LMFDB - Embedded newform 630.2.bz.a.517.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(13,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9, 6]))

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

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

chi := DirichletCharacter("630.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bz (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			517.18
Character	$\chi$	$=$	630.517
Dual form			630.2.bz.a.223.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(1.27527 + 1.17204i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.58256 + 1.57972i) q^{5} +(-1.46217 + 0.928470i) q^{6} +(1.77300 + 1.96379i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.252632 + 2.98934i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(1.27527 + 1.17204i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.58256 + 1.57972i) q^{5} +(-1.46217 + 0.928470i) q^{6} +(1.77300 + 1.96379i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.252632 + 2.98934i) q^{9} +(-1.11630 - 1.93749i) q^{10} +(-0.980360 - 1.69803i) q^{11} +(-0.518396 - 1.65265i) q^{12} +(-5.89543 + 1.57968i) q^{13} +(-2.35576 + 1.20432i) q^{14} +(-3.86969 + 0.159746i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.02765 + 1.02765i) q^{17} +(-2.95287 - 0.529676i) q^{18} +6.70703 q^{19} +(2.16039 - 0.576799i) q^{20} +(-0.0405864 + 4.58240i) q^{21} +(1.89391 - 0.507471i) q^{22} +(-0.704852 - 2.63054i) q^{23} +(1.73051 - 0.0729933i) q^{24} +(0.00897205 - 4.99999i) q^{25} -6.10340i q^{26} +(-3.18147 + 4.10832i) q^{27} +(-0.553570 - 2.58719i) q^{28} +(-7.53914 + 4.35272i) q^{29} +(0.847246 - 3.77918i) q^{30} +(9.45126 + 5.45669i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.739943 - 3.31447i) q^{33} +(-0.726660 - 1.25861i) q^{34} +(-5.90811 - 0.306961i) q^{35} +(1.27589 - 2.71516i) q^{36} +(-5.73811 - 5.73811i) q^{37} +(-1.73591 + 6.47850i) q^{38} +(-9.36972 - 4.89518i) q^{39} +(-0.00200621 + 2.23607i) q^{40} +(4.43101 + 2.55825i) q^{41} +(-4.41575 - 1.22521i) q^{42} +(0.0823739 + 0.0220720i) q^{43} +1.96072i q^{44} +(-5.12213 - 4.33172i) q^{45} +2.72334 q^{46} +(-7.92299 - 2.12296i) q^{47} +(-0.377383 + 1.69044i) q^{48} +(-0.712929 + 6.96360i) q^{49} +(4.82730 + 1.30276i) q^{50} +(-2.51499 + 0.106083i) q^{51} +(5.89543 + 1.57968i) q^{52} +(-0.806198 + 0.806198i) q^{53} +(-3.14491 - 4.13637i) q^{54} +(4.23389 + 1.13854i) q^{55} +(2.64231 + 0.134906i) q^{56} +(8.55329 + 7.86093i) q^{57} +(-2.25314 - 8.40882i) q^{58} +(0.347500 - 0.601888i) q^{59} +(3.43112 + 1.79650i) q^{60} +(2.16932 - 1.25246i) q^{61} +(-7.71692 + 7.71692i) q^{62} +(-5.42252 + 5.79623i) q^{63} -1.00000i q^{64} +(6.83441 - 11.8131i) q^{65} +(3.01003 + 1.57258i) q^{66} +(1.00997 - 0.270620i) q^{67} +(1.40380 - 0.376147i) q^{68} +(2.18423 - 4.18077i) q^{69} +(1.82563 - 5.62735i) q^{70} +12.0505 q^{71} +(2.29242 + 1.93515i) q^{72} +(11.7937 + 11.7937i) q^{73} +(7.02773 - 4.05746i) q^{74} +(5.87165 - 6.36583i) q^{75} +(-5.80846 - 3.35352i) q^{76} +(1.59640 - 4.93583i) q^{77} +(7.15344 - 7.78349i) q^{78} +(6.21197 - 3.58649i) q^{79} +(-2.15936 - 0.580675i) q^{80} +(-8.87235 + 1.51041i) q^{81} +(-3.61791 + 3.61791i) q^{82} +(0.0195572 - 0.0729886i) q^{83} +(2.32635 - 3.94818i) q^{84} +(0.00291567 - 3.24972i) q^{85} +(-0.0426399 + 0.0738544i) q^{86} +(-14.7160 - 3.28529i) q^{87} +(-1.89391 - 0.507471i) q^{88} -9.72011 q^{89} +(5.50982 - 3.82647i) q^{90} +(-13.5548 - 8.77661i) q^{91} +(-0.704852 + 2.63054i) q^{92} +(5.65744 + 18.0360i) q^{93} +(4.10124 - 7.10356i) q^{94} +(-10.6143 + 10.5952i) q^{95} +(-1.53516 - 0.802042i) q^{96} +(7.69510 + 2.06190i) q^{97} +(-6.54180 - 2.49095i) q^{98} +(4.82833 - 3.35961i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} + 24 q^{15} + 96 q^{16} - 8 q^{18} + 8 q^{23} + 48 q^{30} - 24 q^{35} + 8 q^{36} - 44 q^{42} + 48 q^{46} + 32 q^{50} - 160 q^{53} - 4 q^{56} + 88 q^{57} + 24 q^{58} + 8 q^{60} - 48 q^{63} - 8 q^{65} + 16 q^{71} + 16 q^{72} - 16 q^{77} - 16 q^{78} - 8 q^{81} - 16 q^{86} + 8 q^{92} - 120 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) $ 192 * q + 8 * q^11 + 24 * q^15 + 96 * q^16 - 8 * q^18 + 8 * q^23 + 48 * q^30 - 24 * q^35 + 8 * q^36 - 44 * q^42 + 48 * q^46 + 32 * q^50 - 160 * q^53 - 4 * q^56 + 88 * q^57 + 24 * q^58 + 8 * q^60 - 48 * q^63 - 8 * q^65 + 16 * q^71 + 16 * q^72 - 16 * q^77 - 16 * q^78 - 8 * q^81 - 16 * q^86 + 8 * q^92 - 120 * q^93 - 128 * q^95 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	1.27527	+	1.17204i	0.736278	+	0.676679i
$3$	1.27527	+	1.17204i	0.736278	+	0.676679i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−1.58256	+	1.57972i	−0.707741	+	0.706472i
$5$	−1.58256	+	1.57972i	−0.707741	+	0.706472i
$6$	−1.46217	+	0.928470i	−0.596929	+	0.379046i
$7$	1.77300	+	1.96379i	0.670132	+	0.742242i
$7$	1.77300	+	1.96379i	0.670132	+	0.742242i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.252632	+	2.98934i	0.0842105	+	0.996448i
$10$	−1.11630	−	1.93749i	−0.353004	−	0.612689i
$11$	−0.980360	−	1.69803i	−0.295590	−	0.511976i	0.679532	−	0.733646i	$-0.262183\pi$
$11$	−0.980360	−	1.69803i	−0.295590	−	0.511976i	−0.975122	+	0.221669i	$0.928849\pi$
$12$	−0.518396	−	1.65265i	−0.149648	−	0.477080i
$13$	−5.89543	+	1.57968i	−1.63510	+	0.438123i	−0.955387	−	0.295357i	$-0.904561\pi$
$13$	−5.89543	+	1.57968i	−1.63510	+	0.438123i	−0.679711	+	0.733480i	$0.737895\pi$
$14$	−2.35576	+	1.20432i	−0.629603	+	0.321869i
$15$	−3.86969	+	0.159746i	−0.999149	+	0.0412463i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.02765	+	1.02765i	−0.249242	+	0.249242i	−0.820660	−	0.571417i	$-0.806394\pi$
$17$	−1.02765	+	1.02765i	−0.249242	+	0.249242i	0.571417	+	0.820660i	$0.306394\pi$
$18$	−2.95287	−	0.529676i	−0.695998	−	0.124846i
$19$	6.70703			1.53870			0.769350	−	0.638828i	$-0.220580\pi$
$19$	6.70703			1.53870			0.769350	+	0.638828i	$0.220580\pi$
$20$	2.16039	−	0.576799i	0.483079	−	0.128976i
$21$	−0.0405864	+	4.58240i	−0.00885668	+	0.999961i
$22$	1.89391	−	0.507471i	0.403783	−	0.108193i
$23$	−0.704852	−	2.63054i	−0.146972	−	0.548506i	−0.999660	−	0.0260856i	$-0.991696\pi$
$23$	−0.704852	−	2.63054i	−0.146972	−	0.548506i	0.852688	−	0.522421i	$-0.174971\pi$
$24$	1.73051	−	0.0729933i	0.353239	−	0.0148997i
$25$	0.00897205	−	4.99999i	0.00179441	−	0.999998i
$26$		−	6.10340i		−	1.19697i
$27$	−3.18147	+	4.10832i	−0.612273	+	0.790646i
$28$	−0.553570	−	2.58719i	−0.104615	−	0.488933i
$29$	−7.53914	+	4.35272i	−1.39998	+	0.808280i	−0.994390	−	0.105774i	$-0.966268\pi$
$29$	−7.53914	+	4.35272i	−1.39998	+	0.808280i	−0.405593	+	0.914054i	$0.632935\pi$
$30$	0.847246	−	3.77918i	0.154685	−	0.689980i
$31$	9.45126	+	5.45669i	1.69750	+	0.980050i	0.948124	+	0.317900i	$0.102978\pi$
$31$	9.45126	+	5.45669i	1.69750	+	0.980050i	0.749372	+	0.662150i	$0.230356\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	0.739943	−	3.31447i	0.128808	−	0.576976i
$34$	−0.726660	−	1.25861i	−0.124621	−	0.215850i
$35$	−5.90811	−	0.306961i	−0.998653	−	0.0518859i
$36$	1.27589	−	2.71516i	0.212648	−	0.452527i
$37$	−5.73811	−	5.73811i	−0.943340	−	0.943340i	0.0551385	−	0.998479i	$-0.482440\pi$
$37$	−5.73811	−	5.73811i	−0.943340	−	0.943340i	−0.998479	+	0.0551385i	$0.982440\pi$
$38$	−1.73591	+	6.47850i	−0.281602	+	1.05095i
$39$	−9.36972	−	4.89518i	−1.50036	−	0.783856i
$40$	−0.00200621	+	2.23607i	−0.000317210	+	0.353553i
$41$	4.43101	+	2.55825i	0.692008	+	0.399531i	0.804364	−	0.594137i	$-0.202506\pi$
$41$	4.43101	+	2.55825i	0.692008	+	0.399531i	−0.112356	+	0.993668i	$0.535840\pi$
$42$	−4.41575	−	1.22521i	−0.681365	−	0.189055i
$43$	0.0823739	+	0.0220720i	0.0125619	+	0.00336595i	0.265095	−	0.964222i	$-0.414597\pi$
$43$	0.0823739	+	0.0220720i	0.0125619	+	0.00336595i	−0.252533	+	0.967588i	$0.581264\pi$
$44$			1.96072i			0.295590i
$45$	−5.12213	−	4.33172i	−0.763562	−	0.645735i
$46$	2.72334			0.401534
$47$	−7.92299	−	2.12296i	−1.15569	−	0.309665i	−0.370445	−	0.928854i	$-0.620795\pi$
$47$	−7.92299	−	2.12296i	−1.15569	−	0.309665i	−0.785242	+	0.619189i	$0.787461\pi$
$48$	−0.377383	+	1.69044i	−0.0544706	+	0.243994i
$49$	−0.712929	+	6.96360i	−0.101847	+	0.994800i
$50$	4.82730	+	1.30276i	0.682683	+	0.184238i
$51$	−2.51499	+	0.106083i	−0.352169	+	0.0148545i
$52$	5.89543	+	1.57968i	0.817549	+	0.219062i
$53$	−0.806198	+	0.806198i	−0.110740	+	0.110740i	−0.760305	−	0.649566i	$-0.774951\pi$
$53$	−0.806198	+	0.806198i	−0.110740	+	0.110740i	0.649566	+	0.760305i	$0.274951\pi$
$54$	−3.14491	−	4.13637i	−0.427968	−	0.562889i
$55$	4.23389	+	1.13854i	0.570898	+	0.153521i
$56$	2.64231	+	0.134906i	0.353093	+	0.0180276i
$57$	8.55329	+	7.86093i	1.13291	+	1.04121i
$58$	−2.25314	−	8.40882i	−0.295851	−	1.10413i
$59$	0.347500	−	0.601888i	0.0452407	−	0.0783591i	−0.842518	−	0.538668i	$-0.818928\pi$
$59$	0.347500	−	0.601888i	0.0452407	−	0.0783591i	0.887759	+	0.460308i	$0.152261\pi$
$60$	3.43112	+	1.79650i	0.442956	+	0.231927i
$61$	2.16932	−	1.25246i	0.277753	−	0.160361i	−0.354653	−	0.934998i	$-0.615401\pi$
$61$	2.16932	−	1.25246i	0.277753	−	0.160361i	0.632406	+	0.774637i	$0.282068\pi$
$62$	−7.71692	+	7.71692i	−0.980050	+	0.980050i
$63$	−5.42252	+	5.79623i	−0.683174	+	0.730256i
$64$		−	1.00000i		−	0.125000i
$65$	6.83441	−	11.8131i	0.847704	−	1.46523i
$66$	3.01003	+	1.57258i	0.370509	+	0.193571i
$67$	1.00997	−	0.270620i	0.123387	−	0.0330615i	−0.196597	−	0.980484i	$-0.562989\pi$
$67$	1.00997	−	0.270620i	0.123387	−	0.0330615i	0.319984	+	0.947423i	$0.396322\pi$
$68$	1.40380	−	0.376147i	0.170236	−	0.0456145i
$69$	2.18423	−	4.18077i	0.262951	−	0.503306i
$70$	1.82563	−	5.62735i	0.218205	−	0.672597i
$71$	12.0505			1.43013			0.715067	−	0.699056i	$-0.246396\pi$
$71$	12.0505			1.43013			0.715067	+	0.699056i	$0.246396\pi$
$72$	2.29242	+	1.93515i	0.270165	+	0.228059i
$73$	11.7937	+	11.7937i	1.38035	+	1.38035i	0.843982	+	0.536372i	$0.180206\pi$
$73$	11.7937	+	11.7937i	1.38035	+	1.38035i	0.536372	+	0.843982i	$0.319794\pi$
$74$	7.02773	−	4.05746i	0.816957	−	0.471670i
$75$	5.87165	−	6.36583i	0.677999	−	0.735063i
$76$	−5.80846	−	3.35352i	−0.666276	−	0.384675i
$77$	1.59640	−	4.93583i	0.181926	−	0.562490i
$78$	7.15344	−	7.78349i	0.809968	−	0.881306i
$79$	6.21197	−	3.58649i	0.698902	−	0.403511i	−0.108036	−	0.994147i	$-0.534456\pi$
$79$	6.21197	−	3.58649i	0.698902	−	0.403511i	0.806938	+	0.590636i	$0.201123\pi$
$80$	−2.15936	−	0.580675i	−0.241423	−	0.0649214i
$81$	−8.87235	+	1.51041i	−0.985817	+	0.167823i
$82$	−3.61791	+	3.61791i	−0.399531	+	0.399531i
$83$	0.0195572	−	0.0729886i	0.00214669	−	0.00801154i	−0.964844	−	0.262823i	$-0.915347\pi$
$83$	0.0195572	−	0.0729886i	0.00214669	−	0.00801154i	0.966991	+	0.254811i	$0.0820133\pi$
$84$	2.32635	−	3.94818i	0.253825	−	0.430782i
$85$	0.00291567	−	3.24972i	0.000316248	−	0.352482i
$86$	−0.0426399	+	0.0738544i	−0.00459797	+	0.00796393i
$87$	−14.7160	−	3.28529i	−1.57772	−	0.352220i
$88$	−1.89391	−	0.507471i	−0.201891	−	0.0540966i
$89$	−9.72011			−1.03033			−0.515165	−	0.857091i	$-0.672269\pi$
$89$	−9.72011			−1.03033			−0.515165	+	0.857091i	$0.672269\pi$
$90$	5.50982	−	3.82647i	0.580786	−	0.403345i
$91$	−13.5548	−	8.77661i	−1.42092	−	0.920039i
$92$	−0.704852	+	2.63054i	−0.0734859	+	0.274253i
$93$	5.65744	+	18.0360i	0.586650	+	1.87025i
$94$	4.10124	−	7.10356i	0.423011	−	0.732676i
$95$	−10.6143	+	10.5952i	−1.08900	+	1.08705i
$96$	−1.53516	−	0.802042i	−0.156682	−	0.0818581i
$97$	7.69510	+	2.06190i	0.781319	+	0.209354i	0.627366	−	0.778724i	$-0.284133\pi$
$97$	7.69510	+	2.06190i	0.781319	+	0.209354i	0.153953	+	0.988078i	$0.450800\pi$
$98$	−6.54180	−	2.49095i	−0.660822	−	0.251624i
$99$	4.82833	−	3.35961i	0.485266	−	0.337653i
$100$	−2.50777	+	4.32563i	−0.250777	+	0.432563i
$101$	3.18420	−	1.83840i	0.316840	−	0.182928i	−0.333143	−	0.942876i	$-0.608109\pi$
$101$	3.18420	−	1.83840i	0.316840	−	0.182928i	0.649983	+	0.759949i	$0.274776\pi$
$102$	0.548458	−	2.45675i	0.0543055	−	0.243254i
$103$	−6.79575	+	1.82092i	−0.669606	+	0.179420i	−0.577577	−	0.816336i	$-0.696002\pi$
$103$	−6.79575	+	1.82092i	−0.669606	+	0.179420i	−0.0920284	+	0.995756i	$0.529335\pi$
$104$	−3.05170	+	5.28570i	−0.299244	+	0.518305i
$105$	−7.17467	−	7.31602i	−0.700176	−	0.713970i
$106$	−0.570068	−	0.987387i	−0.0553699	−	0.0959035i
$107$	7.76336	+	7.76336i	0.750512	+	0.750512i	0.974575	−	0.224063i	$-0.0719321\pi$
$107$	7.76336	+	7.76336i	0.750512	+	0.750512i	−0.224063	+	0.974575i	$0.571932\pi$
$108$	4.80939	−	1.96718i	0.462784	−	0.189292i
$109$			6.85755i			0.656834i	0.944533	+	0.328417i	$0.106515\pi$
$109$			6.85755i			0.656834i	−0.944533	+	0.328417i	$0.893485\pi$
$110$	−2.19556	+	3.79495i	−0.209338	+	0.361834i
$111$	−0.592335	−	14.0430i	−0.0562219	−	1.33290i
$112$	−0.814190	+	2.51736i	−0.0769337	+	0.237868i
$113$	4.86258	+	18.1474i	0.457433	+	1.70716i	0.680836	+	0.732436i	$0.261617\pi$
$113$	4.86258	+	18.1474i	0.457433	+	1.70716i	−0.223403	+	0.974726i	$0.571717\pi$
$114$	−9.80683	+	6.22728i	−0.918494	+	0.583238i
$115$	5.27099	+	3.04952i	0.491522	+	0.284369i
$116$	8.70545			0.808280
$117$	−6.21157	−	17.2244i	−0.574259	−	1.59240i
$118$	0.491439	+	0.491439i	0.0452407	+	0.0452407i
$119$	−3.84012	−	0.196062i	−0.352023	−	0.0179730i
$120$	−2.62332	+	2.84924i	−0.239476	+	0.260099i
$121$	3.57779	−	6.19691i	0.325254	−	0.563356i
$122$	0.648320	+	2.41957i	0.0586962	+	0.219057i
$123$	2.65237	+	8.45579i	0.239156	+	0.762433i
$124$	−5.45669	−	9.45126i	−0.490025	−	0.848748i
$125$	7.88439	+	7.92694i	0.705201	+	0.709007i
$126$	−4.19527	−	6.73793i	−0.373745	−	0.600262i
$127$	−2.66966	−	2.66966i	−0.236894	−	0.236894i	0.578669	−	0.815563i	$-0.303572\pi$
$127$	−2.66966	−	2.66966i	−0.236894	−	0.236894i	−0.815563	+	0.578669i	$0.803572\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	0.0791797	+	0.124694i	0.00697138	+	0.0109787i
$130$	9.64166	+	9.65897i	0.845629	+	0.847148i
$131$	13.3629	+	7.71510i	1.16753	+	0.674071i	0.953096	−	0.302668i	$-0.0978773\pi$
$131$	13.3629	+	7.71510i	1.16753	+	0.674071i	0.214430	+	0.976739i	$0.431211\pi$
$132$	−2.29805	+	2.50045i	−0.200019	+	0.217636i
$133$	11.8916	+	13.1712i	1.03113	+	1.14209i
$134$			1.04560i			0.0903257i
$135$	−1.45514	−	11.5275i	−0.125239	−	0.992127i
$136$			1.45332i			0.124621i
$137$	2.47371	−	9.23199i	0.211343	−	0.788743i	−0.776079	−	0.630636i	$-0.782794\pi$
$137$	2.47371	−	9.23199i	0.211343	−	0.788743i	0.987422	−	0.158107i	$-0.0505391\pi$
$138$	3.47299	+	3.19187i	0.295641	+	0.271710i
$139$	2.27990	−	3.94890i	0.193379	−	0.334942i	−0.752989	−	0.658033i	$-0.771389\pi$
$139$	2.27990	−	3.94890i	0.193379	−	0.334942i	0.946368	+	0.323091i	$0.104722\pi$
$140$	4.96309	+	3.21989i	0.419458	+	0.272130i
$141$	−7.61576	−	11.9934i	−0.641363	−	1.01003i
$142$	−3.11890	+	11.6399i	−0.261733	+	0.976799i
$143$	8.46198	+	8.46198i	0.707627	+	0.707627i
$144$	−2.46253	+	1.71346i	−0.205211	+	0.142788i
$145$	5.05503	−	18.7982i	0.419798	−	1.56110i
$146$	−14.4443	+	8.33944i	−1.19542	+	0.690177i
$147$	−9.07082	+	8.04489i	−0.748148	+	0.663532i
$148$	2.10030	+	7.83841i	0.172643	+	0.644313i
$149$	0.819226	+	0.472980i	0.0671136	+	0.0387481i	0.533181	−	0.846001i	$-0.320996\pi$
$149$	0.819226	+	0.472980i	0.0671136	+	0.0387481i	−0.466068	+	0.884749i	$0.654330\pi$
$150$	4.62922	+	7.31917i	0.377975	+	0.597608i
$151$	4.61115	+	7.98675i	0.375250	+	0.649953i	0.990364	−	0.138486i	$-0.0442234\pi$
$151$	4.61115	+	7.98675i	0.375250	+	0.649953i	−0.615114	+	0.788438i	$0.710890\pi$
$152$	4.74259	−	4.74259i	0.384675	−	0.384675i
$153$	−3.33162	−	2.81239i	−0.269346	−	0.227368i
$154$	4.35447	+	2.81949i	0.350893	+	0.227201i
$155$	−23.5772	+	6.29482i	−1.89377	+	0.505612i
$156$	5.66682	+	8.92421i	0.453709	+	0.714509i
$157$	−0.919000	−	3.42975i	−0.0733442	−	0.273724i	0.919509	−	0.393070i	$-0.128587\pi$
$157$	−0.919000	−	3.42975i	−0.0733442	−	0.273724i	−0.992853	+	0.119346i	$0.961920\pi$
$158$	1.85650	+	6.92856i	0.147695	+	0.551206i
$159$	−1.97302	+	0.0832223i	−0.156471	+	0.00659996i
$160$	1.11977	−	1.93549i	0.0885257	−	0.153014i
$161$	3.91613	−	6.04814i	0.308634	−	0.476660i
$162$	0.837395	−	8.96096i	0.0657920	−	0.704039i
$163$	6.79104	−	6.79104i	0.531915	−	0.531915i	−0.389227	−	0.921142i	$-0.627258\pi$
$163$	6.79104	−	6.79104i	0.531915	−	0.531915i	0.921142	+	0.389227i	$0.127258\pi$
$164$	−2.55825	−	4.43101i	−0.199765	−	0.346004i
$165$	4.06494	+	6.41425i	0.316455	+	0.499348i
$166$	0.0654398	+	0.0377817i	0.00507912	+	0.00293243i
$167$	3.02482	+	11.2888i	0.234067	+	0.873552i	0.978567	+	0.205929i	$0.0660215\pi$
$167$	3.02482	+	11.2888i	0.234067	+	0.873552i	−0.744500	+	0.667623i	$0.767312\pi$
$168$	3.21154	+	3.26894i	0.247776	+	0.252204i
$169$	21.0024	−	12.1257i	1.61557	−	0.932749i
$170$	3.13823	+	0.843906i	0.240691	+	0.0647246i
$171$	1.69441	+	20.0496i	0.129575	+	1.53323i
$172$	−0.0603019	−	0.0603019i	−0.00459797	−	0.00459797i
$173$	2.94229	−	10.9808i	0.223698	−	0.834853i	−0.759224	−	0.650830i	$-0.774421\pi$
$173$	2.94229	−	10.9808i	0.223698	−	0.834853i	0.982922	−	0.184023i	$-0.0589122\pi$
$174$	6.98213	−	13.3643i	0.529314	−	1.01314i
$175$	9.83483	−	8.84738i	0.743444	−	0.668799i
$176$	0.980360	−	1.69803i	0.0738974	−	0.127994i
$177$	1.14860	−	0.360285i	0.0863337	−	0.0270807i
$178$	2.51575	−	9.38890i	0.188563	−	0.703728i
$179$		−	4.16660i		−	0.311426i	−0.987802	−	0.155713i	$-0.950232\pi$
$179$		−	4.16660i		−	0.311426i	0.987802	−	0.155713i	$-0.0497675\pi$
$180$	2.27003	+	6.31244i	0.169198	+	0.470502i
$181$			8.28357i			0.615713i	0.951433	+	0.307856i	$0.0996117\pi$
$181$			8.28357i			0.615713i	−0.951433	+	0.307856i	$0.900388\pi$
$182$	11.9858	−	10.8213i	0.888445	−	0.802131i
$183$	4.23441	+	0.945314i	0.313017	+	0.0698797i
$184$	−2.35848	−	1.36167i	−0.173870	−	0.100384i
$185$	18.1455	+	0.0162803i	1.33408	+	0.00119695i
$186$	−18.8857	+	0.796603i	−1.38477	+	0.0584098i
$187$	2.75245	+	0.737518i	0.201279	+	0.0539327i
$188$	5.80003	+	5.80003i	0.423011	+	0.423011i
$189$	−13.7086	+	1.03633i	−0.997155	+	0.0753820i
$190$	−7.48704	−	12.9948i	−0.543167	−	0.942745i
$191$	5.18502	+	8.98072i	0.375175	+	0.649822i	0.990353	−	0.138566i	$-0.0442492\pi$
$191$	5.18502	+	8.98072i	0.375175	+	0.649822i	−0.615178	+	0.788388i	$0.710916\pi$
$192$	1.17204	−	1.27527i	0.0845849	−	0.0920347i
$193$	−4.11374	−	15.3527i	−0.296113	−	1.10511i	−0.940329	−	0.340266i	$-0.889483\pi$
$193$	−4.11374	−	15.3527i	−0.296113	−	1.10511i	0.644216	−	0.764843i	$-0.277184\pi$
$194$	−3.98328	+	6.89924i	−0.285983	+	0.495336i
$195$	22.5611	−	7.05462i	1.61564	−	0.505192i
$196$	4.09922	−	5.67419i	0.292801	−	0.405299i
$197$	7.56928	+	7.56928i	0.539289	+	0.539289i	0.923320	−	0.384031i	$-0.125464\pi$
$197$	7.56928	+	7.56928i	0.539289	+	0.539289i	−0.384031	+	0.923320i	$0.625464\pi$
$198$	1.99547	+	5.53334i	0.141812	+	0.393238i
$199$	−4.61561			−0.327192			−0.163596	−	0.986527i	$-0.552309\pi$
$199$	−4.61561			−0.327192			−0.163596	+	0.986527i	$0.552309\pi$
$200$	−3.52918	−	3.54187i	−0.249551	−	0.250448i
$201$	1.60516	+	0.838611i	0.113219	+	0.0591511i
$202$	0.951626	+	3.55152i	0.0669562	+	0.249884i
$203$	−21.9147	−	7.08788i	−1.53811	−	0.497472i
$204$	2.23108	+	1.16562i	0.156207	+	0.0816099i
$205$	−11.0536	+	2.95119i	−0.772019	+	0.206120i
$206$		−	7.03548i		−	0.490185i
$207$	7.68553	−	2.77160i	0.534181	−	0.192640i
$208$	−4.31575	−	4.31575i	−0.299244	−	0.299244i
$209$	−6.57531	−	11.3888i	−0.454823	−	0.787777i
$210$	8.92367	−	5.03667i	0.615792	−	0.347564i
$211$	−2.34571	+	4.06289i	−0.161486	+	0.279701i	−0.935402	−	0.353587i	$-0.884962\pi$
$211$	−2.34571	+	4.06289i	−0.161486	+	0.279701i	0.773916	+	0.633288i	$0.218295\pi$
$212$	1.10129	−	0.295089i	0.0756367	−	0.0202668i
$213$	15.3677	+	14.1237i	1.05298	+	0.967742i
$214$	−9.50813	+	5.48952i	−0.649962	+	0.375256i
$215$	−0.165229	+	0.0951974i	−0.0112685	+	0.00649241i
$216$	0.655384	+	5.15466i	0.0445932	+	0.350730i
$217$	6.04132	+	28.2350i	0.410112	+	1.91672i
$218$	−6.62388	−	1.77486i	−0.448626	−	0.120209i
$219$	1.21745	+	28.8630i	0.0822674	+	1.95038i
$220$	−3.09739	−	3.10295i	−0.208826	−	0.209201i
$221$	4.43509	−	7.68181i	0.298337	−	0.516734i
$222$	13.7178	+	3.06244i	0.920677	+	0.205537i
$223$	−4.89714	+	18.2764i	−0.327937	+	1.22388i	0.583390	+	0.812192i	$0.301726\pi$
$223$	−4.89714	+	18.2764i	−0.327937	+	1.22388i	−0.911326	+	0.411684i	$0.864941\pi$
$224$	−2.22085	−	1.43799i	−0.148387	−	0.0960796i
$225$	14.9490	−	1.23634i	0.996597	−	0.0824223i
$226$	−18.7876			−1.24973
$227$	−17.1211	−	4.58759i	−1.13637	−	0.304489i	−0.358879	−	0.933384i	$-0.616841\pi$
$227$	−17.1211	−	4.58759i	−1.13637	−	0.304489i	−0.777490	+	0.628895i	$0.783508\pi$
$228$	−3.47690	−	11.0844i	−0.230263	−	0.734083i
$229$	0.0252880	−	0.0438001i	0.00167108	−	0.00289439i	−0.865189	−	0.501446i	$-0.832801\pi$
$229$	0.0252880	−	0.0438001i	0.00167108	−	0.00289439i	0.866860	+	0.498552i	$0.166135\pi$
$230$	−4.30984	+	4.30211i	−0.284182	+	0.283673i
$231$	7.82085	−	4.42348i	0.514574	−	0.291044i
$232$	−2.25314	+	8.40882i	−0.147926	+	0.552066i
$233$	19.5066	−	19.5066i	1.27792	−	1.27792i	0.336087	−	0.941831i	$-0.390896\pi$
$233$	19.5066	−	19.5066i	1.27792	−	1.27792i	0.941831	−	0.336087i	$-0.109104\pi$
$234$	18.2452	−	1.54191i	1.19272	−	0.100798i
$235$	15.8923	−	9.15640i	1.03670	−	0.597298i
$236$	−0.601888	+	0.347500i	−0.0391796	+	0.0226203i
$237$	12.1255	+	2.70696i	0.787634	+	0.175836i
$238$	1.18328	−	3.65853i	0.0767005	−	0.237147i
$239$	−9.79417	−	5.65467i	−0.633532	−	0.365770i	0.148586	−	0.988899i	$-0.452528\pi$
$239$	−9.79417	−	5.65467i	−0.633532	−	0.365770i	−0.782119	+	0.623129i	$0.785861\pi$
$240$	−2.07319	−	3.27137i	−0.133824	−	0.211166i
$241$	−7.27293	+	4.19903i	−0.468490	+	0.270483i	−0.715608	−	0.698503i	$-0.753850\pi$
$241$	−7.27293	+	4.19903i	−0.468490	+	0.270483i	0.247117	+	0.968986i	$0.420517\pi$
$242$	5.05976	+	5.05976i	0.325254	+	0.325254i
$243$	−13.0849	−	8.47260i	−0.839398	−	0.543518i
$244$	−2.50492			−0.160361
$245$	−9.87228	−	12.1465i	−0.630717	−	0.776013i
$246$	−8.85415	+	0.373469i	−0.564520	+	0.0238115i
$247$	−39.5409	+	10.5949i	−2.51592	+	0.674140i
$248$	10.5415	−	2.82459i	0.669386	−	0.179362i
$249$	0.110487	−	0.0701584i	0.00700180	−	0.00444610i
$250$	−9.69747	+	5.56409i	−0.613322	+	0.351904i
$251$		−	14.8003i		−	0.934186i	−0.884208	−	0.467093i	$-0.845301\pi$
$251$		−	14.8003i		−	0.934186i	0.884208	−	0.467093i	$-0.154699\pi$
$252$	7.59416	−	2.30842i	0.478387	−	0.145417i
$253$	−3.77574	+	3.77574i	−0.237379	+	0.237379i
$254$	3.26965	−	1.88773i	0.205156	−	0.118447i
$255$	3.81253	−	4.14085i	0.238750	−	0.259310i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.83506	−	14.3126i	−0.239224	−	0.892798i	−0.976199	−	0.216877i	$-0.930413\pi$
$257$	−3.83506	−	14.3126i	−0.239224	−	0.892798i	0.736974	−	0.675921i	$-0.236254\pi$
$258$	−0.140938	+	0.0442086i	−0.00877441	+	0.00275231i
$259$	1.09476	−	21.4421i	0.0680248	−	1.33235i
$260$	−11.8253	+	6.81320i	−0.733374	+	0.422537i
$261$	−14.9164	−	21.4374i	−0.923303	−	1.32694i
$262$	−10.9108	+	10.9108i	−0.674071	+	0.674071i
$263$	6.60977	+	1.77108i	0.407576	+	0.109210i	0.456781	−	0.889579i	$-0.349002\pi$
$263$	6.60977	+	1.77108i	0.407576	+	0.109210i	−0.0492054	+	0.998789i	$0.515669\pi$
$264$	−1.82047	−	2.86691i	−0.112042	−	0.176446i
$265$	0.00228736	−	2.54942i	0.000140511	−	0.156610i
$266$	−15.8002	+	8.07743i	−0.968770	+	0.495259i
$267$	−12.3958	−	11.3924i	−0.758609	−	0.697202i
$268$	−1.00997	−	0.270620i	−0.0616936	−	0.0165307i
$269$	−4.26401			−0.259981			−0.129991	−	0.991515i	$-0.541495\pi$
$269$	−4.26401			−0.259981			−0.129991	+	0.991515i	$0.541495\pi$
$270$	11.5113	+	1.57797i	0.700555	+	0.0960322i
$271$		−	15.6227i		−	0.949010i	−0.880253	−	0.474505i	$-0.842627\pi$
$271$		−	15.6227i		−	0.949010i	0.880253	−	0.474505i	$-0.157373\pi$
$272$	−1.40380	−	0.376147i	−0.0851178	−	0.0228072i
$273$	−6.99943	−	27.0793i	−0.423624	−	1.63891i
$274$	8.27718	+	4.77883i	0.500043	+	0.288700i
$275$	−8.49895	+	4.88656i	−0.512506	+	0.294670i
$276$	−3.98199	+	2.52854i	−0.239687	+	0.152200i
$277$	0.301477	−	1.12513i	0.0181140	−	0.0676023i	−0.956277	−	0.292462i	$-0.905526\pi$
$277$	0.301477	−	1.12513i	0.0181140	−	0.0676023i	0.974391	+	0.224859i	$0.0721923\pi$
$278$	3.22427	+	3.22427i	0.193379	+	0.193379i
$279$	−13.9242	+	29.6316i	−0.833622	+	1.77400i
$280$	−4.39472	+	3.96061i	−0.262635	+	0.236692i
$281$	−7.42502	−	12.8605i	−0.442940	−	0.767194i	0.554966	−	0.831873i	$-0.312731\pi$
$281$	−7.42502	−	12.8605i	−0.442940	−	0.767194i	−0.997906	+	0.0646785i	$0.979398\pi$
$282$	13.5559	−	4.25213i	0.807240	−	0.253211i
$283$	−17.7265	+	4.74981i	−1.05373	+	0.282347i	−0.743793	−	0.668410i	$-0.766975\pi$
$283$	−17.7265	+	4.74981i	−1.05373	+	0.282347i	−0.309939	+	0.950756i	$0.600309\pi$
$284$	−10.4361	−	6.02526i	−0.619266	−	0.357533i
$285$	−25.9541	+	1.07142i	−1.53739	+	0.0634656i
$286$	−10.3638	+	5.98353i	−0.612823	+	0.353813i
$287$	2.83234	+	13.2373i	0.167188	+	0.781376i
$288$	−1.01772	−	2.82210i	−0.0599699	−	0.166294i
$289$			14.8879i			0.875757i
$290$	16.8493	+	9.74811i	0.989424	+	0.572429i
$291$	7.39671	+	11.6485i	0.433603	+	0.682845i
$292$	−4.31681	−	16.1106i	−0.252622	−	0.942799i
$293$	5.23788	−	1.40349i	0.306000	−	0.0819925i	−0.102552	−	0.994728i	$-0.532701\pi$
$293$	5.23788	−	1.40349i	0.306000	−	0.0819925i	0.408552	+	0.912735i	$0.366034\pi$
$294$	−5.42307	−	10.8439i	−0.316280	−	0.632429i
$295$	0.400875	+	1.50147i	0.0233399	+	0.0874192i
$296$	−8.11492			−0.471670
$297$	10.0950	+	1.37460i	0.585774	+	0.0797625i
$298$	−0.668895	+	0.668895i	−0.0387481	+	0.0387481i
$299$	8.31081	+	14.3947i	0.480627	+	0.832470i
$300$	−8.26791	+	2.57715i	−0.477348	+	0.148792i
$301$	0.102704	+	0.200899i	0.00591978	+	0.0115796i
$302$	−8.90806	+	2.38691i	−0.512601	+	0.137351i
$303$	6.21541	+	1.38756i	0.357066	+	0.0797134i
$304$	3.35352	+	5.80846i	0.192337	+	0.333138i
$305$	−1.45454	+	5.40901i	−0.0832868	+	0.309719i
$306$	3.57885	−	2.49020i	0.204589	−	0.142355i
$307$	8.53756	−	8.53756i	0.487264	−	0.487264i	−0.420177	−	0.907442i	$-0.638032\pi$
$307$	8.53756	−	8.53756i	0.487264	−	0.487264i	0.907442	+	0.420177i	$0.138032\pi$
$308$	−3.85044	+	3.47636i	−0.219399	+	0.198084i
$309$	−10.8006	−	5.64275i	−0.614426	−	0.321005i
$310$	0.0218945	−	24.4030i	0.00124353	−	1.38600i
$311$	−2.09420	−	1.20909i	−0.118751	−	0.0685610i	0.439448	−	0.898268i	$-0.355174\pi$
$311$	−2.09420	−	1.20909i	−0.118751	−	0.0685610i	−0.558199	+	0.829707i	$0.688507\pi$
$312$	−10.0868	+	3.16397i	−0.571053	+	0.179125i
$313$	0.417310	−	1.55742i	0.0235878	−	0.0880308i	−0.953129	−	0.302566i	$-0.902157\pi$
$313$	0.417310	−	1.55742i	0.0235878	−	0.0880308i	0.976716	+	0.214535i	$0.0688235\pi$
$314$	3.55074			0.200380
$315$	−0.574963	−	17.7389i	−0.0323955	−	0.999475i
$316$	−7.17297			−0.403511
$317$	5.89971	−	22.0180i	0.331361	−	1.23666i	−0.576400	−	0.817167i	$-0.695543\pi$
$317$	5.89971	−	22.0180i	0.331361	−	1.23666i	0.907761	−	0.419488i	$-0.137790\pi$
$318$	0.430269	−	1.92733i	0.0241283	−	0.108079i
$319$	14.7821	+	8.53447i	0.827641	+	0.477838i
$320$	1.57972	+	1.58256i	0.0883090	+	0.0884676i
$321$	0.801396	+	18.9994i	0.0447296	+	1.06044i
$322$	4.82848	+	5.34806i	0.269081	+	0.298036i
$323$	−6.89250	+	6.89250i	−0.383509	+	0.383509i
$324$	8.43889	+	3.12813i	0.468827	+	0.173785i
$325$	7.84547	+	29.4913i	0.435188	+	1.63588i
$326$	4.80199	+	8.31729i	0.265958	+	0.460652i
$327$	−8.03734	+	8.74523i	−0.444466	+	0.483612i
$328$	4.94215	−	1.32425i	0.272885	−	0.0731192i
$329$	−9.87843	−	19.3231i	−0.544616	−	1.06532i
$330$	−7.24777	+	2.26630i	−0.398977	+	0.124756i
$331$	−6.60904	−	11.4472i	−0.363266	−	0.629195i	0.625230	−	0.780440i	$-0.285005\pi$
$331$	−6.60904	−	11.4472i	−0.363266	−	0.629195i	−0.988496	+	0.151245i	$0.951672\pi$
$332$	−0.0534314	+	0.0534314i	−0.00293243	+	0.00293243i
$333$	15.7036	−	18.6028i	0.860550	−	1.01943i
$334$	−11.6870			−0.639484
$335$	−1.17083	+	2.02374i	−0.0639691	+	0.110569i
$336$	−3.98876	+	2.25605i	−0.217605	+	0.123078i
$337$	−29.0212	+	7.77620i	−1.58088	+	0.423596i	−0.939199	−	0.343372i	$-0.888431\pi$
$337$	−29.0212	+	7.77620i	−1.58088	+	0.423596i	−0.641684	+	0.766969i	$0.721764\pi$
$338$	6.27674	+	23.4251i	0.341410	+	1.27416i
$339$	−15.0684	+	28.8420i	−0.818403	+	1.56648i
$340$	−1.62738	+	2.81288i	−0.0882573	+	0.152550i
$341$		−	21.3981i		−	1.15877i
$342$	−19.8050	−	3.55255i	−1.07093	−	0.192100i
$343$	−14.9391	+	10.9464i	−0.806634	+	0.591052i
$344$	0.0738544	−	0.0426399i	0.00398196	−	0.00229899i
$345$	3.14778	+	10.0668i	0.169471	+	0.541977i
$346$	9.84510	+	5.68407i	0.529276	+	0.305578i
$347$	−1.50748	+	0.403928i	−0.0809257	+	0.0216840i	−0.299055	−	0.954236i	$-0.596671\pi$
$347$	−1.50748	+	0.403928i	−0.0809257	+	0.0216840i	0.218129	+	0.975920i	$0.430005\pi$
$348$	11.1018	+	10.2032i	0.595119	+	0.546947i
$349$	−9.97362	−	17.2748i	−0.533876	−	0.924700i	−0.999217	−	0.0395684i	$-0.987402\pi$
$349$	−9.97362	−	17.2748i	−0.533876	−	0.924700i	0.465341	−	0.885131i	$-0.345932\pi$
$350$	6.00047	+	11.7896i	0.320738	+	0.630180i
$351$	12.2663	−	29.2460i	0.654726	−	1.56104i
$352$	1.38644	+	1.38644i	0.0738974	+	0.0738974i
$353$	−4.33804	+	16.1898i	−0.230891	+	0.861695i	0.749068	+	0.662493i	$0.230502\pi$
$353$	−4.33804	+	16.1898i	−0.230891	+	0.861695i	−0.979958	+	0.199202i	$0.936165\pi$
$354$	0.0507304	+	1.20271i	0.00269629	+	0.0639231i
$355$	−19.0706	+	19.0364i	−1.01216	+	1.01035i
$356$	8.41786	+	4.86005i	0.446146	+	0.257582i
$357$	−4.66740	−	4.75082i	−0.247025	−	0.251440i
$358$	4.02463	+	1.07840i	0.212708	+	0.0569950i
$359$		−	34.9522i		−	1.84471i	−0.386347	−	0.922354i	$-0.626263\pi$
$359$		−	34.9522i		−	1.84471i	0.386347	−	0.922354i	$-0.373737\pi$
$360$	−6.68488	+	0.558904i	−0.352324	+	0.0294568i
$361$	25.9843			1.36760
$362$	−8.00132	−	2.14395i	−0.420540	−	0.112683i
$363$	11.8257	−	3.70942i	0.620688	−	0.194694i
$364$	7.35046	+	14.3781i	0.385269	+	0.753620i
$365$	−37.2951	−	0.0334614i	−1.95211	−	0.00175145i
$366$	−2.00905	+	3.84546i	−0.105015	+	0.201005i
$367$	−3.60188	−	0.965121i	−0.188017	−	0.0503789i	0.163582	−	0.986530i	$-0.447695\pi$
$367$	−3.60188	−	0.965121i	−0.188017	−	0.0503789i	−0.351599	+	0.936151i	$0.614362\pi$
$368$	1.92569	−	1.92569i	0.100384	−	0.100384i
$369$	−6.52806	+	13.8921i	−0.339837	+	0.723194i
$370$	−4.71213	+	17.5230i	−0.244972	+	0.910977i
$371$	−3.01259	−	0.153812i	−0.156406	−	0.00798551i
$372$	4.11853	−	18.4484i	0.213536	−	0.956504i
$373$	−5.66541	−	21.1436i	−0.293344	−	1.09477i	−0.942524	−	0.334139i	$-0.891554\pi$
$373$	−5.66541	−	21.1436i	−0.293344	−	1.09477i	0.649180	−	0.760635i	$-0.275112\pi$
$374$	−1.42478	+	2.46778i	−0.0736734	+	0.127606i
$375$	0.764010	+	19.3498i	0.0394533	+	0.999221i
$376$	−7.10356	+	4.10124i	−0.366338	+	0.211505i
$377$	37.5706	−	37.5706i	1.93498	−	1.93498i
$378$	2.54703	−	13.5097i	0.131005	−	0.694865i
$379$		−	8.38232i		−	0.430571i	−0.976551	−	0.215285i	$-0.930932\pi$
$379$		−	8.38232i		−	0.430571i	0.976551	−	0.215285i	$-0.0690682\pi$
$380$	14.4898	−	3.86861i	0.743313	−	0.198456i
$381$	−0.275584	−	6.53350i	−0.0141186	−	0.334721i
$382$	−10.0167	+	2.68397i	−0.512499	+	0.137324i
$383$	8.89264	−	2.38278i	0.454393	−	0.121754i	−0.0243614	−	0.999703i	$-0.507755\pi$
$383$	8.89264	−	2.38278i	0.454393	−	0.121754i	0.478754	+	0.877949i	$0.341089\pi$
$384$	0.928470	+	1.46217i	0.0473808	+	0.0746161i
$385$	5.27084	+	10.3331i	0.268627	+	0.526623i
$386$	15.8943			0.808996
$387$	−0.0451706	+	0.251820i	−0.00229615	+	0.0128007i
$388$	−5.63320	−	5.63320i	−0.285983	−	0.285983i
$389$	12.7492	−	7.36078i	0.646412	−	0.373206i	−0.140668	−	0.990057i	$-0.544925\pi$
$389$	12.7492	−	7.36078i	0.646412	−	0.373206i	0.787080	+	0.616850i	$0.211592\pi$
$390$	0.974994	+	23.6182i	0.0493707	+	1.19596i
$391$	3.42763	+	1.97894i	0.173342	+	0.100079i
$392$	4.41989	+	5.42813i	0.223238	+	0.274162i
$393$	7.99895	+	25.5008i	0.403494	+	1.28634i
$394$	−9.27044	+	5.35229i	−0.467038	+	0.269645i
$395$	−4.16516	+	15.4890i	−0.209572	+	0.779336i
$396$	−5.86126	+	0.495339i	−0.294540	+	0.0248917i
$397$	−12.9220	+	12.9220i	−0.648538	+	0.648538i	−0.952640	−	0.304102i	$-0.901644\pi$
$397$	−12.9220	+	12.9220i	−0.648538	+	0.648538i	0.304102	+	0.952640i	$0.401644\pi$
$398$	1.19461	−	4.45833i	0.0598802	−	0.223476i
$399$	−0.272214	+	30.7343i	−0.0136278	+	1.53864i
$400$	4.33461	−	2.49223i	0.216730	−	0.124611i
$401$	1.07304	−	1.85855i	0.0535849	−	0.0928117i	−0.837989	−	0.545688i	$-0.816269\pi$
$401$	1.07304	−	1.85855i	0.0535849	−	0.0928117i	0.891574	+	0.452876i	$0.149602\pi$
$402$	−1.22548	+	1.33342i	−0.0611215	+	0.0665048i
$403$	−64.3390	−	17.2396i	−3.20495	−	0.858765i
$404$	−3.67680			−0.182928
$405$	11.6550	−	16.4061i	0.579141	−	0.815227i
$406$	12.5183	−	19.3335i	0.621274	−	0.959507i
$407$	−4.11809	+	15.3689i	−0.204126	+	0.761809i
$408$	−1.70335	+	1.85338i	−0.0843285	+	0.0917558i
$409$	11.2157	−	19.4261i	0.554578	−	0.960558i	−0.443358	−	0.896345i	$-0.646213\pi$
$409$	11.2157	−	19.4261i	0.554578	−	0.960558i	0.997936	−	0.0642130i	$-0.0204537\pi$
$410$	0.0102648	−	11.4408i	0.000506941	−	0.565022i
$411$	13.9749	−	8.87400i	0.689333	−	0.437722i
$412$	6.79575	+	1.82092i	0.334803	+	0.0897101i
$413$	1.79810	−	0.384732i	0.0884787	−	0.0189314i
$414$	0.688001	+	8.14100i	0.0338134	+	0.400108i
$415$	0.0843511	+	0.146404i	0.00414063	+	0.00718667i
$416$	5.28570	−	3.05170i	0.259153	−	0.149622i
$417$	7.53577	−	2.36378i	0.369028	−	0.115755i
$418$	12.7025	−	3.40363i	0.621300	−	0.166477i
$419$	−3.01937	+	5.22970i	−0.147506	+	0.255488i	−0.930305	−	0.366787i	$-0.880458\pi$
$419$	−3.01937	+	5.22970i	−0.147506	+	0.255488i	0.782799	+	0.622274i	$0.213791\pi$
$420$	2.55544	+	9.92319i	0.124693	+	0.484202i
$421$	−2.23614	−	3.87311i	−0.108983	−	0.188764i	0.806376	−	0.591404i	$-0.201426\pi$
$421$	−2.23614	−	3.87311i	−0.108983	−	0.188764i	−0.915358	+	0.402640i	$0.868093\pi$
$422$	−3.31734	−	3.31734i	−0.161486	−	0.161486i
$423$	4.34466	−	24.2209i	0.211244	−	1.17766i
$424$			1.14014i			0.0553699i
$425$	5.12903	+	5.14747i	0.248795	+	0.249689i
$426$	−17.6199	+	11.1885i	−0.853688	+	0.542087i
$427$	6.30578	+	2.03948i	0.305158	+	0.0986973i
$428$	−2.84159	−	10.6049i	−0.137353	−	0.512609i
$429$	0.873514	+	20.7091i	0.0421737	+	0.999846i
$430$	−0.0491892	−	0.184238i	−0.00237212	−	0.00888474i
$431$	−20.1013			−0.968246			−0.484123	−	0.875000i	$-0.660861\pi$
$431$	−20.1013			−0.968246			−0.484123	+	0.875000i	$0.660861\pi$
$432$	−5.14864	−	0.701071i	−0.247714	−	0.0337303i
$433$	−19.5836	−	19.5836i	−0.941128	−	0.941128i	0.0572331	−	0.998361i	$-0.481772\pi$
$433$	−19.5836	−	19.5836i	−0.941128	−	0.941128i	−0.998361	+	0.0572331i	$0.981772\pi$
$434$	−28.8365	−	1.47228i	−1.38420	−	0.0706719i
$435$	28.4788	−	18.0480i	1.36545	−	0.865337i
$436$	3.42877	−	5.93881i	0.164209	−	0.284418i
$437$	−4.72747	−	17.6431i	−0.226145	−	0.843986i
$438$	−28.1946	−	6.29433i	−1.34719	−	0.300755i
$439$	2.78036	+	4.81572i	0.132699	+	0.229842i	0.924716	−	0.380657i	$-0.124302\pi$
$439$	2.78036	+	4.81572i	0.132699	+	0.229842i	−0.792017	+	0.610499i	$0.790969\pi$
$440$	3.79888	−	2.18874i	0.181105	−	0.104344i
$441$	−20.9967	−	0.371966i	−0.999843	−	0.0177127i
$442$	6.27217	+	6.27217i	0.298337	+	0.298337i
$443$	23.4755	+	6.29024i	1.11535	+	0.298858i	0.769002	−	0.639246i	$-0.220754\pi$
$443$	23.4755	+	6.29024i	1.11535	+	0.298858i	0.346352	+	0.938105i	$0.387420\pi$
$444$	−6.50851	+	12.4577i	−0.308880	+	0.591218i
$445$	15.3826	−	15.3550i	0.729206	−	0.727899i
$446$	−16.3862	−	9.46055i	−0.775907	−	0.447970i
$447$	0.490382	+	1.56335i	0.0231943	+	0.0739437i
$448$	1.96379	−	1.77300i	0.0927803	−	0.0837665i
$449$			34.7191i			1.63850i	0.573440	+	0.819248i	$0.305609\pi$
$449$			34.7191i			1.63850i	−0.573440	+	0.819248i	$0.694391\pi$
$450$	−2.67487	+	14.7596i	−0.126094	+	0.695773i
$451$		−	10.0320i		−	0.472389i
$452$	4.86258	−	18.1474i	0.228716	−	0.853581i
$453$	−3.48034	+	15.5897i	−0.163521	+	0.732470i
$454$	8.86255	−	15.3504i	0.415940	−	0.720429i
$455$	35.3158	−	7.52323i	1.65563	−	0.352695i
$456$	11.6066	−	0.489568i	0.543529	−	0.0229261i
$457$	−3.60406	+	13.4505i	−0.168591	+	0.629189i	0.828964	+	0.559302i	$0.188931\pi$
$457$	−3.60406	+	13.4505i	−0.168591	+	0.629189i	−0.997555	+	0.0698875i	$0.977736\pi$
$458$	0.0357627	+	0.0357627i	0.00167108	+	0.00167108i
$459$	−0.952482	−	7.49136i	−0.0444581	−	0.349667i
$460$	−3.04005	−	5.27645i	−0.141743	−	0.246016i
$461$	18.2975	−	10.5641i	0.852199	−	0.492017i	−0.00919325	−	0.999958i	$-0.502926\pi$
$461$	18.2975	−	10.5641i	0.852199	−	0.492017i	0.861392	+	0.507940i	$0.169593\pi$
$462$	2.24857	+	8.69924i	0.104613	+	0.404725i
$463$	2.47907	+	9.25203i	0.115212	+	0.429978i	0.999303	−	0.0373376i	$-0.0118877\pi$
$463$	2.47907	+	9.25203i	0.115212	+	0.429978i	−0.884090	+	0.467316i	$0.845221\pi$
$464$	−7.53914	−	4.35272i	−0.349996	−	0.202070i
$465$	−37.4451	−	19.6059i	−1.73647	−	0.909200i
$466$	13.7932	+	23.8906i	0.638959	+	1.10671i
$467$	17.5749	−	17.5749i	0.813268	−	0.813268i	−0.171855	−	0.985122i	$-0.554976\pi$
$467$	17.5749	−	17.5749i	0.813268	−	0.813268i	0.985122	+	0.171855i	$0.0549759\pi$
$468$	−3.23282	+	18.0225i	−0.149437	+	0.833092i
$469$	2.32211	+	1.50355i	0.107225	+	0.0694276i
$470$	4.73118	+	17.7206i	0.218233	+	0.817390i
$471$	2.84784	−	5.45097i	0.131222	−	0.251168i
$472$	−0.179879	−	0.671319i	−0.00827962	−	0.0309000i
$473$	−0.0432770	−	0.161512i	−0.00198988	−	0.00742633i
$474$	−5.75302	+	11.0117i	−0.264245	+	0.505784i
$475$	0.0601759	−	33.5351i	0.00276106	−	1.53870i
$476$	3.22761	+	2.08985i	0.147937	+	0.0957883i
$477$	−2.61367	−	2.20633i	−0.119672	−	0.101021i
$478$	7.99691	−	7.99691i	0.365770	−	0.365770i
$479$	0.282621	+	0.489515i	0.0129133	+	0.0223665i	0.872410	−	0.488775i	$-0.162556\pi$
$479$	0.282621	+	0.489515i	0.0129133	+	0.0223665i	−0.859497	+	0.511142i	$0.829223\pi$
$480$	3.69649	−	1.15585i	0.168721	−	0.0527572i
$481$	42.8930	+	24.7643i	1.95575	+	1.12915i
$482$	−2.17358	−	8.11190i	−0.0990037	−	0.369487i
$483$	12.0828	−	3.12315i	0.549786	−	0.142108i
$484$	−6.19691	+	3.57779i	−0.281678	+	0.162627i
$485$	−15.4352	+	8.89303i	−0.700874	+	0.403812i
$486$	11.5705	−	10.4462i	0.524850	−	0.473849i
$487$	1.02631	+	1.02631i	0.0465064	+	0.0465064i	0.729978	−	0.683471i	$-0.239530\pi$
$487$	1.02631	+	1.02631i	0.0465064	+	0.0465064i	−0.683471	+	0.729978i	$0.739530\pi$
$488$	0.648320	−	2.41957i	0.0293481	−	0.109529i
$489$	16.6198	−	0.701026i	0.751574	−	0.0317015i
$490$	14.2878	−	6.39214i	0.645456	−	0.288768i
$491$	3.51641	−	6.09060i	0.158693	−	0.274865i	−0.775704	−	0.631096i	$-0.782605\pi$
$491$	3.51641	−	6.09060i	0.158693	−	0.274865i	0.934398	+	0.356231i	$0.115939\pi$
$492$	1.93088	−	8.64911i	0.0870507	−	0.389932i
$493$	3.27452	−	12.2207i	0.147477	−	0.550392i
$494$		−	40.9357i		−	1.84178i
$495$	−2.33387	+	12.9442i	−0.104900	+	0.581798i
$496$			10.9134i			0.490025i
$497$	21.3656	+	23.6647i	0.958378	+	1.06151i
$498$	0.0391717	+	0.124880i	0.00175533	+	0.00559601i
$499$	−17.9552	−	10.3664i	−0.803786	−	0.464066i	0.0410075	−	0.999159i	$-0.486943\pi$
$499$	−17.9552	−	10.3664i	−0.803786	−	0.464066i	−0.844793	+	0.535093i	$0.820277\pi$
$500$	−2.86461	−	10.8071i	−0.128109	−	0.483309i
$501$	−9.37347	+	17.9415i	−0.418776	+	0.801565i
$502$	14.2960	+	3.83060i	0.638061	+	0.170968i
$503$	4.86038	+	4.86038i	0.216714	+	0.216714i	0.807112	−	0.590398i	$-0.201029\pi$
$503$	4.86038	+	4.86038i	0.216714	+	0.216714i	−0.590398	+	0.807112i	$0.701029\pi$
$504$	0.264249	+	7.93285i	0.0117706	+	0.353357i
$505$	−2.13503	+	7.93952i	−0.0950074	+	0.353304i
$506$	−2.66985	−	4.62432i	−0.118689	−	0.205576i
$507$	40.9956	+	9.15210i	1.82068	+	0.406459i
$508$	0.977163	+	3.64682i	0.0433546	+	0.161802i
$509$	−19.1497	+	33.1683i	−0.848796	+	1.47016i	0.0334881	+	0.999439i	$0.489338\pi$
$509$	−19.1497	+	33.1683i	−0.848796	+	1.47016i	−0.882284	+	0.470718i	$0.843995\pi$
$510$	3.01300	+	4.75435i	0.133418	+	0.210526i
$511$	−2.25009	+	44.0708i	−0.0995381	+	1.94958i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−21.3382	+	27.5546i	−0.942104	+	1.21657i
$514$	14.8175			0.653573
$515$	7.87813	−	13.6171i	0.347152	−	0.600041i
$516$	−0.00622485	−	0.147578i	−0.000274034	−	0.00649674i
$517$	4.16253	+	15.5348i	0.183068	+	0.683218i
$518$	20.4282	+	6.60708i	0.897562	+	0.290299i
$519$	16.6222	−	10.5550i	0.729632	−	0.463312i
$520$	−3.52043	−	13.1857i	−0.154381	−	0.578233i
$521$		−	3.59518i		−	0.157508i	−0.996894	−	0.0787539i	$-0.974906\pi$
$521$		−	3.59518i		−	0.157508i	0.996894	−	0.0787539i	$-0.0250941\pi$
$522$	24.5676	−	8.85973i	1.07530	−	0.387780i
$523$	23.5929	+	23.5929i	1.03165	+	1.03165i	0.999483	+	0.0321650i	$0.0102402\pi$
$523$	23.5929	+	23.5929i	1.03165	+	1.03165i	0.0321650	+	0.999483i	$0.489760\pi$
$524$	−7.71510	−	13.3629i	−0.337036	−	0.583763i
$525$	22.9116	+	0.244045i	0.999943	+	0.0106510i
$526$	−3.42147	+	5.92616i	−0.149183	+	0.258393i
$527$	−15.3202	+	4.10503i	−0.667357	+	0.178818i
$528$	3.24039	−	1.01643i	0.141020	−	0.0442344i
$529$	13.4956	−	7.79171i	0.586767	−	0.338770i
$530$	2.46196	+	0.662048i	0.106941	+	0.0287575i
$531$	1.88704	+	0.886742i	0.0818905	+	0.0384813i
$532$	−3.71282	−	17.3524i	−0.160971	−	0.752321i
$533$	−30.1639	−	8.08240i	−1.30654	−	0.350087i
$534$	14.2125	−	9.02483i	0.615033	−	0.390542i
$535$	−24.5499	−	0.0220263i	−1.06138	−	0.000952280i
$536$	0.522798	−	0.905512i	0.0225814	−	0.0391122i
$537$	4.88343	−	5.31354i	0.210736	−	0.229296i
$538$	1.10361	−	4.11872i	0.0475799	−	0.177571i
$539$	12.5233	−	5.61626i	0.539419	−	0.241909i
$540$	−4.50355	+	10.7107i	−0.193802	+	0.460913i
$541$	2.77658			0.119374			0.0596872	−	0.998217i	$-0.480990\pi$
$541$	2.77658			0.119374			0.0596872	+	0.998217i	$0.480990\pi$
$542$	15.0903	+	4.04345i	0.648186	+	0.173681i
$543$	−9.70870	+	10.5638i	−0.416640	+	0.453336i
$544$	0.726660	−	1.25861i	0.0311553	−	0.0539625i
$545$	−10.8330	−	10.8525i	−0.464035	−	0.464868i
$546$	27.9682	+	0.247715i	1.19693	+	0.0106012i
$547$	5.13941	−	19.1805i	0.219745	−	0.820101i	−0.764696	−	0.644391i	$-0.777111\pi$
$547$	5.13941	−	19.1805i	0.219745	−	0.820101i	0.984442	−	0.175710i	$-0.0562222\pi$
$548$	−6.75829	+	6.75829i	−0.288700	+	0.288700i
$549$	4.29207	+	6.16844i	0.183181	+	0.263263i
$550$	−2.52036	−	9.47408i	−0.107469	−	0.403976i
$551$	−50.5653	+	29.1939i	−2.15415	+	1.24370i
$552$	−1.41177	−	4.50074i	−0.0600888	−	0.191564i
$553$	18.0569	+	5.84016i	0.767859	+	0.248349i
$554$	1.00876	+	0.582408i	0.0428581	+	0.0247442i
$555$	23.1214	+	21.2881i	0.981447	+	0.903628i
$556$	−3.94890	+	2.27990i	−0.167471	+	0.0966893i
$557$	−14.9002	−	14.9002i	−0.631343	−	0.631343i	0.317062	−	0.948405i	$-0.397304\pi$
$557$	−14.9002	−	14.9002i	−0.631343	−	0.631343i	−0.948405	+	0.317062i	$0.897304\pi$
$558$	−25.0181	−	21.1190i	−1.05910	−	0.894038i
$559$	−0.520496			−0.0220146
$560$	−2.68822	−	5.27005i	−0.113598	−	0.222700i
$561$	2.64572	+	4.16653i	0.111702	+	0.175911i
$562$	14.3440	−	3.84348i	0.605067	−	0.162127i
$563$	−6.05400	+	1.62216i	−0.255146	+	0.0683661i	−0.384125	−	0.923281i	$-0.625497\pi$
$563$	−6.05400	+	1.62216i	−0.255146	+	0.0683661i	0.128979	+	0.991647i	$0.458830\pi$
$564$	0.598726	+	14.1945i	0.0252109	+	0.597696i
$565$	−36.3631	−	21.0378i	−1.52981	−	0.885065i
$566$		−	18.3519i		−	0.771386i
$567$	−18.6968	−	14.7455i	−0.785192	−	0.619252i
$568$	8.52100	−	8.52100i	0.357533	−	0.357533i
$569$	14.9720	−	8.64409i	0.627659	−	0.362379i	−0.152186	−	0.988352i	$-0.548631\pi$
$569$	14.9720	−	8.64409i	0.627659	−	0.362379i	0.779845	+	0.625973i	$0.215298\pi$
$570$	5.68251	−	25.3471i	0.238014	−	1.06167i
$571$	−21.4296	+	37.1171i	−0.896801	+	1.55330i	−0.0652405	+	0.997870i	$0.520781\pi$
$571$	−21.4296	+	37.1171i	−0.896801	+	1.55330i	−0.831560	+	0.555435i	$0.812552\pi$
$572$	−3.09730	−	11.5593i	−0.129505	−	0.483318i
$573$	−3.91348	+	17.5299i	−0.163488	+	0.732323i
$574$	−13.5194	−	0.690248i	−0.564287	−	0.0288104i
$575$	−13.1590	+	3.50065i	−0.548769	+	0.145987i
$576$	2.98934	−	0.252632i	0.124556	−	0.0105263i
$577$	−13.3350	+	13.3350i	−0.555145	+	0.555145i	−0.927921	−	0.372776i	$-0.878406\pi$
$577$	−13.3350	+	13.3350i	−0.555145	+	0.555145i	0.372776	+	0.927921i	$0.378406\pi$
$578$	−14.3806	−	3.85326i	−0.598153	−	0.160275i
$579$	12.7479	−	24.4003i	0.529783	−	1.01404i
$580$	−13.7769	+	13.7522i	−0.572053	+	0.571028i
$581$	0.178009	−	0.0910027i	0.00738507	−	0.00377543i
$582$	−13.1660	+	4.12983i	−0.545747	+	0.171187i
$583$	2.15932	+	0.578587i	0.0894297	+	0.0239626i
$584$	16.6789			0.690177
$585$	37.0399	+	17.4460i	1.53141	+	0.721305i
$586$			5.42265i			0.224008i
$587$	−31.1488	−	8.34630i	−1.28565	−	0.344488i	−0.449642	−	0.893209i	$-0.648449\pi$
$587$	−31.1488	−	8.34630i	−1.28565	−	0.344488i	−0.836006	+	0.548720i	$0.815115\pi$
$588$	11.8780	−	2.43167i	0.489841	−	0.100281i
$589$	63.3899	+	36.5982i	2.61194	+	1.50800i
$590$	−1.55407	−	0.00139432i	−0.0639799	−	5.74032e-5i
$591$	0.781363	+	18.5244i	0.0321410	+	0.761992i
$592$	2.10030	−	7.83841i	0.0863216	−	0.322157i
$593$	−24.9013	−	24.9013i	−1.02258	−	1.02258i	−0.999739	−	0.0228365i	$-0.992730\pi$
$593$	−24.9013	−	24.9013i	−1.02258	−	1.02258i	−0.0228365	−	0.999739i	$-0.507270\pi$
$594$	−3.94055	+	9.39529i	−0.161683	+	0.385493i
$595$	6.38693	−	5.75603i	0.261839	−	0.235974i
$596$	−0.472980	−	0.819226i	−0.0193740	−	0.0335568i
$597$	−5.88615	−	5.40969i	−0.240904	−	0.221404i
$598$	−16.0553	+	4.30199i	−0.656548	+	0.175922i
$599$	13.6903	+	7.90410i	0.559371	+	0.322953i	0.752893	−	0.658143i	$-0.228658\pi$
$599$	13.6903	+	7.90410i	0.559371	+	0.322953i	−0.193522	+	0.981096i	$0.561991\pi$
$600$	−0.349440	−	8.65320i	−0.0142658	−	0.353265i
$601$	27.2015	−	15.7048i	1.10957	−	0.640611i	0.170852	−	0.985297i	$-0.445348\pi$
$601$	27.2015	−	15.7048i	1.10957	−	0.640611i	0.938718	+	0.344686i	$0.112015\pi$
$602$	−0.220635	+	0.0472083i	−0.00899241	+	0.00192407i
$603$	1.06413	+	2.95077i	0.0433346	+	0.120165i
$604$		−	9.22230i		−	0.375250i
$605$	4.12733	+	15.4589i	0.167800	+	0.628493i
$606$	−2.94895	+	5.64449i	−0.119793	+	0.229292i
$607$	1.97623	+	7.37539i	0.0802127	+	0.299358i	0.994365	−	0.106014i	$-0.0338088\pi$
$607$	1.97623	+	7.37539i	0.0802127	+	0.299358i	−0.914152	+	0.405372i	$0.867142\pi$
$608$	−6.47850	+	1.73591i	−0.262738	+	0.0704004i
$609$	−19.6399	−	34.7240i	−0.795850	−	1.40709i
$610$	−4.84824	−	2.80493i	−0.196299	−	0.113568i
$611$	50.0630			2.02533
$612$	1.47908	+	4.10141i	0.0597881	+	0.165790i
$613$	−10.6309	+	10.6309i	−0.429378	+	0.429378i	−0.888416	−	0.459038i	$-0.848194\pi$
$613$	−10.6309	+	10.6309i	−0.429378	+	0.429378i	0.459038	+	0.888416i	$0.348194\pi$
$614$	6.03697	+	10.4563i	0.243632	+	0.421983i
$615$	−17.5553	−	9.19177i	−0.707898	−	0.370648i
$616$	−2.36134	−	4.61898i	−0.0951410	−	0.186104i
$617$	17.0447	−	4.56712i	0.686195	−	0.183865i	0.101156	−	0.994871i	$-0.467746\pi$
$617$	17.0447	−	4.56712i	0.686195	−	0.183865i	0.585039	+	0.811005i	$0.301079\pi$
$618$	8.24589	−	8.97215i	0.331698	−	0.360913i
$619$	−3.72987	−	6.46032i	−0.149916	−	0.259662i	0.781280	−	0.624181i	$-0.214567\pi$
$619$	−3.72987	−	6.46032i	−0.149916	−	0.259662i	−0.931196	+	0.364518i	$0.881234\pi$
$620$	23.5659	+	6.33712i	0.946427	+	0.254505i
$621$	13.0496	+	5.47323i	0.523661	+	0.219633i
$622$	1.70991	−	1.70991i	0.0685610	−	0.0685610i
$623$	−17.2338	−	19.0882i	−0.690456	−	0.764754i
$624$	−0.445507	−	10.5620i	−0.0178346	−	0.422819i
$625$	−24.9998	−	0.0897204i	−0.999994	−	0.00358881i
$626$	1.39635	+	0.806182i	0.0558093	+	0.0322215i
$627$	4.96282	−	22.2303i	0.198196	−	0.887793i
$628$	−0.919000	+	3.42975i	−0.0366721	+	0.136862i
$629$	11.7936			0.470240
$630$	17.2833	+	4.03580i	0.688583	+	0.160790i
$631$	28.6292			1.13971			0.569855	−	0.821746i	$-0.307000\pi$
$631$	28.6292			1.13971			0.569855	+	0.821746i	$0.307000\pi$
$632$	1.85650	−	6.92856i	0.0738477	−	0.275603i
$633$	−7.75331	+	2.43201i	−0.308166	+	0.0966639i
$634$	19.7408	+	11.3974i	0.784008	+	0.452647i
$635$	8.44220	+	0.00757439i	0.335019	+	0.000300581i
$636$	1.75030	+	0.914437i	0.0694038	+	0.0362598i
$637$	−6.79721	−	42.1796i	−0.269315	−	1.67122i
$638$	−12.0696	+	12.0696i	−0.477838	+	0.477838i
$639$	3.04434	+	36.0231i	0.120432	+	1.42505i
$640$	−1.93749	+	1.11630i	−0.0765862	+	0.0441255i
$641$	12.8189	+	22.2030i	0.506316	+	0.876965i	0.999973	+	0.00730859i	$0.00232642\pi$
$641$	12.8189	+	22.2030i	0.506316	+	0.876965i	−0.493657	+	0.869657i	$0.664340\pi$
$642$	−18.5594	−	4.14331i	−0.732481	−	0.163523i
$643$	35.3494	−	9.47186i	1.39405	−	0.373534i	0.517843	−	0.855476i	$-0.326735\pi$
$643$	35.3494	−	9.47186i	1.39405	−	0.373534i	0.876203	+	0.481942i	$0.160068\pi$
$644$	−6.41553	+	3.27978i	−0.252807	+	0.129241i
$645$	−0.322287	−	0.0722529i	−0.0126900	−	0.00284495i
$646$	−4.87373	−	8.44155i	−0.191754	−	0.332128i
$647$	−7.40772	+	7.40772i	−0.291227	+	0.291227i	−0.837565	−	0.546338i	$-0.816022\pi$
$647$	−7.40772	+	7.40772i	−0.291227	+	0.291227i	0.546338	+	0.837565i	$0.316022\pi$
$648$	−5.20568	+	7.34172i	−0.204499	+	0.288410i
$649$	−1.36270			−0.0534907
$650$	−30.5169	−	0.0547600i	−1.19697	−	0.00214786i
$651$	−25.3883	+	43.0879i	−0.995045	+	1.68875i
$652$	−9.27674	+	2.48569i	−0.363305	+	0.0973473i
$653$	1.99159	+	7.43273i	0.0779371	+	0.290865i	0.993883	−	0.110436i	$-0.0352247\pi$
$653$	1.99159	+	7.43273i	0.0779371	+	0.290865i	−0.915946	+	0.401301i	$0.868558\pi$
$654$	−6.36703	−	10.0269i	−0.248971	−	0.392083i
$655$	−33.3353	+	8.90012i	−1.30252	+	0.347757i
$656$			5.11649i			0.199765i
$657$	−32.2761	+	38.2350i	−1.25921	+	1.49169i
$658$	21.2214	−	4.54065i	0.827296	−	0.177013i
$659$	30.4529	−	17.5820i	1.18628	−	0.684898i	0.228819	−	0.973469i	$-0.426514\pi$
$659$	30.4529	−	17.5820i	1.18628	−	0.684898i	0.957458	+	0.288571i	$0.0931802\pi$
$660$	−0.313217	−	7.58737i	−0.0121920	−	0.295338i
$661$	−3.94277	−	2.27636i	−0.153356	−	0.0885401i	0.421358	−	0.906894i	$-0.361553\pi$
$661$	−3.94277	−	2.27636i	−0.153356	−	0.0885401i	−0.574714	+	0.818354i	$0.694887\pi$
$662$	12.7677	−	3.42109i	0.496230	−	0.132965i
$663$	14.6593	−	4.59827i	0.569322	−	0.178582i
$664$	−0.0377817	−	0.0654398i	−0.00146621	−	0.00253956i
$665$	−39.6259	−	2.05880i	−1.53663	−	0.0798368i
$666$	13.9046	+	19.9832i	0.538791	+	0.774335i
$667$	16.7640	+	16.7640i	0.649105	+	0.649105i
$668$	3.02482	−	11.2888i	0.117034	−	0.436776i
$669$	−27.6659	+	17.5677i	−1.06962	+	0.679206i
$670$	−1.65175	−	1.65471i	−0.0638126	−	0.0639272i
$671$	−4.25343	−	2.45572i	−0.164202	−	0.0948020i
$672$	−1.14681	−	4.43676i	−0.0442391	−	0.171152i
$673$	21.6339	+	5.79679i	0.833926	+	0.223450i	0.650426	−	0.759570i	$-0.274591\pi$
$673$	21.6339	+	5.79679i	0.833926	+	0.223450i	0.183500	+	0.983020i	$0.441257\pi$
$674$		−	30.0449i		−	1.15729i
$675$	20.5130	+	15.9442i	0.789546	+	0.613691i
$676$	−24.2515			−0.932749
$677$	23.5526	+	6.31089i	0.905199	+	0.242547i	0.681248	−	0.732053i	$-0.261438\pi$
$677$	23.5526	+	6.31089i	0.905199	+	0.242547i	0.223951	+	0.974600i	$0.428104\pi$
$678$	−23.9592	−	22.0198i	−0.920148	−	0.845666i
$679$	9.59430	+	18.7673i	0.368195	+	0.720223i
$680$	−2.29584	−	2.29996i	−0.0880413	−	0.0881994i
$681$	−16.4572	−	25.9171i	−0.630642	−	0.993146i
$682$	20.6689	+	5.53822i	0.791454	+	0.212070i
$683$	−8.44527	+	8.44527i	−0.323149	+	0.323149i	−0.849974	−	0.526825i	$-0.823382\pi$
$683$	−8.44527	+	8.44527i	−0.323149	+	0.323149i	0.526825	+	0.849974i	$0.323382\pi$
$684$	8.55742	−	18.2107i	0.327201	−	0.696303i
$685$	10.6692	+	18.5179i	0.407649	+	0.707533i
$686$	−6.70693	−	17.2632i	−0.256072	−	0.659111i
$687$	0.0835847	−	0.0262184i	0.00318896	−	0.00100029i
$688$	0.0220720	+	0.0823739i	0.000841488	+	0.00314047i
$689$	3.47935	−	6.02642i	0.132553	−	0.229588i
$690$	−10.5385	+	0.435043i	−0.401193	+	0.0165618i
$691$	−11.4624	+	6.61781i	−0.436049	+	0.251753i	−0.701920	−	0.712255i	$-0.747674\pi$
$691$	−11.4624	+	6.61781i	−0.436049	+	0.251753i	0.265871	+	0.964009i	$0.414340\pi$
$692$	−8.03849	+	8.03849i	−0.305578	+	0.305578i
$693$	15.1582	+	3.52523i	0.575813	+	0.133913i
$694$		−	1.56066i		−	0.0592417i
$695$	2.63009	+	9.85096i	0.0997649	+	0.373668i
$696$	−12.7288	+	8.08275i	−0.482486	+	0.306376i
$697$	−7.18252	+	1.92455i	−0.272057	+	0.0728976i
$698$	19.2676	−	5.16273i	0.729288	−	0.195412i
$699$	47.7387	−	2.01363i	1.80564	−	0.0761623i
$700$	−12.9409	+	2.74464i	−0.489120	+	0.103737i
$701$	−23.1079			−0.872775			−0.436388	−	0.899759i	$-0.643742\pi$
$701$	−23.1079			−0.872775			−0.436388	+	0.899759i	$0.643742\pi$
$702$	25.0747	+	19.4178i	0.946384	+	0.732876i
$703$	−38.4857	−	38.4857i	−1.45152	−	1.45152i
$704$	−1.69803	+	0.980360i	−0.0639970	+	0.0369487i
$705$	30.9986	+	6.94952i	1.16748	+	0.261734i
$706$	−14.5154	−	8.38045i	−0.546293	−	0.315402i
$707$	9.25583	+	2.99361i	0.348101	+	0.112586i
$708$	−1.17486	−	0.262282i	−0.0441538	−	0.00985714i
$709$	−23.4649	+	13.5475i	−0.881243	+	0.508786i	−0.871068	−	0.491163i	$-0.836572\pi$
$709$	−23.4649	+	13.5475i	−0.881243	+	0.508786i	−0.0101747	+	0.999948i	$0.503239\pi$
$710$	−13.4519	−	23.3478i	−0.504843	−	0.876228i
$711$	12.2906	+	17.6637i	0.460933	+	0.662439i
$712$	−6.87315	+	6.87315i	−0.257582	+	0.257582i
$713$	7.69231	−	28.7081i	0.288079	−	1.07513i
$714$	5.79695	−	3.27876i	0.216945	−	0.122704i
$715$	−26.7591	−	0.0240084i	−1.00073	−	0.000897865i
$716$	−2.08330	+	3.60838i	−0.0778566	+	0.134852i
$717$	−5.86271	−	18.6904i	−0.218947	−	0.698007i
$718$	33.7612	+	9.04630i	1.25996	+	0.337605i
$719$	27.6799			1.03229			0.516143	−	0.856502i	$-0.327367\pi$
$719$	27.6799			1.03229			0.516143	+	0.856502i	$0.327367\pi$
$720$	1.19031	−	6.60175i	0.0443604	−	0.246033i
$721$	−15.6248	−	10.1169i	−0.581897	−	0.376774i
$722$	−6.72523	+	25.0989i	−0.250287	+	0.934085i
$723$	−14.1964	−	3.16929i	−0.527969	−	0.117867i
$724$	4.14179	−	7.17378i	0.153928	−	0.266612i
$725$	21.6959	+	37.7347i	0.805767	+	1.40143i
$726$	0.522309	+	12.3828i	0.0193847	+	0.459569i
$727$	21.7857	+	5.83747i	0.807988	+	0.216500i	0.639088	−	0.769134i	$-0.279312\pi$
$727$	21.7857	+	5.83747i	0.807988	+	0.216500i	0.168900	+	0.985633i	$0.445979\pi$
$728$	−15.7907	+	3.37866i	−0.585241	+	0.125221i
$729$	−6.75656	−	26.1409i	−0.250243	−	0.968183i
$730$	9.68500	−	36.0156i	0.358458	−	1.33300i
$731$	−0.107334	+	0.0619693i	−0.00396989	+	0.00229202i
$732$	−3.19445	−	2.93587i	−0.118070	−	0.108513i
$733$	−17.5609	+	4.70542i	−0.648625	+	0.173799i	−0.568107	−	0.822955i	$-0.692324\pi$
$733$	−17.5609	+	4.70542i	−0.648625	+	0.173799i	−0.0805180	+	0.996753i	$0.525657\pi$
$734$	1.86447	−	3.22936i	0.0688189	−	0.119198i
$735$	1.64641	−	27.0608i	0.0607286	−	0.998154i
$736$	1.36167	+	2.35848i	0.0501918	+	0.0869348i
$737$	−1.44965	−	1.44965i	−0.0533987	−	0.0533987i
$738$	−11.7292	−	9.90117i	−0.431756	−	0.364467i
$739$		−	29.3870i		−	1.08102i	−0.841339	−	0.540508i	$-0.818232\pi$
$739$		−	29.3870i		−	1.08102i	0.841339	−	0.540508i	$-0.181768\pi$
$740$	−15.7063	−	9.08685i	−0.577376	−	0.334039i
$741$	−62.8430	−	32.8322i	−2.30860	−	1.20612i
$742$	0.928287	−	2.87013i	0.0340785	−	0.105366i
$743$	3.95149	+	14.7472i	0.144966	+	0.541021i	0.999757	+	0.0220485i	$0.00701881\pi$
$743$	3.95149	+	14.7472i	0.144966	+	0.541021i	−0.854791	+	0.518973i	$0.826315\pi$
$744$	16.7538	+	8.75298i	0.614225	+	0.320900i
$745$	−2.04365	+	0.545629i	−0.0748735	+	0.0199903i
$746$	21.8895			0.801430
$747$	0.223129	+	0.0400241i	0.00816386	+	0.00146441i
$748$	−2.01494	−	2.01494i	−0.0736734	−	0.0736734i
$749$	−1.48114	+	29.0100i	−0.0541198	+	1.06000i
$750$	−18.8883	−	4.27013i	−0.689701	−	0.155923i
$751$	4.87674	−	8.44676i	0.177955	−	0.308227i	−0.763225	−	0.646133i	$-0.776385\pi$
$751$	4.87674	−	8.44676i	0.177955	−	0.308227i	0.941180	+	0.337906i	$0.109719\pi$
$752$	−2.12296	−	7.92299i	−0.0774163	−	0.288922i
$753$	17.3466	−	18.8744i	0.632144	−	0.687820i
$754$	26.5664	+	46.0144i	0.967491	+	1.67574i
$755$	−19.9142	−	5.35516i	−0.724753	−	0.194894i
$756$	12.3902	+	5.95682i	0.450626	+	0.216647i
$757$	−13.8161	−	13.8161i	−0.502155	−	0.502155i	0.409952	−	0.912107i	$-0.365545\pi$
$757$	−13.8161	−	13.8161i	−0.502155	−	0.502155i	−0.912107	+	0.409952i	$0.865545\pi$
$758$	8.09670	+	2.16950i	0.294085	+	0.0788000i
$759$	−9.24042	+	0.389762i	−0.335406	+	0.0141475i
$760$	−0.0134557	+	14.9974i	−0.000488091	+	0.544012i
$761$	25.9217	+	14.9659i	0.939660	+	0.542513i	0.889854	−	0.456246i	$-0.150806\pi$
$761$	25.9217	+	14.9659i	0.939660	+	0.542513i	0.0498060	+	0.998759i	$0.484140\pi$
$762$	6.38220	+	1.42480i	0.231203	+	0.0516150i
$763$	−13.4668	+	12.1584i	−0.487530	+	0.440165i
$764$		−	10.3700i		−	0.375175i
$765$	9.71526	−	0.812266i	0.351256	−	0.0293675i
$766$			9.20634i			0.332639i
$767$	−1.09788	+	4.09733i	−0.0396420	+	0.147946i
$768$	−1.65265	+	0.518396i	−0.0596350	+	0.0187060i
$769$	−11.9776	+	20.7458i	−0.431922	+	0.748111i	−0.997039	−	0.0768997i	$-0.975498\pi$
$769$	−11.9776	+	20.7458i	−0.431922	+	0.748111i	0.565117	+	0.825011i	$0.308831\pi$
$770$	−11.3452	+	2.41684i	−0.408853	+	0.0870969i
$771$	11.8843	−	22.7473i	0.428002	−	0.819226i
$772$	−4.11374	+	15.3527i	−0.148057	+	0.552555i
$773$	8.02132	+	8.02132i	0.288507	+	0.288507i	0.836490	−	0.547983i	$-0.184604\pi$
$773$	8.02132	+	8.02132i	0.288507	+	0.288507i	−0.547983	+	0.836490i	$0.684604\pi$
$774$	−0.231548	−	0.108807i	−0.00832283	−	0.00391100i
$775$	27.3682	−	47.2073i	0.983094	−	1.69573i
$776$	6.89924	−	3.98328i	0.247668	−	0.142991i
$777$	26.5272	−	26.0614i	0.951658	−	0.934948i
$778$	3.81022	+	14.2199i	0.136603	+	0.509809i
$779$	29.7189	+	17.1582i	1.06479	+	0.614758i
$780$	−23.0658	−	5.17108i	−0.825889	−	0.185154i
$781$	−11.8138	−	20.4622i	−0.422733	−	0.732194i
$782$	−2.79864	+	2.79864i	−0.100079	+	0.100079i
$783$	6.10313	−	44.8212i	0.218108	−	1.60178i
$784$	−6.38712	+	2.86439i	−0.228111	+	0.102299i
$785$	6.87242	+	3.97602i	0.245287	+	0.141910i
$786$	−26.7022	+	1.12630i	−0.952434	+	0.0401738i
$787$	−11.8589	−	44.2581i	−0.422725	−	1.57763i	−0.768842	−	0.639439i	$-0.779167\pi$
$787$	−11.8589	−	44.2581i	−0.422725	−	1.57763i	0.346117	−	0.938191i	$-0.387500\pi$
$788$	−2.77055	−	10.3398i	−0.0986968	−	0.368341i
$789$	6.35346	+	10.0055i	0.226189	+	0.356207i
$790$	−13.8832	−	8.03208i	−0.493942	−	0.285769i
$791$	−27.0163	+	41.7244i	−0.960588	+	1.48355i
$792$	1.03855	−	5.78975i	0.0369031	−	0.205730i
$793$	−10.8106	+	10.8106i	−0.383896	+	0.383896i
$794$	−9.13725	−	15.8262i	−0.324269	−	0.561650i
$795$	2.99095	−	3.24852i	0.106078	−	0.115213i
$796$	3.99723	+	2.30780i	0.141678	+	0.0817979i
$797$	11.3686	+	42.4284i	0.402698	+	1.50289i	0.808262	+	0.588823i	$0.200408\pi$
$797$	11.3686	+	42.4284i	0.402698	+	1.50289i	−0.405564	+	0.914067i	$0.632925\pi$
$798$	−29.6166	−	8.21756i	−1.04842	−	0.290898i
$799$	10.3237	−	5.96041i	0.365228	−	0.210864i
$800$	1.28543	+	4.83194i	0.0454467	+	0.170835i
$801$	−2.45561	−	29.0567i	−0.0867645	−	1.02667i
$802$	1.51750	+	1.51750i	0.0535849	+	0.0535849i
$803$	8.46405	−	31.5883i	0.298690	−	1.11473i
$804$	−0.970804	−	1.52884i	−0.0342376	−	0.0539180i
$805$	3.35687	+	15.7579i	0.118314	+	0.555393i
$806$	33.3043	−	57.6848i	1.17309	−	2.03186i
$807$	−5.43777	−	4.99761i	−0.191419	−	0.175924i
$808$	0.951626	−	3.55152i	0.0334781	−	0.124942i
$809$		−	12.7084i		−	0.446804i	−0.974726	−	0.223402i	$-0.928284\pi$
$809$		−	12.7084i		−	0.446804i	0.974726	−	0.223402i	$-0.0717163\pi$
$810$	12.8306	+	15.5041i	0.450820	+	0.544758i
$811$		−	4.44800i		−	0.156190i	−0.996946	−	0.0780952i	$-0.975116\pi$
$811$		−	4.44800i		−	0.156190i	0.996946	−	0.0780952i	$-0.0248838\pi$
$812$	15.4348	+	17.0957i	0.541654	+	0.599940i
$813$	18.3104	−	19.9231i	0.642175	−	0.698735i
$814$	−13.7794	−	7.95554i	−0.482968	−	0.278842i
$815$	−0.0192676	+	21.4751i	−0.000674916	+	0.752242i
$816$	−1.34936	−	2.12500i	−0.0472372	−	0.0743899i
$817$	0.552484	+	0.148038i	0.0193290	+	0.00517919i
$818$	15.8613	+	15.8613i	0.554578	+	0.554578i
$819$	22.8119	−	42.7371i	0.797114	−	1.49335i
$820$	11.0483	+	2.97102i	0.385824	+	0.103752i
$821$	−0.582450	−	1.00883i	−0.0203277	−	0.0352085i	0.855683	−	0.517501i	$-0.173138\pi$
$821$	−0.582450	−	1.00883i	−0.0203277	−	0.0352085i	−0.876010	+	0.482292i	$0.839804\pi$
$822$	4.95465	+	15.7955i	0.172813	+	0.550932i
$823$	−6.79075	−	25.3434i	−0.236711	−	0.883416i	−0.977370	−	0.211536i	$-0.932154\pi$
$823$	−6.79075	−	25.3434i	−0.236711	−	0.883416i	0.740660	−	0.671880i	$-0.234513\pi$
$824$	−3.51774	+	6.09291i	−0.122546	+	0.212256i
$825$	−16.5657	−	3.72945i	−0.576744	−	0.129843i
$826$	−0.0937600	+	1.83641i	−0.00326233	+	0.0638967i
$827$	37.7974	+	37.7974i	1.31434	+	1.31434i	0.918181	+	0.396162i	$0.129658\pi$
$827$	37.7974	+	37.7974i	1.31434	+	1.31434i	0.396162	+	0.918181i	$0.370342\pi$
$828$	−8.04167	−	1.44249i	−0.279467	−	0.0501299i
$829$	28.3780			0.985610			0.492805	−	0.870140i	$-0.335972\pi$
$829$	28.3780			0.985610			0.492805	+	0.870140i	$0.335972\pi$
$830$	−0.163247	+	0.0435849i	−0.00566638	+	0.00151285i
$831$	1.70316	−	1.08150i	0.0590820	−	0.0375167i
$832$	1.57968	+	5.89543i	0.0547654	+	0.204387i
$833$	−6.42351	−	7.88880i	−0.222562	−	0.273331i
$834$	0.332835	+	7.89079i	0.0115251	+	0.273236i
$835$	−22.6200	−	13.0868i	−0.782799	−	0.452886i
$836$			13.1506i			0.454823i
$837$	−52.4866	+	21.4685i	−1.81420	+	0.742060i
$838$	−4.27003	−	4.27003i	−0.147506	−	0.147506i
$839$	3.46330	+	5.99862i	0.119567	+	0.207095i	0.919596	−	0.392865i	$-0.128516\pi$
$839$	3.46330	+	5.99862i	0.119567	+	0.207095i	−0.800029	+	0.599961i	$0.795183\pi$
$840$	−10.2465	−	0.0999472i	−0.353537	−	0.00344851i
$841$	23.3924	−	40.5168i	0.806634	−	1.39713i
$842$	4.31989	−	1.15751i	0.148873	−	0.0398905i
$843$	5.60416	−	25.1031i	0.193018	−	0.864596i
$844$	4.06289	−	2.34571i	0.139851	−	0.0807428i
$845$	−14.0822	+	52.3676i	−0.484443	+	1.80150i
$846$	22.2711	+	10.4654i	0.765695	+	0.359809i
$847$	18.5129	−	3.96112i	0.636109	−	0.136106i
$848$	−1.10129	−	0.295089i	−0.0378184	−	0.0101334i
$849$	−28.1731	−	14.7190i	−0.966898	−	0.505153i
$850$	−6.29957	+	3.62200i	−0.216073	+	0.124234i
$851$	−11.0498	+	19.1389i	−0.378784	+	0.656072i
$852$	−6.24694	−	19.9153i	−0.214017	−	0.682288i
$853$	−10.9441	+	40.8438i	−0.374717	+	1.39846i	0.479040	+	0.877793i	$0.340985\pi$
$853$	−10.9441	+	40.8438i	−0.374717	+	1.39846i	−0.853757	+	0.520671i	$0.825682\pi$
$854$	−3.60204	+	5.56306i	−0.123259	+	0.190364i
$855$	−34.3543	−	29.0530i	−1.17489	−	0.993591i
$856$	10.9790			0.375256
$857$	37.6945	+	10.1002i	1.28762	+	0.345016i	0.836756	−	0.547577i	$-0.184450\pi$
$857$	37.6945	+	10.1002i	1.28762	+	0.345016i	0.450863	+	0.892593i	$0.351116\pi$
$858$	−20.2296	−	4.51617i	−0.690626	−	0.154179i
$859$	21.8260	−	37.8037i	0.744692	−	1.28984i	−0.205646	−	0.978626i	$-0.565930\pi$
$859$	21.8260	−	37.8037i	0.744692	−	1.28984i	0.950338	−	0.311218i	$-0.100737\pi$
$860$	0.190691		0.000171089i	0.00650252		5.83409e-6i
$861$	−11.9027	+	20.2008i	−0.405644	+	0.688442i
$862$	5.20260	−	19.4164i	0.177201	−	0.661324i
$863$	20.6656	−	20.6656i	0.703467	−	0.703467i	−0.261686	−	0.965153i	$-0.584279\pi$
$863$	20.6656	−	20.6656i	0.703467	−	0.703467i	0.965153	+	0.261686i	$0.0842786\pi$
$864$	2.00975	−	4.79175i	0.0683730	−	0.163019i
$865$	12.6902	+	22.0257i	0.431480	+	0.748896i
$866$	23.9849	−	13.8477i	0.815041	−	0.470564i
$867$	−17.4492	+	18.9861i	−0.592606	+	0.644800i
$868$	8.88555	−	27.4729i	0.301595	−	0.932490i
$869$	−12.1799	−	7.03209i	−0.413176	−	0.238547i
$870$	10.0622	+	32.1796i	0.341141	+	1.09099i
$871$	−5.52670	+	3.19084i	−0.187265	+	0.108118i
$872$	4.84902	+	4.84902i	0.164209	+	0.164209i
$873$	−4.21969	+	23.5242i	−0.142815	+	0.796174i
$874$	18.2655			0.617841
$875$	−1.58781	+	29.5378i	−0.0536778	+	0.998558i
$876$	13.3772	−	25.6048i	0.451972	−	0.865106i
$877$	10.5237	−	2.81981i	0.355360	−	0.0952184i	−0.0767226	−	0.997052i	$-0.524446\pi$
$877$	10.5237	−	2.81981i	0.355360	−	0.0952184i	0.432082	+	0.901834i	$0.357779\pi$
$878$	−5.37124	+	1.43922i	−0.181270	+	0.0485713i
$879$	8.32466	+	4.34919i	0.280784	+	0.146695i
$880$	1.13094	+	4.23593i	0.0381240	+	0.142793i
$881$			8.03298i			0.270638i	0.990802	+	0.135319i	$0.0432059\pi$
$881$			8.03298i			0.270638i	−0.990802	+	0.135319i	$0.956794\pi$
$882$	5.79364	−	20.1850i	0.195082	−	0.679664i
$883$	−36.7064	+	36.7064i	−1.23527	+	1.23527i	−0.273355	+	0.961913i	$0.588133\pi$
$883$	−36.7064	+	36.7064i	−1.23527	+	1.23527i	−0.961913	+	0.273355i	$0.911867\pi$
$884$	−7.68181	+	4.43509i	−0.258367	+	0.149168i
$885$	−1.24857	+	2.38463i	−0.0419701	+	0.0801585i
$886$	−12.1518	+	21.0476i	−0.408248	+	0.707106i
$887$	−2.24625	−	8.38311i	−0.0754216	−	0.281477i	0.917907	−	0.396796i	$-0.129878\pi$
$887$	−2.24625	−	8.38311i	−0.0754216	−	0.281477i	−0.993329	+	0.115318i	$0.963211\pi$
$888$	−10.3487	−	9.51103i	−0.347280	−	0.319169i
$889$	0.509335	−	9.97596i	0.0170826	−	0.334583i
$890$	10.8505	+	18.8326i	0.363710	+	0.631272i
$891$	11.2628	+	13.5848i	0.377319	+	0.455108i
$892$	13.3792	−	13.3792i	0.447970	−	0.447970i
$893$	−53.1398	−	14.2388i	−1.77825	−	0.476482i
$894$	−1.63700	+	0.0690488i	−0.0547494	+	0.00230934i
$895$	6.58206	+	6.59388i	0.220014	+	0.220409i
$896$	1.20432	+	2.35576i	0.0402336	+	0.0787004i
$897$	−6.27272	+	28.0978i	−0.209440	+	0.938159i
$898$	−33.5361	−	8.98596i	−1.11911	−	0.299865i
$899$	−95.0058			−3.16862
$900$	−13.5643	−	6.40378i	−0.452145	−	0.213459i
$901$		−	1.65698i		−	0.0552021i
$902$	9.69017	+	2.59647i	0.322647	+	0.0864531i
$903$	−0.104486	+	0.376574i	−0.00347708	+	0.0125316i
$904$	16.2705	+	9.39378i	0.541149	+	0.312432i
$905$	−13.0857	−	13.1092i	−0.434984	−	0.435765i
$906$	−14.1578	−	7.39668i	−0.470360	−	0.245738i
$907$	6.95995	−	25.9749i	0.231101	−	0.862482i	−0.748767	−	0.662834i	$-0.769354\pi$
$907$	6.95995	−	25.9749i	0.231101	−	0.862482i	0.979868	−	0.199648i	$-0.0639798\pi$
$908$	12.5335	+	12.5335i	0.415940	+	0.415940i
$909$	6.30004	+	9.05424i	0.208959	+	0.300310i
$910$	−1.87350	+	36.0596i	−0.0621061	+	1.19536i
$911$	−7.60533	−	13.1728i	−0.251976	−	0.436435i	0.712094	−	0.702084i	$-0.247747\pi$
$911$	−7.60533	−	13.1728i	−0.251976	−	0.436435i	−0.964070	+	0.265649i	$0.914414\pi$
$912$	−2.53112	+	11.3378i	−0.0838139	+	0.375433i
$913$	−0.143110	+	0.0383463i	−0.00473626	+	0.00126908i
$914$	−12.0594	−	6.96251i	−0.398890	−	0.230299i
$915$	−8.19453	+	5.19317i	−0.270903	+	0.171681i
$916$	−0.0438001	+	0.0252880i	−0.00144720	+	0.000835540i
$917$	8.54170	+	39.9209i	0.282072	+	1.31830i
$918$	7.48262	+	1.01888i	0.246963	+	0.0336280i
$919$		−	24.4822i		−	0.807593i	−0.914849	−	0.403797i	$-0.867690\pi$
$919$		−	24.4822i		−	0.807593i	0.914849	−	0.403797i	$-0.132310\pi$
$920$	5.88349	−	1.57082i	0.193973	−	0.0517884i
$921$	20.8941	−	0.881316i	0.688484	−	0.0290404i
$922$	5.46836	+	20.4082i	0.180091	+	0.672108i
$923$	−71.0430	+	19.0359i	−2.33841	+	0.626575i
$924$	−8.98479	−	0.0795786i	−0.295578	−	0.00261794i
$925$	−28.7420	+	28.6390i	−0.945031	+	0.941646i
$926$	−9.57841			−0.314766
$927$	−7.16017	−	19.8548i	−0.235171	−	0.652118i
$928$	6.15568	−	6.15568i	0.202070	−	0.202070i
$929$	−4.99850	−	8.65766i	−0.163995	−	0.284048i	0.772303	−	0.635255i	$-0.219105\pi$
$929$	−4.99850	−	8.65766i	−0.163995	−	0.284048i	−0.936298	+	0.351206i	$0.885772\pi$
$930$	28.6293	−	31.0948i	0.938792	−	1.01964i
$931$	−4.78164	+	46.7051i	−0.156712	+	1.53070i
$932$	−26.6465	+	7.13990i	−0.872834	+	0.233875i
$933$	−1.25357	−	3.99640i	−0.0410401	−	0.130836i
$934$	12.4273	+	21.5247i	0.406634	+	0.704310i
$935$	−5.52099	+	3.18094i	−0.180556	+	0.104028i
$936$	−16.5717	−	7.78724i	−0.541664	−	0.254534i
$937$	14.2616	−	14.2616i	0.465906	−	0.465906i	−0.434679	−	0.900585i	$-0.643138\pi$
$937$	14.2616	−	14.2616i	0.465906	−	0.465906i	0.900585	+	0.434679i	$0.143138\pi$
$938$	−2.05333	+	1.85384i	−0.0670435	+	0.0605301i
$939$	2.35755	−	1.49703i	0.0769357	−	0.0488538i
$940$	−18.3413	−	0.0164559i	−0.598227	−	0.000536733i
$941$	−26.6786	−	15.4029i	−0.869697	−	0.502120i	−0.00244950	−	0.999997i	$-0.500780\pi$
$941$	−26.6786	−	15.4029i	−0.869697	−	0.502120i	−0.867248	+	0.497877i	$0.834113\pi$
$942$	4.52816	+	4.16162i	0.147535	+	0.135593i
$943$	3.60637	−	13.4592i	0.117440	−	0.438290i
$944$	0.695000			0.0226203
$945$	20.0575	−	23.2958i	0.652472	−	0.757813i
$946$	0.167210			0.00543645
$947$	−7.08246	+	26.4321i	−0.230149	+	0.858928i	0.750127	+	0.661294i	$0.229992\pi$
$947$	−7.08246	+	26.4321i	−0.230149	+	0.858928i	−0.980276	+	0.197634i	$0.936674\pi$
$948$	−9.14748	−	8.40703i	−0.297096	−	0.273048i
$949$	−88.1595	−	50.8989i	−2.86178	−	1.65225i
$950$	32.3769	+	8.73765i	1.05044	+	0.283487i
$951$	33.3298	−	21.1642i	1.08079	−	0.686297i
$952$	−2.85401	+	2.57674i	−0.0924990	+	0.0835125i
$953$	−1.18508	+	1.18508i	−0.0383885	+	0.0383885i	−0.726040	−	0.687652i	$-0.758642\pi$
$953$	−1.18508	+	1.18508i	−0.0383885	+	0.0383885i	0.687652	+	0.726040i	$0.258642\pi$
$954$	2.80762	−	1.95358i	0.0909001	−	0.0632493i
$955$	−22.3926	−	6.02162i	−0.724608	−	0.194855i
$956$	5.65467	+	9.79417i	0.182885	+	0.316766i
$957$	8.84846	+	28.2091i	0.286030	+	0.911869i
$958$	−0.545983	+	0.146296i	−0.0176399	+	0.00472660i
$959$	22.5156	−	11.5105i	0.727066	−	0.371694i
$960$	0.159746	+	3.86969i	0.00515578	+	0.124894i
$961$	44.0508	+	76.2983i	1.42099	+	2.46124i
$962$	−35.0220	+	35.0220i	−1.12915	+	1.12915i
$963$	−21.2461	+	25.1686i	−0.684645	+	0.811047i
$964$	8.39805			0.270483
$965$	30.7631	+	17.7979i	0.990300	+	0.572935i
$966$	−0.110531	+	12.4794i	−0.00355626	+	0.401519i
$967$	6.66891	−	1.78693i	0.214458	−	0.0574637i	−0.149991	−	0.988687i	$-0.547924\pi$
$967$	6.66891	−	1.78693i	0.214458	−	0.0574637i	0.364448	+	0.931224i	$0.381258\pi$
$968$	−1.85200	−	6.91176i	−0.0595255	−	0.222152i
$969$	−16.8681	+	0.711499i	−0.541881	+	0.0228566i
$970$	−4.59510	−	17.2109i	−0.147540	−	0.552609i
$971$			21.4664i			0.688888i	0.938807	+	0.344444i	$0.111933\pi$
$971$			21.4664i			0.688888i	−0.938807	+	0.344444i	$0.888067\pi$
$972$	7.09557	+	13.8799i	0.227590	+	0.445200i
$973$	11.7971	−	2.52417i	0.378197	−	0.0809212i
$974$	−1.25696	+	0.725708i	−0.0402757	+	0.0232532i
$975$	−24.5599	+	46.8046i	−0.786547	+	1.49895i
$976$	2.16932	+	1.25246i	0.0694383	+	0.0400902i
$977$	46.0463	−	12.3381i	1.47315	−	0.394730i	0.569141	−	0.822240i	$-0.307276\pi$
$977$	46.0463	−	12.3381i	1.47315	−	0.394730i	0.904010	+	0.427510i	$0.140609\pi$
$978$	−3.62438	+	16.2349i	−0.115895	+	0.519136i
$979$	9.52920	+	16.5051i	0.304555	+	0.527504i
$980$	2.47639	+	15.4553i	0.0791053	+	0.493703i
$981$	−20.4996	+	1.73243i	−0.654501	+	0.0553123i
$982$	4.97296	+	4.97296i	0.158693	+	0.158693i
$983$	−8.55876	+	31.9417i	−0.272982	+	1.01878i	0.684199	+	0.729295i	$0.260152\pi$
$983$	−8.55876	+	31.9417i	−0.272982	+	1.01878i	−0.957182	+	0.289488i	$0.906515\pi$
$984$	7.85465	+	4.10364i	0.250397	+	0.130819i
$985$	−23.9362	−	0.0214757i	−0.762670	−	0.000684272i
$986$	10.9568	+	6.32590i	0.348935	+	0.201458i
$987$	10.0498	−	36.2201i	0.319889	−	1.15290i
$988$	39.5409	+	10.5949i	1.25796	+	0.337070i
$989$		−	0.232246i		−	0.00738498i
$990$	−11.8991	−	5.60455i	−0.378177	−	0.178124i
$991$	−37.7078			−1.19783			−0.598914	−	0.800813i	$-0.704401\pi$
$991$	−37.7078			−1.19783			−0.598914	+	0.800813i	$0.704401\pi$
$992$	−10.5415	−	2.82459i	−0.334693	−	0.0896808i
$993$	4.98829	−	22.3444i	0.158298	−	0.709077i
$994$	−28.3881	+	14.5127i	−0.900417	+	0.460315i
$995$	7.30446	−	7.29136i	0.231567	−	0.231152i
$996$	−0.130763	+	0.00551562i	−0.00414340	+	0.000174769i
$997$	57.0938	+	15.2982i	1.80818	+	0.484500i	0.995206	−	0.0978000i	$-0.0311806\pi$
$997$	57.0938	+	15.2982i	1.80818	+	0.484500i	0.812974	+	0.582300i	$0.197847\pi$
$998$	14.6604	−	14.6604i	0.464066	−	0.464066i
$999$	41.8296	−	5.31839i	1.32343	−	0.168266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bz.a.517.18	yes	192
5.3	odd	4	inner	630.2.bz.a.13.30	✓	192
7.6	odd	2	inner	630.2.bz.a.517.7	yes	192
9.7	even	3	inner	630.2.bz.a.97.43	yes	192
35.13	even	4	inner	630.2.bz.a.13.43	yes	192
45.43	odd	12	inner	630.2.bz.a.223.7	yes	192
63.34	odd	6	inner	630.2.bz.a.97.30	yes	192
315.223	even	12	inner	630.2.bz.a.223.18	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bz.a.13.30	✓	192	5.3	odd	4	inner
630.2.bz.a.13.43	yes	192	35.13	even	4	inner
630.2.bz.a.97.30	yes	192	63.34	odd	6	inner
630.2.bz.a.97.43	yes	192	9.7	even	3	inner
630.2.bz.a.223.7	yes	192	45.43	odd	12	inner
630.2.bz.a.223.18	yes	192	315.223	even	12	inner
630.2.bz.a.517.7	yes	192	7.6	odd	2	inner
630.2.bz.a.517.18	yes	192	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.27527 + 1.17204i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.58256 + 1.57972i) q^{5} +(-1.46217 + 0.928470i) q^{6} +(1.77300 + 1.96379i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.252632 + 2.98934i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.27527 + 1.17204i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.58256 + 1.57972i) q^{5} +(-1.46217 + 0.928470i) q^{6} +(1.77300 + 1.96379i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.252632 + 2.98934i) q^{9} +(-1.11630 - 1.93749i) q^{10} +(-0.980360 - 1.69803i) q^{11} +(-0.518396 - 1.65265i) q^{12} +(-5.89543 + 1.57968i) q^{13} +(-2.35576 + 1.20432i) q^{14} +(-3.86969 + 0.159746i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.02765 + 1.02765i) q^{17} +(-2.95287 - 0.529676i) q^{18} +6.70703 q^{19} +(2.16039 - 0.576799i) q^{20} +(-0.0405864 + 4.58240i) q^{21} +(1.89391 - 0.507471i) q^{22} +(-0.704852 - 2.63054i) q^{23} +(1.73051 - 0.0729933i) q^{24} +(0.00897205 - 4.99999i) q^{25} -6.10340i q^{26} +(-3.18147 + 4.10832i) q^{27} +(-0.553570 - 2.58719i) q^{28} +(-7.53914 + 4.35272i) q^{29} +(0.847246 - 3.77918i) q^{30} +(9.45126 + 5.45669i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.739943 - 3.31447i) q^{33} +(-0.726660 - 1.25861i) q^{34} +(-5.90811 - 0.306961i) q^{35} +(1.27589 - 2.71516i) q^{36} +(-5.73811 - 5.73811i) q^{37} +(-1.73591 + 6.47850i) q^{38} +(-9.36972 - 4.89518i) q^{39} +(-0.00200621 + 2.23607i) q^{40} +(4.43101 + 2.55825i) q^{41} +(-4.41575 - 1.22521i) q^{42} +(0.0823739 + 0.0220720i) q^{43} +1.96072i q^{44} +(-5.12213 - 4.33172i) q^{45} +2.72334 q^{46} +(-7.92299 - 2.12296i) q^{47} +(-0.377383 + 1.69044i) q^{48} +(-0.712929 + 6.96360i) q^{49} +(4.82730 + 1.30276i) q^{50} +(-2.51499 + 0.106083i) q^{51} +(5.89543 + 1.57968i) q^{52} +(-0.806198 + 0.806198i) q^{53} +(-3.14491 - 4.13637i) q^{54} +(4.23389 + 1.13854i) q^{55} +(2.64231 + 0.134906i) q^{56} +(8.55329 + 7.86093i) q^{57} +(-2.25314 - 8.40882i) q^{58} +(0.347500 - 0.601888i) q^{59} +(3.43112 + 1.79650i) q^{60} +(2.16932 - 1.25246i) q^{61} +(-7.71692 + 7.71692i) q^{62} +(-5.42252 + 5.79623i) q^{63} -1.00000i q^{64} +(6.83441 - 11.8131i) q^{65} +(3.01003 + 1.57258i) q^{66} +(1.00997 - 0.270620i) q^{67} +(1.40380 - 0.376147i) q^{68} +(2.18423 - 4.18077i) q^{69} +(1.82563 - 5.62735i) q^{70} +12.0505 q^{71} +(2.29242 + 1.93515i) q^{72} +(11.7937 + 11.7937i) q^{73} +(7.02773 - 4.05746i) q^{74} +(5.87165 - 6.36583i) q^{75} +(-5.80846 - 3.35352i) q^{76} +(1.59640 - 4.93583i) q^{77} +(7.15344 - 7.78349i) q^{78} +(6.21197 - 3.58649i) q^{79} +(-2.15936 - 0.580675i) q^{80} +(-8.87235 + 1.51041i) q^{81} +(-3.61791 + 3.61791i) q^{82} +(0.0195572 - 0.0729886i) q^{83} +(2.32635 - 3.94818i) q^{84} +(0.00291567 - 3.24972i) q^{85} +(-0.0426399 + 0.0738544i) q^{86} +(-14.7160 - 3.28529i) q^{87} +(-1.89391 - 0.507471i) q^{88} -9.72011 q^{89} +(5.50982 - 3.82647i) q^{90} +(-13.5548 - 8.77661i) q^{91} +(-0.704852 + 2.63054i) q^{92} +(5.65744 + 18.0360i) q^{93} +(4.10124 - 7.10356i) q^{94} +(-10.6143 + 10.5952i) q^{95} +(-1.53516 - 0.802042i) q^{96} +(7.69510 + 2.06190i) q^{97} +(-6.54180 - 2.49095i) q^{98} +(4.82833 - 3.35961i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} + 24 q^{15} + 96 q^{16} - 8 q^{18} + 8 q^{23} + 48 q^{30} - 24 q^{35} + 8 q^{36} - 44 q^{42} + 48 q^{46} + 32 q^{50} - 160 q^{53} - 4 q^{56} + 88 q^{57} + 24 q^{58} + 8 q^{60} - 48 q^{63} - 8 q^{65} + 16 q^{71} + 16 q^{72} - 16 q^{77} - 16 q^{78} - 8 q^{81} - 16 q^{86} + 8 q^{92} - 120 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) \) 192 * q + 8 * q^11 + 24 * q^15 + 96 * q^16 - 8 * q^18 + 8 * q^23 + 48 * q^30 - 24 * q^35 + 8 * q^36 - 44 * q^42 + 48 * q^46 + 32 * q^50 - 160 * q^53 - 4 * q^56 + 88 * q^57 + 24 * q^58 + 8 * q^60 - 48 * q^63 - 8 * q^65 + 16 * q^71 + 16 * q^72 - 16 * q^77 - 16 * q^78 - 8 * q^81 - 16 * q^86 + 8 * q^92 - 120 * q^93 - 128 * q^95 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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