LMFDB - Embedded newform 59.7.b.c.58.12

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			58.12
Character	$\chi$	$=$	59.58
Dual form			59.7.b.c.58.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.66346i q^{2} -37.4041 q^{3} +42.2521 q^{4} +9.17391 q^{5} +174.432i q^{6} +221.670 q^{7} -495.503i q^{8} +670.066 q^{9} -42.7822i q^{10} -1876.98i q^{11} -1580.40 q^{12} +2425.96i q^{13} -1033.75i q^{14} -343.142 q^{15} +393.381 q^{16} -4122.75 q^{17} -3124.83i q^{18} -12156.4 q^{19} +387.617 q^{20} -8291.37 q^{21} -8753.20 q^{22} -15276.1i q^{23} +18533.8i q^{24} -15540.8 q^{25} +11313.4 q^{26} +2204.38 q^{27} +9366.03 q^{28} -10510.9 q^{29} +1600.23i q^{30} +14698.9i q^{31} -33546.7i q^{32} +70206.6i q^{33} +19226.3i q^{34} +2033.58 q^{35} +28311.7 q^{36} -75441.9i q^{37} +56691.1i q^{38} -90740.7i q^{39} -4545.70i q^{40} -30830.6 q^{41} +38666.4i q^{42} -79362.5i q^{43} -79306.2i q^{44} +6147.12 q^{45} -71239.7 q^{46} +94557.7i q^{47} -14714.0 q^{48} -68511.4 q^{49} +72474.1i q^{50} +154208. q^{51} +102502. i q^{52} +63543.3 q^{53} -10280.0i q^{54} -17219.2i q^{55} -109838. i q^{56} +454700. q^{57} +49017.3i q^{58} +(203347. - 28817.0i) q^{59} -14498.5 q^{60} -182254. i q^{61} +68547.8 q^{62} +148534. q^{63} -131267. q^{64} +22255.5i q^{65} +327405. q^{66} +541123. i q^{67} -174195. q^{68} +571390. i q^{69} -9483.52i q^{70} -344464. q^{71} -332019. i q^{72} -230675. i q^{73} -351820. q^{74} +581291. q^{75} -513635. q^{76} -416069. i q^{77} -423166. q^{78} +94875.3 q^{79} +3608.84 q^{80} -570931. q^{81} +143777. i q^{82} -19783.7i q^{83} -350328. q^{84} -37821.7 q^{85} -370104. q^{86} +393152. q^{87} -930046. q^{88} -453016. i q^{89} -28666.9i q^{90} +537762. i q^{91} -645450. i q^{92} -549800. i q^{93} +440966. q^{94} -111522. q^{95} +1.25478e6i q^{96} -1.04599e6i q^{97} +319500. i q^{98} -1.25770e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	4.66346i		−	0.582932i	−0.956581	−	0.291466i	$-0.905857\pi$
$2$		−	4.66346i		−	0.582932i	0.956581	−	0.291466i	$-0.0941431\pi$
$3$	−37.4041			−1.38534			−0.692668	−	0.721256i	$-0.743565\pi$
$3$	−37.4041			−1.38534			−0.692668	+	0.721256i	$0.743565\pi$
$4$	42.2521			0.660190
$5$	9.17391			0.0733913			0.0366956	−	0.999326i	$-0.488317\pi$
$5$	9.17391			0.0733913			0.0366956	+	0.999326i	$0.488317\pi$
$6$			174.432i			0.807558i
$7$	221.670			0.646268			0.323134	−	0.946353i	$-0.395263\pi$
$7$	221.670			0.646268			0.323134	+	0.946353i	$0.395263\pi$
$8$		−	495.503i		−	0.967779i
$9$	670.066			0.919158
$10$		−	42.7822i		−	0.0427822i
$11$		−	1876.98i		−	1.41020i	−0.709108	−	0.705100i	$-0.750902\pi$
$11$		−	1876.98i		−	1.41020i	0.709108	−	0.705100i	$-0.249098\pi$
$12$	−1580.40			−0.914585
$13$			2425.96i			1.10421i	0.833773	+	0.552107i	$0.186176\pi$
$13$			2425.96i			1.10421i	−0.833773	+	0.552107i	$0.813824\pi$
$14$		−	1033.75i		−	0.376731i
$15$	−343.142			−0.101672
$16$	393.381			0.0960402
$17$	−4122.75			−0.839151			−0.419575	−	0.907721i	$-0.637821\pi$
$17$	−4122.75			−0.839151			−0.419575	+	0.907721i	$0.637821\pi$
$18$		−	3124.83i		−	0.535807i
$19$	−12156.4			−1.77233			−0.886167	−	0.463366i	$-0.846641\pi$
$19$	−12156.4			−1.77233			−0.886167	+	0.463366i	$0.846641\pi$
$20$	387.617			0.0484522
$21$	−8291.37			−0.895299
$22$	−8753.20			−0.822051
$23$		−	15276.1i		−	1.25554i	−0.778399	−	0.627770i	$-0.783968\pi$
$23$		−	15276.1i		−	1.25554i	0.778399	−	0.627770i	$-0.216032\pi$
$24$			18533.8i			1.34070i
$25$	−15540.8			−0.994614
$26$	11313.4			0.643682
$27$	2204.38			0.111994
$28$	9366.03			0.426660
$29$	−10510.9			−0.430971			−0.215485	−	0.976507i	$-0.569133\pi$
$29$	−10510.9			−0.430971			−0.215485	+	0.976507i	$0.569133\pi$
$30$			1600.23i			0.0592677i
$31$			14698.9i			0.493401i	0.969092	+	0.246701i	$0.0793464\pi$
$31$			14698.9i			0.493401i	−0.969092	+	0.246701i	$0.920654\pi$
$32$		−	33546.7i		−	1.02376i
$33$			70206.6i			1.95360i
$34$			19226.3i			0.489168i
$35$	2033.58			0.0474305
$36$	28311.7			0.606818
$37$		−	75441.9i		−	1.48939i	−0.667407	−	0.744693i	$-0.732596\pi$
$37$		−	75441.9i		−	1.48939i	0.667407	−	0.744693i	$-0.267404\pi$
$38$			56691.1i			1.03315i
$39$		−	90740.7i		−	1.52971i
$40$		−	4545.70i		−	0.0710265i
$41$	−30830.6			−0.447332			−0.223666	−	0.974666i	$-0.571803\pi$
$41$	−30830.6			−0.447332			−0.223666	+	0.974666i	$0.571803\pi$
$42$			38666.4i			0.521899i
$43$		−	79362.5i		−	0.998183i	−0.866549	−	0.499092i	$-0.833667\pi$
$43$		−	79362.5i		−	0.998183i	0.866549	−	0.499092i	$-0.166333\pi$
$44$		−	79306.2i		−	0.930999i
$45$	6147.12			0.0674581
$46$	−71239.7			−0.731895
$47$			94557.7i			0.910758i	0.890298	+	0.455379i	$0.150496\pi$
$47$			94557.7i			0.910758i	−0.890298	+	0.455379i	$0.849504\pi$
$48$	−14714.0			−0.133048
$49$	−68511.4			−0.582337
$50$			72474.1i			0.579793i
$51$	154208.			1.16251
$52$			102502.i			0.728990i
$53$	63543.3			0.426817			0.213409	−	0.976963i	$-0.431543\pi$
$53$	63543.3			0.426817			0.213409	+	0.976963i	$0.431543\pi$
$54$		−	10280.0i		−	0.0652849i
$55$		−	17219.2i		−	0.103496i
$56$		−	109838.i		−	0.625445i
$57$	454700.			2.45528
$58$			49017.3i			0.251227i
$59$	203347.	−	28817.0i	0.990107	−	0.140311i
$59$	203347.	−	28817.0i	0.990107	−	0.140311i
$60$	−14498.5			−0.0671226
$61$		−	182254.i		−	0.802947i	−0.915871	−	0.401474i	$-0.868498\pi$
$61$		−	182254.i		−	0.802947i	0.915871	−	0.401474i	$-0.131502\pi$
$62$	68547.8			0.287620
$63$	148534.			0.594022
$64$	−131267.			−0.500745
$65$			22255.5i			0.0810396i
$66$	327405.			1.13882
$67$			541123.i			1.79917i	0.436750	+	0.899583i	$0.356130\pi$
$67$			541123.i			1.79917i	−0.436750	+	0.899583i	$0.643870\pi$
$68$	−174195.			−0.553999
$69$			571390.i			1.73934i
$70$		−	9483.52i		−	0.0276488i
$71$	−344464.			−0.962429			−0.481215	−	0.876603i	$-0.659804\pi$
$71$	−344464.			−0.962429			−0.481215	+	0.876603i	$0.659804\pi$
$72$		−	332019.i		−	0.889541i
$73$		−	230675.i		−	0.592970i	−0.955038	−	0.296485i	$-0.904186\pi$
$73$		−	230675.i		−	0.592970i	0.955038	−	0.296485i	$-0.0958144\pi$
$74$	−351820.			−0.868212
$75$	581291.			1.37787
$76$	−513635.			−1.17008
$77$		−	416069.i		−	0.911367i
$78$	−423166.			−0.891716
$79$	94875.3			0.192430			0.0962148	−	0.995361i	$-0.469326\pi$
$79$	94875.3			0.192430			0.0962148	+	0.995361i	$0.469326\pi$
$80$	3608.84			0.00704851
$81$	−570931.			−1.07431
$82$			143777.i			0.260764i
$83$		−	19783.7i		−	0.0345998i	−0.999850	−	0.0172999i	$-0.994493\pi$
$83$		−	19783.7i		−	0.0345998i	0.999850	−	0.0172999i	$-0.00550700\pi$
$84$	−350328.			−0.591067
$85$	−37821.7			−0.0615863
$86$	−370104.			−0.581873
$87$	393152.			0.597039
$88$	−930046.			−1.36476
$89$		−	453016.i		−	0.642605i	−0.946977	−	0.321302i	$-0.895879\pi$
$89$		−	453016.i		−	0.642605i	0.946977	−	0.321302i	$-0.104121\pi$
$90$		−	28666.9i		−	0.0393235i
$91$			537762.i			0.713618i
$92$		−	645450.i		−	0.828894i
$93$		−	549800.i		−	0.683527i
$94$	440966.			0.530911
$95$	−111522.			−0.130074
$96$			1.25478e6i			1.41826i
$97$		−	1.04599e6i		−	1.14607i	−0.819531	−	0.573035i	$-0.805766\pi$
$97$		−	1.04599e6i		−	1.14607i	0.819531	−	0.573035i	$-0.194234\pi$
$98$			319500.i			0.339463i
$99$		−	1.25770e6i		−	1.29620i
$100$	−656634.			−0.656634
$101$			1.27564e6i			1.23813i	0.785341	+	0.619063i	$0.212487\pi$
$101$			1.27564e6i			1.23813i	−0.785341	+	0.619063i	$0.787513\pi$
$102$		−	719141.i		−	0.677663i
$103$		−	446388.i		−	0.408508i	−0.978918	−	0.204254i	$-0.934523\pi$
$103$		−	446388.i		−	0.408508i	0.978918	−	0.204254i	$-0.0654768\pi$
$104$	1.20207e6			1.06863
$105$	−76064.2			−0.0657071
$106$		−	296331.i		−	0.248806i
$107$	1.42306e6			1.16164			0.580819	−	0.814033i	$-0.302732\pi$
$107$	1.42306e6			1.16164			0.580819	+	0.814033i	$0.302732\pi$
$108$	93139.7			0.0739373
$109$			2.08585e6i			1.61066i	0.592829	+	0.805329i	$0.298011\pi$
$109$			2.08585e6i			1.61066i	−0.592829	+	0.805329i	$0.701989\pi$
$110$	−80301.1			−0.0603314
$111$			2.82183e6i			2.06330i
$112$	87200.7			0.0620677
$113$		−	1.20039e6i		−	0.831934i	−0.909380	−	0.415967i	$-0.863443\pi$
$113$		−	1.20039e6i		−	0.831934i	0.909380	−	0.415967i	$-0.136557\pi$
$114$		−	2.12048e6i		−	1.43126i
$115$		−	140142.i		−	0.0921456i
$116$	−444110.			−0.284522
$117$			1.62555e6i			1.01495i
$118$	−134387.	−	948302.i	−0.0817921	−	0.577166i
$119$	−913890.			−0.542316
$120$			170028.i			0.0983956i
$121$	−1.75148e6			−0.988662
$122$	−849933.			−0.468064
$123$	1.15319e6			0.619706
$124$			621061.i			0.325738i
$125$	−285913.			−0.146387
$126$		−	692680.i		−	0.346275i
$127$	1.23925e6			0.604988			0.302494	−	0.953151i	$-0.402181\pi$
$127$	1.23925e6			0.604988			0.302494	+	0.953151i	$0.402181\pi$
$128$		−	1.53483e6i		−	0.731863i
$129$			2.96848e6i			1.38282i
$130$	103788.			0.0472406
$131$		−	3.50861e6i		−	1.56071i	−0.625339	−	0.780353i	$-0.715039\pi$
$131$		−	3.50861e6i		−	1.56071i	0.625339	−	0.780353i	$-0.284961\pi$
$132$			2.96638e6i			1.28975i
$133$	−2.69472e6			−1.14540
$134$	2.52350e6			1.04879
$135$	20222.8			0.00821938
$136$			2.04283e6i			0.812112i
$137$	572795.			0.222760			0.111380	−	0.993778i	$-0.464473\pi$
$137$	572795.			0.222760			0.111380	+	0.993778i	$0.464473\pi$
$138$	2.66466e6			1.01392
$139$	3.78973e6			1.41112			0.705560	−	0.708650i	$-0.250696\pi$
$139$	3.78973e6			1.41112			0.705560	+	0.708650i	$0.250696\pi$
$140$	85923.1			0.0313131
$141$		−	3.53684e6i		−	1.26171i
$142$			1.60639e6i			0.561031i
$143$	4.55346e6			1.55716
$144$	263591.			0.0882761
$145$	−96426.4			−0.0316295
$146$	−1.07574e6			−0.345661
$147$	2.56261e6			0.806733
$148$		−	3.18758e6i		−	0.983277i
$149$			3.00613e6i			0.908758i	0.890808	+	0.454379i	$0.150139\pi$
$149$			3.00613e6i			0.908758i	−0.890808	+	0.454379i	$0.849861\pi$
$150$		−	2.71083e6i		−	0.803208i
$151$			2.46182e6i			0.715031i	0.933907	+	0.357515i	$0.116376\pi$
$151$			2.46182e6i			0.715031i	−0.933907	+	0.357515i	$0.883624\pi$
$152$			6.02355e6i			1.71523i
$153$	−2.76251e6			−0.771312
$154$	−1.94032e6			−0.531265
$155$			134847.i			0.0362113i
$156$		−	3.83399e6i		−	1.00990i
$157$		−	5.78708e6i		−	1.49541i	−0.664030	−	0.747706i	$-0.731155\pi$
$157$		−	5.78708e6i		−	1.49541i	0.664030	−	0.747706i	$-0.268845\pi$
$158$		−	442447.i		−	0.112173i
$159$	−2.37678e6			−0.591285
$160$		−	307754.i		−	0.0751353i
$161$		−	3.38626e6i		−	0.811415i
$162$			2.66251e6i			0.626248i
$163$	6.06682e6			1.40087			0.700436	−	0.713715i	$-0.252989\pi$
$163$	6.06682e6			1.40087			0.700436	+	0.713715i	$0.252989\pi$
$164$	−1.30266e6			−0.295324
$165$			644069.i			0.143377i
$166$	−92260.6			−0.0201693
$167$	6.59870e6			1.41680			0.708400	−	0.705811i	$-0.249417\pi$
$167$	6.59870e6			1.41680			0.708400	+	0.705811i	$0.249417\pi$
$168$			4.10839e6i			0.866451i
$169$	−1.05846e6			−0.219288
$170$			176380.i			0.0359007i
$171$	−8.14561e6			−1.62905
$172$		−	3.35324e6i		−	0.658990i
$173$		−	1.61170e6i		−	0.311277i	−0.987814	−	0.155639i	$-0.950256\pi$
$173$		−	1.61170e6i		−	0.311277i	0.987814	−	0.155639i	$-0.0497435\pi$
$174$		−	1.83345e6i		−	0.348034i
$175$	−3.44494e6			−0.642787
$176$		−	738366.i		−	0.135436i
$177$	−7.60602e6	+	1.07787e6i	−1.37163	+	0.194379i
$178$	−2.11262e6			−0.374595
$179$		−	4.44788e6i		−	0.775522i	−0.921760	−	0.387761i	$-0.873249\pi$
$179$		−	4.44788e6i		−	0.775522i	0.921760	−	0.387761i	$-0.126751\pi$
$180$	259729.			0.0445352
$181$	−5.59004e6			−0.942712			−0.471356	−	0.881943i	$-0.656235\pi$
$181$	−5.59004e6			−0.942712			−0.471356	+	0.881943i	$0.656235\pi$
$182$	2.50783e6			0.415991
$183$			6.81704e6i			1.11235i
$184$	−7.56937e6			−1.21508
$185$		−	692097.i		−	0.109308i
$186$	−2.56397e6			−0.398450
$187$			7.73830e6i			1.18337i
$188$			3.99526e6i			0.601273i
$189$	488644.			0.0723782
$190$			520079.i			0.0758243i
$191$			1.53218e6i			0.219892i	0.993938	+	0.109946i	$0.0350679\pi$
$191$			1.53218e6i			0.219892i	−0.993938	+	0.109946i	$0.964932\pi$
$192$	4.90993e6			0.693700
$193$	−6.01175e6			−0.836236			−0.418118	−	0.908393i	$-0.637310\pi$
$193$	−6.01175e6			−0.836236			−0.418118	+	0.908393i	$0.637310\pi$
$194$	−4.87792e6			−0.668081
$195$		−	832447.i		−	0.112267i
$196$	−2.89475e6			−0.384453
$197$	7.88993e6			1.03199			0.515994	−	0.856592i	$-0.327423\pi$
$197$	7.88993e6			1.03199			0.515994	+	0.856592i	$0.327423\pi$
$198$	−5.86522e6			−0.755594
$199$	−5.83390e6			−0.740286			−0.370143	−	0.928975i	$-0.620691\pi$
$199$	−5.83390e6			−0.740286			−0.370143	+	0.928975i	$0.620691\pi$
$200$			7.70053e6i			0.962566i
$201$		−	2.02402e7i		−	2.49245i
$202$	5.94891e6			0.721744
$203$	−2.32996e6			−0.278523
$204$	6.51560e6			0.767475
$205$	−282837.			−0.0328303
$206$	−2.08171e6			−0.238133
$207$		−	1.02360e7i		−	1.15404i
$208$			954325.i			0.106049i
$209$			2.28173e7i			2.49934i
$210$			354722.i			0.0383028i
$211$		−	6.86056e6i		−	0.730319i	−0.930945	−	0.365159i	$-0.881015\pi$
$211$		−	6.86056e6i		−	0.730319i	0.930945	−	0.365159i	$-0.118985\pi$
$212$	2.68484e6			0.281780
$213$	1.28844e7			1.33329
$214$		−	6.63637e6i		−	0.677157i
$215$		−	728065.i		−	0.0732579i
$216$		−	1.09227e6i		−	0.108385i
$217$			3.25831e6i			0.318870i
$218$	9.72727e6			0.938904
$219$			8.62820e6i			0.821463i
$220$		−	727548.i		−	0.0683272i
$221$		−	1.00016e7i		−	0.926602i
$222$	1.31595e7			1.20277
$223$	−1.30935e7			−1.18071			−0.590353	−	0.807145i	$-0.701011\pi$
$223$	−1.30935e7			−1.18071			−0.590353	+	0.807145i	$0.701011\pi$
$224$		−	7.43629e6i		−	0.661626i
$225$	−1.04134e7			−0.914207
$226$	−5.59799e6			−0.484961
$227$		−	1.12823e7i		−	0.964543i	−0.876022	−	0.482272i	$-0.839812\pi$
$227$		−	1.12823e7i		−	0.964543i	0.876022	−	0.482272i	$-0.160188\pi$
$228$	1.92121e7			1.62095
$229$			1.07738e7i			0.897144i	0.893747	+	0.448572i	$0.148067\pi$
$229$			1.07738e7i			0.897144i	−0.893747	+	0.448572i	$0.851933\pi$
$230$	−653547.			−0.0537147
$231$			1.55627e7i			1.26255i
$232$			5.20820e6i			0.417084i
$233$			776578.i			0.0613928i	0.999529	+	0.0306964i	$0.00977250\pi$
$233$			776578.i			0.0613928i	−0.999529	+	0.0306964i	$0.990228\pi$
$234$	7.58069e6			0.591645
$235$			867463.i			0.0668417i
$236$	8.59186e6	−	1.21758e6i	0.653659	−	0.0926322i
$237$	−3.54872e6			−0.266580
$238$			4.26189e6i			0.316134i
$239$	896008.			0.0656324			0.0328162	−	0.999461i	$-0.489552\pi$
$239$	896008.			0.0656324			0.0328162	+	0.999461i	$0.489552\pi$
$240$	−134985.			−0.00976456
$241$	−3.30996e6			−0.236468			−0.118234	−	0.992986i	$-0.537723\pi$
$241$	−3.30996e6			−0.236468			−0.118234	+	0.992986i	$0.537723\pi$
$242$			8.16794e6i			0.576323i
$243$	1.97482e7			1.37628
$244$		−	7.70061e6i		−	0.530098i
$245$	−628517.			−0.0427385
$246$		−	5.37785e6i		−	0.361247i
$247$		−	2.94910e7i		−	1.95703i
$248$	7.28335e6			0.477503
$249$			739992.i			0.0479324i
$250$			1.33334e6i			0.0853339i
$251$	−3.95442e6			−0.250070			−0.125035	−	0.992152i	$-0.539904\pi$
$251$	−3.95442e6			−0.250070			−0.125035	+	0.992152i	$0.539904\pi$
$252$	6.27586e6			0.392167
$253$	−2.86730e7			−1.77056
$254$		−	5.77918e6i		−	0.352667i
$255$	1.41469e6			0.0853178
$256$	−1.55587e7			−0.927372
$257$	2.02159e7			1.19095			0.595477	−	0.803373i	$-0.296963\pi$
$257$	2.02159e7			1.19095			0.595477	+	0.803373i	$0.296963\pi$
$258$	1.38434e7			0.806090
$259$		−	1.67232e7i		−	0.962543i
$260$			940343.i			0.0535015i
$261$	−7.04302e6			−0.396130
$262$	−1.63623e7			−0.909786
$263$	−1.29640e7			−0.712643			−0.356321	−	0.934363i	$-0.615969\pi$
$263$	−1.29640e7			−0.712643			−0.356321	+	0.934363i	$0.615969\pi$
$264$	3.47875e7			1.89065
$265$	582940.			0.0313247
$266$			1.25667e7i			0.667693i
$267$			1.69447e7i			0.890224i
$268$			2.28636e7i			1.18779i
$269$			2.08133e7i			1.06926i	0.845086	+	0.534630i	$0.179549\pi$
$269$			2.08133e7i			1.06926i	−0.845086	+	0.534630i	$0.820451\pi$
$270$		−	94308.0i		−	0.00479134i
$271$	−3.45377e6			−0.173534			−0.0867671	−	0.996229i	$-0.527654\pi$
$271$	−3.45377e6			−0.173534			−0.0867671	+	0.996229i	$0.527654\pi$
$272$	−1.62181e6			−0.0805922
$273$		−	2.01145e7i		−	0.988601i
$274$		−	2.67121e6i		−	0.129854i
$275$			2.91698e7i			1.40260i
$276$			2.41425e7i			1.14830i
$277$	1.75486e7			0.825663			0.412832	−	0.910807i	$-0.364540\pi$
$277$	1.75486e7			0.825663			0.412832	+	0.910807i	$0.364540\pi$
$278$		−	1.76733e7i		−	0.822588i
$279$			9.84924e6i			0.453513i
$280$		−	1.00764e6i		−	0.0459022i
$281$	3.94952e6			0.178002			0.0890010	−	0.996032i	$-0.471633\pi$
$281$	3.94952e6			0.178002			0.0890010	+	0.996032i	$0.471633\pi$
$282$	−1.64939e7			−0.735490
$283$		−	3.57712e6i		−	0.157824i	−0.996882	−	0.0789122i	$-0.974855\pi$
$283$		−	3.57712e6i		−	0.157824i	0.996882	−	0.0789122i	$-0.0251447\pi$
$284$	−1.45543e7			−0.635386
$285$	4.17138e6			0.180196
$286$		−	2.12349e7i		−	0.907720i
$287$	−6.83422e6			−0.289097
$288$		−	2.24785e7i		−	0.941000i
$289$	−7.14052e6			−0.295826
$290$			449681.i			0.0184378i
$291$			3.91242e7i			1.58769i
$292$		−	9.74652e6i		−	0.391472i
$293$	−4.27637e6			−0.170009			−0.0850045	−	0.996381i	$-0.527090\pi$
$293$	−4.27637e6			−0.170009			−0.0850045	+	0.996381i	$0.527090\pi$
$294$		−	1.19506e7i		−	0.470271i
$295$	1.86549e6	−	264365.i	0.0726652	−	0.0102976i
$296$	−3.73816e7			−1.44140
$297$		−	4.13756e6i		−	0.157934i
$298$	1.40189e7			0.529745
$299$	3.70593e7			1.38638
$300$	2.45608e7			0.909659
$301$		−	1.75923e7i		−	0.645094i
$302$	1.14806e7			0.416815
$303$		−	4.77142e7i		−	1.71522i
$304$	−4.78211e6			−0.170215
$305$		−	1.67198e6i		−	0.0589293i
$306$			1.28829e7i			0.449623i
$307$	1.94010e7			0.670514			0.335257	−	0.942127i	$-0.391177\pi$
$307$	1.94010e7			0.670514			0.335257	+	0.942127i	$0.391177\pi$
$308$		−	1.75798e7i		−	0.601675i
$309$			1.66967e7i			0.565921i
$310$	628851.			0.0211088
$311$	−5.54099e7			−1.84207			−0.921035	−	0.389481i	$-0.872655\pi$
$311$	−5.54099e7			−1.84207			−0.921035	+	0.389481i	$0.872655\pi$
$312$	−4.49623e7			−1.48042
$313$			5.12927e7i			1.67272i	0.548182	+	0.836359i	$0.315320\pi$
$313$			5.12927e7i			1.67272i	−0.548182	+	0.836359i	$0.684680\pi$
$314$	−2.69878e7			−0.871724
$315$	1.36263e6			0.0435961
$316$	4.00868e6			0.127040
$317$	−2.88628e7			−0.906069			−0.453034	−	0.891493i	$-0.649659\pi$
$317$	−2.88628e7			−0.906069			−0.453034	+	0.891493i	$0.649659\pi$
$318$			1.10840e7i			0.344679i
$319$			1.97288e7i			0.607754i
$320$	−1.20423e6			−0.0367503
$321$	−5.32282e7			−1.60926
$322$	−1.57917e7			−0.473000
$323$	5.01179e7			1.48726
$324$	−2.41230e7			−0.709246
$325$		−	3.77014e7i		−	1.09827i
$326$		−	2.82924e7i		−	0.816614i
$327$		−	7.80192e7i		−	2.23130i
$328$			1.52766e7i			0.432919i
$329$			2.09606e7i			0.588594i
$330$	3.00359e6			0.0835793
$331$	8.65891e6			0.238770			0.119385	−	0.992848i	$-0.461908\pi$
$331$	8.65891e6			0.238770			0.119385	+	0.992848i	$0.461908\pi$
$332$		−	835904.i		−	0.0228424i
$333$		−	5.05510e7i		−	1.36898i
$334$		−	3.07728e7i		−	0.825899i
$335$			4.96421e6i			0.132043i
$336$	−3.26166e6			−0.0859847
$337$			3.33853e7i			0.872299i	0.899874	+	0.436149i	$0.143658\pi$
$337$			3.33853e7i			0.872299i	−0.899874	+	0.436149i	$0.856342\pi$
$338$			4.93608e6i			0.127830i
$339$			4.48997e7i			1.15251i
$340$	−1.59805e6			−0.0406587
$341$	2.75895e7			0.695794
$342$			3.79867e7i			0.949628i
$343$	−4.12662e7			−1.02261
$344$	−3.93243e7			−0.966020
$345$			5.24188e6i			0.127653i
$346$	−7.51612e6			−0.181454
$347$			2.72488e6i			0.0652168i	0.999468	+	0.0326084i	$0.0103814\pi$
$347$			2.72488e6i			0.0652168i	−0.999468	+	0.0326084i	$0.989619\pi$
$348$	1.66115e7			0.394159
$349$		−	1.91349e7i		−	0.450143i	−0.974342	−	0.225071i	$-0.927738\pi$
$349$		−	1.91349e7i		−	0.450143i	0.974342	−	0.225071i	$-0.0722615\pi$
$350$			1.60653e7i			0.374702i
$351$			5.34773e6i			0.123665i
$352$	−6.29663e7			−1.44371
$353$		−	6.99509e7i		−	1.59026i	−0.606437	−	0.795132i	$-0.707402\pi$
$353$		−	6.99509e7i		−	1.59026i	0.606437	−	0.795132i	$-0.292598\pi$
$354$	5.02662e6	+	3.54704e7i	0.113310	+	0.799569i
$355$	−3.16008e6			−0.0706339
$356$		−	1.91409e7i		−	0.424241i
$357$	3.41832e7			0.751291
$358$	−2.07425e7			−0.452077
$359$	8.97797e7			1.94042			0.970208	−	0.242272i	$-0.0778927\pi$
$359$	8.97797e7			1.94042			0.970208	+	0.242272i	$0.0778927\pi$
$360$		−	3.04592e6i		−	0.0652845i
$361$	1.00733e8			2.14117
$362$			2.60689e7i			0.549538i
$363$	6.55123e7			1.36963
$364$			2.27216e7i			0.471123i
$365$		−	2.11619e6i		−	0.0435188i
$366$	3.17910e7			0.648426
$367$			8.22941e7i			1.66483i	0.554152	+	0.832416i	$0.313043\pi$
$367$			8.22941e7i			1.66483i	−0.554152	+	0.832416i	$0.686957\pi$
$368$		−	6.00934e6i		−	0.120582i
$369$	−2.06585e7			−0.411169
$370$	−3.22757e6			−0.0637192
$371$	1.40856e7			0.275838
$372$		−	2.32302e7i		−	0.451257i
$373$	−3.31563e6			−0.0638911			−0.0319455	−	0.999490i	$-0.510170\pi$
$373$	−3.31563e6			−0.0638911			−0.0319455	+	0.999490i	$0.510170\pi$
$374$	3.60872e7			0.689825
$375$	1.06943e7			0.202796
$376$	4.68536e7			0.881412
$377$		−	2.54991e7i		−	0.475883i
$378$		−	2.27877e6i		−	0.0421916i
$379$	1.02107e8			1.87559			0.937796	−	0.347186i	$-0.112863\pi$
$379$	1.02107e8			1.87559			0.937796	+	0.347186i	$0.112863\pi$
$380$	−4.71205e6			−0.0858734
$381$	−4.63529e7			−0.838112
$382$	7.14527e6			0.128182
$383$	7.60449e7			1.35355			0.676774	−	0.736190i	$-0.263377\pi$
$383$	7.60449e7			1.35355			0.676774	+	0.736190i	$0.263377\pi$
$384$			5.74088e7i			1.01388i
$385$		−	3.81698e6i		−	0.0668864i
$386$			2.80355e7i			0.487469i
$387$		−	5.31781e7i		−	0.917487i
$388$		−	4.41952e7i		−	0.756623i
$389$	−8.93799e7			−1.51842			−0.759208	−	0.650848i	$-0.774414\pi$
$389$	−8.93799e7			−1.51842			−0.759208	+	0.650848i	$0.774414\pi$
$390$	−3.88208e6			−0.0654442
$391$			6.29797e7i			1.05359i
$392$			3.39476e7i			0.563574i
$393$			1.31236e8i			2.16210i
$394$		−	3.67944e7i		−	0.601579i
$395$	870377.			0.0141226
$396$		−	5.31404e7i		−	0.855735i
$397$			4.00879e7i			0.640682i	0.947302	+	0.320341i	$0.103797\pi$
$397$			4.00879e7i			0.640682i	−0.947302	+	0.320341i	$0.896203\pi$
$398$			2.72061e7i			0.431537i
$399$	1.00793e8			1.58677
$400$	−6.11347e6			−0.0955229
$401$		−	9.20120e7i		−	1.42696i	−0.700676	−	0.713480i	$-0.747118\pi$
$401$		−	9.20120e7i		−	1.42696i	0.700676	−	0.713480i	$-0.252882\pi$
$402$	−9.43894e7			−1.45293
$403$	−3.56589e7			−0.544820
$404$			5.38986e7i			0.817398i
$405$	−5.23767e6			−0.0788448
$406$			1.08657e7i			0.162360i
$407$	−1.41603e8			−2.10033
$408$		−	7.64103e7i		−	1.12505i
$409$		−	5.81927e7i		−	0.850547i	−0.905065	−	0.425274i	$-0.860178\pi$
$409$		−	5.81927e7i		−	0.850547i	0.905065	−	0.425274i	$-0.139822\pi$
$410$			1.31900e6i			0.0191378i
$411$	−2.14249e7			−0.308598
$412$		−	1.88608e7i		−	0.269693i
$413$	4.50760e7	−	6.38787e6i	0.639875	−	0.0906788i
$414$	−4.77353e7			−0.672727
$415$		−	181494.i		−	0.00253932i
$416$	8.13828e7			1.13045
$417$	−1.41751e8			−1.95488
$418$	1.06408e8			1.45695
$419$		−	9.39093e7i		−	1.27663i	−0.769773	−	0.638317i	$-0.779631\pi$
$419$		−	9.39093e7i		−	1.27663i	0.769773	−	0.638317i	$-0.220369\pi$
$420$	−3.21388e6			−0.0433792
$421$			3.33313e7i			0.446690i	0.974739	+	0.223345i	$0.0716976\pi$
$421$			3.33313e7i			0.446690i	−0.974739	+	0.223345i	$0.928302\pi$
$422$	−3.19940e7			−0.425726
$423$			6.33599e7i			0.837130i
$424$		−	3.14859e7i		−	0.413064i
$425$	6.40710e7			0.834631
$426$		−	6.00857e7i		−	0.777217i
$427$		−	4.04002e7i		−	0.518919i
$428$	6.01272e7			0.766902
$429$	−1.70318e8			−2.15719
$430$	−3.39530e6			−0.0427044
$431$		−	1.58784e8i		−	1.98324i	−0.129187	−	0.991620i	$-0.541237\pi$
$431$		−	1.58784e8i		−	1.98324i	0.129187	−	0.991620i	$-0.458763\pi$
$432$	867160.			0.0107559
$433$	1.22323e8			1.50676			0.753380	−	0.657586i	$-0.228422\pi$
$433$	1.22323e8			1.50676			0.753380	+	0.657586i	$0.228422\pi$
$434$	1.51950e7			0.185879
$435$	3.60674e6			0.0438175
$436$			8.81315e7i			1.06334i
$437$			1.85704e8i			2.22523i
$438$	4.02373e7			0.478857
$439$	−4.30639e7			−0.509002			−0.254501	−	0.967072i	$-0.581911\pi$
$439$	−4.30639e7			−0.509002			−0.254501	+	0.967072i	$0.581911\pi$
$440$	−8.53216e6			−0.100162
$441$	−4.59072e7			−0.535260
$442$	−4.66421e7			−0.540146
$443$			8.97610e6i			0.103247i	0.998667	+	0.0516234i	$0.0164395\pi$
$443$			8.97610e6i			0.103247i	−0.998667	+	0.0516234i	$0.983560\pi$
$444$			1.19229e8i			1.36217i
$445$		−	4.15593e6i		−	0.0471616i
$446$			6.10611e7i			0.688271i
$447$		−	1.12441e8i		−	1.25894i
$448$	−2.90980e7			−0.323615
$449$	3.54564e7			0.391702			0.195851	−	0.980634i	$-0.437253\pi$
$449$	3.54564e7			0.391702			0.195851	+	0.980634i	$0.437253\pi$
$450$			4.85624e7i			0.532921i
$451$			5.78682e7i			0.630828i
$452$		−	5.07193e7i		−	0.549234i
$453$		−	9.20820e7i		−	0.990559i
$454$	−5.26147e7			−0.562264
$455$			4.93338e6i			0.0523733i
$456$		−	2.25305e8i		−	2.37617i
$457$		−	1.41739e8i		−	1.48505i	−0.669820	−	0.742524i	$-0.733629\pi$
$457$		−	1.41739e8i		−	1.48505i	0.669820	−	0.742524i	$-0.266371\pi$
$458$	5.02431e7			0.522974
$459$	−9.08809e6			−0.0939798
$460$		−	5.92130e6i		−	0.0608336i
$461$	−1.49779e8			−1.52880			−0.764398	−	0.644745i	$-0.776964\pi$
$461$	−1.49779e8			−1.52880			−0.764398	+	0.644745i	$0.776964\pi$
$462$	7.25760e7			0.735982
$463$			6.59283e7i			0.664246i	0.943236	+	0.332123i	$0.107765\pi$
$463$			6.59283e7i			0.664246i	−0.943236	+	0.332123i	$0.892235\pi$
$464$	−4.13480e6			−0.0413905
$465$		−	5.04381e6i		−	0.0501649i
$466$	3.62154e6			0.0357878
$467$			1.05945e7i			0.104023i	0.998646	+	0.0520116i	$0.0165633\pi$
$467$			1.05945e7i			0.104023i	−0.998646	+	0.0520116i	$0.983437\pi$
$468$			6.86830e7i			0.670057i
$469$			1.19951e8i			1.16274i
$470$	4.04538e6			0.0389642
$471$			2.16461e8i			2.07165i
$472$	−1.42789e7	−	1.00759e8i	−0.135790	−	0.958205i
$473$	−1.48962e8			−1.40764
$474$			1.65493e7i			0.155398i
$475$	1.88921e8			1.76279
$476$	−3.86138e7			−0.358032
$477$	4.25782e7			0.392312
$478$		−	4.17850e6i		−	0.0382592i
$479$	6.65723e7			0.605741			0.302871	−	0.953032i	$-0.402055\pi$
$479$	6.65723e7			0.605741			0.302871	+	0.953032i	$0.402055\pi$
$480$			1.15113e7i			0.104088i
$481$	1.83019e8			1.64460
$482$			1.54359e7i			0.137845i
$483$			1.26660e8i			1.12408i
$484$	−7.40036e7			−0.652705
$485$		−	9.59579e6i		−	0.0841115i
$486$		−	9.20947e7i		−	0.802280i
$487$	−6.66154e7			−0.576750			−0.288375	−	0.957518i	$-0.593115\pi$
$487$	−6.66154e7			−0.576750			−0.288375	+	0.957518i	$0.593115\pi$
$488$	−9.03072e7			−0.777075
$489$	−2.26924e8			−1.94068
$490$			2.93107e6i			0.0249136i
$491$	5.93051e7			0.501012			0.250506	−	0.968115i	$-0.419403\pi$
$491$	5.93051e7			0.501012			0.250506	+	0.968115i	$0.419403\pi$
$492$	4.87247e7			0.409123
$493$	4.33340e7			0.361649
$494$	−1.37530e8			−1.14082
$495$		−	1.15380e7i		−	0.0951294i
$496$			5.78227e6i			0.0473864i
$497$	−7.63574e7			−0.621988
$498$	3.45092e6			0.0279413
$499$	−8.45854e7			−0.680759			−0.340380	−	0.940288i	$-0.610556\pi$
$499$	−8.45854e7			−0.680759			−0.340380	+	0.940288i	$0.610556\pi$
$500$	−1.20804e7			−0.0966434
$501$	−2.46818e8			−1.96275
$502$			1.84413e7i			0.145774i
$503$		−	6.05751e7i		−	0.475981i	−0.971267	−	0.237991i	$-0.923511\pi$
$503$		−	6.05751e7i		−	0.475981i	0.971267	−	0.237991i	$-0.0764888\pi$
$504$		−	7.35987e7i		−	0.574882i
$505$			1.17026e7i			0.0908676i
$506$			1.33715e8i			1.03212i
$507$	3.95907e7			0.303787
$508$	5.23609e7			0.399407
$509$		−	1.72063e8i		−	1.30477i	−0.757889	−	0.652384i	$-0.773769\pi$
$509$		−	1.72063e8i		−	1.30477i	0.757889	−	0.652384i	$-0.226231\pi$
$510$		−	6.59733e6i		−	0.0497345i
$511$		−	5.11338e7i		−	0.383217i
$512$		−	2.56716e7i		−	0.191268i
$513$	−2.67974e7			−0.198491
$514$		−	9.42763e7i		−	0.694245i
$515$		−	4.09512e6i		−	0.0299809i
$516$			1.25425e8i			0.912923i
$517$	1.77482e8			1.28435
$518$	−7.79880e7			−0.561098
$519$			6.02843e7i			0.431223i
$520$	1.10277e7			0.0784284
$521$	−2.57761e8			−1.82265			−0.911327	−	0.411683i	$-0.864941\pi$
$521$	−2.57761e8			−1.82265			−0.911327	+	0.411683i	$0.864941\pi$
$522$			3.28449e7i			0.230917i
$523$	1.99694e8			1.39592			0.697958	−	0.716139i	$-0.254092\pi$
$523$	1.99694e8			1.39592			0.697958	+	0.716139i	$0.254092\pi$
$524$		−	1.48246e8i		−	1.03036i
$525$	1.28855e8			0.890477
$526$			6.04571e7i			0.415423i
$527$		−	6.05999e7i		−	0.414038i
$528$			2.76179e7i			0.187624i
$529$	−8.53248e7			−0.576379
$530$		−	2.71852e6i		−	0.0182602i
$531$	1.36256e8	−	1.93093e7i	0.910065	−	0.128968i
$532$	−1.13858e8			−0.756183
$533$		−	7.47937e7i		−	0.493950i
$534$	7.90208e7			0.518940
$535$	1.30550e7			0.0852541
$536$	2.68128e8			1.74119
$537$			1.66369e8i			1.07436i
$538$	9.70618e7			0.623306
$539$			1.28594e8i			0.821212i
$540$	854455.			0.00542635
$541$			1.88027e8i			1.18749i	0.804655	+	0.593743i	$0.202351\pi$
$541$			1.88027e8i			1.18749i	−0.804655	+	0.593743i	$0.797649\pi$
$542$			1.61065e7i			0.101159i
$543$	2.09090e8			1.30597
$544$			1.38304e8i			0.859092i
$545$			1.91354e7i			0.118208i
$546$	−9.38031e7			−0.576288
$547$	7.42370e7			0.453585			0.226792	−	0.973943i	$-0.427176\pi$
$547$	7.42370e7			0.453585			0.226792	+	0.973943i	$0.427176\pi$
$548$	2.42018e7			0.147064
$549$		−	1.22122e8i		−	0.738035i
$550$	1.36032e8			0.817623
$551$	1.27776e8			0.763824
$552$	2.83125e8			1.68330
$553$	2.10310e7			0.124361
$554$		−	8.18372e7i		−	0.481306i
$555$			2.58873e7i			0.151428i
$556$	1.60124e8			0.931607
$557$	−1.71354e8			−0.991583			−0.495792	−	0.868442i	$-0.665122\pi$
$557$	−1.71354e8			−0.991583			−0.495792	+	0.868442i	$0.665122\pi$
$558$	4.59315e7			0.264368
$559$	1.92530e8			1.10221
$560$	799971.			0.00455523
$561$		−	2.89444e8i		−	1.63937i
$562$		−	1.84184e7i		−	0.103763i
$563$		−	2.01929e8i		−	1.13155i	−0.824560	−	0.565774i	$-0.808578\pi$
$563$		−	2.01929e8i		−	1.13155i	0.824560	−	0.565774i	$-0.191422\pi$
$564$		−	1.49439e8i		−	0.832966i
$565$		−	1.10123e7i		−	0.0610567i
$566$	−1.66818e7			−0.0920010
$567$	−1.26558e8			−0.694290
$568$			1.70683e8i			0.931419i
$569$			4.48510e7i			0.243464i	0.992563	+	0.121732i	$0.0388449\pi$
$569$			4.48510e7i			0.243464i	−0.992563	+	0.121732i	$0.961155\pi$
$570$		−	1.94531e7i		−	0.105042i
$571$		−	2.52904e8i		−	1.35846i	−0.733925	−	0.679231i	$-0.762314\pi$
$571$		−	2.52904e8i		−	1.35846i	0.733925	−	0.679231i	$-0.237686\pi$
$572$	1.92394e8			1.02802
$573$		−	5.73099e7i		−	0.304625i
$574$			3.18711e7i			0.168524i
$575$			2.37404e8i			1.24878i
$576$	−8.79577e7			−0.460263
$577$	−3.42868e8			−1.78484			−0.892420	−	0.451206i	$-0.850994\pi$
$577$	−3.42868e8			−1.78484			−0.892420	+	0.451206i	$0.850994\pi$
$578$			3.32995e7i			0.172447i
$579$	2.24864e8			1.15847
$580$	−4.07422e6			−0.0208815
$581$		−	4.38546e6i		−	0.0223608i
$582$	1.82454e8			0.925517
$583$		−	1.19269e8i		−	0.601897i
$584$	−1.14300e8			−0.573863
$585$			1.49127e7i			0.0744882i
$586$			1.99427e7i			0.0991038i
$587$			3.81349e8i			1.88542i	0.333612	+	0.942711i	$0.391733\pi$
$587$			3.81349e8i			1.88542i	−0.333612	+	0.942711i	$0.608267\pi$
$588$	1.08276e8			0.532597
$589$		−	1.78686e8i		−	0.874472i
$590$	−1.23285e6	−	8.69963e6i	−0.00600283	−	0.0423589i
$591$	−2.95116e8			−1.42965
$592$		−	2.96774e7i		−	0.143041i
$593$	−2.00104e8			−0.959601			−0.479801	−	0.877378i	$-0.659291\pi$
$593$	−2.00104e8			−0.959601			−0.479801	+	0.877378i	$0.659291\pi$
$594$	−1.92954e7			−0.0920648
$595$	−8.38394e6			−0.0398013
$596$			1.27015e8i			0.599953i
$597$	2.18212e8			1.02555
$598$		−	1.72824e8i		−	0.808168i
$599$	−6.89658e7			−0.320888			−0.160444	−	0.987045i	$-0.551293\pi$
$599$	−6.89658e7			−0.320888			−0.160444	+	0.987045i	$0.551293\pi$
$600$		−	2.88031e8i		−	1.33348i
$601$			1.70435e8i			0.785119i	0.919727	+	0.392559i	$0.128410\pi$
$601$			1.70435e8i			0.785119i	−0.919727	+	0.392559i	$0.871590\pi$
$602$	−8.20410e7			−0.376046
$603$			3.62588e8i			1.65372i
$604$			1.04017e8i			0.472056i
$605$	−1.60679e7			−0.0725592
$606$	−2.22513e8			−0.999858
$607$	−4.17835e8			−1.86827			−0.934133	−	0.356926i	$-0.883825\pi$
$607$	−4.17835e8			−1.86827			−0.934133	+	0.356926i	$0.883825\pi$
$608$			4.07808e8i			1.81445i
$609$	8.71500e7			0.385848
$610$	−7.79721e6			−0.0343518
$611$	−2.29393e8			−1.00567
$612$	−1.16722e8			−0.509212
$613$			9.16975e7i			0.398085i	0.979991	+	0.199043i	$0.0637832\pi$
$613$			9.16975e7i			0.398085i	−0.979991	+	0.199043i	$0.936217\pi$
$614$		−	9.04756e7i		−	0.390864i
$615$	1.05793e7			0.0454810
$616$	−2.06163e8			−0.882002
$617$	−1.15089e8			−0.489979			−0.244989	−	0.969526i	$-0.578784\pi$
$617$	−1.15089e8			−0.489979			−0.244989	+	0.969526i	$0.578784\pi$
$618$	7.78645e7			0.329894
$619$	1.33788e8			0.564087			0.282044	−	0.959402i	$-0.408988\pi$
$619$	1.33788e8			0.564087			0.282044	+	0.959402i	$0.408988\pi$
$620$			5.69755e6i			0.0239064i
$621$		−	3.36744e7i		−	0.140613i
$622$			2.58402e8i			1.07380i
$623$		−	1.00420e8i		−	0.415295i
$624$		−	3.56956e7i		−	0.146913i
$625$	2.40203e8			0.983870
$626$	2.39202e8			0.975082
$627$		−	8.53462e8i		−	3.46243i
$628$		−	2.44517e8i		−	0.987255i
$629$			3.11028e8i			1.24982i
$630$		−	6.35458e6i		−	0.0254136i
$631$	−3.82563e8			−1.52270			−0.761352	−	0.648339i	$-0.775464\pi$
$631$	−3.82563e8			−1.52270			−0.761352	+	0.648339i	$0.775464\pi$
$632$		−	4.70109e7i		−	0.186229i
$633$			2.56613e8i			1.01174i
$634$			1.34601e8i			0.528177i
$635$	1.13687e7			0.0444009
$636$	−1.00424e8			−0.390361
$637$		−	1.66206e8i		−	0.643025i
$638$	9.20044e7			0.354280
$639$	−2.30814e8			−0.884624
$640$		−	1.40804e7i		−	0.0537124i
$641$	3.54583e7			0.134631			0.0673153	−	0.997732i	$-0.478557\pi$
$641$	3.54583e7			0.134631			0.0673153	+	0.997732i	$0.478557\pi$
$642$			2.48227e8i			0.938090i
$643$	1.77018e8			0.665864			0.332932	−	0.942951i	$-0.391962\pi$
$643$	1.77018e8			0.665864			0.332932	+	0.942951i	$0.391962\pi$
$644$		−	1.43077e8i		−	0.535688i
$645$			2.72326e7i			0.101487i
$646$		−	2.33723e8i		−	0.866969i
$647$	−3.64728e8			−1.34665			−0.673327	−	0.739344i	$-0.735136\pi$
$647$	−3.64728e8			−1.34665			−0.673327	+	0.739344i	$0.735136\pi$
$648$			2.82898e8i			1.03969i
$649$	−5.40888e7	−	3.81678e8i	−0.197867	−	1.39625i
$650$	−1.75819e8			−0.640215
$651$		−	1.21874e8i		−	0.441742i
$652$	2.56336e8			0.924841
$653$	3.63990e8			1.30722			0.653612	−	0.756830i	$-0.273253\pi$
$653$	3.63990e8			1.30722			0.653612	+	0.756830i	$0.273253\pi$
$654$	−3.63840e8			−1.30070
$655$		−	3.21877e7i		−	0.114542i
$656$	−1.21282e7			−0.0429619
$657$		−	1.54568e8i		−	0.545033i
$658$	9.77489e7			0.343111
$659$		−	2.72225e6i		−	0.00951201i	−0.999989	−	0.00475601i	$-0.998486\pi$
$659$		−	2.72225e6i		−	0.00951201i	0.999989	−	0.00475601i	$-0.00151389\pi$
$660$			2.72133e7i			0.0946562i
$661$	−1.39910e8			−0.484444			−0.242222	−	0.970221i	$-0.577876\pi$
$661$	−1.39910e8			−0.484444			−0.242222	+	0.970221i	$0.577876\pi$
$662$		−	4.03805e7i		−	0.139187i
$663$			3.74101e8i			1.28366i
$664$	−9.80288e6			−0.0334849
$665$	−2.47211e7			−0.0840626
$666$	−2.35743e8			−0.798023
$667$			1.60567e8i			0.541100i
$668$	2.78809e8			0.935357
$669$	4.89751e8			1.63567
$670$	2.31504e7			0.0769722
$671$	−3.42086e8			−1.13232
$672$			2.78148e8i			0.916575i
$673$			8.72886e7i			0.286360i	0.989697	+	0.143180i	$0.0457328\pi$
$673$			8.72886e7i			0.286360i	−0.989697	+	0.143180i	$0.954267\pi$
$674$	1.55691e8			0.508491
$675$	−3.42579e7			−0.111391
$676$	−4.47222e7			−0.144771
$677$	2.35187e8			0.757962			0.378981	−	0.925405i	$-0.376275\pi$
$677$	2.35187e8			0.757962			0.378981	+	0.925405i	$0.376275\pi$
$678$	2.09388e8			0.671835
$679$		−	2.31864e8i		−	0.740668i
$680$			1.87408e7i			0.0596019i
$681$			4.22006e8i			1.33622i
$682$		−	1.28663e8i		−	0.405601i
$683$		−	5.31641e8i		−	1.66862i	−0.551299	−	0.834308i	$-0.685867\pi$
$683$		−	5.31641e8i		−	1.66862i	0.551299	−	0.834308i	$-0.314133\pi$
$684$	−3.44170e8			−1.07548
$685$	5.25477e6			0.0163487
$686$			1.92443e8i			0.596115i
$687$		−	4.02984e8i		−	1.24285i
$688$		−	3.12197e7i		−	0.0958657i
$689$			1.54153e8i			0.471297i
$690$	2.44453e7			0.0744129
$691$		−	1.93656e7i		−	0.0586945i	−0.999569	−	0.0293473i	$-0.990657\pi$
$691$		−	1.93656e7i		−	0.0586945i	0.999569	−	0.0293473i	$-0.00934287\pi$
$692$		−	6.80980e7i		−	0.205502i
$693$		−	2.78794e8i		−	0.837690i
$694$	1.27074e7			0.0380170
$695$	3.47666e7			0.103564
$696$		−	1.94808e8i		−	0.577802i
$697$	1.27107e8			0.375379
$698$	−8.92349e7			−0.262403
$699$		−	2.90472e7i		−	0.0850497i
$700$	−1.45556e8			−0.424362
$701$		−	3.45490e8i		−	1.00296i	−0.865171	−	0.501478i	$-0.832790\pi$
$701$		−	3.45490e8i		−	1.00296i	0.865171	−	0.501478i	$-0.167210\pi$
$702$	2.49389e7			0.0720885
$703$			9.17104e8i			2.63969i
$704$			2.46385e8i			0.706150i
$705$		−	3.24467e7i		−	0.0925983i
$706$	−3.26213e8			−0.927016
$707$			2.82772e8i			0.800162i
$708$	−3.21371e8	+	4.55425e7i	−0.905537	+	0.128327i
$709$	3.59368e8			1.00833			0.504163	−	0.863608i	$-0.331801\pi$
$709$	3.59368e8			1.00833			0.504163	+	0.863608i	$0.331801\pi$
$710$			1.47369e7i			0.0411748i
$711$	6.35727e7			0.176873
$712$	−2.24471e8			−0.621899
$713$	2.24543e8			0.619485
$714$		−	1.59412e8i		−	0.437952i
$715$	4.17730e7			0.114282
$716$		−	1.87932e8i		−	0.511992i
$717$	−3.35143e7			−0.0909229
$718$		−	4.18684e8i		−	1.13113i
$719$		−	4.23162e8i		−	1.13846i	−0.822177	−	0.569232i	$-0.807241\pi$
$719$		−	4.23162e8i		−	1.13846i	0.822177	−	0.569232i	$-0.192759\pi$
$720$	2.41816e6			0.00647869
$721$		−	9.89507e7i		−	0.264006i
$722$		−	4.69765e8i		−	1.24816i
$723$	1.23806e8			0.327587
$724$	−2.36191e8			−0.622369
$725$	1.63349e8			0.428649
$726$		−	3.05514e8i		−	0.798402i
$727$	−3.00784e7			−0.0782801			−0.0391400	−	0.999234i	$-0.512462\pi$
$727$	−3.00784e7			−0.0782801			−0.0391400	+	0.999234i	$0.512462\pi$
$728$	2.66462e8			0.690624
$729$	−3.22453e8			−0.832308
$730$	−9.86879e6			−0.0253685
$731$			3.27192e8i			0.837626i
$732$			2.88034e8i			0.734363i
$733$	1.31344e8			0.333502			0.166751	−	0.985999i	$-0.446672\pi$
$733$	1.31344e8			0.333502			0.166751	+	0.985999i	$0.446672\pi$
$734$	3.83775e8			0.970484
$735$	2.35091e7			0.0592072
$736$	−5.12464e8			−1.28538
$737$	1.01567e9			2.53718
$738$			9.63402e7i			0.239684i
$739$			5.36073e8i			1.32828i	0.747607	+	0.664142i	$0.231203\pi$
$739$			5.36073e8i			1.32828i	−0.747607	+	0.664142i	$0.768797\pi$
$740$		−	2.92426e7i		−	0.0721640i
$741$			1.10308e9i			2.71115i
$742$		−	6.56878e7i		−	0.160795i
$743$	−5.09948e8			−1.24325			−0.621626	−	0.783314i	$-0.713528\pi$
$743$	−5.09948e8			−1.24325			−0.621626	+	0.783314i	$0.713528\pi$
$744$	−2.72427e8			−0.661503
$745$			2.75779e7i			0.0666949i
$746$			1.54623e7i			0.0372442i
$747$		−	1.32564e7i		−	0.0318027i
$748$			3.26960e8i			0.781249i
$749$	3.15449e8			0.750730
$750$		−	4.98724e7i		−	0.118216i
$751$		−	5.16995e8i		−	1.22058i	−0.792178	−	0.610290i	$-0.791053\pi$
$751$		−	5.16995e8i		−	1.22058i	0.792178	−	0.610290i	$-0.208947\pi$
$752$			3.71972e7i			0.0874694i
$753$	1.47911e8			0.346431
$754$	−1.18914e8			−0.277408
$755$			2.25845e7i			0.0524770i
$756$	2.06463e7			0.0477833
$757$	4.35762e8			1.00453			0.502263	−	0.864715i	$-0.332501\pi$
$757$	4.35762e8			1.00453			0.502263	+	0.864715i	$0.332501\pi$
$758$		−	4.76173e8i		−	1.09334i
$759$	1.07249e9			2.45282
$760$			5.52595e7i			0.125883i
$761$	2.10781e8			0.478275			0.239138	−	0.970986i	$-0.423135\pi$
$761$	2.10781e8			0.478275			0.239138	+	0.970986i	$0.423135\pi$
$762$			2.16165e8i			0.488563i
$763$			4.62370e8i			1.04092i
$764$			6.47380e7i			0.145171i
$765$	−2.53430e7			−0.0566075
$766$		−	3.54632e8i		−	0.789028i
$767$	6.99089e7	+	4.93312e8i	0.154934	+	1.09329i
$768$	5.81959e8			1.28472
$769$		−	6.80893e8i		−	1.49727i	−0.662983	−	0.748635i	$-0.730710\pi$
$769$		−	6.80893e8i		−	1.49727i	0.662983	−	0.748635i	$-0.269290\pi$
$770$	−1.78003e7			−0.0389903
$771$	−7.56159e8			−1.64987
$772$	−2.54009e8			−0.552074
$773$		−	1.27276e7i		−	0.0275556i	−0.999905	−	0.0137778i	$-0.995614\pi$
$773$		−	1.27276e7i		−	0.0275556i	0.999905	−	0.0137778i	$-0.00438574\pi$
$774$	−2.47994e8			−0.534833
$775$		−	2.28433e8i		−	0.490744i
$776$	−5.18289e8			−1.10914
$777$			6.25516e8i			1.33345i
$778$			4.16819e8i			0.885134i
$779$	3.74790e8			0.792822
$780$		−	3.51727e7i		−	0.0741176i
$781$			6.46551e8i			1.35722i
$782$	2.93703e8			0.614170
$783$	−2.31701e7			−0.0482661
$784$	−2.69511e7			−0.0559278
$785$		−	5.30902e7i		−	0.109750i
$786$	6.12015e8			1.26036
$787$	6.84602e7			0.140447			0.0702237	−	0.997531i	$-0.477629\pi$
$787$	6.84602e7			0.140447			0.0702237	+	0.997531i	$0.477629\pi$
$788$	3.33366e8			0.681308
$789$	4.84907e8			0.987250
$790$		−	4.05897e6i		−	0.00823255i
$791$		−	2.66092e8i		−	0.537652i
$792$	−6.23192e8			−1.25443
$793$	4.42140e8			0.886625
$794$	1.86948e8			0.373474
$795$	−2.18043e7			−0.0433952
$796$	−2.46495e8			−0.488729
$797$			8.47660e7i			0.167435i	0.996490	+	0.0837176i	$0.0266794\pi$
$797$			8.47660e7i			0.167435i	−0.996490	+	0.0837176i	$0.973321\pi$
$798$		−	4.70046e8i		−	0.924979i
$799$		−	3.89837e8i		−	0.764263i
$800$			5.21344e8i			1.01825i
$801$		−	3.03551e8i		−	0.590655i
$802$	−4.29094e8			−0.831821
$803$	−4.32972e8			−0.836205
$804$		−	8.55192e8i		−	1.64549i
$805$		−	3.10653e7i		−	0.0595508i
$806$			1.66294e8i			0.317593i
$807$		−	7.78501e8i		−	1.48128i
$808$	6.32084e8			1.19823
$809$			3.26264e8i			0.616204i	0.951353	+	0.308102i	$0.0996937\pi$
$809$			3.26264e8i			0.616204i	−0.951353	+	0.308102i	$0.900306\pi$
$810$			2.44256e7i			0.0459612i
$811$			1.97613e8i			0.370470i	0.982694	+	0.185235i	$0.0593047\pi$
$811$			1.97613e8i			0.370470i	−0.982694	+	0.185235i	$0.940695\pi$
$812$	−9.84458e7			−0.183878
$813$	1.29185e8			0.240403
$814$			6.60358e8i			1.22435i
$815$	5.56565e7			0.102812
$816$	6.06623e7			0.111647
$817$			9.64766e8i			1.76911i
$818$	−2.71379e8			−0.495812
$819$			3.60336e8i			0.655928i
$820$	−1.19505e7			−0.0216742
$821$		−	1.06086e9i		−	1.91702i	−0.285053	−	0.958512i	$-0.592011\pi$
$821$		−	1.06086e9i		−	1.91702i	0.285053	−	0.958512i	$-0.407989\pi$
$822$			9.99141e7i			0.179892i
$823$		−	7.67460e8i		−	1.37675i	−0.725353	−	0.688377i	$-0.758324\pi$
$823$		−	7.67460e8i		−	1.37675i	0.725353	−	0.688377i	$-0.241676\pi$
$824$	−2.21186e8			−0.395345
$825$		−	1.09107e9i		−	1.94308i
$826$	−2.97896e7	−	2.10210e8i	−0.0528596	−	0.373004i
$827$	−5.91248e8			−1.04533			−0.522665	−	0.852538i	$-0.675062\pi$
$827$	−5.91248e8			−1.04533			−0.522665	+	0.852538i	$0.675062\pi$
$828$		−	4.32494e8i		−	0.761884i
$829$	−3.99549e8			−0.701304			−0.350652	−	0.936506i	$-0.614040\pi$
$829$	−3.99549e8			−0.701304			−0.350652	+	0.936506i	$0.614040\pi$
$830$	−846390.			−0.00148025
$831$	−6.56389e8			−1.14382
$832$		−	3.18449e8i		−	0.552929i
$833$	2.82455e8			0.488669
$834$			6.61052e8i			1.13956i
$835$	6.05358e7			0.103981
$836$			9.64081e8i			1.65004i
$837$			3.24020e7i			0.0552580i
$838$	−4.37942e8			−0.744192
$839$			3.30724e8i			0.559989i	0.960002	+	0.279995i	$0.0903327\pi$
$839$			3.30724e8i			0.559989i	−0.960002	+	0.279995i	$0.909667\pi$
$840$			3.76900e7i			0.0635900i
$841$	−4.84343e8			−0.814264
$842$	1.55439e8			0.260390
$843$	−1.47728e8			−0.246593
$844$		−	2.89873e8i		−	0.482149i
$845$	−9.71021e6			−0.0160938
$846$	2.95476e8			0.487990
$847$	−3.88250e8			−0.638941
$848$	2.49967e7			0.0409916
$849$			1.33799e8i			0.218640i
$850$		−	2.98792e8i		−	0.486533i
$851$	−1.15246e9			−1.86998
$852$	5.44392e8			0.880224
$853$	−9.43491e8			−1.52016			−0.760082	−	0.649827i	$-0.774841\pi$
$853$	−9.43491e8			−1.52016			−0.760082	+	0.649827i	$0.774841\pi$
$854$	−1.88405e8			−0.302495
$855$	−7.47271e7			−0.119558
$856$		−	7.05129e8i		−	1.12421i
$857$			2.57279e8i			0.408753i	0.978892	+	0.204377i	$0.0655167\pi$
$857$			2.57279e8i			0.408753i	−0.978892	+	0.204377i	$0.934483\pi$
$858$			7.94272e8i			1.25750i
$859$		−	2.58079e8i		−	0.407168i	−0.979058	−	0.203584i	$-0.934741\pi$
$859$		−	2.58079e8i		−	0.407168i	0.979058	−	0.203584i	$-0.0652590\pi$
$860$		−	3.07623e7i		−	0.0483641i
$861$	2.55628e8			0.400496
$862$	−7.40484e8			−1.15610
$863$			3.72841e8i			0.580085i	0.957014	+	0.290043i	$0.0936695\pi$
$863$			3.72841e8i			0.580085i	−0.957014	+	0.290043i	$0.906331\pi$
$864$		−	7.39495e7i		−	0.114655i
$865$		−	1.47856e7i		−	0.0228450i
$866$		−	5.70448e8i		−	0.878339i
$867$	2.67085e8			0.409819
$868$			1.37671e8i			0.210514i
$869$		−	1.78079e8i		−	0.271364i
$870$		−	1.68199e7i		−	0.0255426i
$871$	−1.31274e9			−1.98666
$872$	1.03354e9			1.55876
$873$		−	7.00880e8i		−	1.05342i
$874$	8.66021e8			1.29716
$875$	−6.33782e7			−0.0946054
$876$			3.64560e8i			0.542321i
$877$	1.71955e7			0.0254927			0.0127463	−	0.999919i	$-0.495943\pi$
$877$	1.71955e7			0.0254927			0.0127463	+	0.999919i	$0.495943\pi$
$878$			2.00827e8i			0.296714i
$879$	1.59954e8			0.235520
$880$		−	6.77370e6i		−	0.00993981i
$881$		−	6.96642e7i		−	0.101878i	−0.998702	−	0.0509392i	$-0.983779\pi$
$881$		−	6.96642e7i		−	0.101878i	0.998702	−	0.0509392i	$-0.0162215\pi$
$882$			2.14086e8i			0.312020i
$883$	−1.25832e8			−0.182771			−0.0913857	−	0.995816i	$-0.529130\pi$
$883$	−1.25832e8			−0.182771			−0.0913857	+	0.995816i	$0.529130\pi$
$884$		−	4.22589e8i		−	0.611733i
$885$	−6.97769e7	+	9.88832e6i	−0.100666	+	0.0142657i
$886$	4.18597e7			0.0601859
$887$			3.09682e8i			0.443757i	0.975074	+	0.221879i	$0.0712188\pi$
$887$			3.09682e8i			0.443757i	−0.975074	+	0.221879i	$0.928781\pi$
$888$	1.39823e9			1.99682
$889$	2.74704e8			0.390985
$890$	−1.93810e7			−0.0274920
$891$			1.07162e9i			1.51499i
$892$	−5.53229e8			−0.779489
$893$		−	1.14948e9i		−	1.61417i
$894$	−5.24366e8			−0.733875
$895$		−	4.08045e7i		−	0.0569165i
$896$		−	3.40225e8i		−	0.472980i
$897$	−1.38617e9			−1.92061
$898$		−	1.65350e8i		−	0.228336i
$899$		−	1.54499e8i		−	0.212641i
$900$	−4.39988e8			−0.603550
$901$	−2.61973e8			−0.358164
$902$	2.69866e8			0.367730
$903$			6.58024e8i			0.893672i
$904$	−5.94799e8			−0.805128
$905$	−5.12825e7			−0.0691869
$906$	−4.29421e8			−0.577429
$907$	5.23269e8			0.701299			0.350650	−	0.936507i	$-0.385961\pi$
$907$	5.23269e8			0.701299			0.350650	+	0.936507i	$0.385961\pi$
$908$		−	4.76703e8i		−	0.636781i
$909$			8.54764e8i			1.13803i
$910$	2.30066e7			0.0305301
$911$	1.50080e9			1.98504			0.992518	−	0.122101i	$-0.0389631\pi$
$911$	1.50080e9			1.98504			0.992518	+	0.122101i	$0.0389631\pi$
$912$	1.78870e8			0.235805
$913$	−3.71335e7			−0.0487926
$914$	−6.60994e8			−0.865683
$915$			6.25389e7i			0.0816369i
$916$			4.55216e8i			0.592285i
$917$		−	7.77753e8i		−	1.00863i
$918$			4.23820e7i			0.0547839i
$919$			1.62510e8i			0.209379i	0.994505	+	0.104689i	$0.0333848\pi$
$919$			1.62510e8i			0.209379i	−0.994505	+	0.104689i	$0.966615\pi$
$920$	−6.94407e7			−0.0891766
$921$	−7.25675e8			−0.928888
$922$			6.98491e8i			0.891185i
$923$		−	8.35655e8i		−	1.06273i
$924$			6.57557e8i			0.833523i
$925$			1.17243e9i			1.48136i
$926$	3.07454e8			0.387211
$927$		−	2.99109e8i		−	0.375483i
$928$			3.52607e8i			0.441212i
$929$			9.65223e8i			1.20387i	0.798544	+	0.601936i	$0.205604\pi$
$929$			9.65223e8i			1.20387i	−0.798544	+	0.601936i	$0.794396\pi$
$930$	−2.35216e7			−0.0292427
$931$	8.32855e8			1.03210
$932$			3.28121e7i			0.0405309i
$933$	2.07256e9			2.55189
$934$	4.94071e7			0.0606385
$935$			7.09904e7i			0.0868490i
$936$	8.05465e8			0.982243
$937$		−	2.42385e8i		−	0.294637i	−0.989089	−	0.147319i	$-0.952936\pi$
$937$		−	2.42385e8i		−	0.294637i	0.989089	−	0.147319i	$-0.0470643\pi$
$938$	5.59385e8			0.677801
$939$		−	1.91856e9i		−	2.31728i
$940$			3.66522e7i			0.0441282i
$941$			1.01059e9i			1.21285i	0.795140	+	0.606426i	$0.207397\pi$
$941$			1.01059e9i			1.21285i	−0.795140	+	0.606426i	$0.792603\pi$
$942$	1.00945e9			1.20763
$943$			4.70973e8i			0.561643i
$944$	7.99929e7	−	1.13361e7i	0.0950901	−	0.0134755i
$945$	4.48278e6			0.00531193
$946$			6.94676e8i			0.820557i
$947$	−6.71519e8			−0.790694			−0.395347	−	0.918532i	$-0.629376\pi$
$947$	−6.71519e8			−0.790694			−0.395347	+	0.918532i	$0.629376\pi$
$948$	−1.49941e8			−0.175993
$949$	5.59608e8			0.654765
$950$		−	8.81027e8i		−	1.02759i
$951$	1.07959e9			1.25521
$952$			4.52835e8i			0.524842i
$953$	−1.42930e9			−1.65137			−0.825685	−	0.564132i	$-0.809211\pi$
$953$	−1.42930e9			−1.65137			−0.825685	+	0.564132i	$0.809211\pi$
$954$		−	1.98562e8i		−	0.228692i
$955$			1.40561e7i			0.0161382i
$956$	3.78582e7			0.0433298
$957$		−	7.37937e8i		−	0.841944i
$958$		−	3.10457e8i		−	0.353106i
$959$	1.26972e8			0.143963
$960$	4.50433e7			0.0509115
$961$	6.71446e8			0.756555
$962$		−	8.53501e8i		−	0.958691i
$963$	9.53542e8			1.06773
$964$	−1.39853e8			−0.156113
$965$	−5.51512e7			−0.0613724
$966$	5.90674e8			0.655265
$967$		−	1.38084e9i		−	1.52709i	−0.645754	−	0.763545i	$-0.723457\pi$
$967$		−	1.38084e9i		−	1.52709i	0.645754	−	0.763545i	$-0.276543\pi$
$968$			8.67861e8i			0.956806i
$969$	−1.87462e9			−2.06035
$970$	−4.47496e7			−0.0490313
$971$	−6.60316e8			−0.721263			−0.360632	−	0.932708i	$-0.617439\pi$
$971$	−6.60316e8			−0.721263			−0.360632	+	0.932708i	$0.617439\pi$
$972$	8.34402e8			0.908608
$973$	8.40070e8			0.911962
$974$			3.10658e8i			0.336206i
$975$			1.41019e9i			1.52147i
$976$		−	7.16951e7i		−	0.0771152i
$977$		−	7.87607e8i		−	0.844551i	−0.906468	−	0.422275i	$-0.861232\pi$
$977$		−	7.87607e8i		−	0.844551i	0.906468	−	0.422275i	$-0.138768\pi$
$978$			1.05825e9i			1.13128i
$979$	−8.50301e8			−0.906201
$980$	−2.65562e7			−0.0282155
$981$			1.39766e9i			1.48045i
$982$		−	2.76567e8i		−	0.292056i
$983$			8.93293e8i			0.940445i	0.882548	+	0.470222i	$0.155826\pi$
$983$			8.93293e8i			0.940445i	−0.882548	+	0.470222i	$0.844174\pi$
$984$		−	5.71409e8i		−	0.599738i
$985$	7.23815e7			0.0757389
$986$		−	2.02086e8i		−	0.210817i
$987$		−	7.84012e8i		−	0.815401i
$988$		−	1.24606e9i		−	1.29201i
$989$	−1.21235e9			−1.25326
$990$	−5.38070e7			−0.0554540
$991$		−	1.08986e9i		−	1.11982i	−0.828553	−	0.559910i	$-0.810836\pi$
$991$		−	1.08986e9i		−	1.11982i	0.828553	−	0.559910i	$-0.189164\pi$
$992$	4.93100e8			0.505126
$993$	−3.23879e8			−0.330776
$994$			3.56089e8i			0.362577i
$995$	−5.35196e7			−0.0543305
$996$			3.12662e7i			0.0316445i
$997$	1.56208e9			1.57622			0.788112	−	0.615532i	$-0.211059\pi$
$997$	1.56208e9			1.57622			0.788112	+	0.615532i	$0.211059\pi$
$998$			3.94460e8i			0.396837i
$999$		−	1.66302e8i		−	0.166802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	59.7.b.c.58.12	✓	26
59.58	odd	2	inner	59.7.b.c.58.15	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.7.b.c.58.12	✓	26	1.1	even	1	trivial
59.7.b.c.58.15	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)

\(f(q)\)	\(=\)	\(q-4.66346i q^{2} -37.4041 q^{3} +42.2521 q^{4} +9.17391 q^{5} +174.432i q^{6} +221.670 q^{7} -495.503i q^{8} +670.066 q^{9} -42.7822i q^{10} -1876.98i q^{11} -1580.40 q^{12} +2425.96i q^{13} -1033.75i q^{14} -343.142 q^{15} +393.381 q^{16} -4122.75 q^{17} -3124.83i q^{18} -12156.4 q^{19} +387.617 q^{20} -8291.37 q^{21} -8753.20 q^{22} -15276.1i q^{23} +18533.8i q^{24} -15540.8 q^{25} +11313.4 q^{26} +2204.38 q^{27} +9366.03 q^{28} -10510.9 q^{29} +1600.23i q^{30} +14698.9i q^{31} -33546.7i q^{32} +70206.6i q^{33} +19226.3i q^{34} +2033.58 q^{35} +28311.7 q^{36} -75441.9i q^{37} +56691.1i q^{38} -90740.7i q^{39} -4545.70i q^{40} -30830.6 q^{41} +38666.4i q^{42} -79362.5i q^{43} -79306.2i q^{44} +6147.12 q^{45} -71239.7 q^{46} +94557.7i q^{47} -14714.0 q^{48} -68511.4 q^{49} +72474.1i q^{50} +154208. q^{51} +102502. i q^{52} +63543.3 q^{53} -10280.0i q^{54} -17219.2i q^{55} -109838. i q^{56} +454700. q^{57} +49017.3i q^{58} +(203347. - 28817.0i) q^{59} -14498.5 q^{60} -182254. i q^{61} +68547.8 q^{62} +148534. q^{63} -131267. q^{64} +22255.5i q^{65} +327405. q^{66} +541123. i q^{67} -174195. q^{68} +571390. i q^{69} -9483.52i q^{70} -344464. q^{71} -332019. i q^{72} -230675. i q^{73} -351820. q^{74} +581291. q^{75} -513635. q^{76} -416069. i q^{77} -423166. q^{78} +94875.3 q^{79} +3608.84 q^{80} -570931. q^{81} +143777. i q^{82} -19783.7i q^{83} -350328. q^{84} -37821.7 q^{85} -370104. q^{86} +393152. q^{87} -930046. q^{88} -453016. i q^{89} -28666.9i q^{90} +537762. i q^{91} -645450. i q^{92} -549800. i q^{93} +440966. q^{94} -111522. q^{95} +1.25478e6i q^{96} -1.04599e6i q^{97} +319500. i q^{98} -1.25770e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 10 q^{3} - 1090 q^{4} + 142 q^{5} + 406 q^{7} + 5432 q^{9} - 1124 q^{12} + 14982 q^{15} + 12734 q^{16} - 9108 q^{17} + 3850 q^{19} - 46896 q^{20} - 49034 q^{21} + 11238 q^{22} + 18792 q^{25} - 64590 q^{26}+ \cdots - 2396490 q^{95}+O(q^{100}) \) 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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