LMFDB - Embedded newform 115.7.c.c.114.6

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			114.6
Character	$\chi$	$=$	115.114
Dual form			115.7.c.c.114.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.1333i q^{2} +17.3572i q^{3} -59.9514 q^{4} +(-121.447 - 29.5914i) q^{5} -193.244 q^{6} +504.412 q^{7} +45.0744i q^{8} +427.728 q^{9} +O(q^{10})$	\(q+11.1333i q^{2} +17.3572i q^{3} -59.9514 q^{4} +(-121.447 - 29.5914i) q^{5} -193.244 q^{6} +504.412 q^{7} +45.0744i q^{8} +427.728 q^{9} +(329.451 - 1352.11i) q^{10} -2384.92i q^{11} -1040.59i q^{12} -3159.59i q^{13} +5615.80i q^{14} +(513.623 - 2107.98i) q^{15} -4338.72 q^{16} +7401.20 q^{17} +4762.05i q^{18} -3299.66i q^{19} +(7280.91 + 1774.04i) q^{20} +8755.18i q^{21} +26552.1 q^{22} +(2843.06 - 11830.2i) q^{23} -782.365 q^{24} +(13873.7 + 7187.56i) q^{25} +35176.9 q^{26} +20077.5i q^{27} -30240.2 q^{28} +3460.99 q^{29} +(23468.8 + 5718.34i) q^{30} -49153.9 q^{31} -45419.7i q^{32} +41395.5 q^{33} +82400.2i q^{34} +(-61259.3 - 14926.3i) q^{35} -25642.9 q^{36} -59787.8 q^{37} +36736.3 q^{38} +54841.7 q^{39} +(1333.81 - 5474.15i) q^{40} +71108.4 q^{41} -97474.5 q^{42} +26057.7 q^{43} +142979. i q^{44} +(-51946.3 - 12657.1i) q^{45} +(131709. + 31652.7i) q^{46} -65687.9i q^{47} -75307.9i q^{48} +136783. q^{49} +(-80021.6 + 154461. i) q^{50} +128464. i q^{51} +189422. i q^{52} -91475.0 q^{53} -223530. q^{54} +(-70573.0 + 289641. i) q^{55} +22736.1i q^{56} +57272.8 q^{57} +38532.4i q^{58} +85768.4 q^{59} +(-30792.4 + 126376. i) q^{60} -229731. i q^{61} -547248. i q^{62} +215751. q^{63} +227995. q^{64} +(-93496.7 + 383723. i) q^{65} +460870. i q^{66} +212270. q^{67} -443713. q^{68} +(205338. + 49347.5i) q^{69} +(166179. - 682021. i) q^{70} -295688. q^{71} +19279.6i q^{72} +460048. i q^{73} -665639. i q^{74} +(-124756. + 240808. i) q^{75} +197819. i q^{76} -1.20298e6i q^{77} +610571. i q^{78} +54307.6i q^{79} +(526924. + 128389. i) q^{80} -36675.8 q^{81} +791674. i q^{82} +490873. q^{83} -524885. i q^{84} +(-898853. - 219012. i) q^{85} +290109. i q^{86} +60073.0i q^{87} +107499. q^{88} -151949. i q^{89} +(140915. - 578336. i) q^{90} -1.59374e6i q^{91} +(-170445. + 709235. i) q^{92} -853174. i q^{93} +731326. q^{94} +(-97641.5 + 400734. i) q^{95} +788358. q^{96} +352471. q^{97} +1.52285e6i q^{98} -1.02010e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			11.1333i			1.39167i	0.718202	+	0.695834i	$0.244965\pi$
$2$			11.1333i			1.39167i	−0.718202	+	0.695834i	$0.755035\pi$
$3$			17.3572i			0.642859i	0.946934	+	0.321429i	$0.104163\pi$
$3$			17.3572i			0.642859i	−0.946934	+	0.321429i	$0.895837\pi$
$4$	−59.9514			−0.936741
$5$	−121.447	−	29.5914i	−0.971575	−	0.236731i
$5$	−121.447	−	29.5914i	−0.971575	−	0.236731i
$6$	−193.244			−0.894646
$7$	504.412			1.47059			0.735295	−	0.677747i	$-0.237044\pi$
$7$	504.412			1.47059			0.735295	+	0.677747i	$0.237044\pi$
$8$			45.0744i			0.0880359i
$9$	427.728			0.586733
$10$	329.451	−	1352.11i	0.329451	−	1.35211i
$11$		−	2384.92i		−	1.79182i	−0.444231	−	0.895912i	$-0.646523\pi$
$11$		−	2384.92i		−	1.79182i	0.444231	−	0.895912i	$-0.353477\pi$
$12$		−	1040.59i		−	0.602192i
$13$		−	3159.59i		−	1.43814i	−0.694937	−	0.719070i	$-0.744568\pi$
$13$		−	3159.59i		−	1.43814i	0.694937	−	0.719070i	$-0.255432\pi$
$14$			5615.80i			2.04657i
$15$	513.623	−	2107.98i	0.152185	−	0.624586i
$16$	−4338.72			−1.05926
$17$	7401.20			1.50645			0.753227	−	0.657761i	$-0.228496\pi$
$17$	7401.20			1.50645			0.753227	+	0.657761i	$0.228496\pi$
$18$			4762.05i			0.816537i
$19$		−	3299.66i		−	0.481070i	−0.970640	−	0.240535i	$-0.922677\pi$
$19$		−	3299.66i		−	0.481070i	0.970640	−	0.240535i	$-0.0773229\pi$
$20$	7280.91	+	1774.04i	0.910114	+	0.221756i
$21$			8755.18i			0.945382i
$22$	26552.1			2.49363
$23$	2843.06	−	11830.2i	0.233669	−	0.972316i
$23$	2843.06	−	11830.2i	0.233669	−	0.972316i
$24$	−782.365			−0.0565947
$25$	13873.7	+	7187.56i	0.887917	+	0.460004i
$26$	35176.9			2.00141
$27$			20077.5i			1.02004i
$28$	−30240.2			−1.37756
$29$	3460.99			0.141908			0.0709538	−	0.997480i	$-0.477396\pi$
$29$	3460.99			0.141908			0.0709538	+	0.997480i	$0.477396\pi$
$30$	23468.8	+	5718.34i	0.869216	+	0.211790i
$31$	−49153.9			−1.64996			−0.824980	−	0.565162i	$-0.808814\pi$
$31$	−49153.9			−1.64996			−0.824980	+	0.565162i	$0.808814\pi$
$32$		−	45419.7i		−	1.38610i
$33$	41395.5			1.15189
$34$			82400.2i			2.09648i
$35$	−61259.3	−	14926.3i	−1.42879	−	0.348134i
$36$	−25642.9			−0.549616
$37$	−59787.8			−1.18034			−0.590171	−	0.807278i	$-0.700940\pi$
$37$	−59787.8			−1.18034			−0.590171	+	0.807278i	$0.700940\pi$
$38$	36736.3			0.669490
$39$	54841.7			0.924521
$40$	1333.81	−	5474.15i	0.0208408	−	0.0855335i
$41$	71108.4			1.03174			0.515869	−	0.856668i	$-0.327469\pi$
$41$	71108.4			1.03174			0.515869	+	0.856668i	$0.327469\pi$
$42$	−97474.5			−1.31566
$43$	26057.7			0.327740			0.163870	−	0.986482i	$-0.447602\pi$
$43$	26057.7			0.327740			0.163870	+	0.986482i	$0.447602\pi$
$44$			142979.i			1.67847i
$45$	−51946.3	−	12657.1i	−0.570055	−	0.138898i
$46$	131709.	+	31652.7i	1.35314	+	0.325190i
$47$		−	65687.9i		−	0.632691i	−0.948644	−	0.316345i	$-0.897544\pi$
$47$		−	65687.9i		−	0.632691i	0.948644	−	0.316345i	$-0.102456\pi$
$48$		−	75307.9i		−	0.680953i
$49$	136783.			1.16264
$50$	−80021.6	+	154461.i	−0.640173	+	1.23569i
$51$			128464.i			0.968436i
$52$			189422.i			1.34716i
$53$	−91475.0			−0.614433			−0.307217	−	0.951640i	$-0.599398\pi$
$53$	−91475.0			−0.614433			−0.307217	+	0.951640i	$0.599398\pi$
$54$	−223530.			−1.41956
$55$	−70573.0	+	289641.i	−0.424180	+	1.74089i
$56$			22736.1i			0.129465i
$57$	57272.8			0.309260
$58$			38532.4i			0.197488i
$59$	85768.4			0.417610			0.208805	−	0.977957i	$-0.433043\pi$
$59$	85768.4			0.417610			0.208805	+	0.977957i	$0.433043\pi$
$60$	−30792.4	+	126376.i	−0.142557	+	0.585075i
$61$		−	229731.i		−	1.01212i	−0.862500	−	0.506058i	$-0.831102\pi$
$61$		−	229731.i		−	1.01212i	0.862500	−	0.506058i	$-0.168898\pi$
$62$		−	547248.i		−	2.29620i
$63$	215751.			0.862843
$64$	227995.			0.869733
$65$	−93496.7	+	383723.i	−0.340452	+	1.39726i
$66$			460870.i			1.60305i
$67$	212270.			0.705771			0.352885	−	0.935667i	$-0.385201\pi$
$67$	212270.			0.705771			0.352885	+	0.935667i	$0.385201\pi$
$68$	−443713.			−1.41116
$69$	205338.	+	49347.5i	0.625062	+	0.150216i
$70$	166179.	−	682021.i	0.484487	−	1.98840i
$71$	−295688.			−0.826150			−0.413075	−	0.910697i	$-0.635545\pi$
$71$	−295688.			−0.826150			−0.413075	+	0.910697i	$0.635545\pi$
$72$			19279.6i			0.0516536i
$73$			460048.i			1.18259i	0.806455	+	0.591295i	$0.201383\pi$
$73$			460048.i			1.18259i	−0.806455	+	0.591295i	$0.798617\pi$
$74$		−	665639.i		−	1.64264i
$75$	−124756.	+	240808.i	−0.295718	+	0.570805i
$76$			197819.i			0.450638i
$77$		−	1.20298e6i		−	2.63504i
$78$			610571.i			1.28663i
$79$			54307.6i			0.110149i	0.998482	+	0.0550743i	$0.0175396\pi$
$79$			54307.6i			0.110149i	−0.998482	+	0.0550743i	$0.982460\pi$
$80$	526924.	+	128389.i	1.02915	+	0.250759i
$81$	−36675.8			−0.0690121
$82$			791674.i			1.43584i
$83$	490873.			0.858489			0.429245	−	0.903188i	$-0.358780\pi$
$83$	490873.			0.858489			0.429245	+	0.903188i	$0.358780\pi$
$84$		−	524885.i		−	0.885578i
$85$	−898853.	−	219012.i	−1.46363	−	0.356624i
$86$			290109.i			0.456106i
$87$			60073.0i			0.0912266i
$88$	107499.			0.157745
$89$		−	151949.i		−	0.215540i	−0.994176	−	0.107770i	$-0.965629\pi$
$89$		−	151949.i		−	0.215540i	0.994176	−	0.107770i	$-0.0343711\pi$
$90$	140915.	−	578336.i	0.193300	−	0.793327i
$91$		−	1.59374e6i		−	2.11492i
$92$	−170445.	+	709235.i	−0.218888	+	0.910808i
$93$		−	853174.i		−	1.06069i
$94$	731326.			0.880496
$95$	−97641.5	+	400734.i	−0.113884	+	0.467396i
$96$	788358.			0.891066
$97$	352471.			0.386197			0.193098	−	0.981179i	$-0.438146\pi$
$97$	352471.			0.386197			0.193098	+	0.981179i	$0.438146\pi$
$98$			1.52285e6i			1.61800i
$99$		−	1.02010e6i		−	1.05132i
$100$	−831748.	−	430904.i	−0.831748	−	0.430904i
$101$	480410.			0.466281			0.233140	−	0.972443i	$-0.425100\pi$
$101$	480410.			0.466281			0.233140	+	0.972443i	$0.425100\pi$
$102$	−1.43023e6			−1.34774
$103$	62557.4			0.0572489			0.0286244	−	0.999590i	$-0.490887\pi$
$103$	62557.4			0.0572489			0.0286244	+	0.999590i	$0.490887\pi$
$104$	142417.			0.126608
$105$	259078.	−	1.06329e6i	0.223801	−	0.918510i
$106$		−	1.01842e6i		−	0.855087i
$107$	1.51126e6			1.23364			0.616820	−	0.787104i	$-0.288421\pi$
$107$	1.51126e6			1.23364			0.616820	+	0.787104i	$0.288421\pi$
$108$		−	1.20368e6i		−	0.955518i
$109$		−	650545.i		−	0.502340i	−0.967943	−	0.251170i	$-0.919185\pi$
$109$		−	650545.i		−	0.502340i	0.967943	−	0.251170i	$-0.0808153\pi$
$110$	−3.22467e6	−	785714.i	−2.42274	−	0.590318i
$111$		−	1.03775e6i		−	0.758793i
$112$	−2.18850e6			−1.55773
$113$	820818.			0.568868			0.284434	−	0.958696i	$-0.408194\pi$
$113$	820818.			0.568868			0.284434	+	0.958696i	$0.408194\pi$
$114$			637638.i			0.430388i
$115$	−695351.	+	1.35261e6i	−0.457205	+	0.889361i
$116$	−207491.			−0.132931
$117$		−	1.35145e6i		−	0.843804i
$118$			954889.i			0.581175i
$119$	3.73326e6			2.21538
$120$	95015.8	+	23151.2i	0.0549860	+	0.0133977i
$121$	−3.91627e6			−2.21063
$122$	2.55768e6			1.40853
$123$			1.23424e6i			0.663261i
$124$	2.94685e6			1.54558
$125$	−1.47223e6	−	1.28345e6i	−0.753781	−	0.657126i
$126$			2.40204e6i			1.20079i
$127$			3.79162e6i			1.85103i	0.378713	+	0.925514i	$0.376367\pi$
$127$			3.79162e6i			1.85103i	−0.378713	+	0.925514i	$0.623633\pi$
$128$		−	368511.i		−	0.175720i
$129$			452287.i			0.210691i
$130$	−4.27212e6	−	1.04093e6i	−1.94452	−	0.473797i
$131$	−429749.			−0.191162			−0.0955809	−	0.995422i	$-0.530471\pi$
$131$	−429749.			−0.191162			−0.0955809	+	0.995422i	$0.530471\pi$
$132$	−2.48172e6			−1.07902
$133$		−	1.66439e6i		−	0.707457i
$134$			2.36327e6i			0.982199i
$135$	594122.	−	2.43836e6i	0.241476	−	0.991050i
$136$			333605.i			0.132622i
$137$	2.83452e6			1.10235			0.551173	−	0.834391i	$-0.314180\pi$
$137$	2.83452e6			1.10235			0.551173	+	0.834391i	$0.314180\pi$
$138$	−549402.	+	2.28610e6i	−0.209051	+	0.869879i
$139$	−1.75264e6			−0.652601			−0.326300	−	0.945266i	$-0.605802\pi$
$139$	−1.75264e6			−0.652601			−0.326300	+	0.945266i	$0.605802\pi$
$140$	3.67258e6	+	894850.i	1.33840	+	0.326112i
$141$	1.14016e6			0.406731
$142$		−	3.29200e6i		−	1.14973i
$143$	−7.53537e6			−2.57689
$144$	−1.85579e6			−0.621501
$145$	−420326.	−	102415.i	−0.137874	−	0.0335939i
$146$	−5.12187e6			−1.64577
$147$			2.37417e6i			0.747411i
$148$	3.58436e6			1.10567
$149$		−	1.95787e6i		−	0.591870i	−0.955208	−	0.295935i	$-0.904369\pi$
$149$		−	1.95787e6i		−	0.591870i	0.955208	−	0.295935i	$-0.0956311\pi$
$150$	−2.68100e6	−	1.38895e6i	−0.794371	−	0.411541i
$151$	2.40711e6			0.699141			0.349570	−	0.936910i	$-0.386328\pi$
$151$	2.40711e6			0.699141			0.349570	+	0.936910i	$0.386328\pi$
$152$	148730.			0.0423515
$153$	3.16570e6			0.883885
$154$	1.33932e7			3.66710
$155$	5.96959e6	+	1.45453e6i	1.60306	+	0.390597i
$156$	−3.28783e6			−0.866036
$157$	−7.14269e6			−1.84571			−0.922854	−	0.385151i	$-0.874150\pi$
$157$	−7.14269e6			−1.84571			−0.922854	+	0.385151i	$0.874150\pi$
$158$	−604625.			−0.153290
$159$		−	1.58775e6i		−	0.394994i
$160$	−1.34403e6	+	5.51608e6i	−0.328133	+	1.34670i
$161$	1.43407e6	−	5.96729e6i	0.343632	−	1.42988i
$162$		−	408325.i		−	0.0960419i
$163$			1.83082e6i			0.422749i	0.977405	+	0.211374i	$0.0677939\pi$
$163$			1.83082e6i			0.422749i	−0.977405	+	0.211374i	$0.932206\pi$
$164$	−4.26305e6			−0.966470
$165$	−5.02735e6	−	1.22495e6i	−1.11915	−	0.272688i
$166$			5.46506e6i			1.19473i
$167$			503992.i			0.108212i	0.998535	+	0.0541059i	$0.0172308\pi$
$167$			503992.i			0.108212i	−0.998535	+	0.0541059i	$0.982769\pi$
$168$	−394635.			−0.0832276
$169$	−5.15623e6			−1.06825
$170$	2.43833e6	−	1.00072e7i	0.496302	−	2.03689i
$171$		−	1.41136e6i		−	0.282260i
$172$	−1.56219e6			−0.307008
$173$			9.35549e6i			1.80687i	0.428720	+	0.903437i	$0.358965\pi$
$173$			9.35549e6i			1.80687i	−0.428720	+	0.903437i	$0.641035\pi$
$174$	−668813.			−0.126957
$175$	6.99807e6	+	3.62550e6i	1.30576	+	0.676477i
$176$			1.03475e7i			1.89800i
$177$			1.48870e6i			0.268464i
$178$	1.69170e6			0.299961
$179$	6.18206e6			1.07789			0.538945	−	0.842341i	$-0.318823\pi$
$179$	6.18206e6			1.07789			0.538945	+	0.842341i	$0.318823\pi$
$180$	3.11425e6	+	758809.i	0.533994	+	0.130111i
$181$			5.85400e6i			0.987228i	0.869681	+	0.493614i	$0.164324\pi$
$181$			5.85400e6i			0.987228i	−0.869681	+	0.493614i	$0.835676\pi$
$182$	1.77436e7			2.94326
$183$	3.98748e6			0.650647
$184$	533238.	+	128149.i	0.0855988	+	0.0205713i
$185$	7.26105e6	+	1.76920e6i	1.14679	+	0.279423i
$186$	9.49868e6			1.47613
$187$		−	1.76513e7i		−	2.69930i
$188$			3.93808e6i			0.592667i
$189$			1.01274e7i			1.50007i
$190$	−4.46151e6	−	1.08708e6i	−0.650460	−	0.158489i
$191$		−	1.44986e6i		−	0.208078i	−0.994573	−	0.104039i	$-0.966823\pi$
$191$		−	1.44986e6i		−	0.208078i	0.994573	−	0.104039i	$-0.0331766\pi$
$192$			3.95736e6i			0.559115i
$193$		−	4.58565e6i		−	0.637865i	−0.947777	−	0.318933i	$-0.896676\pi$
$193$		−	4.58565e6i		−	0.637865i	0.947777	−	0.318933i	$-0.103324\pi$
$194$			3.92418e6i			0.537458i
$195$	−6.66035e6	−	1.62284e6i	−0.898242	−	0.218863i
$196$	−8.20033e6			−1.08909
$197$		−	4.79549e6i		−	0.627241i	−0.949548	−	0.313620i	$-0.898458\pi$
$197$		−	4.79549e6i		−	0.627241i	0.949548	−	0.313620i	$-0.101542\pi$
$198$	1.13571e7			1.46309
$199$		−	1.11070e7i		−	1.40942i	−0.709498	−	0.704708i	$-0.751078\pi$
$199$		−	1.11070e7i		−	1.40942i	0.709498	−	0.704708i	$-0.248922\pi$
$200$	−323975.	+	625349.i	−0.0404969	+	0.0781686i
$201$			3.68441e6i			0.453711i
$202$			5.34857e6i			0.648908i
$203$	1.74576e6			0.208688
$204$		−	7.70160e6i		−	0.907174i
$205$	−8.63589e6	−	2.10419e6i	−1.00241	−	0.244244i
$206$			696473.i			0.0796714i
$207$	1.21606e6	−	5.06010e6i	0.137102	−	0.570490i
$208$			1.37086e7i			1.52336i
$209$	−7.86942e6			−0.861993
$210$	1.18380e7	+	2.88440e6i	1.27826	+	0.311457i
$211$	−9.73658e6			−1.03648			−0.518238	−	0.855237i	$-0.673412\pi$
$211$	−9.73658e6			−1.03648			−0.518238	+	0.855237i	$0.673412\pi$
$212$	5.48405e6			0.575565
$213$		−	5.13231e6i		−	0.531097i
$214$			1.68254e7i			1.71682i
$215$	−3.16462e6	−	771082.i	−0.318424	−	0.0775863i
$216$	−904983.			−0.0898006
$217$	−2.47939e7			−2.42641
$218$	7.24274e6			0.699091
$219$	−7.98513e6			−0.760238
$220$	4.23095e6	−	1.73644e7i	0.397347	−	1.63076i
$221$		−	2.33848e7i		−	2.16649i
$222$	1.15536e7			1.05599
$223$			1.45562e7i			1.31261i	0.754497	+	0.656303i	$0.227881\pi$
$223$			1.45562e7i			1.31261i	−0.754497	+	0.656303i	$0.772119\pi$
$224$		−	2.29103e7i		−	2.03838i
$225$	5.93417e6	+	3.07432e6i	0.520970	+	0.269899i
$226$			9.13846e6i			0.791676i
$227$	−1.33660e7			−1.14268			−0.571338	−	0.820715i	$-0.693575\pi$
$227$	−1.33660e7			−1.14268			−0.571338	+	0.820715i	$0.693575\pi$
$228$	−3.43359e6			−0.289697
$229$		−	1.27143e6i		−	0.105873i	−0.998598	−	0.0529366i	$-0.983142\pi$
$229$		−	1.27143e6i		−	0.105873i	0.998598	−	0.0529366i	$-0.0168581\pi$
$230$	−1.50590e7	−	7.74159e6i	−1.23770	−	0.636277i
$231$	2.08804e7			1.69396
$232$			156002.i			0.0124930i
$233$			1.57450e7i			1.24473i	0.782728	+	0.622363i	$0.213827\pi$
$233$			1.57450e7i			1.24473i	−0.782728	+	0.622363i	$0.786173\pi$
$234$	1.50461e7			1.17430
$235$	−1.94379e6	+	7.97759e6i	−0.149778	+	0.614707i
$236$	−5.14193e6			−0.391192
$237$	−942626.			−0.0708100
$238$			4.15637e7i			3.08307i
$239$	−1.04435e7			−0.764985			−0.382492	−	0.923959i	$-0.624934\pi$
$239$	−1.04435e7			−0.764985			−0.382492	+	0.923959i	$0.624934\pi$
$240$	−2.22847e6	+	9.14592e6i	−0.161203	+	0.661597i
$241$		−	915138.i		−	0.0653786i	−0.999466	−	0.0326893i	$-0.989593\pi$
$241$		−	915138.i		−	0.0653786i	0.999466	−	0.0326893i	$-0.0104072\pi$
$242$		−	4.36012e7i		−	3.07647i
$243$			1.39999e7i			0.975680i
$244$			1.37727e7i			0.948090i
$245$	−1.66119e7	−	4.04760e6i	−1.12959	−	0.275232i
$246$	−1.37412e7			−0.923040
$247$	−1.04256e7			−0.691846
$248$		−	2.21558e6i		−	0.145256i
$249$			8.52017e6i			0.551887i
$250$	1.42891e7	−	1.63908e7i	0.914501	−	1.04901i
$251$		−	7.19873e6i		−	0.455234i	−0.973751	−	0.227617i	$-0.926907\pi$
$251$		−	7.19873e6i		−	0.455234i	0.973751	−	0.227617i	$-0.0730934\pi$
$252$	−1.29346e7			−0.808261
$253$	−2.82140e7	−	6.78046e6i	−1.74222	−	0.418695i
$254$	−4.22134e7			−2.57602
$255$	3.80143e6	−	1.56016e7i	0.229259	−	0.940909i
$256$	1.86945e7			1.11428
$257$			3.69241e6i			0.217526i	0.994068	+	0.108763i	$0.0346889\pi$
$257$			3.69241e6i			0.217526i	−0.994068	+	0.108763i	$0.965311\pi$
$258$	−5.03547e6			−0.293212
$259$	−3.01577e7			−1.73580
$260$	5.60526e6	−	2.30047e7i	0.318916	−	1.30887i
$261$	1.48036e6			0.0832619
$262$		−	4.78455e6i		−	0.266034i
$263$	3.73538e6			0.205337			0.102669	−	0.994716i	$-0.467262\pi$
$263$	3.73538e6			0.205337			0.102669	+	0.994716i	$0.467262\pi$
$264$			1.86588e6i			0.101408i
$265$	1.11094e7	+	2.70687e6i	0.596968	+	0.145455i
$266$	1.85302e7			0.984546
$267$	2.63741e6			0.138562
$268$	−1.27259e7			−0.661124
$269$	7.09110e6			0.364298			0.182149	−	0.983271i	$-0.441695\pi$
$269$	7.09110e6			0.364298			0.182149	+	0.983271i	$0.441695\pi$
$270$	2.71471e7	+	6.61457e6i	1.37921	+	0.336055i
$271$	1.73042e7			0.869447			0.434724	−	0.900564i	$-0.356846\pi$
$271$	1.73042e7			0.869447			0.434724	+	0.900564i	$0.356846\pi$
$272$	−3.21117e7			−1.59572
$273$	2.76628e7			1.35959
$274$			3.15577e7i			1.53410i
$275$	1.71417e7	−	3.30876e7i	0.824246	−	1.59099i
$276$	−1.23103e7	−	2.95845e6i	−0.585521	−	0.140714i
$277$			2.67546e7i			1.25881i	0.777079	+	0.629403i	$0.216701\pi$
$277$			2.67546e7i			1.25881i	−0.777079	+	0.629403i	$0.783299\pi$
$278$		−	1.95127e7i		−	0.908204i
$279$	−2.10245e7			−0.968085
$280$	672792.	−	2.76123e6i	0.0306483	−	0.125785i
$281$		−	2.88796e6i		−	0.130158i	−0.997880	−	0.0650792i	$-0.979270\pi$
$281$		−	2.88796e6i		−	0.130158i	0.997880	−	0.0650792i	$-0.0207300\pi$
$282$			1.26938e7i			0.566034i
$283$	−2.96697e7			−1.30904			−0.654521	−	0.756044i	$-0.727130\pi$
$283$	−2.96697e7			−1.30904			−0.654521	+	0.756044i	$0.727130\pi$
$284$	1.77269e7			0.773888
$285$	−6.95561e6	−	1.69478e6i	−0.300470	−	0.0732115i
$286$		−	8.38939e7i		−	3.58618i
$287$	3.58679e7			1.51726
$288$		−	1.94273e7i		−	0.813270i
$289$	3.06403e7			1.26940
$290$	1.14023e6	−	4.67964e6i	0.0467516	−	0.191875i
$291$			6.11791e6i			0.248270i
$292$		−	2.75805e7i		−	1.10778i
$293$	2.81816e7			1.12037			0.560186	−	0.828367i	$-0.310730\pi$
$293$	2.81816e7			1.12037			0.560186	+	0.828367i	$0.310730\pi$
$294$	−2.64324e7			−1.04015
$295$	−1.04163e7	−	2.53800e6i	−0.405740	−	0.0988613i
$296$		−	2.69490e6i		−	0.103912i
$297$	4.78833e7			1.82774
$298$	2.17977e7			0.823686
$299$	−3.73785e7	−	8.98290e6i	−1.39833	−	0.336049i
$300$	7.47929e6	−	1.44368e7i	0.277011	−	0.534696i
$301$	1.31438e7			0.481972
$302$			2.67992e7i			0.972972i
$303$			8.33856e6i			0.299753i
$304$			1.43163e7i			0.509577i
$305$	−6.79806e6	+	2.79001e7i	−0.239599	+	0.983347i
$306$			3.52449e7i			1.23008i
$307$		−	3.12613e7i		−	1.08042i	−0.841531	−	0.540209i	$-0.818345\pi$
$307$		−	3.12613e7i		−	1.08042i	0.841531	−	0.540209i	$-0.181655\pi$
$308$			7.21205e7i			2.46835i
$309$			1.08582e6i			0.0368029i
$310$	−1.61938e7	+	6.64616e7i	−0.543581	+	2.23093i
$311$	2.79448e7			0.929009			0.464504	−	0.885571i	$-0.346232\pi$
$311$	2.79448e7			0.929009			0.464504	+	0.885571i	$0.346232\pi$
$312$			2.47196e6i			0.0813911i
$313$	2.61062e7			0.851354			0.425677	−	0.904875i	$-0.360036\pi$
$313$	2.61062e7			0.851354			0.425677	+	0.904875i	$0.360036\pi$
$314$		−	7.95221e7i		−	2.56861i
$315$	−2.62023e7	−	6.38438e6i	−0.838317	−	0.204262i
$316$		−	3.25581e6i		−	0.103181i
$317$			1.47348e7i			0.462558i	0.972887	+	0.231279i	$0.0742911\pi$
$317$			1.47348e7i			0.462558i	−0.972887	+	0.231279i	$0.925709\pi$
$318$	1.76769e7			0.549700
$319$		−	8.25417e6i		−	0.254274i
$320$	−2.76893e7	−	6.74669e6i	−0.845011	−	0.205893i
$321$			2.62313e7i			0.793056i
$322$	6.64359e7	+	1.59660e7i	1.98992	+	0.478222i
$323$		−	2.44215e7i		−	0.724710i
$324$	2.19877e6			0.0646464
$325$	2.27098e7	−	4.38353e7i	0.661550	−	1.27695i
$326$	−2.03831e7			−0.588326
$327$	1.12916e7			0.322934
$328$			3.20517e6i			0.0908300i
$329$		−	3.31338e7i		−	0.930429i
$330$	1.36378e7	−	5.59712e7i	0.379491	−	1.55748i
$331$	4.79462e7			1.32212			0.661059	−	0.750334i	$-0.270107\pi$
$331$	4.79462e7			1.32212			0.661059	+	0.750334i	$0.270107\pi$
$332$	−2.94285e7			−0.804182
$333$	−2.55729e7			−0.692545
$334$	−5.61112e6			−0.150595
$335$	−2.57795e7	−	6.28135e6i	−0.685709	−	0.167078i
$336$		−	3.79863e7i		−	1.00140i
$337$	−1.17000e7			−0.305701			−0.152850	−	0.988249i	$-0.548845\pi$
$337$	−1.17000e7			−0.305701			−0.152850	+	0.988249i	$0.548845\pi$
$338$		−	5.74061e7i		−	1.48665i
$339$			1.42471e7i			0.365702i
$340$	5.38875e7	+	1.31301e7i	1.37104	+	0.334064i
$341$			1.17228e8i			2.95644i
$342$	1.57131e7			0.392812
$343$	9.65141e6			0.239171
$344$			1.17453e6i			0.0288529i
$345$	−2.34775e7	−	1.20693e7i	−0.571734	−	0.293918i
$346$	−1.04158e8			−2.51457
$347$		−	2.29092e7i		−	0.548305i	−0.961686	−	0.274152i	$-0.911603\pi$
$347$		−	2.29092e7i		−	0.548305i	0.961686	−	0.274152i	$-0.0883973\pi$
$348$		−	3.60146e6i		−	0.0854557i
$349$	−6.88282e7			−1.61916			−0.809581	−	0.587008i	$-0.800306\pi$
$349$	−6.88282e7			−1.61916			−0.809581	+	0.587008i	$0.800306\pi$
$350$	−4.03639e7	+	7.79119e7i	−0.941432	+	1.81719i
$351$	6.34369e7			1.46697
$352$	−1.08322e8			−2.48365
$353$		−	9.03282e6i		−	0.205352i	−0.994715	−	0.102676i	$-0.967259\pi$
$353$		−	9.03282e6i		−	0.205352i	0.994715	−	0.102676i	$-0.0327405\pi$
$354$	−1.65742e7			−0.373613
$355$	3.59104e7	+	8.74981e6i	0.802667	+	0.195575i
$356$			9.10957e6i			0.201905i
$357$			6.47989e7i			1.42417i
$358$			6.88270e7i			1.50006i
$359$			3.63726e7i			0.786124i	0.919512	+	0.393062i	$0.128584\pi$
$359$			3.63726e7i			0.786124i	−0.919512	+	0.393062i	$0.871416\pi$
$360$	570510.	−	2.34145e6i	0.0122280	−	0.0501853i
$361$	3.61581e7			0.768571
$362$	−6.51747e7			−1.37389
$363$		−	6.79755e7i		−	1.42113i
$364$			9.55469e7i			1.98113i
$365$	1.36134e7	−	5.58714e7i	0.279956	−	1.14898i
$366$			4.43940e7i			0.905485i
$367$	4.10259e7			0.829964			0.414982	−	0.909830i	$-0.363788\pi$
$367$	4.10259e7			0.829964			0.414982	+	0.909830i	$0.363788\pi$
$368$	−1.23352e7	+	5.13278e7i	−0.247516	+	1.02993i
$369$	3.04150e7			0.605354
$370$	−1.96972e7	+	8.08398e7i	−0.388865	+	1.59595i
$371$	−4.61411e7			−0.903580
$372$			5.11490e7i			0.993592i
$373$	7.99699e7			1.54099			0.770495	−	0.637446i	$-0.220009\pi$
$373$	7.99699e7			1.54099			0.770495	+	0.637446i	$0.220009\pi$
$374$	1.96518e8			3.75653
$375$	2.22771e7	−	2.55537e7i	0.422439	−	0.484575i
$376$	2.96084e6			0.0556995
$377$		−	1.09353e7i		−	0.204083i
$378$	−1.12751e8			−2.08760
$379$			1.61241e7i			0.296182i	0.988974	+	0.148091i	$0.0473129\pi$
$379$			1.61241e7i			0.296182i	−0.988974	+	0.148091i	$0.952687\pi$
$380$	5.85374e6	−	2.40245e7i	0.106680	−	0.437829i
$381$	−6.58118e7			−1.18995
$382$	1.61418e7			0.289575
$383$	−7.81809e7			−1.39157			−0.695784	−	0.718251i	$-0.744943\pi$
$383$	−7.81809e7			−1.39157			−0.695784	+	0.718251i	$0.744943\pi$
$384$	6.39631e6			0.112963
$385$	−3.55979e7	+	1.46099e8i	−0.623796	+	2.56014i
$386$	5.10536e7			0.887697
$387$	1.11456e7			0.192296
$388$	−2.11311e7			−0.361766
$389$			4.87620e7i			0.828386i	0.910189	+	0.414193i	$0.135936\pi$
$389$			4.87620e7i			0.828386i	−0.910189	+	0.414193i	$0.864064\pi$
$390$	1.80676e7	−	7.41520e7i	0.304584	−	1.25005i
$391$	2.10420e7	−	8.75575e7i	0.352012	−	1.46475i
$392$			6.16541e6i			0.102354i
$393$		−	7.45923e6i		−	0.122890i
$394$	5.33898e7			0.872911
$395$	1.60704e6	−	6.59548e6i	0.0260756	−	0.107018i
$396$			6.11562e7i			0.984816i
$397$		−	1.13874e8i		−	1.81992i	−0.414696	−	0.909960i	$-0.636112\pi$
$397$		−	1.13874e8i		−	1.81992i	0.414696	−	0.909960i	$-0.363888\pi$
$398$	1.23659e8			1.96144
$399$	2.88891e7			0.454795
$400$	−6.01941e7	−	3.11848e7i	−0.940533	−	0.487263i
$401$		−	6.54078e7i		−	1.01437i	−0.861837	−	0.507185i	$-0.830686\pi$
$401$		−	6.54078e7i		−	1.01437i	0.861837	−	0.507185i	$-0.169314\pi$
$402$	−4.10198e7			−0.631415
$403$			1.55307e8i			2.37287i
$404$	−2.88012e7			−0.436784
$405$	4.45417e6	+	1.08529e6i	0.0670504	+	0.0163373i
$406$			1.94362e7i			0.290425i
$407$			1.42589e8i			2.11496i
$408$	−5.79044e6			−0.0852572
$409$	−1.21289e8			−1.77277			−0.886386	−	0.462948i	$-0.846792\pi$
$409$	−1.21289e8			−1.77277			−0.886386	+	0.462948i	$0.846792\pi$
$410$	2.34267e7	−	9.61464e7i	0.339907	−	1.39502i
$411$			4.91993e7i			0.708653i
$412$	−3.75040e6			−0.0536273
$413$	4.32626e7			0.614133
$414$	5.63358e7	+	1.35388e7i	0.793932	+	0.190800i
$415$	−5.96150e7	−	1.45256e7i	−0.834087	−	0.203231i
$416$	−1.43508e8			−1.99341
$417$		−	3.04209e7i		−	0.419530i
$418$		−	8.76130e7i		−	1.19961i
$419$			5.97069e7i			0.811676i	0.913945	+	0.405838i	$0.133020\pi$
$419$			5.97069e7i			0.811676i	−0.913945	+	0.405838i	$0.866980\pi$
$420$	−1.55321e7	+	6.37457e7i	−0.209644	+	0.860405i
$421$			5.85064e7i			0.784074i	0.919950	+	0.392037i	$0.128229\pi$
$421$			5.85064e7i			0.784074i	−0.919950	+	0.392037i	$0.871771\pi$
$422$		−	1.08401e8i		−	1.44243i
$423$		−	2.80965e7i		−	0.371220i
$424$		−	4.12318e6i		−	0.0540922i
$425$	1.02682e8	+	5.31966e7i	1.33761	+	0.692974i
$426$	5.71398e7			0.739112
$427$		−	1.15879e8i		−	1.48841i
$428$	−9.06023e7			−1.15560
$429$		−	1.30793e8i		−	1.65658i
$430$	8.58472e6	−	3.52328e7i	0.107974	−	0.443141i
$431$		−	9.19492e7i		−	1.14846i	−0.818694	−	0.574230i	$-0.805301\pi$
$431$		−	9.19492e7i		−	1.14846i	0.818694	−	0.574230i	$-0.194699\pi$
$432$		−	8.71108e7i		−	1.08049i
$433$	−9.08705e7			−1.11933			−0.559666	−	0.828718i	$-0.689071\pi$
$433$	−9.08705e7			−1.11933			−0.559666	+	0.828718i	$0.689071\pi$
$434$		−	2.76039e8i		−	3.37676i
$435$	1.77764e6	−	7.29568e6i	0.0215962	−	0.0886335i
$436$			3.90011e7i			0.470562i
$437$	−3.90355e7	−	9.38112e6i	−0.467752	−	0.112411i
$438$		−	8.89012e7i		−	1.05800i
$439$	1.50579e8			1.77980			0.889898	−	0.456159i	$-0.150775\pi$
$439$	1.50579e8			1.77980			0.889898	+	0.456159i	$0.150775\pi$
$440$	−1.30554e7	−	3.18104e6i	−0.153261	−	0.0373431i
$441$	5.85059e7			0.682157
$442$	2.60351e8			3.01504
$443$		−	8.50278e7i		−	0.978024i	−0.872277	−	0.489012i	$-0.837357\pi$
$443$		−	8.50278e7i		−	0.978024i	0.872277	−	0.489012i	$-0.162643\pi$
$444$			6.22145e7i			0.710792i
$445$	−4.49639e6	+	1.84538e7i	−0.0510251	+	0.209414i
$446$	−1.62060e8			−1.82671
$447$	3.39832e7			0.380488
$448$	1.15004e8			1.27902
$449$	9.44389e7			1.04331			0.521653	−	0.853158i	$-0.325315\pi$
$449$	9.44389e7			1.04331			0.521653	+	0.853158i	$0.325315\pi$
$450$	−3.42275e7	+	6.60672e7i	−0.375610	+	0.725017i
$451$		−	1.69588e8i		−	1.84869i
$452$	−4.92092e7			−0.532882
$453$			4.17806e7i			0.449449i
$454$		−	1.48808e8i		−	1.59023i
$455$	−4.71609e7	+	1.93555e8i	−0.500666	+	2.05480i
$456$			2.58154e6i			0.0272260i
$457$	8.11904e7			0.850660			0.425330	−	0.905038i	$-0.360158\pi$
$457$	8.11904e7			0.850660			0.425330	+	0.905038i	$0.360158\pi$
$458$	1.41553e7			0.147340
$459$			1.48598e8i			1.53665i
$460$	4.16873e7	−	8.10907e7i	0.428282	−	0.833101i
$461$	9.00424e7			0.919061			0.459531	−	0.888162i	$-0.348018\pi$
$461$	9.00424e7			0.919061			0.459531	+	0.888162i	$0.348018\pi$
$462$			2.32469e8i			2.35743i
$463$		−	4.60376e6i		−	0.0463842i	−0.999731	−	0.0231921i	$-0.992617\pi$
$463$		−	4.60376e6i		−	0.0463842i	0.999731	−	0.0231921i	$-0.00738293\pi$
$464$	−1.50162e7			−0.150317
$465$	−2.52466e7	+	1.03615e8i	−0.251098	+	1.03054i
$466$	−1.75294e8			−1.73225
$467$	−4.69061e7			−0.460552			−0.230276	−	0.973125i	$-0.573963\pi$
$467$	−4.69061e7			−0.460552			−0.230276	+	0.973125i	$0.573963\pi$
$468$			8.10212e7i			0.790426i
$469$	1.07072e8			1.03790
$470$	−8.88172e7	−	2.16409e7i	−0.855468	−	0.208441i
$471$		−	1.23977e8i		−	1.18653i
$472$			3.86596e6i			0.0367647i
$473$		−	6.21454e7i		−	0.587253i
$474$		−	1.04946e7i		−	0.0985440i
$475$	2.37165e7	−	4.57785e7i	0.221294	−	0.427150i
$476$	−2.23814e8			−2.07523
$477$	−3.91264e7			−0.360508
$478$		−	1.16271e8i		−	1.06461i
$479$			1.97258e8i			1.79485i	0.441168	+	0.897425i	$0.354564\pi$
$479$			1.97258e8i			1.79485i	−0.441168	+	0.897425i	$0.645436\pi$
$480$	−9.57437e7	−	2.33286e7i	−0.865738	−	0.210943i
$481$			1.88905e8i			1.69750i
$482$	1.01885e7			0.0909853
$483$	1.03575e8	+	2.48915e7i	0.919210	+	0.220907i
$484$	2.34786e8			2.07079
$485$	−4.28065e7	−	1.04301e7i	−0.375219	−	0.0914247i
$486$	−1.55866e8			−1.35782
$487$			4.46167e7i			0.386287i	0.981171	+	0.193144i	$0.0618683\pi$
$487$			4.46167e7i			0.386287i	−0.981171	+	0.193144i	$0.938132\pi$
$488$	1.03550e7			0.0891026
$489$	−3.17779e7			−0.271768
$490$	4.50633e7	−	1.84946e8i	0.383032	−	1.57201i
$491$	1.47525e7			0.124629			0.0623146	−	0.998057i	$-0.480152\pi$
$491$	1.47525e7			0.124629			0.0623146	+	0.998057i	$0.480152\pi$
$492$		−	7.39945e7i		−	0.621304i
$493$	2.56155e7			0.213777
$494$		−	1.16072e8i		−	0.962821i
$495$	−3.01861e7	+	1.23888e8i	−0.248880	+	1.02144i
$496$	2.13265e8			1.74773
$497$	−1.49149e8			−1.21493
$498$	−9.48580e7			−0.768044
$499$	−9.75908e6			−0.0785429			−0.0392715	−	0.999229i	$-0.512504\pi$
$499$	−9.75908e6			−0.0785429			−0.0392715	+	0.999229i	$0.512504\pi$
$500$	8.82622e7	+	7.69446e7i	0.706097	+	0.615557i
$501$	−8.74788e6			−0.0695648
$502$	8.01459e7			0.633535
$503$	−1.27442e8			−1.00140			−0.500700	−	0.865621i	$-0.666924\pi$
$503$	−1.27442e8			−1.00140			−0.500700	+	0.865621i	$0.666924\pi$
$504$			9.72487e6i			0.0759612i
$505$	−5.83443e7	−	1.42160e7i	−0.453027	−	0.110383i
$506$	7.54892e7	−	3.14116e8i	0.582684	−	2.42459i
$507$		−	8.94976e7i		−	0.686732i
$508$		−	2.27313e8i		−	1.73393i
$509$	6.36575e7			0.482721			0.241360	−	0.970436i	$-0.422406\pi$
$509$	6.36575e7			0.482721			0.241360	+	0.970436i	$0.422406\pi$
$510$	1.73698e8	+	4.23226e7i	1.30943	+	0.319052i
$511$			2.32054e8i			1.73911i
$512$			1.84547e8i			1.37498i
$513$	6.62491e7			0.490713
$514$	−4.11089e7			−0.302724
$515$	−7.59740e6	−	1.85116e6i	−0.0556216	−	0.0135526i
$516$		−	2.71153e7i		−	0.197363i
$517$	−1.56660e8			−1.13367
$518$		−	3.35756e8i		−	2.41566i
$519$	−1.62385e8			−1.16157
$520$	−1.72961e7	−	4.21431e6i	−0.123009	−	0.0299720i
$521$		−	8.49681e6i		−	0.0600818i	−0.999549	−	0.0300409i	$-0.990436\pi$
$521$		−	8.49681e6i		−	0.0600818i	0.999549	−	0.0300409i	$-0.00956375\pi$
$522$			1.64814e7i			0.115873i
$523$	1.41826e8			0.991406			0.495703	−	0.868492i	$-0.334911\pi$
$523$	1.41826e8			0.991406			0.495703	+	0.868492i	$0.334911\pi$
$524$	2.57641e7			0.179069
$525$	−6.29284e7	+	1.21467e8i	−0.434879	+	0.839420i
$526$			4.15873e7i			0.285761i
$527$	−3.63798e8			−2.48559
$528$	−1.79603e8			−1.22015
$529$	−1.31870e8	−	6.72677e7i	−0.890797	−	0.454401i
$530$	−3.01365e7	+	1.23684e8i	−0.202426	+	0.830782i
$531$	3.66855e7			0.245026
$532$			9.97825e7i			0.662704i
$533$		−	2.24674e8i		−	1.48378i
$534$			2.93632e7i			0.192832i
$535$	−1.83538e8	−	4.47203e7i	−1.19857	−	0.292041i
$536$			9.56793e6i			0.0621332i
$537$			1.07303e8i			0.692931i
$538$			7.89477e7i			0.506982i
$539$		−	3.26216e8i		−	2.08324i
$540$	−3.56185e7	+	1.46183e8i	−0.226201	+	0.928357i
$541$	−1.45657e8			−0.919900			−0.459950	−	0.887945i	$-0.652133\pi$
$541$	−1.45657e8			−0.919900			−0.459950	+	0.887945i	$0.652133\pi$
$542$			1.92653e8i			1.20998i
$543$	−1.01609e8			−0.634648
$544$		−	3.36160e8i		−	2.08809i
$545$	−1.92505e7	+	7.90067e7i	−0.118919	+	0.488061i
$546$			3.07980e8i			1.89210i
$547$			2.10359e7i			0.128528i	0.997933	+	0.0642642i	$0.0204700\pi$
$547$			2.10359e7i			0.128528i	−0.997933	+	0.0642642i	$0.979530\pi$
$548$	−1.69934e8			−1.03261
$549$		−	9.82624e7i		−	0.593841i
$550$	3.68376e8	+	1.90845e8i	2.21413	+	1.14708i
$551$		−	1.14201e7i		−	0.0682676i
$552$	−2.22431e6	+	9.25551e6i	−0.0132244	+	0.0550279i
$553$			2.73934e7i			0.161983i
$554$	−2.97868e8			−1.75184
$555$	−3.07084e7	+	1.26031e8i	−0.179630	+	0.737224i
$556$	1.05073e8			0.611318
$557$	1.56424e8			0.905187			0.452593	−	0.891717i	$-0.350499\pi$
$557$	1.56424e8			0.905187			0.452593	+	0.891717i	$0.350499\pi$
$558$		−	2.34073e8i		−	1.34725i
$559$		−	8.23316e7i		−	0.471337i
$560$	2.65787e8	+	6.47608e7i	1.51346	+	0.368764i
$561$	3.06376e8			1.73527
$562$	3.21527e7			0.181137
$563$	−2.92301e8			−1.63797			−0.818985	−	0.573815i	$-0.805463\pi$
$563$	−2.92301e8			−1.63797			−0.818985	+	0.573815i	$0.805463\pi$
$564$	−6.83540e7			−0.381001
$565$	−9.96859e7	−	2.42891e7i	−0.552698	−	0.134669i
$566$		−	3.30323e8i		−	1.82175i
$567$	−1.84997e7			−0.101488
$568$		−	1.33280e7i		−	0.0727309i
$569$			1.36483e8i			0.740870i	0.928858	+	0.370435i	$0.120791\pi$
$569$			1.36483e8i			0.740870i	−0.928858	+	0.370435i	$0.879209\pi$
$570$	1.88686e7	−	7.74392e7i	0.101886	−	0.418154i
$571$		−	2.52207e7i		−	0.135472i	−0.997703	−	0.0677358i	$-0.978423\pi$
$571$		−	2.52207e7i		−	0.135472i	0.997703	−	0.0677358i	$-0.0215775\pi$
$572$	4.51756e8			2.41388
$573$	2.51655e7			0.133765
$574$			3.99330e8i			2.11153i
$575$	1.24474e8	−	1.43694e8i	0.654748	−	0.755847i
$576$	9.75200e7			0.510301
$577$			4.80846e7i			0.250310i	0.992137	+	0.125155i	$0.0399428\pi$
$577$			4.80846e7i			0.250310i	−0.992137	+	0.125155i	$0.960057\pi$
$578$			3.41129e8i			1.76659i
$579$	7.95940e7			0.410057
$580$	2.51991e7	+	6.13994e6i	0.129152	+	0.0314688i
$581$	2.47602e8			1.26249
$582$	−6.81128e7			−0.345509
$583$			2.18160e8i			1.10096i
$584$	−2.07364e7			−0.104110
$585$	−3.99912e7	+	1.64129e8i	−0.199755	+	0.819819i
$586$			3.13755e8i			1.55919i
$587$		−	3.96952e8i		−	1.96256i	−0.192580	−	0.981281i	$-0.561686\pi$
$587$		−	3.96952e8i		−	1.96256i	0.192580	−	0.981281i	$-0.438314\pi$
$588$		−	1.42335e8i		−	0.700130i
$589$			1.62191e8i			0.793746i
$590$	2.82565e7	−	1.15968e8i	0.137582	−	0.564655i
$591$	8.32362e7			0.403227
$592$	2.59403e8			1.25029
$593$			1.99018e8i			0.954397i	0.878796	+	0.477199i	$0.158348\pi$
$593$			1.99018e8i			0.954397i	−0.878796	+	0.477199i	$0.841652\pi$
$594$			5.33101e8i			2.54361i
$595$	−4.53393e8	−	1.10472e8i	−2.15240	−	0.524448i
$596$			1.17377e8i			0.554428i
$597$	1.92787e8			0.906055
$598$	1.00010e8	−	4.16148e8i	0.467669	−	1.94601i
$599$	2.26143e8			1.05221			0.526106	−	0.850419i	$-0.323652\pi$
$599$	2.26143e8			1.05221			0.526106	+	0.850419i	$0.323652\pi$
$600$	−1.08543e7	−	5.62329e6i	−0.0502514	−	0.0260338i
$601$	2.33280e7			0.107462			0.0537309	−	0.998555i	$-0.482889\pi$
$601$	2.33280e7			0.107462			0.0537309	+	0.998555i	$0.482889\pi$
$602$			1.46335e8i			0.670745i
$603$	9.07937e7			0.414099
$604$	−1.44309e8			−0.654914
$605$	4.75619e8	+	1.15888e8i	2.14780	+	0.523326i
$606$	−9.28361e7			−0.417156
$607$			1.73199e8i			0.774424i	0.921991	+	0.387212i	$0.126562\pi$
$607$			1.73199e8i			0.774424i	−0.921991	+	0.387212i	$0.873438\pi$
$608$	−1.49870e8			−0.666811
$609$			3.03016e7i			0.134157i
$610$	−3.10622e8	−	7.56851e7i	−1.36849	−	0.333443i
$611$	−2.07547e8			−0.909898
$612$	−1.89788e8			−0.827971
$613$	1.46366e8			0.635419			0.317710	−	0.948188i	$-0.397086\pi$
$613$	1.46366e8			0.635419			0.317710	+	0.948188i	$0.397086\pi$
$614$	3.48043e8			1.50358
$615$	3.65229e7	−	1.49895e8i	0.157014	−	0.644408i
$616$	5.42237e7			0.231978
$617$	3.19960e8			1.36220			0.681099	−	0.732191i	$-0.261502\pi$
$617$	3.19960e8			1.36220			0.681099	+	0.732191i	$0.261502\pi$
$618$	−1.20888e7			−0.0512175
$619$			4.62664e8i			1.95072i	0.220630	+	0.975358i	$0.429189\pi$
$619$			4.62664e8i			1.95072i	−0.220630	+	0.975358i	$0.570811\pi$
$620$	−3.57886e8	−	8.72013e7i	−1.50165	−	0.365888i
$621$	2.37521e8	+	5.70816e7i	0.991806	+	0.238353i
$622$			3.11119e8i			1.29287i
$623$		−	7.66451e7i		−	0.316972i
$624$	−2.37943e8			−0.979306
$625$	1.40819e8	+	1.99436e8i	0.576793	+	0.816890i
$626$			2.90649e8i			1.18480i
$627$		−	1.36591e8i		−	0.554140i
$628$	4.28214e8			1.72895
$629$	−4.42502e8			−1.77813
$630$	7.10795e7	−	2.91720e8i	0.284265	−	1.16666i
$631$		−	2.73216e8i		−	1.08747i	−0.839257	−	0.543736i	$-0.817009\pi$
$631$		−	2.73216e8i		−	1.08747i	0.839257	−	0.543736i	$-0.182991\pi$
$632$	−2.44788e6			−0.00969704
$633$		−	1.69000e8i		−	0.666307i
$634$	−1.64048e8			−0.643728
$635$	1.12199e8	−	4.60480e8i	0.438196	−	1.79841i
$636$			9.51877e7i			0.370007i
$637$		−	4.32179e8i		−	1.67203i
$638$	9.18965e7			0.353865
$639$	−1.26474e8			−0.484729
$640$	−1.09047e7	+	4.47545e7i	−0.0415983	+	0.170725i
$641$		−	2.84210e8i		−	1.07911i	−0.841951	−	0.539554i	$-0.818593\pi$
$641$		−	2.84210e8i		−	1.07911i	0.841951	−	0.539554i	$-0.181407\pi$
$642$	−2.92042e8			−1.10367
$643$	−2.80541e8			−1.05527			−0.527634	−	0.849472i	$-0.676921\pi$
$643$	−2.80541e8			−1.05527			−0.527634	+	0.849472i	$0.676921\pi$
$644$	−8.59747e7	+	3.57747e8i	−0.321894	+	1.33943i
$645$	1.33838e7	−	5.49289e7i	0.0498770	−	0.204702i
$646$	2.71893e8			1.00856
$647$		−	2.20896e7i		−	0.0815595i	−0.999168	−	0.0407797i	$-0.987016\pi$
$647$		−	2.20896e7i		−	0.0815595i	0.999168	−	0.0407797i	$-0.0129842\pi$
$648$		−	1.65314e6i		−	0.00607554i
$649$		−	2.04551e8i		−	0.748284i
$650$	4.88033e8	+	2.52836e8i	1.77709	+	0.920658i
$651$		−	4.30352e8i		−	1.55984i
$652$		−	1.09760e8i		−	0.396006i
$653$		−	1.67340e8i		−	0.600981i	−0.953785	−	0.300491i	$-0.902850\pi$
$653$		−	1.67340e8i		−	0.600981i	0.953785	−	0.300491i	$-0.0971504\pi$
$654$			1.25714e8i			0.449417i
$655$	5.21917e7	+	1.27169e7i	0.185728	+	0.0452539i
$656$	−3.08519e8			−1.09288
$657$			1.96775e8i			0.693864i
$658$	3.68890e8			1.29485
$659$		−	4.04241e8i		−	1.41249i	−0.707969	−	0.706244i	$-0.750388\pi$
$659$		−	4.04241e8i		−	1.41249i	0.707969	−	0.706244i	$-0.249612\pi$
$660$	3.01397e8	+	7.34374e7i	1.04835	+	0.255438i
$661$			3.52460e8i			1.22041i	0.792244	+	0.610205i	$0.208913\pi$
$661$			3.52460e8i			1.22041i	−0.792244	+	0.610205i	$0.791087\pi$
$662$			5.33802e8i			1.83995i
$663$	4.05894e8			1.39275
$664$			2.21258e7i			0.0755779i
$665$	−4.92516e7	+	2.02135e8i	−0.167477	+	0.687348i
$666$		−	2.84712e8i		−	0.963793i
$667$	9.83978e6	−	4.09441e7i	0.0331595	−	0.137979i
$668$		−	3.02150e7i		−	0.101366i
$669$	−2.52655e8			−0.843821
$670$	6.99325e7	−	2.87012e8i	0.232517	−	0.954280i
$671$	−5.47890e8			−1.81353
$672$	3.97658e8			1.31039
$673$			4.82376e8i			1.58249i	0.611500	+	0.791244i	$0.290566\pi$
$673$			4.82376e8i			1.58249i	−0.611500	+	0.791244i	$0.709434\pi$
$674$		−	1.30260e8i		−	0.425434i
$675$	−1.44309e8	+	2.78550e8i	−0.469225	+	0.905715i
$676$	3.09123e8			1.00067
$677$	−1.34914e8			−0.434802			−0.217401	−	0.976082i	$-0.569758\pi$
$677$	−1.34914e8			−0.434802			−0.217401	+	0.976082i	$0.569758\pi$
$678$	−1.58618e8			−0.508936
$679$	1.77791e8			0.567937
$680$	9.87183e6	−	4.05153e7i	0.0313957	−	0.128852i
$681$		−	2.31996e8i		−	0.734579i
$682$	−1.30514e9			−4.11438
$683$			1.32589e7i			0.0416147i	0.999784	+	0.0208073i	$0.00662366\pi$
$683$			1.32589e7i			0.0416147i	−0.999784	+	0.0208073i	$0.993376\pi$
$684$			8.46129e7i			0.264404i
$685$	−3.44244e8	−	8.38774e7i	−1.07101	−	0.260959i
$686$			1.07452e8i			0.332846i
$687$	2.20685e7			0.0680615
$688$	−1.13057e8			−0.347161
$689$			2.89024e8i			0.883641i
$690$	1.34372e8	−	2.61383e8i	0.409036	−	0.795664i
$691$	4.47546e8			1.35645			0.678224	−	0.734855i	$-0.262750\pi$
$691$	4.47546e8			1.35645			0.678224	+	0.734855i	$0.262750\pi$
$692$		−	5.60874e8i		−	1.69257i
$693$		−	5.14549e8i		−	1.54606i
$694$	2.55056e8			0.763058
$695$	2.12852e8	+	5.18630e7i	0.634051	+	0.154491i
$696$	−2.70775e6			−0.00803122
$697$	5.26288e8			1.55426
$698$		−	7.66289e8i		−	2.25334i
$699$	−2.73288e8			−0.800183
$700$	−4.19544e8	−	2.17354e8i	−1.22316	−	0.633684i
$701$			3.15447e8i			0.915740i	0.889019	+	0.457870i	$0.151387\pi$
$701$			3.15447e8i			0.915740i	−0.889019	+	0.457870i	$0.848613\pi$
$702$			7.06265e8i			2.04153i
$703$			1.97280e8i			0.567827i
$704$		−	5.43750e8i		−	1.55841i
$705$	−1.38468e8	−	3.37388e7i	−0.395170	−	0.0962858i
$706$	1.00566e8			0.285782
$707$	2.42325e8			0.685708
$708$		−	8.92495e7i		−	0.251481i
$709$		−	1.69014e8i		−	0.474224i	−0.971482	−	0.237112i	$-0.923799\pi$
$709$		−	1.69014e8i		−	0.474224i	0.971482	−	0.237112i	$-0.0762008\pi$
$710$	−9.74147e7	+	3.99803e8i	−0.272176	+	1.11705i
$711$			2.32289e7i			0.0646278i
$712$	6.84902e6			0.0189753
$713$	−1.39747e8	+	5.81499e8i	−0.385545	+	1.60428i
$714$	−7.21428e8			−1.98198
$715$	9.15148e8	+	2.22982e8i	2.50365	+	0.610031i
$716$	−3.70623e8			−1.00970
$717$		−	1.81270e8i		−	0.491777i
$718$	−4.04949e8			−1.09402
$719$	−6.88904e8			−1.85341			−0.926707	−	0.375785i	$-0.877373\pi$
$719$	−6.88904e8			−1.85341			−0.926707	+	0.375785i	$0.877373\pi$
$720$	2.25380e8	+	5.49154e7i	0.603835	+	0.147129i
$721$	3.15547e7			0.0841896
$722$			4.02561e8i			1.06960i
$723$	1.58842e7			0.0420292
$724$		−	3.50956e8i		−	0.924776i
$725$	4.80167e7	+	2.48761e7i	0.126002	+	0.0652781i
$726$	7.56795e8			1.97774
$727$	−3.88788e8			−1.01183			−0.505917	−	0.862582i	$-0.668846\pi$
$727$	−3.88788e8			−1.01183			−0.505917	+	0.862582i	$0.668846\pi$
$728$	7.18368e7			0.186189
$729$	−2.69736e8			−0.696236
$730$	6.22035e8	+	1.51563e8i	1.59899	+	0.389605i
$731$	1.92858e8			0.493725
$732$	−2.39055e8			−0.609488
$733$	−4.96714e8			−1.26123			−0.630616	−	0.776095i	$-0.717198\pi$
$733$	−4.96714e8			−1.26123			−0.630616	+	0.776095i	$0.717198\pi$
$734$			4.56755e8i			1.15504i
$735$	7.02549e7	−	2.88335e8i	0.176935	−	0.726166i
$736$	−5.37323e8	−	1.29131e8i	−1.34773	−	0.323889i
$737$		−	5.06246e8i		−	1.26462i
$738$			3.38621e8i			0.842452i
$739$	1.94104e8			0.480950			0.240475	−	0.970655i	$-0.422697\pi$
$739$	1.94104e8			0.480950			0.240475	+	0.970655i	$0.422697\pi$
$740$	−4.35310e8	−	1.06066e8i	−1.07425	−	0.261747i
$741$		−	1.80959e8i		−	0.444760i
$742$		−	5.13705e8i		−	1.25748i
$743$	−1.48648e8			−0.362405			−0.181202	−	0.983446i	$-0.557999\pi$
$743$	−1.48648e8			−0.362405			−0.181202	+	0.983446i	$0.557999\pi$
$744$	3.84563e7			0.0933789
$745$	−5.79362e7	+	2.37778e8i	−0.140114	+	0.575046i
$746$			8.90333e8i			2.14455i
$747$	2.09960e8			0.503704
$748$			1.05822e9i			2.52854i
$749$	7.62299e8			1.81418
$750$	2.84499e8	+	2.48018e8i	0.674367	+	0.587895i
$751$		−	5.81141e8i		−	1.37202i	−0.727590	−	0.686012i	$-0.759360\pi$
$751$		−	5.81141e8i		−	1.37202i	0.727590	−	0.686012i	$-0.240640\pi$
$752$			2.85001e8i			0.670182i
$753$	1.24950e8			0.292651
$754$	1.21747e8			0.284016
$755$	−2.92336e8	−	7.12296e7i	−0.679268	−	0.165508i
$756$		−	6.07150e8i		−	1.40517i
$757$	−5.50730e8			−1.26955			−0.634777	−	0.772696i	$-0.718908\pi$
$757$	−5.50730e8			−1.26955			−0.634777	+	0.772696i	$0.718908\pi$
$758$	−1.79516e8			−0.412188
$759$	1.17690e8	−	4.89715e8i	0.269161	−	1.12000i
$760$	−1.80628e7	−	4.40113e6i	−0.0411476	−	0.0100259i
$761$	−5.38299e7			−0.122143			−0.0610717	−	0.998133i	$-0.519452\pi$
$761$	−5.38299e7			−0.122143			−0.0610717	+	0.998133i	$0.519452\pi$
$762$		−	7.32705e8i		−	1.65602i
$763$		−	3.28143e8i		−	0.738736i
$764$			8.69210e7i			0.194915i
$765$	−3.84465e8	−	9.36775e7i	−0.858761	−	0.209243i
$766$		−	8.70415e8i		−	1.93660i
$767$		−	2.70993e8i		−	0.600582i
$768$			3.24483e8i			0.716322i
$769$		−	1.67530e8i		−	0.368394i	−0.982889	−	0.184197i	$-0.941031\pi$
$769$		−	1.67530e8i		−	0.368394i	0.982889	−	0.184197i	$-0.0589685\pi$
$770$	−1.62657e9	−	3.96324e8i	−3.56286	−	0.868116i
$771$	−6.40899e7			−0.139838
$772$			2.74916e8i			0.597514i
$773$	1.38429e8			0.299700			0.149850	−	0.988709i	$-0.452121\pi$
$773$	1.38429e8			0.299700			0.149850	+	0.988709i	$0.452121\pi$
$774$			1.24088e8i			0.267612i
$775$	−6.81947e8	−	3.53297e8i	−1.46503	−	0.758988i
$776$			1.58874e7i			0.0339992i
$777$		−	5.23453e8i		−	1.11587i
$778$	−5.42884e8			−1.15284
$779$		−	2.34633e8i		−	0.496338i
$780$	3.99297e8	+	9.72915e7i	0.841420	+	0.205018i
$781$			7.05192e8i			1.48032i
$782$	9.74808e8	+	2.34268e8i	2.03844	+	0.489884i
$783$			6.94881e7i			0.144752i
$784$	−5.93463e8			−1.23153
$785$	8.67458e8	+	2.11362e8i	1.79324	+	0.436936i
$786$	8.30462e7			0.171022
$787$	7.10783e7			0.145819			0.0729093	−	0.997339i	$-0.476772\pi$
$787$	7.10783e7			0.145819			0.0729093	+	0.997339i	$0.476772\pi$
$788$			2.87496e8i			0.587562i
$789$			6.48357e7i			0.132003i
$790$	7.34298e7	+	1.78917e7i	0.148933	+	0.0362886i
$791$	4.14031e8			0.836572
$792$	4.59802e7			0.0925541
$793$	−7.25857e8			−1.45556
$794$	1.26780e9			2.53273
$795$	−4.69836e7	+	1.92827e8i	−0.0935073	+	0.383766i
$796$			6.65883e8i			1.32026i
$797$	−6.74277e7			−0.133187			−0.0665937	−	0.997780i	$-0.521213\pi$
$797$	−6.74277e7			−0.133187			−0.0665937	+	0.997780i	$0.521213\pi$
$798$			3.21633e8i			0.632924i
$799$		−	4.86169e8i		−	0.953119i
$800$	3.26457e8	−	6.30139e8i	0.637611	−	1.23074i
$801$		−	6.49930e7i		−	0.126465i
$802$	7.28208e8			1.41167
$803$	1.09718e9			2.11899
$804$		−	2.20885e8i		−	0.425009i
$805$	−3.50744e8	+	6.82272e8i	−0.672361	+	1.30789i
$806$	−1.72908e9			−3.30225
$807$			1.23082e8i			0.234192i
$808$			2.16542e7i			0.0410495i
$809$	2.55099e8			0.481796			0.240898	−	0.970550i	$-0.422558\pi$
$809$	2.55099e8			0.481796			0.240898	+	0.970550i	$0.422558\pi$
$810$	−1.20829e7	+	4.95898e7i	−0.0227361	+	0.0933119i
$811$	−2.36548e8			−0.443463			−0.221731	−	0.975108i	$-0.571171\pi$
$811$	−2.36548e8			−0.443463			−0.221731	+	0.975108i	$0.571171\pi$
$812$	−1.04661e8			−0.195487
$813$			3.00352e8i			0.558932i
$814$	−1.58749e9			−2.94333
$815$	5.41764e7	−	2.22347e8i	0.100078	−	0.410732i
$816$		−	5.57369e8i		−	1.02582i
$817$		−	8.59814e7i		−	0.157666i
$818$		−	1.35036e9i		−	2.46711i
$819$		−	6.81687e8i		−	1.24089i
$820$	5.17734e8	+	1.26149e8i	0.938999	+	0.228793i
$821$	−5.71869e8			−1.03340			−0.516698	−	0.856167i	$-0.672839\pi$
$821$	−5.71869e8			−1.03340			−0.516698	+	0.856167i	$0.672839\pi$
$822$	−5.47753e8			−0.986210
$823$			6.67427e7i			0.119730i	0.998206	+	0.0598652i	$0.0190671\pi$
$823$			6.67427e7i			0.119730i	−0.998206	+	0.0598652i	$0.980933\pi$
$824$			2.81974e6i			0.00503996i
$825$	5.74308e8	+	2.97532e8i	1.02278	+	0.529874i
$826$			4.81658e8i			0.854670i
$827$	4.58111e8			0.809942			0.404971	−	0.914330i	$-0.367282\pi$
$827$	4.58111e8			0.809942			0.404971	+	0.914330i	$0.367282\pi$
$828$	−7.29042e7	+	3.03360e8i	−0.128429	+	0.534401i
$829$	6.47383e8			1.13631			0.568156	−	0.822921i	$-0.307657\pi$
$829$	6.47383e8			1.13631			0.568156	+	0.822921i	$0.307657\pi$
$830$	1.61719e8	−	6.63715e8i	0.282830	−	1.16077i
$831$	−4.64384e8			−0.809235
$832$		−	7.20372e8i		−	1.25080i
$833$	1.01236e9			1.75146
$834$	3.38686e8			0.583847
$835$	1.49138e7	−	6.12083e7i	0.0256171	−	0.105136i
$836$	4.71783e8			0.807464
$837$		−	9.86890e8i		−	1.68303i
$838$	−6.64738e8			−1.12958
$839$			2.85574e8i			0.483541i	0.970333	+	0.241771i	$0.0777281\pi$
$839$			2.85574e8i			0.483541i	−0.970333	+	0.241771i	$0.922272\pi$
$840$	4.79271e7	+	1.16778e7i	0.0808619	+	0.0197025i
$841$	−5.82845e8			−0.979862
$842$	−6.51372e8			−1.09117
$843$	5.01268e7			0.0836734
$844$	5.83722e8			0.970909
$845$	6.26208e8	+	1.52580e8i	1.03788	+	0.252887i
$846$	3.12809e8			0.516616
$847$	−1.97542e9			−3.25094
$848$	3.96884e8			0.650843
$849$		−	5.14982e8i		−	0.841529i
$850$	−5.92256e8	+	1.14320e9i	−0.964390	+	1.86150i
$851$	−1.69980e8	+	7.07300e8i	−0.275810	+	1.14766i
$852$			3.07689e8i			0.497501i
$853$			9.43677e8i			1.52046i	0.649651	+	0.760232i	$0.274915\pi$
$853$			9.43677e8i			1.52046i	−0.649651	+	0.760232i	$0.725085\pi$
$854$	1.29012e9			2.07137
$855$	−4.17640e7	+	1.71405e8i	−0.0668196	+	0.274236i
$856$			6.81192e7i			0.108605i
$857$			9.72069e8i			1.54438i	0.635391	+	0.772191i	$0.280839\pi$
$857$			9.72069e8i			1.54438i	−0.635391	+	0.772191i	$0.719161\pi$
$858$	1.45616e9			2.30541
$859$	7.76782e6			0.0122552			0.00612759	−	0.999981i	$-0.498050\pi$
$859$	7.76782e6			0.0122552			0.00612759	+	0.999981i	$0.498050\pi$
$860$	1.89723e8	+	4.62274e7i	0.298281	+	0.0726782i
$861$			6.22567e8i			0.975386i
$862$	1.02370e9			1.59828
$863$		−	3.23356e8i		−	0.503094i	−0.967845	−	0.251547i	$-0.919061\pi$
$863$		−	3.23356e8i		−	0.503094i	0.967845	−	0.251547i	$-0.0809393\pi$
$864$	9.11916e8			1.41388
$865$	2.76842e8	−	1.13619e9i	0.427743	−	1.75551i
$866$		−	1.01169e9i		−	1.55774i
$867$			5.31829e8i			0.816045i
$868$	1.48643e9			2.27292
$869$	1.29519e8			0.197367
$870$	8.12253e7	+	1.97911e7i	0.123348	+	0.0300547i
$871$		−	6.70686e8i		−	1.01500i
$872$	2.93229e7			0.0442240
$873$	1.50762e8			0.226594
$874$	1.04443e8	−	4.34596e8i	0.156439	−	0.650956i
$875$	−7.42610e8	−	6.47388e8i	−1.10850	−	0.966363i
$876$	4.78720e8			0.712146
$877$			2.63709e8i			0.390955i	0.980708	+	0.195477i	$0.0626256\pi$
$877$			2.63709e8i			0.390955i	−0.980708	+	0.195477i	$0.937374\pi$
$878$			1.67645e9i			2.47689i
$879$			4.89153e8i			0.720241i
$880$	3.06196e8	−	1.25667e9i	0.449316	−	1.84405i
$881$			8.62045e8i			1.26067i	0.776322	+	0.630336i	$0.217083\pi$
$881$			8.62045e8i			1.26067i	−0.776322	+	0.630336i	$0.782917\pi$
$882$			6.51367e8i			0.949336i
$883$			9.37992e7i			0.136244i	0.997677	+	0.0681220i	$0.0217007\pi$
$883$			9.37992e7i			0.136244i	−0.997677	+	0.0681220i	$0.978299\pi$
$884$			1.40195e9i			2.02944i
$885$	4.40526e7	−	1.80798e8i	0.0635538	−	0.260833i
$886$	9.46644e8			1.36109
$887$		−	2.67367e8i		−	0.383121i	−0.981481	−	0.191561i	$-0.938645\pi$
$887$		−	2.67367e8i		−	0.383121i	0.981481	−	0.191561i	$-0.0613549\pi$
$888$	4.67759e7			0.0668010
$889$			1.91254e9i			2.72210i
$890$	−2.05452e8	−	5.00598e7i	−0.291434	−	0.0710100i
$891$			8.74689e7i			0.123657i
$892$		−	8.72667e8i		−	1.22957i
$893$	−2.16748e8			−0.304369
$894$			3.78347e8i			0.529514i
$895$	−7.50792e8	−	1.82936e8i	−1.04725	−	0.255170i
$896$		−	1.85881e8i		−	0.258412i
$897$	1.55918e8	−	6.48786e8i	0.216032	−	0.898927i
$898$			1.05142e9i			1.45194i
$899$	−1.70121e8			−0.234142
$900$	−3.55762e8	−	1.84310e8i	−0.488014	−	0.252826i
$901$	−6.77025e8			−0.925615
$902$	1.88808e9			2.57277
$903$			2.28139e8i			0.309840i
$904$			3.69979e7i			0.0500809i
$905$	1.73228e8	−	7.10951e8i	0.233707	−	0.959166i
$906$	−4.65158e8			−0.625484
$907$	−1.80787e8			−0.242295			−0.121148	−	0.992635i	$-0.538657\pi$
$907$	−1.80787e8			−0.242295			−0.121148	+	0.992635i	$0.538657\pi$
$908$	8.01309e8			1.07039
$909$	2.05485e8			0.273582
$910$	−2.15491e9	−	5.25059e8i	−2.85960	−	0.696761i
$911$			8.88233e8i			1.17482i	0.809289	+	0.587410i	$0.199853\pi$
$911$			8.88233e8i			1.17482i	−0.809289	+	0.587410i	$0.800147\pi$
$912$	−2.48491e8			−0.327586
$913$		−	1.17069e9i		−	1.53826i
$914$			9.03920e8i			1.18384i
$915$	−4.84268e8	−	1.17995e8i	−0.632153	−	0.154028i
$916$			7.62241e7i			0.0991758i
$917$	−2.16771e8			−0.281121
$918$	−1.65439e9			−2.13851
$919$		−	4.88114e8i		−	0.628890i	−0.949276	−	0.314445i	$-0.898182\pi$
$919$		−	4.88114e8i		−	0.628890i	0.949276	−	0.314445i	$-0.101818\pi$
$920$	−6.09680e7	−	3.13425e7i	−0.0782958	−	0.0402505i
$921$	5.42608e8			0.694556
$922$			1.00247e9i			1.27903i
$923$			9.34254e8i			1.18812i
$924$	−1.25181e9			−1.58680
$925$	−8.29479e8	−	4.29729e8i	−1.04805	−	0.542962i
$926$	5.12553e7			0.0645514
$927$	2.67575e7			0.0335898
$928$		−	1.57197e8i		−	0.196698i
$929$	6.24317e8			0.778679			0.389339	−	0.921094i	$-0.372703\pi$
$929$	6.24317e8			0.778679			0.389339	+	0.921094i	$0.372703\pi$
$930$	−1.15359e9	−	2.81079e8i	−1.43417	−	0.349446i
$931$		−	4.51337e8i		−	0.559310i
$932$		−	9.43933e8i		−	1.16599i
$933$			4.85043e8i			0.597221i
$934$		−	5.22222e8i		−	0.640936i
$935$	−5.22325e8	+	2.14369e9i	−0.639008	+	2.62257i
$936$	6.09157e7			0.0742851
$937$	−1.19467e9			−1.45221			−0.726106	−	0.687583i	$-0.758672\pi$
$937$	−1.19467e9			−1.45221			−0.726106	+	0.687583i	$0.758672\pi$
$938$			1.19206e9i			1.44441i
$939$			4.53130e8i			0.547300i
$940$	1.16533e8	−	4.78268e8i	0.140303	−	0.575821i
$941$			2.68684e8i			0.322457i	0.986917	+	0.161229i	$0.0515457\pi$
$941$			2.68684e8i			0.322457i	−0.986917	+	0.161229i	$0.948454\pi$
$942$	1.38028e9			1.65126
$943$	2.02165e8	−	8.41224e8i	0.241085	−	1.00317i
$944$	−3.72125e8			−0.442357
$945$	2.99683e8	−	1.22994e9i	0.355113	−	1.45743i
$946$	6.91886e8			0.817262
$947$			5.41383e8i			0.637462i	0.947845	+	0.318731i	$0.103257\pi$
$947$			5.41383e8i			0.637462i	−0.947845	+	0.318731i	$0.896743\pi$
$948$	5.65118e7			0.0663306
$949$	1.45356e9			1.70073
$950$	5.09668e8	+	2.64044e8i	0.594452	+	0.307968i
$951$	−2.55755e8			−0.297360
$952$			1.68274e8i			0.195033i
$953$	−1.25062e9			−1.44493			−0.722465	−	0.691407i	$-0.756991\pi$
$953$	−1.25062e9			−1.44493			−0.722465	+	0.691407i	$0.756991\pi$
$954$		−	4.35608e8i		−	0.501708i
$955$	−4.29033e7	+	1.76081e8i	−0.0492584	+	0.202163i
$956$	6.26103e8			0.716592
$957$	1.43269e8			0.163462
$958$	−2.19614e9			−2.49783
$959$	1.42977e9			1.62110
$960$	1.17104e8	−	4.80609e8i	0.132360	−	0.543223i
$961$	1.52861e9			1.72237
$962$	−2.10315e9			−2.36235
$963$	6.46409e8			0.723817
$964$			5.48638e7i			0.0612428i
$965$	−1.35696e8	+	5.56913e8i	−0.151002	+	0.619734i
$966$	−2.77125e8	+	1.15314e9i	−0.307429	+	1.27924i
$967$		−	8.12902e8i		−	0.898999i	−0.893281	−	0.449499i	$-0.851602\pi$
$967$		−	8.12902e8i		−	0.898999i	0.893281	−	0.449499i	$-0.148398\pi$
$968$		−	1.76524e8i		−	0.194615i
$969$	4.23888e8			0.465886
$970$	1.16122e8	−	4.76580e8i	0.127233	−	0.522180i
$971$		−	1.48548e9i		−	1.62259i	−0.584637	−	0.811295i	$-0.698763\pi$
$971$		−	1.48548e9i		−	1.62259i	0.584637	−	0.811295i	$-0.301237\pi$
$972$		−	8.39316e8i		−	0.913959i
$973$	−8.84052e8			−0.959709
$974$	−4.96733e8			−0.537583
$975$	7.60857e8	+	3.94178e8i	0.820898	+	0.425283i
$976$			9.96738e8i			1.07209i
$977$	5.48566e8			0.588227			0.294114	−	0.955770i	$-0.404976\pi$
$977$	5.48566e8			0.588227			0.294114	+	0.955770i	$0.404976\pi$
$978$		−	3.53794e8i		−	0.378211i
$979$	−3.62387e8			−0.386210
$980$	9.95905e8	+	2.42659e8i	1.05813	+	0.257821i
$981$		−	2.78256e8i		−	0.294739i
$982$			1.64244e8i			0.173443i
$983$	3.20403e7			0.0337315			0.0168658	−	0.999858i	$-0.494631\pi$
$983$	3.20403e7			0.0337315			0.0168658	+	0.999858i	$0.494631\pi$
$984$	−5.56327e7			−0.0583908
$985$	−1.41905e8	+	5.82397e8i	−0.148487	+	0.609411i
$986$			2.85186e8i			0.297507i
$987$	5.75109e8			0.598134
$988$	6.25029e8			0.648081
$989$	7.40834e7	−	3.08266e8i	0.0765829	−	0.318667i
$990$	−1.37928e9	−	3.36072e8i	−1.42150	−	0.346359i
$991$	−7.00039e8			−0.719285			−0.359643	−	0.933090i	$-0.617101\pi$
$991$	−7.00039e8			−0.719285			−0.359643	+	0.933090i	$0.617101\pi$
$992$			2.23256e9i			2.28701i
$993$			8.32211e8i			0.849935i
$994$		−	1.66052e9i		−	1.69078i
$995$	−3.28673e8	+	1.34892e9i	−0.333652	+	1.36935i
$996$		−	5.10796e8i		−	0.516975i
$997$			1.06039e9i			1.06999i	0.844855	+	0.534995i	$0.179687\pi$
$997$			1.06039e9i			1.06999i	−0.844855	+	0.534995i	$0.820313\pi$
$998$		−	1.08651e8i		−	0.109306i
$999$		−	1.20039e9i		−	1.20400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.7.c.c.114.6	yes	68
5.4	even	2	inner	115.7.c.c.114.63	yes	68
23.22	odd	2	inner	115.7.c.c.114.64	yes	68
115.114	odd	2	inner	115.7.c.c.114.5	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.7.c.c.114.5	✓	68	115.114	odd	2	inner
115.7.c.c.114.6	yes	68	1.1	even	1	trivial
115.7.c.c.114.63	yes	68	5.4	even	2	inner
115.7.c.c.114.64	yes	68	23.22	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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	115.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+11.1333i q^{2} +17.3572i q^{3} -59.9514 q^{4} +(-121.447 - 29.5914i) q^{5} -193.244 q^{6} +504.412 q^{7} +45.0744i q^{8} +427.728 q^{9} +O(q^{10})\)	\(q+11.1333i q^{2} +17.3572i q^{3} -59.9514 q^{4} +(-121.447 - 29.5914i) q^{5} -193.244 q^{6} +504.412 q^{7} +45.0744i q^{8} +427.728 q^{9} +(329.451 - 1352.11i) q^{10} -2384.92i q^{11} -1040.59i q^{12} -3159.59i q^{13} +5615.80i q^{14} +(513.623 - 2107.98i) q^{15} -4338.72 q^{16} +7401.20 q^{17} +4762.05i q^{18} -3299.66i q^{19} +(7280.91 + 1774.04i) q^{20} +8755.18i q^{21} +26552.1 q^{22} +(2843.06 - 11830.2i) q^{23} -782.365 q^{24} +(13873.7 + 7187.56i) q^{25} +35176.9 q^{26} +20077.5i q^{27} -30240.2 q^{28} +3460.99 q^{29} +(23468.8 + 5718.34i) q^{30} -49153.9 q^{31} -45419.7i q^{32} +41395.5 q^{33} +82400.2i q^{34} +(-61259.3 - 14926.3i) q^{35} -25642.9 q^{36} -59787.8 q^{37} +36736.3 q^{38} +54841.7 q^{39} +(1333.81 - 5474.15i) q^{40} +71108.4 q^{41} -97474.5 q^{42} +26057.7 q^{43} +142979. i q^{44} +(-51946.3 - 12657.1i) q^{45} +(131709. + 31652.7i) q^{46} -65687.9i q^{47} -75307.9i q^{48} +136783. q^{49} +(-80021.6 + 154461. i) q^{50} +128464. i q^{51} +189422. i q^{52} -91475.0 q^{53} -223530. q^{54} +(-70573.0 + 289641. i) q^{55} +22736.1i q^{56} +57272.8 q^{57} +38532.4i q^{58} +85768.4 q^{59} +(-30792.4 + 126376. i) q^{60} -229731. i q^{61} -547248. i q^{62} +215751. q^{63} +227995. q^{64} +(-93496.7 + 383723. i) q^{65} +460870. i q^{66} +212270. q^{67} -443713. q^{68} +(205338. + 49347.5i) q^{69} +(166179. - 682021. i) q^{70} -295688. q^{71} +19279.6i q^{72} +460048. i q^{73} -665639. i q^{74} +(-124756. + 240808. i) q^{75} +197819. i q^{76} -1.20298e6i q^{77} +610571. i q^{78} +54307.6i q^{79} +(526924. + 128389. i) q^{80} -36675.8 q^{81} +791674. i q^{82} +490873. q^{83} -524885. i q^{84} +(-898853. - 219012. i) q^{85} +290109. i q^{86} +60073.0i q^{87} +107499. q^{88} -151949. i q^{89} +(140915. - 578336. i) q^{90} -1.59374e6i q^{91} +(-170445. + 709235. i) q^{92} -853174. i q^{93} +731326. q^{94} +(-97641.5 + 400734. i) q^{95} +788358. q^{96} +352471. q^{97} +1.52285e6i q^{98} -1.02010e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9}+O(q^{10}) \) 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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