LMFDB - Embedded newform 115.7.d.a.91.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,7,Mod(91,115)]

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([0, 1]))

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

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

chi := DirichletCharacter("115.91");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	115.d (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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.10
Character	$\chi$	$=$	115.91
Dual form			115.7.d.a.91.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.9049 q^{2} -28.4011 q^{3} +77.7265 q^{4} -55.9017i q^{5} +338.112 q^{6} -365.722i q^{7} -163.412 q^{8} +77.6213 q^{9} +O(q^{10})$	\(q-11.9049 q^{2} -28.4011 q^{3} +77.7265 q^{4} -55.9017i q^{5} +338.112 q^{6} -365.722i q^{7} -163.412 q^{8} +77.6213 q^{9} +665.504i q^{10} -1713.46i q^{11} -2207.52 q^{12} +3283.86 q^{13} +4353.89i q^{14} +1587.67i q^{15} -3029.09 q^{16} +3386.99i q^{17} -924.073 q^{18} +8531.92i q^{19} -4345.04i q^{20} +10386.9i q^{21} +20398.5i q^{22} +(12157.8 + 472.642i) q^{23} +4641.08 q^{24} -3125.00 q^{25} -39094.0 q^{26} +18499.9 q^{27} -28426.3i q^{28} -10257.7 q^{29} -18901.0i q^{30} +26928.8 q^{31} +46519.4 q^{32} +48664.0i q^{33} -40321.7i q^{34} -20444.5 q^{35} +6033.23 q^{36} -30222.2i q^{37} -101572. i q^{38} -93265.1 q^{39} +9135.01i q^{40} -22485.4 q^{41} -123655. i q^{42} +6304.53i q^{43} -133181. i q^{44} -4339.16i q^{45} +(-144737. - 5626.75i) q^{46} +130395. q^{47} +86029.4 q^{48} -16103.8 q^{49} +37202.8 q^{50} -96194.1i q^{51} +255243. q^{52} -266863. i q^{53} -220239. q^{54} -95785.1 q^{55} +59763.5i q^{56} -242316. i q^{57} +122116. q^{58} +213921. q^{59} +123404. i q^{60} +29476.2i q^{61} -320584. q^{62} -28387.8i q^{63} -359946. q^{64} -183573. i q^{65} -579340. i q^{66} +326092. i q^{67} +263259. i q^{68} +(-345295. - 13423.5i) q^{69} +243390. q^{70} +20211.9 q^{71} -12684.3 q^{72} +533200. q^{73} +359792. i q^{74} +88753.4 q^{75} +663156. i q^{76} -626649. q^{77} +1.11031e6 q^{78} +3360.28i q^{79} +169331. i q^{80} -582002. q^{81} +267686. q^{82} +804627. i q^{83} +807338. i q^{84} +189338. q^{85} -75054.8i q^{86} +291328. q^{87} +279999. i q^{88} -1.39482e6i q^{89} +51657.2i q^{90} -1.20098e6i q^{91} +(944984. + 36736.8i) q^{92} -764807. q^{93} -1.55234e6 q^{94} +476949. q^{95} -1.32120e6 q^{96} +719553. i q^{97} +191714. q^{98} -133001. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9}+O(q^{10}) $ 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9	$ 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9} + 4290 q^{12} - 1440 q^{13} + 65400 q^{16} + 4610 q^{18} + 26600 q^{23} + 14940 q^{24} - 150000 q^{25} + 47594 q^{26} + 16080 q^{27} + 131800 q^{29} - 1392 q^{31} - 225040 q^{32} + 5000 q^{35} + 658786 q^{36} - 236320 q^{39} - 351496 q^{41} + 382692 q^{46} + 395680 q^{47} + 1042550 q^{48} - 637848 q^{49} + 62500 q^{50} + 523890 q^{52} - 241250 q^{54} - 402000 q^{55} - 479130 q^{58} - 466312 q^{59} - 1124330 q^{62} + 837582 q^{64} + 1021060 q^{69} - 396000 q^{70} - 114336 q^{71} - 1960750 q^{72} - 498720 q^{73} + 3610400 q^{77} - 1104610 q^{78} + 972888 q^{81} + 124950 q^{82} - 246000 q^{85} - 2090960 q^{87} + 4913480 q^{92} + 3234320 q^{93} - 5550378 q^{94} - 1664000 q^{95} - 776990 q^{96} + 9993220 q^{98}+O(q^{100}) $ 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9 + 4290 * q^12 - 1440 * q^13 + 65400 * q^16 + 4610 * q^18 + 26600 * q^23 + 14940 * q^24 - 150000 * q^25 + 47594 * q^26 + 16080 * q^27 + 131800 * q^29 - 1392 * q^31 - 225040 * q^32 + 5000 * q^35 + 658786 * q^36 - 236320 * q^39 - 351496 * q^41 + 382692 * q^46 + 395680 * q^47 + 1042550 * q^48 - 637848 * q^49 + 62500 * q^50 + 523890 * q^52 - 241250 * q^54 - 402000 * q^55 - 479130 * q^58 - 466312 * q^59 - 1124330 * q^62 + 837582 * q^64 + 1021060 * q^69 - 396000 * q^70 - 114336 * q^71 - 1960750 * q^72 - 498720 * q^73 + 3610400 * q^77 - 1104610 * q^78 + 972888 * q^81 + 124950 * q^82 - 246000 * q^85 - 2090960 * q^87 + 4913480 * q^92 + 3234320 * q^93 - 5550378 * q^94 - 1664000 * q^95 - 776990 * q^96 + 9993220 * q^98

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 $

$2$	−11.9049			−1.48811			−0.744056	−	0.668117i	$-0.767100\pi$
$2$	−11.9049			−1.48811			−0.744056	+	0.668117i	$0.767100\pi$
$3$	−28.4011			−1.05189			−0.525946	−	0.850518i	$-0.676289\pi$
$3$	−28.4011			−1.05189			−0.525946	+	0.850518i	$0.676289\pi$
$4$	77.7265			1.21448
$5$		−	55.9017i		−	0.447214i
$5$		−	55.9017i		−	0.447214i
$6$	338.112			1.56533
$7$		−	365.722i		−	1.06625i	−0.846038	−	0.533123i	$-0.821018\pi$
$7$		−	365.722i		−	1.06625i	0.846038	−	0.533123i	$-0.178982\pi$
$8$	−163.412			−0.319164
$9$	77.6213			0.106476
$10$			665.504i			0.665504i
$11$		−	1713.46i		−	1.28734i	−0.765301	−	0.643672i	$-0.777410\pi$
$11$		−	1713.46i		−	1.28734i	0.765301	−	0.643672i	$-0.222590\pi$
$12$	−2207.52			−1.27750
$13$	3283.86			1.49470			0.747351	−	0.664430i	$-0.231326\pi$
$13$	3283.86			1.49470			0.747351	+	0.664430i	$0.231326\pi$
$14$			4353.89i			1.58669i
$15$			1587.67i			0.470420i
$16$	−3029.09			−0.739524
$17$			3386.99i			0.689393i	0.938714	+	0.344697i	$0.112018\pi$
$17$			3386.99i			0.689393i	−0.938714	+	0.344697i	$0.887982\pi$
$18$	−924.073			−0.158449
$19$			8531.92i			1.24390i	0.783056	+	0.621951i	$0.213660\pi$
$19$			8531.92i			1.24390i	−0.783056	+	0.621951i	$0.786340\pi$
$20$		−	4345.04i		−	0.543130i
$21$			10386.9i			1.12158i
$22$			20398.5i			1.91571i
$23$	12157.8	+	472.642i	0.999245	+	0.0388462i
$23$	12157.8	+	472.642i	0.999245	+	0.0388462i
$24$	4641.08			0.335726
$25$	−3125.00			−0.200000
$26$	−39094.0			−2.22428
$27$	18499.9			0.939890
$28$		−	28426.3i		−	1.29493i
$29$	−10257.7			−0.420585			−0.210293	−	0.977638i	$-0.567442\pi$
$29$	−10257.7			−0.420585			−0.210293	+	0.977638i	$0.567442\pi$
$30$		−	18901.0i		−	0.700038i
$31$	26928.8			0.903924			0.451962	−	0.892037i	$-0.350724\pi$
$31$	26928.8			0.903924			0.451962	+	0.892037i	$0.350724\pi$
$32$	46519.4			1.41966
$33$			48664.0i			1.35415i
$34$		−	40321.7i		−	1.02589i
$35$	−20444.5			−0.476840
$36$	6033.23			0.129313
$37$		−	30222.2i		−	0.596651i	−0.954464	−	0.298326i	$-0.903572\pi$
$37$		−	30222.2i		−	0.596651i	0.954464	−	0.298326i	$-0.0964281\pi$
$38$		−	101572.i		−	1.85106i
$39$	−93265.1			−1.57226
$40$			9135.01i			0.142735i
$41$	−22485.4			−0.326249			−0.163124	−	0.986606i	$-0.552157\pi$
$41$	−22485.4			−0.326249			−0.163124	+	0.986606i	$0.552157\pi$
$42$		−	123655.i		−	1.66903i
$43$			6304.53i			0.0792953i	0.999214	+	0.0396477i	$0.0126235\pi$
$43$			6304.53i			0.0792953i	−0.999214	+	0.0396477i	$0.987376\pi$
$44$		−	133181.i		−	1.56345i
$45$		−	4339.16i		−	0.0476177i
$46$	−144737.	−	5626.75i	−1.48699	−	0.0578075i
$47$	130395.			1.25594			0.627968	−	0.778239i	$-0.283887\pi$
$47$	130395.			1.25594			0.627968	+	0.778239i	$0.283887\pi$
$48$	86029.4			0.777899
$49$	−16103.8			−0.136880
$50$	37202.8			0.297622
$51$		−	96194.1i		−	0.725167i
$52$	255243.			1.81528
$53$		−	266863.i		−	1.79251i	−0.443543	−	0.896253i	$-0.646279\pi$
$53$		−	266863.i		−	1.79251i	0.443543	−	0.896253i	$-0.353721\pi$
$54$	−220239.			−1.39866
$55$	−95785.1			−0.575718
$56$			59763.5i			0.340308i
$57$		−	242316.i		−	1.30845i
$58$	122116.			0.625878
$59$	213921.			1.04159			0.520795	−	0.853682i	$-0.325636\pi$
$59$	213921.			1.04159			0.520795	+	0.853682i	$0.325636\pi$
$60$			123404.i			0.571314i
$61$			29476.2i			0.129862i	0.997890	+	0.0649310i	$0.0206827\pi$
$61$			29476.2i			0.129862i	−0.997890	+	0.0649310i	$0.979317\pi$
$62$	−320584.			−1.34514
$63$		−	28387.8i		−	0.113530i
$64$	−359946.			−1.37309
$65$		−	183573.i		−	0.668451i
$66$		−	579340.i		−	2.01512i
$67$			326092.i			1.08421i	0.840309	+	0.542107i	$0.182373\pi$
$67$			326092.i			1.08421i	−0.840309	+	0.542107i	$0.817627\pi$
$68$			263259.i			0.837251i
$69$	−345295.	−	13423.5i	−1.05110	−	0.0408620i
$70$	243390.			0.709591
$71$	20211.9			0.0564718			0.0282359	−	0.999601i	$-0.491011\pi$
$71$	20211.9			0.0564718			0.0282359	+	0.999601i	$0.491011\pi$
$72$	−12684.3			−0.0339834
$73$	533200.			1.37063			0.685317	−	0.728245i	$-0.259664\pi$
$73$	533200.			1.37063			0.685317	+	0.728245i	$0.259664\pi$
$74$			359792.i			0.887884i
$75$	88753.4			0.210378
$76$			663156.i			1.51069i
$77$	−626649.			−1.37263
$78$	1.11031e6			2.33970
$79$			3360.28i			0.00681545i	0.999994	+	0.00340773i	$0.00108472\pi$
$79$			3360.28i			0.00681545i	−0.999994	+	0.00340773i	$0.998915\pi$
$80$			169331.i			0.330725i
$81$	−582002.			−1.09514
$82$	267686.			0.485495
$83$			804627.i			1.40721i	0.710589	+	0.703607i	$0.248428\pi$
$83$			804627.i			1.40721i	−0.710589	+	0.703607i	$0.751572\pi$
$84$			807338.i			1.36213i
$85$	189338.			0.308306
$86$		−	75054.8i		−	0.118000i
$87$	291328.			0.442410
$88$			279999.i			0.410874i
$89$		−	1.39482e6i		−	1.97856i	−0.146036	−	0.989279i	$-0.546652\pi$
$89$		−	1.39482e6i		−	1.97856i	0.146036	−	0.989279i	$-0.453348\pi$
$90$			51657.2i			0.0708604i
$91$		−	1.20098e6i		−	1.59372i
$92$	944984.	+	36736.8i	1.21356	+	0.0471778i
$93$	−764807.			−0.950830
$94$	−1.55234e6			−1.86897
$95$	476949.			0.556290
$96$	−1.32120e6			−1.49333
$97$			719553.i			0.788402i	0.919024	+	0.394201i	$0.128979\pi$
$97$			719553.i			0.788402i	−0.919024	+	0.394201i	$0.871021\pi$
$98$	191714.			0.203693
$99$		−	133001.i		−	0.137072i
$100$	−242895.			−0.242895
$101$	385831.			0.374484			0.187242	−	0.982314i	$-0.440045\pi$
$101$	385831.			0.374484			0.187242	+	0.982314i	$0.440045\pi$
$102$			1.14518e6i			1.07913i
$103$		−	250983.i		−	0.229685i	−0.993384	−	0.114843i	$-0.963364\pi$
$103$		−	250983.i		−	0.229685i	0.993384	−	0.114843i	$-0.0366364\pi$
$104$	−536622.			−0.477055
$105$	580646.			0.501584
$106$			3.17697e6i			2.66745i
$107$		−	2.00292e6i		−	1.63498i	−0.575943	−	0.817490i	$-0.695365\pi$
$107$		−	2.00292e6i		−	1.63498i	0.575943	−	0.817490i	$-0.304635\pi$
$108$	1.43793e6			1.14147
$109$			1.02367e6i			0.790459i	0.918582	+	0.395229i	$0.129335\pi$
$109$			1.02367e6i			0.790459i	−0.918582	+	0.395229i	$0.870665\pi$
$110$	1.14031e6			0.856733
$111$			858342.i			0.627612i
$112$			1.10781e6i			0.788514i
$113$			264499.i			0.183311i	0.995791	+	0.0916555i	$0.0292159\pi$
$113$			264499.i			0.183311i	−0.995791	+	0.0916555i	$0.970784\pi$
$114$			2.88474e6i			1.94712i
$115$	26421.5	−	679643.i	0.0173725	−	0.446876i
$116$	−797291.			−0.510791
$117$	254897.			0.159150
$118$	−2.54670e6			−1.55000
$119$	1.23870e6			0.735063
$120$		−	259444.i		−	0.150141i
$121$	−1.16437e6			−0.657256
$122$		−	350911.i		−	0.193249i
$123$	638609.			0.343178
$124$	2.09308e6			1.09779
$125$			174693.i			0.0894427i
$126$			337954.i			0.168945i
$127$	−1.20252e6			−0.587060			−0.293530	−	0.955950i	$-0.594830\pi$
$127$	−1.20252e6			−0.587060			−0.293530	+	0.955950i	$0.594830\pi$
$128$	1.30788e6			0.623647
$129$		−	179056.i		−	0.0834101i
$130$			2.18542e6i			0.994729i
$131$	−4.14382e6			−1.84326			−0.921630	−	0.388069i	$-0.873142\pi$
$131$	−4.14382e6			−1.84326			−0.921630	+	0.388069i	$0.873142\pi$
$132$			3.78248e6i			1.64458i
$133$	3.12031e6			1.32631
$134$		−	3.88209e6i		−	1.61343i
$135$		−	1.03417e6i		−	0.420332i
$136$		−	553475.i		−	0.220030i
$137$		−	3.73962e6i		−	1.45434i	−0.686458	−	0.727169i	$-0.740835\pi$
$137$		−	3.73962e6i		−	1.45434i	0.686458	−	0.727169i	$-0.259165\pi$
$138$	4.11070e6	+	159806.i	1.56415	+	0.0608072i
$139$	5.24483e6			1.95293			0.976465	−	0.215675i	$-0.0691951\pi$
$139$	5.24483e6			1.95293			0.976465	+	0.215675i	$0.0691951\pi$
$140$	−1.58908e6			−0.579110
$141$	−3.70336e6			−1.32111
$142$	−240620.			−0.0840363
$143$		−	5.62675e6i		−	1.92420i
$144$	−235122.			−0.0787418
$145$			573420.i			0.188091i
$146$	−6.34769e6			−2.03966
$147$	457366.			0.143983
$148$		−	2.34906e6i		−	0.724619i
$149$		−	5.75857e6i		−	1.74083i	−0.492320	−	0.870414i	$-0.663851\pi$
$149$		−	5.75857e6i		−	1.74083i	0.492320	−	0.870414i	$-0.336149\pi$
$150$	−1.05660e6			−0.313066
$151$	−3.22997e6			−0.938141			−0.469071	−	0.883161i	$-0.655411\pi$
$151$	−3.22997e6			−0.938141			−0.469071	+	0.883161i	$0.655411\pi$
$152$		−	1.39422e6i		−	0.397009i
$153$			262902.i			0.0734041i
$154$	7.46019e6			2.04262
$155$		−	1.50537e6i		−	0.404247i
$156$	−7.24917e6			−1.90948
$157$		−	5.07158e6i		−	1.31052i	−0.755403	−	0.655261i	$-0.772559\pi$
$157$		−	5.07158e6i		−	1.31052i	0.755403	−	0.655261i	$-0.227441\pi$
$158$		−	40003.8i		−	0.0101422i
$159$			7.57919e6i			1.88552i
$160$		−	2.60051e6i		−	0.634891i
$161$	172856.	−	4.44639e6i	0.0414196	−	1.06544i
$162$	6.92867e6			1.62969
$163$	−2.14079e6			−0.494324			−0.247162	−	0.968974i	$-0.579498\pi$
$163$	−2.14079e6			−0.494324			−0.247162	+	0.968974i	$0.579498\pi$
$164$	−1.74771e6			−0.396221
$165$	2.72040e6			0.605593
$166$		−	9.57899e6i		−	2.09409i
$167$	−5.13830e6			−1.10324			−0.551620	−	0.834096i	$-0.685990\pi$
$167$	−5.13830e6			−1.10324			−0.551620	+	0.834096i	$0.685990\pi$
$168$		−	1.69735e6i		−	0.357967i
$169$	5.95692e6			1.23413
$170$	−2.25405e6			−0.458794
$171$			662259.i			0.132446i
$172$			490029.i			0.0963023i
$173$	7.48098e6			1.44484			0.722421	−	0.691454i	$-0.243029\pi$
$173$	7.48098e6			1.44484			0.722421	+	0.691454i	$0.243029\pi$
$174$	−3.46823e6			−0.658356
$175$			1.14288e6i			0.213249i
$176$			5.19021e6i			0.952022i
$177$	−6.07558e6			−1.09564
$178$			1.66052e7i			2.94432i
$179$	−2.12005e6			−0.369648			−0.184824	−	0.982772i	$-0.559171\pi$
$179$	−2.12005e6			−0.369648			−0.184824	+	0.982772i	$0.559171\pi$
$180$		−	337268.i		−	0.0578305i
$181$			1.01078e7i			1.70459i	0.523060	+	0.852296i	$0.324790\pi$
$181$			1.01078e7i			1.70459i	−0.523060	+	0.852296i	$0.675210\pi$
$182$			1.42975e7i			2.37163i
$183$		−	837157.i		−	0.136601i
$184$	−1.98673e6	−	77235.4i	−0.318923	−	0.0123983i
$185$	−1.68947e6			−0.266831
$186$	9.10495e6			1.41494
$187$	5.80345e6			0.887487
$188$	1.01352e7			1.52530
$189$		−	6.76581e6i		−	1.00215i
$190$	−5.67803e6			−0.827821
$191$		−	5.79049e6i		−	0.831027i	−0.909587	−	0.415514i	$-0.863602\pi$
$191$		−	5.79049e6i		−	0.831027i	0.909587	−	0.415514i	$-0.136398\pi$
$192$	1.02229e7			1.44434
$193$	−9.64756e6			−1.34198			−0.670989	−	0.741467i	$-0.734130\pi$
$193$	−9.64756e6			−1.34198			−0.670989	+	0.741467i	$0.734130\pi$
$194$		−	8.56620e6i		−	1.17323i
$195$			5.21368e6i			0.703138i
$196$	−1.25169e6			−0.166238
$197$	−379454.			−0.0496318			−0.0248159	−	0.999692i	$-0.507900\pi$
$197$	−379454.			−0.0496318			−0.0248159	+	0.999692i	$0.507900\pi$
$198$			1.58336e6i			0.203978i
$199$			8.81681e6i			1.11880i	0.828898	+	0.559400i	$0.188968\pi$
$199$			8.81681e6i			1.11880i	−0.828898	+	0.559400i	$0.811032\pi$
$200$	510663.			0.0638329
$201$		−	9.26136e6i		−	1.14048i
$202$	−4.59327e6			−0.557273
$203$			3.75145e6i			0.448447i
$204$		−	7.47683e6i		−	0.880698i
$205$			1.25697e6i			0.145903i
$206$			2.98793e6i			0.341797i
$207$	943705.	+	36687.0i	0.106396	+	0.00413620i
$208$	−9.94710e6			−1.10537
$209$	1.46191e7			1.60133
$210$	−6.91253e6			−0.746413
$211$	−8.32883e6			−0.886619			−0.443309	−	0.896369i	$-0.646196\pi$
$211$	−8.32883e6			−0.886619			−0.443309	+	0.896369i	$0.646196\pi$
$212$		−	2.07423e7i		−	2.17696i
$213$	−574039.			−0.0594022
$214$			2.38445e7i			2.43303i
$215$	352434.			0.0354619
$216$	−3.02310e6			−0.299979
$217$		−	9.84846e6i		−	0.963805i
$218$		−	1.21866e7i		−	1.17629i
$219$	−1.51434e7			−1.44176
$220$	−7.44504e6			−0.699196
$221$			1.11224e7i			1.03044i
$222$		−	1.02185e7i		−	0.933957i
$223$	8.48355e6			0.765003			0.382502	−	0.923955i	$-0.375063\pi$
$223$	8.48355e6			0.765003			0.382502	+	0.923955i	$0.375063\pi$
$224$		−	1.70132e7i		−	1.51371i
$225$	−242566.			−0.0212953
$226$		−	3.14883e6i		−	0.272787i
$227$			6.18130e6i			0.528448i	0.964461	+	0.264224i	$0.0851158\pi$
$227$			6.18130e6i			0.528448i	−0.964461	+	0.264224i	$0.914884\pi$
$228$		−	1.88344e7i		−	1.58908i
$229$			1.02856e7i			0.856490i	0.903663	+	0.428245i	$0.140868\pi$
$229$			1.02856e7i			0.856490i	−0.903663	+	0.428245i	$0.859132\pi$
$230$	−314545.	+	8.09107e6i	−0.0258523	+	0.665001i
$231$	1.77975e7			1.44385
$232$	1.67622e6			0.134236
$233$	6.26129e6			0.494990			0.247495	−	0.968889i	$-0.420393\pi$
$233$	6.26129e6			0.494990			0.247495	+	0.968889i	$0.420393\pi$
$234$	−3.03452e6			−0.236833
$235$		−	7.28931e6i		−	0.561672i
$236$	1.66273e7			1.26499
$237$		−	95435.7i		−	0.00716912i
$238$	−1.47466e7			−1.09386
$239$	−3.38050e6			−0.247621			−0.123810	−	0.992306i	$-0.539511\pi$
$239$	−3.38050e6			−0.247621			−0.123810	+	0.992306i	$0.539511\pi$
$240$		−	4.80919e6i		−	0.347887i
$241$		−	6.27565e6i		−	0.448340i	−0.974550	−	0.224170i	$-0.928033\pi$
$241$		−	6.27565e6i		−	0.448340i	0.974550	−	0.224170i	$-0.0719671\pi$
$242$	1.38617e7			0.978070
$243$	3.04308e6			0.212078
$244$			2.29108e6i			0.157714i
$245$			900232.i			0.0612148i
$246$	−7.60258e6			−0.510688
$247$			2.80176e7i			1.85926i
$248$	−4.40049e6			−0.288500
$249$		−	2.28523e7i		−	1.48024i
$250$		−	2.07970e6i		−	0.133101i
$251$			1.24089e7i			0.784717i	0.919812	+	0.392359i	$0.128341\pi$
$251$			1.24089e7i			0.784717i	−0.919812	+	0.392359i	$0.871659\pi$
$252$		−	2.20649e6i		−	0.137879i
$253$	809851.	−	2.08319e7i	0.0500084	−	1.28637i
$254$	1.43159e7			0.873611
$255$	−5.37742e6			−0.324305
$256$	7.46636e6			0.445030
$257$	7.23578e6			0.426271			0.213136	−	0.977023i	$-0.431632\pi$
$257$	7.23578e6			0.426271			0.213136	+	0.977023i	$0.431632\pi$
$258$			2.13164e6i			0.124124i
$259$	−1.10529e7			−0.636177
$260$		−	1.42685e7i		−	0.811817i
$261$	−796212.			−0.0447824
$262$	4.93317e7			2.74298
$263$			5.03653e6i			0.276863i	0.990372	+	0.138431i	$0.0442060\pi$
$263$			5.03653e6i			0.276863i	−0.990372	+	0.138431i	$0.955794\pi$
$264$		−	7.95228e6i		−	0.432195i
$265$	−1.49181e7			−0.801633
$266$	−3.71470e7			−1.97369
$267$			3.96145e7i			2.08123i
$268$			2.53460e7i			1.31675i
$269$	−5.51009e6			−0.283075			−0.141538	−	0.989933i	$-0.545205\pi$
$269$	−5.51009e6			−0.283075			−0.141538	+	0.989933i	$0.545205\pi$
$270$			1.23117e7i			0.625500i
$271$	3.47681e6			0.174692			0.0873461	−	0.996178i	$-0.472161\pi$
$271$	3.47681e6			0.174692			0.0873461	+	0.996178i	$0.472161\pi$
$272$		−	1.02595e7i		−	0.509823i
$273$			3.41091e7i			1.67642i
$274$			4.45198e7i			2.16422i
$275$			5.35455e6i			0.257469i
$276$	−2.68386e7	−	1.04336e6i	−1.27653	−	0.0496259i
$277$	−2.01930e7			−0.950083			−0.475042	−	0.879963i	$-0.657567\pi$
$277$	−2.01930e7			−0.950083			−0.475042	+	0.879963i	$0.657567\pi$
$278$	−6.24391e7			−2.90618
$279$	2.09025e6			0.0962465
$280$	3.34088e6			0.152190
$281$		−	2.73026e7i		−	1.23051i	−0.788328	−	0.615255i	$-0.789053\pi$
$281$		−	2.73026e7i		−	1.23051i	0.788328	−	0.615255i	$-0.210947\pi$
$282$	4.40881e7			1.96596
$283$		−	1.92399e7i		−	0.848873i	−0.905458	−	0.424437i	$-0.860472\pi$
$283$		−	1.92399e7i		−	0.848873i	0.905458	−	0.424437i	$-0.139528\pi$
$284$	1.57100e6			0.0685836
$285$	−1.35459e7			−0.585157
$286$			6.69858e7i			2.86342i
$287$			8.22341e6i			0.347861i
$288$	3.61089e6			0.151160
$289$	1.26659e7			0.524737
$290$		−	6.82651e6i		−	0.279901i
$291$		−	2.04361e7i		−	0.829313i
$292$	4.14437e7			1.66460
$293$			9.67283e6i			0.384548i	0.981341	+	0.192274i	$0.0615862\pi$
$293$			9.67283e6i			0.384548i	−0.981341	+	0.192274i	$0.938414\pi$
$294$	−5.44490e6			−0.214263
$295$		−	1.19585e7i		−	0.465813i
$296$			4.93867e6i			0.190430i
$297$		−	3.16987e7i		−	1.20996i
$298$			6.85552e7i			2.59055i
$299$	3.99245e7	+	1.55209e6i	1.49357	+	0.0580635i
$300$	6.89849e6			0.255499
$301$	2.30571e6			0.0845483
$302$	3.84525e7			1.39606
$303$	−1.09580e7			−0.393916
$304$		−	2.58440e7i		−	0.919895i
$305$	1.64777e6			0.0580761
$306$		−	3.12982e6i		−	0.109233i
$307$	2.73622e7			0.945660			0.472830	−	0.881154i	$-0.343232\pi$
$307$	2.73622e7			0.945660			0.472830	+	0.881154i	$0.343232\pi$
$308$	−4.87072e7			−1.66702
$309$			7.12820e6i			0.241604i
$310$			1.79212e7i			0.601565i
$311$	−1.17237e7			−0.389748			−0.194874	−	0.980828i	$-0.562430\pi$
$311$	−1.17237e7			−0.389748			−0.194874	+	0.980828i	$0.562430\pi$
$312$	1.52406e7			0.501810
$313$			3.14436e6i			0.102541i	0.998685	+	0.0512706i	$0.0163271\pi$
$313$			3.14436e6i			0.102541i	−0.998685	+	0.0512706i	$0.983673\pi$
$314$			6.03766e7i			1.95020i
$315$	−1.58693e6			−0.0507721
$316$			261183.i			0.00827721i
$317$	−4.87935e6			−0.153174			−0.0765868	−	0.997063i	$-0.524402\pi$
$317$	−4.87935e6			−0.153174			−0.0765868	+	0.997063i	$0.524402\pi$
$318$		−	9.02295e7i		−	2.80587i
$319$			1.75760e7i			0.541438i
$320$			2.01216e7i			0.614063i
$321$			5.68851e7i			1.71982i
$322$	−2.05783e6	+	5.29337e7i	−0.0616370	+	1.58550i
$323$	−2.88975e7			−0.857537
$324$	−4.52369e7			−1.33002
$325$	−1.02621e7			−0.298940
$326$	2.54859e7			0.735609
$327$		−	2.90733e7i		−	0.831477i
$328$	3.67438e6			0.104127
$329$		−	4.76884e7i		−	1.33914i
$330$	−3.23861e7			−0.901190
$331$	−2.78697e7			−0.768507			−0.384254	−	0.923228i	$-0.625541\pi$
$331$	−2.78697e7			−0.768507			−0.384254	+	0.923228i	$0.625541\pi$
$332$			6.25408e7i			1.70903i
$333$		−	2.34588e6i		−	0.0635292i
$334$	6.11709e7			1.64174
$335$	1.82291e7			0.484876
$336$		−	3.14629e7i		−	0.829432i
$337$		−	5.12046e7i		−	1.33789i	−0.743314	−	0.668943i	$-0.766747\pi$
$337$		−	5.12046e7i		−	1.33789i	0.743314	−	0.668943i	$-0.233253\pi$
$338$	−7.09165e7			−1.83653
$339$		−	7.51205e6i		−	0.192823i
$340$	1.47166e7			0.374430
$341$		−	4.61413e7i		−	1.16366i
$342$		−	7.88412e6i		−	0.197095i
$343$		−	3.71373e7i		−	0.920298i
$344$		−	1.03024e6i		−	0.0253082i
$345$	−750398.	+	1.93026e7i	−0.0182740	+	0.470065i
$346$	−8.90603e7			−2.15009
$347$	5.20309e6			0.124530			0.0622649	−	0.998060i	$-0.480168\pi$
$347$	5.20309e6			0.124530			0.0622649	+	0.998060i	$0.480168\pi$
$348$	2.26439e7			0.537297
$349$	2.68495e7			0.631626			0.315813	−	0.948821i	$-0.397723\pi$
$349$	2.68495e7			0.631626			0.315813	+	0.948821i	$0.397723\pi$
$350$		−	1.36059e7i		−	0.317339i
$351$	6.07509e7			1.40485
$352$		−	7.97089e7i		−	1.82759i
$353$	7.81086e7			1.77572			0.887861	−	0.460112i	$-0.152191\pi$
$353$	7.81086e7			1.77572			0.887861	+	0.460112i	$0.152191\pi$
$354$	7.23291e7			1.63043
$355$		−	1.12988e6i		−	0.0252549i
$356$		−	1.08415e8i		−	2.40291i
$357$	−3.51803e7			−0.773206
$358$	2.52390e7			0.550077
$359$		−	1.21399e7i		−	0.262381i	−0.991357	−	0.131190i	$-0.958120\pi$
$359$		−	1.21399e7i		−	0.262381i	0.991357	−	0.131190i	$-0.0418800\pi$
$360$			709071.i			0.0151979i
$361$	−2.57478e7			−0.547292
$362$		−	1.20332e8i		−	2.53662i
$363$	3.30693e7			0.691362
$364$		−	9.33480e7i		−	1.93553i
$365$		−	2.98068e7i		−	0.612966i
$366$			9.96626e6i			0.203277i
$367$		−	1.57546e7i		−	0.318721i	−0.987220	−	0.159360i	$-0.949057\pi$
$367$		−	1.57546e7i		−	0.318721i	0.987220	−	0.159360i	$-0.0509432\pi$
$368$	−3.68271e7	−	1.43167e6i	−0.738966	−	0.0287277i
$369$	−1.74534e6			−0.0347378
$370$	2.01130e7			0.397074
$371$	−9.75977e7			−1.91125
$372$	−5.94457e7			−1.15476
$373$		−	4.48528e7i		−	0.864297i	−0.901802	−	0.432149i	$-0.857756\pi$
$373$		−	4.48528e7i		−	0.864297i	0.901802	−	0.432149i	$-0.142244\pi$
$374$	−6.90895e7			−1.32068
$375$		−	4.96146e6i		−	0.0940841i
$376$	−2.13081e7			−0.400850
$377$	−3.36847e7			−0.628649
$378$			8.05463e7i			1.49132i
$379$		−	6.34492e6i		−	0.116549i	−0.998301	−	0.0582745i	$-0.981440\pi$
$379$		−	6.34492e6i		−	0.116549i	0.998301	−	0.0582745i	$-0.0185599\pi$
$380$	3.70716e7			0.675601
$381$	3.41530e7			0.617524
$382$			6.89351e7i			1.23666i
$383$			7.18346e7i			1.27861i	0.768954	+	0.639304i	$0.220778\pi$
$383$			7.18346e7i			1.27861i	−0.768954	+	0.639304i	$0.779222\pi$
$384$	−3.71453e7			−0.656009
$385$			3.50307e7i			0.613857i
$386$	1.14853e8			1.99701
$387$			489366.i			0.00844307i
$388$			5.59283e7i			0.957495i
$389$		−	9.06162e7i		−	1.53942i	−0.638394	−	0.769710i	$-0.720401\pi$
$389$		−	9.06162e7i		−	1.53942i	0.638394	−	0.769710i	$-0.279599\pi$
$390$		−	6.20683e7i		−	1.04635i
$391$	−1.60083e6	+	4.11784e7i	−0.0267803	+	0.688873i
$392$	2.63156e6			0.0436873
$393$	1.17689e8			1.93891
$394$	4.51735e6			0.0738577
$395$	187846.			0.00304796
$396$		−	1.03377e7i		−	0.166470i
$397$	−8.53591e7			−1.36420			−0.682101	−	0.731258i	$-0.738933\pi$
$397$	−8.53591e7			−1.36420			−0.682101	+	0.731258i	$0.738933\pi$
$398$		−	1.04963e8i		−	1.66490i
$399$	−8.86203e7			−1.39513
$400$	9.46591e6			0.147905
$401$		−	5.61348e7i		−	0.870561i	−0.900295	−	0.435281i	$-0.856649\pi$
$401$		−	5.61348e7i		−	0.870561i	0.900295	−	0.435281i	$-0.143351\pi$
$402$			1.10255e8i			1.69716i
$403$	8.84304e7			1.35110
$404$	2.99893e7			0.454801
$405$			3.25349e7i			0.489761i
$406$		−	4.46606e7i		−	0.667340i
$407$	−5.17844e7			−0.768096
$408$			1.57193e7i			0.231447i
$409$	−2.58188e7			−0.377369			−0.188684	−	0.982038i	$-0.560422\pi$
$409$	−2.58188e7			−0.377369			−0.188684	+	0.982038i	$0.560422\pi$
$410$		−	1.49641e7i		−	0.217120i
$411$			1.06209e8i			1.52981i
$412$		−	1.95081e7i		−	0.278947i
$413$		−	7.82356e7i		−	1.11059i
$414$	−1.12347e7	−	436755.i	−0.158329	−	0.00615513i
$415$	4.49800e7			0.629325
$416$	1.52763e8			2.12197
$417$	−1.48959e8			−2.05427
$418$	−1.74038e8			−2.38296
$419$		−	1.45922e7i		−	0.198371i	−0.995069	−	0.0991853i	$-0.968376\pi$
$419$		−	1.45922e7i		−	0.198371i	0.995069	−	0.0991853i	$-0.0316237\pi$
$420$	4.51316e7			0.609161
$421$			2.73578e7i			0.366636i	0.983054	+	0.183318i	$0.0586837\pi$
$421$			2.73578e7i			0.366636i	−0.983054	+	0.183318i	$0.941316\pi$
$422$	9.91539e7			1.31939
$423$	1.01214e7			0.133728
$424$			4.36086e7i			0.572104i
$425$		−	1.05843e7i		−	0.137879i
$426$	6.83387e6			0.0883971
$427$	1.07801e7			0.138465
$428$		−	1.55680e8i		−	1.98564i
$429$			1.59806e8i			2.02405i
$430$	−4.19569e6			−0.0527713
$431$		−	3.48465e7i		−	0.435238i	−0.976034	−	0.217619i	$-0.930171\pi$
$431$		−	3.48465e7i		−	0.435238i	0.976034	−	0.217619i	$-0.0698291\pi$
$432$	−5.60377e7			−0.695071
$433$			3.55335e7i			0.437698i	0.975759	+	0.218849i	$0.0702301\pi$
$433$			3.55335e7i			0.437698i	−0.975759	+	0.218849i	$0.929770\pi$
$434$			1.17245e8i			1.43425i
$435$		−	1.62858e7i		−	0.197852i
$436$			7.95660e7i			0.959993i
$437$	−4.03254e6	+	1.03730e8i	−0.0483209	+	1.24296i
$438$	1.80281e8			2.14550
$439$	−1.06759e7			−0.126186			−0.0630930	−	0.998008i	$-0.520096\pi$
$439$	−1.06759e7			−0.126186			−0.0630930	+	0.998008i	$0.520096\pi$
$440$	1.56524e7			0.183749
$441$	−1.25000e6			−0.0145745
$442$		−	1.32411e8i		−	1.53340i
$443$	9.48511e7			1.09102			0.545508	−	0.838105i	$-0.316337\pi$
$443$	9.48511e7			1.09102			0.545508	+	0.838105i	$0.316337\pi$
$444$			6.67159e7i			0.762220i
$445$	−7.79729e7			−0.884838
$446$	−1.00996e8			−1.13841
$447$			1.63550e8i			1.83116i
$448$			1.31640e8i			1.46405i
$449$	−9.43551e7			−1.04238			−0.521190	−	0.853440i	$-0.674512\pi$
$449$	−9.43551e7			−1.04238			−0.521190	+	0.853440i	$0.674512\pi$
$450$	2.88773e6			0.0316897
$451$			3.85277e7i			0.419995i
$452$			2.05586e7i			0.222627i
$453$	9.17348e7			0.986823
$454$		−	7.35877e7i		−	0.786389i
$455$	−6.71368e7			−0.712733
$456$			3.95973e7i			0.417611i
$457$			1.41758e8i			1.48525i	0.669706	+	0.742626i	$0.266420\pi$
$457$			1.41758e8i			1.48525i	−0.669706	+	0.742626i	$0.733580\pi$
$458$		−	1.22449e8i		−	1.27455i
$459$			6.26588e7i			0.647954i
$460$	2.05365e6	−	5.28262e7i	0.0210985	−	0.542720i
$461$	−5.03303e7			−0.513720			−0.256860	−	0.966449i	$-0.582688\pi$
$461$	−5.03303e7			−0.513720			−0.256860	+	0.966449i	$0.582688\pi$
$462$	−2.11877e8			−2.14862
$463$	1.86903e8			1.88310			0.941552	−	0.336867i	$-0.109367\pi$
$463$	1.86903e8			1.88310			0.941552	+	0.336867i	$0.109367\pi$
$464$	3.10714e7			0.311033
$465$			4.27540e7i			0.425224i
$466$	−7.45400e7			−0.736600
$467$		−	1.16654e8i		−	1.14538i	−0.819771	−	0.572691i	$-0.805900\pi$
$467$		−	1.16654e8i		−	1.14538i	0.819771	−	0.572691i	$-0.194100\pi$
$468$	1.98123e7			0.193284
$469$	1.19259e8			1.15604
$470$			8.67784e7i			0.835830i
$471$			1.44038e8i			1.37853i
$472$	−3.49572e7			−0.332438
$473$	1.08025e7			0.102080
$474$			1.13615e6i			0.0106685i
$475$		−	2.66623e7i		−	0.248780i
$476$	9.62796e7			0.892716
$477$		−	2.07142e7i		−	0.190859i
$478$	4.02444e7			0.368487
$479$			1.75347e8i			1.59549i	0.602998	+	0.797743i	$0.293973\pi$
$479$			1.75347e8i			1.59549i	−0.602998	+	0.797743i	$0.706027\pi$
$480$			7.38573e7i			0.667836i
$481$		−	9.92453e7i		−	0.891815i
$482$			7.47109e7i			0.667180i
$483$	−4.90929e6	+	1.26282e8i	−0.0435689	+	1.12073i
$484$	−9.05023e7			−0.798222
$485$	4.02242e7			0.352584
$486$	−3.62276e7			−0.315595
$487$	−9.39856e7			−0.813719			−0.406859	−	0.913491i	$-0.633376\pi$
$487$	−9.39856e7			−0.813719			−0.406859	+	0.913491i	$0.633376\pi$
$488$		−	4.81677e6i		−	0.0414473i
$489$	6.08008e7			0.519975
$490$		−	1.07172e7i		−	0.0910944i
$491$	9.16343e7			0.774130			0.387065	−	0.922052i	$-0.373489\pi$
$491$	9.16343e7			0.774130			0.387065	+	0.922052i	$0.373489\pi$
$492$	4.96368e7			0.416782
$493$		−	3.47426e7i		−	0.289949i
$494$		−	3.33547e8i		−	2.76679i
$495$	−7.43496e6			−0.0613003
$496$	−8.15698e7			−0.668474
$497$		−	7.39193e6i		−	0.0602128i
$498$			2.72054e8i			2.20276i
$499$	2.08643e8			1.67920			0.839599	−	0.543207i	$-0.182790\pi$
$499$	2.08643e8			1.67920			0.839599	+	0.543207i	$0.182790\pi$
$500$			1.35783e7i			0.108626i
$501$	1.45933e8			1.16049
$502$		−	1.47727e8i		−	1.16775i
$503$			2.42890e8i			1.90856i	0.298917	+	0.954279i	$0.403375\pi$
$503$			2.42890e8i			1.90856i	−0.298917	+	0.954279i	$0.596625\pi$
$504$			4.63891e6i			0.0362347i
$505$		−	2.15686e7i		−	0.167474i
$506$	−9.64118e6	+	2.48001e8i	−0.0744181	+	1.91427i
$507$	−1.69183e8			−1.29817
$508$	−9.34680e7			−0.712971
$509$	−5.54891e7			−0.420779			−0.210390	−	0.977618i	$-0.567473\pi$
$509$	−5.54891e7			−0.420779			−0.210390	+	0.977618i	$0.567473\pi$
$510$	6.40176e7			0.482601
$511$		−	1.95003e8i		−	1.46143i
$512$	−1.72591e8			−1.28590
$513$			1.57839e8i			1.16913i
$514$	−8.61412e7			−0.634339
$515$	−1.40304e7			−0.102718
$516$		−	1.39174e7i		−	0.101300i
$517$		−	2.23426e8i		−	1.61682i
$518$	1.31584e8			0.946702
$519$	−2.12468e8			−1.51982
$520$			2.99981e7i			0.213346i
$521$			1.01569e8i			0.718206i	0.933298	+	0.359103i	$0.116917\pi$
$521$			1.01569e8i			0.718206i	−0.933298	+	0.359103i	$0.883083\pi$
$522$	9.47882e6			0.0666412
$523$		−	2.36378e8i		−	1.65235i	−0.563415	−	0.826174i	$-0.690513\pi$
$523$		−	2.36378e8i		−	1.65235i	0.563415	−	0.826174i	$-0.309487\pi$
$524$	−3.22084e8			−2.23860
$525$		−	3.24591e7i		−	0.224315i
$526$		−	5.99594e7i		−	0.412002i
$527$			9.12075e7i			0.623159i
$528$		−	1.47408e8i		−	1.00142i
$529$	1.47589e8	+	1.14926e7i	0.996982	+	0.0776338i
$530$	1.77598e8			1.19292
$531$	1.66048e7			0.110905
$532$	2.42531e8			1.61077
$533$	−7.38388e7			−0.487644
$534$		−	4.71606e8i		−	3.09710i
$535$	−1.11967e8			−0.731185
$536$		−	5.32873e7i		−	0.346043i
$537$	6.02118e7			0.388829
$538$	6.55970e7			0.421247
$539$			2.75932e7i			0.176212i
$540$		−	8.03827e7i		−	0.510483i
$541$	−2.44826e8			−1.54620			−0.773100	−	0.634284i	$-0.781295\pi$
$541$	−2.44826e8			−1.54620			−0.773100	+	0.634284i	$0.781295\pi$
$542$	−4.13911e7			−0.259961
$543$		−	2.87072e8i		−	1.79305i
$544$			1.57561e8i			0.978703i
$545$	5.72247e7			0.353504
$546$		−	4.06066e8i		−	2.49470i
$547$	6.54473e7			0.399880			0.199940	−	0.979808i	$-0.435925\pi$
$547$	6.54473e7			0.399880			0.199940	+	0.979808i	$0.435925\pi$
$548$		−	2.90667e8i		−	1.76626i
$549$			2.28798e6i			0.0138272i
$550$		−	6.37453e7i		−	0.383142i
$551$		−	8.75175e7i		−	0.523167i
$552$	5.64254e7	+	2.19357e6i	0.335473	+	0.0130417i
$553$	1.22893e6			0.00726695
$554$	2.40396e8			1.41383
$555$	4.79828e7			0.280677
$556$	4.07662e8			2.37179
$557$		−	1.78236e8i		−	1.03140i	−0.856768	−	0.515702i	$-0.827531\pi$
$557$		−	1.78236e8i		−	1.03140i	0.856768	−	0.515702i	$-0.172469\pi$
$558$	−2.48842e7			−0.143226
$559$			2.07032e7i			0.118523i
$560$	6.19282e7			0.352634
$561$	−1.64824e8			−0.933540
$562$			3.25035e8i			1.83114i
$563$			1.87578e8i			1.05113i	0.850753	+	0.525565i	$0.176146\pi$
$563$			1.87578e8i			1.05113i	−0.850753	+	0.525565i	$0.823854\pi$
$564$	−2.87849e8			−1.60446
$565$	1.47859e7			0.0819792
$566$			2.29049e8i			1.26322i
$567$			2.12851e8i			1.16769i
$568$	−3.30286e6			−0.0180238
$569$			2.13604e8i			1.15951i	0.814792	+	0.579753i	$0.196851\pi$
$569$			2.13604e8i			1.15951i	−0.814792	+	0.579753i	$0.803149\pi$
$570$	1.61262e8			0.870778
$571$			3.53914e7i			0.190103i	0.995472	+	0.0950515i	$0.0303016\pi$
$571$			3.53914e7i			0.190103i	−0.995472	+	0.0950515i	$0.969698\pi$
$572$		−	4.37347e8i		−	2.33689i
$573$			1.64456e8i			0.874150i
$574$		−	9.78988e7i		−	0.517657i
$575$	−3.79932e7	−	1.47701e6i	−0.199849	−	0.00776924i
$576$	−2.79395e7			−0.146201
$577$	−2.64035e7			−0.137446			−0.0687232	−	0.997636i	$-0.521893\pi$
$577$	−2.64035e7			−0.137446			−0.0687232	+	0.997636i	$0.521893\pi$
$578$	−1.50786e8			−0.780867
$579$	2.74001e8			1.41162
$580$			4.45699e7i			0.228433i
$581$	2.94270e8			1.50044
$582$			2.43289e8i			1.23411i
$583$	−4.57258e8			−2.30757
$584$	−8.71313e7			−0.437457
$585$		−	1.42492e7i		−	0.0711742i
$586$		−	1.15154e8i		−	0.572250i
$587$	4.96818e7			0.245631			0.122816	−	0.992430i	$-0.460808\pi$
$587$	4.96818e7			0.245631			0.122816	+	0.992430i	$0.460808\pi$
$588$	3.55495e7			0.174864
$589$			2.29754e8i			1.12439i
$590$			1.42365e8i			0.693182i
$591$	1.07769e7			0.0522073
$592$			9.15457e7i			0.441238i
$593$	−3.80621e8			−1.82528			−0.912638	−	0.408769i	$-0.865958\pi$
$593$	−3.80621e8			−1.82528			−0.912638	+	0.408769i	$0.865958\pi$
$594$			3.77369e8i			1.80056i
$595$		−	6.92453e7i		−	0.328730i
$596$		−	4.47593e8i		−	2.11419i
$597$		−	2.50407e8i		−	1.17686i
$598$	−4.75297e8	−	1.84774e7i	−2.22260	−	0.0864049i
$599$	5.73150e7			0.266679			0.133339	−	0.991070i	$-0.457430\pi$
$599$	5.73150e7			0.266679			0.133339	+	0.991070i	$0.457430\pi$
$600$	−1.45034e7			−0.0671453
$601$	2.12647e8			0.979573			0.489786	−	0.871843i	$-0.337075\pi$
$601$	2.12647e8			0.979573			0.489786	+	0.871843i	$0.337075\pi$
$602$	−2.74492e7			−0.125817
$603$			2.53116e7i			0.115443i
$604$	−2.51054e8			−1.13935
$605$			6.50902e7i			0.293934i
$606$	1.30454e8			0.586191
$607$	1.06712e8			0.477140			0.238570	−	0.971125i	$-0.423321\pi$
$607$	1.06712e8			0.477140			0.238570	+	0.971125i	$0.423321\pi$
$608$			3.96900e8i			1.76592i
$609$		−	1.06545e8i		−	0.471718i
$610$	−1.96165e7			−0.0864237
$611$	4.28199e8			1.87725
$612$			2.04345e7i			0.0891475i
$613$			4.31034e7i			0.187124i	0.995613	+	0.0935622i	$0.0298254\pi$
$613$			4.31034e7i			0.187124i	−0.995613	+	0.0935622i	$0.970175\pi$
$614$	−3.25743e8			−1.40725
$615$		−	3.56993e7i		−	0.153474i
$616$	1.02402e8			0.438093
$617$			2.71509e8i			1.15592i	0.816064	+	0.577961i	$0.196151\pi$
$617$			2.71509e8i			1.15592i	−0.816064	+	0.577961i	$0.803849\pi$
$618$		−	8.48604e7i		−	0.359534i
$619$		−	3.04877e8i		−	1.28544i	−0.766100	−	0.642721i	$-0.777805\pi$
$619$		−	3.04877e8i		−	1.28544i	0.766100	−	0.642721i	$-0.222195\pi$
$620$		−	1.17007e8i		−	0.490948i
$621$	2.24918e8	+	8.74381e6i	0.939181	+	0.0365112i
$622$	1.39570e8			0.579989
$623$	−5.10118e8			−2.10963
$624$	2.82508e8			1.16273
$625$	9.76562e6			0.0400000
$626$		−	3.74332e7i		−	0.152593i
$627$	−4.15197e8			−1.68443
$628$		−	3.94196e8i		−	1.59160i
$629$	1.02362e8			0.411327
$630$	1.88922e7			0.0755546
$631$			2.81889e8i			1.12199i	0.827819	+	0.560995i	$0.189581\pi$
$631$			2.81889e8i			1.12199i	−0.827819	+	0.560995i	$0.810419\pi$
$632$		−	549111.i		−	0.00217525i
$633$	2.36548e8			0.932627
$634$	5.80881e7			0.227939
$635$			6.72232e7i			0.262541i
$636$			5.89104e8i			2.28992i
$637$	−5.28827e7			−0.204595
$638$		−	2.09241e8i		−	0.805720i
$639$	1.56887e6			0.00601291
$640$		−	7.31129e7i		−	0.278903i
$641$		−	1.15901e8i		−	0.440063i	−0.975493	−	0.220031i	$-0.929384\pi$
$641$		−	1.15901e8i		−	0.440063i	0.975493	−	0.220031i	$-0.0706160\pi$
$642$		−	6.77211e8i		−	2.55929i
$643$		−	3.78010e8i		−	1.42190i	−0.703241	−	0.710951i	$-0.748265\pi$
$643$		−	3.78010e8i		−	1.42190i	0.703241	−	0.710951i	$-0.251735\pi$
$644$	1.34355e7	−	3.45602e8i	0.0503031	−	1.29395i
$645$	−1.00095e7			−0.0373021
$646$	3.44022e8			1.27611
$647$	−1.13024e8			−0.417311			−0.208655	−	0.977989i	$-0.566909\pi$
$647$	−1.13024e8			−0.417311			−0.208655	+	0.977989i	$0.566909\pi$
$648$	9.51061e7			0.349529
$649$		−	3.66544e8i		−	1.34089i
$650$	1.22169e8			0.444856
$651$			2.79707e8i			1.01382i
$652$	−1.66396e8			−0.600344
$653$	−2.24393e8			−0.805880			−0.402940	−	0.915226i	$-0.632012\pi$
$653$	−2.24393e8			−0.805880			−0.402940	+	0.915226i	$0.632012\pi$
$654$			3.46114e8i			1.23733i
$655$			2.31646e8i			0.824331i
$656$	6.81103e7			0.241269
$657$	4.13876e7			0.145940
$658$			5.67725e8i			1.99279i
$659$		−	2.08527e8i		−	0.728627i	−0.931276	−	0.364314i	$-0.881304\pi$
$659$		−	2.08527e8i		−	0.728627i	0.931276	−	0.364314i	$-0.118696\pi$
$660$	2.11447e8			0.735478
$661$		−	3.44023e8i		−	1.19119i	−0.803283	−	0.595597i	$-0.796915\pi$
$661$		−	3.44023e8i		−	1.19119i	0.803283	−	0.595597i	$-0.203085\pi$
$662$	3.31785e8			1.14362
$663$		−	3.15888e8i		−	1.08391i
$664$		−	1.31486e8i		−	0.449132i
$665$		−	1.74431e8i		−	0.593142i
$666$			2.79275e7i			0.0945386i
$667$	−1.24711e8	−	4.84819e6i	−0.420268	−	0.0163381i
$668$	−3.99382e8			−1.33986
$669$	−2.40942e8			−0.804700
$670$	−2.17015e8			−0.721549
$671$	5.05062e7			0.167177
$672$			4.83192e8i			1.59225i
$673$	2.97394e8			0.975633			0.487817	−	0.872946i	$-0.337794\pi$
$673$	2.97394e8			0.975633			0.487817	+	0.872946i	$0.337794\pi$
$674$			6.09585e8i			1.99092i
$675$	−5.78121e7			−0.187978
$676$	4.63010e8			1.49882
$677$		−	3.30179e8i		−	1.06410i	−0.846712	−	0.532051i	$-0.821421\pi$
$677$		−	3.30179e8i		−	1.06410i	0.846712	−	0.532051i	$-0.178579\pi$
$678$			8.94302e7i			0.286943i
$679$	2.63157e8			0.840630
$680$	−3.09402e7			−0.0984003
$681$		−	1.75555e8i		−	0.555870i
$682$			5.49307e8i			1.73166i
$683$	2.53904e8			0.796907			0.398453	−	0.917189i	$-0.369547\pi$
$683$	2.53904e8			0.796907			0.398453	+	0.917189i	$0.369547\pi$
$684$			5.14750e7i			0.160853i
$685$	−2.09051e8			−0.650400
$686$			4.42116e8i			1.36951i
$687$		−	2.92122e8i		−	0.900935i
$688$		−	1.90970e7i		−	0.0586408i
$689$		−	8.76340e8i		−	2.67926i
$690$	8.93341e6	−	2.29795e8i	0.0271938	−	0.699510i
$691$	1.31184e8			0.397600			0.198800	−	0.980040i	$-0.436296\pi$
$691$	1.31184e8			0.397600			0.198800	+	0.980040i	$0.436296\pi$
$692$	5.81470e8			1.75473
$693$	−4.86413e7			−0.146152
$694$	−6.19422e7			−0.185314
$695$		−	2.93195e8i		−	0.873377i
$696$	−4.76066e7			−0.141202
$697$		−	7.61578e7i		−	0.224914i
$698$	−3.19641e8			−0.939931
$699$	−1.77827e8			−0.520676
$700$			8.88322e7i			0.258986i
$701$			1.78275e8i			0.517530i	0.965940	+	0.258765i	$0.0833155\pi$
$701$			1.78275e8i			0.517530i	−0.965940	+	0.258765i	$0.916685\pi$
$702$	−7.23233e8			−2.09058
$703$	2.57853e8			0.742175
$704$			6.16752e8i			1.76764i
$705$			2.07024e8i			0.590818i
$706$	−9.29875e8			−2.64247
$707$		−	1.41107e8i		−	0.399292i
$708$	−4.72233e8			−1.33063
$709$		−	1.40744e8i		−	0.394905i	−0.980312	−	0.197452i	$-0.936733\pi$
$709$		−	1.40744e8i		−	0.394905i	0.980312	−	0.197452i	$-0.0632668\pi$
$710$			1.34511e7i			0.0375822i
$711$			260830.i			0.000725685i
$712$			2.27931e8i			0.631485i
$713$	3.27395e8	+	1.27277e7i	0.903242	+	0.0351140i
$714$	4.18818e8			1.15062
$715$	−3.14545e8			−0.860526
$716$	−1.64784e8			−0.448928
$717$	9.60097e7			0.260470
$718$			1.44524e8i			0.390452i
$719$	−5.77479e8			−1.55364			−0.776819	−	0.629724i	$-0.783168\pi$
$719$	−5.77479e8			−1.55364			−0.776819	+	0.629724i	$0.783168\pi$
$720$			1.31437e7i			0.0352144i
$721$	−9.17902e7			−0.244901
$722$	3.06525e8			0.814431
$723$			1.78235e8i			0.471605i
$724$			7.85642e8i			2.07019i
$725$	3.20552e7			0.0841170
$726$	−3.93687e8			−1.02882
$727$			3.84548e8i			1.00080i	0.865794	+	0.500400i	$0.166814\pi$
$727$			3.84548e8i			1.00080i	−0.865794	+	0.500400i	$0.833186\pi$
$728$			1.96255e8i			0.508658i
$729$	3.37853e8			0.872056
$730$			3.54846e8i			0.912162i
$731$	−2.13534e7			−0.0546656
$732$		−	6.50692e7i		−	0.165898i
$733$		−	2.75391e8i		−	0.699258i	−0.936888	−	0.349629i	$-0.886308\pi$
$733$		−	2.75391e8i		−	0.699258i	0.936888	−	0.349629i	$-0.113692\pi$
$734$			1.87557e8i			0.474292i
$735$		−	2.55676e7i		−	0.0643913i
$736$	5.65574e8	+	2.19870e7i	1.41859	+	0.0551483i
$737$	5.58744e8			1.39576
$738$	2.07781e7			0.0516937
$739$	−1.19076e8			−0.295046			−0.147523	−	0.989059i	$-0.547130\pi$
$739$	−1.19076e8			−0.295046			−0.147523	+	0.989059i	$0.547130\pi$
$740$	−1.31317e8			−0.324059
$741$		−	7.95731e8i		−	1.95574i
$742$	1.16189e9			2.84416
$743$			5.12352e8i			1.24911i	0.780980	+	0.624557i	$0.214720\pi$
$743$			5.12352e8i			1.24911i	−0.780980	+	0.624557i	$0.785280\pi$
$744$	1.24979e8			0.303471
$745$	−3.21914e8			−0.778522
$746$			5.33968e8i			1.28617i
$747$			6.24561e7i			0.149835i
$748$	4.51082e8			1.07783
$749$	−7.32513e8			−1.74329
$750$			5.90657e7i			0.140008i
$751$			6.58734e7i			0.155521i	0.996972	+	0.0777607i	$0.0247770\pi$
$751$			6.58734e7i			0.155521i	−0.996972	+	0.0777607i	$0.975223\pi$
$752$	−3.94979e8			−0.928795
$753$		−	3.52427e8i		−	0.825438i
$754$	4.01013e8			0.935500
$755$			1.80561e8i			0.419550i
$756$		−	5.25883e8i		−	1.21709i
$757$			6.88074e7i			0.158616i	0.996850	+	0.0793081i	$0.0252711\pi$
$757$			6.88074e7i			0.158616i	−0.996850	+	0.0793081i	$0.974729\pi$
$758$			7.55356e7i			0.173438i
$759$	−2.30006e7	+	5.91648e8i	−0.0526035	+	1.35313i
$760$	−7.79392e7			−0.177548
$761$	6.55916e8			1.48831			0.744156	−	0.668006i	$-0.232852\pi$
$761$	6.55916e8			1.48831			0.744156	+	0.668006i	$0.232852\pi$
$762$	−4.06588e8			−0.918945
$763$	3.74378e8			0.842824
$764$		−	4.50074e8i		−	1.00926i
$765$	1.46967e7			0.0328273
$766$		−	8.55184e8i		−	1.90271i
$767$	7.02485e8			1.55687
$768$	−2.12053e8			−0.468123
$769$		−	4.09141e8i		−	0.899693i	−0.893106	−	0.449847i	$-0.851479\pi$
$769$		−	4.09141e8i		−	0.899693i	0.893106	−	0.449847i	$-0.148521\pi$
$770$		−	4.17037e8i		−	0.913488i
$771$	−2.05504e8			−0.448391
$772$	−7.49871e8			−1.62980
$773$		−	1.56598e8i		−	0.339038i	−0.985527	−	0.169519i	$-0.945779\pi$
$773$		−	1.56598e8i		−	0.339038i	0.985527	−	0.169519i	$-0.0542214\pi$
$774$		−	5.82585e6i		−	0.0125642i
$775$	−8.41525e7			−0.180785
$776$		−	1.17584e8i		−	0.251630i
$777$	3.13915e8			0.669189
$778$			1.07878e9i			2.29083i
$779$		−	1.91844e8i		−	0.405821i
$780$			4.05241e8i			0.853944i
$781$		−	3.46321e7i		−	0.0726986i
$782$	1.90577e7	−	4.90224e8i	0.0398521	−	1.02512i
$783$	−1.89765e8			−0.395304
$784$	4.87800e7			0.101226
$785$	−2.83510e8			−0.586083
$786$	−1.40107e9			−2.88531
$787$		−	4.50923e8i		−	0.925077i	−0.886599	−	0.462539i	$-0.846939\pi$
$787$		−	4.50923e8i		−	0.925077i	0.886599	−	0.462539i	$-0.153061\pi$
$788$	−2.94936e7			−0.0602766
$789$		−	1.43043e8i		−	0.291229i
$790$	−2.23628e6			−0.00453571
$791$	9.67331e7			0.195455
$792$			2.17339e7i			0.0437484i
$793$			9.67958e7i			0.194105i
$794$	1.01619e9			2.03008
$795$	4.23690e8			0.843231
$796$			6.85300e8i			1.35876i
$797$			8.79632e7i			0.173751i	0.996219	+	0.0868753i	$0.0276882\pi$
$797$			8.79632e7i			0.173751i	−0.996219	+	0.0868753i	$0.972312\pi$
$798$	1.05502e9			2.07611
$799$			4.41647e8i			0.865834i
$800$	−1.45373e8			−0.283932
$801$		−	1.08268e8i		−	0.210670i
$802$			6.68279e8i			1.29549i
$803$		−	9.13614e8i		−	1.76448i
$804$		−	7.19852e8i		−	1.38508i
$805$	−2.48560e8	−	9.66292e6i	−0.476480	−	0.0185234i
$806$	−1.05275e9			−2.01058
$807$	1.56492e8			0.297764
$808$	−6.30494e7			−0.119522
$809$	−6.67149e8			−1.26002			−0.630010	−	0.776587i	$-0.716949\pi$
$809$	−6.67149e8			−1.26002			−0.630010	+	0.776587i	$0.716949\pi$
$810$		−	3.87324e8i		−	0.728819i
$811$	−5.13813e8			−0.963258			−0.481629	−	0.876375i	$-0.659955\pi$
$811$	−5.13813e8			−0.963258			−0.481629	+	0.876375i	$0.659955\pi$
$812$			2.91587e8i			0.544628i
$813$	−9.87453e7			−0.183757
$814$	6.16487e8			1.14301
$815$			1.19674e8i			0.221068i
$816$			2.91381e8i			0.536278i
$817$	−5.37898e7			−0.0986356
$818$	3.07370e8			0.561567
$819$		−	9.32216e7i		−	0.169693i
$820$			9.77000e7i			0.177196i
$821$	−2.92381e8			−0.528347			−0.264173	−	0.964475i	$-0.585099\pi$
$821$	−2.92381e8			−0.528347			−0.264173	+	0.964475i	$0.585099\pi$
$822$		−	1.26441e9i		−	2.27652i
$823$	5.53675e8			0.993244			0.496622	−	0.867967i	$-0.334574\pi$
$823$	5.53675e8			0.993244			0.496622	+	0.867967i	$0.334574\pi$
$824$			4.10137e7i			0.0733074i
$825$		−	1.52075e8i		−	0.270829i
$826$			9.31386e8i			1.65268i
$827$			9.35166e8i			1.65338i	0.562659	+	0.826689i	$0.309778\pi$
$827$			9.35166e8i			1.65338i	−0.562659	+	0.826689i	$0.690222\pi$
$828$	7.33508e7	+	2.85155e6i	0.129215	+	0.00502332i
$829$	−3.34331e8			−0.586831			−0.293416	−	0.955985i	$-0.594792\pi$
$829$	−3.34331e8			−0.586831			−0.293416	+	0.955985i	$0.594792\pi$
$830$	−5.35482e8			−0.936506
$831$	5.73503e8			0.999385
$832$	−1.18201e9			−2.05235
$833$		−	5.45435e7i		−	0.0943644i
$834$	1.77334e9			3.05699
$835$			2.87239e8i			0.493384i
$836$	1.13629e9			1.94478
$837$	4.98179e8			0.849589
$838$			1.73718e8i			0.295198i
$839$			1.13178e9i			1.91636i	0.286174	+	0.958178i	$0.407616\pi$
$839$			1.13178e9i			1.91636i	−0.286174	+	0.958178i	$0.592384\pi$
$840$	−9.48846e7			−0.160088
$841$	−4.89604e8			−0.823108
$842$		−	3.25691e8i		−	0.545595i
$843$			7.75424e8i			1.29436i
$844$	−6.47371e8			−1.07678
$845$		−	3.33002e8i		−	0.551920i
$846$	−1.20495e8			−0.199001
$847$			4.25836e8i			0.700797i
$848$			8.08352e8i			1.32560i
$849$			5.46433e8i			0.892923i
$850$			1.26005e8i			0.205179i
$851$	1.42843e7	−	3.67436e8i	0.0231776	−	0.596201i
$852$	−4.46180e7			−0.0721425
$853$	−6.26786e8			−1.00989			−0.504943	−	0.863153i	$-0.668487\pi$
$853$	−6.26786e8			−1.00989			−0.504943	+	0.863153i	$0.668487\pi$
$854$	−1.28336e8			−0.206051
$855$	3.70214e7			0.0592317
$856$			3.27301e8i			0.521827i
$857$	−8.44407e8			−1.34156			−0.670779	−	0.741658i	$-0.734040\pi$
$857$	−8.44407e8			−1.34156			−0.670779	+	0.741658i	$0.734040\pi$
$858$		−	1.90247e9i		−	3.01201i
$859$	−6.01799e8			−0.949449			−0.474725	−	0.880134i	$-0.657452\pi$
$859$	−6.01799e8			−0.949449			−0.474725	+	0.880134i	$0.657452\pi$
$860$	2.73935e7			0.0430677
$861$		−	2.33554e8i		−	0.365913i
$862$			4.14844e8i			0.647683i
$863$	1.04801e9			1.63054			0.815271	−	0.579080i	$-0.196588\pi$
$863$	1.04801e9			1.63054			0.815271	+	0.579080i	$0.196588\pi$
$864$	8.60602e8			1.33432
$865$		−	4.18200e8i		−	0.646153i
$866$		−	4.23022e8i		−	0.651343i
$867$	−3.59725e8			−0.551967
$868$		−	7.65486e8i		−	1.17052i
$869$	5.75770e6			0.00877384
$870$			1.93880e8i			0.294426i
$871$			1.07084e9i			1.62058i
$872$		−	1.67280e8i		−	0.252286i
$873$			5.58526e7i			0.0839461i
$874$	4.80070e7	−	1.23489e9i	0.0719068	−	1.84967i
$875$	6.38891e7			0.0953679
$876$	−1.17705e9			−1.75098
$877$	−9.73507e8			−1.44325			−0.721623	−	0.692287i	$-0.756603\pi$
$877$	−9.73507e8			−1.44325			−0.721623	+	0.692287i	$0.756603\pi$
$878$	1.27096e8			0.187779
$879$		−	2.74719e8i		−	0.404503i
$880$	2.90142e8			0.425757
$881$		−	2.86924e8i		−	0.419603i	−0.977744	−	0.209801i	$-0.932718\pi$
$881$		−	2.86924e8i		−	0.419603i	0.977744	−	0.209801i	$-0.0672818\pi$
$882$	1.48811e7			0.0216885
$883$	5.11950e7			0.0743611			0.0371805	−	0.999309i	$-0.488162\pi$
$883$	5.11950e7			0.0743611			0.0371805	+	0.999309i	$0.488162\pi$
$884$			8.64504e8i			1.25144i
$885$			3.39635e8i			0.489985i
$886$	−1.12919e9			−1.62355
$887$	1.34996e9			1.93442			0.967209	−	0.253981i	$-0.0817402\pi$
$887$	1.34996e9			1.93442			0.967209	+	0.253981i	$0.0817402\pi$
$888$		−	1.40264e8i		−	0.200311i
$889$			4.39790e8i			0.625951i
$890$	9.28259e8			1.31674
$891$			9.97234e8i			1.40982i
$892$	6.59397e8			0.929078
$893$			1.11252e9i			1.56226i
$894$		−	1.94704e9i		−	2.72497i
$895$			1.18515e8i			0.165311i
$896$		−	4.78322e8i		−	0.664961i
$897$	−1.13390e9	−	4.40810e7i	−1.57108	−	0.0610765i
$898$	1.12329e9			1.55118
$899$	−2.76226e8			−0.380177
$900$	−1.88538e7			−0.0258626
$901$	9.03862e8			1.23574
$902$		−	4.58668e8i		−	0.624999i
$903$	−6.54846e7			−0.0889357
$904$		−	4.32223e7i		−	0.0585063i
$905$	5.65042e8			0.762316
$906$	−1.09209e9			−1.46850
$907$		−	1.42386e9i		−	1.90830i	−0.299330	−	0.954150i	$-0.596763\pi$
$907$		−	1.42386e9i		−	1.90830i	0.299330	−	0.954150i	$-0.403237\pi$
$908$			4.80450e8i			0.641787i
$909$	2.99487e7			0.0398736
$910$	7.99257e8			1.06063
$911$		−	7.42991e8i		−	0.982717i	−0.870957	−	0.491358i	$-0.836501\pi$
$911$		−	7.42991e8i		−	0.982717i	0.870957	−	0.491358i	$-0.163499\pi$
$912$			7.33996e8i			0.967630i
$913$	1.37869e9			1.81157
$914$		−	1.68762e9i		−	2.21022i
$915$	−4.67985e7			−0.0610898
$916$			7.99462e8i			1.04019i
$917$			1.51549e9i			1.96537i
$918$		−	7.45946e8i		−	0.964228i
$919$			7.15568e8i			0.921944i	0.887415	+	0.460972i	$0.152499\pi$
$919$			7.15568e8i			0.921944i	−0.887415	+	0.460972i	$0.847501\pi$
$920$	−4.31759e6	+	1.11062e8i	−0.00554470	+	0.142627i
$921$	−7.77115e8			−0.994732
$922$	5.99177e8			0.764473
$923$	6.63729e7			0.0844084
$924$	1.38334e9			1.75353
$925$			9.44443e7i			0.119330i
$926$	−2.22507e9			−2.80227
$927$		−	1.94816e7i		−	0.0244561i
$928$	−4.77180e8			−0.597087
$929$	−1.19683e9			−1.49275			−0.746374	−	0.665526i	$-0.768207\pi$
$929$	−1.19683e9			−1.49275			−0.746374	+	0.665526i	$0.768207\pi$
$930$		−	5.08982e8i		−	0.632781i
$931$		−	1.37397e8i		−	0.170266i
$932$	4.86668e8			0.601153
$933$	3.32966e8			0.409973
$934$			1.38876e9i			1.70446i
$935$		−	3.24423e8i		−	0.396896i
$936$	−4.16533e7			−0.0507951
$937$		−	1.18386e9i		−	1.43907i	−0.694456	−	0.719535i	$-0.744355\pi$
$937$		−	1.18386e9i		−	1.43907i	0.694456	−	0.719535i	$-0.255645\pi$
$938$	−1.41977e9			−1.72032
$939$		−	8.93031e7i		−	0.107862i
$940$		−	5.66572e8i		−	0.682137i
$941$		−	1.05592e9i		−	1.26725i	−0.773639	−	0.633627i	$-0.781565\pi$
$941$		−	1.05592e9i		−	1.26725i	0.773639	−	0.633627i	$-0.218435\pi$
$942$		−	1.71476e9i		−	2.05140i
$943$	−2.73373e8	−	1.06275e7i	−0.326002	−	0.0126735i
$944$	−6.47985e8			−0.770281
$945$	−3.78220e8			−0.448177
$946$	−1.28603e8			−0.151907
$947$	1.55408e9			1.82989			0.914944	−	0.403580i	$-0.132234\pi$
$947$	1.55408e9			1.82989			0.914944	+	0.403580i	$0.132234\pi$
$948$		−	7.41788e6i		−	0.00870672i
$949$	1.75095e9			2.04869
$950$			3.17411e8i			0.370213i
$951$	1.38579e8			0.161122
$952$	−2.02418e8			−0.234606
$953$		−	1.49188e9i		−	1.72368i	−0.507184	−	0.861838i	$-0.669313\pi$
$953$		−	1.49188e9i		−	1.72368i	0.507184	−	0.861838i	$-0.330687\pi$
$954$			2.46601e8i			0.284020i
$955$	−3.23698e8			−0.371647
$956$	−2.62754e8			−0.300729
$957$		−	4.99178e8i		−	0.569534i
$958$		−	2.08749e9i		−	2.37426i
$959$	−1.36766e9			−1.55068
$960$		−	5.71475e8i		−	0.645928i
$961$	−1.62343e8			−0.182921
$962$			1.18151e9i			1.32712i
$963$		−	1.55469e8i		−	0.174087i
$964$		−	4.87784e8i		−	0.544498i
$965$			5.39315e8i			0.600151i
$966$	5.84445e7	−	1.50338e9i	0.0648354	−	1.66777i
$967$	8.51934e8			0.942164			0.471082	−	0.882089i	$-0.343864\pi$
$967$	8.51934e8			0.942164			0.471082	+	0.882089i	$0.343864\pi$
$968$	1.90272e8			0.209773
$969$	8.20721e8			0.902037
$970$	−4.78865e8			−0.524684
$971$			1.09806e9i			1.19942i	0.800219	+	0.599708i	$0.204717\pi$
$971$			1.09806e9i			1.19942i	−0.800219	+	0.599708i	$0.795283\pi$
$972$	2.36528e8			0.257563
$973$		−	1.91815e9i		−	2.08230i
$974$	1.11889e9			1.21090
$975$	2.91454e8			0.314453
$976$		−	8.92862e7i		−	0.0960361i
$977$		−	6.41123e8i		−	0.687476i	−0.939066	−	0.343738i	$-0.888307\pi$
$977$		−	6.41123e8i		−	0.687476i	0.939066	−	0.343738i	$-0.111693\pi$
$978$	−7.23827e8			−0.773781
$979$	−2.38997e9			−2.54709
$980$			6.99718e7i			0.0743439i
$981$			7.94583e7i			0.0841652i
$982$	−1.09090e9			−1.15199
$983$			2.28724e8i			0.240797i	0.992726	+	0.120398i	$0.0384172\pi$
$983$			2.28724e8i			0.240797i	−0.992726	+	0.120398i	$0.961583\pi$
$984$	−1.04356e8			−0.109530
$985$			2.12121e7i			0.0221960i
$986$			4.13606e8i			0.431476i
$987$			1.35440e9i			1.40863i
$988$			2.17771e9i			2.25803i
$989$	−2.97978e6	+	7.66493e7i	−0.00308032	+	0.0792355i
$990$	8.85124e7			0.0912218
$991$	−1.75028e8			−0.179840			−0.0899200	−	0.995949i	$-0.528661\pi$
$991$	−1.75028e8			−0.179840			−0.0899200	+	0.995949i	$0.528661\pi$
$992$	1.25271e9			1.28326
$993$	7.91529e8			0.808386
$994$			8.80001e7i			0.0896033i
$995$	4.92875e8			0.500342
$996$		−	1.77623e9i		−	1.79771i
$997$	5.87904e8			0.593227			0.296613	−	0.954998i	$-0.404143\pi$
$997$	5.87904e8			0.593227			0.296613	+	0.954998i	$0.404143\pi$
$998$	−2.48387e9			−2.49883
$999$		−	5.59106e8i		−	0.560787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.7.d.a.91.10	yes	48
23.22	odd	2	inner	115.7.d.a.91.9	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.7.d.a.91.9	✓	48	23.22	odd	2	inner
115.7.d.a.91.10	yes	48	1.1	even	1	trivial

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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-11.9049 q^{2} -28.4011 q^{3} +77.7265 q^{4} -55.9017i q^{5} +338.112 q^{6} -365.722i q^{7} -163.412 q^{8} +77.6213 q^{9} +O(q^{10})\)	\(q-11.9049 q^{2} -28.4011 q^{3} +77.7265 q^{4} -55.9017i q^{5} +338.112 q^{6} -365.722i q^{7} -163.412 q^{8} +77.6213 q^{9} +665.504i q^{10} -1713.46i q^{11} -2207.52 q^{12} +3283.86 q^{13} +4353.89i q^{14} +1587.67i q^{15} -3029.09 q^{16} +3386.99i q^{17} -924.073 q^{18} +8531.92i q^{19} -4345.04i q^{20} +10386.9i q^{21} +20398.5i q^{22} +(12157.8 + 472.642i) q^{23} +4641.08 q^{24} -3125.00 q^{25} -39094.0 q^{26} +18499.9 q^{27} -28426.3i q^{28} -10257.7 q^{29} -18901.0i q^{30} +26928.8 q^{31} +46519.4 q^{32} +48664.0i q^{33} -40321.7i q^{34} -20444.5 q^{35} +6033.23 q^{36} -30222.2i q^{37} -101572. i q^{38} -93265.1 q^{39} +9135.01i q^{40} -22485.4 q^{41} -123655. i q^{42} +6304.53i q^{43} -133181. i q^{44} -4339.16i q^{45} +(-144737. - 5626.75i) q^{46} +130395. q^{47} +86029.4 q^{48} -16103.8 q^{49} +37202.8 q^{50} -96194.1i q^{51} +255243. q^{52} -266863. i q^{53} -220239. q^{54} -95785.1 q^{55} +59763.5i q^{56} -242316. i q^{57} +122116. q^{58} +213921. q^{59} +123404. i q^{60} +29476.2i q^{61} -320584. q^{62} -28387.8i q^{63} -359946. q^{64} -183573. i q^{65} -579340. i q^{66} +326092. i q^{67} +263259. i q^{68} +(-345295. - 13423.5i) q^{69} +243390. q^{70} +20211.9 q^{71} -12684.3 q^{72} +533200. q^{73} +359792. i q^{74} +88753.4 q^{75} +663156. i q^{76} -626649. q^{77} +1.11031e6 q^{78} +3360.28i q^{79} +169331. i q^{80} -582002. q^{81} +267686. q^{82} +804627. i q^{83} +807338. i q^{84} +189338. q^{85} -75054.8i q^{86} +291328. q^{87} +279999. i q^{88} -1.39482e6i q^{89} +51657.2i q^{90} -1.20098e6i q^{91} +(944984. + 36736.8i) q^{92} -764807. q^{93} -1.55234e6 q^{94} +476949. q^{95} -1.32120e6 q^{96} +719553. i q^{97} +191714. q^{98} -133001. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9}+O(q^{10}) \) 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9	\( 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9} + 4290 q^{12} - 1440 q^{13} + 65400 q^{16} + 4610 q^{18} + 26600 q^{23} + 14940 q^{24} - 150000 q^{25} + 47594 q^{26} + 16080 q^{27} + 131800 q^{29} - 1392 q^{31} - 225040 q^{32} + 5000 q^{35} + 658786 q^{36} - 236320 q^{39} - 351496 q^{41} + 382692 q^{46} + 395680 q^{47} + 1042550 q^{48} - 637848 q^{49} + 62500 q^{50} + 523890 q^{52} - 241250 q^{54} - 402000 q^{55} - 479130 q^{58} - 466312 q^{59} - 1124330 q^{62} + 837582 q^{64} + 1021060 q^{69} - 396000 q^{70} - 114336 q^{71} - 1960750 q^{72} - 498720 q^{73} + 3610400 q^{77} - 1104610 q^{78} + 972888 q^{81} + 124950 q^{82} - 246000 q^{85} - 2090960 q^{87} + 4913480 q^{92} + 3234320 q^{93} - 5550378 q^{94} - 1664000 q^{95} - 776990 q^{96} + 9993220 q^{98}+O(q^{100}) \) 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9 + 4290 * q^12 - 1440 * q^13 + 65400 * q^16 + 4610 * q^18 + 26600 * q^23 + 14940 * q^24 - 150000 * q^25 + 47594 * q^26 + 16080 * q^27 + 131800 * q^29 - 1392 * q^31 - 225040 * q^32 + 5000 * q^35 + 658786 * q^36 - 236320 * q^39 - 351496 * q^41 + 382692 * q^46 + 395680 * q^47 + 1042550 * q^48 - 637848 * q^49 + 62500 * q^50 + 523890 * q^52 - 241250 * q^54 - 402000 * q^55 - 479130 * q^58 - 466312 * q^59 - 1124330 * q^62 + 837582 * q^64 + 1021060 * q^69 - 396000 * q^70 - 114336 * q^71 - 1960750 * q^72 - 498720 * q^73 + 3610400 * q^77 - 1104610 * q^78 + 972888 * q^81 + 124950 * q^82 - 246000 * q^85 - 2090960 * q^87 + 4913480 * q^92 + 3234320 * q^93 - 5550378 * q^94 - 1664000 * q^95 - 776990 * q^96 + 9993220 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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