LMFDB - Embedded newform 45.4.e.b.16.1

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			16.1
Root			$0.500000 - 0.0378788i$ of defining polynomial
Character	$\chi$	$=$	45.16
Dual form			45.4.e.b.31.1

$q$-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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	0.317255	+	0.948340i	$0.397239\pi$
$2$	−1.87428	+	3.24635i	−0.662659	+	1.14776i	−0.979914	+	0.199419i	$0.936095\pi$
$3$	−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	−0.0380969	−	0.999274i	$-0.512130\pi$
$7$	15.6746	−	27.1492i	0.846348	−	1.46592i	0.884445	−	0.466644i	$-0.154537\pi$
$8$	−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	−0.687214	−	0.726455i	$-0.741166\pi$
$11$	10.4166	−	18.0422i	0.285522	−	0.494538i	0.972736	+	0.231917i	$0.0744998\pi$
$12$	−4.73733	+	31.0869i	−0.113962	+	0.747834i
$13$	−29.9655	−	51.9018i	−0.639303	−	1.10731i	−0.985586	−	0.169175i	$-0.945890\pi$
$13$	−29.9655	−	51.9018i	−0.639303	−	1.10731i	0.346283	−	0.938130i	$-0.387444\pi$
$14$	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	0.930823	−	0.365472i	$-0.119092\pi$
$23$	16.4247	+	28.4484i	0.148904	+	0.257909i	−0.781919	+	0.623380i	$0.785759\pi$
$24$	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	−0.487607	−	0.873063i	$-0.662130\pi$
$29$	80.0044	−	138.572i	0.512291	−	0.887314i	0.999898	−	0.0142513i	$-0.00453647\pi$
$30$	−76.0441	−	60.8458i	−0.462790	−	0.370296i
$31$	127.187	+	220.294i	0.736884	+	1.27632i	0.953892	+	0.300151i	$0.0970371\pi$
$31$	127.187	+	220.294i	0.736884	+	1.27632i	−0.217007	+	0.976170i	$0.569630\pi$
$32$	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	0.698980	−	0.715141i	$-0.253638\pi$
$41$	−70.8407	−	122.700i	−0.269841	−	0.467377i	−0.968820	+	0.247764i	$0.920304\pi$
$42$	91.9908	−	603.654i	0.337964	−	2.21776i
$43$	−68.9529	+	119.430i	−0.244540	+	0.423556i	−0.962002	−	0.273042i	$-0.911970\pi$
$43$	−68.9529	+	119.430i	−0.244540	+	0.423556i	0.717462	+	0.696597i	$0.245304\pi$
$44$	−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	−0.890902	−	0.454195i	$-0.849927\pi$
$47$	−16.7895	+	29.0803i	−0.0521064	+	0.0902509i	0.838796	+	0.544446i	$0.183260\pi$
$48$	−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	−0.975378	−	0.220541i	$-0.929218\pi$
$59$	−307.571	−	532.728i	−0.678683	−	1.17551i	0.296694	−	0.954973i	$-0.404116\pi$
$60$	146.453	−	57.2040i	0.315118	−	0.123083i
$61$	67.1535	−	116.313i	0.140953	−	0.244137i	−0.786903	−	0.617077i	$-0.788317\pi$
$61$	67.1535	−	116.313i	0.140953	−	0.244137i	0.927856	+	0.372939i	$0.121650\pi$
$62$	−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	0.930878	+	0.365329i	$0.119044\pi$
$67$	428.767	+	742.646i	0.781824	+	1.35416i	−0.149055	+	0.988829i	$0.547623\pi$
$68$	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	−0.716503	−	0.697584i	$-0.754259\pi$
$79$	172.644	−	299.029i	0.245873	−	0.425865i	0.962377	+	0.271718i	$0.0875919\pi$
$80$	−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	−0.237023	−	0.971504i	$-0.576172\pi$
$83$	546.584	−	946.711i	0.722836	−	1.25199i	0.959859	−	0.280484i	$-0.0904950\pi$
$84$	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	−0.808494	−	0.588505i	$-0.799717\pi$
$97$	100.705	−	174.427i	0.105413	−	0.182581i	0.913907	+	0.405924i	$0.133050\pi$
$98$	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	−0.923957	−	0.382498i	$-0.875064\pi$
$101$	−132.691	+	229.828i	−0.130726	+	0.226424i	0.793231	+	0.608921i	$0.208397\pi$
$102$	−1343.43	+	524.738i	−1.30411	+	0.509380i
$103$	263.809	+	456.931i	0.252368	+	0.437114i	0.964177	−	0.265259i	$-0.0854574\pi$
$103$	263.809	+	456.931i	0.252368	+	0.437114i	−0.711810	+	0.702373i	$0.752124\pi$
$104$	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	0.729721	−	0.683745i	$-0.239650\pi$
$113$	−273.009	−	472.866i	−0.227279	−	0.393659i	−0.957001	+	0.290085i	$0.906316\pi$
$114$	−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	0.998711	+	0.0507502i	$0.0161612\pi$
$131$	814.614	+	1410.95i	0.543307	+	0.941035i	−0.455405	+	0.890285i	$0.650505\pi$
$132$	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	−0.950529	−	0.310635i	$-0.899458\pi$
$137$	−330.725	+	572.833i	−0.206246	+	0.357229i	0.744283	+	0.667865i	$0.232792\pi$
$138$	499.600	+	399.749i	0.308180	+	0.246586i
$139$	−691.495	−	1197.70i	−0.421955	−	0.730848i	0.574175	−	0.818732i	$-0.305323\pi$
$139$	−691.495	−	1197.70i	−0.421955	−	0.730848i	−0.996131	+	0.0878842i	$0.971989\pi$
$140$	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	−0.862328	−	0.506349i	$-0.830995\pi$
$149$	−1581.75	−	2739.66i	−0.869676	−	1.50632i	−0.00734719	−	0.999973i	$-0.502339\pi$
$150$	−73.3598	+	481.395i	−0.0399320	+	0.262038i
$151$	1279.40	−	2215.98i	0.689509	−	1.19427i	−0.282488	−	0.959271i	$-0.591160\pi$
$151$	1279.40	−	2215.98i	0.689509	−	1.19427i	0.971997	−	0.234994i	$-0.0755071\pi$
$152$	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	−0.840073	−	0.542474i	$-0.817488\pi$
$157$	−1750.48	−	3031.92i	−0.889832	−	1.54123i	−0.0497594	−	0.998761i	$-0.515845\pi$
$158$	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	0.896829	+	0.442377i	$0.145865\pi$
$167$	1794.53	+	3108.21i	0.831524	+	1.44024i	−0.0653054	+	0.997865i	$0.520802\pi$
$168$	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	−0.903853	−	0.427844i	$-0.859273\pi$
$173$	−185.228	+	320.824i	−0.0814024	+	0.140993i	0.822450	+	0.568837i	$0.192607\pi$
$174$	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	−0.803636	−	0.595121i	$-0.797104\pi$
$191$	299.793	−	519.257i	0.113572	−	0.196713i	0.917208	+	0.398409i	$0.130437\pi$
$192$	972.326	+	777.995i	0.365477	+	0.292432i
$193$	2206.87	+	3822.40i	0.823076	+	1.42561i	0.903381	+	0.428839i	$0.141077\pi$
$193$	2206.87	+	3822.40i	0.823076	+	1.42561i	−0.0803048	+	0.996770i	$0.525589\pi$
$194$	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	0.595605	−	0.803277i	$-0.296912\pi$
$211$	−1219.41	−	2112.08i	−0.397856	−	0.689106i	−0.993461	+	0.114171i	$0.963579\pi$
$212$	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	−0.635959	−	0.771722i	$-0.719395\pi$
$223$	1166.71	−	2020.79i	0.350352	−	0.606827i	0.986311	+	0.164896i	$0.0527288\pi$
$224$	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	−0.595313	−	0.803494i	$-0.702972\pi$
$227$	1361.85	−	2358.79i	0.398189	−	0.689684i	0.993503	+	0.113810i	$0.0363054\pi$
$228$	302.426	−	1984.56i	0.0878451	−	0.576449i
$229$	1657.08	+	2870.15i	0.478179	+	0.828230i	0.999687	−	0.0250162i	$-0.00796375\pi$
$229$	1657.08	+	2870.15i	0.478179	+	0.828230i	−0.521508	+	0.853246i	$0.674630\pi$
$230$	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	0.882198	−	0.470878i	$-0.156063\pi$
$239$	123.062	+	213.150i	0.0333064	+	0.0576884i	−0.848892	+	0.528567i	$0.822730\pi$
$240$	1537.50	+	1230.21i	0.413521	+	0.330874i
$241$	2643.87	−	4579.31i	0.706666	−	1.22398i	−0.259421	−	0.965764i	$-0.583532\pi$
$241$	2643.87	−	4579.31i	0.706666	−	1.22398i	0.966087	−	0.258217i	$-0.0831349\pi$
$242$	−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	0.957412	−	0.288725i	$-0.0932313\pi$
$257$	942.096	+	1631.76i	0.228663	+	0.396056i	−0.728749	+	0.684781i	$0.759898\pi$
$258$	−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	−0.896618	−	0.442804i	$-0.853984\pi$
$263$	−276.506	+	478.922i	−0.0648292	+	0.112287i	0.831789	+	0.555092i	$0.187317\pi$
$264$	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	−0.410690	−	0.911775i	$-0.634712\pi$
$277$	2693.63	−	4665.50i	0.584275	−	1.01199i	0.994965	−	0.100220i	$-0.0319546\pi$
$278$	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	−0.993040	−	0.117781i	$-0.962422\pi$
$281$	−1858.35	+	3218.76i	−0.394519	+	0.683327i	0.598521	+	0.801107i	$0.295755\pi$
$282$	−98.5340	+	646.591i	−0.0208071	+	0.136539i
$283$	−1384.38	−	2397.81i	−0.290787	−	0.503658i	0.683209	−	0.730223i	$-0.260584\pi$
$283$	−1384.38	−	2397.81i	−0.290787	−	0.503658i	−0.973996	+	0.226565i	$0.927250\pi$
$284$	−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	0.985703	−	0.168491i	$-0.0538895\pi$
$293$	1740.00	+	3013.76i	0.346934	+	0.600907i	−0.638769	+	0.769398i	$0.720556\pi$
$294$	−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	0.903633	−	0.428308i	$-0.140890\pi$
$311$	443.649	+	768.422i	0.0808907	+	0.140107i	−0.822742	+	0.568415i	$0.807557\pi$
$312$	342.623	−	2248.33i	0.0621706	−	0.407970i
$313$	1107.57	−	1918.36i	0.200011	−	0.346429i	−0.748521	−	0.663111i	$-0.769236\pi$
$313$	1107.57	−	1918.36i	0.200011	−	0.346429i	0.948532	+	0.316682i	$0.102569\pi$
$314$	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	−0.835405	−	0.549635i	$-0.814767\pi$
$317$	329.023	−	569.884i	0.0582958	−	0.100971i	0.893700	+	0.448664i	$0.148100\pi$
$318$	−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	−0.997543	−	0.0700619i	$-0.977680\pi$
$331$	−2638.22	+	4569.53i	−0.438096	+	0.758804i	0.559447	+	0.828866i	$0.311014\pi$
$332$	−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	0.969288	−	0.245930i	$-0.0790934\pi$
$337$	1680.64	+	2910.95i	0.271662	+	0.470532i	−0.697626	+	0.716462i	$0.745760\pi$
$338$	−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	−0.959516	−	0.281653i	$-0.909117\pi$
$347$	−4677.77	−	8102.13i	−0.723677	−	1.25344i	0.235840	−	0.971792i	$-0.424216\pi$
$348$	3928.75	+	3143.55i	0.605182	+	0.484229i
$349$	−3519.65	+	6096.22i	−0.539836	+	0.935023i	0.459077	+	0.888397i	$0.348180\pi$
$349$	−3519.65	+	6096.22i	−0.539836	+	0.935023i	−0.998912	+	0.0466263i	$0.985153\pi$
$350$	−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	−0.979818	−	0.199891i	$-0.935941\pi$
$353$	−2101.09	+	3639.19i	−0.316798	+	0.548710i	0.663020	+	0.748602i	$0.269274\pi$
$354$	−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	−0.444357	−	0.895850i	$-0.646568\pi$
$367$	3892.55	−	6742.10i	0.553650	−	0.958950i	0.998007	−	0.0631004i	$-0.0200988\pi$
$368$	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	0.998727	+	0.0504412i	$0.0160627\pi$
$373$	3912.02	+	6775.81i	0.543047	+	0.940585i	−0.455680	+	0.890144i	$0.650604\pi$
$374$	−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	0.998307	−	0.0581644i	$-0.0185247\pi$
$383$	3363.82	+	5826.31i	0.448782	+	0.777313i	−0.549525	+	0.835477i	$0.685191\pi$
$384$	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	−0.667542	−	0.744572i	$-0.732654\pi$
$389$	2386.44	−	4133.43i	0.311047	−	0.538749i	0.978589	+	0.205823i	$0.0659871\pi$
$390$	−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	0.814314	−	0.580425i	$-0.197114\pi$
$401$	−766.916	−	1328.34i	−0.0955061	−	0.165421i	−0.909820	+	0.415004i	$0.863780\pi$
$402$	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	0.999360	+	0.0357796i	$0.0113914\pi$
$409$	4389.41	+	7602.68i	0.530666	+	0.919140i	−0.468694	+	0.883361i	$0.655275\pi$
$410$	−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	0.963327	−	0.268330i	$-0.0864719\pi$
$419$	2138.02	+	3703.17i	0.249282	+	0.431770i	−0.714044	+	0.700100i	$0.753139\pi$
$420$	742.557	−	4872.74i	0.0862692	−	0.566108i
$421$	−7231.64	+	12525.6i	−0.837169	+	1.45002i	0.0550823	+	0.998482i	$0.482458\pi$
$421$	−7231.64	+	12525.6i	−0.837169	+	1.45002i	−0.892252	+	0.451538i	$0.850875\pi$
$422$	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	0.235504	+	0.971873i	$0.424326\pi$
$439$	−6658.62	+	11533.1i	−0.723915	+	1.25386i	−0.959419	+	0.281984i	$0.909008\pi$
$440$	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	−0.174486	−	0.984660i	$-0.555826\pi$
$443$	7137.55	−	12362.6i	0.765497	−	1.32588i	0.939983	−	0.341220i	$-0.110840\pi$
$444$	−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	−0.643554	−	0.765401i	$-0.722541\pi$
$457$	3332.19	−	5771.53i	0.341080	−	0.590767i	0.984634	+	0.174633i	$0.0558741\pi$
$458$	−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	−0.905063	−	0.425278i	$-0.860176\pi$
$461$	−833.712	+	1444.03i	−0.0842295	+	0.145890i	0.820833	+	0.571168i	$0.193510\pi$
$462$	−9932.99	−	7947.76i	−1.00027	−	0.800354i
$463$	2916.01	+	5050.68i	0.292697	+	0.506966i	0.974446	−	0.224620i	$-0.0721140\pi$
$463$	2916.01	+	5050.68i	0.292697	+	0.506966i	−0.681750	+	0.731585i	$0.738781\pi$
$464$	−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	−0.777164	−	0.629298i	$-0.783343\pi$
$479$	1639.67	−	2839.99i	0.156406	−	0.270903i	0.933570	+	0.358395i	$0.116676\pi$
$480$	−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	0.981756	+	0.190144i	$0.0608956\pi$
$491$	7132.25	+	12353.4i	0.655548	+	1.13544i	−0.326208	+	0.945298i	$0.605771\pi$
$492$	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	0.572534	−	0.819881i	$-0.305961\pi$
$499$	−4723.70	−	8181.68i	−0.423771	−	0.733993i	−0.996305	+	0.0858882i	$0.972627\pi$
$500$	−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	0.622765	−	0.782409i	$-0.286009\pi$
$509$	−4205.32	−	7283.83i	−0.366204	−	0.634283i	−0.988969	+	0.148126i	$0.952676\pi$
$510$	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	−0.263922	−	0.964544i	$-0.585016\pi$
$547$	8998.24	−	15585.4i	0.703358	−	1.21825i	0.967281	−	0.253708i	$-0.0816504\pi$
$548$	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	−0.997922	−	0.0644370i	$-0.979475\pi$
$563$	−7410.91	−	12836.1i	−0.554765	−	0.960881i	0.443157	−	0.896444i	$-0.353858\pi$
$564$	−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	0.0733726	+	0.997305i	$0.476624\pi$
$569$	−11224.7	+	19441.8i	−0.827005	+	1.43241i	−0.900377	+	0.435110i	$0.856710\pi$
$570$	4854.58	+	3884.34i	0.356730	+	0.285433i
$571$	8006.75	+	13868.1i	0.586817	+	1.01640i	0.994646	+	0.103338i	$0.0329523\pi$
$571$	8006.75	+	13868.1i	0.586817	+	1.01640i	−0.407830	+	0.913058i	$0.633714\pi$
$572$	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	0.000582275		1.00000i	$0.499815\pi$
$587$	−12312.4	+	21325.7i	−0.865734	+	1.49950i	−0.866316	+	0.499496i	$0.833519\pi$
$588$	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	0.753862	−	0.657033i	$-0.228189\pi$
$599$	−2815.87	−	4877.24i	−0.192076	−	0.332685i	−0.945938	+	0.324347i	$0.894855\pi$
$600$	−883.692	+	345.166i	−0.0601276	+	0.0234855i
$601$	7375.88	−	12775.4i	0.500613	−	0.867087i	−0.499387	−	0.866379i	$-0.666441\pi$
$601$	7375.88	−	12775.4i	0.500613	−	0.867087i	1.00000		0.000707853i	$-0.000225317\pi$
$602$	−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	0.999978	−	0.00665872i	$-0.00211955\pi$
$607$	7391.04	+	12801.7i	0.494222	+	0.856018i	−0.505756	+	0.862677i	$0.668786\pi$
$608$	−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	0.920609	−	0.390485i	$-0.127693\pi$
$617$	1871.82	+	3242.09i	0.122134	+	0.211543i	−0.798475	+	0.602028i	$0.794360\pi$
$618$	8024.45	+	6420.67i	0.522315	+	0.417924i
$619$	−3069.37	+	5316.30i	−0.199303	+	0.345202i	−0.948303	−	0.317368i	$-0.897201\pi$
$619$	−3069.37	+	5316.30i	−0.199303	+	0.345202i	0.749000	+	0.662570i	$0.230534\pi$
$620$	−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	−0.629927	−	0.776654i	$-0.716915\pi$
$641$	5804.05	−	10052.9i	0.357639	−	0.619448i	0.987566	+	0.157206i	$0.0502487\pi$
$642$	37814.9	−	14770.3i	2.32466	−	0.908002i
$643$	6360.85	+	11017.3i	0.390120	+	0.675708i	0.992465	−	0.122528i	$-0.0391001\pi$
$643$	6360.85	+	11017.3i	0.390120	+	0.675708i	−0.602345	+	0.798236i	$0.705767\pi$
$644$	−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	0.974991	+	0.222247i	$0.0713390\pi$
$653$	11346.4	+	19652.5i	0.679966	+	1.17774i	−0.295024	+	0.955490i	$0.595328\pi$
$654$	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	−0.941007	−	0.338386i	$-0.890119\pi$
$659$	−3002.00	+	5199.61i	−0.177453	+	0.307357i	0.763555	+	0.645743i	$0.223452\pi$
$660$	493.471	−	3238.21i	0.0291035	−	0.190981i
$661$	−5958.18	−	10319.9i	−0.350600	−	0.607256i	0.635755	−	0.771891i	$-0.280689\pi$
$661$	−5958.18	−	10319.9i	−0.350600	−	0.607256i	−0.986355	+	0.164635i	$0.947356\pi$
$662$	−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	−0.539740	−	0.841832i	$-0.681477\pi$
$673$	8016.85	−	13885.6i	0.459178	−	0.795319i	0.998918	+	0.0465125i	$0.0148107\pi$
$674$	−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	−0.980712	−	0.195456i	$-0.937381\pi$
$677$	−5655.94	+	9796.38i	−0.321086	+	0.556138i	0.659626	+	0.751594i	$0.270715\pi$
$678$	−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	−0.985376	−	0.170392i	$-0.945497\pi$
$691$	−6268.93	+	10858.1i	−0.345125	+	0.597774i	0.640252	+	0.768165i	$0.278830\pi$
$692$	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	−0.938308	−	0.345802i	$-0.887607\pi$
$709$	−3203.33	+	5548.33i	−0.169681	+	0.293895i	0.768627	+	0.639697i	$0.220940\pi$
$710$	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	−0.984630	−	0.174655i	$-0.944119\pi$
$727$	−6685.46	+	11579.6i	−0.341059	+	0.590732i	0.643571	+	0.765387i	$0.277452\pi$
$728$	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	−0.942509	−	0.334181i	$-0.891540\pi$
$733$	−15095.5	−	26146.2i	−0.760663	−	1.31751i	0.181846	−	0.983327i	$-0.441793\pi$
$734$	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	0.923568	−	0.383434i	$-0.125259\pi$
$743$	2627.19	+	4550.42i	0.129720	+	0.224682i	−0.793848	+	0.608116i	$0.791925\pi$
$744$	−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	0.964819	+	0.262917i	$0.0846844\pi$
$751$	14614.4	+	25312.9i	0.710102	+	1.22993i	−0.254717	+	0.967016i	$0.581982\pi$
$752$	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	0.979652	−	0.200702i	$-0.0643221\pi$
$761$	6634.11	+	11490.6i	0.316014	+	0.547352i	−0.663639	+	0.748053i	$0.730989\pi$
$762$	−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	−0.917040	−	0.398796i	$-0.869428\pi$
$769$	−17142.9	−	29692.4i	−0.803887	−	1.39237i	0.113153	−	0.993578i	$-0.463905\pi$
$770$	−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	0.861980	−	0.506942i	$-0.169224\pi$
$787$	−177.400	−	307.265i	−0.00803509	−	0.0139172i	−0.870015	+	0.493025i	$0.835891\pi$
$788$	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	0.688011	−	0.725701i	$-0.258484\pi$
$797$	−6400.65	−	11086.2i	−0.284470	−	0.492717i	−0.972481	+	0.232984i	$0.925151\pi$
$798$	−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	−0.102612	+	0.994721i	$0.532720\pi$
$821$	−21471.9	+	37190.5i	−0.912760	+	1.58095i	−0.810148	+	0.586226i	$0.800613\pi$
$822$	−1940.96	+	12736.8i	−0.0823584	+	0.540445i
$823$	3958.46	+	6856.26i	0.167659	+	0.290394i	0.937596	−	0.347726i	$-0.113046\pi$
$823$	3958.46	+	6856.26i	0.167659	+	0.290394i	−0.769937	+	0.638119i	$0.779713\pi$
$824$	−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	−0.0208849	+	0.999782i	$0.506648\pi$
$839$	−21295.4	+	36884.7i	−0.876279	+	1.51776i	−0.855394	+	0.517978i	$0.826685\pi$
$840$	−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	0.468269	+	0.883586i	$0.344878\pi$
$853$	−13230.6	+	22916.0i	−0.531074	+	0.919847i	−0.999342	+	0.0362605i	$0.988455\pi$
$854$	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	−0.594803	−	0.803871i	$-0.702770\pi$
$857$	10004.5	−	17328.3i	0.398772	−	0.690693i	0.993575	+	0.113179i	$0.0361033\pi$
$858$	−22652.9	+	8848.12i	−0.901350	+	0.352063i
$859$	8909.03	+	15430.9i	0.353868	+	0.612917i	0.986923	−	0.161189i	$-0.0515330\pi$
$859$	8909.03	+	15430.9i	0.353868	+	0.612917i	−0.633056	+	0.774106i	$0.718200\pi$
$860$	−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	−0.999429	−	0.0338003i	$-0.989239\pi$
$877$	−13738.6	−	23796.0i	−0.528986	−	0.916231i	0.470442	−	0.882431i	$-0.344094\pi$
$878$	−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	0.750230	−	0.661177i	$-0.229943\pi$
$887$	−5216.89	−	9035.91i	−0.197481	−	0.342048i	−0.947711	+	0.319130i	$0.896609\pi$
$888$	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	−0.990867	−	0.134840i	$-0.956948\pi$
$907$	−10343.3	+	17915.1i	−0.378659	+	0.655856i	0.612209	+	0.790696i	$0.290281\pi$
$908$	−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	−0.566988	−	0.823726i	$-0.691891\pi$
$911$	11820.0	−	20472.9i	0.429874	−	0.744563i	0.996862	+	0.0791627i	$0.0252247\pi$
$912$	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	−0.725270	−	0.688464i	$-0.758285\pi$
$929$	6614.28	−	11456.3i	0.233593	−	0.404594i	0.958863	+	0.283870i	$0.0916184\pi$
$930$	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	−0.758074	−	0.652169i	$-0.773859\pi$
$941$	−27244.5	−	47188.9i	−0.943832	−	1.63476i	−0.185758	−	0.982596i	$-0.559474\pi$
$942$	−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	−0.752855	−	0.658187i	$-0.771324\pi$
$947$	5641.35	−	9771.11i	0.193579	−	0.335289i	0.946434	+	0.322898i	$0.104657\pi$
$948$	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	0.606923	−	0.794761i	$-0.292404\pi$
$967$	−11571.8	−	20042.9i	−0.384822	−	0.666530i	−0.991744	+	0.128230i	$0.959070\pi$
$968$	−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	0.993258	+	0.115921i	$0.0369820\pi$
$977$	18231.8	+	31578.5i	0.597020	+	1.03407i	−0.396239	+	0.918148i	$0.629685\pi$
$978$	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	−0.0568941	−	0.998380i	$-0.518120\pi$
$983$	25770.8	−	44636.3i	0.836176	−	1.44830i	0.893070	−	0.449918i	$-0.148547\pi$
$984$	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	−0.984105	−	0.177589i	$-0.943170\pi$
$997$	−10648.5	+	18443.7i	−0.338256	+	0.585877i	0.645849	+	0.763465i	$0.276504\pi$
$998$	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.16.1	✓	6
3.2	odd	2		135.4.e.b.46.3		6
5.2	odd	4		225.4.k.c.124.2		12
5.3	odd	4		225.4.k.c.124.5		12
5.4	even	2		225.4.e.c.151.3		6
9.2	odd	6		405.4.a.j.1.1		3
9.4	even	3	inner	45.4.e.b.31.1	yes	6
9.5	odd	6		135.4.e.b.91.3		6
9.7	even	3		405.4.a.h.1.3		3
45.4	even	6		225.4.e.c.76.3		6
45.13	odd	12		225.4.k.c.49.2		12
45.22	odd	12		225.4.k.c.49.5		12
45.29	odd	6		2025.4.a.q.1.3		3
45.34	even	6		2025.4.a.s.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.b.16.1	✓	6	1.1	even	1	trivial
45.4.e.b.31.1	yes	6	9.4	even	3	inner
135.4.e.b.46.3		6	3.2	odd	2
135.4.e.b.91.3		6	9.5	odd	6
225.4.e.c.76.3		6	45.4	even	6
225.4.e.c.151.3		6	5.4	even	2
225.4.k.c.49.2		12	45.13	odd	12
225.4.k.c.49.5		12	45.22	odd	12
225.4.k.c.124.2		12	5.2	odd	4
225.4.k.c.124.5		12	5.3	odd	4
405.4.a.h.1.3		3	9.7	even	3
405.4.a.j.1.1		3	9.2	odd	6
2025.4.a.q.1.3		3	45.29	odd	6
2025.4.a.s.1.1		3	45.34	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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