LMFDB - Embedded newform 380.2.n.b.31.15

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			31.15
Character	$\chi$	$=$	380.31
Dual form			380.2.n.b.331.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17905 + 0.780928i) q^{2} +(-0.980171 - 1.69771i) q^{3} +(0.780303 + 1.84150i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.170119 - 2.76712i) q^{6} -1.97181i q^{7} +(-0.518067 + 2.78058i) q^{8} +(-0.421469 + 0.730006i) q^{9} +O(q^{10})$	\(q+(1.17905 + 0.780928i) q^{2} +(-0.980171 - 1.69771i) q^{3} +(0.780303 + 1.84150i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.170119 - 2.76712i) q^{6} -1.97181i q^{7} +(-0.518067 + 2.78058i) q^{8} +(-0.421469 + 0.730006i) q^{9} +(0.0867802 - 1.41155i) q^{10} -5.82590i q^{11} +(2.36150 - 3.12971i) q^{12} +(4.54395 + 2.62345i) q^{13} +(1.53984 - 2.32485i) q^{14} +(-0.980171 + 1.69771i) q^{15} +(-2.78226 + 2.87386i) q^{16} +(-2.29599 - 3.97677i) q^{17} +(-1.06701 + 0.531574i) q^{18} +(4.33715 + 0.434923i) q^{19} +(1.20464 - 1.59651i) q^{20} +(-3.34754 + 1.93271i) q^{21} +(4.54961 - 6.86901i) q^{22} +(-2.54628 - 1.47010i) q^{23} +(5.22839 - 1.84591i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.30880 + 6.64167i) q^{26} -4.22858 q^{27} +(3.63108 - 1.53861i) q^{28} +(4.95320 + 2.85973i) q^{29} +(-2.48145 + 1.23623i) q^{30} -1.56323 q^{31} +(-5.52469 + 1.21567i) q^{32} +(-9.89066 + 5.71038i) q^{33} +(0.398493 - 6.48181i) q^{34} +(-1.70763 + 0.985903i) q^{35} +(-1.67318 - 0.206510i) q^{36} +6.81470i q^{37} +(4.77406 + 3.89979i) q^{38} -10.2857i q^{39} +(2.66708 - 0.941629i) q^{40} +(2.48154 - 1.43272i) q^{41} +(-5.45622 - 0.335441i) q^{42} +(-4.44537 + 2.56654i) q^{43} +(10.7284 - 4.54597i) q^{44} +0.842938 q^{45} +(-1.85415 - 3.72178i) q^{46} +(11.5424 + 6.66401i) q^{47} +(7.60605 + 1.90658i) q^{48} +3.11198 q^{49} +(-1.26583 + 0.630620i) q^{50} +(-4.50093 + 7.79583i) q^{51} +(-1.28543 + 10.4148i) q^{52} +(-11.3578 - 6.55742i) q^{53} +(-4.98569 - 3.30222i) q^{54} +(-5.04538 + 2.91295i) q^{55} +(5.48276 + 1.02153i) q^{56} +(-3.51277 - 7.78950i) q^{57} +(3.60681 + 7.23985i) q^{58} +(5.17758 + 8.96782i) q^{59} +(-3.89116 - 0.480262i) q^{60} +(-3.62484 + 6.27840i) q^{61} +(-1.84313 - 1.22077i) q^{62} +(1.43943 + 0.831055i) q^{63} +(-7.46321 - 2.88105i) q^{64} -5.24690i q^{65} +(-16.1210 - 0.991095i) q^{66} +(-2.99842 + 5.19342i) q^{67} +(5.53167 - 7.33116i) q^{68} +5.76379i q^{69} +(-2.78330 - 0.171114i) q^{70} +(-0.0329647 - 0.0570966i) q^{71} +(-1.81149 - 1.55012i) q^{72} +(-3.29020 - 5.69879i) q^{73} +(-5.32179 + 8.03485i) q^{74} +1.96034 q^{75} +(2.58338 + 8.32623i) q^{76} -11.4875 q^{77} +(8.03240 - 12.1273i) q^{78} +(-1.55084 - 2.68613i) q^{79} +(3.87996 + 0.972575i) q^{80} +(5.40913 + 9.36890i) q^{81} +(4.04470 + 0.248663i) q^{82} +8.28724i q^{83} +(-6.17118 - 4.65641i) q^{84} +(-2.29599 + 3.97677i) q^{85} +(-7.24558 - 0.445449i) q^{86} -11.2121i q^{87} +(16.1994 + 3.01821i) q^{88} +(10.0364 + 5.79452i) q^{89} +(0.993863 + 0.658274i) q^{90} +(5.17293 - 8.95978i) q^{91} +(0.720315 - 5.83611i) q^{92} +(1.53224 + 2.65391i) q^{93} +(8.40492 + 16.8710i) q^{94} +(-1.79192 - 3.97354i) q^{95} +(7.47898 + 8.18772i) q^{96} +(0.927418 - 0.535445i) q^{97} +(3.66917 + 2.43024i) q^{98} +(4.25294 + 2.45544i) 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 $

$2$	1.17905	+	0.780928i	0.833712	+	0.552200i
$2$	1.17905	+	0.780928i	0.833712	+	0.552200i
$3$	−0.980171	−	1.69771i	−0.565902	−	0.980171i	−0.996965	−	0.0778490i	$-0.975195\pi$
$3$	−0.980171	−	1.69771i	−0.565902	−	0.980171i	0.431063	−	0.902322i	$-0.358139\pi$
$4$	0.780303	+	1.84150i	0.390151	+	0.920751i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.170119	−	2.76712i	0.0694507	−	1.12967i
$7$		−	1.97181i		−	0.745272i	−0.927978	−	0.372636i	$-0.878454\pi$
$7$		−	1.97181i		−	0.745272i	0.927978	−	0.372636i	$-0.121546\pi$
$8$	−0.518067	+	2.78058i	−0.183164	+	0.983082i
$9$	−0.421469	+	0.730006i	−0.140490	+	0.243335i
$10$	0.0867802	−	1.41155i	0.0274423	−	0.446371i
$11$		−	5.82590i		−	1.75658i	−0.478132	−	0.878288i	$-0.658686\pi$
$11$		−	5.82590i		−	1.75658i	0.478132	−	0.878288i	$-0.341314\pi$
$12$	2.36150	−	3.12971i	0.681705	−	0.903469i
$13$	4.54395	+	2.62345i	1.26026	+	0.727614i	0.973126	−	0.230275i	$-0.0739625\pi$
$13$	4.54395	+	2.62345i	1.26026	+	0.727614i	0.287139	+	0.957889i	$0.407296\pi$
$14$	1.53984	−	2.32485i	0.411539	−	0.621343i
$15$	−0.980171	+	1.69771i	−0.253079	+	0.438346i
$16$	−2.78226	+	2.87386i	−0.695564	+	0.718464i
$17$	−2.29599	−	3.97677i	−0.556860	−	0.964509i	−0.997756	−	0.0669514i	$-0.978673\pi$
$17$	−2.29599	−	3.97677i	−0.556860	−	0.964509i	0.440897	−	0.897558i	$-0.354661\pi$
$18$	−1.06701	+	0.531574i	−0.251497	+	0.125293i
$19$	4.33715	+	0.434923i	0.995010	+	0.0997781i
$19$	4.33715	+	0.434923i	0.995010	+	0.0997781i
$20$	1.20464	−	1.59651i	0.269365	−	0.356991i
$21$	−3.34754	+	1.93271i	−0.730494	+	0.421751i
$22$	4.54961	−	6.86901i	0.969980	−	1.46448i
$23$	−2.54628	−	1.47010i	−0.530937	−	0.306537i	0.210461	−	0.977602i	$-0.432504\pi$
$23$	−2.54628	−	1.47010i	−0.530937	−	0.306537i	−0.741398	+	0.671066i	$0.765837\pi$
$24$	5.22839	−	1.84591i	1.06724	−	0.376796i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.30880	+	6.64167i	0.648910	+	1.30254i
$27$	−4.22858			−0.813790
$28$	3.63108	−	1.53861i	0.686210	−	0.290769i
$29$	4.95320	+	2.85973i	0.919787	+	0.531039i	0.883567	−	0.468305i	$-0.155135\pi$
$29$	4.95320	+	2.85973i	0.919787	+	0.531039i	0.0362197	+	0.999344i	$0.488468\pi$
$30$	−2.48145	+	1.23623i	−0.453049	+	0.225704i
$31$	−1.56323			−0.280765			−0.140383	−	0.990097i	$-0.544833\pi$
$31$	−1.56323			−0.280765			−0.140383	+	0.990097i	$0.544833\pi$
$32$	−5.52469	+	1.21567i	−0.976636	+	0.214902i
$33$	−9.89066	+	5.71038i	−1.72174	+	0.994049i
$34$	0.398493	−	6.48181i	0.0683410	−	1.11162i
$35$	−1.70763	+	0.985903i	−0.288643	+	0.166648i
$36$	−1.67318	−	0.206510i	−0.278863	−	0.0344184i
$37$			6.81470i			1.12033i	0.828381	+	0.560165i	$0.189262\pi$
$37$			6.81470i			1.12033i	−0.828381	+	0.560165i	$0.810738\pi$
$38$	4.77406	+	3.89979i	0.774454	+	0.632630i
$39$		−	10.2857i		−	1.64703i
$40$	2.66708	−	0.941629i	0.421703	−	0.148885i
$41$	2.48154	−	1.43272i	0.387552	−	0.223753i	−0.293547	−	0.955945i	$-0.594836\pi$
$41$	2.48154	−	1.43272i	0.387552	−	0.223753i	0.681099	+	0.732192i	$0.261502\pi$
$42$	−5.45622	−	0.335441i	−0.841912	−	0.0517597i
$43$	−4.44537	+	2.56654i	−0.677912	+	0.391393i	−0.799068	−	0.601241i	$-0.794673\pi$
$43$	−4.44537	+	2.56654i	−0.677912	+	0.391393i	0.121156	+	0.992634i	$0.461340\pi$
$44$	10.7284	−	4.54597i	1.61737	−	0.685330i
$45$	0.842938			0.125658
$46$	−1.85415	−	3.72178i	−0.273379	−	0.548746i
$47$	11.5424	+	6.66401i	1.68363	+	0.972046i	0.959212	+	0.282689i	$0.0912263\pi$
$47$	11.5424	+	6.66401i	1.68363	+	0.972046i	0.724421	+	0.689357i	$0.242107\pi$
$48$	7.60605	+	1.90658i	1.09784	+	0.275191i
$49$	3.11198			0.444569
$50$	−1.26583	+	0.630620i	−0.179015	+	0.0891832i
$51$	−4.50093	+	7.79583i	−0.630256	+	1.09164i
$52$	−1.28543	+	10.4148i	−0.178257	+	1.44427i
$53$	−11.3578	−	6.55742i	−1.56011	−	0.900731i	−0.997245	−	0.0741832i	$-0.976365\pi$
$53$	−11.3578	−	6.55742i	−1.56011	−	0.900731i	−0.562867	−	0.826548i	$-0.690302\pi$
$54$	−4.98569	−	3.30222i	−0.678467	−	0.449375i
$55$	−5.04538	+	2.91295i	−0.680319	+	0.392782i
$56$	5.48276	+	1.02153i	0.732664	+	0.136507i
$57$	−3.51277	−	7.78950i	−0.465278	−	1.03174i
$58$	3.60681	+	7.23985i	0.473598	+	0.950639i
$59$	5.17758	+	8.96782i	0.674063	+	1.16751i	0.976742	+	0.214419i	$0.0687857\pi$
$59$	5.17758	+	8.96782i	0.674063	+	1.16751i	−0.302679	+	0.953093i	$0.597881\pi$
$60$	−3.89116	−	0.480262i	−0.502346	−	0.0620015i
$61$	−3.62484	+	6.27840i	−0.464113	+	0.803867i	−0.999161	−	0.0409544i	$-0.986960\pi$
$61$	−3.62484	+	6.27840i	−0.464113	+	0.803867i	0.535048	+	0.844822i	$0.320293\pi$
$62$	−1.84313	−	1.22077i	−0.234077	−	0.155038i
$63$	1.43943	+	0.831055i	0.181351	+	0.104703i
$64$	−7.46321	−	2.88105i	−0.932902	−	0.360131i
$65$		−	5.24690i		−	0.650798i
$66$	−16.1210	−	0.991095i	−1.98435	−	0.121995i
$67$	−2.99842	+	5.19342i	−0.366316	+	0.634477i	−0.988986	−	0.148007i	$-0.952714\pi$
$67$	−2.99842	+	5.19342i	−0.366316	+	0.634477i	0.622671	+	0.782484i	$0.286048\pi$
$68$	5.53167	−	7.33116i	0.670813	−	0.889034i
$69$			5.76379i			0.693878i
$70$	−2.78330	−	0.171114i	−0.332668	−	0.0204520i
$71$	−0.0329647	−	0.0570966i	−0.00391219	−	0.00677612i	0.864063	−	0.503384i	$-0.167912\pi$
$71$	−0.0329647	−	0.0570966i	−0.00391219	−	0.00677612i	−0.867975	+	0.496608i	$0.834579\pi$
$72$	−1.81149	−	1.55012i	−0.213486	−	0.182683i
$73$	−3.29020	−	5.69879i	−0.385089	−	0.666993i	0.606693	−	0.794936i	$-0.292496\pi$
$73$	−3.29020	−	5.69879i	−0.385089	−	0.666993i	−0.991782	+	0.127943i	$0.959163\pi$
$74$	−5.32179	+	8.03485i	−0.618645	+	0.934032i
$75$	1.96034			0.226361
$76$	2.58338	+	8.32623i	0.296334	+	0.955084i
$77$	−11.4875			−1.30913
$78$	8.03240	−	12.1273i	0.909491	−	1.37315i
$79$	−1.55084	−	2.68613i	−0.174483	−	0.302213i	0.765499	−	0.643437i	$-0.222492\pi$
$79$	−1.55084	−	2.68613i	−0.174483	−	0.302213i	−0.939982	+	0.341224i	$0.889159\pi$
$80$	3.87996	+	0.972575i	0.433793	+	0.108737i
$81$	5.40913	+	9.36890i	0.601015	+	1.04099i
$82$	4.04470	+	0.248663i	0.446663	+	0.0274603i
$83$			8.28724i			0.909643i	0.890583	+	0.454822i	$0.150297\pi$
$83$			8.28724i			0.909643i	−0.890583	+	0.454822i	$0.849703\pi$
$84$	−6.17118	−	4.65641i	−0.673331	−	0.508056i
$85$	−2.29599	+	3.97677i	−0.249035	+	0.431342i
$86$	−7.24558	−	0.445449i	−0.781311	−	0.0480340i
$87$		−	11.2121i		−	1.20206i
$88$	16.1994	+	3.01821i	1.72686	+	0.321742i
$89$	10.0364	+	5.79452i	1.06386	+	0.614218i	0.926496	−	0.376304i	$-0.122805\pi$
$89$	10.0364	+	5.79452i	1.06386	+	0.614218i	0.137360	+	0.990521i	$0.456138\pi$
$90$	0.993863	+	0.658274i	0.104762	+	0.0693881i
$91$	5.17293	−	8.95978i	0.542271	−	0.939241i
$92$	0.720315	−	5.83611i	0.0750980	−	0.608456i
$93$	1.53224	+	2.65391i	0.158886	+	0.275198i
$94$	8.40492	+	16.8710i	0.866902	+	1.74011i
$95$	−1.79192	−	3.97354i	−0.183847	−	0.407677i
$96$	7.47898	+	8.18772i	0.763321	+	0.835656i
$97$	0.927418	−	0.535445i	0.0941650	−	0.0543662i	−0.452178	−	0.891928i	$-0.649353\pi$
$97$	0.927418	−	0.535445i	0.0941650	−	0.0543662i	0.546343	+	0.837562i	$0.316019\pi$
$98$	3.66917	+	2.43024i	0.370643	+	0.245491i
$99$	4.25294	+	2.45544i	0.427437	+	0.246781i
$100$	−1.98494	−	0.244989i	−0.198494	−	0.0244989i
$101$	2.62941	−	4.55427i	0.261636	−	0.453167i	−0.705041	−	0.709167i	$-0.749071\pi$
$101$	2.62941	−	4.55427i	0.261636	−	0.453167i	0.966677	+	0.256000i	$0.0824047\pi$
$102$	−11.3948	+	5.67675i	−1.12825	+	0.562082i
$103$	4.82415			0.475337			0.237669	−	0.971346i	$-0.423617\pi$
$103$	4.82415			0.475337			0.237669	+	0.971346i	$0.423617\pi$
$104$	−9.64877	+	11.2757i	−0.946140	+	1.10567i
$105$	3.34754	+	1.93271i	0.326687	+	0.188613i
$106$	−8.27048	−	16.6011i	−0.803300	−	1.61244i
$107$	−5.08117			−0.491215			−0.245608	−	0.969369i	$-0.578987\pi$
$107$	−5.08117			−0.491215			−0.245608	+	0.969369i	$0.578987\pi$
$108$	−3.29957	−	7.78693i	−0.317501	−	0.749298i
$109$	9.29330	−	5.36549i	0.890137	−	0.513921i	0.0161497	−	0.999870i	$-0.494859\pi$
$109$	9.29330	−	5.36549i	0.890137	−	0.513921i	0.873987	+	0.485949i	$0.161526\pi$
$110$	−8.22354	−	0.505573i	−0.784084	−	0.0482045i
$111$	11.5693	−	6.67957i	1.09811	−	0.633996i
$112$	5.66669	+	5.48607i	0.535452	+	0.518385i
$113$		−	10.7233i		−	1.00876i	−0.863482	−	0.504380i	$-0.831721\pi$
$113$		−	10.7233i		−	1.00876i	0.863482	−	0.504380i	$-0.168279\pi$
$114$	1.94131	−	11.9274i	0.181820	−	1.11710i
$115$			2.94020i			0.274175i
$116$	−1.40121	+	11.3528i	−0.130099	+	1.05408i
$117$	−3.83027	+	2.21141i	−0.354108	+	0.204444i
$118$	−0.898622	+	14.6168i	−0.0827248	+	1.34559i
$119$	−7.84142	+	4.52725i	−0.718822	+	0.415012i
$120$	−4.21281	−	3.60496i	−0.384575	−	0.329087i
$121$	−22.9411			−2.08556
$122$	−9.17684	+	4.57179i	−0.830832	+	0.413911i
$123$	−4.86467	−	2.80862i	−0.438632	−	0.253245i
$124$	−1.21980	−	2.87870i	−0.109541	−	0.258515i
$125$	1.00000			0.0894427
$126$	1.04816	+	2.10394i	0.0933775	+	0.187434i
$127$	3.56780	−	6.17961i	0.316591	−	0.548352i	−0.663183	−	0.748457i	$-0.730795\pi$
$127$	3.56780	−	6.17961i	0.316591	−	0.548352i	0.979774	+	0.200105i	$0.0641283\pi$
$128$	−6.54959	−	9.22512i	−0.578907	−	0.815394i
$129$	8.71444	+	5.03128i	0.767264	+	0.442980i
$130$	4.09745	−	6.18634i	0.359370	−	0.542578i
$131$	−3.98002	+	2.29786i	−0.347736	+	0.200765i	−0.663687	−	0.748010i	$-0.731010\pi$
$131$	−3.98002	+	2.29786i	−0.347736	+	0.200765i	0.315952	+	0.948775i	$0.397676\pi$
$132$	−18.2334	−	13.7579i	−1.58701	−	1.19747i
$133$	0.857583	−	8.55201i	0.0743618	−	0.741553i
$134$	−7.59097	+	3.78173i	−0.655760	+	0.326692i
$135$	2.11429	+	3.66206i	0.181969	+	0.315180i
$136$	12.2472	−	4.32395i	1.05019	−	0.370775i
$137$	8.17220	−	14.1547i	0.698198	−	1.20931i	−0.270893	−	0.962610i	$-0.587319\pi$
$137$	8.17220	−	14.1547i	0.698198	−	1.20931i	0.969091	−	0.246705i	$-0.0793479\pi$
$138$	−4.50110	+	6.79577i	−0.383159	+	0.578495i
$139$	−7.15182	−	4.12910i	−0.606609	−	0.350226i	0.165028	−	0.986289i	$-0.447229\pi$
$139$	−7.15182	−	4.12910i	−0.606609	−	0.350226i	−0.771637	+	0.636063i	$0.780562\pi$
$140$	−3.14801	−	2.37531i	−0.266056	−	0.200750i
$141$		−	26.1275i		−	2.20033i
$142$	0.00572137	−	0.0930626i	0.000480127	−	0.00780964i
$143$	15.2840	−	26.4726i	1.27811	−	2.21375i
$144$	−0.925297	−	3.24230i	−0.0771081	−	0.270192i
$145$		−	5.71947i		−	0.474976i
$146$	0.571048	−	9.28855i	0.0472603	−	0.768726i
$147$	−3.05027	−	5.28323i	−0.251582	−	0.435754i
$148$	−12.5493	+	5.31753i	−1.03154	+	0.437098i
$149$	5.58383	+	9.67148i	0.457446	+	0.792319i	0.998825	−	0.0484594i	$-0.0154311\pi$
$149$	5.58383	+	9.67148i	0.457446	+	0.792319i	−0.541380	+	0.840778i	$0.682098\pi$
$150$	2.31133	+	1.53089i	0.188720	+	0.124996i
$151$	8.71667			0.709353			0.354676	−	0.934989i	$-0.384591\pi$
$151$	8.71667			0.709353			0.354676	+	0.934989i	$0.384591\pi$
$152$	−3.45627	+	11.8345i	−0.280340	+	0.959901i
$153$	3.87076			0.312932
$154$	−13.5444	−	8.97095i	−1.09144	−	0.722899i
$155$	0.781617	+	1.35380i	0.0627810	+	0.108740i
$156$	18.9412	−	8.02597i	1.51651	−	0.642592i
$157$	5.40678	+	9.36481i	0.431508	+	0.747393i	0.997003	−	0.0773579i	$-0.0246484\pi$
$157$	5.40678	+	9.36481i	0.431508	+	0.747393i	−0.565496	+	0.824751i	$0.691315\pi$
$158$	0.269164	−	4.37816i	0.0214135	−	0.348308i
$159$			25.7096i			2.03890i
$160$	3.81514	+	4.17668i	0.301614	+	0.330196i
$161$	−2.89875	+	5.02078i	−0.228453	+	0.395693i
$162$	−0.938811	+	15.2705i	−0.0737600	+	1.19976i
$163$			8.52260i			0.667541i	0.942654	+	0.333771i	$0.108321\pi$
$163$			8.52260i			0.667541i	−0.942654	+	0.333771i	$0.891679\pi$
$164$	4.57471	+	3.45181i	0.357225	+	0.269541i
$165$	9.89066	+	5.71038i	0.769987	+	0.444552i
$166$	−6.47174	+	9.77105i	−0.502304	+	0.758380i
$167$	−8.33268	+	14.4326i	−0.644802	+	1.11683i	0.339545	+	0.940590i	$0.389727\pi$
$167$	−8.33268	+	14.4326i	−0.644802	+	1.11683i	−0.984347	+	0.176240i	$0.943606\pi$
$168$	−3.63978	−	10.3094i	−0.280815	−	0.795386i
$169$	7.26498	+	12.5833i	0.558845	+	0.967948i
$170$	−5.81266	+	2.89580i	−0.445810	+	0.222098i
$171$	−2.14547	+	2.98283i	−0.164068	+	0.228103i
$172$	−8.19501	−	6.18348i	−0.624864	−	0.471486i
$173$	13.2576	−	7.65428i	1.00796	−	0.581944i	0.0973637	−	0.995249i	$-0.468959\pi$
$173$	13.2576	−	7.65428i	1.00796	−	0.581944i	0.910593	+	0.413305i	$0.135626\pi$
$174$	8.75585	−	13.2196i	0.663779	−	1.00217i
$175$	1.70763	+	0.985903i	0.129085	+	0.0745272i
$176$	16.7428	+	16.2091i	1.26204	+	1.22181i
$177$	10.1498	−	17.5800i	0.762907	−	1.32139i
$178$	7.30828	+	14.6697i	0.547779	+	1.09954i
$179$	−5.42757			−0.405676			−0.202838	−	0.979212i	$-0.565016\pi$
$179$	−5.42757			−0.405676			−0.202838	+	0.979212i	$0.565016\pi$
$180$	0.657747	+	1.55227i	0.0490255	+	0.115699i
$181$	19.3917	+	11.1958i	1.44137	+	0.832178i	0.997942	−	0.0641297i	$-0.0204271\pi$
$181$	19.3917	+	11.1958i	1.44137	+	0.832178i	0.443433	+	0.896308i	$0.353760\pi$
$182$	13.0961	−	6.52432i	0.970746	−	0.483614i
$183$	14.2118			1.05057
$184$	5.40687	−	6.31853i	0.398599	−	0.465808i
$185$	5.90170	−	3.40735i	0.433902	−	0.250513i
$186$	−0.265935	+	4.32565i	−0.0194993	+	0.317172i
$187$	−23.1683	+	13.3762i	−1.69423	+	0.978166i
$188$	−3.26522	+	26.4553i	−0.238140	+	1.92945i
$189$			8.33793i			0.606495i
$190$	0.990293	−	6.08435i	0.0718434	−	0.441405i
$191$		−	22.3172i		−	1.61482i	−0.589993	−	0.807409i	$-0.700869\pi$
$191$		−	22.3172i		−	1.61482i	0.589993	−	0.807409i	$-0.299131\pi$
$192$	2.42405	+	15.4943i	0.174941	+	1.11820i
$193$	−15.8249	+	9.13652i	−1.13910	+	0.657661i	−0.946208	−	0.323558i	$-0.895121\pi$
$193$	−15.8249	+	9.13652i	−1.13910	+	0.657661i	−0.192895	+	0.981219i	$0.561788\pi$
$194$	1.51161	+	0.0929320i	0.108527	+	0.00667213i
$195$	−8.90769	+	5.14286i	−0.637893	+	0.368288i
$196$	2.42829	+	5.73072i	0.173449	+	0.409337i
$197$	0.136754			0.00974330			0.00487165	−	0.999988i	$-0.498449\pi$
$197$	0.136754			0.00974330			0.00487165	+	0.999988i	$0.498449\pi$
$198$	3.09690	+	6.21631i	0.220087	+	0.441774i
$199$	−6.47281	−	3.73708i	−0.458845	−	0.264914i	0.252713	−	0.967541i	$-0.418677\pi$
$199$	−6.47281	−	3.73708i	−0.458845	−	0.264914i	−0.711559	+	0.702627i	$0.752010\pi$
$200$	−2.14902	−	1.83895i	−0.151958	−	0.130033i
$201$	11.7559			0.829195
$202$	6.65676	−	3.31632i	0.468368	−	0.233335i
$203$	5.63884	−	9.76675i	0.395769	−	0.685492i
$204$	−17.8681	−	2.20535i	−1.25102	−	0.154406i
$205$	−2.48154	−	1.43272i	−0.173318	−	0.100065i
$206$	5.68790	+	3.76731i	0.396295	+	0.262481i
$207$	2.14636	−	1.23920i	0.149182	−	0.0861304i
$208$	−20.1818	+	5.75955i	−1.39936	+	0.399353i
$209$	2.53382	−	25.2678i	0.175268	−	1.74781i
$210$	2.43761	+	4.89294i	0.168211	+	0.337645i
$211$	4.49134	+	7.77924i	0.309197	+	0.535545i	0.978187	−	0.207727i	$-0.0666065\pi$
$211$	4.49134	+	7.77924i	0.309197	+	0.535545i	−0.668990	+	0.743271i	$0.733273\pi$
$212$	3.21299	−	26.0321i	0.220669	−	1.78790i
$213$	−0.0646221	+	0.111929i	−0.00442783	+	0.00766924i
$214$	−5.99094	−	3.96803i	−0.409532	−	0.271249i
$215$	4.44537	+	2.56654i	0.303172	+	0.175036i
$216$	2.19069	−	11.7579i	0.149057	−	0.800023i
$217$			3.08239i			0.209247i
$218$	15.1473	+	0.931236i	1.02590	+	0.0630713i
$219$	−6.44992	+	11.1716i	−0.435845	+	0.754905i
$220$	−9.30113	−	7.01809i	−0.627082	−	0.473159i
$221$		−	24.0937i		−	1.62072i
$222$	18.8571	+	1.15931i	1.26560	+	0.0778076i
$223$	−3.65685	−	6.33386i	−0.244881	−	0.424146i	0.717217	−	0.696850i	$-0.245416\pi$
$223$	−3.65685	−	6.33386i	−0.244881	−	0.424146i	−0.962098	+	0.272703i	$0.912082\pi$
$224$	2.39707	+	10.8936i	0.160161	+	0.727860i
$225$	−0.421469	−	0.730006i	−0.0280979	−	0.0486670i
$226$	8.37409	−	12.6432i	0.557036	−	0.841015i
$227$	10.8230			0.718351			0.359175	−	0.933270i	$-0.383058\pi$
$227$	10.8230			0.718351			0.359175	+	0.933270i	$0.383058\pi$
$228$	11.6033	−	12.5469i	0.768450	−	0.830942i
$229$	2.81174			0.185805			0.0929025	−	0.995675i	$-0.470386\pi$
$229$	2.81174			0.185805			0.0929025	+	0.995675i	$0.470386\pi$
$230$	−2.29608	+	3.46663i	−0.151399	+	0.228583i
$231$	11.2598	+	19.5025i	0.740837	+	1.28317i
$232$	−10.5178	+	12.2912i	−0.690527	+	0.806959i
$233$	6.00733	+	10.4050i	0.393554	+	0.681655i	0.992915	−	0.118823i	$-0.0379123\pi$
$233$	6.00733	+	10.4050i	0.393554	+	0.681655i	−0.599362	+	0.800478i	$0.704579\pi$
$234$	−6.24301	−	0.383812i	−0.408118	−	0.0250906i
$235$		−	13.3280i		−	0.869424i
$236$	−12.4742	+	16.5321i	−0.812000	+	1.07615i
$237$	−3.04017	+	5.26573i	−0.197480	+	0.342046i
$238$	−12.7809	−	0.785751i	−0.828460	−	0.0509326i
$239$			6.14204i			0.397296i	0.980071	+	0.198648i	$0.0636550\pi$
$239$			6.14204i			0.397296i	−0.980071	+	0.198648i	$0.936345\pi$
$240$	−2.15188	−	7.54032i	−0.138903	−	0.486726i
$241$	−15.4889	−	8.94251i	−0.997727	−	0.576038i	−0.0901520	−	0.995928i	$-0.528735\pi$
$241$	−15.4889	−	8.94251i	−0.997727	−	0.576038i	−0.907575	+	0.419890i	$0.862069\pi$
$242$	−27.0487	−	17.9154i	−1.73875	−	1.15164i
$243$	4.26088	−	7.38007i	0.273336	−	0.473431i
$244$	−14.3902	−	1.77609i	−0.921236	−	0.113702i
$245$	−1.55599	−	2.69506i	−0.0994087	−	0.172181i
$246$	−3.54234	−	7.11045i	−0.225852	−	0.453346i
$247$	18.5668	+	13.3546i	1.18138	+	0.849730i
$248$	0.809860	−	4.34669i	0.0514262	−	0.276015i
$249$	14.0693	−	8.12291i	0.891605	−	0.514769i
$250$	1.17905	+	0.780928i	0.0745695	+	0.0493902i
$251$	2.93159	+	1.69255i	0.185040	+	0.106833i	0.589659	−	0.807653i	$-0.299262\pi$
$251$	2.93159	+	1.69255i	0.185040	+	0.106833i	−0.404618	+	0.914486i	$0.632596\pi$
$252$	−0.407198	+	3.29918i	−0.0256511	+	0.207829i
$253$	−8.56465	+	14.8344i	−0.538455	+	0.932631i
$254$	9.03244	−	4.49986i	0.566746	−	0.282346i
$255$	9.00185			0.563718
$256$	−0.518109	−	15.9916i	−0.0323818	−	0.999476i
$257$	−14.2817	−	8.24553i	−0.890867	−	0.514342i	−0.0166410	−	0.999862i	$-0.505297\pi$
$257$	−14.2817	−	8.24553i	−0.890867	−	0.514342i	−0.874226	+	0.485519i	$0.838631\pi$
$258$	6.34566	+	12.7375i	0.395064	+	0.793000i
$259$	13.4373			0.834951
$260$	9.66218	−	4.09417i	0.599223	−	0.253910i
$261$	−4.17524	+	2.41058i	−0.258441	+	0.149211i
$262$	−6.48709	−	0.398818i	−0.400774	−	0.0246390i
$263$	−10.7019	+	6.17877i	−0.659910	+	0.380999i	−0.792243	−	0.610206i	$-0.791087\pi$
$263$	−10.7019	+	6.17877i	−0.659910	+	0.380999i	0.132333	+	0.991205i	$0.457753\pi$
$264$	−10.7541	−	30.4601i	−0.661870	−	1.87469i
$265$			13.1148i			0.805638i
$266$	7.68963	−	9.41351i	0.471482	−	0.577179i
$267$		−	22.7185i		−	1.39035i
$268$	−11.9034	−	1.46916i	−0.727114	−	0.0897432i
$269$	−6.45851	+	3.72882i	−0.393782	+	0.227350i	−0.683798	−	0.729672i	$-0.739673\pi$
$269$	−6.45851	+	3.72882i	−0.393782	+	0.227350i	0.290015	+	0.957022i	$0.406340\pi$
$270$	−0.366957	+	5.96884i	−0.0223323	+	0.363252i
$271$	−20.0956	+	11.6022i	−1.22072	+	0.704785i	−0.965072	−	0.261985i	$-0.915623\pi$
$271$	−20.0956	+	11.6022i	−1.22072	+	0.704785i	−0.255651	+	0.966769i	$0.582290\pi$
$272$	17.8167	+	4.46605i	1.08030	+	0.270794i
$273$	−20.2814			−1.22749
$274$	20.6892	−	10.3071i	1.24988	−	0.622675i
$275$	5.04538	+	2.91295i	0.304248	+	0.175658i
$276$	−10.6140	+	4.49750i	−0.638889	+	0.270718i
$277$	14.2912			0.858677			0.429339	−	0.903144i	$-0.358747\pi$
$277$	14.2912			0.858677			0.429339	+	0.903144i	$0.358747\pi$
$278$	−5.20779	−	10.4535i	−0.312343	−	0.626957i
$279$	0.658855	−	1.14117i	0.0394446	−	0.0683200i
$280$	−1.85671	−	5.25897i	−0.110960	−	0.314284i
$281$	−23.1215	−	13.3492i	−1.37931	−	0.796347i	−0.387236	−	0.921981i	$-0.626570\pi$
$281$	−23.1215	−	13.3492i	−1.37931	−	0.796347i	−0.992077	+	0.125634i	$0.959903\pi$
$282$	20.4037	−	30.8055i	1.21502	−	1.83444i
$283$	−0.847564	+	0.489341i	−0.0503825	+	0.0290883i	−0.524980	−	0.851115i	$-0.675927\pi$
$283$	−0.847564	+	0.489341i	−0.0503825	+	0.0290883i	0.474597	+	0.880203i	$0.342594\pi$
$284$	0.0794210	−	0.105257i	0.00471277	−	0.00624587i
$285$	−4.98951	+	6.93690i	−0.295553	+	0.410906i
$286$	38.6937	−	19.2768i	2.28801	−	1.13986i
$287$	−2.82504	−	4.89312i	−0.166757	−	0.288832i
$288$	1.44104	−	4.54542i	0.0849139	−	0.267841i
$289$	−2.04315	+	3.53885i	−0.120185	+	0.208167i
$290$	4.46649	−	6.74352i	0.262281	−	0.395993i
$291$	−1.81806	−	1.04965i	−0.106576	−	0.0615319i
$292$	7.92699	−	10.5057i	0.463892	−	0.614799i
$293$			0.300065i			0.0175300i	0.999962	+	0.00876501i	$0.00279002\pi$
$293$			0.300065i			0.0175300i	−0.999962	+	0.00876501i	$0.997210\pi$
$294$	0.529407	−	8.61122i	0.0308756	−	0.502217i
$295$	5.17758	−	8.96782i	0.301450	−	0.522127i
$296$	−18.9488	−	3.53047i	−1.10138	−	0.205204i
$297$			24.6353i			1.42948i
$298$	−0.969132	+	15.7637i	−0.0561403	+	0.913167i
$299$	−7.71346	−	13.3601i	−0.446081	−	0.772635i
$300$	1.52966	+	3.60997i	0.0883149	+	0.208422i
$301$	5.06071	+	8.76540i	0.291694	+	0.505229i
$302$	10.2774	+	6.80709i	0.591396	+	0.391704i
$303$	−10.3091			−0.592241
$304$	−13.3170	+	11.2543i	−0.763780	+	0.645477i
$305$	7.24968			0.415115
$306$	4.56380	+	3.02278i	0.260895	+	0.172801i
$307$	6.68239	+	11.5742i	0.381384	+	0.660577i	0.991260	−	0.131920i	$-0.0421141\pi$
$307$	6.68239	+	11.5742i	0.381384	+	0.660577i	−0.609876	+	0.792497i	$0.708781\pi$
$308$	−8.96376	−	21.1543i	−0.510758	−	1.20538i
$309$	−4.72849	−	8.18998i	−0.268994	−	0.465912i
$310$	−0.135658	+	2.20658i	−0.00770484	+	0.125325i
$311$		−	2.97658i		−	0.168786i	−0.996433	−	0.0843932i	$-0.973105\pi$
$311$		−	2.97658i		−	0.168786i	0.996433	−	0.0843932i	$-0.0268952\pi$
$312$	28.6002	+	5.32869i	1.61917	+	0.301678i
$313$	−4.86402	+	8.42473i	−0.274931	+	0.476194i	−0.970118	−	0.242635i	$-0.921988\pi$
$313$	−4.86402	+	8.42473i	−0.274931	+	0.476194i	0.695187	+	0.718829i	$0.255322\pi$
$314$	−0.938402	+	15.2639i	−0.0529571	+	0.861389i
$315$		−	1.66211i		−	0.0936492i
$316$	3.73639	−	4.95186i	0.210188	−	0.278564i
$317$	−21.2971	−	12.2959i	−1.19617	−	0.690607i	−0.236467	−	0.971639i	$-0.575990\pi$
$317$	−21.2971	−	12.2959i	−1.19617	−	0.690607i	−0.959698	+	0.281033i	$0.909323\pi$
$318$	−20.0773	+	30.3128i	−1.12588	+	1.69986i
$319$	16.6605	−	28.8569i	0.932810	−	1.61567i
$320$	1.23654	+	7.90386i	0.0691250	+	0.441839i
$321$	4.98041	+	8.62633i	0.277980	+	0.481475i
$322$	−7.33862	+	3.65602i	−0.408966	+	0.203742i
$323$	−8.22846	−	18.2464i	−0.457844	−	1.01526i
$324$	−13.0321	+	17.2715i	−0.724004	+	0.959528i
$325$	−4.54395	+	2.62345i	−0.252053	+	0.145523i
$326$	−6.65554	+	10.0485i	−0.368616	+	0.556537i
$327$	−18.2180	−	10.5182i	−1.00746	−	0.581657i
$328$	2.69818	+	7.64236i	0.148982	+	0.421979i
$329$	13.1401	−	22.7594i	0.724439	−	1.25477i
$330$	7.20216	+	14.4567i	0.396466	+	0.795815i
$331$	5.09793			0.280207			0.140104	−	0.990137i	$-0.455256\pi$
$331$	5.09793			0.280207			0.140104	+	0.990137i	$0.455256\pi$
$332$	−15.2610	+	6.46656i	−0.837555	+	0.354898i
$333$	−4.97477	−	2.87218i	−0.272616	−	0.157395i
$334$	−21.0955	+	10.5095i	−1.15429	+	0.575055i
$335$	5.99685			0.327643
$336$	3.75940	−	14.9976i	0.205092	−	0.818189i
$337$	−15.3602	+	8.86820i	−0.836722	+	0.483082i	−0.856149	−	0.516729i	$-0.827149\pi$
$337$	−15.3602	+	8.86820i	−0.836722	+	0.483082i	0.0194265	+	0.999811i	$0.493816\pi$
$338$	−1.26091	+	20.5098i	−0.0685846	+	1.11558i
$339$	−18.2049	+	10.5106i	−0.988756	+	0.570859i
$340$	−9.11480	−	1.12498i	−0.494320	−	0.0610108i
$341$			9.10725i			0.493185i
$342$	−4.85899	+	1.84145i	−0.262744	+	0.0995740i
$343$		−	19.9389i		−	1.07660i
$344$	−4.83345	−	13.6903i	−0.260602	−	0.738133i
$345$	4.99159	−	2.88189i	0.268738	−	0.155156i
$346$	21.6088	+	1.32848i	1.16169	+	0.0714195i
$347$	−29.6776	+	17.1344i	−1.59318	+	0.919821i	−0.600418	+	0.799686i	$0.704999\pi$
$347$	−29.6776	+	17.1344i	−1.59318	+	0.919821i	−0.992758	+	0.120135i	$0.961667\pi$
$348$	20.6471	−	8.74884i	1.10680	−	0.468987i
$349$	−0.685586			−0.0366986			−0.0183493	−	0.999832i	$-0.505841\pi$
$349$	−0.685586			−0.0366986			−0.0183493	+	0.999832i	$0.505841\pi$
$350$	1.24346	+	2.49596i	0.0664658	+	0.133415i
$351$	−19.2144	−	11.0935i	−1.02559	−	0.592125i
$352$	7.08238	+	32.1863i	0.377492	+	1.71553i
$353$	−21.5256			−1.14569			−0.572846	−	0.819663i	$-0.694161\pi$
$353$	−21.5256			−1.14569			−0.572846	+	0.819663i	$0.694161\pi$
$354$	25.6958	−	12.8014i	1.36572	−	0.680385i
$355$	−0.0329647	+	0.0570966i	−0.00174959	+	0.00303037i
$356$	−2.83918	+	23.0035i	−0.150476	+	1.21918i
$357$	15.3719	+	8.87495i	0.813565	+	0.469712i
$358$	−6.39936	−	4.23854i	−0.338217	−	0.224014i
$359$	18.5922	−	10.7342i	0.981257	−	0.566529i	0.0786075	−	0.996906i	$-0.474953\pi$
$359$	18.5922	−	10.7342i	0.981257	−	0.566529i	0.902649	+	0.430377i	$0.141619\pi$
$360$	−0.436698	+	2.34385i	−0.0230160	+	0.123532i
$361$	18.6217	+	3.77265i	0.980089	+	0.198560i
$362$	14.1206	+	28.3439i	0.742163	+	1.48972i
$363$	22.4862	+	38.9473i	1.18022	+	2.04420i
$364$	20.5359	+	2.53462i	1.07637	+	0.132850i
$365$	−3.29020	+	5.69879i	−0.172217	+	0.298289i
$366$	16.7564	+	11.0984i	0.875872	+	0.580124i
$367$	−3.78351	−	2.18441i	−0.197498	−	0.114025i	0.397990	−	0.917390i	$-0.369708\pi$
$367$	−3.78351	−	2.18441i	−0.197498	−	0.114025i	−0.595488	+	0.803364i	$0.703041\pi$
$368$	11.3093	−	3.22747i	0.589536	−	0.168243i
$369$			2.41539i			0.125740i
$370$	9.61928	+	0.591381i	0.500082	+	0.0307444i
$371$	−12.9300	+	22.3953i	−0.671290	+	1.16271i
$372$	−3.69157	+	4.89247i	−0.191399	+	0.253663i
$373$		−	19.7828i		−	1.02431i	−0.858892	−	0.512156i	$-0.828847\pi$
$373$		−	19.7828i		−	1.02431i	0.858892	−	0.512156i	$-0.171153\pi$
$374$	−37.7624	−	2.32158i	−1.95265	−	0.120046i
$375$	−0.980171	−	1.69771i	−0.0506158	−	0.0876691i
$376$	−24.5095	+	28.6421i	−1.26398	+	1.47711i
$377$	15.0047	+	25.9890i	0.772783	+	1.33850i
$378$	−6.51133	+	9.83081i	−0.334906	+	0.505642i
$379$	5.31924			0.273231			0.136616	−	0.990624i	$-0.456378\pi$
$379$	5.31924			0.273231			0.136616	+	0.990624i	$0.456378\pi$
$380$	5.91904	−	6.40039i	0.303640	−	0.328333i
$381$	−13.9882			−0.716638
$382$	17.4281	−	26.3130i	0.891701	−	1.34629i
$383$	3.30541	+	5.72514i	0.168899	+	0.292541i	0.938033	−	0.346546i	$-0.112646\pi$
$383$	3.30541	+	5.72514i	0.168899	+	0.292541i	−0.769134	+	0.639087i	$0.779312\pi$
$384$	−9.24183	+	20.1615i	−0.471620	+	1.02886i
$385$	5.74377	+	9.94851i	0.292730	+	0.507023i
$386$	−25.7933	−	1.58574i	−1.31284	−	0.0807119i
$387$		−	4.32686i		−	0.219947i
$388$	1.70969	+	1.29003i	0.0867963	+	0.0654915i
$389$	−9.63946	+	16.6960i	−0.488740	+	0.846523i	−0.999916	−	0.0129535i	$-0.995877\pi$
$389$	−9.63946	+	16.6960i	−0.488740	+	0.846523i	0.511176	+	0.859476i	$0.329210\pi$
$390$	−14.5188	−	0.892596i	−0.735187	−	0.0451984i
$391$			13.5013i			0.682792i
$392$	−1.61222	+	8.65311i	−0.0814292	+	0.437048i
$393$	7.80219	+	4.50460i	0.393568	+	0.227227i
$394$	0.161239	+	0.106795i	0.00812310	+	0.00538024i
$395$	−1.55084	+	2.68613i	−0.0780311	+	0.135154i
$396$	−1.20311	+	9.74778i	−0.0604585	+	0.489844i
$397$	4.58902	+	7.94842i	0.230316	+	0.398920i	0.957901	−	0.287098i	$-0.0926905\pi$
$397$	4.58902	+	7.94842i	0.230316	+	0.398920i	−0.727585	+	0.686018i	$0.759357\pi$
$398$	−4.71335	−	9.46098i	−0.236259	−	0.474236i
$399$	−15.3594	+	6.92651i	−0.768930	+	0.346759i
$400$	−1.09771	−	3.84643i	−0.0548853	−	0.192322i
$401$	−18.1229	+	10.4632i	−0.905013	+	0.522509i	−0.878823	−	0.477148i	$-0.841671\pi$
$401$	−18.1229	+	10.4632i	−0.905013	+	0.522509i	−0.0261896	+	0.999657i	$0.508337\pi$
$402$	13.8607	+	9.18048i	0.691310	+	0.457881i
$403$	−7.10326	−	4.10107i	−0.353838	−	0.204289i
$404$	10.4384	+	1.28835i	0.519331	+	0.0640979i
$405$	5.40913	−	9.36890i	0.268782	−	0.465544i
$406$	14.2756	−	7.11193i	0.708485	−	0.352959i
$407$	39.7018			1.96794
$408$	−19.3451	−	16.5539i	−0.957727	−	0.819542i
$409$	−16.1297	−	9.31247i	−0.797561	−	0.460472i	0.0450565	−	0.998984i	$-0.485653\pi$
$409$	−16.1297	−	9.31247i	−0.797561	−	0.460472i	−0.842618	+	0.538512i	$0.818987\pi$
$410$	−1.80700	−	3.62715i	−0.0892416	−	0.179132i
$411$	−32.0406			−1.58045
$412$	3.76430	+	8.88368i	0.185454	+	0.437667i
$413$	17.6828	−	10.2092i	0.870114	−	0.502360i
$414$	3.49838	+	0.215076i	0.171936	+	0.0105704i
$415$	7.17696	−	4.14362i	0.352303	−	0.203402i
$416$	−28.2931	−	8.96979i	−1.38719	−	0.439780i
$417$			16.1889i			0.792774i
$418$	22.7198	−	27.8132i	1.11126	−	1.36039i
$419$			29.5097i			1.44164i	0.693122	+	0.720821i	$0.256235\pi$
$419$			29.5097i			1.44164i	−0.693122	+	0.720821i	$0.743765\pi$
$420$	−0.946983	+	7.67260i	−0.0462080	+	0.374385i
$421$	−17.2407	+	9.95394i	−0.840262	+	0.485125i	−0.857353	−	0.514728i	$-0.827893\pi$
$421$	−17.2407	+	9.95394i	−0.840262	+	0.485125i	0.0170913	+	0.999854i	$0.494559\pi$
$422$	−0.779519	+	12.6795i	−0.0379464	+	0.617228i
$423$	−9.72953	+	5.61735i	−0.473066	+	0.273125i
$424$	24.1175	−	28.1840i	1.17125	−	1.36874i
$425$	4.59198			0.222744
$426$	−0.163601	+	0.0815041i	−0.00792649	+	0.00394888i
$427$	12.3798	+	7.14748i	0.599100	+	0.345891i
$428$	−3.96485	−	9.35698i	−0.191648	−	0.452287i
$429$	−59.9236			−2.89314
$430$	3.23702	+	6.49758i	0.156103	+	0.313341i
$431$	12.6205	−	21.8593i	0.607908	−	1.05293i	−0.383677	−	0.923468i	$-0.625342\pi$
$431$	12.6205	−	21.8593i	0.607908	−	1.05293i	0.991585	−	0.129460i	$-0.0413244\pi$
$432$	11.7650	−	12.1523i	0.566043	−	0.584679i
$433$	22.9388	+	13.2437i	1.10237	+	0.636453i	0.936842	−	0.349752i	$-0.113734\pi$
$433$	22.9388	+	13.2437i	1.10237	+	0.636453i	0.165527	+	0.986205i	$0.447067\pi$
$434$	−2.40713	+	3.63429i	−0.115546	+	0.174451i
$435$	−9.70997	+	5.60605i	−0.465557	+	0.268790i
$436$	17.1321	+	12.9269i	0.820481	+	0.619087i
$437$	−10.4042	−	7.48347i	−0.497702	−	0.357983i
$438$	−16.3290	+	8.13490i	−0.780228	+	0.388700i
$439$	7.46205	+	12.9247i	0.356144	+	0.616860i	0.987313	−	0.158785i	$-0.0507578\pi$
$439$	7.46205	+	12.9247i	0.356144	+	0.616860i	−0.631169	+	0.775646i	$0.717424\pi$
$440$	−5.48584	−	15.5382i	−0.261527	−	0.740753i
$441$	−1.31160	+	2.27177i	−0.0624573	+	0.108179i
$442$	18.8154	−	28.4076i	0.894959	−	1.35121i
$443$	−18.5962	−	10.7365i	−0.883534	−	0.510109i	−0.0117121	−	0.999931i	$-0.503728\pi$
$443$	−18.5962	−	10.7365i	−0.883534	−	0.510109i	−0.871822	+	0.489823i	$0.837062\pi$
$444$	21.3280	+	16.0929i	1.01218	+	0.763735i
$445$		−	11.5890i		−	0.549373i
$446$	0.634685	−	10.3237i	0.0300532	−	0.488839i
$447$	10.9462	−	18.9594i	0.517738	−	0.896749i
$448$	−5.68087	+	14.7160i	−0.268396	+	0.695266i
$449$			15.0746i			0.711412i	0.934598	+	0.355706i	$0.115760\pi$
$449$			15.0746i			0.711412i	−0.934598	+	0.355706i	$0.884240\pi$
$450$	0.0731503	−	1.18985i	0.00344834	−	0.0560900i
$451$	−8.34688	−	14.4572i	−0.393039	−	0.680764i
$452$	19.7469	−	8.36739i	0.928816	−	0.393569i
$453$	−8.54383	−	14.7983i	−0.401424	−	0.695287i
$454$	12.7609	+	8.45202i	0.598898	+	0.396673i
$455$	−10.3459			−0.485022
$456$	23.4791	−	5.73206i	1.09951	−	0.268428i
$457$	−6.98141			−0.326577			−0.163288	−	0.986578i	$-0.552210\pi$
$457$	−6.98141			−0.326577			−0.163288	+	0.986578i	$0.552210\pi$
$458$	3.31517	+	2.19577i	0.154908	+	0.102601i
$459$	9.70878	+	16.8161i	0.453167	+	0.784908i
$460$	−5.41437	+	2.29424i	−0.252447	+	0.106970i
$461$	−16.1247	−	27.9288i	−0.751003	−	1.30078i	−0.947337	−	0.320239i	$-0.896237\pi$
$461$	−16.1247	−	27.9288i	−0.751003	−	1.30078i	0.196333	−	0.980537i	$-0.437097\pi$
$462$	−1.95425	+	31.7874i	−0.0909198	+	1.47888i
$463$			14.3865i			0.668598i	0.942467	+	0.334299i	$0.108499\pi$
$463$			14.3865i			0.668598i	−0.942467	+	0.334299i	$0.891501\pi$
$464$	−21.9995	+	6.27829i	−1.02130	+	0.291462i
$465$	1.53224	−	2.65391i	0.0710558	−	0.123072i
$466$	−1.04263	+	16.9593i	−0.0482991	+	0.785624i
$467$		−	39.7847i		−	1.84102i	−0.390725	−	0.920508i	$-0.627776\pi$
$467$		−	39.7847i		−	1.84102i	0.390725	−	0.920508i	$-0.372224\pi$
$468$	−7.06107	−	5.32788i	−0.326398	−	0.246281i
$469$	10.2404	+	5.91231i	0.472858	+	0.273005i
$470$	10.4082	−	15.7144i	0.480096	−	0.724850i
$471$	10.5991	−	18.3582i	0.488382	−	0.845902i
$472$	−27.6181	+	9.75071i	−1.27122	+	0.448813i
$473$	14.9524	+	25.8983i	0.687511	+	1.19080i
$474$	−7.69666	+	3.83439i	−0.353519	+	0.176119i
$475$	−2.54523	+	3.53862i	−0.116783	+	0.162363i
$476$	−14.4556	−	10.9074i	−0.662572	−	0.499938i
$477$	9.57390	−	5.52750i	0.438359	−	0.253087i
$478$	−4.79650	+	7.24176i	−0.219387	+	0.331230i
$479$	−16.9139	−	9.76523i	−0.772815	−	0.446185i	0.0610629	−	0.998134i	$-0.480551\pi$
$479$	−16.9139	−	9.76523i	−0.772815	−	0.446185i	−0.833878	+	0.551949i	$0.813884\pi$
$480$	3.35128	−	10.5709i	0.152964	−	0.482491i
$481$	−17.8780	+	30.9656i	−0.815168	+	1.41191i
$482$	−11.2787	−	22.6393i	−0.513729	−	1.03119i
$483$	11.3651			0.517128
$484$	−17.9010	−	42.2461i	−0.813683	−	1.92028i
$485$	−0.927418	−	0.535445i	−0.0421119	−	0.0243133i
$486$	10.7871	−	5.37400i	0.489312	−	0.243770i
$487$	22.7373			1.03033			0.515163	−	0.857092i	$-0.327731\pi$
$487$	22.7373			1.03033			0.515163	+	0.857092i	$0.327731\pi$
$488$	−15.5797	−	13.3318i	−0.705259	−	0.603501i
$489$	14.4689	−	8.35360i	0.654304	−	0.377763i
$490$	0.270058	−	4.39272i	0.0122000	−	0.198443i
$491$	−0.936448	+	0.540659i	−0.0422613	+	0.0243996i	−0.520982	−	0.853568i	$-0.674434\pi$
$491$	−0.936448	+	0.540659i	−0.0422613	+	0.0243996i	0.478720	+	0.877967i	$0.341101\pi$
$492$	1.37616	−	11.1499i	0.0620421	−	0.502675i
$493$		−	26.2637i		−	1.18286i
$494$	11.4622	+	30.2450i	0.515707	+	1.36079i
$495$		−	4.91087i		−	0.220727i
$496$	4.34932	−	4.49251i	0.195290	−	0.201720i
$497$	−0.112583	+	0.0650000i	−0.00505005	+	0.00291565i
$498$	22.9318	+	1.40982i	1.02760	+	0.0631753i
$499$	−7.97600	+	4.60494i	−0.357055	+	0.206146i	−0.667788	−	0.744352i	$-0.732759\pi$
$499$	−7.97600	+	4.60494i	−0.357055	+	0.206146i	0.310733	+	0.950497i	$0.399425\pi$
$500$	0.780303	+	1.84150i	0.0348962	+	0.0823545i
$501$	32.6698			1.45958
$502$	2.13472	+	4.28496i	0.0952771	+	0.191247i
$503$	13.2233	+	7.63448i	0.589598	+	0.340405i	0.764939	−	0.644103i	$-0.222769\pi$
$503$	13.2233	+	7.63448i	0.589598	+	0.340405i	−0.175340	+	0.984508i	$0.556103\pi$
$504$	−3.05653	+	3.57190i	−0.136149	+	0.159105i
$505$	−5.25882			−0.234014
$506$	−21.6827	+	10.8021i	−0.963914	+	0.480211i
$507$	14.2418	−	24.6676i	0.632503	−	1.09553i
$508$	14.1637	+	1.74814i	0.628414	+	0.0775613i
$509$	−25.4839	−	14.7131i	−1.12955	−	0.652149i	−0.185732	−	0.982601i	$-0.559465\pi$
$509$	−25.4839	−	14.7131i	−1.12955	−	0.652149i	−0.943823	+	0.330452i	$0.892799\pi$
$510$	10.6136	+	7.02980i	0.469978	+	0.311285i
$511$	−11.2369	+	6.48763i	−0.497092	+	0.286996i
$512$	11.8774	−	19.2595i	0.524913	−	0.851156i
$513$	−18.3400	−	1.83910i	−0.809729	−	0.0811984i
$514$	−10.3996	−	20.8748i	−0.458707	−	0.920750i
$515$	−2.41207	−	4.17783i	−0.106289	−	0.184097i
$516$	−2.46522	+	19.9736i	−0.108525	+	0.879288i
$517$	38.8239	−	67.2449i	1.70747	−	2.95743i
$518$	15.8432	+	10.4935i	0.696108	+	0.461059i
$519$	−25.9894	−	15.0050i	−1.14081	−	0.658646i
$520$	14.5894	+	2.71825i	0.639788	+	0.119203i
$521$			8.90478i			0.390125i	0.980791	+	0.195063i	$0.0624910\pi$
$521$			8.90478i			0.390125i	−0.980791	+	0.195063i	$0.937509\pi$
$522$	−6.80529	−	0.418380i	−0.297860	−	0.0183120i
$523$	−6.54118	+	11.3297i	−0.286026	+	0.495412i	−0.972857	−	0.231405i	$-0.925668\pi$
$523$	−6.54118	+	11.3297i	−0.286026	+	0.495412i	0.686831	+	0.726817i	$0.259001\pi$
$524$	−7.33714	−	5.53618i	−0.320524	−	0.241849i
$525$		−	3.86541i		−	0.168700i
$526$	−17.4433	−	1.07239i	−0.760562	−	0.0467584i
$527$	3.58917	+	6.21663i	0.156347	+	0.270801i
$528$	11.1075	−	44.3121i	0.483394	−	1.92844i
$529$	−7.17762	−	12.4320i	−0.312071	−	0.540522i
$530$	−10.2417	+	15.4630i	−0.444873	+	0.671670i
$531$	−8.72875			−0.378795
$532$	16.4177	−	5.09392i	0.711798	−	0.220849i
$533$	15.0347			0.651224
$534$	17.7415	−	26.7861i	0.767749	−	1.15915i
$535$	2.54059	+	4.40042i	0.109839	+	0.190247i
$536$	−12.8873	−	11.0279i	−0.556647	−	0.476332i
$537$	5.31995	+	9.21442i	0.229573	+	0.397631i
$538$	−10.5268	−	0.647175i	−0.453844	−	0.0279017i
$539$		−	18.1301i		−	0.780919i
$540$	−5.09390	+	6.75098i	−0.219206	+	0.290516i
$541$	2.09301	−	3.62519i	0.0899853	−	0.155859i	−0.817519	−	0.575901i	$-0.804651\pi$
$541$	2.09301	−	3.62519i	0.0899853	−	0.155859i	0.907505	+	0.420042i	$0.137985\pi$
$542$	−32.7542	−	2.01368i	−1.40691	−	0.0864952i
$543$		−	43.8952i		−	1.88372i
$544$	17.5191	+	19.1793i	0.751124	+	0.822304i
$545$	−9.29330	−	5.36549i	−0.398081	−	0.229832i
$546$	−23.9128	−	15.8383i	−1.02337	−	0.677818i
$547$	−14.0870	+	24.3994i	−0.602317	+	1.04324i	0.390153	+	0.920750i	$0.372422\pi$
$547$	−14.0870	+	24.3994i	−0.602317	+	1.04324i	−0.992469	+	0.122493i	$0.960911\pi$
$548$	32.4426	+	4.00419i	1.38588	+	0.171051i
$549$	−3.05551	−	5.29230i	−0.130406	−	0.225870i
$550$	3.67393	+	7.37458i	0.156657	+	0.314453i
$551$	20.2390	+	14.5573i	0.862211	+	0.620164i
$552$	−16.0267	−	2.98603i	−0.682140	−	0.127094i
$553$	−5.29652	+	3.05795i	−0.225231	+	0.130037i
$554$	16.8500	+	11.1604i	0.715889	+	0.474161i
$555$	−11.5693	−	6.67957i	−0.491092	−	0.283532i
$556$	2.02317	−	16.3920i	0.0858014	−	0.695177i
$557$	−16.9711	+	29.3948i	−0.719087	+	1.24550i	0.242274	+	0.970208i	$0.422107\pi$
$557$	−16.9711	+	29.3948i	−0.719087	+	1.24550i	−0.961362	+	0.275288i	$0.911227\pi$
$558$	1.66799	−	0.830974i	0.0706117	−	0.0351780i
$559$	−26.9327			−1.13913
$560$	1.91773	−	7.65053i	0.0810389	−	0.323294i
$561$	45.4178	+	26.2220i	1.91754	+	1.10709i
$562$	−16.8366	−	33.7956i	−0.710207	−	1.42558i
$563$	19.5548			0.824136			0.412068	−	0.911153i	$-0.364807\pi$
$563$	19.5548			0.824136			0.412068	+	0.911153i	$0.364807\pi$
$564$	48.1138	−	20.3873i	2.02596	−	0.858462i
$565$	−9.28661	+	5.36163i	−0.390691	+	0.225565i
$566$	−1.38146	−	0.0849302i	−0.0580670	−	0.00356988i
$567$	18.4736	−	10.6658i	0.775820	−	0.447920i
$568$	0.175839	−	0.0620811i	0.00737806	−	0.00260487i
$569$			29.5258i			1.23779i	0.785476	+	0.618893i	$0.212418\pi$
$569$			29.5258i			1.23779i	−0.785476	+	0.618893i	$0.787582\pi$
$570$	−11.3001	+	4.28248i	−0.473309	+	0.179373i
$571$		−	28.5730i		−	1.19574i	−0.801592	−	0.597871i	$-0.796013\pi$
$571$		−	28.5730i		−	1.19574i	0.801592	−	0.597871i	$-0.203987\pi$
$572$	60.6755	+	7.48880i	2.53697	+	0.313122i
$573$	−37.8881	+	21.8747i	−1.58280	+	0.913828i
$574$	0.490315	−	7.97537i	0.0204654	−	0.332886i
$575$	2.54628	−	1.47010i	0.106187	−	0.0613073i
$576$	5.24869	−	4.23391i	0.218696	−	0.176413i
$577$	22.2421			0.925951			0.462975	−	0.886371i	$-0.346782\pi$
$577$	22.2421			0.925951			0.462975	+	0.886371i	$0.346782\pi$
$578$	−5.17256	+	2.57691i	−0.215150	+	0.107185i
$579$	31.0222	+	17.9107i	1.28924	+	0.744343i
$580$	10.5324	−	4.46291i	0.437334	−	0.185312i
$581$	16.3408			0.677932
$582$	−1.32387	−	2.65736i	−0.0548761	−	0.110151i
$583$	−38.2029	+	66.1693i	−1.58220	+	2.74045i
$584$	17.5505	−	6.19630i	0.726244	−	0.256405i
$585$	3.83027	+	2.21141i	0.158362	+	0.0914304i
$586$	−0.234330	+	0.353791i	−0.00968007	+	0.0146150i
$587$	24.4360	−	14.1081i	1.00858	−	0.582305i	0.0978061	−	0.995205i	$-0.468817\pi$
$587$	24.4360	−	14.1081i	1.00858	−	0.582305i	0.910776	+	0.412900i	$0.135484\pi$
$588$	7.34894	−	9.73960i	0.303065	−	0.401655i
$589$	−6.77998	−	0.679886i	−0.279364	−	0.0280142i
$590$	13.1078	−	6.53017i	0.539641	−	0.268843i
$591$	−0.134042	−	0.232167i	−0.00551375	−	0.00955009i
$592$	−19.5845	−	18.9602i	−0.804917	−	0.779261i
$593$	21.1847	−	36.6929i	0.869950	−	1.50680i	0.00790365	−	0.999969i	$-0.497484\pi$
$593$	21.1847	−	36.6929i	0.869950	−	1.50680i	0.862047	−	0.506829i	$-0.169183\pi$
$594$	−19.2384	+	29.0461i	−0.789360	+	1.19178i
$595$	7.84142	+	4.52725i	0.321467	+	0.185599i
$596$	−13.4530	+	17.8293i	−0.551055	+	0.730318i
$597$			14.6519i			0.599662i
$598$	1.33875	−	21.7758i	0.0547456	−	0.890480i
$599$	0.0932740	−	0.161555i	0.00381107	−	0.00660097i	−0.864114	−	0.503297i	$-0.832120\pi$
$599$	0.0932740	−	0.161555i	0.00381107	−	0.00660097i	0.867925	+	0.496696i	$0.165454\pi$
$600$	−1.01559	+	5.45088i	−0.0414612	+	0.222531i
$601$		−	29.9170i		−	1.22034i	−0.792270	−	0.610171i	$-0.791101\pi$
$601$		−	29.9170i		−	1.22034i	0.792270	−	0.610171i	$-0.208899\pi$
$602$	−0.878338	+	14.2869i	−0.0357984	+	0.582289i
$603$	−2.52748	−	4.37773i	−0.102927	−	0.178275i
$604$	6.80164	+	16.0518i	0.276755	+	0.653137i
$605$	11.4706	+	19.8676i	0.466345	+	0.807733i
$606$	−12.1549	−	8.05065i	−0.493759	−	0.327035i
$607$	13.7069			0.556347			0.278173	−	0.960531i	$-0.410271\pi$
$607$	13.7069			0.556347			0.278173	+	0.960531i	$0.410271\pi$
$608$	−24.4901	+	2.86973i	−0.993204	+	0.116383i
$609$	−22.1081			−0.895865
$610$	8.54771	+	5.66148i	0.346087	+	0.229226i
$611$	34.9654	+	60.5619i	1.41455	+	2.45007i
$612$	3.02036	+	7.12800i	0.122091	+	0.288132i
$613$	3.74362	+	6.48414i	0.151203	+	0.261892i	0.931670	−	0.363305i	$-0.118352\pi$
$613$	3.74362	+	6.48414i	0.151203	+	0.261892i	−0.780467	+	0.625197i	$0.785018\pi$
$614$	−1.15980	+	18.8650i	−0.0468057	+	0.761331i
$615$			5.61724i			0.226509i
$616$	5.95132	−	31.9420i	0.239785	−	1.28698i
$617$	−10.6539	+	18.4531i	−0.428911	+	0.742895i	−0.996777	−	0.0802259i	$-0.974436\pi$
$617$	−10.6539	+	18.4531i	−0.428911	+	0.742895i	0.567866	+	0.823121i	$0.307769\pi$
$618$	0.820678	−	13.3490i	0.0330125	−	0.536975i
$619$		−	7.72485i		−	0.310488i	−0.987876	−	0.155244i	$-0.950384\pi$
$619$		−	7.72485i		−	0.310488i	0.987876	−	0.155244i	$-0.0496164\pi$
$620$	−1.88313	+	2.49572i	−0.0756282	+	0.100231i
$621$	10.7672	+	6.21642i	0.432071	+	0.249456i
$622$	2.32450	−	3.50953i	0.0932038	−	0.140719i
$623$	11.4257	−	19.7898i	0.457759	−	0.792863i
$624$	29.5597	+	28.6175i	1.18333	+	1.14562i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−12.3140	+	6.13470i	−0.492167	+	0.245192i
$627$	−45.3808	+	20.4651i	−1.81234	+	0.817296i
$628$	−13.0264	+	17.2640i	−0.519810	+	0.688908i
$629$	27.1005	−	15.6465i	1.08057	−	0.623866i
$630$	1.29799	−	1.95970i	0.0517131	−	0.0780765i
$631$	−26.0298	−	15.0283i	−1.03623	−	0.598268i	−0.117467	−	0.993077i	$-0.537477\pi$
$631$	−26.0298	−	15.0283i	−1.03623	−	0.598268i	−0.918763	+	0.394809i	$0.870811\pi$
$632$	8.27243	−	2.92063i	0.329059	−	0.116176i
$633$	8.80457	−	15.2500i	0.349950	−	0.606131i
$634$	−15.5081	−	31.1290i	−0.615905	−	1.23629i
$635$	−7.13560			−0.283168
$636$	−47.3442	+	20.0612i	−1.87732	+	0.795480i
$637$	14.1407	+	8.16413i	0.560275	+	0.323475i
$638$	42.1787	−	21.0129i	1.66987	−	0.831910i
$639$	0.0555744			0.00219849
$640$	−4.71440	+	10.2847i	−0.186353	+	0.406537i
$641$	19.4796	−	11.2465i	0.769398	−	0.444212i	−0.0632620	−	0.997997i	$-0.520150\pi$
$641$	19.4796	−	11.2465i	0.769398	−	0.444212i	0.832660	+	0.553785i	$0.186817\pi$
$642$	−0.864402	+	14.0602i	−0.0341152	+	0.554912i
$643$	14.1389	−	8.16307i	0.557582	−	0.321920i	−0.194592	−	0.980884i	$-0.562338\pi$
$643$	14.1389	−	8.16307i	0.557582	−	0.321920i	0.752174	+	0.658964i	$0.229005\pi$
$644$	−11.5077	−	1.42032i	−0.453466	−	0.0559685i
$645$		−	10.0626i		−	0.396213i
$646$	4.54741	−	27.9392i	0.178915	−	1.09925i
$647$			10.3982i			0.408796i	0.978888	+	0.204398i	$0.0655237\pi$
$647$			10.3982i			0.408796i	−0.978888	+	0.204398i	$0.934476\pi$
$648$	−28.8532	+	10.1868i	−1.13346	+	0.400175i
$649$	52.2457	−	30.1640i	2.05082	−	1.18404i
$650$	−7.40625	−	0.455327i	−0.290497	−	0.0178594i
$651$	5.23300	−	3.02127i	0.205097	−	0.118413i
$652$	−15.6944	+	6.65021i	−0.614639	+	0.260442i
$653$	24.4510			0.956844			0.478422	−	0.878130i	$-0.341209\pi$
$653$	24.4510			0.956844			0.478422	+	0.878130i	$0.341209\pi$
$654$	−13.2660	−	26.6284i	−0.518741	−	1.04125i
$655$	3.98002	+	2.29786i	0.155512	+	0.0897849i
$656$	−2.78685	+	11.1178i	−0.108808	+	0.434077i
$657$	5.54687			0.216404
$658$	33.2663	−	16.5729i	1.29685	−	0.646078i
$659$	3.26055	−	5.64745i	0.127013	−	0.219993i	−0.795505	−	0.605947i	$-0.792794\pi$
$659$	3.26055	−	5.64745i	0.127013	−	0.219993i	0.922518	+	0.385954i	$0.126128\pi$
$660$	−2.79796	+	22.6695i	−0.108910	+	0.882409i
$661$	22.4878	+	12.9833i	0.874673	+	0.504993i	0.868898	−	0.494990i	$-0.164828\pi$
$661$	22.4878	+	12.9833i	0.874673	+	0.504993i	0.00577497	+	0.999983i	$0.498162\pi$
$662$	6.01070	+	3.98112i	0.233612	+	0.154730i
$663$	−40.9040	+	23.6159i	−1.58858	+	0.917166i
$664$	−23.0433	−	4.29335i	−0.894254	−	0.166614i
$665$	−7.83505	+	3.53332i	−0.303830	+	0.137016i
$666$	−3.62251	−	7.27137i	−0.140370	−	0.281760i
$667$	−8.40817	−	14.5634i	−0.325566	−	0.563897i
$668$	−33.0797	−	4.08283i	−1.27989	−	0.157969i
$669$	−7.16868	+	12.4165i	−0.277157	+	0.480050i
$670$	7.07056	+	4.68310i	0.273160	+	0.180924i
$671$	36.5774	+	21.1180i	1.41205	+	0.815249i
$672$	16.1446	−	14.7471i	0.622791	−	0.568882i
$673$			2.58867i			0.0997860i	0.998755	+	0.0498930i	$0.0158880\pi$
$673$			2.58867i			0.0997860i	−0.998755	+	0.0498930i	$0.984112\pi$
$674$	−25.0358	−	1.53917i	−0.964343	−	0.0592865i
$675$	2.11429	−	3.66206i	0.0813790	−	0.140953i
$676$	−17.5033	+	23.1973i	−0.673204	+	0.892203i
$677$		−	3.27960i		−	0.126045i	−0.998012	−	0.0630225i	$-0.979926\pi$
$677$		−	3.27960i		−	0.126045i	0.998012	−	0.0630225i	$-0.0200740\pi$
$678$	−29.6725	−	1.82423i	−1.13957	−	0.0700590i
$679$	−1.05579	−	1.82869i	−0.0405176	−	0.0701786i
$680$	−9.86825	−	8.44441i	−0.378430	−	0.323829i
$681$	−10.6084	−	18.3743i	−0.406516	−	0.704106i
$682$	−7.11211	+	10.7379i	−0.272337	+	0.411174i
$683$	26.1204			0.999471			0.499735	−	0.866178i	$-0.333431\pi$
$683$	26.1204			0.999471			0.499735	+	0.866178i	$0.333431\pi$
$684$	−7.16701	−	1.62337i	−0.274037	−	0.0620711i
$685$	−16.3444			−0.624487
$686$	15.5708	−	23.5089i	0.594497	−	0.897572i
$687$	−2.75598	−	4.77350i	−0.105147	−	0.182121i
$688$	4.99230	−	19.9161i	0.190330	−	0.759295i
$689$	−34.4061	−	59.5932i	−1.31077	−	2.27032i
$690$	8.13587	+	0.500182i	0.309727	+	0.0190416i
$691$		−	38.9076i		−	1.48011i	−0.672544	−	0.740057i	$-0.734798\pi$
$691$		−	38.9076i		−	1.48011i	0.672544	−	0.740057i	$-0.265202\pi$
$692$	24.4403	+	18.4412i	0.929081	+	0.701030i
$693$	4.84164	−	8.38597i	0.183919	−	0.318557i
$694$	−48.3720	−	2.97384i	−1.83617	−	0.112886i
$695$			8.25821i			0.313252i
$696$	31.1761	+	5.80862i	1.18173	+	0.220175i
$697$	−11.3952	−	6.57902i	−0.431624	−	0.249198i
$698$	−0.808338	−	0.535394i	−0.0305961	−	0.0202649i
$699$	11.7764	−	20.3974i	0.445425	−	0.771499i
$700$	−0.483070	+	3.91391i	−0.0182583	+	0.147932i
$701$	−9.92728	−	17.1946i	−0.374948	−	0.649429i	0.615371	−	0.788238i	$-0.289006\pi$
$701$	−9.92728	−	17.1946i	−0.374948	−	0.649429i	−0.990319	+	0.138808i	$0.955673\pi$
$702$	−13.9915	−	28.0848i	−0.528076	−	1.05999i
$703$	−2.96387	+	29.5563i	−0.111784	+	1.11474i
$704$	−16.7847	+	43.4799i	−0.632598	+	1.63871i
$705$	−22.6271	+	13.0637i	−0.852184	+	0.492009i
$706$	−25.3797	−	16.8100i	−0.955178	−	0.632651i
$707$	−8.98014	−	5.18468i	−0.337733	−	0.194990i
$708$	40.2935	+	4.97318i	1.51432	+	0.186904i
$709$	−24.4501	+	42.3488i	−0.918243	+	1.59044i	−0.116160	+	0.993231i	$0.537058\pi$
$709$	−24.4501	+	42.3488i	−0.918243	+	1.59044i	−0.802083	+	0.597213i	$0.796275\pi$
$710$	−0.0834553	+	0.0415765i	−0.00313202	+	0.00156034i
$711$	2.61452			0.0980521
$712$	−21.3116	+	24.9050i	−0.798687	+	0.933355i
$713$	3.98044	+	2.29811i	0.149069	+	0.0860648i
$714$	11.1935	+	22.4683i	0.418904	+	0.840855i
$715$	−30.5679			−1.14318
$716$	−4.23515	−	9.99488i	−0.158275	−	0.373526i
$717$	10.4274	−	6.02025i	0.389418	−	0.224830i
$718$	30.3037	+	1.86303i	1.13092	+	0.0695276i
$719$	14.9298	−	8.61971i	0.556787	−	0.321461i	−0.195068	−	0.980790i	$-0.562493\pi$
$719$	14.9298	−	8.61971i	0.556787	−	0.321461i	0.751855	+	0.659329i	$0.229159\pi$
$720$	−2.34527	+	2.42248i	−0.0874030	+	0.0902806i
$721$		−	9.51228i		−	0.354256i
$722$	19.0097	+	18.9903i	0.707467	+	0.706747i
$723$			35.0608i			1.30392i
$724$	−5.48570	+	44.4460i	−0.203874	+	1.65182i
$725$	−4.95320	+	2.85973i	−0.183957	+	0.106208i
$726$	−3.90272	+	63.4808i	−0.144843	+	2.35599i
$727$	1.19700	−	0.691086i	0.0443941	−	0.0256310i	−0.477639	−	0.878556i	$-0.658507\pi$
$727$	1.19700	−	0.691086i	0.0443941	−	0.0256310i	0.522033	+	0.852925i	$0.325174\pi$
$728$	22.2334	+	19.0255i	0.824026	+	0.705132i
$729$	15.7492			0.583305
$730$	−8.32965	+	4.14974i	−0.308294	+	0.153589i
$731$	20.4131	+	11.7855i	0.755004	+	0.435902i
$732$	11.0895	+	26.1711i	0.409881	+	0.967313i
$733$	23.1122			0.853667			0.426834	−	0.904330i	$-0.359629\pi$
$733$	23.1122			0.853667			0.426834	+	0.904330i	$0.359629\pi$
$734$	−2.75507	−	5.53017i	−0.101691	−	0.204122i
$735$	−3.05027	+	5.28323i	−0.112511	+	0.194875i
$736$	15.8546	+	5.02639i	0.584407	+	0.185275i
$737$	30.2564	+	17.4685i	1.11451	+	0.643461i
$738$	−1.88624	+	2.84785i	−0.0694335	+	0.104831i
$739$	0.761232	−	0.439497i	0.0280024	−	0.0161672i	−0.485933	−	0.873996i	$-0.661520\pi$
$739$	0.761232	−	0.439497i	0.0280024	−	0.0161672i	0.513936	+	0.857829i	$0.328187\pi$
$740$	10.8798	+	8.20923i	0.399948	+	0.301777i
$741$	4.47349	−	44.6107i	0.164338	−	1.63881i
$742$	−32.7342	+	16.3078i	−1.20171	+	0.598678i
$743$	−13.9371	−	24.1399i	−0.511304	−	0.885605i	−0.999914	−	0.0131028i	$-0.995829\pi$
$743$	−13.9371	−	24.1399i	−0.511304	−	0.885605i	0.488610	−	0.872502i	$-0.337504\pi$
$744$	−8.17320	+	2.88560i	−0.299644	+	0.105791i
$745$	5.58383	−	9.67148i	0.204576	−	0.354336i
$746$	15.4489	−	23.3248i	0.565625	−	0.853982i
$747$	−6.04973	−	3.49282i	−0.221348	−	0.127795i
$748$	−42.7106	−	32.2269i	−1.56165	−	1.17833i
$749$			10.0191i			0.366089i
$750$	0.170119	−	2.76712i	0.00621186	−	0.101041i
$751$	13.2015	−	22.8657i	0.481731	−	0.834382i	−0.518049	−	0.855351i	$-0.673342\pi$
$751$	13.2015	−	22.8657i	0.481731	−	0.834382i	0.999780	+	0.0209684i	$0.00667493\pi$
$752$	−51.2653	+	14.6302i	−1.86945	+	0.533510i
$753$		−	6.63597i		−	0.241828i
$754$	−2.60423	+	42.3598i	−0.0948403	+	1.54265i
$755$	−4.35834	−	7.54886i	−0.158616	−	0.274731i
$756$	−15.3543	+	6.50611i	−0.558431	+	0.236625i
$757$	−24.7340	−	42.8406i	−0.898973	−	1.55707i	−0.828809	−	0.559532i	$-0.810981\pi$
$757$	−24.7340	−	42.8406i	−0.898973	−	1.55707i	−0.0701643	−	0.997535i	$-0.522352\pi$
$758$	6.27163	+	4.15395i	0.227796	+	0.150878i
$759$	33.5793			1.21885
$760$	11.9771	−	2.92401i	0.434454	−	0.106065i
$761$	35.4470			1.28495			0.642476	−	0.766306i	$-0.277907\pi$
$761$	35.4470			1.28495			0.642476	+	0.766306i	$0.277907\pi$
$762$	−16.4928	−	10.9238i	−0.597470	−	0.395727i
$763$	−10.5797	−	18.3246i	−0.383011	−	0.663395i
$764$	41.0972	−	17.4142i	1.48684	−	0.630023i
$765$	−1.93538	−	3.35217i	−0.0699737	−	0.121198i
$766$	−0.573688	+	9.33149i	−0.0207282	+	0.337161i
$767$			54.3324i			1.96183i
$768$	−26.6412	+	16.5541i	−0.961332	+	0.597345i
$769$	5.94378	−	10.2949i	0.214338	−	0.371245i	−0.738729	−	0.674002i	$-0.764574\pi$
$769$	5.94378	−	10.2949i	0.214338	−	0.371245i	0.953068	+	0.302757i	$0.0979072\pi$
$770$	−0.996891	+	16.2152i	−0.0359255	+	0.584356i
$771$			32.3281i			1.16427i
$772$	−29.1732	−	22.0124i	−1.04996	−	0.792242i
$773$	4.31674	+	2.49227i	0.155262	+	0.0896408i	0.575618	−	0.817719i	$-0.304761\pi$
$773$	4.31674	+	2.49227i	0.155262	+	0.0896408i	−0.420356	+	0.907359i	$0.638095\pi$
$774$	3.37897	−	5.10157i	0.121454	−	0.183372i
$775$	0.781617	−	1.35380i	0.0280765	−	0.0486300i
$776$	1.00838	+	2.85615i	0.0361988	+	0.102530i
$777$	−13.1708	−	22.8125i	−0.472500	−	0.818394i
$778$	−24.4038	+	12.1577i	−0.874918	+	0.435874i
$779$	11.3859	−	5.13463i	0.407943	−	0.183967i
$780$	−16.4213	−	12.3905i	−0.587976	−	0.443653i
$781$	−0.332639	+	0.192049i	−0.0119028	+	0.00687206i
$782$	−10.5436	+	15.9187i	−0.377037	+	0.569251i
$783$	−20.9450	−	12.0926i	−0.748513	−	0.432154i
$784$	−8.65833	+	8.94340i	−0.309226	+	0.319407i
$785$	5.40678	−	9.36481i	0.192976	−	0.334244i
$786$	5.68138	+	11.4041i	0.202648	+	0.406770i
$787$	−2.98394			−0.106366			−0.0531830	−	0.998585i	$-0.516937\pi$
$787$	−2.98394			−0.106366			−0.0531830	+	0.998585i	$0.516937\pi$
$788$	0.106709	+	0.251832i	0.00380136	+	0.00897115i
$789$	20.9794	+	12.1125i	0.746888	+	0.431216i
$790$	−3.92618	+	1.95598i	−0.139687	+	0.0695906i
$791$	−21.1442			−0.751800
$792$	−9.03084	+	10.5535i	−0.320897	+	0.375004i
$793$	−32.9422	+	19.0192i	−1.16981	+	0.675390i
$794$	−0.796472	+	12.9553i	−0.0282657	+	0.459765i
$795$	22.2651	−	12.8548i	0.789663	−	0.455912i
$796$	1.83108	−	14.8357i	0.0649010	−	0.525839i
$797$		−	20.2077i		−	0.715792i	−0.933761	−	0.357896i	$-0.883494\pi$
$797$		−	20.2077i		−	0.715792i	0.933761	−	0.357896i	$-0.116506\pi$
$798$	−23.5185	−	3.82789i	−0.832547	−	0.135506i
$799$		−	61.2021i		−	2.16517i
$800$	1.70954	−	5.39235i	0.0604414	−	0.190648i
$801$	−8.46006	+	4.88442i	−0.298921	+	0.172582i
$802$	−29.5387	−	1.81600i	−1.04305	−	0.0641253i
$803$	−33.2006	+	19.1684i	−1.17162	+	0.676438i
$804$	9.17313	+	21.6484i	0.323511	+	0.763482i
$805$	5.79749			0.204335
$806$	−5.17243	−	10.3825i	−0.182191	−	0.365707i
$807$	12.6609	+	7.30976i	0.445684	+	0.257316i
$808$	11.3013	+	9.67069i	0.397578	+	0.340214i
$809$	−35.4958			−1.24797			−0.623983	−	0.781438i	$-0.714487\pi$
$809$	−35.4958			−1.24797			−0.623983	+	0.781438i	$0.714487\pi$
$810$	13.6941	−	6.82222i	0.481160	−	0.239708i
$811$	6.23098	−	10.7924i	0.218799	−	0.378972i	−0.735642	−	0.677371i	$-0.763119\pi$
$811$	6.23098	−	10.7924i	0.218799	−	0.378972i	0.954441	+	0.298399i	$0.0964527\pi$
$812$	22.3855	+	2.76290i	0.785577	+	0.0969589i
$813$	39.3943	+	22.7443i	1.38162	+	0.797678i
$814$	46.8102	+	31.0042i	1.64070	+	1.08670i
$815$	7.38079	−	4.26130i	0.258538	−	0.149267i
$816$	−9.88138	−	34.6250i	−0.345918	−	1.21212i
$817$	−20.3965	+	9.19805i	−0.713582	+	0.321799i
$818$	−11.7453	−	23.5760i	−0.410664	−	0.824314i
$819$	4.36046	+	7.55254i	0.152367	+	0.263907i
$820$	0.702000	−	5.68772i	0.0245149	−	0.198624i
$821$	−25.4324	+	44.0502i	−0.887596	+	1.53736i	−0.0448868	+	0.998992i	$0.514293\pi$
$821$	−25.4324	+	44.0502i	−0.887596	+	1.53736i	−0.842709	+	0.538369i	$0.819041\pi$
$822$	−37.7774	−	25.0214i	−1.31764	−	0.872722i
$823$	29.9363	+	17.2838i	1.04352	+	0.602474i	0.920827	−	0.389971i	$-0.127515\pi$
$823$	29.9363	+	17.2838i	1.04352	+	0.602474i	0.122688	+	0.992445i	$0.460848\pi$
$824$	−2.49923	+	13.4139i	−0.0870648	+	0.467296i
$825$		−	11.4208i		−	0.397620i
$826$	28.8215	+	1.77191i	1.00283	+	0.0616525i
$827$	−14.1384	+	24.4885i	−0.491642	+	0.851549i	−0.999954	−	0.00962429i	$-0.996936\pi$
$827$	−14.1384	+	24.4885i	−0.491642	+	0.851549i	0.508312	+	0.861173i	$0.330270\pi$
$828$	3.95680	+	2.98557i	0.137508	+	0.103756i
$829$			13.2093i			0.458779i	0.973335	+	0.229390i	$0.0736730\pi$
$829$			13.2093i			0.458779i	−0.973335	+	0.229390i	$0.926327\pi$
$830$	11.6978	+	0.719168i	0.406038	+	0.0249627i
$831$	−14.0078	−	24.2623i	−0.485927	−	0.841650i
$832$	−26.3542	−	32.6707i	−0.913667	−	1.13265i
$833$	−7.14509	−	12.3757i	−0.247563	−	0.428791i
$834$	−12.6424	+	19.0875i	−0.437769	+	0.660945i
$835$	16.6654			0.576729
$836$	48.5078	−	15.0505i	1.67768	−	0.520532i
$837$	6.61026			0.228484
$838$	−23.0449	+	34.7933i	−0.796074	+	1.20191i
$839$	−3.13222	−	5.42517i	−0.108136	−	0.187298i	0.806879	−	0.590717i	$-0.201155\pi$
$839$	−3.13222	−	5.42517i	−0.108136	−	0.187298i	−0.915015	+	0.403419i	$0.867822\pi$
$840$	−7.10829	+	8.30683i	−0.245259	+	0.286613i
$841$	1.85614	+	3.21494i	0.0640050	+	0.110860i
$842$	−28.1009	−	1.72761i	−0.968422	−	0.0595373i
$843$			52.3380i			1.80262i
$844$	−10.8209	+	14.3410i	−0.372470	+	0.493637i
$845$	7.26498	−	12.5833i	0.249923	−	0.432879i
$846$	−15.8583	−	0.974949i	−0.545220	−	0.0335194i
$847$			45.2354i			1.55431i
$848$	50.4453	−	14.3962i	1.73230	−	0.494369i
$849$	1.66151	+	0.959276i	0.0570230	+	0.0329223i
$850$	5.41416	+	3.58601i	0.185704	+	0.122999i
$851$	10.0183	−	17.3522i	0.343422	−	0.594824i
$852$	−0.256542	−	0.0316634i	−0.00878898	−	0.00108477i
$853$	6.57213	+	11.3833i	0.225026	+	0.389756i	0.956327	−	0.292299i	$-0.0944201\pi$
$853$	6.57213	+	11.3833i	0.225026	+	0.389756i	−0.731302	+	0.682054i	$0.761087\pi$
$854$	9.01469	+	18.0949i	0.308476	+	0.619196i
$855$	3.65594	+	0.366613i	0.125031	+	0.0125379i
$856$	2.63239	−	14.1286i	0.0899731	−	0.482905i
$857$	−46.8808	+	27.0667i	−1.60142	+	0.924579i	−0.610214	+	0.792236i	$0.708917\pi$
$857$	−46.8808	+	27.0667i	−1.60142	+	0.924579i	−0.991204	+	0.132343i	$0.957750\pi$
$858$	−70.6527	−	46.7960i	−2.41204	−	1.59759i
$859$	−14.5213	−	8.38389i	−0.495461	−	0.286055i	0.231376	−	0.972864i	$-0.425677\pi$
$859$	−14.5213	−	8.38389i	−0.495461	−	0.286055i	−0.726837	+	0.686810i	$0.759011\pi$
$860$	−1.25754	+	10.1888i	−0.0428819	+	0.347436i
$861$	−5.53805	+	9.59218i	−0.188736	+	0.326901i
$862$	31.9507	−	15.9175i	1.08825	−	0.542152i
$863$	−36.0297			−1.22646			−0.613232	−	0.789903i	$-0.710131\pi$
$863$	−36.0297			−1.22646			−0.613232	+	0.789903i	$0.710131\pi$
$864$	23.3616	−	5.14056i	0.794776	−	0.174885i
$865$	−13.2576	−	7.65428i	−0.450772	−	0.260253i
$866$	16.7035	+	33.5286i	0.567609	+	1.13935i
$867$	8.01056			0.272053
$868$	−5.67623	+	2.40520i	−0.192664	+	0.0816378i
$869$	−15.6491	+	9.03503i	−0.530860	+	0.306492i
$870$	−15.8264	−	0.972988i	−0.536566	−	0.0329874i
$871$	−27.2494	+	15.7324i	−0.923309	+	0.533073i
$872$	10.1046	+	28.6204i	0.342185	+	0.969210i
$873$			0.902694i			0.0305515i
$874$	−6.42302	−	16.9483i	−0.217262	−	0.573285i
$875$		−	1.97181i		−	0.0666592i
$876$	−25.6054	−	3.16031i	−0.865125	−	0.106777i
$877$	38.3700	−	22.1529i	1.29566	−	0.748052i	0.316012	−	0.948755i	$-0.397656\pi$
$877$	38.3700	−	22.1529i	1.29566	−	0.748052i	0.979652	+	0.200704i	$0.0643228\pi$
$878$	−1.29512	+	21.0661i	−0.0437081	+	0.710946i
$879$	0.509423	−	0.294115i	0.0171824	−	0.00992027i
$880$	5.66613	−	22.6043i	0.191005	−	0.761990i
$881$	3.44500			0.116065			0.0580326	−	0.998315i	$-0.481517\pi$
$881$	3.44500			0.116065			0.0580326	+	0.998315i	$0.481517\pi$
$882$	−3.32053	+	1.65425i	−0.111808	+	0.0557015i
$883$	30.8171	+	17.7923i	1.03708	+	0.598757i	0.919004	−	0.394248i	$-0.128995\pi$
$883$	30.8171	+	17.7923i	1.03708	+	0.598757i	0.118074	+	0.993005i	$0.462328\pi$
$884$	44.3685	−	18.8004i	1.49228	−	0.632325i
$885$	−20.2996			−0.682365
$886$	−13.5414	−	27.1812i	−0.454931	−	0.913171i
$887$	7.16791	−	12.4152i	0.240675	−	0.416861i	−0.720232	−	0.693733i	$-0.755965\pi$
$887$	7.16791	−	12.4152i	0.240675	−	0.416861i	0.960907	+	0.276873i	$0.0892980\pi$
$888$	12.5794	+	35.6299i	0.422135	+	1.19566i
$889$	−12.1850	−	7.03501i	−0.408672	−	0.235947i
$890$	9.05020	−	13.6640i	0.303363	−	0.458019i
$891$	54.5823	−	31.5131i	1.82857	−	1.05573i
$892$	8.81035	−	11.6764i	0.294992	−	0.390956i
$893$	47.1628	+	33.9229i	1.57824	+	1.13518i
$894$	27.7120	−	13.8058i	0.926829	−	0.461736i
$895$	2.71379	+	4.70041i	0.0907118	+	0.157118i
$896$	−18.1902	+	12.9145i	−0.607690	+	0.431443i
$897$	−15.1210	+	26.1904i	−0.504876	+	0.874471i
$898$	−11.7721	+	17.7736i	−0.392841	+	0.593113i
$899$	−7.74302	−	4.47043i	−0.258244	−	0.149097i
$900$	1.01543	−	1.34576i	0.0338478	−	0.0448587i
$901$			60.2231i			2.00632i
$902$	1.44869	−	23.5641i	0.0482360	−	0.784597i
$903$	9.92071	−	17.1832i	0.330141	−	0.571820i
$904$	29.8168	+	5.55536i	0.991693	+	0.184769i
$905$		−	22.3916i		−	0.744323i
$906$	1.48287	−	24.1201i	0.0492650	−	0.801335i
$907$	−14.2847	−	24.7418i	−0.474314	−	0.821537i	0.525253	−	0.850946i	$-0.323971\pi$
$907$	−14.2847	−	24.7418i	−0.474314	−	0.821537i	−0.999567	+	0.0294095i	$0.990637\pi$
$908$	8.44525	+	19.9307i	0.280266	+	0.661422i
$909$	2.21643	+	3.83897i	0.0735143	+	0.127331i
$910$	−12.1983	−	8.07938i	−0.404368	−	0.267829i
$911$	−18.0595			−0.598337			−0.299168	−	0.954200i	$-0.596709\pi$
$911$	−18.0595			−0.598337			−0.299168	+	0.954200i	$0.596709\pi$
$912$	32.1593	+	11.5772i	1.06490	+	0.383358i
$913$	48.2807			1.59786
$914$	−8.23141	−	5.45198i	−0.272271	−	0.180335i
$915$	−7.10592	−	12.3078i	−0.234914	−	0.406884i
$916$	2.19401	+	5.17782i	0.0724920	+	0.171080i
$917$	4.53094	+	7.84782i	0.149625	+	0.259158i
$918$	−1.68506	+	27.4088i	−0.0556152	+	0.904626i
$919$			39.3368i			1.29760i	0.760958	+	0.648801i	$0.224729\pi$
$919$			39.3368i			1.29760i	−0.760958	+	0.648801i	$0.775271\pi$
$920$	−8.17544	−	1.52322i	−0.269536	−	0.0502190i
$921$	13.0998	−	22.6895i	0.431652	−	0.747644i
$922$	2.79861	−	45.5217i	0.0921674	−	1.49918i
$923$		−	0.345925i		−	0.0113863i
$924$	−27.1278	+	35.9527i	−0.892439	+	1.18276i
$925$	−5.90170	−	3.40735i	−0.194047	−	0.112033i
$926$	−11.2348	+	16.9624i	−0.369199	+	0.557418i
$927$	−2.03323	+	3.52165i	−0.0667800	+	0.115666i
$928$	−30.8414	−	9.77766i	−1.01242	−	0.320967i
$929$	−8.68327	−	15.0399i	−0.284889	−	0.493442i	0.687693	−	0.726001i	$-0.258623\pi$
$929$	−8.68327	−	15.0399i	−0.284889	−	0.493442i	−0.972582	+	0.232559i	$0.925290\pi$
$930$	3.87909	−	1.93252i	0.127200	−	0.0633698i
$931$	13.4971	+	1.35347i	0.442351	+	0.0443582i
$932$	−14.4733	+	19.1816i	−0.474089	+	0.628313i
$933$	−5.05336	+	2.91756i	−0.165440	+	0.0955165i
$934$	31.0690	−	46.9080i	1.01661	−	1.53488i
$935$	23.1683	+	13.3762i	0.757684	+	0.437449i
$936$	−4.16465	−	11.7960i	−0.136126	−	0.385564i
$937$	28.9619	−	50.1636i	0.946145	−	1.63877i	0.192704	−	0.981257i	$-0.438274\pi$
$937$	28.9619	−	50.1636i	0.946145	−	1.63877i	0.753442	−	0.657515i	$-0.228392\pi$
$938$	7.45684	+	14.9679i	0.243475	+	0.488720i
$939$	19.0703			0.622335
$940$	24.5436	−	10.3999i	0.800523	−	0.339207i
$941$	5.75103	+	3.32036i	0.187478	+	0.108241i	0.590801	−	0.806817i	$-0.298812\pi$
$941$	5.75103	+	3.32036i	0.187478	+	0.108241i	−0.403323	+	0.915058i	$0.632145\pi$
$942$	26.8333	−	13.3681i	0.874277	−	0.435555i
$943$	−8.42495			−0.274354
$944$	−40.1776	−	10.0712i	−1.30767	−	0.327788i
$945$	7.22086	−	4.16897i	0.234895	−	0.135616i
$946$	−2.59514	+	42.2120i	−0.0843753	+	1.37243i
$947$	−48.9721	+	28.2740i	−1.59138	+	0.918783i	−0.598308	+	0.801266i	$0.704160\pi$
$947$	−48.9721	+	28.2740i	−1.59138	+	0.918783i	−0.993071	+	0.117517i	$0.962507\pi$
$948$	−12.0691	−	1.48962i	−0.391986	−	0.0483805i
$949$		−	34.5267i		−	1.12078i
$950$	−5.76435	+	2.18456i	−0.187020	+	0.0708764i
$951$			48.2083i			1.56326i
$952$	−8.52598	−	24.1491i	−0.276329	−	0.782677i
$953$	−13.7609	+	7.94489i	−0.445761	+	0.257360i	−0.706038	−	0.708174i	$-0.749519\pi$
$953$	−13.7609	+	7.94489i	−0.445761	+	0.257360i	0.260277	+	0.965534i	$0.416186\pi$
$954$	15.6047	+	0.959354i	0.505219	+	0.0310602i
$955$	−19.3273	+	11.1586i	−0.625416	+	0.361084i
$956$	−11.3106	+	4.79265i	−0.365810	+	0.155006i
$957$	−65.3206			−2.11152
$958$	−12.3163	−	24.7222i	−0.397922	−	0.798738i
$959$	−27.9102	−	16.1140i	−0.901269	−	0.520348i
$960$	12.2064	−	9.84642i	0.393960	−	0.317792i
$961$	−28.5563			−0.921171
$962$	−45.2610	+	22.5485i	−1.45927	+	0.726993i
$963$	2.14156	−	3.70928i	0.0690107	−	0.119530i
$964$	4.38163	−	35.5007i	0.141123	−	1.14340i
$965$	15.8249	+	9.13652i	0.509422	+	0.294115i
$966$	13.3999	+	8.87530i	0.431136	+	0.285558i
$967$	−1.80783	+	1.04375i	−0.0581360	+	0.0335648i	−0.528786	−	0.848755i	$-0.677353\pi$
$967$	−1.80783	+	1.04375i	−0.0581360	+	0.0335648i	0.470650	+	0.882320i	$0.344019\pi$
$968$	11.8850	−	63.7896i	0.382000	−	2.05027i
$969$	−22.9118	+	31.8541i	−0.736032	+	1.02330i
$970$	−0.675325	−	1.35556i	−0.0216834	−	0.0435245i
$971$	25.4380	+	44.0599i	0.816343	+	1.41395i	0.908359	+	0.418190i	$0.137336\pi$
$971$	25.4380	+	44.0599i	0.816343	+	1.41395i	−0.0920161	+	0.995758i	$0.529331\pi$
$972$	16.9152	+	2.08774i	0.542555	+	0.0669642i
$973$	−8.14179	+	14.1020i	−0.261014	+	0.452089i
$974$	26.8084	+	17.7562i	0.858995	+	0.568946i
$975$	8.90769	+	5.14286i	0.285274	+	0.164703i
$976$	−7.95801	−	27.8854i	−0.254730	−	0.892590i
$977$		−	44.2190i		−	1.41469i	−0.706869	−	0.707345i	$-0.749893\pi$
$977$		−	44.2190i		−	1.41469i	0.706869	−	0.707345i	$-0.250107\pi$
$978$	23.5830	+	1.44985i	0.754102	+	0.0463612i
$979$	33.7583	−	58.4711i	1.07892	−	1.86874i
$980$	3.74881	−	4.96832i	0.119751	−	0.158707i
$981$			9.04555i			0.288802i
$982$	−1.52633	−	0.0938369i	−0.0487072	−	0.00299446i
$983$	0.379884	+	0.657979i	0.0121164	+	0.0209863i	0.872020	−	0.489470i	$-0.162810\pi$
$983$	0.379884	+	0.657979i	0.0121164	+	0.0209863i	−0.859904	+	0.510456i	$0.829476\pi$
$984$	10.3298	−	12.0715i	0.329302	−	0.384826i
$985$	−0.0683768	−	0.118432i	−0.00217867	−	0.00377356i
$986$	20.5101	−	30.9661i	0.653173	−	0.986162i
$987$	−51.5183			−1.63985
$988$	−10.1047	+	44.6113i	−0.321474	+	1.41928i
$989$	15.0922			0.479905
$990$	3.83504	−	5.79015i	0.121886	−	0.184023i
$991$	3.23307	+	5.59985i	0.102702	+	0.177885i	0.912797	−	0.408414i	$-0.133918\pi$
$991$	3.23307	+	5.59985i	0.102702	+	0.177885i	−0.810095	+	0.586299i	$0.800585\pi$
$992$	8.63638	−	1.90038i	0.274205	−	0.0603371i
$993$	−4.99684	−	8.65478i	−0.158570	−	0.274651i
$994$	−0.183501	−	0.0112814i	−0.00582031	−	0.000357825i
$995$			7.47415i			0.236947i
$996$	25.9367	+	19.5703i	0.821835	+	0.620109i
$997$	−15.9475	+	27.6219i	−0.505063	+	0.874796i	0.494919	+	0.868939i	$0.335198\pi$
$997$	−15.9475	+	27.6219i	−0.505063	+	0.874796i	−0.999983	+	0.00585670i	$0.998136\pi$
$998$	−13.0002	−	0.799236i	−0.411514	−	0.0252994i
$999$		−	28.8165i		−	0.911713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.n.b.31.15	yes	40
4.3	odd	2	inner	380.2.n.b.31.9	✓	40
19.8	odd	6	inner	380.2.n.b.331.9	yes	40
76.27	even	6	inner	380.2.n.b.331.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.n.b.31.9	✓	40	4.3	odd	2	inner
380.2.n.b.31.15	yes	40	1.1	even	1	trivial
380.2.n.b.331.9	yes	40	19.8	odd	6	inner
380.2.n.b.331.15	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)

\(f(q)\)	\(=\)	\(q+(1.17905 + 0.780928i) q^{2} +(-0.980171 - 1.69771i) q^{3} +(0.780303 + 1.84150i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.170119 - 2.76712i) q^{6} -1.97181i q^{7} +(-0.518067 + 2.78058i) q^{8} +(-0.421469 + 0.730006i) q^{9} +O(q^{10})\)	\(q+(1.17905 + 0.780928i) q^{2} +(-0.980171 - 1.69771i) q^{3} +(0.780303 + 1.84150i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.170119 - 2.76712i) q^{6} -1.97181i q^{7} +(-0.518067 + 2.78058i) q^{8} +(-0.421469 + 0.730006i) q^{9} +(0.0867802 - 1.41155i) q^{10} -5.82590i q^{11} +(2.36150 - 3.12971i) q^{12} +(4.54395 + 2.62345i) q^{13} +(1.53984 - 2.32485i) q^{14} +(-0.980171 + 1.69771i) q^{15} +(-2.78226 + 2.87386i) q^{16} +(-2.29599 - 3.97677i) q^{17} +(-1.06701 + 0.531574i) q^{18} +(4.33715 + 0.434923i) q^{19} +(1.20464 - 1.59651i) q^{20} +(-3.34754 + 1.93271i) q^{21} +(4.54961 - 6.86901i) q^{22} +(-2.54628 - 1.47010i) q^{23} +(5.22839 - 1.84591i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.30880 + 6.64167i) q^{26} -4.22858 q^{27} +(3.63108 - 1.53861i) q^{28} +(4.95320 + 2.85973i) q^{29} +(-2.48145 + 1.23623i) q^{30} -1.56323 q^{31} +(-5.52469 + 1.21567i) q^{32} +(-9.89066 + 5.71038i) q^{33} +(0.398493 - 6.48181i) q^{34} +(-1.70763 + 0.985903i) q^{35} +(-1.67318 - 0.206510i) q^{36} +6.81470i q^{37} +(4.77406 + 3.89979i) q^{38} -10.2857i q^{39} +(2.66708 - 0.941629i) q^{40} +(2.48154 - 1.43272i) q^{41} +(-5.45622 - 0.335441i) q^{42} +(-4.44537 + 2.56654i) q^{43} +(10.7284 - 4.54597i) q^{44} +0.842938 q^{45} +(-1.85415 - 3.72178i) q^{46} +(11.5424 + 6.66401i) q^{47} +(7.60605 + 1.90658i) q^{48} +3.11198 q^{49} +(-1.26583 + 0.630620i) q^{50} +(-4.50093 + 7.79583i) q^{51} +(-1.28543 + 10.4148i) q^{52} +(-11.3578 - 6.55742i) q^{53} +(-4.98569 - 3.30222i) q^{54} +(-5.04538 + 2.91295i) q^{55} +(5.48276 + 1.02153i) q^{56} +(-3.51277 - 7.78950i) q^{57} +(3.60681 + 7.23985i) q^{58} +(5.17758 + 8.96782i) q^{59} +(-3.89116 - 0.480262i) q^{60} +(-3.62484 + 6.27840i) q^{61} +(-1.84313 - 1.22077i) q^{62} +(1.43943 + 0.831055i) q^{63} +(-7.46321 - 2.88105i) q^{64} -5.24690i q^{65} +(-16.1210 - 0.991095i) q^{66} +(-2.99842 + 5.19342i) q^{67} +(5.53167 - 7.33116i) q^{68} +5.76379i q^{69} +(-2.78330 - 0.171114i) q^{70} +(-0.0329647 - 0.0570966i) q^{71} +(-1.81149 - 1.55012i) q^{72} +(-3.29020 - 5.69879i) q^{73} +(-5.32179 + 8.03485i) q^{74} +1.96034 q^{75} +(2.58338 + 8.32623i) q^{76} -11.4875 q^{77} +(8.03240 - 12.1273i) q^{78} +(-1.55084 - 2.68613i) q^{79} +(3.87996 + 0.972575i) q^{80} +(5.40913 + 9.36890i) q^{81} +(4.04470 + 0.248663i) q^{82} +8.28724i q^{83} +(-6.17118 - 4.65641i) q^{84} +(-2.29599 + 3.97677i) q^{85} +(-7.24558 - 0.445449i) q^{86} -11.2121i q^{87} +(16.1994 + 3.01821i) q^{88} +(10.0364 + 5.79452i) q^{89} +(0.993863 + 0.658274i) q^{90} +(5.17293 - 8.95978i) q^{91} +(0.720315 - 5.83611i) q^{92} +(1.53224 + 2.65391i) q^{93} +(8.40492 + 16.8710i) q^{94} +(-1.79192 - 3.97354i) q^{95} +(7.47898 + 8.18772i) q^{96} +(0.927418 - 0.535445i) q^{97} +(3.66917 + 2.43024i) q^{98} +(4.25294 + 2.45544i) 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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