LMFDB - Embedded newform 145.4.c.b.86.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [145,4,Mod(86,145)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(145, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("145.86");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	145.c (of order $2$, degree $1$, 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:	$8.55527695083$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 95 x^{14} + 3576 x^{12} + 68256 x^{10} + 700479 x^{8} + 3754089 x^{6} + 9373424 x^{4} + \cdots + 2560000 $ x^16 + 95x^14 + 3576x^12 + 68256x^10 + 700479x^8 + 3754089x^6 + 9373424x^4 + 8978880*x^2 + 2560000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			86.12
Root			$3.07662i$ of defining polynomial
Character	$\chi$	$=$	145.86
Dual form			145.4.c.b.86.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.07662i q^{2} +1.74979i q^{3} -1.46560 q^{4} -5.00000 q^{5} -5.38343 q^{6} +25.6180 q^{7} +20.1039i q^{8} +23.9382 q^{9} +O(q^{10})$	\(q+3.07662i q^{2} +1.74979i q^{3} -1.46560 q^{4} -5.00000 q^{5} -5.38343 q^{6} +25.6180 q^{7} +20.1039i q^{8} +23.9382 q^{9} -15.3831i q^{10} +46.7808i q^{11} -2.56449i q^{12} -80.0924 q^{13} +78.8168i q^{14} -8.74893i q^{15} -73.5768 q^{16} +70.7121i q^{17} +73.6489i q^{18} -133.953i q^{19} +7.32802 q^{20} +44.8260i q^{21} -143.927 q^{22} +120.128 q^{23} -35.1775 q^{24} +25.0000 q^{25} -246.414i q^{26} +89.1310i q^{27} -37.5458 q^{28} +(-128.829 - 88.2734i) q^{29} +26.9172 q^{30} +89.0705i q^{31} -65.5372i q^{32} -81.8564 q^{33} -217.554 q^{34} -128.090 q^{35} -35.0840 q^{36} +217.926i q^{37} +412.123 q^{38} -140.144i q^{39} -100.519i q^{40} +76.6386i q^{41} -137.913 q^{42} +164.585i q^{43} -68.5622i q^{44} -119.691 q^{45} +369.588i q^{46} -458.245i q^{47} -128.744i q^{48} +313.281 q^{49} +76.9156i q^{50} -123.731 q^{51} +117.384 q^{52} +572.896 q^{53} -274.223 q^{54} -233.904i q^{55} +515.020i q^{56} +234.389 q^{57} +(271.584 - 396.357i) q^{58} +220.325 q^{59} +12.8225i q^{60} -107.539i q^{61} -274.036 q^{62} +613.249 q^{63} -386.982 q^{64} +400.462 q^{65} -251.841i q^{66} +658.928 q^{67} -103.636i q^{68} +210.198i q^{69} -394.084i q^{70} +267.922 q^{71} +481.251i q^{72} -7.46759i q^{73} -670.476 q^{74} +43.7446i q^{75} +196.322i q^{76} +1198.43i q^{77} +431.172 q^{78} -931.384i q^{79} +367.884 q^{80} +490.372 q^{81} -235.788 q^{82} +139.532 q^{83} -65.6971i q^{84} -353.560i q^{85} -506.366 q^{86} +(154.460 - 225.423i) q^{87} -940.475 q^{88} -705.086i q^{89} -368.245i q^{90} -2051.80 q^{91} -176.060 q^{92} -155.854 q^{93} +1409.85 q^{94} +669.765i q^{95} +114.676 q^{96} -1320.33i q^{97} +963.846i q^{98} +1119.85i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 62 q^{4} - 80 q^{5} + 50 q^{6} + 38 q^{7} - 126 q^{9}+O(q^{10}) $ 16 * q - 62 * q^4 - 80 * q^5 + 50 * q^6 + 38 * q^7 - 126 * q^9	$ 16 q - 62 q^{4} - 80 q^{5} + 50 q^{6} + 38 q^{7} - 126 q^{9} - 14 q^{13} + 210 q^{16} + 310 q^{20} + 88 q^{22} + 42 q^{23} + 62 q^{24} + 400 q^{25} - 346 q^{28} + 28 q^{29} - 250 q^{30} - 460 q^{33} - 626 q^{34} - 190 q^{35} - 12 q^{36} - 292 q^{38} + 584 q^{42} + 630 q^{45} + 1894 q^{49} - 320 q^{51} - 294 q^{52} + 614 q^{53} + 1840 q^{54} - 1360 q^{57} - 644 q^{58} - 2086 q^{59} - 30 q^{62} - 1456 q^{63} - 894 q^{64} + 70 q^{65} - 1604 q^{67} + 792 q^{71} + 1720 q^{74} + 4894 q^{78} - 1050 q^{80} - 192 q^{81} + 1276 q^{82} + 4400 q^{83} - 2042 q^{86} - 2046 q^{87} - 9264 q^{88} + 212 q^{91} - 2030 q^{92} - 1816 q^{93} + 4304 q^{94} + 2234 q^{96}+O(q^{100}) $ 16 * q - 62 * q^4 - 80 * q^5 + 50 * q^6 + 38 * q^7 - 126 * q^9 - 14 * q^13 + 210 * q^16 + 310 * q^20 + 88 * q^22 + 42 * q^23 + 62 * q^24 + 400 * q^25 - 346 * q^28 + 28 * q^29 - 250 * q^30 - 460 * q^33 - 626 * q^34 - 190 * q^35 - 12 * q^36 - 292 * q^38 + 584 * q^42 + 630 * q^45 + 1894 * q^49 - 320 * q^51 - 294 * q^52 + 614 * q^53 + 1840 * q^54 - 1360 * q^57 - 644 * q^58 - 2086 * q^59 - 30 * q^62 - 1456 * q^63 - 894 * q^64 + 70 * q^65 - 1604 * q^67 + 792 * q^71 + 1720 * q^74 + 4894 * q^78 - 1050 * q^80 - 192 * q^81 + 1276 * q^82 + 4400 * q^83 - 2042 * q^86 - 2046 * q^87 - 9264 * q^88 + 212 * q^91 - 2030 * q^92 - 1816 * q^93 + 4304 * q^94 + 2234 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/145\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$-1$	$1$

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 $

$2$			3.07662i			1.08775i	0.839166	+	0.543875i	$0.183043\pi$
$2$			3.07662i			1.08775i	−0.839166	+	0.543875i	$0.816957\pi$
$3$			1.74979i			0.336746i	0.985723	+	0.168373i	$0.0538514\pi$
$3$			1.74979i			0.336746i	−0.985723	+	0.168373i	$0.946149\pi$
$4$	−1.46560			−0.183200
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	−5.38343			−0.366296
$7$	25.6180			1.38324			0.691620	−	0.722261i	$-0.256897\pi$
$7$	25.6180			1.38324			0.691620	+	0.722261i	$0.256897\pi$
$8$			20.1039i			0.888474i
$9$	23.9382			0.886602
$10$		−	15.3831i		−	0.486457i
$11$			46.7808i			1.28227i	0.767429	+	0.641134i	$0.221536\pi$
$11$			46.7808i			1.28227i	−0.767429	+	0.641134i	$0.778464\pi$
$12$		−	2.56449i		−	0.0616921i
$13$	−80.0924			−1.70874			−0.854370	−	0.519665i	$-0.826057\pi$
$13$	−80.0924			−1.70874			−0.854370	+	0.519665i	$0.826057\pi$
$14$			78.8168i			1.50462i
$15$		−	8.74893i		−	0.150598i
$16$	−73.5768			−1.14964
$17$			70.7121i			1.00884i	0.863460	+	0.504418i	$0.168293\pi$
$17$			70.7121i			1.00884i	−0.863460	+	0.504418i	$0.831707\pi$
$18$			73.6489i			0.964401i
$19$		−	133.953i		−	1.61742i	−0.588210	−	0.808708i	$-0.700167\pi$
$19$		−	133.953i		−	1.61742i	0.588210	−	0.808708i	$-0.299833\pi$
$20$	7.32802			0.0819297
$21$			44.8260i			0.465801i
$22$	−143.927			−1.39479
$23$	120.128			1.08906			0.544531	−	0.838741i	$-0.316708\pi$
$23$	120.128			1.08906			0.544531	+	0.838741i	$0.316708\pi$
$24$	−35.1775			−0.299190
$25$	25.0000			0.200000
$26$		−	246.414i		−	1.85868i
$27$			89.1310i			0.635306i
$28$	−37.5458			−0.253410
$29$	−128.829	−	88.2734i	−0.824927	−	0.565240i
$29$	−128.829	−	88.2734i	−0.824927	−	0.565240i
$30$	26.9172			0.163813
$31$			89.0705i			0.516049i	0.966138	+	0.258025i	$0.0830716\pi$
$31$			89.0705i			0.516049i	−0.966138	+	0.258025i	$0.916928\pi$
$32$		−	65.5372i		−	0.362045i
$33$	−81.8564			−0.431799
$34$	−217.554			−1.09736
$35$	−128.090			−0.618604
$36$	−35.0840			−0.162426
$37$			217.926i			0.968293i	0.874987	+	0.484146i	$0.160870\pi$
$37$			217.926i			0.968293i	−0.874987	+	0.484146i	$0.839130\pi$
$38$	412.123			1.75934
$39$		−	140.144i		−	0.575412i
$40$		−	100.519i		−	0.397338i
$41$			76.6386i			0.291925i	0.989290	+	0.145963i	$0.0466279\pi$
$41$			76.6386i			0.291925i	−0.989290	+	0.145963i	$0.953372\pi$
$42$	−137.913			−0.506676
$43$			164.585i			0.583697i	0.956465	+	0.291849i	$0.0942703\pi$
$43$			164.585i			0.583697i	−0.956465	+	0.291849i	$0.905730\pi$
$44$		−	68.5622i		−	0.234912i
$45$	−119.691			−0.396500
$46$			369.588i			1.18463i
$47$		−	458.245i		−	1.42217i	−0.703106	−	0.711085i	$-0.748204\pi$
$47$		−	458.245i		−	1.42217i	0.703106	−	0.711085i	$-0.251796\pi$
$48$		−	128.744i		−	0.387137i
$49$	313.281			0.913354
$50$			76.9156i			0.217550i
$51$	−123.731			−0.339722
$52$	117.384			0.313042
$53$	572.896			1.48478			0.742390	−	0.669968i	$-0.233692\pi$
$53$	572.896			1.48478			0.742390	+	0.669968i	$0.233692\pi$
$54$	−274.223			−0.691055
$55$		−	233.904i		−	0.573448i
$56$			515.020i			1.22897i
$57$	234.389			0.544659
$58$	271.584	−	396.357i	0.614840	−	0.897314i
$59$	220.325			0.486167			0.243083	−	0.970005i	$-0.421841\pi$
$59$	220.325			0.486167			0.243083	+	0.970005i	$0.421841\pi$
$60$			12.8225i			0.0275896i
$61$		−	107.539i		−	0.225721i	−0.993611	−	0.112861i	$-0.963999\pi$
$61$		−	107.539i		−	0.225721i	0.993611	−	0.112861i	$-0.0360013\pi$
$62$	−274.036			−0.561333
$63$	613.249			1.22638
$64$	−386.982			−0.755823
$65$	400.462			0.764172
$66$		−	251.841i		−	0.469690i
$67$	658.928			1.20151			0.600753	−	0.799435i	$-0.294868\pi$
$67$	658.928			1.20151			0.600753	+	0.799435i	$0.294868\pi$
$68$		−	103.636i		−	0.184819i
$69$			210.198i			0.366738i
$70$		−	394.084i		−	0.672887i
$71$	267.922			0.447838			0.223919	−	0.974608i	$-0.428115\pi$
$71$	267.922			0.447838			0.223919	+	0.974608i	$0.428115\pi$
$72$			481.251i			0.787723i
$73$		−	7.46759i		−	0.0119728i	−0.999982	−	0.00598641i	$-0.998094\pi$
$73$		−	7.46759i		−	0.0119728i	0.999982	−	0.00598641i	$-0.00190554\pi$
$74$	−670.476			−1.05326
$75$			43.7446i			0.0673493i
$76$			196.322i			0.296311i
$77$			1198.43i			1.77369i
$78$	431.172			0.625905
$79$		−	931.384i		−	1.32644i	−0.748424	−	0.663221i	$-0.769189\pi$
$79$		−	931.384i		−	1.32644i	0.748424	−	0.663221i	$-0.230811\pi$
$80$	367.884			0.514134
$81$	490.372			0.672665
$82$	−235.788			−0.317542
$83$	139.532			0.184526			0.0922629	−	0.995735i	$-0.470590\pi$
$83$	139.532			0.184526			0.0922629	+	0.995735i	$0.470590\pi$
$84$		−	65.6971i		−	0.0853350i
$85$		−	353.560i		−	0.451165i
$86$	−506.366			−0.634917
$87$	154.460	−	225.423i	0.190342	−	0.277791i
$88$	−940.475			−1.13926
$89$		−	705.086i		−	0.839763i	−0.907579	−	0.419882i	$-0.862072\pi$
$89$		−	705.086i		−	0.839763i	0.907579	−	0.419882i	$-0.137928\pi$
$90$		−	368.245i		−	0.431293i
$91$	−2051.80			−2.36360
$92$	−176.060			−0.199517
$93$	−155.854			−0.173778
$94$	1409.85			1.54696
$95$			669.765i			0.723331i
$96$	114.676			0.121917
$97$		−	1320.33i		−	1.38206i	−0.722827	−	0.691029i	$-0.757158\pi$
$97$		−	1320.33i		−	1.38206i	0.722827	−	0.691029i	$-0.242842\pi$
$98$			963.846i			0.993501i
$99$			1119.85i			1.13686i
$100$	−36.6401			−0.0366401
$101$		−	1008.03i		−	0.993094i	−0.868010	−	0.496547i	$-0.834601\pi$
$101$		−	1008.03i		−	0.993094i	0.868010	−	0.496547i	$-0.165399\pi$
$102$		−	380.674i		−	0.369532i
$103$	1761.28			1.68490			0.842448	−	0.538778i	$-0.181114\pi$
$103$	1761.28			1.68490			0.842448	+	0.538778i	$0.181114\pi$
$104$		−	1610.17i		−	1.51817i
$105$		−	224.130i		−	0.208313i
$106$			1762.58i			1.61507i
$107$	−355.227			−0.320945			−0.160472	−	0.987040i	$-0.551302\pi$
$107$	−355.227			−0.320945			−0.160472	+	0.987040i	$0.551302\pi$
$108$		−	130.631i		−	0.116388i
$109$	−485.241			−0.426401			−0.213200	−	0.977008i	$-0.568389\pi$
$109$	−485.241			−0.426401			−0.213200	+	0.977008i	$0.568389\pi$
$110$	719.635			0.623768
$111$	−381.324			−0.326069
$112$	−1884.89			−1.59023
$113$		−	716.667i		−	0.596622i	−0.954469	−	0.298311i	$-0.903577\pi$
$113$		−	716.667i		−	0.596622i	0.954469	−	0.298311i	$-0.0964233\pi$
$114$			721.126i			0.592453i
$115$	−600.640			−0.487043
$116$	188.812	+	129.374i	0.151127	+	0.103552i
$117$	−1917.27			−1.51497
$118$			677.856i			0.528828i
$119$			1811.50i			1.39546i
$120$	175.887			0.133802
$121$	−857.445			−0.644211
$122$	330.857			0.245528
$123$	−134.101			−0.0983048
$124$		−	130.542i		−	0.0945405i
$125$	−125.000			−0.0894427
$126$			1886.74i			1.33400i
$127$		−	1342.23i		−	0.937825i	−0.883245	−	0.468912i	$-0.844646\pi$
$127$		−	1342.23i		−	0.937825i	0.883245	−	0.468912i	$-0.155354\pi$
$128$		−	1714.89i		−	1.18419i
$129$	−287.989			−0.196558
$130$			1232.07i			0.831228i
$131$			1288.07i			0.859075i	0.903049	+	0.429538i	$0.141323\pi$
$131$			1288.07i			0.859075i	−0.903049	+	0.429538i	$0.858677\pi$
$132$	119.969			0.0791058
$133$		−	3431.60i		−	2.23728i
$134$			2027.27i			1.30694i
$135$		−	445.655i		−	0.284118i
$136$	−1421.59			−0.896324
$137$			2681.67i			1.67234i	0.548469	+	0.836171i	$0.315211\pi$
$137$			2681.67i			1.67234i	−0.548469	+	0.836171i	$0.684789\pi$
$138$	−646.700			−0.398919
$139$	−46.2381			−0.0282148			−0.0141074	−	0.999900i	$-0.504491\pi$
$139$	−46.2381			−0.0282148			−0.0141074	+	0.999900i	$0.504491\pi$
$140$	187.729			0.113329
$141$	801.831			0.478910
$142$			824.295i			0.487136i
$143$		−	3746.79i		−	2.19106i
$144$	−1761.30			−1.01927
$145$	644.143	+	441.367i	0.368918	+	0.252783i
$146$	22.9750			0.0130234
$147$			548.174i			0.307569i
$148$		−	319.393i		−	0.177392i
$149$	2589.52			1.42377			0.711885	−	0.702296i	$-0.247842\pi$
$149$	2589.52			1.42377			0.711885	+	0.702296i	$0.247842\pi$
$150$	−134.586			−0.0732592
$151$	−1827.35			−0.984820			−0.492410	−	0.870363i	$-0.663884\pi$
$151$	−1827.35			−0.984820			−0.492410	+	0.870363i	$0.663884\pi$
$152$	2692.97			1.43703
$153$			1692.72i			0.894435i
$154$	−3687.12			−1.92933
$155$		−	445.352i		−	0.230784i
$156$			205.396i			0.105416i
$157$			1381.88i			0.702461i	0.936289	+	0.351231i	$0.114237\pi$
$157$			1381.88i			0.702461i	−0.936289	+	0.351231i	$0.885763\pi$
$158$	2865.52			1.44284
$159$			1002.45i			0.499994i
$160$			327.686i			0.161912i
$161$	3077.43			1.50643
$162$			1508.69i			0.731691i
$163$			3593.78i			1.72691i	0.504423	+	0.863456i	$0.331705\pi$
$163$			3593.78i			1.72691i	−0.504423	+	0.863456i	$0.668295\pi$
$164$		−	112.322i		−	0.0534808i
$165$	409.282			0.193106
$166$			429.288i			0.200718i
$167$	−1140.05			−0.528263			−0.264132	−	0.964487i	$-0.585085\pi$
$167$	−1140.05			−0.528263			−0.264132	+	0.964487i	$0.585085\pi$
$168$	−901.175			−0.413852
$169$	4217.79			1.91979
$170$	1087.77			0.490755
$171$		−	3206.60i		−	1.43400i
$172$		−	241.216i		−	0.106934i
$173$	−545.729			−0.239832			−0.119916	−	0.992784i	$-0.538263\pi$
$173$	−545.729			−0.239832			−0.119916	+	0.992784i	$0.538263\pi$
$174$	693.540	+	475.214i	0.302167	+	0.207045i
$175$	640.449			0.276648
$176$		−	3441.98i		−	1.47414i
$177$			385.521i			0.163715i
$178$	2169.28			0.913453
$179$	−3472.98			−1.45018			−0.725092	−	0.688652i	$-0.758203\pi$
$179$	−3472.98			−1.45018			−0.725092	+	0.688652i	$0.758203\pi$
$180$	175.420			0.0726391
$181$	−3235.50			−1.32869			−0.664345	−	0.747426i	$-0.731289\pi$
$181$	−3235.50			−1.32869			−0.664345	+	0.747426i	$0.731289\pi$
$182$		−	6312.63i		−	2.57101i
$183$	188.171			0.0760108
$184$			2415.04i			0.967602i
$185$		−	1089.63i		−	0.433034i
$186$		−	479.505i		−	0.189027i
$187$	−3307.97			−1.29360
$188$			671.606i			0.260542i
$189$			2283.36i			0.878782i
$190$	−2060.61			−0.786803
$191$		−	218.654i		−	0.0828339i	−0.999142	−	0.0414170i	$-0.986813\pi$
$191$		−	218.654i		−	0.0828339i	0.999142	−	0.0414170i	$-0.0131872\pi$
$192$		−	677.135i		−	0.254521i
$193$		−	3761.57i		−	1.40292i	−0.712709	−	0.701460i	$-0.752532\pi$
$193$		−	3761.57i		−	1.40292i	0.712709	−	0.701460i	$-0.247468\pi$
$194$	4062.17			1.50333
$195$			700.722i			0.257332i
$196$	−459.145			−0.167327
$197$	−250.457			−0.0905803			−0.0452901	−	0.998974i	$-0.514421\pi$
$197$	−250.457			−0.0905803			−0.0452901	+	0.998974i	$0.514421\pi$
$198$	−3445.36			−1.23662
$199$	880.016			0.313481			0.156740	−	0.987640i	$-0.449901\pi$
$199$	880.016			0.313481			0.156740	+	0.987640i	$0.449901\pi$
$200$			502.597i			0.177695i
$201$			1152.98i			0.404603i
$202$	3101.32			1.08024
$203$	−3300.33	−	2261.38i	−1.14107	−	0.781863i
$204$	181.341			0.0622372
$205$		−	383.193i		−	0.130553i
$206$			5418.80i			1.83275i
$207$	2875.65			0.965564
$208$	5892.94			1.96443
$209$	6266.43			2.07396
$210$	689.563			0.226592
$211$		−	3947.92i		−	1.28808i	−0.764990	−	0.644042i	$-0.777256\pi$
$211$		−	3947.92i		−	1.28808i	0.764990	−	0.644042i	$-0.222744\pi$
$212$	−839.639			−0.272012
$213$			468.807i			0.150808i
$214$		−	1092.90i		−	0.349108i
$215$		−	822.925i		−	0.261037i
$216$	−1791.88			−0.564453
$217$			2281.80i			0.713820i
$218$		−	1492.90i		−	0.463818i
$219$	13.0667			0.00403180
$220$			342.811i			0.105056i
$221$		−	5663.50i		−	1.72384i
$222$		−	1173.19i		−	0.354682i
$223$	305.831			0.0918385			0.0459192	−	0.998945i	$-0.485378\pi$
$223$	305.831			0.0918385			0.0459192	+	0.998945i	$0.485378\pi$
$224$		−	1678.93i		−	0.500796i
$225$	598.456			0.177320
$226$	2204.91			0.648976
$227$	192.331			0.0562356			0.0281178	−	0.999605i	$-0.491049\pi$
$227$	192.331			0.0562356			0.0281178	+	0.999605i	$0.491049\pi$
$228$	−343.521			−0.0997818
$229$		−	5381.32i		−	1.55287i	−0.630196	−	0.776436i	$-0.717026\pi$
$229$		−	5381.32i		−	1.55287i	0.630196	−	0.776436i	$-0.282974\pi$
$230$		−	1847.94i		−	0.529781i
$231$	−2097.00			−0.597282
$232$	1774.64	−	2589.95i	0.502201	−	0.732926i
$233$	−1214.10			−0.341366			−0.170683	−	0.985326i	$-0.554597\pi$
$233$	−1214.10			−0.341366			−0.170683	+	0.985326i	$0.554597\pi$
$234$		−	5898.72i		−	1.64791i
$235$			2291.23i			0.636013i
$236$	−322.909			−0.0890659
$237$	1629.72			0.446675
$238$	−5573.30			−1.51791
$239$	−5284.40			−1.43021			−0.715104	−	0.699018i	$-0.753621\pi$
$239$	−5284.40			−1.43021			−0.715104	+	0.699018i	$0.753621\pi$
$240$			643.719i			0.173133i
$241$	978.748			0.261605			0.130802	−	0.991408i	$-0.458245\pi$
$241$	978.748			0.261605			0.130802	+	0.991408i	$0.458245\pi$
$242$		−	2638.04i		−	0.700741i
$243$			3264.58i			0.861824i
$244$			157.610i			0.0413522i
$245$	−1566.40			−0.408465
$246$		−	412.578i		−	0.106931i
$247$			10728.6i			2.76374i
$248$	−1790.66			−0.458496
$249$			244.151i			0.0621384i
$250$		−	384.578i		−	0.0972913i
$251$			7259.30i			1.82551i	0.408508	+	0.912755i	$0.366049\pi$
$251$			7259.30i			1.82551i	−0.408508	+	0.912755i	$0.633951\pi$
$252$	−898.781			−0.224674
$253$			5619.68i			1.39647i
$254$	4129.54			1.02012
$255$	618.655			0.151928
$256$	2180.23			0.532282
$257$	−94.0579			−0.0228295			−0.0114147	−	0.999935i	$-0.503634\pi$
$257$	−94.0579			−0.0228295			−0.0114147	+	0.999935i	$0.503634\pi$
$258$		−	886.032i		−	0.213806i
$259$			5582.82i			1.33938i
$260$	−586.918			−0.139997
$261$	−3083.93	−	2113.11i	−0.731381	−	0.501143i
$262$	−3962.89			−0.934459
$263$			5613.47i			1.31613i	0.752962	+	0.658064i	$0.228624\pi$
$263$			5613.47i			1.31613i	−0.752962	+	0.658064i	$0.771376\pi$
$264$		−	1645.63i		−	0.383642i
$265$	−2864.48			−0.664014
$266$	10557.7			2.43360
$267$	1233.75			0.282787
$268$	−965.728			−0.220117
$269$		−	696.044i		−	0.157764i	−0.996884	−	0.0788821i	$-0.974865\pi$
$269$		−	696.044i		−	0.157764i	0.996884	−	0.0788821i	$-0.0251351\pi$
$270$	1371.11			0.309049
$271$		−	2597.49i		−	0.582236i	−0.956687	−	0.291118i	$-0.905973\pi$
$271$		−	2597.49i		−	0.582236i	0.956687	−	0.291118i	$-0.0940273\pi$
$272$		−	5202.77i		−	1.15980i
$273$		−	3590.22i		−	0.795934i
$274$	−8250.49			−1.81909
$275$			1169.52i			0.256454i
$276$		−	308.067i		−	0.0671865i
$277$	4182.92			0.907320			0.453660	−	0.891175i	$-0.350118\pi$
$277$	4182.92			0.907320			0.453660	+	0.891175i	$0.350118\pi$
$278$		−	142.257i		−	0.0306907i
$279$			2132.19i			0.457530i
$280$		−	2575.10i		−	0.549613i
$281$	7791.11			1.65402			0.827009	−	0.562189i	$-0.190041\pi$
$281$	7791.11			1.65402			0.827009	+	0.562189i	$0.190041\pi$
$282$			2466.93i			0.520935i
$283$	−1187.74			−0.249483			−0.124742	−	0.992189i	$-0.539810\pi$
$283$	−1187.74			−0.249483			−0.124742	+	0.992189i	$0.539810\pi$
$284$	−392.668			−0.0820442
$285$	−1171.94			−0.243579
$286$	11527.4			2.38333
$287$			1963.33i			0.403803i
$288$		−	1568.85i		−	0.320990i
$289$	−87.1976			−0.0177483
$290$	−1357.92	+	1981.78i	−0.274965	+	0.401291i
$291$	2310.30			0.465403
$292$			10.9445i			0.00219343i
$293$			7646.04i			1.52453i	0.647267	+	0.762263i	$0.275912\pi$
$293$			7646.04i			1.52453i	−0.647267	+	0.762263i	$0.724088\pi$
$294$	−1686.52			−0.334558
$295$	−1101.62			−0.217420
$296$	−4381.16			−0.860303
$297$	−4169.62			−0.814633
$298$			7966.98i			1.54871i
$299$	−9621.33			−1.86092
$300$		−	64.1123i		−	0.0123384i
$301$			4216.33i			0.807394i
$302$		−	5622.07i		−	1.07124i
$303$	1763.83			0.334421
$304$			9855.83i			1.85944i
$305$			537.696i			0.100946i
$306$	−5207.87			−0.972922
$307$		−	4298.80i		−	0.799172i	−0.916696	−	0.399586i	$-0.869154\pi$
$307$		−	4298.80i		−	0.799172i	0.916696	−	0.399586i	$-0.130846\pi$
$308$		−	1756.42i		−	0.324940i
$309$			3081.87i			0.567383i
$310$	1370.18			0.251036
$311$			3775.94i			0.688470i	0.938884	+	0.344235i	$0.111862\pi$
$311$			3775.94i			0.688470i	−0.938884	+	0.344235i	$0.888138\pi$
$312$	2817.45			0.511239
$313$	−6318.75			−1.14108			−0.570538	−	0.821271i	$-0.693265\pi$
$313$	−6318.75			−1.14108			−0.570538	+	0.821271i	$0.693265\pi$
$314$	−4251.54			−0.764102
$315$	−3066.25			−0.548455
$316$			1365.04i			0.243005i
$317$		−	7268.03i		−	1.28774i	−0.765135	−	0.643870i	$-0.777328\pi$
$317$		−	7268.03i		−	1.28774i	0.765135	−	0.643870i	$-0.222672\pi$
$318$	−3084.15			−0.543869
$319$	4129.50	−	6026.71i	0.724789	−	1.05778i
$320$	1934.91			0.338014
$321$		−	621.571i		−	0.108077i
$322$			9468.10i			1.63862i
$323$	9472.09			1.63171
$324$	−718.692			−0.123232
$325$	−2002.31			−0.341748
$326$	−11056.7			−1.87845
$327$		−	849.069i		−	0.143589i
$328$	−1540.73			−0.259368
$329$		−	11739.3i		−	1.96720i
$330$			1259.21i			0.210052i
$331$		−	4395.93i		−	0.729976i	−0.931012	−	0.364988i	$-0.881073\pi$
$331$		−	4395.93i		−	0.729976i	0.931012	−	0.364988i	$-0.118927\pi$
$332$	−204.499			−0.0338052
$333$			5216.77i			0.858490i
$334$		−	3507.51i		−	0.574619i
$335$	−3294.64			−0.537330
$336$		−	3298.15i		−	0.535503i
$337$			303.988i			0.0491373i	0.999698	+	0.0245687i	$0.00782124\pi$
$337$			303.988i			0.0491373i	−0.999698	+	0.0245687i	$0.992179\pi$
$338$			12976.5i			2.08826i
$339$	1254.01			0.200910
$340$			518.179i			0.0826536i
$341$	−4166.79			−0.661713
$342$	9865.49			1.55984
$343$	−761.352			−0.119852
$344$	−3308.80			−0.518600
$345$		−	1050.99i		−	0.164010i
$346$		−	1679.00i		−	0.260878i
$347$	−7323.09			−1.13292			−0.566461	−	0.824089i	$-0.691688\pi$
$347$	−7323.09			−1.13292			−0.566461	+	0.824089i	$0.691688\pi$
$348$	−226.376	+	330.380i	−0.0348708	+	0.0508915i
$349$	2339.83			0.358877			0.179439	−	0.983769i	$-0.442572\pi$
$349$	2339.83			0.358877			0.179439	+	0.983769i	$0.442572\pi$
$350$			1970.42i			0.300924i
$351$		−	7138.71i		−	1.08557i
$352$	3065.88			0.464239
$353$	1925.38			0.290305			0.145152	−	0.989409i	$-0.453633\pi$
$353$	1925.38			0.290305			0.145152	+	0.989409i	$0.453633\pi$
$354$	−1186.10			−0.178081
$355$	−1339.61			−0.200279
$356$			1033.38i			0.153845i
$357$	−3169.74			−0.469917
$358$		−	10685.1i		−	1.57744i
$359$		−	4772.00i		−	0.701551i	−0.936460	−	0.350775i	$-0.885918\pi$
$359$		−	4772.00i		−	0.701551i	0.936460	−	0.350775i	$-0.114082\pi$
$360$		−	2406.26i		−	0.352280i
$361$	−11084.4			−1.61604
$362$		−	9954.41i		−	1.44528i
$363$		−	1500.35i		−	0.216936i
$364$	3007.13			0.433012
$365$			37.3380i			0.00535441i
$366$			578.930i			0.0826807i
$367$			2786.93i			0.396394i	0.980162	+	0.198197i	$0.0635086\pi$
$367$			2786.93i			0.396394i	−0.980162	+	0.198197i	$0.936491\pi$
$368$	−8838.63			−1.25203
$369$			1834.59i			0.258821i
$370$	3352.38			0.471032
$371$	14676.4			2.05381
$372$	228.421			0.0318362
$373$	8227.92			1.14216			0.571080	−	0.820894i	$-0.306525\pi$
$373$	8227.92			1.14216			0.571080	+	0.820894i	$0.306525\pi$
$374$		−	10177.4i		−	1.40711i
$375$		−	218.723i		−	0.0301195i
$376$	9212.50			1.26356
$377$	10318.2	+	7070.02i	1.40959	+	0.965848i
$378$	−7025.03			−0.955895
$379$			356.249i			0.0482830i	0.999709	+	0.0241415i	$0.00768523\pi$
$379$			356.249i			0.0482830i	−0.999709	+	0.0241415i	$0.992315\pi$
$380$		−	981.610i		−	0.132515i
$381$	2348.62			0.315809
$382$	672.717			0.0901026
$383$	−12332.1			−1.64527			−0.822637	−	0.568567i	$-0.807498\pi$
$383$	−12332.1			−1.64527			−0.822637	+	0.568567i	$0.807498\pi$
$384$	3000.70			0.398773
$385$		−	5992.15i		−	0.793216i
$386$	11572.9			1.52603
$387$			3939.88i			0.517507i
$388$			1935.09i			0.253194i
$389$		−	2726.28i		−	0.355342i	−0.984090	−	0.177671i	$-0.943144\pi$
$389$		−	2726.28i		−	0.355342i	0.984090	−	0.177671i	$-0.0568562\pi$
$390$	−2155.86			−0.279913
$391$			8494.50i			1.09868i
$392$			6298.15i			0.811491i
$393$	−2253.84			−0.289291
$394$		−	770.561i		−	0.0985287i
$395$			4656.92i			0.593203i
$396$		−	1641.26i		−	0.208274i
$397$	−10698.1			−1.35245			−0.676223	−	0.736697i	$-0.736384\pi$
$397$	−10698.1			−1.35245			−0.676223	+	0.736697i	$0.736384\pi$
$398$			2707.48i			0.340989i
$399$	6004.57			0.753395
$400$	−1839.42			−0.229928
$401$	8629.87			1.07470			0.537351	−	0.843359i	$-0.319425\pi$
$401$	8629.87			1.07470			0.537351	+	0.843359i	$0.319425\pi$
$402$	−3547.29			−0.440107
$403$		−	7133.86i		−	0.881794i
$404$			1477.37i			0.181935i
$405$	−2451.86			−0.300825
$406$	6957.43	−	10153.9i	0.850471	−	1.24120i
$407$	−10194.8			−1.24161
$408$		−	2487.47i		−	0.301834i
$409$		−	13393.4i		−	1.61923i	−0.586965	−	0.809613i	$-0.699677\pi$
$409$		−	13393.4i		−	1.61923i	0.586965	−	0.809613i	$-0.300323\pi$
$410$	1178.94			0.142009
$411$	−4692.35			−0.563155
$412$	−2581.34			−0.308674
$413$	5644.27			0.672485
$414$			8847.30i			1.05029i
$415$	−697.661			−0.0825224
$416$			5249.03i			0.618641i
$417$		−	80.9067i		−	0.00950125i
$418$			19279.4i			2.25595i
$419$	4639.27			0.540914			0.270457	−	0.962732i	$-0.412825\pi$
$419$	4639.27			0.540914			0.270457	+	0.962732i	$0.412825\pi$
$420$			328.486i			0.0381630i
$421$			2276.42i			0.263530i	0.991281	+	0.131765i	$0.0420644\pi$
$421$			2276.42i			0.263530i	−0.991281	+	0.131765i	$0.957936\pi$
$422$	12146.3			1.40111
$423$		−	10969.6i		−	1.26090i
$424$			11517.4i			1.31919i
$425$			1767.80i			0.201767i
$426$	−1442.34			−0.164041
$427$		−	2754.94i		−	0.312227i
$428$	520.622			0.0587972
$429$	6556.07			0.737833
$430$	2531.83			0.283943
$431$	−5957.44			−0.665800			−0.332900	−	0.942962i	$-0.608027\pi$
$431$	−5957.44			−0.665800			−0.332900	+	0.942962i	$0.608027\pi$
$432$		−	6557.98i		−	0.730373i
$433$			10380.1i			1.15204i	0.817435	+	0.576021i	$0.195395\pi$
$433$			10380.1i			1.15204i	−0.817435	+	0.576021i	$0.804605\pi$
$434$	−7020.25			−0.776458
$435$	−772.298	+	1127.11i	−0.0851238	+	0.124232i
$436$	711.172			0.0781169
$437$		−	16091.5i		−	1.76147i
$438$			40.2013i			0.00438560i
$439$	14707.2			1.59894			0.799471	−	0.600704i	$-0.205113\pi$
$439$	14707.2			1.59894			0.799471	+	0.600704i	$0.205113\pi$
$440$	4702.38			0.509493
$441$	7499.39			0.809782
$442$	17424.4			1.87510
$443$		−	7710.76i		−	0.826973i	−0.910510	−	0.413487i	$-0.864311\pi$
$443$		−	7710.76i		−	0.826973i	0.910510	−	0.413487i	$-0.135689\pi$
$444$	558.870			0.0597360
$445$			3525.43i			0.375554i
$446$			940.928i			0.0998973i
$447$			4531.11i			0.479450i
$448$	−9913.68			−1.04549
$449$			1321.48i			0.138897i	0.997586	+	0.0694484i	$0.0221239\pi$
$449$			1321.48i			0.138897i	−0.997586	+	0.0694484i	$0.977876\pi$
$450$			1841.22i			0.192880i
$451$	−3585.22			−0.374326
$452$			1050.35i			0.109302i
$453$		−	3197.47i		−	0.331635i
$454$			591.731i			0.0611702i
$455$	10259.0			1.05703
$456$			4712.12i			0.483915i
$457$	−4995.16			−0.511299			−0.255650	−	0.966770i	$-0.582289\pi$
$457$	−4995.16			−0.511299			−0.255650	+	0.966770i	$0.582289\pi$
$458$	16556.3			1.68914
$459$	−6302.64			−0.640920
$460$	880.300			0.0892265
$461$			257.723i			0.0260376i	0.999915	+	0.0130188i	$0.00414413\pi$
$461$			257.723i			0.0260376i	−0.999915	+	0.0130188i	$0.995856\pi$
$462$		−	6451.66i		−	0.649694i
$463$	1509.69			0.151536			0.0757679	−	0.997125i	$-0.475859\pi$
$463$	1509.69			0.151536			0.0757679	+	0.997125i	$0.475859\pi$
$464$	9478.80	+	6494.88i	0.948367	+	0.649821i
$465$	779.271			0.0777158
$466$		−	3735.32i		−	0.371321i
$467$			2995.84i			0.296855i	0.988923	+	0.148427i	$0.0474211\pi$
$467$			2995.84i			0.296855i	−0.988923	+	0.148427i	$0.952579\pi$
$468$	2809.96			0.277544
$469$	16880.4			1.66197
$470$	−7049.24			−0.691824
$471$	−2418.00			−0.236551
$472$			4429.38i			0.431946i
$473$	−7699.42			−0.748456
$474$			5014.04i			0.485871i
$475$		−	3348.82i		−	0.323483i
$476$		−	2654.94i		−	0.255649i
$477$	13714.1			1.31641
$478$		−	16258.1i		−	1.55571i
$479$			8143.26i			0.776775i	0.921496	+	0.388387i	$0.126968\pi$
$479$			8143.26i			0.776775i	−0.921496	+	0.388387i	$0.873032\pi$
$480$	−573.380			−0.0545231
$481$		−	17454.2i		−	1.65456i
$482$			3011.24i			0.284560i
$483$			5384.85i			0.507286i
$484$	1256.68			0.118020
$485$			6601.67i			0.618075i
$486$	−10043.9			−0.937449
$487$	−11912.6			−1.10844			−0.554220	−	0.832370i	$-0.686983\pi$
$487$	−11912.6			−1.10844			−0.554220	+	0.832370i	$0.686983\pi$
$488$	2161.95			0.200547
$489$	−6288.35			−0.581532
$490$		−	4819.23i		−	0.444307i
$491$			8565.80i			0.787310i	0.919258	+	0.393655i	$0.128790\pi$
$491$			8565.80i			0.787310i	−0.919258	+	0.393655i	$0.871210\pi$
$492$	196.539			0.0180095
$493$	6241.99	−	9109.74i	0.570234	−	0.832215i
$494$	−33007.9			−3.00626
$495$		−	5599.25i		−	0.508420i
$496$		−	6553.52i		−	0.593270i
$497$	6863.62			0.619468
$498$	−751.161			−0.0675911
$499$	−12919.4			−1.15902			−0.579510	−	0.814965i	$-0.696756\pi$
$499$	−12919.4			−1.15902			−0.579510	+	0.814965i	$0.696756\pi$
$500$	183.200			0.0163859
$501$		−	1994.85i		−	0.177891i
$502$	−22334.1			−1.98570
$503$			1689.00i			0.149719i	0.997194	+	0.0748596i	$0.0238508\pi$
$503$			1689.00i			0.149719i	−0.997194	+	0.0748596i	$0.976149\pi$
$504$			12328.7i			1.08961i
$505$			5040.14i			0.444125i
$506$	−17289.6			−1.51901
$507$			7380.22i			0.646484i
$508$			1967.18i			0.171810i
$509$	1453.42			0.126566			0.0632828	−	0.997996i	$-0.479843\pi$
$509$	1453.42			0.126566			0.0632828	+	0.997996i	$0.479843\pi$
$510$			1903.37i			0.165260i
$511$		−	191.305i		−	0.0165613i
$512$		−	7011.41i		−	0.605202i
$513$	11939.4			1.02756
$514$		−	289.381i		−	0.0248328i
$515$	−8806.41			−0.753508
$516$	422.077			0.0360095
$517$	21437.1			1.82360
$518$	−17176.2			−1.45691
$519$		−	954.909i		−	0.0807627i
$520$			8050.83i			0.678947i
$521$	−12120.7			−1.01922			−0.509612	−	0.860404i	$-0.670211\pi$
$521$	−12120.7			−1.01922			−0.509612	+	0.860404i	$0.670211\pi$
$522$	6501.24	−	9488.09i	0.545118	−	0.795560i
$523$	−6231.35			−0.520990			−0.260495	−	0.965475i	$-0.583886\pi$
$523$	−6231.35			−0.520990			−0.260495	+	0.965475i	$0.583886\pi$
$524$		−	1887.80i		−	0.157383i
$525$			1120.65i			0.0931603i
$526$	−17270.5			−1.43162
$527$	−6298.36			−0.520609
$528$	6022.74			0.496413
$529$	2263.72			0.186054
$530$		−	8812.92i		−	0.722281i
$531$	5274.19			0.431036
$532$			5029.37i			0.409870i
$533$		−	6138.16i		−	0.498824i
$534$			3795.78i			0.307602i
$535$	1776.13			0.143531
$536$			13247.0i			1.06751i
$537$		−	6076.98i		−	0.488344i
$538$	2141.47			0.171608
$539$			14655.5i			1.17117i
$540$			653.154i			0.0520505i
$541$		−	21378.6i		−	1.69896i	−0.527618	−	0.849482i	$-0.676915\pi$
$541$		−	21378.6i		−	1.69896i	0.527618	−	0.849482i	$-0.323085\pi$
$542$	7991.48			0.633328
$543$		−	5661.43i		−	0.447432i
$544$	4634.27			0.365244
$545$	2426.21			0.190692
$546$	11045.7			0.865777
$547$	−22719.5			−1.77590			−0.887949	−	0.459942i	$-0.847870\pi$
$547$	−22719.5			−1.77590			−0.887949	+	0.459942i	$0.847870\pi$
$548$		−	3930.27i		−	0.306374i
$549$		−	2574.30i		−	0.200125i
$550$	−3598.17			−0.278957
$551$	−11824.5	+	17257.0i	−0.914228	+	1.33425i
$552$	−4225.80			−0.325837
$553$		−	23860.2i		−	1.83479i
$554$			12869.3i			0.986937i
$555$	1906.62			0.145823
$556$	67.7667			0.00516897
$557$	−13332.6			−1.01422			−0.507109	−	0.861882i	$-0.669286\pi$
$557$	−13332.6			−1.01422			−0.507109	+	0.861882i	$0.669286\pi$
$558$	−6559.95			−0.497679
$559$		−	13182.0i		−	0.997387i
$560$	9424.45			0.711171
$561$		−	5788.24i		−	0.435614i
$562$			23970.3i			1.79916i
$563$		−	9116.45i		−	0.682438i	−0.939984	−	0.341219i	$-0.889160\pi$
$563$		−	9116.45i		−	0.682438i	0.939984	−	0.341219i	$-0.110840\pi$
$564$	−1175.17			−0.0877366
$565$			3583.33i			0.266818i
$566$		−	3654.23i		−	0.271376i
$567$	12562.3			0.930457
$568$			5386.27i			0.397893i
$569$			18563.3i			1.36769i	0.729627	+	0.683845i	$0.239694\pi$
$569$			18563.3i			1.36769i	−0.729627	+	0.683845i	$0.760306\pi$
$570$		−	3605.63i		−	0.264953i
$571$	23682.8			1.73572			0.867858	−	0.496812i	$-0.165496\pi$
$571$	23682.8			1.73572			0.867858	+	0.496812i	$0.165496\pi$
$572$			5491.30i			0.401404i
$573$	382.598			0.0278940
$574$	−6040.41			−0.439237
$575$	3003.20			0.217812
$576$	−9263.66			−0.670114
$577$			21171.3i			1.52751i	0.645507	+	0.763755i	$0.276646\pi$
$577$			21171.3i			1.52751i	−0.645507	+	0.763755i	$0.723354\pi$
$578$		−	268.274i		−	0.0193058i
$579$	6581.94			0.472428
$580$	−944.059	−	646.869i	−0.0675860	−	0.0463100i
$581$	3574.53			0.255244
$582$			7107.92i			0.506242i
$583$			26800.5i			1.90389i
$584$	150.128			0.0106375
$585$	9586.35			0.677516
$586$	−23524.0			−1.65830
$587$	−15458.7			−1.08697			−0.543484	−	0.839419i	$-0.682895\pi$
$587$	−15458.7			−1.08697			−0.543484	+	0.839419i	$0.682895\pi$
$588$		−	803.406i		−	0.0563468i
$589$	11931.2			0.834666
$590$		−	3389.28i		−	0.236499i
$591$		−	438.246i		−	0.0305026i
$592$		−	16034.3i		−	1.11319i
$593$	−8208.66			−0.568447			−0.284224	−	0.958758i	$-0.591736\pi$
$593$	−8208.66			−0.568447			−0.284224	+	0.958758i	$0.591736\pi$
$594$		−	12828.4i		−	0.886117i
$595$		−	9057.50i		−	0.624069i
$596$	−3795.21			−0.260835
$597$			1539.84i			0.105563i
$598$		−	29601.2i		−	2.02422i
$599$		−	6127.81i		−	0.417989i	−0.977917	−	0.208995i	$-0.932981\pi$
$599$		−	6127.81i		−	0.417989i	0.977917	−	0.208995i	$-0.0670191\pi$
$600$	−879.437			−0.0598381
$601$		−	3297.62i		−	0.223815i	−0.993719	−	0.111908i	$-0.964304\pi$
$601$		−	3297.62i		−	0.223815i	0.993719	−	0.111908i	$-0.0356961\pi$
$602$	−12972.1			−0.878243
$603$	15773.6			1.06526
$604$	2678.17			0.180419
$605$	4287.23			0.288100
$606$			5426.64i			0.363766i
$607$		−	12382.0i		−	0.827958i	−0.910287	−	0.413979i	$-0.864139\pi$
$607$		−	12382.0i		−	0.827958i	0.910287	−	0.413979i	$-0.135861\pi$
$608$	−8778.90			−0.585578
$609$	3956.94	−	5774.87i	0.263289	−	0.384252i
$610$	−1654.29			−0.109804
$611$			36702.0i			2.43012i
$612$		−	2480.86i		−	0.163861i
$613$	9747.57			0.642252			0.321126	−	0.947036i	$-0.395939\pi$
$613$	9747.57			0.642252			0.321126	+	0.947036i	$0.395939\pi$
$614$	13225.8			0.869299
$615$	670.506			0.0439632
$616$	−24093.1			−1.57587
$617$			25023.8i			1.63277i	0.577506	+	0.816387i	$0.304026\pi$
$617$			25023.8i			1.63277i	−0.577506	+	0.816387i	$0.695974\pi$
$618$	−9481.74			−0.617171
$619$			2083.35i			0.135278i	0.997710	+	0.0676388i	$0.0215466\pi$
$619$			2083.35i			0.135278i	−0.997710	+	0.0676388i	$0.978453\pi$
$620$			652.710i			0.0422798i
$621$			10707.1i			0.691888i
$622$	−11617.2			−0.748883
$623$		−	18062.9i		−	1.16159i
$624$			10311.4i			0.661516i
$625$	625.000			0.0400000
$626$		−	19440.4i		−	1.24121i
$627$			10964.9i			0.698399i
$628$		−	2025.30i		−	0.128691i
$629$	−15410.0			−0.976847
$630$		−	9433.68i		−	0.596582i
$631$	7523.41			0.474647			0.237324	−	0.971431i	$-0.423730\pi$
$631$	7523.41			0.474647			0.237324	+	0.971431i	$0.423730\pi$
$632$	18724.4			1.17851
$633$	6908.01			0.433758
$634$	22361.0			1.40074
$635$			6711.16i			0.419408i
$636$		−	1469.19i		−	0.0915992i
$637$	−25091.4			−1.56069
$638$	18541.9	+	12704.9i	1.15060	+	0.788389i
$639$	6413.59			0.397054
$640$			8574.47i			0.529587i
$641$			20222.7i			1.24610i	0.782182	+	0.623050i	$0.214107\pi$
$641$			20222.7i			1.24610i	−0.782182	+	0.623050i	$0.785893\pi$
$642$	1912.34			0.117561
$643$	16700.9			1.02429			0.512145	−	0.858899i	$-0.328851\pi$
$643$	16700.9			1.02429			0.512145	+	0.858899i	$0.328851\pi$
$644$	−4510.30			−0.275979
$645$	1439.94			0.0879034
$646$			29142.0i			1.77489i
$647$	5898.52			0.358415			0.179208	−	0.983811i	$-0.442647\pi$
$647$	5898.52			0.358415			0.179208	+	0.983811i	$0.442647\pi$
$648$			9858.38i			0.597645i
$649$			10307.0i			0.623396i
$650$		−	6160.35i		−	0.371737i
$651$	−3992.67			−0.240376
$652$		−	5267.06i		−	0.316371i
$653$			9860.25i			0.590906i	0.955357	+	0.295453i	$0.0954705\pi$
$653$			9860.25i			0.590906i	−0.955357	+	0.295453i	$0.904529\pi$
$654$	2612.26			0.156189
$655$		−	6440.33i		−	0.384190i
$656$		−	5638.82i		−	0.335608i
$657$		−	178.761i		−	0.0106151i
$658$	36117.4			2.13982
$659$		−	8290.43i		−	0.490059i	−0.969516	−	0.245030i	$-0.921202\pi$
$659$		−	8290.43i		−	0.490059i	0.969516	−	0.245030i	$-0.0787977\pi$
$660$	−599.845			−0.0353772
$661$	11780.7			0.693216			0.346608	−	0.938010i	$-0.387333\pi$
$661$	11780.7			0.693216			0.346608	+	0.938010i	$0.387333\pi$
$662$	13524.6			0.794031
$663$	9909.91			0.580496
$664$			2805.13i			0.163946i
$665$			17158.0i			1.00054i
$666$	−16050.0			−0.933823
$667$	−15475.9	−	10604.1i	−0.898396	−	0.615581i
$668$	1670.87			0.0967781
$669$			535.139i			0.0309263i
$670$		−	10136.4i		−	0.584481i
$671$	5030.77			0.289435
$672$	2937.77			0.168641
$673$	−12161.4			−0.696564			−0.348282	−	0.937390i	$-0.613235\pi$
$673$	−12161.4			−0.696564			−0.348282	+	0.937390i	$0.613235\pi$
$674$	−935.256			−0.0534491
$675$			2228.28i			0.127061i
$676$	−6181.60			−0.351707
$677$		−	30395.0i		−	1.72552i	−0.505615	−	0.862759i	$-0.668734\pi$
$677$		−	30395.0i		−	1.72552i	0.505615	−	0.862759i	$-0.331266\pi$
$678$			3858.12i			0.218540i
$679$		−	33824.3i		−	1.91172i
$680$	7107.93			0.400848
$681$			336.539i			0.0189371i
$682$		−	12819.6i		−	0.719779i
$683$	−12235.2			−0.685456			−0.342728	−	0.939435i	$-0.611351\pi$
$683$	−12235.2			−0.685456			−0.342728	+	0.939435i	$0.611351\pi$
$684$			4699.60i			0.262710i
$685$		−	13408.4i		−	0.747894i
$686$		−	2342.39i		−	0.130369i
$687$	9416.16			0.522924
$688$		−	12109.6i		−	0.671041i
$689$	−45884.6			−2.53710
$690$	3233.50			0.178402
$691$	−15678.9			−0.863174			−0.431587	−	0.902071i	$-0.642046\pi$
$691$	−15678.9			−0.863174			−0.431587	+	0.902071i	$0.642046\pi$
$692$	799.823			0.0439374
$693$			28688.3i			1.57255i
$694$		−	22530.4i		−	1.23234i
$695$	231.190			0.0126181
$696$	4531.86	+	3105.23i	0.246810	+	0.169114i
$697$	−5419.27			−0.294504
$698$			7198.77i			0.390369i
$699$		−	2124.41i		−	0.114954i
$700$	−938.645			−0.0506821
$701$	7407.81			0.399129			0.199564	−	0.979885i	$-0.436047\pi$
$701$	7407.81			0.399129			0.199564	+	0.979885i	$0.436047\pi$
$702$	21963.1			1.18083
$703$	29191.8			1.56613
$704$		−	18103.3i		−	0.969168i
$705$	−4009.16			−0.214175
$706$			5923.67i			0.315779i
$707$		−	25823.6i		−	1.37369i
$708$		−	565.021i		−	0.0299926i
$709$	−18658.5			−0.988342			−0.494171	−	0.869365i	$-0.664528\pi$
$709$	−18658.5			−0.988342			−0.494171	+	0.869365i	$0.664528\pi$
$710$		−	4121.48i		−	0.217854i
$711$		−	22295.7i		−	1.17603i
$712$	14175.0			0.746108
$713$			10699.8i			0.562009i
$714$		−	9752.08i		−	0.511152i
$715$			18733.9i			0.979873i
$716$	5090.02			0.265674
$717$		−	9246.57i		−	0.481617i
$718$	14681.7			0.763112
$719$	29975.3			1.55478			0.777391	−	0.629017i	$-0.216542\pi$
$719$	29975.3			1.55478			0.777391	+	0.629017i	$0.216542\pi$
$720$	8806.50			0.455832
$721$	45120.5			2.33062
$722$		−	34102.5i		−	1.75784i
$723$			1712.60i			0.0880944i
$724$	4741.96			0.243417
$725$	−3220.72	−	2206.83i	−0.164985	−	0.113048i
$726$	4616.00			0.235972
$727$			11591.9i			0.591361i	0.955287	+	0.295681i	$0.0955464\pi$
$727$			11591.9i			0.591361i	−0.955287	+	0.295681i	$0.904454\pi$
$728$		−	41249.2i		−	2.10000i
$729$	7527.73			0.382448
$730$	−114.875			−0.00582426
$731$	−11638.1			−0.588854
$732$	−275.784			−0.0139252
$733$		−	29327.1i		−	1.47779i	−0.673820	−	0.738896i	$-0.735348\pi$
$733$		−	29327.1i		−	1.47779i	0.673820	−	0.738896i	$-0.264652\pi$
$734$	−8574.34			−0.431178
$735$		−	2740.87i		−	0.137549i
$736$		−	7872.85i		−	0.394289i
$737$			30825.2i			1.54065i
$738$	−5644.35			−0.281533
$739$		−	14436.3i		−	0.718603i	−0.933222	−	0.359301i	$-0.883015\pi$
$739$		−	14436.3i		−	0.718603i	0.933222	−	0.359301i	$-0.116985\pi$
$740$			1596.97i			0.0793320i
$741$	−18772.8			−0.930681
$742$			45153.8i			2.23403i
$743$			5564.18i			0.274738i	0.990520	+	0.137369i	$0.0438646\pi$
$743$			5564.18i			0.274738i	−0.990520	+	0.137369i	$0.956135\pi$
$744$		−	3133.27i		−	0.154397i
$745$	−12947.6			−0.636729
$746$			25314.2i			1.24238i
$747$	3340.15			0.163601
$748$	4848.17			0.236988
$749$	−9100.19			−0.443944
$750$	672.929			0.0327625
$751$			19794.2i			0.961787i	0.876779	+	0.480894i	$0.159688\pi$
$751$			19794.2i			0.961787i	−0.876779	+	0.480894i	$0.840312\pi$
$752$			33716.2i			1.63498i
$753$	−12702.2			−0.614734
$754$	−21751.8	+	31745.2i	−1.05060	+	1.53328i
$755$	9136.76			0.440425
$756$		−	3346.50i		−	0.160993i
$757$		−	17778.6i		−	0.853597i	−0.904347	−	0.426798i	$-0.859641\pi$
$757$		−	17778.6i		−	0.853597i	0.904347	−	0.426798i	$-0.140359\pi$
$758$	−1096.04			−0.0525199
$759$	−9833.24			−0.470256
$760$	−13464.9			−0.642660
$761$	15626.7			0.744374			0.372187	−	0.928158i	$-0.378608\pi$
$761$	15626.7			0.744374			0.372187	+	0.928158i	$0.378608\pi$
$762$			7225.81i			0.343522i
$763$	−12430.9			−0.589815
$764$			320.461i			0.0151752i
$765$		−	8463.62i		−	0.400004i
$766$		−	37941.2i		−	1.78965i
$767$	−17646.3			−0.830732
$768$			3814.93i			0.179244i
$769$		−	6083.94i		−	0.285296i	−0.989773	−	0.142648i	$-0.954438\pi$
$769$		−	6083.94i		−	0.285296i	0.989773	−	0.142648i	$-0.0455617\pi$
$770$	18435.6			0.862821
$771$		−	164.581i		−	0.00768774i
$772$			5512.97i			0.257016i
$773$		−	12656.7i		−	0.588915i	−0.955665	−	0.294458i	$-0.904861\pi$
$773$		−	12656.7i		−	0.588915i	0.955665	−	0.294458i	$-0.0951390\pi$
$774$	−12121.5			−0.562918
$775$			2226.76i			0.103210i
$776$	26543.8			1.22792
$777$	−9768.75			−0.451032
$778$	8387.73			0.386523
$779$	10266.0			0.472165
$780$		−	1026.98i		−	0.0471434i
$781$			12533.6i			0.574249i
$782$	−26134.4			−1.19509
$783$	7867.90	−	11482.6i	0.359101	−	0.524081i
$784$	−23050.2			−1.05003
$785$		−	6909.42i		−	0.314150i
$786$		−	6934.22i		−	0.314676i
$787$	20476.9			0.927476			0.463738	−	0.885972i	$-0.346508\pi$
$787$	20476.9			0.927476			0.463738	+	0.885972i	$0.346508\pi$
$788$	367.071			0.0165944
$789$	−9822.38			−0.443201
$790$	−14327.6			−0.645257
$791$		−	18359.5i		−	0.825272i
$792$	−22513.3			−1.01007
$793$			8613.07i			0.385699i
$794$		−	32913.9i		−	1.47112i
$795$		−	5012.23i		−	0.223604i
$796$	−1289.75			−0.0574298
$797$		−	23480.8i		−	1.04358i	−0.853074	−	0.521790i	$-0.825265\pi$
$797$		−	23480.8i		−	1.04358i	0.853074	−	0.521790i	$-0.174735\pi$
$798$			18473.8i			0.819505i
$799$	32403.5			1.43473
$800$		−	1638.43i		−	0.0724090i
$801$		−	16878.5i		−	0.744536i
$802$			26550.9i			1.16901i
$803$	349.340			0.0153524
$804$		−	1689.82i		−	0.0741235i
$805$	−15387.2			−0.673698
$806$	21948.2			0.959172
$807$	1217.93			0.0531265
$808$	20265.2			0.882338
$809$			43637.2i			1.89642i	0.317650	+	0.948208i	$0.397106\pi$
$809$			43637.2i			1.89642i	−0.317650	+	0.948208i	$0.602894\pi$
$810$		−	7543.45i		−	0.327222i
$811$	−34728.4			−1.50367			−0.751837	−	0.659349i	$-0.770832\pi$
$811$	−34728.4			−1.50367			−0.751837	+	0.659349i	$0.770832\pi$
$812$	4836.97	+	3314.29i	0.209045	+	0.143238i
$813$	4545.04			0.196066
$814$		−	31365.4i		−	1.35056i
$815$		−	17968.9i		−	0.772299i
$816$	9103.74			0.390557
$817$	22046.6			0.944081
$818$	41206.6			1.76131
$819$	−49116.6			−2.09557
$820$			561.609i			0.0239174i
$821$	−33882.8			−1.44034			−0.720170	−	0.693798i	$-0.755936\pi$
$821$	−33882.8			−1.44034			−0.720170	+	0.693798i	$0.755936\pi$
$822$		−	14436.6i		−	0.612572i
$823$		−	14478.0i		−	0.613210i	−0.951837	−	0.306605i	$-0.900807\pi$
$823$		−	14478.0i		−	0.613210i	0.951837	−	0.306605i	$-0.0991931\pi$
$824$			35408.6i			1.49699i
$825$	−2046.41			−0.0863598
$826$			17365.3i			0.731496i
$827$		−	1058.20i		−	0.0444947i	−0.999752	−	0.0222473i	$-0.992918\pi$
$827$		−	1058.20i		−	0.0444947i	0.999752	−	0.0222473i	$-0.00708213\pi$
$828$	−4214.57			−0.176892
$829$			33244.9i			1.39282i	0.717646	+	0.696408i	$0.245220\pi$
$829$			33244.9i			1.39282i	−0.717646	+	0.696408i	$0.754780\pi$
$830$		−	2146.44i		−	0.0897638i
$831$			7319.22i			0.305537i
$832$	30994.3			1.29151
$833$			22152.7i			0.921424i
$834$	248.919			0.0103350
$835$	5700.27			0.236247
$836$	−9184.10			−0.379951
$837$	−7938.94			−0.327849
$838$			14273.3i			0.588379i
$839$		−	21224.5i		−	0.873361i	−0.899617	−	0.436680i	$-0.856154\pi$
$839$		−	21224.5i		−	0.873361i	0.899617	−	0.436680i	$-0.143846\pi$
$840$	4505.88			0.185080
$841$	8804.62	+	22744.3i	0.361008	+	0.932563i
$842$	−7003.69			−0.286655
$843$			13632.8i			0.556984i
$844$			5786.08i			0.235978i
$845$	−21088.9			−0.858558
$846$	33749.3			1.37154
$847$	−21966.0			−0.891099
$848$	−42151.9			−1.70696
$849$		−	2078.29i		−	0.0840127i
$850$	−5438.86			−0.219472
$851$			26179.0i			1.05453i
$852$		−	687.085i		−	0.0276281i
$853$			36483.9i			1.46446i	0.681056	+	0.732231i	$0.261521\pi$
$853$			36483.9i			1.46446i	−0.681056	+	0.732231i	$0.738479\pi$
$854$	8475.90			0.339624
$855$			16033.0i			0.641306i
$856$		−	7141.43i		−	0.285151i
$857$	−28349.8			−1.13000			−0.565000	−	0.825091i	$-0.691124\pi$
$857$	−28349.8			−1.13000			−0.565000	+	0.825091i	$0.691124\pi$
$858$			20170.6i			0.802578i
$859$		−	8069.29i		−	0.320513i	−0.987075	−	0.160256i	$-0.948768\pi$
$859$		−	8069.29i		−	0.320513i	0.987075	−	0.160256i	$-0.0512321\pi$
$860$			1206.08i			0.0478222i
$861$	−3435.40			−0.135979
$862$		−	18328.8i		−	0.724224i
$863$	26242.7			1.03512			0.517562	−	0.855645i	$-0.326840\pi$
$863$	26242.7			1.03512			0.517562	+	0.855645i	$0.326840\pi$
$864$	5841.40			0.230010
$865$	2728.65			0.107256
$866$	−31935.5			−1.25313
$867$		−	152.577i		−	0.00597669i
$868$		−	3344.22i		−	0.130772i
$869$	43570.9			1.70085
$870$	−3467.70	−	2376.07i	−0.135133	−	0.0925934i
$871$	−52775.1			−2.05306
$872$		−	9755.23i		−	0.378846i
$873$		−	31606.5i		−	1.22533i
$874$	49507.4			1.91603
$875$	−3202.25			−0.123721
$876$	−19.1506			−0.000738628
$877$	36573.8			1.40822			0.704109	−	0.710092i	$-0.251346\pi$
$877$	36573.8			1.40822			0.704109	+	0.710092i	$0.251346\pi$
$878$			45248.5i			1.73925i
$879$	−13378.9			−0.513379
$880$			17209.9i			0.659257i
$881$			2000.28i			0.0764938i	0.999268	+	0.0382469i	$0.0121773\pi$
$881$			2000.28i			0.0764938i	−0.999268	+	0.0382469i	$0.987823\pi$
$882$			23072.8i			0.880840i
$883$	−36057.6			−1.37422			−0.687109	−	0.726554i	$-0.741121\pi$
$883$	−36057.6			−1.37422			−0.687109	+	0.726554i	$0.741121\pi$
$884$			8300.44i			0.315808i
$885$		−	1927.60i		−	0.0732155i
$886$	23723.1			0.899540
$887$			2827.84i			0.107046i	0.998567	+	0.0535228i	$0.0170450\pi$
$887$			2827.84i			0.107046i	−0.998567	+	0.0535228i	$0.982955\pi$
$888$		−	7666.09i		−	0.289704i
$889$		−	34385.2i		−	1.29724i
$890$	−10846.4			−0.408509
$891$			22940.0i			0.862536i
$892$	−448.228			−0.0168249
$893$	−61383.3			−2.30024
$894$	−13940.5			−0.521521
$895$	17364.9			0.648542
$896$		−	43932.1i		−	1.63802i
$897$		−	16835.3i		−	0.626659i
$898$	−4065.71			−0.151085
$899$	7862.55	−	11474.8i	0.291692	−	0.425703i
$900$	−877.100			−0.0324852
$901$			40510.7i			1.49790i
$902$		−	11030.4i		−	0.407174i
$903$	−7377.68			−0.271887
$904$	14407.8			0.530083
$905$	16177.5			0.594208
$906$	9837.42			0.360736
$907$			46391.0i			1.69833i	0.528126	+	0.849166i	$0.322895\pi$
$907$			46391.0i			1.69833i	−0.528126	+	0.849166i	$0.677105\pi$
$908$	−281.881			−0.0103024
$909$		−	24130.4i		−	0.880479i
$910$			31563.1i			1.14979i
$911$			17736.5i			0.645047i	0.946561	+	0.322524i	$0.104531\pi$
$911$			17736.5i			0.645047i	−0.946561	+	0.322524i	$0.895469\pi$
$912$	−17245.6			−0.626161
$913$			6527.43i			0.236611i
$914$		−	15368.2i		−	0.556166i
$915$	−940.853			−0.0339930
$916$			7886.88i			0.284487i
$917$			32997.6i			1.18831i
$918$		−	19390.8i		−	0.697160i
$919$	7460.97			0.267807			0.133903	−	0.990994i	$-0.457249\pi$
$919$	7460.97			0.267807			0.133903	+	0.990994i	$0.457249\pi$
$920$		−	12075.2i		−	0.432725i
$921$	7521.99			0.269118
$922$	−792.915			−0.0283224
$923$	−21458.5			−0.765239
$924$	3073.37			0.109422
$925$			5448.15i			0.193659i
$926$			4644.74i			0.164833i
$927$	42162.0			1.49383
$928$	−5785.19	+	8443.06i	−0.204642	+	0.298661i
$929$	−48270.9			−1.70475			−0.852377	−	0.522927i	$-0.824840\pi$
$929$	−48270.9			−1.70475			−0.852377	+	0.522927i	$0.824840\pi$
$930$			2397.52i			0.0845353i
$931$		−	41964.8i		−	1.47727i
$932$	1779.39			0.0625384
$933$	−6607.09			−0.231840
$934$	−9217.08			−0.322904
$935$	16539.8			0.578514
$936$		−	38544.6i		−	1.34601i
$937$	14138.7			0.492945			0.246473	−	0.969150i	$-0.420728\pi$
$937$	14138.7			0.492945			0.246473	+	0.969150i	$0.420728\pi$
$938$			51934.6i			1.80781i
$939$		−	11056.5i		−	0.384253i
$940$		−	3358.03i		−	0.116518i
$941$	10287.0			0.356372			0.178186	−	0.983997i	$-0.442977\pi$
$941$	10287.0			0.356372			0.178186	+	0.983997i	$0.442977\pi$
$942$		−	7439.28i		−	0.257309i
$943$			9206.43i			0.317924i
$944$	−16210.8			−0.558916
$945$		−	11416.8i		−	0.393003i
$946$		−	23688.2i		−	0.814133i
$947$		−	52921.3i		−	1.81596i	−0.419018	−	0.907978i	$-0.637626\pi$
$947$		−	52921.3i		−	1.81596i	0.419018	−	0.907978i	$-0.362374\pi$
$948$	−2388.53			−0.0818310
$949$			598.097i			0.0204584i
$950$	10303.1			0.351869
$951$	12717.5			0.433642
$952$	−36418.2			−1.23983
$953$	−12487.2			−0.424450			−0.212225	−	0.977221i	$-0.568071\pi$
$953$	−12487.2			−0.424450			−0.212225	+	0.977221i	$0.568071\pi$
$954$			42193.2i			1.43192i
$955$			1093.27i			0.0370444i
$956$	7744.84			0.262015
$957$	10545.4	+	7225.74i	0.356203	+	0.244070i
$958$	−25053.7			−0.844937
$959$			68699.0i			2.31325i
$960$			3385.67i			0.113825i
$961$	21857.5			0.733693
$962$	53700.0			1.79975
$963$	−8503.51			−0.284550
$964$	−1434.46			−0.0479261
$965$			18807.8i			0.627405i
$966$	−16567.2			−0.551801
$967$			7415.56i			0.246606i	0.992369	+	0.123303i	$0.0393488\pi$
$967$			7415.56i			0.246606i	−0.992369	+	0.123303i	$0.960651\pi$
$968$		−	17238.0i		−	0.572365i
$969$			16574.1i			0.549471i
$970$	−20310.8			−0.672311
$971$		−	37360.3i		−	1.23476i	−0.786666	−	0.617379i	$-0.788195\pi$
$971$		−	37360.3i		−	1.23476i	0.786666	−	0.617379i	$-0.211805\pi$
$972$		−	4784.59i		−	0.157887i
$973$	−1184.53			−0.0390279
$974$		−	36650.5i		−	1.20571i
$975$		−	3503.61i		−	0.115082i
$976$			7912.39i			0.259498i
$977$	−45677.8			−1.49576			−0.747882	−	0.663832i	$-0.768929\pi$
$977$	−45677.8			−1.49576			−0.747882	+	0.663832i	$0.768929\pi$
$978$		−	19346.9i		−	0.632561i
$979$	32984.5			1.07680
$980$	2295.73			0.0748309
$981$	−11615.8			−0.378048
$982$	−26353.7			−0.856397
$983$		−	3354.87i		−	0.108854i	−0.998518	−	0.0544271i	$-0.982667\pi$
$983$		−	3354.87i		−	0.108854i	0.998518	−	0.0544271i	$-0.0173333\pi$
$984$		−	2695.95i		−	0.0873412i
$985$	1252.28			0.0405087
$986$	28027.2	+	19204.3i	0.905242	+	0.620272i
$987$	20541.3			0.662448
$988$		−	15723.9i		−	0.506319i
$989$			19771.3i			0.635682i
$990$	17226.8			0.553034
$991$	−26002.9			−0.833512			−0.416756	−	0.909018i	$-0.636833\pi$
$991$	−26002.9			−0.833512			−0.416756	+	0.909018i	$0.636833\pi$
$992$	5837.43			0.186833
$993$	7691.93			0.245817
$994$			21116.8i			0.673827i
$995$	−4400.08			−0.140193
$996$		−	357.829i		−	0.0113838i
$997$			1814.36i			0.0576343i	0.999585	+	0.0288172i	$0.00917406\pi$
$997$			1814.36i			0.0576343i	−0.999585	+	0.0288172i	$0.990826\pi$
$998$		−	39748.0i		−	1.26072i
$999$	−19424.0			−0.615163

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.4.c.b.86.12	yes	16
29.28	even	2	inner	145.4.c.b.86.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.4.c.b.86.5	✓	16	29.28	even	2	inner
145.4.c.b.86.12	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	145.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.07662i q^{2} +1.74979i q^{3} -1.46560 q^{4} -5.00000 q^{5} -5.38343 q^{6} +25.6180 q^{7} +20.1039i q^{8} +23.9382 q^{9} +O(q^{10})\)	\(q+3.07662i q^{2} +1.74979i q^{3} -1.46560 q^{4} -5.00000 q^{5} -5.38343 q^{6} +25.6180 q^{7} +20.1039i q^{8} +23.9382 q^{9} -15.3831i q^{10} +46.7808i q^{11} -2.56449i q^{12} -80.0924 q^{13} +78.8168i q^{14} -8.74893i q^{15} -73.5768 q^{16} +70.7121i q^{17} +73.6489i q^{18} -133.953i q^{19} +7.32802 q^{20} +44.8260i q^{21} -143.927 q^{22} +120.128 q^{23} -35.1775 q^{24} +25.0000 q^{25} -246.414i q^{26} +89.1310i q^{27} -37.5458 q^{28} +(-128.829 - 88.2734i) q^{29} +26.9172 q^{30} +89.0705i q^{31} -65.5372i q^{32} -81.8564 q^{33} -217.554 q^{34} -128.090 q^{35} -35.0840 q^{36} +217.926i q^{37} +412.123 q^{38} -140.144i q^{39} -100.519i q^{40} +76.6386i q^{41} -137.913 q^{42} +164.585i q^{43} -68.5622i q^{44} -119.691 q^{45} +369.588i q^{46} -458.245i q^{47} -128.744i q^{48} +313.281 q^{49} +76.9156i q^{50} -123.731 q^{51} +117.384 q^{52} +572.896 q^{53} -274.223 q^{54} -233.904i q^{55} +515.020i q^{56} +234.389 q^{57} +(271.584 - 396.357i) q^{58} +220.325 q^{59} +12.8225i q^{60} -107.539i q^{61} -274.036 q^{62} +613.249 q^{63} -386.982 q^{64} +400.462 q^{65} -251.841i q^{66} +658.928 q^{67} -103.636i q^{68} +210.198i q^{69} -394.084i q^{70} +267.922 q^{71} +481.251i q^{72} -7.46759i q^{73} -670.476 q^{74} +43.7446i q^{75} +196.322i q^{76} +1198.43i q^{77} +431.172 q^{78} -931.384i q^{79} +367.884 q^{80} +490.372 q^{81} -235.788 q^{82} +139.532 q^{83} -65.6971i q^{84} -353.560i q^{85} -506.366 q^{86} +(154.460 - 225.423i) q^{87} -940.475 q^{88} -705.086i q^{89} -368.245i q^{90} -2051.80 q^{91} -176.060 q^{92} -155.854 q^{93} +1409.85 q^{94} +669.765i q^{95} +114.676 q^{96} -1320.33i q^{97} +963.846i q^{98} +1119.85i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 62 q^{4} - 80 q^{5} + 50 q^{6} + 38 q^{7} - 126 q^{9}+O(q^{10}) \) 16 * q - 62 * q^4 - 80 * q^5 + 50 * q^6 + 38 * q^7 - 126 * q^9	\( 16 q - 62 q^{4} - 80 q^{5} + 50 q^{6} + 38 q^{7} - 126 q^{9} - 14 q^{13} + 210 q^{16} + 310 q^{20} + 88 q^{22} + 42 q^{23} + 62 q^{24} + 400 q^{25} - 346 q^{28} + 28 q^{29} - 250 q^{30} - 460 q^{33} - 626 q^{34} - 190 q^{35} - 12 q^{36} - 292 q^{38} + 584 q^{42} + 630 q^{45} + 1894 q^{49} - 320 q^{51} - 294 q^{52} + 614 q^{53} + 1840 q^{54} - 1360 q^{57} - 644 q^{58} - 2086 q^{59} - 30 q^{62} - 1456 q^{63} - 894 q^{64} + 70 q^{65} - 1604 q^{67} + 792 q^{71} + 1720 q^{74} + 4894 q^{78} - 1050 q^{80} - 192 q^{81} + 1276 q^{82} + 4400 q^{83} - 2042 q^{86} - 2046 q^{87} - 9264 q^{88} + 212 q^{91} - 2030 q^{92} - 1816 q^{93} + 4304 q^{94} + 2234 q^{96}+O(q^{100}) \) 16 * q - 62 * q^4 - 80 * q^5 + 50 * q^6 + 38 * q^7 - 126 * q^9 - 14 * q^13 + 210 * q^16 + 310 * q^20 + 88 * q^22 + 42 * q^23 + 62 * q^24 + 400 * q^25 - 346 * q^28 + 28 * q^29 - 250 * q^30 - 460 * q^33 - 626 * q^34 - 190 * q^35 - 12 * q^36 - 292 * q^38 + 584 * q^42 + 630 * q^45 + 1894 * q^49 - 320 * q^51 - 294 * q^52 + 614 * q^53 + 1840 * q^54 - 1360 * q^57 - 644 * q^58 - 2086 * q^59 - 30 * q^62 - 1456 * q^63 - 894 * q^64 + 70 * q^65 - 1604 * q^67 + 792 * q^71 + 1720 * q^74 + 4894 * q^78 - 1050 * q^80 - 192 * q^81 + 1276 * q^82 + 4400 * q^83 - 2042 * q^86 - 2046 * q^87 - 9264 * q^88 + 212 * q^91 - 2030 * q^92 - 1816 * q^93 + 4304 * q^94 + 2234 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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