LMFDB - Embedded newform 152.4.t.a.101.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,4,Mod(5,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 16])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	152.t (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.96829032087$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$58$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	152.101
Dual form			152.4.t.a.149.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.82826 - 0.0311153i) q^{2} +(-0.638447 + 1.75412i) q^{3} +(7.99806 + 0.176004i) q^{4} +(19.7279 - 3.47857i) q^{5} +(1.86027 - 4.94123i) q^{6} +(11.8990 - 20.6097i) q^{7} +(-22.6151 - 0.746646i) q^{8} +(18.0139 + 15.1154i) q^{9} +(-55.9039 + 9.22444i) q^{10} +(-20.6968 + 11.9493i) q^{11} +(-5.41507 + 13.9172i) q^{12} +(-31.4808 - 86.4928i) q^{13} +(-34.2947 + 57.9192i) q^{14} +(-6.49342 + 36.8260i) q^{15} +(63.9380 + 2.81538i) q^{16} +(12.1125 - 10.1636i) q^{17} +(-50.4775 - 43.3108i) q^{18} +(-24.5928 + 79.0835i) q^{19} +(158.398 - 24.3496i) q^{20} +(28.5549 + 34.0304i) q^{21} +(58.9076 - 33.1517i) q^{22} +(17.0434 - 96.6578i) q^{23} +(15.7482 - 39.1929i) q^{24} +(259.630 - 94.4974i) q^{25} +(86.3445 + 245.603i) q^{26} +(-81.6635 + 47.1484i) q^{27} +(98.7963 - 162.743i) q^{28} +(53.5466 - 63.8144i) q^{29} +(19.5109 - 103.951i) q^{30} +(49.3503 - 85.4773i) q^{31} +(-180.746 - 9.95207i) q^{32} +(-7.74668 - 43.9336i) q^{33} +(-34.5734 + 28.3683i) q^{34} +(163.051 - 447.978i) q^{35} +(141.416 + 124.065i) q^{36} +158.620i q^{37} +(72.0154 - 222.903i) q^{38} +171.817 q^{39} +(-448.746 + 63.9384i) q^{40} +(231.536 + 84.2722i) q^{41} +(-79.7018 - 97.1353i) q^{42} +(-323.179 + 56.9851i) q^{43} +(-167.637 + 91.9285i) q^{44} +(407.957 + 235.534i) q^{45} +(-51.2106 + 272.843i) q^{46} +(218.747 + 183.550i) q^{47} +(-45.7596 + 110.357i) q^{48} +(-111.672 - 193.422i) q^{49} +(-737.239 + 259.185i) q^{50} +(10.0949 + 27.7356i) q^{51} +(-236.562 - 697.316i) q^{52} +(473.987 + 83.5766i) q^{53} +(232.432 - 130.807i) q^{54} +(-366.739 + 307.730i) q^{55} +(-284.485 + 457.205i) q^{56} +(-123.021 - 93.6292i) q^{57} +(-153.429 + 178.817i) q^{58} +(31.5545 + 37.6052i) q^{59} +(-58.4163 + 293.394i) q^{60} +(-590.177 - 104.064i) q^{61} +(-142.235 + 240.216i) q^{62} +(525.871 - 191.401i) q^{63} +(510.885 + 33.7709i) q^{64} +(-921.923 - 1596.82i) q^{65} +(20.5426 + 124.497i) q^{66} +(-89.8104 + 107.032i) q^{67} +(98.6652 - 79.1571i) q^{68} +(158.668 + 91.6070i) q^{69} +(-475.088 + 1261.92i) q^{70} +(54.0751 + 306.675i) q^{71} +(-396.100 - 355.287i) q^{72} +(626.259 + 227.940i) q^{73} +(4.93551 - 448.618i) q^{74} +515.753i q^{75} +(-210.614 + 628.186i) q^{76} +568.738i q^{77} +(-485.944 - 5.34615i) q^{78} +(-646.316 - 235.240i) q^{79} +(1271.16 - 166.871i) q^{80} +(79.6861 + 451.922i) q^{81} +(-652.221 - 245.548i) q^{82} +(165.283 + 95.4265i) q^{83} +(222.395 + 277.203i) q^{84} +(203.600 - 242.640i) q^{85} +(915.805 - 151.113i) q^{86} +(77.7513 + 134.669i) q^{87} +(476.982 - 254.781i) q^{88} +(-590.353 + 214.871i) q^{89} +(-1146.48 - 678.844i) q^{90} +(-2157.18 - 380.369i) q^{91} +(153.326 - 770.075i) q^{92} +(118.430 + 141.139i) q^{93} +(-612.960 - 525.933i) q^{94} +(-210.067 + 1645.70i) q^{95} +(132.854 - 310.695i) q^{96} +(788.075 - 661.273i) q^{97} +(309.819 + 550.521i) q^{98} +(-553.448 - 97.5879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q - 6 q^{2} + 12 q^{4} - 24 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 75 q^{10} - 3 q^{12} - 81 q^{14} - 12 q^{15} + 192 q^{16} - 12 q^{17} - 12 q^{18} + 558 q^{20} - 30 q^{22} - 12 q^{23} - 108 q^{24}+ \cdots + 8055 q^{98}+O(q^{100}) $ 348 * q - 6 * q^2 + 12 * q^4 - 24 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 75 * q^10 - 3 * q^12 - 81 * q^14 - 12 * q^15 + 192 * q^16 - 12 * q^17 - 12 * q^18 + 558 * q^20 - 30 * q^22 - 12 * q^23 - 108 * q^24 - 12 * q^25 - 411 * q^26 + 1140 * q^28 - 282 * q^30 - 1122 * q^31 + 39 * q^32 - 174 * q^33 + 1536 * q^34 - 2835 * q^36 + 966 * q^38 - 24 * q^39 - 1068 * q^40 + 48 * q^41 + 3015 * q^42 - 1203 * q^44 - 528 * q^46 - 624 * q^47 + 4755 * q^48 - 6768 * q^49 - 1074 * q^50 - 1089 * q^52 + 615 * q^54 - 762 * q^55 + 2046 * q^56 - 12 * q^57 + 4092 * q^58 + 4050 * q^60 + 3120 * q^62 + 2046 * q^63 + 2355 * q^64 - 6 * q^65 + 1716 * q^66 - 1176 * q^68 - 2973 * q^70 - 12 * q^71 - 7122 * q^72 + 636 * q^73 - 9363 * q^74 - 2454 * q^76 - 6897 * q^78 - 12 * q^79 - 6885 * q^80 + 1206 * q^81 - 7311 * q^82 + 1947 * q^84 + 7452 * q^86 - 6 * q^87 - 1131 * q^88 - 12 * q^89 + 4014 * q^90 + 7656 * q^92 + 11898 * q^94 + 1848 * q^95 - 18966 * q^96 - 12 * q^97 + 8055 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−2.82826	−	0.0311153i	−0.999939	−	0.0110009i
$2$	−2.82826	−	0.0311153i	−0.999939	−	0.0110009i
$3$	−0.638447	+	1.75412i	−0.122869	+	0.337580i	−0.985844	−	0.167667i	$-0.946377\pi$
$3$	−0.638447	+	1.75412i	−0.122869	+	0.337580i	0.862974	+	0.505248i	$0.168599\pi$
$4$	7.99806	+	0.176004i	0.999758	+	0.0220005i
$5$	19.7279	−	3.47857i	1.76452	−	0.311133i	0.805106	−	0.593131i	$-0.202108\pi$
$5$	19.7279	−	3.47857i	1.76452	−	0.311133i	0.959415	+	0.281999i	$0.0909974\pi$
$6$	1.86027	−	4.94123i	0.126575	−	0.336208i
$7$	11.8990	−	20.6097i	0.642485	−	1.11282i	−0.342391	−	0.939558i	$-0.611237\pi$
$7$	11.8990	−	20.6097i	0.642485	−	1.11282i	0.984876	−	0.173260i	$-0.0554300\pi$
$8$	−22.6151	−	0.746646i	−0.999455	−	0.0329974i
$9$	18.0139	+	15.1154i	0.667181	+	0.559831i
$10$	−55.9039	+	9.22444i	−1.76784	+	0.291702i
$11$	−20.6968	+	11.9493i	−0.567301	+	0.327532i	−0.756071	−	0.654490i	$-0.772883\pi$
$11$	−20.6968	+	11.9493i	−0.567301	+	0.327532i	0.188769	+	0.982021i	$0.439550\pi$
$12$	−5.41507	+	13.9172i	−0.130266	+	0.334795i
$13$	−31.4808	−	86.4928i	−0.671631	−	1.84529i	−0.513992	−	0.857795i	$-0.671834\pi$
$13$	−31.4808	−	86.4928i	−0.671631	−	1.84529i	−0.157639	−	0.987497i	$-0.550388\pi$
$14$	−34.2947	+	57.9192i	−0.654688	+	1.10568i
$15$	−6.49342	+	36.8260i	−0.111773	+	0.633896i
$16$	63.9380	+	2.81538i	0.999032	+	0.0439903i
$17$	12.1125	−	10.1636i	0.172806	−	0.145002i	−0.552283	−	0.833657i	$-0.686243\pi$
$17$	12.1125	−	10.1636i	0.172806	−	0.145002i	0.725089	+	0.688655i	$0.241799\pi$
$18$	−50.4775	−	43.3108i	−0.660982	−	0.567137i
$19$	−24.5928	+	79.0835i	−0.296946	+	0.954894i
$19$	−24.5928	+	79.0835i	−0.296946	+	0.954894i
$20$	158.398	−	24.3496i	1.77094	−	0.272237i
$21$	28.5549	+	34.0304i	0.296724	+	0.353621i
$22$	58.9076	−	33.1517i	0.570870	−	0.321271i
$23$	17.0434	−	96.6578i	0.154513	−	0.876284i	−0.804717	−	0.593658i	$-0.797683\pi$
$23$	17.0434	−	96.6578i	0.154513	−	0.876284i	0.959230	−	0.282626i	$-0.0912057\pi$
$24$	15.7482	−	39.1929i	0.133942	−	0.333342i
$25$	259.630	−	94.4974i	2.07704	−	0.755980i
$26$	86.3445	+	245.603i	0.651291	+	1.85257i
$27$	−81.6635	+	47.1484i	−0.582080	+	0.336064i
$28$	98.7963	−	162.743i	0.666812	−	1.09841i
$29$	53.5466	−	63.8144i	0.342874	−	0.408622i	−0.566859	−	0.823815i	$-0.691842\pi$
$29$	53.5466	−	63.8144i	0.342874	−	0.408622i	0.909733	+	0.415193i	$0.136286\pi$
$30$	19.5109	−	103.951i	0.118740	−	0.632628i
$31$	49.3503	−	85.4773i	0.285922	−	0.495231i	−0.686910	−	0.726742i	$-0.741034\pi$
$31$	49.3503	−	85.4773i	0.285922	−	0.495231i	0.972832	+	0.231511i	$0.0743668\pi$
$32$	−180.746	−	9.95207i	−0.998488	−	0.0549779i
$33$	−7.74668	−	43.9336i	−0.0408644	−	0.231753i
$34$	−34.5734	+	28.3683i	−0.174391	+	0.143092i
$35$	163.051	−	447.978i	0.787445	−	2.16349i
$36$	141.416	+	124.065i	0.654703	+	0.574374i
$37$			158.620i			0.704783i	0.935853	+	0.352392i	$0.114632\pi$
$37$			158.620i			0.704783i	−0.935853	+	0.352392i	$0.885368\pi$
$38$	72.0154	−	222.903i	0.307432	−	0.951570i
$39$	171.817			0.705457
$40$	−448.746	+	63.9384i	−1.77383	+	0.252739i
$41$	231.536	+	84.2722i	0.881948	+	0.321003i	0.742996	−	0.669296i	$-0.233404\pi$
$41$	231.536	+	84.2722i	0.881948	+	0.321003i	0.138952	+	0.990299i	$0.455627\pi$
$42$	−79.7018	−	97.1353i	−0.292815	−	0.356864i
$43$	−323.179	+	56.9851i	−1.14615	+	0.202097i	−0.714293	−	0.699847i	$-0.753251\pi$
$43$	−323.179	+	56.9851i	−1.14615	+	0.202097i	−0.431854	+	0.901944i	$0.642140\pi$
$44$	−167.637	+	91.9285i	−0.574370	+	0.314971i
$45$	407.957	+	235.534i	1.35144	+	0.780252i
$46$	−51.2106	+	272.843i	−0.164143	+	0.874532i
$47$	218.747	+	183.550i	0.678882	+	0.569650i	0.915680	−	0.401909i	$-0.131653\pi$
$47$	218.747	+	183.550i	0.678882	+	0.569650i	−0.236797	+	0.971559i	$0.576098\pi$
$48$	−45.7596	+	110.357i	−0.137600	+	0.331848i
$49$	−111.672	−	193.422i	−0.325575	−	0.563912i
$50$	−737.239	+	259.185i	−2.08523	+	0.733085i
$51$	10.0949	+	27.7356i	0.0277172	+	0.0761522i
$52$	−236.562	−	697.316i	−0.630871	−	1.85962i
$53$	473.987	+	83.5766i	1.22844	+	0.216606i	0.749953	−	0.661491i	$-0.230076\pi$
$53$	473.987	+	83.5766i	1.22844	+	0.216606i	0.478482	+	0.878097i	$0.341187\pi$
$54$	232.432	−	130.807i	0.585741	−	0.329640i
$55$	−366.739	+	307.730i	−0.899109	+	0.754442i
$56$	−284.485	+	457.205i	−0.678856	+	1.09101i
$57$	−123.021	−	93.6292i	−0.285868	−	0.217570i
$58$	−153.429	+	178.817i	−0.347349	+	0.404825i
$59$	31.5545	+	37.6052i	0.0696279	+	0.0829793i	0.799734	−	0.600354i	$-0.204974\pi$
$59$	31.5545	+	37.6052i	0.0696279	+	0.0829793i	−0.730106	+	0.683334i	$0.760529\pi$
$60$	−58.4163	+	293.394i	−0.125692	+	0.631283i
$61$	−590.177	−	104.064i	−1.23876	−	0.218427i	−0.484376	−	0.874860i	$-0.660953\pi$
$61$	−590.177	−	104.064i	−1.23876	−	0.218427i	−0.754384	+	0.656433i	$0.772065\pi$
$62$	−142.235	+	240.216i	−0.291353	+	0.492056i
$63$	525.871	−	191.401i	1.05164	−	0.382767i
$64$	510.885	+	33.7709i	0.997822	+	0.0659589i
$65$	−921.923	−	1596.82i	−1.75924	−	3.04709i
$66$	20.5426	+	124.497i	0.0383124	+	0.232189i
$67$	−89.8104	+	107.032i	−0.163763	+	0.195165i	−0.841685	−	0.539969i	$-0.818436\pi$
$67$	−89.8104	+	107.032i	−0.163763	+	0.195165i	0.677922	+	0.735133i	$0.262880\pi$
$68$	98.6652	−	79.1571i	0.175955	−	0.141165i
$69$	158.668	+	91.6070i	0.276831	+	0.159829i
$70$	−475.088	+	1261.92i	−0.811198	+	2.15469i
$71$	54.0751	+	306.675i	0.0903878	+	0.512615i	0.996063	+	0.0886435i	$0.0282532\pi$
$71$	54.0751	+	306.675i	0.0903878	+	0.512615i	−0.905676	+	0.423971i	$0.860636\pi$
$72$	−396.100	−	355.287i	−0.648345	−	0.581542i
$73$	626.259	+	227.940i	1.00408	+	0.365456i	0.791158	−	0.611612i	$-0.209479\pi$
$73$	626.259	+	227.940i	1.00408	+	0.365456i	0.212926	+	0.977068i	$0.431701\pi$
$74$	4.93551	−	448.618i	0.00775326	−	0.704741i
$75$			515.753i			0.794053i
$76$	−210.614	+	628.186i	−0.317882	+	0.948130i
$77$			568.738i			0.841737i
$78$	−485.944	−	5.34615i	−0.705414	−	0.00776067i
$79$	−646.316	−	235.240i	−0.920458	−	0.335019i	−0.162037	−	0.986785i	$-0.551807\pi$
$79$	−646.316	−	235.240i	−0.920458	−	0.335019i	−0.758421	+	0.651765i	$0.774029\pi$
$80$	1271.16	−	166.871i	1.77650	−	0.233210i
$81$	79.6861	+	451.922i	0.109309	+	0.619921i
$82$	−652.221	−	245.548i	−0.878363	−	0.330686i
$83$	165.283	+	95.4265i	0.218581	+	0.126198i	0.605293	−	0.796003i	$-0.293056\pi$
$83$	165.283	+	95.4265i	0.218581	+	0.126198i	−0.386712	+	0.922201i	$0.626389\pi$
$84$	222.395	+	277.203i	0.288872	+	0.360064i
$85$	203.600	−	242.640i	0.259806	−	0.309624i
$86$	915.805	−	151.113i	1.14830	−	0.189476i
$87$	77.7513	+	134.669i	0.0958140	+	0.165955i
$88$	476.982	−	254.781i	0.577800	−	0.308634i
$89$	−590.353	+	214.871i	−0.703116	+	0.255913i	−0.668741	−	0.743496i	$-0.733166\pi$
$89$	−590.353	+	214.871i	−0.703116	+	0.255913i	−0.0343750	+	0.999409i	$0.510944\pi$
$90$	−1146.48	−	678.844i	−1.34277	−	0.795072i
$91$	−2157.18	−	380.369i	−2.48499	−	0.438170i
$92$	153.326	−	770.075i	0.173754	−	0.872673i
$93$	118.430	+	141.139i	0.132049	+	0.157370i
$94$	−612.960	−	525.933i	−0.672575	−	0.577084i
$95$	−210.067	+	1645.70i	−0.226868	+	1.77732i
$96$	132.854	−	310.695i	0.141243	−	0.330315i
$97$	788.075	−	661.273i	0.824916	−	0.692187i	−0.129202	−	0.991618i	$-0.541241\pi$
$97$	788.075	−	661.273i	0.824916	−	0.692187i	0.954118	+	0.299432i	$0.0967970\pi$
$98$	309.819	+	550.521i	0.319352	+	0.567460i
$99$	−553.448	−	97.5879i	−0.561855	−	0.0990702i
$100$	2093.17	−	710.101i	2.09317	−	0.710101i
$101$	−47.3548	−	130.106i	−0.0466532	−	0.128179i	0.914178	−	0.405313i	$-0.132837\pi$
$101$	−47.3548	−	130.106i	−0.0466532	−	0.128179i	−0.960831	+	0.277134i	$0.910615\pi$
$102$	−27.6881	−	78.7576i	−0.0268777	−	0.0764526i
$103$	−308.912	−	535.052i	−0.295515	−	0.511847i	0.679590	−	0.733593i	$-0.262158\pi$
$103$	−308.912	−	535.052i	−0.295515	−	0.511847i	−0.975105	+	0.221746i	$0.928825\pi$
$104$	647.362	+	1979.55i	0.610376	+	1.86645i
$105$	681.707	+	572.020i	0.633598	+	0.531652i
$106$	−1337.95	−	251.124i	−1.22598	−	0.230107i
$107$	1152.94	+	665.653i	1.04168	+	0.601412i	0.920308	−	0.391195i	$-0.127938\pi$
$107$	1152.94	+	665.653i	1.04168	+	0.601412i	0.121369	+	0.992608i	$0.461272\pi$
$108$	−661.448	+	362.723i	−0.589332	+	0.323176i
$109$	−98.4666	+	17.3623i	−0.0865265	+	0.0152570i	−0.216744	−	0.976229i	$-0.569544\pi$
$109$	−98.4666	+	17.3623i	−0.0865265	+	0.0152570i	0.130217	+	0.991485i	$0.458433\pi$
$110$	1046.81	−	858.929i	0.907354	−	0.744506i
$111$	−278.238	−	101.271i	−0.237921	−	0.0865961i
$112$	818.823	−	1284.24i	0.690817	−	1.08348i
$113$	416.004			0.346322			0.173161	−	0.984894i	$-0.444602\pi$
$113$	416.004			0.346322			0.173161	+	0.984894i	$0.444602\pi$
$114$	345.020	+	268.635i	0.283457	+	0.220702i
$115$		−	1966.15i		−	1.59430i
$116$	439.501	−	500.967i	0.351781	−	0.400979i
$117$	740.286	−	2033.92i	0.584952	−	1.60714i
$118$	−88.0741	−	107.339i	−0.0687108	−	0.0837402i
$119$	−65.3416	−	370.570i	−0.0503349	−	0.285463i
$120$	174.345	−	827.976i	0.132629	−	0.629863i
$121$	−379.929	+	658.056i	−0.285446	+	0.494407i
$122$	1665.93	+	312.683i	1.23628	+	0.232041i
$123$	−295.647	+	352.338i	−0.216728	+	0.258287i
$124$	409.751	−	674.967i	0.296748	−	0.488821i
$125$	2624.68	−	1515.36i	1.87807	−	1.08430i
$126$	−1493.25	+	524.970i	−1.05579	+	0.371175i
$127$	−2488.74	+	905.827i	−1.73890	+	0.632907i	−0.999198	−	0.0400313i	$-0.987254\pi$
$127$	−2488.74	+	905.827i	−1.73890	+	0.632907i	−0.739699	+	0.672938i	$0.765032\pi$
$128$	−1443.86	−	111.409i	−0.997036	−	0.0769318i
$129$	106.374	−	603.276i	0.0726023	−	0.411748i
$130$	2557.75	+	4544.89i	1.72561	+	3.06626i
$131$	−120.219	−	143.271i	−0.0801799	−	0.0955547i	0.724463	−	0.689314i	$-0.242088\pi$
$131$	−120.219	−	143.271i	−0.0801799	−	0.0955547i	−0.804643	+	0.593759i	$0.797643\pi$
$132$	−54.2260	−	352.747i	−0.0357558	−	0.232596i
$133$	1337.25	+	1447.86i	0.871840	+	0.943952i
$134$	257.337	−	299.919i	0.165900	−	0.193351i
$135$	−1447.04	+	1214.21i	−0.922531	+	0.774095i
$136$	−281.513	+	220.806i	−0.177497	+	0.139221i
$137$	1.83400	−	10.4011i	0.00114372	−	0.00648634i	−0.984231	−	0.176890i	$-0.943396\pi$
$137$	1.83400	−	10.4011i	0.00114372	−	0.00648634i	0.985374	+	0.170404i	$0.0545073\pi$
$138$	−445.903	−	264.025i	−0.275056	−	0.162864i
$139$	15.3836	+	42.2661i	0.00938720	+	0.0257911i	0.944298	−	0.329092i	$-0.106743\pi$
$139$	15.3836	+	42.2661i	0.00938720	+	0.0257911i	−0.934911	+	0.354883i	$0.884521\pi$
$140$	1382.93	−	3554.26i	0.834852	−	2.14564i
$141$	−461.627	+	266.520i	−0.275716	+	0.159185i
$142$	−143.396	−	869.039i	−0.0847431	−	0.513578i
$143$	1685.08	+	1413.95i	0.985409	+	0.826856i
$144$	1109.22	+	1017.17i	0.641908	+	0.588639i
$145$	834.382	−	1445.19i	0.477873	−	0.827701i
$146$	−1764.13	−	664.158i	−1.00000	−	0.376480i
$147$	410.582	−	72.3966i	0.230369	−	0.0406202i
$148$	−27.9178	+	1268.65i	−0.0155056	+	0.704613i
$149$	−862.875	+	2370.73i	−0.474426	+	1.30347i	0.439736	+	0.898127i	$0.355072\pi$
$149$	−862.875	+	2370.73i	−0.474426	+	1.30347i	−0.914162	+	0.405348i	$0.867150\pi$
$150$	16.0478	−	1458.68i	0.00873531	−	0.794005i
$151$	2962.98			1.59685			0.798424	−	0.602095i	$-0.205667\pi$
$151$	2962.98			1.59685			0.798424	+	0.602095i	$0.205667\pi$
$152$	615.215	−	1770.12i	0.328293	−	0.944576i
$153$	371.820			0.196470
$154$	17.6965	−	1608.54i	0.00925988	−	0.841686i
$155$	676.242	−	1857.96i	0.350433	−	0.962806i
$156$	1374.21	+	30.2406i	0.705286	+	0.0155204i
$157$	−2495.40	+	440.006i	−1.26850	+	0.223671i	−0.767090	−	0.641540i	$-0.778296\pi$
$157$	−2495.40	+	440.006i	−1.26850	+	0.223671i	−0.501409	+	0.865210i	$0.667185\pi$
$158$	1820.63	+	685.428i	0.916717	+	0.345125i
$159$	−449.219	+	778.069i	−0.224059	+	0.388081i
$160$	−3600.36	+	432.402i	−1.77896	+	0.213652i
$161$	−1789.29	−	1501.39i	−0.875872	−	0.734944i
$162$	−211.311	−	1280.63i	−0.102482	−	0.621086i
$163$	−2117.85	+	1222.74i	−1.01769	+	0.587562i	−0.913433	−	0.406988i	$-0.866579\pi$
$163$	−2117.85	+	1222.74i	−1.01769	+	0.587562i	−0.104254	+	0.994551i	$0.533246\pi$
$164$	1837.01	+	714.766i	0.874672	+	0.340328i
$165$	−305.652	−	839.772i	−0.144212	−	0.396219i
$166$	−464.495	−	275.033i	−0.217179	−	0.128595i
$167$	−666.101	+	3777.64i	−0.308649	+	1.75044i	0.297161	+	0.954827i	$0.403960\pi$
$167$	−666.101	+	3777.64i	−0.308649	+	1.75044i	−0.605810	+	0.795609i	$0.707151\pi$
$168$	−620.364	−	790.922i	−0.284893	−	0.363220i
$169$	−4806.97	+	4033.52i	−2.18797	+	1.83592i
$170$	−583.381	+	679.914i	−0.263196	+	0.306747i
$171$	−1638.39	+	1052.87i	−0.732696	+	0.470848i
$172$	−2594.83	+	398.890i	−1.15032	+	0.176832i
$173$	−430.750	−	513.347i	−0.189302	−	0.225602i	0.663043	−	0.748581i	$-0.269265\pi$
$173$	−430.750	−	513.347i	−0.189302	−	0.225602i	−0.852345	+	0.522980i	$0.824820\pi$
$174$	−215.710	−	383.298i	−0.0939825	−	0.166999i
$175$	1141.77	−	6475.30i	0.493199	−	2.79707i
$176$	−1356.95	+	705.745i	−0.581161	+	0.302259i
$177$	−86.1098	+	31.3414i	−0.0365673	+	0.0133094i
$178$	1676.35	−	589.341i	0.705888	−	0.248163i
$179$	−90.4307	+	52.2102i	−0.0377604	+	0.0218010i	−0.518761	−	0.854919i	$-0.673607\pi$
$179$	−90.4307	+	52.2102i	−0.0377604	+	0.0218010i	0.481001	+	0.876720i	$0.340273\pi$
$180$	3221.41	+	1955.62i	1.33394	+	0.809795i
$181$	−711.817	+	848.311i	−0.292315	+	0.348367i	−0.892136	−	0.451767i	$-0.850794\pi$
$181$	−711.817	+	848.311i	−0.292315	+	0.348367i	0.599821	+	0.800134i	$0.295238\pi$
$182$	6089.22	+	1142.90i	2.48002	+	0.465481i
$183$	559.337	−	968.801i	0.225942	−	0.391343i
$184$	−457.607	+	2173.20i	−0.183344	+	0.870709i
$185$	551.771	+	3129.25i	0.219281	+	1.24360i
$186$	−330.558	−	402.862i	−0.130310	−	0.158813i
$187$	−129.242	+	355.089i	−0.0505406	+	0.138859i
$188$	1717.24	+	1506.55i	0.666186	+	0.584448i
$189$			2244.08i			0.863664i
$190$	645.331	−	4647.93i	0.246407	−	1.77472i
$191$	3355.14			1.27104			0.635521	−	0.772084i	$-0.280785\pi$
$191$	3355.14			1.27104			0.635521	+	0.772084i	$0.280785\pi$
$192$	−385.411	+	874.592i	−0.144868	+	0.328741i
$193$	−1248.92	−	454.569i	−0.465799	−	0.169537i	0.0984496	−	0.995142i	$-0.468612\pi$
$193$	−1248.92	−	454.569i	−0.465799	−	0.169537i	−0.564248	+	0.825605i	$0.690834\pi$
$194$	−2249.45	+	1845.73i	−0.832481	+	0.683070i
$195$	3389.61	−	597.679i	1.24479	−	0.219491i
$196$	−859.118	−	1566.66i	−0.313090	−	0.570939i
$197$	−3564.39	−	2057.90i	−1.28910	−	0.744262i	−0.310605	−	0.950539i	$-0.600532\pi$
$197$	−3564.39	−	2057.90i	−1.28910	−	0.744262i	−0.978494	+	0.206277i	$0.933865\pi$
$198$	1562.26	+	293.224i	0.560731	+	0.105245i
$199$	−3151.71	−	2644.60i	−1.12271	−	0.942063i	−0.123968	−	0.992286i	$-0.539562\pi$
$199$	−3151.71	−	2644.60i	−1.12271	−	0.942063i	−0.998738	+	0.0502236i	$0.984007\pi$
$200$	−5942.10	+	1943.22i	−2.10085	+	0.687031i
$201$	−130.407	−	225.872i	−0.0457624	−	0.0792627i
$202$	129.883	+	369.447i	0.0452403	+	0.128684i
$203$	−678.042	−	1862.90i	−0.234430	−	0.644090i
$204$	75.8584	+	223.608i	0.0260351	+	0.0767436i
$205$	4860.88	+	857.104i	1.65609	+	0.292013i
$206$	857.035	+	1522.88i	0.289866	+	0.515067i
$207$	1768.04	−	1483.56i	0.593659	−	0.498139i
$208$	−1769.31	−	5618.81i	−0.589806	−	1.87305i
$209$	−436.000	−	1930.64i	−0.144300	−	0.638972i
$210$	−1910.24	−	1639.03i	−0.627711	−	0.538590i
$211$	3140.20	+	3742.35i	1.02455	+	1.22101i	0.974991	+	0.222243i	$0.0713379\pi$
$211$	3140.20	+	3742.35i	1.02455	+	1.22101i	0.0495615	+	0.998771i	$0.484218\pi$
$212$	3776.26	+	751.875i	1.22337	+	0.243580i
$213$	−572.469	−	100.942i	−0.184155	−	0.0324714i
$214$	−3240.11	−	1918.51i	−1.03500	−	0.612835i
$215$	−6177.42	+	2248.40i	−1.95952	+	0.713207i
$216$	1882.03	−	1005.29i	0.592852	−	0.316674i
$217$	−1174.44	−	2034.19i	−0.367401	−	0.636358i
$218$	279.029	−	46.0412i	0.0866891	−	0.0143042i
$219$	−799.667	+	953.005i	−0.246742	+	0.294055i
$220$	−2987.36	+	2396.70i	−0.915490	+	0.734479i
$221$	−1260.39	−	727.685i	−0.383633	−	0.221490i
$222$	783.779	+	295.076i	0.236954	+	0.0892083i
$223$	489.307	+	2775.00i	0.146934	+	0.833307i	0.965794	+	0.259312i	$0.0834959\pi$
$223$	489.307	+	2775.00i	0.146934	+	0.833307i	−0.818859	+	0.573995i	$0.805393\pi$
$224$	−2355.80	+	3606.69i	−0.702694	+	1.07581i
$225$	6105.31	+	2222.15i	1.80898	+	0.658415i
$226$	−1176.57	−	12.9441i	−0.346301	−	0.00380986i
$227$		−	4655.46i		−	1.36121i	−0.732652	−	0.680603i	$-0.761718\pi$
$227$		−	4655.46i		−	1.36121i	0.732652	−	0.680603i	$-0.238282\pi$
$228$	−967.448	−	770.505i	−0.281012	−	0.223807i
$229$		−	3176.25i		−	0.916560i	−0.888808	−	0.458280i	$-0.848466\pi$
$229$		−	3176.25i		−	0.916560i	0.888808	−	0.458280i	$-0.151534\pi$
$230$	−61.1772	+	5560.76i	−0.0175387	+	1.59420i
$231$	−997.635	−	363.109i	−0.284154	−	0.103424i
$232$	−1258.61	+	1403.19i	−0.356171	+	0.397085i
$233$	121.213	+	687.430i	0.0340811	+	0.193283i	0.997095	−	0.0761683i	$-0.0242686\pi$
$233$	121.213	+	687.430i	0.0340811	+	0.193283i	−0.963014	+	0.269452i	$0.913158\pi$
$234$	−2157.00	+	5729.41i	−0.602597	+	1.60061i
$235$	4953.91	+	2860.14i	1.37514	+	0.793937i
$236$	245.756	+	306.322i	0.0677855	+	0.0844911i
$237$	825.277	−	983.526i	0.226192	−	0.269565i
$238$	173.272	+	1050.10i	0.0471915	+	0.286000i
$239$	−3262.26	−	5650.40i	−0.882921	−	1.52926i	−0.848078	−	0.529872i	$-0.822240\pi$
$239$	−3262.26	−	5650.40i	−0.882921	−	1.52926i	−0.0348438	−	0.999393i	$-0.511093\pi$
$240$	−518.856	+	2336.30i	−0.139550	+	0.628365i
$241$	−651.051	+	236.963i	−0.174016	+	0.0633367i	−0.427559	−	0.903987i	$-0.640626\pi$
$241$	−651.051	+	236.963i	−0.174016	+	0.0633367i	0.253543	+	0.967324i	$0.418404\pi$
$242$	1095.01	−	1849.33i	0.290868	−	0.491237i
$243$	−3350.94	−	590.861i	−0.884620	−	0.155982i
$244$	−4701.96	−	936.185i	−1.23366	−	0.245627i
$245$	−2875.89	−	3427.36i	−0.749935	−	0.893738i
$246$	847.129	−	987.304i	0.219557	−	0.255887i
$247$	7614.35	−	362.514i	1.96150	−	0.0933854i
$248$	−1179.88	+	1896.23i	−0.302108	+	0.485527i
$249$	−272.914	+	229.002i	−0.0694587	+	0.0582828i
$250$	−7470.43	+	4204.16i	−1.88989	+	1.06358i
$251$	4751.44	+	837.806i	1.19485	+	0.210685i	0.735472	−	0.677555i	$-0.236960\pi$
$251$	4751.44	+	837.806i	1.19485	+	0.210685i	0.459380	+	0.888240i	$0.348072\pi$
$252$	4239.64	−	1438.29i	1.05981	−	0.359538i
$253$	802.249	+	2204.16i	0.199356	+	0.547725i
$254$	7066.98	−	2484.47i	1.74575	−	0.613739i
$255$	295.633	+	512.051i	0.0726009	+	0.125748i
$256$	4080.15	+	360.020i	0.996130	+	0.0878955i
$257$	1424.58	+	1195.36i	0.345769	+	0.290134i	0.799088	−	0.601214i	$-0.205316\pi$
$257$	1424.58	+	1195.36i	0.345769	+	0.290134i	−0.453320	+	0.891348i	$0.649760\pi$
$258$	−319.623	+	1702.91i	−0.0771275	+	0.410924i
$259$	3269.11	+	1887.42i	0.784295	+	0.452813i
$260$	−7092.55	−	12933.7i	−1.69177	−	3.08506i
$261$	1929.16	−	340.164i	0.457518	−	0.0806728i
$262$	335.552	+	408.948i	0.0791238	+	0.0964309i
$263$	−2775.68	−	1010.27i	−0.650783	−	0.236866i	−0.00453113	−	0.999990i	$-0.501442\pi$
$263$	−2775.68	−	1010.27i	−0.650783	−	0.236866i	−0.646252	+	0.763124i	$0.723665\pi$
$264$	142.389	+	999.347i	0.0331949	+	0.232976i
$265$	9641.51			2.23499
$266$	−3737.05	−	4136.54i	−0.861403	−	0.953486i
$267$		−	1172.73i		−	0.268802i
$268$	−737.148	+	840.241i	−0.168017	+	0.191515i
$269$	−2334.07	+	6412.80i	−0.529036	+	1.45352i	0.331171	+	0.943571i	$0.392556\pi$
$269$	−2334.07	+	6412.80i	−0.529036	+	1.45352i	−0.860207	+	0.509945i	$0.829666\pi$
$270$	4130.39	−	3389.08i	0.930991	−	0.763900i
$271$	−490.430	−	2781.36i	−0.109932	−	0.623453i	−0.989135	−	0.147007i	$-0.953036\pi$
$271$	−490.430	−	2781.36i	−0.109932	−	0.623453i	0.879204	−	0.476446i	$-0.158075\pi$
$272$	803.062	−	615.738i	0.179018	−	0.137260i
$273$	2044.46	−	3541.10i	0.453246	−	0.785045i
$274$	−5.51065	+	29.3600i	−0.00121500	+	0.00647336i
$275$	−4244.32	+	5058.18i	−0.930699	+	1.10916i
$276$	1252.91	+	760.605i	0.273248	+	0.165880i
$277$	1581.74	−	913.217i	0.343096	−	0.198086i	−0.318545	−	0.947908i	$-0.603194\pi$
$277$	1581.74	−	913.217i	0.343096	−	0.198086i	0.661640	+	0.749822i	$0.269861\pi$
$278$	−42.1937	−	120.018i	−0.00910291	−	0.0258928i
$279$	2181.02	−	793.826i	0.468008	−	0.170341i
$280$	−4021.88	+	10009.3i	−0.858406	+	2.13633i
$281$	−213.578	+	1211.26i	−0.0453416	+	0.257145i	−0.999050	−	0.0435894i	$-0.986121\pi$
$281$	−213.578	+	1211.26i	−0.0453416	+	0.257145i	0.953708	+	0.300734i	$0.0972318\pi$
$282$	1313.89	−	739.424i	0.277451	−	0.156142i
$283$	−656.163	−	781.984i	−0.137826	−	0.164255i	0.692716	−	0.721210i	$-0.256414\pi$
$283$	−656.163	−	781.984i	−0.137826	−	0.164255i	−0.830542	+	0.556955i	$0.811969\pi$
$284$	378.520	+	2462.33i	0.0790882	+	0.514479i
$285$	−2752.64	−	1419.18i	−0.572113	−	0.294964i
$286$	−4721.84	−	4051.44i	−0.976253	−	0.837647i
$287$	4491.87	−	3769.13i	0.923856	−	0.775207i
$288$	−3105.50	−	2911.32i	−0.635393	−	0.595665i
$289$	−809.720	+	4592.15i	−0.164812	+	0.934693i
$290$	−2404.81	+	4061.41i	−0.486950	+	0.822394i
$291$	656.808	+	1804.56i	0.132312	+	0.363524i
$292$	4968.74	+	1933.30i	0.995800	+	0.387458i
$293$	−1771.38	+	1022.71i	−0.353191	+	0.203915i	−0.666090	−	0.745871i	$-0.732033\pi$
$293$	−1771.38	+	1022.71i	−0.353191	+	0.203915i	0.312899	+	0.949787i	$0.398700\pi$
$294$	−1163.48	+	191.981i	−0.230802	+	0.0380835i
$295$	753.317	+	632.108i	0.148677	+	0.124755i
$296$	118.433	−	3587.21i	0.0232560	−	0.704400i
$297$	1126.78	−	1951.64i	0.220143	−	0.381299i
$298$	2514.20	−	6678.18i	0.488737	−	1.29818i
$299$	−8896.74	+	1568.74i	−1.72078	+	0.303419i
$300$	−90.7745	+	4125.02i	−0.0174696	+	0.793861i
$301$	−2671.06	+	7338.67i	−0.511486	+	1.40530i
$302$	−8380.07	−	92.1940i	−1.59675	−	0.0175668i
$303$	258.455			0.0490028
$304$	−1795.06	+	4987.20i	−0.338664	+	0.940907i
$305$	−12005.0			−2.25378
$306$	−1051.60	−	11.5693i	−0.196458	−	0.00216134i
$307$	−246.553	+	677.399i	−0.0458356	+	0.125932i	−0.960498	−	0.278285i	$-0.910234\pi$
$307$	−246.553	+	677.399i	−0.0458356	+	0.125932i	0.914663	+	0.404218i	$0.132456\pi$
$308$	−100.100	+	4548.81i	−0.0185186	+	0.841533i
$309$	1135.77	−	200.267i	0.209099	−	0.0368698i
$310$	−1970.40	+	5233.74i	−0.361003	+	0.958892i
$311$	4784.71	−	8287.36i	0.872398	−	1.51104i	0.0128896	−	0.999917i	$-0.495897\pi$
$311$	4784.71	−	8287.36i	0.872398	−	1.51104i	0.859509	−	0.511121i	$-0.170770\pi$
$312$	−3885.67	−	128.287i	−0.705073	−	0.0232782i
$313$	−147.301	−	123.601i	−0.0266005	−	0.0223205i	0.629390	−	0.777089i	$-0.283305\pi$
$313$	−147.301	−	123.601i	−0.0266005	−	0.0223205i	−0.655991	+	0.754769i	$0.727749\pi$
$314$	7071.31	−	1166.80i	1.27088	−	0.209702i
$315$	9708.55	−	5605.24i	1.73656	−	1.00260i
$316$	−5127.87	−	1995.22i	−0.912865	−	0.355189i
$317$	−1015.99	−	2791.41i	−0.180012	−	0.494579i	0.816565	−	0.577254i	$-0.195876\pi$
$317$	−1015.99	−	2791.41i	−0.180012	−	0.494579i	−0.996577	+	0.0826753i	$0.973654\pi$
$318$	1294.71	−	2186.60i	0.228314	−	0.385593i
$319$	−345.706	+	1960.60i	−0.0606766	+	0.344114i
$320$	10196.2	−	1110.92i	1.78120	−	0.194069i
$321$	−1903.73	+	1597.42i	−0.331015	+	0.277754i
$322$	5013.84	+	4301.99i	0.867734	+	0.744535i
$323$	505.891	+	1207.85i	0.0871472	+	0.208069i
$324$	557.794	+	3628.53i	0.0956437	+	0.622175i
$325$	−16346.7	−	19481.2i	−2.79001	−	3.32500i
$326$	6027.88	−	3392.33i	1.02409	−	0.576331i
$327$	32.4101	−	183.807i	0.00548099	−	0.0310842i
$328$	−5173.29	−	2078.70i	−0.870875	−	0.349930i
$329$	6385.77	−	2324.23i	1.07009	−	0.389480i
$330$	838.333	+	2384.60i	0.139845	+	0.397782i
$331$	6168.58	−	3561.43i	1.02434	−	0.591402i	0.108980	−	0.994044i	$-0.465242\pi$
$331$	6168.58	−	3561.43i	1.02434	−	0.591402i	0.915357	+	0.402642i	$0.131908\pi$
$332$	1305.15	+	792.317i	0.215752	+	0.130976i
$333$	−2397.61	+	2857.36i	−0.394560	+	0.470218i
$334$	2001.45	−	10663.4i	0.327887	−	1.74694i
$335$	−1399.46	+	2423.93i	−0.228240	+	0.395324i
$336$	1729.94	+	2256.23i	0.280880	+	0.366332i
$337$	124.101	+	703.812i	0.0200600	+	0.113766i	0.993194	−	0.116475i	$-0.0371596\pi$
$337$	124.101	+	703.812i	0.0200600	+	0.113766i	−0.973134	+	0.230241i	$0.926048\pi$
$338$	13720.8	−	11258.3i	2.20803	−	1.81174i
$339$	−265.597	+	729.721i	−0.0425523	+	0.116912i
$340$	1671.11	−	1904.82i	0.266555	−	0.303833i
$341$			2358.81i			0.374594i
$342$	4666.55	−	2926.81i	0.737832	−	0.462759i
$343$	2847.56			0.448262
$344$	7351.27	−	1047.42i	1.15219	−	0.164167i
$345$	3448.85	+	1255.28i	0.538203	+	0.195890i
$346$	1202.30	+	1465.28i	0.186809	+	0.227670i
$347$	12269.4	−	2163.43i	1.89815	−	0.334694i	0.902720	−	0.430228i	$-0.141567\pi$
$347$	12269.4	−	2163.43i	1.89815	−	0.334694i	0.995426	+	0.0955332i	$0.0304556\pi$
$348$	598.158	+	1090.78i	0.0921397	+	0.168022i
$349$	4735.62	+	2734.11i	0.726338	+	0.419352i	0.817081	−	0.576523i	$-0.195591\pi$
$349$	4735.62	+	2734.11i	0.726338	+	0.419352i	−0.0907429	+	0.995874i	$0.528924\pi$
$350$	−3430.70	+	18278.3i	−0.523939	+	2.79147i
$351$	6648.84	+	5579.04i	1.01108	+	0.848396i
$352$	3859.77	−	1953.81i	0.584450	−	0.295847i
$353$	−368.127	−	637.614i	−0.0555054	−	0.0961381i	0.836938	−	0.547298i	$-0.184344\pi$
$353$	−368.127	−	637.614i	−0.0555054	−	0.0961381i	−0.892443	+	0.451160i	$0.851010\pi$
$354$	244.516	−	85.9622i	0.0367115	−	0.0129063i
$355$	2133.58	+	5861.97i	0.318982	+	0.876397i
$356$	−4759.50	+	1614.65i	−0.708576	+	0.240382i
$357$	691.742	+	121.973i	0.102551	+	0.0180826i
$358$	257.386	−	144.850i	0.0379979	−	0.0213842i
$359$	−652.281	+	547.329i	−0.0958944	+	0.0804650i	−0.689474	−	0.724310i	$-0.742158\pi$
$359$	−652.281	+	547.329i	−0.0958944	+	0.0804650i	0.593580	+	0.804775i	$0.297714\pi$
$360$	−9050.12	−	5631.22i	−1.32495	−	0.824421i
$361$	−5649.39	−	3889.76i	−0.823646	−	0.567104i
$362$	2039.60	−	2377.09i	0.296129	−	0.345130i
$363$	−911.744	−	1086.57i	−0.131830	−	0.157108i
$364$	−17186.3	−	3421.88i	−2.47474	−	0.492735i
$365$	13147.7	+	2318.30i	1.88543	+	0.332452i
$366$	−1612.09	+	2722.61i	−0.230234	+	0.388834i
$367$	1071.10	−	389.848i	0.152346	−	0.0554493i	−0.264722	−	0.964325i	$-0.585280\pi$
$367$	1071.10	−	389.848i	0.152346	−	0.0554493i	0.417067	+	0.908876i	$0.363058\pi$
$368$	1361.85	−	6132.13i	0.192911	−	0.868639i
$369$	2897.05	+	5017.84i	0.408711	+	0.707909i
$370$	−1463.18	−	8867.48i	−0.205587	−	1.24594i
$371$	7362.45	−	8774.23i	1.03029	−	1.22786i
$372$	922.367	+	1149.68i	0.128555	+	0.160237i
$373$	7324.56	+	4228.84i	1.01676	+	0.587026i	0.913164	−	0.407593i	$-0.133632\pi$
$373$	7324.56	+	4228.84i	1.01676	+	0.587026i	0.103596	+	0.994619i	$0.466965\pi$
$374$	376.578	−	1000.26i	0.0520651	−	0.138295i
$375$	982.403	+	5571.49i	0.135283	+	0.767227i
$376$	−4809.93	−	4314.33i	−0.659716	−	0.591741i
$377$	−7205.18	−	2622.47i	−0.984311	−	0.358260i
$378$	69.8251	−	6346.82i	0.00950109	−	0.863612i
$379$		−	2935.06i		−	0.397794i	−0.980020	−	0.198897i	$-0.936264\pi$
$379$		−	2935.06i		−	0.397794i	0.980020	−	0.198897i	$-0.0637358\pi$
$380$	−1969.78	+	13125.5i	−0.265915	+	1.77190i
$381$		−	4943.87i		−	0.664782i
$382$	−9489.18	−	104.396i	−1.27097	−	0.0139826i
$383$	−4252.16	−	1547.66i	−0.567298	−	0.206480i	0.0424173	−	0.999100i	$-0.486494\pi$
$383$	−4252.16	−	1547.66i	−0.567298	−	0.206480i	−0.609716	+	0.792620i	$0.708716\pi$
$384$	1117.25	−	2461.58i	0.148476	−	0.327127i
$385$	1978.40	+	11220.0i	0.261892	+	1.48526i
$386$	3518.12	+	1324.50i	0.463905	+	0.174651i
$387$	−6683.06	−	3858.47i	−0.877827	−	0.506814i
$388$	6419.46	−	5150.20i	0.839945	−	0.673871i
$389$	−5906.06	+	7038.57i	−0.769792	+	0.917403i	−0.998425	−	0.0561101i	$-0.982130\pi$
$389$	−5906.06	+	7038.57i	−0.769792	+	0.917403i	0.228632	+	0.973513i	$0.426575\pi$
$390$	−9605.27	+	1584.92i	−1.24713	+	0.205783i
$391$	−775.951	−	1343.99i	−0.100362	−	0.173832i
$392$	2381.06	+	4457.63i	0.306790	+	0.574348i
$393$	328.068	−	119.407i	0.0421090	−	0.0153264i
$394$	10017.0	+	5931.18i	1.28083	+	0.758398i
$395$	−13568.8	−	2392.54i	−1.72840	−	0.304764i
$396$	−4409.34	−	877.923i	−0.559540	−	0.111407i
$397$	−5472.14	−	6521.44i	−0.691785	−	0.824437i	0.299785	−	0.954007i	$-0.403085\pi$
$397$	−5472.14	−	6521.44i	−0.691785	−	0.824437i	−0.991570	+	0.129569i	$0.958641\pi$
$398$	8831.55	+	7577.66i	1.11228	+	0.954356i
$399$	−3393.49	+	1421.32i	−0.425782	+	0.178333i
$400$	16866.3	−	5311.03i	2.10828	−	0.663878i
$401$	−3509.53	+	2944.85i	−0.437052	+	0.366730i	−0.834605	−	0.550849i	$-0.814304\pi$
$401$	−3509.53	+	2944.85i	−0.437052	+	0.366730i	0.397553	+	0.917579i	$0.369859\pi$
$402$	361.798	+	642.883i	0.0448876	+	0.0797614i
$403$	−8946.76	−	1577.56i	−1.10588	−	0.194997i
$404$	−355.847	−	1048.93i	−0.0438219	−	0.129174i
$405$	3144.08	+	8638.30i	0.385755	+	1.05985i
$406$	1859.71	+	5289.87i	0.227330	+	0.646630i
$407$	−1895.40	−	3282.93i	−0.230839	−	0.399825i
$408$	−207.589	−	634.781i	−0.0251892	−	0.0770254i
$409$	−8139.35	−	6829.72i	−0.984021	−	0.825692i	0.000669754	−	1.00000i	$-0.499787\pi$
$409$	−8139.35	−	6829.72i	−0.984021	−	0.825692i	−0.984691	+	0.174308i	$0.944231\pi$
$410$	−13721.1	−	2575.36i	−1.65278	−	0.310214i
$411$	17.0739	+	9.85762i	0.00204913	+	0.00118307i
$412$	−2376.53	−	4333.75i	−0.284183	−	0.518225i
$413$	1150.50	−	202.864i	0.137076	−	0.0241701i
$414$	−5046.64	+	4140.88i	−0.599103	+	0.491578i
$415$	3592.65	+	1307.62i	0.424955	+	0.154671i
$416$	4829.23	+	15946.5i	0.569165	+	1.87943i
$417$	−83.9614			−0.00985997
$418$	1173.05	+	5473.91i	0.137262	+	0.640521i
$419$			6133.37i			0.715118i	0.933890	+	0.357559i	$0.116391\pi$
$419$			6133.37i			0.715118i	−0.933890	+	0.357559i	$0.883609\pi$
$420$	5351.66	+	4695.04i	0.621748	+	0.545463i
$421$	4878.81	−	13404.4i	0.564795	−	1.55176i	−0.247725	−	0.968830i	$-0.579683\pi$
$421$	4878.81	−	13404.4i	0.564795	−	1.55176i	0.812521	−	0.582932i	$-0.198095\pi$
$422$	−8764.86	−	10682.0i	−1.01106	−	1.23221i
$423$	1166.03	+	6612.90i	0.134030	+	0.760119i
$424$	−10656.8	−	2243.99i	−1.22062	−	0.257023i
$425$	2184.33	−	3783.36i	0.249307	−	0.431812i
$426$	1615.95	+	303.302i	0.183786	+	0.0344953i
$427$	−9167.24	+	10925.1i	−1.03895	+	1.23818i
$428$	9104.17	+	5526.86i	1.02819	+	0.624184i
$429$	−3556.07	+	2053.10i	−0.400207	+	0.231059i
$430$	17541.3	−	6166.83i	1.96725	−	0.691607i
$431$	−10736.3	+	3907.68i	−1.19988	+	0.436720i	−0.863182	−	0.504893i	$-0.831532\pi$
$431$	−10736.3	+	3907.68i	−1.19988	+	0.436720i	−0.336697	+	0.941613i	$0.609310\pi$
$432$	−5354.15	+	2784.67i	−0.596300	+	0.310133i
$433$	−610.998	+	3465.14i	−0.0678122	+	0.384582i	0.931946	+	0.362597i	$0.118110\pi$
$433$	−610.998	+	3465.14i	−0.0678122	+	0.384582i	−0.999758	+	0.0219853i	$0.993001\pi$
$434$	3258.32	+	5789.75i	0.360379	+	0.640361i
$435$	2002.33	+	2386.28i	0.220700	+	0.263020i
$436$	−790.598	+	121.534i	−0.0868412	+	0.0133496i
$437$	7224.89	+	3724.93i	0.790877	+	0.407752i
$438$	2291.31	−	2670.46i	0.249962	−	0.291323i
$439$	1291.54	−	1083.73i	0.140415	−	0.117822i	−0.569875	−	0.821731i	$-0.693008\pi$
$439$	1291.54	−	1083.73i	0.140415	−	0.117822i	0.710290	+	0.703910i	$0.248564\pi$
$440$	8523.59	−	6685.52i	0.923514	−	0.724363i
$441$	912.008	−	5172.25i	0.0984783	−	0.558498i
$442$	3542.05	+	2097.30i	0.381173	+	0.225697i
$443$	−3871.35	−	10636.4i	−0.415199	−	1.14075i	−0.954389	−	0.298566i	$-0.903492\pi$
$443$	−3871.35	−	10636.4i	−0.415199	−	1.14075i	0.539189	−	0.842185i	$-0.318731\pi$
$444$	−2207.54	−	858.939i	−0.235958	−	0.0918096i
$445$	−10899.0	+	6292.54i	−1.16104	+	0.670326i
$446$	−1297.54	−	7863.62i	−0.137758	−	0.834873i
$447$	−3607.64	−	3027.17i	−0.381735	−	0.320314i
$448$	6775.03	−	10127.3i	0.714486	−	1.06802i
$449$	−6353.82	+	11005.1i	−0.667829	+	1.15671i	0.310680	+	0.950514i	$0.399443\pi$
$449$	−6353.82	+	11005.1i	−0.667829	+	1.15671i	−0.978510	+	0.206200i	$0.933890\pi$
$450$	−17198.2	−	6474.78i	−1.80163	−	0.678275i
$451$	−5799.05	+	1022.53i	−0.605469	+	0.106760i
$452$	3327.23	+	73.2184i	0.346238	+	0.00761926i
$453$	−1891.71	+	5197.42i	−0.196203	+	0.539065i
$454$	−144.856	+	13166.8i	−0.0149745	+	1.36112i
$455$	−43879.8			−4.52114
$456$	2712.21	+	2209.29i	0.278533	+	0.226885i
$457$	−11247.4			−1.15127			−0.575636	−	0.817706i	$-0.695245\pi$
$457$	−11247.4			−1.15127			−0.575636	+	0.817706i	$0.695245\pi$
$458$	−98.8298	+	8983.24i	−0.0100830	+	0.916505i
$459$	−509.951	+	1401.08i	−0.0518572	+	0.142476i
$460$	346.049	−	15725.4i	0.0350753	−	1.59391i
$461$	2210.31	−	389.738i	0.223307	−	0.0393751i	−0.0608750	−	0.998145i	$-0.519389\pi$
$461$	2210.31	−	389.738i	0.223307	−	0.0393751i	0.284182	+	0.958770i	$0.408278\pi$
$462$	2810.27	+	1058.01i	0.282999	+	0.106543i
$463$	−3709.03	+	6424.23i	−0.372296	+	0.644836i	−0.989918	−	0.141639i	$-0.954763\pi$
$463$	−3709.03	+	6424.23i	−0.372296	+	0.644836i	0.617622	+	0.786475i	$0.288096\pi$
$464$	3603.33	−	3929.41i	0.360518	−	0.393143i
$465$	2827.34	+	2372.42i	0.281967	+	0.236598i
$466$	−321.430	−	1948.00i	−0.0319527	−	0.193647i
$467$	−4197.77	+	2423.58i	−0.415952	+	0.240150i	−0.693344	−	0.720607i	$-0.743863\pi$
$467$	−4197.77	+	2423.58i	−0.415952	+	0.240150i	0.277392	+	0.960757i	$0.410530\pi$
$468$	6278.83	−	16137.1i	0.620169	−	1.59389i
$469$	1137.24	+	3124.54i	0.111968	+	0.307628i
$470$	−13921.9	−	8243.36i	−1.36632	−	0.809016i
$471$	821.356	−	4658.14i	0.0803526	−	0.455702i
$472$	−685.530	−	874.005i	−0.0668519	−	0.0852316i
$473$	6007.83	−	5041.17i	0.584018	−	0.490049i
$474$	−2364.70	+	2755.99i	−0.229144	+	0.267060i
$475$	1088.17	+	22856.4i	0.105113	+	2.20784i
$476$	−457.384	−	2975.35i	−0.0440424	−	0.286502i
$477$	7275.04	+	8670.06i	0.698325	+	0.832232i
$478$	9050.70	+	16082.3i	0.866045	+	1.53889i
$479$	−1703.49	+	9660.98i	−0.162494	+	0.921548i	0.789117	+	0.614243i	$0.210538\pi$
$479$	−1703.49	+	9660.98i	−0.162494	+	0.921548i	−0.951611	+	0.307305i	$0.900573\pi$
$480$	1540.15	−	6591.52i	0.146454	−	0.626792i
$481$	13719.5	−	4993.49i	1.30053	−	0.473355i
$482$	1848.71	−	649.935i	0.174702	−	0.0614185i
$483$	3775.98	−	2180.06i	0.355720	−	0.205375i
$484$	−3154.51	+	5196.30i	−0.296254	+	0.488007i
$485$	13246.8	−	15786.9i	1.24022	−	1.47804i
$486$	9458.92	+	1775.37i	0.882851	+	0.165705i
$487$	1906.16	−	3301.56i	0.177364	−	0.307203i	−0.763613	−	0.645674i	$-0.776576\pi$
$487$	1906.16	−	3301.56i	0.177364	−	0.307203i	0.940977	+	0.338471i	$0.109910\pi$
$488$	13269.2	+	2794.07i	1.23088	+	0.259184i
$489$	−792.700	−	4495.62i	−0.0733070	−	0.415745i
$490$	8027.12	+	9782.93i	0.740058	+	0.901934i
$491$	−5005.47	+	13752.4i	−0.460068	+	1.26403i	0.465366	+	0.885118i	$0.345923\pi$
$491$	−5005.47	+	13752.4i	−0.460068	+	1.26403i	−0.925434	+	0.378909i	$0.876299\pi$
$492$	−2426.62	+	2765.99i	−0.222358	+	0.253456i
$493$		−	1317.18i		−	0.120330i
$494$	−21546.6	+	788.359i	−1.96241	+	0.0718015i
$495$	−11257.9			−1.02223
$496$	3396.01	−	5326.31i	0.307431	−	0.482174i
$497$	6963.91	+	2534.66i	0.628520	+	0.228762i
$498$	778.996	−	639.185i	0.0700957	−	0.0575152i
$499$	7420.96	−	1308.52i	0.665747	−	0.117389i	0.169446	−	0.985539i	$-0.445802\pi$
$499$	7420.96	−	1308.52i	0.665747	−	0.117389i	0.496301	+	0.868150i	$0.334691\pi$
$500$	21259.1	−	11658.0i	1.90147	−	1.04272i
$501$	−6201.17	−	3580.24i	−0.552989	−	0.319269i
$502$	−13412.2	−	2517.37i	−1.19246	−	0.223816i
$503$	12425.4	+	10426.1i	1.10143	+	0.924211i	0.997521	−	0.0703758i	$-0.0224198\pi$
$503$	12425.4	+	10426.1i	1.10143	+	0.924211i	0.103911	+	0.994587i	$0.466864\pi$
$504$	−12035.5	+	3935.92i	−1.06370	+	0.347857i
$505$	−1386.79	−	2402.00i	−0.122201	−	0.211659i
$506$	−2200.38	−	6258.90i	−0.193318	−	0.549885i
$507$	−4006.29	−	11007.2i	−0.350938	−	0.964193i
$508$	−20064.5	+	6806.84i	−1.75240	+	0.594497i
$509$	9681.91	+	1707.18i	0.843111	+	0.148663i	0.578490	−	0.815689i	$-0.303642\pi$
$509$	9681.91	+	1707.18i	0.843111	+	0.148663i	0.264621	+	0.964353i	$0.414753\pi$
$510$	−820.192	−	1457.41i	−0.0712132	−	0.126540i
$511$	12149.6	−	10194.7i	1.05180	−	0.882561i
$512$	−11528.5	−	1145.18i	−0.995102	−	0.0988485i
$513$	−1720.33	−	7617.74i	−0.148059	−	0.655617i
$514$	−3991.87	−	3425.11i	−0.342556	−	0.293921i
$515$	−7955.42	−	9480.90i	−0.680695	−	0.811220i
$516$	956.963	−	4806.32i	0.0816433	−	0.410051i
$517$	−6720.65	−	1185.03i	−0.571709	−	0.100808i
$518$	−9187.14	−	5439.83i	−0.779266	−	0.461414i
$519$	1175.48	−	427.841i	0.0994180	−	0.0361852i
$520$	19657.1	+	36800.5i	1.65773	+	3.10348i
$521$	4573.68	+	7921.84i	0.384600	+	0.666146i	0.991714	−	0.128469i	$-0.0410061\pi$
$521$	4573.68	+	7921.84i	0.384600	+	0.666146i	−0.607114	+	0.794615i	$0.707673\pi$
$522$	−5466.76	+	902.044i	−0.458378	+	0.0756348i
$523$	10816.8	−	12890.9i	0.904368	−	1.07778i	−0.0922601	−	0.995735i	$-0.529409\pi$
$523$	10816.8	−	12890.9i	0.904368	−	1.07778i	0.996628	−	0.0820491i	$-0.0261464\pi$
$524$	−936.301	−	1167.05i	−0.0780582	−	0.0972955i
$525$	10629.5	+	6136.94i	0.883636	+	0.510168i
$526$	7818.91	+	2943.66i	0.648138	+	0.244011i
$527$	−271.000	−	1536.92i	−0.0224003	−	0.127038i
$528$	−371.618	−	2830.84i	−0.0306299	−	0.233327i
$529$	2380.99	+	866.610i	0.195692	+	0.0712262i
$530$	−27268.6	−	299.998i	−2.23486	−	0.0245869i
$531$			1154.38i			0.0943421i
$532$	10440.6	+	11815.5i	0.850861	+	0.962904i
$533$		−	22679.2i		−	1.84305i
$534$	−36.4899	+	3316.79i	−0.00295706	+	0.268786i
$535$	25060.7	+	9121.36i	2.02518	+	0.737105i
$536$	2110.99	−	2353.48i	0.170113	−	0.189655i
$537$	−33.8477	−	191.960i	−0.00271999	−	0.0154258i
$538$	6800.88	−	18064.4i	0.544994	−	1.44761i
$539$	4622.51	+	2668.81i	0.369398	+	0.213272i
$540$	−11787.3	+	9456.67i	−0.939338	+	0.753612i
$541$	2751.32	−	3278.89i	0.218648	−	0.260574i	−0.645560	−	0.763710i	$-0.723376\pi$
$541$	2751.32	−	3278.89i	0.218648	−	0.260574i	0.864207	+	0.503136i	$0.167820\pi$
$542$	1300.52	+	7881.67i	0.103066	+	0.624625i
$543$	−1033.58	−	1790.21i	−0.0816854	−	0.141483i
$544$	−2290.43	+	1716.48i	−0.180517	+	0.135282i
$545$	−1882.15	+	685.045i	−0.147931	+	0.0538424i
$546$	−5892.43	+	9951.53i	−0.461854	+	0.780011i
$547$	−2689.71	−	474.268i	−0.210244	−	0.0370717i	0.0675340	−	0.997717i	$-0.478487\pi$
$547$	−2689.71	−	474.268i	−0.210244	−	0.0370717i	−0.277778	+	0.960645i	$0.589598\pi$
$548$	16.4991	−	82.8661i	0.00128614	−	0.00645960i
$549$	−9058.40	−	10795.4i	−0.704195	−	0.839227i
$550$	12161.4	−	14173.8i	0.942844	−	1.09886i
$551$	3729.80	+	5804.02i	0.288376	+	0.448747i
$552$	−3519.89	−	2190.17i	−0.271407	−	0.168876i
$553$	−12538.7	+	10521.2i	−0.964196	+	0.809057i
$554$	−4501.98	+	2533.60i	−0.345254	+	0.194300i
$555$	−5841.35	−	1029.99i	−0.446759	−	0.0787757i
$556$	115.600	+	340.755i	0.00881751	+	0.0259914i
$557$	8271.58	+	22726.0i	0.629224	+	1.72878i	0.683194	+	0.730237i	$0.260590\pi$
$557$	8271.58	+	22726.0i	0.629224	+	1.72878i	−0.0539700	+	0.998543i	$0.517188\pi$
$558$	−6193.18	+	2177.28i	−0.469853	+	0.165182i
$559$	15102.7	+	26158.7i	1.14271	+	1.97924i
$560$	11686.4	−	28183.8i	0.881855	−	2.12675i
$561$	−540.354	−	453.411i	−0.0406663	−	0.0341230i
$562$	641.742	−	3419.11i	0.0481677	−	0.256631i
$563$	−451.706	−	260.793i	−0.0338138	−	0.0195224i	0.482998	−	0.875622i	$-0.339548\pi$
$563$	−451.706	−	260.793i	−0.0338138	−	0.0195224i	−0.516812	+	0.856099i	$0.672881\pi$
$564$	−3739.03	+	2050.40i	−0.279152	+	0.153080i
$565$	8206.91	−	1447.10i	0.611093	−	0.107752i
$566$	1831.46	+	2232.07i	0.136011	+	0.165761i
$567$	10262.1	+	3735.12i	0.760088	+	0.276649i
$568$	−993.936	−	6975.87i	−0.0734237	−	0.515318i
$569$	−7213.07			−0.531437			−0.265719	−	0.964051i	$-0.585609\pi$
$569$	−7213.07			−0.531437			−0.265719	+	0.964051i	$0.585609\pi$
$570$	7741.01	+	4099.44i	0.568834	+	0.301240i
$571$		−	8143.69i		−	0.596853i	−0.954433	−	0.298426i	$-0.903538\pi$
$571$		−	8143.69i		−	0.596853i	0.954433	−	0.298426i	$-0.0964618\pi$
$572$	13228.5	+	11605.4i	0.966979	+	0.848336i
$573$	−2142.08	+	5885.30i	−0.156172	+	0.429079i
$574$	−12821.4	+	10520.3i	−0.932328	+	0.764997i
$575$	−4708.95	−	26705.8i	−0.341525	−	1.93688i
$576$	8692.56	+	8330.60i	0.628802	+	0.602619i
$577$	4356.17	−	7545.11i	0.314298	−	0.544380i	−0.664990	−	0.746852i	$-0.731564\pi$
$577$	4356.17	−	7545.11i	0.314298	−	0.544380i	0.979288	+	0.202472i	$0.0648976\pi$
$578$	2432.98	−	12962.6i	0.175084	−	0.932824i
$579$	1594.74	−	1900.53i	0.114465	−	0.136414i
$580$	6927.80	−	11411.9i	0.495967	−	0.816987i
$581$	3933.41	−	2270.96i	0.280870	−	0.162160i
$582$	−1801.47	−	5124.21i	−0.128305	−	0.364957i
$583$	−10808.7	+	3934.04i	−0.767838	+	0.279470i
$584$	−13992.7	−	5622.47i	−0.991478	−	0.398390i
$585$	7529.19	−	42700.1i	0.532126	−	3.01784i
$586$	5041.74	−	2837.36i	0.355413	−	0.200017i
$587$	−5350.84	−	6376.88i	−0.376240	−	0.448385i	0.544384	−	0.838836i	$-0.316763\pi$
$587$	−5350.84	−	6376.88i	−0.376240	−	0.448385i	−0.920624	+	0.390451i	$0.872319\pi$
$588$	3296.60	−	506.769i	0.231207	−	0.0355422i
$589$	5546.18	+	6004.92i	0.387990	+	0.420082i
$590$	−2110.91	−	1811.20i	−0.147296	−	0.126383i
$591$	5885.48	−	4938.51i	0.409639	−	0.343728i
$592$	−446.576	+	10141.9i	−0.0310037	+	0.704101i
$593$	669.763	−	3798.42i	0.0463809	−	0.263039i	−0.952796	−	0.303612i	$-0.901807\pi$
$593$	669.763	−	3798.42i	0.0463809	−	0.263039i	0.999177	+	0.0405730i	$0.0129183\pi$
$594$	−3247.55	+	5484.69i	−0.224324	+	0.378854i
$595$	−2578.11	−	7083.30i	−0.177634	−	0.488045i
$596$	−7318.59	+	18809.4i	−0.502988	+	1.29272i
$597$	6651.13	−	3840.03i	0.455968	−	0.263253i
$598$	25211.1	−	4159.96i	1.72401	−	0.284471i
$599$	8042.03	+	6748.06i	0.548561	+	0.460298i	0.874454	−	0.485109i	$-0.161220\pi$
$599$	8042.03	+	6748.06i	0.548561	+	0.460298i	−0.325892	+	0.945407i	$0.605665\pi$
$600$	385.085	−	11663.8i	0.0262017	−	0.793621i
$601$	6545.43	−	11337.0i	0.444249	−	0.769462i	−0.553751	−	0.832682i	$-0.686804\pi$
$601$	6545.43	−	11337.0i	0.444249	−	0.769462i	0.998000	+	0.0632209i	$0.0201373\pi$
$602$	7782.78	−	20672.5i	0.526914	−	1.39958i
$603$	−3235.67	+	570.536i	−0.218518	+	0.0385307i
$604$	23698.1	+	521.497i	1.59646	+	0.0351314i
$605$	−5206.12	+	14303.7i	−0.349849	+	0.961203i
$606$	−730.977	−	8.04190i	−0.0489999	−	0.000539076i
$607$	15867.9			1.06105			0.530525	−	0.847669i	$-0.321995\pi$
$607$	15867.9			1.06105			0.530525	+	0.847669i	$0.321995\pi$
$608$	5232.08	−	14049.2i	0.348995	−	0.937125i
$609$	3700.65			0.246236
$610$	33953.1	+	373.538i	2.25364	+	0.0247936i
$611$	8989.45	−	24698.3i	0.595212	−	1.63533i
$612$	2973.84	+	65.4417i	0.196422	+	0.00432243i
$613$	2077.18	−	366.263i	0.136862	−	0.0241325i	−0.104797	−	0.994494i	$-0.533419\pi$
$613$	2077.18	−	366.263i	0.136862	−	0.0241325i	0.241660	+	0.970361i	$0.422308\pi$
$614$	718.393	−	1908.19i	0.0472182	−	0.125420i
$615$	−4606.87	+	7979.34i	−0.302060	+	0.523184i
$616$	424.646	−	12862.1i	0.0277751	−	0.841279i
$617$	−12339.5	−	10354.0i	−0.805134	−	0.675588i	0.144307	−	0.989533i	$-0.453905\pi$
$617$	−12339.5	−	10354.0i	−0.805134	−	0.675588i	−0.949441	+	0.313945i	$0.898349\pi$
$618$	−3218.48	+	531.066i	−0.209492	+	0.0345673i
$619$	9600.30	−	5542.74i	0.623374	−	0.359905i	−0.154807	−	0.987945i	$-0.549476\pi$
$619$	9600.30	−	5542.74i	0.623374	−	0.359905i	0.778182	+	0.628039i	$0.216142\pi$
$620$	5735.63	−	14741.1i	0.371530	−	0.954863i
$621$	3165.44	+	8696.98i	0.204549	+	0.561993i
$622$	−13790.2	+	23289.9i	−0.888968	+	1.50135i
$623$	−2596.19	+	14723.7i	−0.166957	+	0.946860i
$624$	10985.7	+	483.732i	0.704774	+	0.0310333i
$625$	20051.8	−	16825.5i	1.28332	−	1.07683i
$626$	412.760	+	354.157i	0.0263534	+	0.0226118i
$627$	3664.93	+	467.815i	0.233434	+	0.0297970i
$628$	−20035.8	+	3079.99i	−1.27311	+	0.195709i
$629$	1612.15	+	1921.28i	0.102195	+	0.121791i
$630$	−27632.7	+	15551.0i	−1.74748	+	0.983437i
$631$	2883.44	−	16352.8i	0.181914	−	1.03169i	−0.747942	−	0.663764i	$-0.768958\pi$
$631$	2883.44	−	16352.8i	0.181914	−	1.03169i	0.929856	−	0.367923i	$-0.119931\pi$
$632$	14440.8	+	5802.54i	0.908902	+	0.365210i
$633$	−8569.38	+	3119.00i	−0.538076	+	0.195844i
$634$	2786.63	+	7926.45i	0.174560	+	0.496529i
$635$	−45946.7	+	26527.4i	−2.87140	+	1.65780i
$636$	−3729.82	+	6143.98i	−0.232543	+	0.383058i
$637$	−13214.1	+	15747.9i	−0.821916	+	0.979522i
$638$	1038.75	−	5534.31i	0.0644585	−	0.343426i
$639$	−3661.43	+	6341.78i	−0.226673	+	0.392609i
$640$	−28872.0	+	2824.70i	−1.78323	+	0.174463i
$641$	−292.766	−	1660.36i	−0.0180399	−	0.102309i	0.974458	−	0.224568i	$-0.0720972\pi$
$641$	−292.766	−	1660.36i	−0.0180399	−	0.102309i	−0.992498	+	0.122259i	$0.960986\pi$
$642$	5433.93	−	4458.67i	0.334050	−	0.274096i
$643$	5145.38	−	14136.8i	0.315574	−	0.867031i	−0.675932	−	0.736964i	$-0.736259\pi$
$643$	5145.38	−	14136.8i	0.315574	−	0.867031i	0.991505	−	0.130067i	$-0.0415192\pi$
$644$	−14046.6	−	12323.1i	−0.859491	−	0.754036i
$645$		−	12271.4i		−	0.749127i
$646$	−1393.21	−	3431.84i	−0.0848530	−	0.209016i
$647$	−9821.73			−0.596804			−0.298402	−	0.954440i	$-0.596454\pi$
$647$	−9821.73			−0.596804			−0.298402	+	0.954440i	$0.596454\pi$
$648$	−1464.68	−	10279.8i	−0.0887934	−	0.623190i
$649$	−1102.43	−	401.252i	−0.0666783	−	0.0242689i
$650$	45626.5	+	55606.6i	2.75326	+	3.35549i
$651$	4318.02	−	761.384i	0.259964	−	0.0458387i
$652$	−17153.9	+	9406.83i	−1.03037	+	0.565030i
$653$	−10736.3	−	6198.61i	−0.643406	−	0.371471i	0.142519	−	0.989792i	$-0.454480\pi$
$653$	−10736.3	−	6198.61i	−0.643406	−	0.371471i	−0.785925	+	0.618321i	$0.787813\pi$
$654$	−97.3833	+	518.845i	−0.00582261	+	0.0310221i
$655$	−2870.05	−	2408.26i	−0.171209	−	0.143662i
$656$	14566.7	+	6040.06i	0.866973	+	0.359489i
$657$	7835.95	+	13572.3i	0.465311	+	0.805943i
$658$	−18132.9	+	6374.83i	−1.07431	+	0.377685i
$659$	8375.48	+	23011.5i	0.495087	+	1.36024i	0.895971	+	0.444112i	$0.146481\pi$
$659$	8375.48	+	23011.5i	0.495087	+	1.36024i	−0.400884	+	0.916129i	$0.631297\pi$
$660$	−2296.82	−	6770.35i	−0.135460	−	0.399296i
$661$	−25007.6	−	4409.52i	−1.47153	−	0.259471i	−0.620344	−	0.784330i	$-0.713007\pi$
$661$	−25007.6	−	4409.52i	−1.47153	−	0.259471i	−0.851189	+	0.524859i	$0.824118\pi$
$662$	−17557.1	+	9880.70i	−1.03078	+	0.580097i
$663$	2081.14	−	1746.28i	0.121907	−	0.102292i
$664$	−3666.65	−	2281.49i	−0.214298	−	0.133342i
$665$	31417.8	+	23911.6i	1.83207	+	1.39436i
$666$	6869.97	−	8006.75i	0.399709	−	0.465849i
$667$	−5255.54	−	6263.31i	−0.305090	−	0.363593i
$668$	−5992.39	+	30096.6i	−0.347085	+	1.74322i
$669$	−5180.07	−	913.386i	−0.299362	−	0.0527855i
$670$	4033.44	−	6811.95i	0.232575	−	0.392789i
$671$	13458.3	−	4898.40i	0.774292	−	0.281819i
$672$	−4822.50	−	6435.03i	−0.276833	−	0.369400i
$673$	12690.6	+	21980.7i	0.726874	+	1.25898i	0.958198	+	0.286106i	$0.0923610\pi$
$673$	12690.6	+	21980.7i	0.726874	+	1.25898i	−0.231324	+	0.972877i	$0.574306\pi$
$674$	−329.090	−	1994.42i	−0.0188072	−	0.113980i
$675$	−16746.9	+	19958.1i	−0.954943	+	1.13806i
$676$	−39156.3	+	31414.3i	−2.22783	+	1.78734i
$677$	166.611	+	96.1931i	0.00945848	+	0.00546086i	0.504722	−	0.863282i	$-0.331595\pi$
$677$	166.611	+	96.1931i	0.00945848	+	0.00546086i	−0.495263	+	0.868743i	$0.664928\pi$
$678$	773.881	−	2055.57i	0.0438359	−	0.116436i
$679$	−4251.32	−	24110.4i	−0.240281	−	1.36270i
$680$	−4785.59	+	5335.32i	−0.269881	+	0.300883i
$681$	8166.23	+	2972.26i	0.459516	+	0.167250i
$682$	73.3949	−	6671.31i	0.00412087	−	0.374571i
$683$		−	83.6066i		−	0.00468392i	−0.999997	−	0.00234196i	$-0.999255\pi$
$683$		−	83.6066i		−	0.00468392i	0.999997	−	0.00234196i	$-0.000745470\pi$
$684$	−13289.3	+	8132.56i	−0.742878	+	0.454614i
$685$		−	211.572i		−	0.0118011i
$686$	−8053.64	−	88.6027i	−0.448235	−	0.00493129i
$687$	5571.51	+	2027.86i	0.309413	+	0.112617i
$688$	−20823.9	+	2733.65i	−1.15393	+	0.151482i
$689$	−7692.70	−	43627.5i	−0.425354	−	2.41230i
$690$	−9715.18	−	3657.56i	−0.536015	−	0.201799i
$691$	2951.03	+	1703.78i	0.162464	+	0.0937986i	0.579028	−	0.815308i	$-0.303432\pi$
$691$	2951.03	+	1703.78i	0.162464	+	0.0937986i	−0.416564	+	0.909107i	$0.636766\pi$
$692$	−3354.81	−	4181.60i	−0.184293	−	0.229712i
$693$	−8596.73	+	10245.2i	−0.471231	+	0.561591i
$694$	−34768.4	+	5736.97i	−1.90171	+	0.313793i
$695$	450.513	+	780.311i	0.0245884	+	0.0425883i
$696$	−1657.80	−	3103.61i	−0.0902857	−	0.169026i
$697$	3660.98	−	1332.49i	0.198952	−	0.0724126i
$698$	−13308.5	−	7880.12i	−0.721681	−	0.427317i
$699$	−1283.22	−	226.267i	−0.0694362	−	0.0122435i
$700$	10271.6	−	51588.9i	0.554616	−	2.78554i
$701$	19234.8	+	22923.1i	1.03636	+	1.23508i	0.971463	+	0.237192i	$0.0762271\pi$
$701$	19234.8	+	22923.1i	1.03636	+	1.23508i	0.0648958	+	0.997892i	$0.479328\pi$
$702$	−18631.0	−	15985.8i	−1.00168	−	0.859467i
$703$	−12544.2	−	3900.91i	−0.672994	−	0.209282i
$704$	−10977.2	+	5405.77i	−0.587670	+	0.289400i
$705$	−8179.84	+	6863.70i	−0.436980	+	0.366669i
$706$	1021.32	+	1814.79i	0.0544444	+	0.0967429i
$707$	−3244.92	−	572.166i	−0.172613	−	0.0304364i
$708$	−694.228	+	235.515i	−0.0368513	+	0.0125017i
$709$	−799.572	−	2196.81i	−0.0423534	−	0.116365i	0.916713	−	0.399546i	$-0.130832\pi$
$709$	−799.572	−	2196.81i	−0.0423534	−	0.116365i	−0.959066	+	0.283181i	$0.908610\pi$
$710$	−5851.92	−	16645.5i	−0.309322	−	0.879853i
$711$	−8086.90	−	14006.9i	−0.426558	−	0.738820i
$712$	13511.3	−	4418.54i	0.711177	−	0.232573i
$713$	−7420.95	−	6226.91i	−0.389785	−	0.327068i
$714$	−1952.63	−	366.494i	−0.102346	−	0.0192096i
$715$	38161.7	+	22032.7i	1.99604	+	1.15241i
$716$	−732.460	+	401.664i	−0.0382309	+	0.0209649i
$717$	11994.3	−	2114.91i	0.624733	−	0.110157i
$718$	1861.85	−	1527.69i	0.0967738	−	0.0794052i
$719$	−24318.8	−	8851.33i	−1.26139	−	0.459109i	−0.377155	−	0.926150i	$-0.623098\pi$
$719$	−24318.8	−	8851.33i	−1.26139	−	0.459109i	−0.884235	+	0.467042i	$0.845320\pi$
$720$	25420.8	+	16208.1i	1.31580	+	0.838947i
$721$	−14703.0			−0.759456
$722$	15856.9	+	11177.0i	0.817358	+	0.576130i
$723$		−	1293.31i		−	0.0665265i
$724$	−5842.47	+	6659.56i	−0.299908	+	0.341852i
$725$	7871.99	−	21628.1i	0.403253	−	1.10793i
$726$	2544.84	+	3101.48i	0.130093	+	0.158549i
$727$	5559.62	+	31530.2i	0.283624	+	1.60851i	0.710158	+	0.704042i	$0.248623\pi$
$727$	5559.62	+	31530.2i	0.283624	+	1.60851i	−0.426534	+	0.904472i	$0.640265\pi$
$728$	48500.8	+	10212.7i	2.46917	+	0.519930i
$729$	−3019.23	+	5229.46i	−0.153393	+	0.265684i
$730$	−37112.9	−	6965.83i	−1.88166	−	0.353174i
$731$	−3335.32	+	3974.88i	−0.168757	+	0.201117i
$732$	4644.13	−	7650.08i	0.234497	−	0.386278i
$733$	18738.5	−	10818.7i	0.944230	−	0.545151i	0.0529462	−	0.998597i	$-0.483139\pi$
$733$	18738.5	−	10818.7i	0.944230	−	0.545151i	0.891284	+	0.453446i	$0.149805\pi$
$734$	−3041.47	+	1069.26i	−0.152947	+	0.0537700i
$735$	7848.09	−	2856.47i	0.393852	−	0.143350i
$736$	−4042.46	+	17300.8i	−0.202455	+	0.866464i
$737$	579.832	−	3288.39i	0.0289802	−	0.164355i
$738$	−8037.47	−	14281.9i	−0.400899	−	0.712362i
$739$	−6211.75	−	7402.88i	−0.309206	−	0.368497i	0.588954	−	0.808167i	$-0.299540\pi$
$739$	−6211.75	−	7402.88i	−0.309206	−	0.368497i	−0.898160	+	0.439670i	$0.855095\pi$
$740$	3862.34	+	25125.0i	0.191868	+	1.24813i
$741$	−4225.47	+	13587.9i	−0.209482	+	0.673637i
$742$	−21095.9	+	24586.7i	−1.04374	+	1.21645i
$743$	13612.3	−	11422.0i	0.672120	−	0.563976i	−0.241572	−	0.970383i	$-0.577663\pi$
$743$	13612.3	−	11422.0i	0.672120	−	0.563976i	0.913692	+	0.406407i	$0.133219\pi$
$744$	−2572.92	−	3280.30i	−0.126785	−	0.161642i
$745$	−8776.00	+	49771.2i	−0.431581	+	2.44762i
$746$	−20584.1	−	12188.1i	−1.01024	−	0.598176i
$747$	1534.98	+	4217.33i	0.0751836	+	0.206565i
$748$	−1096.18	+	2817.28i	−0.0535834	+	0.137714i
$749$	27437.8	−	15841.2i	1.33852	−	0.772797i
$750$	−2605.13	−	15788.2i	−0.126834	−	0.768669i
$751$	−22385.1	−	18783.3i	−1.08767	−	0.912666i	−0.0911375	−	0.995838i	$-0.529050\pi$
$751$	−22385.1	−	18783.3i	−1.08767	−	0.912666i	−0.996535	+	0.0831726i	$0.973495\pi$
$752$	13469.5	+	12351.7i	0.653166	+	0.598963i
$753$	−4503.15	+	7799.69i	−0.217934	+	0.377472i
$754$	20296.5	+	7641.21i	0.980311	+	0.369067i
$755$	58453.5	−	10306.9i	2.81767	−	0.496832i
$756$	−394.966	+	17948.3i	−0.0190010	+	0.863455i
$757$	−177.634	+	488.047i	−0.00852871	+	0.0234324i	−0.943884	−	0.330277i	$-0.892858\pi$
$757$	−177.634	+	488.047i	−0.00852871	+	0.0234324i	0.935355	+	0.353710i	$0.115080\pi$
$758$	−91.3251	+	8301.09i	−0.00437609	+	0.397769i
$759$	−4378.55			−0.209396
$760$	5979.45	−	37060.9i	0.285392	−	1.76887i
$761$	40034.1			1.90701			0.953504	−	0.301379i	$-0.0974470\pi$
$761$	40034.1			1.90701			0.953504	+	0.301379i	$0.0974470\pi$
$762$	−153.830	+	13982.5i	−0.00731321	+	0.664742i
$763$	−813.822	+	2235.96i	−0.0386138	+	0.106091i
$764$	26834.6	+	590.517i	1.27073	+	0.0279635i
$765$	7335.24	−	1293.40i	0.346675	−	0.0611281i
$766$	11978.0	+	4509.49i	0.564992	+	0.212708i
$767$	2259.22	−	3913.08i	0.106357	−	0.184215i
$768$	−3236.48	+	6927.21i	−0.152065	+	0.325474i
$769$	−18739.8	−	15724.6i	−0.878771	−	0.737377i	0.0871549	−	0.996195i	$-0.472222\pi$
$769$	−18739.8	−	15724.6i	−0.878771	−	0.737377i	−0.965926	+	0.258818i	$0.916667\pi$
$770$	−5246.29	−	31794.7i	−0.245537	−	1.48805i
$771$	−3006.32	+	1735.70i	−0.140428	+	0.0810761i
$772$	−9908.93	−	3855.49i	−0.461956	−	0.179744i
$773$	−9580.36	−	26321.8i	−0.445772	−	1.22475i	−0.935641	−	0.352952i	$-0.885178\pi$
$773$	−9580.36	−	26321.8i	−0.445772	−	1.22475i	0.489869	−	0.871796i	$-0.337044\pi$
$774$	18781.3	+	11120.7i	0.872198	+	0.516440i
$775$	4735.42	−	26855.9i	0.219486	−	1.24476i
$776$	−18316.1	+	14366.3i	−0.847307	+	0.664590i
$777$	−5397.91	+	4529.38i	−0.249226	+	0.209126i
$778$	16922.9	−	19723.1i	0.779838	−	0.908879i
$779$	−12358.7	+	16238.2i	−0.568414	+	0.746847i
$780$	27215.5	−	4183.69i	1.24932	−	0.192051i
$781$	−4783.73	−	5701.03i	−0.219175	−	0.261202i
$782$	2152.77	+	3825.28i	0.0984436	+	0.174926i
$783$	−1364.06	+	7735.94i	−0.0622572	+	0.353078i
$784$	−6595.54	−	12681.4i	−0.300453	−	0.577688i
$785$	−47698.4	+	17360.8i	−2.16870	+	0.789343i
$786$	−931.576	+	327.506i	−0.0422751	+	0.0148623i
$787$	16225.3	−	9367.70i	0.734906	−	0.424298i	−0.0853085	−	0.996355i	$-0.527188\pi$
$787$	16225.3	−	9367.70i	0.734906	−	0.424298i	0.820214	+	0.572057i	$0.193854\pi$
$788$	−28146.0	−	17086.6i	−1.27241	−	0.772442i
$789$	3544.25	−	4223.88i	0.159922	−	0.190588i
$790$	38301.5	+	7188.91i	1.72495	+	0.323760i
$791$	4950.04	−	8573.71i	0.222507	−	0.385393i
$792$	12443.4	+	2620.19i	0.558280	+	0.117556i
$793$	9578.45	+	54322.1i	0.428929	+	2.43258i
$794$	15273.7	+	18614.6i	0.682674	+	0.831998i
$795$	−6155.59	+	16912.3i	−0.274612	+	0.754489i
$796$	−24742.1	−	21706.4i	−1.10171	−	0.966535i
$797$		−	9901.49i		−	0.440061i	−0.975493	−	0.220031i	$-0.929384\pi$
$797$		−	9901.49i		−	0.440061i	0.975493	−	0.220031i	$-0.0706157\pi$
$798$	9641.88	−	3914.27i	0.427718	−	0.173639i
$799$	4515.09			0.199915
$800$	−47867.3	+	14496.1i	−2.11546	+	0.640645i
$801$	−13882.4	−	5052.79i	−0.612373	−	0.222886i
$802$	10017.5	−	8219.58i	0.441059	−	0.361900i
$803$	−15685.3	+	2765.74i	−0.689317	+	0.121545i
$804$	−1003.25	−	1829.49i	−0.0440075	−	0.0802503i
$805$	−40521.6	−	23395.2i	−1.77416	−	1.02431i
$806$	25254.6	+	4740.11i	1.10367	+	0.207150i
$807$	−9758.64	−	8188.47i	−0.425676	−	0.357184i
$808$	973.789	+	2977.72i	0.0423982	+	0.129648i
$809$	−3636.65	−	6298.86i	−0.158044	−	0.273741i	0.776119	−	0.630586i	$-0.217186\pi$
$809$	−3636.65	−	6298.86i	−0.158044	−	0.273741i	−0.934163	+	0.356846i	$0.883852\pi$
$810$	−8623.49	−	24529.2i	−0.374072	−	1.06403i
$811$	3410.69	+	9370.80i	0.147676	+	0.405738i	0.991371	−	0.131086i	$-0.0418463\pi$
$811$	3410.69	+	9370.80i	0.147676	+	0.405738i	−0.843695	+	0.536823i	$0.819624\pi$
$812$	−5095.14	−	15019.0i	−0.220203	−	0.649092i
$813$	5191.96	+	915.482i	0.223973	+	0.0394924i
$814$	5258.52	+	9343.93i	0.226426	+	0.402340i
$815$	−37527.5	+	31489.3i	−1.61292	+	1.35340i
$816$	567.365	+	1801.78i	0.0243404	+	0.0772978i
$817$	3441.28	−	26959.5i	0.147362	−	1.15446i
$818$	22807.6	+	19569.5i	0.974879	+	0.836467i
$819$	−33109.7	−	39458.6i	−1.41263	−	1.68351i
$820$	38726.7	+	7710.70i	1.64926	+	0.328377i
$821$	−23742.2	−	4186.39i	−1.00927	−	0.177961i	−0.355516	−	0.934670i	$-0.615695\pi$
$821$	−23742.2	−	4186.39i	−1.00927	−	0.177961i	−0.653752	+	0.756709i	$0.726806\pi$
$822$	−47.9826	−	28.4111i	−0.00203599	−	0.00120554i
$823$	20313.6	−	7393.55i	0.860374	−	0.313151i	0.126111	−	0.992016i	$-0.459750\pi$
$823$	20313.6	−	7393.55i	0.860374	−	0.313151i	0.734263	+	0.678866i	$0.237528\pi$
$824$	6586.59	+	12330.9i	0.278464	+	0.521320i
$825$	−6162.88	−	10674.4i	−0.260078	−	0.450468i
$826$	−3260.21	+	537.952i	−0.137333	+	0.0226607i
$827$	16554.0	−	19728.2i	0.696055	−	0.829526i	−0.296019	−	0.955182i	$-0.595659\pi$
$827$	16554.0	−	19728.2i	0.696055	−	0.829526i	0.992074	+	0.125656i	$0.0401035\pi$
$828$	14402.0	−	11554.5i	0.604475	−	0.484958i
$829$	6748.09	+	3896.01i	0.282715	+	0.163226i	0.634652	−	0.772798i	$-0.281143\pi$
$829$	6748.09	+	3896.01i	0.282715	+	0.163226i	−0.351937	+	0.936024i	$0.614477\pi$
$830$	−10120.2	−	3810.06i	−0.423228	−	0.159336i
$831$	592.035	+	3357.60i	0.0247142	+	0.140161i
$832$	−13162.1	−	45251.0i	−0.548455	−	1.88557i
$833$	−3318.48	−	1207.83i	−0.138030	−	0.0502387i
$834$	237.464	+	2.61248i	0.00985938	+	0.000108469i
$835$			76842.2i			3.18471i
$836$	−3147.36	−	15518.1i	−0.130208	−	0.641992i
$837$			9307.17i			0.384352i
$838$	190.841	−	17346.7i	0.00786695	−	0.715075i
$839$	4565.53	+	1661.72i	0.187866	+	0.0683776i	0.434240	−	0.900797i	$-0.357017\pi$
$839$	4565.53	+	1661.72i	0.187866	+	0.0683776i	−0.246374	+	0.969175i	$0.579239\pi$
$840$	−14989.8	−	13445.3i	−0.615710	−	0.552269i
$841$	3030.07	+	17184.4i	0.124239	+	0.704596i
$842$	−14215.6	+	37759.4i	−0.581832	+	1.54546i
$843$	−1988.34	−	1147.97i	−0.0812360	−	0.0469016i
$844$	24456.9	+	30484.2i	0.997442	+	1.24326i
$845$	−80800.7	+	96294.5i	−3.28950	+	3.92027i
$846$	−3092.08	−	18739.3i	−0.125659	−	0.761548i
$847$	9041.54	+	15660.4i	0.366790	+	0.635299i
$848$	30070.5	+	6678.18i	1.21772	+	0.270436i
$849$	1790.62	−	651.732i	0.0723838	−	0.0263456i
$850$	−6295.55	+	10632.4i	−0.254042	+	0.429043i
$851$	15331.9	+	2703.42i	0.617591	+	0.108898i
$852$	−4560.88	−	908.095i	−0.183396	−	0.0365150i
$853$	−18435.7	−	21970.8i	−0.740005	−	0.881904i	0.256404	−	0.966570i	$-0.417462\pi$
$853$	−18435.7	−	21970.8i	−0.740005	−	0.881904i	−0.996409	+	0.0846655i	$0.973018\pi$
$854$	26267.2	−	30613.7i	1.05251	−	1.22667i
$855$	−28659.6	+	26470.2i	−1.14636	+	1.05879i
$856$	−25576.9	−	15914.6i	−1.02126	−	0.635457i
$857$	9261.00	−	7770.90i	0.369136	−	0.309742i	−0.439284	−	0.898348i	$-0.644768\pi$
$857$	9261.00	−	7770.90i	0.369136	−	0.309742i	0.808420	+	0.588606i	$0.200323\pi$
$858$	10121.4	−	5696.04i	0.402724	−	0.226643i
$859$	5391.81	+	950.722i	0.214163	+	0.0377628i	0.279700	−	0.960087i	$-0.409765\pi$
$859$	5391.81	+	950.722i	0.214163	+	0.0377628i	−0.0655369	+	0.997850i	$0.520876\pi$
$860$	−49803.2	+	16895.6i	−1.97474	+	0.669924i
$861$	3743.67	+	10285.7i	0.148181	+	0.407125i
$862$	30486.5	−	10717.9i	1.20461	−	0.423494i
$863$	−1804.49	−	3125.47i	−0.0711769	−	0.123282i	0.828240	−	0.560373i	$-0.189342\pi$
$863$	−1804.49	−	3125.47i	−0.0711769	−	0.123282i	−0.899417	+	0.437091i	$0.856009\pi$
$864$	15229.5	−	7709.15i	0.599675	−	0.303554i
$865$	−10283.5	−	8628.89i	−0.404220	−	0.339181i
$866$	1835.88	−	9781.30i	0.0720389	−	0.383813i
$867$	−7538.21	−	4352.19i	−0.295284	−	0.170482i
$868$	−9035.21	−	16476.3i	−0.353312	−	0.644287i
$869$	16187.6	−	2854.31i	0.631907	−	0.111422i
$870$	−5588.85	−	6811.32i	−0.217793	−	0.265432i
$871$	12084.8	+	4398.51i	0.470124	+	0.171111i
$872$	2239.79	−	319.131i	0.0869828	−	0.0123935i
$873$	24191.7			0.937876
$874$	−20317.9	−	10759.9i	−0.786344	−	0.416428i
$875$		−	72125.1i		−	2.78660i
$876$	−6563.52	+	7481.45i	−0.253151	+	0.288556i
$877$	13014.7	−	35757.5i	0.501111	−	1.37679i	−0.389080	−	0.921204i	$-0.627207\pi$
$877$	13014.7	−	35757.5i	0.501111	−	1.37679i	0.890191	−	0.455587i	$-0.150571\pi$
$878$	−3686.54	+	3024.89i	−0.141702	+	0.116270i
$879$	−663.017	−	3760.15i	−0.0254414	−	0.144285i
$880$	−24314.9	+	18643.2i	−0.931427	+	0.714160i
$881$	8680.24	−	15034.6i	0.331946	−	0.574948i	−0.650947	−	0.759123i	$-0.725628\pi$
$881$	8680.24	−	15034.6i	0.331946	−	0.574948i	0.982893	+	0.184175i	$0.0589614\pi$
$882$	−2740.33	+	14600.1i	−0.104616	+	0.557381i
$883$	−2663.53	+	3174.27i	−0.101512	+	0.120977i	−0.814408	−	0.580292i	$-0.802938\pi$
$883$	−2663.53	+	3174.27i	−0.101512	+	0.120977i	0.712897	+	0.701269i	$0.247383\pi$
$884$	−9952.58	−	6041.90i	−0.378667	−	0.229877i
$885$	−1589.75	+	917.840i	−0.0603828	+	0.0348620i
$886$	10618.2	+	30203.0i	0.402625	+	1.14525i
$887$	34296.1	−	12482.8i	1.29825	−	0.472525i	0.401825	−	0.915716i	$-0.368376\pi$
$887$	34296.1	−	12482.8i	1.29825	−	0.472525i	0.896427	+	0.443191i	$0.146154\pi$
$888$	6216.78	+	2497.99i	0.234934	+	0.0943998i
$889$	−10944.7	+	62070.5i	−0.412906	+	2.34171i
$890$	31021.0	−	17457.8i	1.16834	−	0.657513i
$891$	−7049.40	−	8401.14i	−0.265055	−	0.315880i
$892$	3425.09	+	22280.7i	0.128566	+	0.836338i
$893$	−19895.4	+	12785.2i	−0.745547	+	0.479106i
$894$	10109.1	+	8673.87i	0.378188	+	0.324494i
$895$	−1602.39	+	1344.57i	−0.0598460	+	0.0502167i
$896$	−19476.6	+	28431.9i	−0.726192	+	1.06009i
$897$	2928.35	−	16607.5i	0.109002	−	0.618181i
$898$	18312.7	−	30927.7i	0.680514	−	1.14930i
$899$	−2812.14	−	7726.28i	−0.104327	−	0.286636i
$900$	48439.5	+	18847.5i	1.79406	+	0.698054i
$901$	6590.59	−	3805.08i	0.243690	−	0.140694i
$902$	16433.0	−	2711.53i	0.606607	−	0.100093i
$903$	−11167.6	−	9370.71i	−0.411554	−	0.345335i
$904$	−9407.98	−	310.608i	−0.346134	−	0.0114277i
$905$	−11091.8	+	19211.5i	−0.407407	+	0.705650i
$906$	5511.95	−	14640.8i	0.202122	−	0.536873i
$907$	7781.42	−	1372.07i	0.284871	−	0.0502304i	−0.0293869	−	0.999568i	$-0.509356\pi$
$907$	7781.42	−	1372.07i	0.284871	−	0.0502304i	0.314258	+	0.949338i	$0.398244\pi$
$908$	819.379	−	37234.7i	0.0299472	−	1.36088i
$909$	1113.57	−	3059.50i	0.0406323	−	0.111636i
$910$	124103.	+	1365.33i	4.52086	+	0.0497366i
$911$	18827.5			0.684724			0.342362	−	0.939568i	$-0.388773\pi$
$911$	18827.5			0.684724			0.342362	+	0.939568i	$0.388773\pi$
$912$	−7602.10	−	6332.82i	−0.276020	−	0.229935i
$913$	−4561.12			−0.165335
$914$	31810.5	+	349.966i	1.15120	+	0.0126650i
$915$	7664.53	−	21058.1i	0.276920	−	0.760831i
$916$	559.032	−	25403.8i	0.0201648	−	0.916338i
$917$	−4383.25	+	772.886i	−0.157849	+	0.0278331i
$918$	1485.87	−	3946.74i	0.0534214	−	0.141897i
$919$	3953.67	−	6847.96i	0.141915	−	0.245803i	−0.786303	−	0.617841i	$-0.788007\pi$
$919$	3953.67	−	6847.96i	0.141915	−	0.245803i	0.928218	+	0.372038i	$0.121341\pi$
$920$	−1468.01	+	44464.6i	−0.0526076	+	1.59343i
$921$	−1030.83	−	864.967i	−0.0368805	−	0.0309464i
$922$	−6263.46	+	1033.50i	−0.223727	+	0.0369161i
$923$	24822.9	−	14331.5i	0.885217	−	0.511080i
$924$	−7915.24	−	3079.76i	−0.281810	−	0.109650i
$925$	14989.2	+	41182.5i	0.532802	+	1.46386i
$926$	10690.0	−	18054.0i	0.379368	−	0.640702i
$927$	2522.84	−	14307.7i	0.0893860	−	0.506933i
$928$	−10313.4	+	11001.3i	−0.364821	+	0.389153i
$929$	−22822.6	+	19150.5i	−0.806014	+	0.676326i	−0.949653	−	0.313304i	$-0.898564\pi$
$929$	−22822.6	+	19150.5i	−0.806014	+	0.676326i	0.143639	+	0.989630i	$0.454120\pi$
$930$	−7922.61	−	6797.78i	−0.279347	−	0.239686i
$931$	18042.8	−	4074.64i	0.635155	−	0.143438i
$932$	848.475	+	5519.44i	0.0298205	+	0.193987i
$933$	11482.2	+	13684.0i	0.402906	+	0.480164i
$934$	11947.8	−	6723.90i	0.418569	−	0.235560i
$935$	−1314.47	+	7454.75i	−0.0459763	+	0.260745i
$936$	−18260.2	+	45444.5i	−0.637665	+	1.58697i
$937$	−9748.45	+	3548.14i	−0.339880	+	0.123706i	−0.506321	−	0.862345i	$-0.668995\pi$
$937$	−9748.45	+	3548.14i	−0.339880	+	0.123706i	0.166441	+	0.986051i	$0.446773\pi$
$938$	−3119.18	−	8872.37i	−0.108577	−	0.308841i
$939$	310.854	−	179.472i	0.0108033	−	0.00623731i
$940$	39118.3	+	23747.5i	1.35734	+	0.823998i
$941$	106.178	−	126.538i	0.00367832	−	0.00438365i	−0.764202	−	0.644977i	$-0.776867\pi$
$941$	106.178	−	126.538i	0.00367832	−	0.00438365i	0.767880	+	0.640593i	$0.221311\pi$
$942$	−2467.94	+	13148.9i	−0.0853609	+	0.454791i
$943$	12091.7	−	20943.5i	0.417562	−	0.723238i
$944$	1911.66	+	2493.24i	0.0659102	+	0.0859619i
$945$	7806.17	+	44271.0i	0.268714	+	1.52395i
$946$	−17148.5	+	14070.8i	−0.589373	+	0.483595i
$947$	−6919.41	+	19010.9i	−0.237435	+	0.652347i	0.762551	+	0.646929i	$0.223947\pi$
$947$	−6919.41	+	19010.9i	−0.237435	+	0.652347i	−0.999985	+	0.00541802i	$0.998275\pi$
$948$	6773.72	−	7721.05i	0.232068	−	0.264523i
$949$		−	61342.6i		−	2.09828i
$950$	−2366.45	−	64677.5i	−0.0808189	−	2.20886i
$951$	5545.13			0.189078
$952$	1201.02	+	8429.27i	0.0408879	+	0.286969i
$953$	−15057.5	−	5480.48i	−0.511815	−	0.186286i	0.0731854	−	0.997318i	$-0.476684\pi$
$953$	−15057.5	−	5480.48i	−0.511815	−	0.186286i	−0.585001	+	0.811033i	$0.698906\pi$
$954$	−20305.9	−	24747.5i	−0.689128	−	0.839864i
$955$	66189.9	−	11671.1i	2.24278	−	0.395463i
$956$	−25097.3	−	45766.5i	−0.849063	−	1.54832i
$957$	−3218.40	−	1858.15i	−0.108711	−	0.0627642i
$958$	5118.52	−	27270.7i	0.172622	−	0.919705i
$959$	−192.541	−	161.561i	−0.00648329	−	0.00544012i
$960$	−4561.04	+	18594.6i	−0.153341	+	0.625143i
$961$	10024.6	+	17363.1i	0.336497	+	0.582830i
$962$	−38957.6	+	13696.0i	−1.30566	+	0.459019i
$963$	10707.4	+	29418.3i	0.358297	+	0.984413i
$964$	−5248.85	+	1780.66i	−0.175367	+	0.0594929i
$965$	−26219.8	−	4623.27i	−0.874660	−	0.154226i
$966$	−10747.3	+	6048.28i	−0.357958	+	0.201450i
$967$	−34818.6	+	29216.3i	−1.15790	+	0.971594i	−0.999875	−	0.0158411i	$-0.994957\pi$
$967$	−34818.6	+	29216.3i	−1.15790	+	0.971594i	−0.158026	+	0.987435i	$0.550513\pi$
$968$	9083.46	−	14598.3i	0.301605	−	0.484719i
$969$	−2441.69	+	116.247i	−0.0809478	+	0.00385387i
$970$	−37956.6	+	44237.3i	−1.25640	+	1.46430i
$971$	−2792.34	−	3327.79i	−0.0922869	−	0.109983i	0.717925	−	0.696121i	$-0.245092\pi$
$971$	−2792.34	−	3327.79i	−0.0922869	−	0.109983i	−0.810212	+	0.586138i	$0.800648\pi$
$972$	−26697.0	−	5315.52i	−0.880974	−	0.175407i
$973$	1054.14	+	185.873i	0.0347319	+	0.00612418i
$974$	−5493.83	+	9278.34i	−0.180733	+	0.305233i
$975$	44608.9	−	16236.3i	1.46526	−	0.533311i
$976$	−37441.8	−	8315.23i	−1.22795	−	0.272709i
$977$	−22126.9	−	38324.9i	−0.724568	−	1.25499i	−0.959152	−	0.282892i	$-0.908706\pi$
$977$	−22126.9	−	38324.9i	−0.724568	−	1.25499i	0.234584	−	0.972096i	$-0.424627\pi$
$978$	2102.07	+	12739.4i	0.0687290	+	0.416526i
$979$	9650.85	−	11501.4i	0.315059	−	0.375472i
$980$	−22398.4	−	27918.4i	−0.730091	−	0.910020i
$981$	−2036.20	−	1175.60i	−0.0662701	−	0.0382611i
$982$	14584.6	−	38739.6i	0.473946	−	1.25889i
$983$	−195.679	−	1109.75i	−0.00634911	−	0.0360076i	0.981469	−	0.191623i	$-0.0613751\pi$
$983$	−195.679	−	1109.75i	−0.00634911	−	0.0360076i	−0.987818	+	0.155615i	$0.950264\pi$
$984$	6949.16	−	7747.42i	0.225133	−	0.250995i
$985$	−77476.7	−	28199.2i	−2.50621	−	0.912184i
$986$	−40.9843	+	3725.31i	−0.00132374	+	0.120323i
$987$			12685.3i			0.409096i
$988$	60963.9	−	1559.25i	1.96308	−	0.0502089i
$989$			32209.0i			1.03558i
$990$	31840.1	+	350.291i	1.02217	+	0.0112454i
$991$	−21950.7	−	7989.41i	−0.703620	−	0.256097i	−0.0346645	−	0.999399i	$-0.511036\pi$
$991$	−21950.7	−	7989.41i	−0.703620	−	0.256097i	−0.668956	+	0.743302i	$0.733258\pi$
$992$	−9770.53	+	14958.5i	−0.312716	+	0.478763i
$993$	2308.86	+	13094.2i	0.0737860	+	0.418461i
$994$	−19616.9	−	7385.34i	−0.625965	−	0.235663i
$995$	−71376.1	−	41209.0i	−2.27415	−	1.31298i
$996$	−2223.09	+	1783.54i	−0.0707242	+	0.0567406i
$997$	2372.06	−	2826.91i	0.0753498	−	0.0897984i	−0.727053	−	0.686582i	$-0.759110\pi$
$997$	2372.06	−	2826.91i	0.0753498	−	0.0897984i	0.802402	+	0.596783i	$0.203555\pi$
$998$	−21029.1	+	3469.91i	−0.666999	+	0.110058i
$999$	−7478.69	−	12953.5i	−0.236852	−	0.410240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.4.t.a.101.1	✓	348
8.5	even	2	inner	152.4.t.a.101.26	yes	348
19.16	even	9	inner	152.4.t.a.149.26	yes	348
152.149	even	18	inner	152.4.t.a.149.1	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.4.t.a.101.1	✓	348	1.1	even	1	trivial
152.4.t.a.101.26	yes	348	8.5	even	2	inner
152.4.t.a.149.1	yes	348	152.149	even	18	inner
152.4.t.a.149.26	yes	348	19.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	152.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.82826 - 0.0311153i) q^{2} +(-0.638447 + 1.75412i) q^{3} +(7.99806 + 0.176004i) q^{4} +(19.7279 - 3.47857i) q^{5} +(1.86027 - 4.94123i) q^{6} +(11.8990 - 20.6097i) q^{7} +(-22.6151 - 0.746646i) q^{8} +(18.0139 + 15.1154i) q^{9} +(-55.9039 + 9.22444i) q^{10} +(-20.6968 + 11.9493i) q^{11} +(-5.41507 + 13.9172i) q^{12} +(-31.4808 - 86.4928i) q^{13} +(-34.2947 + 57.9192i) q^{14} +(-6.49342 + 36.8260i) q^{15} +(63.9380 + 2.81538i) q^{16} +(12.1125 - 10.1636i) q^{17} +(-50.4775 - 43.3108i) q^{18} +(-24.5928 + 79.0835i) q^{19} +(158.398 - 24.3496i) q^{20} +(28.5549 + 34.0304i) q^{21} +(58.9076 - 33.1517i) q^{22} +(17.0434 - 96.6578i) q^{23} +(15.7482 - 39.1929i) q^{24} +(259.630 - 94.4974i) q^{25} +(86.3445 + 245.603i) q^{26} +(-81.6635 + 47.1484i) q^{27} +(98.7963 - 162.743i) q^{28} +(53.5466 - 63.8144i) q^{29} +(19.5109 - 103.951i) q^{30} +(49.3503 - 85.4773i) q^{31} +(-180.746 - 9.95207i) q^{32} +(-7.74668 - 43.9336i) q^{33} +(-34.5734 + 28.3683i) q^{34} +(163.051 - 447.978i) q^{35} +(141.416 + 124.065i) q^{36} +158.620i q^{37} +(72.0154 - 222.903i) q^{38} +171.817 q^{39} +(-448.746 + 63.9384i) q^{40} +(231.536 + 84.2722i) q^{41} +(-79.7018 - 97.1353i) q^{42} +(-323.179 + 56.9851i) q^{43} +(-167.637 + 91.9285i) q^{44} +(407.957 + 235.534i) q^{45} +(-51.2106 + 272.843i) q^{46} +(218.747 + 183.550i) q^{47} +(-45.7596 + 110.357i) q^{48} +(-111.672 - 193.422i) q^{49} +(-737.239 + 259.185i) q^{50} +(10.0949 + 27.7356i) q^{51} +(-236.562 - 697.316i) q^{52} +(473.987 + 83.5766i) q^{53} +(232.432 - 130.807i) q^{54} +(-366.739 + 307.730i) q^{55} +(-284.485 + 457.205i) q^{56} +(-123.021 - 93.6292i) q^{57} +(-153.429 + 178.817i) q^{58} +(31.5545 + 37.6052i) q^{59} +(-58.4163 + 293.394i) q^{60} +(-590.177 - 104.064i) q^{61} +(-142.235 + 240.216i) q^{62} +(525.871 - 191.401i) q^{63} +(510.885 + 33.7709i) q^{64} +(-921.923 - 1596.82i) q^{65} +(20.5426 + 124.497i) q^{66} +(-89.8104 + 107.032i) q^{67} +(98.6652 - 79.1571i) q^{68} +(158.668 + 91.6070i) q^{69} +(-475.088 + 1261.92i) q^{70} +(54.0751 + 306.675i) q^{71} +(-396.100 - 355.287i) q^{72} +(626.259 + 227.940i) q^{73} +(4.93551 - 448.618i) q^{74} +515.753i q^{75} +(-210.614 + 628.186i) q^{76} +568.738i q^{77} +(-485.944 - 5.34615i) q^{78} +(-646.316 - 235.240i) q^{79} +(1271.16 - 166.871i) q^{80} +(79.6861 + 451.922i) q^{81} +(-652.221 - 245.548i) q^{82} +(165.283 + 95.4265i) q^{83} +(222.395 + 277.203i) q^{84} +(203.600 - 242.640i) q^{85} +(915.805 - 151.113i) q^{86} +(77.7513 + 134.669i) q^{87} +(476.982 - 254.781i) q^{88} +(-590.353 + 214.871i) q^{89} +(-1146.48 - 678.844i) q^{90} +(-2157.18 - 380.369i) q^{91} +(153.326 - 770.075i) q^{92} +(118.430 + 141.139i) q^{93} +(-612.960 - 525.933i) q^{94} +(-210.067 + 1645.70i) q^{95} +(132.854 - 310.695i) q^{96} +(788.075 - 661.273i) q^{97} +(309.819 + 550.521i) q^{98} +(-553.448 - 97.5879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q - 6 q^{2} + 12 q^{4} - 24 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 75 q^{10} - 3 q^{12} - 81 q^{14} - 12 q^{15} + 192 q^{16} - 12 q^{17} - 12 q^{18} + 558 q^{20} - 30 q^{22} - 12 q^{23} - 108 q^{24}+ \cdots + 8055 q^{98}+O(q^{100}) \) 348 * q - 6 * q^2 + 12 * q^4 - 24 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 75 * q^10 - 3 * q^12 - 81 * q^14 - 12 * q^15 + 192 * q^16 - 12 * q^17 - 12 * q^18 + 558 * q^20 - 30 * q^22 - 12 * q^23 - 108 * q^24 - 12 * q^25 - 411 * q^26 + 1140 * q^28 - 282 * q^30 - 1122 * q^31 + 39 * q^32 - 174 * q^33 + 1536 * q^34 - 2835 * q^36 + 966 * q^38 - 24 * q^39 - 1068 * q^40 + 48 * q^41 + 3015 * q^42 - 1203 * q^44 - 528 * q^46 - 624 * q^47 + 4755 * q^48 - 6768 * q^49 - 1074 * q^50 - 1089 * q^52 + 615 * q^54 - 762 * q^55 + 2046 * q^56 - 12 * q^57 + 4092 * q^58 + 4050 * q^60 + 3120 * q^62 + 2046 * q^63 + 2355 * q^64 - 6 * q^65 + 1716 * q^66 - 1176 * q^68 - 2973 * q^70 - 12 * q^71 - 7122 * q^72 + 636 * q^73 - 9363 * q^74 - 2454 * q^76 - 6897 * q^78 - 12 * q^79 - 6885 * q^80 + 1206 * q^81 - 7311 * q^82 + 1947 * q^84 + 7452 * q^86 - 6 * q^87 - 1131 * q^88 - 12 * q^89 + 4014 * q^90 + 7656 * q^92 + 11898 * q^94 + 1848 * q^95 - 18966 * q^96 - 12 * q^97 + 8055 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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