LMFDB - Embedded newform 51.7.f.a.38.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,7,Mod(38,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.38"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	51.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$11.7327582646$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			38.6
Character	$\chi$	$=$	51.38
Dual form			51.7.f.a.47.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-11.5147 q^{2} +(-26.9464 + 1.69997i) q^{3} +68.5886 q^{4} +(-61.6662 - 61.6662i) q^{5} +(310.280 - 19.5747i) q^{6} +(157.734 + 157.734i) q^{7} -52.8363 q^{8} +(723.220 - 91.6164i) q^{9} +(710.068 + 710.068i) q^{10} +(373.384 - 373.384i) q^{11} +(-1848.22 + 116.599i) q^{12} +1805.09 q^{13} +(-1816.26 - 1816.26i) q^{14} +(1766.51 + 1556.85i) q^{15} -3781.27 q^{16} +(-3800.81 - 3113.11i) q^{17} +(-8327.67 + 1054.94i) q^{18} +2798.52i q^{19} +(-4229.60 - 4229.60i) q^{20} +(-4518.52 - 3982.23i) q^{21} +(-4299.41 + 4299.41i) q^{22} +(-10216.3 + 10216.3i) q^{23} +(1423.75 - 89.8204i) q^{24} -8019.57i q^{25} -20785.1 q^{26} +(-19332.5 + 3698.19i) q^{27} +(10818.8 + 10818.8i) q^{28} +(1222.32 + 1222.32i) q^{29} +(-20340.9 - 17926.7i) q^{30} +(27939.0 - 27939.0i) q^{31} +46921.8 q^{32} +(-9426.63 + 10696.1i) q^{33} +(43765.2 + 35846.5i) q^{34} -19453.7i q^{35} +(49604.7 - 6283.84i) q^{36} +(-17932.1 + 17932.1i) q^{37} -32224.1i q^{38} +(-48640.8 + 3068.61i) q^{39} +(3258.21 + 3258.21i) q^{40} +(-46941.1 + 46941.1i) q^{41} +(52029.4 + 45854.2i) q^{42} +22657.6i q^{43} +(25609.9 - 25609.9i) q^{44} +(-50247.8 - 38948.6i) q^{45} +(117638. - 117638. i) q^{46} +50789.0i q^{47} +(101892. - 6428.07i) q^{48} -67888.9i q^{49} +92343.0i q^{50} +(107710. + 77425.8i) q^{51} +123809. q^{52} +2415.99 q^{53} +(222608. - 42583.6i) q^{54} -46050.4 q^{55} +(-8334.10 - 8334.10i) q^{56} +(-4757.41 - 75410.1i) q^{57} +(-14074.6 - 14074.6i) q^{58} -273015. q^{59} +(121163. + 106782. i) q^{60} +(-152273. - 152273. i) q^{61} +(-321709. + 321709. i) q^{62} +(128528. + 99625.5i) q^{63} -298290. q^{64} +(-111313. - 111313. i) q^{65} +(108545. - 123163. i) q^{66} -387883. q^{67} +(-260692. - 213524. i) q^{68} +(257926. - 292660. i) q^{69} +224004. i q^{70} +(-246587. - 246587. i) q^{71} +(-38212.3 + 4840.68i) q^{72} +(-540435. + 540435. i) q^{73} +(206483. - 206483. i) q^{74} +(13633.1 + 216099. i) q^{75} +191946. i q^{76} +117791. q^{77} +(560085. - 35334.2i) q^{78} +(34651.0 + 34651.0i) q^{79} +(233177. + 233177. i) q^{80} +(514654. - 132518. i) q^{81} +(540513. - 540513. i) q^{82} -42259.5 q^{83} +(-309919. - 273136. i) q^{84} +(42407.9 + 426355. i) q^{85} -260895. i q^{86} +(-35015.0 - 30859.2i) q^{87} +(-19728.3 + 19728.3i) q^{88} -1.01473e6i q^{89} +(578590. + 448482. i) q^{90} +(284725. + 284725. i) q^{91} +(-700722. + 700722. i) q^{92} +(-705360. + 800351. i) q^{93} -584821. i q^{94} +(172574. - 172574. i) q^{95} +(-1.26438e6 + 79765.9i) q^{96} +(-424226. + 424226. i) q^{97} +781721. i q^{98} +(235831. - 304247. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 18 q^{3} + 2040 q^{4} - 290 q^{6} - 4 q^{7} - 4256 q^{10} + 4182 q^{12} - 1832 q^{13} + 54976 q^{16} + 10940 q^{18} - 1604 q^{21} + 19576 q^{22} + 15110 q^{24} + 37314 q^{27} - 63120 q^{28} + 51360 q^{30}+ \cdots + 203004 q^{99}+O(q^{100}) $ 68 * q + 18 * q^3 + 2040 * q^4 - 290 * q^6 - 4 * q^7 - 4256 * q^10 + 4182 * q^12 - 1832 * q^13 + 54976 * q^16 + 10940 * q^18 - 1604 * q^21 + 19576 * q^22 + 15110 * q^24 + 37314 * q^27 - 63120 * q^28 + 51360 * q^30 - 88660 * q^31 - 128604 * q^33 + 80200 * q^34 + 335180 * q^37 + 31460 * q^39 - 286828 * q^40 + 45484 * q^45 - 85244 * q^46 + 111922 * q^48 - 590566 * q^51 - 904320 * q^52 - 1215638 * q^54 - 731624 * q^55 + 753144 * q^57 - 328292 * q^58 + 751532 * q^61 + 88664 * q^63 + 870368 * q^64 + 174232 * q^67 + 1420428 * q^69 + 1158660 * q^72 + 2397332 * q^73 + 1415042 * q^75 - 1868044 * q^78 - 1438708 * q^79 - 2973932 * q^81 - 617036 * q^82 + 4901976 * q^84 + 2375468 * q^85 + 521156 * q^88 - 3185088 * q^90 + 1741672 * q^91 + 4082570 * q^96 + 2753300 * q^97 + 203004 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−11.5147			−1.43934			−0.719670	−	0.694317i	$-0.755707\pi$
$2$	−11.5147			−1.43934			−0.719670	+	0.694317i	$0.755707\pi$
$3$	−26.9464	+	1.69997i	−0.998016	+	0.0629620i
$3$	−26.9464	+	1.69997i	−0.998016	+	0.0629620i
$4$	68.5886			1.07170
$5$	−61.6662	−	61.6662i	−0.493329	−	0.493329i	0.416024	−	0.909354i	$-0.363423\pi$
$5$	−61.6662	−	61.6662i	−0.493329	−	0.493329i	−0.909354	+	0.416024i	$0.863423\pi$
$6$	310.280	−	19.5747i	1.43648	−	0.0906236i
$7$	157.734	+	157.734i	0.459866	+	0.459866i	0.898612	−	0.438745i	$-0.144577\pi$
$7$	157.734	+	157.734i	0.459866	+	0.459866i	−0.438745	+	0.898612i	$0.644577\pi$
$8$	−52.8363			−0.103196
$9$	723.220	−	91.6164i	0.992072	−	0.125674i
$10$	710.068	+	710.068i	0.710068	+	0.710068i
$11$	373.384	−	373.384i	0.280529	−	0.280529i	−0.552791	−	0.833320i	$-0.686437\pi$
$11$	373.384	−	373.384i	0.280529	−	0.280529i	0.833320	+	0.552791i	$0.186437\pi$
$12$	−1848.22	+	116.599i	−1.06957	+	0.0674762i
$13$	1805.09			0.821618			0.410809	−	0.911721i	$-0.365246\pi$
$13$	1805.09			0.821618			0.410809	+	0.911721i	$0.365246\pi$
$14$	−1816.26	−	1816.26i	−0.661904	−	0.661904i
$15$	1766.51	+	1556.85i	0.523412	+	0.461290i
$16$	−3781.27			−0.923163
$17$	−3800.81	−	3113.11i	−0.773623	−	0.633647i
$17$	−3800.81	−	3113.11i	−0.773623	−	0.633647i
$18$	−8327.67	+	1054.94i	−1.42793	+	0.180888i
$19$			2798.52i			0.408007i	0.978970	+	0.204003i	$0.0653954\pi$
$19$			2798.52i			0.408007i	−0.978970	+	0.204003i	$0.934605\pi$
$20$	−4229.60	−	4229.60i	−0.528699	−	0.528699i
$21$	−4518.52	−	3982.23i	−0.487908	−	0.430000i
$22$	−4299.41	+	4299.41i	−0.403777	+	0.403777i
$23$	−10216.3	+	10216.3i	−0.839673	+	0.839673i	−0.988816	−	0.149142i	$-0.952349\pi$
$23$	−10216.3	+	10216.3i	−0.839673	+	0.839673i	0.149142	+	0.988816i	$0.452349\pi$
$24$	1423.75	−	89.8204i	0.102991	−	0.00649742i
$25$		−	8019.57i		−	0.513252i
$26$	−20785.1			−1.18259
$27$	−19332.5	+	3698.19i	−0.982191	+	0.187888i
$28$	10818.8	+	10818.8i	0.492837	+	0.492837i
$29$	1222.32	+	1222.32i	0.0501175	+	0.0501175i	0.731721	−	0.681604i	$-0.238717\pi$
$29$	1222.32	+	1222.32i	0.0501175	+	0.0501175i	−0.681604	+	0.731721i	$0.738717\pi$
$30$	−20340.9	−	17926.7i	−0.753367	−	0.663952i
$31$	27939.0	−	27939.0i	0.937833	−	0.937833i	−0.0603445	−	0.998178i	$-0.519220\pi$
$31$	27939.0	−	27939.0i	0.937833	−	0.937833i	0.998178	+	0.0603445i	$0.0192199\pi$
$32$	46921.8			1.43194
$33$	−9426.63	+	10696.1i	−0.262310	+	0.297635i
$34$	43765.2	+	35846.5i	1.11351	+	0.912032i
$35$		−	19453.7i		−	0.453731i
$36$	49604.7	−	6283.84i	1.06320	−	0.134685i
$37$	−17932.1	+	17932.1i	−0.354018	+	0.354018i	−0.861602	−	0.507584i	$-0.830539\pi$
$37$	−17932.1	+	17932.1i	−0.354018	+	0.354018i	0.507584	+	0.861602i	$0.330539\pi$
$38$		−	32224.1i		−	0.587260i
$39$	−48640.8	+	3068.61i	−0.819988	+	0.0517307i
$40$	3258.21	+	3258.21i	0.0509096	+	0.0509096i
$41$	−46941.1	+	46941.1i	−0.681086	+	0.681086i	−0.960245	−	0.279159i	$-0.909944\pi$
$41$	−46941.1	+	46941.1i	−0.681086	+	0.681086i	0.279159	+	0.960245i	$0.409944\pi$
$42$	52029.4	+	45854.2i	0.702265	+	0.618916i
$43$			22657.6i			0.284976i	0.989797	+	0.142488i	$0.0455102\pi$
$43$			22657.6i			0.284976i	−0.989797	+	0.142488i	$0.954490\pi$
$44$	25609.9	−	25609.9i	0.300642	−	0.300642i
$45$	−50247.8	−	38948.6i	−0.551417	−	0.427419i
$46$	117638.	−	117638.i	1.20857	−	1.20857i
$47$			50789.0i			0.489189i	0.969625	+	0.244594i	$0.0786548\pi$
$47$			50789.0i			0.489189i	−0.969625	+	0.244594i	$0.921345\pi$
$48$	101892.	−	6428.07i	0.921331	−	0.0581242i
$49$		−	67888.9i		−	0.577046i
$50$			92343.0i			0.738744i
$51$	107710.	+	77425.8i	0.811983	+	0.583681i
$52$	123809.			0.880525
$53$	2415.99			0.0162281			0.00811404	−	0.999967i	$-0.497417\pi$
$53$	2415.99			0.0162281			0.00811404	+	0.999967i	$0.497417\pi$
$54$	222608.	−	42583.6i	1.41371	−	0.270434i
$55$	−46050.4			−0.276787
$56$	−8334.10	−	8334.10i	−0.0474564	−	0.0474564i
$57$	−4757.41	−	75410.1i	−0.0256889	−	0.407197i
$58$	−14074.6	−	14074.6i	−0.0721361	−	0.0721361i
$59$	−273015.			−1.32932			−0.664661	−	0.747145i	$-0.731424\pi$
$59$	−273015.			−1.32932			−0.664661	+	0.747145i	$0.731424\pi$
$60$	121163.	+	106782.i	0.560938	+	0.494363i
$61$	−152273.	−	152273.i	−0.670860	−	0.670860i	0.287054	−	0.957914i	$-0.407324\pi$
$61$	−152273.	−	152273.i	−0.670860	−	0.670860i	−0.957914	+	0.287054i	$0.907324\pi$
$62$	−321709.	+	321709.i	−1.34986	+	1.34986i
$63$	128528.	+	99625.5i	0.514014	+	0.398427i
$64$	−298290.			−1.13788
$65$	−111313.	−	111313.i	−0.405328	−	0.405328i
$66$	108545.	−	123163.i	0.377553	−	0.428398i
$67$	−387883.			−1.28966			−0.644832	−	0.764324i	$-0.723073\pi$
$67$	−387883.			−1.28966			−0.644832	+	0.764324i	$0.723073\pi$
$68$	−260692.	−	213524.i	−0.829089	−	0.679077i
$69$	257926.	−	292660.i	0.785140	−	0.890875i
$70$			224004.i			0.653073i
$71$	−246587.	−	246587.i	−0.688961	−	0.688961i	0.273041	−	0.962002i	$-0.411970\pi$
$71$	−246587.	−	246587.i	−0.688961	−	0.688961i	−0.962002	+	0.273041i	$0.911970\pi$
$72$	−38212.3	+	4840.68i	−0.102378	+	0.0129691i
$73$	−540435.	+	540435.i	−1.38923	+	1.38923i	−0.562298	+	0.826935i	$0.690083\pi$
$73$	−540435.	+	540435.i	−1.38923	+	1.38923i	−0.826935	+	0.562298i	$0.809917\pi$
$74$	206483.	−	206483.i	0.509553	−	0.509553i
$75$	13633.1	+	216099.i	0.0323154	+	0.512234i
$76$			191946.i			0.437260i
$77$	117791.			0.258012
$78$	560085.	−	35334.2i	1.18024	−	0.0744580i
$79$	34651.0	+	34651.0i	0.0702804	+	0.0702804i	0.741373	−	0.671093i	$-0.234175\pi$
$79$	34651.0	+	34651.0i	0.0702804	+	0.0702804i	−0.671093	+	0.741373i	$0.734175\pi$
$80$	233177.	+	233177.i	0.455423	+	0.455423i
$81$	514654.	−	132518.i	0.968412	−	0.249355i
$82$	540513.	−	540513.i	0.980313	−	0.980313i
$83$	−42259.5			−0.0739078			−0.0369539	−	0.999317i	$-0.511765\pi$
$83$	−42259.5			−0.0739078			−0.0369539	+	0.999317i	$0.511765\pi$
$84$	−309919.	−	273136.i	−0.522890	−	0.460830i
$85$	42407.9	+	426355.i	0.0690541	+	0.694247i
$86$		−	260895.i		−	0.410177i
$87$	−35015.0	−	30859.2i	−0.0531736	−	0.0468626i
$88$	−19728.3	+	19728.3i	−0.0289495	+	0.0289495i
$89$		−	1.01473e6i		−	1.43939i	−0.694291	−	0.719695i	$-0.744282\pi$
$89$		−	1.01473e6i		−	1.43939i	0.694291	−	0.719695i	$-0.255718\pi$
$90$	578590.	+	448482.i	0.793676	+	0.615201i
$91$	284725.	+	284725.i	0.377834	+	0.377834i
$92$	−700722.	+	700722.i	−0.899875	+	0.899875i
$93$	−705360.	+	800351.i	−0.876924	+	0.995020i
$94$		−	584821.i		−	0.704108i
$95$	172574.	−	172574.i	0.201282	−	0.201282i
$96$	−1.26438e6	+	79765.9i	−1.42910	+	0.0901578i
$97$	−424226.	+	424226.i	−0.464817	+	0.464817i	−0.900231	−	0.435413i	$-0.856602\pi$
$97$	−424226.	+	424226.i	−0.464817	+	0.464817i	0.435413	+	0.900231i	$0.356602\pi$
$98$			781721.i			0.830564i
$99$	235831.	−	304247.i	0.243050	−	0.313560i
$100$		−	550051.i		−	0.550051i
$101$		−	526697.i		−	0.511207i	−0.966782	−	0.255603i	$-0.917726\pi$
$101$		−	526697.i		−	0.511207i	0.966782	−	0.255603i	$-0.0822741\pi$
$102$	−1.24025e6	−	891536.i	−1.16872	−	0.840114i
$103$	975773.			0.892971			0.446485	−	0.894791i	$-0.352675\pi$
$103$	975773.			0.892971			0.446485	+	0.894791i	$0.352675\pi$
$104$	−95374.6			−0.0847877
$105$	33070.8	+	524208.i	0.0285678	+	0.452831i
$106$	−27819.4			−0.0233577
$107$	1.19525e6	+	1.19525e6i	0.975682	+	0.975682i	0.999711	−	0.0240289i	$-0.00764939\pi$
$107$	1.19525e6	+	1.19525e6i	0.975682	+	0.975682i	−0.0240289	+	0.999711i	$0.507649\pi$
$108$	−1.32599e6	+	253654.i	−1.05261	+	0.201359i
$109$	−1.61689e6	−	1.61689e6i	−1.24853	−	1.24853i	−0.956368	−	0.292166i	$-0.905624\pi$
$109$	−1.61689e6	−	1.61689e6i	−1.24853	−	1.24853i	−0.292166	−	0.956368i	$-0.594376\pi$
$110$	530257.			0.398390
$111$	452722.	−	513690.i	0.331026	−	0.375606i
$112$	−596436.	−	596436.i	−0.424532	−	0.424532i
$113$	−807755.	+	807755.i	−0.559815	+	0.559815i	−0.929255	−	0.369440i	$-0.879550\pi$
$113$	−807755.	+	807755.i	−0.559815	+	0.559815i	0.369440	+	0.929255i	$0.379550\pi$
$114$	54780.2	+	868325.i	0.0369751	+	0.586095i
$115$	1.26000e6			0.828471
$116$	83837.0	+	83837.0i	0.0537108	+	0.0537108i
$117$	1.30548e6	−	165376.i	0.815104	−	0.103256i
$118$	3.14369e6			1.91335
$119$	−108474.	−	1.09056e6i	−0.0643702	−	0.647156i
$120$	−93336.1	−	82258.4i	−0.0540140	−	0.0476032i
$121$			1.49273e6i			0.842607i
$122$	1.75337e6	+	1.75337e6i	0.965595	+	0.965595i
$123$	1.18510e6	−	1.34469e6i	0.636852	−	0.722617i
$124$	1.91630e6	−	1.91630e6i	1.00507	−	1.00507i
$125$	−1.45807e6	+	1.45807e6i	−0.746532	+	0.746532i
$126$	−1.47996e6	−	1.14716e6i	−0.739840	−	0.573472i
$127$			239421.i			0.116883i	0.998291	+	0.0584415i	$0.0186131\pi$
$127$			239421.i			0.116883i	−0.998291	+	0.0584415i	$0.981387\pi$
$128$	431723.			0.205862
$129$	−38517.3	−	610540.i	−0.0179426	−	0.284410i
$130$	1.28174e6	+	1.28174e6i	0.583405	+	0.583405i
$131$	−543834.	−	543834.i	−0.241909	−	0.241909i	0.575730	−	0.817640i	$-0.304718\pi$
$131$	−543834.	−	543834.i	−0.241909	−	0.241909i	−0.817640	+	0.575730i	$0.804718\pi$
$132$	−646559.	+	733632.i	−0.281117	+	0.318975i
$133$	−441422.	+	441422.i	−0.187629	+	0.187629i
$134$	4.46636e6			1.85626
$135$	1.42021e6	+	964105.i	0.577234	+	0.391853i
$136$	200821.	+	164485.i	0.0798347	+	0.0653898i
$137$		−	3.15496e6i		−	1.22697i	−0.789708	−	0.613483i	$-0.789768\pi$
$137$		−	3.15496e6i		−	1.22697i	0.789708	−	0.613483i	$-0.210232\pi$
$138$	−2.96994e6	+	3.36990e6i	−1.13008	+	1.28227i
$139$	−903101.	+	903101.i	−0.336273	+	0.336273i	−0.854963	−	0.518690i	$-0.826420\pi$
$139$	−903101.	+	903101.i	−0.336273	+	0.336273i	0.518690	+	0.854963i	$0.326420\pi$
$140$		−	1.33430e6i		−	0.486262i
$141$	−86340.0	−	1.36858e6i	−0.0308003	−	0.488218i
$142$	2.83938e6	+	2.83938e6i	0.991649	+	0.991649i
$143$	673994.	−	673994.i	0.230488	−	0.230488i
$144$	−2.73469e6	+	346427.i	−0.915844	+	0.116018i
$145$		−	150751.i		−	0.0494489i
$146$	6.22295e6	−	6.22295e6i	1.99958	−	1.99958i
$147$	115409.	+	1.82936e6i	0.0363319	+	0.575901i
$148$	−1.22994e6	+	1.22994e6i	−0.379400	+	0.379400i
$149$			5.81776e6i			1.75872i	0.476155	+	0.879361i	$0.342030\pi$
$149$			5.81776e6i			1.75872i	−0.476155	+	0.879361i	$0.657970\pi$
$150$	−156981.	−	2.48831e6i	−0.0465128	−	0.737278i
$151$		−	2.43957e6i		−	0.708569i	−0.935138	−	0.354284i	$-0.884725\pi$
$151$		−	2.43957e6i		−	0.708569i	0.935138	−	0.354284i	$-0.115275\pi$
$152$		−	147864.i		−	0.0421047i
$153$	−3.03403e6	−	1.90324e6i	−0.847122	−	0.531399i
$154$	−1.35633e6			−0.371367
$155$	−3.44578e6			−0.925321
$156$	−3.33621e6	+	210472.i	−0.878778	+	0.0554396i
$157$	−7.61245e6			−1.96710			−0.983548	−	0.180647i	$-0.942181\pi$
$157$	−7.61245e6			−1.96710			−0.983548	+	0.180647i	$0.942181\pi$
$158$	−398996.	−	398996.i	−0.101157	−	0.101157i
$159$	−65102.2	+	4107.11i	−0.0161959	+	0.00102175i
$160$	−2.89349e6	−	2.89349e6i	−0.706418	−	0.706418i
$161$	−3.22292e6			−0.772275
$162$	−5.92609e6	+	1.52590e6i	−1.39387	+	0.358907i
$163$	−2.99667e6	−	2.99667e6i	−0.691951	−	0.691951i	0.270710	−	0.962661i	$-0.412742\pi$
$163$	−2.99667e6	−	2.99667e6i	−0.691951	−	0.691951i	−0.962661	+	0.270710i	$0.912742\pi$
$164$	−3.21963e6	+	3.21963e6i	−0.729918	+	0.729918i
$165$	1.24089e6	−	78284.4i	0.276237	−	0.0174270i
$166$	486606.			0.106378
$167$	5.17128e6	+	5.17128e6i	1.11032	+	1.11032i	0.993107	+	0.117215i	$0.0373967\pi$
$167$	5.17128e6	+	5.17128e6i	1.11032	+	1.11032i	0.117215	+	0.993107i	$0.462603\pi$
$168$	238742.	+	210406.i	0.0503502	+	0.0443743i
$169$	−1.56844e6			−0.324944
$170$	−488315.	−	4.90935e6i	−0.0993923	−	0.999257i
$171$	256390.	+	2.02395e6i	0.0512759	+	0.404772i
$172$			1.55405e6i			0.305407i
$173$	−614054.	−	614054.i	−0.118596	−	0.118596i	0.645318	−	0.763914i	$-0.276725\pi$
$173$	−614054.	−	614054.i	−0.118596	−	0.118596i	−0.763914	+	0.645318i	$0.776725\pi$
$174$	403187.	+	355334.i	0.0765348	+	0.0674512i
$175$	1.26496e6	−	1.26496e6i	0.236028	−	0.236028i
$176$	−1.41187e6	+	1.41187e6i	−0.258974	+	0.258974i
$177$	7.35678e6	−	464118.i	1.32669	−	0.0836968i
$178$			1.16843e7i			2.07177i
$179$	1.02685e6			0.179039			0.0895194	−	0.995985i	$-0.471467\pi$
$179$	1.02685e6			0.179039			0.0895194	+	0.995985i	$0.471467\pi$
$180$	−3.44643e6	−	2.67143e6i	−0.590952	−	0.458064i
$181$	−6.83763e6	−	6.83763e6i	−1.15311	−	1.15311i	−0.985926	−	0.167181i	$-0.946533\pi$
$181$	−6.83763e6	−	6.83763e6i	−1.15311	−	1.15311i	−0.167181	−	0.985926i	$-0.553467\pi$
$182$	−3.27853e6	−	3.27853e6i	−0.543832	−	0.543832i
$183$	4.36206e6	+	3.84434e6i	0.711768	+	0.627291i
$184$	539792.	−	539792.i	0.0866509	−	0.0866509i
$185$	2.21161e6			0.349295
$186$	8.12202e6	−	9.21582e6i	1.26219	−	1.43217i
$187$	−2.58155e6	+	256777.i	−0.394780	+	0.0392673i
$188$			3.48355e6i			0.524262i
$189$	−3.63272e6	−	2.46606e6i	−0.538080	−	0.365273i
$190$	−1.98714e6	+	1.98714e6i	−0.289713	+	0.289713i
$191$		−	3.39963e6i		−	0.487901i	−0.969788	−	0.243950i	$-0.921557\pi$
$191$		−	3.39963e6i		−	0.487901i	0.969788	−	0.243950i	$-0.0784434\pi$
$192$	8.03784e6	−	507085.i	1.13563	−	0.0716435i
$193$	8.99422e6	+	8.99422e6i	1.25110	+	1.25110i	0.955228	+	0.295871i	$0.0956099\pi$
$193$	8.99422e6	+	8.99422e6i	1.25110	+	1.25110i	0.295871	+	0.955228i	$0.404390\pi$
$194$	4.88484e6	−	4.88484e6i	0.669030	−	0.669030i
$195$	3.18872e6	+	2.81026e6i	0.430044	+	0.379004i
$196$		−	4.65640e6i		−	0.618418i
$197$	−248503.	+	248503.i	−0.0325036	+	0.0325036i	−0.723172	−	0.690668i	$-0.757317\pi$
$197$	−248503.	+	248503.i	−0.0325036	+	0.0325036i	0.690668	+	0.723172i	$0.257317\pi$
$198$	−2.71553e6	+	3.50332e6i	−0.349831	+	0.451320i
$199$	9.45689e6	−	9.45689e6i	1.20002	−	1.20002i	0.225863	−	0.974159i	$-0.427480\pi$
$199$	9.45689e6	−	9.45689e6i	1.20002	−	1.20002i	0.974159	−	0.225863i	$-0.0725203\pi$
$200$			423725.i			0.0529656i
$201$	1.04521e7	−	659391.i	1.28710	−	0.0811998i
$202$			6.06476e6i			0.735800i
$203$			385602.i			0.0460947i
$204$	7.38770e6	+	5.31053e6i	0.870200	+	0.625529i
$205$	5.78936e6			0.671999
$206$	−1.12357e7			−1.28529
$207$	−6.45266e6	+	8.32462e6i	−0.727491	+	0.938541i
$208$	−6.82556e6			−0.758487
$209$	1.04492e6	+	1.04492e6i	0.114458	+	0.114458i
$210$	−380801.	−	6.03611e6i	−0.0411188	−	0.651777i
$211$	8.17710e6	+	8.17710e6i	0.870466	+	0.870466i	0.992523	−	0.122057i	$-0.0389492\pi$
$211$	8.17710e6	+	8.17710e6i	0.870466	+	0.870466i	−0.122057	+	0.992523i	$0.538949\pi$
$212$	165709.			0.0173916
$213$	7.06382e6	+	6.22544e6i	0.730973	+	0.644216i
$214$	−1.37630e7	−	1.37630e7i	−1.40434	−	1.40434i
$215$	1.39720e6	−	1.39720e6i	0.140587	−	0.140587i
$216$	1.02146e6	−	195399.i	0.101358	−	0.0193892i
$217$	8.81387e6			0.862556
$218$	1.86180e7	+	1.86180e7i	1.79706	+	1.79706i
$219$	1.36441e7	−	1.54815e7i	1.29901	−	1.47395i
$220$	−3.15853e6			−0.296631
$221$	−6.86082e6	−	5.61945e6i	−0.635622	−	0.520615i
$222$	−5.21296e6	+	5.91499e6i	−0.476459	+	0.540624i
$223$		−	1.30251e7i		−	1.17454i	−0.809392	−	0.587269i	$-0.800203\pi$
$223$		−	1.30251e7i		−	1.17454i	0.809392	−	0.587269i	$-0.199797\pi$
$224$	7.40117e6	+	7.40117e6i	0.658501	+	0.658501i
$225$	−734724.	−	5.79991e6i	−0.0645025	−	0.509183i
$226$	9.30107e6	−	9.30107e6i	0.805763	−	0.805763i
$227$	−4.21230e6	+	4.21230e6i	−0.360116	+	0.360116i	−0.863855	−	0.503740i	$-0.831957\pi$
$227$	−4.21230e6	+	4.21230e6i	−0.360116	+	0.360116i	0.503740	+	0.863855i	$0.331957\pi$
$228$	−326304.	−	5.17227e6i	−0.0275307	−	0.436392i
$229$			1.87989e7i			1.56540i	0.622398	+	0.782701i	$0.286159\pi$
$229$			1.87989e7i			1.56540i	−0.622398	+	0.782701i	$0.713841\pi$
$230$	−1.45085e7			−1.19245
$231$	−3.17405e6	+	200242.i	−0.257500	+	0.0162449i
$232$	−64582.8	−	64582.8i	−0.00517193	−	0.00517193i
$233$	−1.30746e7	−	1.30746e7i	−1.03362	−	1.03362i	−0.999415	−	0.0342030i	$-0.989111\pi$
$233$	−1.30746e7	−	1.30746e7i	−1.03362	−	1.03362i	−0.0342030	−	0.999415i	$-0.510889\pi$
$234$	−1.50322e7	+	1.90426e6i	−1.17321	+	0.148621i
$235$	3.13197e6	−	3.13197e6i	0.241331	−	0.241331i
$236$	−1.87257e7			−1.42463
$237$	−992626.	−	874815.i	−0.0745660	−	0.0657160i
$238$	1.24905e6	+	1.25575e7i	0.0926505	+	0.931477i
$239$			2.04978e7i			1.50146i	0.660611	+	0.750728i	$0.270297\pi$
$239$			2.04978e7i			1.50146i	−0.660611	+	0.750728i	$0.729703\pi$
$240$	−6.67967e6	−	5.88689e6i	−0.483194	−	0.425845i
$241$	8.17716e6	−	8.17716e6i	0.584186	−	0.584186i	−0.351865	−	0.936051i	$-0.614452\pi$
$241$	8.17716e6	−	8.17716e6i	0.584186	−	0.584186i	0.936051	+	0.351865i	$0.114452\pi$
$242$		−	1.71883e7i		−	1.21280i
$243$	−1.36428e7	+	4.44578e6i	−0.950791	+	0.309834i
$244$	−1.04442e7	−	1.04442e7i	−0.718959	−	0.718959i
$245$	−4.18645e6	+	4.18645e6i	−0.284674	+	0.284674i
$246$	−1.36461e7	+	1.54838e7i	−0.916646	+	1.04009i
$247$			5.05159e6i			0.335226i
$248$	−1.47619e6	+	1.47619e6i	−0.0967806	+	0.0967806i
$249$	1.13874e6	−	71840.1i	0.0737612	−	0.00465338i
$250$	1.67893e7	−	1.67893e7i	1.07451	−	1.07451i
$251$		−	3.18913e6i		−	0.201674i	−0.994903	−	0.100837i	$-0.967848\pi$
$251$		−	3.18913e6i		−	0.201674i	0.994903	−	0.100837i	$-0.0321521\pi$
$252$	8.81553e6	+	6.83317e6i	0.550867	+	0.426993i
$253$			7.62922e6i			0.471106i
$254$		−	2.75686e6i		−	0.168234i
$255$	−1.86753e6	−	1.14166e7i	−0.112628	−	0.688522i
$256$	1.41194e7			0.841580
$257$	9.29112e6			0.547354			0.273677	−	0.961822i	$-0.411760\pi$
$257$	9.29112e6			0.547354			0.273677	+	0.961822i	$0.411760\pi$
$258$	443515.	+	7.03020e6i	0.0258255	+	0.409363i
$259$	−5.65701e6			−0.325602
$260$	−7.63482e6	−	7.63482e6i	−0.434389	−	0.434389i
$261$	995988.	+	772020.i	0.0560187	+	0.0434217i
$262$	6.26209e6	+	6.26209e6i	0.348189	+	0.348189i
$263$	9.95525e6			0.547249			0.273624	−	0.961837i	$-0.411777\pi$
$263$	9.95525e6			0.547249			0.273624	+	0.961837i	$0.411777\pi$
$264$	498069.	−	565144.i	0.0270693	−	0.0307148i
$265$	−148985.	−	148985.i	−0.00800579	−	0.00800579i
$266$	5.08285e6	−	5.08285e6i	0.270061	−	0.270061i
$267$	1.72501e6	+	2.73432e7i	0.0906268	+	1.43653i
$268$	−2.66044e7			−1.38213
$269$	−8.14612e6	−	8.14612e6i	−0.418498	−	0.418498i	0.466187	−	0.884686i	$-0.345627\pi$
$269$	−8.14612e6	−	8.14612e6i	−0.418498	−	0.418498i	−0.884686	+	0.466187i	$0.845627\pi$
$270$	−1.63533e7	−	1.11014e7i	−0.830835	−	0.564009i
$271$	9.37093e6			0.470842			0.235421	−	0.971894i	$-0.424353\pi$
$271$	9.37093e6			0.470842			0.235421	+	0.971894i	$0.424353\pi$
$272$	1.43719e7	+	1.17715e7i	0.714180	+	0.584959i
$273$	−8.15635e6	−	7.18830e6i	−0.400874	−	0.353296i
$274$			3.63285e7i			1.76602i
$275$	−2.99438e6	−	2.99438e6i	−0.143982	−	0.143982i
$276$	1.76908e7	−	2.00732e7i	0.841432	−	0.954748i
$277$	−4.33034e6	+	4.33034e6i	−0.203743	+	0.203743i	−0.801602	−	0.597859i	$-0.796018\pi$
$277$	−4.33034e6	+	4.33034e6i	−0.203743	+	0.203743i	0.597859	+	0.801602i	$0.296018\pi$
$278$	1.03990e7	−	1.03990e7i	0.484011	−	0.484011i
$279$	1.76464e7	−	2.27657e7i	0.812536	−	1.04826i
$280$			1.02786e6i			0.0468232i
$281$	−1.93459e7			−0.871905			−0.435952	−	0.899970i	$-0.643588\pi$
$281$	−1.93459e7			−0.871905			−0.435952	+	0.899970i	$0.643588\pi$
$282$	994181.	+	1.57588e7i	0.0443321	+	0.702711i
$283$	−1.24444e7	−	1.24444e7i	−0.549054	−	0.549054i	0.377113	−	0.926167i	$-0.376917\pi$
$283$	−1.24444e7	−	1.24444e7i	−0.549054	−	0.549054i	−0.926167	+	0.377113i	$0.876917\pi$
$284$	−1.69130e7	−	1.69130e7i	−0.738357	−	0.738357i
$285$	−4.35688e6	+	4.94362e6i	−0.188209	+	0.213555i
$286$	−7.76085e6	+	7.76085e6i	−0.331750	+	0.331750i
$287$	−1.48084e7			−0.626417
$288$	3.39348e7	−	4.29881e6i	1.42059	−	0.179958i
$289$	4.75470e6	+	2.36646e7i	0.196984	+	0.980407i
$290$			1.73586e6i			0.0711737i
$291$	1.07102e7	−	1.21526e7i	0.434629	−	0.493161i
$292$	−3.70677e7	+	3.70677e7i	−1.48884	+	1.48884i
$293$		−	4.65637e7i		−	1.85116i	−0.378547	−	0.925582i	$-0.623576\pi$
$293$		−	4.65637e7i		−	1.85116i	0.378547	−	0.925582i	$-0.376424\pi$
$294$	−1.32890e6	−	2.10646e7i	−0.0522940	−	0.828917i
$295$	1.68358e7	+	1.68358e7i	0.655794	+	0.655794i
$296$	947466.	−	947466.i	0.0365333	−	0.0365333i
$297$	−5.83759e6	+	8.59928e6i	−0.222825	+	0.328241i
$298$		−	6.69899e7i		−	2.53140i
$299$	−1.84414e7	+	1.84414e7i	−0.689891	+	0.689891i
$300$	935072.	+	1.48219e7i	0.0346323	+	0.548960i
$301$	−3.57387e6	+	3.57387e6i	−0.131051	+	0.131051i
$302$			2.80909e7i			1.01987i
$303$	895371.	+	1.41926e7i	0.0321866	+	0.510193i
$304$		−	1.05820e7i		−	0.376657i
$305$			1.87801e7i			0.661910i
$306$	3.49360e7	+	2.19153e7i	1.21930	+	0.764863i
$307$	−2.67230e7			−0.923570			−0.461785	−	0.886992i	$-0.652791\pi$
$307$	−2.67230e7			−0.923570			−0.461785	+	0.886992i	$0.652791\pi$
$308$	8.07912e6			0.276511
$309$	−2.62936e7	+	1.65879e6i	−0.891199	+	0.0562232i
$310$	3.96772e7			1.33185
$311$	−1.52778e7	−	1.52778e7i	−0.507903	−	0.507903i	0.405979	−	0.913882i	$-0.366930\pi$
$311$	−1.52778e7	−	1.52778e7i	−0.507903	−	0.507903i	−0.913882	+	0.405979i	$0.866930\pi$
$312$	2.57000e6	−	162134.i	0.0846194	−	0.00533840i
$313$	−3.63312e7	−	3.63312e7i	−1.18481	−	1.18481i	−0.978484	−	0.206321i	$-0.933851\pi$
$313$	−3.63312e7	−	3.63312e7i	−1.18481	−	1.18481i	−0.206321	−	0.978484i	$-0.566149\pi$
$314$	8.76552e7			2.83132
$315$	−1.78228e6	−	1.40693e7i	−0.0570223	−	0.450134i
$316$	2.37666e6	+	2.37666e6i	0.0753193	+	0.0753193i
$317$	−3.64071e7	+	3.64071e7i	−1.14290	+	1.14290i	−0.154982	+	0.987917i	$0.549532\pi$
$317$	−3.64071e7	+	3.64071e7i	−1.14290	+	1.14290i	−0.987917	+	0.154982i	$0.950468\pi$
$318$	749633.	−	47292.2i	0.0233114	−	0.00147065i
$319$	912788.			0.0281189
$320$	1.83944e7	+	1.83944e7i	0.561352	+	0.561352i
$321$	−3.42397e7	−	3.01759e7i	−1.03518	−	0.912316i
$322$	3.71110e7			1.11157
$323$	8.71209e6	−	1.06366e7i	0.258532	−	0.315643i
$324$	3.52994e7	−	9.08920e6i	1.03784	−	0.267233i
$325$		−	1.44761e7i		−	0.421697i
$326$	3.45058e7	+	3.45058e7i	0.995953	+	0.995953i
$327$	4.63180e7	+	4.08207e7i	1.32467	+	1.16745i
$328$	2.48020e6	−	2.48020e6i	0.0702853	−	0.0702853i
$329$	−8.01117e6	+	8.01117e6i	−0.224961	+	0.224961i
$330$	−1.42885e7	+	901422.i	−0.397599	+	0.0250834i
$331$		−	3.79680e7i		−	1.04697i	−0.852035	−	0.523484i	$-0.824632\pi$
$331$		−	3.79680e7i		−	1.04697i	0.852035	−	0.523484i	$-0.175368\pi$
$332$	−2.89852e6			−0.0792068
$333$	−1.13260e7	+	1.46117e7i	−0.306721	+	0.395703i
$334$	−5.95458e7	−	5.95458e7i	−1.59813	−	1.59813i
$335$	2.39193e7	+	2.39193e7i	0.636229	+	0.636229i
$336$	1.70858e7	+	1.50579e7i	0.450419	+	0.396960i
$337$	−4.18053e7	+	4.18053e7i	−1.09230	+	1.09230i	−0.0970178	+	0.995283i	$0.530930\pi$
$337$	−4.18053e7	+	4.18053e7i	−1.09230	+	1.09230i	−0.995283	+	0.0970178i	$0.969070\pi$
$338$	1.80602e7			0.467705
$339$	2.03929e7	−	2.31393e7i	0.523457	−	0.593951i
$340$	2.90870e6	+	2.92431e7i	0.0740051	+	0.744022i
$341$		−	2.08640e7i		−	0.526179i
$342$	−2.95226e6	−	2.33051e7i	−0.0738034	−	0.582604i
$343$	2.92657e7	−	2.92657e7i	0.725230	−	0.725230i
$344$		−	1.19714e6i		−	0.0294083i
$345$	−3.39525e7	+	2.14197e6i	−0.826827	+	0.0521622i
$346$	7.07066e6	+	7.07066e6i	0.170699	+	0.170699i
$347$	−3.31819e7	+	3.31819e7i	−0.794168	+	0.794168i	−0.982169	−	0.188001i	$-0.939799\pi$
$347$	−3.31819e7	+	3.31819e7i	−0.794168	+	0.794168i	0.188001	+	0.982169i	$0.439799\pi$
$348$	−2.40163e6	−	2.11659e6i	−0.0569860	−	0.0502225i
$349$			1.49621e7i			0.351979i	0.984392	+	0.175990i	$0.0563126\pi$
$349$			1.49621e7i			0.351979i	−0.984392	+	0.175990i	$0.943687\pi$
$350$	−1.45657e7	+	1.45657e7i	−0.339724	+	0.339724i
$351$	−3.48969e7	+	6.67558e6i	−0.806985	+	0.154372i
$352$	1.75199e7	−	1.75199e7i	0.401701	−	0.401701i
$353$		−	7.95855e7i		−	1.80930i	−0.426160	−	0.904648i	$-0.640134\pi$
$353$		−	7.95855e7i		−	1.80930i	0.426160	−	0.904648i	$-0.359866\pi$
$354$	−8.47112e7	+	5.34419e6i	−1.90955	+	0.120468i
$355$			3.04121e7i			0.679769i
$356$		−	6.95986e7i		−	1.54259i
$357$	4.77691e6	+	2.92023e7i	0.104989	+	0.641819i
$358$	−1.18239e7			−0.257697
$359$	3.81461e7			0.824454			0.412227	−	0.911081i	$-0.364751\pi$
$359$	3.81461e7			0.824454			0.412227	+	0.911081i	$0.364751\pi$
$360$	2.65491e6	+	2.05790e6i	0.0569040	+	0.0441080i
$361$	3.92142e7			0.833530
$362$	7.87333e7	+	7.87333e7i	1.65971	+	1.65971i
$363$	−2.53760e6	−	4.02237e7i	−0.0530522	−	0.840935i
$364$	1.95289e7	+	1.95289e7i	0.404924	+	0.404924i
$365$	6.66531e7			1.37070
$366$	−5.02279e7	−	4.42665e7i	−1.02448	−	0.902884i
$367$	2.54511e7	+	2.54511e7i	0.514883	+	0.514883i	0.916019	−	0.401136i	$-0.131384\pi$
$367$	2.54511e7	+	2.54511e7i	0.514883	+	0.514883i	−0.401136	+	0.916019i	$0.631384\pi$
$368$	3.86307e7	−	3.86307e7i	0.775155	−	0.775155i
$369$	−2.96482e7	+	3.82493e7i	−0.590091	+	0.761281i
$370$	−2.54660e7			−0.502754
$371$	381084.	+	381084.i	0.00746275	+	0.00746275i
$372$	−4.83797e7	+	5.48950e7i	−0.939797	+	1.06636i
$373$	1.46444e7			0.282193			0.141096	−	0.989996i	$-0.454937\pi$
$373$	1.46444e7			0.282193			0.141096	+	0.989996i	$0.454937\pi$
$374$	2.97258e7	−	2.95671e6i	0.568222	−	0.0565189i
$375$	3.68111e7	−	4.17685e7i	0.698047	−	0.792054i
$376$		−	2.68351e6i		−	0.0504823i
$377$	2.20640e6	+	2.20640e6i	0.0411775	+	0.0411775i
$378$	4.18297e7	+	2.83959e7i	0.774479	+	0.525752i
$379$	−1.39172e7	+	1.39172e7i	−0.255644	+	0.255644i	−0.823280	−	0.567636i	$-0.807858\pi$
$379$	−1.39172e7	+	1.39172e7i	−0.255644	+	0.255644i	0.567636	+	0.823280i	$0.307858\pi$
$380$	1.18366e7	−	1.18366e7i	0.215713	−	0.215713i
$381$	−407009.	−	6.45154e6i	−0.00735918	−	0.116651i
$382$			3.91458e7i			0.702255i
$383$	1.08474e7			0.193076			0.0965379	−	0.995329i	$-0.469223\pi$
$383$	1.08474e7			0.193076			0.0965379	+	0.995329i	$0.469223\pi$
$384$	−1.16334e7	+	733918.i	−0.205453	+	0.0129614i
$385$	−7.26372e6	−	7.26372e6i	−0.127285	−	0.127285i
$386$	−1.03566e8	−	1.03566e8i	−1.80076	−	1.80076i
$387$	2.07580e6	+	1.63864e7i	0.0358141	+	0.282716i
$388$	−2.90971e7	+	2.90971e7i	−0.498143	+	0.498143i
$389$	1.10201e7			0.187213			0.0936064	−	0.995609i	$-0.470160\pi$
$389$	1.10201e7			0.187213			0.0936064	+	0.995609i	$0.470160\pi$
$390$	−3.67172e7	−	3.23594e7i	−0.618979	−	0.545515i
$391$	7.06347e7	−	7.02576e6i	1.18165	−	0.117534i
$392$			3.58700e6i			0.0595488i
$393$	1.55789e7	+	1.37299e7i	0.256660	+	0.226198i
$394$	2.86143e6	−	2.86143e6i	0.0467838	−	0.0467838i
$395$		−	4.27359e6i		−	0.0693428i
$396$	1.61753e7	−	2.08679e7i	0.260476	−	0.336042i
$397$	1.67272e7	+	1.67272e7i	0.267332	+	0.267332i	0.828024	−	0.560692i	$-0.189465\pi$
$397$	1.67272e7	+	1.67272e7i	0.267332	+	0.267332i	−0.560692	+	0.828024i	$0.689465\pi$
$398$	−1.08893e8	+	1.08893e8i	−1.72724	+	1.72724i
$399$	1.11443e7	−	1.26452e7i	0.175443	−	0.199070i
$400$			3.03242e7i			0.473815i
$401$	−2.36046e7	+	2.36046e7i	−0.366069	+	0.366069i	−0.866041	−	0.499972i	$-0.833344\pi$
$401$	−2.36046e7	+	2.36046e7i	−0.366069	+	0.366069i	0.499972	+	0.866041i	$0.333344\pi$
$402$	−1.20353e8	+	7.59270e6i	−1.85258	+	0.116874i
$403$	5.04325e7	−	5.04325e7i	0.770540	−	0.770540i
$404$		−	3.61254e7i		−	0.547859i
$405$	−3.99086e7	−	2.35649e7i	−0.600760	−	0.354732i
$406$		−	4.44010e6i		−	0.0663460i
$407$			1.33911e7i			0.198625i
$408$	−5.69102e6	−	4.09090e6i	−0.0837934	−	0.0602335i
$409$	−1.91388e7			−0.279734			−0.139867	−	0.990170i	$-0.544667\pi$
$409$	−1.91388e7			−0.279734			−0.139867	+	0.990170i	$0.544667\pi$
$410$	−6.66628e7			−0.967235
$411$	5.36336e6	+	8.50150e7i	0.0772523	+	1.22453i
$412$	6.69269e7			0.956994
$413$	−4.30638e7	−	4.30638e7i	−0.611311	−	0.611311i
$414$	7.43005e7	−	9.58556e7i	1.04711	−	1.35088i
$415$	2.60598e6	+	2.60598e6i	0.0364609	+	0.0364609i
$416$	8.46983e7			1.17651
$417$	2.28001e7	−	2.58706e7i	0.314433	−	0.356778i
$418$	−1.20320e7	−	1.20320e7i	−0.164744	−	0.164744i
$419$	−6.60745e6	+	6.60745e6i	−0.0898238	+	0.0898238i	−0.750591	−	0.660767i	$-0.770231\pi$
$419$	−6.60745e6	+	6.60745e6i	−0.0898238	+	0.0898238i	0.660767	+	0.750591i	$0.270231\pi$
$420$	2.26828e6	+	3.59547e7i	0.0306160	+	0.485297i
$421$	−9.06348e7			−1.21464			−0.607321	−	0.794456i	$-0.707756\pi$
$421$	−9.06348e7			−1.21464			−0.607321	+	0.794456i	$0.707756\pi$
$422$	−9.41569e7	−	9.41569e7i	−1.25290	−	1.25290i
$423$	4.65311e6	+	3.67317e7i	0.0614784	+	0.485310i
$424$	−127652.			−0.00167467
$425$	−2.49658e7	+	3.04808e7i	−0.325221	+	0.397064i
$426$	−8.13379e7	−	7.16842e7i	−1.05212	−	0.927245i
$427$		−	4.80372e7i		−	0.617012i
$428$	8.19807e7	+	8.19807e7i	1.04564	+	1.04564i
$429$	−1.70160e7	+	1.93075e7i	−0.215519	+	0.244542i
$430$	−1.60884e7	+	1.60884e7i	−0.202352	+	0.202352i
$431$	−2.64998e7	+	2.64998e7i	−0.330987	+	0.330987i	−0.852961	−	0.521974i	$-0.825196\pi$
$431$	−2.64998e7	+	2.64998e7i	−0.330987	+	0.330987i	0.521974	+	0.852961i	$0.325196\pi$
$432$	7.31013e7	−	1.39839e7i	0.906722	−	0.173451i
$433$			7.41545e6i			0.0913427i	0.998957	+	0.0456714i	$0.0145427\pi$
$433$			7.41545e6i			0.0913427i	−0.998957	+	0.0456714i	$0.985457\pi$
$434$	−1.01489e8			−1.24151
$435$	256273.	+	4.06221e6i	0.00311340	+	0.0493508i
$436$	−1.10900e8	−	1.10900e8i	−1.33805	−	1.33805i
$437$	−2.85905e7	−	2.85905e7i	−0.342592	−	0.342592i
$438$	−1.57108e8	+	1.78265e8i	−1.86971	+	2.12151i
$439$	−1.64205e7	+	1.64205e7i	−0.194086	+	0.194086i	−0.797459	−	0.603373i	$-0.793823\pi$
$439$	−1.64205e7	+	1.64205e7i	−0.194086	+	0.194086i	0.603373	+	0.797459i	$0.293823\pi$
$440$	2.43313e6			0.0285633
$441$	−6.21974e6	−	4.90986e7i	−0.0725197	−	0.572471i
$442$	7.90003e7	+	6.47064e7i	0.914876	+	0.749342i
$443$		−	6.37703e6i		−	0.0733512i	−0.999327	−	0.0366756i	$-0.988323\pi$
$443$		−	6.37703e6i		−	0.0733512i	0.999327	−	0.0366756i	$-0.0116768\pi$
$444$	3.10516e7	−	3.52333e7i	0.354760	−	0.402535i
$445$	−6.25742e7	+	6.25742e7i	−0.710093	+	0.710093i
$446$			1.49980e8i			1.69056i
$447$	−9.89005e6	−	1.56768e8i	−0.110733	−	1.75523i
$448$	−4.70505e7	−	4.70505e7i	−0.523275	−	0.523275i
$449$	−5.89889e6	+	5.89889e6i	−0.0651675	+	0.0651675i	−0.738939	−	0.673772i	$-0.764673\pi$
$449$	−5.89889e6	+	5.89889e6i	−0.0651675	+	0.0651675i	0.673772	+	0.738939i	$0.264673\pi$
$450$	8.46014e6	+	6.67843e7i	0.0928410	+	0.732887i
$451$			3.50542e7i			0.382129i
$452$	−5.54028e7	+	5.54028e7i	−0.599952	+	0.599952i
$453$	4.14720e6	+	6.57376e7i	0.0446129	+	0.707163i
$454$	4.85035e7	−	4.85035e7i	0.518329	−	0.518329i
$455$		−	3.51158e7i		−	0.372794i
$456$	251364.	+	3.98439e6i	0.00265099	+	0.0420211i
$457$		−	6.90607e7i		−	0.723573i	−0.932261	−	0.361787i	$-0.882167\pi$
$457$		−	6.90607e7i		−	0.723573i	0.932261	−	0.361787i	$-0.117833\pi$
$458$		−	2.16464e8i		−	2.25314i
$459$	8.49918e7	+	4.61279e7i	0.878899	+	0.477008i
$460$	8.64217e7			0.887870
$461$	1.04161e8			1.06317			0.531584	−	0.847005i	$-0.321597\pi$
$461$	1.04161e8			1.06317			0.531584	+	0.847005i	$0.321597\pi$
$462$	3.65482e7	−	2.30572e6i	0.370630	−	0.0233820i
$463$	6.93216e7			0.698435			0.349217	−	0.937042i	$-0.386448\pi$
$463$	6.93216e7			0.698435			0.349217	+	0.937042i	$0.386448\pi$
$464$	−4.62192e6	−	4.62192e6i	−0.0462666	−	0.0462666i
$465$	9.28515e7	−	5.85774e6i	0.923485	−	0.0582601i
$466$	1.50550e8	+	1.50550e8i	1.48773	+	1.48773i
$467$	1.69567e8			1.66491			0.832456	−	0.554091i	$-0.186934\pi$
$467$	1.69567e8			1.66491			0.832456	+	0.554091i	$0.186934\pi$
$468$	8.95411e7	−	1.13429e7i	0.873544	−	0.110659i
$469$	−6.11824e7	−	6.11824e7i	−0.593073	−	0.593073i
$470$	−3.60637e7	+	3.60637e7i	−0.347357	+	0.347357i
$471$	2.05128e8	−	1.29410e7i	1.96319	−	0.123852i
$472$	1.44251e7			0.137181
$473$	8.45998e6	+	8.45998e6i	0.0799440	+	0.0799440i
$474$	1.14298e7	+	1.00732e7i	0.107326	+	0.0945876i
$475$	2.24429e7			0.209410
$476$	−7.44008e6	−	7.48000e7i	−0.0689853	−	0.693555i
$477$	1.74729e6	−	221344.i	0.0160994	−	0.00203945i
$478$		−	2.36026e8i		−	2.16110i
$479$	7.10674e7	+	7.10674e7i	0.646642	+	0.646642i	0.952180	−	0.305538i	$-0.0988363\pi$
$479$	7.10674e7	+	7.10674e7i	0.646642	+	0.646642i	−0.305538	+	0.952180i	$0.598836\pi$
$480$	8.28880e7	+	7.30503e7i	0.749494	+	0.660539i
$481$	−3.23691e7	+	3.23691e7i	−0.290868	+	0.290868i
$482$	−9.41577e7	+	9.41577e7i	−0.840842	+	0.840842i
$483$	8.68462e7	−	5.47888e6i	0.770743	−	0.0486240i
$484$			1.02384e8i			0.903019i
$485$	5.23208e7			0.458616
$486$	1.57093e8	−	5.11918e7i	1.36851	−	0.445956i
$487$	5.21066e7	+	5.21066e7i	0.451134	+	0.451134i	0.895731	−	0.444597i	$-0.146653\pi$
$487$	5.21066e7	+	5.21066e7i	0.451134	+	0.451134i	−0.444597	+	0.895731i	$0.646653\pi$
$488$	8.04552e6	+	8.04552e6i	0.0692301	+	0.0692301i
$489$	8.58437e7	+	7.56552e7i	0.734145	+	0.647012i
$490$	4.82057e7	−	4.82057e7i	0.409742	−	0.409742i
$491$	2.20357e8			1.86158			0.930792	−	0.365549i	$-0.119119\pi$
$491$	2.20357e8			1.86158			0.930792	+	0.365549i	$0.119119\pi$
$492$	8.12841e7	−	9.22307e7i	0.682512	−	0.774426i
$493$	−840588.	−	8.45099e6i	−0.00701524	−	0.0705289i
$494$		−	5.81676e7i		−	0.482503i
$495$	−3.33046e7	+	4.21897e6i	−0.274592	+	0.0347849i
$496$	−1.05645e8	+	1.05645e8i	−0.865773	+	0.865773i
$497$		−	7.77903e7i		−	0.633660i
$498$	−1.31123e7	+	827218.i	−0.106167	+	0.00669779i
$499$	−6.82002e7	−	6.82002e7i	−0.548888	−	0.548888i	0.377231	−	0.926119i	$-0.376876\pi$
$499$	−6.82002e7	−	6.82002e7i	−0.548888	−	0.548888i	−0.926119	+	0.377231i	$0.876876\pi$
$500$	−1.00007e8	+	1.00007e8i	−0.800056	+	0.800056i
$501$	−1.48139e8	−	1.30557e8i	−1.17803	−	1.03821i
$502$			3.67219e7i			0.290278i
$503$	−1.05888e8	+	1.05888e8i	−0.832036	+	0.832036i	−0.987795	−	0.155759i	$-0.950218\pi$
$503$	−1.05888e8	+	1.05888e8i	−0.832036	+	0.832036i	0.155759	+	0.987795i	$0.450218\pi$
$504$	−6.79093e6	−	5.26385e6i	−0.0530442	−	0.0411161i
$505$	−3.24794e7	+	3.24794e7i	−0.252193	+	0.252193i
$506$		−	8.78483e7i		−	0.678081i
$507$	4.22640e7	−	2.66631e6i	0.324300	−	0.0204591i
$508$			1.64215e7i			0.125263i
$509$			9.08426e7i			0.688868i	0.938810	+	0.344434i	$0.111929\pi$
$509$			9.08426e7i			0.688868i	−0.938810	+	0.344434i	$0.888071\pi$
$510$	2.15041e7	+	1.31459e8i	0.162110	+	0.991017i
$511$	−1.70490e8			−1.27772
$512$	−1.90211e8			−1.41718
$513$	−1.03495e7	−	5.41022e7i	−0.0766594	−	0.400740i
$514$	−1.06985e8			−0.787828
$515$	−6.01722e7	−	6.01722e7i	−0.440529	−	0.440529i
$516$	−2.64184e6	−	4.18761e7i	−0.0192291	−	0.304802i
$517$	1.89638e7	+	1.89638e7i	0.137232	+	0.137232i
$518$	6.51388e7			0.468652
$519$	1.75904e7	+	1.55027e7i	0.125827	+	0.110893i
$520$	5.88138e6	+	5.88138e6i	0.0418282	+	0.0418282i
$521$	−4.23302e7	+	4.23302e7i	−0.299321	+	0.299321i	−0.840748	−	0.541427i	$-0.817884\pi$
$521$	−4.23302e7	+	4.23302e7i	−0.299321	+	0.299321i	0.541427	+	0.840748i	$0.317884\pi$
$522$	−1.14685e7	−	8.88959e6i	−0.0806299	−	0.0624986i
$523$	−1.78642e8			−1.24876			−0.624378	−	0.781122i	$-0.714647\pi$
$523$	−1.78642e8			−1.24876			−0.624378	+	0.781122i	$0.714647\pi$
$524$	−3.73008e7	−	3.73008e7i	−0.259253	−	0.259253i
$525$	−3.19358e7	+	3.62366e7i	−0.220698	+	0.250420i
$526$	−1.14632e8			−0.787677
$527$	−1.93168e8	+	1.92137e7i	−1.31978	+	0.131274i
$528$	3.56447e7	−	4.04450e7i	0.242155	−	0.274766i
$529$		−	6.07100e7i		−	0.410103i
$530$	1.71552e6	+	1.71552e6i	0.0115230	+	0.0115230i
$531$	−1.97450e8	+	2.50127e7i	−1.31878	+	0.167061i
$532$	−3.02765e7	+	3.02765e7i	−0.201081	+	0.201081i
$533$	−8.47331e7	+	8.47331e7i	−0.559592	+	0.559592i
$534$	−1.98629e7	−	3.14849e8i	−0.130443	−	2.06766i
$535$		−	1.47413e8i		−	0.962665i
$536$	2.04943e7			0.133088
$537$	−2.76699e7	+	1.74561e6i	−0.178684	+	0.0112726i
$538$	9.38002e7	+	9.38002e7i	0.602361	+	0.602361i
$539$	−2.53486e7	−	2.53486e7i	−0.161878	−	0.161878i
$540$	9.74103e7	+	6.61266e7i	0.618620	+	0.419948i
$541$	3.95257e7	−	3.95257e7i	0.249625	−	0.249625i	−0.571192	−	0.820817i	$-0.693519\pi$
$541$	3.95257e7	−	3.95257e7i	0.249625	−	0.249625i	0.820817	+	0.571192i	$0.193519\pi$
$542$	−1.07904e8			−0.677701
$543$	1.95873e8	+	1.72626e8i	1.22342	+	1.07822i
$544$	−1.78341e8	−	1.46073e8i	−1.10778	−	0.907344i
$545$			1.99414e8i			1.23188i
$546$	9.39180e7	+	8.27712e7i	0.576994	+	0.508512i
$547$	−3.89263e7	+	3.89263e7i	−0.237838	+	0.237838i	−0.815954	−	0.578116i	$-0.803788\pi$
$547$	−3.89263e7	+	3.89263e7i	−0.237838	+	0.237838i	0.578116	+	0.815954i	$0.303788\pi$
$548$		−	2.16395e8i		−	1.31494i
$549$	−1.24077e8	−	9.61759e7i	−0.749851	−	0.581232i
$550$	3.44794e7	+	3.44794e7i	0.207239	+	0.207239i
$551$	−3.42068e6	+	3.42068e6i	−0.0204483	+	0.0204483i
$552$	−1.36278e7	+	1.54631e7i	−0.0810233	+	0.0919347i
$553$			1.09313e7i			0.0646392i
$554$	4.98627e7	−	4.98627e7i	0.293255	−	0.293255i
$555$	−5.95949e7	+	3.75967e6i	−0.348602	+	0.0219923i
$556$	−6.19424e7	+	6.19424e7i	−0.360383	+	0.360383i
$557$		−	3.16238e8i		−	1.82999i	−0.403465	−	0.914995i	$-0.632194\pi$
$557$		−	3.16238e8i		−	1.82999i	0.403465	−	0.914995i	$-0.367806\pi$
$558$	−2.03193e8	+	2.62141e8i	−1.16952	+	1.50880i
$559$			4.08990e7i			0.234141i
$560$			7.35599e7i			0.418868i
$561$	6.91270e7	−	1.13078e7i	0.391525	−	0.0640455i
$562$	2.22762e8			1.25497
$563$	−1.64540e8			−0.922032			−0.461016	−	0.887392i	$-0.652515\pi$
$563$	−1.64540e8			−0.922032			−0.461016	+	0.887392i	$0.652515\pi$
$564$	−5.92194e6	−	9.38692e7i	−0.0330086	−	0.523222i
$565$	9.96223e7			0.552346
$566$	1.43294e8	+	1.43294e8i	0.790274	+	0.790274i
$567$	1.02081e8	+	6.02759e7i	0.560010	+	0.330670i
$568$	1.30287e7	+	1.30287e7i	0.0710980	+	0.0710980i
$569$	1.85974e8			1.00952			0.504760	−	0.863260i	$-0.331581\pi$
$569$	1.85974e8			1.00952			0.504760	+	0.863260i	$0.331581\pi$
$570$	5.01682e7	−	5.69244e7i	0.270897	−	0.307379i
$571$	−5.90462e7	−	5.90462e7i	−0.317164	−	0.317164i	0.530513	−	0.847677i	$-0.321999\pi$
$571$	−5.90462e7	−	5.90462e7i	−0.317164	−	0.317164i	−0.847677	+	0.530513i	$0.821999\pi$
$572$	4.62283e7	−	4.62283e7i	0.247013	−	0.247013i
$573$	5.77928e6	+	9.16079e7i	0.0307192	+	0.486933i
$574$	1.70515e8			0.901627
$575$	8.19304e7	+	8.19304e7i	0.430964	+	0.430964i
$576$	−2.15729e8	+	2.73282e7i	−1.12886	+	0.143003i
$577$	3.15431e8			1.64201			0.821007	−	0.570918i	$-0.193412\pi$
$577$	3.15431e8			1.64201			0.821007	+	0.570918i	$0.193412\pi$
$578$	−5.47491e7	−	2.72491e8i	−0.283526	−	1.41114i
$579$	−2.57652e8	−	2.27072e8i	−1.32739	−	1.16985i
$580$		−	1.03398e7i		−	0.0529942i
$581$	−6.66577e6	−	6.66577e6i	−0.0339877	−	0.0339877i
$582$	−1.23325e8	+	1.39933e8i	−0.625579	+	0.709826i
$583$	902092.	−	902092.i	0.00455245	−	0.00455245i
$584$	2.85546e7	−	2.85546e7i	0.143363	−	0.143363i
$585$	−9.07021e7	−	7.03059e7i	−0.453054	−	0.351175i
$586$			5.36168e8i			2.66445i
$587$	−1.90282e8			−0.940772			−0.470386	−	0.882461i	$-0.655885\pi$
$587$	−1.90282e8			−0.940772			−0.470386	+	0.882461i	$0.655885\pi$
$588$	7.91576e6	+	1.25473e8i	0.0389368	+	0.617191i
$589$	7.81878e7	+	7.81878e7i	0.382642	+	0.382642i
$590$	−1.93859e8	−	1.93859e8i	−0.943910	−	0.943910i
$591$	6.27381e6	−	7.11870e6i	0.0303927	−	0.0344857i
$592$	6.78062e7	−	6.78062e7i	0.326817	−	0.326817i
$593$	3.06416e8			1.46942			0.734711	−	0.678380i	$-0.237318\pi$
$593$	3.06416e8			1.46942			0.734711	+	0.678380i	$0.237318\pi$
$594$	6.72182e7	−	9.90183e7i	0.320721	−	0.472450i
$595$	−6.05615e7	+	7.39399e7i	−0.287505	+	0.351017i
$596$			3.99032e8i			1.88482i
$597$	−2.38753e8	+	2.70906e8i	−1.12209	+	1.27320i
$598$	2.12347e8	−	2.12347e8i	0.992986	−	0.992986i
$599$		−	3.95333e8i		−	1.83943i	−0.392591	−	0.919713i	$-0.628421\pi$
$599$		−	3.95333e8i		−	1.83943i	0.392591	−	0.919713i	$-0.371579\pi$
$600$	−720321.	−	1.14179e7i	−0.00333482	−	0.0528605i
$601$	542212.	+	542212.i	0.00249773	+	0.00249773i	0.708355	−	0.705857i	$-0.249438\pi$
$601$	542212.	+	542212.i	0.00249773	+	0.00249773i	−0.705857	+	0.708355i	$0.749438\pi$
$602$	4.11521e7	−	4.11521e7i	0.188626	−	0.188626i
$603$	−2.80525e8	+	3.55365e7i	−1.27944	+	0.162077i
$604$		−	1.67326e8i		−	0.759371i
$605$	9.20509e7	−	9.20509e7i	0.415683	−	0.415683i
$606$	−1.03099e7	−	1.63424e8i	−0.0463274	−	0.734340i
$607$	−1.47084e8	+	1.47084e8i	−0.657657	+	0.657657i	−0.954825	−	0.297168i	$-0.903958\pi$
$607$	−1.47084e8	+	1.47084e8i	−0.657657	+	0.657657i	0.297168	+	0.954825i	$0.403958\pi$
$608$			1.31312e8i			0.584241i
$609$	−655514.	−	1.03906e7i	−0.00290222	−	0.0460033i
$610$		−	2.16248e8i		−	0.952713i
$611$			9.16790e7i			0.401926i
$612$	−2.08100e8	−	1.30541e8i	−0.907858	−	0.569498i
$613$	1.93205e8			0.838757			0.419379	−	0.907811i	$-0.362248\pi$
$613$	1.93205e8			0.838757			0.419379	+	0.907811i	$0.362248\pi$
$614$	3.07707e8			1.32933
$615$	−1.56003e8	+	9.84176e6i	−0.670666	+	0.0423104i
$616$	−6.22364e6			−0.0266258
$617$	2.30227e8	+	2.30227e8i	0.980170	+	0.980170i	0.999807	−	0.0196374i	$-0.00625118\pi$
$617$	2.30227e8	+	2.30227e8i	0.980170	+	0.980170i	−0.0196374	+	0.999807i	$0.506251\pi$
$618$	3.02763e8	−	1.91005e7i	1.28274	−	0.0809243i
$619$	−3.87498e7	−	3.87498e7i	−0.163379	−	0.163379i	0.620683	−	0.784062i	$-0.286856\pi$
$619$	−3.87498e7	−	3.87498e7i	−0.163379	−	0.163379i	−0.784062	+	0.620683i	$0.786856\pi$
$620$	−2.36341e8			−0.991664
$621$	1.59724e8	−	2.35288e8i	0.666955	−	0.982484i
$622$	1.75920e8	+	1.75920e8i	0.731044	+	0.731044i
$623$	1.60057e8	−	1.60057e8i	0.661927	−	0.661927i
$624$	1.83924e8	−	1.16033e7i	0.756982	−	0.0477558i
$625$	5.45214e7			0.223320
$626$	4.18344e8	+	4.18344e8i	1.70534	+	1.70534i
$627$	−2.99333e7	−	2.63806e7i	−0.121437	−	0.107024i
$628$	−5.22127e8			−2.10813
$629$	1.23981e8	−	1.23319e7i	0.498199	−	0.0495540i
$630$	2.05225e7	+	1.62004e8i	0.0820744	+	0.647895i
$631$			3.80315e8i			1.51376i	0.653557	+	0.756878i	$0.273276\pi$
$631$			3.80315e8i			1.51376i	−0.653557	+	0.756878i	$0.726724\pi$
$632$	−1.83083e6	−	1.83083e6i	−0.00725266	−	0.00725266i
$633$	−2.34244e8	−	2.06443e8i	−0.923545	−	0.813932i
$634$	4.19217e8	−	4.19217e8i	1.64502	−	1.64502i
$635$	1.47642e7	−	1.47642e7i	0.0576618	−	0.0576618i
$636$	−4.46527e6	+	281701.i	−0.0173571	+	0.00109501i
$637$		−	1.22546e8i		−	0.474111i
$638$	−1.05105e7			−0.0404726
$639$	−2.00928e8	−	1.55745e8i	−0.770083	−	0.596914i
$640$	−2.66227e7	−	2.66227e7i	−0.101558	−	0.101558i
$641$	5.34071e6	+	5.34071e6i	0.0202780	+	0.0202780i	0.717173	−	0.696895i	$-0.245436\pi$
$641$	5.34071e6	+	5.34071e6i	0.0202780	+	0.0202780i	−0.696895	+	0.717173i	$0.745436\pi$
$642$	3.94260e8	+	3.47467e8i	1.48997	+	1.31313i
$643$	2.23839e8	−	2.23839e8i	0.841983	−	0.841983i	−0.147133	−	0.989117i	$-0.547005\pi$
$643$	2.23839e8	−	2.23839e8i	0.841983	−	0.841983i	0.989117	+	0.147133i	$0.0470047\pi$
$644$	−2.21056e8			−0.827645
$645$	−3.52745e7	+	4.00249e7i	−0.131456	+	0.149160i
$646$	−1.00317e8	+	1.22478e8i	−0.372115	+	0.454318i
$647$			3.74459e7i			0.138258i	0.997608	+	0.0691291i	$0.0220220\pi$
$647$			3.74459e7i			0.138258i	−0.997608	+	0.0691291i	$0.977978\pi$
$648$	−2.71924e7	+	7.00175e6i	−0.0999362	+	0.0257325i
$649$	−1.01940e8	+	1.01940e8i	−0.372914	+	0.372914i
$650$			1.66688e8i			0.606965i
$651$	−2.37502e8	+	1.49833e7i	−0.860845	+	0.0543082i
$652$	−2.05537e8	−	2.05537e8i	−0.741562	−	0.741562i
$653$	8.36510e7	−	8.36510e7i	0.300422	−	0.300422i	−0.540757	−	0.841179i	$-0.681862\pi$
$653$	8.36510e7	−	8.36510e7i	0.300422	−	0.300422i	0.841179	+	0.540757i	$0.181862\pi$
$654$	−5.33339e8	−	4.70038e8i	−1.90664	−	1.68035i
$655$			6.70723e7i			0.238682i
$656$	1.77497e8	−	1.77497e8i	0.628753	−	0.628753i
$657$	−3.41341e8	+	4.40366e8i	−1.20363	+	1.55281i
$658$	9.22463e7	−	9.22463e7i	0.323796	−	0.323796i
$659$			1.62587e8i			0.568106i	0.958809	+	0.284053i	$0.0916792\pi$
$659$			1.62587e8i			0.568106i	−0.958809	+	0.284053i	$0.908321\pi$
$660$	8.51111e7	−	5.36942e6i	0.296043	−	0.0186765i
$661$		−	2.61278e8i		−	0.904687i	−0.891844	−	0.452343i	$-0.850588\pi$
$661$		−	2.61278e8i		−	0.904687i	0.891844	−	0.452343i	$-0.149412\pi$
$662$			4.37191e8i			1.50694i
$663$	1.94427e8	+	1.39761e8i	0.667140	+	0.479562i
$664$	2.23284e6			0.00762699
$665$	5.44416e7			0.185125
$666$	1.30415e8	−	1.68250e8i	0.441475	−	0.569550i
$667$	−2.49751e7			−0.0841647
$668$	3.54691e8	+	3.54691e8i	1.18993	+	1.18993i
$669$	2.21423e7	+	3.50980e8i	0.0739512	+	1.17221i
$670$	−2.75423e8	−	2.75423e8i	−0.915749	−	0.915749i
$671$	−1.13712e8			−0.376392
$672$	−2.12017e8	−	1.86853e8i	−0.698655	−	0.615734i
$673$	−1.64533e8	−	1.64533e8i	−0.539768	−	0.539768i	0.383693	−	0.923461i	$-0.374652\pi$
$673$	−1.64533e8	−	1.64533e8i	−0.539768	−	0.539768i	−0.923461	+	0.383693i	$0.874652\pi$
$674$	4.81377e8	−	4.81377e8i	1.57219	−	1.57219i
$675$	2.96579e7	+	1.55038e8i	0.0964337	+	0.504112i
$676$	−1.07577e8			−0.348242
$677$	5.61361e7	+	5.61361e7i	0.180916	+	0.180916i	0.791755	−	0.610839i	$-0.209168\pi$
$677$	5.61361e7	+	5.61361e7i	0.180916	+	0.180916i	−0.610839	+	0.791755i	$0.709168\pi$
$678$	−2.34819e8	+	2.66442e8i	−0.753432	+	0.854897i
$679$	−1.33830e8			−0.427508
$680$	−2.24068e6	−	2.25270e7i	−0.00712611	−	0.0716435i
$681$	1.06346e8	−	1.20667e8i	0.336728	−	0.382075i
$682$			2.40243e8i			0.757350i
$683$	−4.41058e8	−	4.41058e8i	−1.38431	−	1.38431i	−0.836793	−	0.547519i	$-0.815572\pi$
$683$	−4.41058e8	−	4.41058e8i	−1.38431	−	1.38431i	−0.547519	−	0.836793i	$-0.684428\pi$
$684$	1.75855e7	+	1.38820e8i	0.0549522	+	0.433793i
$685$	−1.94555e8	+	1.94555e8i	−0.605299	+	0.605299i
$686$	−3.36986e8	+	3.36986e8i	−1.04385	+	1.04385i
$687$	−3.19576e7	−	5.06563e8i	−0.0985608	−	1.56230i
$688$		−	8.56745e7i		−	0.263079i
$689$	4.36108e6			0.0133333
$690$	3.90954e8	−	2.46641e7i	1.19008	−	0.0750791i
$691$	3.78502e8	+	3.78502e8i	1.14719	+	1.14719i	0.987104	+	0.160083i	$0.0511762\pi$
$691$	3.78502e8	+	3.78502e8i	1.14719	+	1.14719i	0.160083	+	0.987104i	$0.448824\pi$
$692$	−4.21171e7	−	4.21171e7i	−0.127098	−	0.127098i
$693$	8.51888e7	−	1.07916e7i	0.255966	−	0.0324254i
$694$	3.82080e8	−	3.82080e8i	1.14308	−	1.14308i
$695$	1.11382e8			0.331787
$696$	1.85006e6	+	1.63049e6i	0.00548730	+	0.00483603i
$697$	3.24547e8	−	3.22815e7i	0.958471	−	0.0953355i
$698$		−	1.72285e8i		−	0.506618i
$699$	3.74540e8	+	3.30087e8i	1.09665	+	0.966489i
$700$	8.67618e7	−	8.67618e7i	0.252950	−	0.252950i
$701$		−	3.19855e8i		−	0.928538i	−0.885694	−	0.464269i	$-0.846317\pi$
$701$		−	3.19855e8i		−	0.928538i	0.885694	−	0.464269i	$-0.153683\pi$
$702$	4.01828e8	−	7.68674e7i	1.16153	−	0.222193i
$703$	−5.01833e7	−	5.01833e7i	−0.144442	−	0.144442i
$704$	−1.11377e8	+	1.11377e8i	−0.319210	+	0.319210i
$705$	−7.90710e7	+	8.97195e7i	−0.225658	+	0.256047i
$706$			9.16404e8i			2.60419i
$707$	8.30781e7	−	8.30781e7i	0.235087	−	0.235087i
$708$	5.04591e8	−	3.18332e7i	1.42180	−	0.0896976i
$709$	−2.02313e8	+	2.02313e8i	−0.567656	+	0.567656i	−0.931471	−	0.363815i	$-0.881474\pi$
$709$	−2.02313e8	+	2.02313e8i	−0.567656	+	0.567656i	0.363815	+	0.931471i	$0.381474\pi$
$710$		−	3.50187e8i		−	0.978419i
$711$	2.82349e7	+	2.18857e7i	0.0785556	+	0.0608908i
$712$			5.36144e7i			0.148539i
$713$			5.70866e8i			1.57495i
$714$	−5.50047e7	−	3.36256e8i	−0.151114	−	0.923795i
$715$	−8.31252e7			−0.227413
$716$	7.04301e7			0.191875
$717$	−3.48456e7	−	5.52341e8i	−0.0945346	−	1.49848i
$718$	−4.39241e8			−1.18667
$719$	−2.99712e8	−	2.99712e8i	−0.806338	−	0.806338i	0.177739	−	0.984078i	$-0.443122\pi$
$719$	−2.99712e8	−	2.99712e8i	−0.806338	−	0.806338i	−0.984078	+	0.177739i	$0.943122\pi$
$720$	1.90001e8	+	1.47275e8i	0.509047	+	0.394578i
$721$	1.53913e8	+	1.53913e8i	0.410647	+	0.410647i
$722$	−4.51540e8			−1.19973
$723$	−2.06444e8	+	2.34246e8i	−0.546246	+	0.619809i
$724$	−4.68983e8	−	4.68983e8i	−1.23578	−	1.23578i
$725$	9.80245e6	−	9.80245e6i	0.0257229	−	0.0257229i
$726$	2.92197e7	+	4.63165e8i	0.0763601	+	1.21039i
$727$	3.54173e8			0.921749			0.460875	−	0.887465i	$-0.347536\pi$
$727$	3.54173e8			0.921749			0.460875	+	0.887465i	$0.347536\pi$
$728$	−1.50438e7	−	1.50438e7i	−0.0389910	−	0.0389910i
$729$	3.60067e8	−	1.42990e8i	0.929397	−	0.369083i
$730$	−7.67491e8			−1.97290
$731$	7.05354e7	−	8.61170e7i	0.180574	−	0.220464i
$732$	2.99188e8	+	2.63678e8i	0.762799	+	0.672265i
$733$		−	3.89496e8i		−	0.988989i	−0.869181	−	0.494494i	$-0.835353\pi$
$733$		−	3.89496e8i		−	0.988989i	0.869181	−	0.494494i	$-0.164647\pi$
$734$	−2.93062e8	−	2.93062e8i	−0.741091	−	0.741091i
$735$	1.05693e8	−	1.19927e8i	0.266185	−	0.302032i
$736$	−4.79368e8	+	4.79368e8i	−1.20236	+	1.20236i
$737$	−1.44830e8	+	1.44830e8i	−0.361788	+	0.361788i
$738$	3.41390e8	−	4.40430e8i	0.849341	−	1.09574i
$739$			3.18602e8i			0.789432i	0.918803	+	0.394716i	$0.129157\pi$
$739$			3.18602e8i			0.789432i	−0.918803	+	0.394716i	$0.870843\pi$
$740$	1.51691e8			0.374339
$741$	−8.58757e6	−	1.36122e8i	−0.0211065	−	0.334561i
$742$	−4.38807e6	−	4.38807e6i	−0.0107414	−	0.0107414i
$743$	−1.35657e7	−	1.35657e7i	−0.0330731	−	0.0330731i	0.690377	−	0.723450i	$-0.257445\pi$
$743$	−1.35657e7	−	1.35657e7i	−0.0330731	−	0.0330731i	−0.723450	+	0.690377i	$0.757445\pi$
$744$	3.72687e7	−	4.22876e7i	0.0904951	−	0.102682i
$745$	3.58759e8	−	3.58759e8i	0.867629	−	0.867629i
$746$	−1.68626e8			−0.406171
$747$	−3.05629e7	+	3.87167e6i	−0.0733218	+	0.00928830i
$748$	−1.77065e8	+	1.76120e7i	−0.423085	+	0.0420826i
$749$			3.77064e8i			0.897367i
$750$	−4.23869e8	+	4.80952e8i	−1.00473	+	1.14003i
$751$	9.17086e7	−	9.17086e7i	0.216516	−	0.216516i	−0.590512	−	0.807029i	$-0.701074\pi$
$751$	9.17086e7	−	9.17086e7i	0.216516	−	0.216516i	0.807029	+	0.590512i	$0.201074\pi$
$752$		−	1.92047e8i		−	0.451601i
$753$	5.42143e6	+	8.59356e7i	0.0126978	+	0.201274i
$754$	−2.54060e7	−	2.54060e7i	−0.0592683	−	0.0592683i
$755$	−1.50439e8	+	1.50439e8i	−0.349558	+	0.349558i
$756$	−2.49163e8	−	1.69143e8i	−0.576658	−	0.391462i
$757$			5.37383e8i			1.23879i	0.785081	+	0.619393i	$0.212621\pi$
$757$			5.37383e8i			1.23879i	−0.785081	+	0.619393i	$0.787379\pi$
$758$	1.60253e8	−	1.60253e8i	0.367958	−	0.367958i
$759$	−1.29695e7	−	2.05580e8i	−0.0296618	−	0.470171i
$760$	−9.11818e6	+	9.11818e6i	−0.0207715	+	0.0207715i
$761$		−	2.80036e8i		−	0.635418i	−0.948188	−	0.317709i	$-0.897086\pi$
$761$		−	2.80036e8i		−	0.635418i	0.948188	−	0.317709i	$-0.102914\pi$
$762$	4.68660e6	+	7.42876e7i	0.0105924	+	0.167900i
$763$		−	5.10077e8i		−	1.14832i
$764$		−	2.33176e8i		−	0.522882i
$765$	6.97313e7	+	3.04463e8i	0.155756	+	0.680065i
$766$	−1.24904e8			−0.277902
$767$	−4.92818e8			−1.09220
$768$	−3.80467e8	+	2.40026e7i	−0.839910	+	0.0529876i
$769$	−1.37568e8			−0.302509			−0.151254	−	0.988495i	$-0.548331\pi$
$769$	−1.37568e8			−0.302509			−0.151254	+	0.988495i	$0.548331\pi$
$770$	8.36396e7	+	8.36396e7i	0.183206	+	0.183206i
$771$	−2.50362e8	+	1.57947e7i	−0.546268	+	0.0344625i
$772$	6.16901e8	+	6.16901e8i	1.34080	+	1.34080i
$773$	2.42814e8			0.525696			0.262848	−	0.964837i	$-0.415338\pi$
$773$	2.42814e8			0.525696			0.262848	+	0.964837i	$0.415338\pi$
$774$	−2.39023e7	−	1.88685e8i	−0.0515486	−	0.406925i
$775$	−2.24059e8	−	2.24059e8i	−0.481345	−	0.481345i
$776$	2.24146e7	−	2.24146e7i	0.0479673	−	0.0479673i
$777$	1.52436e8	−	9.61677e6i	0.324956	−	0.0205006i
$778$	−1.26893e8			−0.269463
$779$	−1.31366e8	−	1.31366e8i	−0.277888	−	0.277888i
$780$	2.18710e8	+	1.92752e8i	0.460877	+	0.406177i
$781$	−1.84143e8			−0.386547
$782$	−8.13338e8	+	8.08996e7i	−1.70079	+	0.169171i
$783$	−2.81507e7	−	1.91100e7i	−0.0586414	−	0.0398085i
$784$			2.56706e8i			0.532707i
$785$	4.69431e8	+	4.69431e8i	0.970426	+	0.970426i
$786$	−1.79386e8	−	1.58096e8i	−0.369421	−	0.325576i
$787$	−5.75603e8	+	5.75603e8i	−1.18086	+	1.18086i	−0.201339	+	0.979522i	$0.564529\pi$
$787$	−5.75603e8	+	5.75603e8i	−1.18086	+	1.18086i	−0.979522	+	0.201339i	$0.935471\pi$
$788$	−1.70444e7	+	1.70444e7i	−0.0348341	+	0.0348341i
$789$	−2.68258e8	+	1.69237e7i	−0.546163	+	0.0344559i
$790$			4.92091e7i			0.0998078i
$791$	−2.54821e8			−0.514880
$792$	−1.24604e7	+	1.60753e7i	−0.0250818	+	0.0323582i
$793$	−2.74866e8	−	2.74866e8i	−0.551191	−	0.551191i
$794$	−1.92609e8	−	1.92609e8i	−0.384782	−	0.384782i
$795$	4.26788e6	+	3.76134e6i	0.00849396	+	0.00748584i
$796$	6.48635e8	−	6.48635e8i	1.28606	−	1.28606i
$797$	2.92253e8			0.577277			0.288638	−	0.957438i	$-0.406797\pi$
$797$	2.92253e8			0.577277			0.288638	+	0.957438i	$0.406797\pi$
$798$	−1.28324e8	+	1.45605e8i	−0.252522	+	0.286529i
$799$	1.58112e8	−	1.93039e8i	0.309973	−	0.378447i
$800$		−	3.76293e8i		−	0.734947i
$801$	−9.29655e7	−	7.33870e8i	−0.180894	−	1.42798i
$802$	2.71800e8	−	2.71800e8i	0.526897	−	0.526897i
$803$			4.03580e8i			0.779441i
$804$	7.16892e8	−	4.52267e7i	1.37939	−	0.0870216i
$805$	1.98745e8	+	1.98745e8i	0.380986	+	0.380986i
$806$	−5.80716e8	+	5.80716e8i	−1.10907	+	1.10907i
$807$	2.33357e8	+	2.05661e8i	0.444018	+	0.391319i
$808$			2.78287e7i			0.0527545i
$809$	3.25364e8	−	3.25364e8i	0.614502	−	0.614502i	−0.329613	−	0.944116i	$-0.606918\pi$
$809$	3.25364e8	−	3.25364e8i	0.614502	−	0.614502i	0.944116	+	0.329613i	$0.106918\pi$
$810$	4.59536e8	+	2.71343e8i	0.864698	+	0.510579i
$811$	6.09253e8	−	6.09253e8i	1.14218	−	1.14218i	0.154132	−	0.988050i	$-0.450742\pi$
$811$	6.09253e8	−	6.09253e8i	1.14218	−	1.14218i	0.988050	−	0.154132i	$-0.0492580\pi$
$812$			2.64479e7i			0.0493996i
$813$	−2.52513e8	+	1.59303e7i	−0.469908	+	0.0296451i
$814$		−	1.54195e8i		−	0.285889i
$815$			3.69586e8i			0.682720i
$816$	−4.07283e8	−	2.92768e8i	−0.749593	−	0.538832i
$817$	−6.34076e7			−0.116272
$818$	2.20378e8			0.402632
$819$	2.32004e8	+	1.79833e8i	0.422323	+	0.327355i
$820$	3.97084e8			0.720179
$821$	−3.52406e7	−	3.52406e7i	−0.0636817	−	0.0636817i	0.674549	−	0.738230i	$-0.264338\pi$
$821$	−3.52406e7	−	3.52406e7i	−0.0636817	−	0.0636817i	−0.738230	+	0.674549i	$0.764338\pi$
$822$	−6.17575e7	−	9.78924e8i	−0.111192	−	1.76252i
$823$	1.10169e8	+	1.10169e8i	0.197633	+	0.197633i	0.798985	−	0.601352i	$-0.205371\pi$
$823$	1.10169e8	+	1.10169e8i	0.197633	+	0.197633i	−0.601352	+	0.798985i	$0.705371\pi$
$824$	−5.15563e7			−0.0921510
$825$	8.57783e7	+	7.55975e7i	0.152762	+	0.134631i
$826$	4.95867e8	+	4.95867e8i	0.879884	+	0.879884i
$827$	−1.87669e8	+	1.87669e8i	−0.331799	+	0.331799i	−0.853269	−	0.521470i	$-0.825384\pi$
$827$	−1.87669e8	+	1.87669e8i	−0.331799	+	0.331799i	0.521470	+	0.853269i	$0.325384\pi$
$828$	−4.42579e8	+	5.70974e8i	−0.779650	+	1.00583i
$829$	1.16251e8			0.204049			0.102025	−	0.994782i	$-0.467468\pi$
$829$	1.16251e8			0.204049			0.102025	+	0.994782i	$0.467468\pi$
$830$	−3.00071e7	−	3.00071e7i	−0.0524796	−	0.0524796i
$831$	1.09326e8	−	1.24049e8i	0.190511	−	0.216167i
$832$	−5.38441e8			−0.934906
$833$	−2.11345e8	+	2.58032e8i	−0.365643	+	0.446416i
$834$	−2.62537e8	+	2.97893e8i	−0.452576	+	0.513525i
$835$		−	6.37786e8i		−	1.09551i
$836$	7.16698e7	+	7.16698e7i	0.122664	+	0.122664i
$837$	−4.36805e8	+	6.43453e8i	−0.744924	+	1.09734i
$838$	7.60828e7	−	7.60828e7i	0.129287	−	0.129287i
$839$	−3.72773e8	+	3.72773e8i	−0.631188	+	0.631188i	−0.948366	−	0.317178i	$-0.897265\pi$
$839$	−3.72773e8	+	3.72773e8i	−0.631188	+	0.631188i	0.317178	+	0.948366i	$0.397265\pi$
$840$	−1.74734e6	−	2.76973e7i	−0.00294808	−	0.0467303i
$841$		−	5.91835e8i		−	0.994976i
$842$	1.04363e9			1.74828
$843$	5.21302e8	−	3.28874e7i	0.870175	−	0.0548969i
$844$	5.60855e8	+	5.60855e8i	0.932875	+	0.932875i
$845$	9.67199e7	+	9.67199e7i	0.160305	+	0.160305i
$846$	−5.35792e7	−	4.22954e8i	−0.0884882	−	0.698526i
$847$	−2.35454e8	+	2.35454e8i	−0.387487	+	0.387487i
$848$	−9.13551e6			−0.0149812
$849$	3.56487e8	+	3.14177e8i	0.582534	+	0.513395i
$850$	2.87474e8	−	3.50978e8i	0.468103	−	0.571509i
$851$		−	3.66400e8i		−	0.594520i
$852$	4.84498e8	+	4.26994e8i	0.783381	+	0.690404i
$853$	2.51527e8	−	2.51527e8i	0.405263	−	0.405263i	−0.474820	−	0.880083i	$-0.657487\pi$
$853$	2.51527e8	−	2.51527e8i	0.405263	−	0.405263i	0.880083	+	0.474820i	$0.157487\pi$
$854$			5.53134e8i			0.888090i
$855$	1.08998e8	−	1.40620e8i	0.174390	−	0.224982i
$856$	−6.31528e7	−	6.31528e7i	−0.100687	−	0.100687i
$857$	6.56319e8	−	6.56319e8i	1.04273	−	1.04273i	0.0436870	−	0.999045i	$-0.486090\pi$
$857$	6.56319e8	−	6.56319e8i	1.04273	−	1.04273i	0.999045	−	0.0436870i	$-0.0139104\pi$
$858$	1.95934e8	−	2.22320e8i	0.310204	−	0.351979i
$859$			7.59843e8i			1.19879i	0.800452	+	0.599397i	$0.204593\pi$
$859$			7.59843e8i			1.19879i	−0.800452	+	0.599397i	$0.795407\pi$
$860$	9.58323e7	−	9.58323e7i	0.150666	−	0.150666i
$861$	3.99035e8	−	2.51740e7i	0.625174	−	0.0394405i
$862$	3.05138e8	−	3.05138e8i	0.476403	−	0.476403i
$863$			2.73815e8i			0.426015i	0.977051	+	0.213007i	$0.0683259\pi$
$863$			2.73815e8i			0.426015i	−0.977051	+	0.213007i	$0.931674\pi$
$864$	−9.07114e8	+	1.73526e8i	−1.40644	+	0.269044i
$865$			7.57327e7i			0.117013i
$866$		−	8.53868e7i		−	0.131473i
$867$	−1.68352e8	−	6.29595e8i	−0.258321	−	0.966059i
$868$	6.04531e8			0.924398
$869$	2.58763e7			0.0394314
$870$	−2.95091e6	−	4.67751e7i	−0.00448124	−	0.0710325i
$871$	−7.00166e8			−1.05961
$872$	8.54304e7	+	8.54304e7i	0.128844	+	0.128844i
$873$	−2.67943e8	+	3.45675e8i	−0.402716	+	0.519547i
$874$	3.29212e8	+	3.29212e8i	0.493107	+	0.493107i
$875$	−4.59975e8			−0.686610
$876$	9.35828e8	−	1.06186e9i	1.39214	−	1.57962i
$877$	2.93573e8	+	2.93573e8i	0.435228	+	0.435228i	0.890402	−	0.455174i	$-0.150423\pi$
$877$	2.93573e8	+	2.93573e8i	0.435228	+	0.435228i	−0.455174	+	0.890402i	$0.650423\pi$
$878$	1.89078e8	−	1.89078e8i	0.279355	−	0.279355i
$879$	7.91571e7	+	1.25473e9i	0.116553	+	1.84749i
$880$	1.74129e8			0.255519
$881$	−1.31531e8	−	1.31531e8i	−0.192353	−	0.192353i	0.604359	−	0.796712i	$-0.293429\pi$
$881$	−1.31531e8	−	1.31531e8i	−0.192353	−	0.192353i	−0.796712	+	0.604359i	$0.793429\pi$
$882$	7.16185e7	+	5.65356e8i	0.104380	+	0.823979i
$883$	7.51463e8			1.09150			0.545752	−	0.837947i	$-0.316244\pi$
$883$	7.51463e8			1.09150			0.545752	+	0.837947i	$0.316244\pi$
$884$	−4.70574e8	−	3.85430e8i	−0.681194	−	0.557942i
$885$	−4.82285e8	−	4.25044e8i	−0.695783	−	0.613203i
$886$			7.34297e7i			0.105577i
$887$	−5.91727e8	−	5.91727e8i	−0.847911	−	0.847911i	0.141961	−	0.989872i	$-0.454659\pi$
$887$	−5.91727e8	−	5.91727e8i	−0.847911	−	0.847911i	−0.989872	+	0.141961i	$0.954659\pi$
$888$	−2.39202e7	+	2.71415e7i	−0.0341606	+	0.0387610i
$889$	−3.77649e7	+	3.77649e7i	−0.0537505	+	0.0537505i
$890$	7.20524e8	−	7.20524e8i	1.02206	−	1.02206i
$891$	1.42684e8	−	2.41644e8i	0.201716	−	0.341619i
$892$		−	8.93374e8i		−	1.25875i
$893$	−1.42134e8			−0.199592
$894$	1.13881e8	+	1.80514e9i	0.159382	+	2.52638i
$895$	−6.33218e7	−	6.33218e7i	−0.0883251	−	0.0883251i
$896$	6.80975e7	+	6.80975e7i	0.0946688	+	0.0946688i
$897$	4.65580e8	−	5.28280e8i	0.645085	−	0.731959i
$898$	6.79240e7	−	6.79240e7i	0.0937982	−	0.0937982i
$899$	6.83006e7			0.0940038
$900$	−5.03937e7	−	3.97808e8i	−0.0691272	−	0.545690i
$901$	−9.18270e6	−	7.52123e6i	−0.0125544	−	0.0102829i
$902$		−	4.03639e8i		−	0.550013i
$903$	9.02276e7	−	1.02379e8i	0.122540	−	0.139042i
$904$	4.26788e7	−	4.26788e7i	0.0577706	−	0.0577706i
$905$			8.43301e8i			1.13772i
$906$	−4.77538e7	−	7.56950e8i	−0.0642131	−	1.01785i
$907$	−1.24658e7	−	1.24658e7i	−0.0167070	−	0.0167070i	0.698704	−	0.715411i	$-0.253760\pi$
$907$	−1.24658e7	−	1.24658e7i	−0.0167070	−	0.0167070i	−0.715411	+	0.698704i	$0.753760\pi$
$908$	−2.88916e8	+	2.88916e8i	−0.385935	+	0.385935i
$909$	−4.82541e7	−	3.80918e8i	−0.0642455	−	0.507154i
$910$			4.04348e8i			0.536576i
$911$	−7.18631e8	+	7.18631e8i	−0.950497	+	0.950497i	−0.998831	−	0.0483342i	$-0.984609\pi$
$911$	−7.18631e8	+	7.18631e8i	−0.950497	+	0.950497i	0.0483342	+	0.998831i	$0.484609\pi$
$912$	1.79891e7	+	2.85146e8i	0.0237151	+	0.375909i
$913$	−1.57790e7	+	1.57790e7i	−0.0207333	+	0.0207333i
$914$			7.95214e8i			1.04147i
$915$	−3.19257e7	−	5.06057e8i	−0.0416752	−	0.660597i
$916$			1.28939e9i			1.67764i
$917$		−	1.71562e8i		−	0.222492i
$918$	−9.78656e8	−	5.31149e8i	−1.26503	−	0.686576i
$919$	−5.78266e8			−0.745043			−0.372521	−	0.928024i	$-0.621507\pi$
$919$	−5.78266e8			−0.745043			−0.372521	+	0.928024i	$0.621507\pi$
$920$	−6.65738e7			−0.0854949
$921$	7.20089e8	−	4.54284e7i	0.921737	−	0.0581498i
$922$	−1.19938e9			−1.53026
$923$	−4.45112e8	−	4.45112e8i	−0.566063	−	0.566063i
$924$	−2.17703e8	+	1.37343e7i	−0.275962	+	0.0174097i
$925$	1.43808e8	+	1.43808e8i	0.181701	+	0.181701i
$926$	−7.98218e8			−1.00528
$927$	7.05699e8	−	8.93969e7i	0.885891	−	0.112223i
$928$	5.73533e7	+	5.73533e7i	0.0717653	+	0.0717653i
$929$	2.87696e8	−	2.87696e8i	0.358828	−	0.358828i	−0.504553	−	0.863381i	$-0.668343\pi$
$929$	2.87696e8	−	2.87696e8i	0.358828	−	0.358828i	0.863381	+	0.504553i	$0.168343\pi$
$930$	−1.06916e9	+	6.74501e7i	−1.32921	+	0.0838560i
$931$	1.89988e8			0.235439
$932$	−8.96767e8	−	8.96767e8i	−1.10773	−	1.10773i
$933$	4.37655e8	+	3.85711e8i	0.538874	+	0.474917i
$934$	−1.95252e9			−2.39637
$935$	1.75029e8	+	1.43360e8i	0.214128	+	0.175385i
$936$	−6.89768e7	+	8.73788e6i	−0.0841154	+	0.0106556i
$937$		−	7.70738e8i		−	0.936889i	−0.883493	−	0.468445i	$-0.844815\pi$
$937$		−	7.70738e8i		−	0.936889i	0.883493	−	0.468445i	$-0.155185\pi$
$938$	7.04498e8	+	7.04498e8i	0.853633	+	0.853633i
$939$	1.04076e9	+	9.17235e8i	1.25705	+	1.10786i
$940$	2.14817e8	−	2.14817e8i	0.258634	−	0.258634i
$941$	2.68161e8	−	2.68161e8i	0.321830	−	0.321830i	−0.527639	−	0.849469i	$-0.676923\pi$
$941$	2.68161e8	−	2.68161e8i	0.321830	−	0.321830i	0.849469	+	0.527639i	$0.176923\pi$
$942$	−2.36199e9	+	1.49012e8i	−2.82570	+	0.178265i
$943$		−	9.59130e8i		−	1.14378i
$944$	1.03234e9			1.22718
$945$	7.19436e7	+	3.76088e8i	0.0852505	+	0.445650i
$946$	−9.74142e7	−	9.74142e7i	−0.115067	−	0.115067i
$947$	4.42634e8	+	4.42634e8i	0.521188	+	0.521188i	0.917930	−	0.396742i	$-0.129859\pi$
$947$	4.42634e8	+	4.42634e8i	0.521188	+	0.521188i	−0.396742	+	0.917930i	$0.629859\pi$
$948$	−6.80828e7	−	6.00023e7i	−0.0799121	−	0.0704276i
$949$	−9.75536e8	+	9.75536e8i	−1.14142	+	1.14142i
$950$	−2.58424e8			−0.301413
$951$	9.19149e8	−	1.04293e9i	1.06867	−	1.21259i
$952$	5.73137e6	+	5.76212e7i	0.00664274	+	0.0667839i
$953$			5.74843e8i			0.664156i	0.943252	+	0.332078i	$0.107750\pi$
$953$			5.74843e8i			0.664156i	−0.943252	+	0.332078i	$0.892250\pi$
$954$	−2.01196e7	+	2.54871e6i	−0.0231725	+	0.00293546i
$955$	−2.09642e8	+	2.09642e8i	−0.240696	+	0.240696i
$956$			1.40591e9i			1.60911i
$957$	−2.45964e7	+	1.55172e6i	−0.0280631	+	0.00177042i
$958$	−8.18320e8	−	8.18320e8i	−0.930737	−	0.930737i
$959$	4.97646e8	−	4.97646e8i	0.564241	−	0.564241i
$960$	−5.26933e8	−	4.64393e8i	−0.595582	−	0.524894i
$961$		−	6.73670e8i		−	0.759062i
$962$	3.72721e8	−	3.72721e8i	0.418657	−	0.418657i
$963$	9.73936e8	+	7.54926e8i	1.09056	+	0.845329i
$964$	5.60860e8	−	5.60860e8i	0.626071	−	0.626071i
$965$		−	1.10928e9i		−	1.23441i
$966$	−1.00001e9	+	6.30877e7i	−1.10936	+	0.0699864i
$967$			1.69437e9i			1.87383i	0.349564	+	0.936913i	$0.386330\pi$
$967$			1.69437e9i			1.87383i	−0.349564	+	0.936913i	$0.613670\pi$
$968$		−	7.88704e7i		−	0.0869536i
$969$	−2.16678e8	+	3.01430e8i	−0.238146	+	0.331295i
$970$	−6.02459e8			−0.660104
$971$	6.95626e8			0.759833			0.379917	−	0.925021i	$-0.375953\pi$
$971$	6.95626e8			0.759833			0.379917	+	0.925021i	$0.375953\pi$
$972$	−9.35741e8	+	3.04930e8i	−1.01896	+	0.332048i
$973$	−2.84900e8			−0.309281
$974$	−5.99992e8	−	5.99992e8i	−0.649335	−	0.649335i
$975$	2.46089e7	+	3.90079e8i	0.0265509	+	0.420861i
$976$	5.75784e8	+	5.75784e8i	0.619313	+	0.619313i
$977$	1.40098e9			1.50228			0.751138	−	0.660145i	$-0.229505\pi$
$977$	1.40098e9			1.50228			0.751138	+	0.660145i	$0.229505\pi$
$978$	−9.88466e8	−	8.71148e8i	−1.05668	−	0.931269i
$979$	−3.78882e8	−	3.78882e8i	−0.403791	−	0.403791i
$980$	−2.87142e8	+	2.87142e8i	−0.305084	+	0.305084i
$981$	−1.31750e9	−	1.02123e9i	−1.39554	−	1.08173i
$982$	−2.53735e9			−2.67945
$983$	−9.35545e8	−	9.35545e8i	−0.984927	−	0.984927i	0.0149611	−	0.999888i	$-0.495238\pi$
$983$	−9.35545e8	−	9.35545e8i	−0.984927	−	0.984927i	−0.999888	+	0.0149611i	$0.995238\pi$
$984$	−6.26162e7	+	7.10487e7i	−0.0657206	+	0.0745712i
$985$	3.06484e7			0.0320700
$986$	9.67913e6	+	9.73107e7i	0.0100973	+	0.101515i
$987$	2.02254e8	−	2.29491e8i	0.210351	−	0.238679i
$988$			3.46481e8i			0.359260i
$989$	−2.31477e8	−	2.31477e8i	−0.239286	−	0.239286i
$990$	3.83492e8	−	4.85802e7i	0.395231	−	0.0500673i
$991$	−7.46418e8	+	7.46418e8i	−0.766940	+	0.766940i	−0.977567	−	0.210627i	$-0.932449\pi$
$991$	−7.46418e8	+	7.46418e8i	−0.766940	+	0.766940i	0.210627	+	0.977567i	$0.432449\pi$
$992$	1.31095e9	−	1.31095e9i	1.34292	−	1.34292i
$993$	6.45446e7	+	1.02310e9i	0.0659192	+	1.04489i
$994$			8.95733e8i			0.912052i
$995$	−1.16634e9			−1.18401
$996$	7.81048e7	−	4.92741e6i	0.0790496	−	0.00498701i
$997$	−4.35451e8	−	4.35451e8i	−0.439393	−	0.439393i	0.452415	−	0.891808i	$-0.350563\pi$
$997$	−4.35451e8	−	4.35451e8i	−0.439393	−	0.439393i	−0.891808	+	0.452415i	$0.850563\pi$
$998$	7.85306e8	+	7.85306e8i	0.790036	+	0.790036i
$999$	2.80355e8	−	4.12988e8i	0.281198	−	0.414229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.7.f.a.38.6	✓	68
3.2	odd	2	inner	51.7.f.a.38.29	yes	68
17.13	even	4	inner	51.7.f.a.47.29	yes	68
51.47	odd	4	inner	51.7.f.a.47.6	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.7.f.a.38.6	✓	68	1.1	even	1	trivial
51.7.f.a.38.29	yes	68	3.2	odd	2	inner
51.7.f.a.47.6	yes	68	51.47	odd	4	inner
51.7.f.a.47.29	yes	68	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	51.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-11.5147 q^{2} +(-26.9464 + 1.69997i) q^{3} +68.5886 q^{4} +(-61.6662 - 61.6662i) q^{5} +(310.280 - 19.5747i) q^{6} +(157.734 + 157.734i) q^{7} -52.8363 q^{8} +(723.220 - 91.6164i) q^{9} +(710.068 + 710.068i) q^{10} +(373.384 - 373.384i) q^{11} +(-1848.22 + 116.599i) q^{12} +1805.09 q^{13} +(-1816.26 - 1816.26i) q^{14} +(1766.51 + 1556.85i) q^{15} -3781.27 q^{16} +(-3800.81 - 3113.11i) q^{17} +(-8327.67 + 1054.94i) q^{18} +2798.52i q^{19} +(-4229.60 - 4229.60i) q^{20} +(-4518.52 - 3982.23i) q^{21} +(-4299.41 + 4299.41i) q^{22} +(-10216.3 + 10216.3i) q^{23} +(1423.75 - 89.8204i) q^{24} -8019.57i q^{25} -20785.1 q^{26} +(-19332.5 + 3698.19i) q^{27} +(10818.8 + 10818.8i) q^{28} +(1222.32 + 1222.32i) q^{29} +(-20340.9 - 17926.7i) q^{30} +(27939.0 - 27939.0i) q^{31} +46921.8 q^{32} +(-9426.63 + 10696.1i) q^{33} +(43765.2 + 35846.5i) q^{34} -19453.7i q^{35} +(49604.7 - 6283.84i) q^{36} +(-17932.1 + 17932.1i) q^{37} -32224.1i q^{38} +(-48640.8 + 3068.61i) q^{39} +(3258.21 + 3258.21i) q^{40} +(-46941.1 + 46941.1i) q^{41} +(52029.4 + 45854.2i) q^{42} +22657.6i q^{43} +(25609.9 - 25609.9i) q^{44} +(-50247.8 - 38948.6i) q^{45} +(117638. - 117638. i) q^{46} +50789.0i q^{47} +(101892. - 6428.07i) q^{48} -67888.9i q^{49} +92343.0i q^{50} +(107710. + 77425.8i) q^{51} +123809. q^{52} +2415.99 q^{53} +(222608. - 42583.6i) q^{54} -46050.4 q^{55} +(-8334.10 - 8334.10i) q^{56} +(-4757.41 - 75410.1i) q^{57} +(-14074.6 - 14074.6i) q^{58} -273015. q^{59} +(121163. + 106782. i) q^{60} +(-152273. - 152273. i) q^{61} +(-321709. + 321709. i) q^{62} +(128528. + 99625.5i) q^{63} -298290. q^{64} +(-111313. - 111313. i) q^{65} +(108545. - 123163. i) q^{66} -387883. q^{67} +(-260692. - 213524. i) q^{68} +(257926. - 292660. i) q^{69} +224004. i q^{70} +(-246587. - 246587. i) q^{71} +(-38212.3 + 4840.68i) q^{72} +(-540435. + 540435. i) q^{73} +(206483. - 206483. i) q^{74} +(13633.1 + 216099. i) q^{75} +191946. i q^{76} +117791. q^{77} +(560085. - 35334.2i) q^{78} +(34651.0 + 34651.0i) q^{79} +(233177. + 233177. i) q^{80} +(514654. - 132518. i) q^{81} +(540513. - 540513. i) q^{82} -42259.5 q^{83} +(-309919. - 273136. i) q^{84} +(42407.9 + 426355. i) q^{85} -260895. i q^{86} +(-35015.0 - 30859.2i) q^{87} +(-19728.3 + 19728.3i) q^{88} -1.01473e6i q^{89} +(578590. + 448482. i) q^{90} +(284725. + 284725. i) q^{91} +(-700722. + 700722. i) q^{92} +(-705360. + 800351. i) q^{93} -584821. i q^{94} +(172574. - 172574. i) q^{95} +(-1.26438e6 + 79765.9i) q^{96} +(-424226. + 424226. i) q^{97} +781721. i q^{98} +(235831. - 304247. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 18 q^{3} + 2040 q^{4} - 290 q^{6} - 4 q^{7} - 4256 q^{10} + 4182 q^{12} - 1832 q^{13} + 54976 q^{16} + 10940 q^{18} - 1604 q^{21} + 19576 q^{22} + 15110 q^{24} + 37314 q^{27} - 63120 q^{28} + 51360 q^{30}+ \cdots + 203004 q^{99}+O(q^{100}) \) 68 * q + 18 * q^3 + 2040 * q^4 - 290 * q^6 - 4 * q^7 - 4256 * q^10 + 4182 * q^12 - 1832 * q^13 + 54976 * q^16 + 10940 * q^18 - 1604 * q^21 + 19576 * q^22 + 15110 * q^24 + 37314 * q^27 - 63120 * q^28 + 51360 * q^30 - 88660 * q^31 - 128604 * q^33 + 80200 * q^34 + 335180 * q^37 + 31460 * q^39 - 286828 * q^40 + 45484 * q^45 - 85244 * q^46 + 111922 * q^48 - 590566 * q^51 - 904320 * q^52 - 1215638 * q^54 - 731624 * q^55 + 753144 * q^57 - 328292 * q^58 + 751532 * q^61 + 88664 * q^63 + 870368 * q^64 + 174232 * q^67 + 1420428 * q^69 + 1158660 * q^72 + 2397332 * q^73 + 1415042 * q^75 - 1868044 * q^78 - 1438708 * q^79 - 2973932 * q^81 - 617036 * q^82 + 4901976 * q^84 + 2375468 * q^85 + 521156 * q^88 - 3185088 * q^90 + 1741672 * q^91 + 4082570 * q^96 + 2753300 * q^97 + 203004 * q^99

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