LMFDB - Embedded newform 930.2.br.b.11.15

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			11.15
Character	$\chi$	$=$	930.11
Dual form			930.2.br.b.761.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(-0.874059 - 1.49533i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.29336 - 1.15205i) q^{6} +(0.359918 + 3.42439i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.47204 + 2.61402i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(-0.874059 - 1.49533i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.29336 - 1.15205i) q^{6} +(0.359918 + 3.42439i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.47204 + 2.61402i) q^{9} +(0.669131 - 0.743145i) q^{10} +(4.28029 + 1.90571i) q^{11} +(-1.58606 - 0.695991i) q^{12} +(0.215242 + 1.01263i) q^{13} +(1.40050 + 3.14556i) q^{14} +(-1.50462 - 0.857967i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.82371 - 2.14765i) q^{17} +(-0.592219 + 2.94097i) q^{18} +(1.67953 + 0.356996i) q^{19} +(0.406737 - 0.913545i) q^{20} +(4.80601 - 3.53131i) q^{21} +(4.65969 + 0.489754i) q^{22} +(-0.800242 - 0.581410i) q^{23} +(-1.72351 - 0.171806i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.517629 + 0.896559i) q^{26} +(5.19548 - 0.0836141i) q^{27} +(2.30398 + 2.55883i) q^{28} +(2.44496 + 7.52482i) q^{29} +(-1.69611 - 0.351021i) q^{30} +(-5.07797 - 2.28347i) q^{31} -1.00000i q^{32} +(-0.891558 - 8.06616i) q^{33} +(3.92396 - 3.53315i) q^{34} +(2.02389 + 2.78565i) q^{35} +(0.345575 + 2.98003i) q^{36} +(-2.37140 - 1.36913i) q^{37} +(1.70765 - 0.179481i) q^{38} +(1.32609 - 1.20696i) q^{39} +(0.104528 - 0.994522i) q^{40} +(-5.93336 - 5.34242i) q^{41} +(3.47955 - 4.84362i) q^{42} +(0.0691375 - 0.325266i) q^{43} +(4.58298 - 0.974141i) q^{44} +(0.0321839 + 2.99983i) q^{45} +(-0.940741 - 0.305665i) q^{46} +(-5.39065 - 1.75153i) q^{47} +(-1.69225 + 0.369196i) q^{48} +(-4.74985 + 1.00961i) q^{49} +(0.207912 - 0.978148i) q^{50} +(-7.42766 - 5.33587i) q^{51} +(0.769346 + 0.692722i) q^{52} +(1.22235 - 11.6299i) q^{53} +(4.91536 - 1.68501i) q^{54} +(4.65969 - 0.489754i) q^{55} +(2.98194 + 1.72162i) q^{56} +(-0.934183 - 2.82349i) q^{57} +(4.65060 + 6.40099i) q^{58} +(2.64517 - 2.38172i) q^{59} +(-1.72157 + 0.190286i) q^{60} +1.89691i q^{61} +(-5.53507 - 0.602535i) q^{62} +(-9.48122 - 4.10001i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.692722 + 0.769346i) q^{65} +(-3.34050 - 7.39587i) q^{66} +(1.43290 + 2.48185i) q^{67} +(2.64010 - 4.57279i) q^{68} +(-0.169943 + 1.70481i) q^{69} +(2.78565 + 2.02389i) q^{70} +(10.5085 + 1.10449i) q^{71} +(1.24954 + 2.72739i) q^{72} +(1.87339 - 4.20771i) q^{73} +(-2.67842 - 0.569316i) q^{74} +(-1.73203 + 0.00929082i) q^{75} +(1.56861 - 0.698389i) q^{76} +(-4.98533 + 15.3433i) q^{77} +(0.888216 - 1.55767i) q^{78} +(4.71772 + 10.5962i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(-4.66619 - 7.69589i) q^{81} +(-7.29386 - 3.24744i) q^{82} +(-4.44010 + 4.93123i) q^{83} +(1.81249 - 5.68179i) q^{84} +(3.10363 - 4.27177i) q^{85} +(-0.0347592 - 0.330711i) q^{86} +(9.11507 - 10.2332i) q^{87} +(4.05764 - 2.34268i) q^{88} +(-7.36112 + 5.34817i) q^{89} +(0.957606 + 2.84306i) q^{90} +(-3.39018 + 1.10154i) q^{91} -0.989153 q^{92} +(1.02389 + 9.58914i) q^{93} -5.66807 q^{94} +(1.63302 - 0.530599i) q^{95} +(-1.49533 + 0.874059i) q^{96} +(4.67822 - 3.39893i) q^{97} +(-4.20539 + 2.42798i) q^{98} +(-11.2823 + 8.38348i) 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
$3$	−0.874059	−	1.49533i	−0.504638	−	0.863331i
$3$	−0.874059	−	1.49533i	−0.504638	−	0.863331i
$4$	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
$6$	−1.29336	−	1.15205i	−0.528013	−	0.470321i
$7$	0.359918	+	3.42439i	0.136036	+	1.29430i	0.823182	+	0.567777i	$0.192197\pi$
$7$	0.359918	+	3.42439i	0.136036	+	1.29430i	−0.687146	+	0.726519i	$0.741137\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	−1.47204	+	2.61402i	−0.490681	+	0.871340i
$10$	0.669131	−	0.743145i	0.211598	−	0.235003i
$11$	4.28029	+	1.90571i	1.29056	+	0.574593i	0.933194	−	0.359373i	$-0.117009\pi$
$11$	4.28029	+	1.90571i	1.29056	+	0.574593i	0.357362	+	0.933966i	$0.383676\pi$
$12$	−1.58606	−	0.695991i	−0.457857	−	0.200915i
$13$	0.215242	+	1.01263i	0.0596974	+	0.280854i	0.997864	−	0.0653308i	$-0.0208103\pi$
$13$	0.215242	+	1.01263i	0.0596974	+	0.280854i	−0.938166	+	0.346185i	$0.887477\pi$
$14$	1.40050	+	3.14556i	0.374298	+	0.840688i
$15$	−1.50462	−	0.857967i	−0.388492	−	0.221526i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	4.82371	−	2.14765i	1.16992	−	0.520882i	0.272542	−	0.962144i	$-0.412136\pi$
$17$	4.82371	−	2.14765i	1.16992	−	0.520882i	0.897378	+	0.441262i	$0.145469\pi$
$18$	−0.592219	+	2.94097i	−0.139587	+	0.693192i
$19$	1.67953	+	0.356996i	0.385311	+	0.0819004i	0.396495	−	0.918037i	$-0.370227\pi$
$19$	1.67953	+	0.356996i	0.385311	+	0.0819004i	−0.0111835	+	0.999937i	$0.503560\pi$
$20$	0.406737	−	0.913545i	0.0909491	−	0.204275i
$21$	4.80601	−	3.53131i	1.04876	−	0.770596i
$22$	4.65969	+	0.489754i	0.993450	+	0.104416i
$23$	−0.800242	−	0.581410i	−0.166862	−	0.121232i	0.501220	−	0.865320i	$-0.332885\pi$
$23$	−0.800242	−	0.581410i	−0.166862	−	0.121232i	−0.668082	+	0.744087i	$0.732885\pi$
$24$	−1.72351	−	0.171806i	−0.351810	−	0.0350698i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	0.517629	+	0.896559i	0.101515	+	0.175830i
$27$	5.19548	−	0.0836141i	0.999871	−	0.0160915i
$28$	2.30398	+	2.55883i	0.435412	+	0.483574i
$29$	2.44496	+	7.52482i	0.454018	+	1.39732i	0.872284	+	0.489000i	$0.162638\pi$
$29$	2.44496	+	7.52482i	0.454018	+	1.39732i	−0.418266	+	0.908325i	$0.637362\pi$
$30$	−1.69611	−	0.351021i	−0.309666	−	0.0640873i
$31$	−5.07797	−	2.28347i	−0.912030	−	0.410124i
$31$	−5.07797	−	2.28347i	−0.912030	−	0.410124i
$32$		−	1.00000i		−	0.176777i
$33$	−0.891558	−	8.06616i	−0.155200	−	1.40414i
$34$	3.92396	−	3.53315i	0.672953	−	0.605929i
$35$	2.02389	+	2.78565i	0.342100	+	0.470860i
$36$	0.345575	+	2.98003i	0.0575958	+	0.496672i
$37$	−2.37140	−	1.36913i	−0.389856	−	0.225083i	0.292242	−	0.956344i	$-0.405599\pi$
$37$	−2.37140	−	1.36913i	−0.389856	−	0.225083i	−0.682098	+	0.731261i	$0.738932\pi$
$38$	1.70765	−	0.179481i	0.277017	−	0.0291157i
$39$	1.32609	−	1.20696i	0.212345	−	0.193268i
$40$	0.104528	−	0.994522i	0.0165274	−	0.157248i
$41$	−5.93336	−	5.34242i	−0.926635	−	0.834346i	0.0598481	−	0.998207i	$-0.480938\pi$
$41$	−5.93336	−	5.34242i	−0.926635	−	0.834346i	−0.986483	+	0.163861i	$0.947605\pi$
$42$	3.47955	−	4.84362i	0.536906	−	0.747386i
$43$	0.0691375	−	0.325266i	0.0105434	−	0.0496027i	−0.972561	−	0.232646i	$-0.925262\pi$
$43$	0.0691375	−	0.325266i	0.0105434	−	0.0496027i	0.983105	+	0.183044i	$0.0585949\pi$
$44$	4.58298	−	0.974141i	0.690910	−	0.146857i
$45$	0.0321839	+	2.99983i	0.00479769	+	0.447188i
$46$	−0.940741	−	0.305665i	−0.138705	−	0.0450679i
$47$	−5.39065	−	1.75153i	−0.786308	−	0.255487i	−0.111777	−	0.993733i	$-0.535654\pi$
$47$	−5.39065	−	1.75153i	−0.786308	−	0.255487i	−0.674531	+	0.738247i	$0.735654\pi$
$48$	−1.69225	+	0.369196i	−0.244255	+	0.0532889i
$49$	−4.74985	+	1.00961i	−0.678550	+	0.144230i
$50$	0.207912	−	0.978148i	0.0294032	−	0.138331i
$51$	−7.42766	−	5.33587i	−1.04008	−	0.747171i
$52$	0.769346	+	0.692722i	0.106689	+	0.0960633i
$53$	1.22235	−	11.6299i	0.167903	−	1.59749i	−0.508567	−	0.861023i	$-0.669824\pi$
$53$	1.22235	−	11.6299i	0.167903	−	1.59749i	0.676470	−	0.736470i	$-0.263509\pi$
$54$	4.91536	−	1.68501i	0.668895	−	0.229301i
$55$	4.65969	−	0.489754i	0.628313	−	0.0660384i
$56$	2.98194	+	1.72162i	0.398479	+	0.230062i
$57$	−0.934183	−	2.82349i	−0.123736	−	0.373981i
$58$	4.65060	+	6.40099i	0.610653	+	0.840492i
$59$	2.64517	−	2.38172i	0.344372	−	0.310074i	−0.478736	−	0.877959i	$-0.658905\pi$
$59$	2.64517	−	2.38172i	0.344372	−	0.310074i	0.823108	+	0.567885i	$0.192238\pi$
$60$	−1.72157	+	0.190286i	−0.222253	+	0.0245658i
$61$			1.89691i			0.242875i	0.992599	+	0.121437i	$0.0387504\pi$
$61$			1.89691i			0.242875i	−0.992599	+	0.121437i	$0.961250\pi$
$62$	−5.53507	−	0.602535i	−0.702954	−	0.0765220i
$63$	−9.48122	−	4.10001i	−1.19452	−	0.516553i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	0.692722	+	0.769346i	0.0859216	+	0.0954256i
$66$	−3.34050	−	7.39587i	−0.411188	−	0.910369i
$67$	1.43290	+	2.48185i	0.175056	+	0.303206i	0.940181	−	0.340676i	$-0.110656\pi$
$67$	1.43290	+	2.48185i	0.175056	+	0.303206i	−0.765125	+	0.643882i	$0.777323\pi$
$68$	2.64010	−	4.57279i	0.320159	−	0.554532i
$69$	−0.169943	+	1.70481i	−0.0204587	+	0.205236i
$70$	2.78565	+	2.02389i	0.332949	+	0.241901i
$71$	10.5085	+	1.10449i	1.24713	+	0.131079i	0.704997	−	0.709211i	$-0.250949\pi$
$71$	10.5085	+	1.10449i	1.24713	+	0.131079i	0.542137	+	0.840290i	$0.317615\pi$
$72$	1.24954	+	2.72739i	0.147260	+	0.321426i
$73$	1.87339	−	4.20771i	0.219264	−	0.492476i	−0.770102	−	0.637921i	$-0.779795\pi$
$73$	1.87339	−	4.20771i	0.219264	−	0.492476i	0.989366	+	0.145445i	$0.0464614\pi$
$74$	−2.67842	−	0.569316i	−0.311360	−	0.0661816i
$75$	−1.73203	+	0.00929082i	−0.199997	+	0.00107281i
$76$	1.56861	−	0.698389i	0.179932	−	0.0801107i
$77$	−4.98533	+	15.3433i	−0.568131	+	1.74853i
$78$	0.888216	−	1.55767i	0.100571	−	0.176372i
$79$	4.71772	+	10.5962i	0.530785	+	1.19216i	0.957673	+	0.287859i	$0.0929433\pi$
$79$	4.71772	+	10.5962i	0.530785	+	1.19216i	−0.426888	+	0.904305i	$0.640390\pi$
$80$	−0.207912	−	0.978148i	−0.0232452	−	0.109360i
$81$	−4.66619	−	7.69589i	−0.518465	−	0.855099i
$82$	−7.29386	−	3.24744i	−0.805472	−	0.358619i
$83$	−4.44010	+	4.93123i	−0.487364	+	0.541273i	−0.935795	−	0.352545i	$-0.885316\pi$
$83$	−4.44010	+	4.93123i	−0.487364	+	0.541273i	0.448431	+	0.893818i	$0.351983\pi$
$84$	1.81249	−	5.68179i	0.197759	−	0.619934i
$85$	3.10363	−	4.27177i	0.336635	−	0.463339i
$86$	−0.0347592	−	0.330711i	−0.00374818	−	0.0356615i
$87$	9.11507	−	10.2332i	0.977238	−	1.09711i
$88$	4.05764	−	2.34268i	0.432546	−	0.249731i
$89$	−7.36112	+	5.34817i	−0.780277	+	0.566905i	−0.905062	−	0.425279i	$-0.860176\pi$
$89$	−7.36112	+	5.34817i	−0.780277	+	0.566905i	0.124785	+	0.992184i	$0.460176\pi$
$90$	0.957606	+	2.84306i	0.100941	+	0.299685i
$91$	−3.39018	+	1.10154i	−0.355388	+	0.115472i
$92$	−0.989153			−0.103126
$93$	1.02389	+	9.58914i	0.106172	+	0.994348i
$94$	−5.66807			−0.584617
$95$	1.63302	−	0.530599i	0.167544	−	0.0544383i
$96$	−1.49533	+	0.874059i	−0.152617	+	0.0892083i
$97$	4.67822	−	3.39893i	0.475002	−	0.345109i	−0.324386	−	0.945925i	$-0.605158\pi$
$97$	4.67822	−	3.39893i	0.475002	−	0.345109i	0.799387	+	0.600816i	$0.205158\pi$
$98$	−4.20539	+	2.42798i	−0.424808	+	0.245263i
$99$	−11.2823	+	8.38348i	−1.13392	+	0.842571i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	3.43741	−	4.73119i	0.342035	−	0.470771i	−0.602999	−	0.797742i	$-0.706028\pi$
$101$	3.43741	−	4.73119i	0.342035	−	0.470771i	0.945035	+	0.326970i	$0.106028\pi$
$102$	−8.71300	−	2.77944i	−0.862715	−	0.275206i
$103$	−7.90146	+	8.77546i	−0.778554	+	0.864672i	−0.993719	−	0.111906i	$-0.964304\pi$
$103$	−7.90146	+	8.77546i	−0.778554	+	0.864672i	0.215165	+	0.976578i	$0.430971\pi$
$104$	0.945754	+	0.421077i	0.0927389	+	0.0412900i
$105$	2.39647	−	5.46121i	0.233872	−	0.532960i
$106$	−2.43132	−	11.4384i	−0.236150	−	1.11100i
$107$	2.20513	+	4.95281i	0.213178	+	0.478806i	0.988208	−	0.153119i	$-0.0489318\pi$
$107$	2.20513	+	4.95281i	0.213178	+	0.478806i	−0.775030	+	0.631925i	$0.782265\pi$
$108$	4.15408	−	3.12147i	0.399727	−	0.300364i
$109$	−4.35524	+	13.4040i	−0.417156	+	1.28387i	0.493152	+	0.869943i	$0.335845\pi$
$109$	−4.35524	+	13.4040i	−0.417156	+	1.28387i	−0.910308	+	0.413931i	$0.864155\pi$
$110$	4.28029	−	1.90571i	0.408110	−	0.181702i
$111$	0.0254407	+	4.74274i	0.00241472	+	0.450161i
$112$	3.36801	+	0.715892i	0.318247	+	0.0676454i
$113$	7.92369	−	17.7969i	0.745398	−	1.67419i	0.00686304	−	0.999976i	$-0.497815\pi$
$113$	7.92369	−	17.7969i	0.745398	−	1.67419i	0.738535	−	0.674215i	$-0.235518\pi$
$114$	−1.76097	−	2.39662i	−0.164930	−	0.224464i
$115$	−0.983734	−	0.103395i	−0.0917337	−	0.00964160i
$116$	6.40099	+	4.65060i	0.594317	+	0.431797i
$117$	−2.96389	−	0.927993i	−0.274012	−	0.0857930i
$118$	1.77971	−	3.08255i	0.163836	−	0.283772i
$119$	9.09053	+	15.7453i	0.833327	+	1.44337i
$120$	−1.57851	+	0.712966i	−0.144097	+	0.0650846i
$121$	7.32873	+	8.13938i	0.666248	+	0.739944i
$122$	0.586179	+	1.80407i	0.0530701	+	0.163333i
$123$	−2.80259	+	13.5419i	−0.252701	+	1.22104i
$124$	−5.45035	+	1.13738i	−0.489456	+	0.102140i
$125$		−	1.00000i		−	0.0894427i
$126$	−10.2842	−	0.969481i	−0.916185	−	0.0863682i
$127$	2.94752	−	2.65396i	0.261550	−	0.235501i	−0.527914	−	0.849298i	$-0.677026\pi$
$127$	2.94752	−	2.65396i	0.261550	−	0.235501i	0.789463	+	0.613798i	$0.210359\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	−0.546812	+	0.180918i	−0.0481441	+	0.0159290i
$130$	0.896559	+	0.517629i	0.0786334	+	0.0453990i
$131$	18.0248	−	1.89449i	1.57484	−	0.165522i	0.723568	−	0.690253i	$-0.242501\pi$
$131$	18.0248	−	1.89449i	1.57484	−	0.165522i	0.851268	+	0.524731i	$0.175834\pi$
$132$	−5.46246	−	6.00162i	−0.475446	−	0.522374i
$133$	−0.617998	+	5.87986i	−0.0535872	+	0.509848i
$134$	2.12970	+	1.91759i	0.183978	+	0.165654i
$135$	4.45761	−	2.67015i	0.383650	−	0.229810i
$136$	1.09782	−	5.16482i	0.0941369	−	0.442880i
$137$	−15.4826	+	3.29093i	−1.32277	+	0.281163i	−0.814564	−	0.580073i	$-0.803024\pi$
$137$	−15.4826	+	3.29093i	−1.32277	+	0.281163i	−0.508204	+	0.861236i	$0.669691\pi$
$138$	0.365192	+	1.67389i	0.0310872	+	0.142491i
$139$	−15.2529	−	4.95597i	−1.29373	−	0.420360i	−0.420337	−	0.907368i	$-0.638088\pi$
$139$	−15.2529	−	4.95597i	−1.29373	−	0.420360i	−0.873397	+	0.487008i	$0.838088\pi$
$140$	3.27472	+	1.06402i	0.276765	+	0.0899263i
$141$	2.09263	+	9.59176i	0.176231	+	0.807772i
$142$	10.3355	−	2.19688i	0.867338	−	0.184358i
$143$	−1.00849	+	4.74456i	−0.0843339	+	0.396760i
$144$	2.03119	+	2.20777i	0.169266	+	0.183981i
$145$	5.87981	+	5.29420i	0.488292	+	0.439660i
$146$	0.481449	−	4.58068i	0.0398450	−	0.379100i
$147$	5.66136	+	6.22015i	0.466941	+	0.513029i
$148$	−2.72326	+	0.286226i	−0.223850	+	0.0235276i
$149$	−20.4618	−	11.8136i	−1.67630	−	0.967811i	−0.963988	−	0.265947i	$-0.914315\pi$
$149$	−20.4618	−	11.8136i	−1.67630	−	0.967811i	−0.712311	−	0.701864i	$-0.752351\pi$
$150$	−1.64438	+	0.544062i	−0.134263	+	0.0444224i
$151$	10.6937	+	14.7187i	0.870244	+	1.19779i	0.979029	+	0.203723i	$0.0653042\pi$
$151$	10.6937	+	14.7187i	0.870244	+	1.19779i	−0.108784	+	0.994065i	$0.534696\pi$
$152$	1.27602	−	1.14893i	0.103499	−	0.0931908i
$153$	−1.48669	+	15.7707i	−0.120192	+	1.27498i
$154$			16.1329i			1.30002i
$155$	−5.53939	+	0.561437i	−0.444934	+	0.0450957i
$156$	0.363397	−	1.75591i	0.0290950	−	0.140585i
$157$	−7.56247	−	23.2749i	−0.603551	−	1.85754i	−0.506459	−	0.862264i	$-0.669046\pi$
$157$	−7.56247	−	23.2749i	−0.603551	−	1.85754i	−0.0970918	−	0.995275i	$-0.530954\pi$
$158$	7.76122	+	8.61971i	0.617450	+	0.685747i
$159$	−18.4590	+	8.33741i	−1.46390	+	0.661200i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	1.70295	−	2.94960i	0.134211	−	0.232461i
$162$	−6.81597	−	5.87729i	−0.535513	−	0.461764i
$163$	−1.62740	−	1.18238i	−0.127468	−	0.0926108i	0.522225	−	0.852808i	$-0.325102\pi$
$163$	−1.62740	−	1.18238i	−0.127468	−	0.0926108i	−0.649692	+	0.760197i	$0.725102\pi$
$164$	−7.94039	−	0.834568i	−0.620040	−	0.0651688i
$165$	−4.80519	−	6.53972i	−0.374084	−	0.509117i
$166$	−2.69895	+	6.06194i	−0.209479	+	0.470498i
$167$	−9.93849	−	2.11249i	−0.769064	−	0.163469i	−0.193360	−	0.981128i	$-0.561938\pi$
$167$	−9.93849	−	2.11249i	−0.769064	−	0.163469i	−0.575704	+	0.817658i	$0.695272\pi$
$168$	−0.0319906	−	5.96380i	−0.00246813	−	0.460117i
$169$	10.8970	−	4.85165i	0.838230	−	0.373204i
$170$	1.63167	−	5.02177i	0.125144	−	0.385152i
$171$	−3.40553	+	3.86482i	−0.260428	+	0.295550i
$172$	−0.135253	−	0.303784i	−0.0103130	−	0.0231633i
$173$	−3.78907	−	17.8262i	−0.288078	−	1.35530i	−0.849421	−	0.527716i	$-0.823049\pi$
$173$	−3.78907	−	17.8262i	−0.288078	−	1.35530i	0.561343	−	0.827583i	$-0.310285\pi$
$174$	5.50672	−	12.5490i	0.417464	−	0.951340i
$175$	3.14556	+	1.40050i	0.237782	+	0.105868i
$176$	3.13512	−	3.48190i	0.236318	−	0.262458i
$177$	−5.87350	−	1.87364i	−0.441479	−	0.140832i
$178$	−5.34817	+	7.36112i	−0.400862	+	0.551739i
$179$	1.51299	+	14.3951i	0.113086	+	1.07594i	0.893000	+	0.450056i	$0.148596\pi$
$179$	1.51299	+	14.3951i	0.113086	+	1.07594i	−0.779914	+	0.625886i	$0.784737\pi$
$180$	1.78929	+	2.40799i	0.133366	+	0.179481i
$181$	−6.32634	+	3.65251i	−0.470233	+	0.271489i	−0.716337	−	0.697754i	$-0.754183\pi$
$181$	−6.32634	+	3.65251i	−0.470233	+	0.271489i	0.246104	+	0.969243i	$0.420849\pi$
$182$	−2.88386	+	2.09525i	−0.213766	+	0.155310i
$183$	2.83652	−	1.65801i	0.209681	−	0.122564i
$184$	−0.940741	+	0.305665i	−0.0693523	+	0.0225339i
$185$	−2.73826			−0.201321
$186$	3.93698	+	8.80342i	0.288674	+	0.645498i
$187$	24.7397			1.80914
$188$	−5.39065	+	1.75153i	−0.393154	+	0.127743i
$189$	2.15627	+	17.7612i	0.156846	+	1.29194i
$190$	1.38913	−	1.00926i	0.100778	−	0.0732193i
$191$	−18.7851	+	10.8456i	−1.35924	+	0.784758i	−0.989522	−	0.144385i	$-0.953879\pi$
$191$	−18.7851	+	10.8456i	−1.35924	+	0.784758i	−0.369719	+	0.929144i	$0.620546\pi$
$192$	−1.15205	+	1.29336i	−0.0831418	+	0.0933404i
$193$	−0.456525	−	4.34355i	−0.0328614	−	0.312655i	−0.998589	−	0.0530986i	$-0.983090\pi$
$193$	−0.456525	−	4.34355i	−0.0328614	−	0.312655i	0.965728	−	0.259557i	$-0.0835764\pi$
$194$	3.39893	−	4.67822i	0.244029	−	0.335877i
$195$	0.544948	−	1.70830i	0.0390246	−	0.122334i
$196$	−3.24928	+	3.60869i	−0.232091	+	0.257763i
$197$	−13.1523	−	5.85576i	−0.937059	−	0.417206i	−0.119360	−	0.992851i	$-0.538084\pi$
$197$	−13.1523	−	5.85576i	−0.937059	−	0.417206i	−0.817700	+	0.575645i	$0.804751\pi$
$198$	−8.13949	+	11.4596i	−0.578448	+	0.814398i
$199$	2.84702	+	13.3942i	0.201820	+	0.949489i	0.956124	+	0.292963i	$0.0946413\pi$
$199$	2.84702	+	13.3942i	0.201820	+	0.949489i	−0.754304	+	0.656526i	$0.772025\pi$
$200$	−0.406737	−	0.913545i	−0.0287606	−	0.0645974i
$201$	2.45875	−	4.31194i	0.173427	−	0.304141i
$202$	1.80716	−	5.56185i	0.127151	−	0.391331i
$203$	−24.8879	+	11.0808i	−1.74679	+	0.777721i
$204$	−9.14545	+	0.0490574i	−0.640309	+	0.00343470i
$205$	−7.80965	−	1.65999i	−0.545450	−	0.115939i
$206$	−4.80297	+	10.7876i	−0.334639	+	0.751611i
$207$	2.69780	−	1.23599i	0.187510	−	0.0859071i
$208$	1.02959	+	0.108214i	0.0713889	+	0.00750328i
$209$	6.50856	+	4.72874i	0.450206	+	0.327094i
$210$	0.591571	−	5.93447i	0.0408223	−	0.409517i
$211$	−10.6572	+	18.4589i	−0.733674	+	1.27076i	0.221628	+	0.975131i	$0.428863\pi$
$211$	−10.6572	+	18.4589i	−0.733674	+	1.27076i	−0.955303	+	0.295630i	$0.904471\pi$
$212$	−5.84699	−	10.1273i	−0.401573	−	0.695545i
$213$	−7.53350	−	16.6792i	−0.516187	−	1.14284i
$214$	3.62771	+	4.02898i	0.247985	+	0.275415i
$215$	−0.102758	−	0.316258i	−0.00700806	−	0.0215686i
$216$	2.98618	−	4.25238i	0.203184	−	0.289338i
$217$	5.99185	−	18.2108i	0.406753	−	1.23623i
$218$			14.0938i			0.954555i
$219$	−7.92939	+	0.876441i	−0.535819	+	0.0592244i
$220$	3.48190	−	3.13512i	0.234750	−	0.211370i
$221$	3.21305	+	4.42238i	0.216133	+	0.297482i
$222$	1.48978	+	4.50275i	0.0999876	+	0.302205i
$223$	11.9544	+	6.90186i	0.800524	+	0.462183i	0.843654	−	0.536886i	$-0.180400\pi$
$223$	11.9544	+	6.90186i	0.800524	+	0.462183i	−0.0431301	+	0.999069i	$0.513733\pi$
$224$	3.42439	−	0.359918i	0.228801	−	0.0240480i
$225$	1.52779	+	2.58183i	0.101852	+	0.172122i
$226$	2.03633	−	19.3744i	0.135455	−	1.28877i
$227$	−8.47556	−	7.63143i	−0.562543	−	0.506516i	0.338080	−	0.941117i	$-0.390223\pi$
$227$	−8.47556	−	7.63143i	−0.562543	−	0.506516i	−0.900623	+	0.434602i	$0.856889\pi$
$228$	−2.41538	−	1.73516i	−0.159962	−	0.114914i
$229$	1.43859	−	6.76801i	0.0950644	−	0.447243i	−0.904711	−	0.426027i	$-0.859913\pi$
$229$	1.43859	−	6.76801i	0.0950644	−	0.447243i	0.999775	−	0.0212160i	$-0.00675376\pi$
$230$	−0.967538	+	0.205657i	−0.0637976	+	0.0135606i
$231$	27.3008	−	5.95619i	1.79626	−	0.391889i
$232$	7.52482	+	2.44496i	0.494029	+	0.160520i
$233$	−8.17971	−	2.65775i	−0.535870	−	0.174115i	0.0285652	−	0.999592i	$-0.490906\pi$
$233$	−8.17971	−	2.65775i	−0.535870	−	0.174115i	−0.564436	+	0.825477i	$0.690906\pi$
$234$	−3.10559	+	0.0333186i	−0.203019	+	0.00217810i
$235$	−5.54421	+	1.17846i	−0.361664	+	0.0768741i
$236$	0.740046	−	3.48164i	0.0481729	−	0.226636i
$237$	11.7212	−	16.3163i	0.761377	−	1.05985i
$238$	13.5112	+	12.1655i	0.875798	+	0.788572i
$239$	0.732522	−	6.96949i	0.0473829	−	0.450819i	−0.944949	−	0.327217i	$-0.893889\pi$
$239$	0.732522	−	6.96949i	0.0473829	−	0.450819i	0.992332	−	0.123601i	$-0.0394443\pi$
$240$	−1.28093	+	1.16586i	−0.0826836	+	0.0752557i
$241$	17.1313	−	1.80057i	1.10352	−	0.115985i	0.464795	−	0.885418i	$-0.346128\pi$
$241$	17.1313	−	1.80057i	1.10352	−	0.115985i	0.638727	+	0.769433i	$0.279461\pi$
$242$	9.48524	+	5.47631i	0.609734	+	0.352030i
$243$	−7.42939	+	13.7042i	−0.476596	+	0.879123i
$244$	1.11498	+	1.53464i	0.0713791	+	0.0982450i
$245$	−3.60869	+	3.24928i	−0.230550	+	0.207589i
$246$	1.51927	+	13.7452i	0.0968649	+	0.876362i
$247$			1.77759i			0.113105i
$248$	−4.83212	+	2.76597i	−0.306840	+	0.175639i
$249$	11.2547	+	2.32924i	0.713240	+	0.147610i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−6.98635	−	7.75912i	−0.440974	−	0.489752i	0.481154	−	0.876636i	$-0.340218\pi$
$251$	−6.98635	−	7.75912i	−0.440974	−	0.489752i	−0.922128	+	0.386885i	$0.873551\pi$
$252$	−10.0804	+	2.25595i	−0.635005	+	0.142111i
$253$	−2.31727	−	4.01363i	−0.145686	−	0.252335i
$254$	1.98314	−	3.43490i	0.124433	−	0.215524i
$255$	−9.10048	−	0.907171i	−0.569894	−	0.0568093i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−12.8632	−	1.35198i	−0.802385	−	0.0843341i	−0.305547	−	0.952177i	$-0.598839\pi$
$257$	−12.8632	−	1.35198i	−0.802385	−	0.0843341i	−0.496838	+	0.867843i	$0.665506\pi$
$258$	−0.464142	+	0.341038i	−0.0288962	+	0.0212321i
$259$	3.83492	−	8.61337i	0.238290	−	0.535209i
$260$	1.01263	+	0.215242i	0.0628009	+	0.0133487i
$261$	−23.2691	−	4.68567i	−1.44032	−	0.290036i
$262$	16.5572	−	7.37174i	1.02291	−	0.455428i
$263$	1.14851	−	3.53476i	0.0708204	−	0.217963i	−0.909382	−	0.415963i	$-0.863445\pi$
$263$	1.14851	−	3.53476i	0.0708204	−	0.217963i	0.980202	+	0.198000i	$0.0634446\pi$
$264$	−7.04971	−	4.01989i	−0.433879	−	0.247407i
$265$	−4.75637	−	10.6830i	−0.292182	−	0.656251i
$266$	1.22922	+	5.78305i	0.0753686	+	0.354581i
$267$	14.4313	+	6.33271i	0.883184	+	0.387556i
$268$	2.61803	+	1.16562i	0.159922	+	0.0712017i
$269$	−17.5444	+	19.4850i	−1.06970	+	1.18802i	−0.0882894	+	0.996095i	$0.528140\pi$
$269$	−17.5444	+	19.4850i	−1.06970	+	1.18802i	−0.981409	+	0.191926i	$0.938527\pi$
$270$	3.41432	−	3.91694i	0.207789	−	0.238378i
$271$	6.01925	−	8.28479i	0.365644	−	0.503265i	−0.586067	−	0.810263i	$-0.699324\pi$
$271$	6.01925	−	8.28479i	0.365644	−	0.503265i	0.951710	+	0.306998i	$0.0993244\pi$
$272$	−0.551932	−	5.25128i	−0.0334658	−	0.318405i
$273$	4.61038	+	4.10664i	0.279033	+	0.248545i
$274$	−13.7079	+	7.91425i	−0.828124	+	0.478117i
$275$	3.79054	−	2.75399i	0.228578	−	0.166072i
$276$	0.864578	+	1.47911i	0.0520415	+	0.0890322i
$277$	−5.14297	+	1.67105i	−0.309011	+	0.100404i	−0.459418	−	0.888220i	$-0.651942\pi$
$277$	−5.14297	+	1.67105i	−0.309011	+	0.100404i	0.150406	+	0.988624i	$0.451942\pi$
$278$	−16.0379			−0.961886
$279$	13.4440	−	9.91253i	0.804873	−	0.593448i
$280$	3.44325			0.205774
$281$	3.88372	−	1.26190i	0.231683	−	0.0752785i	−0.190874	−	0.981614i	$-0.561132\pi$
$281$	3.88372	−	1.26190i	0.231683	−	0.0752785i	0.422558	+	0.906336i	$0.361132\pi$
$282$	4.95423	+	8.47565i	0.295020	+	0.504718i
$283$	8.02626	−	5.83142i	0.477111	−	0.346642i	−0.323095	−	0.946367i	$-0.604723\pi$
$283$	8.02626	−	5.83142i	0.477111	−	0.346642i	0.800206	+	0.599725i	$0.204723\pi$
$284$	9.15079	−	5.28321i	0.542999	−	0.313501i
$285$	−2.22077	−	1.97813i	−0.131547	−	0.117174i
$286$	0.507021	+	4.82398i	0.0299808	+	0.285248i
$287$	16.1590	−	22.2410i	0.953836	−	1.31284i
$288$	2.61402	+	1.47204i	0.154033	+	0.0867409i
$289$	7.28051	−	8.08582i	0.428265	−	0.475637i
$290$	7.22803	+	3.21813i	0.424445	+	0.188975i
$291$	−9.17157	−	4.02464i	−0.537647	−	0.235928i
$292$	−0.957624	−	4.50527i	−0.0560407	−	0.263651i
$293$	11.0412	+	24.7990i	0.645036	+	1.44877i	0.879140	+	0.476563i	$0.158118\pi$
$293$	11.0412	+	24.7990i	0.645036	+	1.44877i	−0.234104	+	0.972211i	$0.575216\pi$
$294$	7.30640	+	4.16626i	0.426118	+	0.242981i
$295$	1.09992	−	3.38521i	0.0640400	−	0.197095i
$296$	−2.50152	+	1.11375i	−0.145398	+	0.0647354i
$297$	22.3975	+	9.54318i	1.29964	+	0.553751i
$298$	−23.1110	−	4.91239i	−1.33878	−	0.284567i
$299$	0.416510	−	0.935496i	0.0240874	−	0.0541011i
$300$	−1.39578	+	1.02558i	−0.0805852	+	0.0592116i
$301$	1.13872	+	0.119685i	0.0656348	+	0.00689850i
$302$	14.7187	+	10.6937i	0.846964	+	0.615356i
$303$	−10.0792	−	1.00474i	−0.579036	−	0.0577205i
$304$	0.858527	−	1.48701i	0.0492399	−	0.0852860i
$305$	0.948457	+	1.64278i	0.0543085	+	0.0940650i
$306$	3.45948	+	15.4582i	0.197765	+	0.883688i
$307$	7.69603	+	8.54730i	0.439236	+	0.487820i	0.921595	−	0.388153i	$-0.126887\pi$
$307$	7.69603	+	8.54730i	0.439236	+	0.487820i	−0.482359	+	0.875973i	$0.660220\pi$
$308$	4.98533	+	15.3433i	0.284066	+	0.874264i
$309$	20.0286	+	4.14504i	1.13939	+	0.235803i
$310$	−5.09477	+	2.24572i	−0.289364	+	0.127548i
$311$		−	22.0667i		−	1.25129i	−0.780109	−	0.625644i	$-0.784836\pi$
$311$		−	22.0667i		−	1.25129i	0.780109	−	0.625644i	$-0.215164\pi$
$312$	−0.196995	−	1.78226i	−0.0111526	−	0.100901i
$313$	3.21364	−	2.89358i	0.181646	−	0.163555i	−0.573292	−	0.819351i	$-0.694334\pi$
$313$	3.21364	−	2.89358i	0.181646	−	0.163555i	0.754938	+	0.655797i	$0.227667\pi$
$314$	−14.3847	−	19.7988i	−0.811774	−	1.11731i
$315$	−10.2610	+	1.18990i	−0.578141	+	0.0670433i
$316$	10.0450	+	5.79948i	0.565075	+	0.326246i
$317$	−18.6915	+	1.96455i	−1.04982	+	0.110340i	−0.613692	−	0.789546i	$-0.710316\pi$
$317$	−18.6915	+	1.96455i	−1.04982	+	0.110340i	−0.436125	+	0.899886i	$0.643650\pi$
$318$	−14.9792	+	13.6335i	−0.839990	+	0.764529i
$319$	−3.87496	+	36.8678i	−0.216956	+	2.06420i
$320$	−0.743145	−	0.669131i	−0.0415431	−	0.0374055i
$321$	5.47868	−	7.62645i	0.305790	−	0.425667i
$322$	0.708127	−	3.33147i	0.0394624	−	0.185656i
$323$	8.86827	−	1.88501i	0.493444	−	0.104885i
$324$	−8.29855	−	3.48339i	−0.461031	−	0.193522i
$325$	0.984588	+	0.319912i	0.0546151	+	0.0177455i
$326$	−1.91312	−	0.621611i	−0.105958	−	0.0344279i
$327$	23.8502	−	5.20339i	1.31892	−	0.287748i
$328$	−7.80965	+	1.65999i	−0.431216	+	0.0916578i
$329$	4.05772	−	19.0901i	0.223710	−	1.05247i
$330$	−6.59090	−	4.73476i	−0.362817	−	0.260640i
$331$	−19.5111	−	17.5679i	−1.07243	−	0.965619i	−0.0729318	−	0.997337i	$-0.523236\pi$
$331$	−19.5111	−	17.5679i	−1.07243	−	0.965619i	−0.999497	+	0.0317179i	$0.989902\pi$
$332$	−0.693612	+	6.59927i	−0.0380669	+	0.362182i
$333$	7.06973	−	4.18347i	0.387419	−	0.229253i
$334$	−10.1049	+	1.06206i	−0.552913	+	0.0581135i
$335$	2.48185	+	1.43290i	0.135598	+	0.0782874i
$336$	−1.87334	−	5.66202i	−0.102199	−	0.308889i
$337$	2.77751	+	3.82292i	0.151301	+	0.208248i	0.877939	−	0.478773i	$-0.158918\pi$
$337$	2.77751	+	3.82292i	0.151301	+	0.208248i	−0.726638	+	0.687020i	$0.758918\pi$
$338$	8.86441	−	7.98155i	0.482160	−	0.434139i
$339$	−33.5381	+	3.70699i	−1.82154	+	0.201336i
$340$		−	5.28020i		−	0.286359i
$341$	−17.3835	−	19.4511i	−0.941371	−	1.05333i
$342$	−2.04456	+	4.72803i	−0.110557	+	0.255662i
$343$	2.28130	+	7.02112i	0.123179	+	0.379105i
$344$	−0.222508	−	0.247120i	−0.0119968	−	0.0133238i
$345$	0.705233	+	1.56138i	0.0379684	+	0.0840621i
$346$	−9.11221	−	15.7828i	−0.489875	−	0.848489i
$347$	6.77714	−	11.7384i	0.363816	−	0.630148i	−0.624769	−	0.780809i	$-0.714807\pi$
$347$	6.77714	−	11.7384i	0.363816	−	0.630148i	0.988585	+	0.150661i	$0.0481403\pi$
$348$	1.35934	−	13.6365i	0.0728683	−	0.730994i
$349$	−9.48771	−	6.89322i	−0.507865	−	0.368986i	0.304148	−	0.952625i	$-0.401628\pi$
$349$	−9.48771	−	6.89322i	−0.507865	−	0.368986i	−0.812013	+	0.583639i	$0.801628\pi$
$350$	3.42439	+	0.359918i	0.183041	+	0.0192384i
$351$	1.20296	+	5.24312i	0.0642091	+	0.279857i
$352$	1.90571	−	4.28029i	0.101575	−	0.228140i
$353$	11.6135	+	2.46852i	0.618122	+	0.131386i	0.506322	−	0.862345i	$-0.331005\pi$
$353$	11.6135	+	2.46852i	0.618122	+	0.131386i	0.111801	+	0.993731i	$0.464338\pi$
$354$	−6.16502	+	0.0330700i	−0.327667	+	0.00175765i
$355$	9.65291	−	4.29775i	0.512323	−	0.228101i
$356$	−2.81170	+	8.65352i	−0.149020	+	0.458635i
$357$	15.5987	−	27.3557i	0.825573	−	1.44781i
$358$	5.88728	+	13.2230i	0.311152	+	0.698860i
$359$	−6.77162	−	31.8579i	−0.357392	−	1.68140i	−0.678694	−	0.734421i	$-0.737454\pi$
$359$	−6.77162	−	31.8579i	−0.357392	−	1.68140i	0.321302	−	0.946977i	$-0.395880\pi$
$360$	2.44583	+	1.73722i	0.128906	+	0.0915594i
$361$	−14.6640	−	6.52883i	−0.771789	−	0.343622i
$362$	−4.88801	+	5.42869i	−0.256908	+	0.285326i
$363$	5.76534	−	18.0732i	0.302602	−	0.948596i
$364$	−2.09525	+	2.88386i	−0.109821	+	0.151155i
$365$	−0.481449	−	4.58068i	−0.0252002	−	0.239764i
$366$	2.18533	−	2.45340i	0.114229	−	0.128241i
$367$	−8.93281	+	5.15736i	−0.466289	+	0.269212i	−0.714685	−	0.699447i	$-0.753430\pi$
$367$	−8.93281	+	5.15736i	−0.466289	+	0.269212i	0.248396	+	0.968659i	$0.420097\pi$
$368$	−0.800242	+	0.581410i	−0.0417155	+	0.0303081i
$369$	22.6993	−	7.64565i	1.18168	−	0.398017i
$370$	−2.60424	+	0.846169i	−0.135388	+	0.0439902i
$371$	40.2653			2.09047
$372$	6.46470	+	7.15595i	0.335179	+	0.371019i
$373$	22.2339			1.15123			0.575614	−	0.817721i	$-0.304763\pi$
$373$	22.2339			1.15123			0.575614	+	0.817721i	$0.304763\pi$
$374$	23.5288	−	7.64498i	1.21665	−	0.395312i
$375$	−1.49533	+	0.874059i	−0.0772187	+	0.0451362i
$376$	−4.58556	+	3.33161i	−0.236482	+	0.171815i
$377$	−7.09363	+	4.09551i	−0.365341	+	0.210930i
$378$	7.53926	+	16.2256i	0.387778	+	0.834556i
$379$	−0.936045	−	8.90587i	−0.0480814	−	0.457464i	−0.991902	−	0.127006i	$-0.959463\pi$
$379$	−0.936045	−	8.90587i	−0.0480814	−	0.457464i	0.943821	−	0.330458i	$-0.107203\pi$
$380$	1.00926	−	1.38913i	0.0517739	−	0.0712606i
$381$	−6.54485	−	2.08781i	−0.335303	−	0.106961i
$382$	−14.5142	+	16.1197i	−0.742611	+	0.824754i
$383$	3.01959	+	1.34441i	0.154294	+	0.0686961i	0.482431	−	0.875934i	$-0.339754\pi$
$383$	3.01959	+	1.34441i	0.154294	+	0.0686961i	−0.328137	+	0.944630i	$0.606421\pi$
$384$	−0.695991	+	1.58606i	−0.0355171	+	0.0809385i
$385$	3.35421	+	15.7803i	0.170946	+	0.804240i
$386$	−1.77641	−	3.98988i	−0.0904169	−	0.203080i
$387$	0.748479	+	0.659533i	0.0380473	+	0.0335259i
$388$	1.78692	−	5.49958i	0.0907172	−	0.279199i
$389$	−26.2835	+	11.7022i	−1.33263	+	0.593324i	−0.944570	−	0.328310i	$-0.893521\pi$
$389$	−26.2835	+	11.7022i	−1.33263	+	0.593324i	−0.388058	+	0.921635i	$0.626854\pi$
$390$	−0.00961838	−	1.79309i	−0.000487046	−	0.0907967i
$391$	−5.10880	−	1.08591i	−0.258363	−	0.0549167i
$392$	−1.97510	+	4.43615i	−0.0997576	+	0.224059i
$393$	−18.5876	−	25.2972i	−0.937623	−	1.27608i
$394$	−14.3181	−	1.50489i	−0.721334	−	0.0758152i
$395$	9.38376	+	6.81770i	0.472148	+	0.343036i
$396$	−4.19991	+	13.4140i	−0.211053	+	0.674077i
$397$	3.19343	−	5.53119i	0.160274	−	0.277602i	−0.774693	−	0.632337i	$-0.782096\pi$
$397$	3.19343	−	5.53119i	0.160274	−	0.277602i	0.934967	+	0.354735i	$0.115429\pi$
$398$	6.84671	+	11.8589i	0.343195	+	0.594430i
$399$	9.33251	−	4.21523i	0.467210	−	0.211025i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	8.40212	+	25.8591i	0.419582	+	1.29134i	0.908088	+	0.418779i	$0.137542\pi$
$401$	8.40212	+	25.8591i	0.419582	+	1.29134i	−0.488506	+	0.872560i	$0.662458\pi$
$402$	1.00595	−	4.86069i	0.0501723	−	0.242429i
$403$	1.21933	−	5.63362i	0.0607393	−	0.280631i
$404$		−	5.84808i		−	0.290953i
$405$	−7.88898	−	4.33174i	−0.392007	−	0.215246i
$406$	−20.2457	+	18.2293i	−1.00477	+	0.904703i
$407$	−7.54113	−	10.3795i	−0.373800	−	0.514491i
$408$	−8.68268	+	2.87276i	−0.429857	+	0.142223i
$409$	20.0478	+	11.5746i	0.991300	+	0.572327i	0.905663	−	0.423999i	$-0.139374\pi$
$409$	20.0478	+	11.5746i	0.991300	+	0.572327i	0.0856374	+	0.996326i	$0.472707\pi$
$410$	−7.94039	+	0.834568i	−0.392148	+	0.0412164i
$411$	18.4538	+	20.2752i	0.910257	+	1.00010i
$412$	−1.23433	+	11.7439i	−0.0608110	+	0.578578i
$413$	9.10797	+	8.20086i	0.448174	+	0.403538i
$414$	2.18382	−	2.00916i	0.107329	−	0.0987449i
$415$	−1.37962	+	6.49062i	−0.0677231	+	0.318612i
$416$	1.01263	−	0.215242i	0.0496485	−	0.0105531i
$417$	5.92111	+	27.1400i	0.289958	+	1.32905i
$418$	7.65127	+	2.48605i	0.374236	+	0.121597i
$419$	19.8273	+	6.44228i	0.968627	+	0.314726i	0.750262	−	0.661141i	$-0.229928\pi$
$419$	19.8273	+	6.44228i	0.968627	+	0.314726i	0.218365	+	0.975867i	$0.429928\pi$
$420$	−1.27123	−	5.82682i	−0.0620299	−	0.284320i
$421$	−32.9634	+	7.00658i	−1.60654	+	0.341480i	−0.921907	−	0.387411i	$-0.873369\pi$
$421$	−32.9634	+	7.00658i	−1.60654	+	0.341480i	−0.684629	+	0.728891i	$0.740036\pi$
$422$	−4.43153	+	20.8487i	−0.215723	+	1.01490i
$423$	12.5138	−	11.5129i	0.608442	−	0.559778i
$424$	−8.69032	−	7.82480i	−0.422039	−	0.380006i
$425$	0.551932	−	5.25128i	0.0267726	−	0.254724i
$426$	−12.3189	−	13.5348i	−0.596854	−	0.655765i
$427$	−6.49577	+	0.682732i	−0.314352	+	0.0330397i
$428$	4.69518	+	2.71076i	0.226950	+	0.131030i
$429$	7.97617	−	2.63900i	0.385093	−	0.127412i
$430$	−0.195458	−	0.269025i	−0.00942582	−	0.0129735i
$431$	7.88657	−	7.10110i	0.379883	−	0.342048i	−0.456964	−	0.889485i	$-0.651063\pi$
$431$	7.88657	−	7.10110i	0.379883	−	0.342048i	0.836847	+	0.547437i	$0.184396\pi$
$432$	1.52597	−	4.96703i	0.0734183	−	0.238976i
$433$		−	11.5612i		−	0.555598i	−0.960639	−	0.277799i	$-0.910395\pi$
$433$		−	11.5612i		−	0.555598i	0.960639	−	0.277799i	$-0.0896049\pi$
$434$	0.0711454	−	19.1711i	0.00341509	−	0.920241i
$435$	2.77730	−	13.4197i	0.133161	−	0.643426i
$436$	4.35524	+	13.4040i	0.208578	+	0.641937i
$437$	−1.13647	−	1.26218i	−0.0543648	−	0.0603782i
$438$	−7.27046	+	3.28386i	−0.347396	+	0.156909i
$439$	−6.04463	−	10.4696i	−0.288494	−	0.499687i	0.684956	−	0.728584i	$-0.259821\pi$
$439$	−6.04463	−	10.4696i	−0.288494	−	0.499687i	−0.973451	+	0.228897i	$0.926488\pi$
$440$	2.34268	−	4.05764i	0.111683	−	0.193441i
$441$	4.35283	−	13.9024i	0.207278	−	0.662019i
$442$	4.42238	+	3.21305i	0.210351	+	0.152829i
$443$	−17.4249	−	1.83143i	−0.827883	−	0.0870140i	−0.318898	−	0.947789i	$-0.603313\pi$
$443$	−17.4249	−	1.83143i	−0.827883	−	0.0870140i	−0.508985	+	0.860775i	$0.669979\pi$
$444$	2.80829	+	3.82200i	0.133276	+	0.181384i
$445$	−3.70083	+	8.31221i	−0.175436	+	0.394037i
$446$	13.5021	+	2.86996i	0.639342	+	0.135896i
$447$	0.219517	+	40.9231i	0.0103828	+	1.93559i
$448$	3.14556	−	1.40050i	0.148614	−	0.0661672i
$449$	−2.83819	+	8.73506i	−0.133943	+	0.412233i	−0.995424	−	0.0955561i	$-0.969537\pi$
$449$	−2.83819	+	8.73506i	−0.133943	+	0.412233i	0.861481	+	0.507789i	$0.169537\pi$
$450$	2.25084	+	1.98336i	0.106106	+	0.0934964i
$451$	−15.2154	−	34.1744i	−0.716466	−	1.60921i
$452$	−4.05036	−	19.0554i	−0.190513	−	0.896292i
$453$	12.6624	−	28.8557i	0.594929	−	1.35576i
$454$	−10.4190	−	4.63883i	−0.488987	−	0.217711i
$455$	−2.38522	+	2.64905i	−0.111821	+	0.124189i
$456$	−2.83335	−	0.903839i	−0.132684	−	0.0423261i
$457$	6.02587	−	8.29389i	0.281878	−	0.387972i	−0.644477	−	0.764624i	$-0.722925\pi$
$457$	6.02587	−	8.29389i	0.281878	−	0.387972i	0.926355	+	0.376652i	$0.122925\pi$
$458$	−0.723255	−	6.88131i	−0.0337955	−	0.321542i
$459$	24.8819	−	11.5614i	1.16139	−	0.539641i
$460$	−0.856632	+	0.494577i	−0.0399407	+	0.0230598i
$461$	2.30103	−	1.67180i	0.107170	−	0.0778634i	−0.532910	−	0.846172i	$-0.678901\pi$
$461$	2.30103	−	1.67180i	0.107170	−	0.0778634i	0.640079	+	0.768309i	$0.278901\pi$
$462$	24.1240	−	14.1011i	1.12235	−	0.656042i
$463$	−20.7720	+	6.74922i	−0.965355	+	0.313663i	−0.748940	−	0.662638i	$-0.769437\pi$
$463$	−20.7720	+	6.74922i	−0.965355	+	0.313663i	−0.216416	+	0.976301i	$0.569437\pi$
$464$	7.91206			0.367308
$465$	5.68128	+	7.79250i	0.263463	+	0.361368i
$466$	−8.60065			−0.398418
$467$	14.8399	−	4.82179i	0.686711	−	0.223126i	0.0551797	−	0.998476i	$-0.482427\pi$
$467$	14.8399	−	4.82179i	0.686711	−	0.223126i	0.631531	+	0.775351i	$0.282427\pi$
$468$	−2.94330	+	0.991369i	−0.136054	+	0.0458260i
$469$	−7.98308	+	5.80005i	−0.368624	+	0.267821i
$470$	−4.90869	+	2.83403i	−0.226421	+	0.130724i
$471$	−28.1937	+	31.6521i	−1.29910	+	1.45845i
$472$	−0.372061	−	3.53993i	−0.0171255	−	0.162938i
$473$	0.915792	−	1.26048i	0.0421081	−	0.0579569i
$474$	6.10557	−	19.1397i	0.280438	−	0.879118i
$475$	1.14893	−	1.27602i	0.0527167	−	0.0585478i
$476$	16.6092	+	7.39490i	0.761282	+	0.338945i
$477$	28.6015	+	20.3150i	1.30957	+	0.930159i
$478$	−1.45702	−	6.85474i	−0.0666425	−	0.313528i
$479$	−1.78766	−	4.01516i	−0.0816805	−	0.183457i	0.868088	−	0.496410i	$-0.165349\pi$
$479$	−1.78766	−	4.01516i	−0.0816805	−	0.183457i	−0.949769	+	0.312952i	$0.898682\pi$
$480$	−0.857967	+	1.50462i	−0.0391607	+	0.0686764i
$481$	0.876002	−	2.69606i	0.0399423	−	0.122930i
$482$	15.7364	−	7.00630i	0.716774	−	0.319128i
$483$	−5.89911	+	0.0316436i	−0.268419	+	0.00143983i
$484$	10.7133	+	2.27718i	0.486967	+	0.103508i
$485$	2.35200	−	5.28267i	0.106799	−	0.239874i
$486$	−2.83095	+	15.3292i	−0.128415	+	0.695349i
$487$	−26.6767	−	2.80383i	−1.20884	−	0.127054i	−0.521408	−	0.853307i	$-0.674593\pi$
$487$	−26.6767	−	2.80383i	−1.20884	−	0.127054i	−0.687427	+	0.726254i	$0.741260\pi$
$488$	1.53464	+	1.11498i	0.0694697	+	0.0504727i
$489$	−0.345601	+	3.46697i	−0.0156286	+	0.156782i
$490$	−2.42798	+	4.20539i	−0.109685	+	0.189980i
$491$	6.35296	+	11.0037i	0.286705	+	0.496588i	0.973021	−	0.230716i	$-0.0741067\pi$
$491$	6.35296	+	11.0037i	0.286705	+	0.496588i	−0.686316	+	0.727303i	$0.740773\pi$
$492$	5.69241	+	12.6030i	0.256634	+	0.568186i
$493$	27.9545	+	31.0466i	1.25901	+	1.39827i
$494$	0.549306	+	1.69059i	0.0247145	+	0.0760633i
$495$	−5.57904	+	12.9015i	−0.250759	+	0.579878i
$496$	−3.74089	+	4.12380i	−0.167971	+	0.185164i
$497$			36.3828i			1.63199i
$498$	11.4237	−	1.26267i	0.511907	−	0.0565814i
$499$	−2.54376	+	2.29041i	−0.113874	+	0.102533i	−0.724101	−	0.689694i	$-0.757745\pi$
$499$	−2.54376	+	2.29041i	−0.113874	+	0.102533i	0.610227	+	0.792227i	$0.291078\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$	5.52795	+	16.7078i	0.246971	+	0.746449i
$502$	−9.04211	−	5.22047i	−0.403569	−	0.233001i
$503$	3.86680	−	0.406417i	0.172412	−	0.0181212i	−0.0179291	−	0.999839i	$-0.505707\pi$
$503$	3.86680	−	0.406417i	0.172412	−	0.0181212i	0.190341	+	0.981718i	$0.439041\pi$
$504$	−8.88990	+	5.26055i	−0.395988	+	0.234323i
$505$	0.611291	−	5.81604i	0.0272021	−	0.258810i
$506$	−3.44413	−	3.10111i	−0.153110	−	0.137861i
$507$	−16.7795	−	12.0540i	−0.745202	−	0.535337i
$508$	0.824635	−	3.87960i	0.0365873	−	0.172130i
$509$	−18.9269	+	4.02304i	−0.838922	+	0.178318i	−0.607285	−	0.794484i	$-0.707741\pi$
$509$	−18.9269	+	4.02304i	−0.838922	+	0.178318i	−0.231637	+	0.972802i	$0.574408\pi$
$510$	−8.93540	+	1.94943i	−0.395666	+	0.0863223i
$511$	15.0831	+	4.90080i	0.667237	+	0.216799i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	8.75582	+	1.71433i	0.386579	+	0.0756895i
$514$	−12.6514	+	2.68914i	−0.558030	+	0.118613i
$515$	−2.45513	+	11.5505i	−0.108186	+	0.508976i
$516$	−0.336039	+	0.467774i	−0.0147933	+	0.0205926i
$517$	−19.7357	−	17.7701i	−0.867973	−	0.781527i
$518$	0.985547	−	9.37686i	0.0433025	−	0.411995i
$519$	−23.3442	+	21.2470i	−1.02470	+	0.932642i
$520$	1.02959	−	0.108214i	0.0451503	−	0.00474549i
$521$	16.3405	+	9.43419i	0.715890	+	0.413319i	0.813238	−	0.581931i	$-0.197703\pi$
$521$	16.3405	+	9.43419i	0.715890	+	0.413319i	−0.0973482	+	0.995250i	$0.531036\pi$
$522$	−23.5782	+	2.73421i	−1.03199	+	0.119673i
$523$	−4.68155	−	6.44359i	−0.204710	−	0.281759i	0.694302	−	0.719684i	$-0.255713\pi$
$523$	−4.68155	−	6.44359i	−0.204710	−	0.281759i	−0.899011	+	0.437925i	$0.855713\pi$
$524$	13.4688	−	12.1274i	0.588389	−	0.529788i
$525$	−0.655202	−	5.92778i	−0.0285954	−	0.258710i
$526$		−	3.71667i		−	0.162054i
$527$	−29.3987	−	0.109101i	−1.28063	−	0.00475251i
$528$	−7.94688	−	1.64466i	−0.345844	−	0.0715746i
$529$	−6.80504	−	20.9438i	−0.295871	−	0.910598i
$530$	−7.82480	−	8.69032i	−0.339888	−	0.377484i
$531$	2.33206	+	10.4205i	0.101203	+	0.452212i
$532$	2.95612	+	5.12015i	0.128164	+	0.221987i
$533$	4.13281	−	7.15824i	0.179012	−	0.310058i
$534$	15.6819	+	1.56324i	0.678624	+	0.0676479i
$535$	4.38610	+	3.18669i	0.189628	+	0.137773i
$536$	2.85009	+	0.299557i	0.123105	+	0.0129389i
$537$	20.2031	−	14.8446i	0.871827	−	0.640593i
$538$	−10.6645	+	23.9528i	−0.459779	+	1.03268i
$539$	−22.2548	−	4.73040i	−0.958581	−	0.203753i
$540$	2.03681	−	4.78032i	0.0876502	−	0.205712i
$541$	24.0868	−	10.7242i	1.03557	−	0.461067i	0.182692	−	0.983170i	$-0.441519\pi$
$541$	24.0868	−	10.7242i	1.03557	−	0.461067i	0.852883	+	0.522103i	$0.174852\pi$
$542$	3.16451	−	9.73936i	0.135927	−	0.418341i
$543$	10.9913	+	6.26747i	0.471682	+	0.268963i
$544$	−2.14765	−	4.82371i	−0.0920798	−	0.206815i
$545$	2.93027	+	13.7859i	0.125519	+	0.590521i
$546$	5.65376	+	2.48096i	0.241958	+	0.106175i
$547$	−13.9964	−	6.23162i	−0.598444	−	0.266445i	0.0850778	−	0.996374i	$-0.472886\pi$
$547$	−13.9964	−	6.23162i	−0.598444	−	0.266445i	−0.683522	+	0.729930i	$0.739553\pi$
$548$	−10.5913	+	11.7629i	−0.452439	+	0.502485i
$549$	−4.95857	−	2.79234i	−0.211626	−	0.119174i
$550$	2.75399	−	3.79054i	0.117430	−	0.161629i
$551$	1.42007	+	13.5110i	0.0604968	+	0.575589i
$552$	1.27933	+	1.13955i	0.0544521	+	0.0485025i
$553$	−34.5874	+	19.9691i	−1.47081	+	0.849171i
$554$	−4.37487	+	3.17853i	−0.185871	+	0.135043i
$555$	2.39340	+	4.09461i	0.101594	+	0.173806i
$556$	−15.2529	+	4.95597i	−0.646867	+	0.210180i
$557$	12.8110			0.542818			0.271409	−	0.962464i	$-0.412510\pi$
$557$	12.8110			0.542818			0.271409	+	0.962464i	$0.412510\pi$
$558$	9.72288	−	13.5818i	0.411603	−	0.574964i
$559$	0.344257			0.0145605
$560$	3.27472	−	1.06402i	0.138382	−	0.0449632i
$561$	−21.6239	−	36.9940i	−0.912963	−	1.56189i
$562$	3.30369	−	2.40027i	0.139358	−	0.101249i
$563$	17.6058	−	10.1647i	0.741995	−	0.428391i	−0.0807995	−	0.996730i	$-0.525747\pi$
$563$	17.6058	−	10.1647i	0.741995	−	0.428391i	0.822794	+	0.568340i	$0.192414\pi$
$564$	7.33087	+	6.52988i	0.308685	+	0.274958i
$565$	−2.03633	−	19.3744i	−0.0856692	−	0.815088i
$566$	5.83142	−	8.02626i	0.245113	−	0.337369i
$567$	24.6743	−	18.7487i	1.03622	−	0.787372i
$568$	7.07032	−	7.85238i	0.296664	−	0.329479i
$569$	37.3367	+	16.6234i	1.56523	+	0.696887i	0.992431	−	0.122806i	$-0.0391891\pi$
$569$	37.3367	+	16.6234i	1.56523	+	0.696887i	0.572803	+	0.819693i	$0.305856\pi$
$570$	−2.72336	−	1.19505i	−0.114069	−	0.0500553i
$571$	5.33557	+	25.1019i	0.223287	+	1.05048i	0.936807	+	0.349847i	$0.113766\pi$
$571$	5.33557	+	25.1019i	0.223287	+	1.05048i	−0.713520	+	0.700635i	$0.752900\pi$
$572$	1.97290	+	4.43120i	0.0824910	+	0.185278i
$573$	32.6370	+	18.6103i	1.36343	+	0.777456i
$574$	8.49529	−	26.1458i	0.354586	−	1.09131i
$575$	−0.903636	+	0.402325i	−0.0376842	+	0.0167781i
$576$	2.94097	+	0.592219i	0.122540	+	0.0246758i
$577$	−22.7188	−	4.82902i	−0.945795	−	0.201035i	−0.290899	−	0.956754i	$-0.593954\pi$
$577$	−22.7188	−	4.82902i	−0.945795	−	0.201035i	−0.654896	+	0.755719i	$0.727288\pi$
$578$	4.42552	−	9.93987i	0.184077	−	0.413444i
$579$	−6.09602	+	4.47917i	−0.253342	+	0.186148i
$580$	7.86872	+	0.827036i	0.326731	+	0.0343408i
$581$	−18.4845	−	13.4298i	−0.766867	−	0.557161i
$582$	−9.96637	−	0.993486i	−0.413119	−	0.0411813i
$583$	27.3953	−	47.4500i	1.13460	−	1.96518i
$584$	−2.30296	−	3.98884i	−0.0952971	−	0.165059i
$585$	−3.03080	+	0.678279i	−0.125308	+	0.0280434i
$586$	18.1642	+	20.1733i	0.750355	+	0.833353i
$587$	−10.9395	−	33.6682i	−0.451520	−	1.38963i	−0.875173	−	0.483810i	$-0.839252\pi$
$587$	−10.9395	−	33.6682i	−0.451520	−	1.38963i	0.423653	−	0.905824i	$-0.360748\pi$
$588$	8.23625	+	1.70454i	0.339657	+	0.0702942i
$589$	−7.71342	−	5.64798i	−0.317826	−	0.232721i
$590$		−	3.55943i		−	0.146539i
$591$	2.73953	+	24.7853i	0.112689	+	1.01953i
$592$	−2.03492	+	1.83225i	−0.0836348	+	0.0753051i
$593$	−0.441382	−	0.607510i	−0.0181254	−	0.0249475i	0.799858	−	0.600189i	$-0.204908\pi$
$593$	−0.441382	−	0.607510i	−0.0181254	−	0.0249475i	−0.817984	+	0.575242i	$0.804908\pi$
$594$	24.2503	+	2.15489i	0.995002	+	0.0884162i
$595$	15.7453	+	9.09053i	0.645493	+	0.372675i
$596$	−23.4979	+	2.46972i	−0.962509	+	0.101164i
$597$	17.5403	−	15.9646i	0.717877	−	0.653386i
$598$	0.107040	−	1.01842i	0.00437719	−	0.0416462i
$599$	5.23864	+	4.71689i	0.214045	+	0.192727i	0.769178	−	0.639035i	$-0.220666\pi$
$599$	5.23864	+	4.71689i	0.214045	+	0.192727i	−0.555133	+	0.831762i	$0.687333\pi$
$600$	−1.01054	+	1.40670i	−0.0412552	+	0.0574283i
$601$	8.32833	−	39.1817i	0.339720	−	1.59826i	−0.394203	−	0.919023i	$-0.628979\pi$
$601$	8.32833	−	39.1817i	0.339720	−	1.59826i	0.733923	−	0.679233i	$-0.237687\pi$
$602$	1.11997	−	0.238058i	0.0456467	−	0.00970251i
$603$	−8.59688	+	0.0922322i	−0.350092	+	0.00375599i
$604$	17.3028	+	5.62203i	0.704042	+	0.228757i
$605$	10.4166	+	3.38454i	0.423493	+	0.137601i
$606$	−9.89638	+	2.15909i	−0.402013	+	0.0877070i
$607$	4.71858	−	1.00297i	0.191521	−	0.0407091i	−0.111152	−	0.993803i	$-0.535454\pi$
$607$	4.71858	−	1.00297i	0.191521	−	0.0407091i	0.302674	+	0.953094i	$0.402121\pi$
$608$	0.356996	−	1.67953i	0.0144781	−	0.0681140i
$609$	38.3230	+	27.5304i	1.55293	+	1.11559i
$610$	1.40968	+	1.26928i	0.0570763	+	0.0513918i
$611$	0.613363	−	5.83576i	0.0248140	−	0.236090i
$612$	8.06702	+	13.6326i	0.326090	+	0.551066i
$613$	36.3747	−	3.82314i	1.46916	−	0.154415i	0.664116	−	0.747629i	$-0.268808\pi$
$613$	36.3747	−	3.82314i	1.46916	−	0.154415i	0.805045	+	0.593214i	$0.202141\pi$
$614$	9.96062	+	5.75077i	0.401978	+	0.232082i
$615$	4.34386	+	13.1290i	0.175161	+	0.529411i
$616$	9.48266	+	13.0518i	0.382067	+	0.525871i
$617$	33.9746	−	30.5909i	1.36777	−	1.23154i	0.422040	−	0.906577i	$-0.361314\pi$
$617$	33.9746	−	30.5909i	1.36777	−	1.23154i	0.945726	−	0.324964i	$-0.105352\pi$
$618$	20.3292	−	2.24700i	0.817760	−	0.0903876i
$619$		−	40.7171i		−	1.63656i	−0.574820	−	0.818280i	$-0.694928\pi$
$619$		−	40.7171i		−	1.63656i	0.574820	−	0.818280i	$-0.305072\pi$
$620$	−4.15145	+	3.71018i	−0.166726	+	0.149004i
$621$	−4.20625	−	2.95379i	−0.168791	−	0.118532i
$622$	−6.81898	−	20.9867i	−0.273416	−	0.841489i
$623$	−20.9636	−	23.2824i	−0.839889	−	0.932791i
$624$	−0.738103	−	1.63416i	−0.0295478	−	0.0654187i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.16219	−	3.74503i	0.0864186	−	0.149681i
$627$	1.38218	−	13.8657i	0.0551991	−	0.553741i
$628$	−19.7988	−	14.3847i	−0.790059	−	0.574011i
$629$	−14.3794	−	1.51133i	−0.573343	−	0.0602607i
$630$	−9.39108	+	4.30248i	−0.374149	+	0.171415i
$631$	−14.6255	+	32.8494i	−0.582232	+	1.30772i	0.346877	+	0.937911i	$0.387242\pi$
$631$	−14.6255	+	32.8494i	−0.582232	+	1.30772i	−0.929109	+	0.369805i	$0.879425\pi$
$632$	11.3455	+	2.41156i	0.451300	+	0.0959267i
$633$	36.9172	−	0.198029i	1.46733	−	0.00787094i
$634$	−17.1696	+	7.64438i	−0.681890	+	0.303597i
$635$	1.22565	−	3.77215i	0.0486383	−	0.149693i
$636$	−10.0331	+	17.5950i	−0.397836	+	0.697689i
$637$	−2.04474	−	4.59255i	−0.0810154	−	0.181963i
$638$	7.70747	+	36.2608i	0.305142	+	1.43558i
$639$	−18.3562	+	25.8437i	−0.726159	+	1.02236i
$640$	−0.913545	−	0.406737i	−0.0361111	−	0.0160777i
$641$	18.1752	−	20.1856i	0.717876	−	0.797282i	−0.268238	−	0.963353i	$-0.586441\pi$
$641$	18.1752	−	20.1856i	0.717876	−	0.797282i	0.986114	+	0.166071i	$0.0531080\pi$
$642$	2.85383	−	8.94619i	0.112632	−	0.353078i
$643$	−10.8641	+	14.9531i	−0.428437	+	0.589692i	−0.967594	−	0.252513i	$-0.918743\pi$
$643$	−10.8641	+	14.9531i	−0.428437	+	0.589692i	0.539157	+	0.842205i	$0.318743\pi$
$644$	−0.356014	−	3.38724i	−0.0140289	−	0.133476i
$645$	−0.383094	+	0.430086i	−0.0150843	+	0.0169346i
$646$	7.85173	−	4.53320i	0.308922	−	0.178356i
$647$	29.9293	−	21.7449i	1.17664	−	0.854881i	0.184854	−	0.982766i	$-0.440819\pi$
$647$	29.9293	−	21.7449i	1.17664	−	0.854881i	0.991789	+	0.127885i	$0.0408189\pi$
$648$	−8.96882	−	0.748505i	−0.352329	−	0.0294041i
$649$	15.8610	−	5.15354i	0.622597	−	0.202294i
$650$	1.03526			0.0406061
$651$	−32.4684	+	6.95749i	−1.27254	+	0.272686i
$652$	−2.01158			−0.0787794
$653$	−15.3928	+	5.00144i	−0.602368	+	0.195721i	−0.594296	−	0.804246i	$-0.702569\pi$
$653$	−15.3928	+	5.00144i	−0.602368	+	0.195721i	−0.00807185	+	0.999967i	$0.502569\pi$
$654$	21.0750	−	12.3188i	0.824097	−	0.481705i
$655$	14.6627	−	10.6531i	0.572920	−	0.416250i
$656$	−6.91445	+	3.99206i	−0.269964	+	0.155864i
$657$	8.24133	+	11.0910i	0.321525	+	0.432702i
$658$	−2.04004	−	19.4097i	−0.0795289	−	0.756667i
$659$	−28.7727	+	39.6023i	−1.12083	+	1.54269i	−0.316408	+	0.948623i	$0.602477\pi$
$659$	−28.7727	+	39.6023i	−1.12083	+	1.54269i	−0.804419	+	0.594063i	$0.797523\pi$
$660$	−7.73144	−	2.46632i	−0.300946	−	0.0960016i
$661$	18.8464	−	20.9311i	0.733042	−	0.814125i	−0.255222	−	0.966882i	$-0.582149\pi$
$661$	18.8464	−	20.9311i	0.733042	−	0.814125i	0.988264	+	0.152757i	$0.0488152\pi$
$662$	−23.9850	−	10.6788i	−0.932202	−	0.415043i
$663$	3.80454	−	8.67001i	0.147756	−	0.336715i
$664$	1.37962	+	6.49062i	0.0535398	+	0.251885i
$665$	2.40473	+	5.40110i	0.0932513	+	0.209446i
$666$	5.43095	−	6.16339i	0.210445	−	0.238826i
$667$	2.41844	−	7.44320i	0.0936425	−	0.288202i
$668$	−9.28210	+	4.13266i	−0.359135	+	0.159897i
$669$	−0.128248	−	23.9084i	−0.00495835	−	0.924353i
$670$	2.80317	+	0.595831i	0.108296	+	0.0230190i
$671$	−3.61496	+	8.11934i	−0.139554	+	0.313444i
$672$	−3.53131	−	4.80601i	−0.136223	−	0.185396i
$673$	13.3377	+	1.40184i	0.514129	+	0.0540371i	0.358041	−	0.933706i	$-0.383445\pi$
$673$	13.3377	+	1.40184i	0.514129	+	0.0540371i	0.156088	+	0.987743i	$0.450112\pi$
$674$	3.82292	+	2.77751i	0.147253	+	0.106986i
$675$	2.52533	−	4.54122i	0.0971999	−	0.174792i
$676$	5.96412	−	10.3302i	0.229389	−	0.397314i
$677$	−0.542697	−	0.939979i	−0.0208576	−	0.0361263i	0.855408	−	0.517954i	$-0.173306\pi$
$677$	−0.542697	−	0.939979i	−0.0208576	−	0.0361263i	−0.876266	+	0.481828i	$0.839973\pi$
$678$	−30.7511	+	13.8894i	−1.18099	+	0.533419i
$679$	13.3230	+	14.7967i	0.511291	+	0.567846i
$680$	−1.63167	−	5.02177i	−0.0625718	−	0.192576i
$681$	−4.00339	+	19.3441i	−0.153410	+	0.741268i
$682$	−22.5434	−	13.1272i	−0.863233	−	0.502668i
$683$			10.7091i			0.409773i	0.978786	+	0.204887i	$0.0656825\pi$
$683$			10.7091i			0.409773i	−0.978786	+	0.204887i	$0.934317\pi$
$684$	−0.483453	+	5.12842i	−0.0184853	+	0.196090i
$685$	−11.7629	+	10.5913i	−0.449436	+	0.404674i
$686$	4.33929	+	5.97252i	0.165675	+	0.228032i
$687$	−11.3778	+	3.76448i	−0.434092	+	0.143624i
$688$	−0.287982	−	0.166267i	−0.0109792	−	0.00633885i
$689$	12.0400	−	1.26545i	0.458686	−	0.0482098i
$690$	1.15321	+	1.26704i	0.0439020	+	0.0482352i
$691$	5.26306	−	50.0746i	0.200216	−	1.90493i	−0.186047	−	0.982541i	$-0.559568\pi$
$691$	5.26306	−	50.0746i	0.200216	−	1.90493i	0.386263	−	0.922389i	$-0.373766\pi$
$692$	−13.5434	−	12.1945i	−0.514842	−	0.463566i
$693$	−32.7690	−	35.6177i	−1.24479	−	1.35300i
$694$	2.81809	−	13.2581i	0.106973	−	0.503270i
$695$	−15.6874	+	3.33446i	−0.595056	+	0.126483i
$696$	−2.92110	−	13.3892i	−0.110724	−	0.507515i
$697$	−40.0945	−	13.0275i	−1.51869	−	0.493451i
$698$	−11.1535	−	3.62398i	−0.422165	−	0.137170i
$699$	3.17533	+	14.5544i	0.120102	+	0.550498i
$700$	3.36801	−	0.715892i	0.127299	−	0.0270582i
$701$	3.97108	−	18.6825i	0.149986	−	0.705627i	−0.837309	−	0.546729i	$-0.815873\pi$
$701$	3.97108	−	18.6825i	0.149986	−	0.705627i	0.987295	−	0.158898i	$-0.0507940\pi$
$702$	2.76429	+	4.61477i	0.104332	+	0.174173i
$703$	−3.49407	−	3.14608i	−0.131781	−	0.118657i
$704$	0.489754	−	4.65969i	0.0184583	−	0.175619i
$705$	6.60815	+	7.26039i	0.248877	+	0.273442i
$706$	11.8079	−	1.24106i	0.444395	−	0.0467078i
$707$	17.4386	+	10.0682i	0.655847	+	0.378653i
$708$	−5.85306	+	1.93655i	−0.219971	+	0.0727799i
$709$	2.39721	+	3.29947i	0.0900290	+	0.123914i	0.851656	−	0.524102i	$-0.175599\pi$
$709$	2.39721	+	3.29947i	0.0900290	+	0.123914i	−0.761627	+	0.648016i	$0.775599\pi$
$710$	7.85238	−	7.07032i	0.294695	−	0.265344i
$711$	−34.6433	−	3.26580i	−1.29923	−	0.122477i
$712$			9.09885i			0.340994i
$713$	2.73597	+	4.77971i	0.102463	+	0.179002i
$714$	6.38193	−	30.8370i	0.238838	−	1.15405i
$715$	1.49890	+	4.61315i	0.0560558	+	0.172522i
$716$	9.68528	+	10.7566i	0.361956	+	0.401993i
$717$	−11.0620	+	4.99638i	−0.413117	+	0.186593i
$718$	−16.2848	−	28.2062i	−0.607745	−	1.05264i
$719$	−9.89179	+	17.1331i	−0.368902	+	0.638956i	−0.989394	−	0.145256i	$-0.953599\pi$
$719$	−9.89179	+	17.1331i	−0.368902	+	0.638956i	0.620493	+	0.784212i	$0.286933\pi$
$720$	2.86295	+	0.896389i	0.106696	+	0.0334064i
$721$	−32.8944	−	23.8992i	−1.22505	−	0.890053i
$722$	−15.9638	−	1.67786i	−0.594111	−	0.0624436i
$723$	−17.6662	−	24.0432i	−0.657013	−	0.894175i
$724$	−2.97122	+	6.67347i	−0.110425	+	0.248018i
$725$	7.73917	+	1.64501i	0.287425	+	0.0610942i
$726$	−0.101759	−	18.9702i	−0.00377662	−	0.704051i
$727$	−36.5797	+	16.2863i	−1.35667	+	0.604027i	−0.950772	−	0.309893i	$-0.899707\pi$
$727$	−36.5797	+	16.2863i	−1.35667	+	0.604027i	−0.405895	+	0.913920i	$0.633040\pi$
$728$	−1.10154	+	3.39018i	−0.0408257	+	0.125649i
$729$	26.9860	−	0.868831i	0.999482	−	0.0321789i
$730$	−1.87339	−	4.20771i	−0.0693374	−	0.155734i
$731$	−0.365060	−	1.71747i	−0.0135022	−	0.0635230i
$732$	1.32023	−	3.00862i	0.0487973	−	0.111202i
$733$	2.03775	+	0.907266i	0.0752661	+	0.0335106i	0.444024	−	0.896015i	$-0.353550\pi$
$733$	2.03775	+	0.907266i	0.0752661	+	0.0335106i	−0.368758	+	0.929525i	$0.620217\pi$
$734$	−6.90190	+	7.66533i	−0.254754	+	0.282933i
$735$	8.01295	+	2.55613i	0.295562	+	0.0942842i
$736$	−0.581410	+	0.800242i	−0.0214310	+	0.0294973i
$737$	1.40353	+	13.3537i	0.0516997	+	0.491890i
$738$	19.2257	−	14.2859i	0.707709	−	0.525872i
$739$	26.9167	−	15.5404i	0.990146	−	0.571661i	0.0848284	−	0.996396i	$-0.472966\pi$
$739$	26.9167	−	15.5404i	0.990146	−	0.571661i	0.905318	+	0.424734i	$0.139632\pi$
$740$	−2.21530	+	1.60951i	−0.0814360	+	0.0591667i
$741$	2.65809	−	1.55372i	0.0976474	−	0.0570773i
$742$	38.2946	−	12.4427i	1.40584	−	0.456785i
$743$	48.2816			1.77128			0.885639	−	0.464374i	$-0.153721\pi$
$743$	48.2816			1.77128			0.885639	+	0.464374i	$0.153721\pi$
$744$	8.35961	+	4.80801i	0.306478	+	0.176270i
$745$	−23.6273			−0.865637
$746$	21.1457	−	6.87066i	0.774200	−	0.251553i
$747$	−6.35432	−	18.8655i	−0.232492	−	0.690252i
$748$	20.0148	−	14.5416i	0.731814	−	0.531694i
$749$	−16.1667	+	9.33383i	−0.590717	+	0.341051i
$750$	−1.15205	+	1.29336i	−0.0420668	+	0.0472269i
$751$	5.30266	+	50.4515i	0.193497	+	1.84100i	0.473250	+	0.880928i	$0.343081\pi$
$751$	5.30266	+	50.4515i	0.193497	+	1.84100i	−0.279753	+	0.960072i	$0.590253\pi$
$752$	−3.33161	+	4.58556i	−0.121491	+	0.167218i
$753$	−5.49599	+	17.2288i	−0.200285	+	0.627854i
$754$	−5.48086	+	6.08712i	−0.199601	+	0.221680i
$755$	16.6204	+	7.39987i	0.604878	+	0.269309i
$756$	12.1843	+	13.1017i	0.443137	+	0.476505i
$757$	10.2228	+	48.0943i	0.371553	+	1.74802i	0.624959	+	0.780658i	$0.285116\pi$
$757$	10.2228	+	48.0943i	0.371553	+	1.74802i	−0.253406	+	0.967360i	$0.581551\pi$
$758$	−3.64230	−	8.18074i	−0.132294	−	0.297138i
$759$	−3.97628	+	6.97324i	−0.144330	+	0.253113i
$760$	0.530599	−	1.63302i	0.0192468	−	0.0592357i
$761$	−35.5096	+	15.8099i	−1.28722	+	0.573108i	−0.932265	−	0.361775i	$-0.882171\pi$
$761$	−35.5096	+	15.8099i	−1.28722	+	0.573108i	−0.354956	+	0.934883i	$0.615504\pi$
$762$	−6.86969	+	0.0368499i	−0.248863	+	0.00133493i
$763$	−47.4681	−	10.0897i	−1.71846	−	0.365270i
$764$	−8.82258	+	19.8158i	−0.319190	+	0.716912i
$765$	6.59783	+	14.4012i	0.238545	+	0.520675i
$766$	3.28725	+	0.345504i	0.118773	+	0.0124835i
$767$	2.98116	+	2.16594i	0.107644	+	0.0782076i
$768$	−0.171806	+	1.72351i	−0.00619952	+	0.0621918i
$769$	4.97345	−	8.61426i	0.179347	−	0.310638i	−0.762310	−	0.647212i	$-0.775935\pi$
$769$	4.97345	−	8.61426i	0.179347	−	0.310638i	0.941657	+	0.336574i	$0.109268\pi$
$770$	8.06643	+	13.9715i	0.290694	+	0.503497i
$771$	9.22155	+	20.4165i	0.332106	+	0.735282i
$772$	−2.92241	−	3.24566i	−0.105180	−	0.116814i
$773$	−5.60124	−	17.2389i	−0.201463	−	0.620039i	−0.999840	−	0.0178811i	$-0.994308\pi$
$773$	−5.60124	−	17.2389i	−0.201463	−	0.620039i	0.798377	−	0.602157i	$-0.205692\pi$
$774$	0.915653	+	0.395960i	0.0329125	+	0.0142325i
$775$	−4.51653	+	3.25591i	−0.162239	+	0.116956i
$776$		−	5.78260i		−	0.207583i
$777$	−16.2318	+	1.79411i	−0.582313	+	0.0643634i
$778$	−21.3810	+	19.2515i	−0.766544	+	0.690200i
$779$	−8.05805	−	11.0910i	−0.288710	−	0.397375i
$780$	−0.563244	−	1.70236i	−0.0201674	−	0.0609543i
$781$	42.8748	+	24.7538i	1.53418	+	0.885759i
$782$	−5.19432	+	0.545945i	−0.185748	+	0.0195229i
$783$	13.3319	+	38.8906i	0.476444	+	1.38984i
$784$	−0.507587	+	4.82936i	−0.0181281	+	0.172477i
$785$	−18.1867	−	16.3754i	−0.649113	−	0.584464i
$786$	−25.4952	−	18.3152i	−0.909383	−	0.653281i
$787$	−9.11705	+	42.8923i	−0.324988	+	1.52895i	0.447714	+	0.894177i	$0.352238\pi$
$787$	−9.11705	+	42.8923i	−0.324988	+	1.52895i	−0.772702	+	0.634770i	$0.781095\pi$
$788$	−14.0823	+	2.99329i	−0.501662	+	0.106632i
$789$	−6.28951	+	1.37218i	−0.223913	+	0.0488509i
$790$	11.0313	+	3.58428i	0.392475	+	0.127523i
$791$	63.7953	+	20.7284i	2.26830	+	0.737016i
$792$	0.150793	+	14.0553i	0.00535820	+	0.499432i
$793$	−1.92088	+	0.408296i	−0.0682124	+	0.0144990i
$794$	1.32790	−	6.24730i	0.0471255	−	0.221708i
$795$	−11.8173	+	16.4499i	−0.419115	+	0.583419i
$796$	10.1762	+	9.16269i	0.360686	+	0.324763i
$797$	−1.43943	+	13.6952i	−0.0509871	+	0.485110i	0.938996	+	0.343927i	$0.111757\pi$
$797$	−1.43943	+	13.6952i	−0.0509871	+	0.485110i	−0.989984	+	0.141183i	$0.954909\pi$
$798$	7.57317	−	6.89282i	0.268087	−	0.244003i
$799$	−29.7646	+	3.12839i	−1.05300	+	0.110674i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	−3.14433	−	27.1148i	−0.111100	−	0.958056i
$802$	15.9818	+	21.9970i	0.564336	+	0.776742i
$803$	16.0373	−	14.4401i	0.565946	−	0.509580i
$804$	−0.545320	−	4.93365i	−0.0192319	−	0.173996i
$805$		−	3.40590i		−	0.120042i
$806$	−0.581231	−	5.73469i	−0.0204730	−	0.201996i
$807$	44.4714	+	9.20364i	1.56547	+	0.323983i
$808$	−1.80716	−	5.56185i	−0.0635755	−	0.195665i
$809$	−12.5366	−	13.9233i	−0.440765	−	0.489519i	0.481299	−	0.876556i	$-0.340165\pi$
$809$	−12.5366	−	13.9233i	−0.440765	−	0.489519i	−0.922064	+	0.387038i	$0.873498\pi$
$810$	−8.84145	−	1.68190i	−0.310657	−	0.0590960i
$811$	−2.44333	−	4.23197i	−0.0857969	−	0.148605i	0.819934	−	0.572459i	$-0.194010\pi$
$811$	−2.44333	−	4.23197i	−0.0857969	−	0.148605i	−0.905731	+	0.423854i	$0.860677\pi$
$812$	−13.6216	+	23.5933i	−0.478025	+	0.827963i
$813$	−17.6497	−	1.75939i	−0.619002	−	0.0617045i
$814$	−10.3795	−	7.54113i	−0.363800	−	0.264316i
$815$	−2.00056	−	0.210267i	−0.0700765	−	0.00736533i
$816$	−7.36999	+	5.41525i	−0.258001	+	0.189572i
$817$	0.232237	−	0.521614i	0.00812496	−	0.0182490i
$818$	22.6433	+	4.81299i	0.791706	+	0.168282i
$819$	2.11105	−	10.4835i	0.0737661	−	0.366323i
$820$	−7.29386	+	3.24744i	−0.254713	+	0.113405i
$821$	−3.97314	+	12.2281i	−0.138663	+	0.426762i	−0.996142	−	0.0877577i	$-0.972030\pi$
$821$	−3.97314	+	12.2281i	−0.138663	+	0.426762i	0.857478	+	0.514520i	$0.172030\pi$
$822$	23.8159	+	13.5803i	0.830676	+	0.473668i
$823$	−0.571113	−	1.28274i	−0.0199078	−	0.0447135i	0.903318	−	0.428972i	$-0.141124\pi$
$823$	−0.571113	−	1.28274i	−0.0199078	−	0.0447135i	−0.923226	+	0.384258i	$0.874457\pi$
$824$	2.45513	+	11.5505i	0.0855287	+	0.402381i
$825$	−7.43128	−	3.26097i	−0.258724	−	0.113532i
$826$	11.1964	+	4.98496i	0.389573	+	0.173449i
$827$	−35.2281	+	39.1248i	−1.22500	+	1.36050i	−0.313297	+	0.949655i	$0.601434\pi$
$827$	−35.2281	+	39.1248i	−1.22500	+	1.36050i	−0.911704	+	0.410847i	$0.865233\pi$
$828$	1.45607	−	2.58566i	0.0506021	−	0.0898581i
$829$	24.8467	−	34.1985i	0.862962	−	1.18776i	−0.117894	−	0.993026i	$-0.537614\pi$
$829$	24.8467	−	34.1985i	0.862962	−	1.18776i	0.980855	−	0.194738i	$-0.0623858\pi$
$830$	0.693612	+	6.59927i	0.0240756	+	0.229064i
$831$	6.99404	+	6.22986i	0.242621	+	0.216111i
$832$	0.896559	−	0.517629i	0.0310826	−	0.0179455i
$833$	−20.7436	+	15.0711i	−0.718723	+	0.522183i
$834$	14.0180	+	23.9819i	0.485405	+	0.830426i
$835$	−9.66323	+	3.13977i	−0.334410	+	0.108656i
$836$	8.04502			0.278243
$837$	−26.5734	−	11.4392i	−0.918511	−	0.395395i
$838$	20.8477			0.720170
$839$	−22.8744	+	7.43234i	−0.789712	+	0.256593i	−0.675981	−	0.736919i	$-0.736280\pi$
$839$	−22.8744	+	7.43234i	−0.789712	+	0.256593i	−0.113731	+	0.993512i	$0.536280\pi$
$840$	−3.00960	−	5.14880i	−0.103841	−	0.177651i
$841$	−27.1836	+	19.7500i	−0.937365	+	0.681036i
$842$	−29.1849	+	16.8499i	−1.00578	+	0.580686i
$843$	−5.28156	−	4.70448i	−0.181907	−	0.162031i
$844$	2.22797	+	21.1977i	0.0766898	+	0.729655i
$845$	7.01125	−	9.65015i	0.241194	−	0.331975i
$846$	8.34363	−	14.8164i	0.286860	−	0.509400i
$847$	−25.2346	+	28.0259i	−0.867073	+	0.962982i
$848$	−10.6830	−	4.75637i	−0.366855	−	0.163334i
$849$	−15.7353	−	6.90492i	−0.540035	−	0.236976i
$850$	−1.09782	−	5.16482i	−0.0376548	−	0.177152i
$851$	1.10167	+	2.47439i	0.0377647	+	0.0848210i
$852$	−15.8985	−	9.06564i	−0.544673	−	0.310584i
$853$	−15.8609	+	48.8149i	−0.543068	+	1.67139i	0.182472	+	0.983211i	$0.441590\pi$
$853$	−15.8609	+	48.8149i	−0.543068	+	1.67139i	−0.725540	+	0.688180i	$0.758410\pi$
$854$	−5.96686	+	2.65662i	−0.204182	+	0.0909076i
$855$	−1.01687	+	5.04980i	−0.0347763	+	0.172699i
$856$	5.30305	+	1.12720i	0.181255	+	0.0385268i
$857$	−19.6264	+	44.0816i	−0.670425	+	1.50580i	0.182192	+	0.983263i	$0.441681\pi$
$857$	−19.6264	+	44.0816i	−0.670425	+	1.50580i	−0.852617	+	0.522536i	$0.824986\pi$
$858$	6.77029	−	4.97461i	0.231134	−	0.169830i
$859$	14.4728	+	1.52115i	0.493806	+	0.0519011i	0.348159	−	0.937436i	$-0.386807\pi$
$859$	14.4728	+	1.52115i	0.493806	+	0.0519011i	0.145647	+	0.989337i	$0.453474\pi$
$860$	−0.269025	−	0.195458i	−0.00917367	−	0.00666506i
$861$	−47.3816	−	4.72318i	−1.61476	−	0.160965i
$862$	5.30622	−	9.19064i	0.180730	−	0.313034i
$863$	−5.95000	−	10.3057i	−0.202540	−	0.350810i	0.746806	−	0.665042i	$-0.231586\pi$
$863$	−5.95000	−	10.3057i	−0.202540	−	0.350810i	−0.949346	+	0.314232i	$0.898253\pi$
$864$	−0.0836141	−	5.19548i	−0.00284461	−	0.176754i
$865$	−12.1945	−	13.5434i	−0.414626	−	0.460489i
$866$	−3.57262	−	10.9954i	−0.121403	−	0.373639i
$867$	−18.4546	−	3.81930i	−0.626751	−	0.129710i
$868$	−5.85652	−	18.2548i	−0.198783	−	0.619607i
$869$			54.3453i			1.84354i
$870$	−1.50555	−	13.6211i	−0.0510431	−	0.461800i
$871$	−2.20478	+	1.98520i	−0.0747063	+	0.0672658i
$872$	8.28415	+	11.4022i	0.280537	+	0.386126i
$873$	1.99832	+	17.2323i	0.0676330	+	0.583226i
$874$	−1.47088	−	0.849215i	−0.0497533	−	0.0287251i
$875$	3.42439	−	0.359918i	0.115765	−	0.0121674i
$876$	−5.89985	+	5.36983i	−0.199338	+	0.181430i
$877$	−3.26222	+	31.0379i	−0.110157	+	1.04808i	0.790178	+	0.612878i	$0.209988\pi$
$877$	−3.26222	+	31.0379i	−0.110157	+	1.04808i	−0.900335	+	0.435198i	$0.856678\pi$
$878$	−8.98407	−	8.08929i	−0.303198	−	0.273000i
$879$	27.4321	−	38.1861i	0.925262	−	1.28799i
$880$	0.974141	−	4.58298i	0.0328383	−	0.154492i
$881$	41.6222	−	8.84708i	1.40229	−	0.298066i	0.556174	−	0.831066i	$-0.312269\pi$
$881$	41.6222	−	8.84708i	1.40229	−	0.298066i	0.846115	+	0.533000i	$0.178936\pi$
$882$	−0.156284	−	14.5671i	−0.00526235	−	0.490498i
$883$	−16.5767	−	5.38610i	−0.557851	−	0.181257i	0.0165032	−	0.999864i	$-0.494747\pi$
$883$	−16.5767	−	5.38610i	−0.557851	−	0.181257i	−0.574354	+	0.818607i	$0.694747\pi$
$884$	5.19882	+	1.68920i	0.174855	+	0.0568140i
$885$	−6.02342	+	1.31413i	−0.202475	+	0.0441739i
$886$	−17.1380	+	3.64280i	−0.575763	+	0.122382i
$887$	6.09281	−	28.6644i	0.204577	−	0.962457i	−0.749294	−	0.662238i	$-0.769607\pi$
$887$	6.09281	−	28.6644i	0.204577	−	0.962457i	0.953870	−	0.300219i	$-0.0970598\pi$
$888$	3.85191	+	2.76713i	0.129262	+	0.0928587i
$889$	10.1490	+	9.13823i	0.340388	+	0.306486i
$890$	−0.951088	+	9.04900i	−0.0318806	+	0.303323i
$891$	−5.30652	−	41.8330i	−0.177775	−	1.40146i
$892$	13.7281	−	1.44288i	0.459651	−	0.0483113i
$893$	−8.42849	−	4.86619i	−0.282049	−	0.162841i
$894$	12.8547	+	38.8523i	0.429925	+	1.29942i
$895$	8.50785	+	11.7101i	0.284386	+	0.391424i
$896$	2.55883	−	2.30398i	0.0854846	−	0.0769707i
$897$	−1.76293	+	0.194858i	−0.0588626	+	0.00650612i
$898$			9.18458i			0.306494i
$899$	4.76730	−	43.7938i	0.158998	−	1.46060i
$900$	2.75357	+	1.19074i	0.0917856	+	0.0396913i
$901$	−19.0808	−	58.7245i	−0.635672	−	1.95640i
$902$	−25.0312	−	27.7999i	−0.833447	−	0.925637i
$903$	−0.816342	−	1.80738i	−0.0271662	−	0.0601458i
$904$	−9.74057	−	16.8712i	−0.323966	−	0.561126i
$905$	−3.65251	+	6.32634i	−0.121414	+	0.210294i
$906$	3.12572	−	31.3563i	0.103845	−	1.04174i
$907$	15.5614	+	11.3060i	0.516708	+	0.375410i	0.815362	−	0.578951i	$-0.196538\pi$
$907$	15.5614	+	11.3060i	0.516708	+	0.375410i	−0.298655	+	0.954361i	$0.596538\pi$
$908$	−11.3425	−	1.19215i	−0.376415	−	0.0395628i
$909$	7.30741	+	15.9500i	0.242372	+	0.529027i
$910$	−1.44987	+	3.25647i	−0.0480628	+	0.107951i
$911$	13.8913	+	2.95269i	0.460240	+	0.0978271i	0.432196	−	0.901780i	$-0.357739\pi$
$911$	13.8913	+	2.95269i	0.460240	+	0.0978271i	0.0280440	+	0.999607i	$0.491072\pi$
$912$	−2.97398	+	0.0159528i	−0.0984784	+	0.000528251i
$913$	−28.4024	+	12.6456i	−0.939982	+	0.418507i
$914$	3.16798	−	9.75005i	0.104788	−	0.322503i
$915$	1.62749	−	2.85414i	0.0538031	−	0.0943550i
$916$	−2.81430	−	6.32102i	−0.0929870	−	0.208852i
$917$	12.9749	+	61.0421i	0.428469	+	2.01579i
$918$	20.0914	−	18.6845i	0.663115	−	0.616680i
$919$	28.1907	+	12.5513i	0.929924	+	0.414029i	0.815076	−	0.579354i	$-0.196695\pi$
$919$	28.1907	+	12.5513i	0.929924	+	0.414029i	0.114848	+	0.993383i	$0.463362\pi$
$920$	−0.661873	+	0.735084i	−0.0218213	+	0.0242350i
$921$	6.05428	−	18.9790i	0.199495	−	0.625378i
$922$	1.67180	−	2.30103i	0.0550577	−	0.0757804i
$923$	1.14343	+	10.8790i	0.0376366	+	0.358088i
$924$	18.5858	−	20.8657i	0.611429	−	0.686430i
$925$	−2.37140	+	1.36913i	−0.0779712	+	0.0450167i
$926$	−17.6697	+	12.8378i	−0.580662	+	0.421876i
$927$	−11.3079	−	33.5724i	−0.371401	−	1.10266i
$928$	7.52482	−	2.44496i	0.247014	−	0.0802598i
$929$	42.6782			1.40023			0.700114	−	0.714032i	$-0.253133\pi$
$929$	42.6782			1.40023			0.700114	+	0.714032i	$0.253133\pi$
$930$	7.81124	+	5.65549i	0.256141	+	0.185451i
$931$	−8.33795			−0.273265
$932$	−8.17971	+	2.65775i	−0.267935	+	0.0870574i
$933$	−32.9971	+	19.2876i	−1.08028	+	0.631447i
$934$	12.6236	−	9.17159i	0.413057	−	0.300104i
$935$	21.4252	−	12.3698i	0.700678	−	0.404537i
$936$	−2.49289	+	1.85238i	−0.0814828	+	0.0605468i
$937$	6.11277	+	58.1591i	0.199695	+	1.89997i	0.394123	+	0.919058i	$0.371049\pi$
$937$	6.11277	+	58.1591i	0.199695	+	1.89997i	−0.194427	+	0.980917i	$0.562285\pi$
$938$	−5.80005	+	7.98308i	−0.189378	+	0.260657i
$939$	−7.13578	−	2.27631i	−0.232867	−	0.0742846i
$940$	−3.79268	+	4.21220i	−0.123704	+	0.137387i
$941$	−28.6666	−	12.7632i	−0.934505	−	0.416069i	−0.117744	−	0.993044i	$-0.537566\pi$
$941$	−28.6666	−	12.7632i	−0.934505	−	0.416069i	−0.816761	+	0.576975i	$0.804233\pi$
$942$	−17.0328	+	38.8152i	−0.554957	+	1.26467i
$943$	1.64199	+	7.72494i	0.0534705	+	0.251559i
$944$	−1.44775	−	3.25170i	−0.0471202	−	0.105834i
$945$	10.7480	+	14.3035i	0.349633	+	0.465294i
$946$	0.481460	−	1.48178i	0.0156536	−	0.0481769i
$947$	−37.0792	+	16.5087i	−1.20491	+	0.536462i	−0.908213	−	0.418509i	$-0.862553\pi$
$947$	−37.0792	+	16.5087i	−1.20491	+	0.536462i	−0.296700	+	0.954971i	$0.595886\pi$
$948$	−0.107764	−	20.0897i	−0.00350001	−	0.652483i
$949$	4.66411	+	0.991387i	0.151403	+	0.0321818i
$950$	0.698389	−	1.56861i	0.0226587	−	0.0508923i
$951$	19.2751	+	26.2328i	0.625038	+	0.850657i
$952$	18.0815	+	1.90044i	0.586023	+	0.0615935i
$953$	−15.4664	−	11.2370i	−0.501005	−	0.364001i	0.308396	−	0.951258i	$-0.400208\pi$
$953$	−15.4664	−	11.2370i	−0.501005	−	0.364001i	−0.809401	+	0.587257i	$0.800208\pi$
$954$	33.4793	+	10.4824i	1.08393	+	0.339379i
$955$	−10.8456	+	18.7851i	−0.350954	+	0.607871i
$956$	−3.50394	−	6.06900i	−0.113325	−	0.196285i
$957$	58.5166	−	26.4303i	1.89157	−	0.854370i
$958$	−2.94092	−	3.26623i	−0.0950169	−	0.105527i
$959$	−16.8419	−	51.8340i	−0.543853	−	1.67381i
$960$	−0.351021	+	1.69611i	−0.0113291	+	0.0547417i
$961$	20.5715	+	23.1908i	0.663597	+	0.748091i
$962$		−	2.83480i		−	0.0913977i
$963$	−16.1928	−	1.52648i	−0.521805	−	0.0491902i
$964$	12.8011	−	11.5262i	0.412297	−	0.371234i
$965$	−2.56714	−	3.53336i	−0.0826390	−	0.113743i
$966$	−5.60061	+	1.85302i	−0.180197	+	0.0596199i
$967$	2.46305	+	1.42204i	0.0792064	+	0.0457298i	0.539080	−	0.842254i	$-0.318772\pi$
$967$	2.46305	+	1.42204i	0.0792064	+	0.0457298i	−0.459874	+	0.887984i	$0.652105\pi$
$968$	10.8926	−	1.14486i	0.350102	−	0.0367972i
$969$	−10.5701	−	11.6134i	−0.339561	−	0.373076i
$970$	0.604447	−	5.75092i	0.0194076	−	0.184651i
$971$	−24.8345	−	22.3611i	−0.796978	−	0.717603i	0.166309	−	0.986074i	$-0.446815\pi$
$971$	−24.8345	−	22.3611i	−0.796978	−	0.717603i	−0.963288	+	0.268471i	$0.913482\pi$
$972$	2.04460	+	15.4538i	0.0655806	+	0.495681i
$973$	11.4814	−	54.0156i	0.368076	−	1.73166i
$974$	−26.2374	+	5.57694i	−0.840702	+	0.178697i
$975$	−0.382213	−	1.75191i	−0.0122406	−	0.0561060i
$976$	1.80407	+	0.586179i	0.0577469	+	0.0187631i
$977$	−41.1447	−	13.3687i	−1.31634	−	0.427704i	−0.435102	−	0.900381i	$-0.643288\pi$
$977$	−41.1447	−	13.3687i	−1.31634	−	0.427704i	−0.881235	+	0.472678i	$0.843288\pi$
$978$	0.742667	+	3.40408i	0.0237479	+	0.108851i
$979$	−41.6998	+	8.86356i	−1.33273	+	0.283281i
$980$	−1.00961	+	4.74985i	−0.0322509	+	0.151728i
$981$	−28.6273	−	31.1160i	−0.914000	−	0.993456i
$982$	9.44234	+	8.50192i	0.301317	+	0.271307i
$983$	2.73304	−	26.0031i	0.0871704	−	0.829371i	−0.860356	−	0.509693i	$-0.829759\pi$
$983$	2.73304	−	26.0031i	0.0871704	−	0.829371i	0.947527	−	0.319677i	$-0.103574\pi$
$984$	9.30834	+	10.2271i	0.296739	+	0.326028i
$985$	−14.3181	+	1.50489i	−0.456212	+	0.0479498i
$986$	36.1802	+	20.8887i	1.15221	+	0.665230i
$987$	−32.0927	+	10.6182i	−1.02152	+	0.337982i
$988$	1.04484	+	1.43810i	0.0332409	+	0.0457521i
$989$	−0.244440	+	0.220095i	−0.00777273	+	0.00699860i
$990$	−1.31921	+	13.9940i	−0.0419272	+	0.444760i
$991$		−	8.74566i		−	0.277815i	−0.990305	−	0.138908i	$-0.955641\pi$
$991$		−	8.74566i		−	0.277815i	0.990305	−	0.138908i	$-0.0443591\pi$
$992$	−2.28347	+	5.07797i	−0.0725004	+	0.161226i
$993$	−9.21598	+	44.5310i	−0.292460	+	1.41315i
$994$	11.2429	+	34.6021i	0.356603	+	1.09751i
$995$	9.16269	+	10.1762i	0.290477	+	0.322607i
$996$	10.4744	−	4.73097i	0.331893	−	0.149907i
$997$	−20.8077	−	36.0400i	−0.658986	−	1.14140i	−0.980878	−	0.194621i	$-0.937652\pi$
$997$	−20.8077	−	36.0400i	−0.658986	−	1.14140i	0.321892	−	0.946776i	$-0.395681\pi$
$998$	−1.71148	+	2.96438i	−0.0541761	+	0.0938357i
$999$	−12.4350	−	6.91500i	−0.393428	−	0.218781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.b.11.15	yes	176
3.2	odd	2	inner	930.2.br.b.11.10	✓	176
31.17	odd	30	inner	930.2.br.b.761.10	yes	176
93.17	even	30	inner	930.2.br.b.761.15	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.10	✓	176	3.2	odd	2	inner
930.2.br.b.11.15	yes	176	1.1	even	1	trivial
930.2.br.b.761.10	yes	176	31.17	odd	30	inner
930.2.br.b.761.15	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)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(-0.874059 - 1.49533i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.29336 - 1.15205i) q^{6} +(0.359918 + 3.42439i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.47204 + 2.61402i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(-0.874059 - 1.49533i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.29336 - 1.15205i) q^{6} +(0.359918 + 3.42439i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.47204 + 2.61402i) q^{9} +(0.669131 - 0.743145i) q^{10} +(4.28029 + 1.90571i) q^{11} +(-1.58606 - 0.695991i) q^{12} +(0.215242 + 1.01263i) q^{13} +(1.40050 + 3.14556i) q^{14} +(-1.50462 - 0.857967i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.82371 - 2.14765i) q^{17} +(-0.592219 + 2.94097i) q^{18} +(1.67953 + 0.356996i) q^{19} +(0.406737 - 0.913545i) q^{20} +(4.80601 - 3.53131i) q^{21} +(4.65969 + 0.489754i) q^{22} +(-0.800242 - 0.581410i) q^{23} +(-1.72351 - 0.171806i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.517629 + 0.896559i) q^{26} +(5.19548 - 0.0836141i) q^{27} +(2.30398 + 2.55883i) q^{28} +(2.44496 + 7.52482i) q^{29} +(-1.69611 - 0.351021i) q^{30} +(-5.07797 - 2.28347i) q^{31} -1.00000i q^{32} +(-0.891558 - 8.06616i) q^{33} +(3.92396 - 3.53315i) q^{34} +(2.02389 + 2.78565i) q^{35} +(0.345575 + 2.98003i) q^{36} +(-2.37140 - 1.36913i) q^{37} +(1.70765 - 0.179481i) q^{38} +(1.32609 - 1.20696i) q^{39} +(0.104528 - 0.994522i) q^{40} +(-5.93336 - 5.34242i) q^{41} +(3.47955 - 4.84362i) q^{42} +(0.0691375 - 0.325266i) q^{43} +(4.58298 - 0.974141i) q^{44} +(0.0321839 + 2.99983i) q^{45} +(-0.940741 - 0.305665i) q^{46} +(-5.39065 - 1.75153i) q^{47} +(-1.69225 + 0.369196i) q^{48} +(-4.74985 + 1.00961i) q^{49} +(0.207912 - 0.978148i) q^{50} +(-7.42766 - 5.33587i) q^{51} +(0.769346 + 0.692722i) q^{52} +(1.22235 - 11.6299i) q^{53} +(4.91536 - 1.68501i) q^{54} +(4.65969 - 0.489754i) q^{55} +(2.98194 + 1.72162i) q^{56} +(-0.934183 - 2.82349i) q^{57} +(4.65060 + 6.40099i) q^{58} +(2.64517 - 2.38172i) q^{59} +(-1.72157 + 0.190286i) q^{60} +1.89691i q^{61} +(-5.53507 - 0.602535i) q^{62} +(-9.48122 - 4.10001i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.692722 + 0.769346i) q^{65} +(-3.34050 - 7.39587i) q^{66} +(1.43290 + 2.48185i) q^{67} +(2.64010 - 4.57279i) q^{68} +(-0.169943 + 1.70481i) q^{69} +(2.78565 + 2.02389i) q^{70} +(10.5085 + 1.10449i) q^{71} +(1.24954 + 2.72739i) q^{72} +(1.87339 - 4.20771i) q^{73} +(-2.67842 - 0.569316i) q^{74} +(-1.73203 + 0.00929082i) q^{75} +(1.56861 - 0.698389i) q^{76} +(-4.98533 + 15.3433i) q^{77} +(0.888216 - 1.55767i) q^{78} +(4.71772 + 10.5962i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(-4.66619 - 7.69589i) q^{81} +(-7.29386 - 3.24744i) q^{82} +(-4.44010 + 4.93123i) q^{83} +(1.81249 - 5.68179i) q^{84} +(3.10363 - 4.27177i) q^{85} +(-0.0347592 - 0.330711i) q^{86} +(9.11507 - 10.2332i) q^{87} +(4.05764 - 2.34268i) q^{88} +(-7.36112 + 5.34817i) q^{89} +(0.957606 + 2.84306i) q^{90} +(-3.39018 + 1.10154i) q^{91} -0.989153 q^{92} +(1.02389 + 9.58914i) q^{93} -5.66807 q^{94} +(1.63302 - 0.530599i) q^{95} +(-1.49533 + 0.874059i) q^{96} +(4.67822 - 3.39893i) q^{97} +(-4.20539 + 2.42798i) q^{98} +(-11.2823 + 8.38348i) 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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