LMFDB - Embedded newform 115.5.i.a.14.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,5,Mod(14,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 21]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("115.14");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	115.i (of order $22$, degree $10$, 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:	$11.8875457546$
Analytic rank:	$0$
Dimension:	$460$
Relative dimension:	$46$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			14.12
Character	$\chi$	$=$	115.14
Dual form			115.5.i.a.74.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33057 - 4.53150i) q^{2} +(-3.81868 + 3.30890i) q^{3} +(-5.30401 + 3.40868i) q^{4} +(-24.7617 + 3.44348i) q^{5} +(20.0753 + 12.9016i) q^{6} +(3.15920 - 6.91768i) q^{7} +(-34.6044 - 29.9848i) q^{8} +(-7.89404 + 54.9042i) q^{9} +O(q^{10})$	\(q+(-1.33057 - 4.53150i) q^{2} +(-3.81868 + 3.30890i) q^{3} +(-5.30401 + 3.40868i) q^{4} +(-24.7617 + 3.44348i) q^{5} +(20.0753 + 12.9016i) q^{6} +(3.15920 - 6.91768i) q^{7} +(-34.6044 - 29.9848i) q^{8} +(-7.89404 + 54.9042i) q^{9} +(48.5512 + 107.626i) q^{10} +(-10.5472 + 35.9204i) q^{11} +(8.97531 - 30.5671i) q^{12} +(208.126 - 95.0478i) q^{13} +(-35.5510 - 5.11146i) q^{14} +(83.1629 - 95.0837i) q^{15} +(-131.739 + 288.468i) q^{16} +(74.6018 + 47.9437i) q^{17} +(259.302 - 37.2820i) q^{18} +(229.805 + 357.584i) q^{19} +(119.599 - 102.669i) q^{20} +(10.8260 + 36.8699i) q^{21} +176.807 q^{22} +(528.810 - 14.1665i) q^{23} +231.360 q^{24} +(601.285 - 170.533i) q^{25} +(-707.634 - 816.654i) q^{26} +(-372.801 - 580.090i) q^{27} +(6.82374 + 47.4601i) q^{28} +(-40.1429 - 25.7983i) q^{29} +(-541.525 - 250.337i) q^{30} +(368.684 - 425.484i) q^{31} +(757.329 + 108.888i) q^{32} +(-78.5808 - 172.068i) q^{33} +(117.994 - 401.850i) q^{34} +(-54.4063 + 182.172i) q^{35} +(-145.281 - 318.121i) q^{36} +(-114.204 + 794.304i) q^{37} +(1314.62 - 1517.15i) q^{38} +(-480.261 + 1051.63i) q^{39} +(960.115 + 623.317i) q^{40} +(-57.4622 - 399.658i) q^{41} +(152.671 - 98.1158i) q^{42} +(629.375 + 726.337i) q^{43} +(-66.4987 - 226.474i) q^{44} +(6.40851 - 1386.71i) q^{45} +(-767.813 - 2377.45i) q^{46} +76.6209i q^{47} +(-451.445 - 1537.48i) q^{48} +(1534.45 + 1770.85i) q^{49} +(-1572.82 - 2497.82i) q^{50} +(-443.521 + 63.7687i) q^{51} +(-779.913 + 1213.57i) q^{52} +(-1683.47 + 3686.29i) q^{53} +(-2132.64 + 2461.20i) q^{54} +(137.475 - 925.769i) q^{55} +(-316.748 + 144.654i) q^{56} +(-2060.76 - 605.095i) q^{57} +(-63.4920 + 216.234i) q^{58} +(2552.80 + 5589.84i) q^{59} +(-116.987 + 787.800i) q^{60} +(2994.32 + 2594.59i) q^{61} +(-2418.64 - 1104.56i) q^{62} +(354.871 + 228.062i) q^{63} +(207.855 + 1445.66i) q^{64} +(-4826.25 + 3070.22i) q^{65} +(-675.169 + 585.037i) q^{66} +(-3601.18 + 1057.40i) q^{67} -559.113 q^{68} +(-1972.48 + 1803.88i) q^{69} +(897.905 + 4.14957i) q^{70} +(-3685.45 + 1082.15i) q^{71} +(1919.46 - 1663.22i) q^{72} +(-972.683 - 1513.52i) q^{73} +(3751.34 - 539.362i) q^{74} +(-1731.84 + 2640.80i) q^{75} +(-2437.78 - 1113.30i) q^{76} +(215.165 + 186.442i) q^{77} +(5404.46 + 777.044i) q^{78} +(4707.01 - 2149.62i) q^{79} +(2268.75 - 7596.61i) q^{80} +(-967.906 - 284.203i) q^{81} +(-1734.59 + 792.162i) q^{82} +(802.374 - 5580.63i) q^{83} +(-183.099 - 158.656i) q^{84} +(-2012.36 - 930.278i) q^{85} +(2453.97 - 3818.45i) q^{86} +(238.657 - 34.3137i) q^{87} +(1442.05 - 926.746i) q^{88} +(-7690.82 + 6664.13i) q^{89} +(-6292.38 + 1816.07i) q^{90} -1740.02i q^{91} +(-2756.53 + 1877.68i) q^{92} +2844.73i q^{93} +(347.208 - 101.949i) q^{94} +(-6921.70 - 8063.06i) q^{95} +(-3252.30 + 2090.12i) q^{96} +(933.932 + 6495.64i) q^{97} +(5982.90 - 9309.57i) q^{98} +(-1888.92 - 862.642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 460 q + 306 q^{4} - 11 q^{5} - 182 q^{6} + 944 q^{9}+O(q^{10}) $ 460 * q + 306 * q^4 - 11 * q^5 - 182 * q^6 + 944 * q^9	$ 460 q + 306 q^{4} - 11 q^{5} - 182 q^{6} + 944 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 1474 q^{15} - 2670 q^{16} - 22 q^{19} + 3157 q^{20} - 22 q^{21} + 3896 q^{24} - 1427 q^{25} - 3166 q^{26} - 2808 q^{29} + 1397 q^{30} + 2684 q^{31} - 12848 q^{34} + 2279 q^{35} + 1114 q^{36} + 12866 q^{39} - 11 q^{40} - 2652 q^{41} + 11110 q^{44} - 5394 q^{46} - 27026 q^{49} - 10931 q^{50} - 22 q^{51} - 51290 q^{54} - 10545 q^{55} + 25322 q^{56} + 41460 q^{59} + 49269 q^{60} - 22506 q^{61} + 68582 q^{64} + 27940 q^{65} - 24332 q^{66} + 7608 q^{69} - 15618 q^{70} + 35838 q^{71} - 59158 q^{74} + 30594 q^{75} - 58520 q^{76} - 17930 q^{79} - 63602 q^{80} + 91888 q^{81} + 92906 q^{84} - 33815 q^{85} + 101486 q^{86} - 22 q^{89} - 37598 q^{90} - 46242 q^{94} + 43336 q^{95} - 210180 q^{96} + 44528 q^{99}+O(q^{100}) $ 460 * q + 306 * q^4 - 11 * q^5 - 182 * q^6 + 944 * q^9 - 11 * q^10 - 22 * q^11 - 22 * q^14 - 1474 * q^15 - 2670 * q^16 - 22 * q^19 + 3157 * q^20 - 22 * q^21 + 3896 * q^24 - 1427 * q^25 - 3166 * q^26 - 2808 * q^29 + 1397 * q^30 + 2684 * q^31 - 12848 * q^34 + 2279 * q^35 + 1114 * q^36 + 12866 * q^39 - 11 * q^40 - 2652 * q^41 + 11110 * q^44 - 5394 * q^46 - 27026 * q^49 - 10931 * q^50 - 22 * q^51 - 51290 * q^54 - 10545 * q^55 + 25322 * q^56 + 41460 * q^59 + 49269 * q^60 - 22506 * q^61 + 68582 * q^64 + 27940 * q^65 - 24332 * q^66 + 7608 * q^69 - 15618 * q^70 + 35838 * q^71 - 59158 * q^74 + 30594 * q^75 - 58520 * q^76 - 17930 * q^79 - 63602 * q^80 + 91888 * q^81 + 92906 * q^84 - 33815 * q^85 + 101486 * q^86 - 22 * q^89 - 37598 * q^90 - 46242 * q^94 + 43336 * q^95 - 210180 * q^96 + 44528 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{21}{22}\right)$

Coefficient data

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

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

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

$2$	−1.33057	−	4.53150i	−0.332642	−	1.13287i	−0.940773	−	0.339038i	$-0.889899\pi$
$2$	−1.33057	−	4.53150i	−0.332642	−	1.13287i	0.608131	−	0.793837i	$-0.291920\pi$
$3$	−3.81868	+	3.30890i	−0.424298	+	0.367656i	−0.840679	−	0.541534i	$-0.817844\pi$
$3$	−3.81868	+	3.30890i	−0.424298	+	0.367656i	0.416381	+	0.909190i	$0.363298\pi$
$4$	−5.30401	+	3.40868i	−0.331501	+	0.213042i
$5$	−24.7617	+	3.44348i	−0.990469	+	0.137739i
$5$	−24.7617	+	3.44348i	−0.990469	+	0.137739i
$6$	20.0753	+	12.9016i	0.557647	+	0.358378i
$7$	3.15920	−	6.91768i	0.0644734	−	0.141177i	−0.874652	−	0.484751i	$-0.838910\pi$
$7$	3.15920	−	6.91768i	0.0644734	−	0.141177i	0.939126	+	0.343574i	$0.111638\pi$
$8$	−34.6044	−	29.9848i	−0.540693	−	0.468513i
$9$	−7.89404	+	54.9042i	−0.0974573	+	0.677830i
$10$	48.5512	+	107.626i	0.485512	+	1.07626i
$11$	−10.5472	+	35.9204i	−0.0871667	+	0.296863i	−0.991526	−	0.129910i	$-0.958531\pi$
$11$	−10.5472	+	35.9204i	−0.0871667	+	0.296863i	0.904359	+	0.426772i	$0.140349\pi$
$12$	8.97531	−	30.5671i	0.0623286	−	0.212272i
$13$	208.126	−	95.0478i	1.23151	−	0.562413i	0.309991	−	0.950739i	$-0.399674\pi$
$13$	208.126	−	95.0478i	1.23151	−	0.562413i	0.921522	+	0.388326i	$0.126947\pi$
$14$	−35.5510	−	5.11146i	−0.181383	−	0.0260789i
$15$	83.1629	−	95.0837i	0.369613	−	0.422594i
$16$	−131.739	+	288.468i	−0.514606	+	1.12683i
$17$	74.6018	+	47.9437i	0.258138	+	0.165895i	0.663309	−	0.748346i	$-0.269152\pi$
$17$	74.6018	+	47.9437i	0.258138	+	0.165895i	−0.405171	+	0.914241i	$0.632788\pi$
$18$	259.302	−	37.2820i	0.800315	−	0.115068i
$19$	229.805	+	357.584i	0.636579	+	0.990537i	0.998302	+	0.0582511i	$0.0185524\pi$
$19$	229.805	+	357.584i	0.636579	+	0.990537i	−0.361723	+	0.932286i	$0.617811\pi$
$20$	119.599	−	102.669i	0.298997	−	0.256672i
$21$	10.8260	+	36.8699i	0.0245487	+	0.0836052i
$22$	176.807			0.365303
$23$	528.810	−	14.1665i	0.999641	−	0.0267798i
$23$	528.810	−	14.1665i	0.999641	−	0.0267798i
$24$	231.360			0.401667
$25$	601.285	−	170.533i	0.962056	−	0.272852i
$26$	−707.634	−	816.654i	−1.04680	−	1.20807i
$27$	−372.801	−	580.090i	−0.511387	−	0.795734i
$28$	6.82374	+	47.4601i	0.00870375	+	0.0605359i
$29$	−40.1429	−	25.7983i	−0.0477324	−	0.0306757i	0.516557	−	0.856253i	$-0.327213\pi$
$29$	−40.1429	−	25.7983i	−0.0477324	−	0.0306757i	−0.564289	+	0.825577i	$0.690850\pi$
$30$	−541.525	−	250.337i	−0.601695	−	0.278153i
$31$	368.684	−	425.484i	0.383646	−	0.442751i	−0.530777	−	0.847512i	$-0.678100\pi$
$31$	368.684	−	425.484i	0.383646	−	0.442751i	0.914423	+	0.404760i	$0.132645\pi$
$32$	757.329	+	108.888i	0.739579	+	0.106335i
$33$	−78.5808	−	172.068i	−0.0721587	−	0.158005i
$34$	117.994	−	401.850i	0.102071	−	0.347621i
$35$	−54.4063	+	182.172i	−0.0444133	+	0.148712i
$36$	−145.281	−	318.121i	−0.112099	−	0.245464i
$37$	−114.204	+	794.304i	−0.0834212	+	0.580207i	0.904644	+	0.426169i	$0.140137\pi$
$37$	−114.204	+	794.304i	−0.0834212	+	0.580207i	−0.988065	+	0.154038i	$0.950772\pi$
$38$	1314.62	−	1517.15i	0.910401	−	1.05066i
$39$	−480.261	+	1051.63i	−0.315753	+	0.691404i
$40$	960.115	+	623.317i	0.600072	+	0.389573i
$41$	−57.4622	−	399.658i	−0.0341833	−	0.237750i	0.965566	−	0.260160i	$-0.0837753\pi$
$41$	−57.4622	−	399.658i	−0.0341833	−	0.237750i	−0.999749	+	0.0224096i	$0.992866\pi$
$42$	152.671	−	98.1158i	0.0865483	−	0.0556212i
$43$	629.375	+	726.337i	0.340387	+	0.392827i	0.899973	−	0.435945i	$-0.143586\pi$
$43$	629.375	+	726.337i	0.340387	+	0.392827i	−0.559587	+	0.828772i	$0.689040\pi$
$44$	−66.4987	−	226.474i	−0.0343485	−	0.116980i
$45$	6.40851	−	1386.71i	0.00316470	−	0.684793i
$46$	−767.813	−	2377.45i	−0.362861	−	1.12356i
$47$			76.6209i			0.0346858i	0.999850	+	0.0173429i	$0.00552069\pi$
$47$			76.6209i			0.0346858i	−0.999850	+	0.0173429i	$0.994479\pi$
$48$	−451.445	−	1537.48i	−0.195940	−	0.667309i
$49$	1534.45	+	1770.85i	0.639087	+	0.737545i
$50$	−1572.82	−	2497.82i	−0.629128	−	0.999127i
$51$	−443.521	+	63.7687i	−0.170520	+	0.0245170i
$52$	−779.913	+	1213.57i	−0.288429	+	0.448805i
$53$	−1683.47	+	3686.29i	−0.599314	+	1.31232i	0.330333	+	0.943864i	$0.392839\pi$
$53$	−1683.47	+	3686.29i	−0.599314	+	1.31232i	−0.929647	+	0.368451i	$0.879888\pi$
$54$	−2132.64	+	2461.20i	−0.731358	+	0.844033i
$55$	137.475	−	925.769i	0.0454463	−	0.306039i
$56$	−316.748	+	144.654i	−0.101004	+	0.0461269i
$57$	−2060.76	−	605.095i	−0.634276	−	0.186240i
$58$	−63.4920	+	216.234i	−0.0188740	+	0.0642788i
$59$	2552.80	+	5589.84i	0.733351	+	1.60582i	0.794191	+	0.607668i	$0.207895\pi$
$59$	2552.80	+	5589.84i	0.733351	+	1.60582i	−0.0608397	+	0.998148i	$0.519378\pi$
$60$	−116.987	+	787.800i	−0.0324964	+	0.218833i
$61$	2994.32	+	2594.59i	0.804708	+	0.697283i	0.956693	−	0.291099i	$-0.0940211\pi$
$61$	2994.32	+	2594.59i	0.804708	+	0.697283i	−0.151985	+	0.988383i	$0.548567\pi$
$62$	−2418.64	−	1104.56i	−0.629199	−	0.287345i
$63$	354.871	+	228.062i	0.0894107	+	0.0574608i
$64$	207.855	+	1445.66i	0.0507458	+	0.352945i
$65$	−4826.25	+	3070.22i	−1.14231	+	0.726680i
$66$	−675.169	+	585.037i	−0.154997	+	0.134306i
$67$	−3601.18	+	1057.40i	−0.802224	+	0.235554i	−0.657045	−	0.753851i	$-0.728194\pi$
$67$	−3601.18	+	1057.40i	−0.802224	+	0.235554i	−0.145179	+	0.989405i	$0.546376\pi$
$68$	−559.113			−0.120915
$69$	−1972.48	+	1803.88i	−0.414300	+	0.378887i
$70$	897.905	+	4.14957i	0.183246	+	0.000846850i
$71$	−3685.45	+	1082.15i	−0.731096	+	0.214669i	−0.626033	−	0.779796i	$-0.715323\pi$
$71$	−3685.45	+	1082.15i	−0.731096	+	0.214669i	−0.105063	+	0.994466i	$0.533504\pi$
$72$	1919.46	−	1663.22i	0.370267	−	0.320838i
$73$	−972.683	−	1513.52i	−0.182526	−	0.284016i	0.737918	−	0.674891i	$-0.235809\pi$
$73$	−972.683	−	1513.52i	−0.182526	−	0.284016i	−0.920444	+	0.390874i	$0.872173\pi$
$74$	3751.34	−	539.362i	0.685051	−	0.0984955i
$75$	−1731.84	+	2640.80i	−0.307882	+	0.469476i
$76$	−2437.78	−	1113.30i	−0.422053	−	0.192745i
$77$	215.165	+	186.442i	0.0362903	+	0.0314457i
$78$	5404.46	+	777.044i	0.888307	+	0.127719i
$79$	4707.01	−	2149.62i	0.754208	−	0.344435i	−0.000931437	−	1.00000i	$-0.500296\pi$
$79$	4707.01	−	2149.62i	0.754208	−	0.344435i	0.755139	+	0.655564i	$0.227569\pi$
$80$	2268.75	−	7596.61i	0.354493	−	1.18697i
$81$	−967.906	−	284.203i	−0.147524	−	0.0433170i
$82$	−1734.59	+	792.162i	−0.257970	+	0.117811i
$83$	802.374	−	5580.63i	0.116472	−	0.810079i	−0.844920	−	0.534893i	$-0.820352\pi$
$83$	802.374	−	5580.63i	0.116472	−	0.810079i	0.961391	−	0.275185i	$-0.0887391\pi$
$84$	−183.099	−	158.656i	−0.0259494	−	0.0224853i
$85$	−2012.36	−	930.278i	−0.278527	−	0.128758i
$86$	2453.97	−	3818.45i	0.331797	−	0.516286i
$87$	238.657	−	34.3137i	0.0315308	−	0.00453345i
$88$	1442.05	−	926.746i	0.186215	−	0.119673i
$89$	−7690.82	+	6664.13i	−0.970941	+	0.841325i	−0.987352	−	0.158541i	$-0.949321\pi$
$89$	−7690.82	+	6664.13i	−0.970941	+	0.841325i	0.0164119	+	0.999865i	$0.494776\pi$
$90$	−6292.38	+	1816.07i	−0.776838	+	0.224206i
$91$		−	1740.02i		−	0.210122i
$92$	−2756.53	+	1877.68i	−0.325676	+	0.221844i
$93$			2844.73i			0.328908i
$94$	347.208	−	101.949i	0.0392947	−	0.0115380i
$95$	−6921.70	−	8063.06i	−0.766947	−	0.893414i
$96$	−3252.30	+	2090.12i	−0.352897	+	0.226793i
$97$	933.932	+	6495.64i	0.0992594	+	0.690364i	0.977313	+	0.211801i	$0.0679330\pi$
$97$	933.932	+	6495.64i	0.0992594	+	0.690364i	−0.878053	+	0.478563i	$0.841158\pi$
$98$	5982.90	−	9309.57i	0.622959	−	0.969343i
$99$	−1888.92	−	862.642i	−0.192727	−	0.0880157i
$100$	−2607.93	+	2954.09i	−0.260793	+	0.295409i
$101$	1523.05	−	10593.0i	0.149304	−	1.03843i	−0.768059	−	0.640379i	$-0.778777\pi$
$101$	1523.05	−	10593.0i	0.149304	−	1.03843i	0.917363	−	0.398051i	$-0.130313\pi$
$102$	879.103	+	1924.97i	0.0844967	+	0.185022i
$103$	1532.54	+	449.994i	0.144457	+	0.0424163i	0.353161	−	0.935562i	$-0.385107\pi$
$103$	1532.54	+	449.994i	0.144457	+	0.0424163i	−0.208705	+	0.977979i	$0.566925\pi$
$104$	−10052.0	−	2951.55i	−0.929368	−	0.272887i
$105$	−395.030	−	875.683i	−0.0358304	−	0.0794270i
$106$	18944.4	+	2723.79i	1.68605	+	0.242417i
$107$	−2098.54	+	2421.84i	−0.183294	+	0.211533i	−0.839959	−	0.542650i	$-0.817421\pi$
$107$	−2098.54	+	2421.84i	−0.183294	+	0.211533i	0.656665	+	0.754182i	$0.271967\pi$
$108$	3954.68	+	1806.04i	0.339050	+	0.154839i
$109$	11661.3	−	18145.4i	0.981511	−	1.52726i	0.137802	−	0.990460i	$-0.455996\pi$
$109$	11661.3	−	18145.4i	0.981511	−	1.52726i	0.843709	−	0.536801i	$-0.180368\pi$
$110$	−4378.04	+	608.830i	−0.361822	+	0.0503165i
$111$	−2192.17	−	3411.08i	−0.177921	−	0.276851i
$112$	1579.34	+	1822.66i	0.125904	+	0.145301i
$113$	14872.6	−	4366.99i	1.16474	−	0.341999i	0.358468	−	0.933542i	$-0.383299\pi$
$113$	14872.6	−	4366.99i	1.16474	−	0.341999i	0.806274	+	0.591543i	$0.201481\pi$
$114$			10143.5i			0.780507i
$115$	−13045.5	+	2171.73i	−0.986425	+	0.164214i
$116$	300.856			0.0223585
$117$	3575.58	+	12177.3i	0.261201	+	0.889568i
$118$	21933.7	−	19005.7i	1.57524	−	1.36496i
$119$	567.341	−	364.608i	0.0400636	−	0.0257473i
$120$	−5728.87	+	796.682i	−0.397838	+	0.0553252i
$121$	11137.8	+	7157.81i	0.760724	+	0.488888i
$122$	7773.24	−	17021.0i	0.522255	−	1.14358i
$123$	1541.86	+	1336.03i	0.101914	+	0.0883092i
$124$	−505.165	+	3513.50i	−0.0328541	+	0.228505i
$125$	−14301.6	+	6293.19i	−0.915304	+	0.402764i
$126$	561.282	−	1911.55i	0.0353541	−	0.120405i
$127$	4249.93	−	14473.9i	0.263496	−	0.897386i	−0.716368	−	0.697723i	$-0.754197\pi$
$127$	4249.93	−	14473.9i	0.263496	−	0.897386i	0.979864	−	0.199664i	$-0.0639850\pi$
$128$	17410.0	−	7950.90i	1.06262	−	0.485284i
$129$	−4806.76	−	691.108i	−0.288850	−	0.0415304i
$130$	20334.4	+	17785.0i	1.20322	+	1.05237i
$131$	−7832.50	+	17150.8i	−0.456413	+	0.999404i	0.531878	+	0.846821i	$0.321486\pi$
$131$	−7832.50	+	17150.8i	−0.456413	+	0.999404i	−0.988291	+	0.152583i	$0.951241\pi$
$132$	1003.32	+	644.793i	0.0575825	+	0.0370060i
$133$	3199.65	−	460.040i	0.180884	−	0.0260071i
$134$	9583.24	+	14911.8i	0.533707	+	0.830464i
$135$	11228.7	+	13080.3i	0.616117	+	0.717712i
$136$	−1143.96	−	3895.98i	−0.0618493	−	0.210639i
$137$	−21499.7			−1.14549			−0.572745	−	0.819734i	$-0.694121\pi$
$137$	−21499.7			−1.14549			−0.572745	+	0.819734i	$0.694121\pi$
$138$	10798.8	+	6538.11i	0.567045	+	0.343316i
$139$	−7382.53			−0.382099			−0.191049	−	0.981580i	$-0.561189\pi$
$139$	−7382.53			−0.382099			−0.191049	+	0.981580i	$0.561189\pi$
$140$	−332.395	−	1151.70i	−0.0169589	−	0.0587600i
$141$	−253.531	−	292.591i	−0.0127524	−	0.0147171i
$142$	9807.50	+	15260.8i	0.486386	+	0.756832i
$143$	1219.02	+	8478.44i	0.0596125	+	0.414614i
$144$	−14798.2	−	9510.22i	−0.713647	−	0.458633i
$145$	1082.84	+	500.579i	0.0515026	+	0.0238087i
$146$	−5564.31	+	6421.56i	−0.261039	+	0.301255i
$147$	−11719.1	−	1684.96i	−0.542326	−	0.0779747i
$148$	−2101.79	−	4602.28i	−0.0959546	−	0.210111i
$149$	6111.19	−	20812.8i	0.275266	−	0.937471i	−0.699573	−	0.714561i	$-0.746626\pi$
$149$	6111.19	−	20812.8i	0.275266	−	0.937471i	0.974839	−	0.222910i	$-0.0715555\pi$
$150$	14271.1	+	4334.05i	0.634272	+	0.192624i
$151$	13419.5	+	29384.5i	0.588547	+	1.28874i	0.936316	+	0.351158i	$0.114212\pi$
$151$	13419.5	+	29384.5i	0.588547	+	1.28874i	−0.347770	+	0.937580i	$0.613061\pi$
$152$	2769.84	−	19264.6i	0.119886	−	0.833822i
$153$	−3221.22	+	3717.49i	−0.137606	+	0.158806i
$154$	558.568	−	1223.09i	0.0235524	−	0.0515725i
$155$	−7664.10	+	11805.3i	−0.319005	+	0.491374i
$156$	−1037.34	−	7214.88i	−0.0426259	−	0.296470i
$157$	443.357	−	284.928i	0.0179868	−	0.0115594i	−0.531617	−	0.846985i	$-0.678415\pi$
$157$	443.357	−	284.928i	0.0179868	−	0.0115594i	0.549603	+	0.835426i	$0.314779\pi$
$158$	−16004.0	−	18469.6i	−0.641083	−	0.739849i
$159$	−5768.95	−	19647.2i	−0.228193	−	0.777154i
$160$	−19127.7	−	88.3966i	−0.747177	−	0.00345299i
$161$	1572.62	−	3702.90i	0.0606696	−	0.142853i
$162$			4764.22i			0.181535i
$163$	9350.26	+	31844.1i	0.351924	+	1.19854i	0.925296	+	0.379247i	$0.123817\pi$
$163$	9350.26	+	31844.1i	0.351924	+	1.19854i	−0.573372	+	0.819295i	$0.694365\pi$
$164$	1667.09	+	1923.92i	0.0619827	+	0.0715319i
$165$	2538.31	+	3990.11i	0.0932344	+	0.146560i
$166$	−26356.2	+	3789.45i	−0.956461	+	0.137518i
$167$	−20069.1	+	31228.1i	−0.719606	+	1.11973i	0.268098	+	0.963392i	$0.413605\pi$
$167$	−20069.1	+	31228.1i	−0.719606	+	1.11973i	−0.987704	+	0.156337i	$0.950031\pi$
$168$	730.912	−	1600.47i	0.0258968	−	0.0567061i
$169$	15578.7	−	17978.8i	0.545455	−	0.629488i
$170$	−1537.97	+	10356.8i	−0.0532169	+	0.358367i
$171$	−21447.0	+	9794.50i	−0.733455	+	0.334958i
$172$	−5814.06	−	1707.16i	−0.196527	−	0.0577056i
$173$	14727.4	−	50157.1i	0.492079	−	1.67587i	−0.221393	−	0.975185i	$-0.571060\pi$
$173$	14727.4	−	50157.1i	0.492079	−	1.67587i	0.713472	−	0.700683i	$-0.247121\pi$
$174$	−473.042	−	1035.82i	−0.0156243	−	0.0342125i
$175$	719.888	−	4698.24i	0.0235065	−	0.153412i
$176$	−8972.42	−	7774.65i	−0.289657	−	0.250989i
$177$	−28244.6	−	12898.9i	−0.901547	−	0.411723i
$178$	40431.7	+	25983.9i	1.27609	+	0.820094i
$179$	−6022.43	−	41886.9i	−0.187960	−	1.30729i	−0.837280	−	0.546775i	$-0.815855\pi$
$179$	−6022.43	−	41886.9i	−0.187960	−	1.30729i	0.649320	−	0.760516i	$-0.275054\pi$
$180$	4692.85	+	7376.95i	0.144841	+	0.227684i
$181$	13946.6	−	12084.8i	0.425709	−	0.368879i	−0.415497	−	0.909595i	$-0.636392\pi$
$181$	13946.6	−	12084.8i	0.425709	−	0.368879i	0.841205	+	0.540716i	$0.181847\pi$
$182$	−7884.91	+	2315.22i	−0.238042	+	0.0698955i
$183$	−20019.6			−0.597796
$184$	−18723.9	−	15366.1i	−0.553046	−	0.453866i
$185$	92.7124	−	20061.6i	0.00270891	−	0.586167i
$186$	12890.9	−	3785.10i	0.372612	−	0.109409i
$187$	−2508.99	+	2174.05i	−0.0717491	+	0.0621709i
$188$	−261.176	−	406.398i	−0.00738955	−	0.0114984i
$189$	−5190.63	+	746.301i	−0.145310	+	0.0208925i
$190$	−27327.9	+	42094.1i	−0.757007	+	1.16604i
$191$	25830.2	+	11796.3i	0.708045	+	0.323353i	0.736685	−	0.676236i	$-0.236390\pi$
$191$	25830.2	+	11796.3i	0.708045	+	0.323353i	−0.0286396	+	0.999590i	$0.509118\pi$
$192$	−5577.28	−	4832.74i	−0.151294	−	0.131097i
$193$	−19233.2	−	2765.32i	−0.516342	−	0.0742388i	−0.120782	−	0.992679i	$-0.538540\pi$
$193$	−19233.2	−	2765.32i	−0.516342	−	0.0742388i	−0.395560	+	0.918440i	$0.629449\pi$
$194$	28192.3	−	12875.0i	0.749078	−	0.342093i
$195$	8270.84	−	27693.8i	0.217511	−	0.728305i
$196$	−14175.0	−	4162.15i	−0.368986	−	0.108344i
$197$	34001.8	−	15528.1i	0.876132	−	0.400116i	0.0739968	−	0.997258i	$-0.476425\pi$
$197$	34001.8	−	15528.1i	0.876132	−	0.400116i	0.802135	+	0.597142i	$0.203697\pi$
$198$	−1395.72	+	9707.45i	−0.0356015	+	0.247614i
$199$	−5005.78	−	4337.53i	−0.126405	−	0.109531i	0.589364	−	0.807868i	$-0.299378\pi$
$199$	−5005.78	−	4337.53i	−0.126405	−	0.109531i	−0.715769	+	0.698337i	$0.753924\pi$
$200$	−25920.5	−	12128.3i	−0.648012	−	0.303207i
$201$	10252.9	−	15953.8i	0.253779	−	0.394887i
$202$	−50028.8	+	7193.05i	−1.22608	+	0.176283i
$203$	−305.284	+	196.194i	−0.00740818	+	0.00476095i
$204$	2135.07	−	1850.05i	0.0513042	−	0.0444553i
$205$	2799.08	+	9698.35i	0.0666050	+	0.230776i
$206$		−	7543.45i		−	0.177761i
$207$	−3396.65	+	29145.8i	−0.0792702	+	0.680197i
$208$			72559.2i			1.67713i
$209$	−15268.3	+	4483.19i	−0.349542	+	0.102635i
$210$	−3442.54	+	2955.23i	−0.0780621	+	0.0670121i
$211$	−10949.6	+	7036.88i	−0.245942	+	0.158057i	−0.657805	−	0.753189i	$-0.728515\pi$
$211$	−10949.6	+	7036.88i	−0.245942	+	0.158057i	0.411862	+	0.911246i	$0.364878\pi$
$212$	−3636.23	−	25290.6i	−0.0809059	−	0.562713i
$213$	10492.8	−	16327.2i	0.231278	−	0.359875i
$214$	13766.8	+	6287.09i	0.300612	+	0.137285i
$215$	−18085.5	−	15818.1i	−0.391250	−	0.342198i
$216$	−4493.37	+	31252.0i	−0.0963084	+	0.669840i
$217$	−1778.62	−	3894.63i	−0.0377714	−	0.0827078i
$218$	−97742.0	−	28699.6i	−2.05669	−	0.603898i
$219$	8722.47	+	2561.15i	0.181866	+	0.0534006i
$220$	2426.48	+	5378.90i	0.0501339	+	0.111134i
$221$	20083.5	+	2887.57i	0.411201	+	0.0591218i
$222$	−12540.5	+	14472.5i	−0.254453	+	0.293655i
$223$	−41554.1	−	18977.1i	−0.835610	−	0.381610i	−0.0488024	−	0.998808i	$-0.515540\pi$
$223$	−41554.1	−	18977.1i	−0.835610	−	0.381610i	−0.786808	+	0.617198i	$0.788268\pi$
$224$	3145.80	−	4894.96i	0.0626954	−	0.0975559i
$225$	4616.40	+	34359.3i	0.0911882	+	0.678702i
$226$	−39578.0	−	61584.5i	−0.774884	−	1.20574i
$227$	54591.9	+	63002.4i	1.05944	+	1.22266i	0.974055	+	0.226311i	$0.0726666\pi$
$227$	54591.9	+	63002.4i	1.05944	+	1.22266i	0.0853850	+	0.996348i	$0.472788\pi$
$228$	12992.9	−	3815.05i	0.249940	−	0.0733890i
$229$			61830.8i			1.17905i	0.807749	+	0.589527i	$0.200686\pi$
$229$			61830.8i			1.17905i	−0.807749	+	0.589527i	$0.799314\pi$
$230$	27199.1	+	56225.9i	0.514160	+	1.06287i
$231$	−1438.56			−0.0269591
$232$	615.562	+	2096.41i	0.0114366	+	0.0389494i
$233$	68050.0	−	58965.7i	1.25348	−	1.08614i	0.260794	−	0.965394i	$-0.416016\pi$
$233$	68050.0	−	58965.7i	1.25348	−	1.08614i	0.992683	−	0.120750i	$-0.0385298\pi$
$234$	50423.8	−	32405.4i	0.920883	−	0.591815i
$235$	−263.842	−	1897.27i	−0.00477759	−	0.0343552i
$236$	−32594.0	−	20946.9i	−0.585213	−	0.376094i
$237$	−10861.7	+	23783.8i	−0.193375	+	0.423432i
$238$	−2407.11	−	2085.77i	−0.0424953	−	0.0368224i
$239$	−3362.20	+	23384.6i	−0.0588611	+	0.409388i	0.938994	+	0.343932i	$0.111759\pi$
$239$	−3362.20	+	23384.6i	−0.0588611	+	0.409388i	−0.997855	+	0.0654553i	$0.979150\pi$
$240$	16472.8	+	36516.1i	0.285987	+	0.633960i
$241$	−14930.9	+	50849.8i	−0.257070	+	0.875498i	0.725282	+	0.688452i	$0.241710\pi$
$241$	−14930.9	+	50849.8i	−0.257070	+	0.875498i	−0.982351	+	0.187046i	$0.940109\pi$
$242$	17616.0	−	59994.7i	0.300800	−	1.02443i
$243$	55443.1	−	25320.0i	0.938933	−	0.428796i
$244$	−24726.0	−	3555.06i	−0.415312	−	0.0597129i
$245$	−44093.4	−	38565.4i	−0.734584	−	0.642488i
$246$	4002.67	−	8764.62i	0.0661423	−	0.144831i
$247$	81815.9	+	52579.9i	1.34105	+	0.861838i
$248$	−25516.1	+	3668.67i	−0.414870	+	0.0596493i
$249$	15401.8	+	23965.6i	0.248412	+	0.386536i
$250$	47546.9	+	56434.2i	0.760750	+	0.902948i
$251$	30659.2	+	104416.i	0.486646	+	1.65737i	0.726968	+	0.686672i	$0.240929\pi$
$251$	30659.2	+	104416.i	0.486646	+	1.65737i	−0.240321	+	0.970693i	$0.577253\pi$
$252$	−2659.63			−0.0418813
$253$	−5068.59	+	19144.5i	−0.0791856	+	0.299090i
$254$	−71243.5			−1.10428
$255$	10762.8	−	3106.28i	0.165517	−	0.0477705i
$256$	−43891.7	−	50653.7i	−0.669734	−	0.772914i
$257$	−47280.6	−	73570.1i	−0.715841	−	1.11387i	−0.988421	−	0.151738i	$-0.951513\pi$
$257$	−47280.6	−	73570.1i	−0.715841	−	1.11387i	0.272579	−	0.962133i	$-0.412123\pi$
$258$	3263.97	+	22701.4i	0.0490350	+	0.341046i
$259$	5133.95	+	3299.39i	0.0765336	+	0.0491851i
$260$	15133.1	−	32735.6i	0.223862	−	0.484255i
$261$	1733.33	−	2000.36i	0.0254448	−	0.0293649i
$262$	88140.4	+	12672.7i	1.28402	+	0.184614i
$263$	−15804.5	−	34607.1i	−0.228491	−	0.500326i	0.760311	−	0.649560i	$-0.225047\pi$
$263$	−15804.5	−	34607.1i	−0.228491	−	0.500326i	−0.988802	+	0.149233i	$0.952319\pi$
$264$	−2440.19	+	8310.54i	−0.0350120	+	0.119240i
$265$	28992.0	−	97076.0i	0.412845	−	1.38236i
$266$	−6342.02	−	13887.1i	−0.0896323	−	0.196267i
$267$	7317.79	−	50896.4i	0.102650	−	0.713944i
$268$	15496.4	−	17883.7i	0.215755	−	0.248994i
$269$	−23051.6	+	50476.0i	−0.318564	+	0.697559i	−0.999391	−	0.0348857i	$-0.988893\pi$
$269$	−23051.6	+	50476.0i	−0.318564	+	0.697559i	0.680827	+	0.732444i	$0.261621\pi$
$270$	44332.8	−	68287.2i	0.608131	−	0.936724i
$271$	−2963.85	−	20614.0i	−0.0403568	−	0.280688i	0.959643	−	0.281221i	$-0.0907394\pi$
$271$	−2963.85	−	20614.0i	−0.0403568	−	0.280688i	−1.00000		0.000533107i	$0.999830\pi$
$272$	−23658.2	+	15204.2i	−0.319775	+	0.205507i
$273$	5757.57	+	6644.59i	0.0772527	+	0.0891544i
$274$	28606.8	+	97425.9i	0.381038	+	1.29770i
$275$	−216.258	+	23397.0i	−0.00285961	+	0.309382i
$276$	4313.21	−	16291.4i	0.0566216	−	0.213865i
$277$		−	41461.0i		−	0.540356i	−0.962810	−	0.270178i	$-0.912917\pi$
$277$		−	41461.0i		−	0.540356i	0.962810	−	0.270178i	$-0.0870826\pi$
$278$	9822.96	+	33453.9i	0.127102	+	0.432870i
$279$	20450.5	+	23601.1i	0.262721	+	0.303196i
$280$	7345.10	−	4672.59i	0.0936875	−	0.0595993i
$281$	48193.4	−	6929.17i	0.610345	−	0.0877544i	0.169790	−	0.985480i	$-0.445691\pi$
$281$	48193.4	−	6929.17i	0.610345	−	0.0877544i	0.440555	+	0.897726i	$0.354782\pi$
$282$	−988.534	+	1538.19i	−0.0124306	+	0.0193424i
$283$	−55612.2	+	121774.i	−0.694380	+	1.52048i	0.152275	+	0.988338i	$0.451340\pi$
$283$	−55612.2	+	121774.i	−0.694380	+	1.52048i	−0.846655	+	0.532142i	$0.821387\pi$
$284$	15859.0	−	18302.3i	0.196625	−	0.226917i
$285$	53111.6	+	7886.99i	0.653883	+	0.0971006i
$286$	36798.0	−	16805.1i	0.449876	−	0.205451i
$287$	−2946.24	−	865.095i	−0.0357688	−	0.0105027i
$288$	−11956.8	+	40721.0i	−0.144155	+	0.490946i
$289$	−31429.0	−	68820.0i	−0.376301	−	0.823984i
$290$	827.575	−	5572.96i	0.00984037	−	0.0662658i
$291$	−25059.8	−	21714.5i	−0.295932	−	0.256427i
$292$	10318.2	+	4712.18i	0.121015	+	0.0552658i
$293$	49728.3	+	31958.5i	0.579253	+	0.372264i	0.797217	−	0.603693i	$-0.206305\pi$
$293$	49728.3	+	31958.5i	0.579253	+	0.372264i	−0.217963	+	0.975957i	$0.569941\pi$
$294$	7957.71	+	55347.1i	0.0920648	+	0.640325i
$295$	−82460.1	−	129624.i	−0.947545	−	1.48950i
$296$	27769.0	−	24062.0i	0.316940	−	0.274630i
$297$	24769.1	−	7272.85i	0.280800	−	0.0824503i
$298$	−102444.			−1.15360
$299$	108713.	−	53210.7i	1.21601	−	0.595191i
$300$	184.029	−	19910.1i	0.00204476	−	0.221224i
$301$	7012.89	−	2059.17i	0.0774041	−	0.0227279i
$302$	115300.	−	99908.3i	1.26420	−	1.09544i
$303$	29235.3	+	45491.0i	0.318436	+	0.495496i
$304$	−133426.	+	19183.8i	−1.44375	+	0.207581i
$305$	−83078.9	−	53935.7i	−0.893081	−	0.579798i
$306$	21131.8	+	9650.59i	0.225681	+	0.103065i
$307$	−30081.3	−	26065.6i	−0.319169	−	0.276561i	0.480510	−	0.876989i	$-0.340452\pi$
$307$	−30081.3	−	26065.6i	−0.319169	−	0.276561i	−0.799679	+	0.600428i	$0.794997\pi$
$308$	−1776.76	−	255.459i	−0.0187295	−	0.00269290i
$309$	−7341.27	+	3352.64i	−0.0768872	+	0.0351132i
$310$	63693.2	+	19022.2i	0.662780	+	0.197941i
$311$	89790.6	+	26364.9i	0.928346	+	0.272587i	0.710744	−	0.703451i	$-0.248358\pi$
$311$	89790.6	+	26364.9i	0.928346	+	0.272587i	0.217602	+	0.976038i	$0.430177\pi$
$312$	48151.9	−	21990.3i	0.494658	−	0.225903i
$313$	17416.5	−	121135.i	0.177776	−	1.23646i	−0.684118	−	0.729371i	$-0.739813\pi$
$313$	17416.5	−	121135.i	0.177776	−	1.23646i	0.861894	−	0.507088i	$-0.169278\pi$
$314$	−1881.07	−	1629.95i	−0.0190785	−	0.0165316i
$315$	−9572.55	−	4425.21i	−0.0964731	−	0.0445978i
$316$	−17638.7	+	27446.3i	−0.176641	+	0.274859i
$317$	−53264.4	+	7658.27i	−0.530052	+	0.0762100i	−0.402145	−	0.915576i	$-0.631735\pi$
$317$	−53264.4	+	7658.27i	−0.530052	+	0.0762100i	−0.127908	+	0.991786i	$0.540826\pi$
$318$	−81355.4	+	52283.9i	−0.804511	+	0.517028i
$319$	1350.08	−	1169.85i	0.0132672	−	0.0114961i
$320$	−10124.9	−	35081.3i	−0.0988763	−	0.342591i
$321$		−	16192.1i		−	0.157142i
$322$	−18872.1	−	2199.36i	−0.182016	−	0.0212121i
$323$			37694.1i			0.361300i
$324$	6102.54	−	1791.87i	0.0581327	−	0.0170693i
$325$	108934.	−	92643.1i	1.03133	−	0.877094i
$326$	131860.	−	84741.4i	1.24073	−	0.797371i
$327$	15510.5	+	107878.i	0.145054	+	1.00887i
$328$	−9995.25	+	15552.9i	−0.0929065	+	0.144565i
$329$	530.039	+	242.061i	0.00489684	+	0.00223631i
$330$	14703.8	−	16811.4i	0.135021	−	0.154375i
$331$	1333.35	−	9273.66i	0.0121699	−	0.0846438i	−0.982831	−	0.184507i	$-0.940931\pi$
$331$	1333.35	−	9273.66i	0.0121699	−	0.0846438i	0.995001	+	0.0998628i	$0.0318404\pi$
$332$	14766.8	+	32334.7i	0.133971	+	0.293355i
$333$	−42709.1	−	12540.5i	−0.385152	−	0.113091i
$334$	168213.	+	49391.9i	1.50788	+	0.442755i
$335$	85530.3	−	38583.7i	0.762132	−	0.343806i
$336$	−12062.0	−	1734.25i	−0.106842	−	0.0153615i
$337$	35630.3	−	41119.6i	0.313733	−	0.362067i	−0.576880	−	0.816829i	$-0.695730\pi$
$337$	35630.3	−	41119.6i	0.313733	−	0.362067i	0.890613	+	0.454762i	$0.150276\pi$
$338$	−102200.	−	46673.0i	−0.894572	−	0.408538i
$339$	−42343.7	+	65888.1i	−0.368459	+	0.573334i
$340$	13844.6	−	1925.29i	0.119763	−	0.0166548i
$341$	11395.0	+	17730.9i	0.0979951	+	0.152483i
$342$	72920.4	+	84154.6i	0.623443	+	0.719492i
$343$	34617.6	−	10164.6i	0.294244	−	0.0863979i
$344$		−	44006.1i		−	0.371874i
$345$	42630.4	−	51459.3i	0.358163	−	0.432341i
$346$	−246882.			−2.06223
$347$	17793.5	+	60599.3i	0.147776	+	0.503278i	0.999795	−	0.0202317i	$-0.00644039\pi$
$347$	17793.5	+	60599.3i	0.147776	+	0.503278i	−0.852019	+	0.523510i	$0.824622\pi$
$348$	−1148.87	+	995.505i	−0.00948668	+	0.00822025i
$349$	−51358.0	+	33005.8i	−0.421655	+	0.270981i	−0.734215	−	0.678917i	$-0.762450\pi$
$349$	−51358.0	+	33005.8i	−0.421655	+	0.270981i	0.312560	+	0.949898i	$0.398813\pi$
$350$	−22247.9	+	2989.16i	−0.181616	+	0.0244013i
$351$	−132726.	−	85297.7i	−1.07731	−	0.692346i
$352$	−11899.0	+	26055.1i	−0.0960337	+	0.210285i
$353$	−164676.	−	142693.i	−1.32154	−	1.14512i	−0.978601	−	0.205765i	$-0.934032\pi$
$353$	−164676.	−	142693.i	−1.32154	−	1.14512i	−0.342940	−	0.939357i	$-0.611423\pi$
$354$	−20869.9	+	145153.i	−0.166538	+	1.15830i
$355$	87531.8	−	39486.6i	0.694559	−	0.313323i
$356$	18076.3	−	61562.2i	0.142629	−	0.485751i
$357$	−960.040	+	3269.60i	−0.00753274	+	0.0256542i
$358$	−181797.	+	83024.0i	−1.41847	+	0.647795i
$359$	−6716.97	−	965.754i	−0.0521176	−	0.00749338i	0.116207	−	0.993225i	$-0.462926\pi$
$359$	−6716.97	−	965.754i	−0.0521176	−	0.00749338i	−0.168324	+	0.985732i	$0.553836\pi$
$360$	−41801.9	+	47793.9i	−0.322546	+	0.368780i
$361$	−20918.5	+	45805.1i	−0.160515	+	0.351479i
$362$	−73319.3	−	47119.5i	−0.559502	−	0.359570i
$363$	−66216.0	+	9520.43i	−0.502516	+	0.0722509i
$364$	5931.18	+	9229.09i	0.0447650	+	0.0696556i
$365$	29297.1	+	34128.0i	0.219907	+	0.256168i
$366$	26637.4	+	90718.8i	0.198852	+	0.677228i
$367$	−201509.			−1.49610			−0.748052	−	0.663640i	$-0.769011\pi$
$367$	−201509.			−1.49610			−0.748052	+	0.663640i	$0.769011\pi$
$368$	−65578.4	+	154411.i	−0.484245	+	1.14021i
$369$	22396.5			0.164486
$370$	−91032.4	+	26273.2i	−0.664955	+	0.191915i
$371$	20182.2	+	23291.5i	0.146629	+	0.169219i
$372$	−9696.76	−	15088.5i	−0.0700714	−	0.109033i
$373$	27956.9	+	194445.i	0.200942	+	1.39759i	0.801496	+	0.598000i	$0.204038\pi$
$373$	27956.9	+	194445.i	0.200942	+	1.39759i	−0.600553	+	0.799585i	$0.705053\pi$
$374$	13190.1	+	8476.77i	0.0942986	+	0.0606020i
$375$	33789.7	−	71354.4i	0.240283	−	0.507409i
$376$	2297.47	−	2651.42i	0.0162508	−	0.0187544i
$377$	−10806.8	−	1553.79i	−0.0760355	−	0.0109322i
$378$	10288.4	+	22528.3i	0.0720049	+	0.157669i
$379$	−2901.93	+	9883.08i	−0.0202027	+	0.0688040i	−0.968977	−	0.247149i	$-0.920506\pi$
$379$	−2901.93	+	9883.08i	−0.0202027	+	0.0688040i	0.948775	+	0.315953i	$0.102324\pi$
$380$	64197.1	+	19172.7i	0.444579	+	0.132775i
$381$	31663.8	+	69334.0i	0.218129	+	0.477635i
$382$	19085.9	−	132745.i	0.130793	−	0.909687i
$383$	−57228.3	+	66045.0i	−0.390134	+	0.450238i	−0.916509	−	0.400014i	$-0.869005\pi$
$383$	−57228.3	+	66045.0i	−0.390134	+	0.450238i	0.526375	+	0.850252i	$0.323551\pi$
$384$	−40174.6	+	87970.1i	−0.272451	+	0.596585i
$385$	−5969.86	−	3875.70i	−0.0402757	−	0.0261474i
$386$	13060.1	+	90834.7i	0.0876538	+	0.609646i
$387$	−44847.3	+	28821.6i	−0.299443	+	0.192440i
$388$	−27095.1	−	31269.4i	−0.179981	−	0.207710i
$389$	40192.3	+	136882.i	0.265609	+	0.904583i	0.979008	+	0.203824i	$0.0653369\pi$
$389$	40192.3	+	136882.i	0.265609	+	0.904583i	−0.713398	+	0.700759i	$0.752845\pi$
$390$	−136499.	−	630.817i	−0.897432	−	0.00414738i
$391$	40129.4	+	24296.3i	0.262488	+	0.158923i
$392$		−	107289.i		−	0.698206i
$393$	−26840.5	−	91410.3i	−0.173782	−	0.591848i
$394$	−115607.	−	133418.i	−0.744720	−	0.859452i
$395$	−109152.	+	69436.8i	−0.699577	+	0.445036i
$396$	12959.3	−	1863.27i	0.0826403	−	0.0118819i
$397$	−55318.2	+	86076.7i	−0.350983	+	0.546141i	−0.971193	−	0.238295i	$-0.923411\pi$
$397$	−55318.2	+	86076.7i	−0.350983	+	0.546141i	0.620209	+	0.784436i	$0.287048\pi$
$398$	−12995.0	+	28455.0i	−0.0820370	+	0.179636i
$399$	−10696.2	+	12344.1i	−0.0671868	+	0.0775377i
$400$	−30019.5	+	195918.i	−0.187622	+	1.22448i
$401$	78659.3	−	35922.5i	0.489172	−	0.223397i	−0.155531	−	0.987831i	$-0.549709\pi$
$401$	78659.3	−	35922.5i	0.489172	−	0.223397i	0.644702	+	0.764434i	$0.276981\pi$
$402$	−85937.0	−	25233.4i	−0.531775	−	0.156143i
$403$	36291.3	−	123597.i	0.223456	−	0.761022i
$404$	28030.0	+	61377.1i	0.171735	+	0.376048i
$405$	24945.7	+	3704.39i	0.152085	+	0.0225843i
$406$	1295.25	+	1122.34i	0.00785783	+	0.00680885i
$407$	−27327.2	−	12479.9i	−0.164970	−	0.0753394i
$408$	17259.9	+	11092.2i	0.103685	+	0.0666345i
$409$	−31907.8	−	221923.i	−0.190743	−	1.32665i	−0.830046	−	0.557695i	$-0.811686\pi$
$409$	−31907.8	−	221923.i	−0.190743	−	1.32665i	0.639303	−	0.768955i	$-0.279223\pi$
$410$	40223.7	−	25588.3i	0.239284	−	0.152221i
$411$	82100.5	−	71140.5i	0.486029	−	0.421146i
$412$	−9662.49	+	2837.16i	−0.0569239	+	0.0167144i
$413$	46733.5			0.273986
$414$	136593.	−	23388.5i	0.796946	−	0.136459i
$415$	−651.380	+	140949.i	−0.00378215	+	0.818400i
$416$	167969.	−	49320.2i	0.970606	−	0.284996i
$417$	28191.5	−	24428.1i	0.162124	−	0.140481i
$418$	40631.1	+	63223.3i	0.232545	+	0.361847i
$419$	−304343.	+	43757.9i	−1.73354	+	0.249246i	−0.935494	−	0.353343i	$-0.885045\pi$
$419$	−304343.	+	43757.9i	−1.73354	+	0.249246i	−0.798051	+	0.602590i	$0.794136\pi$
$420$	5080.17	+	3298.10i	0.0287991	+	0.0186967i
$421$	−39944.9	−	18242.2i	−0.225371	−	0.102923i	0.299530	−	0.954087i	$-0.403170\pi$
$421$	−39944.9	−	18242.2i	−0.225371	−	0.102923i	−0.524900	+	0.851164i	$0.675897\pi$
$422$	46456.8	+	40255.0i	0.260870	+	0.226045i
$423$	−4206.81	−	604.849i	−0.0235111	−	0.00338038i
$424$	168788.	−	77083.1i	0.938882	−	0.428773i
$425$	53032.9	+	16105.8i	0.293608	+	0.0891668i
$426$	−87948.1	−	25823.9i	−0.484627	−	0.142299i
$427$	27408.2	−	12516.9i	0.150323	−	0.0686501i
$428$	2875.38	−	19998.7i	0.0156967	−	0.109173i
$429$	−32709.4	−	28342.8i	−0.177729	−	0.154003i
$430$	−47615.8	+	103002.i	−0.257522	+	0.557067i
$431$	163425.	−	254295.i	0.879762	−	1.36894i	−0.0492107	−	0.998788i	$-0.515671\pi$
$431$	163425.	−	254295.i	0.879762	−	1.36894i	0.928973	−	0.370148i	$-0.120693\pi$
$432$	216450.	−	31120.9i	1.15982	−	0.166757i
$433$	61843.7	−	39744.5i	0.329852	−	0.211983i	−0.365223	−	0.930920i	$-0.619007\pi$
$433$	61843.7	−	39744.5i	0.329852	−	0.211983i	0.695075	+	0.718937i	$0.255371\pi$
$434$	−15281.9	+	13241.9i	−0.0811332	+	0.0703023i
$435$	−5791.40	+	1671.48i	−0.0306059	+	0.00883327i
$436$			135993.i			0.715391i
$437$	126589.	+	185838.i	0.662877	+	0.973134i
$438$		−	42933.6i		−	0.223795i
$439$	204761.	−	60123.4i	1.06248	−	0.311971i	0.296628	−	0.954993i	$-0.404138\pi$
$439$	204761.	−	60123.4i	1.06248	−	0.311971i	0.765848	+	0.643022i	$0.222320\pi$
$440$	−32516.3	+	27913.5i	−0.167956	+	0.144181i
$441$	−109340.	+	70268.5i	−0.562214	+	0.361313i
$442$	−13637.4	−	94850.4i	−0.0698052	−	0.485506i
$443$	−37132.7	+	57779.7i	−0.189212	+	0.294420i	−0.922879	−	0.385089i	$-0.874171\pi$
$443$	−37132.7	+	57779.7i	−0.189212	+	0.294420i	0.733667	+	0.679509i	$0.237807\pi$
$444$	23254.6	+	10620.0i	0.117962	+	0.0538714i
$445$	167490.	−	191499.i	0.845803	−	0.967042i
$446$	−30704.2	+	213552.i	−0.154358	+	1.07358i
$447$	45530.9	+	99698.7i	0.227872	+	0.498970i
$448$	10657.3	+	3129.26i	0.0530995	+	0.0155914i
$449$	−209502.	−	61515.3i	−1.03919	−	0.305134i	−0.282748	−	0.959194i	$-0.591246\pi$
$449$	−209502.	−	61515.3i	−1.03919	−	0.305134i	−0.756442	+	0.654061i	$0.773064\pi$
$450$	149557.	−	66636.6i	0.738551	−	0.329070i
$451$	14961.9	+	2151.20i	0.0735588	+	0.0105762i
$452$	−63998.7	+	73858.4i	−0.313252	+	0.361512i
$453$	−148475.	−	67806.3i	−0.723531	−	0.330426i
$454$	212857.	−	331212.i	1.03271	−	1.60692i
$455$	5991.72	+	43085.9i	0.0289420	+	0.208119i
$456$	53167.7	+	82730.6i	0.255693	+	0.397866i
$457$	−56098.9	−	64741.6i	−0.268610	−	0.309992i	0.605380	−	0.795937i	$-0.293021\pi$
$457$	−56098.9	−	64741.6i	−0.268610	−	0.309992i	−0.873990	+	0.485944i	$0.838476\pi$
$458$	280186.	−	82270.1i	1.33572	−	0.392203i
$459$		−	61149.3i		−	0.290246i
$460$	61790.5	−	55986.7i	0.292016	−	0.264587i
$461$	−283408.			−1.33355			−0.666775	−	0.745259i	$-0.732326\pi$
$461$	−283408.			−1.33355			−0.666775	+	0.745259i	$0.732326\pi$
$462$	1914.11	+	6518.85i	0.00896772	+	0.0305413i
$463$	−177417.	+	153733.i	−0.827627	+	0.717143i	−0.961782	−	0.273818i	$-0.911713\pi$
$463$	−177417.	+	153733.i	−0.827627	+	0.717143i	0.134155	+	0.990960i	$0.457168\pi$
$464$	12730.4	−	8181.32i	0.0591297	−	0.0380003i
$465$	−9795.75	−	70440.3i	−0.0453035	−	0.325773i
$466$	−357748.	−	229911.i	−1.64742	−	1.05874i
$467$	−36648.3	+	80248.6i	−0.168043	+	0.367963i	−0.974853	−	0.222848i	$-0.928465\pi$
$467$	−36648.3	+	80248.6i	−0.168043	+	0.367963i	0.806810	+	0.590811i	$0.201192\pi$
$468$	−60473.4	−	52400.5i	−0.276104	−	0.239245i
$469$	−4062.08	+	28252.4i	−0.0184673	+	0.128443i
$470$	−8246.39	+	3720.04i	−0.0373309	+	0.0168404i
$471$	−750.237	+	2555.07i	−0.00338187	+	0.0115176i
$472$	79272.7	−	269978.i	0.355828	−	1.21184i
$473$	−32728.4	+	14946.6i	−0.146286	+	0.0668066i
$474$	122228.	+	17573.8i	0.544020	+	0.0782183i
$475$	199158.	+	175820.i	0.882695	+	0.779260i
$476$	−1766.35	+	3867.77i	−0.00779584	+	0.0170705i
$477$	−189104.	−	121530.i	−0.831119	−	0.534128i
$478$	110441.	−	15879.0i	0.483365	−	0.0694973i
$479$	−158312.	−	246339.i	−0.689991	−	1.07365i	−0.992705	−	0.120566i	$-0.961529\pi$
$479$	−158312.	−	246339.i	−0.689991	−	1.07365i	0.302714	−	0.953081i	$-0.402107\pi$
$480$	73335.1	−	62954.2i	0.318295	−	0.273239i
$481$	51728.1	+	176170.i	0.223582	+	0.761450i
$482$	250292.			1.07734
$483$	6247.20	+	19343.8i	0.0267788	+	0.0829178i
$484$	−83473.5			−0.356334
$485$	−45493.3	−	157627.i	−0.193403	−	0.670112i
$486$	−188508.	−	217550.i	−0.798101	−	0.921058i
$487$	125133.	+	194711.i	0.527611	+	0.820979i	0.998112	−	0.0614209i	$-0.0195632\pi$
$487$	125133.	+	194711.i	0.527611	+	0.820979i	−0.470501	+	0.882399i	$0.655927\pi$
$488$	−25818.0	−	179568.i	−0.108414	−	0.754033i
$489$	−141075.	−	90663.1i	−0.589972	−	0.379152i
$490$	−116090.	+	251123.i	−0.483505	+	1.04591i
$491$	−102233.	+	117983.i	−0.424061	+	0.489393i	−0.927070	−	0.374889i	$-0.877681\pi$
$491$	−102233.	+	117983.i	−0.424061	+	0.489393i	0.503009	+	0.864281i	$0.332226\pi$
$492$	−12732.1	−	1830.61i	−0.0525982	−	0.00756249i
$493$	−1757.87	−	3849.20i	−0.00723257	−	0.0158371i
$494$	129404.	−	440710.i	0.530266	−	1.80592i
$495$	49743.4	+	14856.0i	0.203014	+	0.0606307i
$496$	74168.6	+	162407.i	0.301479	+	0.660147i
$497$	−4157.14	+	28913.5i	−0.0168299	+	0.117055i
$498$	88107.1	−	101681.i	0.355265	−	0.409997i
$499$	73655.9	−	161284.i	0.295806	−	0.647724i	−0.702123	−	0.712056i	$-0.747764\pi$
$499$	73655.9	−	161284.i	0.295806	−	0.647724i	0.997929	+	0.0643318i	$0.0204916\pi$
$500$	54404.4	−	82128.8i	0.217618	−	0.328515i
$501$	−26693.4	−	185657.i	−0.106348	−	0.739666i
$502$	432365.	−	277864.i	1.71571	−	1.10262i
$503$	153652.	+	177324.i	0.607298	+	0.700859i	0.973243	−	0.229777i	$-0.0737998\pi$
$503$	153652.	+	177324.i	0.607298	+	0.700859i	−0.365945	+	0.930636i	$0.619254\pi$
$504$	−5441.69	−	18532.7i	−0.0214226	−	0.0729588i
$505$	−1236.43	+	267546.i	−0.00484829	+	1.04910i
$506$	93497.3	−	2504.73i	0.365172	−	0.00978274i
$507$			120204.i			0.467630i
$508$	26795.3	+	91256.6i	0.103832	+	0.353620i
$509$	80224.5	+	92584.0i	0.309650	+	0.357355i	0.889149	−	0.457618i	$-0.151297\pi$
$509$	80224.5	+	92584.0i	0.309650	+	0.357355i	−0.579499	+	0.814973i	$0.696752\pi$
$510$	−28396.7	−	44638.3i	−0.109176	−	0.171620i
$511$	−13543.0	+	1947.19i	−0.0518647	+	0.00745702i
$512$	−5573.38	+	8672.34i	−0.0212607	+	0.0330824i
$513$	121759.	−	266616.i	0.462666	−	1.01310i
$514$	−270473.	+	312142.i	−1.02376	+	1.18148i
$515$	−39497.9	−	5865.37i	−0.148922	−	0.0221147i
$516$	27850.9	−	12719.1i	0.104602	−	0.0477701i
$517$	−2752.25	−	808.134i	−0.0102969	−	0.00302345i
$518$	8120.10	−	27654.5i	0.0302623	−	0.103064i
$519$	109726.	+	240265.i	0.407355	+	0.891983i
$520$	259070.	+	38471.4i	0.958097	+	0.142276i
$521$	221907.	+	192283.i	0.817513	+	0.708379i	0.959567	−	0.281480i	$-0.0908253\pi$
$521$	221907.	+	192283.i	0.817513	+	0.708379i	−0.142054	+	0.989859i	$0.545371\pi$
$522$	−11371.0	−	5192.94i	−0.0417307	−	0.0190578i
$523$	235183.	+	151143.i	0.859809	+	0.552566i	0.894620	−	0.446828i	$-0.147447\pi$
$523$	235183.	+	151143.i	0.859809	+	0.552566i	−0.0348109	+	0.999394i	$0.511083\pi$
$524$	−16917.9	−	117666.i	−0.0616145	−	0.428538i
$525$	12797.0	+	20323.1i	0.0464291	+	0.0737347i
$526$	−135793.	+	117665.i	−0.490801	+	0.425281i
$527$	47903.8	−	14065.8i	0.172484	−	0.0506458i
$528$	59988.4			0.215179
$529$	279440.	−	14982.8i	0.998566	−	0.0535403i
$530$	−478475.	−	2211.22i	−1.70337	−	0.00787192i
$531$	−327058.	+	96032.9i	−1.15994	+	0.340589i
$532$	−15402.8	+	13346.6i	−0.0544224	+	0.0471573i
$533$	−49946.0	−	77717.5i	−0.175811	−	0.273567i
$534$	−240374.	+	34560.5i	−0.842955	+	0.121199i
$535$	43623.8	−	67195.2i	0.152411	−	0.234763i
$536$	156323.	+	71390.2i	0.544117	+	0.248490i
$537$	161597.	+	140025.i	0.560384	+	0.485576i
$538$	259404.	+	37296.6i	0.896214	+	0.128856i
$539$	−79793.5	+	36440.5i	−0.274657	+	0.125432i
$540$	−104144.	−	31102.9i	−0.357146	−	0.106663i
$541$	321379.	+	94365.5i	1.09805	+	0.322418i	0.780079	−	0.625682i	$-0.215179\pi$
$541$	321379.	+	94365.5i	1.09805	+	0.322418i	0.317975	+	0.948099i	$0.396997\pi$
$542$	−89468.7	+	40859.0i	−0.304560	+	0.139088i
$543$	−13270.2	+	92296.2i	−0.0450067	+	0.313029i
$544$	51277.7	+	44432.3i	0.173273	+	0.150142i
$545$	−226271.	+	489466.i	−0.761792	+	1.64790i
$546$	22449.1	−	34931.5i	0.0753032	−	0.117174i
$547$	−567350.	+	81572.7i	−1.89617	+	0.272628i	−0.988974	−	0.148086i	$-0.952689\pi$
$547$	−567350.	+	81572.7i	−1.89617	+	0.272628i	−0.907193	+	0.420714i	$0.861780\pi$
$548$	114035.	−	73285.6i	0.379731	−	0.244038i
$549$	−166091.	+	143919.i	−0.551064	+	0.477500i
$550$	106311.	−	30151.4i	0.351442	−	0.0996739i
$551$		−	20283.0i		−	0.0668082i
$552$	122346.	−	3277.56i	0.401522	−	0.0107565i
$553$		−	39352.7i		−	0.128684i
$554$	−187880.	+	55166.7i	−0.612156	+	0.179745i
$555$	66027.8	+	76915.5i	0.214359	+	0.249705i
$556$	39157.0	−	25164.7i	0.126666	−	0.0814033i
$557$	22457.5	+	156195.i	0.0723853	+	0.503451i	0.993470	+	0.114090i	$0.0363951\pi$
$557$	22457.5	+	156195.i	0.0723853	+	0.503451i	−0.921085	+	0.389361i	$0.872696\pi$
$558$	79737.6	−	124074.i	0.256091	−	0.398486i
$559$	200026.	+	91348.7i	0.640122	+	0.292334i
$560$	−45383.5	−	39693.7i	−0.144718	−	0.126574i
$561$	2387.30	−	16604.0i	0.00758545	−	0.0527579i
$562$	−95524.2	−	209169.i	−0.302441	−	0.662254i
$563$	258656.	+	75948.3i	0.816030	+	0.239608i	0.663006	−	0.748614i	$-0.269281\pi$
$563$	258656.	+	75948.3i	0.816030	+	0.239608i	0.153024	+	0.988222i	$0.451099\pi$
$564$	2342.08	+	687.697i	0.00736281	+	0.00216192i
$565$	−353233.	+	159347.i	−1.10653	+	0.499170i
$566$	625813.	+	89978.4i	1.95349	+	0.280870i
$567$	−5023.83	+	5797.81i	−0.0156268	+	0.0180343i
$568$	159981.	+	73060.8i	0.495874	+	0.226458i
$569$	173943.	−	270661.i	0.537258	−	0.835990i	−0.461431	−	0.887176i	$-0.652664\pi$
$569$	173943.	−	270661.i	0.537258	−	0.835990i	0.998689	+	0.0511858i	$0.0163001\pi$
$570$	−34928.8	−	251170.i	−0.107506	−	0.773067i
$571$	30030.7	+	46728.6i	0.0921070	+	0.143321i	0.884249	−	0.467015i	$-0.154671\pi$
$571$	30030.7	+	46728.6i	0.0921070	+	0.143321i	−0.792142	+	0.610336i	$0.791034\pi$
$572$	−35365.9	−	40814.5i	−0.108092	−	0.124745i
$573$	−137670.	+	40423.5i	−0.419305	+	0.123119i
$574$			14502.0i			0.0440152i
$575$	315550.	−	98697.6i	0.954404	−	0.298518i
$576$	−81013.7			−0.244182
$577$	−95716.1	−	325979.i	−0.287497	−	0.979125i	−0.968949	−	0.247262i	$-0.920469\pi$
$577$	−95716.1	−	325979.i	−0.287497	−	0.979125i	0.681452	−	0.731863i	$-0.261349\pi$
$578$	−270039.	+	233990.i	−0.808297	+	0.700394i
$579$	82595.7	−	53081.0i	0.246377	−	0.158337i
$580$	−7449.72	+	1035.99i	−0.0221454	+	0.00307964i
$581$	−36070.2	−	23180.9i	−0.106855	−	0.0686717i
$582$	−65055.3	+	142451.i	−0.192060	+	0.420552i
$583$	−114657.	−	99351.0i	−0.337337	−	0.292304i
$584$	−11723.7	+	81540.3i	−0.0343748	+	0.239082i
$585$	−130470.	−	289218.i	−0.381239	−	0.845112i
$586$	78652.8	−	267867.i	0.229044	−	0.780052i
$587$	−182125.	+	620259.i	−0.528558	+	1.80010i	0.0681898	+	0.997672i	$0.478278\pi$
$587$	−182125.	+	620259.i	−0.528558	+	1.80010i	−0.596747	+	0.802429i	$0.703541\pi$
$588$	67901.8	−	31009.7i	0.196393	−	0.0896898i
$589$	236872.	+	34057.0i	0.682783	+	0.0981694i
$590$	−477670.	+	546141.i	−1.37222	+	1.56892i
$591$	−78461.0	+	171806.i	−0.224636	+	0.491884i
$592$	−214087.	−	137585.i	−0.610866	−	0.392580i
$593$	35004.0	−	5032.81i	0.0995424	−	0.0143120i	−0.0923636	−	0.995725i	$-0.529442\pi$
$593$	35004.0	−	5032.81i	0.0995424	−	0.0143120i	0.191906	+	0.981413i	$0.438533\pi$
$594$	−65913.9	−	102564.i	−0.186812	−	0.290685i
$595$	−12792.8	+	10981.9i	−0.0361353	+	0.0310202i
$596$	38530.4	+	131222.i	0.108470	+	0.369416i
$597$	33467.9			0.0939031
$598$	−385773.	−	421830.i	−1.07877	−	1.17960i
$599$	−160553.			−0.447471			−0.223736	−	0.974650i	$-0.571825\pi$
$599$	−160553.			−0.447471			−0.223736	+	0.974650i	$0.571825\pi$
$600$	139113.	−	39454.4i	0.386426	−	0.109596i
$601$	−166122.	−	191715.i	−0.459915	−	0.530770i	0.477664	−	0.878542i	$-0.341484\pi$
$601$	−166122.	−	191715.i	−0.459915	−	0.530770i	−0.937579	+	0.347773i	$0.886938\pi$
$602$	−18662.3	−	29039.0i	−0.0514957	−	0.0801289i
$603$	−29628.0	−	206067.i	−0.0814832	−	0.566728i
$604$	−171339.	−	110113.i	−0.469659	−	0.301832i
$605$	−300438.	−	138887.i	−0.820812	−	0.379447i
$606$	167243.	−	193008.i	0.455409	−	0.525571i
$607$	−592601.	−	85203.2i	−1.60837	−	0.231248i	−0.721210	−	0.692717i	$-0.756414\pi$
$607$	−592601.	−	85203.2i	−1.60837	−	0.231248i	−0.887157	+	0.461468i	$0.847323\pi$
$608$	135102.	+	295832.i	0.365472	+	0.800272i
$609$	516.594	−	1759.36i	0.00139288	−	0.00474372i
$610$	−133867.	+	448237.i	−0.359762	+	1.20461i
$611$	7282.65	+	15946.8i	0.0195077	+	0.0427160i
$612$	4413.66	−	30697.7i	0.0117841	−	0.0819602i
$613$	441458.	−	509470.i	1.17481	−	1.35581i	0.253333	−	0.967379i	$-0.418473\pi$
$613$	441458.	−	509470.i	1.17481	−	1.35581i	0.921479	−	0.388427i	$-0.126982\pi$
$614$	−78091.1	+	170996.i	−0.207140	+	0.453574i
$615$	−42779.7	−	27773.0i	−0.113106	−	0.0734299i
$616$	−1855.23	−	12903.4i	−0.00488917	−	0.0340050i
$617$	−421178.	+	270675.i	−1.10636	+	0.711012i	−0.960496	−	0.278293i	$-0.910231\pi$
$617$	−421178.	+	270675.i	−1.10636	+	0.711012i	−0.145861	+	0.989305i	$0.546595\pi$
$618$	24960.6	+	28806.0i	0.0653548	+	0.0754234i
$619$	135975.	+	463088.i	0.354877	+	1.20860i	0.922723	+	0.385465i	$0.125959\pi$
$619$	135975.	+	463088.i	0.354877	+	1.20860i	−0.567846	+	0.823135i	$0.692223\pi$
$620$	410.101	−	88739.7i	0.00106686	−	0.230853i
$621$	−205359.	−	301476.i	−0.532514	−	0.781754i
$622$		−	441966.i		−	1.14237i
$623$	21803.5	+	74256.0i	0.0561760	+	0.191318i
$624$	−240092.	−	277080.i	−0.616606	−	0.711601i
$625$	332462.	−	205078.i	0.851103	−	0.524998i
$626$	−572095.	+	82254.9i	−1.45989	+	0.209900i
$627$	43470.5	−	67641.3i	0.110576	−	0.172059i
$628$	−1380.34	+	3022.52i	−0.00349999	+	0.00766390i
$629$	−46601.6	+	53781.1i	−0.117788	+	0.135934i
$630$	−7315.92	+	49266.0i	−0.0184327	+	0.124127i
$631$	−377889.	+	172576.i	−0.949086	+	0.433433i	−0.828949	−	0.559324i	$-0.811061\pi$
$631$	−377889.	+	172576.i	−0.949086	+	0.433433i	−0.120137	+	0.992757i	$0.538333\pi$
$632$	−227339.	−	66752.8i	−0.569167	−	0.167123i
$633$	18528.6	−	63102.7i	0.0462419	−	0.157486i
$634$	105575.	+	231178.i	0.262654	+	0.575132i
$635$	−55395.0	+	373034.i	−0.137380	+	0.925127i
$636$	97569.6	+	84544.6i	0.241213	+	0.209012i
$637$	487673.	+	222713.i	1.20185	+	0.548866i
$638$	−7097.54	−	4561.31i	−0.0174368	−	0.0112059i
$639$	−30321.4	−	210890.i	−0.0742586	−	0.516480i
$640$	−403724.	+	256829.i	−0.985654	+	0.627024i
$641$	583653.	−	505738.i	1.42049	−	1.23086i	0.486444	−	0.873712i	$-0.338294\pi$
$641$	583653.	−	505738.i	1.42049	−	1.23086i	0.934047	−	0.357150i	$-0.116252\pi$
$642$	−73374.4	+	21544.7i	−0.178022	+	0.0522721i
$643$	237918.			0.575446			0.287723	−	0.957714i	$-0.407102\pi$
$643$	237918.			0.575446			0.287723	+	0.957714i	$0.407102\pi$
$644$	4280.81	+	25000.7i	0.0103218	+	0.0602811i
$645$	121403.	+	561.053i	0.291818	+	0.00134860i
$646$	170811.	−	50154.6i	0.409308	−	0.120184i
$647$	−352048.	+	305052.i	−0.840996	+	0.728727i	−0.964632	−	0.263601i	$-0.915090\pi$
$647$	−352048.	+	305052.i	−0.840996	+	0.728727i	0.123636	+	0.992328i	$0.460544\pi$
$648$	24972.0	+	38857.2i	0.0594707	+	0.0925383i
$649$	−227714.	+	32740.3i	−0.540630	+	0.0777309i
$650$	−564756.	−	370367.i	−1.33670	−	0.876608i
$651$	19678.9	+	8987.06i	0.0464343	+	0.0212058i
$652$	−158140.	−	137029.i	−0.372003	−	0.322343i
$653$	73637.9	+	10587.5i	0.172693	+	0.0248295i	0.228119	−	0.973633i	$-0.426743\pi$
$653$	73637.9	+	10587.5i	0.172693	+	0.0248295i	−0.0554258	+	0.998463i	$0.517652\pi$
$654$	468210.	−	213824.i	1.09467	−	0.499921i
$655$	134888.	−	451654.i	0.314405	−	1.05274i
$656$	122859.	+	36074.6i	0.285495	+	0.0838289i
$657$	90777.3	−	41456.6i	0.210303	−	0.0960424i
$658$	391.645	−	2723.95i	0.000904567	−	0.00629140i
$659$	−90383.5	−	78317.8i	−0.208122	−	0.180339i	0.544562	−	0.838721i	$-0.316696\pi$
$659$	−90383.5	−	78317.8i	−0.208122	−	0.180339i	−0.752684	+	0.658382i	$0.771241\pi$
$660$	−27064.2	−	12511.3i	−0.0621309	−	0.0287220i
$661$	405429.	−	630859.i	0.927922	−	1.44387i	0.0320885	−	0.999485i	$-0.489784\pi$
$661$	405429.	−	630859.i	0.927922	−	1.44387i	0.895834	−	0.444390i	$-0.146579\pi$
$662$	−43797.7	+	6297.16i	−0.0999391	+	0.0143691i
$663$	−86247.1	+	55427.6i	−0.196208	+	0.126095i
$664$	−195100.	+	169055.i	−0.442508	+	0.383435i
$665$	−77644.7	+	22409.3i	−0.175577	+	0.0506740i
$666$			210222.i			0.473948i
$667$	−21593.5	−	13073.7i	−0.0485367	−	0.0293865i
$668$		−	234043.i		−	0.524497i
$669$	221475.	−	65030.9i	0.494849	−	0.145301i
$670$	−288646.	−	336242.i	−0.643007	−	0.749036i
$671$	−124780.	+	80191.4i	−0.277141	+	0.178108i
$672$	4184.16	+	29101.5i	0.00926551	+	0.0644431i
$673$	290966.	−	452752.i	0.642410	−	0.999609i	−0.355480	−	0.934684i	$-0.615683\pi$
$673$	290966.	−	452752.i	0.642410	−	0.999609i	0.997890	−	0.0649256i	$-0.0206810\pi$
$674$	−233742.	−	106746.i	−0.514537	−	0.234981i
$675$	−323084.	−	285225.i	−0.709101	−	0.626008i
$676$	−21345.7	+	148463.i	−0.0467108	+	0.324881i
$677$	96385.7	+	211055.i	0.210298	+	0.460489i	0.985159	−	0.171643i	$-0.0549075\pi$
$677$	96385.7	+	211055.i	0.210298	+	0.460489i	−0.774861	+	0.632132i	$0.782180\pi$
$678$	354913.	+	104212.i	0.772080	+	0.226703i
$679$	47885.2	+	14060.4i	0.103863	+	0.0304970i
$680$	41742.2	+	92532.0i	0.0902730	+	0.200112i
$681$	−416938.	−	59946.6i	−0.899036	−	0.129262i
$682$	65185.9	−	75228.5i	0.140147	−	0.161739i
$683$	678203.	+	309725.i	1.45384	+	0.663949i	0.976648	−	0.214848i	$-0.0689255\pi$
$683$	678203.	+	309725.i	1.45384	+	0.663949i	0.477197	+	0.878796i	$0.341653\pi$
$684$	80368.6	−	125056.i	0.171781	−	0.267296i
$685$	532369.	−	74033.7i	1.13457	−	0.157779i
$686$	−92122.0	−	143345.i	−0.195756	−	0.304602i
$687$	−204592.	−	236112.i	−0.433486	−	0.500270i
$688$	−292439.	+	85867.8i	−0.617814	+	0.181407i
$689$			927223.i			1.95320i
$690$	−289911.	−	124709.i	−0.608928	−	0.261940i
$691$	97322.3			0.203825			0.101912	−	0.994793i	$-0.467504\pi$
$691$	97322.3			0.203825			0.101912	+	0.994793i	$0.467504\pi$
$692$	92854.9	+	316235.i	0.193907	+	0.660385i
$693$	−11935.0	+	10341.7i	−0.0248516	+	0.0215340i
$694$	250930.	−	161263.i	0.520995	−	0.334823i
$695$	182804.	−	25421.6i	0.378457	−	0.0526299i
$696$	−9287.46	−	5968.69i	−0.0191725	−	0.0123214i
$697$	14874.3	−	32570.2i	0.0306176	−	0.0670432i
$698$	217901.	+	188812.i	0.447248	+	0.387542i
$699$	−64749.4	+	450342.i	−0.132520	+	0.921697i
$700$	12196.5	+	27373.4i	0.0248908	+	0.0558641i
$701$	98309.2	−	334810.i	0.200059	−	0.681339i	−0.796949	−	0.604046i	$-0.793554\pi$
$701$	98309.2	−	334810.i	0.200059	−	0.681339i	0.997008	−	0.0772925i	$-0.0246275\pi$
$702$	−209926.	+	714942.i	−0.425982	+	1.45076i
$703$	−310275.	+	141698.i	−0.627821	+	0.286716i
$704$	−54121.0	−	7781.42i	−0.109199	−	0.0157005i
$705$	7285.40	+	6372.02i	0.0146580	+	0.0128203i
$706$	−427498.	+	936091.i	−0.857680	+	1.87806i
$707$	−68467.5	−	44001.4i	−0.136976	−	0.0880294i
$708$	193778.	−	27861.0i	0.386578	−	0.0555815i
$709$	115283.	+	179383.i	0.229336	+	0.356853i	0.936782	−	0.349914i	$-0.113789\pi$
$709$	115283.	+	179383.i	0.229336	+	0.356853i	−0.707446	+	0.706767i	$0.750153\pi$
$710$	−295400.	−	344111.i	−0.585996	−	0.682624i
$711$	80865.9	+	275404.i	0.159966	+	0.544793i
$712$	465959.			0.919153
$713$	188936.	−	230223.i	0.371652	−	0.452867i
$714$	16093.6			0.0315687
$715$	−59380.2	−	205743.i	−0.116153	−	0.402451i
$716$	174722.	+	201640.i	0.340817	+	0.393324i
$717$	−64538.3	−	100424.i	−0.125539	−	0.195343i
$718$	4561.07	+	31722.9i	0.00884744	+	0.0615353i
$719$	87751.3	+	56394.3i	0.169744	+	0.109088i	0.622755	−	0.782417i	$-0.286014\pi$
$719$	87751.3	+	56394.3i	0.169744	+	0.109088i	−0.453010	+	0.891505i	$0.649650\pi$
$720$	399177.	+	184532.i	0.770017	+	0.355965i
$721$	7954.52	−	9180.00i	0.0153018	−	0.0176592i
$722$	235399.	+	33845.3i	0.451575	+	0.0649267i
$723$	−111241.	−	243584.i	−0.212808	−	0.465985i
$724$	−32779.8	+	111638.i	−0.0625358	+	0.212977i
$725$	−28536.8	−	8666.44i	−0.0542911	−	0.0164879i
$726$	131247.	+	287390.i	0.249009	+	0.545254i
$727$	51914.7	−	361075.i	0.0982248	−	0.683169i	−0.879901	−	0.475156i	$-0.842391\pi$
$727$	51914.7	−	361075.i	0.0982248	−	0.683169i	0.978126	−	0.208012i	$-0.0666994\pi$
$728$	−52174.3	+	60212.3i	−0.0984450	+	0.113612i
$729$	−93994.1	+	205818.i	−0.176867	+	0.387284i
$730$	115669.	−	178169.i	0.217056	−	0.334339i
$731$	12129.2	+	84360.6i	0.0226986	+	0.157872i
$732$	106184.	−	68240.4i	0.198170	−	0.127356i
$733$	−206319.	−	238104.i	−0.383999	−	0.443159i	0.530538	−	0.847661i	$-0.321990\pi$
$733$	−206319.	−	238104.i	−0.383999	−	0.443159i	−0.914537	+	0.404503i	$0.867445\pi$
$734$	268121.	+	913136.i	0.497667	+	1.69490i
$735$	295988.	+	1367.87i	0.547897	+	0.00253204i
$736$	402026.	+	46852.1i	0.742162	+	0.0864916i
$737$		−	140508.i		−	0.258683i
$738$	−29800.1	−	101490.i	−0.0547149	−	0.186342i
$739$	−37442.8	−	43211.3i	−0.0685613	−	0.0791240i	0.720433	−	0.693525i	$-0.243943\pi$
$739$	−37442.8	−	43211.3i	−0.0685613	−	0.0791240i	−0.788994	+	0.614401i	$0.789398\pi$
$740$	67891.7	+	106723.i	0.123981	+	0.194892i
$741$	−486411.	+	69935.3i	−0.885863	+	0.127368i
$742$	78691.5	−	122446.i	0.142929	−	0.222402i
$743$	154091.	−	337413.i	0.279126	−	0.611201i	−0.717198	−	0.696870i	$-0.754576\pi$
$743$	154091.	−	337413.i	0.279126	−	0.611201i	0.996324	+	0.0856692i	$0.0273028\pi$
$744$	85298.7	−	98440.0i	0.154098	−	0.177838i
$745$	−79655.1	+	536404.i	−0.143516	+	0.966451i
$746$	843927.	−	385408.i	1.51645	−	0.692538i
$747$	300066.	+	88107.4i	0.537745	+	0.157896i
$748$	5897.06	−	20083.6i	0.0105398	−	0.0358953i
$749$	10123.8	+	22168.1i	0.0180460	+	0.0395152i
$750$	−368302.	−	58176.3i	−0.654759	−	0.103424i
$751$	−795848.	−	689606.i	−1.41108	−	1.22270i	−0.940253	−	0.340476i	$-0.889412\pi$
$751$	−795848.	−	689606.i	−1.41108	−	1.22270i	−0.470822	−	0.882228i	$-0.656043\pi$
$752$	−22102.7	−	10094.0i	−0.0390850	−	0.0178495i
$753$	−462579.	−	297282.i	−0.815823	−	0.524298i
$754$	7338.24	+	51038.6i	0.0129077	+	0.0897752i
$755$	−433474.	−	681401.i	−0.760447	−	1.19539i
$756$	24987.3	−	21651.6i	0.0437195	−	0.0378832i
$757$	−242295.	+	71144.2i	−0.422817	+	0.124150i	−0.486217	−	0.873838i	$-0.661624\pi$
$757$	−242295.	+	71144.2i	−0.422817	+	0.124150i	0.0634004	+	0.997988i	$0.479805\pi$
$758$	48646.4			0.0846666
$759$	−43991.9	−	89878.1i	−0.0763642	−	0.156016i
$760$	−2248.60	+	486563.i	−0.00389300	+	0.842388i
$761$	−157478.	+	46239.6i	−0.271925	+	0.0798445i	−0.414852	−	0.909889i	$-0.636167\pi$
$761$	−157478.	+	46239.6i	−0.271925	+	0.0798445i	0.142927	+	0.989733i	$0.454349\pi$
$762$	272056.	−	235738.i	0.468542	−	0.405994i
$763$	−88683.5	−	137994.i	−0.152333	−	0.237035i
$764$	−177213.	+	25479.4i	−0.303605	+	0.0436519i
$765$	66961.9	−	103144.i	0.114421	−	0.176246i
$766$	375429.	+	171453.i	0.639839	+	0.292204i
$767$	1.06260e6	+	920752.i	1.80626	+	1.56514i
$768$	335216.	+	48196.8i	0.568333	+	0.0817139i
$769$	−354651.	+	161964.i	−0.599720	+	0.273883i	−0.692055	−	0.721845i	$-0.743294\pi$
$769$	−354651.	+	161964.i	−0.599720	+	0.273883i	0.0923348	+	0.995728i	$0.470567\pi$
$770$	−9619.41	+	32209.3i	−0.0162243	+	0.0543250i
$771$	423986.	+	124493.i	0.713251	+	0.209429i
$772$	111439.	−	50892.6i	0.186984	−	0.0853926i
$773$	−130748.	+	909374.i	−0.218815	+	1.52189i	0.523607	+	0.851960i	$0.324586\pi$
$773$	−130748.	+	909374.i	−0.218815	+	1.52189i	−0.742422	+	0.669932i	$0.766323\pi$
$774$	190277.	+	164876.i	0.317618	+	0.275218i
$775$	149125.	−	318710.i	0.248283	−	0.530630i
$776$	162453.	−	252781.i	0.269776	−	0.419780i
$777$	−30522.3	+	4388.44i	−0.0505562	+	0.00726889i
$778$	566804.	−	364262.i	0.936426	−	0.601804i
$779$	129706.	−	112391.i	0.213740	−	0.185207i
$780$	50530.7	+	175081.i	0.0830550	+	0.287773i
$781$		−	143797.i		−	0.235747i
$782$	56703.6	−	214174.i	0.0927250	−	0.350230i
$783$			32904.2i			0.0536695i
$784$	−712980.	+	209350.i	−1.15997	+	0.340597i
$785$	−9997.13	+	8581.99i	−0.0162232	+	0.0139267i
$786$	−378512.	+	243255.i	−0.612682	+	0.393747i
$787$	−108932.	−	757641.i	−0.175876	−	1.22325i	−0.866182	−	0.499728i	$-0.833433\pi$
$787$	−108932.	−	757641.i	−0.175876	−	1.22325i	0.690306	−	0.723518i	$-0.257476\pi$
$788$	−127416.	+	198262.i	−0.205197	+	0.319292i
$789$	174864.	+	79857.6i	0.280896	+	0.128281i
$790$	459886.	+	402230.i	0.736879	+	0.644495i
$791$	16776.0	−	116680.i	0.0268125	−	0.186485i
$792$	39498.7	+	86490.2i	0.0629699	+	0.137885i
$793$	869805.	+	255398.i	1.38317	+	0.406135i
$794$	463661.	+	136143.i	0.735461	+	0.215951i
$795$	210504.	+	466634.i	0.333062	+	0.738315i
$796$	41335.9	+	5943.21i	0.0652381	+	0.00937983i
$797$	626941.	−	723529.i	0.986985	−	1.13904i	−0.00330136	−	0.999995i	$-0.501051\pi$
$797$	626941.	−	723529.i	0.986985	−	1.13904i	0.990286	−	0.139046i	$-0.0444037\pi$
$798$	70169.2	+	32045.2i	0.110190	+	0.0503219i
$799$	−3673.49	+	5716.06i	−0.00575420	+	0.00895371i
$800$	473940.	−	63677.0i	0.740531	−	0.0994953i
$801$	−305178.	−	474866.i	−0.475650	−	0.740126i
$802$	−267444.	−	308647.i	−0.415800	−	0.479859i
$803$	64625.4	−	18975.7i	0.100224	−	0.0294285i
$804$			119568.i			0.184971i
$805$	−26189.9	+	97105.3i	−0.0404149	+	0.149848i
$806$	−608367.			−0.936473
$807$	−78993.6	−	269027.i	−0.121296	−	0.413095i
$808$	−370334.	+	320896.i	−0.567246	+	0.491521i
$809$	816420.	−	524681.i	1.24743	−	0.801675i	0.260918	−	0.965361i	$-0.415975\pi$
$809$	816420.	−	524681.i	1.24743	−	0.801675i	0.986513	+	0.163686i	$0.0523384\pi$
$810$	−16405.5	−	117970.i	−0.0250045	−	0.179805i
$811$	−851114.	−	546978.i	−1.29403	−	0.831626i	−0.301486	−	0.953471i	$-0.597483\pi$
$811$	−851114.	−	546978.i	−1.29403	−	0.831626i	−0.992549	+	0.121845i	$0.961119\pi$
$812$	950.465	−	2081.23i	0.00144153	−	0.00315651i
$813$	79527.7	+	68911.2i	0.120320	+	0.104258i
$814$	−20192.0	+	140438.i	−0.0304741	+	0.211952i
$815$	−341183.	−	756316.i	−0.513655	−	1.13864i
$816$	40033.8	−	136343.i	0.0601239	−	0.204763i
$817$	−115093.	+	391970.i	−0.172427	+	0.587231i
$818$	−963190.	+	439874.i	−1.43948	+	0.657388i
$819$	95534.6	+	13735.8i	0.142427	+	0.0204779i
$820$	−47904.9	−	41899.0i	−0.0712447	−	0.0623126i
$821$	53511.3	−	117173.i	0.0793887	−	0.173837i	−0.865775	−	0.500433i	$-0.833174\pi$
$821$	53511.3	−	117173.i	0.0793887	−	0.173837i	0.945164	+	0.326596i	$0.105902\pi$
$822$	−431613.	−	277381.i	−0.638780	−	0.410519i
$823$	271453.	−	39029.0i	0.400769	−	0.0576219i	0.0610167	−	0.998137i	$-0.480566\pi$
$823$	271453.	−	39029.0i	0.400769	−	0.0576219i	0.339753	+	0.940515i	$0.389657\pi$
$824$	−39539.5	−	61524.7i	−0.0582341	−	0.0906140i
$825$	−76592.7	−	90061.3i	−0.112533	−	0.132321i
$826$	−62182.2	−	211773.i	−0.0911393	−	0.310392i
$827$	968868.			1.41662			0.708310	−	0.705901i	$-0.249458\pi$
$827$	968868.			1.41662			0.708310	+	0.705901i	$0.249458\pi$
$828$	−81332.7	−	166167.i	−0.118633	−	0.242374i
$829$	−713898.			−1.03879			−0.519395	−	0.854535i	$-0.673842\pi$
$829$	−713898.			−1.03879			−0.519395	+	0.854535i	$0.673842\pi$
$830$	639577.	−	184590.i	0.928403	−	0.267950i
$831$	137191.	+	158326.i	0.198665	+	0.229272i
$832$	180667.	+	281123.i	0.260995	+	0.406116i
$833$	29571.6	+	205675.i	0.0426173	+	0.296410i
$834$	−148207.	−	95246.6i	−0.213076	−	0.136936i
$835$	389412.	−	842369.i	0.558517	−	1.20817i
$836$	65701.7	−	75823.8i	0.0940078	−	0.108491i
$837$	−384265.	−	55249.0i	−0.548504	−	0.0788630i
$838$	603238.	+	1.32091e6i	0.859014	+	1.88098i
$839$	122649.	−	417703.i	0.174236	−	0.593394i	−0.825350	−	0.564622i	$-0.809022\pi$
$839$	122649.	−	417703.i	0.174236	−	0.593394i	0.999586	−	0.0287724i	$-0.00915980\pi$
$840$	−12587.4	+	42147.4i	−0.0178393	+	0.0597327i
$841$	−292869.	−	641294.i	−0.414078	−	0.906704i
$842$	−29515.2	+	205283.i	−0.0416315	+	0.289553i
$843$	−161107.	+	185928.i	−0.226705	+	0.261631i
$844$	34090.3	−	74647.3i	0.0478570	−	0.104792i
$845$	−323847.	+	498831.i	−0.453551	+	0.698619i
$846$	2856.58	+	19868.0i	0.00399122	+	0.0277596i
$847$	84701.8	−	54434.6i	0.118066	−	0.0758766i
$848$	−841600.	−	971258.i	−1.17035	−	1.35065i
$849$	−190572.	−	649030.i	−0.264390	−	0.900429i
$850$	2419.33	−	261748.i	0.00334856	−	0.362281i
$851$	−49139.6	+	421654.i	−0.0678535	+	0.582233i
$852$			122366.i			0.168571i
$853$	−113213.	−	385569.i	−0.155596	−	0.529912i	0.844387	−	0.535734i	$-0.179965\pi$
$853$	−113213.	−	385569.i	−0.155596	−	0.529912i	−0.999983	+	0.00582187i	$0.998147\pi$
$854$	−93188.8	−	107546.i	−0.127776	−	0.147461i
$855$	497336.	−	316381.i	0.680328	−	0.432791i
$856$	145237.	−	20881.9i	0.198212	−	0.0284986i
$857$	−169281.	+	263406.i	−0.230487	+	0.358644i	−0.937163	−	0.348893i	$-0.886558\pi$
$857$	−169281.	+	263406.i	−0.230487	+	0.358644i	0.706676	+	0.707538i	$0.250194\pi$
$858$	−84913.5	+	185935.i	−0.115346	+	0.252572i
$859$	572467.	−	660662.i	0.775826	−	0.895350i	−0.220975	−	0.975279i	$-0.570924\pi$
$859$	572467.	−	660662.i	0.775826	−	0.895350i	0.996801	+	0.0799291i	$0.0254694\pi$
$860$	149845.	+	22251.7i	0.202602	+	0.0300861i
$861$	14113.3	−	6445.32i	0.0190380	−	0.00869437i
$862$	−1.36979e6	−	402205.i	−1.84348	−	0.541294i
$863$	224329.	−	763995.i	0.301206	−	1.02581i	−0.660293	−	0.751008i	$-0.729568\pi$
$863$	224329.	−	763995.i	0.301206	−	1.02581i	0.961499	−	0.274807i	$-0.0886139\pi$
$864$	−219169.	−	479913.i	−0.293597	−	0.642887i
$865$	−191962.	+	1.29269e6i	−0.256557	+	1.72767i
$866$	−262389.	−	227362.i	−0.349873	−	0.303167i
$867$	347736.	+	158806.i	0.462607	+	0.211265i
$868$	22709.3	+	14594.4i	0.0301415	+	0.0193708i
$869$	27569.5	+	191750.i	0.0365081	+	0.253919i
$870$	15280.1	+	24019.7i	0.0201878	+	0.0317343i
$871$	−648995.	+	562357.i	−0.855470	+	0.741269i
$872$	−947620.	+	278246.i	−1.24624	+	0.365929i
$873$	−364011.			−0.477623
$874$	673691.	−	820909.i	0.881938	−	1.07466i
$875$	−1647.37	+	118815.i	−0.00215167	+	0.155188i
$876$	−54994.2	+	16147.7i	−0.0716652	+	0.0210428i
$877$	−715998.	+	620416.i	−0.930921	+	0.806648i	−0.981380	−	0.192078i	$-0.938477\pi$
$877$	−715998.	+	620416.i	−0.930921	+	0.806648i	0.0504585	+	0.998726i	$0.483932\pi$
$878$	−544898.	−	847878.i	−0.706848	−	1.09988i
$879$	−295644.	+	42507.2i	−0.382641	+	0.0550154i
$880$	248944.	+	161617.i	0.321467	+	0.208700i
$881$	1.09090e6	+	498198.i	1.40551	+	0.641875i	0.966514	−	0.256615i	$-0.0826072\pi$
$881$	1.09090e6	+	498198.i	1.40551	+	0.641875i	0.438995	+	0.898489i	$0.355334\pi$
$882$	463906.	+	401977.i	0.596338	+	0.516730i
$883$	−1.29430e6	−	186093.i	−1.66002	−	0.238675i	−0.752475	−	0.658621i	$-0.771140\pi$
$883$	−1.29430e6	−	186093.i	−1.66002	−	0.238675i	−0.907549	+	0.419946i	$0.862049\pi$
$884$	−116366.	+	53142.5i	−0.148909	+	0.0680044i
$885$	743801.	+	222138.i	0.949664	+	0.283620i
$886$	311236.	+	91387.1i	0.396481	+	0.116417i
$887$	805408.	−	367818.i	1.02369	−	0.467504i	0.168437	−	0.985713i	$-0.446128\pi$
$887$	805408.	−	367818.i	1.02369	−	0.467504i	0.855254	+	0.518209i	$0.173401\pi$
$888$	−26422.1	+	183770.i	−0.0335075	+	0.233050i
$889$	−86699.7	−	75125.7i	−0.109702	−	0.0950573i
$890$	−1.09063e6	−	504179.i	−1.37689	−	0.636510i
$891$	20417.4	−	31770.0i	0.0257184	−	0.0400186i
$892$	285090.	−	40989.7i	0.358304	−	0.0515164i
$893$	−27398.4	+	17607.9i	−0.0343576	+	0.0220803i
$894$	391203.	−	338979.i	0.489471	−	0.424129i
$895$	293362.	+	1.01645e6i	0.366233	+	1.26894i
$896$		−	145556.i		−	0.181306i
$897$	−239069.	+	562914.i	−0.297125	+	0.699612i
$898$			1.03121e6i			1.27877i
$899$	−25776.8	+	7568.76i	−0.0318941	+	0.00936494i
$900$	−141605.	−	166506.i	−0.174821	−	0.205563i
$901$	−302325.	+	194292.i	−0.372412	+	0.239335i
$902$	−10159.7	−	70662.3i	−0.0124873	−	0.0868510i
$903$	−19966.4	+	31068.3i	−0.0244863	+	0.0381015i
$904$	−645600.	−	294836.i	−0.789999	−	0.360780i
$905$	−303729.	+	347266.i	−0.370842	+	0.423999i
$906$	−109708.	+	763036.i	−0.133654	+	0.929584i
$907$	−384424.	−	841771.i	−0.467300	−	1.02324i	−0.985762	−	0.168144i	$-0.946223\pi$
$907$	−384424.	−	841771.i	−0.467300	−	1.02324i	0.518462	−	0.855101i	$-0.326505\pi$
$908$	−504311.	−	148079.i	−0.611683	−	0.179606i
$909$	569579.	+	167243.i	0.689328	+	0.202405i
$910$	187271.	−	84480.2i	0.226146	−	0.102017i
$911$	40885.4	+	5878.43i	0.0492641	+	0.00708312i	0.166903	−	0.985973i	$-0.446623\pi$
$911$	40885.4	+	5878.43i	0.0492641	+	0.00708312i	−0.117639	+	0.993056i	$0.537532\pi$
$912$	446034.	−	514751.i	0.536263	−	0.618881i
$913$	191996.	+	87681.5i	0.230330	+	0.105188i
$914$	−218733.	+	340355.i	−0.261831	+	0.407418i
$915$	495719.	−	68937.0i	0.592098	−	0.0823398i
$916$	−210761.	−	327951.i	−0.251189	−	0.390857i
$917$	93899.2	+	108365.i	0.111667	+	0.128870i
$918$	−277098.	+	81363.2i	−0.328812	+	0.0965479i
$919$			171409.i			0.202957i	0.994838	+	0.101478i	$0.0323573\pi$
$919$			171409.i			0.202957i	−0.994838	+	0.101478i	$0.967643\pi$
$920$	516549.	+	316015.i	0.610290	+	0.373364i
$921$	201120.			0.237102
$922$	377093.	+	1.28426e6i	0.443595	+	1.51075i
$923$	−664182.	+	575517.i	−0.779621	+	0.675546i
$924$	7630.16	−	4903.60i	0.00893695	−	0.00574343i
$925$	66785.8	+	497078.i	0.0780550	+	0.580954i
$926$	932707.	+	599415.i	1.08774	+	0.699045i
$927$	−36804.5	+	80590.7i	−0.0428294	+	0.0937833i
$928$	−27592.3	−	23908.9i	−0.0320400	−	0.0277628i
$929$	163326.	−	1.13596e6i	0.189245	−	1.31623i	−0.644723	−	0.764417i	$-0.723027\pi$
$929$	163326.	−	1.13596e6i	0.189245	−	1.31623i	0.833968	−	0.551813i	$-0.186064\pi$
$930$	−306166.	+	138115.i	−0.353990	+	0.159689i
$931$	−280602.	+	955643.i	−0.323736	+	1.10254i
$932$	−159943.	+	544715.i	−0.184134	+	0.627101i
$933$	−430120.	+	196429.i	−0.494113	+	0.225654i
$934$	412410.	+	59295.6i	0.472754	+	0.0679717i
$935$	54640.7	−	62473.0i	0.0625018	−	0.0714610i
$936$	241404.	−	528601.i	0.275545	−	0.603359i
$937$	−708181.	−	455120.i	−0.806613	−	0.518379i	0.0711547	−	0.997465i	$-0.477332\pi$
$937$	−708181.	−	455120.i	−0.806613	−	0.518379i	−0.877768	+	0.479087i	$0.840968\pi$
$938$	133430.	−	19184.4i	0.151652	−	0.0218043i
$939$	334315.	+	520204.i	0.379162	+	0.589987i
$940$	7866.59	+	9163.76i	0.00890289	+	0.0103709i
$941$	189606.	+	645737.i	0.214127	+	0.729251i	0.994574	+	0.104029i	$0.0331734\pi$
$941$	189606.	+	645737.i	0.214127	+	0.729251i	−0.780447	+	0.625222i	$0.785008\pi$
$942$	12576.5			0.0141729
$943$	−36048.4	−	210529.i	−0.0405380	−	0.236750i
$944$	−1.94880e6			−2.18687
$945$	125959.	−	36353.5i	0.141048	−	0.0407083i
$946$	111278.	+	128421.i	0.124344	+	0.143501i
$947$	−327912.	−	510240.i	−0.365643	−	0.568951i	0.608874	−	0.793267i	$-0.291622\pi$
$947$	−327912.	−	510240.i	−0.365643	−	0.568951i	−0.974516	+	0.224316i	$0.927985\pi$
$948$	−23460.8	−	163173.i	−0.0261051	−	0.181565i
$949$	−346297.	−	222552.i	−0.384518	−	0.247115i
$950$	531737.	−	1.13643e6i	0.589182	−	1.25920i
$951$	178059.	−	205491.i	0.196881	−	0.227213i
$952$	−30565.2	−	4394.61i	−0.0337251	−	0.00484893i
$953$	−323140.	−	707577.i	−0.355799	−	0.779091i	−0.999900	−	0.0141505i	$-0.995496\pi$
$953$	−323140.	−	707577.i	−0.355799	−	0.779091i	0.644101	−	0.764941i	$-0.277232\pi$
$954$	−299096.	+	1.01863e6i	−0.328635	+	1.11923i
$955$	−680220.	−	203150.i	−0.745835	−	0.222746i
$956$	−61877.6	−	135493.i	−0.0677045	−	0.148252i
$957$	−1284.60	+	8934.56i	−0.00140263	+	0.00975550i
$958$	−905638.	+	1.04516e6i	−0.986788	+	1.13881i
$959$	−67921.8	+	148728.i	−0.0738537	+	0.161717i
$960$	154745.	+	100462.i	0.167909	+	0.109008i
$961$	86322.0	+	600383.i	0.0934705	+	0.650102i
$962$	729485.	−	468812.i	0.788255	−	0.506580i
$963$	−116403.	−	134337.i	−0.125520	−	0.144858i
$964$	−94137.4	−	320602.i	−0.101300	−	0.344995i
$965$	485770.	+	2244.93i	0.521646	+	0.00241073i
$966$	79344.1	−	54047.5i	0.0850277	−	0.0579190i
$967$		−	1.42244e6i		−	1.52118i	−0.649234	−	0.760588i	$-0.724911\pi$
$967$		−	1.42244e6i		−	1.52118i	0.649234	−	0.760588i	$-0.275089\pi$
$968$	−170789.	−	581655.i	−0.182268	−	0.620748i
$969$	−124726.	−	143942.i	−0.132834	−	0.153299i
$970$	−653755.	+	415887.i	−0.694819	+	0.442009i
$971$	−170688.	+	24541.2i	−0.181036	+	0.0260290i	−0.232236	−	0.972659i	$-0.574604\pi$
$971$	−170688.	+	24541.2i	−0.181036	+	0.0260290i	0.0512005	+	0.998688i	$0.483695\pi$
$972$	−207763.	+	323285.i	−0.219905	+	0.342179i
$973$	−23322.9	+	51070.0i	−0.0246352	+	0.0539436i
$974$	715833.	−	826115.i	0.754560	−	0.870809i
$975$	−109437.	+	714227.i	−0.115121	+	0.751323i
$976$	−1.14293e6	+	521957.i	−1.19983	+	0.547943i
$977$	−35494.2	−	10422.0i	−0.0371851	−	0.0109185i	0.263087	−	0.964772i	$-0.415259\pi$
$977$	−35494.2	−	10422.0i	−0.0371851	−	0.0109185i	−0.300272	+	0.953854i	$0.597078\pi$
$978$	−223130.	+	759913.i	−0.233282	+	0.794486i
$979$	−158262.	−	346545.i	−0.165124	−	0.361571i
$980$	365329.	+	54250.7i	0.380392	+	0.0564876i
$981$	904204.	+	783497.i	0.939568	+	0.814141i
$982$	670669.	+	306284.i	0.695481	+	0.317616i
$983$	858793.	+	551913.i	0.888754	+	0.571168i	0.903435	−	0.428725i	$-0.141037\pi$
$983$	858793.	+	551913.i	0.888754	+	0.571168i	−0.0146810	+	0.999892i	$0.504673\pi$
$984$	−13294.4	−	92464.9i	−0.0137303	−	0.0954964i
$985$	−788472.	+	501587.i	−0.812670	+	0.516980i
$986$	−15103.7	+	13087.4i	−0.0155356	+	0.0134617i
$987$	−2825.00	+	829.496i	−0.00289991	+	0.000851491i
$988$	−613180.			−0.628166
$989$	343110.	+	375179.i	0.350784	+	0.383571i
$990$	1133.07	−	245179.i	0.00115607	−	0.250157i
$991$	797292.	−	234106.i	0.811839	−	0.238377i	0.150641	−	0.988589i	$-0.451866\pi$
$991$	797292.	−	234106.i	0.811839	−	0.238377i	0.661198	+	0.750211i	$0.270048\pi$
$992$	325545.	−	282086.i	0.330817	−	0.286655i
$993$	25594.0	+	39825.1i	0.0259561	+	0.0403885i
$994$	136553.	−	19633.3i	0.138206	−	0.0198711i
$995$	138888.	+	90167.4i	0.140287	+	0.0910759i
$996$	−163382.	−	74614.2i	−0.164697	−	0.0752147i
$997$	699721.	+	606312.i	0.703938	+	0.609966i	0.931476	−	0.363803i	$-0.118522\pi$
$997$	699721.	+	606312.i	0.703938	+	0.609966i	−0.227537	+	0.973769i	$0.573067\pi$
$998$	−828862.	−	119172.i	−0.832187	−	0.119650i
$999$	503343.	−	229869.i	0.504351	−	0.230330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.5.i.a.14.12	✓	460
5.4	even	2	inner	115.5.i.a.14.35	yes	460
23.5	odd	22	inner	115.5.i.a.74.35	yes	460
115.74	odd	22	inner	115.5.i.a.74.12	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.5.i.a.14.12	✓	460	1.1	even	1	trivial
115.5.i.a.14.35	yes	460	5.4	even	2	inner
115.5.i.a.74.12	yes	460	115.74	odd	22	inner
115.5.i.a.74.35	yes	460	23.5	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	115.i (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33057 - 4.53150i) q^{2} +(-3.81868 + 3.30890i) q^{3} +(-5.30401 + 3.40868i) q^{4} +(-24.7617 + 3.44348i) q^{5} +(20.0753 + 12.9016i) q^{6} +(3.15920 - 6.91768i) q^{7} +(-34.6044 - 29.9848i) q^{8} +(-7.89404 + 54.9042i) q^{9} +O(q^{10})\)	\(q+(-1.33057 - 4.53150i) q^{2} +(-3.81868 + 3.30890i) q^{3} +(-5.30401 + 3.40868i) q^{4} +(-24.7617 + 3.44348i) q^{5} +(20.0753 + 12.9016i) q^{6} +(3.15920 - 6.91768i) q^{7} +(-34.6044 - 29.9848i) q^{8} +(-7.89404 + 54.9042i) q^{9} +(48.5512 + 107.626i) q^{10} +(-10.5472 + 35.9204i) q^{11} +(8.97531 - 30.5671i) q^{12} +(208.126 - 95.0478i) q^{13} +(-35.5510 - 5.11146i) q^{14} +(83.1629 - 95.0837i) q^{15} +(-131.739 + 288.468i) q^{16} +(74.6018 + 47.9437i) q^{17} +(259.302 - 37.2820i) q^{18} +(229.805 + 357.584i) q^{19} +(119.599 - 102.669i) q^{20} +(10.8260 + 36.8699i) q^{21} +176.807 q^{22} +(528.810 - 14.1665i) q^{23} +231.360 q^{24} +(601.285 - 170.533i) q^{25} +(-707.634 - 816.654i) q^{26} +(-372.801 - 580.090i) q^{27} +(6.82374 + 47.4601i) q^{28} +(-40.1429 - 25.7983i) q^{29} +(-541.525 - 250.337i) q^{30} +(368.684 - 425.484i) q^{31} +(757.329 + 108.888i) q^{32} +(-78.5808 - 172.068i) q^{33} +(117.994 - 401.850i) q^{34} +(-54.4063 + 182.172i) q^{35} +(-145.281 - 318.121i) q^{36} +(-114.204 + 794.304i) q^{37} +(1314.62 - 1517.15i) q^{38} +(-480.261 + 1051.63i) q^{39} +(960.115 + 623.317i) q^{40} +(-57.4622 - 399.658i) q^{41} +(152.671 - 98.1158i) q^{42} +(629.375 + 726.337i) q^{43} +(-66.4987 - 226.474i) q^{44} +(6.40851 - 1386.71i) q^{45} +(-767.813 - 2377.45i) q^{46} +76.6209i q^{47} +(-451.445 - 1537.48i) q^{48} +(1534.45 + 1770.85i) q^{49} +(-1572.82 - 2497.82i) q^{50} +(-443.521 + 63.7687i) q^{51} +(-779.913 + 1213.57i) q^{52} +(-1683.47 + 3686.29i) q^{53} +(-2132.64 + 2461.20i) q^{54} +(137.475 - 925.769i) q^{55} +(-316.748 + 144.654i) q^{56} +(-2060.76 - 605.095i) q^{57} +(-63.4920 + 216.234i) q^{58} +(2552.80 + 5589.84i) q^{59} +(-116.987 + 787.800i) q^{60} +(2994.32 + 2594.59i) q^{61} +(-2418.64 - 1104.56i) q^{62} +(354.871 + 228.062i) q^{63} +(207.855 + 1445.66i) q^{64} +(-4826.25 + 3070.22i) q^{65} +(-675.169 + 585.037i) q^{66} +(-3601.18 + 1057.40i) q^{67} -559.113 q^{68} +(-1972.48 + 1803.88i) q^{69} +(897.905 + 4.14957i) q^{70} +(-3685.45 + 1082.15i) q^{71} +(1919.46 - 1663.22i) q^{72} +(-972.683 - 1513.52i) q^{73} +(3751.34 - 539.362i) q^{74} +(-1731.84 + 2640.80i) q^{75} +(-2437.78 - 1113.30i) q^{76} +(215.165 + 186.442i) q^{77} +(5404.46 + 777.044i) q^{78} +(4707.01 - 2149.62i) q^{79} +(2268.75 - 7596.61i) q^{80} +(-967.906 - 284.203i) q^{81} +(-1734.59 + 792.162i) q^{82} +(802.374 - 5580.63i) q^{83} +(-183.099 - 158.656i) q^{84} +(-2012.36 - 930.278i) q^{85} +(2453.97 - 3818.45i) q^{86} +(238.657 - 34.3137i) q^{87} +(1442.05 - 926.746i) q^{88} +(-7690.82 + 6664.13i) q^{89} +(-6292.38 + 1816.07i) q^{90} -1740.02i q^{91} +(-2756.53 + 1877.68i) q^{92} +2844.73i q^{93} +(347.208 - 101.949i) q^{94} +(-6921.70 - 8063.06i) q^{95} +(-3252.30 + 2090.12i) q^{96} +(933.932 + 6495.64i) q^{97} +(5982.90 - 9309.57i) q^{98} +(-1888.92 - 862.642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 460 q + 306 q^{4} - 11 q^{5} - 182 q^{6} + 944 q^{9}+O(q^{10}) \) 460 * q + 306 * q^4 - 11 * q^5 - 182 * q^6 + 944 * q^9	\( 460 q + 306 q^{4} - 11 q^{5} - 182 q^{6} + 944 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 1474 q^{15} - 2670 q^{16} - 22 q^{19} + 3157 q^{20} - 22 q^{21} + 3896 q^{24} - 1427 q^{25} - 3166 q^{26} - 2808 q^{29} + 1397 q^{30} + 2684 q^{31} - 12848 q^{34} + 2279 q^{35} + 1114 q^{36} + 12866 q^{39} - 11 q^{40} - 2652 q^{41} + 11110 q^{44} - 5394 q^{46} - 27026 q^{49} - 10931 q^{50} - 22 q^{51} - 51290 q^{54} - 10545 q^{55} + 25322 q^{56} + 41460 q^{59} + 49269 q^{60} - 22506 q^{61} + 68582 q^{64} + 27940 q^{65} - 24332 q^{66} + 7608 q^{69} - 15618 q^{70} + 35838 q^{71} - 59158 q^{74} + 30594 q^{75} - 58520 q^{76} - 17930 q^{79} - 63602 q^{80} + 91888 q^{81} + 92906 q^{84} - 33815 q^{85} + 101486 q^{86} - 22 q^{89} - 37598 q^{90} - 46242 q^{94} + 43336 q^{95} - 210180 q^{96} + 44528 q^{99}+O(q^{100}) \) 460 * q + 306 * q^4 - 11 * q^5 - 182 * q^6 + 944 * q^9 - 11 * q^10 - 22 * q^11 - 22 * q^14 - 1474 * q^15 - 2670 * q^16 - 22 * q^19 + 3157 * q^20 - 22 * q^21 + 3896 * q^24 - 1427 * q^25 - 3166 * q^26 - 2808 * q^29 + 1397 * q^30 + 2684 * q^31 - 12848 * q^34 + 2279 * q^35 + 1114 * q^36 + 12866 * q^39 - 11 * q^40 - 2652 * q^41 + 11110 * q^44 - 5394 * q^46 - 27026 * q^49 - 10931 * q^50 - 22 * q^51 - 51290 * q^54 - 10545 * q^55 + 25322 * q^56 + 41460 * q^59 + 49269 * q^60 - 22506 * q^61 + 68582 * q^64 + 27940 * q^65 - 24332 * q^66 + 7608 * q^69 - 15618 * q^70 + 35838 * q^71 - 59158 * q^74 + 30594 * q^75 - 58520 * q^76 - 17930 * q^79 - 63602 * q^80 + 91888 * q^81 + 92906 * q^84 - 33815 * q^85 + 101486 * q^86 - 22 * q^89 - 37598 * q^90 - 46242 * q^94 + 43336 * q^95 - 210180 * q^96 + 44528 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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