LMFDB - Embedded newform 380.2.n.b.31.19

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			31.19
Character	$\chi$	$=$	380.31
Dual form			380.2.n.b.331.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35812 + 0.394360i) q^{2} +(1.50046 + 2.59888i) q^{3} +(1.68896 + 1.07117i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.01291 + 4.12130i) q^{6} -4.06445i q^{7} +(1.87138 + 2.12084i) q^{8} +(-3.00277 + 5.20095i) q^{9} +O(q^{10})$	\(q+(1.35812 + 0.394360i) q^{2} +(1.50046 + 2.59888i) q^{3} +(1.68896 + 1.07117i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.01291 + 4.12130i) q^{6} -4.06445i q^{7} +(1.87138 + 2.12084i) q^{8} +(-3.00277 + 5.20095i) q^{9} +(-0.337532 - 1.37334i) q^{10} +3.65062i q^{11} +(-0.249628 + 5.99665i) q^{12} +(-1.47998 - 0.854464i) q^{13} +(1.60286 - 5.51999i) q^{14} +(1.50046 - 2.59888i) q^{15} +(1.70517 + 3.61834i) q^{16} +(-3.34305 - 5.79034i) q^{17} +(-6.12916 + 5.87932i) q^{18} +(0.270060 - 4.35052i) q^{19} +(0.0831836 - 1.99827i) q^{20} +(10.5630 - 6.09855i) q^{21} +(-1.43966 + 4.95797i) q^{22} +(2.43857 + 1.40791i) q^{23} +(-2.70386 + 8.04571i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.67301 - 1.74410i) q^{26} -9.01939 q^{27} +(4.35373 - 6.86469i) q^{28} +(-0.738597 - 0.426429i) q^{29} +(3.06269 - 2.93785i) q^{30} -4.54667 q^{31} +(0.888895 + 5.58658i) q^{32} +(-9.48751 + 5.47762i) q^{33} +(-2.25678 - 9.18232i) q^{34} +(-3.51991 + 2.03222i) q^{35} +(-10.6427 + 5.56771i) q^{36} -2.39078i q^{37} +(2.08245 - 5.80202i) q^{38} -5.12836i q^{39} +(0.901011 - 2.68108i) q^{40} +(-7.85414 + 4.53459i) q^{41} +(16.7508 - 4.11691i) q^{42} +(4.53033 - 2.61559i) q^{43} +(-3.91045 + 6.16575i) q^{44} +6.00554 q^{45} +(2.75663 + 2.87378i) q^{46} +(11.5138 + 6.64747i) q^{47} +(-6.84507 + 9.86071i) q^{48} -9.51973 q^{49} +(-1.02058 + 0.978983i) q^{50} +(10.0322 - 17.3764i) q^{51} +(-1.58434 - 3.02847i) q^{52} +(2.43293 + 1.40465i) q^{53} +(-12.2494 - 3.55689i) q^{54} +(3.16153 - 1.82531i) q^{55} +(8.62003 - 7.60611i) q^{56} +(11.7117 - 5.82594i) q^{57} +(-0.834934 - 0.870413i) q^{58} +(-0.0742391 - 0.128586i) q^{59} +(5.31807 - 2.78214i) q^{60} +(2.45086 - 4.24501i) q^{61} +(-6.17490 - 1.79302i) q^{62} +(21.1390 + 12.2046i) q^{63} +(-0.995901 + 7.93777i) q^{64} +1.70893i q^{65} +(-15.0453 + 3.69775i) q^{66} +(-1.62142 + 2.80837i) q^{67} +(0.556174 - 13.3606i) q^{68} +8.45004i q^{69} +(-5.58188 + 1.37188i) q^{70} +(-6.02376 - 10.4335i) q^{71} +(-16.6497 + 3.36455i) q^{72} +(-0.443085 - 0.767446i) q^{73} +(0.942830 - 3.24696i) q^{74} -3.00092 q^{75} +(5.11629 - 7.05858i) q^{76} +14.8378 q^{77} +(2.02242 - 6.96491i) q^{78} +(3.61536 + 6.26199i) q^{79} +(2.28099 - 3.28589i) q^{80} +(-4.52494 - 7.83742i) q^{81} +(-12.4551 + 3.06114i) q^{82} +14.7014i q^{83} +(24.3731 + 1.01460i) q^{84} +(-3.34305 + 5.79034i) q^{85} +(7.18419 - 1.76569i) q^{86} -2.55936i q^{87} +(-7.74237 + 6.83169i) q^{88} +(-4.29183 - 2.47789i) q^{89} +(8.15622 + 2.36834i) q^{90} +(-3.47292 + 6.01528i) q^{91} +(2.61053 + 4.99003i) q^{92} +(-6.82210 - 11.8162i) q^{93} +(13.0155 + 13.5686i) q^{94} +(-3.90270 + 1.94138i) q^{95} +(-13.1851 + 10.6926i) q^{96} +(-6.44598 + 3.72159i) q^{97} +(-12.9289 - 3.75420i) q^{98} +(-18.9867 - 10.9620i) 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 $

$2$	1.35812	+	0.394360i	0.960333	+	0.278855i
$2$	1.35812	+	0.394360i	0.960333	+	0.278855i
$3$	1.50046	+	2.59888i	0.866292	+	1.50046i	0.865759	+	0.500462i	$0.166836\pi$
$3$	1.50046	+	2.59888i	0.866292	+	1.50046i	0.000533103		1.00000i	$0.499830\pi$
$4$	1.68896	+	1.07117i	0.844480	+	0.535587i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.01291	+	4.12130i	0.413518	+	1.68251i
$7$		−	4.06445i		−	1.53622i	−0.640320	−	0.768108i	$-0.721198\pi$
$7$		−	4.06445i		−	1.53622i	0.640320	−	0.768108i	$-0.278802\pi$
$8$	1.87138	+	2.12084i	0.661631	+	0.749829i
$9$	−3.00277	+	5.20095i	−1.00092	+	1.73365i
$10$	−0.337532	−	1.37334i	−0.106737	−	0.434289i
$11$			3.65062i			1.10070i	0.834933	+	0.550352i	$0.185506\pi$
$11$			3.65062i			1.10070i	−0.834933	+	0.550352i	$0.814494\pi$
$12$	−0.249628	+	5.99665i	−0.0720613	+	1.73108i
$13$	−1.47998	−	0.854464i	−0.410471	−	0.236986i	0.280521	−	0.959848i	$-0.409493\pi$
$13$	−1.47998	−	0.854464i	−0.410471	−	0.236986i	−0.690992	+	0.722862i	$0.742826\pi$
$14$	1.60286	−	5.51999i	0.428381	−	1.47528i
$15$	1.50046	−	2.59888i	0.387417	−	0.671027i
$16$	1.70517	+	3.61834i	0.426293	+	0.904585i
$17$	−3.34305	−	5.79034i	−0.810809	−	1.40436i	−0.912298	−	0.409526i	$-0.865694\pi$
$17$	−3.34305	−	5.79034i	−0.810809	−	1.40436i	0.101489	−	0.994837i	$-0.467639\pi$
$18$	−6.12916	+	5.87932i	−1.44466	+	1.38577i
$19$	0.270060	−	4.35052i	0.0619561	−	0.998079i
$19$	0.270060	−	4.35052i	0.0619561	−	0.998079i
$20$	0.0831836	−	1.99827i	0.0186004	−	0.446827i
$21$	10.5630	−	6.09855i	2.30503	−	1.33081i
$22$	−1.43966	+	4.95797i	−0.306936	+	1.05704i
$23$	2.43857	+	1.40791i	0.508476	+	0.293569i	0.732207	−	0.681082i	$-0.238490\pi$
$23$	2.43857	+	1.40791i	0.508476	+	0.293569i	−0.223731	+	0.974651i	$0.571824\pi$
$24$	−2.70386	+	8.04571i	−0.551924	+	1.64232i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.67301	−	1.74410i	−0.328105	−	0.342047i
$27$	−9.01939			−1.73578
$28$	4.35373	−	6.86469i	0.822778	−	1.29730i
$29$	−0.738597	−	0.426429i	−0.137154	−	0.0791859i	0.429853	−	0.902899i	$-0.358565\pi$
$29$	−0.738597	−	0.426429i	−0.137154	−	0.0791859i	−0.567007	+	0.823713i	$0.691899\pi$
$30$	3.06269	−	2.93785i	0.559169	−	0.536376i
$31$	−4.54667			−0.816605			−0.408303	−	0.912847i	$-0.633879\pi$
$31$	−4.54667			−0.816605			−0.408303	+	0.912847i	$0.633879\pi$
$32$	0.888895	+	5.58658i	0.157136	+	0.987577i
$33$	−9.48751	+	5.47762i	−1.65156	+	0.953531i
$34$	−2.25678	−	9.18232i	−0.387034	−	1.57475i
$35$	−3.51991	+	2.03222i	−0.594974	+	0.343509i
$36$	−10.6427	+	5.56771i	−1.77378	+	0.927951i
$37$		−	2.39078i		−	0.393043i	−0.980500	−	0.196521i	$-0.937036\pi$
$37$		−	2.39078i		−	0.393043i	0.980500	−	0.196521i	$-0.0629645\pi$
$38$	2.08245	−	5.80202i	0.337817	−	0.941212i
$39$		−	5.12836i		−	0.821195i
$40$	0.901011	−	2.68108i	0.142462	−	0.423916i
$41$	−7.85414	+	4.53459i	−1.22661	+	0.708184i	−0.966319	−	0.257346i	$-0.917152\pi$
$41$	−7.85414	+	4.53459i	−1.22661	+	0.708184i	−0.260291	+	0.965530i	$0.583819\pi$
$42$	16.7508	−	4.11691i	2.58470	−	0.635254i
$43$	4.53033	−	2.61559i	0.690868	−	0.398873i	−0.113069	−	0.993587i	$-0.536068\pi$
$43$	4.53033	−	2.61559i	0.690868	−	0.398873i	0.803937	+	0.594714i	$0.202735\pi$
$44$	−3.91045	+	6.16575i	−0.589523	+	0.929523i
$45$	6.00554			0.895253
$46$	2.75663	+	2.87378i	0.406444	+	0.423715i
$47$	11.5138	+	6.64747i	1.67946	+	0.969634i	0.962008	+	0.273021i	$0.0880228\pi$
$47$	11.5138	+	6.64747i	1.67946	+	0.969634i	0.717447	+	0.696613i	$0.245311\pi$
$48$	−6.84507	+	9.86071i	−0.988000	+	1.42327i
$49$	−9.51973			−1.35996
$50$	−1.02058	+	0.978983i	−0.144332	+	0.138449i
$51$	10.0322	−	17.3764i	1.40480	−	2.43318i
$52$	−1.58434	−	3.02847i	−0.219708	−	0.419973i
$53$	2.43293	+	1.40465i	0.334189	+	0.192944i	0.657699	−	0.753280i	$-0.271530\pi$
$53$	2.43293	+	1.40465i	0.334189	+	0.192944i	−0.323510	+	0.946225i	$0.604863\pi$
$54$	−12.2494	−	3.55689i	−1.66693	−	0.484031i
$55$	3.16153	−	1.82531i	0.426301	−	0.246125i
$56$	8.62003	−	7.60611i	1.15190	−	1.01641i
$57$	11.7117	−	5.82594i	1.55125	−	0.771665i
$58$	−0.834934	−	0.870413i	−0.109632	−	0.114291i
$59$	−0.0742391	−	0.128586i	−0.00966511	−	0.0167405i	0.861152	−	0.508347i	$-0.169743\pi$
$59$	−0.0742391	−	0.128586i	−0.00966511	−	0.0167405i	−0.870818	+	0.491606i	$0.836410\pi$
$60$	5.31807	−	2.78214i	0.686560	−	0.359173i
$61$	2.45086	−	4.24501i	0.313800	−	0.543518i	−0.665382	−	0.746503i	$-0.731731\pi$
$61$	2.45086	−	4.24501i	0.313800	−	0.543518i	0.979182	+	0.202986i	$0.0650645\pi$
$62$	−6.17490	−	1.79302i	−0.784213	−	0.227714i
$63$	21.1390	+	12.2046i	2.66326	+	1.53763i
$64$	−0.995901	+	7.93777i	−0.124488	+	0.992221i
$65$			1.70893i			0.211966i
$66$	−15.0453	+	3.69775i	−1.85195	+	0.455161i
$67$	−1.62142	+	2.80837i	−0.198087	+	0.343097i	−0.947908	−	0.318543i	$-0.896806\pi$
$67$	−1.62142	+	2.80837i	−0.198087	+	0.343097i	0.749821	+	0.661641i	$0.230140\pi$
$68$	0.556174	−	13.3606i	0.0674460	−	1.62022i
$69$			8.45004i			1.01727i
$70$	−5.58188	+	1.37188i	−0.667163	+	0.163971i
$71$	−6.02376	−	10.4335i	−0.714888	−	1.23822i	−0.963003	−	0.269492i	$-0.913144\pi$
$71$	−6.02376	−	10.4335i	−0.714888	−	1.23822i	0.248114	−	0.968731i	$-0.420189\pi$
$72$	−16.6497	+	3.36455i	−1.96218	+	0.396516i
$73$	−0.443085	−	0.767446i	−0.0518592	−	0.0898228i	0.838930	−	0.544239i	$-0.183181\pi$
$73$	−0.443085	−	0.767446i	−0.0518592	−	0.0898228i	−0.890790	+	0.454416i	$0.849848\pi$
$74$	0.942830	−	3.24696i	0.109602	−	0.377452i
$75$	−3.00092			−0.346517
$76$	5.11629	−	7.05858i	0.586879	−	0.809675i
$77$	14.8378			1.69092
$78$	2.02242	−	6.96491i	0.228994	−	0.788621i
$79$	3.61536	+	6.26199i	0.406760	+	0.704529i	0.994525	−	0.104503i	$-0.0333252\pi$
$79$	3.61536	+	6.26199i	0.406760	+	0.704529i	−0.587765	+	0.809032i	$0.699992\pi$
$80$	2.28099	−	3.28589i	0.255022	−	0.367374i
$81$	−4.52494	−	7.83742i	−0.502771	−	0.870825i
$82$	−12.4551	+	3.06114i	−1.37544	+	0.338047i
$83$			14.7014i			1.61368i	0.590768	+	0.806842i	$0.298825\pi$
$83$			14.7014i			1.61368i	−0.590768	+	0.806842i	$0.701175\pi$
$84$	24.3731	+	1.01460i	2.65932	+	0.110702i
$85$	−3.34305	+	5.79034i	−0.362605	+	0.628050i
$86$	7.18419	−	1.76569i	0.774692	−	0.190399i
$87$		−	2.55936i		−	0.274392i
$88$	−7.74237	+	6.83169i	−0.825340	+	0.728260i
$89$	−4.29183	−	2.47789i	−0.454934	−	0.262656i	0.254978	−	0.966947i	$-0.417932\pi$
$89$	−4.29183	−	2.47789i	−0.454934	−	0.262656i	−0.709912	+	0.704291i	$0.751265\pi$
$90$	8.15622	+	2.36834i	0.859741	+	0.249645i
$91$	−3.47292	+	6.01528i	−0.364061	+	0.630573i
$92$	2.61053	+	4.99003i	0.272166	+	0.520246i
$93$	−6.82210	−	11.8162i	−0.707419	−	1.22529i
$94$	13.0155	+	13.5686i	1.34245	+	1.39950i
$95$	−3.90270	+	1.94138i	−0.400408	+	0.199182i
$96$	−13.1851	+	10.6926i	−1.34570	+	1.09131i
$97$	−6.44598	+	3.72159i	−0.654490	+	0.377870i	−0.790174	−	0.612882i	$-0.790010\pi$
$97$	−6.44598	+	3.72159i	−0.654490	+	0.377870i	0.135684	+	0.990752i	$0.456677\pi$
$98$	−12.9289	−	3.75420i	−1.30602	−	0.379232i
$99$	−18.9867	−	10.9620i	−1.90823	−	1.10172i
$100$	−1.77214	+	0.927096i	−0.177214	+	0.0927096i
$101$	9.73796	−	16.8666i	0.968963	−	1.67829i	0.270395	−	0.962749i	$-0.412846\pi$
$101$	9.73796	−	16.8666i	0.968963	−	1.67829i	0.698568	−	0.715544i	$-0.253821\pi$
$102$	20.4775	−	19.6428i	2.02757	−	1.94493i
$103$	−4.40113			−0.433656			−0.216828	−	0.976210i	$-0.569571\pi$
$103$	−4.40113			−0.433656			−0.216828	+	0.976210i	$0.569571\pi$
$104$	−0.957411	−	4.73781i	−0.0938819	−	0.464581i
$105$	−10.5630	−	6.09855i	−1.03084	−	0.595157i
$106$	2.75027	+	2.86714i	0.267130	+	0.278481i
$107$	14.0626			1.35949			0.679743	−	0.733450i	$-0.262091\pi$
$107$	14.0626			1.35949			0.679743	+	0.733450i	$0.262091\pi$
$108$	−15.2334	−	9.66133i	−1.46583	−	0.929662i
$109$	−6.68725	+	3.86089i	−0.640522	+	0.369806i	−0.784816	−	0.619729i	$-0.787242\pi$
$109$	−6.68725	+	3.86089i	−0.640522	+	0.369806i	0.144293	+	0.989535i	$0.453909\pi$
$110$	5.01356	−	1.23220i	0.478024	−	0.117486i
$111$	6.21335	−	3.58728i	0.589745	−	0.340490i
$112$	14.7066	−	6.93059i	1.38964	−	0.654879i
$113$			1.76989i			0.166497i	0.996529	+	0.0832487i	$0.0265296\pi$
$113$			1.76989i			0.166497i	−0.996529	+	0.0832487i	$0.973470\pi$
$114$	18.2034	−	3.29368i	1.70490	−	0.308482i
$115$		−	2.81581i		−	0.262576i
$116$	−0.790681	−	1.51139i	−0.0734129	−	0.140329i
$117$	8.88805	−	5.13152i	0.821700	−	0.474409i
$118$	−0.0501162	−	0.203912i	−0.00461357	−	0.0187716i
$119$	−23.5345	+	13.5877i	−2.15741	+	1.24558i
$120$	8.31972	−	1.68124i	0.759483	−	0.153475i
$121$	−2.32704			−0.211549
$122$	5.00261	−	4.79869i	0.452915	−	0.434453i
$123$	−23.5697	−	13.6080i	−2.12521	−	1.22699i
$124$	−7.67914	−	4.87027i	−0.689607	−	0.437363i
$125$	1.00000			0.0894427
$126$	23.8962	+	24.9116i	2.12884	+	2.21930i
$127$	−8.88518	+	15.3896i	−0.788432	+	1.36560i	0.138495	+	0.990363i	$0.455773\pi$
$127$	−8.88518	+	15.3896i	−0.788432	+	1.36560i	−0.926927	+	0.375241i	$0.877560\pi$
$128$	−4.48289	+	10.3877i	−0.396235	+	0.918149i
$129$	13.5952	+	7.84917i	1.19699	+	0.691081i
$130$	−0.673933	+	2.32092i	−0.0591078	+	0.203558i
$131$	−4.43126	+	2.55839i	−0.387161	+	0.223528i	−0.680929	−	0.732349i	$-0.738424\pi$
$131$	−4.43126	+	2.55839i	−0.387161	+	0.223528i	0.293768	+	0.955877i	$0.405091\pi$
$132$	−21.8915	−	0.911296i	−1.90541	−	0.0793181i
$133$	−17.6825	−	1.09765i	−1.53327	−	0.0951780i
$134$	−3.30958	+	3.17468i	−0.285904	+	0.274250i
$135$	4.50969	+	7.81102i	0.388133	+	0.672266i
$136$	6.02425	−	17.9260i	0.516575	−	1.53714i
$137$	−3.13641	+	5.43242i	−0.267962	+	0.464123i	−0.968335	−	0.249653i	$-0.919683\pi$
$137$	−3.13641	+	5.43242i	−0.267962	+	0.464123i	0.700374	+	0.713776i	$0.253017\pi$
$138$	−3.33236	+	11.4761i	−0.283669	+	0.976914i
$139$	7.77964	+	4.49158i	0.659860	+	0.380970i	0.792224	−	0.610231i	$-0.208923\pi$
$139$	7.77964	+	4.49158i	0.659860	+	0.380970i	−0.132364	+	0.991201i	$0.542257\pi$
$140$	−8.12186	−	0.338095i	−0.686423	−	0.0285743i
$141$			39.8971i			3.35994i
$142$	−4.06643	−	16.5454i	−0.341247	−	1.38846i
$143$	3.11932	−	5.40283i	0.260851	−	0.451807i
$144$	−23.9390	−	1.99652i	−1.99492	−	0.166377i
$145$			0.852858i			0.0708260i
$146$	−0.299111	−	1.21702i	−0.0247546	−	0.100721i
$147$	−14.2840	−	24.7406i	−1.17812	−	2.04057i
$148$	2.56095	−	4.03794i	0.210508	−	0.331917i
$149$	1.25425	+	2.17242i	0.102752	+	0.177972i	0.912818	−	0.408368i	$-0.133902\pi$
$149$	1.25425	+	2.17242i	0.102752	+	0.177972i	−0.810065	+	0.586339i	$0.800568\pi$
$150$	−4.07560	−	1.18344i	−0.332772	−	0.0966278i
$151$	−17.0015			−1.38356			−0.691780	−	0.722108i	$-0.743173\pi$
$151$	−17.0015			−1.38356			−0.691780	+	0.722108i	$0.743173\pi$
$152$	9.73214	−	7.56872i	0.789381	−	0.613904i
$153$	40.1537			3.24623
$154$	20.1514	+	5.85142i	1.62385	+	0.471521i
$155$	2.27333	+	3.93753i	0.182599	+	0.316270i
$156$	5.49337	−	8.66160i	0.439821	−	0.693483i
$157$	−7.05683	−	12.2228i	−0.563196	−	0.975484i	−0.997215	−	0.0745804i	$-0.976238\pi$
$157$	−7.05683	−	12.2228i	−0.563196	−	0.975484i	0.434019	−	0.900904i	$-0.357095\pi$
$158$	2.44060	+	9.93026i	0.194164	+	0.790009i
$159$			8.43052i			0.668584i
$160$	4.39367	−	3.56310i	0.347350	−	0.281687i
$161$	5.72236	−	9.91143i	0.450986	−	0.781130i
$162$	−3.05463	−	12.4286i	−0.239994	−	0.976482i
$163$		−	7.37218i		−	0.577434i	−0.957415	−	0.288717i	$-0.906771\pi$
$163$		−	7.37218i		−	0.577434i	0.957415	−	0.288717i	$-0.0932286\pi$
$164$	−18.1227	−	0.754407i	−1.41514	−	0.0589093i
$165$	9.48751	+	5.47762i	0.738602	+	0.426432i
$166$	−5.79763	+	19.9662i	−0.449983	+	1.54967i
$167$	1.33525	−	2.31273i	0.103325	−	0.178964i	−0.809728	−	0.586806i	$-0.800385\pi$
$167$	1.33525	−	2.31273i	0.103325	−	0.178964i	0.913053	+	0.407842i	$0.133718\pi$
$168$	32.7014	+	10.9897i	2.52296	+	0.847875i
$169$	−5.03978	−	8.72916i	−0.387676	−	0.671474i
$170$	−6.82373	+	6.54558i	−0.523356	+	0.502023i
$171$	21.8159	+	14.4682i	1.66831	+	1.10641i
$172$	10.4533	+	0.435148i	0.797056	+	0.0331797i
$173$	0.387275	−	0.223594i	0.0294440	−	0.0169995i	−0.485206	−	0.874400i	$-0.661255\pi$
$173$	0.387275	−	0.223594i	0.0294440	−	0.0169995i	0.514650	+	0.857401i	$0.327922\pi$
$174$	1.00931	−	3.47591i	0.0765156	−	0.263508i
$175$	3.51991	+	2.03222i	0.266081	+	0.153622i
$176$	−13.2092	+	6.22494i	−0.995680	+	0.469223i
$177$	0.222786	−	0.385877i	0.0167456	−	0.0290043i
$178$	−4.85163	−	5.05779i	−0.363645	−	0.379098i
$179$	−8.63304			−0.645263			−0.322632	−	0.946525i	$-0.604568\pi$
$179$	−8.63304			−0.645263			−0.322632	+	0.946525i	$0.604568\pi$
$180$	10.1431	+	6.43298i	0.756023	+	0.479486i
$181$	−6.27009	−	3.62004i	−0.466052	−	0.269075i	0.248533	−	0.968623i	$-0.420051\pi$
$181$	−6.27009	−	3.62004i	−0.466052	−	0.269075i	−0.714586	+	0.699548i	$0.753385\pi$
$182$	−7.08882	+	6.79987i	−0.525458	+	0.504040i
$183$	14.7097			1.08737
$184$	1.57753	+	7.80653i	0.116297	+	0.575505i
$185$	−2.07048	+	1.19539i	−0.152225	+	0.0878870i
$186$	−4.60536	−	18.7382i	−0.337681	−	1.37395i
$187$	21.1383	−	12.2042i	1.54579	−	0.892461i
$188$	12.3257	+	23.5606i	0.898943	+	1.71833i
$189$			36.6588i			2.66654i
$190$	−6.06592	+	1.09756i	−0.440068	+	0.0796252i
$191$			17.0200i			1.23152i	0.787933	+	0.615761i	$0.211151\pi$
$191$			17.0200i			1.23152i	−0.787933	+	0.615761i	$0.788849\pi$
$192$	−22.1236	+	9.32210i	−1.59663	+	0.672764i
$193$	4.53847	−	2.62029i	0.326686	−	0.188612i	−0.327683	−	0.944788i	$-0.606268\pi$
$193$	4.53847	−	2.62029i	0.326686	−	0.188612i	0.654369	+	0.756175i	$0.272934\pi$
$194$	−10.2220	+	2.51231i	−0.733900	+	0.180374i
$195$	−4.44129	+	2.56418i	−0.318047	+	0.183625i
$196$	−16.0785	−	10.1973i	−1.14846	−	0.728378i
$197$	−2.61752			−0.186491			−0.0932453	−	0.995643i	$-0.529724\pi$
$197$	−2.61752			−0.186491			−0.0932453	+	0.995643i	$0.529724\pi$
$198$	−21.4632	−	22.3752i	−1.52532	−	1.59014i
$199$	7.89806	+	4.55995i	0.559879	+	0.323246i	0.753097	−	0.657910i	$-0.228559\pi$
$199$	7.89806	+	4.55995i	0.559879	+	0.323246i	−0.193218	+	0.981156i	$0.561892\pi$
$200$	−2.77239	+	0.560241i	−0.196037	+	0.0396150i
$201$	−9.73149			−0.686406
$202$	19.8768	−	19.0666i	1.39853	−	1.34152i
$203$	−1.73320	+	3.00199i	−0.121647	+	0.210698i
$204$	35.5572	−	18.6017i	2.48950	−	1.30238i
$205$	7.85414	+	4.53459i	0.548557	+	0.316710i
$206$	−5.97725	−	1.73563i	−0.416455	−	0.120927i
$207$	−14.6449	+	8.45524i	−1.01789	+	0.587680i
$208$	0.568127	−	6.81206i	0.0393925	−	0.472332i
$209$	15.8821	+	0.985888i	1.09859	+	0.0681953i
$210$	−11.9408	−	12.4482i	−0.823990	−	0.859005i
$211$	1.10580	+	1.91530i	0.0761265	+	0.131855i	0.901576	−	0.432622i	$-0.142411\pi$
$211$	1.10580	+	1.91530i	0.0761265	+	0.131855i	−0.825449	+	0.564477i	$0.809078\pi$
$212$	2.60450	+	4.97850i	0.178878	+	0.341925i
$213$	18.0768	−	31.3100i	1.23860	−	2.14533i
$214$	19.0987	+	5.54574i	1.30556	+	0.379099i
$215$	−4.53033	−	2.61559i	−0.308966	−	0.178381i
$216$	−16.8787	−	19.1287i	−1.14845	−	1.30154i
$217$			18.4797i			1.25448i
$218$	−10.6046	+	2.60635i	−0.718237	+	0.176524i
$219$	1.32966	−	2.30305i	0.0898504	−	0.155626i
$220$	7.29493	+	0.303672i	0.491824	+	0.0204735i
$221$			11.4261i			0.768601i
$222$	9.85314	−	2.42165i	0.661299	−	0.162530i
$223$	−9.94022	−	17.2170i	−0.665646	−	1.15293i	−0.979110	−	0.203333i	$-0.934823\pi$
$223$	−9.94022	−	17.2170i	−0.665646	−	1.15293i	0.313463	−	0.949600i	$-0.398511\pi$
$224$	22.7064	−	3.61287i	1.51713	−	0.241395i
$225$	−3.00277	−	5.20095i	−0.200185	−	0.346730i
$226$	−0.697975	+	2.40372i	−0.0464286	+	0.159893i
$227$	−7.90411			−0.524614			−0.262307	−	0.964984i	$-0.584483\pi$
$227$	−7.90411			−0.524614			−0.262307	+	0.964984i	$0.584483\pi$
$228$	26.0212	+	2.70547i	1.72329	+	0.179174i
$229$	4.20077			0.277594			0.138797	−	0.990321i	$-0.455676\pi$
$229$	4.20077			0.277594			0.138797	+	0.990321i	$0.455676\pi$
$230$	1.11044	−	3.82420i	0.0732206	−	0.252161i
$231$	22.2635	+	38.5615i	1.46483	+	2.53716i
$232$	−0.477806	−	2.36445i	−0.0313695	−	0.155234i
$233$	8.64423	+	14.9722i	0.566302	+	0.980864i	0.996927	+	0.0783331i	$0.0249598\pi$
$233$	8.64423	+	14.9722i	0.566302	+	0.980864i	−0.430625	+	0.902531i	$0.641707\pi$
$234$	14.0947	−	3.46411i	0.921397	−	0.226456i
$235$		−	13.2949i		−	0.867267i
$236$	0.0123510	−	0.296700i	0.000803979	−	0.0193135i
$237$	−10.8494	+	18.7917i	−0.704746	+	1.22066i
$238$	−37.3211	+	9.17255i	−2.41916	+	0.594568i
$239$		−	19.0862i		−	1.23458i	−0.786734	−	0.617292i	$-0.788230\pi$
$239$		−	19.0862i		−	1.23458i	0.786734	−	0.617292i	$-0.211770\pi$
$240$	11.9622	+	0.997646i	0.772154	+	0.0643978i
$241$	−20.0325	−	11.5657i	−1.29040	−	0.745015i	−0.311679	−	0.950188i	$-0.600891\pi$
$241$	−20.0325	−	11.5657i	−1.29040	−	0.745015i	−0.978726	+	0.205172i	$0.934225\pi$
$242$	−3.16039	−	0.917691i	−0.203157	−	0.0589914i
$243$	0.0499075	−	0.0864424i	0.00320157	−	0.00554528i
$244$	8.68654	−	4.54436i	0.556099	−	0.290923i
$245$	4.75987	+	8.24433i	0.304097	+	0.526711i
$246$	−26.6439	−	27.7761i	−1.69875	−	1.77094i
$247$	−4.11705	+	6.20791i	−0.261962	+	0.395000i
$248$	−8.50853	−	9.64274i	−0.540292	−	0.612315i
$249$	−38.2070	+	22.0588i	−2.42127	+	1.39792i
$250$	1.35812	+	0.394360i	0.0858948	+	0.0249415i
$251$	1.07434	+	0.620270i	0.0678117	+	0.0391511i	0.533522	−	0.845786i	$-0.320868\pi$
$251$	1.07434	+	0.620270i	0.0678117	+	0.0391511i	−0.465711	+	0.884937i	$0.654201\pi$
$252$	22.6297	+	43.2566i	1.42553	+	2.72491i
$253$	−5.13974	+	8.90228i	−0.323132	+	0.559682i
$254$	−18.1361	+	17.3969i	−1.13796	+	1.09158i
$255$	−20.0645			−1.25649
$256$	−10.1848	+	12.3398i	−0.636548	+	0.771237i
$257$	26.1876	+	15.1194i	1.63354	+	0.943124i	0.982990	+	0.183659i	$0.0587944\pi$
$257$	26.1876	+	15.1194i	1.63354	+	0.943124i	0.650549	+	0.759465i	$0.274539\pi$
$258$	15.3684	+	16.0215i	0.956796	+	0.997454i
$259$	−9.71722			−0.603799
$260$	−1.83056	+	2.88631i	−0.113526	+	0.179001i
$261$	4.43567	−	2.56094i	0.274561	−	0.158518i
$262$	−7.02709	+	1.72708i	−0.434135	+	0.106699i
$263$	9.22300	−	5.32490i	0.568715	−	0.328348i	−0.187921	−	0.982184i	$-0.560175\pi$
$263$	9.22300	−	5.32490i	0.568715	−	0.328348i	0.756636	+	0.653837i	$0.226842\pi$
$264$	−29.3718	−	9.87078i	−1.80771	−	0.607505i
$265$		−	2.80931i		−	0.172574i
$266$	−23.5820	−	8.46400i	−1.44591	−	0.518961i
$267$		−	14.8719i		−	0.910147i
$268$	−5.74676	+	3.00641i	−0.351039	+	0.183646i
$269$	2.43148	−	1.40382i	0.148250	−	0.0855922i	−0.424040	−	0.905643i	$-0.639388\pi$
$269$	2.43148	−	1.40382i	0.148250	−	0.0855922i	0.572290	+	0.820051i	$0.306055\pi$
$270$	3.04434	+	12.3867i	0.185272	+	0.753832i
$271$	7.28686	−	4.20707i	0.442646	−	0.255562i	−0.262074	−	0.965048i	$-0.584406\pi$
$271$	7.28686	−	4.20707i	0.442646	−	0.255562i	0.704719	+	0.709486i	$0.251073\pi$
$272$	15.2509	−	21.9698i	0.924723	−	1.33212i
$273$	−20.8440			−1.26153
$274$	−6.40194	+	6.14099i	−0.386755	+	0.370991i
$275$	−3.16153	−	1.82531i	−0.190647	−	0.110070i
$276$	−9.05146	+	14.2718i	−0.544834	+	0.859060i
$277$	0.788700			0.0473884			0.0236942	−	0.999719i	$-0.492457\pi$
$277$	0.788700			0.0473884			0.0236942	+	0.999719i	$0.492457\pi$
$278$	8.79435	+	9.16806i	0.527450	+	0.549864i
$279$	13.6526	−	23.6470i	0.817359	−	1.41571i
$280$	−10.8971	−	3.66211i	−0.651226	−	0.218853i
$281$	22.2686	+	12.8568i	1.32843	+	0.766971i	0.985057	−	0.172227i	$-0.0550962\pi$
$281$	22.2686	+	12.8568i	1.32843	+	0.766971i	0.343376	+	0.939198i	$0.388429\pi$
$282$	−15.7338	+	54.1849i	−0.936936	+	3.22667i
$283$	−7.64565	+	4.41422i	−0.454487	+	0.262398i	−0.709723	−	0.704481i	$-0.751180\pi$
$283$	−7.64565	+	4.41422i	−0.454487	+	0.262398i	0.255236	+	0.966879i	$0.417847\pi$
$284$	1.00216	−	24.0742i	0.0594670	−	1.42854i
$285$	−10.9013	−	7.22965i	−0.645735	−	0.428247i
$286$	6.36707	−	6.10753i	0.376493	−	0.361146i
$287$	18.4306	+	31.9227i	1.08792	+	1.88434i
$288$	−31.7247	−	12.1521i	−1.86939	−	0.716070i
$289$	−13.8520	+	23.9924i	−0.814824	+	1.41132i
$290$	−0.336333	+	1.15828i	−0.0197502	+	0.0680166i
$291$	−19.3439	−	11.1682i	−1.13396	−	0.654692i
$292$	0.0737148	−	1.77081i	0.00431384	−	0.103629i
$293$		−	11.5790i		−	0.676451i	−0.941065	−	0.338225i	$-0.890173\pi$
$293$		−	11.5790i		−	0.676451i	0.941065	−	0.338225i	$-0.109827\pi$
$294$	−9.64262	−	39.2337i	−0.562369	−	2.28815i
$295$	−0.0742391	+	0.128586i	−0.00432237	+	0.00748656i
$296$	5.07047	−	4.47406i	0.294715	−	0.260049i
$297$		−	32.9264i		−	1.91058i
$298$	0.846700	+	3.44503i	0.0490480	+	0.199565i
$299$	−2.40601	−	4.16734i	−0.139143	−	0.241003i
$300$	−5.06844	−	3.21451i	−0.292626	−	0.185590i
$301$	−10.6309	−	18.4133i	−0.612756	−	1.06132i
$302$	−23.0900	−	6.70470i	−1.32868	−	0.385812i
$303$	58.4457			3.35762
$304$	16.2022	−	6.44123i	0.929259	−	0.369430i
$305$	−4.90171			−0.280671
$306$	54.5333	+	15.8350i	3.11746	+	0.905227i
$307$	9.23778	+	16.0003i	0.527228	+	0.913185i	0.999496	+	0.0317307i	$0.0101019\pi$
$307$	9.23778	+	16.0003i	0.527228	+	0.913185i	−0.472269	+	0.881455i	$0.656565\pi$
$308$	25.0604	+	15.8938i	1.42795	+	0.905634i
$309$	−6.60373	−	11.4380i	−0.375673	−	0.650685i
$310$	1.53465	+	6.24413i	0.0871621	+	0.354643i
$311$			17.0624i			0.967517i	0.875201	+	0.483759i	$0.160729\pi$
$311$			17.0624i			0.967517i	−0.875201	+	0.483759i	$0.839271\pi$
$312$	10.8764	−	9.59709i	0.615756	−	0.543329i
$313$	15.4392	−	26.7415i	0.872676	−	1.51152i	0.0134570	−	0.999909i	$-0.495716\pi$
$313$	15.4392	−	26.7415i	0.872676	−	1.51152i	0.859218	−	0.511609i	$-0.170950\pi$
$314$	−4.76381	−	19.3829i	−0.268838	−	1.09384i
$315$		−	24.4092i		−	1.37530i
$316$	−0.601477	+	14.4489i	−0.0338357	+	0.812816i
$317$	−1.78528	−	1.03073i	−0.100272	−	0.0578918i	0.449026	−	0.893519i	$-0.351771\pi$
$317$	−1.78528	−	1.03073i	−0.100272	−	0.0578918i	−0.549297	+	0.835627i	$0.685105\pi$
$318$	−3.32466	+	11.4496i	−0.186438	+	0.642063i
$319$	1.55673	−	2.69634i	0.0871602	−	0.150966i
$320$	7.37226	−	3.10641i	0.412122	−	0.173654i
$321$	21.1005	+	36.5471i	1.17771	+	2.03986i
$322$	11.6803	−	11.2042i	0.650918	−	0.624386i
$323$	−26.0938	+	12.9803i	−1.45190	+	0.722243i
$324$	0.752801	−	18.0841i	0.0418223	−	1.00467i
$325$	1.47998	−	0.854464i	0.0820943	−	0.0473971i
$326$	2.90729	−	10.0123i	0.161020	−	0.554529i
$327$	−20.0679	−	11.5862i	−1.10976	−	0.640720i
$328$	−24.3152	−	8.17143i	−1.34258	−	0.451192i
$329$	27.0183	−	46.7971i	1.48957	−	2.58001i
$330$	10.7250	+	11.1807i	0.590391	+	0.615479i
$331$	20.3110			1.11639			0.558196	−	0.829709i	$-0.311494\pi$
$331$	20.3110			1.11639			0.558196	+	0.829709i	$0.311494\pi$
$332$	−15.7477	+	24.8300i	−0.864268	+	1.36272i
$333$	12.4344	+	7.17898i	0.681398	+	0.393405i
$334$	2.72548	−	2.61438i	0.149132	−	0.143053i
$335$	3.24283			0.177175
$336$	40.0784	+	27.8214i	2.18645	+	1.51778i
$337$	−5.64629	+	3.25989i	−0.307573	+	0.177577i	−0.645840	−	0.763473i	$-0.723493\pi$
$337$	−5.64629	+	3.25989i	−0.307573	+	0.177577i	0.338267	+	0.941050i	$0.390159\pi$
$338$	−3.40218	−	13.8427i	−0.185054	−	0.752944i
$339$	−4.59973	+	2.65565i	−0.249823	+	0.144235i
$340$	−11.8487	+	6.19866i	−0.642588	+	0.336169i
$341$		−	16.5982i		−	0.898841i
$342$	23.9229	+	28.2528i	1.29360	+	1.52774i
$343$			10.2413i			0.552980i
$344$	14.0252	+	4.71334i	0.756187	+	0.254126i
$345$	7.31795	−	4.22502i	0.393985	−	0.227467i
$346$	0.614142	−	0.150940i	0.0330165	−	0.00811459i
$347$	23.7146	−	13.6916i	1.27307	−	0.735005i	0.297502	−	0.954721i	$-0.403846\pi$
$347$	23.7146	−	13.6916i	1.27307	−	0.735005i	0.975564	+	0.219716i	$0.0705130\pi$
$348$	2.74152	−	4.32266i	0.146961	−	0.231719i
$349$	26.9535			1.44279			0.721394	−	0.692525i	$-0.243502\pi$
$349$	26.9535			1.44279			0.721394	+	0.692525i	$0.243502\pi$
$350$	3.97903	+	4.14811i	0.212688	+	0.221726i
$351$	13.3485	+	7.70674i	0.712489	+	0.411356i
$352$	−20.3945	+	3.24502i	−1.08703	+	0.172960i
$353$	−0.186560			−0.00992958			−0.00496479	−	0.999988i	$-0.501580\pi$
$353$	−0.186560			−0.00992958			−0.00496479	+	0.999988i	$0.501580\pi$
$354$	0.454744	−	0.436207i	0.0241693	−	0.0231842i
$355$	−6.02376	+	10.4335i	−0.319708	+	0.553750i
$356$	−4.59448	−	8.78236i	−0.243507	−	0.465464i
$357$	−70.6253	−	40.7755i	−3.73789	−	2.15807i
$358$	−11.7247	−	3.40452i	−0.619668	−	0.179935i
$359$	20.2598	−	11.6970i	1.06927	−	0.617343i	0.141288	−	0.989969i	$-0.454876\pi$
$359$	20.2598	−	11.6970i	1.06927	−	0.617343i	0.927982	+	0.372625i	$0.121542\pi$
$360$	11.2386	+	12.7368i	0.592327	+	0.671287i
$361$	−18.8541	−	2.34981i	−0.992323	−	0.123674i
$362$	−7.08792	−	7.38911i	−0.372533	−	0.388363i
$363$	−3.49163	−	6.04768i	−0.183263	−	0.317421i
$364$	−12.3090	+	6.43947i	−0.645169	+	0.337520i
$365$	−0.443085	+	0.767446i	−0.0231921	+	0.0401700i
$366$	19.9774	+	5.80090i	1.04424	+	0.303218i
$367$	−11.6804	−	6.74365i	−0.609709	−	0.352016i	0.163142	−	0.986603i	$-0.447837\pi$
$367$	−11.6804	−	6.74365i	−0.609709	−	0.352016i	−0.772852	+	0.634587i	$0.781170\pi$
$368$	−0.936107	+	11.2243i	−0.0487980	+	0.585106i
$369$		−	54.4653i		−	2.83535i
$370$	−3.28337	+	0.806967i	−0.170694	+	0.0419522i
$371$	5.70914	−	9.88853i	0.296404	−	0.513387i
$372$	1.13497	−	27.2648i	0.0588456	−	1.41361i
$373$		−	25.2380i		−	1.30677i	−0.757024	−	0.653387i	$-0.773348\pi$
$373$		−	25.2380i		−	1.30677i	0.757024	−	0.653387i	$-0.226652\pi$
$374$	33.5212	−	8.23864i	1.73334	−	0.426010i
$375$	1.50046	+	2.59888i	0.0774835	+	0.134205i
$376$	7.44838	+	36.8587i	0.384121	+	1.90084i
$377$	0.728736	+	1.26221i	0.0375318	+	0.0650070i
$378$	−14.4568	+	49.7870i	−0.743577	+	2.56077i
$379$	−27.8191			−1.42897			−0.714486	−	0.699650i	$-0.753339\pi$
$379$	−27.8191			−1.42897			−0.714486	+	0.699650i	$0.753339\pi$
$380$	−8.67106	−	0.901546i	−0.444816	−	0.0462483i
$381$	−53.3275			−2.73205
$382$	−6.71200	+	23.1151i	−0.343416	+	1.18267i
$383$	−13.7668	−	23.8448i	−0.703451	−	1.21841i	−0.967248	−	0.253834i	$-0.918308\pi$
$383$	−13.7668	−	23.8448i	−0.703451	−	1.21841i	0.263797	−	0.964578i	$-0.415025\pi$
$384$	−33.7227	+	3.93583i	−1.72090	+	0.200850i
$385$	−7.41888	−	12.8499i	−0.378101	−	0.654890i
$386$	7.19711	−	1.76886i	0.366323	−	0.0900328i
$387$			31.4160i			1.59697i
$388$	−14.8735	−	0.619150i	−0.755086	−	0.0314326i
$389$	−9.92603	+	17.1924i	−0.503270	+	0.871689i	0.496723	+	0.867909i	$0.334536\pi$
$389$	−9.92603	+	17.1924i	−0.503270	+	0.871689i	−0.999993	+	0.00377962i	$0.998797\pi$
$390$	−7.04300	+	1.73099i	−0.356636	+	0.0876520i
$391$		−	18.8268i		−	0.952114i
$392$	−17.8150	−	20.1898i	−0.899794	−	1.01974i
$393$	−13.2979	−	7.67753i	−0.670789	−	0.387280i
$394$	−3.55490	−	1.03225i	−0.179093	−	0.0520038i
$395$	3.61536	−	6.26199i	0.181909	−	0.315075i
$396$	−20.3256	−	38.8524i	−1.02140	−	1.95241i
$397$	10.0845	+	17.4668i	0.506125	+	0.876634i	0.999975	+	0.00708686i	$0.00225584\pi$
$397$	10.0845	+	17.4668i	0.506125	+	0.876634i	−0.493850	+	0.869547i	$0.664411\pi$
$398$	8.92823	+	9.30762i	0.447532	+	0.466549i
$399$	−23.6792	−	47.6015i	−1.18544	−	2.38306i
$400$	−3.98616	−	0.332446i	−0.199308	−	0.0166223i
$401$	−15.7590	+	9.09849i	−0.786969	+	0.454357i	−0.838894	−	0.544294i	$-0.816797\pi$
$401$	−15.7590	+	9.09849i	−0.786969	+	0.454357i	0.0519255	+	0.998651i	$0.483464\pi$
$402$	−13.2165	−	3.83771i	−0.659179	−	0.191408i
$403$	6.72895	+	3.88496i	0.335193	+	0.193524i
$404$	34.5141	−	18.0560i	1.71714	−	0.898321i
$405$	−4.52494	+	7.83742i	−0.224846	+	0.389445i
$406$	−3.53775	+	3.39354i	−0.175576	+	0.168419i
$407$	8.72785			0.432624
$408$	55.6265	−	11.2409i	2.75392	−	0.556510i
$409$	−14.4356	−	8.33442i	−0.713796	−	0.412110i	0.0986688	−	0.995120i	$-0.468542\pi$
$409$	−14.4356	−	8.33442i	−0.713796	−	0.412110i	−0.812465	+	0.583010i	$0.801875\pi$
$410$	8.87858	+	9.25586i	0.438482	+	0.457114i
$411$	−18.8243			−0.928532
$412$	−7.43334	−	4.71438i	−0.366214	−	0.232261i
$413$	−0.522631	+	0.301741i	−0.0257170	+	0.0148477i
$414$	−23.2239	+	5.70783i	−1.14139	+	0.280525i
$415$	12.7317	−	7.35068i	0.624977	−	0.360831i
$416$	3.45799	−	9.02753i	0.169542	−	0.442611i
$417$			26.9577i			1.32013i
$418$	21.1810	+	7.60223i	1.03600	+	0.371837i
$419$			21.3815i			1.04455i	0.852776	+	0.522276i	$0.174917\pi$
$419$			21.3815i			1.04455i	−0.852776	+	0.522276i	$0.825083\pi$
$420$	−11.3079	−	21.6150i	−0.551768	−	1.05470i
$421$	12.9546	−	7.47935i	0.631370	−	0.364521i	−0.149913	−	0.988699i	$-0.547899\pi$
$421$	12.9546	−	7.47935i	0.631370	−	0.364521i	0.781282	+	0.624178i	$0.214566\pi$
$422$	0.746488	+	3.03729i	0.0363384	+	0.147853i
$423$	−69.1464	+	39.9217i	−3.36201	+	1.94106i
$424$	1.57389	+	7.78849i	0.0764349	+	0.378243i
$425$	6.68611			0.324324
$426$	36.8979	−	35.3938i	1.78771	−	1.71484i
$427$	−17.2536	−	9.96138i	−0.834961	−	0.482065i
$428$	23.7512	+	15.0635i	1.14806	+	0.728123i
$429$	18.7217			0.903893
$430$	−5.12123	−	5.33885i	−0.246968	−	0.257462i
$431$	3.63535	−	6.29660i	0.175108	−	0.303297i	−0.765090	−	0.643923i	$-0.777306\pi$
$431$	3.63535	−	6.29660i	0.175108	−	0.303297i	0.940199	+	0.340626i	$0.110639\pi$
$432$	−15.3796	−	32.6352i	−0.739952	−	1.57016i
$433$	29.2705	+	16.8993i	1.40665	+	0.812131i	0.995064	−	0.0992395i	$-0.0316410\pi$
$433$	29.2705	+	16.8993i	1.40665	+	0.812131i	0.411588	+	0.911370i	$0.364974\pi$
$434$	−7.28765	+	25.0976i	−0.349818	+	1.20472i
$435$	−2.21647	+	1.27968i	−0.106272	+	0.0613560i
$436$	−15.4302	−	0.642325i	−0.738972	−	0.0307618i
$437$	6.78370	−	10.2288i	0.324508	−	0.489311i
$438$	2.71407	−	2.60344i	0.129683	−	0.124397i
$439$	7.56961	+	13.1109i	0.361278	+	0.625751i	0.988171	−	0.153354i	$-0.0490073\pi$
$439$	7.56961	+	13.1109i	0.361278	+	0.625751i	−0.626894	+	0.779105i	$0.715674\pi$
$440$	9.78760	+	3.28925i	0.466606	+	0.156809i
$441$	28.5856	−	49.5117i	1.36122	−	2.35770i
$442$	−4.50599	+	15.5179i	−0.214328	+	0.738113i
$443$	6.21664	+	3.58918i	0.295362	+	0.170527i	0.640357	−	0.768077i	$-0.278786\pi$
$443$	6.21664	+	3.58918i	0.295362	+	0.170527i	−0.344996	+	0.938604i	$0.612120\pi$
$444$	14.3367	+	0.596806i	0.680390	+	0.0283231i
$445$			4.95578i			0.234927i
$446$	−6.71029	−	27.3027i	−0.317742	−	1.29282i
$447$	−3.76391	+	6.51928i	−0.178027	+	0.308351i
$448$	32.2626	+	4.04779i	1.52427	+	0.191240i
$449$		−	12.4312i		−	0.586667i	−0.956010	−	0.293333i	$-0.905235\pi$
$449$		−	12.4312i		−	0.586667i	0.956010	−	0.293333i	$-0.0947646\pi$
$450$	−2.02706	−	8.24767i	−0.0955567	−	0.388799i
$451$	−16.5541	−	28.6725i	−0.779501	−	1.35014i
$452$	−1.89586	+	2.98928i	−0.0891738	+	0.140604i
$453$	−25.5101	−	44.1847i	−1.19857	−	2.07598i
$454$	−10.7347	−	3.11707i	−0.503804	−	0.146291i
$455$	6.94585			0.325626
$456$	34.2729	+	13.9361i	1.60497	+	0.652615i
$457$	39.7032			1.85724			0.928619	−	0.371034i	$-0.120997\pi$
$457$	39.7032			1.85724			0.928619	+	0.371034i	$0.120997\pi$
$458$	5.70513	+	1.65661i	0.266583	+	0.0774085i
$459$	30.1523	+	52.2253i	1.40739	+	2.43767i
$460$	3.01623	−	4.75580i	0.140632	−	0.221740i
$461$	−7.28315	−	12.6148i	−0.339210	−	0.587529i	0.645074	−	0.764120i	$-0.276826\pi$
$461$	−7.28315	−	12.6148i	−0.339210	−	0.587529i	−0.984284	+	0.176591i	$0.943493\pi$
$462$	15.0293	+	61.1508i	0.699226	+	2.84499i
$463$		−	9.42439i		−	0.437989i	−0.975726	−	0.218994i	$-0.929722\pi$
$463$		−	9.42439i		−	0.437989i	0.975726	−	0.218994i	$-0.0702776\pi$
$464$	0.283530	−	3.39963i	0.0131625	−	0.157824i
$465$	−6.82210	+	11.8162i	−0.316367	+	0.547964i
$466$	5.83541	+	23.7430i	0.270320	+	1.09987i
$467$		−	11.3725i		−	0.526258i	−0.964761	−	0.263129i	$-0.915246\pi$
$467$		−	11.3725i		−	0.526258i	0.964761	−	0.263129i	$-0.0847545\pi$
$468$	20.5083	+	0.853716i	0.947997	+	0.0394630i
$469$	11.4145	+	6.59016i	0.527072	+	0.304305i
$470$	5.24300	−	18.0561i	0.241841	−	0.832865i
$471$	21.1770	−	36.6796i	0.975784	−	1.69011i
$472$	0.133781	−	0.398082i	0.00615775	−	0.0183232i
$473$	9.54851	+	16.5385i	0.439041	+	0.760442i
$474$	−22.1455	+	21.2428i	−1.01718	+	0.975714i
$475$	3.63263	+	2.40914i	0.166677	+	0.110539i
$476$	−54.3036	−	2.26054i	−2.48900	−	0.103612i
$477$	−14.6111	+	8.43571i	−0.668995	+	0.386244i
$478$	7.52684	−	25.9213i	0.344270	−	1.18561i
$479$	24.1524	+	13.9444i	1.10355	+	0.637134i	0.937151	−	0.348924i	$-0.113453\pi$
$479$	24.1524	+	13.9444i	1.10355	+	0.637134i	0.166398	+	0.986059i	$0.446786\pi$
$480$	15.8526	+	6.07232i	0.723568	+	0.277162i
$481$	−2.04284	+	3.53830i	−0.0931455	+	0.161333i
$482$	−22.6453	−	23.6076i	−1.03147	−	1.07530i
$483$	34.3448			1.56274
$484$	−3.93027	−	2.49266i	−0.178649	−	0.113303i
$485$	6.44598	+	3.72159i	0.292697	+	0.168989i
$486$	0.101870	−	0.0977173i	0.00462090	−	0.00443255i
$487$	19.5128			0.884207			0.442104	−	0.896964i	$-0.354232\pi$
$487$	19.5128			0.884207			0.442104	+	0.896964i	$0.354232\pi$
$488$	13.5894	−	2.74614i	0.615165	−	0.124312i
$489$	19.1594	−	11.0617i	0.866417	−	0.500226i
$490$	3.21322	+	13.0739i	0.145158	+	0.590617i
$491$	−19.7574	+	11.4069i	−0.891638	+	0.514788i	−0.874478	−	0.485065i	$-0.838796\pi$
$491$	−19.7574	+	11.4069i	−0.891638	+	0.514788i	−0.0171602	+	0.999853i	$0.505463\pi$
$492$	−25.2318	−	48.2305i	−1.13754	−	2.17440i
$493$			5.70230i			0.256819i
$494$	−8.03959	+	6.80747i	−0.361718	+	0.306282i
$495$			21.9239i			0.985408i
$496$	−7.75286	−	16.4514i	−0.348113	−	0.738689i
$497$	−42.4062	+	24.4832i	−1.90218	+	1.09822i
$498$	−60.5887	+	14.8911i	−2.71504	+	0.667288i
$499$	−17.1123	+	9.87981i	−0.766053	+	0.442281i	−0.831465	−	0.555577i	$-0.812497\pi$
$499$	−17.1123	+	9.87981i	−0.766053	+	0.442281i	0.0654115	+	0.997858i	$0.479164\pi$
$500$	1.68896	+	1.07117i	0.0755326	+	0.0479043i
$501$	8.01399			0.358039
$502$	1.21447	+	1.26608i	0.0542044	+	0.0565077i
$503$	18.6979	+	10.7952i	0.833696	+	0.481335i	0.855117	−	0.518436i	$-0.173485\pi$
$503$	18.6979	+	10.7952i	0.833696	+	0.481335i	−0.0214203	+	0.999771i	$0.506819\pi$
$504$	13.6750	+	67.6717i	0.609134	+	3.01434i
$505$	−19.4759			−0.866667
$506$	−10.4911	+	10.0634i	−0.466385	+	0.447374i
$507$	15.1240	−	26.1955i	0.671680	−	1.16338i
$508$	−31.4916	+	16.4748i	−1.39721	+	0.730952i
$509$	−0.0780100	−	0.0450391i	−0.00345773	−	0.00199632i	0.498270	−	0.867022i	$-0.333969\pi$
$509$	−0.0780100	−	0.0450391i	−0.00345773	−	0.00199632i	−0.501728	+	0.865026i	$0.667302\pi$
$510$	−27.2499	−	7.91263i	−1.20665	−	0.350377i
$511$	−3.11925	+	1.80090i	−0.137987	+	0.0796670i
$512$	−18.6984	+	12.7424i	−0.826361	+	0.563140i
$513$	−2.43578	+	39.2391i	−0.107542	+	1.73245i
$514$	29.6033	+	30.8613i	1.30575	+	1.36123i
$515$	2.20057	+	3.81149i	0.0969685	+	0.167954i
$516$	14.5539	+	27.8197i	0.640698	+	1.22469i
$517$	−24.2674	+	42.0324i	−1.06728	+	1.84858i
$518$	−13.1971	−	3.83208i	−0.579848	−	0.168372i
$519$	1.16218	+	0.670987i	0.0510142	+	0.0294531i
$520$	−3.62436	+	3.19805i	−0.158939	+	0.140244i
$521$			7.39573i			0.324013i	0.986790	+	0.162006i	$0.0517965\pi$
$521$			7.39573i			0.324013i	−0.986790	+	0.162006i	$0.948203\pi$
$522$	7.03409	−	1.72880i	0.307874	−	0.0756674i
$523$	13.1671	−	22.8060i	0.575756	−	0.997239i	−0.420203	−	0.907430i	$-0.638041\pi$
$523$	13.1671	−	22.8060i	0.575756	−	0.997239i	0.995959	−	0.0898087i	$-0.0286256\pi$
$524$	−10.2247	−	0.425632i	−0.446668	−	0.0185938i
$525$			12.1971i			0.532325i
$526$	14.6258	−	3.59465i	0.637717	−	0.156734i
$527$	15.1997	+	26.3267i	0.662111	+	1.14681i
$528$	−35.9977	−	24.9888i	−1.56660	−	1.08750i
$529$	−7.53560	−	13.0520i	−0.327635	−	0.567480i
$530$	1.10788	−	3.81537i	0.0481232	−	0.165729i
$531$	0.891692			0.0386961
$532$	−28.6892	−	20.7949i	−1.24384	−	0.901573i
$533$	15.4986			0.671318
$534$	5.86489	−	20.1978i	0.253799	−	0.874044i
$535$	−7.03132	−	12.1786i	−0.303990	−	0.526527i
$536$	−8.99038	+	1.81677i	−0.388325	+	0.0784724i
$537$	−12.9535	−	22.4362i	−0.558986	−	0.968193i
$538$	3.85585	−	0.947667i	0.166237	−	0.0408568i
$539$		−	34.7529i		−	1.49692i
$540$	−0.750265	+	18.0232i	−0.0322863	+	0.775594i
$541$	−6.47653	+	11.2177i	−0.278448	+	0.482285i	−0.970999	−	0.239083i	$-0.923153\pi$
$541$	−6.47653	+	11.2177i	−0.278448	+	0.482285i	0.692552	+	0.721368i	$0.256487\pi$
$542$	11.5555	−	2.84005i	0.496352	−	0.121990i
$543$		−	21.7269i		−	0.932391i
$544$	29.3766	−	23.8232i	1.25951	−	1.02141i
$545$	6.68725	+	3.86089i	0.286450	+	0.165382i
$546$	−28.3085	−	8.22002i	−1.21149	−	0.351785i
$547$	11.8029	−	20.4432i	0.504655	−	0.874088i	−0.495330	−	0.868705i	$-0.664953\pi$
$547$	11.8029	−	20.4432i	0.504655	−	0.874088i	0.999986	−	0.00538365i	$-0.00171368\pi$
$548$	−11.1163	+	5.81550i	−0.474867	+	0.248426i
$549$	14.7187	+	25.4936i	0.628179	+	1.08804i
$550$	−3.57390	−	3.72577i	−0.152391	−	0.158867i
$551$	−2.05466	+	3.09812i	−0.0875313	+	0.131984i
$552$	−17.9212	+	15.8132i	−0.762775	+	0.673055i
$553$	25.4515	−	14.6944i	1.08231	−	0.624871i
$554$	1.07115	+	0.311032i	0.0455086	+	0.0132145i
$555$	−6.21335	−	3.58728i	−0.263742	−	0.152272i
$556$	8.32824	+	15.9194i	0.353196	+	0.675134i
$557$	−8.02175	+	13.8941i	−0.339893	+	0.588711i	−0.984412	−	0.175877i	$-0.943724\pi$
$557$	−8.02175	+	13.8941i	−0.339893	+	0.588711i	0.644520	+	0.764588i	$0.277057\pi$
$558$	27.8672	−	26.7313i	1.17971	−	1.13163i
$559$	−8.93970			−0.378109
$560$	−13.3553	−	9.27095i	−0.564366	−	0.391769i
$561$	63.4345	+	36.6239i	2.67821	+	1.54626i
$562$	25.1731	+	26.2429i	1.06187	+	1.10699i
$563$	15.9296			0.671352			0.335676	−	0.941978i	$-0.391035\pi$
$563$	15.9296			0.671352			0.335676	+	0.941978i	$0.391035\pi$
$564$	−42.7367	+	67.3846i	−1.79954	+	2.83741i
$565$	1.53277	−	0.884946i	0.0644842	−	0.0372299i
$566$	−12.1245	+	2.97988i	−0.509630	+	0.125254i
$567$	−31.8548	+	18.3914i	−1.33778	+	0.772365i
$568$	10.8549	−	32.3003i	0.455463	−	1.35529i
$569$			10.8647i			0.455472i	0.973723	+	0.227736i	$0.0731324\pi$
$569$			10.8647i			0.455472i	−0.973723	+	0.227736i	$0.926868\pi$
$570$	−11.9541	−	14.1177i	−0.500702	−	0.591326i
$571$		−	42.3109i		−	1.77066i	−0.464967	−	0.885328i	$-0.653934\pi$
$571$		−	42.3109i		−	1.77066i	0.464967	−	0.885328i	$-0.346066\pi$
$572$	11.0558	−	5.78382i	0.462266	−	0.241834i
$573$	−44.2328	+	25.5378i	−1.84785	+	1.06686i
$574$	12.4418	+	50.6231i	0.519313	+	2.11297i
$575$	−2.43857	+	1.40791i	−0.101695	+	0.0587138i
$576$	−38.2935	−	29.0149i	−1.59556	−	1.20895i
$577$	−12.4527			−0.518413			−0.259207	−	0.965822i	$-0.583461\pi$
$577$	−12.4527			−0.518413			−0.259207	+	0.965822i	$0.583461\pi$
$578$	−28.2743	+	27.1218i	−1.17605	+	1.12812i
$579$	13.6196	+	7.86328i	0.566011	+	0.326787i
$580$	−0.913559	+	1.44044i	−0.0379335	+	0.0598111i
$581$	59.7529			2.47897
$582$	−21.8670	−	22.7962i	−0.906415	−	0.944932i
$583$	−5.12786	+	8.88172i	−0.212374	+	0.367843i
$584$	0.798449	−	2.37589i	0.0330401	−	0.0983151i
$585$	−8.88805	−	5.13152i	−0.367476	−	0.212162i
$586$	4.56628	−	15.7256i	0.188631	−	0.649618i
$587$	12.1169	−	6.99570i	0.500119	−	0.288744i	−0.228644	−	0.973510i	$-0.573429\pi$
$587$	12.1169	−	6.99570i	0.500119	−	0.288744i	0.728763	+	0.684766i	$0.240096\pi$
$588$	2.37639	−	57.0865i	0.0980006	−	2.35421i
$589$	−1.22787	+	19.7804i	−0.0505937	+	0.815037i
$590$	−0.151535	+	0.145358i	−0.00623858	+	0.00598428i
$591$	−3.92749	−	6.80261i	−0.161555	−	0.279822i
$592$	8.65067	−	4.07670i	0.355540	−	0.167551i
$593$	−24.0814	+	41.7102i	−0.988905	+	1.71283i	−0.365804	+	0.930692i	$0.619206\pi$
$593$	−24.0814	+	41.7102i	−0.988905	+	1.71283i	−0.623101	+	0.782141i	$0.714127\pi$
$594$	12.9848	−	44.7179i	0.532775	−	1.83480i
$595$	23.5345	+	13.5877i	0.964821	+	0.557040i
$596$	−0.208666	+	5.01266i	−0.00854729	+	0.205326i
$597$			27.3681i			1.12010i
$598$	−1.62421	−	6.60856i	−0.0664190	−	0.270244i
$599$	−16.2746	+	28.1885i	−0.664963	+	1.15175i	0.314333	+	0.949313i	$0.398219\pi$
$599$	−16.2746	+	28.1885i	−0.664963	+	1.15175i	−0.979295	+	0.202436i	$0.935114\pi$
$600$	−5.61586	−	6.36447i	−0.229266	−	0.259828i
$601$			30.8762i			1.25947i	0.776811	+	0.629733i	$0.216836\pi$
$601$			30.8762i			1.25947i	−0.776811	+	0.629733i	$0.783164\pi$
$602$	−7.17655	−	29.1998i	−0.292494	−	1.19009i
$603$	−9.73747	−	16.8658i	−0.396541	−	0.686828i
$604$	−28.7148	−	18.2115i	−1.16839	−	0.741017i
$605$	1.16352	+	2.01527i	0.0473038	+	0.0819325i
$606$	79.3761	+	23.0487i	3.22443	+	0.936288i
$607$	0.809286			0.0328479			0.0164240	−	0.999865i	$-0.494772\pi$
$607$	0.809286			0.0328479			0.0164240	+	0.999865i	$0.494772\pi$
$608$	24.5446	−	2.35845i	0.995415	−	0.0956476i
$609$	−10.4024			−0.421526
$610$	−6.65710	−	1.93304i	−0.269538	−	0.0782665i
$611$	−11.3601	−	19.6762i	−0.459579	−	0.796014i
$612$	67.8179	+	43.0115i	2.74138	+	1.73864i
$613$	1.21467	+	2.10387i	0.0490601	+	0.0849746i	0.889513	−	0.456911i	$-0.151044\pi$
$613$	1.21467	+	2.10387i	0.0490601	+	0.0849746i	−0.840453	+	0.541885i	$0.817711\pi$
$614$	6.23610	+	25.3733i	0.251668	+	1.02398i
$615$			27.2159i			1.09745i
$616$	27.7670	+	31.4685i	1.11877	+	1.26790i
$617$	8.26457	−	14.3146i	0.332719	−	0.576286i	−0.650325	−	0.759656i	$-0.725367\pi$
$617$	8.26457	−	14.3146i	0.332719	−	0.576286i	0.983044	+	0.183370i	$0.0587006\pi$
$618$	−4.45794	−	18.1384i	−0.179325	−	0.729632i
$619$			4.21910i			0.169580i	0.996399	+	0.0847899i	$0.0270219\pi$
$619$			4.21910i			0.169580i	−0.996399	+	0.0847899i	$0.972978\pi$
$620$	−0.378208	+	9.08547i	−0.0151892	+	0.364881i
$621$	−21.9944	−	12.6985i	−0.882604	−	0.509572i
$622$	−6.72871	+	23.1727i	−0.269797	+	0.929139i
$623$	−10.0713	+	17.4439i	−0.403497	+	0.698877i
$624$	18.5562	−	8.74475i	0.742841	−	0.350070i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	31.5140	−	30.2294i	1.25955	−	1.20821i
$627$	21.2683	+	42.7549i	0.849374	+	1.70747i
$628$	1.17402	−	28.2029i	0.0468487	−	1.12542i
$629$	−13.8435	+	7.99252i	−0.551975	+	0.318683i
$630$	9.62601	−	33.1505i	0.383510	−	1.32075i
$631$	−1.58859	−	0.917170i	−0.0632406	−	0.0365120i	0.468046	−	0.883704i	$-0.344958\pi$
$631$	−1.58859	−	0.917170i	−0.0632406	−	0.0365120i	−0.531287	+	0.847192i	$0.678291\pi$
$632$	−6.51496	+	19.3861i	−0.259151	+	0.771139i
$633$	−3.31842	+	5.74768i	−0.131896	+	0.228450i
$634$	−2.01814	−	2.10390i	−0.0801507	−	0.0835566i
$635$	17.7704			0.705195
$636$	−9.03055	+	14.2388i	−0.358085	+	0.564606i
$637$	14.0890	+	8.13427i	0.558225	+	0.322292i
$638$	3.17755	−	3.04803i	0.125800	−	0.120673i
$639$	72.3518			2.86219
$640$	11.2374	−	1.31154i	0.444198	−	0.0518432i
$641$	29.5098	−	17.0375i	1.16557	−	0.672940i	0.212935	−	0.977066i	$-0.431698\pi$
$641$	29.5098	−	17.0375i	1.16557	−	0.672940i	0.952632	+	0.304127i	$0.0983646\pi$
$642$	14.2442	+	57.9563i	0.562172	+	2.28735i
$643$	−21.5349	+	12.4332i	−0.849255	+	0.490317i	−0.860399	−	0.509621i	$-0.829786\pi$
$643$	−21.5349	+	12.4332i	−0.849255	+	0.490317i	0.0111447	+	0.999938i	$0.496452\pi$
$644$	20.2817	−	10.6104i	0.799211	−	0.418107i
$645$		−	15.6983i		−	0.618122i
$646$	−40.5574	+	7.33838i	−1.59571	+	0.288725i
$647$		−	11.2729i		−	0.443183i	−0.975140	−	0.221591i	$-0.928875\pi$
$647$		−	11.2729i		−	0.443183i	0.975140	−	0.221591i	$-0.0711251\pi$
$648$	8.15404	−	24.2634i	0.320321	−	0.953157i
$649$	0.469419	−	0.271019i	0.0184263	−	0.0106384i
$650$	2.34695	−	0.576819i	0.0920548	−	0.0226247i
$651$	−48.0264	+	27.7281i	−1.88230	+	1.08675i
$652$	7.89688	−	12.4513i	0.309266	−	0.487631i
$653$	−40.7789			−1.59580			−0.797901	−	0.602788i	$-0.794056\pi$
$653$	−40.7789			−1.59580			−0.797901	+	0.602788i	$0.794056\pi$
$654$	−22.6854	−	23.6494i	−0.887071	−	0.924766i
$655$	4.43126	+	2.55839i	0.173144	+	0.0999646i
$656$	−29.8004	−	20.6867i	−1.16351	−	0.807679i
$657$	5.32193			0.207628
$658$	55.1489	−	52.9010i	2.14993	−	2.06229i
$659$	13.6726	−	23.6816i	0.532609	−	0.922506i	−0.466666	−	0.884434i	$-0.654545\pi$
$659$	13.6726	−	23.6816i	0.532609	−	0.922506i	0.999275	−	0.0380723i	$-0.0121217\pi$
$660$	10.1565	+	19.4143i	0.395343	+	0.755699i
$661$	16.1909	+	9.34783i	0.629754	+	0.363588i	0.780657	−	0.624960i	$-0.214885\pi$
$661$	16.1909	+	9.34783i	0.629754	+	0.363588i	−0.150903	+	0.988549i	$0.548218\pi$
$662$	27.5846	+	8.00983i	1.07211	+	0.311311i
$663$	−29.6949	+	17.1444i	−1.15326	+	0.665833i
$664$	−31.1792	+	27.5118i	−1.20999	+	1.06766i
$665$	7.89065	+	15.8623i	0.305986	+	0.615114i
$666$	14.0562	+	14.6535i	0.544666	+	0.567811i
$667$	−1.20074	−	2.07975i	−0.0464930	−	0.0805283i
$668$	4.73253	−	2.47582i	0.183107	−	0.0957922i
$669$	29.8298	−	51.6668i	1.15329	−	1.99755i
$670$	4.40414	+	1.27884i	0.170147	+	0.0494060i
$671$	15.4969	+	8.94715i	0.598252	+	0.345401i
$672$	43.4594	+	53.5900i	1.67648	+	2.06728i
$673$		−	16.3791i		−	0.631369i	−0.948864	−	0.315684i	$-0.897766\pi$
$673$		−	16.3791i		−	0.631369i	0.948864	−	0.315684i	$-0.102234\pi$
$674$	−8.95390	+	2.20064i	−0.344891	+	0.0847653i
$675$	4.50969	−	7.81102i	0.173578	−	0.300646i
$676$	0.838454	−	20.1417i	0.0322482	−	0.774680i
$677$		−	49.2868i		−	1.89425i	−0.320871	−	0.947123i	$-0.603976\pi$
$677$		−	49.2868i		−	1.89425i	0.320871	−	0.947123i	$-0.396024\pi$
$678$	−7.29425	+	1.79274i	−0.280134	+	0.0688497i
$679$	15.1262	+	26.1994i	0.580491	+	1.00544i
$680$	−18.5365	+	3.74583i	−0.710841	+	0.143646i
$681$	−11.8598	−	20.5418i	−0.454469	−	0.787163i
$682$	6.54565	−	22.5422i	0.250646	−	0.863187i
$683$	7.14473			0.273385			0.136693	−	0.990614i	$-0.456353\pi$
$683$	7.14473			0.273385			0.136693	+	0.990614i	$0.456353\pi$
$684$	21.3483	+	47.8049i	0.816272	+	1.82786i
$685$	6.27282			0.239672
$686$	−4.03877	+	13.9089i	−0.154201	+	0.531045i
$687$	6.30309	+	10.9173i	0.240478	+	0.416520i
$688$	17.1891	+	11.9322i	0.655327	+	0.454912i
$689$	−2.40045	−	4.15771i	−0.0914500	−	0.158396i
$690$	11.6048	−	2.85216i	0.441787	−	0.108580i
$691$			25.3558i			0.964580i	0.876012	+	0.482290i	$0.160195\pi$
$691$			25.3558i			0.964580i	−0.876012	+	0.482290i	$0.839805\pi$
$692$	0.893601	+	0.0371986i	0.0339696	+	0.00141408i
$693$	−44.5544	+	77.1704i	−1.69248	+	2.93146i
$694$	37.6066	−	9.24274i	1.42753	−	0.350849i
$695$		−	8.98315i		−	0.340750i
$696$	5.42799	−	4.78953i	0.205747	−	0.181547i
$697$	52.5136	+	30.3187i	1.98909	+	1.14840i
$698$	36.6060	+	10.6294i	1.38556	+	0.402328i
$699$	−25.9407	+	44.9305i	−0.981166	+	1.69943i
$700$	3.76813	+	7.20279i	0.142422	+	0.272240i
$701$	−15.1232	−	26.1942i	−0.571196	−	0.989340i	−0.996444	−	0.0842633i	$-0.973146\pi$
$701$	−15.1232	−	26.1942i	−0.571196	−	0.989340i	0.425248	−	0.905077i	$-0.360187\pi$
$702$	15.0895	+	15.7308i	0.569518	+	0.593719i
$703$	−10.4012	−	0.645656i	−0.392288	−	0.0243514i
$704$	−28.9778	−	3.63566i	−1.09214	−	0.137024i
$705$	34.5519	−	19.9486i	1.30130	−	0.751306i
$706$	−0.253370	−	0.0735718i	−0.00953571	−	0.00276891i
$707$	−68.5536	−	39.5794i	−2.57822	−	1.48854i
$708$	0.789617	−	0.413088i	0.0296756	−	0.0155248i
$709$	10.9148	−	18.9050i	0.409914	−	0.709991i	−0.584966	−	0.811058i	$-0.698892\pi$
$709$	10.9148	−	18.9050i	0.409914	−	0.709991i	0.994880	+	0.101067i	$0.0322255\pi$
$710$	−12.2955	+	11.7943i	−0.461442	+	0.442633i
$711$	−43.4244			−1.62854
$712$	−2.77643	−	13.7393i	−0.104051	−	0.514904i
$713$	−11.0874	−	6.40128i	−0.415225	−	0.239730i
$714$	−79.8371	−	83.2297i	−2.98783	−	3.11479i
$715$	−6.23865			−0.233312
$716$	−14.5809	−	9.24748i	−0.544912	−	0.345595i
$717$	49.6027	−	28.6381i	1.85245	−	1.06951i
$718$	32.1279	−	7.89622i	1.19900	−	0.294684i
$719$	−34.8972	+	20.1479i	−1.30145	+	0.751391i	−0.980652	−	0.195758i	$-0.937283\pi$
$719$	−34.8972	+	20.1479i	−1.30145	+	0.751391i	−0.320795	+	0.947149i	$0.603950\pi$
$720$	10.2405	+	21.7301i	0.381640	+	0.809832i
$721$			17.8882i			0.666190i
$722$	−24.6794	−	10.6266i	−0.918474	−	0.395482i
$723$		−	69.4158i		−	2.58160i
$724$	−6.71225	−	12.8305i	−0.249459	−	0.476840i
$725$	0.738597	−	0.426429i	0.0274308	−	0.0158372i
$726$	−2.35708	−	9.59042i	−0.0874793	−	0.355934i
$727$	2.43823	−	1.40771i	0.0904290	−	0.0522092i	−0.454104	−	0.890949i	$-0.650040\pi$
$727$	2.43823	−	1.40771i	0.0904290	−	0.0522092i	0.544533	+	0.838740i	$0.316707\pi$
$728$	−19.2566	+	3.89135i	−0.713696	+	0.144223i
$729$	−26.8501			−0.994448
$730$	−0.904412	+	0.867546i	−0.0334738	+	0.0321093i
$731$	−30.2902	−	17.4881i	−1.12033	−	0.646820i
$732$	24.8440	+	15.7566i	0.918262	+	0.582381i
$733$	−5.71295			−0.211013			−0.105506	−	0.994419i	$-0.533646\pi$
$733$	−5.71295			−0.211013			−0.105506	+	0.994419i	$0.533646\pi$
$734$	−13.2038	−	13.7649i	−0.487363	−	0.508073i
$735$	−14.2840	+	24.7406i	−0.526873	+	0.912571i
$736$	−5.69775	+	14.8747i	−0.210022	+	0.548290i
$737$	−10.2523	−	5.91917i	−0.377649	−	0.218036i
$738$	21.4789	−	73.9702i	0.790651	−	2.72288i
$739$	4.61768	−	2.66602i	0.169864	−	0.0980711i	−0.412658	−	0.910886i	$-0.635399\pi$
$739$	4.61768	−	2.66602i	0.169864	−	0.0980711i	0.582522	+	0.812815i	$0.302066\pi$
$740$	−4.77743	−	0.198874i	−0.175622	−	0.00731076i
$741$	−22.3111	−	1.38497i	−0.819617	−	0.0508781i
$742$	11.6533	−	11.1783i	0.427807	−	0.410369i
$743$	−3.46512	−	6.00176i	−0.127123	−	0.220183i	0.795438	−	0.606035i	$-0.207241\pi$
$743$	−3.46512	−	6.00176i	−0.127123	−	0.220183i	−0.922561	+	0.385852i	$0.873908\pi$
$744$	12.2936	−	36.5812i	0.450704	−	1.34113i
$745$	1.25425	−	2.17242i	0.0459522	−	0.0795915i
$746$	9.95285	−	34.2761i	0.364400	−	1.25494i
$747$	−76.4610	−	44.1448i	−2.79756	−	1.61517i
$748$	48.7746	+	2.03038i	1.78338	+	0.0742381i
$749$		−	57.1569i		−	2.08847i
$750$	1.01291	+	4.12130i	0.0369862	+	0.150489i
$751$	4.24447	−	7.35164i	0.154883	−	0.268265i	−0.778133	−	0.628099i	$-0.783833\pi$
$751$	4.24447	−	7.35164i	0.154883	−	0.268265i	0.933016	+	0.359834i	$0.117167\pi$
$752$	−4.41986	+	52.9958i	−0.161176	+	1.93256i
$753$			3.72276i			0.135665i
$754$	0.491944	+	2.00161i	0.0179156	+	0.0728944i
$755$	8.50074	+	14.7237i	0.309374	+	0.535851i
$756$	−39.2680	+	61.9153i	−1.42816	+	2.25184i
$757$	10.4138	+	18.0373i	0.378497	+	0.655576i	0.990844	−	0.135013i	$-0.0431076\pi$
$757$	10.4138	+	18.0373i	0.378497	+	0.655576i	−0.612347	+	0.790589i	$0.709774\pi$
$758$	−37.7816	−	10.9707i	−1.37229	−	0.398475i
$759$	−30.8479			−1.11971
$760$	−11.4208	−	4.64392i	−0.414275	−	0.168453i
$761$	−32.3556			−1.17289			−0.586446	−	0.809989i	$-0.699473\pi$
$761$	−32.3556			−1.17289			−0.586446	+	0.809989i	$0.699473\pi$
$762$	−72.4249	−	21.0302i	−2.62368	−	0.761845i
$763$	15.6924	+	27.1800i	0.568102	+	0.983981i
$764$	−18.2313	+	28.7461i	−0.659587	+	1.04000i
$765$	−20.0768	−	34.7741i	−0.725879	−	1.25726i
$766$	−9.29348	−	37.8131i	−0.335787	−	1.36624i
$767$			0.253739i			0.00916197i
$768$	−47.3514	−	7.95356i	−1.70865	−	0.286999i
$769$	10.9453	−	18.9579i	0.394699	−	0.683638i	−0.598364	−	0.801224i	$-0.704182\pi$
$769$	10.9453	−	18.9579i	0.394699	−	0.683638i	0.993063	+	0.117586i	$0.0375157\pi$
$770$	−5.00822	−	20.3773i	−0.180484	−	0.734348i
$771$			90.7445i			3.26808i
$772$	10.4721	+	0.435930i	0.376898	+	0.0156895i
$773$	38.9620	+	22.4947i	1.40137	+	0.809079i	0.994533	−	0.104424i	$-0.0333000\pi$
$773$	38.9620	+	22.4947i	1.40137	+	0.809079i	0.406832	+	0.913503i	$0.366633\pi$
$774$	−12.3892	+	42.6666i	−0.445321	+	1.53362i
$775$	2.27333	−	3.93753i	0.0816605	−	0.141440i
$776$	−19.9557	−	6.70638i	−0.716370	−	0.240745i
$777$	−14.5803	−	25.2538i	−0.523066	−	0.905977i
$778$	−20.2607	+	19.4348i	−0.726381	+	0.696773i
$779$	17.6068	+	35.3942i	0.630827	+	1.26813i
$780$	−10.2478	−	0.426595i	−0.366932	−	0.0152746i
$781$	38.0886	−	21.9905i	1.36292	−	0.786880i
$782$	7.42455	−	25.5690i	0.265501	−	0.914347i
$783$	6.66169	+	3.84613i	0.238069	+	0.137449i
$784$	−16.2328	−	34.4456i	−0.579743	−	1.23020i
$785$	−7.05683	+	12.2228i	−0.251869	+	0.436250i
$786$	−15.0323	−	15.6711i	−0.536186	−	0.558971i
$787$	−2.10337			−0.0749770			−0.0374885	−	0.999297i	$-0.511936\pi$
$787$	−2.10337			−0.0749770			−0.0374885	+	0.999297i	$0.511936\pi$
$788$	−4.42089	−	2.80382i	−0.157488	−	0.0998819i
$789$	27.6775	+	15.9796i	0.985346	+	0.568890i
$790$	7.37956	−	7.07876i	0.262553	−	0.251851i
$791$	7.19363			0.255776
$792$	−12.2827	−	60.7817i	−0.436446	−	2.15978i
$793$	−7.25441	+	4.18834i	−0.257612	+	0.148732i
$794$	6.80767	+	27.6989i	0.241595	+	0.982996i
$795$	7.30104	−	4.21526i	0.258941	−	0.149500i
$796$	8.45502	+	16.1618i	0.299680	+	0.572839i
$797$		−	36.8675i		−	1.30591i	−0.757396	−	0.652956i	$-0.773529\pi$
$797$		−	36.8675i		−	1.30591i	0.757396	−	0.652956i	$-0.226471\pi$
$798$	−13.3870	−	73.9866i	−0.473895	−	2.61910i
$799$		−	88.8914i		−	3.14475i
$800$	−5.28257	−	2.02348i	−0.186767	−	0.0715410i
$801$	25.7748	−	14.8811i	0.910707	−	0.525797i
$802$	−24.9907	+	6.14207i	−0.882452	+	0.216884i
$803$	2.80166	−	1.61754i	0.0988683	−	0.0570816i
$804$	−16.4361	−	10.4241i	−0.579656	−	0.367630i
$805$	−11.4447			−0.403374
$806$	7.60663	+	7.92986i	0.267932	+	0.279318i
$807$	7.29669	+	4.21275i	0.256856	+	0.148296i
$808$	53.9948	−	10.9112i	1.89953	−	0.383855i
$809$	−36.9053			−1.29752			−0.648760	−	0.760993i	$-0.724712\pi$
$809$	−36.9053			−1.29752			−0.648760	+	0.760993i	$0.724712\pi$
$810$	−9.23616	+	8.85968i	−0.324526	+	0.311297i
$811$	21.8577	−	37.8587i	0.767529	−	1.32940i	−0.171370	−	0.985207i	$-0.554819\pi$
$811$	21.8577	−	37.8587i	0.767529	−	1.32940i	0.938899	−	0.344193i	$-0.111847\pi$
$812$	−6.14295	+	3.21368i	−0.215575	+	0.112778i
$813$	21.8673	+	12.6251i	0.766920	+	0.442782i
$814$	11.8534	+	3.44192i	0.415463	+	0.120639i
$815$	−6.38449	+	3.68609i	−0.223639	+	0.129118i
$816$	79.9803	+	6.67037i	2.79987	+	0.233510i
$817$	−10.1557	−	20.4157i	−0.355303	−	0.714254i
$818$	−16.3185	−	17.0119i	−0.570563	−	0.594809i
$819$	−20.8568	−	36.1250i	−0.728795	−	1.26231i
$820$	8.40800	+	16.0719i	0.293620	+	0.561255i
$821$	−11.3347	+	19.6322i	−0.395583	+	0.685169i	−0.993175	−	0.116631i	$-0.962791\pi$
$821$	−11.3347	+	19.6322i	−0.395583	+	0.685169i	0.597593	+	0.801800i	$0.296124\pi$
$822$	−25.5655	−	7.42353i	−0.891700	−	0.258925i
$823$	−16.3040	−	9.41310i	−0.568321	−	0.328120i	0.188158	−	0.982139i	$-0.439748\pi$
$823$	−16.3040	−	9.41310i	−0.568321	−	0.328120i	−0.756478	+	0.654019i	$0.773082\pi$
$824$	−8.23617	−	9.33408i	−0.286921	−	0.325168i
$825$		−	10.9552i		−	0.381412i
$826$	−0.828788	+	0.203695i	−0.0288372	+	0.00708745i
$827$	−11.9740	+	20.7396i	−0.416376	+	0.721185i	−0.995572	−	0.0940036i	$-0.970033\pi$
$827$	−11.9740	+	20.7396i	−0.416376	+	0.721185i	0.579195	+	0.815189i	$0.303367\pi$
$828$	−33.7917	−	1.40667i	−1.17434	−	0.0488853i
$829$			5.21491i			0.181121i	0.995891	+	0.0905607i	$0.0288659\pi$
$829$			5.21491i			0.181121i	−0.995891	+	0.0905607i	$0.971134\pi$
$830$	20.1900	−	4.96218i	0.700806	−	0.172240i
$831$	1.18341	+	2.04973i	0.0410522	+	0.0711044i
$832$	8.25645	−	10.8967i	0.286241	−	0.377776i
$833$	31.8250	+	55.1225i	1.10267	+	1.90988i
$834$	−10.6311	+	36.6118i	−0.368123	+	1.26776i
$835$	−2.67051			−0.0924168
$836$	25.7682	+	18.6776i	0.891212	+	0.645980i
$837$	41.0082			1.41745
$838$	−8.43200	+	29.0385i	−0.291278	+	1.00312i
$839$	−10.8783	−	18.8418i	−0.375561	−	0.650491i	0.614850	−	0.788644i	$-0.289217\pi$
$839$	−10.8783	−	18.8418i	−0.375561	−	0.650491i	−0.990411	+	0.138154i	$0.955883\pi$
$840$	−6.83331	−	33.8151i	−0.235772	−	1.16673i
$841$	−14.1363	−	24.4848i	−0.487459	−	0.844304i
$842$	20.5434	−	5.04905i	0.707974	−	0.174002i
$843$			77.1644i			2.65768i
$844$	−0.183969	+	4.41938i	−0.00633248	+	0.152121i
$845$	−5.03978	+	8.72916i	−0.173374	+	0.300292i
$846$	−109.652	+	26.9497i	−3.76992	+	0.926550i
$847$			9.45812i			0.324985i
$848$	−0.933945	+	11.1984i	−0.0320718	+	0.384553i
$849$	−22.9440	−	13.2467i	−0.787437	−	0.454627i
$850$	9.08051	+	2.63673i	0.311459	+	0.0904392i
$851$	3.36600	−	5.83009i	0.115385	−	0.199853i
$852$	64.0695	−	33.5179i	2.19498	−	1.14830i
$853$	−9.35529	−	16.2038i	−0.320319	−	0.554809i	0.660235	−	0.751059i	$-0.270457\pi$
$853$	−9.35529	−	16.2038i	−0.320319	−	0.554809i	−0.980554	+	0.196250i	$0.937123\pi$
$854$	−19.5040	−	20.3328i	−0.667415	−	0.695776i
$855$	1.62186	−	26.1272i	0.0554664	−	0.893533i
$856$	26.3165	+	29.8246i	0.899479	+	1.01938i
$857$	27.0501	−	15.6174i	0.924013	−	0.533479i	0.0390998	−	0.999235i	$-0.487551\pi$
$857$	27.0501	−	15.6174i	0.924013	−	0.533479i	0.884913	+	0.465756i	$0.154218\pi$
$858$	25.4263	+	7.38309i	0.868038	+	0.252055i
$859$	36.4270	+	21.0311i	1.24287	+	0.717573i	0.969678	−	0.244385i	$-0.0785862\pi$
$859$	36.4270	+	21.0311i	1.24287	+	0.717573i	0.273195	+	0.961959i	$0.411920\pi$
$860$	−4.84980	−	9.27039i	−0.165377	−	0.316118i
$861$	−55.3088	+	95.7977i	−1.88492	+	3.26478i
$862$	7.42035	−	7.11789i	0.252738	−	0.242436i
$863$	−15.6416			−0.532446			−0.266223	−	0.963911i	$-0.585776\pi$
$863$	−15.6416			−0.532446			−0.266223	+	0.963911i	$0.585776\pi$
$864$	−8.01729	−	50.3875i	−0.272754	−	1.71422i
$865$	−0.387275	−	0.223594i	−0.0131678	−	0.00760241i
$866$	33.0883	+	34.4944i	1.12439	+	1.17217i
$867$	−83.1376			−2.82350
$868$	−19.7950	+	31.2115i	−0.671885	+	1.05939i
$869$	−22.8602	+	13.1983i	−0.775478	+	0.447722i
$870$	−3.51488	+	0.863867i	−0.119166	+	0.0292878i
$871$	4.79931	−	2.77088i	0.162618	−	0.0938878i
$872$	−20.7027	−	6.95740i	−0.701081	−	0.235607i
$873$		−	44.7003i		−	1.51288i
$874$	13.2469	−	11.2167i	0.448083	−	0.379411i
$875$		−	4.06445i		−	0.137403i
$876$	4.71271	−	2.46545i	0.159228	−	0.0832999i
$877$	−1.87832	+	1.08445i	−0.0634264	+	0.0366193i	−0.531378	−	0.847135i	$-0.678326\pi$
$877$	−1.87832	+	1.08445i	−0.0634264	+	0.0366193i	0.467951	+	0.883754i	$0.344992\pi$
$878$	5.10997	+	20.7913i	0.172453	+	0.701674i
$879$	30.0923	−	17.3738i	1.01499	−	0.586004i
$880$	11.9956	+	8.32702i	0.404370	+	0.280704i
$881$	−23.4038			−0.788496			−0.394248	−	0.919004i	$-0.628995\pi$
$881$	−23.4038			−0.788496			−0.394248	+	0.919004i	$0.628995\pi$
$882$	58.3479	−	55.9696i	1.96468	−	1.88459i
$883$	42.1919	+	24.3595i	1.41987	+	0.819762i	0.996287	−	0.0860959i	$-0.0274392\pi$
$883$	42.1919	+	24.3595i	1.41987	+	0.819762i	0.423582	+	0.905858i	$0.360772\pi$
$884$	−12.2393	+	19.2982i	−0.411653	+	0.649068i
$885$	−0.445572			−0.0149777
$886$	7.02749	+	7.32612i	0.236093	+	0.246126i
$887$	16.4836	−	28.5504i	0.553465	−	0.958630i	−0.444556	−	0.895751i	$-0.646639\pi$
$887$	16.4836	−	28.5504i	0.553465	−	0.958630i	0.998021	−	0.0628787i	$-0.0200281\pi$
$888$	19.2356	+	6.46436i	0.645503	+	0.216930i
$889$	62.5501	+	36.1133i	2.09786	+	1.21120i
$890$	−1.95436	+	6.73053i	−0.0655104	+	0.225608i
$891$	28.6115	−	16.5188i	0.958520	−	0.553402i
$892$	1.65373	−	39.7265i	0.0553709	−	1.33014i
$893$	32.0294	−	48.2957i	1.07182	−	1.61615i
$894$	−7.68277	+	7.36960i	−0.256950	+	0.246476i
$895$	4.31652	+	7.47643i	0.144285	+	0.249909i
$896$	42.2201	+	18.2205i	1.41048	+	0.608703i
$897$	7.22026	−	12.5059i	0.241077	−	0.417558i
$898$	4.90239	−	16.8831i	0.163595	−	0.563395i
$899$	3.35815	+	1.93883i	0.112001	+	0.0646636i
$900$	0.499562	−	12.0007i	0.0166521	−	0.400023i
$901$		−	18.7833i		−	0.625764i
$902$	−11.1751	−	45.4688i	−0.372089	−	1.51395i
$903$	31.9025	−	55.2568i	1.06165	−	1.83883i
$904$	−3.75365	+	3.31213i	−0.124845	+	0.110160i
$905$			7.24008i			0.240668i
$906$	−17.2209	−	70.0682i	−0.572128	−	2.32786i
$907$	14.2473	+	24.6771i	0.473075	+	0.819390i	0.999525	−	0.0308162i	$-0.00981065\pi$
$907$	14.2473	+	24.6771i	0.473075	+	0.819390i	−0.526450	+	0.850206i	$0.676477\pi$
$908$	−13.3497	−	8.46667i	−0.443026	−	0.280976i
$909$	58.4817	+	101.293i	1.93972	+	3.35969i
$910$	9.43327	+	2.73917i	0.312710	+	0.0908025i
$911$	−6.41581			−0.212565			−0.106283	−	0.994336i	$-0.533895\pi$
$911$	−6.41581			−0.212565			−0.106283	+	0.994336i	$0.533895\pi$
$912$	41.0507	+	32.4426i	1.35932	+	1.07428i
$913$	−53.6691			−1.77619
$914$	53.9216	+	15.6574i	1.78357	+	0.517900i
$915$	−7.35483	−	12.7389i	−0.243143	−	0.421136i
$916$	7.09493	+	4.49975i	0.234423	+	0.148676i
$917$	10.3984	+	18.0106i	0.343387	+	0.594763i
$918$	20.3547	+	82.8189i	0.671807	+	2.73343i
$919$			1.28401i			0.0423555i	0.999776	+	0.0211777i	$0.00674159\pi$
$919$			1.28401i			0.0423555i	−0.999776	+	0.0211777i	$0.993258\pi$
$920$	5.97188	−	5.26945i	0.196887	−	0.173729i
$921$	−27.7219	+	48.0157i	−0.913466	+	1.58217i
$922$	−4.91660	−	20.0045i	−0.161920	−	0.658814i
$923$			20.5883i			0.677673i
$924$	−3.70391	+	88.9769i	−0.121850	+	2.92712i
$925$	2.07048	+	1.19539i	0.0680770	+	0.0393043i
$926$	3.71660	−	12.7994i	0.122135	−	0.420615i
$927$	13.2156	−	22.8901i	0.434057	−	0.751808i
$928$	1.72574	−	4.50528i	0.0566503	−	0.147893i
$929$	−16.3457	−	28.3116i	−0.536285	−	0.928873i	−0.999100	−	0.0424182i	$-0.986494\pi$
$929$	−16.3457	−	28.3116i	−0.536285	−	0.928873i	0.462815	−	0.886455i	$-0.346840\pi$
$930$	−13.9250	+	13.3574i	−0.456620	+	0.438008i
$931$	−2.57090	+	41.4158i	−0.0842580	+	1.35735i
$932$	−1.43812	+	34.5470i	−0.0471070	+	1.13162i
$933$	−44.3429	+	25.6014i	−1.45172	+	0.838152i
$934$	4.48487	−	15.4452i	0.146749	−	0.505383i
$935$	−21.1383	−	12.2042i	−0.691297	−	0.399121i
$936$	27.5160	+	9.24710i	0.899388	+	0.302251i
$937$	6.22992	−	10.7905i	0.203523	−	0.352511i	−0.746138	−	0.665791i	$-0.768094\pi$
$937$	6.22992	−	10.7905i	0.203523	−	0.352511i	0.949661	+	0.313279i	$0.101428\pi$
$938$	12.9033	+	13.4516i	0.421308	+	0.439211i
$939$	92.6637			3.02397
$940$	14.2412	−	22.4546i	0.464497	−	0.732390i
$941$	−32.3102	−	18.6543i	−1.05328	−	0.608113i	−0.129716	−	0.991551i	$-0.541407\pi$
$941$	−32.3102	−	18.6543i	−1.05328	−	0.608113i	−0.923567	+	0.383438i	$0.874740\pi$
$942$	43.2258	−	41.4638i	1.40837	−	1.35096i
$943$	−25.5371			−0.831603
$944$	0.338677	−	0.487884i	0.0110230	−	0.0158793i
$945$	31.7475	−	18.3294i	1.03275	−	0.596256i
$946$	6.44586	+	26.2268i	0.209573	+	0.852706i
$947$	6.59519	−	3.80773i	0.214315	−	0.123735i	−0.389000	−	0.921238i	$-0.627179\pi$
$947$	6.59519	−	3.80773i	0.214315	−	0.123735i	0.603315	+	0.797503i	$0.293846\pi$
$948$	−38.4535	+	20.1169i	−1.24891	+	0.653366i
$949$			1.51440i			0.0491596i
$950$	3.98347	+	4.70446i	0.129241	+	0.152633i
$951$		−	6.18631i		−	0.200605i
$952$	−72.8592	−	24.4853i	−2.36138	−	0.793572i
$953$	−27.9964	+	16.1637i	−0.906892	+	0.523595i	−0.879430	−	0.476028i	$-0.842076\pi$
$953$	−27.9964	+	16.1637i	−0.906892	+	0.523595i	−0.0274624	+	0.999623i	$0.508743\pi$
$954$	−23.1702	+	5.69465i	−0.750164	+	0.184371i
$955$	14.7397	−	8.50999i	0.476966	−	0.275377i
$956$	20.4447	−	32.2359i	0.661227	−	1.04258i
$957$	9.34326			0.302025
$958$	27.3026	+	28.4628i	0.882107	+	0.919591i
$959$	22.0798	+	12.7478i	0.712994	+	0.411647i
$960$	19.1350	+	14.4985i	0.617578	+	0.467938i
$961$	−10.3278			−0.333156
$962$	−4.16978	+	3.99981i	−0.134439	+	0.128959i
$963$	−42.2269	+	73.1391i	−1.36074	+	2.35687i
$964$	−21.4451	−	40.9923i	−0.690700	−	1.32027i
$965$	−4.53847	−	2.62029i	−0.146099	−	0.0843500i
$966$	46.6442	+	13.5442i	1.50075	+	0.435777i
$967$	−19.7187	+	11.3846i	−0.634110	+	0.366104i	−0.782342	−	0.622849i	$-0.785975\pi$
$967$	−19.7187	+	11.3846i	−0.634110	+	0.366104i	0.148232	+	0.988953i	$0.452642\pi$
$968$	−4.35476	−	4.93527i	−0.139967	−	0.158626i
$969$	−72.8870	−	48.3382i	−2.34147	−	1.55285i
$970$	7.28675	+	7.59639i	0.233963	+	0.243905i
$971$	18.8364	+	32.6256i	0.604489	+	1.04701i	0.992132	+	0.125196i	$0.0399560\pi$
$971$	18.8364	+	32.6256i	0.604489	+	1.04701i	−0.387643	+	0.921810i	$0.626711\pi$
$972$	0.176887	−	0.0925381i	0.00567364	−	0.00296816i
$973$	18.2558	−	31.6199i	0.585253	−	1.01369i
$974$	26.5006	+	7.69505i	0.849134	+	0.246565i
$975$	4.44129	+	2.56418i	0.142235	+	0.0821195i
$976$	19.5390	+	1.62956i	0.625429	+	0.0521608i
$977$		−	20.2244i		−	0.647035i	−0.946222	−	0.323518i	$-0.895134\pi$
$977$		−	20.2244i		−	0.647035i	0.946222	−	0.323518i	$-0.104866\pi$
$978$	30.3829	−	7.46734i	0.971539	−	0.238779i
$979$	9.04584	−	15.6679i	0.289106	−	0.500747i
$980$	−0.791886	+	19.0230i	−0.0252959	+	0.607667i
$981$		−	46.3734i		−	1.48059i
$982$	−31.3313	+	7.70042i	−0.999821	+	0.245730i
$983$	−4.16727	−	7.21793i	−0.132915	−	0.230216i	0.791884	−	0.610672i	$-0.209101\pi$
$983$	−4.16727	−	7.21793i	−0.132915	−	0.230216i	−0.924799	+	0.380456i	$0.875767\pi$
$984$	−15.2475	−	75.4530i	−0.486071	−	2.40535i
$985$	1.30876	+	2.26684i	0.0417006	+	0.0722275i
$986$	−2.24876	+	7.74438i	−0.0716151	+	0.246631i
$987$	162.160			5.16160
$988$	−13.6033	+	6.07484i	−0.432778	+	0.193266i
$989$	14.7300			0.468387
$990$	−8.64593	+	29.7753i	−0.274786	+	0.946320i
$991$	−9.04215	−	15.6615i	−0.287233	−	0.497503i	0.685915	−	0.727682i	$-0.259402\pi$
$991$	−9.04215	−	15.6615i	−0.287233	−	0.497503i	−0.973148	+	0.230179i	$0.926069\pi$
$992$	−4.04151	−	25.4003i	−0.128318	−	0.806461i
$993$	30.4758	+	52.7856i	0.967120	+	1.67510i
$994$	−67.2478	+	16.5278i	−2.13297	+	0.524229i
$995$		−	9.11990i		−	0.289120i
$996$	−88.1589	−	3.66986i	−2.79342	−	0.116284i
$997$	11.8788	−	20.5747i	0.376207	−	0.651609i	−0.614300	−	0.789072i	$-0.710562\pi$
$997$	11.8788	−	20.5747i	0.376207	−	0.651609i	0.990507	+	0.137463i	$0.0438950\pi$
$998$	−27.1367	+	6.66951i	−0.858999	+	0.211120i
$999$			21.5634i			0.682236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.n.b.31.19	yes	40
4.3	odd	2	inner	380.2.n.b.31.12	✓	40
19.8	odd	6	inner	380.2.n.b.331.12	yes	40
76.27	even	6	inner	380.2.n.b.331.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.n.b.31.12	✓	40	4.3	odd	2	inner
380.2.n.b.31.19	yes	40	1.1	even	1	trivial
380.2.n.b.331.12	yes	40	19.8	odd	6	inner
380.2.n.b.331.19	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)

\(f(q)\)	\(=\)	\(q+(1.35812 + 0.394360i) q^{2} +(1.50046 + 2.59888i) q^{3} +(1.68896 + 1.07117i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.01291 + 4.12130i) q^{6} -4.06445i q^{7} +(1.87138 + 2.12084i) q^{8} +(-3.00277 + 5.20095i) q^{9} +O(q^{10})\)	\(q+(1.35812 + 0.394360i) q^{2} +(1.50046 + 2.59888i) q^{3} +(1.68896 + 1.07117i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.01291 + 4.12130i) q^{6} -4.06445i q^{7} +(1.87138 + 2.12084i) q^{8} +(-3.00277 + 5.20095i) q^{9} +(-0.337532 - 1.37334i) q^{10} +3.65062i q^{11} +(-0.249628 + 5.99665i) q^{12} +(-1.47998 - 0.854464i) q^{13} +(1.60286 - 5.51999i) q^{14} +(1.50046 - 2.59888i) q^{15} +(1.70517 + 3.61834i) q^{16} +(-3.34305 - 5.79034i) q^{17} +(-6.12916 + 5.87932i) q^{18} +(0.270060 - 4.35052i) q^{19} +(0.0831836 - 1.99827i) q^{20} +(10.5630 - 6.09855i) q^{21} +(-1.43966 + 4.95797i) q^{22} +(2.43857 + 1.40791i) q^{23} +(-2.70386 + 8.04571i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.67301 - 1.74410i) q^{26} -9.01939 q^{27} +(4.35373 - 6.86469i) q^{28} +(-0.738597 - 0.426429i) q^{29} +(3.06269 - 2.93785i) q^{30} -4.54667 q^{31} +(0.888895 + 5.58658i) q^{32} +(-9.48751 + 5.47762i) q^{33} +(-2.25678 - 9.18232i) q^{34} +(-3.51991 + 2.03222i) q^{35} +(-10.6427 + 5.56771i) q^{36} -2.39078i q^{37} +(2.08245 - 5.80202i) q^{38} -5.12836i q^{39} +(0.901011 - 2.68108i) q^{40} +(-7.85414 + 4.53459i) q^{41} +(16.7508 - 4.11691i) q^{42} +(4.53033 - 2.61559i) q^{43} +(-3.91045 + 6.16575i) q^{44} +6.00554 q^{45} +(2.75663 + 2.87378i) q^{46} +(11.5138 + 6.64747i) q^{47} +(-6.84507 + 9.86071i) q^{48} -9.51973 q^{49} +(-1.02058 + 0.978983i) q^{50} +(10.0322 - 17.3764i) q^{51} +(-1.58434 - 3.02847i) q^{52} +(2.43293 + 1.40465i) q^{53} +(-12.2494 - 3.55689i) q^{54} +(3.16153 - 1.82531i) q^{55} +(8.62003 - 7.60611i) q^{56} +(11.7117 - 5.82594i) q^{57} +(-0.834934 - 0.870413i) q^{58} +(-0.0742391 - 0.128586i) q^{59} +(5.31807 - 2.78214i) q^{60} +(2.45086 - 4.24501i) q^{61} +(-6.17490 - 1.79302i) q^{62} +(21.1390 + 12.2046i) q^{63} +(-0.995901 + 7.93777i) q^{64} +1.70893i q^{65} +(-15.0453 + 3.69775i) q^{66} +(-1.62142 + 2.80837i) q^{67} +(0.556174 - 13.3606i) q^{68} +8.45004i q^{69} +(-5.58188 + 1.37188i) q^{70} +(-6.02376 - 10.4335i) q^{71} +(-16.6497 + 3.36455i) q^{72} +(-0.443085 - 0.767446i) q^{73} +(0.942830 - 3.24696i) q^{74} -3.00092 q^{75} +(5.11629 - 7.05858i) q^{76} +14.8378 q^{77} +(2.02242 - 6.96491i) q^{78} +(3.61536 + 6.26199i) q^{79} +(2.28099 - 3.28589i) q^{80} +(-4.52494 - 7.83742i) q^{81} +(-12.4551 + 3.06114i) q^{82} +14.7014i q^{83} +(24.3731 + 1.01460i) q^{84} +(-3.34305 + 5.79034i) q^{85} +(7.18419 - 1.76569i) q^{86} -2.55936i q^{87} +(-7.74237 + 6.83169i) q^{88} +(-4.29183 - 2.47789i) q^{89} +(8.15622 + 2.36834i) q^{90} +(-3.47292 + 6.01528i) q^{91} +(2.61053 + 4.99003i) q^{92} +(-6.82210 - 11.8162i) q^{93} +(13.0155 + 13.5686i) q^{94} +(-3.90270 + 1.94138i) q^{95} +(-13.1851 + 10.6926i) q^{96} +(-6.44598 + 3.72159i) q^{97} +(-12.9289 - 3.75420i) q^{98} +(-18.9867 - 10.9620i) 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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