LMFDB - Embedded newform 380.2.n.b.31.17

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			31.17
Character	$\chi$	$=$	380.31
Dual form			380.2.n.b.331.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25364 - 0.654507i) q^{2} +(-1.50479 - 2.60637i) q^{3} +(1.14324 - 1.64104i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-3.59235 - 2.28256i) q^{6} -2.59896i q^{7} +(0.359145 - 2.80553i) q^{8} +(-3.02877 + 5.24598i) q^{9} +O(q^{10})$	\(q+(1.25364 - 0.654507i) q^{2} +(-1.50479 - 2.60637i) q^{3} +(1.14324 - 1.64104i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-3.59235 - 2.28256i) q^{6} -2.59896i q^{7} +(0.359145 - 2.80553i) q^{8} +(-3.02877 + 5.24598i) q^{9} +(-1.19364 - 0.758433i) q^{10} +4.32584i q^{11} +(-5.99748 - 0.510295i) q^{12} +(5.09891 + 2.94386i) q^{13} +(-1.70104 - 3.25817i) q^{14} +(-1.50479 + 2.60637i) q^{15} +(-1.38600 - 3.75220i) 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} +(2.83129 + 5.42305i) q^{22} +(4.53570 + 2.61869i) q^{23} +(-7.85269 + 3.28567i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(8.31899 + 0.353272i) q^{26} +9.20188 q^{27} +(-4.26499 - 2.97124i) q^{28} +(-8.10230 - 4.67787i) q^{29} +(-0.180579 + 4.25235i) q^{30} +5.63734 q^{31} +(-4.19339 - 3.79677i) q^{32} +(11.2747 - 6.50946i) q^{33} +(-1.81349 - 1.15228i) q^{34} +(-2.25077 + 1.29948i) q^{35} +(5.14623 + 10.9677i) q^{36} -5.86885i q^{37} +(-4.61976 - 4.08140i) q^{38} -17.7195i q^{39} +(-2.60924 + 1.09174i) q^{40} +(0.487467 - 0.281439i) q^{41} +(-5.93229 + 9.33639i) q^{42} +(-4.31427 + 2.49085i) q^{43} +(7.09885 + 4.94547i) q^{44} +6.05754 q^{45} +(7.40011 + 0.314251i) q^{46} +(-1.11525 - 0.643888i) q^{47} +(-7.69397 + 9.25869i) q^{48} +0.245391 q^{49} +(-0.0600015 + 1.41294i) q^{50} +(-2.28621 + 3.95983i) q^{51} +(10.6603 - 5.00196i) q^{52} +(3.04525 + 1.75818i) q^{53} +(11.5359 - 6.02270i) 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} +(2.55681 + 5.44912i) q^{60} +(1.65392 - 2.86467i) q^{61} +(7.06721 - 3.68968i) q^{62} +(13.6341 + 7.87166i) q^{63} +(-7.74203 - 2.01519i) q^{64} -5.88772i q^{65} +(9.87398 - 15.5399i) q^{66} +(-0.662378 + 1.14727i) q^{67} +(-3.02765 - 0.257607i) q^{68} -15.7623i q^{69} +(-1.97114 + 3.10223i) q^{70} +(0.864436 + 1.49725i) q^{71} +(13.6300 + 10.3814i) q^{72} +(0.793145 + 1.37377i) q^{73} +(-3.84120 - 7.35744i) q^{74} +3.00957 q^{75} +(-8.46283 - 2.09296i) q^{76} +11.2427 q^{77} +(-11.5976 - 22.2139i) q^{78} +(0.810011 + 1.40298i) q^{79} +(-2.55650 + 3.07641i) q^{80} +(-4.76057 - 8.24555i) q^{81} +(0.426906 - 0.671875i) q^{82} -16.0338i q^{83} +(-1.32624 + 15.5872i) q^{84} +(-0.759646 + 1.31575i) q^{85} +(-3.77828 + 5.94635i) q^{86} +28.1568i q^{87} +(12.1363 + 1.55360i) q^{88} +(13.2176 + 7.63116i) q^{89} +(7.59399 - 3.96470i) q^{90} +(7.65098 - 13.2519i) q^{91} +(9.48277 - 4.44946i) 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} +(0.307633 - 0.160610i) 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 $

$2$	1.25364	−	0.654507i	0.886459	−	0.462806i
$2$	1.25364	−	0.654507i	0.886459	−	0.462806i
$3$	−1.50479	−	2.60637i	−0.868789	−	1.50479i	−0.863235	−	0.504802i	$-0.831565\pi$
$3$	−1.50479	−	2.60637i	−0.868789	−	1.50479i	−0.00555435	−	0.999985i	$-0.501768\pi$
$4$	1.14324	−	1.64104i	0.571620	−	0.820518i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−3.59235	−	2.28256i	−1.46657	−	0.931851i
$7$		−	2.59896i		−	0.982316i	−0.871071	−	0.491158i	$-0.836574\pi$
$7$		−	2.59896i		−	0.982316i	0.871071	−	0.491158i	$-0.163426\pi$
$8$	0.359145	−	2.80553i	0.126977	−	0.991906i
$9$	−3.02877	+	5.24598i	−1.00959	+	1.74866i
$10$	−1.19364	−	0.758433i	−0.377463	−	0.239838i
$11$			4.32584i			1.30429i	0.758095	+	0.652144i	$0.226130\pi$
$11$			4.32584i			1.30429i	−0.758095	+	0.652144i	$0.773870\pi$
$12$	−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	$0.362590\pi$
$14$	−1.70104	−	3.25817i	−0.454622	−	0.870783i
$15$	−1.50479	+	2.60637i	−0.388534	+	0.672961i
$16$	−1.38600	−	3.75220i	−0.346500	−	0.938050i
$17$	−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
$22$	2.83129	+	5.42305i	0.603633	+	1.15620i
$23$	4.53570	+	2.61869i	0.945760	+	0.546035i	0.891761	−	0.452506i	$-0.149470\pi$
$23$	4.53570	+	2.61869i	0.945760	+	0.546035i	0.0539986	+	0.998541i	$0.482803\pi$
$24$	−7.85269	+	3.28567i	−1.60292	+	0.670684i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	8.31899	+	0.353272i	1.63149	+	0.0692823i
$27$	9.20188			1.77090
$28$	−4.26499	−	2.97124i	−0.806008	−	0.561512i
$29$	−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	$-0.331032\pi$
$31$	5.63734			1.01250			0.506248	+	0.862388i	$0.331032\pi$
$32$	−4.19339	−	3.79677i	−0.741294	−	0.671180i
$33$	11.2747	−	6.50946i	1.96268	−	1.13315i
$34$	−1.81349	−	1.15228i	−0.311011	−	0.197615i
$35$	−2.25077	+	1.29948i	−0.380449	+	0.219652i
$36$	5.14623	+	10.9677i	0.857706	+	1.82796i
$37$		−	5.86885i		−	0.964832i	−0.875942	−	0.482416i	$-0.839759\pi$
$37$		−	5.86885i		−	0.964832i	0.875942	−	0.482416i	$-0.160241\pi$
$38$	−4.61976	−	4.08140i	−0.749423	−	0.662091i
$39$		−	17.7195i		−	2.83739i
$40$	−2.60924	+	1.09174i	−0.412556	+	0.172619i
$41$	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	$0.319338\pi$
$42$	−5.93229	+	9.33639i	−0.915372	+	1.44064i
$43$	−4.31427	+	2.49085i	−0.657920	+	0.379850i	−0.791484	−	0.611190i	$-0.790691\pi$
$43$	−4.31427	+	2.49085i	−0.657920	+	0.379850i	0.133564	+	0.991040i	$0.457358\pi$
$44$	7.09885	+	4.94547i	1.07019	+	0.745558i
$45$	6.05754			0.903004
$46$	7.40011	+	0.314251i	1.09109	+	0.0463338i
$47$	−1.11525	−	0.643888i	−0.162675	−	0.0939207i	0.416452	−	0.909158i	$-0.363273\pi$
$47$	−1.11525	−	0.643888i	−0.162675	−	0.0939207i	−0.579128	+	0.815237i	$0.696607\pi$
$48$	−7.69397	+	9.25869i	−1.11053	+	1.33638i
$49$	0.245391			0.0350559
$50$	−0.0600015	+	1.41294i	−0.00848550	+	0.199820i
$51$	−2.28621	+	3.95983i	−0.320134	+	0.554488i
$52$	10.6603	−	5.00196i	1.47831	−	0.693647i
$53$	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	$0.589026\pi$
$54$	11.5359	−	6.02270i	1.56983	−	0.819585i
$55$	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	$0.0110648\pi$
$59$	4.06944	+	7.04847i	0.529796	+	0.917633i	−0.469600	+	0.882879i	$0.655602\pi$
$60$	2.55681	+	5.44912i	0.330083	+	0.703478i
$61$	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	$0.0987463\pi$
$62$	7.06721	−	3.68968i	0.897537	−	0.468590i
$63$	13.6341	+	7.87166i	1.71774	+	0.991736i
$64$	−7.74203	−	2.01519i	−0.967754	−	0.251898i
$65$		−	5.88772i		−	0.730281i
$66$	9.87398	−	15.5399i	1.21540	−	1.91283i
$67$	−0.662378	+	1.14727i	−0.0809223	+	0.140162i	−0.903646	−	0.428279i	$-0.859120\pi$
$67$	−0.662378	+	1.14727i	−0.0809223	+	0.140162i	0.822724	+	0.568441i	$0.192453\pi$
$68$	−3.02765	−	0.257607i	−0.367156	−	0.0312394i
$69$		−	15.7623i		−	1.89756i
$70$	−1.97114	+	3.10223i	−0.235596	+	0.370787i
$71$	0.864436	+	1.49725i	0.102590	+	0.177691i	0.912751	−	0.408517i	$-0.133954\pi$
$71$	0.864436	+	1.49725i	0.102590	+	0.177691i	−0.810161	+	0.586207i	$0.800620\pi$
$72$	13.6300	+	10.3814i	1.60631	+	1.22346i
$73$	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	$0.803742\pi$
$74$	−3.84120	−	7.35744i	−0.446531	−	0.855285i
$75$	3.00957			0.347516
$76$	−8.46283	−	2.09296i	−0.970753	−	0.240079i
$77$	11.2427			1.28122
$78$	−11.5976	−	22.2139i	−1.31316	−	2.51523i
$79$	0.810011	+	1.40298i	0.0911334	+	0.157848i	0.907988	−	0.418996i	$-0.137618\pi$
$79$	0.810011	+	1.40298i	0.0911334	+	0.157848i	−0.816855	+	0.576843i	$0.804284\pi$
$80$	−2.55650	+	3.07641i	−0.285825	+	0.343953i
$81$	−4.76057	−	8.24555i	−0.528952	−	0.916172i
$82$	0.426906	−	0.671875i	0.0471438	−	0.0741962i
$83$		−	16.0338i		−	1.75994i	−0.475032	−	0.879969i	$-0.657563\pi$
$83$		−	16.0338i		−	1.75994i	0.475032	−	0.879969i	$-0.342437\pi$
$84$	−1.32624	+	15.5872i	−0.144704	+	1.70071i
$85$	−0.759646	+	1.31575i	−0.0823952	+	0.142713i
$86$	−3.77828	+	5.94635i	−0.407422	+	0.641212i
$87$			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	$0.366729\pi$
$90$	7.59399	−	3.96470i	0.800477	−	0.417916i
$91$	7.65098	−	13.2519i	0.802040	−	1.38917i
$92$	9.48277	−	4.44946i	0.988647	−	0.463889i
$93$	−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	$0.146096\pi$
$98$	0.307633	−	0.160610i	0.0310757	−	0.0162241i
$99$	−22.6933	−	13.1020i	−2.28076	−	1.31680i
$100$	0.849559	+	1.81059i	0.0849559	+	0.181059i
$101$	−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	$-0.189513\pi$
$103$	16.8053			1.65588			0.827940	+	0.560816i	$0.189513\pi$
$104$	10.0903	−	13.2479i	0.989439	−	1.29906i
$105$	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	$-0.477722\pi$
$107$	1.44673			0.139860			0.0699301	+	0.997552i	$0.477722\pi$
$108$	10.5200	−	15.1006i	1.01228	−	1.45306i
$109$	−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	$0.483682\pi$
$110$	3.28086	−	5.16350i	0.312817	−	0.492320i
$111$	−15.2964	+	8.83136i	−1.45187	+	0.838236i
$112$	−9.75183	+	3.60217i	−0.921461	+	0.340373i
$113$			7.28198i			0.685031i	0.939512	+	0.342516i	$0.111279\pi$
$113$			7.28198i			0.685031i	−0.939512	+	0.342516i	$0.888721\pi$
$114$	−3.68589	+	18.1824i	−0.345215	+	1.70294i
$115$		−	5.23738i		−	0.488388i
$116$	−16.9394	+	7.94825i	−1.57279	+	0.737976i
$117$	−30.8868	+	17.8325i	−2.85549	+	1.64862i
$118$	9.71490	+	6.17279i	0.894329	+	0.568252i
$119$	−3.41957	+	1.97429i	−0.313472	+	0.180983i
$120$	6.77181	+	5.15779i	0.618179	+	0.470840i
$121$	−7.71286			−0.701169
$122$	0.198475	−	4.67378i	0.0179691	−	0.423144i
$123$	−1.46707	−	0.847012i	−0.132281	−	0.0763725i
$124$	6.44484	−	9.25108i	0.578763	−	0.830772i
$125$	1.00000			0.0894427
$126$	22.2444	+	0.944623i	1.98168	+	0.0841537i
$127$	−2.11221	+	3.65845i	−0.187428	+	0.324635i	−0.944392	−	0.328822i	$-0.893349\pi$
$127$	−2.11221	+	3.65845i	−0.187428	+	0.324635i	0.756964	+	0.653457i	$0.226682\pi$
$128$	−11.0247	+	2.54089i	−0.974454	+	0.224585i
$129$	12.9841	+	7.49638i	1.14319	+	0.660020i
$130$	−3.85355	−	7.38109i	−0.337979	−	0.647365i
$131$	4.79102	−	2.76610i	0.418594	−	0.241675i	−0.275882	−	0.961192i	$-0.588970\pi$
$131$	4.79102	−	2.76610i	0.418594	−	0.241675i	0.694475	+	0.719516i	$0.255637\pi$
$132$	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
$136$	−3.96419	+	1.65867i	−0.339927	+	0.142230i
$137$	−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	$0.218423\pi$
$138$	−10.3165	−	19.7603i	−0.878201	−	1.68211i
$139$	−19.1897	−	11.0792i	−1.62765	−	0.939724i	−0.984792	−	0.173737i	$-0.944416\pi$
$139$	−19.1897	−	11.0792i	−1.62765	−	0.939724i	−0.642857	−	0.765986i	$-0.722251\pi$
$140$	−0.440673	+	5.17921i	−0.0372436	+	0.437723i
$141$			3.87566i			0.326389i
$142$	2.06365	+	1.31123i	0.173178	+	0.110036i
$143$	−12.7346	+	22.0571i	−1.06492	+	1.84450i
$144$	23.8818	+	4.09360i	1.99015	+	0.341134i
$145$			9.35573i			0.776951i
$146$	1.89346	+	1.20309i	0.156704	+	0.0995688i
$147$	−0.369262	−	0.639580i	−0.0304562	−	0.0527517i
$148$	−9.63099	−	6.70950i	−0.791663	−	0.551518i
$149$	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	$0.749155\pi$
$150$	3.77293	−	1.96979i	0.308059	−	0.160833i
$151$	−8.52065			−0.693400			−0.346700	−	0.937976i	$-0.612698\pi$
$151$	−8.52065			−0.693400			−0.346700	+	0.937976i	$0.612698\pi$
$152$	−11.9792	+	2.91516i	−0.971643	+	0.236451i
$153$	9.20317			0.744032
$154$	14.0943	−	7.35842i	1.13575	−	0.592958i
$155$	−2.81867	−	4.88208i	−0.226401	−	0.392138i
$156$	−29.0784	−	20.2577i	−2.32813	−	1.62191i
$157$	−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	$0.872465\pi$
$158$	1.93373	+	1.22868i	0.153839	+	0.0977484i
$159$		−	10.5827i		−	0.839264i
$160$	−1.19140	+	5.52997i	−0.0941886	+	0.437182i
$161$	6.80588	−	11.7881i	0.536378	−	0.929035i
$162$	−11.3648	−	7.22114i	−0.892905	−	0.567347i
$163$		−	6.54430i		−	0.512589i	−0.966599	−	0.256295i	$-0.917498\pi$
$163$		−	6.54430i		−	0.512589i	0.966599	−	0.256295i	$-0.0825017\pi$
$164$	0.0954400	−	1.12170i	0.00745262	−	0.0875904i
$165$	−11.2747	−	6.50946i	−0.877736	−	0.506761i
$166$	−10.4942	−	20.1007i	−0.814511	−	1.56011i
$167$	−2.80728	+	4.86236i	−0.217234	+	0.376260i	−0.953961	−	0.299930i	$-0.903037\pi$
$167$	−2.80728	+	4.86236i	−0.217234	+	0.376260i	0.736727	+	0.676190i	$0.236370\pi$
$168$	8.53932	+	20.4088i	0.658823	+	1.57458i
$169$	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	$0.439489\pi$
$174$	18.4288	+	35.2985i	1.39708	+	2.67597i
$175$	2.25077	+	1.29948i	0.170142	+	0.0982316i
$176$	16.2314	−	5.99562i	1.22349	−	0.451937i
$177$	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	$-0.456975\pi$
$179$	3.60586			0.269515			0.134757	+	0.990879i	$0.456975\pi$
$180$	6.92522	−	9.94064i	0.516176	−	0.740931i
$181$	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
$184$	8.97580	−	11.7846i	0.661705	−	0.868771i
$185$	−5.08257	+	2.93442i	−0.373678	+	0.215743i
$186$	−20.2513	−	12.8676i	−1.48490	−	0.943496i
$187$	5.69170	−	3.28610i	0.416218	−	0.240304i
$188$	−2.33164	+	1.09404i	−0.170052	+	0.0797912i
$189$		−	23.9154i		−	1.73959i
$190$	−1.22472	+	6.04153i	−0.0888506	+	0.438298i
$191$			19.2804i			1.39508i	0.716545	+	0.697541i	$0.245722\pi$
$191$			19.2804i			1.39508i	−0.716545	+	0.697541i	$0.754278\pi$
$192$	6.39779	+	23.2110i	0.461721	+	1.67511i
$193$	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	$0.291739\pi$
$194$	8.28961	−	13.0464i	0.595159	−	0.936677i
$195$	−15.3456	+	8.85976i	−1.09892	+	0.634460i
$196$	0.280541	−	0.402696i	0.0200387	−	0.0287640i
$197$	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	0.234343	−	0.972154i	$-0.424706\pi$
$199$	−6.91788	−	3.99404i	−0.490395	−	0.283130i	−0.724739	+	0.689024i	$0.758039\pi$
$200$	2.25009	+	1.71380i	0.159105	+	0.121184i
$201$	3.98695			0.281218
$202$	−1.10060	+	25.9175i	−0.0774382	+	1.82355i
$203$	−12.1576	+	21.0576i	−0.853296	+	1.47795i
$204$	3.88454	+	8.27880i	0.271972	+	0.579632i
$205$	−0.487467	−	0.281439i	−0.0340462	−	0.0196566i
$206$	21.0679	−	10.9992i	1.46787	−	0.766352i
$207$	−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	0.954170	−	0.299266i	$-0.0967419\pi$
$211$	3.16536	+	5.48257i	0.217913	+	0.377436i	−0.736257	+	0.676702i	$0.763409\pi$
$212$	6.36668	−	2.98735i	0.437266	−	0.205172i
$213$	2.60158	−	4.50608i	0.178258	−	0.308751i
$214$	1.81368	−	0.946892i	0.123980	−	0.0647282i
$215$	4.31427	+	2.49085i	0.294231	+	0.169874i
$216$	3.30481	−	25.8162i	0.224864	−	1.75657i
$217$		−	14.6512i		−	0.994591i
$218$	−7.20508	+	11.3395i	−0.487990	+	0.768011i
$219$	2.38703	−	4.13445i	0.161300	−	0.279380i
$220$	0.733476	−	8.62052i	0.0494510	−	0.581196i
$221$		−	8.94516i		−	0.601717i
$222$	−13.3960	+	21.0830i	−0.899080	+	1.41500i
$223$	6.65628	+	11.5290i	0.445738	+	0.772040i	0.998103	−	0.0615618i	$-0.0196081\pi$
$223$	6.65628	+	11.5290i	0.445738	+	0.772040i	−0.552366	+	0.833602i	$0.686275\pi$
$224$	−9.86766	+	10.8985i	−0.659311	+	0.728185i
$225$	−3.02877	−	5.24598i	−0.201918	−	0.349732i
$226$	4.76611	+	9.12901i	0.317037	+	0.607252i
$227$	4.41385			0.292958			0.146479	−	0.989214i	$-0.453206\pi$
$227$	4.41385			0.292958			0.146479	+	0.989214i	$0.453206\pi$
$228$	7.27974	+	25.2067i	0.482113	+	1.66936i
$229$	−6.67515			−0.441106			−0.220553	−	0.975375i	$-0.570786\pi$
$229$	−6.67515			−0.441106			−0.220553	+	0.975375i	$0.570786\pi$
$230$	−3.42790	−	6.56580i	−0.226029	−	0.432936i
$231$	−16.9179	−	29.3026i	−1.11311	−	1.92797i
$232$	−16.0338	+	21.0512i	−1.05267	+	1.38208i
$233$	−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	$-0.441074\pi$
$234$	−27.0495	+	42.5713i	−1.76828	+	2.78297i
$235$			1.28778i			0.0840052i
$236$	16.2192	+	1.38000i	1.05578	+	0.0898306i
$237$	2.43779	−	4.22237i	0.158351	−	0.274273i
$238$	−2.99474	+	4.71319i	−0.194120	+	0.305511i
$239$		−	7.18860i		−	0.464992i	−0.972597	−	0.232496i	$-0.925311\pi$
$239$		−	7.18860i		−	0.464992i	0.972597	−	0.232496i	$-0.0746892\pi$
$240$	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	$0.813218\pi$
$242$	−9.66917	+	5.04812i	−0.621558	+	0.324505i
$243$	−0.524462	+	0.908396i	−0.0336443	+	0.0582736i
$244$	−2.81020	−	5.98915i	−0.179905	−	0.383416i
$245$	−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
$250$	1.25364	−	0.654507i	0.0792873	−	0.0413947i
$251$	−8.48999	−	4.90170i	−0.535883	−	0.309392i	0.207526	−	0.978230i	$-0.433459\pi$
$251$	−8.48999	−	4.90170i	−0.535883	−	0.309392i	−0.743409	+	0.668837i	$0.766792\pi$
$252$	28.5047	−	13.3749i	1.79563	−	0.842538i
$253$	−11.3280	+	19.6207i	−0.712187	+	1.23354i
$254$	−0.253471	+	5.96885i	−0.0159042	+	0.374519i
$255$	4.57242			0.286336
$256$	−12.1580	+	10.4011i	−0.759875	+	0.650069i
$257$	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
$260$	−9.66196	−	6.73108i	−0.599209	−	0.417444i
$261$	49.0800	−	28.3363i	3.03797	−	1.75398i
$262$	4.19580	−	6.60346i	0.259217	−	0.407963i
$263$	−6.86302	+	3.96236i	−0.423192	+	0.244330i	−0.696442	−	0.717613i	$-0.745235\pi$
$263$	−6.86302	+	3.96236i	−0.423192	+	0.244330i	0.273250	+	0.961943i	$0.411901\pi$
$264$	−14.2132	−	33.9694i	−0.874765	−	2.09067i
$265$		−	3.51635i		−	0.216008i
$266$	−10.6074	+	12.0066i	−0.650382	+	0.736170i
$267$		−	45.9331i		−	2.81106i
$268$	1.12546	+	2.39859i	0.0687483	+	0.146517i
$269$	−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	$0.433837\pi$
$270$	−10.9837	−	6.97901i	−0.668450	−	0.424729i
$271$	7.54501	−	4.35611i	0.458327	−	0.264615i	−0.253014	−	0.967463i	$-0.581422\pi$
$271$	7.54501	−	4.35611i	0.458327	−	0.264615i	0.711340	+	0.702848i	$0.248088\pi$
$272$	−3.88407	+	4.67397i	−0.235506	+	0.283401i
$273$	−46.0524			−2.78722
$274$	−0.227378	+	5.35439i	−0.0137364	+	0.323471i
$275$	−3.74628	−	2.16292i	−0.225909	−	0.130429i
$276$	−25.8665	−	18.0201i	−1.55698	−	1.08468i
$277$	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
$280$	2.83739	+	6.78131i	0.169566	+	0.405261i
$281$	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	$0.545309\pi$
$282$	2.53665	+	4.85869i	0.151055	+	0.289331i
$283$	10.3125	−	5.95395i	0.613017	−	0.353926i	−0.161128	−	0.986933i	$-0.551513\pi$
$283$	10.3125	−	5.95395i	0.613017	−	0.353926i	0.774145	+	0.633008i	$0.218180\pi$
$284$	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
$288$	32.6186	−	10.4989i	1.92207	−	0.618655i
$289$	7.34588	−	12.7234i	0.432110	−	0.748437i
$290$	6.12339	+	11.7287i	0.359578	+	0.688736i
$291$	−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	$0.661667\pi$
$294$	−0.881533	−	0.560121i	−0.0514120	−	0.0326669i
$295$	4.06944	−	7.04847i	0.236932	−	0.410378i
$296$	−16.4652	−	2.10777i	−0.957023	−	0.122511i
$297$			39.8058i			2.30977i
$298$	7.61678	+	4.83966i	0.441228	+	0.280354i
$299$	15.4181	+	26.7049i	0.891652	+	1.54439i
$300$	3.44067	−	4.93882i	0.198647	−	0.285143i
$301$	6.47361	+	11.2126i	0.373133	+	0.646285i
$302$	−10.6818	+	5.57683i	−0.614671	+	0.320910i
$303$	55.2044			3.17141
$304$	−13.1097	+	11.4951i	−0.751891	+	0.659287i
$305$	−3.30784			−0.189406
$306$	11.5375	−	6.02354i	0.659554	−	0.344343i
$307$	13.3391	+	23.1039i	0.761301	+	1.31861i	0.942180	+	0.335106i	$0.108772\pi$
$307$	13.3391	+	23.1039i	0.761301	+	1.31861i	−0.180880	+	0.983505i	$0.557895\pi$
$308$	12.8531	−	18.4497i	0.732373	−	1.05127i
$309$	−25.2885	−	43.8009i	−1.43861	−	2.49175i
$310$	−6.72896	−	4.27555i	−0.382179	−	0.242835i
$311$			24.3311i			1.37969i	0.723957	+	0.689845i	$0.242321\pi$
$311$			24.3311i			1.37969i	−0.723957	+	0.689845i	$0.757679\pi$
$312$	−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	$0.0399745\pi$
$314$	−3.66808	−	2.33068i	−0.207002	−	0.131528i
$315$		−	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	$0.621799\pi$
$318$	−6.92647	−	13.2669i	−0.388417	−	0.743974i
$319$	20.2357	−	35.0492i	1.13298	−	1.96238i
$320$	2.12581	+	7.71239i	0.118837	+	0.431136i
$321$	−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
$326$	−4.28329	−	8.20422i	−0.237230	−	0.454389i
$327$	24.7604	+	14.2954i	1.36925	+	0.790538i
$328$	−0.614516	−	1.46868i	−0.0339309	−	0.0810944i
$329$	−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	$-0.311062\pi$
$331$	20.3519			1.11864			0.559321	+	0.828951i	$0.311062\pi$
$332$	−26.3120	−	18.3305i	−1.44406	−	1.00602i
$333$	30.7879	+	17.7754i	1.68716	+	0.974085i
$334$	−0.336883	+	7.93305i	−0.0184334	+	0.434077i
$335$	1.32476			0.0723791
$336$	24.0630	+	19.9964i	1.31274	+	1.09089i
$337$	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	$0.0970653\pi$
$338$	25.8605	+	16.4316i	1.40662	+	0.893761i
$339$	18.9795	−	10.9578i	1.03083	−	0.595148i
$340$	1.29073	+	2.75082i	0.0699996	+	0.149184i
$341$			24.3862i			1.32059i
$342$	35.4031	−	11.8735i	1.91438	−	0.642047i
$343$		−	18.8305i		−	1.01675i
$344$	5.43870	+	12.9984i	0.293235	+	0.700827i
$345$	−13.6505	+	7.88114i	−0.734920	+	0.424306i
$346$	−6.53102	+	10.2787i	−0.351110	+	0.552586i
$347$	−25.1654	+	14.5292i	−1.35095	+	0.779970i	−0.988382	−	0.151988i	$-0.951432\pi$
$347$	−25.1654	+	14.5292i	−1.35095	+	0.779970i	−0.362565	+	0.931958i	$0.618099\pi$
$348$	46.2063	+	32.1900i	2.47692	+	1.72556i
$349$	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
$352$	16.4242	−	18.1399i	0.875413	−	0.966861i
$353$	−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
$356$	27.6339	−	12.9662i	1.46459	−	0.687209i
$357$	10.2915	+	5.94178i	0.544682	+	0.314472i
$358$	4.52046	−	2.36006i	0.238914	−	0.124733i
$359$	−22.5825	+	13.0380i	−1.19186	+	0.688119i	−0.958728	−	0.284326i	$-0.908230\pi$
$359$	−22.5825	+	13.0380i	−1.19186	+	0.688119i	−0.233130	+	0.972446i	$0.574897\pi$
$360$	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
$364$	−12.9999	−	27.7056i	−0.681381	−	1.45217i
$365$	0.793145	−	1.37377i	0.0415151	−	0.0719062i
$366$	−12.4802	+	6.51574i	−0.652353	+	0.340583i
$367$	−5.60010	−	3.23322i	−0.292323	−	0.168773i	0.346666	−	0.937989i	$-0.387314\pi$
$367$	−5.60010	−	3.23322i	−0.292323	−	0.168773i	−0.638989	+	0.769216i	$0.720647\pi$
$368$	3.53935	−	20.6484i	0.184502	−	1.07637i
$369$			3.40966i			0.177500i
$370$	−4.45113	+	7.00530i	−0.231403	+	0.364188i
$371$	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	$0.976044\pi$
$374$	4.98458	−	7.84486i	0.257746	−	0.405648i
$375$	−1.50479	−	2.60637i	−0.0777069	−	0.134592i
$376$	−2.20698	+	2.89761i	−0.113817	+	0.149433i
$377$	−27.5419	−	47.7040i	−1.41848	−	2.45688i
$378$	−15.6528	−	29.9813i	−0.805092	−	1.54207i
$379$	−11.6811			−0.600016			−0.300008	−	0.953937i	$-0.596989\pi$
$379$	−11.6811			−0.600016			−0.300008	+	0.953937i	$0.596989\pi$
$380$	2.41886	+	8.37551i	0.124085	+	0.429654i
$381$	12.7137			0.651342
$382$	12.6192	+	24.1707i	0.645653	+	1.23668i
$383$	−7.50854	−	13.0052i	−0.383668	−	0.664533i	0.607915	−	0.794002i	$-0.292006\pi$
$383$	−7.50854	−	13.0052i	−0.383668	−	0.664533i	−0.991583	+	0.129469i	$0.958673\pi$
$384$	23.2123	+	24.9109i	1.18455	+	1.27123i
$385$	−5.62134	−	9.73645i	−0.286490	−	0.496216i
$386$	2.74580	−	4.32141i	0.139758	−	0.219954i
$387$		−	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	$0.305348\pi$
$390$	−13.4391	+	21.1507i	−0.680513	+	1.07101i
$391$		−	7.95711i		−	0.402408i
$392$	0.0881311	−	0.688454i	0.00445129	−	0.0347722i
$393$	−14.4189	−	8.32478i	−0.727339	−	0.419929i
$394$	14.4871	−	7.56350i	0.729851	−	0.381044i
$395$	0.810011	−	1.40298i	0.0407561	−	0.0705916i
$396$	−47.4446	+	22.2618i	−2.38418	+	1.11870i
$397$	−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	$0.313291\pi$
$402$	4.99821	−	2.60949i	0.249288	−	0.130149i
$403$	28.7443	+	16.5955i	1.43186	+	0.826682i
$404$	15.5834	+	33.2116i	0.775303	+	1.65234i
$405$	−4.76057	+	8.24555i	−0.236555	+	0.409725i
$406$	−1.45895	+	34.3559i	−0.0724064	+	1.70506i
$407$	25.3877			1.25842
$408$	10.2884	+	7.83620i	0.509350	+	0.387950i
$409$	−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
$412$	19.2126	−	27.5782i	0.946535	−	1.35868i
$413$	18.3187	−	10.5763i	0.901405	−	0.520427i
$414$	−24.0618	+	37.8690i	−1.18257	+	1.86116i
$415$	−13.8857	+	8.01690i	−0.681621	+	0.393534i
$416$	−10.2046	−	31.7041i	−0.500321	−	1.55442i
$417$			66.6872i			3.26569i
$418$	17.6555	−	19.9843i	0.863558	−	0.977464i
$419$			13.0559i			0.637822i	0.947785	+	0.318911i	$0.103317\pi$
$419$			13.0559i			0.637822i	−0.947785	+	0.318911i	$0.896683\pi$
$420$	14.1621	−	6.64506i	0.691037	−	0.324246i
$421$	−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	$0.536314\pi$
$422$	7.55662	+	4.80143i	0.367850	+	0.233730i
$423$	6.75565	−	3.90038i	0.328471	−	0.189643i
$424$	6.02631	−	7.91211i	0.292663	−	0.384246i
$425$	1.51929			0.0736965
$426$	0.312198	−	7.35177i	0.0151260	−	0.356194i
$427$	−7.44518	−	4.29847i	−0.360297	−	0.208018i
$428$	1.65396	−	2.37413i	0.0799470	−	0.114758i
$429$	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	$-0.540098\pi$
$431$	16.5325	−	28.6352i	0.796344	−	1.37931i	0.921982	−	0.387232i	$-0.126569\pi$
$432$	−12.7538	−	34.5273i	−0.613619	−	1.66120i
$433$	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	$0.596627\pi$
$434$	−9.58934	−	18.3674i	−0.460303	−	0.881665i
$435$	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	$0.0319981\pi$
$439$	12.2443	+	21.2077i	0.584386	+	1.01219i	−0.410565	+	0.911831i	$0.634669\pi$
$440$	−4.72268	−	11.2871i	−0.225145	−	0.538092i
$441$	−0.743234	+	1.28732i	−0.0353921	+	0.0613009i
$442$	−5.85467	−	11.2140i	−0.278478	−	0.533397i
$443$	−25.3840	−	14.6554i	−1.20603	−	0.696301i	−0.244139	−	0.969740i	$-0.578505\pi$
$443$	−25.3840	−	14.6554i	−1.20603	−	0.696301i	−0.961889	+	0.273439i	$0.911839\pi$
$444$	−2.99484	+	35.1983i	−0.142129	+	1.67044i
$445$		−	15.2623i		−	0.723503i
$446$	15.8904	+	10.0967i	0.752433	+	0.478092i
$447$	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	$0.746779\pi$
$450$	−7.23053	−	4.59424i	−0.340850	−	0.216574i
$451$	1.21746	+	2.10870i	0.0573279	+	0.0992949i
$452$	11.9500	+	8.32506i	0.562081	+	0.391578i
$453$	12.8218	+	22.2079i	0.602419	+	1.04342i
$454$	5.53339	−	2.88890i	0.259695	−	0.135583i
$455$	−15.3020			−0.717367
$456$	25.6242	+	26.8356i	1.19996	+	1.25669i
$457$	−15.2706			−0.714330			−0.357165	−	0.934041i	$-0.616257\pi$
$457$	−15.2706			−0.714330			−0.357165	+	0.934041i	$0.616257\pi$
$458$	−8.36825	+	4.36893i	−0.391023	+	0.204147i
$459$	−6.99017	−	12.1073i	−0.326273	−	0.565122i
$460$	−8.59473	−	5.98759i	−0.400732	−	0.279173i
$461$	−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	$-0.482306\pi$
$462$	−40.3877	−	25.6621i	−1.87901	−	1.19391i
$463$			37.0046i			1.71975i	0.510505	+	0.859875i	$0.329459\pi$
$463$			37.0046i			1.71975i	−0.510505	+	0.859875i	$0.670541\pi$
$464$	−6.32248	+	36.8850i	−0.293514	+	1.71234i
$465$	−8.48300	+	14.6930i	−0.393390	+	0.681371i
$466$	−27.6653	−	17.5784i	−1.28157	−	0.814302i
$467$			8.22282i			0.380507i	0.981735	+	0.190253i	$0.0609310\pi$
$467$			8.22282i			0.380507i	−0.981735	+	0.190253i	$0.939069\pi$
$468$	−6.04726	+	71.0733i	−0.279535	+	3.28536i
$469$	2.98172	+	1.72150i	0.137683	+	0.0794913i
$470$	0.842859	+	1.61441i	0.0388782	+	0.0744672i
$471$	−4.62423	+	8.00941i	−0.213073	+	0.369054i
$472$	21.2362	−	8.88552i	0.977477	−	0.408989i
$473$	−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
$478$	−4.70499	−	9.01194i	−0.215201	−	0.412196i
$479$	20.1915	+	11.6576i	0.922573	+	0.532648i	0.884455	−	0.466625i	$-0.154530\pi$
$479$	20.1915	+	11.6576i	0.922573	+	0.532648i	0.0381180	+	0.999273i	$0.487864\pi$
$480$	16.2059	−	5.21619i	0.739697	−	0.238086i
$481$	17.2770	−	29.9247i	0.787766	−	1.36445i
$482$	−19.4917	−	0.827730i	−0.887823	−	0.0377021i
$483$	−40.9656			−1.86400
$484$	−8.81765	+	12.6571i	−0.400802	+	0.575322i
$485$	−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	$-0.669478\pi$
$487$	−22.4049			−1.01526			−0.507631	+	0.861575i	$0.669478\pi$
$488$	−7.44293	−	5.66896i	−0.336926	−	0.256622i
$489$	−17.0569	+	9.84778i	−0.771338	+	0.445332i
$490$	−0.292909	−	0.186113i	−0.0132323	−	0.00840773i
$491$	−28.8312	+	16.6457i	−1.30114	+	0.751211i	−0.980599	−	0.196025i	$-0.937197\pi$
$491$	−28.8312	+	16.6457i	−1.30114	+	0.751211i	−0.320537	+	0.947236i	$0.603863\pi$
$492$	−3.06719	+	1.43917i	−0.138280	+	0.0648830i
$493$			14.2141i			0.640170i
$494$	−11.5407	−	34.4106i	−0.519239	−	1.54821i
$495$			26.2039i			1.17778i
$496$	−7.81337	−	21.1524i	−0.350830	−	0.949772i
$497$	3.89129	−	2.24664i	0.174548	−	0.100775i
$498$	−36.5981	+	57.5990i	−1.64000	+	2.58107i
$499$	31.6188	−	18.2551i	1.41545	−	0.817211i	0.419556	−	0.907729i	$-0.362186\pi$
$499$	31.6188	−	18.2551i	1.41545	−	0.817211i	0.995895	+	0.0905184i	$0.0288524\pi$
$500$	1.14324	−	1.64104i	0.0511273	−	0.0733894i
$501$	16.8975			0.754923
$502$	−13.8516	−	0.588218i	−0.618227	−	0.0262535i
$503$	−27.5058	−	15.8805i	−1.22642	−	0.708076i	−0.260144	−	0.965570i	$-0.583770\pi$
$503$	−27.5058	−	15.8805i	−1.22642	−	0.708076i	−0.966280	+	0.257493i	$0.917103\pi$
$504$	26.9808	−	35.4239i	1.20182	−	1.57790i
$505$	18.3429			0.816249
$506$	−1.35940	+	32.0116i	−0.0604326	+	1.42309i
$507$	32.6015	−	56.4675i	1.44788	−	2.50781i
$508$	3.58889	+	7.64870i	0.159231	+	0.339356i
$509$	−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	$0.892157\pi$
$510$	5.73218	−	2.99268i	0.253825	−	0.132518i
$511$	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
$516$	27.1458	−	12.7372i	1.19503	−	0.560726i
$517$	2.78535	−	4.82437i	0.122500	−	0.212176i
$518$	−19.1217	+	9.98314i	−0.840160	+	0.438634i
$519$	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	$0.901274\pi$
$522$	42.9824	−	67.6469i	1.88129	−	2.96082i
$523$	11.2431	−	19.4736i	0.491626	−	0.851521i	−0.508328	−	0.861164i	$-0.669736\pi$
$523$	11.2431	−	19.4736i	0.491626	−	0.851521i	0.999954	+	0.00964294i	$0.00306949\pi$
$524$	0.938023	−	11.0246i	0.0409777	−	0.481610i
$525$		−	7.82177i		−	0.341370i
$526$	−6.01037	+	9.45928i	−0.262065	+	0.412444i
$527$	−4.28238	−	7.41731i	−0.186544	−	0.323103i
$528$	−40.0516	−	33.2829i	−1.74302	−	1.44845i
$529$	2.21508	+	3.83663i	0.0963078	+	0.166810i
$530$	−2.30148	−	4.40825i	−0.0999698	−	0.191482i
$531$	−49.3015			−2.13950
$532$	−5.43952	+	21.9946i	−0.235833	+	0.953586i
$533$	3.31407			0.143548
$534$	−30.0635	−	57.5837i	−1.30098	−	2.49189i
$535$	−0.723363	−	1.25290i	−0.0312737	−	0.0541676i
$536$	2.98082	+	2.27036i	0.128752	+	0.0980646i
$537$	−5.42605	−	9.39819i	−0.234151	−	0.405562i
$538$	−7.72529	+	12.1583i	−0.333061	+	0.524180i
$539$			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	$0.921983\pi$
$542$	6.60764	−	10.3993i	0.283822	−	0.446687i
$543$		−	37.7823i		−	1.62140i
$544$	−1.81009	+	8.40164i	−0.0776069	+	0.360217i
$545$	8.22720	+	4.74998i	0.352415	+	0.203467i
$546$	−57.7332	+	30.1416i	−2.47075	+	1.28994i
$547$	−18.7956	+	32.5550i	−0.803643	+	1.39195i	0.113560	+	0.993531i	$0.463775\pi$
$547$	−18.7956	+	32.5550i	−0.803643	+	1.39195i	−0.917203	+	0.398420i	$0.869559\pi$
$548$	3.21944	+	6.86132i	0.137528	+	0.293101i
$549$	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
$554$	14.7079	−	7.67874i	0.624877	−	0.326239i
$555$	15.2964	+	8.83136i	0.649295	+	0.374871i
$556$	−40.1198	+	18.8248i	−1.70146	+	0.798351i
$557$	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
$560$	7.99548	+	6.64425i	0.337871	+	0.280771i
$561$	−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	$-0.449314\pi$
$563$	7.52468			0.317128			0.158564	+	0.987349i	$0.449314\pi$
$564$	6.36010	+	4.43081i	0.267808	+	0.186571i
$565$	6.30638	−	3.64099i	0.265311	−	0.153178i
$566$	9.03134	−	14.2138i	0.379616	−	0.597449i
$567$	−21.4299	+	12.3725i	−0.899970	+	0.519598i
$568$	4.51103	−	1.88747i	0.189279	−	0.0791967i
$569$		−	28.7673i		−	1.20599i	−0.797746	−	0.602993i	$-0.793975\pi$
$569$		−	28.7673i		−	1.20599i	0.797746	−	0.602993i	$-0.206025\pi$
$570$	17.5894	−	5.89914i	0.736738	−	0.247088i
$571$			30.8865i			1.29256i	0.763101	+	0.646280i	$0.223676\pi$
$571$			30.8865i			1.29256i	−0.763101	+	0.646280i	$0.776324\pi$
$572$	21.6377	+	46.1145i	0.904716	+	1.92815i
$573$	50.2518	−	29.0129i	2.09930	−	1.21203i
$574$	−1.74618	−	1.10951i	−0.0728841	−	0.0463101i
$575$	−4.53570	+	2.61869i	−0.189152	+	0.109207i
$576$	34.0204	−	34.5110i	1.41752	−	1.43796i
$577$	−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
$580$	15.3531	+	10.6959i	0.637503	+	0.444121i
$581$	−41.6712			−1.72881
$582$	−46.4778	−	1.97371i	−1.92657	−	0.0818131i
$583$	−7.60558	+	13.1732i	−0.314991	+	0.545580i
$584$	4.13900	−	1.73181i	0.171273	−	0.0716629i
$585$	30.8868	+	17.8325i	1.27701	+	0.737284i
$586$	19.5784	+	37.5004i	0.808775	+	1.54913i
$587$	39.1369	−	22.5957i	1.61535	−	0.932624i	0.627251	−	0.778817i	$-0.284180\pi$
$587$	39.1369	−	22.5957i	1.61535	−	0.932624i	0.988101	−	0.153807i	$-0.0491533\pi$
$588$	−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
$592$	−22.0211	+	8.13423i	−0.905061	+	0.334315i
$593$	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	$0.0182497\pi$
$594$	26.0532	+	49.9023i	1.06898	+	2.04752i
$595$	3.41957	+	1.97429i	0.140189	+	0.0809381i
$596$	12.7163	+	1.08197i	0.520880	+	0.0443190i
$597$			24.0407i			0.983921i
$598$	36.8074	+	23.3872i	1.50517	+	0.956374i
$599$	−6.05996	+	10.4962i	−0.247603	+	0.428861i	−0.962860	−	0.270000i	$-0.912976\pi$
$599$	−6.05996	+	10.4962i	−0.247603	+	0.428861i	0.715257	+	0.698861i	$0.246310\pi$
$600$	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	$-0.189587\pi$
$602$	15.4543	+	9.81961i	0.629872	+	0.400217i
$603$	−4.01238	−	6.94964i	−0.163397	−	0.283011i
$604$	−9.74115	+	13.9827i	−0.396362	+	0.568948i
$605$	3.85643	+	6.67953i	0.156786	+	0.271561i
$606$	69.2066	−	36.1317i	2.81133	−	1.46775i
$607$	−42.1615			−1.71128			−0.855642	−	0.517568i	$-0.826837\pi$
$607$	−42.1615			−1.71128			−0.855642	+	0.517568i	$0.826837\pi$
$608$	−8.91125	+	22.9911i	−0.361399	+	0.932411i
$609$	73.1784			2.96534
$610$	−4.14685	+	2.16500i	−0.167901	+	0.0876584i
$611$	−3.79103	−	6.56626i	−0.153369	−	0.265642i
$612$	10.5214	−	15.1027i	0.425304	−	0.610492i
$613$	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	$0.825168\pi$
$614$	31.8441	+	20.2336i	1.28512	+	0.816560i
$615$			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	$0.162991\pi$
$618$	−60.3707	−	38.3592i	−2.42847	−	1.54303i
$619$			4.33041i			0.174054i	0.996206	+	0.0870269i	$0.0277366\pi$
$619$			4.33041i			0.174054i	−0.996206	+	0.0870269i	$0.972263\pi$
$620$	−11.2341	−	0.955851i	−0.451172	−	0.0383879i
$621$	41.7370	+	24.0969i	1.67485	+	0.966975i
$622$	15.9249	+	30.5025i	0.638530	+	1.22304i
$623$	19.8331	−	34.3519i	0.794596	−	1.37628i
$624$	−66.4872	+	24.5593i	−2.66162	+	0.983158i
$625$	−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
$630$	−10.3041	−	19.7365i	−0.410526	−	0.786321i
$631$	−3.67762	−	2.12328i	−0.146404	−	0.0845264i	0.425009	−	0.905189i	$-0.360271\pi$
$631$	−3.67762	−	2.12328i	−0.146404	−	0.0845264i	−0.571413	+	0.820663i	$0.693604\pi$
$632$	4.22702	−	1.76864i	0.168142	−	0.0703527i
$633$	9.52640	−	16.5002i	0.378640	−	0.655824i
$634$	7.06854	+	0.300171i	0.280728	+	0.0119213i
$635$	4.22442			0.167641
$636$	−17.3666	−	12.0986i	−0.688632	−	0.479740i
$637$	1.25123	+	0.722398i	0.0495755	+	0.0286224i
$638$	2.42834	−	57.1836i	0.0961390	−	2.26392i
$639$	−10.4727			−0.414294
$640$	7.71282	+	8.27722i	0.304876	+	0.327186i
$641$	−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	$0.549383\pi$
$642$	−5.19715	−	3.30224i	−0.205115	−	0.130329i
$643$	9.97978	−	5.76183i	0.393564	−	0.227224i	−0.290139	−	0.956984i	$-0.593702\pi$
$643$	9.97978	−	5.76183i	0.393564	−	0.227224i	0.683703	+	0.729760i	$0.260368\pi$
$644$	−11.5640	−	24.6454i	−0.455685	−	0.971163i
$645$		−	14.9928i		−	0.590340i
$646$	−1.86071	+	9.17885i	−0.0732086	+	0.361137i
$647$		−	22.7092i		−	0.892791i	−0.894836	−	0.446396i	$-0.852707\pi$
$647$		−	22.7092i		−	0.892791i	0.894836	−	0.446396i	$-0.147293\pi$
$648$	−24.8429	+	10.3946i	−0.975921	+	0.408338i
$649$	−30.4905	+	17.6037i	−1.19686	+	0.691007i
$650$	−4.46544	+	7.02782i	−0.175149	+	0.275654i
$651$	−38.1865	+	22.0470i	−1.49665	+	0.864090i
$652$	−10.7394	−	7.48171i	−0.420589	−	0.293006i
$653$	−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
$656$	−1.73165	−	1.43900i	−0.0676094	−	0.0561834i
$657$	−9.60901			−0.374883
$658$	−0.200818	+	4.72894i	−0.00782870	+	0.184353i
$659$	8.39596	−	14.5422i	0.327060	−	0.566485i	−0.654867	−	0.755744i	$-0.727275\pi$
$659$	8.39596	−	14.5422i	0.327060	−	0.566485i	0.981927	+	0.189260i	$0.0606087\pi$
$660$	−23.5720	+	11.0603i	−0.917538	+	0.430523i
$661$	−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	$0.734581\pi$
$662$	25.5140	−	13.3205i	0.991631	−	0.517715i
$663$	−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
$668$	4.76991	+	10.1657i	0.184553	+	0.393323i
$669$	20.0326	−	34.6974i	0.774504	−	1.34148i
$670$	1.66077	−	0.867062i	0.0641612	−	0.0334975i
$671$	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	$-0.130790\pi$
$674$	18.8226	−	29.6235i	0.725019	−	1.14105i
$675$	−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	$-0.128267\pi$
$678$	16.6216	−	26.1594i	0.638347	−	1.00465i
$679$	−14.2032	−	24.6007i	−0.545070	−	0.944089i
$680$	3.41854	+	2.60376i	0.131095	+	0.0998495i
$681$	−6.64190	−	11.5041i	−0.254518	−	0.440839i
$682$	15.9610	+	30.5716i	0.611176	+	1.17065i
$683$	−8.86934			−0.339376			−0.169688	−	0.985498i	$-0.554276\pi$
$683$	−8.86934			−0.339376			−0.169688	+	0.985498i	$0.554276\pi$
$684$	36.6116	−	38.0568i	1.39988	−	1.45514i
$685$	3.78954			0.144791
$686$	−12.3247	−	23.6067i	−0.470559	−	0.901309i
$687$	10.0447	+	17.3979i	0.383228	+	0.663771i
$688$	15.3257	+	12.7357i	0.584288	+	0.485544i
$689$	10.3516	+	17.9296i	0.394366	+	0.683062i
$690$	−11.9546	+	18.8145i	−0.455105	+	0.716256i
$691$			1.45105i			0.0552004i	0.999619	+	0.0276002i	$0.00878653\pi$
$691$			1.45105i			0.0552004i	−0.999619	+	0.0276002i	$0.991213\pi$
$692$	−1.46009	+	17.1604i	−0.0555043	+	0.652341i
$693$	−34.0515	+	58.9789i	−1.29351	+	2.24042i
$694$	−22.0389	+	34.6854i	−0.836585	+	1.31664i
$695$			22.1584i			0.840514i
$696$	78.9947	+	10.1124i	2.99429	+	0.383308i
$697$	−0.740605	−	0.427588i	−0.0280524	−	0.0161961i
$698$	10.5538	−	5.50997i	0.399467	−	0.208555i
$699$	−34.8768	+	60.4083i	−1.31916	+	2.28485i
$700$	4.70567	−	2.20797i	0.177857	−	0.0834535i
$701$	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
$706$	−7.49788	+	3.91453i	−0.282186	+	0.147325i
$707$	41.2857	+	23.8363i	1.55271	+	0.896456i
$708$	−20.8096	−	44.3497i	−0.782072	−	1.66676i
$709$	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
$712$	26.1565	−	34.3416i	0.980256	−	1.28701i
$713$	25.5693	+	14.7625i	0.957578	+	0.552858i
$714$	16.7908	+	0.713032i	0.628378	+	0.0266845i
$715$	25.4693			0.952497
$716$	4.12236	−	5.91735i	0.154060	−	0.221142i
$717$	−18.7361	+	10.8173i	−0.699714	+	0.403980i
$718$	−19.7769	+	31.1254i	−0.738067	+	1.16159i
$719$	28.5881	−	16.5054i	1.06616	−	0.615547i	0.139029	−	0.990288i	$-0.455602\pi$
$719$	28.5881	−	16.5054i	1.06616	−	0.615547i	0.927129	+	0.374742i	$0.122269\pi$
$720$	−8.39576	−	22.7291i	−0.312891	−	0.847063i
$721$		−	43.6765i		−	1.62660i
$722$	−9.40458	+	25.1705i	−0.350002	+	0.936749i
$723$			41.5175i			1.54405i
$724$	22.7303	−	10.6654i	0.844764	−	0.396377i
$725$	8.10230	−	4.67787i	0.300912	−	0.173732i
$726$	27.7073	+	17.6051i	1.02831	+	0.653385i
$727$	−23.3306	+	13.4699i	−0.865283	+	0.499571i	−0.865778	−	0.500428i	$-0.833176\pi$
$727$	−23.3306	+	13.4699i	−0.865283	+	0.499571i	0.000494722		1.00000i	$0.499843\pi$
$728$	−34.4308	−	26.2244i	−1.27609	−	0.971941i
$729$	−25.4066			−0.940985
$730$	0.0951798	−	2.24133i	0.00352276	−	0.0829554i
$731$	6.55464	+	3.78432i	0.242432	+	0.139968i
$732$	−11.3812	+	16.3368i	−0.420660	+	0.603826i
$733$	−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
$736$	−9.07743	−	28.2022i	−0.334598	−	1.03955i
$737$	−4.96291	−	2.86534i	−0.182811	−	0.105546i
$738$	2.23164	+	4.27449i	0.0821480	+	0.157346i
$739$	−20.7716	+	11.9925i	−0.764095	+	0.441150i	−0.830764	−	0.556625i	$-0.812096\pi$
$739$	−20.7716	+	11.9925i	−0.764095	+	0.441150i	0.0666691	+	0.997775i	$0.478763\pi$
$740$	−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	0.968676	−	0.248329i	$-0.0798813\pi$
$743$	7.34001	+	12.7133i	0.269279	+	0.466405i	−0.699397	+	0.714734i	$0.746548\pi$
$744$	−44.2683	+	18.5224i	−1.62295	+	0.679065i
$745$	3.19056	−	5.52622i	0.116893	−	0.202465i
$746$	1.90085	+	3.64088i	0.0695949	+	0.133302i
$747$	84.1130	+	48.5626i	3.07753	+	1.77681i
$748$	1.11436	−	13.0971i	0.0407452	−	0.478877i
$749$		−	3.75999i		−	0.137387i
$750$	−3.59235	−	2.28256i	−0.131174	−	0.0833473i
$751$	17.6143	−	30.5088i	0.642755	−	1.11328i	−0.342061	−	0.939678i	$-0.611125\pi$
$751$	17.6143	−	30.5088i	0.642755	−	1.11328i	0.984815	−	0.173606i	$-0.0555418\pi$
$752$	−0.870262	+	5.07706i	−0.0317352	+	0.185141i
$753$			29.5040i			1.07519i
$754$	−65.7504	−	41.7774i	−2.39449	−	1.52144i
$755$	4.26032	+	7.37910i	0.155049	+	0.268553i
$756$	−39.2460	−	27.3410i	−1.42736	−	0.994383i
$757$	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	$0.673730\pi$
$758$	−14.6439	+	7.64535i	−0.531890	+	0.277691i
$759$	68.1851			2.47496
$760$	8.51422	+	8.91673i	0.308843	+	0.323444i
$761$	−4.66536			−0.169119			−0.0845596	−	0.996418i	$-0.526948\pi$
$761$	−4.66536			−0.169119			−0.0845596	+	0.996418i	$0.526948\pi$
$762$	15.9384	−	8.32121i	0.577388	−	0.301445i
$763$	12.3450	+	21.3822i	0.446920	+	0.774087i
$764$	31.6399	+	22.0421i	1.14469	+	0.797457i
$765$	−4.60158	−	7.97018i	−0.166371	−	0.288162i
$766$	−17.9250	−	11.3894i	−0.647656	−	0.411517i
$767$			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	$0.846336\pi$
$770$	−13.4197	−	8.52682i	−0.483614	−	0.307285i
$771$		−	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	$0.624560\pi$
$774$	−19.7509	−	37.8309i	−0.709932	−	1.35980i
$775$	−2.81867	+	4.88208i	−0.101250	+	0.175370i
$776$	−11.9326	−	28.5187i	−0.428356	−	1.02376i
$777$	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
$782$	−5.20799	−	9.97538i	−0.186237	−	0.356719i
$783$	−74.5564	−	43.0452i	−2.66443	−	1.53831i
$784$	−0.340113	−	0.920758i	−0.0121469	−	0.0328842i
$785$	−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	$-0.751138\pi$
$787$	−39.8153			−1.41926			−0.709630	+	0.704574i	$0.751138\pi$
$788$	13.2113	−	18.9639i	0.470634	−	0.675559i
$789$	20.6548	+	11.9250i	0.735329	+	0.424542i
$790$	0.0972038	−	2.28899i	0.00345836	−	0.0814388i
$791$	18.9256			0.672917
$792$	−44.9081	+	58.9612i	−1.59574	+	2.09509i
$793$	16.8664	−	9.73780i	0.598942	−	0.345800i
$794$	−23.6608	−	15.0339i	−0.839690	−	0.533534i
$795$	−9.16490	+	5.29136i	−0.325046	+	0.187665i
$796$	−14.4632	+	6.78635i	−0.512633	+	0.240536i
$797$		−	4.64787i		−	0.164636i	−0.996606	−	0.0823180i	$-0.973768\pi$
$797$		−	4.64787i		−	0.164636i	0.996606	−	0.0823180i	$-0.0262323\pi$
$798$	47.2555	+	9.57949i	1.67282	+	0.339110i
$799$			1.95651i			0.0692163i
$800$	5.38480	−	1.73320i	0.190381	−	0.0612779i
$801$	−80.0658	+	46.2260i	−2.82899	+	1.63332i
$802$	1.91132	−	3.00809i	0.0674912	−	0.106219i
$803$	−5.94269	+	3.43101i	−0.209713	+	0.121078i
$804$	4.55804	−	6.54273i	0.160750	−	0.230744i
$805$	−13.6118			−0.479751
$806$	46.8970	+	1.99151i	1.65188	+	0.0701481i
$807$	26.5481	+	15.3275i	0.934537	+	0.539555i
$808$	41.2732	+	31.4360i	1.45199	+	1.10592i
$809$	−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	−0.577364	−	0.816487i	$-0.695919\pi$
$811$	11.9157	−	20.6386i	0.418416	−	0.724718i	0.995780	+	0.0917688i	$0.0292521\pi$
$812$	20.6572	+	44.0249i	0.724926	+	1.54497i
$813$	−22.7073	−	13.1100i	−0.796378	−	0.459789i
$814$	31.8271	−	16.6164i	1.11554	−	0.582405i
$815$	−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
$820$	−1.01914	+	0.478198i	−0.0355901	+	0.0166994i
$821$	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	$-0.0163123\pi$
$822$	14.2977	−	7.46459i	0.498688	−	0.260357i
$823$	−28.1635	−	16.2602i	−0.981718	−	0.566795i	−0.0789295	−	0.996880i	$-0.525150\pi$
$823$	−28.1635	−	16.2602i	−0.981718	−	0.566795i	−0.902788	+	0.430085i	$0.858484\pi$
$824$	6.03556	−	47.1480i	0.210259	−	1.64248i
$825$			13.0189i			0.453261i
$826$	16.0429	−	25.2487i	0.558202	−	0.878513i
$827$	8.69607	−	15.0620i	0.302392	−	0.523758i	−0.674285	−	0.738471i	$-0.735548\pi$
$827$	8.69607	−	15.0620i	0.302392	−	0.523758i	0.976677	+	0.214713i	$0.0688815\pi$
$828$	−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	$0.829988\pi$
$830$	−12.1606	+	19.1386i	−0.422099	+	0.664310i
$831$	−17.6543	−	30.5782i	−0.612421	−	1.06074i
$832$	−33.5435	−	33.0667i	−1.16291	−	1.14638i
$833$	−0.186411	−	0.322873i	−0.00645875	−	0.0111869i
$834$	43.6473	+	83.6019i	1.51138	+	2.89490i
$835$	5.61457			0.194300
$836$	9.05379	−	36.6088i	0.313132	−	1.26614i
$837$	51.8742			1.79303
$838$	8.54517	+	16.3674i	0.295188	+	0.565403i
$839$	6.27987	+	10.8771i	0.216805	+	0.375518i	0.953830	−	0.300349i	$-0.0971030\pi$
$839$	6.27987	+	10.8771i	0.216805	+	0.375518i	−0.737024	+	0.675866i	$0.763770\pi$
$840$	13.4049	−	17.5997i	0.462514	−	0.607247i
$841$	29.2649	+	50.6882i	1.00913	+	1.74787i
$842$	−18.5289	+	29.1612i	−0.638547	+	1.00496i
$843$		−	37.5435i		−	1.29307i
$844$	12.6159	+	1.07342i	0.434256	+	0.0369486i
$845$	10.8326	−	18.7626i	0.372653	−	0.645453i
$846$	5.91635	−	9.31130i	0.203408	−	0.320129i
$847$			20.0454i			0.688769i
$848$	2.37630	−	13.8632i	0.0816026	−	0.476065i
$849$	−31.0364	−	17.9189i	−1.06517	−	0.614973i
$850$	1.90465	−	0.994388i	0.0653290	−	0.0341072i
$851$	15.3687	−	26.6194i	0.526832	−	0.912500i
$852$	−4.42040	−	9.42082i	−0.151440	−	0.322752i
$853$	−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	$0.310226\pi$
$858$	96.0939	−	50.1691i	3.28059	−	1.71274i
$859$	−20.1608	−	11.6399i	−0.687878	−	0.397147i	0.114938	−	0.993373i	$-0.463333\pi$
$859$	−20.1608	−	11.6399i	−0.687878	−	0.397147i	−0.802817	+	0.596226i	$0.796666\pi$
$860$	9.01982	−	4.23224i	0.307573	−	0.144318i
$861$	−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	$-0.563030\pi$
$863$	−11.5581			−0.393443			−0.196722	+	0.980459i	$0.563030\pi$
$864$	−38.5871	−	34.9374i	−1.31276	−	1.18860i
$865$	7.45752	+	4.30560i	0.253563	+	0.146395i
$866$	12.8346	+	0.545031i	0.436138	+	0.0185209i
$867$	−44.2159			−1.50165
$868$	−24.0432	−	16.7499i	−0.816080	−	0.568528i
$869$	−6.06906	+	3.50397i	−0.205879	+	0.118864i
$870$	21.3550	−	33.6091i	0.724003	−	1.13945i
$871$	−6.75481	+	3.89989i	−0.228878	+	0.132143i
$872$	10.3715	+	24.7876i	0.351222	+	0.839415i
$873$			66.2084i			2.24081i
$874$	−10.2659	−	30.6098i	−0.347250	−	1.03539i
$875$		−	2.59896i		−	0.0878610i
$876$	−4.05584	−	8.64387i	−0.137034	−	0.292049i
$877$	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	$0.280474\pi$
$878$	29.2305	+	18.5729i	0.986482	+	0.626805i
$879$	77.9646	−	45.0129i	2.62968	−	1.51825i
$880$	−13.3081	−	11.0590i	−0.448614	−	0.372799i
$881$	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	0.0763348	−	0.997082i	$-0.475678\pi$
$883$	−22.2567	−	12.8499i	−0.748996	−	0.432433i	−0.825331	+	0.564649i	$0.809012\pi$
$884$	−14.6793	−	10.2265i	−0.493719	−	0.343953i
$885$	−24.4946			−0.823375
$886$	−41.4145	−	1.75870i	−1.39135	−	0.0590846i
$887$	5.36284	−	9.28872i	0.180067	−	0.311885i	−0.761836	−	0.647769i	$-0.775702\pi$
$887$	5.36284	−	9.28872i	0.180067	−	0.311885i	0.941903	+	0.335885i	$0.109035\pi$
$888$	19.2831	+	46.0862i	0.647097	+	1.54655i
$889$	9.50818	+	5.48955i	0.318894	+	0.184114i
$890$	−9.98930	−	19.1335i	−0.334842	−	0.641356i
$891$	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
$896$	6.60368	+	28.6528i	0.220613	+	0.957222i
$897$	46.4019	−	80.3705i	1.54932	−	2.68349i
$898$	19.8109	+	37.9457i	0.661098	+	1.26627i
$899$	−45.6754	−	26.3707i	−1.52336	−	0.879513i
$900$	−12.0715	−	1.02710i	−0.402382	−	0.0342366i
$901$		−	5.34236i		−	0.177980i
$902$	2.90642	+	1.84672i	0.0967732	+	0.0614892i
$903$	19.4828	−	33.7452i	0.648348	−	1.12297i
$904$	20.4298	+	2.61529i	0.679486	+	0.0869832i
$905$		−	12.5540i		−	0.417311i
$906$	30.6092	+	19.4489i	1.01692	+	0.646146i
$907$	20.1372	+	34.8786i	0.668643	+	1.15812i	0.978284	+	0.207270i	$0.0664579\pi$
$907$	20.1372	+	34.8786i	0.668643	+	1.15812i	−0.309641	+	0.950854i	$0.600209\pi$
$908$	5.04609	−	7.24329i	0.167460	−	0.240377i
$909$	−55.5565	−	96.2266i	−1.84269	−	3.19164i
$910$	−19.1832	+	10.0152i	−0.635916	+	0.332002i
$911$	17.4793			0.579116			0.289558	−	0.957161i	$-0.406492\pi$
$911$	17.4793			0.579116			0.289558	+	0.957161i	$0.406492\pi$
$912$	49.6876	+	16.8710i	1.64532	+	0.558655i
$913$	69.3596			2.29547
$914$	−19.1439	+	9.99474i	−0.633225	+	0.330597i
$915$	4.97759	+	8.62144i	0.164554	+	0.285016i
$916$	−7.63130	+	10.9542i	−0.252145	+	0.361936i
$917$	−7.18899	−	12.4517i	−0.237401	−	0.411191i
$918$	−16.6875	−	10.6032i	−0.550770	−	0.349956i
$919$			40.0640i			1.32159i	0.750567	+	0.660794i	$0.229780\pi$
$919$			40.0640i			1.32159i	−0.750567	+	0.660794i	$0.770220\pi$
$920$	−14.6936	−	1.88098i	−0.484435	−	0.0620141i
$921$	40.1449	−	69.5330i	1.32282	−	2.29119i
$922$	−42.8975	−	27.2568i	−1.41275	−	0.897655i
$923$			10.1791i			0.335049i
$924$	−67.4278	−	5.73708i	−2.21821	−	0.188736i
$925$	5.08257	+	2.93442i	0.167114	+	0.0964832i
$926$	24.2198	+	46.3906i	0.795911	+	1.52449i
$927$	−50.8995	+	88.1605i	−1.67176	+	2.89557i
$928$	16.2154	+	50.3787i	0.532295	+	1.65376i
$929$	−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
$934$	5.38190	+	10.3085i	0.176101	+	0.337304i
$935$	−5.69170	−	3.28610i	−0.186138	−	0.107467i
$936$	38.9369	+	93.0585i	1.27269	+	3.04171i
$937$	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
$940$	2.11329	+	1.47224i	0.0689278	+	0.0480191i
$941$	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
$944$	20.8070	−	25.0385i	0.677211	−	0.814935i
$945$	−20.7113	+	11.9577i	−0.673739	+	0.388983i
$946$	−25.7229	−	16.3442i	−0.836325	−	0.531396i
$947$	20.0897	−	11.5988i	0.652827	−	0.376910i	−0.136711	−	0.990611i	$-0.543653\pi$
$947$	20.0897	−	11.5988i	0.652827	−	0.376910i	0.789539	+	0.613701i	$0.210320\pi$
$948$	−4.14209	−	8.82769i	−0.134529	−	0.286710i
$949$			9.33962i			0.303177i
$950$	5.84448	−	1.96012i	0.189620	−	0.0635948i
$951$		−	15.0561i		−	0.488226i
$952$	4.31082	+	10.3028i	0.139714	+	0.333915i
$953$	−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	$0.337583\pi$
$954$	−16.1549	+	25.4251i	−0.523036	+	0.823167i
$955$	16.6973	−	9.64021i	0.540313	−	0.311950i
$956$	−11.7968	−	8.21830i	−0.381534	−	0.265799i
$957$	−121.802			−3.93728
$958$	32.9429	+	1.39894i	1.06434	+	0.0451978i
$959$	8.52937	+	4.92444i	0.275428	+	0.159018i
$960$	16.9024	−	17.1461i	0.545523	−	0.553390i
$961$	0.779617			0.0251489
$962$	2.07330	−	48.8229i	0.0668458	−	1.57411i
$963$	−4.38180	+	7.58949i	−0.141201	+	0.244568i
$964$	−24.9774	+	11.7198i	−0.804468	+	0.377469i
$965$	−3.13532	−	1.81018i	−0.100930	−	0.0582718i
$966$	−51.3562	+	26.8123i	−1.65236	+	0.862671i
$967$	−34.9088	+	20.1546i	−1.12259	+	0.648128i	−0.942061	−	0.335441i	$-0.891115\pi$
$967$	−34.9088	+	20.1546i	−1.12259	+	0.648128i	−0.180530	+	0.983569i	$0.557781\pi$
$968$	−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	$-0.844070\pi$
$971$	−26.4453	−	45.8046i	−0.848671	−	1.46994i	0.0337239	−	0.999431i	$-0.489263\pi$
$972$	0.891124	+	1.89918i	0.0285828	+	0.0609161i
$973$	−28.7944	+	49.8733i	−0.923105	+	1.59887i
$974$	−28.0877	+	14.6641i	−0.899988	+	0.469869i
$975$	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	$-0.144158\pi$
$978$	−14.9378	+	23.5094i	−0.477657	+	0.751749i
$979$	−33.0111	+	57.1770i	−1.05504	+	1.82738i
$980$	−0.489016	−	0.0416079i	−0.0156210	−	0.00132911i
$981$		−	57.5463i		−	1.83731i
$982$	−25.2493	+	39.7380i	−0.805739	+	1.26809i
$983$	−30.7574	−	53.2733i	−0.981008	−	1.69916i	−0.658485	−	0.752594i	$-0.728802\pi$
$983$	−30.7574	−	53.2733i	−0.981008	−	1.69916i	−0.322523	−	0.946562i	$-0.604531\pi$
$984$	−2.90321	+	3.81171i	−0.0925510	+	0.121513i
$985$	−5.77801	−	10.0078i	−0.184103	−	0.318875i
$986$	9.30322	+	17.8194i	0.296275	+	0.567485i
$987$	10.0727			0.320617
$988$	−36.9899	−	35.5852i	−1.17680	−	1.13212i
$989$	−26.0910			−0.829646
$990$	17.1506	+	32.8503i	0.545083	+	1.04405i
$991$	14.0345	+	24.3085i	0.445821	+	0.772184i	0.998109	−	0.0614691i	$-0.0195786\pi$
$991$	14.0345	+	24.3085i	0.445821	+	0.772184i	−0.552288	+	0.833653i	$0.686245\pi$
$992$	−23.6396	−	21.4037i	−0.750558	−	0.679568i
$993$	−30.6253	−	53.0446i	−0.971865	−	1.68332i
$994$	3.40785	−	5.36336i	0.108090	−	0.170115i
$995$			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	$0.218139\pi$
$998$	27.6906	−	43.5801i	0.876529	−	1.37950i
$999$		−	54.0044i		−	1.70862i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.25364 - 0.654507i) q^{2} +(-1.50479 - 2.60637i) q^{3} +(1.14324 - 1.64104i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-3.59235 - 2.28256i) q^{6} -2.59896i q^{7} +(0.359145 - 2.80553i) q^{8} +(-3.02877 + 5.24598i) q^{9} +O(q^{10})\)	\(q+(1.25364 - 0.654507i) q^{2} +(-1.50479 - 2.60637i) q^{3} +(1.14324 - 1.64104i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-3.59235 - 2.28256i) q^{6} -2.59896i q^{7} +(0.359145 - 2.80553i) q^{8} +(-3.02877 + 5.24598i) q^{9} +(-1.19364 - 0.758433i) q^{10} +4.32584i q^{11} +(-5.99748 - 0.510295i) q^{12} +(5.09891 + 2.94386i) q^{13} +(-1.70104 - 3.25817i) q^{14} +(-1.50479 + 2.60637i) q^{15} +(-1.38600 - 3.75220i) 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} +(2.83129 + 5.42305i) q^{22} +(4.53570 + 2.61869i) q^{23} +(-7.85269 + 3.28567i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(8.31899 + 0.353272i) q^{26} +9.20188 q^{27} +(-4.26499 - 2.97124i) q^{28} +(-8.10230 - 4.67787i) q^{29} +(-0.180579 + 4.25235i) q^{30} +5.63734 q^{31} +(-4.19339 - 3.79677i) q^{32} +(11.2747 - 6.50946i) q^{33} +(-1.81349 - 1.15228i) q^{34} +(-2.25077 + 1.29948i) q^{35} +(5.14623 + 10.9677i) q^{36} -5.86885i q^{37} +(-4.61976 - 4.08140i) q^{38} -17.7195i q^{39} +(-2.60924 + 1.09174i) q^{40} +(0.487467 - 0.281439i) q^{41} +(-5.93229 + 9.33639i) q^{42} +(-4.31427 + 2.49085i) q^{43} +(7.09885 + 4.94547i) q^{44} +6.05754 q^{45} +(7.40011 + 0.314251i) q^{46} +(-1.11525 - 0.643888i) q^{47} +(-7.69397 + 9.25869i) q^{48} +0.245391 q^{49} +(-0.0600015 + 1.41294i) q^{50} +(-2.28621 + 3.95983i) q^{51} +(10.6603 - 5.00196i) q^{52} +(3.04525 + 1.75818i) q^{53} +(11.5359 - 6.02270i) 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} +(2.55681 + 5.44912i) q^{60} +(1.65392 - 2.86467i) q^{61} +(7.06721 - 3.68968i) q^{62} +(13.6341 + 7.87166i) q^{63} +(-7.74203 - 2.01519i) q^{64} -5.88772i q^{65} +(9.87398 - 15.5399i) q^{66} +(-0.662378 + 1.14727i) q^{67} +(-3.02765 - 0.257607i) q^{68} -15.7623i q^{69} +(-1.97114 + 3.10223i) q^{70} +(0.864436 + 1.49725i) q^{71} +(13.6300 + 10.3814i) q^{72} +(0.793145 + 1.37377i) q^{73} +(-3.84120 - 7.35744i) q^{74} +3.00957 q^{75} +(-8.46283 - 2.09296i) q^{76} +11.2427 q^{77} +(-11.5976 - 22.2139i) q^{78} +(0.810011 + 1.40298i) q^{79} +(-2.55650 + 3.07641i) q^{80} +(-4.76057 - 8.24555i) q^{81} +(0.426906 - 0.671875i) q^{82} -16.0338i q^{83} +(-1.32624 + 15.5872i) q^{84} +(-0.759646 + 1.31575i) q^{85} +(-3.77828 + 5.94635i) q^{86} +28.1568i q^{87} +(12.1363 + 1.55360i) q^{88} +(13.2176 + 7.63116i) q^{89} +(7.59399 - 3.96470i) q^{90} +(7.65098 - 13.2519i) q^{91} +(9.48277 - 4.44946i) 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} +(0.307633 - 0.160610i) 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

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