LMFDB - Embedded newform 380.2.n.b.31.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(31,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("380.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.n (of order $6$, degree $2$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.20
Character	$\chi$	$=$	380.31
Dual form			380.2.n.b.331.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40158 - 0.188591i) q^{2} +(-0.0154003 - 0.0266742i) q^{3} +(1.92887 - 0.528652i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0266153 - 0.0344817i) q^{6} -0.370928i q^{7} +(2.60377 - 1.10472i) q^{8} +(1.49953 - 2.59725i) q^{9} +O(q^{10})$	\(q+(1.40158 - 0.188591i) q^{2} +(-0.0154003 - 0.0266742i) q^{3} +(1.92887 - 0.528652i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0266153 - 0.0344817i) q^{6} -0.370928i q^{7} +(2.60377 - 1.10472i) q^{8} +(1.49953 - 2.59725i) q^{9} +(-0.864116 - 1.11951i) q^{10} +1.40398i q^{11} +(-0.0438065 - 0.0433095i) q^{12} +(-1.25941 - 0.727122i) q^{13} +(-0.0699536 - 0.519886i) q^{14} +(-0.0154003 + 0.0266742i) q^{15} +(3.44105 - 2.03940i) q^{16} +(0.606355 + 1.05024i) q^{17} +(1.61189 - 3.92306i) q^{18} +(0.941920 + 4.25591i) q^{19} +(-1.42226 - 1.40612i) q^{20} +(-0.00989418 + 0.00571241i) q^{21} +(0.264778 + 1.96779i) q^{22} +(-0.979966 - 0.565784i) q^{23} +(-0.0695663 - 0.0524403i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.90230 - 0.781608i) q^{26} -0.184775 q^{27} +(-0.196092 - 0.715470i) q^{28} +(2.89291 + 1.67022i) q^{29} +(-0.0165543 + 0.0402904i) q^{30} -3.52962 q^{31} +(4.43831 - 3.50734i) q^{32} +(0.0374499 - 0.0216217i) q^{33} +(1.04792 + 1.35764i) q^{34} +(-0.321233 + 0.185464i) q^{35} +(1.51934 - 5.80249i) q^{36} +3.60258i q^{37} +(2.12281 + 5.78737i) q^{38} +0.0447917i q^{39} +(-2.25860 - 1.70257i) q^{40} +(-6.05954 + 3.49848i) q^{41} +(-0.0127902 + 0.00987237i) q^{42} +(-7.82658 + 4.51868i) q^{43} +(0.742215 + 2.70809i) q^{44} -2.99905 q^{45} +(-1.48021 - 0.608180i) q^{46} +(-9.67501 - 5.58587i) q^{47} +(-0.107393 - 0.0603799i) q^{48} +6.86241 q^{49} +(-0.537467 + 1.30810i) q^{50} +(0.0186761 - 0.0323480i) q^{51} +(-2.81363 - 0.736731i) q^{52} +(2.26850 + 1.30972i) q^{53} +(-0.258977 + 0.0348469i) q^{54} +(1.21588 - 0.701989i) q^{55} +(-0.409770 - 0.965809i) q^{56} +(0.0990170 - 0.0906674i) q^{57} +(4.36964 + 1.79538i) q^{58} +(3.93646 + 6.81814i) q^{59} +(-0.0156039 + 0.0595923i) q^{60} +(-1.29369 + 2.24074i) q^{61} +(-4.94706 + 0.665655i) q^{62} +(-0.963394 - 0.556216i) q^{63} +(5.55921 - 5.75285i) q^{64} +1.45424i q^{65} +(0.0484115 - 0.0373673i) q^{66} +(-1.17370 + 2.03290i) q^{67} +(1.72479 + 1.70522i) q^{68} +0.0348530i q^{69} +(-0.415257 + 0.320524i) q^{70} +(-5.89310 - 10.2071i) q^{71} +(1.03519 - 8.41920i) q^{72} +(2.94165 + 5.09509i) q^{73} +(0.679415 + 5.04932i) q^{74} +0.0308007 q^{75} +(4.06673 + 7.71114i) q^{76} +0.520774 q^{77} +(0.00844731 + 0.0627793i) q^{78} +(6.19301 + 10.7266i) q^{79} +(-3.48670 - 1.96034i) q^{80} +(-4.49573 - 7.78684i) q^{81} +(-7.83316 + 6.04618i) q^{82} -9.54937i q^{83} +(-0.0160647 + 0.0162491i) q^{84} +(0.606355 - 1.05024i) q^{85} +(-10.1174 + 7.80932i) q^{86} -0.102888i q^{87} +(1.55100 + 3.65563i) q^{88} +(-2.29180 - 1.32317i) q^{89} +(-4.20342 + 0.565594i) q^{90} +(-0.269710 + 0.467151i) q^{91} +(-2.18933 - 0.573261i) q^{92} +(0.0543574 + 0.0941498i) q^{93} +(-14.6138 - 6.00444i) q^{94} +(3.21477 - 2.94368i) q^{95} +(-0.161907 - 0.0643741i) q^{96} +(-10.5201 + 6.07377i) q^{97} +(9.61824 - 1.29419i) q^{98} +(3.64649 + 2.10530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9}+O(q^{10}) $ 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9	$ 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} - 18 q^{14} + 9 q^{16} - 12 q^{17} - 2 q^{20} + 12 q^{21} + 20 q^{24} - 20 q^{25} + 34 q^{26} + 12 q^{28} + 10 q^{30} - 12 q^{32} - 6 q^{33} - 27 q^{34} - 6 q^{36} + 12 q^{38} + 36 q^{41} - 21 q^{42} + 28 q^{44} + 44 q^{45} + 36 q^{48} - 60 q^{49} + 15 q^{52} - 66 q^{53} - 31 q^{54} + 28 q^{57} + 2 q^{58} + 3 q^{60} + 4 q^{61} - 57 q^{62} - 80 q^{64} + 18 q^{66} - 20 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} + 30 q^{76} + 12 q^{77} + 144 q^{78} + 9 q^{80} + 16 q^{81} - 41 q^{82} - 12 q^{85} + 18 q^{86} - 18 q^{89} + 39 q^{90} + 40 q^{92} - 8 q^{93} - 160 q^{96} - 18 q^{97} - 66 q^{98}+O(q^{100}) $ 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 - 18 * q^14 + 9 * q^16 - 12 * q^17 - 2 * q^20 + 12 * q^21 + 20 * q^24 - 20 * q^25 + 34 * q^26 + 12 * q^28 + 10 * q^30 - 12 * q^32 - 6 * q^33 - 27 * q^34 - 6 * q^36 + 12 * q^38 + 36 * q^41 - 21 * q^42 + 28 * q^44 + 44 * q^45 + 36 * q^48 - 60 * q^49 + 15 * q^52 - 66 * q^53 - 31 * q^54 + 28 * q^57 + 2 * q^58 + 3 * q^60 + 4 * q^61 - 57 * q^62 - 80 * q^64 + 18 * q^66 - 20 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 + 30 * q^76 + 12 * q^77 + 144 * q^78 + 9 * q^80 + 16 * q^81 - 41 * q^82 - 12 * q^85 + 18 * q^86 - 18 * q^89 + 39 * q^90 + 40 * q^92 - 8 * q^93 - 160 * q^96 - 18 * q^97 - 66 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.40158	−	0.188591i	0.991068	−	0.133354i
$2$	1.40158	−	0.188591i	0.991068	−	0.133354i
$3$	−0.0154003	−	0.0266742i	−0.00889139	−	0.0154003i	0.861545	−	0.507680i	$-0.169497\pi$
$3$	−0.0154003	−	0.0266742i	−0.00889139	−	0.0154003i	−0.870437	+	0.492280i	$0.836164\pi$
$4$	1.92887	−	0.528652i	0.964433	−	0.264326i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.0266153	−	0.0344817i	−0.0108657	−	0.0140771i
$7$		−	0.370928i		−	0.140197i	−0.997540	−	0.0700987i	$-0.977669\pi$
$7$		−	0.370928i		−	0.140197i	0.997540	−	0.0700987i	$-0.0223314\pi$
$8$	2.60377	−	1.10472i	0.920571	−	0.390576i
$9$	1.49953	−	2.59725i	0.499842	−	0.865752i
$10$	−0.864116	−	1.11951i	−0.273257	−	0.354020i
$11$			1.40398i			0.423315i	0.977344	+	0.211658i	$0.0678862\pi$
$11$			1.40398i			0.423315i	−0.977344	+	0.211658i	$0.932114\pi$
$12$	−0.0438065	−	0.0433095i	−0.0126459	−	0.0125024i
$13$	−1.25941	−	0.727122i	−0.349298	−	0.201667i	0.315078	−	0.949066i	$-0.397969\pi$
$13$	−1.25941	−	0.727122i	−0.349298	−	0.201667i	−0.664376	+	0.747398i	$0.731303\pi$
$14$	−0.0699536	−	0.519886i	−0.0186959	−	0.138945i
$15$	−0.0154003	+	0.0266742i	−0.00397635	+	0.00688724i
$16$	3.44105	−	2.03940i	0.860264	−	0.509849i
$17$	0.606355	+	1.05024i	0.147063	+	0.254720i	0.930141	−	0.367204i	$-0.119685\pi$
$17$	0.606355	+	1.05024i	0.147063	+	0.254720i	−0.783078	+	0.621924i	$0.786351\pi$
$18$	1.61189	−	3.92306i	0.379926	−	0.924675i
$19$	0.941920	+	4.25591i	0.216091	+	0.976373i
$19$	0.941920	+	4.25591i	0.216091	+	0.976373i
$20$	−1.42226	−	1.40612i	−0.318027	−	0.314418i
$21$	−0.00989418	+	0.00571241i	−0.00215909	+	0.00124655i
$22$	0.264778	+	1.96779i	0.0564508	+	0.419534i
$23$	−0.979966	−	0.565784i	−0.204337	−	0.117974i	0.394340	−	0.918965i	$-0.370973\pi$
$23$	−0.979966	−	0.565784i	−0.204337	−	0.117974i	−0.598677	+	0.800991i	$0.704307\pi$
$24$	−0.0695663	−	0.0524403i	−0.0142002	−	0.0107043i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.90230	−	0.781608i	−0.373072	−	0.153286i
$27$	−0.184775			−0.0355599
$28$	−0.196092	−	0.715470i	−0.0370578	−	0.135211i
$29$	2.89291	+	1.67022i	0.537200	+	0.310152i	0.743943	−	0.668243i	$-0.232953\pi$
$29$	2.89291	+	1.67022i	0.537200	+	0.310152i	−0.206744	+	0.978395i	$0.566287\pi$
$30$	−0.0165543	+	0.0402904i	−0.00302239	+	0.00735599i
$31$	−3.52962			−0.633939			−0.316970	−	0.948436i	$-0.602665\pi$
$31$	−3.52962			−0.633939			−0.316970	+	0.948436i	$0.602665\pi$
$32$	4.43831	−	3.50734i	0.784590	−	0.620015i
$33$	0.0374499	−	0.0216217i	0.00651919	−	0.00376386i
$34$	1.04792	+	1.35764i	0.179717	+	0.232833i
$35$	−0.321233	+	0.185464i	−0.0542982	+	0.0313491i
$36$	1.51934	−	5.80249i	0.253224	−	0.967081i
$37$			3.60258i			0.592261i	0.955147	+	0.296131i	$0.0956964\pi$
$37$			3.60258i			0.592261i	−0.955147	+	0.296131i	$0.904304\pi$
$38$	2.12281	+	5.78737i	0.344365	+	0.938836i
$39$			0.0447917i			0.00717241i
$40$	−2.25860	−	1.70257i	−0.357115	−	0.269200i
$41$	−6.05954	+	3.49848i	−0.946341	+	0.546370i	−0.891942	−	0.452149i	$-0.850657\pi$
$41$	−6.05954	+	3.49848i	−0.946341	+	0.546370i	−0.0543985	+	0.998519i	$0.517324\pi$
$42$	−0.0127902	+	0.00987237i	−0.00197357	+	0.00152334i
$43$	−7.82658	+	4.51868i	−1.19354	+	0.689092i	−0.959108	−	0.283040i	$-0.908657\pi$
$43$	−7.82658	+	4.51868i	−1.19354	+	0.689092i	−0.234434	+	0.972132i	$0.575324\pi$
$44$	0.742215	+	2.70809i	0.111893	+	0.408259i
$45$	−2.99905			−0.447072
$46$	−1.48021	−	0.608180i	−0.218244	−	0.0896712i
$47$	−9.67501	−	5.58587i	−1.41125	−	0.814783i	−0.415740	−	0.909484i	$-0.636477\pi$
$47$	−9.67501	−	5.58587i	−1.41125	−	0.814783i	−0.995506	+	0.0947005i	$0.969811\pi$
$48$	−0.107393	−	0.0603799i	−0.0155008	−	0.00871508i
$49$	6.86241			0.980345
$50$	−0.537467	+	1.30810i	−0.0760093	+	0.184993i
$51$	0.0186761	−	0.0323480i	0.00261518	−	0.00452963i
$52$	−2.81363	−	0.736731i	−0.390181	−	0.102166i
$53$	2.26850	+	1.30972i	0.311602	+	0.179904i	0.647643	−	0.761944i	$-0.275755\pi$
$53$	2.26850	+	1.30972i	0.311602	+	0.179904i	−0.336041	+	0.941847i	$0.609088\pi$
$54$	−0.258977	+	0.0348469i	−0.0352423	+	0.00474206i
$55$	1.21588	−	0.701989i	0.163949	−	0.0946561i
$56$	−0.409770	−	0.965809i	−0.0547578	−	0.129062i
$57$	0.0990170	−	0.0906674i	0.0131151	−	0.0120092i
$58$	4.36964	+	1.79538i	0.573762	+	0.235744i
$59$	3.93646	+	6.81814i	0.512483	+	0.887646i	0.999895	+	0.0144744i	$0.00460750\pi$
$59$	3.93646	+	6.81814i	0.512483	+	0.887646i	−0.487412	+	0.873172i	$0.662059\pi$
$60$	−0.0156039	+	0.0595923i	−0.00201445	+	0.00769334i
$61$	−1.29369	+	2.24074i	−0.165640	+	0.286897i	−0.936882	−	0.349644i	$-0.886302\pi$
$61$	−1.29369	+	2.24074i	−0.165640	+	0.286897i	0.771242	+	0.636542i	$0.219636\pi$
$62$	−4.94706	+	0.665655i	−0.628277	+	0.0845383i
$63$	−0.963394	−	0.556216i	−0.121376	−	0.0700766i
$64$	5.55921	−	5.75285i	0.694901	−	0.719106i
$65$			1.45424i			0.180377i
$66$	0.0484115	−	0.0373673i	0.00595904	−	0.00459960i
$67$	−1.17370	+	2.03290i	−0.143390	+	0.248359i	−0.928771	−	0.370654i	$-0.879134\pi$
$67$	−1.17370	+	2.03290i	−0.143390	+	0.248359i	0.785381	+	0.619012i	$0.212467\pi$
$68$	1.72479	+	1.70522i	0.209161	+	0.206788i
$69$			0.0348530i			0.00419581i
$70$	−0.415257	+	0.320524i	−0.0496328	+	0.0383100i
$71$	−5.89310	−	10.2071i	−0.699382	−	1.21137i	−0.968681	−	0.248309i	$-0.920125\pi$
$71$	−5.89310	−	10.2071i	−0.699382	−	1.21137i	0.269299	−	0.963057i	$-0.413208\pi$
$72$	1.03519	−	8.41920i	0.121998	−	0.992212i
$73$	2.94165	+	5.09509i	0.344294	+	0.596335i	0.985225	−	0.171263i	$-0.0547849\pi$
$73$	2.94165	+	5.09509i	0.344294	+	0.596335i	−0.640931	+	0.767599i	$0.721452\pi$
$74$	0.679415	+	5.04932i	0.0789804	+	0.586971i
$75$	0.0308007			0.00355655
$76$	4.06673	+	7.71114i	0.466486	+	0.884528i
$77$	0.520774			0.0593477
$78$	0.00844731	+	0.0627793i	0.000956470	+	0.00710835i
$79$	6.19301	+	10.7266i	0.696768	+	1.20684i	0.969581	+	0.244771i	$0.0787127\pi$
$79$	6.19301	+	10.7266i	0.696768	+	1.20684i	−0.272813	+	0.962067i	$0.587954\pi$
$80$	−3.48670	−	1.96034i	−0.389825	−	0.219173i
$81$	−4.49573	−	7.78684i	−0.499526	−	0.865204i
$82$	−7.83316	+	6.04618i	−0.865028	+	0.667688i
$83$		−	9.54937i		−	1.04818i	−0.851663	−	0.524090i	$-0.824406\pi$
$83$		−	9.54937i		−	1.04818i	0.851663	−	0.524090i	$-0.175594\pi$
$84$	−0.0160647	+	0.0162491i	−0.00175280	+	0.00177292i
$85$	0.606355	−	1.05024i	0.0657684	−	0.113914i
$86$	−10.1174	+	7.80932i	−1.09099	+	0.842101i
$87$		−	0.102888i		−	0.0110307i
$88$	1.55100	+	3.65563i	0.165337	+	0.389692i
$89$	−2.29180	−	1.32317i	−0.242931	−	0.140256i	0.373592	−	0.927593i	$-0.378126\pi$
$89$	−2.29180	−	1.32317i	−0.242931	−	0.140256i	−0.616523	+	0.787337i	$0.711459\pi$
$90$	−4.20342	+	0.565594i	−0.443079	+	0.0596188i
$91$	−0.269710	+	0.467151i	−0.0282733	+	0.0489707i
$92$	−2.18933	−	0.573261i	−0.228253	−	0.0597666i
$93$	0.0543574	+	0.0941498i	0.00563660	+	0.00976288i
$94$	−14.6138	−	6.00444i	−1.50730	−	0.619311i
$95$	3.21477	−	2.94368i	0.329828	−	0.302015i
$96$	−0.161907	−	0.0643741i	−0.0165245	−	0.00657015i
$97$	−10.5201	+	6.07377i	−1.06815	+	0.616698i	−0.927676	−	0.373386i	$-0.878197\pi$
$97$	−10.5201	+	6.07377i	−1.06815	+	0.616698i	−0.140476	+	0.990084i	$0.544863\pi$
$98$	9.61824	−	1.29419i	0.971589	−	0.130733i
$99$	3.64649	+	2.10530i	0.366486	+	0.211591i
$100$	−0.506608	+	1.93477i	−0.0506608	+	0.193477i
$101$	−1.01778	+	1.76285i	−0.101273	+	0.175410i	−0.912209	−	0.409724i	$-0.865625\pi$
$101$	−1.01778	+	1.76285i	−0.101273	+	0.175410i	0.810936	+	0.585135i	$0.198958\pi$
$102$	0.0200756	−	0.0488605i	0.00198778	−	0.00483791i
$103$	−4.79558			−0.472522			−0.236261	−	0.971690i	$-0.575922\pi$
$103$	−4.79558			−0.472522			−0.236261	+	0.971690i	$0.575922\pi$
$104$	−4.08248	−	0.501964i	−0.400320	−	0.0492216i
$105$	0.00989418	+	0.00571241i	0.000965574	+	0.000557474i
$106$	3.42649	+	1.40786i	0.332810	+	0.136743i
$107$	0.0989536			0.00956620			0.00478310	−	0.999989i	$-0.498477\pi$
$107$	0.0989536			0.00956620			0.00478310	+	0.999989i	$0.498477\pi$
$108$	−0.356406	+	0.0976815i	−0.0342952	+	0.00939941i
$109$	12.8277	−	7.40605i	1.22867	−	0.709371i	0.261915	−	0.965091i	$-0.415646\pi$
$109$	12.8277	−	7.40605i	1.22867	−	0.709371i	0.966751	+	0.255720i	$0.0823126\pi$
$110$	1.57177	−	1.21320i	0.149862	−	0.115674i
$111$	0.0960959	−	0.0554810i	0.00912102	−	0.00526602i
$112$	−0.756469	−	1.27638i	−0.0714796	−	0.120607i
$113$			1.95433i			0.183847i	0.995766	+	0.0919237i	$0.0293016\pi$
$113$			1.95433i			0.183847i	−0.995766	+	0.0919237i	$0.970698\pi$
$114$	0.121681	−	0.145752i	0.0113965	−	0.0136509i
$115$			1.13157i			0.105519i
$116$	6.46300	+	1.69229i	0.600074	+	0.157126i
$117$	−3.77704	+	2.18068i	−0.349188	+	0.201604i
$118$	6.80311	+	8.81381i	0.626277	+	0.811377i
$119$	0.389562	−	0.224914i	0.0357111	−	0.0206178i
$120$	−0.0106315	+	0.0864663i	−0.000970520	+	0.00789326i
$121$	9.02885			0.820804
$122$	−1.39063	+	3.38456i	−0.125902	+	0.306424i
$123$	0.186638	+	0.107755i	0.0168286	+	0.00971598i
$124$	−6.80818	+	1.86594i	−0.611392	+	0.167567i
$125$	1.00000			0.0894427
$126$	−1.45517	−	0.597895i	−0.129637	−	0.0532647i
$127$	3.16098	−	5.47497i	0.280491	−	0.485825i	−0.691015	−	0.722841i	$-0.742836\pi$
$127$	3.16098	−	5.47497i	0.280491	−	0.485825i	0.971506	+	0.237016i	$0.0761693\pi$
$128$	6.70675	−	9.11150i	0.592799	−	0.805351i
$129$	0.241064	+	0.139178i	0.0212245	+	0.0122540i
$130$	0.274257	+	2.03824i	0.0240540	+	0.178766i
$131$	4.83613	−	2.79214i	0.422534	−	0.243950i	−0.273627	−	0.961836i	$-0.588223\pi$
$131$	4.83613	−	2.79214i	0.422534	−	0.243950i	0.696161	+	0.717886i	$0.254890\pi$
$132$	0.0608056	−	0.0615034i	0.00529244	−	0.00535318i
$133$	1.57864	−	0.349384i	0.136885	−	0.0302955i
$134$	−1.26165	+	3.07063i	−0.108990	+	0.265262i
$135$	0.0923874	+	0.160020i	0.00795144	+	0.0137723i
$136$	2.73902	+	2.06472i	0.234869	+	0.177049i
$137$	2.53519	−	4.39108i	0.216596	−	0.375155i	−0.737169	−	0.675708i	$-0.763838\pi$
$137$	2.53519	−	4.39108i	0.216596	−	0.375155i	0.953765	+	0.300553i	$0.0971712\pi$
$138$	0.00657297	+	0.0488494i	0.000559528	+	0.00415834i
$139$	13.4107	+	7.74267i	1.13748	+	0.656725i	0.945806	−	0.324734i	$-0.105275\pi$
$139$	13.4107	+	7.74267i	1.13748	+	0.656725i	0.191675	+	0.981458i	$0.438608\pi$
$140$	−0.521569	+	0.527555i	−0.0440807	+	0.0445866i
$141$			0.344097i			0.0289782i
$142$	−10.1846	−	13.1948i	−0.854676	−	1.10728i
$143$	1.02086	−	1.76819i	0.0853689	−	0.147863i
$144$	−0.136884	−	11.9954i	−0.0114070	−	0.999619i
$145$		−	3.34044i		−	0.277409i
$146$	5.08386	+	6.58642i	0.420743	+	0.545096i
$147$	−0.105683	−	0.183049i	−0.00871662	−	0.0150976i
$148$	1.90451	+	6.94891i	0.156550	+	0.571197i
$149$	−5.10159	−	8.83621i	−0.417938	−	0.723890i	0.577794	−	0.816183i	$-0.303914\pi$
$149$	−5.10159	−	8.83621i	−0.417938	−	0.723890i	−0.995732	+	0.0922926i	$0.970580\pi$
$150$	0.0431697	−	0.00580873i	0.00352479	−	0.000474281i
$151$	−6.98440			−0.568382			−0.284191	−	0.958768i	$-0.591725\pi$
$151$	−6.98440			−0.568382			−0.284191	+	0.958768i	$0.591725\pi$
$152$	7.15411	+	10.0408i	0.580275	+	0.814420i
$153$	3.63698			0.294032
$154$	0.729908	−	0.0982133i	0.0588176	−	0.00791425i
$155$	1.76481	+	3.05674i	0.141753	+	0.245524i
$156$	0.0236792	+	0.0863972i	0.00189585	+	0.00691731i
$157$	−6.04931	−	10.4777i	−0.482788	−	0.836213i	0.517017	−	0.855975i	$-0.327042\pi$
$157$	−6.04931	−	10.4777i	−0.482788	−	0.836213i	−0.999805	+	0.0197625i	$0.993709\pi$
$158$	10.7030	+	13.8663i	0.851482	+	1.10314i
$159$		−	0.0806804i		−	0.00639837i
$160$	−5.25660	−	2.09002i	−0.415570	−	0.165231i
$161$	−0.209865	+	0.363497i	−0.0165397	+	0.0286475i
$162$	−7.76967	−	10.0660i	−0.610443	−	0.790863i
$163$		−	5.40571i		−	0.423408i	−0.977334	−	0.211704i	$-0.932099\pi$
$163$		−	5.40571i		−	0.423408i	0.977334	−	0.211704i	$-0.0679013\pi$
$164$	−9.83857	+	9.95148i	−0.768263	+	0.777080i
$165$	−0.0374499	−	0.0216217i	−0.00291547	−	0.00168325i
$166$	−1.80093	−	13.3842i	−0.139779	−	1.03882i
$167$	11.1805	−	19.3652i	0.865175	−	1.49853i	−0.00169835	−	0.999999i	$-0.500541\pi$
$167$	11.1805	−	19.3652i	0.865175	−	1.49853i	0.866873	−	0.498528i	$-0.166126\pi$
$168$	−0.0194516	+	0.0258040i	−0.00150072	+	0.00199083i
$169$	−5.44259	−	9.42684i	−0.418661	−	0.725141i
$170$	0.651791	−	1.58635i	0.0499901	−	0.121667i
$171$	12.4661	+	3.93544i	0.953308	+	0.300951i
$172$	−12.7076	+	12.8535i	−0.968947	+	0.980067i
$173$	−11.5378	+	6.66133i	−0.877200	+	0.506451i	−0.869734	−	0.493521i	$-0.835710\pi$
$173$	−11.5378	+	6.66133i	−0.877200	+	0.506451i	−0.00746556	+	0.999972i	$0.502376\pi$
$174$	−0.0194037	−	0.144206i	−0.00147099	−	0.0109322i
$175$	0.321233	+	0.185464i	0.0242829	+	0.0140197i
$176$	2.86327	+	4.83116i	0.215827	+	0.364163i
$177$	0.121245	−	0.210003i	0.00911337	−	0.0157848i
$178$	−3.46169	−	1.42232i	−0.259465	−	0.106608i
$179$	20.4178			1.52610			0.763048	−	0.646341i	$-0.223702\pi$
$179$	20.4178			1.52610			0.763048	+	0.646341i	$0.223702\pi$
$180$	−5.78477	+	1.58545i	−0.431171	+	0.118173i
$181$	1.87734	+	1.08388i	0.139541	+	0.0805643i	0.568145	−	0.822928i	$-0.307661\pi$
$181$	1.87734	+	1.08388i	0.139541	+	0.0805643i	−0.428604	+	0.903492i	$0.640994\pi$
$182$	−0.289920	+	0.705615i	−0.0214903	+	0.0523037i
$183$	0.0796932			0.00589109
$184$	−3.17663	−	0.390585i	−0.234185	−	0.0287943i
$185$	3.11993	−	1.80129i	0.229382	−	0.132434i
$186$	0.0939422	+	0.121707i	0.00688817	+	0.00892402i
$187$	−1.47451	+	0.851308i	−0.107827	+	0.0622538i
$188$	−21.6148	−	5.65969i	−1.57642	−	0.412775i
$189$			0.0685381i			0.00498541i
$190$	3.95061	−	4.73209i	0.286607	−	0.343302i
$191$		−	4.13035i		−	0.298862i	−0.988772	−	0.149431i	$-0.952256\pi$
$191$		−	4.13035i		−	0.298862i	0.988772	−	0.149431i	$-0.0477441\pi$
$192$	−0.239066	−	0.0596914i	−0.0172531	−	0.00430786i
$193$	−3.99542	+	2.30676i	−0.287597	+	0.166044i	−0.636858	−	0.770981i	$-0.719766\pi$
$193$	−3.99542	+	2.30676i	−0.287597	+	0.166044i	0.349261	+	0.937026i	$0.386433\pi$
$194$	−13.5993	+	10.4969i	−0.976373	+	0.753632i
$195$	0.0387907	−	0.0223958i	0.00277786	−	0.00160380i
$196$	13.2367	−	3.62783i	0.945477	−	0.259130i
$197$	−12.0335			−0.857353			−0.428677	−	0.903458i	$-0.641020\pi$
$197$	−12.0335			−0.857353			−0.428677	+	0.903458i	$0.641020\pi$
$198$	5.50789	+	2.26306i	0.391429	+	0.160828i
$199$	9.84314	+	5.68294i	0.697762	+	0.402853i	0.806513	−	0.591216i	$-0.201352\pi$
$199$	9.84314	+	5.68294i	0.697762	+	0.402853i	−0.108752	+	0.994069i	$0.534685\pi$
$200$	−0.345172	+	2.80729i	−0.0244073	+	0.198505i
$201$	0.0723013			0.00509974
$202$	−1.09405	+	2.66273i	−0.0769770	+	0.187349i
$203$	0.619531	−	1.07306i	0.0434826	−	0.0753140i
$204$	0.0189229	−	0.0722682i	0.00132487	−	0.00505978i
$205$	6.05954	+	3.49848i	0.423216	+	0.244344i
$206$	−6.72140	+	0.904402i	−0.468302	+	0.0630127i
$207$	−2.93897	+	1.69681i	−0.204272	+	0.117937i
$208$	−5.81660	+	0.0663753i	−0.403309	+	0.00460230i
$209$	−5.97520	+	1.32244i	−0.413314	+	0.0914747i
$210$	0.0149448	+	0.00614046i	0.00103129	+	0.000423732i
$211$	6.90478	+	11.9594i	0.475344	+	0.823321i	0.999601	−	0.0282397i	$-0.00899016\pi$
$211$	6.90478	+	11.9594i	0.475344	+	0.823321i	−0.524257	+	0.851560i	$0.675657\pi$
$212$	5.06802	+	1.32703i	0.348073	+	0.0911406i
$213$	−0.181511	+	0.314387i	−0.0124370	+	0.0215414i
$214$	0.138692	−	0.0186618i	0.00948076	−	0.00127569i
$215$	7.82658	+	4.51868i	0.533768	+	0.308171i
$216$	−0.481111	+	0.204124i	−0.0327354	+	0.0138889i
$217$			1.30924i			0.0888767i
$218$	16.5823	−	12.7994i	1.12309	−	0.866882i
$219$	0.0906048	−	0.156932i	0.00612251	−	0.0106045i
$220$	1.97416	−	1.99682i	0.133098	−	0.134626i
$221$		−	1.76358i		−	0.118631i
$222$	0.124223	−	0.0958840i	0.00833731	−	0.00643531i
$223$	−9.56991	−	16.5756i	−0.640848	−	1.10998i	−0.985244	−	0.171157i	$-0.945249\pi$
$223$	−9.56991	−	16.5756i	−0.640848	−	1.10998i	0.344395	−	0.938825i	$-0.388084\pi$
$224$	−1.30097	−	1.64629i	−0.0869246	−	0.109998i
$225$	1.49953	+	2.59725i	0.0999684	+	0.173150i
$226$	0.368568	+	2.73915i	0.0245168	+	0.182205i
$227$	1.58729			0.105352			0.0526761	−	0.998612i	$-0.483225\pi$
$227$	1.58729			0.105352			0.0526761	+	0.998612i	$0.483225\pi$
$228$	0.143059	−	0.227231i	0.00947432	−	0.0150487i
$229$	21.4482			1.41734			0.708668	−	0.705542i	$-0.249296\pi$
$229$	21.4482			1.41734			0.708668	+	0.705542i	$0.249296\pi$
$230$	0.213403	+	1.58599i	0.0140714	+	0.104577i
$231$	−0.00802010	−	0.0138912i	−0.000527684	−	0.000913975i
$232$	9.37758	+	1.15303i	0.615668	+	0.0756999i
$233$	−13.1932	−	22.8513i	−0.864317	−	1.49704i	−0.867724	−	0.497047i	$-0.834418\pi$
$233$	−13.1932	−	22.8513i	−0.864317	−	1.49704i	0.00340651	−	0.999994i	$-0.498916\pi$
$234$	−4.88258	+	3.76871i	−0.319184	+	0.246369i
$235$			11.1717i			0.728764i
$236$	11.1973	+	11.0703i	0.728883	+	0.720613i
$237$	0.190749	−	0.330387i	0.0123905	−	0.0214609i
$238$	0.503587	−	0.388703i	0.0326427	−	0.0251959i
$239$		−	20.6501i		−	1.33574i	−0.744277	−	0.667871i	$-0.767206\pi$
$239$		−	20.6501i		−	1.33574i	0.744277	−	0.667871i	$-0.232794\pi$
$240$	0.00140582	+	0.123195i	9.07453e−5	+	0.00795218i
$241$	9.46513	+	5.46469i	0.609702	+	0.352012i	0.772849	−	0.634590i	$-0.218831\pi$
$241$	9.46513	+	5.46469i	0.609702	+	0.352012i	−0.163147	+	0.986602i	$0.552164\pi$
$242$	12.6547	−	1.70276i	0.813473	−	0.109458i
$243$	−0.415634	+	0.719899i	−0.0266629	+	0.0461815i
$244$	−1.31079	+	5.00600i	−0.0839147	+	0.320477i
$245$	−3.43121	−	5.94302i	−0.219212	−	0.379686i
$246$	0.281910	+	0.115830i	0.0179739	+	0.00738504i
$247$	1.90830	−	6.04484i	0.121422	−	0.384624i
$248$	−9.19032	+	3.89923i	−0.583586	+	0.247601i
$249$	−0.254721	+	0.147064i	−0.0161423	+	0.00931977i
$250$	1.40158	−	0.188591i	0.0886439	−	0.0119275i
$251$	−7.34303	−	4.23950i	−0.463488	−	0.267595i	0.250022	−	0.968240i	$-0.419562\pi$
$251$	−7.34303	−	4.23950i	−0.463488	−	0.267595i	−0.713510	+	0.700645i	$0.752895\pi$
$252$	−2.15230	−	0.563566i	−0.135582	−	0.0355013i
$253$	0.794348	−	1.37585i	0.0499402	−	0.0864990i
$254$	3.39784	−	8.26976i	0.213199	−	0.518891i
$255$	−0.0373523			−0.00233909
$256$	7.68172	−	14.0354i	0.480107	−	0.877210i
$257$	−0.257740	−	0.148806i	−0.0160774	−	0.00928227i	0.491940	−	0.870629i	$-0.336288\pi$
$257$	−0.257740	−	0.148806i	−0.0160774	−	0.00928227i	−0.508017	+	0.861347i	$0.669621\pi$
$258$	0.364119	+	0.149607i	0.0226690	+	0.00931415i
$259$	1.33630			0.0830335
$260$	0.768789	+	2.80504i	0.0476782	+	0.173961i
$261$	8.67598	−	5.00908i	0.537030	−	0.310054i
$262$	6.25166	−	4.82546i	0.386229	−	0.298118i
$263$	10.4991	−	6.06168i	0.647405	−	0.373779i	−0.140056	−	0.990144i	$-0.544728\pi$
$263$	10.4991	−	6.06168i	0.647405	−	0.373779i	0.787461	+	0.616364i	$0.211395\pi$
$264$	0.0736250	−	0.0976695i	0.00453131	−	0.00601114i
$265$		−	2.61944i		−	0.160911i
$266$	2.14670	−	0.787407i	0.131622	−	0.0482790i
$267$			0.0815093i			0.00498829i
$268$	−1.18921	+	4.54167i	−0.0726424	+	0.277427i
$269$	−18.7703	+	10.8370i	−1.14444	+	0.660745i	−0.947527	−	0.319675i	$-0.896426\pi$
$269$	−18.7703	+	10.8370i	−1.14444	+	0.660745i	−0.196917	+	0.980420i	$0.563093\pi$
$270$	0.159667	+	0.206857i	0.00971701	+	0.0125889i
$271$	−15.6306	+	9.02435i	−0.949493	+	0.548190i	−0.892923	−	0.450208i	$-0.851350\pi$
$271$	−15.6306	+	9.02435i	−0.949493	+	0.548190i	−0.0565698	+	0.998399i	$0.518016\pi$
$272$	4.22835	+	2.37733i	0.256381	+	0.144147i
$273$	0.0166145			0.00100555
$274$	2.72516	−	6.63257i	0.164633	−	0.400688i
$275$	−1.21588	−	0.701989i	−0.0733203	−	0.0423315i
$276$	0.0184251	+	0.0672269i	0.00110906	+	0.00404658i
$277$	3.32984			0.200070			0.100035	−	0.994984i	$-0.468104\pi$
$277$	3.32984			0.200070			0.100035	+	0.994984i	$0.468104\pi$
$278$	20.2564	+	8.32285i	1.21490	+	0.499172i
$279$	−5.29276	+	9.16733i	−0.316869	+	0.548834i
$280$	−0.631530	+	0.837776i	−0.0377412	+	0.0500667i
$281$	14.6824	+	8.47691i	0.875881	+	0.505690i	0.869298	−	0.494288i	$-0.164571\pi$
$281$	14.6824	+	8.47691i	0.875881	+	0.505690i	0.00658266	+	0.999978i	$0.497905\pi$
$282$	0.0648936	+	0.482281i	0.00386436	+	0.0287194i
$283$	−19.0988	+	11.0267i	−1.13530	+	0.655468i	−0.945264	−	0.326308i	$-0.894195\pi$
$283$	−19.0988	+	11.0267i	−1.13530	+	0.655468i	−0.190041	+	0.981776i	$0.560862\pi$
$284$	−16.7630	−	16.5728i	−0.994703	−	0.983417i
$285$	−0.128029	−	0.0404175i	−0.00758377	−	0.00239413i
$286$	1.09736	−	2.67079i	0.0648882	−	0.157927i
$287$	1.29768	+	2.24765i	0.0765997	+	0.132675i
$288$	−2.45408	−	16.7868i	−0.144608	−	0.989169i
$289$	7.76467	−	13.4488i	0.456745	−	0.791106i
$290$	−0.629977	−	4.68191i	−0.0369935	−	0.274931i
$291$	0.324025	+	0.187076i	0.0189947	+	0.0109666i
$292$	8.36758	+	8.27264i	0.489676	+	0.484120i
$293$		−	18.1081i		−	1.05789i	−0.848657	−	0.528943i	$-0.822588\pi$
$293$		−	18.1081i		−	1.05789i	0.848657	−	0.528943i	$-0.177412\pi$
$294$	−0.182645	−	0.236627i	−0.0106521	−	0.0138004i
$295$	3.93646	−	6.81814i	0.229189	−	0.396967i
$296$	3.97983	+	9.38029i	0.231323	+	0.545218i
$297$		−	0.259420i		−	0.0150531i
$298$	−8.81672	−	11.4226i	−0.510739	−	0.661691i
$299$	0.822788	+	1.42511i	0.0475830	+	0.0824162i
$300$	0.0594104	−	0.0162828i	0.00343006	−	0.000940089i
$301$	1.67610	+	2.90309i	0.0966089	+	0.167332i
$302$	−9.78921	+	1.31719i	−0.563306	+	0.0757960i
$303$	0.0626968			0.00360184
$304$	11.9207	+	12.7239i	0.683699	+	0.729764i
$305$	2.58738			0.148153
$306$	5.09752	−	0.685901i	0.291406	−	0.0392104i
$307$	14.1958	+	24.5879i	0.810199	+	1.40331i	0.912725	+	0.408575i	$0.133974\pi$
$307$	14.1958	+	24.5879i	0.810199	+	1.40331i	−0.102526	+	0.994730i	$0.532692\pi$
$308$	1.00450	−	0.275308i	0.0572369	−	0.0156871i
$309$	0.0738535	+	0.127918i	0.00420138	+	0.00727700i
$310$	3.05000	+	3.95145i	0.173229	+	0.224427i
$311$		−	11.7120i		−	0.664129i	−0.943257	−	0.332065i	$-0.892255\pi$
$311$		−	11.7120i		−	0.664129i	0.943257	−	0.332065i	$-0.107745\pi$
$312$	0.0494821	+	0.116627i	0.00280137	+	0.00660271i
$313$	−16.7858	+	29.0738i	−0.948789	+	1.64335i	−0.200809	+	0.979630i	$0.564357\pi$
$313$	−16.7858	+	29.0738i	−0.948789	+	1.64335i	−0.747981	+	0.663721i	$0.768976\pi$
$314$	−10.4546	−	13.5445i	−0.589988	−	0.764362i
$315$			1.11243i			0.0626784i
$316$	17.6161	+	17.4163i	0.990985	+	0.979741i
$317$	19.7422	+	11.3981i	1.10883	+	0.640183i	0.938526	−	0.345209i	$-0.112192\pi$
$317$	19.7422	+	11.3981i	1.10883	+	0.640183i	0.170304	+	0.985392i	$0.445525\pi$
$318$	−0.0152156	−	0.113080i	−0.000853248	−	0.00634122i
$319$	−2.34495	+	4.06158i	−0.131292	+	0.227405i
$320$	−7.76171	−	1.93799i	−0.433893	−	0.108337i
$321$	−0.00152392	−	0.00263950i	−8.50568e−5	−	0.000147323i
$322$	−0.225591	+	0.549049i	−0.0125717	+	0.0305973i
$323$	−3.89858	+	3.56983i	−0.216923	+	0.198631i
$324$	−12.7882	−	12.6431i	−0.710455	−	0.702394i
$325$	1.25941	−	0.727122i	0.0698596	−	0.0403335i
$326$	−1.01947	−	7.57655i	−0.0564631	−	0.419626i
$327$	−0.395100	−	0.228111i	−0.0218491	−	0.0126146i
$328$	−11.9128	+	15.8033i	−0.657775	+	0.872590i
$329$	−2.07195	+	3.58873i	−0.114231	+	0.197853i
$330$	−0.0565668	−	0.0232419i	−0.00311390	−	0.00127943i
$331$	−21.0140			−1.15503			−0.577517	−	0.816379i	$-0.695978\pi$
$331$	−21.0140			−1.15503			−0.577517	+	0.816379i	$0.695978\pi$
$332$	−5.04829	−	18.4195i	−0.277061	−	1.01090i
$333$	9.35683	+	5.40217i	0.512751	+	0.296037i
$334$	12.0183	−	29.2505i	0.657613	−	1.60052i
$335$	2.34739			0.128252
$336$	−0.0223966	+	0.0398349i	−0.00122183	+	0.00217317i
$337$	11.0807	−	6.39743i	0.603603	−	0.348490i	−0.166855	−	0.985981i	$-0.553361\pi$
$337$	11.0807	−	6.39743i	0.603603	−	0.348490i	0.770458	+	0.637491i	$0.220028\pi$
$338$	−9.40605	−	12.1861i	−0.511622	−	0.662835i
$339$	0.0521300	−	0.0300973i	0.00283131	−	0.00163466i
$340$	0.614368	−	2.34632i	0.0333188	−	0.127247i
$341$		−	4.95551i		−	0.268356i
$342$	18.2145	+	3.16485i	0.984927	+	0.171135i
$343$		−	5.14195i		−	0.277639i
$344$	−15.3867	+	20.4117i	−0.829597	+	1.10053i
$345$	0.0301836	−	0.0174265i	0.00162503	−	0.000938212i
$346$	−14.9149	+	11.5123i	−0.801828	+	0.618906i
$347$	−25.9413	+	14.9772i	−1.39260	+	0.804018i	−0.993603	−	0.112934i	$-0.963975\pi$
$347$	−25.9413	+	14.9772i	−1.39260	+	0.804018i	−0.398998	+	0.916952i	$0.630642\pi$
$348$	−0.0543918	−	0.198457i	−0.00291571	−	0.0106384i
$349$	−23.7928			−1.27360			−0.636800	−	0.771029i	$-0.719742\pi$
$349$	−23.7928			−1.27360			−0.636800	+	0.771029i	$0.719742\pi$
$350$	0.485211	+	0.199361i	0.0259356	+	0.0106563i
$351$	0.232708	+	0.134354i	0.0124210	+	0.00717128i
$352$	4.92422	+	6.23129i	0.262462	+	0.332129i
$353$	13.0078			0.692334			0.346167	−	0.938173i	$-0.387483\pi$
$353$	13.0078			0.692334			0.346167	+	0.938173i	$0.387483\pi$
$354$	0.130331	−	0.317203i	0.00692700	−	0.0168591i
$355$	−5.89310	+	10.2071i	−0.312773	+	0.541739i
$356$	−5.12008	−	1.34066i	−0.271364	−	0.0710548i
$357$	−0.0119988	−	0.00692749i	−0.000635042	−	0.000366642i
$358$	28.6172	−	3.85061i	1.51247	−	0.203511i
$359$	−16.1244	+	9.30940i	−0.851011	+	0.491332i	−0.860992	−	0.508619i	$-0.830156\pi$
$359$	−16.1244	+	9.30940i	−0.851011	+	0.491332i	0.00998076	+	0.999950i	$0.496823\pi$
$360$	−7.80883	+	3.31310i	−0.411562	+	0.174616i
$361$	−17.2256	+	8.01746i	−0.906609	+	0.421972i
$362$	2.83566	+	1.16510i	0.149039	+	0.0612363i
$363$	−0.139047	−	0.240837i	−0.00729809	−	0.0126407i
$364$	−0.273274	+	1.04365i	−0.0143235	+	0.0547024i
$365$	2.94165	−	5.09509i	0.153973	−	0.266689i
$366$	0.111697	−	0.0150294i	0.00583847	−	0.000785600i
$367$	−14.0405	−	8.10629i	−0.732909	−	0.423145i	0.0865766	−	0.996245i	$-0.472407\pi$
$367$	−14.0405	−	8.10629i	−0.732909	−	0.423145i	−0.819485	+	0.573100i	$0.805741\pi$
$368$	−4.52597	+	0.0516476i	−0.235933	+	0.00269232i
$369$			20.9842i			1.09239i
$370$	4.03313	−	3.11305i	0.209672	−	0.161840i
$371$	0.485811	−	0.841449i	0.0252220	−	0.0436858i
$372$	0.154621	+	0.152866i	0.00801671	+	0.00792575i
$373$			31.4802i			1.62998i	0.579472	+	0.814992i	$0.303259\pi$
$373$			31.4802i			1.62998i	−0.579472	+	0.814992i	$0.696741\pi$
$374$	−1.90610	+	1.47126i	−0.0985619	+	0.0760769i
$375$	−0.0154003	−	0.0266742i	−0.000795270	−	0.00137745i
$376$	−31.3623	−	3.85617i	−1.61739	−	0.198867i
$377$	−2.42891	−	4.20700i	−0.125095	−	0.216671i
$378$	0.0129257	+	0.0960618i	0.000664824	+	0.00494088i
$379$	−24.4628			−1.25657			−0.628286	−	0.777983i	$-0.716243\pi$
$379$	−24.4628			−1.25657			−0.628286	+	0.777983i	$0.716243\pi$
$380$	4.64468	−	7.37746i	0.238267	−	0.378456i
$381$	−0.194720			−0.00997583
$382$	−0.778946	−	5.78902i	−0.0398544	−	0.296192i
$383$	−15.8325	−	27.4226i	−0.809000	−	1.40123i	−0.913557	−	0.406711i	$-0.866676\pi$
$383$	−15.8325	−	27.4226i	−0.809000	−	1.40123i	0.104556	−	0.994519i	$-0.466658\pi$
$384$	−0.346328	−	0.0385768i	−0.0176735	−	0.00196861i
$385$	−0.260387	−	0.451004i	−0.0132706	−	0.0229853i
$386$	−5.16488	+	3.98661i	−0.262886	+	0.202913i
$387$			27.1035i			1.37775i
$388$	−17.0809	+	17.2770i	−0.867153	+	0.877104i
$389$	−4.47634	+	7.75324i	−0.226959	+	0.393105i	−0.956905	−	0.290400i	$-0.906212\pi$
$389$	−4.47634	+	7.75324i	−0.226959	+	0.393105i	0.729946	+	0.683505i	$0.239545\pi$
$390$	0.0501448	−	0.0387052i	0.00253918	−	0.00195991i
$391$		−	1.37226i		−	0.0693983i
$392$	17.8681	−	7.58102i	0.902477	−	0.382899i
$393$	−0.148956	−	0.0859998i	−0.00751383	−	0.00433811i
$394$	−16.8660	+	2.26941i	−0.849696	+	0.114331i
$395$	6.19301	−	10.7266i	0.311604	−	0.539714i
$396$	8.14656	+	2.13312i	0.409380	+	0.107193i
$397$	7.16247	+	12.4058i	0.359474	+	0.622627i	0.987873	−	0.155264i	$-0.0496228\pi$
$397$	7.16247	+	12.4058i	0.359474	+	0.622627i	−0.628399	+	0.777891i	$0.716290\pi$
$398$	14.8677	+	6.10878i	0.745252	+	0.306205i
$399$	−0.0336310	−	0.0367281i	−0.00168366	−	0.00183871i
$400$	0.0456425	+	3.99974i	0.00228212	+	0.199987i
$401$	−30.3087	+	17.4987i	−1.51354	+	0.873845i	−0.513669	+	0.857988i	$0.671714\pi$
$401$	−30.3087	+	17.4987i	−1.51354	+	0.873845i	−0.999874	+	0.0158562i	$0.994953\pi$
$402$	0.101336	−	0.0136354i	0.00505419	−	0.000680070i
$403$	4.44525	+	2.56647i	0.221434	+	0.127845i
$404$	−1.03123	+	3.93836i	−0.0513058	+	0.195941i
$405$	−4.49573	+	7.78684i	−0.223395	+	0.386931i
$406$	0.665955	−	1.62082i	0.0330508	−	0.0804399i
$407$	−5.05795			−0.250713
$408$	0.0128929	−	0.104858i	0.000638295	−	0.00519127i
$409$	11.1099	+	6.41428i	0.549347	+	0.317166i	0.748859	−	0.662730i	$-0.230602\pi$
$409$	11.1099	+	6.41428i	0.549347	+	0.317166i	−0.199511	+	0.979896i	$0.563935\pi$
$410$	9.15272	+	3.76063i	0.452021	+	0.185724i
$411$	−0.156171			−0.00770335
$412$	−9.25003	+	2.53519i	−0.455716	+	0.124900i
$413$	2.52904	−	1.46014i	0.124446	−	0.0718488i
$414$	−3.79920	+	2.93249i	−0.186721	+	0.144124i
$415$	−8.27000	+	4.77469i	−0.405958	+	0.234380i
$416$	−8.13992	+	1.18999i	−0.399093	+	0.0583440i
$417$		−	0.476959i		−	0.0233568i
$418$	−8.12534	+	2.98037i	−0.397424	+	0.145775i
$419$		−	19.7926i		−	0.966933i	−0.875363	−	0.483466i	$-0.839378\pi$
$419$		−	19.7926i		−	0.966933i	0.875363	−	0.483466i	$-0.160622\pi$
$420$	0.0221044	+	0.00578790i	0.00107859	+	0.000282421i
$421$	−27.0177	+	15.5987i	−1.31676	+	0.760232i	−0.983206	−	0.182498i	$-0.941582\pi$
$421$	−27.0177	+	15.5987i	−1.31676	+	0.760232i	−0.333555	+	0.942731i	$0.608248\pi$
$422$	11.9331	+	15.4599i	0.580892	+	0.752578i
$423$	−29.0159	+	16.7523i	−1.41080	+	0.814525i
$424$	7.35351	+	0.904155i	0.357118	+	0.0439096i
$425$	−1.21271			−0.0588250
$426$	−0.195113	+	0.474871i	−0.00945324	+	0.0230076i
$427$	0.831153	+	0.479866i	0.0402223	+	0.0232224i
$428$	0.190868	−	0.0523120i	0.00922597	−	0.00252860i
$429$	−0.0628865			−0.00303619
$430$	11.8218	+	4.85728i	0.570097	+	0.234239i
$431$	11.2667	−	19.5145i	0.542698	−	0.939981i	−0.456050	−	0.889954i	$-0.650736\pi$
$431$	11.2667	−	19.5145i	0.542698	−	0.939981i	0.998748	−	0.0500263i	$-0.0159305\pi$
$432$	−0.635820	+	0.376829i	−0.0305909	+	0.0181302i
$433$	6.86997	+	3.96638i	0.330149	+	0.190612i	0.655907	−	0.754841i	$-0.272286\pi$
$433$	6.86997	+	3.96638i	0.330149	+	0.190612i	−0.325758	+	0.945453i	$0.605619\pi$
$434$	0.246910	+	1.83500i	0.0118521	+	0.0880829i
$435$	−0.0891035	+	0.0514439i	−0.00427219	+	0.00246655i
$436$	20.8276	−	21.0666i	0.997462	−	1.00891i
$437$	1.48488	−	4.70357i	0.0710312	−	0.225002i
$438$	0.0973942	−	0.237041i	0.00465367	−	0.0113262i
$439$	−1.05507	−	1.82743i	−0.0503557	−	0.0872186i	0.839749	−	0.542975i	$-0.182702\pi$
$439$	−1.05507	−	1.82743i	−0.0503557	−	0.0872186i	−0.890105	+	0.455756i	$0.849369\pi$
$440$	2.39037	−	3.17102i	0.113956	−	0.151172i
$441$	10.2904	−	17.8234i	0.490017	−	0.848735i
$442$	−0.332594	−	2.47180i	−0.0158199	−	0.117571i
$443$	1.68740	+	0.974219i	0.0801706	+	0.0462865i	0.539549	−	0.841954i	$-0.318595\pi$
$443$	1.68740	+	0.974219i	0.0801706	+	0.0462865i	−0.459379	+	0.888240i	$0.651928\pi$
$444$	0.156026	−	0.157817i	0.00740467	−	0.00748965i
$445$			2.64635i			0.125449i
$446$	−16.5390	−	21.4272i	−0.783145	−	1.01461i
$447$	−0.157132	+	0.272161i	−0.00743210	+	0.0128728i
$448$	−2.13389	−	2.06206i	−0.100817	−	0.0974233i
$449$		−	5.15599i		−	0.243326i	−0.992571	−	0.121663i	$-0.961177\pi$
$449$		−	5.15599i		−	0.243326i	0.992571	−	0.121663i	$-0.0388228\pi$
$450$	2.59153	+	3.35747i	0.122166	+	0.158273i
$451$	−4.91178	−	8.50745i	−0.231287	−	0.400600i
$452$	1.03316	+	3.76963i	0.0485956	+	0.177309i
$453$	0.107562	+	0.186303i	0.00505371	+	0.00875328i
$454$	2.22472	−	0.299349i	0.104411	−	0.0140491i
$455$	0.539419			0.0252884
$456$	0.157655	−	0.345462i	0.00738289	−	0.0161778i
$457$	35.7115			1.67051			0.835257	−	0.549860i	$-0.185319\pi$
$457$	35.7115			1.67051			0.835257	+	0.549860i	$0.185319\pi$
$458$	30.0614	−	4.04494i	1.40468	−	0.189007i
$459$	−0.112039	−	0.194057i	−0.00522953	−	0.00905782i
$460$	0.598205	+	2.18264i	0.0278915	+	0.101766i
$461$	−15.5615	−	26.9534i	−0.724773	−	1.25534i	−0.959067	−	0.283178i	$-0.908611\pi$
$461$	−15.5615	−	26.9534i	−0.724773	−	1.25534i	0.234294	−	0.972166i	$-0.424722\pi$
$462$	−0.0138606	−	0.0179572i	−0.000644853	−	0.000835443i
$463$			18.6241i			0.865534i	0.901506	+	0.432767i	$0.142463\pi$
$463$			18.6241i			0.865534i	−0.901506	+	0.432767i	$0.857537\pi$
$464$	13.3609	−	0.152466i	0.620264	−	0.00707806i
$465$	0.0543574	−	0.0941498i	0.00252076	−	0.00436609i
$466$	−22.8010	−	29.5399i	−1.05623	−	1.36841i
$467$			20.8224i			0.963546i	0.876296	+	0.481773i	$0.160007\pi$
$467$			20.8224i			0.963546i	−0.876296	+	0.481773i	$0.839993\pi$
$468$	−6.13259	+	6.20297i	−0.283479	+	0.286733i
$469$	0.754060	+	0.435357i	0.0348192	+	0.0201029i
$470$	2.10689	+	15.6581i	0.0971836	+	0.722255i
$471$	−0.186323	+	0.322721i	−0.00858530	+	0.0148702i
$472$	17.7817	+	13.4042i	0.818470	+	0.616978i
$473$	−6.34412	−	10.9883i	−0.291703	−	0.505244i
$474$	0.205042	−	0.499038i	0.00941791	−	0.0229216i
$475$	−4.15669	−	1.31223i	−0.190722	−	0.0602092i
$476$	0.632512	−	0.639771i	0.0289911	−	0.0293239i
$477$	6.80334	−	3.92791i	0.311504	−	0.179847i
$478$	−3.89441	−	28.9428i	−0.178126	−	1.32381i
$479$	−27.6141	−	15.9430i	−1.26172	−	0.728456i	−0.288315	−	0.957536i	$-0.593095\pi$
$479$	−27.6141	−	15.9430i	−1.26172	−	0.728456i	−0.973408	+	0.229080i	$0.926428\pi$
$480$	0.0252038	+	0.172402i	0.00115039	+	0.00786905i
$481$	2.61952	−	4.53714i	0.119440	−	0.206876i
$482$	14.2967	+	5.87418i	0.651199	+	0.267562i
$483$	0.0129280			0.000588242
$484$	17.4154	−	4.77312i	0.791611	−	0.216960i
$485$	10.5201	+	6.07377i	0.477692	+	0.275796i
$486$	−0.446779	+	1.08738i	−0.0202663	+	0.0493247i
$487$	35.9431			1.62874			0.814368	−	0.580349i	$-0.197084\pi$
$487$	35.9431			1.62874			0.814368	+	0.580349i	$0.197084\pi$
$488$	−0.893092	+	7.26353i	−0.0404284	+	0.328805i
$489$	−0.144193	+	0.0832498i	−0.00652063	+	0.00376469i
$490$	−5.92992	−	7.68254i	−0.267886	−	0.347062i
$491$	−4.96170	+	2.86464i	−0.223919	+	0.129279i	−0.607763	−	0.794118i	$-0.707933\pi$
$491$	−4.96170	+	2.86464i	−0.223919	+	0.129279i	0.383845	+	0.923398i	$0.374600\pi$
$492$	0.416965	+	0.109179i	0.0187982	+	0.00492219i
$493$			4.05099i			0.182447i
$494$	1.53464	−	8.83223i	0.0690467	−	0.397381i
$495$		−	4.21060i		−	0.189252i
$496$	−12.1456	+	7.19831i	−0.545355	+	0.323214i
$497$	−3.78611	+	2.18591i	−0.169830	+	0.0980516i
$498$	−0.329278	+	0.254160i	−0.0147553	+	0.0113892i
$499$	14.4543	−	8.34522i	0.647065	−	0.373583i	−0.140266	−	0.990114i	$-0.544796\pi$
$499$	14.4543	−	8.34522i	0.647065	−	0.373583i	0.787331	+	0.616531i	$0.211462\pi$
$500$	1.92887	−	0.528652i	0.0862615	−	0.0236420i
$501$	−0.688735			−0.0307704
$502$	−11.0914	−	4.55718i	−0.495033	−	0.203397i
$503$	18.4632	+	10.6597i	0.823234	+	0.475294i	0.851530	−	0.524305i	$-0.175675\pi$
$503$	18.4632	+	10.6597i	0.823234	+	0.475294i	−0.0282965	+	0.999600i	$0.509008\pi$
$504$	−3.12291	−	0.383980i	−0.139106	−	0.0171038i
$505$	2.03557			0.0905815
$506$	0.853871	−	2.07817i	0.0379592	−	0.0923861i
$507$	−0.167635	+	0.290353i	−0.00744495	+	0.0128950i
$508$	3.20275	−	12.2315i	0.142099	−	0.542687i
$509$	6.17222	+	3.56353i	0.273579	+	0.157951i	0.630513	−	0.776179i	$-0.282845\pi$
$509$	6.17222	+	3.56353i	0.273579	+	0.157951i	−0.356934	+	0.934130i	$0.616178\pi$
$510$	−0.0523523	+	0.00704430i	−0.00231820	+	0.000311927i
$511$	1.88991	−	1.09114i	0.0836047	−	0.0482692i
$512$	8.11962	−	21.1204i	0.358840	−	0.933399i
$513$	−0.174043	−	0.786385i	−0.00768419	−	0.0347198i
$514$	−0.389307	−	0.159957i	−0.0171716	−	0.00705539i
$515$	2.39779	+	4.15309i	0.105659	+	0.183007i
$516$	0.538557	+	0.141018i	0.0237086	+	0.00620795i
$517$	7.84244	−	13.5835i	0.344910	−	0.597402i
$518$	1.87293	−	0.252014i	0.0822919	−	0.0110729i
$519$	0.355371	+	0.205173i	0.0155990	+	0.00900611i
$520$	1.60653	+	3.78651i	0.0704509	+	0.166050i
$521$			1.21818i			0.0533696i	0.999644	+	0.0266848i	$0.00849504\pi$
$521$			1.21818i			0.0533696i	−0.999644	+	0.0266848i	$0.991505\pi$
$522$	11.2154	−	8.65685i	0.490886	−	0.378900i
$523$	4.81769	−	8.34448i	0.210663	−	0.364878i	−0.741259	−	0.671219i	$-0.765771\pi$
$523$	4.81769	−	8.34448i	0.210663	−	0.364878i	0.951922	+	0.306340i	$0.0991045\pi$
$524$	7.85218	−	7.94229i	0.343024	−	0.346961i
$525$		−	0.0114248i		−	0.000498620i
$526$	13.5722	−	10.4760i	0.591778	−	0.456775i
$527$	−2.14020	−	3.70694i	−0.0932288	−	0.161477i
$528$	0.0847720	−	0.150777i	0.00368923	−	0.00656172i
$529$	−10.8598	−	18.8097i	−0.472164	−	0.817812i
$530$	−0.494002	−	3.67136i	−0.0214581	−	0.159474i
$531$	23.6113			1.02464
$532$	2.86027	−	1.50846i	0.124009	−	0.0654002i
$533$	10.1753			0.440740
$534$	0.0153719	+	0.114242i	0.000665208	+	0.00494373i
$535$	−0.0494768	−	0.0856963i	−0.00213907	−	0.00370498i
$536$	−0.810253	+	6.58980i	−0.0349976	+	0.284636i
$537$	−0.314441	−	0.544627i	−0.0135691	−	0.0235024i
$538$	−24.2643	+	18.7289i	−1.04611	+	0.807460i
$539$			9.63467i			0.414995i
$540$	0.262798	+	0.259816i	0.0113090	+	0.0111807i
$541$	3.02529	−	5.23996i	0.130068	−	0.225284i	−0.793635	−	0.608394i	$-0.791814\pi$
$541$	3.02529	−	5.23996i	0.130068	−	0.225284i	0.923702	+	0.383111i	$0.125147\pi$
$542$	−20.2057	+	15.5962i	−0.867909	+	0.669913i
$543$		−	0.0667686i		−	0.00286531i
$544$	6.37472	+	2.53459i	0.273314	+	0.108670i
$545$	−12.8277	−	7.40605i	−0.549476	−	0.317240i
$546$	0.0232866	−	0.00313334i	0.000996573	−	0.000134095i
$547$	−6.39858	+	11.0827i	−0.273584	+	0.473861i	−0.969777	−	0.243994i	$-0.921542\pi$
$547$	−6.39858	+	11.0827i	−0.273584	+	0.473861i	0.696193	+	0.717854i	$0.254876\pi$
$548$	2.56869	−	9.81004i	0.109729	−	0.419064i
$549$	3.87985	+	6.72010i	0.165588	+	0.286807i
$550$	−1.83655	−	0.754591i	−0.0783105	−	0.0321759i
$551$	−4.38343	+	13.8852i	−0.186740	+	0.591528i
$552$	0.0385027	+	0.0907492i	0.00163878	+	0.00386254i
$553$	3.97880	−	2.29716i	0.169196	−	0.0976851i
$554$	4.66704	−	0.627977i	0.198284	−	0.0266802i
$555$	−0.0960959	−	0.0554810i	−0.00407904	−	0.00235504i
$556$	29.9606	+	7.84499i	1.27061	+	0.332702i
$557$	16.7108	−	28.9439i	0.708058	−	1.22639i	−0.257519	−	0.966273i	$-0.582905\pi$
$557$	16.7108	−	28.9439i	0.708058	−	1.22639i	0.965577	−	0.260119i	$-0.0837618\pi$
$558$	−5.68937	+	13.8469i	−0.240850	+	0.586188i
$559$	13.1425			0.555869
$560$	−0.727145	+	1.29331i	−0.0307275	+	0.0546524i
$561$	0.0454159	+	0.0262209i	0.00191746	+	0.00110705i
$562$	22.1773	+	9.11211i	0.935493	+	0.384371i
$563$	43.1942			1.82042			0.910208	−	0.414151i	$-0.135921\pi$
$563$	43.1942			1.82042			0.910208	+	0.414151i	$0.135921\pi$
$564$	0.181908	+	0.663718i	0.00765969	+	0.0279476i
$565$	1.69250	−	0.977163i	0.0712038	−	0.0411095i
$566$	−24.6890	+	19.0567i	−1.03776	+	0.801011i
$567$	−2.88835	+	1.66759i	−0.121299	+	0.0700322i
$568$	−26.6203	−	20.0668i	−1.11696	−	0.841986i
$569$			24.4936i			1.02682i	0.858142	+	0.513412i	$0.171619\pi$
$569$			24.4936i			1.02682i	−0.858142	+	0.513412i	$0.828381\pi$
$570$	−0.187065	−	0.0325034i	−0.00783530	−	0.00136142i
$571$			7.91310i			0.331153i	0.986197	+	0.165576i	$0.0529484\pi$
$571$			7.91310i			0.331153i	−0.986197	+	0.165576i	$0.947052\pi$
$572$	1.03435	−	3.95028i	0.0432485	−	0.165169i
$573$	−0.110174	+	0.0636087i	−0.00460257	+	0.00265729i
$574$	2.24269	+	2.90554i	0.0936082	+	0.121275i
$575$	0.979966	−	0.565784i	0.0408674	−	0.0235948i
$576$	−6.60543	−	23.0652i	−0.275226	−	0.961051i
$577$	−17.1770			−0.715088			−0.357544	−	0.933896i	$-0.616386\pi$
$577$	−17.1770			−0.715088			−0.357544	+	0.933896i	$0.616386\pi$
$578$	8.34650	−	20.3139i	0.347169	−	0.844949i
$579$	0.123062	+	0.0710497i	0.00511427	+	0.00295273i
$580$	−1.76593	−	6.44327i	−0.0733263	−	0.267542i
$581$	−3.54213			−0.146952
$582$	0.489429	+	0.201094i	0.0202875	+	0.00833563i
$583$	−1.83882	+	3.18492i	−0.0761559	+	0.131906i
$584$	13.2880	+	10.0167i	0.549862	+	0.414496i
$585$	3.77704	+	2.18068i	0.156162	+	0.0901599i
$586$	−3.41502	−	25.3800i	−0.141073	−	1.04844i
$587$	4.65820	−	2.68942i	0.192265	−	0.111004i	−0.400778	−	0.916175i	$-0.631260\pi$
$587$	4.65820	−	2.68942i	0.192265	−	0.111004i	0.593042	+	0.805171i	$0.297927\pi$
$588$	−0.300619	−	0.297208i	−0.0123973	−	0.0122566i
$589$	−3.32463	−	15.0218i	−0.136989	−	0.618961i
$590$	4.23143	−	10.2986i	0.174205	−	0.423985i
$591$	0.185320	+	0.320984i	0.00762306	+	0.0132035i
$592$	7.34710	+	12.3967i	0.301964	+	0.509501i
$593$	9.11773	−	15.7924i	0.374420	−	0.648515i	−0.615820	−	0.787887i	$-0.711175\pi$
$593$	9.11773	−	15.7924i	0.374420	−	0.648515i	0.990240	+	0.139372i	$0.0445084\pi$
$594$	−0.0489242	−	0.363598i	−0.00200738	−	0.0149186i
$595$	−0.389562	−	0.224914i	−0.0159705	−	0.00922056i
$596$	−14.5116	−	14.3469i	−0.594416	−	0.587672i
$597$		−	0.350077i		−	0.0143277i
$598$	1.42197	+	1.84224i	0.0581486	+	0.0753348i
$599$	−1.16451	+	2.01699i	−0.0475805	+	0.0824118i	−0.888835	−	0.458228i	$-0.848484\pi$
$599$	−1.16451	+	2.01699i	−0.0475805	+	0.0824118i	0.841254	+	0.540640i	$0.181818\pi$
$600$	0.0801978	−	0.0340260i	0.00327406	−	0.00138911i
$601$		−	17.2528i		−	0.703754i	−0.936046	−	0.351877i	$-0.885543\pi$
$601$		−	17.2528i		−	0.703754i	0.936046	−	0.351877i	$-0.114457\pi$
$602$	2.89669	+	3.75283i	0.118060	+	0.152954i
$603$	3.51998	+	6.09678i	0.143345	+	0.248280i
$604$	−13.4720	+	3.69231i	−0.548167	+	0.150238i
$605$	−4.51442	−	7.81921i	−0.183537	−	0.317896i
$606$	0.0878747	−	0.0118241i	0.00356967	−	0.000480319i
$607$	20.3533			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$607$	20.3533			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$608$	19.1074	+	15.5854i	0.774909	+	0.632073i
$609$	−0.0381640			−0.00154648
$610$	3.62643	−	0.487957i	0.146830	−	0.0197568i
$611$	8.12322	+	14.0698i	0.328630	+	0.569204i
$612$	7.01524	−	1.92269i	0.283574	−	0.0777203i
$613$	−20.3973	−	35.3291i	−0.823838	−	1.42693i	−0.902804	−	0.430052i	$-0.858495\pi$
$613$	−20.3973	−	35.3291i	−0.823838	−	1.42693i	0.0789660	−	0.996877i	$-0.474838\pi$
$614$	24.5337	+	31.7848i	0.990099	+	1.28273i
$615$		−	0.215511i		−	0.00869023i
$616$	1.35597	−	0.575307i	0.0546338	−	0.0231798i
$617$	−9.82620	+	17.0195i	−0.395588	+	0.685178i	−0.993176	−	0.116625i	$-0.962792\pi$
$617$	−9.82620	+	17.0195i	−0.395588	+	0.685178i	0.597588	+	0.801803i	$0.296126\pi$
$618$	0.127636	+	0.165359i	0.00513427	+	0.00665173i
$619$		−	41.0912i		−	1.65160i	−0.563966	−	0.825798i	$-0.690725\pi$
$619$		−	41.0912i		−	1.65160i	0.563966	−	0.825798i	$-0.309275\pi$
$620$	5.02004	+	4.96308i	0.201610	+	0.199322i
$621$	0.181073	+	0.104543i	0.00726621	+	0.00419515i
$622$	−2.20879	−	16.4154i	−0.0885643	−	0.658197i
$623$	−0.490802	+	0.850093i	−0.0196636	+	0.0340583i
$624$	0.0913481	+	0.154131i	0.00365685	+	0.00617017i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−18.0436	+	43.9150i	−0.721168	+	1.75520i
$627$	0.127295	+	0.139018i	0.00508367	+	0.00555183i
$628$	−17.2074	−	17.0121i	−0.686649	−	0.678858i
$629$	−3.78357	+	2.18444i	−0.150861	+	0.0870995i
$630$	0.209794	+	1.55916i	0.00835841	+	0.0621186i
$631$	16.4628	+	9.50482i	0.655375	+	0.378381i	0.790513	−	0.612446i	$-0.209814\pi$
$631$	16.4628	+	9.50482i	0.655375	+	0.378381i	−0.135137	+	0.990827i	$0.543148\pi$
$632$	27.9750	+	21.0881i	1.11279	+	0.838839i
$633$	0.212672	−	0.368358i	0.00845294	−	0.0146409i
$634$	29.8198	+	12.2522i	1.18430	+	0.486598i
$635$	−6.32195			−0.250879
$636$	−0.0426518	−	0.155622i	−0.00169125	−	0.00617080i
$637$	−8.64261	−	4.98981i	−0.342433	−	0.197704i
$638$	−2.52067	+	6.13487i	−0.0997942	+	0.242882i
$639$	−35.3474			−1.39832
$640$	−11.2442	−	1.25246i	−0.444465	−	0.0495080i
$641$	22.1928	−	12.8130i	0.876564	−	0.506084i	0.00703994	−	0.999975i	$-0.497759\pi$
$641$	22.1928	−	12.8130i	0.876564	−	0.506084i	0.869524	+	0.493891i	$0.164426\pi$
$642$	−0.00263368	−	0.00341209i	−0.000103943	−	0.000134664i
$643$	27.6129	−	15.9423i	1.08894	−	0.628702i	0.155649	−	0.987812i	$-0.450253\pi$
$643$	27.6129	−	15.9423i	1.08894	−	0.628702i	0.933295	+	0.359110i	$0.116920\pi$
$644$	−0.212638	+	0.812082i	−0.00837912	+	0.0320005i
$645$		−	0.278357i		−	0.0109603i
$646$	−4.79094	+	5.73865i	−0.188497	+	0.225784i
$647$		−	22.1120i		−	0.869312i	−0.900597	−	0.434656i	$-0.856870\pi$
$647$		−	22.1120i		−	0.869312i	0.900597	−	0.434656i	$-0.143130\pi$
$648$	−20.3081	−	15.3086i	−0.797777	−	0.601379i
$649$	−9.57252	+	5.52669i	−0.375754	+	0.216942i
$650$	1.62804	−	1.25664i	0.0638571	−	0.0492893i
$651$	0.0349228	−	0.0201627i	0.00136873	−	0.000790237i
$652$	−2.85774	−	10.4269i	−0.111918	−	0.408349i
$653$	−11.2344			−0.439638			−0.219819	−	0.975541i	$-0.570547\pi$
$653$	−11.2344			−0.439638			−0.219819	+	0.975541i	$0.570547\pi$
$654$	−0.596785	−	0.245204i	−0.0233362	−	0.00958825i
$655$	−4.83613	−	2.79214i	−0.188963	−	0.109098i
$656$	−13.7164	+	24.3963i	−0.535536	+	0.952514i
$657$	17.6443			0.688371
$658$	−2.22721	+	5.42065i	−0.0868258	+	0.211319i
$659$	10.5989	−	18.3579i	0.412876	−	0.715122i	−0.582327	−	0.812955i	$-0.697858\pi$
$659$	10.5989	−	18.3579i	0.412876	−	0.715122i	0.995203	+	0.0978325i	$0.0311909\pi$
$660$	−0.0836663	−	0.0219075i	−0.00325671	−	0.000852747i
$661$	18.5539	+	10.7121i	0.721664	+	0.416653i	0.815365	−	0.578947i	$-0.196536\pi$
$661$	18.5539	+	10.7121i	0.721664	+	0.416653i	−0.0937007	+	0.995600i	$0.529870\pi$
$662$	−29.4528	+	3.96305i	−1.14472	+	0.154028i
$663$	−0.0470419	+	0.0271597i	−0.00182696	+	0.00105479i
$664$	−10.5493	−	24.8643i	−0.409394	−	0.964923i
$665$	−1.09189	−	1.19245i	−0.0423418	−	0.0462411i
$666$	14.1332	+	5.80697i	0.547649	+	0.225016i
$667$	−1.88997	−	3.27352i	−0.0731799	−	0.126751i
$668$	11.3283	−	43.2636i	0.438304	−	1.67392i
$669$	−0.294760	+	0.510539i	−0.0113961	+	0.0197386i
$670$	3.29007	−	0.442697i	0.127106	−	0.0171029i
$671$	−3.14595	−	1.81632i	−0.121448	−	0.0701181i
$672$	−0.0238781	+	0.0600557i	−0.000921118	+	0.00231670i
$673$		−	9.81800i		−	0.378456i	−0.981933	−	0.189228i	$-0.939401\pi$
$673$		−	9.81800i		−	0.378456i	0.981933	−	0.189228i	$-0.0605985\pi$
$674$	14.3240	−	11.0562i	0.551739	−	0.425871i
$675$	0.0923874	−	0.160020i	0.00355599	−	0.00615916i
$676$	−15.4815	−	15.3059i	−0.595444	−	0.588688i
$677$			26.9932i			1.03743i	0.854946	+	0.518717i	$0.173590\pi$
$677$			26.9932i			1.03743i	−0.854946	+	0.518717i	$0.826410\pi$
$678$	0.0673884	−	0.0520151i	0.00258804	−	0.00199763i
$679$	2.25293	+	3.90219i	0.0864595	+	0.149752i
$680$	0.418593	−	3.40442i	0.0160523	−	0.130554i
$681$	−0.0244448	−	0.0423396i	−0.000936727	−	0.00162246i
$682$	−0.934565	−	6.94556i	−0.0357864	−	0.265959i
$683$	38.4771			1.47229			0.736143	−	0.676826i	$-0.236645\pi$
$683$	38.4771			1.47229			0.736143	+	0.676826i	$0.236645\pi$
$684$	26.1260	+	1.00071i	0.998951	+	0.0382630i
$685$	−5.07038			−0.193729
$686$	−0.969726	−	7.20687i	−0.0370243	−	0.275160i
$687$	−0.330309	−	0.572113i	−0.0126021	−	0.0218275i
$688$	−17.7163	+	31.5105i	−0.675428	+	1.20133i
$689$	−1.90465	−	3.29895i	−0.0725614	−	0.125680i
$690$	0.0390183	−	0.0301171i	0.00148540	−	0.00114654i
$691$		−	0.846753i		−	0.0322120i	−0.999870	−	0.0161060i	$-0.994873\pi$
$691$		−	0.846753i		−	0.0322120i	0.999870	−	0.0161060i	$-0.00512692\pi$
$692$	−18.7333	+	18.9483i	−0.712132	+	0.720305i
$693$	0.780914	−	1.35258i	0.0296645	−	0.0513804i
$694$	−33.5343	+	25.8841i	−1.27294	+	0.982546i
$695$		−	15.4853i		−	0.587392i
$696$	−0.113662	−	0.267896i	−0.00430834	−	0.0101546i
$697$	−7.34846	−	4.24263i	−0.278343	−	0.160701i
$698$	−33.3476	+	4.48711i	−1.26223	+	0.169840i
$699$	−0.406360	+	0.703837i	−0.0153700	+	0.0266215i
$700$	0.717661	+	0.187915i	0.0271250	+	0.00710251i
$701$	20.0919	+	34.8002i	0.758861	+	1.31439i	0.943432	+	0.331567i	$0.107577\pi$
$701$	20.0919	+	34.8002i	0.758861	+	1.31439i	−0.184570	+	0.982819i	$0.559089\pi$
$702$	0.351497	+	0.144421i	0.0132664	+	0.00545084i
$703$	−15.3323	+	3.39335i	−0.578268	+	0.127983i
$704$	8.07687	+	7.80500i	0.304408	+	0.294162i
$705$	0.297997	−	0.172049i	0.0112232	−	0.00647972i
$706$	18.2315	−	2.45315i	0.686150	−	0.0923255i
$707$	0.653891	+	0.377524i	0.0245921	+	0.0141982i
$708$	0.122848	−	0.469165i	0.00461690	−	0.0176323i
$709$	3.77286	−	6.53479i	0.141693	−	0.245419i	−0.786441	−	0.617665i	$-0.788079\pi$
$709$	3.77286	−	6.53479i	0.141693	−	0.245419i	0.928134	+	0.372246i	$0.121412\pi$
$710$	−6.33469	+	15.4175i	−0.237737	+	0.578610i
$711$	37.1463			1.39310
$712$	−7.42905	−	0.913444i	−0.278416	−	0.0342328i
$713$	3.45891	+	1.99700i	0.129537	+	0.0747884i
$714$	−0.0181237	−	0.00744659i	−0.000678263	−	0.000278682i
$715$	−2.04173			−0.0763562
$716$	39.3832	−	10.7939i	1.47182	−	0.403387i
$717$	−0.550823	+	0.318018i	−0.0205709	+	0.0118766i
$718$	−20.8439	+	16.0888i	−0.777889	+	0.600429i
$719$	−43.6022	+	25.1738i	−1.62609	+	0.938822i	−0.640843	+	0.767672i	$0.721415\pi$
$719$	−43.6022	+	25.1738i	−1.62609	+	0.938822i	−0.985245	+	0.171151i	$0.945251\pi$
$720$	−10.3199	+	6.11626i	−0.384600	+	0.227939i
$721$			1.77881i			0.0662464i
$722$	−22.6310	+	14.4857i	−0.842240	+	0.539103i
$723$		−	0.336632i		−	0.0125195i
$724$	4.19413	+	1.09821i	0.155874	+	0.0408145i
$725$	−2.89291	+	1.67022i	−0.107440	+	0.0620305i
$726$	−0.240306	−	0.311330i	−0.00891859	−	0.0115545i
$727$	44.6955	−	25.8049i	1.65766	−	0.957052i	0.683874	−	0.729600i	$-0.260294\pi$
$727$	44.6955	−	25.8049i	1.65766	−	0.957052i	0.973789	−	0.227452i	$-0.0730396\pi$
$728$	−0.186192	+	1.51430i	−0.00690074	+	0.0561239i
$729$	−26.9488			−0.998103
$730$	3.16208	−	7.69596i	0.117034	−	0.284840i
$731$	−9.49136	−	5.47984i	−0.351051	−	0.202679i
$732$	0.153718	−	0.0421299i	0.00568156	−	0.00155717i
$733$	−6.85905			−0.253345			−0.126672	−	0.991945i	$-0.540430\pi$
$733$	−6.85905			−0.253345			−0.126672	+	0.991945i	$0.540430\pi$
$734$	−21.2077	−	8.71372i	−0.782791	−	0.321629i
$735$	−0.105683	+	0.183049i	−0.00389819	+	0.00675187i
$736$	−6.33379	+	0.925946i	−0.233466	+	0.0341308i
$737$	−2.85415	−	1.64784i	−0.105134	−	0.0606991i
$738$	3.95743	+	29.4111i	0.145675	+	1.08264i
$739$	33.4709	−	19.3244i	1.23125	−	0.710861i	0.263957	−	0.964534i	$-0.414972\pi$
$739$	33.4709	−	19.3244i	1.23125	−	0.710861i	0.967290	+	0.253674i	$0.0816390\pi$
$740$	5.06567	−	5.12381i	0.186218	−	0.188355i
$741$	−0.190630	+	0.0421902i	−0.00700295	+	0.00154990i
$742$	0.522214	−	1.27098i	0.0191711	−	0.0466591i
$743$	21.4862	+	37.2152i	0.788253	+	1.36530i	0.927036	+	0.374972i	$0.122348\pi$
$743$	21.4862	+	37.2152i	0.788253	+	1.36530i	−0.138783	+	0.990323i	$0.544319\pi$
$744$	0.245543	+	0.185095i	0.00900203	+	0.00678590i
$745$	−5.10159	+	8.83621i	−0.186908	+	0.323734i
$746$	5.93689	+	44.1221i	0.217365	+	1.61543i
$747$	−24.8021	−	14.3195i	−0.907463	−	0.523924i
$748$	−2.39409	+	2.42156i	−0.0875365	+	0.0885411i
$749$		−	0.0367046i		−	0.00134116i
$750$	−0.0266153	−	0.0344817i	−0.000971855	−	0.00125909i
$751$	−8.36777	+	14.4934i	−0.305344	+	0.528872i	−0.977338	−	0.211685i	$-0.932105\pi$
$751$	−8.36777	+	14.4934i	−0.305344	+	0.528872i	0.671994	+	0.740557i	$0.265438\pi$
$752$	−44.6841	+	0.509906i	−1.62946	+	0.0185944i
$753$			0.261159i			0.00951715i
$754$	−4.19772	−	5.43838i	−0.152872	−	0.198054i
$755$	3.49220	+	6.04867i	0.127094	+	0.220133i
$756$	0.0362328	+	0.132201i	0.00131777	+	0.00480810i
$757$	−13.6354	−	23.6173i	−0.495588	−	0.858384i	0.504399	−	0.863471i	$-0.331714\pi$
$757$	−13.6354	−	23.6173i	−0.495588	−	0.858384i	−0.999987	+	0.00508653i	$0.998381\pi$
$758$	−34.2867	+	4.61347i	−1.24535	+	0.167569i
$759$	−0.0489329			−0.00177615
$760$	5.11857	−	11.2161i	0.185670	−	0.406850i
$761$	−16.1484			−0.585378			−0.292689	−	0.956208i	$-0.594550\pi$
$761$	−16.1484			−0.585378			−0.292689	+	0.956208i	$0.594550\pi$
$762$	−0.272917	+	0.0367225i	−0.00988673	+	0.00133032i
$763$	−2.74711	−	4.75813i	−0.0994520	−	0.172256i
$764$	−2.18352	−	7.96689i	−0.0789968	−	0.288232i
$765$	−1.81849	−	3.14971i	−0.0657476	−	0.113878i
$766$	−27.3621	−	35.4492i	−0.988634	−	1.28083i
$767$		−	11.4491i		−	0.413404i
$768$	−0.492682	+	0.0112458i	−0.0177781	+	0.000405799i
$769$	−6.87288	+	11.9042i	−0.247842	+	0.429275i	−0.962927	−	0.269762i	$-0.913055\pi$
$769$	−6.87288	+	11.9042i	−0.247842	+	0.429275i	0.715085	+	0.699038i	$0.246388\pi$
$770$	−0.450009	−	0.583012i	−0.0162172	−	0.0210103i
$771$			0.00916666i			0.000330129i
$772$	−6.48717	+	6.56162i	−0.233478	+	0.236158i
$773$	8.71669	+	5.03258i	0.313517	+	0.181009i	0.648499	−	0.761215i	$-0.275397\pi$
$773$	8.71669	+	5.03258i	0.313517	+	0.181009i	−0.334982	+	0.942225i	$0.608730\pi$
$774$	5.11147	+	37.9878i	0.183728	+	1.36544i
$775$	1.76481	−	3.05674i	0.0633939	−	0.109802i
$776$	−20.6820	+	27.4364i	−0.742442	+	0.984909i
$777$	−0.0205794	−	0.0356446i	−0.000738283	−	0.00127874i
$778$	−4.81176	+	11.7110i	−0.172510	+	0.419860i
$779$	−20.5968	−	22.4936i	−0.737957	−	0.805916i
$780$	0.0629826	−	0.0637054i	0.00225514	−	0.00228102i
$781$	14.3306	−	8.27378i	0.512789	−	0.296059i
$782$	−0.258796	−	1.92334i	−0.00925454	−	0.0687785i
$783$	−0.534537	−	0.308615i	−0.0191028	−	0.0110290i
$784$	23.6139	−	13.9952i	0.843355	−	0.499828i
$785$	−6.04931	+	10.4777i	−0.215909	+	0.373966i
$786$	−0.224993	−	0.0924440i	−0.00802523	−	0.00329737i
$787$	−10.1676			−0.362436			−0.181218	−	0.983443i	$-0.558004\pi$
$787$	−10.1676			−0.362436			−0.181218	+	0.983443i	$0.558004\pi$
$788$	−23.2111	+	6.36154i	−0.826860	+	0.226621i
$789$	−0.323381	−	0.186704i	−0.0115127	−	0.00664683i
$790$	6.65707	−	16.2022i	0.236848	−	0.576447i
$791$	0.724913			0.0257750
$792$	11.8204	+	1.45338i	0.420018	+	0.0516436i
$793$	3.25858	−	1.88134i	0.115716	−	0.0668085i
$794$	12.3784	+	16.0369i	0.439293	+	0.569129i
$795$	−0.0698713	+	0.0403402i	−0.00247808	+	0.00143072i
$796$	21.9904	+	5.75804i	0.779429	+	0.204088i
$797$			41.0384i			1.45365i	0.686821	+	0.726827i	$0.259006\pi$
$797$			41.0384i			1.45365i	−0.686821	+	0.726827i	$0.740994\pi$
$798$	−0.0540633	−	0.0451350i	−0.00191382	−	0.00159776i
$799$		−	13.5481i		−	0.479296i
$800$	0.818287	+	5.59736i	0.0289308	+	0.197896i
$801$	−6.87324	+	3.96827i	−0.242854	+	0.140212i
$802$	−39.1800	+	30.2419i	−1.38349	+	1.06788i
$803$	−7.15339	+	4.13001i	−0.252438	+	0.145745i
$804$	0.139460	−	0.0382222i	0.00491836	−	0.00134799i
$805$	0.419730			0.0147935
$806$	6.71440	+	2.75878i	0.236505	+	0.0971740i
$807$	0.578137	+	0.333788i	0.0203514	+	0.0117499i
$808$	−0.702620	+	5.71442i	−0.0247181	+	0.201033i
$809$	33.7112			1.18522			0.592612	−	0.805488i	$-0.298097\pi$
$809$	33.7112			1.18522			0.592612	+	0.805488i	$0.298097\pi$
$810$	−4.83261	+	11.7617i	−0.169801	+	0.413266i
$811$	8.09031	−	14.0128i	0.284089	−	0.492057i	−0.688299	−	0.725427i	$-0.741642\pi$
$811$	8.09031	−	14.0128i	0.284089	−	0.492057i	0.972388	+	0.233371i	$0.0749755\pi$
$812$	0.627719	−	2.39731i	0.0220286	−	0.0841289i
$813$	0.481434	+	0.277956i	0.0168846	+	0.00974834i
$814$	−7.08913	+	0.953883i	−0.248474	+	0.0334336i
$815$	−4.68148	+	2.70286i	−0.163985	+	0.0946769i
$816$	−0.00170485	−	0.149399i	−5.96817e−5	−	0.00523002i
$817$	−26.6031	−	29.0530i	−0.930725	−	1.01644i
$818$	16.7811	+	6.89492i	0.586736	+	0.241075i
$819$	0.808873	+	1.40101i	0.0282643	+	0.0489552i
$820$	13.5375	+	3.54471i	0.472751	+	0.123787i
$821$	−2.70597	+	4.68688i	−0.0944391	+	0.163573i	−0.909374	−	0.415979i	$-0.863439\pi$
$821$	−2.70597	+	4.68688i	−0.0944391	+	0.163573i	0.814935	+	0.579552i	$0.196772\pi$
$822$	−0.218887	+	0.0294525i	−0.00763455	+	0.00102727i
$823$	4.62640	+	2.67105i	0.161266	+	0.0931071i	0.578461	−	0.815710i	$-0.303653\pi$
$823$	4.62640	+	2.67105i	0.161266	+	0.0931071i	−0.417195	+	0.908817i	$0.636987\pi$
$824$	−12.4866	+	5.29775i	−0.434990	+	0.184556i
$825$			0.0432434i			0.00150554i
$826$	3.26928	−	2.52346i	0.113753	−	0.0878024i
$827$	−8.01052	+	13.8746i	−0.278553	+	0.482468i	−0.971025	−	0.238976i	$-0.923188\pi$
$827$	−8.01052	+	13.8746i	−0.278553	+	0.482468i	0.692472	+	0.721445i	$0.256522\pi$
$828$	−4.77186	+	4.82662i	−0.165833	+	0.167737i
$829$			0.745832i			0.0259038i	0.999916	+	0.0129519i	$0.00412283\pi$
$829$			0.745832i			0.0259038i	−0.999916	+	0.0129519i	$0.995877\pi$
$830$	−10.6906	+	8.25176i	−0.371077	+	0.286423i
$831$	−0.0512806	−	0.0888206i	−0.00177890	−	0.00308115i
$832$	−11.1844	+	3.20298i	−0.387748	+	0.111043i
$833$	4.16106	+	7.20716i	0.144172	+	0.249713i
$834$	−0.0899501	−	0.668497i	−0.00311472	−	0.0231482i
$835$	−22.3610			−0.773836
$836$	−10.8263	+	5.70960i	−0.374434	+	0.197471i
$837$	0.652186			0.0225428
$838$	−3.73271	−	27.7410i	−0.128944	−	0.958297i
$839$	13.1621	+	22.7974i	0.454406	+	0.787055i	0.998654	−	0.0518699i	$-0.0165181\pi$
$839$	13.1621	+	22.7974i	0.454406	+	0.787055i	−0.544248	+	0.838925i	$0.683185\pi$
$840$	0.0320727	+	0.00394352i	0.00110661	+	0.000136064i
$841$	−8.92072	−	15.4511i	−0.307611	−	0.532798i
$842$	−34.9257	+	26.9581i	−1.20362	+	0.929038i
$843$		−	0.522189i		−	0.0179851i
$844$	19.6408	+	19.4179i	0.676063	+	0.668392i
$845$	−5.44259	+	9.42684i	−0.187231	+	0.324293i
$846$	−37.5088	+	28.9519i	−1.28958	+	0.995386i
$847$		−	3.34905i		−	0.115075i
$848$	10.4771	−	0.119558i	0.359784	−	0.00410563i
$849$	0.588255	+	0.339629i	0.0201889	+	0.0116560i
$850$	−1.69971	+	0.228706i	−0.0582996	+	0.00784455i
$851$	2.03828	−	3.53041i	0.0698715	−	0.121021i
$852$	−0.183910	+	0.702367i	−0.00630066	+	0.0240627i
$853$	−7.43882	−	12.8844i	−0.254700	−	0.441154i	0.710114	−	0.704087i	$-0.248643\pi$
$853$	−7.43882	−	12.8844i	−0.254700	−	0.441154i	−0.964814	+	0.262933i	$0.915310\pi$
$854$	1.25543	+	0.515824i	0.0429598	+	0.0176511i
$855$	−2.82487	−	12.7637i	−0.0966084	−	0.436509i
$856$	0.257652	−	0.109316i	0.00880637	−	0.00373633i
$857$	−36.7693	+	21.2288i	−1.25602	+	0.725161i	−0.972298	−	0.233746i	$-0.924902\pi$
$857$	−36.7693	+	21.2288i	−1.25602	+	0.725161i	−0.283719	+	0.958908i	$0.591568\pi$
$858$	−0.0881407	+	0.0118598i	−0.00300907	+	0.000404888i
$859$	−30.8085	−	17.7873i	−1.05117	−	0.606895i	−0.128195	−	0.991749i	$-0.540918\pi$
$859$	−30.8085	−	17.7873i	−1.05117	−	0.606895i	−0.922977	+	0.384854i	$0.874252\pi$
$860$	17.4852	+	4.57839i	0.596241	+	0.156122i
$861$	0.0399695	−	0.0692291i	0.00136216	−	0.00235932i
$862$	12.1110	−	29.4760i	0.412501	−	1.00396i
$863$	−20.3213			−0.691746			−0.345873	−	0.938281i	$-0.612417\pi$
$863$	−20.3213			−0.691746			−0.345873	+	0.938281i	$0.612417\pi$
$864$	−0.820088	+	0.648067i	−0.0279000	+	0.0220477i
$865$	11.5378	+	6.66133i	0.392296	+	0.226492i
$866$	10.3768	+	4.26359i	0.352620	+	0.144883i
$867$	−0.478314			−0.0162444
$868$	0.692129	+	2.52534i	0.0234924	+	0.0857156i
$869$	−15.0599	+	8.69485i	−0.510873	+	0.294953i
$870$	−0.115184	+	0.0889070i	−0.00390511	+	0.00301423i
$871$	2.95634	−	1.70684i	0.100172	−	0.0578341i
$872$	25.2186	−	33.4545i	0.854011	−	1.13291i
$873$			36.4311i			1.23301i
$874$	1.19412	−	6.87248i	0.0403919	−	0.232465i
$875$		−	0.370928i		−	0.0125396i
$876$	0.0918022	−	0.350600i	0.00310171	−	0.0118457i
$877$	−36.7660	+	21.2269i	−1.24150	+	0.716781i	−0.969400	−	0.245488i	$-0.921052\pi$
$877$	−36.7660	+	21.2269i	−1.24150	+	0.716781i	−0.272101	+	0.962269i	$0.587719\pi$
$878$	−1.82340	−	2.36232i	−0.0615368	−	0.0797244i
$879$	−0.483018	+	0.278871i	−0.0162918	+	0.00940608i
$880$	2.75228	−	4.89524i	0.0927792	−	0.165019i
$881$	49.8610			1.67986			0.839929	−	0.542696i	$-0.182596\pi$
$881$	49.8610			1.67986			0.839929	+	0.542696i	$0.182596\pi$
$882$	11.0615	−	26.9217i	0.372459	−	0.906500i
$883$	27.9366	+	16.1292i	0.940142	+	0.542791i	0.890005	−	0.455951i	$-0.150701\pi$
$883$	27.9366	+	16.1292i	0.940142	+	0.542791i	0.0501372	+	0.998742i	$0.484034\pi$
$884$	−0.932317	−	3.40170i	−0.0313572	−	0.114412i
$885$	−0.242491			−0.00815124
$886$	2.54875	+	1.04722i	0.0856271	+	0.0351820i
$887$	6.56597	−	11.3726i	0.220464	−	0.381854i	−0.734485	−	0.678625i	$-0.762576\pi$
$887$	6.56597	−	11.3726i	0.220464	−	0.381854i	0.954949	+	0.296771i	$0.0959097\pi$
$888$	0.188921	−	0.250618i	0.00633976	−	0.00841020i
$889$	−2.03082	−	1.17249i	−0.0681115	−	0.0393242i
$890$	0.499077	+	3.70907i	0.0167291	+	0.124328i
$891$	10.9325	−	6.31191i	0.366254	−	0.211457i
$892$	−27.2218	−	26.9129i	−0.911453	−	0.901111i
$893$	14.6599	−	46.4374i	0.490574	−	1.55397i
$894$	−0.168907	+	0.411090i	−0.00564908	+	0.0137489i
$895$	−10.2089	−	17.6823i	−0.341246	−	0.591055i
$896$	−3.37971	−	2.48772i	−0.112908	−	0.0831089i
$897$	0.0253424	−	0.0438943i	0.000846159	−	0.00146559i
$898$	−0.972374	−	7.22655i	−0.0324485	−	0.241153i
$899$	−10.2109	−	5.89525i	−0.340552	−	0.196618i
$900$	4.26543	+	4.21703i	0.142181	+	0.140568i
$901$			3.17661i			0.105828i
$902$	−8.48870	−	10.9976i	−0.282643	−	0.366179i
$903$	0.0516251	−	0.0894172i	0.00171797	−	0.00297562i
$904$	2.15897	+	5.08861i	0.0718064	+	0.169245i
$905$		−	2.16776i		−	0.0720589i
$906$	0.185892	+	0.240834i	0.00617585	+	0.00800116i
$907$	−7.76230	−	13.4447i	−0.257743	−	0.446424i	0.707894	−	0.706319i	$-0.249645\pi$
$907$	−7.76230	−	13.4447i	−0.257743	−	0.446424i	−0.965637	+	0.259895i	$0.916312\pi$
$908$	3.06167	−	0.839124i	0.101605	−	0.0278473i
$909$	3.05238	+	5.28688i	0.101241	+	0.175355i
$910$	0.756041	−	0.101730i	0.0250625	−	0.00337230i
$911$	−5.36395			−0.177716			−0.0888578	−	0.996044i	$-0.528322\pi$
$911$	−5.36395			−0.177716			−0.0888578	+	0.996044i	$0.528322\pi$
$912$	0.155816	−	0.513926i	0.00515958	−	0.0170178i
$913$	13.4071			0.443710
$914$	50.0526	−	6.73487i	1.65559	−	0.222770i
$915$	−0.0398466	−	0.0690163i	−0.00131729	−	0.00228161i
$916$	41.3707	−	11.3386i	1.36693	−	0.374639i
$917$	−1.03568	−	1.79385i	−0.0342012	−	0.0592383i
$918$	−0.193629	−	0.250858i	−0.00639072	−	0.00827954i
$919$			22.3498i			0.737251i	0.929578	+	0.368625i	$0.120171\pi$
$919$			22.3498i			0.737251i	−0.929578	+	0.368625i	$0.879829\pi$
$920$	1.25006	+	2.94634i	0.0412133	+	0.0971379i
$921$	0.437241	−	0.757324i	0.0144076	−	0.0249547i
$922$	−26.8939	−	34.8426i	−0.885705	−	1.14748i
$923$			17.1400i			0.564170i
$924$	−0.0228133	−	0.0225545i	−0.000750503	−	0.000741987i
$925$	−3.11993	−	1.80129i	−0.102583	−	0.0592261i
$926$	3.51233	+	26.1032i	0.115422	+	0.857804i
$927$	−7.19109	+	12.4553i	−0.236186	+	0.409087i
$928$	18.6977	−	2.73344i	0.613780	−	0.0897295i
$929$	15.5645	+	26.9586i	0.510656	+	0.884482i	0.999924	+	0.0123482i	$0.00393066\pi$
$929$	15.5645	+	26.9586i	0.510656	+	0.884482i	−0.489268	+	0.872133i	$0.662736\pi$
$930$	0.0584306	−	0.142210i	0.00191601	−	0.00466325i
$931$	6.46385	+	29.2058i	0.211844	+	0.957182i
$932$	−37.5284	−	37.1026i	−1.22928	−	1.21534i
$933$	−0.312409	+	0.180369i	−0.0102278	+	0.00590503i
$934$	3.92692	+	29.1843i	0.128493	+	0.954940i
$935$	1.47451	+	0.851308i	0.0482216	+	0.0278408i
$936$	−7.42551	+	9.85053i	−0.242710	+	0.321975i
$937$	25.7081	−	44.5277i	0.839847	−	1.45466i	−0.0501759	−	0.998740i	$-0.515978\pi$
$937$	25.7081	−	44.5277i	0.839847	−	1.45466i	0.890022	−	0.455917i	$-0.150688\pi$
$938$	1.13898	+	0.467979i	0.0371890	+	0.0152801i
$939$	1.03403			0.0337442
$940$	5.90596	+	21.5488i	0.192631	+	0.702844i
$941$	8.15417	+	4.70781i	0.265818	+	0.153470i	0.626986	−	0.779031i	$-0.284288\pi$
$941$	8.15417	+	4.70781i	0.265818	+	0.153470i	−0.361167	+	0.932501i	$0.617622\pi$
$942$	−0.200285	+	0.487458i	−0.00652562	+	0.0158823i
$943$	7.91752			0.257830
$944$	27.4505	+	15.4336i	0.893436	+	0.502321i
$945$	0.0593557	−	0.0342690i	0.00193084	−	0.00111477i
$946$	−10.9641	−	14.2046i	−0.356474	−	0.461832i
$947$	−47.5801	+	27.4704i	−1.54615	+	0.892668i	−0.547716	+	0.836664i	$0.684503\pi$
$947$	−47.5801	+	27.4704i	−1.54615	+	0.892668i	−0.998431	+	0.0560043i	$0.982164\pi$
$948$	0.193270	−	0.738112i	0.00627711	−	0.0239728i
$949$		−	8.55576i		−	0.277732i
$950$	−6.07342	−	1.05528i	−0.197048	−	0.0342379i
$951$		−	0.702140i		−	0.0227685i
$952$	0.765863	−	1.01598i	0.0248218	−	0.0329280i
$953$	44.7973	−	25.8637i	1.45113	−	0.837808i	0.452581	−	0.891723i	$-0.350503\pi$
$953$	44.7973	−	25.8637i	1.45113	−	0.837808i	0.998546	+	0.0539147i	$0.0171699\pi$
$954$	8.79468	−	6.78834i	0.284738	−	0.219781i
$955$	−3.57699	+	2.06517i	−0.115749	+	0.0668275i
$956$	−10.9167	−	39.8312i	−0.353071	−	1.28823i
$957$	0.144452			0.00466948
$958$	−41.7102	−	17.1377i	−1.34760	−	0.553694i
$959$	−1.62877	−	0.940372i	−0.0525958	−	0.0303662i
$960$	0.0678387	+	0.236883i	0.00218948	+	0.00764536i
$961$	−18.5418			−0.598121
$962$	2.81581	−	6.85319i	0.0907853	−	0.220956i
$963$	0.148383	−	0.257008i	0.00478159	−	0.00828196i
$964$	21.1459	+	5.53691i	0.681063	+	0.178332i
$965$	3.99542	+	2.30676i	0.128617	+	0.0742572i
$966$	0.0181196	−	0.00243810i	0.000582988	−	7.84444e-5i
$967$	36.7344	−	21.2086i	1.18130	−	0.682023i	0.224983	−	0.974363i	$-0.427767\pi$
$967$	36.7344	−	21.2086i	1.18130	−	0.682023i	0.956314	+	0.292340i	$0.0944339\pi$
$968$	23.5090	−	9.97431i	0.755608	−	0.320586i
$969$	0.155262	+	0.0490147i	0.00498772	+	0.00157458i
$970$	15.8902	+	6.52890i	0.510204	+	0.209630i
$971$	−4.54659	−	7.87492i	−0.145907	−	0.252718i	0.783804	−	0.621008i	$-0.213277\pi$
$971$	−4.54659	−	7.87492i	−0.145907	−	0.252718i	−0.929711	+	0.368290i	$0.879943\pi$
$972$	−0.421126	+	1.60831i	−0.0135076	+	0.0515867i
$973$	2.87197	−	4.97440i	0.0920712	−	0.159472i
$974$	50.3772	−	6.77854i	1.61419	−	0.217198i
$975$	−0.0387907	−	0.0223958i	−0.00124230	−	0.000717241i
$976$	0.118095	+	10.3489i	0.00378012	+	0.331259i
$977$			10.7763i			0.344764i	0.985030	+	0.172382i	$0.0551463\pi$
$977$			10.7763i			0.344764i	−0.985030	+	0.172382i	$0.944854\pi$
$978$	−0.186398	+	0.143875i	−0.00596035	+	0.00460061i
$979$	1.85771	−	3.21764i	0.0593725	−	0.102836i
$980$	−9.76013	−	9.64939i	−0.311776	−	0.308238i
$981$		−	44.4222i		−	1.41829i
$982$	−6.41399	+	4.95076i	−0.204679	+	0.157985i
$983$	18.3342	+	31.7558i	0.584771	+	1.01285i	0.994904	+	0.100828i	$0.0321491\pi$
$983$	18.3342	+	31.7558i	0.584771	+	1.01285i	−0.410133	+	0.912026i	$0.634518\pi$
$984$	0.605000	+	0.0743882i	0.0192867	+	0.00237141i
$985$	6.01676	+	10.4213i	0.191710	+	0.332051i
$986$	0.763979	+	5.67779i	0.0243301	+	0.180818i
$987$	0.127635			0.00406267
$988$	0.485245	−	12.6685i	0.0154377	−	0.403039i
$989$	10.2264			0.325180
$990$	−0.794081	−	5.90150i	−0.0252376	−	0.187562i
$991$	25.2999	+	43.8208i	0.803679	+	1.39201i	0.917179	+	0.398475i	$0.130460\pi$
$991$	25.2999	+	43.8208i	0.803679	+	1.39201i	−0.113500	+	0.993538i	$0.536206\pi$
$992$	−15.6656	+	12.3796i	−0.497382	+	0.393052i
$993$	0.323622	+	0.560531i	0.0102698	+	0.0177879i
$994$	−4.89431	+	3.77776i	−0.155238	+	0.119823i
$995$		−	11.3659i		−	0.360323i
$996$	−0.413578	+	0.418325i	−0.0131047	+	0.0132551i
$997$	−12.3052	+	21.3132i	−0.389709	+	0.674995i	−0.992410	−	0.122971i	$-0.960758\pi$
$997$	−12.3052	+	21.3132i	−0.389709	+	0.674995i	0.602701	+	0.797967i	$0.294091\pi$
$998$	18.6851	−	14.4225i	0.591467	−	0.456535i
$999$		−	0.665667i		−	0.0210608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.n.b.31.20	yes	40
4.3	odd	2	inner	380.2.n.b.31.14	✓	40
19.8	odd	6	inner	380.2.n.b.331.14	yes	40
76.27	even	6	inner	380.2.n.b.331.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.n.b.31.14	✓	40	4.3	odd	2	inner
380.2.n.b.31.20	yes	40	1.1	even	1	trivial
380.2.n.b.331.14	yes	40	19.8	odd	6	inner
380.2.n.b.331.20	yes	40	76.27	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40158 - 0.188591i) q^{2} +(-0.0154003 - 0.0266742i) q^{3} +(1.92887 - 0.528652i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0266153 - 0.0344817i) q^{6} -0.370928i q^{7} +(2.60377 - 1.10472i) q^{8} +(1.49953 - 2.59725i) q^{9} +O(q^{10})\)	\(q+(1.40158 - 0.188591i) q^{2} +(-0.0154003 - 0.0266742i) q^{3} +(1.92887 - 0.528652i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0266153 - 0.0344817i) q^{6} -0.370928i q^{7} +(2.60377 - 1.10472i) q^{8} +(1.49953 - 2.59725i) q^{9} +(-0.864116 - 1.11951i) q^{10} +1.40398i q^{11} +(-0.0438065 - 0.0433095i) q^{12} +(-1.25941 - 0.727122i) q^{13} +(-0.0699536 - 0.519886i) q^{14} +(-0.0154003 + 0.0266742i) q^{15} +(3.44105 - 2.03940i) q^{16} +(0.606355 + 1.05024i) q^{17} +(1.61189 - 3.92306i) q^{18} +(0.941920 + 4.25591i) q^{19} +(-1.42226 - 1.40612i) q^{20} +(-0.00989418 + 0.00571241i) q^{21} +(0.264778 + 1.96779i) q^{22} +(-0.979966 - 0.565784i) q^{23} +(-0.0695663 - 0.0524403i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.90230 - 0.781608i) q^{26} -0.184775 q^{27} +(-0.196092 - 0.715470i) q^{28} +(2.89291 + 1.67022i) q^{29} +(-0.0165543 + 0.0402904i) q^{30} -3.52962 q^{31} +(4.43831 - 3.50734i) q^{32} +(0.0374499 - 0.0216217i) q^{33} +(1.04792 + 1.35764i) q^{34} +(-0.321233 + 0.185464i) q^{35} +(1.51934 - 5.80249i) q^{36} +3.60258i q^{37} +(2.12281 + 5.78737i) q^{38} +0.0447917i q^{39} +(-2.25860 - 1.70257i) q^{40} +(-6.05954 + 3.49848i) q^{41} +(-0.0127902 + 0.00987237i) q^{42} +(-7.82658 + 4.51868i) q^{43} +(0.742215 + 2.70809i) q^{44} -2.99905 q^{45} +(-1.48021 - 0.608180i) q^{46} +(-9.67501 - 5.58587i) q^{47} +(-0.107393 - 0.0603799i) q^{48} +6.86241 q^{49} +(-0.537467 + 1.30810i) q^{50} +(0.0186761 - 0.0323480i) q^{51} +(-2.81363 - 0.736731i) q^{52} +(2.26850 + 1.30972i) q^{53} +(-0.258977 + 0.0348469i) q^{54} +(1.21588 - 0.701989i) q^{55} +(-0.409770 - 0.965809i) q^{56} +(0.0990170 - 0.0906674i) q^{57} +(4.36964 + 1.79538i) q^{58} +(3.93646 + 6.81814i) q^{59} +(-0.0156039 + 0.0595923i) q^{60} +(-1.29369 + 2.24074i) q^{61} +(-4.94706 + 0.665655i) q^{62} +(-0.963394 - 0.556216i) q^{63} +(5.55921 - 5.75285i) q^{64} +1.45424i q^{65} +(0.0484115 - 0.0373673i) q^{66} +(-1.17370 + 2.03290i) q^{67} +(1.72479 + 1.70522i) q^{68} +0.0348530i q^{69} +(-0.415257 + 0.320524i) q^{70} +(-5.89310 - 10.2071i) q^{71} +(1.03519 - 8.41920i) q^{72} +(2.94165 + 5.09509i) q^{73} +(0.679415 + 5.04932i) q^{74} +0.0308007 q^{75} +(4.06673 + 7.71114i) q^{76} +0.520774 q^{77} +(0.00844731 + 0.0627793i) q^{78} +(6.19301 + 10.7266i) q^{79} +(-3.48670 - 1.96034i) q^{80} +(-4.49573 - 7.78684i) q^{81} +(-7.83316 + 6.04618i) q^{82} -9.54937i q^{83} +(-0.0160647 + 0.0162491i) q^{84} +(0.606355 - 1.05024i) q^{85} +(-10.1174 + 7.80932i) q^{86} -0.102888i q^{87} +(1.55100 + 3.65563i) q^{88} +(-2.29180 - 1.32317i) q^{89} +(-4.20342 + 0.565594i) q^{90} +(-0.269710 + 0.467151i) q^{91} +(-2.18933 - 0.573261i) q^{92} +(0.0543574 + 0.0941498i) q^{93} +(-14.6138 - 6.00444i) q^{94} +(3.21477 - 2.94368i) q^{95} +(-0.161907 - 0.0643741i) q^{96} +(-10.5201 + 6.07377i) q^{97} +(9.61824 - 1.29419i) q^{98} +(3.64649 + 2.10530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9}+O(q^{10}) \) 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9	\( 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} - 18 q^{14} + 9 q^{16} - 12 q^{17} - 2 q^{20} + 12 q^{21} + 20 q^{24} - 20 q^{25} + 34 q^{26} + 12 q^{28} + 10 q^{30} - 12 q^{32} - 6 q^{33} - 27 q^{34} - 6 q^{36} + 12 q^{38} + 36 q^{41} - 21 q^{42} + 28 q^{44} + 44 q^{45} + 36 q^{48} - 60 q^{49} + 15 q^{52} - 66 q^{53} - 31 q^{54} + 28 q^{57} + 2 q^{58} + 3 q^{60} + 4 q^{61} - 57 q^{62} - 80 q^{64} + 18 q^{66} - 20 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} + 30 q^{76} + 12 q^{77} + 144 q^{78} + 9 q^{80} + 16 q^{81} - 41 q^{82} - 12 q^{85} + 18 q^{86} - 18 q^{89} + 39 q^{90} + 40 q^{92} - 8 q^{93} - 160 q^{96} - 18 q^{97} - 66 q^{98}+O(q^{100}) \) 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 - 18 * q^14 + 9 * q^16 - 12 * q^17 - 2 * q^20 + 12 * q^21 + 20 * q^24 - 20 * q^25 + 34 * q^26 + 12 * q^28 + 10 * q^30 - 12 * q^32 - 6 * q^33 - 27 * q^34 - 6 * q^36 + 12 * q^38 + 36 * q^41 - 21 * q^42 + 28 * q^44 + 44 * q^45 + 36 * q^48 - 60 * q^49 + 15 * q^52 - 66 * q^53 - 31 * q^54 + 28 * q^57 + 2 * q^58 + 3 * q^60 + 4 * q^61 - 57 * q^62 - 80 * q^64 + 18 * q^66 - 20 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 + 30 * q^76 + 12 * q^77 + 144 * q^78 + 9 * q^80 + 16 * q^81 - 41 * q^82 - 12 * q^85 + 18 * q^86 - 18 * q^89 + 39 * q^90 + 40 * q^92 - 8 * q^93 - 160 * q^96 - 18 * q^97 - 66 * q^98

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