LMFDB - Embedded newform 380.2.n.b.31.16

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			31.16
Character	$\chi$	$=$	380.31
Dual form			380.2.n.b.331.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19364 - 0.758433i) q^{2} +(1.50479 + 2.60637i) q^{3} +(0.849559 - 1.81059i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(3.77293 + 1.96979i) q^{6} +2.59896i q^{7} +(-0.359145 - 2.80553i) q^{8} +(-3.02877 + 5.24598i) q^{9} +O(q^{10})$	\(q+(1.19364 - 0.758433i) q^{2} +(1.50479 + 2.60637i) q^{3} +(0.849559 - 1.81059i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(3.77293 + 1.96979i) q^{6} +2.59896i q^{7} +(-0.359145 - 2.80553i) q^{8} +(-3.02877 + 5.24598i) q^{9} +(-1.25364 - 0.654507i) q^{10} -4.32584i q^{11} +(5.99748 - 0.510295i) q^{12} +(5.09891 + 2.94386i) q^{13} +(1.97114 + 3.10223i) q^{14} +(1.50479 - 2.60637i) q^{15} +(-2.55650 - 3.07641i) q^{16} +(-0.759646 - 1.31575i) q^{17} +(0.363461 + 8.55894i) q^{18} +(1.56011 + 4.07014i) q^{19} +(-1.99280 + 0.169557i) q^{20} +(-6.77385 + 3.91089i) q^{21} +(-3.28086 - 5.16350i) q^{22} +(-4.53570 - 2.61869i) q^{23} +(6.77181 - 5.15779i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(8.31899 - 0.353272i) q^{26} -9.20188 q^{27} +(4.70567 + 2.20797i) q^{28} +(-8.10230 - 4.67787i) q^{29} +(-0.180579 - 4.25235i) q^{30} -5.63734 q^{31} +(-5.38480 - 1.73320i) q^{32} +(11.2747 - 6.50946i) q^{33} +(-1.90465 - 0.994388i) q^{34} +(2.25077 - 1.29948i) q^{35} +(6.92522 + 9.94064i) q^{36} -5.86885i q^{37} +(4.94914 + 3.67505i) q^{38} +17.7195i q^{39} +(-2.25009 + 1.71380i) q^{40} +(0.487467 - 0.281439i) q^{41} +(-5.11941 + 9.80571i) q^{42} +(4.31427 - 2.49085i) q^{43} +(-7.83233 - 3.67505i) q^{44} +6.05754 q^{45} +(-7.40011 + 0.314251i) q^{46} +(1.11525 + 0.643888i) q^{47} +(4.17128 - 11.2925i) q^{48} +0.245391 q^{49} +(0.0600015 + 1.41294i) q^{50} +(2.28621 - 3.95983i) q^{51} +(9.66196 - 6.73108i) q^{52} +(3.04525 + 1.75818i) q^{53} +(-10.9837 + 6.97901i) q^{54} +(-3.74628 + 2.16292i) q^{55} +(7.29148 - 0.933405i) q^{56} +(-8.26066 + 10.1909i) q^{57} +(-13.2191 + 0.561358i) q^{58} +(-4.06944 - 7.04847i) q^{59} +(-3.44067 - 4.93882i) q^{60} +(1.65392 - 2.86467i) q^{61} +(-6.72896 + 4.27555i) q^{62} +(-13.6341 - 7.87166i) q^{63} +(-7.74203 + 2.01519i) q^{64} -5.88772i q^{65} +(8.52098 - 16.3211i) q^{66} +(0.662378 - 1.14727i) q^{67} +(-3.02765 + 0.257607i) q^{68} -15.7623i q^{69} +(1.70104 - 3.25817i) q^{70} +(-0.864436 - 1.49725i) q^{71} +(15.8055 + 6.61324i) q^{72} +(0.793145 + 1.37377i) q^{73} +(-4.45113 - 7.00530i) q^{74} -3.00957 q^{75} +(8.69478 + 0.633105i) q^{76} +11.2427 q^{77} +(13.4391 + 21.1507i) q^{78} +(-0.810011 - 1.40298i) q^{79} +(-1.38600 + 3.75220i) q^{80} +(-4.76057 - 8.24555i) q^{81} +(0.368408 - 0.705648i) q^{82} +16.0338i q^{83} +(1.32624 + 15.5872i) q^{84} +(-0.759646 + 1.31575i) q^{85} +(3.26055 - 6.24526i) q^{86} -28.1568i q^{87} +(-12.1363 + 1.55360i) q^{88} +(13.2176 + 7.63116i) q^{89} +(7.23053 - 4.59424i) q^{90} +(-7.65098 + 13.2519i) q^{91} +(-8.59473 + 5.98759i) q^{92} +(-8.48300 - 14.6930i) q^{93} +(1.81955 - 0.0772685i) q^{94} +(2.74479 - 3.38616i) q^{95} +(-3.58561 - 16.6429i) q^{96} +(9.46559 - 5.46496i) q^{97} +(0.292909 - 0.186113i) q^{98} +(22.6933 + 13.1020i) 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 $

$2$	1.19364	−	0.758433i	0.844032	−	0.536293i
$2$	1.19364	−	0.758433i	0.844032	−	0.536293i
$3$	1.50479	+	2.60637i	0.868789	+	1.50479i	0.863235	+	0.504802i	$0.168435\pi$
$3$	1.50479	+	2.60637i	0.868789	+	1.50479i	0.00555435	+	0.999985i	$0.498232\pi$
$4$	0.849559	−	1.81059i	0.424780	−	0.905297i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	3.77293	+	1.96979i	1.54029	+	0.804163i
$7$			2.59896i			0.982316i	0.871071	+	0.491158i	$0.163426\pi$
$7$			2.59896i			0.982316i	−0.871071	+	0.491158i	$0.836574\pi$
$8$	−0.359145	−	2.80553i	−0.126977	−	0.991906i
$9$	−3.02877	+	5.24598i	−1.00959	+	1.74866i
$10$	−1.25364	−	0.654507i	−0.396437	−	0.206973i
$11$		−	4.32584i		−	1.30429i	−0.758095	−	0.652144i	$-0.773870\pi$
$11$		−	4.32584i		−	1.30429i	0.758095	−	0.652144i	$-0.226130\pi$
$12$	5.99748	−	0.510295i	1.73132	−	0.147309i
$13$	5.09891	+	2.94386i	1.41418	+	0.816479i	0.995779	−	0.0917817i	$-0.0292562\pi$
$13$	5.09891	+	2.94386i	1.41418	+	0.816479i	0.418404	+	0.908261i	$0.362590\pi$
$14$	1.97114	+	3.10223i	0.526809	+	0.829106i
$15$	1.50479	−	2.60637i	0.388534	−	0.672961i
$16$	−2.55650	−	3.07641i	−0.639125	−	0.769103i
$17$	−0.759646	−	1.31575i	−0.184241	−	0.319115i	0.759079	−	0.650998i	$-0.225649\pi$
$17$	−0.759646	−	1.31575i	−0.184241	−	0.319115i	−0.943321	+	0.331883i	$0.892316\pi$
$18$	0.363461	+	8.55894i	0.0856687	+	2.01736i
$19$	1.56011	+	4.07014i	0.357913	+	0.933755i
$19$	1.56011	+	4.07014i	0.357913	+	0.933755i
$20$	−1.99280	+	0.169557i	−0.445604	+	0.0379141i
$21$	−6.77385	+	3.91089i	−1.47818	+	0.853425i
$22$	−3.28086	−	5.16350i	−0.699481	−	1.10086i
$23$	−4.53570	−	2.61869i	−0.945760	−	0.546035i	−0.0539986	−	0.998541i	$-0.517197\pi$
$23$	−4.53570	−	2.61869i	−0.945760	−	0.546035i	−0.891761	+	0.452506i	$0.850530\pi$
$24$	6.77181	−	5.15779i	1.38229	−	1.05283i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	8.31899	−	0.353272i	1.63149	−	0.0692823i
$27$	−9.20188			−1.77090
$28$	4.70567	+	2.20797i	0.889287	+	0.417268i
$29$	−8.10230	−	4.67787i	−1.50456	−	0.868658i	−0.999986	−	0.00528910i	$-0.998316\pi$
$29$	−8.10230	−	4.67787i	−1.50456	−	0.868658i	−0.504574	−	0.863369i	$-0.668350\pi$
$30$	−0.180579	−	4.25235i	−0.0329691	−	0.776369i
$31$	−5.63734			−1.01250			−0.506248	−	0.862388i	$-0.668968\pi$
$31$	−5.63734			−1.01250			−0.506248	+	0.862388i	$0.668968\pi$
$32$	−5.38480	−	1.73320i	−0.951906	−	0.306389i
$33$	11.2747	−	6.50946i	1.96268	−	1.13315i
$34$	−1.90465	−	0.994388i	−0.326645	−	0.170536i
$35$	2.25077	−	1.29948i	0.380449	−	0.219652i
$36$	6.92522	+	9.94064i	1.15420	+	1.65677i
$37$		−	5.86885i		−	0.964832i	−0.875942	−	0.482416i	$-0.839759\pi$
$37$		−	5.86885i		−	0.964832i	0.875942	−	0.482416i	$-0.160241\pi$
$38$	4.94914	+	3.67505i	0.802856	+	0.596172i
$39$			17.7195i			2.83739i
$40$	−2.25009	+	1.71380i	−0.355771	+	0.270975i
$41$	0.487467	−	0.281439i	0.0761296	−	0.0439534i	−0.461452	−	0.887165i	$-0.652671\pi$
$41$	0.487467	−	0.281439i	0.0761296	−	0.0439534i	0.537582	+	0.843212i	$0.319338\pi$
$42$	−5.11941	+	9.80571i	−0.789942	+	1.51305i
$43$	4.31427	−	2.49085i	0.657920	−	0.379850i	−0.133564	−	0.991040i	$-0.542642\pi$
$43$	4.31427	−	2.49085i	0.657920	−	0.379850i	0.791484	+	0.611190i	$0.209309\pi$
$44$	−7.83233	−	3.67505i	−1.18077	−	0.554035i
$45$	6.05754			0.903004
$46$	−7.40011	+	0.314251i	−1.09109	+	0.0463338i
$47$	1.11525	+	0.643888i	0.162675	+	0.0939207i	0.579128	−	0.815237i	$-0.303393\pi$
$47$	1.11525	+	0.643888i	0.162675	+	0.0939207i	−0.416452	+	0.909158i	$0.636727\pi$
$48$	4.17128	−	11.2925i	0.602072	−	1.62994i
$49$	0.245391			0.0350559
$50$	0.0600015	+	1.41294i	0.00848550	+	0.199820i
$51$	2.28621	−	3.95983i	0.320134	−	0.554488i
$52$	9.66196	−	6.73108i	1.33987	−	0.933432i
$53$	3.04525	+	1.75818i	0.418297	+	0.241504i	0.694348	−	0.719639i	$-0.255693\pi$
$53$	3.04525	+	1.75818i	0.418297	+	0.241504i	−0.276051	+	0.961143i	$0.589026\pi$
$54$	−10.9837	+	6.97901i	−1.49470	+	0.949723i
$55$	−3.74628	+	2.16292i	−0.505149	+	0.291648i
$56$	7.29148	−	0.933405i	0.974364	−	0.124731i
$57$	−8.26066	+	10.1909i	−1.09415	+	1.34982i
$58$	−13.2191	+	0.561358i	−1.73575	+	0.0737099i
$59$	−4.06944	−	7.04847i	−0.529796	−	0.917633i	−0.999396	−	0.0347540i	$-0.988935\pi$
$59$	−4.06944	−	7.04847i	−0.529796	−	0.917633i	0.469600	−	0.882879i	$-0.344398\pi$
$60$	−3.44067	−	4.93882i	−0.444188	−	0.637599i
$61$	1.65392	−	2.86467i	0.211763	−	0.366784i	−0.740504	−	0.672052i	$-0.765413\pi$
$61$	1.65392	−	2.86467i	0.211763	−	0.366784i	0.952266	+	0.305269i	$0.0987463\pi$
$62$	−6.72896	+	4.27555i	−0.854579	+	0.542995i
$63$	−13.6341	−	7.87166i	−1.71774	−	0.991736i
$64$	−7.74203	+	2.01519i	−0.967754	+	0.251898i
$65$		−	5.88772i		−	0.730281i
$66$	8.52098	−	16.3211i	1.04886	−	2.00899i
$67$	0.662378	−	1.14727i	0.0809223	−	0.140162i	−0.822724	−	0.568441i	$-0.807547\pi$
$67$	0.662378	−	1.14727i	0.0809223	−	0.140162i	0.903646	+	0.428279i	$0.140880\pi$
$68$	−3.02765	+	0.257607i	−0.367156	+	0.0312394i
$69$		−	15.7623i		−	1.89756i
$70$	1.70104	−	3.25817i	0.203313	−	0.389426i
$71$	−0.864436	−	1.49725i	−0.102590	−	0.177691i	0.810161	−	0.586207i	$-0.199380\pi$
$71$	−0.864436	−	1.49725i	−0.102590	−	0.177691i	−0.912751	+	0.408517i	$0.866046\pi$
$72$	15.8055	+	6.61324i	1.86270	+	0.779378i
$73$	0.793145	+	1.37377i	0.0928306	+	0.160787i	0.908701	−	0.417447i	$-0.137075\pi$
$73$	0.793145	+	1.37377i	0.0928306	+	0.160787i	−0.815871	+	0.578235i	$0.803742\pi$
$74$	−4.45113	−	7.00530i	−0.517433	−	0.814349i
$75$	−3.00957			−0.347516
$76$	8.69478	+	0.633105i	0.997360	+	0.0726221i
$77$	11.2427			1.28122
$78$	13.4391	+	21.1507i	1.52167	+	2.39485i
$79$	−0.810011	−	1.40298i	−0.0911334	−	0.157848i	0.816855	−	0.576843i	$-0.195716\pi$
$79$	−0.810011	−	1.40298i	−0.0911334	−	0.157848i	−0.907988	+	0.418996i	$0.862382\pi$
$80$	−1.38600	+	3.75220i	−0.154960	+	0.419509i
$81$	−4.76057	−	8.24555i	−0.528952	−	0.916172i
$82$	0.368408	−	0.705648i	0.0406839	−	0.0779258i
$83$			16.0338i			1.75994i	0.475032	+	0.879969i	$0.342437\pi$
$83$			16.0338i			1.75994i	−0.475032	+	0.879969i	$0.657563\pi$
$84$	1.32624	+	15.5872i	0.144704	+	1.70071i
$85$	−0.759646	+	1.31575i	−0.0823952	+	0.142713i
$86$	3.26055	−	6.24526i	0.351594	−	0.673444i
$87$		−	28.1568i		−	3.01872i
$88$	−12.1363	+	1.55360i	−1.29373	+	0.165615i
$89$	13.2176	+	7.63116i	1.40106	+	0.808901i	0.994501	−	0.104725i	$-0.0333961\pi$
$89$	13.2176	+	7.63116i	1.40106	+	0.808901i	0.406557	+	0.913626i	$0.366729\pi$
$90$	7.23053	−	4.59424i	0.762164	−	0.484275i
$91$	−7.65098	+	13.2519i	−0.802040	+	1.38917i
$92$	−8.59473	+	5.98759i	−0.896063	+	0.624249i
$93$	−8.48300	−	14.6930i	−0.879646	−	1.52359i
$94$	1.81955	−	0.0772685i	0.187672	−	0.00796964i
$95$	2.74479	−	3.38616i	0.281610	−	0.347413i
$96$	−3.58561	−	16.6429i	−0.365955	−	1.69860i
$97$	9.46559	−	5.46496i	0.961085	−	0.554883i	0.0645782	−	0.997913i	$-0.479430\pi$
$97$	9.46559	−	5.46496i	0.961085	−	0.554883i	0.896507	+	0.443030i	$0.146096\pi$
$98$	0.292909	−	0.186113i	0.0295883	−	0.0188002i
$99$	22.6933	+	13.1020i	2.28076	+	1.31680i
$100$	1.14324	+	1.64104i	0.114324	+	0.164104i
$101$	−9.17146	+	15.8854i	−0.912594	+	1.58066i	−0.102209	+	0.994763i	$0.532591\pi$
$101$	−9.17146	+	15.8854i	−0.912594	+	1.58066i	−0.810385	+	0.585897i	$0.800742\pi$
$102$	−0.274352	−	6.46056i	−0.0271649	−	0.639691i
$103$	−16.8053			−1.65588			−0.827940	−	0.560816i	$-0.810487\pi$
$103$	−16.8053			−1.65588			−0.827940	+	0.560816i	$0.810487\pi$
$104$	6.42784	−	15.3624i	0.630302	−	1.50641i
$105$	6.77385	+	3.91089i	0.661060	+	0.381663i
$106$	4.96839	−	0.210986i	0.482573	−	0.0204928i
$107$	−1.44673			−0.139860			−0.0699301	−	0.997552i	$-0.522278\pi$
$107$	−1.44673			−0.139860			−0.0699301	+	0.997552i	$0.522278\pi$
$108$	−7.81754	+	16.6609i	−0.752243	+	1.60319i
$109$	−8.22720	+	4.74998i	−0.788023	+	0.454965i	−0.839266	−	0.543721i	$-0.817015\pi$
$109$	−8.22720	+	4.74998i	−0.788023	+	0.454965i	0.0512430	+	0.998686i	$0.483682\pi$
$110$	−2.83129	+	5.42305i	−0.269953	+	0.517068i
$111$	15.2964	−	8.83136i	1.45187	−	0.838236i
$112$	7.99548	−	6.64425i	0.755502	−	0.627822i
$113$			7.28198i			0.685031i	0.939512	+	0.342516i	$0.111279\pi$
$113$			7.28198i			0.685031i	−0.939512	+	0.342516i	$0.888721\pi$
$114$	−2.13114	+	18.4295i	−0.199599	+	1.72608i
$115$			5.23738i			0.488388i
$116$	−15.3531	+	10.6959i	−1.42550	+	0.993085i
$117$	−30.8868	+	17.8325i	−2.85549	+	1.64862i
$118$	−10.2032	−	5.32695i	−0.939285	−	0.490386i
$119$	3.41957	−	1.97429i	0.313472	−	0.180983i
$120$	−7.85269	−	3.28567i	−0.716849	−	0.299939i
$121$	−7.71286			−0.701169
$122$	−0.198475	−	4.67378i	−0.0179691	−	0.423144i
$123$	1.46707	+	0.847012i	0.132281	+	0.0763725i
$124$	−4.78925	+	10.2069i	−0.430088	+	0.916610i
$125$	1.00000			0.0894427
$126$	−22.2444	+	0.944623i	−1.98168	+	0.0841537i
$127$	2.11221	−	3.65845i	0.187428	−	0.324635i	−0.756964	−	0.653457i	$-0.773318\pi$
$127$	2.11221	−	3.65845i	0.187428	−	0.324635i	0.944392	+	0.328822i	$0.106651\pi$
$128$	−7.71282	+	8.27722i	−0.681724	+	0.731610i
$129$	12.9841	+	7.49638i	1.14319	+	0.660020i
$130$	−4.46544	−	7.02782i	−0.391645	−	0.616381i
$131$	−4.79102	+	2.76610i	−0.418594	+	0.241675i	−0.694475	−	0.719516i	$-0.744363\pi$
$131$	−4.79102	+	2.76610i	−0.418594	+	0.241675i	0.275882	+	0.961192i	$0.411030\pi$
$132$	−2.20745	−	25.9441i	−0.192134	−	2.25814i
$133$	−10.5782	+	4.05466i	−0.917242	+	0.351584i
$134$	−0.0794874	−	1.87180i	−0.00686666	−	0.161699i
$135$	4.60094	+	7.96906i	0.395986	+	0.685868i
$136$	−3.41854	+	2.60376i	−0.293138	+	0.223270i
$137$	−1.89477	+	3.28184i	−0.161881	+	0.280386i	−0.935543	−	0.353212i	$-0.885089\pi$
$137$	−1.89477	+	3.28184i	−0.161881	+	0.280386i	0.773662	+	0.633598i	$0.218423\pi$
$138$	−11.9546	−	18.8145i	−1.01765	−	1.60160i
$139$	19.1897	+	11.0792i	1.62765	+	0.939724i	0.984792	+	0.173737i	$0.0555844\pi$
$139$	19.1897	+	11.0792i	1.62765	+	0.939724i	0.642857	+	0.765986i	$0.277749\pi$
$140$	−0.440673	−	5.17921i	−0.0372436	−	0.437723i
$141$			3.87566i			0.326389i
$142$	−2.16739	−	1.13156i	−0.181883	−	0.0949583i
$143$	12.7346	−	22.0571i	1.06492	−	1.84450i
$144$	23.8818	−	4.09360i	1.99015	−	0.341134i
$145$			9.35573i			0.776951i
$146$	1.98864	+	1.03824i	0.164581	+	0.0859252i
$147$	0.369262	+	0.639580i	0.0304562	+	0.0527517i
$148$	−10.6261	−	4.98593i	−0.873460	−	0.409841i
$149$	3.19056	+	5.52622i	0.261381	+	0.452725i	0.966609	−	0.256255i	$-0.0824887\pi$
$149$	3.19056	+	5.52622i	0.261381	+	0.452725i	−0.705228	+	0.708981i	$0.749155\pi$
$150$	−3.59235	+	2.28256i	−0.293314	+	0.186370i
$151$	8.52065			0.693400			0.346700	−	0.937976i	$-0.387302\pi$
$151$	8.52065			0.693400			0.346700	+	0.937976i	$0.387302\pi$
$152$	10.8586	−	5.83871i	0.880750	−	0.473582i
$153$	9.20317			0.744032
$154$	13.4197	−	8.52682i	1.08139	−	0.687111i
$155$	2.81867	+	4.88208i	0.226401	+	0.392138i
$156$	32.0828	+	15.0538i	2.56868	+	1.20527i
$157$	−1.53651	−	2.66131i	−0.122627	−	0.212396i	0.798176	−	0.602424i	$-0.205798\pi$
$157$	−1.53651	−	2.66131i	−0.122627	−	0.212396i	−0.920803	+	0.390029i	$0.872465\pi$
$158$	−2.03093	−	1.06032i	−0.161572	−	0.0843542i
$159$			10.5827i			0.839264i
$160$	1.19140	+	5.52997i	0.0941886	+	0.437182i
$161$	6.80588	−	11.7881i	0.536378	−	0.929035i
$162$	−11.9361	−	6.23165i	−0.937789	−	0.489605i
$163$			6.54430i			0.512589i	0.966599	+	0.256295i	$0.0825017\pi$
$163$			6.54430i			0.512589i	−0.966599	+	0.256295i	$0.917498\pi$
$164$	−0.0954400	−	1.12170i	−0.00745262	−	0.0875904i
$165$	−11.2747	−	6.50946i	−0.877736	−	0.506761i
$166$	12.1606	+	19.1386i	0.943842	+	1.48544i
$167$	2.80728	−	4.86236i	0.217234	−	0.376260i	−0.736727	−	0.676190i	$-0.763630\pi$
$167$	2.80728	−	4.86236i	0.217234	−	0.376260i	0.953961	+	0.299930i	$0.0969632\pi$
$168$	13.4049	+	17.5997i	1.03421	+	1.35785i
$169$	10.8326	+	18.7626i	0.833277	+	1.44328i
$170$	0.0911598	+	2.14667i	0.00699164	+	0.164642i
$171$	−26.0771	−	4.14322i	−1.99417	−	0.316840i
$172$	−0.844681	−	9.92751i	−0.0644063	−	0.756966i
$173$	−7.45752	+	4.30560i	−0.566985	+	0.327349i	−0.755944	−	0.654636i	$-0.772822\pi$
$173$	−7.45752	+	4.30560i	−0.566985	+	0.327349i	0.188959	+	0.981985i	$0.439489\pi$
$174$	−21.3550	−	33.6091i	−1.61892	−	2.54790i
$175$	−2.25077	−	1.29948i	−0.170142	−	0.0982316i
$176$	−13.3081	+	11.0590i	−1.00313	+	0.833603i
$177$	12.2473	−	21.2129i	0.920562	−	1.59446i
$178$	21.5647	−	0.915762i	1.61635	−	0.0686393i
$179$	−3.60586			−0.269515			−0.134757	−	0.990879i	$-0.543025\pi$
$179$	−3.60586			−0.269515			−0.134757	+	0.990879i	$0.543025\pi$
$180$	5.14623	−	10.9677i	0.383578	−	0.817487i
$181$	10.8721	+	6.27702i	0.808119	+	0.466568i	0.846302	−	0.532703i	$-0.178824\pi$
$181$	10.8721	+	6.27702i	0.808119	+	0.466568i	−0.0381835	+	0.999271i	$0.512157\pi$
$182$	0.918141	+	21.6207i	0.0680571	+	1.60264i
$183$	9.95518			0.735908
$184$	−5.71785	+	13.6656i	−0.421525	+	1.00744i
$185$	−5.08257	+	2.93442i	−0.373678	+	0.215743i
$186$	−21.2693	−	11.1044i	−1.55954	−	0.814212i
$187$	−5.69170	+	3.28610i	−0.416218	+	0.240304i
$188$	2.11329	−	1.47224i	0.154127	−	0.107374i
$189$		−	23.9154i		−	1.73959i
$190$	0.708120	−	6.12361i	0.0513724	−	0.444253i
$191$		−	19.2804i		−	1.39508i	−0.716545	−	0.697541i	$-0.754278\pi$
$191$		−	19.2804i		−	1.39508i	0.716545	−	0.697541i	$-0.245722\pi$
$192$	−16.9024	−	17.1461i	−1.21983	−	1.23742i
$193$	3.13532	−	1.81018i	0.225686	−	0.130300i	−0.382895	−	0.923792i	$-0.625073\pi$
$193$	3.13532	−	1.81018i	0.225686	−	0.130300i	0.608580	+	0.793492i	$0.291739\pi$
$194$	7.15371	−	13.7022i	0.513607	−	0.983762i
$195$	15.3456	−	8.85976i	1.09892	−	0.634460i
$196$	0.208475	−	0.444304i	0.0148910	−	0.0317360i
$197$	11.5560			0.823332			0.411666	−	0.911335i	$-0.364947\pi$
$197$	11.5560			0.823332			0.411666	+	0.911335i	$0.364947\pi$
$198$	37.0246	−	1.57227i	2.63122	−	0.111737i
$199$	6.91788	+	3.99404i	0.490395	+	0.283130i	0.724739	−	0.689024i	$-0.241961\pi$
$199$	6.91788	+	3.99404i	0.490395	+	0.283130i	−0.234343	+	0.972154i	$0.575294\pi$
$200$	2.60924	+	1.09174i	0.184501	+	0.0771975i
$201$	3.98695			0.281218
$202$	1.10060	+	25.9175i	0.0774382	+	1.82355i
$203$	12.1576	−	21.0576i	0.853296	−	1.47795i
$204$	−5.22738	−	7.50351i	−0.365990	−	0.525351i
$205$	−0.487467	−	0.281439i	−0.0340462	−	0.0196566i
$206$	−20.0596	+	12.7457i	−1.39762	+	0.888037i
$207$	27.4752	−	15.8628i	1.90966	−	1.10254i
$208$	−3.97884	−	23.2123i	−0.275883	−	1.60948i
$209$	17.6068	−	6.74877i	1.21789	−	0.466822i
$210$	11.0517	−	0.469318i	0.762639	−	0.0323860i
$211$	−3.16536	−	5.48257i	−0.217913	−	0.377436i	0.736257	−	0.676702i	$-0.236591\pi$
$211$	−3.16536	−	5.48257i	−0.217913	−	0.377436i	−0.954170	+	0.299266i	$0.903258\pi$
$212$	5.77046	−	4.02004i	0.396317	−	0.276097i
$213$	2.60158	−	4.50608i	0.178258	−	0.308751i
$214$	−1.72687	+	1.09724i	−0.118046	+	0.0750061i
$215$	−4.31427	−	2.49085i	−0.294231	−	0.169874i
$216$	3.30481	+	25.8162i	0.224864	+	1.75657i
$217$		−	14.6512i		−	0.994591i
$218$	−6.21779	+	11.9096i	−0.421122	+	0.806617i
$219$	−2.38703	+	4.13445i	−0.161300	+	0.279380i
$220$	0.733476	+	8.62052i	0.0494510	+	0.581196i
$221$		−	8.94516i		−	0.601717i
$222$	11.5604	−	22.1428i	0.775882	−	1.48612i
$223$	−6.65628	−	11.5290i	−0.445738	−	0.772040i	0.552366	−	0.833602i	$-0.313725\pi$
$223$	−6.65628	−	11.5290i	−0.445738	−	0.772040i	−0.998103	+	0.0615618i	$0.980392\pi$
$224$	4.50452	−	13.9949i	0.300971	−	0.935072i
$225$	−3.02877	−	5.24598i	−0.201918	−	0.349732i
$226$	5.52290	+	8.69208i	0.367378	+	0.578188i
$227$	−4.41385			−0.292958			−0.146479	−	0.989214i	$-0.546794\pi$
$227$	−4.41385			−0.292958			−0.146479	+	0.989214i	$0.546794\pi$
$228$	11.4337	+	23.6145i	0.757214	+	1.56391i
$229$	−6.67515			−0.441106			−0.220553	−	0.975375i	$-0.570786\pi$
$229$	−6.67515			−0.441106			−0.220553	+	0.975375i	$0.570786\pi$
$230$	3.97220	+	6.25155i	0.261919	+	0.412215i
$231$	16.9179	+	29.3026i	1.11311	+	1.92797i
$232$	−10.2140	+	24.4113i	−0.670582	+	1.60268i
$233$	−11.5886	−	20.0721i	−0.759195	−	1.31496i	−0.943262	−	0.332050i	$-0.892260\pi$
$233$	−11.5886	−	20.0721i	−0.759195	−	1.31496i	0.184067	−	0.982914i	$-0.441074\pi$
$234$	−23.3430	+	44.7112i	−1.52598	+	2.92286i
$235$		−	1.28778i		−	0.0840052i
$236$	−16.2192	+	1.38000i	−1.05578	+	0.0898306i
$237$	2.43779	−	4.22237i	0.158351	−	0.274273i
$238$	2.58438	−	4.95011i	0.167520	−	0.320868i
$239$			7.18860i			0.464992i	0.972597	+	0.232496i	$0.0746892\pi$
$239$			7.18860i			0.464992i	−0.972597	+	0.232496i	$0.925311\pi$
$240$	−11.8652	+	2.03383i	−0.765898	+	0.131283i
$241$	−11.9469	−	6.89757i	−0.769571	−	0.444312i	0.0631508	−	0.998004i	$-0.479885\pi$
$241$	−11.9469	−	6.89757i	−0.769571	−	0.444312i	−0.832721	+	0.553692i	$0.813218\pi$
$242$	−9.20638	+	5.84968i	−0.591809	+	0.376032i
$243$	0.524462	−	0.908396i	0.0336443	−	0.0582736i
$244$	−3.78165	−	5.42828i	−0.242096	−	0.347510i
$245$	−0.122696	−	0.212515i	−0.00783874	−	0.0135771i
$246$	2.39355	−	0.101644i	0.152607	−	0.00648059i
$247$	−4.02707	+	25.3460i	−0.256236	+	1.61273i
$248$	2.02462	+	15.8157i	0.128564	+	1.00430i
$249$	−41.7900	+	24.1274i	−2.64833	+	1.52901i
$250$	1.19364	−	0.758433i	0.0754925	−	0.0479675i
$251$	8.48999	+	4.90170i	0.535883	+	0.309392i	0.743409	−	0.668837i	$-0.233208\pi$
$251$	8.48999	+	4.90170i	0.535883	+	0.309392i	−0.207526	+	0.978230i	$0.566541\pi$
$252$	−25.8354	+	17.9984i	−1.62747	+	1.13379i
$253$	−11.3280	+	19.6207i	−0.712187	+	1.23354i
$254$	−0.253471	−	5.96885i	−0.0159042	−	0.374519i
$255$	−4.57242			−0.286336
$256$	−2.92863	+	15.7297i	−0.183039	+	0.983106i
$257$	7.48480	+	4.32135i	0.466889	+	0.269558i	0.714936	−	0.699189i	$-0.246456\pi$
$257$	7.48480	+	4.32135i	0.466889	+	0.269558i	−0.248048	+	0.968748i	$0.579789\pi$
$258$	21.1839	−	0.899589i	1.31885	−	0.0560060i
$259$	15.2529			0.947770
$260$	−10.6603	−	5.00196i	−0.661121	−	0.310209i
$261$	49.0800	−	28.3363i	3.03797	−	1.75398i
$262$	−3.62086	+	6.93540i	−0.223698	+	0.428470i
$263$	6.86302	−	3.96236i	0.423192	−	0.244330i	−0.273250	−	0.961943i	$-0.588099\pi$
$263$	6.86302	−	3.96236i	0.423192	−	0.244330i	0.696442	+	0.717613i	$0.254765\pi$
$264$	−22.3118	−	29.2938i	−1.37319	−	1.80291i
$265$		−	3.51635i		−	0.216008i
$266$	−9.55133	+	12.8626i	−0.585629	+	0.788658i
$267$			45.9331i			2.81106i
$268$	−1.51451	−	2.17397i	−0.0925137	−	0.132797i
$269$	−8.82121	+	5.09293i	−0.537839	+	0.310521i	−0.744203	−	0.667954i	$-0.767170\pi$
$269$	−8.82121	+	5.09293i	−0.537839	+	0.310521i	0.206364	+	0.978475i	$0.433837\pi$
$270$	11.5359	+	6.02270i	0.702051	+	0.366530i
$271$	−7.54501	+	4.35611i	−0.458327	+	0.264615i	−0.711340	−	0.702848i	$-0.751912\pi$
$271$	−7.54501	+	4.35611i	−0.458327	+	0.264615i	0.253014	+	0.967463i	$0.418578\pi$
$272$	−2.10574	+	5.70069i	−0.127679	+	0.345655i
$273$	−46.0524			−2.78722
$274$	0.227378	+	5.35439i	0.0137364	+	0.323471i
$275$	3.74628	+	2.16292i	0.225909	+	0.130429i
$276$	−28.5391	−	13.3910i	−1.71785	−	0.806043i
$277$	11.7321			0.704914			0.352457	−	0.935828i	$-0.385346\pi$
$277$	11.7321			0.704914			0.352457	+	0.935828i	$0.385346\pi$
$278$	31.3084	−	1.32954i	1.87775	−	0.0797402i
$279$	17.0742	−	29.5734i	1.02221	−	1.77051i
$280$	−4.45409	−	5.84790i	−0.266183	−	0.349479i
$281$	10.8034	+	6.23734i	0.644476	+	0.372088i	0.786337	−	0.617798i	$-0.211975\pi$
$281$	10.8034	+	6.23734i	0.644476	+	0.372088i	−0.141861	+	0.989887i	$0.545309\pi$
$282$	2.93943	+	4.62614i	0.175040	+	0.275483i
$283$	−10.3125	+	5.95395i	−0.613017	+	0.353926i	−0.774145	−	0.633008i	$-0.781820\pi$
$283$	−10.3125	+	5.95395i	−0.613017	+	0.353926i	0.161128	+	0.986933i	$0.448487\pi$
$284$	−3.44530	+	0.293143i	−0.204441	+	0.0173948i
$285$	12.9559	+	2.05848i	0.767442	+	0.121934i
$286$	−1.52820	−	35.9866i	−0.0903641	−	2.12793i
$287$	0.731450	+	1.26691i	0.0431761	+	0.0747833i
$288$	25.4016	−	22.9991i	1.49681	−	1.35523i
$289$	7.34588	−	12.7234i	0.432110	−	0.748437i
$290$	7.09569	+	11.1674i	0.416674	+	0.655772i
$291$	28.4874	+	16.4472i	1.66996	+	0.964152i
$292$	3.16116	−	0.268967i	0.184993	−	0.0157401i
$293$			29.9131i			1.74754i	0.486335	+	0.873772i	$0.338333\pi$
$293$			29.9131i			1.74754i	−0.486335	+	0.873772i	$0.661667\pi$
$294$	0.925845	+	0.483369i	0.0539964	+	0.0281907i
$295$	−4.06944	+	7.04847i	−0.236932	+	0.410378i
$296$	−16.4652	+	2.10777i	−0.957023	+	0.122511i
$297$			39.8058i			2.30977i
$298$	7.99965	+	4.17649i	0.463407	+	0.241938i
$299$	−15.4181	−	26.7049i	−0.891652	−	1.54439i
$300$	−2.55681	+	5.44912i	−0.147618	+	0.314605i
$301$	6.47361	+	11.2126i	0.373133	+	0.646285i
$302$	10.1706	−	6.46234i	0.585252	−	0.371866i
$303$	−55.2044			−3.17141
$304$	8.53302	−	15.2049i	0.489402	−	0.872058i
$305$	−3.30784			−0.189406
$306$	10.9853	−	6.97999i	0.627987	−	0.399019i
$307$	−13.3391	−	23.1039i	−0.761301	−	1.31861i	−0.942180	−	0.335106i	$-0.891228\pi$
$307$	−13.3391	−	23.1039i	−0.761301	−	1.31861i	0.180880	−	0.983505i	$-0.442105\pi$
$308$	9.55133	−	20.3559i	0.544237	−	1.15989i
$309$	−25.2885	−	43.8009i	−1.43861	−	2.49175i
$310$	7.06721	+	3.68968i	0.401391	+	0.209560i
$311$		−	24.3311i		−	1.37969i	−0.723957	−	0.689845i	$-0.757679\pi$
$311$		−	24.3311i		−	1.37969i	0.723957	−	0.689845i	$-0.242321\pi$
$312$	49.7127	−	6.36388i	2.81443	−	0.360284i
$313$	6.85716	−	11.8769i	0.387590	−	0.671325i	−0.604535	−	0.796578i	$-0.706641\pi$
$313$	6.85716	−	11.8769i	0.387590	−	0.671325i	0.992125	+	0.125254i	$0.0399745\pi$
$314$	−3.85246	−	2.01131i	−0.217407	−	0.113505i
$315$			15.7433i			0.887035i
$316$	−3.22838	+	0.274686i	−0.181611	+	0.0154523i
$317$	4.33248	+	2.50136i	0.243336	+	0.140490i	0.616709	−	0.787191i	$-0.288465\pi$
$317$	4.33248	+	2.50136i	0.243336	+	0.140490i	−0.373373	+	0.927681i	$0.621799\pi$
$318$	8.02628	+	12.6320i	0.450092	+	0.708366i
$319$	−20.2357	+	35.0492i	−1.13298	+	1.96238i
$320$	5.61622	+	5.69720i	0.313956	+	0.318483i
$321$	−2.17701	−	3.77070i	−0.121509	−	0.210460i
$322$	−0.816726	−	19.2326i	−0.0455144	−	1.07179i
$323$	4.17014	−	5.14457i	0.232033	−	0.286252i
$324$	−18.9737	+	1.61438i	−1.05410	+	0.0896876i
$325$	−5.09891	+	2.94386i	−0.282837	+	0.163296i
$326$	4.96341	+	7.81155i	0.274898	+	0.432642i
$327$	−24.7604	−	14.2954i	−1.36925	−	0.790538i
$328$	−0.964658	−	1.26653i	−0.0532643	−	0.0699323i
$329$	−1.67344	+	2.89848i	−0.0922598	+	0.159799i
$330$	−18.3950	+	0.781155i	−1.01261	+	0.0430012i
$331$	−20.3519			−1.11864			−0.559321	−	0.828951i	$-0.688938\pi$
$331$	−20.3519			−1.11864			−0.559321	+	0.828951i	$0.688938\pi$
$332$	29.0307	+	13.6217i	1.59327	+	0.747585i
$333$	30.7879	+	17.7754i	1.68716	+	0.974085i
$334$	−0.336883	−	7.93305i	−0.0184334	−	0.434077i
$335$	−1.32476			−0.0723791
$336$	29.3488	+	10.8410i	1.60111	+	0.591425i
$337$	21.4928	−	12.4089i	1.17079	−	0.675954i	0.216921	−	0.976189i	$-0.430399\pi$
$337$	21.4928	−	12.4089i	1.17079	−	0.675954i	0.953865	+	0.300235i	$0.0970653\pi$
$338$	27.1604	+	14.1800i	1.47733	+	0.771292i
$339$	−18.9795	+	10.9578i	−1.03083	+	0.595148i
$340$	1.73692	+	2.49321i	0.0941975	+	0.135214i
$341$			24.3862i			1.32059i
$342$	−34.2691	+	14.8322i	−1.85306	+	0.802034i
$343$			18.8305i			1.01675i
$344$	−8.53760	−	11.2093i	−0.460316	−	0.604362i
$345$	−13.6505	+	7.88114i	−0.734920	+	0.424306i
$346$	−5.63609	+	10.7954i	−0.302998	+	0.580363i
$347$	25.1654	−	14.5292i	1.35095	−	0.779970i	0.362565	−	0.931958i	$-0.381901\pi$
$347$	25.1654	−	14.5292i	1.35095	−	0.779970i	0.988382	+	0.151988i	$0.0485676\pi$
$348$	−50.9805	−	23.9208i	−2.73284	−	1.28229i
$349$	8.41850			0.450632			0.225316	−	0.974286i	$-0.427659\pi$
$349$	8.41850			0.450632			0.225316	+	0.974286i	$0.427659\pi$
$350$	−3.67218	+	0.155942i	−0.196286	+	0.00833544i
$351$	−46.9196	−	27.0890i	−2.50438	−	1.44591i
$352$	−7.49754	+	23.2937i	−0.399620	+	1.24156i
$353$	−5.98088			−0.318330			−0.159165	−	0.987252i	$-0.550880\pi$
$353$	−5.98088			−0.318330			−0.159165	+	0.987252i	$0.550880\pi$
$354$	−1.46971	−	34.6093i	−0.0781142	−	1.83947i
$355$	−0.864436	+	1.49725i	−0.0458795	+	0.0794656i
$356$	25.0460	−	17.4485i	1.32744	−	0.924769i
$357$	10.2915	+	5.94178i	0.544682	+	0.314472i
$358$	−4.30410	+	2.73480i	−0.227479	+	0.144539i
$359$	22.5825	−	13.0380i	1.19186	−	0.688119i	0.233130	−	0.972446i	$-0.425103\pi$
$359$	22.5825	−	13.0380i	1.19186	−	0.688119i	0.958728	+	0.284326i	$0.0917699\pi$
$360$	−2.17553	−	16.9946i	−0.114661	−	0.895695i
$361$	−14.1321	+	12.6997i	−0.743796	+	0.668407i
$362$	17.7381	−	0.753262i	0.932295	−	0.0395906i
$363$	−11.6062	−	20.1025i	−0.609168	−	1.05511i
$364$	17.4938	+	25.1111i	0.916925	+	1.31618i
$365$	0.793145	−	1.37377i	0.0415151	−	0.0719062i
$366$	11.8829	−	7.55034i	0.621130	−	0.394662i
$367$	5.60010	+	3.23322i	0.292323	+	0.168773i	0.638989	−	0.769216i	$-0.279353\pi$
$367$	5.60010	+	3.23322i	0.292323	+	0.168773i	−0.346666	+	0.937989i	$0.612686\pi$
$368$	3.53935	+	20.6484i	0.184502	+	1.07637i
$369$			3.40966i			0.177500i
$370$	−3.84120	+	7.35744i	−0.199695	+	0.382495i
$371$	−4.56943	+	7.91449i	−0.237233	+	0.410900i
$372$	−33.8098	+	2.87671i	−1.75296	+	0.149150i
$373$			2.90424i			0.150376i	0.997169	+	0.0751879i	$0.0239557\pi$
$373$			2.90424i			0.150376i	−0.997169	+	0.0751879i	$0.976044\pi$
$374$	−4.30156	+	8.23920i	−0.222428	+	0.426039i
$375$	1.50479	+	2.60637i	0.0777069	+	0.134592i
$376$	1.40591	−	3.36011i	0.0725045	−	0.173284i
$377$	−27.5419	−	47.7040i	−1.41848	−	2.45688i
$378$	−18.1382	−	28.5464i	−0.932928	−	1.46827i
$379$	11.6811			0.600016			0.300008	−	0.953937i	$-0.403011\pi$
$379$	11.6811			0.600016			0.300008	+	0.953937i	$0.403011\pi$
$380$	−3.79910	−	7.84645i	−0.194890	−	0.402514i
$381$	12.7137			0.651342
$382$	−14.6229	−	23.0139i	−0.748173	−	1.17749i
$383$	7.50854	+	13.0052i	0.383668	+	0.664533i	0.991583	−	0.129469i	$-0.0413273\pi$
$383$	7.50854	+	13.0052i	0.383668	+	0.664533i	−0.607915	+	0.794002i	$0.707994\pi$
$384$	−33.1796	−	7.64700i	−1.69319	−	0.390234i
$385$	−5.62134	−	9.73645i	−0.286490	−	0.496216i
$386$	2.36955	−	4.53864i	0.120607	−	0.231011i
$387$			30.1768i			1.53397i
$388$	−1.85325	−	21.7811i	−0.0940843	−	1.10577i
$389$	−8.32367	+	14.4170i	−0.422027	+	0.730972i	−0.996138	−	0.0878059i	$-0.972014\pi$
$389$	−8.32367	+	14.4170i	−0.422027	+	0.730972i	0.574111	+	0.818778i	$0.305348\pi$
$390$	11.5976	−	22.2139i	0.587265	−	1.12485i
$391$			7.95711i			0.402408i
$392$	−0.0881311	−	0.688454i	−0.00445129	−	0.0347722i
$393$	−14.4189	−	8.32478i	−0.727339	−	0.419929i
$394$	13.7937	−	8.76447i	0.694919	−	0.441547i
$395$	−0.810011	+	1.40298i	−0.0407561	+	0.0705916i
$396$	43.0016	−	29.9574i	2.16091	−	1.50541i
$397$	−9.91118	−	17.1667i	−0.497428	−	0.861571i	0.502568	−	0.864538i	$-0.332389\pi$
$397$	−9.91118	−	17.1667i	−0.497428	−	0.861571i	−0.999996	+	0.00296727i	$0.999055\pi$
$398$	11.2867	−	0.479297i	0.565750	−	0.0240250i
$399$	−26.4858	−	21.4691i	−1.32595	−	1.07480i
$400$	3.94250	−	0.675787i	0.197125	−	0.0337893i
$401$	2.18247	−	1.26005i	0.108987	−	0.0629238i	−0.444516	−	0.895771i	$-0.646624\pi$
$401$	2.18247	−	1.26005i	0.108987	−	0.0629238i	0.553503	+	0.832847i	$0.313291\pi$
$402$	4.75899	−	3.02383i	0.237357	−	0.150815i
$403$	−28.7443	−	16.5955i	−1.43186	−	0.826682i
$404$	20.9704	+	30.1014i	1.04332	+	1.49760i
$405$	−4.76057	+	8.24555i	−0.236555	+	0.409725i
$406$	−1.45895	−	34.3559i	−0.0724064	−	1.70506i
$407$	−25.3877			−1.25842
$408$	−11.9305	−	4.99189i	−0.590649	−	0.247135i
$409$	−13.2179	−	7.63134i	−0.653581	−	0.377345i	0.136246	−	0.990675i	$-0.456496\pi$
$409$	−13.2179	−	7.63134i	−0.653581	−	0.377345i	−0.789827	+	0.613330i	$0.789830\pi$
$410$	−0.795313	+	0.0337736i	−0.0392777	+	0.00166796i
$411$	−11.4049			−0.562562
$412$	−14.2771	+	30.4277i	−0.703384	+	1.49906i
$413$	18.3187	−	10.5763i	0.901405	−	0.520427i
$414$	20.7647	−	39.7726i	1.02053	−	1.95472i
$415$	13.8857	−	8.01690i	0.681621	−	0.393534i
$416$	−22.3543	−	24.6895i	−1.09601	−	1.21050i
$417$			66.6872i			3.26569i
$418$	15.8977	−	21.4092i	0.777581	−	1.04716i
$419$		−	13.0559i		−	0.637822i	−0.947785	−	0.318911i	$-0.896683\pi$
$419$		−	13.0559i		−	0.637822i	0.947785	−	0.318911i	$-0.103317\pi$
$420$	12.8358	−	8.94217i	0.626324	−	0.436333i
$421$	−21.1574	+	12.2152i	−1.03115	+	0.595334i	−0.917314	−	0.398165i	$-0.869647\pi$
$421$	−21.1574	+	12.2152i	−1.03115	+	0.595334i	−0.113836	+	0.993500i	$0.536314\pi$
$422$	−7.93647	−	4.14351i	−0.386341	−	0.201703i
$423$	−6.75565	+	3.90038i	−0.328471	+	0.189643i
$424$	3.83893	−	9.17499i	0.186435	−	0.445577i
$425$	1.51929			0.0736965
$426$	−0.312198	−	7.35177i	−0.0151260	−	0.356194i
$427$	7.44518	+	4.29847i	0.360297	+	0.208018i
$428$	−1.22908	+	2.61943i	−0.0594098	+	0.126615i
$429$	76.6517			3.70078
$430$	−7.03883	+	0.298909i	−0.339443	+	0.0144147i
$431$	−16.5325	+	28.6352i	−0.796344	+	1.37931i	0.125639	+	0.992076i	$0.459902\pi$
$431$	−16.5325	+	28.6352i	−0.796344	+	1.37931i	−0.921982	+	0.387232i	$0.873431\pi$
$432$	23.5246	+	28.3088i	1.13183	+	1.36201i
$433$	7.86664	+	4.54181i	0.378047	+	0.218265i	0.676968	−	0.736012i	$-0.263294\pi$
$433$	7.86664	+	4.54181i	0.378047	+	0.218265i	−0.298921	+	0.954278i	$0.596627\pi$
$434$	−11.1120	−	17.4883i	−0.533392	−	0.839467i
$435$	−24.3845	+	14.0784i	−1.16915	+	0.675007i
$436$	1.61079	+	18.9315i	0.0771426	+	0.906655i
$437$	3.58225	−	22.5464i	0.171362	−	1.07854i
$438$	0.286451	+	6.74545i	0.0136871	+	0.322310i
$439$	−12.2443	−	21.2077i	−0.584386	−	1.01219i	−0.994952	−	0.100356i	$-0.968002\pi$
$439$	−12.2443	−	21.2077i	−0.584386	−	1.01219i	0.410565	−	0.911831i	$-0.365331\pi$
$440$	7.41360	+	9.73352i	0.353429	+	0.464027i
$441$	−0.743234	+	1.28732i	−0.0353921	+	0.0613009i
$442$	−6.78430	−	10.6773i	−0.322696	−	0.507868i
$443$	25.3840	+	14.6554i	1.20603	+	0.696301i	0.961889	−	0.273439i	$-0.0881612\pi$
$443$	25.3840	+	14.6554i	1.20603	+	0.696301i	0.244139	+	0.969740i	$0.421495\pi$
$444$	−2.99484	−	35.1983i	−0.142129	−	1.67044i
$445$		−	15.2623i		−	0.723503i
$446$	−16.6892	−	8.71317i	−0.790256	−	0.412580i
$447$	−9.60224	+	16.6316i	−0.454170	+	0.786646i
$448$	−5.23740	−	20.1212i	−0.247444	−	0.950640i
$449$			30.2684i			1.42845i	0.699914	+	0.714227i	$0.253221\pi$
$449$			30.2684i			1.42845i	−0.699914	+	0.714227i	$0.746779\pi$
$450$	−7.59399	−	3.96470i	−0.357984	−	0.186898i
$451$	−1.21746	−	2.10870i	−0.0573279	−	0.0992949i
$452$	13.1847	+	6.18647i	0.620157	+	0.290987i
$453$	12.8218	+	22.2079i	0.602419	+	1.04342i
$454$	−5.26855	+	3.34761i	−0.247265	+	0.157111i
$455$	15.3020			0.717367
$456$	31.5577	+	19.5155i	1.47783	+	0.913899i
$457$	−15.2706			−0.714330			−0.357165	−	0.934041i	$-0.616257\pi$
$457$	−15.2706			−0.714330			−0.357165	+	0.934041i	$0.616257\pi$
$458$	−7.96773	+	5.06265i	−0.372308	+	0.236562i
$459$	6.99017	+	12.1073i	0.326273	+	0.565122i
$460$	9.48277	+	4.44946i	0.442136	+	0.207457i
$461$	−17.9692	−	31.1235i	−0.836908	−	1.44957i	−0.892468	−	0.451111i	$-0.851028\pi$
$461$	−17.9692	−	31.1235i	−0.836908	−	1.44957i	0.0555603	−	0.998455i	$-0.482306\pi$
$462$	42.4179	+	22.1457i	1.97346	+	1.03031i
$463$		−	37.0046i		−	1.71975i	−0.510505	−	0.859875i	$-0.670541\pi$
$463$		−	37.0046i		−	1.71975i	0.510505	−	0.859875i	$-0.329459\pi$
$464$	6.32248	+	36.8850i	0.293514	+	1.71234i
$465$	−8.48300	+	14.6930i	−0.393390	+	0.681371i
$466$	−29.0560	−	15.1697i	−1.34599	−	0.702721i
$467$		−	8.22282i		−	0.380507i	−0.981735	−	0.190253i	$-0.939069\pi$
$467$		−	8.22282i		−	0.380507i	0.981735	−	0.190253i	$-0.0609310\pi$
$468$	6.04726	+	71.0733i	0.279535	+	3.28536i
$469$	2.98172	+	1.72150i	0.137683	+	0.0794913i
$470$	−0.976692	−	1.53714i	−0.0450514	−	0.0709031i
$471$	4.62423	−	8.00941i	0.213073	−	0.369054i
$472$	−18.3132	+	13.9484i	−0.842934	+	0.642026i
$473$	−10.7750	−	18.6628i	−0.495434	−	0.858118i
$474$	−0.292542	−	6.88890i	−0.0134369	−	0.316418i
$475$	−4.30490	−	0.683978i	−0.197522	−	0.0313831i
$476$	−0.669511	−	7.86874i	−0.0306870	−	0.360663i
$477$	−18.4467	+	10.6502i	−0.844617	+	0.487640i
$478$	5.45207	+	8.58061i	0.249372	+	0.392468i
$479$	−20.1915	−	11.6576i	−0.922573	−	0.532648i	−0.0381180	−	0.999273i	$-0.512136\pi$
$479$	−20.1915	−	11.6576i	−0.922573	−	0.532648i	−0.884455	+	0.466625i	$0.845470\pi$
$480$	−12.6203	+	11.4267i	−0.576036	+	0.521553i
$481$	17.2770	−	29.9247i	0.787766	−	1.36445i
$482$	−19.4917	+	0.827730i	−0.887823	+	0.0377021i
$483$	40.9656			1.86400
$484$	−6.55253	+	13.9648i	−0.297842	+	0.634766i
$485$	−9.46559	−	5.46496i	−0.429810	−	0.248151i
$486$	−0.0629371	−	1.48207i	−0.00285488	−	0.0672280i
$487$	22.4049			1.01526			0.507631	−	0.861575i	$-0.330522\pi$
$487$	22.4049			1.01526			0.507631	+	0.861575i	$0.330522\pi$
$488$	−8.63093	−	3.61129i	−0.390704	−	0.163475i
$489$	−17.0569	+	9.84778i	−0.771338	+	0.445332i
$490$	−0.307633	−	0.160610i	−0.0138975	−	0.00725564i
$491$	28.8312	−	16.6457i	1.30114	−	0.751211i	0.320537	−	0.947236i	$-0.396137\pi$
$491$	28.8312	−	16.6457i	1.30114	−	0.751211i	0.980599	+	0.196025i	$0.0628034\pi$
$492$	2.77996	−	1.93668i	0.125330	−	0.0873122i
$493$			14.2141i			0.640170i
$494$	14.4164	+	33.3083i	0.648624	+	1.49861i
$495$		−	26.2039i		−	1.17778i
$496$	14.4119	+	17.3428i	0.647111	+	0.778714i
$497$	3.89129	−	2.24664i	0.174548	−	0.100775i
$498$	−31.5832	+	60.4944i	−1.41528	+	2.71082i
$499$	−31.6188	+	18.2551i	−1.41545	+	0.817211i	−0.995895	−	0.0905184i	$-0.971148\pi$
$499$	−31.6188	+	18.2551i	−1.41545	+	0.817211i	−0.419556	+	0.907729i	$0.637814\pi$
$500$	0.849559	−	1.81059i	0.0379934	−	0.0809722i
$501$	16.8975			0.754923
$502$	13.8516	−	0.588218i	0.618227	−	0.0262535i
$503$	27.5058	+	15.8805i	1.22642	+	0.708076i	0.966280	−	0.257493i	$-0.0828965\pi$
$503$	27.5058	+	15.8805i	1.22642	+	0.708076i	0.260144	+	0.965570i	$0.416230\pi$
$504$	−17.1876	+	41.0780i	−0.765595	+	1.82976i
$505$	18.3429			0.816249
$506$	1.35940	+	32.0116i	0.0604326	+	1.42309i
$507$	−32.6015	+	56.4675i	−1.44788	+	2.50781i
$508$	−4.82952	−	6.93242i	−0.214276	−	0.307576i
$509$	−25.4241	−	14.6786i	−1.12690	−	0.650618i	−0.183749	−	0.982973i	$-0.558823\pi$
$509$	−25.4241	−	14.6786i	−1.12690	−	0.650618i	−0.943154	+	0.332356i	$0.892157\pi$
$510$	−5.45783	+	3.46788i	−0.241677	+	0.153560i
$511$	−3.57037	+	2.06135i	−0.157944	+	0.0911889i
$512$	8.43418	+	20.9968i	0.372742	+	0.927935i
$513$	−14.3559	−	37.4530i	−0.633830	−	1.65359i
$514$	12.2116	−	0.518575i	0.538631	−	0.0228734i
$515$	8.40267	+	14.5539i	0.370266	+	0.641320i
$516$	24.6037	−	17.1403i	1.08312	−	0.754561i
$517$	2.78535	−	4.82437i	0.122500	−	0.212176i
$518$	18.2065	−	11.5683i	0.799948	−	0.508282i
$519$	−22.4440	−	12.9580i	−0.985181	−	0.568794i
$520$	−16.5182	+	2.11454i	−0.724370	+	0.0927289i
$521$			13.9330i			0.610416i	0.952286	+	0.305208i	$0.0987260\pi$
$521$			13.9330i			0.610416i	−0.952286	+	0.305208i	$0.901274\pi$
$522$	37.0927	−	71.0473i	1.62350	−	3.10966i
$523$	−11.2431	+	19.4736i	−0.491626	+	0.851521i	−0.999954	−	0.00964294i	$-0.996931\pi$
$523$	−11.2431	+	19.4736i	−0.491626	+	0.851521i	0.508328	+	0.861164i	$0.330264\pi$
$524$	0.938023	+	11.0246i	0.0409777	+	0.481610i
$525$		−	7.82177i		−	0.341370i
$526$	5.18679	−	9.93478i	0.226155	−	0.433177i
$527$	4.28238	+	7.41731i	0.186544	+	0.323103i
$528$	−48.8496	−	18.0443i	−2.12591	−	0.785275i
$529$	2.21508	+	3.83663i	0.0963078	+	0.166810i
$530$	−2.66692	−	4.19726i	−0.115843	−	0.182317i
$531$	49.3015			2.13950
$532$	−1.64542	+	22.5974i	−0.0713379	+	0.979722i
$533$	3.31407			0.143548
$534$	34.8372	+	54.8276i	1.50755	+	2.37262i
$535$	0.723363	+	1.25290i	0.0312737	+	0.0541676i
$536$	−3.45660	−	1.44629i	−0.149302	−	0.0624700i
$537$	−5.42605	−	9.39819i	−0.234151	−	0.405562i
$538$	−6.66672	+	12.7694i	−0.287423	+	0.550529i
$539$		−	1.06152i		−	0.0457230i
$540$	18.3375	−	1.56024i	0.789121	−	0.0671422i
$541$	−16.1699	+	28.0071i	−0.695199	+	1.20412i	0.274914	+	0.961469i	$0.411351\pi$
$541$	−16.1699	+	28.0071i	−0.695199	+	1.20412i	−0.970113	+	0.242652i	$0.921983\pi$
$542$	−5.70221	+	10.9220i	−0.244931	+	0.469141i
$543$			37.7823i			1.62140i
$544$	1.81009	+	8.40164i	0.0776069	+	0.360217i
$545$	8.22720	+	4.74998i	0.352415	+	0.203467i
$546$	−54.9700	+	34.9276i	−2.35250	+	1.49476i
$547$	18.7956	−	32.5550i	0.803643	−	1.39195i	−0.113560	−	0.993531i	$-0.536225\pi$
$547$	18.7956	−	32.5550i	0.803643	−	1.39195i	0.917203	−	0.398420i	$-0.130441\pi$
$548$	4.33235	+	6.21877i	0.185069	+	0.265653i
$549$	10.0187	+	17.3529i	0.427587	+	0.740602i
$550$	6.11215	−	0.259557i	0.260623	−	0.0110675i
$551$	6.39912	−	40.2755i	0.272612	−	1.71579i
$552$	−44.2216	+	5.66095i	−1.88220	+	0.240946i
$553$	3.64629	−	2.10519i	0.155056	−	0.0895217i
$554$	14.0039	−	8.89801i	0.594969	−	0.378040i
$555$	−15.2964	−	8.83136i	−0.649295	−	0.374871i
$556$	36.3627	−	25.3323i	1.54212	−	1.07433i
$557$	0.682188	−	1.18158i	0.0289052	−	0.0500653i	−0.851211	−	0.524824i	$-0.824131\pi$
$557$	0.682188	−	1.18158i	0.0289052	−	0.0500653i	0.880116	+	0.474758i	$0.157465\pi$
$558$	−2.04896	−	48.2496i	−0.0867392	−	2.04257i
$559$	29.3308			1.24056
$560$	−9.75183	−	3.60217i	−0.412090	−	0.152219i
$561$	−17.1296	−	9.88977i	−0.723212	−	0.417547i
$562$	17.6260	−	0.748499i	0.743507	−	0.0315735i
$563$	−7.52468			−0.317128			−0.158564	−	0.987349i	$-0.550686\pi$
$563$	−7.52468			−0.317128			−0.158564	+	0.987349i	$0.550686\pi$
$564$	7.01724	+	3.29260i	0.295479	+	0.138643i
$565$	6.30638	−	3.64099i	0.265311	−	0.153178i
$566$	−7.79381	+	14.9283i	−0.327598	+	0.627481i
$567$	21.4299	−	12.3725i	0.899970	−	0.519598i
$568$	−3.89012	+	2.96293i	−0.163226	+	0.124322i
$569$		−	28.7673i		−	1.20599i	−0.797746	−	0.602993i	$-0.793975\pi$
$569$		−	28.7673i		−	1.20599i	0.797746	−	0.602993i	$-0.206025\pi$
$570$	17.0259	−	7.36910i	0.713138	−	0.308658i
$571$		−	30.8865i		−	1.29256i	−0.763101	−	0.646280i	$-0.776324\pi$
$571$		−	30.8865i		−	1.29256i	0.763101	−	0.646280i	$-0.223676\pi$
$572$	−29.1175	−	41.7960i	−1.21746	−	1.74758i
$573$	50.2518	−	29.0129i	2.09930	−	1.21203i
$574$	1.83395	+	0.957479i	0.0765478	+	0.0399644i
$575$	4.53570	−	2.61869i	0.189152	−	0.109207i
$576$	12.8772	−	46.7181i	0.536549	−	1.94659i
$577$	−35.8085			−1.49073			−0.745363	−	0.666659i	$-0.767724\pi$
$577$	−35.8085			−1.49073			−0.745363	+	0.666659i	$0.767724\pi$
$578$	−0.881527	−	20.7586i	−0.0366667	−	0.863442i
$579$	9.43599	+	5.44787i	0.392146	+	0.226406i
$580$	16.9394	+	7.94825i	0.703371	+	0.330033i
$581$	−41.6712			−1.72881
$582$	46.4778	−	1.97371i	1.92657	−	0.0818131i
$583$	7.60558	−	13.1732i	0.314991	−	0.545580i
$584$	3.56929	−	2.71857i	0.147698	−	0.112495i
$585$	30.8868	+	17.8325i	1.27701	+	0.737284i
$586$	22.6871	+	35.7056i	0.937196	+	1.47498i
$587$	−39.1369	+	22.5957i	−1.61535	+	0.932624i	−0.627251	+	0.778817i	$0.715820\pi$
$587$	−39.1369	+	22.5957i	−1.61535	+	0.932624i	−0.988101	+	0.153807i	$0.950847\pi$
$588$	1.47173	−	0.125222i	0.0606931	−	0.00516407i
$589$	−8.79486	−	22.9448i	−0.362386	−	0.945423i
$590$	0.488345	+	11.4997i	0.0201048	+	0.473437i
$591$	17.3894	+	30.1192i	0.715302	+	1.23894i
$592$	−18.0550	+	15.0037i	−0.742056	+	0.616648i
$593$	10.9473	−	18.9614i	0.449554	−	0.778650i	−0.548803	−	0.835952i	$-0.684916\pi$
$593$	10.9473	−	18.9614i	0.449554	−	0.778650i	0.998357	+	0.0573019i	$0.0182497\pi$
$594$	30.1901	+	47.5139i	1.23871	+	1.94952i
$595$	−3.41957	−	1.97429i	−0.140189	−	0.0809381i
$596$	12.7163	−	1.08197i	0.520880	−	0.0443190i
$597$			24.0407i			0.983921i
$598$	−38.6576	−	20.1825i	−1.58083	−	0.825325i
$599$	6.05996	−	10.4962i	0.247603	−	0.428861i	−0.715257	−	0.698861i	$-0.753690\pi$
$599$	6.05996	−	10.4962i	0.247603	−	0.428861i	0.962860	+	0.270000i	$0.0870237\pi$
$600$	1.08087	+	8.44346i	0.0441265	+	0.344703i
$601$		−	27.5066i		−	1.12202i	−0.827810	−	0.561009i	$-0.810413\pi$
$601$		−	27.5066i		−	1.12202i	0.827810	−	0.561009i	$-0.189587\pi$
$602$	16.2312	+	8.47406i	0.661534	+	0.345377i
$603$	4.01238	+	6.94964i	0.163397	+	0.283011i
$604$	7.23879	−	15.4274i	0.294542	−	0.627733i
$605$	3.85643	+	6.67953i	0.156786	+	0.271561i
$606$	−65.8942	+	41.8688i	−2.67677	+	1.70080i
$607$	42.1615			1.71128			0.855642	−	0.517568i	$-0.173163\pi$
$607$	42.1615			1.71128			0.855642	+	0.517568i	$0.173163\pi$
$608$	−1.34649	−	24.6209i	−0.0546074	−	0.998508i
$609$	73.1784			2.96534
$610$	−3.94837	+	2.50877i	−0.159865	+	0.101577i
$611$	3.79103	+	6.56626i	0.153369	+	0.265642i
$612$	7.81863	−	16.6632i	0.316050	−	0.673570i
$613$	0.635023	+	1.09989i	0.0256483	+	0.0444242i	0.878565	−	0.477623i	$-0.158502\pi$
$613$	0.635023	+	1.09989i	0.0256483	+	0.0444242i	−0.852916	+	0.522048i	$0.825168\pi$
$614$	−33.4448	−	17.4610i	−1.34972	−	0.704670i
$615$		−	1.69402i		−	0.0683097i
$616$	−4.03776	−	31.5417i	−0.162686	−	1.27085i
$617$	0.286836	−	0.496814i	0.0115476	−	0.0200010i	−0.860194	−	0.509967i	$-0.829658\pi$
$617$	0.286836	−	0.496814i	0.0115476	−	0.0200010i	0.871741	+	0.489966i	$0.162991\pi$
$618$	−63.4054	−	33.1030i	−2.55054	−	1.33160i
$619$		−	4.33041i		−	0.174054i	−0.996206	−	0.0870269i	$-0.972263\pi$
$619$		−	4.33041i		−	0.174054i	0.996206	−	0.0870269i	$-0.0277366\pi$
$620$	11.2341	−	0.955851i	0.451172	−	0.0383879i
$621$	41.7370	+	24.0969i	1.67485	+	0.966975i
$622$	−18.4535	−	29.0426i	−0.739918	−	1.16450i
$623$	−19.8331	+	34.3519i	−0.794596	+	1.37628i
$624$	54.5125	−	45.2999i	2.18225	−	1.81345i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.822880	−	19.3775i	−0.0328889	−	0.774481i
$627$	44.0842	+	35.7343i	1.76055	+	1.42709i
$628$	−6.12390	+	0.521052i	−0.244370	+	0.0207922i
$629$	−7.72191	+	4.45825i	−0.307893	+	0.177762i
$630$	11.9402	+	18.7919i	0.475711	+	0.748686i
$631$	3.67762	+	2.12328i	0.146404	+	0.0845264i	0.571413	−	0.820663i	$-0.306396\pi$
$631$	3.67762	+	2.12328i	0.146404	+	0.0845264i	−0.425009	+	0.905189i	$0.639729\pi$
$632$	−3.64520	+	2.77639i	−0.144998	+	0.110439i
$633$	9.52640	−	16.5002i	0.378640	−	0.655824i
$634$	7.06854	−	0.300171i	0.280728	−	0.0119213i
$635$	−4.22442			−0.167641
$636$	19.1610	+	8.99064i	0.759783	+	0.356502i
$637$	1.25123	+	0.722398i	0.0495755	+	0.0286224i
$638$	2.42834	+	57.1836i	0.0961390	+	2.26392i
$639$	10.4727			0.414294
$640$	11.0247	+	2.54089i	0.435789	+	0.100438i
$641$	−27.5309	+	15.8950i	−1.08741	+	0.627814i	−0.932885	−	0.360176i	$-0.882717\pi$
$641$	−27.5309	+	15.8950i	−1.08741	+	0.627814i	−0.154521	+	0.987989i	$0.549383\pi$
$642$	−5.45840	−	2.84974i	−0.215426	−	0.112470i
$643$	−9.97978	+	5.76183i	−0.393564	+	0.227224i	−0.683703	−	0.729760i	$-0.739632\pi$
$643$	−9.97978	+	5.76183i	−0.393564	+	0.227224i	0.290139	+	0.956984i	$0.406298\pi$
$644$	−15.5615	−	22.3374i	−0.613210	−	0.880217i
$645$		−	14.9928i		−	0.590340i
$646$	1.07584	−	9.30355i	0.0423284	−	0.366043i
$647$			22.7092i			0.892791i	0.894836	+	0.446396i	$0.147293\pi$
$647$			22.7092i			0.892791i	−0.894836	+	0.446396i	$0.852707\pi$
$648$	−21.4234	+	16.3173i	−0.841591	+	0.641003i
$649$	−30.4905	+	17.6037i	−1.19686	+	0.691007i
$650$	−3.85355	+	7.38109i	−0.151149	+	0.289510i
$651$	38.1865	−	22.0470i	1.49665	−	0.864090i
$652$	11.8491	+	5.55977i	0.464045	+	0.217737i
$653$	−5.75436			−0.225185			−0.112593	−	0.993641i	$-0.535916\pi$
$653$	−5.75436			−0.225185			−0.112593	+	0.993641i	$0.535916\pi$
$654$	−40.3971	+	1.71549i	−1.57965	+	0.0670811i
$655$	4.79102	+	2.76610i	0.187201	+	0.108080i
$656$	−2.11203	−	0.780151i	−0.0824610	−	0.0304598i
$657$	−9.60901			−0.374883
$658$	0.200818	+	4.72894i	0.00782870	+	0.184353i
$659$	−8.39596	+	14.5422i	−0.327060	+	0.566485i	−0.981927	−	0.189260i	$-0.939391\pi$
$659$	−8.39596	+	14.5422i	−0.327060	+	0.566485i	0.654867	+	0.755744i	$0.272725\pi$
$660$	−21.3645	+	14.8838i	−0.831613	+	0.579350i
$661$	−9.42914	−	5.44392i	−0.366751	−	0.211744i	0.305287	−	0.952260i	$-0.401248\pi$
$661$	−9.42914	−	5.44392i	−0.366751	−	0.211744i	−0.672038	+	0.740517i	$0.734581\pi$
$662$	−24.2929	+	15.4356i	−0.944170	+	0.599920i
$663$	23.3144	−	13.4606i	0.905455	−	0.522765i
$664$	44.9833	−	5.75846i	1.74569	−	0.223472i
$665$	8.80052	+	7.13362i	0.341269	+	0.276630i
$666$	50.2311	−	2.13310i	1.94642	−	0.0826559i
$667$	24.4998	+	42.4348i	0.948635	+	1.64308i
$668$	−6.41880	−	9.21371i	−0.248351	−	0.356489i
$669$	20.0326	−	34.6974i	0.774504	−	1.34148i
$670$	−1.58128	+	1.00474i	−0.0610903	+	0.0388164i
$671$	−12.3921	−	7.15458i	−0.478392	−	0.276200i
$672$	43.2542	−	9.31888i	1.66857	−	0.359483i
$673$		−	20.7239i		−	0.798848i	−0.916766	−	0.399424i	$-0.869210\pi$
$673$		−	20.7239i		−	0.798848i	0.916766	−	0.399424i	$-0.130790\pi$
$674$	16.2434	−	31.1126i	0.625672	−	1.19841i
$675$	4.60094	−	7.96906i	0.177090	−	0.306729i
$676$	43.1744	−	3.67349i	1.66055	−	0.141288i
$677$		−	20.4067i		−	0.784293i	−0.919903	−	0.392146i	$-0.871733\pi$
$677$		−	20.4067i		−	0.784293i	0.919903	−	0.392146i	$-0.128267\pi$
$678$	−14.3440	+	27.4744i	−0.550877	+	1.05515i
$679$	14.2032	+	24.6007i	0.545070	+	0.944089i
$680$	3.96419	+	1.65867i	0.152020	+	0.0636070i
$681$	−6.64190	−	11.5041i	−0.254518	−	0.440839i
$682$	18.4953	+	29.1084i	0.708222	+	1.11462i
$683$	8.86934			0.339376			0.169688	−	0.985498i	$-0.445724\pi$
$683$	8.86934			0.339376			0.169688	+	0.985498i	$0.445724\pi$
$684$	−29.6557	+	43.6951i	−1.13392	+	1.67072i
$685$	3.78954			0.144791
$686$	14.2817	+	22.4769i	0.545277	+	0.858171i
$687$	−10.0447	−	17.3979i	−0.383228	−	0.663771i
$688$	−18.6923	−	6.90463i	−0.712637	−	0.263237i
$689$	10.3516	+	17.9296i	0.394366	+	0.683062i
$690$	−10.3165	+	19.7603i	−0.392744	+	0.752261i
$691$		−	1.45105i		−	0.0552004i	−0.999619	−	0.0276002i	$-0.991213\pi$
$691$		−	1.45105i		−	0.0552004i	0.999619	−	0.0276002i	$-0.00878653\pi$
$692$	1.46009	+	17.1604i	0.0555043	+	0.652341i
$693$	−34.0515	+	58.9789i	−1.29351	+	2.24042i
$694$	19.0190	−	36.4289i	0.721950	−	1.38282i
$695$		−	22.1584i		−	0.840514i
$696$	−78.9947	+	10.1124i	−2.99429	+	0.383308i
$697$	−0.740605	−	0.427588i	−0.0280524	−	0.0161961i
$698$	10.0487	−	6.38487i	0.380348	−	0.241671i
$699$	34.8768	−	60.4083i	1.31916	−	2.28485i
$700$	−4.26499	+	2.97124i	−0.161202	+	0.112302i
$701$	17.0583	+	29.5459i	0.644285	+	1.11593i	0.984466	+	0.175574i	$0.0561781\pi$
$701$	17.0583	+	29.5459i	0.644285	+	1.11593i	−0.340182	+	0.940360i	$0.610489\pi$
$702$	−76.5504	+	3.25077i	−2.88921	+	0.122692i
$703$	23.8870	−	9.15603i	0.900917	−	0.345326i
$704$	8.71737	+	33.4907i	0.328548	+	1.26223i
$705$	3.35642	−	1.93783i	0.126410	−	0.0729829i
$706$	−7.13902	+	4.53609i	−0.268681	+	0.170718i
$707$	−41.2857	−	23.8363i	−1.55271	−	0.896456i
$708$	−28.0032	−	40.1965i	−1.05242	−	1.51068i
$709$	1.44002	−	2.49419i	0.0540810	−	0.0936711i	−0.837718	−	0.546104i	$-0.816110\pi$
$709$	1.44002	−	2.49419i	0.0540810	−	0.0936711i	0.891799	+	0.452433i	$0.149444\pi$
$710$	0.103735	+	2.44279i	0.00389310	+	0.0916764i
$711$	9.81334			0.368029
$712$	16.6624	−	39.8230i	0.624452	−	1.49243i
$713$	25.5693	+	14.7625i	0.957578	+	0.552858i
$714$	16.7908	−	0.713032i	0.628378	−	0.0266845i
$715$	−25.4693			−0.952497
$716$	−3.06339	+	6.52875i	−0.114484	+	0.243991i
$717$	−18.7361	+	10.8173i	−0.699714	+	0.403980i
$718$	17.0669	−	32.6900i	0.636932	−	1.21998i
$719$	−28.5881	+	16.5054i	−1.06616	+	0.615547i	−0.927129	−	0.374742i	$-0.877731\pi$
$719$	−28.5881	+	16.5054i	−1.06616	+	0.615547i	−0.139029	+	0.990288i	$0.544398\pi$
$720$	−15.4861	−	18.6355i	−0.577132	−	0.694503i
$721$		−	43.6765i		−	1.62660i
$722$	−7.23680	+	25.8772i	−0.269326	+	0.963049i
$723$		−	41.5175i		−	1.54405i
$724$	20.6017	−	14.3523i	0.765654	−	0.533399i
$725$	8.10230	−	4.67787i	0.300912	−	0.173732i
$726$	−29.1001	−	15.1927i	−1.08000	−	0.563854i
$727$	23.3306	−	13.4699i	0.865283	−	0.499571i	−0.000494722	−	1.00000i	$-0.500157\pi$
$727$	23.3306	−	13.4699i	0.865283	−	0.499571i	0.865778	+	0.500428i	$0.166824\pi$
$728$	39.9264	+	16.7057i	1.47977	+	0.619155i
$729$	−25.4066			−0.940985
$730$	−0.0951798	−	2.24133i	−0.00352276	−	0.0829554i
$731$	−6.55464	−	3.78432i	−0.242432	−	0.139968i
$732$	8.45752	−	18.0248i	0.312599	−	0.666215i
$733$	−2.76001			−0.101943			−0.0509717	−	0.998700i	$-0.516232\pi$
$733$	−2.76001			−0.101943			−0.0509717	+	0.998700i	$0.516232\pi$
$734$	9.13668	−	0.387996i	0.337241	−	0.0143212i
$735$	0.369262	−	0.639580i	0.0136204	−	0.0235913i
$736$	19.8851	+	21.9624i	0.732975	+	0.809545i
$737$	−4.96291	−	2.86534i	−0.182811	−	0.105546i
$738$	2.58600	+	4.06991i	0.0951918	+	0.149815i
$739$	20.7716	−	11.9925i	0.764095	−	0.441150i	−0.0666691	−	0.997775i	$-0.521237\pi$
$739$	20.7716	−	11.9925i	0.764095	−	0.441150i	0.830764	+	0.556625i	$0.187904\pi$
$740$	0.995105	+	11.6954i	0.0365808	+	0.429933i
$741$	−72.1210	+	27.6444i	−2.64943	+	1.01554i
$742$	0.548346	+	12.9127i	0.0201304	+	0.474039i
$743$	−7.34001	−	12.7133i	−0.269279	−	0.466405i	0.699397	−	0.714734i	$-0.253452\pi$
$743$	−7.34001	−	12.7133i	−0.269279	−	0.466405i	−0.968676	+	0.248329i	$0.920119\pi$
$744$	−38.1750	+	29.0762i	−1.39956	+	1.06599i
$745$	3.19056	−	5.52622i	0.116893	−	0.202465i
$746$	2.20267	+	3.46662i	0.0806455	+	0.126922i
$747$	−84.1130	−	48.5626i	−3.07753	−	1.77681i
$748$	1.11436	+	13.0971i	0.0407452	+	0.478877i
$749$		−	3.75999i		−	0.137387i
$750$	3.77293	+	1.96979i	0.137768	+	0.0719265i
$751$	−17.6143	+	30.5088i	−0.642755	+	1.11328i	0.342061	+	0.939678i	$0.388875\pi$
$751$	−17.6143	+	30.5088i	−0.642755	+	1.11328i	−0.984815	+	0.173606i	$0.944458\pi$
$752$	−0.870262	−	5.07706i	−0.0317352	−	0.185141i
$753$			29.5040i			1.07519i
$754$	−69.0555	−	36.0528i	−2.51485	−	1.31297i
$755$	−4.26032	−	7.37910i	−0.155049	−	0.268553i
$756$	−43.3010	−	20.3175i	−1.57484	−	0.738940i
$757$	13.2248	+	22.9060i	0.480662	+	0.832531i	0.999754	−	0.0221874i	$-0.00706304\pi$
$757$	13.2248	+	22.9060i	0.480662	+	0.832531i	−0.519092	+	0.854719i	$0.673730\pi$
$758$	13.9430	−	8.85931i	0.506433	−	0.321785i
$759$	−68.1851			−2.47496
$760$	−10.4858	−	6.48448i	−0.380359	−	0.235217i
$761$	−4.66536			−0.169119			−0.0845596	−	0.996418i	$-0.526948\pi$
$761$	−4.66536			−0.169119			−0.0845596	+	0.996418i	$0.526948\pi$
$762$	15.1756	−	9.64248i	0.549754	−	0.349310i
$763$	−12.3450	−	21.3822i	−0.446920	−	0.774087i
$764$	−34.9090	−	16.3798i	−1.26296	−	0.592602i
$765$	−4.60158	−	7.97018i	−0.166371	−	0.288162i
$766$	18.8260	+	9.82878i	0.680213	+	0.355128i
$767$		−	47.9194i		−	1.73027i
$768$	−45.4043	+	16.0368i	−1.63839	+	0.578677i
$769$	−23.4294	+	40.5808i	−0.844884	+	1.46338i	0.0408373	+	0.999166i	$0.486997\pi$
$769$	−23.4294	+	40.5808i	−0.844884	+	1.46338i	−0.885722	+	0.464217i	$0.846336\pi$
$770$	−14.0943	−	7.35842i	−0.507924	−	0.265179i
$771$			26.0108i			0.936758i
$772$	−0.613858	−	7.21465i	−0.0220932	−	0.259661i
$773$	6.35157	+	3.66708i	0.228450	+	0.131896i	0.609857	−	0.792512i	$-0.291227\pi$
$773$	6.35157	+	3.66708i	0.228450	+	0.131896i	−0.381407	+	0.924407i	$0.624560\pi$
$774$	22.8871	+	36.0202i	0.822658	+	1.29472i
$775$	2.81867	−	4.88208i	0.101250	−	0.175370i
$776$	−18.7316	−	24.5933i	−0.672427	−	0.882848i
$777$	22.9524	+	39.7547i	0.823412	+	1.42619i
$778$	0.998865	+	23.5217i	0.0358111	+	0.843293i
$779$	1.90600	+	1.54498i	0.0682895	+	0.0553548i
$780$	−3.00447	−	35.3114i	−0.107577	−	1.26435i
$781$	−6.47684	+	3.73941i	−0.231760	+	0.133807i
$782$	6.03494	+	9.49794i	0.215809	+	0.339646i
$783$	74.5564	+	43.0452i	2.66443	+	1.53831i
$784$	−0.627343	−	0.754925i	−0.0224051	−	0.0269616i
$785$	−1.53651	+	2.66131i	−0.0548403	+	0.0949862i
$786$	−23.5248	+	0.998999i	−0.839103	+	0.0356331i
$787$	39.8153			1.41926			0.709630	−	0.704574i	$-0.248862\pi$
$787$	39.8153			1.41926			0.709630	+	0.704574i	$0.248862\pi$
$788$	9.81752	−	20.9233i	0.349735	−	0.745360i
$789$	20.6548	+	11.9250i	0.735329	+	0.424542i
$790$	0.0972038	+	2.28899i	0.00345836	+	0.0814388i
$791$	−18.9256			−0.672917
$792$	28.6078	−	68.3722i	1.01653	−	2.42950i
$793$	16.8664	−	9.73780i	0.598942	−	0.345800i
$794$	−24.8502	−	12.9739i	−0.881900	−	0.460426i
$795$	9.16490	−	5.29136i	0.325046	−	0.187665i
$796$	13.1087	−	9.13230i	0.464627	−	0.323686i
$797$		−	4.64787i		−	0.164636i	−0.996606	−	0.0823180i	$-0.973768\pi$
$797$		−	4.64787i		−	0.164636i	0.996606	−	0.0823180i	$-0.0262323\pi$
$798$	−47.8975	−	5.53875i	−1.69555	−	0.196070i
$799$		−	1.95651i		−	0.0692163i
$800$	4.19339	−	3.79677i	0.148259	−	0.134236i
$801$	−80.0658	+	46.2260i	−2.82899	+	1.63332i
$802$	1.64942	−	3.15930i	0.0582431	−	0.111559i
$803$	5.94269	−	3.43101i	0.209713	−	0.121078i
$804$	3.38715	−	7.21875i	0.119456	−	0.254586i
$805$	−13.6118			−0.479751
$806$	−46.8970	+	1.99151i	−1.65188	+	0.0701481i
$807$	−26.5481	−	15.3275i	−0.934537	−	0.539555i
$808$	47.8610	+	20.0257i	1.68374	+	0.704500i
$809$	−1.72993			−0.0608212			−0.0304106	−	0.999537i	$-0.509681\pi$
$809$	−1.72993			−0.0608212			−0.0304106	+	0.999537i	$0.509681\pi$
$810$	0.571283	+	13.4528i	0.0200728	+	0.472683i
$811$	−11.9157	+	20.6386i	−0.418416	+	0.724718i	−0.995780	−	0.0917688i	$-0.970748\pi$
$811$	−11.9157	+	20.6386i	−0.418416	+	0.724718i	0.577364	+	0.816487i	$0.304081\pi$
$812$	−27.7981	−	39.9021i	−0.975523	−	1.40029i
$813$	−22.7073	−	13.1100i	−0.796378	−	0.459789i
$814$	−30.3038	+	19.2548i	−1.06215	+	0.674882i
$815$	5.66753	−	3.27215i	0.198525	−	0.114618i
$816$	−18.0268	+	3.08998i	−0.631064	+	0.108171i
$817$	16.8688	+	13.6737i	0.590165	+	0.478383i
$818$	−21.5652	+	0.915784i	−0.754011	+	0.0320196i
$819$	−46.3461	−	80.2738i	−1.61946	−	2.80499i
$820$	−0.923704	+	0.643505i	−0.0322571	+	0.0224722i
$821$	15.5788	−	26.9833i	0.543705	−	0.941725i	−0.454982	−	0.890501i	$-0.650354\pi$
$821$	15.5788	−	26.9833i	0.543705	−	0.941725i	0.998687	−	0.0512243i	$-0.0163123\pi$
$822$	−13.6134	+	8.64985i	−0.474820	+	0.301698i
$823$	28.1635	+	16.2602i	0.981718	+	0.566795i	0.902788	−	0.430085i	$-0.141516\pi$
$823$	28.1635	+	16.2602i	0.981718	+	0.566795i	0.0789295	+	0.996880i	$0.474850\pi$
$824$	6.03556	+	47.1480i	0.210259	+	1.64248i
$825$			13.0189i			0.453261i
$826$	13.8446	−	26.5179i	0.481714	−	0.922674i
$827$	−8.69607	+	15.0620i	−0.302392	+	0.523758i	−0.976677	−	0.214713i	$-0.931118\pi$
$827$	−8.69607	+	15.0620i	−0.302392	+	0.523758i	0.674285	+	0.738471i	$0.264452\pi$
$828$	−5.37931	−	63.2228i	−0.186944	−	2.19714i
$829$			29.3149i			1.01815i	0.860723	+	0.509074i	$0.170012\pi$
$829$			29.3149i			1.01815i	−0.860723	+	0.509074i	$0.829988\pi$
$830$	10.4942	−	20.1007i	0.364260	−	0.697704i
$831$	17.6543	+	30.5782i	0.612421	+	1.06074i
$832$	−45.4083	−	12.5162i	−1.57425	−	0.433920i
$833$	−0.186411	−	0.322873i	−0.00645875	−	0.0111869i
$834$	50.5778	+	79.6006i	1.75137	+	2.75634i
$835$	−5.61457			−0.194300
$836$	2.73871	−	37.6122i	0.0947202	−	1.30084i
$837$	51.8742			1.79303
$838$	−9.90201	−	15.5840i	−0.342059	−	0.538342i
$839$	−6.27987	−	10.8771i	−0.216805	−	0.375518i	0.737024	−	0.675866i	$-0.236230\pi$
$839$	−6.27987	−	10.8771i	−0.216805	−	0.375518i	−0.953830	+	0.300349i	$0.902897\pi$
$840$	8.53932	−	20.4088i	0.294635	−	0.704172i
$841$	29.2649	+	50.6882i	1.00913	+	1.74787i
$842$	−15.9899	+	30.6271i	−0.551049	+	1.05548i
$843$			37.5435i			1.29307i
$844$	−12.6159	+	1.07342i	−0.434256	+	0.0369486i
$845$	10.8326	−	18.7626i	0.372653	−	0.645453i
$846$	−5.10565	+	9.77935i	−0.175536	+	0.336221i
$847$		−	20.0454i		−	0.688769i
$848$	−2.37630	−	13.8632i	−0.0816026	−	0.476065i
$849$	−31.0364	−	17.9189i	−1.06517	−	0.614973i
$850$	1.81349	−	1.15228i	0.0622022	−	0.0395229i
$851$	−15.3687	+	26.6194i	−0.526832	+	0.912500i
$852$	−5.94847	−	8.53859i	−0.203791	−	0.292527i
$853$	−16.4707	−	28.5281i	−0.563947	−	0.976785i	−0.997147	−	0.0754869i	$-0.975949\pi$
$853$	−16.4707	−	28.5281i	−0.563947	−	0.976785i	0.433200	−	0.901298i	$-0.357384\pi$
$854$	12.1470	−	0.515830i	0.415661	−	0.0176513i
$855$	9.45041	+	24.6550i	0.323197	+	0.843185i
$856$	0.519584	+	4.05884i	0.0177590	+	0.138728i
$857$	3.67766	−	2.12330i	0.125626	−	0.0725305i	−0.435870	−	0.900010i	$-0.643559\pi$
$857$	3.67766	−	2.12330i	0.125626	−	0.0725305i	0.561496	+	0.827479i	$0.310226\pi$
$858$	91.4947	−	58.1352i	3.12358	−	1.98470i
$859$	20.1608	+	11.6399i	0.687878	+	0.397147i	0.802817	−	0.596226i	$-0.203334\pi$
$859$	20.1608	+	11.6399i	0.687878	+	0.397147i	−0.114938	+	0.993373i	$0.536667\pi$
$860$	−8.17514	+	5.69527i	−0.278770	+	0.194207i
$861$	−2.20135	+	3.81286i	−0.0750219	+	0.129942i
$862$	1.98395	+	46.7189i	0.0675737	+	1.59125i
$863$	11.5581			0.393443			0.196722	−	0.980459i	$-0.436970\pi$
$863$	11.5581			0.393443			0.196722	+	0.980459i	$0.436970\pi$
$864$	49.5503	+	15.9487i	1.68573	+	0.542586i
$865$	7.45752	+	4.30560i	0.253563	+	0.146395i
$866$	12.8346	−	0.545031i	0.436138	−	0.0185209i
$867$	44.2159			1.50165
$868$	−26.5274	−	12.4471i	−0.900400	−	0.422482i
$869$	−6.06906	+	3.50397i	−0.205879	+	0.118864i
$870$	−18.4288	+	35.2985i	−0.624795	+	1.19673i
$871$	6.75481	−	3.89989i	0.228878	−	0.132143i
$872$	16.2810	+	21.3758i	0.551344	+	0.723875i
$873$			66.2084i			2.24081i
$874$	−12.8240	−	29.6292i	−0.433779	−	1.00222i
$875$			2.59896i			0.0878610i
$876$	5.45789	+	7.83440i	0.184405	+	0.264700i
$877$	8.47883	−	4.89526i	0.286310	−	0.165301i	−0.349967	−	0.936762i	$-0.613807\pi$
$877$	8.47883	−	4.89526i	0.286310	−	0.165301i	0.636277	+	0.771461i	$0.280474\pi$
$878$	−30.6998	−	16.0279i	−1.03607	−	0.540916i
$879$	−77.9646	+	45.0129i	−2.62968	+	1.51825i
$880$	16.2314	+	5.99562i	0.547160	+	0.202112i
$881$	31.2058			1.05135			0.525676	−	0.850685i	$-0.323813\pi$
$881$	31.2058			1.05135			0.525676	+	0.850685i	$0.323813\pi$
$882$	0.0891903	+	2.10029i	0.00300319	+	0.0707204i
$883$	22.2567	+	12.8499i	0.748996	+	0.432433i	0.825331	−	0.564649i	$-0.190988\pi$
$883$	22.2567	+	12.8499i	0.748996	+	0.432433i	−0.0763348	+	0.997082i	$0.524322\pi$
$884$	−16.1961	−	7.59944i	−0.544732	−	0.255597i
$885$	−24.4946			−0.823375
$886$	41.4145	−	1.75870i	1.39135	−	0.0590846i
$887$	−5.36284	+	9.28872i	−0.180067	+	0.311885i	−0.941903	−	0.335885i	$-0.890965\pi$
$887$	−5.36284	+	9.28872i	−0.180067	+	0.311885i	0.761836	+	0.647769i	$0.224298\pi$
$888$	−30.2703	−	39.7427i	−1.01580	−	1.33368i
$889$	9.50818	+	5.48955i	0.318894	+	0.184114i
$890$	−11.5754	−	18.2177i	−0.388010	−	0.610660i
$891$	−35.6689	+	20.5934i	−1.19495	+	0.689906i
$892$	−26.5293	+	2.25724i	−0.888266	+	0.0755780i
$893$	−0.880811	+	5.54375i	−0.0294752	+	0.185514i
$894$	1.15230	+	27.1348i	0.0385386	+	0.907522i
$895$	1.80293	+	3.12277i	0.0602653	+	0.104383i
$896$	−21.5122	−	20.0453i	−0.718672	−	0.669668i
$897$	46.4019	−	80.3705i	1.54932	−	2.68349i
$898$	22.9565	+	36.1296i	0.766070	+	1.20566i
$899$	45.6754	+	26.3707i	1.52336	+	0.879513i
$900$	−12.0715	+	1.02710i	−0.402382	+	0.0342366i
$901$		−	5.34236i		−	0.177980i
$902$	−3.05252	−	1.59367i	−0.101638	−	0.0530635i
$903$	−19.4828	+	33.7452i	−0.648348	+	1.12297i
$904$	20.4298	−	2.61529i	0.679486	−	0.0869832i
$905$		−	12.5540i		−	0.417311i
$906$	32.1478	+	16.7839i	1.06804	+	0.557607i
$907$	−20.1372	−	34.8786i	−0.668643	−	1.15812i	−0.978284	−	0.207270i	$-0.933542\pi$
$907$	−20.1372	−	34.8786i	−0.668643	−	1.15812i	0.309641	−	0.950854i	$-0.399791\pi$
$908$	−3.74983	+	7.99169i	−0.124442	+	0.265213i
$909$	−55.5565	−	96.2266i	−1.84269	−	3.19164i
$910$	18.2650	−	11.6055i	0.605480	−	0.384719i
$911$	−17.4793			−0.579116			−0.289558	−	0.957161i	$-0.593508\pi$
$911$	−17.4793			−0.579116			−0.289558	+	0.957161i	$0.593508\pi$
$912$	52.4698	−	0.639866i	1.73745	−	0.0211881i
$913$	69.3596			2.29547
$914$	−18.2277	+	11.5818i	−0.602917	+	0.383090i
$915$	−4.97759	−	8.62144i	−0.164554	−	0.285016i
$916$	−5.67093	+	12.0860i	−0.187373	+	0.399332i
$917$	−7.18899	−	12.4517i	−0.237401	−	0.411191i
$918$	17.5264	+	9.15024i	0.578456	+	0.302003i
$919$		−	40.0640i		−	1.32159i	−0.750567	−	0.660794i	$-0.770220\pi$
$919$		−	40.0640i		−	1.32159i	0.750567	−	0.660794i	$-0.229780\pi$
$920$	14.6936	−	1.88098i	0.484435	−	0.0620141i
$921$	40.1449	−	69.5330i	1.32282	−	2.29119i
$922$	−45.0538	−	23.5219i	−1.48377	−	0.774653i
$923$		−	10.1791i		−	0.335049i
$924$	67.4278	−	5.73708i	2.21821	−	0.188736i
$925$	5.08257	+	2.93442i	0.167114	+	0.0964832i
$926$	−28.0655	−	44.1702i	−0.922290	−	1.45152i
$927$	50.8995	−	88.1605i	1.67176	−	2.89557i
$928$	35.5216	+	39.2323i	1.16605	+	1.28786i
$929$	−1.94843	−	3.37477i	−0.0639258	−	0.110723i	0.832291	−	0.554339i	$-0.187029\pi$
$929$	−1.94843	−	3.37477i	−0.0639258	−	0.110723i	−0.896217	+	0.443616i	$0.853695\pi$
$930$	1.01799	+	23.9719i	0.0333811	+	0.786071i
$931$	0.382837	+	0.998778i	0.0125470	+	0.0327336i
$932$	−46.1875	+	3.92986i	−1.51292	+	0.128727i
$933$	63.4158	−	36.6131i	2.07614	−	1.19866i
$934$	−6.23646	−	9.81510i	−0.204063	−	0.321160i
$935$	5.69170	+	3.28610i	0.186138	+	0.107467i
$936$	61.1226	+	80.2496i	1.99785	+	2.62304i
$937$	20.3964	−	35.3276i	0.666321	−	1.15410i	−0.312605	−	0.949883i	$-0.601202\pi$
$937$	20.3964	−	35.3276i	0.666321	−	1.15410i	0.978925	−	0.204218i	$-0.0654651\pi$
$938$	4.86474	−	0.206585i	0.158839	−	0.00674523i
$939$	41.2743			1.34693
$940$	−2.33164	−	1.09404i	−0.0760497	−	0.0356837i
$941$	2.68518	+	1.55029i	0.0875345	+	0.0505381i	0.543128	−	0.839650i	$-0.317240\pi$
$941$	2.68518	+	1.55029i	0.0875345	+	0.0505381i	−0.455594	+	0.890188i	$0.650573\pi$
$942$	−0.554922	−	13.0675i	−0.0180803	−	0.425763i
$943$	−2.94801			−0.0960004
$944$	−11.2805	+	30.5387i	−0.367149	+	0.993950i
$945$	−20.7113	+	11.9577i	−0.673739	+	0.388983i
$946$	−27.0160	−	14.1046i	−0.878365	−	0.458581i
$947$	−20.0897	+	11.5988i	−0.652827	+	0.376910i	−0.789539	−	0.613701i	$-0.789680\pi$
$947$	−20.0897	+	11.5988i	−0.652827	+	0.376910i	0.136711	+	0.990611i	$0.456347\pi$
$948$	−5.57396	−	8.00100i	−0.181034	−	0.259860i
$949$			9.33962i			0.303177i
$950$	−5.65726	+	2.44855i	−0.183546	+	0.0794416i
$951$			15.0561i			0.488226i
$952$	−6.76706	−	8.88467i	−0.219322	−	0.287954i
$953$	−0.713832	+	0.412131i	−0.0231233	+	0.0133502i	−0.511517	−	0.859273i	$-0.670916\pi$
$953$	−0.713832	+	0.412131i	−0.0231233	+	0.0133502i	0.488394	+	0.872623i	$0.337583\pi$
$954$	−13.9413	+	26.7031i	−0.451366	+	0.864546i
$955$	−16.6973	+	9.64021i	−0.540313	+	0.311950i
$956$	13.0156	+	6.10714i	0.420956	+	0.197519i
$957$	−121.802			−3.93728
$958$	−32.9429	+	1.39894i	−1.06434	+	0.0451978i
$959$	−8.52937	−	4.92444i	−0.275428	−	0.159018i
$960$	−6.39779	+	23.2110i	−0.206488	+	0.749132i
$961$	0.779617			0.0251489
$962$	−2.07330	−	48.8229i	−0.0668458	−	1.57411i
$963$	4.38180	−	7.58949i	0.141201	−	0.244568i
$964$	−22.6383	+	15.7712i	−0.729132	+	0.507955i
$965$	−3.13532	−	1.81018i	−0.100930	−	0.0582718i
$966$	48.8982	−	31.0697i	1.57327	−	0.999650i
$967$	34.9088	−	20.1546i	1.12259	−	0.648128i	0.180530	−	0.983569i	$-0.442219\pi$
$967$	34.9088	−	20.1546i	1.12259	−	0.648128i	0.942061	+	0.335441i	$0.108885\pi$
$968$	2.77003	+	21.6387i	0.0890323	+	0.695493i
$969$	19.6838	+	3.12744i	0.632336	+	0.100468i
$970$	−15.4433	+	0.655812i	−0.495855	+	0.0210569i
$971$	26.4453	+	45.8046i	0.848671	+	1.46994i	0.882395	+	0.470510i	$0.155930\pi$
$971$	26.4453	+	45.8046i	0.848671	+	1.46994i	−0.0337239	+	0.999431i	$0.510737\pi$
$972$	−1.19917	−	1.72132i	−0.0384635	−	0.0552115i
$973$	−28.7944	+	49.8733i	−0.923105	+	1.59887i
$974$	26.7434	−	16.9926i	0.856913	−	0.544477i
$975$	−15.3456	−	8.85976i	−0.491451	−	0.283739i
$976$	−13.0412	+	2.23539i	−0.417437	+	0.0715532i
$977$		−	27.3538i		−	0.875126i	−0.899188	−	0.437563i	$-0.855842\pi$
$977$		−	27.3538i		−	0.875126i	0.899188	−	0.437563i	$-0.144158\pi$
$978$	−12.8909	+	24.6912i	−0.412205	+	0.789537i
$979$	33.0111	−	57.1770i	1.05504	−	1.82738i
$980$	−0.489016	+	0.0416079i	−0.0156210	+	0.00132911i
$981$		−	57.5463i		−	1.83731i
$982$	21.7895	−	41.7356i	0.695331	−	1.33184i
$983$	30.7574	+	53.2733i	0.981008	+	1.69916i	0.658485	+	0.752594i	$0.271198\pi$
$983$	30.7574	+	53.2733i	0.981008	+	1.69916i	0.322523	+	0.946562i	$0.395469\pi$
$984$	1.84943	−	4.42011i	0.0589577	−	0.140908i
$985$	−5.77801	−	10.0078i	−0.184103	−	0.318875i
$986$	10.7804	+	16.9665i	0.343319	+	0.540324i
$987$	−10.0727			−0.320617
$988$	42.4701	+	28.8243i	1.35115	+	0.917024i
$989$	−26.0910			−0.829646
$990$	−19.8739	−	31.2781i	−0.631634	−	0.994082i
$991$	−14.0345	−	24.3085i	−0.445821	−	0.772184i	0.552288	−	0.833653i	$-0.313755\pi$
$991$	−14.0345	−	24.3085i	−0.445821	−	0.772184i	−0.998109	+	0.0614691i	$0.980421\pi$
$992$	30.3559	+	9.77064i	0.963802	+	0.310218i
$993$	−30.6253	−	53.0446i	−0.971865	−	1.68332i
$994$	2.94088	−	5.63296i	0.0932791	−	0.178667i
$995$		−	7.98808i		−	0.253239i
$996$	8.18196	+	96.1623i	0.259255	+	3.04702i
$997$	−5.08362	+	8.80508i	−0.161000	+	0.278860i	−0.935228	−	0.354047i	$-0.884805\pi$
$997$	−5.08362	+	8.80508i	−0.161000	+	0.278860i	0.774228	+	0.632907i	$0.218139\pi$
$998$	−23.8962	+	45.7708i	−0.756421	+	1.44885i
$999$			54.0044i			1.70862i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.n.b.31.16	✓	40
4.3	odd	2	inner	380.2.n.b.31.17	yes	40
19.8	odd	6	inner	380.2.n.b.331.17	yes	40
76.27	even	6	inner	380.2.n.b.331.16	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.n.b.31.16	✓	40	1.1	even	1	trivial
380.2.n.b.31.17	yes	40	4.3	odd	2	inner
380.2.n.b.331.16	yes	40	76.27	even	6	inner
380.2.n.b.331.17	yes	40	19.8	odd	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)

\(f(q)\)	\(=\)	\(q+(1.19364 - 0.758433i) q^{2} +(1.50479 + 2.60637i) q^{3} +(0.849559 - 1.81059i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(3.77293 + 1.96979i) q^{6} +2.59896i q^{7} +(-0.359145 - 2.80553i) q^{8} +(-3.02877 + 5.24598i) q^{9} +O(q^{10})\)	\(q+(1.19364 - 0.758433i) q^{2} +(1.50479 + 2.60637i) q^{3} +(0.849559 - 1.81059i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(3.77293 + 1.96979i) q^{6} +2.59896i q^{7} +(-0.359145 - 2.80553i) q^{8} +(-3.02877 + 5.24598i) q^{9} +(-1.25364 - 0.654507i) q^{10} -4.32584i q^{11} +(5.99748 - 0.510295i) q^{12} +(5.09891 + 2.94386i) q^{13} +(1.97114 + 3.10223i) q^{14} +(1.50479 - 2.60637i) q^{15} +(-2.55650 - 3.07641i) q^{16} +(-0.759646 - 1.31575i) q^{17} +(0.363461 + 8.55894i) q^{18} +(1.56011 + 4.07014i) q^{19} +(-1.99280 + 0.169557i) q^{20} +(-6.77385 + 3.91089i) q^{21} +(-3.28086 - 5.16350i) q^{22} +(-4.53570 - 2.61869i) q^{23} +(6.77181 - 5.15779i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(8.31899 - 0.353272i) q^{26} -9.20188 q^{27} +(4.70567 + 2.20797i) q^{28} +(-8.10230 - 4.67787i) q^{29} +(-0.180579 - 4.25235i) q^{30} -5.63734 q^{31} +(-5.38480 - 1.73320i) q^{32} +(11.2747 - 6.50946i) q^{33} +(-1.90465 - 0.994388i) q^{34} +(2.25077 - 1.29948i) q^{35} +(6.92522 + 9.94064i) q^{36} -5.86885i q^{37} +(4.94914 + 3.67505i) q^{38} +17.7195i q^{39} +(-2.25009 + 1.71380i) q^{40} +(0.487467 - 0.281439i) q^{41} +(-5.11941 + 9.80571i) q^{42} +(4.31427 - 2.49085i) q^{43} +(-7.83233 - 3.67505i) q^{44} +6.05754 q^{45} +(-7.40011 + 0.314251i) q^{46} +(1.11525 + 0.643888i) q^{47} +(4.17128 - 11.2925i) q^{48} +0.245391 q^{49} +(0.0600015 + 1.41294i) q^{50} +(2.28621 - 3.95983i) q^{51} +(9.66196 - 6.73108i) q^{52} +(3.04525 + 1.75818i) q^{53} +(-10.9837 + 6.97901i) q^{54} +(-3.74628 + 2.16292i) q^{55} +(7.29148 - 0.933405i) q^{56} +(-8.26066 + 10.1909i) q^{57} +(-13.2191 + 0.561358i) q^{58} +(-4.06944 - 7.04847i) q^{59} +(-3.44067 - 4.93882i) q^{60} +(1.65392 - 2.86467i) q^{61} +(-6.72896 + 4.27555i) q^{62} +(-13.6341 - 7.87166i) q^{63} +(-7.74203 + 2.01519i) q^{64} -5.88772i q^{65} +(8.52098 - 16.3211i) q^{66} +(0.662378 - 1.14727i) q^{67} +(-3.02765 + 0.257607i) q^{68} -15.7623i q^{69} +(1.70104 - 3.25817i) q^{70} +(-0.864436 - 1.49725i) q^{71} +(15.8055 + 6.61324i) q^{72} +(0.793145 + 1.37377i) q^{73} +(-4.45113 - 7.00530i) q^{74} -3.00957 q^{75} +(8.69478 + 0.633105i) q^{76} +11.2427 q^{77} +(13.4391 + 21.1507i) q^{78} +(-0.810011 - 1.40298i) q^{79} +(-1.38600 + 3.75220i) q^{80} +(-4.76057 - 8.24555i) q^{81} +(0.368408 - 0.705648i) q^{82} +16.0338i q^{83} +(1.32624 + 15.5872i) q^{84} +(-0.759646 + 1.31575i) q^{85} +(3.26055 - 6.24526i) q^{86} -28.1568i q^{87} +(-12.1363 + 1.55360i) q^{88} +(13.2176 + 7.63116i) q^{89} +(7.23053 - 4.59424i) q^{90} +(-7.65098 + 13.2519i) q^{91} +(-8.59473 + 5.98759i) q^{92} +(-8.48300 - 14.6930i) q^{93} +(1.81955 - 0.0772685i) q^{94} +(2.74479 - 3.38616i) q^{95} +(-3.58561 - 16.6429i) q^{96} +(9.46559 - 5.46496i) q^{97} +(0.292909 - 0.186113i) q^{98} +(22.6933 + 13.1020i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more