LMFDB - Embedded newform 930.2.br.b.11.6

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			11.6
Character	$\chi$	$=$	930.11
Dual form			930.2.br.b.761.6

$q$-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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

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	0.770986	+	0.636852i	$0.219764\pi$
$7$	0.394896	+	3.75719i	0.149257	+	1.42008i	−0.621730	+	0.783232i	$0.713570\pi$
$8$	−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	0.882888	−	0.469584i	$-0.155596\pi$
$11$	3.73016	+	1.66078i	1.12469	+	0.500743i	0.241799	+	0.970326i	$0.422263\pi$
$12$	1.05474	+	1.37387i	0.304477	+	0.396603i
$13$	1.26376	+	5.94554i	0.350505	+	1.64900i	0.701538	+	0.712632i	$0.252497\pi$
$13$	1.26376	+	5.94554i	0.350505	+	1.64900i	−0.351033	+	0.936363i	$0.614170\pi$
$14$	−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	0.532754	−	0.846270i	$-0.321157\pi$
$17$	6.25944	−	2.78688i	1.51814	−	0.675918i	0.985383	+	0.170352i	$0.0544904\pi$
$18$	2.80022	−	1.07647i	0.660018	−	0.253725i
$19$	0.190708	+	0.0405362i	0.0437513	+	0.00929964i	0.229735	−	0.973253i	$-0.426214\pi$
$19$	0.190708	+	0.0405362i	0.0437513	+	0.00929964i	−0.185984	+	0.982553i	$0.559547\pi$
$20$	−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	0.286857	−	0.957973i	$-0.407390\pi$
$23$	−2.56858	−	1.86618i	−0.535586	−	0.389126i	−0.822443	+	0.568847i	$0.807390\pi$
$24$	−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	0.995282	−	0.0970211i	$-0.0309314\pi$
$29$	0.716520	+	2.20522i	0.133054	+	0.409500i	−0.862228	+	0.506521i	$0.830931\pi$
$30$	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	0.998917	+	0.0465234i	$0.0148142\pi$
$37$	9.35934	+	5.40362i	1.53867	+	0.888349i	0.539749	+	0.841826i	$0.318519\pi$
$38$	−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	−0.968165	−	0.250314i	$-0.919466\pi$
$41$	−8.44129	−	7.60057i	−1.31831	−	1.18701i	−0.350144	−	0.936696i	$-0.613867\pi$
$42$	5.90537	−	2.81848i	0.911218	−	0.434901i
$43$	0.0402884	−	0.189542i	0.00614393	−	0.0289049i	−0.974969	−	0.222341i	$-0.928630\pi$
$43$	0.0402884	−	0.189542i	0.00614393	−	0.0289049i	0.981113	+	0.193437i	$0.0619634\pi$
$44$	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	−0.0517303	−	0.998661i	$-0.516474\pi$
$47$	−4.66582	−	1.51602i	−0.680579	−	0.221134i	−0.628849	+	0.777527i	$0.716474\pi$
$48$	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	0.943975	+	0.330017i	$0.107054\pi$
$53$	−0.349345	+	3.32380i	−0.0479863	+	0.456559i	−0.991961	+	0.126542i	$0.959612\pi$
$54$	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	0.0852275	−	0.996362i	$-0.472838\pi$
$59$	8.33435	−	7.50428i	1.08504	−	0.976974i	0.999812	+	0.0193875i	$0.00617163\pi$
$60$	−1.60037	−	0.662438i	−0.206607	−	0.0855204i
$61$			7.43838i			0.952387i	0.879340	+	0.476194i	$0.157984\pi$
$61$			7.43838i			0.952387i	−0.879340	+	0.476194i	$0.842016\pi$
$62$	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	−0.992983	−	0.118256i	$-0.962270\pi$
$67$	−4.90224	−	8.49093i	−0.598904	−	1.03733i	0.394079	−	0.919077i	$-0.371064\pi$
$68$	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	−0.0775319	−	0.996990i	$-0.524704\pi$
$71$	−3.03894	−	0.319405i	−0.360655	−	0.0379064i	−0.283123	+	0.959083i	$0.591371\pi$
$72$	1.63269	−	2.51681i	0.192415	−	0.296608i
$73$	−2.09217	+	4.69909i	−0.244870	+	0.549986i	−0.993609	−	0.112878i	$-0.963993\pi$
$73$	−2.09217	+	4.69909i	−0.244870	+	0.549986i	0.748739	+	0.662865i	$0.230660\pi$
$74$	−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	0.715318	−	0.698799i	$-0.246282\pi$
$79$	−2.51209	−	5.64224i	−0.282632	−	0.634802i	−0.997950	+	0.0639971i	$0.979615\pi$
$80$	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	0.0105201	+	0.999945i	$0.496651\pi$
$83$	−8.97420	+	9.96686i	−0.985046	+	1.09400i	−0.995567	+	0.0940602i	$0.970015\pi$
$84$	−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	−0.310492	−	0.950576i	$-0.600494\pi$
$89$	4.69447	−	3.41073i	0.497613	−	0.361537i	0.808104	+	0.589039i	$0.200494\pi$
$90$	−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	0.0917622	−	0.995781i	$-0.470750\pi$
$97$	10.5103	−	7.63620i	1.06716	−	0.775339i	0.975400	+	0.220442i	$0.0707500\pi$
$98$	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	−0.996615	−	0.0822054i	$-0.973804\pi$
$101$	−6.13507	+	8.44420i	−0.610462	+	0.840229i	0.386153	+	0.922435i	$0.373804\pi$
$102$	−8.17127	−	8.60653i	−0.809076	−	0.852173i
$103$	6.45892	−	7.17335i	0.636416	−	0.706811i	−0.335526	−	0.942031i	$-0.608914\pi$
$103$	6.45892	−	7.17335i	0.636416	−	0.706811i	0.971942	+	0.235219i	$0.0755809\pi$
$104$	−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	−0.981191	−	0.193040i	$-0.938165\pi$
$107$	−4.84209	−	10.8755i	−0.468103	−	1.05138i	0.513088	−	0.858336i	$-0.328501\pi$
$108$	−3.37751	−	3.94872i	−0.325001	−	0.379966i
$109$	3.27050	−	10.0656i	0.313257	−	0.964107i	−0.663209	−	0.748435i	$-0.730806\pi$
$109$	3.27050	−	10.0656i	0.313257	−	0.964107i	0.976466	−	0.215672i	$-0.0691942\pi$
$110$	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	−0.904024	−	0.427481i	$-0.859401\pi$
$113$	0.197367	−	0.443294i	0.0185668	−	0.0417016i	0.922591	+	0.385780i	$0.126068\pi$
$114$	−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	−0.998270	−	0.0587972i	$-0.981273\pi$
$127$	−11.7669	+	10.5950i	−1.04414	+	0.940150i	−0.0458725	+	0.998947i	$0.514607\pi$
$128$	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	0.0628709	−	0.998022i	$-0.479974\pi$
$131$	3.79841	−	0.399229i	0.331868	−	0.0348808i	0.268997	+	0.963141i	$0.413308\pi$
$132$	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	0.563367	−	0.826207i	$-0.309506\pi$
$137$	16.5513	−	3.51810i	1.41408	−	0.300571i	0.850710	+	0.525636i	$0.176173\pi$
$138$	−1.56056	+	5.27308i	−0.132844	+	0.448875i
$139$	−6.52978	−	2.12165i	−0.553849	−	0.179956i	0.0187029	−	0.999825i	$-0.494046\pi$
$139$	−6.52978	−	2.12165i	−0.553849	−	0.179956i	−0.572551	+	0.819869i	$0.694046\pi$
$140$	−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	0.629265	−	0.777191i	$-0.283356\pi$
$149$	3.30591	+	1.90867i	0.270831	+	0.156364i	−0.358434	+	0.933555i	$0.616689\pi$
$150$	−1.70312	−	0.315227i	−0.139060	−	0.0257382i
$151$	2.32612	+	3.20162i	0.189297	+	0.260544i	0.893108	−	0.449843i	$-0.148520\pi$
$151$	2.32612	+	3.20162i	0.189297	+	0.260544i	−0.703811	+	0.710387i	$0.748520\pi$
$152$	−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	−0.908632	−	0.417599i	$-0.862872\pi$
$157$	−5.24995	−	16.1577i	−0.418992	−	1.28952i	0.489640	−	0.871925i	$-0.337128\pi$
$158$	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	0.859510	−	0.511120i	$-0.170769\pi$
$163$	8.15832	+	5.92737i	0.639009	+	0.464267i	−0.220501	+	0.975387i	$0.570769\pi$
$164$	−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	0.581750	−	0.813367i	$-0.302368\pi$
$167$	10.1106	+	2.14907i	0.782380	+	0.166300i	0.200629	+	0.979667i	$0.435701\pi$
$168$	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	0.964737	−	0.263216i	$-0.0847833\pi$
$173$	−0.311118	−	1.46369i	−0.0236538	−	0.111283i	−0.988391	+	0.151934i	$0.951450\pi$
$174$	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	0.883080	+	0.469222i	$0.155466\pi$
$179$	1.56340	+	14.8748i	0.116854	+	1.11179i	−0.766226	+	0.642571i	$0.777868\pi$
$180$	1.07374	−	2.80126i	0.0800320	−	0.208794i
$181$	15.1547	−	8.74960i	1.12644	−	0.650352i	0.183405	−	0.983037i	$-0.441288\pi$
$181$	15.1547	−	8.74960i	1.12644	−	0.650352i	0.943038	+	0.332685i	$0.107955\pi$
$182$	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	−0.0986365	−	0.995124i	$-0.531448\pi$
$191$	9.86557	−	5.69589i	0.713848	−	0.412140i	0.812484	+	0.582983i	$0.198115\pi$
$192$	1.63256	−	0.578567i	0.117820	−	0.0417545i
$193$	2.24885	+	21.3964i	0.161876	+	1.54015i	0.710272	+	0.703928i	$0.248572\pi$
$193$	2.24885	+	21.3964i	0.161876	+	1.54015i	−0.548396	+	0.836219i	$0.684761\pi$
$194$	−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	0.296692	−	0.954973i	$-0.404117\pi$
$197$	−3.01017	−	1.34021i	−0.214466	−	0.0954862i	−0.511158	+	0.859487i	$0.670783\pi$
$198$	12.2330	+	0.635141i	0.869364	+	0.0451375i
$199$	0.0158454	+	0.0745467i	0.00112325	+	0.00528448i	0.978706	−	0.205269i	$-0.0658068\pi$
$199$	0.0158454	+	0.0745467i	0.00112325	+	0.00528448i	−0.977582	+	0.210553i	$0.932473\pi$
$200$	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	−0.831341	−	0.555763i	$-0.812426\pi$
$211$	0.953391	−	1.65132i	0.0656342	−	0.113682i	0.896975	+	0.442081i	$0.145760\pi$
$212$	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	0.923666	−	0.383198i	$-0.125177\pi$
$223$	15.7342	+	9.08415i	1.05364	+	0.608319i	0.129974	+	0.991517i	$0.458511\pi$
$224$	−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	0.917422	−	0.397915i	$-0.130266\pi$
$227$	9.30484	+	8.37812i	0.617584	+	0.556075i	−0.299838	+	0.953990i	$0.596933\pi$
$228$	0.145456	+	0.304763i	0.00963303	+	0.0201834i
$229$	3.32576	−	15.6465i	0.219772	−	1.03395i	−0.720482	−	0.693474i	$-0.756079\pi$
$229$	3.32576	−	15.6465i	0.219772	−	1.03395i	0.940254	−	0.340473i	$-0.110587\pi$
$230$	−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	0.617648	−	0.786455i	$-0.288086\pi$
$233$	9.99918	+	3.24893i	0.655068	+	0.212845i	0.0374207	+	0.999300i	$0.488086\pi$
$234$	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	0.685330	+	0.728233i	$0.259658\pi$
$239$	−2.10919	+	20.0676i	−0.136432	+	1.29806i	−0.821762	+	0.569831i	$0.807009\pi$
$240$	−1.68410	+	0.404749i	−0.108708	+	0.0261264i
$241$	10.7058	−	1.12523i	0.689624	−	0.0724824i	0.246767	−	0.969075i	$-0.420632\pi$
$241$	10.7058	−	1.12523i	0.689624	−	0.0724824i	0.442857	+	0.896592i	$0.353965\pi$
$242$	−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	−0.965999	−	0.258546i	$-0.916757\pi$
$251$	−17.7783	−	19.7448i	−1.12215	−	1.24628i	−0.156155	−	0.987733i	$-0.549910\pi$
$252$	−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	0.451122	−	0.892463i	$-0.351024\pi$
$257$	11.3314	+	1.19098i	0.706832	+	0.0742910i	0.255710	+	0.966754i	$0.417691\pi$
$258$	−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	−0.902147	−	0.431428i	$-0.858010\pi$
$263$	1.31834	−	4.05744i	0.0812925	−	0.250193i	0.983440	+	0.181236i	$0.0580097\pi$
$264$	−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	−0.803416	−	0.595418i	$-0.796987\pi$
$269$	−2.08755	+	2.31846i	−0.127280	+	0.141359i	0.676136	+	0.736777i	$0.263653\pi$
$270$	−4.12469	−	3.16021i	−0.251021	−	0.192324i
$271$	5.68849	−	7.82954i	0.345551	−	0.475611i	−0.600501	−	0.799624i	$-0.705032\pi$
$271$	5.68849	−	7.82954i	0.345551	−	0.475611i	0.946053	+	0.324013i	$0.105032\pi$
$272$	−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	0.839644	−	0.543137i	$-0.182763\pi$
$277$	30.5934	−	9.94039i	1.83818	−	0.597260i	0.998534	−	0.0541239i	$-0.0172366\pi$
$278$	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	−0.932140	−	0.362099i	$-0.882060\pi$
$281$	−24.6990	+	8.02520i	−1.47342	+	0.478743i	−0.541280	+	0.840842i	$0.682060\pi$
$282$	0.224499	+	8.49435i	0.0133687	+	0.505831i
$283$	−6.84152	+	4.97065i	−0.406686	+	0.295475i	−0.772259	−	0.635308i	$-0.780873\pi$
$283$	−6.84152	+	4.97065i	−0.406686	+	0.295475i	0.365573	+	0.930783i	$0.380873\pi$
$284$	−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	0.779192	−	0.626786i	$-0.215630\pi$
$293$	−3.56007	−	7.99605i	−0.207982	−	0.467135i	−0.987174	+	0.159651i	$0.948963\pi$
$294$	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	0.843353	−	0.537360i	$-0.180578\pi$
$307$	3.86841	+	4.29630i	0.220782	+	0.245203i	−0.622571	+	0.782563i	$0.713912\pi$
$308$	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	$-0.769516\pi$
$311$		−	23.3649i		−	1.32490i	0.749105	−	0.662451i	$-0.230484\pi$
$312$	4.02654	−	9.72762i	0.227958	−	0.550718i
$313$	−4.09463	+	3.68682i	−0.231442	+	0.208391i	−0.776689	−	0.629884i	$-0.783102\pi$
$313$	−4.09463	+	3.68682i	−0.231442	+	0.208391i	0.545247	+	0.838275i	$0.316436\pi$
$314$	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	−0.453138	−	0.891440i	$-0.649696\pi$
$317$	−12.6596	+	1.33058i	−0.711034	+	0.0747327i	−0.257895	+	0.966173i	$0.583029\pi$
$318$	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	0.971101	−	0.238667i	$-0.0767105\pi$
$331$	15.1960	+	13.6826i	0.835249	+	0.752062i	−0.135852	+	0.990729i	$0.543377\pi$
$332$	−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	0.985715	−	0.168424i	$-0.0538677\pi$
$337$	9.56303	+	13.1624i	0.520932	+	0.717001i	−0.464783	+	0.885425i	$0.653868\pi$
$338$	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	0.446550	+	0.894759i	$0.352653\pi$
$347$	−10.2753	+	17.7974i	−0.551609	+	0.955415i	−0.998159	+	0.0606558i	$0.980681\pi$
$348$	−2.27395	+	3.31034i	−0.121897	+	0.177453i
$349$	18.6496	+	13.5497i	0.998289	+	0.725299i	0.961721	−	0.274032i	$-0.0883573\pi$
$349$	18.6496	+	13.5497i	0.998289	+	0.725299i	0.0365684	+	0.999331i	$0.488357\pi$
$350$	−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	−0.0693816	−	0.997590i	$-0.522103\pi$
$353$	−10.1179	−	2.15063i	−0.538521	−	0.114466i	−0.469140	+	0.883124i	$0.655436\pi$
$354$	−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	0.983244	+	0.182292i	$0.0583518\pi$
$359$	3.01548	+	14.1867i	0.159151	+	0.748746i	−0.824093	+	0.566454i	$0.808315\pi$
$360$	−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	−0.899849	−	0.436202i	$-0.856323\pi$
$367$	−18.6210	+	10.7509i	−0.972011	+	0.561191i	−0.0721622	+	0.997393i	$0.522990\pi$
$368$	−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	0.925619	+	0.378458i	$0.123546\pi$
$379$	1.92563	+	18.3211i	0.0989128	+	0.941092i	−0.826706	+	0.562635i	$0.809788\pi$
$380$	−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	0.00306103	−	0.999995i	$-0.499026\pi$
$383$	−14.4436	−	6.43069i	−0.738032	−	0.328593i	−0.741093	+	0.671402i	$0.765692\pi$
$384$	−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	−0.166812	−	0.985989i	$-0.553347\pi$
$389$	8.96023	−	3.98935i	0.454302	−	0.202268i	0.621114	+	0.783721i	$0.286681\pi$
$390$	−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	−0.992479	−	0.122411i	$-0.960937\pi$
$397$	−7.77524	+	13.4671i	−0.390228	+	0.675895i	0.602251	+	0.798307i	$0.294271\pi$
$398$	−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	0.649527	+	0.760338i	$0.274967\pi$
$401$	11.4336	+	35.1889i	0.570964	+	1.75725i	−0.0785627	+	0.996909i	$0.525033\pi$
$402$	−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	−0.200335	−	0.979727i	$-0.564203\pi$
$409$	−23.2365	−	13.4156i	−1.14897	−	0.663359i	−0.948636	+	0.316368i	$0.897536\pi$
$410$	−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	0.0241629	−	0.999708i	$-0.492308\pi$
$419$	−11.1334	−	3.61746i	−0.543903	−	0.176725i	−0.568065	+	0.822983i	$0.692308\pi$
$420$	1.85693	−	6.27448i	0.0906087	−	0.306163i
$421$	10.1854	−	2.16498i	0.496408	−	0.105515i	0.0470974	−	0.998890i	$-0.485003\pi$
$421$	10.1854	−	2.16498i	0.496408	−	0.105515i	0.449311	+	0.893375i	$0.351670\pi$
$422$	−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	−0.930956	−	0.365131i	$-0.881024\pi$
$431$	−13.8086	+	12.4333i	−0.665136	+	0.598891i	0.265820	+	0.964023i	$0.414357\pi$
$432$	−5.05347	−	1.20933i	−0.243135	−	0.0581840i
$433$			33.7931i			1.62399i	0.583662	+	0.811997i	$0.301619\pi$
$433$			33.7931i			1.62399i	−0.583662	+	0.811997i	$0.698381\pi$
$434$	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	0.729937	−	0.683515i	$-0.239549\pi$
$439$	−4.75560	−	8.23694i	−0.226973	−	0.393128i	−0.956909	+	0.290387i	$0.906216\pi$
$440$	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	0.628730	−	0.777624i	$-0.283575\pi$
$443$	22.7744	+	2.39368i	1.08204	+	0.113727i	0.453313	+	0.891351i	$0.350242\pi$
$444$	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	0.768189	+	0.640223i	$0.221158\pi$
$449$	−4.86519	+	14.9735i	−0.229602	+	0.706644i	−0.997792	+	0.0664209i	$0.978842\pi$
$450$	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	−0.773847	−	0.633373i	$-0.781670\pi$
$457$	1.44637	−	1.99076i	0.0676584	−	0.0931238i	0.841505	+	0.540249i	$0.181670\pi$
$458$	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	0.0203171	−	0.999794i	$-0.493532\pi$
$461$	20.9869	−	15.2478i	0.977456	−	0.710163i	0.957139	+	0.289630i	$0.0935324\pi$
$462$	26.7089	−	0.705895i	1.24261	−	0.0328412i
$463$	−25.5865	+	8.31357i	−1.18911	+	0.386364i	−0.835742	−	0.549122i	$-0.814962\pi$
$463$	−25.5865	+	8.31357i	−1.18911	+	0.386364i	−0.353364	+	0.935486i	$0.614962\pi$
$464$	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	−0.706001	−	0.708211i	$-0.749503\pi$
$467$	−18.6040	+	6.04482i	−0.860892	+	0.279721i	−0.154891	+	0.987932i	$0.549503\pi$
$468$	−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	−0.826249	−	0.563305i	$-0.809530\pi$
$479$	−15.1451	−	34.0165i	−0.691998	−	1.55425i	0.134251	−	0.990947i	$-0.457137\pi$
$480$	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	0.964069	−	0.265652i	$-0.0855872\pi$
$487$	40.8665	+	4.29524i	1.85184	+	0.194636i	0.887770	+	0.460288i	$0.152254\pi$
$488$	−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	0.735876	−	0.677116i	$-0.236771\pi$
$491$	−4.84079	−	8.38450i	−0.218462	−	0.378387i	−0.954338	+	0.298729i	$0.903437\pi$
$492$	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	0.172202	−	0.985062i	$-0.444912\pi$
$499$	26.1329	−	23.5301i	1.16987	−	1.05335i	0.997665	−	0.0682915i	$-0.0217548\pi$
$500$	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	−0.929202	−	0.369573i	$-0.879504\pi$
$503$	−39.5009	+	4.15172i	−1.76126	+	0.185116i	−0.832058	+	0.554689i	$0.812837\pi$
$504$	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	0.253457	−	0.967347i	$-0.418432\pi$
$509$	19.8189	−	4.21264i	0.878457	−	0.186722i	0.625000	+	0.780625i	$0.285099\pi$
$510$	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	0.0720117	−	0.997404i	$-0.477058\pi$
$521$	−17.2505	−	9.95960i	−0.755759	−	0.436338i	−0.827771	+	0.561066i	$0.810391\pi$
$522$	4.38026	+	5.40379i	0.191719	+	0.236518i
$523$	11.9938	+	16.5080i	0.524452	+	0.721846i	0.986272	−	0.165127i	$-0.0528035\pi$
$523$	11.9938	+	16.5080i	0.524452	+	0.721846i	−0.461820	+	0.886974i	$0.652803\pi$
$524$	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	0.199219	−	0.979955i	$-0.436159\pi$
$541$	24.6729	−	10.9851i	1.06077	−	0.472286i	0.861552	+	0.507669i	$0.169493\pi$
$542$	−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	0.260621	−	0.965441i	$-0.416073\pi$
$547$	−6.60600	−	2.94118i	−0.282452	−	0.125756i	−0.543073	+	0.839685i	$0.682739\pi$
$548$	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	−0.522877	−	0.852408i	$-0.675141\pi$
$563$	−1.09405	+	0.631649i	−0.0461086	+	0.0266208i	0.476768	+	0.879029i	$0.341808\pi$
$564$	−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	0.450188	−	0.892934i	$-0.351357\pi$
$569$	2.09538	+	0.932923i	0.0878429	+	0.0391102i	−0.362345	+	0.932044i	$0.618024\pi$
$570$	0.205641	+	0.267861i	0.00861334	+	0.0112195i
$571$	−1.50969	−	7.10253i	−0.0631785	−	0.297231i	0.935202	−	0.354114i	$-0.115217\pi$
$571$	−1.50969	−	7.10253i	−0.0631785	−	0.297231i	−0.998381	+	0.0568822i	$0.981884\pi$
$572$	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	−0.380598	−	0.924741i	$-0.624282\pi$
$577$	−26.5290	−	5.63891i	−1.10442	−	0.234751i	−0.723819	+	0.689990i	$0.757615\pi$
$578$	−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	0.982341	−	0.187097i	$-0.0599080\pi$
$587$	1.88101	+	5.78914i	0.0776375	+	0.238944i	−0.904704	+	0.426041i	$0.859908\pi$
$588$	−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	0.456905	−	0.889516i	$-0.348958\pi$
$593$	−12.9128	−	17.7730i	−0.530266	−	0.729849i	−0.987171	+	0.159667i	$0.948958\pi$
$594$	−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	0.772652	−	0.634829i	$-0.218930\pi$
$599$	5.43492	+	4.89363i	0.222065	+	0.199948i	−0.550587	+	0.834777i	$0.685596\pi$
$600$	−1.56314	+	0.746047i	−0.0638150	+	0.0304572i
$601$	4.38550	−	20.6321i	0.178888	−	0.841602i	−0.793562	−	0.608490i	$-0.791776\pi$
$601$	4.38550	−	20.6321i	0.178888	−	0.841602i	0.972450	−	0.233113i	$-0.0748910\pi$
$602$	−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	−0.0391847	−	0.999232i	$-0.512476\pi$
$607$	8.16587	−	1.73571i	0.331442	−	0.0704503i	0.370627	+	0.928782i	$0.379143\pi$
$608$	−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	0.492634	−	0.870237i	$-0.336034\pi$
$613$	28.6072	−	3.00674i	1.15544	−	0.121441i	0.662801	+	0.748795i	$0.269367\pi$
$614$	−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	0.0953243	−	0.995446i	$-0.469611\pi$
$617$	27.2062	−	24.4966i	1.09528	−	0.986196i	0.999957	+	0.00925034i	$0.00294452\pi$
$618$	−15.4479	−	6.39431i	−0.621404	−	0.257217i
$619$		−	30.5542i		−	1.22808i	−0.789276	−	0.614038i	$-0.789544\pi$
$619$		−	30.5542i		−	1.22808i	0.789276	−	0.614038i	$-0.210456\pi$
$620$	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	−0.675131	−	0.737698i	$-0.735913\pi$
$631$	8.15980	−	18.3272i	0.324836	−	0.729595i	0.999967	+	0.00810345i	$0.00257944\pi$
$632$	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	−0.315760	−	0.948839i	$-0.602260\pi$
$641$	16.7323	−	18.5831i	0.660887	−	0.733989i	0.976647	+	0.214850i	$0.0689262\pi$
$642$	−14.9535	+	14.1972i	−0.590167	+	0.560320i
$643$	14.1651	−	19.4966i	0.558616	−	0.768869i	−0.432534	−	0.901618i	$-0.642380\pi$
$643$	14.1651	−	19.4966i	0.558616	−	0.768869i	0.991150	+	0.132749i	$0.0423803\pi$
$644$	−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	−0.270257	−	0.962788i	$-0.587109\pi$
$647$	14.2925	−	10.3841i	0.561895	−	0.408241i	0.832152	+	0.554548i	$0.187109\pi$
$648$	−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	−0.419362	−	0.907819i	$-0.637746\pi$
$653$	−5.75041	+	1.86842i	−0.225031	+	0.0731169i	0.194331	+	0.980936i	$0.437746\pi$
$654$	−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	−0.910039	−	0.414524i	$-0.863948\pi$
$659$	−6.02205	+	8.28864i	−0.234586	+	0.322880i	0.675453	+	0.737403i	$0.263948\pi$
$660$	−4.86947	−	5.12885i	−0.189544	−	0.199640i
$661$	−12.3972	+	13.7685i	−0.482195	+	0.535531i	−0.934326	−	0.356420i	$-0.883997\pi$
$661$	−12.3972	+	13.7685i	−0.482195	+	0.535531i	0.452131	+	0.891951i	$0.350664\pi$
$662$	−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	0.633653	−	0.773618i	$-0.281555\pi$
$673$	28.3449	+	2.97917i	1.09261	+	0.114838i	0.458962	+	0.888456i	$0.348222\pi$
$674$	−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	0.726921	−	0.686721i	$-0.240951\pi$
$677$	−6.01713	−	10.4220i	−0.231257	−	0.400549i	−0.958178	+	0.286172i	$0.907617\pi$
$678$	−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	$-0.869399\pi$
$683$		−	20.8488i		−	0.797758i	0.917003	−	0.398879i	$-0.130601\pi$
$684$	−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	−0.972818	−	0.231570i	$-0.925614\pi$
$691$	0.706793	−	6.72469i	0.0268877	−	0.255819i	0.999706	−	0.0242493i	$-0.00771954\pi$
$692$	−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	0.824721	+	0.565540i	$0.191332\pi$
$701$	−4.20247	+	19.7711i	−0.158725	+	0.746743i	−0.983446	+	0.181203i	$0.942001\pi$
$702$	−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	0.602489	−	0.798127i	$-0.294176\pi$
$709$	−9.12653	−	12.5616i	−0.342754	−	0.471760i	−0.945243	+	0.326367i	$0.894176\pi$
$710$	−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	0.210930	+	0.977501i	$0.432351\pi$
$719$	−19.8713	+	34.4182i	−0.741076	+	1.28358i	−0.952006	+	0.306080i	$0.900983\pi$
$720$	−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	−0.475760	−	0.879575i	$-0.657827\pi$
$727$	−3.78705	+	1.68610i	−0.140454	+	0.0625340i	0.335306	+	0.942109i	$0.391160\pi$
$728$	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	0.783158	−	0.621823i	$-0.213608\pi$
$733$	22.8799	+	10.1868i	0.845088	+	0.376257i	0.0619303	+	0.998080i	$0.480274\pi$
$734$	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	−0.673571	−	0.739123i	$-0.735240\pi$
$739$	−10.0653	+	5.81119i	−0.370257	+	0.213768i	0.303314	+	0.952891i	$0.401907\pi$
$740$	−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	−0.887929	−	0.459981i	$-0.847856\pi$
$751$	−3.15257	−	29.9947i	−0.115039	−	1.09452i	0.772890	−	0.634540i	$-0.218810\pi$
$752$	−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	0.999933	+	0.0116136i	$0.00369681\pi$
$757$	2.50848	+	11.8015i	0.0911724	+	0.428932i	−0.908760	+	0.417319i	$0.862970\pi$
$758$	−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	−0.0373193	−	0.999303i	$-0.511882\pi$
$761$	18.7679	−	8.35601i	0.680336	−	0.302905i	0.717656	+	0.696398i	$0.245215\pi$
$762$	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	−0.883738	−	0.467981i	$-0.844981\pi$
$769$	−1.01455	+	1.75725i	−0.0365855	+	0.0633680i	0.847153	+	0.531349i	$0.178315\pi$
$770$	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	0.999850	+	0.0173156i	$0.00551201\pi$
$773$	5.59205	+	17.2106i	0.201132	+	0.619021i	−0.798718	+	0.601706i	$0.794488\pi$
$774$	−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	0.701130	+	0.713033i	$0.252679\pi$
$787$	−6.43550	+	30.2767i	−0.229401	+	1.07925i	−0.930531	+	0.366213i	$0.880654\pi$
$788$	−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	0.900462	+	0.434934i	$0.143228\pi$
$797$	−1.99737	+	19.0037i	−0.0707506	+	0.673147i	−0.971213	+	0.238213i	$0.923438\pi$
$798$	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	0.974117	−	0.226046i	$-0.0725800\pi$
$809$	18.4164	+	20.4535i	0.647486	+	0.719106i	−0.326631	+	0.945152i	$0.605913\pi$
$810$	5.28298	−	7.28629i	0.185625	−	0.256014i
$811$	−18.8309	−	32.6161i	−0.661243	−	1.14531i	−0.980289	−	0.197568i	$-0.936696\pi$
$811$	−18.8309	−	32.6161i	−0.661243	−	1.14531i	0.319046	−	0.947739i	$-0.396638\pi$
$812$	−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	−0.608346	−	0.793672i	$-0.708167\pi$
$821$	10.0379	−	30.8935i	0.350325	−	1.07819i	0.958671	−	0.284518i	$-0.0918334\pi$
$822$	−15.3196	−	24.9856i	−0.534332	−	0.871474i
$823$	14.4593	+	32.4762i	0.504021	+	1.13205i	0.969075	+	0.246767i	$0.0793683\pi$
$823$	14.4593	+	32.4762i	0.504021	+	1.13205i	−0.465054	+	0.885282i	$0.653965\pi$
$824$	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	−0.881652	−	0.471899i	$-0.843569\pi$
$827$	−9.20762	+	10.2261i	−0.320180	+	0.355596i	0.561472	+	0.827496i	$0.310235\pi$
$828$	9.51153	−	0.503116i	0.330548	−	0.0174845i
$829$	−13.6674	+	18.8116i	−0.474689	+	0.653353i	−0.977473	−	0.211059i	$-0.932309\pi$
$829$	−13.6674	+	18.8116i	−0.474689	+	0.653353i	0.502785	+	0.864412i	$0.332309\pi$
$830$	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	0.130988	−	0.991384i	$-0.458185\pi$
$839$	23.7425	−	7.71439i	0.819681	−	0.266330i	0.688693	+	0.725054i	$0.258185\pi$
$840$	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	−0.332805	−	0.942996i	$-0.607995\pi$
$853$	14.3320	−	44.1094i	0.490719	−	1.51028i	0.823524	−	0.567281i	$-0.192005\pi$
$854$	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	0.447334	+	0.894367i	$0.352374\pi$
$857$	−15.1243	+	33.9697i	−0.516635	+	1.16038i	−0.963969	+	0.266014i	$0.914293\pi$
$858$	42.6186	−	5.62139i	1.45498	−	0.191911i
$859$	−42.3173	−	4.44773i	−1.44385	−	0.151754i	−0.650029	−	0.759910i	$-0.725243\pi$
$859$	−42.3173	−	4.44773i	−1.44385	−	0.151754i	−0.793818	+	0.608155i	$0.791910\pi$
$860$	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	0.913781	−	0.406208i	$-0.133149\pi$
$863$	3.08762	+	5.34792i	0.105104	+	0.182045i	−0.808677	+	0.588253i	$0.799816\pi$
$864$	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	0.926497	+	0.376303i	$0.122805\pi$
$877$	−1.71737	+	16.3397i	−0.0579915	+	0.551752i	−0.984488	+	0.175450i	$0.943862\pi$
$878$	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	−0.173858	−	0.984771i	$-0.555623\pi$
$881$	2.01413	−	0.428117i	0.0678578	−	0.0144236i	0.241715	+	0.970347i	$0.422290\pi$
$882$	−18.2917	+	11.8914i	−0.615913	+	0.400405i
$883$	13.5584	+	4.40539i	0.456276	+	0.148253i	0.528133	−	0.849162i	$-0.322892\pi$
$883$	13.5584	+	4.40539i	0.456276	+	0.148253i	−0.0718567	+	0.997415i	$0.522892\pi$
$884$	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	0.542588	+	0.839999i	$0.317445\pi$
$887$	−8.77839	+	41.2991i	−0.294749	+	1.38669i	−0.837337	+	0.546687i	$0.815889\pi$
$888$	−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	−0.0589541	−	0.998261i	$-0.518777\pi$
$907$	−30.9168	−	22.4623i	−1.02657	−	0.745850i	−0.967620	+	0.252411i	$0.918777\pi$
$908$	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	−0.387730	−	0.921773i	$-0.626741\pi$
$911$	−33.7099	−	7.16526i	−1.11686	−	0.237395i	−0.729128	+	0.684377i	$0.760074\pi$
$912$	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	0.932575	−	0.360976i	$-0.117556\pi$
$919$	39.0558	+	17.3888i	1.28833	+	0.573603i	0.355758	+	0.934578i	$0.384223\pi$
$920$	−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	0.934427	+	0.356153i	$0.115912\pi$
$937$	2.89171	+	27.5128i	0.0944679	+	0.898802i	−0.839960	+	0.542649i	$0.817421\pi$
$938$	−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	−0.0360511	−	0.999350i	$-0.511478\pi$
$941$	−24.6276	−	10.9649i	−0.802836	−	0.357446i	−0.766785	+	0.641904i	$0.778145\pi$
$942$	−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	0.489980	−	0.871734i	$-0.337004\pi$
$947$	45.1034	−	20.0813i	1.46566	−	0.652556i	0.975685	+	0.219178i	$0.0703375\pi$
$948$	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	0.999053	−	0.0435081i	$-0.0138534\pi$
$953$	39.0946	+	28.4039i	1.26640	+	0.920093i	0.267346	+	0.963601i	$0.413853\pi$
$954$	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	0.0570410	−	0.998372i	$-0.481833\pi$
$967$	−24.2259	−	13.9869i	−0.779054	−	0.449787i	−0.836095	+	0.548585i	$0.815167\pi$
$968$	−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	0.575889	−	0.817528i	$-0.304656\pi$
$971$	−5.51434	−	4.96514i	−0.176964	−	0.159339i	−0.752853	+	0.658189i	$0.771323\pi$
$972$	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	0.948653	−	0.316318i	$-0.102447\pi$
$977$	47.8295	+	15.5408i	1.53020	+	0.497193i	0.581550	+	0.813511i	$0.302447\pi$
$978$	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	0.974920	+	0.222556i	$0.0714402\pi$
$983$	−0.782810	+	7.44794i	−0.0249677	+	0.237552i	−0.999888	+	0.0149958i	$0.995227\pi$
$984$	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	$0.187639\pi$
$991$			35.0017i			1.11186i	−0.831228	+	0.555932i	$0.812361\pi$
$992$	−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	0.994281	−	0.106793i	$-0.0340582\pi$
$997$	12.7771	+	22.1306i	0.404655	+	0.700883i	−0.589626	+	0.807676i	$0.700725\pi$
$998$	−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.11.6	✓	176
3.2	odd	2	inner	930.2.br.b.11.12	yes	176
31.17	odd	30	inner	930.2.br.b.761.12	yes	176
93.17	even	30	inner	930.2.br.b.761.6	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.6	✓	176	1.1	even	1	trivial
930.2.br.b.11.12	yes	176	3.2	odd	2	inner
930.2.br.b.761.6	yes	176	93.17	even	30	inner
930.2.br.b.761.12	yes	176	31.17	odd	30	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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