LMFDB - Embedded newform 930.2.br.b.11.14

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			11.14
Character	$\chi$	$=$	930.11
Dual form			930.2.br.b.761.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(-1.47317 + 0.910922i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.11958 + 1.32157i) q^{6} +(0.140936 + 1.34092i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.34044 - 2.68388i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(-1.47317 + 0.910922i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.11958 + 1.32157i) q^{6} +(0.140936 + 1.34092i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.34044 - 2.68388i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-3.37088 - 1.50081i) q^{11} +(-0.656391 + 1.60286i) q^{12} +(-1.36284 - 6.41167i) q^{13} +(0.548405 + 1.23174i) q^{14} +(-0.820340 + 1.52546i) q^{15} +(0.309017 - 0.951057i) q^{16} +(5.12286 - 2.28084i) q^{17} +(0.445473 - 2.96674i) q^{18} +(-1.80634 - 0.383949i) q^{19} +(0.406737 - 0.913545i) q^{20} +(-1.42910 - 1.84702i) q^{21} +(-3.66968 - 0.385699i) q^{22} +(4.04207 + 2.93674i) q^{23} +(-0.128955 + 1.72724i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-3.27746 - 5.67672i) q^{26} +(0.470106 + 5.17484i) q^{27} +(0.902193 + 1.00199i) q^{28} +(0.419623 + 1.29147i) q^{29} +(-0.308795 + 1.70430i) q^{30} +(4.68202 - 3.01308i) q^{31} -1.00000i q^{32} +(6.33300 - 0.859661i) q^{33} +(4.16731 - 3.75226i) q^{34} +(0.792514 + 1.09080i) q^{35} +(-0.493103 - 2.95920i) q^{36} +(-3.11169 - 1.79653i) q^{37} +(-1.83658 + 0.193032i) q^{38} +(7.84822 + 8.20402i) q^{39} +(0.104528 - 0.994522i) q^{40} +(1.81154 + 1.63112i) q^{41} +(-1.92991 - 1.31500i) q^{42} +(2.02409 - 9.52259i) q^{43} +(-3.60926 + 0.767172i) q^{44} +(-0.181081 - 2.99453i) q^{45} +(4.75174 + 1.54393i) q^{46} +(-2.26952 - 0.737413i) q^{47} +(0.411104 + 1.68256i) q^{48} +(5.06883 - 1.07741i) q^{49} +(0.207912 - 0.978148i) q^{50} +(-5.46916 + 8.02659i) q^{51} +(-4.87125 - 4.38609i) q^{52} +(0.959748 - 9.13139i) q^{53} +(2.04621 + 4.77630i) q^{54} +(-3.66968 + 0.385699i) q^{55} +(1.16767 + 0.674153i) q^{56} +(3.01079 - 1.07981i) q^{57} +(0.798170 + 1.09859i) q^{58} +(-7.31627 + 6.58760i) q^{59} +(0.232977 + 1.71631i) q^{60} -1.70177i q^{61} +(3.52177 - 4.31244i) q^{62} +(3.78779 + 1.41917i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-4.38609 - 4.87125i) q^{65} +(5.75739 - 2.77459i) q^{66} +(-0.0499869 - 0.0865799i) q^{67} +(2.80383 - 4.85638i) q^{68} +(-8.62978 - 0.644295i) q^{69} +(1.09080 + 0.792514i) q^{70} +(8.04344 + 0.845399i) q^{71} +(-1.38341 - 2.66199i) q^{72} +(1.50175 - 3.37300i) q^{73} +(-3.51455 - 0.747040i) q^{74} +(0.0522975 + 1.73126i) q^{75} +(-1.68704 + 0.751118i) q^{76} +(1.53739 - 4.73161i) q^{77} +(9.99929 + 5.37725i) q^{78} +(0.331778 + 0.745186i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(-5.40642 - 7.19518i) q^{81} +(2.22693 + 0.991491i) q^{82} +(-3.07491 + 3.41503i) q^{83} +(-2.24181 - 0.654267i) q^{84} +(3.29610 - 4.53670i) q^{85} +(-1.01762 - 9.68200i) q^{86} +(-1.79460 - 1.52030i) q^{87} +(-3.19554 + 1.84495i) q^{88} +(-9.31870 + 6.77043i) q^{89} +(-1.09758 - 2.79201i) q^{90} +(8.40546 - 2.73110i) q^{91} +4.99627 q^{92} +(-4.15272 + 8.70373i) q^{93} -2.38632 q^{94} +(-1.75631 + 0.570660i) q^{95} +(0.910922 + 1.47317i) q^{96} +(13.8287 - 10.0471i) q^{97} +(4.48780 - 2.59104i) q^{98} +(-8.54649 + 7.03529i) 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
$3$	−1.47317	+	0.910922i	−0.850534	+	0.525921i
$3$	−1.47317	+	0.910922i	−0.850534	+	0.525921i
$4$	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
$6$	−1.11958	+	1.32157i	−0.457065	+	0.539529i
$7$	0.140936	+	1.34092i	0.0532689	+	0.506820i	0.988329	+	0.152332i	$0.0486782\pi$
$7$	0.140936	+	1.34092i	0.0532689	+	0.506820i	−0.935060	+	0.354488i	$0.884655\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	1.34044	−	2.68388i	0.446815	−	0.894627i
$10$	0.669131	−	0.743145i	0.211598	−	0.235003i
$11$	−3.37088	−	1.50081i	−1.01636	−	0.452513i	−0.170182	−	0.985413i	$-0.554436\pi$
$11$	−3.37088	−	1.50081i	−1.01636	−	0.452513i	−0.846178	+	0.532900i	$0.821102\pi$
$12$	−0.656391	+	1.60286i	−0.189484	+	0.462705i
$13$	−1.36284	−	6.41167i	−0.377985	−	1.77828i	−0.596675	−	0.802483i	$-0.703512\pi$
$13$	−1.36284	−	6.41167i	−0.377985	−	1.77828i	0.218690	−	0.975794i	$-0.429822\pi$
$14$	0.548405	+	1.23174i	0.146568	+	0.329196i
$15$	−0.820340	+	1.52546i	−0.211811	+	0.393873i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	5.12286	−	2.28084i	1.24248	−	0.553186i	0.323025	−	0.946390i	$-0.395300\pi$
$17$	5.12286	−	2.28084i	1.24248	−	0.553186i	0.919451	+	0.393204i	$0.128634\pi$
$18$	0.445473	−	2.96674i	0.104999	−	0.699268i
$19$	−1.80634	−	0.383949i	−0.414403	−	0.0880840i	−0.00400785	−	0.999992i	$-0.501276\pi$
$19$	−1.80634	−	0.383949i	−0.414403	−	0.0880840i	−0.410395	+	0.911908i	$0.634609\pi$
$20$	0.406737	−	0.913545i	0.0909491	−	0.204275i
$21$	−1.42910	−	1.84702i	−0.311854	−	0.403052i
$22$	−3.66968	−	0.385699i	−0.782378	−	0.0822313i
$23$	4.04207	+	2.93674i	0.842830	+	0.612352i	0.923160	−	0.384417i	$-0.125597\pi$
$23$	4.04207	+	2.93674i	0.842830	+	0.612352i	−0.0803298	+	0.996768i	$0.525597\pi$
$24$	−0.128955	+	1.72724i	−0.0263228	+	0.352572i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−3.27746	−	5.67672i	−0.642762	−	1.11330i
$27$	0.470106	+	5.17484i	0.0904719	+	0.995899i
$28$	0.902193	+	1.00199i	0.170498	+	0.189358i
$29$	0.419623	+	1.29147i	0.0779220	+	0.239819i	0.982428	−	0.186641i	$-0.0597603\pi$
$29$	0.419623	+	1.29147i	0.0779220	+	0.239819i	−0.904506	+	0.426461i	$0.859760\pi$
$30$	−0.308795	+	1.70430i	−0.0563779	+	0.311162i
$31$	4.68202	−	3.01308i	0.840916	−	0.541166i
$31$	4.68202	−	3.01308i	0.840916	−	0.541166i
$32$		−	1.00000i		−	0.176777i
$33$	6.33300	−	0.859661i	1.10243	−	0.149648i
$34$	4.16731	−	3.75226i	0.714688	−	0.643508i
$35$	0.792514	+	1.09080i	0.133959	+	0.184379i
$36$	−0.493103	−	2.95920i	−0.0821838	−	0.493200i
$37$	−3.11169	−	1.79653i	−0.511558	−	0.295348i	0.221916	−	0.975066i	$-0.428769\pi$
$37$	−3.11169	−	1.79653i	−0.511558	−	0.295348i	−0.733474	+	0.679718i	$0.762102\pi$
$38$	−1.83658	+	0.193032i	−0.297932	+	0.0313139i
$39$	7.84822	+	8.20402i	1.25672	+	1.31369i
$40$	0.104528	−	0.994522i	0.0165274	−	0.157248i
$41$	1.81154	+	1.63112i	0.282916	+	0.254738i	0.798354	−	0.602188i	$-0.205704\pi$
$41$	1.81154	+	1.63112i	0.282916	+	0.254738i	−0.515439	+	0.856927i	$0.672371\pi$
$42$	−1.92991	−	1.31500i	−0.297792	−	0.202909i
$43$	2.02409	−	9.52259i	0.308671	−	1.45218i	−0.501077	−	0.865403i	$-0.667063\pi$
$43$	2.02409	−	9.52259i	0.308671	−	1.45218i	0.809747	−	0.586779i	$-0.199604\pi$
$44$	−3.60926	+	0.767172i	−0.544116	+	0.115656i
$45$	−0.181081	−	2.99453i	−0.0269940	−	0.446398i
$46$	4.75174	+	1.54393i	0.700606	+	0.227641i
$47$	−2.26952	−	0.737413i	−0.331044	−	0.107563i	0.138779	−	0.990323i	$-0.455682\pi$
$47$	−2.26952	−	0.737413i	−0.331044	−	0.107563i	−0.469823	+	0.882761i	$0.655682\pi$
$48$	0.411104	+	1.68256i	0.0593378	+	0.242856i
$49$	5.06883	−	1.07741i	0.724119	−	0.153916i
$50$	0.207912	−	0.978148i	0.0294032	−	0.138331i
$51$	−5.46916	+	8.02659i	−0.765836	+	1.12395i
$52$	−4.87125	−	4.38609i	−0.675521	−	0.608241i
$53$	0.959748	−	9.13139i	0.131832	−	1.25429i	−0.705940	−	0.708272i	$-0.749475\pi$
$53$	0.959748	−	9.13139i	0.131832	−	1.25429i	0.837771	−	0.546021i	$-0.183858\pi$
$54$	2.04621	+	4.77630i	0.278454	+	0.649972i
$55$	−3.66968	+	0.385699i	−0.494819	+	0.0520076i
$56$	1.16767	+	0.674153i	0.156036	+	0.0900875i
$57$	3.01079	−	1.07981i	0.398789	−	0.143025i
$58$	0.798170	+	1.09859i	0.104805	+	0.144251i
$59$	−7.31627	+	6.58760i	−0.952497	+	0.857632i	−0.989914	−	0.141667i	$-0.954754\pi$
$59$	−7.31627	+	6.58760i	−0.952497	+	0.857632i	0.0374170	+	0.999300i	$0.488087\pi$
$60$	0.232977	+	1.71631i	0.0300772	+	0.221575i
$61$		−	1.70177i		−	0.217889i	−0.994048	−	0.108944i	$-0.965253\pi$
$61$		−	1.70177i		−	0.217889i	0.994048	−	0.108944i	$-0.0347471\pi$
$62$	3.52177	−	4.31244i	0.447266	−	0.547680i
$63$	3.78779	+	1.41917i	0.477216	+	0.178799i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−4.38609	−	4.87125i	−0.544028	−	0.604204i
$66$	5.75739	−	2.77459i	0.708686	−	0.341529i
$67$	−0.0499869	−	0.0865799i	−0.00610687	−	0.0105774i	0.862956	−	0.505279i	$-0.168611\pi$
$67$	−0.0499869	−	0.0865799i	−0.00610687	−	0.0105774i	−0.869063	+	0.494702i	$0.835277\pi$
$68$	2.80383	−	4.85638i	0.340015	−	0.588923i
$69$	−8.62978	−	0.644295i	−1.03890	−	0.0775640i
$70$	1.09080	+	0.792514i	0.130376	+	0.0947236i
$71$	8.04344	+	0.845399i	0.954580	+	0.100330i	0.568994	−	0.822341i	$-0.307333\pi$
$71$	8.04344	+	0.845399i	0.954580	+	0.100330i	0.385586	+	0.922672i	$0.373999\pi$
$72$	−1.38341	−	2.66199i	−0.163037	−	0.313718i
$73$	1.50175	−	3.37300i	0.175767	−	0.394779i	−0.804082	−	0.594518i	$-0.797343\pi$
$73$	1.50175	−	3.37300i	0.175767	−	0.394779i	0.979849	+	0.199739i	$0.0640094\pi$
$74$	−3.51455	−	0.747040i	−0.408558	−	0.0868417i
$75$	0.0522975	+	1.73126i	0.00603880	+	0.199909i
$76$	−1.68704	+	0.751118i	−0.193517	+	0.0861591i
$77$	1.53739	−	4.73161i	0.175202	−	0.539217i
$78$	9.99929	+	5.37725i	1.13220	+	0.608854i
$79$	0.331778	+	0.745186i	0.0373280	+	0.0838400i	0.931247	−	0.364388i	$-0.118722\pi$
$79$	0.331778	+	0.745186i	0.0373280	+	0.0838400i	−0.893919	+	0.448228i	$0.852055\pi$
$80$	−0.207912	−	0.978148i	−0.0232452	−	0.109360i
$81$	−5.40642	−	7.19518i	−0.600713	−	0.799464i
$82$	2.22693	+	0.991491i	0.245923	+	0.109492i
$83$	−3.07491	+	3.41503i	−0.337515	+	0.374849i	−0.887880	−	0.460076i	$-0.847822\pi$
$83$	−3.07491	+	3.41503i	−0.337515	+	0.374849i	0.550364	+	0.834925i	$0.314489\pi$
$84$	−2.24181	−	0.654267i	−0.244602	−	0.0713864i
$85$	3.29610	−	4.53670i	0.357513	−	0.492074i
$86$	−1.01762	−	9.68200i	−0.109733	−	1.04404i
$87$	−1.79460	−	1.52030i	−0.192401	−	0.162993i
$88$	−3.19554	+	1.84495i	−0.340646	+	0.196672i
$89$	−9.31870	+	6.77043i	−0.987780	+	0.717664i	−0.959434	−	0.281934i	$-0.909024\pi$
$89$	−9.31870	+	6.77043i	−0.987780	+	0.717664i	−0.0283463	+	0.999598i	$0.509024\pi$
$90$	−1.09758	−	2.79201i	−0.115695	−	0.294304i
$91$	8.40546	−	2.73110i	0.881132	−	0.286297i
$92$	4.99627			0.520898
$93$	−4.15272	+	8.70373i	−0.430617	+	0.902535i
$94$	−2.38632			−0.246130
$95$	−1.75631	+	0.570660i	−0.180194	+	0.0585485i
$96$	0.910922	+	1.47317i	0.0929705	+	0.150355i
$97$	13.8287	−	10.0471i	1.40409	−	1.02013i	0.409938	−	0.912113i	$-0.365550\pi$
$97$	13.8287	−	10.0471i	1.40409	−	1.02013i	0.994149	−	0.108016i	$-0.0344497\pi$
$98$	4.48780	−	2.59104i	0.453337	−	0.261734i
$99$	−8.54649	+	7.03529i	−0.858954	+	0.707073i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−7.89339	+	10.8643i	−0.785422	+	1.08104i	0.209241	+	0.977864i	$0.432901\pi$
$101$	−7.89339	+	10.8643i	−0.785422	+	1.08104i	−0.994663	+	0.103177i	$0.967099\pi$
$102$	−2.72113	+	9.32380i	−0.269432	+	0.923194i
$103$	5.22200	−	5.79962i	0.514539	−	0.571453i	−0.428751	−	0.903423i	$-0.641046\pi$
$103$	5.22200	−	5.79962i	0.514539	−	0.571453i	0.943290	+	0.331969i	$0.107713\pi$
$104$	−5.98821	−	2.66612i	−0.587192	−	0.261435i
$105$	−2.16114	−	0.885016i	−0.210906	−	0.0863687i
$106$	−1.90898	−	8.98105i	−0.185417	−	0.872317i
$107$	−2.63935	−	5.92808i	−0.255156	−	0.573089i	0.739865	−	0.672755i	$-0.234889\pi$
$107$	−2.63935	−	5.92808i	−0.255156	−	0.573089i	−0.995021	+	0.0996658i	$0.968223\pi$
$108$	3.42202	+	3.91021i	0.329284	+	0.376261i
$109$	−6.04369	+	18.6006i	−0.578880	+	1.78161i	0.0436890	+	0.999045i	$0.486089\pi$
$109$	−6.04369	+	18.6006i	−0.578880	+	1.78161i	−0.622569	+	0.782565i	$0.713911\pi$
$110$	−3.37088	+	1.50081i	−0.321401	+	0.143097i
$111$	6.22054	−	0.187908i	0.590427	−	0.0178355i
$112$	1.31884	+	0.280329i	0.124619	+	0.0264886i
$113$	−6.93720	+	15.5812i	−0.652597	+	1.46576i	0.219096	+	0.975703i	$0.429689\pi$
$113$	−6.93720	+	15.5812i	−0.652597	+	1.46576i	−0.871693	+	0.490053i	$0.836977\pi$
$114$	2.52975	−	1.95735i	0.236933	−	0.183322i
$115$	4.96890	+	0.522253i	0.463353	+	0.0487003i
$116$	1.09859	+	0.798170i	0.102001	+	0.0741082i
$117$	−19.0350	−	4.93678i	−1.75978	−	0.456405i
$118$	−4.92251	+	8.52603i	−0.453153	+	0.784885i
$119$	3.78043	+	6.54789i	0.346551	+	0.600244i
$120$	0.751943	+	1.56031i	0.0686427	+	0.142437i
$121$	1.74998	+	1.94355i	0.159089	+	0.176687i
$122$	−0.525875	−	1.61848i	−0.0476105	−	0.146530i
$123$	−4.15453	−	0.752741i	−0.374602	−	0.0678723i
$124$	2.01679	−	5.18966i	0.181113	−	0.466045i
$125$		−	1.00000i		−	0.0894427i
$126$	4.04095	+	0.179223i	0.359996	+	0.0159664i
$127$	−13.4400	+	12.1014i	−1.19261	+	1.07383i	−0.196979	+	0.980408i	$0.563113\pi$
$127$	−13.4400	+	12.1014i	−1.19261	+	1.07383i	−0.995627	+	0.0934189i	$0.970220\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	5.69251	+	15.8722i	0.501198	+	1.39747i
$130$	−5.67672	−	3.27746i	−0.497881	−	0.287452i
$131$	12.7882	−	1.34410i	1.11731	−	0.117434i	0.472178	−	0.881503i	$-0.343468\pi$
$131$	12.7882	−	1.34410i	1.11731	−	0.117434i	0.645135	+	0.764069i	$0.276801\pi$
$132$	4.61821	−	4.41793i	0.401964	−	0.384531i
$133$	0.260266	−	2.47627i	0.0225679	−	0.214720i
$134$	−0.0742950	−	0.0668956i	−0.00641811	−	0.00577890i
$135$	2.99454	+	4.24649i	0.257729	+	0.365480i
$136$	1.16590	−	5.48513i	0.0999751	−	0.470346i
$137$	3.58631	−	0.762293i	0.306399	−	0.0651271i	−0.0521463	−	0.998639i	$-0.516606\pi$
$137$	3.58631	−	0.762293i	0.306399	−	0.0651271i	0.358545	+	0.933512i	$0.383273\pi$
$138$	−8.40651	+	2.05399i	−0.715610	+	0.174847i
$139$	6.94795	+	2.25753i	0.589318	+	0.191481i	0.588471	−	0.808519i	$-0.299730\pi$
$139$	6.94795	+	2.25753i	0.589318	+	0.191481i	0.000847313		1.00000i	$0.499730\pi$
$140$	1.28232	+	0.416649i	0.108375	+	0.0352133i
$141$	4.01511	−	0.981025i	0.338133	−	0.0826172i
$142$	7.91101	−	1.68154i	0.663877	−	0.141111i
$143$	−5.02874	+	23.6584i	−0.420525	+	1.97841i
$144$	−2.13830	−	2.10420i	−0.178192	−	0.175350i
$145$	1.00914	+	0.908631i	0.0838042	+	0.0754577i
$146$	0.385940	−	3.67198i	0.0319407	−	0.303895i
$147$	−6.48580	+	6.20452i	−0.534939	+	0.511740i
$148$	−3.57338	+	0.375578i	−0.293730	+	0.0308723i
$149$	19.0580	+	11.0032i	1.56130	+	0.901414i	0.997126	+	0.0757551i	$0.0241367\pi$
$149$	19.0580	+	11.0032i	1.56130	+	0.901414i	0.564169	+	0.825659i	$0.309197\pi$
$150$	0.584727	+	1.63037i	0.0477428	+	0.133119i
$151$	−11.7273	−	16.1412i	−0.954354	−	1.31356i	−0.949566	−	0.313567i	$-0.898476\pi$
$151$	−11.7273	−	16.1412i	−0.954354	−	1.31356i	−0.00478737	−	0.999989i	$-0.501524\pi$
$152$	−1.37236	+	1.23568i	−0.111313	+	0.100227i
$153$	0.745395	−	16.8065i	0.0602616	−	1.35872i
$154$		−	4.97511i		−	0.400905i
$155$	2.54821	−	4.95042i	0.204677	−	0.397627i
$156$	11.1715	+	2.02412i	0.894440	+	0.162059i
$157$	2.69616	+	8.29793i	0.215177	+	0.662247i	0.999141	+	0.0414407i	$0.0131948\pi$
$157$	2.69616	+	8.29793i	0.215177	+	0.662247i	−0.783964	+	0.620807i	$0.786805\pi$
$158$	0.545815	+	0.606189i	0.0434227	+	0.0482258i
$159$	6.90411	+	14.3263i	0.547532	+	1.13615i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−3.36825	+	5.83399i	−0.265456	+	0.459782i
$162$	−7.36524	−	5.17235i	−0.578668	−	0.406378i
$163$	−7.44782	−	5.41116i	−0.583358	−	0.423835i	0.256575	−	0.966524i	$-0.417406\pi$
$163$	−7.44782	−	5.41116i	−0.583358	−	0.423835i	−0.839933	+	0.542690i	$0.817406\pi$
$164$	2.42432	+	0.254806i	0.189308	+	0.0198970i
$165$	5.05471	−	3.91099i	0.393509	−	0.304470i
$166$	−1.86911	+	4.19809i	−0.145071	+	0.325835i
$167$	4.72701	+	1.00476i	0.365787	+	0.0777504i	0.387138	−	0.922022i	$-0.373464\pi$
$167$	4.72701	+	1.00476i	0.365787	+	0.0777504i	−0.0213516	+	0.999772i	$0.506797\pi$
$168$	−2.33427	+	0.0705131i	−0.180093	+	0.00544020i
$169$	−27.3761	+	12.1886i	−2.10585	+	0.937586i
$170$	1.73286	−	5.33321i	0.132905	−	0.409038i
$171$	−3.45177	+	4.33333i	−0.263963	+	0.331378i
$172$	−3.95972	−	8.89367i	−0.301926	−	0.678136i
$173$	−3.24242	−	15.2544i	−0.246517	−	1.15977i	−0.910980	−	0.412450i	$-0.864673\pi$
$173$	−3.24242	−	15.2544i	−0.246517	−	1.15977i	0.664463	−	0.747321i	$-0.268660\pi$
$174$	−2.17656	−	0.891332i	−0.165005	−	0.0675717i
$175$	1.23174	+	0.548405i	0.0931107	+	0.0414556i
$176$	−2.46902	+	2.74212i	−0.186109	+	0.206695i
$177$	4.77730	−	16.3692i	0.359084	−	1.23038i
$178$	−6.77043	+	9.31870i	−0.507465	+	0.698466i
$179$	1.50880	+	14.3553i	0.112773	+	1.07296i	0.893800	+	0.448467i	$0.148030\pi$
$179$	1.50880	+	14.3553i	0.112773	+	1.07296i	−0.781026	+	0.624498i	$0.785304\pi$
$180$	−1.90664	−	2.31619i	−0.142112	−	0.172639i
$181$	−8.35728	+	4.82508i	−0.621192	+	0.358645i	−0.777333	−	0.629089i	$-0.783428\pi$
$181$	−8.35728	+	4.82508i	−0.621192	+	0.358645i	0.156141	+	0.987735i	$0.450095\pi$
$182$	7.15011	−	5.19486i	0.530002	−	0.385069i
$183$	1.55018	+	2.50699i	0.114592	+	0.185322i
$184$	4.75174	−	1.54393i	0.350303	−	0.113820i
$185$	−3.59307			−0.264167
$186$	−1.25987	+	9.56100i	−0.0923782	+	0.701047i
$187$	−20.6917			−1.51313
$188$	−2.26952	+	0.737413i	−0.165522	+	0.0537814i
$189$	−6.87280	+	1.35970i	−0.499922	+	0.0989034i
$190$	−1.49401	+	1.08546i	−0.108387	+	0.0787475i
$191$	−6.84297	+	3.95079i	−0.495140	+	0.285869i	−0.726704	−	0.686951i	$-0.758949\pi$
$191$	−6.84297	+	3.95079i	−0.495140	+	0.285869i	0.231564	+	0.972820i	$0.425616\pi$
$192$	1.32157	+	1.11958i	0.0953762	+	0.0807984i
$193$	0.947966	+	9.01929i	0.0682361	+	0.649223i	0.974172	+	0.225808i	$0.0725022\pi$
$193$	0.947966	+	9.01929i	0.0682361	+	0.649223i	−0.905936	+	0.423415i	$0.860831\pi$
$194$	10.0471	−	13.8287i	0.721340	−	0.992840i
$195$	10.8988	+	3.18078i	0.780477	+	0.227780i
$196$	3.46748	−	3.85103i	0.247677	−	0.275074i
$197$	−9.03839	−	4.02415i	−0.643958	−	0.286709i	0.0586575	−	0.998278i	$-0.481318\pi$
$197$	−9.03839	−	4.02415i	−0.643958	−	0.286709i	−0.702616	+	0.711569i	$0.747985\pi$
$198$	−5.95417	+	9.33197i	−0.423144	+	0.663194i
$199$	−0.000289787	−	0.00136334i	−2.05424e−5	−	9.66446e-5i	0.978137	−	0.207960i	$-0.0666824\pi$
$199$	−0.000289787	−	0.00136334i	−2.05424e−5	−	9.66446e-5i	−0.978158	+	0.207863i	$0.933349\pi$
$200$	−0.406737	−	0.913545i	−0.0287606	−	0.0645974i
$201$	0.152507	+	0.0820125i	0.0107570	+	0.00578472i
$202$	−4.14980	+	12.7718i	−0.291979	+	0.898619i
$203$	−1.67261	+	0.744695i	−0.117394	+	0.0522673i
$204$	0.293267	+	9.70834i	0.0205328	+	0.679720i
$205$	2.38440	+	0.506821i	0.166534	+	0.0353979i
$206$	3.17424	−	7.12945i	0.221160	−	0.496732i
$207$	13.3000	−	6.91190i	0.924415	−	0.480410i
$208$	−6.51900	−	0.685175i	−0.452011	−	0.0475083i
$209$	5.51272	+	4.00523i	0.381323	+	0.277047i
$210$	−2.32885	−	0.173871i	−0.160706	−	0.0119982i
$211$	−6.86283	+	11.8868i	−0.472457	+	0.818319i	−0.999503	−	0.0315172i	$-0.989966\pi$
$211$	−6.86283	+	11.8868i	−0.472457	+	0.818319i	0.527046	+	0.849837i	$0.323299\pi$
$212$	−4.59085	−	7.95158i	−0.315301	−	0.546117i
$213$	−12.6194	+	6.08153i	−0.864668	+	0.416699i
$214$	−4.34205	−	4.82234i	−0.296817	−	0.329648i
$215$	−3.00838	−	9.25885i	−0.205170	−	0.631448i
$216$	4.46286	+	2.66137i	0.303659	+	0.181083i
$217$	4.70017	+	5.85356i	0.319068	+	0.397366i
$218$			19.5578i			1.32462i
$219$	0.860199	+	6.33697i	0.0581269	+	0.428213i
$220$	−2.74212	+	2.46902i	−0.184874	+	0.166461i
$221$	−21.6057	−	29.7377i	−1.45335	−	2.00037i
$222$	5.85801	−	2.10096i	0.393164	−	0.141007i
$223$	−10.9442	−	6.31865i	−0.732880	−	0.423128i	0.0865949	−	0.996244i	$-0.472401\pi$
$223$	−10.9442	−	6.31865i	−0.732880	−	0.423128i	−0.819475	+	0.573115i	$0.805735\pi$
$224$	1.34092	−	0.140936i	0.0895940	−	0.00941671i
$225$	−1.65409	−	2.50280i	−0.110272	−	0.166853i
$226$	−1.78281	+	16.9623i	−0.118591	+	1.12832i
$227$	8.30198	+	7.47513i	0.551022	+	0.496142i	0.896958	−	0.442116i	$-0.145772\pi$
$227$	8.30198	+	7.47513i	0.551022	+	0.496142i	−0.345936	+	0.938258i	$0.612439\pi$
$228$	1.80108	−	2.64328i	0.119279	−	0.175056i
$229$	2.48323	−	11.6827i	0.164096	−	0.772013i	−0.816713	−	0.577044i	$-0.804206\pi$
$229$	2.48323	−	11.6827i	0.164096	−	0.772013i	0.980809	−	0.194969i	$-0.0624606\pi$
$230$	4.88709	−	1.03878i	0.322245	−	0.0684954i
$231$	2.04529	+	8.37089i	0.134570	+	0.550764i
$232$	1.29147	+	0.419623i	0.0847889	+	0.0275496i
$233$	10.9052	+	3.54332i	0.714424	+	0.232130i	0.643604	−	0.765359i	$-0.277438\pi$
$233$	10.9052	+	3.54332i	0.714424	+	0.232130i	0.0708198	+	0.997489i	$0.477438\pi$
$234$	−19.6289	+	1.18697i	−1.28318	+	0.0775948i
$235$	−2.33417	+	0.496143i	−0.152265	+	0.0323648i
$236$	−2.04689	+	9.62988i	−0.133241	+	0.626852i
$237$	−1.16757	−	0.795560i	−0.0758419	−	0.0516772i
$238$	5.61881	+	5.05920i	0.364213	+	0.327939i
$239$	−1.50610	+	14.3295i	−0.0974212	+	0.926901i	0.831225	+	0.555936i	$0.187640\pi$
$239$	−1.50610	+	14.3295i	−0.0974212	+	0.926901i	−0.928647	+	0.370966i	$0.879027\pi$
$240$	1.19730	+	1.25158i	0.0772857	+	0.0807894i
$241$	−12.5968	+	1.32397i	−0.811429	+	0.0852846i	−0.501149	−	0.865361i	$-0.667089\pi$
$241$	−12.5968	+	1.32397i	−0.811429	+	0.0852846i	−0.310279	+	0.950645i	$0.600423\pi$
$242$	2.26492	+	1.30765i	0.145595	+	0.0840592i
$243$	14.5188	+	5.67488i	0.931382	+	0.364044i
$244$	−1.00027	−	1.37676i	−0.0640359	−	0.0881379i
$245$	3.85103	−	3.46748i	0.246033	−	0.221529i
$246$	−4.18380	+	0.567922i	−0.266750	+	0.0362094i
$247$			12.1049i			0.770217i
$248$	0.314388	−	5.55888i	0.0199637	−	0.352989i
$249$	1.41903	−	7.83192i	0.0899273	−	0.496328i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	1.34486	+	1.49361i	0.0848865	+	0.0942760i	0.784092	−	0.620645i	$-0.213129\pi$
$251$	1.34486	+	1.49361i	0.0848865	+	0.0942760i	−0.699205	+	0.714921i	$0.746463\pi$
$252$	3.89855	−	1.07827i	0.245586	−	0.0679246i
$253$	−9.21786	−	15.9658i	−0.579522	−	1.00376i
$254$	−9.04264	+	15.6623i	−0.567386	+	0.982741i
$255$	−0.723137	+	9.68581i	−0.0452846	+	0.606549i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−3.03046	−	0.318514i	−0.189035	−	0.0198684i	0.00953794	−	0.999955i	$-0.496964\pi$
$257$	−3.03046	−	0.318514i	−0.189035	−	0.0198684i	−0.198573	+	0.980086i	$0.563631\pi$
$258$	10.3187	+	13.3362i	0.642412	+	0.830278i
$259$	1.97046	−	4.42572i	0.122438	−	0.275001i
$260$	−6.41167	−	1.36284i	−0.397635	−	0.0845199i
$261$	4.02862	+	0.604921i	0.249365	+	0.0374437i
$262$	11.7470	−	5.23009i	0.725731	−	0.323116i
$263$	−0.850313	+	2.61699i	−0.0524325	+	0.161371i	−0.973844	−	0.227218i	$-0.927037\pi$
$263$	−0.850313	+	2.61699i	−0.0524325	+	0.161371i	0.921411	+	0.388588i	$0.127037\pi$
$264$	3.02697	−	5.62880i	0.186297	−	0.346429i
$265$	−3.73453	−	8.38789i	−0.229410	−	0.515264i
$266$	−0.517681	−	2.43550i	−0.0317411	−	0.149330i
$267$	7.56067	−	18.4626i	0.462706	−	1.12989i
$268$	−0.0913306	−	0.0406630i	−0.00557891	−	0.00248389i
$269$	15.4577	−	17.1675i	0.942473	−	1.04672i	−0.0563592	−	0.998411i	$-0.517949\pi$
$269$	15.4577	−	17.1675i	0.942473	−	1.04672i	0.998832	−	0.0483118i	$-0.0153841\pi$
$270$	4.16022	+	3.11329i	0.253183	+	0.189469i
$271$	11.5470	−	15.8931i	0.701431	−	0.965437i	−0.298508	−	0.954407i	$-0.596489\pi$
$271$	11.5470	−	15.8931i	0.701431	−	0.965437i	0.999939	−	0.0110298i	$-0.00351096\pi$
$272$	−0.586161	−	5.57695i	−0.0355412	−	0.338152i
$273$	−9.89483	+	11.6801i	−0.598863	+	0.706911i
$274$	3.17522	−	1.83321i	0.191822	−	0.110748i
$275$	−2.98519	+	2.16886i	−0.180013	+	0.130787i
$276$	−7.36035	+	4.55121i	−0.443041	+	0.273951i
$277$	−1.45337	+	0.472230i	−0.0873248	+	0.0283736i	−0.352354	−	0.935867i	$-0.614619\pi$
$277$	−1.45337	+	0.472230i	−0.0873248	+	0.0283736i	0.265029	+	0.964241i	$0.414619\pi$
$278$	7.30551			0.438156
$279$	−1.81076	−	16.6049i	−0.108408	−	0.994107i
$280$	1.34831			0.0805767
$281$	14.8517	−	4.82562i	0.885980	−	0.287872i	0.169542	−	0.985523i	$-0.445771\pi$
$281$	14.8517	−	4.82562i	0.885980	−	0.287872i	0.716438	+	0.697650i	$0.245771\pi$
$282$	3.51545	−	2.17375i	0.209342	−	0.129445i
$283$	20.2186	−	14.6897i	1.20187	−	0.873209i	0.207402	−	0.978256i	$-0.433499\pi$
$283$	20.2186	−	14.6897i	1.20187	−	0.873209i	0.994467	+	0.105047i	$0.0334992\pi$
$284$	7.00419	−	4.04387i	0.415622	−	0.239960i
$285$	2.06751	−	2.44054i	0.122469	−	0.144565i
$286$	2.52822	+	24.0544i	0.149497	+	1.42237i
$287$	−1.93189	+	2.65902i	−0.114036	+	0.156957i
$288$	−2.68388	−	1.34044i	−0.158149	−	0.0789864i
$289$	9.66622	−	10.7354i	0.568601	−	0.631496i
$290$	1.24053	+	0.552319i	0.0728463	+	0.0324333i
$291$	−11.2198	+	27.3979i	−0.657716	+	1.60609i
$292$	−0.767652	−	3.61152i	−0.0449235	−	0.211348i
$293$	7.63171	+	17.1411i	0.445850	+	1.00139i	0.987037	+	0.160493i	$0.0513083\pi$
$293$	7.63171	+	17.1411i	0.445850	+	1.00139i	−0.541188	+	0.840902i	$0.682025\pi$
$294$	−4.25106	+	7.90507i	−0.247927	+	0.461033i
$295$	−3.04228	+	9.36316i	−0.177128	+	0.545144i
$296$	−3.28243	+	1.46143i	−0.190787	+	0.0849440i
$297$	6.18181	−	18.1493i	0.358705	−	1.05313i
$298$	21.5254	+	4.57537i	1.24694	+	0.265044i
$299$	13.3207	−	29.9187i	0.770355	−	1.73024i
$300$	1.05992	+	1.36988i	0.0611945	+	0.0790901i
$301$	13.0543	+	1.37206i	0.752437	+	0.0790844i
$302$	−16.1412	−	11.7273i	−0.928824	−	0.674830i
$303$	1.73174	−	23.1952i	0.0994860	−	1.33253i
$304$	−0.923347	+	1.59928i	−0.0529576	+	0.0917252i
$305$	−0.850883	−	1.47377i	−0.0487214	−	0.0843880i
$306$	−4.48458	−	16.2143i	−0.256366	−	0.926907i
$307$	7.18730	+	7.98230i	0.410201	+	0.455574i	0.912474	−	0.409135i	$-0.134169\pi$
$307$	7.18730	+	7.98230i	0.410201	+	0.455574i	−0.502273	+	0.864709i	$0.667503\pi$
$308$	−1.53739	−	4.73161i	−0.0876010	−	0.269608i
$309$	−2.40988	+	13.3006i	−0.137093	+	0.756647i
$310$	0.893727	−	5.49557i	0.0507603	−	0.312127i
$311$		−	8.76227i		−	0.496863i	−0.968649	−	0.248431i	$-0.920085\pi$
$311$		−	8.76227i		−	0.496863i	0.968649	−	0.248431i	$-0.0799151\pi$
$312$	11.2503	−	1.52714i	0.636921	−	0.0864575i
$313$	6.50542	−	5.85750i	0.367708	−	0.331086i	−0.464476	−	0.885586i	$-0.653757\pi$
$313$	6.50542	−	5.85750i	0.367708	−	0.331086i	0.832184	+	0.554500i	$0.187091\pi$
$314$	5.12841	+	7.05864i	0.289413	+	0.398342i
$315$	3.98990	−	0.664854i	0.224806	−	0.0374603i
$316$	0.706424	+	0.407854i	0.0397394	+	0.0229436i
$317$	22.0209	−	2.31449i	1.23682	−	0.129995i	0.536546	−	0.843871i	$-0.319729\pi$
$317$	22.0209	−	2.31449i	1.23682	−	0.129995i	0.700272	+	0.713876i	$0.253062\pi$
$318$	10.9933	+	11.4917i	0.616473	+	0.644420i
$319$	0.523751	−	4.98316i	0.0293244	−	0.279003i
$320$	−0.743145	−	0.669131i	−0.0415431	−	0.0374055i
$321$	9.28823	+	6.32881i	0.518418	+	0.353240i
$322$	−1.40060	+	6.58930i	−0.0780523	+	0.367207i
$323$	−10.1293	+	2.15306i	−0.563612	+	0.119799i
$324$	−8.60311	−	2.64321i	−0.477950	−	0.146845i
$325$	−6.23409	−	2.02558i	−0.345805	−	0.112359i
$326$	−8.75544	−	2.84481i	−0.484919	−	0.157560i
$327$	−8.04028	−	32.9071i	−0.444629	−	1.81976i
$328$	2.38440	−	0.506821i	0.131657	−	0.0279845i
$329$	0.668953	−	3.14718i	0.0368806	−	0.173509i
$330$	3.59875	−	5.28156i	0.198105	−	0.290740i
$331$	17.6480	+	15.8903i	0.970023	+	0.873412i	0.991986	−	0.126347i	$-0.0403251\pi$
$331$	17.6480	+	15.8903i	0.970023	+	0.873412i	−0.0219636	+	0.999759i	$0.506992\pi$
$332$	−0.480348	+	4.57021i	−0.0263625	+	0.250823i
$333$	−8.99272	+	5.94324i	−0.492798	+	0.325688i
$334$	4.80614	−	0.505145i	0.262980	−	0.0276403i
$335$	−0.0865799	−	0.0499869i	−0.00473036	−	0.00273108i
$336$	−2.19823	+	0.788391i	−0.119923	+	0.0430103i
$337$	−13.0598	−	17.9753i	−0.711413	−	0.979176i	−0.999766	−	0.0216513i	$-0.993108\pi$
$337$	−13.0598	−	17.9753i	−0.711413	−	0.979176i	0.288353	−	0.957524i	$-0.406892\pi$
$338$	−22.2697	+	20.0517i	−1.21131	+	1.09067i
$339$	−3.97360	−	29.2730i	−0.215816	−	1.58989i
$340$		−	5.60767i		−	0.304119i
$341$	−20.3046	+	3.12991i	−1.09956	+	0.169494i
$342$	−1.94375	+	5.18790i	−0.105106	+	0.280530i
$343$	5.07565	+	15.6213i	0.274060	+	0.843469i
$344$	−6.51421	−	7.23476i	−0.351223	−	0.390072i
$345$	−7.79576	+	3.75692i	−0.419709	+	0.202266i
$346$	−7.79760	−	13.5058i	−0.419201	−	0.726078i
$347$	−12.6018	+	21.8270i	−0.676500	+	1.17173i	0.299528	+	0.954088i	$0.403171\pi$
$347$	−12.6018	+	21.8270i	−0.676500	+	1.17173i	−0.976028	+	0.217645i	$0.930162\pi$
$348$	−2.34547	−	0.175112i	−0.125730	−	0.00938697i
$349$	28.7820	+	20.9114i	1.54067	+	1.11936i	0.949917	+	0.312504i	$0.101168\pi$
$349$	28.7820	+	20.9114i	1.54067	+	1.11936i	0.590749	+	0.806855i	$0.298832\pi$
$350$	1.34092	+	0.140936i	0.0716752	+	0.00753337i
$351$	32.5387	−	10.0667i	1.73679	−	0.537319i
$352$	−1.50081	+	3.37088i	−0.0799937	+	0.179669i
$353$	27.9373	+	5.93825i	1.48695	+	0.316061i	0.878581	−	0.477593i	$-0.158491\pi$
$353$	27.9373	+	5.93825i	1.48695	+	0.316061i	0.608369	+	0.793654i	$0.291824\pi$
$354$	−0.514870	−	17.0443i	−0.0273650	−	0.905894i
$355$	7.38852	−	3.28958i	0.392142	−	0.174593i
$356$	−3.55943	+	10.9548i	−0.188649	+	0.580603i
$357$	−11.5338	−	6.20247i	−0.610434	−	0.328269i
$358$	5.87098	+	13.1864i	0.310291	+	0.696925i
$359$	6.16257	+	28.9926i	0.325248	+	1.53017i	0.772064	+	0.635545i	$0.219225\pi$
$359$	6.16257	+	28.9926i	0.325248	+	1.53017i	−0.446816	+	0.894626i	$0.647442\pi$
$360$	−2.52906	−	1.61364i	−0.133293	−	0.0850464i
$361$	−14.2419	−	6.34091i	−0.749575	−	0.333732i
$362$	−6.45722	+	7.17147i	−0.339384	+	0.376924i
$363$	−4.34844	−	1.26908i	−0.228234	−	0.0666095i
$364$	5.19486	−	7.15011i	0.272285	−	0.374768i
$365$	−0.385940	−	3.67198i	−0.0202010	−	0.192200i
$366$	2.24901	+	1.90526i	0.117557	+	0.0995893i
$367$	13.0415	−	7.52949i	0.680759	−	0.393036i	−0.119382	−	0.992848i	$-0.538091\pi$
$367$	13.0415	−	7.52949i	0.680759	−	0.393036i	0.800141	+	0.599812i	$0.204758\pi$
$368$	4.04207	−	2.93674i	0.210707	−	0.153088i
$369$	6.80601	−	2.67554i	0.354307	−	0.139283i
$370$	−3.41721	+	1.11032i	−0.177652	+	0.0577227i
$371$	12.3797			0.642724
$372$	1.75630	+	9.48237i	0.0910601	+	0.491638i
$373$	−7.27462			−0.376665			−0.188333	−	0.982105i	$-0.560308\pi$
$373$	−7.27462			−0.376665			−0.188333	+	0.982105i	$0.560308\pi$
$374$	−19.6790	+	6.39409i	−1.01758	+	0.330630i
$375$	0.910922	+	1.47317i	0.0470398	+	0.0760740i
$376$	−1.93057	+	1.40264i	−0.0995616	+	0.0723358i
$377$	7.70857	−	4.45055i	0.397012	−	0.229215i
$378$	−6.11625	+	3.41696i	−0.314586	+	0.175749i
$379$	2.67747	+	25.4745i	0.137533	+	1.30853i	0.817771	+	0.575544i	$0.195210\pi$
$379$	2.67747	+	25.4745i	0.137533	+	1.30853i	−0.680238	+	0.732991i	$0.738124\pi$
$380$	−1.08546	+	1.49401i	−0.0556829	+	0.0766409i
$381$	8.77590	−	30.0702i	0.449603	−	1.54054i
$382$	−5.28719	+	5.87202i	−0.270516	+	0.300438i
$383$	9.47373	+	4.21798i	0.484085	+	0.215528i	0.634243	−	0.773133i	$-0.281312\pi$
$383$	9.47373	+	4.21798i	0.484085	+	0.215528i	−0.150158	+	0.988662i	$0.547978\pi$
$384$	1.60286	+	0.656391i	0.0817955	+	0.0334963i
$385$	−1.03438	−	4.86639i	−0.0527170	−	0.248014i
$386$	3.68868	+	8.28492i	0.187749	+	0.421691i
$387$	−22.8443	−	18.1969i	−1.16124	−	0.925001i
$388$	5.28208	−	16.2566i	0.268157	−	0.825302i
$389$	5.12581	−	2.28216i	0.259889	−	0.115710i	−0.272657	−	0.962111i	$-0.587902\pi$
$389$	5.12581	−	2.28216i	0.259889	−	0.115710i	0.532545	+	0.846401i	$0.321236\pi$
$390$	11.3483	−	0.342806i	0.574642	−	0.0173586i
$391$	27.4052	+	5.82515i	1.38594	+	0.294591i
$392$	2.10774	−	4.73406i	0.106457	−	0.239106i
$393$	−17.6148	+	13.6292i	−0.888551	+	0.687500i
$394$	−9.83955	−	1.03418i	−0.495709	−	0.0521011i
$395$	0.659922	+	0.479461i	0.0332043	+	0.0241243i
$396$	−2.77901	+	10.7152i	−0.139651	+	0.538458i
$397$	9.09073	−	15.7456i	0.456251	−	0.790249i	−0.542509	−	0.840050i	$-0.682525\pi$
$397$	9.09073	−	15.7456i	0.456251	−	0.790249i	0.998759	+	0.0498011i	$0.0158588\pi$
$398$	−0.000696899	−	0.00120706i	−3.49324e−5	−	6.05047e-5i
$399$	1.87227	+	3.88504i	0.0937308	+	0.194495i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	−4.54601	−	13.9912i	−0.227017	−	0.698686i	−0.998081	−	0.0619279i	$-0.980275\pi$
$401$	−4.54601	−	13.9912i	−0.227017	−	0.698686i	0.771064	−	0.636758i	$-0.219725\pi$
$402$	0.170386	+	0.0308714i	0.00849806	+	0.00153973i
$403$	−25.6998	−	25.9132i	−1.28020	−	1.29083i
$404$			13.4290i			0.668120i
$405$	−8.27969	−	3.52800i	−0.411421	−	0.175308i
$406$	−1.36063	+	1.22511i	−0.0675267	+	0.0608013i
$407$	7.79287	+	10.7260i	0.386278	+	0.531667i
$408$	3.27896	+	9.14255i	0.162332	+	0.452624i
$409$	14.5021	+	8.37278i	0.717082	+	0.414007i	0.813678	−	0.581316i	$-0.197462\pi$
$409$	14.5021	+	8.37278i	0.717082	+	0.414007i	−0.0965959	+	0.995324i	$0.530795\pi$
$410$	2.42432	−	0.254806i	0.119729	−	0.0125840i
$411$	−4.58884	+	4.38983i	−0.226351	+	0.216534i
$412$	0.815757	−	7.76141i	0.0401894	−	0.382377i
$413$	−9.86457	−	8.88210i	−0.485404	−	0.437060i
$414$	10.5132	−	10.6835i	0.516694	−	0.525067i
$415$	−0.955433	+	4.49496i	−0.0469004	+	0.220649i
$416$	−6.41167	+	1.36284i	−0.314358	+	0.0668189i
$417$	−12.2919	+	3.00333i	−0.601938	+	0.147074i
$418$	6.48060	+	2.10567i	0.316976	+	0.102992i
$419$	−35.0985	−	11.4042i	−1.71468	−	0.557132i	−0.723575	−	0.690246i	$-0.757502\pi$
$419$	−35.0985	−	11.4042i	−1.71468	−	0.557132i	−0.991101	+	0.133114i	$0.957502\pi$
$420$	−2.26860	+	0.554294i	−0.110696	+	0.0270468i
$421$	−26.3891	+	5.60917i	−1.28613	+	0.273374i	−0.799728	−	0.600363i	$-0.795023\pi$
$421$	−26.3891	+	5.60917i	−1.28613	+	0.273374i	−0.486398	+	0.873737i	$0.661689\pi$
$422$	−2.85373	+	13.4257i	−0.138917	+	0.653554i
$423$	−5.02130	+	5.10267i	−0.244144	+	0.248100i
$424$	−6.82333	−	6.14375i	−0.331370	−	0.298367i
$425$	0.586161	−	5.57695i	0.0284330	−	0.270522i
$426$	−10.1225	+	9.68349i	−0.490436	+	0.469167i
$427$	2.28193	−	0.239841i	0.110430	−	0.0116067i
$428$	−5.61972	−	3.24455i	−0.271639	−	0.156831i
$429$	−14.1427	−	39.4335i	−0.682818	−	1.90387i
$430$	−5.72228	−	7.87605i	−0.275953	−	0.379817i
$431$	−18.9781	+	17.0880i	−0.914144	+	0.823099i	−0.984673	−	0.174411i	$-0.944198\pi$
$431$	−18.9781	+	17.0880i	−0.914144	+	0.823099i	0.0705290	+	0.997510i	$0.477531\pi$
$432$	5.06684	+	1.15202i	0.243778	+	0.0554265i
$433$		−	24.3011i		−	1.16783i	−0.811813	−	0.583917i	$-0.801519\pi$
$433$		−	24.3011i		−	1.16783i	0.811813	−	0.583917i	$-0.198481\pi$
$434$	6.27898	+	4.11464i	0.301401	+	0.197509i
$435$	−2.31432	−	0.419321i	−0.110963	−	0.0201049i
$436$	6.04369	+	18.6006i	0.289440	+	0.890805i
$437$	−6.17379	−	6.85669i	−0.295333	−	0.328000i
$438$	2.77633	+	5.76100i	0.132658	+	0.275271i
$439$	−13.2566	−	22.9611i	−0.632702	−	1.09587i	−0.986997	−	0.160738i	$-0.948612\pi$
$439$	−13.2566	−	22.9611i	−0.632702	−	1.09587i	0.354295	−	0.935134i	$-0.384721\pi$
$440$	−1.84495	+	3.19554i	−0.0879544	+	0.152341i
$441$	3.90284	−	15.0483i	0.185849	−	0.716588i
$442$	−29.7377	−	21.6057i	−1.41448	−	1.02768i
$443$	−20.8207	−	2.18835i	−0.989223	−	0.103972i	−0.403927	−	0.914791i	$-0.632355\pi$
$443$	−20.8207	−	2.18835i	−0.989223	−	0.103972i	−0.585296	+	0.810820i	$0.699022\pi$
$444$	4.92207	−	3.80836i	0.233591	−	0.180737i
$445$	−4.68501	+	10.5227i	−0.222091	+	0.498825i
$446$	−12.3612	−	2.62744i	−0.585318	−	0.124413i
$447$	−38.0987	+	1.15088i	−1.80201	+	0.0544346i
$448$	1.23174	−	0.548405i	0.0581942	−	0.0259097i
$449$	−4.74159	+	14.5931i	−0.223770	+	0.688692i	0.774644	+	0.632397i	$0.217929\pi$
$449$	−4.74159	+	14.5931i	−0.223770	+	0.688692i	−0.998414	+	0.0562953i	$0.982071\pi$
$450$	−2.34654	−	1.86916i	−0.110617	−	0.0881131i
$451$	−3.65850	−	8.21712i	−0.172272	−	0.386929i
$452$	3.54609	+	16.6830i	0.166794	+	0.784704i
$453$	31.9797	+	13.0961i	1.50254	+	0.615308i
$454$	10.2056	+	4.54382i	0.478972	+	0.213252i
$455$	5.91379	−	6.56793i	0.277243	−	0.307909i
$456$	0.896110	−	3.07048i	0.0419642	−	0.143788i
$457$	−14.7381	+	20.2853i	−0.689420	+	0.948906i	−0.999999	−	0.00164220i	$-0.999477\pi$
$457$	−14.7381	+	20.2853i	−0.689420	+	0.948906i	0.310578	+	0.950548i	$0.399477\pi$
$458$	−1.24845	−	11.8782i	−0.0583364	−	0.555034i
$459$	14.2113	+	25.4378i	0.663326	+	1.18733i
$460$	4.32690	−	2.49814i	0.201743	−	0.116476i
$461$	2.19286	−	1.59321i	0.102132	−	0.0742030i	−0.535547	−	0.844505i	$-0.679895\pi$
$461$	2.19286	−	1.59321i	0.102132	−	0.0742030i	0.637679	+	0.770302i	$0.279895\pi$
$462$	4.53193	+	7.32916i	0.210844	+	0.340983i
$463$	−5.76377	+	1.87276i	−0.267865	+	0.0870346i	−0.439870	−	0.898061i	$-0.644975\pi$
$463$	−5.76377	+	1.87276i	−0.267865	+	0.0870346i	0.172005	+	0.985096i	$0.444975\pi$
$464$	1.35793			0.0630402
$465$	0.755504	+	9.61401i	0.0350357	+	0.445839i
$466$	11.4664			0.531171
$467$	38.1428	−	12.3933i	1.76504	−	0.573495i	0.767335	−	0.641247i	$-0.221583\pi$
$467$	38.1428	−	12.3933i	1.76504	−	0.573495i	0.997702	+	0.0677518i	$0.0215826\pi$
$468$	−18.3014	+	7.19453i	−0.845981	+	0.332567i
$469$	0.109052	−	0.0792307i	0.00503554	−	0.00365853i
$470$	−2.06661	+	1.19316i	−0.0953257	+	0.0550363i
$471$	−11.5307	−	9.76825i	−0.531305	−	0.450097i
$472$	1.02908	+	9.79108i	0.0473674	+	0.450671i
$473$	−21.1146	+	29.0618i	−0.970851	+	1.33626i
$474$	−1.35627	−	0.395823i	−0.0622954	−	0.0181808i
$475$	−1.23568	+	1.37236i	−0.0566969	+	0.0629682i
$476$	6.90718	+	3.07528i	0.316590	+	0.140955i
$477$	−23.2211	−	14.8160i	−1.06322	−	0.678377i
$478$	2.99569	+	14.0936i	0.137020	+	0.644627i
$479$	6.66205	+	14.9632i	0.304397	+	0.683687i	0.999375	−	0.0353439i	$-0.0112527\pi$
$479$	6.66205	+	14.9632i	0.304397	+	0.683687i	−0.694978	+	0.719031i	$0.744586\pi$
$480$	1.52546	+	0.820340i	0.0696276	+	0.0374432i
$481$	−7.27804	+	22.3995i	−0.331850	+	1.02133i
$482$	−11.5711	+	5.15179i	−0.527049	+	0.234657i
$483$	−0.352303	−	11.6627i	−0.0160303	−	0.530669i
$484$	2.55816	+	0.543754i	0.116280	+	0.0247161i
$485$	6.95241	−	15.6154i	0.315693	−	0.709058i
$486$	15.5618	+	0.910574i	0.705899	+	0.0413045i
$487$	16.9421	+	1.78068i	0.767719	+	0.0806905i	0.480288	−	0.877111i	$-0.340532\pi$
$487$	16.9421	+	1.78068i	0.767719	+	0.0806905i	0.287431	+	0.957801i	$0.407199\pi$
$488$	−1.37676	−	1.00027i	−0.0623229	−	0.0452802i
$489$	15.9010	+	1.18716i	0.719069	+	0.0536853i
$490$	2.59104	−	4.48780i	0.117051	−	0.202738i
$491$	−17.0000	−	29.4448i	−0.767197	−	1.32882i	−0.939077	−	0.343706i	$-0.888318\pi$
$491$	−17.0000	−	29.4448i	−0.767197	−	1.32882i	0.171880	−	0.985118i	$-0.445016\pi$
$492$	−3.80354	+	1.83299i	−0.171477	+	0.0826377i
$493$	5.09530	+	5.65890i	0.229481	+	0.254864i
$494$	3.74062	+	11.5125i	0.168299	+	0.517970i
$495$	−3.88383	+	10.3660i	−0.174565	+	0.465916i
$496$	−1.41879	−	5.38396i	−0.0637055	−	0.241747i
$497$			10.9048i			0.489145i
$498$	−1.07062	−	7.88710i	−0.0479756	−	0.353429i
$499$	23.7219	−	21.3593i	1.06194	−	0.956175i	0.0628161	−	0.998025i	$-0.479992\pi$
$499$	23.7219	−	21.3593i	1.06194	−	0.956175i	0.999124	+	0.0418500i	$0.0133252\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$	−7.87892	+	2.82576i	−0.352004	+	0.126246i
$502$	1.74059	+	1.00493i	0.0776861	+	0.0448521i
$503$	−14.4287	+	1.51652i	−0.643344	+	0.0676182i	−0.420582	−	0.907255i	$-0.638174\pi$
$503$	−14.4287	+	1.51652i	−0.643344	+	0.0676182i	−0.222762	+	0.974873i	$0.571507\pi$
$504$	3.37454	−	2.23021i	0.150314	−	0.0993416i
$505$	−1.40372	+	13.3555i	−0.0624646	+	0.594311i
$506$	−13.7004	−	12.3359i	−0.609057	−	0.548398i
$507$	29.2267	−	42.8933i	1.29800	−	1.90496i
$508$	−3.76014	+	17.6901i	−0.166829	+	0.784870i
$509$	22.9726	−	4.88298i	1.01824	−	0.216434i	0.331593	−	0.943423i	$-0.392414\pi$
$509$	22.9726	−	4.88298i	1.01824	−	0.216434i	0.686650	+	0.726989i	$0.259081\pi$
$510$	2.30534	+	9.43521i	0.102082	+	0.417798i
$511$	4.73457	+	1.53835i	0.209445	+	0.0680528i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	1.13771	−	9.52802i	0.0502310	−	0.420672i
$514$	−2.98056	+	0.633538i	−0.131467	+	0.0279442i
$515$	1.62258	−	7.63362i	0.0714992	−	0.336377i
$516$	13.9348	+	9.49487i	0.613444	+	0.417988i
$517$	6.54358	+	5.89187i	0.287786	+	0.259124i
$518$	0.506394	−	4.81801i	0.0222497	−	0.211691i
$519$	18.6722	+	19.5187i	0.819619	+	0.856776i
$520$	−6.51900	+	0.685175i	−0.285877	+	0.0300469i
$521$	0.279080	+	0.161127i	0.0122267	+	0.00705909i	0.506101	−	0.862474i	$-0.331086\pi$
$521$	0.279080	+	0.161127i	0.0122267	+	0.00705909i	−0.493874	+	0.869533i	$0.664420\pi$
$522$	4.01838	−	0.669598i	0.175880	−	0.0293075i
$523$	−2.32621	−	3.20175i	−0.101718	−	0.140003i	0.755124	−	0.655582i	$-0.227577\pi$
$523$	−2.32621	−	3.20175i	−0.101718	−	0.140003i	−0.856842	+	0.515579i	$0.827577\pi$
$524$	9.55586	−	8.60413i	0.417449	−	0.375873i
$525$	−2.31411	+	0.314124i	−0.100996	+	0.0137095i
$526$			2.75167i			0.119978i
$527$	17.1130	−	26.1146i	0.745453	−	1.13757i
$528$	1.13942	−	6.28869i	0.0495869	−	0.273680i
$529$	0.606523	+	1.86669i	0.0263706	+	0.0811603i
$530$	−6.14375	−	6.82333i	−0.266867	−	0.296386i
$531$	7.87327	+	28.4663i	0.341671	+	1.23533i
$532$	−1.24495	−	2.15632i	−0.0539756	−	0.0934885i
$533$	7.98937	−	13.8380i	0.346058	−	0.599390i
$534$	1.48537	−	19.8953i	0.0642784	−	0.860955i
$535$	−5.24979	−	3.81419i	−0.226968	−	0.164902i
$536$	−0.0994262	−	0.0104501i	−0.00429456	−	0.000451376i
$537$	−15.2993	−	19.7733i	−0.660212	−	0.853283i
$538$	9.39610	−	21.1040i	0.405095	−	0.909857i
$539$	−18.7034	−	3.97554i	−0.805614	−	0.171239i
$540$	4.91866	+	1.67534i	0.211666	+	0.0720950i
$541$	−21.9320	+	9.76476i	−0.942931	+	0.419820i	−0.819851	−	0.572577i	$-0.805944\pi$
$541$	−21.9320	+	9.76476i	−0.942931	+	0.419820i	−0.123080	+	0.992397i	$0.539277\pi$
$542$	6.07062	−	18.6835i	0.260756	−	0.802523i
$543$	7.91641	−	14.7210i	0.339726	−	0.631738i
$544$	−2.28084	−	5.12286i	−0.0977904	−	0.219641i
$545$	4.06629	+	19.1304i	0.174181	+	0.819456i
$546$	−5.80120	+	14.1661i	−0.248269	+	0.606253i
$547$	35.6735	+	15.8829i	1.52529	+	0.679103i	0.986564	−	0.163378i	$-0.0522390\pi$
$547$	35.6735	+	15.8829i	1.52529	+	0.679103i	0.538726	+	0.842481i	$0.318906\pi$
$548$	2.45332	−	2.72469i	0.104801	−	0.116393i
$549$	−4.56734	−	2.28112i	−0.194929	−	0.0973559i
$550$	−2.16886	+	2.98519i	−0.0924807	+	0.127289i
$551$	−0.262124	−	2.49394i	−0.0111668	−	0.106245i
$552$	−5.59370	+	6.60293i	−0.238084	+	0.281040i
$553$	−0.952476	+	0.549912i	−0.0405034	+	0.0233846i
$554$	−1.23631	+	0.898235i	−0.0525260	+	0.0381624i
$555$	5.29319	−	3.27300i	0.224683	−	0.138931i
$556$	6.94795	−	2.25753i	0.294659	−	0.0957405i
$557$	7.27305			0.308169			0.154085	−	0.988058i	$-0.450757\pi$
$557$	7.27305			0.308169			0.154085	+	0.988058i	$0.450757\pi$
$558$	−6.85332	−	15.2326i	−0.290124	−	0.644847i
$559$	−63.8142			−2.69905
$560$	1.28232	−	0.416649i	0.0541877	−	0.0176067i
$561$	30.4823	−	18.8485i	1.28696	−	0.795785i
$562$	12.6336	−	9.17888i	0.532918	−	0.387188i
$563$	7.52484	−	4.34447i	0.317134	−	0.183098i	−0.332980	−	0.942934i	$-0.608054\pi$
$563$	7.52484	−	4.34447i	0.317134	−	0.183098i	0.650114	+	0.759836i	$0.274721\pi$
$564$	2.67166	−	3.15369i	0.112497	−	0.132794i
$565$	1.78281	+	16.9623i	0.0750034	+	0.713610i
$566$	14.6897	−	20.2186i	0.617452	−	0.849850i
$567$	8.88620	−	8.26364i	0.373185	−	0.347040i
$568$	5.41176	−	6.01036i	0.227072	−	0.252189i
$569$	31.4886	+	14.0196i	1.32007	+	0.587734i	0.941242	−	0.337732i	$-0.109660\pi$
$569$	31.4886	+	14.0196i	1.32007	+	0.587734i	0.378830	+	0.925466i	$0.376326\pi$
$570$	1.21215	−	2.95999i	0.0507715	−	0.123980i
$571$	3.60439	+	16.9573i	0.150839	+	0.709641i	0.986943	+	0.161070i	$0.0514946\pi$
$571$	3.60439	+	16.9573i	0.150839	+	0.709641i	−0.836104	+	0.548571i	$0.815172\pi$
$572$	9.83771	+	22.0959i	0.411335	+	0.923874i
$573$	6.48198	−	12.0536i	0.270788	−	0.503545i
$574$	−1.01566	+	3.12587i	−0.0423926	+	0.130471i
$575$	4.56432	−	2.03217i	0.190345	−	0.0847472i
$576$	−2.96674	−	0.445473i	−0.123614	−	0.0185614i
$577$	34.1756	+	7.26426i	1.42275	+	0.302415i	0.854076	−	0.520148i	$-0.174123\pi$
$577$	34.1756	+	7.26426i	1.42275	+	0.302415i	0.568674	+	0.822563i	$0.307456\pi$
$578$	5.87569	−	13.1970i	0.244397	−	0.548924i
$579$	−9.61238	−	12.4234i	−0.399477	−	0.516299i
$580$	1.35049	+	0.141942i	0.0560760	+	0.00589382i
$581$	−5.01265	−	3.64191i	−0.207960	−	0.151092i
$582$	−2.20425	+	29.5240i	−0.0913690	+	1.22381i
$583$	−16.9397	+	29.3405i	−0.701572	+	1.21516i
$584$	−1.84610	−	3.19754i	−0.0763922	−	0.132315i
$585$	−18.9532	+	5.24211i	−0.783616	+	0.216734i
$586$	12.5551	+	13.9438i	0.518646	+	0.576015i
$587$	3.57253	+	10.9951i	0.147454	+	0.453817i	0.997318	−	0.0731846i	$-0.0233162\pi$
$587$	3.57253	+	10.9951i	0.147454	+	0.453817i	−0.849864	+	0.527001i	$0.823316\pi$
$588$	−1.60020	+	8.83181i	−0.0659910	+	0.364218i
$589$	−9.61419	+	3.64499i	−0.396146	+	0.150189i
$590$			9.84501i			0.405313i
$591$	16.9807	−	2.30502i	0.698494	−	0.0948157i
$592$	−2.67017	+	2.40423i	−0.109743	+	0.0988133i
$593$	−23.8530	−	32.8309i	−0.979527	−	1.34820i	−0.937084	−	0.349104i	$-0.886486\pi$
$593$	−23.8530	−	32.8309i	−0.979527	−	1.34820i	−0.0424432	−	0.999099i	$-0.513514\pi$
$594$	0.270794	−	19.1713i	0.0111108	−	0.786609i
$595$	6.54789	+	3.78043i	0.268437	+	0.154982i
$596$	21.8858	−	2.30029i	0.896476	−	0.0942235i
$597$	0.00166880	+	0.00174445i	6.82994e−5	+	7.13958e-5i
$598$	3.42332	−	32.5707i	0.139990	−	1.33192i
$599$	−14.6629	−	13.2025i	−0.599109	−	0.539440i	0.312807	−	0.949817i	$-0.398731\pi$
$599$	−14.6629	−	13.2025i	−0.599109	−	0.539440i	−0.911916	+	0.410377i	$0.865397\pi$
$600$	1.43136	+	0.975300i	0.0584350	+	0.0398165i
$601$	−4.27992	+	20.1354i	−0.174581	+	0.821341i	0.800472	+	0.599370i	$0.204582\pi$
$601$	−4.27992	+	20.1354i	−0.174581	+	0.821341i	−0.975053	+	0.221971i	$0.928751\pi$
$602$	12.8394	−	2.72909i	0.523294	−	0.111229i
$603$	−0.299375	+	0.0181034i	−0.0121915	+	0.000737227i
$604$	−18.9752	−	6.16540i	−0.772088	−	0.250867i
$605$	2.48731	+	0.808175i	0.101123	+	0.0328570i
$606$	−5.52074	−	22.5951i	−0.224265	−	0.917864i
$607$	11.6656	−	2.47959i	0.473491	−	0.100644i	0.0350154	−	0.999387i	$-0.488852\pi$
$607$	11.6656	−	2.47959i	0.473491	−	0.100644i	0.438475	+	0.898743i	$0.355519\pi$
$608$	−0.383949	+	1.80634i	−0.0155712	+	0.0732567i
$609$	1.78568	−	2.62068i	0.0723594	−	0.106195i
$610$	−1.26466	−	1.13870i	−0.0512045	−	0.0461048i
$611$	−1.63504	+	15.5564i	−0.0661468	+	0.629345i
$612$	−9.27557	−	14.0349i	−0.374943	−	0.567326i
$613$	6.57914	−	0.691495i	0.265729	−	0.0279292i	0.0292730	−	0.999571i	$-0.490681\pi$
$613$	6.57914	−	0.691495i	0.265729	−	0.0279292i	0.236456	+	0.971642i	$0.424014\pi$
$614$	9.30219	+	5.37062i	0.375406	+	0.216741i
$615$	−3.97430	+	1.42537i	−0.160259	+	0.0574766i
$616$	−2.92429	−	4.02494i	−0.117823	−	0.162170i
$617$	−25.7361	+	23.1729i	−1.03610	+	0.932905i	−0.997796	−	0.0663609i	$-0.978861\pi$
$617$	−25.7361	+	23.1729i	−1.03610	+	0.932905i	−0.0383007	+	0.999266i	$0.512194\pi$
$618$	1.81819	+	13.3944i	0.0731383	+	0.538800i
$619$		−	27.1275i		−	1.09035i	−0.838323	−	0.545174i	$-0.816464\pi$
$619$		−	27.1275i		−	1.09035i	0.838323	−	0.545174i	$-0.183536\pi$
$620$	−0.848238	−	5.50277i	−0.0340661	−	0.220997i
$621$	−13.2969	+	22.2977i	−0.533588	+	0.894774i
$622$	−2.70769	−	8.33342i	−0.108569	−	0.334140i
$623$	−10.3919	−	11.5414i	−0.416345	−	0.462398i
$624$	10.2277	−	4.92892i	0.409437	−	0.197315i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.37695	−	7.58110i	0.174938	−	0.303002i
$627$	−11.7696	−	0.878713i	−0.470033	−	0.0350924i
$628$	7.05864	+	5.12841i	0.281671	+	0.204646i
$629$	−20.0383	−	2.10611i	−0.798981	−	0.0839763i
$630$	3.58917	−	1.86526i	0.142996	−	0.0743138i
$631$	5.92265	−	13.3025i	0.235777	−	0.529564i	−0.756443	−	0.654059i	$-0.773065\pi$
$631$	5.92265	−	13.3025i	0.235777	−	0.529564i	0.992220	+	0.124496i	$0.0397313\pi$
$632$	0.797883	+	0.169595i	0.0317381	+	0.00674614i
$633$	−0.717818	−	23.7627i	−0.0285307	−	0.944483i
$634$	20.2279	−	9.00605i	0.803353	−	0.357676i
$635$	−5.58866	+	17.2001i	−0.221779	+	0.682566i
$636$	14.0063	+	7.53211i	0.555388	+	0.298667i
$637$	−13.8160	−	31.0313i	−0.547411	−	1.22951i
$638$	−1.04176	−	4.90111i	−0.0412438	−	0.194037i
$639$	13.0507	−	20.4544i	0.516279	−	0.809164i
$640$	−0.913545	−	0.406737i	−0.0361111	−	0.0160777i
$641$	−21.8840	+	24.3046i	−0.864364	+	0.959974i	−0.999524	−	0.0308500i	$-0.990179\pi$
$641$	−21.8840	+	24.3046i	−0.864364	+	0.959974i	0.135160	+	0.990824i	$0.456845\pi$
$642$	10.7893	+	3.14884i	0.425821	+	0.124275i
$643$	−4.77787	+	6.57618i	−0.188421	+	0.259339i	−0.892768	−	0.450516i	$-0.851240\pi$
$643$	−4.77787	+	6.57618i	−0.188421	+	0.259339i	0.704347	+	0.709856i	$0.251240\pi$
$644$	0.704157	+	6.69960i	0.0277477	+	0.264001i
$645$	12.8659	+	10.8994i	0.506596	+	0.429165i
$646$	−8.96825	+	5.17782i	−0.352851	+	0.203719i
$647$	−23.6320	+	17.1696i	−0.929068	+	0.675008i	−0.945764	−	0.324853i	$-0.894685\pi$
$647$	−23.6320	+	17.1696i	−0.929068	+	0.675008i	0.0166963	+	0.999861i	$0.494685\pi$
$648$	−8.99884	+	0.144665i	−0.353508	+	0.00568298i
$649$	34.5491	−	11.2257i	1.35617	−	0.440646i
$650$	−6.55491			−0.257105
$651$	−12.2563	−	4.34179i	−0.480361	−	0.170168i
$652$	−9.20601			−0.360535
$653$	33.8569	−	11.0008i	1.32492	−	0.430493i	0.440739	−	0.897635i	$-0.354716\pi$
$653$	33.8569	−	11.0008i	1.32492	−	0.430493i	0.884182	+	0.467142i	$0.154716\pi$
$654$	−17.8156	−	28.8119i	−0.696645	−	1.12663i
$655$	10.4029	−	7.55814i	0.406474	−	0.295321i
$656$	2.11109	−	1.21884i	0.0824241	−	0.0475876i
$657$	−7.03970	−	8.55184i	−0.274645	−	0.333639i
$658$	−0.336319	−	3.19986i	−0.0131111	−	0.124744i
$659$	−3.17686	+	4.37258i	−0.123753	+	0.170331i	−0.866398	−	0.499354i	$-0.833571\pi$
$659$	−3.17686	+	4.37258i	−0.123753	+	0.170331i	0.742645	+	0.669685i	$0.233571\pi$
$660$	1.79052	−	6.13514i	0.0696961	−	0.238810i
$661$	17.8559	−	19.8310i	0.694513	−	0.771335i	−0.287979	−	0.957637i	$-0.592983\pi$
$661$	17.8559	−	19.8310i	0.694513	−	0.771335i	0.982493	+	0.186302i	$0.0596502\pi$
$662$	21.6946	+	9.65908i	0.843186	+	0.375411i
$663$	58.9174	+	24.1275i	2.28816	+	0.937033i
$664$	0.955433	+	4.49496i	0.0370780	+	0.174438i
$665$	−1.01274	−	2.27464i	−0.0392723	−	0.0882069i
$666$	−6.71602	+	8.43126i	−0.260241	+	0.326705i
$667$	−2.09655	+	6.45252i	−0.0811787	+	0.249842i
$668$	4.41481	−	1.96560i	0.170814	−	0.0760513i
$669$	21.8785	−	0.660900i	0.845871	−	0.0255519i
$670$	−0.0977892	−	0.0207857i	−0.00377793	−	0.000803023i
$671$	−2.55404	+	5.73646i	−0.0985975	+	0.221454i
$672$	−1.84702	+	1.42910i	−0.0712502	+	0.0551286i
$673$	−0.998611	−	0.104958i	−0.0384936	−	0.00404584i	0.0852621	−	0.996359i	$-0.472827\pi$
$673$	−0.998611	−	0.104958i	−0.0384936	−	0.00404584i	−0.123756	+	0.992313i	$0.539494\pi$
$674$	−17.9753	−	13.0598i	−0.692382	−	0.503045i
$675$	4.71660	+	2.18030i	0.181542	+	0.0839197i
$676$	−14.9834	+	25.9521i	−0.576286	+	0.998156i
$677$	0.696025	+	1.20555i	0.0267504	+	0.0463331i	0.879091	−	0.476655i	$-0.158151\pi$
$677$	0.696025	+	1.20555i	0.0267504	+	0.0463331i	−0.852340	+	0.522988i	$0.824817\pi$
$678$	−12.8250	−	26.6123i	−0.492540	−	1.02204i
$679$	15.4213	+	17.1271i	0.591816	+	0.657278i
$680$	−1.73286	−	5.33321i	−0.0664523	−	0.204519i
$681$	−19.0395	−	3.44967i	−0.729594	−	0.132192i
$682$	−18.3437	+	9.25120i	−0.702415	+	0.354247i
$683$		−	35.0354i		−	1.34059i	−0.742093	−	0.670297i	$-0.766167\pi$
$683$		−	35.0354i		−	1.34059i	0.742093	−	0.670297i	$-0.233833\pi$
$684$	−0.245470	+	5.53464i	−0.00938579	+	0.211622i
$685$	2.72469	−	2.45332i	0.104105	−	0.0937365i
$686$	9.65447	+	13.2882i	0.368609	+	0.507347i
$687$	6.98379	+	19.4726i	0.266448	+	0.742924i
$688$	−8.43104	−	4.86767i	−0.321431	−	0.185578i
$689$	−59.8555	+	6.29106i	−2.28031	+	0.239670i
$690$	−6.25326	+	5.98206i	−0.238057	+	0.227733i
$691$	−3.69038	+	35.1116i	−0.140389	+	1.33571i	0.666721	+	0.745307i	$0.267697\pi$
$691$	−3.69038	+	35.1116i	−0.140389	+	1.33571i	−0.807110	+	0.590402i	$0.798969\pi$
$692$	−11.5895	−	10.4352i	−0.440566	−	0.396688i
$693$	−10.6383	−	10.4686i	−0.404115	−	0.397670i
$694$	−5.24013	+	24.6529i	−0.198912	+	0.935809i
$695$	7.14587	−	1.51890i	0.271058	−	0.0576152i
$696$	−2.28479	+	0.558250i	−0.0866047	+	0.0211604i
$697$	13.0006	+	4.22416i	0.492434	+	0.160001i
$698$	33.8353	+	10.9937i	1.28068	+	0.416120i
$699$	−19.2929	+	4.71389i	−0.729724	+	0.178296i
$700$	1.31884	−	0.280329i	0.0498476	−	0.0105954i
$701$	7.03182	−	33.0821i	0.265588	−	1.24949i	−0.619844	−	0.784725i	$-0.712804\pi$
$701$	7.03182	−	33.0821i	0.265588	−	1.24949i	0.885432	−	0.464769i	$-0.153862\pi$
$702$	27.8354	−	19.6290i	1.05058	−	0.740848i
$703$	4.93098	+	4.43988i	0.185976	+	0.167453i
$704$	−0.385699	+	3.66968i	−0.0145366	+	0.138306i
$705$	2.98668	−	2.85715i	0.112485	−	0.107606i
$706$	28.4049	−	2.98548i	1.06903	−	0.112360i
$707$	−15.6807	−	9.05323i	−0.589732	−	0.340482i
$708$	−5.75665	−	16.0510i	−0.216348	−	0.603233i
$709$	10.7375	+	14.7790i	0.403257	+	0.555035i	0.961558	−	0.274603i	$-0.0885465\pi$
$709$	10.7375	+	14.7790i	0.403257	+	0.555035i	−0.558301	+	0.829639i	$0.688547\pi$
$710$	6.01036	−	5.41176i	0.225565	−	0.203100i
$711$	2.44472	+	0.108427i	0.0916842	+	0.00406634i
$712$			11.5185i			0.431676i
$713$	27.7737	+	1.57077i	1.04013	+	0.0588258i
$714$	−12.8860	−	2.33475i	−0.482246	−	0.0873759i
$715$	7.47417	+	23.0031i	0.279518	+	0.860268i
$716$	9.65847	+	10.7268i	0.360954	+	0.400880i
$717$	−10.8344	−	22.4817i	−0.404616	−	0.839596i
$718$	14.8202	+	25.6693i	0.553083	+	0.957969i
$719$	12.9139	−	22.3676i	0.481608	−	0.834170i	−0.518169	−	0.855278i	$-0.673386\pi$
$719$	12.9139	−	22.3676i	0.481608	−	0.834170i	0.999777	+	0.0211085i	$0.00671956\pi$
$720$	−2.90392	−	0.753142i	−0.108223	−	0.0280679i
$721$	8.51279	+	6.18491i	0.317033	+	0.230338i
$722$	−15.5043	−	1.62957i	−0.577011	−	0.0606463i
$723$	17.3511	−	13.4251i	0.645294	−	0.499285i
$724$	−3.92507	+	8.81586i	−0.145874	+	0.327639i
$725$	1.32825	+	0.282329i	0.0493301	+	0.0104854i
$726$	−4.52778	+	0.136774i	−0.168042	+	0.00507617i
$727$	−18.0501	+	8.03641i	−0.669440	+	0.298054i	−0.713172	−	0.700989i	$-0.752742\pi$
$727$	−18.0501	+	8.03641i	−0.669440	+	0.298054i	0.0437315	+	0.999043i	$0.486075\pi$
$728$	2.73110	−	8.40546i	0.101221	−	0.311527i
$729$	−26.5580	+	4.86545i	−0.983630	+	0.180202i
$730$	−1.50175	−	3.37300i	−0.0555824	−	0.124840i
$731$	−11.3504	−	53.3995i	−0.419811	−	1.97505i
$732$	2.72769	+	1.11702i	0.100818	+	0.0412864i
$733$	25.0288	+	11.1435i	0.924459	+	0.411596i	0.813060	−	0.582180i	$-0.197800\pi$
$733$	25.0288	+	11.1435i	0.924459	+	0.411596i	0.111399	+	0.993776i	$0.464467\pi$
$734$	10.0764	−	11.1910i	0.371928	−	0.413068i
$735$	−2.51461	+	8.61617i	−0.0927526	+	0.317812i
$736$	2.93674	−	4.04207i	0.108250	−	0.148993i
$737$	0.0385598	+	0.366872i	0.00142037	+	0.0135139i
$738$	5.64611	−	4.64776i	0.207836	−	0.171086i
$739$	−33.9689	+	19.6120i	−1.24957	+	0.721438i	−0.971023	−	0.238985i	$-0.923185\pi$
$739$	−33.9689	+	19.6120i	−1.24957	+	0.721438i	−0.278545	+	0.960423i	$0.589852\pi$
$740$	−2.90685	+	2.11195i	−0.106858	+	0.0776369i
$741$	−11.0266	−	17.8326i	−0.405073	−	0.655096i
$742$	11.7738	−	3.82555i	0.432231	−	0.140440i
$743$	44.4963			1.63241			0.816206	−	0.577761i	$-0.196073\pi$
$743$	44.4963			1.63241			0.816206	+	0.577761i	$0.196073\pi$
$744$	4.60056	+	8.47554i	0.168665	+	0.310729i
$745$	22.0063			0.806250
$746$	−6.91857	+	2.24798i	−0.253307	+	0.0823044i
$747$	5.04379	+	12.8303i	0.184543	+	0.469438i
$748$	−16.7399	+	12.1623i	−0.612073	+	0.444697i
$749$	7.57710	−	4.37464i	0.276861	−	0.159846i
$750$	1.32157	+	1.11958i	0.0482570	+	0.0408811i
$751$	−2.67618	−	25.4622i	−0.0976552	−	0.929127i	−0.928176	−	0.372140i	$-0.878624\pi$
$751$	−2.67618	−	25.4622i	−0.0976552	−	0.929127i	0.830521	−	0.556987i	$-0.188043\pi$
$752$	−1.40264	+	1.93057i	−0.0511491	+	0.0704007i
$753$	−3.34176	−	0.975285i	−0.121781	−	0.0355413i
$754$	5.95599	−	6.61480i	0.216905	−	0.240897i
$755$	−18.2268	−	8.11507i	−0.663339	−	0.295338i
$756$	−4.76100	+	5.13975i	−0.173156	+	0.186931i
$757$	−3.34305	−	15.7278i	−0.121505	−	0.571637i	−0.996210	−	0.0869808i	$-0.972278\pi$
$757$	−3.34305	−	15.7278i	−0.121505	−	0.571637i	0.874705	−	0.484656i	$-0.161055\pi$
$758$	10.4185	+	23.4003i	0.378416	+	0.849936i
$759$	28.1230	+	15.1235i	1.02080	+	0.548950i
$760$	−0.570660	+	1.75631i	−0.0207000	+	0.0637081i
$761$	41.2290	−	18.3564i	1.49455	−	0.665417i	0.513311	−	0.858203i	$-0.328419\pi$
$761$	41.2290	−	18.3564i	1.49455	−	0.665417i	0.981241	+	0.192786i	$0.0617522\pi$
$762$	−0.945815	−	31.3103i	−0.0342633	−	1.13425i
$763$	−25.7936	−	5.48261i	−0.933792	−	0.198484i
$764$	−3.21386	+	7.21845i	−0.116273	+	0.261154i
$765$	−7.75771	−	14.9275i	−0.280481	−	0.539706i
$766$	10.3135	+	1.08399i	0.372641	+	0.0391662i
$767$	52.2084	+	37.9317i	1.88514	+	1.36963i
$768$	1.72724	+	0.128955i	0.0623265	+	0.00465326i
$769$	−22.4501	+	38.8847i	−0.809571	+	1.40222i	0.103591	+	0.994620i	$0.466967\pi$
$769$	−22.4501	+	38.8847i	−0.809571	+	1.40222i	−0.913162	+	0.407597i	$0.866367\pi$
$770$	−2.48755	−	4.30857i	−0.0896452	−	0.155270i
$771$	4.75451	−	2.29129i	0.171230	−	0.0825186i
$772$	6.06833	+	6.73956i	0.218404	+	0.242562i
$773$	0.132270	+	0.407084i	0.00475741	+	0.0146418i	0.953407	−	0.301687i	$-0.0975497\pi$
$773$	0.132270	+	0.407084i	0.00475741	+	0.0146418i	−0.948650	+	0.316329i	$0.897550\pi$
$774$	−27.3494	−	10.2470i	−0.983053	−	0.368321i
$775$	−0.268395	−	5.56129i	−0.00964105	−	0.199767i
$776$		−	17.0932i		−	0.613609i
$777$	1.12867	+	8.31476i	0.0404908	+	0.298290i
$778$	4.16971	−	3.75442i	0.149491	−	0.134603i
$779$	−2.64600	−	3.64190i	−0.0948026	−	0.130485i
$780$	10.6869	−	3.83283i	0.382653	−	0.137237i
$781$	−25.8447	−	14.9215i	−0.924797	−	0.533932i
$782$	27.8640	−	2.92862i	0.996413	−	0.104727i
$783$	−6.48587	+	2.77861i	−0.231786	+	0.0992993i
$784$	0.541674	−	5.15368i	0.0193455	−	0.184060i
$785$	6.48391	+	5.83814i	0.231421	+	0.208372i
$786$	−12.5411	+	18.4054i	−0.447325	+	0.656498i
$787$	−0.941742	+	4.43055i	−0.0335695	+	0.157932i	−0.991740	−	0.128267i	$-0.959059\pi$
$787$	−0.941742	+	4.43055i	−0.0335695	+	0.157932i	0.958170	+	0.286199i	$0.0923919\pi$
$788$	−9.67754	+	2.05703i	−0.344748	+	0.0732785i
$789$	−1.13122	−	4.62984i	−0.0402726	−	0.164827i
$790$	0.775784	+	0.252068i	0.0276012	+	0.00896816i
$791$	−21.8708	−	7.10627i	−0.777638	−	0.252670i
$792$	0.668171	+	11.0495i	0.0237424	+	0.392627i
$793$	−10.9112	+	2.31924i	−0.387467	+	0.0823586i
$794$	3.78014	−	17.7841i	0.134152	−	0.631136i
$795$	13.1423	+	8.95491i	0.466109	+	0.317598i
$796$	−0.00103579		0.000932633i	−3.67127e−5		3.30563e-5i
$797$	−2.04193	+	19.4276i	−0.0723288	+	0.688162i	0.896939	+	0.442154i	$0.145786\pi$
$797$	−2.04193	+	19.4276i	−0.0723288	+	0.688162i	−0.969268	+	0.246008i	$0.920881\pi$
$798$	2.98118	+	3.11633i	0.105533	+	0.110317i
$799$	−13.3084	+	1.39877i	−0.470816	+	0.0494848i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	5.67983	+	34.0856i	0.200687	+	1.20436i
$802$	−8.64702	−	11.9016i	−0.305337	−	0.420260i
$803$	−10.1245	+	9.11613i	−0.357285	+	0.321701i
$804$	0.171586	−	0.0232916i	0.00605138	−	0.000821432i
$805$			6.73651i			0.237431i
$806$	−32.4495	−	16.7033i	−1.14299	−	0.588348i
$807$	−7.13352	+	39.3714i	−0.251112	+	1.38594i
$808$	4.14980	+	12.7718i	0.145990	+	0.449310i
$809$	24.1219	+	26.7901i	0.848081	+	0.941889i	0.998910	−	0.0466704i	$-0.0148610\pi$
$809$	24.1219	+	26.7901i	0.848081	+	0.941889i	−0.150829	+	0.988560i	$0.548194\pi$
$810$	−8.96466	−	0.796762i	−0.314986	−	0.0279954i
$811$	8.66146	+	15.0021i	0.304145	+	0.526794i	0.977071	−	0.212916i	$-0.0682960\pi$
$811$	8.66146	+	15.0021i	0.304145	+	0.526794i	−0.672926	+	0.739710i	$0.734963\pi$
$812$	−0.915451	+	1.58561i	−0.0321260	+	0.0556439i
$813$	−2.53331	+	33.9316i	−0.0888472	+	1.19003i
$814$	10.7260	+	7.79287i	0.375945	+	0.273140i
$815$	−9.15558	−	0.962290i	−0.320706	−	0.0337076i
$816$	5.94368	+	7.68183i	0.208070	+	0.268918i
$817$	−7.31238	+	16.4239i	−0.255828	+	0.574599i
$818$	16.3796	+	3.48160i	0.572700	+	0.121731i
$819$	3.93711	−	26.2201i	0.137574	−	0.916206i
$820$	2.22693	−	0.991491i	0.0777676	−	0.0346244i
$821$	−3.74543	+	11.5272i	−0.130716	+	0.402303i	−0.994899	−	0.100874i	$-0.967836\pi$
$821$	−3.74543	+	11.5272i	−0.130716	+	0.402303i	0.864183	+	0.503178i	$0.167836\pi$
$822$	−3.00772	+	5.59301i	−0.104906	+	0.195078i
$823$	−11.0633	−	24.8485i	−0.385641	−	0.866164i	−0.997187	−	0.0749553i	$-0.976119\pi$
$823$	−11.0633	−	24.8485i	−0.385641	−	0.866164i	0.611546	−	0.791209i	$-0.290548\pi$
$824$	−1.62258	−	7.63362i	−0.0565251	−	0.265930i
$825$	2.42201	−	5.91437i	0.0843237	−	0.205912i
$826$	−12.1265	−	5.39906i	−0.421934	−	0.187857i
$827$	−20.3136	+	22.5605i	−0.706373	+	0.784506i	−0.984377	−	0.176074i	$-0.943660\pi$
$827$	−20.3136	+	22.5605i	−0.706373	+	0.784506i	0.278004	+	0.960580i	$0.410327\pi$
$828$	6.69722	−	13.4094i	0.232745	−	0.466009i
$829$	−29.0086	+	39.9269i	−1.00751	+	1.38672i	−0.0869083	+	0.996216i	$0.527699\pi$
$829$	−29.0086	+	39.9269i	−1.00751	+	1.38672i	−0.920602	+	0.390502i	$0.872301\pi$
$830$	0.480348	+	4.57021i	0.0166731	+	0.158634i
$831$	1.71090	−	2.01958i	0.0593505	−	0.0700586i
$832$	−5.67672	+	3.27746i	−0.196805	+	0.113625i
$833$	23.5095	−	17.0806i	0.814556	−	0.591809i
$834$	−10.7622	+	6.65475i	−0.372666	+	0.230435i
$835$	4.59609	−	1.49336i	0.159054	−	0.0516798i
$836$	6.81410			0.235671
$837$	17.7933	+	22.8123i	0.615026	+	0.788507i
$838$	−36.9048			−1.27485
$839$	23.0855	−	7.50095i	0.797002	−	0.258961i	0.117919	−	0.993023i	$-0.462378\pi$
$839$	23.0855	−	7.50095i	0.797002	−	0.258961i	0.679083	+	0.734062i	$0.262378\pi$
$840$	−1.98628	+	1.22820i	−0.0685332	+	0.0423770i
$841$	21.9697	−	15.9619i	0.757576	−	0.550411i
$842$	−23.3642	+	13.4893i	−0.805183	+	0.464873i
$843$	−17.4833	+	20.6377i	−0.602158	+	0.710801i
$844$	1.43472	+	13.6505i	0.0493852	+	0.469869i
$845$	−17.6141	+	24.2437i	−0.605943	+	0.834008i
$846$	−3.19873	+	6.40459i	−0.109974	+	0.220194i
$847$	−2.35951	+	2.62051i	−0.0810739	+	0.0900416i
$848$	−8.38789	−	3.73453i	−0.288041	−	0.128244i
$849$	−16.4042	+	40.0578i	−0.562991	+	1.37478i
$850$	−1.16590	−	5.48513i	−0.0399900	−	0.188138i
$851$	−7.30171	−	16.3999i	−0.250299	−	0.562182i
$852$	−6.63469	+	12.3376i	−0.227301	+	0.422678i
$853$	−13.8830	+	42.7275i	−0.475345	+	1.46296i	0.370146	+	0.928974i	$0.379308\pi$
$853$	−13.8830	+	42.7275i	−0.475345	+	1.46296i	−0.845491	+	0.533989i	$0.820692\pi$
$854$	2.09613	−	0.933258i	0.0717281	−	0.0319354i
$855$	−0.822653	+	5.47866i	−0.0281341	+	0.187366i
$856$	−6.34729	−	1.34916i	−0.216946	−	0.0461133i
$857$	−12.9651	+	29.1201i	−0.442879	+	0.994722i	0.544849	+	0.838534i	$0.316587\pi$
$857$	−12.9651	+	29.1201i	−0.442879	+	0.994722i	−0.987727	+	0.156188i	$0.950080\pi$
$858$	−25.6362	−	33.1332i	−0.875205	−	1.13115i
$859$	23.3886	+	2.45824i	0.798007	+	0.0838739i	0.494751	−	0.869035i	$-0.335259\pi$
$859$	23.3886	+	2.45824i	0.798007	+	0.0838739i	0.303257	+	0.952909i	$0.401926\pi$
$860$	−7.87605	−	5.72228i	−0.268571	−	0.195128i
$861$	0.423840	−	5.67698i	0.0144444	−	0.193471i
$862$	−12.7688	+	22.1162i	−0.434907	+	0.753281i
$863$	12.5904	+	21.8072i	0.428582	+	0.742326i	0.996747	−	0.0805883i	$-0.0256799\pi$
$863$	12.5904	+	21.8072i	0.428582	+	0.742326i	−0.568165	+	0.822914i	$0.692347\pi$
$864$	5.17484	−	0.470106i	0.176052	−	0.0159933i
$865$	−10.4352	−	11.5895i	−0.354808	−	0.394054i
$866$	−7.50944	−	23.1117i	−0.255181	−	0.785367i
$867$	−4.46083	+	24.6203i	−0.151498	+	0.836148i
$868$	7.24316	+	1.97294i	0.245849	+	0.0669660i
$869$		−	3.00988i		−	0.102103i
$870$	−2.33063	+	0.316366i	−0.0790156	+	0.0107258i
$871$	−0.486997	+	0.438494i	−0.0165013	+	0.0148578i
$872$	11.4958	+	15.8226i	0.389296	+	0.535820i
$873$	−8.42869	−	50.5820i	−0.285268	−	1.71194i
$874$	−7.99046	−	4.61329i	−0.270281	−	0.156047i
$875$	1.34092	−	0.140936i	0.0453314	−	0.00476452i
$876$	4.42069	+	4.62110i	0.149361	+	0.156133i
$877$	3.94150	−	37.5009i	0.133095	−	1.26631i	−0.700385	−	0.713765i	$-0.746989\pi$
$877$	3.94150	−	37.5009i	0.133095	−	1.26631i	0.833480	−	0.552549i	$-0.186345\pi$
$878$	−19.7031	−	17.7408i	−0.664948	−	0.598722i
$879$	−26.8570	−	18.2998i	−0.905864	−	0.617238i
$880$	−0.767172	+	3.60926i	−0.0258614	+	0.121668i
$881$	9.45978	−	2.01074i	0.318708	−	0.0677435i	−0.0457800	−	0.998952i	$-0.514577\pi$
$881$	9.45978	−	2.01074i	0.318708	−	0.0677435i	0.364488	+	0.931208i	$0.381244\pi$
$882$	−0.938376	−	15.5179i	−0.0315968	−	0.522514i
$883$	−37.8679	−	12.3040i	−1.27436	−	0.414064i	−0.407768	−	0.913086i	$-0.633693\pi$
$883$	−37.8679	−	12.3040i	−1.27436	−	0.414064i	−0.866589	+	0.499022i	$0.833693\pi$
$884$	−34.9587	−	11.3588i	−1.17579	−	0.382037i
$885$	−4.04733	−	16.5648i	−0.136049	−	0.556819i
$886$	−20.4779	+	4.35272i	−0.687970	+	0.146233i
$887$	8.85496	−	41.6593i	0.297320	−	1.39878i	−0.535171	−	0.844744i	$-0.679753\pi$
$887$	8.85496	−	41.6593i	0.297320	−	1.39878i	0.832491	−	0.554039i	$-0.186914\pi$
$888$	3.50432	−	5.14297i	0.117597	−	0.172587i
$889$	−18.1212	−	16.3164i	−0.607766	−	0.547235i
$890$	−1.20402	+	11.4554i	−0.0403587	+	0.383987i
$891$	7.42579	+	32.3682i	0.248773	+	1.08437i
$892$	−12.5681	+	1.32096i	−0.420810	+	0.0442290i
$893$	3.81640	+	2.20340i	0.127711	+	0.0737339i
$894$	−35.8784	+	12.8677i	−1.19995	+	0.430360i
$895$	8.48430	+	11.6776i	0.283599	+	0.390341i
$896$	1.00199	−	0.902193i	0.0334740	−	0.0301401i
$897$	7.63003	+	56.2094i	0.254759	+	1.87678i
$898$			15.3441i			0.512040i
$899$	5.85598	+	4.78231i	0.195308	+	0.159499i
$900$	−2.80929	−	1.05256i	−0.0936431	−	0.0350853i
$901$	−15.9106	−	48.9679i	−0.530060	−	1.63136i
$902$	−6.01867	−	6.68441i	−0.200400	−	0.222566i
$903$	−20.4810	+	9.87017i	−0.681565	+	0.328459i
$904$	8.52787	+	14.7707i	0.283633	+	0.491267i
$905$	−4.82508	+	8.35728i	−0.160391	+	0.277806i
$906$	34.4614	+	2.57287i	1.14490	+	0.0854778i
$907$	−48.3277	−	35.1121i	−1.60469	−	1.16588i	−0.877670	−	0.479265i	$-0.840903\pi$
$907$	−48.3277	−	35.1121i	−1.60469	−	1.16588i	−0.727023	−	0.686613i	$-0.759097\pi$
$908$	11.1102	+	1.16773i	0.368705	+	0.0387525i
$909$	18.5779	+	35.7479i	0.616190	+	1.18568i
$910$	3.59475	−	8.07394i	0.119165	−	0.267648i
$911$	16.0098	+	3.40298i	0.530428	+	0.112746i	0.465337	−	0.885133i	$-0.345933\pi$
$911$	16.0098	+	3.40298i	0.530428	+	0.112746i	0.0650905	+	0.997879i	$0.479266\pi$
$912$	−0.0965775	−	3.19711i	−0.00319800	−	0.105867i
$913$	15.4905	−	6.89682i	0.512661	−	0.228251i
$914$	−7.74829	+	23.8468i	−0.256291	+	0.788781i
$915$	2.59598	+	1.39603i	0.0858206	+	0.0461512i
$916$	−4.85793	−	10.9111i	−0.160510	−	0.360512i
$917$	3.60465	+	16.9586i	0.119036	+	0.560021i
$918$	21.3764	+	19.8012i	0.705528	+	0.653537i
$919$	−6.94664	−	3.09284i	−0.229149	−	0.102024i	0.288951	−	0.957344i	$-0.406694\pi$
$919$	−6.94664	−	3.09284i	−0.229149	−	0.102024i	−0.518099	+	0.855320i	$0.673360\pi$
$920$	3.34316	−	3.71295i	0.110221	−	0.122412i
$921$	−17.8593	−	5.21220i	−0.588485	−	0.171748i
$922$	1.59321	−	2.19286i	0.0524694	−	0.0722180i
$923$	−5.54152	−	52.7240i	−0.182401	−	1.73543i
$924$	6.57496	+	5.57000i	0.216300	+	0.183240i
$925$	−3.11169	+	1.79653i	−0.102312	+	0.0590696i
$926$	−4.90295	+	3.56220i	−0.161121	+	0.117061i
$927$	−8.56568	−	21.7893i	−0.281334	−	0.715654i
$928$	1.29147	−	0.419623i	0.0423944	−	0.0137748i
$929$	−12.7080			−0.416935			−0.208468	−	0.978029i	$-0.566848\pi$
$929$	−12.7080			−0.416935			−0.208468	+	0.978029i	$0.566848\pi$
$930$	3.68942	+	8.91000i	0.120981	+	0.292171i
$931$	−9.56970			−0.313634
$932$	10.9052	−	3.54332i	0.357212	−	0.116065i
$933$	7.98174	+	12.9083i	0.261311	+	0.422599i
$934$	32.4462	−	23.5735i	1.06167	−	0.771349i
$935$	−17.9195	+	10.3458i	−0.586031	+	0.338345i
$936$	−15.1824	+	12.4978i	−0.496253	+	0.408505i
$937$	5.57929	+	53.0834i	0.182267	+	1.73416i	0.578215	+	0.815885i	$0.303750\pi$
$937$	5.57929	+	53.0834i	0.182267	+	1.73416i	−0.395948	+	0.918273i	$0.629584\pi$
$938$	0.0792307	−	0.109052i	0.00258697	−	0.00356066i
$939$	−4.24784	+	14.5550i	−0.138623	+	0.474985i
$940$	−1.59676	+	1.77338i	−0.0520805	+	0.0578413i
$941$	43.9165	+	19.5529i	1.43164	+	0.637406i	0.968530	−	0.248897i	$-0.0800680\pi$
$941$	43.9165	+	19.5529i	1.43164	+	0.637406i	0.463107	+	0.886303i	$0.346735\pi$
$942$	−13.9849	−	5.72699i	−0.455652	−	0.186595i
$943$	2.53222	+	11.9131i	0.0824603	+	0.387945i
$944$	4.00433	+	8.99387i	0.130330	+	0.292725i
$945$	−5.27217	+	4.61393i	−0.171504	+	0.150091i
$946$	−11.1006	+	34.1642i	−0.360912	+	1.11077i
$947$	−11.5723	+	5.15233i	−0.376050	+	0.167428i	−0.586053	−	0.810272i	$-0.699319\pi$
$947$	−11.5723	+	5.15233i	−0.376050	+	0.167428i	0.210003	+	0.977701i	$0.432652\pi$
$948$	−1.41220	+	0.0426595i	−0.0458662	+	0.00138552i
$949$	−23.6732	−	5.03189i	−0.768464	−	0.163342i
$950$	−0.751118	+	1.68704i	−0.0243695	+	0.0547348i
$951$	−30.3322	+	23.4690i	−0.983588	+	0.761033i
$952$	7.51943	+	0.790324i	0.243706	+	0.0256146i
$953$	−37.9206	−	27.5509i	−1.22837	−	0.892462i	−0.231602	−	0.972811i	$-0.574397\pi$
$953$	−37.9206	−	27.5509i	−1.22837	−	0.892462i	−0.996767	+	0.0803485i	$0.974397\pi$
$954$	−26.6629	−	6.91512i	−0.863245	−	0.223885i
$955$	−3.95079	+	6.84297i	−0.127845	+	0.221433i
$956$	7.20424	+	12.4781i	0.233002	+	0.403571i
$957$	3.76769	+	7.81812i	0.121792	+	0.252724i
$958$	10.9599	+	12.1722i	0.354098	+	0.393265i
$959$	1.52762	+	4.70152i	0.0493293	+	0.151820i
$960$	1.70430	+	0.308795i	0.0550061	+	0.00996631i
$961$	12.8427	−	28.2146i	0.414279	−	0.910150i
$962$			23.5522i			0.759354i
$963$	−19.4482	−	0.862558i	−0.626708	−	0.0277955i
$964$	−9.41278	+	8.47531i	−0.303165	+	0.272971i
$965$	5.33061	+	7.33696i	0.171598	+	0.236185i
$966$	−3.93902	−	10.9830i	−0.126736	−	0.353371i
$967$	32.7635	+	18.9160i	1.05360	+	0.608299i	0.923656	−	0.383222i	$-0.125186\pi$
$967$	32.7635	+	18.9160i	1.05360	+	0.608299i	0.129948	+	0.991521i	$0.458519\pi$
$968$	2.60098	−	0.273374i	0.0835988	−	0.00878658i
$969$	12.9610	−	12.3989i	0.416366	−	0.398309i
$970$	1.78672	−	16.9995i	0.0573682	−	0.545822i
$971$	−27.4472	−	24.7136i	−0.880824	−	0.793097i	0.0985548	−	0.995132i	$-0.468578\pi$
$971$	−27.4472	−	24.7136i	−0.880824	−	0.793097i	−0.979378	+	0.202035i	$0.935245\pi$
$972$	15.0816	−	3.94287i	0.483742	−	0.126467i
$973$	−2.04794	+	9.63482i	−0.0656541	+	0.308878i
$974$	16.6631	−	3.54186i	0.533921	−	0.113489i
$975$	11.0290	−	2.69475i	0.353211	−	0.0863011i
$976$	−1.61848	−	0.525875i	−0.0518061	−	0.0168328i
$977$	38.1953	+	12.4104i	1.22198	+	0.397044i	0.847801	−	0.530314i	$-0.177926\pi$
$977$	38.1953	+	12.4104i	1.22198	+	0.397044i	0.374175	+	0.927358i	$0.377926\pi$
$978$	15.4896	−	3.78463i	0.495304	−	0.121019i
$979$	41.5734	−	8.83670i	1.32869	−	0.282422i
$980$	1.07741	−	5.06883i	0.0344167	−	0.161918i
$981$	41.8204	+	41.1535i	1.33522	+	1.31393i
$982$	−25.2669	−	22.7504i	−0.806298	−	0.725994i
$983$	−2.12031	+	20.1734i	−0.0676273	+	0.643431i	0.907235	+	0.420624i	$0.138189\pi$
$983$	−2.12031	+	20.1734i	−0.0676273	+	0.643431i	−0.974863	+	0.222807i	$0.928478\pi$
$984$	−3.05095	+	2.91864i	−0.0972608	+	0.0930428i
$985$	−9.83955	+	1.03418i	−0.313514	+	0.0329516i
$986$	6.59462	+	3.80740i	0.210015	+	0.121252i
$987$	1.88135	+	5.24568i	0.0598841	+	0.166972i
$988$	7.11509	+	9.79308i	0.226361	+	0.311559i
$989$	36.1468	−	32.5468i	1.14940	−	1.03493i
$990$	−0.490476	+	11.0588i	−0.0155884	+	0.351472i
$991$			57.7953i			1.83593i	0.396663	+	0.917964i	$0.370168\pi$
$991$			57.7953i			1.83593i	−0.396663	+	0.917964i	$0.629832\pi$
$992$	−3.01308	−	4.68202i	−0.0956655	−	0.148654i
$993$	−40.4733	−	7.33318i	−1.28438	−	0.232711i
$994$	3.36975	+	10.3710i	0.106882	+	0.328949i
$995$	−0.000932633	−	0.00103579i	−2.95664e−5	−	3.28369e-5i
$996$	−3.45547	−	7.17024i	−0.109491	−	0.227198i
$997$	11.8843	+	20.5842i	0.376380	+	0.651909i	0.990533	−	0.137278i	$-0.0438354\pi$
$997$	11.8843	+	20.5842i	0.376380	+	0.651909i	−0.614153	+	0.789187i	$0.710502\pi$
$998$	15.9605	−	27.6444i	0.505221	−	0.875069i
$999$	7.83395	−	16.9470i	0.247855	−	0.536181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.b.11.14	yes	176
3.2	odd	2	inner	930.2.br.b.11.4	✓	176
31.17	odd	30	inner	930.2.br.b.761.4	yes	176
93.17	even	30	inner	930.2.br.b.761.14	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.4	✓	176	3.2	odd	2	inner
930.2.br.b.11.14	yes	176	1.1	even	1	trivial
930.2.br.b.761.4	yes	176	31.17	odd	30	inner
930.2.br.b.761.14	yes	176	93.17	even	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)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(-1.47317 + 0.910922i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.11958 + 1.32157i) q^{6} +(0.140936 + 1.34092i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.34044 - 2.68388i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(-1.47317 + 0.910922i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.11958 + 1.32157i) q^{6} +(0.140936 + 1.34092i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.34044 - 2.68388i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-3.37088 - 1.50081i) q^{11} +(-0.656391 + 1.60286i) q^{12} +(-1.36284 - 6.41167i) q^{13} +(0.548405 + 1.23174i) q^{14} +(-0.820340 + 1.52546i) q^{15} +(0.309017 - 0.951057i) q^{16} +(5.12286 - 2.28084i) q^{17} +(0.445473 - 2.96674i) q^{18} +(-1.80634 - 0.383949i) q^{19} +(0.406737 - 0.913545i) q^{20} +(-1.42910 - 1.84702i) q^{21} +(-3.66968 - 0.385699i) q^{22} +(4.04207 + 2.93674i) q^{23} +(-0.128955 + 1.72724i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-3.27746 - 5.67672i) q^{26} +(0.470106 + 5.17484i) q^{27} +(0.902193 + 1.00199i) q^{28} +(0.419623 + 1.29147i) q^{29} +(-0.308795 + 1.70430i) q^{30} +(4.68202 - 3.01308i) q^{31} -1.00000i q^{32} +(6.33300 - 0.859661i) q^{33} +(4.16731 - 3.75226i) q^{34} +(0.792514 + 1.09080i) q^{35} +(-0.493103 - 2.95920i) q^{36} +(-3.11169 - 1.79653i) q^{37} +(-1.83658 + 0.193032i) q^{38} +(7.84822 + 8.20402i) q^{39} +(0.104528 - 0.994522i) q^{40} +(1.81154 + 1.63112i) q^{41} +(-1.92991 - 1.31500i) q^{42} +(2.02409 - 9.52259i) q^{43} +(-3.60926 + 0.767172i) q^{44} +(-0.181081 - 2.99453i) q^{45} +(4.75174 + 1.54393i) q^{46} +(-2.26952 - 0.737413i) q^{47} +(0.411104 + 1.68256i) q^{48} +(5.06883 - 1.07741i) q^{49} +(0.207912 - 0.978148i) q^{50} +(-5.46916 + 8.02659i) q^{51} +(-4.87125 - 4.38609i) q^{52} +(0.959748 - 9.13139i) q^{53} +(2.04621 + 4.77630i) q^{54} +(-3.66968 + 0.385699i) q^{55} +(1.16767 + 0.674153i) q^{56} +(3.01079 - 1.07981i) q^{57} +(0.798170 + 1.09859i) q^{58} +(-7.31627 + 6.58760i) q^{59} +(0.232977 + 1.71631i) q^{60} -1.70177i q^{61} +(3.52177 - 4.31244i) q^{62} +(3.78779 + 1.41917i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-4.38609 - 4.87125i) q^{65} +(5.75739 - 2.77459i) q^{66} +(-0.0499869 - 0.0865799i) q^{67} +(2.80383 - 4.85638i) q^{68} +(-8.62978 - 0.644295i) q^{69} +(1.09080 + 0.792514i) q^{70} +(8.04344 + 0.845399i) q^{71} +(-1.38341 - 2.66199i) q^{72} +(1.50175 - 3.37300i) q^{73} +(-3.51455 - 0.747040i) q^{74} +(0.0522975 + 1.73126i) q^{75} +(-1.68704 + 0.751118i) q^{76} +(1.53739 - 4.73161i) q^{77} +(9.99929 + 5.37725i) q^{78} +(0.331778 + 0.745186i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(-5.40642 - 7.19518i) q^{81} +(2.22693 + 0.991491i) q^{82} +(-3.07491 + 3.41503i) q^{83} +(-2.24181 - 0.654267i) q^{84} +(3.29610 - 4.53670i) q^{85} +(-1.01762 - 9.68200i) q^{86} +(-1.79460 - 1.52030i) q^{87} +(-3.19554 + 1.84495i) q^{88} +(-9.31870 + 6.77043i) q^{89} +(-1.09758 - 2.79201i) q^{90} +(8.40546 - 2.73110i) q^{91} +4.99627 q^{92} +(-4.15272 + 8.70373i) q^{93} -2.38632 q^{94} +(-1.75631 + 0.570660i) q^{95} +(0.910922 + 1.47317i) q^{96} +(13.8287 - 10.0471i) q^{97} +(4.48780 - 2.59104i) q^{98} +(-8.54649 + 7.03529i) 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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