LMFDB - Embedded newform 690.2.q.a.11.6

Newspace parameters

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (of order $22$, degree $10$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	690.11
Dual form			690.2.q.a.251.6

$q$-expansion

$f(q)$	$=$	$q+(-0.540641 - 0.841254i) q^{2} +(1.20125 + 1.24780i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.400274 - 1.68516i) q^{6} +(-1.03609 + 0.897775i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-0.114014 + 2.99783i) q^{9} +O(q^{10})$	\(q+(-0.540641 - 0.841254i) q^{2} +(1.20125 + 1.24780i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.400274 - 1.68516i) q^{6} +(-1.03609 + 0.897775i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-0.114014 + 2.99783i) q^{9} +(0.755750 + 0.654861i) q^{10} +(0.339703 + 0.218314i) q^{11} +(-1.63406 + 0.574337i) q^{12} +(-4.17553 + 4.81882i) q^{13} +(1.31541 + 0.386239i) q^{14} +(-1.50413 - 0.858826i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-2.37786 - 5.20678i) q^{17} +(2.58358 - 1.52484i) q^{18} +(-7.48553 - 3.41853i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-2.36484 - 0.214382i) q^{21} -0.403806i q^{22} +(2.16418 + 4.27976i) q^{23} +(1.36660 + 1.06414i) q^{24} +(0.841254 - 0.540641i) q^{25} +(6.31131 + 0.907429i) q^{26} +(-3.87766 + 3.45887i) q^{27} +(-0.386239 - 1.31541i) q^{28} +(3.60769 - 1.64758i) q^{29} +(0.0907058 + 1.72967i) q^{30} +(0.0831939 + 0.578626i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(0.135655 + 0.686131i) q^{33} +(-3.09466 + 4.81538i) q^{34} +(0.741187 - 1.15331i) q^{35} +(-2.67956 - 1.34906i) q^{36} +(0.143089 - 0.487316i) q^{37} +(1.17114 + 8.14542i) q^{38} +(-11.0288 + 0.578359i) q^{39} +(-0.909632 + 0.415415i) q^{40} +(1.20245 + 4.09517i) q^{41} +(1.09818 + 2.10534i) q^{42} +(-1.84231 - 0.264885i) q^{43} +(-0.339703 + 0.218314i) q^{44} +(-0.735192 - 2.90852i) q^{45} +(2.43032 - 4.13444i) q^{46} +9.15703i q^{47} +(0.156376 - 1.72498i) q^{48} +(-0.728726 + 5.06840i) q^{49} +(-0.909632 - 0.415415i) q^{50} +(3.64063 - 9.22172i) q^{51} +(-2.64877 - 5.80000i) q^{52} +(-2.93753 - 3.39009i) q^{53} +(5.00621 + 1.39209i) q^{54} +(-0.387449 - 0.113765i) q^{55} +(-0.897775 + 1.03609i) q^{56} +(-4.72633 - 13.4469i) q^{57} +(-3.33649 - 2.14423i) q^{58} +(-0.376830 - 0.326525i) q^{59} +(1.40606 - 1.01144i) q^{60} +(-5.55432 + 0.798591i) q^{61} +(0.441794 - 0.382816i) q^{62} +(-2.57325 - 3.20838i) q^{63} +(0.959493 - 0.281733i) q^{64} +(2.64877 - 5.80000i) q^{65} +(0.503869 - 0.485070i) q^{66} +(1.46086 + 2.27314i) q^{67} +5.72405 q^{68} +(-2.74057 + 7.84151i) q^{69} -1.37094 q^{70} +(-2.81276 - 4.37673i) q^{71} +(0.313783 + 2.98354i) q^{72} +(-4.54208 + 9.94576i) q^{73} +(-0.487316 + 0.143089i) q^{74} +(1.68516 + 0.400274i) q^{75} +(6.21920 - 5.38897i) q^{76} +(-0.547959 + 0.0787847i) q^{77} +(6.44915 + 8.96530i) q^{78} +(8.40212 + 7.28048i) q^{79} +(0.841254 + 0.540641i) q^{80} +(-8.97400 - 0.683588i) q^{81} +(2.79499 - 3.22559i) q^{82} +(10.4602 + 3.07139i) q^{83} +(1.17740 - 2.06208i) q^{84} +(3.74846 + 4.32595i) q^{85} +(0.773195 + 1.69306i) q^{86} +(6.38957 + 2.52253i) q^{87} +(0.367315 + 0.167747i) q^{88} +(-0.413934 + 2.87897i) q^{89} +(-2.04933 + 2.19095i) q^{90} -8.74141i q^{91} +(-4.79204 + 0.190732i) q^{92} +(-0.622074 + 0.798882i) q^{93} +(7.70338 - 4.95066i) q^{94} +(8.14542 + 1.17114i) q^{95} +(-1.53569 + 0.801041i) q^{96} +(5.21815 + 17.7714i) q^{97} +(4.65779 - 2.12714i) q^{98} +(-0.693199 + 0.993482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} + O(q^{10}) $	$ 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} - 12q^{11} - 12q^{14} - 16q^{16} - 8q^{18} + 16q^{20} + 62q^{21} + 4q^{23} + 2q^{24} - 16q^{25} + 42q^{27} - 2q^{30} - 4q^{31} + 16q^{33} + 2q^{36} + 72q^{38} - 124q^{39} + 44q^{41} + 44q^{43} + 12q^{44} - 2q^{45} + 4q^{46} + 70q^{49} - 2q^{51} - 52q^{53} + 92q^{54} + 10q^{55} - 54q^{56} - 38q^{57} - 36q^{58} - 44q^{61} - 220q^{63} + 16q^{64} - 34q^{66} - 44q^{67} + 22q^{69} - 12q^{70} - 36q^{72} - 28q^{73} - 24q^{74} - 88q^{77} - 54q^{78} - 44q^{79} - 16q^{80} - 66q^{81} - 28q^{82} + 4q^{83} - 18q^{84} + 158q^{86} - 64q^{87} + 80q^{89} - 8q^{90} - 4q^{92} + 4q^{93} + 24q^{94} - 2q^{96} - 88q^{98} + 190q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.540641	−	0.841254i	−0.382291	−	0.594856i
$2$	−0.540641	−	0.841254i	−0.382291	−	0.594856i
$3$	1.20125	+	1.24780i	0.693540	+	0.720418i
$3$	1.20125	+	1.24780i	0.693540	+	0.720418i
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	0.400274	−	1.68516i	0.163411	−	0.687966i
$7$	−1.03609	+	0.897775i	−0.391605	+	0.339327i	−0.828303	−	0.560281i	$-0.810693\pi$
$7$	−1.03609	+	0.897775i	−0.391605	+	0.339327i	0.436698	+	0.899608i	$0.356148\pi$
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	−0.114014	+	2.99783i	−0.0380046	+	0.999278i
$10$	0.755750	+	0.654861i	0.238989	+	0.207085i
$11$	0.339703	+	0.218314i	0.102424	+	0.0658241i	0.590850	−	0.806781i	$-0.298792\pi$
$11$	0.339703	+	0.218314i	0.102424	+	0.0658241i	−0.488426	+	0.872605i	$0.662429\pi$
$12$	−1.63406	+	0.574337i	−0.471711	+	0.165797i
$13$	−4.17553	+	4.81882i	−1.15808	+	1.33650i	−0.226055	+	0.974115i	$0.572583\pi$
$13$	−4.17553	+	4.81882i	−1.15808	+	1.33650i	−0.932028	+	0.362385i	$0.881963\pi$
$14$	1.31541	+	0.386239i	0.351558	+	0.103227i
$15$	−1.50413	−	0.858826i	−0.388366	−	0.221748i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−2.37786	−	5.20678i	−0.576715	−	1.26283i	−0.943144	−	0.332384i	$-0.892147\pi$
$17$	−2.37786	−	5.20678i	−0.576715	−	1.26283i	0.366429	−	0.930446i	$-0.380580\pi$
$18$	2.58358	−	1.52484i	0.608955	−	0.359407i
$19$	−7.48553	−	3.41853i	−1.71730	−	0.784264i	−0.995770	−	0.0918787i	$-0.970713\pi$
$19$	−7.48553	−	3.41853i	−1.71730	−	0.784264i	−0.721528	−	0.692385i	$-0.756560\pi$
$20$	0.142315	−	0.989821i	0.0318226	−	0.221331i
$21$	−2.36484	−	0.214382i	−0.516051	−	0.0467820i
$22$		−	0.403806i		−	0.0860917i
$23$	2.16418	+	4.27976i	0.451263	+	0.892391i
$23$	2.16418	+	4.27976i	0.451263	+	0.892391i
$24$	1.36660	+	1.06414i	0.278956	+	0.217218i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	6.31131	+	0.907429i	1.23775	+	0.177962i
$27$	−3.87766	+	3.45887i	−0.746255	+	0.665660i
$28$	−0.386239	−	1.31541i	−0.0729923	−	0.248589i
$29$	3.60769	−	1.64758i	0.669931	−	0.305947i	−0.0512583	−	0.998685i	$-0.516323\pi$
$29$	3.60769	−	1.64758i	0.669931	−	0.305947i	0.721189	+	0.692738i	$0.243596\pi$
$30$	0.0907058	+	1.72967i	0.0165605	+	0.315794i
$31$	0.0831939	+	0.578626i	0.0149421	+	0.103924i	0.995928	−	0.0901564i	$-0.0287367\pi$
$31$	0.0831939	+	0.578626i	0.0149421	+	0.103924i	−0.980986	+	0.194081i	$0.937828\pi$
$32$	−0.281733	+	0.959493i	−0.0498038	+	0.169616i
$33$	0.135655	+	0.686131i	0.0236145	+	0.119440i
$34$	−3.09466	+	4.81538i	−0.530729	+	0.825830i
$35$	0.741187	−	1.15331i	0.125283	−	0.194945i
$36$	−2.67956	−	1.34906i	−0.446594	−	0.224843i
$37$	0.143089	−	0.487316i	0.0235236	−	0.0801142i	−0.946895	−	0.321544i	$-0.895798\pi$
$37$	0.143089	−	0.487316i	0.0235236	−	0.0801142i	0.970418	+	0.241430i	$0.0776164\pi$
$38$	1.17114	+	8.14542i	0.189983	+	1.32136i
$39$	−11.0288	+	0.578359i	−1.76602	+	0.0926116i
$40$	−0.909632	+	0.415415i	−0.143825	+	0.0656829i
$41$	1.20245	+	4.09517i	0.187791	+	0.639559i	0.998533	+	0.0541541i	$0.0172462\pi$
$41$	1.20245	+	4.09517i	0.187791	+	0.639559i	−0.810741	+	0.585405i	$0.800936\pi$
$42$	1.09818	+	2.10534i	0.169453	+	0.324860i
$43$	−1.84231	−	0.264885i	−0.280950	−	0.0403945i	0.000399236	−	1.00000i	$-0.499873\pi$
$43$	−1.84231	−	0.264885i	−0.280950	−	0.0403945i	−0.281349	+	0.959605i	$0.590782\pi$
$44$	−0.339703	+	0.218314i	−0.0512122	+	0.0329121i
$45$	−0.735192	−	2.90852i	−0.109596	−	0.433577i
$46$	2.43032	−	4.13444i	0.358331	−	0.609589i
$47$			9.15703i			1.33569i	0.744300	+	0.667845i	$0.232783\pi$
$47$			9.15703i			1.33569i	−0.744300	+	0.667845i	$0.767217\pi$
$48$	0.156376	−	1.72498i	0.0225709	−	0.248979i
$49$	−0.728726	+	5.06840i	−0.104104	+	0.724057i
$50$	−0.909632	−	0.415415i	−0.128641	−	0.0587486i
$51$	3.64063	−	9.22172i	0.509790	−	1.29130i
$52$	−2.64877	−	5.80000i	−0.367319	−	0.804316i
$53$	−2.93753	−	3.39009i	−0.403501	−	0.465665i	0.517239	−	0.855841i	$-0.326960\pi$
$53$	−2.93753	−	3.39009i	−0.403501	−	0.465665i	−0.920740	+	0.390176i	$0.872414\pi$
$54$	5.00621	+	1.39209i	0.681258	+	0.189439i
$55$	−0.387449	−	0.113765i	−0.0522436	−	0.0153401i
$56$	−0.897775	+	1.03609i	−0.119970	+	0.138453i
$57$	−4.72633	−	13.4469i	−0.626017	−	1.78109i
$58$	−3.33649	−	2.14423i	−0.438103	−	0.281552i
$59$	−0.376830	−	0.326525i	−0.0490591	−	0.0425099i	0.629986	−	0.776606i	$-0.283061\pi$
$59$	−0.376830	−	0.326525i	−0.0490591	−	0.0425099i	−0.679045	+	0.734096i	$0.737606\pi$
$60$	1.40606	−	1.01144i	0.181521	−	0.130576i
$61$	−5.55432	+	0.798591i	−0.711158	+	0.102249i	−0.488394	−	0.872623i	$-0.662417\pi$
$61$	−5.55432	+	0.798591i	−0.711158	+	0.102249i	−0.222764	+	0.974872i	$0.571508\pi$
$62$	0.441794	−	0.382816i	0.0561078	−	0.0486177i
$63$	−2.57325	−	3.20838i	−0.324199	−	0.404218i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	2.64877	−	5.80000i	0.328540	−	0.719402i
$66$	0.503869	−	0.485070i	0.0620220	−	0.0597080i
$67$	1.46086	+	2.27314i	0.178472	+	0.277708i	0.918951	−	0.394371i	$-0.129038\pi$
$67$	1.46086	+	2.27314i	0.178472	+	0.277708i	−0.740479	+	0.672080i	$0.765401\pi$
$68$	5.72405			0.694143
$69$	−2.74057	+	7.84151i	−0.329926	+	0.944007i
$70$	−1.37094			−0.163859
$71$	−2.81276	−	4.37673i	−0.333813	−	0.519423i	0.633255	−	0.773944i	$-0.281719\pi$
$71$	−2.81276	−	4.37673i	−0.333813	−	0.519423i	−0.967067	+	0.254521i	$0.918082\pi$
$72$	0.313783	+	2.98354i	0.0369797	+	0.351614i
$73$	−4.54208	+	9.94576i	−0.531610	+	1.16406i	0.433244	+	0.901277i	$0.357369\pi$
$73$	−4.54208	+	9.94576i	−0.531610	+	1.16406i	−0.964854	+	0.262787i	$0.915358\pi$
$74$	−0.487316	+	0.143089i	−0.0566493	+	0.0166337i
$75$	1.68516	+	0.400274i	0.194586	+	0.0462197i
$76$	6.21920	−	5.38897i	0.713391	−	0.618157i
$77$	−0.547959	+	0.0787847i	−0.0624458	+	0.00897834i
$78$	6.44915	+	8.96530i	0.730222	+	1.01512i
$79$	8.40212	+	7.28048i	0.945313	+	0.819118i	0.983640	−	0.180147i	$-0.0576574\pi$
$79$	8.40212	+	7.28048i	0.945313	+	0.819118i	−0.0383271	+	0.999265i	$0.512203\pi$
$80$	0.841254	+	0.540641i	0.0940550	+	0.0604455i
$81$	−8.97400	−	0.683588i	−0.997111	−	0.0759542i
$82$	2.79499	−	3.22559i	0.308655	−	0.356206i
$83$	10.4602	+	3.07139i	1.14815	+	0.337129i	0.799819	−	0.600241i	$-0.204929\pi$
$83$	10.4602	+	3.07139i	1.14815	+	0.337129i	0.348336	+	0.937370i	$0.386747\pi$
$84$	1.17740	−	2.06208i	0.128465	−	0.224991i
$85$	3.74846	+	4.32595i	0.406577	+	0.469215i
$86$	0.773195	+	1.69306i	0.0833757	+	0.182567i
$87$	6.38957	+	2.52253i	0.685034	+	0.270444i
$88$	0.367315	+	0.167747i	0.0391559	+	0.0178819i
$89$	−0.413934	+	2.87897i	−0.0438769	+	0.305171i	0.956051	+	0.293199i	$0.0947199\pi$
$89$	−0.413934	+	2.87897i	−0.0438769	+	0.305171i	−0.999928	+	0.0119716i	$0.996189\pi$
$90$	−2.04933	+	2.19095i	−0.216018	+	0.230946i
$91$		−	8.74141i		−	0.916349i
$92$	−4.79204	+	0.190732i	−0.499604	+	0.0198852i
$93$	−0.622074	+	0.798882i	−0.0645061	+	0.0828403i
$94$	7.70338	−	4.95066i	0.794543	−	0.510622i
$95$	8.14542	+	1.17114i	0.835703	+	0.120156i
$96$	−1.53569	+	0.801041i	−0.156735	+	0.0817560i
$97$	5.21815	+	17.7714i	0.529822	+	1.80441i	0.591489	+	0.806313i	$0.298540\pi$
$97$	5.21815	+	17.7714i	0.529822	+	1.80441i	−0.0616669	+	0.998097i	$0.519642\pi$
$98$	4.65779	−	2.12714i	0.470508	−	0.214874i
$99$	−0.693199	+	0.993482i	−0.0696692	+	0.0998487i
$100$	0.142315	+	0.989821i	0.0142315	+	0.0989821i
$101$	3.61987	−	12.3282i	0.360191	−	1.22670i	−0.557760	−	0.830003i	$-0.688339\pi$
$101$	3.61987	−	12.3282i	0.360191	−	1.22670i	0.917950	−	0.396695i	$-0.129843\pi$
$102$	−9.72608	+	1.92294i	−0.963025	+	0.190400i
$103$	−0.0748719	+	0.116503i	−0.00737734	+	0.0114794i	−0.844923	−	0.534889i	$-0.820354\pi$
$103$	−0.0748719	+	0.116503i	−0.00737734	+	0.0114794i	0.837545	+	0.546368i	$0.183990\pi$
$104$	−3.44724	+	5.36401i	−0.338030	+	0.525984i
$105$	2.32945	−	0.460555i	0.227331	−	0.0449456i
$106$	−1.26378	+	4.30403i	−0.122749	+	0.418044i
$107$	−0.764728	−	5.31880i	−0.0739291	−	0.514188i	−0.992814	−	0.119664i	$-0.961818\pi$
$107$	−0.764728	−	5.31880i	−0.0739291	−	0.514188i	0.918885	−	0.394525i	$-0.129091\pi$
$108$	−1.53546	−	4.96411i	−0.147750	−	0.477671i
$109$	8.11507	−	3.70603i	0.777283	−	0.354973i	0.0130511	−	0.999915i	$-0.495846\pi$
$109$	8.11507	−	3.70603i	0.777283	−	0.354973i	0.764232	+	0.644942i	$0.223118\pi$
$110$	0.113765	+	0.387449i	0.0108471	+	0.0369418i
$111$	0.779958	−	0.406840i	0.0740303	−	0.0386155i
$112$	1.35699	+	0.195105i	0.128223	+	0.0184357i
$113$	1.64447	−	1.05684i	0.154699	−	0.0994189i	−0.461001	−	0.887399i	$-0.652510\pi$
$113$	1.64447	−	1.05684i	0.154699	−	0.0994189i	0.615700	+	0.787981i	$0.288873\pi$
$114$	−8.75704	+	11.2460i	−0.820172	+	1.05328i
$115$	−3.28226	−	3.49668i	−0.306073	−	0.326067i
$116$			3.96610i			0.368243i
$117$	−13.9699	−	13.0670i	−1.29152	−	1.20804i
$118$	−0.0709607	+	0.493542i	−0.00653246	+	0.0454342i
$119$	7.13819	+	3.25990i	0.654357	+	0.298835i
$120$	−1.61105	−	0.636024i	−0.147068	−	0.0580608i
$121$	−4.50183	−	9.85763i	−0.409257	−	0.896148i
$122$	3.67471	+	4.24084i	0.332693	+	0.383948i
$123$	−3.66552	+	6.41973i	−0.330509	+	0.578848i
$124$	−0.560897	−	0.164694i	−0.0503701	−	0.0147900i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−1.30785	+	3.89934i	−0.116513	+	0.347381i
$127$	13.2936	+	8.54326i	1.17961	+	0.758091i	0.975315	−	0.220817i	$-0.0708725\pi$
$127$	13.2936	+	8.54326i	1.17961	+	0.758091i	0.204298	+	0.978909i	$0.434509\pi$
$128$	−0.755750	−	0.654861i	−0.0667995	−	0.0578821i
$129$	−1.88255	−	2.61703i	−0.165749	−	0.230417i
$130$	−6.31131	+	0.907429i	−0.553538	+	0.0795868i
$131$	10.5952	−	9.18077i	0.925704	−	0.802127i	−0.0548259	−	0.998496i	$-0.517460\pi$
$131$	10.5952	−	9.18077i	0.925704	−	0.802127i	0.980530	+	0.196369i	$0.0629149\pi$
$132$	−0.680480	−	0.161633i	−0.0592281	−	0.0140683i
$133$	10.8247	−	3.17843i	0.938624	−	0.275605i
$134$	1.12249	−	2.45790i	0.0969682	−	0.212331i
$135$	2.74611	−	4.41122i	0.236347	−	0.379658i
$136$	−3.09466	−	4.81538i	−0.265365	−	0.412915i
$137$	−18.5500			−1.58483			−0.792415	−	0.609982i	$-0.791177\pi$
$137$	−18.5500			−1.58483			−0.792415	+	0.609982i	$0.791177\pi$
$138$	8.07836	−	1.93393i	0.687676	−	0.164627i
$139$	12.7611			1.08238			0.541191	−	0.840899i	$-0.317973\pi$
$139$	12.7611			1.08238			0.541191	+	0.840899i	$0.317973\pi$
$140$	0.741187	+	1.15331i	0.0626417	+	0.0974724i
$141$	−11.4262	+	10.9999i	−0.962255	+	0.926355i
$142$	−2.16125	+	4.73248i	−0.181368	+	0.397141i
$143$	−2.47046	+	0.725391i	−0.206590	+	0.0606603i
$144$	2.34027	−	1.87700i	0.195023	−	0.156416i
$145$	−2.99737	+	2.59724i	−0.248918	+	0.215689i
$146$	10.8225	−	1.55605i	0.895680	−	0.128779i
$147$	−7.19973	+	5.17909i	−0.593824	+	0.427164i
$148$	0.383837	+	0.332596i	0.0315512	+	0.0273392i
$149$	2.03122	+	1.30539i	0.166404	+	0.106941i	0.621192	−	0.783658i	$-0.286649\pi$
$149$	2.03122	+	1.30539i	0.166404	+	0.106941i	−0.454788	+	0.890600i	$0.650285\pi$
$150$	−0.574337	−	1.63406i	−0.0468944	−	0.133420i
$151$	0.821694	−	0.948286i	0.0668685	−	0.0771704i	−0.721330	−	0.692592i	$-0.756469\pi$
$151$	0.821694	−	0.948286i	0.0668685	−	0.0771704i	0.788198	+	0.615421i	$0.211014\pi$
$152$	−7.89584	−	2.31843i	−0.640438	−	0.188049i
$153$	15.8802	−	6.53477i	1.28384	−	0.528305i
$154$	0.362527	+	0.418378i	0.0292133	+	0.0337139i
$155$	−0.242842	−	0.531750i	−0.0195055	−	0.0427112i
$156$	4.05542	−	10.2724i	0.324694	−	0.822448i
$157$	18.4276	+	8.41562i	1.47068	+	0.671639i	0.979872	−	0.199626i	$-0.0639726\pi$
$157$	18.4276	+	8.41562i	1.47068	+	0.671639i	0.490813	+	0.871265i	$0.336700\pi$
$158$	1.58220	−	11.0044i	0.125873	−	0.875466i
$159$	0.701460	−	7.73779i	0.0556294	−	0.613647i
$160$		−	1.00000i		−	0.0790569i
$161$	−6.08454	−	2.49126i	−0.479529	−	0.196339i
$162$	4.27664	+	7.91899i	0.336005	+	0.622174i
$163$	−11.9210	+	7.66117i	−0.933726	+	0.600069i	−0.916609	−	0.399784i	$-0.869085\pi$
$163$	−11.9210	+	7.66117i	−0.933726	+	0.600069i	−0.0171170	+	0.999853i	$0.505449\pi$
$164$	−4.22462	−	0.607408i	−0.329887	−	0.0474306i
$165$	−0.323465	−	0.620119i	−0.0251817	−	0.0482762i
$166$	−3.07139	−	10.4602i	−0.238386	−	0.811868i
$167$	11.7086	−	5.34714i	0.906040	−	0.413774i	0.0927876	−	0.995686i	$-0.470422\pi$
$167$	11.7086	−	5.34714i	0.906040	−	0.413774i	0.813252	+	0.581911i	$0.197695\pi$
$168$	−2.37128	+	0.124352i	−0.182948	+	0.00959399i
$169$	−3.93587	−	27.3746i	−0.302759	−	2.10574i
$170$	1.61265	−	5.49219i	0.123685	−	0.421231i
$171$	11.1016	−	22.0506i	0.848962	−	1.68625i
$172$	1.00627	−	1.56579i	0.0767276	−	0.119390i
$173$	−10.1607	+	15.8104i	−0.772504	+	1.20204i	0.202375	+	0.979308i	$0.435134\pi$
$173$	−10.1607	+	15.8104i	−0.772504	+	1.20204i	−0.974880	+	0.222732i	$0.928502\pi$
$174$	−1.33237	−	6.73903i	−0.101007	−	0.510885i
$175$	−0.386239	+	1.31541i	−0.0291969	+	0.0994355i
$176$	−0.0574676	−	0.399696i	−0.00433178	−	0.0301282i
$177$	−0.0452275	−	0.862446i	−0.00339951	−	0.0648254i
$178$	2.64574	−	1.20827i	0.198306	−	0.0905635i
$179$	−5.48870	−	18.6928i	−0.410244	−	1.39716i	−0.862853	−	0.505455i	$-0.831325\pi$
$179$	−5.48870	−	18.6928i	−0.410244	−	1.39716i	0.452609	−	0.891709i	$-0.350493\pi$
$180$	2.95109	+	0.539489i	0.219962	+	0.0402112i
$181$	10.9455	+	1.57373i	0.813574	+	0.116974i	0.536528	−	0.843882i	$-0.319736\pi$
$181$	10.9455	+	1.57373i	0.813574	+	0.116974i	0.277046	+	0.960857i	$0.410645\pi$
$182$	−7.35374	+	4.72596i	−0.545096	+	0.350312i
$183$	−7.66859	−	5.97138i	−0.566879	−	0.441417i
$184$	2.75123	+	3.92820i	0.202823	+	0.289591i
$185$			0.507889i			0.0373407i
$186$	1.00838	+	0.0914136i	0.0739381	+	0.00670277i
$187$	0.328947	−	2.28788i	0.0240550	−	0.167306i
$188$	−8.32953	−	3.80397i	−0.607493	−	0.277433i
$189$	0.912306	−	7.06496i	0.0663605	−	0.513900i
$190$	−3.41853	−	7.48553i	−0.248006	−	0.543057i
$191$	−5.31393	−	6.13261i	−0.384503	−	0.443740i	0.530197	−	0.847875i	$-0.322118\pi$
$191$	−5.31393	−	6.13261i	−0.384503	−	0.443740i	−0.914699	+	0.404135i	$0.867573\pi$
$192$	1.50413	+	0.858826i	0.108551	+	0.0619804i
$193$	−19.2594	−	5.65508i	−1.38633	−	0.407062i	−0.498359	−	0.866971i	$-0.666064\pi$
$193$	−19.2594	−	5.65508i	−1.38633	−	0.407062i	−0.887966	+	0.459909i	$0.847882\pi$
$194$	12.1291	−	13.9977i	0.870818	−	1.00498i
$195$	10.4191	−	3.66209i	0.746126	−	0.262248i
$196$	−4.30766	−	2.76836i	−0.307690	−	0.197740i
$197$	12.4468	+	10.7852i	0.886799	+	0.768415i	0.973708	−	0.227801i	$-0.0731535\pi$
$197$	12.4468	+	10.7852i	0.886799	+	0.768415i	−0.0869091	+	0.996216i	$0.527699\pi$
$198$	1.21054	+	0.0460394i	0.0860295	+	0.00327188i
$199$	−17.1194	+	2.46140i	−1.21356	+	0.174484i	−0.719220	−	0.694782i	$-0.755501\pi$
$199$	−17.1194	+	2.46140i	−1.21356	+	0.174484i	−0.494344	+	0.869266i	$0.664592\pi$
$200$	0.755750	−	0.654861i	0.0534396	−	0.0463056i
$201$	−1.08158	+	4.55346i	−0.0762884	+	0.321176i
$202$	−12.3282	+	3.61987i	−0.867406	+	0.254693i
$203$	−2.25873	+	4.94593i	−0.158532	+	0.347136i
$204$	6.87600	+	7.14247i	0.481416	+	0.500073i
$205$	−2.30749	−	3.59052i	−0.161162	−	0.250773i
$206$	0.138487			0.00964886
$207$	−13.0767	+	5.99990i	−0.908896	+	0.417022i
$208$	6.37621			0.442111
$209$	−1.79655	−	2.79548i	−0.124270	−	0.193367i
$210$	−1.64684	−	1.71066i	−0.113643	−	0.118047i
$211$	7.81051	−	17.1026i	0.537698	−	1.17739i	−0.424596	−	0.905383i	$-0.639584\pi$
$211$	7.81051	−	17.1026i	0.537698	−	1.17739i	0.962294	−	0.272011i	$-0.0876888\pi$
$212$	4.30403	−	1.26378i	0.295602	−	0.0867966i
$213$	2.08248	−	8.76730i	0.142689	−	0.600725i
$214$	−4.06102	+	3.51889i	−0.277606	+	0.240547i
$215$	1.84231	−	0.264885i	0.125645	−	0.0180650i
$216$	−3.34594	+	3.97551i	−0.227662	+	0.270499i
$217$	−0.605673	−	0.524819i	−0.0411158	−	0.0356270i
$218$	−7.50505	−	4.82320i	−0.508306	−	0.326669i
$219$	−17.8665	+	6.27970i	−1.20730	+	0.424343i
$220$	0.264437	−	0.305176i	0.0178283	−	0.0205750i
$221$	35.0193	+	10.2826i	2.35566	+	0.691683i
$222$	−0.763932	−	0.436188i	−0.0512718	−	0.0292750i
$223$	7.59769	+	8.76820i	0.508779	+	0.587162i	0.950786	−	0.309850i	$-0.100279\pi$
$223$	7.59769	+	8.76820i	0.508779	+	0.587162i	−0.442007	+	0.897012i	$0.645733\pi$
$224$	−0.569510	−	1.24705i	−0.0380520	−	0.0833222i
$225$	1.52484	+	2.58358i	0.101656	+	0.172239i
$226$	−1.77814	−	0.812048i	−0.118280	−	0.0540166i
$227$	0.676097	−	4.70236i	0.0448741	−	0.312107i	−0.955005	−	0.296588i	$-0.904151\pi$
$227$	0.676097	−	4.70236i	0.0448741	−	0.312107i	0.999880	−	0.0155183i	$-0.00493982\pi$
$228$	14.1952	+	1.28685i	0.940097	+	0.0852234i
$229$			0.284547i			0.0188034i	0.999956	+	0.00940171i	$0.00299270\pi$
$229$			0.284547i			0.0188034i	−0.999956	+	0.00940171i	$0.997007\pi$
$230$	−1.16707	+	4.65166i	−0.0769541	+	0.306721i
$231$	−0.756542	−	0.589104i	−0.0497768	−	0.0387602i
$232$	3.33649	−	2.14423i	0.219051	−	0.140776i
$233$	−16.1092	−	2.31616i	−1.05535	−	0.151736i	−0.407269	−	0.913308i	$-0.633519\pi$
$233$	−16.1092	−	2.31616i	−1.05535	−	0.151736i	−0.648081	+	0.761572i	$0.724428\pi$
$234$	−3.43990	+	18.8168i	−0.224873	+	1.23009i
$235$	−2.57983	−	8.78611i	−0.168290	−	0.573142i
$236$	0.453558	−	0.207133i	0.0295241	−	0.0134832i
$237$	1.00843	+	19.2298i	0.0655046	+	1.24911i
$238$	−1.11679	−	7.76746i	−0.0723909	−	0.503490i
$239$	−3.97555	+	13.5395i	−0.257157	+	0.875797i	0.725161	+	0.688579i	$0.241765\pi$
$239$	−3.97555	+	13.5395i	−0.257157	+	0.875797i	−0.982318	+	0.187218i	$0.940053\pi$
$240$	0.335941	+	1.69916i	0.0216849	+	0.109680i
$241$	−2.70342	+	4.20660i	−0.174142	+	0.270971i	−0.917343	−	0.398098i	$-0.869670\pi$
$241$	−2.70342	+	4.20660i	−0.174142	+	0.270971i	0.743201	+	0.669069i	$0.233307\pi$
$242$	−5.85889	+	9.11661i	−0.376624	+	0.586038i
$243$	−9.92701	−	12.0189i	−0.636818	−	0.771014i
$244$	1.58092	−	5.38414i	0.101208	−	0.344684i
$245$	−0.728726	−	5.06840i	−0.0465566	−	0.323808i
$246$	7.38236	−	0.387138i	0.470682	−	0.0246830i
$247$	47.7293	−	21.7972i	3.03694	−	1.38693i
$248$	0.164694	+	0.560897i	0.0104581	+	0.0356170i
$249$	8.73278	+	16.7417i	0.553418	+	1.06096i
$250$	0.989821	+	0.142315i	0.0626018	+	0.00900078i
$251$	6.63388	−	4.26334i	0.418727	−	0.269099i	−0.314267	−	0.949335i	$-0.601759\pi$
$251$	6.63388	−	4.26334i	0.418727	−	0.269099i	0.732994	+	0.680235i	$0.238122\pi$
$252$	3.98741	−	1.00790i	0.251183	−	0.0634920i
$253$	−0.199152	+	1.92632i	−0.0125206	+	0.121107i
$254$		−	15.8021i		−	0.991511i
$255$	−0.895103	+	9.87386i	−0.0560535	+	0.618325i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	13.4220	+	6.12962i	0.837241	+	0.382355i	0.787430	−	0.616404i	$-0.211411\pi$
$257$	13.4220	+	6.12962i	0.837241	+	0.382355i	0.0498105	+	0.998759i	$0.484138\pi$
$258$	−1.18380	+	2.99858i	−0.0737005	+	0.186683i
$259$	0.289247	+	0.633363i	0.0179730	+	0.0393553i
$260$	4.17553	+	4.81882i	0.258955	+	0.298850i
$261$	4.52783	+	11.0031i	0.280266	+	0.681074i
$262$	−13.4515	−	3.94973i	−0.831038	−	0.244015i
$263$	19.8762	−	22.9383i	1.22562	−	1.41444i	0.346352	−	0.938105i	$-0.387420\pi$
$263$	19.8762	−	22.9383i	1.22562	−	1.41444i	0.879265	−	0.476333i	$-0.158034\pi$
$264$	0.231921	+	0.659841i	0.0142737	+	0.0406104i
$265$	3.77364	+	2.42517i	0.231813	+	0.148977i
$266$	−8.52616	−	7.38796i	−0.522772	−	0.452985i
$267$	−4.08962	+	2.94185i	−0.250281	+	0.180038i
$268$	−2.67458	+	0.384547i	−0.163376	+	0.0234900i
$269$	−18.4954	+	16.0263i	−1.12768	+	0.977143i	−0.999893	−	0.0146579i	$-0.995334\pi$
$269$	−18.4954	+	16.0263i	−1.12768	+	0.977143i	−0.127791	+	0.991801i	$0.540789\pi$
$270$	−5.19562	+	0.0747141i	−0.316195	+	0.00454696i
$271$	9.00422	−	2.64388i	0.546967	−	0.160604i	0.00343777	−	0.999994i	$-0.498906\pi$
$271$	9.00422	−	2.64388i	0.546967	−	0.160604i	0.543530	+	0.839390i	$0.317088\pi$
$272$	−2.37786	+	5.20678i	−0.144179	+	0.315707i
$273$	10.9075	−	10.5006i	0.660154	−	0.635524i
$274$	10.0289	+	15.6052i	0.605866	+	0.942746i
$275$	0.403806			0.0243504
$276$	−5.99441	−	5.75039i	−0.360821	−	0.346133i
$277$	−14.7786			−0.887960			−0.443980	−	0.896037i	$-0.646434\pi$
$277$	−14.7786			−0.887960			−0.443980	+	0.896037i	$0.646434\pi$
$278$	−6.89917	−	10.7353i	−0.413785	−	0.643862i
$279$	−1.74411	+	0.183430i	−0.104417	+	0.0109817i
$280$	0.569510	−	1.24705i	0.0340347	−	0.0745256i
$281$	−10.1480	+	2.97972i	−0.605379	+	0.177755i	−0.570036	−	0.821620i	$-0.693071\pi$
$281$	−10.1480	+	2.97972i	−0.605379	+	0.177755i	−0.0353434	+	0.999375i	$0.511252\pi$
$282$	15.4311	+	3.66532i	0.918909	+	0.218267i
$283$	−17.1110	+	14.8268i	−1.01715	+	0.881361i	−0.992972	−	0.118346i	$-0.962241\pi$
$283$	−17.1110	+	14.8268i	−1.01715	+	0.881361i	−0.0241728	+	0.999708i	$0.507695\pi$
$284$	5.14968	−	0.740412i	0.305577	−	0.0439354i
$285$	8.32332	+	11.5707i	0.493031	+	0.685388i
$286$	1.94587	+	1.68610i	0.115062	+	0.0997014i
$287$	−4.92239	−	3.16343i	−0.290560	−	0.186731i
$288$	−2.84428	−	0.953982i	−0.167601	−	0.0562140i
$289$	−10.3237	+	11.9142i	−0.607278	+	0.700836i
$290$	3.80544	+	1.11738i	0.223463	+	0.0656147i
$291$	−15.9069	+	27.8590i	−0.932476	+	1.63312i
$292$	−7.16013	−	8.26324i	−0.419015	−	0.483569i
$293$	3.55717	+	7.78911i	0.207812	+	0.455045i	0.984624	−	0.174688i	$-0.0558917\pi$
$293$	3.55717	+	7.78911i	0.207812	+	0.455045i	−0.776812	+	0.629733i	$0.783164\pi$
$294$	8.24940	+	3.25677i	0.481115	+	0.189939i
$295$	0.453558	+	0.207133i	0.0264072	+	0.0120598i
$296$	0.0722801	−	0.502719i	0.00420119	−	0.0292200i
$297$	−2.07237	+	0.328442i	−0.120251	+	0.0190582i
$298$		−	2.41452i		−	0.139869i
$299$	−29.6600	−	7.44146i	−1.71528	−	0.430351i
$300$	−1.06414	+	1.36660i	−0.0614384	+	0.0789007i
$301$	2.14661	−	1.37954i	0.123728	−	0.0795154i
$302$	−1.24199	−	0.178571i	−0.0714685	−	0.0102756i
$303$	19.7314	−	10.2923i	1.13354	−	0.591276i
$304$	2.31843	+	7.89584i	0.132971	+	0.452858i
$305$	5.10434	−	2.33108i	0.292274	−	0.133477i
$306$	−14.0829	−	9.82628i	−0.805064	−	0.561731i
$307$	0.000241553		0.00168004i	1.37862e−5		9.58849e-5i	0.989828	−	0.142267i	$-0.0454391\pi$
$307$	0.000241553		0.00168004i	1.37862e−5		9.58849e-5i	−0.989815	+	0.142363i	$0.954530\pi$
$308$	0.155965	−	0.531170i	0.00888696	−	0.0302662i
$309$	−0.235312	+	0.0465235i	−0.0133864	+	0.00264663i
$310$	−0.316046	+	0.491777i	−0.0179502	+	0.0279311i
$311$	−15.2226	+	23.6868i	−0.863194	+	1.34316i	0.0750490	+	0.997180i	$0.476089\pi$
$311$	−15.2226	+	23.6868i	−0.863194	+	1.34316i	−0.938243	+	0.345977i	$0.887548\pi$
$312$	−10.8342	+	2.14203i	−0.613366	+	0.121269i
$313$	−0.414295	+	1.41096i	−0.0234173	+	0.0797521i	−0.970373	−	0.241613i	$-0.922324\pi$
$313$	−0.414295	+	1.41096i	−0.0234173	+	0.0797521i	0.946955	+	0.321365i	$0.104142\pi$
$314$	−2.88306	−	20.0521i	−0.162701	−	1.13161i
$315$	3.37292	+	2.35345i	0.190043	+	0.132602i
$316$	−10.1129	+	4.61842i	−0.568896	+	0.259806i
$317$	6.98427	+	23.7862i	0.392276	+	1.33597i	0.884922	+	0.465739i	$0.154211\pi$
$317$	6.98427	+	23.7862i	0.392276	+	1.33597i	−0.492646	+	0.870230i	$0.663970\pi$
$318$	−6.88868	+	3.59326i	−0.386298	+	0.201500i
$319$	1.58523	+	0.227922i	0.0887559	+	0.0127612i
$320$	−0.841254	+	0.540641i	−0.0470275	+	0.0302227i
$321$	5.71818	−	7.34342i	0.319158	−	0.409870i
$322$	1.19377	+	6.46552i	0.0665264	+	0.360309i
$323$			47.1043i			2.62095i
$324$	4.34975	−	7.87907i	0.241653	−	0.437726i
$325$	−0.907429	+	6.31131i	−0.0503351	+	0.350088i
$326$	12.8900	+	5.88666i	0.713910	+	0.326032i
$327$	14.3726	+	5.67414i	0.794806	+	0.313781i
$328$	1.77302	+	3.88237i	0.0978985	+	0.214368i
$329$	−8.22096	−	9.48749i	−0.453236	−	0.523062i
$330$	−0.346799	+	0.607378i	−0.0190907	+	0.0334351i
$331$	0.0124577	+	0.00365790i	0.000684735	+	0.000201056i	0.282075	−	0.959392i	$-0.408977\pi$
$331$	0.0124577	+	0.00365790i	0.000684735	+	0.000201056i	−0.281390	+	0.959593i	$0.590796\pi$
$332$	−7.13915	+	8.23902i	−0.391812	+	0.452175i
$333$	1.44458	+	0.484517i	0.0791623	+	0.0265514i
$334$	−10.8285	−	6.95903i	−0.592507	−	0.380781i
$335$	−2.04210	−	1.76949i	−0.111572	−	0.0966776i
$336$	1.38662	+	1.92762i	0.0756465	+	0.105160i
$337$	−19.8278	+	2.85081i	−1.08009	+	0.155293i	−0.659311	−	0.751870i	$-0.729152\pi$
$337$	−19.8278	+	2.85081i	−1.08009	+	0.155293i	−0.420778	+	0.907164i	$0.638243\pi$
$338$	−20.9011	+	18.1109i	−1.13687	+	0.985101i
$339$	3.29414	+	0.782450i	0.178913	+	0.0424969i
$340$	−5.49219	+	1.61265i	−0.297856	+	0.0874583i
$341$	−0.0980610	+	0.214724i	−0.00531030	+	0.0116279i
$342$	−24.5521	+	2.58218i	−1.32763	+	0.139628i
$343$	−8.98357	−	13.9787i	−0.485067	−	0.754779i
$344$	−1.86126			−0.100352
$345$	0.420350	−	8.29598i	0.0226309	−	0.446641i
$346$	18.7938			1.01036
$347$	−1.62527	−	2.52897i	−0.0872490	−	0.135762i	0.794886	−	0.606759i	$-0.207531\pi$
$347$	−1.62527	−	2.52897i	−0.0872490	−	0.135762i	−0.882135	+	0.470997i	$0.843894\pi$
$348$	−4.94890	+	4.76426i	−0.265289	+	0.255391i
$349$	−5.31186	+	11.6314i	−0.284337	+	0.622612i	−0.996873	−	0.0790243i	$-0.974820\pi$
$349$	−5.31186	+	11.6314i	−0.284337	+	0.622612i	0.712535	+	0.701636i	$0.247547\pi$
$350$	1.31541	−	0.386239i	0.0703115	−	0.0206453i
$351$	−0.476393	−	33.1283i	−0.0254280	−	1.76826i
$352$	−0.305176	+	0.264437i	−0.0162659	+	0.0140945i
$353$	−32.2167	+	4.63207i	−1.71472	+	0.246540i	−0.928482	−	0.371379i	$-0.878885\pi$
$353$	−32.2167	+	4.63207i	−1.71472	+	0.246540i	−0.786242	+	0.617919i	$0.787976\pi$
$354$	−0.701084	+	0.504321i	−0.0372622	+	0.0268044i
$355$	3.93189	+	3.40700i	0.208683	+	0.180825i
$356$	−2.44685	−	1.57250i	−0.129683	−	0.0833422i
$357$	4.50702	+	12.8230i	0.238537	+	0.678664i
$358$	−12.7580	+	14.7235i	−0.674279	+	0.778159i
$359$	29.4460	+	8.64613i	1.55410	+	0.456326i	0.942323	−	0.334704i	$-0.108636\pi$
$359$	29.4460	+	8.64613i	1.55410	+	0.456326i	0.611778	+	0.791029i	$0.290454\pi$
$360$	−1.14163	−	2.77429i	−0.0601694	−	0.146218i
$361$	31.9045	+	36.8197i	1.67918	+	1.93788i
$362$	−4.59369	−	10.0588i	−0.241439	−	0.528677i
$363$	6.89255	−	17.4588i	0.361765	−	0.916351i
$364$	7.95146	+	3.63131i	0.416770	+	0.190332i
$365$	1.55605	−	10.8225i	0.0814472	−	0.566478i
$366$	−0.877493	+	9.67960i	−0.0458673	+	0.505961i
$367$			34.1297i			1.78156i	0.454440	+	0.890778i	$0.349840\pi$
$367$			34.1297i			1.78156i	−0.454440	+	0.890778i	$0.650160\pi$
$368$	1.81719	−	4.43822i	0.0947275	−	0.231358i
$369$	−12.4137	+	3.13784i	−0.646234	+	0.163350i
$370$	0.427263	−	0.274585i	0.0222124	−	0.0142750i
$371$	6.08708	+	0.875190i	0.316026	+	0.0454376i
$372$	−0.468270	−	0.897726i	−0.0242787	−	0.0465449i
$373$	−8.56531	−	29.1708i	−0.443495	−	1.51041i	−0.813605	−	0.581417i	$-0.802498\pi$
$373$	−8.56531	−	29.1708i	−0.443495	−	1.51041i	0.370110	−	0.928988i	$-0.379320\pi$
$374$	−2.10253	+	0.960192i	−0.108719	+	0.0496504i
$375$	−1.72967	+	0.0907058i	−0.0893200	+	0.00468403i
$376$	1.30318	+	9.06383i	0.0672064	+	0.467431i
$377$	−7.12464	+	24.2643i	−0.366938	+	1.24967i
$378$	−6.43665	+	3.05212i	−0.331066	+	0.156984i
$379$	14.6211	−	22.7509i	0.751036	−	1.16864i	−0.229693	−	0.973263i	$-0.573772\pi$
$379$	14.6211	−	22.7509i	0.751036	−	1.16864i	0.980729	−	0.195372i	$-0.0625914\pi$
$380$	−4.44903	+	6.92283i	−0.228231	+	0.355134i
$381$	5.30857	+	26.8503i	0.271966	+	1.37558i
$382$	−2.28615	+	7.78590i	−0.116969	+	0.398361i
$383$	−0.820838	−	5.70905i	−0.0419428	−	0.291719i	−0.999987	−	0.00509823i	$-0.998377\pi$
$383$	−0.820838	−	5.70905i	−0.0419428	−	0.291719i	0.958044	−	0.286621i	$-0.0925319\pi$
$384$	−0.0907058	−	1.72967i	−0.00462881	−	0.0882671i
$385$	0.503567	−	0.229971i	0.0256641	−	0.0117204i
$386$	5.65508	+	19.2594i	0.287836	+	0.980280i
$387$	1.00413	−	5.49275i	0.0510428	−	0.279212i
$388$	−18.3331	−	2.63590i	−0.930722	−	0.133818i
$389$	3.43506	−	2.20758i	0.174165	−	0.111929i	−0.450654	−	0.892699i	$-0.648809\pi$
$389$	3.43506	−	2.20758i	0.174165	−	0.111929i	0.624819	+	0.780770i	$0.285173\pi$
$390$	−8.71373	−	6.78521i	−0.441237	−	0.343583i
$391$	17.1376	−	21.4451i	0.866688	−	1.08452i
$392$			5.12052i			0.258625i
$393$	24.1832	+	2.19230i	1.21988	+	0.110587i
$394$	2.34385	−	16.3019i	0.118082	−	0.821276i
$395$	−10.1129	−	4.61842i	−0.508836	−	0.232378i
$396$	−0.615738	−	1.04326i	−0.0309420	−	0.0524260i
$397$	1.28656	+	2.81718i	0.0645706	+	0.141390i	0.939166	−	0.343464i	$-0.111600\pi$
$397$	1.28656	+	2.81718i	0.0645706	+	0.141390i	−0.874595	+	0.484854i	$0.838873\pi$
$398$	11.3261	+	13.0711i	0.567728	+	0.655193i
$399$	16.9692	+	9.68904i	0.849524	+	0.485059i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	−18.5602	+	21.4196i	−0.926850	+	1.06964i	0.0705448	+	0.997509i	$0.477526\pi$
$401$	−18.5602	+	21.4196i	−0.926850	+	1.06964i	−0.997395	+	0.0721336i	$0.977019\pi$
$402$	4.41536	−	1.55191i	0.220218	−	0.0774022i
$403$	−3.13567	−	2.01518i	−0.156199	−	0.100383i
$404$	9.71034	+	8.41406i	0.483107	+	0.418615i
$405$	8.80308	−	1.87237i	0.437429	−	0.0930388i
$406$	5.38194	−	0.773806i	0.267101	−	0.0384034i
$407$	0.154995	−	0.134304i	0.00768284	−	0.00665722i
$408$	2.29119	−	9.64597i	0.113431	−	0.477547i
$409$	−23.5077	+	6.90247i	−1.16238	+	0.341305i	−0.805357	−	0.592791i	$-0.798026\pi$
$409$	−23.5077	+	6.90247i	−1.16238	+	0.341305i	−0.357022	+	0.934096i	$0.616208\pi$
$410$	−1.77302	+	3.88237i	−0.0875631	+	0.191736i
$411$	−22.2831	−	23.1467i	−1.09914	−	1.14174i
$412$	−0.0748719	−	0.116503i	−0.00368867	−	0.00573969i
$413$	0.683575			0.0336365
$414$	12.1173	+	7.75707i	0.595531	+	0.381239i
$415$	−10.9018			−0.535148
$416$	−3.44724	−	5.36401i	−0.169015	−	0.262992i
$417$	15.3292	+	15.9233i	0.750676	+	0.779768i
$418$	−1.38042	+	3.02270i	−0.0675186	+	0.147845i
$419$	23.1205	−	6.78879i	1.12951	−	0.331654i	0.336995	−	0.941506i	$-0.390589\pi$
$419$	23.1205	−	6.78879i	1.12951	−	0.331654i	0.792515	+	0.609852i	$0.208771\pi$
$420$	−0.548752	+	2.31026i	−0.0267764	+	0.112729i
$421$	−12.5394	+	10.8654i	−0.611132	+	0.529548i	−0.904512	−	0.426447i	$-0.859765\pi$
$421$	−12.5394	+	10.8654i	−0.611132	+	0.529548i	0.293381	+	0.955996i	$0.405220\pi$
$422$	−18.6103	+	2.67576i	−0.905937	+	0.130254i
$423$	−27.4512	−	1.04403i	−1.33473	−	0.0507623i
$424$	−3.39009	−	2.93753i	−0.164637	−	0.142659i
$425$	−4.81538	−	3.09466i	−0.233580	−	0.150113i
$426$	−8.50139	+	2.98807i	−0.411894	+	0.144772i
$427$	5.03781	−	5.81394i	0.243797	−	0.281356i
$428$	5.15583	+	1.51389i	0.249217	+	0.0731766i
$429$	−3.87277	−	2.21126i	−0.186979	−	0.106761i
$430$	−1.21887	−	1.40665i	−0.0587789	−	0.0678345i
$431$	−11.1779	−	24.4762i	−0.538421	−	1.17898i	−0.961983	−	0.273110i	$-0.911948\pi$
$431$	−11.1779	−	24.4762i	−0.538421	−	1.17898i	0.423562	−	0.905867i	$-0.360779\pi$
$432$	5.15336	+	0.665459i	0.247941	+	0.0320169i
$433$	24.9796	+	11.4078i	1.20044	+	0.548223i	0.912362	−	0.409384i	$-0.134256\pi$
$433$	24.9796	+	11.4078i	1.20044	+	0.548223i	0.288079	+	0.957607i	$0.406984\pi$
$434$	−0.114054	+	0.793263i	−0.00547477	+	0.0380778i
$435$	−6.84142	−	0.620201i	−0.328021	−	0.0297364i
$436$			8.92127i			0.427251i
$437$	−1.56957	−	39.4346i	−0.0750827	−	1.88641i
$438$	14.9422	+	11.6352i	0.713965	+	0.555950i
$439$	−7.04000	+	4.52433i	−0.336001	+	0.215935i	−0.697751	−	0.716340i	$-0.745816\pi$
$439$	−7.04000	+	4.52433i	−0.336001	+	0.215935i	0.361750	+	0.932275i	$0.382179\pi$
$440$	−0.399696	−	0.0574676i	−0.0190547	−	0.00273966i
$441$	−15.1111	−	2.76247i	−0.719578	−	0.131546i
$442$	−10.2826	−	35.0193i	−0.489094	−	1.66570i
$443$	21.6350	−	9.88038i	1.02791	−	0.469431i	0.171204	−	0.985236i	$-0.445234\pi$
$443$	21.6350	−	9.88038i	1.02791	−	0.469431i	0.856706	+	0.515805i	$0.172507\pi$
$444$	0.0460684	+	0.878482i	0.00218631	+	0.0416909i
$445$	−0.413934	−	2.87897i	−0.0196224	−	0.136476i
$446$	3.26866	−	11.1320i	0.154775	−	0.527117i
$447$	0.811135	+	4.10265i	0.0383654	+	0.194049i
$448$	−0.741187	+	1.15331i	−0.0350178	+	0.0544887i
$449$	5.45849	−	8.49357i	0.257602	−	0.400836i	−0.688230	−	0.725492i	$-0.741612\pi$
$449$	5.45849	−	8.49357i	0.257602	−	0.400836i	0.945832	+	0.324656i	$0.105248\pi$
$450$	1.34906	−	2.67956i	0.0635951	−	0.126316i
$451$	−0.485557	+	1.65366i	−0.0228640	+	0.0778676i
$452$	0.278195	+	1.93489i	0.0130852	+	0.0910096i
$453$	2.17033	−	0.113814i	0.101971	−	0.00534745i
$454$	−4.32140	+	1.97352i	−0.202813	+	0.0926218i
$455$	2.46274	+	8.38732i	0.115455	+	0.393204i
$456$	−6.59192	−	12.6374i	−0.308695	−	0.591803i
$457$	−26.9812	−	3.87930i	−1.26213	−	0.181466i	−0.521422	−	0.853299i	$-0.674598\pi$
$457$	−26.9812	−	3.87930i	−1.26213	−	0.181466i	−0.740703	+	0.671833i	$0.765507\pi$
$458$	0.239376	−	0.153838i	0.0111853	−	0.00718837i
$459$	27.2301	+	11.9654i	1.27099	+	0.558497i
$460$	4.54419	−	1.53308i	0.211874	−	0.0714802i
$461$		−	0.702074i		−	0.0326989i	−0.999866	−	0.0163494i	$-0.994796\pi$
$461$		−	0.702074i		−	0.0326989i	0.999866	−	0.0163494i	$-0.00520442\pi$
$462$	−0.0865687	+	0.954937i	−0.00402754	+	0.0444277i
$463$	4.25598	−	29.6010i	0.197792	−	1.37568i	−0.612880	−	0.790176i	$-0.709989\pi$
$463$	4.25598	−	29.6010i	0.197792	−	1.37568i	0.810673	−	0.585500i	$-0.199102\pi$
$464$	−3.60769	−	1.64758i	−0.167483	−	0.0764868i
$465$	0.371805	−	0.941781i	0.0172420	−	0.0436740i
$466$	6.76083	+	14.8041i	0.313189	+	0.685789i
$467$	−14.1475	−	16.3271i	−0.654669	−	0.755528i	0.327228	−	0.944945i	$-0.393886\pi$
$467$	−14.1475	−	16.3271i	−0.654669	−	0.755528i	−0.981897	+	0.189417i	$0.939340\pi$
$468$	17.6894	−	7.27930i	0.817695	−	0.336486i
$469$	−3.55435	−	1.04365i	−0.164125	−	0.0481913i
$470$	−5.99658	+	6.92042i	−0.276602	+	0.319215i
$471$	11.6351	+	33.1032i	0.536118	+	1.52532i
$472$	−0.419464	−	0.269573i	−0.0193074	−	0.0124081i
$473$	−0.568012	−	0.492185i	−0.0261172	−	0.0226307i
$474$	15.6320	−	11.2448i	0.718000	−	0.516490i
$475$	−8.14542	+	1.17114i	−0.373738	+	0.0537354i
$476$	−5.93062	+	5.13891i	−0.271830	+	0.235542i
$477$	10.4978	−	8.41971i	0.480663	−	0.385512i
$478$	13.5395	−	3.97555i	0.619282	−	0.181838i
$479$	−10.3362	+	22.6331i	−0.472272	+	1.03413i	0.512244	+	0.858840i	$0.328814\pi$
$479$	−10.3362	+	22.6331i	−0.472272	+	1.03413i	−0.984516	+	0.175292i	$0.943913\pi$
$480$	1.24780	−	1.20125i	0.0569541	−	0.0548292i
$481$	1.75081	+	2.72432i	0.0798302	+	0.124218i
$482$	5.00039			0.227762
$483$	−4.20044	−	10.5849i	−0.191127	−	0.481630i
$484$	10.8369			0.492588
$485$	−10.0135	−	15.5814i	−0.454692	−	0.707514i
$486$	−4.74402	+	14.8491i	−0.215193	+	0.673567i
$487$	4.16130	−	9.11198i	0.188567	−	0.412903i	−0.791611	−	0.611026i	$-0.790757\pi$
$487$	4.16130	−	9.11198i	0.188567	−	0.412903i	0.980177	+	0.198123i	$0.0634844\pi$
$488$	−5.38414	+	1.58092i	−0.243728	+	0.0715651i
$489$	−23.8797	−	5.67210i	−1.07988	−	0.256501i
$490$	−3.86983	+	3.35323i	−0.174821	+	0.151483i
$491$	11.8700	−	1.70664i	0.535684	−	0.0770198i	0.130837	−	0.991404i	$-0.458234\pi$
$491$	11.8700	−	1.70664i	0.535684	−	0.0770198i	0.404848	+	0.914384i	$0.367325\pi$
$492$	−4.31688	−	6.00113i	−0.194620	−	0.270552i
$493$	−17.1571	−	14.8667i	−0.772718	−	0.669564i
$494$	−44.1414	−	28.3680i	−1.98602	−	1.27634i
$495$	0.385224	−	1.14854i	0.0173145	−	0.0516229i
$496$	0.382816	−	0.441794i	0.0171890	−	0.0198371i
$497$	6.84359	+	2.00946i	0.306977	+	0.0901366i
$498$	9.36273	−	16.3977i	0.419554	−	0.734800i
$499$	16.3850	+	18.9092i	0.733491	+	0.846494i	0.992860	−	0.119284i	$-0.0380599\pi$
$499$	16.3850	+	18.9092i	0.733491	+	0.846494i	−0.259369	+	0.965778i	$0.583514\pi$
$500$	−0.415415	−	0.909632i	−0.0185779	−	0.0406800i
$501$	20.7371	+	8.18678i	0.926465	+	0.365758i
$502$	−7.17309	−	3.27584i	−0.320151	−	0.146208i
$503$	−1.02098	+	7.10104i	−0.0455231	+	0.316620i	0.954318	+	0.298793i	$0.0965839\pi$
$503$	−1.02098	+	7.10104i	−0.0455231	+	0.316620i	−0.999841	+	0.0178271i	$0.994325\pi$
$504$	−3.00366	−	2.80951i	−0.133794	−	0.125145i
$505$			12.8486i			0.571756i
$506$	1.72819	−	0.873909i	0.0768275	−	0.0388500i
$507$	29.4300	−	37.7948i	1.30703	−	1.67852i
$508$	−13.2936	+	8.54326i	−0.589807	+	0.379046i
$509$	3.69012	+	0.530559i	0.163562	+	0.0235166i	0.223609	−	0.974679i	$-0.428216\pi$
$509$	3.69012	+	0.530559i	0.163562	+	0.0235166i	−0.0600475	+	0.998196i	$0.519125\pi$
$510$	8.79035	−	4.58520i	0.389243	−	0.203036i
$511$	−4.22307	−	14.3824i	−0.186818	−	0.636242i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	40.8506	−	12.6356i	1.80360	−	0.557875i
$514$	−2.09991	−	14.6052i	−0.0926232	−	0.644209i
$515$	0.0390164	−	0.132878i	0.00171927	−	0.00585528i
$516$	3.16258	−	0.625273i	0.139225	−	0.0275261i
$517$	−1.99911	+	3.11067i	−0.0879206	+	0.136807i
$518$	0.376440	−	0.585753i	0.0165398	−	0.0257365i
$519$	−31.9337	+	6.31361i	−1.40173	+	0.277137i
$520$	1.79639	−	6.11793i	0.0787767	−	0.268289i
$521$	−1.00592	−	6.99634i	−0.0440703	−	0.306515i	−0.999920	−	0.0126591i	$-0.995970\pi$
$521$	−1.00592	−	6.99634i	−0.0440703	−	0.306515i	0.955850	−	0.293856i	$-0.0949387\pi$
$522$	6.80846	−	9.75777i	0.297998	−	0.427086i
$523$	−13.5095	+	6.16959i	−0.590730	+	0.269777i	−0.688270	−	0.725454i	$-0.741630\pi$
$523$	−13.5095	+	6.16959i	−0.590730	+	0.269777i	0.0975404	+	0.995232i	$0.468902\pi$
$524$	3.94973	+	13.4515i	0.172545	+	0.587633i
$525$	−2.10534	+	1.09818i	−0.0918844	+	0.0479285i
$526$	−30.0428	−	4.31950i	−1.30993	−	0.188339i
$527$	2.81496	−	1.80906i	0.122621	−	0.0788040i
$528$	0.429708	−	0.551841i	0.0187006	−	0.0240158i
$529$	−13.6326	+	18.5243i	−0.592724	+	0.805406i
$530$		−	4.48573i		−	0.194848i
$531$	1.02183	−	1.09244i	0.0443437	−	0.0474081i
$532$	−1.60556	+	11.1669i	−0.0696097	+	0.484146i
$533$	−24.7548	−	11.3051i	−1.07225	−	0.489679i
$534$	4.68586	+	1.84993i	0.202777	+	0.0800541i
$535$	2.23223	+	4.88791i	0.0965078	+	0.211323i
$536$	1.76949	+	2.04210i	0.0764304	+	0.0882053i
$537$	16.7316	−	29.3034i	0.722021	−	1.26454i
$538$	23.4816	+	6.89481i	1.01236	+	0.297256i
$539$	−1.35405	+	1.56266i	−0.0583232	+	0.0673086i
$540$	2.87182	+	4.33044i	0.123583	+	0.186352i
$541$	25.2953	+	16.2563i	1.08753	+	0.698912i	0.956284	−	0.292438i	$-0.0944665\pi$
$541$	25.2953	+	16.2563i	1.08753	+	0.698912i	0.131244	+	0.991350i	$0.458103\pi$
$542$	−7.09222	−	6.14544i	−0.304637	−	0.263969i
$543$	11.1846	+	15.5483i	0.479976	+	0.667240i
$544$	5.66579	−	0.814617i	0.242919	−	0.0349264i
$545$	−6.74225	+	5.84219i	−0.288806	+	0.250252i
$546$	−14.7307	−	3.49896i	−0.630416	−	0.149742i
$547$	18.3940	−	5.40095i	0.786469	−	0.230928i	0.136249	−	0.990675i	$-0.456495\pi$
$547$	18.3940	−	5.40095i	0.786469	−	0.230928i	0.650219	+	0.759747i	$0.274677\pi$
$548$	7.70593	−	16.8736i	0.329181	−	0.720806i
$549$	−1.76077	−	16.7420i	−0.0751480	−	0.714530i
$550$	−0.218314	−	0.339703i	−0.00930894	−	0.0144850i
$551$	−32.6377			−1.39041
$552$	−1.59671	+	8.15172i	−0.0679606	+	0.346960i
$553$	−15.2416			−0.648138
$554$	7.98991	+	12.4326i	0.339459	+	0.528208i
$555$	−0.633744	+	0.610099i	−0.0269009	+	0.0258973i
$556$	−5.30116	+	11.6079i	−0.224819	+	0.492285i
$557$	40.2355	−	11.8142i	1.70483	−	0.500584i	0.723083	−	0.690761i	$-0.242725\pi$
$557$	40.2355	−	11.8142i	1.70483	−	0.500584i	0.981750	+	0.190178i	$0.0609064\pi$
$558$	1.09725	+	1.36807i	0.0464502	+	0.0579150i
$559$	8.96907	−	7.77174i	0.379351	−	0.328710i
$560$	−1.35699	+	0.195105i	−0.0573432	+	0.00824470i
$561$	3.24996	−	2.33785i	0.137214	−	0.0987039i
$562$	7.99313	+	6.92608i	0.337170	+	0.292159i
$563$	−7.17869	−	4.61346i	−0.302546	−	0.194434i	0.380555	−	0.924758i	$-0.375733\pi$
$563$	−7.17869	−	4.61346i	−0.302546	−	0.194434i	−0.683101	+	0.730324i	$0.739369\pi$
$564$	−5.25922	−	14.9631i	−0.221453	−	0.630060i
$565$	−1.28011	+	1.47733i	−0.0538548	+	0.0621517i
$566$	21.7240	+	6.37875i	0.913128	+	0.268119i
$567$	9.91157	−	7.34838i	0.416247	−	0.308603i
$568$	−3.40700	−	3.93189i	−0.142955	−	0.164978i
$569$	3.28662	+	7.19670i	0.137782	+	0.301701i	0.965928	−	0.258812i	$-0.0833311\pi$
$569$	3.28662	+	7.19670i	0.137782	+	0.301701i	−0.828145	+	0.560513i	$0.810604\pi$
$570$	5.23396	−	13.2576i	0.219226	−	0.555300i
$571$	−6.88888	−	3.14605i	−0.288291	−	0.131658i	0.266021	−	0.963967i	$-0.414291\pi$
$571$	−6.88888	−	3.14605i	−0.288291	−	0.131658i	−0.554311	+	0.832309i	$0.687018\pi$
$572$	0.366425	−	2.54854i	0.0153210	−	0.106560i
$573$	1.26893	−	13.9975i	0.0530102	−	0.584754i
$574$			5.85126i			0.244227i
$575$	4.13444	+	2.43032i	0.172418	+	0.101351i
$576$	0.735192	+	2.90852i	0.0306330	+	0.121188i
$577$	24.7927	−	15.9333i	1.03213	−	0.663311i	0.0891033	−	0.996022i	$-0.471600\pi$
$577$	24.7927	−	15.9333i	1.03213	−	0.663311i	0.943029	+	0.332711i	$0.107963\pi$
$578$	15.6043	+	2.24356i	0.649053	+	0.0933197i
$579$	−16.0789	−	30.8251i	−0.668217	−	1.28105i
$580$	−1.11738	−	3.80544i	−0.0463966	−	0.158012i
$581$	−13.5951	+	6.20867i	−0.564019	+	0.257579i
$582$	32.0364	−	1.68002i	1.32795	−	0.0696390i
$583$	−0.257784	−	1.79293i	−0.0106763	−	0.0742555i
$584$	−3.08042	+	10.4909i	−0.127468	+	0.434118i
$585$	17.0854	+	8.60186i	0.706396	+	0.355643i
$586$	4.62947	−	7.20359i	0.191242	−	0.297578i
$587$	17.2670	−	26.8681i	0.712687	−	1.10896i	−0.276315	−	0.961067i	$-0.589113\pi$
$587$	17.2670	−	26.8681i	0.712687	−	1.10896i	0.989003	−	0.147896i	$-0.0472502\pi$
$588$	−1.72019	−	8.70058i	−0.0709395	−	0.358806i
$589$	1.35530	−	4.61573i	0.0558441	−	0.190188i
$590$	−0.0709607	−	0.493542i	−0.00292140	−	0.0203188i
$591$	1.49388	+	28.4869i	0.0614499	+	1.17179i
$592$	−0.461992	+	0.210985i	−0.0189877	+	0.00867141i
$593$	−1.19659	−	4.07520i	−0.0491379	−	0.167348i	0.931269	−	0.364333i	$-0.118703\pi$
$593$	−1.19659	−	4.07520i	−0.0491379	−	0.167348i	−0.980406	+	0.196985i	$0.936885\pi$
$594$	1.39671	+	1.56582i	0.0573078	+	0.0642464i
$595$	−7.76746	−	1.11679i	−0.318435	−	0.0457840i
$596$	−2.03122	+	1.30539i	−0.0832021	+	0.0534707i
$597$	−23.6360	−	18.4049i	−0.967357	−	0.753262i
$598$	9.77523	+	28.9747i	0.399739	+	1.18486i
$599$			35.1729i			1.43713i	0.695461	+	0.718564i	$0.255200\pi$
$599$			35.1729i			1.43713i	−0.695461	+	0.718564i	$0.744800\pi$
$600$	1.72498	+	0.156376i	0.0704219	+	0.00638401i
$601$	2.76791	−	19.2512i	0.112905	−	0.785274i	−0.852163	−	0.523276i	$-0.824710\pi$
$601$	2.76791	−	19.2512i	0.112905	−	0.785274i	0.965068	−	0.261998i	$-0.0843814\pi$
$602$	−2.32109	−	1.06000i	−0.0946004	−	0.0432026i
$603$	−6.98105	+	4.12024i	−0.284290	+	0.167789i
$604$	0.521247	+	1.14137i	0.0212092	+	0.0464417i
$605$	7.09669	+	8.19001i	0.288521	+	0.332971i
$606$	−19.3260	−	11.0347i	−0.785067	−	0.448255i
$607$	−17.7035	−	5.19821i	−0.718562	−	0.210989i	−0.0980451	−	0.995182i	$-0.531259\pi$
$607$	−17.7035	−	5.19821i	−0.718562	−	0.210989i	−0.620517	+	0.784193i	$0.713077\pi$
$608$	5.38897	−	6.21920i	0.218552	−	0.252222i
$609$	−8.88482	+	3.12283i	−0.360031	+	0.126544i
$610$	−4.72064	−	3.03377i	−0.191133	−	0.122834i
$611$	−44.1261	−	38.2355i	−1.78515	−	1.54684i
$612$	−0.652620	+	17.1597i	−0.0263806	+	0.693642i
$613$	−23.1683	+	3.33110i	−0.935759	+	0.134542i	−0.593292	−	0.804988i	$-0.702172\pi$
$613$	−23.1683	+	3.33110i	−0.935759	+	0.134542i	−0.342468	+	0.939530i	$0.611263\pi$
$614$	0.00128275	−	0.00111151i	5.17674e−5	−	4.48567e-5i
$615$	1.70839	−	7.19239i	0.0688891	−	0.290025i
$616$	−0.531170	+	0.155965i	−0.0214014	+	0.00628403i
$617$	−4.50903	+	9.87339i	−0.181527	+	0.397488i	−0.978418	−	0.206635i	$-0.933749\pi$
$617$	−4.50903	+	9.87339i	−0.181527	+	0.397488i	0.796892	+	0.604122i	$0.206476\pi$
$618$	0.166357	+	0.172804i	0.00669187	+	0.00695122i
$619$	−4.05753	−	6.31364i	−0.163086	−	0.253767i	0.750087	−	0.661339i	$-0.230012\pi$
$619$	−4.05753	−	6.31364i	−0.163086	−	0.253767i	−0.913173	+	0.407573i	$0.866375\pi$
$620$	0.584577			0.0234772
$621$	−23.1951	−	9.10981i	−0.930786	−	0.365564i
$622$	28.1566			1.12898
$623$	−2.15580	−	3.35449i	−0.0863703	−	0.134395i
$624$	7.65940	+	7.95624i	0.306621	+	0.318505i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	1.41096	−	0.414295i	0.0563933	−	0.0165586i
$627$	1.33011	−	5.59979i	0.0531194	−	0.223634i
$628$	−15.3102	+	13.2664i	−0.610945	+	0.529387i
$629$	−2.87759	+	0.413735i	−0.114737	+	0.0164967i
$630$	0.156306	−	4.10985i	0.00622738	−	0.163740i
$631$	16.0437	+	13.9020i	0.638690	+	0.553428i	0.912870	−	0.408250i	$-0.133861\pi$
$631$	16.0437	+	13.9020i	0.638690	+	0.553428i	−0.274180	+	0.961678i	$0.588406\pi$
$632$	9.35272	+	6.01063i	0.372031	+	0.239090i
$633$	30.7230	−	10.7985i	1.22113	−	0.429203i
$634$	16.2343	−	18.7354i	0.644746	−	0.744076i
$635$	−15.1620	−	4.45196i	−0.601685	−	0.176671i
$636$	6.74714	+	3.85246i	0.267542	+	0.152760i
$637$	−21.3809	−	24.6749i	−0.847142	−	0.977653i
$638$	−0.665301	−	1.45681i	−0.0263395	−	0.0576755i
$639$	13.4414	−	7.93317i	0.531734	−	0.313831i
$640$	0.909632	+	0.415415i	0.0359564	+	0.0164207i
$641$	−3.68330	+	25.6179i	−0.145482	+	1.01185i	0.778016	+	0.628244i	$0.216226\pi$
$641$	−3.68330	+	25.6179i	−0.145482	+	1.01185i	−0.923498	+	0.383603i	$0.874683\pi$
$642$	−9.26916	−	0.840285i	−0.365825	−	0.0331634i
$643$			36.6855i			1.44673i	0.690464	+	0.723367i	$0.257406\pi$
$643$			36.6855i			1.44673i	−0.690464	+	0.723367i	$0.742594\pi$
$644$	4.79374	−	4.49979i	0.188900	−	0.177317i
$645$	2.54360	+	1.98065i	0.100154	+	0.0779880i
$646$	39.6266	−	25.4665i	1.55909	−	1.00197i
$647$	−21.6513	−	3.11299i	−0.851202	−	0.122384i	−0.297113	−	0.954842i	$-0.596024\pi$
$647$	−21.6513	−	3.11299i	−0.851202	−	0.122384i	−0.554088	+	0.832458i	$0.686933\pi$
$648$	−8.97994	+	0.600503i	−0.352766	+	0.0235900i
$649$	−0.0567253	−	0.193189i	−0.00222666	−	0.00758332i
$650$	5.80000	−	2.64877i	0.227495	−	0.103893i
$651$	−0.0726934	−	1.38620i	−0.00284908	−	0.0543293i
$652$	−2.01668	−	14.0263i	−0.0789792	−	0.549313i
$653$	4.27934	−	14.5741i	0.167463	−	0.570328i	−0.832406	−	0.554166i	$-0.813037\pi$
$653$	4.27934	−	14.5741i	0.167463	−	0.570328i	0.999869	−	0.0161617i	$-0.00514466\pi$
$654$	−2.99702	−	15.1587i	−0.117193	−	0.592751i
$655$	−7.57947	+	11.7939i	−0.296154	+	0.460825i
$656$	2.30749	−	3.59052i	0.0900923	−	0.140186i
$657$	−29.2979	−	14.7503i	−1.14302	−	0.575466i
$658$	−3.53680	+	12.0452i	−0.137879	+	0.469572i
$659$	−1.13675	−	7.90628i	−0.0442815	−	0.307985i	−0.999910	−	0.0134105i	$-0.995731\pi$
$659$	−1.13675	−	7.90628i	−0.0442815	−	0.307985i	0.955629	−	0.294574i	$-0.0951779\pi$
$660$	0.698453	−	0.0366275i	0.0271872	−	0.00142572i
$661$	−31.5144	+	14.3921i	−1.22577	+	0.559790i	−0.919851	−	0.392268i	$-0.871690\pi$
$661$	−31.5144	+	14.3921i	−1.22577	+	0.559790i	−0.305917	+	0.952058i	$0.598963\pi$
$662$	−0.00365790	−	0.0124577i	−0.000142168	−	0.000484181i
$663$	29.2362	+	56.0491i	1.13544	+	2.17677i
$664$	10.7908	+	1.55149i	0.418765	+	0.0602093i
$665$	−9.49079	+	6.09936i	−0.368037	+	0.236523i
$666$	−0.373395	−	1.47720i	−0.0144688	−	0.0572405i
$667$	14.8589	+	11.8744i	0.575339	+	0.459778i
$668$			12.8718i			0.498025i
$669$	−1.81427	+	20.0132i	−0.0701437	+	0.773754i
$670$	−0.384547	+	2.67458i	−0.0148563	+	0.103328i
$671$	−2.06116	−	0.941302i	−0.0795703	−	0.0363386i
$672$	0.871951	−	2.20865i	0.0336362	−	0.0852006i
$673$	7.46626	+	16.3488i	0.287803	+	0.630201i	0.997214	−	0.0745943i	$-0.0237662\pi$
$673$	7.46626	+	16.3488i	0.287803	+	0.630201i	−0.709411	+	0.704795i	$0.751039\pi$
$674$	13.1180	+	15.1389i	0.505285	+	0.583131i
$675$	−1.39209	+	5.00621i	−0.0535814	+	0.192689i
$676$	26.5358	+	7.79161i	1.02061	+	0.299677i
$677$	16.5525	−	19.1026i	0.636165	−	0.734174i	−0.342527	−	0.939508i	$-0.611283\pi$
$677$	16.5525	−	19.1026i	0.636165	−	0.734174i	0.978692	+	0.205334i	$0.0658281\pi$
$678$	−1.12271	−	3.19423i	−0.0431173	−	0.122674i
$679$	−21.3612	−	13.7280i	−0.819766	−	0.526832i
$680$	4.32595	+	3.74846i	0.165893	+	0.143747i
$681$	6.67977	−	4.80506i	0.255969	−	0.184130i
$682$	0.233653	−	0.0335942i	0.00894703	−	0.00128639i
$683$	11.7811	−	10.2084i	0.450793	−	0.390614i	−0.399662	−	0.916663i	$-0.630872\pi$
$683$	11.7811	−	10.2084i	0.450793	−	0.390614i	0.850455	+	0.526048i	$0.176327\pi$
$684$	15.4462	+	19.2585i	0.590599	+	0.736369i
$685$	17.7986	−	5.22613i	0.680048	−	0.199680i
$686$	−6.90275	+	15.1149i	−0.263548	+	0.577090i
$687$	−0.355058	+	0.341812i	−0.0135463	+	0.0130409i
$688$	1.00627	+	1.56579i	0.0383638	+	0.0596952i
$689$	28.6020			1.08965
$690$	−7.20628	+	4.13153i	−0.274338	+	0.157284i
$691$	3.45676			0.131501			0.0657507	−	0.997836i	$-0.479056\pi$
$691$	3.45676			0.131501			0.0657507	+	0.997836i	$0.479056\pi$
$692$	−10.1607	−	15.8104i	−0.386252	−	0.601020i
$693$	−0.173708	−	1.65167i	−0.00659863	−	0.0627419i
$694$	−1.24882	+	2.73453i	−0.0474044	+	0.103801i
$695$	−12.2442	+	3.59522i	−0.464449	+	0.136374i
$696$	6.68352	+	1.58752i	0.253338	+	0.0601750i
$697$	18.4634	−	15.9986i	0.699352	−	0.605992i
$698$	12.6567	−	1.81976i	0.479064	−	0.0688790i
$699$	−16.4610	−	22.8834i	−0.622614	−	0.865529i
$700$	−1.03609	−	0.897775i	−0.0391605	−	0.0339327i
$701$	−26.9091	−	17.2934i	−1.01634	−	0.653163i	−0.0773151	−	0.997007i	$-0.524635\pi$
$701$	−26.9091	−	17.2934i	−1.01634	−	0.653163i	−0.939027	+	0.343843i	$0.888271\pi$
$702$	−27.6118	+	18.3113i	−1.04214	+	0.691115i
$703$	−2.73700	+	3.15866i	−0.103228	+	0.119131i
$704$	0.387449	+	0.113765i	0.0146025	+	0.00428769i
$705$	7.86429	−	13.7734i	0.296186	−	0.518736i
$706$	21.3144	+	24.5982i	0.802179	+	0.925764i
$707$	7.31741	+	16.0229i	0.275200	+	0.602603i
$708$	0.803296	+	0.317133i	0.0301897	+	0.0119186i
$709$	6.52880	+	2.98160i	0.245194	+	0.111976i	0.534222	−	0.845344i	$-0.320605\pi$
$709$	6.52880	+	2.98160i	0.245194	+	0.111976i	−0.289028	+	0.957321i	$0.593332\pi$
$710$	0.740412	−	5.14968i	0.0277872	−	0.193264i
$711$	−22.7836	+	24.3581i	−0.854452	+	0.913499i
$712$			2.90858i			0.109004i
$713$	−2.29633	+	1.60830i	−0.0859984	+	0.0602314i
$714$	8.35070	−	10.7242i	0.312517	−	0.401342i
$715$	2.16602	−	1.39202i	0.0810045	−	0.0520584i
$716$	19.2836	+	2.77257i	0.720663	+	0.103616i
$717$	−21.6702	+	11.3036i	−0.809288	+	0.422139i
$718$	−8.64613	−	29.4460i	−0.322671	−	1.09892i
$719$	−9.50565	+	4.34108i	−0.354501	+	0.161895i	−0.584702	−	0.811248i	$-0.698789\pi$
$719$	−9.50565	+	4.34108i	−0.354501	+	0.161895i	0.230202	+	0.973143i	$0.426061\pi$
$720$	−1.71667	+	2.46030i	−0.0639763	+	0.0916899i
$721$	−0.0270196	−	0.187925i	−0.00100626	−	0.00699871i
$722$	13.7259	−	46.7460i	0.510824	−	1.73971i
$723$	−8.49646	+	1.67984i	−0.315987	+	0.0624738i
$724$	−5.97844	+	9.30264i	−0.222187	+	0.345730i
$725$	2.14423	−	3.33649i	0.0796348	−	0.123914i
$726$	−18.4137	+	3.64057i	−0.683396	+	0.135114i
$727$	−1.75247	+	5.96835i	−0.0649954	+	0.221354i	−0.985586	−	0.169175i	$-0.945890\pi$
$727$	−1.75247	+	5.96835i	−0.0649954	+	0.221354i	0.920591	+	0.390529i	$0.127708\pi$
$728$	−1.24403	−	8.65243i	−0.0461069	−	0.320681i
$729$	3.07244	−	26.8246i	0.113794	−	0.993504i
$730$	−9.94576	+	4.54208i	−0.368109	+	0.168110i
$731$	3.00156	+	10.2224i	0.111017	+	0.378088i
$732$	8.61741	−	4.49499i	0.318509	−	0.166140i
$733$	24.2811	+	3.49110i	0.896844	+	0.128947i	0.575295	−	0.817946i	$-0.304887\pi$
$733$	24.2811	+	3.49110i	0.896844	+	0.128947i	0.321549	+	0.946893i	$0.395796\pi$
$734$	28.7117	−	18.4519i	1.05977	−	0.681072i
$735$	5.44898	−	6.99770i	0.200988	−	0.258114i
$736$	−4.71612	+	0.870769i	−0.173838	+	0.0320970i
$737$			1.09112i			0.0401919i
$738$	9.35110	+	8.74666i	0.344219	+	0.321969i
$739$	−4.98729	+	34.6874i	−0.183461	+	1.27600i	0.665042	+	0.746806i	$0.268413\pi$
$739$	−4.98729	+	34.6874i	−0.183461	+	1.27600i	−0.848503	+	0.529191i	$0.822496\pi$
$740$	−0.461992	−	0.210985i	−0.0169832	−	0.00775595i
$741$	84.5333	+	33.3728i	3.10541	+	1.22598i
$742$	−2.55467	−	5.59394i	−0.0937848	−	0.205360i
$743$	21.0635	+	24.3086i	0.772744	+	0.891794i	0.996563	−	0.0828363i	$-0.0263979\pi$
$743$	21.0635	+	24.3086i	0.772744	+	0.891794i	−0.223819	+	0.974631i	$0.571852\pi$
$744$	−0.502050	+	0.879281i	−0.0184060	+	0.0322360i
$745$	−2.31671	−	0.680248i	−0.0848778	−	0.0249224i
$746$	−19.9093	+	22.9765i	−0.728930	+	0.841230i
$747$	−10.4001	+	31.0077i	−0.380520	+	1.13451i
$748$	1.94448	+	1.24964i	0.0710972	+	0.0456914i
$749$	5.56742	+	4.82419i	0.203429	+	0.176272i
$750$	1.01144	+	1.40606i	0.0369325	+	0.0513419i
$751$	12.0076	−	1.72643i	0.438163	−	0.0629983i	0.0802962	−	0.996771i	$-0.474413\pi$
$751$	12.0076	−	1.72643i	0.438163	−	0.0629983i	0.357866	+	0.933773i	$0.383504\pi$
$752$	6.92042	−	5.99658i	0.252362	−	0.218673i
$753$	13.2887	+	3.15644i	0.484268	+	0.115027i
$754$	24.2643	−	7.12464i	0.883653	−	0.259464i
$755$	−0.521247	+	1.14137i	−0.0189701	+	0.0415388i
$756$	6.04753	+	3.76475i	0.219946	+	0.136923i
$757$	−2.34534	−	3.64942i	−0.0852427	−	0.132640i	0.796014	−	0.605278i	$-0.206938\pi$
$757$	−2.34534	−	3.64942i	−0.0852427	−	0.132640i	−0.881257	+	0.472638i	$0.843302\pi$
$758$	−27.0440			−0.982284
$759$	−2.64289	+	2.06548i	−0.0959309	+	0.0749722i
$760$	8.22918			0.298504
$761$	2.63228	+	4.09591i	0.0954202	+	0.148477i	0.885682	−	0.464293i	$-0.153692\pi$
$761$	2.63228	+	4.09591i	0.0954202	+	0.148477i	−0.790261	+	0.612770i	$0.790055\pi$
$762$	19.7179	−	18.9822i	0.714303	−	0.687653i
$763$	−5.08075	+	11.1253i	−0.183935	+	0.402762i
$764$	7.78590	−	2.28615i	0.281684	−	0.0827099i
$765$	−13.3958	+	10.7440i	−0.484328	+	0.388451i
$766$	−4.35898	+	3.77708i	−0.157496	+	0.136471i
$767$	3.14693	−	0.452460i	0.113629	−	0.0163374i
$768$	−1.40606	+	1.01144i	−0.0507366	+	0.0364972i
$769$	1.52299	+	1.31968i	0.0549204	+	0.0475888i	0.681889	−	0.731456i	$-0.261159\pi$
$769$	1.52299	+	1.31968i	0.0549204	+	0.0475888i	−0.626968	+	0.779045i	$0.715704\pi$
$770$	−0.465713	−	0.299296i	−0.0167831	−	0.0107859i
$771$	8.47458	+	24.1112i	0.305204	+	0.868342i
$772$	13.1447	−	15.1698i	0.473088	−	0.545973i
$773$	−36.7030	−	10.7770i	−1.32011	−	0.387620i	−0.455580	−	0.890195i	$-0.650568\pi$
$773$	−36.7030	−	10.7770i	−1.32011	−	0.387620i	−0.864534	+	0.502574i

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540641 - 0.841254i) q^{2} +(1.20125 + 1.24780i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.400274 - 1.68516i) q^{6} +(-1.03609 + 0.897775i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-0.114014 + 2.99783i) q^{9} +O(q^{10})\)	\(q+(-0.540641 - 0.841254i) q^{2} +(1.20125 + 1.24780i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.400274 - 1.68516i) q^{6} +(-1.03609 + 0.897775i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-0.114014 + 2.99783i) q^{9} +(0.755750 + 0.654861i) q^{10} +(0.339703 + 0.218314i) q^{11} +(-1.63406 + 0.574337i) q^{12} +(-4.17553 + 4.81882i) q^{13} +(1.31541 + 0.386239i) q^{14} +(-1.50413 - 0.858826i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-2.37786 - 5.20678i) q^{17} +(2.58358 - 1.52484i) q^{18} +(-7.48553 - 3.41853i) q^{19} +(0.142315 - 0.989821i) q^{20} +(-2.36484 - 0.214382i) q^{21} -0.403806i q^{22} +(2.16418 + 4.27976i) q^{23} +(1.36660 + 1.06414i) q^{24} +(0.841254 - 0.540641i) q^{25} +(6.31131 + 0.907429i) q^{26} +(-3.87766 + 3.45887i) q^{27} +(-0.386239 - 1.31541i) q^{28} +(3.60769 - 1.64758i) q^{29} +(0.0907058 + 1.72967i) q^{30} +(0.0831939 + 0.578626i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(0.135655 + 0.686131i) q^{33} +(-3.09466 + 4.81538i) q^{34} +(0.741187 - 1.15331i) q^{35} +(-2.67956 - 1.34906i) q^{36} +(0.143089 - 0.487316i) q^{37} +(1.17114 + 8.14542i) q^{38} +(-11.0288 + 0.578359i) q^{39} +(-0.909632 + 0.415415i) q^{40} +(1.20245 + 4.09517i) q^{41} +(1.09818 + 2.10534i) q^{42} +(-1.84231 - 0.264885i) q^{43} +(-0.339703 + 0.218314i) q^{44} +(-0.735192 - 2.90852i) q^{45} +(2.43032 - 4.13444i) q^{46} +9.15703i q^{47} +(0.156376 - 1.72498i) q^{48} +(-0.728726 + 5.06840i) q^{49} +(-0.909632 - 0.415415i) q^{50} +(3.64063 - 9.22172i) q^{51} +(-2.64877 - 5.80000i) q^{52} +(-2.93753 - 3.39009i) q^{53} +(5.00621 + 1.39209i) q^{54} +(-0.387449 - 0.113765i) q^{55} +(-0.897775 + 1.03609i) q^{56} +(-4.72633 - 13.4469i) q^{57} +(-3.33649 - 2.14423i) q^{58} +(-0.376830 - 0.326525i) q^{59} +(1.40606 - 1.01144i) q^{60} +(-5.55432 + 0.798591i) q^{61} +(0.441794 - 0.382816i) q^{62} +(-2.57325 - 3.20838i) q^{63} +(0.959493 - 0.281733i) q^{64} +(2.64877 - 5.80000i) q^{65} +(0.503869 - 0.485070i) q^{66} +(1.46086 + 2.27314i) q^{67} +5.72405 q^{68} +(-2.74057 + 7.84151i) q^{69} -1.37094 q^{70} +(-2.81276 - 4.37673i) q^{71} +(0.313783 + 2.98354i) q^{72} +(-4.54208 + 9.94576i) q^{73} +(-0.487316 + 0.143089i) q^{74} +(1.68516 + 0.400274i) q^{75} +(6.21920 - 5.38897i) q^{76} +(-0.547959 + 0.0787847i) q^{77} +(6.44915 + 8.96530i) q^{78} +(8.40212 + 7.28048i) q^{79} +(0.841254 + 0.540641i) q^{80} +(-8.97400 - 0.683588i) q^{81} +(2.79499 - 3.22559i) q^{82} +(10.4602 + 3.07139i) q^{83} +(1.17740 - 2.06208i) q^{84} +(3.74846 + 4.32595i) q^{85} +(0.773195 + 1.69306i) q^{86} +(6.38957 + 2.52253i) q^{87} +(0.367315 + 0.167747i) q^{88} +(-0.413934 + 2.87897i) q^{89} +(-2.04933 + 2.19095i) q^{90} -8.74141i q^{91} +(-4.79204 + 0.190732i) q^{92} +(-0.622074 + 0.798882i) q^{93} +(7.70338 - 4.95066i) q^{94} +(8.14542 + 1.17114i) q^{95} +(-1.53569 + 0.801041i) q^{96} +(5.21815 + 17.7714i) q^{97} +(4.65779 - 2.12714i) q^{98} +(-0.693199 + 0.993482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} + O(q^{10}) \)	\( 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} - 12q^{11} - 12q^{14} - 16q^{16} - 8q^{18} + 16q^{20} + 62q^{21} + 4q^{23} + 2q^{24} - 16q^{25} + 42q^{27} - 2q^{30} - 4q^{31} + 16q^{33} + 2q^{36} + 72q^{38} - 124q^{39} + 44q^{41} + 44q^{43} + 12q^{44} - 2q^{45} + 4q^{46} + 70q^{49} - 2q^{51} - 52q^{53} + 92q^{54} + 10q^{55} - 54q^{56} - 38q^{57} - 36q^{58} - 44q^{61} - 220q^{63} + 16q^{64} - 34q^{66} - 44q^{67} + 22q^{69} - 12q^{70} - 36q^{72} - 28q^{73} - 24q^{74} - 88q^{77} - 54q^{78} - 44q^{79} - 16q^{80} - 66q^{81} - 28q^{82} + 4q^{83} - 18q^{84} + 158q^{86} - 64q^{87} + 80q^{89} - 8q^{90} - 4q^{92} + 4q^{93} + 24q^{94} - 2q^{96} - 88q^{98} + 190q^{99} + O(q^{100}) \)

Introduction

L-functions

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