LMFDB - Embedded newform 930.2.br.b.761.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (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:	$7.42608738798$
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			761.6
Character	$\chi$	$=$	930.761
Dual form			930.2.br.b.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(0.0457608 - 1.73145i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.578567 + 1.63256i) q^{6} +(0.394896 - 3.75719i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-2.99581 - 0.158465i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(0.0457608 - 1.73145i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.578567 + 1.63256i) q^{6} +(0.394896 - 3.75719i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-2.99581 - 0.158465i) q^{9} +(0.669131 + 0.743145i) q^{10} +(3.73016 - 1.66078i) q^{11} +(1.05474 - 1.37387i) q^{12} +(1.26376 - 5.94554i) q^{13} +(-1.53660 + 3.45127i) q^{14} +(-0.905353 + 1.47660i) q^{15} +(0.309017 + 0.951057i) q^{16} +(6.25944 + 2.78688i) q^{17} +(2.80022 + 1.07647i) q^{18} +(0.190708 - 0.0405362i) q^{19} +(-0.406737 - 0.913545i) q^{20} +(-6.48730 - 0.855674i) q^{21} +(-4.06080 + 0.426808i) q^{22} +(-2.56858 + 1.86618i) q^{23} +(-1.42767 + 0.980697i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-3.03918 + 5.26402i) q^{26} +(-0.411464 + 5.17984i) q^{27} +(2.52790 - 2.80751i) q^{28} +(0.716520 - 2.20522i) q^{29} +(1.31734 - 1.12456i) q^{30} +(-5.12643 - 2.17250i) q^{31} -1.00000i q^{32} +(-2.70485 - 6.53458i) q^{33} +(-5.09189 - 4.58476i) q^{34} +(-2.22058 + 3.05637i) q^{35} +(-2.33052 - 1.88909i) q^{36} +(9.35934 - 5.40362i) q^{37} +(-0.193900 - 0.0203797i) q^{38} +(-10.2365 - 2.46021i) q^{39} +(0.104528 + 0.994522i) q^{40} +(-8.44129 + 7.60057i) q^{41} +(5.90537 + 2.81848i) q^{42} +(0.0402884 + 0.189542i) q^{43} +(3.99395 + 0.848939i) q^{44} +(2.51522 + 1.63514i) q^{45} +(3.01955 - 0.981111i) q^{46} +(-4.66582 + 1.51602i) q^{47} +(1.66084 - 0.491525i) q^{48} +(-7.11349 - 1.51202i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(5.11177 - 10.7104i) q^{51} +(4.51710 - 4.06722i) q^{52} +(-0.349345 - 3.32380i) q^{53} +(1.99198 - 4.79917i) q^{54} +(-4.06080 - 0.426808i) q^{55} +(-3.27174 + 1.88894i) q^{56} +(-0.0614593 - 0.332055i) q^{57} +(-1.36290 + 1.87587i) q^{58} +(8.33435 + 7.50428i) q^{59} +(-1.60037 + 0.662438i) q^{60} -7.43838i q^{61} +(4.20418 + 3.65032i) q^{62} +(-1.77842 + 11.1933i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-4.06722 + 4.51710i) q^{65} +(0.553169 + 7.05059i) q^{66} +(-4.90224 + 8.49093i) q^{67} +(3.42591 + 5.93384i) q^{68} +(3.11366 + 4.53276i) q^{69} +(3.05637 - 2.22058i) q^{70} +(-3.03894 + 0.319405i) q^{71} +(1.63269 + 2.51681i) q^{72} +(-2.09217 - 4.69909i) q^{73} +(-10.5711 + 2.24695i) q^{74} +(1.52236 - 0.826093i) q^{75} +(0.178112 + 0.0793007i) q^{76} +(-4.76682 - 14.6708i) q^{77} +(8.97529 + 5.50307i) q^{78} +(-2.51209 + 5.64224i) q^{79} +(0.207912 - 0.978148i) q^{80} +(8.94978 + 0.949461i) q^{81} +(10.3769 - 4.62007i) q^{82} +(-8.97420 - 9.96686i) q^{83} +(-4.74538 - 4.50539i) q^{84} +(-4.02739 - 5.54323i) q^{85} +(0.0202552 - 0.192715i) q^{86} +(-3.78544 - 1.34153i) q^{87} +(-3.53613 - 2.04159i) q^{88} +(4.69447 + 3.41073i) q^{89} +(-1.88683 - 2.33236i) q^{90} +(-21.8394 - 7.09607i) q^{91} -3.17494 q^{92} +(-3.99616 + 8.77672i) q^{93} +4.90593 q^{94} +(-0.185426 - 0.0602485i) q^{95} +(-1.73145 - 0.0457608i) q^{96} +(10.5103 + 7.63620i) q^{97} +(6.29809 + 3.63620i) q^{98} +(-11.4380 + 4.38427i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{30}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	0.0457608	−	1.73145i	0.0264200	−	0.999651i
$3$	0.0457608	−	1.73145i	0.0264200	−	0.999651i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−0.578567	+	1.63256i	−0.236199	+	0.666491i
$7$	0.394896	−	3.75719i	0.149257	−	1.42008i	−0.621730	−	0.783232i	$-0.713570\pi$
$7$	0.394896	−	3.75719i	0.149257	−	1.42008i	0.770986	−	0.636852i	$-0.219764\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	−2.99581	−	0.158465i	−0.998604	−	0.0528216i
$10$	0.669131	+	0.743145i	0.211598	+	0.235003i
$11$	3.73016	−	1.66078i	1.12469	−	0.500743i	0.241799	−	0.970326i	$-0.422263\pi$
$11$	3.73016	−	1.66078i	1.12469	−	0.500743i	0.882888	+	0.469584i	$0.155596\pi$
$12$	1.05474	−	1.37387i	0.304477	−	0.396603i
$13$	1.26376	−	5.94554i	0.350505	−	1.64900i	−0.351033	−	0.936363i	$-0.614170\pi$
$13$	1.26376	−	5.94554i	0.350505	−	1.64900i	0.701538	−	0.712632i	$-0.252497\pi$
$14$	−1.53660	+	3.45127i	−0.410675	+	0.922390i
$15$	−0.905353	+	1.47660i	−0.233761	+	0.381255i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	6.25944	+	2.78688i	1.51814	+	0.675918i	0.985383	−	0.170352i	$-0.0544904\pi$
$17$	6.25944	+	2.78688i	1.51814	+	0.675918i	0.532754	+	0.846270i	$0.321157\pi$
$18$	2.80022	+	1.07647i	0.660018	+	0.253725i
$19$	0.190708	−	0.0405362i	0.0437513	−	0.00929964i	−0.185984	−	0.982553i	$-0.559547\pi$
$19$	0.190708	−	0.0405362i	0.0437513	−	0.00929964i	0.229735	+	0.973253i	$0.426214\pi$
$20$	−0.406737	−	0.913545i	−0.0909491	−	0.204275i
$21$	−6.48730	−	0.855674i	−1.41564	−	0.186723i
$22$	−4.06080	+	0.426808i	−0.865766	+	0.0909957i
$23$	−2.56858	+	1.86618i	−0.535586	+	0.389126i	−0.822443	−	0.568847i	$-0.807390\pi$
$23$	−2.56858	+	1.86618i	−0.535586	+	0.389126i	0.286857	+	0.957973i	$0.407390\pi$
$24$	−1.42767	+	0.980697i	−0.291421	+	0.200184i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−3.03918	+	5.26402i	−0.596033	+	1.03236i
$27$	−0.411464	+	5.17984i	−0.0791863	+	0.996860i
$28$	2.52790	−	2.80751i	0.477728	−	0.530570i
$29$	0.716520	−	2.20522i	0.133054	−	0.409500i	−0.862228	−	0.506521i	$-0.830931\pi$
$29$	0.716520	−	2.20522i	0.133054	−	0.409500i	0.995282	+	0.0970211i	$0.0309314\pi$
$30$	1.31734	−	1.12456i	0.240511	−	0.205315i
$31$	−5.12643	−	2.17250i	−0.920733	−	0.390193i
$31$	−5.12643	−	2.17250i	−0.920733	−	0.390193i
$32$		−	1.00000i		−	0.176777i
$33$	−2.70485	−	6.53458i	−0.470854	−	1.13752i
$34$	−5.09189	−	4.58476i	−0.873252	−	0.786279i
$35$	−2.22058	+	3.05637i	−0.375347	+	0.516621i
$36$	−2.33052	−	1.88909i	−0.388420	−	0.314849i
$37$	9.35934	−	5.40362i	1.53867	−	0.888349i	0.539749	−	0.841826i	$-0.318519\pi$
$37$	9.35934	−	5.40362i	1.53867	−	0.888349i	0.998917	−	0.0465234i	$-0.0148142\pi$
$38$	−0.193900	−	0.0203797i	−0.0314548	−	0.00330603i
$39$	−10.2365	−	2.46021i	−1.63916	−	0.393949i
$40$	0.104528	+	0.994522i	0.0165274	+	0.157248i
$41$	−8.44129	+	7.60057i	−1.31831	+	1.18701i	−0.350144	+	0.936696i	$0.613867\pi$
$41$	−8.44129	+	7.60057i	−1.31831	+	1.18701i	−0.968165	+	0.250314i	$0.919466\pi$
$42$	5.90537	+	2.81848i	0.911218	+	0.434901i
$43$	0.0402884	+	0.189542i	0.00614393	+	0.0289049i	0.981113	−	0.193437i	$-0.0619634\pi$
$43$	0.0402884	+	0.189542i	0.00614393	+	0.0289049i	−0.974969	+	0.222341i	$0.928630\pi$
$44$	3.99395	+	0.848939i	0.602110	+	0.127982i
$45$	2.51522	+	1.63514i	0.374946	+	0.243752i
$46$	3.01955	−	0.981111i	0.445208	−	0.144657i
$47$	−4.66582	+	1.51602i	−0.680579	+	0.221134i	−0.628849	−	0.777527i	$-0.716474\pi$
$47$	−4.66582	+	1.51602i	−0.680579	+	0.221134i	−0.0517303	+	0.998661i	$0.516474\pi$
$48$	1.66084	−	0.491525i	0.239722	−	0.0709455i
$49$	−7.11349	−	1.51202i	−1.01621	−	0.216003i
$50$	−0.207912	−	0.978148i	−0.0294032	−	0.138331i
$51$	5.11177	−	10.7104i	0.715792	−	1.49975i
$52$	4.51710	−	4.06722i	0.626410	−	0.564022i
$53$	−0.349345	−	3.32380i	−0.0479863	−	0.456559i	−0.991961	−	0.126542i	$-0.959612\pi$
$53$	−0.349345	−	3.32380i	−0.0479863	−	0.456559i	0.943975	−	0.330017i	$-0.107054\pi$
$54$	1.99198	−	4.79917i	0.271075	−	0.653084i
$55$	−4.06080	−	0.426808i	−0.547559	−	0.0575507i
$56$	−3.27174	+	1.88894i	−0.437205	+	0.252420i
$57$	−0.0614593	−	0.332055i	−0.00814048	−	0.0439818i
$58$	−1.36290	+	1.87587i	−0.178958	+	0.246314i
$59$	8.33435	+	7.50428i	1.08504	+	0.976974i	0.999812	−	0.0193875i	$-0.00617163\pi$
$59$	8.33435	+	7.50428i	1.08504	+	0.976974i	0.0852275	+	0.996362i	$0.472838\pi$
$60$	−1.60037	+	0.662438i	−0.206607	+	0.0855204i
$61$		−	7.43838i		−	0.952387i	−0.879340	−	0.476194i	$-0.842016\pi$
$61$		−	7.43838i		−	0.952387i	0.879340	−	0.476194i	$-0.157984\pi$
$62$	4.20418	+	3.65032i	0.533932	+	0.463591i
$63$	−1.77842	+	11.1933i	−0.224060	+	1.41022i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−4.06722	+	4.51710i	−0.504476	+	0.560278i
$66$	0.553169	+	7.05059i	0.0680904	+	0.867868i
$67$	−4.90224	+	8.49093i	−0.598904	+	1.03733i	0.394079	+	0.919077i	$0.371064\pi$
$67$	−4.90224	+	8.49093i	−0.598904	+	1.03733i	−0.992983	+	0.118256i	$0.962270\pi$
$68$	3.42591	+	5.93384i	0.415452	+	0.719584i
$69$	3.11366	+	4.53276i	0.374840	+	0.545680i
$70$	3.05637	−	2.22058i	0.365306	−	0.265411i
$71$	−3.03894	+	0.319405i	−0.360655	+	0.0379064i	−0.283123	−	0.959083i	$-0.591371\pi$
$71$	−3.03894	+	0.319405i	−0.360655	+	0.0379064i	−0.0775319	+	0.996990i	$0.524704\pi$
$72$	1.63269	+	2.51681i	0.192415	+	0.296608i
$73$	−2.09217	−	4.69909i	−0.244870	−	0.549986i	0.748739	−	0.662865i	$-0.230660\pi$
$73$	−2.09217	−	4.69909i	−0.244870	−	0.549986i	−0.993609	+	0.112878i	$0.963993\pi$
$74$	−10.5711	+	2.24695i	−1.22886	+	0.261203i
$75$	1.52236	−	0.826093i	0.175787	−	0.0953890i
$76$	0.178112	+	0.0793007i	0.0204309	+	0.00909642i
$77$	−4.76682	−	14.6708i	−0.543229	−	1.67189i
$78$	8.97529	+	5.50307i	1.01625	+	0.623099i
$79$	−2.51209	+	5.64224i	−0.282632	+	0.634802i	−0.997950	−	0.0639971i	$-0.979615\pi$
$79$	−2.51209	+	5.64224i	−0.282632	+	0.634802i	0.715318	+	0.698799i	$0.246282\pi$
$80$	0.207912	−	0.978148i	0.0232452	−	0.109360i
$81$	8.94978	+	0.949461i	0.994420	+	0.105496i
$82$	10.3769	−	4.62007i	1.14593	−	0.510202i
$83$	−8.97420	−	9.96686i	−0.985046	−	1.09400i	−0.995567	−	0.0940602i	$-0.970015\pi$
$83$	−8.97420	−	9.96686i	−0.985046	−	1.09400i	0.0105201	−	0.999945i	$-0.496651\pi$
$84$	−4.74538	−	4.50539i	−0.517764	−	0.491579i
$85$	−4.02739	−	5.54323i	−0.436832	−	0.601248i
$86$	0.0202552	−	0.192715i	0.00218417	−	0.0207810i
$87$	−3.78544	−	1.34153i	−0.405841	−	0.143827i
$88$	−3.53613	−	2.04159i	−0.376953	−	0.217634i
$89$	4.69447	+	3.41073i	0.497613	+	0.361537i	0.808104	−	0.589039i	$-0.200494\pi$
$89$	4.69447	+	3.41073i	0.497613	+	0.361537i	−0.310492	+	0.950576i	$0.600494\pi$
$90$	−1.88683	−	2.33236i	−0.198889	−	0.245852i
$91$	−21.8394	−	7.09607i	−2.28940	−	0.743870i
$92$	−3.17494			−0.331011
$93$	−3.99616	+	8.77672i	−0.414382	+	0.910103i
$94$	4.90593			0.506008
$95$	−0.185426	−	0.0602485i	−0.0190243	−	0.00618137i
$96$	−1.73145	−	0.0457608i	−0.176715	−	0.00467044i
$97$	10.5103	+	7.63620i	1.06716	+	0.775339i	0.975400	−	0.220442i	$-0.0707500\pi$
$97$	10.5103	+	7.63620i	1.06716	+	0.775339i	0.0917622	+	0.995781i	$0.470750\pi$
$98$	6.29809	+	3.63620i	0.636203	+	0.367312i
$99$	−11.4380	+	4.38427i	−1.14957	+	0.440636i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	−6.13507	−	8.44420i	−0.610462	−	0.840229i	0.386153	−	0.922435i	$-0.373804\pi$
$101$	−6.13507	−	8.44420i	−0.610462	−	0.840229i	−0.996615	+	0.0822054i	$0.973804\pi$
$102$	−8.17127	+	8.60653i	−0.809076	+	0.852173i
$103$	6.45892	+	7.17335i	0.636416	+	0.706811i	0.971942	−	0.235219i	$-0.0755809\pi$
$103$	6.45892	+	7.17335i	0.636416	+	0.706811i	−0.335526	+	0.942031i	$0.608914\pi$
$104$	−5.55286	+	2.47229i	−0.544503	+	0.242428i
$105$	5.19033	+	3.98468i	0.506524	+	0.388865i
$106$	−0.694863	+	3.26907i	−0.0674911	+	0.317521i
$107$	−4.84209	+	10.8755i	−0.468103	+	1.05138i	0.513088	+	0.858336i	$0.328501\pi$
$107$	−4.84209	+	10.8755i	−0.468103	+	1.05138i	−0.981191	+	0.193040i	$0.938165\pi$
$108$	−3.37751	+	3.94872i	−0.325001	+	0.379966i
$109$	3.27050	+	10.0656i	0.313257	+	0.964107i	0.976466	+	0.215672i	$0.0691942\pi$
$109$	3.27050	+	10.0656i	0.313257	+	0.964107i	−0.663209	+	0.748435i	$0.730806\pi$
$110$	3.73016	+	1.66078i	0.355657	+	0.158349i
$111$	−8.92778	−	16.4525i	−0.847388	−	1.56160i
$112$	3.69533	−	0.785466i	0.349176	−	0.0742196i
$113$	0.197367	+	0.443294i	0.0185668	+	0.0417016i	0.922591	−	0.385780i	$-0.126068\pi$
$113$	0.197367	+	0.443294i	0.0185668	+	0.0417016i	−0.904024	+	0.427481i	$0.859401\pi$
$114$	−0.0441594	+	0.334795i	−0.00413591	+	0.0313564i
$115$	3.15755	−	0.331872i	0.294443	−	0.0309472i
$116$	1.87587	−	1.36290i	0.174171	−	0.126542i
$117$	−4.72815	+	17.6114i	−0.437118	+	1.62818i
$118$	−5.60748	−	9.71245i	−0.516211	−	0.894103i
$119$	12.9427	−	22.4174i	1.18645	−	2.05500i
$120$	1.72674	−	0.135475i	0.157629	−	0.0123671i
$121$	3.79551	−	4.21534i	0.345046	−	0.383212i
$122$	−2.29859	+	7.07432i	−0.208104	+	0.640479i
$123$	12.7737	+	14.9635i	1.15177	+	1.34921i
$124$	−2.87040	−	4.77083i	−0.257770	−	0.428433i
$125$		−	1.00000i		−	0.0894427i
$126$	5.15028	−	10.0959i	0.458823	−	0.899410i
$127$	−11.7669	−	10.5950i	−1.04414	−	0.940150i	−0.0458725	−	0.998947i	$-0.514607\pi$
$127$	−11.7669	−	10.5950i	−1.04414	−	0.940150i	−0.998270	+	0.0587972i	$0.981273\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	0.330026	−	0.0610837i	0.0290572	−	0.00537812i
$130$	5.26402	−	3.03918i	0.461685	−	0.266554i
$131$	3.79841	+	0.399229i	0.331868	+	0.0348808i	0.268997	−	0.963141i	$-0.413308\pi$
$131$	3.79841	+	0.399229i	0.331868	+	0.0348808i	0.0628709	+	0.998022i	$0.479974\pi$
$132$	1.65266	−	6.87645i	0.143845	−	0.598518i
$133$	−0.0769923	−	0.732532i	−0.00667607	−	0.0635186i
$134$	7.28615	−	6.56048i	0.629428	−	0.566739i
$135$	2.94626	−	4.28014i	0.253573	−	0.368376i
$136$	−1.42457	−	6.70208i	−0.122156	−	0.574699i
$137$	16.5513	+	3.51810i	1.41408	+	0.300571i	0.850710	−	0.525636i	$-0.176173\pi$
$137$	16.5513	+	3.51810i	1.41408	+	0.300571i	0.563367	+	0.826207i	$0.309506\pi$
$138$	−1.56056	−	5.27308i	−0.132844	−	0.448875i
$139$	−6.52978	+	2.12165i	−0.553849	+	0.179956i	−0.572551	−	0.819869i	$-0.694046\pi$
$139$	−6.52978	+	2.12165i	−0.553849	+	0.179956i	0.0187029	+	0.999825i	$0.494046\pi$
$140$	−3.59298	+	1.16743i	−0.303662	+	0.0986659i
$141$	2.41139	+	8.14798i	0.203075	+	0.686184i
$142$	2.98890	+	0.635311i	0.250823	+	0.0533141i
$143$	−5.16016	−	24.2767i	−0.431514	−	2.03012i
$144$	−0.775048	−	2.89815i	−0.0645873	−	0.241513i
$145$	−1.72314	+	1.55152i	−0.143099	+	0.128847i
$146$	0.537672	+	5.11561i	0.0444981	+	0.423371i
$147$	−2.94350	+	12.2474i	−0.242776	+	1.01015i
$148$	10.7480	+	1.12966i	0.883483	+	0.0928578i
$149$	3.30591	−	1.90867i	0.270831	−	0.156364i	−0.358434	−	0.933555i	$-0.616689\pi$
$149$	3.30591	−	1.90867i	0.270831	−	0.156364i	0.629265	+	0.777191i	$0.283356\pi$
$150$	−1.70312	+	0.315227i	−0.139060	+	0.0257382i
$151$	2.32612	−	3.20162i	0.189297	−	0.260544i	−0.703811	−	0.710387i	$-0.748520\pi$
$151$	2.32612	−	3.20162i	0.189297	−	0.260544i	0.893108	+	0.449843i	$0.148520\pi$
$152$	−0.144890	−	0.130459i	−0.0117521	−	0.0105816i
$153$	−18.3105	−	9.34088i	−1.48032	−	0.755165i
$154$			15.4258i			1.24304i
$155$	3.35337	+	4.44465i	0.269349	+	0.357003i
$156$	−6.83546	−	8.00724i	−0.547275	−	0.641093i
$157$	−5.24995	+	16.1577i	−0.418992	+	1.28952i	0.489640	+	0.871925i	$0.337128\pi$
$157$	−5.24995	+	16.1577i	−0.418992	+	1.28952i	−0.908632	+	0.417599i	$0.862872\pi$
$158$	4.13269	−	4.58981i	0.328779	−	0.365146i
$159$	−5.77097	+	0.452773i	−0.457667	+	0.0359072i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	5.99728	+	10.3876i	0.472652	+	0.818657i
$162$	−8.21834	−	3.66862i	−0.645694	−	0.288234i
$163$	8.15832	−	5.92737i	0.639009	−	0.464267i	−0.220501	−	0.975387i	$-0.570769\pi$
$163$	8.15832	−	5.92737i	0.639009	−	0.464267i	0.859510	+	0.511120i	$0.170769\pi$
$164$	−11.2967	+	1.18733i	−0.882120	+	0.0927146i
$165$	−0.924820	+	7.01153i	−0.0719972	+	0.545847i
$166$	5.45504	+	12.2522i	0.423393	+	0.950957i
$167$	10.1106	−	2.14907i	0.782380	−	0.166300i	0.200629	−	0.979667i	$-0.435701\pi$
$167$	10.1106	−	2.14907i	0.782380	−	0.166300i	0.581750	+	0.813367i	$0.302368\pi$
$168$	3.12088	+	5.75129i	0.240781	+	0.443721i
$169$	−21.8762	−	9.73992i	−1.68279	−	0.749225i
$170$	2.11733	+	6.51646i	0.162392	+	0.499790i
$171$	−0.577748	+	0.0912183i	−0.0441815	+	0.00697564i
$172$	−0.0788161	+	0.177024i	−0.00600967	+	0.0134979i
$173$	−0.311118	+	1.46369i	−0.0236538	+	0.111283i	−0.988391	−	0.151934i	$-0.951450\pi$
$173$	−0.311118	+	1.46369i	−0.0236538	+	0.111283i	0.964737	+	0.263216i	$0.0847833\pi$
$174$	3.18561	+	2.44563i	0.241500	+	0.185403i
$175$	3.45127	−	1.53660i	0.260891	−	0.116156i
$176$	2.73218	+	3.03439i	0.205945	+	0.228726i
$177$	13.3746	−	14.0871i	1.00530	−	1.05885i
$178$	−3.41073	−	4.69447i	−0.255645	−	0.351865i
$179$	1.56340	−	14.8748i	0.116854	−	1.11179i	−0.766226	−	0.642571i	$-0.777868\pi$
$179$	1.56340	−	14.8748i	0.116854	−	1.11179i	0.883080	−	0.469222i	$-0.155466\pi$
$180$	1.07374	+	2.80126i	0.0800320	+	0.208794i
$181$	15.1547	+	8.74960i	1.12644	+	0.650352i	0.943038	−	0.332685i	$-0.107955\pi$
$181$	15.1547	+	8.74960i	1.12644	+	0.650352i	0.183405	+	0.983037i	$0.441288\pi$
$182$	18.5777	+	13.4975i	1.37707	+	1.00050i
$183$	−12.8792	−	0.340386i	−0.952055	−	0.0251621i
$184$	3.01955	+	0.981111i	0.222604	+	0.0723285i
$185$	−10.8072			−0.794564
$186$	6.51272	−	7.11227i	0.477536	−	0.521497i
$187$	27.9771			2.04589
$188$	−4.66582	−	1.51602i	−0.340290	−	0.110567i
$189$	19.2991	+	3.59145i	1.40381	+	0.261239i
$190$	0.157733	+	0.114599i	0.0114431	+	0.00831392i
$191$	9.86557	+	5.69589i	0.713848	+	0.412140i	0.812484	−	0.582983i	$-0.198115\pi$
$191$	9.86557	+	5.69589i	0.713848	+	0.412140i	−0.0986365	+	0.995124i	$0.531448\pi$
$192$	1.63256	+	0.578567i	0.117820	+	0.0417545i
$193$	2.24885	−	21.3964i	0.161876	−	1.54015i	−0.548396	−	0.836219i	$-0.684761\pi$
$193$	2.24885	−	21.3964i	0.161876	−	1.54015i	0.710272	−	0.703928i	$-0.248572\pi$
$194$	−7.63620	−	10.5103i	−0.548247	−	0.754598i
$195$	7.63500	+	7.24888i	0.546754	+	0.519103i
$196$	−4.86619	−	5.40445i	−0.347585	−	0.386032i
$197$	−3.01017	+	1.34021i	−0.214466	+	0.0954862i	−0.511158	−	0.859487i	$-0.670783\pi$
$197$	−3.01017	+	1.34021i	−0.214466	+	0.0954862i	0.296692	+	0.954973i	$0.404117\pi$
$198$	12.2330	−	0.635141i	0.869364	−	0.0451375i
$199$	0.0158454	−	0.0745467i	0.00112325	−	0.00528448i	−0.977582	−	0.210553i	$-0.932473\pi$
$199$	0.0158454	−	0.0745467i	0.00112325	−	0.00528448i	0.978706	+	0.205269i	$0.0658068\pi$
$200$	0.406737	−	0.913545i	0.0287606	−	0.0645974i
$201$	14.4773	+	8.87652i	1.02115	+	0.626102i
$202$	3.22540	+	9.92675i	0.226938	+	0.698444i
$203$	−8.00248	−	3.56294i	−0.561664	−	0.250069i
$204$	10.4309	−	5.66023i	0.730309	−	0.396296i
$205$	11.1107	−	2.36164i	0.776002	−	0.164944i
$206$	−3.92611	−	8.81818i	−0.273545	−	0.614392i
$207$	7.99071	−	5.18371i	0.555393	−	0.360292i
$208$	6.04507	−	0.635362i	0.419150	−	0.0440544i
$209$	0.644049	−	0.467929i	0.0445498	−	0.0323673i
$210$	−3.70496	−	5.39356i	−0.255667	−	0.372191i
$211$	0.953391	+	1.65132i	0.0656342	+	0.113682i	0.896975	−	0.442081i	$-0.145760\pi$
$211$	0.953391	+	1.65132i	0.0656342	+	0.113682i	−0.831341	+	0.555763i	$0.812426\pi$
$212$	1.67105	−	2.89435i	0.114768	−	0.198785i
$213$	0.413969	+	5.27637i	0.0283647	+	0.361531i
$214$	7.96582	−	8.84694i	0.544532	−	0.604764i
$215$	0.0598803	−	0.184293i	0.00408380	−	0.0125687i
$216$	4.43243	−	2.71175i	0.301588	−	0.184511i
$217$	−10.1869	+	18.4030i	−0.691532	+	1.24928i
$218$		−	10.5836i		−	0.716810i
$219$	−8.23195	+	3.40744i	−0.556264	+	0.230254i
$220$	−3.03439	−	2.73218i	−0.204578	−	0.184203i
$221$	24.4800	−	33.6938i	1.64670	−	2.26649i
$222$	3.40673	+	18.4061i	0.228645	+	1.23533i
$223$	15.7342	−	9.08415i	1.05364	−	0.608319i	0.129974	−	0.991517i	$-0.458511\pi$
$223$	15.7342	−	9.08415i	1.05364	−	0.608319i	0.923666	+	0.383198i	$0.125177\pi$
$224$	−3.75719	−	0.394896i	−0.251038	−	0.0263851i
$225$	−1.36067	−	2.67368i	−0.0907114	−	0.178245i
$226$	−0.0507220	−	0.482588i	−0.00337398	−	0.0321013i
$227$	9.30484	−	8.37812i	0.617584	−	0.556075i	−0.299838	−	0.953990i	$-0.596933\pi$
$227$	9.30484	−	8.37812i	0.617584	−	0.556075i	0.917422	+	0.397915i	$0.130266\pi$
$228$	0.145456	−	0.304763i	0.00963303	−	0.0201834i
$229$	3.32576	+	15.6465i	0.219772	+	1.03395i	0.940254	+	0.340473i	$0.110587\pi$
$229$	3.32576	+	15.6465i	0.219772	+	1.03395i	−0.720482	+	0.693474i	$0.756079\pi$
$230$	−3.10556	−	0.660107i	−0.204775	−	0.0435262i
$231$	−25.6198	+	7.58214i	−1.68566	+	0.498869i
$232$	−2.20522	+	0.716520i	−0.144780	+	0.0470419i
$233$	9.99918	−	3.24893i	0.655068	−	0.212845i	0.0374207	−	0.999300i	$-0.488086\pi$
$233$	9.99918	−	3.24893i	0.655068	−	0.212845i	0.617648	+	0.786455i	$0.288086\pi$
$234$	9.93898	−	15.2884i	0.649731	−	0.999434i
$235$	4.79872	+	1.02000i	0.313034	+	0.0665375i
$236$	2.33172	+	10.9699i	0.151782	+	0.714079i
$237$	9.65428	+	4.60774i	0.627113	+	0.299305i
$238$	−19.2366	+	17.3207i	−1.24692	+	1.12273i
$239$	−2.10919	−	20.0676i	−0.136432	−	1.29806i	−0.821762	−	0.569831i	$-0.807009\pi$
$239$	−2.10919	−	20.0676i	−0.136432	−	1.29806i	0.685330	−	0.728233i	$-0.259658\pi$
$240$	−1.68410	−	0.404749i	−0.108708	−	0.0261264i
$241$	10.7058	+	1.12523i	0.689624	+	0.0724824i	0.442857	−	0.896592i	$-0.353965\pi$
$241$	10.7058	+	1.12523i	0.689624	+	0.0724824i	0.246767	+	0.969075i	$0.420632\pi$
$242$	−4.91235	+	2.83615i	−0.315778	+	0.182314i
$243$	2.05349	−	15.4526i	0.131731	−	0.991285i
$244$	4.37217	−	6.01778i	0.279900	−	0.385249i
$245$	5.40445	+	4.86619i	0.345278	+	0.310889i
$246$	−7.52455	−	18.1784i	−0.479748	−	1.15901i
$247$		−	1.18509i		−	0.0754053i
$248$	1.25565	+	5.42433i	0.0797337	+	0.344445i
$249$	−17.6677	+	15.0823i	−1.11965	+	0.955799i
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	−17.7783	+	19.7448i	−1.12215	+	1.24628i	−0.156155	+	0.987733i	$0.549910\pi$
$251$	−17.7783	+	19.7448i	−1.12215	+	1.24628i	−0.965999	+	0.258546i	$0.916757\pi$
$252$	−8.01800	+	8.01020i	−0.505086	+	0.504595i
$253$	−6.48192	+	11.2270i	−0.407515	+	0.705836i
$254$	7.91695	+	13.7126i	0.496754	+	0.860403i
$255$	−9.78210	+	6.71955i	−0.612579	+	0.420795i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	11.3314	−	1.19098i	0.706832	−	0.0742910i	0.255710	−	0.966754i	$-0.417691\pi$
$257$	11.3314	−	1.19098i	0.706832	−	0.0742910i	0.451122	+	0.892463i	$0.351024\pi$
$258$	−0.332749	−	0.0438896i	−0.0207161	−	0.00273244i
$259$	−16.6064	−	37.2987i	−1.03187	−	2.31763i
$260$	−5.94554	+	1.26376i	−0.368727	+	0.0783752i
$261$	−2.49601	+	6.49289i	−0.154499	+	0.401900i
$262$	−3.48913	−	1.55346i	−0.215559	−	0.0959731i
$263$	1.31834	+	4.05744i	0.0812925	+	0.250193i	0.983440	−	0.181236i	$-0.0580097\pi$
$263$	1.31834	+	4.05744i	0.0812925	+	0.250193i	−0.902147	+	0.431428i	$0.858010\pi$
$264$	−3.69671	+	6.02920i	−0.227517	+	0.371071i
$265$	−1.35936	+	3.05317i	−0.0835047	+	0.187555i
$266$	−0.153141	+	0.720472i	−0.00938967	+	0.0441749i
$267$	6.12032	−	7.97214i	0.374558	−	0.487887i
$268$	−8.95684	+	3.98784i	−0.547126	+	0.243596i
$269$	−2.08755	−	2.31846i	−0.127280	−	0.141359i	0.676136	−	0.736777i	$-0.263653\pi$
$269$	−2.08755	−	2.31846i	−0.127280	−	0.141359i	−0.803416	+	0.595418i	$0.796987\pi$
$270$	−4.12469	+	3.16021i	−0.251021	+	0.192324i
$271$	5.68849	+	7.82954i	0.345551	+	0.475611i	0.946053	−	0.324013i	$-0.105032\pi$
$271$	5.68849	+	7.82954i	0.345551	+	0.475611i	−0.600501	+	0.799624i	$0.705032\pi$
$272$	−0.716209	+	6.81428i	−0.0434266	+	0.413176i
$273$	−13.2858	+	37.4891i	−0.804096	+	2.26894i
$274$	−14.6541	−	8.46055i	−0.885287	−	0.511121i
$275$	3.30336	+	2.40003i	0.199200	+	0.144727i
$276$	−0.145288	+	5.49724i	−0.00874530	+	0.330895i
$277$	30.5934	+	9.94039i	1.83818	+	0.597260i	0.998534	+	0.0541239i	$0.0172366\pi$
$277$	30.5934	+	9.94039i	1.83818	+	0.597260i	0.839644	+	0.543137i	$0.182763\pi$
$278$	6.86581			0.411784
$279$	15.0135	+	7.32076i	0.898837	+	0.438282i
$280$	3.77788			0.225772
$281$	−24.6990	−	8.02520i	−1.47342	−	0.478743i	−0.541280	−	0.840842i	$-0.682060\pi$
$281$	−24.6990	−	8.02520i	−1.47342	−	0.478743i	−0.932140	+	0.362099i	$0.882060\pi$
$282$	0.224499	−	8.49435i	0.0133687	−	0.505831i
$283$	−6.84152	−	4.97065i	−0.406686	−	0.295475i	0.365573	−	0.930783i	$-0.380873\pi$
$283$	−6.84152	−	4.97065i	−0.406686	−	0.295475i	−0.772259	+	0.635308i	$0.780873\pi$
$284$	−2.64629	−	1.52784i	−0.157029	−	0.0906605i
$285$	−0.112802	+	0.318298i	−0.00668183	+	0.0188543i
$286$	−2.59429	+	24.6830i	−0.153404	+	1.45954i
$287$	25.2234	+	34.7170i	1.48889	+	2.04928i
$288$	−0.158465	+	2.99581i	−0.00933763	+	0.176530i
$289$	20.0387	+	22.2552i	1.17875	+	1.30913i
$290$	2.11825	−	0.943104i	0.124388	−	0.0553809i
$291$	13.7026	−	17.8486i	0.803263	−	1.04631i
$292$	1.06945	−	5.03139i	0.0625851	−	0.294440i
$293$	−3.56007	+	7.99605i	−0.207982	+	0.467135i	−0.987174	−	0.159651i	$-0.948963\pi$
$293$	−3.56007	+	7.99605i	−0.207982	+	0.467135i	0.779192	+	0.626786i	$0.215630\pi$
$294$	6.58410	−	10.7384i	0.383992	−	0.626277i
$295$	−3.46562	−	10.6661i	−0.201776	−	0.621003i
$296$	−9.87290	−	4.39570i	−0.573851	−	0.255495i
$297$	7.06772	+	20.0050i	0.410111	+	1.16081i
$298$	−3.73392	+	0.793670i	−0.216300	+	0.0459760i
$299$	7.84939	+	17.6300i	0.453942	+	1.01957i
$300$	1.71718	+	0.226496i	0.0991413	+	0.0130767i
$301$	0.728056	−	0.0765217i	0.0419644	−	0.00441064i
$302$	−3.20162	+	2.32612i	−0.184233	+	0.133853i
$303$	−14.9014	+	10.2361i	−0.856064	+	0.588050i
$304$	0.0974841	+	0.168847i	0.00559110	+	0.00968406i
$305$	−3.71919	+	6.44183i	−0.212960	+	0.368858i
$306$	14.5278	+	14.5420i	0.830500	+	0.831308i
$307$	3.86841	−	4.29630i	0.220782	−	0.245203i	−0.622571	−	0.782563i	$-0.713912\pi$
$307$	3.86841	−	4.29630i	0.220782	−	0.245203i	0.843353	+	0.537360i	$0.180578\pi$
$308$	4.76682	−	14.6708i	0.271615	−	0.835944i
$309$	12.7158	−	10.8550i	0.723379	−	0.617520i
$310$	−1.81577	−	5.26336i	−0.103129	−	0.298939i
$311$			23.3649i			1.32490i	0.749105	+	0.662451i	$0.230484\pi$
$311$			23.3649i			1.32490i	−0.749105	+	0.662451i	$0.769516\pi$
$312$	4.02654	+	9.72762i	0.227958	+	0.550718i
$313$	−4.09463	−	3.68682i	−0.231442	−	0.208391i	0.545247	−	0.838275i	$-0.316436\pi$
$313$	−4.09463	−	3.68682i	−0.231442	−	0.208391i	−0.776689	+	0.629884i	$0.783102\pi$
$314$	9.98600	−	13.7445i	0.563542	−	0.775650i
$315$	7.13678	−	8.80443i	0.402112	−	0.496074i
$316$	−5.34875	+	3.08810i	−0.300891	+	0.173719i
$317$	−12.6596	−	1.33058i	−0.711034	−	0.0747327i	−0.257895	−	0.966173i	$-0.583029\pi$
$317$	−12.6596	−	1.33058i	−0.711034	−	0.0747327i	−0.453138	+	0.891440i	$0.649696\pi$
$318$	5.62843	+	1.35271i	0.315627	+	0.0758564i
$319$	−0.989643	−	9.41582i	−0.0554093	−	0.527185i
$320$	0.743145	−	0.669131i	0.0415431	−	0.0374055i
$321$	18.6088	+	8.88149i	1.03864	+	0.495717i
$322$	−2.49381	−	11.7325i	−0.138975	−	0.653824i
$323$	1.30669	+	0.277746i	0.0727064	+	0.0154542i
$324$	6.68244	+	6.02868i	0.371247	+	0.334927i
$325$	5.78087	−	1.87832i	0.320665	−	0.104190i
$326$	−9.59068	+	3.11620i	−0.531179	+	0.172590i
$327$	17.5777	−	5.20209i	0.972046	−	0.287676i
$328$	11.1107	+	2.36164i	0.613484	+	0.130400i
$329$	3.85344	+	18.1290i	0.212447	+	0.999485i
$330$	3.04624	−	6.38258i	0.167690	−	0.351349i
$331$	15.1960	−	13.6826i	0.835249	−	0.752062i	−0.135852	−	0.990729i	$-0.543377\pi$
$331$	15.1960	−	13.6826i	0.835249	−	0.752062i	0.971101	+	0.238667i	$0.0767105\pi$
$332$	−1.40191	−	13.3383i	−0.0769397	−	0.732032i
$333$	−28.8951	+	14.7051i	−1.58344	+	0.805834i
$334$	−10.2798	−	1.08045i	−0.562487	−	0.0591198i
$335$	8.49093	−	4.90224i	0.463909	−	0.267838i
$336$	−1.19089	−	6.43421i	−0.0649684	−	0.351015i
$337$	9.56303	−	13.1624i	0.520932	−	0.717001i	−0.464783	−	0.885425i	$-0.653868\pi$
$337$	9.56303	−	13.1624i	0.520932	−	0.717001i	0.985715	+	0.168424i	$0.0538677\pi$
$338$	17.7957	+	16.0233i	0.967960	+	0.871555i
$339$	0.776572	−	0.321445i	0.0421776	−	0.0174585i
$340$		−	6.85181i		−	0.371592i
$341$	−22.7304	+	0.410064i	−1.23092	+	0.0222062i
$342$	0.577659	+	0.0917802i	0.0312362	+	0.00496290i
$343$	−0.318016	+	0.978754i	−0.0171713	+	0.0528477i
$344$	0.129662	−	0.144004i	0.00699090	−	0.00776418i
$345$	−0.430126	−	5.48231i	−0.0231572	−	0.295158i
$346$	0.748196	−	1.29591i	0.0402233	−	0.0696688i
$347$	−10.2753	−	17.7974i	−0.551609	−	0.955415i	−0.998159	−	0.0606558i	$-0.980681\pi$
$347$	−10.2753	−	17.7974i	−0.551609	−	0.955415i	0.446550	−	0.894759i	$-0.352653\pi$
$348$	−2.27395	−	3.31034i	−0.121897	−	0.177453i
$349$	18.6496	−	13.5497i	0.998289	−	0.725299i	0.0365684	−	0.999331i	$-0.488357\pi$
$349$	18.6496	−	13.5497i	0.998289	−	0.725299i	0.961721	+	0.274032i	$0.0883573\pi$
$350$	−3.75719	+	0.394896i	−0.200830	+	0.0211081i
$351$	30.2769	+	8.99246i	1.61606	+	0.479982i
$352$	−1.66078	−	3.73016i	−0.0885196	−	0.198818i
$353$	−10.1179	+	2.15063i	−0.538521	+	0.114466i	−0.469140	−	0.883124i	$-0.655436\pi$
$353$	−10.1179	+	2.15063i	−0.538521	+	0.114466i	−0.0693816	+	0.997590i	$0.522103\pi$
$354$	−17.0732	+	9.26461i	−0.907430	+	0.492408i
$355$	2.79150	+	1.24286i	0.148157	+	0.0659639i
$356$	1.79313	+	5.51868i	0.0950356	+	0.292489i
$357$	−38.2222	−	23.4354i	−2.02293	−	1.24033i
$358$	−6.08345	+	13.6636i	−0.321520	+	0.722146i
$359$	3.01548	−	14.1867i	0.159151	−	0.748746i	−0.824093	−	0.566454i	$-0.808315\pi$
$359$	3.01548	−	14.1867i	0.159151	−	0.748746i	0.983244	−	0.182292i	$-0.0583518\pi$
$360$	−0.155551	−	2.99596i	−0.00819825	−	0.157901i
$361$	−17.3226	+	7.71254i	−0.911718	+	0.405923i
$362$	−11.7092	−	13.0044i	−0.615424	−	0.683498i
$363$	−7.12494	−	6.76461i	−0.373963	−	0.355050i
$364$	−13.4975	−	18.5777i	−0.707462	−	0.973738i
$365$	−0.537672	+	5.11561i	−0.0281431	+	0.267763i
$366$	12.1436	+	4.30360i	0.634757	+	0.224953i
$367$	−18.6210	−	10.7509i	−0.972011	−	0.561191i	−0.0721622	−	0.997393i	$-0.522990\pi$
$367$	−18.6210	−	10.7509i	−0.972011	−	0.561191i	−0.899849	+	0.436202i	$0.856323\pi$
$368$	−2.56858	−	1.86618i	−0.133897	−	0.0972816i
$369$	26.4929	−	21.4322i	1.37917	−	1.11572i
$370$	10.2783	+	3.33962i	0.534343	+	0.173619i
$371$	−12.6261			−0.655514
$372$	−8.39178	+	4.75163i	−0.435094	+	0.246361i
$373$	−21.6657			−1.12181			−0.560904	−	0.827881i	$-0.689546\pi$
$373$	−21.6657			−1.12181			−0.560904	+	0.827881i	$0.689546\pi$
$374$	−26.6078	−	8.64541i	−1.37586	−	0.447043i
$375$	−1.73145	−	0.0457608i	−0.0894115	−	0.00236308i
$376$	3.96898	+	2.88363i	0.204685	+	0.148712i
$377$	−12.2057	−	7.04698i	−0.628627	−	0.362938i
$378$	−17.2447	−	9.37943i	−0.886974	−	0.482426i
$379$	1.92563	−	18.3211i	0.0989128	−	0.941092i	−0.826706	−	0.562635i	$-0.809788\pi$
$379$	1.92563	−	18.3211i	0.0989128	−	0.941092i	0.925619	−	0.378458i	$-0.123546\pi$
$380$	−0.114599	−	0.157733i	−0.00587883	−	0.00809151i
$381$	−18.8831	+	19.8889i	−0.967408	+	1.01894i
$382$	−7.62259	−	8.46574i	−0.390005	−	0.433145i
$383$	−14.4436	+	6.43069i	−0.738032	+	0.328593i	−0.741093	−	0.671402i	$-0.765692\pi$
$383$	−14.4436	+	6.43069i	−0.738032	+	0.328593i	0.00306103	+	0.999995i	$0.499026\pi$
$384$	−1.37387	−	1.05474i	−0.0701101	−	0.0538245i
$385$	−3.20719	+	15.0887i	−0.163454	+	0.768989i
$386$	−8.75064	+	19.6542i	−0.445396	+	1.00037i
$387$	−0.0906608	−	0.574217i	−0.00460855	−	0.0291891i
$388$	4.01459	+	12.3556i	0.203810	+	0.627262i
$389$	8.96023	+	3.98935i	0.454302	+	0.202268i	0.621114	−	0.783721i	$-0.286681\pi$
$389$	8.96023	+	3.98935i	0.454302	+	0.202268i	−0.166812	+	0.985989i	$0.553347\pi$
$390$	−5.02129	−	9.25344i	−0.254263	−	0.468566i
$391$	−21.2787	+	4.52293i	−1.07611	+	0.228734i
$392$	2.95795	+	6.64367i	0.149399	+	0.335556i
$393$	0.865061	−	6.55847i	0.0436366	−	0.330831i
$394$	3.27699	−	0.344425i	0.165092	−	0.0173519i
$395$	4.99665	−	3.63028i	0.251409	−	0.182659i
$396$	−11.8306	−	3.17616i	−0.594509	−	0.159608i
$397$	−7.77524	−	13.4671i	−0.390228	−	0.675895i	0.602251	−	0.798307i	$-0.294271\pi$
$397$	−7.77524	−	13.4671i	−0.390228	−	0.675895i	−0.992479	+	0.122411i	$0.960937\pi$
$398$	−0.0381061	+	0.0660017i	−0.00191008	+	0.00330836i
$399$	−1.27186	+	0.0997867i	−0.0636728	+	0.00499558i
$400$	−0.669131	+	0.743145i	−0.0334565	+	0.0371572i
$401$	11.4336	−	35.1889i	0.570964	−	1.75725i	−0.0785627	−	0.996909i	$-0.525033\pi$
$401$	11.4336	−	35.1889i	0.570964	−	1.75725i	0.649527	−	0.760338i	$-0.274967\pi$
$402$	−11.0257	−	12.9158i	−0.549912	−	0.644181i
$403$	−19.3953	+	27.7338i	−0.966147	+	1.38152i
$404$		−	10.4376i		−	0.519290i
$405$	−7.27600	−	5.29715i	−0.361548	−	0.263217i
$406$	6.50981	+	5.86146i	0.323076	+	0.290899i
$407$	25.9377	−	35.7001i	1.28568	−	1.76959i
$408$	−11.6695	+	2.15988i	−0.577726	+	0.106930i
$409$	−23.2365	+	13.4156i	−1.14897	+	0.663359i	−0.948636	−	0.316368i	$-0.897536\pi$
$409$	−23.2365	+	13.4156i	−1.14897	+	0.663359i	−0.200335	+	0.979727i	$0.564203\pi$
$410$	−11.2967	−	1.18733i	−0.557902	−	0.0586379i
$411$	6.84880	−	28.4968i	0.337826	−	1.40564i
$412$	1.00898	+	9.59982i	0.0497090	+	0.472949i
$413$	31.4862	−	28.3503i	1.54933	−	1.39503i
$414$	−9.20147	+	2.46073i	−0.452228	+	0.120938i
$415$	2.78846	+	13.1187i	0.136880	+	0.643969i
$416$	−5.94554	−	1.26376i	−0.291504	−	0.0619611i
$417$	3.37472	+	11.4030i	0.165261	+	0.558410i
$418$	−0.757125	+	0.246005i	−0.0370322	+	0.0120325i
$419$	−11.1334	+	3.61746i	−0.543903	+	0.176725i	−0.568065	−	0.822983i	$-0.692308\pi$
$419$	−11.1334	+	3.61746i	−0.543903	+	0.176725i	0.0241629	+	0.999708i	$0.492308\pi$
$420$	1.85693	+	6.27448i	0.0906087	+	0.306163i
$421$	10.1854	+	2.16498i	0.496408	+	0.105515i	0.449311	−	0.893375i	$-0.351670\pi$
$421$	10.1854	+	2.16498i	0.496408	+	0.105515i	0.0470974	+	0.998890i	$0.485003\pi$
$422$	−0.396442	−	1.86512i	−0.0192985	−	0.0907924i
$423$	14.2181	−	3.80233i	0.691310	−	0.184876i
$424$	−2.48367	+	2.23631i	−0.120618	+	0.108605i
$425$	0.716209	+	6.81428i	0.0347413	+	0.330541i
$426$	1.23678	−	5.14605i	0.0599222	−	0.249327i
$427$	−27.9474	−	2.93739i	−1.35247	−	0.142150i
$428$	−10.3098	+	5.95237i	−0.498343	+	0.287718i
$429$	−42.2698	+	7.82362i	−2.04081	+	0.377728i
$430$	−0.113899	+	0.156769i	−0.00549270	+	0.00756006i
$431$	−13.8086	−	12.4333i	−0.665136	−	0.598891i	0.265820	−	0.964023i	$-0.414357\pi$
$431$	−13.8086	−	12.4333i	−0.665136	−	0.598891i	−0.930956	+	0.365131i	$0.881024\pi$
$432$	−5.05347	+	1.20933i	−0.243135	+	0.0581840i
$433$		−	33.7931i		−	1.62399i	−0.583662	−	0.811997i	$-0.698381\pi$
$433$		−	33.7931i		−	1.62399i	0.583662	−	0.811997i	$-0.301619\pi$
$434$	15.3752	−	14.3544i	0.738032	−	0.689033i
$435$	2.60752	+	3.05452i	0.125021	+	0.146453i
$436$	−3.27050	+	10.0656i	−0.156629	+	0.482053i
$437$	−0.414200	+	0.460016i	−0.0198139	+	0.0220056i
$438$	8.88201	−	0.696856i	0.424399	−	0.0332971i
$439$	−4.75560	+	8.23694i	−0.226973	+	0.393128i	−0.956909	−	0.290387i	$-0.906216\pi$
$439$	−4.75560	+	8.23694i	−0.226973	+	0.393128i	0.729937	+	0.683515i	$0.239549\pi$
$440$	2.04159	+	3.53613i	0.0973288	+	0.168578i
$441$	21.0711	+	5.65696i	1.00338	+	0.269379i
$442$	−33.6938	+	24.4800i	−1.60265	+	1.16439i
$443$	22.7744	−	2.39368i	1.08204	−	0.113727i	0.453313	−	0.891351i	$-0.350242\pi$
$443$	22.7744	−	2.39368i	1.08204	−	0.113727i	0.628730	+	0.777624i	$0.283575\pi$
$444$	2.44779	−	18.5579i	0.116167	−	0.880721i
$445$	−2.36016	−	5.30102i	−0.111883	−	0.251292i
$446$	−17.7713	+	3.77740i	−0.841494	+	0.178865i
$447$	−3.15348	−	5.81135i	−0.149154	−	0.274868i
$448$	3.45127	+	1.53660i	0.163057	+	0.0725977i
$449$	−4.86519	−	14.9735i	−0.229602	−	0.706644i	−0.997792	−	0.0664209i	$-0.978842\pi$
$449$	−4.86519	−	14.9735i	−0.229602	−	0.706644i	0.768189	−	0.640223i	$-0.221158\pi$
$450$	0.467862	+	2.96329i	0.0220552	+	0.139691i
$451$	−18.8646	+	42.3705i	−0.888297	+	1.99515i
$452$	−0.100888	+	0.474642i	−0.00474539	+	0.0223253i
$453$	−5.43699	−	4.17405i	−0.255452	−	0.196114i
$454$	−11.4384	+	5.09271i	−0.536831	+	0.239013i
$455$	15.3655	+	17.0651i	0.720345	+	0.800024i
$456$	−0.232513	+	0.244899i	−0.0108884	+	0.0114684i
$457$	1.44637	+	1.99076i	0.0676584	+	0.0931238i	0.841505	−	0.540249i	$-0.181670\pi$
$457$	1.44637	+	1.99076i	0.0676584	+	0.0931238i	−0.773847	+	0.633373i	$0.781670\pi$
$458$	1.67204	−	15.9084i	0.0781292	−	0.743350i
$459$	−17.0111	+	31.2762i	−0.794012	+	1.45985i
$460$	2.74958	+	1.58747i	0.128200	+	0.0740162i
$461$	20.9869	+	15.2478i	0.977456	+	0.710163i	0.957139	−	0.289630i	$-0.0935324\pi$
$461$	20.9869	+	15.2478i	0.977456	+	0.710163i	0.0203171	+	0.999794i	$0.493532\pi$
$462$	26.7089	+	0.705895i	1.24261	+	0.0328412i
$463$	−25.5865	−	8.31357i	−1.18911	−	0.386364i	−0.353364	−	0.935486i	$-0.614962\pi$
$463$	−25.5865	−	8.31357i	−1.18911	−	0.386364i	−0.835742	+	0.549122i	$0.814962\pi$
$464$	2.31871			0.107643
$465$	7.84913	−	5.60278i	0.363995	−	0.259823i
$466$	−10.5138			−0.487041
$467$	−18.6040	−	6.04482i	−0.860892	−	0.279721i	−0.154891	−	0.987932i	$-0.549503\pi$
$467$	−18.6040	−	6.04482i	−0.860892	−	0.279721i	−0.706001	+	0.708211i	$0.749503\pi$
$468$	−14.1769	+	11.4688i	−0.655328	+	0.530146i
$469$	29.9662	+	21.7717i	1.38371	+	1.00532i
$470$	−4.24866	−	2.45296i	−0.195976	−	0.113147i
$471$	27.7359	+	9.82939i	1.27800	+	0.452915i
$472$	1.17228	−	11.1535i	0.0539587	−	0.513383i
$473$	0.465070	+	0.640113i	0.0213839	+	0.0294324i
$474$	−7.75790	−	7.36556i	−0.356332	−	0.338311i
$475$	0.130459	+	0.144890i	0.00598588	+	0.00664799i
$476$	23.6474	−	10.5285i	1.08388	−	0.482574i
$477$	0.519868	+	10.0128i	0.0238031	+	0.458456i
$478$	−4.19526	+	19.7372i	−0.191887	+	0.902757i
$479$	−15.1451	+	34.0165i	−0.691998	+	1.55425i	0.134251	+	0.990947i	$0.457137\pi$
$479$	−15.1451	+	34.0165i	−0.691998	+	1.55425i	−0.826249	+	0.563305i	$0.809530\pi$
$480$	1.47660	+	0.905353i	0.0673971	+	0.0413235i
$481$	−20.2994	−	62.4752i	−0.925574	−	2.84862i
$482$	−9.83415	−	4.37844i	−0.447933	−	0.199433i
$483$	18.2600	−	9.90862i	0.830859	−	0.450858i
$484$	5.54834	−	1.17934i	0.252197	−	0.0536062i
$485$	−5.28411	−	11.8683i	−0.239939	−	0.538912i
$486$	−6.72810	+	14.0617i	−0.305193	+	0.637854i
$487$	40.8665	−	4.29524i	1.85184	−	0.194636i	0.887770	−	0.460288i	$-0.152254\pi$
$487$	40.8665	−	4.29524i	1.85184	−	0.194636i	0.964069	+	0.265652i	$0.0855872\pi$
$488$	−6.01778	+	4.37217i	−0.272412	+	0.197919i
$489$	−9.88959	−	14.3969i	−0.447223	−	0.651052i
$490$	−3.63620	−	6.29809i	−0.164267	−	0.284519i
$491$	−4.84079	+	8.38450i	−0.218462	+	0.378387i	−0.954338	−	0.298729i	$-0.903437\pi$
$491$	−4.84079	+	8.38450i	−0.218462	+	0.378387i	0.735876	+	0.677116i	$0.236771\pi$
$492$	1.53885	+	19.6139i	0.0693766	+	0.884262i
$493$	10.6307	−	11.8066i	0.478783	−	0.531743i
$494$	−0.366212	+	1.12709i	−0.0164767	+	0.0507100i
$495$	12.0978	+	1.92213i	0.543754	+	0.0863933i
$496$	0.482017	−	5.54686i	0.0216432	−	0.249061i
$497$			11.5440i			0.517819i
$498$	21.4637	−	8.88444i	0.961811	−	0.398121i
$499$	26.1329	+	23.5301i	1.16987	+	1.05335i	0.997665	+	0.0682915i	$0.0217548\pi$
$499$	26.1329	+	23.5301i	1.16987	+	1.05335i	0.172202	+	0.985062i	$0.444912\pi$
$500$	0.587785	−	0.809017i	0.0262866	−	0.0361803i
$501$	−3.25833	−	17.6043i	−0.145571	−	0.786500i
$502$	23.0096	−	13.2846i	1.02697	−	0.592921i
$503$	−39.5009	−	4.15172i	−1.76126	−	0.185116i	−0.832058	−	0.554689i	$-0.812837\pi$
$503$	−39.5009	−	4.15172i	−1.76126	−	0.185116i	−0.929202	+	0.369573i	$0.879504\pi$
$504$	10.1009	−	5.14046i	0.449928	−	0.228974i
$505$	1.09103	+	10.3804i	0.0485501	+	0.461923i
$506$	9.63400	−	8.67450i	0.428284	−	0.385628i
$507$	−17.8652	+	37.4318i	−0.793422	+	1.66240i
$508$	−3.29205	−	15.4879i	−0.146061	−	0.687164i
$509$	19.8189	+	4.21264i	0.878457	+	0.186722i	0.625000	−	0.780625i	$-0.285099\pi$
$509$	19.8189	+	4.21264i	0.878457	+	0.186722i	0.253457	+	0.967347i	$0.418432\pi$
$510$	11.3798	−	3.36784i	0.503906	−	0.149130i
$511$	−18.4815	+	6.00502i	−0.817575	+	0.265646i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	0.131501	+	1.00451i	0.00580593	+	0.0443504i
$514$	−11.1448	−	2.36890i	−0.491576	−	0.104488i
$515$	−2.00691	−	9.44176i	−0.0884350	−	0.416054i
$516$	0.302901	+	0.144567i	0.0133345	+	0.00636419i
$517$	−14.8865	+	13.4039i	−0.654707	+	0.589501i
$518$	4.26774	+	40.6048i	0.187514	+	1.78407i
$519$	2.52007	+	0.605663i	0.110619	+	0.0265857i
$520$	6.04507	+	0.635362i	0.265094	+	0.0278625i
$521$	−17.2505	+	9.95960i	−0.755759	+	0.436338i	−0.827771	−	0.561066i	$-0.810391\pi$
$521$	−17.2505	+	9.95960i	−0.755759	+	0.436338i	0.0720117	+	0.997404i	$0.477058\pi$
$522$	4.38026	−	5.40379i	0.191719	−	0.236518i
$523$	11.9938	−	16.5080i	0.524452	−	0.721846i	−0.461820	−	0.886974i	$-0.652803\pi$
$523$	11.9938	−	16.5080i	0.524452	−	0.721846i	0.986272	+	0.165127i	$0.0528035\pi$
$524$	2.83831	+	2.55563i	0.123992	+	0.111643i
$525$	−2.50261	−	6.04600i	−0.109223	−	0.263869i
$526$		−	4.26625i		−	0.186017i
$527$	−26.0341	−	27.8854i	−1.13406	−	1.21471i
$528$	5.37891	−	4.59176i	0.234087	−	0.199831i
$529$	−3.99242	+	12.2874i	−0.173584	+	0.534235i
$530$	2.23631	−	2.48367i	0.0971389	−	0.107884i
$531$	−23.7790	−	23.8021i	−1.03192	−	1.03292i
$532$	0.368284	−	0.637886i	0.0159671	−	0.0276559i
$533$	34.5217	+	59.7933i	1.49530	+	2.58994i
$534$	−8.28430	+	5.69068i	−0.358497	+	0.246260i
$535$	9.63113	−	6.99743i	0.416390	−	0.302525i
$536$	9.75078	−	1.02485i	0.421169	−	0.0442667i
$537$	−25.6833	−	3.38763i	−1.10832	−	0.146187i
$538$	1.26894	+	2.85008i	0.0547077	+	0.122875i
$539$	−29.0456	+	6.17383i	−1.25108	+	0.265926i
$540$	4.89937	−	1.73094i	0.210835	−	0.0744877i
$541$	24.6729	+	10.9851i	1.06077	+	0.472286i	0.861552	−	0.507669i	$-0.169493\pi$
$541$	24.6729	+	10.9851i	1.06077	+	0.472286i	0.199219	+	0.979955i	$0.436159\pi$
$542$	−2.99062	−	9.20418i	−0.128458	−	0.395353i
$543$	15.8429	−	25.8392i	0.679886	−	1.10887i
$544$	2.78688	−	6.25944i	0.119487	−	0.268371i
$545$	2.20045	−	10.3523i	0.0942568	−	0.443443i
$546$	24.2204	−	31.5487i	1.03654	−	1.35016i
$547$	−6.60600	+	2.94118i	−0.282452	+	0.125756i	−0.543073	−	0.839685i	$-0.682739\pi$
$547$	−6.60600	+	2.94118i	−0.282452	+	0.125756i	0.260621	+	0.965441i	$0.416073\pi$
$548$	11.3224	+	12.5748i	0.483670	+	0.537170i
$549$	−1.17872	+	22.2840i	−0.0503066	+	0.951058i
$550$	−2.40003	−	3.30336i	−0.102338	−	0.140856i
$551$	0.0472546	−	0.449598i	0.00201312	−	0.0191535i
$552$	1.83692	−	5.18329i	0.0781844	−	0.220615i
$553$	20.2070	+	11.6665i	0.859287	+	0.496110i
$554$	−26.0243	−	18.9078i	−1.10567	−	0.803314i
$555$	−0.494548	+	18.7121i	−0.0209924	+	0.794286i
$556$	−6.52978	−	2.12165i	−0.276924	−	0.0899781i
$557$	−31.5183			−1.33547			−0.667737	−	0.744397i	$-0.732737\pi$
$557$	−31.5183			−1.33547			−0.667737	+	0.744397i	$0.732737\pi$
$558$	−12.0165	−	11.6019i	−0.508699	−	0.491147i
$559$	1.17785			0.0498175
$560$	−3.59298	−	1.16743i	−0.151831	−	0.0493329i
$561$	1.28026	−	48.4409i	0.0540525	−	2.04518i
$562$	21.0102	+	15.2648i	0.886264	+	0.643908i
$563$	−1.09405	−	0.631649i	−0.0461086	−	0.0266208i	0.476768	−	0.879029i	$-0.341808\pi$
$563$	−1.09405	−	0.631649i	−0.0461086	−	0.0266208i	−0.522877	+	0.852408i	$0.675141\pi$
$564$	−2.83841	+	8.00924i	−0.119519	+	0.337250i
$565$	0.0507220	−	0.482588i	0.00213389	−	0.0203026i
$566$	4.97065	+	6.84152i	0.208932	+	0.287570i
$567$	7.10154	−	33.2511i	0.298237	−	1.39641i
$568$	2.04465	+	2.27081i	0.0857914	+	0.0952811i
$569$	2.09538	−	0.932923i	0.0878429	−	0.0391102i	−0.362345	−	0.932044i	$-0.618024\pi$
$569$	2.09538	−	0.932923i	0.0878429	−	0.0391102i	0.450188	+	0.892934i	$0.351357\pi$
$570$	0.205641	−	0.267861i	0.00861334	−	0.0112195i
$571$	−1.50969	+	7.10253i	−0.0631785	+	0.297231i	−0.998381	−	0.0568822i	$-0.981884\pi$
$571$	−1.50969	+	7.10253i	−0.0631785	+	0.297231i	0.935202	+	0.354114i	$0.115217\pi$
$572$	10.0948	−	22.6733i	0.422085	−	0.948018i
$573$	10.3136	−	16.8211i	0.430856	−	0.702710i
$574$	−13.2607	−	40.8122i	−0.553491	−	1.70347i
$575$	−2.90045	−	1.29136i	−0.120957	−	0.0538536i
$576$	1.07647	−	2.80022i	0.0448527	−	0.116676i
$577$	−26.5290	+	5.63891i	−1.10442	+	0.234751i	−0.723819	−	0.689990i	$-0.757615\pi$
$577$	−26.5290	+	5.63891i	−1.10442	+	0.234751i	−0.380598	+	0.924741i	$0.624282\pi$
$578$	−12.1807	−	27.3582i	−0.506649	−	1.13795i
$579$	−36.9438	−	4.87288i	−1.53533	−	0.202510i
$580$	−2.30601	+	0.242371i	−0.0957517	+	0.0100639i
$581$	−40.9912	+	29.7819i	−1.70060	+	1.23556i
$582$	−18.5475	+	12.7407i	−0.768819	+	0.528119i
$583$	−6.82320	−	11.8181i	−0.282588	−	0.489457i
$584$	−2.57190	+	4.45465i	−0.106426	+	0.184335i
$585$	12.9004	−	12.8879i	0.533367	−	0.532848i
$586$	5.85675	−	6.50458i	0.241940	−	0.268702i
$587$	1.88101	−	5.78914i	0.0776375	−	0.238944i	−0.904704	−	0.426041i	$-0.859908\pi$
$587$	1.88101	−	5.78914i	0.0776375	−	0.238944i	0.982341	+	0.187097i	$0.0599080\pi$
$588$	−9.58020	+	8.17823i	−0.395081	+	0.337265i
$589$	−1.06571	−	0.206507i	−0.0439120	−	0.00850896i
$590$			11.2150i			0.461713i
$591$	2.18276	+	5.27327i	0.0897867	+	0.216914i
$592$	8.03134	+	7.23145i	0.330086	+	0.297211i
$593$	−12.9128	+	17.7730i	−0.530266	+	0.729849i	−0.987171	−	0.159667i	$-0.948958\pi$
$593$	−12.9128	+	17.7730i	−0.530266	+	0.729849i	0.456905	+	0.889516i	$0.348958\pi$
$594$	−0.539919	−	21.2099i	−0.0221531	−	0.870253i
$595$	−22.4174	+	12.9427i	−0.919023	+	0.530598i
$596$	3.79643	+	0.399021i	0.155508	+	0.0163445i
$597$	−0.128349	−	0.0308468i	−0.00525296	−	0.00126247i
$598$	−2.01724	−	19.1927i	−0.0824910	−	0.784849i
$599$	5.43492	−	4.89363i	0.222065	−	0.199948i	−0.550587	−	0.834777i	$-0.685596\pi$
$599$	5.43492	−	4.89363i	0.222065	−	0.199948i	0.772652	+	0.634829i	$0.218930\pi$
$600$	−1.56314	−	0.746047i	−0.0638150	−	0.0304572i
$601$	4.38550	+	20.6321i	0.178888	+	0.841602i	0.972450	+	0.233113i	$0.0748910\pi$
$601$	4.38550	+	20.6321i	0.178888	+	0.841602i	−0.793562	+	0.608490i	$0.791776\pi$
$602$	−0.716069	−	0.152205i	−0.0291848	−	0.00620342i
$603$	16.0317	−	24.6604i	0.652862	−	1.00425i
$604$	3.76373	−	1.22291i	0.153144	−	0.0497596i
$605$	−5.39467	+	1.75284i	−0.219325	+	0.0712629i
$606$	17.3352	−	5.13035i	0.704196	−	0.208406i
$607$	8.16587	+	1.73571i	0.331442	+	0.0704503i	0.370627	−	0.928782i	$-0.379143\pi$
$607$	8.16587	+	1.73571i	0.331442	+	0.0704503i	−0.0391847	+	0.999232i	$0.512476\pi$
$608$	−0.0405362	−	0.190708i	−0.00164396	−	0.00773422i
$609$	−6.53523	+	13.6928i	−0.264821	+	0.554861i
$610$	5.52779	−	4.97725i	0.223814	−	0.201523i
$611$	3.11704	+	29.6567i	0.126102	+	1.19978i
$612$	−9.32306	−	18.3196i	−0.376863	−	0.740524i
$613$	28.6072	+	3.00674i	1.15544	+	0.121441i	0.662801	−	0.748795i	$-0.269367\pi$
$613$	28.6072	+	3.00674i	1.15544	+	0.121441i	0.492634	+	0.870237i	$0.336034\pi$
$614$	−5.00671	+	2.89062i	−0.202054	+	0.116656i
$615$	−3.58063	−	19.3456i	−0.144385	−	0.780089i
$616$	−9.06703	+	12.4797i	−0.365321	+	0.502821i
$617$	27.2062	+	24.4966i	1.09528	+	0.986196i	0.999957	−	0.00925034i	$-0.00294452\pi$
$617$	27.2062	+	24.4966i	1.09528	+	0.986196i	0.0953243	+	0.995446i	$0.469611\pi$
$618$	−15.4479	+	6.39431i	−0.621404	+	0.257217i
$619$			30.5542i			1.22808i	0.789276	+	0.614038i	$0.210456\pi$
$619$			30.5542i			1.22808i	−0.789276	+	0.614038i	$0.789544\pi$
$620$	0.100428	+	5.56686i	0.00403328	+	0.223570i
$621$	−8.60965	−	14.0727i	−0.345493	−	0.564718i
$622$	7.22015	−	22.2213i	0.289502	−	0.890995i
$623$	14.6686	−	16.2911i	0.587685	−	0.652690i
$624$	−0.823468	−	10.4958i	−0.0329651	−	0.420168i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	2.75493	+	4.77168i	0.110109	+	0.190715i
$627$	−0.780722	−	1.13655i	−0.0311790	−	0.0453894i
$628$	−13.7445	+	9.98600i	−0.548467	+	0.398485i
$629$	73.6435	−	7.74024i	2.93636	−	0.308624i
$630$	−9.50820	+	6.16813i	−0.378816	+	0.245744i
$631$	8.15980	+	18.3272i	0.324836	+	0.729595i	0.999967	−	0.00810345i	$-0.00257944\pi$
$631$	8.15980	+	18.3272i	0.324836	+	0.729595i	−0.675131	+	0.737698i	$0.735913\pi$
$632$	6.04124	−	1.28410i	0.240308	−	0.0510790i
$633$	2.90280	−	1.57518i	0.115376	−	0.0626078i
$634$	11.6288	+	5.17749i	0.461840	+	0.205624i
$635$	4.89295	+	15.0589i	0.194171	+	0.597596i
$636$	−4.93494	−	3.02579i	−0.195683	−	0.119980i
$637$	−17.9795	+	40.3827i	−0.712375	+	1.60002i
$638$	−1.96844	+	9.26079i	−0.0779314	+	0.366638i
$639$	9.15470	−	0.475313i	0.362154	−	0.0188031i
$640$	−0.913545	+	0.406737i	−0.0361111	+	0.0160777i
$641$	16.7323	+	18.5831i	0.660887	+	0.733989i	0.976647	−	0.214850i	$-0.0689262\pi$
$641$	16.7323	+	18.5831i	0.660887	+	0.733989i	−0.315760	+	0.948839i	$0.602260\pi$
$642$	−14.9535	−	14.1972i	−0.590167	−	0.560320i
$643$	14.1651	+	19.4966i	0.558616	+	0.768869i	0.991150	−	0.132749i	$-0.0423803\pi$
$643$	14.1651	+	19.4966i	0.558616	+	0.768869i	−0.432534	+	0.901618i	$0.642380\pi$
$644$	−1.25377	+	11.9289i	−0.0494056	+	0.470063i
$645$	−0.316353	−	0.112113i	−0.0124564	−	0.00441444i
$646$	−1.15691	−	0.667943i	−0.0455180	−	0.0262799i
$647$	14.2925	+	10.3841i	0.561895	+	0.408241i	0.832152	−	0.554548i	$-0.187109\pi$
$647$	14.2925	+	10.3841i	0.561895	+	0.408241i	−0.270257	+	0.962788i	$0.587109\pi$
$648$	−4.49242	−	7.79860i	−0.176479	−	0.306358i
$649$	43.5514	+	14.1507i	1.70954	+	0.555464i
$650$	−6.07836			−0.238413
$651$	31.3977	+	18.4802i	1.23057	+	0.724296i
$652$	10.0842			0.394929
$653$	−5.75041	−	1.86842i	−0.225031	−	0.0731169i	0.194331	−	0.980936i	$-0.437746\pi$
$653$	−5.75041	−	1.86842i	−0.225031	−	0.0731169i	−0.419362	+	0.907819i	$0.637746\pi$
$654$	−18.3249	−	0.484313i	−0.716559	−	0.0189381i
$655$	−3.08990	−	2.24495i	−0.120732	−	0.0877173i
$656$	−9.83708	−	5.67944i	−0.384073	−	0.221745i
$657$	5.52310	+	14.4091i	0.215477	+	0.562153i
$658$	1.93733	−	18.4325i	0.0755251	−	0.718574i
$659$	−6.02205	−	8.28864i	−0.234586	−	0.322880i	0.675453	−	0.737403i	$-0.263948\pi$
$659$	−6.02205	−	8.28864i	−0.234586	−	0.322880i	−0.910039	+	0.414524i	$0.863948\pi$
$660$	−4.86947	+	5.12885i	−0.189544	+	0.199640i
$661$	−12.3972	−	13.7685i	−0.482195	−	0.535531i	0.452131	−	0.891951i	$-0.350664\pi$
$661$	−12.3972	−	13.7685i	−0.482195	−	0.535531i	−0.934326	+	0.356420i	$0.883997\pi$
$662$	−18.6804	+	8.31706i	−0.726036	+	0.323252i
$663$	−57.2187	−	43.9276i	−2.22219	−	1.70601i
$664$	−2.78846	+	13.1187i	−0.108213	+	0.509102i
$665$	−0.299589	+	0.672888i	−0.0116176	+	0.0260935i
$666$	32.0250	−	5.05630i	1.24094	−	0.195928i
$667$	2.27491	+	7.00145i	0.0880849	+	0.271097i
$668$	9.44282	+	4.20421i	0.365353	+	0.162666i
$669$	−15.0087	−	27.6586i	−0.580270	−	1.06934i
$670$	−9.59023	+	2.03847i	−0.370503	+	0.0787529i
$671$	−12.3535	−	27.7464i	−0.476901	−	1.07114i
$672$	−0.855674	+	6.48730i	−0.0330083	+	0.250253i
$673$	28.3449	−	2.97917i	1.09261	−	0.114838i	0.458962	−	0.888456i	$-0.348222\pi$
$673$	28.3449	−	2.97917i	1.09261	−	0.114838i	0.633653	+	0.773618i	$0.281555\pi$
$674$	−13.1624	+	9.56303i	−0.506996	+	0.368354i
$675$	−4.69160	+	2.23358i	−0.180580	+	0.0859705i
$676$	−11.9733	−	20.7383i	−0.460510	−	0.797626i
$677$	−6.01713	+	10.4220i	−0.231257	+	0.400549i	−0.958178	−	0.286172i	$-0.907617\pi$
$677$	−6.01713	+	10.4220i	−0.231257	+	0.400549i	0.726921	+	0.686721i	$0.240951\pi$
$678$	−0.837896	+	0.0657388i	−0.0321792	+	0.00252468i
$679$	32.8411	−	36.4738i	1.26033	−	1.39974i
$680$	−2.11733	+	6.51646i	−0.0811958	+	0.249895i
$681$	−14.0805	−	16.4942i	−0.539564	−	0.632060i
$682$	21.7447	+	6.63410i	0.832646	+	0.254033i
$683$			20.8488i			0.797758i	0.917003	+	0.398879i	$0.130601\pi$
$683$			20.8488i			0.797758i	−0.917003	+	0.398879i	$0.869399\pi$
$684$	−0.521025	−	0.265795i	−0.0199219	−	0.0101629i
$685$	−12.5748	−	11.3224i	−0.480460	−	0.432608i
$686$	0.604903	−	0.832578i	0.0230953	−	0.0317880i
$687$	27.2432	−	5.04237i	1.03939	−	0.192379i
$688$	−0.167816	+	0.0968884i	−0.00639791	+	0.00369383i
$689$	−20.2033	−	2.12345i	−0.769683	−	0.0808969i
$690$	−1.28505	+	5.34691i	−0.0489212	+	0.203553i
$691$	0.706793	+	6.72469i	0.0268877	+	0.255819i	0.999706	+	0.0242493i	$0.00771954\pi$
$691$	0.706793	+	6.72469i	0.0268877	+	0.255819i	−0.972818	+	0.231570i	$0.925614\pi$
$692$	−1.11204	+	1.00128i	−0.0422733	+	0.0380630i
$693$	11.9557	+	44.7062i	0.454159	+	1.69825i
$694$	4.27272	+	20.1016i	0.162190	+	0.763046i
$695$	6.71578	+	1.42748i	0.254744	+	0.0541475i
$696$	1.13970	+	3.85101i	0.0432003	+	0.145972i
$697$	−74.0197	+	24.0505i	−2.80370	+	0.910976i
$698$	−21.9239	+	7.12351i	−0.829832	+	0.269629i
$699$	−5.16778	−	17.4617i	−0.195463	−	0.660463i
$700$	3.69533	+	0.785466i	0.139670	+	0.0296878i
$701$	−4.20247	−	19.7711i	−0.158725	−	0.746743i	−0.983446	−	0.181203i	$-0.942001\pi$
$701$	−4.20247	−	19.7711i	−0.158725	−	0.746743i	0.824721	−	0.565540i	$-0.191332\pi$
$702$	−26.0162	−	17.9084i	−0.981919	−	0.675910i
$703$	1.56586	−	1.40990i	0.0590574	−	0.0531755i
$704$	0.426808	+	4.06080i	0.0160859	+	0.153047i
$705$	1.98567	−	8.26205i	0.0747846	−	0.311167i
$706$	10.2873	+	1.08124i	0.387167	+	0.0406928i
$707$	−34.1492	+	19.7160i	−1.28431	+	0.741498i
$708$	19.1005	−	3.53526i	0.717840	−	0.132863i
$709$	−9.12653	+	12.5616i	−0.342754	+	0.471760i	−0.945243	−	0.326367i	$-0.894176\pi$
$709$	−9.12653	+	12.5616i	−0.342754	+	0.471760i	0.602489	+	0.798127i	$0.294176\pi$
$710$	−2.27081	−	2.04465i	−0.0852220	−	0.0767342i
$711$	8.41984	−	16.5050i	0.315769	−	0.618987i
$712$		−	5.80268i		−	0.217465i
$713$	17.2219	−	3.98661i	0.644966	−	0.149300i
$714$	29.1095	+	34.0997i	1.08940	+	1.27615i
$715$	−7.66949	+	23.6043i	−0.286823	+	0.882750i
$716$	10.0080	−	11.1150i	0.374017	−	0.415387i
$717$	−34.8424	+	2.73363i	−1.30121	+	0.102089i
$718$	−7.25183	+	12.5605i	−0.270636	+	0.468755i
$719$	−19.8713	−	34.4182i	−0.741076	−	1.28358i	−0.952006	−	0.306080i	$-0.900983\pi$
$719$	−19.8713	−	34.4182i	−0.741076	−	1.28358i	0.210930	−	0.977501i	$-0.432351\pi$
$720$	−0.777866	+	2.89740i	−0.0289894	+	0.107980i
$721$	29.5022	−	21.4346i	1.09872	−	0.798267i
$722$	18.8581	−	1.98207i	0.701826	−	0.0737649i
$723$	2.43818	−	18.4851i	0.0906770	−	0.687468i
$724$	7.11756	+	15.9863i	0.264522	+	0.594126i
$725$	2.26804	−	0.482087i	0.0842328	−	0.0179042i
$726$	4.68584	+	8.63526i	0.173908	+	0.320484i
$727$	−3.78705	−	1.68610i	−0.140454	−	0.0625340i	0.335306	−	0.942109i	$-0.391160\pi$
$727$	−3.78705	−	1.68610i	−0.140454	−	0.0625340i	−0.475760	+	0.879575i	$0.657827\pi$
$728$	7.09607	+	21.8394i	0.262998	+	0.809424i
$729$	−26.6614	−	4.26263i	−0.987459	−	0.157875i
$730$	2.09217	−	4.69909i	0.0774346	−	0.173921i
$731$	−0.276049	+	1.29871i	−0.0102100	+	0.0480344i
$732$	−10.2194	−	7.84556i	−0.377719	−	0.289980i
$733$	22.8799	−	10.1868i	0.845088	−	0.376257i	0.0619303	−	0.998080i	$-0.480274\pi$
$733$	22.8799	−	10.1868i	0.845088	−	0.376257i	0.783158	+	0.621823i	$0.213608\pi$
$734$	14.3875	+	15.9789i	0.531051	+	0.589792i
$735$	8.67286	−	9.13484i	0.319903	−	0.336944i
$736$	1.86618	+	2.56858i	0.0687884	+	0.0946792i
$737$	−4.18463	+	39.8141i	−0.154143	+	1.46657i
$738$	−31.8192	+	12.1965i	−1.17128	+	0.448959i
$739$	−10.0653	−	5.81119i	−0.370257	−	0.213768i	0.303314	−	0.952891i	$-0.401907\pi$
$739$	−10.0653	−	5.81119i	−0.370257	−	0.213768i	−0.673571	+	0.739123i	$0.735240\pi$
$740$	−8.74324	−	6.35233i	−0.321408	−	0.233516i
$741$	−2.05192	−	0.0542306i	−0.0753790	−	0.00199221i
$742$	12.0081	+	3.90168i	0.440832	+	0.143235i
$743$	−13.7011			−0.502645			−0.251323	−	0.967903i	$-0.580866\pi$
$743$	−13.7011			−0.502645			−0.251323	+	0.967903i	$0.580866\pi$
$744$	9.44939	−	1.92587i	0.346432	−	0.0706057i
$745$	−3.81734			−0.139857
$746$	20.6053	+	6.69507i	0.754414	+	0.245124i
$747$	25.3056	+	31.2809i	0.925884	+	1.14451i
$748$	22.6340	+	16.4445i	0.827580	+	0.601272i
$749$	38.9492	+	22.4873i	1.42317	+	0.821670i
$750$	1.63256	+	0.578567i	0.0596127	+	0.0211263i
$751$	−3.15257	+	29.9947i	−0.115039	+	1.09452i	0.772890	+	0.634540i	$0.218810\pi$
$751$	−3.15257	+	29.9947i	−0.115039	+	1.09452i	−0.887929	+	0.459981i	$0.847856\pi$
$752$	−2.88363	−	3.96898i	−0.105155	−	0.144734i
$753$	33.3734	+	31.6856i	1.21620	+	1.15469i
$754$	9.43069	+	10.4738i	0.343446	+	0.381435i
$755$	−3.61529	+	1.60963i	−0.131574	+	0.0585804i
$756$	13.5023	+	14.2493i	0.491075	+	0.518242i
$757$	2.50848	−	11.8015i	0.0911724	−	0.428932i	−0.908760	−	0.417319i	$-0.862970\pi$
$757$	2.50848	−	11.8015i	0.0911724	−	0.428932i	0.999933	−	0.0116136i	$-0.00369681\pi$
$758$	−7.49292	+	16.8294i	−0.272155	+	0.611270i
$759$	19.1423	+	11.7368i	0.694823	+	0.426021i
$760$	0.0602485	+	0.185426i	0.00218544	+	0.00672610i
$761$	18.7679	+	8.35601i	0.680336	+	0.302905i	0.717656	−	0.696398i	$-0.245215\pi$
$761$	18.7679	+	8.35601i	0.680336	+	0.302905i	−0.0373193	+	0.999303i	$0.511882\pi$
$762$	24.1049	−	13.0803i	0.873227	−	0.473849i
$763$	39.1097	−	8.31303i	1.41587	−	0.300952i
$764$	4.63345	+	10.4069i	0.167632	+	0.376509i
$765$	11.1869	+	17.2447i	0.404463	+	0.623483i
$766$	15.7238	−	1.65264i	0.568126	−	0.0597124i
$767$	55.1496	−	40.0685i	1.99134	−	1.44679i
$768$	0.980697	+	1.42767i	0.0353879	+	0.0515165i
$769$	−1.01455	−	1.75725i	−0.0365855	−	0.0633680i	0.847153	−	0.531349i	$-0.178315\pi$
$769$	−1.01455	−	1.75725i	−0.0365855	−	0.0633680i	−0.883738	+	0.467981i	$0.844981\pi$
$770$	7.71288	−	13.3591i	0.277953	−	0.481428i
$771$	−1.54358	−	19.6742i	−0.0555906	−	0.708548i
$772$	14.3958	−	15.9882i	0.518118	−	0.575428i
$773$	5.59205	−	17.2106i	0.201132	−	0.619021i	−0.798718	−	0.601706i	$-0.794488\pi$
$773$	5.59205	−	17.2106i	0.201132	−	0.619021i	0.999850	−	0.0173156i	$-0.00551201\pi$
$774$	−0.0912193	+	0.574129i	−0.00327881	+	0.0206366i
$775$	−0.681773	−	5.52587i	−0.0244900	−	0.198495i
$776$		−	12.9915i		−	0.466367i
$777$	−65.3406	+	27.0463i	−2.34408	+	0.970282i
$778$	−7.28891	−	6.56296i	−0.261320	−	0.235294i
$779$	−1.30172	+	1.79167i	−0.0466390	+	0.0641931i
$780$	1.91606	+	10.3522i	0.0686061	+	0.370669i
$781$	−10.8053	+	6.23842i	−0.386643	+	0.223228i
$782$	21.6349	+	2.27392i	0.773663	+	0.0813153i
$783$	11.1279	+	4.61883i	0.397678	+	0.165063i
$784$	−0.760174	−	7.23257i	−0.0271491	−	0.258306i
$785$	12.6254	−	11.3680i	0.450621	−	0.405741i
$786$	−2.84940	+	5.97015i	−0.101635	+	0.212948i
$787$	−6.43550	−	30.2767i	−0.229401	−	1.07925i	−0.930531	−	0.366213i	$-0.880654\pi$
$787$	−6.43550	−	30.2767i	−0.229401	−	1.07925i	0.701130	−	0.713033i	$-0.252679\pi$
$788$	−3.22304	−	0.685077i	−0.114816	−	0.0244049i
$789$	7.08557	−	2.09697i	0.252253	−	0.0746540i
$790$	−5.87392	+	1.90855i	−0.208985	+	0.0679032i
$791$	1.74348	−	0.566491i	0.0619910	−	0.0201421i
$792$	10.2701	+	6.67656i	0.364931	+	0.237241i
$793$	−44.2252	−	9.40035i	−1.57048	−	0.333816i
$794$	3.23313	+	15.2107i	0.114739	+	0.539807i
$795$	5.22419	+	2.49337i	0.185283	+	0.0884307i
$796$	0.0566367	−	0.0509959i	0.00200743	−	0.00180750i
$797$	−1.99737	−	19.0037i	−0.0707506	−	0.673147i	−0.971213	−	0.238213i	$-0.923438\pi$
$797$	−1.99737	−	19.0037i	−0.0707506	−	0.673147i	0.900462	−	0.434934i	$-0.143228\pi$
$798$	1.24045	+	0.298125i	0.0439115	+	0.0105535i
$799$	−33.4304	−	3.51367i	−1.18268	−	0.124305i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−13.5233	−	10.9618i	−0.477821	−	0.387317i
$802$	−21.7479	+	29.9334i	−0.767945	+	1.05699i
$803$	−15.6083	−	14.0537i	−0.550803	−	0.495946i
$804$	6.49486	+	15.6908i	0.229056	+	0.553371i
$805$		−	11.9946i		−	0.422753i
$806$	27.0162	−	20.3830i	0.951606	−	0.717960i
$807$	−4.10982	+	3.50839i	−0.144672	+	0.123501i
$808$	−3.22540	+	9.92675i	−0.113469	+	0.349222i
$809$	18.4164	−	20.4535i	0.647486	−	0.719106i	−0.326631	−	0.945152i	$-0.605913\pi$
$809$	18.4164	−	20.4535i	0.647486	−	0.719106i	0.974117	+	0.226046i	$0.0725800\pi$
$810$	5.28298	+	7.28629i	0.185625	+	0.256014i
$811$	−18.8309	+	32.6161i	−0.661243	+	1.14531i	0.319046	+	0.947739i	$0.396638\pi$
$811$	−18.8309	+	32.6161i	−0.661243	+	1.14531i	−0.980289	+	0.197568i	$0.936696\pi$
$812$	−4.37991	−	7.58622i	−0.153705	−	0.266224i
$813$	13.8167	−	9.49103i	0.484574	−	0.332865i
$814$	−35.7001	+	25.9377i	−1.25129	+	0.909115i
$815$	−10.0290	+	1.05409i	−0.351300	+	0.0369232i
$816$	11.7658	+	1.55190i	0.411885	+	0.0543275i
$817$	0.0153666	+	0.0345140i	0.000537610	+	0.00120749i
$818$	26.2449	−	5.57852i	0.917631	−	0.195048i
$819$	64.3024	+	24.7193i	2.24691	+	0.863761i
$820$	10.3769	+	4.62007i	0.362375	+	0.161340i
$821$	10.0379	+	30.8935i	0.350325	+	1.07819i	0.958671	+	0.284518i	$0.0918334\pi$
$821$	10.0379	+	30.8935i	0.350325	+	1.07819i	−0.608346	+	0.793672i	$0.708167\pi$
$822$	−15.3196	+	24.9856i	−0.534332	+	0.871474i
$823$	14.4593	−	32.4762i	0.504021	−	1.13205i	−0.465054	−	0.885282i	$-0.653965\pi$
$823$	14.4593	−	32.4762i	0.504021	−	1.13205i	0.969075	−	0.246767i	$-0.0793683\pi$
$824$	2.00691	−	9.44176i	0.0699140	−	0.328919i
$825$	4.30668	−	5.60976i	0.149940	−	0.195307i
$826$	−38.7059	+	17.2330i	−1.34675	+	0.599612i
$827$	−9.20762	−	10.2261i	−0.320180	−	0.355596i	0.561472	−	0.827496i	$-0.310235\pi$
$827$	−9.20762	−	10.2261i	−0.320180	−	0.355596i	−0.881652	+	0.471899i	$0.843569\pi$
$828$	9.51153	+	0.503116i	0.330548	+	0.0174845i
$829$	−13.6674	−	18.8116i	−0.474689	−	0.653353i	0.502785	−	0.864412i	$-0.332309\pi$
$829$	−13.6674	−	18.8116i	−0.474689	−	0.653353i	−0.977473	+	0.211059i	$0.932309\pi$
$830$	1.40191	−	13.3383i	0.0486609	−	0.462978i
$831$	18.6112	−	52.5159i	0.645617	−	1.82176i
$832$	5.26402	+	3.03918i	0.182497	+	0.105365i
$833$	−40.3126	−	29.2888i	−1.39675	−	1.01480i
$834$	0.314185	−	11.8878i	0.0108793	−	0.411640i
$835$	−9.83055	−	3.19414i	−0.340200	−	0.110538i
$836$	0.796089			0.0275333
$837$	13.3625	−	25.6601i	0.461877	−	0.886944i
$838$	11.7064			0.404389
$839$	23.7425	+	7.71439i	0.819681	+	0.266330i	0.688693	−	0.725054i	$-0.258185\pi$
$839$	23.7425	+	7.71439i	0.819681	+	0.266330i	0.130988	+	0.991384i	$0.458185\pi$
$840$	0.172879	−	6.54120i	0.00596489	−	0.225693i
$841$	19.1119	+	13.8856i	0.659031	+	0.478814i
$842$	−9.01792	−	5.20650i	−0.310778	−	0.179428i
$843$	−15.0254	+	42.3978i	−0.517504	+	1.46026i
$844$	−0.199313	+	1.89634i	−0.00686064	+	0.0652746i
$845$	14.0754	+	19.3731i	0.484209	+	0.666456i
$846$	−14.6972	−	0.777417i	−0.505302	−	0.0267281i
$847$	−14.3390	−	15.9251i	−0.492693	−	0.547191i
$848$	3.05317	−	1.35936i	0.104846	−	0.0466805i
$849$	−8.91949	+	11.6183i	−0.306116	+	0.398738i
$850$	1.42457	−	6.70208i	0.0488624	−	0.229880i
$851$	−13.9561	+	31.3459i	−0.478408	+	1.07452i
$852$	−2.76647	+	4.51200i	−0.0947775	+	0.154579i
$853$	14.3320	+	44.1094i	0.490719	+	1.51028i	0.823524	+	0.567281i	$0.192005\pi$
$853$	14.3320	+	44.1094i	0.490719	+	1.51028i	−0.332805	+	0.942996i	$0.607995\pi$
$854$	25.6719	+	11.4298i	0.878473	+	0.391121i
$855$	0.545954	+	0.209877i	0.0186712	+	0.00717763i
$856$	11.6446	−	2.47513i	0.398004	−	0.0845983i
$857$	−15.1243	−	33.9697i	−0.516635	−	1.16038i	−0.963969	−	0.266014i	$-0.914293\pi$
$857$	−15.1243	−	33.9697i	−0.516635	−	1.16038i	0.447334	−	0.894367i	$-0.352374\pi$
$858$	42.6186	+	5.62139i	1.45498	+	0.191911i
$859$	−42.3173	+	4.44773i	−1.44385	+	0.151754i	−0.793818	−	0.608155i	$-0.791910\pi$
$859$	−42.3173	+	4.44773i	−1.44385	+	0.151754i	−0.650029	+	0.759910i	$0.725243\pi$
$860$	0.156769	−	0.113899i	0.00534577	−	0.00388393i
$861$	61.2648	−	42.0842i	2.08790	−	1.43423i
$862$	9.29064	+	16.0919i	0.316441	+	0.548091i
$863$	3.08762	−	5.34792i	0.105104	−	0.182045i	−0.808677	−	0.588253i	$-0.799816\pi$
$863$	3.08762	−	5.34792i	0.105104	−	0.182045i	0.913781	+	0.406208i	$0.133149\pi$
$864$	5.17984	+	0.411464i	0.176222	+	0.0139983i
$865$	1.00128	−	1.11204i	0.0340446	−	0.0378104i
$866$	−10.4426	+	32.1392i	−0.354856	+	1.09213i
$867$	39.4507	−	33.6775i	1.33981	−	1.14375i
$868$	−19.0584	+	8.90066i	−0.646884	+	0.302108i
$869$			25.2185i			0.855479i
$870$	−1.53600	−	3.71078i	−0.0520753	−	0.125807i
$871$	44.2879	+	39.8770i	1.50064	+	1.35118i
$872$	6.22086	−	8.56228i	0.210665	−	0.289956i
$873$	−30.2769	−	24.5421i	−1.02472	−	0.830626i
$874$	0.536081	−	0.309506i	0.0181332	−	0.0104692i
$875$	−3.75719	−	0.394896i	−0.127016	−	0.0133499i
$876$	−8.66264	−	2.08194i	−0.292683	−	0.0703423i
$877$	−1.71737	−	16.3397i	−0.0579915	−	0.551752i	−0.984488	−	0.175450i	$-0.943862\pi$
$877$	−1.71737	−	16.3397i	−0.0579915	−	0.551752i	0.926497	−	0.376303i	$-0.122805\pi$
$878$	7.06820	−	6.36424i	0.238540	−	0.214783i
$879$	13.6818	+	6.52998i	0.461477	+	0.220251i
$880$	−0.848939	−	3.99395i	−0.0286177	−	0.134636i
$881$	2.01413	+	0.428117i	0.0678578	+	0.0144236i	0.241715	−	0.970347i	$-0.422290\pi$
$881$	2.01413	+	0.428117i	0.0678578	+	0.0144236i	−0.173858	+	0.984771i	$0.555623\pi$
$882$	−18.2917	−	11.8914i	−0.615913	−	0.400405i
$883$	13.5584	−	4.40539i	0.456276	−	0.148253i	−0.0718567	−	0.997415i	$-0.522892\pi$
$883$	13.5584	−	4.40539i	0.456276	−	0.148253i	0.528133	+	0.849162i	$0.322892\pi$
$884$	39.6094	−	12.8699i	1.33221	−	0.432861i
$885$	−18.6263	+	5.51244i	−0.626117	+	0.185299i
$886$	−22.3994	−	4.76114i	−0.752523	−	0.159954i
$887$	−8.77839	−	41.2991i	−0.294749	−	1.38669i	−0.837337	−	0.546687i	$-0.815889\pi$
$887$	−8.77839	−	41.2991i	−0.294749	−	1.38669i	0.542588	−	0.839999i	$-0.317445\pi$
$888$	−8.06271	+	16.8932i	−0.270567	+	0.566900i
$889$	−44.4539	+	40.0265i	−1.49094	+	1.34245i
$890$	0.606546	+	5.77090i	0.0203315	+	0.193441i
$891$	34.9610	−	11.3219i	1.17124	−	0.379299i
$892$	18.0688	+	1.89910i	0.604987	+	0.0635867i
$893$	−0.828354	+	0.478250i	−0.0277198	+	0.0160040i
$894$	1.20333	+	6.50140i	0.0402453	+	0.217439i
$895$	−8.79134	+	12.1002i	−0.293862	+	0.404466i
$896$	−2.80751	−	2.52790i	−0.0937925	−	0.0844511i
$897$	30.8846	−	12.7840i	1.03121	−	0.426846i
$898$			15.7441i			0.525387i
$899$	−8.46403	+	9.74827i	−0.282291	+	0.325123i
$900$	0.470744	−	2.96284i	0.0156915	−	0.0987612i
$901$	7.07633	−	21.7787i	0.235747	−	0.725554i
$902$	31.0345	−	34.4672i	1.03333	−	1.14763i
$903$	−0.0991768	−	1.26409i	−0.00330040	−	0.0420663i
$904$	0.242623	−	0.420235i	0.00806952	−	0.0139768i
$905$	−8.74960	−	15.1547i	−0.290846	−	0.503761i
$906$	3.88104	+	5.64988i	0.128939	+	0.187705i
$907$	−30.9168	+	22.4623i	−1.02657	+	0.745850i	−0.967620	−	0.252411i	$-0.918777\pi$
$907$	−30.9168	+	22.4623i	−1.02657	+	0.745850i	−0.0589541	+	0.998261i	$0.518777\pi$
$908$	12.4523	−	1.30879i	0.413244	−	0.0434337i
$909$	17.0414	+	26.2694i	0.565228	+	0.871302i
$910$	−9.34004	−	20.9781i	−0.309619	−	0.695416i
$911$	−33.7099	+	7.16526i	−1.11686	+	0.237395i	−0.729128	−	0.684377i	$-0.760074\pi$
$911$	−33.7099	+	7.16526i	−1.11686	+	0.237395i	−0.387730	+	0.921773i	$0.626741\pi$
$912$	0.296811	−	0.161062i	0.00982840	−	0.00533329i
$913$	−50.0279	−	22.2739i	−1.65568	−	0.737158i
$914$	−0.760402	−	2.34028i	−0.0251519	−	0.0774095i
$915$	10.9835	+	6.73436i	0.363103	+	0.222631i
$916$	−6.50616	+	14.6131i	−0.214970	+	0.482830i
$917$	2.99995	−	14.1137i	0.0990672	−	0.466075i
$918$	25.8434	−	24.4887i	0.852960	−	0.808247i
$919$	39.0558	−	17.3888i	1.28833	−	0.573603i	0.355758	−	0.934578i	$-0.384223\pi$
$919$	39.0558	−	17.3888i	1.28833	−	0.573603i	0.932575	+	0.360976i	$0.117556\pi$
$920$	−2.12445	−	2.35944i	−0.0700411	−	0.0777885i
$921$	−7.26180	−	6.89455i	−0.239284	−	0.227183i
$922$	−15.2478	−	20.9869i	−0.502161	−	0.691166i
$923$	−1.94146	+	18.4718i	−0.0639039	+	0.608005i
$924$	−25.1835	−	8.92484i	−0.828476	−	0.293606i
$925$	9.35934	+	5.40362i	0.307733	+	0.177670i
$926$	21.7652	+	15.8133i	0.715249	+	0.519659i
$927$	−18.2130	−	22.5135i	−0.598192	−	0.739441i
$928$	−2.20522	−	0.716520i	−0.0723900	−	0.0235209i
$929$	−22.4936			−0.737992			−0.368996	−	0.929431i	$-0.620298\pi$
$929$	−22.4936			−0.737992			−0.368996	+	0.929431i	$0.620298\pi$
$930$	−9.19632	+	2.90305i	−0.301559	+	0.0951946i
$931$	−1.41789			−0.0464694
$932$	9.99918	+	3.24893i	0.327534	+	0.106422i
$933$	40.4551	+	1.06920i	1.32444	+	0.0350039i
$934$	15.8255	+	11.4979i	0.517827	+	0.376224i
$935$	−24.2289	−	13.9886i	−0.792370	−	0.457475i
$936$	17.0271	−	6.52659i	0.556548	−	0.213328i
$937$	2.89171	−	27.5128i	0.0944679	−	0.898802i	−0.839960	−	0.542649i	$-0.817421\pi$
$937$	2.89171	−	27.5128i	0.0944679	−	0.898802i	0.934427	−	0.356153i	$-0.115912\pi$
$938$	−21.7717	−	29.9662i	−0.710871	−	0.978430i
$939$	−6.57090	+	6.92091i	−0.214433	+	0.225856i
$940$	3.28271	+	3.64582i	0.107070	+	0.118913i
$941$	−24.6276	+	10.9649i	−0.802836	+	0.357446i	−0.766785	−	0.641904i	$-0.778145\pi$
$941$	−24.6276	+	10.9649i	−0.802836	+	0.357446i	−0.0360511	+	0.999350i	$0.511478\pi$
$942$	−23.3410	−	17.9192i	−0.760490	−	0.583838i
$943$	7.49808	−	35.2757i	0.244171	−	1.14873i
$944$	−4.56154	+	10.2454i	−0.148465	+	0.333459i
$945$	−14.9178	−	12.7598i	−0.485277	−	0.415078i
$946$	−0.244502	−	0.752498i	−0.00794943	−	0.0244658i
$947$	45.1034	+	20.0813i	1.46566	+	0.652556i	0.975685	−	0.219178i	$-0.0703375\pi$
$947$	45.1034	+	20.0813i	1.46566	+	0.652556i	0.489980	+	0.871734i	$0.337004\pi$
$948$	5.10212	+	9.40239i	0.165709	+	0.305375i
$949$	−30.5826	+	6.50053i	−0.992753	+	0.211016i
$950$	−0.0793007	−	0.178112i	−0.00257286	−	0.00577873i
$951$	−2.88314	+	21.8585i	−0.0934921	+	0.708811i
$952$	−25.7435	+	2.70576i	−0.834353	+	0.0876940i
$953$	39.0946	−	28.4039i	1.26640	−	0.920093i	0.267346	−	0.963601i	$-0.413853\pi$
$953$	39.0946	−	28.4039i	1.26640	−	0.920093i	0.999053	+	0.0435081i	$0.0138534\pi$
$954$	2.59971	−	9.68342i	0.0841688	−	0.313512i
$955$	−5.69589	−	9.86557i	−0.184315	−	0.319242i
$956$	10.0891	−	17.4748i	0.326303	−	0.565174i
$957$	−16.3483	+	1.28264i	−0.528465	+	0.0414618i
$958$	24.9155	−	27.6715i	0.804984	−	0.894025i
$959$	19.7542	−	60.7972i	0.637897	−	1.96324i
$960$	−1.12456	−	1.31734i	−0.0362949	−	0.0425168i
$961$	21.5605	+	22.2743i	0.695500	+	0.718526i
$962$			65.6903i			2.11794i
$963$	16.2294	−	31.8137i	0.522984	−	1.02518i
$964$	7.99982	+	7.20307i	0.257657	+	0.231995i
$965$	−12.6458	+	17.4054i	−0.407081	+	0.560300i
$966$	−20.4282	+	3.78101i	−0.657267	+	0.121652i
$967$	−24.2259	+	13.9869i	−0.779054	+	0.449787i	−0.836095	−	0.548585i	$-0.815167\pi$
$967$	−24.2259	+	13.9869i	−0.779054	+	0.449787i	0.0570410	+	0.998372i	$0.481833\pi$
$968$	−5.64122	−	0.592916i	−0.181316	−	0.0190571i
$969$	0.540698	−	2.24976i	0.0173697	−	0.0722727i
$970$	1.35798	+	12.9203i	0.0436021	+	0.414846i
$971$	−5.51434	+	4.96514i	−0.176964	+	0.159339i	−0.752853	−	0.658189i	$-0.771323\pi$
$971$	−5.51434	+	4.96514i	−0.176964	+	0.159339i	0.575889	+	0.817528i	$0.304656\pi$
$972$	10.7441	−	11.2944i	0.344618	−	0.362268i
$973$	5.39287	+	25.3714i	0.172887	+	0.813371i
$974$	−40.1937	−	8.54343i	−1.28789	−	0.273749i
$975$	−2.98767	−	10.0952i	−0.0956820	−	0.323306i
$976$	7.07432	−	2.29859i	0.226443	−	0.0735760i
$977$	47.8295	−	15.5408i	1.53020	−	0.497193i	0.581550	−	0.813511i	$-0.302447\pi$
$977$	47.8295	−	15.5408i	1.53020	−	0.497193i	0.948653	+	0.316318i	$0.102447\pi$
$978$	4.95666	+	16.7484i	0.158496	+	0.535553i
$979$	23.1756	+	4.92613i	0.740695	+	0.157440i
$980$	1.51202	+	7.11349i	0.0482997	+	0.227232i
$981$	−8.20277	−	30.6728i	−0.261894	−	0.979307i
$982$	7.19482	−	6.47824i	0.229596	−	0.206729i
$983$	−0.782810	−	7.44794i	−0.0249677	−	0.237552i	−0.999888	−	0.0149958i	$-0.995227\pi$
$983$	−0.782810	−	7.44794i	−0.0249677	−	0.237552i	0.974920	−	0.222556i	$-0.0714402\pi$
$984$	4.59749	−	19.1294i	0.146563	−	0.609824i
$985$	3.27699	+	0.344425i	0.104414	+	0.0109743i
$986$	−13.7588	+	7.94368i	−0.438171	+	0.252978i
$987$	31.5658	−	5.84243i	1.00475	−	0.185967i
$988$	0.696577	−	0.958756i	0.0221611	−	0.0305021i
$989$	−0.457205	−	0.411669i	−0.0145383	−	0.0130903i
$990$	−10.9117	−	5.56647i	−0.346796	−	0.176914i
$991$		−	35.0017i		−	1.11186i	−0.831228	−	0.555932i	$-0.812361\pi$
$991$		−	35.0017i		−	1.11186i	0.831228	−	0.555932i	$-0.187639\pi$
$992$	−2.17250	+	5.12643i	−0.0689769	+	0.162764i
$993$	−22.9952	−	26.9372i	−0.729732	−	0.854827i
$994$	3.56729	−	10.9790i	0.113148	−	0.348232i
$995$	−0.0509959	+	0.0566367i	−0.00161668	+	0.00179550i
$996$	−23.1586	+	1.81696i	−0.733809	+	0.0575725i
$997$	12.7771	−	22.1306i	0.404655	−	0.700883i	−0.589626	−	0.807676i	$-0.700725\pi$
$997$	12.7771	−	22.1306i	0.404655	−	0.700883i	0.994281	+	0.106793i	$0.0340582\pi$
$998$	−17.5826	−	30.4540i	−0.556568	−	0.964004i
$999$	24.1388	+	50.7032i	0.763719	+	1.60418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.b.761.6	yes	176
3.2	odd	2	inner	930.2.br.b.761.12	yes	176
31.11	odd	30	inner	930.2.br.b.11.12	yes	176
93.11	even	30	inner	930.2.br.b.11.6	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.6	✓	176	93.11	even	30	inner
930.2.br.b.11.12	yes	176	31.11	odd	30	inner
930.2.br.b.761.6	yes	176	1.1	even	1	trivial
930.2.br.b.761.12	yes	176	3.2	odd	2	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.0457608 - 1.73145i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.578567 + 1.63256i) q^{6} +(0.394896 - 3.75719i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-2.99581 - 0.158465i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.0457608 - 1.73145i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.578567 + 1.63256i) q^{6} +(0.394896 - 3.75719i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-2.99581 - 0.158465i) q^{9} +(0.669131 + 0.743145i) q^{10} +(3.73016 - 1.66078i) q^{11} +(1.05474 - 1.37387i) q^{12} +(1.26376 - 5.94554i) q^{13} +(-1.53660 + 3.45127i) q^{14} +(-0.905353 + 1.47660i) q^{15} +(0.309017 + 0.951057i) q^{16} +(6.25944 + 2.78688i) q^{17} +(2.80022 + 1.07647i) q^{18} +(0.190708 - 0.0405362i) q^{19} +(-0.406737 - 0.913545i) q^{20} +(-6.48730 - 0.855674i) q^{21} +(-4.06080 + 0.426808i) q^{22} +(-2.56858 + 1.86618i) q^{23} +(-1.42767 + 0.980697i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-3.03918 + 5.26402i) q^{26} +(-0.411464 + 5.17984i) q^{27} +(2.52790 - 2.80751i) q^{28} +(0.716520 - 2.20522i) q^{29} +(1.31734 - 1.12456i) q^{30} +(-5.12643 - 2.17250i) q^{31} -1.00000i q^{32} +(-2.70485 - 6.53458i) q^{33} +(-5.09189 - 4.58476i) q^{34} +(-2.22058 + 3.05637i) q^{35} +(-2.33052 - 1.88909i) q^{36} +(9.35934 - 5.40362i) q^{37} +(-0.193900 - 0.0203797i) q^{38} +(-10.2365 - 2.46021i) q^{39} +(0.104528 + 0.994522i) q^{40} +(-8.44129 + 7.60057i) q^{41} +(5.90537 + 2.81848i) q^{42} +(0.0402884 + 0.189542i) q^{43} +(3.99395 + 0.848939i) q^{44} +(2.51522 + 1.63514i) q^{45} +(3.01955 - 0.981111i) q^{46} +(-4.66582 + 1.51602i) q^{47} +(1.66084 - 0.491525i) q^{48} +(-7.11349 - 1.51202i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(5.11177 - 10.7104i) q^{51} +(4.51710 - 4.06722i) q^{52} +(-0.349345 - 3.32380i) q^{53} +(1.99198 - 4.79917i) q^{54} +(-4.06080 - 0.426808i) q^{55} +(-3.27174 + 1.88894i) q^{56} +(-0.0614593 - 0.332055i) q^{57} +(-1.36290 + 1.87587i) q^{58} +(8.33435 + 7.50428i) q^{59} +(-1.60037 + 0.662438i) q^{60} -7.43838i q^{61} +(4.20418 + 3.65032i) q^{62} +(-1.77842 + 11.1933i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-4.06722 + 4.51710i) q^{65} +(0.553169 + 7.05059i) q^{66} +(-4.90224 + 8.49093i) q^{67} +(3.42591 + 5.93384i) q^{68} +(3.11366 + 4.53276i) q^{69} +(3.05637 - 2.22058i) q^{70} +(-3.03894 + 0.319405i) q^{71} +(1.63269 + 2.51681i) q^{72} +(-2.09217 - 4.69909i) q^{73} +(-10.5711 + 2.24695i) q^{74} +(1.52236 - 0.826093i) q^{75} +(0.178112 + 0.0793007i) q^{76} +(-4.76682 - 14.6708i) q^{77} +(8.97529 + 5.50307i) q^{78} +(-2.51209 + 5.64224i) q^{79} +(0.207912 - 0.978148i) q^{80} +(8.94978 + 0.949461i) q^{81} +(10.3769 - 4.62007i) q^{82} +(-8.97420 - 9.96686i) q^{83} +(-4.74538 - 4.50539i) q^{84} +(-4.02739 - 5.54323i) q^{85} +(0.0202552 - 0.192715i) q^{86} +(-3.78544 - 1.34153i) q^{87} +(-3.53613 - 2.04159i) q^{88} +(4.69447 + 3.41073i) q^{89} +(-1.88683 - 2.33236i) q^{90} +(-21.8394 - 7.09607i) q^{91} -3.17494 q^{92} +(-3.99616 + 8.77672i) q^{93} +4.90593 q^{94} +(-0.185426 - 0.0602485i) q^{95} +(-1.73145 - 0.0457608i) q^{96} +(10.5103 + 7.63620i) q^{97} +(6.29809 + 3.63620i) q^{98} +(-11.4380 + 4.38427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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