LMFDB - Embedded newform 335.2.w.a.2.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [335,2,Mod(2,335)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(335, base_ring=CyclotomicField(132))

chi = DirichletCharacter(H, H._module([33, 2]))

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

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

chi := DirichletCharacter("335.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 335 = 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	335.w (of order $132$, degree $40$, 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:	$2.67498846771$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$32$ over $\Q(\zeta_{132})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{132}]$

Embedding invariants

Embedding label			2.16
Character	$\chi$	$=$	335.2
Dual form			335.2.w.a.168.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173696 - 0.191073i) q^{2} +(-0.850181 - 1.55699i) q^{3} +(0.183774 - 1.92457i) q^{4} +(2.08783 + 0.800609i) q^{5} +(-0.149825 + 0.432890i) q^{6} +(0.268681 - 0.840506i) q^{7} +(-0.813089 + 0.608671i) q^{8} +(-0.0794885 + 0.123687i) q^{9} +O(q^{10})$	\(q+(-0.173696 - 0.191073i) q^{2} +(-0.850181 - 1.55699i) q^{3} +(0.183774 - 1.92457i) q^{4} +(2.08783 + 0.800609i) q^{5} +(-0.149825 + 0.432890i) q^{6} +(0.268681 - 0.840506i) q^{7} +(-0.813089 + 0.608671i) q^{8} +(-0.0794885 + 0.123687i) q^{9} +(-0.209674 - 0.537990i) q^{10} +(3.11583 - 1.07840i) q^{11} +(-3.15277 + 1.35010i) q^{12} +(3.37845 + 0.403943i) q^{13} +(-0.207267 + 0.0946554i) q^{14} +(-0.528491 - 3.93139i) q^{15} +(-3.53924 - 0.682132i) q^{16} +(-4.44995 - 3.67419i) q^{17} +(0.0374400 - 0.00629584i) q^{18} +(-3.52513 + 6.83781i) q^{19} +(1.92451 - 3.87103i) q^{20} +(-1.53709 + 0.296249i) q^{21} +(-0.747261 - 0.408035i) q^{22} +(-4.23604 - 2.58200i) q^{23} +(1.63897 + 0.748491i) q^{24} +(3.71805 + 3.34307i) q^{25} +(-0.509643 - 0.715693i) q^{26} +(-5.04824 - 0.361057i) q^{27} +(-1.56823 - 0.671557i) q^{28} +(1.04030 + 0.600615i) q^{29} +(-0.659384 + 0.783849i) q^{30} +(3.81611 - 4.85258i) q^{31} +(1.54167 + 2.52927i) q^{32} +(-4.32808 - 3.93448i) q^{33} +(0.0709040 + 1.48846i) q^{34} +(1.23388 - 1.53972i) q^{35} +(0.223435 + 0.175711i) q^{36} +(-1.41547 + 5.28260i) q^{37} +(1.91882 - 0.514146i) q^{38} +(-2.24336 - 5.60364i) q^{39} +(-2.18490 + 0.619834i) q^{40} +(8.27616 - 5.89342i) q^{41} +(0.323592 + 0.242238i) q^{42} +(-0.759129 + 0.283141i) q^{43} +(-1.50284 - 6.19480i) q^{44} +(-0.264983 + 0.194597i) q^{45} +(0.242435 + 1.25787i) q^{46} +(-1.75490 - 0.0417745i) q^{47} +(1.94692 + 6.09049i) q^{48} +(5.06777 + 3.60874i) q^{49} +(-0.00704372 - 1.29110i) q^{50} +(-1.93741 + 10.0523i) q^{51} +(1.39829 - 6.42782i) q^{52} +(-3.58256 + 9.60522i) q^{53} +(0.807873 + 1.02729i) q^{54} +(7.36869 + 0.243050i) q^{55} +(0.293130 + 0.846944i) q^{56} +(13.6434 - 0.324773i) q^{57} +(-0.0659346 - 0.303097i) q^{58} +(6.75739 + 0.971565i) q^{59} +(-7.66335 + 0.294630i) q^{60} +(9.44224 + 3.26799i) q^{61} +(-1.59004 + 0.113722i) q^{62} +(0.0826022 + 0.100043i) q^{63} +(-1.81545 + 6.18284i) q^{64} +(6.73022 + 3.54818i) q^{65} +1.51038i q^{66} +(8.08321 - 1.28907i) q^{67} +(-7.88901 + 7.88901i) q^{68} +(-0.418749 + 8.79063i) q^{69} +(-0.508519 + 0.0316848i) q^{70} +(-12.3123 - 1.17568i) q^{71} +(-0.0106531 - 0.148950i) q^{72} +(-1.14920 - 2.36572i) q^{73} +(1.25522 - 0.647112i) q^{74} +(2.04411 - 8.63118i) q^{75} +(12.5120 + 8.04096i) q^{76} +(-0.0692381 - 2.90862i) q^{77} +(-0.681038 + 1.40198i) q^{78} +(-6.14383 - 2.45962i) q^{79} +(-6.84319 - 4.25772i) q^{80} +(3.91299 + 8.56824i) q^{81} +(-2.56361 - 0.557679i) q^{82} +(-2.25607 + 1.52695i) q^{83} +(0.287675 + 3.01267i) q^{84} +(-6.34914 - 11.2337i) q^{85} +(0.185958 + 0.0958683i) q^{86} +(0.0507121 - 2.13036i) q^{87} +(-1.87706 + 2.77335i) q^{88} +(2.84439 + 9.68712i) q^{89} +(0.0832087 + 0.0168301i) q^{90} +(1.24724 - 2.73108i) q^{91} +(-5.74770 + 7.67803i) q^{92} +(-10.7998 - 1.81607i) q^{93} +(0.296839 + 0.342570i) q^{94} +(-12.8343 + 11.4539i) q^{95} +(2.62734 - 4.55069i) q^{96} +(1.04623 + 0.280338i) q^{97} +(-0.190722 - 1.59514i) q^{98} +(-0.114289 + 0.471106i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 38 q^{2} - 44 q^{3} - 44 q^{5} - 80 q^{6} - 38 q^{7} - 110 q^{8}+O(q^{10}) $ 1280 * q - 38 * q^2 - 44 * q^3 - 44 * q^5 - 80 * q^6 - 38 * q^7 - 110 * q^8	$ 1280 q - 38 q^{2} - 44 q^{3} - 44 q^{5} - 80 q^{6} - 38 q^{7} - 110 q^{8} - 42 q^{10} - 76 q^{11} - 20 q^{12} - 38 q^{13} - 52 q^{15} - 136 q^{16} - 42 q^{17} - 68 q^{18} - 68 q^{20} + 44 q^{21} - 68 q^{22} - 24 q^{23} - 24 q^{25} - 68 q^{26} - 44 q^{27} - 2 q^{28} - 150 q^{30} - 164 q^{31} - 70 q^{32} - 26 q^{33} - 36 q^{35} - 28 q^{36} - 32 q^{37} - 18 q^{38} + 118 q^{40} - 76 q^{41} - 44 q^{42} - 88 q^{43} - 44 q^{45} - 160 q^{46} - 26 q^{47} - 402 q^{48} + 94 q^{50} - 100 q^{51} - 44 q^{52} - 44 q^{53} + 112 q^{55} - 64 q^{56} - 62 q^{57} - 88 q^{58} + 234 q^{60} - 152 q^{61} + 84 q^{62} - 98 q^{63} + 140 q^{65} - 118 q^{67} + 420 q^{68} + 440 q^{70} - 124 q^{71} + 176 q^{72} - 26 q^{73} + 308 q^{75} + 56 q^{76} - 322 q^{77} + 196 q^{78} + 250 q^{80} + 152 q^{81} + 44 q^{82} - 30 q^{83} + 10 q^{85} - 60 q^{86} - 134 q^{87} - 32 q^{88} - 256 q^{90} - 56 q^{91} - 24 q^{92} - 304 q^{93} - 14 q^{95} + 228 q^{96} - 120 q^{97} + 70 q^{98}+O(q^{100}) $ 1280 * q - 38 * q^2 - 44 * q^3 - 44 * q^5 - 80 * q^6 - 38 * q^7 - 110 * q^8 - 42 * q^10 - 76 * q^11 - 20 * q^12 - 38 * q^13 - 52 * q^15 - 136 * q^16 - 42 * q^17 - 68 * q^18 - 68 * q^20 + 44 * q^21 - 68 * q^22 - 24 * q^23 - 24 * q^25 - 68 * q^26 - 44 * q^27 - 2 * q^28 - 150 * q^30 - 164 * q^31 - 70 * q^32 - 26 * q^33 - 36 * q^35 - 28 * q^36 - 32 * q^37 - 18 * q^38 + 118 * q^40 - 76 * q^41 - 44 * q^42 - 88 * q^43 - 44 * q^45 - 160 * q^46 - 26 * q^47 - 402 * q^48 + 94 * q^50 - 100 * q^51 - 44 * q^52 - 44 * q^53 + 112 * q^55 - 64 * q^56 - 62 * q^57 - 88 * q^58 + 234 * q^60 - 152 * q^61 + 84 * q^62 - 98 * q^63 + 140 * q^65 - 118 * q^67 + 420 * q^68 + 440 * q^70 - 124 * q^71 + 176 * q^72 - 26 * q^73 + 308 * q^75 + 56 * q^76 - 322 * q^77 + 196 * q^78 + 250 * q^80 + 152 * q^81 + 44 * q^82 - 30 * q^83 + 10 * q^85 - 60 * q^86 - 134 * q^87 - 32 * q^88 - 256 * q^90 - 56 * q^91 - 24 * q^92 - 304 * q^93 - 14 * q^95 + 228 * q^96 - 120 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/335\mathbb{Z}\right)^\times$.

$n$	$136$	$202$
$\chi(n)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.173696	−	0.191073i	−0.122822	−	0.135109i	0.675450	−	0.737406i	$-0.263949\pi$
$2$	−0.173696	−	0.191073i	−0.122822	−	0.135109i	−0.798272	+	0.602297i	$0.794252\pi$
$3$	−0.850181	−	1.55699i	−0.490852	−	0.898929i	−0.999284	−	0.0378267i	$-0.987957\pi$
$3$	−0.850181	−	1.55699i	−0.490852	−	0.898929i	0.508432	−	0.861102i	$-0.330225\pi$
$4$	0.183774	−	1.92457i	0.0918869	−	0.962283i
$5$	2.08783	+	0.800609i	0.933705	+	0.358043i
$5$	2.08783	+	0.800609i	0.933705	+	0.358043i
$6$	−0.149825	+	0.432890i	−0.0611657	+	0.176727i
$7$	0.268681	−	0.840506i	0.101552	−	0.317681i	−0.888403	−	0.459064i	$-0.848185\pi$
$7$	0.268681	−	0.840506i	0.101552	−	0.317681i	0.989955	+	0.141382i	$0.0451547\pi$
$8$	−0.813089	+	0.608671i	−0.287470	+	0.215198i
$9$	−0.0794885	+	0.123687i	−0.0264962	+	0.0412288i
$10$	−0.209674	−	0.537990i	−0.0663047	−	0.170127i
$11$	3.11583	−	1.07840i	0.939458	−	0.325150i	0.185928	−	0.982563i	$-0.440471\pi$
$11$	3.11583	−	1.07840i	0.939458	−	0.325150i	0.753530	+	0.657414i	$0.228350\pi$
$12$	−3.15277	+	1.35010i	−0.910127	+	0.389739i
$13$	3.37845	+	0.403943i	0.937014	+	0.112034i	0.573179	−	0.819430i	$-0.305710\pi$
$13$	3.37845	+	0.403943i	0.937014	+	0.112034i	0.363834	+	0.931464i	$0.381467\pi$
$14$	−0.207267	+	0.0946554i	−0.0553943	+	0.0252977i
$15$	−0.528491	−	3.93139i	−0.136456	−	1.01508i
$16$	−3.53924	−	0.682132i	−0.884809	−	0.170533i
$17$	−4.44995	−	3.67419i	−1.07927	−	0.891122i	−0.0848287	−	0.996396i	$-0.527034\pi$
$17$	−4.44995	−	3.67419i	−1.07927	−	0.891122i	−0.994443	+	0.105273i	$0.966428\pi$
$18$	0.0374400	−	0.00629584i	0.00882468	−	0.00148394i
$19$	−3.52513	+	6.83781i	−0.808721	+	1.56870i	0.0137584	+	0.999905i	$0.495620\pi$
$19$	−3.52513	+	6.83781i	−0.808721	+	1.56870i	−0.822480	+	0.568795i	$0.807410\pi$
$20$	1.92451	−	3.87103i	0.430334	−	0.865589i
$21$	−1.53709	+	0.296249i	−0.335420	+	0.0646469i
$22$	−0.747261	−	0.408035i	−0.159317	−	0.0869934i
$23$	−4.23604	−	2.58200i	−0.883274	−	0.538384i	0.00380910	−	0.999993i	$-0.498788\pi$
$23$	−4.23604	−	2.58200i	−0.883274	−	0.538384i	−0.887084	+	0.461609i	$0.847272\pi$
$24$	1.63897	+	0.748491i	0.334553	+	0.152785i
$25$	3.71805	+	3.34307i	0.743610	+	0.668614i
$26$	−0.509643	−	0.715693i	−0.0999491	−	0.140359i
$27$	−5.04824	−	0.361057i	−0.971534	−	0.0694855i
$28$	−1.56823	−	0.671557i	−0.296368	−	0.126912i
$29$	1.04030	+	0.600615i	0.193178	+	0.111531i	0.593469	−	0.804856i	$-0.297758\pi$
$29$	1.04030	+	0.600615i	0.193178	+	0.111531i	−0.400291	+	0.916388i	$0.631091\pi$
$30$	−0.659384	+	0.783849i	−0.120386	+	0.143111i
$31$	3.81611	−	4.85258i	0.685393	−	0.871548i	−0.311506	−	0.950244i	$-0.600833\pi$
$31$	3.81611	−	4.85258i	0.685393	−	0.871548i	0.996899	+	0.0786961i	$0.0250757\pi$
$32$	1.54167	+	2.52927i	0.272531	+	0.447115i
$33$	−4.32808	−	3.93448i	−0.753421	−	0.684906i
$34$	0.0709040	+	1.48846i	0.0121599	+	0.255268i
$35$	1.23388	−	1.53972i	0.208563	−	0.260261i
$36$	0.223435	+	0.175711i	0.0372392	+	0.0292852i
$37$	−1.41547	+	5.28260i	−0.232702	+	0.868455i	0.746470	+	0.665419i	$0.231747\pi$
$37$	−1.41547	+	5.28260i	−0.232702	+	0.868455i	−0.979171	+	0.203035i	$0.934919\pi$
$38$	1.91882	−	0.514146i	0.311274	−	0.0834055i
$39$	−2.24336	−	5.60364i	−0.359225	−	0.897301i
$40$	−2.18490	+	0.619834i	−0.345463	+	0.0980043i
$41$	8.27616	−	5.89342i	1.29252	−	0.920398i	0.293155	−	0.956065i	$-0.405295\pi$
$41$	8.27616	−	5.89342i	1.29252	−	0.920398i	0.999364	+	0.0356669i	$0.0113555\pi$
$42$	0.323592	+	0.242238i	0.0499313	+	0.0373781i
$43$	−0.759129	+	0.283141i	−0.115766	+	0.0431785i	−0.406680	−	0.913571i	$-0.633314\pi$
$43$	−0.759129	+	0.283141i	−0.115766	+	0.0431785i	0.290914	+	0.956749i	$0.406041\pi$
$44$	−1.50284	−	6.19480i	−0.226562	−	0.933902i
$45$	−0.264983	+	0.194597i	−0.0395013	+	0.0290088i
$46$	0.242435	+	1.25787i	0.0357451	+	0.185463i
$47$	−1.75490	−	0.0417745i	−0.255979	−	0.00609344i	−0.104388	−	0.994537i	$-0.533288\pi$
$47$	−1.75490	−	0.0417745i	−0.255979	−	0.00609344i	−0.151591	+	0.988443i	$0.548440\pi$
$48$	1.94692	+	6.09049i	0.281013	+	0.879087i
$49$	5.06777	+	3.60874i	0.723967	+	0.515535i
$50$	−0.00704372	−	1.29110i	−0.000996132	−	0.182589i
$51$	−1.93741	+	10.0523i	−0.271292	+	1.40760i
$52$	1.39829	−	6.42782i	0.193907	−	0.891378i
$53$	−3.58256	+	9.60522i	−0.492103	+	1.31938i	0.419294	+	0.907850i	$0.362278\pi$
$53$	−3.58256	+	9.60522i	−0.492103	+	1.31938i	−0.911397	+	0.411528i	$0.864995\pi$
$54$	0.807873	+	1.02729i	0.109938	+	0.139797i
$55$	7.36869	+	0.243050i	0.993594	+	0.0327728i
$56$	0.293130	+	0.846944i	0.0391712	+	0.113178i
$57$	13.6434	−	0.324773i	1.80711	−	0.0430173i
$58$	−0.0659346	−	0.303097i	−0.00865764	−	0.0397985i
$59$	6.75739	+	0.971565i	0.879737	+	0.126487i	0.567359	−	0.823471i	$-0.307965\pi$
$59$	6.75739	+	0.971565i	0.879737	+	0.126487i	0.312378	+	0.949958i	$0.398874\pi$
$60$	−7.66335	+	0.294630i	−0.989334	+	0.0380365i
$61$	9.44224	+	3.26799i	1.20895	+	0.418423i	0.855881	−	0.517172i	$-0.173015\pi$
$61$	9.44224	+	3.26799i	1.20895	+	0.418423i	0.353073	+	0.935596i	$0.385137\pi$
$62$	−1.59004	+	0.113722i	−0.201935	+	0.0144427i
$63$	0.0826022	+	0.100043i	0.0104069	+	0.0126042i
$64$	−1.81545	+	6.18284i	−0.226931	+	0.772855i
$65$	6.73022	+	3.54818i	0.834782	+	0.440098i
$66$			1.51038i			0.185915i
$67$	8.08321	−	1.28907i	0.987521	−	0.157485i
$67$	8.08321	−	1.28907i	0.987521	−	0.157485i
$68$	−7.88901	+	7.88901i	−0.956683	+	0.956683i
$69$	−0.418749	+	8.79063i	−0.0504115	+	1.05827i
$70$	−0.508519	+	0.0316848i	−0.0607796	+	0.00378706i
$71$	−12.3123	−	1.17568i	−1.46120	−	0.139528i	−0.666035	−	0.745921i	$-0.732010\pi$
$71$	−12.3123	−	1.17568i	−1.46120	−	0.139528i	−0.795165	+	0.606393i	$0.792616\pi$
$72$	−0.0106531	−	0.148950i	−0.00125549	−	0.0175540i
$73$	−1.14920	−	2.36572i	−0.134503	−	0.276887i	0.821519	−	0.570182i	$-0.193127\pi$
$73$	−1.14920	−	2.36572i	−0.134503	−	0.276887i	−0.956022	+	0.293294i	$0.905248\pi$
$74$	1.25522	−	0.647112i	0.145917	−	0.0752253i
$75$	2.04411	−	8.63118i	0.236033	−	0.996643i
$76$	12.5120	+	8.04096i	1.43522	+	0.922362i
$77$	−0.0692381	−	2.90862i	−0.00789041	−	0.331468i
$78$	−0.681038	+	1.40198i	−0.0771124	+	0.158743i
$79$	−6.14383	−	2.45962i	−0.691234	−	0.276728i	−0.000670343	−	1.00000i	$-0.500213\pi$
$79$	−6.14383	−	2.45962i	−0.691234	−	0.276728i	−0.690564	+	0.723271i	$0.742638\pi$
$80$	−6.84319	−	4.25772i	−0.765092	−	0.476027i
$81$	3.91299	+	8.56824i	0.434776	+	0.952027i
$82$	−2.56361	−	0.557679i	−0.283103	−	0.0615854i
$83$	−2.25607	+	1.52695i	−0.247636	+	0.167605i	−0.678025	−	0.735039i	$-0.737164\pi$
$83$	−2.25607	+	1.52695i	−0.247636	+	0.167605i	0.430390	+	0.902643i	$0.358376\pi$
$84$	0.287675	+	3.01267i	0.0313879	+	0.328709i
$85$	−6.34914	−	11.2337i	−0.688661	−	1.21847i
$86$	0.185958	+	0.0958683i	0.0200524	+	0.0103377i
$87$	0.0507121	−	2.13036i	0.00543690	−	0.228399i
$88$	−1.87706	+	2.77335i	−0.200095	+	0.295640i
$89$	2.84439	+	9.68712i	0.301505	+	1.02683i	0.961327	+	0.275410i	$0.0888137\pi$
$89$	2.84439	+	9.68712i	0.301505	+	1.02683i	−0.659822	+	0.751422i	$0.729368\pi$
$90$	0.0832087	+	0.0168301i	0.00877097	+	0.00177405i
$91$	1.24724	−	2.73108i	0.130746	−	0.286295i
$92$	−5.74770	+	7.67803i	−0.599239	+	0.800490i
$93$	−10.7998	−	1.81607i	−1.11989	−	0.188318i
$94$	0.296839	+	0.342570i	0.0306166	+	0.0353334i
$95$	−12.8343	+	11.4539i	−1.31677	+	1.17515i
$96$	2.62734	−	4.55069i	0.268152	−	0.464453i
$97$	1.04623	+	0.280338i	0.106229	+	0.0284640i	0.311542	−	0.950232i	$-0.399155\pi$
$97$	1.04623	+	0.280338i	0.106229	+	0.0284640i	−0.205313	+	0.978696i	$0.565821\pi$
$98$	−0.190722	−	1.59514i	−0.0192658	−	0.161133i
$99$	−0.114289	+	0.471106i	−0.0114865	+	0.0473480i
$100$	7.11724	−	6.54127i	0.711724	−	0.654127i
$101$	3.58658	−	0.170850i	0.356878	−	0.0170002i	0.131622	−	0.991300i	$-0.457981\pi$
$101$	3.58658	−	0.170850i	0.356878	−	0.0170002i	0.225255	+	0.974300i	$0.427678\pi$
$102$	2.25723	−	1.37586i	0.223499	−	0.136230i
$103$	7.48974	−	0.895508i	0.737986	−	0.0882370i	0.258776	−	0.965937i	$-0.416681\pi$
$103$	7.48974	−	0.895508i	0.737986	−	0.0882370i	0.479210	+	0.877700i	$0.340923\pi$
$104$	−2.99285	+	1.72792i	−0.293473	+	0.169437i
$105$	−3.44635	−	0.612088i	−0.336330	−	0.0597337i
$106$	2.45757	−	0.983864i	0.238701	−	0.0955613i
$107$	1.24163	−	17.3603i	0.120033	−	1.67828i	−0.479199	−	0.877706i	$-0.659073\pi$
$107$	1.24163	−	17.3603i	0.120033	−	1.67828i	0.599232	−	0.800575i	$-0.295473\pi$
$108$	−1.62261	+	9.64932i	−0.156136	+	0.928506i
$109$	−0.286334	−	1.99150i	−0.0274259	−	0.190751i	0.971503	−	0.237028i	$-0.0761734\pi$
$109$	−0.286334	−	1.99150i	−0.0274259	−	0.190751i	−0.998929	+	0.0462771i	$0.985264\pi$
$110$	−1.23348	−	1.45017i	−0.117607	−	0.138268i
$111$	9.42837	−	2.28730i	0.894901	−	0.217101i
$112$	−1.52426	+	2.79147i	−0.144029	+	0.263769i
$113$	8.59770	+	5.81909i	0.808804	+	0.547414i	0.893537	−	0.448989i	$-0.148216\pi$
$113$	8.59770	+	5.81909i	0.808804	+	0.547414i	−0.0847332	+	0.996404i	$0.527004\pi$
$114$	−2.43186	−	2.55047i	−0.227765	−	0.238873i
$115$	−6.77694	−	8.78218i	−0.631953	−	0.818942i
$116$	1.34710	−	1.89174i	0.125075	−	0.175644i
$117$	−0.318510	+	0.385760i	−0.0294463	+	0.0356635i
$118$	−0.988094	−	1.45991i	−0.0909615	−	0.134395i
$119$	−4.28380	+	2.75303i	−0.392695	+	0.252370i
$120$	2.82263	+	2.87489i	0.257670	+	0.262441i
$121$	−0.101132	+	0.0795308i	−0.00919378	+	0.00723007i
$122$	−1.01566	−	2.37179i	−0.0919535	−	0.214732i
$123$	−16.2122	−	7.87542i	−1.46181	−	0.710102i
$124$	−8.63780	−	8.23613i	−0.775698	−	0.739626i
$125$	5.08616	+	9.95645i	0.454920	+	0.890532i
$126$	0.00476770	−	0.0331601i	0.000424741	−	0.00295414i
$127$	15.4334	+	4.93351i	1.36949	+	0.437778i	0.896403	−	0.443239i	$-0.146171\pi$
$127$	15.4334	+	4.93351i	1.36949	+	0.437778i	0.473085	+	0.881017i	$0.343140\pi$
$128$	6.82542	−	3.31559i	0.603288	−	0.293059i
$129$	1.08624	+	0.941236i	0.0956385	+	0.0828712i
$130$	−0.491056	−	1.90227i	−0.0430684	−	0.166840i
$131$	−10.9009	−	3.20080i	−0.952419	−	0.279656i	−0.231626	−	0.972805i	$-0.574404\pi$
$131$	−10.9009	−	3.20080i	−0.952419	−	0.279656i	−0.720794	+	0.693149i	$0.756223\pi$
$132$	−8.36756	+	7.60662i	−0.728303	+	0.662071i
$133$	4.80008	+	4.80008i	0.416220	+	0.416220i
$134$	−1.65033	−	1.32057i	−0.142567	−	0.114080i
$135$	−10.2508	−	4.79549i	−0.882248	−	0.412730i
$136$	5.85458	+	0.278888i	0.502026	+	0.0239145i
$137$	−4.15924	+	2.27112i	−0.355348	+	0.194034i	−0.647000	−	0.762490i	$-0.723977\pi$
$137$	−4.15924	+	2.27112i	−0.355348	+	0.194034i	0.291653	+	0.956524i	$0.405795\pi$
$138$	1.75238	−	1.44689i	0.149173	−	0.123167i
$139$	3.52766	−	4.07113i	0.299212	−	0.345309i	−0.586158	−	0.810197i	$-0.699360\pi$
$139$	3.52766	−	4.07113i	0.299212	−	0.345309i	0.885369	+	0.464888i	$0.153905\pi$
$140$	−2.73655	−	2.65764i	−0.231280	−	0.224611i
$141$	1.42694	+	2.76789i	0.120170	+	0.233098i
$142$	1.91396	+	2.55675i	0.160616	+	0.214558i
$143$	10.9623	−	2.38470i	0.916713	−	0.199419i
$144$	0.365699	−	0.383534i	0.0304749	−	0.0319612i
$145$	1.69110	+	2.08685i	0.140438	+	0.173304i
$146$	−0.252413	+	0.630498i	−0.0208899	+	0.0521804i
$147$	1.31026	−	10.9586i	0.108068	−	0.903846i
$148$	9.90660	+	3.69497i	0.814317	+	0.303725i
$149$	−4.54740	−	7.07589i	−0.372538	−	0.579680i	0.603478	−	0.797380i	$-0.293781\pi$
$149$	−4.54740	−	7.07589i	−0.372538	−	0.579680i	−0.976016	+	0.217700i	$0.930145\pi$
$150$	−2.00424	+	1.10863i	−0.163645	+	0.0905195i
$151$	15.9572	−	1.52373i	1.29858	−	0.124000i	0.577238	−	0.816576i	$-0.304131\pi$
$151$	15.9572	−	1.52373i	1.29858	−	0.124000i	0.721344	+	0.692577i	$0.243525\pi$
$152$	−1.29573	−	7.70539i	−0.105097	−	0.624990i
$153$	0.808168	−	0.258343i	0.0653365	−	0.0208858i
$154$	−0.543731	+	0.518446i	−0.0438151	+	0.0417776i
$155$	11.8524	−	7.07613i	0.952007	−	0.568369i
$156$	−11.1969	+	3.28769i	−0.896466	+	0.263226i
$157$	−3.26217	+	5.35193i	−0.260350	+	0.427131i	−0.956917	−	0.290360i	$-0.906225\pi$
$157$	−3.26217	+	5.35193i	−0.260350	+	0.427131i	0.696568	+	0.717491i	$0.254710\pi$
$158$	0.597195	+	1.60114i	0.0475103	+	0.127380i
$159$	18.0011	−	2.58816i	1.42758	−	0.205255i
$160$	1.19378	+	6.51494i	0.0943769	+	0.515051i
$161$	−3.30833	+	2.86668i	−0.260733	+	0.225926i
$162$	0.957484	−	2.23594i	0.0752271	−	0.175672i
$163$	4.53354	+	16.9194i	0.355094	+	1.32523i	0.880366	+	0.474295i	$0.157297\pi$
$163$	4.53354	+	16.9194i	0.355094	+	1.32523i	−0.525272	+	0.850935i	$0.676036\pi$
$164$	−9.82135	−	17.0111i	−0.766918	−	1.32834i
$165$	−5.88630	−	11.6796i	−0.458248	−	0.909257i
$166$	0.683630	+	0.165847i	0.0530599	+	0.0128722i
$167$	−2.27573	+	2.50338i	−0.176101	+	0.193718i	−0.821635	−	0.570014i	$-0.806938\pi$
$167$	−2.27573	+	2.50338i	−0.176101	+	0.193718i	0.645534	+	0.763731i	$0.276635\pi$
$168$	1.06947	−	1.17646i	0.0825114	−	0.0907656i
$169$	−1.38279	−	0.335461i	−0.106368	−	0.0258047i
$170$	−1.04364	+	3.16441i	−0.0800433	+	0.242699i
$171$	−0.565537	−	0.979538i	−0.0432477	−	0.0749072i
$172$	0.405415	+	1.51303i	0.0309126	+	0.115367i
$173$	6.64606	−	15.5200i	0.505291	−	1.17997i	−0.452308	−	0.891862i	$-0.649399\pi$
$173$	6.64606	−	15.5200i	0.505291	−	1.17997i	0.957599	−	0.288104i	$-0.0930249\pi$
$174$	−0.415862	+	0.360347i	−0.0315264	+	0.0273178i
$175$	3.80884	−	2.22683i	0.287921	−	0.168332i
$176$	−11.7633	+	1.69130i	−0.886690	+	0.127487i
$177$	−4.23228	−	11.3472i	−0.318118	−	0.852907i
$178$	1.35688	−	2.22610i	0.101703	−	0.166854i
$179$	−7.10338	+	2.08574i	−0.530931	+	0.155896i	−0.536201	−	0.844091i	$-0.680141\pi$
$179$	−7.10338	+	2.08574i	−0.530931	+	0.155896i	0.00526919	+	0.999986i	$0.498323\pi$
$180$	0.325818	+	0.545739i	0.0242850	+	0.0406770i
$181$	−10.6733	+	10.1770i	−0.793343	+	0.756451i	−0.973867	−	0.227119i	$-0.927069\pi$
$181$	−10.6733	+	10.1770i	−0.793343	+	0.756451i	0.180524	+	0.983571i	$0.442221\pi$
$182$	−0.738475	+	0.236065i	−0.0547394	+	0.0174983i
$183$	−2.93938	−	17.4799i	−0.217285	−	1.29215i
$184$	5.01586	−	0.478957i	0.369774	−	0.0353092i
$185$	−7.18456	+	9.89593i	−0.528219	+	0.727563i
$186$	1.52888	+	2.37899i	0.112103	+	0.174436i
$187$	−17.8275	−	6.64933i	−1.30368	−	0.486247i
$188$	−0.402903	+	3.36975i	−0.0293848	+	0.245765i
$189$	−1.65984	+	4.14607i	−0.120735	+	0.301582i
$190$	4.41780	+	0.462776i	0.320501	+	0.0335733i
$191$	−14.1252	+	14.8141i	−1.02206	+	1.07191i	−0.0246735	+	0.999696i	$0.507855\pi$
$191$	−14.1252	+	14.8141i	−1.02206	+	1.07191i	−0.997389	+	0.0722130i	$0.976994\pi$
$192$	11.1701	−	2.42990i	0.806131	−	0.175363i
$193$	−14.0269	−	18.7378i	−1.00968	−	1.34877i	−0.936196	−	0.351477i	$-0.885679\pi$
$193$	−14.0269	−	18.7378i	−1.00968	−	1.34877i	−0.0734832	−	0.997296i	$-0.523412\pi$
$194$	−0.128162	−	0.248600i	−0.00920152	−	0.0178485i
$195$	−0.197423	−	13.4955i	−0.0141377	−	0.966432i
$196$	7.87659	−	9.09007i	0.562614	−	0.649291i
$197$	−11.0617	+	9.13328i	−0.788111	+	0.650719i	−0.941336	−	0.337472i	$-0.890428\pi$
$197$	−11.0617	+	9.13328i	−0.788111	+	0.650719i	0.153225	+	0.988191i	$0.451034\pi$
$198$	0.109867	−	0.0599920i	0.00780792	−	0.00426345i
$199$	−21.9343	−	1.04486i	−1.55488	−	0.0740681i	−0.747566	−	0.664188i	$-0.768777\pi$
$199$	−21.9343	−	1.04486i	−1.55488	−	0.0740681i	−0.807316	+	0.590120i	$0.799080\pi$
$200$	−5.05793	−	0.455143i	−0.357650	−	0.0321835i
$201$	−8.87926	−	11.4895i	−0.626295	−	0.810410i
$202$	−0.655620	−	0.655620i	−0.0461293	−	0.0461293i
$203$	0.784328	−	0.713001i	0.0550490	−	0.0500429i
$204$	18.9902	+	5.57602i	1.32958	+	0.390400i
$205$	21.9975	−	5.67849i	1.53637	−	0.396603i
$206$	−1.47205	−	1.27554i	−0.102562	−	0.0888709i
$207$	0.656074	−	0.318701i	0.0456003	−	0.0221513i
$208$	−11.6816	−	3.73420i	−0.809973	−	0.258920i
$209$	−3.60983	+	25.1069i	−0.249697	+	1.73668i
$210$	0.481666	+	0.764821i	0.0332381	+	0.0527777i
$211$	14.7290	+	14.0441i	1.01399	+	0.966837i	0.999453	−	0.0330577i	$-0.0105245\pi$
$211$	14.7290	+	14.0441i	1.01399	+	0.966837i	0.0145356	+	0.999894i	$0.495373\pi$
$212$	17.8275	+	8.66007i	1.22440	+	0.594776i
$213$	8.63715	+	20.1697i	0.591808	+	1.38200i
$214$	−3.53274	+	2.77818i	−0.241493	+	0.189912i
$215$	−1.81162	−	0.0166170i	−0.123551	−	0.00113327i
$216$	4.32443	−	2.77915i	0.294240	−	0.189097i
$217$	−3.05330	−	4.51125i	−0.207272	−	0.306244i
$218$	−0.330785	+	0.400627i	−0.0224036	+	0.0271339i
$219$	−2.70638	+	3.80058i	−0.182880	+	0.256820i
$220$	1.82194	−	14.1369i	0.122835	−	0.953108i
$221$	−13.5498	−	14.2106i	−0.911457	−	0.955909i
$222$	−2.07471	−	1.40421i	−0.139246	−	0.0942442i
$223$	0.937182	−	1.71632i	0.0627583	−	0.114933i	−0.844416	−	0.535687i	$-0.820053\pi$
$223$	0.937182	−	1.71632i	0.0627583	−	0.114933i	0.907175	+	0.420754i	$0.138234\pi$
$224$	2.54008	−	0.616216i	0.169716	−	0.0411727i
$225$	−0.709035	+	0.194137i	−0.0472690	+	0.0129425i
$226$	−0.381522	−	2.65354i	−0.0253784	−	0.176511i
$227$	1.28528	−	7.64330i	0.0853073	−	0.507303i	−0.910321	−	0.413902i	$-0.864165\pi$
$227$	1.28528	−	7.64330i	0.0853073	−	0.507303i	0.995629	−	0.0934011i	$-0.0297739\pi$
$228$	1.88225	−	26.3173i	0.124655	−	1.74291i
$229$	11.7409	−	4.70036i	0.775862	−	0.310608i	0.0502721	−	0.998736i	$-0.483991\pi$
$229$	11.7409	−	4.70036i	0.775862	−	0.310608i	0.725590	+	0.688127i	$0.241567\pi$
$230$	−0.500902	+	2.82032i	−0.0330285	+	0.185966i
$231$	−4.46983	+	2.58066i	−0.294093	+	0.169795i
$232$	−1.21143	+	0.144844i	−0.0795343	+	0.00950949i
$233$	10.4940	−	6.39643i	0.687485	−	0.419044i	−0.132689	−	0.991158i	$-0.542361\pi$
$233$	10.4940	−	6.39643i	0.687485	−	0.419044i	0.820174	+	0.572114i	$0.193876\pi$
$234$	0.129032	−	0.00614656i	0.00843510	−	0.000401813i
$235$	−3.63049	−	1.49221i	−0.236827	−	0.0973411i
$236$	3.11167	−	12.8265i	0.202553	−	0.834933i
$237$	1.39376	+	11.6570i	0.0905347	+	0.757203i
$238$	1.27011	+	0.340324i	0.0823289	+	0.0220600i
$239$	−4.97778	+	8.62177i	−0.321986	+	0.557696i	−0.980898	−	0.194524i	$-0.937684\pi$
$239$	−4.97778	+	8.62177i	−0.321986	+	0.557696i	0.658912	+	0.752220i	$0.271017\pi$
$240$	−0.811271	+	14.2746i	−0.0523673	+	0.921423i
$241$	−12.6591	−	14.6094i	−0.815447	−	0.941076i	0.183675	−	0.982987i	$-0.441201\pi$
$241$	−12.6591	−	14.6094i	−0.815447	−	0.941076i	−0.999121	+	0.0419114i	$0.986655\pi$
$242$	0.0327623	+	0.00550926i	0.00210604	+	0.000354149i
$243$	0.914851	−	1.22210i	0.0586877	−	0.0783976i
$244$	8.02470	−	17.5716i	0.513729	−	1.12491i
$245$	7.69144	+	11.5917i	0.491388	+	0.740569i
$246$	1.31123	+	4.46564i	0.0836011	+	0.284719i
$247$	−14.6716	+	21.6772i	−0.933530	+	1.37929i
$248$	−0.149214	+	6.26833i	−0.00947510	+	0.398039i
$249$	4.29551	+	2.21449i	0.272217	+	0.140338i
$250$	1.01896	−	2.70123i	0.0644445	−	0.170841i
$251$	−1.18716	−	12.4325i	−0.0749330	−	0.784733i	−0.952350	−	0.305006i	$-0.901342\pi$
$251$	−1.18716	−	12.4325i	−0.0749330	−	0.784733i	0.877418	−	0.479728i	$-0.159264\pi$
$252$	0.207719	−	0.140588i	0.0130851	−	0.00885623i
$253$	−15.9832	−	3.47693i	−1.00485	−	0.218593i
$254$	−1.73806	−	3.80582i	−0.109056	−	0.238798i
$255$	−12.0929	+	19.4363i	−0.757288	+	1.21715i
$256$	10.1455	+	4.06164i	0.634093	+	0.253852i
$257$	8.16893	−	16.8165i	0.509564	−	1.04898i	−0.475963	−	0.879465i	$-0.657900\pi$
$257$	8.16893	−	16.8165i	0.509564	−	1.04898i	0.985527	−	0.169517i	$-0.0542207\pi$
$258$	−0.00883242	−	0.371041i	−0.000549883	−	0.0231000i
$259$	4.05975	+	2.60904i	0.252261	+	0.162118i
$260$	8.06555	−	12.3007i	0.500204	−	0.762857i
$261$	−0.156979	+	0.0809286i	−0.00971679	+	0.00500935i
$262$	1.28187	+	2.63884i	0.0791941	+	0.163028i
$263$	1.42776	+	19.9628i	0.0880398	+	1.23096i	0.828938	+	0.559340i	$0.188945\pi$
$263$	1.42776	+	19.9628i	0.0880398	+	1.23096i	−0.740899	+	0.671617i	$0.765600\pi$
$264$	5.91392	+	0.564711i	0.363976	+	0.0347555i
$265$	−15.1698	+	17.1858i	−0.931873	+	1.05572i
$266$	0.0834066	−	1.75092i	0.00511399	−	0.107356i
$267$	12.6645	−	12.6645i	0.775055	−	0.775055i
$268$	−0.995414	−	15.7936i	−0.0608046	−	0.964746i
$269$		−	5.83885i		−	0.356001i	−0.984030	−	0.178001i	$-0.943037\pi$
$269$		−	5.83885i		−	0.356001i	0.984030	−	0.178001i	$-0.0569629\pi$
$270$	0.864239	+	2.79160i	0.0525959	+	0.169892i
$271$	−4.74519	+	16.1606i	−0.288249	+	0.981688i	0.680314	+	0.732921i	$0.261843\pi$
$271$	−4.74519	+	16.1606i	−0.288249	+	0.981688i	−0.968563	+	0.248767i	$0.919975\pi$
$272$	13.2431	+	16.0393i	0.802984	+	0.972524i
$273$	−5.31264	+	0.379968i	−0.321536	+	0.0229967i
$274$	1.15639	+	0.400231i	0.0698602	+	0.0241789i
$275$	15.1900	+	6.40689i	0.915990	+	0.386350i
$276$	16.8412	+	2.42140i	1.01372	+	0.145751i
$277$	5.28774	+	24.3074i	0.317710	+	1.46049i	0.808131	+	0.589003i	$0.200479\pi$
$277$	5.28774	+	24.3074i	0.317710	+	1.46049i	−0.490421	+	0.871485i	$0.663157\pi$
$278$	−1.39062	+	0.0331030i	−0.0834040	+	0.00198539i
$279$	0.296861	+	0.857725i	0.0177726	+	0.0513506i
$280$	−0.0660657	+	2.00296i	−0.00394818	+	0.119700i
$281$	−11.3918	−	14.4859i	−0.679578	−	0.864154i	0.316861	−	0.948472i	$-0.397371\pi$
$281$	−11.3918	−	14.4859i	−0.679578	−	0.864154i	−0.996439	+	0.0843182i	$0.973129\pi$
$282$	0.281012	−	0.753422i	0.0167340	−	0.0448656i
$283$	−4.04444	+	18.5920i	−0.240417	+	1.10518i	0.685682	+	0.727901i	$0.259504\pi$
$283$	−4.04444	+	18.5920i	−0.240417	+	1.10518i	−0.926100	+	0.377279i	$0.876860\pi$
$284$	−4.52535	+	23.4798i	−0.268530	+	1.39327i
$285$	28.7451	+	10.2450i	1.70271	+	0.606859i
$286$	−2.35976	−	1.68038i	−0.139536	−	0.0993629i
$287$	−2.72982	−	8.53961i	−0.161136	−	0.504077i
$288$	−0.435381	−	0.0103640i	−0.0256551	−	0.000610704i
$289$	3.08513	+	16.0072i	0.181478	+	0.941598i
$290$	0.105002	−	0.685601i	0.00616591	−	0.0402599i
$291$	−0.453006	−	1.86731i	−0.0265557	−	0.109464i
$292$	−4.76419	+	1.77695i	−0.278803	+	0.103988i
$293$	3.94917	+	2.95631i	0.230713	+	0.172710i	0.708380	−	0.705832i	$-0.249426\pi$
$293$	3.94917	+	2.95631i	0.230713	+	0.172710i	−0.477667	+	0.878541i	$0.658517\pi$
$294$	−2.32147	+	1.65311i	−0.135391	+	0.0964112i
$295$	13.3304	+	7.43849i	0.776127	+	0.433085i
$296$	−2.06446	−	5.15678i	−0.119995	−	0.299732i
$297$	−16.1188	+	4.31903i	−0.935309	+	0.250615i
$298$	−0.562142	+	2.09794i	−0.0325640	+	0.121530i
$299$	−13.2683	−	10.4343i	−0.767323	−	0.603430i
$300$	−16.2356	−	5.52021i	−0.937364	−	0.318709i
$301$	0.0340181	+	0.714127i	0.00196077	+	0.0411616i
$302$	−3.06286	−	2.78432i	−0.176248	−	0.160220i
$303$	−3.31525	−	5.43901i	−0.190456	−	0.312463i
$304$	17.1406	−	21.7960i	0.983079	−	1.25009i
$305$	17.0974	+	14.3825i	0.978993	+	0.823542i
$306$	−0.189738	−	0.109545i	−0.0108466	−	0.00626229i
$307$	−1.60238	−	0.686178i	−0.0914525	−	0.0391622i	0.347437	−	0.937703i	$-0.387052\pi$
$307$	−1.60238	−	0.686178i	−0.0914525	−	0.0391622i	−0.438889	+	0.898541i	$0.644628\pi$
$308$	−5.61056	−	0.401275i	−0.319691	−	0.0228648i
$309$	−7.76193	−	10.9001i	−0.441561	−	0.620085i
$310$	−3.41077	−	1.03557i	−0.193719	−	0.0588163i
$311$	−20.4945	−	9.35954i	−1.16214	−	0.530731i	−0.261459	−	0.965215i	$-0.584203\pi$
$311$	−20.4945	−	9.35954i	−1.16214	−	0.530731i	−0.900680	+	0.434484i	$0.856931\pi$
$312$	5.23482	+	3.19079i	0.296364	+	0.180643i
$313$	18.3594	+	10.0250i	1.03773	+	0.566646i	0.905400	−	0.424560i	$-0.139571\pi$
$313$	18.3594	+	10.0250i	1.03773	+	0.566646i	0.132334	+	0.991205i	$0.457753\pi$
$314$	1.58924	−	0.306300i	0.0896857	−	0.0172855i
$315$	0.0923642	+	0.275004i	0.00520413	+	0.0154947i
$316$	−5.86277	+	11.3722i	−0.329807	+	0.639736i
$317$	−24.3243	+	4.09034i	−1.36619	+	0.229736i	−0.802699	−	0.596385i	$-0.796603\pi$
$317$	−24.3243	+	4.09034i	−1.36619	+	0.229736i	−0.563493	+	0.826121i	$0.690543\pi$
$318$	−3.62125	−	2.98995i	−0.203069	−	0.167668i
$319$	3.88909	+	0.749560i	0.217747	+	0.0419673i
$320$	−8.74038	+	11.4552i	−0.488602	+	0.640368i
$321$	−28.0854	+	12.8262i	−1.56757	+	0.715887i
$322$	1.12239	+	0.134198i	0.0625483	+	0.00747856i
$323$	40.8101	−	17.4759i	2.27073	−	0.972385i
$324$	17.2093	−	5.95618i	0.956070	−	0.330899i
$325$	11.2108	+	12.7963i	0.621866	+	0.709810i
$326$	2.44537	−	3.80508i	0.135437	−	0.210744i
$327$	−2.85731	+	2.13895i	−0.158010	+	0.118284i
$328$	−3.14210	+	9.82933i	−0.173493	+	0.542734i
$329$	−0.506621	+	1.46378i	−0.0279309	+	0.0807010i
$330$	−1.20923	+	3.15342i	−0.0665657	+	0.173590i
$331$	−1.26726	+	13.2714i	−0.0696550	+	0.729460i	0.891421	+	0.453176i	$0.149709\pi$
$331$	−1.26726	+	13.2714i	−0.0696550	+	0.729460i	−0.961076	+	0.276284i	$0.910897\pi$
$332$	2.52411	+	4.62257i	0.138529	+	0.253696i
$333$	−0.540873	−	0.594981i	−0.0296397	−	0.0326047i
$334$	0.873613			0.0478020
$335$	17.9084	+	3.78014i	0.978440	+	0.206531i
$336$	5.64219			0.307807
$337$	5.31443	+	5.84606i	0.289495	+	0.318455i	0.867364	−	0.497674i	$-0.165812\pi$
$337$	5.31443	+	5.84606i	0.289495	+	0.318455i	−0.577869	+	0.816130i	$0.696115\pi$
$338$	0.176088	+	0.322481i	0.00957792	+	0.0175406i
$339$	1.75067	−	18.3338i	0.0950832	−	0.995757i
$340$	−22.7869	+	10.1549i	−1.23579	+	0.550726i
$341$	6.65733	−	19.2351i	0.360515	−	1.04164i
$342$	−0.0889311	+	0.278201i	−0.00480885	+	0.0150434i
$343$	9.33960	−	6.99153i	0.504291	−	0.377507i
$344$	0.444900	−	0.692279i	0.0239874	−	0.0373252i
$345$	−7.91214	+	18.0181i	−0.425975	+	0.970060i
$346$	−4.11985	+	1.42589i	−0.221484	+	0.0766565i
$347$	3.53693	−	1.51460i	0.189872	−	0.0813081i	−0.296609	−	0.954999i	$-0.595856\pi$
$347$	3.53693	−	1.51460i	0.189872	−	0.0813081i	0.486482	+	0.873691i	$0.338280\pi$
$348$	−4.09070	−	0.489103i	−0.219285	−	0.0262187i
$349$	24.7539	−	11.3047i	1.32505	−	0.605129i	0.377876	−	0.925856i	$-0.376655\pi$
$349$	24.7539	−	11.3047i	1.32505	−	0.605129i	0.947171	+	0.320728i	$0.103927\pi$
$350$	−1.08707	−	0.340972i	−0.0581062	−	0.0182257i
$351$	−16.9094	−	3.25902i	−0.902556	−	0.173953i
$352$	7.53113	+	6.21823i	0.401411	+	0.331433i
$353$	2.60639	−	0.438286i	0.138724	−	0.0233276i	−0.0960573	−	0.995376i	$-0.530623\pi$
$353$	2.60639	−	0.438286i	0.138724	−	0.0233276i	0.234781	+	0.972048i	$0.424563\pi$
$354$	−1.43300	+	2.77964i	−0.0761633	+	0.147736i
$355$	−24.7647	−	12.3119i	−1.31437	−	0.653450i
$356$	19.1662	−	3.69399i	1.01581	−	0.195781i
$357$	7.92844	+	4.32926i	0.419618	+	0.229129i
$358$	1.63236	+	0.994975i	0.0862729	+	0.0525861i
$359$	0.684758	+	0.312719i	0.0361402	+	0.0165047i	0.433403	−	0.901200i	$-0.357313\pi$
$359$	0.684758	+	0.312719i	0.0361402	+	0.0165047i	−0.397263	+	0.917705i	$0.630040\pi$
$360$	0.0970092	−	0.319512i	0.00511283	−	0.0168398i
$361$	−23.3079	−	32.7314i	−1.22673	−	1.72271i
$362$	3.79847	+	0.271672i	0.199643	+	0.0142788i
$363$	0.209809	+	0.0898454i	0.0110121	+	0.00471566i
$364$	−5.02693	−	2.90230i	−0.263483	−	0.152122i
$365$	−0.505307	−	5.85928i	−0.0264490	−	0.306689i
$366$	−2.82936	+	3.59782i	−0.147893	+	0.188061i
$367$	1.80088	+	2.95454i	0.0940053	+	0.154225i	0.897395	−	0.441228i	$-0.145457\pi$
$367$	1.80088	+	2.95454i	0.0940053	+	0.154225i	−0.803390	+	0.595454i	$0.796972\pi$
$368$	13.2311	+	12.0278i	0.689717	+	0.626994i
$369$	0.0710779	+	1.49211i	0.00370017	+	0.0776760i
$370$	3.13877	−	0.346116i	0.163177	−	0.0179937i
$371$	7.11068	+	5.59190i	0.369168	+	0.290317i
$372$	−5.47988	+	20.4512i	−0.284118	+	1.06034i
$373$	−31.6966	+	8.49308i	−1.64119	+	0.439755i	−0.957127	−	0.289669i	$-0.906455\pi$
$373$	−31.6966	+	8.49308i	−1.64119	+	0.439755i	−0.684062	+	0.729424i	$0.739788\pi$
$374$	1.82608	+	4.56132i	0.0944242	+	0.235860i
$375$	11.1779	−	16.3839i	0.577227	−	0.846060i
$376$	1.45232	−	1.03419i	0.0748977	−	0.0533344i
$377$	3.27197	+	2.44937i	0.168515	+	0.126149i
$378$	1.08051	−	0.403008i	0.0555753	−	0.0207285i
$379$	3.16830	+	13.0599i	0.162745	+	0.670844i	0.993463	+	0.114151i	$0.0364147\pi$
$379$	3.16830	+	13.0599i	0.162745	+	0.670844i	−0.830719	+	0.556693i	$0.812070\pi$
$380$	19.6852	+	26.8054i	1.00983	+	1.37509i
$381$	−5.43972	−	28.2239i	−0.278685	−	1.44596i
$382$	5.28406	+	0.125784i	0.270356	+	0.00643567i
$383$	−5.42384	−	16.9672i	−0.277145	−	0.866986i	−0.986731	−	0.162366i	$-0.948087\pi$
$383$	−5.42384	−	16.9672i	−0.277145	−	0.866986i	0.709585	−	0.704619i	$-0.248882\pi$
$384$	−10.9652	−	7.80827i	−0.559564	−	0.398464i
$385$	2.18411	−	6.12813i	0.111313	−	0.312318i
$386$	−1.14385	+	5.93484i	−0.0582203	+	0.302075i
$387$	0.0253214	−	0.116400i	0.00128716	−	0.00591697i
$388$	0.731799	−	1.96203i	0.0371515	−	0.0996069i
$389$	8.37993	+	10.6559i	0.424879	+	0.540278i	0.950616	−	0.310369i	$-0.100453\pi$
$389$	8.37993	+	10.6559i	0.424879	+	0.540278i	−0.525737	+	0.850647i	$0.676210\pi$
$390$	−2.54433	+	2.38184i	−0.128837	+	0.120609i
$391$	9.36340	+	27.0538i	0.473528	+	1.36817i
$392$	−6.31709	+	0.150375i	−0.319061	+	0.00759507i
$393$	4.28415	+	19.6939i	0.216107	+	0.993427i
$394$	3.66649	+	0.527162i	0.184715	+	0.0265580i
$395$	−10.8581	−	10.0541i	−0.546328	−	0.505875i
$396$	0.885672	+	0.306534i	0.0445067	+	0.0154039i
$397$	17.9059	−	1.28066i	0.898672	−	0.0642743i	0.385645	−	0.922647i	$-0.373979\pi$
$397$	17.9059	−	1.28066i	0.898672	−	0.0642743i	0.513026	+	0.858373i	$0.328524\pi$
$398$	3.61027	+	4.37253i	0.180966	+	0.219175i
$399$	3.39274	−	11.5546i	0.169850	−	0.578454i
$400$	−10.8786	−	14.3681i	−0.543932	−	0.718405i
$401$			35.2658i			1.76109i	0.473964	+	0.880544i	$0.342823\pi$
$401$			35.2658i			1.76109i	−0.473964	+	0.880544i	$0.657177\pi$
$402$	−0.653040	+	3.69227i	−0.0325707	+	0.184154i
$403$	14.8527	−	14.8527i	0.739866	−	0.739866i
$404$	0.330307	−	6.93400i	0.0164334	−	0.344980i
$405$	1.30983	+	21.0218i	0.0650859	+	1.04458i
$406$	−0.272470	−	0.0260177i	−0.0135225	−	0.00129124i
$407$	1.28639	+	17.9861i	0.0637642	+	0.891540i
$408$	−4.54323	−	9.35263i	−0.224923	−	0.463024i
$409$	−19.7165	+	10.1646i	−0.974919	+	0.502605i	−0.870628	−	0.491941i	$-0.836287\pi$
$409$	−19.7165	+	10.1646i	−0.974919	+	0.502605i	−0.104290	+	0.994547i	$0.533257\pi$
$410$	−4.90589	−	3.21679i	−0.242285	−	0.158866i
$411$	7.07221	+	4.54503i	0.348846	+	0.224190i
$412$	−0.347047	−	14.5791i	−0.0170978	−	0.718259i
$413$	2.63219	−	5.41858i	0.129521	−	0.266631i
$414$	−0.174853	−	0.0700005i	−0.00859355	−	0.00344034i
$415$	−5.93277	+	1.38178i	−0.291228	+	0.0678290i
$416$	4.18677	+	9.16775i	0.205273	+	0.449486i
$417$	−9.33786	−	2.03133i	−0.457277	−	0.0994745i
$418$	5.42426	−	3.67125i	0.265309	−	0.179567i
$419$	−1.94078	−	20.3248i	−0.0948133	−	0.992930i	−0.910243	−	0.414074i	$-0.864105\pi$
$419$	−1.94078	−	20.3248i	−0.0948133	−	0.992930i	0.815430	−	0.578856i	$-0.196501\pi$
$420$	−1.81135	+	6.52025i	−0.0883850	+	0.318156i
$421$	−17.2719	−	8.90431i	−0.841783	−	0.433969i	−0.0172963	−	0.999850i	$-0.505506\pi$
$421$	−17.2719	−	8.90431i	−0.841783	−	0.433969i	−0.824487	+	0.565881i	$0.808536\pi$
$422$	0.125062	−	5.25373i	0.00608793	−	0.255747i
$423$	0.144662	−	0.213737i	0.00703369	−	0.0103923i
$424$	−2.93348	−	9.99050i	−0.142462	−	0.485182i
$425$	−4.26208	−	28.5373i	−0.206741	−	1.38426i
$426$	2.35362	−	5.15372i	0.114033	−	0.249698i
$427$	5.28371	−	7.05821i	0.255697	−	0.341571i
$428$	−33.1828	−	5.57997i	−1.60395	−	0.269718i
$429$	−13.0329	−	15.0408i	−0.629234	−	0.726175i
$430$	0.311496	+	0.349036i	0.0150217	+	0.0168320i
$431$	11.7304	−	20.3177i	0.565036	−	0.978671i	−0.432011	−	0.901868i	$-0.642196\pi$
$431$	11.7304	−	20.3177i	0.565036	−	0.978671i	0.997046	−	0.0768020i	$-0.0244709\pi$
$432$	17.6206	+	4.72143i	0.847773	+	0.227160i
$433$	2.40432	+	20.1089i	0.115544	+	0.966374i	0.925203	+	0.379473i	$0.123895\pi$
$433$	2.40432	+	20.1089i	0.115544	+	0.966374i	−0.809659	+	0.586901i	$0.800348\pi$
$434$	−0.331629	+	1.36699i	−0.0159187	+	0.0656177i
$435$	1.81146	−	4.40723i	0.0868531	−	0.211310i
$436$	−3.88539	+	0.185084i	−0.186077	+	0.00886392i
$437$	32.5878	−	19.8633i	1.55889	−	0.950190i
$438$	1.19628	−	0.143032i	0.0571603	−	0.00683435i
$439$	−2.08769	+	1.20533i	−0.0996402	+	0.0575273i	−0.548992	−	0.835828i	$-0.684988\pi$
$439$	−2.08769	+	1.20533i	−0.0996402	+	0.0575273i	0.449352	+	0.893355i	$0.351655\pi$
$440$	−6.13934	+	4.28749i	−0.292682	+	0.204398i
$441$	−0.849182	+	0.339961i	−0.0404372	+	0.0161886i
$442$	−0.361707	+	5.05732i	−0.0172046	+	0.240552i
$443$	−3.45459	+	20.5437i	−0.164133	+	0.976061i	0.774862	+	0.632130i	$0.217819\pi$
$443$	−3.45459	+	20.5437i	−0.164133	+	0.976061i	−0.938995	+	0.343931i	$0.888241\pi$
$444$	−2.66937	−	18.5659i	−0.126683	−	0.881097i
$445$	−1.81699	+	22.5023i	−0.0861335	+	1.06671i
$446$	−0.490727	+	0.119049i	−0.0232366	+	0.00563713i
$447$	−7.15099	+	13.0961i	−0.338230	+	0.619422i
$448$	4.70894	+	3.18710i	0.222477	+	0.150577i
$449$	−17.5830	−	18.4405i	−0.829792	−	0.870261i	0.163423	−	0.986556i	$-0.447747\pi$
$449$	−17.5830	−	18.4405i	−0.829792	−	0.870261i	−0.993215	+	0.116295i	$0.962898\pi$
$450$	0.160251	+	0.101756i	0.00755431	+	0.00479683i
$451$	19.4316	−	27.2879i	0.915000	−	1.28494i
$452$	12.7793	−	15.4775i	0.601086	−	0.727998i
$453$	−15.9390	−	23.5498i	−0.748879	−	1.10647i
$454$	−1.68367	+	1.08203i	−0.0790187	+	0.0507822i
$455$	4.79055	−	4.70347i	0.224584	−	0.220502i
$456$	−10.8956	+	8.56841i	−0.510234	+	0.401253i
$457$	−11.6844	−	27.2856i	−0.546572	−	1.27637i	−0.934922	−	0.354854i	$-0.884531\pi$
$457$	−11.6844	−	27.2856i	−0.546572	−	1.27637i	0.388350	−	0.921512i	$-0.373045\pi$
$458$	−2.93747	−	1.42693i	−0.137259	−	0.0666762i
$459$	21.1378	+	20.1549i	0.986630	+	0.940749i
$460$	−18.1473	+	11.4287i	−0.846123	+	0.532868i
$461$	−1.26899	+	8.82599i	−0.0591026	+	0.411067i	0.938696	+	0.344747i	$0.112035\pi$
$461$	−1.26899	+	8.82599i	−0.0591026	+	0.411067i	−0.997798	+	0.0663208i	$0.978874\pi$
$462$	1.26949	+	0.405810i	0.0590618	+	0.0188800i
$463$	−3.72270	+	1.80838i	−0.173009	+	0.0840424i	−0.521424	−	0.853298i	$-0.674599\pi$
$463$	−3.72270	+	1.80838i	−0.173009	+	0.0840424i	0.348415	+	0.937340i	$0.386720\pi$
$464$	−3.27215	−	2.83534i	−0.151906	−	0.131627i
$465$	−21.0941	−	12.4381i	−0.978218	−	0.576801i
$466$	−3.04495	−	0.894079i	−0.141055	−	0.0414174i
$467$	1.94595	−	1.76898i	0.0900478	−	0.0818588i	−0.626390	−	0.779510i	$-0.715468\pi$
$467$	1.94595	−	1.76898i	0.0900478	−	0.0818588i	0.716438	+	0.697651i	$0.245771\pi$
$468$	0.683887	+	0.683887i	0.0316127	+	0.0316127i
$469$	1.08833	−	7.14034i	0.0502545	−	0.329710i
$470$	0.345483	+	0.952879i	0.0159360	+	0.0439530i
$471$	11.1063	+	0.529060i	0.511753	+	0.0243778i
$472$	−6.08572	+	3.32305i	−0.280118	+	0.152956i
$473$	−2.05998	+	1.70086i	−0.0947180	+	0.0782058i
$474$	1.98524	−	2.29109i	0.0911851	−	0.105233i
$475$	−35.9659	+	13.6385i	−1.65023	+	0.625779i
$476$	4.51114	+	8.75038i	0.206768	+	0.401073i
$477$	−0.903264	−	1.20662i	−0.0413576	−	0.0552473i
$478$	2.51201	−	0.546454i	0.114897	−	0.0249942i
$479$	−0.272405	+	0.285691i	−0.0124465	+	0.0130535i	−0.729928	−	0.683524i	$-0.760446\pi$
$479$	−0.272405	+	0.285691i	−0.0124465	+	0.0130535i	0.717481	+	0.696578i	$0.245295\pi$
$480$	9.12877	−	7.39759i	0.416669	−	0.337652i
$481$	−6.91597	+	17.2752i	−0.315341	+	0.787684i
$482$	−0.592612	+	4.95642i	−0.0269928	+	0.225759i
$483$	7.27607	+	2.71383i	0.331073	+	0.123484i
$484$	0.134477	+	0.209250i	0.00611259	+	0.00951137i
$485$	1.95992	+	1.42292i	0.0889952	+	0.0646115i
$486$	−0.392416	+	0.0374711i	−0.0178003	+	0.00169973i
$487$	−5.49054	−	32.6510i	−0.248800	−	1.47956i	−0.776495	−	0.630124i	$-0.783004\pi$
$487$	−5.49054	−	32.6510i	−0.248800	−	1.47956i	0.527695	−	0.849434i	$-0.323057\pi$
$488$	−9.66651	+	3.09005i	−0.437582	+	0.139880i
$489$	22.4890	−	21.4432i	1.01699	−	0.969697i
$490$	0.878887	−	3.48307i	0.0397041	−	0.157349i
$491$	0.179511	−	0.0527092i	0.00810123	−	0.00237873i	−0.277679	−	0.960674i	$-0.589565\pi$
$491$	0.179511	−	0.0527092i	0.00810123	−	0.00237873i	0.285781	+	0.958295i	$0.407747\pi$
$492$	−18.1361	+	29.7542i	−0.817641	+	1.34142i
$493$	−2.42249	−	6.49495i	−0.109104	−	0.292518i
$494$	6.69033	−	0.961924i	0.301012	−	0.0432790i
$495$	−0.615788	+	0.892088i	−0.0276776	+	0.0400964i
$496$	−16.8162	+	14.5713i	−0.755070	+	0.654271i
$497$	−4.29624	+	10.0327i	−0.192713	+	0.450027i
$498$	−0.322987	−	1.20540i	−0.0144734	−	0.0540155i
$499$	−14.6030	−	25.2932i	−0.653722	−	1.13228i	−0.982213	−	0.187772i	$-0.939873\pi$
$499$	−14.6030	−	25.2932i	−0.653722	−	1.13228i	0.328491	−	0.944507i	$-0.393460\pi$
$500$	20.0966	−	7.95892i	0.898746	−	0.355934i
$501$	5.83252	+	1.41495i	0.260578	+	0.0632155i
$502$	−2.16931	+	2.38632i	−0.0968209	+	0.106507i
$503$	−3.28417	+	3.61271i	−0.146434	+	0.161083i	−0.808772	−	0.588122i	$-0.799867\pi$
$503$	−3.28417	+	3.61271i	−0.146434	+	0.161083i	0.662338	+	0.749205i	$0.269564\pi$
$504$	−0.128056	−	0.0310661i	−0.00570407	−	0.00138379i
$505$	7.62494	+	2.51474i	0.339305	+	0.111904i
$506$	2.11188	+	3.65788i	0.0938844	+	0.162613i
$507$	0.653311	+	2.43819i	0.0290145	+	0.108284i
$508$	12.3311	−	28.7959i	0.547104	−	1.27761i
$509$	−7.33526	+	6.35604i	−0.325130	+	0.281727i	−0.802096	−	0.597195i	$-0.796282\pi$
$509$	−7.33526	+	6.35604i	−0.325130	+	0.281727i	0.476966	+	0.878922i	$0.341736\pi$
$510$	5.81424	−	1.06539i	0.257459	−	0.0471762i
$511$	−2.29717	+	0.330284i	−0.101621	+	0.0146109i
$512$	−6.28972	−	16.8634i	−0.277969	−	0.745263i
$513$	20.2646	−	33.2461i	0.894702	−	1.46785i
$514$	−4.63208	+	1.36010i	−0.204312	+	0.0599915i
$515$	16.3542	+	4.12669i	0.720654	+	0.181844i
$516$	2.01110	−	1.91758i	0.0885335	−	0.0844166i
$517$	−5.51303	+	1.76233i	−0.242463	+	0.0775070i
$518$	−0.206648	−	1.22889i	−0.00907958	−	0.0539943i
$519$	−29.8149	+	2.84698i	−1.30873	+	0.124968i
$520$	−7.63195	+	1.21150i	−0.334683	+	0.0531279i
$521$	−15.1246	−	23.5343i	−0.662619	−	1.03106i	−0.996094	−	0.0882970i	$-0.971858\pi$
$521$	−15.1246	−	23.5343i	−0.662619	−	1.03106i	0.333475	−	0.942759i	$-0.391779\pi$
$522$	0.0427300	+	0.0159375i	0.00187024	+	0.000697564i
$523$	0.0900183	−	0.752884i	0.00393623	−	0.0329213i	−0.990823	−	0.135163i	$-0.956844\pi$
$523$	0.0900183	−	0.752884i	0.00393623	−	0.0329213i	0.994760	+	0.102242i	$0.0326016\pi$
$524$	−8.16347	+	20.3914i	−0.356623	+	0.890801i
$525$	−6.70535	−	4.03712i	−0.292645	−	0.176194i
$526$	3.56634	−	3.74027i	0.155500	−	0.163083i
$527$	−34.8108	+	7.57262i	−1.51638	+	0.329869i
$528$	12.6342	+	16.8774i	0.549835	+	0.734494i
$529$	0.738071	+	1.43166i	0.0320901	+	0.0622460i
$530$	5.91868	−	0.0865831i	0.257091	−	0.00376093i
$531$	−0.657304	+	0.758569i	−0.0285246	+	0.0329191i
$532$	10.1202	−	8.35595i	0.438767	−	0.362276i
$533$	30.3412	−	16.5675i	1.31422	−	0.717620i
$534$	−4.61962	−	0.220059i	−0.199910	−	0.00952290i
$535$	16.4911	−	35.2512i	0.712973	−	1.52404i
$536$	−5.78775	+	5.96814i	−0.249993	+	0.257785i
$537$	9.28663	+	9.28663i	0.400748	+	0.400748i
$538$	−1.11564	+	1.01419i	−0.0480989	+	0.0437248i
$539$	19.6820	+	5.77915i	0.847763	+	0.248926i
$540$	−11.1131	+	18.8470i	−0.478230	+	0.811048i
$541$	−6.19315	−	5.36639i	−0.266264	−	0.230719i	0.511488	−	0.859291i	$-0.329095\pi$
$541$	−6.19315	−	5.36639i	−0.266264	−	0.230719i	−0.777752	+	0.628571i	$0.783640\pi$
$542$	3.91207	−	1.90037i	0.168038	−	0.0816278i
$543$	24.9198	+	7.96599i	1.06941	+	0.341853i
$544$	2.43266	−	16.9195i	0.104299	−	0.725417i
$545$	0.996595	−	4.38715i	0.0426894	−	0.187925i
$546$	0.995388	+	0.949101i	0.0425987	+	0.0406178i
$547$	−16.7689	−	8.14584i	−0.716988	−	0.348291i	0.0422478	−	0.999107i	$-0.486548\pi$
$547$	−16.7689	−	8.14584i	−0.716988	−	0.348291i	−0.759235	+	0.650816i	$0.774427\pi$
$548$	3.60655	+	8.42210i	0.154064	+	0.359774i
$549$	−1.15476	+	0.908110i	−0.0492838	+	0.0387572i
$550$	−1.41426	−	4.01524i	−0.0603044	−	0.171210i
$551$	−7.77407	+	4.99609i	−0.331186	+	0.212841i
$552$	−5.01012	−	7.40245i	−0.213245	−	0.315069i
$553$	−3.71805	+	4.50307i	−0.158108	+	0.191490i
$554$	3.72601	−	5.23245i	0.158303	−	0.222305i
$555$	21.5160	+	2.77295i	0.913305	+	0.117705i
$556$	−7.18687	−	7.53738i	−0.304791	−	0.319656i
$557$	−11.7285	−	7.93810i	−0.496954	−	0.336348i	0.286206	−	0.958168i	$-0.407606\pi$
$557$	−11.7285	−	7.93810i	−0.496954	−	0.336348i	−0.783160	+	0.621820i	$0.786394\pi$
$558$	0.112324	−	0.205706i	0.00475505	−	0.00870822i
$559$	−2.67905	+	0.649932i	−0.113312	+	0.0274892i
$560$	−5.41727	+	4.60778i	−0.228921	+	0.194714i
$561$	4.80370	+	33.4104i	0.202812	+	1.41059i
$562$	−0.789134	+	4.69280i	−0.0332876	+	0.197954i
$563$	2.25568	−	31.5386i	0.0950658	−	1.32919i	−0.696256	−	0.717793i	$-0.745152\pi$
$563$	2.25568	−	31.5386i	0.0950658	−	1.32919i	0.791322	−	0.611400i	$-0.209393\pi$
$564$	5.58921	−	2.23758i	0.235348	−	0.0942193i
$565$	13.2917	+	19.0327i	0.559186	+	0.800710i
$566$	4.25493	−	2.45658i	0.178848	−	0.103258i
$567$	8.25301	−	0.986768i	0.346594	−	0.0414403i
$568$	10.7266	−	6.53820i	0.450078	−	0.274337i
$569$	−19.7669	+	0.941611i	−0.828670	+	0.0394744i	−0.457630	−	0.889143i	$-0.651302\pi$
$569$	−19.7669	+	0.941611i	−0.828670	+	0.0394744i	−0.371040	+	0.928617i	$0.620999\pi$
$570$	−3.03539	−	7.27191i	−0.127138	−	0.304587i
$571$	−0.587872	+	2.42324i	−0.0246017	+	0.101409i	−0.982789	−	0.184733i	$-0.940858\pi$
$571$	−0.587872	+	2.42324i	−0.0246017	+	0.101409i	0.958187	+	0.286143i	$0.0923731\pi$
$572$	−2.57493	−	21.5359i	−0.107663	−	0.900462i
$573$	35.0743	+	9.39814i	1.46525	+	0.392613i
$574$	−1.15753	+	2.00489i	−0.0483142	+	0.0836826i
$575$	−7.11800	−	23.7614i	−0.296841	−	0.990917i
$576$	−0.620427	−	0.716011i	−0.0258511	−	0.0298338i
$577$	−0.708247	−	0.119098i	−0.0294847	−	0.00495810i	0.151069	−	0.988523i	$-0.451728\pi$
$577$	−0.708247	−	0.119098i	−0.0294847	−	0.00495810i	−0.180554	+	0.983565i	$0.557789\pi$
$578$	2.52265	−	3.36987i	0.104929	−	0.140168i
$579$	−17.2491	+	37.7703i	−0.716848	+	1.56968i
$580$	4.32706	−	2.87113i	0.179672	−	0.119217i
$581$	0.677250	+	2.30650i	0.0280971	+	0.0956898i
$582$	−0.278107	+	0.410903i	−0.0115279	+	0.0170325i
$583$	−0.804392	+	33.7917i	−0.0333145	+	1.39951i
$584$	2.37435	+	1.22406i	0.0982512	+	0.0506520i
$585$	−0.973838	+	0.550398i	−0.0402632	+	0.0227562i
$586$	−0.121087	−	1.26808i	−0.00500205	−	0.0523838i
$587$	23.3167	−	15.7812i	0.962384	−	0.651360i	0.0250108	−	0.999687i	$-0.492038\pi$
$587$	23.3167	−	15.7812i	0.962384	−	0.651360i	0.937373	+	0.348327i	$0.113250\pi$
$588$	−20.8497	−	4.53557i	−0.859826	−	0.187044i
$589$	19.7287	+	43.1998i	0.812906	+	1.78002i
$590$	−0.894155	−	3.83911i	−0.0368118	−	0.158054i
$591$	23.6248	+	9.45796i	0.971796	+	0.389048i
$592$	8.61311	−	17.7308i	0.353997	−	0.728733i
$593$	0.624174	+	26.2209i	0.0256317	+	1.07676i	0.855181	+	0.518329i	$0.173446\pi$
$593$	0.624174	+	26.2209i	0.0256317	+	1.07676i	−0.829549	+	0.558433i	$0.811403\pi$
$594$	3.62503	+	2.32966i	0.148737	+	0.0955873i
$595$	−11.1479	+	2.31820i	−0.457020	+	0.0950371i
$596$	−14.4537	+	7.45141i	−0.592048	+	0.305222i
$597$	17.0213	+	35.0398i	0.696635	+	1.43408i
$598$	0.310946	+	4.34760i	0.0127155	+	0.177786i
$599$	−17.7093	−	1.69103i	−0.723581	−	0.0690936i	−0.273234	−	0.961947i	$-0.588093\pi$
$599$	−17.7093	−	1.69103i	−0.723581	−	0.0690936i	−0.450346	+	0.892854i	$0.648700\pi$
$600$	3.59151	+	8.26211i	0.146623	+	0.337299i
$601$	0.819041	−	17.1938i	0.0334094	−	0.701349i	−0.918583	−	0.395228i	$-0.870666\pi$
$601$	0.819041	−	17.1938i	0.0334094	−	0.701349i	0.951993	−	0.306121i	$-0.0990313\pi$
$602$	0.130541	−	0.130541i	0.00532047	−	0.00532047i
$603$	−0.483082	+	1.10225i	−0.0196726	+	0.0448871i
$604$		−	30.9908i		−	1.26100i
$605$	−0.274818	+	0.0850797i	−0.0111730	+	0.00345898i
$606$	−0.463398	+	1.57819i	−0.0188243	+	0.0641096i
$607$	−19.1057	−	23.1397i	−0.775478	−	0.939211i	0.223895	−	0.974613i	$-0.428123\pi$
$607$	−19.1057	−	23.1397i	−0.775478	−	0.939211i	−0.999373	+	0.0354022i	$0.988729\pi$
$608$	−22.7292	+	1.62562i	−0.921791	+	0.0659278i
$609$	−1.77696	−	0.615011i	−0.0720059	−	0.0249215i
$610$	−0.221646	−	5.76504i	−0.00897419	−	0.233420i
$611$	−5.91199	−	0.850015i	−0.239173	−	0.0343879i
$612$	−0.348679	−	1.60285i	−0.0140945	−	0.0647914i
$613$	1.02837	−	0.0244798i	0.0415356	−	0.000988731i	−0.00302478	−	0.999995i	$-0.500963\pi$
$613$	1.02837	−	0.0244798i	0.0415356	−	0.000988731i	0.0445603	+	0.999007i	$0.485811\pi$
$614$	0.147217	+	0.425357i	0.00594121	+	0.0171660i
$615$	−27.5432	−	29.4222i	−1.11065	−	1.18642i
$616$	1.82669	+	2.32282i	0.0735994	+	0.0935892i
$617$	−13.0968	+	35.1138i	−0.527256	+	1.41363i	0.351424	+	0.936216i	$0.385698\pi$
$617$	−13.0968	+	35.1138i	−0.527256	+	1.41363i	−0.878680	+	0.477411i	$0.841575\pi$
$618$	−0.734491	+	3.37640i	−0.0295456	+	0.135819i
$619$	−2.63609	+	13.6774i	−0.105954	+	0.549739i	0.889695	+	0.456555i	$0.150917\pi$
$619$	−2.63609	+	13.6774i	−0.105954	+	0.549739i	−0.995649	+	0.0931846i	$0.970295\pi$
$620$	−11.4403	−	24.1111i	−0.459455	−	0.968326i
$621$	20.4523	+	14.5640i	0.820722	+	0.584433i
$622$	1.77148	+	5.54166i	0.0710297	+	0.222200i
$623$	8.90632	+	0.212010i	0.356824	+	0.00849400i
$624$	4.11736	+	21.3629i	0.164826	+	0.855199i
$625$	2.64780	+	24.8594i	0.105912	+	0.994376i
$626$	−1.27346	−	5.24928i	−0.0508977	−	0.209803i
$627$	42.1603	−	15.7250i	1.68372	−	0.627995i
$628$	9.70065	+	7.26182i	0.387098	+	0.289778i
$629$	25.7081	−	18.3066i	1.02505	−	0.729933i
$630$	0.0365024	−	0.0654155i	0.00145429	−	0.00260622i
$631$	6.63332	+	16.5692i	0.264068	+	0.659611i	0.999845	−	0.0176136i	$-0.00560688\pi$
$631$	6.63332	+	16.5692i	0.264068	+	0.659611i	−0.735777	+	0.677224i	$0.763183\pi$
$632$	6.49257	−	1.73968i	0.258261	−	0.0692008i
$633$	9.34420	−	34.8730i	0.371398	−	1.38608i
$634$	5.00660	+	3.93724i	0.198838	+	0.156368i
$635$	28.2724	+	22.6564i	1.12195	+	0.899091i
$636$	−1.67297	−	35.1199i	−0.0663374	−	1.39259i
$637$	15.6635	+	14.2391i	0.620610	+	0.564172i
$638$	−0.532300	−	0.873294i	−0.0210740	−	0.0345740i
$639$	1.12410	−	1.42941i	0.0444687	−	0.0565466i
$640$	16.9048	−	1.45788i	0.668221	−	0.0576276i
$641$	−0.721359	−	0.416477i	−0.0284920	−	0.0164498i	0.485686	−	0.874133i	$-0.338570\pi$
$641$	−0.721359	−	0.416477i	−0.0284920	−	0.0164498i	−0.514178	+	0.857683i	$0.671903\pi$
$642$	7.32906	+	3.13849i	0.289255	+	0.123866i
$643$	−29.4489	−	2.10623i	−1.16135	−	0.0830615i	−0.522672	−	0.852534i	$-0.675065\pi$
$643$	−29.4489	−	2.10623i	−1.16135	−	0.0830615i	−0.638680	+	0.769473i	$0.720519\pi$
$644$	4.90913	+	6.89391i	0.193447	+	0.271658i
$645$	1.51433	+	2.83480i	0.0596267	+	0.111620i
$646$	−10.4277	−	4.76218i	−0.410273	−	0.187366i
$647$	3.11556	+	1.89903i	0.122485	+	0.0746588i	0.580370	−	0.814353i	$-0.302908\pi$
$647$	3.11556	+	1.89903i	0.122485	+	0.0746588i	−0.457885	+	0.889012i	$0.651393\pi$
$648$	−8.39685	−	4.58503i	−0.329859	−	0.180117i
$649$	22.1026	−	4.25993i	0.867603	−	0.167217i
$650$	0.497733	−	4.36475i	0.0195227	−	0.171200i
$651$	−4.42812	+	8.58935i	−0.173552	+	0.336643i
$652$	33.3957	−	5.61576i	1.30788	−	0.219930i
$653$	−1.31598	−	1.08656i	−0.0514981	−	0.0425204i	0.610586	−	0.791950i	$-0.290934\pi$
$653$	−1.31598	−	1.08656i	−0.0514981	−	0.0425204i	−0.662084	+	0.749429i	$0.730328\pi$
$654$	0.905000	+	0.174424i	0.0353883	+	0.00682053i
$655$	−20.1967	−	15.4101i	−0.789150	−	0.602123i
$656$	−33.3114	+	15.2128i	−1.30059	+	0.593959i
$657$	0.383956	+	0.0459076i	0.0149796	+	0.00179103i
$658$	0.367687	−	0.157453i	0.0143339	−	0.00613815i
$659$	−41.2866	+	14.2894i	−1.60830	+	0.556638i	−0.975940	−	0.218038i	$-0.930034\pi$
$659$	−41.2866	+	14.2894i	−1.60830	+	0.556638i	−0.632359	+	0.774676i	$0.717913\pi$
$660$	−23.5600	+	9.18216i	−0.917070	+	0.357415i
$661$	12.0011	−	18.6741i	0.466789	−	0.726337i	−0.525431	−	0.850836i	$-0.676096\pi$
$661$	12.0011	−	18.6741i	0.466789	−	0.726337i	0.992220	+	0.124499i	$0.0397323\pi$
$662$	2.75591	−	2.06305i	0.107112	−	0.0801827i
$663$	−10.6060	+	33.1785i	−0.411903	+	1.28854i
$664$	0.904974	−	2.61475i	0.0351198	−	0.101472i
$665$	6.17876	+	13.8647i	0.239602	+	0.537651i
$666$	−0.0197367	+	0.206692i	−0.000764781	+	0.00800915i
$667$	−2.85594	−	5.23027i	−0.110583	−	0.202517i
$668$	4.39971	+	4.83984i	0.170230	+	0.187259i
$669$	−3.46907			−0.134122
$670$	−2.38834	−	4.07840i	−0.0922697	−	0.157562i
$671$	32.9446			1.27181
$672$	−3.11897	−	3.43098i	−0.120317	−	0.132353i
$673$	8.08906	+	14.8140i	0.311810	+	0.571038i	0.985844	−	0.167662i	$-0.0536218\pi$
$673$	8.08906	+	14.8140i	0.311810	+	0.571038i	−0.674034	+	0.738700i	$0.735440\pi$
$674$	0.193926	−	2.03088i	0.00746974	−	0.0782266i
$675$	−17.5626	−	18.2190i	−0.675984	−	0.701251i
$676$	−0.899736	+	2.59962i	−0.0346052	+	0.0999853i
$677$	5.13284	−	16.0569i	0.197271	−	0.617117i	−0.802519	−	0.596626i	$-0.796507\pi$
$677$	5.13284	−	16.0569i	0.197271	−	0.617117i	0.999790	−	0.0204907i	$-0.00652284\pi$
$678$	−3.80717	+	2.85002i	−0.146214	+	0.109454i
$679$	0.516728	−	0.804045i	0.0198302	−	0.0308564i
$680$	12.0001	+	5.26950i	0.460182	+	0.202076i
$681$	−12.9933	+	4.49701i	−0.497903	+	0.172326i
$682$	−4.83165	+	2.06903i	−0.185013	+	0.0792274i
$683$	−15.6308	−	1.86889i	−0.598096	−	0.0715112i	−0.185841	−	0.982580i	$-0.559501\pi$
$683$	−15.6308	−	1.86889i	−0.598096	−	0.0715112i	−0.412255	+	0.911069i	$0.635259\pi$
$684$	−1.98912	+	0.908400i	−0.0760558	+	0.0347335i
$685$	−10.5020	+	1.41177i	−0.401263	+	0.0539411i
$686$	−2.95815	−	0.570136i	−0.112943	−	0.0217679i
$687$	−17.3003	−	14.2844i	−0.660048	−	0.544982i
$688$	2.87988	−	0.484275i	0.109794	−	0.0184628i
$689$	−15.9835	+	31.0036i	−0.608922	+	1.18114i
$690$	4.81707	−	1.61788i	0.183383	−	0.0615918i
$691$	0.452329	−	0.0871794i	0.0172074	−	0.00331646i	−0.180640	−	0.983549i	$-0.557817\pi$
$691$	0.452329	−	0.0871794i	0.0172074	−	0.00331646i	0.197848	+	0.980233i	$0.436605\pi$
$692$	−28.6479	−	15.6430i	−1.08903	−	0.594656i
$693$	0.365261	+	0.222638i	0.0138751	+	0.00845732i
$694$	−0.903751	−	0.412729i	−0.0343059	−	0.0156670i
$695$	10.6245	−	5.67555i	0.403011	−	0.215286i
$696$	1.25546	+	1.76304i	0.0475879	+	0.0668279i
$697$	−58.4821	−	4.18272i	−2.21517	−	0.158432i
$698$	−6.45969	−	2.76620i	−0.244503	−	0.104702i
$699$	−18.8810	−	10.9009i	−0.714144	−	0.412311i
$700$	−3.58571	−	7.73959i	−0.135527	−	0.292529i
$701$	26.6435	−	33.8800i	1.00631	−	1.27963i	0.0465194	−	0.998917i	$-0.485187\pi$
$701$	26.6435	−	33.8800i	1.00631	−	1.27963i	0.959792	−	0.280712i	$-0.0905705\pi$
$702$	2.31439	+	3.79700i	0.0873511	+	0.143308i
$703$	−31.1317	−	28.3006i	−1.17415	−	1.06738i
$704$	1.01095	+	21.2225i	0.0381016	+	0.799852i
$705$	0.763220	+	6.92129i	0.0287445	+	0.260671i
$706$	−0.536465	−	0.421881i	−0.0201901	−	0.0158777i
$707$	0.820043	−	3.06044i	0.0308409	−	0.115100i
$708$	−22.6162	+	6.05999i	−0.849969	+	0.227749i
$709$	−1.29582	−	3.23680i	−0.0486656	−	0.121561i	0.902043	−	0.431645i	$-0.142067\pi$
$709$	−1.29582	−	3.23680i	−0.0486656	−	0.121561i	−0.950709	+	0.310085i	$0.899643\pi$
$710$	1.94906	+	6.87039i	0.0731470	+	0.257841i
$711$	0.792585	−	0.564397i	0.0297243	−	0.0211665i
$712$	−8.20901	−	6.14519i	−0.307646	−	0.230301i
$713$	−28.6945	+	10.7025i	−1.07462	+	0.400812i
$714$	−0.549940	−	2.26688i	−0.0205810	−	0.0848360i
$715$	24.7966	+	3.79767i	0.927340	+	0.142025i
$716$	2.70873	+	14.0542i	0.101230	+	0.525231i
$717$	17.6560	+	0.420292i	0.659376	+	0.0156961i
$718$	−0.0591881	−	0.185157i	−0.00220888	−	0.00690998i
$719$	−3.17566	−	2.26138i	−0.118432	−	0.0843352i	0.519306	−	0.854588i	$-0.326190\pi$
$719$	−3.17566	−	2.26138i	−0.118432	−	0.0843352i	−0.637738	+	0.770253i	$0.720130\pi$
$720$	1.07058	−	0.507971i	0.0398981	−	0.0189310i
$721$	1.25967	−	6.53578i	0.0469125	−	0.243405i
$722$	−2.20557	+	10.1388i	−0.0820828	+	0.377328i
$723$	−11.9842	+	32.1308i	−0.445696	+	1.19496i
$724$	17.6249	+	22.4118i	0.655022	+	0.832929i
$725$	1.85998	+	5.71090i	0.0690777	+	0.212097i
$726$	−0.0192761	−	0.0556945i	−0.000715402	−	0.00206702i
$727$	7.17692	−	0.170843i	0.266177	−	0.00633620i	0.109503	−	0.993986i	$-0.465074\pi$
$727$	7.17692	−	0.170843i	0.266177	−	0.00633620i	0.156674	+	0.987650i	$0.449923\pi$
$728$	0.648209	+	2.97977i	0.0240242	+	0.110438i
$729$	25.2902	+	3.63618i	0.936673	+	0.134673i
$730$	−1.03178	+	1.11429i	−0.0381878	+	0.0412416i
$731$	4.41840	+	1.52922i	0.163421	+	0.0565604i
$732$	−34.1813	+	2.44470i	−1.26338	+	0.0903586i
$733$	−25.2727	−	30.6087i	−0.933467	−	1.13056i	−0.991219	−	0.132227i	$-0.957787\pi$
$733$	−25.2727	−	30.6087i	−0.933467	−	1.13056i	0.0577523	−	0.998331i	$-0.481607\pi$
$734$	0.251724	−	0.857292i	0.00929128	−	0.0316432i
$735$	11.5091	−	21.8306i	0.424520	−	0.805233i
$736$		−	14.6946i		−	0.541652i
$737$	23.7958	−	12.7334i	0.876529	−	0.469042i
$738$	0.272755	−	0.272755i	0.0100402	−	0.0100402i
$739$	−1.60320	+	33.6554i	−0.0589747	+	1.23803i	0.754448	+	0.656360i	$0.227905\pi$
$739$	−1.60320	+	33.6554i	−0.0589747	+	1.23803i	−0.813423	+	0.581673i	$0.802398\pi$
$740$	17.7250	+	15.6458i	0.651585	+	0.575150i
$741$	46.2247	+	4.41393i	1.69811	+	0.162150i
$742$	−0.166641	−	2.32995i	−0.00611759	−	0.0855351i
$743$	7.47599	+	15.3900i	0.274267	+	0.564603i	0.991174	−	0.132566i	$-0.0423215\pi$
$743$	7.47599	+	15.3900i	0.274267	+	0.564603i	−0.716907	+	0.697169i	$0.754443\pi$
$744$	9.88659	−	5.09689i	0.362460	−	0.186861i
$745$	−3.82917	−	18.4139i	−0.140290	−	0.674635i
$746$	7.12839	+	4.58114i	0.260989	+	0.167727i
$747$	−0.00953178	−	0.400420i	−0.000348750	−	0.0146506i
$748$	−16.0733	+	33.0883i	−0.587698	+	1.20983i
$749$	−14.2578	−	5.70797i	−0.520969	−	0.208565i
$750$	−5.07208	+	0.710025i	−0.185206	+	0.0259264i
$751$	15.5959	+	34.1502i	0.569101	+	1.24616i	0.947275	+	0.320423i	$0.103825\pi$
$751$	15.5959	+	34.1502i	0.569101	+	1.24616i	−0.378173	+	0.925735i	$0.623448\pi$
$752$	6.18253	+	1.34493i	0.225453	+	0.0490444i
$753$	−18.3480	+	12.4183i	−0.668638	+	0.452548i
$754$	−0.100323	−	1.05063i	−0.00365355	−	0.0382617i
$755$	34.5359	+	9.59422i	1.25689	+	0.349169i
$756$	7.67435	+	3.95640i	0.279113	+	0.143893i
$757$	−1.07084	+	44.9851i	−0.0389205	+	1.63501i	0.555969	+	0.831203i	$0.312347\pi$
$757$	−1.07084	+	44.9851i	−0.0389205	+	1.63501i	−0.594889	+	0.803808i	$0.702804\pi$
$758$	1.94507	−	2.87384i	0.0706482	−	0.104383i
$759$	8.17506	+	27.8417i	0.296736	+	1.01059i
$760$	3.46375	−	17.1249i	0.125644	−	0.621185i
$761$	−1.95855	+	4.28863i	−0.0709975	+	0.155463i	−0.941803	−	0.336164i	$-0.890870\pi$
$761$	−1.95855	+	4.28863i	−0.0709975	+	0.155463i	0.870806	+	0.491627i	$0.163598\pi$
$762$	−4.44796	+	5.94178i	−0.161133	+	0.215248i
$763$	−1.75080	−	0.294411i	−0.0633832	−	0.0106584i
$764$	25.9148	+	29.9073i	0.937565	+	1.08201i
$765$	1.89415	+	0.107650i	0.0684830	+	0.00389211i
$766$	−2.29987	+	3.98350i	−0.0830978	+	0.143930i
$767$	22.4370	+	6.01199i	0.810155	+	0.217080i
$768$	−2.30157	−	19.2496i	−0.0830506	−	0.694608i
$769$	6.54870	−	26.9941i	0.236152	−	0.973433i	−0.723069	−	0.690776i	$-0.757269\pi$
$769$	6.54870	−	26.9941i	0.236152	−	0.973433i	0.959221	−	0.282657i	$-0.0912158\pi$
$770$	−1.55029	+	0.647111i	−0.0558685	+	0.0233203i
$771$	−33.1281	+	1.57809i	−1.19308	+	0.0568334i
$772$	−38.6399	+	23.5522i	−1.39068	+	0.847663i
$773$	13.1316	−	1.57008i	0.472311	−	0.0564717i	0.120843	−	0.992672i	$-0.461440\pi$
$773$	13.1316	−	1.57008i	0.472311	−	0.0564717i	0.351468	+	0.936200i	$0.385683\pi$
$774$	−0.0266392	+	0.0153801i	−0.000957525	+	0.000552827i
$775$	30.4110	−	5.28461i	1.09239	−	0.189829i
$776$	−1.02132	+	0.408873i	−0.0366631	+	0.0146777i
$777$	0.610732	−	8.53915i	0.0219099	−	0.306340i
$778$	0.580495	−	3.45207i	0.0208117	−	0.123763i
$779$	11.1235	+	77.3658i	0.398542	+	2.77192i
$780$	−26.0093	−	2.10016i	−0.931281	−	0.0751980i
$781$	−39.6308	+	9.61434i	−1.41810	+	0.344028i
$782$	3.54284	−	6.48823i	0.126692	−	0.232019i
$783$	−5.03481	−	3.40765i	−0.179929	−	0.121780i
$784$	−15.4744	−	16.2291i	−0.552657	−	0.579610i
$785$	−11.0957	+	8.56219i	−0.396021	+	0.305598i
$786$	3.01883	−	4.23935i	0.107678	−	0.151212i
$787$	−2.57237	+	3.11549i	−0.0916950	+	0.111055i	−0.814965	−	0.579510i	$-0.803244\pi$
$787$	−2.57237	+	3.11549i	−0.0916950	+	0.111055i	0.723270	+	0.690565i	$0.242638\pi$
$788$	15.5448	+	22.9674i	0.553759	+	0.818178i
$789$	29.8680	−	19.1950i	1.06333	−	0.683359i
$790$	−0.0350482	+	3.82103i	−0.00124696	+	0.135946i
$791$	7.20102	−	5.66294i	0.256039	−	0.201351i
$792$	−0.193822	−	0.452616i	−0.00688715	−	0.0160830i
$793$	30.5801	+	14.8549i	1.08593	+	0.527512i
$794$	−3.35489	−	3.19888i	−0.119061	−	0.113524i
$795$	39.6552	+	9.00818i	1.40643	+	0.319487i
$796$	−6.04185	+	42.0220i	−0.214148	+	1.48943i
$797$	−16.3873	−	5.23846i	−0.580469	−	0.185556i	−0.000226938	−	1.00000i	$-0.500072\pi$
$797$	−16.3873	−	5.23846i	−0.580469	−	0.185556i	−0.580242	+	0.814444i	$0.697042\pi$
$798$	−2.79708	+	1.35874i	−0.0990155	+	0.0480987i
$799$	7.65575	+	6.63375i	0.270841	+	0.234685i
$800$	−2.72351	+	14.5578i	−0.0962905	+	0.514697i
$801$	−1.42426	−	0.418201i	−0.0503238	−	0.0147764i
$802$	6.73832	−	6.12554i	0.237938	−	0.216300i
$803$	−6.13190	−	6.13190i	−0.216390	−	0.216390i
$804$	−23.7442	+	14.9772i	−0.837392	+	0.528207i
$805$	−9.20231	+	3.33646i	−0.324339	+	0.117595i
$806$	−5.41780	−	0.258082i	−0.190834	−	0.00909054i
$807$	−9.09104	+	4.96408i	−0.320020	+	0.174744i
$808$	−2.81222	+	2.32196i	−0.0989334	+	0.0816863i
$809$	17.9042	−	20.6625i	0.629477	−	0.726455i	−0.348001	−	0.937494i	$-0.613139\pi$
$809$	17.9042	−	20.6625i	0.629477	−	0.726455i	0.977478	+	0.211039i	$0.0676848\pi$
$810$	3.78917	−	3.90168i	0.133138	−	0.137091i
$811$	−13.1644	−	25.5353i	−0.462264	−	0.896666i	−0.998612	−	0.0526697i	$-0.983227\pi$
$811$	−13.1644	−	25.5353i	−0.462264	−	0.896666i	0.536348	−	0.843997i	$-0.319803\pi$
$812$	−1.22808	−	1.64052i	−0.0430971	−	0.0575710i
$813$	29.1962	−	6.35124i	1.02396	−	0.222748i
$814$	3.21321	−	3.36992i	0.112623	−	0.118116i
$815$	−4.08058	+	38.9544i	−0.142936	+	1.36451i
$816$	13.7139	−	34.2557i	0.480084	−	1.19919i
$817$	0.739972	−	6.18889i	0.0258883	−	0.216522i
$818$	5.36686	+	2.00173i	0.187648	+	0.0699890i
$819$	0.238656	+	0.371356i	0.00833932	+	0.0129762i
$820$	−6.88606	−	43.3792i	−0.240472	−	1.51487i
$821$	20.3651	−	1.94464i	0.710748	−	0.0678682i	0.266582	−	0.963812i	$-0.414106\pi$
$821$	20.3651	−	1.94464i	0.710748	−	0.0678682i	0.444167	+	0.895944i	$0.353500\pi$
$822$	−0.359987	−	2.14076i	−0.0125560	−	0.0746676i
$823$	3.57781	−	1.14370i	0.124714	−	0.0398669i	−0.241476	−	0.970407i	$-0.577632\pi$
$823$	3.57781	−	1.14370i	0.124714	−	0.0398669i	0.366191	+	0.930540i	$0.380662\pi$
$824$	−5.54476	+	5.28691i	−0.193161	+	0.184178i
$825$	−2.93877	−	29.0977i	−0.102315	−	1.01305i
$826$	−1.49254	+	0.438250i	−0.0519322	+	0.0152487i
$827$	2.56680	−	4.21111i	0.0892565	−	0.146435i	−0.806108	−	0.591768i	$-0.798430\pi$
$827$	2.56680	−	4.21111i	0.0892565	−	0.146435i	0.895365	+	0.445334i	$0.146915\pi$
$828$	−0.492793	−	1.32123i	−0.0171257	−	0.0459158i
$829$	−32.2875	+	4.64224i	−1.12139	+	0.161232i	−0.677976	−	0.735084i	$-0.737143\pi$
$829$	−32.2875	+	4.64224i	−1.12139	+	0.161232i	−0.443416	+	0.896316i	$0.646234\pi$
$830$	1.29452	+	0.893579i	0.0449335	+	0.0310166i
$831$	33.3508	−	28.8986i	1.15693	−	1.00248i
$832$	−8.63092	+	20.1551i	−0.299223	+	0.698752i
$833$	−9.29213	−	34.6787i	−0.321953	−	1.20155i
$834$	1.23382	+	2.13704i	0.0427238	+	0.0739997i
$835$	−6.75556	+	3.40467i	−0.233786	+	0.117823i
$836$	47.6566	+	11.5614i	1.64824	+	0.399858i
$837$	−21.0167	+	23.1191i	−0.726443	+	0.799114i
$838$	−3.54640	+	3.90117i	−0.122508	+	0.134764i
$839$	3.39426	+	0.823438i	0.117183	+	0.0284282i	0.293921	−	0.955830i	$-0.405040\pi$
$839$	3.39426	+	0.823438i	0.117183	+	0.0284282i	−0.176739	+	0.984258i	$0.556555\pi$
$840$	3.17475	−	1.60001i	0.109539	−	0.0552057i
$841$	−13.7785	−	23.8651i	−0.475121	−	0.822935i
$842$	1.29871	+	4.84684i	0.0447564	+	0.167033i
$843$	−12.8692	+	30.0525i	−0.443240	+	1.03506i
$844$	29.7356	−	25.7661i	1.02354	−	0.886905i
$845$	−2.61845	−	1.80746i	−0.0900774	−	0.0621784i
$846$	−0.0659666	+	0.00948456i	−0.00226798	+	0.000326086i
$847$	0.0396740	+	0.106370i	0.00136321	+	0.00365492i
$848$	19.2316	−	31.5514i	0.660414	−	1.08348i
$849$	32.3861	−	9.50941i	1.11149	−	0.326362i
$850$	−4.71239	+	5.77120i	−0.161634	+	0.197950i
$851$	19.6357	−	18.7226i	0.673101	−	0.641801i
$852$	40.4051	−	12.9161i	1.38426	−	0.442499i
$853$	−1.93019	−	11.4784i	−0.0660884	−	0.393013i	−0.999422	−	0.0340022i	$-0.989175\pi$
$853$	−1.93019	−	11.4784i	−0.0660884	−	0.393013i	0.933333	−	0.359011i	$-0.116886\pi$
$854$	−2.26639	+	0.216414i	−0.0775544	+	0.00740554i
$855$	−0.396516	−	2.49788i	−0.0135606	−	0.0854257i
$856$	9.55714	+	14.8712i	0.326656	+	0.508287i
$857$	0.816263	+	0.304450i	0.0278830	+	0.0103998i	0.363367	−	0.931646i	$-0.381627\pi$
$857$	0.816263	+	0.304450i	0.0278830	+	0.0103998i	−0.335484	+	0.942046i	$0.608900\pi$
$858$	−0.610109	+	5.10275i	−0.0208288	+	0.174205i
$859$	12.1224	−	30.2803i	0.413611	−	1.03315i	−0.564568	−	0.825386i	$-0.690957\pi$
$859$	12.1224	−	30.2803i	0.413611	−	1.03315i	0.978179	−	0.207763i	$-0.0666184\pi$
$860$	−0.364908	+	3.48352i	−0.0124433	+	0.118787i
$861$	−10.9752	+	11.5105i	−0.374035	+	0.392277i
$862$	−5.91970	+	1.28775i	−0.201626	+	0.0438610i
$863$	30.8298	+	41.1838i	1.04946	+	1.40191i	0.911415	+	0.411488i	$0.134991\pi$
$863$	30.8298	+	41.1838i	1.04946	+	1.40191i	0.138044	+	0.990426i	$0.455918\pi$
$864$	−6.86950	−	13.3250i	−0.233705	−	0.453325i
$865$	26.3013	−	27.0822i	0.894271	−	0.920824i
$866$	3.42464	−	3.95225i	0.116374	−	0.134303i
$867$	22.3001	−	18.4125i	0.757350	−	0.625321i
$868$	−9.24333	+	5.04724i	−0.313739	+	0.171314i
$869$	−21.7956	−	1.03825i	−0.739364	−	0.0352202i
$870$	−1.15675	+	0.419399i	−0.0392173	+	0.0142189i
$871$	27.8294	−	1.08989i	0.942965	−	0.0369296i
$872$	1.44498	+	1.44498i	0.0489333	+	0.0489333i
$873$	−0.117838	+	0.107121i	−0.00398820	+	0.00362551i
$874$	−9.45571	−	2.77645i	−0.319844	−	0.0939148i
$875$	9.73501	−	1.59984i	0.329104	−	0.0540845i
$876$	6.81711	+	5.90706i	0.230329	+	0.199581i
$877$	27.2752	−	13.2495i	0.921017	−	0.447403i	0.0851711	−	0.996366i	$-0.472856\pi$
$877$	27.2752	−	13.2495i	0.921017	−	0.447403i	0.835846	+	0.548964i	$0.184978\pi$
$878$	0.592931	+	0.189539i	0.0200104	+	0.00639664i
$879$	1.24544	−	8.66222i	0.0420076	−	0.292169i
$880$	−25.9137	−	5.88663i	−0.873552	−	0.198438i
$881$	−25.8033	−	24.6034i	−0.869334	−	0.828908i	0.117091	−	0.993121i	$-0.462643\pi$
$881$	−25.8033	−	24.6034i	−0.869334	−	0.828908i	−0.986425	+	0.164213i	$0.947492\pi$
$882$	0.212457	+	0.103205i	0.00715381	+	0.00347510i
$883$	−16.9031	−	39.4725i	−0.568835	−	1.32836i	−0.919954	−	0.392026i	$-0.871774\pi$
$883$	−16.9031	−	39.4725i	−0.568835	−	1.32836i	0.351119	−	0.936331i	$-0.385801\pi$
$884$	−29.8393	+	23.4659i	−1.00361	+	0.789244i
$885$	0.248384	−	27.0794i	0.00834935	−	0.910264i
$886$	4.52539	−	2.90829i	0.152033	−	0.0977059i
$887$	29.8601	+	44.1183i	1.00261	+	1.48135i	0.871753	+	0.489946i	$0.162984\pi$
$887$	29.8601	+	44.1183i	1.00261	+	1.48135i	0.130853	+	0.991402i	$0.458228\pi$
$888$	−6.27389	+	7.59855i	−0.210538	+	0.254991i
$889$	8.29328	−	11.6463i	0.278148	−	0.390604i
$890$	4.61517	−	3.56139i	0.154701	−	0.119378i
$891$	21.4322	+	22.4774i	0.718005	+	0.753022i
$892$	−3.13094	−	2.11908i	−0.104832	−	0.0709522i
$893$	6.47192	−	11.8524i	0.216575	−	0.396627i
$894$	3.74440	−	0.908381i	0.125231	−	0.0303808i
$895$	−16.5005	−	1.33236i	−0.551551	−	0.0445360i
$896$	−0.952911	−	6.62764i	−0.0318345	−	0.221414i
$897$	−4.96564	+	29.5296i	−0.165798	+	0.985964i
$898$	−0.469372	+	6.56267i	−0.0156631	+	0.218999i
$899$	6.88441	−	2.75610i	0.229608	−	0.0919211i
$900$	0.243328	+	1.40026i	0.00811094	+	0.0466754i
$901$	51.2336	−	29.5798i	1.70684	−	0.985445i
$902$	−8.58917	+	1.02696i	−0.285988	+	0.0341941i
$903$	1.08297	−	0.660103i	0.0360389	−	0.0219669i
$904$	−10.5326	+	0.501730i	−0.350309	+	0.0166873i
$905$	−30.4319	+	12.7027i	−1.01159	+	0.422251i
$906$	−1.73118	+	7.13602i	−0.0575146	+	0.237078i
$907$	4.91992	+	41.1487i	0.163363	+	1.36632i	0.802236	+	0.597006i	$0.203643\pi$
$907$	4.91992	+	41.1487i	0.163363	+	1.36632i	−0.638873	+	0.769312i	$0.720599\pi$
$908$	−14.4738	−	3.87825i	−0.480331	−	0.128704i
$909$	−0.263960	+	0.457192i	−0.00875499	+	0.0151641i
$910$	−1.73080	−	0.0983671i	−0.0573756	−	0.00326084i
$911$	8.86118	+	10.2263i	0.293584	+	0.338814i	0.883310	−	0.468790i	$-0.155310\pi$
$911$	8.86118	+	10.2263i	0.293584	+	0.338814i	−0.589726	+	0.807603i	$0.700764\pi$
$912$	−48.5087	−	8.15714i	−1.60628	−	0.270110i
$913$	−5.38286	+	7.19066i	−0.178147	+	0.237976i
$914$	−3.18399	+	6.97197i	−0.105317	+	0.230612i
$915$	7.85761	−	38.8482i	0.259764	−	1.28428i
$916$	−6.88848	−	23.4600i	−0.227602	−	0.775140i
$917$	−5.61917	+	8.30231i	−0.185561	+	0.274166i
$918$	0.179478	−	7.53969i	0.00592366	−	0.248847i
$919$	14.3796	+	7.41321i	0.474340	+	0.244539i	0.678783	−	0.734339i	$-0.262508\pi$
$919$	14.3796	+	7.41321i	0.474340	+	0.244539i	−0.204442	+	0.978879i	$0.565538\pi$
$920$	10.8557	+	3.01577i	0.357902	+	0.0994268i
$921$	0.293938	+	3.07826i	0.00968559	+	0.101432i
$922$	1.90682	−	1.29058i	0.0627979	−	0.0425028i
$923$	−41.1216	−	8.94545i	−1.35353	−	0.294443i
$924$	4.14521	+	9.07674i	0.136367	+	0.298603i
$925$	−22.9229	+	14.9090i	−0.753700	+	0.490204i
$926$	0.992151	+	0.397197i	0.0326041	+	0.0130527i
$927$	−0.484586	+	0.997562i	−0.0159159	+	0.0327642i
$928$	0.0846755	+	3.55713i	0.00277961	+	0.116769i
$929$	−9.67764	−	6.21944i	−0.317513	−	0.204053i	0.372170	−	0.928165i	$-0.378614\pi$
$929$	−9.67764	−	6.21944i	−0.317513	−	0.204053i	−0.689683	+	0.724111i	$0.742250\pi$
$930$	1.28741	+	6.19096i	0.0422157	+	0.203010i
$931$	−42.5404	+	21.9311i	−1.39421	+	0.718764i
$932$	−10.3818	−	21.3719i	−0.340068	−	0.700060i
$933$	2.85135	+	39.8671i	0.0933490	+	1.30519i
$934$	−0.676009	−	0.0645510i	−0.0221197	−	0.00211217i
$935$	−31.8973	−	28.1555i	−1.04315	−	0.920785i
$936$	0.0241764	−	0.507525i	0.000790231	−	0.0165890i
$937$	−21.7910	+	21.7910i	−0.711881	+	0.711881i	−0.966929	−	0.255048i	$-0.917909\pi$
$937$	−21.7910	+	21.7910i	−0.711881	+	0.711881i	0.255048	+	0.966929i	$0.417909\pi$
$938$	−1.55336	+	1.03230i	−0.0507191	+	0.0337058i
$939$		−	37.1084i		−	1.21099i
$940$	−3.53905	+	6.71290i	−0.115431	+	0.218951i
$941$	−1.67445	+	5.70265i	−0.0545855	+	0.185901i	−0.982273	−	0.187457i	$-0.939975\pi$
$941$	−1.67445	+	5.70265i	−0.0545855	+	0.185901i	0.927687	+	0.373358i	$0.121794\pi$
$942$	−1.82804	−	2.21401i	−0.0595609	−	0.0721365i
$943$	−50.2749	+	3.59573i	−1.63718	+	0.117093i
$944$	−23.2532	−	8.04803i	−0.756829	−	0.261941i
$945$	−6.78483	+	7.32740i	−0.220711	+	0.238360i
$946$	0.682799	+	0.0981717i	0.0221997	+	0.00319184i
$947$	−4.51184	−	20.7406i	−0.146615	−	0.673979i	−0.990507	−	0.137465i	$-0.956104\pi$
$947$	−4.51184	−	20.7406i	−0.146615	−	0.673979i	0.843891	−	0.536514i	$-0.180259\pi$
$948$	22.6908	−	0.540142i	0.736963	−	0.0175430i
$949$	−2.92689	−	8.45669i	−0.0950109	−	0.274516i
$950$	8.85309	+	4.50312i	0.287232	+	0.146101i
$951$	27.0487	+	34.3952i	0.877115	+	1.11534i
$952$	1.80742	−	4.84588i	0.0585788	−	0.157056i
$953$	7.98095	−	36.6878i	0.258528	−	1.18843i	−0.646443	−	0.762962i	$-0.723744\pi$
$953$	7.98095	−	36.6878i	0.258528	−	1.18843i	0.904971	−	0.425473i	$-0.139892\pi$
$954$	−0.0736581	+	0.382174i	−0.00238477	+	0.0123734i
$955$	−41.3512	+	19.6205i	−1.33809	+	0.634904i
$956$	15.6784	+	11.1645i	0.507075	+	0.361087i
$957$	−2.13937	−	6.69253i	−0.0691560	−	0.216339i
$958$	0.101903	+	0.00242576i	0.00329235	+	7.83726e-5i
$959$	0.791380	+	4.10607i	0.0255550	+	0.132592i
$960$	25.2666	+	3.86965i	0.815477	+	0.124892i
$961$	−1.67628	−	6.90973i	−0.0540737	−	0.222895i
$962$	4.50210	−	1.67920i	0.145154	−	0.0541395i
$963$	2.04854	+	1.53352i	0.0660132	+	0.0494168i
$964$	−30.4432	+	21.6785i	−0.980510	+	0.698218i
$965$	−14.2842	−	50.3513i	−0.459823	−	1.62087i
$966$	−0.745288	−	1.86164i	−0.0239793	−	0.0598973i
$967$	33.7321	−	9.03849i	1.08475	−	0.290658i	0.328211	−	0.944605i	$-0.393554\pi$
$967$	33.7321	−	9.03849i	1.08475	−	0.290658i	0.756541	+	0.653946i	$0.226888\pi$
$968$	0.0338209	−	0.126221i	0.00108705	−	0.00405691i
$969$	−61.9057	−	48.6832i	−1.98870	−	1.56393i
$970$	−0.0685493	−	0.621643i	−0.00220099	−	0.0199597i
$971$	0.379945	+	7.97603i	0.0121930	+	0.255963i	0.996731	+	0.0807918i	$0.0257449\pi$
$971$	0.379945	+	7.97603i	0.0121930	+	0.255963i	−0.984538	+	0.175171i	$0.943952\pi$
$972$	−2.18388	−	1.98528i	−0.0700481	−	0.0636779i
$973$	−2.47400	−	4.05885i	−0.0793127	−	0.130121i
$974$	−5.28502	+	6.72045i	−0.169343	+	0.215337i
$975$	10.3924	−	28.3343i	0.332824	−	0.907424i
$976$	−31.1891	−	18.0070i	−0.998339	−	0.576391i
$977$	−0.155432	−	0.0665599i	−0.00497272	−	0.00212944i	0.391162	−	0.920322i	$-0.372073\pi$
$977$	−0.155432	−	0.0665599i	−0.00497272	−	0.00212944i	−0.396135	+	0.918192i	$0.629649\pi$
$978$	−8.00348	−	0.572420i	−0.255923	−	0.0183040i
$979$	19.3092	+	27.1160i	0.617126	+	0.866632i
$980$	23.7226	−	12.6724i	0.757789	−	0.404806i
$981$	0.269082	+	0.122886i	0.00859112	+	0.00392343i
$982$	−0.0412517	−	0.0251443i	−0.00131640	−	0.000802385i
$983$	−44.9958	−	24.5696i	−1.43514	−	0.783648i	−0.441613	−	0.897206i	$-0.645593\pi$
$983$	−44.9958	−	24.5696i	−1.43514	−	0.783648i	−0.993531	+	0.113558i	$0.963775\pi$
$984$	17.9755	−	3.46450i	0.573039	−	0.110444i
$985$	−30.4070	+	10.2126i	−0.968849	+	0.325402i
$986$	−0.820229	+	1.59102i	−0.0261214	+	0.0506685i
$987$	2.70982	−	0.455678i	0.0862544	−	0.0145044i
$988$	39.0230	+	32.2201i	1.24149	+	1.02506i
$989$	3.94677	+	0.760677i	0.125500	+	0.0241881i
$990$	0.277414	−	0.0372923i	0.00881679	−	0.00118523i
$991$	−5.89325	+	2.69136i	−0.187205	+	0.0854937i	−0.506812	−	0.862056i	$-0.669176\pi$
$991$	−5.89325	+	2.69136i	−0.187205	+	0.0854937i	0.319607	+	0.947550i	$0.396449\pi$
$992$	18.1566	+	2.17089i	0.576473	+	0.0689258i
$993$	21.7408	−	9.30995i	0.689923	−	0.295442i
$994$	2.66321	−	0.921746i	0.0844719	−	0.0292360i
$995$	−44.9585	−	19.7423i	−1.42528	−	0.625873i
$996$	5.05134	−	7.86004i	0.160058	−	0.249055i
$997$	7.88195	−	5.90036i	0.249624	−	0.186866i	−0.467137	−	0.884185i	$-0.654715\pi$
$997$	7.88195	−	5.90036i	0.249624	−	0.186866i	0.716761	+	0.697319i	$0.245624\pi$
$998$	−2.29634	+	7.18358i	−0.0726894	+	0.227392i
$999$	9.05295	−	26.1568i	0.286423	−	0.827564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	335.2.w.a.2.16	✓	1280
5.3	odd	4	inner	335.2.w.a.203.16	yes	1280
67.34	odd	66	inner	335.2.w.a.302.16	yes	1280
335.168	even	132	inner	335.2.w.a.168.16	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
335.2.w.a.2.16	✓	1280	1.1	even	1	trivial
335.2.w.a.168.16	yes	1280	335.168	even	132	inner
335.2.w.a.203.16	yes	1280	5.3	odd	4	inner
335.2.w.a.302.16	yes	1280	67.34	odd	66	inner

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:	\( N \)	\(=\)	\( 335 = 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	335.w (of order \(132\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173696 - 0.191073i) q^{2} +(-0.850181 - 1.55699i) q^{3} +(0.183774 - 1.92457i) q^{4} +(2.08783 + 0.800609i) q^{5} +(-0.149825 + 0.432890i) q^{6} +(0.268681 - 0.840506i) q^{7} +(-0.813089 + 0.608671i) q^{8} +(-0.0794885 + 0.123687i) q^{9} +O(q^{10})\)	\(q+(-0.173696 - 0.191073i) q^{2} +(-0.850181 - 1.55699i) q^{3} +(0.183774 - 1.92457i) q^{4} +(2.08783 + 0.800609i) q^{5} +(-0.149825 + 0.432890i) q^{6} +(0.268681 - 0.840506i) q^{7} +(-0.813089 + 0.608671i) q^{8} +(-0.0794885 + 0.123687i) q^{9} +(-0.209674 - 0.537990i) q^{10} +(3.11583 - 1.07840i) q^{11} +(-3.15277 + 1.35010i) q^{12} +(3.37845 + 0.403943i) q^{13} +(-0.207267 + 0.0946554i) q^{14} +(-0.528491 - 3.93139i) q^{15} +(-3.53924 - 0.682132i) q^{16} +(-4.44995 - 3.67419i) q^{17} +(0.0374400 - 0.00629584i) q^{18} +(-3.52513 + 6.83781i) q^{19} +(1.92451 - 3.87103i) q^{20} +(-1.53709 + 0.296249i) q^{21} +(-0.747261 - 0.408035i) q^{22} +(-4.23604 - 2.58200i) q^{23} +(1.63897 + 0.748491i) q^{24} +(3.71805 + 3.34307i) q^{25} +(-0.509643 - 0.715693i) q^{26} +(-5.04824 - 0.361057i) q^{27} +(-1.56823 - 0.671557i) q^{28} +(1.04030 + 0.600615i) q^{29} +(-0.659384 + 0.783849i) q^{30} +(3.81611 - 4.85258i) q^{31} +(1.54167 + 2.52927i) q^{32} +(-4.32808 - 3.93448i) q^{33} +(0.0709040 + 1.48846i) q^{34} +(1.23388 - 1.53972i) q^{35} +(0.223435 + 0.175711i) q^{36} +(-1.41547 + 5.28260i) q^{37} +(1.91882 - 0.514146i) q^{38} +(-2.24336 - 5.60364i) q^{39} +(-2.18490 + 0.619834i) q^{40} +(8.27616 - 5.89342i) q^{41} +(0.323592 + 0.242238i) q^{42} +(-0.759129 + 0.283141i) q^{43} +(-1.50284 - 6.19480i) q^{44} +(-0.264983 + 0.194597i) q^{45} +(0.242435 + 1.25787i) q^{46} +(-1.75490 - 0.0417745i) q^{47} +(1.94692 + 6.09049i) q^{48} +(5.06777 + 3.60874i) q^{49} +(-0.00704372 - 1.29110i) q^{50} +(-1.93741 + 10.0523i) q^{51} +(1.39829 - 6.42782i) q^{52} +(-3.58256 + 9.60522i) q^{53} +(0.807873 + 1.02729i) q^{54} +(7.36869 + 0.243050i) q^{55} +(0.293130 + 0.846944i) q^{56} +(13.6434 - 0.324773i) q^{57} +(-0.0659346 - 0.303097i) q^{58} +(6.75739 + 0.971565i) q^{59} +(-7.66335 + 0.294630i) q^{60} +(9.44224 + 3.26799i) q^{61} +(-1.59004 + 0.113722i) q^{62} +(0.0826022 + 0.100043i) q^{63} +(-1.81545 + 6.18284i) q^{64} +(6.73022 + 3.54818i) q^{65} +1.51038i q^{66} +(8.08321 - 1.28907i) q^{67} +(-7.88901 + 7.88901i) q^{68} +(-0.418749 + 8.79063i) q^{69} +(-0.508519 + 0.0316848i) q^{70} +(-12.3123 - 1.17568i) q^{71} +(-0.0106531 - 0.148950i) q^{72} +(-1.14920 - 2.36572i) q^{73} +(1.25522 - 0.647112i) q^{74} +(2.04411 - 8.63118i) q^{75} +(12.5120 + 8.04096i) q^{76} +(-0.0692381 - 2.90862i) q^{77} +(-0.681038 + 1.40198i) q^{78} +(-6.14383 - 2.45962i) q^{79} +(-6.84319 - 4.25772i) q^{80} +(3.91299 + 8.56824i) q^{81} +(-2.56361 - 0.557679i) q^{82} +(-2.25607 + 1.52695i) q^{83} +(0.287675 + 3.01267i) q^{84} +(-6.34914 - 11.2337i) q^{85} +(0.185958 + 0.0958683i) q^{86} +(0.0507121 - 2.13036i) q^{87} +(-1.87706 + 2.77335i) q^{88} +(2.84439 + 9.68712i) q^{89} +(0.0832087 + 0.0168301i) q^{90} +(1.24724 - 2.73108i) q^{91} +(-5.74770 + 7.67803i) q^{92} +(-10.7998 - 1.81607i) q^{93} +(0.296839 + 0.342570i) q^{94} +(-12.8343 + 11.4539i) q^{95} +(2.62734 - 4.55069i) q^{96} +(1.04623 + 0.280338i) q^{97} +(-0.190722 - 1.59514i) q^{98} +(-0.114289 + 0.471106i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 38 q^{2} - 44 q^{3} - 44 q^{5} - 80 q^{6} - 38 q^{7} - 110 q^{8}+O(q^{10}) \) 1280 * q - 38 * q^2 - 44 * q^3 - 44 * q^5 - 80 * q^6 - 38 * q^7 - 110 * q^8	\( 1280 q - 38 q^{2} - 44 q^{3} - 44 q^{5} - 80 q^{6} - 38 q^{7} - 110 q^{8} - 42 q^{10} - 76 q^{11} - 20 q^{12} - 38 q^{13} - 52 q^{15} - 136 q^{16} - 42 q^{17} - 68 q^{18} - 68 q^{20} + 44 q^{21} - 68 q^{22} - 24 q^{23} - 24 q^{25} - 68 q^{26} - 44 q^{27} - 2 q^{28} - 150 q^{30} - 164 q^{31} - 70 q^{32} - 26 q^{33} - 36 q^{35} - 28 q^{36} - 32 q^{37} - 18 q^{38} + 118 q^{40} - 76 q^{41} - 44 q^{42} - 88 q^{43} - 44 q^{45} - 160 q^{46} - 26 q^{47} - 402 q^{48} + 94 q^{50} - 100 q^{51} - 44 q^{52} - 44 q^{53} + 112 q^{55} - 64 q^{56} - 62 q^{57} - 88 q^{58} + 234 q^{60} - 152 q^{61} + 84 q^{62} - 98 q^{63} + 140 q^{65} - 118 q^{67} + 420 q^{68} + 440 q^{70} - 124 q^{71} + 176 q^{72} - 26 q^{73} + 308 q^{75} + 56 q^{76} - 322 q^{77} + 196 q^{78} + 250 q^{80} + 152 q^{81} + 44 q^{82} - 30 q^{83} + 10 q^{85} - 60 q^{86} - 134 q^{87} - 32 q^{88} - 256 q^{90} - 56 q^{91} - 24 q^{92} - 304 q^{93} - 14 q^{95} + 228 q^{96} - 120 q^{97} + 70 q^{98}+O(q^{100}) \) 1280 * q - 38 * q^2 - 44 * q^3 - 44 * q^5 - 80 * q^6 - 38 * q^7 - 110 * q^8 - 42 * q^10 - 76 * q^11 - 20 * q^12 - 38 * q^13 - 52 * q^15 - 136 * q^16 - 42 * q^17 - 68 * q^18 - 68 * q^20 + 44 * q^21 - 68 * q^22 - 24 * q^23 - 24 * q^25 - 68 * q^26 - 44 * q^27 - 2 * q^28 - 150 * q^30 - 164 * q^31 - 70 * q^32 - 26 * q^33 - 36 * q^35 - 28 * q^36 - 32 * q^37 - 18 * q^38 + 118 * q^40 - 76 * q^41 - 44 * q^42 - 88 * q^43 - 44 * q^45 - 160 * q^46 - 26 * q^47 - 402 * q^48 + 94 * q^50 - 100 * q^51 - 44 * q^52 - 44 * q^53 + 112 * q^55 - 64 * q^56 - 62 * q^57 - 88 * q^58 + 234 * q^60 - 152 * q^61 + 84 * q^62 - 98 * q^63 + 140 * q^65 - 118 * q^67 + 420 * q^68 + 440 * q^70 - 124 * q^71 + 176 * q^72 - 26 * q^73 + 308 * q^75 + 56 * q^76 - 322 * q^77 + 196 * q^78 + 250 * q^80 + 152 * q^81 + 44 * q^82 - 30 * q^83 + 10 * q^85 - 60 * q^86 - 134 * q^87 - 32 * q^88 - 256 * q^90 - 56 * q^91 - 24 * q^92 - 304 * q^93 - 14 * q^95 + 228 * q^96 - 120 * q^97 + 70 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more