LMFDB - Embedded newform 930.2.bg.h.391.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, 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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			391.2
Character	$\chi$	$=$	930.391
Dual form			930.2.bg.h.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.334019 - 0.370966i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.334019 - 0.370966i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.913545 + 0.406737i) q^{10} +(1.48307 + 0.315236i) q^{11} +(0.104528 - 0.994522i) q^{12} +(0.0540005 + 0.513781i) q^{13} +(0.488275 - 0.103786i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.01506 + 0.215758i) q^{17} +(0.104528 + 0.994522i) q^{18} +(-0.712864 + 6.78245i) q^{19} +(-0.978148 - 0.207912i) q^{20} +(-0.456027 + 0.203036i) q^{21} +(1.01454 + 1.12676i) q^{22} +(-1.07483 + 3.30799i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.258305 + 0.447398i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.456027 + 0.203036i) q^{28} +(3.15052 + 2.28899i) q^{29} +1.00000 q^{30} +(5.07551 - 2.28893i) q^{31} -1.00000 q^{32} +(-1.22663 - 0.891201i) q^{33} +(-0.948019 - 0.422085i) q^{34} +(0.154256 + 0.474752i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.95182 + 5.11271i) q^{37} +(-4.56334 + 5.06811i) q^{38} +(0.159642 - 0.491326i) q^{39} +(-0.669131 - 0.743145i) q^{40} +(-9.93869 + 4.42499i) q^{41} +(-0.488275 - 0.103786i) q^{42} +(-0.0609742 + 0.580131i) q^{43} +(0.158486 + 1.50790i) q^{44} +(-0.978148 + 0.207912i) q^{45} +(-2.81394 + 2.04445i) q^{46} +(-7.33533 + 5.32943i) q^{47} +(0.978148 - 0.207912i) q^{48} +(0.705652 + 6.71383i) q^{49} +(0.104528 - 0.994522i) q^{50} +(1.01506 + 0.215758i) q^{51} +(-0.471948 + 0.210125i) q^{52} +(-3.19079 - 3.54374i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-1.01454 + 1.12676i) q^{55} +(0.249592 + 0.432306i) q^{56} +(3.40990 - 5.90613i) q^{57} +(1.20339 + 3.70366i) q^{58} +(6.42597 + 2.86102i) q^{59} +(0.809017 + 0.587785i) q^{60} -5.45783 q^{61} +(5.45157 + 1.13153i) q^{62} +0.499184 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.471948 - 0.210125i) q^{65} +(-0.468532 - 1.44199i) q^{66} +(4.91335 - 8.51018i) q^{67} +(-0.518868 - 0.898706i) q^{68} +(2.32738 - 2.58482i) q^{69} +(-0.154256 + 0.474752i) q^{70} +(1.38120 + 1.53398i) q^{71} +(-0.913545 + 0.406737i) q^{72} +(0.946846 + 0.201258i) q^{73} +(-0.617099 + 5.87131i) q^{74} +(0.104528 + 0.994522i) q^{75} +(-6.67078 + 1.41792i) q^{76} +(0.612315 - 0.444873i) q^{77} +(0.417947 - 0.303656i) q^{78} +(12.4087 - 2.63754i) q^{79} +(-0.104528 - 0.994522i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-10.6415 - 2.26192i) q^{82} +(2.58021 - 1.14878i) q^{83} +(-0.334019 - 0.370966i) q^{84} +(0.320678 - 0.986946i) q^{85} +(-0.390321 + 0.433496i) q^{86} +(-1.94713 - 3.37253i) q^{87} +(-0.758101 + 1.31307i) q^{88} +(2.80670 + 8.63815i) q^{89} +(-0.913545 - 0.406737i) q^{90} +(0.208632 + 0.151580i) q^{91} -3.47822 q^{92} +(-5.56770 + 0.0266443i) q^{93} -9.06697 q^{94} +(-5.51734 - 4.00858i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-0.749715 - 2.30739i) q^{97} +(-3.37541 + 5.84638i) q^{98} +(0.758101 + 1.31307i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{10} - 5 q^{11} - 3 q^{12} - 13 q^{13} - 4 q^{14} + 6 q^{15} - 6 q^{16} + 31 q^{17} - 3 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} + 5 q^{22} - 9 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} + 6 q^{27} + 4 q^{28} + 11 q^{29} + 24 q^{30} + 17 q^{31} - 24 q^{32} + 10 q^{33} + 9 q^{34} + 7 q^{35} - 12 q^{36} + 8 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + 12 q^{41} + 4 q^{42} - 7 q^{43} - 10 q^{44} + 3 q^{45} - 6 q^{46} - 46 q^{47} - 3 q^{48} + 20 q^{49} - 3 q^{50} - 31 q^{51} + 17 q^{52} + 48 q^{53} - 6 q^{54} - 5 q^{55} + q^{56} - 2 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{61} + 13 q^{62} + 2 q^{63} - 6 q^{64} + 17 q^{65} + 10 q^{66} - 33 q^{67} + q^{68} - 12 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 19 q^{73} + 7 q^{74} - 3 q^{75} + 2 q^{76} + 26 q^{77} - 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 12 q^{82} + 11 q^{84} - 2 q^{85} - 48 q^{86} + 3 q^{87} + 21 q^{89} - 3 q^{90} + 72 q^{91} + 6 q^{92} + 19 q^{93} - 14 q^{94} + 6 q^{95} + 3 q^{96} - 35 q^{97} - 5 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9 - 3 * q^10 - 5 * q^11 - 3 * q^12 - 13 * q^13 - 4 * q^14 + 6 * q^15 - 6 * q^16 + 31 * q^17 - 3 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 + 5 * q^22 - 9 * q^23 + 3 * q^24 - 12 * q^25 + 3 * q^26 + 6 * q^27 + 4 * q^28 + 11 * q^29 + 24 * q^30 + 17 * q^31 - 24 * q^32 + 10 * q^33 + 9 * q^34 + 7 * q^35 - 12 * q^36 + 8 * q^37 - 2 * q^38 - q^39 - 3 * q^40 + 12 * q^41 + 4 * q^42 - 7 * q^43 - 10 * q^44 + 3 * q^45 - 6 * q^46 - 46 * q^47 - 3 * q^48 + 20 * q^49 - 3 * q^50 - 31 * q^51 + 17 * q^52 + 48 * q^53 - 6 * q^54 - 5 * q^55 + q^56 - 2 * q^57 + 14 * q^58 + 12 * q^59 + 6 * q^60 - 4 * q^61 + 13 * q^62 + 2 * q^63 - 6 * q^64 + 17 * q^65 + 10 * q^66 - 33 * q^67 + q^68 - 12 * q^69 - 7 * q^70 - 35 * q^71 - 3 * q^72 + 19 * q^73 + 7 * q^74 - 3 * q^75 + 2 * q^76 + 26 * q^77 - 4 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 - 12 * q^82 + 11 * q^84 - 2 * q^85 - 48 * q^86 + 3 * q^87 + 21 * q^89 - 3 * q^90 + 72 * q^91 + 6 * q^92 + 19 * q^93 - 14 * q^94 + 6 * q^95 + 3 * q^96 - 35 * q^97 - 5 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	0.334019	−	0.370966i	0.126247	−	0.140212i	−0.676707	−	0.736252i	$-0.736594\pi$
$7$	0.334019	−	0.370966i	0.126247	−	0.140212i	0.802954	+	0.596041i	$0.203260\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	−0.913545	+	0.406737i	−0.288888	+	0.128621i
$11$	1.48307	+	0.315236i	0.447162	+	0.0950473i	0.425989	−	0.904729i	$-0.359926\pi$
$11$	1.48307	+	0.315236i	0.447162	+	0.0950473i	0.0211737	+	0.999776i	$0.493260\pi$
$12$	0.104528	−	0.994522i	0.0301748	−	0.287094i
$13$	0.0540005	+	0.513781i	0.0149771	+	0.142497i	0.999455	−	0.0330113i	$-0.0105097\pi$
$13$	0.0540005	+	0.513781i	0.0149771	+	0.142497i	−0.984478	+	0.175508i	$0.943843\pi$
$14$	0.488275	−	0.103786i	0.130497	−	0.0277380i
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.01506	+	0.215758i	−0.246188	+	0.0523289i	−0.329353	−	0.944207i	$-0.606831\pi$
$17$	−1.01506	+	0.215758i	−0.246188	+	0.0523289i	0.0831648	+	0.996536i	$0.473497\pi$
$18$	0.104528	+	0.994522i	0.0246376	+	0.234411i
$19$	−0.712864	+	6.78245i	−0.163542	+	1.55600i	0.537736	+	0.843113i	$0.319280\pi$
$19$	−0.712864	+	6.78245i	−0.163542	+	1.55600i	−0.701279	+	0.712887i	$0.747387\pi$
$20$	−0.978148	−	0.207912i	−0.218720	−	0.0464905i
$21$	−0.456027	+	0.203036i	−0.0995132	+	0.0443061i
$22$	1.01454	+	1.12676i	0.216300	+	0.240226i
$23$	−1.07483	+	3.30799i	−0.224117	+	0.689763i	0.774262	+	0.632865i	$0.218121\pi$
$23$	−1.07483	+	3.30799i	−0.224117	+	0.689763i	−0.998380	+	0.0568981i	$0.981879\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.258305	+	0.447398i	−0.0506579	+	0.0877420i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	0.456027	+	0.203036i	0.0861810	+	0.0383702i
$29$	3.15052	+	2.28899i	0.585038	+	0.425055i	0.840537	−	0.541755i	$-0.182240\pi$
$29$	3.15052	+	2.28899i	0.585038	+	0.425055i	−0.255499	+	0.966809i	$0.582240\pi$
$30$	1.00000			0.182574
$31$	5.07551	−	2.28893i	0.911589	−	0.411104i
$31$	5.07551	−	2.28893i	0.911589	−	0.411104i
$32$	−1.00000			−0.176777
$33$	−1.22663	−	0.891201i	−0.213529	−	0.155138i
$34$	−0.948019	−	0.422085i	−0.162584	−	0.0723870i
$35$	0.154256	+	0.474752i	0.0260741	+	0.0802477i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	2.95182	+	5.11271i	0.485277	+	0.840524i	0.999857	−	0.0169182i	$-0.00538548\pi$
$37$	2.95182	+	5.11271i	0.485277	+	0.840524i	−0.514580	+	0.857442i	$0.672052\pi$
$38$	−4.56334	+	5.06811i	−0.740272	+	0.822155i
$39$	0.159642	−	0.491326i	0.0255631	−	0.0786751i
$40$	−0.669131	−	0.743145i	−0.105799	−	0.117502i
$41$	−9.93869	+	4.42499i	−1.55216	+	0.691067i	−0.990653	−	0.136403i	$-0.956446\pi$
$41$	−9.93869	+	4.42499i	−1.55216	+	0.691067i	−0.561510	+	0.827470i	$0.689779\pi$
$42$	−0.488275	−	0.103786i	−0.0753425	−	0.0160145i
$43$	−0.0609742	+	0.580131i	−0.00929848	+	0.0884691i	−0.998187	−	0.0601905i	$-0.980829\pi$
$43$	−0.0609742	+	0.580131i	−0.00929848	+	0.0884691i	0.988888	+	0.148660i	$0.0474959\pi$
$44$	0.158486	+	1.50790i	0.0238927	+	0.227324i
$45$	−0.978148	+	0.207912i	−0.145814	+	0.0309936i
$46$	−2.81394	+	2.04445i	−0.414893	+	0.301437i
$47$	−7.33533	+	5.32943i	−1.06997	+	0.777378i	−0.975907	−	0.218189i	$-0.929985\pi$
$47$	−7.33533	+	5.32943i	−1.06997	+	0.777378i	−0.0940619	+	0.995566i	$0.529985\pi$
$48$	0.978148	−	0.207912i	0.141183	−	0.0300095i
$49$	0.705652	+	6.71383i	0.100807	+	0.959119i
$50$	0.104528	−	0.994522i	0.0147826	−	0.140647i
$51$	1.01506	+	0.215758i	0.142137	+	0.0302121i
$52$	−0.471948	+	0.210125i	−0.0654473	+	0.0291390i
$53$	−3.19079	−	3.54374i	−0.438289	−	0.486770i	0.483015	−	0.875612i	$-0.339542\pi$
$53$	−3.19079	−	3.54374i	−0.438289	−	0.486770i	−0.921304	+	0.388843i	$0.872875\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	−1.01454	+	1.12676i	−0.136800	+	0.151932i
$56$	0.249592	+	0.432306i	0.0333531	+	0.0577693i
$57$	3.40990	−	5.90613i	0.451653	−	0.782286i
$58$	1.20339	+	3.70366i	0.158013	+	0.486315i
$59$	6.42597	+	2.86102i	0.836590	+	0.372474i	0.779889	−	0.625918i	$-0.215275\pi$
$59$	6.42597	+	2.86102i	0.836590	+	0.372474i	0.0567004	+	0.998391i	$0.481942\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	−5.45783			−0.698804			−0.349402	−	0.936973i	$-0.613615\pi$
$61$	−5.45783			−0.698804			−0.349402	+	0.936973i	$0.613615\pi$
$62$	5.45157	+	1.13153i	0.692350	+	0.143704i
$63$	0.499184			0.0628912
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.471948	−	0.210125i	−0.0585379	−	0.0260627i
$66$	−0.468532	−	1.44199i	−0.0576723	−	0.177497i
$67$	4.91335	−	8.51018i	0.600262	−	1.03968i	−0.392520	−	0.919744i	$-0.628396\pi$
$67$	4.91335	−	8.51018i	0.600262	−	1.03968i	0.992781	−	0.119940i	$-0.0382702\pi$
$68$	−0.518868	−	0.898706i	−0.0629220	−	0.108984i
$69$	2.32738	−	2.58482i	0.280184	−	0.311176i
$70$	−0.154256	+	0.474752i	−0.0184371	+	0.0567437i
$71$	1.38120	+	1.53398i	0.163919	+	0.182050i	0.819508	−	0.573067i	$-0.194247\pi$
$71$	1.38120	+	1.53398i	0.163919	+	0.182050i	−0.655590	+	0.755117i	$0.727580\pi$
$72$	−0.913545	+	0.406737i	−0.107662	+	0.0479344i
$73$	0.946846	+	0.201258i	0.110820	+	0.0235555i	0.262988	−	0.964799i	$-0.415292\pi$
$73$	0.946846	+	0.201258i	0.110820	+	0.0235555i	−0.152168	+	0.988355i	$0.548625\pi$
$74$	−0.617099	+	5.87131i	−0.0717363	+	0.682526i
$75$	0.104528	+	0.994522i	0.0120699	+	0.114837i
$76$	−6.67078	+	1.41792i	−0.765191	+	0.162646i
$77$	0.612315	−	0.444873i	0.0697798	−	0.0506980i
$78$	0.417947	−	0.303656i	0.0473232	−	0.0343823i
$79$	12.4087	−	2.63754i	1.39608	−	0.296747i	0.552396	−	0.833582i	$-0.313714\pi$
$79$	12.4087	−	2.63754i	1.39608	−	0.296747i	0.843687	+	0.536835i	$0.180380\pi$
$80$	−0.104528	−	0.994522i	−0.0116866	−	0.111191i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	−10.6415	−	2.26192i	−1.17516	−	0.249788i
$83$	2.58021	−	1.14878i	0.283214	−	0.126095i	−0.260213	−	0.965551i	$-0.583793\pi$
$83$	2.58021	−	1.14878i	0.283214	−	0.126095i	0.543428	+	0.839456i	$0.317126\pi$
$84$	−0.334019	−	0.370966i	−0.0364445	−	0.0404757i
$85$	0.320678	−	0.986946i	0.0347824	−	0.107049i
$86$	−0.390321	+	0.433496i	−0.0420894	+	0.0467451i
$87$	−1.94713	−	3.37253i	−0.208754	−	0.361573i
$88$	−0.758101	+	1.31307i	−0.0808139	+	0.139974i
$89$	2.80670	+	8.63815i	0.297510	+	0.915642i	0.982367	+	0.186964i	$0.0598647\pi$
$89$	2.80670	+	8.63815i	0.297510	+	0.915642i	−0.684857	+	0.728678i	$0.740135\pi$
$90$	−0.913545	−	0.406737i	−0.0962961	−	0.0428738i
$91$	0.208632	+	0.151580i	0.0218706	+	0.0158899i
$92$	−3.47822			−0.362630
$93$	−5.56770	+	0.0266443i	−0.577344	+	0.00276289i
$94$	−9.06697			−0.935187
$95$	−5.51734	−	4.00858i	−0.566067	−	0.411272i
$96$	0.913545	+	0.406737i	0.0932383	+	0.0415124i
$97$	−0.749715	−	2.30739i	−0.0761221	−	0.234280i	0.905754	−	0.423804i	$-0.139305\pi$
$97$	−0.749715	−	2.30739i	−0.0761221	−	0.234280i	−0.981876	+	0.189524i	$0.939305\pi$
$98$	−3.37541	+	5.84638i	−0.340968	+	0.590573i
$99$	0.758101	+	1.31307i	0.0761920	+	0.131968i
$100$	0.669131	−	0.743145i	0.0669131	−	0.0743145i
$101$	2.29613	−	7.06677i	0.228474	−	0.703170i	−0.769447	−	0.638711i	$-0.779468\pi$
$101$	2.29613	−	7.06677i	0.228474	−	0.703170i	0.997920	−	0.0644587i	$-0.0205321\pi$
$102$	0.694381	+	0.771188i	0.0687540	+	0.0763590i
$103$	9.15801	−	4.07741i	0.902365	−	0.401759i	0.0975131	−	0.995234i	$-0.468911\pi$
$103$	9.15801	−	4.07741i	0.902365	−	0.401759i	0.804852	+	0.593475i	$0.202245\pi$
$104$	−0.505322	−	0.107409i	−0.0495509	−	0.0105324i
$105$	0.0521789	−	0.496449i	0.00509214	−	0.0484485i
$106$	−0.498451	−	4.74244i	−0.0484138	−	0.460627i
$107$	8.51309	−	1.80951i	0.822992	−	0.174932i	0.222877	−	0.974846i	$-0.428455\pi$
$107$	8.51309	−	1.80951i	0.822992	−	0.174932i	0.600114	+	0.799914i	$0.295122\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	4.43842	−	3.22470i	0.425123	−	0.308870i	−0.354573	−	0.935028i	$-0.615374\pi$
$109$	4.43842	−	3.22470i	0.425123	−	0.308870i	0.779696	+	0.626158i	$0.215374\pi$
$110$	−1.48307	+	0.315236i	−0.141405	+	0.0300566i
$111$	−0.617099	−	5.87131i	−0.0585725	−	0.557280i
$112$	−0.0521789	+	0.496449i	−0.00493044	+	0.0469100i
$113$	−16.3515	−	3.47562i	−1.53822	−	0.326959i	−0.640652	−	0.767831i	$-0.721336\pi$
$113$	−16.3515	−	3.47562i	−1.53822	−	0.326959i	−0.897570	+	0.440872i	$0.854669\pi$
$114$	6.23020	−	2.77387i	0.583512	−	0.259796i
$115$	−2.32738	−	2.58482i	−0.217030	−	0.241036i
$116$	−1.20339	+	3.70366i	−0.111732	+	0.343877i
$117$	−0.345680	+	0.383917i	−0.0319581	+	0.0354931i
$118$	3.51705	+	6.09171i	0.323771	+	0.560787i
$119$	−0.259010	+	0.448619i	−0.0237434	+	0.0411249i
$120$	0.309017	+	0.951057i	0.0282093	+	0.0868192i
$121$	−7.94888	−	3.53907i	−0.722625	−	0.321734i
$122$	−4.41548	−	3.20803i	−0.399759	−	0.290442i
$123$	10.8793			0.980949
$124$	3.74532	+	4.11978i	0.336340	+	0.369967i
$125$	1.00000			0.0894427
$126$	0.403848	+	0.293413i	0.0359776	+	0.0261393i
$127$	4.76236	+	2.12034i	0.422591	+	0.188150i	0.607003	−	0.794699i	$-0.292372\pi$
$127$	4.76236	+	2.12034i	0.422591	+	0.188150i	−0.184412	+	0.982849i	$0.559038\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	0.291663	−	0.505175i	0.0256795	−	0.0444782i
$130$	−0.258305	−	0.447398i	−0.0226549	−	0.0392394i
$131$	−0.910113	+	1.01078i	−0.0795170	+	0.0883125i	−0.781590	−	0.623792i	$-0.785591\pi$
$131$	−0.910113	+	1.01078i	−0.0795170	+	0.0883125i	0.702073	+	0.712105i	$0.252258\pi$
$132$	0.468532	−	1.44199i	0.0407805	−	0.125509i
$133$	2.27795	+	2.52991i	0.197523	+	0.219371i
$134$	8.97714	−	3.99688i	0.775507	−	0.345278i
$135$	0.978148	+	0.207912i	0.0841855	+	0.0178942i
$136$	0.108473	−	1.03205i	0.00930148	−	0.0884977i
$137$	−1.88751	−	17.9585i	−0.161261	−	1.53430i	−0.713527	−	0.700628i	$-0.752903\pi$
$137$	−1.88751	−	17.9585i	−0.161261	−	1.53430i	0.552266	−	0.833668i	$-0.313763\pi$
$138$	3.40221	−	0.723163i	0.289616	−	0.0615597i
$139$	5.71237	−	4.15028i	0.484517	−	0.352022i	−0.318555	−	0.947904i	$-0.603197\pi$
$139$	5.71237	−	4.15028i	0.484517	−	0.352022i	0.803072	+	0.595882i	$0.203197\pi$
$140$	−0.403848	+	0.293413i	−0.0341314	+	0.0247979i
$141$	8.86884	−	1.88513i	0.746891	−	0.158757i
$142$	0.215765	+	2.05287i	0.0181066	+	0.172273i
$143$	−0.0818757	+	0.778996i	−0.00684679	+	0.0651429i
$144$	−0.978148	−	0.207912i	−0.0815123	−	0.0173260i
$145$	−3.55759	+	1.58394i	−0.295441	+	0.131539i
$146$	0.647718	+	0.719363i	0.0536055	+	0.0595349i
$147$	2.08612	−	6.42041i	0.172060	−	0.529546i
$148$	−3.95031	+	4.38727i	−0.324714	+	0.360631i
$149$	−0.431325	−	0.747076i	−0.0353355	−	0.0612029i	0.847817	−	0.530289i	$-0.177917\pi$
$149$	−0.431325	−	0.747076i	−0.0353355	−	0.0612029i	−0.883152	+	0.469086i	$0.844583\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−0.285324	−	0.878137i	−0.0232193	−	0.0714618i	0.938775	−	0.344530i	$-0.111962\pi$
$151$	−0.285324	−	0.878137i	−0.0232193	−	0.0714618i	−0.961995	+	0.273068i	$0.911962\pi$
$152$	−6.23020	−	2.77387i	−0.505336	−	0.224990i
$153$	−0.839546	−	0.609966i	−0.0678733	−	0.0493128i
$154$	0.756863			0.0609898
$155$	−0.555485	+	5.53999i	−0.0446176	+	0.444982i
$156$	0.516611			0.0413620
$157$	−7.15963	−	5.20178i	−0.571401	−	0.415147i	0.264213	−	0.964464i	$-0.414888\pi$
$157$	−7.15963	−	5.20178i	−0.571401	−	0.415147i	−0.835614	+	0.549317i	$0.814888\pi$
$158$	11.5891	+	5.15981i	0.921981	+	0.410492i
$159$	1.47357	+	4.53518i	0.116862	+	0.359663i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	0.868136	+	1.50366i	0.0684187	+	0.118505i
$162$	−0.669131	+	0.743145i	−0.0525719	+	0.0583870i
$163$	4.16894	−	12.8307i	0.326537	−	1.00498i	−0.644206	−	0.764852i	$-0.722812\pi$
$163$	4.16894	−	12.8307i	0.326537	−	1.00498i	0.970742	−	0.240124i	$-0.0771881\pi$
$164$	−7.27964	−	8.08486i	−0.568444	−	0.631322i
$165$	1.38512	−	0.616695i	0.107831	−	0.0480096i
$166$	2.76267	+	0.587223i	0.214425	+	0.0455774i
$167$	−0.558718	+	5.31585i	−0.0432349	+	0.411352i	0.951404	+	0.307945i	$0.0996413\pi$
$167$	−0.558718	+	5.31585i	−0.0432349	+	0.411352i	−0.994639	+	0.103408i	$0.967025\pi$
$168$	−0.0521789	−	0.496449i	−0.00402569	−	0.0383019i
$169$	12.4549	−	2.64736i	0.958066	−	0.203643i
$170$	0.839546	−	0.609966i	0.0643903	−	0.0467823i
$171$	−5.51734	+	4.00858i	−0.421922	+	0.306544i
$172$	−0.570579	+	0.121280i	−0.0435062	+	0.00924754i
$173$	−1.18312	−	11.2567i	−0.0899512	−	0.855828i	−0.942730	−	0.333556i	$-0.891751\pi$
$173$	−1.18312	−	11.2567i	−0.0899512	−	0.855828i	0.852779	−	0.522272i	$-0.174915\pi$
$174$	0.407061	−	3.87293i	0.0308592	−	0.293606i
$175$	−0.488275	−	0.103786i	−0.0369101	−	0.00784549i
$176$	−1.38512	+	0.616695i	−0.104407	+	0.0464851i
$177$	−4.70673	−	5.22735i	−0.353779	−	0.392912i
$178$	−2.80670	+	8.63815i	−0.210371	+	0.647456i
$179$	5.26086	−	5.84278i	0.393215	−	0.436710i	−0.513734	−	0.857949i	$-0.671738\pi$
$179$	5.26086	−	5.84278i	0.393215	−	0.436710i	0.906949	+	0.421240i	$0.138405\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	10.9897	−	19.0347i	0.816859	−	1.41484i	−0.0911266	−	0.995839i	$-0.529047\pi$
$181$	10.9897	−	19.0347i	0.816859	−	1.41484i	0.907985	−	0.419002i	$-0.137620\pi$
$182$	0.0796904	+	0.245262i	0.00590705	+	0.0181800i
$183$	4.98598	+	2.21990i	0.368574	+	0.164100i
$184$	−2.81394	−	2.04445i	−0.207446	−	0.150719i
$185$	−5.90365			−0.434045
$186$	−4.52003	−	3.25106i	−0.331424	−	0.238379i
$187$	−1.57342			−0.115060
$188$	−7.33533	−	5.32943i	−0.534984	−	0.388689i
$189$	−0.456027	−	0.203036i	−0.0331711	−	0.0147687i
$190$	−2.10744	−	6.48602i	−0.152890	−	0.470546i
$191$	−12.0172	+	20.8143i	−0.869531	+	1.50607i	−0.00705492	+	0.999975i	$0.502246\pi$
$191$	−12.0172	+	20.8143i	−0.869531	+	1.50607i	−0.862476	+	0.506097i	$0.831088\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	13.4367	−	14.9230i	0.967197	−	1.07418i	−0.0300139	−	0.999549i	$-0.509555\pi$
$193$	13.4367	−	14.9230i	0.967197	−	1.07418i	0.997211	−	0.0746319i	$-0.0237782\pi$
$194$	0.749715	−	2.30739i	0.0538264	−	0.165661i
$195$	0.345680	+	0.383917i	0.0247547	+	0.0274928i
$196$	−6.16718	+	2.74580i	−0.440513	+	0.196129i
$197$	−16.9788	−	3.60895i	−1.20969	−	0.257127i	−0.441446	−	0.897288i	$-0.645534\pi$
$197$	−16.9788	−	3.60895i	−1.20969	−	0.257127i	−0.768241	+	0.640161i	$0.778868\pi$
$198$	−0.158486	+	1.50790i	−0.0112631	+	0.107162i
$199$	1.62943	+	15.5030i	0.115507	+	1.09898i	0.886690	+	0.462365i	$0.152999\pi$
$199$	1.62943	+	15.5030i	0.115507	+	1.09898i	−0.771183	+	0.636614i	$0.780334\pi$
$200$	0.978148	−	0.207912i	0.0691655	−	0.0147016i
$201$	−7.94997	+	5.77599i	−0.560748	+	0.407407i
$202$	6.01135	−	4.36750i	0.422957	−	0.307296i
$203$	1.90147	−	0.404170i	0.133457	−	0.0283672i
$204$	0.108473	+	1.03205i	0.00759463	+	0.0722581i
$205$	1.13719	−	10.8197i	0.0794249	−	0.755678i
$206$	9.80562	+	2.08425i	0.683190	+	0.145217i
$207$	−3.17751	+	1.41472i	−0.220852	+	0.0983299i
$208$	−0.345680	−	0.383917i	−0.0239686	−	0.0266198i
$209$	−3.19530	+	9.83412i	−0.221024	+	0.680241i
$210$	0.334019	−	0.370966i	0.0230495	−	0.0255991i
$211$	−8.75660	−	15.1669i	−0.602829	−	1.04413i	−0.992391	−	0.123130i	$-0.960707\pi$
$211$	−8.75660	−	15.1669i	−0.602829	−	1.04413i	0.389561	−	0.921001i	$-0.372627\pi$
$212$	2.38428	−	4.12970i	0.163753	−	0.283629i
$213$	−0.637865	−	1.96315i	−0.0437058	−	0.134513i
$214$	7.95084	+	3.53994i	0.543508	+	0.241986i
$215$	−0.471921	−	0.342871i	−0.0321847	−	0.0233836i
$216$	1.00000			0.0680414
$217$	0.846203	−	2.64739i	0.0574440	−	0.179716i
$218$	5.48618			0.371571
$219$	−0.783127	−	0.568975i	−0.0529188	−	0.0384478i
$220$	−1.38512	−	0.616695i	−0.0933848	−	0.0415776i
$221$	−0.165666	−	0.509867i	−0.0111439	−	0.0342974i
$222$	2.95182	−	5.11271i	0.198113	−	0.343143i
$223$	6.68328	+	11.5758i	0.447546	+	0.775172i	0.998226	−	0.0595445i	$-0.0189648\pi$
$223$	6.68328	+	11.5758i	0.447546	+	0.775172i	−0.550680	+	0.834717i	$0.685631\pi$
$224$	−0.334019	+	0.370966i	−0.0223176	+	0.0247862i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	−11.1857	−	12.4230i	−0.744064	−	0.826367i
$227$	−6.65041	+	2.96095i	−0.441403	+	0.196525i	−0.615390	−	0.788223i	$-0.711002\pi$
$227$	−6.65041	+	2.96095i	−0.441403	+	0.196525i	0.173987	+	0.984748i	$0.444335\pi$
$228$	6.67078	+	1.41792i	0.441783	+	0.0939039i
$229$	−1.05219	+	10.0109i	−0.0695307	+	0.661540i	0.903139	+	0.429348i	$0.141257\pi$
$229$	−1.05219	+	10.0109i	−0.0695307	+	0.661540i	−0.972670	+	0.232192i	$0.925410\pi$
$230$	−0.363573	−	3.45917i	−0.0239733	−	0.228091i
$231$	−0.740324	+	0.157361i	−0.0487097	+	0.0103536i
$232$	−3.15052	+	2.28899i	−0.206842	+	0.150280i
$233$	1.72235	−	1.25136i	0.112835	−	0.0819795i	−0.529937	−	0.848037i	$-0.677784\pi$
$233$	1.72235	−	1.25136i	0.112835	−	0.0819795i	0.642772	+	0.766058i	$0.277784\pi$
$234$	−0.505322	+	0.107409i	−0.0330339	+	0.00702157i
$235$	−0.947757	−	9.01730i	−0.0618248	−	0.588224i
$236$	−0.735263	+	6.99556i	−0.0478616	+	0.455372i
$237$	−12.4087	−	2.63754i	−0.806029	−	0.171327i
$238$	−0.473236	+	0.210698i	−0.0306753	+	0.0136575i
$239$	14.2093	+	15.7810i	0.919123	+	1.02079i	0.999711	+	0.0240422i	$0.00765360\pi$
$239$	14.2093	+	15.7810i	0.919123	+	1.02079i	−0.0805878	+	0.996748i	$0.525680\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	9.04565	−	10.0462i	0.582681	−	0.647133i	−0.377665	−	0.925942i	$-0.623273\pi$
$241$	9.04565	−	10.0462i	0.582681	−	0.647133i	0.960347	+	0.278809i	$0.0899396\pi$
$242$	−4.35057	−	7.53540i	−0.279665	−	0.484394i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−1.68656	−	5.19071i	−0.107971	−	0.332301i
$245$	−6.16718	−	2.74580i	−0.394006	−	0.175423i
$246$	8.80150	+	6.39466i	0.561163	+	0.407709i
$247$	−3.52319			−0.224175
$248$	0.608482	+	5.53442i	0.0386386	+	0.351436i
$249$	−2.82439			−0.178988
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	17.2523	+	7.68120i	1.08895	+	0.484833i	0.871079	−	0.491144i	$-0.163421\pi$
$251$	17.2523	+	7.68120i	1.08895	+	0.484833i	0.217875	+	0.975977i	$0.430088\pi$
$252$	0.154256	+	0.474752i	0.00971723	+	0.0299066i
$253$	−2.63684	+	4.56715i	−0.165777	+	0.287134i
$254$	2.60652	+	4.51463i	0.163548	+	0.283273i
$255$	−0.694381	+	0.771188i	−0.0434838	+	0.0482937i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−10.7437	−	11.9321i	−0.670176	−	0.744306i	0.308159	−	0.951335i	$-0.400287\pi$
$257$	−10.7437	−	11.9321i	−0.670176	−	0.744306i	−0.978335	+	0.207029i	$0.933621\pi$
$258$	0.532895	−	0.237260i	0.0331766	−	0.0147712i
$259$	2.88260	+	0.612717i	0.179116	+	0.0380724i
$260$	0.0540005	−	0.513781i	0.00334897	−	0.0318633i
$261$	0.407061	+	3.87293i	0.0251965	+	0.239728i
$262$	−1.33042	+	0.282790i	−0.0821936	+	0.0174708i
$263$	9.76357	−	7.09365i	0.602048	−	0.437413i	−0.244558	−	0.969635i	$-0.578643\pi$
$263$	9.76357	−	7.09365i	0.602048	−	0.437413i	0.846605	+	0.532222i	$0.178643\pi$
$264$	1.22663	−	0.891201i	0.0754941	−	0.0548497i
$265$	4.66436	−	0.991441i	0.286530	−	0.0609037i
$266$	0.355850	+	3.38569i	0.0218186	+	0.207590i
$267$	0.949399	−	9.03293i	0.0581023	−	0.552806i
$268$	9.61197	+	2.04309i	0.587144	+	0.124801i
$269$	−9.78952	+	4.35857i	−0.596877	+	0.265747i	−0.682860	−	0.730550i	$-0.739264\pi$
$269$	−9.78952	+	4.35857i	−0.596877	+	0.265747i	0.0859820	+	0.996297i	$0.472597\pi$
$270$	0.669131	+	0.743145i	0.0407220	+	0.0452264i
$271$	0.727507	−	2.23904i	0.0441929	−	0.136012i	−0.926526	−	0.376232i	$-0.877220\pi$
$271$	0.727507	−	2.23904i	0.0441929	−	0.136012i	0.970718	+	0.240220i	$0.0772196\pi$
$272$	0.694381	−	0.771188i	0.0421030	−	0.0467602i
$273$	−0.128942	−	0.223334i	−0.00780391	−	0.0135168i
$274$	9.02870	−	15.6382i	0.545444	−	0.944736i
$275$	−0.468532	−	1.44199i	−0.0282536	−	0.0869555i
$276$	3.17751	+	1.41472i	0.191264	+	0.0851562i
$277$	1.78618	+	1.29774i	0.107321	+	0.0779736i	0.640152	−	0.768249i	$-0.278872\pi$
$277$	1.78618	+	1.29774i	0.107321	+	0.0779736i	−0.532830	+	0.846222i	$0.678872\pi$
$278$	7.06088			0.423484
$279$	5.09718	+	2.24025i	0.305160	+	0.134120i
$280$	−0.499184			−0.0298319
$281$	23.1584	+	16.8256i	1.38151	+	1.00373i	0.996737	+	0.0807196i	$0.0257218\pi$
$281$	23.1584	+	16.8256i	1.38151	+	1.00373i	0.384778	+	0.923009i	$0.374278\pi$
$282$	8.28309	+	3.68787i	0.493251	+	0.219609i
$283$	−2.04919	−	6.30676i	−0.121812	−	0.374898i	0.871495	−	0.490404i	$-0.163151\pi$
$283$	−2.04919	−	6.30676i	−0.121812	−	0.374898i	−0.993307	+	0.115506i	$0.963151\pi$
$284$	−1.03209	+	1.78763i	−0.0612431	+	0.106076i
$285$	3.40990	+	5.90613i	0.201985	+	0.349849i
$286$	−0.524121	+	0.582095i	−0.0309919	+	0.0344200i
$287$	−1.67819	+	5.16494i	−0.0990606	+	0.304877i
$288$	−0.669131	−	0.743145i	−0.0394289	−	0.0437902i
$289$	−14.5465	+	6.47651i	−0.855675	+	0.380971i
$290$	−3.80916	−	0.809663i	−0.223682	−	0.0475450i
$291$	−0.253600	+	2.41284i	−0.0148663	+	0.141443i
$292$	0.101183	+	0.962696i	0.00592131	+	0.0563375i
$293$	−17.2394	+	3.66435i	−1.00714	+	0.214074i	−0.681811	−	0.731528i	$-0.738807\pi$
$293$	−17.2394	+	3.66435i	−1.00714	+	0.214074i	−0.325326	+	0.945602i	$0.605474\pi$
$294$	5.46152	−	3.96803i	0.318523	−	0.231420i
$295$	−5.69070	+	4.13454i	−0.331326	+	0.240722i
$296$	−5.77464	+	1.22744i	−0.335644	+	0.0713434i
$297$	−0.158486	−	1.50790i	−0.00919631	−	0.0874970i
$298$	0.0901714	−	0.857924i	0.00522349	−	0.0496982i
$299$	−1.75762	−	0.373594i	−0.101646	−	0.0216055i
$300$	−0.913545	+	0.406737i	−0.0527436	+	0.0234830i
$301$	0.194842	+	0.216394i	0.0112305	+	0.0124727i
$302$	0.285324	−	0.878137i	0.0164186	−	0.0505311i
$303$	−4.97194	+	5.52189i	−0.285630	+	0.317224i
$304$	−3.40990	−	5.90613i	−0.195571	−	0.338740i
$305$	2.72892	−	4.72662i	0.156257	−	0.270646i
$306$	−0.320678	−	0.986946i	−0.0183319	−	0.0564199i
$307$	0.606377	+	0.269976i	0.0346078	+	0.0154084i	0.423968	−	0.905677i	$-0.360637\pi$
$307$	0.606377	+	0.269976i	0.0346078	+	0.0154084i	−0.389360	+	0.921086i	$0.627304\pi$
$308$	0.612315	+	0.444873i	0.0348899	+	0.0253490i
$309$	−10.0247			−0.570284
$310$	−3.70572	+	4.15544i	−0.210471	+	0.236013i
$311$	−16.2091			−0.919136			−0.459568	−	0.888143i	$-0.651996\pi$
$311$	−16.2091			−0.919136			−0.459568	+	0.888143i	$0.651996\pi$
$312$	0.417947	+	0.303656i	0.0236616	+	0.0171912i
$313$	24.6471	+	10.9736i	1.39314	+	0.620265i	0.959728	−	0.280931i	$-0.0906433\pi$
$313$	24.6471	+	10.9736i	1.39314	+	0.620265i	0.433411	+	0.901196i	$0.357310\pi$
$314$	−2.73474	−	8.41665i	−0.154330	−	0.474979i
$315$	−0.249592	+	0.432306i	−0.0140629	+	0.0243577i
$316$	6.34294	+	10.9863i	0.356818	+	0.618027i
$317$	4.87256	−	5.41152i	0.273670	−	0.303941i	−0.590605	−	0.806961i	$-0.701111\pi$
$317$	4.87256	−	5.41152i	0.273670	−	0.303941i	0.864275	+	0.503019i	$0.167778\pi$
$318$	−1.47357	+	4.53518i	−0.0826336	+	0.254320i
$319$	3.95087	+	4.38789i	0.221207	+	0.245675i
$320$	0.913545	−	0.406737i	0.0510687	−	0.0227373i
$321$	−8.51309	−	1.80951i	−0.475154	−	0.100997i
$322$	−0.181490	+	1.72676i	−0.0101140	+	0.0962286i
$323$	−0.739765	−	7.03839i	−0.0411616	−	0.391627i
$324$	−0.978148	+	0.207912i	−0.0543415	+	0.0115506i
$325$	0.417947	−	0.303656i	0.0231835	−	0.0168438i
$326$	10.9144	−	7.92979i	0.604494	−	0.439191i
$327$	−5.36630	+	1.14064i	−0.296757	+	0.0630776i
$328$	−1.13719	−	10.8197i	−0.0627909	−	0.597416i
$329$	−0.473105	+	4.50129i	−0.0260831	+	0.248164i
$330$	1.48307	+	0.315236i	0.0816403	+	0.0173532i
$331$	12.3482	−	5.49776i	0.678717	−	0.302184i	−0.0382734	−	0.999267i	$-0.512186\pi$
$331$	12.3482	−	5.49776i	0.678717	−	0.302184i	0.716990	+	0.697083i	$0.245519\pi$
$332$	1.88988	+	2.09893i	0.103721	+	0.115194i
$333$	−1.82433	+	5.61470i	−0.0999725	+	0.307684i
$334$	−3.57659	+	3.97220i	−0.195702	+	0.217349i
$335$	4.91335	+	8.51018i	0.268445	+	0.464961i
$336$	0.249592	−	0.432306i	0.0136163	−	0.0235842i
$337$	5.43424	+	16.7249i	0.296022	+	0.911062i	0.982876	+	0.184267i	$0.0589911\pi$
$337$	5.43424	+	16.7249i	0.296022	+	0.911062i	−0.686854	+	0.726795i	$0.741009\pi$
$338$	11.6323	+	5.17902i	0.632712	+	0.281702i
$339$	13.5242	+	9.82590i	0.734534	+	0.533670i
$340$	1.03774			0.0562792
$341$	8.24889	−	1.79466i	0.446702	−	0.0971861i
$342$	−6.81981			−0.368773
$343$	5.55324	+	4.03466i	0.299847	+	0.217851i
$344$	−0.532895	−	0.237260i	−0.0287318	−	0.0127922i
$345$	1.07483	+	3.30799i	0.0578669	+	0.178096i
$346$	5.65934	−	9.80226i	0.304248	−	0.526973i
$347$	12.3507	+	21.3920i	0.663021	+	1.14839i	0.979818	+	0.199892i	$0.0640591\pi$
$347$	12.3507	+	21.3920i	0.663021	+	1.14839i	−0.316797	+	0.948493i	$0.602608\pi$
$348$	2.60577	−	2.89400i	0.139684	−	0.155135i
$349$	−8.50886	+	26.1876i	−0.455469	+	1.40179i	0.415116	+	0.909769i	$0.363741\pi$
$349$	−8.50886	+	26.1876i	−0.455469	+	1.40179i	−0.870584	+	0.492019i	$0.836259\pi$
$350$	−0.334019	−	0.370966i	−0.0178541	−	0.0198289i
$351$	0.471948	−	0.210125i	0.0251907	−	0.0112156i
$352$	−1.48307	−	0.315236i	−0.0790479	−	0.0168021i
$353$	−1.06639	+	10.1460i	−0.0567579	+	0.540016i	0.928788	+	0.370610i	$0.120851\pi$
$353$	−1.06639	+	10.1460i	−0.0567579	+	0.540016i	−0.985546	+	0.169406i	$0.945815\pi$
$354$	−0.735263	−	6.99556i	−0.0390788	−	0.371810i
$355$	−2.01907	+	0.429166i	−0.107161	+	0.0227778i
$356$	−7.34805	+	5.33867i	−0.389446	+	0.282949i
$357$	0.419088	−	0.304485i	0.0221805	−	0.0161151i
$358$	7.69042	−	1.63465i	0.406451	−	0.0863939i
$359$	−0.464783	−	4.42211i	−0.0245303	−	0.233390i	−0.999917	−	0.0128887i	$-0.995897\pi$
$359$	−0.464783	−	4.42211i	−0.0245303	−	0.233390i	0.975387	−	0.220501i	$-0.0707694\pi$
$360$	0.104528	−	0.994522i	0.00550913	−	0.0524159i
$361$	−26.9086	−	5.71961i	−1.41624	−	0.301032i
$362$	20.0792	−	8.93984i	1.05534	−	0.469867i
$363$	5.82219	+	6.46620i	0.305586	+	0.339387i
$364$	−0.0796904	+	0.245262i	−0.00417691	+	0.0128552i
$365$	−0.647718	+	0.719363i	−0.0339031	+	0.0376532i
$366$	2.72892	+	4.72662i	0.142643	+	0.247065i
$367$	9.57165	−	16.5786i	0.499636	−	0.865395i	−0.500364	−	0.865815i	$-0.666800\pi$
$367$	9.57165	−	16.5786i	0.499636	−	0.865395i	1.00000		0.000419958i	$0.000133677\pi$
$368$	−1.07483	−	3.30799i	−0.0560294	−	0.172441i
$369$	−9.93869	−	4.42499i	−0.517388	−	0.230356i
$370$	−4.77615	−	3.47008i	−0.248300	−	0.180401i
$371$	−2.38039			−0.123584
$372$	−1.74585	−	5.28696i	−0.0905183	−	0.274116i
$373$	3.95594			0.204831			0.102415	−	0.994742i	$-0.467343\pi$
$373$	3.95594			0.204831			0.102415	+	0.994742i	$0.467343\pi$
$374$	−1.27292	−	0.924832i	−0.0658212	−	0.0478219i
$375$	−0.913545	−	0.406737i	−0.0471753	−	0.0210038i
$376$	−2.80185	−	8.62320i	−0.144494	−	0.444708i
$377$	−1.00591	+	1.74229i	−0.0518070	+	0.0897323i
$378$	−0.249592	−	0.432306i	−0.0128376	−	0.0222354i
$379$	−11.0687	+	12.2931i	−0.568563	+	0.631453i	−0.957023	−	0.290013i	$-0.906341\pi$
$379$	−11.0687	+	12.2931i	−0.568563	+	0.631453i	0.388460	+	0.921466i	$0.373007\pi$
$380$	2.10744	−	6.48602i	0.108109	−	0.332726i
$381$	−3.48821	−	3.87405i	−0.178706	−	0.198474i
$382$	−21.9564	+	9.77564i	−1.12339	+	0.500165i
$383$	−29.2442	−	6.21605i	−1.49431	−	0.317625i	−0.612969	−	0.790107i	$-0.710025\pi$
$383$	−29.2442	−	6.21605i	−1.49431	−	0.317625i	−0.881340	+	0.472482i	$0.843358\pi$
$384$	−0.104528	+	0.994522i	−0.00533420	+	0.0507515i
$385$	0.0791138	+	0.752717i	0.00403201	+	0.0383620i
$386$	19.6421	−	4.17505i	0.999755	−	0.212504i
$387$	−0.471921	+	0.342871i	−0.0239891	+	0.0174291i
$388$	1.96278	−	1.42604i	0.0996451	−	0.0723964i
$389$	−4.35654	+	0.926012i	−0.220886	+	0.0469507i	−0.317025	−	0.948417i	$-0.602684\pi$
$389$	−4.35654	+	0.926012i	−0.220886	+	0.0469507i	0.0961393	+	0.995368i	$0.469351\pi$
$390$	0.0540005	+	0.513781i	0.00273442	+	0.0260163i
$391$	0.377293	−	3.58970i	0.0190805	−	0.181539i
$392$	−6.60329	−	1.40357i	−0.333517	−	0.0708912i
$393$	1.24255	−	0.553220i	0.0626785	−	0.0279063i
$394$	−11.6148	−	12.8996i	−0.585146	−	0.649870i
$395$	−3.92015	+	12.0650i	−0.197244	+	0.607055i
$396$	−1.01454	+	1.12676i	−0.0509824	+	0.0566217i
$397$	−9.60721	−	16.6402i	−0.482172	−	0.835146i	0.517619	−	0.855611i	$-0.326819\pi$
$397$	−9.60721	−	16.6402i	−0.482172	−	0.835146i	−0.999791	+	0.0204652i	$0.993485\pi$
$398$	−7.79420	+	13.4999i	−0.390688	+	0.676691i
$399$	−1.05200	−	3.23772i	−0.0526658	−	0.162089i
$400$	0.913545	+	0.406737i	0.0456773	+	0.0203368i
$401$	5.63844	+	4.09656i	0.281570	+	0.204573i	0.719602	−	0.694387i	$-0.244324\pi$
$401$	5.63844	+	4.09656i	0.281570	+	0.204573i	−0.438032	+	0.898959i	$0.644324\pi$
$402$	−9.82671			−0.490112
$403$	1.45009	+	2.48410i	0.0722340	+	0.123742i
$404$	7.43044			0.369678
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$	1.77589	+	0.790676i	0.0881359	+	0.0392406i
$407$	2.76605	+	8.51303i	0.137108	+	0.421975i
$408$	−0.518868	+	0.898706i	−0.0256878	+	0.0444926i
$409$	−4.20302	−	7.27984i	−0.207826	−	0.359965i	0.743204	−	0.669065i	$-0.233305\pi$
$409$	−4.20302	−	7.27984i	−0.207826	−	0.359965i	−0.951029	+	0.309100i	$0.899972\pi$
$410$	7.27964	−	8.08486i	0.359516	−	0.399283i
$411$	−5.58004	+	17.1736i	−0.275243	+	0.847112i
$412$	6.70782	+	7.44979i	0.330471	+	0.367025i
$413$	3.20774	−	1.42818i	0.157842	−	0.0702760i
$414$	−3.40221	−	0.723163i	−0.167210	−	0.0355415i
$415$	−0.295229	+	2.80892i	−0.0144922	+	0.137884i
$416$	−0.0540005	−	0.513781i	−0.00264759	−	0.0251902i
$417$	−6.90659	+	1.46804i	−0.338217	+	0.0718902i
$418$	−8.36540	+	6.07782i	−0.409165	+	0.297276i
$419$	1.54418	−	1.12191i	0.0754380	−	0.0548089i	−0.549427	−	0.835542i	$-0.685154\pi$
$419$	1.54418	−	1.12191i	0.0754380	−	0.0548089i	0.624865	+	0.780733i	$0.285154\pi$
$420$	0.488275	−	0.103786i	0.0238254	−	0.00506424i
$421$	−1.52281	−	14.4885i	−0.0742170	−	0.706127i	−0.966850	−	0.255344i	$-0.917811\pi$
$421$	−1.52281	−	14.4885i	−0.0742170	−	0.706127i	0.892633	−	0.450784i	$-0.148855\pi$
$422$	1.83063	−	17.4173i	0.0891136	−	0.847859i
$423$	−8.86884	−	1.88513i	−0.431218	−	0.0916581i
$424$	4.35630	−	1.93955i	0.211561	−	0.0941929i
$425$	0.694381	+	0.771188i	0.0336824	+	0.0374081i
$426$	0.637865	−	1.96315i	0.0309047	−	0.0951148i
$427$	−1.82302	+	2.02467i	−0.0882221	+	0.0979806i
$428$	4.35164	+	7.53726i	0.210344	+	0.364327i
$429$	0.391643	−	0.678346i	0.0189087	−	0.0327509i
$430$	−0.180258	−	0.554776i	−0.00869280	−	0.0267537i
$431$	27.4172	+	12.2069i	1.32064	+	0.587987i	0.941394	−	0.337309i	$-0.109517\pi$
$431$	27.4172	+	12.2069i	1.32064	+	0.587987i	0.379246	+	0.925296i	$0.376183\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	−18.6204			−0.894840			−0.447420	−	0.894324i	$-0.647657\pi$
$433$	−18.6204			−0.894840			−0.447420	+	0.894324i	$0.647657\pi$
$434$	2.24069	−	1.64439i	0.107556	−	0.0789335i
$435$	3.89426			0.186716
$436$	4.43842	+	3.22470i	0.212562	+	0.154435i
$437$	−21.6700	−	9.64812i	−1.03662	−	0.461532i
$438$	−0.299128	−	0.920621i	−0.0142929	−	0.0439890i
$439$	−13.0041	+	22.5238i	−0.620653	+	1.07500i	0.368711	+	0.929544i	$0.379799\pi$
$439$	−13.0041	+	22.5238i	−0.620653	+	1.07500i	−0.989364	+	0.145459i	$0.953534\pi$
$440$	−0.758101	−	1.31307i	−0.0361411	−	0.0625981i
$441$	−4.51718	+	5.01683i	−0.215104	+	0.238897i
$442$	0.165666	−	0.509867i	0.00787992	−	0.0242519i
$443$	−5.54921	−	6.16302i	−0.263651	−	0.292814i	0.596755	−	0.802424i	$-0.296456\pi$
$443$	−5.54921	−	6.16302i	−0.263651	−	0.292814i	−0.860406	+	0.509610i	$0.829790\pi$
$444$	5.39325	−	2.40123i	0.255952	−	0.113957i
$445$	−8.88421	−	1.88840i	−0.421152	−	0.0895186i
$446$	−1.39719	+	13.2933i	−0.0661587	+	0.629458i
$447$	0.0901714	+	0.857924i	0.00426496	+	0.0405784i
$448$	−0.488275	+	0.103786i	−0.0230688	+	0.00490343i
$449$	1.89134	−	1.37414i	0.0892579	−	0.0648497i	−0.542261	−	0.840210i	$-0.682432\pi$
$449$	1.89134	−	1.37414i	0.0892579	−	0.0648497i	0.631519	+	0.775360i	$0.282432\pi$
$450$	0.809017	−	0.587785i	0.0381374	−	0.0277085i
$451$	−16.1347	+	3.42953i	−0.759753	+	0.161490i
$452$	−1.74738	−	16.6252i	−0.0821900	−	0.781986i
$453$	−0.0965141	+	0.918270i	−0.00453463	+	0.0431441i
$454$	−7.12070	−	1.51355i	−0.334191	−	0.0710345i
$455$	−0.235588	+	0.104891i	−0.0110446	+	0.00491735i
$456$	4.56334	+	5.06811i	0.213698	+	0.237336i
$457$	−2.31465	+	7.12375i	−0.108275	+	0.333235i	−0.990485	−	0.137620i	$-0.956055\pi$
$457$	−2.31465	+	7.12375i	−0.108275	+	0.333235i	0.882211	+	0.470855i	$0.156055\pi$
$458$	−6.73551	+	7.48054i	−0.314730	+	0.349543i
$459$	0.518868	+	0.898706i	0.0242187	+	0.0419480i
$460$	1.73911	−	3.01223i	0.0810865	−	0.140446i
$461$	1.57247	+	4.83957i	0.0732372	+	0.225401i	0.980974	−	0.194139i	$-0.0621913\pi$
$461$	1.57247	+	4.83957i	0.0732372	+	0.225401i	−0.907737	+	0.419540i	$0.862191\pi$
$462$	−0.691429	−	0.307844i	−0.0321682	−	0.0143222i
$463$	−2.66735	−	1.93794i	−0.123962	−	0.0900638i	0.524077	−	0.851671i	$-0.324411\pi$
$463$	−2.66735	−	1.93794i	−0.123962	−	0.0900638i	−0.648039	+	0.761607i	$0.724411\pi$
$464$	−3.89426			−0.180787
$465$	2.76078	−	4.83509i	0.128028	−	0.224222i
$466$	2.12894			0.0986214
$467$	−22.3939	−	16.2701i	−1.03627	−	0.752893i	−0.0667142	−	0.997772i	$-0.521252\pi$
$467$	−22.3939	−	16.2701i	−1.03627	−	0.752893i	−0.969554	+	0.244880i	$0.921252\pi$
$468$	−0.471948	−	0.210125i	−0.0218158	−	0.00971301i
$469$	−1.51583	−	4.66525i	−0.0699945	−	0.215421i
$470$	4.53349	−	7.85223i	0.209114	−	0.362196i
$471$	4.42490	+	7.66415i	0.203888	+	0.353145i
$472$	−4.70673	+	5.22735i	−0.216645	+	0.240608i
$473$	−0.273307	+	0.841153i	−0.0125667	+	0.0386763i
$474$	−8.48851	−	9.42744i	−0.389890	−	0.433017i
$475$	6.23020	−	2.77387i	0.285861	−	0.127274i
$476$	−0.506701	−	0.107703i	−0.0232246	−	0.00493654i
$477$	0.498451	−	4.74244i	0.0228225	−	0.217142i
$478$	2.21971	+	21.1191i	0.101527	+	0.965967i
$479$	0.223800	−	0.0475702i	0.0102257	−	0.00217354i	−0.202796	−	0.979221i	$-0.565003\pi$
$479$	0.223800	−	0.0475702i	0.0102257	−	0.00217354i	0.213022	+	0.977047i	$0.431669\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	−2.46741	+	1.79268i	−0.112504	+	0.0817392i
$482$	13.2231	−	2.81066i	0.602296	−	0.128022i
$483$	−0.181490	−	1.72676i	−0.00825807	−	0.0785703i
$484$	0.909516	−	8.65346i	0.0413416	−	0.393339i
$485$	2.37311	+	0.504421i	0.107757	+	0.0229046i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	−6.37194	−	7.07676i	−0.288740	−	0.320678i	0.581271	−	0.813710i	$-0.302555\pi$
$487$	−6.37194	−	7.07676i	−0.288740	−	0.320678i	−0.870012	+	0.493031i	$0.835889\pi$
$488$	1.68656	−	5.19071i	0.0763471	−	0.234972i
$489$	−9.02722	+	10.0257i	−0.408225	+	0.453380i
$490$	−3.37541	−	5.84638i	−0.152485	−	0.264112i
$491$	14.5249	−	25.1579i	0.655501	−	1.13536i	−0.326267	−	0.945278i	$-0.605791\pi$
$491$	14.5249	−	25.1579i	0.655501	−	1.13536i	0.981768	−	0.190083i	$-0.0608758\pi$
$492$	3.36187	+	10.3468i	0.151565	+	0.466469i
$493$	−3.69184	−	1.64371i	−0.166272	−	0.0740290i
$494$	−2.85032	−	2.07088i	−0.128242	−	0.0931732i
$495$	−1.51620			−0.0681482
$496$	−2.76078	+	4.83509i	−0.123962	+	0.217102i
$497$	1.03040			0.0462199
$498$	−2.28498	−	1.66013i	−0.102392	−	0.0743924i
$499$	−0.00516482	−	0.00229952i	−0.000231209	−	0.000102941i	0.406621	−	0.913597i	$-0.366707\pi$
$499$	−0.00516482	−	0.00229952i	−0.000231209	−	0.000102941i	−0.406852	+	0.913494i	$0.633374\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	2.67256	−	4.62902i	0.119401	−	0.206809i
$502$	9.44248	+	16.3548i	0.421438	+	0.729953i
$503$	10.2612	−	11.3963i	0.457526	−	0.508134i	−0.469602	−	0.882878i	$-0.655603\pi$
$503$	10.2612	−	11.3963i	0.457526	−	0.508134i	0.927128	+	0.374744i	$0.122269\pi$
$504$	−0.154256	+	0.474752i	−0.00687112	+	0.0211471i
$505$	4.97194	+	5.52189i	0.221248	+	0.245721i
$506$	−4.81775	+	2.14500i	−0.214175	+	0.0953570i
$507$	−12.4549	−	2.64736i	−0.553140	−	0.117574i
$508$	−0.544912	+	5.18449i	−0.0241766	+	0.230025i
$509$	−3.24467	−	30.8709i	−0.143817	−	1.36833i	−0.793706	−	0.608301i	$-0.791851\pi$
$509$	−3.24467	−	30.8709i	−0.143817	−	1.36833i	0.649889	−	0.760029i	$-0.274815\pi$
$510$	−1.01506	+	0.215758i	−0.0449476	+	0.00955390i
$511$	0.390924	−	0.284023i	0.0172935	−	0.0125644i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	6.67078	−	1.41792i	0.294522	−	0.0626026i
$514$	−1.67834	−	15.9683i	−0.0740283	−	0.704332i
$515$	−1.04787	+	9.96977i	−0.0461745	+	0.439321i
$516$	0.570579	+	0.121280i	0.0251183	+	0.00533907i
$517$	−12.5588	+	5.59156i	−0.552337	+	0.245916i
$518$	1.97193	+	2.19005i	0.0866417	+	0.0962253i
$519$	−3.49766	+	10.7647i	−0.153530	+	0.472518i
$520$	0.345680	−	0.383917i	0.0151591	−	0.0168359i
$521$	0.572752	+	0.992036i	0.0250927	+	0.0434619i	0.878299	−	0.478112i	$-0.158679\pi$
$521$	0.572752	+	0.992036i	0.0250927	+	0.0434619i	−0.853206	+	0.521574i	$0.825345\pi$
$522$	−1.94713	+	3.37253i	−0.0852236	+	0.147612i
$523$	2.46920	+	7.59943i	0.107971	+	0.332300i	0.990416	−	0.138115i	$-0.0441044\pi$
$523$	2.46920	+	7.59943i	0.107971	+	0.332300i	−0.882445	+	0.470415i	$0.844104\pi$
$524$	−1.24255	−	0.553220i	−0.0542811	−	0.0241675i
$525$	0.403848	+	0.293413i	0.0176254	+	0.0128056i
$526$	12.0684			0.526209
$527$	−4.65809	+	3.41848i	−0.202910	+	0.148911i
$528$	1.51620			0.0659842
$529$	8.81988	+	6.40802i	0.383473	+	0.278609i
$530$	4.35630	+	1.93955i	0.189226	+	0.0842487i
$531$	2.17366	+	6.68982i	0.0943286	+	0.290314i
$532$	−1.70217	+	2.94824i	−0.0737983	+	0.127822i
$533$	−2.81017	−	4.86736i	−0.121722	−	0.210829i
$534$	6.07750	−	6.74975i	0.262999	−	0.292090i
$535$	−2.68946	+	8.27731i	−0.116276	+	0.357859i
$536$	6.57535	+	7.30267i	0.284012	+	0.315427i
$537$	−7.18251	+	3.19786i	−0.309948	+	0.137998i
$538$	−10.4818	−	2.22797i	−0.451902	−	0.0960548i
$539$	−1.06991	+	10.1795i	−0.0460844	+	0.438463i
$540$	0.104528	+	0.994522i	0.00449819	+	0.0427974i
$541$	13.5497	−	2.88007i	0.582546	−	0.123824i	0.0927933	−	0.995685i	$-0.470420\pi$
$541$	13.5497	−	2.88007i	0.582546	−	0.123824i	0.489753	+	0.871861i	$0.337087\pi$
$542$	1.90464	−	1.38380i	0.0818113	−	0.0594394i
$543$	−17.7817	+	12.9192i	−0.763087	+	0.554415i
$544$	1.01506	−	0.215758i	0.0435203	−	0.00925053i
$545$	0.573462	+	5.45613i	0.0245644	+	0.233715i
$546$	0.0269562	−	0.256471i	0.00115362	−	0.0109759i
$547$	13.1785	+	2.80118i	0.563472	+	0.119770i	0.480837	−	0.876810i	$-0.340333\pi$
$547$	13.1785	+	2.80118i	0.563472	+	0.119770i	0.0826356	+	0.996580i	$0.473666\pi$
$548$	16.4963	−	7.34461i	0.704685	−	0.313746i
$549$	−3.65200	−	4.05596i	−0.155864	−	0.173104i
$550$	0.468532	−	1.44199i	0.0199783	−	0.0614868i
$551$	−17.7709	+	19.7365i	−0.757064	+	0.840805i
$552$	1.73911	+	3.01223i	0.0740215	+	0.128209i
$553$	3.16629	−	5.48418i	0.134644	−	0.233211i
$554$	0.682262	+	2.09979i	0.0289865	+	0.0892114i
$555$	5.39325	+	2.40123i	0.228931	+	0.101927i
$556$	5.71237	+	4.15028i	0.242259	+	0.176011i
$557$	13.1761			0.558287			0.279144	−	0.960249i	$-0.409949\pi$
$557$	13.1761			0.558287			0.279144	+	0.960249i	$0.409949\pi$
$558$	2.80692	+	4.80845i	0.118827	+	0.203558i
$559$	−0.301353			−0.0127459
$560$	−0.403848	−	0.293413i	−0.0170657	−	0.0123990i
$561$	1.43739	+	0.639967i	0.0606866	+	0.0270194i
$562$	8.84572	+	27.2243i	0.373134	+	1.14839i
$563$	7.39990	−	12.8170i	0.311869	−	0.540172i	−0.666898	−	0.745149i	$-0.732378\pi$
$563$	7.39990	−	12.8170i	0.311869	−	0.540172i	0.978767	+	0.204976i	$0.0657118\pi$
$564$	4.53349	+	7.85223i	0.190894	+	0.330638i
$565$	11.1857	−	12.4230i	0.470588	−	0.522641i
$566$	2.04919	−	6.30676i	0.0861339	−	0.265093i
$567$	0.334019	+	0.370966i	0.0140275	+	0.0155791i
$568$	−1.88572	+	0.839576i	−0.0791230	+	0.0352278i
$569$	−15.8511	−	3.36925i	−0.664513	−	0.141247i	−0.136707	−	0.990612i	$-0.543652\pi$
$569$	−15.8511	−	3.36925i	−0.664513	−	0.141247i	−0.527806	+	0.849365i	$0.676985\pi$
$570$	−0.712864	+	6.78245i	−0.0298586	+	0.284086i
$571$	−2.13658	−	20.3282i	−0.0894130	−	0.850707i	−0.943677	−	0.330868i	$-0.892658\pi$
$571$	−2.13658	−	20.3282i	−0.0894130	−	0.850707i	0.854264	−	0.519839i	$-0.174008\pi$
$572$	−0.766170	+	0.162854i	−0.0320352	+	0.00680929i
$573$	19.4442	−	14.1270i	0.812292	−	0.590165i
$574$	−4.39356	+	3.19211i	−0.183384	+	0.133236i
$575$	3.40221	−	0.723163i	0.141882	−	0.0301580i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−4.87934	+	46.4239i	−0.203130	+	1.93265i	0.133572	+	0.991039i	$0.457355\pi$
$577$	−4.87934	+	46.4239i	−0.203130	+	1.93265i	−0.336702	+	0.941611i	$0.609311\pi$
$578$	−15.5751	−	3.31060i	−0.647841	−	0.137703i
$579$	−18.3448	+	8.16763i	−0.762384	+	0.339435i
$580$	−2.60577	−	2.89400i	−0.108199	−	0.120167i
$581$	0.435679	−	1.34088i	0.0180750	−	0.0556292i
$582$	−1.62340	+	1.80297i	−0.0672920	+	0.0747353i
$583$	−3.61506	−	6.26146i	−0.149720	−	0.259323i
$584$	−0.483999	+	0.838311i	−0.0200280	+	0.0346896i
$585$	−0.159642	−	0.491326i	−0.00660037	−	0.0203138i
$586$	−16.1008	−	7.16855i	−0.665119	−	0.296130i
$587$	15.9998	+	11.6245i	0.660383	+	0.479796i	0.866792	−	0.498670i	$-0.166178\pi$
$587$	15.9998	+	11.6245i	0.660383	+	0.479796i	−0.206410	+	0.978466i	$0.566178\pi$
$588$	6.75082			0.278399
$589$	11.9064	+	36.0561i	0.490594	+	1.48567i
$590$	−7.03410			−0.289589
$591$	14.0430	+	10.2028i	0.577651	+	0.419688i
$592$	−5.39325	−	2.40123i	−0.221661	−	0.0986899i
$593$	−9.46424	−	29.1279i	−0.388650	−	1.19614i	−0.933798	−	0.357801i	$-0.883527\pi$
$593$	−9.46424	−	29.1279i	−0.388650	−	1.19614i	0.545148	−	0.838340i	$-0.316473\pi$
$594$	0.758101	−	1.31307i	0.0311053	−	0.0538759i
$595$	−0.259010	−	0.448619i	−0.0106184	−	0.0183916i
$596$	0.577225	−	0.641073i	0.0236441	−	0.0262594i
$597$	4.81708	−	14.8254i	0.197150	−	0.606765i
$598$	−1.20235	−	1.33535i	−0.0491678	−	0.0546064i
$599$	−0.387944	+	0.172724i	−0.0158510	+	0.00705731i	−0.414647	−	0.909982i	$-0.636095\pi$
$599$	−0.387944	+	0.172724i	−0.0158510	+	0.00705731i	0.398796	+	0.917040i	$0.369428\pi$
$600$	−0.978148	−	0.207912i	−0.0399327	−	0.00848796i
$601$	−2.19707	+	20.9038i	−0.0896205	+	0.852682i	0.853692	+	0.520777i	$0.174358\pi$
$601$	−2.19707	+	20.9038i	−0.0896205	+	0.852682i	−0.943313	+	0.331905i	$0.892309\pi$
$602$	0.0304373	+	0.289592i	0.00124053	+	0.0118029i
$603$	9.61197	−	2.04309i	0.391430	−	0.0832009i
$604$	0.746988	−	0.542719i	0.0303945	−	0.0220829i
$605$	7.03936	−	5.11440i	0.286191	−	0.207930i
$606$	−7.26807	+	1.54488i	−0.295245	+	0.0627563i
$607$	1.73128	+	16.4720i	0.0702704	+	0.668579i	0.971791	+	0.235843i	$0.0757850\pi$
$607$	1.73128	+	16.4720i	0.0702704	+	0.668579i	−0.901521	+	0.432736i	$0.857548\pi$
$608$	0.712864	−	6.78245i	0.0289105	−	0.275065i
$609$	−1.90147	−	0.404170i	−0.0770515	−	0.0163778i
$610$	4.98598	−	2.21990i	0.201876	−	0.0898812i
$611$	−3.13427	−	3.48096i	−0.126799	−	0.140825i
$612$	0.320678	−	0.986946i	0.0129626	−	0.0398949i
$613$	−29.4595	+	32.7181i	−1.18986	+	1.32147i	−0.254796	+	0.966995i	$0.582008\pi$
$613$	−29.4595	+	32.7181i	−1.18986	+	1.32147i	−0.935064	+	0.354478i	$0.884658\pi$
$614$	0.331881	+	0.574835i	0.0133936	+	0.0231984i
$615$	−5.43963	+	9.42171i	−0.219347	+	0.379920i
$616$	0.233884	+	0.719820i	0.00942344	+	0.0290024i
$617$	−0.910347	−	0.405313i	−0.0366492	−	0.0163173i	0.388330	−	0.921520i	$-0.373052\pi$
$617$	−0.910347	−	0.405313i	−0.0366492	−	0.0163173i	−0.424979	+	0.905203i	$0.639719\pi$
$618$	−8.11014	−	5.89236i	−0.326238	−	0.237026i
$619$	34.8802			1.40195			0.700976	−	0.713185i	$-0.252748\pi$
$619$	34.8802			1.40195			0.700976	+	0.713185i	$0.252748\pi$
$620$	−5.44049	+	1.18365i	−0.218495	+	0.0475366i
$621$	3.47822			0.139576
$622$	−13.1135	−	9.52749i	−0.525802	−	0.382018i
$623$	4.14195	+	1.84411i	0.165944	+	0.0738829i
$624$	0.159642	+	0.491326i	0.00639078	+	0.0196688i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	13.4898	+	23.3651i	0.539162	+	0.933856i
$627$	6.91895	−	7.68427i	0.276316	−	0.306880i
$628$	2.73474	−	8.41665i	0.109128	−	0.335861i
$629$	−4.09938	−	4.55282i	−0.163453	−	0.181533i
$630$	−0.456027	+	0.203036i	−0.0181685	+	0.00808916i
$631$	−41.3099	−	8.78068i	−1.64452	−	0.349553i	−0.709652	−	0.704552i	$-0.751148\pi$
$631$	−41.3099	−	8.78068i	−1.64452	−	0.349553i	−0.934867	+	0.354999i	$0.884481\pi$
$632$	−1.32604	+	12.6164i	−0.0527468	+	0.501853i
$633$	1.83063	+	17.4173i	0.0727609	+	0.692274i
$634$	7.12279	−	1.51400i	0.282882	−	0.0601285i
$635$	−4.21745	+	3.06415i	−0.167364	+	0.121597i
$636$	−3.85785	+	2.80289i	−0.152974	+	0.111142i
$637$	−3.41133	+	0.725101i	−0.135162	+	0.0287296i
$638$	0.617187	+	5.87214i	0.0244347	+	0.232480i
$639$	−0.215765	+	2.05287i	−0.00853554	+	0.0812102i
$640$	0.978148	+	0.207912i	0.0386647	+	0.00821843i
$641$	29.2131	−	13.0065i	1.15385	−	0.513727i	0.261558	−	0.965188i	$-0.415764\pi$
$641$	29.2131	−	13.0065i	1.15385	−	0.513727i	0.892291	+	0.451461i	$0.149097\pi$
$642$	−5.82363	−	6.46780i	−0.229840	−	0.255264i
$643$	−5.61665	+	17.2863i	−0.221499	+	0.681704i	0.777129	+	0.629341i	$0.216675\pi$
$643$	−5.61665	+	17.2863i	−0.221499	+	0.681704i	−0.998628	+	0.0523627i	$0.983325\pi$
$644$	−1.16179	+	1.29030i	−0.0457810	+	0.0508450i
$645$	0.291663	+	0.505175i	0.0114842	+	0.0198913i
$646$	3.53858	−	6.12900i	0.139224	−	0.241142i
$647$	−4.60533	−	14.1737i	−0.181054	−	0.557227i	0.818804	−	0.574073i	$-0.194638\pi$
$647$	−4.60533	−	14.1737i	−0.181054	−	0.557227i	−0.999858	+	0.0168459i	$0.994638\pi$
$648$	−0.913545	−	0.406737i	−0.0358875	−	0.0159781i
$649$	8.62826	+	6.26880i	0.338689	+	0.246072i
$650$	0.516611			0.0202631
$651$	−1.84983	+	2.07433i	−0.0725007	+	0.0812992i
$652$	13.4910			0.528347
$653$	−7.95624	−	5.78055i	−0.311352	−	0.226210i	0.421125	−	0.907003i	$-0.361636\pi$
$653$	−7.95624	−	5.78055i	−0.311352	−	0.226210i	−0.732476	+	0.680793i	$0.761636\pi$
$654$	−5.01188	−	2.23143i	−0.195980	−	0.0872559i
$655$	−0.420307	−	1.29357i	−0.0164228	−	0.0505441i
$656$	5.43963	−	9.42171i	0.212382	−	0.367856i
$657$	0.483999	+	0.838311i	0.0188826	+	0.0327056i
$658$	−3.02854	+	3.36354i	−0.118065	+	0.131124i
$659$	11.2156	−	34.5181i	0.436898	−	1.34463i	−0.454231	−	0.890884i	$-0.650086\pi$
$659$	11.2156	−	34.5181i	0.436898	−	1.34463i	0.891129	−	0.453750i	$-0.149914\pi$
$660$	1.01454	+	1.12676i	0.0394908	+	0.0438590i
$661$	12.6758	−	5.64363i	0.493032	−	0.219512i	−0.145132	−	0.989412i	$-0.546361\pi$
$661$	12.6758	−	5.64363i	0.493032	−	0.219512i	0.638164	+	0.769900i	$0.279694\pi$
$662$	13.2214	+	2.81029i	0.513864	+	0.109225i
$663$	−0.0560383	+	0.533169i	−0.00217635	+	0.0207066i
$664$	0.295229	+	2.80892i	0.0114571	+	0.109007i
$665$	−3.32994	+	0.707801i	−0.129130	+	0.0274474i
$666$	−4.77615	+	3.47008i	−0.185072	+	0.134463i
$667$	−10.9582	+	7.96162i	−0.424304	+	0.308275i
$668$	−5.22832	+	1.11131i	−0.202290	+	0.0429980i
$669$	−1.39719	−	13.2933i	−0.0540184	−	0.513950i
$670$	−1.02717	+	9.77287i	−0.0396831	+	0.377559i
$671$	−8.09435	−	1.72051i	−0.312479	−	0.0664194i
$672$	0.456027	−	0.203036i	0.0175916	−	0.00783229i
$673$	17.8645	+	19.8406i	0.688627	+	0.764797i	0.981522	−	0.191347i	$-0.0612856\pi$
$673$	17.8645	+	19.8406i	0.688627	+	0.764797i	−0.292896	+	0.956144i	$0.594619\pi$
$674$	−5.43424	+	16.7249i	−0.209319	+	0.644218i
$675$	−0.669131	+	0.743145i	−0.0257548	+	0.0286037i
$676$	6.36656	+	11.0272i	0.244868	+	0.424123i
$677$	−6.12305	+	10.6054i	−0.235328	+	0.407600i	−0.959368	−	0.282158i	$-0.908950\pi$
$677$	−6.12305	+	10.6054i	−0.235328	+	0.407600i	0.724040	+	0.689758i	$0.242283\pi$
$678$	5.16578	+	15.8986i	0.198391	+	0.610584i
$679$	−1.10638	−	0.492592i	−0.0424590	−	0.0189040i
$680$	0.839546	+	0.609966i	0.0321951	+	0.0233911i
$681$	7.27978			0.278962
$682$	7.72836	+	3.39667i	0.295934	+	0.130065i
$683$	33.5514			1.28381			0.641905	−	0.766784i	$-0.278144\pi$
$683$	33.5514			1.28381			0.641905	+	0.766784i	$0.278144\pi$
$684$	−5.51734	−	4.00858i	−0.210961	−	0.153272i
$685$	16.4963	+	7.34461i	0.630290	+	0.280623i
$686$	2.12115	+	6.52822i	0.0809858	+	0.249249i
$687$	5.03303	−	8.71746i	0.192022	−	0.332592i
$688$	−0.291663	−	0.505175i	−0.0111196	−	0.0192596i
$689$	1.64840	−	1.83073i	0.0627990	−	0.0697454i
$690$	−1.07483	+	3.30799i	−0.0409181	+	0.125933i
$691$	−5.24104	−	5.82076i	−0.199379	−	0.221432i	0.635162	−	0.772379i	$-0.280933\pi$
$691$	−5.24104	−	5.82076i	−0.199379	−	0.221432i	−0.834540	+	0.550947i	$0.814267\pi$
$692$	10.3401	−	4.60372i	0.393072	−	0.175007i
$693$	0.740324	+	0.157361i	0.0281226	+	0.00597764i
$694$	−2.58200	+	24.5661i	−0.0980114	+	0.932516i
$695$	0.738063	+	7.02220i	0.0279963	+	0.266367i
$696$	3.80916	−	0.809663i	0.144386	−	0.0306902i
$697$	9.13364	−	6.63598i	0.345961	−	0.251356i
$698$	−22.2765	+	16.1848i	−0.843177	+	0.612604i
$699$	−2.08242	+	0.442632i	−0.0787644	+	0.0167419i
$700$	−0.0521789	−	0.496449i	−0.00197218	−	0.0187640i
$701$	2.03243	−	19.3373i	0.0767638	−	0.730359i	−0.886668	−	0.462406i	$-0.846986\pi$
$701$	2.03243	−	19.3373i	0.0767638	−	0.730359i	0.963432	−	0.267953i	$-0.0863471\pi$
$702$	0.505322	+	0.107409i	0.0190721	+	0.00405391i
$703$	−36.7809	+	16.3759i	−1.38722	+	0.617630i
$704$	−1.01454	−	1.12676i	−0.0382368	−	0.0424663i
$705$	−2.80185	+	8.62320i	−0.105524	+	0.324769i
$706$	−6.82638	+	7.58146i	−0.256914	+	0.285332i
$707$	−1.85458	−	3.21222i	−0.0697485	−	0.120808i
$708$	3.51705	−	6.09171i	0.132179	−	0.228940i
$709$	12.0330	+	37.0337i	0.451908	+	1.39083i	0.874728	+	0.484615i	$0.161040\pi$
$709$	12.0330	+	37.0337i	0.451908	+	1.39083i	−0.422820	+	0.906214i	$0.638960\pi$
$710$	−1.88572	−	0.839576i	−0.0707697	−	0.0315087i
$711$	10.2631	+	7.45657i	0.384896	+	0.279643i
$712$	−9.08268			−0.340388
$713$	2.11643	+	19.2499i	0.0792611	+	0.720915i
$714$	0.518021			0.0193864
$715$	−0.633692	−	0.460404i	−0.0236987	−	0.0172181i
$716$	7.18251	+	3.19786i	0.268423	+	0.119510i
$717$	−6.56212	−	20.1961i	−0.245067	−	0.754238i
$718$	2.22324	−	3.85076i	0.0829704	−	0.143709i
$719$	16.1953	+	28.0511i	0.603983	+	1.04613i	0.992211	+	0.124566i	$0.0397539\pi$
$719$	16.1953	+	28.0511i	0.603983	+	1.04613i	−0.388228	+	0.921563i	$0.626913\pi$
$720$	0.669131	−	0.743145i	0.0249370	−	0.0276954i
$721$	1.54637	−	4.75924i	0.0575898	−	0.177243i
$722$	−18.4076	−	20.4438i	−0.685061	−	0.760838i
$723$	−12.3498	+	5.49847i	−0.459293	+	0.204490i
$724$	21.4991	+	4.56978i	0.799009	+	0.169835i
$725$	0.407061	−	3.87293i	0.0151179	−	0.143837i
$726$	0.909516	+	8.65346i	0.0337553	+	0.321160i
$727$	1.92759	−	0.409723i	0.0714905	−	0.0151958i	−0.172028	−	0.985092i	$-0.555032\pi$
$727$	1.92759	−	0.409723i	0.0714905	−	0.0151958i	0.243518	+	0.969896i	$0.421698\pi$
$728$	−0.208632	+	0.151580i	−0.00773243	+	0.00561794i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−0.946846	+	0.201258i	−0.0350443	+	0.00744890i
$731$	−0.0632751	−	0.602023i	−0.00234032	−	0.0222666i
$732$	−0.570499	+	5.42794i	−0.0210863	+	0.200622i
$733$	−46.0071	−	9.77912i	−1.69931	−	0.361200i	−0.746647	−	0.665221i	$-0.768337\pi$
$733$	−46.0071	−	9.77912i	−1.69931	−	0.361200i	−0.952665	+	0.304021i	$0.901671\pi$
$734$	17.4883	−	7.78628i	0.645504	−	0.287397i
$735$	4.51718	+	5.01683i	0.166619	+	0.185049i
$736$	1.07483	−	3.30799i	0.0396188	−	0.121934i
$737$	9.96956	−	11.0723i	0.367233	−	0.407854i
$738$	−5.43963	−	9.42171i	−0.200235	−	0.346818i
$739$	21.4075	−	37.0788i	0.787487	−	1.36397i	−0.140016	−	0.990149i	$-0.544715\pi$
$739$	21.4075	−	37.0788i	0.787487	−	1.36397i	0.927502	−	0.373817i	$-0.121951\pi$
$740$	−1.82433	−	5.61470i	−0.0670636	−	0.206401i
$741$	3.21859	+	1.43301i	0.118238	+	0.0526429i
$742$	−1.92578	−	1.39916i	−0.0706975	−	0.0513647i
$743$	31.6073			1.15956			0.579780	−	0.814773i	$-0.303138\pi$
$743$	31.6073			1.15956			0.579780	+	0.814773i	$0.303138\pi$
$744$	1.69517	−	5.30343i	0.0621481	−	0.194433i
$745$	0.862649			0.0316050
$746$	3.20042	+	2.32524i	0.117176	+	0.0851331i
$747$	2.58021	+	1.14878i	0.0944048	+	0.0420317i
$748$	−0.486213	−	1.49641i	−0.0177777	−	0.0547142i
$749$	2.17227	−	3.76248i	0.0793729	−	0.137478i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	20.3619	−	22.6142i	0.743016	−	0.825203i	−0.246573	−	0.969124i	$-0.579304\pi$
$751$	20.3619	−	22.6142i	0.743016	−	0.825203i	0.989589	+	0.143921i	$0.0459712\pi$
$752$	2.80185	−	8.62320i	0.102173	−	0.314456i
$753$	−12.6365	−	14.0343i	−0.460500	−	0.511437i
$754$	−1.83789	+	0.818280i	−0.0669319	+	0.0298000i
$755$	0.903151	+	0.191971i	0.0328690	+	0.00698653i
$756$	0.0521789	−	0.496449i	0.00189773	−	0.0180557i
$757$	2.60731	+	24.8069i	0.0947642	+	0.901621i	0.933860	+	0.357638i	$0.116418\pi$
$757$	2.60731	+	24.8069i	0.0947642	+	0.901621i	−0.839096	+	0.543983i	$0.816916\pi$
$758$	−16.1805	+	3.43927i	−0.587702	+	0.124920i
$759$	4.26650	−	3.09980i	0.154864	−	0.112515i
$760$	5.51734	−	4.00858i	0.200135	−	0.145407i
$761$	24.8949	−	5.29157i	0.902438	−	0.191819i	0.266751	−	0.963766i	$-0.414050\pi$
$761$	24.8949	−	5.29157i	0.902438	−	0.191819i	0.635688	+	0.771946i	$0.280717\pi$
$762$	−0.544912	−	5.18449i	−0.0197401	−	0.187814i
$763$	0.286263	−	2.72361i	0.0103634	−	0.0986013i
$764$	−23.5091	−	4.99702i	−0.850530	−	0.180786i
$765$	0.948019	−	0.422085i	0.0342757	−	0.0152605i
$766$	−20.0054	−	22.2182i	−0.722823	−	0.802776i
$767$	−1.12293	+	3.45604i	−0.0405468	+	0.124790i
$768$	−0.669131	+	0.743145i	−0.0241452	+	0.0268159i
$769$	−17.0823	−	29.5873i	−0.616002	−	1.06695i	−0.990208	−	0.139601i	$-0.955418\pi$
$769$	−17.0823	−	29.5873i	−0.616002	−	1.06695i	0.374206	−	0.927346i	$-0.377915\pi$
$770$	−0.378432	+	0.655463i	−0.0136377	+	0.0236212i
$771$	4.96166	+	15.2704i	0.178690	+	0.549951i
$772$	18.3448	+	8.16763i	0.660244	+	0.293959i
$773$	−7.30379	−	5.30651i	−0.262699	−	0.190862i	0.448637	−	0.893714i	$-0.351910\pi$
$773$	−7.30379	−	5.30651i	−0.262699	−	0.190862i	−0.711336	+	0.702852i	$0.751910\pi$
$774$	−0.583326			−0.0209672
$775$	−4.52003	−	3.25106i	−0.162364	−	0.116781i
$776$	2.42613			0.0870930
$777$	−2.38418	−	1.73221i	−0.0855318	−	0.0621425i
$778$	−4.06881	−	1.81155i	−0.145874	−	0.0649473i
$779$	−22.9273	−	70.5631i	−0.821457	−	2.52819i
$780$	−0.258305	+	0.447398i	−0.00924882	+	0.0160194i
$781$	1.56485	+	2.71041i	0.0559949	+	0.0969860i
$782$	2.41521	−	2.68236i	0.0863678	−	0.0959212i
$783$	1.20339	−	3.70366i	0.0430058	−	0.132358i
$784$	−4.51718	−	5.01683i	−0.161328	−	0.179173i
$785$	8.08469	−	3.59954i	0.288555	−	0.128473i
$786$	1.33042	+	0.282790i	0.0474545	+	0.0100868i
$787$	−1.59646	+	15.1893i	−0.0569075	+	0.541439i	0.928513	+	0.371301i	$0.121088\pi$
$787$	−1.59646	+	15.1893i	−0.0569075	+	0.541439i	−0.985420	+	0.170138i	$0.945579\pi$
$788$	−1.81441	−	17.2630i	−0.0646358	−	0.614968i
$789$	−11.8047	+	2.50917i	−0.420259	+	0.0893288i
$790$	−10.2631	+	7.45657i	−0.365144	+	0.265293i
$791$	−6.75106	+	4.90493i	−0.240040	+	0.174399i
$792$	−1.48307	+	0.315236i	−0.0526986	+	0.0112014i
$793$	−0.294726	−	2.80413i	−0.0104660	−	0.0995776i
$794$	2.00845	−	19.1092i	0.0712773	−	0.678159i
$795$	−4.66436	−	0.991441i	−0.165428	−	0.0351628i
$796$	−14.2407	+	6.34037i	−0.504748	+	0.224728i
$797$	23.5373	+	26.1408i	0.833733	+	0.925954i	0.998172	−	0.0604329i	$-0.0192481\pi$
$797$	23.5373	+	26.1408i	0.833733	+	0.925954i	−0.164439	+	0.986387i	$0.552581\pi$
$798$	1.05200	−	3.23772i	0.0372403	−	0.114614i
$799$	6.29593	−	6.99234i	0.222734	−	0.247371i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−4.54134	+	7.86583i	−0.160460	+	0.277926i
$802$	2.15369	+	6.62838i	0.0760495	+	0.234056i
$803$	1.34079	+	0.596960i	0.0473156	+	0.0210663i
$804$	−7.94997	−	5.77599i	−0.280374	−	0.203704i
$805$	−1.73627			−0.0611955
$806$	−0.286970	+	2.86202i	−0.0101081	+	0.100810i
$807$	10.7160			0.377220
$808$	6.01135	+	4.36750i	0.211479	+	0.153648i
$809$	−26.1510	−	11.6432i	−0.919419	−	0.409352i	−0.108224	−	0.994127i	$-0.534516\pi$
$809$	−26.1510	−	11.6432i	−0.919419	−	0.409352i	−0.811196	+	0.584775i	$0.801183\pi$
$810$	−0.309017	−	0.951057i	−0.0108578	−	0.0334167i
$811$	5.66602	−	9.81383i	0.198961	−	0.344610i	−0.749231	−	0.662309i	$-0.769577\pi$
$811$	5.66602	−	9.81383i	0.198961	−	0.344610i	0.948192	+	0.317699i	$0.102910\pi$
$812$	0.971976	+	1.68351i	0.0341097	+	0.0590797i
$813$	−1.57531	+	1.74956i	−0.0552485	+	0.0613597i
$814$	−2.76605	+	8.51303i	−0.0969500	+	0.298381i
$815$	9.02722	+	10.0257i	0.316210	+	0.351187i
$816$	−0.948019	+	0.422085i	−0.0331873	+	0.0147759i
$817$	−3.89124	−	0.827109i	−0.136137	−	0.0289369i
$818$	0.878670	−	8.35999i	0.0307220	−	0.292300i
$819$	0.0269562	+	0.256471i	0.000941925	+	0.00896182i
$820$	10.6415	−	2.26192i	0.371618	−	0.0789898i
$821$	30.7704	−	22.3560i	1.07389	−	0.780229i	0.0972850	−	0.995257i	$-0.468984\pi$
$821$	30.7704	−	22.3560i	1.07389	−	0.780229i	0.976608	+	0.215028i	$0.0689842\pi$
$822$	−14.6087	+	10.6139i	−0.509538	+	0.370201i
$823$	−36.5782	+	7.77494i	−1.27504	+	0.271017i	−0.795203	−	0.606343i	$-0.792636\pi$
$823$	−36.5782	+	7.77494i	−1.27504	+	0.271017i	−0.479832	+	0.877360i	$0.659303\pi$
$824$	1.04787	+	9.96977i	0.0365041	+	0.347313i
$825$	−0.158486	+	1.50790i	−0.00551778	+	0.0524982i
$826$	3.43457	+	0.730041i	0.119504	+	0.0254014i
$827$	35.2495	−	15.6941i	1.22575	−	0.545737i	0.311248	−	0.950329i	$-0.399253\pi$
$827$	35.2495	−	15.6941i	1.22575	−	0.545737i	0.914497	+	0.404592i	$0.132586\pi$
$828$	−2.32738	−	2.58482i	−0.0808822	−	0.0898288i
$829$	−11.3714	+	34.9975i	−0.394944	+	1.21551i	0.534061	+	0.845446i	$0.320665\pi$
$829$	−11.3714	+	34.9975i	−0.394944	+	1.21551i	−0.929005	+	0.370067i	$0.879335\pi$
$830$	−1.88988	+	2.09893i	−0.0655988	+	0.0728549i
$831$	−1.10392	−	1.91205i	−0.0382947	−	0.0663283i
$832$	0.258305	−	0.447398i	0.00895513	−	0.0155107i
$833$	−2.16484	−	6.66269i	−0.0750072	−	0.230849i
$834$	−6.45044	−	2.87192i	−0.223360	−	0.0994464i
$835$	−4.32430	−	3.14179i	−0.149649	−	0.108726i
$836$	−10.3402			−0.357624
$837$	−3.74532	−	4.11978i	−0.129457	−	0.142400i
$838$	1.90871			0.0659352
$839$	11.4555	+	8.32294i	0.395489	+	0.287340i	0.767701	−	0.640808i	$-0.221401\pi$
$839$	11.4555	+	8.32294i	0.395489	+	0.287340i	−0.372212	+	0.928148i	$0.621401\pi$
$840$	0.456027	+	0.203036i	0.0157344	+	0.00700542i
$841$	−4.27516	−	13.1576i	−0.147419	−	0.453710i
$842$	7.28417	−	12.6165i	0.251029	−	0.434795i
$843$	−14.3127	−	24.7903i	−0.492955	−	0.853823i
$844$	11.7186	−	13.0148i	0.403371	−	0.447989i
$845$	−3.93475	+	12.1099i	−0.135359	+	0.416594i
$846$	−6.06699	−	6.73807i	−0.208587	−	0.231660i
$847$	−3.96795	+	1.76664i	−0.136340	+	0.0607026i
$848$	4.66436	+	0.991441i	0.160175	+	0.0340462i
$849$	−0.693162	+	6.59499i	−0.0237893	+	0.226340i
$850$	0.108473	+	1.03205i	0.00372059	+	0.0353991i
$851$	−20.0855	+	4.26930i	−0.688521	+	0.146350i
$852$	1.66995	−	1.21329i	0.0572116	−	0.0415667i
$853$	25.2351	−	18.3344i	0.864033	−	0.627757i	−0.0649462	−	0.997889i	$-0.520688\pi$
$853$	25.2351	−	18.3344i	0.864033	−	0.627757i	0.928979	+	0.370132i	$0.120688\pi$
$854$	−2.66493	+	0.566447i	−0.0911919	+	0.0193834i
$855$	−0.712864	−	6.78245i	−0.0243794	−	0.231955i
$856$	−0.909740	+	8.65560i	−0.0310943	+	0.295842i
$857$	−5.46420	−	1.16145i	−0.186654	−	0.0396744i	0.113636	−	0.993522i	$-0.463750\pi$
$857$	−5.46420	−	1.16145i	−0.186654	−	0.0396744i	−0.300290	+	0.953848i	$0.597083\pi$
$858$	0.715568	−	0.318591i	0.0244291	−	0.0108765i
$859$	−24.6055	−	27.3271i	−0.839528	−	0.932390i	0.158964	−	0.987284i	$-0.449185\pi$
$859$	−24.6055	−	27.3271i	−0.839528	−	0.932390i	−0.998492	+	0.0548941i	$0.982518\pi$
$860$	0.180258	−	0.554776i	0.00614674	−	0.0189177i
$861$	3.63388	−	4.03583i	0.123842	−	0.137541i
$862$	15.0059	+	25.9910i	0.511104	+	0.885258i
$863$	22.0778	−	38.2399i	0.751538	−	1.30170i	−0.195539	−	0.980696i	$-0.562646\pi$
$863$	22.0778	−	38.2399i	0.751538	−	1.30170i	0.947077	−	0.321007i	$-0.104021\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	10.3401	+	4.60372i	0.351575	+	0.156531i
$866$	−15.0642	−	10.9448i	−0.511904	−	0.371920i
$867$	15.9231			0.540777
$868$	2.77930	−	0.0133004i	0.0943357	−	0.000451445i
$869$	19.2344			0.652481
$870$	3.15052	+	2.28899i	0.106813	+	0.0776040i
$871$	4.63769	+	2.06483i	0.157142	+	0.0699642i
$872$	1.69532	+	5.21767i	0.0574109	+	0.176693i
$873$	1.21306	−	2.10109i	0.0410560	−	0.0711111i
$874$	−11.8604	−	20.5428i	−0.401184	−	0.694871i
$875$	0.334019	−	0.370966i	0.0112919	−	0.0125409i
$876$	0.299128	−	0.920621i	0.0101066	−	0.0311049i
$877$	37.0123	+	41.1063i	1.24982	+	1.38806i	0.890587	+	0.454812i	$0.150294\pi$
$877$	37.0123	+	41.1063i	1.24982	+	1.38806i	0.359229	+	0.933249i	$0.383040\pi$
$878$	−23.7597	+	10.5785i	−0.801852	+	0.357007i
$879$	17.2394	+	3.66435i	0.581471	+	0.123595i
$880$	0.158486	−	1.50790i	0.00534257	−	0.0508312i
$881$	−3.71328	−	35.3295i	−0.125104	−	1.19028i	−0.859346	−	0.511394i	$-0.829129\pi$
$881$	−3.71328	−	35.3295i	−0.125104	−	1.19028i	0.734243	−	0.678887i	$-0.237537\pi$
$882$	−6.60329	+	1.40357i	−0.222344	+	0.0472608i
$883$	42.4793	−	30.8630i	1.42954	−	1.03862i	0.439441	−	0.898272i	$-0.355177\pi$
$883$	42.4793	−	30.8630i	1.42954	−	1.03862i	0.990102	−	0.140352i	$-0.0448234\pi$
$884$	0.433719	−	0.315115i	0.0145875	−	0.0105985i
$885$	6.88038	−	1.46247i	0.231282	−	0.0491604i
$886$	−0.866871	−	8.24773i	−0.0291231	−	0.277088i
$887$	−1.39628	+	13.2848i	−0.0468827	+	0.446059i	0.945750	+	0.324895i	$0.105329\pi$
$887$	−1.39628	+	13.2848i	−0.0468827	+	0.446059i	−0.992633	+	0.121163i	$0.961338\pi$
$888$	5.77464	+	1.22744i	0.193784	+	0.0411901i
$889$	2.37729	−	1.05844i	0.0797318	−	0.0354989i
$890$	−6.07750	−	6.74975i	−0.203718	−	0.226252i
$891$	−0.468532	+	1.44199i	−0.0156964	+	0.0483086i
$892$	−8.94398	+	9.93329i	−0.299467	+	0.332591i
$893$	−30.9175	−	53.5507i	−1.03461	−	1.79201i
$894$	−0.431325	+	0.747076i	−0.0144257	+	0.0249860i
$895$	2.42956	+	7.47743i	0.0812113	+	0.249943i
$896$	−0.456027	−	0.203036i	−0.0152348	−	0.00678296i
$897$	1.45371	+	1.05618i	0.0485380	+	0.0352650i
$898$	2.33783			0.0780143
$899$	21.2299	+	4.40647i	0.708055	+	0.146964i
$900$	1.00000			0.0333333
$901$	4.00343	+	2.90866i	0.133374	+	0.0969017i
$902$	−15.0691	−	6.70918i	−0.501745	−	0.223391i
$903$	−0.0899817	−	0.276935i	−0.00299440	−	0.00921582i
$904$	8.35841	−	14.4772i	0.277997	−	0.481504i
$905$	10.9897	+	19.0347i	0.365310	+	0.632736i
$906$	−0.617827	+	0.686166i	−0.0205259	+	0.0227964i
$907$	16.5902	−	51.0593i	0.550867	−	1.69539i	−0.155748	−	0.987797i	$-0.549779\pi$
$907$	16.5902	−	51.0593i	0.550867	−	1.69539i	0.706615	−	0.707598i	$-0.250221\pi$
$908$	−4.87112	−	5.40993i	−0.161654	−	0.179535i
$909$	6.78805	−	3.02223i	0.225145	−	0.100241i
$910$	−0.252248	−	0.0536170i	−0.00836195	−	0.00177739i
$911$	2.47320	−	23.5309i	0.0819408	−	0.779614i	−0.873974	−	0.485972i	$-0.838466\pi$
$911$	2.47320	−	23.5309i	0.0819408	−	0.779614i	0.955915	−	0.293643i	$-0.0948676\pi$
$912$	0.712864	+	6.78245i	0.0236053	+	0.224589i
$913$	4.18876	−	0.890349i	0.138628	−	0.0294663i
$914$	−6.05982	+	4.40272i	−0.200441	+	0.145629i
$915$	−4.41548	+	3.20803i	−0.145971	+	0.106054i
$916$	−9.84609	+	2.09285i	−0.325324	+	0.0691498i
$917$	0.0709707	+	0.675241i	0.00234366	+	0.0222984i
$918$	−0.108473	+	1.03205i	−0.00358014	+	0.0340628i
$919$	−2.80291	−	0.595777i	−0.0924594	−	0.0196529i	0.161450	−	0.986881i	$-0.448383\pi$
$919$	−2.80291	−	0.595777i	−0.0924594	−	0.0196529i	−0.253909	+	0.967228i	$0.581716\pi$
$920$	3.17751	−	1.41472i	0.104760	−	0.0466419i
$921$	−0.444144	−	0.493271i	−0.0146350	−	0.0162538i
$922$	−1.57247	+	4.83957i	−0.0517865	+	0.159383i
$923$	−0.713545	+	0.792471i	−0.0234866	+	0.0260845i
$924$	−0.378432	−	0.655463i	−0.0124495	−	0.0215631i
$925$	2.95182	−	5.11271i	0.0970554	−	0.168105i
$926$	−1.01884	−	3.13566i	−0.0334810	−	0.103044i
$927$	9.15801	+	4.07741i	0.300788	+	0.133920i
$928$	−3.15052	−	2.28899i	−0.103421	−	0.0751398i
$929$	16.5867			0.544193			0.272096	−	0.962270i	$-0.412283\pi$
$929$	16.5867			0.544193			0.272096	+	0.962270i	$0.412283\pi$
$930$	5.07551	−	2.28893i	0.166433	−	0.0750569i
$931$	−46.0393			−1.50888
$932$	1.72235	+	1.25136i	0.0564175	+	0.0409897i
$933$	14.8078	+	6.59285i	0.484785	+	0.215840i
$934$	−8.55372	−	26.3256i	−0.279886	−	0.861402i
$935$	0.786709	−	1.36262i	0.0257281	−	0.0445624i
$936$	−0.258305	−	0.447398i	−0.00844298	−	0.0146237i
$937$	16.1644	−	17.9524i	0.528067	−	0.586478i	−0.418810	−	0.908074i	$-0.637553\pi$
$937$	16.1644	−	17.9524i	0.528067	−	0.586478i	0.946877	+	0.321596i	$0.104219\pi$
$938$	1.51583	−	4.66525i	0.0494936	−	0.152326i
$939$	−18.0529	−	20.0498i	−0.589135	−	0.654300i
$940$	8.28309	−	3.68787i	0.270165	−	0.120285i
$941$	−37.1928	−	7.90557i	−1.21245	−	0.257714i	−0.443059	−	0.896492i	$-0.646107\pi$
$941$	−37.1928	−	7.90557i	−1.21245	−	0.257714i	−0.769391	+	0.638778i	$0.779440\pi$
$942$	−0.925055	+	8.80131i	−0.0301399	+	0.286762i
$943$	−3.95541	−	37.6332i	−0.128806	−	1.22550i
$944$	−6.88038	+	1.46247i	−0.223937	+	0.0475994i
$945$	0.403848	−	0.293413i	0.0131372	−	0.00954472i
$946$	−0.715527	+	0.519861i	−0.0232638	+	0.0169021i
$947$	−6.19894	+	1.31762i	−0.201438	+	0.0428171i	−0.307526	−	0.951540i	$-0.599501\pi$
$947$	−6.19894	+	1.31762i	−0.201438	+	0.0428171i	0.106087	+	0.994357i	$0.466168\pi$
$948$	−1.32604	−	12.6164i	−0.0430676	−	0.409761i
$949$	−0.0522725	+	0.497339i	−0.00169684	+	0.0161443i
$950$	6.67078	+	1.41792i	0.216429	+	0.0460033i
$951$	−6.65237	+	2.96182i	−0.215718	+	0.0960437i
$952$	−0.346624	−	0.384965i	−0.0112341	−	0.0124768i
$953$	8.90912	−	27.4194i	0.288595	−	0.888203i	−0.696704	−	0.717359i	$-0.745351\pi$
$953$	8.90912	−	27.4194i	0.288595	−	0.888203i	0.985298	−	0.170844i	$-0.0546493\pi$
$954$	3.19079	−	3.54374i	0.103306	−	0.114733i
$955$	−12.0172	−	20.8143i	−0.388866	−	0.673536i
$956$	−10.6177	+	18.3905i	−0.343402	+	0.594790i
$957$	−1.82459	−	5.61550i	−0.0589805	−	0.181523i
$958$	0.209019	+	0.0930614i	0.00675311	+	0.00300668i
$959$	−7.29244	−	5.29827i	−0.235485	−	0.171090i
$960$	−1.00000			−0.0322749
$961$	20.5216	−	23.2350i	0.661987	−	0.749515i
$962$	−3.04989			−0.0983324
$963$	7.04110	+	5.11566i	0.226896	+	0.164850i
$964$	12.3498	+	5.49847i	0.397759	+	0.177094i
$965$	6.20533	+	19.0981i	0.199757	+	0.614788i
$966$	0.868136	−	1.50366i	0.0279318	−	0.0483793i
$967$	18.9046	+	32.7437i	0.607931	+	1.05297i	0.991581	+	0.129489i	$0.0413335\pi$
$967$	18.9046	+	32.7437i	0.607931	+	1.05297i	−0.383650	+	0.923479i	$0.625333\pi$
$968$	5.82219	−	6.46620i	0.187132	−	0.207832i
$969$	−2.18696	+	6.73078i	−0.0702554	+	0.216224i
$970$	1.62340	+	1.80297i	0.0521242	+	0.0578897i
$971$	−24.8096	+	11.0459i	−0.796178	+	0.354481i	−0.764177	−	0.645006i	$-0.776855\pi$
$971$	−24.8096	+	11.0459i	−0.796178	+	0.354481i	−0.0320011	+	0.999488i	$0.510188\pi$
$972$	0.978148	+	0.207912i	0.0313741	+	0.00666877i
$973$	0.368429	−	3.50537i	0.0118113	−	0.112377i
$974$	−0.995395	−	9.47055i	−0.0318945	−	0.303456i
$975$	−0.505322	+	0.107409i	−0.0161832	+	0.00343986i
$976$	4.41548	−	3.20803i	0.141336	−	0.102687i
$977$	−32.6445	+	23.7176i	−1.04439	+	0.758793i	−0.971137	−	0.238521i	$-0.923338\pi$
$977$	−32.6445	+	23.7176i	−1.04439	+	0.758793i	−0.0732514	+	0.997314i	$0.523338\pi$
$978$	−13.1962	+	2.80493i	−0.421967	+	0.0896918i
$979$	1.43948	+	13.6957i	0.0460060	+	0.437718i
$980$	0.705652	−	6.71383i	0.0225412	−	0.214466i
$981$	5.36630	+	1.14064i	0.171333	+	0.0364179i
$982$	26.5384	−	11.8156i	0.846873	−	0.377052i
$983$	33.1958	+	36.8676i	1.05878	+	1.17589i	0.983903	+	0.178702i	$0.0571897\pi$
$983$	33.1958	+	36.8676i	1.05878	+	1.17589i	0.0748767	+	0.997193i	$0.476144\pi$
$984$	−3.36187	+	10.3468i	−0.107173	+	0.329843i
$985$	11.6148	−	12.8996i	0.370079	−	0.411014i
$986$	−2.02061	−	3.49980i	−0.0643493	−	0.111456i
$987$	2.26304	−	3.91970i	0.0720334	−	0.124766i
$988$	−1.08872	−	3.35075i	−0.0346369	−	0.106602i
$989$	−1.85353	−	0.825243i	−0.0589387	−	0.0262412i
$990$	−1.22663	−	0.891201i	−0.0389850	−	0.0283242i
$991$	−58.4308			−1.85612			−0.928058	−	0.372434i	$-0.878523\pi$
$991$	−58.4308			−1.85612			−0.928058	+	0.372434i	$0.878523\pi$
$992$	−5.07551	+	2.28893i	−0.161148	+	0.0726736i
$993$	−13.5168			−0.428941
$994$	0.833613	+	0.605655i	0.0264406	+	0.0192102i
$995$	−14.2407	−	6.34037i	−0.451461	−	0.201003i
$996$	−0.872784	−	2.68615i	−0.0276552	−	0.0851140i
$997$	20.8469	−	36.1079i	0.660229	−	1.14355i	−0.320327	−	0.947307i	$-0.603793\pi$
$997$	20.8469	−	36.1079i	0.660229	−	1.14355i	0.980555	−	0.196243i	$-0.0628740\pi$
$998$	−0.00282680	−	0.00489616i	−8.94807e−5	−	0.000154985i
$999$	3.95031	−	4.38727i	0.124982	−	0.138807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.h.391.2	✓	24
31.18	even	15	inner	930.2.bg.h.421.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.h.391.2	✓	24	1.1	even	1	trivial
930.2.bg.h.421.2	yes	24	31.18	even	15	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.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.334019 - 0.370966i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.334019 - 0.370966i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.913545 + 0.406737i) q^{10} +(1.48307 + 0.315236i) q^{11} +(0.104528 - 0.994522i) q^{12} +(0.0540005 + 0.513781i) q^{13} +(0.488275 - 0.103786i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.01506 + 0.215758i) q^{17} +(0.104528 + 0.994522i) q^{18} +(-0.712864 + 6.78245i) q^{19} +(-0.978148 - 0.207912i) q^{20} +(-0.456027 + 0.203036i) q^{21} +(1.01454 + 1.12676i) q^{22} +(-1.07483 + 3.30799i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.258305 + 0.447398i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.456027 + 0.203036i) q^{28} +(3.15052 + 2.28899i) q^{29} +1.00000 q^{30} +(5.07551 - 2.28893i) q^{31} -1.00000 q^{32} +(-1.22663 - 0.891201i) q^{33} +(-0.948019 - 0.422085i) q^{34} +(0.154256 + 0.474752i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.95182 + 5.11271i) q^{37} +(-4.56334 + 5.06811i) q^{38} +(0.159642 - 0.491326i) q^{39} +(-0.669131 - 0.743145i) q^{40} +(-9.93869 + 4.42499i) q^{41} +(-0.488275 - 0.103786i) q^{42} +(-0.0609742 + 0.580131i) q^{43} +(0.158486 + 1.50790i) q^{44} +(-0.978148 + 0.207912i) q^{45} +(-2.81394 + 2.04445i) q^{46} +(-7.33533 + 5.32943i) q^{47} +(0.978148 - 0.207912i) q^{48} +(0.705652 + 6.71383i) q^{49} +(0.104528 - 0.994522i) q^{50} +(1.01506 + 0.215758i) q^{51} +(-0.471948 + 0.210125i) q^{52} +(-3.19079 - 3.54374i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-1.01454 + 1.12676i) q^{55} +(0.249592 + 0.432306i) q^{56} +(3.40990 - 5.90613i) q^{57} +(1.20339 + 3.70366i) q^{58} +(6.42597 + 2.86102i) q^{59} +(0.809017 + 0.587785i) q^{60} -5.45783 q^{61} +(5.45157 + 1.13153i) q^{62} +0.499184 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.471948 - 0.210125i) q^{65} +(-0.468532 - 1.44199i) q^{66} +(4.91335 - 8.51018i) q^{67} +(-0.518868 - 0.898706i) q^{68} +(2.32738 - 2.58482i) q^{69} +(-0.154256 + 0.474752i) q^{70} +(1.38120 + 1.53398i) q^{71} +(-0.913545 + 0.406737i) q^{72} +(0.946846 + 0.201258i) q^{73} +(-0.617099 + 5.87131i) q^{74} +(0.104528 + 0.994522i) q^{75} +(-6.67078 + 1.41792i) q^{76} +(0.612315 - 0.444873i) q^{77} +(0.417947 - 0.303656i) q^{78} +(12.4087 - 2.63754i) q^{79} +(-0.104528 - 0.994522i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-10.6415 - 2.26192i) q^{82} +(2.58021 - 1.14878i) q^{83} +(-0.334019 - 0.370966i) q^{84} +(0.320678 - 0.986946i) q^{85} +(-0.390321 + 0.433496i) q^{86} +(-1.94713 - 3.37253i) q^{87} +(-0.758101 + 1.31307i) q^{88} +(2.80670 + 8.63815i) q^{89} +(-0.913545 - 0.406737i) q^{90} +(0.208632 + 0.151580i) q^{91} -3.47822 q^{92} +(-5.56770 + 0.0266443i) q^{93} -9.06697 q^{94} +(-5.51734 - 4.00858i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-0.749715 - 2.30739i) q^{97} +(-3.37541 + 5.84638i) q^{98} +(0.758101 + 1.31307i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{10} - 5 q^{11} - 3 q^{12} - 13 q^{13} - 4 q^{14} + 6 q^{15} - 6 q^{16} + 31 q^{17} - 3 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} + 5 q^{22} - 9 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} + 6 q^{27} + 4 q^{28} + 11 q^{29} + 24 q^{30} + 17 q^{31} - 24 q^{32} + 10 q^{33} + 9 q^{34} + 7 q^{35} - 12 q^{36} + 8 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + 12 q^{41} + 4 q^{42} - 7 q^{43} - 10 q^{44} + 3 q^{45} - 6 q^{46} - 46 q^{47} - 3 q^{48} + 20 q^{49} - 3 q^{50} - 31 q^{51} + 17 q^{52} + 48 q^{53} - 6 q^{54} - 5 q^{55} + q^{56} - 2 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{61} + 13 q^{62} + 2 q^{63} - 6 q^{64} + 17 q^{65} + 10 q^{66} - 33 q^{67} + q^{68} - 12 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 19 q^{73} + 7 q^{74} - 3 q^{75} + 2 q^{76} + 26 q^{77} - 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 12 q^{82} + 11 q^{84} - 2 q^{85} - 48 q^{86} + 3 q^{87} + 21 q^{89} - 3 q^{90} + 72 q^{91} + 6 q^{92} + 19 q^{93} - 14 q^{94} + 6 q^{95} + 3 q^{96} - 35 q^{97} - 5 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9 - 3 * q^10 - 5 * q^11 - 3 * q^12 - 13 * q^13 - 4 * q^14 + 6 * q^15 - 6 * q^16 + 31 * q^17 - 3 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 + 5 * q^22 - 9 * q^23 + 3 * q^24 - 12 * q^25 + 3 * q^26 + 6 * q^27 + 4 * q^28 + 11 * q^29 + 24 * q^30 + 17 * q^31 - 24 * q^32 + 10 * q^33 + 9 * q^34 + 7 * q^35 - 12 * q^36 + 8 * q^37 - 2 * q^38 - q^39 - 3 * q^40 + 12 * q^41 + 4 * q^42 - 7 * q^43 - 10 * q^44 + 3 * q^45 - 6 * q^46 - 46 * q^47 - 3 * q^48 + 20 * q^49 - 3 * q^50 - 31 * q^51 + 17 * q^52 + 48 * q^53 - 6 * q^54 - 5 * q^55 + q^56 - 2 * q^57 + 14 * q^58 + 12 * q^59 + 6 * q^60 - 4 * q^61 + 13 * q^62 + 2 * q^63 - 6 * q^64 + 17 * q^65 + 10 * q^66 - 33 * q^67 + q^68 - 12 * q^69 - 7 * q^70 - 35 * q^71 - 3 * q^72 + 19 * q^73 + 7 * q^74 - 3 * q^75 + 2 * q^76 + 26 * q^77 - 4 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 - 12 * q^82 + 11 * q^84 - 2 * q^85 - 48 * q^86 + 3 * q^87 + 21 * q^89 - 3 * q^90 + 72 * q^91 + 6 * q^92 + 19 * q^93 - 14 * q^94 + 6 * q^95 + 3 * q^96 - 35 * q^97 - 5 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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