LMFDB - Embedded newform 59.7.b.c.58.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [59,7,Mod(58,59)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(59, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("59.58");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 59 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	59.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:	$13.5731909336$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.13
Character	$\chi$	$=$	59.58
Dual form			59.7.b.c.58.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.85246i q^{2} +13.0960 q^{3} +49.1585 q^{4} -100.422 q^{5} -50.4519i q^{6} -365.384 q^{7} -435.939i q^{8} -557.495 q^{9} +386.871i q^{10} +61.8507i q^{11} +643.780 q^{12} -4006.24i q^{13} +1407.63i q^{14} -1315.12 q^{15} +1466.71 q^{16} -670.367 q^{17} +2147.73i q^{18} -4252.09 q^{19} -4936.59 q^{20} -4785.07 q^{21} +238.277 q^{22} -6238.59i q^{23} -5709.06i q^{24} -5540.46 q^{25} -15433.9 q^{26} -16847.9 q^{27} -17961.8 q^{28} -741.535 q^{29} +5066.47i q^{30} +49303.7i q^{31} -33550.5i q^{32} +809.997i q^{33} +2582.56i q^{34} +36692.6 q^{35} -27405.6 q^{36} -58183.7i q^{37} +16381.0i q^{38} -52465.7i q^{39} +43777.8i q^{40} +67462.6 q^{41} +18434.3i q^{42} +40630.5i q^{43} +3040.49i q^{44} +55984.6 q^{45} -24033.9 q^{46} -19917.3i q^{47} +19208.0 q^{48} +15856.6 q^{49} +21344.4i q^{50} -8779.13 q^{51} -196941. i q^{52} +164402. q^{53} +64906.1i q^{54} -6211.16i q^{55} +159285. i q^{56} -55685.4 q^{57} +2856.73i q^{58} +(197780. - 55351.3i) q^{59} -64649.6 q^{60} +101054. i q^{61} +189941. q^{62} +203700. q^{63} -35382.9 q^{64} +402314. i q^{65} +3120.48 q^{66} -120981. i q^{67} -32954.3 q^{68} -81700.6i q^{69} -141357. i q^{70} +43899.5 q^{71} +243034. i q^{72} +49458.8i q^{73} -224150. q^{74} -72557.8 q^{75} -209026. q^{76} -22599.3i q^{77} -202122. q^{78} -658281. q^{79} -147289. q^{80} +185773. q^{81} -259897. i q^{82} -930063. i q^{83} -235227. q^{84} +67319.5 q^{85} +156528. q^{86} -9711.14 q^{87} +26963.1 q^{88} -383075. i q^{89} -215679. i q^{90} +1.46382e6i q^{91} -306680. i q^{92} +645682. i q^{93} -76730.8 q^{94} +427002. q^{95} -439378. i q^{96} +379358. i q^{97} -61087.1i q^{98} -34481.4i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 10 q^{3} - 1090 q^{4} + 142 q^{5} + 406 q^{7} + 5432 q^{9} - 1124 q^{12} + 14982 q^{15} + 12734 q^{16} - 9108 q^{17} + 3850 q^{19} - 46896 q^{20} - 49034 q^{21} + 11238 q^{22} + 18792 q^{25} - 64590 q^{26}+ \cdots - 2396490 q^{95}+O(q^{100}) $ 26 * q + 10 * q^3 - 1090 * q^4 + 142 * q^5 + 406 * q^7 + 5432 * q^9 - 1124 * q^12 + 14982 * q^15 + 12734 * q^16 - 9108 * q^17 + 3850 * q^19 - 46896 * q^20 - 49034 * q^21 + 11238 * q^22 + 18792 * q^25 - 64590 * q^26 + 3550 * q^27 - 45542 * q^28 - 31730 * q^29 + 163558 * q^35 - 325266 * q^36 + 91914 * q^41 + 736396 * q^45 + 287148 * q^46 + 479572 * q^48 - 462900 * q^49 + 329932 * q^51 + 8238 * q^53 - 187506 * q^57 + 326182 * q^59 - 970064 * q^60 + 630140 * q^62 + 630508 * q^63 - 1800262 * q^64 - 869200 * q^66 - 319586 * q^68 + 1763840 * q^71 - 2294090 * q^74 + 354736 * q^75 + 247144 * q^76 - 375064 * q^78 + 4702 * q^79 + 1920984 * q^80 - 2435946 * q^81 - 1007672 * q^84 + 864044 * q^85 + 5031110 * q^86 - 1519202 * q^87 + 725994 * q^88 + 2835768 * q^94 - 2396490 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/59\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	3.85246i		−	0.481558i	−0.970580	−	0.240779i	$-0.922597\pi$
$2$		−	3.85246i		−	0.481558i	0.970580	−	0.240779i	$-0.0774029\pi$
$3$	13.0960			0.485037			0.242519	−	0.970147i	$-0.422026\pi$
$3$	13.0960			0.485037			0.242519	+	0.970147i	$0.422026\pi$
$4$	49.1585			0.768102
$5$	−100.422			−0.803375			−0.401687	−	0.915777i	$-0.631576\pi$
$5$	−100.422			−0.803375			−0.401687	+	0.915777i	$0.631576\pi$
$6$		−	50.4519i		−	0.233573i
$7$	−365.384			−1.06526			−0.532630	−	0.846348i	$-0.678796\pi$
$7$	−365.384			−1.06526			−0.532630	+	0.846348i	$0.678796\pi$
$8$		−	435.939i		−	0.851443i
$9$	−557.495			−0.764739
$10$			386.871i			0.386871i
$11$			61.8507i			0.0464693i	0.999730	+	0.0232347i	$0.00739649\pi$
$11$			61.8507i			0.0464693i	−0.999730	+	0.0232347i	$0.992604\pi$
$12$	643.780			0.372558
$13$		−	4006.24i		−	1.82350i	−0.410742	−	0.911752i	$-0.634730\pi$
$13$		−	4006.24i		−	1.82350i	0.410742	−	0.911752i	$-0.365270\pi$
$14$			1407.63i			0.512984i
$15$	−1315.12			−0.389667
$16$	1466.71			0.358083
$17$	−670.367			−0.136448			−0.0682238	−	0.997670i	$-0.521733\pi$
$17$	−670.367			−0.136448			−0.0682238	+	0.997670i	$0.521733\pi$
$18$			2147.73i			0.368266i
$19$	−4252.09			−0.619928			−0.309964	−	0.950748i	$-0.600317\pi$
$19$	−4252.09			−0.619928			−0.309964	+	0.950748i	$0.600317\pi$
$20$	−4936.59			−0.617074
$21$	−4785.07			−0.516691
$22$	238.277			0.0223777
$23$		−	6238.59i		−	0.512747i	−0.966578	−	0.256373i	$-0.917472\pi$
$23$		−	6238.59i		−	0.512747i	0.966578	−	0.256373i	$-0.0825277\pi$
$24$		−	5709.06i		−	0.412982i
$25$	−5540.46			−0.354589
$26$	−15433.9			−0.878122
$27$	−16847.9			−0.855964
$28$	−17961.8			−0.818229
$29$	−741.535			−0.0304045			−0.0152022	−	0.999884i	$-0.504839\pi$
$29$	−741.535			−0.0304045			−0.0152022	+	0.999884i	$0.504839\pi$
$30$			5066.47i			0.187647i
$31$			49303.7i			1.65499i	0.561476	+	0.827493i	$0.310234\pi$
$31$			49303.7i			1.65499i	−0.561476	+	0.827493i	$0.689766\pi$
$32$		−	33550.5i		−	1.02388i
$33$			809.997i			0.0225394i
$34$			2582.56i			0.0657074i
$35$	36692.6			0.855803
$36$	−27405.6			−0.587398
$37$		−	58183.7i		−	1.14867i	−0.818620	−	0.574336i	$-0.805260\pi$
$37$		−	58183.7i		−	1.14867i	0.818620	−	0.574336i	$-0.194740\pi$
$38$			16381.0i			0.298531i
$39$		−	52465.7i		−	0.884467i
$40$			43777.8i			0.684028i
$41$	67462.6			0.978840			0.489420	−	0.872048i	$-0.337208\pi$
$41$	67462.6			0.978840			0.489420	+	0.872048i	$0.337208\pi$
$42$			18434.3i			0.248816i
$43$			40630.5i			0.511031i	0.966805	+	0.255515i	$0.0822451\pi$
$43$			40630.5i			0.511031i	−0.966805	+	0.255515i	$0.917755\pi$
$44$			3040.49i			0.0356932i
$45$	55984.6			0.614372
$46$	−24033.9			−0.246917
$47$		−	19917.3i		−	0.191839i	−0.995389	−	0.0959197i	$-0.969421\pi$
$47$		−	19917.3i		−	0.191839i	0.995389	−	0.0959197i	$-0.0305792\pi$
$48$	19208.0			0.173684
$49$	15856.6			0.134779
$50$			21344.4i			0.170755i
$51$	−8779.13			−0.0661822
$52$		−	196941.i		−	1.40064i
$53$	164402.			1.10428			0.552142	−	0.833750i	$-0.313811\pi$
$53$	164402.			1.10428			0.552142	+	0.833750i	$0.313811\pi$
$54$			64906.1i			0.412196i
$55$		−	6211.16i		−	0.0373323i
$56$			159285.i			0.907009i
$57$	−55685.4			−0.300688
$58$			2856.73i			0.0146415i
$59$	197780.	−	55351.3i	0.962998	−	0.269508i
$59$	197780.	−	55351.3i	0.962998	−	0.269508i
$60$	−64649.6			−0.299304
$61$			101054.i			0.445208i	0.974909	+	0.222604i	$0.0714558\pi$
$61$			101054.i			0.445208i	−0.974909	+	0.222604i	$0.928544\pi$
$62$	189941.			0.796972
$63$	203700.			0.814646
$64$	−35382.9			−0.134975
$65$			402314.i			1.46496i
$66$	3120.48			0.0108540
$67$		−	120981.i		−	0.402247i	−0.979566	−	0.201124i	$-0.935541\pi$
$67$		−	120981.i		−	0.402247i	0.979566	−	0.201124i	$-0.0644593\pi$
$68$	−32954.3			−0.104806
$69$		−	81700.6i		−	0.248701i
$70$		−	141357.i		−	0.412119i
$71$	43899.5			0.122655			0.0613274	−	0.998118i	$-0.480467\pi$
$71$	43899.5			0.122655			0.0613274	+	0.998118i	$0.480467\pi$
$72$			243034.i			0.651132i
$73$			49458.8i			0.127138i	0.997977	+	0.0635690i	$0.0202483\pi$
$73$			49458.8i			0.127138i	−0.997977	+	0.0635690i	$0.979752\pi$
$74$	−224150.			−0.553152
$75$	−72557.8			−0.171989
$76$	−209026.			−0.476168
$77$		−	22599.3i		−	0.0495019i
$78$	−202122.			−0.425922
$79$	−658281.			−1.33515			−0.667575	−	0.744542i	$-0.732668\pi$
$79$	−658281.			−1.33515			−0.667575	+	0.744542i	$0.732668\pi$
$80$	−147289.			−0.287675
$81$	185773.			0.349565
$82$		−	259897.i		−	0.471368i
$83$		−	930063.i		−	1.62659i	−0.581851	−	0.813295i	$-0.697671\pi$
$83$		−	930063.i		−	1.62659i	0.581851	−	0.813295i	$-0.302329\pi$
$84$	−235227.			−0.396871
$85$	67319.5			0.109619
$86$	156528.			0.246091
$87$	−9711.14			−0.0147473
$88$	26963.1			0.0395660
$89$		−	383075.i		−	0.543393i	−0.962383	−	0.271697i	$-0.912415\pi$
$89$		−	383075.i		−	0.543393i	0.962383	−	0.271697i	$-0.0875847\pi$
$90$		−	215679.i		−	0.295856i
$91$			1.46382e6i			1.94251i
$92$		−	306680.i		−	0.393842i
$93$			645682.i			0.802730i
$94$	−76730.8			−0.0923817
$95$	427002.			0.498035
$96$		−	439378.i		−	0.496620i
$97$			379358.i			0.415655i	0.978165	+	0.207828i	$0.0666393\pi$
$97$			379358.i			0.415655i	−0.978165	+	0.207828i	$0.933361\pi$
$98$		−	61087.1i		−	0.0649040i
$99$		−	34481.4i		−	0.0355369i
$100$	−272361.			−0.272361
$101$		−	1.80479e6i		−	1.75171i	−0.482576	−	0.875854i	$-0.660299\pi$
$101$		−	1.80479e6i		−	1.75171i	0.482576	−	0.875854i	$-0.339701\pi$
$102$			33821.3i			0.0318705i
$103$			715784.i			0.655043i	0.944844	+	0.327522i	$0.106213\pi$
$103$			715784.i			0.655043i	−0.944844	+	0.327522i	$0.893787\pi$
$104$	−1.74647e6			−1.55261
$105$	480526.			0.415096
$106$		−	633354.i		−	0.531776i
$107$	−863588.			−0.704945			−0.352473	−	0.935822i	$-0.614659\pi$
$107$	−863588.			−0.704945			−0.352473	+	0.935822i	$0.614659\pi$
$108$	−828220.			−0.657468
$109$		−	2.03282e6i		−	1.56971i	−0.619681	−	0.784854i	$-0.712738\pi$
$109$		−	2.03282e6i		−	1.56971i	0.619681	−	0.784854i	$-0.287262\pi$
$110$	−23928.3			−0.0179777
$111$		−	761973.i		−	0.557148i
$112$	−535912.			−0.381452
$113$			2.15310e6i			1.49221i	0.665829	+	0.746104i	$0.268078\pi$
$113$			2.15310e6i			1.49221i	−0.665829	+	0.746104i	$0.731922\pi$
$114$			214526.i			0.144799i
$115$			626491.i			0.411928i
$116$	−36452.8			−0.0233537
$117$			2.23346e6i			1.39450i
$118$	−213239.	−	761938.i	−0.129784	−	0.463739i
$119$	244942.			0.145352
$120$			573314.i			0.331779i
$121$	1.76774e6			0.997841
$122$	389306.			0.214394
$123$	883491.			0.474774
$124$			2.42370e6i			1.27120i
$125$	2.12547e6			1.08824
$126$		−	784746.i		−	0.392299i
$127$	1.41290e6			0.689764			0.344882	−	0.938646i	$-0.387919\pi$
$127$	1.41290e6			0.689764			0.344882	+	0.938646i	$0.387919\pi$
$128$		−	2.01092e6i		−	0.958883i
$129$			532097.i			0.247869i
$130$	1.54990e6			0.705461
$131$			1.54310e6i			0.686407i	0.939261	+	0.343203i	$0.111512\pi$
$131$			1.54310e6i			0.686407i	−0.939261	+	0.343203i	$0.888488\pi$
$132$			39818.3i			0.0173125i
$133$	1.55365e6			0.660385
$134$	−466075.			−0.193705
$135$	1.69190e6			0.687660
$136$			292239.i			0.116177i
$137$	1.60884e6			0.625678			0.312839	−	0.949806i	$-0.398720\pi$
$137$	1.60884e6			0.625678			0.312839	+	0.949806i	$0.398720\pi$
$138$	−314748.			−0.119764
$139$	−3.53355e6			−1.31573			−0.657865	−	0.753136i	$-0.728540\pi$
$139$	−3.53355e6			−1.31573			−0.657865	+	0.753136i	$0.728540\pi$
$140$	1.80375e6			0.657344
$141$		−	260837.i		−	0.0930492i
$142$		−	169121.i		−	0.0590653i
$143$	247788.			0.0847370
$144$	−817682.			−0.273840
$145$	74466.3			0.0244262
$146$	190538.			0.0612242
$147$	207659.			0.0653729
$148$		−	2.86022e6i		−	0.882297i
$149$			2.56276e6i			0.774729i	0.921927	+	0.387364i	$0.126614\pi$
$149$			2.56276e6i			0.774729i	−0.921927	+	0.387364i	$0.873386\pi$
$150$			279526.i			0.0828226i
$151$			52811.7i			0.0153391i	0.999971	+	0.00766955i	$0.00244132\pi$
$151$			52811.7i			0.0153391i	−0.999971	+	0.00766955i	$0.997559\pi$
$152$			1.85365e6i			0.527834i
$153$	373726.			0.104347
$154$	−87062.8			−0.0238380
$155$		−	4.95117e6i		−	1.32957i
$156$		−	2.57914e6i		−	0.679361i
$157$		−	4.83449e6i		−	1.24926i	−0.780923	−	0.624628i	$-0.785251\pi$
$157$		−	4.83449e6i		−	1.24926i	0.780923	−	0.624628i	$-0.214749\pi$
$158$			2.53600e6i			0.642952i
$159$	2.15302e6			0.535619
$160$			3.36921e6i			0.822560i
$161$			2.27948e6i			0.546209i
$162$		−	715683.i		−	0.168336i
$163$	−5.54610e6			−1.28063			−0.640317	−	0.768111i	$-0.721197\pi$
$163$	−5.54610e6			−1.28063			−0.640317	+	0.768111i	$0.721197\pi$
$164$	3.31636e6			0.751849
$165$		−	81341.4i		−	0.0181075i
$166$	−3.58303e6			−0.783297
$167$	566652.			0.121665			0.0608326	−	0.998148i	$-0.480624\pi$
$167$	566652.			0.121665			0.0608326	+	0.998148i	$0.480624\pi$
$168$			2.08600e6i			0.439933i
$169$	−1.12231e7			−2.32516
$170$		−	259346.i		−	0.0527877i
$171$	2.37052e6			0.474083
$172$			1.99734e6i			0.392524i
$173$		−	5.16399e6i		−	0.997350i	−0.866789	−	0.498675i	$-0.833820\pi$
$173$		−	5.16399e6i		−	0.997350i	0.866789	−	0.498675i	$-0.166180\pi$
$174$			37411.8i			0.00710168i
$175$	2.02440e6			0.377730
$176$			90716.9i			0.0166399i
$177$	2.59012e6	−	724881.i	0.467090	−	0.130722i
$178$	−1.47578e6			−0.261675
$179$		−	6.59206e6i		−	1.14938i	−0.818373	−	0.574688i	$-0.805124\pi$
$179$		−	6.59206e6i		−	1.14938i	0.818373	−	0.574688i	$-0.194876\pi$
$180$	2.75212e6			0.471900
$181$	−1.00148e7			−1.68890			−0.844452	−	0.535631i	$-0.820074\pi$
$181$	−1.00148e7			−1.68890			−0.844452	+	0.535631i	$0.820074\pi$
$182$	5.63929e6			0.935428
$183$			1.32340e6i			0.215943i
$184$	−2.71964e6			−0.436575
$185$			5.84291e6i			0.922814i
$186$	2.48746e6			0.386561
$187$		−	41462.7i		−	0.00634063i
$188$		−	979107.i		−	0.147352i
$189$	6.15597e6			0.911824
$190$		−	1.64501e6i		−	0.239832i
$191$			5.95686e6i			0.854904i	0.904038	+	0.427452i	$0.140589\pi$
$191$			5.95686e6i			0.854904i	−0.904038	+	0.427452i	$0.859411\pi$
$192$	−463374.			−0.0654678
$193$	−9.07562e6			−1.26242			−0.631211	−	0.775611i	$-0.717442\pi$
$193$	−9.07562e6			−1.26242			−0.631211	+	0.775611i	$0.717442\pi$
$194$	1.46146e6			0.200162
$195$			5.26870e6i			0.710558i
$196$	779489.			0.103524
$197$	−1.05343e7			−1.37787			−0.688933	−	0.724825i	$-0.741921\pi$
$197$	−1.05343e7			−1.37787			−0.688933	+	0.724825i	$0.741921\pi$
$198$	−132838.			−0.0171131
$199$	−87774.8			−0.0111381			−0.00556904	−	0.999984i	$-0.501773\pi$
$199$	−87774.8			−0.0111381			−0.00556904	+	0.999984i	$0.501773\pi$
$200$			2.41530e6i			0.301913i
$201$		−	1.58437e6i		−	0.195105i
$202$	−6.95287e6			−0.843548
$203$	270945.			0.0323887
$204$	−431569.			−0.0508347
$205$	−6.77472e6			−0.786375
$206$	2.75753e6			0.315441
$207$			3.47798e6i			0.392117i
$208$		−	5.87598e6i		−	0.652965i
$209$		−	262995.i		−	0.0288077i
$210$		−	1.85121e6i		−	0.199893i
$211$		−	1.40276e7i		−	1.49326i	−0.665239	−	0.746630i	$-0.731670\pi$
$211$		−	1.40276e7i		−	1.49326i	0.665239	−	0.746630i	$-0.268330\pi$
$212$	8.08178e6			0.848203
$213$	574908.			0.0594921
$214$			3.32694e6i			0.339472i
$215$		−	4.08019e6i		−	0.410549i
$216$			7.34467e6i			0.728805i
$217$		−	1.80148e7i		−	1.76299i
$218$	−7.83135e6			−0.755905
$219$			647713.i			0.0616666i
$220$		−	305331.i		−	0.0286750i
$221$			2.68565e6i			0.248813i
$222$	−2.93547e6			−0.268299
$223$	7.40039e6			0.667329			0.333665	−	0.942692i	$-0.391715\pi$
$223$	7.40039e6			0.667329			0.333665	+	0.942692i	$0.391715\pi$
$224$			1.22588e7i			1.09070i
$225$	3.08877e6			0.271168
$226$	8.29475e6			0.718585
$227$			1.47756e7i			1.26319i	0.775300	+	0.631593i	$0.217599\pi$
$227$			1.47756e7i			1.26319i	−0.775300	+	0.631593i	$0.782401\pi$
$228$	−2.73741e6			−0.230959
$229$			8.53576e6i			0.710781i	0.934718	+	0.355390i	$0.115652\pi$
$229$			8.53576e6i			0.710781i	−0.934718	+	0.355390i	$0.884348\pi$
$230$	2.41353e6			0.198367
$231$		−	295960.i		−	0.0240103i
$232$			323264.i			0.0258877i
$233$		−	1.67507e7i		−	1.32423i	−0.749400	−	0.662117i	$-0.769658\pi$
$233$		−	1.67507e7i		−	1.32423i	0.749400	−	0.662117i	$-0.230342\pi$
$234$	8.60430e6			0.671534
$235$			2.00013e6i			0.154119i
$236$	9.72255e6	−	2.72099e6i	0.739681	−	0.207010i
$237$	−8.62086e6			−0.647598
$238$		−	943629.i		−	0.0699955i
$239$	1.52021e7			1.11355			0.556777	−	0.830662i	$-0.312038\pi$
$239$	1.52021e7			1.11355			0.556777	+	0.830662i	$0.312038\pi$
$240$	−1.92890e6			−0.139533
$241$	1.32876e7			0.949280			0.474640	−	0.880180i	$-0.342578\pi$
$241$	1.32876e7			0.949280			0.474640	+	0.880180i	$0.342578\pi$
$242$		−	6.81013e6i		−	0.480518i
$243$	1.47150e7			1.02552
$244$			4.96766e6i			0.341965i
$245$	−1.59235e6			−0.108278
$246$		−	3.40362e6i		−	0.228631i
$247$			1.70349e7i			1.13044i
$248$	2.14934e7			1.40913
$249$		−	1.21801e7i		−	0.788957i
$250$		−	8.18831e6i		−	0.524052i
$251$	−8.00471e6			−0.506203			−0.253101	−	0.967440i	$-0.581451\pi$
$251$	−8.00471e6			−0.506203			−0.253101	+	0.967440i	$0.581451\pi$
$252$	1.00136e7			0.625731
$253$	385861.			0.0238270
$254$		−	5.44314e6i		−	0.332161i
$255$	881617.			0.0531691
$256$	−1.00115e7			−0.596732
$257$	−2.13967e7			−1.26052			−0.630258	−	0.776386i	$-0.717051\pi$
$257$	−2.13967e7			−1.26052			−0.630258	+	0.776386i	$0.717051\pi$
$258$	2.04989e6			0.119363
$259$			2.12594e7i			1.22363i
$260$			1.97771e7i			1.12524i
$261$	413402.			0.0232515
$262$	5.94475e6			0.330544
$263$	1.61578e7			0.888210			0.444105	−	0.895975i	$-0.353522\pi$
$263$	1.61578e7			0.888210			0.444105	+	0.895975i	$0.353522\pi$
$264$	353109.			0.0191910
$265$	−1.65096e7			−0.887153
$266$		−	5.98536e6i		−	0.318013i
$267$		−	5.01676e6i		−	0.263566i
$268$		−	5.94725e6i		−	0.308967i
$269$			2.45278e7i			1.26009i	0.776557	+	0.630047i	$0.216964\pi$
$269$			2.45278e7i			1.26009i	−0.776557	+	0.630047i	$0.783036\pi$
$270$		−	6.51798e6i		−	0.331148i
$271$	9.86272e6			0.495551			0.247776	−	0.968817i	$-0.420300\pi$
$271$	9.86272e6			0.495551			0.247776	+	0.968817i	$0.420300\pi$
$272$	−983233.			−0.0488596
$273$			1.91701e7i			0.942187i
$274$		−	6.19799e6i		−	0.301300i
$275$		−	342681.i		−	0.0164775i
$276$		−	4.01628e6i		−	0.191028i
$277$	−8.09034e6			−0.380651			−0.190326	−	0.981721i	$-0.560954\pi$
$277$	−8.09034e6			−0.380651			−0.190326	+	0.981721i	$0.560954\pi$
$278$			1.36129e7i			0.633600i
$279$		−	2.74866e7i		−	1.26563i
$280$		−	1.59957e7i		−	0.728668i
$281$	−1.57261e7			−0.708763			−0.354381	−	0.935101i	$-0.615308\pi$
$281$	−1.57261e7			−0.708763			−0.354381	+	0.935101i	$0.615308\pi$
$282$	−1.00487e6			−0.0448086
$283$		−	5.75507e6i		−	0.253917i	−0.991908	−	0.126958i	$-0.959479\pi$
$283$		−	5.75507e6i		−	0.253917i	0.991908	−	0.126958i	$-0.0405215\pi$
$284$	2.15803e6			0.0942114
$285$	5.59203e6			0.241565
$286$		−	954596.i		−	0.0408058i
$287$	−2.46498e7			−1.04272
$288$			1.87042e7i			0.783002i
$289$	−2.36882e7			−0.981382
$290$		−	286879.i		−	0.0117626i
$291$			4.96807e6i			0.201608i
$292$			2.43132e6i			0.0976549i
$293$	3.69070e7			1.46726			0.733628	−	0.679551i	$-0.237825\pi$
$293$	3.69070e7			1.46726			0.733628	+	0.679551i	$0.237825\pi$
$294$		−	799997.i		−	0.0314809i
$295$	−1.98614e7	+	5.55848e6i	−0.773648	+	0.216516i
$296$	−2.53645e7			−0.978029
$297$		−	1.04206e6i		−	0.0397761i
$298$	9.87295e6			0.373077
$299$	−2.49933e7			−0.934995
$300$	−3.56684e6			−0.132105
$301$		−	1.48458e7i		−	0.544381i
$302$	203455.			0.00738666
$303$		−	2.36355e7i		−	0.849643i
$304$	−6.23657e6			−0.221986
$305$		−	1.01480e7i		−	0.357669i
$306$		−	1.43977e6i		−	0.0502490i
$307$	9.50053e6			0.328347			0.164173	−	0.986432i	$-0.447504\pi$
$307$	9.50053e6			0.328347			0.164173	+	0.986432i	$0.447504\pi$
$308$		−	1.11095e6i		−	0.0380225i
$309$			9.37391e6i			0.317720i
$310$	−1.90742e7			−0.640267
$311$	5.71200e7			1.89892			0.949461	−	0.313886i	$-0.101631\pi$
$311$	5.71200e7			1.89892			0.949461	+	0.313886i	$0.101631\pi$
$312$	−2.28718e7			−0.753073
$313$		−	8.44025e6i		−	0.275247i	−0.990485	−	0.137623i	$-0.956054\pi$
$313$		−	8.44025e6i		−	0.275247i	0.990485	−	0.137623i	$-0.0439464\pi$
$314$	−1.86247e7			−0.601589
$315$	−2.04559e7			−0.654466
$316$	−3.23602e7			−1.02553
$317$	4.24509e6			0.133263			0.0666315	−	0.997778i	$-0.478775\pi$
$317$	4.24509e6			0.133263			0.0666315	+	0.997778i	$0.478775\pi$
$318$		−	8.29441e6i		−	0.257931i
$319$		−	45864.4i		−	0.00141288i
$320$	3.55321e6			0.108435
$321$	−1.13096e7			−0.341925
$322$	8.78162e6			0.263031
$323$	2.85046e6			0.0845878
$324$	9.13232e6			0.268501
$325$			2.21964e7i			0.646595i
$326$			2.13662e7i			0.616699i
$327$		−	2.66218e7i		−	0.761367i
$328$		−	2.94096e7i		−	0.833427i
$329$			7.27748e6i			0.204359i
$330$	−313365.			−0.00871983
$331$	2.21198e7			0.609955			0.304977	−	0.952360i	$-0.401351\pi$
$331$	2.21198e7			0.609955			0.304977	+	0.952360i	$0.401351\pi$
$332$		−	4.57206e7i		−	1.24939i
$333$			3.24371e7i			0.878434i
$334$		−	2.18300e6i		−	0.0585889i
$335$			1.21491e7i			0.323155i
$336$	−7.01830e6			−0.185018
$337$		−	2.82265e7i		−	0.737508i	−0.929527	−	0.368754i	$-0.879784\pi$
$337$		−	2.82265e7i		−	0.737508i	0.929527	−	0.368754i	$-0.120216\pi$
$338$			4.32366e7i			1.11970i
$339$			2.81970e7i			0.723777i
$340$	3.30933e6			0.0841983
$341$	−3.04947e6			−0.0769061
$342$		−	9.13232e6i		−	0.228298i
$343$	3.71933e7			0.921685
$344$	1.77124e7			0.435114
$345$			8.20452e6i			0.199800i
$346$	−1.98941e7			−0.480281
$347$		−	6.72750e7i		−	1.61015i	−0.593176	−	0.805073i	$-0.702126\pi$
$347$		−	6.72750e7i		−	1.61015i	0.593176	−	0.805073i	$-0.297874\pi$
$348$	−477386.			−0.0113274
$349$		−	4.28546e7i		−	1.00814i	−0.863663	−	0.504070i	$-0.831835\pi$
$349$		−	4.28546e7i		−	1.00814i	0.863663	−	0.504070i	$-0.168165\pi$
$350$		−	7.79891e6i		−	0.181899i
$351$			6.74968e7i			1.56085i
$352$	2.07512e6			0.0475791
$353$		−	2.65945e7i		−	0.604599i	−0.953213	−	0.302300i	$-0.902246\pi$
$353$		−	2.65945e7i		−	0.604599i	0.953213	−	0.302300i	$-0.0977543\pi$
$354$	−2.79258e6	−	9.97835e6i	−0.0629500	−	0.224931i
$355$	−4.40847e6			−0.0985377
$356$		−	1.88314e7i		−	0.417381i
$357$	3.20776e6			0.0705013
$358$	−2.53957e7			−0.553491
$359$	1.72238e7			0.372259			0.186130	−	0.982525i	$-0.440406\pi$
$359$	1.72238e7			0.372259			0.186130	+	0.982525i	$0.440406\pi$
$360$		−	2.44059e7i		−	0.523103i
$361$	−2.89656e7			−0.615689
$362$			3.85815e7i			0.813305i
$363$	2.31503e7			0.483990
$364$			7.19590e7i			1.49204i
$365$		−	4.96674e6i		−	0.102139i
$366$	5.09835e6			0.103989
$367$			9.01317e7i			1.82339i	0.410868	+	0.911695i	$0.365226\pi$
$367$			9.01317e7i			1.82339i	−0.410868	+	0.911695i	$0.634774\pi$
$368$		−	9.15019e6i		−	0.183606i
$369$	−3.76101e7			−0.748557
$370$	2.25096e7			0.444388
$371$	−6.00701e7			−1.17635
$372$			3.17408e7i			0.616579i
$373$	1.01073e7			0.194764			0.0973821	−	0.995247i	$-0.468953\pi$
$373$	1.01073e7			0.194764			0.0973821	+	0.995247i	$0.468953\pi$
$374$	−159733.			−0.00305338
$375$	2.78352e7			0.527838
$376$	−8.68274e6			−0.163340
$377$			2.97076e6i			0.0554427i
$378$		−	2.37156e7i		−	0.439096i
$379$	1.03143e7			0.189462			0.0947309	−	0.995503i	$-0.469801\pi$
$379$	1.03143e7			0.189462			0.0947309	+	0.995503i	$0.469801\pi$
$380$	2.09908e7			0.382541
$381$	1.85033e7			0.334561
$382$	2.29486e7			0.411686
$383$	7.40568e7			1.31816			0.659081	−	0.752072i	$-0.270946\pi$
$383$	7.40568e7			1.31816			0.659081	+	0.752072i	$0.270946\pi$
$384$		−	2.63351e7i		−	0.465094i
$385$			2.26946e6i			0.0397686i
$386$			3.49635e7i			0.607929i
$387$		−	2.26513e7i		−	0.390805i
$388$			1.86487e7i			0.319266i
$389$	3.85680e7			0.655207			0.327603	−	0.944815i	$-0.393759\pi$
$389$	3.85680e7			0.655207			0.327603	+	0.944815i	$0.393759\pi$
$390$	2.02975e7			0.342175
$391$			4.18215e6i			0.0699631i
$392$		−	6.91253e6i		−	0.114757i
$393$			2.02085e7i			0.332933i
$394$			4.05830e7i			0.663522i
$395$	6.61058e7			1.07263
$396$		−	1.69506e6i		−	0.0272960i
$397$		−	4.94217e7i		−	0.789852i	−0.918713	−	0.394926i	$-0.870770\pi$
$397$		−	4.94217e7i		−	0.789852i	0.918713	−	0.394926i	$-0.129230\pi$
$398$			338149.i			0.00536363i
$399$	2.03466e7			0.320311
$400$	−8.12623e6			−0.126972
$401$		−	6.59077e7i		−	1.02212i	−0.859544	−	0.511061i	$-0.829252\pi$
$401$		−	6.59077e7i		−	1.02212i	0.859544	−	0.511061i	$-0.170748\pi$
$402$	−6.10372e6			−0.0939543
$403$	1.97522e8			3.01787
$404$		−	8.87206e7i		−	1.34549i
$405$	−1.86557e7			−0.280831
$406$		−	1.04381e6i		−	0.0155970i
$407$	3.59870e6			0.0533780
$408$			3.82717e6i			0.0563504i
$409$			7.62298e7i			1.11418i	0.830453	+	0.557089i	$0.188082\pi$
$409$			7.62298e7i			1.11418i	−0.830453	+	0.557089i	$0.811918\pi$
$410$			2.60994e7i			0.378685i
$411$	2.10693e7			0.303477
$412$			3.51869e7i			0.503140i
$413$	−7.22655e7	+	2.02245e7i	−1.02584	+	0.287096i
$414$	1.33988e7			0.188827
$415$			9.33987e7i			1.30676i
$416$	−1.34411e8			−1.86705
$417$	−4.62754e7			−0.638178
$418$	−1.01318e6			−0.0138726
$419$			1.12782e8i			1.53320i	0.642127	+	0.766598i	$0.278052\pi$
$419$			1.12782e8i			1.53320i	−0.642127	+	0.766598i	$0.721948\pi$
$420$	2.36219e7			0.318836
$421$		−	1.34931e8i		−	1.80828i	−0.427235	−	0.904140i	$-0.640512\pi$
$421$		−	1.34931e8i		−	1.80828i	0.427235	−	0.904140i	$-0.359488\pi$
$422$	−5.40408e7			−0.719091
$423$			1.11038e7i			0.146707i
$424$		−	7.16694e7i		−	0.940235i
$425$	3.71414e6			0.0483829
$426$		−	2.21481e6i		−	0.0286489i
$427$		−	3.69235e7i		−	0.474263i
$428$	−4.24527e7			−0.541470
$429$	3.24504e6			0.0411006
$430$	−1.57188e7			−0.197703
$431$		−	9.09928e7i		−	1.13652i	−0.822851	−	0.568258i	$-0.807618\pi$
$431$		−	9.09928e7i		−	1.13652i	0.822851	−	0.568258i	$-0.192382\pi$
$432$	−2.47110e7			−0.306506
$433$	−6.71992e7			−0.827753			−0.413876	−	0.910333i	$-0.635825\pi$
$433$	−6.71992e7			−0.827753			−0.413876	+	0.910333i	$0.635825\pi$
$434$	−6.94013e7			−0.848982
$435$	975211.			0.0118476
$436$		−	9.99303e7i		−	1.20570i
$437$			2.65270e7i			0.317866i
$438$	2.49529e6			0.0296960
$439$	5.45084e7			0.644273			0.322136	−	0.946693i	$-0.395599\pi$
$439$	5.45084e7			0.644273			0.322136	+	0.946693i	$0.395599\pi$
$440$	−2.70769e6			−0.0317863
$441$	−8.83999e6			−0.103071
$442$	1.03464e7			0.119818
$443$		−	4.88666e7i		−	0.562083i	−0.959696	−	0.281042i	$-0.909320\pi$
$443$		−	4.88666e7i		−	0.562083i	0.959696	−	0.281042i	$-0.0906799\pi$
$444$		−	3.74575e7i		−	0.427947i
$445$			3.84691e7i			0.436548i
$446$		−	2.85097e7i		−	0.321358i
$447$			3.35620e7i			0.375772i
$448$	1.29283e7			0.143783
$449$	−7.09118e7			−0.783392			−0.391696	−	0.920095i	$-0.628112\pi$
$449$	−7.09118e7			−0.783392			−0.391696	+	0.920095i	$0.628112\pi$
$450$		−	1.18994e7i		−	0.130583i
$451$			4.17261e6i			0.0454861i
$452$			1.05843e8i			1.14617i
$453$			691623.i			0.00744003i
$454$	5.69224e7			0.608297
$455$		−	1.46999e8i		−	1.56056i
$456$			2.42754e7i			0.256019i
$457$			4.96671e7i			0.520380i	0.965557	+	0.260190i	$0.0837852\pi$
$457$			4.96671e7i			0.520380i	−0.965557	+	0.260190i	$0.916215\pi$
$458$	3.28837e7			0.342282
$459$	1.12943e7			0.116794
$460$			3.07974e7i			0.316403i
$461$	−8.74372e6			−0.0892469			−0.0446235	−	0.999004i	$-0.514209\pi$
$461$	−8.74372e6			−0.0892469			−0.0446235	+	0.999004i	$0.514209\pi$
$462$	−1.14018e6			−0.0115623
$463$		−	1.83059e6i		−	0.0184437i	−0.999957	−	0.00922183i	$-0.997065\pi$
$463$		−	1.83059e6i		−	0.0184437i	0.999957	−	0.00922183i	$-0.00293544\pi$
$464$	−1.08761e6			−0.0108873
$465$		−	6.48405e7i		−	0.644893i
$466$	−6.45314e7			−0.637695
$467$			1.14057e8i			1.11988i	0.828532	+	0.559942i	$0.189177\pi$
$467$			1.14057e8i			1.11988i	−0.828532	+	0.559942i	$0.810823\pi$
$468$			1.09793e8i			1.07112i
$469$			4.42046e7i			0.428498i
$470$	7.70544e6			0.0742171
$471$		−	6.33124e7i		−	0.605935i
$472$	−2.41298e7	−	8.62198e7i	−0.229471	−	0.819938i
$473$	−2.51303e6			−0.0237473
$474$			3.32115e7i			0.311856i
$475$	2.35585e7			0.219820
$476$	1.20410e7			0.111645
$477$	−9.16535e7			−0.844489
$478$		−	5.85657e7i		−	0.536240i
$479$	−1.20850e8			−1.09961			−0.549806	−	0.835293i	$-0.685298\pi$
$479$	−1.20850e8			−1.09961			−0.549806	+	0.835293i	$0.685298\pi$
$480$			4.41231e7i			0.398972i
$481$	−2.33097e8			−2.09461
$482$		−	5.11898e7i		−	0.457133i
$483$			2.98521e7i			0.264932i
$484$	8.68993e7			0.766443
$485$		−	3.80958e7i		−	0.333927i
$486$		−	5.66891e7i		−	0.493845i
$487$	2.47607e7			0.214376			0.107188	−	0.994239i	$-0.465815\pi$
$487$	2.47607e7			0.214376			0.107188	+	0.994239i	$0.465815\pi$
$488$	4.40533e7			0.379070
$489$	−7.26318e7			−0.621155
$490$			6.13448e6i			0.0521422i
$491$	−1.03559e8			−0.874873			−0.437436	−	0.899249i	$-0.644113\pi$
$491$	−1.03559e8			−0.874873			−0.437436	+	0.899249i	$0.644113\pi$
$492$	4.34311e7			0.364675
$493$	497101.			0.00414862
$494$	6.56262e7			0.544373
$495$			3.46269e6i			0.0285495i
$496$			7.23141e7i			0.592623i
$497$	−1.60402e7			−0.130659
$498$	−4.69234e7			−0.379928
$499$	−1.56611e7			−0.126043			−0.0630217	−	0.998012i	$-0.520074\pi$
$499$	−1.56611e7			−0.126043			−0.0630217	+	0.998012i	$0.520074\pi$
$500$	1.04485e8			0.835881
$501$	7.42087e6			0.0590122
$502$			3.08378e7i			0.243766i
$503$			1.00136e8i			0.786839i	0.919359	+	0.393419i	$0.128708\pi$
$503$			1.00136e8i			0.786839i	−0.919359	+	0.393419i	$0.871292\pi$
$504$		−	8.88007e7i		−	0.693625i
$505$			1.81240e8i			1.40728i
$506$		−	1.48652e6i		−	0.0114741i
$507$	−1.46978e8			−1.12779
$508$	6.94561e7			0.529809
$509$		−	8.35577e6i		−	0.0633626i	−0.999498	−	0.0316813i	$-0.989914\pi$
$509$		−	8.35577e6i		−	0.0633626i	0.999498	−	0.0316813i	$-0.0100862\pi$
$510$		−	3.39639e6i		−	0.0256040i
$511$		−	1.80715e7i		−	0.135435i
$512$		−	9.01301e7i		−	0.671522i
$513$	7.16389e7			0.530636
$514$			8.24301e7i			0.607011i
$515$		−	7.18803e7i		−	0.526245i
$516$			2.61571e7i			0.190389i
$517$	1.23190e6			0.00891465
$518$	8.19010e7			0.589251
$519$		−	6.76277e7i		−	0.483752i
$520$	1.75384e8			1.24733
$521$	−1.01557e8			−0.718120			−0.359060	−	0.933314i	$-0.616903\pi$
$521$	−1.01557e8			−0.718120			−0.359060	+	0.933314i	$0.616903\pi$
$522$		−	1.59261e6i		−	0.0111969i
$523$	1.66508e8			1.16394			0.581970	−	0.813210i	$-0.302282\pi$
$523$	1.66508e8			1.16394			0.581970	+	0.813210i	$0.302282\pi$
$524$			7.58568e7i			0.527230i
$525$	2.65115e7			0.183213
$526$		−	6.22474e7i		−	0.427724i
$527$		−	3.30516e7i		−	0.225819i
$528$			1.18803e6i			0.00807096i
$529$	1.09116e8			0.737091
$530$			6.36026e7i			0.427216i
$531$	−1.10261e8	+	3.08581e7i	−0.736442	+	0.206103i
$532$	7.63750e7			0.507243
$533$		−	2.70271e8i		−	1.78492i
$534$	−1.93269e7			−0.126922
$535$	8.67231e7			0.566335
$536$	−5.27404e7			−0.342491
$537$		−	8.63296e7i		−	0.557490i
$538$	9.44926e7			0.606808
$539$			980744.i			0.00626310i
$540$	8.31714e7			0.528193
$541$			1.87749e8i			1.18573i	0.805301	+	0.592866i	$0.202004\pi$
$541$			1.87749e8i			1.18573i	−0.805301	+	0.592866i	$0.797996\pi$
$542$		−	3.79957e7i		−	0.238637i
$543$	−1.31153e8			−0.819182
$544$			2.24912e7i			0.139706i
$545$			2.04139e8i			1.26106i
$546$	7.38522e7			0.453718
$547$	−9.98669e6			−0.0610182			−0.0305091	−	0.999534i	$-0.509713\pi$
$547$	−9.98669e6			−0.0610182			−0.0305091	+	0.999534i	$0.509713\pi$
$548$	7.90881e7			0.480584
$549$		−	5.63370e7i		−	0.340468i
$550$	−1.32017e6			−0.00793488
$551$	3.15307e6			0.0188486
$552$	−3.56165e7			−0.211755
$553$	2.40526e8			1.42228
$554$			3.11677e7i			0.183306i
$555$			7.65188e7i			0.447599i
$556$	−1.73704e8			−1.01062
$557$	2.02606e8			1.17243			0.586214	−	0.810156i	$-0.300618\pi$
$557$	2.02606e8			1.17243			0.586214	+	0.810156i	$0.300618\pi$
$558$	−1.05891e8			−0.609475
$559$	1.62775e8			0.931866
$560$	5.38173e7			0.306448
$561$		−	542995.i		−	0.00307544i
$562$			6.05840e7i			0.341310i
$563$			1.46234e8i			0.819454i	0.912208	+	0.409727i	$0.134376\pi$
$563$			1.46234e8i			0.819454i	−0.912208	+	0.409727i	$0.865624\pi$
$564$		−	1.28224e7i		−	0.0714713i
$565$		−	2.16219e8i		−	1.19880i
$566$	−2.21712e7			−0.122276
$567$	−6.78785e7			−0.372377
$568$		−	1.91375e7i		−	0.104434i
$569$		−	2.76599e8i		−	1.50146i	−0.660608	−	0.750731i	$-0.729701\pi$
$569$		−	2.76599e8i		−	1.50146i	0.660608	−	0.750731i	$-0.270299\pi$
$570$		−	2.15431e7i		−	0.116328i
$571$		−	6.30200e7i		−	0.338509i	−0.985572	−	0.169255i	$-0.945864\pi$
$571$		−	6.30200e7i		−	0.338509i	0.985572	−	0.169255i	$-0.0541360\pi$
$572$	1.21809e7			0.0650867
$573$			7.80111e7i			0.414660i
$574$			9.49624e7i			0.502130i
$575$			3.45646e7i			0.181814i
$576$	1.97258e7			0.103221
$577$	1.74799e8			0.909935			0.454968	−	0.890508i	$-0.349651\pi$
$577$	1.74799e8			0.909935			0.454968	+	0.890508i	$0.349651\pi$
$578$			9.12578e7i			0.472592i
$579$	−1.18854e8			−0.612321
$580$	3.66065e6			0.0187618
$581$			3.39830e8i			1.73274i
$582$	1.91393e7			0.0970861
$583$			1.01684e7i			0.0513153i
$584$	2.15610e7			0.108251
$585$		−	2.24288e8i		−	1.12031i
$586$		−	1.42183e8i		−	0.706569i
$587$		−	2.17853e8i		−	1.07708i	−0.842599	−	0.538541i	$-0.818976\pi$
$587$		−	2.17853e8i		−	1.07708i	0.842599	−	0.538541i	$-0.181024\pi$
$588$	1.02082e7			0.0502131
$589$		−	2.09644e8i		−	1.02597i
$590$	2.14138e7	+	7.65152e7i	0.104265	+	0.372556i
$591$	−1.37957e8			−0.668317
$592$		−	8.53384e7i		−	0.411320i
$593$	7.86680e7			0.377254			0.188627	−	0.982049i	$-0.439596\pi$
$593$	7.86680e7			0.377254			0.188627	+	0.982049i	$0.439596\pi$
$594$	−4.01448e6			−0.0191545
$595$	−2.45975e7			−0.116772
$596$			1.25982e8i			0.595071i
$597$	−1.14950e6			−0.00540239
$598$			9.62856e7i			0.450254i
$599$	−2.90673e8			−1.35246			−0.676230	−	0.736691i	$-0.736387\pi$
$599$	−2.90673e8			−1.35246			−0.676230	+	0.736691i	$0.736387\pi$
$600$			3.16308e7i			0.146439i
$601$			1.60588e8i			0.739757i	0.929080	+	0.369879i	$0.120601\pi$
$601$			1.60588e8i			0.739757i	−0.929080	+	0.369879i	$0.879399\pi$
$602$	−5.71927e7			−0.262151
$603$			6.74463e7i			0.307614i
$604$			2.59615e6i			0.0117820i
$605$	−1.77519e8			−0.801640
$606$	−9.10548e7			−0.409152
$607$	2.16250e8			0.966917			0.483459	−	0.875367i	$-0.339380\pi$
$607$	2.16250e8			0.966917			0.483459	+	0.875367i	$0.339380\pi$
$608$			1.42660e8i			0.634733i
$609$	3.54830e6			0.0157097
$610$	−3.90948e7			−0.172238
$611$	−7.97935e7			−0.349820
$612$	1.83718e7			0.0801490
$613$			2.74279e8i			1.19072i	0.803458	+	0.595362i	$0.202991\pi$
$613$			2.74279e8i			1.19072i	−0.803458	+	0.595362i	$0.797009\pi$
$614$		−	3.66004e7i		−	0.158118i
$615$	−8.87218e7			−0.381421
$616$	−9.85190e6			−0.0421481
$617$	2.96247e7			0.126124			0.0630621	−	0.998010i	$-0.479913\pi$
$617$	2.96247e7			0.126124			0.0630621	+	0.998010i	$0.479913\pi$
$618$	3.61126e7			0.153001
$619$	−8.18362e7			−0.345043			−0.172522	−	0.985006i	$-0.555191\pi$
$619$	−8.18362e7			−0.345043			−0.172522	+	0.985006i	$0.555191\pi$
$620$		−	2.43392e8i		−	1.02125i
$621$			1.05107e8i			0.438893i
$622$		−	2.20053e8i		−	0.914440i
$623$			1.39970e8i			0.578855i
$624$		−	7.69518e7i		−	0.316712i
$625$	−1.26874e8			−0.519677
$626$	−3.25158e7			−0.132547
$627$		−	3.44418e6i		−	0.0139728i
$628$		−	2.37656e8i		−	0.959556i
$629$			3.90044e7i			0.156734i
$630$			7.88056e7i			0.315163i
$631$	8.79839e6			0.0350199			0.0175100	−	0.999847i	$-0.494426\pi$
$631$	8.79839e6			0.0350199			0.0175100	+	0.999847i	$0.494426\pi$
$632$			2.86971e8i			1.13681i
$633$		−	1.83705e8i		−	0.724287i
$634$		−	1.63541e7i		−	0.0641738i
$635$	−1.41886e8			−0.554138
$636$	1.05839e8			0.411410
$637$		−	6.35255e7i		−	0.245770i
$638$	−176691.			−0.000680381
$639$	−2.44737e7			−0.0937989
$640$			2.01941e8i			0.770342i
$641$	1.15671e8			0.439186			0.219593	−	0.975592i	$-0.429527\pi$
$641$	1.15671e8			0.439186			0.219593	+	0.975592i	$0.429527\pi$
$642$			4.35696e7i			0.164656i
$643$	4.96348e8			1.86704			0.933519	−	0.358528i	$-0.116721\pi$
$643$	4.96348e8			1.86704			0.933519	+	0.358528i	$0.116721\pi$
$644$			1.12056e8i			0.419544i
$645$		−	5.34342e7i		−	0.199132i
$646$		−	1.09813e7i		−	0.0407339i
$647$	−2.68052e8			−0.989706			−0.494853	−	0.868977i	$-0.664778\pi$
$647$	−2.68052e8			−0.989706			−0.494853	+	0.868977i	$0.664778\pi$
$648$		−	8.09857e7i		−	0.297634i
$649$	3.42352e6	+	1.22328e7i	0.0125239	+	0.0447499i
$650$	8.55107e7			0.311373
$651$		−	2.35922e8i		−	0.855116i
$652$	−2.72638e8			−0.983658
$653$	9.83343e7			0.353155			0.176578	−	0.984287i	$-0.443497\pi$
$653$	9.83343e7			0.353155			0.176578	+	0.984287i	$0.443497\pi$
$654$	−1.02559e8			−0.366642
$655$		−	1.54961e8i		−	0.551442i
$656$	9.89480e7			0.350506
$657$		−	2.75730e7i		−	0.0972273i
$658$	2.80362e7			0.0984106
$659$		−	1.27306e8i		−	0.444828i	−0.974952	−	0.222414i	$-0.928606\pi$
$659$		−	1.27306e8i		−	0.444828i	0.974952	−	0.222414i	$-0.0713936\pi$
$660$		−	3.99862e6i		−	0.0139084i
$661$	−4.05361e8			−1.40358			−0.701790	−	0.712384i	$-0.747616\pi$
$661$	−4.05361e8			−1.40358			−0.701790	+	0.712384i	$0.747616\pi$
$662$		−	8.52158e7i		−	0.293729i
$663$			3.51713e7i			0.120683i
$664$	−4.05451e8			−1.38495
$665$	−1.56020e8			−0.530536
$666$	1.24963e8			0.423017
$667$			4.62613e6i			0.0155898i
$668$	2.78558e7			0.0934514
$669$	9.69156e7			0.323680
$670$	4.68041e7			0.155618
$671$	−6.25025e6			−0.0206885
$672$			1.60542e8i			0.529030i
$673$			3.25005e8i			1.06622i	0.846047	+	0.533108i	$0.178976\pi$
$673$			3.25005e8i			1.06622i	−0.846047	+	0.533108i	$0.821024\pi$
$674$	−1.08741e8			−0.355153
$675$	9.33453e7			0.303516
$676$	−5.51712e8			−1.78596
$677$	−4.44051e8			−1.43109			−0.715544	−	0.698567i	$-0.753821\pi$
$677$	−4.44051e8			−1.43109			−0.715544	+	0.698567i	$0.753821\pi$
$678$	1.08628e8			0.348540
$679$		−	1.38611e8i		−	0.442781i
$680$		−	2.93472e7i		−	0.0933340i
$681$			1.93501e8i			0.612693i
$682$			1.17480e7i			0.0370347i
$683$		−	2.66562e8i		−	0.836636i	−0.908301	−	0.418318i	$-0.862620\pi$
$683$		−	2.66562e8i		−	0.836636i	0.908301	−	0.418318i	$-0.137380\pi$
$684$	1.16531e8			0.364144
$685$	−1.61562e8			−0.502654
$686$		−	1.43286e8i		−	0.443845i
$687$			1.11784e8i			0.344755i
$688$			5.95931e7i			0.182991i
$689$		−	6.58635e8i		−	2.01366i
$690$	3.16076e7			0.0962154
$691$		−	4.07668e8i		−	1.23558i	−0.786341	−	0.617792i	$-0.788027\pi$
$691$		−	4.07668e8i		−	1.23558i	0.786341	−	0.617792i	$-0.211973\pi$
$692$		−	2.53854e8i		−	0.766066i
$693$			1.25990e7i			0.0378561i
$694$	−2.59174e8			−0.775378
$695$	3.54846e8			1.05702
$696$			4.23347e6i			0.0125565i
$697$	−4.52248e7			−0.133560
$698$	−1.65096e8			−0.485478
$699$		−	2.19367e8i		−	0.642303i
$700$	9.95163e7			0.290135
$701$			3.70097e8i			1.07439i	0.843459	+	0.537194i	$0.180516\pi$
$701$			3.70097e8i			1.07439i	−0.843459	+	0.537194i	$0.819484\pi$
$702$	2.60029e8			0.751641
$703$			2.47402e8i			0.712094i
$704$		−	2.18845e6i		−	0.00627219i
$705$			2.61938e7i			0.0747534i
$706$	−1.02454e8			−0.291149
$707$			6.59440e8i			1.86602i
$708$	1.27327e8	−	3.56341e7i	0.358773	−	0.100407i
$709$	1.09757e8			0.307960			0.153980	−	0.988074i	$-0.450791\pi$
$709$	1.09757e8			0.307960			0.153980	+	0.988074i	$0.450791\pi$
$710$			1.69834e7i			0.0474516i
$711$	3.66988e8			1.02104
$712$	−1.66997e8			−0.462668
$713$	3.07586e8			0.848589
$714$		−	1.23578e7i		−	0.0339504i
$715$	−2.48834e7			−0.0680755
$716$		−	3.24056e8i		−	0.882838i
$717$	1.99087e8			0.540115
$718$		−	6.63540e7i		−	0.179264i
$719$			5.43118e8i			1.46119i	0.682810	+	0.730596i	$0.260758\pi$
$719$			5.43118e8i			1.46119i	−0.682810	+	0.730596i	$0.739242\pi$
$720$	8.21131e7			0.219996
$721$		−	2.61536e8i		−	0.697792i
$722$			1.11589e8i			0.296490i
$723$	1.74014e8			0.460436
$724$	−4.92311e8			−1.29725
$725$	4.10844e6			0.0107811
$726$		−	8.91855e7i		−	0.233069i
$727$	7.19307e8			1.87202			0.936011	−	0.351971i	$-0.114489\pi$
$727$	7.19307e8			1.87202			0.936011	+	0.351971i	$0.114489\pi$
$728$	6.38134e8			1.65393
$729$	5.72797e7			0.147849
$730$	−1.91342e7			−0.0491860
$731$		−	2.72374e7i		−	0.0697289i
$732$			6.50565e7i			0.165866i
$733$	4.44144e8			1.12775			0.563874	−	0.825861i	$-0.309310\pi$
$733$	4.44144e8			1.12775			0.563874	+	0.825861i	$0.309310\pi$
$734$	3.47229e8			0.878068
$735$	−2.08535e7			−0.0525190
$736$	−2.09308e8			−0.524992
$737$	7.48277e6			0.0186922
$738$			1.44891e8i			0.360474i
$739$			7.57423e7i			0.187675i	0.995588	+	0.0938373i	$0.0299133\pi$
$739$			7.57423e7i			0.187675i	−0.995588	+	0.0938373i	$0.970087\pi$
$740$			2.87229e8i			0.708815i
$741$			2.23089e8i			0.548306i
$742$			2.31418e8i			0.566480i
$743$	3.64938e7			0.0889719			0.0444860	−	0.999010i	$-0.485835\pi$
$743$	3.64938e7			0.0889719			0.0444860	+	0.999010i	$0.485835\pi$
$744$	2.81478e8			0.683479
$745$		−	2.57357e8i		−	0.622397i
$746$		−	3.89380e7i		−	0.0937902i
$747$			5.18505e8i			1.24392i
$748$		−	2.03824e6i		−	0.00487025i
$749$	3.15541e8			0.750950
$750$		−	1.07234e8i		−	0.254185i
$751$			1.82821e7i			0.0431625i	0.999767	+	0.0215813i	$0.00687007\pi$
$751$			1.82821e7i			0.0431625i	−0.999767	+	0.0215813i	$0.993130\pi$
$752$		−	2.92129e7i		−	0.0686944i
$753$	−1.04830e8			−0.245527
$754$	1.14448e7			0.0266988
$755$		−	5.30345e6i		−	0.0123230i
$756$	3.02619e8			0.700374
$757$	−7.22256e8			−1.66496			−0.832480	−	0.554056i	$-0.813079\pi$
$757$	−7.22256e8			−1.66496			−0.832480	+	0.554056i	$0.813079\pi$
$758$		−	3.97354e7i		−	0.0912368i
$759$	5.05324e6			0.0115570
$760$		−	1.86147e8i		−	0.424048i
$761$	6.07648e8			1.37879			0.689394	−	0.724386i	$-0.257877\pi$
$761$	6.07648e8			1.37879			0.689394	+	0.724386i	$0.257877\pi$
$762$		−	7.12834e7i		−	0.161110i
$763$			7.42760e8i			1.67215i
$764$			2.92831e8i			0.656654i
$765$	−3.75303e7			−0.0838296
$766$		−	2.85301e8i		−	0.634771i
$767$	−2.21751e8	−	7.92352e8i	−0.491449	−	1.75603i
$768$	−1.31111e8			−0.289437
$769$			3.21651e7i			0.0707305i	0.999374	+	0.0353652i	$0.0112595\pi$
$769$			3.21651e7i			0.0707305i	−0.999374	+	0.0353652i	$0.988741\pi$
$770$	8.74301e6			0.0191509
$771$	−2.80212e8			−0.611397
$772$	−4.46144e8			−0.969669
$773$			4.64920e8i			1.00656i	0.864123	+	0.503280i	$0.167874\pi$
$773$			4.64920e8i			1.00656i	−0.864123	+	0.503280i	$0.832126\pi$
$774$	−8.72633e7			−0.188195
$775$		−	2.73165e8i		−	0.586840i
$776$	1.65377e8			0.353907
$777$			2.78413e8i			0.593508i
$778$		−	1.48582e8i		−	0.315520i
$779$	−2.86857e8			−0.606811
$780$			2.59002e8i			0.545781i
$781$			2.71521e6i			0.00569968i
$782$	1.61116e7			0.0336913
$783$	1.24933e7			0.0260251
$784$	2.32571e7			0.0482621
$785$			4.85488e8i			1.00362i
$786$	7.78525e7			0.160326
$787$	2.36271e8			0.484714			0.242357	−	0.970187i	$-0.422079\pi$
$787$	2.36271e8			0.484714			0.242357	+	0.970187i	$0.422079\pi$
$788$	−5.17851e8			−1.05834
$789$	2.11603e8			0.430815
$790$		−	2.54670e8i		−	0.516532i
$791$		−	7.86710e8i		−	1.58959i
$792$	−1.50318e7			−0.0302577
$793$	4.04846e8			0.811839
$794$	−1.90395e8			−0.380359
$795$	−2.16210e8			−0.430302
$796$	−4.31488e6			−0.00855519
$797$		−	7.76241e8i		−	1.53328i	−0.642077	−	0.766640i	$-0.721927\pi$
$797$		−	7.76241e8i		−	1.53328i	0.642077	−	0.766640i	$-0.278073\pi$
$798$		−	7.83843e7i		−	0.154248i
$799$			1.33519e7i			0.0261760i
$800$			1.85885e8i			0.363057i
$801$			2.13562e8i			0.415554i
$802$	−2.53907e8			−0.492211
$803$	−3.05906e6			−0.00590801
$804$		−	7.78853e7i		−	0.149860i
$805$		−	2.28910e8i		−	0.438810i
$806$		−	7.60947e8i		−	1.45328i
$807$			3.21217e8i			0.611192i
$808$	−7.86777e8			−1.49148
$809$			4.85806e8i			0.917524i	0.888559	+	0.458762i	$0.151707\pi$
$809$			4.85806e8i			0.917524i	−0.888559	+	0.458762i	$0.848293\pi$
$810$			7.18702e7i			0.135236i
$811$			3.65498e8i			0.685208i	0.939480	+	0.342604i	$0.111309\pi$
$811$			3.65498e8i			0.685208i	−0.939480	+	0.342604i	$0.888691\pi$
$812$	1.33193e7			0.0248778
$813$	1.29162e8			0.240361
$814$		−	1.38639e7i		−	0.0257046i
$815$	5.56950e8			1.02883
$816$	−1.28764e7			−0.0236987
$817$		−	1.72765e8i		−	0.316802i
$818$	2.93672e8			0.536541
$819$		−	8.16069e8i		−	1.48551i
$820$	−3.33035e8			−0.604017
$821$			8.63585e7i			0.156054i	0.996951	+	0.0780271i	$0.0248621\pi$
$821$			8.63585e7i			0.156054i	−0.996951	+	0.0780271i	$0.975138\pi$
$822$		−	8.11689e7i		−	0.146142i
$823$			9.30819e8i			1.66981i	0.550397	+	0.834903i	$0.314476\pi$
$823$			9.30819e8i			1.66981i	−0.550397	+	0.834903i	$0.685524\pi$
$824$	3.12038e8			0.557732
$825$		−	4.48775e6i		−	0.00799221i
$826$	7.79142e7	+	2.78400e8i	0.138254	+	0.494003i
$827$	−6.55263e8			−1.15851			−0.579254	−	0.815147i	$-0.696656\pi$
$827$	−6.55263e8			−1.15851			−0.579254	+	0.815147i	$0.696656\pi$
$828$			1.70972e8i			0.301186i
$829$	6.10083e8			1.07084			0.535421	−	0.844585i	$-0.320153\pi$
$829$	6.10083e8			1.07084			0.535421	+	0.844585i	$0.320153\pi$
$830$	3.59815e8			0.629281
$831$	−1.05951e8			−0.184630
$832$			1.41752e8i			0.246127i
$833$	−1.06298e7			−0.0183903
$834$			1.78274e8i			0.307320i
$835$	−5.69042e7			−0.0977428
$836$		−	1.29284e7i		−	0.0221272i
$837$		−	8.30666e8i		−	1.41661i
$838$	4.34488e8			0.738322
$839$			1.08243e9i			1.83280i	0.400266	+	0.916399i	$0.368918\pi$
$839$			1.08243e9i			1.83280i	−0.400266	+	0.916399i	$0.631082\pi$
$840$		−	2.09480e8i		−	0.353431i
$841$	−5.94273e8			−0.999076
$842$	−5.19817e8			−0.870792
$843$	−2.05948e8			−0.343776
$844$		−	6.89576e8i		−	1.14698i
$845$	1.12705e9			1.86798
$846$	4.27770e7			0.0706479
$847$	−6.45903e8			−1.06296
$848$	2.41130e8			0.395425
$849$		−	7.53684e7i		−	0.123159i
$850$		−	1.43086e7i		−	0.0232991i
$851$	−3.62984e8			−0.588978
$852$	2.82616e7			0.0456960
$853$	2.71040e8			0.436702			0.218351	−	0.975870i	$-0.429932\pi$
$853$	2.71040e8			0.436702			0.218351	+	0.975870i	$0.429932\pi$
$854$	−1.42246e8			−0.228385
$855$	−2.38052e8			−0.380866
$856$			3.76472e8i			0.600221i
$857$		−	1.12202e8i		−	0.178262i	−0.996020	−	0.0891309i	$-0.971591\pi$
$857$		−	1.12202e8i		−	0.178262i	0.996020	−	0.0891309i	$-0.0284090\pi$
$858$		−	1.25014e7i		−	0.0197923i
$859$		−	1.23565e9i		−	1.94947i	−0.223368	−	0.974734i	$-0.571705\pi$
$859$		−	1.23565e9i		−	1.94947i	0.223368	−	0.974734i	$-0.428295\pi$
$860$		−	2.00576e8i		−	0.315344i
$861$	−3.22814e8			−0.505758
$862$	−3.50546e8			−0.547298
$863$		−	1.21090e9i		−	1.88398i	−0.335645	−	0.941988i	$-0.608954\pi$
$863$		−	1.21090e9i		−	1.88398i	0.335645	−	0.941988i	$-0.391046\pi$
$864$			5.65257e8i			0.876405i
$865$			5.18578e8i			0.801245i
$866$			2.58882e8i			0.398611i
$867$	−3.10220e8			−0.476007
$868$		−	8.85581e8i		−	1.35416i
$869$		−	4.07152e7i		−	0.0620436i
$870$		−	3.75696e6i		−	0.00570531i
$871$	−4.84679e8			−0.733499
$872$	−8.86185e8			−1.33652
$873$		−	2.11490e8i		−	0.317868i
$874$	1.02194e8			0.153071
$875$	−7.76615e8			−1.15926
$876$			3.18406e7i			0.0473663i
$877$	1.01315e9			1.50202			0.751010	−	0.660291i	$-0.229567\pi$
$877$	1.01315e9			1.50202			0.751010	+	0.660291i	$0.229567\pi$
$878$		−	2.09991e8i		−	0.310255i
$879$	4.83334e8			0.711674
$880$		−	9.10996e6i		−	0.0133681i
$881$		−	3.47745e7i		−	0.0508550i	−0.999677	−	0.0254275i	$-0.991905\pi$
$881$		−	3.47745e7i		−	0.0508550i	0.999677	−	0.0254275i	$-0.00809469\pi$
$882$			3.40557e7i			0.0496346i
$883$	−6.87142e8			−0.998078			−0.499039	−	0.866580i	$-0.666314\pi$
$883$	−6.87142e8			−0.998078			−0.499039	+	0.866580i	$0.666314\pi$
$884$			1.32023e8i			0.191114i
$885$	−2.60105e8	+	7.27939e7i	−0.375248	+	0.105018i
$886$	−1.88257e8			−0.270676
$887$			7.79510e7i			0.111699i	0.998439	+	0.0558497i	$0.0177868\pi$
$887$			7.79510e7i			0.111699i	−0.998439	+	0.0558497i	$0.982213\pi$
$888$	−3.32174e8			−0.474380
$889$	−5.16251e8			−0.734778
$890$	1.48201e8			0.210223
$891$			1.14902e7i			0.0162440i
$892$	3.63793e8			0.512577
$893$			8.46902e7i			0.118927i
$894$	1.29296e8			0.180956
$895$			6.61987e8i			0.923379i
$896$			7.34760e8i			1.02146i
$897$	−3.27312e8			−0.453507
$898$			2.73185e8i			0.377249i
$899$		−	3.65604e7i		−	0.0503190i
$900$	1.51840e8			0.208285
$901$	−1.10210e8			−0.150677
$902$	1.60748e7			0.0219042
$903$		−	1.94420e8i		−	0.264045i
$904$	9.38622e8			1.27053
$905$	1.00570e9			1.35682
$906$	2.66445e6			0.00358280
$907$	−1.30550e9			−1.74967			−0.874835	−	0.484422i	$-0.839030\pi$
$907$	−1.30550e9			−1.74967			−0.874835	+	0.484422i	$0.839030\pi$
$908$			7.26347e8i			0.970256i
$909$			1.00616e9i			1.33960i
$910$	−5.66308e8			−0.751500
$911$	−3.16348e8			−0.418418			−0.209209	−	0.977871i	$-0.567089\pi$
$911$	−3.16348e8			−0.418418			−0.209209	+	0.977871i	$0.567089\pi$
$912$	−8.16742e7			−0.107671
$913$	5.75251e7			0.0755866
$914$	1.91341e8			0.250593
$915$		−	1.32898e8i		−	0.173483i
$916$			4.19605e8i			0.545952i
$917$		−	5.63826e8i		−	0.731202i
$918$		−	4.35109e7i		−	0.0562432i
$919$		−	3.91774e8i		−	0.504765i	−0.967628	−	0.252382i	$-0.918786\pi$
$919$		−	3.91774e8i		−	0.504765i	0.967628	−	0.252382i	$-0.0812140\pi$
$920$	2.73112e8			0.350733
$921$	1.24419e8			0.159260
$922$			3.36848e7i			0.0429776i
$923$		−	1.75872e8i		−	0.223661i
$924$		−	1.45490e7i		−	0.0184423i
$925$			3.22364e8i			0.407307i
$926$	−7.05226e6			−0.00888168
$927$		−	3.99046e8i		−	0.500937i
$928$			2.48789e7i			0.0311306i
$929$			1.07348e8i			0.133889i	0.997757	+	0.0669446i	$0.0213251\pi$
$929$			1.07348e8i			0.133889i	−0.997757	+	0.0669446i	$0.978675\pi$
$930$	−2.49796e8			−0.310553
$931$	−6.74238e7			−0.0835535
$932$		−	8.23439e8i		−	1.01715i
$933$	7.48044e8			0.921048
$934$	4.39402e8			0.539289
$935$			4.16376e6i			0.00509390i
$936$	9.73650e8			1.18734
$937$			2.50556e8i			0.304569i	0.988337	+	0.152285i	$0.0486631\pi$
$937$			2.50556e8i			0.304569i	−0.988337	+	0.152285i	$0.951337\pi$
$938$	1.70297e8			0.206347
$939$		−	1.10534e8i		−	0.133505i
$940$			9.83237e7i			0.118379i
$941$			5.17515e8i			0.621090i	0.950559	+	0.310545i	$0.100511\pi$
$941$			5.17515e8i			0.621090i	−0.950559	+	0.310545i	$0.899489\pi$
$942$	−2.43909e8			−0.291793
$943$		−	4.20872e8i		−	0.501897i
$944$	2.90085e8	−	8.11842e7i	0.344833	−	0.0965063i
$945$	−6.18194e8			−0.732537
$946$			9.68134e6i			0.0114357i
$947$	1.46435e9			1.72423			0.862113	−	0.506716i	$-0.169141\pi$
$947$	1.46435e9			1.72423			0.862113	+	0.506716i	$0.169141\pi$
$948$	−4.23789e8			−0.497421
$949$	1.98144e8			0.231836
$950$		−	9.07583e7i		−	0.105856i
$951$	5.55938e7			0.0646375
$952$		−	1.06780e8i		−	0.123759i
$953$	−1.33904e9			−1.54709			−0.773543	−	0.633743i	$-0.781518\pi$
$953$	−1.33904e9			−1.54709			−0.773543	+	0.633743i	$0.781518\pi$
$954$			3.53092e8i			0.406670i
$955$		−	5.98199e8i		−	0.686808i
$956$	7.47315e8			0.855323
$957$		−	600641.i		−	0.000685297i
$958$			4.65569e8i			0.529526i
$959$	−5.87844e8			−0.666509
$960$	4.65329e7			0.0525952
$961$	−1.54335e9			−1.73898
$962$			8.97999e8i			1.00867i
$963$	4.81446e8			0.539099
$964$	6.53197e8			0.729144
$965$	9.11390e8			1.01420
$966$	1.15004e8			0.127580
$967$		−	1.06877e9i		−	1.18196i	−0.806685	−	0.590982i	$-0.798741\pi$
$967$		−	1.06877e9i		−	1.18196i	0.806685	−	0.590982i	$-0.201259\pi$
$968$		−	7.70625e8i		−	0.849605i
$969$	3.73296e7			0.0410282
$970$	−1.46763e8			−0.160805
$971$	3.47954e6			0.00380070			0.00190035	−	0.999998i	$-0.499395\pi$
$971$	3.47954e6			0.00380070			0.00190035	+	0.999998i	$0.499395\pi$
$972$	7.23369e8			0.787701
$973$	1.29110e9			1.40160
$974$		−	9.53896e7i		−	0.103234i
$975$			2.90684e8i			0.313622i
$976$			1.48216e8i			0.159422i
$977$			7.50772e8i			0.805053i	0.915408	+	0.402526i	$0.131868\pi$
$977$			7.50772e8i			0.805053i	−0.915408	+	0.402526i	$0.868132\pi$
$978$			2.79811e8i			0.299122i
$979$	2.36935e7			0.0252511
$980$	−7.82777e7			−0.0831687
$981$			1.13329e9i			1.20042i
$982$			3.98959e8i			0.421302i
$983$			2.01448e8i			0.212082i	0.994362	+	0.106041i	$0.0338174\pi$
$983$			2.01448e8i			0.212082i	−0.994362	+	0.106041i	$0.966183\pi$
$984$		−	3.85148e8i		−	0.404243i
$985$	1.05787e9			1.10694
$986$		−	1.91506e6i		−	0.00199780i
$987$			9.53059e7i			0.0991216i
$988$			8.37409e8i			0.868294i
$989$	2.53477e8			0.262029
$990$	1.33399e7			0.0137482
$991$		−	2.03555e8i		−	0.209151i	−0.994517	−	0.104575i	$-0.966652\pi$
$991$		−	2.03555e8i		−	0.209151i	0.994517	−	0.104575i	$-0.0333484\pi$
$992$	1.65417e9			1.69451
$993$	2.89681e8			0.295851
$994$			6.17942e7i			0.0629200i
$995$	8.81450e6			0.00894806
$996$		−	5.98757e8i		−	0.606000i
$997$	9.82929e8			0.991829			0.495915	−	0.868371i	$-0.334833\pi$
$997$	9.82929e8			0.991829			0.495915	+	0.868371i	$0.334833\pi$
$998$			6.03337e7i			0.0606972i
$999$			9.80275e8i			0.983222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	59.7.b.c.58.13	✓	26
59.58	odd	2	inner	59.7.b.c.58.14	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.7.b.c.58.13	✓	26	1.1	even	1	trivial
59.7.b.c.58.14	yes	26	59.58	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:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	59.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.85246i q^{2} +13.0960 q^{3} +49.1585 q^{4} -100.422 q^{5} -50.4519i q^{6} -365.384 q^{7} -435.939i q^{8} -557.495 q^{9} +386.871i q^{10} +61.8507i q^{11} +643.780 q^{12} -4006.24i q^{13} +1407.63i q^{14} -1315.12 q^{15} +1466.71 q^{16} -670.367 q^{17} +2147.73i q^{18} -4252.09 q^{19} -4936.59 q^{20} -4785.07 q^{21} +238.277 q^{22} -6238.59i q^{23} -5709.06i q^{24} -5540.46 q^{25} -15433.9 q^{26} -16847.9 q^{27} -17961.8 q^{28} -741.535 q^{29} +5066.47i q^{30} +49303.7i q^{31} -33550.5i q^{32} +809.997i q^{33} +2582.56i q^{34} +36692.6 q^{35} -27405.6 q^{36} -58183.7i q^{37} +16381.0i q^{38} -52465.7i q^{39} +43777.8i q^{40} +67462.6 q^{41} +18434.3i q^{42} +40630.5i q^{43} +3040.49i q^{44} +55984.6 q^{45} -24033.9 q^{46} -19917.3i q^{47} +19208.0 q^{48} +15856.6 q^{49} +21344.4i q^{50} -8779.13 q^{51} -196941. i q^{52} +164402. q^{53} +64906.1i q^{54} -6211.16i q^{55} +159285. i q^{56} -55685.4 q^{57} +2856.73i q^{58} +(197780. - 55351.3i) q^{59} -64649.6 q^{60} +101054. i q^{61} +189941. q^{62} +203700. q^{63} -35382.9 q^{64} +402314. i q^{65} +3120.48 q^{66} -120981. i q^{67} -32954.3 q^{68} -81700.6i q^{69} -141357. i q^{70} +43899.5 q^{71} +243034. i q^{72} +49458.8i q^{73} -224150. q^{74} -72557.8 q^{75} -209026. q^{76} -22599.3i q^{77} -202122. q^{78} -658281. q^{79} -147289. q^{80} +185773. q^{81} -259897. i q^{82} -930063. i q^{83} -235227. q^{84} +67319.5 q^{85} +156528. q^{86} -9711.14 q^{87} +26963.1 q^{88} -383075. i q^{89} -215679. i q^{90} +1.46382e6i q^{91} -306680. i q^{92} +645682. i q^{93} -76730.8 q^{94} +427002. q^{95} -439378. i q^{96} +379358. i q^{97} -61087.1i q^{98} -34481.4i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 10 q^{3} - 1090 q^{4} + 142 q^{5} + 406 q^{7} + 5432 q^{9} - 1124 q^{12} + 14982 q^{15} + 12734 q^{16} - 9108 q^{17} + 3850 q^{19} - 46896 q^{20} - 49034 q^{21} + 11238 q^{22} + 18792 q^{25} - 64590 q^{26}+ \cdots - 2396490 q^{95}+O(q^{100}) \) 26 * q + 10 * q^3 - 1090 * q^4 + 142 * q^5 + 406 * q^7 + 5432 * q^9 - 1124 * q^12 + 14982 * q^15 + 12734 * q^16 - 9108 * q^17 + 3850 * q^19 - 46896 * q^20 - 49034 * q^21 + 11238 * q^22 + 18792 * q^25 - 64590 * q^26 + 3550 * q^27 - 45542 * q^28 - 31730 * q^29 + 163558 * q^35 - 325266 * q^36 + 91914 * q^41 + 736396 * q^45 + 287148 * q^46 + 479572 * q^48 - 462900 * q^49 + 329932 * q^51 + 8238 * q^53 - 187506 * q^57 + 326182 * q^59 - 970064 * q^60 + 630140 * q^62 + 630508 * q^63 - 1800262 * q^64 - 869200 * q^66 - 319586 * q^68 + 1763840 * q^71 - 2294090 * q^74 + 354736 * q^75 + 247144 * q^76 - 375064 * q^78 + 4702 * q^79 + 1920984 * q^80 - 2435946 * q^81 - 1007672 * q^84 + 864044 * q^85 + 5031110 * q^86 - 1519202 * q^87 + 725994 * q^88 + 2835768 * q^94 - 2396490 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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