LMFDB - Embedded newform 731.2.k.a.35.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(35,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("731.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.k (of order $7$, degree $6$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$30$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			35.11
Character	$\chi$	$=$	731.35
Dual form			731.2.k.a.188.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.265151 + 1.16170i) q^{2} +(0.558598 + 2.44738i) q^{3} +(0.522689 + 0.251714i) q^{4} +(0.802903 - 1.00681i) q^{5} -2.99124 q^{6} -4.26133 q^{7} +(-1.91688 + 2.40369i) q^{8} +(-2.97472 + 1.43255i) q^{9} +O(q^{10})$	\(q+(-0.265151 + 1.16170i) q^{2} +(0.558598 + 2.44738i) q^{3} +(0.522689 + 0.251714i) q^{4} +(0.802903 - 1.00681i) q^{5} -2.99124 q^{6} -4.26133 q^{7} +(-1.91688 + 2.40369i) q^{8} +(-2.97472 + 1.43255i) q^{9} +(0.956722 + 1.19969i) q^{10} +(-0.515272 + 0.248142i) q^{11} +(-0.324065 + 1.41982i) q^{12} +(-0.401997 + 0.504088i) q^{13} +(1.12990 - 4.95041i) q^{14} +(2.91254 + 1.40261i) q^{15} +(-1.56069 - 1.95705i) q^{16} +(0.623490 + 0.781831i) q^{17} +(-0.875447 - 3.83559i) q^{18} +(-4.37796 - 2.10832i) q^{19} +(0.673095 - 0.324146i) q^{20} +(-2.38037 - 10.4291i) q^{21} +(-0.151642 - 0.664388i) q^{22} +(-1.52600 + 0.734883i) q^{23} +(-6.95351 - 3.34864i) q^{24} +(0.743595 + 3.25790i) q^{25} +(-0.479011 - 0.600661i) q^{26} +(-0.472194 - 0.592113i) q^{27} +(-2.22735 - 1.07264i) q^{28} +(-0.0857115 + 0.375527i) q^{29} +(-2.40167 + 3.01160i) q^{30} +(0.414847 - 1.81756i) q^{31} +(-2.85262 + 1.37375i) q^{32} +(-0.895127 - 1.12245i) q^{33} +(-1.07358 + 0.517007i) q^{34} +(-3.42144 + 4.29035i) q^{35} -1.91544 q^{36} +3.73207 q^{37} +(3.61006 - 4.52687i) q^{38} +(-1.45825 - 0.702256i) q^{39} +(0.880989 + 3.85986i) q^{40} +(-0.723599 + 3.17030i) q^{41} +12.7467 q^{42} +(-4.56029 + 4.71209i) q^{43} -0.331788 q^{44} +(-0.946108 + 4.14517i) q^{45} +(-0.449095 - 1.96761i) q^{46} +(4.70673 + 2.26664i) q^{47} +(3.91783 - 4.91281i) q^{48} +11.1590 q^{49} -3.98188 q^{50} +(-1.56516 + 1.96264i) q^{51} +(-0.337005 + 0.162293i) q^{52} +(4.92257 + 6.17271i) q^{53} +(0.813062 - 0.391550i) q^{54} +(-0.163882 + 0.718014i) q^{55} +(8.16847 - 10.2429i) q^{56} +(2.71432 - 11.8922i) q^{57} +(-0.413524 - 0.199143i) q^{58} +(-3.11525 - 3.90640i) q^{59} +(1.16930 + 1.46625i) q^{60} +(2.68748 + 11.7746i) q^{61} +(2.00147 + 0.963858i) q^{62} +(12.6763 - 6.10457i) q^{63} +(-1.95352 - 8.55895i) q^{64} +(0.184756 + 0.809467i) q^{65} +(1.54130 - 0.742252i) q^{66} +(8.64947 + 4.16536i) q^{67} +(0.129093 + 0.565595i) q^{68} +(-2.65096 - 3.32419i) q^{69} +(-4.07691 - 5.11228i) q^{70} +(-7.62825 - 3.67357i) q^{71} +(2.25878 - 9.89635i) q^{72} +(1.88246 - 2.36053i) q^{73} +(-0.989562 + 4.33556i) q^{74} +(-7.55795 + 3.63972i) q^{75} +(-1.75762 - 2.20399i) q^{76} +(2.19575 - 1.05742i) q^{77} +(1.20247 - 1.50785i) q^{78} +3.81279 q^{79} -3.22345 q^{80} +(-4.99036 + 6.25771i) q^{81} +(-3.49108 - 1.68122i) q^{82} +(0.0628882 + 0.275531i) q^{83} +(1.38095 - 6.05034i) q^{84} +1.28776 q^{85} +(-4.26488 - 6.54712i) q^{86} -0.966934 q^{87} +(0.391258 - 1.71422i) q^{88} +(-3.74368 - 16.4021i) q^{89} +(-4.56460 - 2.19819i) q^{90} +(1.71304 - 2.14809i) q^{91} -0.982603 q^{92} +4.68000 q^{93} +(-3.88116 + 4.86682i) q^{94} +(-5.63775 + 2.71500i) q^{95} +(-4.95556 - 6.21407i) q^{96} +(6.94335 - 3.34374i) q^{97} +(-2.95881 + 12.9634i) q^{98} +(1.17731 - 1.47631i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9}+O(q^{10}) $ 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9	\( 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9} - 8 q^{10} - 12 q^{11} - 24 q^{12} - 5 q^{13} - 8 q^{14} - q^{15} - 58 q^{16} - 30 q^{17} + 36 q^{18} - 24 q^{19} - 36 q^{20} - 28 q^{21} + 5 q^{22} + 27 q^{23} - 46 q^{24} - 38 q^{25} + 6 q^{26} - 36 q^{27} - 54 q^{28} + 28 q^{29} - 21 q^{30} + 36 q^{31} + 11 q^{32} + 5 q^{33} - 4 q^{34} + 6 q^{35} + 192 q^{36} + 164 q^{37} + 32 q^{38} - 34 q^{39} + 2 q^{40} + 42 q^{41} - 2 q^{42} - 22 q^{43} + 14 q^{44} + 58 q^{45} - 53 q^{46} + 21 q^{47} - 20 q^{48} + 166 q^{49} + 18 q^{50} - 6 q^{51} + 54 q^{52} + 8 q^{53} - 154 q^{54} - 5 q^{55} - 35 q^{56} + 8 q^{57} + 9 q^{58} - 13 q^{59} - 88 q^{60} - 34 q^{61} - 36 q^{62} - 31 q^{63} - 18 q^{64} + 9 q^{65} + 222 q^{66} - 48 q^{67} - 27 q^{68} + 2 q^{69} - 64 q^{70} - 42 q^{71} + 77 q^{72} - 44 q^{73} - 35 q^{74} - 21 q^{75} + 44 q^{76} - 32 q^{77} + 124 q^{78} - 96 q^{79} + 490 q^{80} - 12 q^{81} - 130 q^{82} - 8 q^{83} + 170 q^{84} + 22 q^{85} - 12 q^{86} - 90 q^{87} - 122 q^{88} - 81 q^{89} + 49 q^{90} - 27 q^{91} - 116 q^{92} + 18 q^{93} - 124 q^{94} + 117 q^{95} + 52 q^{96} - 79 q^{97} - 54 q^{98} - 39 q^{99}+O(q^{100}) \) 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9 - 8 * q^10 - 12 * q^11 - 24 * q^12 - 5 * q^13 - 8 * q^14 - q^15 - 58 * q^16 - 30 * q^17 + 36 * q^18 - 24 * q^19 - 36 * q^20 - 28 * q^21 + 5 * q^22 + 27 * q^23 - 46 * q^24 - 38 * q^25 + 6 * q^26 - 36 * q^27 - 54 * q^28 + 28 * q^29 - 21 * q^30 + 36 * q^31 + 11 * q^32 + 5 * q^33 - 4 * q^34 + 6 * q^35 + 192 * q^36 + 164 * q^37 + 32 * q^38 - 34 * q^39 + 2 * q^40 + 42 * q^41 - 2 * q^42 - 22 * q^43 + 14 * q^44 + 58 * q^45 - 53 * q^46 + 21 * q^47 - 20 * q^48 + 166 * q^49 + 18 * q^50 - 6 * q^51 + 54 * q^52 + 8 * q^53 - 154 * q^54 - 5 * q^55 - 35 * q^56 + 8 * q^57 + 9 * q^58 - 13 * q^59 - 88 * q^60 - 34 * q^61 - 36 * q^62 - 31 * q^63 - 18 * q^64 + 9 * q^65 + 222 * q^66 - 48 * q^67 - 27 * q^68 + 2 * q^69 - 64 * q^70 - 42 * q^71 + 77 * q^72 - 44 * q^73 - 35 * q^74 - 21 * q^75 + 44 * q^76 - 32 * q^77 + 124 * q^78 - 96 * q^79 + 490 * q^80 - 12 * q^81 - 130 * q^82 - 8 * q^83 + 170 * q^84 + 22 * q^85 - 12 * q^86 - 90 * q^87 - 122 * q^88 - 81 * q^89 + 49 * q^90 - 27 * q^91 - 116 * q^92 + 18 * q^93 - 124 * q^94 + 117 * q^95 + 52 * q^96 - 79 * q^97 - 54 * q^98 - 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{3}{7}\right)$

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 $

$2$	−0.265151	+	1.16170i	−0.187490	+	0.821448i	0.790444	+	0.612534i	$0.209850\pi$
$2$	−0.265151	+	1.16170i	−0.187490	+	0.821448i	−0.977934	+	0.208914i	$0.933007\pi$
$3$	0.558598	+	2.44738i	0.322507	+	1.41299i	0.833076	+	0.553158i	$0.186577\pi$
$3$	0.558598	+	2.44738i	0.322507	+	1.41299i	−0.510570	+	0.859836i	$0.670565\pi$
$4$	0.522689	+	0.251714i	0.261344	+	0.125857i
$5$	0.802903	−	1.00681i	0.359069	−	0.450258i	−0.569183	−	0.822211i	$-0.692740\pi$
$5$	0.802903	−	1.00681i	0.359069	−	0.450258i	0.928252	+	0.371953i	$0.121312\pi$
$6$	−2.99124			−1.22117
$7$	−4.26133			−1.61063			−0.805316	−	0.592845i	$-0.798005\pi$
$7$	−4.26133			−1.61063			−0.805316	+	0.592845i	$0.798005\pi$
$8$	−1.91688	+	2.40369i	−0.677720	+	0.849834i
$9$	−2.97472	+	1.43255i	−0.991574	+	0.477517i
$10$	0.956722	+	1.19969i	0.302542	+	0.379376i
$11$	−0.515272	+	0.248142i	−0.155360	+	0.0748176i	−0.509948	−	0.860205i	$-0.670335\pi$
$11$	−0.515272	+	0.248142i	−0.155360	+	0.0748176i	0.354588	+	0.935023i	$0.384621\pi$
$12$	−0.324065	+	1.41982i	−0.0935496	+	0.409868i
$13$	−0.401997	+	0.504088i	−0.111494	+	0.139809i	−0.834447	−	0.551088i	$-0.814213\pi$
$13$	−0.401997	+	0.504088i	−0.111494	+	0.139809i	0.722953	+	0.690897i	$0.242784\pi$
$14$	1.12990	−	4.95041i	0.301978	−	1.32305i
$15$	2.91254	+	1.40261i	0.752015	+	0.362151i
$16$	−1.56069	−	1.95705i	−0.390173	−	0.489262i
$17$	0.623490	+	0.781831i	0.151218	+	0.189622i
$17$	0.623490	+	0.781831i	0.151218	+	0.189622i
$18$	−0.875447	−	3.83559i	−0.206345	−	0.904056i
$19$	−4.37796	−	2.10832i	−1.00437	−	0.483681i	−0.141953	−	0.989873i	$-0.545338\pi$
$19$	−4.37796	−	2.10832i	−1.00437	−	0.483681i	−0.862420	+	0.506193i	$0.831053\pi$
$20$	0.673095	−	0.324146i	0.150509	−	0.0724812i
$21$	−2.38037	−	10.4291i	−0.519440	−	2.27582i
$22$	−0.151642	−	0.664388i	−0.0323302	−	0.141648i
$23$	−1.52600	+	0.734883i	−0.318193	+	0.153234i	−0.586162	−	0.810194i	$-0.699362\pi$
$23$	−1.52600	+	0.734883i	−0.318193	+	0.153234i	0.267969	+	0.963428i	$0.413648\pi$
$24$	−6.95351	−	3.34864i	−1.41938	−	0.683538i
$25$	0.743595	+	3.25790i	0.148719	+	0.651580i
$26$	−0.479011	−	0.600661i	−0.0939417	−	0.117799i
$27$	−0.472194	−	0.592113i	−0.0908738	−	0.113952i
$28$	−2.22735	−	1.07264i	−0.420930	−	0.202709i
$29$	−0.0857115	+	0.375527i	−0.0159162	+	0.0697335i	−0.982262	−	0.187512i	$-0.939958\pi$
$29$	−0.0857115	+	0.375527i	−0.0159162	+	0.0697335i	0.966346	+	0.257245i	$0.0828149\pi$
$30$	−2.40167	+	3.01160i	−0.438484	+	0.549841i
$31$	0.414847	−	1.81756i	0.0745087	−	0.326444i	−0.923913	−	0.382602i	$-0.875028\pi$
$31$	0.414847	−	1.81756i	0.0745087	−	0.326444i	0.998422	+	0.0561582i	$0.0178851\pi$
$32$	−2.85262	+	1.37375i	−0.504277	+	0.242847i
$33$	−0.895127	−	1.12245i	−0.155822	−	0.195394i
$34$	−1.07358	+	0.517007i	−0.184117	+	0.0886659i
$35$	−3.42144	+	4.29035i	−0.578328	+	0.725201i
$36$	−1.91544			−0.319241
$37$	3.73207			0.613548			0.306774	−	0.951782i	$-0.400750\pi$
$37$	3.73207			0.613548			0.306774	+	0.951782i	$0.400750\pi$
$38$	3.61006	−	4.52687i	0.585629	−	0.734355i
$39$	−1.45825	−	0.702256i	−0.233507	−	0.112451i
$40$	0.880989	+	3.85986i	0.139297	+	0.610298i
$41$	−0.723599	+	3.17030i	−0.113007	+	0.495117i	0.886470	+	0.462786i	$0.153150\pi$
$41$	−0.723599	+	3.17030i	−0.113007	+	0.495117i	−0.999477	+	0.0323309i	$0.989707\pi$
$42$	12.7467			1.96685
$43$	−4.56029	+	4.71209i	−0.695438	+	0.718586i
$43$	−4.56029	+	4.71209i	−0.695438	+	0.718586i
$44$	−0.331788			−0.0500189
$45$	−0.946108	+	4.14517i	−0.141037	+	0.617926i
$46$	−0.449095	−	1.96761i	−0.0662154	−	0.290109i
$47$	4.70673	+	2.26664i	0.686547	+	0.330624i	0.744431	−	0.667700i	$-0.232721\pi$
$47$	4.70673	+	2.26664i	0.686547	+	0.330624i	−0.0578835	+	0.998323i	$0.518435\pi$
$48$	3.91783	−	4.91281i	0.565490	−	0.709102i
$49$	11.1590			1.59414
$50$	−3.98188			−0.563123
$51$	−1.56516	+	1.96264i	−0.219166	+	0.274825i
$52$	−0.337005	+	0.162293i	−0.0467342	+	0.0225060i
$53$	4.92257	+	6.17271i	0.676167	+	0.847886i	0.994995	−	0.0999263i	$-0.0318607\pi$
$53$	4.92257	+	6.17271i	0.676167	+	0.847886i	−0.318828	+	0.947813i	$0.603289\pi$
$54$	0.813062	−	0.391550i	0.110644	−	0.0532832i
$55$	−0.163882	+	0.718014i	−0.0220978	+	0.0968170i
$56$	8.16847	−	10.2429i	1.09156	−	1.36877i
$57$	2.71432	−	11.8922i	0.359521	−	1.57516i
$58$	−0.413524	−	0.199143i	−0.0542984	−	0.0261487i
$59$	−3.11525	−	3.90640i	−0.405571	−	0.508570i	0.536538	−	0.843876i	$-0.319732\pi$
$59$	−3.11525	−	3.90640i	−0.405571	−	0.508570i	−0.942109	+	0.335306i	$0.891160\pi$
$60$	1.16930	+	1.46625i	0.150956	+	0.189292i
$61$	2.68748	+	11.7746i	0.344097	+	1.50759i	0.790336	+	0.612674i	$0.209906\pi$
$61$	2.68748	+	11.7746i	0.344097	+	1.50759i	−0.446239	+	0.894914i	$0.647237\pi$
$62$	2.00147	+	0.963858i	0.254187	+	0.122410i
$63$	12.6763	−	6.10457i	1.59706	−	0.769104i
$64$	−1.95352	−	8.55895i	−0.244190	−	1.06987i
$65$	0.184756	+	0.809467i	0.0229161	+	0.100402i
$66$	1.54130	−	0.742252i	0.189721	−	0.0913649i
$67$	8.64947	+	4.16536i	1.05670	+	0.508880i	0.879798	−	0.475348i	$-0.157678\pi$
$67$	8.64947	+	4.16536i	1.05670	+	0.508880i	0.176903	+	0.984228i	$0.443392\pi$
$68$	0.129093	+	0.565595i	0.0156549	+	0.0685885i
$69$	−2.65096	−	3.32419i	−0.319138	−	0.400186i
$70$	−4.07691	−	5.11228i	−0.487284	−	0.611035i
$71$	−7.62825	−	3.67357i	−0.905307	−	0.435973i	−0.0775041	−	0.996992i	$-0.524695\pi$
$71$	−7.62825	−	3.67357i	−0.905307	−	0.435973i	−0.827803	+	0.561019i	$0.810409\pi$
$72$	2.25878	−	9.89635i	0.266199	−	1.16630i
$73$	1.88246	−	2.36053i	0.220325	−	0.276279i	−0.659368	−	0.751820i	$-0.729176\pi$
$73$	1.88246	−	2.36053i	0.220325	−	0.276279i	0.879694	+	0.475541i	$0.157748\pi$
$74$	−0.989562	+	4.33556i	−0.115034	+	0.503998i
$75$	−7.55795	+	3.63972i	−0.872717	+	0.420278i
$76$	−1.75762	−	2.20399i	−0.201613	−	0.252814i
$77$	2.19575	−	1.05742i	0.250229	−	0.120504i
$78$	1.20247	−	1.50785i	0.136153	−	0.170730i
$79$	3.81279			0.428973			0.214486	−	0.976727i	$-0.431192\pi$
$79$	3.81279			0.428973			0.214486	+	0.976727i	$0.431192\pi$
$80$	−3.22345			−0.360393
$81$	−4.99036	+	6.25771i	−0.554484	+	0.695301i
$82$	−3.49108	−	1.68122i	−0.385525	−	0.185659i
$83$	0.0628882	+	0.275531i	0.00690287	+	0.0302435i	0.978262	−	0.207372i	$-0.0664912\pi$
$83$	0.0628882	+	0.275531i	0.00690287	+	0.0302435i	−0.971359	+	0.237616i	$0.923634\pi$
$84$	1.38095	−	6.05034i	0.150674	−	0.660146i
$85$	1.28776			0.139677
$86$	−4.26488	−	6.54712i	−0.459894	−	0.705994i
$87$	−0.966934			−0.103666
$88$	0.391258	−	1.71422i	0.0417083	−	0.182736i
$89$	−3.74368	−	16.4021i	−0.396830	−	1.73862i	−0.639755	−	0.768579i	$-0.720964\pi$
$89$	−3.74368	−	16.4021i	−0.396830	−	1.73862i	0.242925	−	0.970045i	$-0.421893\pi$
$90$	−4.56460	−	2.19819i	−0.481151	−	0.231710i
$91$	1.71304	−	2.14809i	0.179576	−	0.225181i
$92$	−0.982603			−0.102443
$93$	4.68000			0.485293
$94$	−3.88116	+	4.86682i	−0.400311	+	0.501974i
$95$	−5.63775	+	2.71500i	−0.578421	+	0.278553i
$96$	−4.95556	−	6.21407i	−0.505775	−	0.634221i
$97$	6.94335	−	3.34374i	0.704991	−	0.339506i	−0.0468030	−	0.998904i	$-0.514903\pi$
$97$	6.94335	−	3.34374i	0.704991	−	0.339506i	0.751794	+	0.659399i	$0.229189\pi$
$98$	−2.95881	+	12.9634i	−0.298885	+	1.30950i
$99$	1.17731	−	1.47631i	0.118325	−	0.148374i
$100$	−0.431390	+	1.89004i	−0.0431390	+	0.189004i
$101$	14.3071	+	6.88992i	1.42361	+	0.685573i	0.977797	−	0.209554i	$-0.0672013\pi$
$101$	14.3071	+	6.88992i	1.42361	+	0.685573i	0.445810	+	0.895127i	$0.352916\pi$
$102$	−1.86501	−	2.33865i	−0.184663	−	0.231560i
$103$	8.52031	+	10.6841i	0.839531	+	1.05274i	0.997862	+	0.0653522i	$0.0208171\pi$
$103$	8.52031	+	10.6841i	0.839531	+	1.05274i	−0.158332	+	0.987386i	$0.550611\pi$
$104$	−0.441093	−	1.93255i	−0.0432527	−	0.189503i
$105$	−12.4113	−	5.97697i	−1.21122	−	0.583292i
$106$	−8.47608	+	4.08186i	−0.823269	+	0.396466i
$107$	−2.29419	−	10.0515i	−0.221788	−	0.971717i	−0.956131	−	0.292939i	$-0.905367\pi$
$107$	−2.29419	−	10.0515i	−0.221788	−	0.971717i	0.734343	−	0.678779i	$-0.237490\pi$
$108$	−0.0977677	−	0.428348i	−0.00940770	−	0.0412178i
$109$	−0.796867	+	0.383751i	−0.0763260	+	0.0367567i	−0.471657	−	0.881782i	$-0.656344\pi$
$109$	−0.796867	+	0.383751i	−0.0763260	+	0.0367567i	0.395331	+	0.918539i	$0.370630\pi$
$110$	−0.790666	−	0.380764i	−0.0753870	−	0.0363045i
$111$	2.08473	+	9.13378i	0.197873	+	0.866940i
$112$	6.65063	+	8.33963i	0.628426	+	0.788021i
$113$	−5.55374	−	6.96417i	−0.522452	−	0.655134i	0.448676	−	0.893695i	$-0.351896\pi$
$113$	−5.55374	−	6.96417i	−0.522452	−	0.655134i	−0.971128	+	0.238561i	$0.923324\pi$
$114$	13.0955	+	6.30648i	1.22651	+	0.590656i
$115$	−0.485343	+	2.12643i	−0.0452585	+	0.198290i
$116$	−0.139326	+	0.174709i	−0.0129361	+	0.0162213i
$117$	0.473697	−	2.07540i	0.0437933	−	0.191871i
$118$	5.36409	−	2.58321i	0.493805	−	0.237804i
$119$	−2.65690	−	3.33165i	−0.243557	−	0.305411i
$120$	−8.95443	+	4.31223i	−0.817424	+	0.393651i
$121$	−6.65446	+	8.34443i	−0.604951	+	0.758584i
$122$	−14.3912			−1.30292
$123$	−8.16311			−0.736043
$124$	0.674341	−	0.845597i	0.0605576	−	0.0759369i
$125$	9.67826	+	4.66080i	0.865649	+	0.416875i
$126$	3.73057	+	16.3447i	0.332346	+	1.45610i
$127$	−4.44530	+	19.4761i	−0.394457	+	1.72823i	0.254205	+	0.967150i	$0.418186\pi$
$127$	−4.44530	+	19.4761i	−0.394457	+	1.72823i	−0.648662	+	0.761077i	$0.724671\pi$
$128$	4.12859			0.364919
$129$	−14.0796	−	8.52859i	−1.23964	−	0.750901i
$130$	−0.989349			−0.0867716
$131$	−0.768726	+	3.36801i	−0.0671639	+	0.294264i	−0.997344	−	0.0728401i	$-0.976794\pi$
$131$	−0.768726	+	3.36801i	−0.0671639	+	0.294264i	0.930180	+	0.367105i	$0.119651\pi$
$132$	−0.185336	−	0.812010i	−0.0161314	−	0.0706764i
$133$	18.6560	+	8.98424i	1.61768	+	0.779032i
$134$	−7.13233	+	8.94366i	−0.616140	+	0.772615i
$135$	−0.975270			−0.0839379
$136$	−3.07444			−0.263631
$137$	−1.70431	+	2.13714i	−0.145609	+	0.182588i	−0.849288	−	0.527931i	$-0.822968\pi$
$137$	−1.70431	+	2.13714i	−0.145609	+	0.182588i	0.703679	+	0.710518i	$0.251540\pi$
$138$	4.56463	−	2.19821i	0.388567	−	0.187124i
$139$	−6.33413	−	7.94275i	−0.537254	−	0.673695i	0.436918	−	0.899501i	$-0.356070\pi$
$139$	−6.33413	−	7.94275i	−0.537254	−	0.673695i	−0.974172	+	0.225806i	$0.927498\pi$
$140$	−2.86828	+	1.38129i	−0.242414	+	0.116741i
$141$	−2.91816	+	12.7853i	−0.245753	+	1.07672i
$142$	6.29024	−	7.88771i	0.527865	−	0.661922i
$143$	0.0820523	−	0.359495i	0.00686156	−	0.0300625i
$144$	7.44619	+	3.58590i	0.620516	+	0.298825i
$145$	0.309265	+	0.387806i	0.0256831	+	0.0322056i
$146$	2.24310	+	2.81276i	0.185640	+	0.232786i
$147$	6.23338	+	27.3102i	0.514120	+	2.25251i
$148$	1.95071	+	0.939412i	0.160347	+	0.0772192i
$149$	8.61977	−	4.15106i	0.706159	−	0.340068i	−0.0460991	−	0.998937i	$-0.514679\pi$
$149$	8.61977	−	4.15106i	0.706159	−	0.340068i	0.752258	+	0.658869i	$0.228965\pi$
$150$	−2.22427	−	9.74517i	−0.181611	−	0.795690i
$151$	2.66570	+	11.6792i	0.216931	+	0.950438i	0.959730	+	0.280924i	$0.0906407\pi$
$151$	2.66570	+	11.6792i	0.216931	+	0.950438i	−0.742799	+	0.669515i	$0.766502\pi$
$152$	13.4598	−	6.48189i	1.09173	−	0.525751i
$153$	−2.97472	−	1.43255i	−0.240492	−	0.115815i
$154$	0.646199	+	2.83118i	0.0520722	+	0.228143i
$155$	−1.49686	−	1.87700i	−0.120230	−	0.150764i
$156$	−0.585443	−	0.734122i	−0.0468729	−	0.0587768i
$157$	3.45551	+	1.66408i	0.275779	+	0.132808i	0.566662	−	0.823950i	$-0.308235\pi$
$157$	3.45551	+	1.66408i	0.275779	+	0.132808i	−0.290882	+	0.956759i	$0.593949\pi$
$158$	−1.01097	+	4.42933i	−0.0804282	+	0.352379i
$159$	−12.3572	+	15.4954i	−0.979990	+	1.22887i
$160$	−0.907275	+	3.97503i	−0.0717264	+	0.314254i
$161$	6.50279	−	3.13158i	0.512492	−	0.246803i
$162$	−5.94640	−	7.45655i	−0.467193	−	0.585842i
$163$	−0.317026	+	0.152672i	−0.0248314	+	0.0119582i	−0.446258	−	0.894904i	$-0.647244\pi$
$163$	−0.317026	+	0.152672i	−0.0248314	+	0.0119582i	0.421427	+	0.906862i	$0.361529\pi$
$164$	−1.17622	+	1.47494i	−0.0918476	+	0.115173i
$165$	−1.84880			−0.143929
$166$	−0.336760			−0.0261377
$167$	−4.30145	+	5.39385i	−0.332856	+	0.417388i	−0.919892	−	0.392173i	$-0.871724\pi$
$167$	−4.30145	+	5.39385i	−0.332856	+	0.417388i	0.587035	+	0.809561i	$0.300295\pi$
$168$	29.6312	+	14.2697i	2.28610	+	1.10093i
$169$	2.80027	+	12.2688i	0.215405	+	0.943752i
$170$	−0.341450	+	1.49599i	−0.0261880	+	0.114737i
$171$	16.0435			1.22688
$172$	−3.56971	+	1.31507i	−0.272188	+	0.100273i
$173$	−14.8004			−1.12525			−0.562626	−	0.826712i	$-0.690209\pi$
$173$	−14.8004			−1.12525			−0.562626	+	0.826712i	$0.690209\pi$
$174$	0.256384	−	1.12329i	0.0194364	−	0.0851564i
$175$	−3.16871	−	13.8830i	−0.239532	−	1.04946i
$176$	1.28981	+	0.621138i	0.0972228	+	0.0468200i
$177$	7.82027	−	9.80631i	0.587808	−	0.737087i
$178$	20.0471			1.50259
$179$	16.7301			1.25046			0.625232	−	0.780439i	$-0.285004\pi$
$179$	16.7301			1.25046			0.625232	+	0.780439i	$0.285004\pi$
$180$	−1.53792	+	1.92849i	−0.114629	+	0.143741i
$181$	19.7132	−	9.49339i	1.46527	−	0.705638i	0.480102	−	0.877213i	$-0.340600\pi$
$181$	19.7132	−	9.49339i	1.46527	−	0.705638i	0.985171	+	0.171575i	$0.0548855\pi$
$182$	2.04122	+	2.55961i	0.151306	+	0.189731i
$183$	−27.3158	+	13.1546i	−2.01924	+	0.972415i
$184$	1.15873	−	5.07672i	0.0854226	−	0.374261i
$185$	2.99649	−	3.75748i	0.220306	−	0.276255i
$186$	−1.24091	+	5.43677i	−0.0909877	+	0.398643i
$187$	−0.515272	−	0.248142i	−0.0376804	−	0.0181459i
$188$	1.88961	+	2.36950i	0.137814	+	0.172813i
$189$	2.01218	+	2.52319i	0.146364	+	0.183535i
$190$	−1.65916	−	7.26927i	−0.120368	−	0.527368i
$191$	−2.11054	−	1.01638i	−0.152713	−	0.0735429i	0.355966	−	0.934499i	$-0.384152\pi$
$191$	−2.11054	−	1.01638i	−0.152713	−	0.0735429i	−0.508679	+	0.860956i	$0.669866\pi$
$192$	19.8557	−	9.56202i	1.43296	−	0.690080i
$193$	2.44757	+	10.7235i	0.176180	+	0.771896i	0.983371	+	0.181606i	$0.0581295\pi$
$193$	2.44757	+	10.7235i	0.176180	+	0.771896i	−0.807191	+	0.590290i	$0.799013\pi$
$194$	2.04340	+	8.95271i	0.146707	+	0.642767i
$195$	−1.87787	+	0.904334i	−0.134477	+	0.0647607i
$196$	5.83266	+	2.80886i	0.416619	+	0.200633i
$197$	−5.26806	−	23.0809i	−0.375334	−	1.64445i	−0.711532	−	0.702654i	$-0.751998\pi$
$197$	−5.26806	−	23.0809i	−0.375334	−	1.64445i	0.336198	−	0.941791i	$-0.390859\pi$
$198$	1.40286	+	1.75913i	0.0996971	+	0.125016i
$199$	−14.3059	−	17.9390i	−1.01412	−	1.27166i	−0.962008	−	0.273020i	$-0.911978\pi$
$199$	−14.3059	−	17.9390i	−1.01412	−	1.27166i	−0.0521077	−	0.998641i	$-0.516594\pi$
$200$	−9.25638	−	4.45764i	−0.654525	−	0.315203i
$201$	−5.36264	+	23.4953i	−0.378252	+	1.65723i
$202$	−11.7976	+	14.7937i	−0.830075	+	1.04088i
$203$	0.365245	−	1.60024i	0.0256352	−	0.112315i
$204$	−1.31211	+	0.631881i	−0.0918664	+	0.0442405i
$205$	2.61090	+	3.27396i	0.182353	+	0.228664i
$206$	−14.6710	+	7.06516i	−1.02217	+	0.492253i
$207$	3.48667	−	4.37214i	0.242340	−	0.303885i
$208$	1.61392			0.111905
$209$	2.77900			0.192228
$210$	10.2343	−	12.8335i	0.706236	−	0.885592i
$211$	−17.0415	−	8.20677i	−1.17319	−	0.564977i	−0.257268	−	0.966340i	$-0.582822\pi$
$211$	−17.0415	−	8.20677i	−1.17319	−	0.564977i	−0.915919	+	0.401363i	$0.868537\pi$
$212$	1.01922	+	4.46548i	0.0700001	+	0.306690i
$213$	4.72949	−	20.7213i	0.324060	−	1.41980i
$214$	12.2852			0.839799
$215$	1.08270	+	8.37468i	0.0738393	+	0.571149i
$216$	2.32840			0.158427
$217$	−1.76780	+	7.74524i	−0.120006	+	0.525781i
$218$	−0.234514	−	1.02747i	−0.0158833	−	0.0695894i
$219$	6.82865	+	3.28851i	0.461438	+	0.222217i
$220$	−0.266393	+	0.334046i	−0.0179602	+	0.0225214i
$221$	−0.644753			−0.0433708
$222$	−11.1635			−0.749246
$223$	−4.73723	+	5.94030i	−0.317228	+	0.397792i	−0.914723	−	0.404081i	$-0.867591\pi$
$223$	−4.73723	+	5.94030i	−0.317228	+	0.397792i	0.597495	+	0.801873i	$0.296163\pi$
$224$	12.1560	−	5.85401i	0.812206	−	0.391138i
$225$	−6.87910	−	8.62611i	−0.458606	−	0.575074i
$226$	9.56288	−	4.60524i	0.636113	−	0.306336i
$227$	−2.14003	+	9.37606i	−0.142038	+	0.622311i	0.852922	+	0.522039i	$0.174828\pi$
$227$	−2.14003	+	9.37606i	−0.142038	+	0.622311i	−0.994960	+	0.100272i	$0.968029\pi$
$228$	4.41218	−	5.53270i	0.292204	−	0.366412i
$229$	−0.548495	+	2.40311i	−0.0362456	+	0.158802i	−0.989812	−	0.142381i	$-0.954524\pi$
$229$	−0.548495	+	2.40311i	−0.0362456	+	0.158802i	0.953566	+	0.301183i	$0.0973815\pi$
$230$	−2.34159	−	1.12765i	−0.154400	−	0.0743550i
$231$	3.81444	+	4.78315i	0.250971	+	0.314708i
$232$	−0.738352	−	0.925864i	−0.0484752	−	0.0607860i
$233$	−2.95154	−	12.9315i	−0.193362	−	0.847174i	−0.974780	−	0.223166i	$-0.928361\pi$
$233$	−2.95154	−	12.9315i	−0.193362	−	0.847174i	0.781419	−	0.624007i	$-0.214496\pi$
$234$	2.28540	+	1.10059i	0.149401	+	0.0719478i
$235$	6.06112	−	2.91888i	0.395384	−	0.190407i
$236$	−0.645012	−	2.82598i	−0.0419867	−	0.183956i
$237$	2.12982	+	9.33135i	0.138347	+	0.606136i
$238$	4.57486	−	2.20314i	0.296544	−	0.142808i
$239$	4.06520	+	1.95770i	0.262956	+	0.126633i	0.560717	−	0.828008i	$-0.310526\pi$
$239$	4.06520	+	1.95770i	0.262956	+	0.126633i	−0.297761	+	0.954640i	$0.596240\pi$
$240$	−1.80061	−	7.88901i	−0.116229	−	0.509233i
$241$	6.76276	+	8.48024i	0.435628	+	0.546260i	0.950385	−	0.311076i	$-0.100689\pi$
$241$	6.76276	+	8.48024i	0.435628	+	0.546260i	−0.514757	+	0.857336i	$0.672118\pi$
$242$	−7.92931	−	9.94304i	−0.509715	−	0.639163i
$243$	−20.1496	−	9.70354i	−1.29260	−	0.622482i
$244$	−1.55912	+	6.83094i	−0.0998123	+	0.437306i
$245$	8.95956	−	11.2349i	0.572406	−	0.717774i
$246$	2.16446	−	9.48311i	0.138001	−	0.604621i
$247$	2.82270	−	1.35934i	0.179604	−	0.0864929i
$248$	3.57365	+	4.48122i	0.226927	+	0.284558i
$249$	−0.639199	+	0.307822i	−0.0405076	+	0.0195074i
$250$	−7.98067	+	10.0074i	−0.504742	+	0.632926i
$251$	−27.1912			−1.71629			−0.858146	−	0.513405i	$-0.828384\pi$
$251$	−27.1912			−1.71629			−0.858146	+	0.513405i	$0.828384\pi$
$252$	8.16235			0.514180
$253$	0.603950	−	0.757329i	0.0379700	−	0.0476129i
$254$	−21.4468	−	10.3282i	−1.34569	−	0.648051i
$255$	0.719338	+	3.15163i	0.0450467	+	0.197362i
$256$	2.81235	−	12.3217i	0.175772	−	0.770106i
$257$	−18.5105			−1.15465			−0.577327	−	0.816513i	$-0.695904\pi$
$257$	−18.5105			−1.15465			−0.577327	+	0.816513i	$0.695904\pi$
$258$	13.6409	−	14.0950i	0.849247	−	0.877515i
$259$	−15.9036			−0.988201
$260$	−0.107184	+	0.469605i	−0.00664728	+	0.0291236i
$261$	−0.282993	−	1.23987i	−0.0175168	−	0.0767462i
$262$	−3.70880	−	1.78606i	−0.229130	−	0.110343i
$263$	9.15911	−	11.4852i	0.564775	−	0.708205i	−0.414657	−	0.909978i	$-0.636099\pi$
$263$	9.15911	−	11.4852i	0.564775	−	0.708205i	0.979433	+	0.201772i	$0.0646700\pi$
$264$	4.41389			0.271656
$265$	10.1671			0.624558
$266$	−15.3837	+	19.2905i	−0.943233	+	1.18278i
$267$	38.0510	−	18.3244i	2.32869	−	1.12144i
$268$	3.47250	+	4.35438i	0.212117	+	0.265986i
$269$	0.576853	−	0.277798i	0.0351714	−	0.0169376i	−0.416215	−	0.909266i	$-0.636644\pi$
$269$	0.576853	−	0.277798i	0.0351714	−	0.0169376i	0.451387	+	0.892328i	$0.350929\pi$
$270$	0.258594	−	1.13297i	0.0157375	−	0.0689506i
$271$	0.189666	−	0.237834i	0.0115214	−	0.0144474i	−0.776037	−	0.630687i	$-0.782773\pi$
$271$	0.189666	−	0.237834i	0.0115214	−	0.0144474i	0.787559	+	0.616240i	$0.211345\pi$
$272$	0.557005	−	2.44040i	0.0337734	−	0.147971i
$273$	6.21408	+	2.99255i	0.376094	+	0.181117i
$274$	−2.03082	−	2.54657i	−0.122686	−	0.153844i
$275$	−1.19158	−	1.49419i	−0.0718547	−	0.0901030i
$276$	−0.548880	−	2.40480i	−0.0330387	−	0.144752i
$277$	28.9994	+	13.9654i	1.74241	+	0.839098i	0.981808	+	0.189875i	$0.0608081\pi$
$277$	28.9994	+	13.9654i	1.74241	+	0.839098i	0.760597	+	0.649224i	$0.224906\pi$
$278$	10.9066	−	5.25235i	0.654136	−	0.315015i
$279$	1.36970	+	6.00103i	0.0820016	+	0.359272i
$280$	−3.75419	−	16.4482i	−0.224356	−	0.982966i
$281$	−1.18574	+	0.571021i	−0.0707352	+	0.0340643i	−0.468917	−	0.883242i	$-0.655356\pi$
$281$	−1.18574	+	0.571021i	−0.0707352	+	0.0340643i	0.398182	+	0.917307i	$0.369641\pi$
$282$	−14.0790	−	6.78007i	−0.838390	−	0.403747i
$283$	2.35260	+	10.3074i	0.139848	+	0.612713i	0.995467	+	0.0951074i	$0.0303194\pi$
$283$	2.35260	+	10.3074i	0.139848	+	0.612713i	−0.855619	+	0.517606i	$0.826823\pi$
$284$	−3.06251	−	3.84027i	−0.181727	−	0.227878i
$285$	−9.79386	−	12.2811i	−0.580138	−	0.727470i
$286$	0.395870	+	0.190641i	0.0234083	+	0.0112728i
$287$	3.08350	−	13.5097i	0.182013	−	0.797452i
$288$	6.51779	−	8.17305i	0.384065	−	0.481602i
$289$	−0.222521	+	0.974928i	−0.0130895	+	0.0573487i
$290$	−0.532518	+	0.256447i	−0.0312705	+	0.0150591i
$291$	12.0619	+	15.1252i	0.707084	+	0.886655i
$292$	1.57812	−	0.759982i	0.0923524	−	0.0444746i
$293$	−10.1607	+	12.7411i	−0.593595	+	0.744345i	−0.984364	−	0.176144i	$-0.943638\pi$
$293$	−10.1607	+	12.7411i	−0.593595	+	0.744345i	0.390769	+	0.920489i	$0.372209\pi$
$294$	−33.3791			−1.94671
$295$	−6.43424			−0.374616
$296$	−7.15394	+	8.97075i	−0.415814	+	0.521414i
$297$	0.390236	+	0.187928i	0.0226438	+	0.0109047i
$298$	2.53676	+	11.1143i	0.146951	+	0.643832i
$299$	0.243001	−	1.06466i	0.0140531	−	0.0615708i
$300$	−4.86662			−0.280974
$301$	19.4329	−	20.0798i	1.12009	−	1.15738i
$302$	−14.2746			−0.821408
$303$	−8.87035	+	38.8635i	−0.509588	+	2.23265i
$304$	2.70658	+	11.8583i	0.155233	+	0.680121i
$305$	14.0126	+	6.74811i	0.802358	+	0.386395i
$306$	2.45295	−	3.07590i	0.140226	−	0.175838i
$307$	−3.77970			−0.215719			−0.107860	−	0.994166i	$-0.534400\pi$
$307$	−3.77970			−0.215719			−0.107860	+	0.994166i	$0.534400\pi$
$308$	1.41386			0.0805620
$309$	−21.3887	+	26.8205i	−1.21676	+	1.52577i
$310$	2.57741	−	1.24121i	0.146387	−	0.0704962i
$311$	14.0227	+	17.5839i	0.795156	+	0.997094i	0.999833	+	0.0182643i	$0.00581403\pi$
$311$	14.0227	+	17.5839i	0.795156	+	0.997094i	−0.204677	+	0.978829i	$0.565615\pi$
$312$	4.48330	−	2.15904i	0.253817	−	0.122232i
$313$	−1.66250	+	7.28390i	−0.0939703	+	0.411711i	−0.999932	−	0.0116486i	$-0.996292\pi$
$313$	−1.66250	+	7.28390i	−0.0939703	+	0.411711i	0.905962	+	0.423359i	$0.139149\pi$
$314$	−2.84940	+	3.57304i	−0.160801	+	0.201638i
$315$	4.03168	−	17.6640i	0.227160	−	0.995251i
$316$	1.99290	+	0.959732i	0.112110	+	0.0539891i
$317$	−1.91665	−	2.40340i	−0.107650	−	0.134988i	0.725088	−	0.688656i	$-0.241799\pi$
$317$	−1.91665	−	2.40340i	−0.107650	−	0.134988i	−0.832738	+	0.553668i	$0.813228\pi$
$318$	−14.7246	−	18.4640i	−0.825714	−	1.03541i
$319$	−0.0490192	−	0.214767i	−0.00274455	−	0.0120246i
$320$	−10.1857	−	4.90518i	−0.569398	−	0.274208i
$321$	23.3183	−	11.2295i	1.30150	−	0.626771i
$322$	1.91374	+	8.38466i	0.106649	+	0.467259i
$323$	−1.08127	−	4.73734i	−0.0601633	−	0.263593i
$324$	−4.18355	+	2.01469i	−0.232420	+	0.111927i
$325$	−1.94119	−	0.934829i	−0.107678	−	0.0518550i
$326$	−0.0932994	−	0.408771i	−0.00516738	−	0.0226398i
$327$	−1.38431	−	1.73587i	−0.0765526	−	0.0959940i
$328$	−6.23337	−	7.81639i	−0.344180	−	0.431588i
$329$	−20.0570	−	9.65892i	−1.10578	−	0.532514i
$330$	0.490210	−	2.14775i	0.0269852	−	0.118230i
$331$	−7.55643	+	9.47546i	−0.415339	+	0.520818i	−0.944858	−	0.327479i	$-0.893801\pi$
$331$	−7.55643	+	9.47546i	−0.415339	+	0.520818i	0.529520	+	0.848298i	$0.322372\pi$
$332$	−0.0364840	+	0.159847i	−0.00200232	+	0.00877273i
$333$	−11.1019	+	5.34638i	−0.608378	+	0.292980i
$334$	−5.12552	−	6.42719i	−0.280456	−	0.351680i
$335$	11.1384	−	5.36397i	0.608556	−	0.293065i
$336$	−16.6952	+	20.9351i	−0.910797	+	1.14210i
$337$	18.1184			0.986972			0.493486	−	0.869754i	$-0.335722\pi$
$337$	18.1184			0.986972			0.493486	+	0.869754i	$0.335722\pi$
$338$	−14.9952			−0.815630
$339$	13.9416	−	17.4823i	0.757206	−	0.949507i
$340$	0.673095	+	0.324146i	0.0365037	+	0.0175793i
$341$	0.237255	+	1.03948i	0.0128481	+	0.0562910i
$342$	−4.25395	+	18.6378i	−0.230027	+	1.00782i
$343$	−17.7227			−0.956938
$344$	−2.58487	−	19.9941i	−0.139367	−	1.07801i
$345$	−5.47529			−0.294779
$346$	3.92434	−	17.1936i	0.210974	−	0.924336i
$347$	−0.616986	−	2.70319i	−0.0331215	−	0.145115i	0.955663	−	0.294461i	$-0.0951402\pi$
$347$	−0.616986	−	2.70319i	−0.0331215	−	0.145115i	−0.988785	+	0.149346i	$0.952283\pi$
$348$	−0.505405	−	0.243390i	−0.0270926	−	0.0130471i
$349$	20.5819	−	25.8089i	1.10172	−	1.38152i	0.184650	−	0.982804i	$-0.440885\pi$
$349$	20.5819	−	25.8089i	1.10172	−	1.38152i	0.917075	−	0.398715i	$-0.130544\pi$
$350$	16.9681			0.906984
$351$	0.488297			0.0260634
$352$	1.12899	−	1.41571i	0.0601755	−	0.0754577i
$353$	16.7510	−	8.06683i	0.891563	−	0.429354i	0.0687288	−	0.997635i	$-0.478106\pi$
$353$	16.7510	−	8.06683i	0.891563	−	0.429354i	0.822834	+	0.568281i	$0.192391\pi$
$354$	9.31847	+	11.6850i	0.495271	+	0.621050i
$355$	−9.82333	+	4.73066i	−0.521368	+	0.251078i
$356$	2.17186	−	9.51555i	0.115108	−	0.504323i
$357$	6.66966	−	8.36349i	0.352996	−	0.442643i
$358$	−4.43600	+	19.4354i	−0.234450	+	1.02719i
$359$	−14.0701	−	6.77580i	−0.742591	−	0.357613i	0.0240314	−	0.999711i	$-0.492350\pi$
$359$	−14.0701	−	6.77580i	−0.742591	−	0.357613i	−0.766622	+	0.642098i	$0.778064\pi$
$360$	−8.15015	−	10.2200i	−0.429550	−	0.538639i
$361$	2.87526	+	3.60546i	0.151329	+	0.189761i
$362$	5.80152	+	25.4181i	0.304921	+	1.33595i
$363$	−24.1391	−	11.6248i	−1.26698	−	0.610143i
$364$	1.43609	−	0.691585i	0.0752716	−	0.0362489i
$365$	−0.865169	−	3.79055i	−0.0452850	−	0.198407i
$366$	−8.03891	−	35.2208i	−0.420201	−	1.84102i
$367$	33.2459	−	16.0104i	1.73542	−	0.835736i	0.750916	−	0.660397i	$-0.229612\pi$
$367$	33.2459	−	16.0104i	1.73542	−	0.835736i	0.984508	−	0.175339i	$-0.0561021\pi$
$368$	3.81982	+	1.83953i	0.199122	+	0.0958919i
$369$	−2.38910	−	10.4673i	−0.124372	−	0.544908i
$370$	3.57055	+	4.47733i	0.185624	+	0.232765i
$371$	−20.9767	−	26.3040i	−1.08906	−	1.36563i
$372$	2.44618	+	1.17802i	0.126829	+	0.0610774i
$373$	−1.93770	+	8.48962i	−0.100330	+	0.439576i	0.899665	+	0.436581i	$0.143811\pi$
$373$	−1.93770	+	8.48962i	−0.100330	+	0.439576i	−0.999996	+	0.00299537i	$0.999047\pi$
$374$	0.424892	−	0.532798i	0.0219707	−	0.0275503i
$375$	−6.00049	+	26.2899i	−0.309864	+	1.35760i
$376$	−14.4706	+	6.96866i	−0.746262	+	0.359381i
$377$	−0.154843	−	0.194167i	−0.00797481	−	0.0100001i
$378$	−3.46473	+	1.66853i	−0.178206	+	0.0858197i
$379$	−0.917552	+	1.15057i	−0.0471315	+	0.0591010i	−0.804839	−	0.593494i	$-0.797748\pi$
$379$	−0.917552	+	1.15057i	−0.0471315	+	0.0591010i	0.757707	+	0.652595i	$0.226320\pi$
$380$	−3.63019			−0.186225
$381$	−50.1486			−2.56919
$382$	1.74035	−	2.18233i	0.0890440	−	0.111658i
$383$	1.38958	+	0.669186i	0.0710042	+	0.0341938i	0.469049	−	0.883172i	$-0.344597\pi$
$383$	1.38958	+	0.669186i	0.0710042	+	0.0341938i	−0.398045	+	0.917366i	$0.630311\pi$
$384$	2.30622	+	10.1042i	0.117689	+	0.515629i
$385$	0.698356	−	3.05970i	0.0355915	−	0.155937i
$386$	−13.1065			−0.667104
$387$	6.81529	−	20.5500i	0.346441	−	1.04461i
$388$	4.47088			0.226974
$389$	3.13098	−	13.7177i	0.158747	−	0.695516i	−0.831422	−	0.555641i	$-0.812473\pi$
$389$	3.13098	−	13.7177i	0.158747	−	0.695516i	0.990169	−	0.139875i	$-0.0446700\pi$
$390$	−0.552648	−	2.42131i	−0.0279844	−	0.122608i
$391$	−1.52600	−	0.734883i	−0.0771731	−	0.0371646i
$392$	−21.3904	+	26.8227i	−1.08038	+	1.35475i
$393$	−8.67220			−0.437455
$394$	28.2100			1.42120
$395$	3.06130	−	3.83875i	0.154031	−	0.193149i
$396$	0.986975	−	0.475302i	0.0495974	−	0.0238848i
$397$	0.964415	+	1.20934i	0.0484026	+	0.0606949i	0.805444	−	0.592672i	$-0.201927\pi$
$397$	0.964415	+	1.20934i	0.0484026	+	0.0606949i	−0.757041	+	0.653367i	$0.773356\pi$
$398$	24.6330	−	11.8626i	1.23474	−	0.594620i
$399$	−11.5666	+	50.6768i	−0.579056	+	2.53701i
$400$	5.21534	−	6.53983i	0.260767	−	0.326992i
$401$	7.94345	−	34.8025i	0.396677	−	1.73795i	−0.243661	−	0.969861i	$-0.578348\pi$
$401$	7.94345	−	34.8025i	0.396677	−	1.73795i	0.640337	−	0.768094i	$-0.278795\pi$
$402$	−25.8726	−	12.4596i	−1.29041	−	0.621428i
$403$	0.749445	+	0.939774i	0.0373325	+	0.0468135i
$404$	5.74386	+	7.20257i	0.285768	+	0.358341i
$405$	2.29354	+	10.0487i	0.113967	+	0.499322i
$406$	1.76216	+	0.848613i	0.0874547	+	0.0421160i
$407$	−1.92303	+	0.926083i	−0.0953211	+	0.0459042i
$408$	−1.71738	−	7.52432i	−0.0850228	−	0.372509i
$409$	0.226705	+	0.993257i	0.0112098	+	0.0491134i	0.980224	−	0.197894i	$-0.0634101\pi$
$409$	0.226705	+	0.993257i	0.0112098	+	0.0491134i	−0.969014	+	0.247007i	$0.920553\pi$
$410$	−4.49566	+	2.16499i	−0.222025	+	0.106921i
$411$	−6.18241	−	2.97729i	−0.304956	−	0.146859i
$412$	1.76413	+	7.72915i	0.0869123	+	0.380788i
$413$	13.2751	+	16.6465i	0.653226	+	0.819120i
$414$	4.15464	+	5.20975i	0.204189	+	0.256045i
$415$	0.327900	+	0.157908i	0.0160960	+	0.00775141i
$416$	0.454254	−	1.99022i	0.0222716	−	0.0975784i
$417$	15.9007	−	19.9388i	0.778660	−	0.976408i
$418$	−0.736856	+	3.22838i	−0.0360408	+	0.157905i
$419$	−4.61284	+	2.22143i	−0.225352	+	0.108524i	−0.543153	−	0.839634i	$-0.682770\pi$
$419$	−4.61284	+	2.22143i	−0.225352	+	0.108524i	0.317801	+	0.948157i	$0.397055\pi$
$420$	−4.98276	−	6.24819i	−0.243134	−	0.304880i
$421$	−3.46045	+	1.66647i	−0.168652	+	0.0812186i	−0.516305	−	0.856405i	$-0.672693\pi$
$421$	−3.46045	+	1.66647i	−0.168652	+	0.0812186i	0.347653	+	0.937623i	$0.386979\pi$
$422$	14.0524	−	17.6212i	0.684061	−	0.857785i
$423$	−17.2483			−0.838641
$424$	−24.2733			−1.17881
$425$	−2.08351	+	2.61263i	−0.101065	+	0.126731i
$426$	22.8179	+	10.9885i	1.10553	+	0.532396i
$427$	−11.4523	−	50.1757i	−0.554214	−	2.42817i
$428$	1.33096	−	5.83130i	0.0643341	−	0.281866i
$429$	0.925654			0.0446910
$430$	−10.0160	−	0.962784i	−0.483013	−	0.0464296i
$431$	−2.95017			−0.142105			−0.0710523	−	0.997473i	$-0.522636\pi$
$431$	−2.95017			−0.142105			−0.0710523	+	0.997473i	$0.522636\pi$
$432$	−0.421842	+	1.84821i	−0.0202959	+	0.0889221i
$433$	−2.19152	−	9.60168i	−0.105318	−	0.461427i	−0.999895	−	0.0145132i	$-0.995380\pi$
$433$	−2.19152	−	9.60168i	−0.105318	−	0.461427i	0.894577	−	0.446914i	$-0.147477\pi$
$434$	−8.52894	−	4.10732i	−0.409402	−	0.197158i
$435$	−0.776354	+	0.973517i	−0.0372233	+	0.0466766i
$436$	−0.513109			−0.0245734
$437$	8.23014			0.393701
$438$	−5.63089	+	7.06092i	−0.269055	+	0.337384i
$439$	19.8070	−	9.53856i	0.945337	−	0.455250i	0.103288	−	0.994651i	$-0.467064\pi$
$439$	19.8070	−	9.53856i	0.945337	−	0.455250i	0.842049	+	0.539401i	$0.181349\pi$
$440$	−1.41174	−	1.77027i	−0.0673022	−	0.0843943i
$441$	−33.1948	+	15.9858i	−1.58071	+	0.761228i
$442$	0.170957	−	0.749011i	0.00813159	−	0.0356268i
$443$	−0.804299	+	1.00856i	−0.0382134	+	0.0479181i	−0.800571	−	0.599238i	$-0.795470\pi$
$443$	−0.804299	+	1.00856i	−0.0382134	+	0.0479181i	0.762358	+	0.647156i	$0.224042\pi$
$444$	−1.20943	+	5.29888i	−0.0573972	+	0.251474i
$445$	−19.5196	−	9.40016i	−0.925319	−	0.445610i
$446$	−5.64478	−	7.07833i	−0.267288	−	0.335169i
$447$	14.9742	+	18.7771i	0.708255	+	0.888124i
$448$	8.32462	+	36.4725i	0.393301	+	1.72317i
$449$	5.70134	+	2.74562i	0.269063	+	0.129574i	0.563551	−	0.826081i	$-0.309435\pi$
$449$	5.70134	+	2.74562i	0.269063	+	0.129574i	−0.294488	+	0.955655i	$0.595149\pi$
$450$	11.8450	−	5.70424i	0.558378	−	0.268901i
$451$	−0.413833	−	1.81312i	−0.0194866	−	0.0853765i
$452$	−1.14990	−	5.03804i	−0.0540868	−	0.236970i
$453$	−27.0943	+	13.0479i	−1.27300	+	0.613046i
$454$	−10.3248	−	4.97215i	−0.484566	−	0.233354i
$455$	−0.787305	−	3.44941i	−0.0369094	−	0.161711i
$456$	23.3822	+	29.3204i	1.09497	+	1.37305i
$457$	0.573142	+	0.718697i	0.0268105	+	0.0336192i	0.795056	−	0.606536i	$-0.207441\pi$
$457$	0.573142	+	0.718697i	0.0268105	+	0.0336192i	−0.768246	+	0.640155i	$0.778870\pi$
$458$	−2.64627	−	1.27438i	−0.123652	−	0.0595477i
$459$	0.168524	−	0.738352i	0.00786603	−	0.0344633i
$460$	−0.788934	+	0.989292i	−0.0367842	+	0.0461260i
$461$	0.599633	−	2.62716i	0.0279277	−	0.122359i	−0.959043	−	0.283262i	$-0.908583\pi$
$461$	0.599633	−	2.62716i	0.0279277	−	0.122359i	0.986970	+	0.160903i	$0.0514405\pi$
$462$	−6.56800	+	3.16298i	−0.305571	+	0.147155i
$463$	17.8121	+	22.3357i	0.827801	+	1.03803i	0.998609	+	0.0527248i	$0.0167906\pi$
$463$	17.8121	+	22.3357i	0.827801	+	1.03803i	−0.170809	+	0.985304i	$0.554638\pi$
$464$	0.868692	−	0.418340i	0.0403280	−	0.0194210i
$465$	3.75758	−	4.71186i	0.174254	−	0.218507i
$466$	15.8052			0.732163
$467$	12.6855			0.587016			0.293508	−	0.955957i	$-0.405177\pi$
$467$	12.6855			0.587016			0.293508	+	0.955957i	$0.405177\pi$
$468$	0.770003	−	0.965553i	0.0355934	−	0.0446327i
$469$	−36.8583	−	17.7500i	−1.70196	−	0.819619i
$470$	1.78376	+	7.81517i	0.0822788	+	0.360487i
$471$	−2.14240	+	9.38649i	−0.0987168	+	0.432506i
$472$	15.3614			0.707064
$473$	1.18052	−	3.55961i	0.0542806	−	0.163671i
$474$	−11.4050			−0.523848
$475$	3.61326	−	15.8307i	0.165788	−	0.726363i
$476$	−0.550110	−	2.41019i	−0.0252143	−	0.110471i
$477$	−23.4860	−	11.3103i	−1.07535	−	0.517861i
$478$	−3.35216	+	4.20347i	−0.153324	+	0.192262i
$479$	18.2539			0.834044			0.417022	−	0.908896i	$-0.363074\pi$
$479$	18.2539			0.834044			0.417022	+	0.908896i	$0.363074\pi$
$480$	−10.2352			−0.467171
$481$	−1.50028	+	1.88129i	−0.0684069	+	0.0857795i
$482$	−11.6447	+	5.60778i	−0.530400	+	0.255427i
$483$	11.2966	+	14.1655i	0.514014	+	0.644553i
$484$	−5.57861	+	2.68652i	−0.253573	+	0.122114i
$485$	2.20833	−	9.67532i	0.100275	−	0.439334i
$486$	16.6153	−	20.8350i	0.753686	−	0.945093i
$487$	3.40222	−	14.9061i	0.154169	−	0.675459i	−0.837477	−	0.546472i	$-0.815970\pi$
$487$	3.40222	−	14.9061i	0.154169	−	0.675459i	0.991646	−	0.128987i	$-0.0411724\pi$
$488$	−33.4542	−	16.1107i	−1.51440	−	0.729297i
$489$	−0.550736	−	0.690601i	−0.0249051	−	0.0312300i
$490$	10.6760	+	13.3873i	0.482294	+	0.604777i
$491$	−6.78871	−	29.7433i	−0.306370	−	1.34230i	−0.860324	−	0.509748i	$-0.829739\pi$
$491$	−6.78871	−	29.7433i	−0.306370	−	1.34230i	0.553954	−	0.832548i	$-0.313118\pi$
$492$	−4.26677	−	2.05477i	−0.192361	−	0.0926360i
$493$	−0.347039	+	0.167125i	−0.0156298	+	0.00752693i
$494$	0.830709	+	3.63958i	0.0373754	+	0.163752i
$495$	−0.541088	−	2.37066i	−0.0243201	−	0.106553i
$496$	−4.20450	+	2.02478i	−0.188788	+	0.0909154i
$497$	32.5065	+	15.6543i	1.45812	+	0.702192i
$498$	−0.188114	−	0.824179i	−0.00842957	−	0.0369324i
$499$	−11.3027	−	14.1732i	−0.505980	−	0.634478i	0.461587	−	0.887095i	$-0.347280\pi$
$499$	−11.3027	−	14.1732i	−0.505980	−	0.634478i	−0.967566	+	0.252617i	$0.918709\pi$
$500$	3.88553	+	4.87230i	0.173766	+	0.217896i
$501$	−15.6036	−	7.51428i	−0.697116	−	0.335713i
$502$	7.20978	−	31.5881i	0.321788	−	1.40985i
$503$	24.6587	−	30.9210i	1.09948	−	1.37870i	0.180880	−	0.983505i	$-0.442105\pi$
$503$	24.6587	−	30.9210i	1.09948	−	1.37870i	0.918597	−	0.395196i	$-0.129323\pi$
$504$	−9.62540	+	42.1716i	−0.428750	+	1.87847i
$505$	18.4240	−	8.87254i	0.819858	−	0.394823i
$506$	0.719654	+	0.902417i	0.0319925	+	0.0401173i
$507$	−28.4621	+	13.7066i	−1.26405	+	0.608733i
$508$	−7.22591	+	9.06101i	−0.320598	+	0.402017i
$509$	6.44305			0.285583			0.142792	−	0.989753i	$-0.454392\pi$
$509$	6.44305			0.285583			0.142792	+	0.989753i	$0.454392\pi$
$510$	−3.85199			−0.170569
$511$	−8.02180	+	10.0590i	−0.354863	+	0.444985i
$512$	21.0079	+	10.1169i	0.928428	+	0.447107i
$513$	0.818888	+	3.58778i	0.0361548	+	0.158404i
$514$	4.90808	−	21.5037i	0.216486	−	0.948489i
$515$	17.5978			0.775453
$516$	−5.21250	−	8.00183i	−0.229467	−	0.352261i
$517$	−2.98770			−0.131399
$518$	4.21686	−	18.4753i	0.185278	−	0.811756i
$519$	−8.26746	−	36.2221i	−0.362901	−	1.58997i
$520$	−2.29987	−	1.10756i	−0.100856	−	0.0485696i
$521$	19.5362	−	24.4976i	0.855895	−	1.07326i	−0.140638	−	0.990061i	$-0.544916\pi$
$521$	19.5362	−	24.4976i	0.855895	−	1.07326i	0.996533	−	0.0831970i	$-0.0265131\pi$
$522$	1.51540			0.0663273
$523$	12.9942			0.568195			0.284097	−	0.958795i	$-0.408306\pi$
$523$	12.9942			0.568195			0.284097	+	0.958795i	$0.408306\pi$
$524$	−1.24958	+	1.56692i	−0.0545881	+	0.0684513i
$525$	32.2069	−	15.5100i	1.40563	−	0.676914i
$526$	10.9138	+	13.6855i	0.475864	+	0.596715i
$527$	1.67968	−	0.808892i	0.0731681	−	0.0352359i
$528$	−0.799676	+	3.50361i	−0.0348014	+	0.152475i
$529$	−12.5516	+	15.7393i	−0.545724	+	0.684316i
$530$	−2.69581	+	11.8111i	−0.117099	+	0.513042i
$531$	14.8631	+	7.15770i	0.645005	+	0.310618i
$532$	7.48980	+	9.39192i	0.324724	+	0.407191i
$533$	−1.30722	−	1.63921i	−0.0566221	−	0.0710019i
$534$	11.1983	+	49.0628i	0.484596	+	2.12315i
$535$	−11.9620	−	5.76058i	−0.517161	−	0.249052i
$536$	−26.5923	+	12.8062i	−1.14861	+	0.553142i
$537$	9.34539	+	40.9448i	0.403283	+	1.76690i
$538$	0.169765	+	0.743791i	0.00731910	+	0.0320671i
$539$	−5.74990	+	2.76901i	−0.247666	+	0.119270i
$540$	−0.509762	−	0.245489i	−0.0219367	−	0.0105641i
$541$	−0.261598	−	1.14613i	−0.0112470	−	0.0492761i	0.968993	−	0.247088i	$-0.0794737\pi$
$541$	−0.261598	−	1.14613i	−0.0112470	−	0.0492761i	−0.980240	+	0.197812i	$0.936617\pi$
$542$	0.226002	+	0.283398i	0.00970762	+	0.0121730i
$543$	34.2457	+	42.9427i	1.46962	+	1.84285i
$544$	−2.85262	−	1.37375i	−0.122305	−	0.0588991i
$545$	−0.253443	+	1.11041i	−0.0108563	+	0.0475646i
$546$	−5.12412	+	6.42544i	−0.219292	+	0.274984i
$547$	6.24471	−	27.3599i	0.267005	−	1.16982i	−0.646474	−	0.762936i	$-0.723757\pi$
$547$	6.24471	−	27.3599i	0.267005	−	1.16982i	0.913478	−	0.406887i	$-0.133386\pi$
$548$	−1.42877	+	0.688059i	−0.0610340	+	0.0293924i
$549$	−24.8623	−	31.1763i	−1.06110	−	1.33057i
$550$	2.05175	−	0.988072i	0.0874870	−	0.0421315i
$551$	1.16697	−	1.46333i	0.0497146	−	0.0623402i
$552$	13.0719			0.556378
$553$	−16.2476			−0.690918
$554$	−23.9129	+	29.9858i	−1.01596	+	1.27397i
$555$	10.8698	+	5.23462i	0.461397	+	0.222197i
$556$	−1.31148	−	5.74597i	−0.0556192	−	0.243683i
$557$	−4.46043	+	19.5424i	−0.188994	+	0.828039i	0.788153	+	0.615479i	$0.211037\pi$
$557$	−4.46043	+	19.5424i	−0.188994	+	0.828039i	−0.977148	+	0.212560i	$0.931820\pi$
$558$	−7.33460			−0.310498
$559$	−0.542084	−	4.19303i	−0.0229277	−	0.177346i
$560$	13.7362			0.580461
$561$	0.319467	−	1.39968i	0.0134879	−	0.0590944i
$562$	−0.348957	−	1.52888i	−0.0147199	−	0.0644920i
$563$	19.0901	+	9.19331i	0.804552	+	0.387452i	0.790509	−	0.612450i	$-0.209816\pi$
$563$	19.0901	+	9.19331i	0.804552	+	0.387452i	0.0140421	+	0.999901i	$0.495530\pi$
$564$	−4.74352	+	5.94819i	−0.199738	+	0.250464i
$565$	−11.4707			−0.482576
$566$	−12.5980			−0.529532
$567$	21.2656	−	26.6662i	0.893070	−	1.11987i
$568$	23.4526	−	11.2942i	0.984049	−	0.473893i
$569$	20.6293	+	25.8684i	0.864827	+	1.08446i	0.995661	+	0.0930547i	$0.0296632\pi$
$569$	20.6293	+	25.8684i	0.864827	+	1.08446i	−0.130834	+	0.991404i	$0.541765\pi$
$570$	16.8639	−	8.12120i	0.706349	−	0.340160i
$571$	2.04663	−	8.96685i	0.0856486	−	0.375251i	−0.913879	−	0.405987i	$-0.866928\pi$
$571$	2.04663	−	8.96685i	0.0856486	−	0.375251i	0.999528	+	0.0307357i	$0.00978501\pi$
$572$	0.133378	−	0.167250i	0.00557679	−	0.00699308i
$573$	1.30853	−	5.73304i	0.0546646	−	0.239501i
$574$	14.8767	+	7.16422i	0.620940	+	0.299029i
$575$	−3.52890	−	4.42510i	−0.147165	−	0.184540i
$576$	18.0723	+	22.6620i	0.753013	+	0.944248i
$577$	6.02342	+	26.3903i	0.250758	+	1.09864i	0.930817	+	0.365486i	$0.119097\pi$
$577$	6.02342	+	26.3903i	0.250758	+	1.09864i	−0.680059	+	0.733158i	$0.738046\pi$
$578$	−1.07358	−	0.517007i	−0.0446548	−	0.0215046i
$579$	−24.8773	+	11.9803i	−1.03387	+	0.497883i
$580$	0.0640333	+	0.280548i	0.00265884	+	0.0116491i
$581$	−0.267987	−	1.17413i	−0.0111180	−	0.0487111i
$582$	−20.7692	+	10.0019i	−0.860912	+	0.414594i
$583$	−4.06817	−	1.95913i	−0.168486	−	0.0811388i
$584$	2.06554	+	9.04972i	0.0854727	+	0.374480i
$585$	−1.70920	−	2.14327i	−0.0706667	−	0.0886132i
$586$	−12.1073	−	15.1821i	−0.500148	−	0.627165i
$587$	34.8872	+	16.8008i	1.43995	+	0.693443i	0.980818	−	0.194925i	$-0.0624465\pi$
$587$	34.8872	+	16.8008i	1.43995	+	0.693443i	0.459131	+	0.888368i	$0.348161\pi$
$588$	−3.61623	+	15.8438i	−0.149131	+	0.653386i
$589$	−5.64818	+	7.08260i	−0.232729	+	0.291833i
$590$	1.70605	−	7.47468i	0.0702368	−	0.307728i
$591$	53.5449	−	25.7859i	2.20254	−	1.06069i
$592$	−5.82461	−	7.30383i	−0.239390	−	0.300186i
$593$	−18.3278	+	8.82622i	−0.752634	+	0.362450i	−0.770541	−	0.637390i	$-0.780014\pi$
$593$	−18.3278	+	8.82622i	−0.752634	+	0.362450i	0.0179071	+	0.999840i	$0.494300\pi$
$594$	−0.321788	+	0.403510i	−0.0132031	+	0.0165562i
$595$	−5.48756			−0.224968
$596$	5.55033			0.227350
$597$	35.9123	−	45.0326i	1.46979	−	1.84306i
$598$	1.17239	+	0.564591i	0.0479424	+	0.0230878i
$599$	2.76173	+	12.0999i	0.112841	+	0.494389i	0.999490	+	0.0319453i	$0.0101702\pi$
$599$	2.76173	+	12.0999i	0.112841	+	0.494389i	−0.886648	+	0.462444i	$0.846973\pi$
$600$	5.73893	−	25.1439i	0.234291	−	1.02650i
$601$	−26.7739			−1.09213			−0.546066	−	0.837742i	$-0.683875\pi$
$601$	−26.7739			−1.09213			−0.546066	+	0.837742i	$0.683875\pi$
$602$	18.1741	+	27.8995i	0.740720	+	1.13710i
$603$	−31.6968			−1.29080
$604$	−1.54648	+	6.77557i	−0.0629253	+	0.275694i
$605$	3.05835	+	13.3995i	0.124340	+	0.544768i
$606$	−42.7959	−	20.6094i	−1.73846	−	0.837200i
$607$	13.5348	−	16.9722i	0.549362	−	0.688878i	−0.427189	−	0.904162i	$-0.640496\pi$
$607$	13.5348	−	16.9722i	0.549362	−	0.688878i	0.976552	+	0.215284i	$0.0690676\pi$
$608$	15.3850			0.623943
$609$	4.12043			0.166968
$610$	−11.5548	+	14.4892i	−0.467838	+	0.586651i
$611$	−3.03468	+	1.46142i	−0.122770	+	0.0591229i
$612$	−1.19426	−	1.49756i	−0.0482751	−	0.0605351i
$613$	31.4348	−	15.1382i	1.26964	−	0.611426i	0.326933	−	0.945048i	$-0.393985\pi$
$613$	31.4348	−	15.1382i	1.26964	−	0.611426i	0.942707	+	0.333621i	$0.108271\pi$
$614$	1.00219	−	4.39089i	0.0404452	−	0.177202i
$615$	−6.55418	+	8.21869i	−0.264290	+	0.331409i
$616$	−1.66728	+	7.30484i	−0.0671767	+	0.294321i
$617$	−34.5086	−	16.6185i	−1.38926	−	0.669034i	−0.418311	−	0.908304i	$-0.637378\pi$
$617$	−34.5086	−	16.6185i	−1.38926	−	0.669034i	−0.970953	+	0.239270i	$0.923092\pi$
$618$	−25.4863	−	31.9588i	−1.02521	−	1.28557i
$619$	28.3950	+	35.6062i	1.14129	+	1.43113i	0.885645	+	0.464362i	$0.153716\pi$
$619$	28.3950	+	35.6062i	1.14129	+	1.43113i	0.255645	+	0.966771i	$0.417712\pi$
$620$	−0.309924	−	1.35786i	−0.0124468	−	0.0545331i
$621$	1.15570	+	0.556557i	0.0463767	+	0.0223338i
$622$	−24.1455	+	11.6278i	−0.968145	+	0.466234i
$623$	15.9531	+	69.8950i	0.639147	+	2.80029i
$624$	0.901531	+	3.94986i	0.0360901	+	0.158121i
$625$	−2.59054	+	1.24754i	−0.103622	+	0.0499016i
$626$	−8.02092	−	3.86267i	−0.320580	−	0.154383i
$627$	1.55235	+	6.80127i	0.0619947	+	0.271617i
$628$	1.38728	+	1.73960i	0.0553586	+	0.0694174i
$629$	2.32691	+	2.91785i	0.0927799	+	0.116342i
$630$	19.4513	+	9.36724i	0.774957	+	0.373200i
$631$	−8.12038	+	35.5777i	−0.323267	+	1.41633i	0.508433	+	0.861102i	$0.330225\pi$
$631$	−8.12038	+	35.5777i	−0.323267	+	1.41633i	−0.831700	+	0.555225i	$0.812632\pi$
$632$	−7.30868	+	9.16479i	−0.290723	+	0.364556i
$633$	10.5657	−	46.2913i	0.419949	−	1.83992i
$634$	3.30024	−	1.58931i	0.131069	−	0.0631196i
$635$	16.0396	+	20.1130i	0.636511	+	0.798160i
$636$	−10.3594	+	4.98882i	−0.410776	+	0.197819i
$637$	−4.48587	+	5.62510i	−0.177737	+	0.222875i
$638$	0.262493			0.0103922
$639$	27.9545			1.10586
$640$	3.31485	−	4.15670i	0.131031	−	0.164308i
$641$	7.48412	+	3.60416i	0.295605	+	0.142356i	0.575808	−	0.817585i	$-0.304688\pi$
$641$	7.48412	+	3.60416i	0.295605	+	0.142356i	−0.280203	+	0.959941i	$0.590402\pi$
$642$	6.86249	+	30.0665i	0.270841	+	1.18663i
$643$	−9.22328	+	40.4098i	−0.363731	+	1.59361i	0.379906	+	0.925025i	$0.375956\pi$
$643$	−9.22328	+	40.4098i	−0.363731	+	1.59361i	−0.743637	+	0.668583i	$0.766901\pi$
$644$	4.18720			0.164999
$645$	−19.8912	+	7.32785i	−0.783216	+	0.288534i
$646$	5.79009			0.227808
$647$	−1.17064	+	5.12891i	−0.0460227	+	0.201638i	−0.992712	−	0.120509i	$-0.961547\pi$
$647$	−1.17064	+	5.12891i	−0.0460227	+	0.201638i	0.946690	+	0.322147i	$0.104405\pi$
$648$	−5.47569	−	23.9906i	−0.215106	−	0.942439i
$649$	2.57455	+	1.23984i	0.101060	+	0.0486678i
$650$	1.60070	−	2.00722i	0.0627847	−	0.0787296i
$651$	−19.9430			−0.781629
$652$	−0.204136			−0.00799456
$653$	−20.9275	+	26.2422i	−0.818956	+	1.02694i	0.180107	+	0.983647i	$0.442356\pi$
$653$	−20.9275	+	26.2422i	−0.818956	+	1.02694i	−0.999063	+	0.0432911i	$0.986216\pi$
$654$	2.38362	−	1.14789i	0.0932069	−	0.0448861i
$655$	2.77373	+	3.47814i	0.108379	+	0.135902i
$656$	7.33373	−	3.53174i	0.286334	−	0.137891i
$657$	−2.21822	+	9.71865i	−0.0865409	+	0.379160i
$658$	16.5389	−	20.7392i	0.644754	−	0.808496i
$659$	8.64524	−	37.8773i	0.336771	−	1.47549i	−0.468966	−	0.883216i	$-0.655373\pi$
$659$	8.64524	−	37.8773i	0.336771	−	1.47549i	0.805737	−	0.592273i	$-0.201769\pi$
$660$	−0.966344	−	0.465367i	−0.0376149	−	0.0181144i
$661$	−0.401902	−	0.503969i	−0.0156322	−	0.0196021i	0.773954	−	0.633242i	$-0.218276\pi$
$661$	−0.401902	−	0.503969i	−0.0156322	−	0.0196021i	−0.789586	+	0.613640i	$0.789705\pi$
$662$	−9.00408	−	11.2908i	−0.349953	−	0.438828i
$663$	−0.360158	−	1.57795i	−0.0139874	−	0.0612827i
$664$	−0.782842	−	0.376997i	−0.0303801	−	0.0146303i
$665$	24.0243	−	11.5695i	0.931623	−	0.448646i
$666$	−3.26723	−	14.3147i	−0.126603	−	0.554682i
$667$	−0.145172	−	0.636041i	−0.00562109	−	0.0246276i
$668$	−3.60602	+	1.73657i	−0.139521	+	0.0671899i
$669$	−17.1844	−	8.27555i	−0.664386	−	0.319951i
$670$	3.27798	+	14.3618i	0.126640	+	0.554844i
$671$	−4.30657	−	5.40027i	−0.166253	−	0.208475i
$672$	21.1173	+	26.4802i	0.814617	+	1.02150i
$673$	−33.5280	−	16.1462i	−1.29241	−	0.622392i	−0.343860	−	0.939021i	$-0.611735\pi$
$673$	−33.5280	−	16.1462i	−1.29241	−	0.622392i	−0.948549	+	0.316629i	$0.897449\pi$
$674$	−4.80412	+	21.0482i	−0.185048	+	0.810747i
$675$	1.57792	−	1.97865i	0.0607343	−	0.0761584i
$676$	−1.62455	+	7.11762i	−0.0624827	+	0.273754i
$677$	−25.3918	+	12.2281i	−0.975886	+	0.469962i	−0.852688	−	0.522420i	$-0.825029\pi$
$677$	−25.3918	+	12.2281i	−0.975886	+	0.469962i	−0.123198	+	0.992382i	$0.539315\pi$
$678$	16.6126	+	20.8315i	0.638002	+	0.800029i
$679$	−29.5879	+	14.2488i	−1.13548	+	0.546819i
$680$	−2.46848	+	3.09537i	−0.0946617	+	0.118702i
$681$	−24.1422			−0.925131
$682$	−1.27048			−0.0486491
$683$	8.97377	−	11.2527i	0.343372	−	0.430574i	−0.579920	−	0.814673i	$-0.696916\pi$
$683$	8.97377	−	11.2527i	0.343372	−	0.430574i	0.923292	+	0.384099i	$0.125488\pi$
$684$	8.38575	+	4.03836i	0.320637	+	0.154411i
$685$	0.783292	+	3.43183i	0.0299280	+	0.131123i
$686$	4.69921	−	20.5886i	0.179417	−	0.786075i
$687$	−6.18772			−0.236076
$688$	16.3390	+	1.57058i	0.622918	+	0.0598779i
$689$	−5.09044			−0.193930
$690$	1.45178	−	6.36066i	0.0552683	−	0.242146i
$691$	−4.55934	−	19.9758i	−0.173445	−	0.759914i	−0.984563	−	0.175031i	$-0.943998\pi$
$691$	−4.55934	−	19.9758i	−0.173445	−	0.759914i	0.811118	−	0.584883i	$-0.198860\pi$
$692$	−7.73599	−	3.72545i	−0.294078	−	0.141621i
$693$	−5.01693	+	6.29103i	−0.190577	+	0.238977i
$694$	3.30390			0.125414
$695$	−13.0825			−0.496248
$696$	1.85350	−	2.32421i	0.0702567	−	0.0880991i
$697$	−2.92979	+	1.41091i	−0.110974	+	0.0534422i
$698$	24.5250	+	30.7533i	0.928284	+	1.16403i
$699$	29.9997	−	14.4471i	1.13469	−	0.546438i
$700$	1.83829	−	8.05410i	0.0694810	−	0.304416i
$701$	24.9775	−	31.3208i	0.943389	−	1.18297i	−0.0395832	−	0.999216i	$-0.512603\pi$
$701$	24.9775	−	31.3208i	0.943389	−	1.18297i	0.982972	−	0.183756i	$-0.0588256\pi$
$702$	−0.129473	+	0.567257i	−0.00488663	+	0.0214097i
$703$	−16.3389	−	7.86838i	−0.616232	−	0.296762i
$704$	3.13043	+	3.92544i	0.117983	+	0.147945i
$705$	10.5293	+	13.2034i	0.396558	+	0.497268i
$706$	4.92973	+	21.5986i	0.185533	+	0.812873i
$707$	−60.9672	−	29.3603i	−2.29291	−	1.10421i
$708$	6.55595	−	3.15718i	0.246388	−	0.118654i
$709$	1.15556	+	5.06283i	0.0433979	+	0.190138i	0.991980	−	0.126391i	$-0.0403395\pi$
$709$	1.15556	+	5.06283i	0.0433979	+	0.190138i	−0.948583	+	0.316530i	$0.897482\pi$
$710$	−2.89096	−	12.6661i	−0.108496	−	0.475351i
$711$	−11.3420	+	5.46202i	−0.425358	+	0.204842i
$712$	46.6019	+	22.4423i	1.74648	+	0.841061i
$713$	0.702640	+	3.07847i	0.0263141	+	0.115289i
$714$	7.94742	+	9.96575i	0.297425	+	0.372959i
$715$	−0.296062	−	0.371250i	−0.0110721	−	0.0138840i
$716$	8.74462	+	4.21119i	0.326802	+	0.157379i
$717$	−2.52041	+	11.0426i	−0.0941265	+	0.412395i
$718$	11.6022	−	14.5487i	0.432989	−	0.542951i
$719$	−6.05570	+	26.5318i	−0.225840	+	0.989468i	0.727153	+	0.686475i	$0.240843\pi$
$719$	−6.05570	+	26.5318i	−0.225840	+	0.989468i	−0.952993	+	0.302993i	$0.902014\pi$
$720$	9.58887	−	4.61776i	0.357356	−	0.172094i
$721$	−36.3079	−	45.5286i	−1.35218	−	1.69557i
$722$	−4.95085	+	2.38420i	−0.184252	+	0.0887309i
$723$	−16.9767	+	21.2881i	−0.631370	+	0.791713i
$724$	12.6935			0.471750
$725$	−1.28716			−0.0478041
$726$	19.9051	−	24.9602i	0.738747	−	0.926359i
$727$	−22.1634	−	10.6733i	−0.821995	−	0.395852i	−0.0248884	−	0.999690i	$-0.507923\pi$
$727$	−22.1634	−	10.6733i	−0.821995	−	0.395852i	−0.797107	+	0.603838i	$0.793637\pi$
$728$	1.87964	+	8.23526i	0.0696643	+	0.305219i
$729$	7.14958	−	31.3244i	0.264799	−	1.16016i
$730$	4.63290			0.171471
$731$	−6.52735	−	0.627441i	−0.241423	−	0.0232067i
$732$	−17.5888			−0.650102
$733$	1.11860	−	4.90091i	0.0413164	−	0.181019i	−0.950059	−	0.312069i	$-0.898978\pi$
$733$	1.11860	−	4.90091i	0.0413164	−	0.181019i	0.991376	+	0.131050i	$0.0418350\pi$
$734$	9.78414	+	42.8671i	0.361139	+	1.58225i
$735$	32.5009	+	15.6516i	1.19882	+	0.577319i
$736$	3.34356	−	4.19269i	0.123245	−	0.154545i
$737$	−5.49043			−0.202243
$738$	12.7934			0.470932
$739$	−13.5989	+	17.0525i	−0.500245	+	0.627287i	−0.966284	−	0.257477i	$-0.917109\pi$
$739$	−13.5989	+	17.0525i	−0.500245	+	0.627287i	0.466040	+	0.884764i	$0.345680\pi$
$740$	2.51204	−	1.20973i	0.0923443	−	0.0444707i
$741$	4.90358	+	6.14890i	0.180138	+	0.225885i
$742$	36.1194	−	17.3942i	1.32598	−	0.638561i
$743$	−10.4863	+	45.9433i	−0.384704	+	1.68550i	0.297810	+	0.954625i	$0.403744\pi$
$743$	−10.4863	+	45.9433i	−0.384704	+	1.68550i	−0.682514	+	0.730873i	$0.739113\pi$
$744$	−8.97100	+	11.2493i	−0.328893	+	0.412419i
$745$	2.74151	−	12.0113i	0.100441	−	0.440062i
$746$	−9.34864	−	4.50207i	−0.342278	−	0.164832i
$747$	−0.581787	−	0.729538i	−0.0212865	−	0.0266924i
$748$	−0.206866	−	0.259402i	−0.00756378	−	0.00948467i
$749$	9.77633	+	42.8329i	0.357219	+	1.56508i
$750$	−28.9500	−	13.9416i	−1.05710	−	0.509074i
$751$	9.01471	−	4.34126i	0.328951	−	0.158415i	−0.262117	−	0.965036i	$-0.584421\pi$
$751$	9.01471	−	4.34126i	0.328951	−	0.158415i	0.591068	+	0.806621i	$0.298706\pi$
$752$	−2.90984	−	12.7488i	−0.106111	−	0.464902i
$753$	−15.1889	−	66.5471i	−0.553516	−	2.42511i
$754$	0.266621	−	0.128398i	0.00970975	−	0.00467597i
$755$	13.8990	+	6.69340i	0.505836	+	0.243598i
$756$	0.416621	+	1.82533i	0.0151523	+	0.0663868i
$757$	−21.9142	−	27.4795i	−0.796484	−	0.998760i	−0.999807	−	0.0196481i	$-0.993745\pi$
$757$	−21.9142	−	27.4795i	−0.796484	−	0.998760i	0.203322	−	0.979112i	$-0.434826\pi$
$758$	−1.09334	−	1.37100i	−0.0397117	−	0.0497969i
$759$	2.19084	+	1.05505i	0.0795223	+	0.0382959i
$760$	4.28088	−	18.7557i	0.155284	−	0.680342i
$761$	−23.5861	+	29.5760i	−0.854995	+	1.07213i	0.141620	+	0.989921i	$0.454769\pi$
$761$	−23.5861	+	29.5760i	−0.854995	+	1.07213i	−0.996615	+	0.0822091i	$0.973802\pi$
$762$	13.2970	−	58.2578i	0.481698	−	2.11046i
$763$	3.39572	−	1.63529i	0.122933	−	0.0592015i
$764$	−0.847319	−	1.06250i	−0.0306549	−	0.0384400i
$765$	−3.83071	+	1.84477i	−0.138500	+	0.0666980i
$766$	−1.14584	+	1.43684i	−0.0414010	+	0.0519153i
$767$	3.22149			0.116321
$768$	31.7268			1.14484
$769$	19.2356	−	24.1207i	0.693655	−	0.869816i	−0.302877	−	0.953030i	$-0.597947\pi$
$769$	19.2356	−	24.1207i	0.693655	−	0.869816i	0.996532	+	0.0832141i	$0.0265185\pi$
$770$	3.36929	+	1.62256i	0.121421	+	0.0584732i
$771$	−10.3399	−	45.3022i	−0.372384	−	1.63152i
$772$	−1.41994	+	6.22115i	−0.0511046	+	0.223904i
$773$	−8.47879			−0.304961			−0.152480	−	0.988306i	$-0.548726\pi$
$773$	−8.47879			−0.304961			−0.152480	+	0.988306i	$0.548726\pi$
$774$	22.0659	+	13.3662i	0.793142	+	0.480438i
$775$	6.22992			0.223785
$776$	−5.27225	+	23.0993i	−0.189263	+	0.829215i
$777$	−8.88372	−	38.9221i	−0.318702	−	1.39632i
$778$	15.1057	+	7.27454i	0.541567	+	0.260805i
$779$	9.85188	−	12.3539i	0.352980	−	0.442623i
$780$	−1.20917			−0.0432953
$781$	4.84219			0.173267
$782$	1.25834	−	1.57790i	0.0449980	−	0.0564257i
$783$	0.262827	−	0.126571i	0.00939265	−	0.00452326i
$784$	−17.4157	−	21.8386i	−0.621990	−	0.779950i
$785$	4.44985	−	2.14293i	0.158822	−	0.0764846i
$786$	2.29945	−	10.0745i	0.0820185	−	0.359346i
$787$	31.2626	−	39.2020i	1.11439	−	1.39740i	0.206370	−	0.978474i	$-0.433835\pi$
$787$	31.2626	−	39.2020i	1.11439	−	1.39740i	0.908020	−	0.418927i	$-0.137594\pi$
$788$	3.05622	−	13.3902i	0.108873	−	0.477005i
$789$	33.2248	+	16.0002i	1.18283	+	0.569623i
$790$	3.64778	+	4.57417i	0.129782	+	0.162742i
$791$	23.6663	+	29.6767i	0.841478	+	1.05518i
$792$	1.29181	+	5.65981i	0.0459026	+	0.201113i
$793$	−7.01581	−	3.37864i	−0.249139	−	0.119979i
$794$	−1.66061	+	0.799707i	−0.0589328	+	0.0283805i
$795$	5.67931	+	24.8827i	0.201424	+	0.882497i
$796$	−2.96203	−	12.9775i	−0.104986	−	0.459975i
$797$	−33.7495	+	16.2529i	−1.19547	+	0.575708i	−0.922381	−	0.386281i	$-0.873760\pi$
$797$	−33.7495	+	16.2529i	−1.19547	+	0.575708i	−0.273089	+	0.961989i	$0.588045\pi$
$798$	−55.8045	−	26.8740i	−1.97546	−	0.951330i
$799$	1.16247	+	5.09310i	0.0411251	+	0.180181i
$800$	−6.59674	−	8.27205i	−0.233230	−	0.292461i
$801$	34.6333	+	43.4288i	1.22371	+	1.53448i
$802$	38.3240	+	18.4559i	1.35327	+	0.651699i
$803$	−0.384233	+	1.68343i	−0.0135593	+	0.0594071i
$804$	−8.71707	+	10.9309i	−0.307427	+	0.385502i
$805$	2.06821	−	9.06142i	0.0728948	−	0.319373i
$806$	−1.29045	+	0.621450i	−0.0454543	+	0.0218897i
$807$	1.00211	+	1.25660i	0.0352758	+	0.0442344i
$808$	−43.9863	+	21.1827i	−1.54743	+	0.745203i
$809$	−30.3178	+	38.0173i	−1.06592	+	1.33662i	−0.127219	+	0.991875i	$0.540605\pi$
$809$	−30.3178	+	38.0173i	−1.06592	+	1.33662i	−0.938697	+	0.344742i	$0.887966\pi$
$810$	−12.2817			−0.431535
$811$	−13.8697			−0.487031			−0.243515	−	0.969897i	$-0.578301\pi$
$811$	−13.8697			−0.487031			−0.243515	+	0.969897i	$0.578301\pi$
$812$	0.593713	−	0.744492i	0.0208352	−	0.0261266i
$813$	0.688016	+	0.331331i	0.0241298	+	0.0116203i
$814$	−0.565940	−	2.47954i	−0.0198362	−	0.0869079i
$815$	−0.100830	+	0.441765i	−0.00353192	+	0.0154744i
$816$	6.28371			0.219974
$817$	29.8993	−	11.0148i	1.04605	−	0.385359i
$818$	−1.21398			−0.0424459
$819$	−2.01858	+	8.84398i	−0.0705349	+	0.309034i
$820$	0.540586	+	2.36846i	0.0188781	+	0.0827103i
$821$	−15.4287	−	7.43007i	−0.538466	−	0.259311i	0.144826	−	0.989457i	$-0.453738\pi$
$821$	−15.4287	−	7.43007i	−0.538466	−	0.259311i	−0.683291	+	0.730146i	$0.739452\pi$
$822$	5.09800	−	6.39269i	0.177813	−	0.222971i
$823$	−53.0127			−1.84791			−0.923954	−	0.382505i	$-0.875062\pi$
$823$	−53.0127			−1.84791			−0.923954	+	0.382505i	$0.875062\pi$
$824$	−42.0138			−1.46362
$825$	2.99123	−	3.75089i	0.104141	−	0.130589i
$826$	−22.8582	+	11.0079i	−0.795338	+	0.383015i
$827$	25.9475	+	32.5371i	0.902282	+	1.13143i	0.990798	+	0.135351i	$0.0432162\pi$
$827$	25.9475	+	32.5371i	0.902282	+	1.13143i	−0.0885158	+	0.996075i	$0.528212\pi$
$828$	2.92297	−	1.40763i	0.101580	−	0.0489184i
$829$	−6.35147	+	27.8276i	−0.220596	+	0.966493i	0.736435	+	0.676508i	$0.236508\pi$
$829$	−6.35147	+	27.8276i	−0.220596	+	0.966493i	−0.957031	+	0.289985i	$0.906350\pi$
$830$	−0.270386	+	0.339053i	−0.00938522	+	0.0117687i
$831$	−17.9796	+	78.7736i	−0.623704	+	2.73262i
$832$	5.09977	+	2.45592i	0.176803	+	0.0851438i
$833$	6.95750	+	8.72443i	0.241063	+	0.302284i
$834$	18.9469	+	23.7587i	0.656078	+	0.822696i
$835$	1.97692	+	8.66147i	0.0684143	+	0.299742i
$836$	1.45255	+	0.699513i	0.0502376	+	0.0241932i
$837$	−1.27209	+	0.612607i	−0.0439699	+	0.0211748i
$838$	−1.35754	−	5.94776i	−0.0468954	−	0.205462i
$839$	6.50492	+	28.4999i	0.224575	+	0.983927i	0.953986	+	0.299851i	$0.0969370\pi$
$839$	6.50492	+	28.4999i	0.224575	+	0.983927i	−0.729411	+	0.684076i	$0.760206\pi$
$840$	38.1578	−	18.3758i	1.31657	−	0.634027i
$841$	25.9944	+	12.5183i	0.896359	+	0.431664i
$842$	−1.01840	−	4.46189i	−0.0350963	−	0.153767i
$843$	−2.05986	−	2.58298i	−0.0709452	−	0.0889625i
$844$	−6.84166	−	8.57917i	−0.235500	−	0.295307i
$845$	14.6006	+	7.03130i	0.502278	+	0.241884i
$846$	4.57341	−	20.0374i	0.157237	−	0.688900i
$847$	28.3569	−	35.5584i	0.974353	−	1.22180i
$848$	4.39766	−	19.2674i	0.151016	−	0.661645i
$849$	−23.9120	+	11.5154i	−0.820658	+	0.395208i
$850$	−2.48266	−	3.11316i	−0.0851546	−	0.106780i
$851$	−5.69514	+	2.74263i	−0.195227	+	0.0940163i
$852$	7.68788	−	9.64029i	0.263382	−	0.330271i
$853$	51.4295			1.76091			0.880457	−	0.474127i	$-0.157236\pi$
$853$	51.4295			1.76091			0.880457	+	0.474127i	$0.157236\pi$
$854$	61.3258			2.09853
$855$	12.8814	−	16.1527i	0.440533	−	0.552411i
$856$	28.5585	+	13.7530i	0.976109	+	0.470069i
$857$	−7.17169	−	31.4212i	−0.244980	−	1.07333i	−0.936416	−	0.350891i	$-0.885879\pi$
$857$	−7.17169	−	31.4212i	−0.244980	−	1.07333i	0.691436	−	0.722438i	$-0.256978\pi$
$858$	−0.245438	+	1.07534i	−0.00837912	+	0.0367113i
$859$	22.2094			0.757775			0.378887	−	0.925443i	$-0.376307\pi$
$859$	22.2094			0.757775			0.378887	+	0.925443i	$0.376307\pi$
$860$	−1.54211	+	4.64988i	−0.0525854	+	0.158560i
$861$	34.7858			1.18550
$862$	0.782241	−	3.42722i	0.0266432	−	0.116732i
$863$	6.62983	+	29.0472i	0.225682	+	0.988778i	0.953117	+	0.302602i	$0.0978552\pi$
$863$	6.62983	+	29.0472i	0.225682	+	0.988778i	−0.727435	+	0.686177i	$0.759288\pi$
$864$	2.16041	+	1.04040i	0.0734986	+	0.0353950i
$865$	−11.8833	+	14.9011i	−0.404043	+	0.506654i
$866$	11.7354			0.398784
$867$	−2.51032			−0.0852548
$868$	−2.87359	+	3.60337i	−0.0975361	+	0.122306i
$869$	−1.96463	+	0.946114i	−0.0666454	+	0.0320947i
$870$	−0.925086	−	1.16002i	−0.0313634	−	0.0393284i
$871$	−5.57677	+	2.68563i	−0.188962	+	0.0909991i
$872$	0.605080	−	2.65103i	0.0204906	−	0.0897752i
$873$	−15.8645	+	19.8934i	−0.536930	+	0.673290i
$874$	−2.18223	+	9.56097i	−0.0738150	+	0.323405i
$875$	−41.2423	−	19.8612i	−1.39424	−	0.671432i
$876$	2.74150	+	3.43773i	0.0926266	+	0.116150i
$877$	−15.7157	−	19.7069i	−0.530682	−	0.665454i	0.442157	−	0.896938i	$-0.354213\pi$
$877$	−15.7157	−	19.7069i	−0.530682	−	0.665454i	−0.972839	+	0.231484i	$0.925642\pi$
$878$	5.82912	+	25.5390i	0.196723	+	0.861901i
$879$	−36.8581	−	17.7499i	−1.24319	−	0.598691i
$880$	1.66096	−	0.799874i	0.0559908	−	0.0269638i
$881$	−8.43119	−	36.9395i	−0.284054	−	1.24452i	−0.892544	−	0.450961i	$-0.851082\pi$
$881$	−8.43119	−	36.9395i	−0.284054	−	1.24452i	0.608490	−	0.793562i	$-0.291776\pi$
$882$	−9.76909	−	42.8012i	−0.328942	−	1.44119i
$883$	10.3756	−	4.99662i	0.349166	−	0.168150i	−0.251077	−	0.967967i	$-0.580785\pi$
$883$	10.3756	−	4.99662i	0.349166	−	0.168150i	0.600243	+	0.799818i	$0.295070\pi$
$884$	−0.337005	−	0.162293i	−0.0113347	−	0.00545850i
$885$	−3.59416	−	15.7470i	−0.120816	−	0.529330i
$886$	−0.958386	−	1.20178i	−0.0321976	−	0.0403745i
$887$	34.1865	+	42.8685i	1.14787	+	1.43938i	0.879392	+	0.476099i	$0.157949\pi$
$887$	34.1865	+	42.8685i	1.14787	+	1.43938i	0.268479	+	0.963286i	$0.413479\pi$
$888$	−25.9510	−	12.4973i	−0.870858	−	0.419383i
$889$	18.9429	−	82.9943i	0.635325	−	2.78354i
$890$	16.0958	−	20.1836i	0.539534	−	0.676554i
$891$	1.01859	−	4.46274i	0.0341241	−	0.149507i
$892$	−3.97135	+	1.91250i	−0.132971	+	0.0640353i
$893$	−15.8271	−	19.8466i	−0.529634	−	0.664140i
$894$	−25.7838	+	12.4168i	−0.862339	+	0.415281i
$895$	13.4326	−	16.8440i	0.449003	−	0.563032i
$896$	−17.5933			−0.587751
$897$	2.74136			0.0915314
$898$	−4.70131	+	5.89526i	−0.156885	+	0.196727i
$899$	0.646986	+	0.311572i	0.0215782	+	0.0103915i
$900$	−1.42432	−	6.24033i	−0.0474772	−	0.208011i
$901$	−1.75684	+	7.69724i	−0.0585290	+	0.256432i
$902$	2.21604			0.0737859
$903$	59.9980	+	36.3432i	1.99661	+	1.20943i
$904$	27.3856			0.910831
$905$	6.26978	−	27.4697i	0.208415	−	0.913124i
$906$	−7.97374	−	34.9352i	−0.264910	−	1.16065i
$907$	−8.22653	−	3.96169i	−0.273158	−	0.131546i	0.292291	−	0.956330i	$-0.405583\pi$
$907$	−8.22653	−	3.96169i	−0.273158	−	0.131546i	−0.565448	+	0.824784i	$0.691297\pi$
$908$	−3.47865	+	4.36209i	−0.115443	+	0.144761i
$909$	−52.4297			−1.73898
$910$	4.21595			0.139757
$911$	15.8182	−	19.8354i	0.524081	−	0.657177i	−0.447389	−	0.894339i	$-0.647646\pi$
$911$	15.8182	−	19.8354i	0.524081	−	0.657177i	0.971470	+	0.237163i	$0.0762175\pi$
$912$	−27.5099	+	13.2481i	−0.910943	+	0.438687i
$913$	−0.100775	−	0.126368i	−0.00333518	−	0.00418218i
$914$	−0.986882	+	0.475257i	−0.0326432	+	0.0157201i
$915$	−8.68776	+	38.0636i	−0.287209	+	1.25834i
$916$	−0.891589	+	1.11802i	−0.0294589	+	0.0369403i
$917$	3.27580	−	14.3522i	0.108176	−	0.473952i
$918$	0.813062	+	0.391550i	0.0268350	+	0.0129231i
$919$	18.4387	+	23.1214i	0.608237	+	0.762705i	0.986636	−	0.162937i	$-0.0520969\pi$
$919$	18.4387	+	23.1214i	0.608237	+	0.762705i	−0.378400	+	0.925642i	$0.623525\pi$
$920$	−4.18094	−	5.24273i	−0.137841	−	0.172848i
$921$	−2.11133	−	9.25036i	−0.0695708	−	0.304810i
$922$	2.89299	+	1.39319i	0.0952756	+	0.0458823i
$923$	4.91834	−	2.36855i	0.161889	−	0.0779616i
$924$	0.789778	+	3.46024i	0.0259818	+	0.113834i
$925$	2.77515	+	12.1587i	0.0912463	+	0.399776i
$926$	−30.6704	+	14.7701i	−1.00789	+	0.485375i
$927$	−40.6511	−	19.5765i	−1.33516	−	0.642978i
$928$	−0.271377	−	1.18898i	−0.00890840	−	0.0390303i
$929$	−1.77028	−	2.21986i	−0.0580811	−	0.0728314i	0.751942	−	0.659229i	$-0.229117\pi$
$929$	−1.77028	−	2.21986i	−0.0580811	−	0.0728314i	−0.810023	+	0.586397i	$0.800546\pi$
$930$	4.47745	+	5.61455i	0.146822	+	0.184108i
$931$	−48.8535	−	23.5266i	−1.60111	−	0.771054i
$932$	1.71231	−	7.50211i	0.0560885	−	0.245740i
$933$	−35.2015	+	44.1413i	−1.15244	+	1.44512i
$934$	−3.36358	+	14.7368i	−0.110060	+	0.482204i
$935$	−0.663545	+	0.319546i	−0.0217002	+	0.0104503i
$936$	4.08061	+	5.11692i	0.133379	+	0.167252i
$937$	−8.61713	+	4.14979i	−0.281509	+	0.135568i	−0.569311	−	0.822122i	$-0.692790\pi$
$937$	−8.61713	+	4.14979i	−0.281509	+	0.135568i	0.287802	+	0.957690i	$0.407076\pi$
$938$	30.3933	−	38.1119i	0.992375	−	1.24440i
$939$	−18.7551			−0.612051
$940$	3.90280			0.127295
$941$	24.9546	−	31.2921i	0.813498	−	1.02009i	−0.185799	−	0.982588i	$-0.559487\pi$
$941$	24.9546	−	31.2921i	0.813498	−	1.02009i	0.999296	−	0.0375062i	$-0.0119414\pi$
$942$	−10.3363	−	4.97768i	−0.336773	−	0.162181i
$943$	−1.22558	−	5.36963i	−0.0399105	−	0.174859i
$944$	−2.78306	+	12.1934i	−0.0905809	+	0.396861i
$945$	4.15595			0.135193
$946$	3.82219	+	2.31525i	0.124270	+	0.0752753i
$947$	−24.8559			−0.807709			−0.403855	−	0.914823i	$-0.632330\pi$
$947$	−24.8559			−0.807709			−0.403855	+	0.914823i	$0.632330\pi$
$948$	−1.23559	+	5.41349i	−0.0401302	+	0.175822i
$949$	0.433173	+	1.89785i	0.0140614	+	0.0616069i
$950$	17.4325	+	8.39506i	0.565586	+	0.272372i
$951$	4.81139	−	6.03330i	0.156020	−	0.195643i
$952$	13.1012			0.424613
$953$	12.4566			0.403509			0.201754	−	0.979436i	$-0.435336\pi$
$953$	12.4566			0.403509			0.201754	+	0.979436i	$0.435336\pi$
$954$	19.3665	−	24.2848i	0.627013	−	0.786250i
$955$	−2.71786	+	1.30885i	−0.0879480	+	0.0423535i
$956$	1.63205	+	2.04653i	0.0527844	+	0.0661896i
$957$	0.498234	−	0.239937i	0.0161056	−	0.00775606i
$958$	−4.84005	+	21.2057i	−0.156375	+	0.685124i
$959$	7.26263	−	9.10705i	0.234523	−	0.294082i
$960$	6.31511	−	27.6683i	0.203819	−	0.892990i
$961$	24.7986	+	11.9424i	0.799955	+	0.385238i
$962$	−1.78770	−	2.24171i	−0.0576378	−	0.0722755i
$963$	21.2239	+	26.6139i	0.683931	+	0.857622i
$964$	1.40023	+	6.13480i	0.0450983	+	0.197589i
$965$	12.7617	+	6.14571i	0.410813	+	0.197837i
$966$	−19.4514	+	9.36731i	−0.625839	+	0.301388i
$967$	−9.20843	−	40.3448i	−0.296123	−	1.29740i	−0.875847	−	0.482588i	$-0.839697\pi$
$967$	−9.20843	−	40.3448i	−0.296123	−	1.29740i	0.579724	−	0.814813i	$-0.303160\pi$
$968$	−7.30164	−	31.9906i	−0.234683	−	1.02822i
$969$	10.9901	−	5.29254i	0.353052	−	0.170021i
$970$	10.6543	+	5.13085i	0.342089	+	0.164742i
$971$	10.5095	+	46.0453i	0.337267	+	1.47766i	0.804725	+	0.593648i	$0.202313\pi$
$971$	10.5095	+	46.0453i	0.337267	+	1.47766i	−0.467458	+	0.884015i	$0.654830\pi$
$972$	−8.08945	−	10.1439i	−0.259469	−	0.325364i
$973$	26.9919	+	33.8467i	0.865319	+	1.08508i
$974$	16.4143	+	7.90473i	0.525949	+	0.253284i
$975$	1.20353	−	5.27302i	0.0385439	−	0.168872i
$976$	18.8492	−	23.6361i	0.603347	−	0.756574i
$977$	12.8190	−	56.1637i	0.410116	−	1.79684i	−0.173531	−	0.984828i	$-0.555518\pi$
$977$	12.8190	−	56.1637i	0.410116	−	1.79684i	0.583647	−	0.812008i	$-0.301625\pi$
$978$	0.948301	−	0.456678i	0.0303233	−	0.0146029i
$979$	5.99908	+	7.52260i	0.191731	+	0.240423i
$980$	7.51105	−	3.61713i	0.239932	−	0.115545i
$981$	1.82071	−	2.28310i	0.0581309	−	0.0728939i
$982$	36.3529			1.16007
$983$	−15.2186			−0.485399			−0.242700	−	0.970101i	$-0.578033\pi$
$983$	−15.2186			−0.485399			−0.242700	+	0.970101i	$0.578033\pi$
$984$	15.6477	−	19.6216i	0.498831	−	0.625515i
$985$	−27.4678	−	13.2278i	−0.875196	−	0.421472i
$986$	−0.102132	−	0.447469i	−0.00325254	−	0.0142503i
$987$	12.4353	−	54.4824i	0.395819	−	1.73419i
$988$	1.81756			0.0578243
$989$	3.49617	−	10.5419i	0.111172	−	0.335214i
$990$	2.89747			0.0920878
$991$	1.11782	−	4.89748i	0.0355086	−	0.155574i	−0.954065	−	0.299598i	$-0.903147\pi$
$991$	1.11782	−	4.89748i	0.0355086	−	0.155574i	0.989574	+	0.144025i	$0.0460045\pi$
$992$	1.31348	+	5.75472i	0.0417030	+	0.182713i
$993$	−27.4110	−	13.2005i	−0.869863	−	0.418904i
$994$	−26.8048	+	33.6122i	−0.850197	+	1.06611i
$995$	−29.5473			−0.936714
$996$	−0.411585			−0.0130416
$997$	−24.5539	+	30.7896i	−0.777630	+	0.975118i	0.222370	+	0.974962i	$0.428621\pi$
$997$	−24.5539	+	30.7896i	−0.777630	+	0.975118i	−1.00000		0.000155103i	$0.999951\pi$
$998$	19.4620	−	9.37238i	0.616057	−	0.296678i
$999$	−1.76226	−	2.20981i	−0.0557555	−	0.0699152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.k.a.35.11	✓	180
43.16	even	7	inner	731.2.k.a.188.11	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.k.a.35.11	✓	180	1.1	even	1	trivial
731.2.k.a.188.11	yes	180	43.16	even	7	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.265151 + 1.16170i) q^{2} +(0.558598 + 2.44738i) q^{3} +(0.522689 + 0.251714i) q^{4} +(0.802903 - 1.00681i) q^{5} -2.99124 q^{6} -4.26133 q^{7} +(-1.91688 + 2.40369i) q^{8} +(-2.97472 + 1.43255i) q^{9} +O(q^{10})\)	\(q+(-0.265151 + 1.16170i) q^{2} +(0.558598 + 2.44738i) q^{3} +(0.522689 + 0.251714i) q^{4} +(0.802903 - 1.00681i) q^{5} -2.99124 q^{6} -4.26133 q^{7} +(-1.91688 + 2.40369i) q^{8} +(-2.97472 + 1.43255i) q^{9} +(0.956722 + 1.19969i) q^{10} +(-0.515272 + 0.248142i) q^{11} +(-0.324065 + 1.41982i) q^{12} +(-0.401997 + 0.504088i) q^{13} +(1.12990 - 4.95041i) q^{14} +(2.91254 + 1.40261i) q^{15} +(-1.56069 - 1.95705i) q^{16} +(0.623490 + 0.781831i) q^{17} +(-0.875447 - 3.83559i) q^{18} +(-4.37796 - 2.10832i) q^{19} +(0.673095 - 0.324146i) q^{20} +(-2.38037 - 10.4291i) q^{21} +(-0.151642 - 0.664388i) q^{22} +(-1.52600 + 0.734883i) q^{23} +(-6.95351 - 3.34864i) q^{24} +(0.743595 + 3.25790i) q^{25} +(-0.479011 - 0.600661i) q^{26} +(-0.472194 - 0.592113i) q^{27} +(-2.22735 - 1.07264i) q^{28} +(-0.0857115 + 0.375527i) q^{29} +(-2.40167 + 3.01160i) q^{30} +(0.414847 - 1.81756i) q^{31} +(-2.85262 + 1.37375i) q^{32} +(-0.895127 - 1.12245i) q^{33} +(-1.07358 + 0.517007i) q^{34} +(-3.42144 + 4.29035i) q^{35} -1.91544 q^{36} +3.73207 q^{37} +(3.61006 - 4.52687i) q^{38} +(-1.45825 - 0.702256i) q^{39} +(0.880989 + 3.85986i) q^{40} +(-0.723599 + 3.17030i) q^{41} +12.7467 q^{42} +(-4.56029 + 4.71209i) q^{43} -0.331788 q^{44} +(-0.946108 + 4.14517i) q^{45} +(-0.449095 - 1.96761i) q^{46} +(4.70673 + 2.26664i) q^{47} +(3.91783 - 4.91281i) q^{48} +11.1590 q^{49} -3.98188 q^{50} +(-1.56516 + 1.96264i) q^{51} +(-0.337005 + 0.162293i) q^{52} +(4.92257 + 6.17271i) q^{53} +(0.813062 - 0.391550i) q^{54} +(-0.163882 + 0.718014i) q^{55} +(8.16847 - 10.2429i) q^{56} +(2.71432 - 11.8922i) q^{57} +(-0.413524 - 0.199143i) q^{58} +(-3.11525 - 3.90640i) q^{59} +(1.16930 + 1.46625i) q^{60} +(2.68748 + 11.7746i) q^{61} +(2.00147 + 0.963858i) q^{62} +(12.6763 - 6.10457i) q^{63} +(-1.95352 - 8.55895i) q^{64} +(0.184756 + 0.809467i) q^{65} +(1.54130 - 0.742252i) q^{66} +(8.64947 + 4.16536i) q^{67} +(0.129093 + 0.565595i) q^{68} +(-2.65096 - 3.32419i) q^{69} +(-4.07691 - 5.11228i) q^{70} +(-7.62825 - 3.67357i) q^{71} +(2.25878 - 9.89635i) q^{72} +(1.88246 - 2.36053i) q^{73} +(-0.989562 + 4.33556i) q^{74} +(-7.55795 + 3.63972i) q^{75} +(-1.75762 - 2.20399i) q^{76} +(2.19575 - 1.05742i) q^{77} +(1.20247 - 1.50785i) q^{78} +3.81279 q^{79} -3.22345 q^{80} +(-4.99036 + 6.25771i) q^{81} +(-3.49108 - 1.68122i) q^{82} +(0.0628882 + 0.275531i) q^{83} +(1.38095 - 6.05034i) q^{84} +1.28776 q^{85} +(-4.26488 - 6.54712i) q^{86} -0.966934 q^{87} +(0.391258 - 1.71422i) q^{88} +(-3.74368 - 16.4021i) q^{89} +(-4.56460 - 2.19819i) q^{90} +(1.71304 - 2.14809i) q^{91} -0.982603 q^{92} +4.68000 q^{93} +(-3.88116 + 4.86682i) q^{94} +(-5.63775 + 2.71500i) q^{95} +(-4.95556 - 6.21407i) q^{96} +(6.94335 - 3.34374i) q^{97} +(-2.95881 + 12.9634i) q^{98} +(1.17731 - 1.47631i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9}+O(q^{10}) \) 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9	\( 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9} - 8 q^{10} - 12 q^{11} - 24 q^{12} - 5 q^{13} - 8 q^{14} - q^{15} - 58 q^{16} - 30 q^{17} + 36 q^{18} - 24 q^{19} - 36 q^{20} - 28 q^{21} + 5 q^{22} + 27 q^{23} - 46 q^{24} - 38 q^{25} + 6 q^{26} - 36 q^{27} - 54 q^{28} + 28 q^{29} - 21 q^{30} + 36 q^{31} + 11 q^{32} + 5 q^{33} - 4 q^{34} + 6 q^{35} + 192 q^{36} + 164 q^{37} + 32 q^{38} - 34 q^{39} + 2 q^{40} + 42 q^{41} - 2 q^{42} - 22 q^{43} + 14 q^{44} + 58 q^{45} - 53 q^{46} + 21 q^{47} - 20 q^{48} + 166 q^{49} + 18 q^{50} - 6 q^{51} + 54 q^{52} + 8 q^{53} - 154 q^{54} - 5 q^{55} - 35 q^{56} + 8 q^{57} + 9 q^{58} - 13 q^{59} - 88 q^{60} - 34 q^{61} - 36 q^{62} - 31 q^{63} - 18 q^{64} + 9 q^{65} + 222 q^{66} - 48 q^{67} - 27 q^{68} + 2 q^{69} - 64 q^{70} - 42 q^{71} + 77 q^{72} - 44 q^{73} - 35 q^{74} - 21 q^{75} + 44 q^{76} - 32 q^{77} + 124 q^{78} - 96 q^{79} + 490 q^{80} - 12 q^{81} - 130 q^{82} - 8 q^{83} + 170 q^{84} + 22 q^{85} - 12 q^{86} - 90 q^{87} - 122 q^{88} - 81 q^{89} + 49 q^{90} - 27 q^{91} - 116 q^{92} + 18 q^{93} - 124 q^{94} + 117 q^{95} + 52 q^{96} - 79 q^{97} - 54 q^{98} - 39 q^{99}+O(q^{100}) \) 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9 - 8 * q^10 - 12 * q^11 - 24 * q^12 - 5 * q^13 - 8 * q^14 - q^15 - 58 * q^16 - 30 * q^17 + 36 * q^18 - 24 * q^19 - 36 * q^20 - 28 * q^21 + 5 * q^22 + 27 * q^23 - 46 * q^24 - 38 * q^25 + 6 * q^26 - 36 * q^27 - 54 * q^28 + 28 * q^29 - 21 * q^30 + 36 * q^31 + 11 * q^32 + 5 * q^33 - 4 * q^34 + 6 * q^35 + 192 * q^36 + 164 * q^37 + 32 * q^38 - 34 * q^39 + 2 * q^40 + 42 * q^41 - 2 * q^42 - 22 * q^43 + 14 * q^44 + 58 * q^45 - 53 * q^46 + 21 * q^47 - 20 * q^48 + 166 * q^49 + 18 * q^50 - 6 * q^51 + 54 * q^52 + 8 * q^53 - 154 * q^54 - 5 * q^55 - 35 * q^56 + 8 * q^57 + 9 * q^58 - 13 * q^59 - 88 * q^60 - 34 * q^61 - 36 * q^62 - 31 * q^63 - 18 * q^64 + 9 * q^65 + 222 * q^66 - 48 * q^67 - 27 * q^68 + 2 * q^69 - 64 * q^70 - 42 * q^71 + 77 * q^72 - 44 * q^73 - 35 * q^74 - 21 * q^75 + 44 * q^76 - 32 * q^77 + 124 * q^78 - 96 * q^79 + 490 * q^80 - 12 * q^81 - 130 * q^82 - 8 * q^83 + 170 * q^84 + 22 * q^85 - 12 * q^86 - 90 * q^87 - 122 * q^88 - 81 * q^89 + 49 * q^90 - 27 * q^91 - 116 * q^92 + 18 * q^93 - 124 * q^94 + 117 * q^95 + 52 * q^96 - 79 * q^97 - 54 * q^98 - 39 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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