LMFDB - Embedded newform 60.7.l.a.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(23,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.1
Character	$\chi$	$=$	60.23
Dual form			60.7.l.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.99914 + 0.117326i) q^{2} +(-11.4327 - 24.4601i) q^{3} +(63.9725 - 1.87701i) q^{4} +(124.485 - 11.3316i) q^{5} +(94.3213 + 194.318i) q^{6} +(152.267 + 152.267i) q^{7} +(-511.504 + 22.5201i) q^{8} +(-467.588 + 559.287i) q^{9} +O(q^{10})$	\(q+(-7.99914 + 0.117326i) q^{2} +(-11.4327 - 24.4601i) q^{3} +(63.9725 - 1.87701i) q^{4} +(124.485 - 11.3316i) q^{5} +(94.3213 + 194.318i) q^{6} +(152.267 + 152.267i) q^{7} +(-511.504 + 22.5201i) q^{8} +(-467.588 + 559.287i) q^{9} +(-994.446 + 105.248i) q^{10} -980.987 q^{11} +(-777.288 - 1543.31i) q^{12} +(2132.91 + 2132.91i) q^{13} +(-1235.87 - 1200.14i) q^{14} +(-1700.37 - 2915.37i) q^{15} +(4088.95 - 240.154i) q^{16} +(3763.23 + 3763.23i) q^{17} +(3674.68 - 4528.68i) q^{18} -5096.33 q^{19} +(7942.36 - 958.570i) q^{20} +(1983.63 - 5465.26i) q^{21} +(7847.05 - 115.095i) q^{22} +(7614.05 + 7614.05i) q^{23} +(6398.70 + 12254.0i) q^{24} +(15368.2 - 2821.23i) q^{25} +(-17311.7 - 16811.2i) q^{26} +(19026.0 + 5043.08i) q^{27} +(10026.7 + 9455.06i) q^{28} +20018.2 q^{29} +(13943.5 + 23120.9i) q^{30} -26355.1i q^{31} +(-32679.9 + 2400.77i) q^{32} +(11215.3 + 23995.0i) q^{33} +(-30544.1 - 29661.1i) q^{34} +(20680.4 + 17229.5i) q^{35} +(-28863.0 + 36656.7i) q^{36} +(34575.9 - 34575.9i) q^{37} +(40766.2 - 597.931i) q^{38} +(27786.2 - 76555.8i) q^{39} +(-63419.6 + 8599.58i) q^{40} +62637.0i q^{41} +(-15226.2 + 43950.1i) q^{42} +(-24457.9 + 24457.9i) q^{43} +(-62756.2 + 1841.32i) q^{44} +(-51870.3 + 74921.6i) q^{45} +(-61799.2 - 60012.5i) q^{46} +(128570. - 128570. i) q^{47} +(-52621.8 - 97270.4i) q^{48} -71278.8i q^{49} +(-122601. + 24370.5i) q^{50} +(49025.0 - 135072. i) q^{51} +(140451. + 132444. i) q^{52} +(-60472.2 + 60472.2i) q^{53} +(-152783. - 38108.1i) q^{54} +(-122118. + 11116.1i) q^{55} +(-81314.1 - 74456.0i) q^{56} +(58264.6 + 124656. i) q^{57} +(-160128. + 2348.65i) q^{58} +316059. i q^{59} +(-114249. - 183312. i) q^{60} -249370. q^{61} +(3092.14 + 210818. i) q^{62} +(-156359. + 13962.7i) q^{63} +(261130. - 23038.3i) q^{64} +(289685. + 241346. i) q^{65} +(-92528.0 - 190623. i) q^{66} +(-49804.5 - 49804.5i) q^{67} +(247807. + 233679. i) q^{68} +(99191.1 - 273289. i) q^{69} +(-167447. - 135395. i) q^{70} +407414. q^{71} +(226578. - 296608. i) q^{72} +(324061. + 324061. i) q^{73} +(-272521. + 280634. i) q^{74} +(-244707. - 343653. i) q^{75} +(-326025. + 9565.87i) q^{76} +(-149371. - 149371. i) q^{77} +(-213284. + 615641. i) q^{78} +602371. q^{79} +(506293. - 76230.0i) q^{80} +(-94163.6 - 523032. i) q^{81} +(-7348.94 - 501042. i) q^{82} +(95886.0 + 95886.0i) q^{83} +(116640. - 353349. i) q^{84} +(511110. + 425823. i) q^{85} +(192773. - 198512. i) q^{86} +(-228861. - 489646. i) q^{87} +(501779. - 22091.9i) q^{88} -499957. q^{89} +(406127. - 605394. i) q^{90} +649541. i q^{91} +(501381. + 472798. i) q^{92} +(-644648. + 301310. i) q^{93} +(-1.01337e6 + 1.04353e6i) q^{94} +(-634418. + 57749.4i) q^{95} +(432342. + 771906. i) q^{96} +(695245. - 695245. i) q^{97} +(8362.85 + 570169. i) q^{98} +(458698. - 548654. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 4 q^{6}+O(q^{10}) $ 136 * q - 4 * q^6	$ 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) $ 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−7.99914	+	0.117326i	−0.999892	+	0.0146657i
$2$	−7.99914	+	0.117326i	−0.999892	+	0.0146657i
$3$	−11.4327	−	24.4601i	−0.423432	−	0.905928i
$3$	−11.4327	−	24.4601i	−0.423432	−	0.905928i
$4$	63.9725	−	1.87701i	0.999570	−	0.0293283i
$5$	124.485	−	11.3316i	0.995883	−	0.0906527i
$5$	124.485	−	11.3316i	0.995883	−	0.0906527i
$6$	94.3213	+	194.318i	0.436673	+	0.899620i
$7$	152.267	+	152.267i	0.443926	+	0.443926i	0.893329	−	0.449403i	$-0.148363\pi$
$7$	152.267	+	152.267i	0.443926	+	0.443926i	−0.449403	+	0.893329i	$0.648363\pi$
$8$	−511.504	+	22.5201i	−0.999032	+	0.0439846i
$9$	−467.588	+	559.287i	−0.641410	+	0.767198i
$10$	−994.446	+	105.248i	−0.994446	+	0.105248i
$11$	−980.987			−0.737030			−0.368515	−	0.929622i	$-0.620134\pi$
$11$	−980.987			−0.737030			−0.368515	+	0.929622i	$0.620134\pi$
$12$	−777.288	−	1543.31i	−0.449819	−	0.893120i
$13$	2132.91	+	2132.91i	0.970827	+	0.970827i	0.999586	−	0.0287596i	$-0.00915573\pi$
$13$	2132.91	+	2132.91i	0.970827	+	0.970827i	−0.0287596	+	0.999586i	$0.509156\pi$
$14$	−1235.87	−	1200.14i	−0.450389	−	0.437368i
$15$	−1700.37	−	2915.37i	−0.503814	−	0.863812i
$16$	4088.95	−	240.154i	0.998280	−	0.0586314i
$17$	3763.23	+	3763.23i	0.765973	+	0.765973i	0.977395	−	0.211422i	$-0.0678093\pi$
$17$	3763.23	+	3763.23i	0.765973	+	0.765973i	−0.211422	+	0.977395i	$0.567809\pi$
$18$	3674.68	−	4528.68i	0.630090	−	0.776522i
$19$	−5096.33			−0.743013			−0.371506	−	0.928430i	$-0.621159\pi$
$19$	−5096.33			−0.743013			−0.371506	+	0.928430i	$0.621159\pi$
$20$	7942.36	−	958.570i	0.992795	−	0.119821i
$21$	1983.63	−	5465.26i	0.214192	−	0.590137i
$22$	7847.05	−	115.095i	0.736951	−	0.0108091i
$23$	7614.05	+	7614.05i	0.625795	+	0.625795i	0.947007	−	0.321212i	$-0.104090\pi$
$23$	7614.05	+	7614.05i	0.625795	+	0.625795i	−0.321212	+	0.947007i	$0.604090\pi$
$24$	6398.70	+	12254.0i	0.462869	+	0.886427i
$25$	15368.2	−	2821.23i	0.983564	−	0.180559i
$26$	−17311.7	−	16811.2i	−0.984960	−	0.956484i
$27$	19026.0	+	5043.08i	0.966620	+	0.256215i
$28$	10026.7	+	9455.06i	0.456754	+	0.430715i
$29$	20018.2			0.820787			0.410394	−	0.911909i	$-0.365391\pi$
$29$	20018.2			0.820787			0.410394	+	0.911909i	$0.365391\pi$
$30$	13943.5	+	23120.9i	0.516428	+	0.856331i
$31$		−	26355.1i		−	0.884668i	−0.896850	−	0.442334i	$-0.854151\pi$
$31$		−	26355.1i		−	0.884668i	0.896850	−	0.442334i	$-0.145849\pi$
$32$	−32679.9	+	2400.77i	−0.997312	+	0.0732656i
$33$	11215.3	+	23995.0i	0.312082	+	0.667696i
$34$	−30544.1	−	29661.1i	−0.777125	−	0.754657i
$35$	20680.4	+	17229.5i	0.482341	+	0.401855i
$36$	−28863.0	+	36656.7i	−0.618634	+	0.785679i
$37$	34575.9	−	34575.9i	0.682603	−	0.682603i	−0.277983	−	0.960586i	$-0.589666\pi$
$37$	34575.9	−	34575.9i	0.682603	−	0.682603i	0.960586	+	0.277983i	$0.0896658\pi$
$38$	40766.2	−	597.931i	0.742933	−	0.0108968i
$39$	27786.2	−	76555.8i	0.468420	−	1.29058i
$40$	−63419.6	+	8599.58i	−0.990931	+	0.134368i
$41$			62637.0i			0.908823i	0.890792	+	0.454412i	$0.150150\pi$
$41$			62637.0i			0.908823i	−0.890792	+	0.454412i	$0.849850\pi$
$42$	−15226.2	+	43950.1i	−0.205514	+	0.593215i
$43$	−24457.9	+	24457.9i	−0.307620	+	0.307620i	−0.843986	−	0.536366i	$-0.819797\pi$
$43$	−24457.9	+	24457.9i	−0.307620	+	0.307620i	0.536366	+	0.843986i	$0.319797\pi$
$44$	−62756.2	+	1841.32i	−0.736713	+	0.0216159i
$45$	−51870.3	+	74921.6i	−0.569221	+	0.822185i
$46$	−61799.2	−	60012.5i	−0.634905	−	0.616550i
$47$	128570.	−	128570.i	1.23836	−	1.23836i	0.277687	−	0.960672i	$-0.410432\pi$
$47$	128570.	−	128570.i	1.23836	−	1.23836i	0.960672	−	0.277687i	$-0.0895677\pi$
$48$	−52621.8	−	97270.4i	−0.475820	−	0.879543i
$49$		−	71278.8i		−	0.605860i
$50$	−122601.	+	24370.5i	−0.980810	+	0.194964i
$51$	49025.0	−	135072.i	0.369579	−	1.01825i
$52$	140451.	+	132444.i	0.998882	+	0.941936i
$53$	−60472.2	+	60472.2i	−0.406189	+	0.406189i	−0.880407	−	0.474218i	$-0.842731\pi$
$53$	−60472.2	+	60472.2i	−0.406189	+	0.406189i	0.474218	+	0.880407i	$0.342731\pi$
$54$	−152783.	−	38108.1i	−0.970273	−	0.242011i
$55$	−122118.	+	11116.1i	−0.733995	+	0.0668137i
$56$	−81314.1	−	74456.0i	−0.463022	−	0.423970i
$57$	58264.6	+	124656.i	0.314616	+	0.673116i
$58$	−160128.	+	2348.65i	−0.820699	+	0.0120374i
$59$			316059.i			1.53891i	0.638702	+	0.769454i	$0.279472\pi$
$59$			316059.i			1.53891i	−0.638702	+	0.769454i	$0.720528\pi$
$60$	−114249.	−	183312.i	−0.528931	−	0.848665i
$61$	−249370.			−1.09864			−0.549319	−	0.835613i	$-0.685113\pi$
$61$	−249370.			−1.09864			−0.549319	+	0.835613i	$0.685113\pi$
$62$	3092.14	+	210818.i	0.0129743	+	0.884573i
$63$	−156359.	+	13962.7i	−0.625318	+	0.0558404i
$64$	261130.	−	23038.3i	0.996131	−	0.0878841i
$65$	289685.	+	241346.i	1.05484	+	0.878821i
$66$	−92528.0	−	190623.i	−0.321841	−	0.663047i
$67$	−49804.5	−	49804.5i	−0.165594	−	0.165594i	0.619446	−	0.785040i	$-0.287357\pi$
$67$	−49804.5	−	49804.5i	−0.165594	−	0.165594i	−0.785040	+	0.619446i	$0.787357\pi$
$68$	247807.	+	233679.i	0.788109	+	0.743179i
$69$	99191.1	−	273289.i	0.301943	−	0.831907i
$70$	−167447.	−	135395.i	−0.488183	−	0.394738i
$71$	407414.			1.13831			0.569156	−	0.822230i	$-0.307270\pi$
$71$	407414.			1.13831			0.569156	+	0.822230i	$0.307270\pi$
$72$	226578.	−	296608.i	0.607045	−	0.794668i
$73$	324061.	+	324061.i	0.833025	+	0.833025i	0.987929	−	0.154905i	$-0.0495070\pi$
$73$	324061.	+	324061.i	0.833025	+	0.833025i	−0.154905	+	0.987929i	$0.549507\pi$
$74$	−272521.	+	280634.i	−0.672519	+	0.692541i
$75$	−244707.	−	343653.i	−0.580046	−	0.814584i
$76$	−326025.	+	9565.87i	−0.742693	+	0.0217913i
$77$	−149371.	−	149371.i	−0.327187	−	0.327187i
$78$	−213284.	+	615641.i	−0.449442	+	1.29731i
$79$	602371.			1.22175			0.610876	−	0.791726i	$-0.290817\pi$
$79$	602371.			1.22175			0.610876	+	0.791726i	$0.290817\pi$
$80$	506293.	−	76230.0i	0.988854	−	0.148887i
$81$	−94163.6	−	523032.i	−0.177185	−	0.984177i
$82$	−7348.94	−	501042.i	−0.0133286	−	0.908725i
$83$	95886.0	+	95886.0i	0.167695	+	0.167695i	0.785966	−	0.618270i	$-0.212166\pi$
$83$	95886.0	+	95886.0i	0.167695	+	0.167695i	−0.618270	+	0.785966i	$0.712166\pi$
$84$	116640.	−	353349.i	0.196792	−	0.596165i
$85$	511110.	+	425823.i	0.832257	+	0.693382i
$86$	192773.	−	198512.i	0.303075	−	0.312098i
$87$	−228861.	−	489646.i	−0.347548	−	0.743574i
$88$	501779.	−	22091.9i	0.736317	−	0.0324180i
$89$	−499957.			−0.709190			−0.354595	−	0.935020i	$-0.615381\pi$
$89$	−499957.			−0.709190			−0.354595	+	0.935020i	$0.615381\pi$
$90$	406127.	−	605394.i	0.557102	−	0.830444i
$91$			649541.i			0.861950i
$92$	501381.	+	472798.i	0.643879	+	0.607172i
$93$	−644648.	+	301310.i	−0.801445	+	0.374597i
$94$	−1.01337e6	+	1.04353e6i	−1.22006	+	1.25639i
$95$	−634418.	+	57749.4i	−0.739954	+	0.0673561i
$96$	432342.	+	771906.i	0.488668	+	0.872470i
$97$	695245.	−	695245.i	0.761768	−	0.761768i	−0.214874	−	0.976642i	$-0.568934\pi$
$97$	695245.	−	695245.i	0.761768	−	0.761768i	0.976642	+	0.214874i	$0.0689340\pi$
$98$	8362.85	+	570169.i	0.00888538	+	0.605795i
$99$	458698.	−	548654.i	0.472739	−	0.565448i
$100$	977846.	−	209327.i	0.977846	−	0.209327i
$101$		−	2.02471e6i		−	1.96517i	−0.185820	−	0.982584i	$-0.559494\pi$
$101$		−	2.02471e6i		−	1.96517i	0.185820	−	0.982584i	$-0.440506\pi$
$102$	−376310.	+	1.08622e6i	−0.354606	+	1.02357i
$103$	−1.01467e6	+	1.01467e6i	−0.928570	+	0.928570i	−0.997614	−	0.0690437i	$-0.978005\pi$
$103$	−1.01467e6	+	1.01467e6i	−0.928570	+	0.928570i	0.0690437	+	0.997614i	$0.478005\pi$
$104$	−1.13902e6	−	1.04296e6i	−1.01259	−	0.927186i
$105$	185003.	−	702822.i	0.159813	−	0.607124i
$106$	476631.	−	490821.i	0.400188	−	0.412102i
$107$	−1.11504e6	+	1.11504e6i	−0.910205	+	0.910205i	−0.996288	−	0.0860826i	$-0.972565\pi$
$107$	−1.11504e6	+	1.11504e6i	−0.910205	+	0.910205i	0.0860826	+	0.996288i	$0.472565\pi$
$108$	1.22660e6	+	286906.i	0.973718	+	0.227756i
$109$			1.30388e6i			1.00684i	0.864043	+	0.503418i	$0.167924\pi$
$109$			1.30388e6i			1.00684i	−0.864043	+	0.503418i	$0.832076\pi$
$110$	975538.	−	103247.i	0.732936	−	0.0775711i
$111$	−1.24102e6	−	450434.i	−0.907426	−	0.329353i
$112$	659178.	+	586043.i	0.469190	+	0.417134i
$113$	−659406.	+	659406.i	−0.457002	+	0.457002i	−0.897670	−	0.440668i	$-0.854742\pi$
$113$	−659406.	+	659406.i	−0.457002	+	0.457002i	0.440668	+	0.897670i	$0.354742\pi$
$114$	−480692.	−	990308.i	−0.324454	−	0.668430i
$115$	1.03412e6	+	861558.i	0.679948	+	0.566488i
$116$	1.28061e6	−	37574.4i	0.820434	−	0.0240723i
$117$	−2.19023e6	+	195586.i	−1.36751	+	0.122118i
$118$	−37082.0	−	2.52820e6i	−0.0225692	−	1.53874i
$119$			1.14603e6i			0.680071i
$120$	935402.	+	1.45293e6i	0.541320	+	0.840816i
$121$	−809226.			−0.456787
$122$	1.99474e6	−	29257.5i	1.09852	−	0.0161123i
$123$	1.53210e6	−	716108.i	0.823328	−	0.384825i
$124$	−49468.9	−	1.68600e6i	−0.0259458	−	0.884287i
$125$	1.88115e6	−	525348.i	0.963146	−	0.268978i
$126$	1.24910e6	−	130035.i	0.624431	−	0.0650051i
$127$	−531347.	−	531347.i	−0.259398	−	0.259398i	0.565411	−	0.824809i	$-0.308718\pi$
$127$	−531347.	−	531347.i	−0.259398	−	0.259398i	−0.824809	+	0.565411i	$0.808718\pi$
$128$	−2.08611e6	+	214924.i	−0.994735	+	0.102484i
$129$	877862.	+	318623.i	0.408937	+	0.148425i
$130$	−2.34554e6	−	1.89658e6i	−1.06761	−	0.863257i
$131$	389456.			0.173239			0.0866194	−	0.996241i	$-0.472394\pi$
$131$	389456.			0.173239			0.0866194	+	0.996241i	$0.472394\pi$
$132$	762509.	+	1.51397e6i	0.331530	+	0.658256i
$133$	−776000.	−	776000.i	−0.329843	−	0.329843i
$134$	404237.	+	392550.i	0.168005	+	0.163148i
$135$	2.42560e6	+	412195.i	0.985866	+	0.167534i
$136$	−2.00966e6	−	1.84016e6i	−0.798923	−	0.731541i
$137$	1.54905e6	+	1.54905e6i	0.602425	+	0.602425i	0.940956	−	0.338530i	$-0.109930\pi$
$137$	1.54905e6	+	1.54905e6i	0.602425	+	0.602425i	−0.338530	+	0.940956i	$0.609930\pi$
$138$	−761380.	+	2.19771e6i	−0.289710	+	0.836246i
$139$	−3.51381e6			−1.30838			−0.654190	−	0.756330i	$-0.726990\pi$
$139$	−3.51381e6			−1.30838			−0.654190	+	0.756330i	$0.726990\pi$
$140$	1.35531e6	+	1.06340e6i	0.493919	+	0.387536i
$141$	−4.61473e6	−	1.67493e6i	−1.64622	−	0.597502i
$142$	−3.25896e6	+	47800.3i	−1.13819	+	0.0166942i
$143$	−2.09235e6	−	2.09235e6i	−0.715528	−	0.715528i
$144$	−1.77763e6	+	2.39919e6i	−0.595325	+	0.803485i
$145$	2.49197e6	−	226838.i	0.817408	−	0.0744065i
$146$	−2.63023e6	−	2.55419e6i	−0.845152	−	0.820718i
$147$	−1.74348e6	+	814907.i	−0.548865	+	0.256541i
$148$	2.14701e6	−	2.27681e6i	0.662290	−	0.702329i
$149$	−5.17826e6			−1.56540			−0.782699	−	0.622401i	$-0.786157\pi$
$149$	−5.17826e6			−1.56540			−0.782699	+	0.622401i	$0.786157\pi$
$150$	1.99776e6	+	2.72021e6i	0.591930	+	0.805989i
$151$			4.66549e6i			1.35508i	0.735484	+	0.677542i	$0.236955\pi$
$151$			4.66549e6i			1.35508i	−0.735484	+	0.677542i	$0.763045\pi$
$152$	2.60679e6	−	114770.i	0.742294	−	0.0326811i
$153$	−3.86437e6	+	345085.i	−1.07896	+	0.0963500i
$154$	1.21237e6	+	1.17732e6i	0.331950	+	0.322353i
$155$	−298645.	−	3.28083e6i	−0.0801975	−	0.881025i
$156$	1.63385e6	−	4.94962e6i	0.430368	−	1.30376i
$157$	3.02389e6	−	3.02389e6i	0.781389	−	0.781389i	−0.198676	−	0.980065i	$-0.563664\pi$
$157$	3.02389e6	−	3.02389e6i	0.781389	−	0.781389i	0.980065	+	0.198676i	$0.0636642\pi$
$158$	−4.81845e6	+	70673.7i	−1.22162	+	0.0179179i
$159$	2.17051e6	+	787795.i	0.539972	+	0.195984i
$160$	−4.04097e6	+	669176.i	−0.986564	+	0.163373i
$161$			2.31873e6i			0.555613i
$162$	814593.	+	4.17276e6i	0.191600	+	0.981473i
$163$	1.24764e6	−	1.24764e6i	0.288088	−	0.288088i	−0.548236	−	0.836324i	$-0.684700\pi$
$163$	1.24764e6	−	1.24764e6i	0.288088	−	0.288088i	0.836324	+	0.548236i	$0.184700\pi$
$164$	117570.	+	4.00704e6i	0.0266543	+	0.908432i
$165$	1.66804e6	+	2.85994e6i	0.371326	+	0.636656i
$166$	−778256.	−	755756.i	−0.170137	−	0.165218i
$167$	3.66670e6	−	3.66670e6i	0.787275	−	0.787275i	−0.193772	−	0.981047i	$-0.562072\pi$
$167$	3.66670e6	−	3.66670e6i	0.787275	−	0.787275i	0.981047	+	0.193772i	$0.0620722\pi$
$168$	−891560.	+	2.84018e6i	−0.188028	+	0.598987i
$169$			4.27177e6i			0.885009i
$170$	−4.13840e6	−	3.34625e6i	−0.842337	−	0.681102i
$171$	2.38298e6	−	2.85031e6i	0.476576	−	0.570038i
$172$	−1.51873e6	+	1.61054e6i	−0.298466	+	0.316509i
$173$	−3014.84	+	3014.84i	−0.000582273	+	0.000582273i	−0.707398	−	0.706816i	$-0.750131\pi$
$173$	−3014.84	+	3014.84i	−0.000582273	+	0.000582273i	0.706816	+	0.707398i	$0.250131\pi$
$174$	1.88814e6	+	3.88989e6i	0.358415	+	0.738397i
$175$	2.76964e6	+	1.91048e6i	0.516784	+	0.356475i
$176$	−4.01121e6	+	235588.i	−0.735762	+	0.0432131i
$177$	7.73083e6	−	3.61340e6i	1.39414	−	0.651623i
$178$	3.99922e6	−	58657.9i	0.709113	−	0.0104008i
$179$		−	5.42748e6i		−	0.946322i	−0.880976	−	0.473161i	$-0.843113\pi$
$179$		−	5.42748e6i		−	0.946322i	0.880976	−	0.473161i	$-0.156887\pi$
$180$	−3.17764e6	+	4.89028e6i	−0.544863	+	0.838525i
$181$	7.18857e6			1.21229			0.606145	−	0.795354i	$-0.292715\pi$
$181$	7.18857e6			1.21229			0.606145	+	0.795354i	$0.292715\pi$
$182$	−76207.9	−	5.19577e6i	−0.0126411	−	0.861857i
$183$	2.85096e6	+	6.09960e6i	0.465198	+	0.995286i
$184$	−4.06609e6	−	3.72315e6i	−0.652715	−	0.597664i
$185$	3.91239e6	−	4.69599e6i	0.617913	−	0.741673i
$186$	5.12128e6	−	2.48585e6i	0.795865	−	0.386310i
$187$	−3.69168e6	−	3.69168e6i	−0.564545	−	0.564545i
$188$	7.98362e6	−	8.46627e6i	1.20151	−	1.27414i
$189$	2.12913e6	+	3.66491e6i	0.315367	+	0.542848i
$190$	5.06802e6	−	536380.i	0.738886	−	0.0782008i
$191$	3.54551e6			0.508837			0.254419	−	0.967094i	$-0.418116\pi$
$191$	3.54551e6			0.508837			0.254419	+	0.967094i	$0.418116\pi$
$192$	−3.54893e6	−	6.12386e6i	−0.501410	−	0.865210i
$193$	2.43996e6	+	2.43996e6i	0.339400	+	0.339400i	0.856141	−	0.516742i	$-0.172855\pi$
$193$	2.43996e6	+	2.43996e6i	0.339400	+	0.339400i	−0.516742	+	0.856141i	$0.672855\pi$
$194$	−5.47979e6	+	5.64293e6i	−0.750514	+	0.772858i
$195$	2.59147e6	−	9.84494e6i	0.349497	−	1.32773i
$196$	−133791.	−	4.55988e6i	−0.0177689	−	0.605599i
$197$	2.83325e6	+	2.83325e6i	0.370584	+	0.370584i	0.867690	−	0.497106i	$-0.165604\pi$
$197$	2.83325e6	+	2.83325e6i	0.370584	+	0.370584i	−0.497106	+	0.867690i	$0.665604\pi$
$198$	−3.60482e6	+	4.44257e6i	−0.464395	+	0.572320i
$199$	1.75342e6			0.222498			0.111249	−	0.993793i	$-0.464515\pi$
$199$	1.75342e6			0.222498			0.111249	+	0.993793i	$0.464515\pi$
$200$	−7.79736e6	+	1.78917e6i	−0.974670	+	0.223646i
$201$	−648822.	+	1.78762e6i	−0.0798983	+	0.220134i
$202$	237551.	+	1.61960e7i	0.0288206	+	1.96496i
$203$	3.04810e6	+	3.04810e6i	0.364369	+	0.364369i
$204$	2.88272e6	−	8.73294e6i	0.339556	−	1.02866i
$205$	709776.	+	7.79739e6i	0.0823873	+	0.905081i
$206$	7.99747e6	−	8.23556e6i	0.914852	−	0.942088i
$207$	−7.81868e6	+	698202.i	−0.881500	+	0.0787173i
$208$	9.23358e6	+	8.20913e6i	1.02608	+	0.912236i
$209$	4.99943e6			0.547623
$210$	−1.39741e6	+	5.64368e6i	−0.150892	+	0.609403i
$211$			9.86205e6i			1.04983i	0.851154	+	0.524916i	$0.175903\pi$
$211$			9.86205e6i			1.04983i	−0.851154	+	0.524916i	$0.824097\pi$
$212$	−3.75505e6	+	3.98206e6i	−0.394102	+	0.417927i
$213$	−4.65783e6	−	9.96537e6i	−0.481998	−	1.03123i
$214$	8.78854e6	−	9.05019e6i	0.896759	−	0.923456i
$215$	−2.76751e6	+	3.32180e6i	−0.278467	+	0.334240i
$216$	−9.84544e6	−	2.15109e6i	−0.976954	−	0.213451i
$217$	4.01301e6	−	4.01301e6i	0.392727	−	0.392727i
$218$	−152979.	−	1.04299e7i	−0.0147660	−	1.00673i
$219$	4.22166e6	−	1.16314e7i	0.401931	−	1.10739i
$220$	−7.79135e6	+	940344.i	−0.731720	+	0.0883118i
$221$			1.60532e7i			1.48725i
$222$	9.97997e6	+	3.45748e6i	0.912158	+	0.316010i
$223$	−1.07535e7	+	1.07535e7i	−0.969696	+	0.969696i	−0.999554	−	0.0298580i	$-0.990494\pi$
$223$	−1.07535e7	+	1.07535e7i	−0.969696	+	0.969696i	0.0298580	+	0.999554i	$0.490494\pi$
$224$	−5.34162e6	−	4.61050e6i	−0.475257	−	0.410208i
$225$	−5.60810e6	+	9.91441e6i	−0.492344	+	0.870401i
$226$	5.19732e6	−	5.35205e6i	0.450250	−	0.463655i
$227$	−5.71992e6	+	5.71992e6i	−0.489004	+	0.489004i	−0.907992	−	0.418988i	$-0.862385\pi$
$227$	−5.71992e6	+	5.71992e6i	−0.489004	+	0.489004i	0.418988	+	0.907992i	$0.362385\pi$
$228$	3.96131e6	+	7.86521e6i	0.334222	+	0.663599i
$229$		−	3.76832e6i		−	0.313792i	−0.987615	−	0.156896i	$-0.949851\pi$
$229$		−	3.76832e6i		−	0.313792i	0.987615	−	0.156896i	$-0.0501487\pi$
$230$	−8.37312e6	−	6.77039e6i	−0.688183	−	0.556455i
$231$	−1.94592e6	+	5.36135e6i	−0.157866	+	0.434949i
$232$	−1.02394e7	+	450812.i	−0.819993	+	0.0361020i
$233$	−2.17672e6	+	2.17672e6i	−0.172082	+	0.172082i	−0.787893	−	0.615812i	$-0.788828\pi$
$233$	−2.17672e6	+	2.17672e6i	−0.172082	+	0.172082i	0.615812	+	0.787893i	$0.288828\pi$
$234$	1.74970e7	−	1.82149e6i	1.36558	−	0.142160i
$235$	1.45482e7	−	1.74620e7i	1.12100	−	1.34552i
$236$	593247.	+	2.02191e7i	0.0451336	+	1.53825i
$237$	−6.88671e6	−	1.47340e7i	−0.517329	−	1.10682i
$238$	−134459.	−	9.16723e6i	−0.00997374	−	0.679998i
$239$			510599.i			0.0374013i	0.999825	+	0.0187006i	$0.00595294\pi$
$239$			510599.i			0.0374013i	−0.999825	+	0.0187006i	$0.994047\pi$
$240$	−7.65287e6	−	1.15124e7i	−0.553593	−	0.832787i
$241$	−2.49088e7			−1.77951			−0.889757	−	0.456435i	$-0.849126\pi$
$241$	−2.49088e7			−1.77951			−0.889757	+	0.456435i	$0.849126\pi$
$242$	6.47311e6	−	94943.1i	0.456738	−	0.00669912i
$243$	−1.17169e7	+	8.28290e6i	−0.816568	+	0.577250i
$244$	−1.59528e7	+	468070.i	−1.09816	+	0.0322212i
$245$	−807702.	−	8.87316e6i	−0.0549228	−	0.603365i
$246$	−1.21715e7	+	5.90800e6i	−0.817596	+	0.396858i
$247$	−1.08700e7	−	1.08700e7i	−0.721337	−	0.721337i
$248$	593521.	+	1.34808e7i	0.0389118	+	0.883812i
$249$	1.24914e6	−	3.44161e6i	0.0809123	−	0.222928i
$250$	−1.49859e7	+	4.42304e6i	−0.959098	+	0.283074i
$251$	−1.75528e6			−0.111001			−0.0555003	−	0.998459i	$-0.517675\pi$
$251$	−1.75528e6			−0.111001			−0.0555003	+	0.998459i	$0.517675\pi$
$252$	−9.97645e6	+	1.18672e6i	−0.623411	+	0.0741559i
$253$	−7.46928e6	−	7.46928e6i	−0.461230	−	0.461230i
$254$	4.31266e6	+	4.18798e6i	0.263175	+	0.255566i
$255$	4.57231e6	−	1.73701e7i	0.275750	−	1.04757i
$256$	1.66619e7	−	1.96396e6i	0.993125	−	0.117061i
$257$	−1.46827e7	−	1.46827e7i	−0.864982	−	0.864982i	0.126930	−	0.991912i	$-0.459488\pi$
$257$	−1.46827e7	−	1.46827e7i	−0.864982	−	0.864982i	−0.991912	+	0.126930i	$0.959488\pi$
$258$	−7.05952e6	−	2.44571e6i	−0.411070	−	0.142412i
$259$	1.05295e7			0.606050
$260$	1.89849e7	+	1.48958e7i	1.08016	+	0.847507i
$261$	−9.36026e6	+	1.11959e7i	−0.526461	+	0.629706i
$262$	−3.11532e6	+	45693.3i	−0.173220	+	0.00254067i
$263$	8.09073e6	+	8.09073e6i	0.444755	+	0.444755i	0.893606	−	0.448852i	$-0.148167\pi$
$263$	8.09073e6	+	8.09073e6i	0.444755	+	0.444755i	−0.448852	+	0.893606i	$0.648167\pi$
$264$	−6.27705e6	−	1.20210e7i	−0.341148	−	0.653323i
$265$	−6.84266e6	+	8.21315e6i	−0.367694	+	0.441339i
$266$	6.29838e6	+	6.11629e6i	0.334645	+	0.324970i
$267$	5.71584e6	+	1.22290e7i	0.300294	+	0.642475i
$268$	−3.27960e6	−	3.09263e6i	−0.170379	−	0.160666i
$269$	−1.88557e6			−0.0968693			−0.0484346	−	0.998826i	$-0.515423\pi$
$269$	−1.88557e6			−0.0968693			−0.0484346	+	0.998826i	$0.515423\pi$
$270$	−1.94511e7	−	3.01262e6i	−0.988217	−	0.153057i
$271$			1.55070e7i			0.779150i	0.920995	+	0.389575i	$0.127378\pi$
$271$			1.55070e7i			0.779150i	−0.920995	+	0.389575i	$0.872622\pi$
$272$	1.62914e7	+	1.44839e7i	0.809566	+	0.719746i
$273$	1.58878e7	−	7.42598e6i	0.780865	−	0.364977i
$274$	−1.25728e7	−	1.22093e7i	−0.611196	−	0.593526i
$275$	−1.50760e7	+	2.76759e6i	−0.724916	+	0.133077i
$276$	5.83253e6	−	1.76691e7i	0.277415	−	0.840404i
$277$	1.51271e7	−	1.51271e7i	0.711734	−	0.711734i	−0.255164	−	0.966898i	$-0.582129\pi$
$277$	1.51271e7	−	1.51271e7i	0.711734	−	0.711734i	0.966898	+	0.255164i	$0.0821295\pi$
$278$	2.81075e7	−	412261.i	1.30824	−	0.0191884i
$279$	1.47401e7	+	1.23234e7i	0.678715	+	0.567435i
$280$	−1.09661e7	−	8.34726e6i	−0.499550	−	0.380250i
$281$		−	1.51539e7i		−	0.682976i	−0.939886	−	0.341488i	$-0.889069\pi$
$281$		−	1.51539e7i		−	0.682976i	0.939886	−	0.341488i	$-0.110931\pi$
$282$	3.71104e7	+	1.28566e7i	1.65481	+	0.573295i
$283$	2.21304e7	−	2.21304e7i	0.976407	−	0.976407i	−0.0233215	−	0.999728i	$-0.507424\pi$
$283$	2.21304e7	−	2.21304e7i	0.976407	−	0.976407i	0.999728	+	0.0233215i	$0.00742413\pi$
$284$	2.60633e7	−	764722.i	1.13782	−	0.0333848i
$285$	8.66564e6	+	1.48577e7i	0.374340	+	0.641824i
$286$	1.69825e7	+	1.64915e7i	0.725945	+	0.704958i
$287$	−9.53752e6	+	9.53752e6i	−0.403450	+	0.403450i
$288$	1.39380e7	−	1.94000e7i	0.583477	−	0.812129i
$289$			4.18619e6i			0.173430i
$290$	−1.99070e7	+	2.10688e6i	−0.816228	+	0.0863864i
$291$	−2.49542e7	−	9.05722e6i	−1.01266	−	0.367550i
$292$	2.13392e7	+	2.01227e7i	0.857098	+	0.808235i
$293$	1.26983e7	−	1.26983e7i	0.504827	−	0.504827i	−0.408107	−	0.912934i	$-0.633811\pi$
$293$	1.26983e7	−	1.26983e7i	0.504827	−	0.504827i	0.912934	+	0.408107i	$0.133811\pi$
$294$	1.38508e7	−	6.72311e6i	0.545044	−	0.264562i
$295$	3.58145e6	+	3.93448e7i	0.139506	+	1.53257i
$296$	−1.69071e7	+	1.84644e7i	−0.651919	+	0.711967i
$297$	−1.86642e7	−	4.94720e6i	−0.712428	−	0.188838i
$298$	4.14216e7	−	607543.i	1.56523	−	0.0229577i
$299$			3.24801e7i			1.21508i
$300$	−1.62995e7	−	2.15250e7i	−0.603687	−	0.797222i
$301$	−7.44825e6			−0.273121
$302$	−547383.	−	3.73199e7i	−0.0198733	−	1.35494i
$303$	−4.95246e7	+	2.31479e7i	−1.78030	+	0.832115i
$304$	−2.08386e7	+	1.22390e6i	−0.741735	+	0.0435639i
$305$	−3.10429e7	+	2.82575e6i	−1.09411	+	0.0995944i
$306$	3.08711e7	−	3.21377e6i	1.07743	−	0.112163i
$307$	−3.91941e7	−	3.91941e7i	−1.35458	−	1.35458i	−0.880455	−	0.474129i	$-0.842763\pi$
$307$	−3.91941e7	−	3.91941e7i	−1.35458	−	1.35458i	−0.474129	−	0.880455i	$-0.657237\pi$
$308$	−9.83603e6	−	9.27529e6i	−0.336642	−	0.317450i
$309$	3.64194e7	+	1.32185e7i	1.23440	+	0.448031i
$310$	2.77383e6	+	2.62088e7i	0.0931098	+	0.879754i
$311$	4.22866e7			1.40579			0.702896	−	0.711293i	$-0.251890\pi$
$311$	4.22866e7			1.40579			0.702896	+	0.711293i	$0.251890\pi$
$312$	−1.24887e7	+	3.97844e7i	−0.411201	+	1.30993i
$313$	−2.65137e7	−	2.65137e7i	−0.864644	−	0.864644i	0.127229	−	0.991873i	$-0.459392\pi$
$313$	−2.65137e7	−	2.65137e7i	−0.864644	−	0.864644i	−0.991873	+	0.127229i	$0.959392\pi$
$314$	−2.38338e7	+	2.45433e7i	−0.769845	+	0.792765i
$315$	−1.93062e7	+	3.50995e6i	−0.617681	+	0.112297i
$316$	3.85352e7	−	1.13066e6i	1.22123	−	0.0358319i
$317$	−1.35411e7	−	1.35411e7i	−0.425085	−	0.425085i	0.461865	−	0.886950i	$-0.347180\pi$
$317$	−1.35411e7	−	1.35411e7i	−0.425085	−	0.425085i	−0.886950	+	0.461865i	$0.847180\pi$
$318$	−1.74547e7	−	6.04702e6i	−0.542788	−	0.188044i
$319$	−1.96376e7			−0.604945
$320$	3.22458e7	−	5.82694e6i	0.984062	−	0.177824i
$321$	4.00218e7	+	1.45261e7i	1.20999	+	0.439170i
$322$	−272047.	−	1.85478e7i	−0.00814848	−	0.555553i
$323$	−1.91786e7	−	1.91786e7i	−0.569128	−	0.569128i
$324$	−7.00562e6	−	3.32829e7i	−0.205974	−	0.978558i
$325$	3.87963e7	+	2.67615e7i	1.13016	+	0.779579i
$326$	−9.83363e6	+	1.01264e7i	−0.283832	+	0.292282i
$327$	3.18930e7	−	1.49068e7i	0.912120	−	0.426327i
$328$	−1.41059e6	−	3.20391e7i	−0.0399742	−	0.907944i
$329$	3.91538e7			1.09948
$330$	−1.36784e7	−	2.26813e7i	−0.380623	−	0.631141i
$331$		−	3.47980e7i		−	0.959557i	−0.877390	−	0.479778i	$-0.840717\pi$
$331$		−	3.47980e7i		−	0.959557i	0.877390	−	0.479778i	$-0.159283\pi$
$332$	6.31405e6	+	5.95409e6i	0.172541	+	0.162705i
$333$	3.17058e6	+	3.55052e7i	0.0858630	+	0.961521i
$334$	−2.89003e7	+	2.97607e7i	−0.775644	+	0.798736i
$335$	−6.76430e6	−	5.63557e6i	−0.179924	−	0.149901i
$336$	6.79848e6	−	2.28236e7i	0.179223	−	0.601680i
$337$	−1.84367e7	+	1.84367e7i	−0.481718	+	0.481718i	−0.905680	−	0.423962i	$-0.860639\pi$
$337$	−1.84367e7	+	1.84367e7i	−0.481718	+	0.481718i	0.423962	+	0.905680i	$0.360639\pi$
$338$	−501189.	−	3.41705e7i	−0.0129793	−	0.884914i
$339$	2.36679e7	+	8.59034e6i	0.607520	+	0.220501i
$340$	3.34962e7	+	2.62816e7i	0.852235	+	0.668675i
$341$			2.58540e7i			0.652027i
$342$	−1.87274e7	+	2.30796e7i	−0.468165	+	0.576966i
$343$	2.87674e7	−	2.87674e7i	0.712883	−	0.712883i
$344$	1.19595e7	−	1.30611e7i	0.293792	−	0.320853i
$345$	9.25104e6	−	3.51444e7i	0.225286	−	0.855853i
$346$	23762.4	−	24469.9i	0.000573671	−	0.000590750i
$347$	1.14456e7	−	1.14456e7i	0.273938	−	0.273938i	−0.556746	−	0.830683i	$-0.687950\pi$
$347$	1.14456e7	−	1.14456e7i	0.273938	−	0.273938i	0.830683	+	0.556746i	$0.187950\pi$
$348$	−1.55599e7	−	3.08943e7i	−0.369206	−	0.733061i
$349$			105831.i			0.00248964i	0.999999	+	0.00124482i	$0.000396239\pi$
$349$			105831.i			0.00248964i	−0.999999	+	0.00124482i	$0.999604\pi$
$350$	−2.23789e7	−	1.49573e7i	−0.521957	−	0.348857i
$351$	2.98242e7	+	5.13371e7i	0.689680	+	1.18716i
$352$	3.20586e7	−	2.35512e6i	0.735049	−	0.0539989i
$353$	−2.11684e7	+	2.11684e7i	−0.481242	+	0.481242i	−0.905528	−	0.424286i	$-0.860525\pi$
$353$	−2.11684e7	+	2.11684e7i	−0.481242	+	0.481242i	0.424286	+	0.905528i	$0.360525\pi$
$354$	−6.14160e7	+	2.98111e7i	−1.38443	+	0.671999i
$355$	5.07171e7	−	4.61665e6i	1.13362	−	0.103191i
$356$	−3.19835e7	+	938425.i	−0.708885	+	0.0207993i
$357$	2.80319e7	−	1.31021e7i	0.616095	−	0.287964i
$358$	636784.	+	4.34151e7i	0.0138785	+	0.946220i
$359$		−	4.53272e7i		−	0.979660i	−0.871818	−	0.489830i	$-0.837059\pi$
$359$		−	4.53272e7i		−	0.979660i	0.871818	−	0.489830i	$-0.162941\pi$
$360$	2.48446e7	−	3.94908e7i	0.532507	−	0.846426i
$361$	−2.10733e7			−0.447932
$362$	−5.75024e7	+	843406.i	−1.21216	+	0.0177791i
$363$	9.25161e6	+	1.97937e7i	0.193418	+	0.413816i
$364$	1.21920e6	+	4.15527e7i	0.0252795	+	0.861579i
$365$	4.40129e7	+	3.66687e7i	0.905111	+	0.754079i
$366$	−2.35209e7	−	4.84570e7i	−0.479745	−	0.988356i
$367$	−4.60238e6	−	4.60238e6i	−0.0931074	−	0.0931074i	0.659019	−	0.752126i	$-0.270972\pi$
$367$	−4.60238e6	−	4.60238e6i	−0.0931074	−	0.0931074i	−0.752126	+	0.659019i	$0.770972\pi$
$368$	3.29620e7	+	2.93049e7i	0.661410	+	0.588027i
$369$	−3.50321e7	−	2.92883e7i	−0.697247	−	0.582929i
$370$	−3.07448e7	+	3.80229e7i	−0.606969	+	0.750655i
$371$	−1.84158e7			−0.360636
$372$	−4.06742e7	+	2.04855e7i	−0.790114	+	0.397941i
$373$	−5.03635e7	−	5.03635e7i	−0.970487	−	0.970487i	0.0290898	−	0.999577i	$-0.490739\pi$
$373$	−5.03635e7	−	5.03635e7i	−0.970487	−	0.970487i	−0.999577	+	0.0290898i	$0.990739\pi$
$374$	2.99634e7	+	2.90971e7i	0.572764	+	0.556205i
$375$	−3.43565e7	−	4.00068e7i	−0.651502	−	0.758647i
$376$	−6.28688e7	+	6.86596e7i	−1.18269	+	1.29163i
$377$	4.26969e7	+	4.26969e7i	0.796842	+	0.796842i
$378$	−1.74612e7	−	2.90663e7i	−0.323294	−	0.538164i
$379$	−1.08688e7			−0.199648			−0.0998240	−	0.995005i	$-0.531828\pi$
$379$	−1.08688e7			−0.199648			−0.0998240	+	0.995005i	$0.531828\pi$
$380$	−4.04769e7	+	4.88518e6i	−0.737660	+	0.0890287i
$381$	−6.92206e6	+	1.90715e7i	−0.125159	+	0.344834i
$382$	−2.83610e7	+	415980.i	−0.508783	+	0.00746247i
$383$	2.65015e7	+	2.65015e7i	0.471709	+	0.471709i	0.902467	−	0.430758i	$-0.141754\pi$
$383$	2.65015e7	+	2.65015e7i	0.471709	+	0.471709i	−0.430758	+	0.902467i	$0.641754\pi$
$384$	2.91068e7	+	4.85692e7i	0.514045	+	0.857763i
$385$	−2.02872e7	−	1.69019e7i	−0.355500	−	0.296179i
$386$	−1.98039e7	−	1.92313e7i	−0.344341	−	0.334386i
$387$	−2.24277e6	−	2.51152e7i	−0.0386948	−	0.433316i
$388$	4.31716e7	−	4.57815e7i	0.739099	−	0.783782i
$389$	−6.40339e6			−0.108783			−0.0543915	−	0.998520i	$-0.517322\pi$
$389$	−6.40339e6			−0.108783			−0.0543915	+	0.998520i	$0.517322\pi$
$390$	−1.95745e7	+	7.90551e7i	−0.329987	+	1.33271i
$391$			5.73068e7i			0.958685i
$392$	1.60521e6	+	3.64594e7i	0.0266485	+	0.605273i
$393$	−4.45253e6	−	9.52612e6i	−0.0733548	−	0.156942i
$394$	−2.29960e7	−	2.23311e7i	−0.375979	−	0.365109i
$395$	7.49864e7	−	6.82582e6i	1.21672	−	0.110755i
$396$	2.83142e7	−	3.59597e7i	0.455952	−	0.579069i
$397$	9.16365e6	−	9.16365e6i	0.146453	−	0.146453i	−0.630079	−	0.776531i	$-0.716977\pi$
$397$	9.16365e6	−	9.16365e6i	0.146453	−	0.146453i	0.776531	+	0.630079i	$0.216977\pi$
$398$	−1.40258e7	+	205721.i	−0.222474	+	0.00326310i
$399$	−1.01092e7	+	2.78527e7i	−0.159148	+	0.438480i
$400$	6.21623e7	−	1.52266e7i	0.971286	−	0.237916i
$401$		−	6.14309e7i		−	0.952694i	−0.879257	−	0.476347i	$-0.841961\pi$
$401$		−	6.14309e7i		−	0.952694i	0.879257	−	0.476347i	$-0.158039\pi$
$402$	4.98029e6	−	1.43755e7i	0.0766613	−	0.221282i
$403$	5.62131e7	−	5.62131e7i	0.858859	−	0.858859i
$404$	−3.80041e6	−	1.29526e8i	−0.0576351	−	1.96432i
$405$	−1.76488e7	−	6.40428e7i	−0.265674	−	0.964063i
$406$	−2.47398e7	−	2.40245e7i	−0.369673	−	0.358986i
$407$	−3.39185e7	+	3.39185e7i	−0.503099	+	0.503099i
$408$	−2.20347e7	+	7.01942e7i	−0.324434	+	1.03352i
$409$			1.58416e6i			0.0231542i	0.999933	+	0.0115771i	$0.00368518\pi$
$409$			1.58416e6i			0.0231542i	−0.999933	+	0.0115771i	$0.996315\pi$
$410$	−6.59244e6	−	6.22891e7i	−0.0956521	−	0.903776i
$411$	2.01800e7	−	5.55996e7i	0.290668	−	0.800840i
$412$	−6.30066e7	+	6.68157e7i	−0.900937	+	0.955404i
$413$	−4.81253e7	+	4.81253e7i	−0.683161	+	0.683161i
$414$	6.24608e7	−	6.50235e6i	0.880251	−	0.0916366i
$415$	1.30229e7	+	1.08499e7i	0.182207	+	0.151803i
$416$	−7.48239e7	−	6.45826e7i	−1.03935	−	0.897089i
$417$	4.01722e7	+	8.59480e7i	0.554010	+	1.18530i
$418$	−3.99911e7	+	586562.i	−0.547564	+	0.00803129i
$419$		−	1.29898e8i		−	1.76587i	−0.469495	−	0.882935i	$-0.655564\pi$
$419$		−	1.29898e8i		−	1.76587i	0.469495	−	0.882935i	$-0.344436\pi$
$420$	1.05159e7	−	4.53085e7i	0.141938	−	0.611550i
$421$	−4.31187e7			−0.577855			−0.288928	−	0.957351i	$-0.593299\pi$
$421$	−4.31187e7			−0.577855			−0.288928	+	0.957351i	$0.593299\pi$
$422$	−1.15707e6	−	7.88879e7i	−0.0153966	−	1.04972i
$423$	1.17898e7	+	1.32025e8i	0.155770	+	1.74436i
$424$	2.95700e7	−	3.22936e7i	0.387930	−	0.423662i
$425$	6.84509e7	+	4.72171e7i	0.891687	+	0.615081i
$426$	3.84279e7	+	7.91679e7i	0.497070	+	1.02405i
$427$	−3.79707e7	−	3.79707e7i	−0.487713	−	0.487713i
$428$	−6.92390e7	+	7.34249e7i	−0.883119	+	0.936509i
$429$	−2.72579e7	+	7.51002e7i	−0.345239	+	0.951195i
$430$	2.17479e7	−	2.68962e7i	0.273535	−	0.338288i
$431$	−7.15947e6			−0.0894230			−0.0447115	−	0.999000i	$-0.514237\pi$
$431$	−7.15947e6			−0.0894230			−0.0447115	+	0.999000i	$0.514237\pi$
$432$	7.90075e7	+	1.60518e7i	0.979979	+	0.199100i
$433$	1.05709e8	+	1.05709e8i	1.30211	+	1.30211i	0.926966	+	0.375144i	$0.122407\pi$
$433$	1.05709e8	+	1.05709e8i	1.30211	+	1.30211i	0.375144	+	0.926966i	$0.377593\pi$
$434$	−3.16298e7	+	3.25714e7i	−0.386925	+	0.398444i
$435$	−3.40383e7	−	5.83603e7i	−0.413524	−	0.709006i
$436$	2.44740e6	+	8.34125e7i	0.0295288	+	1.00640i
$437$	−3.88037e7	−	3.88037e7i	−0.464974	−	0.464974i
$438$	−3.24050e7	+	9.35367e7i	−0.385647	+	1.11317i
$439$	−7.27138e7			−0.859455			−0.429728	−	0.902959i	$-0.641390\pi$
$439$	−7.27138e7			−0.859455			−0.429728	+	0.902959i	$0.641390\pi$
$440$	6.22138e7	−	8.43607e6i	0.730346	−	0.0990336i
$441$	3.98653e7	+	3.33291e7i	0.464814	+	0.388605i
$442$	−1.88346e6	−	1.28412e8i	−0.0218117	−	1.48709i
$443$	−1.08243e8	−	1.08243e8i	−1.24505	−	1.24505i	−0.957879	−	0.287171i	$-0.907285\pi$
$443$	−1.08243e8	−	1.08243e8i	−1.24505	−	1.24505i	−0.287171	−	0.957879i	$-0.592715\pi$
$444$	−8.02368e7	−	2.64859e7i	−0.916695	−	0.302598i
$445$	−6.22373e7	+	5.66530e6i	−0.706270	+	0.0642899i
$446$	8.47572e7	−	8.72805e7i	0.955371	−	0.983813i
$447$	5.92013e7	+	1.26660e8i	0.662840	+	1.41814i
$448$	4.32693e7	+	3.62534e7i	0.481222	+	0.403194i
$449$	−9.90816e7			−1.09460			−0.547298	−	0.836938i	$-0.684344\pi$
$449$	−9.90816e7			−1.09460			−0.547298	+	0.836938i	$0.684344\pi$
$450$	4.36968e7	−	7.99647e7i	0.479526	−	0.877528i
$451$		−	6.14461e7i		−	0.669830i
$452$	−4.09461e7	+	4.34216e7i	−0.443402	+	0.470208i
$453$	1.14118e8	−	5.33390e7i	1.22761	−	0.573786i
$454$	4.50833e7	−	4.64255e7i	0.481780	−	0.496123i
$455$	7.36032e6	+	8.08583e7i	0.0781381	+	0.858401i
$456$	−3.26099e7	−	6.24502e7i	−0.343918	−	0.658626i
$457$	4.13400e7	−	4.13400e7i	0.433134	−	0.433134i	−0.456559	−	0.889693i	$-0.650918\pi$
$457$	4.13400e7	−	4.13400e7i	0.433134	−	0.433134i	0.889693	+	0.456559i	$0.150918\pi$
$458$	442122.	+	3.01433e7i	0.00460199	+	0.313758i
$459$	5.26208e7	+	9.05773e7i	0.544151	+	0.936659i
$460$	6.77721e7	+	5.31749e7i	0.696270	+	0.546303i
$461$		−	1.11922e8i		−	1.14238i	−0.820816	−	0.571192i	$-0.806481\pi$
$461$		−	1.11922e8i		−	1.14238i	0.820816	−	0.571192i	$-0.193519\pi$
$462$	1.49367e7	−	4.31145e7i	0.151470	−	0.437217i
$463$	−5.91997e7	+	5.91997e7i	−0.596454	+	0.596454i	−0.939367	−	0.342913i	$-0.888586\pi$
$463$	−5.91997e7	+	5.91997e7i	−0.596454	+	0.596454i	0.342913	+	0.939367i	$0.388586\pi$
$464$	8.18534e7	−	4.80745e6i	0.819375	−	0.0481239i
$465$	−7.68349e7	+	4.48135e7i	−0.764187	+	0.445708i
$466$	1.71565e7	−	1.76673e7i	0.169540	−	0.174587i
$467$	−4.00561e7	+	4.00561e7i	−0.393295	+	0.393295i	−0.875860	−	0.482565i	$-0.839705\pi$
$467$	−4.00561e7	+	4.00561e7i	−0.393295	+	0.393295i	0.482565	+	0.875860i	$0.339705\pi$
$468$	−1.39747e8	+	1.66232e7i	−1.36334	+	0.162172i
$469$		−	1.51671e7i		−	0.147023i
$470$	−1.14324e8	+	1.41388e8i	−1.10115	+	1.36182i
$471$	−1.08536e8	−	3.93934e7i	−1.03875	−	0.377017i
$472$	−7.11769e6	−	1.61666e8i	−0.0676883	−	1.53742i
$473$	2.39929e7	−	2.39929e7i	0.226725	−	0.226725i
$474$	5.68164e7	+	1.17052e8i	0.533506	+	1.09911i
$475$	−7.83213e7	+	1.43779e7i	−0.730801	+	0.134158i
$476$	2.15111e6	+	7.33142e7i	0.0199453	+	0.679778i
$477$	−5.54525e6	−	6.20974e7i	−0.0510935	−	0.572161i
$478$	−59906.5	−	4.08435e6i	−0.000548517	−	0.0373972i
$479$			2.30845e7i			0.210046i	0.994470	+	0.105023i	$0.0334916\pi$
$479$			2.30845e7i			0.210046i	−0.994470	+	0.105023i	$0.966508\pi$
$480$	6.25671e7	+	9.11918e7i	0.565747	+	0.824579i
$481$	1.47494e8			1.32538
$482$	1.99249e8	−	2.92245e6i	1.77932	−	0.0260979i
$483$	5.67162e7	−	2.65093e7i	0.503345	−	0.235264i
$484$	−5.17682e7	+	1.51893e6i	−0.456590	+	0.0133968i
$485$	7.86696e7	−	9.44260e7i	0.689575	−	0.827688i
$486$	9.27530e7	−	6.76308e7i	0.808014	−	0.589163i
$487$	1.44925e8	+	1.44925e8i	1.25475	+	1.25475i	0.953566	+	0.301184i	$0.0973817\pi$
$487$	1.44925e8	+	1.44925e8i	1.25475	+	1.25475i	0.301184	+	0.953566i	$0.402618\pi$
$488$	1.27554e8	−	5.61583e6i	1.09757	−	0.0483231i
$489$	−4.47810e7	−	1.62534e7i	−0.382972	−	0.139001i
$490$	7.50197e6	+	7.08829e7i	0.0637657	+	0.602495i
$491$	2.29116e7			0.193558			0.0967790	−	0.995306i	$-0.469146\pi$
$491$	2.29116e7			0.193558			0.0967790	+	0.995306i	$0.469146\pi$
$492$	9.66684e7	−	4.86870e7i	0.811688	−	0.408806i
$493$	7.53329e7	+	7.53329e7i	0.628701	+	0.628701i
$494$	8.82259e7	+	8.56752e7i	0.731838	+	0.710680i
$495$	5.08840e7	−	7.34971e7i	0.419533	−	0.605975i
$496$	−6.32930e6	−	1.07765e8i	−0.0518693	−	0.883146i
$497$	6.20356e7	+	6.20356e7i	0.505326	+	0.505326i
$498$	−9.58829e6	+	2.76765e7i	−0.0776342	+	0.224090i
$499$	−3.28161e7			−0.264110			−0.132055	−	0.991242i	$-0.542158\pi$
$499$	−3.28161e7			−0.264110			−0.132055	+	0.991242i	$0.542158\pi$
$500$	1.19355e8	−	3.71387e7i	0.954843	−	0.297110i
$501$	−1.31608e8	−	4.77675e7i	−1.04657	−	0.379857i
$502$	1.40407e7	−	205940.i	0.110989	−	0.00162791i
$503$	1.63511e7	+	1.63511e7i	0.128482	+	0.128482i	0.768424	−	0.639942i	$-0.221041\pi$
$503$	1.63511e7	+	1.63511e7i	0.128482	+	0.128482i	−0.639942	+	0.768424i	$0.721041\pi$
$504$	7.96638e7	−	1.06632e7i	0.622256	−	0.0832907i
$505$	−2.29432e7	−	2.52047e8i	−0.178148	−	1.95708i
$506$	6.06242e7	+	5.88715e7i	0.467944	+	0.454416i
$507$	1.04488e8	−	4.88377e7i	0.801754	−	0.374741i
$508$	−3.49889e7	−	3.29942e7i	−0.266894	−	0.251679i
$509$	−1.78774e8			−1.35566			−0.677832	−	0.735217i	$-0.737080\pi$
$509$	−1.78774e8			−1.35566			−0.677832	+	0.735217i	$0.737080\pi$
$510$	−3.45366e7	+	1.39482e8i	−0.260357	+	1.05150i
$511$			9.86872e7i			0.739602i
$512$	−1.33050e8	+	1.76649e7i	−0.991301	+	0.131613i
$513$	−9.69626e7	−	2.57012e7i	−0.718211	−	0.190371i
$514$	1.19172e8	+	1.15726e8i	0.877574	+	0.852203i
$515$	−1.14814e8	+	1.37810e8i	−0.840569	+	1.00892i
$516$	5.67570e7	+	1.87353e7i	0.413115	+	0.136368i
$517$	−1.26126e8	+	1.26126e8i	−0.912707	+	0.912707i
$518$	−8.42270e7	+	1.23538e6i	−0.605985	+	0.00888818i
$519$	108211.	+	39275.5i	0.000774050	+	0.000280944i
$520$	−1.53610e8	−	1.16926e8i	−1.09247	−	0.831574i
$521$		−	2.62127e8i		−	1.85353i	−0.375644	−	0.926764i	$-0.622578\pi$
$521$		−	2.62127e8i		−	1.85353i	0.375644	−	0.926764i	$-0.377422\pi$
$522$	7.35605e7	−	9.06559e7i	0.517170	−	0.637359i
$523$	9.92793e7	−	9.92793e7i	0.693990	−	0.693990i	−0.269117	−	0.963107i	$-0.586732\pi$
$523$	9.92793e7	−	9.92793e7i	0.693990	−	0.693990i	0.963107	+	0.269117i	$0.0867319\pi$
$524$	2.49145e7	−	731014.i	0.173164	−	0.00508080i
$525$	1.50661e7	−	8.95875e7i	0.104117	−	0.619112i
$526$	−6.56681e7	−	6.37696e7i	−0.451229	−	0.438184i
$527$	9.91804e7	−	9.91804e7i	0.677632	−	0.677632i
$528$	5.16213e7	+	9.54210e7i	0.350693	+	0.648249i
$529$		−	3.20884e7i		−	0.216761i
$530$	5.37718e7	−	6.65009e7i	0.361182	−	0.446684i
$531$	−1.76768e8	−	1.47786e8i	−1.18065	−	0.987072i
$532$	−5.10992e7	−	4.81861e7i	−0.339374	−	0.320027i
$533$	−1.33599e8	+	1.33599e8i	−0.882310	+	0.882310i
$534$	−4.71566e7	−	9.71506e7i	−0.309684	−	0.638002i
$535$	−1.26171e8	+	1.51441e8i	−0.823945	+	0.988970i
$536$	2.65968e7	+	2.43536e7i	0.172717	+	0.158150i
$537$	−1.32756e8	+	6.20506e7i	−0.857299	+	0.400703i
$538$	1.50829e7	−	221226.i	0.0968588	−	0.00142066i
$539$			6.99236e7i			0.446537i
$540$	1.55945e8	+	2.18163e7i	0.990356	+	0.138548i
$541$	7.86139e7			0.496487			0.248243	−	0.968698i	$-0.420147\pi$
$541$	7.86139e7			0.496487			0.248243	+	0.968698i	$0.420147\pi$
$542$	−1.81938e6	−	1.24043e8i	−0.0114268	−	0.779066i
$543$	−8.21845e7	−	1.75833e8i	−0.513323	−	1.09825i
$544$	−1.32017e8	−	1.13947e8i	−0.820034	−	0.707795i
$545$	1.47750e7	+	1.62314e8i	0.0912723	+	1.00269i
$546$	−1.26217e8	+	6.12655e7i	−0.775428	+	0.376390i
$547$	1.27038e8	+	1.27038e8i	0.776194	+	0.776194i	0.979181	−	0.202987i	$-0.0650650\pi$
$547$	1.27038e8	+	1.27038e8i	0.776194	+	0.776194i	−0.202987	+	0.979181i	$0.565065\pi$
$548$	1.02004e8	+	9.61889e7i	0.619834	+	0.584498i
$549$	1.16602e8	−	1.39469e8i	0.704677	−	0.842872i
$550$	1.20270e8	−	2.39072e7i	0.722887	−	0.143694i
$551$	−1.02019e8			−0.609855
$552$	−4.45822e7	+	1.42022e8i	−0.265060	+	0.844383i
$553$	9.17210e7	+	9.17210e7i	0.542367	+	0.542367i
$554$	−1.19229e8	+	1.22779e8i	−0.701219	+	0.722095i
$555$	−1.59593e8	−	4.20096e7i	−0.933546	−	0.245736i
$556$	−2.24787e8	+	6.59547e6i	−1.30782	+	0.0383726i
$557$	8.64577e7	+	8.64577e7i	0.500309	+	0.500309i	0.911534	−	0.411225i	$-0.134899\pi$
$557$	8.64577e7	+	8.64577e7i	0.500309	+	0.500309i	−0.411225	+	0.911534i	$0.634899\pi$
$558$	−1.19354e8	−	9.68468e7i	−0.686964	−	0.557420i
$559$	−1.04333e8			−0.597291
$560$	8.86988e7	+	6.54843e7i	0.505073	+	0.372883i
$561$	−4.80929e7	+	1.32504e8i	−0.272391	+	0.750484i
$562$	1.77794e6	+	1.21218e8i	0.0100163	+	0.682902i
$563$	7.68334e7	+	7.68334e7i	0.430551	+	0.430551i	0.888816	−	0.458265i	$-0.151529\pi$
$563$	7.68334e7	+	7.68334e7i	0.430551	+	0.430551i	−0.458265	+	0.888816i	$0.651529\pi$
$564$	−2.98360e8	−	9.84876e7i	−1.66304	−	0.548964i
$565$	−7.46143e7	+	8.95585e7i	−0.413692	+	0.496549i
$566$	−1.74428e8	+	1.79621e8i	−0.961982	+	0.990621i
$567$	6.53023e7	−	9.39783e7i	0.358245	−	0.515559i
$568$	−2.08394e8	+	9.17502e6i	−1.13721	+	0.0500682i
$569$	6.14058e7			0.333328			0.166664	−	0.986014i	$-0.446700\pi$
$569$	6.14058e7			0.333328			0.166664	+	0.986014i	$0.446700\pi$
$570$	−7.10609e7	−	1.17832e8i	−0.383713	−	0.636265i
$571$		−	7.85184e7i		−	0.421758i	−0.977512	−	0.210879i	$-0.932367\pi$
$571$		−	7.85184e7i		−	0.421758i	0.977512	−	0.210879i	$-0.0676326\pi$
$572$	−1.37780e8	−	1.29926e8i	−0.736206	−	0.694235i
$573$	−4.05347e7	−	8.67234e7i	−0.215458	−	0.460970i
$574$	7.51730e7	−	7.74110e7i	0.397490	−	0.409324i
$575$	1.38495e8	+	9.55331e7i	0.728502	+	0.502517i
$576$	−1.09216e8	+	1.56819e8i	−0.571504	+	0.820599i
$577$	−1.73612e8	+	1.73612e8i	−0.903761	+	0.903761i	−0.995759	−	0.0919986i	$-0.970674\pi$
$577$	−1.73612e8	+	1.73612e8i	−0.903761	+	0.903761i	0.0919986	+	0.995759i	$0.470674\pi$
$578$	−491149.	−	3.34859e7i	−0.00254349	−	0.173412i
$579$	3.17863e7	−	8.75769e7i	0.163759	−	0.451184i
$580$	1.58992e8	−	1.91888e7i	0.814874	−	0.0983477i
$581$			2.92005e7i			0.148889i
$582$	2.00675e8	+	6.95222e7i	1.01795	+	0.352659i
$583$	5.93224e7	−	5.93224e7i	0.299374	−	0.299374i
$584$	−1.73056e8	−	1.58461e8i	−0.868859	−	0.795578i
$585$	−2.70435e8	+	4.91663e7i	−1.35081	+	0.245584i
$586$	−1.00086e8	+	1.03065e8i	−0.497369	+	0.512177i
$587$	−2.30417e8	+	2.30417e8i	−1.13920	+	1.13920i	−0.150607	+	0.988594i	$0.548123\pi$
$587$	−2.30417e8	+	2.30417e8i	−1.13920	+	1.13920i	−0.988594	+	0.150607i	$0.951877\pi$
$588$	−1.10005e8	+	5.54041e7i	−0.541105	+	0.272527i
$589$			1.34314e8i			0.657320i
$590$	−3.32647e7	−	3.14304e8i	−0.161967	−	1.53036i
$591$	3.69098e7	−	1.01693e8i	0.178805	−	0.492639i
$592$	1.33076e8	−	1.49683e8i	0.641407	−	0.721451i
$593$	1.28393e8	−	1.28393e8i	0.615713	−	0.615713i	−0.328716	−	0.944429i	$-0.606616\pi$
$593$	1.28393e8	−	1.28393e8i	0.615713	−	0.615713i	0.944429	+	0.328716i	$0.106616\pi$
$594$	1.49878e8	+	3.73835e7i	0.715121	+	0.178370i
$595$	1.29863e7	+	1.42664e8i	0.0616502	+	0.677271i
$596$	−3.31266e8	+	9.71965e6i	−1.56472	+	0.0459105i
$597$	−2.00462e7	−	4.28887e7i	−0.0942129	−	0.201567i
$598$	−3.81076e6	−	2.59813e8i	−0.0178200	−	1.21495i
$599$		−	5.89659e7i		−	0.274360i	−0.990546	−	0.137180i	$-0.956196\pi$
$599$		−	5.89659e7i		−	0.274360i	0.990546	−	0.137180i	$-0.0438038\pi$
$600$	1.32908e8	+	1.70269e8i	0.615314	+	0.788282i
$601$	2.19502e8			1.01115			0.505575	−	0.862783i	$-0.331280\pi$
$601$	2.19502e8			1.01115			0.505575	+	0.862783i	$0.331280\pi$
$602$	5.95796e7	−	873872.i	0.273091	−	0.00400552i
$603$	5.11430e7	−	4.56703e6i	0.233257	−	0.0208297i
$604$	8.75718e6	+	2.98463e8i	0.0397423	+	1.35450i
$605$	−1.00737e8	+	9.16981e6i	−0.454906	+	0.0414089i
$606$	3.93438e8	−	1.90974e8i	1.76791	−	0.858135i
$607$	−1.61143e8	−	1.61143e8i	−0.720518	−	0.720518i	0.248193	−	0.968711i	$-0.420163\pi$
$607$	−1.61143e8	−	1.61143e8i	−0.720518	−	0.720518i	−0.968711	+	0.248193i	$0.920163\pi$
$608$	1.66548e8	−	1.22351e7i	0.741016	−	0.0544373i
$609$	3.97087e7	−	1.09405e8i	0.175806	−	0.484377i
$610$	2.47985e8	−	2.62457e7i	1.09254	−	0.115630i
$611$	5.48456e8			2.40446
$612$	−2.46565e8	+	2.93294e7i	−1.07567	+	0.127952i
$613$	−8.75185e7	−	8.75185e7i	−0.379943	−	0.379943i	0.491138	−	0.871082i	$-0.336581\pi$
$613$	−8.75185e7	−	8.75185e7i	−0.379943	−	0.379943i	−0.871082	+	0.491138i	$0.836581\pi$
$614$	3.18118e8	+	3.08921e8i	1.37430	+	1.33457i
$615$	1.82610e8	−	1.06506e8i	0.785053	−	0.457877i
$616$	7.97680e7	+	7.30403e7i	0.341261	+	0.312479i
$617$	1.61445e8	+	1.61445e8i	0.687335	+	0.687335i	0.961642	−	0.274307i	$-0.0884486\pi$
$617$	1.61445e8	+	1.61445e8i	0.687335	+	0.687335i	−0.274307	+	0.961642i	$0.588449\pi$
$618$	−2.92875e8	−	1.01464e8i	−1.24084	−	0.429879i
$619$	−2.40836e7			−0.101543			−0.0507715	−	0.998710i	$-0.516168\pi$
$619$	−2.40836e7			−0.101543			−0.0507715	+	0.998710i	$0.516168\pi$
$620$	−2.52632e7	−	2.09322e8i	−0.106002	−	0.878294i
$621$	1.06466e8	+	1.83263e8i	0.444568	+	0.765244i
$622$	−3.38256e8	+	4.96131e6i	−1.40564	+	0.0206170i
$623$	−7.61267e7	−	7.61267e7i	−0.314828	−	0.314828i
$624$	9.52312e7	−	3.19706e8i	0.391945	−	1.31582i
$625$	2.28222e8	−	8.67145e7i	0.934797	−	0.355182i
$626$	2.15198e8	+	2.08976e8i	0.877232	+	0.851871i
$627$	−5.71568e7	−	1.22286e8i	−0.231881	−	0.496107i
$628$	1.87770e8	−	1.99122e8i	0.758136	−	0.803970i
$629$	2.60234e8			1.04571
$630$	1.54021e8	−	3.03417e7i	0.615967	−	0.121344i
$631$			4.84706e7i			0.192926i	0.995337	+	0.0964629i	$0.0307529\pi$
$631$			4.84706e7i			0.192926i	−0.995337	+	0.0964629i	$0.969247\pi$
$632$	−3.08116e8	+	1.35655e7i	−1.22057	+	0.0537382i
$633$	2.41226e8	−	1.12750e8i	0.951072	−	0.444533i
$634$	1.09906e8	+	1.06728e8i	0.431274	+	0.418805i
$635$	−7.21659e7	−	6.01239e7i	−0.281845	−	0.234815i
$636$	1.40332e8	+	4.63231e7i	0.545487	+	0.180064i
$637$	1.52031e8	−	1.52031e8i	0.588185	−	0.588185i
$638$	1.57084e8	−	2.30400e6i	0.604880	−	0.00887196i
$639$	−1.90502e8	+	2.27862e8i	−0.730125	+	0.873310i
$640$	−2.57255e8	+	5.03938e7i	−0.981349	+	0.192237i
$641$			1.35555e8i			0.514686i	0.966320	+	0.257343i	$0.0828470\pi$
$641$			1.35555e8i			0.514686i	−0.966320	+	0.257343i	$0.917153\pi$
$642$	−3.21845e8	−	1.11500e8i	−1.21630	−	0.421377i
$643$	−1.05466e8	+	1.05466e8i	−0.396715	+	0.396715i	−0.877073	−	0.480357i	$-0.840507\pi$
$643$	−1.05466e8	+	1.05466e8i	−0.396715	+	0.396715i	0.480357	+	0.877073i	$0.340507\pi$
$644$	4.35228e6	+	1.48335e8i	0.0162952	+	0.555374i
$645$	1.12891e8	+	2.97163e7i	0.420709	+	0.110743i
$646$	1.55663e8	+	1.51162e8i	0.577414	+	0.560720i
$647$	2.90203e8	−	2.90203e8i	1.07149	−	1.07149i	0.0742529	−	0.997239i	$-0.476343\pi$
$647$	2.90203e8	−	2.90203e8i	1.07149	−	1.07149i	0.997239	−	0.0742529i	$-0.0236572\pi$
$648$	5.99439e7	+	2.65413e8i	0.220303	+	0.975432i
$649$		−	3.10050e8i		−	1.13422i
$650$	−3.13477e8	−	2.09517e8i	−1.14147	−	0.762921i
$651$	−1.44038e8	−	5.22790e7i	−0.522075	−	0.189489i
$652$	7.74725e7	−	8.21561e7i	0.279515	−	0.296413i
$653$	−2.02185e8	+	2.02185e8i	−0.726121	+	0.726121i	−0.969845	−	0.243724i	$-0.921631\pi$
$653$	−2.02185e8	+	2.02185e8i	−0.726121	+	0.726121i	0.243724	+	0.969845i	$0.421631\pi$
$654$	−2.53368e8	+	1.22984e8i	−0.905770	+	0.439658i
$655$	4.84816e7	−	4.41316e6i	0.172525	−	0.0157046i
$656$	1.50425e7	+	2.56120e8i	0.0532856	+	0.907260i
$657$	−3.32770e8	+	2.97161e7i	−1.17341	+	0.104784i
$658$	−3.13197e8	+	4.59376e6i	−1.09936	+	0.0161247i
$659$			9.43320e7i			0.329612i	0.986326	+	0.164806i	$0.0526998\pi$
$659$			9.43320e7i			0.329612i	−0.986326	+	0.164806i	$0.947300\pi$
$660$	1.12077e8	+	1.79826e8i	0.389838	+	0.625491i
$661$	1.53583e8			0.531789			0.265894	−	0.964002i	$-0.414333\pi$
$661$	1.53583e8			0.531789			0.265894	+	0.964002i	$0.414333\pi$
$662$	4.08271e6	+	2.78354e8i	0.0140726	+	0.959454i
$663$	3.92663e8	−	1.83531e8i	1.34735	−	0.629752i
$664$	−5.12055e7	−	4.68868e7i	−0.174909	−	0.160157i
$665$	−1.05394e8	−	8.78073e7i	−0.358386	−	0.298583i
$666$	−2.95276e7	−	2.83639e8i	−0.0999552	−	0.960158i
$667$	1.52419e8	+	1.52419e8i	0.513644	+	0.513644i
$668$	2.27686e8	−	2.41450e8i	0.763846	−	0.810025i
$669$	3.85973e8	+	1.40090e8i	1.28908	+	0.467874i
$670$	5.47697e7	+	4.42861e7i	0.182103	+	0.147246i
$671$	2.44628e8			0.809728
$672$	−5.17042e7	+	1.83367e8i	−0.170380	+	0.604244i
$673$	2.36318e8	+	2.36318e8i	0.775267	+	0.775267i	0.979022	−	0.203755i	$-0.0653146\pi$
$673$	2.36318e8	+	2.36318e8i	0.775267	+	0.775267i	−0.203755	+	0.979022i	$0.565315\pi$
$674$	1.45314e8	−	1.49641e8i	0.474601	−	0.488731i
$675$	3.06623e8	+	2.38264e7i	0.996995	+	0.0774723i
$676$	8.01817e6	+	2.73276e8i	0.0259558	+	0.884629i
$677$	−1.31071e8	−	1.31071e8i	−0.422418	−	0.422418i	0.463618	−	0.886035i	$-0.346551\pi$
$677$	−1.31071e8	−	1.31071e8i	−0.422418	−	0.422418i	−0.886035	+	0.463618i	$0.846551\pi$
$678$	−1.90331e8	−	6.59385e7i	−0.610688	−	0.211568i
$679$	2.11725e8			0.676337
$680$	−2.71025e8	−	2.06300e8i	−0.861950	−	0.656104i
$681$	2.05304e8	+	7.45156e7i	0.650062	+	0.235942i
$682$	−3.03335e6	−	2.06810e8i	−0.00956245	−	0.651957i
$683$	−3.40687e8	−	3.40687e8i	−1.06928	−	1.06928i	−0.997414	−	0.0718694i	$-0.977104\pi$
$683$	−3.40687e8	−	3.40687e8i	−1.06928	−	1.06928i	−0.0718694	−	0.997414i	$-0.522896\pi$
$684$	1.47095e8	−	1.86814e8i	0.459653	−	0.583770i
$685$	2.10387e8	+	1.75281e8i	0.654556	+	0.545333i
$686$	−2.26739e8	+	2.33489e8i	−0.702351	+	0.723261i
$687$	−9.21734e7	+	4.30820e7i	−0.284273	+	0.132870i
$688$	−9.41337e7	+	1.05881e8i	−0.289054	+	0.325127i
$689$	−2.57963e8			−0.788678
$690$	−6.98770e7	+	2.82211e8i	−0.212710	+	0.859065i
$691$		−	1.79903e8i		−	0.545259i	−0.962119	−	0.272630i	$-0.912107\pi$
$691$		−	1.79903e8i		−	0.545259i	0.962119	−	0.272630i	$-0.0878934\pi$
$692$	−187208.	+	198526.i	−0.000564945	+	0.000599099i
$693$	1.53386e8	−	1.36972e7i	0.460878	−	0.0411560i
$694$	−9.02124e7	+	9.28981e7i	−0.269891	+	0.277926i
$695$	−4.37418e8	+	3.98170e7i	−1.30299	+	0.118608i
$696$	1.28090e8	+	2.45302e8i	0.379917	+	0.727567i
$697$	−2.35717e8	+	2.35717e8i	−0.696134	+	0.696134i
$698$	−12416.7	−	846558.i	−3.65124e−5	−	0.00248938i
$699$	7.81285e7	+	2.83570e7i	0.228759	+	0.0830288i
$700$	1.80767e8	+	1.17020e8i	0.527017	+	0.341165i
$701$			7.00273e7i			0.203289i	0.994821	+	0.101644i	$0.0324104\pi$
$701$			7.00273e7i			0.203289i	−0.994821	+	0.101644i	$0.967590\pi$
$702$	−2.44591e8	−	4.07153e8i	−0.707016	−	1.17692i
$703$	−1.76210e8	+	1.76210e8i	−0.507183	+	0.507183i
$704$	−2.56165e8	+	2.26002e7i	−0.734178	+	0.0647732i
$705$	−5.93446e8	−	1.56212e8i	−1.69361	−	0.445808i
$706$	1.66845e8	−	1.71813e8i	0.474133	−	0.488248i
$707$	3.08296e8	−	3.08296e8i	0.872389	−	0.872389i
$708$	4.87778e8	−	2.45669e8i	1.37443	−	0.692231i
$709$		−	3.37893e8i		−	0.948071i	−0.880506	−	0.474035i	$-0.842797\pi$
$709$		−	3.37893e8i		−	0.948071i	0.880506	−	0.474035i	$-0.157203\pi$
$710$	−4.05152e8	+	4.28797e7i	−1.13199	+	0.119805i
$711$	−2.81662e8	+	3.36899e8i	−0.783644	+	0.937325i
$712$	2.55730e8	−	1.12591e7i	0.708503	−	0.0311934i
$713$	2.00669e8	−	2.00669e8i	0.553621	−	0.553621i
$714$	−2.22694e8	+	1.08095e8i	−0.611805	+	0.296968i
$715$	−2.84177e8	−	2.36758e8i	−0.777447	−	0.647718i
$716$	−1.01874e7	−	3.47209e8i	−0.0277540	−	0.945915i
$717$	1.24893e7	−	5.83751e6i	0.0338828	−	0.0158369i
$718$	5.31805e6	+	3.62578e8i	0.0143674	+	0.979555i
$719$		−	8.08138e7i		−	0.217420i	−0.994074	−	0.108710i	$-0.965328\pi$
$719$		−	8.08138e7i		−	0.217420i	0.994074	−	0.108710i	$-0.0346719\pi$
$720$	−1.94102e8	+	3.18808e8i	−0.520036	+	0.854144i
$721$	−3.09002e8			−0.824432
$722$	1.68569e8	−	2.47245e6i	0.447884	−	0.00656925i
$723$	2.84774e8	+	6.09270e8i	0.753503	+	1.61211i
$724$	4.59871e8	−	1.34930e7i	1.21177	−	0.0355545i
$725$	3.07643e8	−	5.64759e7i	0.807297	−	0.148200i
$726$	−7.63272e7	−	1.57247e8i	−0.199466	−	0.410935i
$727$	−1.10052e7	−	1.10052e7i	−0.0286414	−	0.0286414i	0.692641	−	0.721282i	$-0.256447\pi$
$727$	−1.10052e7	−	1.10052e7i	−0.0286414	−	0.0286414i	−0.721282	+	0.692641i	$0.756447\pi$
$728$	−1.46277e7	−	3.32243e8i	−0.0379125	−	0.861116i
$729$	3.36555e8	+	1.91899e8i	0.868708	+	0.495325i
$730$	−3.56368e8	−	2.88154e8i	−0.916072	−	0.740724i
$731$	−1.84081e8			−0.471257
$732$	1.93832e8	+	3.84855e8i	0.494188	+	0.981214i
$733$	−3.51791e8	−	3.51791e8i	−0.893250	−	0.893250i	0.101577	−	0.994828i	$-0.467611\pi$
$733$	−3.51791e8	−	3.51791e8i	−0.893250	−	0.893250i	−0.994828	+	0.101577i	$0.967611\pi$
$734$	3.73551e7	+	3.62751e7i	0.0944629	+	0.0917319i
$735$	−2.07804e8	+	1.21200e8i	−0.523349	+	0.305240i
$736$	−2.67106e8	−	2.30547e8i	−0.669962	−	0.578264i
$737$	4.88576e7	+	4.88576e7i	0.122048	+	0.122048i
$738$	2.83663e8	+	2.30171e8i	0.705721	+	0.572640i
$739$	−1.00652e8			−0.249396			−0.124698	−	0.992195i	$-0.539796\pi$
$739$	−1.00652e8			−0.249396			−0.124698	+	0.992195i	$0.539796\pi$
$740$	2.41471e8	−	3.07758e8i	0.595895	−	0.759476i
$741$	−1.41607e8	+	3.90153e8i	−0.348042	+	0.958916i
$742$	1.47310e8	−	2.16065e6i	0.360597	−	0.00528899i
$743$	−1.27406e8	−	1.27406e8i	−0.310616	−	0.310616i	0.534532	−	0.845148i	$-0.320488\pi$
$743$	−1.27406e8	−	1.27406e8i	−0.310616	−	0.310616i	−0.845148	+	0.534532i	$0.820488\pi$
$744$	3.22955e8	−	1.68639e8i	0.784193	−	0.409486i
$745$	−6.44617e8	+	5.86778e7i	−1.55895	+	0.141907i
$746$	4.08774e8	+	3.96956e8i	0.984616	+	0.956150i
$747$	−9.84630e7	+	8.79267e6i	−0.236217	+	0.0210940i
$748$	−2.43095e8	−	2.29236e8i	−0.580860	−	0.547745i
$749$	−3.39567e8			−0.808127
$750$	2.79517e8	+	3.15989e8i	0.662558	+	0.749011i
$751$		−	8.43414e8i		−	1.99123i	−0.0935592	−	0.995614i	$-0.529824\pi$
$751$		−	8.43414e8i		−	1.99123i	0.0935592	−	0.995614i	$-0.470176\pi$
$752$	4.94840e8	−	5.56594e8i	1.16362	−	1.30883i
$753$	2.00676e7	+	4.29343e7i	0.0470013	+	0.100559i
$754$	−3.46548e8	−	3.36529e8i	−0.808443	−	0.785070i
$755$	5.28674e7	+	5.80785e8i	0.122842	+	1.34950i
$756$	1.43085e8	+	2.30457e8i	0.331152	+	0.533365i
$757$	2.77095e8	−	2.77095e8i	0.638764	−	0.638764i	−0.311486	−	0.950251i	$-0.600827\pi$
$757$	2.77095e8	−	2.77095e8i	0.638764	−	0.638764i	0.950251	+	0.311486i	$0.100827\pi$
$758$	8.69413e7	−	1.27519e6i	0.199627	−	0.00292799i
$759$	−9.73052e7	+	2.68093e8i	−0.222541	+	0.613140i
$760$	3.23207e8	−	4.38263e7i	0.736275	−	0.0998375i
$761$		−	3.06203e8i		−	0.694793i	−0.937718	−	0.347396i	$-0.887066\pi$
$761$		−	3.06203e8i		−	0.694793i	0.937718	−	0.347396i	$-0.112934\pi$
$762$	5.31329e7	−	1.53368e8i	0.120088	−	0.346632i
$763$	−1.98537e8	+	1.98537e8i	−0.446960	+	0.446960i
$764$	2.26815e8	−	6.65497e6i	0.508618	−	0.0149233i
$765$	−4.77146e8	+	8.67474e7i	−1.06578	+	0.193764i
$766$	−2.15099e8	−	2.08880e8i	−0.478576	−	0.464740i
$767$	−6.74125e8	+	6.74125e8i	−1.49401	+	1.49401i
$768$	−2.38528e8	−	3.85097e8i	−0.526570	−	0.850132i
$769$			6.02937e8i			1.32584i	0.748688	+	0.662922i	$0.230684\pi$
$769$			6.02937e8i			1.32584i	−0.748688	+	0.662922i	$0.769316\pi$
$770$	1.64263e8	+	1.32821e8i	0.359805	+	0.290934i
$771$	−1.91277e8	+	5.27002e8i	−0.417350	+	1.14987i
$772$	1.60670e8	+	1.51511e8i	0.349208	+	0.329300i
$773$	−1.08244e8	+	1.08244e8i	−0.234350	+	0.234350i	−0.814506	−	0.580156i	$-0.802992\pi$
$773$	−1.08244e8	+	1.08244e8i	−0.234350	+	0.234350i	0.580156	+	0.814506i	$0.302992\pi$
$774$	2.08869e7	+	2.00637e8i	0.0450455	+	0.432702i
$775$	−7.43540e7	−	4.05031e8i	−0.159735	−	0.870128i
$776$	−3.39964e8	+	3.71278e8i	−0.727525	+	0.794537i
$777$	−1.20380e8	−	2.57552e8i	−0.256621	−	0.549038i
$778$	5.12216e7	−	751284.i	0.108771	−	0.00159538i
$779$		−	3.19219e8i		−	0.675267i
$780$	1.47304e8	−	6.34669e8i	0.310406	−	1.33741i
$781$	−3.99668e8			−0.838970
$782$	−6.72357e6	−	4.58405e8i	−0.0140598	−	0.958582i
$783$	3.80865e8	+	1.00953e8i	0.793389	+	0.210298i
$784$	−1.71179e7	−	2.91456e8i	−0.0355224	−	0.604818i
$785$	3.42165e8	−	4.10696e8i	0.707337	−	0.849007i
$786$	3.67340e7	+	7.56784e7i	0.0756486	+	0.155849i
$787$	3.72559e8	+	3.72559e8i	0.764312	+	0.764312i	0.977099	−	0.212787i	$-0.0682539\pi$
$787$	3.72559e8	+	3.72559e8i	0.764312	+	0.764312i	−0.212787	+	0.977099i	$0.568254\pi$
$788$	1.86568e8	+	1.75932e8i	0.381293	+	0.359556i
$789$	1.05401e8	−	2.90398e8i	0.214592	−	0.591239i
$790$	−5.99026e8	+	6.33985e7i	−1.21497	+	0.128587i
$791$	−2.00811e8			−0.405750
$792$	−2.22270e8	+	2.90969e8i	−0.447410	+	0.585694i
$793$	−5.31882e8	−	5.31882e8i	−1.06659	−	1.06659i
$794$	−7.22262e7	+	7.43764e7i	−0.144289	+	0.148585i
$795$	2.79124e8	+	7.34735e7i	0.555515	+	0.146228i
$796$	1.12170e8	−	3.29119e6i	0.222402	−	0.00652550i
$797$	−1.29841e8	−	1.29841e8i	−0.256470	−	0.256470i	0.567147	−	0.823617i	$-0.308047\pi$
$797$	−1.29841e8	−	1.29841e8i	−0.256470	−	0.256470i	−0.823617	+	0.567147i	$0.808047\pi$
$798$	7.75974e7	−	2.23984e8i	0.152700	−	0.440766i
$799$	9.67677e8			1.89710
$800$	−4.95458e8	+	1.29093e8i	−0.967692	+	0.252135i
$801$	2.33774e8	−	2.79619e8i	0.454882	−	0.544089i
$802$	7.20743e6	+	4.91394e8i	0.0139720	+	0.952591i
$803$	−3.17899e8	−	3.17899e8i	−0.613964	−	0.613964i
$804$	−3.81514e7	+	1.15576e8i	−0.0734078	+	0.222382i
$805$	2.62749e7	+	2.88648e8i	0.0503678	+	0.553325i
$806$	−4.43061e8	+	4.56251e8i	−0.846171	+	0.871363i
$807$	2.15571e7	+	4.61212e7i	0.0410176	+	0.0877566i
$808$	4.55968e7	+	1.03565e9i	0.0864371	+	1.96327i
$809$	−3.44355e8			−0.650370			−0.325185	−	0.945650i	$-0.605427\pi$
$809$	−3.44355e8			−0.650370			−0.325185	+	0.945650i	$0.605427\pi$
$810$	1.48689e8	+	5.10217e8i	0.279784	+	0.960063i
$811$			9.74265e8i			1.82648i	0.407424	+	0.913239i	$0.366427\pi$
$811$			9.74265e8i			1.82648i	−0.407424	+	0.913239i	$0.633573\pi$
$812$	2.00716e8	+	1.89273e8i	0.374898	+	0.353525i
$813$	3.79303e8	−	1.77287e8i	0.705854	−	0.329917i
$814$	2.67339e8	−	2.75298e8i	0.495667	−	0.510423i
$815$	1.41175e8	−	1.69450e8i	0.260786	−	0.313017i
$816$	1.68023e8	−	5.64079e8i	0.309241	−	1.03817i
$817$	1.24646e8	−	1.24646e8i	0.228566	−	0.228566i
$818$	−185863.	−	1.26719e7i	−0.000339573	−	0.0231517i
$819$	−3.63280e8	−	3.03717e8i	−0.661286	−	0.552864i
$820$	6.00419e7	+	4.97486e8i	0.108896	+	0.902276i
$821$			1.99444e8i			0.360406i	0.983629	+	0.180203i	$0.0576754\pi$
$821$			1.99444e8i			0.360406i	−0.983629	+	0.180203i	$0.942325\pi$
$822$	−1.54900e8	+	4.47116e8i	−0.278891	+	0.805017i
$823$	2.60107e8	−	2.60107e8i	0.466608	−	0.466608i	−0.434206	−	0.900814i	$-0.642971\pi$
$823$	2.60107e8	−	2.60107e8i	0.466608	−	0.466608i	0.900814	+	0.434206i	$0.142971\pi$
$824$	4.96159e8	−	5.41861e8i	0.886828	−	0.968514i
$825$	2.40054e8	+	3.37119e8i	0.427511	+	0.600373i
$826$	3.79314e8	−	3.90607e8i	0.673068	−	0.693107i
$827$	−1.66713e8	+	1.66713e8i	−0.294749	+	0.294749i	−0.838953	−	0.544204i	$-0.816832\pi$
$827$	−1.66713e8	+	1.66713e8i	−0.294749	+	0.294749i	0.544204	+	0.838953i	$0.316832\pi$
$828$	−4.98870e8	+	5.93415e7i	−0.878812	+	0.104536i
$829$			1.57027e8i			0.275620i	0.990459	+	0.137810i	$0.0440063\pi$
$829$			1.57027e8i			0.275620i	−0.990459	+	0.137810i	$0.955994\pi$
$830$	−1.05445e8	−	8.52617e7i	−0.184414	−	0.149114i
$831$	−5.42954e8	−	1.97067e8i	−0.946150	−	0.343408i
$832$	6.06104e8	+	5.07827e8i	1.05239	+	0.881750i
$833$	2.68238e8	−	2.68238e8i	0.464072	−	0.464072i
$834$	−3.31427e8	−	6.82797e8i	−0.571334	−	1.17705i
$835$	4.14901e8	−	4.98000e8i	0.712664	−	0.855402i
$836$	3.19826e8	−	9.38399e6i	0.547387	−	0.0160609i
$837$	1.32911e8	−	5.01432e8i	0.226665	−	0.855137i
$838$	1.52403e7	+	1.03907e9i	0.0258978	+	1.76568i
$839$		−	2.65259e8i		−	0.449142i	−0.974458	−	0.224571i	$-0.927902\pi$
$839$		−	2.65259e8i		−	0.449142i	0.974458	−	0.224571i	$-0.0720981\pi$
$840$	−7.88024e7	+	3.63663e8i	−0.132954	+	0.613566i
$841$	−1.94096e8			−0.326309
$842$	3.44912e8	−	5.05894e6i	0.577793	−	0.00847467i
$843$	−3.70665e8	+	1.73249e8i	−0.618727	+	0.289194i
$844$	1.85112e7	+	6.30900e8i	0.0307898	+	1.04938i
$845$	4.84059e7	+	5.31773e8i	0.0802284	+	0.881365i
$846$	−1.09798e8	−	1.05471e9i	−0.181336	−	1.74189i
$847$	−1.23218e8	−	1.23218e8i	−0.202779	−	0.202779i
$848$	−2.32745e8	+	2.61791e8i	−0.381675	+	0.429306i
$849$	−7.94322e8	−	2.88302e8i	−1.29800	−	0.471112i
$850$	−5.53088e8	−	3.69665e8i	−0.900612	−	0.601937i
$851$	5.26525e8			0.854339
$852$	−3.16678e8	−	6.28767e8i	−0.512035	−	1.01665i
$853$	4.13025e8	+	4.13025e8i	0.665471	+	0.665471i	0.956664	−	0.291193i	$-0.0940523\pi$
$853$	4.13025e8	+	4.13025e8i	0.665471	+	0.665471i	−0.291193	+	0.956664i	$0.594052\pi$
$854$	3.08188e8	+	2.99278e8i	0.494814	+	0.480508i
$855$	2.64348e8	−	3.81825e8i	0.422939	−	0.610894i
$856$	5.45238e8	−	5.95459e8i	0.869290	−	0.949360i
$857$	2.23660e8	+	2.23660e8i	0.355342	+	0.355342i	0.862093	−	0.506751i	$-0.169154\pi$
$857$	2.23660e8	+	2.23660e8i	0.355342	+	0.355342i	−0.506751	+	0.862093i	$0.669154\pi$
$858$	2.09228e8	−	6.03935e8i	0.331252	−	0.956156i
$859$	−7.31416e8			−1.15394			−0.576972	−	0.816764i	$-0.695766\pi$
$859$	−7.31416e8			−1.15394			−0.576972	+	0.816764i	$0.695766\pi$
$860$	−1.70809e8	+	2.17698e8i	−0.268544	+	0.342263i
$861$	3.42328e8	+	1.24249e8i	0.536330	+	0.194663i
$862$	5.72696e7	−	839991.i	0.0894133	−	0.00131145i
$863$	8.33536e7	+	8.33536e7i	0.129686	+	0.129686i	0.768970	−	0.639285i	$-0.220769\pi$
$863$	8.33536e7	+	8.33536e7i	0.129686	+	0.129686i	−0.639285	+	0.768970i	$0.720769\pi$
$864$	−6.33875e8	−	1.19131e8i	−0.982794	−	0.184707i
$865$	−341141.	+	409467.i	−0.000527091	+	0.000632660i
$866$	−8.57983e8	−	8.33178e8i	−1.32107	−	1.28287i
$867$	1.02394e8	−	4.78593e7i	0.157115	−	0.0734360i
$868$	2.49189e8	−	2.64254e8i	0.381040	−	0.404076i
$869$	−5.90918e8			−0.900467
$870$	2.79124e8	+	4.62839e8i	0.423877	+	0.702865i
$871$		−	2.12457e8i		−	0.321526i
$872$	−2.93636e7	−	6.66941e8i	−0.0442853	−	1.00586i
$873$	6.37534e7	+	7.13930e8i	0.0958210	+	1.07303i
$874$	3.14949e8	+	3.05843e8i	0.471743	+	0.458105i
$875$	3.66428e8	+	2.06443e8i	0.546972	+	0.308159i
$876$	2.48238e8	−	7.52015e8i	0.369280	−	1.11870i
$877$	1.96125e8	−	1.96125e8i	0.290759	−	0.290759i	−0.546621	−	0.837380i	$-0.684086\pi$
$877$	1.96125e8	−	1.96125e8i	0.290759	−	0.290759i	0.837380	+	0.546621i	$0.184086\pi$
$878$	5.81648e8	−	8.53121e6i	0.859363	−	0.0126045i
$879$	−4.55777e8	−	1.65426e8i	−0.671097	−	0.243577i
$880$	−4.96667e8	+	7.47806e7i	−0.728815	+	0.109734i
$881$		−	6.18867e8i		−	0.905043i	−0.891753	−	0.452522i	$-0.850525\pi$
$881$		−	6.18867e8i		−	0.905043i	0.891753	−	0.452522i	$-0.149475\pi$
$882$	−3.22799e8	−	2.61927e8i	−0.470464	−	0.381746i
$883$	−2.27672e8	+	2.27672e8i	−0.330694	+	0.330694i	−0.852850	−	0.522156i	$-0.825128\pi$
$883$	−2.27672e8	+	2.27672e8i	−0.330694	+	0.330694i	0.522156	+	0.852850i	$0.325128\pi$
$884$	3.01321e7	+	1.02696e9i	0.0436187	+	1.48662i
$885$	9.21429e8	−	5.37418e8i	1.32933	−	0.775323i
$886$	8.78547e8	+	8.53148e8i	1.26318	+	1.22666i
$887$	−1.64345e8	+	1.64345e8i	−0.235497	+	0.235497i	−0.814983	−	0.579485i	$-0.803254\pi$
$887$	−1.64345e8	+	1.64345e8i	−0.235497	+	0.235497i	0.579485	+	0.814983i	$0.303254\pi$
$888$	6.44933e8	+	2.02451e8i	0.921034	+	0.289122i
$889$		−	1.61813e8i		−	0.230307i
$890$	4.97180e8	−	5.26196e7i	0.705251	−	0.0746410i
$891$	9.23733e7	+	5.13088e8i	0.130591	+	0.725368i
$892$	−6.67744e8	+	7.08113e8i	−0.940839	+	0.997719i
$893$	−6.55235e8	+	6.55235e8i	−0.920116	+	0.920116i
$894$	−4.88420e8	−	1.00623e9i	−0.683566	−	1.40826i
$895$	−6.15019e7	−	6.75641e8i	−0.0857866	−	0.942426i
$896$	−3.50370e8	−	2.84919e8i	−0.487083	−	0.396093i
$897$	7.94465e8	−	3.71334e8i	1.10077	−	0.514503i
$898$	7.92568e8	−	1.16248e7i	1.09448	−	0.0160531i
$899$		−	5.27582e8i		−	0.726124i
$900$	−3.40155e8	+	6.44776e8i	−0.466605	+	0.884466i
$901$	−4.55141e8			−0.622260
$902$	7.20922e6	+	4.91516e8i	0.00982355	+	0.669758i
$903$	8.51534e7	+	1.82185e8i	0.115648	+	0.247428i
$904$	3.22439e8	−	3.52139e8i	0.436458	−	0.476661i
$905$	8.94872e8	−	8.14579e7i	1.20730	−	0.109897i
$906$	−9.06588e8	+	4.40055e8i	−1.21906	+	0.591728i
$907$	−6.77377e8	−	6.77377e8i	−0.907839	−	0.907839i	0.0882589	−	0.996098i	$-0.471870\pi$
$907$	−6.77377e8	−	6.77377e8i	−0.907839	−	0.907839i	−0.996098	+	0.0882589i	$0.971870\pi$
$908$	−3.55181e8	+	3.76654e8i	−0.474452	+	0.503135i
$909$	1.13240e9	+	9.46732e8i	1.50767	+	1.26048i
$910$	−6.83630e7	−	6.45933e8i	−0.0907188	−	0.857163i
$911$	7.94414e8			1.05073			0.525366	−	0.850877i	$-0.323929\pi$
$911$	7.94414e8			1.05073			0.525366	+	0.850877i	$0.323929\pi$
$912$	2.68178e8	+	4.95722e8i	0.353540	+	0.653512i
$913$	−9.40630e7	−	9.40630e7i	−0.123597	−	0.123597i
$914$	−3.25834e8	+	3.35535e8i	−0.426735	+	0.439439i
$915$	4.24021e8	+	7.27004e8i	0.553508	+	0.949016i
$916$	−7.07319e6	−	2.41069e8i	−0.00920299	−	0.313657i
$917$	5.93012e7	+	5.93012e7i	0.0769051	+	0.0769051i
$918$	−4.31548e8	−	7.18367e8i	−0.557829	−	0.928578i
$919$	1.37387e9			1.77011			0.885055	−	0.465486i	$-0.154120\pi$
$919$	1.37387e9			1.77011			0.885055	+	0.465486i	$0.154120\pi$
$920$	−5.48358e8	−	4.17402e8i	−0.704207	−	0.536033i
$921$	−5.10597e8	+	1.40678e9i	−0.653581	+	1.80073i
$922$	1.31313e7	+	8.95279e8i	0.0167539	+	1.14226i
$923$	8.68977e8	+	8.68977e8i	1.10510	+	1.10510i
$924$	−1.14422e8	+	3.46631e8i	−0.145042	+	0.439392i
$925$	4.33822e8	−	6.28916e8i	0.548134	−	0.794634i
$926$	4.66601e8	−	4.80493e8i	0.587642	−	0.605137i
$927$	−9.30447e7	−	1.04194e9i	−0.116803	−	1.30799i
$928$	−6.54193e8	+	4.80590e7i	−0.818581	+	0.0601355i
$929$	6.61758e8			0.825376			0.412688	−	0.910872i	$-0.364590\pi$
$929$	6.61758e8			0.825376			0.412688	+	0.910872i	$0.364590\pi$
$930$	6.09355e8	−	3.67484e8i	0.757568	−	0.456867i
$931$			3.63260e8i			0.450162i
$932$	−1.35165e8	+	1.43336e8i	−0.166961	+	0.177055i
$933$	−4.83448e8	−	1.03433e9i	−0.595258	−	1.27355i
$934$	3.15715e8	−	3.25114e8i	0.387484	−	0.399020i
$935$	−5.01392e8	−	4.17727e8i	−0.613398	−	0.511043i
$936$	1.11591e9	−	1.49367e8i	1.36082	−	0.182149i
$937$	1.25830e8	−	1.25830e8i	0.152956	−	0.152956i	−0.626481	−	0.779437i	$-0.715505\pi$
$937$	1.25830e8	−	1.25830e8i	0.152956	−	0.152956i	0.779437	+	0.626481i	$0.215505\pi$
$938$	1.77950e6	+	1.21324e8i	0.00215620	+	0.147007i
$939$	−3.45404e8	+	9.51649e8i	−0.417187	+	1.14942i
$940$	8.97907e8	−	1.14439e9i	1.08105	−	1.37782i
$941$		−	8.66832e8i		−	1.04032i	−0.854069	−	0.520159i	$-0.825873\pi$
$941$		−	8.66832e8i		−	1.04032i	0.854069	−	0.520159i	$-0.174127\pi$
$942$	8.72814e8	+	3.02379e8i	1.04416	+	0.361742i
$943$	−4.76921e8	+	4.76921e8i	−0.568737	+	0.568737i
$944$	7.59030e7	+	1.29235e9i	0.0902284	+	1.53626i
$945$	3.06574e8	+	4.32101e8i	0.363279	+	0.512024i
$946$	−1.89108e8	+	1.94738e8i	−0.223376	+	0.230026i
$947$	−3.17909e8	+	3.17909e8i	−0.374328	+	0.374328i	−0.869051	−	0.494723i	$-0.835270\pi$
$947$	−3.17909e8	+	3.17909e8i	−0.374328	+	0.374328i	0.494723	+	0.869051i	$0.335270\pi$
$948$	−4.68216e8	−	9.29646e8i	−0.549568	−	1.09117i
$949$			1.38238e9i			1.61745i
$950$	6.24816e8	−	1.24200e8i	0.728755	−	0.144861i
$951$	−1.76405e8	+	4.86027e8i	−0.205102	+	0.565091i
$952$	−2.58087e7	−	5.86198e8i	−0.0299126	−	0.679412i
$953$	−6.52473e8	+	6.52473e8i	−0.753848	+	0.753848i	−0.975195	−	0.221347i	$-0.928955\pi$
$953$	−6.52473e8	+	6.52473e8i	−0.753848	+	0.753848i	0.221347	+	0.975195i	$0.428955\pi$
$954$	5.16429e7	+	4.96075e8i	0.0594792	+	0.571350i
$955$	4.41364e8	−	4.01763e7i	0.506742	−	0.0461275i
$956$	958401.	+	3.26643e7i	0.00109692	+	0.0373852i
$957$	2.24510e8	+	4.80336e8i	0.256153	+	0.548036i
$958$	−2.70841e6	−	1.84656e8i	−0.00308048	−	0.210024i
$959$			4.71736e8i			0.534864i
$960$	−5.11182e8	−	7.22115e8i	−0.577779	−	0.816193i
$961$	1.92910e8			0.217363
$962$	−1.17983e9	+	1.73049e7i	−1.32524	+	0.0194377i
$963$	−1.02248e8	−	1.14501e9i	−0.114493	−	1.28212i
$964$	−1.59348e9	+	4.67541e7i	−1.77875	+	0.0521901i
$965$	3.31388e8	+	2.76091e8i	0.368770	+	0.307235i
$966$	−4.50571e8	+	2.18706e8i	−0.499841	+	0.242621i
$967$	−1.13905e9	−	1.13905e9i	−1.25969	−	1.25969i	−0.951240	−	0.308451i	$-0.900189\pi$
$967$	−1.13905e9	−	1.13905e9i	−1.25969	−	1.25969i	−0.308451	−	0.951240i	$-0.599811\pi$
$968$	4.13923e8	−	1.82239e7i	0.456345	−	0.0200916i
$969$	−2.49847e8	+	6.88373e8i	−0.274602	+	0.756576i
$970$	−6.18210e8	+	7.64557e8i	−0.677362	+	0.837712i
$971$	1.19853e9			1.30916			0.654580	−	0.755993i	$-0.272846\pi$
$971$	1.19853e9			1.30916			0.654580	+	0.755993i	$0.272846\pi$
$972$	−7.34009e8	+	5.51870e8i	−0.799287	+	0.600950i
$973$	−5.35036e8	−	5.35036e8i	−0.580824	−	0.580824i
$974$	−1.17628e9	−	1.14227e9i	−1.27302	−	1.23621i
$975$	2.11042e8	−	1.25492e9i	0.227696	−	1.35394i
$976$	−1.01966e9	+	5.98872e7i	−1.09675	+	0.0644146i
$977$	9.05317e8	+	9.05317e8i	0.970771	+	0.970771i	0.999585	−	0.0288137i	$-0.00917296\pi$
$977$	9.05317e8	+	9.05317e8i	0.970771	+	0.970771i	−0.0288137	+	0.999585i	$0.509173\pi$
$978$	3.60117e8	+	1.24759e8i	0.384970	+	0.133370i
$979$	4.90451e8			0.522694
$980$	−6.83257e7	−	5.66122e8i	−0.0725949	−	0.601495i
$981$	−7.29244e8	−	6.09679e8i	−0.772442	−	0.645795i
$982$	−1.83273e8	+	2.68812e6i	−0.193537	+	0.00283867i
$983$	1.73853e8	+	1.73853e8i	0.183030	+	0.183030i	0.792675	−	0.609645i	$-0.208688\pi$
$983$	1.73853e8	+	1.73853e8i	0.183030	+	0.183030i	−0.609645	+	0.792675i	$0.708688\pi$
$984$	−7.67551e8	+	4.00796e8i	−0.805605	+	0.420666i
$985$	3.84803e8	+	3.20593e8i	0.402652	+	0.335463i
$986$	−6.11437e8	−	5.93760e8i	−0.637854	−	0.619413i
$987$	−4.47633e8	−	9.57705e8i	−0.465555	−	0.996048i
$988$	−7.15783e8	−	6.74977e8i	−0.742182	−	0.699871i
$989$	−3.72448e8			−0.385014
$990$	−3.98405e8	+	5.93883e8i	−0.410601	+	0.612062i
$991$		−	9.50775e8i		−	0.976915i	−0.872588	−	0.488458i	$-0.837560\pi$
$991$		−	9.50775e8i		−	0.976915i	0.872588	−	0.488458i	$-0.162440\pi$
$992$	6.32726e7	+	8.61284e8i	0.0648157	+	0.882290i
$993$	−8.51162e8	+	3.97834e8i	−0.869289	+	0.406307i
$994$	−5.03510e8	−	4.88953e8i	−0.512683	−	0.497861i
$995$	2.18275e8	−	1.98690e7i	0.221582	−	0.0201700i
$996$	7.34509e7	−	2.22513e8i	0.0743394	−	0.225205i
$997$	4.93372e8	−	4.93372e8i	0.497839	−	0.497839i	−0.412926	−	0.910765i	$-0.635493\pi$
$997$	4.93372e8	−	4.93372e8i	0.497839	−	0.497839i	0.910765	+	0.412926i	$0.135493\pi$
$998$	2.62500e8	−	3.85018e6i	0.264082	−	0.00387337i
$999$	8.32210e8	−	4.83471e8i	0.834711	−	0.484925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.l.a.23.1	✓	136
3.2	odd	2	inner	60.7.l.a.23.68	yes	136
4.3	odd	2	inner	60.7.l.a.23.35	yes	136
5.2	odd	4	inner	60.7.l.a.47.34	yes	136
12.11	even	2	inner	60.7.l.a.23.34	yes	136
15.2	even	4	inner	60.7.l.a.47.35	yes	136
20.7	even	4	inner	60.7.l.a.47.68	yes	136
60.47	odd	4	inner	60.7.l.a.47.1	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.l.a.23.1	✓	136	1.1	even	1	trivial
60.7.l.a.23.34	yes	136	12.11	even	2	inner
60.7.l.a.23.35	yes	136	4.3	odd	2	inner
60.7.l.a.23.68	yes	136	3.2	odd	2	inner
60.7.l.a.47.1	yes	136	60.47	odd	4	inner
60.7.l.a.47.34	yes	136	5.2	odd	4	inner
60.7.l.a.47.35	yes	136	15.2	even	4	inner
60.7.l.a.47.68	yes	136	20.7	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.99914 + 0.117326i) q^{2} +(-11.4327 - 24.4601i) q^{3} +(63.9725 - 1.87701i) q^{4} +(124.485 - 11.3316i) q^{5} +(94.3213 + 194.318i) q^{6} +(152.267 + 152.267i) q^{7} +(-511.504 + 22.5201i) q^{8} +(-467.588 + 559.287i) q^{9} +O(q^{10})\)	\(q+(-7.99914 + 0.117326i) q^{2} +(-11.4327 - 24.4601i) q^{3} +(63.9725 - 1.87701i) q^{4} +(124.485 - 11.3316i) q^{5} +(94.3213 + 194.318i) q^{6} +(152.267 + 152.267i) q^{7} +(-511.504 + 22.5201i) q^{8} +(-467.588 + 559.287i) q^{9} +(-994.446 + 105.248i) q^{10} -980.987 q^{11} +(-777.288 - 1543.31i) q^{12} +(2132.91 + 2132.91i) q^{13} +(-1235.87 - 1200.14i) q^{14} +(-1700.37 - 2915.37i) q^{15} +(4088.95 - 240.154i) q^{16} +(3763.23 + 3763.23i) q^{17} +(3674.68 - 4528.68i) q^{18} -5096.33 q^{19} +(7942.36 - 958.570i) q^{20} +(1983.63 - 5465.26i) q^{21} +(7847.05 - 115.095i) q^{22} +(7614.05 + 7614.05i) q^{23} +(6398.70 + 12254.0i) q^{24} +(15368.2 - 2821.23i) q^{25} +(-17311.7 - 16811.2i) q^{26} +(19026.0 + 5043.08i) q^{27} +(10026.7 + 9455.06i) q^{28} +20018.2 q^{29} +(13943.5 + 23120.9i) q^{30} -26355.1i q^{31} +(-32679.9 + 2400.77i) q^{32} +(11215.3 + 23995.0i) q^{33} +(-30544.1 - 29661.1i) q^{34} +(20680.4 + 17229.5i) q^{35} +(-28863.0 + 36656.7i) q^{36} +(34575.9 - 34575.9i) q^{37} +(40766.2 - 597.931i) q^{38} +(27786.2 - 76555.8i) q^{39} +(-63419.6 + 8599.58i) q^{40} +62637.0i q^{41} +(-15226.2 + 43950.1i) q^{42} +(-24457.9 + 24457.9i) q^{43} +(-62756.2 + 1841.32i) q^{44} +(-51870.3 + 74921.6i) q^{45} +(-61799.2 - 60012.5i) q^{46} +(128570. - 128570. i) q^{47} +(-52621.8 - 97270.4i) q^{48} -71278.8i q^{49} +(-122601. + 24370.5i) q^{50} +(49025.0 - 135072. i) q^{51} +(140451. + 132444. i) q^{52} +(-60472.2 + 60472.2i) q^{53} +(-152783. - 38108.1i) q^{54} +(-122118. + 11116.1i) q^{55} +(-81314.1 - 74456.0i) q^{56} +(58264.6 + 124656. i) q^{57} +(-160128. + 2348.65i) q^{58} +316059. i q^{59} +(-114249. - 183312. i) q^{60} -249370. q^{61} +(3092.14 + 210818. i) q^{62} +(-156359. + 13962.7i) q^{63} +(261130. - 23038.3i) q^{64} +(289685. + 241346. i) q^{65} +(-92528.0 - 190623. i) q^{66} +(-49804.5 - 49804.5i) q^{67} +(247807. + 233679. i) q^{68} +(99191.1 - 273289. i) q^{69} +(-167447. - 135395. i) q^{70} +407414. q^{71} +(226578. - 296608. i) q^{72} +(324061. + 324061. i) q^{73} +(-272521. + 280634. i) q^{74} +(-244707. - 343653. i) q^{75} +(-326025. + 9565.87i) q^{76} +(-149371. - 149371. i) q^{77} +(-213284. + 615641. i) q^{78} +602371. q^{79} +(506293. - 76230.0i) q^{80} +(-94163.6 - 523032. i) q^{81} +(-7348.94 - 501042. i) q^{82} +(95886.0 + 95886.0i) q^{83} +(116640. - 353349. i) q^{84} +(511110. + 425823. i) q^{85} +(192773. - 198512. i) q^{86} +(-228861. - 489646. i) q^{87} +(501779. - 22091.9i) q^{88} -499957. q^{89} +(406127. - 605394. i) q^{90} +649541. i q^{91} +(501381. + 472798. i) q^{92} +(-644648. + 301310. i) q^{93} +(-1.01337e6 + 1.04353e6i) q^{94} +(-634418. + 57749.4i) q^{95} +(432342. + 771906. i) q^{96} +(695245. - 695245. i) q^{97} +(8362.85 + 570169. i) q^{98} +(458698. - 548654. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 4 q^{6}+O(q^{10}) \) 136 * q - 4 * q^6	\( 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) \) 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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