LMFDB - Embedded newform 115.7.c.c.114.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,7,Mod(114,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("115.114");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	115.c (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:	$26.4562196163$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			114.19
Character	$\chi$	$=$	115.114
Dual form			115.7.c.c.114.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.58308i q^{2} +53.1699i q^{3} +6.49696 q^{4} +(-65.6908 + 106.347i) q^{5} +403.191 q^{6} -232.063 q^{7} -534.584i q^{8} -2098.04 q^{9} +O(q^{10})$	\(q-7.58308i q^{2} +53.1699i q^{3} +6.49696 q^{4} +(-65.6908 + 106.347i) q^{5} +403.191 q^{6} -232.063 q^{7} -534.584i q^{8} -2098.04 q^{9} +(806.439 + 498.138i) q^{10} +2126.02i q^{11} +345.443i q^{12} -1028.42i q^{13} +1759.75i q^{14} +(-5654.47 - 3492.77i) q^{15} -3637.98 q^{16} +6732.26 q^{17} +15909.6i q^{18} +427.331i q^{19} +(-426.790 + 690.934i) q^{20} -12338.7i q^{21} +16121.8 q^{22} +(-10806.0 - 5591.65i) q^{23} +28423.8 q^{24} +(-6994.45 - 13972.1i) q^{25} -7798.62 q^{26} -72791.6i q^{27} -1507.70 q^{28} -16125.5 q^{29} +(-26485.9 + 42878.3i) q^{30} +6944.68 q^{31} -6626.26i q^{32} -113040. q^{33} -51051.2i q^{34} +(15244.4 - 24679.2i) q^{35} -13630.9 q^{36} +52591.8 q^{37} +3240.48 q^{38} +54681.2 q^{39} +(56851.5 + 35117.2i) q^{40} +73926.6 q^{41} -93565.7 q^{42} -22440.8 q^{43} +13812.7i q^{44} +(137822. - 223120. i) q^{45} +(-42401.9 + 81942.6i) q^{46} +28207.0i q^{47} -193431. i q^{48} -63795.9 q^{49} +(-105951. + 53039.4i) q^{50} +357954. i q^{51} -6681.64i q^{52} -206293. q^{53} -551984. q^{54} +(-226097. - 139660. i) q^{55} +124057. i q^{56} -22721.1 q^{57} +122281. i q^{58} +75321.3 q^{59} +(-36736.9 - 22692.4i) q^{60} -179559. i q^{61} -52662.0i q^{62} +486876. q^{63} -283078. q^{64} +(109370. + 67558.0i) q^{65} +857194. i q^{66} -551385. q^{67} +43739.2 q^{68} +(297308. - 574553. i) q^{69} +(-187144. - 115599. i) q^{70} -371411. q^{71} +1.12158e6i q^{72} +188063. i q^{73} -398807. i q^{74} +(742893. - 371894. i) q^{75} +2776.35i q^{76} -493371. i q^{77} -414652. i q^{78} +126019. i q^{79} +(238982. - 386889. i) q^{80} +2.34085e6 q^{81} -560591. i q^{82} -541715. q^{83} -80164.4i q^{84} +(-442247. + 715957. i) q^{85} +170170. i q^{86} -857393. i q^{87} +1.13654e6 q^{88} +823856. i q^{89} +(-1.69194e6 - 1.04511e6i) q^{90} +238659. i q^{91} +(-70206.1 - 36328.8i) q^{92} +369248. i q^{93} +213896. q^{94} +(-45445.4 - 28071.7i) q^{95} +352317. q^{96} +781061. q^{97} +483769. i q^{98} -4.46048e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9}+O(q^{10}) $ 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9	$ 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9} + 66968 q^{16} - 30916 q^{24} + 32588 q^{25} - 22072 q^{26} + 103360 q^{29} - 17256 q^{31} - 358168 q^{35} + 451984 q^{36} + 192432 q^{39} - 183552 q^{41} - 397956 q^{46} + 806756 q^{49} - 749960 q^{50} - 1638436 q^{54} - 1752 q^{55} - 505552 q^{59} - 4095100 q^{64} + 1354876 q^{69} + 1196604 q^{70} + 493688 q^{71} + 3178568 q^{75} + 2473820 q^{81} + 3306336 q^{85} - 3770196 q^{94} + 896144 q^{95} + 16928136 q^{96}+O(q^{100}) $ 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9 + 66968 * q^16 - 30916 * q^24 + 32588 * q^25 - 22072 * q^26 + 103360 * q^29 - 17256 * q^31 - 358168 * q^35 + 451984 * q^36 + 192432 * q^39 - 183552 * q^41 - 397956 * q^46 + 806756 * q^49 - 749960 * q^50 - 1638436 * q^54 - 1752 * q^55 - 505552 * q^59 - 4095100 * q^64 + 1354876 * q^69 + 1196604 * q^70 + 493688 * q^71 + 3178568 * q^75 + 2473820 * q^81 + 3306336 * q^85 - 3770196 * q^94 + 896144 * q^95 + 16928136 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	7.58308i		−	0.947884i	−0.880556	−	0.473942i	$-0.842831\pi$
$2$		−	7.58308i		−	0.947884i	0.880556	−	0.473942i	$-0.157169\pi$
$3$			53.1699i			1.96926i	0.174666	+	0.984628i	$0.444115\pi$
$3$			53.1699i			1.96926i	−0.174666	+	0.984628i	$0.555885\pi$
$4$	6.49696			0.101515
$5$	−65.6908	+	106.347i	−0.525526	+	0.850777i
$5$	−65.6908	+	106.347i	−0.525526	+	0.850777i
$6$	403.191			1.86663
$7$	−232.063			−0.676568			−0.338284	−	0.941044i	$-0.609846\pi$
$7$	−232.063			−0.676568			−0.338284	+	0.941044i	$0.609846\pi$
$8$		−	534.584i		−	1.04411i
$9$	−2098.04			−2.87797
$10$	806.439	+	498.138i	0.806439	+	0.498138i
$11$			2126.02i			1.59731i	0.601787	+	0.798656i	$0.294455\pi$
$11$			2126.02i			1.59731i	−0.601787	+	0.798656i	$0.705545\pi$
$12$			345.443i			0.199909i
$13$		−	1028.42i		−	0.468104i	−0.972224	−	0.234052i	$-0.924801\pi$
$13$		−	1028.42i		−	0.468104i	0.972224	−	0.234052i	$-0.0751986\pi$
$14$			1759.75i			0.641308i
$15$	−5654.47	−	3492.77i	−1.67540	−	1.03490i
$16$	−3637.98			−0.888180
$17$	6732.26			1.37030			0.685148	−	0.728404i	$-0.259738\pi$
$17$	6732.26			1.37030			0.685148	+	0.728404i	$0.259738\pi$
$18$			15909.6i			2.72798i
$19$			427.331i			0.0623022i	0.999515	+	0.0311511i	$0.00991730\pi$
$19$			427.331i			0.0623022i	−0.999515	+	0.0311511i	$0.990083\pi$
$20$	−426.790	+	690.934i	−0.0533488	+	0.0863667i
$21$		−	12338.7i		−	1.33233i
$22$	16121.8			1.51407
$23$	−10806.0	−	5591.65i	−0.888139	−	0.459575i
$23$	−10806.0	−	5591.65i	−0.888139	−	0.459575i
$24$	28423.8			2.05612
$25$	−6994.45	−	13972.1i	−0.447645	−	0.894212i
$26$	−7798.62			−0.443709
$27$		−	72791.6i		−	3.69820i
$28$	−1507.70			−0.0686818
$29$	−16125.5			−0.661180			−0.330590	−	0.943774i	$-0.607248\pi$
$29$	−16125.5			−0.661180			−0.330590	+	0.943774i	$0.607248\pi$
$30$	−26485.9	+	42878.3i	−0.980961	+	1.58808i
$31$	6944.68			0.233113			0.116557	−	0.993184i	$-0.462814\pi$
$31$	6944.68			0.233113			0.116557	+	0.993184i	$0.462814\pi$
$32$		−	6626.26i		−	0.202217i
$33$	−113040.			−3.14552
$34$		−	51051.2i		−	1.29888i
$35$	15244.4	−	24679.2i	0.355554	−	0.575608i
$36$	−13630.9			−0.292157
$37$	52591.8			1.03828			0.519138	−	0.854691i	$-0.326253\pi$
$37$	52591.8			1.03828			0.519138	+	0.854691i	$0.326253\pi$
$38$	3240.48			0.0590553
$39$	54681.2			0.921817
$40$	56851.5	+	35117.2i	0.888304	+	0.548706i
$41$	73926.6			1.07263			0.536314	−	0.844019i	$-0.319816\pi$
$41$	73926.6			1.07263			0.536314	+	0.844019i	$0.319816\pi$
$42$	−93565.7			−1.26290
$43$	−22440.8			−0.282250			−0.141125	−	0.989992i	$-0.545072\pi$
$43$	−22440.8			−0.282250			−0.141125	+	0.989992i	$0.545072\pi$
$44$			13812.7i			0.162151i
$45$	137822.	−	223120.i	1.51245	−	2.44851i
$46$	−42401.9	+	81942.6i	−0.435624	+	0.841853i
$47$			28207.0i			0.271684i	0.990731	+	0.135842i	$0.0433739\pi$
$47$			28207.0i			0.271684i	−0.990731	+	0.135842i	$0.956626\pi$
$48$		−	193431.i		−	1.74905i
$49$	−63795.9			−0.542256
$50$	−105951.	+	53039.4i	−0.847609	+	0.424315i
$51$			357954.i			2.69846i
$52$		−	6681.64i		−	0.0475196i
$53$	−206293.			−1.38566			−0.692831	−	0.721100i	$-0.743637\pi$
$53$	−206293.			−1.38566			−0.692831	+	0.721100i	$0.743637\pi$
$54$	−551984.			−3.50546
$55$	−226097.	−	139660.i	−1.35896	−	0.839429i
$56$			124057.i			0.706410i
$57$	−22721.1			−0.122689
$58$			122281.i			0.626723i
$59$	75321.3			0.366743			0.183371	−	0.983044i	$-0.441299\pi$
$59$	75321.3			0.366743			0.183371	+	0.983044i	$0.441299\pi$
$60$	−36736.9	−	22692.4i	−0.170078	−	0.105057i
$61$		−	179559.i		−	0.791077i	−0.918449	−	0.395538i	$-0.870558\pi$
$61$		−	179559.i		−	0.791077i	0.918449	−	0.395538i	$-0.129442\pi$
$62$		−	52662.0i		−	0.220964i
$63$	486876.			1.94714
$64$	−283078.			−1.07986
$65$	109370.	+	67558.0i	0.398252	+	0.246001i
$66$			857194.i			2.98159i
$67$	−551385.			−1.83329			−0.916644	−	0.399705i	$-0.869113\pi$
$67$	−551385.			−1.83329			−0.916644	+	0.399705i	$0.869113\pi$
$68$	43739.2			0.139106
$69$	297308.	−	574553.i	0.905021	−	1.74897i
$70$	−187144.	−	115599.i	−0.545610	−	0.337024i
$71$	−371411.			−1.03772			−0.518860	−	0.854859i	$-0.673643\pi$
$71$	−371411.			−1.03772			−0.518860	+	0.854859i	$0.673643\pi$
$72$			1.12158e6i			3.00491i
$73$			188063.i			0.483431i	0.970347	+	0.241716i	$0.0777101\pi$
$73$			188063.i			0.483431i	−0.970347	+	0.241716i	$0.922290\pi$
$74$		−	398807.i		−	0.984165i
$75$	742893.	−	371894.i	1.76093	−	0.881527i
$76$			2776.35i			0.00632461i
$77$		−	493371.i		−	1.08069i
$78$		−	414652.i		−	0.873776i
$79$			126019.i			0.255597i	0.991800	+	0.127798i	$0.0407911\pi$
$79$			126019.i			0.255597i	−0.991800	+	0.127798i	$0.959209\pi$
$80$	238982.	−	386889.i	0.466762	−	0.755643i
$81$	2.34085e6			4.40473
$82$		−	560591.i		−	1.01673i
$83$	−541715.			−0.947407			−0.473703	−	0.880684i	$-0.657083\pi$
$83$	−541715.			−0.947407			−0.473703	+	0.880684i	$0.657083\pi$
$84$		−	80164.4i		−	0.135252i
$85$	−442247.	+	715957.i	−0.720126	+	1.16582i
$86$			170170.i			0.267540i
$87$		−	857393.i		−	1.30203i
$88$	1.13654e6			1.66777
$89$			823856.i			1.16864i	0.811523	+	0.584321i	$0.198639\pi$
$89$			823856.i			1.16864i	−0.811523	+	0.584321i	$0.801361\pi$
$90$	−1.69194e6	−	1.04511e6i	−2.32090	−	1.43362i
$91$			238659.i			0.316704i
$92$	−70206.1	−	36328.8i	−0.0901595	−	0.0466538i
$93$			369248.i			0.459060i
$94$	213896.			0.257525
$95$	−45445.4	−	28071.7i	−0.0530053	−	0.0327414i
$96$	352317.			0.398218
$97$	781061.			0.855795			0.427898	−	0.903827i	$-0.359254\pi$
$97$	781061.			0.855795			0.427898	+	0.903827i	$0.359254\pi$
$98$			483769.i			0.513996i
$99$		−	4.46048e6i		−	4.59701i
$100$	−45442.7	−	90775.9i	−0.0454427	−	0.0907759i
$101$	918788.			0.891767			0.445884	−	0.895091i	$-0.352890\pi$
$101$	918788.			0.891767			0.445884	+	0.895091i	$0.352890\pi$
$102$	2.71439e6			2.55783
$103$	−1.27954e6			−1.17096			−0.585479	−	0.810688i	$-0.699093\pi$
$103$	−1.27954e6			−1.17096			−0.585479	+	0.810688i	$0.699093\pi$
$104$	−549779.			−0.488752
$105$	1.31219e6	+	810542.i	1.13352	+	0.700176i
$106$			1.56434e6i			1.31345i
$107$	−752025.			−0.613877			−0.306938	−	0.951729i	$-0.599305\pi$
$107$	−752025.			−0.613877			−0.306938	+	0.951729i	$0.599305\pi$
$108$		−	472924.i		−	0.375423i
$109$		−	148621.i		−	0.114763i	−0.998352	−	0.0573815i	$-0.981725\pi$
$109$		−	148621.i		−	0.114763i	0.998352	−	0.0573815i	$-0.0182751\pi$
$110$	−1.05905e6	+	1.71451e6i	−0.795682	+	1.28813i
$111$			2.79630e6i			2.04463i
$112$	844240.			0.600914
$113$	671991.			0.465723			0.232862	−	0.972510i	$-0.425191\pi$
$113$	671991.			0.465723			0.232862	+	0.972510i	$0.425191\pi$
$114$			172296.i			0.116295i
$115$	1.30451e6	−	781866.i	0.857736	−	0.514090i
$116$	−104767.			−0.0671198
$117$			2.15767e6i			1.34719i
$118$		−	571167.i		−	0.347630i
$119$	−1.56231e6			−0.927097
$120$	−1.86718e6	+	3.02279e6i	−1.08054	+	1.74930i
$121$	−2.74841e6			−1.55141
$122$	−1.36161e6			−0.749849
$123$			3.93067e6i			2.11228i
$124$	45119.3			0.0236645
$125$	1.94536e6	+	173995.i	0.996024	+	0.0890854i
$126$		−	3.69202e6i		−	1.84566i
$127$			2.85729e6i			1.39490i	0.716634	+	0.697450i	$0.245682\pi$
$127$			2.85729e6i			1.39490i	−0.716634	+	0.697450i	$0.754318\pi$
$128$			1.72252e6i			0.821364i
$129$		−	1.19318e6i		−	0.555822i
$130$	512297.	−	829362.i	0.233180	−	0.377497i
$131$	41035.1			0.0182533			0.00912666	−	0.999958i	$-0.497095\pi$
$131$	41035.1			0.0182533			0.00912666	+	0.999958i	$0.497095\pi$
$132$	−734420.			−0.319317
$133$		−	99167.5i		−	0.0421516i
$134$			4.18120e6i			1.73775i
$135$	7.74118e6	+	4.78174e6i	3.14634	+	1.94350i
$136$		−	3.59896e6i		−	1.43074i
$137$	2.18343e6			0.849135			0.424567	−	0.905396i	$-0.360426\pi$
$137$	2.18343e6			0.849135			0.424567	+	0.905396i	$0.360426\pi$
$138$	−4.35688e6	−	2.25451e6i	−1.65782	−	0.857855i
$139$	−3.55338e6			−1.32311			−0.661557	−	0.749895i	$-0.730104\pi$
$139$	−3.55338e6			−1.32311			−0.661557	+	0.749895i	$0.730104\pi$
$140$	99042.1	−	160340.i	0.0360941	−	0.0584329i
$141$	−1.49976e6			−0.535015
$142$			2.81644e6i			0.983638i
$143$	2.18645e6			0.747709
$144$	7.63263e6			2.55615
$145$	1.05930e6	−	1.71490e6i	0.347468	−	0.562517i
$146$	1.42610e6			0.458237
$147$		−	3.39202e6i		−	1.06784i
$148$	341687.			0.105401
$149$		−	170007.i		−	0.0513936i	−0.999670	−	0.0256968i	$-0.991820\pi$
$149$		−	170007.i		−	0.0513936i	0.999670	−	0.0256968i	$-0.00818044\pi$
$150$	−2.82010e6	−	5.63341e6i	−0.835586	−	1.66916i
$151$	−3.62362e6			−1.05248			−0.526238	−	0.850337i	$-0.676398\pi$
$151$	−3.62362e6			−1.05248			−0.526238	+	0.850337i	$0.676398\pi$
$152$	228444.			0.0650503
$153$	−1.41245e7			−3.94366
$154$	−3.74127e6			−1.02437
$155$	−456201.	+	738547.i	−0.122507	+	0.198327i
$156$	355262.			0.0935783
$157$	−4.29423e6			−1.10965			−0.554826	−	0.831967i	$-0.687215\pi$
$157$	−4.29423e6			−1.10965			−0.554826	+	0.831967i	$0.687215\pi$
$158$	955614.			0.242276
$159$		−	1.09686e7i		−	2.72872i
$160$	704684.	+	435284.i	0.172042	+	0.106270i
$161$	2.50767e6	+	1.29761e6i	0.600886	+	0.310934i
$162$		−	1.77509e7i		−	4.17517i
$163$			3.89642e6i			0.899710i	0.893102	+	0.449855i	$0.148524\pi$
$163$			3.89642e6i			0.899710i	−0.893102	+	0.449855i	$0.851476\pi$
$164$	480298.			0.108888
$165$	7.42571e6	−	1.20215e7i	1.65305	−	2.67613i
$166$			4.10786e6i			0.898032i
$167$			1.69124e6i			0.363126i	0.983379	+	0.181563i	$0.0581156\pi$
$167$			1.69124e6i			0.363126i	−0.983379	+	0.181563i	$0.941884\pi$
$168$	−6.59610e6			−1.39110
$169$	3.76915e6			0.780879
$170$	5.42916e6	+	3.35359e6i	1.10506	+	0.682596i
$171$		−	896556.i		−	0.179304i
$172$	−145797.			−0.0286526
$173$			786475.i			0.151896i	0.997112	+	0.0759481i	$0.0241983\pi$
$173$			786475.i			0.151896i	−0.997112	+	0.0759481i	$0.975802\pi$
$174$	−6.50167e6			−1.23418
$175$	1.62315e6	+	3.24239e6i	0.302862	+	0.604994i
$176$		−	7.73444e6i		−	1.41870i
$177$			4.00482e6i			0.722210i
$178$	6.24736e6			1.10774
$179$	1.79827e6			0.313542			0.156771	−	0.987635i	$-0.449892\pi$
$179$	1.79827e6			0.313542			0.156771	+	0.987635i	$0.449892\pi$
$180$	895423.	−	1.44961e6i	0.153536	−	0.248561i
$181$			7.56123e6i			1.27514i	0.770394	+	0.637568i	$0.220060\pi$
$181$			7.56123e6i			1.27514i	−0.770394	+	0.637568i	$0.779940\pi$
$182$	1.80977e6			0.300199
$183$	9.54715e6			1.55783
$184$	−2.98921e6	+	5.77671e6i	−0.479847	+	0.927314i
$185$	−3.45479e6	+	5.59299e6i	−0.545641	+	0.883342i
$186$	2.80003e6			0.435135
$187$			1.43129e7i			2.18879i
$188$			183260.i			0.0275800i
$189$			1.68922e7i			2.50208i
$190$	−212870.	+	344616.i	−0.0310351	+	0.0502429i
$191$		−	1.01386e7i		−	1.45505i	−0.686084	−	0.727523i	$-0.740672\pi$
$191$		−	1.01386e7i		−	1.45505i	0.686084	−	0.727523i	$-0.259328\pi$
$192$		−	1.50512e7i		−	2.12652i
$193$			4.12584e6i			0.573905i	0.957945	+	0.286953i	$0.0926422\pi$
$193$			4.12584e6i			0.573905i	−0.957945	+	0.286953i	$0.907358\pi$
$194$		−	5.92285e6i		−	0.811195i
$195$	−3.59205e6	+	5.81520e6i	−0.484439	+	0.784261i
$196$	−414480.			−0.0550472
$197$		−	1.09528e7i		−	1.43260i	−0.697791	−	0.716301i	$-0.745834\pi$
$197$		−	1.09528e7i		−	1.43260i	0.697791	−	0.716301i	$-0.254166\pi$
$198$	−3.38241e7			−4.35744
$199$			8.28135e6i			1.05085i	0.850839	+	0.525426i	$0.176094\pi$
$199$			8.28135e6i			1.05085i	−0.850839	+	0.525426i	$0.823906\pi$
$200$	−7.46923e6	+	3.73912e6i	−0.933654	+	0.467390i
$201$		−	2.93171e7i		−	3.61021i
$202$		−	6.96724e6i		−	0.845292i
$203$	3.74213e6			0.447333
$204$			2.32561e6i			0.273934i
$205$	−4.85629e6	+	7.86188e6i	−0.563694	+	0.912567i
$206$			9.70283e6i			1.10993i
$207$	2.26714e7	+	1.17315e7i	2.55603	+	1.32264i
$208$			3.74139e6i			0.415761i
$209$	−908515.			−0.0995160
$210$	6.14640e6	−	9.95045e6i	0.663686	−	1.07445i
$211$	−1.66299e7			−1.77029			−0.885143	−	0.465320i	$-0.845939\pi$
$211$	−1.66299e7			−1.77029			−0.885143	+	0.465320i	$0.845939\pi$
$212$	−1.34028e6			−0.140666
$213$		−	1.97479e7i		−	2.04354i
$214$			5.70266e6i			0.581884i
$215$	1.47415e6	−	2.38652e6i	0.148330	−	0.240132i
$216$	−3.89132e7			−3.86132
$217$	−1.61160e6			−0.157717
$218$	−1.12701e6			−0.108782
$219$	−9.99929e6			−0.952000
$220$	−1.46894e6	−	907366.i	−0.137955	−	0.0852147i
$221$		−	6.92362e6i		−	0.641441i
$222$	2.12046e7			1.93807
$223$		−	1.25985e7i		−	1.13607i	−0.823006	−	0.568033i	$-0.807704\pi$
$223$		−	1.25985e7i		−	1.13607i	0.823006	−	0.568033i	$-0.192296\pi$
$224$			1.53771e6i			0.136814i
$225$	1.46746e7	+	2.93139e7i	1.28831	+	2.57351i
$226$		−	5.09575e6i		−	0.441452i
$227$	−1.18073e7			−1.00942			−0.504710	−	0.863289i	$-0.668401\pi$
$227$	−1.18073e7			−1.00942			−0.504710	+	0.863289i	$0.668401\pi$
$228$	−147618.			−0.0124548
$229$		−	4.09707e6i		−	0.341167i	−0.985343	−	0.170583i	$-0.945435\pi$
$229$		−	4.09707e6i		−	0.341167i	0.985343	−	0.170583i	$-0.0545652\pi$
$230$	−5.92895e6	−	9.89220e6i	−0.487298	−	0.813035i
$231$	2.62325e7			2.12815
$232$			8.62045e6i			0.690344i
$233$		−	5.28397e6i		−	0.417727i	−0.977945	−	0.208863i	$-0.933024\pi$
$233$		−	5.28397e6i		−	0.417727i	0.977945	−	0.208863i	$-0.0669764\pi$
$234$	1.63618e7			1.27698
$235$	−2.99974e6	−	1.85294e6i	−0.231142	−	0.142777i
$236$	489360.			0.0372299
$237$	−6.70043e6			−0.503336
$238$			1.18471e7i			0.878781i
$239$	2.33341e7			1.70922			0.854610	−	0.519270i	$-0.173796\pi$
$239$	2.33341e7			1.70922			0.854610	+	0.519270i	$0.173796\pi$
$240$	2.05709e7	+	1.27066e7i	1.48805	+	0.919173i
$241$			2.29077e7i			1.63655i	0.574825	+	0.818277i	$0.305070\pi$
$241$			2.29077e7i			1.63655i	−0.574825	+	0.818277i	$0.694930\pi$
$242$			2.08414e7i			1.47056i
$243$			7.13978e7i			4.97584i
$244$		−	1.16659e6i		−	0.0803062i
$245$	4.19080e6	−	6.78452e6i	0.284970	−	0.461340i
$246$	2.98065e7			2.00220
$247$	439477.			0.0291639
$248$		−	3.71251e6i		−	0.243396i
$249$		−	2.88029e7i		−	1.86569i
$250$	1.31942e6	−	1.47518e7i	0.0844427	−	0.944116i
$251$			7.48396e6i			0.473271i	0.971598	+	0.236636i	$0.0760448\pi$
$251$			7.48396e6i			0.473271i	−0.971598	+	0.236636i	$0.923955\pi$
$252$	3.16322e6			0.197664
$253$	1.18880e7	−	2.29738e7i	0.734085	−	1.41864i
$254$	2.16670e7			1.32220
$255$	−3.80674e7	−	2.35142e7i	−2.29579	−	1.41811i
$256$	−5.05498e6			−0.301301
$257$		−	1.35267e7i		−	0.796879i	−0.917195	−	0.398440i	$-0.869552\pi$
$257$		−	1.35267e7i		−	0.796879i	0.917195	−	0.398440i	$-0.130448\pi$
$258$	−9.04795e6			−0.526855
$259$	−1.22046e7			−0.702464
$260$	710573.	+	438922.i	0.0404286	+	0.0249728i
$261$	3.38320e7			1.90286
$262$		−	311172.i		−	0.0173020i
$263$	6.87040e6			0.377672			0.188836	−	0.982009i	$-0.439529\pi$
$263$	6.87040e6			0.377672			0.188836	+	0.982009i	$0.439529\pi$
$264$			6.04296e7i			3.28426i
$265$	1.35516e7	−	2.19387e7i	0.728202	−	1.17889i
$266$	−751995.			−0.0399549
$267$	−4.38043e7			−2.30135
$268$	−3.58233e6			−0.186106
$269$	5.56604e6			0.285950			0.142975	−	0.989726i	$-0.454333\pi$
$269$	5.56604e6			0.285950			0.142975	+	0.989726i	$0.454333\pi$
$270$	3.62603e7	−	5.87020e7i	1.84221	−	2.98237i
$271$	−1.78687e7			−0.897814			−0.448907	−	0.893579i	$-0.648187\pi$
$271$	−1.78687e7			−0.897814			−0.448907	+	0.893579i	$0.648187\pi$
$272$	−2.44919e7			−1.21707
$273$	−1.26895e7			−0.623671
$274$		−	1.65571e7i		−	0.804882i
$275$	2.97049e7	−	1.48704e7i	1.42834	−	0.715029i
$276$	1.93160e6	−	3.73285e6i	0.0918732	−	0.177547i
$277$			1.24642e6i			0.0586442i	0.999570	+	0.0293221i	$0.00933485\pi$
$277$			1.24642e6i			0.0586442i	−0.999570	+	0.0293221i	$0.990665\pi$
$278$			2.69455e7i			1.25416i
$279$	−1.45702e7			−0.670892
$280$	−1.31931e7	−	8.14939e6i	−0.600998	−	0.371237i
$281$			9.85982e6i			0.444375i	0.975004	+	0.222188i	$0.0713198\pi$
$281$			9.85982e6i			0.444375i	−0.975004	+	0.222188i	$0.928680\pi$
$282$			1.13728e7i			0.507132i
$283$	−2.53158e7			−1.11695			−0.558474	−	0.829522i	$-0.688613\pi$
$283$	−2.53158e7			−1.11695			−0.558474	+	0.829522i	$0.688613\pi$
$284$	−2.41305e6			−0.105344
$285$	1.49257e6	−	2.41633e6i	0.0644762	−	0.104381i
$286$		−	1.65801e7i		−	0.708741i
$287$	−1.71556e7			−0.725705
$288$			1.39021e7i			0.581975i
$289$	2.11858e7			0.877709
$290$	−1.30043e7	−	8.03274e6i	−0.533202	−	0.329359i
$291$			4.15290e7i			1.68528i
$292$			1.22184e6i			0.0490755i
$293$	−4.49983e6			−0.178893			−0.0894464	−	0.995992i	$-0.528510\pi$
$293$	−4.49983e6			−0.178893			−0.0894464	+	0.995992i	$0.528510\pi$
$294$	−2.57220e7			−1.01219
$295$	−4.94791e6	+	8.01021e6i	−0.192733	+	0.312017i
$296$		−	2.81147e7i		−	1.08407i
$297$	1.54757e8			5.90718
$298$	−1.28918e6			−0.0487152
$299$	−5.75059e6	+	1.11131e7i	−0.215129	+	0.415741i
$300$	4.82655e6	−	2.41618e6i	0.178761	−	0.0894882i
$301$	5.20768e6			0.190961
$302$			2.74782e7i			0.997625i
$303$			4.88519e7i			1.75612i
$304$		−	1.55462e6i		−	0.0553355i
$305$	1.90956e7	+	1.17954e7i	0.673030	+	0.415731i
$306$			1.07107e8i			3.73814i
$307$		−	3.03703e7i		−	1.04962i	−0.851218	−	0.524812i	$-0.824136\pi$
$307$		−	3.03703e7i		−	1.04962i	0.851218	−	0.524812i	$-0.175864\pi$
$308$		−	3.20541e6i		−	0.109706i
$309$		−	6.80328e7i		−	2.30591i
$310$	5.60046e6	+	3.45941e6i	0.187992	+	0.116123i
$311$	1.45520e7			0.483773			0.241887	−	0.970305i	$-0.422234\pi$
$311$	1.45520e7			0.483773			0.241887	+	0.970305i	$0.422234\pi$
$312$		−	2.92317e7i		−	0.962477i
$313$	−4.85041e6			−0.158178			−0.0790889	−	0.996868i	$-0.525201\pi$
$313$	−4.85041e6			−0.158178			−0.0790889	+	0.996868i	$0.525201\pi$
$314$			3.25635e7i			1.05182i
$315$	−3.19833e7	+	5.17779e7i	−1.02327	+	1.65658i
$316$			818743.i			0.0259469i
$317$			1.81206e6i			0.0568845i	0.999595	+	0.0284423i	$0.00905468\pi$
$317$			1.81206e6i			0.0568845i	−0.999595	+	0.0284423i	$0.990945\pi$
$318$	−8.31756e7			−2.58651
$319$		−	3.42832e7i		−	1.05611i
$320$	1.85956e7	−	3.01046e7i	0.567494	−	0.918719i
$321$		−	3.99851e7i		−	1.20888i
$322$	9.83990e6	−	1.90158e7i	0.294729	−	0.569570i
$323$			2.87690e6i			0.0853724i
$324$	1.52084e7			0.447146
$325$	−1.43692e7	+	7.19326e6i	−0.418584	+	0.209544i
$326$	2.95468e7			0.852821
$327$	7.90218e6			0.225998
$328$		−	3.95199e7i		−	1.11994i
$329$		−	6.54580e6i		−	0.183812i
$330$	−9.11602e7	−	5.63097e7i	−2.53667	−	1.56690i
$331$	1.47257e7			0.406063			0.203031	−	0.979172i	$-0.434921\pi$
$331$	1.47257e7			0.406063			0.203031	+	0.979172i	$0.434921\pi$
$332$	−3.51950e6			−0.0961760
$333$	−1.10340e8			−2.98812
$334$	1.28248e7			0.344201
$335$	3.62209e7	−	5.86383e7i	0.963441	−	1.55972i
$336$			4.48882e7i			1.18335i
$337$	−1.92010e7			−0.501689			−0.250844	−	0.968027i	$-0.580708\pi$
$337$	−1.92010e7			−0.501689			−0.250844	+	0.968027i	$0.580708\pi$
$338$		−	2.85818e7i		−	0.740183i
$339$			3.57297e7i			0.917128i
$340$	−2.87326e6	+	4.65155e6i	−0.0731036	+	0.118348i
$341$			1.47645e7i			0.372355i
$342$	−6.79865e6			−0.169959
$343$	4.21066e7			1.04344
$344$			1.19965e7i			0.294699i
$345$	4.15718e7	+	6.93607e7i	1.01237	+	1.68910i
$346$	5.96390e6			0.143980
$347$		−	6.26899e6i		−	0.150041i	−0.997182	−	0.0750203i	$-0.976098\pi$
$347$		−	6.26899e6i		−	0.150041i	0.997182	−	0.0750203i	$-0.0239022\pi$
$348$		−	5.57045e6i		−	0.132176i
$349$	−3.59098e7			−0.844766			−0.422383	−	0.906418i	$-0.638806\pi$
$349$	−3.59098e7			−0.844766			−0.422383	+	0.906418i	$0.638806\pi$
$350$	2.45873e7	−	1.23085e7i	0.573465	−	0.287078i
$351$	−7.48607e7			−1.73114
$352$	1.40876e7			0.323004
$353$			6.87784e7i			1.56361i	0.623525	+	0.781804i	$0.285700\pi$
$353$			6.87784e7i			1.56361i	−0.623525	+	0.781804i	$0.714300\pi$
$354$	3.03689e7			0.684572
$355$	2.43983e7	−	3.94985e7i	0.545349	−	0.882869i
$356$			5.35256e6i			0.118635i
$357$		−	8.30677e7i		−	1.82569i
$358$		−	1.36364e7i		−	0.297201i
$359$			6.10668e7i			1.31984i	0.751335	+	0.659920i	$0.229410\pi$
$359$			6.10668e7i			1.31984i	−0.751335	+	0.659920i	$0.770590\pi$
$360$	−1.19277e8	−	7.36773e7i	−2.55651	−	1.57916i
$361$	4.68633e7			0.996118
$362$	5.73374e7			1.20868
$363$		−	1.46133e8i		−	3.05512i
$364$			1.55056e6i			0.0321502i
$365$	−2.00000e7	−	1.23540e7i	−0.411292	−	0.254056i
$366$		−	7.23968e7i		−	1.47664i
$367$	−3.64048e7			−0.736480			−0.368240	−	0.929731i	$-0.620039\pi$
$367$	−3.64048e7			−0.736480			−0.368240	+	0.929731i	$0.620039\pi$
$368$	3.93120e7	+	2.03423e7i	0.788827	+	0.408185i
$369$	−1.55101e8			−3.08699
$370$	4.24121e7	+	2.61980e7i	0.837306	+	0.517205i
$371$	4.78730e7			0.937494
$372$			2.39899e6i			0.0466015i
$373$	−9.13914e7			−1.76108			−0.880539	−	0.473974i	$-0.842819\pi$
$373$	−9.13914e7			−1.76108			−0.880539	+	0.473974i	$0.842819\pi$
$374$	1.08536e8			2.07472
$375$	−9.25129e6	+	1.03435e8i	−0.175432	+	1.96143i
$376$	1.50790e7			0.283667
$377$			1.65839e7i			0.309501i
$378$	1.28095e8			2.37168
$379$			6.98508e6i			0.128308i	0.997940	+	0.0641540i	$0.0204349\pi$
$379$			6.98508e6i			0.128308i	−0.997940	+	0.0641540i	$0.979565\pi$
$380$	−295257.	−	182381.i	−0.00538083	−	0.00332375i
$381$	−1.51922e8			−2.74691
$382$	−7.68815e7			−1.37921
$383$	2.67383e7			0.475925			0.237962	−	0.971274i	$-0.423521\pi$
$383$	2.67383e7			0.475925			0.237962	+	0.971274i	$0.423521\pi$
$384$	−9.15864e7			−1.61747
$385$	5.24686e7	+	3.24099e7i	0.919427	+	0.567931i
$386$	3.12865e7			0.543996
$387$	4.70817e7			0.812305
$388$	5.07453e6			0.0868761
$389$		−	4.08571e7i		−	0.694095i	−0.937848	−	0.347047i	$-0.887184\pi$
$389$		−	4.08571e7i		−	0.694095i	0.937848	−	0.347047i	$-0.112816\pi$
$390$	4.40971e7	+	2.72388e7i	0.743389	+	0.459192i
$391$	−7.27487e7	−	3.76444e7i	−1.21701	−	0.629754i
$392$			3.41043e7i			0.566175i
$393$			2.18183e6i			0.0359454i
$394$	−8.30557e7			−1.35794
$395$	−1.34018e7	−	8.27830e6i	−0.217456	−	0.134323i
$396$		−	2.89796e7i		−	0.466666i
$397$		−	4.55383e7i		−	0.727789i	−0.931440	−	0.363895i	$-0.881447\pi$
$397$		−	4.55383e7i		−	0.727789i	0.931440	−	0.363895i	$-0.118553\pi$
$398$	6.27981e7			0.996087
$399$	5.27272e6			0.0830073
$400$	2.54457e7	+	5.08301e7i	0.397589	+	0.794220i
$401$		−	1.00581e8i		−	1.55986i	−0.625869	−	0.779928i	$-0.715255\pi$
$401$		−	1.00581e8i		−	1.55986i	0.625869	−	0.779928i	$-0.284745\pi$
$402$	−2.22314e8			−3.42206
$403$		−	7.14208e6i		−	0.109121i
$404$	5.96934e6			0.0905278
$405$	−1.53772e8	+	2.48943e8i	−2.31480	+	3.74744i
$406$		−	2.83769e7i		−	0.424020i
$407$			1.11811e8i			1.65845i
$408$	1.91356e8			2.81749
$409$	5.44472e7			0.795804			0.397902	−	0.917428i	$-0.369738\pi$
$409$	5.44472e7			0.795804			0.397902	+	0.917428i	$0.369738\pi$
$410$	5.96172e7	+	3.68256e7i	0.865008	+	0.534317i
$411$			1.16092e8i			1.67216i
$412$	−8.31310e6			−0.118870
$413$	−1.74793e7			−0.248126
$414$	8.89608e7	−	1.71919e8i	1.25371	−	2.42283i
$415$	3.55857e7	−	5.76098e7i	0.497887	−	0.806032i
$416$	−6.81461e6			−0.0946588
$417$		−	1.88933e8i		−	2.60555i
$418$			6.88934e6i			0.0943297i
$419$		−	2.82846e7i		−	0.384510i	−0.981345	−	0.192255i	$-0.938420\pi$
$419$		−	2.82846e7i		−	0.384510i	0.981345	−	0.192255i	$-0.0615801\pi$
$420$	8.52526e6	+	5.26606e6i	0.115069	+	0.0710784i
$421$		−	6.91760e7i		−	0.927063i	−0.886081	−	0.463531i	$-0.846582\pi$
$421$		−	6.91760e7i		−	0.927063i	0.886081	−	0.463531i	$-0.153418\pi$
$422$			1.26106e8i			1.67803i
$423$		−	5.91794e7i		−	0.781897i
$424$			1.10281e8i			1.44678i
$425$	−4.70884e7	−	9.40635e7i	−0.613405	−	1.22533i
$426$	−1.49750e8			−1.93704
$427$			4.16690e7i			0.535217i
$428$	−4.88588e6			−0.0623177
$429$			1.16254e8i			1.47243i
$430$	−1.80971e7	−	1.11786e7i	−0.227617	−	0.140599i
$431$		−	5.43951e7i		−	0.679403i	−0.940533	−	0.339702i	$-0.889674\pi$
$431$		−	5.43951e7i		−	0.679403i	0.940533	−	0.339702i	$-0.110326\pi$
$432$			2.64815e8i			3.28466i
$433$	7.83526e7			0.965139			0.482569	−	0.875858i	$-0.339704\pi$
$433$	7.83526e7			0.965139			0.482569	+	0.875858i	$0.339704\pi$
$434$			1.22209e7i			0.149497i
$435$	9.11813e7	+	5.63228e7i	1.10774	+	0.684252i
$436$		−	965588.i		−	0.0116502i
$437$	2.38948e6	−	4.61773e6i	0.0286325	−	0.0553330i
$438$			7.58254e7i			0.902386i
$439$	1.23278e8			1.45711			0.728553	−	0.684990i	$-0.240193\pi$
$439$	1.23278e8			1.45711			0.728553	+	0.684990i	$0.240193\pi$
$440$	−7.46600e7	+	1.20868e8i	−0.876456	+	1.41890i
$441$	1.33846e8			1.56060
$442$	−5.25024e7			−0.608012
$443$			1.10361e8i			1.26942i	0.772751	+	0.634709i	$0.218880\pi$
$443$			1.10361e8i			1.26942i	−0.772751	+	0.634709i	$0.781120\pi$
$444$			1.81675e7i			0.207561i
$445$	−8.76147e7	−	5.41197e7i	−0.994254	−	0.614151i
$446$	−9.55353e7			−1.07686
$447$	9.03927e6			0.101207
$448$	6.56919e7			0.730597
$449$	−6.95657e7			−0.768522			−0.384261	−	0.923225i	$-0.625544\pi$
$449$	−6.95657e7			−0.768522			−0.384261	+	0.923225i	$0.625544\pi$
$450$	2.22290e8	−	1.11279e8i	2.43939	−	1.22117i
$451$			1.57170e8i			1.71332i
$452$	4.36590e6			0.0472779
$453$		−	1.92668e8i		−	2.07259i
$454$			8.95354e7i			0.956814i
$455$	−2.53807e7	−	1.56777e7i	−0.269445	−	0.166436i
$456$			1.21463e7i			0.128101i
$457$	−1.07689e8			−1.12830			−0.564149	−	0.825673i	$-0.690796\pi$
$457$	−1.07689e8			−1.12830			−0.564149	+	0.825673i	$0.690796\pi$
$458$	−3.10684e7			−0.323387
$459$		−	4.90052e8i		−	5.06762i
$460$	8.47535e6	−	5.07976e6i	0.0870732	−	0.0521879i
$461$	4.47625e7			0.456890			0.228445	−	0.973557i	$-0.426636\pi$
$461$	4.47625e7			0.456890			0.228445	+	0.973557i	$0.426636\pi$
$462$		−	1.98923e8i		−	2.01724i
$463$			8.23010e7i			0.829205i	0.910003	+	0.414603i	$0.136079\pi$
$463$			8.23010e7i			0.829205i	−0.910003	+	0.414603i	$0.863921\pi$
$464$	5.86644e7			0.587247
$465$	−3.92685e7	−	2.42562e7i	−0.390558	−	0.241248i
$466$	−4.00687e7			−0.395957
$467$	−1.70238e8			−1.67150			−0.835750	−	0.549110i	$-0.814967\pi$
$467$	−1.70238e8			−1.67150			−0.835750	+	0.549110i	$0.814967\pi$
$468$			1.40183e7i			0.136760i
$469$	1.27956e8			1.24034
$470$	−1.40510e7	+	2.27472e7i	−0.135336	+	0.219096i
$471$		−	2.28324e8i		−	2.18519i
$472$		−	4.02655e7i		−	0.382919i
$473$		−	4.77097e7i		−	0.450841i
$474$			5.08099e7i			0.477104i
$475$	5.97069e6	−	2.98894e6i	0.0557113	−	0.0278892i
$476$	−1.01502e7			−0.0941143
$477$	4.32811e8			3.98789
$478$		−	1.76945e8i		−	1.62014i
$479$			6.86388e7i			0.624544i	0.949993	+	0.312272i	$0.101090\pi$
$479$			6.86388e7i			0.624544i	−0.949993	+	0.312272i	$0.898910\pi$
$480$	−2.31440e7	+	3.74680e7i	−0.209274	+	0.338795i
$481$		−	5.40867e7i		−	0.486021i
$482$	1.73711e8			1.55126
$483$	−6.89940e7	+	1.33332e8i	−0.612308	+	1.18330i
$484$	−1.78563e7			−0.157491
$485$	−5.13085e7	+	8.30637e7i	−0.449743	+	0.728092i
$486$	5.41415e8			4.71652
$487$		−	7.10106e7i		−	0.614803i	−0.951580	−	0.307402i	$-0.900540\pi$
$487$		−	7.10106e7i		−	0.614803i	0.951580	−	0.307402i	$-0.0994595\pi$
$488$	−9.59895e7			−0.825970
$489$	−2.07172e8			−1.77176
$490$	−5.14475e7	−	3.17792e7i	−0.437297	−	0.270118i
$491$	1.82112e8			1.53849			0.769244	−	0.638955i	$-0.220633\pi$
$491$	1.82112e8			1.53849			0.769244	+	0.638955i	$0.220633\pi$
$492$			2.55374e7i			0.214428i
$493$	−1.08561e8			−0.906012
$494$		−	3.33259e6i		−	0.0276440i
$495$	4.74359e8	+	2.93012e8i	3.91104	+	2.41585i
$496$	−2.52646e7			−0.207046
$497$	8.61907e7			0.702087
$498$	−2.18415e8			−1.76845
$499$	8.35943e7			0.672783			0.336392	−	0.941722i	$-0.390793\pi$
$499$	8.35943e7			0.672783			0.336392	+	0.941722i	$0.390793\pi$
$500$	1.26389e7	+	1.13044e6i	0.101111	+	0.00904351i
$501$	−8.99233e7			−0.715087
$502$	5.67514e7			0.448607
$503$	2.09636e8			1.64726			0.823629	−	0.567129i	$-0.191946\pi$
$503$	2.09636e8			1.64726			0.823629	+	0.567129i	$0.191946\pi$
$504$		−	2.60276e8i		−	2.03303i
$505$	−6.03559e7	+	9.77106e7i	−0.468647	+	0.758695i
$506$	−1.74212e8	−	9.01474e7i	−1.34470	−	0.695828i
$507$			2.00405e8i			1.53775i
$508$			1.85637e7i			0.141603i
$509$	−8.27771e7			−0.627707			−0.313854	−	0.949471i	$-0.601620\pi$
$509$	−8.27771e7			−0.627707			−0.313854	+	0.949471i	$0.601620\pi$
$510$	−1.78310e8	+	2.88668e8i	−1.34421	+	2.17614i
$511$		−	4.36424e7i		−	0.327074i
$512$			1.48574e8i			1.10696i
$513$	3.11061e7			0.230406
$514$	−1.02574e8			−0.755350
$515$	8.40537e7	−	1.36075e8i	0.615369	−	0.996224i
$516$		−	7.75202e6i		−	0.0564243i
$517$	−5.99688e7			−0.433964
$518$			9.25483e7i			0.665854i
$519$	−4.18168e7			−0.299122
$520$	3.61154e7	−	5.84675e7i	0.256852	−	0.415819i
$521$			3.78036e7i			0.267313i	0.991028	+	0.133657i	$0.0426719\pi$
$521$			3.78036e7i			0.267313i	−0.991028	+	0.133657i	$0.957328\pi$
$522$		−	2.56550e8i		−	1.80369i
$523$	1.39000e8			0.971653			0.485826	−	0.874055i	$-0.338519\pi$
$523$	1.39000e8			0.971653			0.485826	+	0.874055i	$0.338519\pi$
$524$	266604.			0.00185299
$525$	−1.72398e8	+	8.63027e7i	−1.19139	+	0.596412i
$526$		−	5.20987e7i		−	0.357989i
$527$	4.67534e7			0.319434
$528$	4.11239e8			2.79378
$529$	8.55028e7	+	1.20847e8i	0.577581	+	0.816333i
$530$	−1.66363e8	−	1.02762e8i	−1.11745	−	0.690251i
$531$	−1.58027e8			−1.05547
$532$		−	644288.i		−	0.00427902i
$533$		−	7.60279e7i		−	0.502101i
$534$			3.32172e8i			2.18142i
$535$	4.94011e7	−	7.99758e7i	0.322608	−	0.522272i
$536$			2.94762e8i			1.91415i
$537$			9.56137e7i			0.617443i
$538$		−	4.22077e7i		−	0.271047i
$539$		−	1.35632e8i		−	0.866153i
$540$	5.02942e7	+	3.10668e7i	0.319401	+	0.197294i
$541$	−2.93540e8			−1.85385			−0.926927	−	0.375242i	$-0.877560\pi$
$541$	−2.93540e8			−1.85385			−0.926927	+	0.375242i	$0.877560\pi$
$542$			1.35500e8i			0.851024i
$543$	−4.02030e8			−2.51107
$544$		−	4.46097e7i		−	0.277097i
$545$	1.58055e7	+	9.76305e6i	0.0976377	+	0.0603109i
$546$			9.62252e7i			0.591168i
$547$		−	1.19021e8i		−	0.727216i	−0.931552	−	0.363608i	$-0.881545\pi$
$547$		−	1.19021e8i		−	0.727216i	0.931552	−	0.363608i	$-0.118455\pi$
$548$	1.41856e7			0.0862000
$549$			3.76722e8i			2.27669i
$550$	−1.12763e8	−	2.25255e8i	−0.677764	−	1.35390i
$551$		−	6.89093e6i		−	0.0411930i
$552$	−3.07147e8	−	1.58936e8i	−1.82612	−	0.944940i
$553$		−	2.92444e7i		−	0.172929i
$554$	9.45169e6			0.0555879
$555$	−2.97379e8	−	1.83691e8i	−1.73953	−	1.07451i
$556$	−2.30862e7			−0.134316
$557$	9.14563e7			0.529234			0.264617	−	0.964354i	$-0.414754\pi$
$557$	9.14563e7			0.529234			0.264617	+	0.964354i	$0.414754\pi$
$558$			1.10487e8i			0.635928i
$559$			2.30787e7i			0.132122i
$560$	−5.54588e7	+	8.97826e7i	−0.315796	+	0.511244i
$561$	−7.61018e8			−4.31029
$562$	7.47678e7			0.421217
$563$	6.52111e7			0.365423			0.182712	−	0.983167i	$-0.441513\pi$
$563$	6.52111e7			0.365423			0.182712	+	0.983167i	$0.441513\pi$
$564$	−9.74392e6			−0.0543121
$565$	−4.41436e7	+	7.14643e7i	−0.244750	+	0.396227i
$566$			1.91972e8i			1.05874i
$567$	−5.43225e8			−2.98010
$568$			1.98550e8i			1.08349i
$569$			6.16702e7i			0.334764i	0.985892	+	0.167382i	$0.0535313\pi$
$569$			6.16702e7i			0.334764i	−0.985892	+	0.167382i	$0.946469\pi$
$570$	−1.83232e7	−	1.13183e7i	−0.0989411	−	0.0611160i
$571$			8.15627e7i			0.438110i	0.975713	+	0.219055i	$0.0702974\pi$
$571$			8.15627e7i			0.438110i	−0.975713	+	0.219055i	$0.929703\pi$
$572$	1.42053e7			0.0759037
$573$	5.39067e8			2.86536
$574$			1.30092e8i			0.687884i
$575$	−2.54494e6	+	1.90092e8i	−0.0133867	+	0.999910i
$576$	5.93909e8			3.10780
$577$			8.04228e7i			0.418650i	0.977846	+	0.209325i	$0.0671267\pi$
$577$			8.04228e7i			0.418650i	−0.977846	+	0.209325i	$0.932873\pi$
$578$		−	1.60653e8i		−	0.831967i
$579$	−2.19370e8			−1.13017
$580$	6.88222e6	−	1.11417e7i	0.0352732	−	0.0571040i
$581$	1.25712e8			0.640985
$582$	3.14917e8			1.59745
$583$		−	4.38584e8i		−	2.21334i
$584$	1.00535e8			0.504755
$585$	−2.29463e8	−	1.41739e8i	−1.14616	−	0.707983i
$586$			3.41225e7i			0.169570i
$587$			2.23911e8i			1.10704i	0.832837	+	0.553518i	$0.186715\pi$
$587$			2.23911e8i			1.10704i	−0.832837	+	0.553518i	$0.813285\pi$
$588$		−	2.20378e7i		−	0.108402i
$589$			2.96767e6i			0.0145235i
$590$	6.07420e7	+	3.75204e7i	0.295756	+	0.182689i
$591$	5.82358e8			2.82116
$592$	−1.91328e8			−0.922175
$593$			2.58003e8i			1.23726i	0.785683	+	0.618629i	$0.212312\pi$
$593$			2.58003e8i			1.23726i	−0.785683	+	0.618629i	$0.787688\pi$
$594$		−	1.17353e9i		−	5.59932i
$595$	1.02629e8	−	1.66147e8i	0.487214	−	0.788753i
$596$		−	1.10453e6i		−	0.00521722i
$597$	−4.40319e8			−2.06940
$598$	8.42718e7	+	4.36072e7i	0.394075	+	0.203917i
$599$	−2.63170e8			−1.22449			−0.612246	−	0.790667i	$-0.709734\pi$
$599$	−2.63170e8			−1.22449			−0.612246	+	0.790667i	$0.709734\pi$
$600$	−1.98809e8	−	3.97138e8i	−0.920410	−	1.83860i
$601$	2.72942e8			1.25732			0.628661	−	0.777679i	$-0.283603\pi$
$601$	2.72942e8			1.25732			0.628661	+	0.777679i	$0.283603\pi$
$602$		−	3.94902e7i		−	0.181009i
$603$	1.15683e9			5.27614
$604$	−2.35425e7			−0.106842
$605$	1.80545e8	−	2.92286e8i	0.815305	−	1.31990i
$606$	3.70448e8			1.66460
$607$			1.15274e8i			0.515427i	0.966221	+	0.257713i	$0.0829690\pi$
$607$			1.15274e8i			0.515427i	−0.966221	+	0.257713i	$0.917031\pi$
$608$	2.83160e6			0.0125986
$609$			1.98969e8i			0.880913i
$610$	8.94453e7	−	1.44804e8i	0.394065	−	0.637955i
$611$	2.90088e7			0.127176
$612$	−9.17666e7			−0.400341
$613$	−2.25722e8			−0.979923			−0.489962	−	0.871744i	$-0.662989\pi$
$613$	−2.25722e8			−0.979923			−0.489962	+	0.871744i	$0.662989\pi$
$614$	−2.30300e8			−0.994922
$615$	−4.18015e8	−	2.58209e8i	−1.79708	−	1.11006i
$616$	−2.63748e8			−1.12836
$617$	−1.26687e8			−0.539355			−0.269678	−	0.962951i	$-0.586917\pi$
$617$	−1.26687e8			−0.539355			−0.269678	+	0.962951i	$0.586917\pi$
$618$	−5.15898e8			−2.18574
$619$			3.39348e8i			1.43078i	0.698725	+	0.715391i	$0.253751\pi$
$619$			3.39348e8i			1.43078i	−0.698725	+	0.715391i	$0.746249\pi$
$620$	−2.96392e6	+	4.79831e6i	−0.0124363	+	0.0201332i
$621$	−4.07025e8	+	7.86585e8i	−1.69960	+	3.28451i
$622$		−	1.10349e8i		−	0.458561i
$623$		−	1.91186e8i		−	0.790665i
$624$	−1.98929e8			−0.818739
$625$	−1.46296e8	+	1.95454e8i	−0.599228	+	0.800578i
$626$			3.67811e7i			0.149934i
$627$		−	4.83056e7i		−	0.195973i
$628$	−2.78995e7			−0.112646
$629$	3.54062e8			1.42274
$630$	3.92636e8	+	2.42532e8i	1.57025	+	0.969944i
$631$		−	2.81908e8i		−	1.12207i	−0.827793	−	0.561034i	$-0.810404\pi$
$631$		−	2.81908e8i		−	1.12207i	0.827793	−	0.561034i	$-0.189596\pi$
$632$	6.73679e7			0.266871
$633$		−	8.84212e8i		−	3.48614i
$634$	1.37410e7			0.0539200
$635$	−3.03865e8	−	1.87697e8i	−1.18675	−	0.733056i
$636$		−	7.12625e7i		−	0.277006i
$637$			6.56093e7i			0.253832i
$638$	−2.59972e8			−1.00107
$639$	7.79235e8			2.98652
$640$	−1.83186e8	−	1.13154e8i	−0.698798	−	0.431648i
$641$			8.49424e7i			0.322515i	0.986912	+	0.161258i	$0.0515550\pi$
$641$			8.49424e7i			0.322515i	−0.986912	+	0.161258i	$0.948445\pi$
$642$	−3.03210e8			−1.14588
$643$	−2.01464e8			−0.757816			−0.378908	−	0.925434i	$-0.623700\pi$
$643$	−2.01464e8			−0.757816			−0.378908	+	0.925434i	$0.623700\pi$
$644$	1.62922e7	+	8.43055e6i	0.0609990	+	0.0315644i
$645$	1.26891e8	+	7.83807e7i	0.472881	+	0.292099i
$646$	2.18158e7			0.0809231
$647$		−	2.91400e8i		−	1.07591i	−0.842973	−	0.537955i	$-0.819197\pi$
$647$		−	2.91400e8i		−	1.07591i	0.842973	−	0.537955i	$-0.180803\pi$
$648$		−	1.25138e9i		−	4.59902i
$649$			1.60135e8i			0.585803i
$650$	5.45471e7	+	1.08963e8i	0.198624	+	0.396769i
$651$		−	8.56886e7i		−	0.310585i
$652$			2.53149e7i			0.0913341i
$653$			7.56209e7i			0.271583i	0.990737	+	0.135791i	$0.0433577\pi$
$653$			7.56209e7i			0.271583i	−0.990737	+	0.135791i	$0.956642\pi$
$654$		−	5.99229e7i		−	0.214220i
$655$	−2.69563e6	+	4.36397e6i	−0.00959259	+	0.0155295i
$656$	−2.68944e8			−0.952686
$657$		−	3.94563e8i		−	1.39130i
$658$	−4.96373e7			−0.174233
$659$			1.85799e8i			0.649211i	0.945849	+	0.324606i	$0.105232\pi$
$659$			1.85799e8i			0.649211i	−0.945849	+	0.324606i	$0.894768\pi$
$660$	4.82446e7	−	7.81035e7i	0.167810	−	0.271668i
$661$		−	4.71920e8i		−	1.63405i	−0.576605	−	0.817023i	$-0.695623\pi$
$661$		−	4.71920e8i		−	1.63405i	0.576605	−	0.817023i	$-0.304377\pi$
$662$		−	1.11666e8i		−	0.384901i
$663$	3.68128e8			1.26316
$664$			2.89592e8i			0.989196i
$665$	1.05462e7	+	6.51439e6i	0.0358617	+	0.0221518i
$666$			8.36713e8i			2.83240i
$667$	1.74252e8	+	9.01683e7i	0.587220	+	0.303862i
$668$			1.09880e7i			0.0368627i
$669$	6.69860e8			2.23721
$670$	−4.44658e8	−	2.74666e8i	−1.47843	−	0.913230i
$671$	3.81747e8			1.26360
$672$	−8.17597e7			−0.269421
$673$			5.48271e8i			1.79866i	0.437267	+	0.899332i	$0.355947\pi$
$673$			5.48271e8i			1.79866i	−0.437267	+	0.899332i	$0.644053\pi$
$674$			1.45603e8i			0.475543i
$675$	−1.01705e9	+	5.09137e8i	−3.30697	+	1.65548i
$676$	2.44880e7			0.0792709
$677$	2.77473e7			0.0894242			0.0447121	−	0.999000i	$-0.485763\pi$
$677$	2.77473e7			0.0894242			0.0447121	+	0.999000i	$0.485763\pi$
$678$	2.70941e8			0.869331
$679$	−1.81255e8			−0.579003
$680$	3.82739e8	+	2.36418e8i	1.21724	+	0.751890i
$681$		−	6.27791e8i		−	1.98781i
$682$	1.11961e8			0.352949
$683$			2.54060e8i			0.797395i	0.917083	+	0.398697i	$0.130538\pi$
$683$			2.54060e8i			0.797395i	−0.917083	+	0.398697i	$0.869462\pi$
$684$		−	5.82489e6i		−	0.0182020i
$685$	−1.43431e8	+	2.32201e8i	−0.446242	+	0.722425i
$686$		−	3.19297e8i		−	0.989061i
$687$	2.17841e8			0.671844
$688$	8.16393e7			0.250688
$689$			2.12157e8i			0.648634i
$690$	5.25967e8	−	3.15242e8i	1.60107	−	0.959614i
$691$	−2.58044e7			−0.0782094			−0.0391047	−	0.999235i	$-0.512451\pi$
$691$	−2.58044e7			−0.0782094			−0.0391047	+	0.999235i	$0.512451\pi$
$692$			5.10970e6i			0.0154197i
$693$			1.03511e9i			3.11019i
$694$	−4.75382e7			−0.142221
$695$	2.33424e8	−	3.77892e8i	0.695331	−	1.12568i
$696$	−4.58348e8			−1.35946
$697$	4.97693e8			1.46982
$698$			2.72306e8i			0.800740i
$699$	2.80948e8			0.822611
$700$	1.05455e7	+	2.10657e7i	0.0307450	+	0.0614160i
$701$			3.86143e8i			1.12097i	0.828164	+	0.560486i	$0.189385\pi$
$701$			3.86143e8i			1.12097i	−0.828164	+	0.560486i	$0.810615\pi$
$702$			5.67674e8i			1.64092i
$703$			2.24741e7i			0.0646868i
$704$		−	6.01831e8i		−	1.72487i
$705$	9.85207e7	−	1.59496e8i	0.281164	−	0.455179i
$706$	5.21552e8			1.48212
$707$	−2.13217e8			−0.603341
$708$			2.60192e7i			0.0733152i
$709$		−	8.08257e7i		−	0.226783i	−0.993550	−	0.113392i	$-0.963829\pi$
$709$		−	8.08257e7i		−	0.226783i	0.993550	−	0.113392i	$-0.0361714\pi$
$710$	−2.99520e8	−	1.85014e8i	−0.836857	−	0.516928i
$711$		−	2.64393e8i		−	0.735600i
$712$	4.40420e8			1.22019
$713$	−7.50441e7	−	3.88322e7i	−0.207037	−	0.107133i
$714$	−6.29908e8			−1.73054
$715$	−1.43630e8	+	2.32523e8i	−0.392940	+	0.636134i
$716$	1.16833e7			0.0318292
$717$			1.24067e9i			3.36589i
$718$	4.63074e8			1.25106
$719$	4.88617e8			1.31456			0.657282	−	0.753645i	$-0.271706\pi$
$719$	4.88617e8			1.31456			0.657282	+	0.753645i	$0.271706\pi$
$720$	−5.01393e8	+	8.11709e8i	−1.34332	+	2.17472i
$721$	2.96933e8			0.792232
$722$		−	3.55368e8i		−	0.944205i
$723$	−1.21800e9			−3.22279
$724$			4.91250e7i			0.129446i
$725$	1.12789e8	+	2.25307e8i	0.295974	+	0.591235i
$726$	−1.10814e9			−2.89590
$727$	5.58598e8			1.45377			0.726886	−	0.686758i	$-0.240967\pi$
$727$	5.58598e8			1.45377			0.726886	+	0.686758i	$0.240967\pi$
$728$	1.27583e8			0.330674
$729$	−2.08973e9			−5.39397
$730$	−9.36813e7	+	1.51661e8i	−0.240815	+	0.389858i
$731$	−1.51077e8			−0.386765
$732$	6.20275e7			0.158143
$733$	−1.91761e8			−0.486910			−0.243455	−	0.969912i	$-0.578281\pi$
$733$	−1.91761e8			−0.486910			−0.243455	+	0.969912i	$0.578281\pi$
$734$			2.76061e8i			0.698098i
$735$	3.60732e8	+	2.22825e8i	0.908495	+	0.561178i
$736$	−3.70517e7	+	7.16032e7i	−0.0929341	+	0.179597i
$737$		−	1.17226e9i		−	2.92833i
$738$			1.17614e9i			2.92611i
$739$	−3.79395e7			−0.0940067			−0.0470033	−	0.998895i	$-0.514967\pi$
$739$	−3.79395e7			−0.0940067			−0.0470033	+	0.998895i	$0.514967\pi$
$740$	−2.24457e7	+	3.63374e7i	−0.0553908	+	0.0896725i
$741$			2.33670e7i			0.0574312i
$742$		−	3.63024e8i		−	0.888636i
$743$	−4.71712e8			−1.15003			−0.575017	−	0.818142i	$-0.695004\pi$
$743$	−4.71712e8			−1.15003			−0.575017	+	0.818142i	$0.695004\pi$
$744$	1.97394e8			0.479308
$745$	1.80798e7	+	1.11679e7i	0.0437245	+	0.0270087i
$746$			6.93028e8i			1.66930i
$747$	1.13654e9			2.72661
$748$			9.29907e7i			0.222195i
$749$	1.74517e8			0.415329
$750$	7.84352e8	+	7.01533e7i	1.85920	+	0.166289i
$751$		−	5.54903e8i		−	1.31008i	−0.755595	−	0.655039i	$-0.772652\pi$
$751$		−	5.54903e8i		−	1.31008i	0.755595	−	0.655039i	$-0.227348\pi$
$752$		−	1.02617e8i		−	0.241304i
$753$	−3.97921e8			−0.931992
$754$	1.25757e8			0.293371
$755$	2.38038e8	−	3.85362e8i	0.553103	−	0.895423i
$756$			1.09748e8i			0.253999i
$757$	−3.15658e7			−0.0727660			−0.0363830	−	0.999338i	$-0.511584\pi$
$757$	−3.15658e7			−0.0727660			−0.0363830	+	0.999338i	$0.511584\pi$
$758$	5.29684e7			0.121621
$759$	1.22151e9	+	6.32083e8i	2.79366	+	1.44560i
$760$	−1.50067e7	+	2.42944e7i	−0.0341856	+	0.0553433i
$761$	−3.30365e8			−0.749619			−0.374809	−	0.927102i	$-0.622292\pi$
$761$	−3.30365e8			−0.749619			−0.374809	+	0.927102i	$0.622292\pi$
$762$			1.15203e9i			2.60376i
$763$			3.44895e7i			0.0776449i
$764$		−	6.58699e7i		−	0.147709i
$765$	9.27852e8	−	1.50210e9i	2.07250	−	3.35518i
$766$		−	2.02759e8i		−	0.451122i
$767$		−	7.74623e7i		−	0.171674i
$768$		−	2.68773e8i		−	0.593338i
$769$			6.23158e8i			1.37031i	0.728397	+	0.685155i	$0.240266\pi$
$769$			6.23158e8i			1.37031i	−0.728397	+	0.685155i	$0.759734\pi$
$770$	2.45767e8	−	3.97873e8i	0.538333	−	0.871510i
$771$	7.19213e8			1.56926
$772$			2.68054e7i			0.0582600i
$773$	4.91213e8			1.06348			0.531742	−	0.846906i	$-0.321537\pi$
$773$	4.91213e8			1.06348			0.531742	+	0.846906i	$0.321537\pi$
$774$		−	3.57024e8i		−	0.769972i
$775$	−4.85742e7	−	9.70314e7i	−0.104352	−	0.208453i
$776$		−	4.17543e8i		−	0.893544i
$777$		−	6.48917e8i		−	1.38333i
$778$	−3.09822e8			−0.657921
$779$			3.15911e7i			0.0668270i
$780$	−2.33374e7	+	3.77811e7i	−0.0491778	+	0.0796143i
$781$		−	7.89629e8i		−	1.65756i
$782$	−2.85461e8	+	5.51659e8i	−0.596934	+	1.15359i
$783$			1.17380e9i			2.44518i
$784$	2.32089e8			0.481621
$785$	2.82091e8	−	4.56680e8i	0.583151	−	0.944066i
$786$	1.65450e7			0.0340721
$787$	4.39645e8			0.901940			0.450970	−	0.892539i	$-0.351078\pi$
$787$	4.39645e8			0.901940			0.450970	+	0.892539i	$0.351078\pi$
$788$		−	7.11598e7i		−	0.145431i
$789$			3.65298e8i			0.743732i
$790$	−6.27750e7	+	1.01627e8i	−0.127323	+	0.206123i
$791$	−1.55944e8			−0.315093
$792$	−2.38450e9			−4.79978
$793$	−1.84663e8			−0.370306
$794$	−3.45321e8			−0.689860
$795$	1.16648e9	+	7.20535e8i	2.32154	+	1.43401i
$796$			5.38036e7i			0.106677i
$797$	−1.61515e8			−0.319034			−0.159517	−	0.987195i	$-0.550994\pi$
$797$	−1.61515e8			−0.319034			−0.159517	+	0.987195i	$0.550994\pi$
$798$		−	3.99835e7i		−	0.0786814i
$799$			1.89897e8i			0.372287i
$800$	−9.25824e7	+	4.63470e7i	−0.180825	+	0.0905215i
$801$		−	1.72848e9i		−	3.36331i
$802$	−7.62717e8			−1.47856
$803$	−3.99826e8			−0.772191
$804$		−	1.90472e8i		−	0.366491i
$805$	−3.02728e8	+	1.81442e8i	−0.580317	+	0.347817i
$806$	−5.41589e7			−0.103434
$807$			2.95946e8i			0.563108i
$808$		−	4.91169e8i		−	0.931102i
$809$	8.44049e8			1.59412			0.797062	−	0.603898i	$-0.206387\pi$
$809$	8.44049e8			1.59412			0.797062	+	0.603898i	$0.206387\pi$
$810$	1.88775e9	+	1.16607e9i	3.55214	+	2.19416i
$811$	−3.14047e8			−0.588752			−0.294376	−	0.955690i	$-0.595112\pi$
$811$	−3.14047e8			−0.588752			−0.294376	+	0.955690i	$0.595112\pi$
$812$	2.43125e7			0.0454111
$813$		−	9.50079e8i		−	1.76802i
$814$	8.47874e8			1.57202
$815$	−4.14373e8	−	2.55959e8i	−0.765453	−	0.472821i
$816$		−	1.30223e9i		−	2.39672i
$817$		−	9.58965e6i		−	0.0175848i
$818$		−	4.12877e8i		−	0.754330i
$819$		−	5.00716e8i		−	0.911464i
$820$	−3.15512e7	+	5.10784e7i	−0.0572234	+	0.0926393i
$821$	9.37526e8			1.69416			0.847079	−	0.531466i	$-0.178359\pi$
$821$	9.37526e8			1.69416			0.847079	+	0.531466i	$0.178359\pi$
$822$	8.80338e8			1.58502
$823$			5.24343e8i			0.940624i	0.882500	+	0.470312i	$0.155859\pi$
$823$			5.24343e8i			0.940624i	−0.882500	+	0.470312i	$0.844141\pi$
$824$			6.84020e8i			1.22261i
$825$	7.90655e8	+	1.57941e9i	1.40807	+	2.81276i
$826$			1.32547e8i			0.235195i
$827$	9.62539e7			0.170177			0.0850887	−	0.996373i	$-0.472883\pi$
$827$	9.62539e7			0.170177			0.0850887	+	0.996373i	$0.472883\pi$
$828$	1.47295e8	+	7.62191e7i	0.259476	+	0.134268i
$829$	3.13872e8			0.550920			0.275460	−	0.961312i	$-0.411170\pi$
$829$	3.13872e8			0.550920			0.275460	+	0.961312i	$0.411170\pi$
$830$	−4.36860e8	−	2.69849e8i	−0.764025	−	0.471939i
$831$	−6.62720e7			−0.115485
$832$			2.91125e8i			0.505486i
$833$	−4.29491e8			−0.743051
$834$	−1.43269e9			−2.46976
$835$	−1.79859e8	−	1.11099e8i	−0.308939	−	0.190832i
$836$	−5.90259e6			−0.0101024
$837$		−	5.05514e8i		−	0.862099i
$838$	−2.14484e8			−0.364471
$839$		−	6.38090e8i		−	1.08043i	−0.841528	−	0.540214i	$-0.818343\pi$
$839$		−	6.38090e8i		−	1.08043i	0.841528	−	0.540214i	$-0.181657\pi$
$840$	4.33302e8	−	7.01476e8i	0.731061	−	1.18352i
$841$	−3.34791e8			−0.562840
$842$	−5.24567e8			−0.878748
$843$	−5.24246e8			−0.875089
$844$	−1.08044e8			−0.179711
$845$	−2.47598e8	+	4.00839e8i	−0.410372	+	0.664354i
$846$	−4.48762e8			−0.741148
$847$	6.37804e8			1.04963
$848$	7.50491e8			1.23072
$849$		−	1.34604e9i		−	2.19955i
$850$	−7.13291e8	+	3.57075e8i	−1.16147	+	0.581437i
$851$	−5.68306e8	−	2.94075e8i	−0.922133	−	0.477166i
$852$		−	1.28301e8i		−	0.207450i
$853$		−	2.57225e8i		−	0.414445i	−0.978294	−	0.207222i	$-0.933558\pi$
$853$		−	2.57225e8i		−	0.414445i	0.978294	−	0.207222i	$-0.0664424\pi$
$854$	3.15979e8			0.507324
$855$	9.53462e7	+	5.88954e7i	0.152547	+	0.0942287i
$856$			4.02021e8i			0.640954i
$857$		−	6.50353e8i		−	1.03325i	−0.856211	−	0.516627i	$-0.827188\pi$
$857$		−	6.50353e8i		−	1.03325i	0.856211	−	0.516627i	$-0.172812\pi$
$858$	8.81560e8			1.39569
$859$	2.16113e8			0.340958			0.170479	−	0.985361i	$-0.445468\pi$
$859$	2.16113e8			0.340958			0.170479	+	0.985361i	$0.445468\pi$
$860$	9.57753e6	−	1.55051e7i	0.0150577	−	0.0243770i
$861$		−	9.12161e8i		−	1.42910i
$862$	−4.12482e8			−0.643996
$863$		−	6.47959e8i		−	1.00813i	−0.863667	−	0.504063i	$-0.831838\pi$
$863$		−	6.47959e8i		−	1.00813i	0.863667	−	0.504063i	$-0.168162\pi$
$864$	−4.82336e8			−0.747840
$865$	−8.36394e7	−	5.16642e7i	−0.129230	−	0.0798254i
$866$		−	5.94154e8i		−	0.914840i
$867$			1.12644e9i			1.72843i
$868$	−1.04705e7			−0.0160106
$869$	−2.67920e8			−0.408268
$870$	4.27100e8	−	6.91435e8i	0.648592	−	1.05001i
$871$			5.67058e8i			0.858169i
$872$	−7.94506e7			−0.119825
$873$	−1.63870e9			−2.46295
$874$	−3.50166e7	−	1.81196e7i	−0.0524493	−	0.0271403i
$875$	−4.51445e8	−	4.03777e7i	−0.673878	−	0.0602723i
$876$	−6.49650e7			−0.0966423
$877$		−	2.75436e8i		−	0.408341i	−0.978935	−	0.204170i	$-0.934550\pi$
$877$		−	2.75436e8i		−	0.408341i	0.978935	−	0.204170i	$-0.0654497\pi$
$878$		−	9.34824e8i		−	1.38117i
$879$		−	2.39255e8i		−	0.352286i
$880$	8.22536e8	+	5.08081e8i	1.20700	+	0.745564i
$881$			8.43571e8i			1.23366i	0.787098	+	0.616828i	$0.211583\pi$
$881$			8.43571e8i			1.23366i	−0.787098	+	0.616828i	$0.788417\pi$
$882$		−	1.01497e9i		−	1.47926i
$883$			1.11197e9i			1.61514i	0.589773	+	0.807569i	$0.299217\pi$
$883$			1.11197e9i			1.61514i	−0.589773	+	0.807569i	$0.700783\pi$
$884$		−	4.49825e7i		−	0.0651159i
$885$	−4.25902e8	−	2.63080e8i	−0.614440	−	0.379540i
$886$	8.36876e8			1.20326
$887$		−	1.76991e8i		−	0.253618i	−0.991927	−	0.126809i	$-0.959527\pi$
$887$		−	1.76991e8i		−	0.253618i	0.991927	−	0.126809i	$-0.0404735\pi$
$888$	1.49486e9			2.13482
$889$		−	6.63070e8i		−	0.943744i
$890$	−4.10394e8	+	6.64389e8i	−0.582145	+	0.942437i
$891$			4.97671e9i			7.03573i
$892$		−	8.18519e7i		−	0.115328i
$893$	−1.20537e7			−0.0169265
$894$		−	6.85455e7i		−	0.0959326i
$895$	−1.18130e8	+	1.91241e8i	−0.164774	+	0.266754i
$896$		−	3.99734e8i		−	0.555708i
$897$	−5.90885e8	−	3.05758e8i	−0.818701	−	0.423644i
$898$			5.27522e8i			0.728470i
$899$	−1.11987e8			−0.154130
$900$	9.53405e7	+	1.90451e8i	0.130783	+	0.261250i
$901$	−1.38882e9			−1.89877
$902$	1.19183e9			1.62403
$903$			2.76892e8i			0.376051i
$904$		−	3.59235e8i		−	0.486266i
$905$	−8.04115e8	−	4.96703e8i	−1.08486	−	0.670117i
$906$	−1.46101e9			−1.96458
$907$	1.04782e9			1.40431			0.702157	−	0.712022i	$-0.252220\pi$
$907$	1.04782e9			1.40431			0.702157	+	0.712022i	$0.252220\pi$
$908$	−7.67114e7			−0.102471
$909$	−1.92765e9			−2.56648
$910$	−1.18885e8	+	1.92464e8i	−0.157762	+	0.255402i
$911$			8.07113e8i			1.06753i	0.845634	+	0.533764i	$0.179223\pi$
$911$			8.07113e8i			1.06753i	−0.845634	+	0.533764i	$0.820777\pi$
$912$	8.26591e7			0.108970
$913$		−	1.15170e9i		−	1.51330i
$914$			8.16615e8i			1.06950i
$915$	−6.27160e8	+	1.01531e9i	−0.818681	+	1.32537i
$916$		−	2.66185e7i		−	0.0346336i
$917$	−9.52272e6			−0.0123496
$918$	−3.71610e9			−4.80352
$919$			1.01474e9i			1.30740i	0.756752	+	0.653702i	$0.226785\pi$
$919$			1.01474e9i			1.30740i	−0.756752	+	0.653702i	$0.773215\pi$
$920$	−4.17973e8	−	6.97370e8i	−0.536766	−	0.895570i
$921$	1.61478e9			2.06698
$922$		−	3.39438e8i		−	0.433079i
$923$			3.81969e8i			0.485761i
$924$	1.70431e8			0.216040
$925$	−3.67851e8	−	7.34815e8i	−0.464779	−	0.928438i
$926$	6.24094e8			0.785991
$927$	2.68452e9			3.36998
$928$			1.06852e8i			0.133702i
$929$	−9.19700e7			−0.114709			−0.0573547	−	0.998354i	$-0.518267\pi$
$929$	−9.19700e7			−0.114709			−0.0573547	+	0.998354i	$0.518267\pi$
$930$	−1.83936e8	+	2.97776e8i	−0.228675	+	0.370203i
$931$		−	2.72619e7i		−	0.0337837i
$932$		−	3.43298e7i		−	0.0424056i
$933$			7.73729e8i			0.952673i
$934$			1.29093e9i			1.58439i
$935$	−1.52214e9	−	9.40228e8i	−1.86217	−	1.15027i
$936$	1.15346e9			1.40661
$937$	−7.33180e8			−0.891235			−0.445617	−	0.895224i	$-0.647016\pi$
$937$	−7.33180e8			−0.891235			−0.445617	+	0.895224i	$0.647016\pi$
$938$		−	9.70299e8i		−	1.17570i
$939$		−	2.57896e8i		−	0.311493i
$940$	−1.94892e7	−	1.20385e7i	−0.0234644	−	0.0144940i
$941$		−	8.60489e7i		−	0.103271i	−0.998666	−	0.0516353i	$-0.983557\pi$
$941$		−	8.60489e7i		−	0.103271i	0.998666	−	0.0516353i	$-0.0164433\pi$
$942$	−1.73140e9			−2.07131
$943$	−7.98849e8	−	4.13372e8i	−0.952642	−	0.492953i
$944$	−2.74018e8			−0.325733
$945$	−1.79644e9	−	1.10966e9i	−2.12871	−	1.31491i
$946$	−3.61786e8			−0.427345
$947$		−	1.36294e9i		−	1.60482i	−0.596770	−	0.802412i	$-0.703550\pi$
$947$		−	1.36294e9i		−	1.60482i	0.596770	−	0.802412i	$-0.296450\pi$
$948$	−4.35325e7			−0.0510962
$949$	1.93409e8			0.226296
$950$	−2.26654e7	−	4.52762e7i	−0.0264358	−	0.0528079i
$951$	−9.63469e7			−0.112020
$952$			8.35184e8i			0.967991i
$953$	1.33663e8			0.154431			0.0772153	−	0.997014i	$-0.475397\pi$
$953$	1.33663e8			0.154431			0.0772153	+	0.997014i	$0.475397\pi$
$954$		−	3.28204e9i		−	3.78006i
$955$	1.07821e9	+	6.66010e8i	1.23792	+	0.764664i
$956$	1.51601e8			0.173512
$957$	1.82284e9			2.07975
$958$	5.20493e8			0.591996
$959$	−5.06691e8			−0.574497
$960$	1.60066e9	+	9.88728e8i	1.80919	+	1.11754i
$961$	−8.39275e8			−0.945658
$962$	−4.10143e8			−0.460692
$963$	1.57778e9			1.76672
$964$			1.48830e8i			0.166135i
$965$	−4.38771e8	−	2.71029e8i	−0.488266	−	0.301602i
$966$	1.01107e9	+	5.23187e8i	1.12163	+	0.580397i
$967$			3.57658e8i			0.395538i	0.980249	+	0.197769i	$0.0633697\pi$
$967$			3.57658e8i			0.395538i	−0.980249	+	0.197769i	$0.936630\pi$
$968$			1.46926e9i			1.61984i
$969$	−1.52965e8			−0.168120
$970$	6.29878e8	+	3.89076e8i	0.690147	+	0.426304i
$971$			1.92300e8i			0.210050i	0.994470	+	0.105025i	$0.0334922\pi$
$971$			1.92300e8i			0.210050i	−0.994470	+	0.105025i	$0.966508\pi$
$972$			4.63869e8i			0.505122i
$973$	8.24607e8			0.895176
$974$	−5.38479e8			−0.582763
$975$	−3.82465e8	−	7.64009e8i	−0.412646	−	0.824299i
$976$			6.53234e8i			0.702618i
$977$	−2.77695e8			−0.297772			−0.148886	−	0.988854i	$-0.547569\pi$
$977$	−2.77695e8			−0.297772			−0.148886	+	0.988854i	$0.547569\pi$
$978$			1.57100e9i			1.67942i
$979$	−1.75154e9			−1.86669
$980$	2.72275e7	−	4.40788e7i	0.0289287	−	0.0468329i
$981$			3.11813e8i			0.330284i
$982$		−	1.38097e9i		−	1.45831i
$983$	−1.50916e9			−1.58882			−0.794410	−	0.607382i	$-0.792220\pi$
$983$	−1.50916e9			−1.58882			−0.794410	+	0.607382i	$0.792220\pi$
$984$	2.10127e9			2.20545
$985$	1.16480e9	+	7.19496e8i	1.21883	+	0.752870i
$986$			8.23228e8i			0.858795i
$987$	3.48039e8			0.361974
$988$	2.85527e6			0.00296058
$989$	2.42495e8	+	1.25481e8i	0.250677	+	0.129715i
$990$	2.22193e9	−	3.59710e9i	2.28995	−	3.70721i
$991$	1.21301e9			1.24636			0.623178	−	0.782080i	$-0.285841\pi$
$991$	1.21301e9			1.24636			0.623178	+	0.782080i	$0.285841\pi$
$992$		−	4.60172e7i		−	0.0471395i
$993$			7.82966e8i			0.799641i
$994$		−	6.53591e8i		−	0.665498i
$995$	−8.80698e8	−	5.44008e8i	−0.894042	−	0.552251i
$996$		−	1.87132e8i		−	0.189395i
$997$			7.45906e8i			0.752659i	0.926486	+	0.376330i	$0.122814\pi$
$997$			7.45906e8i			0.752659i	−0.926486	+	0.376330i	$0.877186\pi$
$998$		−	6.33902e8i		−	0.637721i
$999$		−	3.82824e9i		−	3.83975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.7.c.c.114.19	✓	68
5.4	even	2	inner	115.7.c.c.114.50	yes	68
23.22	odd	2	inner	115.7.c.c.114.49	yes	68
115.114	odd	2	inner	115.7.c.c.114.20	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.7.c.c.114.19	✓	68	1.1	even	1	trivial
115.7.c.c.114.20	yes	68	115.114	odd	2	inner
115.7.c.c.114.49	yes	68	23.22	odd	2	inner
115.7.c.c.114.50	yes	68	5.4	even	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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	115.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-7.58308i q^{2} +53.1699i q^{3} +6.49696 q^{4} +(-65.6908 + 106.347i) q^{5} +403.191 q^{6} -232.063 q^{7} -534.584i q^{8} -2098.04 q^{9} +O(q^{10})\)	\(q-7.58308i q^{2} +53.1699i q^{3} +6.49696 q^{4} +(-65.6908 + 106.347i) q^{5} +403.191 q^{6} -232.063 q^{7} -534.584i q^{8} -2098.04 q^{9} +(806.439 + 498.138i) q^{10} +2126.02i q^{11} +345.443i q^{12} -1028.42i q^{13} +1759.75i q^{14} +(-5654.47 - 3492.77i) q^{15} -3637.98 q^{16} +6732.26 q^{17} +15909.6i q^{18} +427.331i q^{19} +(-426.790 + 690.934i) q^{20} -12338.7i q^{21} +16121.8 q^{22} +(-10806.0 - 5591.65i) q^{23} +28423.8 q^{24} +(-6994.45 - 13972.1i) q^{25} -7798.62 q^{26} -72791.6i q^{27} -1507.70 q^{28} -16125.5 q^{29} +(-26485.9 + 42878.3i) q^{30} +6944.68 q^{31} -6626.26i q^{32} -113040. q^{33} -51051.2i q^{34} +(15244.4 - 24679.2i) q^{35} -13630.9 q^{36} +52591.8 q^{37} +3240.48 q^{38} +54681.2 q^{39} +(56851.5 + 35117.2i) q^{40} +73926.6 q^{41} -93565.7 q^{42} -22440.8 q^{43} +13812.7i q^{44} +(137822. - 223120. i) q^{45} +(-42401.9 + 81942.6i) q^{46} +28207.0i q^{47} -193431. i q^{48} -63795.9 q^{49} +(-105951. + 53039.4i) q^{50} +357954. i q^{51} -6681.64i q^{52} -206293. q^{53} -551984. q^{54} +(-226097. - 139660. i) q^{55} +124057. i q^{56} -22721.1 q^{57} +122281. i q^{58} +75321.3 q^{59} +(-36736.9 - 22692.4i) q^{60} -179559. i q^{61} -52662.0i q^{62} +486876. q^{63} -283078. q^{64} +(109370. + 67558.0i) q^{65} +857194. i q^{66} -551385. q^{67} +43739.2 q^{68} +(297308. - 574553. i) q^{69} +(-187144. - 115599. i) q^{70} -371411. q^{71} +1.12158e6i q^{72} +188063. i q^{73} -398807. i q^{74} +(742893. - 371894. i) q^{75} +2776.35i q^{76} -493371. i q^{77} -414652. i q^{78} +126019. i q^{79} +(238982. - 386889. i) q^{80} +2.34085e6 q^{81} -560591. i q^{82} -541715. q^{83} -80164.4i q^{84} +(-442247. + 715957. i) q^{85} +170170. i q^{86} -857393. i q^{87} +1.13654e6 q^{88} +823856. i q^{89} +(-1.69194e6 - 1.04511e6i) q^{90} +238659. i q^{91} +(-70206.1 - 36328.8i) q^{92} +369248. i q^{93} +213896. q^{94} +(-45445.4 - 28071.7i) q^{95} +352317. q^{96} +781061. q^{97} +483769. i q^{98} -4.46048e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9}+O(q^{10}) \) 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9	\( 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9} + 66968 q^{16} - 30916 q^{24} + 32588 q^{25} - 22072 q^{26} + 103360 q^{29} - 17256 q^{31} - 358168 q^{35} + 451984 q^{36} + 192432 q^{39} - 183552 q^{41} - 397956 q^{46} + 806756 q^{49} - 749960 q^{50} - 1638436 q^{54} - 1752 q^{55} - 505552 q^{59} - 4095100 q^{64} + 1354876 q^{69} + 1196604 q^{70} + 493688 q^{71} + 3178568 q^{75} + 2473820 q^{81} + 3306336 q^{85} - 3770196 q^{94} + 896144 q^{95} + 16928136 q^{96}+O(q^{100}) \) 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9 + 66968 * q^16 - 30916 * q^24 + 32588 * q^25 - 22072 * q^26 + 103360 * q^29 - 17256 * q^31 - 358168 * q^35 + 451984 * q^36 + 192432 * q^39 - 183552 * q^41 - 397956 * q^46 + 806756 * q^49 - 749960 * q^50 - 1638436 * q^54 - 1752 * q^55 - 505552 * q^59 - 4095100 * q^64 + 1354876 * q^69 + 1196604 * q^70 + 493688 * q^71 + 3178568 * q^75 + 2473820 * q^81 + 3306336 * q^85 - 3770196 * q^94 + 896144 * q^95 + 16928136 * q^96

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