LMFDB - Embedded newform 930.2.v.b.401.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(401,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("930.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.v (of order $10$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			401.16
Character	$\chi$	$=$	930.401
Dual form			930.2.v.b.821.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(0.206116 + 1.71974i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(1.51245 + 0.844088i) q^{6} +(1.04544 + 3.21754i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-2.91503 + 0.708934i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(0.206116 + 1.71974i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(1.51245 + 0.844088i) q^{6} +(1.04544 + 3.21754i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-2.91503 + 0.708934i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(-0.169909 - 0.522925i) q^{11} +(1.57188 - 0.727458i) q^{12} +(3.02952 + 4.16977i) q^{13} +(3.21754 + 1.04544i) q^{14} +(1.71974 - 0.206116i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.761416 + 2.34340i) q^{17} +(-1.13987 + 2.77501i) q^{18} +(-3.99611 - 2.90335i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(-5.31787 + 2.46108i) q^{21} +(-0.522925 - 0.169909i) q^{22} +(-2.08643 + 6.42136i) q^{23} +(0.335402 - 1.69927i) q^{24} -1.00000 q^{25} +5.15412 q^{26} +(-1.82002 - 4.86698i) q^{27} +(2.73701 - 1.98855i) q^{28} +(4.67275 + 3.39495i) q^{29} +(0.844088 - 1.51245i) q^{30} +(5.00837 - 2.43233i) q^{31} +1.00000i q^{32} +(0.864276 - 0.399982i) q^{33} +(1.44830 + 1.99341i) q^{34} +(3.21754 - 1.04544i) q^{35} +(1.57503 + 2.55329i) q^{36} +3.43934i q^{37} +(-4.69771 + 1.52638i) q^{38} +(-6.54650 + 6.06944i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(5.22598 - 7.19295i) q^{41} +(-1.13471 + 5.74883i) q^{42} +(-6.02817 + 8.29706i) q^{43} +(-0.444827 + 0.323185i) q^{44} +(0.708934 + 2.91503i) q^{45} +(3.96862 + 5.46234i) q^{46} +(4.14987 + 5.71181i) q^{47} +(-1.17759 - 1.27015i) q^{48} +(-3.59652 + 2.61302i) q^{49} +(-0.587785 + 0.809017i) q^{50} +(-4.18698 - 0.826427i) q^{51} +(3.02952 - 4.16977i) q^{52} +(-0.703300 + 2.16453i) q^{53} +(-5.00725 - 1.38831i) q^{54} +(-0.522925 + 0.169909i) q^{55} -3.38313i q^{56} +(4.16934 - 7.47071i) q^{57} +(5.49315 - 1.78483i) q^{58} +(-3.03322 - 4.17488i) q^{59} +(-0.727458 - 1.57188i) q^{60} +5.16980i q^{61} +(0.976048 - 5.48154i) q^{62} +(-5.32853 - 8.63809i) q^{63} +(0.809017 + 0.587785i) q^{64} +(4.16977 - 3.02952i) q^{65} +(0.184416 - 0.934317i) q^{66} +11.6647 q^{67} +2.46399 q^{68} +(-11.4731 - 2.26457i) q^{69} +(1.04544 - 3.21754i) q^{70} +(-9.53148 - 3.09697i) q^{71} +(2.99143 + 0.226558i) q^{72} +(7.71362 - 2.50631i) q^{73} +(2.78249 + 2.02159i) q^{74} +(-0.206116 - 1.71974i) q^{75} +(-1.52638 + 4.69771i) q^{76} +(1.50490 - 1.09338i) q^{77} +(1.06235 + 8.86376i) q^{78} +(-10.0834 - 3.27629i) q^{79} +(0.587785 + 0.809017i) q^{80} +(7.99483 - 4.13313i) q^{81} +(-2.74746 - 8.45582i) q^{82} +(-6.33776 - 4.60465i) q^{83} +(3.98394 + 4.29707i) q^{84} +(2.34340 + 0.761416i) q^{85} +(3.16920 + 9.75378i) q^{86} +(-4.87532 + 8.73569i) q^{87} +0.549836i q^{88} +(2.01596 + 6.20448i) q^{89} +(2.77501 + 1.13987i) q^{90} +(-10.2492 + 14.1069i) q^{91} +6.75182 q^{92} +(5.21529 + 8.11176i) q^{93} +7.06018 q^{94} +(-2.90335 + 3.99611i) q^{95} +(-1.71974 + 0.206116i) q^{96} +(-3.85307 - 11.8585i) q^{97} +4.44554i q^{98} +(0.866008 + 1.40389i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9	$ 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9} - 20 q^{10} + 10 q^{13} - 20 q^{16} - 4 q^{18} - 12 q^{19} - 30 q^{21} - 10 q^{22} - 80 q^{25} + 60 q^{27} + 18 q^{28} + 8 q^{31} - 20 q^{33} + 10 q^{34} - 8 q^{36} - 46 q^{39} + 20 q^{40} + 50 q^{43} - 16 q^{45} - 10 q^{46} - 8 q^{49} - 20 q^{51} + 10 q^{52} - 10 q^{55} + 10 q^{58} + 44 q^{63} + 20 q^{64} - 10 q^{66} - 132 q^{67} - 16 q^{69} + 12 q^{70} + 4 q^{72} - 20 q^{73} - 18 q^{76} + 48 q^{78} - 120 q^{79} + 48 q^{81} - 20 q^{82} + 20 q^{84} - 136 q^{87} - 12 q^{90} - 110 q^{91} - 20 q^{93} - 28 q^{94} + 22 q^{97}+O(q^{100}) $ 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9 - 20 * q^10 + 10 * q^13 - 20 * q^16 - 4 * q^18 - 12 * q^19 - 30 * q^21 - 10 * q^22 - 80 * q^25 + 60 * q^27 + 18 * q^28 + 8 * q^31 - 20 * q^33 + 10 * q^34 - 8 * q^36 - 46 * q^39 + 20 * q^40 + 50 * q^43 - 16 * q^45 - 10 * q^46 - 8 * q^49 - 20 * q^51 + 10 * q^52 - 10 * q^55 + 10 * q^58 + 44 * q^63 + 20 * q^64 - 10 * q^66 - 132 * q^67 - 16 * q^69 + 12 * q^70 + 4 * q^72 - 20 * q^73 - 18 * q^76 + 48 * q^78 - 120 * q^79 + 48 * q^81 - 20 * q^82 + 20 * q^84 - 136 * q^87 - 12 * q^90 - 110 * q^91 - 20 * q^93 - 28 * q^94 + 22 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	0.206116	+	1.71974i	0.119001	+	0.992894i
$3$	0.206116	+	1.71974i	0.119001	+	0.992894i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.51245	+	0.844088i	0.617457	+	0.344597i
$7$	1.04544	+	3.21754i	0.395140	+	1.21612i	0.928852	+	0.370451i	$0.120797\pi$
$7$	1.04544	+	3.21754i	0.395140	+	1.21612i	−0.533712	+	0.845667i	$0.679203\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−2.91503	+	0.708934i	−0.971677	+	0.236311i
$10$	−0.809017	−	0.587785i	−0.255834	−	0.185874i
$11$	−0.169909	−	0.522925i	−0.0512294	−	0.157668i	0.922169	−	0.386787i	$-0.126415\pi$
$11$	−0.169909	−	0.522925i	−0.0512294	−	0.157668i	−0.973398	+	0.229120i	$0.926415\pi$
$12$	1.57188	−	0.727458i	0.453762	−	0.209999i
$13$	3.02952	+	4.16977i	0.840236	+	1.15649i	0.985930	+	0.167156i	$0.0534585\pi$
$13$	3.02952	+	4.16977i	0.840236	+	1.15649i	−0.145694	+	0.989330i	$0.546542\pi$
$14$	3.21754	+	1.04544i	0.859925	+	0.279406i
$15$	1.71974	−	0.206116i	0.444036	−	0.0532190i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.761416	+	2.34340i	−0.184670	+	0.568357i	−0.999943	−	0.0107210i	$-0.996587\pi$
$17$	−0.761416	+	2.34340i	−0.184670	+	0.568357i	0.815272	+	0.579078i	$0.196587\pi$
$18$	−1.13987	+	2.77501i	−0.268671	+	0.654076i
$19$	−3.99611	−	2.90335i	−0.916771	−	0.666073i	0.0259471	−	0.999663i	$-0.491740\pi$
$19$	−3.99611	−	2.90335i	−0.916771	−	0.666073i	−0.942718	+	0.333590i	$0.891740\pi$
$20$	−0.951057	+	0.309017i	−0.212663	+	0.0690983i
$21$	−5.31787	+	2.46108i	−1.16045	+	0.537052i
$22$	−0.522925	−	0.169909i	−0.111488	−	0.0362246i
$23$	−2.08643	+	6.42136i	−0.435050	+	1.33895i	0.457985	+	0.888960i	$0.348571\pi$
$23$	−2.08643	+	6.42136i	−0.435050	+	1.33895i	−0.893035	+	0.449987i	$0.851429\pi$
$24$	0.335402	−	1.69927i	0.0684636	−	0.346861i
$25$	−1.00000			−0.200000
$26$	5.15412			1.01081
$27$	−1.82002	−	4.86698i	−0.350263	−	0.936651i
$28$	2.73701	−	1.98855i	0.517246	−	0.375801i
$29$	4.67275	+	3.39495i	0.867708	+	0.630427i	0.929971	−	0.367633i	$-0.119832\pi$
$29$	4.67275	+	3.39495i	0.867708	+	0.630427i	−0.0622629	+	0.998060i	$0.519832\pi$
$30$	0.844088	−	1.51245i	0.154109	−	0.276135i
$31$	5.00837	−	2.43233i	0.899530	−	0.436860i
$31$	5.00837	−	2.43233i	0.899530	−	0.436860i
$32$			1.00000i			0.176777i
$33$	0.864276	−	0.399982i	0.150451	−	0.0696280i
$34$	1.44830	+	1.99341i	0.248381	+	0.341867i
$35$	3.21754	−	1.04544i	0.543864	−	0.176712i
$36$	1.57503	+	2.55329i	0.262505	+	0.425548i
$37$			3.43934i			0.565424i	0.959205	+	0.282712i	$0.0912341\pi$
$37$			3.43934i			0.565424i	−0.959205	+	0.282712i	$0.908766\pi$
$38$	−4.69771	+	1.52638i	−0.762070	+	0.247611i
$39$	−6.54650	+	6.06944i	−1.04828	+	0.971889i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	5.22598	−	7.19295i	0.816162	−	1.12335i	−0.174182	−	0.984714i	$-0.555728\pi$
$41$	5.22598	−	7.19295i	0.816162	−	1.12335i	0.990343	−	0.138637i	$-0.0442720\pi$
$42$	−1.13471	+	5.74883i	−0.175089	+	0.887064i
$43$	−6.02817	+	8.29706i	−0.919287	+	1.26529i	0.0446068	+	0.999005i	$0.485797\pi$
$43$	−6.02817	+	8.29706i	−0.919287	+	1.26529i	−0.963894	+	0.266286i	$0.914203\pi$
$44$	−0.444827	+	0.323185i	−0.0670601	+	0.0487220i
$45$	0.708934	+	2.91503i	0.105682	+	0.434547i
$46$	3.96862	+	5.46234i	0.585141	+	0.805378i
$47$	4.14987	+	5.71181i	0.605321	+	0.833153i	0.996182	−	0.0872969i	$-0.0278229\pi$
$47$	4.14987	+	5.71181i	0.605321	+	0.833153i	−0.390862	+	0.920449i	$0.627823\pi$
$48$	−1.17759	−	1.27015i	−0.169971	−	0.183330i
$49$	−3.59652	+	2.61302i	−0.513788	+	0.373289i
$50$	−0.587785	+	0.809017i	−0.0831254	+	0.114412i
$51$	−4.18698	−	0.826427i	−0.586294	−	0.115723i
$52$	3.02952	−	4.16977i	0.420118	−	0.578243i
$53$	−0.703300	+	2.16453i	−0.0966057	+	0.297322i	−0.987669	−	0.156558i	$-0.949960\pi$
$53$	−0.703300	+	2.16453i	−0.0966057	+	0.297322i	0.891063	+	0.453879i	$0.149960\pi$
$54$	−5.00725	−	1.38831i	−0.681401	−	0.188926i
$55$	−0.522925	+	0.169909i	−0.0705112	+	0.0229105i
$56$		−	3.38313i		−	0.452089i
$57$	4.16934	−	7.47071i	0.552243	−	0.989520i
$58$	5.49315	−	1.78483i	0.721286	−	0.234360i
$59$	−3.03322	−	4.17488i	−0.394892	−	0.543522i	0.564561	−	0.825392i	$-0.309046\pi$
$59$	−3.03322	−	4.17488i	−0.394892	−	0.543522i	−0.959453	+	0.281869i	$0.909046\pi$
$60$	−0.727458	−	1.57188i	−0.0939144	−	0.202929i
$61$			5.16980i			0.661925i	0.943644	+	0.330963i	$0.107373\pi$
$61$			5.16980i			0.661925i	−0.943644	+	0.330963i	$0.892627\pi$
$62$	0.976048	−	5.48154i	0.123958	−	0.696157i
$63$	−5.32853	−	8.63809i	−0.671331	−	1.08830i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	4.16977	−	3.02952i	0.517196	−	0.375765i
$66$	0.184416	−	0.934317i	0.0227000	−	0.115007i
$67$	11.6647			1.42507			0.712533	−	0.701639i	$-0.247548\pi$
$67$	11.6647			1.42507			0.712533	+	0.701639i	$0.247548\pi$
$68$	2.46399			0.298803
$69$	−11.4731	−	2.26457i	−1.38120	−	0.272622i
$70$	1.04544	−	3.21754i	0.124954	−	0.384570i
$71$	−9.53148	−	3.09697i	−1.13118	−	0.367542i	−0.317155	−	0.948374i	$-0.602728\pi$
$71$	−9.53148	−	3.09697i	−1.13118	−	0.367542i	−0.814024	+	0.580831i	$0.802728\pi$
$72$	2.99143	+	0.226558i	0.352544	+	0.0267001i
$73$	7.71362	−	2.50631i	0.902811	−	0.293341i	0.179414	−	0.983774i	$-0.442580\pi$
$73$	7.71362	−	2.50631i	0.902811	−	0.293341i	0.723397	+	0.690433i	$0.242580\pi$
$74$	2.78249	+	2.02159i	0.323457	+	0.235006i
$75$	−0.206116	−	1.71974i	−0.0238003	−	0.198579i
$76$	−1.52638	+	4.69771i	−0.175088	+	0.538865i
$77$	1.50490	−	1.09338i	0.171500	−	0.124602i
$78$	1.06235	+	8.86376i	0.120287	+	1.00362i
$79$	−10.0834	−	3.27629i	−1.13447	−	0.368611i	−0.319196	−	0.947689i	$-0.603413\pi$
$79$	−10.0834	−	3.27629i	−1.13447	−	0.368611i	−0.815272	+	0.579078i	$0.803413\pi$
$80$	0.587785	+	0.809017i	0.0657164	+	0.0904508i
$81$	7.99483	−	4.13313i	0.888314	−	0.459237i
$82$	−2.74746	−	8.45582i	−0.303406	−	0.933789i
$83$	−6.33776	−	4.60465i	−0.695660	−	0.505426i	0.182856	−	0.983140i	$-0.441466\pi$
$83$	−6.33776	−	4.60465i	−0.695660	−	0.505426i	−0.878516	+	0.477713i	$0.841466\pi$
$84$	3.98394	+	4.29707i	0.434683	+	0.468849i
$85$	2.34340	+	0.761416i	0.254177	+	0.0825871i
$86$	3.16920	+	9.75378i	0.341743	+	1.05178i
$87$	−4.87532	+	8.73569i	−0.522689	+	0.936564i
$88$			0.549836i			0.0586127i
$89$	2.01596	+	6.20448i	0.213691	+	0.657674i	0.999244	+	0.0388790i	$0.0123787\pi$
$89$	2.01596	+	6.20448i	0.213691	+	0.657674i	−0.785553	+	0.618795i	$0.787621\pi$
$90$	2.77501	+	1.13987i	0.292512	+	0.120153i
$91$	−10.2492	+	14.1069i	−1.07441	+	1.47880i
$92$	6.75182			0.703926
$93$	5.21529	+	8.11176i	0.540801	+	0.841151i
$94$	7.06018			0.728202
$95$	−2.90335	+	3.99611i	−0.297877	+	0.409993i
$96$	−1.71974	+	0.206116i	−0.175521	+	0.0210367i
$97$	−3.85307	−	11.8585i	−0.391220	−	1.20405i	−0.931866	−	0.362802i	$-0.881820\pi$
$97$	−3.85307	−	11.8585i	−0.391220	−	1.20405i	0.540646	−	0.841250i	$-0.318180\pi$
$98$			4.44554i			0.449067i
$99$	0.866008	+	1.40389i	0.0870371	+	0.141096i
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	14.3521	+	4.66328i	1.42809	+	0.464014i	0.918162	−	0.396205i	$-0.129673\pi$
$101$	14.3521	+	4.66328i	1.42809	+	0.464014i	0.509926	+	0.860219i	$0.329673\pi$
$102$	−3.12964	+	2.90158i	−0.309880	+	0.287299i
$103$	3.95712	+	2.87502i	0.389907	+	0.283284i	0.765417	−	0.643534i	$-0.222533\pi$
$103$	3.95712	+	2.87502i	0.389907	+	0.283284i	−0.375510	+	0.926818i	$0.622533\pi$
$104$	−1.59271	−	4.90186i	−0.156178	−	0.480667i
$105$	2.46108	+	5.31787i	0.240177	+	0.518971i
$106$	1.33776	+	1.84126i	0.129934	+	0.178839i
$107$	0.546372	+	0.177527i	0.0528198	+	0.0171622i	0.335308	−	0.942109i	$-0.391160\pi$
$107$	0.546372	+	0.177527i	0.0528198	+	0.0171622i	−0.282488	+	0.959271i	$0.591160\pi$
$108$	−4.06636	+	3.23492i	−0.391286	+	0.311281i
$109$	8.31993	−	6.04478i	0.796905	−	0.578985i	−0.113100	−	0.993584i	$-0.536078\pi$
$109$	8.31993	−	6.04478i	0.796905	−	0.578985i	0.910005	+	0.414598i	$0.136078\pi$
$110$	−0.169909	+	0.522925i	−0.0162002	+	0.0498589i
$111$	−5.91478	+	0.708904i	−0.561407	+	0.0672862i
$112$	−2.73701	−	1.98855i	−0.258623	−	0.187900i
$113$	−6.85077	+	2.22595i	−0.644466	+	0.209400i	−0.612973	−	0.790104i	$-0.710026\pi$
$113$	−6.85077	+	2.22595i	−0.644466	+	0.209400i	−0.0314936	+	0.999504i	$0.510026\pi$
$114$	−3.59325	−	7.76425i	−0.336539	−	0.727188i
$115$	6.42136	+	2.08643i	0.598795	+	0.194560i
$116$	1.78483	−	5.49315i	0.165717	−	0.510026i
$117$	−11.7872	−	10.0073i	−1.08973	−	0.925174i
$118$	−5.16043			−0.475056
$119$	−8.33600			−0.764160
$120$	−1.69927	−	0.335402i	−0.155121	−	0.0306178i
$121$	8.65461	−	6.28794i	0.786782	−	0.571631i
$122$	4.18246	+	3.03873i	0.378662	+	0.275114i
$123$	13.4472	+	7.50477i	1.21249	+	0.676682i
$124$	−3.86096	−	4.01161i	−0.346724	−	0.360253i
$125$			1.00000i			0.0894427i
$126$	−10.1204	−	0.766475i	−0.901596	−	0.0682830i
$127$	−10.6242	−	14.6229i	−0.942742	−	1.29757i	−0.954677	−	0.297645i	$-0.903799\pi$
$127$	−10.6242	−	14.6229i	−0.942742	−	1.29757i	0.0119345	−	0.999929i	$-0.496201\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	−15.5113	−	8.65674i	−1.36570	−	0.762184i
$130$		−	5.15412i		−	0.452046i
$131$	−3.55333	+	1.15455i	−0.310456	+	0.100873i	−0.460101	−	0.887867i	$-0.652187\pi$
$131$	−3.55333	+	1.15455i	−0.310456	+	0.100873i	0.149645	+	0.988740i	$0.452187\pi$
$132$	−0.647482	−	0.698374i	−0.0563561	−	0.0607856i
$133$	5.16393	−	15.8930i	0.447770	−	1.37809i
$134$	6.85632	−	9.43691i	0.592295	−	0.815225i
$135$	−4.86698	+	1.82002i	−0.418883	+	0.156642i
$136$	1.44830	−	1.99341i	0.124191	−	0.170934i
$137$	13.0821	−	9.50473i	1.11768	−	0.812044i	0.133826	−	0.991005i	$-0.457274\pi$
$137$	13.0821	−	9.50473i	1.11768	−	0.812044i	0.983856	+	0.178961i	$0.0572736\pi$
$138$	−8.57582	+	7.95088i	−0.730022	+	0.676824i
$139$	−2.43702	−	3.35426i	−0.206705	−	0.284505i	0.693060	−	0.720880i	$-0.256262\pi$
$139$	−2.43702	−	3.35426i	−0.206705	−	0.284505i	−0.899765	+	0.436375i	$0.856262\pi$
$140$	−1.98855	−	2.73701i	−0.168063	−	0.231319i
$141$	−8.96748	+	8.31401i	−0.755198	+	0.700166i
$142$	−8.10796	+	5.89078i	−0.680405	+	0.494343i
$143$	1.66574	−	2.29269i	0.139296	−	0.191724i
$144$	1.94161	−	2.28695i	0.161801	−	0.190579i
$145$	3.39495	−	4.67275i	0.281935	−	0.388051i
$146$	2.50631	−	7.71362i	0.207423	−	0.638384i
$147$	−5.23503	−	5.64650i	−0.431778	−	0.465715i
$148$	3.27101	−	1.06282i	0.268875	−	0.0873629i
$149$		−	5.09209i		−	0.417160i	−0.978005	−	0.208580i	$-0.933116\pi$
$149$		−	5.09209i		−	0.417160i	0.978005	−	0.208580i	$-0.0668842\pi$
$150$	−1.51245	−	0.844088i	−0.123491	−	0.0689195i
$151$	14.6059	−	4.74576i	1.18861	−	0.386204i	0.353054	−	0.935603i	$-0.385143\pi$
$151$	14.6059	−	4.74576i	1.18861	−	0.386204i	0.835561	+	0.549398i	$0.185143\pi$
$152$	2.90335	+	3.99611i	0.235492	+	0.324128i
$153$	0.558238	−	7.37087i	0.0451308	−	0.595899i
$154$		−	1.86016i		−	0.149896i
$155$	−2.43233	−	5.00837i	−0.195370	−	0.402282i
$156$	7.79536	+	4.35053i	0.624129	+	0.348321i
$157$	−5.97010	−	4.33753i	−0.476466	−	0.346173i	0.323490	−	0.946232i	$-0.395144\pi$
$157$	−5.97010	−	4.33753i	−0.476466	−	0.346173i	−0.799956	+	0.600059i	$0.795144\pi$
$158$	−8.57743	+	6.23187i	−0.682384	+	0.495781i
$159$	−3.86740	−	0.763349i	−0.306705	−	0.0605375i
$160$	1.00000			0.0790569
$161$	−22.8423			−1.80022
$162$	1.35547	−	8.89734i	0.106496	−	0.699041i
$163$	2.36388	−	7.27529i	0.185154	−	0.569844i	−0.814797	−	0.579746i	$-0.803152\pi$
$163$	2.36388	−	7.27529i	0.185154	−	0.569844i	0.999951	+	0.00990157i	$0.00315182\pi$
$164$	−8.45582	−	2.74746i	−0.660289	−	0.214541i
$165$	−0.399982	−	0.864276i	−0.0311386	−	0.0672838i
$166$	−7.45048	+	2.42081i	−0.578270	+	0.187891i
$167$	10.4067	+	7.56094i	0.805298	+	0.585083i	0.912464	−	0.409158i	$-0.134178\pi$
$167$	10.4067	+	7.56094i	0.805298	+	0.585083i	−0.107166	+	0.994241i	$0.534178\pi$
$168$	5.81811	−	0.697317i	0.448877	−	0.0537992i
$169$	−4.19180	+	12.9010i	−0.322446	+	0.992387i
$170$	1.99341	−	1.44830i	0.152888	−	0.111079i
$171$	13.7071	+	5.63037i	1.04821	+	0.430565i
$172$	9.75378	+	3.16920i	0.743719	+	0.241649i
$173$	−8.66268	−	11.9232i	−0.658611	−	0.906501i	0.340823	−	0.940127i	$-0.389294\pi$
$173$	−8.66268	−	11.9232i	−0.658611	−	0.906501i	−0.999434	+	0.0336267i	$0.989294\pi$
$174$	4.20168	+	9.07892i	0.318529	+	0.688271i
$175$	−1.04544	−	3.21754i	−0.0790281	−	0.243223i
$176$	0.444827	+	0.323185i	0.0335301	+	0.0243610i
$177$	6.55452	−	6.07688i	0.492668	−	0.456766i
$178$	6.20448	+	2.01596i	0.465045	+	0.151102i
$179$	−6.81513	−	20.9748i	−0.509387	−	1.56773i	−0.793268	−	0.608872i	$-0.791622\pi$
$179$	−6.81513	−	20.9748i	−0.509387	−	1.56773i	0.283881	−	0.958859i	$-0.408378\pi$
$180$	2.55329	−	1.57503i	0.190311	−	0.117396i
$181$		−	13.4005i		−	0.996049i	−0.867163	−	0.498025i	$-0.834059\pi$
$181$		−	13.4005i		−	0.996049i	0.867163	−	0.498025i	$-0.165941\pi$
$182$	5.38834	+	16.5836i	0.399410	+	1.22926i
$183$	−8.89073	+	1.06558i	−0.657222	+	0.0787699i
$184$	3.96862	−	5.46234i	0.292571	−	0.402689i
$185$	3.43934			0.252865
$186$	9.62803	+	0.548716i	0.705961	+	0.0402338i
$187$	1.35479			0.0990722
$188$	4.14987	−	5.71181i	0.302660	−	0.416576i
$189$	13.7570	−	10.9441i	1.00067	−	0.796070i
$190$	1.52638	+	4.69771i	0.110735	+	0.340808i
$191$		−	7.46469i		−	0.540126i	−0.962843	−	0.270063i	$-0.912955\pi$
$191$		−	7.46469i		−	0.540126i	0.962843	−	0.270063i	$-0.0870445\pi$
$192$	−0.844088	+	1.51245i	−0.0609168	+	0.109152i
$193$	−2.15402	−	6.62938i	−0.155050	−	0.477193i	0.843116	−	0.537731i	$-0.180718\pi$
$193$	−2.15402	−	6.62938i	−0.155050	−	0.477193i	−0.998166	+	0.0605377i	$0.980718\pi$
$194$	−11.8585	−	3.85307i	−0.851393	−	0.276634i
$195$	6.06944	+	6.54650i	0.434642	+	0.468805i
$196$	3.59652	+	2.61302i	0.256894	+	0.186644i
$197$	4.07120	+	12.5299i	0.290061	+	0.892717i	0.984836	+	0.173489i	$0.0555042\pi$
$197$	4.07120	+	12.5299i	0.290061	+	0.892717i	−0.694775	+	0.719228i	$0.744496\pi$
$198$	1.64480	+	0.124570i	0.116891	+	0.00885279i
$199$	13.7514	+	18.9272i	0.974814	+	1.34172i	0.939577	+	0.342337i	$0.111218\pi$
$199$	13.7514	+	18.9272i	0.974814	+	1.34172i	0.0352363	+	0.999379i	$0.488782\pi$
$200$	0.951057	+	0.309017i	0.0672499	+	0.0218508i
$201$	2.40428	+	20.0602i	0.169585	+	1.41494i
$202$	12.2086	−	8.87009i	0.858996	−	0.624097i
$203$	−6.03831	+	18.5840i	−0.423806	+	1.30434i
$204$	0.507869	+	4.23743i	0.0355579	+	0.296680i
$205$	−7.19295	−	5.22598i	−0.502377	−	0.364999i
$206$	4.65188	−	1.51149i	0.324112	−	0.105310i
$207$	1.52968	−	20.1976i	0.106320	−	1.40383i
$208$	−4.90186	−	1.59271i	−0.339883	−	0.110435i
$209$	−0.839258	+	2.58297i	−0.0580527	+	0.178668i
$210$	5.74883	+	1.13471i	0.396707	+	0.0783021i
$211$	12.1026			0.833175			0.416587	−	0.909096i	$-0.363226\pi$
$211$	12.1026			0.833175			0.416587	+	0.909096i	$0.363226\pi$
$212$	2.27593			0.156311
$213$	3.36139	−	17.0300i	0.230319	−	1.16688i
$214$	0.464772	−	0.337677i	0.0317712	−	0.0230831i
$215$	8.29706	+	6.02817i	0.565855	+	0.411118i
$216$	0.226961	+	5.19119i	0.0154428	+	0.353216i
$217$	13.0621	+	13.5718i	0.886713	+	0.921313i
$218$		−	10.2840i		−	0.696520i
$219$	5.90011	+	12.7489i	0.398692	+	0.861488i
$220$	0.323185	+	0.444827i	0.0217892	+	0.0299902i
$221$	−12.0781	+	3.92443i	−0.812464	+	0.263985i
$222$	−2.90311	+	5.20185i	−0.194844	+	0.349125i
$223$		−	18.2599i		−	1.22278i	−0.791331	−	0.611388i	$-0.790612\pi$
$223$		−	18.2599i		−	1.22278i	0.791331	−	0.611388i	$-0.209388\pi$
$224$	−3.21754	+	1.04544i	−0.214981	+	0.0698516i
$225$	2.91503	−	0.708934i	0.194335	−	0.0472623i
$226$	−2.22595	+	6.85077i	−0.148068	+	0.455706i
$227$	−12.0690	+	16.6116i	−0.801051	+	1.10255i	0.191592	+	0.981475i	$0.438635\pi$
$227$	−12.0690	+	16.6116i	−0.801051	+	1.10255i	−0.992643	+	0.121077i	$0.961365\pi$
$228$	−8.39347	−	1.65671i	−0.555871	−	0.109718i
$229$	−0.197387	+	0.271679i	−0.0130437	+	0.0179531i	−0.815489	−	0.578773i	$-0.803532\pi$
$229$	−0.197387	+	0.271679i	−0.0130437	+	0.0179531i	0.802445	+	0.596726i	$0.203532\pi$
$230$	5.46234	−	3.96862i	0.360176	−	0.261683i
$231$	2.19051	+	2.36269i	0.144125	+	0.155453i
$232$	−3.39495	−	4.67275i	−0.222890	−	0.306781i
$233$	−9.13597	−	12.5746i	−0.598517	−	0.823788i	0.397055	−	0.917795i	$-0.370032\pi$
$233$	−9.13597	−	12.5746i	−0.598517	−	0.823788i	−0.995572	+	0.0940071i	$0.970032\pi$
$234$	−15.0244	+	3.65393i	−0.982177	+	0.238865i
$235$	5.71181	−	4.14987i	0.372597	−	0.270708i
$236$	−3.03322	+	4.17488i	−0.197446	+	0.271761i
$237$	3.55602	−	18.0161i	0.230989	−	1.17027i
$238$	−4.89978	+	6.74396i	−0.317605	+	0.437146i
$239$	−8.64963	+	26.6208i	−0.559498	+	1.72196i	0.124261	+	0.992250i	$0.460344\pi$
$239$	−8.64963	+	26.6208i	−0.559498	+	1.72196i	−0.683759	+	0.729708i	$0.739656\pi$
$240$	−1.27015	+	1.17759i	−0.0819878	+	0.0760132i
$241$	−19.3067	+	6.27312i	−1.24365	+	0.404087i	−0.855642	−	0.517568i	$-0.826838\pi$
$241$	−19.3067	+	6.27312i	−1.24365	+	0.404087i	−0.388010	+	0.921655i	$0.626838\pi$
$242$		−	10.6977i		−	0.687673i
$243$	8.75579	+	12.8971i	0.561684	+	0.827352i
$244$	4.91677	−	1.59756i	0.314764	−	0.102273i
$245$	2.61302	+	3.59652i	0.166940	+	0.229773i
$246$	13.9755	−	6.46781i	0.891048	−	0.412373i
$247$		−	25.4586i		−	1.61989i
$248$	−5.51487	+	0.765614i	−0.350195	+	0.0486165i
$249$	6.61250	−	11.8484i	0.419050	−	0.750863i
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	−19.2975	+	14.0204i	−1.21805	+	0.884962i	−0.995936	−	0.0900599i	$-0.971294\pi$
$251$	−19.2975	+	14.0204i	−1.21805	+	0.884962i	−0.222109	+	0.975022i	$0.571294\pi$
$252$	−6.56871	+	7.73705i	−0.413790	+	0.487388i
$253$	3.71239			0.233396
$254$	−18.0749			−1.13412
$255$	−0.826427	+	4.18698i	−0.0517529	+	0.262199i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−5.21057	−	1.69302i	−0.325027	−	0.105608i	0.141959	−	0.989873i	$-0.454660\pi$
$257$	−5.21057	−	1.69302i	−0.325027	−	0.105608i	−0.466985	+	0.884265i	$0.654660\pi$
$258$	−16.1208	+	7.46062i	−1.00364	+	0.464478i
$259$	−11.0662	+	3.59564i	−0.687622	+	0.223422i
$260$	−4.16977	−	3.02952i	−0.258598	−	0.187883i
$261$	−16.0280	−	6.58372i	−0.992109	−	0.407522i
$262$	−1.15455	+	3.55333i	−0.0713281	+	0.219525i
$263$	−0.504862	+	0.366804i	−0.0311311	+	0.0226181i	−0.603242	−	0.797558i	$-0.706125\pi$
$263$	−0.504862	+	0.366804i	−0.0311311	+	0.0226181i	0.572111	+	0.820176i	$0.306125\pi$
$264$	−0.945576	+	0.113330i	−0.0581962	+	0.00697499i
$265$	2.16453	+	0.703300i	0.132966	+	0.0432034i
$266$	−9.82238	−	13.5194i	−0.602249	−	0.828925i
$267$	−10.2546	+	4.74577i	−0.627571	+	0.290437i
$268$	−3.60458	−	11.0938i	−0.220185	−	0.677659i
$269$	12.5417	+	9.11211i	0.764684	+	0.555575i	0.900343	−	0.435180i	$-0.143315\pi$
$269$	12.5417	+	9.11211i	0.764684	+	0.555575i	−0.135660	+	0.990756i	$0.543315\pi$
$270$	−1.38831	+	5.00725i	−0.0844901	+	0.304732i
$271$	19.6199	+	6.37489i	1.19182	+	0.387247i	0.836747	−	0.547590i	$-0.184455\pi$
$271$	19.6199	+	6.37489i	1.19182	+	0.387247i	0.355077	+	0.934837i	$0.384455\pi$
$272$	−0.761416	−	2.34340i	−0.0461676	−	0.142089i
$273$	−26.3727	−	14.7184i	−1.59615	−	0.890797i
$274$		−	16.1704i		−	0.976890i
$275$	0.169909	+	0.522925i	0.0102459	+	0.0315336i
$276$	1.39166	+	11.6114i	0.0837681	+	0.698924i
$277$	1.77807	−	2.44730i	0.106834	−	0.147044i	−0.752252	−	0.658875i	$-0.771033\pi$
$277$	1.77807	−	2.44730i	0.106834	−	0.147044i	0.859086	+	0.511831i	$0.171033\pi$
$278$	−4.14610			−0.248666
$279$	−12.8752	+	10.6409i	−0.770818	+	0.637056i
$280$	−3.38313			−0.202180
$281$	7.35028	−	10.1168i	0.438481	−	0.603517i	−0.531393	−	0.847126i	$-0.678331\pi$
$281$	7.35028	−	10.1168i	0.438481	−	0.603517i	0.969874	+	0.243608i	$0.0783311\pi$
$282$	1.45522	+	12.1417i	0.0866570	+	0.723028i
$283$	0.705987	+	2.17280i	0.0419666	+	0.129160i	0.969845	−	0.243724i	$-0.0783691\pi$
$283$	0.705987	+	2.17280i	0.0419666	+	0.129160i	−0.927878	+	0.372884i	$0.878369\pi$
$284$			10.0220i			0.594696i
$285$	−7.47071	−	4.16934i	−0.442527	−	0.246971i
$286$	−0.875729	−	2.69522i	−0.0517830	−	0.159372i
$287$	28.6071	+	9.29501i	1.68862	+	0.548667i
$288$	−0.708934	−	2.91503i	−0.0417743	−	0.171770i
$289$	8.84154	+	6.42375i	0.520090	+	0.377868i
$290$	−1.78483	−	5.49315i	−0.104809	−	0.322569i
$291$	19.5995	−	9.07053i	1.14894	−	0.531724i
$292$	−4.76728	−	6.56160i	−0.278984	−	0.383988i
$293$	1.24850	+	0.405663i	0.0729383	+	0.0236991i	0.345259	−	0.938508i	$-0.387791\pi$
$293$	1.24850	+	0.405663i	0.0729383	+	0.0236991i	−0.272321	+	0.962207i	$0.587791\pi$
$294$	−7.64519	+	0.916298i	−0.445876	+	0.0534396i
$295$	−4.17488	+	3.03322i	−0.243071	+	0.176601i
$296$	1.06282	−	3.27101i	0.0617749	−	0.190124i
$297$	−2.23583	+	1.77868i	−0.129736	+	0.103209i
$298$	−4.11959	−	2.99306i	−0.238641	−	0.173383i
$299$	−33.0965	+	10.7537i	−1.91402	+	0.621902i
$300$	−1.57188	+	0.727458i	−0.0907525	+	0.0419998i
$301$	−32.9983	−	10.7218i	−1.90199	−	0.617994i
$302$	4.74576	−	14.6059i	0.273088	−	0.840478i
$303$	−5.06144	+	25.6431i	−0.290772	+	1.47316i
$304$	4.93947			0.283298
$305$	5.16980			0.296022
$306$	−5.63503	−	4.78411i	−0.322133	−	0.273489i
$307$	3.71259	−	2.69736i	0.211889	−	0.153946i	−0.476779	−	0.879023i	$-0.658196\pi$
$307$	3.71259	−	2.69736i	0.211889	−	0.153946i	0.688668	+	0.725077i	$0.258196\pi$
$308$	−1.50490	−	1.09338i	−0.0857499	−	0.0623009i
$309$	−4.12867	+	7.39782i	−0.234872	+	0.420848i
$310$	−5.48154	−	0.976048i	−0.311331	−	0.0554358i
$311$		−	28.9842i		−	1.64354i	−0.569818	−	0.821771i	$-0.692986\pi$
$311$		−	28.9842i		−	1.64354i	0.569818	−	0.821771i	$-0.307014\pi$
$312$	8.10165	−	3.74941i	0.458666	−	0.212268i
$313$	−5.04576	−	6.94489i	−0.285203	−	0.392548i	0.642245	−	0.766499i	$-0.278003\pi$
$313$	−5.04576	−	6.94489i	−0.285203	−	0.392548i	−0.927449	+	0.373951i	$0.878003\pi$
$314$	−7.01827	+	2.28037i	−0.396064	+	0.128689i
$315$	−8.63809	+	5.32853i	−0.486701	+	0.300228i
$316$			10.6023i			0.596425i
$317$	0.136489	−	0.0443480i	0.00766600	−	0.00249083i	−0.305181	−	0.952294i	$-0.598717\pi$
$317$	0.136489	−	0.0443480i	0.00766600	−	0.00249083i	0.312847	+	0.949803i	$0.398717\pi$
$318$	−2.89077	+	2.68011i	−0.162106	+	0.150293i
$319$	0.981365	−	3.02033i	0.0549459	−	0.169106i
$320$	0.587785	−	0.809017i	0.0328582	−	0.0452254i
$321$	−0.192685	+	0.976211i	−0.0107546	+	0.0544868i
$322$	−13.4263	+	18.4798i	−0.748221	+	1.02984i
$323$	9.84639	−	7.15382i	0.547868	−	0.398049i
$324$	−6.40138	−	6.32632i	−0.355632	−	0.351462i
$325$	−3.02952	−	4.16977i	−0.168047	−	0.231297i
$326$	−4.49637	−	6.18873i	−0.249031	−	0.342762i
$327$	12.1103	+	13.0622i	0.669704	+	0.722342i
$328$	−7.19295	+	5.22598i	−0.397164	+	0.288557i
$329$	−14.0395	+	19.3238i	−0.774024	+	1.06535i
$330$	−0.934317	−	0.184416i	−0.0514325	−	0.0101518i
$331$	16.3645	−	22.5237i	0.899472	−	1.23802i	−0.0711645	−	0.997465i	$-0.522672\pi$
$331$	16.3645	−	22.5237i	0.899472	−	1.23802i	0.970636	−	0.240552i	$-0.0773285\pi$
$332$	−2.42081	+	7.45048i	−0.132859	+	0.408898i
$333$	−2.43827	−	10.0258i	−0.133616	−	0.549410i
$334$	12.2339	−	3.97502i	0.669407	−	0.217504i
$335$		−	11.6647i		−	0.637309i
$336$	2.85566	−	5.11682i	0.155789	−	0.279145i
$337$	3.16177	−	1.02732i	0.172232	−	0.0559617i	−0.221631	−	0.975131i	$-0.571138\pi$
$337$	3.16177	−	1.02732i	0.172232	−	0.0559617i	0.393864	+	0.919169i	$0.371138\pi$
$338$	7.97327	+	10.9743i	0.433689	+	0.596921i
$339$	−5.24012	−	11.3228i	−0.284604	−	0.614968i
$340$		−	2.46399i		−	0.133629i
$341$	−2.12289	−	2.20573i	−0.114961	−	0.119447i
$342$	12.6119	−	7.77981i	0.681972	−	0.420684i
$343$	6.99157	+	5.07968i	0.377509	+	0.274277i
$344$	8.29706	−	6.02817i	0.447348	−	0.325017i
$345$	−2.26457	+	11.4731i	−0.121920	+	0.617693i
$346$	−14.7378			−0.792311
$347$	10.9495			0.587800			0.293900	−	0.955836i	$-0.405047\pi$
$347$	10.9495			0.587800			0.293900	+	0.955836i	$0.405047\pi$
$348$	9.81469	+	1.93723i	0.526122	+	0.103846i
$349$	−9.79784	+	30.1547i	−0.524467	+	1.61414i	0.240902	+	0.970550i	$0.422557\pi$
$349$	−9.79784	+	30.1547i	−0.524467	+	1.61414i	−0.765368	+	0.643593i	$0.777443\pi$
$350$	−3.21754	−	1.04544i	−0.171985	−	0.0558813i
$351$	14.7804	−	22.3337i	0.788921	−	1.19208i
$352$	0.522925	−	0.169909i	0.0278720	−	0.00905616i
$353$	13.6035	+	9.88349i	0.724039	+	0.526045i	0.887672	−	0.460476i	$-0.152321\pi$
$353$	13.6035	+	9.88349i	0.724039	+	0.526045i	−0.163633	+	0.986521i	$0.552321\pi$
$354$	−1.06365	−	8.87461i	−0.0565323	−	0.471680i
$355$	−3.09697	+	9.53148i	−0.164370	+	0.505879i
$356$	5.27785	−	3.83458i	0.279725	−	0.203232i
$357$	−1.71818	−	14.3358i	−0.0909360	−	0.758729i
$358$	−20.9748	−	6.81513i	−1.10855	−	0.360191i
$359$	16.8109	+	23.1383i	0.887247	+	1.22119i	0.974360	+	0.224993i	$0.0722358\pi$
$359$	16.8109	+	23.1383i	0.887247	+	1.22119i	−0.0871133	+	0.996198i	$0.527764\pi$
$360$	0.226558	−	2.99143i	0.0119407	−	0.157662i
$361$	1.66818	+	5.13412i	0.0877988	+	0.270217i
$362$	−10.8412	−	7.87660i	−0.569801	−	0.413985i
$363$	12.5975	+	13.5877i	0.661197	+	0.713167i
$364$	16.5836	+	5.38834i	0.869217	+	0.282426i
$365$	−2.50631	−	7.71362i	−0.131186	−	0.403749i
$366$	−4.36377	+	7.81908i	−0.228098	+	0.408710i
$367$			34.8317i			1.81820i	0.416581	+	0.909099i	$0.363228\pi$
$367$			34.8317i			1.81820i	−0.416581	+	0.909099i	$0.636772\pi$
$368$	−2.08643	−	6.42136i	−0.108763	−	0.334737i
$369$	−10.1346	+	24.6726i	−0.527585	+	1.28440i
$370$	2.02159	−	2.78249i	0.105098	−	0.144655i
$371$	−7.69974			−0.399751
$372$	6.10313	−	7.46671i	0.316433	−	0.387131i
$373$	−13.9927			−0.724514			−0.362257	−	0.932078i	$-0.617994\pi$
$373$	−13.9927			−0.724514			−0.362257	+	0.932078i	$0.617994\pi$
$374$	0.796326	−	1.09605i	0.0411771	−	0.0566754i
$375$	−1.71974	+	0.206116i	−0.0888071	+	0.0106438i
$376$	−2.18172	−	6.71463i	−0.112513	−	0.346281i
$377$			29.7694i			1.53320i
$378$	−0.767838	−	17.5625i	−0.0394933	−	0.903315i
$379$	10.2518	+	31.5518i	0.526600	+	1.62071i	0.761130	+	0.648599i	$0.224645\pi$
$379$	10.2518	+	31.5518i	0.526600	+	1.62071i	−0.234530	+	0.972109i	$0.575355\pi$
$380$	4.69771	+	1.52638i	0.240988	+	0.0783016i
$381$	22.9578	−	21.2849i	1.17617	−	1.09046i
$382$	−6.03906	−	4.38763i	−0.308985	−	0.224491i
$383$	−4.28275	−	13.1809i	−0.218838	−	0.673514i	−0.998859	−	0.0477607i	$-0.984792\pi$
$383$	−4.28275	−	13.1809i	−0.218838	−	0.673514i	0.780021	−	0.625754i	$-0.215208\pi$
$384$	0.727458	+	1.57188i	0.0371229	+	0.0802146i
$385$	−1.09338	−	1.50490i	−0.0557236	−	0.0766970i
$386$	−6.62938	−	2.15402i	−0.337427	−	0.109637i
$387$	11.6902	−	28.4598i	0.594248	−	1.44669i
$388$	−10.0875	+	7.32898i	−0.512114	+	0.372073i
$389$	0.320181	−	0.985415i	0.0162338	−	0.0499625i	−0.942611	−	0.333892i	$-0.891638\pi$
$389$	0.320181	−	0.985415i	0.0162338	−	0.0499625i	0.958845	+	0.283929i	$0.0916380\pi$
$390$	8.86376	−	1.06235i	0.448834	−	0.0537941i
$391$	−13.4592	−	9.77865i	−0.680659	−	0.494528i
$392$	4.22796	−	1.37375i	0.213544	−	0.0693847i
$393$	−2.71792	−	5.87284i	−0.137101	−	0.296246i
$394$	12.5299	+	4.07120i	0.631246	+	0.205104i
$395$	−3.27629	+	10.0834i	−0.164848	+	0.507349i
$396$	1.06757	−	1.25745i	0.0536472	−	0.0631892i
$397$	16.9525			0.850819			0.425410	−	0.905001i	$-0.360130\pi$
$397$	16.9525			0.850819			0.425410	+	0.905001i	$0.360130\pi$
$398$	23.3953			1.17270
$399$	28.3962	+	5.60484i	1.42159	+	0.280593i
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	−2.68632	−	1.95172i	−0.134148	−	0.0974645i	0.518687	−	0.854964i	$-0.326421\pi$
$401$	−2.68632	−	1.95172i	−0.134148	−	0.0974645i	−0.652836	+	0.757499i	$0.726421\pi$
$402$	17.6423	+	9.84600i	0.879916	+	0.491074i
$403$	25.3152	+	13.5150i	1.26104	+	0.673228i
$404$		−	15.0907i		−	0.750790i
$405$	−4.13313	−	7.99483i	−0.205377	−	0.397266i
$406$	11.4856	+	15.8085i	0.570018	+	0.784563i
$407$	1.79852	−	0.584374i	0.0891492	−	0.0289663i
$408$	3.72667	+	2.07983i	0.184498	+	0.102967i
$409$			3.74275i			0.185067i	0.995710	+	0.0925336i	$0.0294966\pi$
$409$			3.74275i			0.185067i	−0.995710	+	0.0925336i	$0.970503\pi$
$410$	−8.45582	+	2.74746i	−0.417603	+	0.135688i
$411$	19.0421	+	20.5388i	0.939279	+	1.01311i
$412$	1.51149	−	4.65188i	0.0744656	−	0.229182i
$413$	10.2618	−	14.1241i	0.504949	−	0.695003i
$414$	−15.4411	−	13.1094i	−0.758888	−	0.644292i
$415$	−4.60465	+	6.33776i	−0.226033	+	0.311108i
$416$	−4.16977	+	3.02952i	−0.204440	+	0.148534i
$417$	5.26616	−	4.88241i	0.257885	−	0.239093i
$418$	1.59636	+	2.19721i	0.0780807	+	0.107469i
$419$	4.30094	+	5.91973i	0.210114	+	0.289198i	0.901047	−	0.433722i	$-0.142800\pi$
$419$	4.30094	+	5.91973i	0.210114	+	0.289198i	−0.690933	+	0.722919i	$0.742800\pi$
$420$	4.29707	−	3.98394i	0.209676	−	0.194396i
$421$	−24.4023	+	17.7293i	−1.18930	+	0.864073i	−0.993190	−	0.116509i	$-0.962829\pi$
$421$	−24.4023	+	17.7293i	−1.18930	+	0.864073i	−0.196105	+	0.980583i	$0.562829\pi$
$422$	7.11371	−	9.79118i	0.346290	−	0.476627i
$423$	−16.1463	−	13.7081i	−0.785060	−	0.666511i
$424$	1.33776	−	1.84126i	0.0649672	−	0.0894196i
$425$	0.761416	−	2.34340i	0.0369341	−	0.113671i
$426$	−11.8018	−	12.7294i	−0.571800	−	0.616743i
$427$	−16.6341	+	5.40473i	−0.804979	+	0.261553i
$428$		−	0.574490i		−	0.0277690i
$429$	4.28617	+	2.39208i	0.206938	+	0.115491i
$430$	9.75378	−	3.16920i	0.470369	−	0.152832i
$431$	6.55061	+	9.01614i	0.315532	+	0.434292i	0.937096	−	0.349071i	$-0.113503\pi$
$431$	6.55061	+	9.01614i	0.315532	+	0.434292i	−0.621565	+	0.783363i	$0.713503\pi$
$432$	4.33317	+	2.86769i	0.208480	+	0.137972i
$433$			7.14146i			0.343197i	0.985167	+	0.171598i	$0.0548932\pi$
$433$			7.14146i			0.343197i	−0.985167	+	0.171598i	$0.945107\pi$
$434$	18.6575	−	2.59017i	0.895589	−	0.124332i
$435$	8.73569	+	4.87532i	0.418844	+	0.233753i
$436$	−8.31993	−	6.04478i	−0.398452	−	0.289493i
$437$	26.9810	−	19.6029i	1.29068	−	0.937732i
$438$	13.7820	+	2.72030i	0.658531	+	0.129981i
$439$	−30.2115			−1.44192			−0.720959	−	0.692978i	$-0.756298\pi$
$439$	−30.2115			−1.44192			−0.720959	+	0.692978i	$0.756298\pi$
$440$	0.549836			0.0262124
$441$	8.63150	−	10.1667i	0.411024	−	0.484130i
$442$	−3.92443	+	12.0781i	−0.186666	+	0.574499i
$443$	−3.21847	−	1.04574i	−0.152914	−	0.0496848i	0.231560	−	0.972821i	$-0.425617\pi$
$443$	−3.21847	−	1.04574i	−0.152914	−	0.0496848i	−0.384474	+	0.923136i	$0.625617\pi$
$444$	2.50198	+	5.40623i	0.118739	+	0.256568i
$445$	6.20448	−	2.01596i	0.294121	−	0.0955656i
$446$	−14.7726	−	10.7329i	−0.699503	−	0.508218i
$447$	8.75709	−	1.04956i	0.414196	−	0.0496426i
$448$	−1.04544	+	3.21754i	−0.0493926	+	0.152015i
$449$	18.2973	−	13.2937i	0.863501	−	0.627370i	−0.0653344	−	0.997863i	$-0.520811\pi$
$449$	18.2973	−	13.2937i	0.863501	−	0.627370i	0.928835	+	0.370493i	$0.120811\pi$
$450$	1.13987	−	2.77501i	0.0537341	−	0.130815i
$451$	−4.64931	−	1.51065i	−0.218928	−	0.0711339i
$452$	4.23401	+	5.82761i	0.199151	+	0.274108i
$453$	11.1720	+	24.1403i	0.524907	+	1.13421i
$454$	6.34507	+	19.5281i	0.297789	+	0.916501i
$455$	14.1069	+	10.2492i	0.661340	+	0.480491i
$456$	−6.27386	+	5.81667i	−0.293800	+	0.272391i
$457$	31.1066	+	10.1072i	1.45511	+	0.472793i	0.926571	−	0.376119i	$-0.122742\pi$
$457$	31.1066	+	10.1072i	1.45511	+	0.472793i	0.528535	+	0.848911i	$0.322742\pi$
$458$	0.103772	+	0.319378i	0.00484896	+	0.0149236i
$459$	12.7911	−	0.559231i	0.597036	−	0.0261027i
$460$		−	6.75182i		−	0.314805i
$461$	−3.77695	−	11.6243i	−0.175910	−	0.541396i	0.823764	−	0.566933i	$-0.191870\pi$
$461$	−3.77695	−	11.6243i	−0.175910	−	0.541396i	−0.999674	+	0.0255373i	$0.991870\pi$
$462$	3.19900	−	0.383410i	0.148831	−	0.0178378i
$463$	22.8258	−	31.4170i	1.06080	−	1.46007i	0.181750	−	0.983345i	$-0.441824\pi$
$463$	22.8258	−	31.4170i	1.06080	−	1.46007i	0.879053	−	0.476725i	$-0.158176\pi$
$464$	−5.77584			−0.268137
$465$	8.11176	−	5.21529i	0.376174	−	0.241853i
$466$	−15.5430			−0.720017
$467$	−21.7231	+	29.8993i	−1.00522	+	1.38357i	−0.0831609	+	0.996536i	$0.526502\pi$
$467$	−21.7231	+	29.8993i	−1.00522	+	1.38357i	−0.922064	+	0.387037i	$0.873498\pi$
$468$	−5.87504	+	14.3027i	−0.271574	+	0.661144i
$469$	12.1947	+	37.5316i	0.563101	+	1.73305i
$470$		−	7.06018i		−	0.325662i
$471$	6.22890	−	11.1611i	0.287013	−	0.514275i
$472$	1.59466	+	4.90786i	0.0734002	+	0.225903i
$473$	5.36298	+	1.74254i	0.246590	+	0.0801220i
$474$	−12.4852	−	13.4665i	−0.573462	−	0.618536i
$475$	3.99611	+	2.90335i	0.183354	+	0.133215i
$476$	2.57596	+	7.92800i	0.118069	+	0.363379i
$477$	0.515630	−	6.80828i	0.0236091	−	0.311730i
$478$	16.4526	+	22.6450i	0.752523	+	1.03576i
$479$	25.5169	+	8.29094i	1.16590	+	0.378823i	0.827110	−	0.562041i	$-0.189984\pi$
$479$	25.5169	+	8.29094i	1.16590	+	0.378823i	0.338786	+	0.940863i	$0.389984\pi$
$480$	0.206116	+	1.71974i	0.00940788	+	0.0784952i
$481$	−14.3413	+	10.4195i	−0.653905	+	0.475090i
$482$	−6.27312	+	19.3067i	−0.285733	+	0.879395i
$483$	−4.70816	−	39.2828i	−0.214229	−	1.78743i
$484$	−8.65461	−	6.28794i	−0.393391	−	0.285815i
$485$	−11.8585	+	3.85307i	−0.538468	+	0.174959i
$486$	15.5805	+	0.497168i	0.706747	+	0.0225520i
$487$	−20.0070	−	6.50066i	−0.906603	−	0.294573i	−0.181643	−	0.983364i	$-0.558142\pi$
$487$	−20.0070	−	6.50066i	−0.906603	−	0.294573i	−0.724960	+	0.688791i	$0.758142\pi$
$488$	1.59756	−	4.91677i	0.0723180	−	0.222572i
$489$	12.9989	+	2.56572i	0.587829	+	0.116026i
$490$	4.44554			0.200829
$491$	−8.27978			−0.373661			−0.186831	−	0.982392i	$-0.559822\pi$
$491$	−8.27978			−0.373661			−0.186831	+	0.982392i	$0.559822\pi$
$492$	2.98205	−	15.1081i	0.134441	−	0.681127i
$493$	−11.5136	+	8.36514i	−0.518548	+	0.376747i
$494$	−20.5964	−	14.9642i	−0.926678	−	0.673271i
$495$	1.40389	−	0.866008i	0.0631001	−	0.0389242i
$496$	−2.62217	+	4.91164i	−0.117739	+	0.220539i
$497$		−	33.9057i		−	1.52088i
$498$	−5.69884	−	12.3139i	−0.255371	−	0.551801i
$499$	−11.5751	−	15.9317i	−0.518172	−	0.713202i	0.467099	−	0.884205i	$-0.345299\pi$
$499$	−11.5751	−	15.9317i	−0.518172	−	0.713202i	−0.985271	+	0.171003i	$0.945299\pi$
$500$	0.951057	−	0.309017i	0.0425325	−	0.0138197i
$501$	−10.8579	+	19.4554i	−0.485094	+	0.869201i
$502$			23.8530i			1.06461i
$503$	−4.31270	+	1.40128i	−0.192294	+	0.0624800i	−0.403581	−	0.914944i	$-0.632235\pi$
$503$	−4.31270	+	1.40128i	−0.192294	+	0.0624800i	0.211287	+	0.977424i	$0.432235\pi$
$504$	2.39841	+	9.86192i	0.106834	+	0.439285i
$505$	4.66328	−	14.3521i	0.207513	−	0.638660i
$506$	2.18209	−	3.00339i	0.0970057	−	0.133517i
$507$	−23.0504	−	4.54970i	−1.02371	−	0.202059i
$508$	−10.6242	+	14.6229i	−0.471371	+	0.648787i
$509$	28.4494	−	20.6697i	1.26100	−	0.916168i	0.262191	−	0.965016i	$-0.415555\pi$
$509$	28.4494	−	20.6697i	1.26100	−	0.916168i	0.998806	+	0.0488477i	$0.0155549\pi$
$510$	2.90158	+	3.12964i	0.128484	+	0.138583i
$511$	16.1283	+	22.1987i	0.713474	+	0.982013i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	−6.85753	+	24.7332i	−0.302767	+	1.09200i
$514$	−4.43238	+	3.22031i	−0.195504	+	0.142042i
$515$	2.87502	−	3.95712i	0.126688	−	0.174372i
$516$	−3.43979	+	17.4272i	−0.151428	+	0.767191i
$517$	2.28175	−	3.14056i	0.100351	−	0.138121i
$518$	−3.59564	+	11.0662i	−0.157983	+	0.486222i
$519$	18.7192	−	17.3551i	0.821684	−	0.761806i
$520$	−4.90186	+	1.59271i	−0.214961	+	0.0698450i
$521$			20.8735i			0.914485i	0.889342	+	0.457242i	$0.151163\pi$
$521$			20.8735i			0.914485i	−0.889342	+	0.457242i	$0.848837\pi$
$522$	−14.7474	+	9.09712i	−0.645475	+	0.398170i
$523$	−10.8883	+	3.53784i	−0.476114	+	0.154699i	−0.537237	−	0.843431i	$-0.680532\pi$
$523$	−10.8883	+	3.53784i	−0.476114	+	0.154699i	0.0611228	+	0.998130i	$0.480532\pi$
$524$	2.19608	+	3.02264i	0.0959361	+	0.132045i
$525$	5.31787	−	2.46108i	0.232091	−	0.107410i
$526$			0.624044i			0.0272096i
$527$	1.88647	+	13.5886i	0.0821758	+	0.591929i
$528$	−0.464110	+	0.831601i	−0.0201978	+	0.0361908i
$529$	−18.2733	−	13.2763i	−0.794492	−	0.577232i
$530$	1.84126	−	1.33776i	0.0799794	−	0.0581084i
$531$	11.8017	+	10.0195i	0.512148	+	0.434811i
$532$	−16.7108			−0.724507
$533$	45.8251			1.98491
$534$	−2.18809	+	11.0856i	−0.0946877	+	0.479722i
$535$	0.177527	−	0.546372i	0.00767516	−	0.0236217i
$536$	−11.0938	−	3.60458i	−0.479177	−	0.155694i
$537$	34.6666	−	16.0435i	1.49597	−	0.692329i
$538$	14.7437	−	4.79052i	0.635646	−	0.206534i
$539$	1.97749	+	1.43673i	0.0851767	+	0.0618845i
$540$	3.23492	+	4.06636i	0.139209	+	0.174988i
$541$	4.28853	−	13.1987i	0.184378	−	0.567458i	−0.815559	−	0.578674i	$-0.803570\pi$
$541$	4.28853	−	13.1987i	0.184378	−	0.567458i	0.999937	+	0.0112160i	$0.00357024\pi$
$542$	16.6897	−	12.1258i	0.716883	−	0.520846i
$543$	23.0454	−	2.76205i	0.988971	−	0.118531i
$544$	−2.34340	−	0.761416i	−0.100472	−	0.0326454i
$545$	−6.04478	−	8.31993i	−0.258930	−	0.356387i
$546$	−27.4089	+	12.6847i	−1.17299	+	0.542855i
$547$	4.39632	+	13.5305i	0.187973	+	0.578521i	0.999987	−	0.00511685i	$-0.00162875\pi$
$547$	4.39632	+	13.5305i	0.187973	+	0.578521i	−0.812014	+	0.583638i	$0.801629\pi$
$548$	−13.0821	−	9.50473i	−0.558841	−	0.406022i
$549$	−3.66505	−	15.0701i	−0.156420	−	0.643178i
$550$	0.522925	+	0.169909i	0.0222976	+	0.00724493i
$551$	−8.81612	−	27.1332i	−0.375579	−	1.15591i
$552$	10.2118	+	5.69913i	0.434644	+	0.242571i
$553$		−	35.8689i		−	1.52530i
$554$	−0.934787	−	2.87698i	−0.0397153	−	0.122231i
$555$	0.708904	+	5.91478i	0.0300913	+	0.251069i
$556$	−2.43702	+	3.35426i	−0.103352	+	0.142252i
$557$	18.1135			0.767493			0.383746	−	0.923439i	$-0.374634\pi$
$557$	18.1135			0.767493			0.383746	+	0.923439i	$0.374634\pi$
$558$	1.04084	+	16.6708i	0.0440624	+	0.705733i
$559$	−52.8593			−2.23571
$560$	−1.98855	+	2.73701i	−0.0840316	+	0.115660i
$561$	0.279245	+	2.32989i	0.0117897	+	0.0983682i
$562$	−3.86427	−	11.8930i	−0.163004	−	0.501676i
$563$			21.3786i			0.901002i	0.892776	+	0.450501i	$0.148755\pi$
$563$			21.3786i			0.901002i	−0.892776	+	0.450501i	$0.851245\pi$
$564$	10.6782	+	5.95941i	0.449633	+	0.250937i
$565$	2.22595	+	6.85077i	0.0936464	+	0.288214i
$566$	2.17280	+	0.705987i	0.0913298	+	0.0296748i
$567$	21.6567	+	21.4027i	0.909495	+	0.898831i
$568$	8.10796	+	5.89078i	0.340203	+	0.247172i
$569$	11.3905	+	35.0563i	0.477513	+	1.46964i	0.842538	+	0.538637i	$0.181061\pi$
$569$	11.3905	+	35.0563i	0.477513	+	1.46964i	−0.365024	+	0.930998i	$0.618939\pi$
$570$	−7.76425	+	3.59325i	−0.325208	+	0.150505i
$571$	2.73381	+	3.76277i	0.114406	+	0.157467i	0.862380	−	0.506262i	$-0.168973\pi$
$571$	2.73381	+	3.76277i	0.114406	+	0.157467i	−0.747974	+	0.663729i	$0.768973\pi$
$572$	−2.69522	−	0.875729i	−0.112693	−	0.0366161i
$573$	12.8373	−	1.53859i	0.536288	−	0.0642757i
$574$	24.3347	−	17.6802i	1.01571	−	0.737956i
$575$	2.08643	−	6.42136i	0.0870100	−	0.267789i
$576$	−2.77501	−	1.13987i	−0.115625	−	0.0474947i
$577$	8.40465	+	6.10634i	0.349890	+	0.254210i	0.748823	−	0.662770i	$-0.230619\pi$
$577$	8.40465	+	6.10634i	0.349890	+	0.254210i	−0.398933	+	0.916980i	$0.630619\pi$
$578$	10.3939	−	3.37717i	0.432327	−	0.140472i
$579$	10.9569	−	5.07078i	0.455351	−	0.210734i
$580$	−5.49315	−	1.78483i	−0.228091	−	0.0741111i
$581$	8.18990	−	25.2059i	0.339774	−	1.04572i
$582$	4.18206	−	21.1878i	0.173352	−	0.878263i
$583$	1.25139			0.0518271
$584$	−8.11058			−0.335618
$585$	−10.0073	+	11.7872i	−0.413750	+	0.487342i
$586$	1.06204	−	0.771617i	0.0438724	−	0.0318752i
$587$	−33.3471	−	24.2281i	−1.37638	−	1.00000i	−0.997208	−	0.0746772i	$-0.976207\pi$
$587$	−33.3471	−	24.2281i	−1.37638	−	1.00000i	−0.379176	−	0.925324i	$-0.623793\pi$
$588$	−3.75243	+	6.72367i	−0.154747	+	0.277280i
$589$	−27.0759	−	4.82116i	−1.11564	−	0.198652i
$590$			5.16043i			0.212452i
$591$	−20.7090	+	9.58404i	−0.851856	+	0.394235i
$592$	−2.02159	−	2.78249i	−0.0830870	−	0.114359i
$593$	12.8683	−	4.18117i	0.528438	−	0.171700i	−0.0326332	−	0.999467i	$-0.510389\pi$
$593$	12.8683	−	4.18117i	0.528438	−	0.171700i	0.561071	+	0.827767i	$0.310389\pi$
$594$	0.124791	+	2.85430i	0.00512025	+	0.117114i
$595$			8.33600i			0.341743i
$596$	−4.84287	+	1.57354i	−0.198372	+	0.0644548i
$597$	−29.7156	+	27.5502i	−1.21618	+	1.12755i
$598$	−10.7537	+	33.0965i	−0.439751	+	1.35341i
$599$	22.5419	−	31.0263i	0.921037	−	1.26770i	−0.0422169	−	0.999108i	$-0.513442\pi$
$599$	22.5419	−	31.0263i	0.921037	−	1.26770i	0.963254	−	0.268591i	$-0.0865579\pi$
$600$	−0.335402	+	1.69927i	−0.0136927	+	0.0693723i
$601$	−11.1534	+	15.3513i	−0.454956	+	0.626194i	−0.973453	−	0.228886i	$-0.926492\pi$
$601$	−11.1534	+	15.3513i	−0.454956	+	0.626194i	0.518497	+	0.855079i	$0.326492\pi$
$602$	−28.0700	+	20.3941i	−1.14405	+	0.831200i
$603$	−34.0029	+	8.26948i	−1.38470	+	0.336759i
$604$	−9.02697	−	12.4246i	−0.367302	−	0.505548i
$605$	−6.28794	−	8.65461i	−0.255641	−	0.351860i
$606$	17.7707	+	19.1674i	0.721884	+	0.778624i
$607$	11.2724	−	8.18986i	0.457532	−	0.332416i	−0.335030	−	0.942207i	$-0.608747\pi$
$607$	11.2724	−	8.18986i	0.457532	−	0.332416i	0.792562	+	0.609791i	$0.208747\pi$
$608$	2.90335	−	3.99611i	0.117746	−	0.162064i
$609$	−33.2043	−	6.55388i	−1.34551	−	0.265576i
$610$	3.03873	−	4.18246i	0.123035	−	0.169343i
$611$	−11.2448	+	34.6080i	−0.454917	+	1.40009i
$612$	−7.18262	+	1.74681i	−0.290340	+	0.0706105i
$613$	−7.93230	+	2.57736i	−0.320383	+	0.104099i	−0.464793	−	0.885419i	$-0.653871\pi$
$613$	−7.93230	+	2.57736i	−0.320383	+	0.104099i	0.144411	+	0.989518i	$0.453871\pi$
$614$		−	4.58902i		−	0.185198i
$615$	7.50477	−	13.4472i	0.302621	−	0.542243i
$616$	−1.76912	+	0.574822i	−0.0712799	+	0.0231602i
$617$	−12.8922	−	17.7446i	−0.519021	−	0.714371i	0.466387	−	0.884581i	$-0.345556\pi$
$617$	−12.8922	−	17.7446i	−0.519021	−	0.714371i	−0.985408	+	0.170210i	$0.945556\pi$
$618$	3.55820	+	7.68849i	0.143132	+	0.309277i
$619$		−	40.1731i		−	1.61469i	−0.590078	−	0.807346i	$-0.700903\pi$
$619$		−	40.1731i		−	1.61469i	0.590078	−	0.807346i	$-0.299097\pi$
$620$	−4.01161	+	3.86096i	−0.161110	+	0.155060i
$621$	35.0500	−	1.53240i	1.40651	−	0.0614931i
$622$	−23.4487	−	17.0365i	−0.940207	−	0.683100i
$623$	−17.8556	+	12.9729i	−0.715370	+	0.519747i
$624$	1.72870	−	8.75822i	0.0692034	−	0.350609i
$625$	1.00000			0.0400000
$626$	−8.58436			−0.343100
$627$	−4.61503	−	0.910916i	−0.184307	−	0.0363785i
$628$	−2.28037	+	7.01827i	−0.0909968	+	0.280059i
$629$	−8.05974	−	2.61877i	−0.321363	−	0.104417i
$630$	−0.766475	+	10.1204i	−0.0305371	+	0.403206i
$631$	42.1790	−	13.7048i	1.67912	−	0.545579i	0.694379	−	0.719609i	$-0.255679\pi$
$631$	42.1790	−	13.7048i	1.67912	−	0.545579i	0.984740	+	0.174030i	$0.0556791\pi$
$632$	8.57743	+	6.23187i	0.341192	+	0.247890i
$633$	2.49453	+	20.8133i	0.0991488	+	0.827254i
$634$	0.0443480	−	0.136489i	0.00176129	−	0.00542068i
$635$	−14.6229	+	10.6242i	−0.580292	+	0.421607i
$636$	0.469105	+	3.91401i	0.0186012	+	0.155201i
$637$	−21.7914	−	7.08046i	−0.863407	−	0.280538i
$638$	−1.86667	−	2.56925i	−0.0739020	−	0.101717i
$639$	29.9801	+	2.27056i	1.18600	+	0.0898222i
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	21.2492	+	15.4385i	0.839294	+	0.609783i	0.922173	−	0.386776i	$-0.126412\pi$
$641$	21.2492	+	15.4385i	0.839294	+	0.609783i	−0.0828790	+	0.996560i	$0.526412\pi$
$642$	0.676514	+	0.729688i	0.0266999	+	0.0287985i
$643$	−7.78668	−	2.53005i	−0.307077	−	0.0997753i	0.151425	−	0.988469i	$-0.451614\pi$
$643$	−7.78668	−	2.53005i	−0.307077	−	0.0997753i	−0.458502	+	0.888693i	$0.651614\pi$
$644$	7.05864	+	21.7243i	0.278150	+	0.856056i
$645$	−8.65674	+	15.5113i	−0.340859	+	0.610758i
$646$		−	12.1708i		−	0.478854i
$647$	12.6614	+	38.9679i	0.497772	+	1.53199i	0.812591	+	0.582834i	$0.198056\pi$
$647$	12.6614	+	38.9679i	0.497772	+	1.53199i	−0.314819	+	0.949152i	$0.601944\pi$
$648$	−8.88074	+	1.46030i	−0.348868	+	0.0573662i
$649$	−1.66778	+	2.29550i	−0.0654659	+	0.0901061i
$650$	−5.15412			−0.202161
$651$	−20.6477	+	25.2608i	−0.809246	+	0.990050i
$652$	−7.64969			−0.299585
$653$	−19.2633	+	26.5136i	−0.753831	+	1.03756i	0.243871	+	0.969808i	$0.421583\pi$
$653$	−19.2633	+	26.5136i	−0.753831	+	1.03756i	−0.997702	+	0.0677516i	$0.978417\pi$
$654$	17.6858	−	2.11970i	0.691571	−	0.0828868i
$655$	1.15455	+	3.55333i	0.0451119	+	0.138840i
$656$			8.89098i			0.347134i
$657$	−20.7086	+	12.7744i	−0.807921	+	0.498377i
$658$	7.38102	+	22.7164i	0.287742	+	0.885579i
$659$	−20.6974	−	6.72500i	−0.806257	−	0.261969i	−0.123245	−	0.992376i	$-0.539330\pi$
$659$	−20.6974	−	6.72500i	−0.806257	−	0.261969i	−0.683012	+	0.730407i	$0.739330\pi$
$660$	−0.698374	+	0.647482i	−0.0271842	+	0.0252032i
$661$	−33.2742	−	24.1752i	−1.29422	−	0.940304i	−0.294337	−	0.955702i	$-0.595099\pi$
$661$	−33.2742	−	24.1752i	−1.29422	−	0.940304i	−0.999881	+	0.0153974i	$0.995099\pi$
$662$	−8.60330	−	26.4782i	−0.334377	−	1.02911i
$663$	−9.23851	−	19.9624i	−0.358794	−	0.775276i
$664$	4.60465	+	6.33776i	0.178695	+	0.245953i
$665$	−15.8930	−	5.16393i	−0.616302	−	0.200249i
$666$	−9.54421	−	3.92041i	−0.369831	−	0.151913i
$667$	−31.5496	+	22.9221i	−1.22160	+	0.887547i
$668$	3.97502	−	12.2339i	0.153798	−	0.473342i
$669$	31.4024	−	3.76367i	1.21409	−	0.145512i
$670$	−9.43691	−	6.85632i	−0.364580	−	0.264883i
$671$	2.70342	−	0.878394i	0.104364	−	0.0339100i
$672$	−2.46108	−	5.31787i	−0.0949383	−	0.205141i
$673$	−0.652552	−	0.212027i	−0.0251540	−	0.00817305i	0.296413	−	0.955060i	$-0.404210\pi$
$673$	−0.652552	−	0.212027i	−0.0251540	−	0.00817305i	−0.321567	+	0.946887i	$0.604210\pi$
$674$	1.02732	−	3.16177i	0.0395709	−	0.121787i
$675$	1.82002	+	4.86698i	0.0700526	+	0.187330i
$676$	13.5649			0.521729
$677$	17.8770			0.687069			0.343535	−	0.939140i	$-0.388376\pi$
$677$	17.8770			0.687069			0.343535	+	0.939140i	$0.388376\pi$
$678$	−12.2404	−	2.41601i	−0.470088	−	0.0927862i
$679$	34.1272	−	24.7949i	1.30968	−	0.951539i
$680$	−1.99341	−	1.44830i	−0.0764439	−	0.0555397i
$681$	−31.0553	−	17.3317i	−1.19004	−	0.664154i
$682$	−3.03228	+	0.420962i	−0.116112	+	0.0161195i
$683$			16.1092i			0.616402i	0.951321	+	0.308201i	$0.0997269\pi$
$683$			16.1092i			0.616402i	−0.951321	+	0.308201i	$0.900273\pi$
$684$	1.11908	−	14.7761i	0.0427890	−	0.564978i
$685$	−9.50473	−	13.0821i	−0.363157	−	0.499843i
$686$	8.21909	−	2.67054i	0.313806	−	0.101962i
$687$	−0.507903	−	0.283457i	−0.0193777	−	0.0108145i
$688$		−	10.2557i		−	0.390996i
$689$	−11.1563	+	3.62489i	−0.425020	+	0.138097i
$690$	7.95088	+	8.57582i	0.302685	+	0.326476i
$691$	1.12795	−	3.47148i	0.0429093	−	0.132061i	−0.927307	−	0.374302i	$-0.877882\pi$
$691$	1.12795	−	3.47148i	0.0429093	−	0.132061i	0.970216	+	0.242241i	$0.0778824\pi$
$692$	−8.66268	+	11.9232i	−0.329306	+	0.453250i
$693$	−3.61171	+	4.25411i	−0.137198	+	0.161600i
$694$	6.43596	−	8.85834i	0.244306	−	0.336258i
$695$	−3.35426	+	2.43702i	−0.127234	+	0.0924413i
$696$	7.33618	−	6.80158i	0.278077	−	0.257813i
$697$	12.8768	+	17.7234i	0.487743	+	0.671321i
$698$	18.6366	+	25.6511i	0.705406	+	0.970908i
$699$	19.7420	−	18.3033i	0.746710	−	0.692296i
$700$	−2.73701	+	1.98855i	−0.103449	+	0.0751602i
$701$	26.9134	−	37.0432i	1.01651	−	1.39910i	0.101883	−	0.994796i	$-0.467513\pi$
$701$	26.9134	−	37.0432i	1.01651	−	1.39910i	0.914624	−	0.404305i	$-0.132487\pi$
$702$	−9.38060	−	25.0850i	−0.354048	−	0.946773i
$703$	9.98560	−	13.7440i	0.376614	−	0.518365i
$704$	0.169909	−	0.522925i	0.00640367	−	0.0197085i
$705$	8.31401	+	8.96748i	0.313124	+	0.337735i
$706$	15.9918	−	5.19606i	0.601860	−	0.195556i
$707$			51.0537i			1.92007i
$708$	−7.80491	−	4.35586i	−0.293326	−	0.163703i
$709$	3.88522	−	1.26238i	0.145912	−	0.0474098i	−0.235150	−	0.971959i	$-0.575558\pi$
$709$	3.88522	−	1.26238i	0.145912	−	0.0474098i	0.381063	+	0.924549i	$0.375558\pi$
$710$	5.89078	+	8.10796i	0.221077	+	0.304287i
$711$	31.7160	+	2.40203i	1.18944	+	0.0900833i
$712$		−	6.52378i		−	0.244489i
$713$	5.16929	+	37.2354i	0.193591	+	1.39448i
$714$	−12.6078	−	7.03631i	−0.471835	−	0.263327i
$715$	−2.29269	−	1.66574i	−0.0857417	−	0.0622950i
$716$	−17.8422	+	12.9632i	−0.666796	+	0.484456i
$717$	−47.5638	−	9.38815i	−1.77630	−	0.350607i
$718$	28.6005			1.06736
$719$	14.1526			0.527803			0.263902	−	0.964550i	$-0.414991\pi$
$719$	14.1526			0.527803			0.263902	+	0.964550i	$0.414991\pi$
$720$	−2.28695	−	1.94161i	−0.0852297	−	0.0723595i
$721$	−5.11355	+	15.7379i	−0.190439	+	0.586110i
$722$	5.13412	+	1.66818i	0.191072	+	0.0620831i
$723$	−14.7676	−	31.9095i	−0.549212	−	1.18673i
$724$	−12.7446	+	4.14097i	−0.473649	+	0.153898i
$725$	−4.67275	−	3.39495i	−0.173542	−	0.126085i
$726$	18.3973	−	2.20497i	0.682786	−	0.0818340i
$727$	1.58149	−	4.86733i	0.0586543	−	0.180519i	−0.917437	−	0.397882i	$-0.869745\pi$
$727$	1.58149	−	4.86733i	0.0586543	−	0.180519i	0.976091	+	0.217362i	$0.0697454\pi$
$728$	14.1069	−	10.2492i	0.522835	−	0.379862i
$729$	−20.3751	+	17.7160i	−0.754632	+	0.656149i
$730$	−7.71362	−	2.50631i	−0.285494	−	0.0927626i
$731$	−14.8534	−	20.4439i	−0.549372	−	0.756145i
$732$	3.76081	+	8.12630i	0.139004	+	0.300357i
$733$	−12.1753	−	37.4717i	−0.449704	−	1.38405i	−0.877241	−	0.480049i	$-0.840619\pi$
$733$	−12.1753	−	37.4717i	−0.449704	−	1.38405i	0.427537	−	0.903998i	$-0.359381\pi$
$734$	28.1794	+	20.4735i	1.04012	+	0.755692i
$735$	−5.64650	+	5.23503i	−0.208274	+	0.193097i
$736$	−6.42136	−	2.08643i	−0.236695	−	0.0769067i
$737$	−1.98193	−	6.09974i	−0.0730052	−	0.224687i
$738$	14.0036	+	22.7012i	0.515478	+	0.835643i
$739$			39.5004i			1.45304i	0.687143	+	0.726522i	$0.258865\pi$
$739$			39.5004i			1.45304i	−0.687143	+	0.726522i	$0.741135\pi$
$740$	−1.06282	−	3.27101i	−0.0390699	−	0.120245i
$741$	43.7822	−	5.24743i	1.60838	−	0.192769i
$742$	−4.52580	+	6.22922i	−0.166147	+	0.228682i
$743$	−11.4842			−0.421315			−0.210657	−	0.977560i	$-0.567560\pi$
$743$	−11.4842			−0.421315			−0.210657	+	0.977560i	$0.567560\pi$
$744$	−2.45336	−	9.32636i	−0.0899447	−	0.341921i
$745$	−5.09209			−0.186560
$746$	−8.22470	+	11.3203i	−0.301128	+	0.414467i
$747$	21.7392	+	8.92966i	0.795395	+	0.326719i
$748$	−0.418654	−	1.28848i	−0.0153075	−	0.0471116i
$749$			1.94357i			0.0710165i
$750$	−0.844088	+	1.51245i	−0.0308217	+	0.0552270i
$751$	1.16999	+	3.60084i	0.0426934	+	0.131397i	0.970131	−	0.242580i	$-0.0779938\pi$
$751$	1.16999	+	3.60084i	0.0426934	+	0.131397i	−0.927438	+	0.373977i	$0.877994\pi$
$752$	−6.71463	−	2.18172i	−0.244857	−	0.0795590i
$753$	−28.0891	−	30.2969i	−1.02362	−	1.10408i
$754$	24.0839	+	17.4980i	0.877084	+	0.637239i
$755$	−4.74576	−	14.6059i	−0.172716	−	0.531565i
$756$	−14.6597	−	9.70176i	−0.533166	−	0.352850i
$757$	9.40665	+	12.9471i	0.341890	+	0.470572i	0.944992	−	0.327092i	$-0.106069\pi$
$757$	9.40665	+	12.9471i	0.341890	+	0.470572i	−0.603102	+	0.797664i	$0.706069\pi$
$758$	31.5518	+	10.2518i	1.14601	+	0.372362i
$759$	0.765184	+	6.38436i	0.0277744	+	0.231738i
$760$	3.99611	−	2.90335i	0.144954	−	0.105315i
$761$	0.559484	−	1.72192i	0.0202813	−	0.0624194i	−0.940404	−	0.340060i	$-0.889553\pi$
$761$	0.559484	−	1.72192i	0.0202813	−	0.0624194i	0.960685	+	0.277641i	$0.0895525\pi$
$762$	−3.72553	−	31.0842i	−0.134962	−	1.12606i
$763$	28.1474	+	20.4503i	1.01900	+	0.740349i
$764$	−7.09934	+	2.30672i	−0.256845	+	0.0834541i
$765$	−7.37087	−	0.558238i	−0.266494	−	0.0201831i
$766$	−13.1809	−	4.28275i	−0.476247	−	0.154742i
$767$	8.21907	−	25.2957i	0.296773	−	0.913375i
$768$	1.69927	+	0.335402i	0.0613170	+	0.0121028i
$769$	−9.20645			−0.331993			−0.165997	−	0.986126i	$-0.553084\pi$
$769$	−9.20645			−0.331993			−0.165997	+	0.986126i	$0.553084\pi$
$770$	−1.86016			−0.0670356
$771$	1.83757	−	9.30980i	0.0661785	−	0.335284i
$772$	−5.63929	+	4.09718i	−0.202962	+	0.147461i
$773$	−23.4286	−	17.0219i	−0.842667	−	0.612234i	0.0804471	−	0.996759i	$-0.474365\pi$
$773$	−23.4286	−	17.0219i	−0.842667	−	0.612234i	−0.923114	+	0.384525i	$0.874365\pi$
$774$	−16.1531	−	26.1858i	−0.580611	−	0.941231i
$775$	−5.00837	+	2.43233i	−0.179906	+	0.0873719i
$776$			12.4688i			0.447604i
$777$	−8.46450	−	18.2900i	−0.303662	−	0.656149i
$778$	−0.609020	−	0.838244i	−0.0218344	−	0.0300525i
$779$	−41.7672	+	13.5710i	−1.49647	+	0.486232i
$780$	4.35053	−	7.79536i	0.155774	−	0.279119i
$781$			5.51045i			0.197179i
$782$	−15.8222	+	5.14094i	−0.565800	+	0.183840i
$783$	8.01868	−	28.9211i	0.286564	−	1.03356i
$784$	1.37375	−	4.22796i	0.0490624	−	0.150999i
$785$	−4.33753	+	5.97010i	−0.154813	+	0.213082i
$786$	−6.34878	−	1.25312i	−0.226454	−	0.0446975i
$787$	−4.31484	+	5.93886i	−0.153807	+	0.211698i	−0.878966	−	0.476884i	$-0.841766\pi$
$787$	−4.31484	+	5.93886i	−0.153807	+	0.211698i	0.725159	+	0.688581i	$0.241766\pi$
$788$	10.6585	−	7.74389i	0.379695	−	0.275865i
$789$	−0.734869	−	0.792629i	−0.0261620	−	0.0282183i
$790$	6.23187	+	8.57743i	0.221720	+	0.305171i
$791$	−14.3242	−	19.7155i	−0.509309	−	0.701004i
$792$	−0.389797	−	1.60279i	−0.0138508	−	0.0569526i
$793$	−21.5569	+	15.6620i	−0.765507	+	0.556174i
$794$	9.96440	−	13.7148i	0.353623	−	0.486721i
$795$	−0.763349	+	3.86740i	−0.0270732	+	0.137163i
$796$	13.7514	−	18.9272i	0.487407	−	0.670858i
$797$	4.43336	−	13.6445i	0.157038	−	0.483312i	−0.841324	−	0.540531i	$-0.818223\pi$
$797$	4.43336	−	13.6445i	0.157038	−	0.483312i	0.998362	+	0.0572188i	$0.0182233\pi$
$798$	21.2253	−	19.6785i	0.751366	−	0.696613i
$799$	−16.5448	+	5.37573i	−0.585313	+	0.190180i
$800$		−	1.00000i		−	0.0353553i
$801$	−10.2751	−	16.6571i	−0.363055	−	0.588549i
$802$	−3.15796	+	1.02608i	−0.111511	+	0.0362322i
$803$	−2.62122	−	3.60780i	−0.0925009	−	0.127317i
$804$	18.3354	−	8.48555i	0.646641	−	0.299262i
$805$			22.8423i			0.805084i
$806$	25.8137	−	12.5365i	0.909250	−	0.441580i
$807$	−13.0854	+	23.4467i	−0.460629	+	0.825364i
$808$	−12.2086	−	8.87009i	−0.429498	−	0.312049i
$809$	22.9262	−	16.6569i	0.806044	−	0.585625i	−0.106637	−	0.994298i	$-0.534008\pi$
$809$	22.9262	−	16.6569i	0.806044	−	0.585625i	0.912681	+	0.408673i	$0.134008\pi$
$810$	−8.89734	−	1.35547i	−0.312621	−	0.0476263i
$811$	−31.3482			−1.10079			−0.550393	−	0.834906i	$-0.685522\pi$
$811$	−31.3482			−1.10079			−0.550393	+	0.834906i	$0.685522\pi$
$812$	19.5404			0.685733
$813$	−6.91920	+	35.0552i	−0.242667	+	1.22944i
$814$	0.584374	−	1.79852i	0.0204823	−	0.0630380i
$815$	−7.27529	−	2.36388i	−0.254842	−	0.0828032i
$816$	3.87310	−	1.79245i	0.135586	−	0.0627483i
$817$	48.1785	−	15.6541i	1.68555	−	0.547669i
$818$	3.02795	+	2.19993i	0.105870	+	0.0769189i
$819$	19.8760	−	48.3880i	0.694524	−	1.69081i
$820$	−2.74746	+	8.45582i	−0.0959456	+	0.295290i
$821$	−23.5910	+	17.1399i	−0.823331	+	0.598185i	−0.917665	−	0.397355i	$-0.869928\pi$
$821$	−23.5910	+	17.1399i	−0.823331	+	0.598185i	0.0943334	+	0.995541i	$0.469928\pi$
$822$	27.8089	−	3.33298i	0.969949	−	0.116251i
$823$	−46.2285	−	15.0206i	−1.61142	−	0.523584i	−0.641528	−	0.767100i	$-0.721699\pi$
$823$	−46.2285	−	15.0206i	−1.61142	−	0.523584i	−0.969897	+	0.243516i	$0.921699\pi$
$824$	−2.87502	−	3.95712i	−0.100156	−	0.137853i
$825$	−0.864276	+	0.399982i	−0.0300902	+	0.0139256i
$826$	−5.39494	−	16.6039i	−0.187714	−	0.577724i
$827$	−6.28220	−	4.56429i	−0.218454	−	0.158716i	0.473177	−	0.880968i	$-0.343107\pi$
$827$	−6.28220	−	4.56429i	−0.218454	−	0.158716i	−0.691630	+	0.722252i	$0.743107\pi$
$828$	−19.6818	+	4.78659i	−0.683989	+	0.166346i
$829$	−30.7049	−	9.97663i	−1.06643	−	0.346503i	−0.277331	−	0.960774i	$-0.589450\pi$
$829$	−30.7049	−	9.97663i	−1.06643	−	0.346503i	−0.789094	+	0.614272i	$0.789450\pi$
$830$	2.42081	+	7.45048i	0.0840275	+	0.258610i
$831$	4.57522	+	2.55339i	0.158713	+	0.0885763i
$832$			5.15412i			0.178687i
$833$	−3.38490	−	10.4177i	−0.117280	−	0.360951i
$834$	−0.854578	−	7.13022i	−0.0295916	−	0.246899i
$835$	7.56094	−	10.4067i	0.261657	−	0.360140i
$836$	2.71590			0.0939312
$837$	−20.9535	−	19.9488i	−0.724257	−	0.689530i
$838$	7.31719			0.252768
$839$	−10.7687	+	14.8218i	−0.371775	+	0.511705i	−0.953382	−	0.301765i	$-0.902424\pi$
$839$	−10.7687	+	14.8218i	−0.371775	+	0.511705i	0.581607	+	0.813470i	$0.302424\pi$
$840$	−0.697317	−	5.81811i	−0.0240597	−	0.200744i
$841$	1.34741	+	4.14690i	0.0464624	+	0.142996i
$842$			30.1629i			1.03948i
$843$	18.9133	+	10.5554i	0.651409	+	0.363546i
$844$	−3.73990	−	11.5102i	−0.128733	−	0.396198i
$845$	12.9010	+	4.19180i	0.443809	+	0.144202i
$846$	−20.5807	+	5.00520i	−0.707577	+	0.172082i
$847$	29.2796	+	21.2729i	1.00606	+	0.730945i
$848$	−0.703300	−	2.16453i	−0.0241514	−	0.0743304i
$849$	−3.59115	+	1.66197i	−0.123248	+	0.0570385i
$850$	−1.44830	−	1.99341i	−0.0496762	−	0.0683735i
$851$	−22.0853	−	7.17594i	−0.757073	−	0.245988i
$852$	−17.2353	+	2.06570i	−0.590470	+	0.0707696i
$853$	−14.0430	+	10.2028i	−0.480823	+	0.349339i	−0.801644	−	0.597801i	$-0.796041\pi$
$853$	−14.0430	+	10.2028i	−0.480823	+	0.349339i	0.320821	+	0.947140i	$0.396041\pi$
$854$	−5.40473	+	16.6341i	−0.184946	+	0.569206i
$855$	5.63037	−	13.7071i	0.192554	−	0.468772i
$856$	−0.464772	−	0.337677i	−0.0158856	−	0.0115415i
$857$	4.70310	−	1.52813i	0.160655	−	0.0521999i	−0.227585	−	0.973758i	$-0.573083\pi$
$857$	4.70310	−	1.52813i	0.160655	−	0.0521999i	0.388240	+	0.921558i	$0.373083\pi$
$858$	4.45458	−	2.06156i	0.152077	−	0.0703804i
$859$	−39.4883	−	12.8305i	−1.34732	−	0.437772i	−0.455532	−	0.890219i	$-0.650551\pi$
$859$	−39.4883	−	12.8305i	−1.34732	−	0.437772i	−0.891791	+	0.452447i	$0.850551\pi$
$860$	3.16920	−	9.75378i	0.108069	−	0.332601i
$861$	−10.0886	+	51.1127i	−0.343820	+	1.74192i
$862$	11.1446			0.379585
$863$	−29.8281			−1.01536			−0.507679	−	0.861546i	$-0.669497\pi$
$863$	−29.8281			−1.01536			−0.507679	+	0.861546i	$0.669497\pi$
$864$	4.86698	−	1.82002i	0.165578	−	0.0619183i
$865$	−11.9232	+	8.66268i	−0.405399	+	0.294540i
$866$	5.77757	+	4.19765i	0.196330	+	0.142642i
$867$	−9.22482	+	16.5292i	−0.313291	+	0.561361i
$868$	8.87112	−	16.6167i	0.301105	−	0.564008i
$869$			5.82952i			0.197753i
$870$	9.07892	−	4.20168i	0.307804	−	0.142450i
$871$	35.3383	+	48.6390i	1.19739	+	1.64807i
$872$	−9.78067	+	3.17793i	−0.331215	+	0.107618i
$873$	19.6388	+	31.8364i	0.664671	+	1.07750i
$874$		−	33.3504i		−	1.12809i
$875$	−3.21754	+	1.04544i	−0.108773	+	0.0353424i
$876$	10.3016	−	9.55095i	0.348060	−	0.322697i
$877$	8.51676	−	26.2119i	0.287590	−	0.885112i	−0.698020	−	0.716078i	$-0.745935\pi$
$877$	8.51676	−	26.2119i	0.287590	−	0.885112i	0.985610	−	0.169034i	$-0.0540647\pi$
$878$	−17.7579	+	24.4416i	−0.599300	+	0.824865i
$879$	−0.440299	+	2.23072i	−0.0148509	+	0.0752402i
$880$	0.323185	−	0.444827i	0.0108946	−	0.0149951i
$881$	34.6806	−	25.1969i	1.16842	−	0.848907i	0.177601	−	0.984103i	$-0.443166\pi$
$881$	34.6806	−	25.1969i	1.16842	−	0.848907i	0.990819	+	0.135196i	$0.0431664\pi$
$882$	−3.15159	−	12.9589i	−0.106120	−	0.436349i
$883$	7.69172	+	10.5867i	0.258847	+	0.356272i	0.918585	−	0.395223i	$-0.129333\pi$
$883$	7.69172	+	10.5867i	0.258847	+	0.356272i	−0.659738	+	0.751496i	$0.729333\pi$
$884$	7.46470	+	10.2743i	0.251065	+	0.345561i
$885$	−6.07688	−	6.55452i	−0.204272	−	0.220328i
$886$	−2.73779	+	1.98912i	−0.0919780	+	0.0668259i
$887$	−30.2306	+	41.6088i	−1.01504	+	1.39709i	−0.0994220	+	0.995045i	$0.531699\pi$
$887$	−30.2306	+	41.6088i	−1.01504	+	1.39709i	−0.915621	+	0.402042i	$0.868301\pi$
$888$	5.84436	+	1.15356i	0.196124	+	0.0387110i
$889$	35.9429	−	49.4711i	1.20549	−	1.65921i
$890$	2.01596	−	6.20448i	0.0675751	−	0.207975i
$891$	−3.51971	−	3.47844i	−0.117915	−	0.116532i
$892$	−17.3662	+	5.64263i	−0.581464	+	0.188929i
$893$		−	34.8735i		−	1.16700i
$894$	4.29817	−	7.70155i	0.143752	−	0.257578i
$895$	−20.9748	+	6.81513i	−0.701111	+	0.227805i
$896$	1.98855	+	2.73701i	0.0664328	+	0.0914370i
$897$	−25.3153	−	54.7009i	−0.845253	−	1.82641i
$898$		−	22.6166i		−	0.754727i
$899$	31.6605	+	5.63749i	1.05594	+	0.188021i
$900$	−1.57503	−	2.55329i	−0.0525010	−	0.0851096i
$901$	−4.53686	−	3.29622i	−0.151145	−	0.109813i
$902$	−3.95494	+	2.87343i	−0.131685	+	0.0956749i
$903$	11.6372	−	58.9585i	0.387263	−	1.96202i
$904$	7.20332			0.239579
$905$	−13.4005			−0.445447
$906$	26.0966	+	5.15096i	0.867003	+	0.171129i
$907$	−11.5988	+	35.6975i	−0.385133	+	1.18532i	0.551251	+	0.834339i	$0.314151\pi$
$907$	−11.5988	+	35.6975i	−0.385133	+	1.18532i	−0.936384	+	0.350978i	$0.885849\pi$
$908$	19.5281	+	6.34507i	0.648064	+	0.210569i
$909$	−45.1428	−	3.41892i	−1.49729	−	0.113398i
$910$	16.5836	−	5.38834i	0.549741	−	0.178622i
$911$	4.36433	+	3.17087i	0.144597	+	0.105056i	0.657732	−	0.753252i	$-0.271516\pi$
$911$	4.36433	+	3.17087i	0.144597	+	0.105056i	−0.513135	+	0.858308i	$0.671516\pi$
$912$	1.01810	+	8.49461i	0.0337128	+	0.281285i
$913$	−1.33105	+	4.09654i	−0.0440512	+	0.135576i
$914$	26.4609	−	19.2250i	0.875248	−	0.635905i
$915$	1.06558	+	8.89073i	0.0352270	+	0.293918i
$916$	0.319378	+	0.103772i	0.0105526	+	0.00342873i
$917$	−7.42961	−	10.2260i	−0.245347	−	0.337692i
$918$	7.06597	−	10.6769i	0.233212	−	0.352390i
$919$	−11.8809	−	36.5658i	−0.391916	−	1.20619i	−0.931337	−	0.364158i	$-0.881357\pi$
$919$	−11.8809	−	36.5658i	−0.391916	−	1.20619i	0.539421	−	0.842036i	$-0.318643\pi$
$920$	−5.46234	−	3.96862i	−0.180088	−	0.130842i
$921$	5.40399	+	5.82874i	0.178067	+	0.192063i
$922$	−11.6243	−	3.77695i	−0.382825	−	0.124387i
$923$	−15.9621	−	49.1264i	−0.525400	−	1.61702i
$924$	1.57014	−	2.81341i	0.0516539	−	0.0925544i
$925$		−	3.43934i		−	0.113085i
$926$	−12.0002	−	36.9328i	−0.394351	−	1.21369i
$927$	−13.5733	−	5.57543i	−0.445807	−	0.183121i
$928$	−3.39495	+	4.67275i	−0.111445	+	0.153391i
$929$	22.3096			0.731954			0.365977	−	0.930624i	$-0.380735\pi$
$929$	22.3096			0.731954			0.365977	+	0.930624i	$0.380735\pi$
$930$	0.548716	−	9.62803i	0.0179931	−	0.315715i
$931$	21.9586			0.719664
$932$	−9.13597	+	12.5746i	−0.299258	+	0.411894i
$933$	49.8453	−	5.97411i	1.63186	−	0.195584i
$934$	11.4205	+	35.1487i	0.373690	+	1.15010i
$935$		−	1.35479i		−	0.0443064i
$936$	8.11790	+	13.1599i	0.265342	+	0.430146i
$937$	13.2024	+	40.6328i	0.431304	+	1.32742i	0.896827	+	0.442381i	$0.145866\pi$
$937$	13.2024	+	40.6328i	0.431304	+	1.32742i	−0.465523	+	0.885036i	$0.654134\pi$
$938$	37.5316	+	12.1947i	1.22545	+	0.398172i
$939$	10.9034	−	10.1089i	0.355820	−	0.329890i
$940$	−5.71181	−	4.14987i	−0.186299	−	0.135354i
$941$	−17.5949	−	54.1516i	−0.573578	−	1.76529i	−0.640972	−	0.767565i	$-0.721468\pi$
$941$	−17.5949	−	54.1516i	−0.573578	−	1.76529i	0.0673937	−	0.997726i	$-0.478532\pi$
$942$	−5.36824	−	11.5996i	−0.174907	−	0.377935i
$943$	35.2849	+	48.5655i	1.14903	+	1.58151i
$944$	4.90786	+	1.59466i	0.159737	+	0.0519018i
$945$	−10.9441	−	13.7570i	−0.356013	−	0.447515i
$946$	4.56202	−	3.31450i	0.148324	−	0.107764i
$947$	−8.92758	+	27.4763i	−0.290107	+	0.892858i	0.694714	+	0.719286i	$0.255531\pi$
$947$	−8.92758	+	27.4763i	−0.290107	+	0.892858i	−0.984821	+	0.173572i	$0.944469\pi$
$948$	−18.2332	+	2.18530i	−0.592187	+	0.0709753i
$949$	33.8193	+	24.5711i	1.09782	+	0.797613i
$950$	4.69771	−	1.52638i	0.152414	−	0.0495223i
$951$	0.104400	+	0.225586i	0.00338540	+	0.00731511i
$952$	7.92800	+	2.57596i	0.256948	+	0.0834875i
$953$	7.67618	−	23.6248i	0.248656	−	0.765284i	−0.746358	−	0.665545i	$-0.768199\pi$
$953$	7.67618	−	23.6248i	0.248656	−	0.765284i	0.995014	−	0.0997390i	$-0.0318008\pi$
$954$	−5.20494	−	4.41896i	−0.168516	−	0.143069i
$955$	−7.46469			−0.241552
$956$	27.9908			0.905287
$957$	5.39647	+	1.06516i	0.174443	+	0.0344316i
$958$	21.7060	−	15.7703i	0.701288	−	0.509515i
$959$	44.2585	+	32.1557i	1.42918	+	1.03836i
$960$	1.51245	+	0.844088i	0.0488142	+	0.0272428i
$961$	19.1675	−	24.3640i	0.618307	−	0.785936i
$962$			17.7268i			0.571534i
$963$	−1.71855	−	0.130155i	−0.0553794	−	0.00419420i
$964$	11.9322	+	16.4232i	0.384310	+	0.528957i
$965$	−6.62938	+	2.15402i	−0.213407	+	0.0693403i
$966$	−34.5478	−	19.2809i	−1.11156	−	0.620352i
$967$		−	29.2209i		−	0.939679i	−0.882752	−	0.469840i	$-0.844312\pi$
$967$		−	29.2209i		−	0.939679i	0.882752	−	0.469840i	$-0.155688\pi$
$968$	−10.1741	+	3.30577i	−0.327008	+	0.106251i
$969$	14.3322	+	15.4587i	0.460418	+	0.496606i
$970$	−3.85307	+	11.8585i	−0.123715	+	0.380755i
$971$	17.8721	−	24.5989i	0.573544	−	0.789415i	−0.419425	−	0.907790i	$-0.637768\pi$
$971$	17.8721	−	24.5989i	0.573544	−	0.789415i	0.992969	+	0.118375i	$0.0377684\pi$
$972$	9.56022	−	12.3127i	0.306644	−	0.394929i
$973$	8.24473	−	11.3479i	0.264314	−	0.363797i
$974$	−17.0190	+	12.3650i	−0.545323	+	0.396200i
$975$	6.54650	−	6.06944i	0.209656	−	0.194378i
$976$	−3.03873	−	4.18246i	−0.0972675	−	0.133877i
$977$	−29.4297	−	40.5065i	−0.941540	−	1.29592i	−0.955184	−	0.296012i	$-0.904343\pi$
$977$	−29.4297	−	40.5065i	−0.941540	−	1.29592i	0.0136442	−	0.999907i	$-0.495657\pi$
$978$	9.71625	−	9.00820i	0.310691	−	0.288051i
$979$	2.90195	−	2.10839i	0.0927467	−	0.0673844i
$980$	2.61302	−	3.59652i	0.0834699	−	0.114887i
$981$	−19.9675	+	23.5190i	−0.637514	+	0.750905i
$982$	−4.86673	+	6.69848i	−0.155304	+	0.213757i
$983$	0.120320	−	0.370307i	0.00383762	−	0.0118110i	−0.949119	−	0.314917i	$-0.898023\pi$
$983$	0.120320	−	0.370307i	0.00383762	−	0.0118110i	0.952957	+	0.303106i	$0.0980235\pi$
$984$	−10.4699	−	11.2929i	−0.333769	−	0.360003i
$985$	12.5299	−	4.07120i	0.399235	−	0.129719i
$986$			14.2316i			0.453227i
$987$	−36.1257	−	20.1614i	−1.14989	−	0.641746i
$988$	−24.2126	+	7.86714i	−0.770304	+	0.250287i
$989$	−40.7011	−	56.0203i	−1.29422	−	1.78134i
$990$	0.124570	−	1.64480i	0.00395909	−	0.0522751i
$991$		−	15.6203i		−	0.496196i	−0.968735	−	0.248098i	$-0.920195\pi$
$991$		−	15.6203i		−	0.496196i	0.968735	−	0.248098i	$-0.0798054\pi$
$992$	2.43233	+	5.00837i	0.0772266	+	0.159016i
$993$	42.1080	+	23.5001i	1.33626	+	0.745755i
$994$	−27.4303	−	19.9293i	−0.870035	−	0.632118i
$995$	18.9272	−	13.7514i	0.600034	−	0.435950i
$996$	−13.3119	−	2.62750i	−0.421803	−	0.0832556i
$997$	−2.25253			−0.0713384			−0.0356692	−	0.999364i	$-0.511356\pi$
$997$	−2.25253			−0.0713384			−0.0356692	+	0.999364i	$0.511356\pi$
$998$	−19.6927			−0.623362
$999$	16.7392	−	6.25967i	0.529606	−	0.198047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.v.b.401.16	yes	80
3.2	odd	2	inner	930.2.v.b.401.8	✓	80
31.15	odd	10	inner	930.2.v.b.821.8	yes	80
93.77	even	10	inner	930.2.v.b.821.16	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.v.b.401.8	✓	80	3.2	odd	2	inner
930.2.v.b.401.16	yes	80	1.1	even	1	trivial
930.2.v.b.821.8	yes	80	31.15	odd	10	inner
930.2.v.b.821.16	yes	80	93.77	even	10	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.v (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.206116 + 1.71974i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(1.51245 + 0.844088i) q^{6} +(1.04544 + 3.21754i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-2.91503 + 0.708934i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.206116 + 1.71974i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(1.51245 + 0.844088i) q^{6} +(1.04544 + 3.21754i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-2.91503 + 0.708934i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(-0.169909 - 0.522925i) q^{11} +(1.57188 - 0.727458i) q^{12} +(3.02952 + 4.16977i) q^{13} +(3.21754 + 1.04544i) q^{14} +(1.71974 - 0.206116i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.761416 + 2.34340i) q^{17} +(-1.13987 + 2.77501i) q^{18} +(-3.99611 - 2.90335i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(-5.31787 + 2.46108i) q^{21} +(-0.522925 - 0.169909i) q^{22} +(-2.08643 + 6.42136i) q^{23} +(0.335402 - 1.69927i) q^{24} -1.00000 q^{25} +5.15412 q^{26} +(-1.82002 - 4.86698i) q^{27} +(2.73701 - 1.98855i) q^{28} +(4.67275 + 3.39495i) q^{29} +(0.844088 - 1.51245i) q^{30} +(5.00837 - 2.43233i) q^{31} +1.00000i q^{32} +(0.864276 - 0.399982i) q^{33} +(1.44830 + 1.99341i) q^{34} +(3.21754 - 1.04544i) q^{35} +(1.57503 + 2.55329i) q^{36} +3.43934i q^{37} +(-4.69771 + 1.52638i) q^{38} +(-6.54650 + 6.06944i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(5.22598 - 7.19295i) q^{41} +(-1.13471 + 5.74883i) q^{42} +(-6.02817 + 8.29706i) q^{43} +(-0.444827 + 0.323185i) q^{44} +(0.708934 + 2.91503i) q^{45} +(3.96862 + 5.46234i) q^{46} +(4.14987 + 5.71181i) q^{47} +(-1.17759 - 1.27015i) q^{48} +(-3.59652 + 2.61302i) q^{49} +(-0.587785 + 0.809017i) q^{50} +(-4.18698 - 0.826427i) q^{51} +(3.02952 - 4.16977i) q^{52} +(-0.703300 + 2.16453i) q^{53} +(-5.00725 - 1.38831i) q^{54} +(-0.522925 + 0.169909i) q^{55} -3.38313i q^{56} +(4.16934 - 7.47071i) q^{57} +(5.49315 - 1.78483i) q^{58} +(-3.03322 - 4.17488i) q^{59} +(-0.727458 - 1.57188i) q^{60} +5.16980i q^{61} +(0.976048 - 5.48154i) q^{62} +(-5.32853 - 8.63809i) q^{63} +(0.809017 + 0.587785i) q^{64} +(4.16977 - 3.02952i) q^{65} +(0.184416 - 0.934317i) q^{66} +11.6647 q^{67} +2.46399 q^{68} +(-11.4731 - 2.26457i) q^{69} +(1.04544 - 3.21754i) q^{70} +(-9.53148 - 3.09697i) q^{71} +(2.99143 + 0.226558i) q^{72} +(7.71362 - 2.50631i) q^{73} +(2.78249 + 2.02159i) q^{74} +(-0.206116 - 1.71974i) q^{75} +(-1.52638 + 4.69771i) q^{76} +(1.50490 - 1.09338i) q^{77} +(1.06235 + 8.86376i) q^{78} +(-10.0834 - 3.27629i) q^{79} +(0.587785 + 0.809017i) q^{80} +(7.99483 - 4.13313i) q^{81} +(-2.74746 - 8.45582i) q^{82} +(-6.33776 - 4.60465i) q^{83} +(3.98394 + 4.29707i) q^{84} +(2.34340 + 0.761416i) q^{85} +(3.16920 + 9.75378i) q^{86} +(-4.87532 + 8.73569i) q^{87} +0.549836i q^{88} +(2.01596 + 6.20448i) q^{89} +(2.77501 + 1.13987i) q^{90} +(-10.2492 + 14.1069i) q^{91} +6.75182 q^{92} +(5.21529 + 8.11176i) q^{93} +7.06018 q^{94} +(-2.90335 + 3.99611i) q^{95} +(-1.71974 + 0.206116i) q^{96} +(-3.85307 - 11.8585i) q^{97} +4.44554i q^{98} +(0.866008 + 1.40389i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9	\( 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9} - 20 q^{10} + 10 q^{13} - 20 q^{16} - 4 q^{18} - 12 q^{19} - 30 q^{21} - 10 q^{22} - 80 q^{25} + 60 q^{27} + 18 q^{28} + 8 q^{31} - 20 q^{33} + 10 q^{34} - 8 q^{36} - 46 q^{39} + 20 q^{40} + 50 q^{43} - 16 q^{45} - 10 q^{46} - 8 q^{49} - 20 q^{51} + 10 q^{52} - 10 q^{55} + 10 q^{58} + 44 q^{63} + 20 q^{64} - 10 q^{66} - 132 q^{67} - 16 q^{69} + 12 q^{70} + 4 q^{72} - 20 q^{73} - 18 q^{76} + 48 q^{78} - 120 q^{79} + 48 q^{81} - 20 q^{82} + 20 q^{84} - 136 q^{87} - 12 q^{90} - 110 q^{91} - 20 q^{93} - 28 q^{94} + 22 q^{97}+O(q^{100}) \) 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9 - 20 * q^10 + 10 * q^13 - 20 * q^16 - 4 * q^18 - 12 * q^19 - 30 * q^21 - 10 * q^22 - 80 * q^25 + 60 * q^27 + 18 * q^28 + 8 * q^31 - 20 * q^33 + 10 * q^34 - 8 * q^36 - 46 * q^39 + 20 * q^40 + 50 * q^43 - 16 * q^45 - 10 * q^46 - 8 * q^49 - 20 * q^51 + 10 * q^52 - 10 * q^55 + 10 * q^58 + 44 * q^63 + 20 * q^64 - 10 * q^66 - 132 * q^67 - 16 * q^69 + 12 * q^70 + 4 * q^72 - 20 * q^73 - 18 * q^76 + 48 * q^78 - 120 * q^79 + 48 * q^81 - 20 * q^82 + 20 * q^84 - 136 * q^87 - 12 * q^90 - 110 * q^91 - 20 * q^93 - 28 * q^94 + 22 * q^97

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