LMFDB - Embedded newform 185.2.e.b.26.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [185,2,Mod(26,185)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(185, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("185.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.e (of order $3$, 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:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 13 x^{12} - 16 x^{11} + 98 x^{10} - 116 x^{9} + 378 x^{8} - 264 x^{7} + 795 x^{6} + \cdots + 9 $ x^14 - 2x^13 + 13x^12 - 16x^11 + 98x^10 - 116x^9 + 378x^8 - 264x^7 + 795x^6 - 520x^5 + 927x^4 - 71x^3 + 94x^2 - 3*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.4
Root			$0.167462 - 0.290053i$ of defining polynomial
Character	$\chi$	$=$	185.26
Dual form			185.2.e.b.121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.167462 + 0.290053i) q^{2} +(1.19442 - 2.06880i) q^{3} +(0.943913 - 1.63491i) q^{4} +(0.500000 - 0.866025i) q^{5} +0.800081 q^{6} +(-2.21517 + 3.83679i) q^{7} +1.30213 q^{8} +(-1.35329 - 2.34397i) q^{9} +O(q^{10})$	\(q+(0.167462 + 0.290053i) q^{2} +(1.19442 - 2.06880i) q^{3} +(0.943913 - 1.63491i) q^{4} +(0.500000 - 0.866025i) q^{5} +0.800081 q^{6} +(-2.21517 + 3.83679i) q^{7} +1.30213 q^{8} +(-1.35329 - 2.34397i) q^{9} +0.334924 q^{10} -2.13807 q^{11} +(-2.25486 - 3.90553i) q^{12} +(-0.0906236 + 0.156965i) q^{13} -1.48383 q^{14} +(-1.19442 - 2.06880i) q^{15} +(-1.66977 - 2.89213i) q^{16} +(2.46466 + 4.26892i) q^{17} +(0.453249 - 0.785050i) q^{18} +(-0.626920 + 1.08586i) q^{19} +(-0.943913 - 1.63491i) q^{20} +(5.29171 + 9.16550i) q^{21} +(-0.358045 - 0.620152i) q^{22} +6.29996 q^{23} +(1.55529 - 2.69384i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.0607040 q^{26} +0.700938 q^{27} +(4.18186 + 7.24320i) q^{28} -1.75180 q^{29} +(0.400041 - 0.692891i) q^{30} -3.74502 q^{31} +(1.86137 - 3.22399i) q^{32} +(-2.55376 + 4.42324i) q^{33} +(-0.825475 + 1.42976i) q^{34} +(2.21517 + 3.83679i) q^{35} -5.10955 q^{36} +(2.13771 - 5.69475i) q^{37} -0.419941 q^{38} +(0.216486 + 0.374964i) q^{39} +(0.651063 - 1.12767i) q^{40} +(-1.47512 + 2.55498i) q^{41} +(-1.77232 + 3.06975i) q^{42} -12.0533 q^{43} +(-2.01815 + 3.49554i) q^{44} -2.70658 q^{45} +(1.05500 + 1.82732i) q^{46} +0.334924 q^{47} -7.97764 q^{48} +(-6.31399 - 10.9361i) q^{49} +(0.167462 - 0.290053i) q^{50} +11.7754 q^{51} +(0.171082 + 0.296322i) q^{52} +(6.01987 + 10.4267i) q^{53} +(0.117380 + 0.203309i) q^{54} +(-1.06903 + 1.85162i) q^{55} +(-2.88443 + 4.99599i) q^{56} +(1.49761 + 2.59394i) q^{57} +(-0.293359 - 0.508113i) q^{58} +(-2.79575 - 4.84238i) q^{59} -4.50972 q^{60} +(5.78204 - 10.0148i) q^{61} +(-0.627148 - 1.08625i) q^{62} +11.9911 q^{63} -5.43224 q^{64} +(0.0906236 + 0.156965i) q^{65} -1.71063 q^{66} +(-6.32800 + 10.9604i) q^{67} +9.30571 q^{68} +(7.52481 - 13.0334i) q^{69} +(-0.741914 + 1.28503i) q^{70} +(-2.95872 + 5.12465i) q^{71} +(-1.76215 - 3.05214i) q^{72} -12.2065 q^{73} +(2.00976 - 0.333606i) q^{74} -2.38884 q^{75} +(1.18352 + 2.04991i) q^{76} +(4.73619 - 8.20333i) q^{77} +(-0.0725062 + 0.125584i) q^{78} +(-2.34202 + 4.05649i) q^{79} -3.33954 q^{80} +(4.89708 - 8.48200i) q^{81} -0.988105 q^{82} +(3.60894 + 6.25087i) q^{83} +19.9796 q^{84} +4.92933 q^{85} +(-2.01848 - 3.49610i) q^{86} +(-2.09238 + 3.62411i) q^{87} -2.78403 q^{88} +(-6.59322 - 11.4198i) q^{89} +(-0.453249 - 0.785050i) q^{90} +(-0.401494 - 0.695408i) q^{91} +(5.94661 - 10.2998i) q^{92} +(-4.47313 + 7.74769i) q^{93} +(0.0560870 + 0.0971455i) q^{94} +(0.626920 + 1.08586i) q^{95} +(-4.44653 - 7.70161i) q^{96} +4.49570 q^{97} +(2.11471 - 3.66278i) q^{98} +(2.89342 + 5.01156i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9} + 4 q^{10} - 10 q^{11} - 8 q^{12} + 6 q^{13} - 36 q^{14} + 2 q^{15} - 14 q^{16} - q^{17} - 4 q^{18} + 6 q^{19} + 8 q^{20} + 13 q^{21} - q^{22} + 12 q^{23} - 21 q^{24} - 7 q^{25} + 2 q^{26} + 22 q^{27} + 13 q^{28} - 12 q^{29} + 2 q^{30} - 8 q^{31} + 18 q^{32} + q^{33} - 11 q^{34} - 2 q^{35} - 8 q^{36} + 12 q^{37} + 16 q^{38} + 23 q^{39} - 3 q^{40} - 3 q^{41} + 29 q^{42} - 38 q^{43} + 25 q^{44} - 10 q^{45} + 10 q^{46} + 4 q^{47} - 20 q^{48} - 7 q^{49} + 2 q^{50} - 14 q^{51} + 46 q^{52} - 2 q^{53} + 23 q^{54} - 5 q^{55} + 19 q^{56} + 22 q^{57} - 12 q^{58} - 18 q^{59} - 16 q^{60} - 20 q^{61} - 21 q^{62} + 46 q^{63} + 50 q^{64} - 6 q^{65} - 42 q^{66} - 20 q^{67} + 110 q^{68} + 17 q^{69} - 18 q^{70} - 11 q^{71} - 29 q^{72} - 36 q^{73} - 66 q^{74} + 4 q^{75} + 40 q^{76} - q^{77} + 6 q^{78} + 23 q^{79} - 28 q^{80} + 29 q^{81} - 24 q^{82} - 9 q^{83} + 8 q^{84} - 2 q^{85} - 3 q^{86} - 43 q^{87} - 116 q^{88} - 16 q^{89} + 4 q^{90} + 12 q^{91} - 33 q^{92} + 25 q^{93} + 22 q^{94} - 6 q^{95} - 67 q^{96} - 62 q^{97} - 24 q^{98} + 4 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9 + 4 * q^10 - 10 * q^11 - 8 * q^12 + 6 * q^13 - 36 * q^14 + 2 * q^15 - 14 * q^16 - q^17 - 4 * q^18 + 6 * q^19 + 8 * q^20 + 13 * q^21 - q^22 + 12 * q^23 - 21 * q^24 - 7 * q^25 + 2 * q^26 + 22 * q^27 + 13 * q^28 - 12 * q^29 + 2 * q^30 - 8 * q^31 + 18 * q^32 + q^33 - 11 * q^34 - 2 * q^35 - 8 * q^36 + 12 * q^37 + 16 * q^38 + 23 * q^39 - 3 * q^40 - 3 * q^41 + 29 * q^42 - 38 * q^43 + 25 * q^44 - 10 * q^45 + 10 * q^46 + 4 * q^47 - 20 * q^48 - 7 * q^49 + 2 * q^50 - 14 * q^51 + 46 * q^52 - 2 * q^53 + 23 * q^54 - 5 * q^55 + 19 * q^56 + 22 * q^57 - 12 * q^58 - 18 * q^59 - 16 * q^60 - 20 * q^61 - 21 * q^62 + 46 * q^63 + 50 * q^64 - 6 * q^65 - 42 * q^66 - 20 * q^67 + 110 * q^68 + 17 * q^69 - 18 * q^70 - 11 * q^71 - 29 * q^72 - 36 * q^73 - 66 * q^74 + 4 * q^75 + 40 * q^76 - q^77 + 6 * q^78 + 23 * q^79 - 28 * q^80 + 29 * q^81 - 24 * q^82 - 9 * q^83 + 8 * q^84 - 2 * q^85 - 3 * q^86 - 43 * q^87 - 116 * q^88 - 16 * q^89 + 4 * q^90 + 12 * q^91 - 33 * q^92 + 25 * q^93 + 22 * q^94 - 6 * q^95 - 67 * q^96 - 62 * q^97 - 24 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.167462	+	0.290053i	0.118413	+	0.205098i	0.919139	−	0.393933i	$-0.128886\pi$
$2$	0.167462	+	0.290053i	0.118413	+	0.205098i	−0.800726	+	0.599031i	$0.795553\pi$
$3$	1.19442	−	2.06880i	0.689600	−	1.19442i	−0.282367	−	0.959306i	$-0.591120\pi$
$3$	1.19442	−	2.06880i	0.689600	−	1.19442i	0.971967	−	0.235116i	$-0.0755470\pi$
$4$	0.943913	−	1.63491i	0.471957	−	0.817453i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.800081			0.326632
$7$	−2.21517	+	3.83679i	−0.837257	+	1.45017i	0.0549226	+	0.998491i	$0.482509\pi$
$7$	−2.21517	+	3.83679i	−0.837257	+	1.45017i	−0.892180	+	0.451681i	$0.850825\pi$
$8$	1.30213			0.460371
$9$	−1.35329	−	2.34397i	−0.451096	−	0.781322i
$10$	0.334924			0.105912
$11$	−2.13807			−0.644652			−0.322326	−	0.946629i	$-0.604465\pi$
$11$	−2.13807			−0.644652			−0.322326	+	0.946629i	$0.604465\pi$
$12$	−2.25486	−	3.90553i	−0.650922	−	1.12743i
$13$	−0.0906236	+	0.156965i	−0.0251345	+	0.0435342i	−0.878319	−	0.478075i	$-0.841335\pi$
$13$	−0.0906236	+	0.156965i	−0.0251345	+	0.0435342i	0.853185	+	0.521609i	$0.174668\pi$
$14$	−1.48383			−0.396570
$15$	−1.19442	−	2.06880i	−0.308399	−	0.534162i
$16$	−1.66977	−	2.89213i	−0.417442	−	0.723031i
$17$	2.46466	+	4.26892i	0.597769	+	1.03537i	0.993150	+	0.116849i	$0.0372793\pi$
$17$	2.46466	+	4.26892i	0.597769	+	1.03537i	−0.395381	+	0.918517i	$0.629387\pi$
$18$	0.453249	−	0.785050i	0.106832	−	0.185038i
$19$	−0.626920	+	1.08586i	−0.143825	+	0.249113i	−0.928934	−	0.370245i	$-0.879274\pi$
$19$	−0.626920	+	1.08586i	−0.143825	+	0.249113i	0.785109	+	0.619358i	$0.212607\pi$
$20$	−0.943913	−	1.63491i	−0.211065	−	0.365576i
$21$	5.29171	+	9.16550i	1.15474	+	2.00008i
$22$	−0.358045	−	0.620152i	−0.0763355	−	0.132217i
$23$	6.29996			1.31363			0.656816	−	0.754051i	$-0.271903\pi$
$23$	6.29996			1.31363			0.656816	+	0.754051i	$0.271903\pi$
$24$	1.55529	−	2.69384i	0.317472	−	0.549877i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.0607040			−0.0119050
$27$	0.700938			0.134896
$28$	4.18186	+	7.24320i	0.790298	+	1.36884i
$29$	−1.75180			−0.325300			−0.162650	−	0.986684i	$-0.552004\pi$
$29$	−1.75180			−0.325300			−0.162650	+	0.986684i	$0.552004\pi$
$30$	0.400041	−	0.692891i	0.0730371	−	0.126504i
$31$	−3.74502			−0.672625			−0.336313	−	0.941750i	$-0.609180\pi$
$31$	−3.74502			−0.672625			−0.336313	+	0.941750i	$0.609180\pi$
$32$	1.86137	−	3.22399i	0.329047	−	0.569926i
$33$	−2.55376	+	4.42324i	−0.444552	+	0.769987i
$34$	−0.825475	+	1.42976i	−0.141568	+	0.245203i
$35$	2.21517	+	3.83679i	0.374433	+	0.648536i
$36$	−5.10955			−0.851592
$37$	2.13771	−	5.69475i	0.351437	−	0.936211i
$37$	2.13771	−	5.69475i	0.351437	−	0.936211i
$38$	−0.419941			−0.0681234
$39$	0.216486	+	0.374964i	0.0346655	+	0.0600423i
$40$	0.651063	−	1.12767i	0.102942	−	0.178301i
$41$	−1.47512	+	2.55498i	−0.230375	+	0.399021i	−0.957918	−	0.287040i	$-0.907329\pi$
$41$	−1.47512	+	2.55498i	−0.230375	+	0.399021i	0.727544	+	0.686061i	$0.240662\pi$
$42$	−1.77232	+	3.06975i	−0.273475	+	0.473672i
$43$	−12.0533			−1.83812			−0.919059	−	0.394121i	$-0.871049\pi$
$43$	−12.0533			−1.83812			−0.919059	+	0.394121i	$0.871049\pi$
$44$	−2.01815	+	3.49554i	−0.304248	+	0.526972i
$45$	−2.70658			−0.403473
$46$	1.05500	+	1.82732i	0.155552	+	0.269423i
$47$	0.334924			0.0488537			0.0244268	−	0.999702i	$-0.492224\pi$
$47$	0.334924			0.0488537			0.0244268	+	0.999702i	$0.492224\pi$
$48$	−7.97764			−1.15147
$49$	−6.31399	−	10.9361i	−0.901998	−	1.56231i
$50$	0.167462	−	0.290053i	0.0236827	−	0.0410196i
$51$	11.7754			1.64889
$52$	0.171082	+	0.296322i	0.0237247	+	0.0410925i
$53$	6.01987	+	10.4267i	0.826893	+	1.43222i	0.900464	+	0.434931i	$0.143227\pi$
$53$	6.01987	+	10.4267i	0.826893	+	1.43222i	−0.0735704	+	0.997290i	$0.523439\pi$
$54$	0.117380	+	0.203309i	0.0159734	+	0.0276668i
$55$	−1.06903	+	1.85162i	−0.144149	+	0.249673i
$56$	−2.88443	+	4.99599i	−0.385449	+	0.667617i
$57$	1.49761	+	2.59394i	0.198364	+	0.343576i
$58$	−0.293359	−	0.508113i	−0.0385199	−	0.0667185i
$59$	−2.79575	−	4.84238i	−0.363976	−	0.630424i	0.624636	−	0.780916i	$-0.285247\pi$
$59$	−2.79575	−	4.84238i	−0.363976	−	0.630424i	−0.988611	+	0.150492i	$0.951914\pi$
$60$	−4.50972			−0.582203
$61$	5.78204	−	10.0148i	0.740315	−	1.28226i	−0.212038	−	0.977262i	$-0.568010\pi$
$61$	5.78204	−	10.0148i	0.740315	−	1.28226i	0.952352	−	0.305001i	$-0.0986568\pi$
$62$	−0.627148	−	1.08625i	−0.0796479	−	0.137954i
$63$	11.9911			1.51073
$64$	−5.43224			−0.679030
$65$	0.0906236	+	0.156965i	0.0112405	+	0.0194691i
$66$	−1.71063			−0.210564
$67$	−6.32800	+	10.9604i	−0.773088	+	1.33903i	0.162774	+	0.986663i	$0.447956\pi$
$67$	−6.32800	+	10.9604i	−0.773088	+	1.33903i	−0.935863	+	0.352365i	$0.885378\pi$
$68$	9.30571			1.12848
$69$	7.52481	−	13.0334i	0.905881	−	1.56903i
$70$	−0.741914	+	1.28503i	−0.0886757	+	0.153591i
$71$	−2.95872	+	5.12465i	−0.351135	+	0.608184i	−0.986449	−	0.164070i	$-0.947538\pi$
$71$	−2.95872	+	5.12465i	−0.351135	+	0.608184i	0.635314	+	0.772254i	$0.280871\pi$
$72$	−1.76215	−	3.05214i	−0.207672	−	0.359698i
$73$	−12.2065			−1.42866			−0.714330	−	0.699809i	$-0.753269\pi$
$73$	−12.2065			−1.42866			−0.714330	+	0.699809i	$0.753269\pi$
$74$	2.00976	−	0.333606i	0.233630	−	0.0387809i
$75$	−2.38884			−0.275840
$76$	1.18352	+	2.04991i	0.135759	+	0.235141i
$77$	4.73619	−	8.20333i	0.539739	−	0.934856i
$78$	−0.0725062	+	0.125584i	−0.00820971	+	0.0142196i
$79$	−2.34202	+	4.05649i	−0.263497	+	0.456391i	−0.967169	−	0.254135i	$-0.918209\pi$
$79$	−2.34202	+	4.05649i	−0.263497	+	0.456391i	0.703672	+	0.710525i	$0.251543\pi$
$80$	−3.33954			−0.373372
$81$	4.89708	−	8.48200i	0.544120	−	0.942444i
$82$	−0.988105			−0.109118
$83$	3.60894	+	6.25087i	0.396133	+	0.686122i	0.993245	−	0.116036i	$-0.0370187\pi$
$83$	3.60894	+	6.25087i	0.396133	+	0.686122i	−0.597112	+	0.802158i	$0.703685\pi$
$84$	19.9796			2.17996
$85$	4.92933			0.534661
$86$	−2.01848	−	3.49610i	−0.217658	−	0.376994i
$87$	−2.09238	+	3.62411i	−0.224327	+	0.388546i
$88$	−2.78403			−0.296779
$89$	−6.59322	−	11.4198i	−0.698880	−	1.21050i	−0.968855	−	0.247628i	$-0.920349\pi$
$89$	−6.59322	−	11.4198i	−0.698880	−	1.21050i	0.269975	−	0.962867i	$-0.412984\pi$
$90$	−0.453249	−	0.785050i	−0.0477766	−	0.0827515i
$91$	−0.401494	−	0.695408i	−0.0420880	−	0.0728986i
$92$	5.94661	−	10.2998i	0.619977	−	1.07383i
$93$	−4.47313	+	7.74769i	−0.463842	+	0.803398i
$94$	0.0560870	+	0.0971455i	0.00578493	+	0.0100198i
$95$	0.626920	+	1.08586i	0.0643206	+	0.111407i
$96$	−4.44653	−	7.70161i	−0.453822	−	0.786042i
$97$	4.49570			0.456469			0.228234	−	0.973606i	$-0.426705\pi$
$97$	4.49570			0.456469			0.228234	+	0.973606i	$0.426705\pi$
$98$	2.11471	−	3.66278i	0.213618	−	0.369996i
$99$	2.89342	+	5.01156i	0.290800	+	0.503681i
$100$	−1.88783			−0.188783
$101$	19.1503			1.90552			0.952762	−	0.303719i	$-0.0982283\pi$
$101$	19.1503			1.90552			0.952762	+	0.303719i	$0.0982283\pi$
$102$	1.97193	+	3.41549i	0.195250	+	0.338183i
$103$	4.42494			0.436002			0.218001	−	0.975949i	$-0.430046\pi$
$103$	4.42494			0.436002			0.218001	+	0.975949i	$0.430046\pi$
$104$	−0.118003	+	0.204388i	−0.0115712	+	0.0200419i
$105$	10.5834			1.03284
$106$	−2.01620	+	3.49216i	−0.195831	+	0.339189i
$107$	−0.924693	+	1.60162i	−0.0893935	+	0.154834i	−0.907255	−	0.420581i	$-0.861826\pi$
$107$	−0.924693	+	1.60162i	−0.0893935	+	0.154834i	0.817861	+	0.575415i	$0.195160\pi$
$108$	0.661624	−	1.14597i	0.0636648	−	0.110271i
$109$	4.57340	+	7.92137i	0.438052	+	0.758729i	0.997539	−	0.0701101i	$-0.0223351\pi$
$109$	4.57340	+	7.92137i	0.438052	+	0.758729i	−0.559487	+	0.828839i	$0.689002\pi$
$110$	−0.716090			−0.0682765
$111$	−9.22798	−	11.2244i	−0.875881	−	1.06538i
$112$	14.7953			1.39803
$113$	−9.07433	−	15.7172i	−0.853642	−	1.47855i	−0.877900	−	0.478845i	$-0.841056\pi$
$113$	−9.07433	−	15.7172i	−0.853642	−	1.47855i	0.0242580	−	0.999706i	$-0.492278\pi$
$114$	−0.501587	+	0.868774i	−0.0469779	+	0.0813681i
$115$	3.14998	−	5.45592i	0.293737	−	0.508767i
$116$	−1.65354	+	2.86402i	−0.153528	+	0.265918i
$117$	0.490560			0.0453523
$118$	0.936363	−	1.62183i	0.0861992	−	0.149301i
$119$	−21.8386			−2.00194
$120$	−1.55529	−	2.69384i	−0.141978	−	0.245913i
$121$	−6.42866			−0.584424
$122$	3.87309			0.350653
$123$	3.52383	+	6.10345i	0.317733	+	0.550330i
$124$	−3.53497	+	6.12275i	−0.317450	+	0.549839i
$125$	−1.00000			−0.0894427
$126$	2.00805	+	3.47804i	0.178891	+	0.309849i
$127$	−7.40743	−	12.8301i	−0.657303	−	1.13848i	−0.981311	−	0.192428i	$-0.938364\pi$
$127$	−7.40743	−	12.8301i	−0.657303	−	1.13848i	0.324008	−	0.946054i	$-0.394970\pi$
$128$	−4.63244	−	8.02362i	−0.409453	−	0.709194i
$129$	−14.3968	+	24.9360i	−1.26757	+	2.19549i
$130$	−0.0303520	+	0.0525712i	−0.00266205	+	0.00461080i
$131$	−3.87564	−	6.71280i	−0.338616	−	0.586500i	0.645557	−	0.763712i	$-0.276625\pi$
$131$	−3.87564	−	6.71280i	−0.338616	−	0.586500i	−0.984173	+	0.177212i	$0.943292\pi$
$132$	4.82105	+	8.35030i	0.419618	+	0.726800i
$133$	−2.77747	−	4.81072i	−0.240837	−	0.417143i
$134$	−4.23880			−0.366176
$135$	0.350469	−	0.607030i	0.0301636	−	0.0522448i
$136$	3.20930	+	5.55868i	0.275195	+	0.476652i
$137$	−2.52416			−0.215653			−0.107827	−	0.994170i	$-0.534389\pi$
$137$	−2.52416			−0.215653			−0.107827	+	0.994170i	$0.534389\pi$
$138$	5.04048			0.429074
$139$	−2.33923	−	4.05166i	−0.198411	−	0.343658i	0.749603	−	0.661888i	$-0.230245\pi$
$139$	−2.33923	−	4.05166i	−0.198411	−	0.343658i	−0.948013	+	0.318231i	$0.896911\pi$
$140$	8.36372			0.706864
$141$	0.400041	−	0.692891i	0.0336895	−	0.0583519i
$142$	−1.98189			−0.166316
$143$	0.193759	−	0.335601i	0.0162030	−	0.0280644i
$144$	−4.51936	+	7.82777i	−0.376614	+	0.652314i
$145$	−0.875898	+	1.51710i	−0.0727393	+	0.125988i
$146$	−2.04412	−	3.54052i	−0.169173	−	0.293016i
$147$	−30.1663			−2.48807
$148$	−7.29257	−	8.87030i	−0.599445	−	0.729134i
$149$	17.6991			1.44997			0.724983	−	0.688767i	$-0.241848\pi$
$149$	17.6991			1.44997			0.724983	+	0.688767i	$0.241848\pi$
$150$	−0.400041	−	0.692891i	−0.0326632	−	0.0565743i
$151$	0.177623	−	0.307652i	0.0144548	−	0.0250364i	−0.858708	−	0.512466i	$-0.828732\pi$
$151$	0.177623	−	0.307652i	0.0144548	−	0.0250364i	0.873162	+	0.487430i	$0.162065\pi$
$152$	−0.816328	+	1.41392i	−0.0662130	+	0.114684i
$153$	6.67081	−	11.5542i	0.539303	−	0.934100i
$154$	3.17253			0.255650
$155$	−1.87251	+	3.24328i	−0.150404	+	0.260507i
$156$	0.817375			0.0654423
$157$	4.19375	+	7.26379i	0.334698	+	0.579713i	0.983427	−	0.181306i	$-0.0580325\pi$
$157$	4.19375	+	7.26379i	0.334698	+	0.579713i	−0.648729	+	0.761019i	$0.724699\pi$
$158$	−1.56879			−0.124807
$159$	28.7611			2.28090
$160$	−1.86137	−	3.22399i	−0.147154	−	0.254879i
$161$	−13.9555	+	24.1716i	−1.09985	+	1.90499i
$162$	3.28030			0.257725
$163$	1.81038	+	3.13567i	0.141800	+	0.245604i	0.928174	−	0.372146i	$-0.121378\pi$
$163$	1.81038	+	3.13567i	0.141800	+	0.245604i	−0.786375	+	0.617750i	$0.788044\pi$
$164$	2.78477	+	4.82336i	0.217454	+	0.376641i
$165$	2.55376	+	4.42324i	0.198810	+	0.344348i
$166$	−1.20872	+	2.09357i	−0.0938149	+	0.162492i
$167$	2.89722	−	5.01814i	0.224194	−	0.388315i	−0.731883	−	0.681430i	$-0.761358\pi$
$167$	2.89722	−	5.01814i	0.224194	−	0.388315i	0.956077	+	0.293115i	$0.0946918\pi$
$168$	6.89047	+	11.9346i	0.531611	+	0.920777i
$169$	6.48357	+	11.2299i	0.498737	+	0.863837i
$170$	0.825475	+	1.42976i	0.0633110	+	0.109658i
$171$	3.39362			0.259516
$172$	−11.3773	+	19.7061i	−0.867511	+	1.50257i
$173$	−7.52631	−	13.0360i	−0.572215	−	0.991105i	−0.996338	−	0.0855007i	$-0.972751\pi$
$173$	−7.52631	−	13.0360i	−0.572215	−	0.991105i	0.424123	−	0.905604i	$-0.360582\pi$
$174$	−1.40158			−0.106253
$175$	4.43035			0.334903
$176$	3.57008	+	6.18356i	0.269105	+	0.466104i
$177$	−13.3572			−1.00399
$178$	2.20823	−	3.82476i	0.165514	−	0.286678i
$179$	5.86114			0.438083			0.219041	−	0.975716i	$-0.429707\pi$
$179$	5.86114			0.438083			0.219041	+	0.975716i	$0.429707\pi$
$180$	−2.55477	+	4.42500i	−0.190422	+	0.329820i
$181$	6.30702	−	10.9241i	0.468797	−	0.811980i	−0.530567	−	0.847643i	$-0.678021\pi$
$181$	6.30702	−	10.9241i	0.468797	−	0.811980i	0.999364	+	0.0356628i	$0.0113542\pi$
$182$	0.134470	−	0.232909i	0.00996757	−	0.0172643i
$183$	−13.8124	−	23.9238i	−1.02104	−	1.76850i
$184$	8.20334			0.604758
$185$	−3.86295	−	4.69869i	−0.284009	−	0.345454i
$186$	−2.99632			−0.219701
$187$	−5.26962	−	9.12725i	−0.385353	−	0.667451i
$188$	0.316139	−	0.547569i	0.0230568	−	0.0399356i
$189$	−1.55270	+	2.68935i	−0.112942	+	0.195622i
$190$	−0.209970	+	0.363679i	−0.0152329	+	0.0263841i
$191$	−1.95503			−0.141461			−0.0707305	−	0.997495i	$-0.522533\pi$
$191$	−1.95503			−0.141461			−0.0707305	+	0.997495i	$0.522533\pi$
$192$	−6.48839	+	11.2382i	−0.468259	+	0.811049i
$193$	−0.669377			−0.0481828			−0.0240914	−	0.999710i	$-0.507669\pi$
$193$	−0.669377			−0.0481828			−0.0240914	+	0.999710i	$0.507669\pi$
$194$	0.752858	+	1.30399i	0.0540520	+	0.0936209i
$195$	0.432971			0.0310057
$196$	−23.8394			−1.70282
$197$	12.4497	+	21.5634i	0.887002	+	1.53633i	0.843402	+	0.537283i	$0.180549\pi$
$197$	12.4497	+	21.5634i	0.887002	+	1.53633i	0.0435994	+	0.999049i	$0.486117\pi$
$198$	−0.969077	+	1.67849i	−0.0688693	+	0.119285i
$199$	−21.6009			−1.53125			−0.765624	−	0.643288i	$-0.777570\pi$
$199$	−21.6009			−1.53125			−0.765624	+	0.643288i	$0.777570\pi$
$200$	−0.651063	−	1.12767i	−0.0460371	−	0.0797386i
$201$	15.1166	+	26.1827i	1.06624	+	1.84679i
$202$	3.20694	+	5.55459i	0.225640	+	0.390819i
$203$	3.88053	−	6.72128i	0.272360	−	0.471741i
$204$	11.1150	−	19.2517i	0.778202	−	1.34789i
$205$	1.47512	+	2.55498i	0.103027	+	0.178448i
$206$	0.741009	+	1.28346i	0.0516285	+	0.0894232i
$207$	−8.52567	−	14.7669i	−0.592575	−	1.02637i
$208$	0.605282			0.0419688
$209$	1.34040	−	2.32164i	0.0927172	−	0.160591i
$210$	1.77232	+	3.06975i	0.122302	+	0.211833i
$211$	−11.6062			−0.799001			−0.399501	−	0.916733i	$-0.630816\pi$
$211$	−11.6062			−0.799001			−0.399501	+	0.916733i	$0.630816\pi$
$212$	22.7290			1.56103
$213$	7.06792	+	12.2420i	0.484286	+	0.838807i
$214$	−0.619404			−0.0423416
$215$	−6.02667	+	10.4385i	−0.411015	+	0.711900i
$216$	0.912709			0.0621020
$217$	8.29587	−	14.3689i	0.563160	−	0.975422i
$218$	−1.53174	+	2.65305i	−0.103743	+	0.179687i
$219$	−14.5797	+	25.2528i	−0.985205	+	1.70642i
$220$	2.01815	+	3.49554i	0.136064	+	0.235669i
$221$	−0.893427			−0.0600984
$222$	1.71034	−	4.55626i	0.114791	−	0.305796i
$223$	20.1196			1.34731			0.673653	−	0.739048i	$-0.264724\pi$
$223$	20.1196			1.34731			0.673653	+	0.739048i	$0.264724\pi$
$224$	8.24652	+	14.2834i	0.550994	+	0.954349i
$225$	−1.35329	+	2.34397i	−0.0902193	+	0.156264i
$226$	3.03921	−	5.26407i	0.202165	−	0.350161i
$227$	4.81525	−	8.34026i	0.319599	−	0.553562i	−0.660805	−	0.750558i	$-0.729785\pi$
$227$	4.81525	−	8.34026i	0.319599	−	0.553562i	0.980404	+	0.196995i	$0.0631184\pi$
$228$	5.65447			0.374476
$229$	3.91839	−	6.78686i	0.258935	−	0.448488i	−0.707022	−	0.707191i	$-0.749962\pi$
$229$	3.91839	−	6.78686i	0.258935	−	0.448488i	0.965957	+	0.258703i	$0.0832952\pi$
$230$	2.11001			0.139130
$231$	−11.3140	−	19.5965i	−0.744408	−	1.28935i
$232$	−2.28106			−0.149759
$233$	−10.7159			−0.702023			−0.351011	−	0.936371i	$-0.614162\pi$
$233$	−10.7159			−0.702023			−0.351011	+	0.936371i	$0.614162\pi$
$234$	0.0821501	+	0.142288i	0.00537032	+	0.00930167i
$235$	0.167462	−	0.290053i	0.0109240	−	0.0189209i
$236$	−10.5558			−0.687122
$237$	5.59471	+	9.69032i	0.363416	+	0.629454i
$238$	−3.65714	−	6.33435i	−0.237057	−	0.410595i
$239$	−6.11462	−	10.5908i	−0.395522	−	0.685064i	0.597646	−	0.801760i	$-0.296103\pi$
$239$	−6.11462	−	10.5908i	−0.395522	−	0.685064i	−0.993168	+	0.116696i	$0.962770\pi$
$240$	−3.98882	+	6.90884i	−0.257477	+	0.445964i
$241$	11.6936	−	20.2538i	0.753248	−	1.30466i	−0.192992	−	0.981200i	$-0.561819\pi$
$241$	11.6936	−	20.2538i	0.753248	−	1.30466i	0.946240	−	0.323464i	$-0.104848\pi$
$242$	−1.07656	−	1.86465i	−0.0692037	−	0.119864i
$243$	−10.6470	−	18.4411i	−0.683003	−	1.18300i
$244$	−10.9155	−	18.9062i	−0.698793	−	1.21034i
$245$	−12.6280			−0.806772
$246$	−1.18021	+	2.04419i	−0.0752478	+	0.130333i
$247$	−0.113627	−	0.196809i	−0.00722994	−	0.0125226i
$248$	−4.87648			−0.309657
$249$	17.2424			1.09269
$250$	−0.167462	−	0.290053i	−0.0105912	−	0.0183445i
$251$	12.2588			0.773771			0.386886	−	0.922128i	$-0.373551\pi$
$251$	12.2588			0.773771			0.386886	+	0.922128i	$0.373551\pi$
$252$	11.3185	−	19.6043i	0.713001	−	1.23495i
$253$	−13.4697			−0.846835
$254$	2.48093	−	4.29709i	0.155667	−	0.269623i
$255$	5.88770	−	10.1978i	0.368702	−	0.638611i
$256$	−3.88073	+	6.72162i	−0.242546	+	0.420101i
$257$	−5.90961	−	10.2357i	−0.368631	−	0.638488i	0.620721	−	0.784032i	$-0.286840\pi$
$257$	−5.90961	−	10.2357i	−0.368631	−	0.638488i	−0.989352	+	0.145544i	$0.953507\pi$
$258$	−9.64365			−0.600387
$259$	17.1142	+	20.8168i	1.06342	+	1.29349i
$260$	0.342163			0.0212201
$261$	2.37069	+	4.10615i	0.146742	+	0.254164i
$262$	1.29804	−	2.24828i	0.0801934	−	0.138899i
$263$	−9.07983	+	15.7267i	−0.559886	+	0.969751i	0.437619	+	0.899160i	$0.355822\pi$
$263$	−9.07983	+	15.7267i	−0.559886	+	0.969751i	−0.997505	+	0.0705909i	$0.977512\pi$
$264$	−3.32531	+	5.75961i	−0.204659	+	0.354479i
$265$	12.0397			0.739596
$266$	0.930242	−	1.61123i	0.0570368	−	0.0987906i
$267$	−31.5003			−1.92779
$268$	11.9462	+	20.6914i	0.729728	+	1.26393i
$269$	13.1678			0.802858			0.401429	−	0.915890i	$-0.368514\pi$
$269$	13.1678			0.802858			0.401429	+	0.915890i	$0.368514\pi$
$270$	0.234761			0.0142871
$271$	−4.94962	−	8.57299i	−0.300668	−	0.520772i	0.675620	−	0.737250i	$-0.263876\pi$
$271$	−4.94962	−	8.57299i	−0.300668	−	0.520772i	−0.976287	+	0.216479i	$0.930543\pi$
$272$	8.23084	−	14.2562i	0.499068	−	0.864411i
$273$	−1.91821			−0.116096
$274$	−0.422700	−	0.732138i	−0.0255363	−	0.0442301i
$275$	1.06903	+	1.85162i	0.0644652	+	0.111657i
$276$	−14.2055	−	24.6047i	−0.855073	−	1.48103i
$277$	6.59332	−	11.4200i	0.396154	−	0.686159i	−0.597094	−	0.802172i	$-0.703678\pi$
$277$	6.59332	−	11.4200i	0.396154	−	0.686159i	0.993248	+	0.116012i	$0.0370113\pi$
$278$	0.783463	−	1.35700i	0.0469890	−	0.0813874i
$279$	5.06809	+	8.77820i	0.303419	+	0.525537i
$280$	2.88443	+	4.99599i	0.172378	+	0.298567i
$281$	5.56142	+	9.63265i	0.331766	+	0.574636i	0.982858	−	0.184363i	$-0.0590221\pi$
$281$	5.56142	+	9.63265i	0.331766	+	0.574636i	−0.651092	+	0.758999i	$0.725689\pi$
$282$	0.267966			0.0159572
$283$	3.43351	−	5.94701i	0.204101	−	0.353513i	−0.745745	−	0.666231i	$-0.767906\pi$
$283$	3.43351	−	5.94701i	0.204101	−	0.353513i	0.949846	+	0.312719i	$0.101240\pi$
$284$	5.58554	+	9.67444i	0.331441	+	0.574073i
$285$	2.99523			0.177422
$286$	0.129789			0.00767460
$287$	−6.53529	−	11.3195i	−0.385766	−	0.668166i
$288$	−10.0759			−0.593728
$289$	−3.64914	+	6.32050i	−0.214655	+	0.371794i
$290$	−0.586718			−0.0344533
$291$	5.36976	−	9.30070i	0.314781	−	0.545216i
$292$	−11.5219	+	19.9564i	−0.674266	+	1.16786i
$293$	−15.0762	+	26.1127i	−0.880761	+	1.52552i	−0.0302644	+	0.999542i	$0.509635\pi$
$293$	−15.0762	+	26.1127i	−0.880761	+	1.52552i	−0.850496	+	0.525981i	$0.823698\pi$
$294$	−5.05170	−	8.74981i	−0.294621	−	0.510299i
$295$	−5.59150			−0.325550
$296$	2.78357	−	7.41528i	0.161791	−	0.431005i
$297$	−1.49865			−0.0869606
$298$	2.96392	+	5.13367i	0.171695	+	0.297385i
$299$	−0.570925	+	0.988871i	−0.0330174	+	0.0571879i
$300$	−2.25486	+	3.90553i	−0.130184	+	0.225486i
$301$	26.7002	−	46.2462i	1.53898	−	2.66559i
$302$	0.118980			0.00684656
$303$	22.8735	−	39.6181i	1.31405	−	2.27600i
$304$	4.18725			0.240155
$305$	−5.78204	−	10.0148i	−0.331079	−	0.573445i
$306$	4.46843			0.255443
$307$	21.7098			1.23905			0.619523	−	0.784979i	$-0.287326\pi$
$307$	21.7098			1.23905			0.619523	+	0.784979i	$0.287326\pi$
$308$	−8.94111	−	15.4865i	−0.509467	−	0.882422i
$309$	5.28525	−	9.15431i	0.300667	−	0.520771i
$310$	−1.25430			−0.0712392
$311$	16.7652	+	29.0382i	0.950668	+	1.64661i	0.743984	+	0.668198i	$0.232934\pi$
$311$	16.7652	+	29.0382i	0.950668	+	1.64661i	0.206684	+	0.978408i	$0.433733\pi$
$312$	0.281892	+	0.488251i	0.0159590	+	0.0276417i
$313$	16.6765	+	28.8846i	0.942613	+	1.63265i	0.760462	+	0.649383i	$0.224973\pi$
$313$	16.6765	+	28.8846i	0.942613	+	1.63265i	0.182151	+	0.983271i	$0.441694\pi$
$314$	−1.40459	+	2.43282i	−0.0792654	+	0.137292i
$315$	5.99554	−	10.3846i	0.337811	−	0.585105i
$316$	4.42132	+	7.65795i	0.248719	+	0.430793i
$317$	−3.69820	−	6.40547i	−0.207712	−	0.359767i	0.743282	−	0.668979i	$-0.233268\pi$
$317$	−3.69820	−	6.40547i	−0.207712	−	0.359767i	−0.950993	+	0.309212i	$0.899935\pi$
$318$	4.81639	+	8.34223i	0.270090	+	0.467809i
$319$	3.74546			0.209705
$320$	−2.71612	+	4.70446i	−0.151836	+	0.262987i
$321$	2.20895	+	3.82601i	0.123291	+	0.213547i
$322$	−9.34806			−0.520947
$323$	−6.18059			−0.343897
$324$	−9.24484	−	16.0125i	−0.513602	−	0.889585i
$325$	0.181247			0.0100538
$326$	−0.606339	+	1.05021i	−0.0335820	+	0.0581657i
$327$	21.8503			1.20832
$328$	−1.92079	+	3.32691i	−0.106058	+	0.183698i
$329$	−0.741914	+	1.28503i	−0.0409031	+	0.0708462i
$330$	−0.855314	+	1.48145i	−0.0470835	+	0.0815510i
$331$	14.1299	+	24.4738i	0.776652	+	1.34520i	0.933861	+	0.357636i	$0.116417\pi$
$331$	14.1299	+	24.4738i	0.776652	+	1.34520i	−0.157209	+	0.987565i	$0.550250\pi$
$332$	13.6261			0.747830
$333$	−16.2412	+	2.69593i	−0.890015	+	0.147736i
$334$	1.94070			0.106190
$335$	6.32800	+	10.9604i	0.345736	+	0.598832i
$336$	17.6719	−	30.6086i	0.964079	−	1.66983i
$337$	7.86211	−	13.6176i	0.428277	−	0.741797i	−0.568444	−	0.822722i	$-0.692454\pi$
$337$	7.86211	−	13.6176i	0.428277	−	0.741797i	0.996720	+	0.0809255i	$0.0257876\pi$
$338$	−2.17150	+	3.76115i	−0.118114	+	0.204580i
$339$	−43.3544			−2.35469
$340$	4.65286	−	8.05899i	0.252337	−	0.437060i
$341$	8.00710			0.433609
$342$	0.568301	+	0.984327i	0.0307302	+	0.0532263i
$343$	24.9339			1.34630
$344$	−15.6950			−0.846216
$345$	−7.52481	−	13.0334i	−0.405122	−	0.701692i
$346$	2.52074	−	4.36605i	0.135516	−	0.234720i
$347$	−15.4749			−0.830734			−0.415367	−	0.909654i	$-0.636347\pi$
$347$	−15.4749			−0.830734			−0.415367	+	0.909654i	$0.636347\pi$
$348$	3.95006	+	6.84170i	0.211745	+	0.366753i
$349$	1.61859	+	2.80349i	0.0866413	+	0.150067i	0.906089	−	0.423086i	$-0.139053\pi$
$349$	1.61859	+	2.80349i	0.0866413	+	0.150067i	−0.819448	+	0.573153i	$0.805720\pi$
$350$	0.741914	+	1.28503i	0.0396570	+	0.0686879i
$351$	−0.0635215	+	0.110022i	−0.00339053	+	0.00587256i
$352$	−3.97974	+	6.89311i	−0.212121	+	0.367404i
$353$	1.27659	+	2.21111i	0.0679458	+	0.117686i	0.897997	−	0.440002i	$-0.145022\pi$
$353$	1.27659	+	2.21111i	0.0679458	+	0.117686i	−0.830051	+	0.557687i	$0.811689\pi$
$354$	−2.23683	−	3.87430i	−0.118886	−	0.205916i
$355$	2.95872	+	5.12465i	0.157032	+	0.271988i
$356$	−24.8937			−1.31936
$357$	−26.0846	+	45.1798i	−1.38054	+	2.39117i
$358$	0.981519	+	1.70004i	0.0518749	+	0.0898499i
$359$	5.82088			0.307214			0.153607	−	0.988132i	$-0.450911\pi$
$359$	5.82088			0.307214			0.153607	+	0.988132i	$0.450911\pi$
$360$	−3.52431			−0.185747
$361$	8.71394	+	15.0930i	0.458629	+	0.794368i
$362$	4.22474			0.222048
$363$	−7.67854	+	13.2996i	−0.403019	+	0.698049i
$364$	−1.51590			−0.0794548
$365$	−6.10324	+	10.5711i	−0.319458	+	0.553318i
$366$	4.62610	−	8.01264i	0.241810	−	0.418828i
$367$	−1.58961	+	2.75329i	−0.0829771	+	0.143721i	−0.904527	−	0.426415i	$-0.859776\pi$
$367$	−1.58961	+	2.75329i	−0.0829771	+	0.143721i	0.821550	+	0.570136i	$0.193110\pi$
$368$	−10.5195	−	18.2203i	−0.548366	−	0.949797i
$369$	7.98505			0.415685
$370$	0.715970	−	1.90731i	0.0372215	−	0.0991562i
$371$	−53.3403			−2.76929
$372$	8.44450	+	14.6263i	0.437827	+	0.758338i
$373$	−9.11005	+	15.7791i	−0.471701	+	0.817009i	−0.999476	−	0.0323748i	$-0.989693\pi$
$373$	−9.11005	+	15.7791i	−0.471701	+	0.817009i	0.527775	+	0.849384i	$0.323026\pi$
$374$	1.76492	−	3.05693i	0.0912619	−	0.158070i
$375$	−1.19442	+	2.06880i	−0.0616797	+	0.106832i
$376$	0.436113			0.0224908
$377$	0.158754	−	0.274970i	0.00817625	−	0.0141617i
$378$	−1.04007			−0.0534955
$379$	10.3230	+	17.8799i	0.530255	+	0.918429i	0.999377	+	0.0352952i	$0.0112371\pi$
$379$	10.3230	+	17.8799i	0.530255	+	0.918429i	−0.469122	+	0.883133i	$0.655430\pi$
$380$	2.36703			0.121426
$381$	−35.3904			−1.81311
$382$	−0.327393	−	0.567061i	−0.0167509	−	0.0290134i
$383$	−2.90691	+	5.03491i	−0.148536	+	0.257272i	−0.930687	−	0.365818i	$-0.880789\pi$
$383$	−2.90691	+	5.03491i	−0.148536	+	0.257272i	0.782151	+	0.623089i	$0.214123\pi$
$384$	−22.1323			−1.12944
$385$	−4.73619	−	8.20333i	−0.241379	−	0.418080i
$386$	−0.112095	−	0.194154i	−0.00570549	−	0.00988220i
$387$	16.3117	+	28.2526i	0.829168	+	1.43616i
$388$	4.24355	−	7.35004i	0.215433	−	0.373142i
$389$	12.8066	−	22.1817i	0.649321	−	1.12466i	−0.333964	−	0.942586i	$-0.608387\pi$
$389$	12.8066	−	22.1817i	0.649321	−	1.12466i	0.983285	−	0.182071i	$-0.0582801\pi$
$390$	0.0725062	+	0.125584i	0.00367150	+	0.00635922i
$391$	15.5273	+	26.8940i	0.785248	+	1.36009i
$392$	−8.22161	−	14.2402i	−0.415254	−	0.719241i
$393$	−18.5166			−0.934039
$394$	−4.16969	+	7.22211i	−0.210066	+	0.363845i
$395$	2.34202	+	4.05649i	0.117840	+	0.204104i
$396$	10.9246			0.548980
$397$	−26.1740			−1.31364			−0.656818	−	0.754049i	$-0.728098\pi$
$397$	−26.1740			−1.31364			−0.656818	+	0.754049i	$0.728098\pi$
$398$	−3.61733	−	6.26540i	−0.181320	−	0.314056i
$399$	−13.2699			−0.664326
$400$	−1.66977	+	2.89213i	−0.0834885	+	0.144606i
$401$	−2.05863			−0.102803			−0.0514017	−	0.998678i	$-0.516369\pi$
$401$	−2.05863			−0.102803			−0.0514017	+	0.998678i	$0.516369\pi$
$402$	−5.06291	+	8.76923i	−0.252515	+	0.437369i
$403$	0.339387	−	0.587836i	0.0169061	−	0.0292822i
$404$	18.0762	−	31.3089i	0.899324	−	1.55768i
$405$	−4.89708	−	8.48200i	−0.243338	−	0.421474i
$406$	2.59936			0.129004
$407$	−4.57057	+	12.1758i	−0.226555	+	0.603530i
$408$	15.3331			0.759099
$409$	−8.31961	−	14.4100i	−0.411378	−	0.712528i	0.583663	−	0.811996i	$-0.301619\pi$
$409$	−8.31961	−	14.4100i	−0.411378	−	0.712528i	−0.995041	+	0.0994685i	$0.968286\pi$
$410$	−0.494053	+	0.855724i	−0.0243995	+	0.0422612i
$411$	−3.01491	+	5.22198i	−0.148715	+	0.257581i
$412$	4.17676	−	7.23436i	0.205774	−	0.356411i
$413$	24.7723			1.21896
$414$	2.85545	−	4.94578i	0.140338	−	0.243072i
$415$	7.21788			0.354312
$416$	0.337368	+	0.584339i	0.0165408	+	0.0286496i
$417$	−11.1761			−0.547296
$418$	0.897862			0.0439159
$419$	1.51927	+	2.63145i	0.0742211	+	0.128555i	0.900747	−	0.434344i	$-0.143020\pi$
$419$	1.51927	+	2.63145i	0.0742211	+	0.128555i	−0.826526	+	0.562898i	$0.809686\pi$
$420$	9.98982	−	17.3029i	0.487453	−	0.844294i
$421$	−24.9080			−1.21394			−0.606972	−	0.794723i	$-0.707616\pi$
$421$	−24.9080			−1.21394			−0.606972	+	0.794723i	$0.707616\pi$
$422$	−1.94359	−	3.36640i	−0.0946125	−	0.163874i
$423$	−0.453249	−	0.785050i	−0.0220377	−	0.0381704i
$424$	7.83863	+	13.5769i	0.380678	+	0.659353i
$425$	2.46466	−	4.26892i	0.119554	−	0.207073i
$426$	−2.36721	+	4.10013i	−0.114692	+	0.198652i
$427$	25.6165	+	44.3690i	1.23967	+	2.14717i
$428$	1.74566	+	3.02357i	0.0843797	+	0.146150i
$429$	−0.462861	−	0.801699i	−0.0223471	−	0.0387064i
$430$	−4.03695			−0.194679
$431$	2.52281	−	4.36964i	0.121520	−	0.210478i	−0.798848	−	0.601534i	$-0.794557\pi$
$431$	2.52281	−	4.36964i	0.121520	−	0.210478i	0.920367	+	0.391056i	$0.127890\pi$
$432$	−1.17040	−	2.02720i	−0.0563111	−	0.0975337i
$433$	20.9589			1.00722			0.503609	−	0.863932i	$-0.332005\pi$
$433$	20.9589			1.00722			0.503609	+	0.863932i	$0.332005\pi$
$434$	5.55697			0.266743
$435$	2.09238	+	3.62411i	0.100322	+	0.173763i
$436$	17.2676			0.826967
$437$	−3.94957	+	6.84085i	−0.188933	+	0.327242i
$438$	−9.76618			−0.466646
$439$	0.408895	−	0.708227i	0.0195155	−	0.0338018i	−0.856103	−	0.516806i	$-0.827121\pi$
$439$	0.408895	−	0.708227i	0.0195155	−	0.0338018i	0.875618	+	0.483004i	$0.160454\pi$
$440$	−1.39202	+	2.41104i	−0.0663618	+	0.114942i
$441$	−17.0893	+	29.5996i	−0.813777	+	1.40950i
$442$	−0.149615	−	0.259141i	−0.00711646	−	0.0123261i
$443$	1.23825			0.0588311			0.0294156	−	0.999567i	$-0.490635\pi$
$443$	1.23825			0.0588311			0.0294156	+	0.999567i	$0.490635\pi$
$444$	−27.0613	+	4.49198i	−1.28427	+	0.213180i
$445$	−13.1864			−0.625097
$446$	3.36926	+	5.83573i	0.159539	+	0.276330i
$447$	21.1402	−	36.6159i	0.999896	−	1.73187i
$448$	12.0334	−	20.8424i	0.568523	−	0.984711i
$449$	−3.30605	+	5.72625i	−0.156022	+	0.270239i	−0.933431	−	0.358757i	$-0.883201\pi$
$449$	−3.30605	+	5.72625i	−0.156022	+	0.270239i	0.777408	+	0.628996i	$0.216534\pi$
$450$	−0.906498			−0.0427327
$451$	3.15391	−	5.46272i	0.148512	−	0.257230i
$452$	−34.2615			−1.61153
$453$	−0.424314	−	0.734934i	−0.0199360	−	0.0345302i
$454$	3.22548			0.151379
$455$	−0.802988			−0.0376447
$456$	1.95008	+	3.37764i	0.0913210	+	0.158173i
$457$	−3.19221	+	5.52907i	−0.149325	+	0.258639i	−0.930978	−	0.365075i	$-0.881043\pi$
$457$	−3.19221	+	5.52907i	−0.149325	+	0.258639i	0.781653	+	0.623713i	$0.214377\pi$
$458$	2.62473			0.122645
$459$	1.72758	+	2.99225i	0.0806363	+	0.139666i
$460$	−5.94661	−	10.2998i	−0.277262	−	0.480232i
$461$	17.7231	+	30.6972i	0.825445	+	1.42971i	0.901579	+	0.432615i	$0.142409\pi$
$461$	17.7231	+	30.6972i	0.825445	+	1.42971i	−0.0761338	+	0.997098i	$0.524258\pi$
$462$	3.78934	−	6.56333i	0.176296	−	0.305354i
$463$	−6.23017	+	10.7910i	−0.289540	+	0.501499i	−0.973700	−	0.227834i	$-0.926836\pi$
$463$	−6.23017	+	10.7910i	−0.289540	+	0.501499i	0.684160	+	0.729332i	$0.260169\pi$
$464$	2.92509	+	5.06641i	0.135794	+	0.235202i
$465$	4.47313	+	7.74769i	0.207437	+	0.359291i
$466$	−1.79451	−	3.10818i	−0.0831289	−	0.143984i
$467$	35.6089			1.64778			0.823892	−	0.566747i	$-0.191798\pi$
$467$	35.6089			1.64778			0.823892	+	0.566747i	$0.191798\pi$
$468$	0.463046	−	0.802019i	0.0214043	−	0.0370733i
$469$	−28.0352	−	48.5585i	−1.29455	−	2.24222i
$470$	0.112174			0.00517420
$471$	20.0364			0.923230
$472$	−3.64042	−	6.30539i	−0.167564	−	0.290229i
$473$	25.7709			1.18495
$474$	−1.87380	+	3.24552i	−0.0860666	+	0.149072i
$475$	1.25384			0.0575301
$476$	−20.6138	+	35.7041i	−0.944831	+	1.63649i
$477$	16.2933	−	28.2208i	0.746017	−	1.29214i
$478$	2.04793	−	3.54712i	0.0936702	−	0.162242i
$479$	−18.5377	−	32.1083i	−0.847011	−	1.46707i	−0.883863	−	0.467746i	$-0.845066\pi$
$479$	−18.5377	−	32.1083i	−0.847011	−	1.46707i	0.0368518	−	0.999321i	$-0.488267\pi$
$480$	−8.89305			−0.405911
$481$	0.700148	+	0.851624i	0.0319240	+	0.0388307i
$482$	7.83290			0.356779
$483$	33.3375	+	57.7423i	1.51691	+	2.62736i
$484$	−6.06810	+	10.5103i	−0.275823	+	0.477739i
$485$	2.24785	−	3.89339i	0.102070	−	0.176790i
$486$	3.56592	−	6.17636i	0.161754	−	0.280165i
$487$	−18.3258			−0.830423			−0.415211	−	0.909725i	$-0.636292\pi$
$487$	−18.3258			−0.830423			−0.415211	+	0.909725i	$0.636292\pi$
$488$	7.52894	−	13.0405i	0.340819	−	0.590316i
$489$	8.64942			0.391140
$490$	−2.11471	−	3.66278i	−0.0955327	−	0.165467i
$491$	−30.5557			−1.37896			−0.689481	−	0.724304i	$-0.742161\pi$
$491$	−30.5557			−1.37896			−0.689481	+	0.724304i	$0.742161\pi$
$492$	13.3048			0.599825
$493$	−4.31759	−	7.47828i	−0.194454	−	0.336805i
$494$	0.0380565	−	0.0659159i	0.00171225	−	0.00296570i
$495$	5.78685			0.260100
$496$	6.25332	+	10.8311i	0.280782	+	0.486329i
$497$	−13.1081	−	22.7040i	−0.587981	−	1.01841i
$498$	2.88745	+	5.00120i	0.129390	+	0.224109i
$499$	7.72653	−	13.3827i	0.345887	−	0.599094i	−0.639627	−	0.768685i	$-0.720911\pi$
$499$	7.72653	−	13.3827i	0.345887	−	0.599094i	0.985515	+	0.169591i	$0.0542447\pi$
$500$	−0.943913	+	1.63491i	−0.0422131	+	0.0731152i
$501$	−6.92102	−	11.9876i	−0.309208	−	0.535564i
$502$	2.05289	+	3.55571i	0.0916250	+	0.158699i
$503$	10.8485	+	18.7901i	0.483710	+	0.837811i	0.999825	−	0.0187086i	$-0.00595549\pi$
$503$	10.8485	+	18.7901i	0.483710	+	0.837811i	−0.516115	+	0.856520i	$0.672622\pi$
$504$	15.6139			0.695498
$505$	9.57514	−	16.5846i	0.426088	−	0.738006i
$506$	−2.25567	−	3.90693i	−0.100277	−	0.173684i
$507$	30.9765			1.37571
$508$	−27.9679			−1.24087
$509$	−5.04468	−	8.73764i	−0.223601	−	0.387289i	0.732298	−	0.680985i	$-0.238448\pi$
$509$	−5.04468	−	8.73764i	−0.223601	−	0.387289i	−0.955899	+	0.293696i	$0.905115\pi$
$510$	3.94386			0.174637
$511$	27.0395	−	46.8338i	1.19616	−	2.07180i
$512$	−21.1292			−0.933789
$513$	−0.439432	+	0.761118i	−0.0194014	+	0.0336042i
$514$	1.97927	−	3.42819i	0.0873018	−	0.151211i
$515$	2.21247	−	3.83211i	0.0974930	−	0.168863i
$516$	27.1786	+	47.0747i	1.19647	+	2.07235i
$517$	−0.716090			−0.0314936
$518$	−3.17199	+	8.45004i	−0.139369	+	0.371273i
$519$	−35.9584			−1.57840
$520$	0.118003	+	0.204388i	0.00517479	+	0.00896299i
$521$	2.93802	−	5.08880i	0.128717	−	0.222944i	−0.794463	−	0.607313i	$-0.792247\pi$
$521$	2.93802	−	5.08880i	0.128717	−	0.222944i	0.923180	+	0.384368i	$0.125581\pi$
$522$	−0.793999	+	1.37525i	−0.0347524	+	0.0601929i
$523$	19.8137	−	34.3184i	0.866394	−	1.50064i	0.000736955	−	1.00000i	$-0.499765\pi$
$523$	19.8137	−	34.3184i	0.866394	−	1.50064i	0.865657	−	0.500638i	$-0.166901\pi$
$524$	−14.6331			−0.639248
$525$	5.29171	−	9.16550i	0.230949	−	0.400015i
$526$	−6.08210			−0.265192
$527$	−9.23021	−	15.9872i	−0.402074	−	0.696413i
$528$	17.0567			0.742299
$529$	16.6895			0.725629
$530$	2.01620	+	3.49216i	0.0875781	+	0.151690i
$531$	−7.56691	+	13.1063i	−0.328376	+	0.568764i
$532$	−10.4868			−0.454659
$533$	−0.267361	−	0.463083i	−0.0115807	−	0.0200584i
$534$	−5.27511	−	9.13676i	−0.228276	−	0.395386i
$535$	0.924693	+	1.60162i	0.0399780	+	0.0692439i
$536$	−8.23985	+	14.2718i	−0.355907	+	0.616450i
$537$	7.00068	−	12.1255i	0.302102	−	0.523256i
$538$	2.20511	+	3.81937i	0.0950692	+	0.164665i
$539$	13.4997	+	23.3822i	0.581475	+	1.00714i
$540$	−0.661624	−	1.14597i	−0.0284718	−	0.0493146i
$541$	5.79599			0.249189			0.124595	−	0.992208i	$-0.460237\pi$
$541$	5.79599			0.249189			0.124595	+	0.992208i	$0.460237\pi$
$542$	1.65774	−	2.87130i	0.0712062	−	0.123333i
$543$	−15.0665	−	26.0959i	−0.646565	−	1.11988i
$544$	18.3506			0.786776
$545$	9.14680			0.391806
$546$	−0.321228	−	0.556383i	−0.0137473	−	0.0238110i
$547$	4.84878			0.207319			0.103659	−	0.994613i	$-0.466945\pi$
$547$	4.84878			0.207319			0.103659	+	0.994613i	$0.466945\pi$
$548$	−2.38259	+	4.12676i	−0.101779	+	0.176286i
$549$	−31.2991			−1.33581
$550$	−0.358045	+	0.620152i	−0.0152671	+	0.0264434i
$551$	1.09824	−	1.90220i	0.0467864	−	0.0810364i
$552$	9.79825	−	16.9711i	0.417041	−	0.722336i
$553$	−10.3759	−	17.9717i	−0.441230	−	0.764233i
$554$	4.41652			0.187640
$555$	−14.3346	+	2.37945i	−0.608471	+	0.101002i
$556$	−8.83211			−0.374565
$557$	−3.47811	−	6.02427i	−0.147372	−	0.255256i	0.782883	−	0.622169i	$-0.213748\pi$
$557$	−3.47811	−	6.02427i	−0.147372	−	0.255256i	−0.930256	+	0.366912i	$0.880415\pi$
$558$	−1.69743	+	2.94003i	−0.0718577	+	0.124461i
$559$	1.09232	−	1.89195i	0.0462001	−	0.0800209i
$560$	7.39766	−	12.8131i	0.312608	−	0.541453i
$561$	−25.1766			−1.06296
$562$	−1.86265	+	3.22621i	−0.0785712	+	0.136089i
$563$	−31.5941			−1.33153			−0.665767	−	0.746160i	$-0.731895\pi$
$563$	−31.5941			−1.33153			−0.665767	+	0.746160i	$0.731895\pi$
$564$	−0.755207	−	1.30806i	−0.0317999	−	0.0550791i
$565$	−18.1487			−0.763520
$566$	2.29993			0.0966731
$567$	21.6958	+	37.5782i	0.911137	+	1.57814i
$568$	−3.85262	+	6.67294i	−0.161652	+	0.279990i
$569$	8.67259			0.363574			0.181787	−	0.983338i	$-0.441812\pi$
$569$	8.67259			0.363574			0.181787	+	0.983338i	$0.441812\pi$
$570$	0.501587	+	0.868774i	0.0210092	+	0.0363889i
$571$	−5.07464	−	8.78954i	−0.212367	−	0.367831i	0.740088	−	0.672510i	$-0.234784\pi$
$571$	−5.07464	−	8.78954i	−0.212367	−	0.367831i	−0.952455	+	0.304680i	$0.901451\pi$
$572$	−0.365784	−	0.633557i	−0.0152942	−	0.0264903i
$573$	−2.33513	+	4.04456i	−0.0975515	+	0.168964i
$574$	2.18882	−	3.79116i	0.0913598	−	0.158240i
$575$	−3.14998	−	5.45592i	−0.131363	−	0.227528i
$576$	7.35140	+	12.7330i	0.306308	+	0.530541i
$577$	−1.15161	−	1.99464i	−0.0479420	−	0.0830380i	0.841059	−	0.540944i	$-0.181933\pi$
$577$	−1.15161	−	1.99464i	−0.0479420	−	0.0830380i	−0.889001	+	0.457906i	$0.848600\pi$
$578$	−2.44437			−0.101672
$579$	−0.799518	+	1.38481i	−0.0332268	+	0.0575506i
$580$	1.65354	+	2.86402i	0.0686596	+	0.118922i
$581$	−31.9777			−1.32666
$582$	3.59692			0.149097
$583$	−12.8709	−	22.2931i	−0.533058	−	0.923284i
$584$	−15.8944			−0.657714
$585$	0.245280	−	0.424837i	0.0101411	−	0.0175649i
$586$	−10.0988			−0.417176
$587$	22.8189	−	39.5236i	0.941839	−	1.63131i	0.179878	−	0.983689i	$-0.442430\pi$
$587$	22.8189	−	39.5236i	0.941839	−	1.63131i	0.761960	−	0.647624i	$-0.224237\pi$
$588$	−28.4743	+	49.3190i	−1.17426	+	2.03388i
$589$	2.34783	−	4.06655i	0.0967405	−	0.167559i
$590$	−0.936363	−	1.62183i	−0.0385495	−	0.0667696i
$591$	59.4806			2.44671
$592$	−20.0394	+	3.32640i	−0.823615	+	0.136714i
$593$	−8.56939			−0.351903			−0.175951	−	0.984399i	$-0.556300\pi$
$593$	−8.56939			−0.351903			−0.175951	+	0.984399i	$0.556300\pi$
$594$	−0.250967	−	0.434688i	−0.0102973	−	0.0178355i
$595$	−10.9193	+	18.9128i	−0.447648	+	0.775350i
$596$	16.7064	−	28.9363i	0.684321	−	1.18528i
$597$	−25.8006	+	44.6880i	−1.05595	+	1.82896i
$598$	−0.382433			−0.0156388
$599$	15.0983	−	26.1511i	0.616901	−	1.06850i	−0.373147	−	0.927772i	$-0.621721\pi$
$599$	15.0983	−	26.1511i	0.616901	−	1.06850i	0.990048	−	0.140732i	$-0.0449455\pi$
$600$	−3.11058			−0.126989
$601$	−14.9298	−	25.8591i	−0.608997	−	1.05481i	−0.991406	−	0.130821i	$-0.958239\pi$
$601$	−14.9298	−	25.8591i	−0.608997	−	1.05481i	0.382409	−	0.923993i	$-0.375095\pi$
$602$	17.8851			0.728942
$603$	34.2545			1.39495
$604$	−0.335322	−	0.580794i	−0.0136440	−	0.0236322i
$605$	−3.21433	+	5.56739i	−0.130681	+	0.226346i
$606$	15.3218			0.622404
$607$	5.37280	+	9.30596i	0.218075	+	0.377717i	0.954219	−	0.299107i	$-0.0966889\pi$
$607$	5.37280	+	9.30596i	0.218075	+	0.377717i	−0.736144	+	0.676825i	$0.763356\pi$
$608$	2.33386	+	4.04237i	0.0946506	+	0.163940i
$609$	−9.26998	−	16.0561i	−0.375639	−	0.650625i
$610$	1.93654	−	3.35419i	0.0784084	−	0.135807i
$611$	−0.0303520	+	0.0525712i	−0.00122791	+	0.00212680i
$612$	−12.5933	−	21.8123i	−0.509055	−	0.881709i
$613$	−0.756038	−	1.30950i	−0.0305361	−	0.0528900i	0.850354	−	0.526212i	$-0.176388\pi$
$613$	−0.756038	−	1.30950i	−0.0305361	−	0.0528900i	−0.880890	+	0.473322i	$0.843055\pi$
$614$	3.63557	+	6.29699i	0.146720	+	0.254126i
$615$	7.04766			0.284189
$616$	6.16712	−	10.6818i	0.248480	−	0.430380i
$617$	6.63675	+	11.4952i	0.267186	+	0.462779i	0.968134	−	0.250433i	$-0.0805730\pi$
$617$	6.63675	+	11.4952i	0.267186	+	0.462779i	−0.700948	+	0.713212i	$0.747240\pi$
$618$	3.54031			0.142412
$619$	−18.0083			−0.723815			−0.361907	−	0.932214i	$-0.617874\pi$
$619$	−18.0083			−0.723815			−0.361907	+	0.932214i	$0.617874\pi$
$620$	3.53497	+	6.12275i	0.141968	+	0.245896i
$621$	4.41588			0.177203
$622$	−5.61507	+	9.72559i	−0.225144	+	0.389960i
$623$	58.4205			2.34057
$624$	0.722962	−	1.25221i	0.0289417	−	0.0501284i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−5.58537	+	9.67414i	−0.223236	+	0.386656i
$627$	−3.20200	−	5.54603i	−0.127876	−	0.221487i
$628$	15.8341			0.631851
$629$	29.5792	−	4.90993i	1.17940	−	0.195772i
$630$	4.01610			0.160005
$631$	11.3139	+	19.5963i	0.450399	+	0.780114i	0.998411	−	0.0563564i	$-0.0179483\pi$
$631$	11.3139	+	19.5963i	0.450399	+	0.780114i	−0.548011	+	0.836471i	$0.684615\pi$
$632$	−3.04960	+	5.28206i	−0.121307	+	0.210109i
$633$	−13.8627	+	24.0108i	−0.550991	+	0.954345i
$634$	1.23862	−	2.14534i	0.0491917	−	0.0852025i
$635$	−14.8149			−0.587910
$636$	27.1480	−	47.0217i	1.07649	−	1.86453i
$637$	2.28879			0.0906850
$638$	0.627222	+	1.08638i	0.0248319	+	0.0430102i
$639$	16.0160			0.633583
$640$	−9.26487			−0.366226
$641$	−11.4338	−	19.8040i	−0.451609	−	0.782210i	0.546877	−	0.837213i	$-0.315817\pi$
$641$	−11.4338	−	19.8040i	−0.451609	−	0.782210i	−0.998486	+	0.0550030i	$0.982483\pi$
$642$	−0.739830	+	1.28142i	−0.0291987	+	0.0505737i
$643$	−17.7885			−0.701510			−0.350755	−	0.936467i	$-0.614075\pi$
$643$	−17.7885			−0.701510			−0.350755	+	0.936467i	$0.614075\pi$
$644$	26.3456	+	45.6318i	1.03816	+	1.79815i
$645$	14.3968	+	24.9360i	0.566873	+	0.981852i
$646$	−1.03501	−	1.79270i	−0.0407221	−	0.0705327i
$647$	7.41271	−	12.8392i	0.291424	−	0.504761i	−0.682723	−	0.730677i	$-0.739204\pi$
$647$	7.41271	−	12.8392i	0.291424	−	0.504761i	0.974147	+	0.225917i	$0.0725377\pi$
$648$	6.37662	−	11.0446i	0.250497	−	0.433874i
$649$	5.97750	+	10.3533i	0.234637	+	0.406404i
$650$	0.0303520	+	0.0525712i	0.00119050	+	0.00206201i
$651$	−19.8175	−	34.3250i	−0.776710	−	1.34530i
$652$	6.83536			0.267693
$653$	7.01613	−	12.1523i	0.274562	−	0.475556i	−0.695462	−	0.718563i	$-0.744800\pi$
$653$	7.01613	−	12.1523i	0.274562	−	0.475556i	0.970025	+	0.243007i	$0.0781337\pi$
$654$	3.65909	+	6.33773i	0.143082	+	0.247825i
$655$	−7.75128			−0.302867
$656$	9.85244			0.384673
$657$	16.5189	+	28.6116i	0.644464	+	1.11624i
$658$	−0.496970			−0.0193739
$659$	0.0601313	−	0.104150i	0.00234238	−	0.00405712i	−0.864852	−	0.502027i	$-0.832588\pi$
$659$	0.0601313	−	0.104150i	0.00234238	−	0.00405712i	0.867194	+	0.497970i	$0.165921\pi$
$660$	9.64210			0.375318
$661$	0.772445	−	1.33791i	0.0300446	−	0.0520388i	−0.850612	−	0.525794i	$-0.823768\pi$
$661$	0.772445	−	1.33791i	0.0300446	−	0.0520388i	0.880657	+	0.473755i	$0.157102\pi$
$662$	−4.73246	+	8.19685i	−0.183932	+	0.318580i
$663$	−1.06713	+	1.84832i	−0.0414439	+	0.0717829i
$664$	4.69930	+	8.13942i	0.182368	+	0.315871i
$665$	−5.55495			−0.215412
$666$	−3.50175	−	4.25935i	−0.135690	−	0.165046i
$667$	−11.0362			−0.427325
$668$	−5.46945	−	9.47337i	−0.211619	−	0.366536i
$669$	24.0313	−	41.6234i	0.929102	−	1.60925i
$670$	−2.11940	+	3.67091i	−0.0818795	+	0.141819i
$671$	−12.3624	+	21.4123i	−0.477245	+	0.826613i
$672$	39.3993			1.51986
$673$	−21.9574	+	38.0313i	−0.846394	+	1.46600i	0.0380102	+	0.999277i	$0.487898\pi$
$673$	−21.9574	+	38.0313i	−0.846394	+	1.46600i	−0.884405	+	0.466721i	$0.845435\pi$
$674$	5.26642			0.202855
$675$	−0.350469	−	0.607030i	−0.0134896	−	0.0233646i
$676$	24.4797			0.941528
$677$	−14.5886			−0.560684			−0.280342	−	0.959900i	$-0.590448\pi$
$677$	−14.5886			−0.560684			−0.280342	+	0.959900i	$0.590448\pi$
$678$	−7.26020	−	12.5750i	−0.278826	−	0.482942i
$679$	−9.95875	+	17.2491i	−0.382182	+	0.661958i
$680$	6.41861			0.246142
$681$	−11.5029	−	19.9236i	−0.440791	−	0.763473i
$682$	1.34089	+	2.32248i	0.0513451	+	0.0889324i
$683$	1.29256	+	2.23878i	0.0494585	+	0.0856646i	0.889695	−	0.456556i	$-0.150917\pi$
$683$	1.29256	+	2.23878i	0.0494585	+	0.0856646i	−0.840236	+	0.542220i	$0.817584\pi$
$684$	3.20328	−	5.54824i	0.122480	−	0.212142i
$685$	−1.26208	+	2.18598i	−0.0482216	+	0.0835222i
$686$	4.17548	+	7.23214i	0.159420	+	0.276124i
$687$	−9.36043	−	16.2127i	−0.357123	−	0.618555i
$688$	20.1263	+	34.8598i	0.767308	+	1.32902i
$689$	−2.18217			−0.0831341
$690$	2.52024	−	4.36518i	0.0959438	−	0.166180i
$691$	8.86369	+	15.3524i	0.337191	+	0.584031i	0.983903	−	0.178703i	$-0.0571900\pi$
$691$	8.86369	+	15.3524i	0.337191	+	0.584031i	−0.646713	+	0.762734i	$0.723857\pi$
$692$	−28.4167			−1.08024
$693$	−25.6378			−0.973898
$694$	−2.59145	−	4.48852i	−0.0983701	−	0.170382i
$695$	−4.67846			−0.177464
$696$	−2.72455	+	4.71905i	−0.103274	+	0.178875i
$697$	−14.5427			−0.550844
$698$	−0.542106	+	0.938954i	−0.0205190	+	0.0355399i
$699$	−12.7993	+	22.1691i	−0.484115	+	0.838512i
$700$	4.18186	−	7.24320i	0.158060	−	0.273767i
$701$	1.76799	+	3.06224i	0.0667760	+	0.115659i	0.897480	−	0.441054i	$-0.145395\pi$
$701$	1.76799	+	3.06224i	0.0667760	+	0.115659i	−0.830704	+	0.556714i	$0.812062\pi$
$702$	−0.0425497			−0.00160594
$703$	4.84351	+	5.89140i	0.182677	+	0.222198i
$704$	11.6145			0.437738
$705$	−0.400041	−	0.692891i	−0.0150664	−	0.0260958i
$706$	−0.427559	+	0.740554i	−0.0160914	+	0.0278711i
$707$	−42.4212	+	73.4756i	−1.59541	+	2.76334i
$708$	−12.6081	+	21.8378i	−0.473840	+	0.820714i
$709$	17.1968			0.645839			0.322920	−	0.946426i	$-0.395336\pi$
$709$	17.1968			0.645839			0.322920	+	0.946426i	$0.395336\pi$
$710$	−0.990945	+	1.71637i	−0.0371895	+	0.0644141i
$711$	12.6777			0.475451
$712$	−8.58520	−	14.8700i	−0.321744	−	0.557277i
$713$	−23.5935			−0.883582
$714$	−17.4727			−0.653899
$715$	−0.193759	−	0.335601i	−0.00724619	−	0.0125508i
$716$	5.53241	−	9.58242i	0.206756	−	0.358112i
$717$	−29.2138			−1.09101
$718$	0.974776	+	1.68836i	0.0363783	+	0.0630091i
$719$	13.4572	+	23.3085i	0.501868	+	0.869261i	0.999998	+	0.00215861i	$0.000687109\pi$
$719$	13.4572	+	23.3085i	0.501868	+	0.869261i	−0.498129	+	0.867103i	$0.665980\pi$
$720$	4.51936	+	7.82777i	0.168427	+	0.291724i
$721$	−9.80201	+	16.9776i	−0.365046	+	0.632278i
$722$	−2.91851	+	5.05500i	−0.108616	+	0.188128i
$723$	−27.9341	−	48.3833i	−1.03888	−	1.79939i
$724$	−11.9066	−	20.6228i	−0.442504	−	0.766439i
$725$	0.875898	+	1.51710i	0.0325300	+	0.0563436i
$726$	−5.14345			−0.190891
$727$	−9.13049	+	15.8145i	−0.338631	+	0.586526i	−0.984176	−	0.177196i	$-0.943297\pi$
$727$	−9.13049	+	15.8145i	−0.338631	+	0.586526i	0.645544	+	0.763723i	$0.276631\pi$
$728$	−0.522796	−	0.905509i	−0.0193761	−	0.0335604i
$729$	−21.4854			−0.795755
$730$	−4.08824			−0.151313
$731$	−29.7074	−	51.4548i	−1.09877	−	1.90312i
$732$	−52.1508			−1.92755
$733$	−2.92592	+	5.06785i	−0.108071	+	0.187185i	−0.914989	−	0.403479i	$-0.867801\pi$
$733$	−2.92592	+	5.06785i	−0.108071	+	0.187185i	0.806917	+	0.590664i	$0.201134\pi$
$734$	−1.06480			−0.0393024
$735$	−15.0831	+	26.1248i	−0.556350	+	0.963626i
$736$	11.7266	−	20.3110i	0.432247	−	0.748673i
$737$	13.5297	−	23.4341i	0.498373	−	0.863207i
$738$	1.33719	+	2.31608i	0.0492227	+	0.0852563i
$739$	−23.9849			−0.882298			−0.441149	−	0.897434i	$-0.645429\pi$
$739$	−23.9849			−0.882298			−0.441149	+	0.897434i	$0.645429\pi$
$740$	−11.3282	+	1.88040i	−0.416433	+	0.0691248i
$741$	−0.542877			−0.0199431
$742$	−8.93246	−	15.4715i	−0.327921	−	0.567976i
$743$	−3.88794	+	6.73411i	−0.142635	+	0.247051i	−0.928488	−	0.371362i	$-0.878891\pi$
$743$	−3.88794	+	6.73411i	−0.142635	+	0.247051i	0.785853	+	0.618413i	$0.212224\pi$
$744$	−5.82458	+	10.0885i	−0.213540	+	0.369861i
$745$	8.84954	−	15.3279i	0.324222	−	0.561569i
$746$	−6.10235			−0.223423
$747$	9.76788	−	16.9185i	0.357388	−	0.619015i
$748$	−19.8963			−0.727479
$749$	−4.09671	−	7.09571i	−0.149691	−	0.259272i
$750$	−0.800081			−0.0292148
$751$	−3.71415			−0.135531			−0.0677657	−	0.997701i	$-0.521587\pi$
$751$	−3.71415			−0.135531			−0.0677657	+	0.997701i	$0.521587\pi$
$752$	−0.559246	−	0.968642i	−0.0203936	−	0.0353227i
$753$	14.6422	−	25.3611i	0.533593	−	0.924210i
$754$	0.106341			0.00387271
$755$	−0.177623	−	0.307652i	−0.00646437	−	0.0111966i
$756$	2.93122	+	5.07703i	0.106608	+	0.184650i
$757$	−4.22993	−	7.32646i	−0.153740	−	0.266285i	0.778860	−	0.627198i	$-0.215798\pi$
$757$	−4.22993	−	7.32646i	−0.153740	−	0.266285i	−0.932599	+	0.360913i	$0.882465\pi$
$758$	−3.45741	+	5.98840i	−0.125579	+	0.217509i
$759$	−16.0886	+	27.8662i	−0.583978	+	1.01148i
$760$	0.816328	+	1.41392i	0.0296113	+	0.0512884i
$761$	17.5451	+	30.3890i	0.636009	+	1.10160i	0.986300	+	0.164959i	$0.0527492\pi$
$761$	17.5451	+	30.3890i	0.636009	+	1.10160i	−0.350291	+	0.936641i	$0.613917\pi$
$762$	−5.92655	−	10.2651i	−0.214696	−	0.371865i
$763$	−40.5235			−1.46705
$764$	−1.84538	+	3.19629i	−0.0667634	+	0.115638i
$765$	−6.67081	−	11.5542i	−0.241184	−	0.417742i
$766$	−1.94719			−0.0703547
$767$	1.01344			0.0365933
$768$	9.27046	+	16.0569i	0.334519	+	0.579404i
$769$	−10.3177			−0.372067			−0.186034	−	0.982543i	$-0.559563\pi$
$769$	−10.3177			−0.372067			−0.186034	+	0.982543i	$0.559563\pi$
$770$	1.58626	−	2.74749i	0.0571650	−	0.0990126i
$771$	−28.2343			−1.01683
$772$	−0.631833	+	1.09437i	−0.0227402	+	0.0393871i
$773$	−20.1066	+	34.8257i	−0.723186	+	1.25259i	0.236531	+	0.971624i	$0.423990\pi$
$773$	−20.1066	+	34.8257i	−0.723186	+	1.25259i	−0.959716	+	0.280971i	$0.909344\pi$
$774$	−5.46316	+	9.46248i	−0.196369	+	0.340122i
$775$	1.87251	+	3.24328i	0.0672625	+	0.116502i
$776$	5.85396			0.210145
$777$	63.5074	−	10.5418i	2.27832	−	0.378184i
$778$	8.57848			0.307553
$779$	−1.84956	−	3.20354i	−0.0662675	−	0.114779i
$780$	0.408687	−	0.707867i	0.0146334	−	0.0253457i
$781$	6.32594	−	10.9568i	0.226360	−	0.392067i
$782$	−5.20046	+	9.00746i	−0.185968	+	0.322106i
$783$	−1.22790			−0.0438815
$784$	−21.0858	+	36.5217i	−0.753065	+	1.30435i
$785$	8.38750			0.299363
$786$	−3.10082	−	5.37079i	−0.110603	−	0.191570i
$787$	31.0424			1.10654			0.553272	−	0.833001i	$-0.313379\pi$
$787$	31.0424			1.10654			0.553272	+	0.833001i	$0.313379\pi$
$788$	47.0056			1.67450
$789$	21.6903	+	37.5687i	0.772195	+	1.33748i
$790$	−0.784397	+	1.35862i	−0.0279076	+	0.0483374i
$791$	80.4049			2.85887
$792$	3.76760	+	6.52568i	0.133876	+	0.231880i
$793$	1.04798	+	1.81515i	0.0372148	+	0.0644580i
$794$	−4.38315	−	7.59184i	−0.155552	−	0.269424i
$795$	14.3805	−	24.9078i	0.510025	−	0.883390i
$796$	−20.3894	+	35.3155i	−0.722683	+	1.25172i
$797$	20.7314	+	35.9079i	0.734346	+	1.27192i	0.955010	+	0.296574i	$0.0958441\pi$
$797$	20.7314	+	35.9079i	0.734346	+	1.27192i	−0.220664	+	0.975350i	$0.570823\pi$
$798$	−2.22220	−	3.84897i	−0.0786651	−	0.136252i
$799$	0.825475	+	1.42976i	0.0292032	+	0.0505814i
$800$	−3.72274			−0.131619
$801$	−17.8451	+	30.9086i	−0.630524	+	1.09210i
$802$	−0.344743	−	0.597112i	−0.0121733	−	0.0210848i
$803$	26.0983			0.920989
$804$	57.0751			2.01288
$805$	13.9555	+	24.1716i	0.491867	+	0.851938i
$806$	0.227338			0.00800763
$807$	15.7280	−	27.2416i	0.553651	−	0.958951i
$808$	24.9361			0.877248
$809$	−3.71881	+	6.44116i	−0.130746	+	0.226459i	−0.923964	−	0.382478i	$-0.875071\pi$
$809$	−3.71881	+	6.44116i	−0.130746	+	0.226459i	0.793218	+	0.608938i	$0.208404\pi$
$810$	1.64015	−	2.84082i	0.0576290	−	0.0998164i
$811$	−6.27095	+	10.8616i	−0.220203	+	0.381402i	−0.954869	−	0.297026i	$-0.904005\pi$
$811$	−6.27095	+	10.8616i	−0.220203	+	0.381402i	0.734667	+	0.678428i	$0.237339\pi$
$812$	−7.32577	−	12.6886i	−0.257084	−	0.445283i
$813$	−23.6477			−0.829362
$814$	−4.29701	+	0.713272i	−0.150610	+	0.0250002i
$815$	3.62076			0.126830
$816$	−19.6622	−	34.0559i	−0.688315	−	1.19220i
$817$	7.55648	−	13.0882i	0.264368	−	0.457898i
$818$	2.78643	−	4.82625i	0.0974254	−	0.168746i
$819$	−1.08668	+	1.88218i	−0.0379715	+	0.0657686i
$820$	5.56954			0.194497
$821$	−3.53505	+	6.12288i	−0.123374	+	0.213690i	−0.921096	−	0.389335i	$-0.872705\pi$
$821$	−3.53505	+	6.12288i	−0.123374	+	0.213690i	0.797722	+	0.603025i	$0.206038\pi$
$822$	−2.01953			−0.0704392
$823$	−9.52287	−	16.4941i	−0.331946	−	0.574948i	0.650947	−	0.759123i	$-0.274372\pi$
$823$	−9.52287	−	16.4941i	−0.331946	−	0.574948i	−0.982893	+	0.184175i	$0.941039\pi$
$824$	5.76183			0.200723
$825$	5.10751			0.177821
$826$	4.14841	+	7.18526i	0.144342	+	0.250007i
$827$	14.5656	−	25.2283i	0.506495	−	0.877275i	−0.493477	−	0.869759i	$-0.664274\pi$
$827$	14.5656	−	25.2283i	0.506495	−	0.877275i	0.999972	−	0.00751613i	$-0.00239248\pi$
$828$	−32.1899			−1.11868
$829$	20.7804	+	35.9926i	0.721732	+	1.25008i	0.960305	+	0.278952i	$0.0899869\pi$
$829$	20.7804	+	35.9926i	0.721732	+	1.25008i	−0.238573	+	0.971124i	$0.576680\pi$
$830$	1.20872	+	2.09357i	0.0419553	+	0.0726687i
$831$	−15.7504	−	27.2805i	−0.546376	−	0.946351i
$832$	0.492289	−	0.852670i	0.0170671	−	0.0295610i
$833$	31.1237	−	53.9079i	1.07837	−	1.86780i
$834$	−1.87157	−	3.24166i	−0.0648072	−	0.112249i
$835$	−2.89722	−	5.01814i	−0.100263	−	0.173660i
$836$	−2.53044	−	4.38285i	−0.0875170	−	0.151584i
$837$	−2.62502			−0.0907341
$838$	−0.508839	+	0.881335i	−0.0175776	+	0.0304452i
$839$	−12.4449	−	21.5553i	−0.429647	−	0.744170i	0.567195	−	0.823584i	$-0.308029\pi$
$839$	−12.4449	−	21.5553i	−0.429647	−	0.744170i	−0.996842	+	0.0794133i	$0.974695\pi$
$840$	13.7809			0.475487
$841$	−25.9312			−0.894180
$842$	−4.17115	−	7.22464i	−0.143747	−	0.248978i
$843$	26.5707			0.915144
$844$	−10.9552	+	18.9750i	−0.377094	+	0.653146i
$845$	12.9671			0.446084
$846$	0.151804	−	0.262932i	0.00521912	−	0.00903979i
$847$	14.2406	−	24.6655i	0.489313	−	0.847515i
$848$	20.1036	−	34.8205i	0.690361	−	1.19574i
$849$	−8.20211	−	14.2065i	−0.281496	−	0.487565i
$850$	1.65095			0.0566271
$851$	13.4675	−	35.8767i	0.461659	−	1.22984i
$852$	26.6860			0.914247
$853$	−19.4733	−	33.7287i	−0.666752	−	1.15485i	−0.978807	−	0.204785i	$-0.934351\pi$
$853$	−19.4733	−	33.7287i	−0.666752	−	1.15485i	0.312055	−	0.950064i	$-0.398983\pi$
$854$	−8.57956	+	14.8602i	−0.293587	+	0.508507i
$855$	1.69681	−	2.93896i	0.0580296	−	0.100510i
$856$	−1.20407	+	2.08550i	−0.0411542	+	0.0712811i
$857$	4.63879			0.158458			0.0792290	−	0.996856i	$-0.474754\pi$
$857$	4.63879			0.158458			0.0792290	+	0.996856i	$0.474754\pi$
$858$	0.155023	−	0.268508i	0.00529241	−	0.00916672i
$859$	33.1569			1.13130			0.565649	−	0.824646i	$-0.308626\pi$
$859$	33.1569			1.13130			0.565649	+	0.824646i	$0.308626\pi$
$860$	11.3773	+	19.7061i	0.387963	+	0.671971i
$861$	−31.2236			−1.06410
$862$	1.68990			0.0575582
$863$	6.85507	+	11.8733i	0.233349	+	0.404173i	0.958792	−	0.284110i	$-0.0916982\pi$
$863$	6.85507	+	11.8733i	0.233349	+	0.404173i	−0.725442	+	0.688283i	$0.758365\pi$
$864$	1.30471	−	2.25982i	0.0443870	−	0.0768805i
$865$	−15.0526			−0.511805
$866$	3.50981	+	6.07917i	0.119268	+	0.206579i
$867$	8.71723	+	15.0987i	0.296053	+	0.512778i
$868$	−15.6612	−	27.1259i	−0.531574	−	0.920713i
$869$	5.00739	−	8.67305i	0.169864	−	0.294213i
$870$	−0.700789	+	1.21380i	−0.0237590	+	0.0411518i
$871$	−1.14693	−	1.98655i	−0.0388623	−	0.0673115i
$872$	5.95514	+	10.3146i	0.201667	+	0.349297i
$873$	−6.08398	−	10.5378i	−0.205911	−	0.356649i
$874$	−2.64561			−0.0894891
$875$	2.21517	−	3.83679i	0.0748865	−	0.129707i
$876$	27.5239	+	47.6729i	0.929948	+	1.61072i
$877$	−51.3567			−1.73419			−0.867096	−	0.498141i	$-0.834016\pi$
$877$	−51.3567			−1.73419			−0.867096	+	0.498141i	$0.834016\pi$
$878$	0.273897			0.00924359
$879$	36.0147	+	62.3793i	1.21475	+	2.10400i
$880$	7.14016			0.240695
$881$	−17.8394	+	30.8987i	−0.601024	+	1.04100i	0.391642	+	0.920118i	$0.371907\pi$
$881$	−17.8394	+	30.8987i	−0.601024	+	1.04100i	−0.992666	+	0.120887i	$0.961426\pi$
$882$	−11.4472			−0.385448
$883$	−0.886492	+	1.53545i	−0.0298328	+	0.0516720i	−0.880556	−	0.473941i	$-0.842831\pi$
$883$	−0.886492	+	1.53545i	−0.0298328	+	0.0516720i	0.850724	+	0.525613i	$0.176164\pi$
$884$	−0.843317	+	1.46067i	−0.0283638	+	0.0491276i
$885$	−6.67861	+	11.5677i	−0.224499	+	0.388844i
$886$	0.207360	+	0.359158i	0.00696640	+	0.0120662i
$887$	17.3058			0.581072			0.290536	−	0.956864i	$-0.406166\pi$
$887$	17.3058			0.581072			0.290536	+	0.956864i	$0.406166\pi$
$888$	−12.0160	−	14.6156i	−0.403230	−	0.490468i
$889$	65.6350			2.20133
$890$	−2.20823	−	3.82476i	−0.0740199	−	0.128206i
$891$	−10.4703	+	18.1351i	−0.350768	+	0.607548i
$892$	18.9911	−	32.8936i	0.635870	−	1.10136i
$893$	−0.209970	+	0.363679i	−0.00702639	+	0.0121701i
$894$	14.1607			0.473605
$895$	2.93057	−	5.07590i	0.0979582	−	0.169669i
$896$	41.0466			1.37127
$897$	1.36385	+	2.36226i	0.0455377	+	0.0788735i
$898$	−2.21455			−0.0739006
$899$	6.56050			0.218805
$900$	2.55477	+	4.42500i	0.0851592	+	0.147500i
$901$	−29.6739	+	51.3968i	−0.988582	+	1.71227i
$902$	2.11264			0.0703431
$903$	−63.7827	−	110.475i	−2.12256	−	3.67638i
$904$	−11.8159	−	20.4658i	−0.392992	−	0.680682i
$905$	−6.30702	−	10.9241i	−0.209652	−	0.363129i
$906$	0.142113	−	0.246147i	0.00472139	−	0.00817768i
$907$	−14.2058	+	24.6051i	−0.471695	+	0.816999i	−0.999476	−	0.0323815i	$-0.989691\pi$
$907$	−14.2058	+	24.6051i	−0.471695	+	0.816999i	0.527781	+	0.849381i	$0.323024\pi$
$908$	−9.09035	−	15.7450i	−0.301674	−	0.522515i
$909$	−25.9159	−	44.8876i	−0.859575	−	1.48883i
$910$	−0.134470	−	0.232909i	−0.00445763	−	0.00772085i
$911$	−47.0535			−1.55895			−0.779476	−	0.626433i	$-0.784514\pi$
$911$	−47.0535			−1.55895			−0.779476	+	0.626433i	$0.784514\pi$
$912$	5.00134	−	8.66258i	0.165611	−	0.286847i
$913$	−7.71616	−	13.3648i	−0.255368	−	0.442310i
$914$	−2.13829			−0.0707284
$915$	−27.6248			−0.913248
$916$	−7.39724	−	12.8124i	−0.244412	−	0.423334i
$917$	34.3408			1.13403
$918$	−0.578606	+	1.00218i	−0.0190969	+	0.0330767i
$919$	8.35104			0.275475			0.137738	−	0.990469i	$-0.456017\pi$
$919$	8.35104			0.275475			0.137738	+	0.990469i	$0.456017\pi$
$920$	4.10167	−	7.10430i	0.135228	−	0.234222i
$921$	25.9307	−	44.9133i	0.854446	−	1.47994i
$922$	−5.93587	+	10.2812i	−0.195488	+	0.338594i
$923$	−0.536259	−	0.928828i	−0.0176512	−	0.0305727i
$924$	−42.7178			−1.40531
$925$	−6.00065	+	0.996065i	−0.197300	+	0.0327504i
$926$	−4.17326			−0.137142
$927$	−5.98822	−	10.3719i	−0.196679	−	0.340658i
$928$	−3.26074	+	5.64777i	−0.107039	+	0.185397i
$929$	1.56597	−	2.71234i	0.0513779	−	0.0889891i	−0.839193	−	0.543834i	$-0.816972\pi$
$929$	1.56597	−	2.71234i	0.0513779	−	0.0889891i	0.890571	+	0.454845i	$0.150305\pi$
$930$	−1.49816	+	2.59489i	−0.0491266	+	0.0850897i
$931$	15.8335			0.518921
$932$	−10.1149	+	17.5195i	−0.331324	+	0.573870i
$933$	80.0990			2.62232
$934$	5.96314	+	10.3285i	0.195120	+	0.337957i
$935$	−10.5392			−0.344670
$936$	0.638771			0.0208789
$937$	1.82786	+	3.16595i	0.0597136	+	0.103427i	0.894337	−	0.447394i	$-0.147648\pi$
$937$	1.82786	+	3.16595i	0.0597136	+	0.103427i	−0.834623	+	0.550821i	$0.814315\pi$
$938$	9.38967	−	16.2634i	0.306584	−	0.531019i
$939$	79.6753			2.60010
$940$	−0.316139	−	0.547569i	−0.0103113	−	0.0178597i
$941$	−6.23199	−	10.7941i	−0.203157	−	0.351879i	0.746387	−	0.665512i	$-0.231787\pi$
$941$	−6.23199	−	10.7941i	−0.203157	−	0.351879i	−0.949544	+	0.313634i	$0.898454\pi$
$942$	3.35534	+	5.81162i	0.109323	+	0.189353i
$943$	−9.29319	+	16.0963i	−0.302628	+	0.524167i
$944$	−9.33651	+	16.1713i	−0.303878	+	0.526331i
$945$	1.55270	+	2.68935i	0.0505093	+	0.0874847i
$946$	4.31564	+	7.47490i	0.140314	+	0.243030i
$947$	−7.17885	−	12.4341i	−0.233281	−	0.404055i	0.725490	−	0.688232i	$-0.241613\pi$
$947$	−7.17885	−	12.4341i	−0.233281	−	0.404055i	−0.958772	+	0.284177i	$0.908280\pi$
$948$	21.1237			0.686065
$949$	1.10620	−	1.91599i	0.0359086	−	0.0621956i
$950$	0.209970	+	0.363679i	0.00681234	+	0.0117993i
$951$	−17.6688			−0.572952
$952$	−28.4367			−0.921637
$953$	18.3278	+	31.7447i	0.593695	+	1.02831i	0.993730	+	0.111810i	$0.0356648\pi$
$953$	18.3278	+	31.7447i	0.593695	+	1.02831i	−0.400034	+	0.916500i	$0.631002\pi$
$954$	10.9140			0.353354
$955$	−0.977514	+	1.69310i	−0.0316316	+	0.0547876i
$956$	−23.0867			−0.746677
$957$	4.47366	−	7.74860i	0.144613	−	0.250477i
$958$	6.20873	−	10.7538i	0.200595	−	0.347441i
$959$	5.59145	−	9.68467i	0.180557	−	0.312734i
$960$	6.48839	+	11.2382i	0.209412	+	0.362712i
$961$	−16.9748			−0.547575
$962$	−0.129768	+	0.345694i	−0.00418387	+	0.0111456i
$963$	5.00551			0.161300
$964$	−22.0754	−	38.2357i	−0.711001	−	1.23149i
$965$	−0.334688	+	0.579697i	−0.0107740	+	0.0186611i
$966$	−11.1655	+	19.3393i	−0.359245	+	0.622231i
$967$	−6.35194	+	11.0019i	−0.204265	+	0.353797i	−0.949898	−	0.312559i	$-0.898814\pi$
$967$	−6.35194	+	11.0019i	−0.204265	+	0.353797i	0.745633	+	0.666356i	$0.232147\pi$
$968$	−8.37093			−0.269052
$969$	−7.38223	+	12.7864i	−0.237151	+	0.410758i
$970$	1.50572			0.0483456
$971$	14.2760	+	24.7267i	0.458138	+	0.793519i	0.998863	−	0.0476812i	$-0.0151831\pi$
$971$	14.2760	+	24.7267i	0.458138	+	0.793519i	−0.540724	+	0.841200i	$0.681850\pi$
$972$	−40.1992			−1.28939
$973$	20.7272			0.664483
$974$	−3.06888	−	5.31545i	−0.0983332	−	0.170318i
$975$	0.216486	−	0.374964i	0.00693309	−	0.0120085i
$976$	−38.6187			−1.23615
$977$	−22.7323	−	39.3736i	−0.727272	−	1.25967i	−0.958032	−	0.286661i	$-0.907455\pi$
$977$	−22.7323	−	39.3736i	−0.727272	−	1.25967i	0.230760	−	0.973011i	$-0.425879\pi$
$978$	1.44845	+	2.50879i	0.0463163	+	0.0802222i
$979$	14.0967	+	24.4163i	0.450534	+	0.780348i
$980$	−11.9197	+	20.6455i	−0.380761	+	0.659498i
$981$	12.3783	−	21.4398i	0.395208	−	0.684520i
$982$	−5.11692	−	8.86277i	−0.163288	−	0.282822i
$983$	−16.9637	−	29.3820i	−0.541059	−	0.937141i	−0.998844	−	0.0480781i	$-0.984690\pi$
$983$	−16.9637	−	29.3820i	−0.541059	−	0.937141i	0.457785	−	0.889063i	$-0.348643\pi$
$984$	4.58847	+	7.94746i	0.146275	+	0.253356i
$985$	24.8993			0.793358
$986$	1.44606	−	2.50465i	0.0460520	−	0.0797644i
$987$	1.77232	+	3.06975i	0.0564135	+	0.0977111i
$988$	−0.429018			−0.0136489
$989$	−75.9355			−2.41461
$990$	0.969077	+	1.67849i	0.0307993	+	0.0533459i
$991$	2.27283			0.0721987			0.0360993	−	0.999348i	$-0.488507\pi$
$991$	2.27283			0.0721987			0.0360993	+	0.999348i	$0.488507\pi$
$992$	−6.97087	+	12.0739i	−0.221325	+	0.383347i
$993$	67.5085			2.14232
$994$	4.39023	−	7.60410i	0.139250	−	0.241187i
$995$	−10.8005	+	18.7069i	−0.342398	+	0.593050i
$996$	16.2753	−	28.1897i	0.515703	−	0.893225i
$997$	−1.78555	−	3.09267i	−0.0565491	−	0.0979459i	0.836365	−	0.548173i	$-0.184676\pi$
$997$	−1.78555	−	3.09267i	−0.0565491	−	0.0979459i	−0.892914	+	0.450227i	$0.851343\pi$
$998$	5.17560			0.163831
$999$	1.49840	−	3.99167i	0.0474073	−	0.126291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.e.b.26.4	✓	14
5.2	odd	4		925.2.o.c.174.6		28
5.3	odd	4		925.2.o.c.174.9		28
5.4	even	2		925.2.e.b.26.4		14
37.10	even	3	inner	185.2.e.b.121.4	yes	14
37.11	even	6		6845.2.a.m.1.4		7
37.26	even	3		6845.2.a.j.1.4		7
185.47	odd	12		925.2.o.c.824.9		28
185.84	even	6		925.2.e.b.676.4		14
185.158	odd	12		925.2.o.c.824.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.e.b.26.4	✓	14	1.1	even	1	trivial
185.2.e.b.121.4	yes	14	37.10	even	3	inner
925.2.e.b.26.4		14	5.4	even	2
925.2.e.b.676.4		14	185.84	even	6
925.2.o.c.174.6		28	5.2	odd	4
925.2.o.c.174.9		28	5.3	odd	4
925.2.o.c.824.6		28	185.158	odd	12
925.2.o.c.824.9		28	185.47	odd	12
6845.2.a.j.1.4		7	37.26	even	3
6845.2.a.m.1.4		7	37.11	even	6

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:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.167462 + 0.290053i) q^{2} +(1.19442 - 2.06880i) q^{3} +(0.943913 - 1.63491i) q^{4} +(0.500000 - 0.866025i) q^{5} +0.800081 q^{6} +(-2.21517 + 3.83679i) q^{7} +1.30213 q^{8} +(-1.35329 - 2.34397i) q^{9} +O(q^{10})\)	\(q+(0.167462 + 0.290053i) q^{2} +(1.19442 - 2.06880i) q^{3} +(0.943913 - 1.63491i) q^{4} +(0.500000 - 0.866025i) q^{5} +0.800081 q^{6} +(-2.21517 + 3.83679i) q^{7} +1.30213 q^{8} +(-1.35329 - 2.34397i) q^{9} +0.334924 q^{10} -2.13807 q^{11} +(-2.25486 - 3.90553i) q^{12} +(-0.0906236 + 0.156965i) q^{13} -1.48383 q^{14} +(-1.19442 - 2.06880i) q^{15} +(-1.66977 - 2.89213i) q^{16} +(2.46466 + 4.26892i) q^{17} +(0.453249 - 0.785050i) q^{18} +(-0.626920 + 1.08586i) q^{19} +(-0.943913 - 1.63491i) q^{20} +(5.29171 + 9.16550i) q^{21} +(-0.358045 - 0.620152i) q^{22} +6.29996 q^{23} +(1.55529 - 2.69384i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.0607040 q^{26} +0.700938 q^{27} +(4.18186 + 7.24320i) q^{28} -1.75180 q^{29} +(0.400041 - 0.692891i) q^{30} -3.74502 q^{31} +(1.86137 - 3.22399i) q^{32} +(-2.55376 + 4.42324i) q^{33} +(-0.825475 + 1.42976i) q^{34} +(2.21517 + 3.83679i) q^{35} -5.10955 q^{36} +(2.13771 - 5.69475i) q^{37} -0.419941 q^{38} +(0.216486 + 0.374964i) q^{39} +(0.651063 - 1.12767i) q^{40} +(-1.47512 + 2.55498i) q^{41} +(-1.77232 + 3.06975i) q^{42} -12.0533 q^{43} +(-2.01815 + 3.49554i) q^{44} -2.70658 q^{45} +(1.05500 + 1.82732i) q^{46} +0.334924 q^{47} -7.97764 q^{48} +(-6.31399 - 10.9361i) q^{49} +(0.167462 - 0.290053i) q^{50} +11.7754 q^{51} +(0.171082 + 0.296322i) q^{52} +(6.01987 + 10.4267i) q^{53} +(0.117380 + 0.203309i) q^{54} +(-1.06903 + 1.85162i) q^{55} +(-2.88443 + 4.99599i) q^{56} +(1.49761 + 2.59394i) q^{57} +(-0.293359 - 0.508113i) q^{58} +(-2.79575 - 4.84238i) q^{59} -4.50972 q^{60} +(5.78204 - 10.0148i) q^{61} +(-0.627148 - 1.08625i) q^{62} +11.9911 q^{63} -5.43224 q^{64} +(0.0906236 + 0.156965i) q^{65} -1.71063 q^{66} +(-6.32800 + 10.9604i) q^{67} +9.30571 q^{68} +(7.52481 - 13.0334i) q^{69} +(-0.741914 + 1.28503i) q^{70} +(-2.95872 + 5.12465i) q^{71} +(-1.76215 - 3.05214i) q^{72} -12.2065 q^{73} +(2.00976 - 0.333606i) q^{74} -2.38884 q^{75} +(1.18352 + 2.04991i) q^{76} +(4.73619 - 8.20333i) q^{77} +(-0.0725062 + 0.125584i) q^{78} +(-2.34202 + 4.05649i) q^{79} -3.33954 q^{80} +(4.89708 - 8.48200i) q^{81} -0.988105 q^{82} +(3.60894 + 6.25087i) q^{83} +19.9796 q^{84} +4.92933 q^{85} +(-2.01848 - 3.49610i) q^{86} +(-2.09238 + 3.62411i) q^{87} -2.78403 q^{88} +(-6.59322 - 11.4198i) q^{89} +(-0.453249 - 0.785050i) q^{90} +(-0.401494 - 0.695408i) q^{91} +(5.94661 - 10.2998i) q^{92} +(-4.47313 + 7.74769i) q^{93} +(0.0560870 + 0.0971455i) q^{94} +(0.626920 + 1.08586i) q^{95} +(-4.44653 - 7.70161i) q^{96} +4.49570 q^{97} +(2.11471 - 3.66278i) q^{98} +(2.89342 + 5.01156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9} + 4 q^{10} - 10 q^{11} - 8 q^{12} + 6 q^{13} - 36 q^{14} + 2 q^{15} - 14 q^{16} - q^{17} - 4 q^{18} + 6 q^{19} + 8 q^{20} + 13 q^{21} - q^{22} + 12 q^{23} - 21 q^{24} - 7 q^{25} + 2 q^{26} + 22 q^{27} + 13 q^{28} - 12 q^{29} + 2 q^{30} - 8 q^{31} + 18 q^{32} + q^{33} - 11 q^{34} - 2 q^{35} - 8 q^{36} + 12 q^{37} + 16 q^{38} + 23 q^{39} - 3 q^{40} - 3 q^{41} + 29 q^{42} - 38 q^{43} + 25 q^{44} - 10 q^{45} + 10 q^{46} + 4 q^{47} - 20 q^{48} - 7 q^{49} + 2 q^{50} - 14 q^{51} + 46 q^{52} - 2 q^{53} + 23 q^{54} - 5 q^{55} + 19 q^{56} + 22 q^{57} - 12 q^{58} - 18 q^{59} - 16 q^{60} - 20 q^{61} - 21 q^{62} + 46 q^{63} + 50 q^{64} - 6 q^{65} - 42 q^{66} - 20 q^{67} + 110 q^{68} + 17 q^{69} - 18 q^{70} - 11 q^{71} - 29 q^{72} - 36 q^{73} - 66 q^{74} + 4 q^{75} + 40 q^{76} - q^{77} + 6 q^{78} + 23 q^{79} - 28 q^{80} + 29 q^{81} - 24 q^{82} - 9 q^{83} + 8 q^{84} - 2 q^{85} - 3 q^{86} - 43 q^{87} - 116 q^{88} - 16 q^{89} + 4 q^{90} + 12 q^{91} - 33 q^{92} + 25 q^{93} + 22 q^{94} - 6 q^{95} - 67 q^{96} - 62 q^{97} - 24 q^{98} + 4 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9 + 4 * q^10 - 10 * q^11 - 8 * q^12 + 6 * q^13 - 36 * q^14 + 2 * q^15 - 14 * q^16 - q^17 - 4 * q^18 + 6 * q^19 + 8 * q^20 + 13 * q^21 - q^22 + 12 * q^23 - 21 * q^24 - 7 * q^25 + 2 * q^26 + 22 * q^27 + 13 * q^28 - 12 * q^29 + 2 * q^30 - 8 * q^31 + 18 * q^32 + q^33 - 11 * q^34 - 2 * q^35 - 8 * q^36 + 12 * q^37 + 16 * q^38 + 23 * q^39 - 3 * q^40 - 3 * q^41 + 29 * q^42 - 38 * q^43 + 25 * q^44 - 10 * q^45 + 10 * q^46 + 4 * q^47 - 20 * q^48 - 7 * q^49 + 2 * q^50 - 14 * q^51 + 46 * q^52 - 2 * q^53 + 23 * q^54 - 5 * q^55 + 19 * q^56 + 22 * q^57 - 12 * q^58 - 18 * q^59 - 16 * q^60 - 20 * q^61 - 21 * q^62 + 46 * q^63 + 50 * q^64 - 6 * q^65 - 42 * q^66 - 20 * q^67 + 110 * q^68 + 17 * q^69 - 18 * q^70 - 11 * q^71 - 29 * q^72 - 36 * q^73 - 66 * q^74 + 4 * q^75 + 40 * q^76 - q^77 + 6 * q^78 + 23 * q^79 - 28 * q^80 + 29 * q^81 - 24 * q^82 - 9 * q^83 + 8 * q^84 - 2 * q^85 - 3 * q^86 - 43 * q^87 - 116 * q^88 - 16 * q^89 + 4 * q^90 + 12 * q^91 - 33 * q^92 + 25 * q^93 + 22 * q^94 - 6 * q^95 - 67 * q^96 - 62 * q^97 - 24 * q^98 + 4 * q^99

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