LMFDB - Embedded newform 946.2.t.a.7.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(7,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("946.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.t (of order $30$, degree $8$, 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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			7.18
Character	$\chi$	$=$	946.7
Dual form			946.2.t.a.811.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.408426 + 1.92149i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.341490 + 0.766999i) q^{5} +(0.799001 - 1.79459i) q^{6} +(4.50849 + 0.958309i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.784684 + 0.349364i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.408426 + 1.92149i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.341490 + 0.766999i) q^{5} +(0.799001 - 1.79459i) q^{6} +(4.50849 + 0.958309i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.784684 + 0.349364i) q^{9} +(0.727102 - 0.419793i) q^{10} +(-2.84411 + 1.70617i) q^{11} +(-1.70124 + 0.982210i) q^{12} +(0.115267 + 0.258894i) q^{13} +(-3.08416 - 3.42531i) q^{14} +(-1.61326 - 0.342908i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(7.11733 - 0.748061i) q^{17} +(0.840174 + 0.178584i) q^{18} +(6.78687 - 1.44259i) q^{19} +(-0.834986 - 0.0877606i) q^{20} +9.05442i q^{21} +(3.30380 + 0.291402i) q^{22} +(-1.47428 - 2.55353i) q^{23} +(1.95366 + 0.205338i) q^{24} +(2.87398 + 3.19188i) q^{25} +(0.0589212 - 0.277202i) q^{26} +(2.47219 + 3.40267i) q^{27} +(0.481794 + 4.58396i) q^{28} +(-4.69187 - 0.997287i) q^{29} +(1.10360 + 1.22567i) q^{30} +(0.376924 - 3.58619i) q^{31} +1.00000 q^{32} +(-4.44001 - 4.76809i) q^{33} +(-6.19774 - 3.57827i) q^{34} +(-2.27463 + 3.13076i) q^{35} +(-0.574746 - 0.638320i) q^{36} +(-6.20377 - 5.58590i) q^{37} +(-6.33863 - 2.82214i) q^{38} +(-0.450385 + 0.327224i) q^{39} +(0.623933 + 0.561792i) q^{40} +(-7.38095 - 2.39822i) q^{41} +(5.32206 - 7.32518i) q^{42} +(-5.28872 + 3.87678i) q^{43} +(-2.50155 - 2.17767i) q^{44} -0.721157i q^{45} +(-0.308209 + 2.93241i) q^{46} +(1.29074 - 3.97249i) q^{47} +(-1.45985 - 1.31445i) q^{48} +(13.0133 + 5.79389i) q^{49} +(-0.448960 - 4.27157i) q^{50} +(4.34429 + 13.3704i) q^{51} +(-0.210604 + 0.189628i) q^{52} +(-0.635449 + 6.04589i) q^{53} -4.20593i q^{54} +(-0.337399 - 2.76407i) q^{55} +(2.30461 - 3.99169i) q^{56} +(5.54387 + 12.4517i) q^{57} +(3.20961 + 3.56463i) q^{58} +(2.24651 + 6.91405i) q^{59} +(-0.172399 - 1.64026i) q^{60} +(1.16687 + 11.1021i) q^{61} +(-2.41285 + 2.67974i) q^{62} +(-3.87254 + 0.823134i) q^{63} +(-0.809017 - 0.587785i) q^{64} -0.237934 q^{65} +(0.789429 + 6.46724i) q^{66} +(-6.00792 - 10.4060i) q^{67} +(2.91082 + 6.53782i) q^{68} +(4.30446 - 3.87575i) q^{69} +(3.68042 - 1.19584i) q^{70} +(-8.91636 + 0.937148i) q^{71} +(0.0897841 + 0.854238i) q^{72} +(4.99027 + 1.06072i) q^{73} +(1.73565 + 8.16558i) q^{74} +(-4.95936 + 6.82598i) q^{75} +(3.46925 + 6.00892i) q^{76} +(-14.4577 + 4.96673i) q^{77} +0.556707 q^{78} +(1.80710 + 4.05881i) q^{79} +(-0.174560 - 0.821238i) q^{80} +(-7.25274 + 8.05498i) q^{81} +(4.56168 + 6.27861i) q^{82} +(6.37834 - 14.3260i) q^{83} +(-8.61127 + 2.79797i) q^{84} +(-1.85673 + 5.71444i) q^{85} +(6.55738 - 0.0277458i) q^{86} -9.42270i q^{87} +(0.743790 + 3.23215i) q^{88} +(2.87816 - 1.66170i) q^{89} +(-0.423885 + 0.583428i) q^{90} +(0.271580 + 1.27768i) q^{91} +(1.97298 - 2.19121i) q^{92} +(7.04478 - 0.740436i) q^{93} +(-3.37920 + 2.45513i) q^{94} +(-1.21118 + 5.69816i) q^{95} +(0.408426 + 1.92149i) q^{96} +(1.40469 + 1.02057i) q^{97} +(-7.12241 - 12.3364i) q^{98} +(1.63565 - 2.33244i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 44 q^{2} - 44 q^{4} - 5 q^{6} - 15 q^{7} - 44 q^{8} - 20 q^{9}+O(q^{10}) $ 176 * q - 44 * q^2 - 44 * q^4 - 5 * q^6 - 15 * q^7 - 44 * q^8 - 20 * q^9	$ 176 q - 44 q^{2} - 44 q^{4} - 5 q^{6} - 15 q^{7} - 44 q^{8} - 20 q^{9} - 5 q^{11} - 5 q^{13} + 15 q^{14} + 41 q^{15} - 44 q^{16} - 2 q^{17} - 25 q^{18} + 34 q^{19} + 5 q^{22} - 4 q^{23} + 5 q^{24} - 24 q^{25} + 20 q^{26} - 60 q^{27} - 3 q^{29} - 49 q^{30} + 40 q^{31} + 176 q^{32} - 47 q^{33} + 3 q^{34} - 60 q^{35} - 25 q^{36} - 8 q^{37} + 14 q^{38} + 12 q^{39} - 19 q^{43} - 10 q^{44} + 26 q^{46} - 4 q^{47} - 21 q^{49} + 6 q^{50} + 45 q^{51} - 20 q^{52} - 27 q^{53} + 68 q^{55} + 71 q^{57} - 3 q^{58} - 21 q^{59} + 6 q^{60} + 30 q^{61} + 71 q^{63} - 44 q^{64} - 16 q^{65} + 43 q^{66} - 3 q^{67} + 8 q^{68} - 42 q^{69} + 3 q^{71} - 20 q^{72} - 19 q^{73} - 28 q^{74} + 9 q^{76} + 38 q^{77} + 92 q^{78} + 32 q^{79} - 23 q^{81} - 5 q^{82} - 26 q^{83} + 2 q^{85} + 36 q^{86} + 5 q^{88} + 57 q^{89} + 30 q^{91} + 6 q^{92} - 10 q^{93} + 6 q^{94} - 58 q^{95} - 37 q^{97} - 106 q^{98} - 119 q^{99}+O(q^{100}) $ 176 * q - 44 * q^2 - 44 * q^4 - 5 * q^6 - 15 * q^7 - 44 * q^8 - 20 * q^9 - 5 * q^11 - 5 * q^13 + 15 * q^14 + 41 * q^15 - 44 * q^16 - 2 * q^17 - 25 * q^18 + 34 * q^19 + 5 * q^22 - 4 * q^23 + 5 * q^24 - 24 * q^25 + 20 * q^26 - 60 * q^27 - 3 * q^29 - 49 * q^30 + 40 * q^31 + 176 * q^32 - 47 * q^33 + 3 * q^34 - 60 * q^35 - 25 * q^36 - 8 * q^37 + 14 * q^38 + 12 * q^39 - 19 * q^43 - 10 * q^44 + 26 * q^46 - 4 * q^47 - 21 * q^49 + 6 * q^50 + 45 * q^51 - 20 * q^52 - 27 * q^53 + 68 * q^55 + 71 * q^57 - 3 * q^58 - 21 * q^59 + 6 * q^60 + 30 * q^61 + 71 * q^63 - 44 * q^64 - 16 * q^65 + 43 * q^66 - 3 * q^67 + 8 * q^68 - 42 * q^69 + 3 * q^71 - 20 * q^72 - 19 * q^73 - 28 * q^74 + 9 * q^76 + 38 * q^77 + 92 * q^78 + 32 * q^79 - 23 * q^81 - 5 * q^82 - 26 * q^83 + 2 * q^85 + 36 * q^86 + 5 * q^88 + 57 * q^89 + 30 * q^91 + 6 * q^92 - 10 * q^93 + 6 * q^94 - 58 * q^95 - 37 * q^97 - 106 * q^98 - 119 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/946\mathbb{Z}\right)^\times$.

$n$	$89$	$431$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	0.408426	+	1.92149i	0.235805	+	1.10937i	0.923567	+	0.383438i	$0.125260\pi$
$3$	0.408426	+	1.92149i	0.235805	+	1.10937i	−0.687762	+	0.725936i	$0.741407\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.341490	+	0.766999i	−0.152719	+	0.343013i	−0.973662	−	0.227998i	$-0.926782\pi$
$5$	−0.341490	+	0.766999i	−0.152719	+	0.343013i	0.820943	+	0.571011i	$0.193449\pi$
$6$	0.799001	−	1.79459i	0.326191	−	0.732637i
$7$	4.50849	+	0.958309i	1.70405	+	0.362207i	0.954146	−	0.299341i	$-0.0967670\pi$
$7$	4.50849	+	0.958309i	1.70405	+	0.362207i	0.749903	+	0.661548i	$0.230100\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.784684	+	0.349364i	−0.261561	+	0.116455i
$10$	0.727102	−	0.419793i	0.229930	−	0.132750i
$11$	−2.84411	+	1.70617i	−0.857532	+	0.514431i
$11$	−2.84411	+	1.70617i	−0.857532	+	0.514431i
$12$	−1.70124	+	0.982210i	−0.491105	+	0.283540i
$13$	0.115267	+	0.258894i	0.0319694	+	0.0718044i	0.928824	−	0.370520i	$-0.120821\pi$
$13$	0.115267	+	0.258894i	0.0319694	+	0.0718044i	−0.896855	+	0.442325i	$0.854154\pi$
$14$	−3.08416	−	3.42531i	−0.824278	−	0.915453i
$15$	−1.61326	−	0.342908i	−0.416541	−	0.0885385i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	7.11733	−	0.748061i	1.72621	−	0.181432i	0.811172	−	0.584808i	$-0.198830\pi$
$17$	7.11733	−	0.748061i	1.72621	−	0.181432i	0.915034	+	0.403377i	$0.132164\pi$
$18$	0.840174	+	0.178584i	0.198031	+	0.0420928i
$19$	6.78687	−	1.44259i	1.55702	−	0.330954i	0.652632	−	0.757675i	$-0.273665\pi$
$19$	6.78687	−	1.44259i	1.55702	−	0.330954i	0.904383	+	0.426721i	$0.140331\pi$
$20$	−0.834986	−	0.0877606i	−0.186709	−	0.0196239i
$21$			9.05442i			1.97584i
$22$	3.30380	+	0.291402i	0.704372	+	0.0621272i
$23$	−1.47428	−	2.55353i	−0.307409	−	0.532449i	0.670386	−	0.742013i	$-0.266129\pi$
$23$	−1.47428	−	2.55353i	−0.307409	−	0.532449i	−0.977795	+	0.209564i	$0.932795\pi$
$24$	1.95366	+	0.205338i	0.398789	+	0.0419144i
$25$	2.87398	+	3.19188i	0.574796	+	0.638376i
$26$	0.0589212	−	0.277202i	0.0115554	−	0.0543638i
$27$	2.47219	+	3.40267i	0.475772	+	0.654844i
$28$	0.481794	+	4.58396i	0.0910505	+	0.866287i
$29$	−4.69187	−	0.997287i	−0.871258	−	0.185192i	−0.249475	−	0.968381i	$-0.580258\pi$
$29$	−4.69187	−	0.997287i	−0.871258	−	0.185192i	−0.621783	+	0.783190i	$0.713591\pi$
$30$	1.10360	+	1.22567i	0.201488	+	0.223775i
$31$	0.376924	−	3.58619i	0.0676975	−	0.644099i	−0.907086	−	0.420946i	$-0.861698\pi$
$31$	0.376924	−	3.58619i	0.0676975	−	0.644099i	0.974783	−	0.223153i	$-0.0716350\pi$
$32$	1.00000			0.176777
$33$	−4.44001	−	4.76809i	−0.772906	−	0.830018i
$34$	−6.19774	−	3.57827i	−1.06290	−	0.613668i
$35$	−2.27463	+	3.13076i	−0.384482	+	0.529194i
$36$	−0.574746	−	0.638320i	−0.0957909	−	0.106387i
$37$	−6.20377	−	5.58590i	−1.01989	−	0.918317i	−0.0232136	−	0.999731i	$-0.507390\pi$
$37$	−6.20377	−	5.58590i	−1.01989	−	0.918317i	−0.996680	+	0.0814138i	$0.974056\pi$
$38$	−6.33863	−	2.82214i	−1.02826	−	0.457812i
$39$	−0.450385	+	0.327224i	−0.0721194	+	0.0523978i
$40$	0.623933	+	0.561792i	0.0986525	+	0.0888271i
$41$	−7.38095	−	2.39822i	−1.15271	−	0.374539i	−0.330547	−	0.943789i	$-0.607233\pi$
$41$	−7.38095	−	2.39822i	−1.15271	−	0.374539i	−0.822164	+	0.569251i	$0.807233\pi$
$42$	5.32206	−	7.32518i	0.821211	−	1.13030i
$43$	−5.28872	+	3.87678i	−0.806523	+	0.591203i
$43$	−5.28872	+	3.87678i	−0.806523	+	0.591203i
$44$	−2.50155	−	2.17767i	−0.377122	−	0.328297i
$45$		−	0.721157i		−	0.107504i
$46$	−0.308209	+	2.93241i	−0.0454430	+	0.432361i
$47$	1.29074	−	3.97249i	0.188274	−	0.579447i	−0.811716	−	0.584053i	$-0.801466\pi$
$47$	1.29074	−	3.97249i	0.188274	−	0.579447i	0.999989	+	0.00460562i	$0.00146602\pi$
$48$	−1.45985	−	1.31445i	−0.210711	−	0.189725i
$49$	13.0133	+	5.79389i	1.85904	+	0.827699i
$50$	−0.448960	−	4.27157i	−0.0634925	−	0.604091i
$51$	4.34429	+	13.3704i	0.608323	+	1.87223i
$52$	−0.210604	+	0.189628i	−0.0292055	+	0.0262967i
$53$	−0.635449	+	6.04589i	−0.0872856	+	0.830467i	0.860047	+	0.510215i	$0.170434\pi$
$53$	−0.635449	+	6.04589i	−0.0872856	+	0.830467i	−0.947332	+	0.320252i	$0.896232\pi$
$54$		−	4.20593i		−	0.572355i
$55$	−0.337399	−	2.76407i	−0.0454949	−	0.372708i
$56$	2.30461	−	3.99169i	0.307966	−	0.533413i
$57$	5.54387	+	12.4517i	0.734303	+	1.64927i
$58$	3.20961	+	3.56463i	0.421442	+	0.468059i
$59$	2.24651	+	6.91405i	0.292471	+	0.900133i	0.984059	+	0.177841i	$0.0569112\pi$
$59$	2.24651	+	6.91405i	0.292471	+	0.900133i	−0.691588	+	0.722292i	$0.743089\pi$
$60$	−0.172399	−	1.64026i	−0.0222566	−	0.211757i
$61$	1.16687	+	11.1021i	0.149403	+	1.42147i	0.770351	+	0.637620i	$0.220081\pi$
$61$	1.16687	+	11.1021i	0.149403	+	1.42147i	−0.620948	+	0.783852i	$0.713252\pi$
$62$	−2.41285	+	2.67974i	−0.306432	+	0.340327i
$63$	−3.87254	+	0.823134i	−0.487894	+	0.103705i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.237934			−0.0295121
$66$	0.789429	+	6.46724i	0.0971720	+	0.796062i
$67$	−6.00792	−	10.4060i	−0.733984	−	1.27130i	−0.955168	−	0.296066i	$-0.904325\pi$
$67$	−6.00792	−	10.4060i	−0.733984	−	1.27130i	0.221184	−	0.975232i	$-0.429008\pi$
$68$	2.91082	+	6.53782i	0.352989	+	0.792827i
$69$	4.30446	−	3.87575i	0.518196	−	0.466586i
$70$	3.68042	−	1.19584i	0.439895	−	0.142930i
$71$	−8.91636	+	0.937148i	−1.05818	+	0.111219i	−0.617598	−	0.786494i	$-0.711894\pi$
$71$	−8.91636	+	0.937148i	−1.05818	+	0.111219i	−0.440580	+	0.897713i	$0.645227\pi$
$72$	0.0897841	+	0.854238i	0.0105812	+	0.100673i
$73$	4.99027	+	1.06072i	0.584067	+	0.124147i	0.490463	−	0.871462i	$-0.336828\pi$
$73$	4.99027	+	1.06072i	0.584067	+	0.124147i	0.0936046	+	0.995609i	$0.470161\pi$
$74$	1.73565	+	8.16558i	0.201765	+	0.949229i
$75$	−4.95936	+	6.82598i	−0.572658	+	0.788196i
$76$	3.46925	+	6.00892i	0.397950	+	0.689270i
$77$	−14.4577	+	4.96673i	−1.64761	+	0.566012i
$78$	0.556707			0.0630347
$79$	1.80710	+	4.05881i	0.203314	+	0.456651i	0.986209	−	0.165502i	$-0.0529246\pi$
$79$	1.80710	+	4.05881i	0.203314	+	0.456651i	−0.782895	+	0.622154i	$0.786258\pi$
$80$	−0.174560	−	0.821238i	−0.0195164	−	0.0918172i
$81$	−7.25274	+	8.05498i	−0.805860	+	0.894998i
$82$	4.56168	+	6.27861i	0.503753	+	0.693357i
$83$	6.37834	−	14.3260i	0.700114	−	1.57248i	−0.115122	−	0.993351i	$-0.536726\pi$
$83$	6.37834	−	14.3260i	0.700114	−	1.57248i	0.815235	−	0.579130i	$-0.196608\pi$
$84$	−8.61127	+	2.79797i	−0.939567	+	0.305284i
$85$	−1.85673	+	5.71444i	−0.201391	+	0.619818i
$86$	6.55738	−	0.0277458i	0.707100	−	0.00299191i
$87$		−	9.42270i		−	1.01022i
$88$	0.743790	+	3.23215i	0.0792883	+	0.344548i
$89$	2.87816	−	1.66170i	0.305084	−	0.176140i	−0.339641	−	0.940555i	$-0.610305\pi$
$89$	2.87816	−	1.66170i	0.305084	−	0.176140i	0.644725	+	0.764415i	$0.276972\pi$
$90$	−0.423885	+	0.583428i	−0.0446814	+	0.0614987i
$91$	0.271580	+	1.27768i	0.0284693	+	0.133938i
$92$	1.97298	−	2.19121i	0.205697	−	0.228450i
$93$	7.04478	−	0.740436i	0.730510	−	0.0767797i
$94$	−3.37920	+	2.45513i	−0.348538	+	0.253228i
$95$	−1.21118	+	5.69816i	−0.124265	+	0.584619i
$96$	0.408426	+	1.92149i	0.0416848	+	0.196111i
$97$	1.40469	+	1.02057i	0.142625	+	0.103623i	0.656810	−	0.754056i	$-0.271905\pi$
$97$	1.40469	+	1.02057i	0.142625	+	0.103623i	−0.514185	+	0.857679i	$0.671905\pi$
$98$	−7.12241	−	12.3364i	−0.719473	−	1.24616i
$99$	1.63565	−	2.33244i	0.164389	−	0.234419i
$100$	−2.14755	+	3.71966i	−0.214755	+	0.371966i
$101$	3.31428	+	7.44399i	0.329783	+	0.740705i	0.999999	−	0.00146135i	$-0.000465161\pi$
$101$	3.31428	+	7.44399i	0.329783	+	0.740705i	−0.670216	+	0.742166i	$0.733798\pi$
$102$	4.34429	−	13.3704i	0.430149	−	1.32386i
$103$	8.69039	+	1.84720i	0.856289	+	0.182010i	0.615081	−	0.788464i	$-0.289123\pi$
$103$	8.69039	+	1.84720i	0.856289	+	0.182010i	0.241208	+	0.970473i	$0.422456\pi$
$104$	0.281843	−	0.0296229i	0.0276370	−	0.00290476i
$105$	−6.94474	−	3.09200i	−0.677737	−	0.301748i
$106$	4.06778	−	4.51772i	0.395097	−	0.438800i
$107$	−0.786912	−	0.255683i	−0.0760736	−	0.0247178i	0.270733	−	0.962654i	$-0.412734\pi$
$107$	−0.786912	−	0.255683i	−0.0760736	−	0.0247178i	−0.346807	+	0.937937i	$0.612734\pi$
$108$	−2.47219	+	3.40267i	−0.237886	+	0.327422i
$109$	−14.7060	+	8.49050i	−1.40858	+	0.813242i	−0.995251	−	0.0973408i	$-0.968966\pi$
$109$	−14.7060	+	8.49050i	−1.40858	+	0.813242i	−0.413326	+	0.910583i	$0.635633\pi$
$110$	−1.35172	+	2.43450i	−0.128881	+	0.232120i
$111$	8.19949	−	14.2019i	0.778261	−	1.34799i
$112$	−4.21072	+	1.87474i	−0.397876	+	0.177146i
$113$	−15.4858	−	5.03165i	−1.45678	−	0.473338i	−0.529697	−	0.848187i	$-0.677695\pi$
$113$	−15.4858	−	5.03165i	−1.45678	−	0.473338i	−0.927086	+	0.374849i	$0.877695\pi$
$114$	2.83386	−	13.3323i	0.265415	−	1.24868i
$115$	2.46201	−	0.258768i	0.229584	−	0.0241302i
$116$	−0.501390	−	4.77041i	−0.0465529	−	0.442921i
$117$	−0.180897	−	0.162880i	−0.0167239	−	0.0150583i
$118$	2.24651	−	6.91405i	0.206808	−	0.636490i
$119$	32.8053	+	3.44797i	3.00725	+	0.316075i
$120$	−0.824649	+	1.42833i	−0.0752798	+	0.130388i
$121$	5.17794	−	9.70510i	0.470721	−	0.882282i
$122$	5.58160	−	9.66762i	0.505334	−	0.875265i
$123$	1.59358	−	15.1619i	0.143689	−	1.36711i
$124$	3.52714	−	0.749718i	0.316747	−	0.0673266i
$125$	−7.42207	+	2.41158i	−0.663850	+	0.215698i
$126$	3.61678	+	1.61029i	0.322208	+	0.143456i
$127$	−8.00650	−	11.0200i	−0.710462	−	0.977867i	−0.999787	−	0.0206360i	$-0.993431\pi$
$127$	−8.00650	−	11.0200i	−0.710462	−	0.977867i	0.289325	−	0.957231i	$-0.406569\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−9.60925	−	8.57886i	−0.846047	−	0.755327i
$130$	0.192493	+	0.139854i	0.0168828	+	0.0122660i
$131$	−13.0040			−1.13617			−0.568083	−	0.822971i	$-0.692315\pi$
$131$	−13.0040			−1.13617			−0.568083	+	0.822971i	$0.692315\pi$
$132$	3.16269	−	5.69612i	0.275276	−	0.495784i
$133$	31.9810			2.77310
$134$	−1.25600	+	11.9500i	−0.108502	+	1.03232i
$135$	−3.45407	+	0.734186i	−0.297279	+	0.0631887i
$136$	1.48793	−	7.00015i	0.127589	−	0.600258i
$137$	10.3867	+	14.2961i	0.887400	+	1.22140i	0.974316	+	0.225185i	$0.0722988\pi$
$137$	10.3867	+	14.2961i	0.887400	+	1.22140i	−0.0869160	+	0.996216i	$0.527701\pi$
$138$	−5.76049	+	0.605452i	−0.490366	+	0.0515395i
$139$	−10.1665	−	9.15399i	−0.862314	−	0.776431i	0.113842	−	0.993499i	$-0.463684\pi$
$139$	−10.1665	−	9.15399i	−0.862314	−	0.776431i	−0.976157	+	0.217068i	$0.930351\pi$
$140$	−3.68042	−	1.19584i	−0.311053	−	0.101067i
$141$	8.16028	+	0.857680i	0.687220	+	0.0722297i
$142$	7.76433	+	4.48274i	0.651568	+	0.376183i
$143$	−0.769552	−	0.539658i	−0.0643531	−	0.0451285i
$144$	0.429472	−	0.743867i	0.0357893	−	0.0619889i
$145$	2.36714	−	3.25809i	0.196581	−	0.270570i
$146$	−3.41374	−	3.79135i	−0.282523	−	0.313774i
$147$	−5.81796	+	27.3713i	−0.479857	+	2.25755i
$148$	3.39544	−	7.62628i	0.279103	−	0.626876i
$149$	−5.55741	−	2.47432i	−0.455281	−	0.202704i	0.166266	−	0.986081i	$-0.446829\pi$
$149$	−5.55741	−	2.47432i	−0.455281	−	0.202704i	−0.621547	+	0.783377i	$0.713496\pi$
$150$	8.02442	−	2.60729i	0.655191	−	0.212884i
$151$	−0.327716	+	1.00861i	−0.0266692	+	0.0820793i	−0.963505	−	0.267690i	$-0.913740\pi$
$151$	−0.327716	+	1.00861i	−0.0266692	+	0.0820793i	0.936836	+	0.349769i	$0.113740\pi$
$152$	0.725271	−	6.90049i	0.0588272	−	0.559703i
$153$	−5.32351	+	3.07353i	−0.430380	+	0.248480i
$154$	14.6159	+	4.47984i	1.17778	+	0.360996i
$155$	2.62189	+	1.51375i	0.210595	+	0.121587i
$156$	−0.450385	−	0.327224i	−0.0360597	−	0.0261989i
$157$	2.12685	−	1.91502i	0.169741	−	0.152835i	−0.579882	−	0.814700i	$-0.696901\pi$
$157$	2.12685	−	1.91502i	0.169741	−	0.152835i	0.749623	+	0.661865i	$0.230235\pi$
$158$	0.923734	−	4.34583i	0.0734883	−	0.345735i
$159$	−11.8767	+	1.24829i	−0.941881	+	0.0989957i
$160$	−0.341490	+	0.766999i	−0.0269972	+	0.0606366i
$161$	−4.19972	−	12.9254i	−0.330984	−	1.01866i
$162$	10.6022	−	2.25356i	0.832987	−	0.177057i
$163$	6.04292	+	13.5726i	0.473318	+	1.06309i	0.979643	+	0.200748i	$0.0643371\pi$
$163$	6.04292	+	13.5726i	0.473318	+	1.06309i	−0.506325	+	0.862343i	$0.668996\pi$
$164$		−	7.76079i		−	0.606016i
$165$	5.17334	−	1.77723i	0.402744	−	0.138357i
$166$	−13.5808	+	7.84087i	−1.05407	+	0.608570i
$167$	−9.36956	−	0.984780i	−0.725038	−	0.0762046i	−0.265182	−	0.964198i	$-0.585432\pi$
$167$	−9.36956	−	0.984780i	−0.725038	−	0.0762046i	−0.459856	+	0.887994i	$0.652099\pi$
$168$	8.61127	+	2.79797i	0.664374	+	0.215868i
$169$	8.64496	−	9.60120i	0.664997	−	0.738554i
$170$	4.86099	−	3.53172i	0.372821	−	0.270871i
$171$	−4.82156	+	3.50307i	−0.368714	+	0.267887i
$172$	−5.32134	−	3.83188i	−0.405748	−	0.292178i
$173$	17.8510	+	5.80014i	1.35719	+	0.440977i	0.895103	−	0.445860i	$-0.147102\pi$
$173$	17.8510	+	5.80014i	1.35719	+	0.440977i	0.462084	+	0.886836i	$0.347102\pi$
$174$	−5.53852	+	7.62312i	−0.419874	+	0.577908i
$175$	9.89850	+	17.1447i	0.748257	+	1.29602i
$176$	1.29807	−	3.05205i	0.0978457	−	0.230057i
$177$	−12.3678	+	7.14053i	−0.929618	+	0.536715i
$178$	−3.30520	−	0.347391i	−0.247735	−	0.0260380i
$179$	14.1654	−	12.7546i	1.05877	−	0.953324i	0.0597813	−	0.998211i	$-0.480960\pi$
$179$	14.1654	−	12.7546i	1.05877	−	0.953324i	0.998992	+	0.0448877i	$0.0142930\pi$
$180$	0.685861	−	0.222850i	0.0511210	−	0.0166102i
$181$	−1.80080	−	17.1335i	−0.133852	−	1.27352i	−0.830870	−	0.556466i	$-0.812157\pi$
$181$	−1.80080	−	17.1335i	−0.133852	−	1.27352i	0.697018	−	0.717054i	$-0.254510\pi$
$182$	0.531291	−	1.19330i	0.0393819	−	0.0884532i
$183$	−20.8559	+	6.77650i	−1.54171	+	0.500933i
$184$	−2.88413	+	0.613041i	−0.212621	+	0.0451940i
$185$	6.40291	−	2.85076i	0.470751	−	0.209592i
$186$	−6.13456	−	3.54179i	−0.449808	−	0.259697i
$187$	−18.9662	+	14.2710i	−1.38694	+	1.04360i
$188$	4.17692			0.304634
$189$	7.88501	+	17.7100i	0.573550	+	1.28821i
$190$	4.32916	−	3.89799i	0.314070	−	0.282790i
$191$	−11.1029	−	9.99709i	−0.803377	−	0.723364i	0.161270	−	0.986910i	$-0.448441\pi$
$191$	−11.1029	−	9.99709i	−0.803377	−	0.723364i	−0.964647	+	0.263546i	$0.915108\pi$
$192$	0.799001	−	1.79459i	0.0576630	−	0.129513i
$193$	−7.04905	−	9.70218i	−0.507402	−	0.698378i	0.476077	−	0.879404i	$-0.342058\pi$
$193$	−7.04905	−	9.70218i	−0.507402	−	0.698378i	−0.983478	+	0.181025i	$0.942058\pi$
$194$	−0.536544	−	1.65131i	−0.0385216	−	0.118557i
$195$	−0.0971785	−	0.457189i	−0.00695910	−	0.0327400i
$196$	−1.48899	+	14.1668i	−0.106356	+	1.01191i
$197$	−14.6027	−	8.43085i	−1.04040	−	0.600673i	−0.120451	−	0.992719i	$-0.538434\pi$
$197$	−14.6027	−	8.43085i	−1.04040	−	0.600673i	−0.919946	+	0.392046i	$0.871767\pi$
$198$	−2.69424	+	0.925569i	−0.191472	+	0.0657773i
$199$			0.839399i			0.0595034i	0.999557	+	0.0297517i	$0.00947166\pi$
$199$			0.839399i			0.0595034i	−0.999557	+	0.0297517i	$0.990528\pi$
$200$	3.92377	−	1.74697i	0.277452	−	0.123530i
$201$	17.5413	−	15.7943i	1.23727	−	1.11404i
$202$	1.69416	−	7.97040i	0.119201	−	0.560795i
$203$	−20.1975	−	8.99251i	−1.41759	−	0.631151i
$204$	−11.3735	+	8.26334i	−0.796305	+	0.578549i
$205$	4.35995	−	4.84222i	0.304512	−	0.338195i
$206$	−5.94491	−	6.60250i	−0.414202	−	0.460018i
$207$	2.04896	+	1.48866i	0.142413	+	0.103469i
$208$	−0.245427	−	0.141698i	−0.0170173	−	0.00982496i
$209$	−16.8413	+	15.6825i	−1.16494	+	1.08478i
$210$	3.80098	+	6.58349i	0.262293	+	0.454304i
$211$	2.54954	+	1.85235i	0.175518	+	0.127521i	0.672076	−	0.740482i	$-0.265403\pi$
$211$	2.54954	+	1.85235i	0.175518	+	0.127521i	−0.496558	+	0.868004i	$0.665403\pi$
$212$	−5.94635	+	1.26394i	−0.408397	+	0.0868075i
$213$	−5.44240	−	16.7500i	−0.372907	−	1.14769i
$214$	0.486338	+	0.669387i	0.0332454	+	0.0457584i
$215$	−1.16744	−	5.38033i	−0.0796187	−	0.366935i
$216$	4.00008	−	1.29970i	0.272171	−	0.0884337i
$217$	5.13603	−	15.8071i	0.348657	−	1.07305i
$218$	16.8880	+	1.77500i	1.14380	+	0.120218i
$219$			10.0220i			0.677224i
$220$	2.52453	−	1.17503i	0.170204	−	0.0792206i
$221$	1.01406	+	1.75641i	0.0682133	+	0.118149i
$222$	−14.9812	+	6.67006i	−1.00547	+	0.447665i
$223$	−18.0088	−	5.85142i	−1.20596	−	0.391840i	−0.364010	−	0.931395i	$-0.618592\pi$
$223$	−18.0088	−	5.85142i	−1.20596	−	0.391840i	−0.841950	+	0.539555i	$0.818592\pi$
$224$	4.50849	+	0.958309i	0.301236	+	0.0640297i
$225$	−3.37029	−	1.50055i	−0.224686	−	0.100037i
$226$	9.57076	+	13.1730i	0.636638	+	0.876256i
$227$	12.1803	−	13.5276i	0.808437	−	0.897860i	−0.188003	−	0.982168i	$-0.560201\pi$
$227$	12.1803	−	13.5276i	0.808437	−	0.897860i	0.996440	+	0.0843085i	$0.0268681\pi$
$228$	−10.1292	+	9.12033i	−0.670820	+	0.604009i
$229$	26.8754	−	11.9657i	1.77598	−	0.790715i	0.792452	−	0.609934i	$-0.208804\pi$
$229$	26.8754	−	11.9657i	1.77598	−	0.790715i	0.983523	−	0.180781i	$-0.0578625\pi$
$230$	−2.14391	−	1.23779i	−0.141365	−	0.0816172i
$231$	−15.4484	−	25.7518i	−1.01643	−	1.69434i
$232$	−2.39834	+	4.15405i	−0.157459	+	0.272727i
$233$	8.77811	−	3.90827i	0.575073	−	0.256039i	−0.0985277	−	0.995134i	$-0.531413\pi$
$233$	8.77811	−	3.90827i	0.575073	−	0.256039i	0.673601	+	0.739095i	$0.264747\pi$
$234$	0.0506100	+	0.238101i	0.00330848	+	0.0155652i
$235$	2.60612	+	2.34656i	0.170005	+	0.153073i
$236$	−5.88144	+	4.27312i	−0.382849	+	0.278156i
$237$	−7.06090	+	5.13004i	−0.458655	+	0.333232i
$238$	−24.5134	−	22.0719i	−1.58896	−	1.43071i
$239$	2.01416	+	9.47586i	0.130285	+	0.612942i	0.994039	+	0.109028i	$0.0347738\pi$
$239$	2.01416	+	9.47586i	0.130285	+	0.612942i	−0.863754	+	0.503914i	$0.831893\pi$
$240$	1.50671	−	0.670830i	0.0972576	−	0.0433019i
$241$	8.01686	−	13.8856i	0.516412	−	0.894451i	−0.483407	−	0.875396i	$-0.660601\pi$
$241$	8.01686	−	13.8856i	0.516412	−	0.894451i	0.999818	−	0.0190553i	$-0.00606586\pi$
$242$	−9.89355	+	4.80808i	−0.635982	+	0.309075i
$243$	−7.51246	−	4.33732i	−0.481924	−	0.278239i
$244$	−10.1981	+	4.54048i	−0.652866	+	0.290675i
$245$	−8.88783	+	8.00263i	−0.567822	+	0.511270i
$246$	−10.2012	+	11.3296i	−0.650405	+	0.722348i
$247$	1.15578	+	1.59080i	0.0735408	+	0.101220i
$248$	−3.29419	−	1.46667i	−0.209181	−	0.0931336i
$249$	30.1323	+	6.40483i	1.90956	+	0.405889i
$250$	7.42207	+	2.41158i	0.469413	+	0.152522i
$251$	−0.0985048	+	0.0438572i	−0.00621757	+	0.00276824i	−0.409843	−	0.912156i	$-0.634417\pi$
$251$	−0.0985048	+	0.0438572i	−0.00621757	+	0.00276824i	0.403626	+	0.914924i	$0.367750\pi$
$252$	−1.97953	−	3.42864i	−0.124698	−	0.215984i
$253$	8.54980	+	4.74715i	0.537521	+	0.298451i
$254$			13.6215i			0.854687i
$255$	−11.7386	−	1.23378i	−0.735099	−	0.0772620i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	3.64961	−	1.18583i	0.227657	−	0.0739701i	−0.192967	−	0.981205i	$-0.561811\pi$
$257$	3.64961	−	1.18583i	0.227657	−	0.0739701i	0.420624	+	0.907235i	$0.361811\pi$
$258$	2.73152	+	12.5886i	0.170057	+	0.783733i
$259$	−22.6166	−	31.1291i	−1.40533	−	1.93427i
$260$	−0.0735258	−	0.226289i	−0.00455988	−	0.0140339i
$261$	4.03005	−	0.856613i	0.249454	−	0.0530230i
$262$	10.5205	+	7.64357i	0.649957	+	0.472221i
$263$	5.41551	+	9.37995i	0.333935	+	0.578392i	0.983280	−	0.182102i	$-0.0582901\pi$
$263$	5.41551	+	9.37995i	0.333935	+	0.578392i	−0.649345	+	0.760494i	$0.724957\pi$
$264$	−5.90676	+	2.74928i	−0.363536	+	0.169206i
$265$	−4.42020	−	2.55200i	−0.271531	−	0.156768i
$266$	−25.8732	−	18.7980i	−1.58639	−	1.15258i
$267$	4.36847	+	4.85167i	0.267346	+	0.296918i
$268$	8.04016	−	8.92951i	0.491131	−	0.545456i
$269$	18.9775	−	13.7880i	1.15708	−	0.840667i	0.167673	−	0.985843i	$-0.446375\pi$
$269$	18.9775	−	13.7880i	1.15708	−	0.840667i	0.989406	+	0.145175i	$0.0463746\pi$
$270$	3.22595	+	1.43628i	0.196325	+	0.0874095i
$271$	3.28523	−	15.4558i	0.199564	−	0.938874i	−0.758357	−	0.651840i	$-0.773997\pi$
$271$	3.28523	−	15.4558i	0.199564	−	0.938874i	0.957920	−	0.287034i	$-0.0926692\pi$
$272$	−5.31834	+	4.78866i	−0.322472	+	0.290355i
$273$	−2.34414	+	1.04368i	−0.141874	+	0.0631663i
$274$		−	17.6710i		−	1.06754i
$275$	−13.6198	−	4.17455i	−0.821306	−	0.251735i
$276$	5.01621	+	2.89611i	0.301940	+	0.174325i
$277$	−1.12969	+	10.7483i	−0.0678767	+	0.645804i	0.906704	+	0.421767i	$0.138590\pi$
$277$	−1.12969	+	10.7483i	−0.0678767	+	0.645804i	−0.974581	+	0.224036i	$0.928077\pi$
$278$	2.84432	+	13.3815i	0.170591	+	0.802567i
$279$	0.957119	+	2.94571i	0.0573012	+	0.176355i
$280$	2.27463	+	3.13076i	0.135935	+	0.187098i
$281$	−3.32014	+	7.45715i	−0.198063	+	0.444857i	−0.985085	−	0.172068i	$-0.944955\pi$
$281$	−3.32014	+	7.45715i	−0.198063	+	0.444857i	0.787022	+	0.616925i	$0.211622\pi$
$282$	−6.09768	−	5.49037i	−0.363111	−	0.326947i
$283$	4.32636	−	3.89547i	0.257175	−	0.231562i	−0.530450	−	0.847716i	$-0.677977\pi$
$283$	4.32636	−	3.89547i	0.257175	−	0.231562i	0.787625	+	0.616155i	$0.211310\pi$
$284$	−3.64659	−	8.19037i	−0.216385	−	0.486009i
$285$	−11.4436			−0.677863
$286$	0.305377	+	0.888924i	0.0180573	+	0.0525632i
$287$	−30.9787	−	17.8856i	−1.82862	−	1.05575i
$288$	−0.784684	+	0.349364i	−0.0462380	+	0.0205865i
$289$	33.4683	−	7.11390i	1.96872	−	0.418465i
$290$	−3.83012	+	1.24448i	−0.224912	+	0.0730785i
$291$	−1.38730	+	3.11593i	−0.0813250	+	0.182659i
$292$	0.533279	+	5.07381i	0.0312078	+	0.296922i
$293$	0.288001	−	0.0935772i	0.0168252	−	0.00546684i	−0.300592	−	0.953753i	$-0.597184\pi$
$293$	0.288001	−	0.0935772i	0.0168252	−	0.00546684i	0.317417	+	0.948286i	$0.397184\pi$
$294$	20.7953	−	18.7242i	1.21281	−	1.09202i
$295$	−6.07023	−	0.638007i	−0.353423	−	0.0371462i
$296$	−7.22958	+	4.17400i	−0.420211	+	0.242609i
$297$	−12.8367	−	5.45959i	−0.744862	−	0.316798i
$298$	3.04167	+	5.26833i	0.176199	+	0.305186i
$299$	0.491159	−	0.676022i	0.0284045	−	0.0390954i
$300$	−8.02442	−	2.60729i	−0.463290	−	0.150532i
$301$	−27.5593	+	12.4102i	−1.58849	+	0.715311i
$302$	0.857972	−	0.623353i	0.0493708	−	0.0358700i
$303$	−12.9499	+	9.40868i	−0.743954	+	0.540514i
$304$	−4.64276	+	5.15631i	−0.266281	+	0.295735i
$305$	−8.91374	−	2.89625i	−0.510399	−	0.165839i
$306$	6.11339	+	0.642543i	0.349479	+	0.0367317i
$307$	−21.2635	+	12.2765i	−1.21357	+	0.700658i	−0.963536	−	0.267578i	$-0.913777\pi$
$307$	−21.2635	+	12.2765i	−1.21357	+	0.700658i	−0.250038	+	0.968236i	$0.580443\pi$
$308$	−9.19131	−	12.2153i	−0.523724	−	0.696030i
$309$			17.4530i			0.992864i
$310$	−1.23139	−	2.76576i	−0.0699385	−	0.157084i
$311$	−15.2496	+	3.24141i	−0.864728	+	0.183804i	−0.618861	−	0.785500i	$-0.712406\pi$
$311$	−15.2496	+	3.24141i	−0.864728	+	0.183804i	−0.245866	+	0.969304i	$0.579072\pi$
$312$	0.172032	+	0.529460i	0.00973939	+	0.0299748i
$313$	3.78199	−	8.49448i	0.213770	−	0.480136i	−0.774553	−	0.632510i	$-0.782025\pi$
$313$	3.78199	−	8.49448i	0.213770	−	0.480136i	0.988323	+	0.152373i	$0.0486916\pi$
$314$	−2.84628	+	0.299156i	−0.160625	+	0.0168823i
$315$	0.691091	−	3.25133i	0.0389386	−	0.183192i
$316$	−3.30173	+	2.97289i	−0.185737	+	0.167238i
$317$	−11.9839	−	8.70678i	−0.673081	−	0.489022i	0.197974	−	0.980207i	$-0.436564\pi$
$317$	−11.9839	−	8.70678i	−0.673081	−	0.489022i	−0.871055	+	0.491185i	$0.836564\pi$
$318$	10.3422	+	5.97105i	0.579959	+	0.334840i
$319$	15.0457	−	5.16875i	0.842399	−	0.289394i
$320$	0.727102	−	0.419793i	0.0406462	−	0.0234671i
$321$	0.169898	−	1.61647i	0.00948279	−	0.0902227i
$322$	−4.19972	+	12.9254i	−0.234041	+	0.720304i
$323$	47.2253	−	15.3444i	2.62768	−	0.853786i
$324$	−9.90196	−	4.40864i	−0.550109	−	0.244924i
$325$	−0.495084	+	1.11198i	−0.0274623	+	0.0616813i
$326$	3.08896	−	14.5324i	0.171082	−	0.804877i
$327$	−22.3207	−	24.7897i	−1.23434	−	1.37087i
$328$	−4.56168	+	6.27861i	−0.251877	+	0.346678i
$329$	9.62616	−	16.6730i	0.530708	−	0.919212i
$330$	−5.22995	−	1.60301i	−0.287899	−	0.0882426i
$331$	−22.9018	−	13.2224i	−1.25880	−	0.726767i	−0.285957	−	0.958243i	$-0.592311\pi$
$331$	−22.9018	−	13.2224i	−1.25880	−	0.726767i	−0.972841	+	0.231476i	$0.925645\pi$
$332$	15.5958	+	1.63919i	0.855933	+	0.0899622i
$333$	6.81952	+	2.21580i	0.373707	+	0.121425i
$334$	7.00129	+	6.30399i	0.383094	+	0.344939i
$335$	10.0331	−	1.05452i	0.548164	−	0.0576144i
$336$	−5.32206	−	7.32518i	−0.290342	−	0.399622i
$337$	−1.82241	+	8.57377i	−0.0992730	+	0.467043i	0.900227	+	0.435421i	$0.143401\pi$
$337$	−1.82241	+	8.57377i	−0.0992730	+	0.467043i	−0.999500	+	0.0316218i	$0.989933\pi$
$338$	−12.6374	+	2.68615i	−0.687382	+	0.146108i
$339$	3.34346	−	31.8109i	0.181592	−	1.72773i
$340$	−6.00852			−0.325858
$341$	5.04665	+	10.8426i	0.273292	+	0.587161i
$342$	5.95978			0.322268
$343$	27.0155	+	19.6279i	1.45870	+	1.05981i
$344$	2.05273	+	6.22786i	0.110676	+	0.335784i
$345$	1.50277	+	4.62505i	0.0809064	+	0.249004i
$346$	−11.0325	−	15.1850i	−0.593112	−	0.816349i
$347$	21.0107	+	9.35458i	1.12792	+	0.502180i	0.883940	−	0.467601i	$-0.154882\pi$
$347$	21.0107	+	9.35458i	1.12792	+	0.502180i	0.243976	+	0.969781i	$0.421548\pi$
$348$	8.96152	−	2.91177i	0.480388	−	0.156088i
$349$	5.54933	−	1.17955i	0.297049	−	0.0631397i	−0.0569764	−	0.998376i	$-0.518146\pi$
$349$	5.54933	−	1.17955i	0.297049	−	0.0631397i	0.354025	+	0.935236i	$0.384813\pi$
$350$	2.06935	−	19.6886i	0.110611	−	1.05240i
$351$	−0.595970	+	1.03225i	−0.0318106	+	0.0550975i
$352$	−2.84411	+	1.70617i	−0.151592	+	0.0909394i
$353$	−0.372243	+	0.644743i	−0.0198125	+	0.0343162i	−0.875762	−	0.482744i	$-0.839640\pi$
$353$	−0.372243	+	0.644743i	−0.0198125	+	0.0343162i	0.855949	+	0.517060i	$0.172974\pi$
$354$	14.2028	+	1.49278i	0.754872	+	0.0793402i
$355$	2.32606	−	7.15887i	0.123454	−	0.379954i
$356$	2.46977	+	2.22379i	0.130898	+	0.117861i
$357$	6.77327	+	64.4433i	0.358479	+	3.41070i
$358$	−18.9570	+	1.99246i	−1.00191	+	0.105305i
$359$	−0.916845	+	4.31342i	−0.0483892	+	0.227653i	−0.995697	−	0.0926724i	$-0.970459\pi$
$359$	−0.916845	+	4.31342i	−0.0483892	+	0.227653i	0.947307	+	0.320326i	$0.103792\pi$
$360$	−0.685861	−	0.222850i	−0.0361480	−	0.0117452i
$361$	26.6232	−	11.8534i	1.40122	−	0.623864i
$362$	−8.61392	+	14.9197i	−0.452738	+	0.784165i
$363$	20.7631	+	5.98555i	1.08978	+	0.314160i
$364$	−1.13123	+	0.653114i	−0.0592924	+	0.0342325i
$365$	−2.51770	+	3.46531i	−0.131782	+	0.181383i
$366$	20.8559	+	6.77650i	1.09016	+	0.354213i
$367$	−9.99591	+	11.1016i	−0.521782	+	0.579498i	−0.945223	−	0.326426i	$-0.894156\pi$
$367$	−9.99591	+	11.1016i	−0.521782	+	0.579498i	0.423441	+	0.905924i	$0.360822\pi$
$368$	2.69365	+	1.19929i	0.140416	+	0.0625173i
$369$	6.62957	−	0.696796i	0.345122	−	0.0362737i
$370$	−6.85570	−	1.45722i	−0.356411	−	0.0757574i
$371$	−8.65875	+	26.6489i	−0.449540	+	1.38354i
$372$	2.88115	+	6.47118i	0.149381	+	0.335515i
$373$	−15.0989	+	26.1521i	−0.781793	+	1.35411i	0.149103	+	0.988822i	$0.452361\pi$
$373$	−15.0989	+	26.1521i	−0.781793	+	1.35411i	−0.930896	+	0.365284i	$0.880972\pi$
$374$	23.7322	−	0.397438i	1.22716	−	0.0205510i
$375$	−7.66519	−	13.2765i	−0.395829	−	0.685595i
$376$	−3.37920	−	2.45513i	−0.174269	−	0.126614i
$377$	−0.282626	−	1.32965i	−0.0145560	−	0.0684806i
$378$	4.03058	−	18.9624i	0.207311	−	0.975321i
$379$	−21.2105	+	15.4104i	−1.08951	+	0.791577i	−0.979317	−	0.202333i	$-0.935148\pi$
$379$	−21.2105	+	15.4104i	−1.08951	+	0.791577i	−0.110196	+	0.993910i	$0.535148\pi$
$380$	−5.79355	+	0.608926i	−0.297203	+	0.0312373i
$381$	17.9048	−	19.8853i	0.917290	−	1.01875i
$382$	3.10629	+	14.6139i	0.158931	+	0.747714i
$383$	−0.382061	+	0.525862i	−0.0195224	+	0.0268703i	−0.818667	−	0.574269i	$-0.805286\pi$
$383$	−0.382061	+	0.525862i	−0.0195224	+	0.0268703i	0.799144	+	0.601139i	$0.205286\pi$
$384$	−1.70124	+	0.982210i	−0.0868159	+	0.0501232i
$385$	1.12768	−	12.7851i	0.0574717	−	0.651590i
$386$			11.9926i			0.610405i
$387$	2.79557	−	4.88974i	0.142107	−	0.248559i
$388$	−0.536544	+	1.65131i	−0.0272389	+	0.0838327i
$389$	8.08147	−	2.62583i	0.409747	−	0.133135i	−0.0968887	−	0.995295i	$-0.530889\pi$
$389$	8.08147	−	2.62583i	0.409747	−	0.133135i	0.506635	+	0.862160i	$0.330889\pi$
$390$	−0.190110	+	0.426994i	−0.00962659	+	0.0216217i
$391$	−12.4032	−	17.0715i	−0.627255	−	0.863342i
$392$	9.53165	−	10.5860i	0.481421	−	0.534672i
$393$	−5.31118	−	24.9871i	−0.267913	−	1.26043i
$394$	6.85827	+	15.4039i	0.345515	+	0.776039i
$395$	−3.73021			−0.187687
$396$	2.72373	+	0.834836i	0.136872	+	0.0419521i
$397$	14.1200	+	24.4566i	0.708664	+	1.22744i	0.965353	+	0.260947i	$0.0840349\pi$
$397$	14.1200	+	24.4566i	0.708664	+	1.22744i	−0.256690	+	0.966494i	$0.582632\pi$
$398$	0.493386	−	0.679088i	0.0247312	−	0.0340396i
$399$	13.0619	+	61.4512i	0.653911	+	3.07641i
$400$	−4.20124	−	0.893001i	−0.210062	−	0.0446500i
$401$	−1.35679	−	12.9090i	−0.0677550	−	0.644646i	−0.974718	−	0.223437i	$-0.928272\pi$
$401$	−1.35679	−	12.9090i	−0.0677550	−	0.644646i	0.906963	−	0.421209i	$-0.138394\pi$
$402$	−23.4748	+	2.46731i	−1.17082	+	0.123058i
$403$	0.971891	−	0.315787i	0.0484133	−	0.0157304i
$404$	−6.05549	+	5.45239i	−0.301272	+	0.271266i
$405$	−3.70143	−	8.31354i	−0.183925	−	0.413103i
$406$	11.0545	+	19.1469i	0.548624	+	0.950245i
$407$	27.1747	+	5.30221i	1.34700	+	0.262821i
$408$	14.0584			0.695996
$409$	21.2058	+	15.4069i	1.04856	+	0.761822i	0.971938	−	0.235239i	$-0.0755872\pi$
$409$	21.2058	+	15.4069i	1.04856	+	0.761822i	0.0766199	+	0.997060i	$0.475587\pi$
$410$	−6.37346	+	1.35472i	−0.314763	+	0.0669049i
$411$	−23.2277	+	25.7970i	−1.14574	+	1.27247i
$412$	0.928687	+	8.83586i	0.0457531	+	0.435312i
$413$	3.50257	+	33.3248i	0.172350	+	1.63980i
$414$	−0.782633	−	2.40870i	−0.0384643	−	0.118381i
$415$	8.80988	+	9.78436i	0.432460	+	0.480296i
$416$	0.115267	+	0.258894i	0.00565144	+	0.0126933i
$417$	13.4370	−	23.2736i	0.658015	−	1.13972i
$418$	22.8428	−	2.78833i	1.11728	−	0.136382i
$419$		−	10.9635i		−	0.535602i	−0.963474	−	0.267801i	$-0.913703\pi$
$419$		−	10.9635i		−	0.535602i	0.963474	−	0.267801i	$-0.0862970\pi$
$420$	0.794621	−	7.56032i	0.0387736	−	0.368906i
$421$	21.8568	−	19.6800i	1.06524	−	0.959144i	0.0659852	−	0.997821i	$-0.478981\pi$
$421$	21.8568	−	19.6800i	1.06524	−	0.959144i	0.999252	+	0.0386769i	$0.0123143\pi$
$422$	−0.973839	−	2.99717i	−0.0474058	−	0.145900i
$423$	0.375021	+	3.56809i	0.0182342	+	0.173486i
$424$	5.55362	+	2.47263i	0.269708	+	0.120082i
$425$	22.8428	+	20.5677i	1.10804	+	0.997682i
$426$	−5.44240	+	16.7500i	−0.263685	+	0.811539i
$427$	−5.37836	+	51.1717i	−0.260277	+	2.47637i
$428$		−	0.827408i		−	0.0399943i
$429$	0.722645	−	1.69910i	0.0348896	−	0.0820332i
$430$	−2.21800	+	5.03898i	−0.106961	+	0.243001i
$431$	13.3099	−	18.3196i	0.641117	−	0.882422i	−0.357558	−	0.933891i	$-0.616390\pi$
$431$	13.3099	−	18.3196i	0.641117	−	0.882422i	0.998675	+	0.0514692i	$0.0163904\pi$
$432$	−4.00008	−	1.29970i	−0.192454	−	0.0625321i
$433$	16.3251	+	14.6992i	0.784536	+	0.706399i	0.960586	−	0.277982i	$-0.0896656\pi$
$433$	16.3251	+	14.6992i	0.784536	+	0.706399i	−0.176051	+	0.984381i	$0.556332\pi$
$434$	−13.4463	+	9.76932i	−0.645444	+	0.468942i
$435$	7.22721	+	3.21776i	0.346518	+	0.154280i
$436$	−12.6193	−	11.3625i	−0.604357	−	0.544165i
$437$	−13.6895	−	15.2037i	−0.654857	−	0.727293i
$438$	5.89078	−	8.10797i	0.281472	−	0.387414i
$439$	5.37388	+	3.10261i	0.256481	+	0.148079i	0.622728	−	0.782438i	$-0.286024\pi$
$439$	5.37388	+	3.10261i	0.256481	+	0.148079i	−0.366247	+	0.930518i	$0.619358\pi$
$440$	−2.73305	−	0.533260i	−0.130293	−	0.0254222i
$441$	−12.2355			−0.582643
$442$	0.211997	−	2.01702i	0.0100837	−	0.0959397i
$443$	−16.4002	−	18.2143i	−0.779197	−	0.865386i	0.214587	−	0.976705i	$-0.431159\pi$
$443$	−16.4002	−	18.2143i	−0.779197	−	0.865386i	−0.993785	+	0.111318i	$0.964493\pi$
$444$	16.0406	+	3.40954i	0.761254	+	0.161810i
$445$	0.291664	+	2.77500i	0.0138262	+	0.131548i
$446$	11.1301	+	15.3192i	0.527024	+	0.725386i
$447$	2.48459	−	11.6891i	0.117517	−	0.552875i
$448$	−3.08416	−	3.42531i	−0.145713	−	0.161831i
$449$	−7.19043	−	0.755745i	−0.339338	−	0.0356658i	−0.0666727	−	0.997775i	$-0.521238\pi$
$449$	−7.19043	−	0.755745i	−0.339338	−	0.0356658i	−0.272665	+	0.962109i	$0.587905\pi$
$450$	1.84462	+	3.19498i	0.0869564	+	0.150613i
$451$	25.0840	−	5.77240i	1.18116	−	0.271812i
$452$		−	16.2828i		−	0.765876i
$453$	−2.07188	−	0.217763i	−0.0973453	−	0.0102314i
$454$	−17.8054	+	3.78466i	−0.835650	+	0.177623i
$455$	−1.07272	−	0.228015i	−0.0502901	−	0.0106895i
$456$	13.5555	−	1.42474i	0.634792	−	0.0667194i
$457$	−0.978361	+	0.710821i	−0.0457658	+	0.0332508i	−0.610433	−	0.792068i	$-0.709005\pi$
$457$	−0.978361	+	0.710821i	−0.0457658	+	0.0332508i	0.564667	+	0.825319i	$0.309005\pi$
$458$	−28.7759	−	6.11651i	−1.34461	−	0.285806i
$459$	20.1408	+	22.3686i	0.940090	+	1.04408i
$460$	1.00691	+	2.26155i	0.0469472	+	0.105445i
$461$	20.3578	−	11.7536i	0.948157	−	0.547419i	0.0556489	−	0.998450i	$-0.482277\pi$
$461$	20.3578	−	11.7536i	0.948157	−	0.547419i	0.892508	+	0.451032i	$0.148944\pi$
$462$	−2.63848	+	29.9140i	−0.122753	+	1.39172i
$463$	−2.65722	+	1.53414i	−0.123491	+	0.0712977i	−0.560473	−	0.828173i	$-0.689381\pi$
$463$	−2.65722	+	1.53414i	−0.123491	+	0.0712977i	0.436982	+	0.899470i	$0.356047\pi$
$464$	4.38199	−	1.95099i	0.203429	−	0.0905723i
$465$	−1.83781	+	5.65619i	−0.0852263	+	0.262300i
$466$	−9.39886	−	1.99779i	−0.435394	−	0.0925458i
$467$	1.88423	−	4.23206i	0.0871919	−	0.195836i	−0.864687	−	0.502312i	$-0.832483\pi$
$467$	1.88423	−	4.23206i	0.0871919	−	0.195836i	0.951879	+	0.306475i	$0.0991497\pi$
$468$	0.0990081	−	0.222376i	0.00457665	−	0.0102793i
$469$	−17.1145	−	52.6729i	−0.790272	−	2.43221i
$470$	−0.729122	−	3.43025i	−0.0336319	−	0.158226i
$471$	4.54836	+	3.30457i	0.209577	+	0.152267i
$472$	7.26986			0.334623
$473$	8.42726	−	20.0495i	0.387486	−	0.921876i
$474$	8.72775			0.400879
$475$	24.1099	+	17.5169i	1.10624	+	0.803730i
$476$	6.85817	+	32.2652i	0.314344	+	1.47887i
$477$	−1.61359	−	4.96612i	−0.0738812	−	0.227383i
$478$	3.94028	−	8.85002i	0.180224	−	0.404790i
$479$	−3.45663	+	7.76371i	−0.157937	+	0.354733i	−0.975131	−	0.221630i	$-0.928862\pi$
$479$	−3.45663	+	7.76371i	−0.157937	+	0.354733i	0.817193	+	0.576364i	$0.195529\pi$
$480$	−1.61326	−	0.342908i	−0.0736348	−	0.0156515i
$481$	0.731067	−	2.24999i	0.0333338	−	0.102591i
$482$	−14.6475	+	6.52150i	−0.667177	+	0.297046i
$483$	23.1208	−	13.3488i	1.05203	−	0.607391i
$484$	10.8302	+	1.92547i	0.492280	+	0.0875213i
$485$	−1.26246	+	0.728883i	−0.0573255	+	0.0330969i
$486$	3.52829	+	7.92468i	0.160047	+	0.359471i
$487$	−1.89224	−	2.10155i	−0.0857456	−	0.0952301i	0.698745	−	0.715371i	$-0.253742\pi$
$487$	−1.89224	−	2.10155i	−0.0857456	−	0.0952301i	−0.784491	+	0.620141i	$0.787076\pi$
$488$	10.9193	+	2.32096i	0.494292	+	0.105065i
$489$	−23.6116	+	17.1548i	−1.06775	+	0.775769i
$490$	11.8942	−	1.25013i	0.537327	−	0.0564753i
$491$	−12.4371	−	2.64359i	−0.561278	−	0.119303i	−0.0814685	−	0.996676i	$-0.525961\pi$
$491$	−12.4371	−	2.64359i	−0.561278	−	0.119303i	−0.479810	+	0.877373i	$0.659294\pi$
$492$	14.9123	−	3.16971i	0.672299	−	0.142901i
$493$	−34.1396	−	3.58821i	−1.53757	−	0.161605i
$494$		−	1.96634i		−	0.0884697i
$495$	1.23042	+	2.05105i	0.0553032	+	0.0921878i
$496$	1.80297	+	3.12284i	0.0809558	+	0.140220i
$497$	−41.0974	−	4.31951i	−1.84347	−	0.193757i
$498$	−20.6129	−	22.8930i	−0.923687	−	1.02586i
$499$	6.96322	−	32.7594i	0.311717	−	1.46651i	−0.491528	−	0.870862i	$-0.663561\pi$
$499$	6.96322	−	32.7594i	0.311717	−	1.46651i	0.803245	−	0.595649i	$-0.203105\pi$
$500$	−4.58709	−	6.31359i	−0.205141	−	0.282352i
$501$	−1.93452	−	18.4057i	−0.0864280	−	0.822308i
$502$	0.105471	+	0.0224185i	0.00470739	+	0.00100059i
$503$	−12.9401	−	14.3714i	−0.576971	−	0.640791i	0.382045	−	0.924144i	$-0.375220\pi$
$503$	−12.9401	−	14.3714i	−0.576971	−	0.640791i	−0.959016	+	0.283353i	$0.908553\pi$
$504$	−0.413834	+	3.93737i	−0.0184336	+	0.175384i
$505$	−6.84133			−0.304435
$506$	−4.12663	−	8.86597i	−0.183451	−	0.394140i
$507$	21.9795	+	12.6898i	0.976142	+	0.563576i
$508$	8.00650	−	11.0200i	0.355231	−	0.488933i
$509$	1.79820	+	1.99710i	0.0797037	+	0.0885199i	0.781677	−	0.623683i	$-0.214364\pi$
$509$	1.79820	+	1.99710i	0.0797037	+	0.0885199i	−0.701974	+	0.712203i	$0.747698\pi$
$510$	8.77153	+	7.89792i	0.388410	+	0.349726i
$511$	21.4821	+	9.56445i	0.950312	+	0.423106i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	21.6871	+	19.5271i	0.957508	+	0.862144i
$514$	−3.64961	−	1.18583i	−0.160978	−	0.0523048i
$515$	−4.38448	+	6.03472i	−0.193203	+	0.265922i
$516$	5.18956	−	11.7900i	0.228458	−	0.519024i
$517$	3.10675	+	13.5004i	0.136635	+	0.593748i
$518$			38.4777i			1.69061i
$519$	−3.85412	+	36.6695i	−0.169177	+	1.60961i
$520$	−0.0735258	+	0.226289i	−0.00322432	+	0.00992343i
$521$	15.0322	+	13.5351i	0.658573	+	0.592982i	0.929144	−	0.369718i	$-0.120546\pi$
$521$	15.0322	+	13.5351i	0.658573	+	0.592982i	−0.270571	+	0.962700i	$0.587212\pi$
$522$	−3.76388	−	1.67579i	−0.164741	−	0.0733473i
$523$	2.51194	+	23.8995i	0.109839	+	1.04505i	0.901111	+	0.433588i	$0.142753\pi$
$523$	2.51194	+	23.8995i	0.109839	+	1.04505i	−0.791272	+	0.611465i	$0.790581\pi$
$524$	−4.01846	−	12.3676i	−0.175547	−	0.540279i
$525$	−28.9006	+	26.0222i	−1.26133	+	1.13570i
$526$	1.13215	−	10.7717i	0.0493641	−	0.469668i
$527$		−	25.8060i		−	1.12413i
$528$	6.39466	+	1.24769i	0.278292	+	0.0542990i
$529$	7.15298	−	12.3893i	0.310999	−	0.538666i
$530$	2.07599	+	4.66274i	0.0901750	+	0.202536i
$531$	−4.17832	−	4.64050i	−0.181324	−	0.201380i
$532$	9.88267	+	30.4157i	0.428468	+	1.31869i
$533$	−0.229897	−	2.18732i	−0.00995794	−	0.0947435i
$534$	−0.682421	−	6.49280i	−0.0295313	−	0.280971i
$535$	0.464831	−	0.516247i	0.0200964	−	0.0223193i
$536$	−11.7533	+	2.49823i	−0.507664	+	0.107907i
$537$	30.2934	+	22.0094i	1.30726	+	0.949777i
$538$	−23.4575			−1.01132
$539$	−46.8967	+	5.72448i	−2.01998	+	0.246571i
$540$	−1.76562	−	3.05814i	−0.0759802	−	0.131602i
$541$	4.88457	+	10.9709i	0.210004	+	0.471677i	0.987581	−	0.157111i	$-0.0502180\pi$
$541$	4.88457	+	10.9709i	0.210004	+	0.471677i	−0.777577	+	0.628788i	$0.783551\pi$
$542$	−11.7425	+	10.5730i	−0.504384	+	0.454149i
$543$	32.1863	−	10.4580i	1.38125	−	0.448795i
$544$	7.11733	−	0.748061i	0.305153	−	0.0320729i
$545$	−1.49026	−	14.1789i	−0.0638358	−	0.607357i
$546$	2.50991	+	0.533497i	0.107414	+	0.0228316i
$547$	5.77517	+	27.1700i	0.246928	+	1.16171i	0.910472	+	0.413570i	$0.135718\pi$
$547$	5.77517	+	27.1700i	0.246928	+	1.16171i	−0.663544	+	0.748137i	$0.730948\pi$
$548$	−10.3867	+	14.2961i	−0.443700	+	0.610701i
$549$	−4.79428	−	8.30394i	−0.204615	−	0.354404i
$550$	8.56493	+	11.3828i	0.365210	+	0.485365i
$551$	−33.2818			−1.41785
$552$	−2.35591	−	5.29146i	−0.100274	−	0.225219i
$553$	4.25769	+	20.0308i	0.181055	+	0.851798i
$554$	7.23164	−	8.03155i	0.307243	−	0.341228i
$555$	8.09283	+	11.1388i	0.343521	+	0.472817i
$556$	5.56433	−	12.4977i	0.235980	−	0.530020i
$557$	−17.6176	+	5.72429i	−0.746480	+	0.242546i	−0.657466	−	0.753484i	$-0.728372\pi$
$557$	−17.6176	+	5.72429i	−0.746480	+	0.242546i	−0.0890141	+	0.996030i	$0.528372\pi$
$558$	0.957119	−	2.94571i	0.0405181	−	0.124702i
$559$	−1.61329	−	0.922355i	−0.0682350	−	0.0390115i
$560$		−	3.86983i		−	0.163530i
$561$	−35.1678	−	30.6147i	−1.48479	−	1.29255i
$562$	7.06925	−	4.08144i	0.298199	−	0.172165i
$563$	−11.6246	+	15.9999i	−0.489919	+	0.674316i	−0.980373	−	0.197151i	$-0.936831\pi$
$563$	−11.6246	+	15.9999i	−0.489919	+	0.674316i	0.490454	+	0.871467i	$0.336831\pi$
$564$	1.70596	+	8.02593i	0.0718340	+	0.337953i
$565$	9.14752	−	10.1594i	0.384839	−	0.427407i
$566$	−5.78980	+	0.608532i	−0.243363	+	0.0255785i
$567$	−40.4181	+	29.3654i	−1.69740	+	1.23323i
$568$	−1.86403	+	8.76956i	−0.0782129	+	0.367963i
$569$	−2.33557	−	10.9880i	−0.0979122	−	0.460641i	−0.999601	−	0.0282546i	$-0.991005\pi$
$569$	−2.33557	−	10.9880i	−0.0979122	−	0.460641i	0.901689	−	0.432386i	$-0.142328\pi$
$570$	9.25811	+	6.72641i	0.387779	+	0.281738i
$571$	−18.3278	−	31.7446i	−0.766993	−	1.32847i	−0.939186	−	0.343408i	$-0.888419\pi$
$571$	−18.3278	−	31.7446i	−0.766993	−	1.32847i	0.172193	−	0.985063i	$-0.444915\pi$
$572$	0.275441	−	0.898651i	0.0115168	−	0.0375745i
$573$	14.6746	−	25.4172i	0.613041	−	1.06182i
$574$	14.5494	+	32.6786i	0.607282	+	1.36398i
$575$	3.91351	−	12.0445i	0.163205	−	0.502292i
$576$	0.840174	+	0.178584i	0.0350072	+	0.00744102i
$577$	26.4976	−	2.78501i	1.10311	−	0.115941i	0.464574	−	0.885534i	$-0.346207\pi$
$577$	26.4976	−	2.78501i	1.10311	−	0.115941i	0.638535	+	0.769593i	$0.279541\pi$
$578$	−31.2578	−	13.9169i	−1.30015	−	0.578866i
$579$	15.7637	−	17.5073i	0.655115	−	0.727579i
$580$	3.83012	+	1.24448i	0.159037	+	0.0516743i
$581$	42.4854	−	58.4761i	1.76259	−	2.42600i
$582$	2.95385	−	1.70540i	0.122441	−	0.0706913i
$583$	−8.50806	−	18.2794i	−0.352368	−	0.757055i
$584$	2.55088	−	4.41825i	0.105556	−	0.182829i
$585$	0.186703	−	0.0831257i	0.00771924	−	0.00343683i
$586$	−0.288001	−	0.0935772i	−0.0118972	−	0.00386564i
$587$	0.00827662	−	0.0389384i	0.000341613	−	0.00160716i	−0.977976	−	0.208715i	$-0.933072\pi$
$587$	0.00827662	−	0.0389384i	0.000341613	−	0.00160716i	0.978318	+	0.207108i	$0.0664052\pi$
$588$	−27.8295	+	2.92500i	−1.14767	+	0.120625i
$589$	−2.61528	−	24.8828i	−0.107761	−	1.02528i
$590$	4.53591	+	4.08415i	0.186740	+	0.168142i
$591$	10.2357	−	31.5023i	0.421041	−	1.29583i
$592$	8.30227	+	0.872604i	0.341221	+	0.0358638i
$593$	−16.3064	+	28.2434i	−0.669622	+	1.15982i	0.308388	+	0.951261i	$0.400211\pi$
$593$	−16.3064	+	28.2434i	−0.669622	+	1.15982i	−0.978010	+	0.208559i	$0.933123\pi$
$594$	7.17606	+	11.9621i	0.294437	+	0.490813i
$595$	−13.8473	+	23.9842i	−0.567683	+	0.983255i
$596$	0.635882	−	6.05002i	0.0260468	−	0.247818i
$597$	−1.61290	+	0.342832i	−0.0660116	+	0.0140312i
$598$	−0.794712	+	0.258218i	−0.0324982	+	0.0105593i
$599$	5.14254	+	2.28960i	0.210118	+	0.0935507i	0.509097	−	0.860709i	$-0.329979\pi$
$599$	5.14254	+	2.28960i	0.210118	+	0.0935507i	−0.298979	+	0.954260i	$0.596646\pi$
$600$	4.95936	+	6.82598i	0.202465	+	0.278669i
$601$	9.59323	+	29.5249i	0.391316	+	1.20435i	0.931793	+	0.362989i	$0.118244\pi$
$601$	9.59323	+	29.5249i	0.391316	+	1.20435i	−0.540477	+	0.841359i	$0.681756\pi$
$602$	29.5905	+	6.15890i	1.20602	+	0.251018i
$603$	8.34981	+	6.06649i	0.340030	+	0.247047i
$604$	−1.06051			−0.0431516
$605$	5.67559	+	7.28567i	0.230746	+	0.296205i
$606$	16.0070			0.650240
$607$	1.04442	−	9.93697i	0.0423916	−	0.403329i	−0.952665	−	0.304021i	$-0.901671\pi$
$607$	1.04442	−	9.93697i	0.0423916	−	0.403329i	0.995057	−	0.0993077i	$-0.0316628\pi$
$608$	6.78687	−	1.44259i	0.275244	−	0.0585049i
$609$	9.02986	−	42.4821i	0.365908	−	1.72146i
$610$	5.50899	+	7.58248i	0.223053	+	0.307006i
$611$	1.17724	−	0.123732i	0.0476259	−	0.00500568i
$612$	−4.56816	−	4.11319i	−0.184657	−	0.166266i
$613$	−16.5840	−	5.38846i	−0.669821	−	0.217638i	−0.0456873	−	0.998956i	$-0.514548\pi$
$613$	−16.5840	−	5.38846i	−0.669821	−	0.217638i	−0.624133	+	0.781318i	$0.714548\pi$
$614$	24.4185	+	2.56649i	0.985451	+	0.103575i
$615$	11.0850	+	6.39993i	0.446990	+	0.258070i
$616$	0.255973	+	15.2849i	0.0103134	+	0.615845i
$617$	2.35541	−	4.07970i	0.0948254	−	0.164242i	−0.814710	−	0.579868i	$-0.803104\pi$
$617$	2.35541	−	4.07970i	0.0948254	−	0.164242i	0.909536	+	0.415626i	$0.136437\pi$
$618$	10.2586	−	14.1197i	0.412661	−	0.567979i
$619$	23.7117	+	26.3345i	0.953055	+	1.05847i	0.998229	+	0.0594955i	$0.0189492\pi$
$619$	23.7117	+	26.3345i	0.953055	+	1.05847i	−0.0451737	+	0.998979i	$0.514384\pi$
$620$	−0.629452	+	2.96134i	−0.0252794	+	0.118930i
$621$	5.04413	−	11.3293i	0.202414	−	0.454629i
$622$	14.2425	+	6.34116i	0.571071	+	0.254257i
$623$	14.5686	−	4.73361i	0.583677	−	0.189648i
$624$	0.172032	−	0.529460i	0.00688679	−	0.0211954i
$625$	−1.55991	+	14.8416i	−0.0623965	+	0.593663i
$626$	−8.05262	+	4.64918i	−0.321847	+	0.185819i
$627$	−37.0122	−	25.9553i	−1.47813	−	1.03656i
$628$	2.47852	+	1.43098i	0.0989039	+	0.0571022i
$629$	−48.3329	−	35.1159i	−1.92716	−	1.40016i
$630$	−2.47019	+	2.22417i	−0.0984146	+	0.0886129i
$631$	2.29348	−	10.7900i	0.0913020	−	0.429542i	−0.908627	−	0.417609i	$-0.862868\pi$
$631$	2.29348	−	10.7900i	0.0913020	−	0.429542i	0.999929	−	0.0119331i	$-0.00379850\pi$
$632$	4.41858	−	0.464411i	0.175762	−	0.0184733i
$633$	−2.51798	+	5.65548i	−0.100081	+	0.224785i
$634$	4.57743	+	14.0879i	0.181793	+	0.559501i
$635$	11.1865	−	2.37776i	0.443922	−	0.0943585i
$636$	−4.85729	−	10.9096i	−0.192604	−	0.432595i
$637$			4.03692i			0.159948i
$638$	−15.2104	−	4.66205i	−0.602184	−	0.184573i
$639$	6.66913	−	3.85042i	0.263827	−	0.152320i
$640$	−0.834986	−	0.0877606i	−0.0330057	−	0.00346904i
$641$	29.7226	+	9.65747i	1.17397	+	0.381447i	0.830124	−	0.557578i	$-0.188269\pi$
$641$	29.7226	+	9.65747i	1.17397	+	0.381447i	0.343849	+	0.939025i	$0.388269\pi$
$642$	−1.08759	+	1.20789i	−0.0429237	+	0.0476716i
$643$	6.04571	−	4.39246i	0.238419	−	0.173222i	−0.462159	−	0.886797i	$-0.652925\pi$
$643$	6.04571	−	4.39246i	0.238419	−	0.173222i	0.700579	+	0.713575i	$0.252925\pi$
$644$	10.9950	−	7.98833i	0.433264	−	0.314784i
$645$	9.86145	−	4.44069i	0.388294	−	0.174852i
$646$	−47.2253	−	15.3444i	−1.85805	−	0.603718i
$647$	2.54418	−	3.50177i	0.100022	−	0.137669i	−0.756072	−	0.654488i	$-0.772884\pi$
$647$	2.54418	−	3.50177i	0.100022	−	0.137669i	0.856094	+	0.516820i	$0.172884\pi$
$648$	5.41952	+	9.38689i	0.212899	+	0.368752i
$649$	−18.1859	−	15.8314i	−0.713859	−	0.621436i
$650$	1.05413	−	0.608605i	0.0413466	−	0.0238714i
$651$	32.4709	+	3.41283i	1.27263	+	0.133759i
$652$	−11.0410	+	9.94134i	−0.432398	+	0.389333i
$653$	−33.8242	+	10.9902i	−1.32364	+	0.430078i	−0.883745	−	0.467969i	$-0.844986\pi$
$653$	−33.8242	+	10.9902i	−1.32364	+	0.430078i	−0.439900	+	0.898047i	$0.644986\pi$
$654$	3.48684	+	33.1751i	0.136346	+	1.29725i
$655$	4.44074	−	9.97407i	0.173514	−	0.389719i
$656$	7.38095	−	2.39822i	0.288178	−	0.0936346i
$657$	−4.28637	+	0.911095i	−0.167227	+	0.0355452i
$658$	−17.5879	+	7.83063i	−0.685647	+	0.305270i
$659$	14.4112	+	8.32030i	0.561380	+	0.324113i	0.753699	−	0.657220i	$-0.228268\pi$
$659$	14.4112	+	8.32030i	0.561380	+	0.324113i	−0.192319	+	0.981332i	$0.561601\pi$
$660$	3.28890	+	4.37095i	0.128020	+	0.170139i
$661$	−46.7664			−1.81900			−0.909501	−	0.415701i	$-0.863536\pi$
$661$	−46.7664			−1.81900			−0.909501	+	0.415701i	$0.863536\pi$
$662$	10.7560	+	24.1585i	0.418045	+	0.938945i
$663$	−2.96076	+	2.66588i	−0.114986	+	0.103534i
$664$	−11.6538	−	10.4931i	−0.452255	−	0.407213i
$665$	−10.9212	+	24.5294i	−0.423506	+	0.951210i
$666$	−4.21469	−	5.80103i	−0.163316	−	0.224785i
$667$	4.37053	+	13.4511i	0.169228	+	0.520829i
$668$	−1.95877	−	9.21529i	−0.0757871	−	0.356550i
$669$	3.88819	−	36.9937i	0.150326	−	1.43026i
$670$	−8.73674	−	5.04416i	−0.337530	−	0.194873i
$671$	−22.2608	−	29.5846i	−0.859367	−	1.14210i
$672$			9.05442i			0.349282i
$673$	−39.0914	+	17.4046i	−1.50686	+	0.670898i	−0.983450	−	0.181181i	$-0.942008\pi$
$673$	−39.0914	+	17.4046i	−1.50686	+	0.670898i	−0.523413	+	0.852079i	$0.675341\pi$
$674$	6.51390	−	5.86514i	0.250906	−	0.225917i
$675$	−3.75590	+	17.6701i	−0.144565	+	0.680123i
$676$	11.8027	+	5.25491i	0.453951	+	0.202112i
$677$	40.4083	−	29.3584i	1.55302	−	1.12833i	0.611564	−	0.791195i	$-0.290541\pi$
$677$	40.4083	−	29.3584i	1.55302	−	1.12833i	0.941455	−	0.337139i	$-0.109459\pi$
$678$	−21.4029	+	23.7703i	−0.821974	+	0.912895i
$679$	5.35502	+	5.94735i	0.205507	+	0.228238i
$680$	4.86099	+	3.53172i	0.186411	+	0.135435i
$681$	30.9680	+	17.8794i	1.18670	+	0.685139i
$682$	2.29030	−	11.7382i	0.0877003	−	0.449479i
$683$	−17.3795	−	30.1022i	−0.665008	−	1.15183i	−0.979283	−	0.202495i	$-0.935095\pi$
$683$	−17.3795	−	30.1022i	−0.665008	−	1.15183i	0.314275	−	0.949332i	$-0.398238\pi$
$684$	−4.82156	−	3.50307i	−0.184357	−	0.133943i
$685$	−14.5121	+	3.08464i	−0.554479	+	0.117858i
$686$	−10.3190	−	31.7586i	−0.393981	−	1.21255i
$687$	33.9686	+	46.7537i	1.29598	+	1.78377i
$688$	1.99995	−	6.24501i	0.0762475	−	0.238089i
$689$	−1.63849	+	0.532379i	−0.0624217	+	0.0202820i
$690$	1.50277	−	4.62505i	0.0572095	−	0.176073i
$691$	7.70434	+	0.809759i	0.293087	+	0.0308047i	0.249931	−	0.968264i	$-0.419592\pi$
$691$	7.70434	+	0.809759i	0.293087	+	0.0308047i	0.0431560	+	0.999068i	$0.486259\pi$
$692$			18.7697i			0.713515i
$693$	9.60952	−	8.94831i	0.365036	−	0.339918i
$694$	−11.4996	−	19.9178i	−0.436517	−	0.756070i
$695$	10.4929	−	4.67173i	0.398017	−	0.177209i
$696$	−8.96152	−	2.91177i	−0.339686	−	0.110371i
$697$	−54.3267	−	11.5475i	−2.05777	−	0.437392i
$698$	−5.18283	−	2.30754i	−0.196173	−	0.0873418i
$699$	11.0949	+	15.2708i	0.419648	+	0.577596i
$700$	−13.2468	+	14.7120i	−0.500681	+	0.556063i
$701$	−33.9137	+	30.5361i	−1.28090	+	1.15333i	−0.301052	+	0.953608i	$0.597338\pi$
$701$	−33.9137	+	30.5361i	−1.28090	+	1.15333i	−0.979852	+	0.199723i	$0.935996\pi$
$702$	1.08889	−	0.484806i	0.0410976	−	0.0182978i
$703$	−50.1624	−	28.9613i	−1.89191	−	1.09230i
$704$	3.30380	+	0.291402i	0.124517	+	0.0109826i
$705$	−3.44450	+	5.96604i	−0.129727	+	0.224694i
$706$	0.680121	−	0.302810i	0.0255967	−	0.0113964i
$707$	7.80875	+	36.7373i	0.293678	+	1.38165i
$708$	−10.6129	−	9.55589i	−0.398857	−	0.359132i
$709$	−36.6417	+	26.6217i	−1.37611	+	0.999800i	−0.378874	+	0.925448i	$0.623689\pi$
$709$	−36.6417	+	26.6217i	−1.37611	+	0.999800i	−0.997232	+	0.0743514i	$0.976311\pi$
$710$	−6.08970	+	4.42443i	−0.228542	+	0.166046i
$711$	−2.83600	−	2.55355i	−0.106358	−	0.0957655i
$712$	−0.690976	−	3.25078i	−0.0258954	−	0.121828i
$713$	−9.71315	+	4.32457i	−0.363760	+	0.161956i
$714$	32.3991	−	56.1170i	1.21251	−	2.10012i
$715$	0.676712	−	0.405958i	0.0253076	−	0.0151820i
$716$	16.5077	+	9.53073i	0.616922	+	0.356180i
$717$	−17.3851	+	7.74037i	−0.649260	+	0.289069i
$718$	3.27711	−	2.95072i	0.122301	−	0.110120i
$719$	−27.8997	+	30.9858i	−1.04048	+	1.15557i	−0.0528809	+	0.998601i	$0.516840\pi$
$719$	−27.8997	+	30.9858i	−1.04048	+	1.15557i	−0.987603	+	0.156973i	$0.949826\pi$
$720$	0.423885	+	0.583428i	0.0157973	+	0.0217431i
$721$	37.4103	+	16.6561i	1.39323	+	0.620307i
$722$	−28.5059	−	6.05912i	−1.06088	−	0.225497i
$723$	29.9554	+	9.73310i	1.11405	+	0.361978i
$724$	15.7384	−	7.00719i	0.584914	−	0.260420i
$725$	−10.3011	−	17.8420i	−0.382574	−	0.662637i
$726$	−13.2795	−	17.0466i	−0.492847	−	0.632660i
$727$		−	20.2319i		−	0.750360i	−0.926952	−	0.375180i	$-0.877581\pi$
$727$		−	20.2319i		−	0.750360i	0.926952	−	0.375180i	$-0.122419\pi$
$728$	1.29907	+	0.136538i	0.0481468	+	0.00506044i
$729$	−4.78251	+	14.7190i	−0.177130	+	0.545150i
$730$	4.07372	−	1.32363i	0.150775	−	0.0489898i
$731$	−34.7415	+	31.5486i	−1.28496	+	1.16687i
$732$	−12.8897	−	17.7411i	−0.476416	−	0.655730i
$733$	5.50697	+	16.9487i	0.203405	+	0.626015i	0.999775	+	0.0212058i	$0.00675053\pi$
$733$	5.50697	+	16.9487i	0.203405	+	0.626015i	−0.796371	+	0.604809i	$0.793249\pi$
$734$	14.6122	−	3.10592i	0.539346	−	0.114642i
$735$	−19.0070	−	13.8094i	−0.701084	−	0.509368i
$736$	−1.47428	−	2.55353i	−0.0543428	−	0.0941245i
$737$	34.8417	+	19.3453i	1.28341	+	0.712594i
$738$	−5.77300	−	3.33304i	−0.212507	−	0.122691i
$739$	−4.54593	−	3.30281i	−0.167225	−	0.121496i	0.501025	−	0.865433i	$-0.332956\pi$
$739$	−4.54593	−	3.30281i	−0.167225	−	0.121496i	−0.668250	+	0.743937i	$0.732956\pi$
$740$	4.68984	+	5.20860i	0.172402	+	0.191472i
$741$	−2.58466	+	2.87055i	−0.0949498	+	0.105452i
$742$	22.6689	−	16.4699i	0.832201	−	0.604630i
$743$	32.8526	+	14.6269i	1.20525	+	0.536610i	0.908314	−	0.418289i	$-0.137370\pi$
$743$	32.8526	+	14.6269i	1.20525	+	0.536610i	0.296932	+	0.954899i	$0.404037\pi$
$744$	1.47276	−	6.92879i	0.0539940	−	0.254022i
$745$	3.79560	−	3.41757i	0.139060	−	0.125210i
$746$	27.5871	−	12.2826i	1.01004	−	0.449697i
$747$			13.4697i			0.492832i
$748$	−19.4334	−	13.6279i	−0.710554	−	0.498286i
$749$	−3.30276	−	1.90685i	−0.120680	−	0.0696747i
$750$	−1.60246	+	15.2464i	−0.0585136	+	0.556720i
$751$	−7.79403	−	36.6680i	−0.284408	−	1.33804i	−0.855778	−	0.517343i	$-0.826921\pi$
$751$	−7.79403	−	36.6680i	−0.284408	−	1.33804i	0.571370	−	0.820693i	$-0.306412\pi$
$752$	1.29074	+	3.97249i	0.0470685	+	0.144862i
$753$	−0.124503	−	0.171364i	−0.00453715	−	0.00624485i
$754$	−0.552900	+	1.24183i	−0.0201354	+	0.0452249i
$755$	−0.661689	−	0.595787i	−0.0240813	−	0.0216829i
$756$	−14.4066	+	12.9718i	−0.523964	+	0.471779i
$757$	7.05404	+	15.8436i	0.256383	+	0.575847i	0.995178	−	0.0980839i	$-0.0312714\pi$
$757$	7.05404	+	15.8436i	0.256383	+	0.575847i	−0.738795	+	0.673931i	$0.764605\pi$
$758$	26.2177			0.952269
$759$	−5.62965	+	18.3672i	−0.204343	+	0.666688i
$760$	5.04500	+	2.91273i	0.183001	+	0.105656i
$761$	−6.19329	+	2.75743i	−0.224507	+	0.0999568i	−0.515908	−	0.856644i	$-0.672545\pi$
$761$	−6.19329	+	2.75743i	−0.224507	+	0.0999568i	0.291401	+	0.956601i	$0.405879\pi$
$762$	−26.1735	+	5.56336i	−0.948168	+	0.201539i
$763$	−74.4383	+	24.1865i	−2.69485	+	0.875608i
$764$	6.07681	−	13.6487i	0.219851	−	0.493794i
$765$	−0.539469	−	5.13271i	−0.0195046	−	0.185573i
$766$	0.618188	−	0.200861i	0.0223360	−	0.00725742i
$767$	−1.53106	+	1.37857i	−0.0552834	+	0.0497774i
$768$	1.95366	+	0.205338i	0.0704966	+	0.00740949i
$769$	−16.5191	+	9.53733i	−0.595695	+	0.343925i	−0.767346	−	0.641233i	$-0.778423\pi$
$769$	−16.5191	+	9.53733i	−0.595695	+	0.343925i	0.171651	+	0.985158i	$0.445090\pi$
$770$	−8.42722	+	9.68055i	−0.303696	+	0.348863i
$771$	3.76916	+	6.52838i	0.135743	+	0.235114i
$772$	7.04905	−	9.70218i	0.253701	−	0.349189i
$773$	21.1444	+	6.87024i	0.760512	+	0.247105i	0.663498	−	0.748178i	$-0.269071\pi$
$773$	21.1444	+	6.87024i	0.760512	+	0.247105i	0.0970136	+	0.995283i	$0.469071\pi$
$774$	−5.13578	+	2.31268i	−0.184602	+	0.0831277i
$775$	12.5300	−	9.10354i	0.450089	−	0.327009i
$776$	1.40469	−	1.02057i	0.0504255	−	0.0366363i
$777$	50.5771	−	56.1716i	1.81444	−	2.01514i
$778$	−8.08147	−	2.62583i	−0.289735	−	0.0941405i
$779$	−53.5533	−	5.62867i	−1.91874	−	0.201668i
$780$	0.404783	−	0.233702i	0.0144936	−	0.00836786i
$781$	23.7602	−	17.8782i	0.850207	−	0.639733i
$782$			21.1015i			0.754589i
$783$	−8.20572	−	18.4304i	−0.293249	−	0.658647i
$784$	−13.9335	+	2.96167i	−0.497627	+	0.105774i
$785$	0.742523	+	2.28525i	0.0265018	+	0.0815641i
$786$	−10.3902	+	23.3368i	−0.370607	+	0.832397i
$787$	31.2011	−	3.27937i	1.11220	−	0.116897i	0.469439	−	0.882965i	$-0.344456\pi$
$787$	31.2011	−	3.27937i	1.11220	−	0.116897i	0.642760	+	0.766068i	$0.277789\pi$
$788$	3.50575	−	16.4932i	0.124887	−	0.587547i
$789$	−15.8117	+	14.2369i	−0.562910	+	0.506846i
$790$	3.01780	+	2.19256i	0.107369	+	0.0780078i
$791$	−64.9958	−	37.5253i	−2.31098	−	1.33425i
$792$	−1.71284	−	2.27636i	−0.0608630	−	0.0808870i
$793$	−2.73976	+	1.58180i	−0.0972916	+	0.0561713i
$794$	2.95189	−	28.0853i	0.104759	−	0.996711i
$795$	3.09833	−	9.53568i	0.109886	−	0.338196i
$796$	−0.798316	+	0.259389i	−0.0282956	+	0.00919378i
$797$	−35.4536	−	15.7850i	−1.25583	−	0.559132i	−0.332488	−	0.943108i	$-0.607888\pi$
$797$	−35.4536	−	15.7850i	−1.25583	−	0.559132i	−0.923343	+	0.383976i	$0.874555\pi$
$798$	25.5529	−	57.3927i	0.904562	−	2.03168i
$799$	6.21496	−	29.2391i	0.219869	−	1.03440i
$800$	2.87398	+	3.19188i	0.101611	+	0.112850i
$801$	−1.67790	+	2.30944i	−0.0592858	+	0.0816000i
$802$	−6.49006	+	11.2411i	−0.229172	+	0.396938i
$803$	−16.0027	+	5.49749i	−0.564722	+	0.194002i
$804$	20.4418	+	11.8021i	0.720926	+	0.416227i
$805$	11.3479	+	1.19272i	0.399962	+	0.0420377i
$806$	−0.971891	−	0.315787i	−0.0342334	−	0.0111231i
$807$	34.2444	+	30.8338i	1.20546	+	1.08540i
$808$	8.10383	−	0.851746i	0.285092	−	0.0299643i
$809$	17.6936	+	24.3531i	0.622074	+	0.856211i	0.997502	−	0.0706407i	$-0.0225044\pi$
$809$	17.6936	+	24.3531i	0.622074	+	0.856211i	−0.375428	+	0.926851i	$0.622504\pi$
$810$	−1.89206	+	8.90144i	−0.0664802	+	0.312765i
$811$	−32.0271	+	6.80757i	−1.12462	+	0.239046i	−0.732434	−	0.680838i	$-0.761616\pi$
$811$	−32.0271	+	6.80757i	−1.12462	+	0.239046i	−0.392190	+	0.919884i	$0.628282\pi$
$812$	2.31101	−	21.9878i	0.0811006	−	0.771621i
$813$	31.0400			1.08862
$814$	−18.8683	−	20.2625i	−0.661333	−	0.710200i
$815$	−12.4738			−0.436938
$816$	−11.3735	−	8.26334i	−0.398153	−	0.289275i
$817$	−30.3013	+	33.9407i	−1.06011	+	1.18743i
$818$	−8.09988	−	24.9289i	−0.283206	−	0.871618i
$819$	−0.659481	−	0.907698i	−0.0230441	−	0.0317175i
$820$	5.95252	+	2.65023i	0.207871	+	0.0925502i
$821$	27.0384	−	8.78531i	0.943647	−	0.306609i	0.203515	−	0.979072i	$-0.434763\pi$
$821$	27.0384	−	8.78531i	0.943647	−	0.306609i	0.740131	+	0.672462i	$0.234763\pi$
$822$	33.9547	−	7.21729i	1.18431	−	0.251732i
$823$	3.11666	−	29.6530i	0.108640	−	1.03364i	−0.795369	−	0.606126i	$-0.792723\pi$
$823$	3.11666	−	29.6530i	0.108640	−	1.03364i	0.904009	−	0.427514i	$-0.140611\pi$
$824$	4.44227	−	7.69423i	0.154754	−	0.268041i
$825$	2.45867	−	27.8754i	0.0855999	−	0.970496i
$826$	16.7542	−	29.0191i	0.582952	−	1.00970i
$827$	14.5707	+	1.53144i	0.506674	+	0.0532535i	0.354417	−	0.935087i	$-0.384679\pi$
$827$	14.5707	+	1.53144i	0.506674	+	0.0532535i	0.152257	+	0.988341i	$0.451346\pi$
$828$	−0.782633	+	2.40870i	−0.0271984	+	0.0837080i
$829$	−6.06296	−	5.45912i	−0.210575	−	0.189603i	0.557093	−	0.830450i	$-0.311917\pi$
$829$	−6.06296	−	5.45912i	−0.210575	−	0.189603i	−0.767669	+	0.640847i	$0.778583\pi$
$830$	−1.37624	−	13.0940i	−0.0477699	−	0.454501i
$831$	−21.1142	+	2.21919i	−0.732444	+	0.0769829i
$832$	0.0589212	−	0.277202i	0.00204272	−	0.00961026i
$833$	96.9541	+	31.5023i	3.35926	+	1.09149i
$834$	−24.5507	+	10.9307i	−0.850121	+	0.378498i
$835$	3.95494	−	6.85015i	0.136866	−	0.237059i
$836$	−20.1192	−	11.1709i	−0.695837	−	0.386353i
$837$	13.1344	−	7.58318i	0.453993	−	0.262113i
$838$	−6.44418	+	8.86966i	−0.222611	+	0.306397i
$839$	−29.9403	−	9.72820i	−1.03365	−	0.335855i	−0.257420	−	0.966300i	$-0.582873\pi$
$839$	−29.9403	−	9.72820i	−1.03365	−	0.335855i	−0.776234	+	0.630445i	$0.782873\pi$
$840$	−5.08671	+	5.64936i	−0.175508	+	0.194921i
$841$	−5.47380	−	2.43709i	−0.188752	−	0.0840376i
$842$	−29.2502	+	3.07432i	−1.00803	+	0.105948i
$843$	−15.6849	−	3.33393i	−0.540216	−	0.114827i
$844$	−0.973839	+	2.99717i	−0.0335209	+	0.103167i
$845$	4.41195	+	9.90939i	0.151776	+	0.340893i
$846$	1.79387	−	3.10708i	0.0616746	−	0.106824i
$847$	32.6452	−	38.7933i	1.12170	−	1.33295i
$848$	−3.03960	−	5.26474i	−0.104380	−	0.180792i
$849$	9.25211	+	6.72205i	0.317532	+	0.230700i
$850$	−6.39079	−	30.0663i	−0.219202	−	1.03127i
$851$	−5.11767	+	24.0767i	−0.175431	+	0.825340i
$852$	14.2484	−	10.3521i	0.488141	−	0.354655i
$853$	−32.7110	+	3.43806i	−1.12000	+	0.117717i	−0.646384	−	0.763013i	$-0.723719\pi$
$853$	−32.7110	+	3.43806i	−1.12000	+	0.117717i	−0.473619	+	0.880730i	$0.657053\pi$
$854$	34.4292	−	38.2375i	1.17814	−	1.30846i
$855$	−1.04034	−	4.89440i	−0.0355788	−	0.167385i
$856$	−0.486338	+	0.669387i	−0.0166227	+	0.0228792i
$857$	−25.4649	+	14.7021i	−0.869863	+	0.502216i	−0.867303	−	0.497781i	$-0.834148\pi$
$857$	−25.4649	+	14.7021i	−0.869863	+	0.502216i	−0.00256051	+	0.999997i	$0.500815\pi$
$858$	−1.58334	+	0.949839i	−0.0540542	+	0.0324270i
$859$		−	33.4198i		−	1.14027i	−0.821552	−	0.570134i	$-0.806891\pi$
$859$		−	33.4198i		−	1.14027i	0.821552	−	0.570134i	$-0.193109\pi$
$860$	4.75624	−	2.77291i	0.162186	−	0.0945556i
$861$	21.7145	−	66.8303i	0.740027	−	2.27757i
$862$	−21.5359	+	6.99745i	−0.733517	+	0.238334i
$863$	3.79907	−	8.53286i	0.129322	−	0.290462i	−0.837267	−	0.546795i	$-0.815848\pi$
$863$	3.79907	−	8.53286i	0.129322	−	0.290462i	0.966589	+	0.256333i	$0.0825144\pi$
$864$	2.47219	+	3.40267i	0.0841054	+	0.115761i
$865$	−10.5446	+	11.7110i	−0.358529	+	0.398186i
$866$	−4.56733	−	21.4876i	−0.155204	−	0.730178i
$867$	27.3386	+	61.4035i	0.928468	+	2.08537i
$868$	16.6206			0.564138
$869$	−12.0646	−	8.46047i	−0.409264	−	0.287002i
$870$	−3.95558	−	6.85127i	−0.134107	−	0.232280i
$871$	2.00154	−	2.75489i	0.0678197	−	0.0933459i
$872$	3.53055	+	16.6099i	0.119559	+	0.562483i
$873$	−1.45879	−	0.310075i	−0.0493725	−	0.0104945i
$874$	2.13851	+	20.3465i	0.0723361	+	0.688232i
$875$	−35.7734	+	3.75993i	−1.20936	+	0.127109i
$876$	−9.53149	+	3.09697i	−0.322039	+	0.104637i
$877$	−17.3511	+	15.6230i	−0.585905	+	0.527551i	−0.907898	−	0.419191i	$-0.862314\pi$
$877$	−17.3511	+	15.6230i	−0.585905	+	0.527551i	0.321993	+	0.946742i	$0.395647\pi$
$878$	−2.52389	−	5.66875i	−0.0851772	−	0.191311i
$879$	0.297435	+	0.515172i	0.0100322	+	0.0173763i
$880$	1.89764	+	2.03786i	0.0639695	+	0.0686964i
$881$	15.2030			0.512202			0.256101	−	0.966650i	$-0.417562\pi$
$881$	15.2030			0.512202			0.256101	+	0.966650i	$0.417562\pi$
$882$	9.89873	+	7.19185i	0.333308	+	0.242162i
$883$	−0.394626	+	0.0838802i	−0.0132802	+	0.00282279i	−0.214547	−	0.976714i	$-0.568828\pi$
$883$	−0.394626	+	0.0838802i	−0.0132802	+	0.00282279i	0.201267	+	0.979536i	$0.435494\pi$
$884$	−1.35708	+	1.50719i	−0.0456436	+	0.0506924i
$885$	−1.25331	−	11.9245i	−0.0421297	−	0.400837i
$886$	2.56196	+	24.3755i	0.0860709	+	0.818910i
$887$	11.2571	+	34.6458i	0.377976	+	1.16329i	0.941449	+	0.337157i	$0.109465\pi$
$887$	11.2571	+	34.6458i	0.377976	+	1.16329i	−0.563472	+	0.826135i	$0.690535\pi$
$888$	−10.9731	−	12.1868i	−0.368232	−	0.408963i
$889$	−25.5366	−	57.3562i	−0.856472	−	1.92367i
$890$	1.39514	−	2.41646i	0.0467653	−	0.0809998i
$891$	6.88439	−	35.2837i	0.230636	−	1.18205i
$892$		−	18.9356i		−	0.634011i
$893$	3.02940	−	28.8228i	0.101375	−	0.964519i
$894$	−8.88076	+	7.99627i	−0.297017	+	0.267435i
$895$	4.94542	+	15.2204i	0.165307	+	0.508763i
$896$	0.481794	+	4.58396i	0.0160956	+	0.153139i
$897$	1.49957	+	0.667653i	0.0500693	+	0.0222923i
$898$	5.37297	+	4.83784i	0.179298	+	0.161441i
$899$	−5.34493	+	16.4500i	−0.178264	+	0.548639i
$900$	0.385631	−	3.66904i	0.0128544	−	0.122301i
$901$			43.5060i			1.44939i
$902$	−23.6863	−	10.0741i	−0.788669	−	0.335429i
$903$	−35.1020	−	47.8863i	−1.16812	−	1.59356i
$904$	−9.57076	+	13.1730i	−0.318319	+	0.438128i
$905$	13.7563	+	4.46970i	0.457275	+	0.148578i
$906$	1.54819	+	1.39399i	0.0514351	+	0.0463123i
$907$	−9.65931	+	7.01790i	−0.320732	+	0.233026i	−0.736488	−	0.676451i	$-0.763517\pi$
$907$	−9.65931	+	7.01790i	−0.320732	+	0.233026i	0.415756	+	0.909476i	$0.363517\pi$
$908$	16.6295	+	7.40391i	0.551868	+	0.245708i
$909$	−5.20132	−	4.68329i	−0.172517	−	0.155335i
$910$	0.733829	+	0.815000i	0.0243262	+	0.0270170i
$911$	10.9445	−	15.0638i	0.362608	−	0.499087i	−0.588265	−	0.808668i	$-0.700189\pi$
$911$	10.9445	−	15.0638i	0.362608	−	0.499087i	0.950873	+	0.309581i	$0.100189\pi$
$912$	−11.8040	−	6.81506i	−0.390870	−	0.225669i
$913$	6.30193	+	51.6273i	0.208563	+	1.70861i
$914$	1.20932			0.0400008
$915$	1.92452	−	18.3106i	0.0636227	−	0.605329i
$916$	19.6850	+	21.8624i	0.650411	+	0.722354i
$917$	−58.6285	−	12.4619i	−1.93608	−	0.411527i
$918$	−3.14630	−	29.9350i	−0.103843	−	0.988002i
$919$	7.94183	+	10.9310i	0.261977	+	0.360580i	0.919661	−	0.392714i	$-0.128464\pi$
$919$	7.94183	+	10.9310i	0.261977	+	0.360580i	−0.657684	+	0.753294i	$0.728464\pi$
$920$	0.514701	−	2.42148i	0.0169692	−	0.0798337i
$921$	−32.2738	−	35.8437i	−1.06346	−	1.18109i
$922$	−23.3784	−	2.45717i	−0.769926	−	0.0809225i
$923$	−1.27039	−	2.20037i	−0.0418153	−	0.0724262i
$924$	19.7176	−	22.6501i	0.648661	−	0.745133i
$925$		−	35.8555i		−	1.17892i
$926$	3.05148	+	0.320724i	0.100278	+	0.0105396i
$927$	−7.46455	+	1.58664i	−0.245168	+	0.0521121i
$928$	−4.69187	−	0.997287i	−0.154018	−	0.0327375i
$929$	−0.112868	+	0.0118629i	−0.00370309	+	0.000389210i	−0.106380	−	0.994326i	$-0.533926\pi$
$929$	−0.112868	+	0.0118629i	−0.00370309	+	0.000389210i	0.102677	+	0.994715i	$0.467259\pi$
$930$	4.81145	−	3.49572i	0.157773	−	0.114629i
$931$	96.6779	+	20.5495i	3.16849	+	0.673483i
$932$	6.42957	+	7.14076i	0.210608	+	0.233903i
$933$	−12.4567	−	27.9782i	−0.407814	−	0.915965i
$934$	−4.01192	+	2.31628i	−0.131274	+	0.0757911i
$935$	−4.46908	−	19.4204i	−0.146154	−	0.635116i
$936$	−0.210808	+	0.121710i	−0.00689049	+	0.00397822i
$937$	21.4015	−	9.52855i	0.699155	−	0.311284i	−0.0262019	−	0.999657i	$-0.508341\pi$
$937$	21.4015	−	9.52855i	0.699155	−	0.311284i	0.725357	+	0.688373i	$0.241675\pi$
$938$	−17.1145	+	52.6729i	−0.558807	+	1.71983i
$939$	17.8667	+	3.79769i	0.583059	+	0.123933i
$940$	−1.42638	+	3.20370i	−0.0465233	+	0.104493i
$941$	9.18902	−	20.6389i	0.299554	−	0.672808i	−0.699574	−	0.714560i	$-0.746627\pi$
$941$	9.18902	−	20.6389i	0.299554	−	0.672808i	0.999128	+	0.0417514i	$0.0132937\pi$
$942$	−1.73732	−	5.34691i	−0.0566049	−	0.174212i
$943$	4.75769	+	22.3832i	0.154932	+	0.728896i
$944$	−5.88144	−	4.27312i	−0.191425	−	0.139078i
$945$	−16.2762			−0.529466
$946$	−18.6026	+	11.2669i	−0.604822	+	0.366320i
$947$	−8.60189			−0.279524			−0.139762	−	0.990185i	$-0.544634\pi$
$947$	−8.60189			−0.279524			−0.139762	+	0.990185i	$0.544634\pi$
$948$	−7.06090	−	5.13004i	−0.229327	−	0.166616i
$949$	0.300602	+	1.41422i	0.00975794	+	0.0459075i
$950$	−9.20918	−	28.3429i	−0.298785	−	0.919566i
$951$	11.8355	−	26.5830i	0.383792	−	0.862012i
$952$	13.4166	−	30.1342i	0.434835	−	0.976655i
$953$	60.1611	+	12.7876i	1.94881	+	0.414232i	0.992577	+	0.121621i	$0.0388092\pi$
$953$	60.1611	+	12.7876i	1.94881	+	0.414232i	0.956232	+	0.292611i	$0.0945241\pi$
$954$	−1.61359	+	4.96612i	−0.0522419	+	0.160784i
$955$	11.4593	−	5.10200i	0.370814	−	0.165097i
$956$	−8.38967	+	4.84378i	−0.271341	+	0.156659i
$957$	16.0768	+	26.7992i	0.519688	+	0.866295i
$958$	7.35987	−	4.24922i	0.237787	−	0.137286i
$959$	33.1284	+	74.4077i	1.06977	+	2.40275i
$960$	1.10360	+	1.22567i	0.0356184	+	0.0395582i
$961$	17.6039	+	3.74182i	0.567868	+	0.120704i
$962$	−1.91396	+	1.39057i	−0.0617085	+	0.0448339i
$963$	0.706804	−	0.0742881i	0.0227764	−	0.00239390i
$964$	15.6834	+	3.33360i	0.505127	+	0.107368i
$965$	9.84875	−	2.09342i	0.317042	−	0.0673894i
$966$	−26.5513	−	2.79066i	−0.854275	−	0.0897879i
$967$		−	35.6122i		−	1.14521i	−0.819831	−	0.572606i	$-0.805932\pi$
$967$		−	35.6122i		−	1.14521i	0.819831	−	0.572606i	$-0.194068\pi$
$968$	−7.63003	−	7.92355i	−0.245238	−	0.254673i
$969$	48.7722	+	84.4759i	1.56679	+	2.71376i
$970$	1.44978	+	0.152378i	0.0465497	+	0.00489257i
$971$	10.8657	+	12.0676i	0.348698	+	0.387268i	0.891824	−	0.452383i	$-0.149426\pi$
$971$	10.8657	+	12.0676i	0.348698	+	0.387268i	−0.543126	+	0.839651i	$0.682759\pi$
$972$	1.80356	−	8.48508i	0.0578492	−	0.272159i
$973$	−37.0634	−	51.0133i	−1.18820	−	1.63541i
$974$	0.295597	+	2.81242i	0.00947154	+	0.0901157i
$975$	−2.33886	−	0.497140i	−0.0749034	−	0.0159212i
$976$	−7.46964	−	8.29588i	−0.239097	−	0.265545i
$977$	−4.38247	+	41.6964i	−0.140208	+	1.33399i	0.667591	+	0.744528i	$0.267326\pi$
$977$	−4.38247	+	41.6964i	−0.140208	+	1.33399i	−0.807798	+	0.589459i	$0.799341\pi$
$978$	29.1856			0.933251
$979$	−5.35064	+	9.63671i	−0.171007	+	0.307991i
$980$	−10.3574	−	5.97987i	−0.330857	−	0.191020i
$981$	8.57327	−	11.8001i	0.273724	−	0.376748i
$982$	8.50796	+	9.44905i	0.271500	+	0.301531i
$983$	24.1361	+	21.7323i	0.769823	+	0.693152i	0.957293	−	0.289119i	$-0.0933622\pi$
$983$	24.1361	+	21.7323i	0.769823	+	0.693152i	−0.187470	+	0.982270i	$0.560029\pi$
$984$	−13.9274	−	6.20088i	−0.443990	−	0.197677i
$985$	11.4531	−	8.32118i	0.364927	−	0.265135i
$986$	25.5104	+	22.9697i	0.812417	+	0.731503i
$987$	35.9686	+	11.6869i	1.14489	+	0.371999i
$988$	−1.15578	+	1.59080i	−0.0367704	+	0.0506101i
$989$	17.6966	+	7.78946i	0.562718	+	0.247691i
$990$	0.210147	−	2.38256i	0.00667890	−	0.0757226i
$991$		−	12.1840i		−	0.387038i	−0.981097	−	0.193519i	$-0.938010\pi$
$991$		−	12.1840i		−	0.387038i	0.981097	−	0.193519i	$-0.0619902\pi$
$992$	0.376924	−	3.58619i	0.0119673	−	0.113862i
$993$	16.0530	−	49.4060i	0.509426	−	1.56785i
$994$	30.7096	+	27.6510i	0.974048	+	0.877037i
$995$	−0.643819	−	0.286646i	−0.0204104	−	0.00908730i
$996$	3.22005	+	30.6368i	0.102031	+	0.970763i
$997$	−6.08607	−	18.7310i	−0.192748	−	0.593217i	−0.999995	−	0.00300407i	$-0.999044\pi$
$997$	−6.08607	−	18.7310i	−0.192748	−	0.593217i	0.807248	−	0.590213i	$-0.200956\pi$
$998$	−24.8888	+	22.4100i	−0.787843	+	0.709377i
$999$	3.67011	−	34.9188i	0.116117	−	1.10478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.t.a.7.18	✓	176
11.8	odd	10		946.2.t.b.437.5	yes	176
43.37	odd	6		946.2.t.b.381.5	yes	176
473.338	even	30	inner	946.2.t.a.811.18	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.t.a.7.18	✓	176	1.1	even	1	trivial
946.2.t.a.811.18	yes	176	473.338	even	30	inner
946.2.t.b.381.5	yes	176	43.37	odd	6
946.2.t.b.437.5	yes	176	11.8	odd	10

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:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.t (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.408426 + 1.92149i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.341490 + 0.766999i) q^{5} +(0.799001 - 1.79459i) q^{6} +(4.50849 + 0.958309i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.784684 + 0.349364i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.408426 + 1.92149i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.341490 + 0.766999i) q^{5} +(0.799001 - 1.79459i) q^{6} +(4.50849 + 0.958309i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.784684 + 0.349364i) q^{9} +(0.727102 - 0.419793i) q^{10} +(-2.84411 + 1.70617i) q^{11} +(-1.70124 + 0.982210i) q^{12} +(0.115267 + 0.258894i) q^{13} +(-3.08416 - 3.42531i) q^{14} +(-1.61326 - 0.342908i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(7.11733 - 0.748061i) q^{17} +(0.840174 + 0.178584i) q^{18} +(6.78687 - 1.44259i) q^{19} +(-0.834986 - 0.0877606i) q^{20} +9.05442i q^{21} +(3.30380 + 0.291402i) q^{22} +(-1.47428 - 2.55353i) q^{23} +(1.95366 + 0.205338i) q^{24} +(2.87398 + 3.19188i) q^{25} +(0.0589212 - 0.277202i) q^{26} +(2.47219 + 3.40267i) q^{27} +(0.481794 + 4.58396i) q^{28} +(-4.69187 - 0.997287i) q^{29} +(1.10360 + 1.22567i) q^{30} +(0.376924 - 3.58619i) q^{31} +1.00000 q^{32} +(-4.44001 - 4.76809i) q^{33} +(-6.19774 - 3.57827i) q^{34} +(-2.27463 + 3.13076i) q^{35} +(-0.574746 - 0.638320i) q^{36} +(-6.20377 - 5.58590i) q^{37} +(-6.33863 - 2.82214i) q^{38} +(-0.450385 + 0.327224i) q^{39} +(0.623933 + 0.561792i) q^{40} +(-7.38095 - 2.39822i) q^{41} +(5.32206 - 7.32518i) q^{42} +(-5.28872 + 3.87678i) q^{43} +(-2.50155 - 2.17767i) q^{44} -0.721157i q^{45} +(-0.308209 + 2.93241i) q^{46} +(1.29074 - 3.97249i) q^{47} +(-1.45985 - 1.31445i) q^{48} +(13.0133 + 5.79389i) q^{49} +(-0.448960 - 4.27157i) q^{50} +(4.34429 + 13.3704i) q^{51} +(-0.210604 + 0.189628i) q^{52} +(-0.635449 + 6.04589i) q^{53} -4.20593i q^{54} +(-0.337399 - 2.76407i) q^{55} +(2.30461 - 3.99169i) q^{56} +(5.54387 + 12.4517i) q^{57} +(3.20961 + 3.56463i) q^{58} +(2.24651 + 6.91405i) q^{59} +(-0.172399 - 1.64026i) q^{60} +(1.16687 + 11.1021i) q^{61} +(-2.41285 + 2.67974i) q^{62} +(-3.87254 + 0.823134i) q^{63} +(-0.809017 - 0.587785i) q^{64} -0.237934 q^{65} +(0.789429 + 6.46724i) q^{66} +(-6.00792 - 10.4060i) q^{67} +(2.91082 + 6.53782i) q^{68} +(4.30446 - 3.87575i) q^{69} +(3.68042 - 1.19584i) q^{70} +(-8.91636 + 0.937148i) q^{71} +(0.0897841 + 0.854238i) q^{72} +(4.99027 + 1.06072i) q^{73} +(1.73565 + 8.16558i) q^{74} +(-4.95936 + 6.82598i) q^{75} +(3.46925 + 6.00892i) q^{76} +(-14.4577 + 4.96673i) q^{77} +0.556707 q^{78} +(1.80710 + 4.05881i) q^{79} +(-0.174560 - 0.821238i) q^{80} +(-7.25274 + 8.05498i) q^{81} +(4.56168 + 6.27861i) q^{82} +(6.37834 - 14.3260i) q^{83} +(-8.61127 + 2.79797i) q^{84} +(-1.85673 + 5.71444i) q^{85} +(6.55738 - 0.0277458i) q^{86} -9.42270i q^{87} +(0.743790 + 3.23215i) q^{88} +(2.87816 - 1.66170i) q^{89} +(-0.423885 + 0.583428i) q^{90} +(0.271580 + 1.27768i) q^{91} +(1.97298 - 2.19121i) q^{92} +(7.04478 - 0.740436i) q^{93} +(-3.37920 + 2.45513i) q^{94} +(-1.21118 + 5.69816i) q^{95} +(0.408426 + 1.92149i) q^{96} +(1.40469 + 1.02057i) q^{97} +(-7.12241 - 12.3364i) q^{98} +(1.63565 - 2.33244i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 44 q^{2} - 44 q^{4} - 5 q^{6} - 15 q^{7} - 44 q^{8} - 20 q^{9}+O(q^{10}) \) 176 * q - 44 * q^2 - 44 * q^4 - 5 * q^6 - 15 * q^7 - 44 * q^8 - 20 * q^9	\( 176 q - 44 q^{2} - 44 q^{4} - 5 q^{6} - 15 q^{7} - 44 q^{8} - 20 q^{9} - 5 q^{11} - 5 q^{13} + 15 q^{14} + 41 q^{15} - 44 q^{16} - 2 q^{17} - 25 q^{18} + 34 q^{19} + 5 q^{22} - 4 q^{23} + 5 q^{24} - 24 q^{25} + 20 q^{26} - 60 q^{27} - 3 q^{29} - 49 q^{30} + 40 q^{31} + 176 q^{32} - 47 q^{33} + 3 q^{34} - 60 q^{35} - 25 q^{36} - 8 q^{37} + 14 q^{38} + 12 q^{39} - 19 q^{43} - 10 q^{44} + 26 q^{46} - 4 q^{47} - 21 q^{49} + 6 q^{50} + 45 q^{51} - 20 q^{52} - 27 q^{53} + 68 q^{55} + 71 q^{57} - 3 q^{58} - 21 q^{59} + 6 q^{60} + 30 q^{61} + 71 q^{63} - 44 q^{64} - 16 q^{65} + 43 q^{66} - 3 q^{67} + 8 q^{68} - 42 q^{69} + 3 q^{71} - 20 q^{72} - 19 q^{73} - 28 q^{74} + 9 q^{76} + 38 q^{77} + 92 q^{78} + 32 q^{79} - 23 q^{81} - 5 q^{82} - 26 q^{83} + 2 q^{85} + 36 q^{86} + 5 q^{88} + 57 q^{89} + 30 q^{91} + 6 q^{92} - 10 q^{93} + 6 q^{94} - 58 q^{95} - 37 q^{97} - 106 q^{98} - 119 q^{99}+O(q^{100}) \) 176 * q - 44 * q^2 - 44 * q^4 - 5 * q^6 - 15 * q^7 - 44 * q^8 - 20 * q^9 - 5 * q^11 - 5 * q^13 + 15 * q^14 + 41 * q^15 - 44 * q^16 - 2 * q^17 - 25 * q^18 + 34 * q^19 + 5 * q^22 - 4 * q^23 + 5 * q^24 - 24 * q^25 + 20 * q^26 - 60 * q^27 - 3 * q^29 - 49 * q^30 + 40 * q^31 + 176 * q^32 - 47 * q^33 + 3 * q^34 - 60 * q^35 - 25 * q^36 - 8 * q^37 + 14 * q^38 + 12 * q^39 - 19 * q^43 - 10 * q^44 + 26 * q^46 - 4 * q^47 - 21 * q^49 + 6 * q^50 + 45 * q^51 - 20 * q^52 - 27 * q^53 + 68 * q^55 + 71 * q^57 - 3 * q^58 - 21 * q^59 + 6 * q^60 + 30 * q^61 + 71 * q^63 - 44 * q^64 - 16 * q^65 + 43 * q^66 - 3 * q^67 + 8 * q^68 - 42 * q^69 + 3 * q^71 - 20 * q^72 - 19 * q^73 - 28 * q^74 + 9 * q^76 + 38 * q^77 + 92 * q^78 + 32 * q^79 - 23 * q^81 - 5 * q^82 - 26 * q^83 + 2 * q^85 + 36 * q^86 + 5 * q^88 + 57 * q^89 + 30 * q^91 + 6 * q^92 - 10 * q^93 + 6 * q^94 - 58 * q^95 - 37 * q^97 - 106 * q^98 - 119 * q^99

Introduction

L-functions

Modular forms

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