LMFDB - Embedded newform 312.2.bt.b.115.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,2,Mod(19,312)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 0, 5]))

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

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

chi := DirichletCharacter("312.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.bt (of order $12$, degree $4$, 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:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	312.115
Dual form			312.2.bt.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36603 - 0.366025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-0.366025 + 0.366025i) q^{5} +(-1.00000 - 1.00000i) q^{6} +(2.36603 - 0.633975i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.366025 + 0.633975i) q^{10} +(-3.36603 - 0.901924i) q^{11} +(-1.73205 - 1.00000i) q^{12} +(3.50000 - 0.866025i) q^{13} +(3.00000 - 1.73205i) q^{14} +(0.500000 + 0.133975i) q^{15} +(2.00000 - 3.46410i) q^{16} +(0.232051 + 0.133975i) q^{17} +(-0.366025 + 1.36603i) q^{18} +(-4.09808 + 1.09808i) q^{19} +(-0.267949 + 1.00000i) q^{20} +(-1.73205 - 1.73205i) q^{21} -4.92820 q^{22} +(0.366025 + 0.633975i) q^{23} +(-2.73205 - 0.732051i) q^{24} +4.73205i q^{25} +(4.46410 - 2.46410i) q^{26} +1.00000 q^{27} +(3.46410 - 3.46410i) q^{28} +(-2.59808 + 1.50000i) q^{29} +0.732051 q^{30} +(4.00000 - 4.00000i) q^{31} +(1.46410 - 5.46410i) q^{32} +(0.901924 + 3.36603i) q^{33} +(0.366025 + 0.0980762i) q^{34} +(-0.633975 + 1.09808i) q^{35} +2.00000i q^{36} +(-1.86603 + 6.96410i) q^{37} +(-5.19615 + 3.00000i) q^{38} +(-2.50000 - 2.59808i) q^{39} +1.46410i q^{40} +(-2.50000 + 9.33013i) q^{41} +(-3.00000 - 1.73205i) q^{42} +(-0.633975 - 0.366025i) q^{43} +(-6.73205 + 1.80385i) q^{44} +(-0.133975 - 0.500000i) q^{45} +(0.732051 + 0.732051i) q^{46} +(2.26795 + 2.26795i) q^{47} -4.00000 q^{48} +(-0.866025 + 0.500000i) q^{49} +(1.73205 + 6.46410i) q^{50} -0.267949i q^{51} +(5.19615 - 5.00000i) q^{52} +8.66025i q^{53} +(1.36603 - 0.366025i) q^{54} +(1.56218 - 0.901924i) q^{55} +(3.46410 - 6.00000i) q^{56} +(3.00000 + 3.00000i) q^{57} +(-3.00000 + 3.00000i) q^{58} +(-2.80385 - 10.4641i) q^{59} +(1.00000 - 0.267949i) q^{60} +(1.66987 + 0.964102i) q^{61} +(4.00000 - 6.92820i) q^{62} +(-0.633975 + 2.36603i) q^{63} -8.00000i q^{64} +(-0.964102 + 1.59808i) q^{65} +(2.46410 + 4.26795i) q^{66} +(-1.56218 + 5.83013i) q^{67} +0.535898 q^{68} +(0.366025 - 0.633975i) q^{69} +(-0.464102 + 1.73205i) q^{70} +(1.83013 + 6.83013i) q^{71} +(0.732051 + 2.73205i) q^{72} +(7.83013 - 7.83013i) q^{73} +10.1962i q^{74} +(4.09808 - 2.36603i) q^{75} +(-6.00000 + 6.00000i) q^{76} -8.53590 q^{77} +(-4.36603 - 2.63397i) q^{78} +1.07180i q^{79} +(0.535898 + 2.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +13.6603i q^{82} +(-7.92820 - 7.92820i) q^{83} +(-4.73205 - 1.26795i) q^{84} +(-0.133975 + 0.0358984i) q^{85} +(-1.00000 - 0.267949i) q^{86} +(2.59808 + 1.50000i) q^{87} +(-8.53590 + 4.92820i) q^{88} +(-12.5622 - 3.36603i) q^{89} +(-0.366025 - 0.633975i) q^{90} +(7.73205 - 4.26795i) q^{91} +(1.26795 + 0.732051i) q^{92} +(-5.46410 - 1.46410i) q^{93} +(3.92820 + 2.26795i) q^{94} +(1.09808 - 1.90192i) q^{95} +(-5.46410 + 1.46410i) q^{96} +(15.2942 - 4.09808i) q^{97} +(-1.00000 + 1.00000i) q^{98} +(2.46410 - 2.46410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} + 2 q^{5} - 4 q^{6} + 6 q^{7} + 8 q^{8} - 2 q^{9} + 2 q^{10} - 10 q^{11} + 14 q^{13} + 12 q^{14} + 2 q^{15} + 8 q^{16} - 6 q^{17} + 2 q^{18} - 6 q^{19} - 8 q^{20} + 8 q^{22} - 2 q^{23}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^5 - 4 * q^6 + 6 * q^7 + 8 * q^8 - 2 * q^9 + 2 * q^10 - 10 * q^11 + 14 * q^13 + 12 * q^14 + 2 * q^15 + 8 * q^16 - 6 * q^17 + 2 * q^18 - 6 * q^19 - 8 * q^20 + 8 * q^22 - 2 * q^23 - 4 * q^24 + 4 * q^26 + 4 * q^27 - 4 * q^30 + 16 * q^31 - 8 * q^32 + 14 * q^33 - 2 * q^34 - 6 * q^35 - 4 * q^37 - 10 * q^39 - 10 * q^41 - 12 * q^42 - 6 * q^43 - 20 * q^44 - 4 * q^45 - 4 * q^46 + 16 * q^47 - 16 * q^48 + 2 * q^54 - 18 * q^55 + 12 * q^57 - 12 * q^58 - 32 * q^59 + 4 * q^60 + 24 * q^61 + 16 * q^62 - 6 * q^63 + 10 * q^65 - 4 * q^66 + 18 * q^67 + 16 * q^68 - 2 * q^69 + 12 * q^70 - 10 * q^71 - 4 * q^72 + 14 * q^73 + 6 * q^75 - 24 * q^76 - 48 * q^77 - 14 * q^78 + 16 * q^80 - 2 * q^81 - 4 * q^83 - 12 * q^84 - 4 * q^85 - 4 * q^86 - 48 * q^88 - 26 * q^89 + 2 * q^90 + 24 * q^91 + 12 * q^92 - 8 * q^93 - 12 * q^94 - 6 * q^95 - 8 * q^96 + 30 * q^97 - 4 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

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 $

$2$	1.36603	−	0.366025i	0.965926	−	0.258819i
$2$	1.36603	−	0.366025i	0.965926	−	0.258819i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$	−0.366025	+	0.366025i	−0.163692	+	0.163692i	−0.784200	−	0.620508i	$-0.786926\pi$
$5$	−0.366025	+	0.366025i	−0.163692	+	0.163692i	0.620508	+	0.784200i	$0.286926\pi$
$6$	−1.00000	−	1.00000i	−0.408248	−	0.408248i
$7$	2.36603	−	0.633975i	0.894274	−	0.239620i	0.217718	−	0.976012i	$-0.430139\pi$
$7$	2.36603	−	0.633975i	0.894274	−	0.239620i	0.676555	+	0.736392i	$0.263472\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.366025	+	0.633975i	−0.115747	+	0.200480i
$11$	−3.36603	−	0.901924i	−1.01489	−	0.271940i	−0.287222	−	0.957864i	$-0.592732\pi$
$11$	−3.36603	−	0.901924i	−1.01489	−	0.271940i	−0.727673	+	0.685924i	$0.759398\pi$
$12$	−1.73205	−	1.00000i	−0.500000	−	0.288675i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$	3.00000	−	1.73205i	0.801784	−	0.462910i
$15$	0.500000	+	0.133975i	0.129099	+	0.0345921i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	0.232051	+	0.133975i	0.0562806	+	0.0324936i	0.527876	−	0.849321i	$-0.322988\pi$
$17$	0.232051	+	0.133975i	0.0562806	+	0.0324936i	−0.471596	+	0.881815i	$0.656322\pi$
$18$	−0.366025	+	1.36603i	−0.0862730	+	0.321975i
$19$	−4.09808	+	1.09808i	−0.940163	+	0.251916i	−0.696183	−	0.717864i	$-0.745120\pi$
$19$	−4.09808	+	1.09808i	−0.940163	+	0.251916i	−0.243980	+	0.969780i	$0.578453\pi$
$20$	−0.267949	+	1.00000i	−0.0599153	+	0.223607i
$21$	−1.73205	−	1.73205i	−0.377964	−	0.377964i
$22$	−4.92820			−1.05070
$23$	0.366025	+	0.633975i	0.0763216	+	0.132193i	0.901660	−	0.432445i	$-0.142349\pi$
$23$	0.366025	+	0.633975i	0.0763216	+	0.132193i	−0.825339	+	0.564638i	$0.809016\pi$
$24$	−2.73205	−	0.732051i	−0.557678	−	0.149429i
$25$			4.73205i			0.946410i
$26$	4.46410	−	2.46410i	0.875482	−	0.483250i
$27$	1.00000			0.192450
$28$	3.46410	−	3.46410i	0.654654	−	0.654654i
$29$	−2.59808	+	1.50000i	−0.482451	+	0.278543i	−0.721437	−	0.692480i	$-0.756518\pi$
$29$	−2.59808	+	1.50000i	−0.482451	+	0.278543i	0.238987	+	0.971023i	$0.423185\pi$
$30$	0.732051			0.133654
$31$	4.00000	−	4.00000i	0.718421	−	0.718421i	−0.249861	−	0.968282i	$-0.580385\pi$
$31$	4.00000	−	4.00000i	0.718421	−	0.718421i	0.968282	+	0.249861i	$0.0803848\pi$
$32$	1.46410	−	5.46410i	0.258819	−	0.965926i
$33$	0.901924	+	3.36603i	0.157005	+	0.585950i
$34$	0.366025	+	0.0980762i	0.0627728	+	0.0168199i
$35$	−0.633975	+	1.09808i	−0.107161	+	0.185609i
$36$			2.00000i			0.333333i
$37$	−1.86603	+	6.96410i	−0.306773	+	1.14489i	0.624636	+	0.780916i	$0.285247\pi$
$37$	−1.86603	+	6.96410i	−0.306773	+	1.14489i	−0.931409	+	0.363975i	$0.881419\pi$
$38$	−5.19615	+	3.00000i	−0.842927	+	0.486664i
$39$	−2.50000	−	2.59808i	−0.400320	−	0.416025i
$40$			1.46410i			0.231495i
$41$	−2.50000	+	9.33013i	−0.390434	+	1.45712i	0.438985	+	0.898494i	$0.355338\pi$
$41$	−2.50000	+	9.33013i	−0.390434	+	1.45712i	−0.829419	+	0.558627i	$0.811329\pi$
$42$	−3.00000	−	1.73205i	−0.462910	−	0.267261i
$43$	−0.633975	−	0.366025i	−0.0966802	−	0.0558184i	0.450880	−	0.892584i	$-0.351110\pi$
$43$	−0.633975	−	0.366025i	−0.0966802	−	0.0558184i	−0.547561	+	0.836766i	$0.684443\pi$
$44$	−6.73205	+	1.80385i	−1.01489	+	0.271940i
$45$	−0.133975	−	0.500000i	−0.0199718	−	0.0745356i
$46$	0.732051	+	0.732051i	0.107935	+	0.107935i
$47$	2.26795	+	2.26795i	0.330814	+	0.330814i	0.852896	−	0.522081i	$-0.174844\pi$
$47$	2.26795	+	2.26795i	0.330814	+	0.330814i	−0.522081	+	0.852896i	$0.674844\pi$
$48$	−4.00000			−0.577350
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	1.73205	+	6.46410i	0.244949	+	0.914162i
$51$		−	0.267949i		−	0.0375204i
$52$	5.19615	−	5.00000i	0.720577	−	0.693375i
$53$			8.66025i			1.18958i	0.803882	+	0.594789i	$0.202764\pi$
$53$			8.66025i			1.18958i	−0.803882	+	0.594789i	$0.797236\pi$
$54$	1.36603	−	0.366025i	0.185893	−	0.0498097i
$55$	1.56218	−	0.901924i	0.210644	−	0.121615i
$56$	3.46410	−	6.00000i	0.462910	−	0.801784i
$57$	3.00000	+	3.00000i	0.397360	+	0.397360i
$58$	−3.00000	+	3.00000i	−0.393919	+	0.393919i
$59$	−2.80385	−	10.4641i	−0.365030	−	1.36231i	−0.867380	−	0.497646i	$-0.834198\pi$
$59$	−2.80385	−	10.4641i	−0.365030	−	1.36231i	0.502350	−	0.864664i	$-0.332469\pi$
$60$	1.00000	−	0.267949i	0.129099	−	0.0345921i
$61$	1.66987	+	0.964102i	0.213805	+	0.123441i	0.603079	−	0.797682i	$-0.293941\pi$
$61$	1.66987	+	0.964102i	0.213805	+	0.123441i	−0.389273	+	0.921122i	$0.627274\pi$
$62$	4.00000	−	6.92820i	0.508001	−	0.879883i
$63$	−0.633975	+	2.36603i	−0.0798733	+	0.298091i
$64$		−	8.00000i		−	1.00000i
$65$	−0.964102	+	1.59808i	−0.119582	+	0.198217i
$66$	2.46410	+	4.26795i	0.303310	+	0.525348i
$67$	−1.56218	+	5.83013i	−0.190850	+	0.712263i	0.802452	+	0.596717i	$0.203529\pi$
$67$	−1.56218	+	5.83013i	−0.190850	+	0.712263i	−0.993302	+	0.115546i	$0.963138\pi$
$68$	0.535898			0.0649872
$69$	0.366025	−	0.633975i	0.0440643	−	0.0763216i
$70$	−0.464102	+	1.73205i	−0.0554708	+	0.207020i
$71$	1.83013	+	6.83013i	0.217196	+	0.810587i	0.985382	+	0.170360i	$0.0544930\pi$
$71$	1.83013	+	6.83013i	0.217196	+	0.810587i	−0.768186	+	0.640227i	$0.778840\pi$
$72$	0.732051	+	2.73205i	0.0862730	+	0.321975i
$73$	7.83013	−	7.83013i	0.916447	−	0.916447i	−0.0803219	−	0.996769i	$-0.525595\pi$
$73$	7.83013	−	7.83013i	0.916447	−	0.916447i	0.996769	+	0.0803219i	$0.0255948\pi$
$74$			10.1962i			1.18528i
$75$	4.09808	−	2.36603i	0.473205	−	0.273205i
$76$	−6.00000	+	6.00000i	−0.688247	+	0.688247i
$77$	−8.53590			−0.972756
$78$	−4.36603	−	2.63397i	−0.494355	−	0.298239i
$79$			1.07180i			0.120587i	0.998181	+	0.0602933i	$0.0192036\pi$
$79$			1.07180i			0.120587i	−0.998181	+	0.0602933i	$0.980796\pi$
$80$	0.535898	+	2.00000i	0.0599153	+	0.223607i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			13.6603i			1.50852i
$83$	−7.92820	−	7.92820i	−0.870233	−	0.870233i	0.122264	−	0.992498i	$-0.460984\pi$
$83$	−7.92820	−	7.92820i	−0.870233	−	0.870233i	−0.992498	+	0.122264i	$0.960984\pi$
$84$	−4.73205	−	1.26795i	−0.516309	−	0.138345i
$85$	−0.133975	+	0.0358984i	−0.0145316	+	0.00389373i
$86$	−1.00000	−	0.267949i	−0.107833	−	0.0288937i
$87$	2.59808	+	1.50000i	0.278543	+	0.160817i
$88$	−8.53590	+	4.92820i	−0.909930	+	0.525348i
$89$	−12.5622	−	3.36603i	−1.33159	−	0.356798i	−0.478281	−	0.878207i	$-0.658740\pi$
$89$	−12.5622	−	3.36603i	−1.33159	−	0.356798i	−0.853307	+	0.521409i	$0.825407\pi$
$90$	−0.366025	−	0.633975i	−0.0385825	−	0.0668268i
$91$	7.73205	−	4.26795i	0.810539	−	0.447403i
$92$	1.26795	+	0.732051i	0.132193	+	0.0763216i
$93$	−5.46410	−	1.46410i	−0.566601	−	0.151820i
$94$	3.92820	+	2.26795i	0.405163	+	0.233921i
$95$	1.09808	−	1.90192i	0.112660	−	0.195133i
$96$	−5.46410	+	1.46410i	−0.557678	+	0.149429i
$97$	15.2942	−	4.09808i	1.55289	−	0.416097i	0.622488	−	0.782629i	$-0.286122\pi$
$97$	15.2942	−	4.09808i	1.55289	−	0.416097i	0.930405	+	0.366532i	$0.119455\pi$
$98$	−1.00000	+	1.00000i	−0.101015	+	0.101015i
$99$	2.46410	−	2.46410i	0.247652	−	0.247652i
$100$	4.73205	+	8.19615i	0.473205	+	0.819615i
$101$	−6.42820	−	11.1340i	−0.639630	−	1.10787i	−0.985514	−	0.169595i	$-0.945754\pi$
$101$	−6.42820	−	11.1340i	−0.639630	−	1.10787i	0.345884	−	0.938277i	$-0.387579\pi$
$102$	−0.0980762	−	0.366025i	−0.00971099	−	0.0362419i
$103$	−12.1962			−1.20172			−0.600861	−	0.799353i	$-0.705176\pi$
$103$	−12.1962			−1.20172			−0.600861	+	0.799353i	$0.705176\pi$
$104$	5.26795	−	8.73205i	0.516565	−	0.856248i
$105$	1.26795			0.123739
$106$	3.16987	+	11.8301i	0.307885	+	1.14904i
$107$	−1.90192	−	3.29423i	−0.183866	−	0.318465i	0.759328	−	0.650708i	$-0.225528\pi$
$107$	−1.90192	−	3.29423i	−0.183866	−	0.318465i	−0.943194	+	0.332243i	$0.892195\pi$
$108$	1.73205	−	1.00000i	0.166667	−	0.0962250i
$109$	14.1244	−	14.1244i	1.35287	−	1.35287i	0.470431	−	0.882437i	$-0.344098\pi$
$109$	14.1244	−	14.1244i	1.35287	−	1.35287i	0.882437	−	0.470431i	$-0.155902\pi$
$110$	1.80385	−	1.80385i	0.171990	−	0.171990i
$111$	6.96410	−	1.86603i	0.661003	−	0.177115i
$112$	2.53590	−	9.46410i	0.239620	−	0.894274i
$113$	−1.96410	+	3.40192i	−0.184767	+	0.320026i	−0.943498	−	0.331378i	$-0.892486\pi$
$113$	−1.96410	+	3.40192i	−0.184767	+	0.320026i	0.758731	+	0.651404i	$0.225820\pi$
$114$	5.19615	+	3.00000i	0.486664	+	0.280976i
$115$	−0.366025	−	0.0980762i	−0.0341320	−	0.00914565i
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	−1.00000	+	3.46410i	−0.0924500	+	0.320256i
$118$	−7.66025	−	13.2679i	−0.705184	−	1.22141i
$119$	0.633975	+	0.169873i	0.0581164	+	0.0155722i
$120$	1.26795	−	0.732051i	0.115747	−	0.0668268i
$121$	0.990381	+	0.571797i	0.0900346	+	0.0519815i
$122$	2.63397	+	0.705771i	0.238469	+	0.0638975i
$123$	9.33013	−	2.50000i	0.841269	−	0.225417i
$124$	2.92820	−	10.9282i	0.262960	−	0.981382i
$125$	−3.56218	−	3.56218i	−0.318611	−	0.318611i
$126$			3.46410i			0.308607i
$127$	0.267949	+	0.464102i	0.0237766	+	0.0411824i	0.877669	−	0.479267i	$-0.159098\pi$
$127$	0.267949	+	0.464102i	0.0237766	+	0.0411824i	−0.853892	+	0.520450i	$0.825764\pi$
$128$	−2.92820	−	10.9282i	−0.258819	−	0.965926i
$129$			0.732051i			0.0644535i
$130$	−0.732051	+	2.53590i	−0.0642051	+	0.222413i
$131$	13.8564			1.21064			0.605320	−	0.795982i	$-0.293045\pi$
$131$	13.8564			1.21064			0.605320	+	0.795982i	$0.293045\pi$
$132$	4.92820	+	4.92820i	0.428945	+	0.428945i
$133$	−9.00000	+	5.19615i	−0.780399	+	0.450564i
$134$			8.53590i			0.737389i
$135$	−0.366025	+	0.366025i	−0.0315025	+	0.0315025i
$136$	0.732051	−	0.196152i	0.0627728	−	0.0168199i
$137$	−1.33013	−	4.96410i	−0.113640	−	0.424112i	0.885541	−	0.464561i	$-0.153788\pi$
$137$	−1.33013	−	4.96410i	−0.113640	−	0.424112i	−0.999182	+	0.0404491i	$0.987121\pi$
$138$	0.267949	−	1.00000i	0.0228093	−	0.0851257i
$139$	−7.66025	+	13.2679i	−0.649734	+	1.12537i	0.333452	+	0.942767i	$0.391786\pi$
$139$	−7.66025	+	13.2679i	−0.649734	+	1.12537i	−0.983186	+	0.182606i	$0.941547\pi$
$140$			2.53590i			0.214323i
$141$	0.830127	−	3.09808i	0.0699093	−	0.260905i
$142$	5.00000	+	8.66025i	0.419591	+	0.726752i
$143$	−12.5622	−	0.241670i	−1.05050	−	0.0202094i
$144$	2.00000	+	3.46410i	0.166667	+	0.288675i
$145$	0.401924	−	1.50000i	0.0333780	−	0.124568i
$146$	7.83013	−	13.5622i	0.648026	−	1.12241i
$147$	0.866025	+	0.500000i	0.0714286	+	0.0412393i
$148$	3.73205	+	13.9282i	0.306773	+	1.14489i
$149$	4.30385	+	16.0622i	0.352585	+	1.31586i	0.883497	+	0.468438i	$0.155183\pi$
$149$	4.30385	+	16.0622i	0.352585	+	1.31586i	−0.530912	+	0.847427i	$0.678150\pi$
$150$	4.73205	−	4.73205i	0.386370	−	0.386370i
$151$	−14.6603	−	14.6603i	−1.19303	−	1.19303i	−0.976211	−	0.216824i	$-0.930430\pi$
$151$	−14.6603	−	14.6603i	−1.19303	−	1.19303i	−0.216824	−	0.976211i	$-0.569570\pi$
$152$	−6.00000	+	10.3923i	−0.486664	+	0.842927i
$153$	−0.232051	+	0.133975i	−0.0187602	+	0.0108312i
$154$	−11.6603	+	3.12436i	−0.939610	+	0.251768i
$155$			2.92820i			0.235199i
$156$	−6.92820	−	2.00000i	−0.554700	−	0.160128i
$157$			0.803848i			0.0641540i	0.999485	+	0.0320770i	$0.0102122\pi$
$157$			0.803848i			0.0641540i	−0.999485	+	0.0320770i	$0.989788\pi$
$158$	0.392305	+	1.46410i	0.0312101	+	0.116478i
$159$	7.50000	−	4.33013i	0.594789	−	0.343401i
$160$	1.46410	+	2.53590i	0.115747	+	0.200480i
$161$	1.26795	+	1.26795i	0.0999284	+	0.0999284i
$162$	−1.00000	−	1.00000i	−0.0785674	−	0.0785674i
$163$	−2.26795	−	8.46410i	−0.177639	−	0.662960i	−0.996087	−	0.0883783i	$-0.971832\pi$
$163$	−2.26795	−	8.46410i	−0.177639	−	0.662960i	0.818447	−	0.574581i	$-0.194835\pi$
$164$	5.00000	+	18.6603i	0.390434	+	1.45712i
$165$	−1.56218	−	0.901924i	−0.121615	−	0.0702147i
$166$	−13.7321	−	7.92820i	−1.06581	−	0.615348i
$167$	5.26795	−	19.6603i	0.407646	−	1.52136i	−0.391476	−	0.920188i	$-0.628036\pi$
$167$	5.26795	−	19.6603i	0.407646	−	1.52136i	0.799123	−	0.601168i	$-0.205298\pi$
$168$	−6.92820			−0.534522
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	−0.169873	+	0.0980762i	−0.0130287	+	0.00752210i
$171$	1.09808	−	4.09808i	0.0839720	−	0.313388i
$172$	−1.46410			−0.111637
$173$	9.46410	−	16.3923i	0.719542	−	1.24628i	−0.241639	−	0.970366i	$-0.577685\pi$
$173$	9.46410	−	16.3923i	0.719542	−	1.24628i	0.961181	−	0.275918i	$-0.0889817\pi$
$174$	4.09808	+	1.09808i	0.310674	+	0.0832449i
$175$	3.00000	+	11.1962i	0.226779	+	0.846350i
$176$	−9.85641	+	9.85641i	−0.742955	+	0.742955i
$177$	−7.66025	+	7.66025i	−0.575780	+	0.575780i
$178$	−18.3923			−1.37856
$179$	−1.09808	+	0.633975i	−0.0820741	+	0.0473855i	−0.540475	−	0.841360i	$-0.681756\pi$
$179$	−1.09808	+	0.633975i	−0.0820741	+	0.0473855i	0.458401	+	0.888745i	$0.348422\pi$
$180$	−0.732051	−	0.732051i	−0.0545638	−	0.0545638i
$181$	1.92820			0.143322			0.0716611	−	0.997429i	$-0.477170\pi$
$181$	1.92820			0.143322			0.0716611	+	0.997429i	$0.477170\pi$
$182$	9.00000	−	8.66025i	0.667124	−	0.641941i
$183$		−	1.92820i		−	0.142537i
$184$	2.00000	+	0.535898i	0.147442	+	0.0395070i
$185$	−1.86603	−	3.23205i	−0.137193	−	0.237625i
$186$	−8.00000			−0.586588
$187$	−0.660254	−	0.660254i	−0.0482826	−	0.0482826i
$188$	6.19615	+	1.66025i	0.451901	+	0.121086i
$189$	2.36603	−	0.633975i	0.172103	−	0.0461149i
$190$	0.803848	−	3.00000i	0.0583172	−	0.217643i
$191$	16.3923	+	9.46410i	1.18611	+	0.684798i	0.957419	−	0.288702i	$-0.0932236\pi$
$191$	16.3923	+	9.46410i	1.18611	+	0.684798i	0.228686	+	0.973500i	$0.426557\pi$
$192$	−6.92820	+	4.00000i	−0.500000	+	0.288675i
$193$	−16.0622	−	4.30385i	−1.15618	−	0.309798i	−0.370741	−	0.928736i	$-0.620896\pi$
$193$	−16.0622	−	4.30385i	−1.15618	−	0.309798i	−0.785440	+	0.618938i	$0.787563\pi$
$194$	19.3923	−	11.1962i	1.39229	−	0.803837i
$195$	1.86603	+	0.0358984i	0.133629	+	0.00257074i
$196$	−1.00000	+	1.73205i	−0.0714286	+	0.123718i
$197$	9.56218	+	2.56218i	0.681277	+	0.182548i	0.582829	−	0.812595i	$-0.301946\pi$
$197$	9.56218	+	2.56218i	0.681277	+	0.182548i	0.0984477	+	0.995142i	$0.468612\pi$
$198$	2.46410	−	4.26795i	0.175116	−	0.303310i
$199$	5.36603	−	9.29423i	0.380387	−	0.658850i	−0.610730	−	0.791839i	$-0.709124\pi$
$199$	5.36603	−	9.29423i	0.380387	−	0.658850i	0.991118	+	0.132988i	$0.0424573\pi$
$200$	9.46410	+	9.46410i	0.669213	+	0.669213i
$201$	5.83013	−	1.56218i	0.411225	−	0.110188i
$202$	−12.8564	−	12.8564i	−0.904574	−	0.904574i
$203$	−5.19615	+	5.19615i	−0.364698	+	0.364698i
$204$	−0.267949	−	0.464102i	−0.0187602	−	0.0324936i
$205$	−2.50000	−	4.33013i	−0.174608	−	0.302429i
$206$	−16.6603	+	4.46410i	−1.16077	+	0.311029i
$207$	−0.732051			−0.0508810
$208$	4.00000	−	13.8564i	0.277350	−	0.960769i
$209$	14.7846			1.02267
$210$	1.73205	−	0.464102i	0.119523	−	0.0320261i
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	0.944237	+	0.329266i	$0.106801\pi$
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	−0.186966	+	0.982366i	$0.559865\pi$
$212$	8.66025	+	15.0000i	0.594789	+	1.03020i
$213$	5.00000	−	5.00000i	0.342594	−	0.342594i
$214$	−3.80385	−	3.80385i	−0.260026	−	0.260026i
$215$	0.366025	−	0.0980762i	0.0249627	−	0.00668874i
$216$	2.00000	−	2.00000i	0.136083	−	0.136083i
$217$	6.92820	−	12.0000i	0.470317	−	0.814613i
$218$	14.1244	−	24.4641i	0.956622	−	1.65692i
$219$	−10.6962	−	2.86603i	−0.722779	−	0.193668i
$220$	1.80385	−	3.12436i	0.121615	−	0.210644i
$221$	0.928203	+	0.267949i	0.0624377	+	0.0180242i
$222$	8.83013	−	5.09808i	0.592639	−	0.342160i
$223$	−17.9282	−	4.80385i	−1.20056	−	0.321689i	−0.397509	−	0.917598i	$-0.630125\pi$
$223$	−17.9282	−	4.80385i	−1.20056	−	0.321689i	−0.803052	+	0.595909i	$0.796792\pi$
$224$		−	13.8564i		−	0.925820i
$225$	−4.09808	−	2.36603i	−0.273205	−	0.157735i
$226$	−1.43782	+	5.36603i	−0.0956425	+	0.356943i
$227$	1.09808	−	0.294229i	0.0728819	−	0.0195286i	−0.222194	−	0.975003i	$-0.571322\pi$
$227$	1.09808	−	0.294229i	0.0728819	−	0.0195286i	0.295076	+	0.955474i	$0.404655\pi$
$228$	8.19615	+	2.19615i	0.542803	+	0.145444i
$229$	5.00000	+	5.00000i	0.330409	+	0.330409i	0.852742	−	0.522333i	$-0.174938\pi$
$229$	5.00000	+	5.00000i	0.330409	+	0.330409i	−0.522333	+	0.852742i	$0.674938\pi$
$230$	−0.535898			−0.0353361
$231$	4.26795	+	7.39230i	0.280810	+	0.486378i
$232$	−2.19615	+	8.19615i	−0.144184	+	0.538104i
$233$		−	9.07180i		−	0.594313i	−0.954829	−	0.297157i	$-0.903962\pi$
$233$		−	9.07180i		−	0.594313i	0.954829	−	0.297157i	$-0.0960383\pi$
$234$	−0.0980762	+	5.09808i	−0.00641144	+	0.333272i
$235$	−1.66025			−0.108303
$236$	−15.3205	−	15.3205i	−0.997280	−	0.997280i
$237$	0.928203	−	0.535898i	0.0602933	−	0.0348103i
$238$	0.928203			0.0601665
$239$	−13.0000	+	13.0000i	−0.840900	+	0.840900i	−0.988976	−	0.148076i	$-0.952692\pi$
$239$	−13.0000	+	13.0000i	−0.840900	+	0.840900i	0.148076	+	0.988976i	$0.452692\pi$
$240$	1.46410	−	1.46410i	0.0945074	−	0.0945074i
$241$	−3.83975	−	14.3301i	−0.247340	−	0.923085i	−0.972193	−	0.234181i	$-0.924759\pi$
$241$	−3.83975	−	14.3301i	−0.247340	−	0.923085i	0.724853	−	0.688903i	$-0.241908\pi$
$242$	1.56218	+	0.418584i	0.100421	+	0.0269076i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	3.85641			0.246881
$245$	0.133975	−	0.500000i	0.00855932	−	0.0319438i
$246$	11.8301	−	6.83013i	0.754261	−	0.435473i
$247$	−13.3923	+	7.39230i	−0.852132	+	0.470361i
$248$		−	16.0000i		−	1.01600i
$249$	−2.90192	+	10.8301i	−0.183902	+	0.686331i
$250$	−6.16987	−	3.56218i	−0.390217	−	0.225292i
$251$	24.9282	+	14.3923i	1.57345	+	0.908434i	0.995741	+	0.0921944i	$0.0293881\pi$
$251$	24.9282	+	14.3923i	1.57345	+	0.908434i	0.577713	+	0.816240i	$0.303945\pi$
$252$	1.26795	+	4.73205i	0.0798733	+	0.298091i
$253$	−0.660254	−	2.46410i	−0.0415098	−	0.154917i
$254$	0.535898	+	0.535898i	0.0336253	+	0.0336253i
$255$	0.0980762	+	0.0980762i	0.00614177	+	0.00614177i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	2.13397	−	1.23205i	0.133114	−	0.0768532i	−0.431964	−	0.901891i	$-0.642179\pi$
$257$	2.13397	−	1.23205i	0.133114	−	0.0768532i	0.565078	+	0.825037i	$0.308846\pi$
$258$	0.267949	+	1.00000i	0.0166818	+	0.0622573i
$259$			17.6603i			1.09735i
$260$	−0.0717968	+	3.73205i	−0.00445265	+	0.231452i
$261$		−	3.00000i		−	0.185695i
$262$	18.9282	−	5.07180i	1.16939	−	0.313337i
$263$	−1.56218	+	0.901924i	−0.0963280	+	0.0556150i	−0.547390	−	0.836878i	$-0.684379\pi$
$263$	−1.56218	+	0.901924i	−0.0963280	+	0.0556150i	0.451062	+	0.892493i	$0.351045\pi$
$264$	8.53590	+	4.92820i	0.525348	+	0.303310i
$265$	−3.16987	−	3.16987i	−0.194724	−	0.194724i
$266$	−10.3923	+	10.3923i	−0.637193	+	0.637193i
$267$	3.36603	+	12.5622i	0.205997	+	0.768793i
$268$	3.12436	+	11.6603i	0.190850	+	0.712263i
$269$	7.85641	+	4.53590i	0.479014	+	0.276559i	0.720005	−	0.693969i	$-0.244139\pi$
$269$	7.85641	+	4.53590i	0.479014	+	0.276559i	−0.240992	+	0.970527i	$0.577473\pi$
$270$	−0.366025	+	0.633975i	−0.0222756	+	0.0385825i
$271$	0.196152	−	0.732051i	0.0119154	−	0.0444689i	−0.959712	−	0.280985i	$-0.909339\pi$
$271$	0.196152	−	0.732051i	0.0119154	−	0.0444689i	0.971628	+	0.236516i	$0.0760056\pi$
$272$	0.928203	−	0.535898i	0.0562806	−	0.0324936i
$273$	−7.56218	−	4.56218i	−0.457684	−	0.276116i
$274$	−3.63397	−	6.29423i	−0.219536	−	0.380248i
$275$	4.26795	−	15.9282i	0.257367	−	0.960507i
$276$		−	1.46410i		−	0.0881286i
$277$	−14.0622	+	24.3564i	−0.844914	+	1.46343i	0.0407812	+	0.999168i	$0.487015\pi$
$277$	−14.0622	+	24.3564i	−0.844914	+	1.46343i	−0.885696	+	0.464267i	$0.846318\pi$
$278$	−5.60770	+	20.9282i	−0.336327	+	1.25519i
$279$	1.46410	+	5.46410i	0.0876535	+	0.327127i
$280$	0.928203	+	3.46410i	0.0554708	+	0.207020i
$281$	−13.2942	+	13.2942i	−0.793067	+	0.793067i	−0.981992	−	0.188924i	$-0.939500\pi$
$281$	−13.2942	+	13.2942i	−0.793067	+	0.793067i	0.188924	+	0.981992i	$0.439500\pi$
$282$		−	4.53590i		−	0.270109i
$283$	−27.2942	+	15.7583i	−1.62247	+	0.936736i	−0.636218	+	0.771510i	$0.719502\pi$
$283$	−27.2942	+	15.7583i	−1.62247	+	0.936736i	−0.986256	+	0.165226i	$0.947165\pi$
$284$	10.0000	+	10.0000i	0.593391	+	0.593391i
$285$	−2.19615			−0.130089
$286$	−17.2487	+	4.26795i	−1.01994	+	0.252369i
$287$			23.6603i			1.39662i
$288$	4.00000	+	4.00000i	0.235702	+	0.235702i
$289$	−8.46410	−	14.6603i	−0.497888	−	0.862368i
$290$		−	2.19615i		−	0.128963i
$291$	−11.1962	−	11.1962i	−0.656330	−	0.656330i
$292$	5.73205	−	21.3923i	0.335443	−	1.25189i
$293$	−6.59808	+	1.76795i	−0.385464	+	0.103285i	−0.446346	−	0.894860i	$-0.647275\pi$
$293$	−6.59808	+	1.76795i	−0.385464	+	0.103285i	0.0608827	+	0.998145i	$0.480608\pi$
$294$	1.36603	+	0.366025i	0.0796682	+	0.0213470i
$295$	4.85641	+	2.80385i	0.282751	+	0.163246i
$296$	10.1962	+	17.6603i	0.592639	+	1.02648i
$297$	−3.36603	−	0.901924i	−0.195317	−	0.0523349i
$298$	11.7583	+	20.3660i	0.681142	+	1.17977i
$299$	1.83013	+	1.90192i	0.105839	+	0.109991i
$300$	4.73205	−	8.19615i	0.273205	−	0.473205i
$301$	−1.73205	−	0.464102i	−0.0998337	−	0.0267504i
$302$	−25.3923	−	14.6603i	−1.46116	−	0.843603i
$303$	−6.42820	+	11.1340i	−0.369291	+	0.639630i
$304$	−4.39230	+	16.3923i	−0.251916	+	0.940163i
$305$	−0.964102	+	0.258330i	−0.0552043	+	0.0147919i
$306$	−0.267949	+	0.267949i	−0.0153176	+	0.0153176i
$307$	−7.73205	+	7.73205i	−0.441291	+	0.441291i	−0.892446	−	0.451154i	$-0.851012\pi$
$307$	−7.73205	+	7.73205i	−0.441291	+	0.441291i	0.451154	+	0.892446i	$0.351012\pi$
$308$	−14.7846	+	8.53590i	−0.842431	+	0.486378i
$309$	6.09808	+	10.5622i	0.346907	+	0.600861i
$310$	1.07180	+	4.00000i	0.0608740	+	0.227185i
$311$	10.7321			0.608559			0.304279	−	0.952583i	$-0.401584\pi$
$311$	10.7321			0.608559			0.304279	+	0.952583i	$0.401584\pi$
$312$	−10.1962	−	0.196152i	−0.577243	−	0.0111049i
$313$	−19.8564			−1.12235			−0.561175	−	0.827697i	$-0.689651\pi$
$313$	−19.8564			−1.12235			−0.561175	+	0.827697i	$0.689651\pi$
$314$	0.294229	+	1.09808i	0.0166043	+	0.0619680i
$315$	−0.633975	−	1.09808i	−0.0357204	−	0.0618696i
$316$	1.07180	+	1.85641i	0.0602933	+	0.104431i
$317$	21.3660	−	21.3660i	1.20004	−	1.20004i	0.225881	−	0.974155i	$-0.427474\pi$
$317$	21.3660	−	21.3660i	1.20004	−	1.20004i	0.974155	−	0.225881i	$-0.0725259\pi$
$318$	8.66025	−	8.66025i	0.485643	−	0.485643i
$319$	10.0981	−	2.70577i	0.565384	−	0.151494i
$320$	2.92820	+	2.92820i	0.163692	+	0.163692i
$321$	−1.90192	+	3.29423i	−0.106155	+	0.183866i
$322$	2.19615	+	1.26795i	0.122387	+	0.0706600i
$323$	−1.09808	−	0.294229i	−0.0610986	−	0.0163713i
$324$	−1.73205	−	1.00000i	−0.0962250	−	0.0555556i
$325$	4.09808	+	16.5622i	0.227320	+	0.918704i
$326$	−6.19615	−	10.7321i	−0.343173	−	0.594393i
$327$	−19.2942	−	5.16987i	−1.06697	−	0.285895i
$328$	13.6603	+	23.6603i	0.754261	+	1.30642i
$329$	6.80385	+	3.92820i	0.375108	+	0.216569i
$330$	−2.46410	−	0.660254i	−0.135644	−	0.0363458i
$331$	12.6603	−	3.39230i	0.695870	−	0.186458i	0.106490	−	0.994314i	$-0.466039\pi$
$331$	12.6603	−	3.39230i	0.695870	−	0.186458i	0.589380	+	0.807856i	$0.299372\pi$
$332$	−21.6603	−	5.80385i	−1.18876	−	0.318528i
$333$	−5.09808	−	5.09808i	−0.279373	−	0.279373i
$334$		−	28.7846i		−	1.57502i
$335$	−1.56218	−	2.70577i	−0.0853509	−	0.147832i
$336$	−9.46410	+	2.53590i	−0.516309	+	0.138345i
$337$			20.8564i			1.13612i	0.822987	+	0.568060i	$0.192306\pi$
$337$			20.8564i			1.13612i	−0.822987	+	0.568060i	$0.807694\pi$
$338$	13.4904	−	12.4904i	0.733780	−	0.679387i
$339$	3.92820			0.213351
$340$	−0.196152	+	0.196152i	−0.0106379	+	0.0106379i
$341$	−17.0718	+	9.85641i	−0.924490	+	0.533754i
$342$		−	6.00000i		−	0.324443i
$343$	−13.8564	+	13.8564i	−0.748176	+	0.748176i
$344$	−2.00000	+	0.535898i	−0.107833	+	0.0288937i
$345$	0.0980762	+	0.366025i	0.00528025	+	0.0197061i
$346$	6.92820	−	25.8564i	0.372463	−	1.39005i
$347$	−2.36603	+	4.09808i	−0.127015	+	0.219996i	−0.922519	−	0.385952i	$-0.873873\pi$
$347$	−2.36603	+	4.09808i	−0.127015	+	0.219996i	0.795504	+	0.605949i	$0.207206\pi$
$348$	6.00000			0.321634
$349$	4.68653	−	17.4904i	0.250864	−	0.936239i	−0.719480	−	0.694513i	$-0.755620\pi$
$349$	4.68653	−	17.4904i	0.250864	−	0.936239i	0.970345	−	0.241726i	$-0.0777134\pi$
$350$	8.19615	+	14.1962i	0.438103	+	0.758816i
$351$	3.50000	−	0.866025i	0.186816	−	0.0462250i
$352$	−9.85641	+	17.0718i	−0.525348	+	0.909930i
$353$	−0.866025	+	3.23205i	−0.0460939	+	0.172025i	−0.985136	−	0.171779i	$-0.945049\pi$
$353$	−0.866025	+	3.23205i	−0.0460939	+	0.172025i	0.939042	+	0.343803i	$0.111715\pi$
$354$	−7.66025	+	13.2679i	−0.407138	+	0.705184i
$355$	−3.16987	−	1.83013i	−0.168239	−	0.0971331i
$356$	−25.1244	+	6.73205i	−1.33159	+	0.356798i
$357$	−0.169873	−	0.633975i	−0.00899063	−	0.0335535i
$358$	−1.26795	+	1.26795i	−0.0670132	+	0.0670132i
$359$	4.07180	+	4.07180i	0.214901	+	0.214901i	0.806346	−	0.591444i	$-0.201442\pi$
$359$	4.07180	+	4.07180i	0.214901	+	0.214901i	−0.591444	+	0.806346i	$0.701442\pi$
$360$	−1.26795	−	0.732051i	−0.0668268	−	0.0385825i
$361$	−0.866025	+	0.500000i	−0.0455803	+	0.0263158i
$362$	2.63397	−	0.705771i	0.138439	−	0.0370945i
$363$		−	1.14359i		−	0.0600231i
$364$	9.12436	−	15.1244i	0.478246	−	0.792732i
$365$			5.73205i			0.300029i
$366$	−0.705771	−	2.63397i	−0.0368913	−	0.137680i
$367$	6.16987	−	3.56218i	0.322065	−	0.185944i	−0.330248	−	0.943894i	$-0.607132\pi$
$367$	6.16987	−	3.56218i	0.322065	−	0.185944i	0.652313	+	0.757950i	$0.273799\pi$
$368$	2.92820			0.152643
$369$	−6.83013	−	6.83013i	−0.355562	−	0.355562i
$370$	−3.73205	−	3.73205i	−0.194020	−	0.194020i
$371$	5.49038	+	20.4904i	0.285046	+	1.06381i
$372$	−10.9282	+	2.92820i	−0.566601	+	0.151820i
$373$	14.3038	+	8.25833i	0.740625	+	0.427600i	0.822297	−	0.569059i	$-0.192692\pi$
$373$	14.3038	+	8.25833i	0.740625	+	0.427600i	−0.0816714	+	0.996659i	$0.526026\pi$
$374$	−1.14359	−	0.660254i	−0.0591338	−	0.0341409i
$375$	−1.30385	+	4.86603i	−0.0673304	+	0.251280i
$376$	9.07180			0.467842
$377$	−7.79423	+	7.50000i	−0.401423	+	0.386270i
$378$	3.00000	−	1.73205i	0.154303	−	0.0890871i
$379$	−6.07180	+	22.6603i	−0.311887	+	1.16398i	0.614966	+	0.788554i	$0.289170\pi$
$379$	−6.07180	+	22.6603i	−0.311887	+	1.16398i	−0.926853	+	0.375425i	$0.877497\pi$
$380$		−	4.39230i		−	0.225320i
$381$	0.267949	−	0.464102i	0.0137275	−	0.0237766i
$382$	25.8564	+	6.92820i	1.32293	+	0.354478i
$383$	−4.19615	−	15.6603i	−0.214413	−	0.800202i	−0.986372	−	0.164529i	$-0.947390\pi$
$383$	−4.19615	−	15.6603i	−0.214413	−	0.800202i	0.771959	−	0.635672i	$-0.219277\pi$
$384$	−8.00000	+	8.00000i	−0.408248	+	0.408248i
$385$	3.12436	−	3.12436i	0.159232	−	0.159232i
$386$	−23.5167			−1.19697
$387$	0.633975	−	0.366025i	0.0322267	−	0.0186061i
$388$	22.3923	−	22.3923i	1.13680	−	1.13680i
$389$	−1.73205			−0.0878185			−0.0439092	−	0.999036i	$-0.513981\pi$
$389$	−1.73205			−0.0878185			−0.0439092	+	0.999036i	$0.513981\pi$
$390$	2.56218	−	0.633975i	0.129741	−	0.0321026i
$391$			0.196152i			0.00991985i
$392$	−0.732051	+	2.73205i	−0.0369741	+	0.137989i
$393$	−6.92820	−	12.0000i	−0.349482	−	0.605320i
$394$	14.0000			0.705310
$395$	−0.392305	−	0.392305i	−0.0197390	−	0.0197390i
$396$	1.80385	−	6.73205i	0.0906468	−	0.338298i
$397$	7.29423	−	1.95448i	0.366087	−	0.0980927i	−0.0710860	−	0.997470i	$-0.522646\pi$
$397$	7.29423	−	1.95448i	0.366087	−	0.0980927i	0.437173	+	0.899378i	$0.355980\pi$
$398$	3.92820	−	14.6603i	0.196903	−	0.734852i
$399$	9.00000	+	5.19615i	0.450564	+	0.260133i
$400$	16.3923	+	9.46410i	0.819615	+	0.473205i
$401$	2.13397	+	0.571797i	0.106566	+	0.0285542i	0.311708	−	0.950178i	$-0.399099\pi$
$401$	2.13397	+	0.571797i	0.106566	+	0.0285542i	−0.205142	+	0.978732i	$0.565766\pi$
$402$	7.39230	−	4.26795i	0.368695	−	0.212866i
$403$	10.5359	−	17.4641i	0.524830	−	0.869949i
$404$	−22.2679	−	12.8564i	−1.10787	−	0.639630i
$405$	0.500000	+	0.133975i	0.0248452	+	0.00665725i
$406$	−5.19615	+	9.00000i	−0.257881	+	0.446663i
$407$	12.5622	−	21.7583i	0.622684	−	1.07852i
$408$	−0.535898	−	0.535898i	−0.0265309	−	0.0265309i
$409$	−2.33013	+	0.624356i	−0.115217	+	0.0308724i	−0.315967	−	0.948770i	$-0.602329\pi$
$409$	−2.33013	+	0.624356i	−0.115217	+	0.0308724i	0.200750	+	0.979643i	$0.435662\pi$
$410$	−5.00000	−	5.00000i	−0.246932	−	0.246932i
$411$	−3.63397	+	3.63397i	−0.179251	+	0.179251i
$412$	−21.1244	+	12.1962i	−1.04072	+	0.600861i
$413$	−13.2679	−	22.9808i	−0.652873	−	1.13081i
$414$	−1.00000	+	0.267949i	−0.0491473	+	0.0131690i
$415$	5.80385			0.284900
$416$	0.392305	−	20.3923i	0.0192343	−	0.999815i
$417$	15.3205			0.750249
$418$	20.1962	−	5.41154i	0.987826	−	0.264687i
$419$	4.80385	+	8.32051i	0.234683	+	0.406483i	0.959181	−	0.282794i	$-0.0912614\pi$
$419$	4.80385	+	8.32051i	0.234683	+	0.406483i	−0.724497	+	0.689278i	$0.757928\pi$
$420$	2.19615	−	1.26795i	0.107161	−	0.0618696i
$421$	26.3660	−	26.3660i	1.28500	−	1.28500i	0.347216	−	0.937785i	$-0.387127\pi$
$421$	26.3660	−	26.3660i	1.28500	−	1.28500i	0.937785	−	0.347216i	$-0.112873\pi$
$422$	22.0000	+	22.0000i	1.07094	+	1.07094i
$423$	−3.09808	+	0.830127i	−0.150634	+	0.0403622i
$424$	17.3205	+	17.3205i	0.841158	+	0.841158i
$425$	−0.633975	+	1.09808i	−0.0307523	+	0.0532645i
$426$	5.00000	−	8.66025i	0.242251	−	0.419591i
$427$	4.56218	+	1.22243i	0.220779	+	0.0591576i
$428$	−6.58846	−	3.80385i	−0.318465	−	0.183866i
$429$	6.07180	+	11.0000i	0.293149	+	0.531085i
$430$	0.464102	−	0.267949i	0.0223810	−	0.0129217i
$431$	−39.4186	−	10.5622i	−1.89873	−	0.508762i	−0.997087	−	0.0762738i	$-0.975698\pi$
$431$	−39.4186	−	10.5622i	−1.89873	−	0.508762i	−0.901639	−	0.432488i	$-0.857636\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	−8.42820	−	4.86603i	−0.405034	−	0.233846i	0.283620	−	0.958937i	$-0.408465\pi$
$433$	−8.42820	−	4.86603i	−0.405034	−	0.233846i	−0.688654	+	0.725090i	$0.741798\pi$
$434$	5.07180	−	18.9282i	0.243454	−	0.908583i
$435$	−1.50000	+	0.401924i	−0.0719195	+	0.0192708i
$436$	10.3397	−	38.5885i	0.495184	−	1.84805i
$437$	−2.19615	−	2.19615i	−0.105056	−	0.105056i
$438$	−15.6603			−0.748276
$439$	16.8301	+	29.1506i	0.803258	+	1.39128i	0.917461	+	0.397826i	$0.130235\pi$
$439$	16.8301	+	29.1506i	0.803258	+	1.39128i	−0.114203	+	0.993457i	$0.536431\pi$
$440$	1.32051	−	4.92820i	0.0629528	−	0.234943i
$441$		−	1.00000i		−	0.0476190i
$442$	1.36603	+	0.0262794i	0.0649752	+	0.00124999i
$443$	12.1436			0.576960			0.288480	−	0.957486i	$-0.406850\pi$
$443$	12.1436			0.576960			0.288480	+	0.957486i	$0.406850\pi$
$444$	10.1962	−	10.1962i	0.483888	−	0.483888i
$445$	5.83013	−	3.36603i	0.276375	−	0.159565i
$446$	−26.2487			−1.24291
$447$	11.7583	−	11.7583i	0.556150	−	0.556150i
$448$	−5.07180	−	18.9282i	−0.239620	−	0.894274i
$449$	−7.02628	−	26.2224i	−0.331591	−	1.23751i	−0.907518	−	0.420012i	$-0.862026\pi$
$449$	−7.02628	−	26.2224i	−0.331591	−	1.23751i	0.575928	−	0.817501i	$-0.304641\pi$
$450$	−6.46410	−	1.73205i	−0.304721	−	0.0816497i
$451$	16.8301	−	29.1506i	0.792500	−	1.37265i
$452$			7.85641i			0.369534i
$453$	−5.36603	+	20.0263i	−0.252118	+	0.940917i
$454$	1.39230	−	0.803848i	0.0653441	−	0.0377264i
$455$	−1.26795	+	4.39230i	−0.0594424	+	0.205914i
$456$	12.0000			0.561951
$457$	−1.59808	+	5.96410i	−0.0747549	+	0.278989i	−0.993178	−	0.116611i	$-0.962797\pi$
$457$	−1.59808	+	5.96410i	−0.0747549	+	0.278989i	0.918423	+	0.395600i	$0.129463\pi$
$458$	8.66025	+	5.00000i	0.404667	+	0.233635i
$459$	0.232051	+	0.133975i	0.0108312	+	0.00625340i
$460$	−0.732051	+	0.196152i	−0.0341320	+	0.00914565i
$461$	−7.28461	−	27.1865i	−0.339278	−	1.26620i	−0.899156	−	0.437628i	$-0.855819\pi$
$461$	−7.28461	−	27.1865i	−0.339278	−	1.26620i	0.559878	−	0.828575i	$-0.310848\pi$
$462$	8.53590	+	8.53590i	0.397126	+	0.397126i
$463$	−0.660254	−	0.660254i	−0.0306846	−	0.0306846i	0.691598	−	0.722283i	$-0.256907\pi$
$463$	−0.660254	−	0.660254i	−0.0306846	−	0.0306846i	−0.722283	+	0.691598i	$0.756907\pi$
$464$			12.0000i			0.557086i
$465$	2.53590	−	1.46410i	0.117599	−	0.0678961i
$466$	−3.32051	−	12.3923i	−0.153820	−	0.574062i
$467$			14.1962i			0.656920i	0.944518	+	0.328460i	$0.106530\pi$
$467$			14.1962i			0.656920i	−0.944518	+	0.328460i	$0.893470\pi$
$468$	1.73205	+	7.00000i	0.0800641	+	0.323575i
$469$			14.7846i			0.682690i
$470$	−2.26795	+	0.607695i	−0.104613	+	0.0280309i
$471$	0.696152	−	0.401924i	0.0320770	−	0.0185197i
$472$	−26.5359	−	15.3205i	−1.22141	−	0.705184i
$473$	1.80385	+	1.80385i	0.0829410	+	0.0829410i
$474$	1.07180	−	1.07180i	0.0492293	−	0.0492293i
$475$	−5.19615	−	19.3923i	−0.238416	−	0.889780i
$476$	1.26795	−	0.339746i	0.0581164	−	0.0155722i
$477$	−7.50000	−	4.33013i	−0.343401	−	0.198263i
$478$	−13.0000	+	22.5167i	−0.594606	+	1.02989i
$479$	10.1244	−	37.7846i	0.462594	−	1.72642i	−0.202153	−	0.979354i	$-0.564794\pi$
$479$	10.1244	−	37.7846i	0.462594	−	1.72642i	0.664747	−	0.747069i	$-0.268540\pi$
$480$	1.46410	−	2.53590i	0.0668268	−	0.115747i
$481$	−0.500000	+	25.9904i	−0.0227980	+	1.18506i
$482$	−10.4904	−	18.1699i	−0.477824	−	0.827615i
$483$	0.464102	−	1.73205i	0.0211174	−	0.0788110i
$484$	2.28719			0.103963
$485$	−4.09808	+	7.09808i	−0.186084	+	0.322307i
$486$	−0.366025	+	1.36603i	−0.0166032	+	0.0619642i
$487$	3.29423	+	12.2942i	0.149276	+	0.557105i	0.999528	+	0.0307288i	$0.00978283\pi$
$487$	3.29423	+	12.2942i	0.149276	+	0.557105i	−0.850252	+	0.526376i	$0.823550\pi$
$488$	5.26795	−	1.41154i	0.238469	−	0.0638975i
$489$	−6.19615	+	6.19615i	−0.280200	+	0.280200i
$490$		−	0.732051i		−	0.0330707i
$491$	−4.09808	+	2.36603i	−0.184944	+	0.106777i	−0.589613	−	0.807686i	$-0.700720\pi$
$491$	−4.09808	+	2.36603i	−0.184944	+	0.106777i	0.404670	+	0.914463i	$0.367387\pi$
$492$	13.6603	−	13.6603i	0.615852	−	0.615852i
$493$	−0.803848			−0.0362035
$494$	−15.5885	+	15.0000i	−0.701358	+	0.674882i
$495$			1.80385i			0.0810769i
$496$	−5.85641	−	21.8564i	−0.262960	−	0.981382i
$497$	8.66025	+	15.0000i	0.388465	+	0.672842i
$498$			15.8564i			0.710543i
$499$	−13.0718	−	13.0718i	−0.585174	−	0.585174i	0.351147	−	0.936321i	$-0.385792\pi$
$499$	−13.0718	−	13.0718i	−0.585174	−	0.585174i	−0.936321	+	0.351147i	$0.885792\pi$
$500$	−9.73205	−	2.60770i	−0.435231	−	0.116620i
$501$	−19.6603	+	5.26795i	−0.878355	+	0.235355i
$502$	39.3205	+	10.5359i	1.75496	+	0.470240i
$503$	22.8109	+	13.1699i	1.01709	+	0.587216i	0.913259	−	0.407380i	$-0.133557\pi$
$503$	22.8109	+	13.1699i	1.01709	+	0.587216i	0.103828	+	0.994595i	$0.466891\pi$
$504$	3.46410	+	6.00000i	0.154303	+	0.267261i
$505$	6.42820	+	1.72243i	0.286051	+	0.0766472i
$506$	−1.80385	−	3.12436i	−0.0801908	−	0.138895i
$507$	−11.0000	−	6.92820i	−0.488527	−	0.307692i
$508$	0.928203	+	0.535898i	0.0411824	+	0.0237766i
$509$	29.4545	+	7.89230i	1.30555	+	0.349820i	0.843545	−	0.537059i	$-0.180465\pi$
$509$	29.4545	+	7.89230i	1.30555	+	0.349820i	0.462002	+	0.886879i	$0.347131\pi$
$510$	0.169873	+	0.0980762i	0.00752210	+	0.00434289i
$511$	13.5622	−	23.4904i	0.599955	−	1.03915i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	−4.09808	+	1.09808i	−0.180934	+	0.0484812i
$514$	2.46410	−	2.46410i	0.108687	−	0.108687i
$515$	4.46410	−	4.46410i	0.196712	−	0.196712i
$516$	0.732051	+	1.26795i	0.0322267	+	0.0558184i
$517$	−5.58846	−	9.67949i	−0.245780	−	0.425704i
$518$	6.46410	+	24.1244i	0.284016	+	1.05996i
$519$	−18.9282			−0.830856
$520$	1.26795	+	5.12436i	0.0556033	+	0.224718i
$521$	34.7128			1.52080			0.760398	−	0.649457i	$-0.225004\pi$
$521$	34.7128			1.52080			0.760398	+	0.649457i	$0.225004\pi$
$522$	−1.09808	−	4.09808i	−0.0480615	−	0.179368i
$523$	−5.36603	−	9.29423i	−0.234640	−	0.406408i	0.724528	−	0.689245i	$-0.242058\pi$
$523$	−5.36603	−	9.29423i	−0.234640	−	0.406408i	−0.959168	+	0.282837i	$0.908724\pi$
$524$	24.0000	−	13.8564i	1.04844	−	0.605320i
$525$	8.19615	−	8.19615i	0.357709	−	0.357709i
$526$	−1.80385	+	1.80385i	−0.0786515	+	0.0786515i
$527$	1.46410	−	0.392305i	0.0637773	−	0.0170891i
$528$	13.4641	+	3.60770i	0.585950	+	0.157005i
$529$	11.2321	−	19.4545i	0.488350	−	0.845847i
$530$	−5.49038	−	3.16987i	−0.238487	−	0.137690i
$531$	10.4641	+	2.80385i	0.454103	+	0.121677i
$532$	−10.3923	+	18.0000i	−0.450564	+	0.780399i
$533$	−0.669873	+	34.8205i	−0.0290154	+	1.50824i
$534$	9.19615	+	15.9282i	0.397956	+	0.689281i
$535$	1.90192	+	0.509619i	0.0822273	+	0.0220327i
$536$	8.53590	+	14.7846i	0.368695	+	0.638598i
$537$	1.09808	+	0.633975i	0.0473855	+	0.0273580i
$538$	12.3923	+	3.32051i	0.534270	+	0.143157i
$539$	3.36603	−	0.901924i	0.144985	−	0.0388486i
$540$	−0.267949	+	1.00000i	−0.0115307	+	0.0430331i
$541$	−20.2942	−	20.2942i	−0.872517	−	0.872517i	0.120229	−	0.992746i	$-0.461637\pi$
$541$	−20.2942	−	20.2942i	−0.872517	−	0.872517i	−0.992746	+	0.120229i	$0.961637\pi$
$542$		−	1.07180i		−	0.0460376i
$543$	−0.964102	−	1.66987i	−0.0413736	−	0.0716611i
$544$	1.07180	−	1.07180i	0.0459529	−	0.0459529i
$545$			10.3397i			0.442906i
$546$	−12.0000	−	3.46410i	−0.513553	−	0.148250i
$547$	−4.33975			−0.185554			−0.0927771	−	0.995687i	$-0.529574\pi$
$547$	−4.33975			−0.185554			−0.0927771	+	0.995687i	$0.529574\pi$
$548$	−7.26795	−	7.26795i	−0.310471	−	0.310471i
$549$	−1.66987	+	0.964102i	−0.0712684	+	0.0411469i
$550$		−	23.3205i		−	0.994390i
$551$	9.00000	−	9.00000i	0.383413	−	0.383413i
$552$	−0.535898	−	2.00000i	−0.0228093	−	0.0851257i
$553$	0.679492	+	2.53590i	0.0288949	+	0.107837i
$554$	−10.2942	+	38.4186i	−0.437360	+	1.63225i
$555$	−1.86603	+	3.23205i	−0.0792084	+	0.137193i
$556$			30.6410i			1.29947i
$557$	4.13397	−	15.4282i	0.175162	−	0.653714i	−0.821362	−	0.570407i	$-0.806785\pi$
$557$	4.13397	−	15.4282i	0.175162	−	0.653714i	0.996524	−	0.0833065i	$-0.0265480\pi$
$558$	4.00000	+	6.92820i	0.169334	+	0.293294i
$559$	−2.53590	−	0.732051i	−0.107257	−	0.0309625i
$560$	2.53590	+	4.39230i	0.107161	+	0.185609i
$561$	−0.241670	+	0.901924i	−0.0102033	+	0.0380793i
$562$	−13.2942	+	23.0263i	−0.560783	+	0.971305i
$563$	−35.7846	−	20.6603i	−1.50814	−	0.870726i	−0.999955	−	0.00947879i	$-0.996983\pi$
$563$	−35.7846	−	20.6603i	−1.50814	−	0.870726i	−0.508186	−	0.861247i	$-0.669684\pi$
$564$	−1.66025	−	6.19615i	−0.0699093	−	0.260905i
$565$	−0.526279	−	1.96410i	−0.0221407	−	0.0826304i
$566$	−31.5167	+	31.5167i	−1.32474	+	1.32474i
$567$	−1.73205	−	1.73205i	−0.0727393	−	0.0727393i
$568$	17.3205	+	10.0000i	0.726752	+	0.419591i
$569$	35.1962	−	20.3205i	1.47550	−	0.851880i	0.475881	−	0.879510i	$-0.342129\pi$
$569$	35.1962	−	20.3205i	1.47550	−	0.851880i	0.999618	+	0.0276295i	$0.00879587\pi$
$570$	−3.00000	+	0.803848i	−0.125656	+	0.0336695i
$571$		−	25.6603i		−	1.07385i	−0.843631	−	0.536924i	$-0.819586\pi$
$571$		−	25.6603i		−	1.07385i	0.843631	−	0.536924i	$-0.180414\pi$
$572$	−22.0000	+	12.1436i	−0.919866	+	0.507749i
$573$		−	18.9282i		−	0.790737i
$574$	8.66025	+	32.3205i	0.361472	+	1.34903i
$575$	−3.00000	+	1.73205i	−0.125109	+	0.0722315i
$576$	6.92820	+	4.00000i	0.288675	+	0.166667i
$577$	29.0263	+	29.0263i	1.20838	+	1.20838i	0.971552	+	0.236828i	$0.0761079\pi$
$577$	29.0263	+	29.0263i	1.20838	+	1.20838i	0.236828	+	0.971552i	$0.423892\pi$
$578$	−16.9282	−	16.9282i	−0.704120	−	0.704120i
$579$	4.30385	+	16.0622i	0.178862	+	0.667521i
$580$	−0.803848	−	3.00000i	−0.0333780	−	0.124568i
$581$	−23.7846	−	13.7321i	−0.986752	−	0.569701i
$582$	−19.3923	−	11.1962i	−0.803837	−	0.464095i
$583$	7.81089	−	29.1506i	0.323494	−	1.20730i
$584$		−	31.3205i		−	1.29605i
$585$	−0.901924	−	1.63397i	−0.0372900	−	0.0675565i
$586$	−8.36603	+	4.83013i	−0.345597	+	0.199531i
$587$	9.58846	−	35.7846i	0.395758	−	1.47699i	−0.424727	−	0.905321i	$-0.639630\pi$
$587$	9.58846	−	35.7846i	0.395758	−	1.47699i	0.820485	−	0.571668i	$-0.193703\pi$
$588$	2.00000			0.0824786
$589$	−12.0000	+	20.7846i	−0.494451	+	0.856415i
$590$	7.66025	+	2.05256i	0.315368	+	0.0845025i
$591$	−2.56218	−	9.56218i	−0.105394	−	0.393335i
$592$	20.3923	+	20.3923i	0.838119	+	0.838119i
$593$	5.75833	−	5.75833i	0.236466	−	0.236466i	−0.578919	−	0.815385i	$-0.696525\pi$
$593$	5.75833	−	5.75833i	0.236466	−	0.236466i	0.815385	+	0.578919i	$0.196525\pi$
$594$	−4.92820			−0.202207
$595$	−0.294229	+	0.169873i	−0.0120622	+	0.00696411i
$596$	23.5167	+	23.5167i	0.963280	+	0.963280i
$597$	−10.7321			−0.439234
$598$	3.19615	+	1.92820i	0.130700	+	0.0788501i
$599$			18.5359i			0.757356i	0.925528	+	0.378678i	$0.123621\pi$
$599$			18.5359i			0.757356i	−0.925528	+	0.378678i	$0.876379\pi$
$600$	3.46410	−	12.9282i	0.141421	−	0.527792i
$601$	−0.205771	−	0.356406i	−0.00839359	−	0.0145381i	0.861798	−	0.507251i	$-0.169338\pi$
$601$	−0.205771	−	0.356406i	−0.00839359	−	0.0145381i	−0.870192	+	0.492713i	$0.836005\pi$
$602$	−2.53590			−0.103356
$603$	−4.26795	−	4.26795i	−0.173804	−	0.173804i
$604$	−40.0526	−	10.7321i	−1.62972	−	0.436681i
$605$	−0.571797	+	0.153212i	−0.0232468	+	0.00622897i
$606$	−4.70577	+	17.5622i	−0.191159	+	0.713415i
$607$	28.0526	+	16.1962i	1.13862	+	0.657382i	0.946088	−	0.323910i	$-0.104997\pi$
$607$	28.0526	+	16.1962i	1.13862	+	0.657382i	0.192530	+	0.981291i	$0.438331\pi$
$608$			24.0000i			0.973329i
$609$	7.09808	+	1.90192i	0.287629	+	0.0770698i
$610$	−1.22243	+	0.705771i	−0.0494948	+	0.0285758i
$611$	9.90192	+	5.97372i	0.400589	+	0.241671i
$612$	−0.267949	+	0.464102i	−0.0108312	+	0.0187602i
$613$	−29.2583	−	7.83975i	−1.18173	−	0.316644i	−0.386119	−	0.922449i	$-0.626185\pi$
$613$	−29.2583	−	7.83975i	−1.18173	−	0.316644i	−0.795614	+	0.605805i	$0.792851\pi$
$614$	−7.73205	+	13.3923i	−0.312040	+	0.540469i
$615$	−2.50000	+	4.33013i	−0.100810	+	0.174608i
$616$	−17.0718	+	17.0718i	−0.687842	+	0.687842i
$617$	2.33013	−	0.624356i	0.0938074	−	0.0251356i	−0.211610	−	0.977354i	$-0.567871\pi$
$617$	2.33013	−	0.624356i	0.0938074	−	0.0251356i	0.305417	+	0.952219i	$0.401204\pi$
$618$	12.1962	+	12.1962i	0.490601	+	0.490601i
$619$	17.1244	−	17.1244i	0.688286	−	0.688286i	−0.273567	−	0.961853i	$-0.588204\pi$
$619$	17.1244	−	17.1244i	0.688286	−	0.688286i	0.961853	+	0.273567i	$0.0882035\pi$
$620$	2.92820	+	5.07180i	0.117599	+	0.203688i
$621$	0.366025	+	0.633975i	0.0146881	+	0.0254405i
$622$	14.6603	−	3.92820i	0.587823	−	0.157507i
$623$	−31.8564			−1.27630
$624$	−14.0000	+	3.46410i	−0.560449	+	0.138675i
$625$	−21.0526			−0.842102
$626$	−27.1244	+	7.26795i	−1.08411	+	0.290486i
$627$	−7.39230	−	12.8038i	−0.295220	−	0.511336i
$628$	0.803848	+	1.39230i	0.0320770	+	0.0555590i
$629$	−1.36603	+	1.36603i	−0.0544670	+	0.0544670i
$630$	−1.26795	−	1.26795i	−0.0505163	−	0.0505163i
$631$	−32.5167	+	8.71281i	−1.29447	+	0.346852i	−0.839356	−	0.543583i	$-0.817067\pi$
$631$	−32.5167	+	8.71281i	−1.29447	+	0.346852i	−0.455112	+	0.890434i	$0.650401\pi$
$632$	2.14359	+	2.14359i	0.0852676	+	0.0852676i
$633$	11.0000	−	19.0526i	0.437211	−	0.757271i
$634$	21.3660	−	37.0070i	0.848553	−	1.46974i
$635$	−0.267949	−	0.0717968i	−0.0106332	−	0.00284917i
$636$	8.66025	−	15.0000i	0.343401	−	0.594789i
$637$	−2.59808	+	2.50000i	−0.102940	+	0.0990536i
$638$	12.8038	−	7.39230i	0.506909	−	0.292664i
$639$	−6.83013	−	1.83013i	−0.270196	−	0.0723987i
$640$	5.07180	+	2.92820i	0.200480	+	0.115747i
$641$	−14.5526	−	8.40192i	−0.574792	−	0.331856i	0.184269	−	0.982876i	$-0.441008\pi$
$641$	−14.5526	−	8.40192i	−0.574792	−	0.331856i	−0.759061	+	0.651020i	$0.774341\pi$
$642$	−1.39230	+	5.19615i	−0.0549499	+	0.205076i
$643$	−16.1962	+	4.33975i	−0.638714	+	0.171143i	−0.563621	−	0.826034i	$-0.690592\pi$
$643$	−16.1962	+	4.33975i	−0.638714	+	0.171143i	−0.0750931	+	0.997177i	$0.523925\pi$
$644$	3.46410	+	0.928203i	0.136505	+	0.0365763i
$645$	−0.267949	−	0.267949i	−0.0105505	−	0.0105505i
$646$	−1.60770			−0.0632539
$647$	−5.19615	−	9.00000i	−0.204282	−	0.353827i	0.745622	−	0.666369i	$-0.232153\pi$
$647$	−5.19615	−	9.00000i	−0.204282	−	0.353827i	−0.949904	+	0.312543i	$0.898819\pi$
$648$	−2.73205	−	0.732051i	−0.107325	−	0.0287577i
$649$			37.7513i			1.48187i
$650$	11.6603	+	21.1244i	0.457353	+	0.828565i
$651$	−13.8564			−0.543075
$652$	−12.3923	−	12.3923i	−0.485320	−	0.485320i
$653$	−36.2487	+	20.9282i	−1.41852	+	0.818984i	−0.996169	−	0.0874477i	$-0.972129\pi$
$653$	−36.2487	+	20.9282i	−1.41852	+	0.818984i	−0.422353	+	0.906432i	$0.638796\pi$
$654$	−28.2487			−1.10461
$655$	−5.07180	+	5.07180i	−0.198171	+	0.198171i
$656$	27.3205	+	27.3205i	1.06669	+	1.06669i
$657$	2.86603	+	10.6962i	0.111814	+	0.417297i
$658$	10.7321	+	2.87564i	0.418379	+	0.112104i
$659$	1.92820	−	3.33975i	0.0751121	−	0.130098i	−0.826023	−	0.563637i	$-0.809402\pi$
$659$	1.92820	−	3.33975i	0.0751121	−	0.130098i	0.901135	+	0.433539i	$0.142735\pi$
$660$	−3.60770			−0.140429
$661$	−9.59808	+	35.8205i	−0.373322	+	1.39326i	0.482459	+	0.875918i	$0.339744\pi$
$661$	−9.59808	+	35.8205i	−0.373322	+	1.39326i	−0.855781	+	0.517338i	$0.826923\pi$
$662$	16.0526	−	9.26795i	0.623900	−	0.360209i
$663$	−0.232051	−	0.937822i	−0.00901211	−	0.0364220i
$664$	−31.7128			−1.23070
$665$	1.39230	−	5.19615i	0.0539913	−	0.201498i
$666$	−8.83013	−	5.09808i	−0.342160	−	0.197546i
$667$	−1.90192	−	1.09808i	−0.0736428	−	0.0425177i
$668$	−10.5359	−	39.3205i	−0.407646	−	1.52136i
$669$	4.80385	+	17.9282i	0.185727	+	0.693144i
$670$	−3.12436	−	3.12436i	−0.120704	−	0.120704i
$671$	−4.75129	−	4.75129i	−0.183421	−	0.183421i
$672$	−12.0000	+	6.92820i	−0.462910	+	0.267261i
$673$	15.0622	−	8.69615i	0.580604	−	0.335212i	−0.180769	−	0.983526i	$-0.557859\pi$
$673$	15.0622	−	8.69615i	0.580604	−	0.335212i	0.761373	+	0.648314i	$0.224525\pi$
$674$	7.63397	+	28.4904i	0.294050	+	1.09741i
$675$			4.73205i			0.182137i
$676$	13.8564	−	22.0000i	0.532939	−	0.846154i
$677$			36.2487i			1.39315i	0.717483	+	0.696576i	$0.245294\pi$
$677$			36.2487i			1.39315i	−0.717483	+	0.696576i	$0.754706\pi$
$678$	5.36603	−	1.43782i	0.206081	−	0.0552192i
$679$	33.5885	−	19.3923i	1.28901	−	0.744208i
$680$	−0.196152	+	0.339746i	−0.00752210	+	0.0130287i
$681$	−0.803848	−	0.803848i	−0.0308035	−	0.0308035i
$682$	−19.7128	+	19.7128i	−0.754843	+	0.754843i
$683$	4.12436	+	15.3923i	0.157814	+	0.588970i	0.998848	+	0.0479877i	$0.0152808\pi$
$683$	4.12436	+	15.3923i	0.157814	+	0.588970i	−0.841034	+	0.540983i	$0.818053\pi$
$684$	−2.19615	−	8.19615i	−0.0839720	−	0.313388i
$685$	2.30385	+	1.33013i	0.0880255	+	0.0508215i
$686$	−13.8564	+	24.0000i	−0.529040	+	0.916324i
$687$	1.83013	−	6.83013i	0.0698237	−	0.260586i
$688$	−2.53590	+	1.46410i	−0.0966802	+	0.0558184i
$689$	7.50000	+	30.3109i	0.285727	+	1.15475i
$690$	0.267949	+	0.464102i	0.0102007	+	0.0176680i
$691$	0.241670	−	0.901924i	0.00919355	−	0.0343108i	−0.961177	−	0.275934i	$-0.911013\pi$
$691$	0.241670	−	0.901924i	0.00919355	−	0.0343108i	0.970370	+	0.241623i	$0.0776797\pi$
$692$		−	37.8564i		−	1.43908i
$693$	4.26795	−	7.39230i	0.162126	−	0.280810i
$694$	−1.73205	+	6.46410i	−0.0657477	+	0.245374i
$695$	−2.05256	−	7.66025i	−0.0778580	−	0.290570i
$696$	8.19615	−	2.19615i	0.310674	−	0.0832449i
$697$	−1.83013	+	1.83013i	−0.0693210	+	0.0693210i
$698$		−	25.6077i		−	0.969266i
$699$	−7.85641	+	4.53590i	−0.297157	+	0.171563i
$700$	16.3923	+	16.3923i	0.619571	+	0.619571i
$701$	36.6410			1.38391			0.691956	−	0.721940i	$-0.256749\pi$
$701$	36.6410			1.38391			0.691956	+	0.721940i	$0.256749\pi$
$702$	4.46410	−	2.46410i	0.168487	−	0.0930015i
$703$		−	30.5885i		−	1.15367i
$704$	−7.21539	+	26.9282i	−0.271940	+	1.01489i
$705$	0.830127	+	1.43782i	0.0312644	+	0.0541515i
$706$			4.73205i			0.178093i
$707$	−22.2679	−	22.2679i	−0.837472	−	0.837472i
$708$	−5.60770	+	20.9282i	−0.210750	+	0.786530i
$709$	−14.3301	+	3.83975i	−0.538179	+	0.144205i	−0.517663	−	0.855585i	$-0.673198\pi$
$709$	−14.3301	+	3.83975i	−0.538179	+	0.144205i	−0.0205166	+	0.999790i	$0.506531\pi$
$710$	−5.00000	−	1.33975i	−0.187647	−	0.0502798i
$711$	−0.928203	−	0.535898i	−0.0348103	−	0.0200978i
$712$	−31.8564	+	18.3923i	−1.19387	+	0.689281i
$713$	4.00000	+	1.07180i	0.149801	+	0.0401391i
$714$	−0.464102	−	0.803848i	−0.0173686	−	0.0300832i
$715$	4.68653	−	4.50962i	0.175266	−	0.168650i
$716$	−1.26795	+	2.19615i	−0.0473855	+	0.0820741i
$717$	17.7583	+	4.75833i	0.663197	+	0.177703i
$718$	7.05256	+	4.07180i	0.263199	+	0.151958i
$719$	−19.4641	+	33.7128i	−0.725889	+	1.25728i	0.232719	+	0.972544i	$0.425238\pi$
$719$	−19.4641	+	33.7128i	−0.725889	+	1.25728i	−0.958607	+	0.284732i	$0.908095\pi$
$720$	−2.00000	−	0.535898i	−0.0745356	−	0.0199718i
$721$	−28.8564	+	7.73205i	−1.07467	+	0.287957i
$722$	−1.00000	+	1.00000i	−0.0372161	+	0.0372161i
$723$	−10.4904	+	10.4904i	−0.390141	+	0.390141i
$724$	3.33975	−	1.92820i	0.124121	−	0.0716611i
$725$	−7.09808	−	12.2942i	−0.263616	−	0.456596i
$726$	−0.418584	−	1.56218i	−0.0155351	−	0.0579779i
$727$	−32.5885			−1.20864			−0.604319	−	0.796742i	$-0.706555\pi$
$727$	−32.5885			−1.20864			−0.604319	+	0.796742i	$0.706555\pi$
$728$	6.92820	−	24.0000i	0.256776	−	0.889499i
$729$	1.00000			0.0370370
$730$	2.09808	+	7.83013i	0.0776533	+	0.289806i
$731$	−0.0980762	−	0.169873i	−0.00362748	−	0.00628298i
$732$	−1.92820	−	3.33975i	−0.0712684	−	0.123441i
$733$	4.68653	−	4.68653i	0.173101	−	0.173101i	−0.615239	−	0.788340i	$-0.710941\pi$
$733$	4.68653	−	4.68653i	0.173101	−	0.173101i	0.788340	+	0.615239i	$0.210941\pi$
$734$	7.12436	−	7.12436i	0.262965	−	0.262965i
$735$	−0.500000	+	0.133975i	−0.0184428	+	0.00494173i
$736$	4.00000	−	1.07180i	0.147442	−	0.0395070i
$737$	10.5167	−	18.2154i	0.387386	−	0.670973i
$738$	−11.8301	−	6.83013i	−0.435473	−	0.251420i
$739$	24.5885	+	6.58846i	0.904501	+	0.242360i	0.680948	−	0.732332i	$-0.261568\pi$
$739$	24.5885	+	6.58846i	0.904501	+	0.242360i	0.223553	+	0.974692i	$0.428235\pi$
$740$	−6.46410	−	3.73205i	−0.237625	−	0.137193i
$741$	13.0981	+	7.90192i	0.481170	+	0.290284i
$742$	15.0000	+	25.9808i	0.550667	+	0.953784i
$743$	47.7846	+	12.8038i	1.75305	+	0.469728i	0.985272	−	0.170992i	$-0.0546972\pi$
$743$	47.7846	+	12.8038i	1.75305	+	0.469728i	0.767775	+	0.640720i	$0.221364\pi$
$744$	−13.8564	+	8.00000i	−0.508001	+	0.293294i
$745$	−7.45448	−	4.30385i	−0.273111	−	0.157681i
$746$	22.5622	+	6.04552i	0.826060	+	0.221342i
$747$	10.8301	−	2.90192i	0.396254	−	0.106176i
$748$	−1.80385	−	0.483340i	−0.0659552	−	0.0176726i
$749$	−6.58846	−	6.58846i	−0.240737	−	0.240737i
$750$			7.12436i			0.260145i
$751$	22.9545	+	39.7583i	0.837621	+	1.45080i	0.891878	+	0.452275i	$0.149387\pi$
$751$	22.9545	+	39.7583i	0.837621	+	1.45080i	−0.0542575	+	0.998527i	$0.517279\pi$
$752$	12.3923	−	3.32051i	0.451901	−	0.121086i
$753$		−	28.7846i		−	1.04897i
$754$	−7.90192	+	13.0981i	−0.287771	+	0.477004i
$755$	10.7321			0.390579
$756$	3.46410	−	3.46410i	0.125988	−	0.125988i
$757$	−11.6603	+	6.73205i	−0.423799	+	0.244681i	−0.696701	−	0.717361i	$-0.745350\pi$
$757$	−11.6603	+	6.73205i	−0.423799	+	0.244681i	0.272902	+	0.962042i	$0.412016\pi$
$758$			33.1769i			1.20504i
$759$	−1.80385	+	1.80385i	−0.0654755	+	0.0654755i
$760$	−1.60770	−	6.00000i	−0.0583172	−	0.217643i
$761$	11.9545	+	44.6147i	0.433350	+	1.61728i	0.744985	+	0.667081i	$0.232457\pi$
$761$	11.9545	+	44.6147i	0.433350	+	1.61728i	−0.311635	+	0.950202i	$0.600877\pi$
$762$	0.196152	−	0.732051i	0.00710585	−	0.0265194i
$763$	24.4641	−	42.3731i	0.885660	−	1.53401i
$764$	37.8564			1.36960
$765$	0.0358984	−	0.133975i	0.00129791	−	0.00484386i
$766$	−11.4641	−	19.8564i	−0.414215	−	0.717441i
$767$	−18.8756	−	34.1962i	−0.681560	−	1.23475i
$768$	−8.00000	+	13.8564i	−0.288675	+	0.500000i
$769$	−5.95448	+	22.2224i	−0.214724	+	0.801361i	0.771539	+	0.636182i	$0.219487\pi$
$769$	−5.95448	+	22.2224i	−0.214724	+	0.801361i	−0.986263	+	0.165180i	$0.947180\pi$
$770$	3.12436	−	5.41154i	0.112594	−	0.195018i
$771$	−2.13397	−	1.23205i	−0.0768532	−	0.0443712i
$772$	−32.1244	+	8.60770i	−1.15618	+	0.309798i
$773$	3.95448	+	14.7583i	0.142233	+	0.530820i	0.999863	+	0.0165532i	$0.00526930\pi$
$773$	3.95448	+	14.7583i	0.142233	+	0.530820i	−0.857630	+	0.514267i	$0.828064\pi$
$774$	0.732051	−	0.732051i	0.0263130	−	0.0263130i
$775$	18.9282	+	18.9282i	0.679921	+	0.679921i
$776$	22.3923	−	38.7846i	0.803837	−	1.39229i
$777$	15.2942	−	8.83013i	0.548677	−	0.316779i
$778$	−2.36603	+	0.633975i	−0.0848261	+	0.0227291i
$779$		−	40.9808i		−	1.46829i
$780$	3.26795	−	1.80385i	0.117011	−	0.0645881i
$781$		−	24.6410i		−	0.881725i
$782$	0.0717968	+	0.267949i	0.00256745	+	0.00958184i
$783$	−2.59808	+	1.50000i	−0.0928477	+	0.0536056i
$784$			4.00000i			0.142857i
$785$	−0.294229	−	0.294229i	−0.0105015	−	0.0105015i
$786$	−13.8564	−	13.8564i	−0.494242	−	0.494242i
$787$	−2.87564	−	10.7321i	−0.102506	−	0.382556i	0.895545	−	0.444972i	$-0.146786\pi$
$787$	−2.87564	−	10.7321i	−0.102506	−	0.382556i	−0.998050	+	0.0624155i	$0.980120\pi$
$788$	19.1244	−	5.12436i	0.681277	−	0.182548i
$789$	1.56218	+	0.901924i	0.0556150	+	0.0321093i
$790$	−0.679492	−	0.392305i	−0.0241752	−	0.0139576i
$791$	−2.49038	+	9.29423i	−0.0885478	+	0.330465i
$792$		−	9.85641i		−	0.350232i
$793$	6.67949	+	1.92820i	0.237196	+	0.0684725i
$794$	9.24871	−	5.33975i	0.328224	−	0.189500i
$795$	−1.16025	+	4.33013i	−0.0411500	+	0.153574i
$796$		−	21.4641i		−	0.760775i
$797$	1.85641	−	3.21539i	0.0657573	−	0.113895i	−0.831272	−	0.555865i	$-0.812387\pi$
$797$	1.85641	−	3.21539i	0.0657573	−	0.113895i	0.897030	+	0.441970i	$0.145720\pi$
$798$	14.1962	+	3.80385i	0.502538	+	0.134655i
$799$	0.222432	+	0.830127i	0.00786907	+	0.0293678i
$800$	25.8564	+	6.92820i	0.914162	+	0.244949i
$801$	9.19615	−	9.19615i	0.324930	−	0.324930i
$802$	3.12436			0.110325
$803$	−33.4186	+	19.2942i	−1.17932	+	0.680879i
$804$	8.53590	−	8.53590i	0.301038	−	0.301038i
$805$	−0.928203			−0.0327149
$806$	8.00000	−	27.7128i	0.281788	−	0.976142i
$807$		−	9.07180i		−	0.319342i
$808$	−35.1244	−	9.41154i	−1.23567	−	0.331097i
$809$	−22.0885	−	38.2583i	−0.776589	−	1.34509i	−0.933897	−	0.357542i	$-0.883615\pi$
$809$	−22.0885	−	38.2583i	−0.776589	−	1.34509i	0.157308	−	0.987550i	$-0.449718\pi$
$810$	0.732051			0.0257216
$811$	16.9808	+	16.9808i	0.596275	+	0.596275i	0.939319	−	0.343044i	$-0.111458\pi$
$811$	16.9808	+	16.9808i	0.596275	+	0.596275i	−0.343044	+	0.939319i	$0.611458\pi$
$812$	−3.80385	+	14.1962i	−0.133489	+	0.498187i
$813$	−0.732051	+	0.196152i	−0.0256741	+	0.00687937i
$814$	9.19615	−	34.3205i	0.322325	−	1.20293i
$815$	3.92820	+	2.26795i	0.137599	+	0.0794428i
$816$	−0.928203	−	0.535898i	−0.0324936	−	0.0187602i
$817$	3.00000	+	0.803848i	0.104957	+	0.0281231i
$818$	−2.95448	+	1.70577i	−0.103301	+	0.0596409i
$819$	−0.169873	+	8.83013i	−0.00593584	+	0.308550i
$820$	−8.66025	−	5.00000i	−0.302429	−	0.174608i
$821$	34.4186	+	9.22243i	1.20122	+	0.321865i	0.803310	−	0.595561i	$-0.203070\pi$
$821$	34.4186	+	9.22243i	1.20122	+	0.321865i	0.397907	+	0.917426i	$0.369737\pi$
$822$	−3.63397	+	6.29423i	−0.126749	+	0.219536i
$823$	18.2679	−	31.6410i	0.636781	−	1.10294i	−0.349354	−	0.936991i	$-0.613599\pi$
$823$	18.2679	−	31.6410i	0.636781	−	1.10294i	0.986135	−	0.165946i	$-0.0530677\pi$
$824$	−24.3923	+	24.3923i	−0.849746	+	0.849746i
$825$	−15.9282	+	4.26795i	−0.554549	+	0.148591i
$826$	−26.5359	−	26.5359i	−0.923302	−	0.923302i
$827$	−30.1962	+	30.1962i	−1.05002	+	1.05002i	−0.0513420	+	0.998681i	$0.516350\pi$
$827$	−30.1962	+	30.1962i	−1.05002	+	1.05002i	−0.998681	+	0.0513420i	$0.983650\pi$
$828$	−1.26795	+	0.732051i	−0.0440643	+	0.0254405i
$829$	−24.4545	−	42.3564i	−0.849339	−	1.47110i	−0.881799	−	0.471626i	$-0.843667\pi$
$829$	−24.4545	−	42.3564i	−0.849339	−	1.47110i	0.0324595	−	0.999473i	$-0.489666\pi$
$830$	7.92820	−	2.12436i	0.275192	−	0.0737375i
$831$	28.1244			0.975623
$832$	−6.92820	−	28.0000i	−0.240192	−	0.970725i
$833$	−0.267949			−0.00928389
$834$	20.9282	−	5.60770i	0.724684	−	0.194179i
$835$	5.26795	+	9.12436i	0.182305	+	0.315761i
$836$	25.6077	−	14.7846i	0.885661	−	0.511336i
$837$	4.00000	−	4.00000i	0.138260	−	0.138260i
$838$	9.60770	+	9.60770i	0.331892	+	0.331892i
$839$	38.3205	−	10.2679i	1.32297	−	0.354489i	0.472881	−	0.881126i	$-0.343214\pi$
$839$	38.3205	−	10.2679i	1.32297	−	0.354489i	0.850090	+	0.526637i	$0.176547\pi$
$840$	2.53590	−	2.53590i	0.0874968	−	0.0874968i
$841$	−10.0000	+	17.3205i	−0.344828	+	0.597259i
$842$	26.3660	−	45.6673i	0.908633	−	1.57380i
$843$	18.1603	+	4.86603i	0.625472	+	0.167595i
$844$	38.1051	+	22.0000i	1.31163	+	0.757271i
$845$	−1.99038	+	6.42820i	−0.0684712	+	0.221137i
$846$	−3.92820	+	2.26795i	−0.135054	+	0.0779737i
$847$	2.70577	+	0.725009i	0.0929714	+	0.0249116i
$848$	30.0000	+	17.3205i	1.03020	+	0.594789i
$849$	27.2942	+	15.7583i	0.936736	+	0.540824i
$850$	−0.464102	+	1.73205i	−0.0159186	+	0.0594089i
$851$	−5.09808	+	1.36603i	−0.174760	+	0.0468267i
$852$	3.66025	−	13.6603i	0.125398	−	0.467993i
$853$	−7.77757	−	7.77757i	−0.266299	−	0.266299i	0.561308	−	0.827607i	$-0.310298\pi$
$853$	−7.77757	−	7.77757i	−0.266299	−	0.266299i	−0.827607	+	0.561308i	$0.810298\pi$
$854$	6.67949			0.228568
$855$	1.09808	+	1.90192i	0.0375534	+	0.0650444i
$856$	−10.3923	−	2.78461i	−0.355202	−	0.0951760i
$857$			3.39230i			0.115879i	0.998320	+	0.0579395i	$0.0184530\pi$
$857$			3.39230i			0.115879i	−0.998320	+	0.0579395i	$0.981547\pi$
$858$	12.3205	+	12.8038i	0.420615	+	0.437116i
$859$	−33.6603			−1.14847			−0.574237	−	0.818689i	$-0.694701\pi$
$859$	−33.6603			−1.14847			−0.574237	+	0.818689i	$0.694701\pi$
$860$	0.535898	−	0.535898i	0.0182740	−	0.0182740i
$861$	20.4904	−	11.8301i	0.698310	−	0.403170i
$862$	−57.7128			−1.96571
$863$	−33.6410	+	33.6410i	−1.14515	+	1.14515i	−0.157660	+	0.987493i	$0.550395\pi$
$863$	−33.6410	+	33.6410i	−1.14515	+	1.14515i	−0.987493	+	0.157660i	$0.949605\pi$
$864$	1.46410	−	5.46410i	0.0498097	−	0.185893i
$865$	2.53590	+	9.46410i	0.0862231	+	0.321789i
$866$	−13.2942	−	3.56218i	−0.451756	−	0.121048i
$867$	−8.46410	+	14.6603i	−0.287456	+	0.497888i
$868$		−	27.7128i		−	0.940634i
$869$	0.966679	−	3.60770i	0.0327923	−	0.122383i
$870$	−1.90192	+	1.09808i	−0.0644813	+	0.0372283i
$871$	−0.418584	+	21.7583i	−0.0141832	+	0.737253i
$872$		−	56.4974i		−	1.91324i
$873$	−4.09808	+	15.2942i	−0.138699	+	0.517631i
$874$	−3.80385	−	2.19615i	−0.128667	−	0.0742860i
$875$	−10.6865	−	6.16987i	−0.361271	−	0.208580i
$876$	−21.3923	+	5.73205i	−0.722779	+	0.193668i
$877$	2.83975	+	10.5981i	0.0958914	+	0.357872i	0.997153	−	0.0754036i	$-0.0240245\pi$
$877$	2.83975	+	10.5981i	0.0958914	+	0.357872i	−0.901262	+	0.433275i	$0.857358\pi$
$878$	33.6603	+	33.6603i	1.13598	+	1.13598i
$879$	4.83013	+	4.83013i	0.162916	+	0.162916i
$880$		−	7.21539i		−	0.243231i
$881$	−37.7942	+	21.8205i	−1.27332	+	0.735152i	−0.975611	−	0.219505i	$-0.929556\pi$
$881$	−37.7942	+	21.8205i	−1.27332	+	0.735152i	−0.297709	+	0.954657i	$0.596222\pi$
$882$	−0.366025	−	1.36603i	−0.0123247	−	0.0459965i
$883$		−	12.7846i		−	0.430236i	−0.976588	−	0.215118i	$-0.930986\pi$
$883$		−	12.7846i		−	0.430236i	0.976588	−	0.215118i	$-0.0690137\pi$
$884$	1.87564	−	0.464102i	0.0630847	−	0.0156094i
$885$		−	5.60770i		−	0.188501i
$886$	16.5885	−	4.44486i	0.557300	−	0.149328i
$887$	24.8038	−	14.3205i	0.832832	−	0.480836i	−0.0219895	−	0.999758i	$-0.507000\pi$
$887$	24.8038	−	14.3205i	0.832832	−	0.480836i	0.854821	+	0.518923i	$0.173667\pi$
$888$	10.1962	−	17.6603i	0.342160	−	0.592639i
$889$	0.928203	+	0.928203i	0.0311309	+	0.0311309i
$890$	6.73205	−	6.73205i	0.225659	−	0.225659i
$891$	0.901924	+	3.36603i	0.0302156	+	0.112766i
$892$	−35.8564	+	9.60770i	−1.20056	+	0.321689i
$893$	−11.7846	−	6.80385i	−0.394357	−	0.227682i
$894$	11.7583	−	20.3660i	0.393257	−	0.681142i
$895$	0.169873	−	0.633975i	0.00567823	−	0.0211914i
$896$	−13.8564	−	24.0000i	−0.462910	−	0.801784i
$897$	0.732051	−	2.53590i	0.0244425	−	0.0846712i
$898$	−19.1962	−	33.2487i	−0.640584	−	1.10952i
$899$	−4.39230	+	16.3923i	−0.146492	+	0.546714i
$900$	−9.46410			−0.315470
$901$	−1.16025	+	2.00962i	−0.0386537	+	0.0669501i
$902$	12.3205	−	45.9808i	0.410228	−	1.53099i
$903$	0.464102	+	1.73205i	0.0154443	+	0.0576390i
$904$	2.87564	+	10.7321i	0.0956425	+	0.356943i
$905$	−0.705771	+	0.705771i	−0.0234606	+	0.0234606i
$906$			29.3205i			0.974109i
$907$	1.85641	−	1.07180i	0.0616410	−	0.0355884i	−0.468863	−	0.883271i	$-0.655336\pi$
$907$	1.85641	−	1.07180i	0.0616410	−	0.0355884i	0.530504	+	0.847683i	$0.322003\pi$
$908$	1.60770	−	1.60770i	0.0533532	−	0.0533532i
$909$	12.8564			0.426420
$910$	−0.124356	+	6.46410i	−0.00412235	+	0.214283i
$911$			50.7846i			1.68257i	0.540592	+	0.841285i	$0.318200\pi$
$911$			50.7846i			1.68257i	−0.540592	+	0.841285i	$0.681800\pi$
$912$	16.3923	−	4.39230i	0.542803	−	0.145444i
$913$	19.5359	+	33.8372i	0.646544	+	1.11985i
$914$			8.73205i			0.288831i
$915$	0.705771	+	0.705771i	0.0233321	+	0.0233321i
$916$	13.6603	+	3.66025i	0.451347	+	0.120938i
$917$	32.7846	−	8.78461i	1.08264	−	0.290093i
$918$	0.366025	+	0.0980762i	0.0120806	+	0.00323700i
$919$	−30.9282	−	17.8564i	−1.02023	−	0.589028i	−0.106058	−	0.994360i	$-0.533823\pi$
$919$	−30.9282	−	17.8564i	−1.02023	−	0.589028i	−0.914170	+	0.405331i	$0.867156\pi$
$920$	−0.928203	+	0.535898i	−0.0306020	+	0.0176680i
$921$	10.5622	+	2.83013i	0.348036	+	0.0932559i
$922$	−19.9019	−	34.4711i	−0.655435	−	1.13525i
$923$	12.3205	+	22.3205i	0.405534	+	0.734688i
$924$	14.7846	+	8.53590i	0.486378	+	0.280810i
$925$	−32.9545	−	8.83013i	−1.08354	−	0.290333i
$926$	−1.14359	−	0.660254i	−0.0375808	−	0.0216973i
$927$	6.09808	−	10.5622i	0.200287	−	0.346907i
$928$	4.39230	+	16.3923i	0.144184	+	0.538104i
$929$	−27.3564	+	7.33013i	−0.897535	+	0.240494i	−0.677957	−	0.735101i	$-0.737135\pi$
$929$	−27.3564	+	7.33013i	−0.897535	+	0.240494i	−0.219577	+	0.975595i	$0.570468\pi$
$930$	2.92820	−	2.92820i	0.0960196	−	0.0960196i
$931$	3.00000	−	3.00000i	0.0983210	−	0.0983210i
$932$	−9.07180	−	15.7128i	−0.297157	−	0.514690i
$933$	−5.36603	−	9.29423i	−0.175676	−	0.304279i
$934$	5.19615	+	19.3923i	0.170023	+	0.634536i
$935$	0.483340			0.0158069
$936$	4.92820	+	8.92820i	0.161083	+	0.291827i
$937$	−46.7128			−1.52604			−0.763021	−	0.646374i	$-0.776285\pi$
$937$	−46.7128			−1.52604			−0.763021	+	0.646374i	$0.776285\pi$
$938$	5.41154	+	20.1962i	0.176693	+	0.659428i
$939$	9.92820	+	17.1962i	0.323995	+	0.561175i
$940$	−2.87564	+	1.66025i	−0.0937932	+	0.0541515i
$941$	−5.19615	+	5.19615i	−0.169390	+	0.169390i	−0.786711	−	0.617321i	$-0.788218\pi$
$941$	−5.19615	+	5.19615i	−0.169390	+	0.169390i	0.617321	+	0.786711i	$0.288218\pi$
$942$	0.803848	−	0.803848i	0.0261908	−	0.0261908i
$943$	−6.83013	+	1.83013i	−0.222420	+	0.0595971i
$944$	−41.8564	−	11.2154i	−1.36231	−	0.365030i
$945$	−0.633975	+	1.09808i	−0.0206232	+	0.0357204i
$946$	3.12436	+	1.80385i	0.101582	+	0.0586481i
$947$	−12.3923	−	3.32051i	−0.402696	−	0.107902i	0.0517856	−	0.998658i	$-0.483509\pi$
$947$	−12.3923	−	3.32051i	−0.402696	−	0.107902i	−0.454481	+	0.890756i	$0.650175\pi$
$948$	1.07180	−	1.85641i	0.0348103	−	0.0602933i
$949$	20.6244	−	34.1865i	0.669495	−	1.10974i
$950$	−14.1962	−	24.5885i	−0.460584	−	0.797755i
$951$	−29.1865	−	7.82051i	−0.946438	−	0.253597i
$952$	1.60770	−	0.928203i	0.0521057	−	0.0300832i
$953$	−34.2679	−	19.7846i	−1.11005	−	0.640886i	−0.171206	−	0.985235i	$-0.554766\pi$
$953$	−34.2679	−	19.7846i	−1.11005	−	0.640886i	−0.938842	+	0.344349i	$0.888100\pi$
$954$	−11.8301	−	3.16987i	−0.383015	−	0.102628i
$955$	−9.46410	+	2.53590i	−0.306251	+	0.0820597i
$956$	−9.51666	+	35.5167i	−0.307791	+	1.14869i
$957$	−7.39230	−	7.39230i	−0.238959	−	0.238959i
$958$		−	55.3205i		−	1.78732i
$959$	−6.29423	−	10.9019i	−0.203251	−	0.352041i
$960$	1.07180	−	4.00000i	0.0345921	−	0.129099i
$961$		−	1.00000i		−	0.0322581i
$962$	8.83013	+	35.6865i	0.284695	+	1.15058i
$963$	3.80385			0.122577
$964$	−20.9808	−	20.9808i	−0.675745	−	0.675745i
$965$	7.45448	−	4.30385i	0.239968	−	0.138546i
$966$		−	2.53590i		−	0.0815912i
$967$	−19.0526	+	19.0526i	−0.612689	+	0.612689i	−0.943646	−	0.330957i	$-0.892629\pi$
$967$	−19.0526	+	19.0526i	−0.612689	+	0.612689i	0.330957	+	0.943646i	$0.392629\pi$
$968$	3.12436	−	0.837169i	0.100421	−	0.0269076i
$969$	0.294229	+	1.09808i	0.00945199	+	0.0352753i
$970$	−3.00000	+	11.1962i	−0.0963242	+	0.359487i
$971$	−20.1244	+	34.8564i	−0.645821	+	1.11860i	0.338290	+	0.941042i	$0.390152\pi$
$971$	−20.1244	+	34.8564i	−0.645821	+	1.11860i	−0.984111	+	0.177553i	$0.943182\pi$
$972$			2.00000i			0.0641500i
$973$	−9.71281	+	36.2487i	−0.311378	+	1.16208i
$974$	9.00000	+	15.5885i	0.288379	+	0.499486i
$975$	12.2942	−	11.8301i	0.393730	−	0.378867i
$976$	6.67949	−	3.85641i	0.213805	−	0.123441i
$977$	11.8397	−	44.1865i	0.378787	−	1.41365i	−0.468945	−	0.883227i	$-0.655366\pi$
$977$	11.8397	−	44.1865i	0.378787	−	1.41365i	0.847732	−	0.530425i	$-0.177968\pi$
$978$	−6.19615	+	10.7321i	−0.198131	+	0.343173i
$979$	39.2487	+	22.6603i	1.25439	+	0.724225i
$980$	−0.267949	−	1.00000i	−0.00855932	−	0.0319438i
$981$	5.16987	+	19.2942i	0.165061	+	0.616017i
$982$	−4.73205	+	4.73205i	−0.151006	+	0.151006i
$983$	6.33975	+	6.33975i	0.202206	+	0.202206i	0.800945	−	0.598738i	$-0.204331\pi$
$983$	6.33975	+	6.33975i	0.202206	+	0.202206i	−0.598738	+	0.800945i	$0.704331\pi$
$984$	13.6603	−	23.6603i	0.435473	−	0.754261i
$985$	−4.43782	+	2.56218i	−0.141401	+	0.0816378i
$986$	−1.09808	+	0.294229i	−0.0349699	+	0.00937015i
$987$		−	7.85641i		−	0.250072i
$988$	−15.8038	+	26.1962i	−0.502787	+	0.833411i
$989$		−	0.535898i		−	0.0170406i
$990$	0.660254	+	2.46410i	0.0209843	+	0.0783143i
$991$	34.8109	−	20.0981i	1.10580	−	0.638436i	0.168065	−	0.985776i	$-0.446248\pi$
$991$	34.8109	−	20.0981i	1.10580	−	0.638436i	0.937739	+	0.347340i	$0.112915\pi$
$992$	−16.0000	−	27.7128i	−0.508001	−	0.879883i
$993$	−9.26795	−	9.26795i	−0.294109	−	0.294109i
$994$	17.3205	+	17.3205i	0.549373	+	0.549373i
$995$	1.43782	+	5.36603i	0.0455820	+	0.170114i
$996$	5.80385	+	21.6603i	0.183902	+	0.686331i
$997$	6.86603	+	3.96410i	0.217449	+	0.125544i	0.604769	−	0.796401i	$-0.293266\pi$
$997$	6.86603	+	3.96410i	0.217449	+	0.125544i	−0.387319	+	0.921946i	$0.626599\pi$
$998$	−22.6410	−	13.0718i	−0.716689	−	0.413780i
$999$	−1.86603	+	6.96410i	−0.0590384	+	0.220334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bt.b.115.1	yes	4
3.2	odd	2		936.2.ed.a.739.1		4
8.3	odd	2		312.2.bt.a.115.1	yes	4
13.6	odd	12		312.2.bt.a.19.1	✓	4
24.11	even	2		936.2.ed.b.739.1		4
39.32	even	12		936.2.ed.b.19.1		4
104.19	even	12	inner	312.2.bt.b.19.1	yes	4
312.227	odd	12		936.2.ed.a.19.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.a.19.1	✓	4	13.6	odd	12
312.2.bt.a.115.1	yes	4	8.3	odd	2
312.2.bt.b.19.1	yes	4	104.19	even	12	inner
312.2.bt.b.115.1	yes	4	1.1	even	1	trivial
936.2.ed.a.19.1		4	312.227	odd	12
936.2.ed.a.739.1		4	3.2	odd	2
936.2.ed.b.19.1		4	39.32	even	12
936.2.ed.b.739.1		4	24.11	even	2

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-0.366025 + 0.366025i) q^{5} +(-1.00000 - 1.00000i) q^{6} +(2.36603 - 0.633975i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.366025 + 0.633975i) q^{10} +(-3.36603 - 0.901924i) q^{11} +(-1.73205 - 1.00000i) q^{12} +(3.50000 - 0.866025i) q^{13} +(3.00000 - 1.73205i) q^{14} +(0.500000 + 0.133975i) q^{15} +(2.00000 - 3.46410i) q^{16} +(0.232051 + 0.133975i) q^{17} +(-0.366025 + 1.36603i) q^{18} +(-4.09808 + 1.09808i) q^{19} +(-0.267949 + 1.00000i) q^{20} +(-1.73205 - 1.73205i) q^{21} -4.92820 q^{22} +(0.366025 + 0.633975i) q^{23} +(-2.73205 - 0.732051i) q^{24} +4.73205i q^{25} +(4.46410 - 2.46410i) q^{26} +1.00000 q^{27} +(3.46410 - 3.46410i) q^{28} +(-2.59808 + 1.50000i) q^{29} +0.732051 q^{30} +(4.00000 - 4.00000i) q^{31} +(1.46410 - 5.46410i) q^{32} +(0.901924 + 3.36603i) q^{33} +(0.366025 + 0.0980762i) q^{34} +(-0.633975 + 1.09808i) q^{35} +2.00000i q^{36} +(-1.86603 + 6.96410i) q^{37} +(-5.19615 + 3.00000i) q^{38} +(-2.50000 - 2.59808i) q^{39} +1.46410i q^{40} +(-2.50000 + 9.33013i) q^{41} +(-3.00000 - 1.73205i) q^{42} +(-0.633975 - 0.366025i) q^{43} +(-6.73205 + 1.80385i) q^{44} +(-0.133975 - 0.500000i) q^{45} +(0.732051 + 0.732051i) q^{46} +(2.26795 + 2.26795i) q^{47} -4.00000 q^{48} +(-0.866025 + 0.500000i) q^{49} +(1.73205 + 6.46410i) q^{50} -0.267949i q^{51} +(5.19615 - 5.00000i) q^{52} +8.66025i q^{53} +(1.36603 - 0.366025i) q^{54} +(1.56218 - 0.901924i) q^{55} +(3.46410 - 6.00000i) q^{56} +(3.00000 + 3.00000i) q^{57} +(-3.00000 + 3.00000i) q^{58} +(-2.80385 - 10.4641i) q^{59} +(1.00000 - 0.267949i) q^{60} +(1.66987 + 0.964102i) q^{61} +(4.00000 - 6.92820i) q^{62} +(-0.633975 + 2.36603i) q^{63} -8.00000i q^{64} +(-0.964102 + 1.59808i) q^{65} +(2.46410 + 4.26795i) q^{66} +(-1.56218 + 5.83013i) q^{67} +0.535898 q^{68} +(0.366025 - 0.633975i) q^{69} +(-0.464102 + 1.73205i) q^{70} +(1.83013 + 6.83013i) q^{71} +(0.732051 + 2.73205i) q^{72} +(7.83013 - 7.83013i) q^{73} +10.1962i q^{74} +(4.09808 - 2.36603i) q^{75} +(-6.00000 + 6.00000i) q^{76} -8.53590 q^{77} +(-4.36603 - 2.63397i) q^{78} +1.07180i q^{79} +(0.535898 + 2.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +13.6603i q^{82} +(-7.92820 - 7.92820i) q^{83} +(-4.73205 - 1.26795i) q^{84} +(-0.133975 + 0.0358984i) q^{85} +(-1.00000 - 0.267949i) q^{86} +(2.59808 + 1.50000i) q^{87} +(-8.53590 + 4.92820i) q^{88} +(-12.5622 - 3.36603i) q^{89} +(-0.366025 - 0.633975i) q^{90} +(7.73205 - 4.26795i) q^{91} +(1.26795 + 0.732051i) q^{92} +(-5.46410 - 1.46410i) q^{93} +(3.92820 + 2.26795i) q^{94} +(1.09808 - 1.90192i) q^{95} +(-5.46410 + 1.46410i) q^{96} +(15.2942 - 4.09808i) q^{97} +(-1.00000 + 1.00000i) q^{98} +(2.46410 - 2.46410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} + 2 q^{5} - 4 q^{6} + 6 q^{7} + 8 q^{8} - 2 q^{9} + 2 q^{10} - 10 q^{11} + 14 q^{13} + 12 q^{14} + 2 q^{15} + 8 q^{16} - 6 q^{17} + 2 q^{18} - 6 q^{19} - 8 q^{20} + 8 q^{22} - 2 q^{23}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^5 - 4 * q^6 + 6 * q^7 + 8 * q^8 - 2 * q^9 + 2 * q^10 - 10 * q^11 + 14 * q^13 + 12 * q^14 + 2 * q^15 + 8 * q^16 - 6 * q^17 + 2 * q^18 - 6 * q^19 - 8 * q^20 + 8 * q^22 - 2 * q^23 - 4 * q^24 + 4 * q^26 + 4 * q^27 - 4 * q^30 + 16 * q^31 - 8 * q^32 + 14 * q^33 - 2 * q^34 - 6 * q^35 - 4 * q^37 - 10 * q^39 - 10 * q^41 - 12 * q^42 - 6 * q^43 - 20 * q^44 - 4 * q^45 - 4 * q^46 + 16 * q^47 - 16 * q^48 + 2 * q^54 - 18 * q^55 + 12 * q^57 - 12 * q^58 - 32 * q^59 + 4 * q^60 + 24 * q^61 + 16 * q^62 - 6 * q^63 + 10 * q^65 - 4 * q^66 + 18 * q^67 + 16 * q^68 - 2 * q^69 + 12 * q^70 - 10 * q^71 - 4 * q^72 + 14 * q^73 + 6 * q^75 - 24 * q^76 - 48 * q^77 - 14 * q^78 + 16 * q^80 - 2 * q^81 - 4 * q^83 - 12 * q^84 - 4 * q^85 - 4 * q^86 - 48 * q^88 - 26 * q^89 + 2 * q^90 + 24 * q^91 + 12 * q^92 - 8 * q^93 - 12 * q^94 - 6 * q^95 - 8 * q^96 + 30 * q^97 - 4 * q^98 - 4 * q^99

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