LMFDB - Embedded newform 930.2.br.b.11.5

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			11.5
Character	$\chi$	$=$	930.11
Dual form			930.2.br.b.761.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(0.0316079 - 1.73176i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.505083 + 1.65677i) q^{6} +(-0.0802420 - 0.763452i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.99800 - 0.109475i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(0.0316079 - 1.73176i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.505083 + 1.65677i) q^{6} +(-0.0802420 - 0.763452i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.99800 - 0.109475i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-0.551428 - 0.245511i) q^{11} +(-0.992333 - 1.41960i) q^{12} +(1.24517 + 5.85808i) q^{13} +(0.312234 + 0.701289i) q^{14} +(0.838508 + 1.51555i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.895018 + 0.398488i) q^{17} +(2.88510 - 0.822317i) q^{18} +(-4.05438 - 0.861785i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(-1.32465 + 0.114829i) q^{21} +(0.600306 + 0.0630947i) q^{22} +(0.492054 + 0.357498i) q^{23} +(1.38245 + 1.04348i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.99448 - 5.18659i) q^{26} +(-0.284345 + 5.18837i) q^{27} +(-0.513663 - 0.570480i) q^{28} +(2.63625 + 8.11355i) q^{29} +(-1.26580 - 1.18226i) q^{30} +(1.97759 + 5.20472i) q^{31} +1.00000i q^{32} +(-0.442597 + 0.947182i) q^{33} +(0.728073 - 0.655560i) q^{34} +(0.451217 + 0.621047i) q^{35} +(-2.48978 + 1.67361i) q^{36} +(-9.50309 - 5.48661i) q^{37} +(4.12225 - 0.433266i) q^{38} +(10.1842 - 1.97118i) q^{39} +(0.104528 - 0.994522i) q^{40} +(8.20129 + 7.38447i) q^{41} +(1.22434 - 0.518549i) q^{42} +(0.784850 - 3.69243i) q^{43} +(-0.590422 + 0.125498i) q^{44} +(2.65108 - 1.40419i) q^{45} +(-0.578444 - 0.187948i) q^{46} +(-9.44864 - 3.07005i) q^{47} +(-1.63724 - 0.565205i) q^{48} +(6.27061 - 1.33286i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(0.661796 + 1.56255i) q^{51} +(4.45066 + 4.00739i) q^{52} +(-0.409227 + 3.89354i) q^{53} +(-1.33287 - 5.02230i) q^{54} +(0.600306 - 0.0630947i) q^{55} +(0.664810 + 0.383828i) q^{56} +(-1.62056 + 6.99398i) q^{57} +(-5.01445 - 6.90180i) q^{58} +(7.27371 - 6.54928i) q^{59} +(1.56919 + 0.733246i) q^{60} +11.7984i q^{61} +(-3.48915 - 4.33888i) q^{62} +(0.156987 + 2.29761i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-4.00739 - 4.45066i) q^{65} +(0.128239 - 1.03759i) q^{66} +(-0.364290 - 0.630968i) q^{67} +(-0.489859 + 0.848461i) q^{68} +(0.634655 - 0.840821i) q^{69} +(-0.621047 - 0.451217i) q^{70} +(6.35088 + 0.667504i) q^{71} +(1.85075 - 2.36109i) q^{72} +(-5.73753 + 12.8867i) q^{73} +(10.7334 + 2.28146i) q^{74} +(-1.48395 - 0.893254i) q^{75} +(-3.78661 + 1.68591i) q^{76} +(-0.143188 + 0.440689i) q^{77} +(-9.07658 + 5.02178i) q^{78} +(2.71470 + 6.09731i) q^{79} +(0.207912 + 0.978148i) q^{80} +(8.97603 + 0.656411i) q^{81} +(-10.0818 - 4.48871i) q^{82} +(4.71869 - 5.24064i) q^{83} +(-1.00417 + 0.871510i) q^{84} +(0.575864 - 0.792609i) q^{85} +(0.394587 + 3.75424i) q^{86} +(14.1341 - 4.30891i) q^{87} +(0.522744 - 0.301806i) q^{88} +(4.80921 - 3.49409i) q^{89} +(-2.08741 + 2.15470i) q^{90} +(4.37244 - 1.42069i) q^{91} +0.608212 q^{92} +(9.07585 - 3.26020i) q^{93} +9.93488 q^{94} +(3.94209 - 1.28086i) q^{95} +(1.73176 + 0.0316079i) q^{96} +(7.85424 - 5.70644i) q^{97} +(-5.55183 + 3.20535i) q^{98} +(1.62630 + 0.796411i) 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
$3$	0.0316079	−	1.73176i	0.0182488	−	0.999833i
$3$	0.0316079	−	1.73176i	0.0182488	−	0.999833i
$4$	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
$6$	0.505083	+	1.65677i	0.206199	+	0.676374i
$7$	−0.0802420	−	0.763452i	−0.0303286	−	0.288558i	−0.999165	−	0.0408561i	$-0.986991\pi$
$7$	−0.0802420	−	0.763452i	−0.0303286	−	0.288558i	0.968836	−	0.247701i	$-0.0796752\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	−2.99800	−	0.109475i	−0.999334	−	0.0364916i
$10$	0.669131	−	0.743145i	0.211598	−	0.235003i
$11$	−0.551428	−	0.245511i	−0.166262	−	0.0740245i	0.321918	−	0.946767i	$-0.395672\pi$
$11$	−0.551428	−	0.245511i	−0.166262	−	0.0740245i	−0.488180	+	0.872743i	$0.662339\pi$
$12$	−0.992333	−	1.41960i	−0.286462	−	0.409804i
$13$	1.24517	+	5.85808i	0.345349	+	1.62474i	0.717494	+	0.696565i	$0.245289\pi$
$13$	1.24517	+	5.85808i	0.345349	+	1.62474i	−0.372145	+	0.928175i	$0.621378\pi$
$14$	0.312234	+	0.701289i	0.0834481	+	0.187427i
$15$	0.838508	+	1.51555i	0.216502	+	0.391314i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.895018	+	0.398488i	−0.217074	+	0.0966474i	−0.512393	−	0.858751i	$-0.671241\pi$
$17$	−0.895018	+	0.398488i	−0.217074	+	0.0966474i	0.295319	+	0.955399i	$0.404574\pi$
$18$	2.88510	−	0.822317i	0.680024	−	0.193822i
$19$	−4.05438	−	0.861785i	−0.930138	−	0.197707i	−0.282161	−	0.959367i	$-0.591051\pi$
$19$	−4.05438	−	0.861785i	−0.930138	−	0.197707i	−0.647977	+	0.761660i	$0.724385\pi$
$20$	−0.406737	+	0.913545i	−0.0909491	+	0.204275i
$21$	−1.32465	+	0.114829i	−0.289063	+	0.0250577i
$22$	0.600306	+	0.0630947i	0.127986	+	0.0134518i
$23$	0.492054	+	0.357498i	0.102600	+	0.0745435i	0.637903	−	0.770117i	$-0.279802\pi$
$23$	0.492054	+	0.357498i	0.102600	+	0.0745435i	−0.535302	+	0.844661i	$0.679802\pi$
$24$	1.38245	+	1.04348i	0.282191	+	0.212999i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.99448	−	5.18659i	−0.587265	−	1.01717i
$27$	−0.284345	+	5.18837i	−0.0547222	+	0.998502i
$28$	−0.513663	−	0.570480i	−0.0970731	−	0.107811i
$29$	2.63625	+	8.11355i	0.489540	+	1.50665i	0.825296	+	0.564700i	$0.191008\pi$
$29$	2.63625	+	8.11355i	0.489540	+	1.50665i	−0.335756	+	0.941949i	$0.608992\pi$
$30$	−1.26580	−	1.18226i	−0.231102	−	0.215851i
$31$	1.97759	+	5.20472i	0.355185	+	0.934796i
$31$	1.97759	+	5.20472i	0.355185	+	0.934796i
$32$			1.00000i			0.176777i
$33$	−0.442597	+	0.947182i	−0.0770462	+	0.164883i
$34$	0.728073	−	0.655560i	0.124863	−	0.112428i
$35$	0.451217	+	0.621047i	0.0762697	+	0.104976i
$36$	−2.48978	+	1.67361i	−0.414964	+	0.278936i
$37$	−9.50309	−	5.48661i	−1.56230	−	0.901993i	−0.997024	−	0.0770894i	$-0.975437\pi$
$37$	−9.50309	−	5.48661i	−1.56230	−	0.901993i	−0.565273	−	0.824904i	$-0.691229\pi$
$38$	4.12225	−	0.433266i	0.668717	−	0.0702850i
$39$	10.1842	−	1.97118i	1.63077	−	0.315642i
$40$	0.104528	−	0.994522i	0.0165274	−	0.157248i
$41$	8.20129	+	7.38447i	1.28083	+	1.15326i	0.979873	+	0.199621i	$0.0639713\pi$
$41$	8.20129	+	7.38447i	1.28083	+	1.15326i	0.300953	+	0.953639i	$0.402695\pi$
$42$	1.22434	−	0.518549i	0.188919	−	0.0800139i
$43$	0.784850	−	3.69243i	0.119689	−	0.563090i	−0.876908	−	0.480658i	$-0.840398\pi$
$43$	0.784850	−	3.69243i	0.119689	−	0.563090i	0.996597	−	0.0824323i	$-0.0262688\pi$
$44$	−0.590422	+	0.125498i	−0.0890095	+	0.0189196i
$45$	2.65108	−	1.40419i	0.395200	−	0.209325i
$46$	−0.578444	−	0.187948i	−0.0852870	−	0.0277114i
$47$	−9.44864	−	3.07005i	−1.37823	−	0.447813i	−0.476140	−	0.879370i	$-0.657964\pi$
$47$	−9.44864	−	3.07005i	−1.37823	−	0.447813i	−0.902086	+	0.431557i	$0.857964\pi$
$48$	−1.63724	−	0.565205i	−0.236315	−	0.0815803i
$49$	6.27061	−	1.33286i	0.895802	−	0.190409i
$50$	−0.207912	+	0.978148i	−0.0294032	+	0.138331i
$51$	0.661796	+	1.56255i	0.0926700	+	0.218801i
$52$	4.45066	+	4.00739i	0.617195	+	0.555725i
$53$	−0.409227	+	3.89354i	−0.0562117	+	0.534818i	0.929791	+	0.368088i	$0.119988\pi$
$53$	−0.409227	+	3.89354i	−0.0562117	+	0.534818i	−0.986003	+	0.166730i	$0.946679\pi$
$54$	−1.33287	−	5.02230i	−0.181380	−	0.683448i
$55$	0.600306	−	0.0630947i	0.0809453	−	0.00850769i
$56$	0.664810	+	0.383828i	0.0888390	+	0.0512912i
$57$	−1.62056	+	6.99398i	−0.214648	+	0.926376i
$58$	−5.01445	−	6.90180i	−0.658430	−	0.906251i
$59$	7.27371	−	6.54928i	0.946957	−	0.852644i	−0.0422593	−	0.999107i	$-0.513456\pi$
$59$	7.27371	−	6.54928i	0.946957	−	0.852644i	0.989216	+	0.146463i	$0.0467889\pi$
$60$	1.56919	+	0.733246i	0.202581	+	0.0946617i
$61$			11.7984i			1.51063i	0.655359	+	0.755317i	$0.272517\pi$
$61$			11.7984i			1.51063i	−0.655359	+	0.755317i	$0.727483\pi$
$62$	−3.48915	−	4.33888i	−0.443122	−	0.551038i
$63$	0.156987	+	2.29761i	0.0197785	+	0.289472i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−4.00739	−	4.45066i	−0.497056	−	0.552036i
$66$	0.128239	−	1.03759i	0.0157852	−	0.127719i
$67$	−0.364290	−	0.630968i	−0.0445051	−	0.0770851i	0.842915	−	0.538047i	$-0.180838\pi$
$67$	−0.364290	−	0.630968i	−0.0445051	−	0.0770851i	−0.887420	+	0.460962i	$0.847504\pi$
$68$	−0.489859	+	0.848461i	−0.0594042	+	0.102891i
$69$	0.634655	−	0.840821i	0.0764035	−	0.101223i
$70$	−0.621047	−	0.451217i	−0.0742294	−	0.0539308i
$71$	6.35088	+	0.667504i	0.753711	+	0.0792182i	0.473589	−	0.880746i	$-0.342958\pi$
$71$	6.35088	+	0.667504i	0.753711	+	0.0792182i	0.280122	+	0.959964i	$0.409625\pi$
$72$	1.85075	−	2.36109i	0.218113	−	0.278257i
$73$	−5.73753	+	12.8867i	−0.671527	+	1.50827i	0.179835	+	0.983697i	$0.442444\pi$
$73$	−5.73753	+	12.8867i	−0.671527	+	1.50827i	−0.851362	+	0.524578i	$0.824223\pi$
$74$	10.7334	+	2.28146i	1.24774	+	0.265214i
$75$	−1.48395	−	0.893254i	−0.171351	−	0.103144i
$76$	−3.78661	+	1.68591i	−0.434353	+	0.193387i
$77$	−0.143188	+	0.440689i	−0.0163178	+	0.0502211i
$78$	−9.07658	+	5.02178i	−1.02772	+	0.568605i
$79$	2.71470	+	6.09731i	0.305427	+	0.686001i	0.999423	−	0.0339789i	$-0.0108179\pi$
$79$	2.71470	+	6.09731i	0.305427	+	0.686001i	−0.693995	+	0.719979i	$0.744151\pi$
$80$	0.207912	+	0.978148i	0.0232452	+	0.109360i
$81$	8.97603	+	0.656411i	0.997337	+	0.0729346i
$82$	−10.0818	−	4.48871i	−1.11335	−	0.495695i
$83$	4.71869	−	5.24064i	0.517944	−	0.575235i	−0.426258	−	0.904602i	$-0.640169\pi$
$83$	4.71869	−	5.24064i	0.517944	−	0.575235i	0.944202	+	0.329367i	$0.106835\pi$
$84$	−1.00417	+	0.871510i	−0.109564	+	0.0950895i
$85$	0.575864	−	0.792609i	0.0624613	−	0.0859705i
$86$	0.394587	+	3.75424i	0.0425494	+	0.404830i
$87$	14.1341	−	4.30891i	1.51533	−	0.461964i
$88$	0.522744	−	0.301806i	0.0557247	−	0.0321727i
$89$	4.80921	−	3.49409i	0.509775	−	0.370373i	−0.302963	−	0.953002i	$-0.597976\pi$
$89$	4.80921	−	3.49409i	0.509775	−	0.370373i	0.812738	+	0.582629i	$0.197976\pi$
$90$	−2.08741	+	2.15470i	−0.220032	+	0.227125i
$91$	4.37244	−	1.42069i	0.458357	−	0.148929i
$92$	0.608212			0.0634105
$93$	9.07585	−	3.26020i	0.941122	−	0.338067i
$94$	9.93488			1.02471
$95$	3.94209	−	1.28086i	0.404450	−	0.131414i
$96$	1.73176	+	0.0316079i	0.176747	+	0.00322597i
$97$	7.85424	−	5.70644i	0.797477	−	0.579401i	−0.112696	−	0.993630i	$-0.535949\pi$
$97$	7.85424	−	5.70644i	0.797477	−	0.579401i	0.910173	+	0.414228i	$0.135949\pi$
$98$	−5.55183	+	3.20535i	−0.560820	+	0.323789i
$99$	1.62630	+	0.796411i	0.163450	+	0.0800423i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−7.75539	+	10.6744i	−0.771690	+	1.06214i	0.224460	+	0.974483i	$0.427938\pi$
$101$	−7.75539	+	10.6744i	−0.771690	+	1.06214i	−0.996151	+	0.0876573i	$0.972062\pi$
$102$	−1.11226	−	1.28157i	−0.110130	−	0.126894i
$103$	−10.7089	+	11.8935i	−1.05518	+	1.17190i	−0.0705052	+	0.997511i	$0.522461\pi$
$103$	−10.7089	+	11.8935i	−1.05518	+	1.17190i	−0.984677	+	0.174387i	$0.944206\pi$
$104$	−5.47118	−	2.43593i	−0.536493	−	0.238862i
$105$	1.08977	−	0.761771i	0.106351	−	0.0743413i
$106$	−0.813971	−	3.82943i	−0.0790598	−	0.371947i
$107$	5.63995	+	12.6675i	0.545235	+	1.22462i	0.950587	+	0.310457i	$0.100482\pi$
$107$	5.63995	+	12.6675i	0.545235	+	1.22462i	−0.405353	+	0.914160i	$0.632851\pi$
$108$	2.81961	+	4.36461i	0.271317	+	0.419985i
$109$	−2.77250	+	8.53289i	−0.265558	+	0.817302i	0.726007	+	0.687688i	$0.241374\pi$
$109$	−2.77250	+	8.53289i	−0.265558	+	0.817302i	−0.991564	+	0.129615i	$0.958626\pi$
$110$	−0.551428	+	0.245511i	−0.0525766	+	0.0234086i
$111$	−9.80188	+	16.2837i	−0.930353	+	1.54558i
$112$	−0.750882	−	0.159605i	−0.0709517	−	0.0150812i
$113$	0.875218	−	1.96577i	0.0823336	−	0.184924i	−0.867687	−	0.497110i	$-0.834394\pi$
$113$	0.875218	−	1.96577i	0.0823336	−	0.184924i	0.950021	+	0.312186i	$0.101061\pi$
$114$	−0.620018	−	7.15245i	−0.0580700	−	0.669888i
$115$	−0.604881	−	0.0635755i	−0.0564054	−	0.00592845i
$116$	6.90180	+	5.01445i	0.640816	+	0.465580i
$117$	−3.09172	−	17.6988i	−0.285830	−	1.63626i
$118$	−4.89387	+	8.47644i	−0.450518	+	0.780319i
$119$	0.376044	+	0.651327i	0.0344719	+	0.0597071i
$120$	−1.71897	−	0.212453i	−0.156920	−	0.0193942i
$121$	−7.11664	−	7.90383i	−0.646967	−	0.718530i
$122$	−3.64592	−	11.2210i	−0.330086	−	1.01590i
$123$	13.0474	−	13.9693i	1.17644	−	1.25957i
$124$	4.65916	+	3.04831i	0.418405	+	0.273747i
$125$			1.00000i			0.0894427i
$126$	−0.859305	−	2.13665i	−0.0765530	−	0.190348i
$127$	−7.31430	+	6.58582i	−0.649039	+	0.584397i	−0.926479	−	0.376346i	$-0.877181\pi$
$127$	−7.31430	+	6.58582i	−0.649039	+	0.584397i	0.277441	+	0.960743i	$0.410514\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	−6.36960	−	1.47588i	−0.560812	−	0.129944i
$130$	5.18659	+	2.99448i	0.454894	+	0.262633i
$131$	−13.9640	+	1.46768i	−1.22004	+	0.128232i	−0.692577	−	0.721344i	$-0.743525\pi$
$131$	−13.9640	+	1.46768i	−1.22004	+	0.128232i	−0.527467	+	0.849575i	$0.676858\pi$
$132$	0.198671	+	1.02644i	0.0172921	+	0.0893400i
$133$	−0.332600	+	3.16447i	−0.0288400	+	0.274395i
$134$	0.541440	+	0.487515i	0.0467733	+	0.0421149i
$135$	−2.34793	−	4.63543i	−0.202078	−	0.398954i
$136$	0.203695	−	0.958310i	0.0174667	−	0.0821744i
$137$	−7.78117	+	1.65394i	−0.664790	+	0.141305i	−0.527934	−	0.849286i	$-0.677033\pi$
$137$	−7.78117	+	1.65394i	−0.664790	+	0.141305i	−0.136856	+	0.990591i	$0.543700\pi$
$138$	−0.343765	+	0.995788i	−0.0292632	+	0.0847671i
$139$	−13.3149	−	4.32629i	−1.12936	−	0.366951i	−0.316027	−	0.948750i	$-0.602349\pi$
$139$	−13.3149	−	4.32629i	−1.12936	−	0.366951i	−0.813332	+	0.581799i	$0.802349\pi$
$140$	0.730085	+	0.237219i	0.0617034	+	0.0200487i
$141$	−5.61525	+	16.2658i	−0.472889	+	1.36982i
$142$	−6.24631	+	1.32770i	−0.524179	+	0.111418i
$143$	0.751603	−	3.53601i	0.0628522	−	0.295696i
$144$	−1.03055	+	2.81744i	−0.0858792	+	0.234787i
$145$	−6.33984	−	5.70842i	−0.526495	−	0.474058i
$146$	1.47451	−	14.0290i	0.122031	−	1.16105i
$147$	−2.11000	−	10.9013i	−0.174030	−	0.899128i
$148$	−10.9131	+	1.14701i	−0.897052	+	0.0942839i
$149$	−2.08442	−	1.20344i	−0.170762	−	0.0985897i	0.412183	−	0.911101i	$-0.364766\pi$
$149$	−2.08442	−	1.20344i	−0.170762	−	0.0985897i	−0.582945	+	0.812511i	$0.698100\pi$
$150$	1.68735	+	0.390971i	0.137771	+	0.0319226i
$151$	2.52073	+	3.46948i	0.205134	+	0.282343i	0.899172	−	0.437596i	$-0.144170\pi$
$151$	2.52073	+	3.46948i	0.205134	+	0.282343i	−0.694038	+	0.719939i	$0.744170\pi$
$152$	3.08030	−	2.77352i	0.249846	−	0.224962i
$153$	2.72689	−	1.09668i	0.220456	−	0.0886617i
$154$		−	0.463368i		−	0.0373392i
$155$	−4.31500	−	3.51863i	−0.346589	−	0.282623i
$156$	7.08053	−	7.58082i	0.566896	−	0.606951i
$157$	−3.61004	−	11.1106i	−0.288113	−	0.886720i	−0.985448	−	0.169975i	$-0.945631\pi$
$157$	−3.61004	−	11.1106i	−0.288113	−	0.886720i	0.697336	−	0.716745i	$-0.254369\pi$
$158$	−4.46600	−	4.96000i	−0.355296	−	0.394596i
$159$	6.72974	+	0.831751i	0.533703	+	0.0659621i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	0.233449	−	0.404346i	0.0183984	−	0.0318669i
$162$	−8.73955	+	2.14946i	−0.686644	+	0.168878i
$163$	4.01111	+	2.91424i	0.314175	+	0.228261i	0.733686	−	0.679489i	$-0.237798\pi$
$163$	4.01111	+	2.91424i	0.314175	+	0.228261i	−0.419511	+	0.907750i	$0.637798\pi$
$164$	10.9755	+	1.15357i	0.857040	+	0.0900785i
$165$	−0.0902907	−	1.04158i	−0.00702912	−	0.0810870i
$166$	−2.86830	+	6.44230i	−0.222623	+	0.500020i
$167$	−8.79381	−	1.86918i	−0.680485	−	0.144642i	−0.145314	−	0.989386i	$-0.546419\pi$
$167$	−8.79381	−	1.86918i	−0.680485	−	0.144642i	−0.535171	+	0.844744i	$0.679753\pi$
$168$	0.685713	−	1.13916i	0.0529039	−	0.0878882i
$169$	−20.8906	+	9.30107i	−1.60697	+	0.715467i
$170$	−0.302750	+	0.931768i	−0.0232198	+	0.0714633i
$171$	12.0607	+	3.02748i	0.922304	+	0.231518i
$172$	−1.53540	−	3.44856i	−0.117073	−	0.262950i
$173$	1.89714	+	8.92535i	0.144237	+	0.678582i	0.989536	+	0.144288i	$0.0460891\pi$
$173$	1.89714	+	8.92535i	0.144237	+	0.678582i	−0.845299	+	0.534294i	$0.820578\pi$
$174$	−12.1108	+	8.46569i	−0.918115	+	0.641782i
$175$	−0.701289	−	0.312234i	−0.0530125	−	0.0236027i
$176$	−0.403896	+	0.448572i	−0.0304448	+	0.0338124i
$177$	−11.1119	−	12.8034i	−0.835221	−	0.962359i
$178$	−3.49409	+	4.80921i	−0.261893	+	0.360465i
$179$	−0.898176	−	8.54557i	−0.0671328	−	0.638726i	−0.975416	−	0.220371i	$-0.929273\pi$
$179$	−0.898176	−	8.54557i	−0.0671328	−	0.638726i	0.908283	−	0.418355i	$-0.137393\pi$
$180$	1.31941	−	2.69428i	0.0983428	−	0.200820i
$181$	16.9711	−	9.79829i	1.26145	−	0.728301i	0.288099	−	0.957601i	$-0.406977\pi$
$181$	16.9711	−	9.79829i	1.26145	−	0.728301i	0.973356	+	0.229299i	$0.0736435\pi$
$182$	−3.71942	+	2.70232i	−0.275702	+	0.200309i
$183$	20.4321	+	0.372924i	1.51038	+	0.0275673i
$184$	−0.578444	+	0.187948i	−0.0426435	+	0.0138557i
$185$	10.9732			0.806767
$186$	−7.62419	+	5.90523i	−0.559033	+	0.432992i
$187$	0.591371			0.0432453
$188$	−9.44864	+	3.07005i	−0.689113	+	0.223906i
$189$	3.98388	−	0.199241i	0.289785	−	0.0144927i
$190$	−3.35334	+	2.43634i	−0.243277	+	0.176751i
$191$	11.6486	−	6.72532i	0.842862	−	0.486627i	−0.0153738	−	0.999882i	$-0.504894\pi$
$191$	11.6486	−	6.72532i	0.842862	−	0.486627i	0.858236	+	0.513255i	$0.171560\pi$
$192$	−1.65677	+	0.505083i	−0.119567	+	0.0364512i
$193$	−2.58308	−	24.5763i	−0.185934	−	1.76904i	−0.547605	−	0.836737i	$-0.684460\pi$
$193$	−2.58308	−	24.5763i	−0.185934	−	1.76904i	0.361671	−	0.932306i	$-0.382206\pi$
$194$	−5.70644	+	7.85424i	−0.409698	+	0.563902i
$195$	−7.83415	+	6.79917i	−0.561015	+	0.486899i
$196$	4.28960	−	4.76408i	0.306400	−	0.340291i
$197$	−15.6853	−	6.98356i	−1.11753	−	0.497558i	−0.236984	−	0.971513i	$-0.576159\pi$
$197$	−15.6853	−	6.98356i	−1.11753	−	0.497558i	−0.880549	+	0.473956i	$0.842826\pi$
$198$	−1.79281	−	0.254876i	−0.127410	−	0.0181133i
$199$	−0.529552	−	2.49134i	−0.0375389	−	0.176607i	0.955384	−	0.295366i	$-0.0954416\pi$
$199$	−0.529552	−	2.49134i	−0.0375389	−	0.176607i	−0.992923	+	0.118759i	$0.962108\pi$
$200$	0.406737	+	0.913545i	0.0287606	+	0.0645974i
$201$	−1.10420	+	0.610920i	−0.0778844	+	0.0430910i
$202$	4.07725	−	12.5485i	0.286874	−	0.882908i
$203$	5.98277	−	2.66370i	0.419908	−	0.186955i
$204$	1.45385	+	0.875138i	0.101790	+	0.0612719i
$205$	−10.7948	−	2.29450i	−0.753939	−	0.160255i
$206$	6.50951	−	14.6206i	0.453539	−	1.01867i
$207$	−1.43604	−	1.12565i	−0.0998118	−	0.0782379i
$208$	5.95614	+	0.626016i	0.412984	+	0.0434064i
$209$	2.02412	+	1.47061i	0.140011	+	0.101724i
$210$	−0.801031	+	1.06124i	−0.0552764	+	0.0732328i
$211$	6.82631	−	11.8235i	0.469943	−	0.813964i	−0.529467	−	0.848331i	$-0.677608\pi$
$211$	6.82631	−	11.8235i	0.469943	−	0.813964i	0.999409	+	0.0343663i	$0.0109413\pi$
$212$	1.95749	+	3.39047i	0.134441	+	0.232859i
$213$	1.35670	−	10.9771i	0.0929593	−	0.752139i
$214$	−9.27840	−	10.3047i	−0.634258	−	0.704415i
$215$	1.16651	+	3.59016i	0.0795556	+	0.244847i
$216$	−4.03034	−	3.27969i	−0.274230	−	0.223154i
$217$	3.81487	−	1.92743i	0.258970	−	0.130842i
$218$		−	8.97201i		−	0.607661i
$219$	22.1354	+	10.3434i	1.49577	+	0.698940i
$220$	0.448572	−	0.403896i	0.0302427	−	0.0272307i
$221$	−3.44882	−	4.74690i	−0.231993	−	0.319311i
$222$	4.29021	−	18.5156i	0.287940	−	1.24269i
$223$	10.3800	+	5.99290i	0.695097	+	0.401314i	0.805519	−	0.592570i	$-0.201887\pi$
$223$	10.3800	+	5.99290i	0.695097	+	0.401314i	−0.110422	+	0.993885i	$0.535220\pi$
$224$	0.763452	−	0.0802420i	0.0510103	−	0.00536139i
$225$	−1.59381	+	2.54161i	−0.106254	+	0.169441i
$226$	−0.224925	+	2.14002i	−0.0149618	+	0.142352i
$227$	16.1577	+	14.5485i	1.07242	+	0.965615i	0.999497	−	0.0317220i	$-0.0100991\pi$
$227$	16.1577	+	14.5485i	1.07242	+	0.965615i	0.0729276	+	0.997337i	$0.476766\pi$
$228$	2.79990	+	6.61079i	0.185428	+	0.437810i
$229$	−2.87446	+	13.5233i	−0.189950	+	0.893644i	0.775153	+	0.631773i	$0.217673\pi$
$229$	−2.87446	+	13.5233i	−0.189950	+	0.893644i	−0.965103	+	0.261870i	$0.915661\pi$
$230$	0.594922	−	0.126454i	0.0392280	−	0.00833816i
$231$	0.758642	+	0.261898i	0.0499150	+	0.0172316i
$232$	−8.11355	−	2.63625i	−0.532681	−	0.173078i
$233$	2.31438	+	0.751987i	0.151620	+	0.0492643i	0.383844	−	0.923398i	$-0.374600\pi$
$233$	2.31438	+	0.751987i	0.151620	+	0.0492643i	−0.232224	+	0.972662i	$0.574600\pi$
$234$	8.40965	+	15.8772i	0.549756	+	1.03793i
$235$	9.71778	−	2.06558i	0.633918	−	0.134743i
$236$	2.03499	−	9.57386i	0.132466	−	0.623205i
$237$	10.6449	−	4.50848i	0.691460	−	0.292858i
$238$	−0.558910	−	0.503245i	−0.0362288	−	0.0326205i
$239$	2.71745	−	25.8548i	0.175777	−	1.67241i	−0.450477	−	0.892788i	$-0.648746\pi$
$239$	2.71745	−	25.8548i	0.175777	−	1.67241i	0.626254	−	0.779619i	$-0.284587\pi$
$240$	1.70049	−	0.329136i	0.109766	−	0.0212457i
$241$	−14.1209	+	1.48417i	−0.909607	+	0.0956035i	−0.547761	−	0.836635i	$-0.684520\pi$
$241$	−14.1209	+	1.48417i	−0.909607	+	0.0956035i	−0.361845	+	0.932238i	$0.617853\pi$
$242$	9.21074	+	5.31783i	0.592089	+	0.341843i
$243$	1.42046	−	15.5236i	0.0911226	−	0.995840i
$244$	6.93495	+	9.54513i	0.443964	+	0.611065i
$245$	−4.76408	+	4.28960i	−0.304366	+	0.274052i
$246$	−8.09205	+	17.3174i	−0.515930	+	1.10412i
$247$		−	24.8239i		−	1.57951i
$248$	−5.37311	−	1.45936i	−0.341193	−	0.0926693i
$249$	−8.92640	−	8.33730i	−0.565687	−	0.528355i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−7.86589	−	8.73596i	−0.496491	−	0.551409i	0.441864	−	0.897082i	$-0.354317\pi$
$251$	−7.86589	−	8.73596i	−0.496491	−	0.551409i	−0.938355	+	0.345673i	$0.887651\pi$
$252$	1.47751	+	1.76653i	0.0930743	+	0.111281i
$253$	−0.183562	−	0.317939i	−0.0115405	−	0.0199887i
$254$	4.92118	−	8.52373i	0.308782	−	0.534826i
$255$	−1.35441	−	1.02231i	−0.0848164	−	0.0640197i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−20.1391	−	2.11671i	−1.25624	−	0.132037i	−0.547080	−	0.837080i	$-0.684261\pi$
$257$	−20.1391	−	2.11671i	−1.25624	−	0.132037i	−0.709164	+	0.705043i	$0.750927\pi$
$258$	6.51393	−	0.564667i	0.405539	−	0.0351546i
$259$	−3.42621	+	7.69540i	−0.212895	+	0.478169i
$260$	−5.85808	−	1.24517i	−0.363303	−	0.0772224i
$261$	−7.01526	−	24.6130i	−0.434234	−	1.52351i
$262$	12.8271	−	5.71098i	0.792459	−	0.352825i
$263$	−6.78381	+	20.8784i	−0.418308	+	1.28742i	0.490951	+	0.871187i	$0.336649\pi$
$263$	−6.78381	+	20.8784i	−0.418308	+	1.28742i	−0.909259	+	0.416232i	$0.863351\pi$
$264$	−0.506134	−	0.914808i	−0.0311504	−	0.0563025i
$265$	−1.59237	−	3.57651i	−0.0978183	−	0.219704i
$266$	−0.661555	−	3.11237i	−0.0405625	−	0.190832i
$267$	−5.89893	−	8.43885i	−0.361009	−	0.516449i
$268$	−0.665591	−	0.296340i	−0.0406574	−	0.0181018i
$269$	−10.7519	+	11.9412i	−0.655553	+	0.728065i	−0.975653	−	0.219318i	$-0.929617\pi$
$269$	−10.7519	+	11.9412i	−0.655553	+	0.728065i	0.320100	+	0.947384i	$0.396283\pi$
$270$	3.66544	+	3.68300i	0.223072	+	0.224141i
$271$	−0.374862	+	0.515953i	−0.0227712	+	0.0313419i	−0.820251	−	0.572004i	$-0.806166\pi$
$271$	−0.374862	+	0.515953i	−0.0227712	+	0.0313419i	0.797480	+	0.603346i	$0.206166\pi$
$272$	0.102409	+	0.974352i	0.00620943	+	0.0590788i
$273$	−2.32210	−	7.61694i	−0.140540	−	0.460998i
$274$	6.88923	−	3.97750i	0.416194	−	0.240290i
$275$	−0.488333	+	0.354795i	−0.0294476	+	0.0213949i
$276$	0.0192243	−	1.05328i	0.00115717	−	0.0634000i
$277$	−3.10775	+	1.00977i	−0.186726	+	0.0606711i	−0.400888	−	0.916127i	$-0.631298\pi$
$277$	−3.10775	+	1.00977i	−0.186726	+	0.0606711i	0.214161	+	0.976798i	$0.431298\pi$
$278$	14.0002			0.839674
$279$	−5.35903	−	15.8203i	−0.320837	−	0.947135i
$280$	−0.767657			−0.0458763
$281$	5.35691	−	1.74057i	0.319567	−	0.103833i	−0.144841	−	0.989455i	$-0.546267\pi$
$281$	5.35691	−	1.74057i	0.319567	−	0.103833i	0.464408	+	0.885621i	$0.346267\pi$
$282$	0.314021	−	17.2049i	0.0186997	−	1.02453i
$283$	−16.4777	+	11.9717i	−0.979495	+	0.711645i	−0.957596	−	0.288115i	$-0.906971\pi$
$283$	−16.4777	+	11.9717i	−0.979495	+	0.711645i	−0.0218994	+	0.999760i	$0.506971\pi$
$284$	5.53032	−	3.19293i	0.328164	−	0.189466i
$285$	−2.09355	−	6.86724i	−0.124011	−	0.406780i
$286$	0.377871	+	3.59521i	0.0223440	+	0.212589i
$287$	4.97960	−	6.85383i	0.293936	−	0.404569i
$288$	0.109475	−	2.99800i	0.00645086	−	0.176659i
$289$	−10.7330	+	11.9202i	−0.631350	+	0.701186i
$290$	7.79354	+	3.46991i	0.457653	+	0.203760i
$291$	−9.63394	−	13.7820i	−0.564752	−	0.807918i
$292$	2.93286	+	13.7980i	0.171632	+	0.807467i
$293$	−3.61021	−	8.10866i	−0.210911	−	0.473713i	0.776851	−	0.629685i	$-0.216816\pi$
$293$	−3.61021	−	8.10866i	−0.210911	−	0.473713i	−0.987762	+	0.155971i	$0.950149\pi$
$294$	5.37543	+	9.71577i	0.313501	+	0.566635i
$295$	−3.02458	+	9.30870i	−0.176098	+	0.541974i
$296$	10.0245	−	4.46321i	0.582664	−	0.259419i
$297$	1.43060	−	2.79120i	0.0830118	−	0.161962i
$298$	2.35428	+	0.500419i	0.136380	+	0.0289885i
$299$	−1.48156	+	3.32764i	−0.0856809	+	0.192442i
$300$	−1.72558	+	0.149584i	−0.0996264	+	0.00863622i
$301$	−2.88197	−	0.302907i	−0.166114	−	0.0174593i
$302$	−3.46948	−	2.52073i	−0.199646	−	0.145052i
$303$	18.2404	+	13.7679i	1.04788	+	0.790945i
$304$	−2.07248	+	3.58964i	−0.118865	+	0.205880i
$305$	−5.89922	−	10.2177i	−0.337788	−	0.585066i
$306$	−2.25453	+	1.88566i	−0.128883	+	0.107796i
$307$	−3.54030	−	3.93190i	−0.202056	−	0.224405i	0.633598	−	0.773663i	$-0.281577\pi$
$307$	−3.54030	−	3.93190i	−0.202056	−	0.224405i	−0.835653	+	0.549257i	$0.814911\pi$
$308$	0.143188	+	0.440689i	0.00815892	+	0.0251106i
$309$	20.2582	+	18.9213i	1.15245	+	1.07639i
$310$	5.19113	+	2.01301i	0.294836	+	0.114331i
$311$		−	9.87218i		−	0.559800i	−0.960029	−	0.279900i	$-0.909699\pi$
$311$		−	9.87218i		−	0.559800i	0.960029	−	0.279900i	$-0.0903013\pi$
$312$	−4.39138	+	9.39779i	−0.248613	+	0.532045i
$313$	10.7290	−	9.66046i	0.606441	−	0.546042i	−0.307677	−	0.951491i	$-0.599552\pi$
$313$	10.7290	−	9.66046i	0.606441	−	0.546042i	0.914118	+	0.405449i	$0.132885\pi$
$314$	6.86671	+	9.45122i	0.387511	+	0.533363i
$315$	−1.28476	−	1.91130i	−0.0723881	−	0.107689i
$316$	5.78014	+	3.33717i	0.325158	+	0.187730i
$317$	−6.87909	+	0.723022i	−0.386368	+	0.0406089i	−0.295722	−	0.955274i	$-0.595560\pi$
$317$	−6.87909	+	0.723022i	−0.386368	+	0.0406089i	−0.0906467	+	0.995883i	$0.528893\pi$
$318$	−6.65739	+	1.28856i	−0.373328	+	0.0722591i
$319$	0.538267	−	5.12127i	0.0301372	−	0.286736i
$320$	0.743145	+	0.669131i	0.0415431	+	0.0374055i
$321$	22.1154	−	9.36666i	1.23436	−	0.522796i
$322$	−0.0970736	+	0.456696i	−0.00540970	+	0.0254506i
$323$	3.97215	−	0.844307i	0.221016	−	0.0469785i
$324$	7.64759	−	4.74493i	0.424866	−	0.263607i
$325$	5.69583	+	1.85069i	0.315948	+	0.102658i
$326$	−4.71535	−	1.53211i	−0.261159	−	0.0848557i
$327$	14.6893	+	5.07102i	0.812320	+	0.280428i
$328$	−10.7948	+	2.29450i	−0.596041	+	0.126692i
$329$	−1.58566	+	7.45992i	−0.0874200	+	0.411279i
$330$	0.407738	+	0.962702i	0.0224452	+	0.0529950i
$331$	9.95446	+	8.96303i	0.547146	+	0.492653i	0.895714	−	0.444631i	$-0.146665\pi$
$331$	9.95446	+	8.96303i	0.547146	+	0.492653i	−0.348568	+	0.937284i	$0.613332\pi$
$332$	0.737132	−	7.01335i	0.0404554	−	0.384907i
$333$	27.8896	+	17.4892i	1.52834	+	0.958403i
$334$	8.94101	−	0.939739i	0.489231	−	0.0514202i
$335$	0.630968	+	0.364290i	0.0344735	+	0.0199033i
$336$	−0.300131	+	1.29530i	−0.0163735	+	0.0706646i
$337$	−4.02343	−	5.53778i	−0.219170	−	0.301662i	0.685247	−	0.728311i	$-0.259694\pi$
$337$	−4.02343	−	5.53778i	−0.219170	−	0.301662i	−0.904417	+	0.426649i	$0.859694\pi$
$338$	16.9939	−	15.3014i	0.924347	−	0.832285i
$339$	−3.37659	−	1.57780i	−0.183391	−	0.0856945i
$340$		−	0.979719i		−	0.0531327i
$341$	0.187322	−	3.35555i	0.0101441	−	0.181713i
$342$	−12.4059	+	0.847650i	−0.670837	+	0.0458357i
$343$	−3.18127	−	9.79095i	−0.171773	−	0.528662i
$344$	2.52592	+	2.80531i	0.136188	+	0.151252i
$345$	−0.129217	+	1.04550i	−0.00695679	+	0.0562878i
$346$	−4.56237	−	7.90226i	−0.245275	−	0.424828i
$347$	−17.8507	+	30.9184i	−0.958278	+	1.65979i	−0.231595	+	0.972812i	$0.574394\pi$
$347$	−17.8507	+	30.9184i	−0.958278	+	1.65979i	−0.726683	+	0.686973i	$0.758939\pi$
$348$	8.90199	−	11.7938i	0.477197	−	0.632213i
$349$	−2.89439	−	2.10290i	−0.154933	−	0.112565i	0.507618	−	0.861582i	$-0.330526\pi$
$349$	−2.89439	−	2.10290i	−0.154933	−	0.112565i	−0.662551	+	0.749017i	$0.730526\pi$
$350$	0.763452	+	0.0802420i	0.0408082	+	0.00428911i
$351$	−30.7479	+	4.79470i	−1.64120	+	0.255922i
$352$	0.245511	−	0.551428i	0.0130858	−	0.0293912i
$353$	−4.63748	−	0.985728i	−0.246828	−	0.0524650i	0.0828360	−	0.996563i	$-0.473602\pi$
$353$	−4.63748	−	0.985728i	−0.246828	−	0.0524650i	−0.329664	+	0.944098i	$0.606936\pi$
$354$	14.5245	+	8.74295i	0.771968	+	0.464682i
$355$	−5.83377	+	2.59736i	−0.309625	+	0.137854i
$356$	1.83695	−	5.65356i	0.0973584	−	0.299638i
$357$	1.13983	−	0.630632i	0.0603262	−	0.0333766i
$358$	3.49494	+	7.84977i	0.184713	+	0.414873i
$359$	−4.69762	−	22.1006i	−0.247931	−	1.16642i	−0.909228	−	0.416299i	$-0.863327\pi$
$359$	−4.69762	−	22.1006i	−0.247931	−	1.16642i	0.661297	−	0.750125i	$-0.270006\pi$
$360$	−0.422252	+	2.97014i	−0.0222546	+	0.156540i
$361$	−1.66205	−	0.739991i	−0.0874762	−	0.0389469i
$362$	−13.1127	+	14.5631i	−0.689187	+	0.765419i
$363$	−13.9125	+	12.0745i	−0.730217	+	0.633747i
$364$	2.70232	−	3.71942i	0.141640	−	0.194951i
$365$	−1.47451	−	14.0290i	−0.0771791	−	0.734310i
$366$	−19.5473	+	5.95919i	−1.02175	+	0.311492i
$367$	18.2142	−	10.5160i	0.950772	−	0.548929i	0.0574515	−	0.998348i	$-0.481703\pi$
$367$	18.2142	−	10.5160i	0.950772	−	0.548929i	0.893321	+	0.449420i	$0.148369\pi$
$368$	0.492054	−	0.357498i	0.0256501	−	0.0186359i
$369$	−23.7791	−	23.0365i	−1.23789	−	1.19923i
$370$	−10.4362	+	3.39091i	−0.542550	+	0.176285i
$371$	3.00536			0.156031
$372$	5.42622	−	7.97221i	0.281336	−	0.413340i
$373$	9.76782			0.505758			0.252879	−	0.967498i	$-0.418622\pi$
$373$	9.76782			0.505758			0.252879	+	0.967498i	$0.418622\pi$
$374$	−0.562427	+	0.182744i	−0.0290824	+	0.00944945i
$375$	1.73176	+	0.0316079i	0.0894278	+	0.00163222i
$376$	8.03749	−	5.83958i	0.414502	−	0.301153i
$377$	−44.2472	+	25.5462i	−2.27885	+	1.31569i
$378$	−3.72733	+	1.42058i	−0.191713	+	0.0730666i
$379$	2.78074	+	26.4570i	0.142837	+	1.35900i	0.797608	+	0.603176i	$0.206098\pi$
$379$	2.78074	+	26.4570i	0.142837	+	1.35900i	−0.654771	+	0.755827i	$0.727235\pi$
$380$	2.43634	−	3.35334i	0.124982	−	0.172023i
$381$	11.1739	+	12.8748i	0.572456	+	0.659595i
$382$	−9.00023	+	9.99577i	−0.460492	+	0.511428i
$383$	24.8972	+	11.0849i	1.27219	+	0.566413i	0.928032	−	0.372500i	$-0.121499\pi$
$383$	24.8972	+	11.0849i	1.27219	+	0.566413i	0.344153	+	0.938914i	$0.388166\pi$
$384$	1.41960	−	0.992333i	0.0724439	−	0.0506398i
$385$	−0.0963395	−	0.453242i	−0.00490992	−	0.0230993i
$386$	10.0512	+	22.5753i	0.511590	+	1.14905i
$387$	−2.75721	+	10.9840i	−0.140157	+	0.558348i
$388$	3.00005	−	9.23321i	0.152305	−	0.468745i
$389$	−20.0853	+	8.94256i	−1.01837	+	0.453406i	−0.846882	−	0.531781i	$-0.821523\pi$
$389$	−20.0853	+	8.94256i	−1.01837	+	0.453406i	−0.171484	+	0.985187i	$0.554856\pi$
$390$	5.34966	−	8.88728i	0.270890	−	0.450025i
$391$	−0.582856	−	0.123890i	−0.0294763	−	0.00626538i
$392$	−2.60747	+	5.85647i	−0.131697	+	0.295796i
$393$	2.10030	+	24.2288i	0.105946	+	1.22218i
$394$	17.0757	+	1.79473i	0.860260	+	0.0904169i
$395$	−5.39965	−	3.92307i	−0.271686	−	0.197391i
$396$	1.78383	−	0.311607i	0.0896407	−	0.0156589i
$397$	5.90865	−	10.2341i	0.296547	−	0.513634i	−0.678797	−	0.734326i	$-0.737498\pi$
$397$	5.90865	−	10.2341i	0.296547	−	0.513634i	0.975344	+	0.220692i	$0.0708316\pi$
$398$	1.27350	+	2.20577i	0.0638349	+	0.110565i
$399$	5.46960	+	0.676006i	0.273823	+	0.0338426i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	2.15585	+	6.63504i	0.107658	+	0.331338i	0.990345	−	0.138623i	$-0.0442678\pi$
$401$	2.15585	+	6.63504i	0.107658	+	0.331338i	−0.882687	+	0.469962i	$0.844268\pi$
$402$	0.861374	−	0.922236i	0.0429614	−	0.0459970i
$403$	−28.0272	+	18.0657i	−1.39614	+	0.899914i
$404$			13.1943i			0.656439i
$405$	−8.10168	+	3.91955i	−0.402576	+	0.194764i
$406$	−4.86682	+	4.38210i	−0.241536	+	0.217480i
$407$	3.89324	+	5.35859i	0.192981	+	0.265615i
$408$	−1.65313	−	0.383042i	−0.0818419	−	0.0189634i
$409$	12.0644	+	6.96539i	0.596547	+	0.344417i	0.767682	−	0.640831i	$-0.221410\pi$
$409$	12.0644	+	6.96539i	0.596547	+	0.344417i	−0.171135	+	0.985248i	$0.554743\pi$
$410$	10.9755	−	1.15357i	0.542039	−	0.0569706i
$411$	2.61828	+	13.5274i	0.129150	+	0.667258i
$412$	−1.67290	+	15.9166i	−0.0824178	+	0.784153i
$413$	−5.58372	−	5.02760i	−0.274757	−	0.247392i
$414$	1.71360	+	0.626793i	0.0842189	+	0.0308052i
$415$	−1.46619	+	6.89787i	−0.0719724	+	0.338603i
$416$	−5.85808	+	1.24517i	−0.287216	+	0.0610496i
$417$	−7.91296	+	22.9216i	−0.387499	+	1.12247i
$418$	−2.37949	−	0.773145i	−0.116385	−	0.0378157i
$419$	11.8830	+	3.86102i	0.580522	+	0.188623i	0.584534	−	0.811369i	$-0.301277\pi$
$419$	11.8830	+	3.86102i	0.580522	+	0.188623i	−0.00401257	+	0.999992i	$0.501277\pi$
$420$	0.433883	−	1.25684i	0.0211713	−	0.0613273i
$421$	−4.57066	+	0.971523i	−0.222760	+	0.0473491i	−0.317940	−	0.948111i	$-0.602991\pi$
$421$	−4.57066	+	0.971523i	−0.222760	+	0.0473491i	0.0951793	+	0.995460i	$0.469658\pi$
$422$	−2.83854	+	13.3543i	−0.138178	+	0.650076i
$423$	27.9909	+	10.2384i	1.36097	+	0.497808i
$424$	−2.90940	−	2.61963i	−0.141293	−	0.127221i
$425$	−0.102409	+	0.974352i	−0.00496754	+	0.0472630i
$426$	2.10182	+	10.8591i	0.101833	+	0.526125i
$427$	9.00753	−	0.946730i	0.435905	−	0.0458155i
$428$	12.0086	+	6.93317i	0.580458	+	0.335128i
$429$	−6.09978	−	1.41336i	−0.294500	−	0.0682378i
$430$	−2.21884	−	3.05398i	−0.107002	−	0.147276i
$431$	12.9255	−	11.6382i	0.622602	−	0.560593i	−0.296292	−	0.955097i	$-0.595750\pi$
$431$	12.9255	−	11.6382i	0.622602	−	0.560593i	0.918894	+	0.394504i	$0.129084\pi$
$432$	4.84656	+	1.87372i	0.233180	+	0.0901495i
$433$		−	5.30566i		−	0.254974i	−0.991840	−	0.127487i	$-0.959309\pi$
$433$		−	5.30566i		−	0.254974i	0.991840	−	0.127487i	$-0.0406911\pi$
$434$	−3.03255	+	3.01195i	−0.145567	+	0.144578i
$435$	−10.0860	+	10.7987i	−0.483587	+	0.517756i
$436$	2.77250	+	8.53289i	0.132779	+	0.408651i
$437$	−1.68689	−	1.87348i	−0.0806948	−	0.0896206i
$438$	−24.2483	−	2.99692i	−1.15863	−	0.143198i
$439$	14.6196	+	25.3219i	0.697757	+	1.20855i	0.969243	+	0.246107i	$0.0791516\pi$
$439$	14.6196	+	25.3219i	0.697757	+	1.20855i	−0.271486	+	0.962442i	$0.587515\pi$
$440$	−0.301806	+	0.522744i	−0.0143881	+	0.0249208i
$441$	−18.9452	+	3.30944i	−0.902154	+	0.157593i
$442$	4.74690	+	3.44882i	0.225787	+	0.164044i
$443$	−35.7573	−	3.75825i	−1.69888	−	0.178560i	−0.795078	−	0.606507i	$-0.792570\pi$
$443$	−35.7573	−	3.75825i	−1.69888	−	0.178560i	−0.903803	+	0.427948i	$0.859237\pi$
$444$	1.64141	+	18.9352i	0.0778981	+	0.898623i
$445$	−2.41785	+	5.43058i	−0.114617	+	0.257434i
$446$	−11.7239	−	2.49199i	−0.555142	−	0.117999i
$447$	−2.14996	+	3.57168i	−0.101689	+	0.168935i
$448$	−0.701289	+	0.312234i	−0.0331328	+	0.0147517i
$449$	−5.85188	+	18.0102i	−0.276167	+	0.849956i	0.712741	+	0.701428i	$0.247454\pi$
$449$	−5.85188	+	18.0102i	−0.276167	+	0.849956i	−0.988908	+	0.148528i	$0.952546\pi$
$450$	0.730402	−	2.90973i	0.0344315	−	0.137166i
$451$	−2.70944	−	6.08551i	−0.127583	−	0.286556i
$452$	−0.447385	−	2.10478i	−0.0210432	−	0.0990007i
$453$	6.08799	−	4.25564i	0.286039	−	0.199947i
$454$	−19.8626	−	8.84340i	−0.932198	−	0.415041i
$455$	−3.07630	+	3.41658i	−0.144219	+	0.160172i
$456$	−4.70571	−	5.42202i	−0.220365	−	0.253909i
$457$	16.3923	−	22.5621i	0.766800	−	1.05541i	−0.229818	−	0.973234i	$-0.573813\pi$
$457$	16.3923	−	22.5621i	0.766800	−	1.05541i	0.996618	−	0.0821756i	$-0.0261868\pi$
$458$	−1.44515	−	13.7497i	−0.0675273	−	0.642479i
$459$	−1.81301	−	4.75699i	−0.0846239	−	0.222037i
$460$	−0.526727	+	0.304106i	−0.0245588	+	0.0141790i
$461$	12.7484	−	9.26226i	0.593752	−	0.431386i	−0.249903	−	0.968271i	$-0.580399\pi$
$461$	12.7484	−	9.26226i	0.593752	−	0.431386i	0.843656	+	0.536884i	$0.180399\pi$
$462$	−0.802442	−	0.0146461i	−0.0373330	−	0.000681397i
$463$	38.6431	−	12.5559i	1.79590	−	0.583522i	0.796130	−	0.605125i	$-0.206877\pi$
$463$	38.6431	−	12.5559i	1.79590	−	0.583522i	0.999767	+	0.0216027i	$0.00687687\pi$
$464$	8.53109			0.396046
$465$	−6.22982	+	7.36134i	−0.288901	+	0.341374i
$466$	−2.43348			−0.112729
$467$	−2.79854	+	0.909299i	−0.129501	+	0.0420774i	−0.373050	−	0.927811i	$-0.621688\pi$
$467$	−2.79854	+	0.909299i	−0.129501	+	0.0420774i	0.243550	+	0.969888i	$0.421688\pi$
$468$	−12.9044	−	12.5014i	−0.596505	−	0.577878i
$469$	−0.452482	+	0.328748i	−0.0208937	+	0.0151802i
$470$	−8.60386	+	4.96744i	−0.396867	+	0.229131i
$471$	−19.3550	+	5.90056i	−0.891830	+	0.271883i
$472$	1.02310	+	9.73413i	0.0470919	+	0.448050i
$473$	−1.33932	+	1.84342i	−0.0615821	+	0.0847605i
$474$	−8.73069	+	7.57728i	−0.401014	+	0.348036i
$475$	−2.77352	+	3.08030i	−0.127258	+	0.141334i
$476$	0.687067	+	0.305902i	0.0314916	+	0.0140210i
$477$	1.65311	−	11.6280i	0.0756906	−	0.532411i
$478$	5.40512	+	25.4291i	0.247225	+	1.16310i
$479$	3.55451	+	7.98357i	0.162410	+	0.364779i	0.976358	−	0.216159i	$-0.0693528\pi$
$479$	3.55451	+	7.98357i	0.162410	+	0.364779i	−0.813948	+	0.580937i	$0.802686\pi$
$480$	−1.51555	+	0.838508i	−0.0691753	+	0.0382725i
$481$	20.3080	−	62.5016i	0.925965	−	2.84983i
$482$	12.9711	−	5.77512i	0.590819	−	0.263050i
$483$	−0.692852	−	0.417059i	−0.0315259	−	0.0189768i
$484$	−10.4032	−	2.21128i	−0.472874	−	0.100513i
$485$	−3.94875	+	8.86904i	−0.179304	+	0.402722i
$486$	3.44612	+	15.2028i	0.156319	+	0.689612i
$487$	26.6813	+	2.80431i	1.20904	+	0.127076i	0.687523	−	0.726163i	$-0.258698\pi$
$487$	26.6813	+	2.80431i	1.20904	+	0.127076i	0.521521	+	0.853238i	$0.325365\pi$
$488$	−9.54513	−	6.93495i	−0.432088	−	0.313930i
$489$	5.17356	−	6.85418i	0.233957	−	0.309957i
$490$	3.20535	−	5.55183i	0.144803	−	0.250806i
$491$	17.5497	+	30.3970i	0.792007	+	1.37180i	0.924722	+	0.380643i	$0.124297\pi$
$491$	17.5497	+	30.3970i	0.792007	+	1.37180i	−0.132715	+	0.991154i	$0.542369\pi$
$492$	2.34462	−	18.9704i	0.105703	−	0.855253i
$493$	−5.59264	−	6.21126i	−0.251880	−	0.279741i
$494$	7.67102	+	23.6090i	0.345136	+	1.06222i
$495$	−1.80663	+	0.123440i	−0.0812018	+	0.00554820i
$496$	5.56109	−	0.272450i	0.249701	−	0.0122334i
$497$		−	4.90215i		−	0.219891i
$498$	11.0659	+	5.17084i	0.495874	+	0.231711i
$499$	−11.6663	+	10.5043i	−0.522253	+	0.470239i	−0.887589	−	0.460637i	$-0.847621\pi$
$499$	−11.6663	+	10.5043i	−0.522253	+	0.470239i	0.365335	+	0.930876i	$0.380954\pi$
$500$	0.587785	+	0.809017i	0.0262866	+	0.0361803i
$501$	−3.51493	+	15.1697i	−0.157036	+	0.677732i
$502$	10.1805	+	5.87769i	0.454376	+	0.262334i
$503$	−24.8068	+	2.60730i	−1.10608	+	0.116254i	−0.639916	−	0.768445i	$-0.721031\pi$
$503$	−24.8068	+	2.60730i	−1.10608	+	0.116254i	−0.466164	+	0.884698i	$0.654364\pi$
$504$	−1.95108	−	1.22350i	−0.0869081	−	0.0544989i
$505$	1.37918	−	13.1220i	0.0613725	−	0.583920i
$506$	0.272827	+	0.245654i	0.0121286	+	0.0109207i
$507$	15.4469	+	36.4715i	0.686023	+	1.61975i
$508$	−2.04634	+	9.62728i	−0.0907917	+	0.427141i
$509$	−24.6479	+	5.23906i	−1.09250	+	0.232217i	−0.718719	−	0.695301i	$-0.755271\pi$
$509$	−24.6479	+	5.23906i	−1.09250	+	0.232217i	−0.373778	+	0.927518i	$0.621938\pi$
$510$	1.60403	+	0.553742i	0.0710277	+	0.0245201i
$511$	10.2988	+	3.34627i	0.455591	+	0.148030i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	5.62410	−	20.7906i	0.248310	−	0.917926i
$514$	19.8076	−	4.21023i	0.873674	−	0.185705i
$515$	3.32747	−	15.6545i	0.146626	−	0.689820i
$516$	−6.02062	+	2.54994i	−0.265043	+	0.112255i
$517$	4.45651	+	4.01266i	0.195997	+	0.176477i
$518$	0.880513	−	8.37752i	0.0386875	−	0.368087i
$519$	15.5165	−	3.00329i	0.681101	−	0.131830i
$520$	5.95614	−	0.626016i	0.261194	−	0.0274526i
$521$	31.1524	+	17.9859i	1.36481	+	0.787975i	0.990260	−	0.139230i	$-0.0444629\pi$
$521$	31.1524	+	17.9859i	1.36481	+	0.787975i	0.374553	+	0.927206i	$0.377796\pi$
$522$	14.2778	+	21.2406i	0.624921	+	0.929674i
$523$	−2.45922	−	3.38483i	−0.107534	−	0.148008i	0.751858	−	0.659325i	$-0.229158\pi$
$523$	−2.45922	−	3.38483i	−0.107534	−	0.148008i	−0.859392	+	0.511317i	$0.829158\pi$
$524$	−10.4345	+	9.39524i	−0.455832	+	0.410433i
$525$	−0.562882	+	1.20460i	−0.0245662	+	0.0525729i
$526$		−	21.9529i		−	0.957191i
$527$	−3.84399	−	3.87028i	−0.167447	−	0.168592i
$528$	0.764053	+	0.713630i	0.0332512	+	0.0310568i
$529$	−6.99308	−	21.5225i	−0.304047	−	0.935760i
$530$	2.61963	+	2.90940i	0.113790	+	0.126376i
$531$	−22.5236	+	18.8385i	−0.977441	+	0.817520i
$532$	1.59095	+	2.75561i	0.0689765	+	0.119471i
$533$	−33.0468	+	57.2387i	−1.43142	+	2.47928i
$534$	8.21797	+	6.20295i	0.355626	+	0.268428i
$535$	−11.2181	−	8.15043i	−0.485001	−	0.352374i
$536$	0.724588	+	0.0761573i	0.0312974	+	0.00328949i
$537$	−14.8273	+	1.28532i	−0.639845	+	0.0554656i
$538$	6.53561	−	14.6792i	0.281770	−	0.632867i
$539$	−3.78502	−	0.804531i	−0.163032	−	0.0346536i
$540$	−4.62416	−	2.37006i	−0.198992	−	0.101991i
$541$	25.5168	−	11.3608i	1.09705	−	0.488440i	0.223271	−	0.974756i	$-0.428327\pi$
$541$	25.5168	−	11.3608i	1.09705	−	0.488440i	0.873782	+	0.486317i	$0.161660\pi$
$542$	0.197076	−	0.606539i	0.00846515	−	0.0260531i
$543$	−16.4319	−	29.6997i	−0.705160	−	1.27454i
$544$	−0.398488	−	0.895018i	−0.0170850	−	0.0383736i
$545$	−1.86539	−	8.77595i	−0.0799043	−	0.375920i
$546$	4.56221	+	6.52657i	0.195245	+	0.279312i
$547$	−5.66523	−	2.52232i	−0.242228	−	0.107847i	0.282032	−	0.959405i	$-0.408991\pi$
$547$	−5.66523	−	2.52232i	−0.242228	−	0.107847i	−0.524260	+	0.851558i	$0.675658\pi$
$548$	−5.32294	+	5.91172i	−0.227385	+	0.252536i
$549$	1.29163	−	35.3717i	0.0551254	−	1.50963i
$550$	0.354795	−	0.488333i	0.0151285	−	0.0208226i
$551$	−3.69623	−	35.1673i	−0.157465	−	1.49818i
$552$	0.307198	+	1.00767i	0.0130752	+	0.0428892i
$553$	4.43717	−	2.56180i	0.188687	−	0.108939i
$554$	2.64361	−	1.92069i	0.112316	−	0.0816025i
$555$	0.346840	−	19.0030i	0.0147226	−	0.806633i
$556$	−13.3149	+	4.32629i	−0.564680	+	0.183476i
$557$	−17.7658			−0.752762			−0.376381	−	0.926465i	$-0.622832\pi$
$557$	−17.7658			−0.752762			−0.376381	+	0.926465i	$0.622832\pi$
$558$	9.98547	+	13.3899i	0.422719	+	0.566841i
$559$	22.6078			0.956209
$560$	0.730085	−	0.237219i	0.0308517	−	0.0100243i
$561$	0.0186920	−	1.02411i	0.000789177	−	0.0432381i
$562$	−4.55686	+	3.31075i	−0.192220	+	0.139656i
$563$	29.2058	−	16.8620i	1.23088	−	0.710648i	0.263665	−	0.964614i	$-0.415069\pi$
$563$	29.2058	−	16.8620i	1.23088	−	0.710648i	0.967213	+	0.253967i	$0.0817354\pi$
$564$	5.01794	+	16.4598i	0.211293	+	0.693084i
$565$	0.224925	+	2.14002i	0.00946266	+	0.0900312i
$566$	11.9717	−	16.4777i	0.503209	−	0.692608i
$567$	−0.219117	−	6.90544i	−0.00920203	−	0.290001i
$568$	−4.27297	+	4.74562i	−0.179290	+	0.199122i
$569$	12.3040	+	5.47810i	0.515811	+	0.229654i	0.648097	−	0.761558i	$-0.275565\pi$
$569$	12.3040	+	5.47810i	0.515811	+	0.229654i	−0.132286	+	0.991212i	$0.542232\pi$
$570$	4.11318	+	5.88420i	0.172282	+	0.246462i
$571$	6.91088	+	32.5131i	0.289211	+	1.36063i	0.847416	+	0.530929i	$0.178157\pi$
$571$	6.91088	+	32.5131i	0.289211	+	1.36063i	−0.558205	+	0.829703i	$0.688510\pi$
$572$	−1.47036	−	3.30248i	−0.0614787	−	0.138083i
$573$	−11.2785	−	20.3852i	−0.471165	−	0.851602i
$574$	−2.61793	+	8.05716i	−0.109270	+	0.336299i
$575$	0.555630	−	0.247382i	0.0231714	−	0.0103166i
$576$	0.822317	+	2.88510i	0.0342632	+	0.120212i
$577$	33.6546	+	7.15351i	1.40106	+	0.297804i	0.845635	−	0.533762i	$-0.179222\pi$
$577$	33.6546	+	7.15351i	1.40106	+	0.297804i	0.555425	+	0.831567i	$0.312556\pi$
$578$	6.52412	−	14.6534i	0.271367	−	0.609501i
$579$	−42.6420	+	3.69647i	−1.77214	+	0.153620i
$580$	−8.48436	−	0.891742i	−0.352294	−	0.0370276i
$581$	−4.37961	−	3.18197i	−0.181697	−	0.132011i
$582$	13.4213	+	10.1305i	0.556331	+	0.419921i
$583$	1.18157	−	2.04653i	0.0489355	−	0.0847588i
$584$	−7.05313	−	12.2164i	−0.291861	−	0.505517i
$585$	11.5269	+	13.7818i	0.476580	+	0.569807i
$586$	5.93923	+	6.59618i	0.245347	+	0.272486i
$587$	3.10175	+	9.54622i	0.128023	+	0.394015i	0.994440	−	0.105307i	$-0.0335826\pi$
$587$	3.10175	+	9.54622i	0.128023	+	0.394015i	−0.866417	+	0.499322i	$0.833583\pi$
$588$	−8.11467	−	7.57915i	−0.334643	−	0.312559i
$589$	−3.53254	−	22.8062i	−0.145556	−	0.939712i
$590$		−	9.78775i		−	0.402955i
$591$	−12.5896	+	26.9425i	−0.517869	+	1.10827i
$592$	−8.15469	+	7.34252i	−0.335156	+	0.301776i
$593$	15.7259	+	21.6449i	0.645786	+	0.888848i	0.998908	−	0.0467297i	$-0.0148800\pi$
$593$	15.7259	+	21.6449i	0.645786	+	0.888848i	−0.353122	+	0.935577i	$0.614880\pi$
$594$	−0.498053	+	3.09667i	−0.0204353	+	0.127058i
$595$	−0.651327	−	0.376044i	−0.0267018	−	0.0154163i
$596$	−2.39370	+	0.251587i	−0.0980496	+	0.0103054i
$597$	−4.33115	+	0.838311i	−0.177262	+	0.0343098i
$598$	0.380751	−	3.62260i	0.0155701	−	0.148139i
$599$	0.788528	+	0.709994i	0.0322184	+	0.0290096i	0.685083	−	0.728465i	$-0.259766\pi$
$599$	0.788528	+	0.709994i	0.0322184	+	0.0290096i	−0.652864	+	0.757475i	$0.726433\pi$
$600$	1.59490	−	0.675496i	0.0651115	−	0.0275770i
$601$	−2.82272	+	13.2799i	−0.115141	+	0.541697i	0.882330	+	0.470630i	$0.155973\pi$
$601$	−2.82272	+	13.2799i	−0.115141	+	0.541697i	−0.997472	+	0.0710661i	$0.977360\pi$
$602$	2.83452	−	0.602496i	0.115526	−	0.0245559i
$603$	1.02307	+	1.93153i	0.0416625	+	0.0786578i
$604$	4.07862	+	1.32522i	0.165957	+	0.0539226i
$605$	10.1151	+	3.28660i	0.411238	+	0.133619i
$606$	−21.6021	−	7.45746i	−0.877526	−	0.302939i
$607$	−2.96992	+	0.631277i	−0.120545	+	0.0256227i	−0.267789	−	0.963477i	$-0.586293\pi$
$607$	−2.96992	+	0.631277i	−0.120545	+	0.0256227i	0.147244	+	0.989100i	$0.452960\pi$
$608$	0.861785	−	4.05438i	0.0349500	−	0.164427i
$609$	−4.42379	−	10.4449i	−0.179261	−	0.423250i
$610$	8.76795	+	7.89469i	0.355004	+	0.319647i
$611$	6.21940	−	59.1736i	0.251610	−	2.39391i
$612$	1.56148	−	2.49006i	0.0631193	−	0.100655i
$613$	25.2070	−	2.64936i	1.01810	−	0.107007i	0.419253	−	0.907869i	$-0.362292\pi$
$613$	25.2070	−	2.64936i	1.01810	−	0.107007i	0.598848	+	0.800863i	$0.295625\pi$
$614$	4.58205	+	2.64545i	0.184917	+	0.106762i
$615$	−4.31472	+	18.6214i	−0.173986	+	0.750889i
$616$	−0.272361	−	0.374872i	−0.0109737	−	0.0151040i
$617$	5.39004	−	4.85322i	0.216995	−	0.195383i	−0.553463	−	0.832874i	$-0.686694\pi$
$617$	5.39004	−	4.85322i	0.216995	−	0.195383i	0.770458	+	0.637490i	$0.220027\pi$
$618$	−25.1137	−	11.7351i	−1.01022	−	0.472053i
$619$		−	8.74465i		−	0.351477i	−0.984437	−	0.175739i	$-0.943769\pi$
$619$		−	8.74465i		−	0.351477i	0.984437	−	0.175739i	$-0.0562313\pi$
$620$	−5.55911	−	0.310335i	−0.223259	−	0.0124634i
$621$	−1.99475	+	2.45130i	−0.0800464	+	0.0983675i
$622$	3.05067	+	9.38900i	0.122321	+	0.376465i
$623$	−3.05347	−	3.39122i	−0.122335	−	0.135867i
$624$	1.27237	−	10.2948i	0.0509357	−	0.412123i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.21867	+	12.5031i	−0.288516	+	0.499724i
$627$	2.61072	−	3.45881i	0.104262	−	0.138132i
$628$	−9.45122	−	6.86671i	−0.377145	−	0.274012i
$629$	10.6918	+	1.12375i	0.426309	+	0.0448069i
$630$	1.81250	+	1.42074i	0.0722119	+	0.0566036i
$631$	−17.7257	+	39.8127i	−0.705651	+	1.58492i	0.101679	+	0.994817i	$0.467579\pi$
$631$	−17.7257	+	39.8127i	−0.705651	+	1.58492i	−0.807330	+	0.590100i	$0.799088\pi$
$632$	−6.52848	−	1.38767i	−0.259689	−	0.0551986i
$633$	−20.2598	−	12.1953i	−0.805253	−	0.484718i
$634$	6.31898	−	2.81339i	0.250959	−	0.111734i
$635$	3.04146	−	9.36064i	0.120696	−	0.371466i
$636$	5.93337	−	3.28274i	0.235273	−	0.130169i
$637$	15.6160	+	35.0741i	0.618729	+	1.38969i
$638$	1.07064	+	5.03695i	0.0423869	+	0.199415i
$639$	−18.9669	−	2.69644i	−0.750318	−	0.106670i
$640$	−0.913545	−	0.406737i	−0.0361111	−	0.0160777i
$641$	3.20094	−	3.55500i	0.126429	−	0.140414i	−0.676606	−	0.736345i	$-0.736550\pi$
$641$	3.20094	−	3.55500i	0.126429	−	0.140414i	0.803036	+	0.595931i	$0.203217\pi$
$642$	−18.1386	+	15.7423i	−0.715872	+	0.621298i
$643$	9.33028	−	12.8420i	0.367950	−	0.506440i	−0.584392	−	0.811471i	$-0.698667\pi$
$643$	9.33028	−	12.8420i	0.367950	−	0.506440i	0.952342	+	0.305031i	$0.0986670\pi$
$644$	−0.0488042	−	0.464341i	−0.00192315	−	0.0182976i
$645$	6.25418	−	1.90665i	0.246258	−	0.0750742i
$646$	−3.51684	+	2.03045i	−0.138368	+	0.0798868i
$647$	10.8392	−	7.87517i	0.426135	−	0.309605i	−0.353967	−	0.935258i	$-0.615167\pi$
$647$	10.8392	−	7.87517i	0.426135	−	0.309605i	0.780101	+	0.625653i	$0.215167\pi$
$648$	−5.80703	+	6.87593i	−0.228122	+	0.270112i
$649$	−5.61885	+	1.82568i	−0.220559	+	0.0716640i
$650$	−5.98895			−0.234906
$651$	−3.21727	−	6.66737i	−0.126095	−	0.261315i
$652$	4.95801			0.194171
$653$	10.0828	−	3.27611i	0.394571	−	0.128204i	−0.105010	−	0.994471i	$-0.533487\pi$
$653$	10.0828	−	3.27611i	0.394571	−	0.128204i	0.499581	+	0.866267i	$0.333487\pi$
$654$	−15.5374	−	0.283586i	−0.607560	−	0.0110891i
$655$	11.3594	−	8.25307i	0.443848	−	0.322474i
$656$	9.55739	−	5.51796i	0.373153	−	0.215440i
$657$	18.6119	−	38.0063i	0.726119	−	1.48277i
$658$	−0.797195	−	7.58480i	−0.0310779	−	0.295686i
$659$	−28.8165	+	39.6624i	−1.12253	+	1.54503i	−0.320995	+	0.947081i	$0.604017\pi$
$659$	−28.8165	+	39.6624i	−1.12253	+	1.54503i	−0.801535	+	0.597948i	$0.795983\pi$
$660$	−0.685273	−	0.789586i	−0.0266742	−	0.0307346i
$661$	−5.57231	+	6.18868i	−0.216738	+	0.240712i	−0.841703	−	0.539941i	$-0.818447\pi$
$661$	−5.57231	+	6.18868i	−0.216738	+	0.240712i	0.624965	+	0.780653i	$0.285113\pi$
$662$	−12.2370	−	5.44825i	−0.475604	−	0.211752i
$663$	−8.32951	+	5.82250i	−0.323491	+	0.226127i
$664$	1.46619	+	6.89787i	0.0568991	+	0.267689i
$665$	−1.29420	−	2.90681i	−0.0501868	−	0.112721i
$666$	−31.9291	−	8.01486i	−1.23723	−	0.310570i
$667$	−1.60340	+	4.93476i	−0.0620840	+	0.191075i
$668$	−8.21302	+	3.65667i	−0.317771	+	0.141481i
$669$	10.7064	−	17.7863i	0.413932	−	0.687658i
$670$	−0.712658	−	0.151480i	−0.0275324	−	0.00585219i
$671$	2.89665	−	6.50598i	0.111824	−	0.251161i
$672$	−0.114829	−	1.32465i	−0.00442962	−	0.0510996i
$673$	−14.3216	−	1.50526i	−0.552057	−	0.0580235i	−0.175607	−	0.984460i	$-0.556189\pi$
$673$	−14.3216	−	1.50526i	−0.552057	−	0.0580235i	−0.376450	+	0.926437i	$0.622855\pi$
$674$	5.53778	+	4.02343i	0.213307	+	0.154977i
$675$	4.35108	+	2.84043i	0.167473	+	0.109328i
$676$	−11.4338	+	19.8039i	−0.439761	+	0.761688i
$677$	18.8427	+	32.6365i	0.724184	+	1.25432i	0.959309	+	0.282359i	$0.0911168\pi$
$677$	18.8427	+	32.6365i	0.724184	+	1.25432i	−0.235125	+	0.971965i	$0.575550\pi$
$678$	3.69889	+	0.457158i	0.142055	+	0.0175570i
$679$	−4.98683	−	5.53844i	−0.191377	−	0.212546i
$680$	0.302750	+	0.931768i	0.0116099	+	0.0357317i
$681$	25.7052	−	27.5215i	0.985025	−	1.05462i
$682$	0.858768	+	3.24920i	0.0328839	+	0.124418i
$683$		−	4.55653i		−	0.174351i	−0.996193	−	0.0871755i	$-0.972216\pi$
$683$		−	4.55653i		−	0.174351i	0.996193	−	0.0871755i	$-0.0277841\pi$
$684$	11.5368	−	4.63981i	0.441121	−	0.177408i
$685$	5.91172	−	5.32294i	0.225875	−	0.203379i
$686$	6.05114	+	8.32868i	0.231034	+	0.317991i
$687$	23.3283	+	5.40533i	0.890028	+	0.206226i
$688$	−3.26918	−	1.88746i	−0.124636	−	0.0719588i
$689$	−23.3182	+	2.45084i	−0.888353	+	0.0933696i
$690$	−0.200185	−	1.03426i	−0.00762091	−	0.0393736i
$691$	1.85137	−	17.6146i	0.0704294	−	0.670091i	−0.901171	−	0.433464i	$-0.857291\pi$
$691$	1.85137	−	17.6146i	0.0704294	−	0.670091i	0.971600	−	0.236627i	$-0.0760420\pi$
$692$	6.78101	+	6.10565i	0.257775	+	0.232102i
$693$	0.477524	−	1.30551i	0.0181396	−	0.0495922i
$694$	7.42275	−	34.9213i	0.281764	−	1.32559i
$695$	13.6942	−	2.91080i	0.519452	−	0.110413i
$696$	−4.82182	+	13.9674i	−0.182770	+	0.529434i
$697$	−10.2829	−	3.34112i	−0.389493	−	0.126554i
$698$	3.40256	+	1.10556i	0.128789	+	0.0418460i
$699$	1.37542	−	3.98418i	0.0520230	−	0.150696i
$700$	−0.750882	+	0.159605i	−0.0283807	+	0.00603250i
$701$	2.71288	−	12.7631i	0.102464	−	0.482055i	−0.896754	−	0.442528i	$-0.854082\pi$
$701$	2.71288	−	12.7631i	0.102464	−	0.482055i	0.999219	−	0.0395270i	$-0.0125851\pi$
$702$	27.7614	−	14.0617i	1.04779	−	0.530723i
$703$	33.8008	+	30.4344i	1.27482	+	1.14786i
$704$	−0.0630947	+	0.600306i	−0.00237797	+	0.0226249i
$705$	−3.26993	−	16.8942i	−0.123153	−	0.636272i
$706$	4.71512	−	0.495579i	0.177456	−	0.0186513i
$707$	8.77168	+	5.06433i	0.329893	+	0.190464i
$708$	−16.5153	−	3.82672i	−0.620684	−	0.143817i
$709$	12.3468	+	16.9940i	0.463695	+	0.638221i	0.975270	−	0.221017i	$-0.0709377\pi$
$709$	12.3468	+	16.9940i	0.463695	+	0.638221i	−0.511575	+	0.859239i	$0.670938\pi$
$710$	4.74562	−	4.27297i	0.178100	−	0.160362i
$711$	−7.47116	−	18.5769i	−0.280190	−	0.696689i
$712$			5.94451i			0.222780i
$713$	−0.887599	+	3.26799i	−0.0332409	+	0.122387i
$714$	−0.889167	+	0.951993i	−0.0332762	+	0.0356275i
$715$	1.11710	+	3.43808i	0.0417771	+	0.128577i
$716$	−5.74960	−	6.38558i	−0.214873	−	0.238640i
$717$	−44.6884	−	5.52319i	−1.66892	−	0.206267i
$718$	11.2972	+	19.5673i	0.421606	+	0.730243i
$719$	22.0550	−	38.2004i	0.822512	−	1.42463i	−0.0812933	−	0.996690i	$-0.525905\pi$
$719$	22.0550	−	38.2004i	0.822512	−	1.42463i	0.903806	−	0.427943i	$-0.140762\pi$
$720$	−0.516237	−	2.95525i	−0.0192390	−	0.110136i
$721$	9.93940	+	7.22139i	0.370162	+	0.268939i
$722$	1.80937	+	0.190173i	0.0673378	+	0.00707749i
$723$	2.12389	+	24.5010i	0.0789884	+	0.911200i
$724$	7.97065	−	17.9024i	0.296227	−	0.665336i
$725$	8.34467	+	1.77371i	0.309913	+	0.0658741i
$726$	9.50034	−	15.7827i	0.352591	−	0.585752i
$727$	−8.76250	+	3.90132i	−0.324983	+	0.144692i	−0.562742	−	0.826632i	$-0.690254\pi$
$727$	−8.76250	+	3.90132i	−0.324983	+	0.144692i	0.237759	+	0.971324i	$0.423587\pi$
$728$	−1.42069	+	4.37244i	−0.0526544	+	0.162054i
$729$	−26.8383	−	2.95057i	−0.994011	−	0.109280i
$730$	5.73753	+	12.8867i	0.212356	+	0.476958i
$731$	0.768933	+	3.61754i	0.0284400	+	0.133800i
$732$	16.7491	−	11.7080i	0.619065	−	0.432739i
$733$	8.69275	+	3.87026i	0.321074	+	0.142951i	0.560944	−	0.827854i	$-0.310438\pi$
$733$	8.69275	+	3.87026i	0.321074	+	0.142951i	−0.239870	+	0.970805i	$0.577105\pi$
$734$	−14.0731	+	15.6298i	−0.519448	+	0.576905i
$735$	7.27798	+	8.38584i	0.268452	+	0.309316i
$736$	−0.357498	+	0.492054i	−0.0131776	+	0.0181374i
$737$	0.0459695	+	0.437371i	0.00169331	+	0.0161108i
$738$	29.7339	+	14.5609i	1.09452	+	0.535993i
$739$	24.7823	−	14.3080i	0.911630	−	0.526330i	0.0306750	−	0.999529i	$-0.490234\pi$
$739$	24.7823	−	14.3080i	0.911630	−	0.526330i	0.880955	+	0.473199i	$0.156901\pi$
$740$	8.87752	−	6.44990i	0.326344	−	0.237103i
$741$	−42.9892	−	0.784633i	−1.57925	−	0.0288242i
$742$	−2.85827	+	0.928708i	−0.104930	+	0.0340940i
$743$	31.0820			1.14029			0.570144	−	0.821545i	$-0.306888\pi$
$743$	31.0820			1.14029			0.570144	+	0.821545i	$0.306888\pi$
$744$	−2.69709	+	9.25882i	−0.0988802	+	0.339445i
$745$	2.40688			0.0881813
$746$	−9.28974	+	3.01842i	−0.340122	+	0.110512i
$747$	−14.7204	+	15.1949i	−0.538590	+	0.555951i
$748$	0.478429	−	0.347599i	0.0174931	−	0.0127095i
$749$	9.21849	−	5.32230i	0.336836	−	0.194473i
$750$	−1.65677	+	0.505083i	−0.0604967	+	0.0184430i
$751$	−3.16153	−	30.0799i	−0.115366	−	1.09763i	−0.887065	−	0.461644i	$-0.847260\pi$
$751$	−3.16153	−	30.0799i	−0.115366	−	1.09763i	0.771699	−	0.635988i	$-0.219407\pi$
$752$	−5.83958	+	8.03749i	−0.212948	+	0.293097i
$753$	−15.3772	+	13.3457i	−0.560377	+	0.486345i
$754$	34.1874	−	37.9690i	1.24503	−	1.38275i
$755$	−3.91775	−	1.74430i	−0.142582	−	0.0634815i
$756$	3.10592	−	2.50286i	0.112961	−	0.0910280i
$757$	−4.20373	−	19.7770i	−0.152787	−	0.718807i	−0.986120	−	0.166035i	$-0.946903\pi$
$757$	−4.20373	−	19.7770i	−0.152787	−	0.718807i	0.833333	−	0.552772i	$-0.186430\pi$
$758$	−10.8203	−	24.3028i	−0.393011	−	0.882716i
$759$	−0.556398	+	0.307837i	−0.0201960	+	0.0111738i
$760$	−1.28086	+	3.94209i	−0.0464617	+	0.142995i
$761$	4.50194	−	2.00439i	0.163195	−	0.0726592i	−0.323513	−	0.946224i	$-0.604864\pi$
$761$	4.50194	−	2.00439i	0.163195	−	0.0726592i	0.486708	+	0.873564i	$0.338197\pi$
$762$	−14.6055	−	8.79173i	−0.529102	−	0.318491i
$763$	6.73692	+	1.43198i	0.243893	+	0.0518410i
$764$	5.47087	−	12.2878i	0.197929	−	0.444556i
$765$	−1.81321	+	2.31320i	−0.0655569	+	0.0836340i
$766$	−27.1040	−	2.84875i	−0.979309	−	0.102929i
$767$	47.4232	+	34.4550i	1.71235	+	1.24410i
$768$	−1.04348	+	1.38245i	−0.0376532	+	0.0498847i
$769$	27.2147	−	47.1372i	0.981387	−	1.69981i	0.324383	−	0.945926i	$-0.394843\pi$
$769$	27.2147	−	47.1372i	0.981387	−	1.69981i	0.657004	−	0.753887i	$-0.271823\pi$
$770$	0.231684	+	0.401288i	0.00834930	+	0.0144614i
$771$	−4.30219	+	34.8093i	−0.154940	+	1.25363i
$772$	−16.5354	−	18.3644i	−0.595120	−	0.660948i
$773$	7.77843	+	23.9396i	0.279771	+	0.861046i	0.987918	+	0.154981i	$0.0495315\pi$
$773$	7.77843	+	23.9396i	0.279771	+	0.861046i	−0.708147	+	0.706065i	$0.750468\pi$
$774$	−0.771977	−	11.2984i	−0.0277481	−	0.406113i
$775$	5.49622	+	0.889720i	0.197430	+	0.0319597i
$776$			9.70837i			0.348510i
$777$	13.2183	+	6.17662i	0.474204	+	0.221585i
$778$	16.3389	−	14.7116i	0.585777	−	0.527436i
$779$	−26.8873	−	37.0072i	−0.963337	−	1.32592i
$780$	−2.34151	+	10.1054i	−0.0838394	+	0.361833i
$781$	−3.33817	−	1.92729i	−0.119449	−	0.0689640i
$782$	0.592613	−	0.0622861i	0.0211918	−	0.00222735i
$783$	−42.8457	+	11.3708i	−1.53118	+	0.406359i
$784$	0.670101	−	6.37558i	0.0239322	−	0.227699i
$785$	8.68167	+	7.81701i	0.309862	+	0.279001i
$786$	−9.48462	−	22.3939i	−0.338305	−	0.798765i
$787$	9.53085	−	44.8391i	0.339738	−	1.59834i	−0.394133	−	0.919053i	$-0.628955\pi$
$787$	9.53085	−	44.8391i	0.339738	−	1.59834i	0.733871	−	0.679288i	$-0.237711\pi$
$788$	−16.7945	+	3.56979i	−0.598280	+	0.127168i
$789$	35.9420	+	12.4079i	1.27957	+	0.441732i
$790$	6.34767	+	2.06248i	0.225840	+	0.0733798i
$791$	−1.57100	−	0.510449i	−0.0558584	−	0.0181495i
$792$	−1.60023	+	0.847589i	−0.0568616	+	0.0301178i
$793$	−69.1162	+	14.6911i	−2.45439	+	0.521696i
$794$	−2.45696	+	11.5591i	−0.0871941	+	0.410216i
$795$	−6.24401	+	2.64456i	−0.221452	+	0.0937927i
$796$	−1.89279	−	1.70428i	−0.0670882	−	0.0604065i
$797$	4.10138	−	39.0220i	0.145278	−	1.38223i	−0.642506	−	0.766280i	$-0.722105\pi$
$797$	4.10138	−	39.0220i	0.145278	−	1.38223i	0.787785	−	0.615951i	$-0.211228\pi$
$798$	−5.41080	+	1.04728i	−0.191540	+	0.0370733i
$799$	9.68007	−	1.01742i	0.342456	−	0.0359936i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	−14.8005	+	9.94882i	−0.522951	+	0.351524i
$802$	−4.10068	−	5.64410i	−0.144800	−	0.199300i
$803$	6.32767	−	5.69746i	0.223299	−	0.201059i
$804$	−0.534228	+	1.14328i	−0.0188408	+	0.0403203i
$805$			0.466898i			0.0164560i
$806$	21.0729	−	25.8424i	0.742261	−	0.910258i
$807$	20.3394	+	18.9971i	0.715981	+	0.668730i
$808$	−4.07725	−	12.5485i	−0.143437	−	0.441454i
$809$	−24.9455	−	27.7048i	−0.877037	−	0.974049i	0.122794	−	0.992432i	$-0.460815\pi$
$809$	−24.9455	−	27.7048i	−0.877037	−	0.974049i	−0.999831	+	0.0183835i	$0.994148\pi$
$810$	6.49395	−	6.23127i	0.228174	−	0.218944i
$811$	−2.21449	−	3.83562i	−0.0777614	−	0.134687i	0.824522	−	0.565829i	$-0.191444\pi$
$811$	−2.21449	−	3.83562i	−0.0777614	−	0.134687i	−0.902284	+	0.431143i	$0.858111\pi$
$812$	3.27448	−	5.67156i	0.114912	−	0.199033i
$813$	0.881659	+	0.665479i	0.0309211	+	0.0233394i
$814$	−5.35859	−	3.89324i	−0.187818	−	0.136458i
$815$	−4.93085	−	0.518253i	−0.172720	−	0.0181536i
$816$	1.69058	−	0.146550i	0.0591822	−	0.00513028i
$817$	−6.36416	+	14.2941i	−0.222654	+	0.500089i
$818$	−13.6264	−	2.89637i	−0.476435	−	0.101269i
$819$	−13.2641	+	3.78057i	−0.463486	+	0.132104i
$820$	−10.0818	+	4.48871i	−0.352072	+	0.156753i
$821$	−2.29451	+	7.06176i	−0.0800788	+	0.246457i	−0.983079	−	0.183183i	$-0.941360\pi$
$821$	−2.29451	+	7.06176i	−0.0800788	+	0.246457i	0.903000	+	0.429641i	$0.141360\pi$
$822$	−6.67033	−	12.0562i	−0.232655	−	0.420510i
$823$	−1.47241	−	3.30708i	−0.0513249	−	0.115278i	0.886063	−	0.463565i	$-0.153430\pi$
$823$	−1.47241	−	3.30708i	−0.0513249	−	0.115278i	−0.937388	+	0.348287i	$0.886763\pi$
$824$	−3.32747	−	15.6545i	−0.115918	−	0.545351i
$825$	0.598985	+	0.856891i	0.0208540	+	0.0298331i
$826$	6.86404	+	3.05607i	0.238831	+	0.106334i
$827$	15.6373	−	17.3670i	0.543761	−	0.603908i	−0.407154	−	0.913360i	$-0.633479\pi$
$827$	15.6373	−	17.3670i	0.543761	−	0.603908i	0.950915	+	0.309451i	$0.100145\pi$
$828$	−1.82342	−	0.0665839i	−0.0633683	−	0.00231395i
$829$	−5.09618	+	7.01428i	−0.176998	+	0.243616i	−0.888293	−	0.459277i	$-0.848109\pi$
$829$	−5.09618	+	7.01428i	−0.176998	+	0.243616i	0.711296	+	0.702893i	$0.248109\pi$
$830$	−0.737132	−	7.01335i	−0.0255862	−	0.243437i
$831$	1.65045	+	5.41380i	0.0572535	+	0.187803i
$832$	5.18659	−	2.99448i	0.179812	−	0.103815i
$833$	−5.08118	+	3.69170i	−0.176053	+	0.127910i
$834$	0.442516	−	24.2450i	0.0153231	−	0.839534i
$835$	8.55025	−	2.77814i	0.295894	−	0.0961417i
$836$	2.50195			0.0865317
$837$	−27.5663	+	8.78052i	−0.952832	+	0.303499i
$838$	−12.4945			−0.431616
$839$	8.87796	−	2.88462i	0.306501	−	0.0995882i	−0.151728	−	0.988422i	$-0.548484\pi$
$839$	8.87796	−	2.88462i	0.306501	−	0.0995882i	0.458229	+	0.888834i	$0.348484\pi$
$840$	−0.0242640	+	1.32940i	−0.000837188	+	0.0458686i
$841$	−35.4184	+	25.7330i	−1.22132	+	0.887344i
$842$	4.04674	−	2.33638i	0.139460	−	0.0805171i
$843$	−2.84493	−	9.33191i	−0.0979844	−	0.321408i
$844$	−1.42709	−	13.5778i	−0.0491224	−	0.467368i
$845$	13.4412	−	18.5002i	0.462392	−	0.636428i
$846$	−29.7848	−	1.08762i	−1.02402	−	0.0373931i
$847$	−5.46314	+	6.06743i	−0.187716	+	0.208479i
$848$	3.57651	+	1.59237i	0.122818	+	0.0546821i
$849$	20.2114	+	28.9138i	0.693652	+	0.992319i
$850$	−0.203695	−	0.958310i	−0.00698668	−	0.0328698i
$851$	−2.71458	−	6.09705i	−0.0930546	−	0.209004i
$852$	−5.35459	−	9.67812i	−0.183445	−	0.331567i
$853$	1.04568	−	3.21829i	0.0358036	−	0.110192i	−0.931558	−	0.363594i	$-0.881550\pi$
$853$	1.04568	−	3.21829i	0.0358036	−	0.110192i	0.967361	+	0.253402i	$0.0815495\pi$
$854$	−8.27412	+	3.68387i	−0.283134	+	0.126060i
$855$	−11.9586	+	3.40847i	−0.408976	+	0.116567i
$856$	−13.5633	−	2.88298i	−0.463585	−	0.0985381i
$857$	16.2380	−	36.4712i	0.554681	−	1.24583i	−0.390897	−	0.920435i	$-0.627835\pi$
$857$	16.2380	−	36.4712i	0.554681	−	1.24583i	0.945577	−	0.325398i	$-0.105498\pi$
$858$	6.23799	−	0.540746i	0.212961	−	0.0184608i
$859$	−1.55912	−	0.163870i	−0.0531965	−	0.00559118i	0.0778928	−	0.996962i	$-0.475181\pi$
$859$	−1.55912	−	0.163870i	−0.0531965	−	0.00559118i	−0.131089	+	0.991371i	$0.541847\pi$
$860$	3.05398	+	2.21884i	0.104140	+	0.0756619i
$861$	−11.7118	−	8.84012i	−0.399137	−	0.301270i
$862$	−8.69652	+	15.0628i	−0.296205	+	0.513041i
$863$	−18.3647	−	31.8086i	−0.625141	−	1.08278i	−0.988514	−	0.151132i	$-0.951708\pi$
$863$	−18.3647	−	31.8086i	−0.625141	−	1.08278i	0.363373	−	0.931644i	$-0.381625\pi$
$864$	−5.18837	−	0.284345i	−0.176512	−	0.00967361i
$865$	−6.10565	−	6.78101i	−0.207598	−	0.230561i
$866$	1.63954	+	5.04598i	0.0557138	+	0.171469i
$867$	20.3036	+	18.9637i	0.689547	+	0.644041i
$868$	1.95338	−	3.80165i	0.0663020	−	0.129036i
$869$		−	4.02871i		−	0.136665i
$870$	6.25539	−	13.3869i	0.212078	−	0.453858i
$871$	3.24266	−	2.91970i	0.109873	−	0.0989304i
$872$	−5.27361	−	7.25851i	−0.178587	−	0.245804i
$873$	−24.1717	+	16.2481i	−0.818089	+	0.549914i
$874$	2.18326	+	1.26051i	0.0738499	+	0.0426373i
$875$	0.763452	−	0.0802420i	0.0258094	−	0.00271267i
$876$	23.9876	−	4.64288i	0.810465	−	0.156868i
$877$	−4.21572	+	40.1098i	−0.142355	+	1.35441i	0.657153	+	0.753757i	$0.271761\pi$
$877$	−4.21572	+	40.1098i	−0.142355	+	1.35441i	−0.799507	+	0.600656i	$0.794906\pi$
$878$	−21.7290	−	19.5649i	−0.733318	−	0.660283i
$879$	−14.1564	+	5.99573i	−0.477483	+	0.202231i
$880$	0.125498	−	0.590422i	0.00423054	−	0.0199031i
$881$	10.7650	−	2.28817i	0.362681	−	0.0770903i	−0.0229669	−	0.999736i	$-0.507311\pi$
$881$	10.7650	−	2.28817i	0.362681	−	0.0770903i	0.385648	+	0.922646i	$0.373978\pi$
$882$	16.9953	−	9.00186i	0.572262	−	0.303109i
$883$	−18.9906	−	6.17043i	−0.639086	−	0.207652i	−0.0284902	−	0.999594i	$-0.509070\pi$
$883$	−18.9906	−	6.17043i	−0.639086	−	0.207652i	−0.610596	+	0.791942i	$0.709070\pi$
$884$	−5.58032	−	1.81315i	−0.187686	−	0.0609830i
$885$	16.0249	+	5.53208i	0.538670	+	0.185959i
$886$	35.1686	−	7.47531i	1.18151	−	0.251138i
$887$	2.25929	−	10.6291i	0.0758595	−	0.356891i	−0.923803	−	0.382868i	$-0.874936\pi$
$887$	2.25929	−	10.6291i	0.0758595	−	0.356891i	0.999663	+	0.0259771i	$0.00826971\pi$
$888$	−7.41236	−	17.5012i	−0.248743	−	0.587301i
$889$	5.61487	+	5.05565i	0.188317	+	0.169561i
$890$	0.621370	−	5.91194i	0.0208284	−	0.198169i
$891$	−4.78848	−	2.56568i	−0.160420	−	0.0859536i
$892$	11.9201	−	1.25286i	0.399116	−	0.0419488i
$893$	35.6626	+	20.5898i	1.19340	+	0.689012i
$894$	0.941020	−	4.06124i	0.0314724	−	0.135828i
$895$	5.05063	+	6.95159i	0.168824	+	0.232366i
$896$	0.570480	−	0.513663i	0.0190584	−	0.0171603i
$897$	5.71585	+	2.67089i	0.190847	+	0.0891785i
$898$		−	18.9371i		−	0.631939i
$899$	−37.0154	+	29.7662i	−1.23453	+	0.992759i
$900$	0.204502	+	2.99302i	0.00681672	+	0.0997674i
$901$	−1.18526	−	3.64786i	−0.0394867	−	0.121528i
$902$	4.45736	+	4.95040i	0.148414	+	0.164830i
$903$	−0.615656	+	4.98131i	−0.0204878	+	0.165768i
$904$	1.07590	+	1.86352i	0.0357840	+	0.0619797i
$905$	−9.79829	+	16.9711i	−0.325706	+	0.564140i
$906$	−4.47496	+	5.92865i	−0.148671	+	0.196966i
$907$	−22.0320	−	16.0072i	−0.731561	−	0.531510i	0.158496	−	0.987360i	$-0.449335\pi$
$907$	−22.0320	−	16.0072i	−0.731561	−	0.531510i	−0.890057	+	0.455850i	$0.849335\pi$
$908$	21.6232	+	2.27269i	0.717592	+	0.0754220i
$909$	24.4193	−	31.1528i	0.809935	−	1.03327i
$910$	1.86996	−	4.19999i	0.0619884	−	0.139228i
$911$	20.8411	+	4.42992i	0.690498	+	0.146770i	0.539779	−	0.841807i	$-0.318508\pi$
$911$	20.8411	+	4.42992i	0.690498	+	0.146770i	0.150719	+	0.988577i	$0.451841\pi$
$912$	6.15089	+	3.70250i	0.203676	+	0.122602i
$913$	−3.88866	+	1.73134i	−0.128696	+	0.0572990i
$914$	−8.61794	+	26.5233i	−0.285056	+	0.877313i
$915$	−17.8812	+	9.89308i	−0.591133	+	0.327055i
$916$	5.62330	+	12.6301i	0.185799	+	0.417311i
$917$	2.24101	+	10.5431i	0.0740045	+	0.348164i
$918$	3.19426	+	3.96391i	0.105426	+	0.130829i
$919$	−46.7705	−	20.8236i	−1.54282	−	0.686906i	−0.553521	−	0.832835i	$-0.686716\pi$
$919$	−46.7705	−	20.8236i	−1.54282	−	0.686906i	−0.989295	+	0.145929i	$0.953383\pi$
$920$	0.406974	−	0.451990i	0.0134175	−	0.0149017i
$921$	−6.92102	+	6.00668i	−0.228055	+	0.197927i
$922$	−9.26226	+	12.7484i	−0.305036	+	0.419846i
$923$	3.99765	+	38.0351i	0.131584	+	1.25194i
$924$	0.767694	−	0.234039i	0.0252553	−	0.00769932i
$925$	−9.50309	+	5.48661i	−0.312460	+	0.180399i
$926$	−32.8718	+	23.8827i	−1.08023	+	0.784836i
$927$	33.4074	−	34.4843i	1.09724	−	1.13261i
$928$	−8.11355	+	2.63625i	−0.266340	+	0.0865392i
$929$	33.5885			1.10200			0.551002	−	0.834504i	$-0.314246\pi$
$929$	33.5885			1.10200			0.551002	+	0.834504i	$0.314246\pi$
$930$	3.65013	−	8.92617i	0.119692	−	0.292701i
$931$	−26.5721			−0.870865
$932$	2.31438	−	0.751987i	0.0758100	−	0.0246322i
$933$	−17.0963	−	0.312039i	−0.559707	−	0.0102157i
$934$	2.38058	−	1.72959i	0.0778948	−	0.0565939i
$935$	−0.512142	+	0.295685i	−0.0167488	+	0.00966995i
$936$	16.1359	+	7.90187i	0.527420	+	0.258281i
$937$	2.88244	+	27.4246i	0.0941651	+	0.895921i	0.935004	+	0.354636i	$0.115395\pi$
$937$	2.88244	+	27.4246i	0.0941651	+	0.895921i	−0.840839	+	0.541285i	$0.817938\pi$
$938$	0.328748	−	0.452482i	0.0107340	−	0.0147741i
$939$	−16.3905	−	18.8855i	−0.534884	−	0.616304i
$940$	6.64773	−	7.38306i	0.216825	−	0.240809i
$941$	32.5513	+	14.4928i	1.06114	+	0.472451i	0.861678	−	0.507455i	$-0.169414\pi$
$941$	32.5513	+	14.4928i	1.06114	+	0.472451i	0.199463	+	0.979905i	$0.436080\pi$
$942$	16.5843	−	11.5928i	0.540346	−	0.377713i
$943$	1.39554	+	6.56551i	0.0454451	+	0.213802i
$944$	−3.98104	−	8.94155i	−0.129572	−	0.291023i
$945$	−3.35052	+	2.16449i	−0.108993	+	0.0704109i
$946$	0.704123	−	2.16707i	0.0228930	−	0.0704575i
$947$	1.54311	−	0.687036i	0.0501443	−	0.0223257i	−0.381511	−	0.924364i	$-0.624596\pi$
$947$	1.54311	−	0.687036i	0.0501443	−	0.0223257i	0.431656	+	0.902039i	$0.357930\pi$
$948$	5.96188	−	9.90435i	0.193633	−	0.321678i
$949$	−82.6356	−	17.5647i	−2.68246	−	0.570175i
$950$	1.68591	−	3.78661i	0.0546980	−	0.122854i
$951$	1.03467	+	11.9358i	0.0335514	+	0.387045i
$952$	−0.747968	−	0.0786146i	−0.0242418	−	0.00254791i
$953$	−12.0812	−	8.77751i	−0.391349	−	0.284331i	0.374659	−	0.927163i	$-0.377760\pi$
$953$	−12.0812	−	8.77751i	−0.391349	−	0.284331i	−0.766008	+	0.642831i	$0.777760\pi$
$954$	2.02106	+	11.5698i	0.0654342	+	0.374585i
$955$	−6.72532	+	11.6486i	−0.217626	+	0.376940i
$956$	−12.9986	−	22.5142i	−0.420405	−	0.728162i
$957$	−8.85181	−	1.09402i	−0.286138	−	0.0353647i
$958$	−5.84760	−	6.49442i	−0.188927	−	0.209825i
$959$	1.88708	+	5.80783i	0.0609369	+	0.187545i
$960$	1.18226	−	1.26580i	0.0381574	−	0.0408535i
$961$	−23.1783	+	20.5856i	−0.747687	+	0.664052i
$962$			65.7181i			2.11884i
$963$	−15.5218	−	38.5947i	−0.500183	−	1.24370i
$964$	−10.5517	+	9.50077i	−0.339847	+	0.305999i
$965$	14.5252	+	19.9922i	0.467582	+	0.643571i
$966$	0.787820	+	0.182544i	0.0253477	+	0.00587325i
$967$	−4.76122	−	2.74889i	−0.153111	−	0.0883984i	0.421487	−	0.906834i	$-0.361508\pi$
$967$	−4.76122	−	2.74889i	−0.153111	−	0.0883984i	−0.574598	+	0.818436i	$0.694842\pi$
$968$	10.5774	−	1.11173i	0.339970	−	0.0357323i
$969$	−1.33659	−	6.90551i	−0.0429374	−	0.221837i
$970$	1.01480	−	9.65519i	0.0325833	−	0.310009i
$971$	−16.6815	−	15.0201i	−0.535336	−	0.482018i	0.356552	−	0.934276i	$-0.383952\pi$
$971$	−16.6815	−	15.0201i	−0.535336	−	0.482018i	−0.891888	+	0.452257i	$0.850619\pi$
$972$	−7.97537	−	13.3938i	−0.255810	−	0.429606i
$973$	−2.23449	+	10.5125i	−0.0716346	+	0.337014i
$974$	−26.2420	+	5.57790i	−0.840847	+	0.178728i
$975$	3.38499	−	9.80533i	0.108406	−	0.314022i
$976$	11.2210	+	3.64592i	0.359175	+	0.116703i
$977$	7.68850	+	2.49815i	0.245977	+	0.0799228i	0.429411	−	0.903109i	$-0.358721\pi$
$977$	7.68850	+	2.49815i	0.245977	+	0.0799228i	−0.183434	+	0.983032i	$0.558721\pi$
$978$	−2.80229	+	8.11743i	−0.0896074	+	0.259567i
$979$	−3.50977	+	0.746025i	−0.112173	+	0.0238431i
$980$	−1.33286	+	6.27061i	−0.0425767	+	0.200307i
$981$	9.24611	−	25.2781i	0.295205	−	0.807067i
$982$	−26.0840	−	23.4861i	−0.832372	−	0.749472i
$983$	2.40628	−	22.8942i	0.0767484	−	0.730213i	−0.886705	−	0.462336i	$-0.847011\pi$
$983$	2.40628	−	22.8942i	0.0767484	−	0.730213i	0.963453	−	0.267877i	$-0.0863219\pi$
$984$	3.63232	+	18.7665i	0.115794	+	0.598253i
$985$	17.0757	−	1.79473i	0.544076	−	0.0571847i
$986$	7.23830	+	4.17904i	0.230515	+	0.133088i
$987$	12.8687	+	2.98177i	0.409615	+	0.0949108i
$988$	−14.5912	−	20.0830i	−0.464206	−	0.638925i
$989$	1.70623	−	1.53629i	0.0542548	−	0.0488513i
$990$	1.68006	−	0.675676i	0.0533958	−	0.0214744i
$991$		−	3.07934i		−	0.0978185i	−0.998803	−	0.0489093i	$-0.984425\pi$
$991$		−	3.07934i		−	0.0978185i	0.998803	−	0.0489093i	$-0.0155745\pi$
$992$	−5.20472	+	1.97759i	−0.165250	+	0.0627885i
$993$	15.8365	−	16.9554i	0.502556	−	0.538065i
$994$	1.51485	+	4.66222i	0.0480480	+	0.147877i
$995$	1.70428	+	1.89279i	0.0540292	+	0.0600055i
$996$	−12.1221	−	1.49822i	−0.384105	−	0.0474728i
$997$	22.7959	+	39.4837i	0.721953	+	1.25046i	0.960216	+	0.279259i	$0.0900889\pi$
$997$	22.7959	+	39.4837i	0.721953	+	1.25046i	−0.238262	+	0.971201i	$0.576578\pi$
$998$	7.84924	−	13.5953i	0.248463	−	0.430351i
$999$	31.1687	−	47.7454i	0.986134	−	1.51060i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.b.11.5	✓	176
3.2	odd	2	inner	930.2.br.b.11.22	yes	176
31.17	odd	30	inner	930.2.br.b.761.22	yes	176
93.17	even	30	inner	930.2.br.b.761.5	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.5	✓	176	1.1	even	1	trivial
930.2.br.b.11.22	yes	176	3.2	odd	2	inner
930.2.br.b.761.5	yes	176	93.17	even	30	inner
930.2.br.b.761.22	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)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.0316079 - 1.73176i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.505083 + 1.65677i) q^{6} +(-0.0802420 - 0.763452i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.99800 - 0.109475i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.0316079 - 1.73176i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.505083 + 1.65677i) q^{6} +(-0.0802420 - 0.763452i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.99800 - 0.109475i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-0.551428 - 0.245511i) q^{11} +(-0.992333 - 1.41960i) q^{12} +(1.24517 + 5.85808i) q^{13} +(0.312234 + 0.701289i) q^{14} +(0.838508 + 1.51555i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.895018 + 0.398488i) q^{17} +(2.88510 - 0.822317i) q^{18} +(-4.05438 - 0.861785i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(-1.32465 + 0.114829i) q^{21} +(0.600306 + 0.0630947i) q^{22} +(0.492054 + 0.357498i) q^{23} +(1.38245 + 1.04348i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.99448 - 5.18659i) q^{26} +(-0.284345 + 5.18837i) q^{27} +(-0.513663 - 0.570480i) q^{28} +(2.63625 + 8.11355i) q^{29} +(-1.26580 - 1.18226i) q^{30} +(1.97759 + 5.20472i) q^{31} +1.00000i q^{32} +(-0.442597 + 0.947182i) q^{33} +(0.728073 - 0.655560i) q^{34} +(0.451217 + 0.621047i) q^{35} +(-2.48978 + 1.67361i) q^{36} +(-9.50309 - 5.48661i) q^{37} +(4.12225 - 0.433266i) q^{38} +(10.1842 - 1.97118i) q^{39} +(0.104528 - 0.994522i) q^{40} +(8.20129 + 7.38447i) q^{41} +(1.22434 - 0.518549i) q^{42} +(0.784850 - 3.69243i) q^{43} +(-0.590422 + 0.125498i) q^{44} +(2.65108 - 1.40419i) q^{45} +(-0.578444 - 0.187948i) q^{46} +(-9.44864 - 3.07005i) q^{47} +(-1.63724 - 0.565205i) q^{48} +(6.27061 - 1.33286i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(0.661796 + 1.56255i) q^{51} +(4.45066 + 4.00739i) q^{52} +(-0.409227 + 3.89354i) q^{53} +(-1.33287 - 5.02230i) q^{54} +(0.600306 - 0.0630947i) q^{55} +(0.664810 + 0.383828i) q^{56} +(-1.62056 + 6.99398i) q^{57} +(-5.01445 - 6.90180i) q^{58} +(7.27371 - 6.54928i) q^{59} +(1.56919 + 0.733246i) q^{60} +11.7984i q^{61} +(-3.48915 - 4.33888i) q^{62} +(0.156987 + 2.29761i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-4.00739 - 4.45066i) q^{65} +(0.128239 - 1.03759i) q^{66} +(-0.364290 - 0.630968i) q^{67} +(-0.489859 + 0.848461i) q^{68} +(0.634655 - 0.840821i) q^{69} +(-0.621047 - 0.451217i) q^{70} +(6.35088 + 0.667504i) q^{71} +(1.85075 - 2.36109i) q^{72} +(-5.73753 + 12.8867i) q^{73} +(10.7334 + 2.28146i) q^{74} +(-1.48395 - 0.893254i) q^{75} +(-3.78661 + 1.68591i) q^{76} +(-0.143188 + 0.440689i) q^{77} +(-9.07658 + 5.02178i) q^{78} +(2.71470 + 6.09731i) q^{79} +(0.207912 + 0.978148i) q^{80} +(8.97603 + 0.656411i) q^{81} +(-10.0818 - 4.48871i) q^{82} +(4.71869 - 5.24064i) q^{83} +(-1.00417 + 0.871510i) q^{84} +(0.575864 - 0.792609i) q^{85} +(0.394587 + 3.75424i) q^{86} +(14.1341 - 4.30891i) q^{87} +(0.522744 - 0.301806i) q^{88} +(4.80921 - 3.49409i) q^{89} +(-2.08741 + 2.15470i) q^{90} +(4.37244 - 1.42069i) q^{91} +0.608212 q^{92} +(9.07585 - 3.26020i) q^{93} +9.93488 q^{94} +(3.94209 - 1.28086i) q^{95} +(1.73176 + 0.0316079i) q^{96} +(7.85424 - 5.70644i) q^{97} +(-5.55183 + 3.20535i) q^{98} +(1.62630 + 0.796411i) 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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