LMFDB - Embedded newform 260.2.bg.c.23.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(23,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("260.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bg (of order $12$, degree $4$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.12
Character	$\chi$	$=$	260.23
Dual form			260.2.bg.c.147.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.849309 - 1.13078i) q^{2} +(-0.754665 - 0.202212i) q^{3} +(-0.557348 + 1.92077i) q^{4} +(0.282716 + 2.21812i) q^{5} +(0.412286 + 1.02510i) q^{6} +(-0.814984 - 3.04156i) q^{7} +(2.64534 - 1.00109i) q^{8} +(-2.06945 - 1.19480i) q^{9} +O(q^{10})$	\(q+(-0.849309 - 1.13078i) q^{2} +(-0.754665 - 0.202212i) q^{3} +(-0.557348 + 1.92077i) q^{4} +(0.282716 + 2.21812i) q^{5} +(0.412286 + 1.02510i) q^{6} +(-0.814984 - 3.04156i) q^{7} +(2.64534 - 1.00109i) q^{8} +(-2.06945 - 1.19480i) q^{9} +(2.26811 - 2.20356i) q^{10} +(-0.846561 - 1.46629i) q^{11} +(0.809013 - 1.33684i) q^{12} +(-2.00244 - 2.99837i) q^{13} +(-2.74718 + 3.50480i) q^{14} +(0.235175 - 1.73111i) q^{15} +(-3.37873 - 2.14107i) q^{16} +(-1.49691 - 5.58654i) q^{17} +(0.406544 + 3.35485i) q^{18} +(1.47839 + 0.853551i) q^{19} +(-4.41808 - 0.693234i) q^{20} +2.46016i q^{21} +(-0.939062 + 2.20261i) q^{22} +(1.69316 + 0.453682i) q^{23} +(-2.19878 + 0.220568i) q^{24} +(-4.84014 + 1.25420i) q^{25} +(-1.68982 + 4.81087i) q^{26} +(2.97750 + 2.97750i) q^{27} +(6.29637 + 0.129809i) q^{28} +(1.31383 - 0.758542i) q^{29} +(-2.15725 + 1.20431i) q^{30} -8.65488 q^{31} +(0.448491 + 5.63905i) q^{32} +(0.342369 + 1.27774i) q^{33} +(-5.04584 + 6.43738i) q^{34} +(6.51615 - 2.66763i) q^{35} +(3.44833 - 3.30902i) q^{36} +(-0.693362 + 2.58766i) q^{37} +(-0.290431 - 2.39667i) q^{38} +(0.904867 + 2.66768i) q^{39} +(2.96842 + 5.58467i) q^{40} +(-1.12125 + 0.647352i) q^{41} +(2.78191 - 2.08944i) q^{42} +(-2.38355 - 8.89553i) q^{43} +(3.28823 - 0.808819i) q^{44} +(2.06514 - 4.92808i) q^{45} +(-0.925003 - 2.29992i) q^{46} +(7.31398 - 7.31398i) q^{47} +(2.11686 + 2.29901i) q^{48} +(-2.52472 + 1.45765i) q^{49} +(5.52900 + 4.40796i) q^{50} +4.51866i q^{51} +(6.87524 - 2.17510i) q^{52} +(4.69463 + 4.69463i) q^{53} +(0.838091 - 5.89572i) q^{54} +(3.01307 - 2.29232i) q^{55} +(-5.20078 - 7.23009i) q^{56} +(-0.943094 - 0.943094i) q^{57} +(-1.97360 - 0.841425i) q^{58} +(5.38925 + 3.11149i) q^{59} +(3.19399 + 1.41655i) q^{60} +(1.75935 - 3.04729i) q^{61} +(7.35067 + 9.78681i) q^{62} +(-1.94748 + 7.26809i) q^{63} +(5.99564 - 5.29644i) q^{64} +(6.08463 - 5.28935i) q^{65} +(1.15407 - 1.47234i) q^{66} +(-13.9381 - 3.73469i) q^{67} +(11.5648 + 0.238424i) q^{68} +(-1.18603 - 0.684755i) q^{69} +(-8.55074 - 5.10272i) q^{70} +(-2.41646 + 4.18543i) q^{71} +(-6.67049 - 1.08894i) q^{72} +(-8.10316 + 8.10316i) q^{73} +(3.51497 - 1.41368i) q^{74} +(3.90630 + 0.0322366i) q^{75} +(-2.46346 + 2.36393i) q^{76} +(-3.76987 + 3.76987i) q^{77} +(2.24806 - 3.28890i) q^{78} +9.28225 q^{79} +(3.79395 - 8.09975i) q^{80} +(1.93946 + 3.35924i) q^{81} +(1.68430 + 0.718086i) q^{82} +(7.11624 + 7.11624i) q^{83} +(-4.72540 - 1.37116i) q^{84} +(11.9684 - 4.89973i) q^{85} +(-8.03456 + 10.2503i) q^{86} +(-1.14489 + 0.306772i) q^{87} +(-3.70732 - 3.03134i) q^{88} +(0.710435 + 1.23051i) q^{89} +(-7.32653 + 1.85023i) q^{90} +(-7.48777 + 8.53417i) q^{91} +(-1.81510 + 2.99932i) q^{92} +(6.53153 + 1.75012i) q^{93} +(-14.4824 - 2.05871i) q^{94} +(-1.47532 + 3.52057i) q^{95} +(0.801822 - 4.34628i) q^{96} +(-3.76899 + 1.00990i) q^{97} +(3.79255 + 1.61692i) q^{98} +4.04587i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 6 q^{2} - 12 q^{6}+O(q^{10}) $ 144 * q - 6 * q^2 - 12 * q^6	$ 144 q - 6 q^{2} - 12 q^{6} + 12 q^{10} - 12 q^{12} + 4 q^{13} - 12 q^{16} - 24 q^{17} - 42 q^{20} - 12 q^{22} - 24 q^{25} - 36 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 76 q^{36} + 48 q^{37} - 16 q^{38} + 76 q^{40} - 72 q^{41} + 40 q^{42} - 120 q^{45} - 12 q^{46} - 40 q^{48} + 120 q^{50} - 10 q^{52} + 8 q^{53} - 20 q^{56} + 126 q^{58} + 16 q^{61} - 44 q^{62} + 32 q^{65} + 96 q^{66} - 64 q^{68} - 54 q^{72} - 12 q^{76} + 40 q^{77} - 100 q^{78} - 24 q^{80} - 32 q^{81} - 78 q^{82} - 24 q^{85} - 10 q^{88} - 8 q^{90} + 100 q^{92} - 48 q^{93} - 12 q^{97} - 162 q^{98}+O(q^{100}) $ 144 * q - 6 * q^2 - 12 * q^6 + 12 * q^10 - 12 * q^12 + 4 * q^13 - 12 * q^16 - 24 * q^17 - 42 * q^20 - 12 * q^22 - 24 * q^25 - 36 * q^26 - 6 * q^28 - 36 * q^32 - 12 * q^33 - 76 * q^36 + 48 * q^37 - 16 * q^38 + 76 * q^40 - 72 * q^41 + 40 * q^42 - 120 * q^45 - 12 * q^46 - 40 * q^48 + 120 * q^50 - 10 * q^52 + 8 * q^53 - 20 * q^56 + 126 * q^58 + 16 * q^61 - 44 * q^62 + 32 * q^65 + 96 * q^66 - 64 * q^68 - 54 * q^72 - 12 * q^76 + 40 * q^77 - 100 * q^78 - 24 * q^80 - 32 * q^81 - 78 * q^82 - 24 * q^85 - 10 * q^88 - 8 * q^90 + 100 * q^92 - 48 * q^93 - 12 * q^97 - 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.849309	−	1.13078i	−0.600552	−	0.799585i
$2$	−0.849309	−	1.13078i	−0.600552	−	0.799585i
$3$	−0.754665	−	0.202212i	−0.435706	−	0.116747i	0.0342975	−	0.999412i	$-0.489081\pi$
$3$	−0.754665	−	0.202212i	−0.435706	−	0.116747i	−0.470003	+	0.882665i	$0.655747\pi$
$4$	−0.557348	+	1.92077i	−0.278674	+	0.960386i
$5$	0.282716	+	2.21812i	0.126434	+	0.991975i
$5$	0.282716	+	2.21812i	0.126434	+	0.991975i
$6$	0.412286	+	1.02510i	0.168315	+	0.418497i
$7$	−0.814984	−	3.04156i	−0.308035	−	1.14960i	−0.930301	−	0.366796i	$-0.880455\pi$
$7$	−0.814984	−	3.04156i	−0.308035	−	1.14960i	0.622266	−	0.782806i	$-0.286212\pi$
$8$	2.64534	−	1.00109i	0.935269	−	0.353938i
$9$	−2.06945	−	1.19480i	−0.689816	−	0.398265i
$10$	2.26811	−	2.20356i	0.717238	−	0.696828i
$11$	−0.846561	−	1.46629i	−0.255248	−	0.442102i	0.709715	−	0.704489i	$-0.248824\pi$
$11$	−0.846561	−	1.46629i	−0.255248	−	0.442102i	−0.964963	+	0.262387i	$0.915490\pi$
$12$	0.809013	−	1.33684i	0.233542	−	0.385911i
$13$	−2.00244	−	2.99837i	−0.555378	−	0.831598i
$13$	−2.00244	−	2.99837i	−0.555378	−	0.831598i
$14$	−2.74718	+	3.50480i	−0.734214	+	0.936697i
$15$	0.235175	−	1.73111i	0.0607220	−	0.446970i
$16$	−3.37873	−	2.14107i	−0.844682	−	0.535269i
$17$	−1.49691	−	5.58654i	−0.363054	−	1.35494i	−0.870040	−	0.492981i	$-0.835907\pi$
$17$	−1.49691	−	5.58654i	−0.363054	−	1.35494i	0.506986	−	0.861954i	$-0.330760\pi$
$18$	0.406544	+	3.35485i	0.0958233	+	0.790746i
$19$	1.47839	+	0.853551i	0.339167	+	0.195818i	0.659904	−	0.751350i	$-0.270597\pi$
$19$	1.47839	+	0.853551i	0.339167	+	0.195818i	−0.320737	+	0.947168i	$0.603930\pi$
$20$	−4.41808	−	0.693234i	−0.987913	−	0.155012i
$21$			2.46016i			0.536851i
$22$	−0.939062	+	2.20261i	−0.200209	+	0.469598i
$23$	1.69316	+	0.453682i	0.353049	+	0.0945991i	0.430985	−	0.902359i	$-0.358166\pi$
$23$	1.69316	+	0.453682i	0.353049	+	0.0945991i	−0.0779359	+	0.996958i	$0.524833\pi$
$24$	−2.19878	+	0.220568i	−0.448823	+	0.0450232i
$25$	−4.84014	+	1.25420i	−0.968029	+	0.250839i
$26$	−1.68982	+	4.81087i	−0.331401	+	0.943490i
$27$	2.97750	+	2.97750i	0.573019	+	0.573019i
$28$	6.29637	+	0.129809i	1.18990	+	0.0245315i
$29$	1.31383	−	0.758542i	0.243973	−	0.140858i	−0.373029	−	0.927820i	$-0.621681\pi$
$29$	1.31383	−	0.758542i	0.243973	−	0.140858i	0.617001	+	0.786962i	$0.288347\pi$
$30$	−2.15725	+	1.20431i	−0.393858	+	0.219877i
$31$	−8.65488			−1.55446			−0.777231	−	0.629215i	$-0.783376\pi$
$31$	−8.65488			−1.55446			−0.777231	+	0.629215i	$0.783376\pi$
$32$	0.448491	+	5.63905i	0.0792827	+	0.996852i
$33$	0.342369	+	1.27774i	0.0595988	+	0.222426i
$34$	−5.04584	+	6.43738i	−0.865354	+	1.10400i
$35$	6.51615	−	2.66763i	1.10143	−	0.450912i
$36$	3.44833	−	3.30902i	0.574722	−	0.551503i
$37$	−0.693362	+	2.58766i	−0.113988	+	0.425409i	−0.999209	−	0.0397611i	$-0.987340\pi$
$37$	−0.693362	+	2.58766i	−0.113988	+	0.425409i	0.885221	+	0.465170i	$0.154007\pi$
$38$	−0.290431	−	2.39667i	−0.0471142	−	0.388792i
$39$	0.904867	+	2.66768i	0.144895	+	0.427171i
$40$	2.96842	+	5.58467i	0.469348	+	0.883013i
$41$	−1.12125	+	0.647352i	−0.175109	+	0.101099i	−0.584993	−	0.811038i	$-0.698903\pi$
$41$	−1.12125	+	0.647352i	−0.175109	+	0.101099i	0.409884	+	0.912138i	$0.365569\pi$
$42$	2.78191	−	2.08944i	0.429258	−	0.322407i
$43$	−2.38355	−	8.89553i	−0.363488	−	1.35656i	−0.869459	−	0.494005i	$-0.835532\pi$
$43$	−2.38355	−	8.89553i	−0.363488	−	1.35656i	0.505971	−	0.862551i	$-0.331134\pi$
$44$	3.28823	−	0.808819i	0.495719	−	0.121934i
$45$	2.06514	−	4.92808i	0.307853	−	0.734634i
$46$	−0.925003	−	2.29992i	−0.136384	−	0.339104i
$47$	7.31398	−	7.31398i	1.06685	−	1.06685i	0.0692551	−	0.997599i	$-0.477938\pi$
$47$	7.31398	−	7.31398i	1.06685	−	1.06685i	0.997599	−	0.0692551i	$-0.0220622\pi$
$48$	2.11686	+	2.29901i	0.305542	+	0.331834i
$49$	−2.52472	+	1.45765i	−0.360674	+	0.208235i
$50$	5.52900	+	4.40796i	0.781919	+	0.623380i
$51$			4.51866i			0.632739i
$52$	6.87524	−	2.17510i	0.953424	−	0.301632i
$53$	4.69463	+	4.69463i	0.644857	+	0.644857i	0.951746	−	0.306888i	$-0.0992878\pi$
$53$	4.69463	+	4.69463i	0.644857	+	0.644857i	−0.306888	+	0.951746i	$0.599288\pi$
$54$	0.838091	−	5.89572i	0.114050	−	0.802306i
$55$	3.01307	−	2.29232i	0.406282	−	0.309096i
$56$	−5.20078	−	7.23009i	−0.694984	−	0.966161i
$57$	−0.943094	−	0.943094i	−0.124916	−	0.124916i
$58$	−1.97360	−	0.841425i	−0.259146	−	0.110485i
$59$	5.38925	+	3.11149i	0.701621	+	0.405081i	0.807951	−	0.589250i	$-0.200577\pi$
$59$	5.38925	+	3.11149i	0.701621	+	0.405081i	−0.106330	+	0.994331i	$0.533910\pi$
$60$	3.19399	+	1.41655i	0.412342	+	0.182875i
$61$	1.75935	−	3.04729i	0.225262	−	0.390165i	−0.731136	−	0.682232i	$-0.761010\pi$
$61$	1.75935	−	3.04729i	0.225262	−	0.390165i	0.956398	+	0.292066i	$0.0943428\pi$
$62$	7.35067	+	9.78681i	0.933536	+	1.24293i
$63$	−1.94748	+	7.26809i	−0.245359	+	0.915693i
$64$	5.99564	−	5.29644i	0.749455	−	0.662055i
$65$	6.08463	−	5.28935i	0.754706	−	0.656063i
$66$	1.15407	−	1.47234i	0.142056	−	0.181233i
$67$	−13.9381	−	3.73469i	−1.70281	−	0.456265i	−0.729162	−	0.684341i	$-0.760090\pi$
$67$	−13.9381	−	3.73469i	−1.70281	−	0.456265i	−0.973643	+	0.228076i	$0.926757\pi$
$68$	11.5648	+	0.238424i	1.40243	+	0.0289132i
$69$	−1.18603	−	0.684755i	−0.142781	−	0.0824348i
$70$	−8.55074	−	5.10272i	−1.02201	−	0.609891i
$71$	−2.41646	+	4.18543i	−0.286781	+	0.496719i	−0.973040	−	0.230638i	$-0.925919\pi$
$71$	−2.41646	+	4.18543i	−0.286781	+	0.496719i	0.686258	+	0.727358i	$0.259252\pi$
$72$	−6.67049	−	1.08894i	−0.786124	−	0.128333i
$73$	−8.10316	+	8.10316i	−0.948404	+	0.948404i	−0.998733	−	0.0503291i	$-0.983973\pi$
$73$	−8.10316	+	8.10316i	−0.948404	+	0.948404i	0.0503291	+	0.998733i	$0.483973\pi$
$74$	3.51497	−	1.41368i	0.408607	−	0.164337i
$75$	3.90630	+	0.0322366i	0.451061	+	0.00372237i
$76$	−2.46346	+	2.36393i	−0.282578	+	0.271162i
$77$	−3.76987	+	3.76987i	−0.429616	+	0.429616i
$78$	2.24806	−	3.28890i	0.254543	−	0.372394i
$79$	9.28225			1.04433			0.522167	−	0.852843i	$-0.325124\pi$
$79$	9.28225			1.04433			0.522167	+	0.852843i	$0.325124\pi$
$80$	3.79395	−	8.09975i	0.424176	−	0.905580i
$81$	1.93946	+	3.35924i	0.215496	+	0.373249i
$82$	1.68430	+	0.718086i	0.186000	+	0.0792993i
$83$	7.11624	+	7.11624i	0.781109	+	0.781109i	0.980018	−	0.198909i	$-0.0637398\pi$
$83$	7.11624	+	7.11624i	0.781109	+	0.781109i	−0.198909	+	0.980018i	$0.563740\pi$
$84$	−4.72540	−	1.37116i	−0.515584	−	0.149606i
$85$	11.9684	−	4.89973i	1.29816	−	0.531451i
$86$	−8.03456	+	10.2503i	−0.866389	+	1.10532i
$87$	−1.14489	+	0.306772i	−0.122745	+	0.0328894i
$88$	−3.70732	−	3.03134i	−0.395202	−	0.323142i
$89$	0.710435	+	1.23051i	0.0753060	+	0.130434i	0.901219	−	0.433363i	$-0.142673\pi$
$89$	0.710435	+	1.23051i	0.0753060	+	0.130434i	−0.825913	+	0.563797i	$0.809340\pi$
$90$	−7.32653	+	1.85023i	−0.772285	+	0.195032i
$91$	−7.48777	+	8.53417i	−0.784931	+	0.894625i
$92$	−1.81510	+	2.99932i	−0.189237	+	0.312701i
$93$	6.53153	+	1.75012i	0.677288	+	0.181479i
$94$	−14.4824	−	2.05871i	−1.49374	−	0.212339i
$95$	−1.47532	+	3.52057i	−0.151364	+	0.361203i
$96$	0.801822	−	4.34628i	0.0818356	−	0.443590i
$97$	−3.76899	+	1.00990i	−0.382683	+	0.102540i	−0.445032	−	0.895515i	$-0.646808\pi$
$97$	−3.76899	+	1.00990i	−0.382683	+	0.102540i	0.0623486	+	0.998054i	$0.480141\pi$
$98$	3.79255	+	1.61692i	0.383106	+	0.163334i
$99$			4.04587i			0.406625i
$100$	0.288618	−	9.99583i	0.0288618	−	0.999583i
$101$	1.80715	+	3.13008i	0.179818	+	0.311454i	0.941818	−	0.336123i	$-0.109116\pi$
$101$	1.80715	+	3.13008i	0.179818	+	0.311454i	−0.762000	+	0.647577i	$0.775782\pi$
$102$	5.10963	−	3.83774i	0.505929	−	0.379993i
$103$	−5.35764	+	5.35764i	−0.527904	+	0.527904i	−0.919947	−	0.392043i	$-0.871768\pi$
$103$	−5.35764	+	5.35764i	−0.527904	+	0.527904i	0.392043	+	0.919947i	$0.371768\pi$
$104$	−8.29878	−	5.92708i	−0.813762	−	0.581198i
$105$	−5.45694	+	0.695525i	−0.532542	+	0.0678763i
$106$	1.32142	−	9.29581i	0.128348	−	0.902889i
$107$	4.98393	−	18.6003i	0.481815	−	1.79816i	−0.112177	−	0.993688i	$-0.535782\pi$
$107$	4.98393	−	18.6003i	0.481815	−	1.79816i	0.593993	−	0.804471i	$-0.297551\pi$
$108$	−7.37859	+	4.05959i	−0.710005	+	0.390634i
$109$	13.0909			1.25388			0.626940	−	0.779067i	$-0.284307\pi$
$109$	13.0909			1.25388			0.626940	+	0.779067i	$0.284307\pi$
$110$	−5.15115	−	1.46024i	−0.491143	−	0.139229i
$111$	1.04651	−	1.81261i	0.0993306	−	0.172046i
$112$	−3.75860	+	12.0215i	−0.355154	+	1.13593i
$113$	4.40696	−	1.18084i	0.414572	−	0.111084i	−0.0455031	−	0.998964i	$-0.514489\pi$
$113$	4.40696	−	1.18084i	0.414572	−	0.111084i	0.460075	+	0.887880i	$0.347822\pi$
$114$	−0.265458	+	1.86741i	−0.0248624	+	0.174899i
$115$	−0.527638	+	3.88391i	−0.0492025	+	0.362176i
$116$	0.724724	+	2.94634i	0.0672889	+	0.273561i
$117$	0.561508	+	8.59748i	0.0519114	+	0.794837i
$118$	−1.05872	−	8.73669i	−0.0974632	−	0.804278i
$119$	−15.7719	+	9.10588i	−1.44580	+	0.834735i
$120$	−1.11088	−	4.81480i	−0.101409	−	0.439529i
$121$	4.06667	−	7.04368i	0.369697	−	0.640334i
$122$	−4.94006	+	0.598641i	−0.447252	+	0.0541984i
$123$	0.977067	−	0.261804i	0.0880992	−	0.0236061i
$124$	4.82378	−	16.6240i	0.433188	−	1.49288i
$125$	−4.15035	−	10.3815i	−0.371218	−	0.928546i
$126$	9.87265	−	3.97068i	0.879526	−	0.353736i
$127$	1.51107	−	5.63940i	0.134086	−	0.500416i	−0.865914	−	0.500193i	$-0.833262\pi$
$127$	1.51107	−	5.63940i	0.134086	−	0.500416i	1.00000		0.000223043i	$-7.09966e-5\pi$
$128$	−11.0813	−	2.28146i	−0.979457	−	0.201655i
$129$			7.19513i			0.633496i
$130$	−11.1489	−	2.38812i	−0.977819	−	0.209452i
$131$			1.50749i			0.131710i	0.997829	+	0.0658548i	$0.0209774\pi$
$131$			1.50749i			0.131710i	−0.997829	+	0.0658548i	$0.979023\pi$
$132$	−2.64506	−	0.0545317i	−0.230223	−	0.00474638i
$133$	1.39126	−	5.19226i	0.120638	−	0.450226i
$134$	7.61459	+	18.9329i	0.657801	+	1.63555i
$135$	−5.76267	+	7.44624i	−0.495972	+	0.640870i
$136$	−9.55246	−	13.2798i	−0.819117	−	1.13873i
$137$	−18.4924	+	4.95502i	−1.57991	+	0.423336i	−0.938898	−	0.344195i	$-0.888152\pi$
$137$	−18.4924	+	4.95502i	−1.57991	+	0.423336i	−0.641012	+	0.767531i	$0.721485\pi$
$138$	0.232996	+	1.92271i	0.0198340	+	0.163672i
$139$	−6.83643	+	11.8410i	−0.579858	+	1.00434i	0.415637	+	0.909531i	$0.363559\pi$
$139$	−6.83643	+	11.8410i	−0.579858	+	1.00434i	−0.995495	+	0.0948132i	$0.969775\pi$
$140$	1.49215	+	14.0028i	0.126110	+	1.18346i
$141$	−6.99858	+	4.04063i	−0.589387	+	0.340283i
$142$	6.78515	−	0.822230i	0.569397	−	0.0690000i
$143$	−2.70128	+	5.47446i	−0.225892	+	0.457797i
$144$	4.43395	+	8.46773i	0.369496	+	0.705644i
$145$	2.05398	+	2.69979i	0.170574	+	0.224205i
$146$	16.0450	+	2.28084i	1.32790	+	0.188764i
$147$	2.20007	−	0.589507i	0.181459	−	0.0486217i
$148$	−4.58387	−	2.77402i	−0.376792	−	0.228023i
$149$	8.14994	−	14.1161i	0.667669	−	1.15644i	−0.310885	−	0.950447i	$-0.600625\pi$
$149$	8.14994	−	14.1161i	0.667669	−	1.15644i	0.978554	−	0.205989i	$-0.0660412\pi$
$150$	−3.28120	−	4.44456i	−0.267909	−	0.362897i
$151$	−13.2716			−1.08003			−0.540013	−	0.841656i	$-0.681581\pi$
$151$	−13.2716			−1.08003			−0.540013	+	0.841656i	$0.681581\pi$
$152$	4.76533	+	0.777928i	0.386520	+	0.0630983i
$153$	−3.57700	+	13.3496i	−0.289184	+	1.07925i
$154$	7.46469	+	1.06112i	0.601522	+	0.0855078i
$155$	−2.44687	−	19.1976i	−0.196537	−	1.54199i
$156$	−5.62833	+	0.251217i	−0.450627	+	0.0201134i
$157$	13.8068	−	13.8068i	1.10191	−	1.10191i	0.107725	−	0.994181i	$-0.465643\pi$
$157$	13.8068	−	13.8068i	1.10191	−	1.10191i	0.994181	−	0.107725i	$-0.0343566\pi$
$158$	−7.88350	−	10.4962i	−0.627178	−	0.835035i
$159$	−2.59356	−	4.49218i	−0.205683	−	0.356253i
$160$	−12.3813	+	2.58905i	−0.978828	+	0.204683i
$161$		−	5.51960i		−	0.435005i
$162$	2.15138	−	5.04615i	0.169028	−	0.396463i
$163$	−11.4151	+	3.05866i	−0.894099	+	0.239573i	−0.676480	−	0.736461i	$-0.736496\pi$
$163$	−11.4151	+	3.05866i	−0.894099	+	0.239573i	−0.217619	+	0.976034i	$0.569829\pi$
$164$	−0.618491	−	2.51446i	−0.0482961	−	0.196346i
$165$	−2.73739	+	1.12065i	−0.213106	+	0.0872428i
$166$	2.00305	−	14.0908i	0.155467	−	1.09366i
$167$	7.68440	+	2.05903i	0.594637	+	0.159333i	0.543572	−	0.839363i	$-0.317072\pi$
$167$	7.68440	+	2.05903i	0.594637	+	0.159333i	0.0510655	+	0.998695i	$0.483738\pi$
$168$	2.46284	+	6.50795i	0.190012	+	0.502100i
$169$	−4.98045	+	12.0081i	−0.383111	+	0.923702i
$170$	−15.7055	−	9.37234i	−1.20455	−	0.718826i
$171$	−2.03964	−	3.53276i	−0.155975	−	0.270157i
$172$	18.4148	+	0.379646i	1.40411	+	0.0289477i
$173$	−8.22963	+	2.20512i	−0.625687	+	0.167652i	−0.557712	−	0.830035i	$-0.688321\pi$
$173$	−8.22963	+	2.20512i	−0.625687	+	0.167652i	−0.0679752	+	0.997687i	$0.521654\pi$
$174$	1.31926	+	1.03408i	0.100013	+	0.0783933i
$175$	7.75935	+	13.6994i	0.586552	+	1.03558i
$176$	−0.279130	+	6.76673i	−0.0210402	+	0.510062i
$177$	−3.43790	−	3.43790i	−0.258408	−	0.258408i
$178$	0.788063	−	1.84843i	0.0590678	−	0.138546i
$179$	−6.66957	−	11.5520i	−0.498507	−	0.863439i	0.501492	−	0.865162i	$-0.332785\pi$
$179$	−6.66957	−	11.5520i	−0.498507	−	0.863439i	−0.999999	+	0.00172335i	$0.999451\pi$
$180$	8.31471	+	6.71331i	0.619742	+	0.500381i
$181$	18.9562			1.40901			0.704503	−	0.709701i	$-0.251170\pi$
$181$	18.9562			1.40901			0.704503	+	0.709701i	$0.251170\pi$
$182$	16.0097	+	1.21890i	1.18672	+	0.0903509i
$183$	−1.94392	+	1.94392i	−0.143699	+	0.143699i
$184$	4.93317	−	0.494865i	0.363678	−	0.0364819i
$185$	−5.93578	−	0.806391i	−0.436407	−	0.0592870i
$186$	−3.56828	−	8.87215i	−0.261639	−	0.650538i
$187$	−6.92425	+	6.92425i	−0.506351	+	0.506351i
$188$	9.97206	+	18.1249i	0.727287	+	1.32190i
$189$	6.62962	−	11.4828i	0.482234	−	0.835254i
$190$	5.23401	−	1.32179i	0.379715	−	0.0958927i
$191$	11.6625	+	6.73335i	0.843869	+	0.487208i	0.858578	−	0.512684i	$-0.171349\pi$
$191$	11.6625	+	6.73335i	0.843869	+	0.487208i	−0.0147083	+	0.999892i	$0.504682\pi$
$192$	−5.59570	+	2.78465i	−0.403835	+	0.200965i
$193$	−4.40750	−	1.18099i	−0.317259	−	0.0850092i	0.0966757	−	0.995316i	$-0.469179\pi$
$193$	−4.40750	−	1.18099i	−0.317259	−	0.0850092i	−0.413934	+	0.910307i	$0.635846\pi$
$194$	4.34302	+	3.40420i	0.311810	+	0.244407i
$195$	−5.66143	+	2.76130i	−0.405423	+	0.197741i
$196$	−1.39266	−	5.66182i	−0.0994758	−	0.404416i
$197$	2.58333	−	9.64110i	0.184054	−	0.686900i	−0.810777	−	0.585356i	$-0.800955\pi$
$197$	2.58333	−	9.64110i	0.184054	−	0.686900i	0.994831	−	0.101545i	$-0.0323784\pi$
$198$	4.57501	−	3.43619i	0.325132	−	0.244200i
$199$	9.35295	−	16.1998i	0.663013	−	1.14837i	−0.316807	−	0.948490i	$-0.602611\pi$
$199$	9.35295	−	16.1998i	0.663013	−	1.14837i	0.979820	−	0.199882i	$-0.0640560\pi$
$200$	−11.5483	+	8.16319i	−0.816585	+	0.577225i
$201$	9.76337	+	5.63688i	0.688655	+	0.397595i
$202$	2.00461	−	4.70190i	0.141044	−	0.330824i
$203$	−3.37790	−	3.37790i	−0.237082	−	0.237082i
$204$	−8.67931	−	2.51846i	−0.607673	−	0.176328i
$205$	−1.75290	−	2.30405i	−0.122428	−	0.160922i
$206$	10.6086	+	1.50804i	0.739138	+	0.105070i
$207$	−2.96185	−	2.96185i	−0.205863	−	0.205863i
$208$	0.345973	+	14.4181i	0.0239889	+	0.999712i
$209$		−	2.89033i		−	0.199928i
$210$	5.42111	+	5.57990i	0.374092	+	0.385050i
$211$	19.2027	−	11.0867i	1.32197	−	0.763239i	0.337927	−	0.941172i	$-0.390274\pi$
$211$	19.2027	−	11.0867i	1.32197	−	0.763239i	0.984043	+	0.177933i	$0.0569411\pi$
$212$	−11.6339	+	6.40077i	−0.799017	+	0.439607i
$213$	2.66996	−	2.66996i	0.182943	−	0.182943i
$214$	−25.2658	+	10.1616i	−1.72714	+	0.694636i
$215$	19.0575	−	7.80191i	1.29971	−	0.532086i
$216$	10.8572	+	4.89575i	0.738741	+	0.333113i
$217$	7.05359	+	26.3243i	0.478829	+	1.78701i
$218$	−11.1182	−	14.8030i	−0.753021	−	1.00258i
$219$	7.75373	−	4.47662i	0.523948	−	0.302502i
$220$	2.72369	+	7.06504i	0.183631	+	0.476325i
$221$	−13.7530	+	15.6750i	−0.925130	+	1.05442i
$222$	−2.93849	+	0.356089i	−0.197218	+	0.0238991i
$223$	6.10355	−	22.7788i	0.408724	−	1.52538i	−0.388359	−	0.921508i	$-0.626958\pi$
$223$	6.10355	−	22.7788i	0.408724	−	1.52538i	0.797083	−	0.603870i	$-0.206376\pi$
$224$	16.7860	−	5.95984i	1.12156	−	0.398209i
$225$	11.5149	+	3.18749i	0.767662	+	0.212499i
$226$	−5.07815	−	3.98043i	−0.337794	−	0.264774i
$227$	6.68762	+	24.9585i	0.443873	+	1.65656i	0.718896	+	0.695118i	$0.244648\pi$
$227$	6.68762	+	24.9585i	0.443873	+	1.65656i	−0.275023	+	0.961438i	$0.588685\pi$
$228$	2.33710	−	1.28584i	0.154778	−	0.0851566i
$229$	0.143658			0.00949318			0.00474659	−	0.999989i	$-0.498489\pi$
$229$	0.143658			0.00949318			0.00474659	+	0.999989i	$0.498489\pi$
$230$	4.83999	−	2.70199i	0.319139	−	0.178164i
$231$	3.60730	−	2.08267i	0.237343	−	0.137030i
$232$	2.71617	−	3.32186i	0.178325	−	0.218091i
$233$	−9.50636	−	9.50636i	−0.622782	−	0.622782i	0.323460	−	0.946242i	$-0.395154\pi$
$233$	−9.50636	−	9.50636i	−0.622782	−	0.622782i	−0.946242	+	0.323460i	$0.895154\pi$
$234$	9.24500	−	7.93686i	0.604365	−	0.518849i
$235$	18.2911	+	14.1555i	1.19318	+	0.923406i
$236$	−8.98014	+	8.61734i	−0.584557	+	0.560941i
$237$	−7.00499	−	1.87698i	−0.455023	−	0.121923i
$238$	23.6920	+	10.1009i	1.53572	+	0.654741i
$239$		−	5.42372i		−	0.350831i	−0.984494	−	0.175416i	$-0.943873\pi$
$239$		−	5.42372i		−	0.350831i	0.984494	−	0.175416i	$-0.0561269\pi$
$240$	−4.50102	+	5.34541i	−0.290540	+	0.345045i
$241$	−1.46196	−	0.844062i	−0.0941730	−	0.0543708i	0.452174	−	0.891930i	$-0.350649\pi$
$241$	−1.46196	−	0.844062i	−0.0941730	−	0.0543708i	−0.546347	+	0.837559i	$0.683982\pi$
$242$	−11.4187	+	1.38373i	−0.734024	+	0.0889498i
$243$	−4.05388	−	15.1293i	−0.260057	−	0.970544i
$244$	4.87258	+	5.07771i	0.311935	+	0.325067i
$245$	−3.94702	−	5.18804i	−0.252166	−	0.331452i
$246$	−1.12588	−	0.882500i	−0.0717833	−	0.0562661i
$247$	−0.401136	−	6.14196i	−0.0255237	−	0.390804i
$248$	−22.8951	+	8.66431i	−1.45384	+	0.550184i
$249$	−3.93139	−	6.80936i	−0.249142	−	0.431526i
$250$	−8.21426	+	13.5102i	−0.519516	+	0.854461i
$251$	7.32610	+	4.22972i	0.462419	+	0.266978i	0.713061	−	0.701102i	$-0.247308\pi$
$251$	7.32610	+	4.22972i	0.462419	+	0.266978i	−0.250642	+	0.968080i	$0.580642\pi$
$252$	−12.8749	−	7.79151i	−0.811044	−	0.490819i
$253$	−0.768138	−	2.86673i	−0.0482924	−	0.180230i
$254$	−7.66032	+	3.08090i	−0.480651	+	0.193313i
$255$	−10.0229	+	1.27750i	−0.627661	+	0.0799999i
$256$	6.83160	+	14.4682i	0.426975	+	0.904263i
$257$	−16.5218	−	4.42700i	−1.03060	−	0.276149i	−0.296388	−	0.955068i	$-0.595782\pi$
$257$	−16.5218	−	4.42700i	−1.03060	−	0.276149i	−0.734213	+	0.678919i	$0.762449\pi$
$258$	8.13614	−	6.11089i	0.506534	−	0.380447i
$259$	8.43562			0.524164
$260$	6.76838	+	14.6352i	0.419757	+	0.907637i
$261$	−3.62521			−0.224395
$262$	1.70464	−	1.28032i	0.105313	−	0.0790985i
$263$	−2.96017	−	0.793174i	−0.182532	−	0.0489092i	0.166395	−	0.986059i	$-0.446787\pi$
$263$	−2.96017	−	0.793174i	−0.182532	−	0.0489092i	−0.348927	+	0.937150i	$0.613454\pi$
$264$	2.18481	+	3.03731i	0.134466	+	0.186934i
$265$	−9.08603	+	11.7405i	−0.558150	+	0.721214i
$266$	−7.05293	+	2.83662i	−0.432443	+	0.173924i
$267$	−0.287317	−	1.07228i	−0.0175835	−	0.0656225i
$268$	14.9418	−	24.6903i	0.912718	−	1.50820i
$269$	−6.66060	−	3.84550i	−0.406104	−	0.234464i	0.283010	−	0.959117i	$-0.408667\pi$
$269$	−6.66060	−	3.84550i	−0.406104	−	0.234464i	−0.689114	+	0.724653i	$0.742000\pi$
$270$	13.3144	+	0.192178i	0.810287	+	0.0116956i
$271$	−2.51715	−	4.35983i	−0.152906	−	0.264841i	0.779389	−	0.626541i	$-0.215530\pi$
$271$	−2.51715	−	4.35983i	−0.152906	−	0.264841i	−0.932295	+	0.361700i	$0.882196\pi$
$272$	−6.90355	+	22.0804i	−0.418589	+	1.33882i
$273$	7.37647	−	4.92633i	0.446444	−	0.298155i
$274$	21.3088	+	16.7025i	1.28731	+	1.00904i
$275$	5.93649	+	6.03528i	0.357984	+	0.363941i
$276$	1.97629	−	1.89645i	0.118959	−	0.114153i
$277$	−2.43660	−	9.09352i	−0.146401	−	0.546376i	−0.999689	−	0.0249364i	$-0.992062\pi$
$277$	−2.43660	−	9.09352i	−0.146401	−	0.546376i	0.853288	−	0.521440i	$-0.174605\pi$
$278$	19.1959	−	2.32618i	1.15129	−	0.139515i
$279$	17.9108	+	10.3408i	1.07229	+	0.619088i
$280$	14.5669	−	13.5800i	0.870538	−	0.811563i
$281$		−	16.4775i		−	0.982967i	−0.870887	−	0.491484i	$-0.836455\pi$
$281$		−	16.4775i		−	0.982967i	0.870887	−	0.491484i	$-0.163545\pi$
$282$	10.5130	+	4.48214i	0.626043	+	0.266908i
$283$	−7.40783	−	1.98492i	−0.440350	−	0.117991i	0.0318306	−	0.999493i	$-0.489866\pi$
$283$	−7.40783	−	1.98492i	−0.440350	−	0.117991i	−0.472181	+	0.881502i	$0.656533\pi$
$284$	−6.69245	−	6.97421i	−0.397124	−	0.413843i
$285$	1.82527	−	2.35853i	0.108120	−	0.139707i
$286$	8.48466	−	1.59494i	0.501708	−	0.0943108i
$287$	2.88276	+	2.88276i	0.170164	+	0.170164i
$288$	5.80938	−	12.2056i	0.342321	−	0.719220i
$289$	−14.2463	+	8.22510i	−0.838017	+	0.483829i
$290$	1.30842	−	4.61557i	0.0768330	−	0.271035i
$291$	3.04854			0.178708
$292$	−11.0480	−	20.0806i	−0.646538	−	1.17513i
$293$	4.38556	+	16.3671i	0.256207	+	0.956179i	0.967415	+	0.253197i	$0.0814820\pi$
$293$	4.38556	+	16.3671i	0.256207	+	0.956179i	−0.711207	+	0.702982i	$0.751851\pi$
$294$	−2.53514	−	1.98713i	−0.147853	−	0.115892i
$295$	−5.37803	+	12.8337i	−0.313121	+	0.747206i
$296$	0.756303	+	7.53937i	0.0439592	+	0.438217i
$297$	1.84523	−	6.88649i	0.107071	−	0.399595i
$298$	−22.8841	+	2.77312i	−1.32564	+	0.160642i
$299$	−2.03016	−	5.98520i	−0.117407	−	0.346133i
$300$	−2.23909	+	7.48514i	−0.129274	+	0.432155i
$301$	−25.1138	+	14.4994i	−1.44753	+	0.835733i
$302$	11.2717	+	15.0073i	0.648613	+	0.863574i
$303$	−0.730854	−	2.72758i	−0.0419865	−	0.156696i
$304$	−3.16757	−	6.04927i	−0.181673	−	0.346949i
$305$	7.25666	+	3.04095i	0.415515	+	0.174124i
$306$	18.1335	−	7.29308i	1.03662	−	0.416918i
$307$	8.97585	−	8.97585i	0.512279	−	0.512279i	−0.402945	−	0.915224i	$-0.632014\pi$
$307$	8.97585	−	8.97585i	0.512279	−	0.512279i	0.915224	+	0.402945i	$0.132014\pi$
$308$	−5.13993	−	9.34218i	−0.292875	−	0.532320i
$309$	5.12660	−	2.95984i	0.291642	−	0.168380i
$310$	−19.6302	+	19.0716i	−1.11492	+	1.08319i
$311$			5.17060i			0.293198i	0.989196	+	0.146599i	$0.0468326\pi$
$311$			5.17060i			0.293198i	−0.989196	+	0.146599i	$0.953167\pi$
$312$	5.06427	+	6.15107i	0.286708	+	0.348236i
$313$	−12.0985	−	12.0985i	−0.683847	−	0.683847i	0.277018	−	0.960865i	$-0.410654\pi$
$313$	−12.0985	−	12.0985i	−0.683847	−	0.683847i	−0.960865	+	0.277018i	$0.910654\pi$
$314$	−27.3388	−	3.88628i	−1.54282	−	0.219316i
$315$	−16.6721	−	2.26495i	−0.939367	−	0.127615i
$316$	−5.17344	+	17.8291i	−0.291029	+	1.00296i
$317$	5.65270	+	5.65270i	0.317487	+	0.317487i	0.847801	−	0.530314i	$-0.177926\pi$
$317$	5.65270	+	5.65270i	0.317487	+	0.317487i	−0.530314	+	0.847801i	$0.677926\pi$
$318$	−2.87695	+	6.74801i	−0.161332	+	0.378410i
$319$	−2.22448	−	1.28430i	−0.124547	−	0.0719072i
$320$	13.4432	+	11.8017i	0.751499	+	0.659734i
$321$	−7.52240	+	13.0292i	−0.419859	+	0.727218i
$322$	−6.24148	+	4.68785i	−0.347824	+	0.261244i
$323$	2.55538	−	9.53680i	0.142185	−	0.530642i
$324$	−7.53330	+	1.85299i	−0.418516	+	0.102944i
$325$	13.4527	+	12.0011i	0.746219	+	0.665701i
$326$	13.1536	+	10.3103i	0.728512	+	0.571032i
$327$	−9.87924	−	2.64713i	−0.546323	−	0.146387i
$328$	−2.31802	+	2.83493i	−0.127991	+	0.156533i
$329$	−28.2067	−	16.2851i	−1.55509	−	0.897829i
$330$	3.59211	+	2.14362i	0.197739	+	0.118002i
$331$	−8.22026	+	14.2379i	−0.451827	+	0.782587i	−0.998500	−	0.0547597i	$-0.982561\pi$
$331$	−8.22026	+	14.2379i	−0.451827	+	0.782587i	0.546673	+	0.837346i	$0.315894\pi$
$332$	−17.6349	+	9.70246i	−0.967841	+	0.532491i
$333$	4.52661	−	4.52661i	0.248057	−	0.248057i
$334$	−4.19812	−	10.4382i	−0.229711	−	0.571151i
$335$	4.34350	−	31.9722i	0.237311	−	1.74683i
$336$	5.26738	−	8.31221i	0.287359	−	0.453468i
$337$	−1.54306	+	1.54306i	−0.0840560	+	0.0840560i	−0.747885	−	0.663829i	$-0.768930\pi$
$337$	−1.54306	+	1.54306i	−0.0840560	+	0.0840560i	0.663829	+	0.747885i	$0.268930\pi$
$338$	17.8085	−	4.56680i	0.968657	−	0.248401i
$339$	−3.56456			−0.193600
$340$	2.74069	+	25.7195i	0.148635	+	1.39484i
$341$	7.32688	+	12.6905i	0.396773	+	0.687231i
$342$	−2.26250	+	5.30680i	−0.122342	+	0.286959i
$343$	−9.09491	−	9.09491i	−0.491079	−	0.491079i
$344$	−15.2105	−	21.1456i	−0.820096	−	1.14009i
$345$	1.18356	−	2.82435i	0.0637208	−	0.152058i
$346$	9.48302	+	7.43311i	0.509810	+	0.399606i
$347$	−19.7182	+	5.28346i	−1.05853	+	0.283631i	−0.745771	−	0.666203i	$-0.767919\pi$
$347$	−19.7182	+	5.28346i	−1.05853	+	0.283631i	−0.312755	+	0.949834i	$0.601252\pi$
$348$	0.0488619	−	2.37005i	0.00261927	−	0.127048i
$349$	10.6734	+	18.4869i	0.571335	+	0.989581i	0.996429	+	0.0844316i	$0.0269075\pi$
$349$	10.6734	+	18.4869i	0.571335	+	0.989581i	−0.425095	+	0.905149i	$0.639759\pi$
$350$	8.90103	−	20.4092i	0.475780	−	1.09092i
$351$	2.96537	−	14.8899i	0.158280	−	0.794764i
$352$	7.88879	−	5.43141i	0.420474	−	0.289495i
$353$	21.0821	+	5.64894i	1.12209	+	0.300663i	0.771728	−	0.635952i	$-0.219392\pi$
$353$	21.0821	+	5.64894i	1.12209	+	0.300663i	0.350360	+	0.936615i	$0.386059\pi$
$354$	−0.967683	+	6.80736i	−0.0514318	+	0.361807i
$355$	−9.96698	−	4.17672i	−0.528992	−	0.221677i
$356$	−2.75949	+	0.678762i	−0.146253	+	0.0359743i
$357$	13.7438	−	3.68263i	0.727398	−	0.194906i
$358$	−7.39833	+	17.3531i	−0.391014	+	0.917139i
$359$		−	21.9019i		−	1.15594i	−0.816059	−	0.577969i	$-0.803846\pi$
$359$		−	21.9019i		−	1.15594i	0.816059	−	0.577969i	$-0.196154\pi$
$360$	0.529551	−	15.1038i	0.0279098	−	0.796041i
$361$	−8.04290	−	13.9307i	−0.423311	−	0.733195i
$362$	−16.0997	−	21.4354i	−0.846182	−	1.12662i
$363$	−4.49329	+	4.49329i	−0.235836	+	0.235836i
$364$	−12.2189	−	19.1388i	−0.640445	−	1.00315i
$365$	−20.2647	−	15.6829i	−1.06070	−	0.820882i
$366$	3.84914	+	0.547165i	0.201198	+	0.0286008i
$367$	−0.898235	+	3.35226i	−0.0468875	+	0.174987i	−0.985399	−	0.170262i	$-0.945539\pi$
$367$	−0.898235	+	3.35226i	−0.0468875	+	0.174987i	0.938511	+	0.345248i	$0.112205\pi$
$368$	−4.74937	−	5.15805i	−0.247578	−	0.268882i
$369$	3.09381			0.161057
$370$	4.12946	+	7.39697i	0.214680	+	0.384550i
$371$	10.4530	−	18.1051i	0.542691	−	0.939968i
$372$	−7.00191	+	11.5702i	−0.363032	+	0.599885i
$373$	21.2313	−	5.68892i	1.09932	−	0.294561i	0.336831	−	0.941565i	$-0.390645\pi$
$373$	21.2313	−	5.68892i	1.09932	−	0.294561i	0.762487	+	0.647004i	$0.223978\pi$
$374$	13.7107	+	1.94900i	0.708961	+	0.100781i
$375$	1.03287	+	8.67377i	0.0533370	+	0.447911i
$376$	12.0260	−	26.6699i	0.620195	−	1.37540i
$377$	−4.90526	−	2.42042i	−0.252634	−	0.124658i
$378$	−18.6152	+	2.25581i	−0.957464	+	0.116026i
$379$	−28.7721	+	16.6116i	−1.47792	+	0.853279i	−0.999689	−	0.0249543i	$-0.992056\pi$
$379$	−28.7721	+	16.6116i	−1.47792	+	0.853279i	−0.478233	+	0.878233i	$0.658723\pi$
$380$	−5.93995	−	4.79593i	−0.304713	−	0.246026i
$381$	−2.28071	+	3.95030i	−0.116844	+	0.202380i
$382$	−2.29110	−	18.9065i	−0.117223	−	0.967340i
$383$	27.0424	−	7.24598i	1.38180	−	0.370252i	0.510026	−	0.860159i	$-0.329636\pi$
$383$	27.0424	−	7.24598i	1.38180	−	0.370252i	0.871775	+	0.489907i	$0.162969\pi$
$384$	7.90132	+	3.96251i	0.403212	+	0.202211i
$385$	−9.42783	−	7.29623i	−0.480487	−	0.371850i
$386$	2.40789	+	5.98695i	0.122558	+	0.304728i
$387$	−5.69571	+	21.2567i	−0.289529	+	1.08054i
$388$	0.160854	−	7.80224i	0.00816613	−	0.396099i
$389$			5.22428i			0.264882i	0.991191	+	0.132441i	$0.0422814\pi$
$389$			5.22428i			0.264882i	−0.991191	+	0.132441i	$0.957719\pi$
$390$	7.93074	+	4.05666i	0.401589	+	0.205417i
$391$		−	10.1380i		−	0.512703i
$392$	−5.21950	+	6.38344i	−0.263625	+	0.322412i
$393$	0.304831	−	1.13765i	0.0153767	−	0.0573867i
$394$	−13.0961	+	5.26709i	−0.659770	+	0.265352i
$395$	2.62424	+	20.5892i	0.132040	+	1.03595i
$396$	−7.77119	−	2.25496i	−0.390517	−	0.113316i
$397$	24.3214	−	6.51689i	1.22065	−	0.327073i	0.409720	−	0.912211i	$-0.365626\pi$
$397$	24.3214	−	6.51689i	1.22065	−	0.327073i	0.810934	+	0.585138i	$0.198960\pi$
$398$	−26.2620	+	3.18246i	−1.31640	+	0.159522i
$399$	−2.09987	+	3.63708i	−0.105125	+	0.182082i
$400$	19.0389	+	6.12552i	0.951943	+	0.306276i
$401$	30.6071	−	17.6710i	1.52845	−	0.882449i	0.529018	−	0.848610i	$-0.322560\pi$
$401$	30.6071	−	17.6710i	1.52845	−	0.882449i	0.999427	−	0.0338383i	$-0.0107731\pi$
$402$	−1.91802	−	15.8277i	−0.0956620	−	0.789415i
$403$	17.3309	+	25.9505i	0.863314	+	1.29269i
$404$	−7.01937	+	1.72658i	−0.349227	+	0.0859007i
$405$	−6.90290	+	5.25167i	−0.343008	+	0.260958i
$406$	−0.950796	+	6.68857i	−0.0471872	+	0.331948i
$407$	4.38123	−	1.17395i	0.217170	−	0.0581904i
$408$	4.52358	+	11.9534i	0.223951	+	0.591781i
$409$	14.9070	−	25.8196i	0.737103	−	1.27670i	−0.216692	−	0.976240i	$-0.569527\pi$
$409$	14.9070	−	25.8196i	0.737103	−	1.27670i	0.953795	−	0.300459i	$-0.0971399\pi$
$410$	−1.11663	+	3.93900i	−0.0551462	+	0.194533i
$411$	14.9575			0.737799
$412$	−7.30473	−	13.2769i	−0.359878	−	0.654104i
$413$	5.07162	−	18.9275i	0.249558	−	0.931364i
$414$	−0.833688	+	5.86475i	−0.0409736	+	0.288237i
$415$	−13.7728	+	17.7966i	−0.676082	+	0.873600i
$416$	16.0099	−	12.6366i	0.784949	−	0.619561i
$417$	7.55361	−	7.55361i	0.369902	−	0.369902i
$418$	−3.26834	+	2.45479i	−0.159860	+	0.120068i
$419$	−5.24342	−	9.08187i	−0.256158	−	0.443679i	0.709051	−	0.705157i	$-0.249123\pi$
$419$	−5.24342	−	9.08187i	−0.256158	−	0.443679i	−0.965209	+	0.261478i	$0.915790\pi$
$420$	1.70546	−	10.8692i	0.0832181	−	0.530361i
$421$		−	15.1565i		−	0.738683i	−0.929294	−	0.369341i	$-0.879583\pi$
$421$		−	15.1565i		−	0.738683i	0.929294	−	0.369341i	$-0.120417\pi$
$422$	−28.8457	−	12.2981i	−1.40419	−	0.598662i
$423$	−23.8746	+	6.39718i	−1.16082	+	0.311042i
$424$	17.1186	+	7.71915i	0.831355	+	0.374875i
$425$	14.2519	+	25.1623i	0.691318	+	1.22055i
$426$	−5.28677	−	0.751528i	−0.256145	−	0.0364117i
$427$	−10.7024	−	2.86769i	−0.517924	−	0.138777i
$428$	32.9491	+	19.9398i	1.59266	+	0.963828i
$429$	3.14556	−	3.58515i	0.151869	−	0.173093i
$430$	−25.0080	−	14.9237i	−1.20599	−	0.719685i
$431$	2.55968	+	4.43350i	0.123295	+	0.213554i	0.921065	−	0.389408i	$-0.127320\pi$
$431$	2.55968	+	4.43350i	0.123295	+	0.213554i	−0.797770	+	0.602962i	$0.793987\pi$
$432$	−3.68511	−	16.4352i	−0.177300	−	0.790738i
$433$	−18.2830	+	4.89892i	−0.878625	+	0.235427i	−0.669814	−	0.742529i	$-0.733626\pi$
$433$	−18.2830	+	4.89892i	−0.878625	+	0.235427i	−0.208811	+	0.977956i	$0.566959\pi$
$434$	23.7765	−	30.3336i	1.14131	−	1.45606i
$435$	−1.00414	−	2.45278i	−0.0481447	−	0.117602i
$436$	−7.29618	+	25.1446i	−0.349424	+	1.20421i
$437$	2.11592	+	2.11592i	0.101218	+	0.101218i
$438$	−11.6474	−	4.96576i	−0.556534	−	0.237273i
$439$	8.96000	+	15.5192i	0.427637	+	0.740690i	0.996663	−	0.0816304i	$-0.0260127\pi$
$439$	8.96000	+	15.5192i	0.427637	+	0.740690i	−0.569025	+	0.822320i	$0.692679\pi$
$440$	5.67577	−	9.08031i	0.270582	−	0.432887i
$441$	6.96636			0.331732
$442$	29.4057	+	2.23880i	1.39868	+	0.106489i
$443$	−9.03180	+	9.03180i	−0.429114	+	0.429114i	−0.888326	−	0.459213i	$-0.848132\pi$
$443$	−9.03180	+	9.03180i	−0.429114	+	0.429114i	0.459213	+	0.888326i	$0.348132\pi$
$444$	2.89834	+	3.02037i	0.137549	+	0.143340i
$445$	−2.52857	+	1.92372i	−0.119866	+	0.0911930i
$446$	−30.9417	+	12.4444i	−1.46513	+	0.589260i
$447$	−9.00492	+	9.00492i	−0.425918	+	0.425918i
$448$	−20.9958	−	13.9196i	−0.991958	−	0.657639i
$449$	−13.7192	+	23.7623i	−0.647448	+	1.12141i	0.336283	+	0.941761i	$0.390830\pi$
$449$	−13.7192	+	23.7623i	−0.647448	+	1.12141i	−0.983730	+	0.179651i	$0.942503\pi$
$450$	−6.17537	−	15.7281i	−0.291110	−	0.741428i
$451$	1.89841	+	1.09605i	0.0893925	+	0.0516108i
$452$	−0.188082	+	9.12291i	−0.00884662	+	0.429106i
$453$	10.0156	+	2.68367i	0.470574	+	0.126090i
$454$	22.5429	−	28.7598i	1.05799	−	1.34976i
$455$	−21.0468	−	14.1961i	−0.986687	−	0.665521i
$456$	−3.43892	−	1.55068i	−0.161042	−	0.0726173i
$457$	−3.16969	+	11.8295i	−0.148272	+	0.553359i	0.851316	+	0.524653i	$0.175805\pi$
$457$	−3.16969	+	11.8295i	−0.148272	+	0.553359i	−0.999588	+	0.0287053i	$0.990862\pi$
$458$	−0.122010	−	0.162446i	−0.00570115	−	0.00759061i
$459$	12.1769	−	21.0909i	0.568367	−	0.984441i
$460$	−7.16602	−	3.17816i	−0.334117	−	0.148182i
$461$	−14.7686	−	8.52663i	−0.687840	−	0.397125i	0.114962	−	0.993370i	$-0.463325\pi$
$461$	−14.7686	−	8.52663i	−0.687840	−	0.397125i	−0.802803	+	0.596245i	$0.796659\pi$
$462$	−5.41877	−	2.31024i	−0.252104	−	0.107482i
$463$	14.8781	+	14.8781i	0.691442	+	0.691442i	0.962549	−	0.271107i	$-0.0873898\pi$
$463$	14.8781	+	14.8781i	0.691442	+	0.691442i	−0.271107	+	0.962549i	$0.587390\pi$
$464$	−6.06318	−	0.250108i	−0.281476	−	0.0116110i
$465$	−2.03541	+	14.9825i	−0.0943901	+	0.694798i
$466$	−2.67580	+	18.8235i	−0.123954	+	0.871981i
$467$	2.73760	+	2.73760i	0.126681	+	0.126681i	0.767605	−	0.640924i	$-0.221448\pi$
$467$	2.73760	+	2.73760i	0.126681	+	0.126681i	−0.640924	+	0.767605i	$0.721448\pi$
$468$	−16.8267	−	3.71325i	−0.777817	−	0.171645i
$469$			45.4372i			2.09809i
$470$	0.472071	−	32.7057i	0.0217750	−	1.50860i
$471$	−13.2114	+	7.62763i	−0.608751	+	0.351463i
$472$	17.3713	+	2.83581i	0.799578	+	0.130529i
$473$	−11.0256	+	11.0256i	−0.506957	+	0.506957i
$474$	3.82694	+	9.51527i	0.175777	+	0.437051i
$475$	−8.22616	−	2.27711i	−0.377442	−	0.104481i
$476$	−8.69992	−	35.3693i	−0.398760	−	1.62115i
$477$	−4.10616	−	15.3244i	−0.188008	−	0.701657i
$478$	−6.13306	+	4.60642i	−0.280520	+	0.210693i
$479$	−28.6298	+	16.5294i	−1.30813	+	0.755249i	−0.981784	−	0.190002i	$-0.939151\pi$
$479$	−28.6298	+	16.5294i	−1.30813	+	0.755249i	−0.326346	+	0.945251i	$0.605817\pi$
$480$	9.86727	+	0.549779i	0.450377	+	0.0250939i
$481$	9.14719	−	3.10269i	0.417076	−	0.141471i
$482$	0.287202	+	2.37003i	0.0130817	+	0.107952i
$483$	−1.11613	+	4.16545i	−0.0507856	+	0.189534i
$484$	11.2627	+	11.7369i	0.511943	+	0.533496i
$485$	−3.30563	−	8.07457i	−0.150101	−	0.366648i
$486$	−13.6650	+	17.4335i	−0.619856	+	0.790800i
$487$	−3.56225	−	13.2945i	−0.161421	−	0.602431i	−0.998470	−	0.0553028i	$-0.982388\pi$
$487$	−3.56225	−	13.2945i	−0.161421	−	0.602431i	0.837049	−	0.547128i	$-0.184279\pi$
$488$	1.60348	−	9.82238i	0.0725860	−	0.444638i
$489$	9.23306			0.417534
$490$	−2.51431	+	8.86948i	−0.113585	+	0.400682i
$491$	1.20988	−	0.698526i	0.0546012	−	0.0315240i	−0.472451	−	0.881357i	$-0.656631\pi$
$491$	1.20988	−	0.698526i	0.0546012	−	0.0315240i	0.527052	+	0.849833i	$0.323297\pi$
$492$	−0.0416996	+	2.02264i	−0.00187996	+	0.0911876i
$493$	−6.20431	−	6.20431i	−0.279428	−	0.279428i
$494$	−6.60454	+	5.67002i	−0.297152	+	0.255106i
$495$	−8.97424	+	1.14383i	−0.403362	+	0.0514114i
$496$	29.2425	+	18.5307i	1.31303	+	0.832055i
$497$	14.6996	+	3.93875i	0.659368	+	0.176677i
$498$	−4.36096	+	10.2288i	−0.195419	+	0.458364i
$499$		−	14.5051i		−	0.649336i	−0.945828	−	0.324668i	$-0.894747\pi$
$499$		−	14.5051i		−	0.649336i	0.945828	−	0.324668i	$-0.105253\pi$
$500$	22.2536	−	2.18579i	0.995211	−	0.0977514i
$501$	−5.38279	−	3.10775i	−0.240485	−	0.138844i
$502$	−1.43922	−	11.8766i	−0.0642353	−	0.530078i
$503$	1.09005	+	4.06814i	0.0486031	+	0.181389i	0.985960	−	0.166981i	$-0.0534018\pi$
$503$	1.09005	+	4.06814i	0.0486031	+	0.181389i	−0.937357	+	0.348370i	$0.886735\pi$
$504$	2.12426	+	21.1762i	0.0946222	+	0.943261i
$505$	−6.43198	+	4.89340i	−0.286220	+	0.217754i
$506$	−2.58927	+	3.30334i	−0.115107	+	0.146851i
$507$	6.18675	−	8.05500i	0.274763	−	0.357735i
$508$	9.98981	+	6.04554i	0.443226	+	0.268227i
$509$	15.2703	+	26.4489i	0.676844	+	1.17233i	0.975926	+	0.218101i	$0.0699861\pi$
$509$	15.2703	+	26.4489i	0.676844	+	1.17233i	−0.299082	+	0.954227i	$0.596681\pi$
$510$	9.95715	+	10.2488i	0.440910	+	0.453825i
$511$	31.2502	+	18.0423i	1.38243	+	0.798145i
$512$	10.5583	−	20.0131i	0.466615	−	0.884461i
$513$	1.86047	+	6.94336i	0.0821416	+	0.306557i
$514$	9.02613	+	22.4425i	0.398126	+	0.989896i
$515$	−13.3986	−	10.3692i	−0.590412	−	0.456922i
$516$	−13.8202	−	4.01019i	−0.608400	−	0.176539i
$517$	−16.9161	−	4.53266i	−0.743970	−	0.199346i
$518$	−7.16445	−	9.53887i	−0.314788	−	0.419114i
$519$	6.65651			0.292188
$520$	10.8008	−	20.0834i	0.473647	−	0.880715i
$521$	−4.04849			−0.177368			−0.0886838	−	0.996060i	$-0.528266\pi$
$521$	−4.04849			−0.177368			−0.0886838	+	0.996060i	$0.528266\pi$
$522$	3.07892	+	4.09933i	0.134761	+	0.179423i
$523$	33.4902	+	8.97367i	1.46442	+	0.392391i	0.901016	−	0.433787i	$-0.142823\pi$
$523$	33.4902	+	8.97367i	1.46442	+	0.392391i	0.563409	+	0.826178i	$0.309490\pi$
$524$	−2.89554	−	0.840193i	−0.126492	−	0.0367040i
$525$	−3.08552	−	11.9075i	−0.134663	−	0.519687i
$526$	1.61719	+	4.02096i	0.0705127	+	0.175322i
$527$	12.9556	+	48.3509i	0.564354	+	2.10620i
$528$	1.57896	−	5.05017i	0.0687155	−	0.219781i
$529$	−17.2576	−	9.96369i	−0.750331	−	0.433204i
$530$	20.9928	+	0.303008i	0.911871	+	0.0131618i
$531$	−7.43518	−	12.8781i	−0.322659	−	0.558862i
$532$	9.19772	+	5.56619i	0.398772	+	0.241325i
$533$	4.18623	+	2.06563i	0.181326	+	0.0894722i
$534$	−0.968498	+	1.23559i	−0.0419110	+	0.0534693i
$535$	42.6668	+	5.79639i	1.84465	+	0.250600i
$536$	−40.6097	+	4.07372i	−1.75407	+	0.175958i
$537$	2.69733	+	10.0666i	0.116398	+	0.434405i
$538$	1.30848	+	10.7977i	0.0564125	+	0.465523i
$539$	4.27466	+	2.46797i	0.184123	+	0.106303i
$540$	−11.0907	−	15.2189i	−0.477268	−	0.654918i
$541$			27.0286i			1.16205i	0.813886	+	0.581024i	$0.197348\pi$
$541$			27.0286i			1.16205i	−0.813886	+	0.581024i	$0.802652\pi$
$542$	−2.79219	+	6.54920i	−0.119935	+	0.281312i
$543$	−14.3056	−	3.83317i	−0.613912	−	0.164497i
$544$	30.8314	−	10.9467i	1.32189	−	0.469334i
$545$	3.70100	+	29.0372i	0.158533	+	1.24382i
$546$	−11.8355	−	4.15722i	−0.506513	−	0.177913i
$547$	7.43836	+	7.43836i	0.318041	+	0.318041i	0.848014	−	0.529973i	$-0.177798\pi$
$547$	7.43836	+	7.43836i	0.318041	+	0.318041i	−0.529973	+	0.848014i	$0.677798\pi$
$548$	0.789223	−	38.2813i	0.0337139	−	1.63530i
$549$	−7.28178	+	4.20414i	−0.310779	+	0.179428i
$550$	1.78269	−	11.8387i	0.0760143	−	0.504804i
$551$	2.58982			0.110330
$552$	−3.82295	−	0.624087i	−0.162716	−	0.0265629i
$553$	−7.56489	−	28.2325i	−0.321692	−	1.20057i
$554$	−8.21338	+	10.4785i	−0.348953	+	0.445188i
$555$	4.31646	+	1.80884i	0.183224	+	0.0767810i
$556$	−18.9337	−	19.7308i	−0.802966	−	0.836772i
$557$	−2.93335	+	10.9474i	−0.124290	+	0.463857i	−0.999813	−	0.0193188i	$-0.993850\pi$
$557$	−2.93335	+	10.9474i	−0.124290	+	0.463857i	0.875523	+	0.483176i	$0.160517\pi$
$558$	−3.51859	−	29.0358i	−0.148954	−	1.22918i
$559$	−21.8992	+	24.9596i	−0.926236	+	1.05568i
$560$	−27.7279	−	4.93836i	−1.17172	−	0.208684i
$561$	6.62565	−	3.82532i	0.279735	−	0.161505i
$562$	−18.6325	+	13.9945i	−0.785966	+	0.590323i
$563$	1.63124	+	6.08786i	0.0687485	+	0.256573i	0.991743	−	0.128240i	$-0.0409327\pi$
$563$	1.63124	+	6.08786i	0.0687485	+	0.256573i	−0.922995	+	0.384813i	$0.874266\pi$
$564$	−3.86049	−	15.6947i	−0.162556	−	0.660866i
$565$	3.86517	+	9.44135i	0.162609	+	0.397200i
$566$	4.04702	+	10.0625i	0.170109	+	0.422957i
$567$	8.63672	−	8.63672i	0.362708	−	0.362708i
$568$	−2.20237	+	13.4910i	−0.0924093	+	0.566069i
$569$	34.6883	−	20.0273i	1.45421	−	0.839587i	0.455491	−	0.890240i	$-0.349464\pi$
$569$	34.6883	−	20.0273i	1.45421	−	0.839587i	0.998716	+	0.0506534i	$0.0161304\pi$
$570$	−4.21720	−	0.0608707i	−0.176639	−	0.00254959i
$571$		−	19.2559i		−	0.805835i	−0.915236	−	0.402918i	$-0.867996\pi$
$571$		−	19.2559i		−	0.805835i	0.915236	−	0.402918i	$-0.132004\pi$
$572$	−9.00963	−	8.23972i	−0.376712	−	0.344520i
$573$	−7.43972	−	7.43972i	−0.310799	−	0.310799i
$574$	0.811425	−	5.70813i	0.0338682	−	0.238253i
$575$	−8.76416	−	0.0723260i	−0.365491	−	0.00301620i
$576$	−18.7358	+	3.79714i	−0.780659	+	0.158214i
$577$	20.0863	+	20.0863i	0.836202	+	0.836202i	0.988357	−	0.152154i	$-0.0486211\pi$
$577$	20.0863	+	20.0863i	0.836202	+	0.836202i	−0.152154	+	0.988357i	$0.548621\pi$
$578$	21.4003	+	9.12383i	0.890136	+	0.379501i
$579$	3.08737	+	1.78250i	0.128307	+	0.0740780i
$580$	−6.33046	+	2.44050i	−0.262858	+	0.101336i
$581$	15.8449	−	27.4441i	0.657356	−	1.13857i
$582$	−2.58915	−	3.44724i	−0.107324	−	0.142893i
$583$	2.90938	−	10.8580i	0.120494	−	0.449691i
$584$	−13.3236	+	29.5476i	−0.551336	+	1.22269i
$585$	−18.9115	+	3.67614i	−0.781895	+	0.151989i
$586$	14.7830	−	18.8599i	0.610681	−	0.779095i
$587$	15.8873	+	4.25698i	0.655738	+	0.175705i	0.571322	−	0.820726i	$-0.306431\pi$
$587$	15.8873	+	4.25698i	0.655738	+	0.175705i	0.0844163	+	0.996431i	$0.473097\pi$
$588$	−0.0938952	+	4.55439i	−0.00387217	+	0.187820i
$589$	−12.7953	−	7.38738i	−0.527222	−	0.304392i
$590$	19.0797	−	4.81837i	0.785501	−	0.198369i
$591$	−3.89909	+	6.75342i	−0.160387	+	0.277799i
$592$	7.88306	−	7.25847i	0.323992	−	0.298321i
$593$	8.97210	−	8.97210i	0.368440	−	0.368440i	−0.498468	−	0.866908i	$-0.666104\pi$
$593$	8.97210	−	8.97210i	0.368440	−	0.368440i	0.866908	+	0.498468i	$0.166104\pi$
$594$	−9.35431	+	3.76220i	−0.383812	+	0.154365i
$595$	−24.6569	−	32.4095i	−1.01084	−	1.32866i
$596$	22.5715	+	23.5217i	0.924564	+	0.963488i
$597$	−10.3341	+	10.3341i	−0.422948	+	0.422948i
$598$	−5.04374	+	7.37895i	−0.206254	+	0.301748i
$599$	6.53440			0.266988			0.133494	−	0.991050i	$-0.457380\pi$
$599$	6.53440			0.266988			0.133494	+	0.991050i	$0.457380\pi$
$600$	10.3658	−	3.82528i	0.423180	−	0.156166i
$601$	−9.84509	−	17.0522i	−0.401590	−	0.695574i	0.592328	−	0.805697i	$-0.298209\pi$
$601$	−9.84509	−	17.0522i	−0.401590	−	0.695574i	−0.993918	+	0.110123i	$0.964876\pi$
$602$	37.7251	+	16.0837i	1.53756	+	0.655524i
$603$	24.3819	+	24.3819i	0.992907	+	0.992907i
$604$	7.39689	−	25.4917i	0.300975	−	1.03724i
$605$	16.7735	+	7.02902i	0.681938	+	0.285770i
$606$	−2.46359	+	3.14300i	−0.100076	+	0.127676i
$607$	1.40422	−	0.376259i	0.0569954	−	0.0152719i	−0.230209	−	0.973141i	$-0.573941\pi$
$607$	1.40422	−	0.376259i	0.0569954	−	0.0152719i	0.287204	+	0.957869i	$0.407274\pi$
$608$	−4.15017	+	8.71954i	−0.168312	+	0.353624i
$609$	1.86613	+	3.23224i	0.0756195	+	0.130977i
$610$	−2.72449	−	10.7884i	−0.110312	−	0.436810i
$611$	−36.5759	−	7.28420i	−1.47970	−	0.294687i
$612$	−23.6478	−	14.3109i	−0.955906	−	0.578486i
$613$	−10.0891	−	2.70337i	−0.407496	−	0.109188i	0.0492476	−	0.998787i	$-0.484318\pi$
$613$	−10.0891	−	2.70337i	−0.407496	−	0.109188i	−0.456744	+	0.889598i	$0.650984\pi$
$614$	−17.7730	−	2.52648i	−0.717261	−	0.101960i
$615$	0.856947	+	2.09324i	0.0345554	+	0.0844076i
$616$	−6.19860	+	13.7466i	−0.249749	+	0.553864i
$617$	7.95408	−	2.13129i	0.320219	−	0.0858025i	−0.0951291	−	0.995465i	$-0.530326\pi$
$617$	7.95408	−	2.13129i	0.320219	−	0.0858025i	0.415348	+	0.909662i	$0.363660\pi$
$618$	−7.70101	−	3.28326i	−0.309780	−	0.132072i
$619$			2.83419i			0.113916i	0.998377	+	0.0569578i	$0.0181401\pi$
$619$			2.83419i			0.113916i	−0.998377	+	0.0569578i	$0.981860\pi$
$620$	38.2379	+	5.99985i	1.53567	+	0.240960i
$621$	3.69055	+	6.39222i	0.148097	+	0.256511i
$622$	5.84683	−	4.39144i	0.234437	−	0.176081i
$623$	3.16368	−	3.16368i	0.126750	−	0.126750i
$624$	2.65441	−	10.9508i	0.106261	−	0.438381i
$625$	21.8540	−	12.1410i	0.874159	−	0.485639i
$626$	−3.40543	+	23.9561i	−0.136108	+	0.957480i
$627$	−0.584459	+	2.18123i	−0.0233411	+	0.0871100i
$628$	18.8246	+	34.2150i	0.751182	+	1.36533i
$629$	15.4940			0.617786
$630$	11.5986	+	20.7762i	0.462099	+	0.827743i
$631$	8.56140	−	14.8288i	0.340824	−	0.590324i	−0.643762	−	0.765226i	$-0.722627\pi$
$631$	8.56140	−	14.8288i	0.340824	−	0.590324i	0.984586	+	0.174901i	$0.0559606\pi$
$632$	24.5547	−	9.29236i	0.976734	−	0.369630i
$633$	−16.7335	+	4.48372i	−0.665096	+	0.178212i
$634$	1.59109	−	11.1929i	0.0631904	−	0.444526i
$635$	12.9361	+	1.75740i	0.513353	+	0.0697403i
$636$	10.0740	−	2.47794i	0.399459	−	0.0982565i
$637$	9.42617	+	4.65119i	0.373478	+	0.184287i
$638$	0.437000	+	3.60618i	0.0173010	+	0.142770i
$639$	10.0015	−	5.77435i	0.395652	−	0.228430i
$640$	1.92771	−	25.2247i	0.0761994	−	0.997093i
$641$	8.48826	−	14.7021i	0.335266	−	0.580698i	−0.648270	−	0.761411i	$-0.724507\pi$
$641$	8.48826	−	14.7021i	0.335266	−	0.580698i	0.983536	+	0.180713i	$0.0578405\pi$
$642$	21.1220	−	2.55959i	0.833620	−	0.101019i
$643$	34.9369	−	9.36132i	1.37778	−	0.369174i	0.507464	−	0.861673i	$-0.330583\pi$
$643$	34.9369	−	9.36132i	1.37778	−	0.369174i	0.870313	+	0.492498i	$0.163916\pi$
$644$	10.6019	+	3.07634i	0.417773	+	0.121225i
$645$	−15.9597	+	2.03417i	−0.628412	+	0.0800955i
$646$	−12.9544	+	5.21011i	−0.509683	+	0.204989i
$647$	−6.81778	+	25.4443i	−0.268035	+	1.00032i	0.692332	+	0.721579i	$0.256583\pi$
$647$	−6.81778	+	25.4443i	−0.268035	+	1.00032i	−0.960367	+	0.278740i	$0.910083\pi$
$648$	8.49344	+	6.94477i	0.333654	+	0.272816i
$649$		−	10.5362i		−	0.413584i
$650$	2.14518	−	25.4047i	0.0841410	−	0.996454i
$651$		−	21.2924i		−	0.834514i
$652$	0.487176	−	23.6305i	0.0190793	−	0.925443i
$653$	−3.16533	+	11.8132i	−0.123869	+	0.462285i	−0.999797	−	0.0201568i	$-0.993583\pi$
$653$	−3.16533	+	11.8132i	−0.123869	+	0.462285i	0.875928	+	0.482442i	$0.160250\pi$
$654$	5.39719	+	13.4195i	0.211047	+	0.524745i
$655$	−3.34379	+	0.426190i	−0.130653	+	0.0166526i
$656$	5.17441	+	0.213446i	0.202027	+	0.00833368i
$657$	26.4507	−	7.08744i	1.03194	−	0.276507i
$658$	5.54122	+	45.7268i	0.216019	+	1.78262i
$659$	5.23202	−	9.06212i	0.203811	−	0.353010i	−0.745943	−	0.666010i	$-0.768001\pi$
$659$	5.23202	−	9.06212i	0.203811	−	0.353010i	0.949753	+	0.313000i	$0.101334\pi$
$660$	−0.626843	−	5.88250i	−0.0243998	−	0.228976i
$661$	−15.8313	+	9.14020i	−0.615766	+	0.355512i	−0.775219	−	0.631693i	$-0.782360\pi$
$661$	−15.8313	+	9.14020i	−0.615766	+	0.355512i	0.159453	+	0.987206i	$0.449027\pi$
$662$	23.0816	−	2.79705i	0.897090	−	0.108710i
$663$	13.5486	−	9.04836i	0.526185	−	0.351409i
$664$	25.9489	+	11.7009i	1.00701	+	0.454082i
$665$	11.9104	+	1.61806i	0.461865	+	0.0627455i
$666$	−8.96311	−	1.27413i	−0.347313	−	0.0493715i
$667$	2.56867	−	0.688273i	0.0994592	−	0.0266500i
$668$	−8.23781	+	13.6124i	−0.318730	+	0.526679i
$669$	−9.21227	+	15.9561i	−0.356167	+	0.616899i
$670$	−39.8426	+	22.2427i	−1.53926	+	0.859311i
$671$	−5.95760			−0.229991
$672$	−13.8730	+	1.10336i	−0.535161	+	0.0425630i
$673$	−2.60915	+	9.73748i	−0.100575	+	0.375352i	−0.997806	−	0.0662106i	$-0.978909\pi$
$673$	−2.60915	+	9.73748i	−0.100575	+	0.375352i	0.897230	+	0.441563i	$0.145576\pi$
$674$	3.05541	+	0.434334i	0.117690	+	0.0167299i
$675$	−18.1459	−	10.6771i	−0.698435	−	0.410963i
$676$	−20.2890	−	16.2590i	−0.780347	−	0.625346i
$677$	24.0253	−	24.0253i	0.923368	−	0.923368i	−0.0738979	−	0.997266i	$-0.523544\pi$
$677$	24.0253	−	24.0253i	0.923368	−	0.923368i	0.997266	+	0.0738979i	$0.0235439\pi$
$678$	3.02741	+	4.03075i	0.116267	+	0.154800i
$679$	6.14333	+	10.6406i	0.235760	+	0.408348i
$680$	26.7555	−	24.9429i	1.02603	−	0.956518i
$681$		−	20.1876i		−	0.773592i
$682$	8.12747	−	19.0633i	0.311217	−	0.729972i
$683$	−19.3626	+	5.18818i	−0.740888	+	0.198520i	−0.609473	−	0.792807i	$-0.708619\pi$
$683$	−19.3626	+	5.18818i	−0.740888	+	0.198520i	−0.131415	+	0.991327i	$0.541952\pi$
$684$	7.92241	−	1.94871i	0.302921	−	0.0745106i
$685$	−16.2189	−	39.6175i	−0.619693	−	1.51371i
$686$	−2.55999	+	18.0088i	−0.0977410	+	0.687579i
$687$	−0.108414	−	0.0290493i	−0.00413623	−	0.00110830i
$688$	−10.9926	+	35.1589i	−0.419090	+	1.34042i
$689$	4.67551	−	23.4770i	0.178123	−	0.894401i
$690$	−4.19894	+	1.06040i	−0.159851	+	0.0403686i
$691$	9.17627	+	15.8938i	0.349082	+	0.604627i	0.986087	−	0.166232i	$-0.0531602\pi$
$691$	9.17627	+	15.8938i	0.349082	+	0.604627i	−0.637005	+	0.770860i	$0.719827\pi$
$692$	0.351226	−	17.0363i	0.0133516	−	0.647621i
$693$	12.3058	−	3.29732i	0.467457	−	0.125255i
$694$	22.7213	+	17.8097i	0.862487	+	0.676046i
$695$	−28.1977	−	11.8164i	−1.06960	−	0.448221i
$696$	−2.72151	+	1.95765i	−0.103159	+	0.0742046i
$697$	5.29486	+	5.29486i	0.200557	+	0.200557i
$698$	11.8397	−	27.7704i	0.448138	−	1.05113i
$699$	5.25181	+	9.09641i	0.198642	+	0.344058i
$700$	−30.6382	+	7.26860i	−1.15801	+	0.274727i
$701$	−52.3785			−1.97831			−0.989154	−	0.146880i	$-0.953077\pi$
$701$	−52.3785			−1.97831			−0.989154	+	0.146880i	$0.953077\pi$
$702$	−19.3558	+	9.29293i	−0.730537	+	0.350739i
$703$	−3.23377	+	3.23377i	−0.121964	+	0.121964i
$704$	−12.8418	−	4.30757i	−0.483993	−	0.162348i
$705$	−10.9412	−	14.3814i	−0.412070	−	0.541633i
$706$	−11.5175	−	28.6371i	−0.433468	−	1.07777i
$707$	8.04752	−	8.04752i	0.302658	−	0.302658i
$708$	8.51952	−	4.68731i	0.320183	−	0.176160i
$709$	−4.87478	+	8.44336i	−0.183076	+	0.317097i	−0.942927	−	0.333001i	$-0.891939\pi$
$709$	−4.87478	+	8.44336i	−0.183076	+	0.317097i	0.759850	+	0.650098i	$0.225272\pi$
$710$	3.74207	+	14.8178i	0.140438	+	0.556103i
$711$	−19.2091	−	11.0904i	−0.720399	−	0.415922i
$712$	3.11119	+	2.54391i	0.116597	+	0.0953370i
$713$	−14.6541	−	3.92656i	−0.548801	−	0.147051i
$714$	−15.8370	−	12.4136i	−0.592684	−	0.464566i
$715$	−12.9067	−	4.44406i	−0.482684	−	0.166198i
$716$	25.9061	−	6.37222i	0.968155	−	0.238141i
$717$	−1.09674	+	4.09309i	−0.0409585	+	0.152859i
$718$	−24.7663	+	18.6015i	−0.924271	+	0.694201i
$719$	10.5808	−	18.3266i	0.394599	−	0.683465i	−0.598451	−	0.801159i	$-0.704217\pi$
$719$	10.5808	−	18.3266i	0.394599	−	0.683465i	0.993050	+	0.117694i	$0.0375502\pi$
$720$	−17.5289	+	12.2290i	−0.653264	+	0.455748i
$721$	20.6620	+	11.9292i	0.769492	+	0.444266i
$722$	−8.92173	+	20.9263i	−0.332032	+	0.778795i
$723$	0.932609	+	0.932609i	0.0346841	+	0.0346841i
$724$	−10.5652	+	36.4106i	−0.392653	+	1.35319i
$725$	−5.40778	+	5.31925i	−0.200840	+	0.197552i
$726$	8.89713	+	1.26475i	0.330203	+	0.0469392i
$727$	−19.9764	−	19.9764i	−0.740883	−	0.740883i	0.231865	−	0.972748i	$-0.425517\pi$
$727$	−19.9764	−	19.9764i	−0.740883	−	0.740883i	−0.972748	+	0.231865i	$0.925517\pi$
$728$	−11.2642	+	30.0717i	−0.417480	+	1.11453i
$729$			0.600519i			0.0222414i
$730$	−0.523007	+	36.2347i	−0.0193574	+	1.34111i
$731$	−46.1273	+	26.6316i	−1.70608	+	0.985006i
$732$	−2.65039	−	4.81726i	−0.0979611	−	0.178051i
$733$	−12.8558	+	12.8558i	−0.474838	+	0.474838i	−0.903476	−	0.428638i	$-0.858994\pi$
$733$	−12.8558	+	12.8558i	−0.474838	+	0.474838i	0.428638	+	0.903476i	$0.358994\pi$
$734$	4.55356	−	1.83139i	0.168075	−	0.0675980i
$735$	1.92959	+	4.71336i	0.0711741	+	0.173855i
$736$	−1.79896	+	9.75130i	−0.0663107	+	0.359438i
$737$	6.32329	+	23.5988i	0.232921	+	0.869274i
$738$	−2.62760	−	3.49844i	−0.0967234	−	0.128779i
$739$	−2.85108	+	1.64607i	−0.104879	+	0.0605518i	−0.551522	−	0.834160i	$-0.685953\pi$
$739$	−2.85108	+	1.64607i	−0.104879	+	0.0605518i	0.446643	+	0.894712i	$0.352619\pi$
$740$	4.85719	−	10.9518i	0.178554	−	0.402598i
$741$	−0.939253	+	4.71623i	−0.0345043	+	0.173255i
$742$	−29.3507	+	3.55675i	−1.07750	+	0.130572i
$743$	−0.808647	+	3.01791i	−0.0296664	+	0.110716i	−0.979171	−	0.203035i	$-0.934919\pi$
$743$	−0.808647	+	3.01791i	−0.0296664	+	0.110716i	0.949505	+	0.313752i	$0.101586\pi$
$744$	19.0301	−	1.90899i	0.697679	−	0.0699869i
$745$	33.6154	+	14.0867i	1.23157	+	0.516098i
$746$	−24.4649	−	19.1764i	−0.895725	−	0.702099i
$747$	−6.22423	−	23.2291i	−0.227733	−	0.849910i
$748$	−9.44069	−	17.1591i	−0.345186	−	0.627399i
$749$	−60.6358			−2.21558
$750$	8.93094	−	8.53466i	0.326112	−	0.311642i
$751$	−2.04172	+	1.17878i	−0.0745032	+	0.0430145i	−0.536789	−	0.843717i	$-0.680363\pi$
$751$	−2.04172	+	1.17878i	−0.0745032	+	0.0430145i	0.462286	+	0.886731i	$0.347029\pi$
$752$	−40.3717	+	9.05217i	−1.47221	+	0.330099i
$753$	−4.67345	−	4.67345i	−0.170310	−	0.170310i
$754$	1.42911	+	7.60248i	0.0520451	+	0.276866i
$755$	−3.75209	−	29.4380i	−0.136552	−	1.07136i
$756$	18.3609	+	19.1339i	0.667780	+	0.695894i
$757$	−6.35228	−	1.70209i	−0.230878	−	0.0618635i	0.141525	−	0.989935i	$-0.454799\pi$
$757$	−6.35228	−	1.70209i	−0.230878	−	0.0618635i	−0.372403	+	0.928071i	$0.621466\pi$
$758$	43.2205	+	18.4267i	1.56984	+	0.669286i
$759$			2.31875i			0.0841652i
$760$	−0.378306	+	10.7900i	−0.0137226	+	0.391396i
$761$	−45.8866	−	26.4926i	−1.66339	−	0.960357i	−0.971080	−	0.238753i	$-0.923261\pi$
$761$	−45.8866	−	26.4926i	−1.66339	−	0.960357i	−0.692306	−	0.721604i	$-0.743405\pi$
$762$	6.40397	−	0.776039i	0.231991	−	0.0281129i
$763$	−10.6689	−	39.8168i	−0.386239	−	1.44146i
$764$	−19.4333	+	18.6482i	−0.703072	+	0.674668i
$765$	−30.6222	−	4.16011i	−1.10715	−	0.150409i
$766$	−31.1610	−	24.4250i	−1.12589	−	0.882512i
$767$	−1.46228	−	22.3895i	−0.0527998	−	0.808439i
$768$	−2.22992	−	12.3001i	−0.0804654	−	0.443841i
$769$	−14.4966	−	25.1089i	−0.522762	−	0.905451i	−0.999649	−	0.0264861i	$-0.991568\pi$
$769$	−14.4966	−	25.1089i	−0.522762	−	0.905451i	0.476887	−	0.878965i	$-0.341765\pi$
$770$	−0.243321	+	16.8576i	−0.00876867	+	0.607506i
$771$	11.5732	+	6.68181i	0.416800	+	0.240639i
$772$	4.72491	−	7.80758i	0.170053	−	0.281001i
$773$	2.90313	+	10.8346i	0.104418	+	0.389694i	0.998279	−	0.0586513i	$-0.0186800\pi$
$773$	2.90313	+	10.8346i	0.104418	+	0.389694i	−0.893860	+	0.448346i	$0.852013\pi$
$774$	28.8742	−	11.6129i	1.03786	−	0.417416i
$775$	41.8909	−	10.8549i	1.50476	−	0.389920i
$776$	−8.95926	+	6.44462i	−0.321619	+	0.231348i
$777$	−6.36606	−	1.70578i	−0.228381	−	0.0611946i
$778$	5.90754	−	4.43703i	0.211795	−	0.159075i
$779$	−2.21019			−0.0791883
$780$	−2.14845	−	12.4133i	−0.0769267	−	0.444468i
$781$	8.18273			0.292801
$782$	−11.4639	+	8.61034i	−0.409950	+	0.307905i
$783$	6.17049	+	1.65338i	0.220515	+	0.0590869i
$784$	11.6513	+	0.480619i	0.416117	+	0.0171650i
$785$	34.5287	+	26.7219i	1.23238	+	0.953744i
$786$	−1.54533	+	0.621515i	−0.0551201	+	0.0221687i
$787$	12.2197	+	45.6045i	0.435585	+	1.62562i	0.739663	+	0.672977i	$0.234985\pi$
$787$	12.2197	+	45.6045i	0.435585	+	1.62562i	−0.304079	+	0.952647i	$0.598349\pi$
$788$	17.0785	+	10.3354i	0.608398	+	0.368184i
$789$	2.07354	+	1.19716i	0.0738201	+	0.0426201i
$790$	21.0531	−	20.4540i	0.749037	−	0.727722i
$791$	−7.18321	−	12.4417i	−0.255405	−	0.442375i
$792$	4.05028	+	10.7027i	0.143920	+	0.380304i
$793$	−12.6599	+	0.826828i	−0.449566	+	0.0293615i
$794$	−28.0256	−	21.9674i	−0.994590	−	0.779593i
$795$	9.23098	−	7.02285i	0.327389	−	0.249075i
$796$	25.9033	+	26.9938i	0.918116	+	0.956770i
$797$	5.44521	+	20.3218i	0.192879	+	0.719835i	0.992806	+	0.119737i	$0.0382051\pi$
$797$	5.44521	+	20.3218i	0.192879	+	0.719835i	−0.799926	+	0.600098i	$0.795128\pi$
$798$	5.89620	−	0.714507i	0.208723	−	0.0252933i
$799$	−51.8083	−	29.9115i	−1.83284	−	1.05819i
$800$	−9.24323	−	26.7313i	−0.326798	−	0.945094i
$801$		−	3.39530i		−	0.119967i
$802$	−45.9770	−	19.6019i	−1.62350	−	0.692166i
$803$	18.7414	+	5.02174i	0.661369	+	0.177213i
$804$	−16.2688	+	15.6115i	−0.573755	+	0.550575i
$805$	12.2432	−	1.56048i	0.431515	−	0.0549996i
$806$	14.6252	−	41.6375i	0.515150	−	1.46662i
$807$	4.24892	+	4.24892i	0.149569	+	0.149569i
$808$	7.91401	+	6.47099i	0.278414	+	0.227649i
$809$	14.4601	−	8.34856i	0.508391	−	0.293520i	−0.223781	−	0.974639i	$-0.571840\pi$
$809$	14.4601	−	8.34856i	0.508391	−	0.293520i	0.732172	+	0.681120i	$0.238507\pi$
$810$	11.8012	+	3.34540i	0.414652	+	0.117545i
$811$	13.2397			0.464909			0.232455	−	0.972607i	$-0.425324\pi$
$811$	13.2397			0.464909			0.232455	+	0.972607i	$0.425324\pi$
$812$	8.37085	−	4.60552i	0.293759	−	0.161622i
$813$	1.01799	+	3.79921i	0.0357026	+	0.133244i
$814$	−5.04850	−	3.95718i	−0.176950	−	0.138699i
$815$	−10.0117	−	24.4553i	−0.350695	−	0.856633i
$816$	9.67479	−	15.2673i	0.338685	−	0.534463i
$817$	4.06896	−	15.1856i	0.142355	−	0.531276i
$818$	−41.8571	+	5.07228i	−1.46350	+	0.177348i
$819$	25.6921	−	8.71467i	0.897756	−	0.304515i
$820$	5.40252	−	2.08277i	0.188664	−	0.0727334i
$821$	−10.6131	+	6.12745i	−0.370398	+	0.213849i	−0.673632	−	0.739067i	$-0.735267\pi$
$821$	−10.6131	+	6.12745i	−0.370398	+	0.213849i	0.303234	+	0.952916i	$0.401934\pi$
$822$	−12.7035	−	16.9137i	−0.443087	−	0.589934i
$823$	−1.82886	−	6.82538i	−0.0637499	−	0.237918i	0.926698	−	0.375808i	$-0.122635\pi$
$823$	−1.82886	−	6.82538i	−0.0637499	−	0.237918i	−0.990448	+	0.137890i	$0.955968\pi$
$824$	−8.80930	+	19.5362i	−0.306886	+	0.680577i
$825$	−3.25965	−	5.75504i	−0.113487	−	0.200365i
$826$	−25.7104	+	10.3404i	−0.894578	+	0.359790i
$827$	4.66045	−	4.66045i	0.162060	−	0.162060i	−0.621419	−	0.783478i	$-0.713443\pi$
$827$	4.66045	−	4.66045i	0.162060	−	0.162060i	0.783478	+	0.621419i	$0.213443\pi$
$828$	7.33983	−	4.03826i	0.255077	−	0.140339i
$829$	−20.3479	+	11.7479i	−0.706711	+	0.408020i	−0.809842	−	0.586648i	$-0.800447\pi$
$829$	−20.3479	+	11.7479i	−0.706711	+	0.408020i	0.103131	+	0.994668i	$0.467114\pi$
$830$	31.8215	+	0.459308i	1.10454	+	0.0159428i
$831$			7.35527i			0.255151i
$832$	−27.8866	−	7.37133i	−0.966795	−	0.255555i
$833$	11.9225	+	11.9225i	0.413090	+	0.413090i
$834$	−14.9569	−	2.12615i	−0.517913	−	0.0736227i
$835$	−2.39468	+	17.6271i	−0.0828714	+	0.610010i
$836$	5.55167	+	1.61092i	0.192008	+	0.0557148i
$837$	−25.7699	−	25.7699i	−0.890737	−	0.890737i
$838$	−5.81636	+	13.6425i	−0.200923	+	0.471272i
$839$	−5.55502	−	3.20719i	−0.191781	−	0.110725i	0.401035	−	0.916063i	$-0.368650\pi$
$839$	−5.55502	−	3.20719i	−0.191781	−	0.110725i	−0.592816	+	0.805338i	$0.701984\pi$
$840$	−13.7392	+	7.30278i	−0.474046	+	0.251970i
$841$	−13.3492	+	23.1215i	−0.460318	+	0.797295i
$842$	−17.1387	+	12.8726i	−0.590640	+	0.443618i
$843$	−3.33195	+	12.4350i	−0.114759	+	0.428285i
$844$	10.5924	+	43.0632i	0.364606	+	1.48230i
$845$	−28.0436	−	7.65237i	−0.964728	−	0.263249i
$846$	27.5108	+	21.5639i	0.945840	+	0.741381i
$847$	−24.7380	−	6.62854i	−0.850009	−	0.227759i
$848$	−5.81032	−	25.9134i	−0.199527	−	0.889871i
$849$	5.18906	+	2.99590i	0.178088	+	0.102819i
$850$	16.3488	−	37.4863i	0.560760	−	1.28577i
$851$	−2.34795	+	4.06677i	−0.0804867	+	0.139407i
$852$	3.64029	+	6.61648i	0.124714	+	0.226677i
$853$	19.7870	−	19.7870i	0.677494	−	0.677494i	−0.281938	−	0.959432i	$-0.590977\pi$
$853$	19.7870	−	19.7870i	0.677494	−	0.677494i	0.959432	+	0.281938i	$0.0909774\pi$
$854$	5.84688	+	14.5376i	0.200076	+	0.497467i
$855$	7.25945	−	5.52294i	0.248268	−	0.188880i
$856$	−5.43636	−	54.1935i	−0.185811	−	1.85229i
$857$	33.3074	−	33.3074i	1.13776	−	1.13776i	0.148907	−	0.988851i	$-0.452425\pi$
$857$	33.3074	−	33.3074i	1.13776	−	1.13776i	0.988851	−	0.148907i	$-0.0475755\pi$
$858$	−6.72559	−	0.512052i	−0.229608	−	0.0174812i
$859$	21.8062			0.744019			0.372009	−	0.928229i	$-0.378669\pi$
$859$	21.8062			0.744019			0.372009	+	0.928229i	$0.378669\pi$
$860$	4.36404	+	40.9535i	0.148812	+	1.39650i
$861$	−1.59259	−	2.75844i	−0.0542753	−	0.0940075i
$862$	2.83937	−	6.65985i	0.0967093	−	0.226836i
$863$	−5.02124	−	5.02124i	−0.170925	−	0.170925i	0.616461	−	0.787386i	$-0.288566\pi$
$863$	−5.02124	−	5.02124i	−0.170925	−	0.170925i	−0.787386	+	0.616461i	$0.788566\pi$
$864$	−15.4549	+	18.1256i	−0.525785	+	0.616646i
$865$	−7.21788	−	17.6309i	−0.245415	−	0.599469i
$866$	21.0676	+	16.5134i	0.715905	+	0.561150i
$867$	12.4144	−	3.32642i	0.421615	−	0.112971i
$868$	−54.4944	−	1.12348i	−1.84966	−	0.0381333i
$869$	−7.85799	−	13.6104i	−0.266564	−	0.461703i
$870$	−1.92074	+	3.21863i	−0.0651192	+	0.109122i
$871$	16.7122	+	49.2700i	0.566270	+	1.66945i
$872$	34.6299	−	13.1052i	1.17272	−	0.443797i
$873$	9.00635	+	2.41324i	0.304819	+	0.0816759i
$874$	0.595579	−	4.18972i	0.0201458	−	0.141719i
$875$	−28.1934	+	21.0843i	−0.953110	+	0.712778i
$876$	4.27704	+	17.3882i	0.144508	+	0.587492i
$877$	−47.7238	+	12.7876i	−1.61152	+	0.431805i	−0.948495	−	0.316792i	$-0.897394\pi$
$877$	−47.7238	+	12.7876i	−1.61152	+	0.431805i	−0.663025	+	0.748597i	$0.730728\pi$
$878$	9.93903	−	23.3124i	0.335426	−	0.786755i
$879$		−	13.2385i		−	0.446524i
$880$	−15.0884	+	1.29392i	−0.508629	+	0.0436179i
$881$	24.2806	+	42.0552i	0.818033	+	1.41688i	0.907129	+	0.420852i	$0.138269\pi$
$881$	24.2806	+	42.0552i	0.818033	+	1.41688i	−0.0890958	+	0.996023i	$0.528398\pi$
$882$	−5.91660	−	7.87745i	−0.199222	−	0.265248i
$883$	6.57308	−	6.57308i	0.221202	−	0.221202i	−0.587803	−	0.809004i	$-0.700007\pi$
$883$	6.57308	−	6.57308i	0.221202	−	0.221202i	0.809004	+	0.587803i	$0.200007\pi$
$884$	−22.4429	−	35.1529i	−0.754837	−	1.18232i
$885$	6.65374	−	8.59763i	0.223663	−	0.289006i
$886$	17.8838	+	2.54223i	0.600819	+	0.0854079i
$887$	−10.2024	+	38.0759i	−0.342564	+	1.27847i	0.552869	+	0.833268i	$0.313533\pi$
$887$	−10.2024	+	38.0759i	−0.342564	+	1.27847i	−0.895433	+	0.445197i	$0.853134\pi$
$888$	0.953793	−	5.84263i	0.0320072	−	0.196066i
$889$	−18.3841			−0.616583
$890$	4.32285	+	1.22544i	0.144902	+	0.0410768i
$891$	3.28374	−	5.68761i	0.110010	−	0.190542i
$892$	40.3510	+	24.4192i	1.35105	+	0.817616i
$893$	17.0558	−	4.57009i	0.570751	−	0.152932i
$894$	17.8306	+	2.53466i	0.596344	+	0.0847718i
$895$	23.7382	−	18.0599i	0.793482	−	0.603675i
$896$	2.09187	+	35.5638i	0.0698844	+	1.18810i
$897$	0.321808	+	4.92734i	0.0107449	+	0.164519i
$898$	38.5219	−	4.66812i	1.28549	−	0.155777i
$899$	−11.3711	+	6.56509i	−0.379246	+	0.218958i
$900$	−12.5403	+	20.3410i	−0.418009	+	0.678034i
$901$	19.1993	−	33.2542i	0.639622	−	1.10786i
$902$	−0.372943	−	3.07757i	−0.0124176	−	0.102472i
$903$	21.8844	−	5.86391i	0.728268	−	0.195139i
$904$	10.4758	−	7.53549i	0.348419	−	0.250627i
$905$	5.35922	+	42.0473i	0.178147	+	1.39770i
$906$	−5.47169	−	13.6048i	−0.181785	−	0.451988i
$907$	3.82965	−	14.2924i	0.127161	−	0.474573i	−0.872746	−	0.488174i	$-0.837663\pi$
$907$	3.82965	−	14.2924i	0.127161	−	0.474573i	0.999907	+	0.0136016i	$0.00432966\pi$
$908$	−51.6670	−	1.06519i	−1.71463	−	0.0353495i
$909$		−	8.63670i		−	0.286461i
$910$	1.82253	+	35.8562i	0.0604164	+	1.18862i
$911$		−	56.7680i		−	1.88081i	−0.340060	−	0.940404i	$-0.610448\pi$
$911$		−	56.7680i		−	1.88081i	0.340060	−	0.940404i	$-0.389552\pi$
$912$	1.16722	+	5.20569i	0.0386506	+	0.172378i
$913$	4.41012	−	16.4588i	0.145954	−	0.544706i
$914$	16.0686	−	6.46263i	0.531503	−	0.213765i
$915$	−4.86143	−	3.76228i	−0.160714	−	0.124377i
$916$	−0.0800674	+	0.275934i	−0.00264550	+	0.00911712i
$917$	4.58511	−	1.22858i	0.151414	−	0.0405712i
$918$	−34.1912	+	4.14333i	−1.12848	+	0.136750i
$919$	−21.1517	+	36.6358i	−0.697729	+	1.20850i	0.271523	+	0.962432i	$0.412473\pi$
$919$	−21.1517	+	36.6358i	−0.697729	+	1.20850i	−0.969252	+	0.246070i	$0.920861\pi$
$920$	2.49235	+	10.8025i	0.0821705	+	0.356147i
$921$	−8.58878	+	4.95873i	−0.283010	+	0.163396i
$922$	2.90129	+	23.9418i	0.0955489	+	0.788481i
$923$	17.3883	−	1.13564i	0.572343	−	0.0373802i
$924$	1.98982	+	8.08957i	0.0654604	+	0.266127i
$925$	0.110536	−	13.3943i	0.00363440	−	0.440401i
$926$	4.18781	−	29.4600i	0.137620	−	0.968114i
$927$	17.4886	−	4.68606i	0.574402	−	0.153911i
$928$	4.86669	+	7.06857i	0.159757	+	0.232037i
$929$	−1.96558	+	3.40448i	−0.0644884	+	0.111697i	−0.896467	−	0.443111i	$-0.853875\pi$
$929$	−1.96558	+	3.40448i	−0.0644884	+	0.111697i	0.831979	+	0.554808i	$0.187208\pi$
$930$	18.6707	−	10.4232i	0.612237	−	0.341790i
$931$	−4.97671			−0.163105
$932$	23.5579	−	12.9612i	0.771664	−	0.424558i
$933$	1.04556	−	3.90207i	0.0342300	−	0.127748i
$934$	0.770568	−	5.42071i	0.0252138	−	0.177371i
$935$	−17.3164	−	13.4012i	−0.566308	−	0.438268i
$936$	10.0922	+	22.1811i	0.329875	+	0.725013i
$937$	−32.4683	+	32.4683i	−1.06069	+	1.06069i	−0.0626596	+	0.998035i	$0.519958\pi$
$937$	−32.4683	+	32.4683i	−1.06069	+	1.06069i	−0.998035	+	0.0626596i	$0.980042\pi$
$938$	51.3797	−	38.5902i	1.67761	−	1.26002i
$939$	6.68385	+	11.5768i	0.218119	+	0.377793i
$940$	−37.3841	+	27.2435i	−1.21933	+	0.888584i
$941$			37.8083i			1.23252i	0.787545	+	0.616258i	$0.211352\pi$
$941$			37.8083i			1.23252i	−0.787545	+	0.616258i	$0.788648\pi$
$942$	19.8458	+	8.46108i	0.646611	+	0.275677i
$943$	−2.19214	+	0.587383i	−0.0713860	+	0.0191278i
$944$	−11.5469	−	22.0516i	−0.375819	−	0.717720i
$945$	27.3447	+	11.4589i	0.889522	+	0.372760i
$946$	21.8317	+	3.10343i	0.709809	+	0.100901i
$947$	−6.07236	−	1.62708i	−0.197325	−	0.0528731i	0.158803	−	0.987310i	$-0.449237\pi$
$947$	−6.07236	−	1.62708i	−0.197325	−	0.0528731i	−0.356128	+	0.934437i	$0.615903\pi$
$948$	7.50947	−	12.4089i	0.243896	−	0.403021i
$949$	40.5224	+	8.07017i	1.31541	+	0.261969i
$950$	4.41163	+	11.2360i	0.143132	+	0.364544i
$951$	−3.12285	−	5.40893i	−0.101265	−	0.175397i
$952$	−32.6061	+	39.8772i	−1.05677	+	1.29243i
$953$	−43.2508	+	11.5890i	−1.40103	+	0.375405i	−0.878715	−	0.477347i	$-0.841599\pi$
$953$	−43.2508	+	11.5890i	−1.40103	+	0.375405i	−0.522316	+	0.852752i	$0.674932\pi$
$954$	−13.8412	+	17.6584i	−0.448126	+	0.571710i
$955$	−11.6382	+	27.7725i	−0.376604	+	0.898697i
$956$	10.4177	+	3.02290i	0.336933	+	0.0977675i
$957$	1.41903	+	1.41903i	0.0458709	+	0.0458709i
$958$	43.0068	+	18.3356i	1.38949	+	0.592395i
$959$	30.1420	+	52.2074i	0.973335	+	1.68587i
$960$	−7.75869	−	11.6247i	−0.250411	−	0.375185i
$961$	43.9070			1.41635
$962$	−11.2773	−	7.70836i	−0.363594	−	0.248528i
$963$	−32.5375	+	32.5375i	−1.04851	+	1.04851i
$964$	2.43607	−	2.33765i	0.0784605	−	0.0752907i
$965$	1.37350	−	10.1103i	0.0442146	−	0.325461i
$966$	5.65816	−	2.27565i	0.182048	−	0.0732179i
$967$	35.9460	−	35.9460i	1.15595	−	1.15595i	0.170607	−	0.985339i	$-0.445427\pi$
$967$	35.9460	−	35.9460i	1.15595	−	1.15595i	0.985339	−	0.170607i	$-0.0545727\pi$
$968$	3.70637	−	22.7040i	0.119127	−	0.729735i
$969$	−3.85691	+	6.68036i	−0.123902	+	0.214604i
$970$	−6.32310	+	10.5958i	−0.203023	+	0.340210i
$971$	22.7373	+	13.1274i	0.729675	+	0.421278i	0.818303	−	0.574787i	$-0.194915\pi$
$971$	22.7373	+	13.1274i	0.729675	+	0.421278i	−0.0886283	+	0.996065i	$0.528248\pi$
$972$	31.3193	+	0.645692i	1.00457	+	0.0207106i
$973$	41.5868	+	11.1432i	1.33321	+	0.357233i
$974$	−12.0078	+	15.3193i	−0.384754	+	0.490861i
$975$	−7.72548	−	11.7771i	−0.247413	−	0.377169i
$976$	−12.4688	+	6.52905i	−0.399118	+	0.208990i
$977$	6.44653	−	24.0588i	0.206243	−	0.769709i	−0.782824	−	0.622243i	$-0.786222\pi$
$977$	6.44653	−	24.0588i	0.206243	−	0.769709i	0.989067	−	0.147466i	$-0.0471117\pi$
$978$	−7.84173	−	10.4406i	−0.250751	−	0.333854i
$979$	1.20285	−	2.08340i	0.0384434	−	0.0665859i
$980$	12.1649	−	4.68978i	0.388593	−	0.149810i
$981$	−27.0909	−	15.6409i	−0.864946	−	0.499377i
$982$	−1.81745	−	0.774852i	−0.0579971	−	0.0247265i
$983$	8.45425	+	8.45425i	0.269649	+	0.269649i	0.828959	−	0.559310i	$-0.188934\pi$
$983$	8.45425	+	8.45425i	0.269649	+	0.269649i	−0.559310	+	0.828959i	$0.688934\pi$
$984$	2.32258	−	1.67069i	0.0740413	−	0.0532597i
$985$	22.1155	+	3.00445i	0.704659	+	0.0957296i
$986$	−1.74636	+	12.2851i	−0.0556155	+	0.391238i
$987$	17.9936	+	17.9936i	0.572741	+	0.572741i
$988$	12.0209	+	2.65271i	0.382435	+	0.0843941i
$989$		−	16.1430i		−	0.513316i
$990$	8.91533	+	9.17647i	0.283348	+	0.291647i
$991$	−24.3058	+	14.0330i	−0.772100	+	0.445772i	−0.833623	−	0.552334i	$-0.813737\pi$
$991$	−24.3058	+	14.0330i	−0.772100	+	0.445772i	0.0615233	+	0.998106i	$0.480404\pi$
$992$	−3.88163	−	48.8053i	−0.123242	−	1.54957i
$993$	9.08262	−	9.08262i	0.288228	−	0.288228i
$994$	−8.03065	−	19.9673i	−0.254717	−	0.633325i
$995$	38.5774	+	16.1661i	1.22298	+	0.512499i
$996$	15.2704	−	3.75612i	0.483861	−	0.119017i
$997$	−15.5675	−	58.0986i	−0.493026	−	1.84000i	−0.540814	−	0.841142i	$-0.681884\pi$
$997$	−15.5675	−	58.0986i	−0.493026	−	1.84000i	0.0477878	−	0.998858i	$-0.484783\pi$
$998$	−16.4021	+	12.3193i	−0.519200	+	0.389960i
$999$	−9.76924	+	5.64027i	−0.309085	+	0.178450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bg.c.23.12	✓	144
4.3	odd	2	inner	260.2.bg.c.23.31	yes	144
5.2	odd	4	inner	260.2.bg.c.127.31	yes	144
13.4	even	6	inner	260.2.bg.c.43.25	yes	144
20.7	even	4	inner	260.2.bg.c.127.25	yes	144
52.43	odd	6	inner	260.2.bg.c.43.31	yes	144
65.17	odd	12	inner	260.2.bg.c.147.31	yes	144
260.147	even	12	inner	260.2.bg.c.147.12	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bg.c.23.12	✓	144	1.1	even	1	trivial
260.2.bg.c.23.31	yes	144	4.3	odd	2	inner
260.2.bg.c.43.25	yes	144	13.4	even	6	inner
260.2.bg.c.43.31	yes	144	52.43	odd	6	inner
260.2.bg.c.127.25	yes	144	20.7	even	4	inner
260.2.bg.c.127.31	yes	144	5.2	odd	4	inner
260.2.bg.c.147.12	yes	144	260.147	even	12	inner
260.2.bg.c.147.31	yes	144	65.17	odd	12	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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.849309 - 1.13078i) q^{2} +(-0.754665 - 0.202212i) q^{3} +(-0.557348 + 1.92077i) q^{4} +(0.282716 + 2.21812i) q^{5} +(0.412286 + 1.02510i) q^{6} +(-0.814984 - 3.04156i) q^{7} +(2.64534 - 1.00109i) q^{8} +(-2.06945 - 1.19480i) q^{9} +O(q^{10})\)	\(q+(-0.849309 - 1.13078i) q^{2} +(-0.754665 - 0.202212i) q^{3} +(-0.557348 + 1.92077i) q^{4} +(0.282716 + 2.21812i) q^{5} +(0.412286 + 1.02510i) q^{6} +(-0.814984 - 3.04156i) q^{7} +(2.64534 - 1.00109i) q^{8} +(-2.06945 - 1.19480i) q^{9} +(2.26811 - 2.20356i) q^{10} +(-0.846561 - 1.46629i) q^{11} +(0.809013 - 1.33684i) q^{12} +(-2.00244 - 2.99837i) q^{13} +(-2.74718 + 3.50480i) q^{14} +(0.235175 - 1.73111i) q^{15} +(-3.37873 - 2.14107i) q^{16} +(-1.49691 - 5.58654i) q^{17} +(0.406544 + 3.35485i) q^{18} +(1.47839 + 0.853551i) q^{19} +(-4.41808 - 0.693234i) q^{20} +2.46016i q^{21} +(-0.939062 + 2.20261i) q^{22} +(1.69316 + 0.453682i) q^{23} +(-2.19878 + 0.220568i) q^{24} +(-4.84014 + 1.25420i) q^{25} +(-1.68982 + 4.81087i) q^{26} +(2.97750 + 2.97750i) q^{27} +(6.29637 + 0.129809i) q^{28} +(1.31383 - 0.758542i) q^{29} +(-2.15725 + 1.20431i) q^{30} -8.65488 q^{31} +(0.448491 + 5.63905i) q^{32} +(0.342369 + 1.27774i) q^{33} +(-5.04584 + 6.43738i) q^{34} +(6.51615 - 2.66763i) q^{35} +(3.44833 - 3.30902i) q^{36} +(-0.693362 + 2.58766i) q^{37} +(-0.290431 - 2.39667i) q^{38} +(0.904867 + 2.66768i) q^{39} +(2.96842 + 5.58467i) q^{40} +(-1.12125 + 0.647352i) q^{41} +(2.78191 - 2.08944i) q^{42} +(-2.38355 - 8.89553i) q^{43} +(3.28823 - 0.808819i) q^{44} +(2.06514 - 4.92808i) q^{45} +(-0.925003 - 2.29992i) q^{46} +(7.31398 - 7.31398i) q^{47} +(2.11686 + 2.29901i) q^{48} +(-2.52472 + 1.45765i) q^{49} +(5.52900 + 4.40796i) q^{50} +4.51866i q^{51} +(6.87524 - 2.17510i) q^{52} +(4.69463 + 4.69463i) q^{53} +(0.838091 - 5.89572i) q^{54} +(3.01307 - 2.29232i) q^{55} +(-5.20078 - 7.23009i) q^{56} +(-0.943094 - 0.943094i) q^{57} +(-1.97360 - 0.841425i) q^{58} +(5.38925 + 3.11149i) q^{59} +(3.19399 + 1.41655i) q^{60} +(1.75935 - 3.04729i) q^{61} +(7.35067 + 9.78681i) q^{62} +(-1.94748 + 7.26809i) q^{63} +(5.99564 - 5.29644i) q^{64} +(6.08463 - 5.28935i) q^{65} +(1.15407 - 1.47234i) q^{66} +(-13.9381 - 3.73469i) q^{67} +(11.5648 + 0.238424i) q^{68} +(-1.18603 - 0.684755i) q^{69} +(-8.55074 - 5.10272i) q^{70} +(-2.41646 + 4.18543i) q^{71} +(-6.67049 - 1.08894i) q^{72} +(-8.10316 + 8.10316i) q^{73} +(3.51497 - 1.41368i) q^{74} +(3.90630 + 0.0322366i) q^{75} +(-2.46346 + 2.36393i) q^{76} +(-3.76987 + 3.76987i) q^{77} +(2.24806 - 3.28890i) q^{78} +9.28225 q^{79} +(3.79395 - 8.09975i) q^{80} +(1.93946 + 3.35924i) q^{81} +(1.68430 + 0.718086i) q^{82} +(7.11624 + 7.11624i) q^{83} +(-4.72540 - 1.37116i) q^{84} +(11.9684 - 4.89973i) q^{85} +(-8.03456 + 10.2503i) q^{86} +(-1.14489 + 0.306772i) q^{87} +(-3.70732 - 3.03134i) q^{88} +(0.710435 + 1.23051i) q^{89} +(-7.32653 + 1.85023i) q^{90} +(-7.48777 + 8.53417i) q^{91} +(-1.81510 + 2.99932i) q^{92} +(6.53153 + 1.75012i) q^{93} +(-14.4824 - 2.05871i) q^{94} +(-1.47532 + 3.52057i) q^{95} +(0.801822 - 4.34628i) q^{96} +(-3.76899 + 1.00990i) q^{97} +(3.79255 + 1.61692i) q^{98} +4.04587i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 6 q^{2} - 12 q^{6}+O(q^{10}) \) 144 * q - 6 * q^2 - 12 * q^6	\( 144 q - 6 q^{2} - 12 q^{6} + 12 q^{10} - 12 q^{12} + 4 q^{13} - 12 q^{16} - 24 q^{17} - 42 q^{20} - 12 q^{22} - 24 q^{25} - 36 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 76 q^{36} + 48 q^{37} - 16 q^{38} + 76 q^{40} - 72 q^{41} + 40 q^{42} - 120 q^{45} - 12 q^{46} - 40 q^{48} + 120 q^{50} - 10 q^{52} + 8 q^{53} - 20 q^{56} + 126 q^{58} + 16 q^{61} - 44 q^{62} + 32 q^{65} + 96 q^{66} - 64 q^{68} - 54 q^{72} - 12 q^{76} + 40 q^{77} - 100 q^{78} - 24 q^{80} - 32 q^{81} - 78 q^{82} - 24 q^{85} - 10 q^{88} - 8 q^{90} + 100 q^{92} - 48 q^{93} - 12 q^{97} - 162 q^{98}+O(q^{100}) \) 144 * q - 6 * q^2 - 12 * q^6 + 12 * q^10 - 12 * q^12 + 4 * q^13 - 12 * q^16 - 24 * q^17 - 42 * q^20 - 12 * q^22 - 24 * q^25 - 36 * q^26 - 6 * q^28 - 36 * q^32 - 12 * q^33 - 76 * q^36 + 48 * q^37 - 16 * q^38 + 76 * q^40 - 72 * q^41 + 40 * q^42 - 120 * q^45 - 12 * q^46 - 40 * q^48 + 120 * q^50 - 10 * q^52 + 8 * q^53 - 20 * q^56 + 126 * q^58 + 16 * q^61 - 44 * q^62 + 32 * q^65 + 96 * q^66 - 64 * q^68 - 54 * q^72 - 12 * q^76 + 40 * q^77 - 100 * q^78 - 24 * q^80 - 32 * q^81 - 78 * q^82 - 24 * q^85 - 10 * q^88 - 8 * q^90 + 100 * q^92 - 48 * q^93 - 12 * q^97 - 162 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more