LMFDB - Embedded newform 45.4.e.b.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(16,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("45.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.15759792.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 16x^{4} - 27x^{3} + 52x^{2} - 39x + 9 $ x^6 - 3x^5 + 16x^4 - 27x^3 + 52x^2 - 39*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			31.1
Root			$0.500000 + 0.0378788i$ of defining polynomial
Character	$\chi$	$=$	45.31
Dual form			45.4.e.b.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87428 - 3.24635i) q^{2} +(-4.05724 + 3.24635i) q^{3} +(-3.02587 + 5.24096i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(18.1432 + 7.08665i) q^{6} +(15.6746 + 27.1492i) q^{7} -7.30318 q^{8} +(5.92239 - 26.3425i) q^{9} +O(q^{10})$	\(q+(-1.87428 - 3.24635i) q^{2} +(-4.05724 + 3.24635i) q^{3} +(-3.02587 + 5.24096i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(18.1432 + 7.08665i) q^{6} +(15.6746 + 27.1492i) q^{7} -7.30318 q^{8} +(5.92239 - 26.3425i) q^{9} +18.7428 q^{10} +(10.4166 + 18.0422i) q^{11} +(-4.73733 - 31.0869i) q^{12} +(-29.9655 + 51.9018i) q^{13} +(58.7572 - 101.770i) q^{14} +(-3.91402 - 25.6842i) q^{15} +(37.8952 + 65.6364i) q^{16} -74.0460 q^{17} +(-96.6172 + 30.1471i) q^{18} -63.8390 q^{19} +(-15.1294 - 26.2048i) q^{20} +(-151.731 - 59.2655i) q^{21} +(39.0475 - 67.6322i) q^{22} +(16.4247 - 28.4484i) q^{23} +(29.6307 - 23.7087i) q^{24} +(-12.5000 - 21.6506i) q^{25} +224.655 q^{26} +(61.4884 + 126.104i) q^{27} -189.717 q^{28} +(80.0044 + 138.572i) q^{29} +(-76.0441 + 60.8458i) q^{30} +(127.187 - 220.294i) q^{31} +(112.840 - 195.444i) q^{32} +(-100.834 - 39.3853i) q^{33} +(138.783 + 240.379i) q^{34} -156.746 q^{35} +(120.139 + 110.748i) q^{36} +215.365 q^{37} +(119.652 + 207.244i) q^{38} +(-46.9143 - 307.857i) q^{39} +(18.2579 - 31.6237i) q^{40} +(-70.8407 + 122.700i) q^{41} +(91.9908 + 603.654i) q^{42} +(-68.9529 - 119.430i) q^{43} -126.078 q^{44} +(99.2602 + 91.5008i) q^{45} -123.138 q^{46} +(-16.7895 - 29.0803i) q^{47} +(-366.829 - 143.281i) q^{48} +(-319.885 + 554.058i) q^{49} +(-46.8571 + 81.1588i) q^{50} +(300.422 - 240.379i) q^{51} +(-181.344 - 314.096i) q^{52} -41.9914 q^{53} +(294.131 - 435.967i) q^{54} -104.166 q^{55} +(-114.474 - 198.275i) q^{56} +(259.010 - 207.244i) q^{57} +(299.902 - 519.445i) q^{58} +(-307.571 + 532.728i) q^{59} +(146.453 + 57.2040i) q^{60} +(67.1535 + 116.313i) q^{61} -953.535 q^{62} +(808.007 - 252.119i) q^{63} -239.652 q^{64} +(-149.828 - 259.509i) q^{65} +(61.1331 + 401.162i) q^{66} +(428.767 - 742.646i) q^{67} +(224.054 - 388.072i) q^{68} +(25.7146 + 168.742i) q^{69} +(293.786 + 508.852i) q^{70} +588.665 q^{71} +(-43.2522 + 192.384i) q^{72} -618.191 q^{73} +(-403.655 - 699.152i) q^{74} +(121.001 + 47.2624i) q^{75} +(193.169 - 334.578i) q^{76} +(-326.553 + 565.607i) q^{77} +(-911.481 + 729.311i) q^{78} +(172.644 + 299.029i) q^{79} -378.952 q^{80} +(-658.851 - 312.021i) q^{81} +531.102 q^{82} +(546.584 + 946.711i) q^{83} +(769.728 - 615.889i) q^{84} +(185.115 - 320.629i) q^{85} +(-258.474 + 447.691i) q^{86} +(-774.450 - 302.496i) q^{87} +(-76.0746 - 131.765i) q^{88} +414.849 q^{89} +(111.002 - 493.732i) q^{90} -1878.79 q^{91} +(99.3979 + 172.162i) q^{92} +(199.125 + 1306.68i) q^{93} +(-62.9366 + 109.009i) q^{94} +(159.598 - 276.431i) q^{95} +(176.663 + 1159.28i) q^{96} +(100.705 + 174.427i) q^{97} +2398.22 q^{98} +(536.967 - 167.547i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + 9 q^{3} - 11 q^{4} - 15 q^{5} + 84 q^{6} + 43 q^{7} - 54 q^{8} + 57 q^{9}+O(q^{10}) $ 6 * q + q^2 + 9 * q^3 - 11 * q^4 - 15 * q^5 + 84 * q^6 + 43 * q^7 - 54 * q^8 + 57 * q^9	\( 6 q + q^{2} + 9 q^{3} - 11 q^{4} - 15 q^{5} + 84 q^{6} + 43 q^{7} - 54 q^{8} + 57 q^{9} - 10 q^{10} - 14 q^{11} + 75 q^{12} - 40 q^{13} + 27 q^{14} - 15 q^{15} + 13 q^{16} - 332 q^{17} + 3 q^{18} - 328 q^{19} - 55 q^{20} - 144 q^{21} + 376 q^{22} - 171 q^{23} - 63 q^{24} - 75 q^{25} + 868 q^{26} + 162 q^{27} - 1034 q^{28} + 335 q^{29} - 315 q^{30} + 352 q^{31} + 77 q^{32} - 708 q^{33} + 52 q^{34} - 430 q^{35} + 1086 q^{36} + 804 q^{37} + 178 q^{38} - 390 q^{39} + 135 q^{40} - 187 q^{41} + 513 q^{42} + 602 q^{43} + 1964 q^{44} + 330 q^{45} - 402 q^{46} - 665 q^{47} - 1074 q^{48} - 430 q^{49} + 25 q^{50} - 180 q^{51} + 456 q^{52} - 1460 q^{53} + 639 q^{54} + 140 q^{55} - 705 q^{56} - 486 q^{57} - 217 q^{58} + 298 q^{59} - 150 q^{60} + 1439 q^{61} - 3228 q^{62} + 2205 q^{63} - 3138 q^{64} - 200 q^{65} - 966 q^{66} + 1849 q^{67} + 710 q^{68} - 873 q^{69} + 135 q^{70} + 140 q^{71} + 261 q^{72} - 736 q^{73} + 320 q^{74} - 150 q^{75} - 204 q^{76} + 948 q^{77} - 432 q^{78} + 382 q^{79} - 130 q^{80} - 1251 q^{81} - 1150 q^{82} + 831 q^{83} - 909 q^{84} + 830 q^{85} - 1580 q^{86} + 258 q^{87} + 1428 q^{88} + 3438 q^{89} + 375 q^{90} - 1420 q^{91} + 1623 q^{92} + 2178 q^{93} + 2077 q^{94} + 820 q^{95} + 1155 q^{96} + 282 q^{97} + 4328 q^{98} - 762 q^{99}+O(q^{100}) \) 6 * q + q^2 + 9 * q^3 - 11 * q^4 - 15 * q^5 + 84 * q^6 + 43 * q^7 - 54 * q^8 + 57 * q^9 - 10 * q^10 - 14 * q^11 + 75 * q^12 - 40 * q^13 + 27 * q^14 - 15 * q^15 + 13 * q^16 - 332 * q^17 + 3 * q^18 - 328 * q^19 - 55 * q^20 - 144 * q^21 + 376 * q^22 - 171 * q^23 - 63 * q^24 - 75 * q^25 + 868 * q^26 + 162 * q^27 - 1034 * q^28 + 335 * q^29 - 315 * q^30 + 352 * q^31 + 77 * q^32 - 708 * q^33 + 52 * q^34 - 430 * q^35 + 1086 * q^36 + 804 * q^37 + 178 * q^38 - 390 * q^39 + 135 * q^40 - 187 * q^41 + 513 * q^42 + 602 * q^43 + 1964 * q^44 + 330 * q^45 - 402 * q^46 - 665 * q^47 - 1074 * q^48 - 430 * q^49 + 25 * q^50 - 180 * q^51 + 456 * q^52 - 1460 * q^53 + 639 * q^54 + 140 * q^55 - 705 * q^56 - 486 * q^57 - 217 * q^58 + 298 * q^59 - 150 * q^60 + 1439 * q^61 - 3228 * q^62 + 2205 * q^63 - 3138 * q^64 - 200 * q^65 - 966 * q^66 + 1849 * q^67 + 710 * q^68 - 873 * q^69 + 135 * q^70 + 140 * q^71 + 261 * q^72 - 736 * q^73 + 320 * q^74 - 150 * q^75 - 204 * q^76 + 948 * q^77 - 432 * q^78 + 382 * q^79 - 130 * q^80 - 1251 * q^81 - 1150 * q^82 + 831 * q^83 - 909 * q^84 + 830 * q^85 - 1580 * q^86 + 258 * q^87 + 1428 * q^88 + 3438 * q^89 + 375 * q^90 - 1420 * q^91 + 1623 * q^92 + 2178 * q^93 + 2077 * q^94 + 820 * q^95 + 1155 * q^96 + 282 * q^97 + 4328 * q^98 - 762 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.87428	−	3.24635i	−0.662659	−	1.14776i	−0.979914	−	0.199419i	$-0.936095\pi$
$2$	−1.87428	−	3.24635i	−0.662659	−	1.14776i	0.317255	−	0.948340i	$-0.397239\pi$
$3$	−4.05724	+	3.24635i	−0.780816	+	0.624761i
$3$	−4.05724	+	3.24635i	−0.780816	+	0.624761i
$4$	−3.02587	+	5.24096i	−0.378234	+	0.655120i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$	18.1432	+	7.08665i	1.23449	+	0.482185i
$7$	15.6746	+	27.1492i	0.846348	+	1.46592i	0.884445	+	0.466644i	$0.154537\pi$
$7$	15.6746	+	27.1492i	0.846348	+	1.46592i	−0.0380969	+	0.999274i	$0.512130\pi$
$8$	−7.30318			−0.322758
$9$	5.92239	−	26.3425i	0.219348	−	0.975647i
$10$	18.7428			0.592700
$11$	10.4166	+	18.0422i	0.285522	+	0.494538i	0.972736	−	0.231917i	$-0.0744998\pi$
$11$	10.4166	+	18.0422i	0.285522	+	0.494538i	−0.687214	+	0.726455i	$0.741166\pi$
$12$	−4.73733	−	31.0869i	−0.113962	−	0.747834i
$13$	−29.9655	+	51.9018i	−0.639303	+	1.10731i	0.346283	+	0.938130i	$0.387444\pi$
$13$	−29.9655	+	51.9018i	−0.639303	+	1.10731i	−0.985586	+	0.169175i	$0.945890\pi$
$14$	58.7572	−	101.770i	1.12168	−	1.94281i
$15$	−3.91402	−	25.6842i	−0.0673730	−	0.442110i
$16$	37.8952	+	65.6364i	0.592112	+	1.02557i
$17$	−74.0460			−1.05640			−0.528200	−	0.849120i	$-0.677133\pi$
$17$	−74.0460			−1.05640			−0.528200	+	0.849120i	$0.677133\pi$
$18$	−96.6172	+	30.1471i	−1.26516	+	0.394763i
$19$	−63.8390			−0.770825			−0.385413	−	0.922744i	$-0.625941\pi$
$19$	−63.8390			−0.770825			−0.385413	+	0.922744i	$0.625941\pi$
$20$	−15.1294	−	26.2048i	−0.169151	−	0.292979i
$21$	−151.731	−	59.2655i	−1.57669	−	0.615847i
$22$	39.0475	−	67.6322i	0.378407	−	0.655420i
$23$	16.4247	−	28.4484i	0.148904	−	0.257909i	−0.781919	−	0.623380i	$-0.785759\pi$
$23$	16.4247	−	28.4484i	0.148904	−	0.257909i	0.930823	+	0.365472i	$0.119092\pi$
$24$	29.6307	−	23.7087i	0.252015	−	0.201646i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	224.655			1.69456
$27$	61.4884	+	126.104i	0.438276	+	0.898841i
$28$	−189.717			−1.28047
$29$	80.0044	+	138.572i	0.512291	+	0.887314i	0.999898	+	0.0142513i	$0.00453647\pi$
$29$	80.0044	+	138.572i	0.512291	+	0.887314i	−0.487607	+	0.873063i	$0.662130\pi$
$30$	−76.0441	+	60.8458i	−0.462790	+	0.370296i
$31$	127.187	−	220.294i	0.736884	−	1.27632i	−0.217007	−	0.976170i	$-0.569630\pi$
$31$	127.187	−	220.294i	0.736884	−	1.27632i	0.953892	−	0.300151i	$-0.0970371\pi$
$32$	112.840	−	195.444i	0.623358	−	1.07969i
$33$	−100.834	−	39.3853i	−0.531908	−	0.207760i
$34$	138.783	+	240.379i	0.700033	+	1.21249i
$35$	−156.746			−0.756997
$36$	120.139	+	110.748i	0.556201	+	0.512722i
$37$	215.365			0.956914			0.478457	−	0.878111i	$-0.341196\pi$
$37$	215.365			0.956914			0.478457	+	0.878111i	$0.341196\pi$
$38$	119.652	+	207.244i	0.510794	+	0.884722i
$39$	−46.9143	−	307.857i	−0.192623	−	1.26401i
$40$	18.2579	−	31.6237i	0.0721708	−	0.125004i
$41$	−70.8407	+	122.700i	−0.269841	+	0.467377i	−0.968820	−	0.247764i	$-0.920304\pi$
$41$	−70.8407	+	122.700i	−0.269841	+	0.467377i	0.698980	+	0.715141i	$0.253638\pi$
$42$	91.9908	+	603.654i	0.337964	+	2.21776i
$43$	−68.9529	−	119.430i	−0.244540	−	0.423556i	0.717462	−	0.696597i	$-0.245304\pi$
$43$	−68.9529	−	119.430i	−0.244540	−	0.423556i	−0.962002	+	0.273042i	$0.911970\pi$
$44$	−126.078			−0.431976
$45$	99.2602	+	91.5008i	0.328819	+	0.303114i
$46$	−123.138			−0.394689
$47$	−16.7895	−	29.0803i	−0.0521064	−	0.0902509i	0.838796	−	0.544446i	$-0.183260\pi$
$47$	−16.7895	−	29.0803i	−0.0521064	−	0.0902509i	−0.890902	+	0.454195i	$0.849927\pi$
$48$	−366.829	−	143.281i	−1.10307	−	0.430852i
$49$	−319.885	+	554.058i	−0.932611	+	1.61533i
$50$	−46.8571	+	81.1588i	−0.132532	+	0.229552i
$51$	300.422	−	240.379i	0.824854	−	0.659997i
$52$	−181.344	−	314.096i	−0.483612	−	0.837641i
$53$	−41.9914			−0.108829			−0.0544147	−	0.998518i	$-0.517329\pi$
$53$	−41.9914			−0.108829			−0.0544147	+	0.998518i	$0.517329\pi$
$54$	294.131	−	435.967i	0.741225	−	1.09866i
$55$	−104.166			−0.255378
$56$	−114.474	−	198.275i	−0.273166	−	0.473137i
$57$	259.010	−	207.244i	0.601873	−	0.481581i
$58$	299.902	−	519.445i	0.678949	−	1.17597i
$59$	−307.571	+	532.728i	−0.678683	+	1.17551i	0.296694	+	0.954973i	$0.404116\pi$
$59$	−307.571	+	532.728i	−0.678683	+	1.17551i	−0.975378	+	0.220541i	$0.929218\pi$
$60$	146.453	+	57.2040i	0.315118	+	0.123083i
$61$	67.1535	+	116.313i	0.140953	+	0.244137i	0.927856	−	0.372939i	$-0.121650\pi$
$61$	67.1535	+	116.313i	0.140953	+	0.244137i	−0.786903	+	0.617077i	$0.788317\pi$
$62$	−953.535			−1.95321
$63$	808.007	−	252.119i	1.61586	−	0.504191i
$64$	−239.652			−0.468071
$65$	−149.828	−	259.509i	−0.285905	−	0.495202i
$66$	61.1331	+	401.162i	0.114015	+	0.748176i
$67$	428.767	−	742.646i	0.781824	−	1.35416i	−0.149055	−	0.988829i	$-0.547623\pi$
$67$	428.767	−	742.646i	0.781824	−	1.35416i	0.930878	−	0.365329i	$-0.119044\pi$
$68$	224.054	−	388.072i	0.399566	−	0.692069i
$69$	25.7146	+	168.742i	0.0448649	+	0.294408i
$70$	293.786	+	508.852i	0.501631	+	0.868850i
$71$	588.665			0.983968			0.491984	−	0.870604i	$-0.336272\pi$
$71$	588.665			0.983968			0.491984	+	0.870604i	$0.336272\pi$
$72$	−43.2522	+	192.384i	−0.0707962	+	0.314898i
$73$	−618.191			−0.991148			−0.495574	−	0.868566i	$-0.665042\pi$
$73$	−618.191			−0.991148			−0.495574	+	0.868566i	$0.665042\pi$
$74$	−403.655	−	699.152i	−0.634108	−	1.09831i
$75$	121.001	+	47.2624i	0.186293	+	0.0727652i
$76$	193.169	−	334.578i	0.291552	−	0.504983i
$77$	−326.553	+	565.607i	−0.483301	+	0.837103i
$78$	−911.481	+	729.311i	−1.32314	+	1.05869i
$79$	172.644	+	299.029i	0.245873	+	0.425865i	0.962377	−	0.271718i	$-0.0875919\pi$
$79$	172.644	+	299.029i	0.245873	+	0.425865i	−0.716503	+	0.697584i	$0.754259\pi$
$80$	−378.952			−0.529601
$81$	−658.851	−	312.021i	−0.903773	−	0.428012i
$82$	531.102			0.715249
$83$	546.584	+	946.711i	0.722836	+	1.25199i	0.959859	+	0.280484i	$0.0904950\pi$
$83$	546.584	+	946.711i	0.722836	+	1.25199i	−0.237023	+	0.971504i	$0.576172\pi$
$84$	769.728	−	615.889i	0.999812	−	0.799988i
$85$	185.115	−	320.629i	0.236218	−	0.409142i
$86$	−258.474	+	447.691i	−0.324093	+	0.561346i
$87$	−774.450	−	302.496i	−0.954365	−	0.372770i
$88$	−76.0746	−	131.765i	−0.0921543	−	0.159616i
$89$	414.849			0.494089			0.247045	−	0.969004i	$-0.420541\pi$
$89$	414.849			0.494089			0.247045	+	0.969004i	$0.420541\pi$
$90$	111.002	−	493.732i	0.130007	−	0.578266i
$91$	−1878.79			−2.16429
$92$	99.3979	+	172.162i	0.112641	+	0.195100i
$93$	199.125	+	1306.68i	0.222024	+	1.45695i
$94$	−62.9366	+	109.009i	−0.0690576	+	0.119611i
$95$	159.598	−	276.431i	0.172362	−	0.298539i
$96$	176.663	+	1159.28i	0.187819	+	1.23249i
$97$	100.705	+	174.427i	0.105413	+	0.182581i	0.913907	−	0.405924i	$-0.133050\pi$
$97$	100.705	+	174.427i	0.105413	+	0.182581i	−0.808494	+	0.588505i	$0.799717\pi$
$98$	2398.22			2.47201
$99$	536.967	−	167.547i	0.545123	−	0.170092i
$100$	151.294			0.151294
$101$	−132.691	−	229.828i	−0.130726	−	0.226424i	0.793231	−	0.608921i	$-0.208397\pi$
$101$	−132.691	−	229.828i	−0.130726	−	0.226424i	−0.923957	+	0.382498i	$0.875064\pi$
$102$	−1343.43	−	524.738i	−1.30411	−	0.509380i
$103$	263.809	−	456.931i	0.252368	−	0.437114i	−0.711810	−	0.702373i	$-0.752124\pi$
$103$	263.809	−	456.931i	0.252368	−	0.437114i	0.964177	+	0.265259i	$0.0854574\pi$
$104$	218.843	−	379.048i	0.206340	−	0.357391i
$105$	635.956	−	508.852i	0.591075	−	0.472942i
$106$	78.7038	+	136.319i	0.0721168	+	0.124910i
$107$	2084.24			1.88310			0.941549	−	0.336877i	$-0.109371\pi$
$107$	2084.24			1.88310			0.941549	+	0.336877i	$0.109371\pi$
$108$	−846.961	−	59.3157i	−0.754619	−	0.0528487i
$109$	925.651			0.813406			0.406703	−	0.913560i	$-0.366678\pi$
$109$	925.651			0.813406			0.406703	+	0.913560i	$0.366678\pi$
$110$	195.237	+	338.161i	0.169229	+	0.293113i
$111$	−873.788	+	699.152i	−0.747174	+	0.597843i
$112$	−1187.98	+	2057.65i	−1.00227	+	1.73598i
$113$	−273.009	+	472.866i	−0.227279	+	0.393659i	−0.957001	−	0.290085i	$-0.906316\pi$
$113$	−273.009	+	472.866i	−0.227279	+	0.393659i	0.729721	+	0.683745i	$0.239650\pi$
$114$	−1158.25	−	452.405i	−0.951576	−	0.371681i
$115$	82.1234	+	142.242i	0.0665917	+	0.115340i
$116$	−968.332			−0.775063
$117$	1189.75	+	1096.75i	0.940109	+	0.866619i
$118$	2305.90			1.79894
$119$	−1160.64	−	2010.29i	−0.894082	−	1.54860i
$120$	28.5848	+	187.577i	0.0217452	+	0.142694i
$121$	448.487	−	776.802i	0.336955	−	0.583623i
$122$	251.729	−	436.008i	0.186807	−	0.323560i
$123$	−110.909	−	727.796i	−0.0813033	−	0.533522i
$124$	769.701	+	1333.16i	0.557429	+	0.965495i
$125$	125.000			0.0894427
$126$	−2332.90	−	2150.53i	−1.64946	−	1.52051i
$127$	−975.972			−0.681918			−0.340959	−	0.940078i	$-0.610752\pi$
$127$	−975.972			−0.681918			−0.340959	+	0.940078i	$0.610752\pi$
$128$	−453.543	−	785.559i	−0.313187	−	0.542455i
$129$	667.470	+	260.710i	0.455562	+	0.177940i
$130$	−561.639	+	972.786i	−0.378915	+	0.656300i
$131$	814.614	−	1410.95i	0.543307	−	0.941035i	−0.455405	−	0.890285i	$-0.650505\pi$
$131$	814.614	−	1410.95i	0.543307	−	0.941035i	0.998711	−	0.0507502i	$-0.0161612\pi$
$132$	511.528	−	409.293i	0.337294	−	0.269882i
$133$	−1000.65	−	1733.18i	−0.652387	−	1.12997i
$134$	−3214.52			−2.07233
$135$	−699.767	−	49.0071i	−0.446121	−	0.0312434i
$136$	540.771			0.340961
$137$	−330.725	−	572.833i	−0.206246	−	0.357229i	0.744283	−	0.667865i	$-0.232792\pi$
$137$	−330.725	−	572.833i	−0.206246	−	0.357229i	−0.950529	+	0.310635i	$0.899458\pi$
$138$	499.600	−	399.749i	0.308180	−	0.246586i
$139$	−691.495	+	1197.70i	−0.421955	+	0.730848i	−0.996131	−	0.0878842i	$-0.971989\pi$
$139$	−691.495	+	1197.70i	−0.421955	+	0.730848i	0.574175	+	0.818732i	$0.305323\pi$
$140$	474.293	−	821.499i	0.286322	−	0.495924i
$141$	162.524	+	63.4810i	0.0970708	+	0.0379153i
$142$	−1103.33	−	1911.02i	−0.652035	−	1.12936i
$143$	−1248.56			−0.730139
$144$	1953.45	−	609.528i	1.13047	−	0.352736i
$145$	−800.044			−0.458207
$146$	1158.66	+	2006.87i	0.656793	+	1.13760i
$147$	−500.815	−	3286.41i	−0.280997	−	1.84393i
$148$	−651.667	+	1128.72i	−0.361937	+	0.626894i
$149$	−1581.75	+	2739.66i	−0.869676	+	1.50632i	−0.00734719	+	0.999973i	$0.502339\pi$
$149$	−1581.75	+	2739.66i	−0.869676	+	1.50632i	−0.862328	+	0.506349i	$0.830995\pi$
$150$	−73.3598	−	481.395i	−0.0399320	−	0.262038i
$151$	1279.40	+	2215.98i	0.689509	+	1.19427i	0.971997	+	0.234994i	$0.0755071\pi$
$151$	1279.40	+	2215.98i	0.689509	+	1.19427i	−0.282488	+	0.959271i	$0.591160\pi$
$152$	466.228			0.248790
$153$	−438.529	+	1950.55i	−0.231719	+	1.03067i
$154$	2448.21			1.28106
$155$	635.934	+	1101.47i	0.329545	+	0.570788i
$156$	1755.42	+	685.659i	0.900937	+	0.351901i
$157$	−1750.48	+	3031.92i	−0.889832	+	1.54123i	−0.0497594	+	0.998761i	$0.515845\pi$
$157$	−1750.48	+	3031.92i	−0.889832	+	1.54123i	−0.840073	+	0.542474i	$0.817488\pi$
$158$	647.168	−	1120.93i	0.325860	−	0.564407i
$159$	170.369	−	136.319i	0.0849758	−	0.0679924i
$160$	564.199	+	977.222i	0.278774	+	0.482851i
$161$	1029.80			0.504097
$162$	221.943	+	2723.68i	0.107639	+	1.32094i
$163$	263.950			0.126835			0.0634176	−	0.997987i	$-0.479800\pi$
$163$	263.950			0.126835			0.0634176	+	0.997987i	$0.479800\pi$
$164$	−428.710	−	742.547i	−0.204126	−	0.353556i
$165$	422.628	−	338.161i	0.199404	−	0.159550i
$166$	2048.90	−	3548.81i	0.957987	−	1.65928i
$167$	1794.53	−	3108.21i	0.831524	−	1.44024i	−0.0653054	−	0.997865i	$-0.520802\pi$
$167$	1794.53	−	3108.21i	0.831524	−	1.44024i	0.896829	−	0.442377i	$-0.145865\pi$
$168$	1108.12	+	432.826i	0.508889	+	0.198770i
$169$	−697.365	−	1207.87i	−0.317417	−	0.549782i
$170$	−1387.83			−0.626128
$171$	−378.080	+	1681.68i	−0.169079	+	0.752053i
$172$	834.570			0.369973
$173$	−185.228	−	320.824i	−0.0814024	−	0.140993i	0.822450	−	0.568837i	$-0.192607\pi$
$173$	−185.228	−	320.824i	−0.0814024	−	0.140993i	−0.903853	+	0.427844i	$0.859273\pi$
$174$	469.529	+	3081.10i	0.204568	+	1.34240i
$175$	391.865	−	678.730i	0.169270	−	0.293184i
$176$	−789.482	+	1367.42i	−0.338122	+	0.585644i
$177$	−481.535	−	3159.89i	−0.204488	−	1.34188i
$178$	−777.545	−	1346.75i	−0.327413	−	0.567095i
$179$	446.898			0.186607			0.0933036	−	0.995638i	$-0.470257\pi$
$179$	446.898			0.186607			0.0933036	+	0.995638i	$0.470257\pi$
$180$	−779.901	+	243.349i	−0.322947	+	0.100768i
$181$	−904.046			−0.371255			−0.185628	−	0.982620i	$-0.559432\pi$
$181$	−904.046			−0.371255			−0.185628	+	0.982620i	$0.559432\pi$
$182$	3521.38	+	6099.21i	1.43419	+	2.48409i
$183$	−650.051	−	253.907i	−0.262586	−	0.102565i
$184$	−119.952	+	207.764i	−0.0480598	+	0.0832420i
$185$	−538.413	+	932.559i	−0.213973	+	0.370611i
$186$	3868.72	−	3095.51i	1.52510	−	1.22029i
$187$	−771.311	−	1335.95i	−0.301625	−	0.522430i
$188$	203.211			0.0788336
$189$	−2459.81	+	3645.99i	−0.946693	+	1.40321i
$190$	−1196.52			−0.456868
$191$	299.793	+	519.257i	0.113572	+	0.196713i	0.917208	−	0.398409i	$-0.130437\pi$
$191$	299.793	+	519.257i	0.113572	+	0.196713i	−0.803636	+	0.595121i	$0.797104\pi$
$192$	972.326	−	777.995i	0.365477	−	0.292432i
$193$	2206.87	−	3822.40i	0.823076	−	1.42561i	−0.0803048	−	0.996770i	$-0.525589\pi$
$193$	2206.87	−	3822.40i	0.823076	−	1.42561i	0.903381	−	0.428839i	$-0.141077\pi$
$194$	377.500	−	653.850i	0.139706	−	0.241978i
$195$	1450.34	+	566.497i	0.532622	+	0.208039i
$196$	−1935.86	−	3353.01i	−0.705490	−	1.22194i
$197$	−4807.15			−1.73855			−0.869277	−	0.494325i	$-0.835415\pi$
$197$	−4807.15			−1.73855			−0.869277	+	0.494325i	$0.835415\pi$
$198$	−1550.35	−	1429.15i	−0.556456	−	0.512956i
$199$	313.833			0.111794			0.0558970	−	0.998437i	$-0.482198\pi$
$199$	313.833			0.111794			0.0558970	+	0.998437i	$0.482198\pi$
$200$	91.2897	+	158.118i	0.0322758	+	0.0559033i
$201$	671.281	+	4405.02i	0.235565	+	1.54580i
$202$	−497.403	+	861.527i	−0.173253	+	0.300083i
$203$	−2508.07	+	4344.11i	−0.867153	+	1.50195i
$204$	350.780	+	2301.86i	0.120390	+	0.790012i
$205$	−354.204	−	613.499i	−0.120676	−	0.209018i
$206$	−1977.81			−0.668935
$207$	−652.127	−	601.149i	−0.218966	−	0.201849i
$208$	−4542.20			−1.51416
$209$	−664.989	−	1151.79i	−0.220087	−	0.381202i
$210$	−2843.88	−	1110.80i	−0.934505	−	0.365013i
$211$	−1219.41	+	2112.08i	−0.397856	+	0.689106i	−0.993461	−	0.114171i	$-0.963579\pi$
$211$	−1219.41	+	2112.08i	−0.397856	+	0.689106i	0.595605	+	0.803277i	$0.296912\pi$
$212$	127.061	−	220.075i	0.0411630	−	0.0712964i
$213$	−2388.36	+	1911.02i	−0.768298	+	0.614745i
$214$	−3906.46	−	6766.19i	−1.24785	−	2.16134i
$215$	689.529			0.218723
$216$	−449.060	−	920.959i	−0.141457	−	0.290108i
$217$	7974.40			2.49464
$218$	−1734.93	−	3004.99i	−0.539011	−	0.933594i
$219$	2508.15	−	2006.87i	0.773904	−	0.619230i
$220$	315.194	−	545.933i	0.0965927	−	0.167303i
$221$	2218.83	−	3843.12i	0.675360	−	1.16976i
$222$	3907.42	+	1526.22i	1.18130	+	0.461410i
$223$	1166.71	+	2020.79i	0.350352	+	0.606827i	0.986311	−	0.164896i	$-0.0527288\pi$
$223$	1166.71	+	2020.79i	0.350352	+	0.606827i	−0.635959	+	0.771722i	$0.719395\pi$
$224$	7074.87			2.11031
$225$	−644.361	+	201.057i	−0.190922	+	0.0595725i
$226$	2046.79			0.602435
$227$	1361.85	+	2358.79i	0.398189	+	0.689684i	0.993503	−	0.113810i	$-0.0363054\pi$
$227$	1361.85	+	2358.79i	0.398189	+	0.689684i	−0.595313	+	0.803494i	$0.702972\pi$
$228$	302.426	+	1984.56i	0.0878451	+	0.576449i
$229$	1657.08	−	2870.15i	0.478179	−	0.828230i	−0.521508	−	0.853246i	$-0.674630\pi$
$229$	1657.08	−	2870.15i	0.478179	−	0.828230i	0.999687	+	0.0250162i	$0.00796375\pi$
$230$	307.845	−	533.203i	0.0882552	−	0.152863i
$231$	−511.255	−	3354.91i	−0.145619	−	0.955571i
$232$	−584.286	−	1012.01i	−0.165346	−	0.286388i
$233$	−3175.44			−0.892833			−0.446416	−	0.894825i	$-0.647300\pi$
$233$	−3175.44			−0.892833			−0.446416	+	0.894825i	$0.647300\pi$
$234$	1330.50	−	5917.98i	0.371698	−	1.65329i
$235$	167.895			0.0466054
$236$	−1861.34	−	3223.93i	−0.513402	−	0.889238i
$237$	−1671.21	−	652.767i	−0.458046	−	0.178910i
$238$	−4350.74	+	7535.70i	−1.18494	+	2.05238i
$239$	123.062	−	213.150i	0.0333064	−	0.0576884i	−0.848892	−	0.528567i	$-0.822730\pi$
$239$	123.062	−	213.150i	0.0333064	−	0.0576884i	0.882198	+	0.470878i	$0.156063\pi$
$240$	1537.50	−	1230.21i	0.413521	−	0.330874i
$241$	2643.87	+	4579.31i	0.706666	+	1.22398i	0.966087	+	0.258217i	$0.0831349\pi$
$241$	2643.87	+	4579.31i	0.706666	+	1.22398i	−0.259421	+	0.965764i	$0.583532\pi$
$242$	−3362.36			−0.893144
$243$	3686.04	−	872.919i	0.973086	−	0.230444i
$244$	−812.791			−0.213252
$245$	−1599.43	−	2770.29i	−0.417076	−	0.722397i
$246$	−2154.81	+	1724.14i	−0.558478	+	0.446860i
$247$	1912.97	−	3313.36i	0.492791	−	0.853539i
$248$	−928.867	+	1608.84i	−0.237835	+	0.411943i
$249$	−5290.98	−	2066.63i	−1.34659	−	0.525973i
$250$	−234.285	−	405.794i	−0.0592700	−	0.102659i
$251$	2821.23			0.709459			0.354730	−	0.934969i	$-0.384573\pi$
$251$	2821.23			0.709459			0.354730	+	0.934969i	$0.384573\pi$
$252$	−1123.58	+	4997.62i	−0.280868	+	1.24929i
$253$	684.361			0.170061
$254$	1829.25	+	3168.35i	0.451879	+	0.782677i
$255$	289.818	+	1901.82i	0.0711729	+	0.467044i
$256$	−2658.74	+	4605.08i	−0.649107	+	1.12429i
$257$	942.096	−	1631.76i	0.228663	−	0.396056i	−0.728749	−	0.684781i	$-0.759898\pi$
$257$	942.096	−	1631.76i	0.228663	−	0.396056i	0.957412	+	0.288725i	$0.0932313\pi$
$258$	−404.670	−	2655.49i	−0.0976497	−	0.640789i
$259$	3375.76	+	5846.99i	0.809883	+	1.40276i
$260$	1813.44			0.432556
$261$	4124.14	−	1286.84i	0.978075	−	0.305185i
$262$	−6107.27			−1.44011
$263$	−276.506	−	478.922i	−0.0648292	−	0.112287i	0.831789	−	0.555092i	$-0.187317\pi$
$263$	−276.506	−	478.922i	−0.0648292	−	0.112287i	−0.896618	+	0.442804i	$0.853984\pi$
$264$	736.409	+	287.638i	0.171677	+	0.0670563i
$265$	104.979	−	181.828i	0.0243350	−	0.0421495i
$266$	−3751.00	+	6496.93i	−0.864620	+	1.49757i
$267$	−1683.14	+	1346.75i	−0.385793	+	0.308688i
$268$	2594.78	+	4494.30i	0.591424	+	1.02438i
$269$	3363.48			0.762361			0.381180	−	0.924501i	$-0.375518\pi$
$269$	3363.48			0.762361			0.381180	+	0.924501i	$0.375518\pi$
$270$	1152.47	+	2363.54i	0.259766	+	0.532743i
$271$	−3333.85			−0.747295			−0.373648	−	0.927571i	$-0.621893\pi$
$271$	−3333.85			−0.747295			−0.373648	+	0.927571i	$0.621893\pi$
$272$	−2805.99	−	4860.11i	−0.625507	−	1.08341i
$273$	7622.70	−	6099.21i	1.68991	−	1.35217i
$274$	−1239.75	+	2147.30i	−0.273342	+	0.473443i
$275$	260.416	−	451.054i	0.0571043	−	0.0989076i
$276$	−962.181	−	375.823i	−0.209842	−	0.0819633i
$277$	2693.63	+	4665.50i	0.584275	+	1.01199i	0.994965	+	0.100220i	$0.0319546\pi$
$277$	2693.63	+	4665.50i	0.584275	+	1.01199i	−0.410690	+	0.911775i	$0.634712\pi$
$278$	5184.23			1.11845
$279$	−5049.83	−	4655.08i	−1.08360	−	0.998897i
$280$	1144.74			0.244327
$281$	−1858.35	−	3218.76i	−0.394519	−	0.683327i	0.598521	−	0.801107i	$-0.295755\pi$
$281$	−1858.35	−	3218.76i	−0.394519	−	0.683327i	−0.993040	+	0.117781i	$0.962422\pi$
$282$	−98.5340	−	646.591i	−0.0208071	−	0.136539i
$283$	−1384.38	+	2397.81i	−0.290787	+	0.503658i	−0.973996	−	0.226565i	$-0.927250\pi$
$283$	−1384.38	+	2397.81i	−0.290787	+	0.503658i	0.683209	+	0.730223i	$0.260584\pi$
$284$	−1781.23	+	3085.17i	−0.372170	+	0.644617i
$285$	249.867	+	1639.66i	0.0519328	+	0.340789i
$286$	2340.16	+	4053.27i	0.483833	+	0.838024i
$287$	−4441.60			−0.913516
$288$	−4480.20	−	4129.98i	−0.916662	−	0.845004i
$289$	569.810			0.115980
$290$	1499.51	+	2597.23i	0.303635	+	0.525911i
$291$	−974.836	−	380.766i	−0.196378	−	0.0767041i
$292$	1870.57	−	3239.91i	0.374886	−	0.649321i
$293$	1740.00	−	3013.76i	0.346934	−	0.600907i	−0.638769	−	0.769398i	$-0.720556\pi$
$293$	1740.00	−	3013.76i	0.346934	−	0.600907i	0.985703	+	0.168491i	$0.0538895\pi$
$294$	−9730.17	+	7785.48i	−1.93019	+	1.54442i
$295$	−1537.85	−	2663.64i	−0.303516	−	0.525706i
$296$	−1572.85			−0.308852
$297$	−1634.68	+	2422.96i	−0.319374	+	0.473382i
$298$	11858.6			2.30519
$299$	984.348	+	1704.94i	0.190389	+	0.329764i
$300$	−613.834	+	491.152i	−0.118132	+	0.0945223i
$301$	2161.62	−	3744.03i	0.413932	−	0.716951i
$302$	4795.91	−	8306.75i	0.913819	−	1.58278i
$303$	1284.47	+	501.705i	0.243533	+	0.0951229i
$304$	−2419.19	−	4190.16i	−0.456415	−	0.790534i
$305$	−671.535			−0.126072
$306$	7154.11	−	2232.27i	1.33651	−	0.417027i
$307$	−1810.36			−0.336555			−0.168278	−	0.985740i	$-0.553821\pi$
$307$	−1810.36			−0.336555			−0.168278	+	0.985740i	$0.553821\pi$
$308$	−1976.22	−	3422.91i	−0.365602	−	0.633241i
$309$	413.021	+	2710.29i	0.0760387	+	0.498975i
$310$	2383.84	−	4128.93i	0.436751	−	0.756476i
$311$	443.649	−	768.422i	0.0808907	−	0.140107i	−0.822742	−	0.568415i	$-0.807557\pi$
$311$	443.649	−	768.422i	0.0808907	−	0.140107i	0.903633	+	0.428308i	$0.140890\pi$
$312$	342.623	+	2248.33i	0.0621706	+	0.407970i
$313$	1107.57	+	1918.36i	0.200011	+	0.346429i	0.948532	−	0.316682i	$-0.102569\pi$
$313$	1107.57	+	1918.36i	0.200011	+	0.346429i	−0.748521	+	0.663111i	$0.769236\pi$
$314$	13123.6			2.35862
$315$	−928.310	+	4129.07i	−0.166046	+	0.738562i
$316$	−2089.60			−0.371990
$317$	329.023	+	569.884i	0.0582958	+	0.100971i	0.893700	−	0.448664i	$-0.148100\pi$
$317$	329.023	+	569.884i	0.0582958	+	0.100971i	−0.835405	+	0.549635i	$0.814767\pi$
$318$	−761.859	−	297.578i	−0.134349	−	0.0524760i
$319$	−1666.76	+	2886.91i	−0.292540	+	0.506695i
$320$	599.130	−	1037.72i	0.104664	−	0.181283i
$321$	−8456.28	+	6766.19i	−1.47035	+	1.17649i
$322$	−1930.14	−	3343.10i	−0.334045	−	0.578582i
$323$	4727.03			0.814299
$324$	3628.88	−	2508.88i	0.622237	−	0.430192i
$325$	1498.28			0.255721
$326$	−494.717	−	856.875i	−0.0840485	−	0.145576i
$327$	−3755.59	+	3004.99i	−0.635121	+	0.508184i
$328$	517.362	−	896.098i	0.0870931	−	0.150850i
$329$	526.337	−	911.643i	0.0882003	−	0.152767i
$330$	−1889.92	−	738.191i	−0.315262	−	0.123140i
$331$	−2638.22	−	4569.53i	−0.438096	−	0.758804i	0.559447	−	0.828866i	$-0.311014\pi$
$331$	−2638.22	−	4569.53i	−0.438096	−	0.758804i	−0.997543	+	0.0700619i	$0.977680\pi$
$332$	−6615.57			−1.09360
$333$	1275.48	−	5673.25i	0.209897	−	0.933610i
$334$	−13453.8			−2.20407
$335$	2143.83	+	3713.23i	0.349642	+	0.605598i
$336$	−1859.92	−	12205.0i	−0.301984	−	1.98165i
$337$	1680.64	−	2910.95i	0.271662	−	0.470532i	−0.697626	−	0.716462i	$-0.745760\pi$
$337$	1680.64	−	2910.95i	0.271662	−	0.470532i	0.969288	+	0.245930i	$0.0790934\pi$
$338$	−2614.12	+	4527.78i	−0.420678	+	0.728636i
$339$	−427.426	−	2804.82i	−0.0684796	−	0.449371i
$340$	1120.27	+	1940.36i	0.178691	+	0.309503i
$341$	5299.44			0.841586
$342$	6167.95	−	1924.56i	0.975217	−	0.304293i
$343$	−9303.52			−1.46456
$344$	503.575	+	872.218i	0.0789272	+	0.136706i
$345$	−794.962	−	310.508i	−0.124056	−	0.0484556i
$346$	−694.339	+	1202.63i	−0.107884	+	0.186861i
$347$	−4677.77	+	8102.13i	−0.723677	+	1.25344i	0.235840	+	0.971792i	$0.424216\pi$
$347$	−4677.77	+	8102.13i	−0.723677	+	1.25344i	−0.959516	+	0.281653i	$0.909117\pi$
$348$	3928.75	−	3143.55i	0.605182	−	0.484229i
$349$	−3519.65	−	6096.22i	−0.539836	−	0.935023i	−0.998912	−	0.0466263i	$-0.985153\pi$
$349$	−3519.65	−	6096.22i	−0.539836	−	0.935023i	0.459077	−	0.888397i	$-0.348180\pi$
$350$	−2937.86			−0.448672
$351$	−8387.55	−	587.410i	−1.27548	−	0.0893266i
$352$	4701.65			0.711929
$353$	−2101.09	−	3639.19i	−0.316798	−	0.548710i	0.663020	−	0.748602i	$-0.269274\pi$
$353$	−2101.09	−	3639.19i	−0.316798	−	0.548710i	−0.979818	+	0.199891i	$0.935941\pi$
$354$	−9355.58	+	7485.76i	−1.40464	+	1.12391i
$355$	−1471.66	+	2549.00i	−0.220022	+	0.381089i
$356$	−1255.28	+	2174.21i	−0.186881	+	0.323688i
$357$	11235.1	+	4388.37i	1.66562	+	0.650581i
$358$	−837.612	−	1450.79i	−0.123657	−	0.214180i
$359$	588.013			0.0864461			0.0432230	−	0.999065i	$-0.486237\pi$
$359$	588.013			0.0864461			0.0432230	+	0.999065i	$0.486237\pi$
$360$	−724.915	−	668.247i	−0.106129	−	0.0978325i
$361$	−2783.58			−0.405828
$362$	1694.44	+	2934.85i	0.246016	+	0.426112i
$363$	702.155	+	4607.62i	0.101525	+	0.666218i
$364$	5684.97	−	9846.66i	0.818608	−	1.41787i
$365$	1545.48	−	2676.85i	0.221627	−	0.383870i
$366$	394.109	+	2586.19i	0.0562853	+	0.369350i
$367$	3892.55	+	6742.10i	0.553650	+	0.958950i	0.998007	+	0.0631004i	$0.0200988\pi$
$367$	3892.55	+	6742.10i	0.553650	+	0.958950i	−0.444357	+	0.895850i	$0.646568\pi$
$368$	2489.67			0.352671
$369$	2812.67	+	2592.79i	0.396806	+	0.365787i
$370$	4036.55			0.567163
$371$	−658.198	−	1140.03i	−0.0921077	−	0.159535i
$372$	−7450.77	−	2910.23i	−1.03845	−	0.405615i
$373$	3912.02	−	6775.81i	0.543047	−	0.940585i	−0.455680	−	0.890144i	$-0.650604\pi$
$373$	3912.02	−	6775.81i	0.543047	−	0.940585i	0.998727	−	0.0504412i	$-0.0160627\pi$
$374$	−2891.31	+	5007.90i	−0.399749	+	0.692385i
$375$	−507.155	+	405.794i	−0.0698383	+	0.0558803i
$376$	122.617	+	212.378i	0.0168177	+	0.0291292i
$377$	−9589.49			−1.31004
$378$	16446.5	+	1151.81i	2.23788	+	0.156727i
$379$	−4679.90			−0.634275			−0.317138	−	0.948379i	$-0.602722\pi$
$379$	−4679.90			−0.634275			−0.317138	+	0.948379i	$0.602722\pi$
$380$	965.843	+	1672.89i	0.130386	+	0.225835i
$381$	3959.75	−	3168.35i	0.532452	−	0.426036i
$382$	1123.79	−	1946.47i	0.150519	−	0.260707i
$383$	3363.82	−	5826.31i	0.448782	−	0.777313i	−0.549525	−	0.835477i	$-0.685191\pi$
$383$	3363.82	−	5826.31i	0.448782	−	0.777313i	0.998307	+	0.0581644i	$0.0185247\pi$
$384$	4390.33	+	1714.84i	0.583446	+	0.227891i
$385$	−1632.77	−	2828.04i	−0.216139	−	0.374364i
$386$	−16545.2			−2.18167
$387$	−3554.44	+	1109.08i	−0.466880	+	0.145679i
$388$	−1218.89			−0.159483
$389$	2386.44	+	4133.43i	0.311047	+	0.538749i	0.978589	−	0.205823i	$-0.0659871\pi$
$389$	2386.44	+	4133.43i	0.311047	+	0.538749i	−0.667542	+	0.744572i	$0.732654\pi$
$390$	−879.306	−	5770.10i	−0.114168	−	0.749181i
$391$	−1216.18	+	2106.49i	−0.157302	+	0.272455i
$392$	2336.18	−	4046.38i	0.301007	−	0.521360i
$393$	1275.37	+	8369.10i	0.163699	+	1.07421i
$394$	9009.95	+	15605.7i	1.15207	+	1.99544i
$395$	−1726.44			−0.219916
$396$	−746.681	+	3321.20i	−0.0947529	+	0.421456i
$397$	−4688.95			−0.592775			−0.296388	−	0.955068i	$-0.595782\pi$
$397$	−4688.95			−0.592775			−0.296388	+	0.955068i	$0.595782\pi$
$398$	−588.211	−	1018.81i	−0.0740813	−	0.128313i
$399$	9686.39	+	3783.45i	1.21535	+	0.474711i
$400$	947.379	−	1640.91i	0.118422	−	0.205114i
$401$	−766.916	+	1328.34i	−0.0955061	+	0.165421i	−0.909820	−	0.415004i	$-0.863780\pi$
$401$	−766.916	+	1328.34i	−0.0955061	+	0.165421i	0.814314	+	0.580425i	$0.197114\pi$
$402$	13042.1	−	10435.5i	1.61811	−	1.29471i
$403$	7622.43	+	13202.4i	0.942185	+	1.63191i
$404$	1606.03			0.197780
$405$	2998.22	−	2072.86i	0.367858	−	0.254323i
$406$	18803.3			2.29851
$407$	2243.38	+	3885.66i	0.273220	+	0.473230i
$408$	−2194.04	+	1755.53i	−0.266228	+	0.213019i
$409$	4389.41	−	7602.68i	0.530666	−	0.919140i	−0.468694	−	0.883361i	$-0.655275\pi$
$409$	4389.41	−	7602.68i	0.530666	−	0.919140i	0.999360	−	0.0357796i	$-0.0113914\pi$
$410$	−1327.76	+	2299.74i	−0.159935	+	0.277015i
$411$	3201.45	+	1250.47i	0.384224	+	0.150076i
$412$	1596.50	+	2765.23i	0.190908	+	0.330662i
$413$	−19284.2			−2.29761
$414$	−729.271	+	3243.76i	−0.0865742	+	0.385077i
$415$	−5465.84			−0.646524
$416$	6762.61	+	11713.2i	0.797029	+	1.38050i
$417$	−1082.61	−	7104.21i	−0.127136	−	0.834279i
$418$	−2492.75	+	4317.58i	−0.291686	+	0.505214i
$419$	2138.02	−	3703.17i	0.249282	−	0.431770i	−0.714044	−	0.700100i	$-0.753139\pi$
$419$	2138.02	−	3703.17i	0.249282	−	0.431770i	0.963327	+	0.268330i	$0.0864719\pi$
$420$	742.557	+	4872.74i	0.0862692	+	0.566108i
$421$	−7231.64	−	12525.6i	−0.837169	−	1.45002i	−0.892252	−	0.451538i	$-0.850875\pi$
$421$	−7231.64	−	12525.6i	−0.837169	−	1.45002i	0.0550823	−	0.998482i	$-0.482458\pi$
$422$	9142.07			1.05457
$423$	−865.480	+	270.052i	−0.0994825	+	0.0310411i
$424$	306.671			0.0351256
$425$	925.575	+	1603.14i	0.105640	+	0.182974i
$426$	10680.3	+	4171.66i	1.21470	+	0.474455i
$427$	−2105.21	+	3646.32i	−0.238590	+	0.413250i
$428$	−6306.65	+	10923.4i	−0.712251	+	1.23366i
$429$	5065.71	−	4053.27i	0.570105	−	0.456163i
$430$	−1292.37	−	2238.45i	−0.144939	−	0.251042i
$431$	−2208.11			−0.246777			−0.123389	−	0.992358i	$-0.539376\pi$
$431$	−2208.11			−0.246777			−0.123389	+	0.992358i	$0.539376\pi$
$432$	−5946.89	+	8814.60i	−0.662314	+	0.981696i
$433$	−10062.3			−1.11677			−0.558386	−	0.829581i	$-0.688579\pi$
$433$	−10062.3			−1.11677			−0.558386	+	0.829581i	$0.688579\pi$
$434$	−14946.3	−	25887.7i	−1.65310	−	2.86325i
$435$	3245.97	−	2597.23i	0.357776	−	0.286270i
$436$	−2800.90	+	4851.30i	−0.307658	+	0.532879i
$437$	−1048.54	+	1816.12i	−0.114779	+	0.198803i
$438$	−11216.0	−	4380.90i	−1.22356	−	0.477917i
$439$	−6658.62	−	11533.1i	−0.723915	−	1.25386i	−0.959419	−	0.281984i	$-0.909008\pi$
$439$	−6658.62	−	11533.1i	−0.723915	−	1.25386i	0.235504	−	0.971873i	$-0.424326\pi$
$440$	760.746			0.0824253
$441$	12700.8	+	11707.9i	1.37142	+	1.26422i
$442$	−16634.8			−1.79013
$443$	7137.55	+	12362.6i	0.765497	+	1.32588i	0.939983	+	0.341220i	$0.110840\pi$
$443$	7137.55	+	12362.6i	0.765497	+	1.32588i	−0.174486	+	0.984660i	$0.555826\pi$
$444$	−1020.26	−	6695.03i	−0.109052	−	0.715613i
$445$	−1037.12	+	1796.35i	−0.110482	+	0.191360i
$446$	4373.47	−	7575.08i	0.464327	−	0.804238i
$447$	−2476.39	−	16250.4i	−0.262034	−	1.71950i
$448$	−3756.45	−	6506.36i	−0.396151	−	0.686153i
$449$	−1690.02			−0.177632			−0.0888162	−	0.996048i	$-0.528308\pi$
$449$	−1690.02			−0.177632			−0.0888162	+	0.996048i	$0.528308\pi$
$450$	1860.42	+	1714.98i	0.194891	+	0.179656i
$451$	−2951.69			−0.308181
$452$	−1652.18	−	2861.66i	−0.171929	−	0.297791i
$453$	−12384.7	−	4837.39i	−1.28451	−	0.501723i
$454$	5104.97	−	8842.07i	0.527727	−	0.914051i
$455$	4696.97	−	8135.39i	0.483950	−	0.838227i
$456$	−1891.60	+	1513.54i	−0.194259	+	0.155434i
$457$	3332.19	+	5771.53i	0.341080	+	0.590767i	0.984634	−	0.174633i	$-0.0558741\pi$
$457$	3332.19	+	5771.53i	0.341080	+	0.590767i	−0.643554	+	0.765401i	$0.722541\pi$
$458$	−12423.3			−1.26748
$459$	−4552.97	−	9337.49i	−0.462994	−	0.949535i
$460$	−993.979			−0.100749
$461$	−833.712	−	1444.03i	−0.0842295	−	0.145890i	0.820833	−	0.571168i	$-0.193510\pi$
$461$	−833.712	−	1444.03i	−0.0842295	−	0.145890i	−0.905063	+	0.425278i	$0.860176\pi$
$462$	−9932.99	+	7947.76i	−1.00027	+	0.800354i
$463$	2916.01	−	5050.68i	0.292697	−	0.506966i	−0.681750	−	0.731585i	$-0.738781\pi$
$463$	2916.01	−	5050.68i	0.292697	−	0.506966i	0.974446	+	0.224620i	$0.0721140\pi$
$464$	−6063.56	+	10502.4i	−0.606668	+	1.05078i
$465$	−6155.89	−	2404.46i	−0.613920	−	0.239794i
$466$	5951.67	+	10308.6i	0.591644	+	1.02476i
$467$	17410.6			1.72519			0.862597	−	0.505892i	$-0.168837\pi$
$467$	17410.6			1.72519			0.862597	+	0.505892i	$0.168837\pi$
$468$	−9348.06	+	2916.84i	−0.923321	+	0.288100i
$469$	26883.0			2.64678
$470$	−314.683	−	545.047i	−0.0308835	−	0.0534918i
$471$	−2740.57	−	17983.9i	−0.268108	−	1.75935i
$472$	2246.24	−	3890.61i	0.219050	−	0.379406i
$473$	1436.52	−	2488.12i	0.139643	−	0.241869i
$474$	1013.21	+	6648.81i	0.0981822	+	0.644283i
$475$	797.988	+	1382.16i	0.0770825	+	0.133511i
$476$	14047.8			1.35269
$477$	−248.689	+	1106.16i	−0.0238715	+	0.106179i
$478$	−922.614			−0.0882832
$479$	1639.67	+	2839.99i	0.156406	+	0.270903i	0.933570	−	0.358395i	$-0.116676\pi$
$479$	1639.67	+	2839.99i	0.156406	+	0.270903i	−0.777164	+	0.629298i	$0.783343\pi$
$480$	−5461.50	−	2133.23i	−0.519338	−	0.202851i
$481$	−6453.53	+	11177.8i	−0.611758	+	1.05960i
$482$	9910.71	−	17165.9i	0.936557	−	1.62216i
$483$	−4178.15	+	3343.10i	−0.393607	+	0.314940i
$484$	2714.13	+	4701.00i	0.254895	+	0.441492i
$485$	−1007.05			−0.0942844
$486$	−9742.49	−	10330.1i	−0.909318	−	0.964162i
$487$	−10506.7			−0.977624			−0.488812	−	0.872389i	$-0.662570\pi$
$487$	−10506.7			−0.977624			−0.488812	+	0.872389i	$0.662570\pi$
$488$	−490.433	−	849.456i	−0.0454936	−	0.0787972i
$489$	−1070.91	+	856.875i	−0.0990350	+	0.0792417i
$490$	−5995.56	+	10384.6i	−0.552759	+	0.957406i
$491$	7132.25	−	12353.4i	0.655548	−	1.13544i	−0.326208	−	0.945298i	$-0.605771\pi$
$491$	7132.25	−	12353.4i	0.655548	−	1.13544i	0.981756	−	0.190144i	$-0.0608956\pi$
$492$	4149.95	+	1620.95i	0.380272	+	0.148532i
$493$	−5924.01	−	10260.7i	−0.541184	−	0.937359i
$494$	−14341.8			−1.30621
$495$	−616.914	+	2744.00i	−0.0560167	+	0.249159i
$496$	19279.1			1.74527
$497$	9227.09	+	15981.8i	0.832780	+	1.44242i
$498$	3207.78	+	21049.8i	0.288643	+	1.89411i
$499$	−4723.70	+	8181.68i	−0.423771	+	0.733993i	−0.996305	−	0.0858882i	$-0.972627\pi$
$499$	−4723.70	+	8181.68i	−0.423771	+	0.733993i	0.572534	+	0.819881i	$0.305961\pi$
$500$	−378.234	+	655.120i	−0.0338303	+	0.0585957i
$501$	2809.52	+	18436.4i	0.250539	+	1.64407i
$502$	−5287.78	−	9158.70i	−0.470130	−	0.814288i
$503$	14579.2			1.29235			0.646177	−	0.763188i	$-0.276367\pi$
$503$	14579.2			1.29235			0.646177	+	0.763188i	$0.276367\pi$
$504$	−5901.02	+	1841.27i	−0.521532	+	0.162732i
$505$	1326.91			0.116925
$506$	−1282.69	−	2221.68i	−0.112692	−	0.195189i
$507$	6750.55	+	2636.73i	0.591327	+	0.230969i
$508$	2953.17	−	5115.03i	0.257924	−	0.446738i
$509$	−4205.32	+	7283.83i	−0.366204	+	0.634283i	−0.988969	−	0.148126i	$-0.952676\pi$
$509$	−4205.32	+	7283.83i	−0.366204	+	0.634283i	0.622765	+	0.782409i	$0.286009\pi$
$510$	5630.76	−	4505.39i	0.488891	−	0.391180i
$511$	−9689.89	−	16783.4i	−0.838856	−	1.45294i
$512$	12676.3			1.09417
$513$	−3925.36	−	8050.35i	−0.337834	−	0.692849i
$514$	−7063.02			−0.606102
$515$	1319.04	+	2284.65i	0.112862	+	0.195483i
$516$	−3386.05	+	2709.31i	−0.288881	+	0.231145i
$517$	349.781	−	605.838i	0.0297550	−	0.0515372i
$518$	12654.3	−	21917.8i	1.07335	−	1.85910i
$519$	1793.02	+	700.345i	0.151647	+	0.0592327i
$520$	1094.22	+	1895.24i	0.0922781	+	0.159830i
$521$	10058.1			0.845781			0.422890	−	0.906181i	$-0.361016\pi$
$521$	10058.1			0.845781			0.422890	+	0.906181i	$0.361016\pi$
$522$	−11907.3	−	10976.5i	−0.998409	−	0.920361i
$523$	20006.3			1.67269			0.836344	−	0.548205i	$-0.184688\pi$
$523$	20006.3			1.67269			0.836344	+	0.548205i	$0.184688\pi$
$524$	4929.83	+	8538.72i	0.410994	+	0.711862i
$525$	613.507	+	4025.90i	0.0510012	+	0.334676i
$526$	−1036.50	+	1795.27i	−0.0859192	+	0.148817i
$527$	−9417.67	+	16311.9i	−0.778444	+	1.34830i
$528$	−1236.02	−	8110.90i	−0.101877	−	0.668525i
$529$	5543.96	+	9602.42i	0.455655	+	0.789218i
$530$	−787.038			−0.0645033
$531$	12211.8	+	11257.2i	0.998019	+	0.920001i
$532$	12111.4			0.987019
$533$	−4245.56	−	7353.52i	−0.345020	−	0.597592i
$534$	7526.70	+	2939.89i	0.609948	+	0.238243i
$535$	−5210.61	+	9025.04i	−0.421073	+	0.729320i
$536$	−3131.36	+	5423.67i	−0.252340	+	0.437065i
$537$	−1813.17	+	1450.79i	−0.145706	+	0.116585i
$538$	−6304.11	−	10919.0i	−0.505185	−	0.875006i
$539$	−13328.5			−1.06512
$540$	2374.25	−	3519.16i	0.189206	−	0.280445i
$541$	−1884.15			−0.149734			−0.0748668	−	0.997194i	$-0.523853\pi$
$541$	−1884.15			−0.149734			−0.0748668	+	0.997194i	$0.523853\pi$
$542$	6248.58	+	10822.9i	0.495202	+	0.857715i
$543$	3667.93	−	2934.85i	0.289882	−	0.231946i
$544$	−8355.34	+	14471.9i	−0.658515	+	1.14058i
$545$	−2314.13	+	4008.19i	−0.181883	+	0.315031i
$546$	−34087.3	−	13314.3i	−2.67180	−	1.04359i
$547$	8998.24	+	15585.4i	0.703358	+	1.21825i	0.967281	+	0.253708i	$0.0816504\pi$
$547$	8998.24	+	15585.4i	0.703358	+	1.21825i	−0.263922	+	0.964544i	$0.585016\pi$
$548$	4002.93			0.312038
$549$	3461.68	−	1080.14i	0.269109	−	0.0839691i
$550$	−1952.37			−0.151363
$551$	−5107.40	−	8846.28i	−0.394887	−	0.683964i
$552$	−187.798	−	1232.35i	−0.0144805	−	0.0950226i
$553$	−5412.25	+	9374.30i	−0.416189	+	0.720860i
$554$	10097.2	−	17488.9i	0.774351	−	1.34121i
$555$	−842.944	−	5531.49i	−0.0644702	−	0.423061i
$556$	−4184.75	−	7248.19i	−0.319196	−	0.552863i
$557$	−3615.76			−0.275054			−0.137527	−	0.990498i	$-0.543915\pi$
$557$	−3615.76			−0.275054			−0.137527	+	0.990498i	$0.543915\pi$
$558$	−5647.21	+	25118.5i	−0.428433	+	1.90564i
$559$	8264.84			0.625341
$560$	−5939.91	−	10288.2i	−0.448227	−	0.776352i
$561$	7466.36	+	2916.32i	0.561907	+	0.219478i
$562$	−6966.14	+	12065.7i	−0.522863	+	0.905625i
$563$	−7410.91	+	12836.1i	−0.554765	+	0.960881i	0.443157	+	0.896444i	$0.353858\pi$
$563$	−7410.91	+	12836.1i	−0.554765	+	0.960881i	−0.997922	+	0.0644370i	$0.979475\pi$
$564$	−824.478	+	659.696i	−0.0615546	+	0.0492522i
$565$	−1365.05	−	2364.33i	−0.101642	−	0.176050i
$566$	10378.9			0.770771
$567$	−1856.11	−	22778.1i	−0.137477	−	1.68710i
$568$	−4299.13			−0.317583
$569$	−11224.7	−	19441.8i	−0.827005	−	1.43241i	−0.900377	−	0.435110i	$-0.856710\pi$
$569$	−11224.7	−	19441.8i	−0.827005	−	1.43241i	0.0733726	−	0.997305i	$-0.476624\pi$
$570$	4854.58	−	3884.34i	0.356730	−	0.285433i
$571$	8006.75	−	13868.1i	0.586817	−	1.01640i	−0.407830	−	0.913058i	$-0.633714\pi$
$571$	8006.75	−	13868.1i	0.586817	−	1.01640i	0.994646	−	0.103338i	$-0.0329523\pi$
$572$	3777.98	−	6543.66i	0.276163	−	0.478329i
$573$	−2902.03	−	1133.52i	−0.211577	−	0.0826410i
$574$	8324.81	+	14419.0i	0.605350	+	1.04850i
$575$	−821.234			−0.0595615
$576$	−1419.31	+	6313.03i	−0.102670	+	0.456672i
$577$	3096.97			0.223446			0.111723	−	0.993739i	$-0.464363\pi$
$577$	3096.97			0.223446			0.111723	+	0.993739i	$0.464363\pi$
$578$	−1067.99	−	1849.81i	−0.0768553	−	0.133117i
$579$	3455.09	+	22672.7i	0.247994	+	1.62736i
$580$	2420.83	−	4193.00i	0.173309	−	0.300181i
$581$	−17135.0	+	29678.6i	−1.22354	+	2.11924i
$582$	591.018	+	3878.33i	0.0420936	+	0.276223i
$583$	−437.410	−	757.616i	−0.0310732	−	0.0538203i
$584$	4514.76			0.319901
$585$	−7723.44	+	2409.91i	−0.545855	+	0.170321i
$586$	−13045.0			−0.919595
$587$	−12312.4	−	21325.7i	−0.865734	−	1.49950i	−0.866316	−	0.499496i	$-0.833519\pi$
$587$	−12312.4	−	21325.7i	−0.865734	−	1.49950i	0.000582275	−	1.00000i	$-0.499815\pi$
$588$	18739.3	+	7319.49i	1.31428	+	0.513351i
$589$	−8119.48	+	14063.3i	−0.568009	+	0.983820i
$590$	−5764.75	+	9984.83i	−0.402256	+	0.696727i
$591$	19503.8	−	15605.7i	1.35749	−	1.08618i
$592$	8161.30	+	14135.8i	0.566601	+	0.981381i
$593$	27128.8			1.87866			0.939330	−	0.343014i	$-0.111448\pi$
$593$	27128.8			1.87866			0.939330	+	0.343014i	$0.111448\pi$
$594$	10929.7	+	765.442i	0.754965	+	0.0528729i
$595$	11606.4			0.799691
$596$	−9572.32	−	16579.7i	−0.657881	−	1.13948i
$597$	−1273.29	+	1018.81i	−0.0872906	+	0.0698445i
$598$	3689.89	−	6391.08i	0.252326	−	0.437042i
$599$	−2815.87	+	4877.24i	−0.192076	+	0.332685i	−0.945938	−	0.324347i	$-0.894855\pi$
$599$	−2815.87	+	4877.24i	−0.192076	+	0.332685i	0.753862	+	0.657033i	$0.228189\pi$
$600$	−883.692	−	345.166i	−0.0601276	−	0.0234855i
$601$	7375.88	+	12775.4i	0.500613	+	0.867087i	1.00000		0.000707853i	$0.000225317\pi$
$601$	7375.88	+	12775.4i	0.500613	+	0.867087i	−0.499387	+	0.866379i	$0.666441\pi$
$602$	−16205.9			−1.09718
$603$	−17023.8	−	15693.0i	−1.14969	−	1.05982i
$604$	−15485.2			−1.04318
$605$	2242.43	+	3884.01i	0.150691	+	0.261004i
$606$	−778.738	−	5110.16i	−0.0522014	−	0.342552i
$607$	7391.04	−	12801.7i	0.494222	−	0.856018i	−0.505756	−	0.862677i	$-0.668786\pi$
$607$	7391.04	−	12801.7i	0.494222	−	0.856018i	0.999978	+	0.00665872i	$0.00211955\pi$
$608$	−7203.59	+	12477.0i	−0.480500	+	0.832251i
$609$	−3926.66	−	25767.2i	−0.261275	−	1.71451i
$610$	1258.65	+	2180.04i	0.0835427	+	0.144700i
$611$	2012.43			0.133247
$612$	−8895.85	−	8200.44i	−0.587571	−	0.541639i
$613$	4947.28			0.325969			0.162984	−	0.986629i	$-0.447888\pi$
$613$	4947.28			0.325969			0.162984	+	0.986629i	$0.447888\pi$
$614$	3393.12	+	5877.06i	0.223021	+	0.386284i
$615$	3428.72	+	1339.24i	0.224812	+	0.0878104i
$616$	2384.88	−	4130.73i	0.155989	−	0.270181i
$617$	1871.82	−	3242.09i	0.122134	−	0.211543i	−0.798475	−	0.602028i	$-0.794360\pi$
$617$	1871.82	−	3242.09i	0.122134	−	0.211543i	0.920609	+	0.390485i	$0.127693\pi$
$618$	8024.45	−	6420.67i	0.522315	−	0.417924i
$619$	−3069.37	−	5316.30i	−0.199303	−	0.345202i	0.749000	−	0.662570i	$-0.230534\pi$
$619$	−3069.37	−	5316.30i	−0.199303	−	0.345202i	−0.948303	+	0.317368i	$0.897201\pi$
$620$	−7697.01			−0.498580
$621$	4597.38	+	321.971i	0.297080	+	0.0208055i
$622$	−3326.09			−0.214412
$623$	6502.59	+	11262.8i	0.418171	+	0.724294i
$624$	18428.8	−	14745.6i	1.18228	−	0.945986i
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	4151.79	−	7191.11i	0.265078	−	0.459128i
$627$	6437.15	+	2514.32i	0.410008	+	0.160147i
$628$	−10593.5	−	18348.4i	−0.673129	−	1.16589i
$629$	−15946.9			−1.01088
$630$	15144.3	−	4725.43i	0.957722	−	0.298834i
$631$	−5548.00			−0.350019			−0.175010	−	0.984567i	$-0.555996\pi$
$631$	−5548.00			−0.350019			−0.175010	+	0.984567i	$0.555996\pi$
$632$	−1260.85	−	2183.86i	−0.0793575	−	0.137451i
$633$	−1909.12	−	12527.8i	−0.119874	−	0.786630i
$634$	1233.36	−	2136.25i	0.0772605	−	0.133819i
$635$	2439.93	−	4226.08i	0.152481	−	0.264106i
$636$	198.927	+	1305.38i	0.0124025	+	0.0813864i
$637$	−19171.1	−	33205.3i	−1.19244	−	2.06537i
$638$	12495.9			0.775418
$639$	3486.31	−	15506.9i	0.215831	−	0.960005i
$640$	4535.43			0.280123
$641$	5804.05	+	10052.9i	0.357639	+	0.619448i	0.987566	−	0.157206i	$-0.0502487\pi$
$641$	5804.05	+	10052.9i	0.357639	+	0.619448i	−0.629927	+	0.776654i	$0.716915\pi$
$642$	37814.9	+	14770.3i	2.32466	+	0.908002i
$643$	6360.85	−	11017.3i	0.390120	−	0.675708i	−0.602345	−	0.798236i	$-0.705767\pi$
$643$	6360.85	−	11017.3i	0.390120	−	0.675708i	0.992465	+	0.122528i	$0.0391001\pi$
$644$	−3116.04	+	5397.15i	−0.190667	+	0.330244i
$645$	−2797.58	+	2238.45i	−0.170783	+	0.136650i
$646$	−8859.78	−	15345.6i	−0.539603	−	0.934620i
$647$	−28203.7			−1.71376			−0.856879	−	0.515518i	$-0.827600\pi$
$647$	−28203.7			−1.71376			−0.856879	+	0.515518i	$0.827600\pi$
$648$	4811.70	+	2278.74i	0.291700	+	0.138144i
$649$	−12815.4			−0.775115
$650$	−2808.19	−	4863.93i	−0.169456	−	0.293506i
$651$	−32354.0	+	25887.7i	−1.94786	+	1.55856i
$652$	−798.678	+	1383.35i	−0.0479734	+	0.0830924i
$653$	11346.4	−	19652.5i	0.679966	−	1.17774i	−0.295024	−	0.955490i	$-0.595328\pi$
$653$	11346.4	−	19652.5i	0.679966	−	1.17774i	0.974991	−	0.222247i	$-0.0713390\pi$
$654$	16794.3	+	6559.76i	1.00414	+	0.392213i
$655$	4073.07	+	7054.77i	0.242974	+	0.420844i
$656$	−10738.1			−0.639103
$657$	−3661.17	+	16284.7i	−0.217406	+	0.967010i
$658$	−3946.02			−0.233787
$659$	−3002.00	−	5199.61i	−0.177453	−	0.307357i	0.763555	−	0.645743i	$-0.223452\pi$
$659$	−3002.00	−	5199.61i	−0.177453	−	0.307357i	−0.941007	+	0.338386i	$0.890119\pi$
$660$	493.471	+	3238.21i	0.0291035	+	0.190981i
$661$	−5958.18	+	10319.9i	−0.350600	+	0.607256i	−0.986355	−	0.164635i	$-0.947356\pi$
$661$	−5958.18	+	10319.9i	−0.350600	+	0.607256i	0.635755	+	0.771891i	$0.280689\pi$
$662$	−9889.54	+	17129.2i	−0.580616	+	1.00566i
$663$	3473.81	+	22795.6i	0.203487	+	1.33530i
$664$	−3991.80	−	6914.00i	−0.233301	−	0.404089i
$665$	10006.5			0.583512
$666$	−20808.0	+	6492.63i	−1.21065	+	0.377754i
$667$	5256.19			0.305128
$668$	10860.0	+	18810.1i	0.629021	+	1.08950i
$669$	−11293.8	−	4411.31i	−0.652682	−	0.254934i
$670$	8036.30	−	13919.3i	0.463387	−	0.802610i
$671$	−1399.03	+	2423.19i	−0.0804901	+	0.139413i
$672$	−28704.5	+	22967.5i	−1.64777	+	1.31844i
$673$	8016.85	+	13885.6i	0.459178	+	0.795319i	0.998918	−	0.0465125i	$-0.0148107\pi$
$673$	8016.85	+	13885.6i	0.459178	+	0.795319i	−0.539740	+	0.841832i	$0.681477\pi$
$674$	−12599.9			−0.720077
$675$	1961.62	−	2907.56i	0.111856	−	0.165796i
$676$	8440.54			0.480231
$677$	−5655.94	−	9796.38i	−0.321086	−	0.556138i	0.659626	−	0.751594i	$-0.270715\pi$
$677$	−5655.94	−	9796.38i	−0.321086	−	0.556138i	−0.980712	+	0.195456i	$0.937381\pi$
$678$	−8304.31	+	6644.59i	−0.470391	+	0.376378i
$679$	−3157.03	+	5468.14i	−0.178432	+	0.309054i
$680$	−1351.93	+	2341.61i	−0.0762413	+	0.132054i
$681$	−13182.8	−	5149.13i	−0.741800	−	0.289743i
$682$	−9932.64	−	17203.8i	−0.557684	−	0.965937i
$683$	−652.395			−0.0365493			−0.0182747	−	0.999833i	$-0.505817\pi$
$683$	−652.395			−0.0365493			−0.0182747	+	0.999833i	$0.505817\pi$
$684$	−7669.59	−	7070.04i	−0.428734	−	0.395219i
$685$	3307.25			0.184472
$686$	17437.4	+	30202.5i	0.970502	+	1.68096i
$687$	2594.34	+	17024.3i	0.144076	+	0.945443i
$688$	5225.96	−	9051.64i	0.289590	−	0.501585i
$689$	1258.29	−	2179.43i	0.0695750	−	0.120507i
$690$	481.965	+	3162.71i	0.0265914	+	0.174496i
$691$	−6268.93	−	10858.1i	−0.345125	−	0.597774i	0.640252	−	0.768165i	$-0.278830\pi$
$691$	−6268.93	−	10858.1i	−0.345125	−	0.597774i	−0.985376	+	0.170392i	$0.945497\pi$
$692$	2241.90			0.123157
$693$	12965.5	+	11952.0i	0.710705	+	0.655148i
$694$	35069.8			1.91820
$695$	−3457.47	−	5988.52i	−0.188704	−	0.326845i
$696$	5655.94	+	2209.18i	0.308029	+	0.120314i
$697$	5245.47	−	9085.42i	0.285059	−	0.493737i
$698$	−13193.6	+	22852.1i	−0.715454	+	1.23920i
$699$	12883.5	−	10308.6i	0.697138	−	0.557807i
$700$	2371.46	+	4107.50i	0.128047	+	0.221784i
$701$	5880.60			0.316844			0.158422	−	0.987372i	$-0.449359\pi$
$701$	5880.60			0.316844			0.158422	+	0.987372i	$0.449359\pi$
$702$	13813.7	+	28329.9i	0.742684	+	1.52314i
$703$	−13748.7			−0.737614
$704$	−2496.37	−	4323.84i	−0.133644	−	0.231479i
$705$	−681.190	+	545.047i	−0.0363902	+	0.0291172i
$706$	−7876.07	+	13641.8i	−0.419858	+	0.727216i
$707$	4159.77	−	7204.93i	0.221279	−	0.383266i
$708$	18017.9	+	7037.71i	0.956434	+	0.373578i
$709$	−3203.33	−	5548.33i	−0.169681	−	0.293895i	0.768627	−	0.639697i	$-0.220940\pi$
$709$	−3203.33	−	5548.33i	−0.169681	−	0.293895i	−0.938308	+	0.345802i	$0.887607\pi$
$710$	11033.3			0.583198
$711$	8899.62	−	2776.91i	0.469426	−	0.146473i
$712$	−3029.72			−0.159471
$713$	−4178.00	−	7236.52i	−0.219449	−	0.380098i
$714$	−6811.55	−	44698.2i	−0.357025	−	2.34284i
$715$	3121.40	−	5406.43i	0.163264	−	0.282782i
$716$	−1352.25	+	2342.17i	−0.0705812	+	0.122250i
$717$	192.667	+	1264.30i	0.0100353	+	0.0658526i
$718$	−1102.10	−	1908.90i	−0.0572843	−	0.0992193i
$719$	21907.0			1.13629			0.568144	−	0.822929i	$-0.307662\pi$
$719$	21907.0			1.13629			0.568144	+	0.822929i	$0.307662\pi$
$720$	−2244.30	+	9982.52i	−0.116167	+	0.516704i
$721$	16540.4			0.854364
$722$	5217.21	+	9036.47i	0.268926	+	0.465793i
$723$	−25592.9	−	9996.44i	−1.31647	−	0.514207i
$724$	2735.53	−	4738.07i	0.140421	−	0.243217i
$725$	2000.11	−	3464.29i	0.102458	−	0.177463i
$726$	13641.9	−	10915.4i	0.697382	−	0.558002i
$727$	−6685.46	−	11579.6i	−0.341059	−	0.590732i	0.643571	−	0.765387i	$-0.277452\pi$
$727$	−6685.46	−	11579.6i	−0.341059	−	0.590732i	−0.984630	+	0.174655i	$0.944119\pi$
$728$	13721.1			0.698542
$729$	−12121.4	+	15507.8i	−0.615829	+	0.787880i
$730$	−11586.6			−0.587453
$731$	5105.69	+	8843.31i	0.258332	+	0.447444i
$732$	3297.69	−	2638.61i	0.166511	−	0.133232i
$733$	−15095.5	+	26146.2i	−0.760663	+	1.31751i	0.181846	+	0.983327i	$0.441793\pi$
$733$	−15095.5	+	26146.2i	−0.760663	+	1.31751i	−0.942509	+	0.334181i	$0.891540\pi$
$734$	14591.5	−	25273.2i	0.733762	−	1.27091i
$735$	15482.6	+	6047.42i	0.776985	+	0.303486i
$736$	−3706.72	−	6420.22i	−0.185641	−	0.321539i
$737$	17865.2			0.892910
$738$	3145.39	−	13990.5i	0.156888	−	0.697830i
$739$	−11624.7			−0.578650			−0.289325	−	0.957231i	$-0.593431\pi$
$739$	−11624.7			−0.578650			−0.289325	+	0.957231i	$0.593431\pi$
$740$	−3258.34	−	5643.60i	−0.161863	−	0.280355i
$741$	2994.96	+	19653.3i	0.148479	+	0.974334i
$742$	−2467.30	+	4273.49i	−0.122072	+	0.211435i
$743$	2627.19	−	4550.42i	0.129720	−	0.224682i	−0.793848	−	0.608116i	$-0.791925\pi$
$743$	2627.19	−	4550.42i	0.129720	−	0.224682i	0.923568	+	0.383434i	$0.125259\pi$
$744$	−1454.24	−	9542.90i	−0.0716601	−	0.470241i
$745$	−7908.73	−	13698.3i	−0.388931	−	0.673648i
$746$	−29328.9			−1.43942
$747$	28175.8	−	8791.57i	1.38005	−	0.430612i
$748$	9335.55			0.456339
$749$	32669.7	+	56585.5i	1.59376	+	2.76047i
$750$	2267.90	+	885.831i	0.110416	+	0.0431280i
$751$	14614.4	−	25312.9i	0.710102	−	1.22993i	−0.254717	−	0.967016i	$-0.581982\pi$
$751$	14614.4	−	25312.9i	0.710102	−	1.22993i	0.964819	−	0.262917i	$-0.0846844\pi$
$752$	1272.48	−	2204.00i	0.0617057	−	0.106877i
$753$	−11446.4	+	9158.70i	−0.553957	+	0.443242i
$754$	17973.4	+	31130.9i	0.868108	+	1.50361i
$755$	−12794.0			−0.616716
$756$	−11665.4	−	23924.1i	−0.561199	−	1.15094i
$757$	32885.9			1.57894			0.789470	−	0.613789i	$-0.210355\pi$
$757$	32885.9			1.57894			0.789470	+	0.613789i	$0.210355\pi$
$758$	8771.46	+	15192.6i	0.420308	+	0.727995i
$759$	−2776.62	+	2221.68i	−0.132786	+	0.106247i
$760$	−1165.57	+	2018.83i	−0.0556311	+	0.0963559i
$761$	6634.11	−	11490.6i	0.316014	−	0.547352i	−0.663639	−	0.748053i	$-0.730989\pi$
$761$	6634.11	−	11490.6i	0.316014	−	0.547352i	0.979652	+	0.200702i	$0.0643221\pi$
$762$	−17707.3	−	6916.37i	−0.841820	−	0.328811i
$763$	14509.2	+	25130.7i	0.688425	+	1.19239i
$764$	−3628.54			−0.171827
$765$	−7349.82	−	6775.27i	−0.347364	−	0.320210i
$766$	−25219.0			−1.18956
$767$	−18433.0	−	31927.0i	−0.867769	−	1.50302i
$768$	−4162.55	−	27315.1i	−0.195577	−	1.28340i
$769$	−17142.9	+	29692.4i	−0.803887	+	1.39237i	0.113153	+	0.993578i	$0.463905\pi$
$769$	−17142.9	+	29692.4i	−0.803887	+	1.39237i	−0.917040	+	0.398796i	$0.869428\pi$
$770$	−6120.53	+	10601.1i	−0.286453	+	0.496151i
$771$	1474.95	+	9678.81i	0.0688964	+	0.452106i
$772$	13355.4	+	23132.2i	0.622630	+	1.07843i
$773$	−27987.1			−1.30223			−0.651117	−	0.758978i	$-0.725699\pi$
$773$	−27987.1			−1.30223			−0.651117	+	0.758978i	$0.725699\pi$
$774$	10262.5	+	9460.25i	0.476586	+	0.439330i
$775$	−6359.34			−0.294754
$776$	−735.469	−	1273.87i	−0.0340229	−	0.0589294i
$777$	−32677.7	−	12763.7i	−1.50876	−	0.589313i
$778$	8945.72	−	15494.4i	0.412236	−	0.714014i
$779$	4522.40	−	7833.03i	0.208000	−	0.360266i
$780$	−7357.54	+	5887.05i	−0.337747	+	0.270244i
$781$	6131.92	+	10620.8i	0.280944	+	0.486610i
$782$	9117.88			0.416950
$783$	−12555.1	+	18609.4i	−0.573029	+	0.849356i
$784$	−48488.5			−2.20884
$785$	−8752.41	−	15159.6i	−0.397945	−	0.689261i
$786$	24778.7	−	19826.3i	1.12446	−	0.899723i
$787$	−177.400	+	307.265i	−0.00803509	+	0.0139172i	−0.870015	−	0.493025i	$-0.835891\pi$
$787$	−177.400	+	307.265i	−0.00803509	+	0.0139172i	0.861980	+	0.506942i	$0.169224\pi$
$788$	14545.8	−	25194.1i	0.657580	−	1.13896i
$789$	2676.60	+	1045.47i	0.120772	+	0.0471731i
$790$	3235.84	+	5604.64i	0.145729	+	0.252410i
$791$	−17117.2			−0.769430
$792$	−3921.56	+	1223.63i	−0.175943	+	0.0548987i
$793$	−8049.15			−0.360446
$794$	8788.42	+	15222.0i	0.392808	+	0.680363i
$795$	164.355	+	1078.52i	0.00733217	+	0.0481146i
$796$	−949.617	+	1644.78i	−0.0422843	+	0.0732385i
$797$	−6400.65	+	11086.2i	−0.284470	+	0.492717i	−0.972481	−	0.232984i	$-0.925151\pi$
$797$	−6400.65	+	11086.2i	−0.284470	+	0.492717i	0.688011	+	0.725701i	$0.258484\pi$
$798$	−5872.60	−	38536.7i	−0.260511	−	1.70950i
$799$	1243.20	+	2153.28i	0.0550452	+	0.0953411i
$800$	−5641.99			−0.249343
$801$	2456.90	−	10928.2i	0.108377	−	0.482056i
$802$	5749.67			0.253152
$803$	−6439.48	−	11153.5i	−0.282994	−	0.490160i
$804$	−25117.7	−	9810.86i	−1.10178	−	0.430351i
$805$	−2574.50	+	4459.17i	−0.112720	+	0.195236i
$806$	28573.2	−	49490.2i	1.24869	−	2.16280i
$807$	−13646.4	+	10919.0i	−0.595264	+	0.476293i
$808$	969.069	+	1678.48i	0.0421927	+	0.0730800i
$809$	−16374.9			−0.711632			−0.355816	−	0.934556i	$-0.615797\pi$
$809$	−16374.9			−0.711632			−0.355816	+	0.934556i	$0.615797\pi$
$810$	−12348.7	−	5848.15i	−0.535667	−	0.253683i
$811$	−35518.2			−1.53787			−0.768936	−	0.639326i	$-0.779214\pi$
$811$	−35518.2			−1.53787			−0.768936	+	0.639326i	$0.779214\pi$
$812$	−15178.2	−	26289.4i	−0.655974	−	1.13618i
$813$	13526.2	−	10822.9i	0.583500	−	0.466881i
$814$	8409.47	−	14565.6i	0.362103	−	0.627181i
$815$	−659.875	+	1142.94i	−0.0283612	+	0.0491231i
$816$	27162.2	+	10609.4i	1.16528	+	0.455152i
$817$	4401.89	+	7624.29i	0.188498	+	0.326487i
$818$	−32908.0			−1.40660
$819$	−11126.9	+	49491.9i	−0.474733	+	2.11158i
$820$	4287.10			0.182576
$821$	−21471.9	−	37190.5i	−0.912760	−	1.58095i	−0.810148	−	0.586226i	$-0.800613\pi$
$821$	−21471.9	−	37190.5i	−0.912760	−	1.58095i	−0.102612	−	0.994721i	$-0.532720\pi$
$822$	−1940.96	−	12736.8i	−0.0823584	−	0.540445i
$823$	3958.46	−	6856.26i	0.167659	−	0.290394i	−0.769937	−	0.638119i	$-0.779713\pi$
$823$	3958.46	−	6856.26i	0.167659	−	0.290394i	0.937596	+	0.347726i	$0.113046\pi$
$824$	−1926.64	+	3337.04i	−0.0814536	+	0.141082i
$825$	407.710	+	2675.44i	0.0172056	+	0.112905i
$826$	36144.0	+	62603.3i	1.52253	+	2.63710i
$827$	18774.4			0.789421			0.394710	−	0.918806i	$-0.370845\pi$
$827$	18774.4			0.789421			0.394710	+	0.918806i	$0.370845\pi$
$828$	5123.85	−	1598.77i	0.215056	−	0.0671030i
$829$	22166.1			0.928661			0.464330	−	0.885662i	$-0.346295\pi$
$829$	22166.1			0.928661			0.464330	+	0.885662i	$0.346295\pi$
$830$	10244.5	+	17744.0i	0.428425	+	0.742054i
$831$	−26074.5	−	10184.6i	−1.08847	−	0.425149i
$832$	7181.30	−	12438.4i	0.299239	−	0.518297i
$833$	23686.2	−	41025.8i	0.985210	−	1.70643i
$834$	−21033.6	+	16829.8i	−0.873304	+	0.698764i
$835$	8972.63	+	15541.0i	0.371869	+	0.644096i
$836$	8048.68			0.332978
$837$	35600.4	+	2493.22i	1.47017	+	0.102961i
$838$	−16029.1			−0.660757
$839$	−21295.4	−	36884.7i	−0.876279	−	1.51776i	−0.855394	−	0.517978i	$-0.826685\pi$
$839$	−21295.4	−	36884.7i	−0.876279	−	1.51776i	−0.0208849	−	0.999782i	$-0.506648\pi$
$840$	−4644.50	+	3716.24i	−0.190774	+	0.152646i
$841$	−606.908	+	1051.20i	−0.0248845	+	0.0431012i
$842$	−27108.3	+	46952.9i	−1.10952	+	1.92174i
$843$	17989.0	+	7026.40i	0.734963	+	0.287073i
$844$	−7379.55	−	12781.7i	−0.300965	−	0.521287i
$845$	6973.65			0.283906
$846$	2498.84	+	2303.50i	0.101551	+	0.0936122i
$847$	28119.4			1.14072
$848$	−1591.27	−	2756.16i	−0.0644393	−	0.111612i
$849$	−2167.39	−	14222.7i	−0.0876145	−	0.574937i
$850$	3469.58	−	6009.49i	0.140007	−	0.242498i
$851$	3537.31	−	6126.79i	0.142488	−	0.246796i
$852$	−2788.70	−	18299.8i	−0.112135	−	0.735845i
$853$	−13230.6	−	22916.0i	−0.531074	−	0.919847i	−0.999342	−	0.0362605i	$-0.988455\pi$
$853$	−13230.6	−	22916.0i	−0.531074	−	0.919847i	0.468269	−	0.883586i	$-0.344878\pi$
$854$	15783.0			0.632416
$855$	−6336.68	−	5841.33i	−0.253462	−	0.233648i
$856$	−15221.6			−0.607784
$857$	10004.5	+	17328.3i	0.398772	+	0.690693i	0.993575	−	0.113179i	$-0.0361033\pi$
$857$	10004.5	+	17328.3i	0.398772	+	0.690693i	−0.594803	+	0.803871i	$0.702770\pi$
$858$	−22652.9	−	8848.12i	−0.901350	−	0.352063i
$859$	8909.03	−	15430.9i	0.353868	−	0.612917i	−0.633056	−	0.774106i	$-0.718200\pi$
$859$	8909.03	−	15430.9i	0.353868	−	0.612917i	0.986923	+	0.161189i	$0.0515330\pi$
$860$	−2086.43	+	3613.79i	−0.0827285	+	0.143290i
$861$	18020.6	−	14419.0i	0.713288	−	0.570729i
$862$	4138.63	+	7168.31i	0.163529	+	0.283241i
$863$	12769.5			0.503683			0.251841	−	0.967769i	$-0.418964\pi$
$863$	12769.5			0.503683			0.251841	+	0.967769i	$0.418964\pi$
$864$	31584.6	+	2211.98i	1.24367	+	0.0870986i
$865$	1852.28			0.0728085
$866$	18859.6	+	32665.7i	0.740039	+	1.28179i
$867$	−2311.86	+	1849.81i	−0.0905592	+	0.0724598i
$868$	−24129.5	+	41793.5i	−0.943558	+	1.63429i
$869$	−3596.75	+	6229.75i	−0.140404	+	0.243187i
$870$	−14515.4	−	5669.63i	−0.565652	−	0.220941i
$871$	25696.4	+	44507.5i	0.999644	+	1.73144i
$872$	−6760.19			−0.262533
$873$	5191.25	−	1619.80i	0.201257	−	0.0627973i
$874$	7861.01			0.304236
$875$	1959.32	+	3393.65i	0.0756997	+	0.131116i
$876$	2928.57	+	19217.6i	0.112954	+	0.741214i
$877$	−13738.6	+	23796.0i	−0.528986	+	0.916231i	0.470442	+	0.882431i	$0.344094\pi$
$877$	−13738.6	+	23796.0i	−0.528986	+	0.916231i	−0.999429	+	0.0338003i	$0.989239\pi$
$878$	−24960.3	+	43232.5i	−0.959417	+	1.66176i
$879$	2724.15	+	17876.2i	0.104532	+	0.685948i
$880$	−3947.41	−	6837.11i	−0.151213	−	0.261908i
$881$	31509.1			1.20496			0.602480	−	0.798134i	$-0.294179\pi$
$881$	31509.1			1.20496			0.602480	+	0.798134i	$0.294179\pi$
$882$	14203.2	−	63175.1i	0.542230	−	2.41181i
$883$	5271.46			0.200905			0.100452	−	0.994942i	$-0.467971\pi$
$883$	5271.46			0.200905			0.100452	+	0.994942i	$0.467971\pi$
$884$	13427.8	+	23257.6i	0.510888	+	0.884883i
$885$	14886.6	+	5814.62i	0.565431	+	0.220854i
$886$	26755.6	−	46342.0i	1.01453	−	1.75721i
$887$	−5216.89	+	9035.91i	−0.197481	+	0.342048i	−0.947711	−	0.319130i	$-0.896609\pi$
$887$	−5216.89	+	9035.91i	−0.197481	+	0.342048i	0.750230	+	0.661177i	$0.229943\pi$
$888$	6381.43	−	5106.03i	0.241156	−	0.192958i
$889$	−15298.0	−	26496.9i	−0.577140	−	0.999636i
$890$	7775.45			0.292847
$891$	−1233.49	−	15137.3i	−0.0463787	−	0.569157i
$892$	−14121.2			−0.530059
$893$	1071.83	+	1856.46i	0.0401649	+	0.0695677i
$894$	−48113.0	+	38497.1i	−1.79993	+	1.44019i
$895$	−1117.24	+	1935.12i	−0.0417266	+	0.0722727i
$896$	14218.2	−	24626.6i	0.530130	−	0.918212i
$897$	−9528.58	−	3721.81i	−0.354682	−	0.138537i
$898$	3167.57	+	5486.40i	0.117710	+	0.203879i
$899$	40702.0			1.51000
$900$	896.019	−	3985.44i	0.0331859	−	0.147609i
$901$	3109.30			0.114967
$902$	5532.30	+	9582.23i	0.204219	+	0.353718i
$903$	3384.24	+	22207.8i	0.124718	+	0.818415i
$904$	1993.84	−	3453.43i	0.0733562	−	0.127057i
$905$	2260.11	−	3914.63i	0.0830152	−	0.143787i
$906$	7508.51	+	49271.7i	0.275335	+	1.80678i
$907$	−10343.3	−	17915.1i	−0.378659	−	0.655856i	0.612209	−	0.790696i	$-0.290281\pi$
$907$	−10343.3	−	17915.1i	−0.378659	−	0.655856i	−0.990867	+	0.134840i	$0.956948\pi$
$908$	−16483.1			−0.602434
$909$	−6840.10	+	2134.29i	−0.249584	+	0.0778766i
$910$	−35213.8			−1.28278
$911$	11820.0	+	20472.9i	0.429874	+	0.744563i	0.996862	−	0.0791627i	$-0.0252247\pi$
$911$	11820.0	+	20472.9i	0.429874	+	0.744563i	−0.566988	+	0.823726i	$0.691891\pi$
$912$	23418.0	+	9146.95i	0.850271	+	0.332111i
$913$	−11387.1	+	19723.1i	−0.412770	+	0.714939i
$914$	12490.9	−	21635.0i	0.452039	−	0.782955i
$915$	2724.58	−	2180.04i	0.0984390	−	0.0787648i
$916$	10028.2	+	17369.4i	0.361727	+	0.626529i
$917$	51075.0			1.83931
$918$	−21779.2	+	32281.6i	−0.783030	+	1.16062i
$919$	27335.2			0.981180			0.490590	−	0.871390i	$-0.336781\pi$
$919$	27335.2			0.981180			0.490590	+	0.871390i	$0.336781\pi$
$920$	−599.762	−	1038.82i	−0.0214930	−	0.0372270i
$921$	7345.05	−	5877.06i	0.262788	−	0.210267i
$922$	−3125.22	+	5413.04i	−0.111631	+	0.193350i
$923$	−17639.7	+	30552.8i	−0.629054	+	1.08955i
$924$	19129.9	+	7472.06i	0.681092	+	0.266031i
$925$	−2692.07	−	4662.79i	−0.0956914	−	0.165742i
$926$	−21861.7			−0.775832
$927$	−10474.3	−	9655.50i	−0.371112	−	0.342102i
$928$	36110.7			1.27736
$929$	6614.28	+	11456.3i	0.233593	+	0.404594i	0.958863	−	0.283870i	$-0.0916184\pi$
$929$	6614.28	+	11456.3i	0.233593	+	0.404594i	−0.725270	+	0.688464i	$0.758285\pi$
$930$	3732.16	+	24490.8i	0.131594	+	0.863534i
$931$	20421.2	−	35370.5i	0.718880	−	1.24514i
$932$	9608.47	−	16642.4i	0.337700	−	0.584913i
$933$	694.580	+	4557.91i	0.0243725	+	0.159935i
$934$	−32632.3	−	56520.9i	−1.14321	−	1.98011i
$935$	7713.11			0.269782
$936$	−8688.98	−	8009.75i	−0.303428	−	0.279708i
$937$	−18740.4			−0.653387			−0.326693	−	0.945130i	$-0.605934\pi$
$937$	−18740.4			−0.653387			−0.326693	+	0.945130i	$0.605934\pi$
$938$	−50386.3	−	87271.6i	−1.75391	−	3.03787i
$939$	−10721.3	−	4187.70i	−0.372607	−	0.145538i
$940$	−508.029	+	879.932i	−0.0176277	+	0.0305321i
$941$	−27244.5	+	47188.9i	−0.943832	+	1.63476i	−0.185758	+	0.982596i	$0.559474\pi$
$941$	−27244.5	+	47188.9i	−0.943832	+	1.63476i	−0.758074	+	0.652169i	$0.773859\pi$
$942$	−53245.6	+	42603.8i	−1.84165	+	1.47357i
$943$	2327.07	+	4030.61i	0.0803605	+	0.139188i
$944$	−46621.8			−1.60743
$945$	−9638.05	−	19766.3i	−0.331773	−	0.680420i
$946$	−10769.7			−0.370142
$947$	5641.35	+	9771.11i	0.193579	+	0.335289i	0.946434	−	0.322898i	$-0.104657\pi$
$947$	5641.35	+	9771.11i	0.193579	+	0.335289i	−0.752855	+	0.658187i	$0.771324\pi$
$948$	8477.99	−	6783.57i	0.290456	−	0.232405i
$949$	18524.4	−	32085.2i	0.633644	−	1.09750i
$950$	2991.31	−	5181.10i	0.102159	−	0.176944i
$951$	−3184.97	−	1244.03i	−0.108601	−	0.0424191i
$952$	8476.36	+	14681.5i	0.288572	+	0.499821i
$953$	−51190.0			−1.73999			−0.869994	−	0.493063i	$-0.835877\pi$
$953$	−51190.0			−1.73999			−0.869994	+	0.493063i	$0.835877\pi$
$954$	4057.09	−	1265.92i	0.137687	−	0.0429618i
$955$	−2997.93			−0.101582
$956$	744.741	+	1289.93i	0.0251952	+	0.0436394i
$957$	−2609.49	−	17123.7i	−0.0881428	−	0.578403i
$958$	6146.41	−	10645.9i	0.207288	−	0.359033i
$959$	10368.0	−	17957.8i	0.349113	−	0.604681i
$960$	938.003	+	6155.29i	0.0315353	+	0.206939i
$961$	−17457.4	−	30237.2i	−0.585997	−	1.01498i
$962$	48383.0			1.62155
$963$	12343.7	−	54904.1i	0.413053	−	1.83724i
$964$	−32000.0			−1.06914
$965$	11034.3	+	19112.0i	0.368091	+	0.637552i
$966$	18683.9	+	7297.84i	0.622303	+	0.243068i
$967$	−11571.8	+	20042.9i	−0.384822	+	0.666530i	−0.991744	−	0.128230i	$-0.959070\pi$
$967$	−11571.8	+	20042.9i	−0.384822	+	0.666530i	0.606923	+	0.794761i	$0.292404\pi$
$968$	−3275.38	+	5673.12i	−0.108755	+	0.188369i
$969$	−19178.7	+	15345.6i	−0.635818	+	0.508742i
$970$	1887.50	+	3269.25i	0.0624784	+	0.108216i
$971$	−34124.5			−1.12782			−0.563908	−	0.825838i	$-0.690703\pi$
$971$	−34124.5			−1.12782			−0.563908	+	0.825838i	$0.690703\pi$
$972$	−6578.56	+	21959.8i	−0.217086	+	0.724650i
$973$	−43355.6			−1.42848
$974$	19692.5	+	34108.4i	0.647831	+	1.12208i
$975$	−6078.87	+	4863.93i	−0.199671	+	0.159765i
$976$	−5089.58	+	8815.42i	−0.166920	+	0.289113i
$977$	18231.8	−	31578.5i	0.597020	−	1.03407i	−0.396239	−	0.918148i	$-0.629685\pi$
$977$	18231.8	−	31578.5i	0.597020	−	1.03407i	0.993258	−	0.115921i	$-0.0369820\pi$
$978$	4788.90	+	1870.52i	0.156577	+	0.0611581i
$979$	4321.34	+	7484.78i	0.141073	+	0.244346i
$980$	19358.6			0.631009
$981$	5482.06	−	24383.9i	0.178419	−	0.793597i
$982$	−53471.4			−1.73762
$983$	25770.8	+	44636.3i	0.836176	+	1.44830i	0.893070	+	0.449918i	$0.148547\pi$
$983$	25770.8	+	44636.3i	0.836176	+	1.44830i	−0.0568941	+	0.998380i	$0.518120\pi$
$984$	809.986	+	5315.22i	0.0262413	+	0.172198i
$985$	12017.9	−	20815.6i	0.388752	−	0.673339i
$986$	−22206.5	+	38462.8i	−0.717241	+	1.24230i
$987$	824.038	+	5407.43i	0.0265749	+	0.174387i
$988$	11576.8	+	20051.6i	0.372780	+	0.645675i
$989$	−4530.12			−0.145652
$990$	10064.3	−	3140.31i	0.323094	−	0.100814i
$991$	34299.1			1.09944			0.549721	−	0.835348i	$-0.314734\pi$
$991$	34299.1			1.09944			0.549721	+	0.835348i	$0.314734\pi$
$992$	−28703.5	−	49715.9i	−0.918685	−	1.59121i
$993$	25538.2	+	9975.10i	0.816144	+	0.318782i
$994$	34588.3	−	59908.8i	1.10370	−	1.91166i
$995$	−784.582	+	1358.94i	−0.0249979	+	0.0432976i
$996$	26840.9	−	21476.5i	0.853903	−	0.683241i
$997$	−10648.5	−	18443.7i	−0.338256	−	0.585877i	0.645849	−	0.763465i	$-0.276504\pi$
$997$	−10648.5	−	18443.7i	−0.338256	−	0.585877i	−0.984105	+	0.177589i	$0.943170\pi$
$998$	35414.2			1.12326
$999$	13242.5	+	27158.4i	0.419392	+	0.860113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.e.b.31.1	yes	6
3.2	odd	2		135.4.e.b.91.3		6
5.2	odd	4		225.4.k.c.49.5		12
5.3	odd	4		225.4.k.c.49.2		12
5.4	even	2		225.4.e.c.76.3		6
9.2	odd	6		135.4.e.b.46.3		6
9.4	even	3		405.4.a.h.1.3		3
9.5	odd	6		405.4.a.j.1.1		3
9.7	even	3	inner	45.4.e.b.16.1	✓	6
45.4	even	6		2025.4.a.s.1.1		3
45.7	odd	12		225.4.k.c.124.2		12
45.14	odd	6		2025.4.a.q.1.3		3
45.34	even	6		225.4.e.c.151.3		6
45.43	odd	12		225.4.k.c.124.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.b.16.1	✓	6	9.7	even	3	inner
45.4.e.b.31.1	yes	6	1.1	even	1	trivial
135.4.e.b.46.3		6	9.2	odd	6
135.4.e.b.91.3		6	3.2	odd	2
225.4.e.c.76.3		6	5.4	even	2
225.4.e.c.151.3		6	45.34	even	6
225.4.k.c.49.2		12	5.3	odd	4
225.4.k.c.49.5		12	5.2	odd	4
225.4.k.c.124.2		12	45.7	odd	12
225.4.k.c.124.5		12	45.43	odd	12
405.4.a.h.1.3		3	9.4	even	3
405.4.a.j.1.1		3	9.5	odd	6
2025.4.a.q.1.3		3	45.14	odd	6
2025.4.a.s.1.1		3	45.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87428 - 3.24635i) q^{2} +(-4.05724 + 3.24635i) q^{3} +(-3.02587 + 5.24096i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(18.1432 + 7.08665i) q^{6} +(15.6746 + 27.1492i) q^{7} -7.30318 q^{8} +(5.92239 - 26.3425i) q^{9} +O(q^{10})\)	\(q+(-1.87428 - 3.24635i) q^{2} +(-4.05724 + 3.24635i) q^{3} +(-3.02587 + 5.24096i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(18.1432 + 7.08665i) q^{6} +(15.6746 + 27.1492i) q^{7} -7.30318 q^{8} +(5.92239 - 26.3425i) q^{9} +18.7428 q^{10} +(10.4166 + 18.0422i) q^{11} +(-4.73733 - 31.0869i) q^{12} +(-29.9655 + 51.9018i) q^{13} +(58.7572 - 101.770i) q^{14} +(-3.91402 - 25.6842i) q^{15} +(37.8952 + 65.6364i) q^{16} -74.0460 q^{17} +(-96.6172 + 30.1471i) q^{18} -63.8390 q^{19} +(-15.1294 - 26.2048i) q^{20} +(-151.731 - 59.2655i) q^{21} +(39.0475 - 67.6322i) q^{22} +(16.4247 - 28.4484i) q^{23} +(29.6307 - 23.7087i) q^{24} +(-12.5000 - 21.6506i) q^{25} +224.655 q^{26} +(61.4884 + 126.104i) q^{27} -189.717 q^{28} +(80.0044 + 138.572i) q^{29} +(-76.0441 + 60.8458i) q^{30} +(127.187 - 220.294i) q^{31} +(112.840 - 195.444i) q^{32} +(-100.834 - 39.3853i) q^{33} +(138.783 + 240.379i) q^{34} -156.746 q^{35} +(120.139 + 110.748i) q^{36} +215.365 q^{37} +(119.652 + 207.244i) q^{38} +(-46.9143 - 307.857i) q^{39} +(18.2579 - 31.6237i) q^{40} +(-70.8407 + 122.700i) q^{41} +(91.9908 + 603.654i) q^{42} +(-68.9529 - 119.430i) q^{43} -126.078 q^{44} +(99.2602 + 91.5008i) q^{45} -123.138 q^{46} +(-16.7895 - 29.0803i) q^{47} +(-366.829 - 143.281i) q^{48} +(-319.885 + 554.058i) q^{49} +(-46.8571 + 81.1588i) q^{50} +(300.422 - 240.379i) q^{51} +(-181.344 - 314.096i) q^{52} -41.9914 q^{53} +(294.131 - 435.967i) q^{54} -104.166 q^{55} +(-114.474 - 198.275i) q^{56} +(259.010 - 207.244i) q^{57} +(299.902 - 519.445i) q^{58} +(-307.571 + 532.728i) q^{59} +(146.453 + 57.2040i) q^{60} +(67.1535 + 116.313i) q^{61} -953.535 q^{62} +(808.007 - 252.119i) q^{63} -239.652 q^{64} +(-149.828 - 259.509i) q^{65} +(61.1331 + 401.162i) q^{66} +(428.767 - 742.646i) q^{67} +(224.054 - 388.072i) q^{68} +(25.7146 + 168.742i) q^{69} +(293.786 + 508.852i) q^{70} +588.665 q^{71} +(-43.2522 + 192.384i) q^{72} -618.191 q^{73} +(-403.655 - 699.152i) q^{74} +(121.001 + 47.2624i) q^{75} +(193.169 - 334.578i) q^{76} +(-326.553 + 565.607i) q^{77} +(-911.481 + 729.311i) q^{78} +(172.644 + 299.029i) q^{79} -378.952 q^{80} +(-658.851 - 312.021i) q^{81} +531.102 q^{82} +(546.584 + 946.711i) q^{83} +(769.728 - 615.889i) q^{84} +(185.115 - 320.629i) q^{85} +(-258.474 + 447.691i) q^{86} +(-774.450 - 302.496i) q^{87} +(-76.0746 - 131.765i) q^{88} +414.849 q^{89} +(111.002 - 493.732i) q^{90} -1878.79 q^{91} +(99.3979 + 172.162i) q^{92} +(199.125 + 1306.68i) q^{93} +(-62.9366 + 109.009i) q^{94} +(159.598 - 276.431i) q^{95} +(176.663 + 1159.28i) q^{96} +(100.705 + 174.427i) q^{97} +2398.22 q^{98} +(536.967 - 167.547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + 9 q^{3} - 11 q^{4} - 15 q^{5} + 84 q^{6} + 43 q^{7} - 54 q^{8} + 57 q^{9}+O(q^{10}) \) 6 * q + q^2 + 9 * q^3 - 11 * q^4 - 15 * q^5 + 84 * q^6 + 43 * q^7 - 54 * q^8 + 57 * q^9	\( 6 q + q^{2} + 9 q^{3} - 11 q^{4} - 15 q^{5} + 84 q^{6} + 43 q^{7} - 54 q^{8} + 57 q^{9} - 10 q^{10} - 14 q^{11} + 75 q^{12} - 40 q^{13} + 27 q^{14} - 15 q^{15} + 13 q^{16} - 332 q^{17} + 3 q^{18} - 328 q^{19} - 55 q^{20} - 144 q^{21} + 376 q^{22} - 171 q^{23} - 63 q^{24} - 75 q^{25} + 868 q^{26} + 162 q^{27} - 1034 q^{28} + 335 q^{29} - 315 q^{30} + 352 q^{31} + 77 q^{32} - 708 q^{33} + 52 q^{34} - 430 q^{35} + 1086 q^{36} + 804 q^{37} + 178 q^{38} - 390 q^{39} + 135 q^{40} - 187 q^{41} + 513 q^{42} + 602 q^{43} + 1964 q^{44} + 330 q^{45} - 402 q^{46} - 665 q^{47} - 1074 q^{48} - 430 q^{49} + 25 q^{50} - 180 q^{51} + 456 q^{52} - 1460 q^{53} + 639 q^{54} + 140 q^{55} - 705 q^{56} - 486 q^{57} - 217 q^{58} + 298 q^{59} - 150 q^{60} + 1439 q^{61} - 3228 q^{62} + 2205 q^{63} - 3138 q^{64} - 200 q^{65} - 966 q^{66} + 1849 q^{67} + 710 q^{68} - 873 q^{69} + 135 q^{70} + 140 q^{71} + 261 q^{72} - 736 q^{73} + 320 q^{74} - 150 q^{75} - 204 q^{76} + 948 q^{77} - 432 q^{78} + 382 q^{79} - 130 q^{80} - 1251 q^{81} - 1150 q^{82} + 831 q^{83} - 909 q^{84} + 830 q^{85} - 1580 q^{86} + 258 q^{87} + 1428 q^{88} + 3438 q^{89} + 375 q^{90} - 1420 q^{91} + 1623 q^{92} + 2178 q^{93} + 2077 q^{94} + 820 q^{95} + 1155 q^{96} + 282 q^{97} + 4328 q^{98} - 762 q^{99}+O(q^{100}) \) 6 * q + q^2 + 9 * q^3 - 11 * q^4 - 15 * q^5 + 84 * q^6 + 43 * q^7 - 54 * q^8 + 57 * q^9 - 10 * q^10 - 14 * q^11 + 75 * q^12 - 40 * q^13 + 27 * q^14 - 15 * q^15 + 13 * q^16 - 332 * q^17 + 3 * q^18 - 328 * q^19 - 55 * q^20 - 144 * q^21 + 376 * q^22 - 171 * q^23 - 63 * q^24 - 75 * q^25 + 868 * q^26 + 162 * q^27 - 1034 * q^28 + 335 * q^29 - 315 * q^30 + 352 * q^31 + 77 * q^32 - 708 * q^33 + 52 * q^34 - 430 * q^35 + 1086 * q^36 + 804 * q^37 + 178 * q^38 - 390 * q^39 + 135 * q^40 - 187 * q^41 + 513 * q^42 + 602 * q^43 + 1964 * q^44 + 330 * q^45 - 402 * q^46 - 665 * q^47 - 1074 * q^48 - 430 * q^49 + 25 * q^50 - 180 * q^51 + 456 * q^52 - 1460 * q^53 + 639 * q^54 + 140 * q^55 - 705 * q^56 - 486 * q^57 - 217 * q^58 + 298 * q^59 - 150 * q^60 + 1439 * q^61 - 3228 * q^62 + 2205 * q^63 - 3138 * q^64 - 200 * q^65 - 966 * q^66 + 1849 * q^67 + 710 * q^68 - 873 * q^69 + 135 * q^70 + 140 * q^71 + 261 * q^72 - 736 * q^73 + 320 * q^74 - 150 * q^75 - 204 * q^76 + 948 * q^77 - 432 * q^78 + 382 * q^79 - 130 * q^80 - 1251 * q^81 - 1150 * q^82 + 831 * q^83 - 909 * q^84 + 830 * q^85 - 1580 * q^86 + 258 * q^87 + 1428 * q^88 + 3438 * q^89 + 375 * q^90 - 1420 * q^91 + 1623 * q^92 + 2178 * q^93 + 2077 * q^94 + 820 * q^95 + 1155 * q^96 + 282 * q^97 + 4328 * q^98 - 762 * q^99

Introduction

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