.0403518	+	0.538457i	0.939997	+	0.341184i	$0.110828\pi$
$599$	−0.987589	+	13.1785i	−0.0403518	+	0.538457i	−0.980348	+	0.197274i	$0.936791\pi$
$600$	0.139742	−	0.356057i	0.00570495	−	0.0145360i
$601$	−19.9810	+	9.62234i	−0.815042	+	0.392504i	−0.794484	−	0.607285i	$-0.792259\pi$
$601$	−19.9810	+	9.62234i	−0.815042	+	0.392504i	−0.0205581	+	0.999789i	$0.506544\pi$
$602$	−20.0774	+	5.72651i	−0.818295	+	0.233395i
$603$	1.77533	+	0.854956i	0.0722972	+	0.0348165i
$604$	−13.8578	+	12.8581i	−0.563864	+	0.523189i
$605$	4.81647	−	0.725966i	0.195817	−	0.0295147i
$606$	0.582696	−	1.00926i	0.0236704	−	0.0409984i
$607$	10.1257	+	17.5382i	0.410990	+	0.711856i	0.994998	−	0.0998922i	$-0.0318498\pi$
$607$	10.1257	+	17.5382i	0.410990	+	0.711856i	−0.584008	+	0.811748i	$0.698516\pi$
$608$	3.12286	+	3.91594i	0.126649	+	0.158812i
$609$	−0.975702	+	0.635133i	−0.0395374	+	0.0257369i
$610$	1.73214	−	2.17203i	0.0701321	−	0.0879429i
$611$	−36.7769	−	5.54323i	−1.48783	−	0.224255i
$612$	3.29535	−	2.24673i	0.133207	−	0.0908189i
$613$	−1.81069	+	1.23451i	−0.0731330	+	0.0498612i	−0.599335	−	0.800499i	$-0.704568\pi$
$613$	−1.81069	+	1.23451i	−0.0731330	+	0.0498612i	0.526202	+	0.850360i	$0.323616\pi$
$614$	6.14976	+	0.926926i	0.248184	+	0.0374077i
$615$	0.112450	−	0.141008i	0.00453442	−	0.00568599i
$616$	4.27633	+	11.6196i	0.172298	+	0.468167i
$617$	−17.4124	−	21.8344i	−0.700996	−	0.879022i	0.296101	−	0.955157i	$-0.404313\pi$
$617$	−17.4124	−	21.8344i	−0.700996	−	0.879022i	−0.997098	+	0.0761350i	$0.975742\pi$
$618$	0.271077	+	0.469519i	0.0109043	+	0.0188868i
$619$	−2.54627	+	4.41026i	−0.102343	+	0.177263i	−0.912650	−	0.408743i	$-0.865967\pi$
$619$	−2.54627	+	4.41026i	−0.102343	+	0.177263i	0.810307	+	0.586006i	$0.199301\pi$
$620$	−1.84433	+	0.277989i	−0.0740703	+	0.0111643i
$621$	1.15290	−	1.06974i	0.0462644	−	0.0429271i
$622$	26.6835	+	12.8501i	1.06991	+	0.515242i
$623$	16.3255	−	14.5116i	0.654067	−	0.581393i
$624$	0.499839	−	0.240710i	0.0200096	−	0.00963611i
$625$	8.05381	−	20.5208i	0.322153	−	0.820831i
$626$	0.728483	−	9.72093i	0.0291160	−	0.388527i
$627$	−1.78472	−	0.550514i	−0.0712750	−	0.0219854i
$628$	0.526778	+	7.02936i	0.0210207	+	0.280502i
$629$	0.530927	−	2.32614i	0.0211694	−	0.0927494i
$630$	−3.22088	+	1.46721i	−0.128323	+	0.0584549i
$631$	−7.41251	−	32.4763i	−0.295087	−	1.29286i	−0.877346	−	0.479859i	$-0.840688\pi$
$631$	−7.41251	−	32.4763i	−0.295087	−	1.29286i	0.582258	−	0.813004i	$-0.302169\pi$
$632$	1.77408	−	0.547231i	0.0705691	−	0.0217677i
$633$	−0.403245	−	1.02745i	−0.0160275	−	0.0408375i
$634$	5.46824	+	5.07379i	0.217172	+	0.201506i
$635$	−0.472246	−	0.321972i	−0.0187405	−	0.0127771i
$636$	0.717244			0.0284406
$637$	−8.80630	−	47.9349i	−0.348918	−	1.89925i
$638$	25.8433			1.02315
$639$	−0.629022	−	0.428860i	−0.0248837	−	0.0169654i
$640$	0.327570	+	0.303940i	0.0129483	+	0.0120143i
$641$	10.3798	+	26.4473i	0.409978	+	1.04461i	0.975525	+	0.219890i	$0.0705699\pi$
$641$	10.3798	+	26.4473i	0.409978	+	1.04461i	−0.565547	+	0.824716i	$0.691335\pi$
$642$	0.122458	−	0.0377732i	0.00483302	−	0.00149079i
$643$	7.00563	+	30.6937i	0.276275	+	1.21044i	0.902463	+	0.430768i	$0.141757\pi$
$643$	7.00563	+	30.6937i	0.276275	+	1.21044i	−0.626188	+	0.779672i	$0.715386\pi$
$644$	−5.57655	+	6.69436i	−0.219747	+	0.263795i
$645$	0.0625233	−	0.273933i	0.00246185	−	0.0107861i
$646$	−0.498671	−	6.65430i	−0.0196199	−	0.261810i
$647$	−38.1776	−	11.7762i	−1.50092	−	0.462972i	−0.567990	−	0.823036i	$-0.692279\pi$
$647$	−38.1776	−	11.7762i	−1.50092	−	0.462972i	−0.932928	+	0.360064i	$0.882755\pi$
$648$	0.668304	−	8.91789i	0.0262534	−	0.350328i
$649$	17.1914	−	43.8031i	0.674823	−	1.71942i
$650$	30.1121	−	14.5012i	1.18109	−	0.568785i
$651$	0.716296	+	0.511105i	0.0280739	+	0.0200318i
$652$	−16.1931	−	7.79821i	−0.634173	−	0.305401i
$653$	−29.7896	+	27.6407i	−1.16576	+	1.08167i	−0.170405	+	0.985374i	$0.554508\pi$
$653$	−29.7896	+	27.6407i	−1.16576	+	1.08167i	−0.995353	+	0.0962913i	$0.969302\pi$
$654$	−0.187650	+	0.0282836i	−0.00733768	+	0.00110598i
$655$	−2.93368	+	5.08129i	−0.114629	+	0.198542i
$656$	−2.53263	−	4.38665i	−0.0988826	−	0.171270i
$657$	7.63802	+	9.57777i	0.297987	+	0.373664i
$658$	−7.32636	+	12.0860i	−0.285611	+	0.471162i
$659$	−11.9814	+	15.0242i	−0.466731	+	0.585262i	−0.958367	−	0.285539i	$-0.907827\pi$
$659$	−11.9814	+	15.0242i	−0.466731	+	0.585262i	0.491637	+	0.870800i	$0.336399\pi$
$660$	−0.164769	−	0.0248349i	−0.00641362	−	0.000966698i
$661$	28.5957	−	19.4962i	1.11225	−	0.758316i	0.139507	−	0.990221i	$-0.455448\pi$
$661$	28.5957	−	19.4962i	1.11225	−	0.758316i	0.972738	+	0.231905i	$0.0744959\pi$
$662$	−1.50849	+	1.02847i	−0.0586291	+	0.0399727i
$663$	−0.730867	−	0.110160i	−0.0283845	−	0.00427828i
$664$	9.76719	−	12.2477i	0.379040	−	0.475302i
$665$	−0.568521	+	5.89427i	−0.0220463	+	0.228570i
$666$	−3.34271	−	4.19163i	−0.129527	−	0.162422i
$667$	9.09287	+	15.7493i	0.352077	+	0.609816i
$668$	−2.31150	+	4.00364i	−0.0894347	+	0.154905i
$669$	1.43876	−	0.216858i	0.0556255	−	0.00838420i
$670$	0.215612	−	0.200059i	0.00832982	−	0.00772894i
$671$	26.2131	+	12.6236i	1.01194	+	0.487327i
$672$	−0.0112616	−	0.210517i	−0.000434426	−	0.00812088i
$673$	4.23514	−	2.03954i	0.163253	−	0.0786183i	−0.350473	−	0.936573i	$-0.613979\pi$
$673$	4.23514	−	2.03954i	0.163253	−	0.0786183i	0.513726	+	0.857954i	$0.328265\pi$
$674$	−9.99559	+	25.4683i	−0.385016	+	0.981004i
$675$	−0.171323	+	2.28615i	−0.00659423	+	0.0879939i
$676$	33.8995	+	10.4566i	1.30383	+	0.402177i
$677$	1.83663	+	24.5081i	0.0705873	+	0.941922i	0.914277	+	0.405090i	$0.132760\pi$
$677$	1.83663	+	24.5081i	0.0705873	+	0.941922i	−0.843689	+	0.536832i	$0.819621\pi$
$678$	0.126385	−	0.553730i	0.00485379	−	0.0212659i
$679$	26.9807	+	35.3560i	1.03543	+	1.35684i
$680$	−0.132475	−	0.580413i	−0.00508020	−	0.0222578i
$681$	0.319471	−	0.0985436i	0.0122421	−	0.00377620i
$682$	−7.13628	−	18.1830i	−0.273262	−	0.696261i
$683$	17.8669	+	16.5780i	0.683657	+	0.634341i	0.943524	−	0.331303i	$-0.107488\pi$
$683$	17.8669	+	16.5780i	0.683657	+	0.634341i	−0.259867	+	0.965644i	$0.583679\pi$
$684$	−12.3888	−	8.44655i	−0.473698	−	0.322962i
$685$	−3.40941			−0.130267
$686$	−18.0991	−	3.92713i	−0.691027	−	0.149938i
$687$	−0.266373			−0.0101628
$688$	−6.52001	−	4.44527i	−0.248573	−	0.169474i
$689$	45.9414	+	42.6274i	1.75023	+	1.62397i
$690$	−0.0428385	−	0.109151i	−0.00163083	−	0.00415529i
$691$	13.6363	−	4.20624i	0.518749	−	0.160013i	−0.0243148	−	0.999704i	$-0.507740\pi$
$691$	13.6363	−	4.20624i	0.518749	−	0.160013i	0.543064	+	0.839692i	$0.317264\pi$
$692$	−1.24882	−	5.47142i	−0.0474729	−	0.207992i
$693$	−22.4861	−	29.4662i	−0.854178	−	1.11933i
$694$	4.30045	−	18.8415i	0.163243	−	0.715214i
$695$	0.186169	+	2.48426i	0.00706180	+	0.0942332i
$696$	−0.420481	−	0.129701i	−0.0159383	−	0.00491632i
$697$	−0.504305	+	6.72948i	−0.0191019	+	0.254897i
$698$	−8.84905	+	22.5470i	−0.334941	+	0.853417i
$699$	1.61589	−	0.778174i	0.0611187	−	0.0294332i
$700$	−0.678440	−	12.6823i	−0.0256426	−	0.479346i
$701$	33.9759	+	16.3619i	1.28325	+	0.617982i	0.946224	−	0.323512i	$-0.104864\pi$
$701$	33.9759	+	16.3619i	1.28325	+	0.617982i	0.337029	+	0.941494i	$0.390578\pi$
$702$	−2.43751	+	2.26168i	−0.0919980	+	0.0853616i
$703$	−8.86979	+	1.33691i	−0.334531	+	0.0504224i
$704$	−2.33989	+	4.05280i	−0.0881878	+	0.152746i
$705$	−0.0951021	−	0.164722i	−0.00358175	−	0.00620378i
$706$	−16.2518	−	20.3791i	−0.611645	−	0.766979i
$707$	3.71507	−	38.5169i	0.139720	−	1.44858i
$708$	−0.499548	+	0.626414i	−0.0187742	+	0.0235421i
$709$	24.7413	+	3.72915i	0.929179	+	0.140051i	0.596157	−	0.802868i	$-0.296693\pi$
$709$	24.7413	+	3.72915i	0.929179	+	0.140051i	0.333022	+	0.942919i	$0.391932\pi$
$710$	−0.0938932	+	0.0640153i	−0.00352375	+	0.00240245i
$711$	−4.59215	+	3.13087i	−0.172219	+	0.117417i
$712$	8.16358	+	1.23046i	0.305943	+	0.0461135i
$713$	8.57008	−	10.7465i	0.320952	−	0.402461i
$714$	−0.145597	+	0.240185i	−0.00544882	+	0.00898871i
$715$	−9.07789	−	11.3833i	−0.339494	−	0.425712i
$716$	7.22371	+	12.5118i	0.269963	+	0.467589i
$717$	−0.532816	+	0.922865i	−0.0198984	+	0.0344650i
$718$	3.24907	−	0.489719i	0.121254	−	0.0182761i
$719$	1.11847	−	1.03779i	0.0417118	−	0.0387029i	−0.659041	−	0.752107i	$-0.729038\pi$
$719$	1.11847	−	1.03779i	0.0417118	−	0.0387029i	0.700753	+	0.713404i	$0.252847\pi$
$720$	−1.20526	−	0.580422i	−0.0449173	−	0.0216310i
$721$	14.6537	+	10.4560i	0.545733	+	0.389401i
$722$	−5.48406	+	2.64098i	−0.204096	+	0.0982873i
$723$	0.308803	−	0.786817i	0.0114845	−	0.0292620i
$724$	−1.01348	+	13.5239i	−0.0376656	+	0.502613i
$725$	−25.3313	−	7.81367i	−0.940781	−	0.290192i
$726$	−0.0649072	−	0.866126i	−0.00240893	−	0.0321450i
$727$	4.02231	−	17.6229i	0.149179	−	0.653597i	−0.843935	−	0.536446i	$-0.819767\pi$
$727$	4.02231	−	17.6229i	0.149179	−	0.653597i	0.993114	−	0.117151i	$-0.0373762\pi$
$728$	11.7902	−	14.1535i	0.436972	−	0.524563i
$729$	5.93191	+	25.9894i	0.219700	+	0.962570i
$730$	1.74736	−	0.538990i	0.0646728	−	0.0199489i
$731$	3.84093	+	9.78653i	0.142062	+	0.361968i
$732$	−0.363143	−	0.336947i	−0.0134221	−	0.0124539i
$733$	43.2568	+	29.4920i	1.59773	+	1.08931i	0.942668	+	0.333733i	$0.108308\pi$
$733$	43.2568	+	29.4920i	1.59773	+	1.08931i	0.655059	+	0.755578i	$0.272644\pi$
$734$	2.66803			0.0984790
$735$	0.163581	−	0.188054i	0.00603376	−	0.00693649i
$736$	−3.29312			−0.121386
$737$	2.54507	+	1.73520i	0.0937488	+	0.0639169i
$738$	11.1157	+	10.3139i	0.409176	+	0.379659i
$739$	−7.00237	−	17.8417i	−0.257586	−	0.656319i	0.742320	−	0.670046i	$-0.233726\pi$
$739$	−7.00237	−	17.8417i	−0.257586	−	0.656319i	−0.999906	+	0.0137270i	$0.995630\pi$
$740$	−0.764718	+	0.235884i	−0.0281116	+	0.00867128i
$741$	0.618322	+	2.70904i	0.0227146	+	0.0995193i
$742$	21.6726	−	9.87254i	0.795628	−	0.362432i
$743$	−6.19260	+	27.1316i	−0.227185	+	0.995361i	0.724739	+	0.689024i	$0.241961\pi$
$743$	−6.19260	+	27.1316i	−0.227185	+	0.995361i	−0.951923	+	0.306337i	$0.900897\pi$
$744$	0.0248544	+	0.331659i	0.000911207	+	0.0121592i
$745$	0.324783	+	0.100182i	0.0118991	+	0.00367040i
$746$	−1.16321	+	15.5220i	−0.0425882	+	0.568300i
$747$	−17.1332	+	43.6548i	−0.626873	+	1.59725i
$748$	5.61733	−	2.70516i	0.205390	−	0.0989106i
$749$	3.18032	−	2.82695i	0.116206	−	0.103295i
$750$	0.314397	+	0.151406i	0.0114802	+	0.00552855i
$751$	6.46920	−	6.00254i	0.236065	−	0.219036i	−0.553266	−	0.833005i	$-0.686619\pi$
$751$	6.46920	−	6.00254i	0.236065	−	0.219036i	0.789330	+	0.613969i	$0.210428\pi$
$752$	−5.28219	+	0.796161i	−0.192622	+	0.0290330i
$753$	0.313319	−	0.542684i	0.0114180	−	0.0197765i
$754$	−19.2245	−	33.2978i	−0.700115	−	1.21263i
$755$	−5.26692	−	6.60451i	−0.191683	−	0.240363i
$756$	0.436412	+	1.18581i	0.0158721	+	0.0431277i
$757$	−29.8250	+	37.3994i	−1.08401	+	1.35931i	−0.155569	+	0.987825i	$0.549721\pi$
$757$	−29.8250	+	37.3994i	−1.08401	+	1.35931i	−0.928441	+	0.371480i	$0.878850\pi$
$758$	16.9133	+	2.54927i	0.614318	+	0.0925936i
$759$	1.01460	−	0.691746i	0.0368278	−	0.0251088i
$760$	−1.84926	+	1.26080i	−0.0670797	+	0.0457341i
$761$	7.05385	+	1.06320i	0.255702	+	0.0385409i	0.275642	−	0.961260i	$-0.411110\pi$
$761$	7.05385	+	1.06320i	0.255702	+	0.0385409i	−0.0199403	+	0.999801i	$0.506348\pi$
$762$	−0.0635452	+	0.0796831i	−0.00230200	+	0.00288662i
$763$	−5.28081	+	3.43754i	−0.191178	+	0.124447i
$764$	−12.7406	−	15.9762i	−0.460937	−	0.577997i
$765$	0.891119	+	1.54346i	0.0322185	+	0.0558040i
$766$	3.63272	−	6.29205i	0.131255	−	0.227341i
$767$	−69.2265	+	10.4342i	−2.49962	+	0.376758i
$768$	0.0584109	−	0.0541974i	0.00210772	−	0.00195568i
$769$	−21.8541	−	10.5244i	−0.788080	−	0.379519i	−0.00385239	−	0.999993i	$-0.501226\pi$
$769$	−21.8541	−	10.5244i	−0.788080	−	0.379519i	−0.784228	+	0.620473i	$0.786941\pi$
$770$	−5.32059	+	1.51754i	−0.191741	+	0.0546885i
$771$	−1.34142	+	0.645995i	−0.0483101	+	0.0232649i
$772$	−4.38857	+	11.1819i	−0.157948	+	0.402445i
$773$	−0.0304992	+	0.406984i	−0.00109698	+	0.0146382i	−0.997725	−	0.0674090i	$-0.978527\pi$
$773$	−0.0304992	+	0.406984i	−0.00109698	+	0.0146382i	0.996628	+	0.0820472i	$0.0261458\pi$
$774$	22.5740	+	6.96314i	0.811404	+	0.250285i
$775$	1.49732	+	19.9803i	0.0537853	+	0.717715i
$776$	−3.74055	+	16.3884i	−0.134278	+	0.588310i
$777$	0.336587	+	0.171040i	0.0120750	+	0.00613603i
$778$	−4.44269	−	19.4647i	−0.159278	−	0.697844i
$779$	24.2431	−	7.47802i	0.868601	−	0.267928i
$780$	0.0905708	+	0.230771i	0.00324296	+	0.00826291i
$781$	−0.872407	−	0.809475i	−0.0312172	−	0.0289653i
$782$	3.62500	+	2.47148i	0.129630	+	0.0883801i
$783$	2.63739			0.0942526
$784$	−3.23796	−	6.20609i	−0.115641	−	0.221646i
$785$	−3.14993			−0.112426
$786$	0.864448	+	0.589371i	0.0308339	+	0.0210222i
$787$	4.04448	+	3.75272i	0.144170	+	0.133770i	0.748961	−	0.662614i	$-0.230553\pi$
$787$	4.04448	+	3.75272i	0.144170	+	0.133770i	−0.604791	+	0.796384i	$0.706743\pi$
$788$	−6.25915	−	15.9480i	−0.222973	−	0.568126i
$789$	0.639610	−	0.197293i	0.0227707	−	0.00702383i
$790$	0.184607	+	0.808818i	0.00656804	+	0.0287764i
$791$	−3.80291	−	18.4714i	−0.135216	−	0.656768i
$792$	3.11743	−	13.6584i	0.110773	−	0.485329i
$793$	−3.23475	−	43.1647i	−0.114869	−	1.53282i
$794$	−27.0859	−	8.35490i	−0.961244	−	0.296504i
$795$	−0.0239515	+	0.319610i	−0.000849470	+	0.0113354i
$796$	8.19853	−	20.8895i	0.290589	−	0.740409i
$797$	45.6273	−	21.9730i	1.61620	−	0.778322i	0.616245	−	0.787554i	$-0.288653\pi$
$797$	45.6273	−	21.9730i	1.61620	−	0.778322i	0.999957	+	0.00923199i	$0.00293868\pi$
$798$	1.04053	+	0.179637i	0.0368343	+	0.00635909i
$799$	6.41205	+	3.08788i	0.226842	+	0.109241i
$800$	3.51888	−	3.26505i	0.124411	−	0.115437i
$801$	−24.4389	+	3.68357i	−0.863507	+	0.130153i
$802$	0.468216	−	0.810974i	0.0165333	−	0.0286365i
$803$	9.57514	+	16.5846i	0.337899	+	0.585259i
$804$	−0.0327007	−	0.0410054i	−0.00115327	−	0.00144615i
$805$	−2.79684	−	2.70850i	−0.0985756	−	0.0954622i
$806$	−18.1192	+	22.7208i	−0.638222	+	0.800305i
$807$	−1.04814	−	0.157982i	−0.0368964	−	0.00556123i
$808$	12.0842	−	8.23888i	0.425121	−	0.289843i
$809$	29.9081	−	20.3910i	1.05151	−	0.716910i	0.0911999	−	0.995833i	$-0.470930\pi$
$809$	29.9081	−	20.3910i	1.05151	−	0.716910i	0.960314	+	0.278923i	$0.0899774\pi$
$810$	3.95157	+	0.595603i	0.138844	+	0.0209274i
$811$	−15.0068	+	18.8180i	−0.526962	+	0.660789i	−0.972071	−	0.234687i	$-0.924593\pi$
$811$	−15.0068	+	18.8180i	−0.526962	+	0.660789i	0.445109	+	0.895476i	$0.353165\pi$
$812$	−14.4908	+	1.86861i	−0.508526	+	0.0655753i
$813$	−0.0629189	−	0.0788978i	−0.00220666	−	0.00276707i
$814$	−4.19048	−	7.25812i	−0.146876	−	0.254397i
$815$	4.01569	−	6.95539i	0.140664	−	0.243637i
$816$	−0.104973	+	0.0158221i	−0.00367478	+	0.000553884i
$817$	28.9735	−	26.8834i	1.01365	−	0.940533i
$818$	−16.1606	−	7.78256i	−0.565044	−	0.272111i
$819$	−21.2386	+	50.8917i	−0.742136	+	1.77830i
$820$	2.03930	−	0.982075i	0.0712154	−	0.0342955i
$821$	−7.55367	+	19.2464i	−0.263625	+	0.671706i	−0.999988	−	0.00488102i	$-0.998446\pi$
$821$	−7.55367	+	19.2464i	−0.263625	+	0.671706i	0.736363	+	0.676587i	$0.236542\pi$
$822$	−0.0454324	+	0.606253i	−0.00158464	+	0.0211455i
$823$	2.44783	+	0.755055i	0.0853259	+	0.0263196i	0.337124	−	0.941460i	$-0.390546\pi$
$823$	2.44783	+	0.755055i	0.0853259	+	0.0263196i	−0.251798	+	0.967780i	$0.581022\pi$
$824$	0.508462	+	6.78495i	0.0177131	+	0.236365i
$825$	−0.398314	+	1.74513i	−0.0138675	+	0.0607575i
$826$	−6.47232	+	25.8041i	−0.225201	+	0.897840i
$827$	−4.01538	−	17.5925i	−0.139629	−	0.611753i	−0.995516	−	0.0945909i	$-0.969846\pi$
$827$	−4.01538	−	17.5925i	−0.139629	−	0.611753i	0.855888	−	0.517162i	$-0.173011\pi$
$828$	9.42046	−	2.90583i	0.327384	−	0.100984i
$829$	−8.28721	−	21.1155i	−0.287827	−	0.733370i	−0.999523	−	0.0308831i	$-0.990168\pi$
$829$	−8.28721	−	21.1155i	−0.287827	−	0.733370i	0.711696	−	0.702487i	$-0.247927\pi$
$830$	5.13150	+	4.76133i	0.178117	+	0.165268i
$831$	−1.19840	−	0.817058i	−0.0415722	−	0.0283434i
$832$	6.96244			0.241379
$833$	−1.09339	+	9.26164i	−0.0378836	+	0.320897i
$834$	0.444225			0.0153822
$835$	−1.70686	−	1.16372i	−0.0590685	−	0.0402722i
$836$	−17.1824	−	15.9429i	−0.594264	−	0.551397i
$837$	−0.728279	−	1.85562i	−0.0251730	−	0.0641398i
$838$	−22.3521	+	6.89470i	−0.772140	+	0.238174i
$839$	10.0547	+	44.0524i	0.347126	+	1.52086i	0.783671	+	0.621176i	$0.213345\pi$
$839$	10.0547	+	44.0524i	0.347126	+	1.52086i	−0.436545	+	0.899682i	$0.643798\pi$
$840$	0.0941843	+	0.00201168i	0.00324967	+	6.94097e-5i
$841$	−0.332962	+	1.45880i	−0.0114815	+	0.0503035i
$842$	1.40889	+	18.8004i	0.0485536	+	0.647903i
$843$	1.07852	+	0.332681i	0.0371464	+	0.0114581i
$844$	1.03516	−	13.8132i	0.0356316	−	0.475471i
$845$	−5.79158	+	14.7567i	−0.199236	+	0.507646i
$846$	14.4080	−	6.93851i	0.495356	−	0.238551i
$847$	−13.8831	−	25.2779i	−0.477029	−	0.868560i
$848$	8.10994	+	3.90554i	0.278497	+	0.134117i
$849$	0.911330	−	0.845590i	0.0312768	−	0.0290206i
$850$	−6.32394	+	0.953180i	−0.216909	+	0.0326938i
$851$	2.94880	−	5.10747i	0.101084	−	0.175082i
$852$	0.0101318	+	0.0175489i	0.000347111	+	0.000601215i
$853$	−16.6074	−	20.8250i	−0.568626	−	0.713034i	0.411500	−	0.911410i	$-0.365005\pi$
$853$	−16.6074	−	20.8250i	−0.568626	−	0.713034i	−0.980126	+	0.198375i	$0.936434\pi$
$854$	−15.6108	−	5.18289i	−0.534192	−	0.177355i
$855$	4.17756	−	5.23849i	0.142870	−	0.179153i
$856$	1.59032	+	0.239703i	0.0543561	+	0.00819287i
$857$	40.8523	−	27.8526i	1.39549	−	0.951427i	0.396037	−	0.918234i	$-0.370385\pi$
$857$	40.8523	−	27.8526i	1.39549	−	0.951427i	0.999449	−	0.0331922i	$-0.0105674\pi$
$858$	−2.14512	+	1.46252i	−0.0732331	+	0.0499295i
$859$	−25.4530	−	3.83642i	−0.868444	−	0.130897i	−0.300318	−	0.953839i	$-0.597093\pi$
$859$	−25.4530	−	3.83642i	−0.868444	−	0.130897i	−0.568125	+	0.822942i	$0.692331\pi$
$860$	2.19857	−	2.75693i	0.0749708	−	0.0940104i
$861$	−1.01345	−	0.336472i	−0.0345384	−	0.0114670i
$862$	6.64031	+	8.32669i	0.226170	+	0.283608i
$863$	−13.1220	−	22.7280i	−0.446679	−	0.773671i	0.551488	−	0.834183i	$-0.314060\pi$
$863$	−13.1220	−	22.7280i	−0.446679	−	0.773671i	−0.998167	+	0.0605116i	$0.980727\pi$
$864$	−0.238793	+	0.413601i	−0.00812389	+	0.0140710i
$865$	2.47981	−	0.373772i	0.0843162	−	0.0127086i
$866$	−5.25406	+	4.87505i	−0.178540	+	0.165661i
$867$	−1.09302	−	0.526370i	−0.0371208	−	0.0178764i
$868$	5.31615	+	9.67948i	0.180442	+	0.328543i
$869$	−7.82787	+	3.76970i	−0.265542	+	0.127878i
$870$	0.0718374	−	0.183039i	0.00243552	−	0.00620559i
$871$	0.342473	−	4.56998i	0.0116042	−	0.154848i
$872$	−2.27578	−	0.701985i	−0.0770676	−	0.0237722i
$873$	−3.76064	−	50.1822i	−0.127278	−	1.69841i
$874$	3.67030	−	16.0806i	0.124150	−	0.543935i
$875$	11.5840	+	0.247423i	0.391611	+	0.00836443i
$876$	−0.0725571	−	0.317894i	−0.00245148	−	0.0107406i
$877$	−11.8787	+	3.66410i	−0.401116	+	0.123728i	−0.488748	−	0.872425i	$-0.662546\pi$
$877$	−11.8787	+	3.66410i	−0.401116	+	0.123728i	0.0876321	+	0.996153i	$0.472070\pi$
$878$	−9.07748	−	23.1290i	−0.306350	−	0.780567i
$879$	1.38682	+	1.28678i	0.0467761	+	0.0434019i
$880$	−1.72782	−	1.17801i	−0.0582450	−	0.0397107i
$881$	−30.3136			−1.02129			−0.510645	−	0.859792i	$-0.670593\pi$
$881$	−30.3136			−1.02129			−0.510645	+	0.859792i	$0.670593\pi$
$882$	14.7389	+	14.8963i	0.496285	+	0.501585i
$883$	30.3184			1.02030			0.510148	−	0.860087i	$-0.329591\pi$
$883$	30.3184			1.02030			0.510148	+	0.860087i	$0.329591\pi$
$884$	−7.66412	−	5.22531i	−0.257772	−	0.175746i
$885$	−0.262453	−	0.243521i	−0.00882227	−	0.00818587i
$886$	−6.49873	−	16.5585i	−0.218329	−	0.556293i
$887$	−26.7618	+	8.25492i	−0.898573	+	0.277173i	−0.709430	−	0.704776i	$-0.751047\pi$
$887$	−26.7618	+	8.25492i	−0.898573	+	0.277173i	−0.189144	+	0.981949i	$0.560571\pi$
$888$	0.0317540	+	0.139123i	0.00106559	+	0.00466868i
$889$	−0.823314	+	3.28242i	−0.0276131	+	0.110089i
$890$	−0.820916	+	3.59667i	−0.0275172	+	0.120561i
$891$	3.12751	+	41.7337i	0.104776	+	1.39813i
$892$	17.4490	+	5.38229i	0.584235	+	0.180212i
$893$	1.99945	−	26.6808i	0.0669090	−	0.892839i
$894$	0.0221421	−	0.0564171i	0.000740542	−	0.00188687i
$895$	−5.81660	+	2.80113i	−0.194427	+	0.0936313i
$896$	1.01897	−	2.44166i	0.0340415	−	0.0815701i
$897$	−1.64603	−	0.792686i	−0.0549593	−	0.0264670i
$898$	17.5216	−	16.2577i	0.584704	−	0.542526i
$899$	22.7926	−	3.43544i	0.760177	−	0.114578i
$900$	−7.18524	+	12.4452i	−0.239508	+	0.414840i
$901$	−5.99616	−	10.3857i	−0.199761	−	0.345996i
$902$	14.7794	+	18.5328i	0.492100	+	0.617073i
$903$	−1.64995	+	0.212763i	−0.0549068	+	0.00708032i
$904$	4.44422	−	5.57287i	0.147812	−	0.185351i
$905$	−5.99253	−	0.903228i	−0.199198	−	0.0300243i
$906$	−1.24458	+	0.848541i	−0.0413484	+	0.0281909i
$907$	−15.3137	+	10.4407i	−0.508482	+	0.346677i	−0.790229	−	0.612812i	$-0.790038\pi$
$907$	−15.3137	+	10.4407i	−0.508482	+	0.346677i	0.281747	+	0.959489i	$0.409086\pi$
$908$	4.14887	+	0.625342i	0.137685	+	0.0207527i
$909$	−27.2988	+	34.2316i	−0.905444	+	1.13539i
$910$	5.91319	+	5.72643i	0.196020	+	0.189829i
$911$	−25.2743	−	31.6929i	−0.837374	−	1.05003i	−0.998012	−	0.0630208i	$-0.979927\pi$
$911$	−25.2743	−	31.6929i	−0.837374	−	1.05003i	0.160638	−	0.987013i	$-0.448645\pi$
$912$	0.199550	+	0.345631i	0.00660777	+	0.0114450i
$913$	−36.6552	+	63.4886i	−1.21311	+	2.10117i
$914$	−9.14156	+	1.37787i	−0.302376	+	0.0455758i
$915$	0.162273	−	0.150567i	0.00536458	−	0.00497760i
$916$	−3.01191	−	1.45046i	−0.0995162	−	0.0479245i
$917$	34.2331	+	5.91002i	1.13048	+	0.195166i
$918$	0.573266	−	0.276070i	0.0189206	−	0.00911167i
$919$	15.4139	−	39.2741i	0.508459	−	1.29553i	−0.414295	−	0.910142i	$-0.635972\pi$
$919$	15.4139	−	39.2741i	0.508459	−	1.29553i	0.922754	−	0.385389i	$-0.125933\pi$
$920$	0.109969	−	1.46744i	0.00362558	−	0.0483800i
$921$	0.473542	+	0.146068i	0.0156038	+	0.00481312i
$922$	1.43322	+	19.1250i	0.0472006	+	0.629849i
$923$	−0.393996	+	1.72621i	−0.0129685	+	0.0568189i
$924$	0.198946	+	0.966315i	0.00654483	+	0.0317894i
$925$	1.91298	+	8.38129i	0.0628982	+	0.275575i
$926$	−5.27586	+	1.62739i	−0.173375	+	0.0534792i
$927$	−7.44153	−	18.9607i	−0.244412	−	0.622752i
$928$	−4.04817	−	3.75615i	−0.132888	−	0.123302i
$929$	−46.1075	−	31.4356i	−1.51274	−	1.03137i	−0.983084	−	0.183154i	$-0.941369\pi$
$929$	−46.1075	−	31.4356i	−1.51274	−	1.03137i	−0.529655	−	0.848213i	$-0.677678\pi$
$930$	−0.148620			−0.00487344
$931$	33.9138	−	8.89438i	1.11148	−	0.291501i
$932$	22.5084			0.737286
$933$	1.94983	+	1.32937i	0.0638347	+	0.0435218i
$934$	25.9994	+	24.1239i	0.850727	+	0.789359i
$935$	1.01786	+	2.59346i	0.0332876	+	0.0848153i
$936$	−19.9171	+	6.14361i	−0.651011	+	0.200810i
$937$	−4.81598	−	21.1002i	−0.157331	−	0.689313i	−0.990639	−	0.136504i	$-0.956413\pi$
$937$	−4.81598	−	21.1002i	−0.157331	−	0.689313i	0.833308	−	0.552808i	$-0.186444\pi$
$938$	−1.55252	−	0.788932i	−0.0506917	−	0.0257595i
$939$	0.172844	−	0.757279i	0.00564055	−	0.0247129i
$940$	−0.178384	−	2.38037i	−0.00581825	−	0.0776392i
$941$	−3.87230	−	1.19445i	−0.126233	−	0.0389379i	0.230995	−	0.972955i	$-0.425802\pi$
$941$	−3.87230	−	1.19445i	−0.126233	−	0.0389379i	−0.357228	+	0.934017i	$0.616278\pi$
$942$	−0.0419746	+	0.560112i	−0.00136761	+	0.0182494i
$943$	−6.09407	+	15.5274i	−0.198450	+	0.505643i
$944$	−9.05938	+	4.36277i	−0.294858	+	0.141996i
$945$	−0.542982	+	0.154870i	−0.0176632	+	0.00503792i
$946$	33.2719	+	16.0229i	1.08176	+	0.520949i
$947$	35.0517	−	32.5232i	1.13903	−	1.05686i	0.141265	−	0.989972i	$-0.454883\pi$
$947$	35.0517	−	32.5232i	1.13903	−	1.05686i	0.997760	−	0.0668895i	$-0.0213075\pi$
$948$	0.146282	−	0.0220484i	0.00475101	−	0.000716100i
$949$	14.2456	−	24.6741i	0.462433	−	0.800957i
$950$	12.0216	+	20.8221i	0.390033	+	0.675557i
$951$	0.370597	+	0.464713i	0.0120174	+	0.0150694i
$952$	−2.95413	+	1.92299i	−0.0957439	+	0.0623245i
$953$	3.50558	−	4.39586i	0.113557	−	0.142396i	−0.721804	−	0.692097i	$-0.756687\pi$
$953$	3.50558	−	4.39586i	0.113557	−	0.142396i	0.835361	+	0.549701i	$0.185258\pi$
$954$	−26.6459	−	4.01623i	−0.862694	−	0.130030i
$955$	7.54456	−	5.14379i	0.244136	−	0.166449i
$956$	−11.0498	+	7.53362i	−0.357376	+	0.243655i
$957$	2.03624	+	0.306914i	0.0658224	+	0.00992113i
$958$	−16.5438	+	20.7452i	−0.534505	+	0.670248i
$959$	6.97199	+	18.9442i	0.225137	+	0.611741i
$960$	0.0222002	+	0.0278382i	0.000716510	+	0.000898475i
$961$	6.78901	+	11.7589i	0.219000	+	0.379320i
$962$	−6.23448	+	10.7984i	−0.201008	+	0.348155i
$963$	−4.76087	+	0.717586i	−0.153417	+	0.0231239i
$964$	7.77604	−	7.21511i	0.250449	−	0.232383i
$965$	−4.83619	−	2.32899i	−0.155682	−	0.0749727i
$966$	−0.518888	+	0.461234i	−0.0166950	+	0.0148400i
$967$	22.7403	−	10.9511i	0.731278	−	0.352165i	−0.0309089	−	0.999522i	$-0.509840\pi$
$967$	22.7403	−	10.9511i	0.731278	−	0.352165i	0.762187	+	0.647357i	$0.224126\pi$
$968$	3.98232	−	10.1468i	0.127997	−	0.326130i
$969$	0.0397350	−	0.530227i	0.00127647	−	0.0170333i
$970$	−7.17790	−	2.21409i	−0.230469	−	0.0710901i
$971$	−3.86896	−	51.6277i	−0.124161	−	1.65681i	−0.617201	−	0.786806i	$-0.711733\pi$
$971$	−3.86896	−	51.6277i	−0.124161	−	1.65681i	0.493040	−	0.870007i	$-0.335886\pi$
$972$	0.477383	−	2.09155i	0.0153121	−	0.0670866i
$973$	13.4229	−	6.11455i	0.430320	−	0.196023i
$974$	−4.25322	−	18.6346i	−0.136282	−	0.597090i
$975$	2.54480	−	0.784968i	0.0814990	−	0.0251391i
$976$	−2.27134	−	5.78727i	−0.0727038	−	0.185246i
$977$	13.5712	+	12.5923i	0.434182	+	0.402862i	0.866753	−	0.498738i	$-0.166203\pi$
$977$	13.5712	+	12.5923i	0.434182	+	0.402862i	−0.432571	+	0.901600i	$0.642393\pi$
$978$	−1.18328	−	0.806744i	−0.0378370	−	0.0257968i
$979$	−38.6353			−1.23479
$980$	2.87361	−	1.23562i	0.0917942	−	0.0394704i
$981$	7.12964			0.227632
$982$	26.0290	+	17.7463i	0.830619	+	0.566306i
$983$	14.1740	+	13.1515i	0.452080	+	0.419469i	0.873069	−	0.487597i	$-0.162126\pi$
$983$	14.1740	+	13.1515i	0.452080	+	0.419469i	−0.420989	+	0.907066i	$0.638317\pi$
$984$	−0.147455	−	0.375709i	−0.00470070	−	0.0119772i
$985$	7.31559	−	2.25656i	0.233094	−	0.0719000i
$986$	1.63716	+	7.17285i	0.0521377	+	0.228430i
$987$	−0.720791	+	0.865273i	−0.0229430	+	0.0275419i
$988$	−7.75989	+	33.9983i	−0.246875	+	1.08163i
$989$	1.94198	+	25.9140i	0.0617515	+	0.824016i
$990$	5.98217	+	1.84526i	0.190126	+	0.0586461i
$991$	3.56039	−	47.5102i	0.113100	−	1.50921i	−0.595360	−	0.803459i	$-0.702991\pi$
$991$	3.56039	−	47.5102i	0.113100	−	1.50921i	0.708460	−	0.705751i	$-0.249390\pi$
$992$	−1.52492	+	3.88543i	−0.0484163	+	0.123363i
$993$	−0.131071	+	0.0631203i	−0.00415940	+	0.00200306i
$994$	0.547702	+	0.390806i	0.0173720	+	0.0123956i
$995$	9.03475	+	4.35091i	0.286421	+	0.137933i
$996$	0.915027	−	0.849021i	0.0289938	−	0.0269023i
$997$	−8.65494	+	1.30452i	−0.274105	+	0.0413146i	−0.284656	−	0.958630i	$-0.591879\pi$
$997$	−8.65494	+	1.30452i	−0.274105	+	0.0413146i	0.0105515	+	0.999944i	$0.496641\pi$
$998$	10.8652	−	18.8190i	0.343931	−	0.595706i
$999$	−0.427651	−	0.740713i	−0.0135303	−	0.0234351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.g.b.53.2	yes	24
3.2	odd	2		882.2.z.b.739.2		24
4.3	odd	2		784.2.bg.b.641.1		24
7.2	even	3		686.2.g.f.275.1		24
7.3	odd	6		686.2.e.d.491.2		24
7.4	even	3		686.2.e.c.491.3		24
7.5	odd	6		686.2.g.d.275.2		24
7.6	odd	2		686.2.g.e.263.1		24
49.12	odd	42		686.2.g.e.373.1		24
49.17	odd	42		686.2.e.d.197.2		24
49.20	odd	14		686.2.g.d.459.2		24
49.24	odd	42		4802.2.a.l.1.8		12
49.25	even	21		4802.2.a.o.1.5		12
49.29	even	7		686.2.g.f.459.1		24
49.32	even	21		686.2.e.c.197.3		24
49.37	even	21	inner	98.2.g.b.37.2	✓	24
147.86	odd	42		882.2.z.b.37.2		24
196.135	odd	42		784.2.bg.b.625.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.b.37.2	✓	24	49.37	even	21	inner
98.2.g.b.53.2	yes	24	1.1	even	1	trivial
686.2.e.c.197.3		24	49.32	even	21
686.2.e.c.491.3		24	7.4	even	3
686.2.e.d.197.2		24	49.17	odd	42
686.2.e.d.491.2		24	7.3	odd	6
686.2.g.d.275.2		24	7.5	odd	6
686.2.g.d.459.2		24	49.20	odd	14
686.2.g.e.263.1		24	7.6	odd	2
686.2.g.e.373.1		24	49.12	odd	42
686.2.g.f.275.1		24	7.2	even	3
686.2.g.f.459.1		24	49.29	even	7
784.2.bg.b.625.1		24	196.135	odd	42
784.2.bg.b.641.1		24	4.3	odd	2
882.2.z.b.37.2		24	147.86	odd	42
882.2.z.b.739.2		24	3.2	odd	2
4802.2.a.l.1.8		12	49.24	odd	42
4802.2.a.o.1.5		12	49.25	even	21

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.826239 + 0.563320i) q^{2} +(0.0584109 + 0.0541974i) q^{3} +(0.365341 + 0.930874i) q^{4} +(-0.427005 + 0.131714i) q^{5} +(0.0177309 + 0.0776840i) q^{6} +(1.60505 + 2.10329i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.223716 - 2.98528i) q^{9} +O(q^{10})\)	\(q+(0.826239 + 0.563320i) q^{2} +(0.0584109 + 0.0541974i) q^{3} +(0.365341 + 0.930874i) q^{4} +(-0.427005 + 0.131714i) q^{5} +(0.0177309 + 0.0776840i) q^{6} +(1.60505 + 2.10329i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.223716 - 2.98528i) q^{9} +(-0.427005 - 0.131714i) q^{10} +(0.349720 - 4.66669i) q^{11} +(-0.0291110 + 0.0741737i) q^{12} +(-6.27294 + 3.02089i) q^{13} +(0.141332 + 2.64197i) q^{14} +(-0.0320803 - 0.0154490i) q^{15} +(-0.733052 + 0.680173i) q^{16} +(1.31740 - 0.198566i) q^{17} +(1.49683 - 2.59258i) q^{18} +(-2.50434 - 4.33764i) q^{19} +(-0.278611 - 0.349367i) q^{20} +(-0.0202401 + 0.209844i) q^{21} +(2.91779 - 3.65879i) q^{22} +(3.25634 + 0.490814i) q^{23} +(-0.0658362 + 0.0448864i) q^{24} +(-3.96621 + 2.70412i) q^{25} +(-6.88467 - 1.03770i) q^{26} +(0.297769 - 0.373391i) q^{27} +(-1.37150 + 2.26252i) q^{28} +(3.44313 + 4.31754i) q^{29} +(-0.0178032 - 0.0308361i) q^{30} +(2.08698 - 3.61476i) q^{31} +(-0.988831 + 0.149042i) q^{32} +(0.273350 - 0.253632i) q^{33} +(1.20034 + 0.578055i) q^{34} +(-0.962396 - 0.686706i) q^{35} +(2.69719 - 1.29890i) q^{36} +(0.654285 - 1.66709i) q^{37} +(0.374299 - 4.99467i) q^{38} +(-0.530133 - 0.163524i) q^{39} +(-0.0333937 - 0.445608i) q^{40} +(-1.12713 + 4.93827i) q^{41} +(-0.134933 + 0.161980i) q^{42} +(1.75596 + 7.69334i) q^{43} +(4.47187 - 1.37939i) q^{44} +(0.488730 + 1.24526i) q^{45} +(2.41403 + 2.23989i) q^{46} +(4.41364 + 3.00917i) q^{47} -0.0796818 q^{48} +(-1.84762 + 6.75176i) q^{49} -4.80032 q^{50} +(0.0877122 + 0.0598012i) q^{51} +(-5.10383 - 4.73566i) q^{52} +(-3.28856 - 8.37913i) q^{53} +(0.456367 - 0.140771i) q^{54} +(0.465334 + 2.03876i) q^{55} +(-2.40771 + 1.09678i) q^{56} +(0.0888082 - 0.389094i) q^{57} +(0.412686 + 5.50691i) q^{58} +(9.60843 + 2.96381i) q^{59} +(0.00266087 - 0.0355069i) q^{60} +(-2.27134 + 5.78727i) q^{61} +(3.76061 - 1.81101i) q^{62} +(5.91982 - 5.26207i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(2.28068 - 2.11617i) q^{65} +(0.368728 - 0.0555768i) q^{66} +(-0.329108 + 0.570033i) q^{67} +(0.666140 + 1.15379i) q^{68} +(0.163605 + 0.205154i) q^{69} +(-0.408333 - 1.10952i) q^{70} +(0.158558 - 0.198826i) q^{71} +(2.96021 + 0.446181i) q^{72} +(-3.38108 + 2.30518i) q^{73} +(1.47970 - 1.00884i) q^{74} +(-0.378226 - 0.0570084i) q^{75} +(3.12286 - 3.91594i) q^{76} +(10.3767 - 6.75471i) q^{77} +(-0.345900 - 0.433744i) q^{78} +(-0.928280 - 1.60783i) q^{79} +(0.223429 - 0.386990i) q^{80} +(-8.84301 + 1.33287i) q^{81} +(-3.71310 + 3.44525i) q^{82} +(-14.1140 - 6.79694i) q^{83} +(-0.202733 + 0.0578238i) q^{84} +(-0.536382 + 0.258308i) q^{85} +(-2.88298 + 7.34570i) q^{86} +(-0.0328835 + 0.438800i) q^{87} +(4.47187 + 1.37939i) q^{88} +(-0.616956 - 8.23271i) q^{89} +(-0.297674 + 1.30420i) q^{90} +(-16.4222 - 8.34511i) q^{91} +(0.732787 + 3.21055i) q^{92} +(0.317813 - 0.0980323i) q^{93} +(1.95160 + 4.97259i) q^{94} +(1.64069 + 1.52234i) q^{95} +(-0.0658362 - 0.0448864i) q^{96} +16.8099 q^{97} +(-5.32998 + 4.53777i) q^{98} -14.0096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9	\( 24 q + 2 q^{2} - 7 q^{3} + 2 q^{4} - 7 q^{6} - 4 q^{8} + 19 q^{9} - 11 q^{11} - 14 q^{13} + 9 q^{15} + 2 q^{16} - 7 q^{17} - 9 q^{18} - 14 q^{19} - 7 q^{20} - 7 q^{21} + q^{22} - 29 q^{23} - 8 q^{25} - 7 q^{26} - 7 q^{27} + 14 q^{28} + 13 q^{29} - 8 q^{30} - 28 q^{31} + 2 q^{32} - 14 q^{33} - 7 q^{34} - 35 q^{35} - 17 q^{36} + 20 q^{37} + 35 q^{38} + 56 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 6 q^{43} + 3 q^{44} + 7 q^{45} + 34 q^{46} + 42 q^{47} + 14 q^{48} + 28 q^{49} + 16 q^{50} + 32 q^{51} - 7 q^{52} - 60 q^{53} + 21 q^{54} - 14 q^{55} + 7 q^{56} + 23 q^{57} + 18 q^{58} + 49 q^{59} + 6 q^{60} - 14 q^{61} - 28 q^{63} - 4 q^{64} - 28 q^{65} + 21 q^{66} + 24 q^{67} - 14 q^{68} + 7 q^{69} - 28 q^{70} + 6 q^{71} - 2 q^{72} - 35 q^{73} - 15 q^{74} - 56 q^{75} + 49 q^{77} + 6 q^{79} - 14 q^{80} - 45 q^{81} - 14 q^{82} - 77 q^{83} - 21 q^{84} - 33 q^{85} - 38 q^{86} + 63 q^{87} + 3 q^{88} - 21 q^{90} - 21 q^{91} - 5 q^{92} - 38 q^{93} - 35 q^{94} + 86 q^{95} + 98 q^{97} + 28 q^{98} - 106 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 7 * q^3 + 2 * q^4 - 7 * q^6 - 4 * q^8 + 19 * q^9 - 11 * q^11 - 14 * q^13 + 9 * q^15 + 2 * q^16 - 7 * q^17 - 9 * q^18 - 14 * q^19 - 7 * q^20 - 7 * q^21 + q^22 - 29 * q^23 - 8 * q^25 - 7 * q^26 - 7 * q^27 + 14 * q^28 + 13 * q^29 - 8 * q^30 - 28 * q^31 + 2 * q^32 - 14 * q^33 - 7 * q^34 - 35 * q^35 - 17 * q^36 + 20 * q^37 + 35 * q^38 + 56 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 6 * q^43 + 3 * q^44 + 7 * q^45 + 34 * q^46 + 42 * q^47 + 14 * q^48 + 28 * q^49 + 16 * q^50 + 32 * q^51 - 7 * q^52 - 60 * q^53 + 21 * q^54 - 14 * q^55 + 7 * q^56 + 23 * q^57 + 18 * q^58 + 49 * q^59 + 6 * q^60 - 14 * q^61 - 28 * q^63 - 4 * q^64 - 28 * q^65 + 21 * q^66 + 24 * q^67 - 14 * q^68 + 7 * q^69 - 28 * q^70 + 6 * q^71 - 2 * q^72 - 35 * q^73 - 15 * q^74 - 56 * q^75 + 49 * q^77 + 6 * q^79 - 14 * q^80 - 45 * q^81 - 14 * q^82 - 77 * q^83 - 21 * q^84 - 33 * q^85 - 38 * q^86 + 63 * q^87 + 3 * q^88 - 21 * q^90 - 21 * q^91 - 5 * q^92 - 38 * q^93 - 35 * q^94 + 86 * q^95 + 98 * q^97 + 28 * q^98 - 106 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more