LMFDB - Embedded newform 354.5.b.a.119.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,5,Mod(119,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("354.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	354.b (of order $2$, degree $1$, 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:	$36.5929669317$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.8
Character	$\chi$	$=$	354.119
Dual form			354.5.b.a.119.46

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} +(-7.33533 - 5.21468i) q^{3} -8.00000 q^{4} +49.1667i q^{5} +(-14.7493 + 20.7475i) q^{6} -32.7313 q^{7} +22.6274i q^{8} +(26.6142 + 76.5028i) q^{9} +O(q^{10})$	\(q-2.82843i q^{2} +(-7.33533 - 5.21468i) q^{3} -8.00000 q^{4} +49.1667i q^{5} +(-14.7493 + 20.7475i) q^{6} -32.7313 q^{7} +22.6274i q^{8} +(26.6142 + 76.5028i) q^{9} +139.065 q^{10} -179.360i q^{11} +(58.6827 + 41.7175i) q^{12} +156.423 q^{13} +92.5780i q^{14} +(256.389 - 360.654i) q^{15} +64.0000 q^{16} +442.293i q^{17} +(216.383 - 75.2762i) q^{18} +523.992 q^{19} -393.334i q^{20} +(240.095 + 170.683i) q^{21} -507.306 q^{22} +466.789i q^{23} +(117.995 - 165.980i) q^{24} -1792.37 q^{25} -442.431i q^{26} +(203.714 - 699.958i) q^{27} +261.850 q^{28} -526.472i q^{29} +(-1020.08 - 725.177i) q^{30} -442.968 q^{31} -181.019i q^{32} +(-935.305 + 1315.66i) q^{33} +1250.99 q^{34} -1609.29i q^{35} +(-212.913 - 612.023i) q^{36} -294.659 q^{37} -1482.07i q^{38} +(-1147.41 - 815.696i) q^{39} -1112.52 q^{40} +668.443i q^{41} +(482.765 - 679.091i) q^{42} -2718.94 q^{43} +1434.88i q^{44} +(-3761.39 + 1308.53i) q^{45} +1320.28 q^{46} +1740.30i q^{47} +(-469.461 - 333.740i) q^{48} -1329.66 q^{49} +5069.58i q^{50} +(2306.42 - 3244.37i) q^{51} -1251.38 q^{52} -702.011i q^{53} +(-1979.78 - 576.191i) q^{54} +8818.54 q^{55} -740.624i q^{56} +(-3843.66 - 2732.45i) q^{57} -1489.09 q^{58} +453.188i q^{59} +(-2051.11 + 2885.23i) q^{60} -930.423 q^{61} +1252.90i q^{62} +(-871.116 - 2504.04i) q^{63} -512.000 q^{64} +7690.81i q^{65} +(3721.26 + 2645.44i) q^{66} +591.000 q^{67} -3538.35i q^{68} +(2434.16 - 3424.05i) q^{69} -4551.76 q^{70} +8542.75i q^{71} +(-1731.06 + 602.210i) q^{72} -6204.14 q^{73} +833.421i q^{74} +(13147.6 + 9346.63i) q^{75} -4191.94 q^{76} +5870.68i q^{77} +(-2307.14 + 3245.38i) q^{78} +555.300 q^{79} +3146.67i q^{80} +(-5144.37 + 4072.12i) q^{81} +1890.64 q^{82} -11275.7i q^{83} +(-1920.76 - 1365.47i) q^{84} -21746.1 q^{85} +7690.33i q^{86} +(-2745.39 + 3861.85i) q^{87} +4058.45 q^{88} -12396.7i q^{89} +(3701.09 + 10638.8i) q^{90} -5119.92 q^{91} -3734.31i q^{92} +(3249.32 + 2309.94i) q^{93} +4922.32 q^{94} +25763.0i q^{95} +(-943.958 + 1327.84i) q^{96} -1632.36 q^{97} +3760.86i q^{98} +(13721.5 - 4773.52i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9}+O(q^{10}) $ 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9	$ 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9} + 256 q^{10} - 200 q^{13} - 26 q^{15} + 4864 q^{16} - 512 q^{18} + 616 q^{19} + 330 q^{21} + 640 q^{22} + 512 q^{24} - 10540 q^{25} - 354 q^{27} + 1472 q^{28} - 832 q^{30} - 3920 q^{31} - 188 q^{33} + 2560 q^{34} - 1344 q^{36} - 1440 q^{37} + 8204 q^{39} - 2048 q^{40} - 5760 q^{42} - 1944 q^{43} + 3886 q^{45} + 4864 q^{46} + 33636 q^{49} - 7544 q^{51} + 1600 q^{52} + 3392 q^{54} - 10536 q^{55} - 12182 q^{57} - 7168 q^{58} + 208 q^{60} + 6360 q^{61} + 10860 q^{63} - 38912 q^{64} + 19712 q^{66} + 30744 q^{67} - 34208 q^{69} - 23808 q^{70} + 4096 q^{72} + 4032 q^{73} + 22324 q^{75} - 4928 q^{76} + 12864 q^{78} - 29824 q^{79} - 22584 q^{81} + 13184 q^{82} - 2640 q^{84} + 9240 q^{85} + 32850 q^{87} - 5120 q^{88} - 16448 q^{90} - 31160 q^{91} - 1780 q^{93} + 5248 q^{94} - 4096 q^{96} + 77504 q^{97} - 15412 q^{99}+O(q^{100}) $ 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9 + 256 * q^10 - 200 * q^13 - 26 * q^15 + 4864 * q^16 - 512 * q^18 + 616 * q^19 + 330 * q^21 + 640 * q^22 + 512 * q^24 - 10540 * q^25 - 354 * q^27 + 1472 * q^28 - 832 * q^30 - 3920 * q^31 - 188 * q^33 + 2560 * q^34 - 1344 * q^36 - 1440 * q^37 + 8204 * q^39 - 2048 * q^40 - 5760 * q^42 - 1944 * q^43 + 3886 * q^45 + 4864 * q^46 + 33636 * q^49 - 7544 * q^51 + 1600 * q^52 + 3392 * q^54 - 10536 * q^55 - 12182 * q^57 - 7168 * q^58 + 208 * q^60 + 6360 * q^61 + 10860 * q^63 - 38912 * q^64 + 19712 * q^66 + 30744 * q^67 - 34208 * q^69 - 23808 * q^70 + 4096 * q^72 + 4032 * q^73 + 22324 * q^75 - 4928 * q^76 + 12864 * q^78 - 29824 * q^79 - 22584 * q^81 + 13184 * q^82 - 2640 * q^84 + 9240 * q^85 + 32850 * q^87 - 5120 * q^88 - 16448 * q^90 - 31160 * q^91 - 1780 * q^93 + 5248 * q^94 - 4096 * q^96 + 77504 * q^97 - 15412 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	2.82843i		−	0.707107i
$2$		−	2.82843i		−	0.707107i
$3$	−7.33533	−	5.21468i	−0.815037	−	0.579409i
$3$	−7.33533	−	5.21468i	−0.815037	−	0.579409i
$4$	−8.00000			−0.500000
$5$			49.1667i			1.96667i	0.181805	+	0.983335i	$0.441806\pi$
$5$			49.1667i			1.96667i	−0.181805	+	0.983335i	$0.558194\pi$
$6$	−14.7493	+	20.7475i	−0.409704	+	0.576318i
$7$	−32.7313			−0.667985			−0.333993	−	0.942576i	$-0.608396\pi$
$7$	−32.7313			−0.667985			−0.333993	+	0.942576i	$0.608396\pi$
$8$			22.6274i			0.353553i
$9$	26.6142	+	76.5028i	0.328570	+	0.944480i
$10$	139.065			1.39065
$11$		−	179.360i		−	1.48231i	−0.671332	−	0.741157i	$-0.734278\pi$
$11$		−	179.360i		−	1.48231i	0.671332	−	0.741157i	$-0.265722\pi$
$12$	58.6827	+	41.7175i	0.407518	+	0.289705i
$13$	156.423			0.925580			0.462790	−	0.886468i	$-0.346848\pi$
$13$	156.423			0.925580			0.462790	+	0.886468i	$0.346848\pi$
$14$			92.5780i			0.472337i
$15$	256.389	−	360.654i	1.13951	−	1.60291i
$16$	64.0000			0.250000
$17$			442.293i			1.53043i	0.643777	+	0.765213i	$0.277366\pi$
$17$			442.293i			1.53043i	−0.643777	+	0.765213i	$0.722634\pi$
$18$	216.383	−	75.2762i	0.667848	−	0.232334i
$19$	523.992			1.45150			0.725751	−	0.687958i	$-0.241493\pi$
$19$	523.992			1.45150			0.725751	+	0.687958i	$0.241493\pi$
$20$		−	393.334i		−	0.983335i
$21$	240.095	+	170.683i	0.544433	+	0.387037i
$22$	−507.306			−1.04815
$23$			466.789i			0.882400i	0.897409	+	0.441200i	$0.145447\pi$
$23$			466.789i			0.882400i	−0.897409	+	0.441200i	$0.854553\pi$
$24$	117.995	−	165.980i	0.204852	−	0.288159i
$25$	−1792.37			−2.86779
$26$		−	442.431i		−	0.654484i
$27$	203.714	−	699.958i	0.279443	−	0.960162i
$28$	261.850			0.333993
$29$		−	526.472i		−	0.626008i	−0.949752	−	0.313004i	$-0.898665\pi$
$29$		−	526.472i		−	0.626008i	0.949752	−	0.313004i	$-0.101335\pi$
$30$	−1020.08	−	725.177i	−1.13343	−	0.805753i
$31$	−442.968			−0.460945			−0.230472	−	0.973079i	$-0.574027\pi$
$31$	−442.968			−0.460945			−0.230472	+	0.973079i	$0.574027\pi$
$32$		−	181.019i		−	0.176777i
$33$	−935.305	+	1315.66i	−0.858866	+	1.20814i
$34$	1250.99			1.08217
$35$		−	1609.29i		−	1.31371i
$36$	−212.913	−	612.023i	−0.164285	−	0.472240i
$37$	−294.659			−0.215237			−0.107618	−	0.994192i	$-0.534322\pi$
$37$	−294.659			−0.215237			−0.107618	+	0.994192i	$0.534322\pi$
$38$		−	1482.07i		−	1.02637i
$39$	−1147.41	−	815.696i	−0.754382	−	0.536289i
$40$	−1112.52			−0.695323
$41$			668.443i			0.397646i	0.980035	+	0.198823i	$0.0637119\pi$
$41$			668.443i			0.397646i	−0.980035	+	0.198823i	$0.936288\pi$
$42$	482.765	−	679.091i	0.273676	−	0.384972i
$43$	−2718.94			−1.47049			−0.735247	−	0.677799i	$-0.762934\pi$
$43$	−2718.94			−1.47049			−0.735247	+	0.677799i	$0.762934\pi$
$44$			1434.88i			0.741157i
$45$	−3761.39	+	1308.53i	−1.85748	+	0.646189i
$46$	1320.28			0.623951
$47$			1740.30i			0.787825i	0.919148	+	0.393912i	$0.128879\pi$
$47$			1740.30i			0.787825i	−0.919148	+	0.393912i	$0.871121\pi$
$48$	−469.461	−	333.740i	−0.203759	−	0.144852i
$49$	−1329.66			−0.553796
$50$			5069.58i			2.02783i
$51$	2306.42	−	3244.37i	0.886743	−	1.24735i
$52$	−1251.38			−0.462790
$53$		−	702.011i		−	0.249915i	−0.992162	−	0.124958i	$-0.960121\pi$
$53$		−	702.011i		−	0.249915i	0.992162	−	0.124958i	$-0.0398795\pi$
$54$	−1979.78	−	576.191i	−0.678937	−	0.197596i
$55$	8818.54			2.91522
$56$		−	740.624i		−	0.236168i
$57$	−3843.66	−	2732.45i	−1.18303	−	0.841013i
$58$	−1489.09			−0.442654
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	−2051.11	+	2885.23i	−0.569753	+	0.801454i
$61$	−930.423			−0.250047			−0.125023	−	0.992154i	$-0.539901\pi$
$61$	−930.423			−0.250047			−0.125023	+	0.992154i	$0.539901\pi$
$62$			1252.90i			0.325937i
$63$	−871.116	−	2504.04i	−0.219480	−	0.630898i
$64$	−512.000			−0.125000
$65$			7690.81i			1.82031i
$66$	3721.26	+	2645.44i	0.854284	+	0.607310i
$67$	591.000			0.131655			0.0658276	−	0.997831i	$-0.479031\pi$
$67$	591.000			0.131655			0.0658276	+	0.997831i	$0.479031\pi$
$68$		−	3538.35i		−	0.765213i
$69$	2434.16	−	3424.05i	0.511270	−	0.719188i
$70$	−4551.76			−0.928930
$71$			8542.75i			1.69465i	0.531072	+	0.847327i	$0.321790\pi$
$71$			8542.75i			1.69465i	−0.531072	+	0.847327i	$0.678210\pi$
$72$	−1731.06	+	602.210i	−0.333924	+	0.116167i
$73$	−6204.14			−1.16422			−0.582111	−	0.813109i	$-0.697773\pi$
$73$	−6204.14			−1.16422			−0.582111	+	0.813109i	$0.697773\pi$
$74$			833.421i			0.152195i
$75$	13147.6	+	9346.63i	2.33735	+	1.66162i
$76$	−4191.94			−0.725751
$77$			5870.68i			0.990163i
$78$	−2307.14	+	3245.38i	−0.379214	+	0.533428i
$79$	555.300			0.0889761			0.0444881	−	0.999010i	$-0.485834\pi$
$79$	555.300			0.0889761			0.0444881	+	0.999010i	$0.485834\pi$
$80$			3146.67i			0.491667i
$81$	−5144.37	+	4072.12i	−0.784083	+	0.620655i
$82$	1890.64			0.281178
$83$		−	11275.7i		−	1.63678i	−0.574667	−	0.818388i	$-0.694868\pi$
$83$		−	11275.7i		−	1.63678i	0.574667	−	0.818388i	$-0.305132\pi$
$84$	−1920.76	−	1365.47i	−0.272216	−	0.193518i
$85$	−21746.1			−3.00984
$86$			7690.33i			1.03980i
$87$	−2745.39	+	3861.85i	−0.362715	+	0.510219i
$88$	4058.45			0.524077
$89$		−	12396.7i		−	1.56504i	−0.622625	−	0.782520i	$-0.713934\pi$
$89$		−	12396.7i		−	1.56504i	0.622625	−	0.782520i	$-0.286066\pi$
$90$	3701.09	+	10638.8i	0.456924	+	1.31344i
$91$	−5119.92			−0.618274
$92$		−	3734.31i		−	0.441200i
$93$	3249.32	+	2309.94i	0.375687	+	0.267076i
$94$	4922.32			0.557076
$95$			25763.0i			2.85462i
$96$	−943.958	+	1327.84i	−0.102426	+	0.144080i
$97$	−1632.36			−0.173489			−0.0867444	−	0.996231i	$-0.527646\pi$
$97$	−1632.36			−0.173489			−0.0867444	+	0.996231i	$0.527646\pi$
$98$			3760.86i			0.391593i
$99$	13721.5	−	4773.52i	1.40001	−	0.487044i
$100$	14338.9			1.43389
$101$		−	3682.10i		−	0.360955i	−0.983579	−	0.180477i	$-0.942236\pi$
$101$		−	3682.10i		−	0.360955i	0.983579	−	0.180477i	$-0.0577642\pi$
$102$	−9176.46	−	6523.54i	−0.882012	−	0.627022i
$103$	6597.41			0.621870			0.310935	−	0.950431i	$-0.399358\pi$
$103$	6597.41			0.621870			0.310935	+	0.950431i	$0.399358\pi$
$104$			3539.45i			0.327242i
$105$	−8391.93	+	11804.7i	−0.761173	+	1.07072i
$106$	−1985.59			−0.176717
$107$		−	17165.6i		−	1.49931i	−0.661829	−	0.749654i	$-0.730220\pi$
$107$		−	17165.6i		−	1.49931i	0.661829	−	0.749654i	$-0.269780\pi$
$108$	−1629.71	+	5599.67i	−0.139722	+	0.480081i
$109$	9191.39			0.773621			0.386810	−	0.922159i	$-0.373577\pi$
$109$	9191.39			0.773621			0.386810	+	0.922159i	$0.373577\pi$
$110$		−	24942.6i		−	2.06137i
$111$	2161.42	+	1536.55i	0.175426	+	0.124710i
$112$	−2094.80			−0.166996
$113$		−	11083.7i		−	0.868018i	−0.900908	−	0.434009i	$-0.857099\pi$
$113$		−	11083.7i		−	0.868018i	0.900908	−	0.434009i	$-0.142901\pi$
$114$	−7728.54	+	10871.5i	−0.594686	+	0.836527i
$115$	−22950.5			−1.73539
$116$			4211.78i			0.313004i
$117$	4163.07	+	11966.8i	0.304118	+	0.874191i
$118$	1281.81			0.0920575
$119$		−	14476.8i		−	1.02230i
$120$	8160.67	+	5801.42i	0.566713	+	0.402876i
$121$	−17529.0			−1.19725
$122$			2631.63i			0.176810i
$123$	3485.72	−	4903.25i	0.230400	−	0.324096i
$124$	3543.75			0.230472
$125$		−	57395.6i		−	3.67332i
$126$	−7082.48	+	2463.89i	−0.446113	+	0.155196i
$127$	−24393.0			−1.51237			−0.756184	−	0.654359i	$-0.772939\pi$
$127$	−24393.0			−1.51237			−0.756184	+	0.654359i	$0.772939\pi$
$128$			1448.15i			0.0883883i
$129$	19944.3	+	14178.4i	1.19851	+	0.852018i
$130$	21752.9			1.28715
$131$		−	16567.4i		−	0.965409i	−0.875783	−	0.482704i	$-0.839655\pi$
$131$		−	16567.4i		−	0.965409i	0.875783	−	0.482704i	$-0.160345\pi$
$132$	7482.44	−	10525.3i	0.429433	−	0.604070i
$133$	−17150.9			−0.969582
$134$		−	1671.60i		−	0.0930943i
$135$	34414.7	+	10016.0i	1.88832	+	0.549573i
$136$	−10008.0			−0.541087
$137$			19716.4i			1.05047i	0.850956	+	0.525237i	$0.176023\pi$
$137$			19716.4i			1.05047i	−0.850956	+	0.525237i	$0.823977\pi$
$138$	−9684.69	−	6884.84i	−0.508543	−	0.361523i
$139$	−36780.8			−1.90367			−0.951835	−	0.306612i	$-0.900805\pi$
$139$	−36780.8			−1.90367			−0.951835	+	0.306612i	$0.900805\pi$
$140$			12874.3i			0.656853i
$141$	9075.14	−	12765.7i	0.456473	−	0.642106i
$142$	24162.5			1.19830
$143$		−	28056.0i		−	1.37200i
$144$	1703.31	+	4896.18i	0.0821425	+	0.236120i
$145$	25884.9			1.23115
$146$			17547.9i			0.823229i
$147$	9753.52	+	6933.77i	0.451364	+	0.320874i
$148$	2357.27			0.107618
$149$			17714.4i			0.797911i	0.916970	+	0.398956i	$0.130627\pi$
$149$			17714.4i			0.797911i	−0.916970	+	0.398956i	$0.869373\pi$
$150$	26436.2	−	37187.0i	1.17494	−	1.65276i
$151$	−19658.8			−0.862190			−0.431095	−	0.902307i	$-0.641873\pi$
$151$	−19658.8			−0.862190			−0.431095	+	0.902307i	$0.641873\pi$
$152$			11856.6i			0.513183i
$153$	−33836.7	+	11771.3i	−1.44546	+	0.502852i
$154$	16604.8			0.700151
$155$		−	21779.3i		−	0.906526i
$156$	9179.31	+	6525.57i	0.377191	+	0.268145i
$157$	−10789.1			−0.437711			−0.218855	−	0.975757i	$-0.570232\pi$
$157$	−10789.1			−0.437711			−0.218855	+	0.975757i	$0.570232\pi$
$158$		−	1570.63i		−	0.0629156i
$159$	−3660.77	+	5149.49i	−0.144803	+	0.203690i
$160$	8900.13			0.347661
$161$		−	15278.6i		−	0.589430i
$162$	11517.7	+	14550.5i	0.438870	+	0.554431i
$163$	−20629.6			−0.776455			−0.388227	−	0.921564i	$-0.626913\pi$
$163$	−20629.6			−0.776455			−0.388227	+	0.921564i	$0.626913\pi$
$164$		−	5347.54i		−	0.198823i
$165$	−64686.9	−	45985.9i	−2.37601	−	1.68911i
$166$	−31892.6			−1.15737
$167$			30691.0i			1.10047i	0.835009	+	0.550236i	$0.185462\pi$
$167$			30691.0i			1.10047i	−0.835009	+	0.550236i	$0.814538\pi$
$168$	−3862.12	+	5432.72i	−0.136838	+	0.192486i
$169$	−4092.86			−0.143302
$170$			61507.3i			2.12828i
$171$	13945.6	+	40086.9i	0.476920	+	1.37091i
$172$	21751.5			0.735247
$173$			39243.8i			1.31123i	0.755095	+	0.655615i	$0.227591\pi$
$173$			39243.8i			1.31123i	−0.755095	+	0.655615i	$0.772409\pi$
$174$	10923.0	+	7765.13i	0.360780	+	0.256478i
$175$	58666.5			1.91564
$176$		−	11479.0i		−	0.370578i
$177$	2363.23	−	3324.28i	0.0754326	−	0.106109i
$178$	−35063.1			−1.10665
$179$		−	27131.2i		−	0.846766i	−0.905951	−	0.423383i	$-0.860843\pi$
$179$		−	27131.2i		−	0.846766i	0.905951	−	0.423383i	$-0.139157\pi$
$180$	30091.2	−	10468.3i	0.928739	−	0.323094i
$181$	5250.57			0.160269			0.0801345	−	0.996784i	$-0.474465\pi$
$181$	5250.57			0.160269			0.0801345	+	0.996784i	$0.474465\pi$
$182$			14481.3i			0.437185i
$183$	6824.96	+	4851.86i	0.203797	+	0.144879i
$184$	−10562.2			−0.311975
$185$		−	14487.4i		−	0.423299i
$186$	6533.49	−	9190.46i	0.188851	−	0.265651i
$187$	79329.7			2.26857
$188$		−	13922.4i		−	0.393912i
$189$	−6667.83	+	22910.5i	−0.186664	+	0.641374i
$190$	72868.7			2.01852
$191$			36928.7i			1.01227i	0.862454	+	0.506136i	$0.168927\pi$
$191$			36928.7i			1.01227i	−0.862454	+	0.506136i	$0.831073\pi$
$192$	3755.69	+	2669.92i	0.101880	+	0.0724261i
$193$	−34955.3			−0.938423			−0.469211	−	0.883086i	$-0.655462\pi$
$193$	−34955.3			−0.938423			−0.469211	+	0.883086i	$0.655462\pi$
$194$			4617.00i			0.122675i
$195$	40105.1	−	56414.6i	1.05470	−	1.48362i
$196$	10637.3			0.276898
$197$			39741.8i			1.02403i	0.858975	+	0.512017i	$0.171102\pi$
$197$			39741.8i			1.02403i	−0.858975	+	0.512017i	$0.828898\pi$
$198$	−13501.5	−	38810.4i	−0.344392	−	0.989960i
$199$	402.244			0.0101574			0.00507871	−	0.999987i	$-0.498383\pi$
$199$	402.244			0.0101574			0.00507871	+	0.999987i	$0.498383\pi$
$200$		−	40556.6i		−	1.01392i
$201$	−4335.18	−	3081.88i	−0.107304	−	0.0762823i
$202$	−10414.5			−0.255233
$203$			17232.1i			0.418164i
$204$	−18451.4	+	25954.9i	−0.443372	+	0.623677i
$205$	−32865.2			−0.782038
$206$		−	18660.3i		−	0.439728i
$207$	−35710.7	+	12423.2i	−0.833408	+	0.289930i
$208$	10011.1			0.231395
$209$		−	93983.2i		−	2.15158i
$210$	33388.7	+	23736.0i	0.757112	+	0.538231i
$211$	−10730.3			−0.241016			−0.120508	−	0.992712i	$-0.538452\pi$
$211$	−10730.3			−0.241016			−0.120508	+	0.992712i	$0.538452\pi$
$212$			5616.09i			0.124958i
$213$	44547.7	−	62663.9i	0.981898	−	1.38121i
$214$	−48551.6			−1.06017
$215$		−	133682.i		−	2.89197i
$216$	15838.2	+	4609.53i	0.339469	+	0.0987982i
$217$	14498.9			0.307904
$218$		−	25997.2i		−	0.547032i
$219$	45509.4	+	32352.6i	0.948883	+	0.674561i
$220$	−70548.3			−1.45761
$221$			69184.8i			1.41653i
$222$	4346.03	−	6113.42i	0.0881833	−	0.124045i
$223$	−53797.2			−1.08181			−0.540903	−	0.841085i	$-0.681917\pi$
$223$	−53797.2			−1.08181			−0.540903	+	0.841085i	$0.681917\pi$
$224$			5924.99i			0.118084i
$225$	−47702.4	−	137121.i	−0.942269	−	2.70857i
$226$	−31349.5			−0.613782
$227$		−	91713.6i		−	1.77985i	−0.456112	−	0.889923i	$-0.650758\pi$
$227$		−	91713.6i		−	1.77985i	0.456112	−	0.889923i	$-0.349242\pi$
$228$	30749.2	+	21859.6i	0.591514	+	0.420507i
$229$	−36340.1			−0.692970			−0.346485	−	0.938055i	$-0.612625\pi$
$229$	−36340.1			−0.692970			−0.346485	+	0.938055i	$0.612625\pi$
$230$			64913.8i			1.22710i
$231$	30613.7	−	43063.4i	0.573710	−	0.807020i
$232$	11912.7			0.221327
$233$			38359.1i			0.706572i	0.935515	+	0.353286i	$0.114936\pi$
$233$			38359.1i			0.706572i	−0.935515	+	0.353286i	$0.885064\pi$
$234$	33847.2	−	11774.9i	0.618146	−	0.215044i
$235$	−85565.1			−1.54939
$236$		−	3625.50i		−	0.0650945i
$237$	−4073.31	−	2895.71i	−0.0725188	−	0.0515536i
$238$	−40946.6			−0.722877
$239$		−	78839.1i		−	1.38021i	−0.723708	−	0.690106i	$-0.757564\pi$
$239$		−	78839.1i		−	1.38021i	0.723708	−	0.690106i	$-0.242436\pi$
$240$	16408.9	−	23081.9i	0.284877	−	0.400727i
$241$	107676.			1.85390			0.926949	−	0.375187i	$-0.122422\pi$
$241$	107676.			1.85390			0.926949	+	0.375187i	$0.122422\pi$
$242$			49579.4i			0.846586i
$243$	58970.5	−	3044.08i	0.998670	−	0.0515518i
$244$	7443.39			0.125023
$245$		−	65375.2i		−	1.08913i
$246$	−13868.5	−	9859.10i	−0.229171	−	0.162917i
$247$	81964.4			1.34348
$248$		−	10023.2i		−	0.162969i
$249$	−58799.4	+	82711.3i	−0.948363	+	1.33403i
$250$	−162339.			−2.59743
$251$		−	23123.4i		−	0.367032i	−0.983017	−	0.183516i	$-0.941252\pi$
$251$		−	23123.4i		−	0.367032i	0.983017	−	0.183516i	$-0.0587480\pi$
$252$	6968.93	+	20032.3i	0.109740	+	0.315449i
$253$	83723.3			1.30799
$254$			68993.8i			1.06941i
$255$	159515.	+	113399.i	2.45313	+	1.74393i
$256$	4096.00			0.0625000
$257$			28699.2i			0.434514i	0.976114	+	0.217257i	$0.0697109\pi$
$257$			28699.2i			0.434514i	−0.976114	+	0.217257i	$0.930289\pi$
$258$	40102.6	−	56411.1i	0.602467	−	0.847472i
$259$	9644.56			0.143775
$260$		−	61526.4i		−	0.910154i
$261$	40276.6	−	14011.6i	0.591251	−	0.205687i
$262$	−46859.6			−0.682647
$263$			16674.4i			0.241068i	0.992709	+	0.120534i	$0.0384606\pi$
$263$			16674.4i			0.241068i	−0.992709	+	0.120534i	$0.961539\pi$
$264$	−29770.1	−	21163.5i	−0.427142	−	0.303655i
$265$	34515.6			0.491500
$266$			48510.1i			0.685598i
$267$	−64644.8	+	90933.8i	−0.906799	+	1.27557i
$268$	−4728.00			−0.0658276
$269$			113717.i			1.57153i	0.618528	+	0.785763i	$0.287729\pi$
$269$			113717.i			1.57153i	−0.618528	+	0.785763i	$0.712271\pi$
$270$	28329.4	−	97339.3i	0.388607	−	1.33524i
$271$	−46631.5			−0.634952			−0.317476	−	0.948266i	$-0.602835\pi$
$271$	−46631.5			−0.634952			−0.317476	+	0.948266i	$0.602835\pi$
$272$			28306.8i			0.382607i
$273$	37556.3	+	26698.8i	0.503916	+	0.358233i
$274$	55766.3			0.742798
$275$			321479.i			4.25096i
$276$	−19473.3	+	27392.4i	−0.255635	+	0.359594i
$277$	112811.			1.47025			0.735127	−	0.677930i	$-0.237123\pi$
$277$	112811.			1.47025			0.735127	+	0.677930i	$0.237123\pi$
$278$			104032.i			1.34610i
$279$	−11789.2	−	33888.3i	−0.151453	−	0.435353i
$280$	36414.1			0.464465
$281$		−	142752.i		−	1.80788i	−0.427656	−	0.903941i	$-0.640661\pi$
$281$		−	142752.i		−	1.80788i	0.427656	−	0.903941i	$-0.359339\pi$
$282$	−36106.9	−	25668.4i	−0.454038	−	0.322775i
$283$	93541.3			1.16797			0.583983	−	0.811766i	$-0.301493\pi$
$283$	93541.3			1.16797			0.583983	+	0.811766i	$0.301493\pi$
$284$		−	68342.0i		−	0.847327i
$285$	134346.	−	188980.i	1.65399	−	2.32662i
$286$	−79354.4			−0.970150
$287$		−	21879.0i		−	0.265622i
$288$	13848.5	−	4817.68i	0.166962	−	0.0580835i
$289$	−112102.			−1.34220
$290$		−	73213.6i		−	0.870554i
$291$	11973.9	+	8512.21i	0.141400	+	0.100521i
$292$	49633.1			0.582111
$293$		−	22416.3i		−	0.261113i	−0.991441	−	0.130557i	$-0.958324\pi$
$293$		−	22416.3i		−	0.261113i	0.991441	−	0.130557i	$-0.0416764\pi$
$294$	19611.7	−	27587.1i	0.226892	−	0.319162i
$295$	−22281.8			−0.256039
$296$		−	6667.37i		−	0.0760976i
$297$	−125544.	−	36538.2i	−1.42326	−	0.414223i
$298$	50104.0			0.564208
$299$			73016.6i			0.816731i
$300$	−105181.	−	74773.0i	−1.16868	−	0.830811i
$301$	88994.5			0.982268
$302$			55603.4i			0.609660i
$303$	−19201.0	+	27009.4i	−0.209140	+	0.294191i
$304$	33535.5			0.362875
$305$		−	45745.9i		−	0.491759i
$306$	33294.2	+	95704.6i	0.355570	+	1.02209i
$307$	−29935.3			−0.317619			−0.158809	−	0.987309i	$-0.550766\pi$
$307$	−29935.3			−0.317619			−0.158809	+	0.987309i	$0.550766\pi$
$308$		−	46965.4i		−	0.495082i
$309$	−48394.2	−	34403.4i	−0.506847	−	0.360317i
$310$	−61601.1			−0.641011
$311$		−	112925.i		−	1.16753i	−0.811922	−	0.583766i	$-0.801579\pi$
$311$		−	112925.i		−	1.16753i	0.811922	−	0.583766i	$-0.198421\pi$
$312$	18457.1	−	25963.0i	0.189607	−	0.266714i
$313$	−6005.62			−0.0613012			−0.0306506	−	0.999530i	$-0.509758\pi$
$313$	−6005.62			−0.0613012			−0.0306506	+	0.999530i	$0.509758\pi$
$314$			30516.3i			0.309508i
$315$	123115.	−	42829.9i	1.24077	−	0.431644i
$316$	−4442.40			−0.0444881
$317$			31984.9i			0.318293i	0.987255	+	0.159146i	$0.0508742\pi$
$317$			31984.9i			0.318293i	−0.987255	+	0.159146i	$0.949126\pi$
$318$	14564.9	+	10354.2i	0.144031	+	0.102391i
$319$	−94428.1			−0.927940
$320$		−	25173.4i		−	0.245834i
$321$	−89513.1	+	125915.i	−0.868713	+	1.22199i
$322$	−43214.4			−0.416790
$323$			231758.i			2.22142i
$324$	41155.0	−	32577.0i	0.392042	−	0.310328i
$325$	−280367.			−2.65437
$326$			58349.4i			0.549037i
$327$	−67421.9	−	47930.2i	−0.630529	−	0.448243i
$328$	−15125.1			−0.140589
$329$		−	56962.4i		−	0.526255i
$330$	−130068.	+	182962.i	−1.19438	+	1.68009i
$331$	40597.6			0.370548			0.185274	−	0.982687i	$-0.440683\pi$
$331$	40597.6			0.370548			0.185274	+	0.982687i	$0.440683\pi$
$332$			90206.0i			0.818388i
$333$	−7842.10	−	22542.2i	−0.0707203	−	0.203287i
$334$	86807.4			0.778151
$335$			29057.6i			0.258922i
$336$	15366.1	+	10923.7i	0.136108	+	0.0967592i
$337$	18286.6			0.161017			0.0805087	−	0.996754i	$-0.474346\pi$
$337$	18286.6			0.161017			0.0805087	+	0.996754i	$0.474346\pi$
$338$			11576.3i			0.101330i
$339$	−57798.1	+	81302.8i	−0.502938	+	0.707467i
$340$	173969.			1.50492
$341$			79450.7i			0.683265i
$342$	113383.	−	39444.2i	0.969382	−	0.337233i
$343$	122109.			1.03791
$344$		−	61522.7i		−	0.519898i
$345$	168350.	+	119680.i	1.41441	+	1.00550i
$346$	110998.			0.927180
$347$			86629.0i			0.719456i	0.933057	+	0.359728i	$0.117131\pi$
$347$			86629.0i			0.719456i	−0.933057	+	0.359728i	$0.882869\pi$
$348$	21963.1	−	30894.8i	0.181357	−	0.255110i
$349$	9132.62			0.0749799			0.0374899	−	0.999297i	$-0.488064\pi$
$349$	9132.62			0.0749799			0.0374899	+	0.999297i	$0.488064\pi$
$350$		−	165934.i		−	1.35456i
$351$	31865.6	−	109490.i	0.258647	−	0.888707i
$352$	−32467.6			−0.262038
$353$			216298.i			1.73582i	0.496725	+	0.867908i	$0.334536\pi$
$353$			216298.i			1.73582i	−0.496725	+	0.867908i	$0.665464\pi$
$354$	−9402.49	−	6684.22i	−0.0750302	−	0.0533389i
$355$	−420019.			−3.33282
$356$			99173.5i			0.782520i
$357$	−75492.0	+	106192.i	−0.592331	+	0.833214i
$358$	−76738.7			−0.598754
$359$		−	104709.i		−	0.812448i	−0.913773	−	0.406224i	$-0.866845\pi$
$359$		−	104709.i		−	0.812448i	0.913773	−	0.406224i	$-0.133155\pi$
$360$	−29608.7	−	85110.6i	−0.228462	−	0.656718i
$361$	144247.			1.10686
$362$		−	14850.9i		−	0.113327i
$363$	128581.	+	91408.1i	0.975805	+	0.693699i
$364$	40959.4			0.309137
$365$		−	305037.i		−	2.28964i
$366$	13723.1	−	19303.9i	0.102445	−	0.144106i
$367$	−13049.9			−0.0968893			−0.0484446	−	0.998826i	$-0.515426\pi$
$367$	−13049.9			−0.0968893			−0.0484446	+	0.998826i	$0.515426\pi$
$368$			29874.5i			0.220600i
$369$	−51137.8	+	17790.1i	−0.375569	+	0.130655i
$370$	−40976.6			−0.299318
$371$			22977.7i			0.166940i
$372$	−25994.5	−	18479.5i	−0.187844	−	0.133538i
$373$	−65736.7			−0.472488			−0.236244	−	0.971694i	$-0.575916\pi$
$373$	−65736.7			−0.472488			−0.236244	+	0.971694i	$0.575916\pi$
$374$		−	224378.i		−	1.60412i
$375$	−299300.	+	421016.i	−2.12836	+	2.99389i
$376$	−39378.6			−0.278538
$377$		−	82352.4i		−	0.579420i
$378$	64800.7	+	18859.5i	0.453520	+	0.131991i
$379$	−35491.2			−0.247083			−0.123541	−	0.992339i	$-0.539425\pi$
$379$	−35491.2			−0.247083			−0.123541	+	0.992339i	$0.539425\pi$
$380$		−	206104.i		−	1.42731i
$381$	178931.	+	127202.i	1.23264	+	0.876280i
$382$	104450.			0.715784
$383$			232563.i			1.58542i	0.609601	+	0.792709i	$0.291330\pi$
$383$			232563.i			1.58542i	−0.609601	+	0.792709i	$0.708670\pi$
$384$	7551.67	−	10622.7i	0.0512130	−	0.0720398i
$385$	−288642.			−1.94732
$386$			98868.5i			0.663565i
$387$	−72362.4	−	208007.i	−0.483160	−	1.38885i
$388$	13058.8			0.0867444
$389$		−	208400.i		−	1.37720i	−0.725139	−	0.688602i	$-0.758225\pi$
$389$		−	208400.i		−	1.37720i	0.725139	−	0.688602i	$-0.241775\pi$
$390$	−159565.	−	113434.i	−1.04908	−	0.745788i
$391$	−206458.			−1.35045
$392$		−	30086.9i		−	0.195796i
$393$	−86393.6	+	121527.i	−0.559367	+	0.786844i
$394$	112407.			0.724102
$395$			27302.3i			0.174987i
$396$	−109772.	+	38188.1i	−0.700007	+	0.243522i
$397$	−150140.			−0.952614			−0.476307	−	0.879279i	$-0.658025\pi$
$397$	−150140.			−0.952614			−0.476307	+	0.879279i	$0.658025\pi$
$398$		−	1137.72i		−	0.00718238i
$399$	125808.	+	89436.6i	0.790245	+	0.561784i
$400$	−114711.			−0.716947
$401$			94015.2i			0.584668i	0.956316	+	0.292334i	$0.0944319\pi$
$401$			94015.2i			0.584668i	−0.956316	+	0.292334i	$0.905568\pi$
$402$	−8716.87	+	12261.8i	−0.0539397	+	0.0758753i
$403$	−69290.4			−0.426641
$404$			29456.8i			0.180477i
$405$	−200213.	−	252932.i	−1.22062	−	1.54203i
$406$	48739.8			0.295687
$407$			52850.0i			0.319048i
$408$	73411.7	+	52188.3i	0.441006	+	0.313511i
$409$	−140295.			−0.838677			−0.419339	−	0.907830i	$-0.637738\pi$
$409$	−140295.			−0.838677			−0.419339	+	0.907830i	$0.637738\pi$
$410$			92956.7i			0.552984i
$411$	102815.	−	144626.i	0.608655	−	0.856175i
$412$	−52779.3			−0.310935
$413$		−	14833.4i		−	0.0869643i
$414$	35138.1	+	101005.i	0.205011	+	0.589309i
$415$	554391.			3.21900
$416$		−	28315.6i		−	0.163621i
$417$	269799.	+	191800.i	1.55156	+	1.10300i
$418$	−265825.			−1.52140
$419$			169649.i			0.966323i	0.875531	+	0.483161i	$0.160512\pi$
$419$			169649.i			0.966323i	−0.875531	+	0.483161i	$0.839488\pi$
$420$	67135.5	−	94437.4i	0.380587	−	0.535359i
$421$	3072.01			0.0173324			0.00866620	−	0.999962i	$-0.497241\pi$
$421$	3072.01			0.0173324			0.00866620	+	0.999962i	$0.497241\pi$
$422$			30349.8i			0.170424i
$423$	−133138.	+	46316.8i	−0.744084	+	0.258856i
$424$	15884.7			0.0883583
$425$		−	792752.i		−	4.38894i
$426$	−177240.	−	126000.i	−0.976660	−	0.694307i
$427$	30453.9			0.167027
$428$			137325.i			0.749654i
$429$	−146303.	+	205800.i	−0.794949	+	1.11823i
$430$	−378108.			−2.04493
$431$			49116.3i			0.264406i	0.991223	+	0.132203i	$0.0422050\pi$
$431$			49116.3i			0.264406i	−0.991223	+	0.132203i	$0.957795\pi$
$432$	13037.7	−	44797.3i	0.0698609	−	0.240041i
$433$	−16836.7			−0.0898008			−0.0449004	−	0.998991i	$-0.514297\pi$
$433$	−16836.7			−0.0898008			−0.0449004	+	0.998991i	$0.514297\pi$
$434$		−	41009.1i		−	0.217721i
$435$	−189875.	−	134982.i	−1.00343	−	0.713340i
$436$	−73531.1			−0.386810
$437$			244594.i			1.28080i
$438$	91507.0	−	128720.i	0.476986	−	0.670962i
$439$	157998.			0.819827			0.409913	−	0.912124i	$-0.365559\pi$
$439$	157998.			0.819827			0.409913	+	0.912124i	$0.365559\pi$
$440$			199541.i			1.03069i
$441$	−35387.9	−	101723.i	−0.181961	−	0.523049i
$442$	195684.			1.00164
$443$		−	31837.1i		−	0.162228i	−0.996705	−	0.0811140i	$-0.974152\pi$
$443$		−	31837.1i		−	0.162228i	0.996705	−	0.0811140i	$-0.0258478\pi$
$444$	−17291.4	−	12292.4i	−0.0877129	−	0.0623550i
$445$	609504.			3.07792
$446$			152161.i			0.764953i
$447$	92375.1	−	129941.i	0.462317	−	0.650327i
$448$	16758.4			0.0834982
$449$			330642.i			1.64008i	0.572304	+	0.820042i	$0.306050\pi$
$449$			330642.i			1.64008i	−0.572304	+	0.820042i	$0.693950\pi$
$450$	−387837.	+	134923.i	−1.91525	+	0.666285i
$451$	119892.			0.589436
$452$			88669.8i			0.434009i
$453$	144204.	+	102514.i	0.702716	+	0.499561i
$454$	−259405.			−1.25854
$455$		−	251730.i		−	1.21594i
$456$	61828.3	−	86972.0i	0.297343	−	0.418263i
$457$	−172496.			−0.825935			−0.412968	−	0.910746i	$-0.635508\pi$
$457$	−172496.			−0.825935			−0.412968	+	0.910746i	$0.635508\pi$
$458$			102785.i			0.490004i
$459$	309587.	+	90101.5i	1.46946	+	0.427668i
$460$	183604.			0.867694
$461$		−	327769.i		−	1.54229i	−0.636660	−	0.771145i	$-0.719684\pi$
$461$		−	327769.i		−	1.54229i	0.636660	−	0.771145i	$-0.280316\pi$
$462$	−121802.	−	86588.7i	−0.570649	−	0.405674i
$463$	125432.			0.585123			0.292561	−	0.956247i	$-0.405492\pi$
$463$	125432.			0.585123			0.292561	+	0.956247i	$0.405492\pi$
$464$		−	33694.2i		−	0.156502i
$465$	−113572.	+	159758.i	−0.525250	+	0.738852i
$466$	108496.			0.499622
$467$			235253.i			1.07870i	0.842081	+	0.539350i	$0.181330\pi$
$467$			235253.i			1.07870i	−0.842081	+	0.539350i	$0.818670\pi$
$468$	−33304.5	−	95734.4i	−0.152059	−	0.437096i
$469$	−19344.2			−0.0879438
$470$			242015.i			1.09558i
$471$	79141.8	+	56261.9i	0.356750	+	0.253614i
$472$	−10254.5			−0.0460287
$473$			487669.i			2.17973i
$474$	−8190.31	+	11521.1i	−0.0364539	+	0.0512785i
$475$	−939186.			−4.16260
$476$			115815.i			0.511151i
$477$	53705.9	−	18683.5i	0.236040	−	0.0821146i
$478$	−222991.			−0.975957
$479$		−	28232.7i		−	0.123050i	−0.998106	−	0.0615249i	$-0.980404\pi$
$479$		−	28232.7i		−	0.123050i	0.998106	−	0.0615249i	$-0.0195964\pi$
$480$	−65285.4	−	46411.3i	−0.283357	−	0.201438i
$481$	−46091.4			−0.199219
$482$		−	304554.i		−	1.31090i
$483$	−79673.1	+	112074.i	−0.341521	+	0.480407i
$484$	140232.			0.598626
$485$		−	80257.6i		−	0.341195i
$486$	−8609.97	−	166794.i	−0.0364526	−	0.706167i
$487$	−164473.			−0.693482			−0.346741	−	0.937961i	$-0.612712\pi$
$487$	−164473.			−0.693482			−0.346741	+	0.937961i	$0.612712\pi$
$488$		−	21053.1i		−	0.0884048i
$489$	151325.	+	107577.i	0.632839	+	0.449885i
$490$	−184909.			−0.770133
$491$		−	371814.i		−	1.54228i	−0.636666	−	0.771140i	$-0.719687\pi$
$491$		−	371814.i		−	1.54228i	0.636666	−	0.771140i	$-0.280313\pi$
$492$	−27885.7	+	39226.0i	−0.115200	+	0.162048i
$493$	232855.			0.958059
$494$		−	231830.i		−	0.949984i
$495$	234698.	+	674643.i	0.957854	+	2.75337i
$496$	−28350.0			−0.115236
$497$		−	279615.i		−	1.13200i
$498$	233943.	+	166310.i	0.943303	+	0.670594i
$499$	−248828.			−0.999305			−0.499653	−	0.866226i	$-0.666539\pi$
$499$	−248828.			−0.999305			−0.499653	+	0.866226i	$0.666539\pi$
$500$			459165.i			1.83666i
$501$	160044.	−	225129.i	0.637623	−	0.896925i
$502$	−65402.9			−0.259531
$503$		−	170477.i		−	0.673799i	−0.941541	−	0.336899i	$-0.890622\pi$
$503$		−	170477.i		−	0.673799i	0.941541	−	0.336899i	$-0.109378\pi$
$504$	56659.9	−	19711.1i	0.223056	−	0.0775979i
$505$	181037.			0.709878
$506$		−	236805.i		−	0.924890i
$507$	30022.5	+	21342.9i	0.116797	+	0.0830307i
$508$	195144.			0.756184
$509$		−	21635.4i		−	0.0835082i	−0.999128	−	0.0417541i	$-0.986705\pi$
$509$		−	21635.4i		−	0.0835082i	0.999128	−	0.0417541i	$-0.0132946\pi$
$510$	320741.	−	451176.i	1.23314	−	1.73463i
$511$	203069.			0.777683
$512$		−	11585.2i		−	0.0441942i
$513$	106745.	−	366773.i	0.405613	−	1.39368i
$514$	81173.6			0.307248
$515$			324373.i			1.22301i
$516$	−159555.	−	113427.i	−0.599253	−	0.426009i
$517$	312141.			1.16780
$518$		−	27278.9i		−	0.101664i
$519$	204644.	−	287866.i	0.759739	−	1.06870i
$520$	−174023.			−0.643576
$521$		−	461333.i		−	1.69957i	−0.527128	−	0.849786i	$-0.676731\pi$
$521$		−	461333.i		−	1.69957i	0.527128	−	0.849786i	$-0.323269\pi$
$522$	−39630.9	−	113920.i	−0.145443	−	0.418078i
$523$	−86398.1			−0.315865			−0.157932	−	0.987450i	$-0.550483\pi$
$523$	−86398.1			−0.315865			−0.157932	+	0.987450i	$0.550483\pi$
$524$			132539.i			0.482704i
$525$	−430338.	−	305927.i	−1.56132	−	1.10994i
$526$	47162.3			0.170461
$527$		−	195922.i		−	0.705442i
$528$	−59859.5	+	84202.5i	−0.214716	+	0.302035i
$529$	61948.7			0.221371
$530$		−	97624.9i		−	0.347543i
$531$	−34670.1	+	12061.2i	−0.122961	+	0.0427762i
$532$	137207.			0.484791
$533$			104560.i			0.368053i
$534$	257200.	+	182843.i	0.901961	+	0.641204i
$535$	843976.			2.94864
$536$			13372.8i			0.0465472i
$537$	−141481.	+	199016.i	−0.490624	+	0.690145i
$538$	321641.			1.11124
$539$			238488.i			0.820899i
$540$	−275317.	−	80127.7i	−0.944161	−	0.274786i
$541$	−217386.			−0.742739			−0.371370	−	0.928485i	$-0.621112\pi$
$541$	−217386.			−0.742739			−0.371370	+	0.928485i	$0.621112\pi$
$542$			131894.i			0.448979i
$543$	−38514.7	−	27380.1i	−0.130625	−	0.0928614i
$544$	80063.6			0.270544
$545$			451910.i			1.52146i
$546$	75515.5	−	106225.i	0.253309	−	0.356322i
$547$	63693.0			0.212871			0.106436	−	0.994320i	$-0.466056\pi$
$547$	63693.0			0.212871			0.106436	+	0.994320i	$0.466056\pi$
$548$		−	157731.i		−	0.525237i
$549$	−24762.4	−	71180.0i	−0.0821578	−	0.236164i
$550$	909279.			3.00588
$551$		−	275867.i		−	0.908651i
$552$	77477.5	+	55078.7i	0.254271	+	0.180761i
$553$	−18175.7			−0.0594347
$554$		−	319078.i		−	1.03963i
$555$	−75547.3	+	106270.i	−0.245263	+	0.345004i
$556$	294246.			0.951835
$557$			370499.i			1.19420i	0.802168	+	0.597099i	$0.203680\pi$
$557$			370499.i			1.19420i	−0.802168	+	0.597099i	$0.796320\pi$
$558$	−95850.7	+	33345.0i	−0.307841	+	0.107093i
$559$	−425305.			−1.36106
$560$		−	102995.i		−	0.328426i
$561$	−581909.	−	413679.i	−1.84897	−	1.31443i
$562$	−403764.			−1.27837
$563$			524227.i			1.65388i	0.562293	+	0.826938i	$0.309919\pi$
$563$			524227.i			1.65388i	−0.562293	+	0.826938i	$0.690081\pi$
$564$	−72601.1	+	102126.i	−0.228236	+	0.321053i
$565$	544951.			1.70710
$566$		−	264575.i		−	0.825877i
$567$	168382.	−	133286.i	0.523756	−	0.414589i
$568$	−193300.			−0.599151
$569$		−	69554.9i		−	0.214834i	−0.994214	−	0.107417i	$-0.965742\pi$
$569$		−	69554.9i		−	0.214834i	0.994214	−	0.107417i	$-0.0342580\pi$
$570$	−534516.	−	379987.i	−1.64517	−	1.16955i
$571$	160407.			0.491985			0.245993	−	0.969272i	$-0.420886\pi$
$571$	160407.			0.491985			0.245993	+	0.969272i	$0.420886\pi$
$572$			224448.i			0.686000i
$573$	192571.	−	270884.i	0.586520	−	0.825039i
$574$	−61883.1			−0.187823
$575$		−	836658.i		−	2.53053i
$576$	−13626.5	−	39169.5i	−0.0410713	−	0.118060i
$577$	−161917.			−0.486340			−0.243170	−	0.969984i	$-0.578187\pi$
$577$	−161917.			−0.486340			−0.243170	+	0.969984i	$0.578187\pi$
$578$			317073.i			0.949082i
$579$	256409.	+	182281.i	0.764849	+	0.543731i
$580$	−207079.			−0.615575
$581$			369070.i			1.09334i
$582$	24076.2	−	33867.2i	0.0710790	−	0.0999847i
$583$	−125913.			−0.370452
$584$		−	140384.i		−	0.411614i
$585$	−588369.	+	204684.i	−1.71924	+	0.598099i
$586$	−63402.9			−0.184635
$587$			193558.i			0.561740i	0.959746	+	0.280870i	$0.0906230\pi$
$587$			193558.i			0.561740i	−0.959746	+	0.280870i	$0.909377\pi$
$588$	−78028.2	−	55470.2i	−0.225682	−	0.160437i
$589$	−232112.			−0.669062
$590$			63022.3i			0.181047i
$591$	207241.	−	291519.i	0.593335	−	0.834626i
$592$	−18858.2			−0.0538092
$593$			85583.1i			0.243376i	0.992568	+	0.121688i	$0.0388308\pi$
$593$			85583.1i			0.243376i	−0.992568	+	0.121688i	$0.961169\pi$
$594$	−103346.	+	355093.i	−0.292900	+	1.00640i
$595$	711778.			2.01053
$596$		−	141715.i		−	0.398956i
$597$	−2950.59	−	2097.58i	−0.00827867	−	0.00588530i
$598$	206522.			0.577516
$599$			224298.i			0.625131i	0.949896	+	0.312565i	$0.101188\pi$
$599$			224298.i			0.625131i	−0.949896	+	0.312565i	$0.898812\pi$
$600$	−211490.	+	297496.i	−0.587472	+	0.826379i
$601$	−102659.			−0.284215			−0.142107	−	0.989851i	$-0.545388\pi$
$601$	−102659.			−0.284215			−0.142107	+	0.989851i	$0.545388\pi$
$602$		−	251714.i		−	0.694568i
$603$	15729.0	+	45213.2i	0.0432580	+	0.124346i
$604$	157270.			0.431095
$605$		−	861843.i		−	2.35460i
$606$	76394.1	+	54308.6i	0.208025	+	0.147885i
$607$	587588.			1.59476			0.797380	−	0.603478i	$-0.206219\pi$
$607$	587588.			1.59476			0.797380	+	0.603478i	$0.206219\pi$
$608$		−	94852.7i		−	0.256592i
$609$	89860.0	−	126403.i	0.242288	−	0.340819i
$610$	−129389.			−0.347726
$611$			272224.i			0.729194i
$612$	270694.	−	94170.1i	0.722728	−	0.251426i
$613$	−80795.3			−0.215013			−0.107507	−	0.994204i	$-0.534287\pi$
$613$	−80795.3			−0.215013			−0.107507	+	0.994204i	$0.534287\pi$
$614$			84669.7i			0.224590i
$615$	241077.	+	171381.i	0.637390	+	0.453120i
$616$	−132838.			−0.350076
$617$		−	313732.i		−	0.824117i	−0.911157	−	0.412059i	$-0.864810\pi$
$617$		−	313732.i		−	0.824117i	0.911157	−	0.412059i	$-0.135190\pi$
$618$	−97307.6	+	136880.i	−0.254783	+	0.358395i
$619$	−67404.0			−0.175916			−0.0879578	−	0.996124i	$-0.528034\pi$
$619$	−67404.0			−0.175916			−0.0879578	+	0.996124i	$0.528034\pi$
$620$			174234.i			0.453263i
$621$	326733.	+	95091.7i	0.847247	+	0.246581i
$622$	−319400.			−0.825569
$623$			405759.i			1.04542i
$624$	−73434.5	−	52204.6i	−0.188595	−	0.134072i
$625$	1.70173e6			4.35642
$626$			16986.5i			0.0433465i
$627$	−490092.	+	689398.i	−1.24665	+	1.75362i
$628$	86313.0			0.218855
$629$		−	130326.i		−	0.329404i
$630$	−121141.	−	348223.i	−0.305219	−	0.877356i
$631$	−123366.			−0.309840			−0.154920	−	0.987927i	$-0.549512\pi$
$631$	−123366.			−0.309840			−0.154920	+	0.987927i	$0.549512\pi$
$632$			12565.0i			0.0314578i
$633$	78710.2	+	55955.0i	0.196437	+	0.139647i
$634$	90467.0			0.225067
$635$		−	1.19932e6i		−	2.97433i
$636$	29286.1	−	41195.9i	0.0724015	−	0.101845i
$637$	−207990.			−0.512582
$638$			267083.i			0.656152i
$639$	−653545.	+	227358.i	−1.60057	+	0.556812i
$640$	−71201.0			−0.173831
$641$			408405.i			0.993974i	0.867758	+	0.496987i	$0.165560\pi$
$641$			408405.i			0.993974i	−0.867758	+	0.496987i	$0.834440\pi$
$642$	356142.	+	253181.i	0.864079	+	0.614273i
$643$	59343.2			0.143532			0.0717661	−	0.997421i	$-0.477136\pi$
$643$	59343.2			0.143532			0.0717661	+	0.997421i	$0.477136\pi$
$644$			122229.i			0.294715i
$645$	−697107.	+	980598.i	−1.67564	+	2.35707i
$646$	655511.			1.57078
$647$			40240.4i			0.0961290i	0.998844	+	0.0480645i	$0.0153053\pi$
$647$			40240.4i			0.0961290i	−0.998844	+	0.0480645i	$0.984695\pi$
$648$	−92141.6	−	116404.i	−0.219435	−	0.277215i
$649$	81283.7			0.192981
$650$			792999.i			1.87692i
$651$	−106354.	−	75607.2i	−0.250953	−	0.178403i
$652$	165037.			0.388227
$653$		−	332773.i		−	0.780408i	−0.920728	−	0.390204i	$-0.872404\pi$
$653$		−	332773.i		−	0.780408i	0.920728	−	0.390204i	$-0.127596\pi$
$654$	−135567.	+	190698.i	−0.316956	+	0.445852i
$655$	814564.			1.89864
$656$			42780.3i			0.0994115i
$657$	−165118.	−	474634.i	−0.382528	−	1.09958i
$658$	−161114.			−0.372119
$659$			364963.i			0.840384i	0.907435	+	0.420192i	$0.138037\pi$
$659$			364963.i			0.840384i	−0.907435	+	0.420192i	$0.861963\pi$
$660$	517495.	+	367887.i	1.18801	+	0.844553i
$661$	72296.9			0.165469			0.0827345	−	0.996572i	$-0.473635\pi$
$661$	72296.9			0.165469			0.0827345	+	0.996572i	$0.473635\pi$
$662$		−	114827.i		−	0.262017i
$663$	360777.	−	507494.i	0.820751	−	1.15453i
$664$	255141.			0.578687
$665$		−	843255.i		−	1.90685i
$666$	−63759.1	+	22180.8i	−0.143745	+	0.0500068i
$667$	245752.			0.552389
$668$		−	245528.i		−	0.550236i
$669$	394620.	+	280535.i	0.881712	+	0.626809i
$670$	82187.2			0.183086
$671$			166881.i			0.370647i
$672$	30897.0	−	43461.8i	0.0684191	−	0.0962430i
$673$	480315.			1.06046			0.530232	−	0.847853i	$-0.322105\pi$
$673$	480315.			1.06046			0.530232	+	0.847853i	$0.322105\pi$
$674$		−	51722.3i		−	0.113856i
$675$	−365131.	+	1.25458e6i	−0.801385	+	2.75354i
$676$	32742.9			0.0716511
$677$		−	73980.4i		−	0.161413i	−0.996738	−	0.0807066i	$-0.974282\pi$
$677$		−	73980.4i		−	0.161413i	0.996738	−	0.0807066i	$-0.0257177\pi$
$678$	229959.	+	163478.i	0.500255	+	0.355631i
$679$	53429.1			0.115888
$680$		−	492058.i		−	1.06414i
$681$	−478258.	+	672750.i	−1.03126	+	1.45064i
$682$	224721.			0.483141
$683$			2144.82i			0.00459780i	0.999997	+	0.00229890i	$0.000731763\pi$
$683$			2144.82i			0.00459780i	−0.999997	+	0.00229890i	$0.999268\pi$
$684$	−111565.	−	320695.i	−0.238460	−	0.685457i
$685$	−969389.			−2.06594
$686$		−	345377.i		−	0.733915i
$687$	266566.	+	189502.i	0.564796	+	0.401513i
$688$	−174012.			−0.367623
$689$		−	109811.i		−	0.231316i
$690$	338505.	−	476164.i	0.710996	−	1.00014i
$691$	−530973.			−1.11203			−0.556015	−	0.831172i	$-0.687670\pi$
$691$	−530973.			−1.11203			−0.556015	+	0.831172i	$0.687670\pi$
$692$		−	313950.i		−	0.655615i
$693$	−449124.	+	156243.i	−0.935189	+	0.325338i
$694$	245024.			0.508732
$695$		−	1.80839e6i		−	3.74389i
$696$	−87383.7	−	62121.0i	−0.180390	−	0.128239i
$697$	−295648.			−0.608568
$698$		−	25831.0i		−	0.0530188i
$699$	200031.	−	281377.i	0.409395	−	0.575883i
$700$	−469332.			−0.957820
$701$			536037.i			1.09083i	0.838165	+	0.545417i	$0.183629\pi$
$701$			536037.i			1.09083i	−0.838165	+	0.545417i	$0.816371\pi$
$702$	−309683.	−	90129.5i	−0.628410	−	0.182891i
$703$	−154399.			−0.312416
$704$			91832.3i			0.185289i
$705$	627648.	+	446195.i	1.26281	+	0.897731i
$706$	611784.			1.22741
$707$			120520.i			0.241112i
$708$	−18905.8	+	26594.2i	−0.0377163	+	0.0530544i
$709$	−926579.			−1.84327			−0.921637	−	0.388053i	$-0.873148\pi$
$709$	−926579.			−1.84327			−0.921637	+	0.388053i	$0.873148\pi$
$710$			1.18799e6i			2.35666i
$711$	14778.8	+	42482.0i	0.0292349	+	0.0840361i
$712$	280505.			0.553325
$713$		−	206773.i		−	0.406738i
$714$	300357.	+	213524.i	0.589171	+	0.418841i
$715$	1.37942e6			2.69827
$716$			217050.i			0.423383i
$717$	−411121.	+	578311.i	−0.799707	+	1.12492i
$718$	−296162.			−0.574488
$719$			81615.9i			0.157876i	0.996880	+	0.0789382i	$0.0251530\pi$
$719$			81615.9i			0.157876i	−0.996880	+	0.0789382i	$0.974847\pi$
$720$	−240729.	+	83746.0i	−0.464370	+	0.161547i
$721$	−215942.			−0.415400
$722$		−	407991.i		−	0.782666i
$723$	−789841.	−	561498.i	−1.51100	−	1.07417i
$724$	−42004.6			−0.0801345
$725$			943632.i			1.79526i
$726$	258541.	−	363682.i	0.490519	−	0.689998i
$727$	225315.			0.426305			0.213153	−	0.977019i	$-0.431627\pi$
$727$	225315.			0.426305			0.213153	+	0.977019i	$0.431627\pi$
$728$		−	115851.i		−	0.218593i
$729$	−448442.	−	285183.i	−0.843823	−	0.536622i
$730$	−862775.			−1.61902
$731$		−	1.20257e6i		−	2.25048i
$732$	−54599.7	−	38814.9i	−0.101899	−	0.0724396i
$733$	706541.			1.31501			0.657505	−	0.753450i	$-0.271612\pi$
$733$	706541.			1.31501			0.657505	+	0.753450i	$0.271612\pi$
$734$			36910.7i			0.0685111i
$735$	−340911.	+	479549.i	−0.631054	+	0.887684i
$736$	84497.9			0.155988
$737$		−	106002.i		−	0.195154i
$738$	50317.9	+	144640.i	0.0923867	+	0.265567i
$739$	−358370.			−0.656211			−0.328105	−	0.944641i	$-0.606410\pi$
$739$	−358370.			−0.656211			−0.328105	+	0.944641i	$0.606410\pi$
$740$			115899.i			0.211650i
$741$	−601236.	−	427418.i	−1.09499	−	0.778425i
$742$	64990.8			0.118044
$743$		−	224110.i		−	0.405961i	−0.979183	−	0.202981i	$-0.934937\pi$
$743$		−	224110.i		−	0.405961i	0.979183	−	0.202981i	$-0.0650628\pi$
$744$	−52267.9	+	73523.7i	−0.0944255	+	0.132825i
$745$	−870960.			−1.56923
$746$			185932.i			0.334099i
$747$	862627.	−	300095.i	1.54590	−	0.537795i
$748$	−634637.			−1.13429
$749$			561852.i			1.00152i
$750$	1.19081e6	+	846548.i	2.11700	+	1.50497i
$751$	−887658.			−1.57386			−0.786929	−	0.617043i	$-0.788330\pi$
$751$	−887658.			−1.57386			−0.786929	+	0.617043i	$0.788330\pi$
$752$			111380.i			0.196956i
$753$	−120581.	+	169618.i	−0.212662	+	0.299145i
$754$	−232928.			−0.409712
$755$		−	966558.i		−	1.69564i
$756$	53342.6	−	183284.i	0.0933321	−	0.320687i
$757$	20307.6			0.0354377			0.0177189	−	0.999843i	$-0.494360\pi$
$757$	20307.6			0.0354377			0.0177189	+	0.999843i	$0.494360\pi$
$758$			100384.i			0.174714i
$759$	−614138.	−	436590.i	−1.06606	−	0.757863i
$760$	−582950.			−1.00926
$761$			108330.i			0.187060i	0.995616	+	0.0935298i	$0.0298151\pi$
$761$			108330.i			0.187060i	−0.995616	+	0.0935298i	$0.970185\pi$
$762$	359781.	−	506092.i	0.619624	−	0.871605i
$763$	−300846.			−0.516767
$764$		−	295430.i		−	0.506136i
$765$	−578755.	−	1.66364e6i	−0.988944	−	2.84273i
$766$	657788.			1.12106
$767$			70888.9i			0.120500i
$768$	−30045.5	−	21359.3i	−0.0509398	−	0.0362131i
$769$	−1.03772e6			−1.75480			−0.877401	−	0.479759i	$-0.840724\pi$
$769$	−1.03772e6			−1.75480			−0.877401	+	0.479759i	$0.840724\pi$
$770$			816403.i			1.37697i
$771$	149657.	−	210518.i	0.251761	−	0.354145i
$772$	279642.			0.469211
$773$		−	1.04554e6i		−	1.74978i	−0.484325	−	0.874888i	$-0.660935\pi$
$773$		−	1.04554e6i		−	1.74978i	0.484325	−	0.874888i	$-0.339065\pi$
$774$	−588332.	+	204672.i	−0.982066	+	0.341646i
$775$	793962.			1.32189
$776$		−	36936.0i		−	0.0613375i
$777$	−70746.1	−	50293.3i	−0.117182	−	0.0833045i
$778$	−589444.			−0.973831
$779$			350259.i			0.577184i
$780$	−320841.	+	451317.i	−0.527352	+	0.741809i
$781$	1.53223e6			2.51201
$782$			583951.i			0.954911i
$783$	−368509.	−	107250.i	−0.601069	−	0.174934i
$784$	−85098.5			−0.138449
$785$		−	530466.i		−	0.860832i
$786$	343731.	+	244358.i	0.556382	+	0.395532i
$787$	439610.			0.709770			0.354885	−	0.934910i	$-0.384520\pi$
$787$	439610.			0.709770			0.354885	+	0.934910i	$0.384520\pi$
$788$		−	317934.i		−	0.512017i
$789$	86951.7	−	122312.i	0.139677	−	0.196479i
$790$	77222.5			0.123734
$791$			362784.i			0.579823i
$792$	108012.	+	310483.i	0.172196	+	0.494980i
$793$	−145540.			−0.231438
$794$			424661.i			0.673600i
$795$	−253183.	−	179988.i	−0.400591	−	0.284780i
$796$	−3217.95			−0.00507871
$797$			1.05421e6i			1.65963i	0.558039	+	0.829815i	$0.311554\pi$
$797$			1.05421e6i			1.65963i	−0.558039	+	0.829815i	$0.688446\pi$
$798$	252965.	−	355838.i	0.397242	−	0.558787i
$799$	−769725.			−1.20571
$800$			324453.i			0.506958i
$801$	948382.	−	329928.i	1.47815	−	0.514225i
$802$	265915.			0.413423
$803$			1.11277e6i			1.72574i
$804$	34681.5	+	24655.0i	0.0536519	+	0.0381411i
$805$	751199.			1.15921
$806$			195983.i			0.301681i
$807$	592999.	−	834153.i	0.910556	−	1.28085i
$808$	83316.4			0.127617
$809$		−	980771.i		−	1.49855i	−0.662261	−	0.749274i	$-0.730403\pi$
$809$		−	980771.i		−	1.49855i	0.662261	−	0.749274i	$-0.269597\pi$
$810$	−715400.	+	566287.i	−1.09038	+	0.863111i
$811$	1.23176e6			1.87277			0.936387	−	0.350968i	$-0.114148\pi$
$811$	1.23176e6			1.87277			0.936387	+	0.350968i	$0.114148\pi$
$812$		−	137857.i		−	0.209082i
$813$	342058.	+	243169.i	0.517510	+	0.367897i
$814$	149482.			0.225601
$815$		−	1.01429e6i		−	1.52703i
$816$	147611.	−	207640.i	0.221686	−	0.311838i
$817$	−1.42470e6			−2.13442
$818$			396814.i			0.593034i
$819$	−136263.	−	391689.i	−0.203146	−	0.583947i
$820$	262921.			0.391019
$821$			39208.8i			0.0581697i	0.999577	+	0.0290849i	$0.00925930\pi$
$821$			39208.8i			0.0581697i	−0.999577	+	0.0290849i	$0.990741\pi$
$822$	−409064.	−	290803.i	−0.605407	−	0.430384i
$823$	−144695.			−0.213626			−0.106813	−	0.994279i	$-0.534065\pi$
$823$	−144695.			−0.213626			−0.106813	+	0.994279i	$0.534065\pi$
$824$			149282.i			0.219864i
$825$	1.67641e6	−	2.35815e6i	2.46304	−	3.46469i
$826$	−41955.2			−0.0614930
$827$		−	667141.i		−	0.975453i	−0.872996	−	0.487726i	$-0.837826\pi$
$827$		−	667141.i		−	0.975453i	0.872996	−	0.487726i	$-0.162174\pi$
$828$	285686.	−	99385.7i	0.416704	−	0.144965i
$829$	−916659.			−1.33382			−0.666912	−	0.745136i	$-0.732384\pi$
$829$	−916659.			−1.33382			−0.666912	+	0.745136i	$0.732384\pi$
$830$		−	1.56806e6i		−	2.27617i
$831$	−827507.	−	588274.i	−1.19831	−	0.851878i
$832$	−80088.6			−0.115697
$833$		−	588101.i		−	0.847544i
$834$	542493.	−	763108.i	0.779941	−	1.09712i
$835$	−1.50898e6			−2.16426
$836$			751865.i			1.07579i
$837$	−90238.9	+	310059.i	−0.128808	+	0.442582i
$838$	479839.			0.683293
$839$			904805.i			1.28538i	0.766127	+	0.642689i	$0.222181\pi$
$839$			904805.i			1.28538i	−0.766127	+	0.642689i	$0.777819\pi$
$840$	−267109.	−	189888.i	−0.378556	−	0.269115i
$841$	430108.			0.608114
$842$		−	8688.96i		−	0.0122559i
$843$	−744408.	+	1.04713e6i	−1.04750	+	1.47349i
$844$	85842.2			0.120508
$845$		−	201232.i		−	0.281828i
$846$	131004.	+	376572.i	0.183039	+	0.526147i
$847$	573746.			0.799747
$848$		−	44928.7i		−	0.0624788i
$849$	−686156.	−	487788.i	−0.951936	−	0.676731i
$850$	−2.24224e6			−3.10345
$851$		−	137544.i		−	0.189925i
$852$	−356382.	+	501311.i	−0.490949	+	0.690603i
$853$	328616.			0.451639			0.225819	−	0.974169i	$-0.427494\pi$
$853$	328616.			0.451639			0.225819	+	0.974169i	$0.427494\pi$
$854$		−	86136.8i		−	0.118106i
$855$	−1.97094e6	+	685660.i	−2.69613	+	0.937944i
$856$	388413.			0.530086
$857$			116351.i			0.158420i	0.996858	+	0.0792099i	$0.0252397\pi$
$857$			116351.i			0.158420i	−0.996858	+	0.0792099i	$0.974760\pi$
$858$	582091.	+	413808.i	0.790708	+	0.562114i
$859$	−458253.			−0.621039			−0.310519	−	0.950567i	$-0.600503\pi$
$859$	−458253.			−0.621039			−0.310519	+	0.950567i	$0.600503\pi$
$860$			1.06945e6i			1.44599i
$861$	−114092.	+	160490.i	−0.153904	+	0.216491i
$862$	138922.			0.186963
$863$			493616.i			0.662778i	0.943494	+	0.331389i	$0.107517\pi$
$863$			493616.i			0.662778i	−0.943494	+	0.331389i	$0.892483\pi$
$864$	−126706.	−	36876.2i	−0.169734	−	0.0493991i
$865$	−1.92949e6			−2.57876
$866$			47621.2i			0.0634987i
$867$	822307.	+	584578.i	1.09395	+	0.777686i
$868$	−115991.			−0.153952
$869$		−	99598.6i		−	0.131890i
$870$	−381786.	+	537046.i	−0.504407	+	0.709534i
$871$	92446.0			0.121857
$872$			207977.i			0.273516i
$873$	−43443.8	−	124880.i	−0.0570032	−	0.163857i
$874$	691816.			0.905665
$875$			1.87863e6i			2.45372i
$876$	−364075.	−	258821.i	−0.474442	−	0.337280i
$877$	−653158.			−0.849217			−0.424609	−	0.905377i	$-0.639588\pi$
$877$	−653158.			−0.849217			−0.424609	+	0.905377i	$0.639588\pi$
$878$		−	446885.i		−	0.579705i
$879$	−116894.	+	164431.i	−0.151291	+	0.212817i
$880$	564387.			0.728805
$881$		−	4741.79i		−	0.00610928i	−0.999995	−	0.00305464i	$-0.999028\pi$
$881$		−	4741.79i		−	0.00610928i	0.999995	−	0.00305464i	$-0.000972324\pi$
$882$	−287716.	+	100092.i	−0.369851	+	0.128666i
$883$	−359603.			−0.461213			−0.230607	−	0.973047i	$-0.574071\pi$
$883$	−359603.			−0.461213			−0.230607	+	0.973047i	$0.574071\pi$
$884$		−	553479.i		−	0.708266i
$885$	163444.	+	116192.i	0.208681	+	0.148351i
$886$	−90048.9			−0.114713
$887$			1.07871e6i			1.37106i	0.728045	+	0.685530i	$0.240429\pi$
$887$			1.07871e6i			1.37106i	−0.728045	+	0.685530i	$0.759571\pi$
$888$	−34768.2	+	48907.4i	−0.0440917	+	0.0620224i
$889$	798414.			1.01024
$890$		−	1.72394e6i		−	2.17642i
$891$	730375.	+	922694.i	0.920006	+	1.16226i
$892$	430377.			0.540903
$893$			911906.i			1.14353i
$894$	−367529.	−	261276.i	−0.459851	−	0.326907i
$895$	1.33395e6			1.66531
$896$		−	47399.9i		−	0.0590421i
$897$	380758.	−	535601.i	0.473221	−	0.665666i
$898$	935198.			1.15971
$899$			233211.i			0.288555i
$900$	381619.	+	1.09697e6i	0.471134	+	1.35428i
$901$	310495.			0.382477
$902$		−	339105.i		−	0.416794i
$903$	−652804.	−	464078.i	−0.800585	−	0.569135i
$904$	250796.			0.306891
$905$			258154.i			0.315196i
$906$	289954.	−	407870.i	0.353243	−	0.496896i
$907$	1.39312e6			1.69346			0.846728	−	0.532026i	$-0.178569\pi$
$907$	1.39312e6			1.69346			0.846728	+	0.532026i	$0.178569\pi$
$908$			733709.i			0.889923i
$909$	281691.	−	97996.0i	0.340914	−	0.118599i
$910$	−712000.			−0.859799
$911$			842819.i			1.01554i	0.861492	+	0.507770i	$0.169530\pi$
$911$			842819.i			1.01554i	−0.861492	+	0.507770i	$0.830470\pi$
$912$	−245994.	−	174877.i	−0.295757	−	0.210253i
$913$	−2.02242e6			−2.42621
$914$			487892.i			0.584024i
$915$	−238550.	+	335561.i	−0.284930	+	0.400802i
$916$	290720.			0.346485
$917$			542271.i			0.644879i
$918$	254845.	−	875644.i	0.302407	−	1.03906i
$919$	1.45676e6			1.72488			0.862438	−	0.506162i	$-0.168936\pi$
$919$	1.45676e6			1.72488			0.862438	+	0.506162i	$0.168936\pi$
$920$		−	519311.i		−	0.613552i
$921$	219585.	+	156103.i	0.258871	+	0.184031i
$922$	−927071.			−1.09056
$923$			1.33628e6i			1.56854i
$924$	−244910.	+	344507.i	−0.286855	+	0.403510i
$925$	528137.			0.617253
$926$		−	354776.i		−	0.413744i
$927$	175585.	+	504721.i	0.204328	+	0.587343i
$928$	−95301.7			−0.110664
$929$			1.49385e6i			1.73091i	0.500988	+	0.865454i	$0.332970\pi$
$929$			1.49385e6i			1.73091i	−0.500988	+	0.865454i	$0.667030\pi$
$930$	451865.	+	321230.i	0.522447	+	0.371408i
$931$	−696733.			−0.803835
$932$		−	306873.i		−	0.353286i
$933$	−588867.	+	828341.i	−0.676478	+	0.951581i
$934$	665395.			0.762757
$935$			3.90038e6i			4.46153i
$936$	−270778.	+	94199.5i	−0.309073	+	0.107522i
$937$	25883.0			0.0294805			0.0147402	−	0.999891i	$-0.495308\pi$
$937$	25883.0			0.0294805			0.0147402	+	0.999891i	$0.495308\pi$
$938$			54713.6i			0.0621856i
$939$	44053.2	+	31317.4i	0.0499627	+	0.0355185i
$940$	684521.			0.774695
$941$		−	1.51289e6i		−	1.70855i	−0.519820	−	0.854276i	$-0.674001\pi$
$941$		−	1.51289e6i		−	1.70855i	0.519820	−	0.854276i	$-0.325999\pi$
$942$	159133.	−	223847.i	0.179332	−	0.252261i
$943$	−312022.			−0.350883
$944$			29004.0i			0.0325472i
$945$	−1.12644e6	−	327835.i	−1.26137	−	0.367107i
$946$	1.37934e6			1.54130
$947$			909836.i			1.01453i	0.861791	+	0.507263i	$0.169343\pi$
$947$			909836.i			1.01453i	−0.861791	+	0.507263i	$0.830657\pi$
$948$	32586.5	+	23165.7i	0.0362594	+	0.0257768i
$949$	−970469.			−1.07758
$950$			2.65642e6i			2.94340i
$951$	166791.	−	234620.i	0.184422	−	0.259420i
$952$	327573.			0.361438
$953$		−	81106.0i		−	0.0893032i	−0.999003	−	0.0446516i	$-0.985782\pi$
$953$		−	81106.0i		−	0.0893032i	0.999003	−	0.0446516i	$-0.0142178\pi$
$954$	−52844.8	−	151903.i	−0.0580638	−	0.166905i
$955$	−1.81566e6			−1.99080
$956$			630713.i			0.690106i
$957$	692661.	+	492412.i	0.756305	+	0.537657i
$958$	−79854.1			−0.0870094
$959$		−	645341.i		−	0.701701i
$960$	−131271.	+	184655.i	−0.142438	+	0.200363i
$961$	−727300.			−0.787530
$962$			130366.i			0.140869i
$963$	1.31322e6	−	456848.i	1.41607	−	0.492628i
$964$	−861410.			−0.926949
$965$		−	1.71864e6i		−	1.84557i
$966$	316992.	+	225350.i	0.339699	+	0.241492i
$967$	−833275.			−0.891119			−0.445559	−	0.895252i	$-0.646995\pi$
$967$	−833275.			−0.891119			−0.445559	+	0.895252i	$0.646995\pi$
$968$		−	396636.i		−	0.423293i
$969$	1.20855e6	−	1.70002e6i	1.28711	−	1.81054i
$970$	−227003.			−0.241261
$971$		−	38558.4i		−	0.0408959i	−0.999791	−	0.0204480i	$-0.993491\pi$
$971$		−	38558.4i		−	0.0408959i	0.999791	−	0.0204480i	$-0.00650924\pi$
$972$	−471764.	+	24352.7i	−0.499335	+	0.0257759i
$973$	1.20388e6			1.27162
$974$			465199.i			0.490366i
$975$	2.05659e6	+	1.46203e6i	2.16341	+	1.53796i
$976$	−59547.1			−0.0625116
$977$			128219.i			0.134327i	0.997742	+	0.0671635i	$0.0213949\pi$
$977$			128219.i			0.134327i	−0.997742	+	0.0671635i	$0.978605\pi$
$978$	304274.	−	428012.i	0.318117	−	0.447485i
$979$	−2.22347e6			−2.31988
$980$			523002.i			0.544567i
$981$	244621.	+	703167.i	0.254189	+	0.730669i
$982$	−1.05165e6			−1.09056
$983$			761733.i			0.788308i	0.919044	+	0.394154i	$0.128962\pi$
$983$			761733.i			0.788308i	−0.919044	+	0.394154i	$0.871038\pi$
$984$	110948.	+	78872.8i	0.114585	+	0.0814586i
$985$	−1.95397e6			−2.01394
$986$		−	658614.i		−	0.677450i
$987$	−297041.	+	417838.i	−0.304917	+	0.428917i
$988$	−655715.			−0.671740
$989$		−	1.26917e6i		−	1.29756i
$990$	1.90818e6	−	663827.i	1.94692	−	0.677305i
$991$	−995749.			−1.01392			−0.506959	−	0.861970i	$-0.669230\pi$
$991$	−995749.			−1.01392			−0.506959	+	0.861970i	$0.669230\pi$
$992$			80185.8i			0.0814843i
$993$	−297797.	−	211703.i	−0.302010	−	0.214699i
$994$	−790871.			−0.800448
$995$			19777.0i			0.0199763i
$996$	470395.	−	661691.i	0.474181	−	0.667016i
$997$	1.82384e6			1.83484			0.917419	−	0.397923i	$-0.130269\pi$
$997$	1.82384e6			1.83484			0.917419	+	0.397923i	$0.130269\pi$
$998$			703792.i			0.706615i
$999$	−60026.2	+	206249.i	−0.0601465	+	0.206662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.5.b.a.119.8	✓	76
3.2	odd	2	inner	354.5.b.a.119.46	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.5.b.a.119.8	✓	76	1.1	even	1	trivial
354.5.b.a.119.46	yes	76	3.2	odd	2	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	354.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} +(-7.33533 - 5.21468i) q^{3} -8.00000 q^{4} +49.1667i q^{5} +(-14.7493 + 20.7475i) q^{6} -32.7313 q^{7} +22.6274i q^{8} +(26.6142 + 76.5028i) q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} +(-7.33533 - 5.21468i) q^{3} -8.00000 q^{4} +49.1667i q^{5} +(-14.7493 + 20.7475i) q^{6} -32.7313 q^{7} +22.6274i q^{8} +(26.6142 + 76.5028i) q^{9} +139.065 q^{10} -179.360i q^{11} +(58.6827 + 41.7175i) q^{12} +156.423 q^{13} +92.5780i q^{14} +(256.389 - 360.654i) q^{15} +64.0000 q^{16} +442.293i q^{17} +(216.383 - 75.2762i) q^{18} +523.992 q^{19} -393.334i q^{20} +(240.095 + 170.683i) q^{21} -507.306 q^{22} +466.789i q^{23} +(117.995 - 165.980i) q^{24} -1792.37 q^{25} -442.431i q^{26} +(203.714 - 699.958i) q^{27} +261.850 q^{28} -526.472i q^{29} +(-1020.08 - 725.177i) q^{30} -442.968 q^{31} -181.019i q^{32} +(-935.305 + 1315.66i) q^{33} +1250.99 q^{34} -1609.29i q^{35} +(-212.913 - 612.023i) q^{36} -294.659 q^{37} -1482.07i q^{38} +(-1147.41 - 815.696i) q^{39} -1112.52 q^{40} +668.443i q^{41} +(482.765 - 679.091i) q^{42} -2718.94 q^{43} +1434.88i q^{44} +(-3761.39 + 1308.53i) q^{45} +1320.28 q^{46} +1740.30i q^{47} +(-469.461 - 333.740i) q^{48} -1329.66 q^{49} +5069.58i q^{50} +(2306.42 - 3244.37i) q^{51} -1251.38 q^{52} -702.011i q^{53} +(-1979.78 - 576.191i) q^{54} +8818.54 q^{55} -740.624i q^{56} +(-3843.66 - 2732.45i) q^{57} -1489.09 q^{58} +453.188i q^{59} +(-2051.11 + 2885.23i) q^{60} -930.423 q^{61} +1252.90i q^{62} +(-871.116 - 2504.04i) q^{63} -512.000 q^{64} +7690.81i q^{65} +(3721.26 + 2645.44i) q^{66} +591.000 q^{67} -3538.35i q^{68} +(2434.16 - 3424.05i) q^{69} -4551.76 q^{70} +8542.75i q^{71} +(-1731.06 + 602.210i) q^{72} -6204.14 q^{73} +833.421i q^{74} +(13147.6 + 9346.63i) q^{75} -4191.94 q^{76} +5870.68i q^{77} +(-2307.14 + 3245.38i) q^{78} +555.300 q^{79} +3146.67i q^{80} +(-5144.37 + 4072.12i) q^{81} +1890.64 q^{82} -11275.7i q^{83} +(-1920.76 - 1365.47i) q^{84} -21746.1 q^{85} +7690.33i q^{86} +(-2745.39 + 3861.85i) q^{87} +4058.45 q^{88} -12396.7i q^{89} +(3701.09 + 10638.8i) q^{90} -5119.92 q^{91} -3734.31i q^{92} +(3249.32 + 2309.94i) q^{93} +4922.32 q^{94} +25763.0i q^{95} +(-943.958 + 1327.84i) q^{96} -1632.36 q^{97} +3760.86i q^{98} +(13721.5 - 4773.52i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9}+O(q^{10}) \) 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9	\( 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9} + 256 q^{10} - 200 q^{13} - 26 q^{15} + 4864 q^{16} - 512 q^{18} + 616 q^{19} + 330 q^{21} + 640 q^{22} + 512 q^{24} - 10540 q^{25} - 354 q^{27} + 1472 q^{28} - 832 q^{30} - 3920 q^{31} - 188 q^{33} + 2560 q^{34} - 1344 q^{36} - 1440 q^{37} + 8204 q^{39} - 2048 q^{40} - 5760 q^{42} - 1944 q^{43} + 3886 q^{45} + 4864 q^{46} + 33636 q^{49} - 7544 q^{51} + 1600 q^{52} + 3392 q^{54} - 10536 q^{55} - 12182 q^{57} - 7168 q^{58} + 208 q^{60} + 6360 q^{61} + 10860 q^{63} - 38912 q^{64} + 19712 q^{66} + 30744 q^{67} - 34208 q^{69} - 23808 q^{70} + 4096 q^{72} + 4032 q^{73} + 22324 q^{75} - 4928 q^{76} + 12864 q^{78} - 29824 q^{79} - 22584 q^{81} + 13184 q^{82} - 2640 q^{84} + 9240 q^{85} + 32850 q^{87} - 5120 q^{88} - 16448 q^{90} - 31160 q^{91} - 1780 q^{93} + 5248 q^{94} - 4096 q^{96} + 77504 q^{97} - 15412 q^{99}+O(q^{100}) \) 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9 + 256 * q^10 - 200 * q^13 - 26 * q^15 + 4864 * q^16 - 512 * q^18 + 616 * q^19 + 330 * q^21 + 640 * q^22 + 512 * q^24 - 10540 * q^25 - 354 * q^27 + 1472 * q^28 - 832 * q^30 - 3920 * q^31 - 188 * q^33 + 2560 * q^34 - 1344 * q^36 - 1440 * q^37 + 8204 * q^39 - 2048 * q^40 - 5760 * q^42 - 1944 * q^43 + 3886 * q^45 + 4864 * q^46 + 33636 * q^49 - 7544 * q^51 + 1600 * q^52 + 3392 * q^54 - 10536 * q^55 - 12182 * q^57 - 7168 * q^58 + 208 * q^60 + 6360 * q^61 + 10860 * q^63 - 38912 * q^64 + 19712 * q^66 + 30744 * q^67 - 34208 * q^69 - 23808 * q^70 + 4096 * q^72 + 4032 * q^73 + 22324 * q^75 - 4928 * q^76 + 12864 * q^78 - 29824 * q^79 - 22584 * q^81 + 13184 * q^82 - 2640 * q^84 + 9240 * q^85 + 32850 * q^87 - 5120 * q^88 - 16448 * q^90 - 31160 * q^91 - 1780 * q^93 + 5248 * q^94 - 4096 * q^96 + 77504 * q^97 - 15412 * q^99

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