LMFDB - Embedded newform 115.7.d.a.91.13

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			91.13
Character	$\chi$	$=$	115.91
Dual form			115.7.d.a.91.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.10890 q^{2} -4.25404 q^{3} +1.75429 q^{4} -55.9017i q^{5} +34.4956 q^{6} +124.794i q^{7} +504.744 q^{8} -710.903 q^{9} +O(q^{10})$	\(q-8.10890 q^{2} -4.25404 q^{3} +1.75429 q^{4} -55.9017i q^{5} +34.4956 q^{6} +124.794i q^{7} +504.744 q^{8} -710.903 q^{9} +453.301i q^{10} -346.155i q^{11} -7.46283 q^{12} -1902.93 q^{13} -1011.94i q^{14} +237.808i q^{15} -4205.20 q^{16} -6961.06i q^{17} +5764.64 q^{18} +3806.82i q^{19} -98.0678i q^{20} -530.879i q^{21} +2806.93i q^{22} +(-8740.95 - 8463.55i) q^{23} -2147.20 q^{24} -3125.00 q^{25} +15430.6 q^{26} +6125.41 q^{27} +218.925i q^{28} -19154.6 q^{29} -1928.36i q^{30} +23102.9 q^{31} +1795.89 q^{32} +1472.56i q^{33} +56446.5i q^{34} +6976.20 q^{35} -1247.13 q^{36} +38375.1i q^{37} -30869.1i q^{38} +8095.13 q^{39} -28216.1i q^{40} +7756.70 q^{41} +4304.85i q^{42} +101329. i q^{43} -607.256i q^{44} +39740.7i q^{45} +(70879.5 + 68630.1i) q^{46} +193627. q^{47} +17889.1 q^{48} +102075. q^{49} +25340.3 q^{50} +29612.6i q^{51} -3338.29 q^{52} +277214. i q^{53} -49670.4 q^{54} -19350.6 q^{55} +62989.1i q^{56} -16194.4i q^{57} +155323. q^{58} +181634. q^{59} +417.185i q^{60} -217213. i q^{61} -187339. q^{62} -88716.4i q^{63} +254570. q^{64} +106377. i q^{65} -11940.8i q^{66} +455833. i q^{67} -12211.7i q^{68} +(37184.4 + 36004.3i) q^{69} -56569.3 q^{70} +200562. q^{71} -358824. q^{72} -555408. q^{73} -311180. i q^{74} +13293.9 q^{75} +6678.26i q^{76} +43198.0 q^{77} -65642.6 q^{78} -79710.6i q^{79} +235078. i q^{80} +492191. q^{81} -62898.3 q^{82} +147726. i q^{83} -931.316i q^{84} -389135. q^{85} -821670. i q^{86} +81484.6 q^{87} -174720. i q^{88} -486500. i q^{89} -322253. i q^{90} -237474. i q^{91} +(-15334.2 - 14847.5i) q^{92} -98280.7 q^{93} -1.57010e6 q^{94} +212808. q^{95} -7639.80 q^{96} -1.66220e6i q^{97} -827720. q^{98} +246082. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.10890			−1.01361			−0.506806	−	0.862060i	$-0.669174\pi$
$2$	−8.10890			−1.01361			−0.506806	+	0.862060i	$0.669174\pi$
$3$	−4.25404			−0.157557			−0.0787786	−	0.996892i	$-0.525102\pi$
$3$	−4.25404			−0.157557			−0.0787786	+	0.996892i	$0.525102\pi$
$4$	1.75429			0.0274108
$5$		−	55.9017i		−	0.447214i
$5$		−	55.9017i		−	0.447214i
$6$	34.4956			0.159702
$7$			124.794i			0.363831i	0.983314	+	0.181915i	$0.0582297\pi$
$7$			124.794i			0.363831i	−0.983314	+	0.181915i	$0.941770\pi$
$8$	504.744			0.985829
$9$	−710.903			−0.975176
$10$			453.301i			0.453301i
$11$		−	346.155i		−	0.260071i	−0.991509	−	0.130036i	$-0.958491\pi$
$11$		−	346.155i		−	0.260071i	0.991509	−	0.130036i	$-0.0415092\pi$
$12$	−7.46283			−0.00431877
$13$	−1902.93			−0.866147			−0.433074	−	0.901359i	$-0.642571\pi$
$13$	−1902.93			−0.866147			−0.433074	+	0.901359i	$0.642571\pi$
$14$		−	1011.94i		−	0.368784i
$15$			237.808i			0.0704617i
$16$	−4205.20			−1.02666
$17$		−	6961.06i		−	1.41687i	−0.705778	−	0.708433i	$-0.749403\pi$
$17$		−	6961.06i		−	1.41687i	0.705778	−	0.708433i	$-0.250597\pi$
$18$	5764.64			0.988451
$19$			3806.82i			0.555010i	0.960724	+	0.277505i	$0.0895076\pi$
$19$			3806.82i			0.555010i	−0.960724	+	0.277505i	$0.910492\pi$
$20$		−	98.0678i		−	0.0122585i
$21$		−	530.879i		−	0.0573242i
$22$			2806.93i			0.263611i
$23$	−8740.95	−	8463.55i	−0.718414	−	0.695615i
$23$	−8740.95	−	8463.55i	−0.718414	−	0.695615i
$24$	−2147.20			−0.155324
$25$	−3125.00			−0.200000
$26$	15430.6			0.877938
$27$	6125.41			0.311203
$28$			218.925i			0.00997289i
$29$	−19154.6			−0.785380			−0.392690	−	0.919671i	$-0.628455\pi$
$29$	−19154.6			−0.785380			−0.392690	+	0.919671i	$0.628455\pi$
$30$		−	1928.36i		−	0.0714209i
$31$	23102.9			0.775499			0.387749	−	0.921765i	$-0.373253\pi$
$31$	23102.9			0.775499			0.387749	+	0.921765i	$0.373253\pi$
$32$	1795.89			0.0548063
$33$			1472.56i			0.0409761i
$34$			56446.5i			1.43615i
$35$	6976.20			0.162710
$36$	−1247.13			−0.0267303
$37$			38375.1i			0.757608i	0.925477	+	0.378804i	$0.123665\pi$
$37$			38375.1i			0.757608i	−0.925477	+	0.378804i	$0.876335\pi$
$38$		−	30869.1i		−	0.562566i
$39$	8095.13			0.136468
$40$		−	28216.1i		−	0.440876i
$41$	7756.70			0.112545			0.0562724	−	0.998415i	$-0.482078\pi$
$41$	7756.70			0.112545			0.0562724	+	0.998415i	$0.482078\pi$
$42$			4304.85i			0.0581045i
$43$			101329.i			1.27447i	0.770669	+	0.637235i	$0.219922\pi$
$43$			101329.i			1.27447i	−0.770669	+	0.637235i	$0.780078\pi$
$44$		−	607.256i		−	0.00712876i
$45$			39740.7i			0.436112i
$46$	70879.5	+	68630.1i	0.728194	+	0.705085i
$47$	193627.			1.86497			0.932486	−	0.361206i	$-0.117635\pi$
$47$	193627.			1.86497			0.932486	+	0.361206i	$0.117635\pi$
$48$	17889.1			0.161758
$49$	102075.			0.867627
$50$	25340.3			0.202723
$51$			29612.6i			0.223237i
$52$	−3338.29			−0.0237418
$53$			277214.i			1.86203i	0.364979	+	0.931016i	$0.381076\pi$
$53$			277214.i			1.86203i	−0.364979	+	0.931016i	$0.618924\pi$
$54$	−49670.4			−0.315439
$55$	−19350.6			−0.116307
$56$			62989.1i			0.358675i
$57$		−	16194.4i		−	0.0874459i
$58$	155323.			0.796071
$59$	181634.			0.884383			0.442192	−	0.896921i	$-0.354201\pi$
$59$	181634.			0.884383			0.442192	+	0.896921i	$0.354201\pi$
$60$			417.185i			0.00193141i
$61$		−	217213.i		−	0.956965i	−0.878097	−	0.478483i	$-0.841187\pi$
$61$		−	217213.i		−	0.956965i	0.878097	−	0.478483i	$-0.158813\pi$
$62$	−187339.			−0.786056
$63$		−	88716.4i		−	0.354799i
$64$	254570.			0.971107
$65$			106377.i			0.387353i
$66$		−	11940.8i		−	0.0415339i
$67$			455833.i			1.51559i	0.652494	+	0.757794i	$0.273723\pi$
$67$			455833.i			1.51559i	−0.652494	+	0.757794i	$0.726277\pi$
$68$		−	12211.7i		−	0.0388374i
$69$	37184.4	+	36004.3i	0.113191	+	0.109599i
$70$	−56569.3			−0.164925
$71$	200562.			0.560367			0.280184	−	0.959946i	$-0.409605\pi$
$71$	200562.			0.560367			0.280184	+	0.959946i	$0.409605\pi$
$72$	−358824.			−0.961356
$73$	−555408.			−1.42772			−0.713861	−	0.700287i	$-0.753055\pi$
$73$	−555408.			−1.42772			−0.713861	+	0.700287i	$0.753055\pi$
$74$		−	311180.i		−	0.767921i
$75$	13293.9			0.0315114
$76$			6678.26i			0.0152133i
$77$	43198.0			0.0946219
$78$	−65642.6			−0.138325
$79$		−	79710.6i		−	0.161672i	−0.996727	−	0.0808360i	$-0.974241\pi$
$79$		−	79710.6i		−	0.161672i	0.996727	−	0.0808360i	$-0.0257590\pi$
$80$			235078.i			0.459136i
$81$	492191.			0.926143
$82$	−62898.3			−0.114077
$83$			147726.i			0.258358i	0.991621	+	0.129179i	$0.0412342\pi$
$83$			147726.i			0.258358i	−0.991621	+	0.129179i	$0.958766\pi$
$84$		−	931.316i		−	0.00157130i
$85$	−389135.			−0.633641
$86$		−	821670.i		−	1.29182i
$87$	81484.6			0.123742
$88$		−	174720.i		−	0.256386i
$89$		−	486500.i		−	0.690102i	−0.938584	−	0.345051i	$-0.887862\pi$
$89$		−	486500.i		−	0.690102i	0.938584	−	0.345051i	$-0.112138\pi$
$90$		−	322253.i		−	0.442049i
$91$		−	237474.i		−	0.315131i
$92$	−15334.2	−	14847.5i	−0.0196923	−	0.0190674i
$93$	−98280.7			−0.122185
$94$	−1.57010e6			−1.89036
$95$	212808.			0.248208
$96$	−7639.80			−0.00863512
$97$		−	1.66220e6i		−	1.82124i	−0.413243	−	0.910621i	$-0.635604\pi$
$97$		−	1.66220e6i		−	1.82124i	0.413243	−	0.910621i	$-0.364396\pi$
$98$	−827720.			−0.879438
$99$			246082.i			0.253615i
$100$	−5482.16			−0.00548216
$101$	−179312.			−0.174039			−0.0870194	−	0.996207i	$-0.527734\pi$
$101$	−179312.			−0.174039			−0.0870194	+	0.996207i	$0.527734\pi$
$102$		−	240126.i		−	0.226276i
$103$			934664.i			0.855350i	0.903933	+	0.427675i	$0.140667\pi$
$103$			934664.i			0.855350i	−0.903933	+	0.427675i	$0.859333\pi$
$104$	−960491.			−0.853873
$105$	−29677.0			−0.0256361
$106$		−	2.24790e6i		−	1.88738i
$107$		−	682153.i		−	0.556840i	−0.960459	−	0.278420i	$-0.910189\pi$
$107$		−	682153.i		−	0.556840i	0.960459	−	0.278420i	$-0.0898107\pi$
$108$	10745.7			0.00853032
$109$			1.56595e6i			1.20920i	0.796529	+	0.604600i	$0.206667\pi$
$109$			1.56595e6i			1.20920i	−0.796529	+	0.604600i	$0.793333\pi$
$110$	156912.			0.117891
$111$		−	163249.i		−	0.119367i
$112$		−	524783.i		−	0.373530i
$113$			609866.i			0.422667i	0.977414	+	0.211334i	$0.0677807\pi$
$113$			609866.i			0.422667i	−0.977414	+	0.211334i	$0.932219\pi$
$114$			131319.i			0.0886363i
$115$	−473127.	+	488634.i	−0.311089	+	0.321285i
$116$	−33602.8			−0.0215279
$117$	1.35280e6			0.844646
$118$	−1.47285e6			−0.896422
$119$	868698.			0.515499
$120$			120032.i			0.0694632i
$121$	1.65174e6			0.932363
$122$			1.76136e6i			0.969992i
$123$	−32997.3			−0.0177322
$124$	40529.2			0.0212570
$125$			174693.i			0.0894427i
$126$			719393.i			0.359629i
$127$	−1.25305e6			−0.611728			−0.305864	−	0.952075i	$-0.598945\pi$
$127$	−1.25305e6			−0.611728			−0.305864	+	0.952075i	$0.598945\pi$
$128$	−2.17922e6			−1.03913
$129$		−	431059.i		−	0.200802i
$130$		−	862599.i		−	0.392626i
$131$	1.82833e6			0.813282			0.406641	−	0.913588i	$-0.366700\pi$
$131$	1.82833e6			0.813282			0.406641	+	0.913588i	$0.366700\pi$
$132$			2583.29i			0.00112319i
$133$	−475068.			−0.201930
$134$		−	3.69630e6i		−	1.53622i
$135$		−	342421.i		−	0.139174i
$136$		−	3.51355e6i		−	1.39679i
$137$			3.36730e6i			1.30954i	0.755827	+	0.654771i	$0.227235\pi$
$137$			3.36730e6i			1.30954i	−0.755827	+	0.654771i	$0.772765\pi$
$138$	−301524.	−	291955.i	−0.114732	−	0.111091i
$139$	266955.			0.0994017			0.0497009	−	0.998764i	$-0.484173\pi$
$139$	266955.			0.0994017			0.0497009	+	0.998764i	$0.484173\pi$
$140$	12238.3			0.00446001
$141$	−823698.			−0.293840
$142$	−1.62633e6			−0.567995
$143$			658707.i			0.225260i
$144$	2.98949e6			1.00117
$145$			1.07078e6i			0.351233i
$146$	4.50375e6			1.44716
$147$	−434233.			−0.136701
$148$			67321.1i			0.0207666i
$149$			5.97281e6i			1.80559i	0.430068	+	0.902796i	$0.358489\pi$
$149$			5.97281e6i			1.80559i	−0.430068	+	0.902796i	$0.641511\pi$
$150$	−107799.			−0.0319404
$151$	4.75312e6			1.38054			0.690269	−	0.723553i	$-0.257492\pi$
$151$	4.75312e6			1.38054			0.690269	+	0.723553i	$0.257492\pi$
$152$			1.92147e6i			0.547145i
$153$			4.94864e6i			1.38169i
$154$	−350289.			−0.0959100
$155$		−	1.29149e6i		−	0.346814i
$156$	14201.2			0.00374069
$157$			374149.i			0.0966820i	0.998831	+	0.0483410i	$0.0153934\pi$
$157$			374149.i			0.0966820i	−0.998831	+	0.0483410i	$0.984607\pi$
$158$			646365.i			0.163873i
$159$		−	1.17928e6i		−	0.293376i
$160$		−	100393.i		−	0.0245101i
$161$	1.05620e6	−	1.09082e6i	0.253086	−	0.261381i
$162$	−3.99113e6			−0.938751
$163$	−2.64317e6			−0.610326			−0.305163	−	0.952300i	$-0.598711\pi$
$163$	−2.64317e6			−0.610326			−0.305163	+	0.952300i	$0.598711\pi$
$164$	13607.5			0.00308494
$165$	82318.4			0.0183251
$166$		−	1.19789e6i		−	0.261875i
$167$	3.73270e6			0.801446			0.400723	−	0.916199i	$-0.368759\pi$
$167$	3.73270e6			0.801446			0.400723	+	0.916199i	$0.368759\pi$
$168$		−	267958.i		−	0.0565118i
$169$	−1.20568e6			−0.249789
$170$	3.15546e6			0.642267
$171$		−	2.70628e6i		−	0.541233i
$172$			177761.i			0.0349342i
$173$	5.53638e6			1.06927			0.534636	−	0.845083i	$-0.320449\pi$
$173$	5.53638e6			1.06927			0.534636	+	0.845083i	$0.320449\pi$
$174$	−660751.			−0.125427
$175$		−	389981.i		−	0.0727662i
$176$			1.45565e6i			0.267004i
$177$	−772678.			−0.139341
$178$			3.94498e6i			0.699496i
$179$	−2.14164e6			−0.373412			−0.186706	−	0.982416i	$-0.559781\pi$
$179$	−2.14164e6			−0.373412			−0.186706	+	0.982416i	$0.559781\pi$
$180$			69716.7i			0.0119542i
$181$		−	5.49835e6i		−	0.927249i	−0.886032	−	0.463624i	$-0.846549\pi$
$181$		−	5.49835e6i		−	0.927249i	0.886032	−	0.463624i	$-0.153451\pi$
$182$			1.92565e6i			0.319421i
$183$			924033.i			0.150777i
$184$	−4.41194e6	−	4.27193e6i	−0.708234	−	0.685758i
$185$	2.14523e6			0.338813
$186$	796948.			0.123849
$187$	−2.40960e6			−0.368486
$188$	339678.			0.0511204
$189$			764414.i			0.113225i
$190$	−1.72564e6			−0.251587
$191$			410531.i			0.0589177i	0.999566	+	0.0294589i	$0.00937841\pi$
$191$			410531.i			0.0589177i	−0.999566	+	0.0294589i	$0.990622\pi$
$192$	−1.08295e6			−0.153005
$193$	−370493.			−0.0515357			−0.0257678	−	0.999668i	$-0.508203\pi$
$193$	−370493.			−0.0515357			−0.0257678	+	0.999668i	$0.508203\pi$
$194$			1.34786e7i			1.84603i
$195$		−	452531.i		−	0.0610302i
$196$	179070.			0.0237823
$197$	−8.53751e6			−1.11669			−0.558345	−	0.829609i	$-0.688563\pi$
$197$	−8.53751e6			−1.11669			−0.558345	+	0.829609i	$0.688563\pi$
$198$		−	1.99546e6i		−	0.257067i
$199$		−	1.01982e6i		−	0.129408i	−0.997904	−	0.0647042i	$-0.979390\pi$
$199$		−	1.01982e6i		−	0.129408i	0.997904	−	0.0647042i	$-0.0206104\pi$
$200$	−1.57733e6			−0.197166
$201$		−	1.93913e6i		−	0.238792i
$202$	1.45403e6			0.176408
$203$		−	2.39038e6i		−	0.285745i
$204$			51949.2i			0.00611911i
$205$		−	433613.i		−	0.0503316i
$206$		−	7.57909e6i		−	0.866993i
$207$	6.21397e6	+	6.01677e6i	0.700580	+	0.678347i
$208$	8.00218e6			0.889238
$209$	1.31775e6			0.144342
$210$	240648.			0.0259851
$211$	1.32426e7			1.40970			0.704849	−	0.709358i	$-0.251015\pi$
$211$	1.32426e7			1.40970			0.704849	+	0.709358i	$0.251015\pi$
$212$			486313.i			0.0510398i
$213$	−853197.			−0.0882898
$214$			5.53151e6i			0.564420i
$215$	5.66448e6			0.569961
$216$	3.09177e6			0.306793
$217$			2.88310e6i			0.282150i
$218$		−	1.26981e7i		−	1.22566i
$219$	2.36273e6			0.224948
$220$	−33946.6			−0.00318808
$221$			1.32464e7i			1.22721i
$222$			1.32377e6i			0.120992i
$223$	−1.49941e7			−1.35209			−0.676047	−	0.736858i	$-0.736308\pi$
$223$	−1.49941e7			−1.35209			−0.676047	+	0.736858i	$0.736308\pi$
$224$			224117.i			0.0199402i
$225$	2.22157e6			0.195035
$226$		−	4.94534e6i		−	0.428421i
$227$			1.57821e7i			1.34923i	0.738169	+	0.674616i	$0.235691\pi$
$227$			1.57821e7i			1.34923i	−0.738169	+	0.674616i	$0.764309\pi$
$228$		−	28409.6i		−	0.00239696i
$229$			7.35801e6i			0.612708i	0.951918	+	0.306354i	$0.0991092\pi$
$229$			7.35801e6i			0.612708i	−0.951918	+	0.306354i	$0.900891\pi$
$230$	3.83654e6	−	3.96228e6i	0.315323	−	0.325658i
$231$	−183766.			−0.0149084
$232$	−9.66819e6			−0.774250
$233$	2.35303e7			1.86020			0.930100	−	0.367307i	$-0.119720\pi$
$233$	2.35303e7			1.86020			0.930100	+	0.367307i	$0.119720\pi$
$234$	−1.09697e7			−0.856144
$235$		−	1.08241e7i		−	0.834041i
$236$	318638.			0.0242416
$237$			339092.i			0.0254726i
$238$	−7.04419e6			−0.522517
$239$	−1.51325e7			−1.10845			−0.554226	−	0.832366i	$-0.686986\pi$
$239$	−1.51325e7			−1.10845			−0.554226	+	0.832366i	$0.686986\pi$
$240$		−	1.00003e6i		−	0.0723402i
$241$		−	2.19013e7i		−	1.56465i	−0.622868	−	0.782327i	$-0.714032\pi$
$241$		−	2.19013e7i		−	1.56465i	0.622868	−	0.782327i	$-0.285968\pi$
$242$	−1.33938e7			−0.945055
$243$	−6.55922e6			−0.457124
$244$		−	381055.i		−	0.0262312i
$245$		−	5.70619e6i		−	0.388015i
$246$	267572.			0.0179736
$247$		−	7.24409e6i		−	0.480721i
$248$	1.16611e7			0.764509
$249$		−	628432.i		−	0.0407062i
$250$		−	1.41657e6i		−	0.0906603i
$251$			9.95887e6i			0.629780i	0.949128	+	0.314890i	$0.101968\pi$
$251$			9.95887e6i			0.629780i	−0.949128	+	0.314890i	$0.898032\pi$
$252$		−	155634.i		−	0.00972532i
$253$	−2.92970e6	+	3.02572e6i	−0.180909	+	0.186839i
$254$	1.01609e7			0.620055
$255$	1.65540e6			0.0998347
$256$	1.37860e6			0.0821712
$257$	−7.39852e6			−0.435858			−0.217929	−	0.975965i	$-0.569930\pi$
$257$	−7.39852e6			−0.435858			−0.217929	+	0.975965i	$0.569930\pi$
$258$			3.49542e6i			0.203535i
$259$	−4.78899e6			−0.275641
$260$			186616.i			0.0106176i
$261$	1.36171e7			0.765883
$262$	−1.48258e7			−0.824353
$263$			3.89170e6i			0.213930i	0.994263	+	0.106965i	$0.0341133\pi$
$263$			3.89170e6i			0.213930i	−0.994263	+	0.106965i	$0.965887\pi$
$264$			743265.i			0.0403954i
$265$	1.54967e7			0.832726
$266$	3.85228e6			0.204679
$267$			2.06959e6i			0.108730i
$268$			799663.i			0.0415435i
$269$	1.29120e7			0.663343			0.331672	−	0.943395i	$-0.392387\pi$
$269$	1.29120e7			0.663343			0.331672	+	0.943395i	$0.392387\pi$
$270$			2.77666e6i			0.141069i
$271$	−3.31473e7			−1.66548			−0.832741	−	0.553663i	$-0.813230\pi$
$271$	−3.31473e7			−1.66548			−0.832741	+	0.553663i	$0.813230\pi$
$272$			2.92726e7i			1.45464i
$273$			1.01022e6i			0.0496512i
$274$		−	2.73051e7i		−	1.32737i
$275$			1.08173e6i			0.0520142i
$276$	65232.2	+	63162.0i	0.00310266	+	0.00300420i
$277$	−1.49639e7			−0.704055			−0.352027	−	0.935990i	$-0.614508\pi$
$277$	−1.49639e7			−0.704055			−0.352027	+	0.935990i	$0.614508\pi$
$278$	−2.16471e6			−0.100755
$279$	−1.64239e7			−0.756248
$280$	3.52120e6			0.160404
$281$		−	2.08219e7i		−	0.938427i	−0.883085	−	0.469214i	$-0.844537\pi$
$281$		−	2.08219e7i		−	0.938427i	0.883085	−	0.469214i	$-0.155463\pi$
$282$	6.67928e6			0.297840
$283$		−	3.65386e7i		−	1.61210i	−0.591846	−	0.806051i	$-0.701601\pi$
$283$		−	3.65386e7i		−	1.61210i	0.591846	−	0.806051i	$-0.298399\pi$
$284$	351843.			0.0153601
$285$	−905292.			−0.0391070
$286$		−	5.34139e6i		−	0.228326i
$287$			967989.i			0.0409473i
$288$	−1.27671e6			−0.0534457
$289$	−2.43188e7			−1.00751
$290$		−	8.68282e6i		−	0.356014i
$291$			7.07106e6i			0.286950i
$292$	−974348.			−0.0391350
$293$		−	2.35946e7i		−	0.938016i	−0.883194	−	0.469008i	$-0.844612\pi$
$293$		−	2.35946e7i		−	0.938016i	0.883194	−	0.469008i	$-0.155388\pi$
$294$	3.52116e6			0.138562
$295$		−	1.01536e7i		−	0.395508i
$296$			1.93696e7i			0.746872i
$297$		−	2.12034e6i		−	0.0809349i
$298$		−	4.84329e7i		−	1.83017i
$299$	1.66334e7	+	1.61055e7i	0.622253	+	0.602505i
$300$	23321.3			0.000863753
$301$	−1.26453e7			−0.463692
$302$	−3.85426e7			−1.39933
$303$	762803.			0.0274211
$304$		−	1.60084e7i		−	0.569807i
$305$	−1.21426e7			−0.427968
$306$		−	4.01280e7i		−	1.40050i
$307$	−4.02487e7			−1.39103			−0.695515	−	0.718511i	$-0.744824\pi$
$307$	−4.02487e7			−1.39103			−0.695515	+	0.718511i	$0.744824\pi$
$308$	75781.9			0.00259366
$309$		−	3.97610e6i		−	0.134766i
$310$			1.04726e7i			0.351535i
$311$	2.18139e7			0.725192			0.362596	−	0.931946i	$-0.381890\pi$
$311$	2.18139e7			0.725192			0.362596	+	0.931946i	$0.381890\pi$
$312$	4.08597e6			0.134534
$313$			5.20853e7i			1.69856i	0.527939	+	0.849282i	$0.322965\pi$
$313$			5.20853e7i			1.69856i	−0.527939	+	0.849282i	$0.677035\pi$
$314$		−	3.03394e6i		−	0.0979981i
$315$	−4.95940e6			−0.158671
$316$		−	139835.i		−	0.00443155i
$317$	1.02997e7			0.323329			0.161665	−	0.986846i	$-0.448314\pi$
$317$	1.02997e7			0.323329			0.161665	+	0.986846i	$0.448314\pi$
$318$			9.56266e6i			0.297370i
$319$			6.63046e6i			0.204255i
$320$		−	1.42309e7i		−	0.434292i
$321$			2.90191e6i			0.0877341i
$322$	−8.56463e6	+	8.84533e6i	−0.256532	+	0.264939i
$323$	2.64995e7			0.786375
$324$	863445.			0.0253863
$325$	5.94664e6			0.173229
$326$	2.14332e7			0.618634
$327$		−	6.66162e6i		−	0.190518i
$328$	3.91515e6			0.110950
$329$			2.41635e7i			0.678535i
$330$	−667512.			−0.0185745
$331$	5.23270e7			1.44292			0.721459	−	0.692457i	$-0.243472\pi$
$331$	5.23270e7			1.44292			0.721459	+	0.692457i	$0.243472\pi$
$332$			259154.i			0.00708180i
$333$		−	2.72810e7i		−	0.738801i
$334$	−3.02681e7			−0.812356
$335$	2.54818e7			0.677791
$336$			2.23245e6i			0.0588524i
$337$			6.87676e7i			1.79678i	0.439201	+	0.898389i	$0.355262\pi$
$337$			6.87676e7i			1.79678i	−0.439201	+	0.898389i	$0.644738\pi$
$338$	9.77676e6			0.253189
$339$		−	2.59439e6i		−	0.0665943i
$340$	−682656.			−0.0173686
$341$		−	7.99717e6i		−	0.201685i
$342$			2.19449e7i			0.548600i
$343$			2.74203e7i			0.679500i
$344$			5.11454e7i			1.25641i
$345$	2.01270e6	−	2.07867e6i	0.0490142	−	0.0506207i
$346$	−4.48940e7			−1.08383
$347$	5.51640e7			1.32028			0.660142	−	0.751141i	$-0.270496\pi$
$347$	5.51640e7			1.32028			0.660142	+	0.751141i	$0.270496\pi$
$348$	142948.			0.00339187
$349$	1.26824e7			0.298349			0.149175	−	0.988811i	$-0.452338\pi$
$349$	1.26824e7			0.298349			0.149175	+	0.988811i	$0.452338\pi$
$350$			3.16232e6i			0.0737567i
$351$	−1.16562e7			−0.269548
$352$		−	621656.i		−	0.0142535i
$353$	990314.			0.0225138			0.0112569	−	0.999937i	$-0.496417\pi$
$353$	990314.			0.0225138			0.0112569	+	0.999937i	$0.496417\pi$
$354$	6.26557e6			0.141238
$355$		−	1.12117e7i		−	0.250604i
$356$		−	853463.i		−	0.0189162i
$357$	−3.69548e6			−0.0812206
$358$	1.73664e7			0.378495
$359$			1.79559e7i			0.388083i	0.980993	+	0.194042i	$0.0621597\pi$
$359$			1.79559e7i			0.388083i	−0.980993	+	0.194042i	$0.937840\pi$
$360$			2.00589e7i			0.429932i
$361$	3.25540e7			0.691963
$362$			4.45855e7i			0.939871i
$363$	−7.02656e6			−0.146900
$364$		−	416598.i		−	0.00863799i
$365$			3.10483e7i			0.638497i
$366$		−	7.49289e6i		−	0.152829i
$367$		−	8.76120e7i		−	1.77241i	−0.463289	−	0.886207i	$-0.653331\pi$
$367$		−	8.76120e7i		−	1.77241i	0.463289	−	0.886207i	$-0.346669\pi$
$368$	3.67574e7	+	3.55909e7i	0.737567	+	0.714160i
$369$	−5.51426e6			−0.109751
$370$	−1.73955e7			−0.343425
$371$	−3.45946e7			−0.677465
$372$	−172413.			−0.00334920
$373$			2.25019e6i			0.0433603i	0.999765	+	0.0216801i	$0.00690154\pi$
$373$			2.25019e6i			0.0433603i	−0.999765	+	0.0216801i	$0.993098\pi$
$374$	1.95392e7			0.373502
$375$		−	743151.i		−	0.0140923i
$376$	9.77322e7			1.83854
$377$	3.64498e7			0.680255
$378$		−	6.19856e6i		−	0.114767i
$379$			2.96678e7i			0.544963i	0.962161	+	0.272482i	$0.0878444\pi$
$379$			2.96678e7i			0.544963i	−0.962161	+	0.272482i	$0.912156\pi$
$380$	373326.			0.00680358
$381$	5.33054e6			0.0963821
$382$		−	3.32896e6i		−	0.0597198i
$383$			1.03235e8i			1.83751i	0.394830	+	0.918754i	$0.370804\pi$
$383$			1.03235e8i			1.83751i	−0.394830	+	0.918754i	$0.629196\pi$
$384$	9.27049e6			0.163723
$385$		−	2.41484e6i		−	0.0423162i
$386$	3.00429e6			0.0522372
$387$		−	7.20353e7i		−	1.24283i
$388$		−	2.91598e6i		−	0.0499217i
$389$		−	3.64900e7i		−	0.619905i	−0.950752	−	0.309952i	$-0.899687\pi$
$389$		−	3.64900e7i		−	0.619905i	0.950752	−	0.309952i	$-0.100313\pi$
$390$			3.66953e6i			0.0618610i
$391$	−5.89153e7	+	6.08463e7i	−0.985593	+	1.01790i
$392$	5.15220e7			0.855332
$393$	−7.77780e6			−0.128138
$394$	6.92298e7			1.13189
$395$	−4.45596e6			−0.0723019
$396$			431700.i			0.00695179i
$397$	9.14361e7			1.46132			0.730662	−	0.682740i	$-0.239212\pi$
$397$	9.14361e7			1.46132			0.730662	+	0.682740i	$0.239212\pi$
$398$			8.26958e6i			0.131170i
$399$	2.02096e6			0.0318155
$400$	1.31412e7			0.205332
$401$			6.42295e7i			0.996097i	0.867149	+	0.498049i	$0.165950\pi$
$401$			6.42295e7i			0.996097i	−0.867149	+	0.498049i	$0.834050\pi$
$402$			1.57242e7i			0.242042i
$403$	−4.39631e7			−0.671696
$404$	−314566.			−0.00477054
$405$		−	2.75143e7i		−	0.414184i
$406$			1.93834e7i			0.289635i
$407$	1.32837e7			0.197032
$408$			1.49468e7i			0.220074i
$409$	3.94371e6			0.0576415			0.0288208	−	0.999585i	$-0.490825\pi$
$409$	3.94371e6			0.0576415			0.0288208	+	0.999585i	$0.490825\pi$
$410$			3.51612e6i			0.0510167i
$411$		−	1.43246e7i		−	0.206328i
$412$			1.63967e6i			0.0234458i
$413$			2.26668e7i			0.321766i
$414$	−5.03885e7	−	4.87894e7i	−0.710117	−	0.687581i
$415$	8.25812e6			0.115541
$416$	−3.41745e6			−0.0474703
$417$	−1.13564e6			−0.0156615
$418$	−1.06855e7			−0.146307
$419$		−	9.62017e7i		−	1.30780i	−0.756582	−	0.653899i	$-0.773132\pi$
$419$		−	9.62017e7i		−	1.30780i	0.756582	−	0.653899i	$-0.226868\pi$
$420$	−52062.2			−0.000702707
$421$		−	2.76772e6i		−	0.0370916i	−0.999828	−	0.0185458i	$-0.994096\pi$
$421$		−	2.76772e6i		−	0.0370916i	0.999828	−	0.0185458i	$-0.00590365\pi$
$422$	−1.07383e8			−1.42889
$423$	−1.37650e8			−1.81868
$424$			1.39922e8i			1.83564i
$425$			2.17533e7i			0.283373i
$426$	6.91849e6			0.0894917
$427$	2.71069e7			0.348173
$428$		−	1.19669e6i		−	0.0152634i
$429$		−	2.80217e6i		−	0.0354913i
$430$	−4.59327e7			−0.577719
$431$		−	1.04474e8i		−	1.30490i	−0.757832	−	0.652450i	$-0.773741\pi$
$431$		−	1.04474e8i		−	1.30490i	0.757832	−	0.652450i	$-0.226259\pi$
$432$	−2.57586e7			−0.319500
$433$		−	7.30703e7i		−	0.900071i	−0.893011	−	0.450036i	$-0.851411\pi$
$433$		−	7.30703e7i		−	0.900071i	0.893011	−	0.450036i	$-0.148589\pi$
$434$		−	2.33788e7i		−	0.285991i
$435$		−	4.55513e6i		−	0.0553392i
$436$			2.74713e6i			0.0331451i
$437$	3.22192e7	−	3.32752e7i	0.386074	−	0.398728i
$438$	−1.91592e7			−0.228010
$439$	5.10374e7			0.603247			0.301624	−	0.953427i	$-0.402471\pi$
$439$	5.10374e7			0.603247			0.301624	+	0.953427i	$0.402471\pi$
$440$	−9.76712e6			−0.114659
$441$	−7.25658e7			−0.846089
$442$		−	1.07414e8i		−	1.24392i
$443$	−1.33803e8			−1.53906			−0.769528	−	0.638613i	$-0.779509\pi$
$443$	−1.33803e8			−1.53906			−0.769528	+	0.638613i	$0.779509\pi$
$444$		−	286387.i		−	0.00327193i
$445$	−2.71962e7			−0.308623
$446$	1.21586e8			1.37050
$447$		−	2.54086e7i		−	0.284484i
$448$			3.17688e7i			0.353319i
$449$	−7.91961e7			−0.874913			−0.437457	−	0.899240i	$-0.644121\pi$
$449$	−7.91961e7			−0.874913			−0.437457	+	0.899240i	$0.644121\pi$
$450$	−1.80145e7			−0.197690
$451$		−	2.68502e6i		−	0.0292696i
$452$			1.06988e6i			0.0115856i
$453$	−2.02200e7			−0.217514
$454$		−	1.27975e8i		−	1.36760i
$455$	−1.32752e7			−0.140931
$456$		−	8.17401e6i		−	0.0862067i
$457$		−	6.49001e6i		−	0.0679980i	−0.999422	−	0.0339990i	$-0.989176\pi$
$457$		−	6.49001e6i		−	0.0679980i	0.999422	−	0.0339990i	$-0.0108243\pi$
$458$		−	5.96654e7i		−	0.621049i
$459$		−	4.26393e7i		−	0.440933i
$460$	−830002.	+	857206.i	−0.00852719	+	0.00880667i
$461$	1.61825e7			0.165174			0.0825872	−	0.996584i	$-0.473682\pi$
$461$	1.61825e7			0.165174			0.0825872	+	0.996584i	$0.473682\pi$
$462$	1.49014e6			0.0151113
$463$	−3.26864e7			−0.329325			−0.164662	−	0.986350i	$-0.552653\pi$
$463$	−3.26864e7			−0.329325			−0.164662	+	0.986350i	$0.552653\pi$
$464$	8.05490e7			0.806318
$465$			5.49406e6i			0.0546430i
$466$	−1.90805e8			−1.88552
$467$		−	9.52131e6i		−	0.0934859i	−0.998907	−	0.0467429i	$-0.985116\pi$
$467$		−	9.52131e6i		−	0.0934859i	0.998907	−	0.0467429i	$-0.0148842\pi$
$468$	2.37320e6			0.0231524
$469$	−5.68852e7			−0.551418
$470$			8.77714e7i			0.845395i
$471$		−	1.59165e6i		−	0.0152329i
$472$	9.16786e7			0.871851
$473$	3.50756e7			0.331453
$474$		−	2.74966e6i		−	0.0258193i
$475$		−	1.18963e7i		−	0.111002i
$476$	1.52395e6			0.0141302
$477$		−	1.97072e8i		−	1.81581i
$478$	1.22708e8			1.12354
$479$		−	1.07217e8i		−	0.975568i	−0.872964	−	0.487784i	$-0.837805\pi$
$479$		−	1.07217e8i		−	0.975568i	0.872964	−	0.487784i	$-0.162195\pi$
$480$			427078.i			0.00386174i
$481$		−	7.30250e7i		−	0.656200i
$482$			1.77595e8i			1.58595i
$483$	−4.49312e6	+	4.64039e6i	−0.0398756	+	0.0411825i
$484$	2.89763e6			0.0255568
$485$	−9.29197e7			−0.814484
$486$	5.31881e7			0.463346
$487$	−9.42621e7			−0.816113			−0.408056	−	0.912957i	$-0.633793\pi$
$487$	−9.42621e7			−0.816113			−0.408056	+	0.912957i	$0.633793\pi$
$488$		−	1.09637e8i		−	0.943404i
$489$	1.12441e7			0.0961612
$490$			4.62709e7i			0.393297i
$491$	−8.40480e7			−0.710040			−0.355020	−	0.934859i	$-0.615526\pi$
$491$	−8.40480e7			−0.710040			−0.355020	+	0.934859i	$0.615526\pi$
$492$	−57886.9			−0.000486055
$493$			1.33337e8i			1.11278i
$494$			5.87416e7i			0.487265i
$495$	1.37564e7			0.113420
$496$	−9.71522e7			−0.796173
$497$			2.50289e7i			0.203879i
$498$			5.09589e6i			0.0412603i
$499$	−4.98643e7			−0.401317			−0.200659	−	0.979661i	$-0.564308\pi$
$499$	−4.98643e7			−0.401317			−0.200659	+	0.979661i	$0.564308\pi$
$500$			306462.i			0.00245170i
$501$	−1.58791e7			−0.126274
$502$		−	8.07555e7i		−	0.638353i
$503$			7.85187e6i			0.0616977i	0.999524	+	0.0308489i	$0.00982105\pi$
$503$			7.85187e6i			0.0616977i	−0.999524	+	0.0308489i	$0.990179\pi$
$504$		−	4.47791e7i		−	0.349771i
$505$			1.00239e7i			0.0778325i
$506$	2.37566e7	−	2.45353e7i	0.183372	−	0.189382i
$507$	5.12902e6			0.0393560
$508$	−2.19822e6			−0.0167679
$509$	6.27692e7			0.475985			0.237992	−	0.971267i	$-0.423511\pi$
$509$	6.27692e7			0.475985			0.237992	+	0.971267i	$0.423511\pi$
$510$	−1.34235e7			−0.101194
$511$		−	6.93116e7i		−	0.519450i
$512$	1.28291e8			0.955843
$513$			2.33183e7i			0.172721i
$514$	5.99938e7			0.441791
$515$	5.22493e7			0.382524
$516$		−	756203.i		−	0.00550414i
$517$		−	6.70249e7i		−	0.485025i
$518$	3.88334e7			0.279393
$519$	−2.35520e7			−0.168471
$520$			5.36931e7i			0.381864i
$521$			2.24178e8i			1.58518i	0.609752	+	0.792592i	$0.291269\pi$
$521$			2.24178e8i			1.58518i	−0.609752	+	0.792592i	$0.708731\pi$
$522$	−1.10420e8			−0.776309
$523$		−	3.20476e7i		−	0.224022i	−0.993707	−	0.112011i	$-0.964271\pi$
$523$		−	3.20476e7i		−	0.224022i	0.993707	−	0.112011i	$-0.0357292\pi$
$524$	3.20743e6			0.0222927
$525$			1.65900e6i			0.0114648i
$526$		−	3.15574e7i		−	0.216842i
$527$		−	1.60821e8i		−	1.09878i
$528$		−	6.19239e6i		−	0.0420685i
$529$	4.77247e6	+	1.47959e8i	0.0322386	+	0.999480i
$530$	−1.25661e8			−0.844062
$531$	−1.29124e8			−0.862429
$532$	−833407.			−0.00553506
$533$	−1.47604e7			−0.0974804
$534$		−	1.67821e7i		−	0.110211i
$535$	−3.81335e7			−0.249026
$536$			2.30079e8i			1.49411i
$537$	9.11065e6			0.0588337
$538$	−1.04702e8			−0.672373
$539$		−	3.53339e7i		−	0.225645i
$540$		−	600706.i		−	0.00381488i
$541$	4.11533e7			0.259904			0.129952	−	0.991520i	$-0.458518\pi$
$541$	4.11533e7			0.259904			0.129952	+	0.991520i	$0.458518\pi$
$542$	2.68788e8			1.68815
$543$			2.33902e7i			0.146095i
$544$		−	1.25013e7i		−	0.0776531i
$545$	8.75393e7			0.540771
$546$		−	8.19180e6i		−	0.0503271i
$547$	1.69031e8			1.03277			0.516386	−	0.856356i	$-0.327277\pi$
$547$	1.69031e8			1.03277			0.516386	+	0.856356i	$0.327277\pi$
$548$			5.90722e6i			0.0358956i
$549$			1.54417e8i			0.933209i
$550$		−	8.77167e6i		−	0.0527223i
$551$		−	7.29182e7i		−	0.435894i
$552$	1.87686e7	+	1.81730e7i	0.111587	+	0.108046i
$553$	9.94740e6			0.0588212
$554$	1.21341e8			0.713639
$555$	−9.12592e6			−0.0533824
$556$	468317.			0.00272468
$557$		−	1.98497e8i		−	1.14865i	−0.818626	−	0.574327i	$-0.805264\pi$
$557$		−	1.98497e8i		−	1.14865i	0.818626	−	0.574327i	$-0.194736\pi$
$558$	1.33180e8			0.766542
$559$		−	1.92822e8i		−	1.10388i
$560$	−2.93363e7			−0.167048
$561$	1.02506e7			0.0580576
$562$			1.68842e8i			0.951202i
$563$			1.42948e8i			0.801035i	0.916289	+	0.400518i	$0.131170\pi$
$563$			1.42948e8i			0.801035i	−0.916289	+	0.400518i	$0.868830\pi$
$564$	−1.44501e6			−0.00805438
$565$	3.40925e7			0.189023
$566$			2.96288e8i			1.63405i
$567$			6.14224e7i			0.336960i
$568$	1.01232e8			0.552426
$569$			4.67711e7i			0.253887i	0.991910	+	0.126944i	$0.0405167\pi$
$569$			4.67711e7i			0.253887i	−0.991910	+	0.126944i	$0.959483\pi$
$570$	7.34093e6			0.0396393
$571$			1.86472e8i			1.00163i	0.865555	+	0.500814i	$0.166966\pi$
$571$			1.86472e8i			1.00163i	−0.865555	+	0.500814i	$0.833034\pi$
$572$			1.15556e6i			0.00617455i
$573$		−	1.74642e6i		−	0.00928291i
$574$		−	7.84933e6i		−	0.0415047i
$575$	2.73155e7	+	2.64486e7i	0.143683	+	0.139123i
$576$	−1.80975e8			−0.947000
$577$	2.71762e8			1.41469			0.707345	−	0.706868i	$-0.249893\pi$
$577$	2.71762e8			1.41469			0.707345	+	0.706868i	$0.249893\pi$
$578$	1.97198e8			1.02122
$579$	1.57609e6			0.00811981
$580$			1.87845e6i			0.00962756i
$581$	−1.84353e7			−0.0939986
$582$		−	5.73386e7i		−	0.290856i
$583$	9.59588e7			0.484261
$584$	−2.80339e8			−1.40749
$585$		−	7.56236e7i		−	0.377737i
$586$			1.91326e8i			0.950785i
$587$	−1.05279e8			−0.520510			−0.260255	−	0.965540i	$-0.583807\pi$
$587$	−1.05279e8			−0.520510			−0.260255	+	0.965540i	$0.583807\pi$
$588$	−761772.			−0.00374708
$589$			8.79485e7i			0.430410i
$590$			8.23348e7i			0.400892i
$591$	3.63189e7			0.175942
$592$		−	1.61375e8i		−	0.777806i
$593$	−2.10408e8			−1.00902			−0.504508	−	0.863407i	$-0.668326\pi$
$593$	−2.10408e8			−1.00902			−0.504508	+	0.863407i	$0.668326\pi$
$594$			1.71936e7i			0.0820367i
$595$		−	4.85617e7i		−	0.230538i
$596$			1.04780e7i			0.0494927i
$597$			4.33834e6i			0.0203892i
$598$	−1.34878e8	−	1.30598e8i	−0.630723	−	0.610707i
$599$	2.48897e8			1.15808			0.579040	−	0.815299i	$-0.303428\pi$
$599$	2.48897e8			1.15808			0.579040	+	0.815299i	$0.303428\pi$
$600$	6.71001e6			0.0310649
$601$	6.19754e7			0.285494			0.142747	−	0.989759i	$-0.454407\pi$
$601$	6.19754e7			0.285494			0.142747	+	0.989759i	$0.454407\pi$
$602$	1.02539e8			0.470004
$603$		−	3.24053e8i		−	1.47796i
$604$	8.33836e6			0.0378416
$605$		−	9.23350e7i		−	0.416965i
$606$	−6.18549e6			−0.0277943
$607$	2.35512e7			0.105304			0.0526522	−	0.998613i	$-0.483233\pi$
$607$	2.35512e7			0.105304			0.0526522	+	0.998613i	$0.483233\pi$
$608$			6.83663e6i			0.0304181i
$609$			1.01688e7i			0.0450212i
$610$	9.84629e7			0.433794
$611$	−3.68458e8			−1.61534
$612$			8.68135e6i			0.0378733i
$613$			2.88190e8i			1.25112i	0.780178	+	0.625558i	$0.215128\pi$
$613$			2.88190e8i			1.25112i	−0.780178	+	0.625558i	$0.784872\pi$
$614$	3.26373e8			1.40997
$615$			1.84461e6i			0.00793010i
$616$	2.18040e7			0.0932810
$617$			2.53165e8i			1.07782i	0.842362	+	0.538912i	$0.181164\pi$
$617$			2.53165e8i			1.07782i	−0.842362	+	0.538912i	$0.818836\pi$
$618$			3.22418e7i			0.136601i
$619$		−	2.89798e8i		−	1.22186i	−0.791683	−	0.610932i	$-0.790795\pi$
$619$		−	2.89798e8i		−	1.22186i	0.791683	−	0.610932i	$-0.209205\pi$
$620$		−	2.26565e6i		−	0.00950644i
$621$	−5.35419e7	−	5.18427e7i	−0.223573	−	0.216478i
$622$	−1.76887e8			−0.735064
$623$	6.07123e7			0.251080
$624$	−3.40416e7			−0.140106
$625$	9.76562e6			0.0400000
$626$		−	4.22354e8i		−	1.72169i
$627$	−5.60575e6			−0.0227421
$628$			656366.i			0.00265013i
$629$	2.67132e8			1.07343
$630$	4.02153e7			0.160831
$631$			3.48381e8i			1.38665i	0.720626	+	0.693324i	$0.243854\pi$
$631$			3.48381e8i			1.38665i	−0.720626	+	0.693324i	$0.756146\pi$
$632$		−	4.02335e7i		−	0.159381i
$633$	−5.63346e7			−0.222108
$634$	−8.35189e7			−0.327730
$635$			7.00478e7i			0.273573i
$636$		−	2.06880e6i		−	0.00804168i
$637$	−1.94242e8			−0.751493
$638$		−	5.37658e7i		−	0.207035i
$639$	−1.42580e8			−0.546456
$640$			1.21822e8i			0.464714i
$641$			2.59872e8i			0.986701i	0.869831	+	0.493350i	$0.164228\pi$
$641$			2.59872e8i			0.986701i	−0.869831	+	0.493350i	$0.835772\pi$
$642$		−	2.35313e7i		−	0.0889284i
$643$		−	2.08353e8i		−	0.783732i	−0.920022	−	0.391866i	$-0.871830\pi$
$643$		−	2.08353e8i		−	0.783732i	0.920022	−	0.391866i	$-0.128170\pi$
$644$	1.85288e6	−	1.91361e6i	0.00693730	−	0.00716467i
$645$	−2.40970e7			−0.0898014
$646$	−2.14882e8			−0.797080
$647$	−2.77940e8			−1.02622			−0.513108	−	0.858324i	$-0.671506\pi$
$647$	−2.77940e8			−1.02622			−0.513108	+	0.858324i	$0.671506\pi$
$648$	2.48430e8			0.913019
$649$		−	6.28734e7i		−	0.230003i
$650$	−4.82207e7			−0.175588
$651$		−	1.22648e7i		−	0.0444548i
$652$	−4.63688e6			−0.0167295
$653$	4.68214e8			1.68153			0.840765	−	0.541400i	$-0.182106\pi$
$653$	4.68214e8			1.68153			0.840765	+	0.541400i	$0.182106\pi$
$654$			5.40184e7i			0.193112i
$655$		−	1.02207e8i		−	0.363711i
$656$	−3.26184e7			−0.115545
$657$	3.94842e8			1.39228
$658$		−	1.95939e8i		−	0.687771i
$659$			5.17814e8i			1.80933i	0.426124	+	0.904665i	$0.359879\pi$
$659$			5.17814e8i			1.80933i	−0.426124	+	0.904665i	$0.640121\pi$
$660$	144410.			0.000502304
$661$			2.63249e8i			0.911513i	0.890104	+	0.455756i	$0.150631\pi$
$661$			2.63249e8i			0.911513i	−0.890104	+	0.455756i	$0.849369\pi$
$662$	−4.24314e8			−1.46256
$663$		−	5.63507e7i		−	0.193356i
$664$			7.45638e7i			0.254697i
$665$			2.65571e7i			0.0903058i
$666$			2.21219e8i			0.748858i
$667$	1.67430e8	+	1.62116e8i	0.564228	+	0.546322i
$668$	6.54825e6			0.0219683
$669$	6.37857e7			0.213032
$670$	−2.06630e8			−0.687018
$671$	−7.51893e7			−0.248879
$672$		−	953401.i		−	0.00314172i
$673$	1.61261e8			0.529033			0.264517	−	0.964381i	$-0.414788\pi$
$673$	1.61261e8			0.529033			0.264517	+	0.964381i	$0.414788\pi$
$674$		−	5.57630e8i		−	1.82124i
$675$	−1.91419e7			−0.0622406
$676$	−2.11512e6			−0.00684690
$677$			2.62775e8i			0.846871i	0.905926	+	0.423436i	$0.139176\pi$
$677$			2.62775e8i			0.846871i	−0.905926	+	0.423436i	$0.860824\pi$
$678$			2.10377e7i			0.0675008i
$679$	2.07432e8			0.662624
$680$	−1.96414e8			−0.624662
$681$		−	6.71377e7i		−	0.212581i
$682$			6.48483e7i			0.204430i
$683$	2.81643e8			0.883967			0.441984	−	0.897023i	$-0.354275\pi$
$683$	2.81643e8			0.883967			0.441984	+	0.897023i	$0.354275\pi$
$684$		−	4.74760e6i		−	0.0148356i
$685$	1.88238e8			0.585645
$686$		−	2.22348e8i		−	0.688750i
$687$		−	3.13013e7i		−	0.0965366i
$688$		−	4.26110e8i		−	1.30845i
$689$		−	5.27517e8i		−	1.61279i
$690$	−1.63208e7	+	1.68557e7i	−0.0496815	+	0.0513098i
$691$	−1.81811e8			−0.551042			−0.275521	−	0.961295i	$-0.588850\pi$
$691$	−1.81811e8			−0.551042			−0.275521	+	0.961295i	$0.588850\pi$
$692$	9.71243e6			0.0293096
$693$	−3.07096e7			−0.0922730
$694$	−4.47319e8			−1.33826
$695$		−	1.49232e7i		−	0.0444538i
$696$	4.11289e7			0.121989
$697$		−	5.39948e7i		−	0.159461i
$698$	−1.02840e8			−0.302411
$699$	−1.00099e8			−0.293088
$700$		−	684140.i		−	0.00199458i
$701$			3.03442e7i			0.0880890i	0.999030	+	0.0440445i	$0.0140243\pi$
$701$			3.03442e7i			0.0880890i	−0.999030	+	0.0440445i	$0.985976\pi$
$702$	9.45190e7			0.273217
$703$	−1.46087e8			−0.420481
$704$		−	8.81206e7i		−	0.252557i
$705$			4.60461e7i			0.131409i
$706$	−8.03036e6			−0.0228203
$707$		−	2.23771e7i		−	0.0633207i
$708$	−1.35550e6			−0.00381945
$709$			4.05139e8i			1.13675i	0.822769	+	0.568376i	$0.192428\pi$
$709$			4.05139e8i			1.13675i	−0.822769	+	0.568376i	$0.807572\pi$
$710$			9.09148e7i			0.254015i
$711$			5.66665e7i			0.157659i
$712$		−	2.45558e8i		−	0.680322i
$713$	−2.01941e8	−	1.95532e8i	−0.557130	−	0.539449i
$714$	2.99663e7			0.0823262
$715$	3.68228e7			0.100739
$716$	−3.75707e6			−0.0102355
$717$	6.43743e7			0.174645
$718$		−	1.45603e8i		−	0.393366i
$719$	−1.36720e8			−0.367828			−0.183914	−	0.982942i	$-0.558877\pi$
$719$	−1.36720e8			−0.367828			−0.183914	+	0.982942i	$0.558877\pi$
$720$		−	1.67117e8i		−	0.447738i
$721$	−1.16640e8			−0.311203
$722$	−2.63977e8			−0.701383
$723$			9.31690e7i			0.246523i
$724$		−	9.64570e6i		−	0.0254166i
$725$	5.98582e7			0.157076
$726$	5.69777e7			0.148900
$727$			3.67729e8i			0.957028i	0.878080	+	0.478514i	$0.158824\pi$
$727$			3.67729e8i			0.957028i	−0.878080	+	0.478514i	$0.841176\pi$
$728$		−	1.19864e8i		−	0.310665i
$729$	−3.30904e8			−0.854120
$730$		−	2.51767e8i		−	0.647189i
$731$	7.05359e8			1.80575
$732$			1.62102e6i			0.00413291i
$733$			2.02970e8i			0.515371i	0.966229	+	0.257686i	$0.0829599\pi$
$733$			2.02970e8i			0.515371i	−0.966229	+	0.257686i	$0.917040\pi$
$734$			7.10437e8i			1.79654i
$735$			2.42744e7i			0.0611345i
$736$	−1.56978e7	−	1.51996e7i	−0.0393736	−	0.0381241i
$737$	1.57789e8			0.394161
$738$	4.47146e7			0.111245
$739$	2.64831e8			0.656200			0.328100	−	0.944643i	$-0.393592\pi$
$739$	2.64831e8			0.656200			0.328100	+	0.944643i	$0.393592\pi$
$740$	3.76337e6			0.00928712
$741$			3.08167e7i			0.0757410i
$742$	2.80524e8			0.686687
$743$		−	1.15323e7i		−	0.0281156i	−0.999901	−	0.0140578i	$-0.995525\pi$
$743$		−	1.15323e7i		−	0.0281156i	0.999901	−	0.0140578i	$-0.00447489\pi$
$744$	−4.96066e7			−0.120454
$745$	3.33890e8			0.807486
$746$		−	1.82465e7i		−	0.0439505i
$747$		−	1.05019e8i		−	0.251945i
$748$	−4.22714e6			−0.0101005
$749$	8.51286e7			0.202596
$750$			6.02614e6i			0.0142842i
$751$			6.21974e7i			0.146843i	0.997301	+	0.0734213i	$0.0233918\pi$
$751$			6.21974e7i			0.146843i	−0.997301	+	0.0734213i	$0.976608\pi$
$752$	−8.14240e8			−1.91469
$753$		−	4.23655e7i		−	0.0992264i
$754$	−2.95568e8			−0.689515
$755$		−	2.65708e8i		−	0.617395i
$756$			1.34100e6i			0.00310359i
$757$		−	1.89778e8i		−	0.437481i	−0.975783	−	0.218740i	$-0.929805\pi$
$757$		−	1.89778e8i		−	0.437481i	0.975783	−	0.218740i	$-0.0701948\pi$
$758$		−	2.40573e8i		−	0.552382i
$759$	1.24631e7	−	1.28715e7i	0.0285036	−	0.0294378i
$760$	1.07413e8			0.244691
$761$	−1.69185e8			−0.383891			−0.191945	−	0.981406i	$-0.561480\pi$
$761$	−1.69185e8			−0.383891			−0.191945	+	0.981406i	$0.561480\pi$
$762$	−4.32248e7			−0.0976942
$763$	−1.95421e8			−0.439945
$764$			720191.i			0.00161498i
$765$	2.76637e8			0.617912
$766$		−	8.37120e8i		−	1.86252i
$767$	−3.45636e8			−0.766006
$768$	−5.86464e6			−0.0129467
$769$			7.36339e7i			0.161919i	0.996717	+	0.0809597i	$0.0257985\pi$
$769$			7.36339e7i			0.161919i	−0.996717	+	0.0809597i	$0.974201\pi$
$770$			1.95817e7i			0.0428922i
$771$	3.14736e7			0.0686726
$772$	−649952.			−0.00141263
$773$			6.26611e8i			1.35662i	0.734774	+	0.678312i	$0.237288\pi$
$773$			6.26611e8i			1.35662i	−0.734774	+	0.678312i	$0.762712\pi$
$774$			5.84128e8i			1.25975i
$775$	−7.21965e7			−0.155100
$776$		−	8.38985e8i		−	1.79543i
$777$	2.03726e7			0.0434293
$778$			2.95894e8i			0.628343i
$779$			2.95283e7i			0.0624635i
$780$		−	793872.i		−	0.00167289i
$781$		−	6.94253e7i		−	0.145735i
$782$	4.77738e8	−	4.93396e8i	0.999010	−	1.03175i
$783$	−1.17330e8			−0.244413
$784$	−4.29247e8			−0.890758
$785$	2.09156e7			0.0432375
$786$	6.30695e7			0.129883
$787$		−	1.71242e8i		−	0.351306i	−0.984452	−	0.175653i	$-0.943796\pi$
$787$		−	1.71242e8i		−	0.351306i	0.984452	−	0.175653i	$-0.0562037\pi$
$788$	−1.49773e7			−0.0306094
$789$		−	1.65555e7i		−	0.0337062i
$790$	3.61329e7			0.0732861
$791$	−7.61076e7			−0.153779
$792$			1.24209e8i			0.250021i
$793$			4.13340e8i			0.828873i
$794$	−7.41447e8			−1.48122
$795$	−6.59237e7			−0.131202
$796$		−	1.78905e6i		−	0.00354719i
$797$			7.21389e8i			1.42493i	0.701706	+	0.712466i	$0.252422\pi$
$797$			7.21389e8i			1.42493i	−0.701706	+	0.712466i	$0.747578\pi$
$798$	−1.63878e7			−0.0322486
$799$		−	1.34785e9i		−	2.64241i
$800$	−5.61216e6			−0.0109613
$801$			3.45855e8i			0.672970i
$802$		−	5.20831e8i		−	1.00966i
$803$			1.92257e8i			0.371309i
$804$		−	3.40180e6i		−	0.00654547i
$805$	−6.09786e7	−	5.90434e7i	−0.116893	−	0.113184i
$806$	3.56492e8			0.680840
$807$	−5.49284e7			−0.104514
$808$	−9.05069e7			−0.171573
$809$	8.56556e8			1.61775			0.808873	−	0.587983i	$-0.200078\pi$
$809$	8.56556e8			1.61775			0.808873	+	0.587983i	$0.200078\pi$
$810$			2.23111e8i			0.419822i
$811$	−6.03761e8			−1.13189			−0.565943	−	0.824444i	$-0.691488\pi$
$811$	−6.03761e8			−1.13189			−0.565943	+	0.824444i	$0.691488\pi$
$812$		−	4.19343e6i		−	0.00783251i
$813$	1.41010e8			0.262409
$814$	−1.07716e8			−0.199714
$815$			1.47757e8i			0.272946i
$816$		−	1.24527e8i		−	0.229189i
$817$	−3.85742e8			−0.707345
$818$	−3.19792e7			−0.0584262
$819$			1.68821e8i			0.307308i
$820$		−	760683.i		−	0.00137963i
$821$	2.33546e8			0.422030			0.211015	−	0.977483i	$-0.432323\pi$
$821$	2.33546e8			0.422030			0.211015	+	0.977483i	$0.432323\pi$
$822$			1.16157e8i			0.209137i
$823$	−8.22627e8			−1.47572			−0.737860	−	0.674954i	$-0.764163\pi$
$823$	−8.22627e8			−1.47572			−0.737860	+	0.674954i	$0.764163\pi$
$824$			4.71766e8i			0.843228i
$825$		−	4.60174e6i		−	0.00819521i
$826$		−	1.83803e8i		−	0.326146i
$827$		−	5.13063e7i		−	0.0907097i	−0.998971	−	0.0453549i	$-0.985558\pi$
$827$		−	5.13063e7i		−	0.0907097i	0.998971	−	0.0453549i	$-0.0144419\pi$
$828$	1.09011e7	+	1.05552e7i	0.0192035	+	0.0185940i
$829$	5.82477e8			1.02239			0.511193	−	0.859466i	$-0.329204\pi$
$829$	5.82477e8			1.02239			0.511193	+	0.859466i	$0.329204\pi$
$830$	−6.69643e7			−0.117114
$831$	6.36572e7			0.110929
$832$	−4.84428e8			−0.841122
$833$		−	7.10553e8i		−	1.22931i
$834$	9.20878e6			0.0158747
$835$		−	2.08664e8i		−	0.358417i
$836$	2.31171e6			0.00395653
$837$	1.41515e8			0.241338
$838$			7.80090e8i			1.32560i
$839$		−	8.50938e8i		−	1.44083i	−0.693545	−	0.720414i	$-0.743952\pi$
$839$		−	8.50938e8i		−	1.44083i	0.693545	−	0.720414i	$-0.256048\pi$
$840$	−1.49793e7			−0.0252728
$841$	−2.27923e8			−0.383178
$842$			2.24432e7i			0.0375965i
$843$			8.85771e7i			0.147856i
$844$	2.32314e7			0.0386409
$845$			6.73997e7i			0.111709i
$846$	1.11619e9			1.84343
$847$			2.06127e8i			0.339222i
$848$		−	1.16574e9i		−	1.91167i
$849$			1.55437e8i			0.253998i
$850$		−	1.76395e8i		−	0.287231i
$851$	3.24790e8	−	3.35435e8i	0.527004	−	0.544277i
$852$	−1.49676e6			−0.00242009
$853$	−7.95002e7			−0.128092			−0.0640459	−	0.997947i	$-0.520400\pi$
$853$	−7.95002e7			−0.128092			−0.0640459	+	0.997947i	$0.520400\pi$
$854$	−2.19807e8			−0.352913
$855$	−1.51286e8			−0.242047
$856$		−	3.44313e8i		−	0.548949i
$857$	−5.80260e8			−0.921893			−0.460946	−	0.887428i	$-0.652490\pi$
$857$	−5.80260e8			−0.921893			−0.460946	+	0.887428i	$0.652490\pi$
$858$			2.27225e7i			0.0359745i
$859$	1.50022e8			0.236688			0.118344	−	0.992973i	$-0.462242\pi$
$859$	1.50022e8			0.236688			0.118344	+	0.992973i	$0.462242\pi$
$860$	9.93715e6			0.0156231
$861$		−	4.11787e6i		−	0.00645154i
$862$			8.47171e8i			1.32266i
$863$	1.72082e7			0.0267734			0.0133867	−	0.999910i	$-0.495739\pi$
$863$	1.72082e7			0.0267734			0.0133867	+	0.999910i	$0.495739\pi$
$864$	1.10006e7			0.0170559
$865$		−	3.09493e8i		−	0.478193i
$866$			5.92520e8i			0.912324i
$867$	1.03453e8			0.158740
$868$			5.05780e6i			0.00773397i
$869$	−2.75922e7			−0.0420462
$870$			3.69371e7i			0.0560925i
$871$		−	8.67416e8i		−	1.31272i
$872$			7.90404e8i			1.19206i
$873$			1.18166e9i			1.77603i
$874$	−2.61262e8	+	2.69825e8i	−0.391329	+	0.404155i
$875$	−2.18006e7			−0.0325420
$876$	4.14492e6			0.00616600
$877$	2.23707e8			0.331650			0.165825	−	0.986155i	$-0.446971\pi$
$877$	2.23707e8			0.331650			0.165825	+	0.986155i	$0.446971\pi$
$878$	−4.13858e8			−0.611459
$879$			1.00373e8i			0.147791i
$880$	8.13732e7			0.119408
$881$		−	3.64549e7i		−	0.0533124i	−0.999645	−	0.0266562i	$-0.991514\pi$
$881$		−	3.64549e7i		−	0.0533124i	0.999645	−	0.0266562i	$-0.00848593\pi$
$882$	5.88429e8			0.857606
$883$	−7.00642e8			−1.01769			−0.508843	−	0.860859i	$-0.669927\pi$
$883$	−7.00642e8			−1.01769			−0.508843	+	0.860859i	$0.669927\pi$
$884$			2.32380e7i			0.0336389i
$885$			4.31940e7i			0.0623152i
$886$	1.08499e9			1.56001
$887$	2.82653e8			0.405026			0.202513	−	0.979280i	$-0.435089\pi$
$887$	2.82653e8			0.405026			0.202513	+	0.979280i	$0.435089\pi$
$888$		−	8.23992e7i		−	0.117675i
$889$		−	1.56374e8i		−	0.222566i
$890$	2.20531e8			0.312824
$891$		−	1.70374e8i		−	0.240863i
$892$	−2.63041e7			−0.0370620
$893$			7.37103e8i			1.03508i
$894$			2.06036e8i			0.288357i
$895$			1.19722e8i			0.166995i
$896$		−	2.71953e8i		−	0.378069i
$897$	−7.07591e7	−	6.85135e7i	−0.0980404	−	0.0949290i
$898$	6.42194e8			0.886823
$899$	−4.42527e8			−0.609061
$900$	3.89728e6			0.00534607
$901$	1.92970e9			2.63825
$902$			2.17725e7i			0.0296681i
$903$	5.37936e7			0.0730580
$904$			3.07826e8i			0.416678i
$905$	−3.07367e8			−0.414678
$906$	1.63962e8			0.220475
$907$			4.37312e8i			0.586097i	0.956098	+	0.293048i	$0.0946697\pi$
$907$			4.37312e8i			0.586097i	−0.956098	+	0.293048i	$0.905330\pi$
$908$			2.76864e7i			0.0369835i
$909$	1.27474e8			0.169718
$910$	1.07647e8			0.142849
$911$		−	7.29648e8i		−	0.965068i	−0.875877	−	0.482534i	$-0.839716\pi$
$911$		−	7.29648e8i		−	0.965068i	0.875877	−	0.482534i	$-0.160284\pi$
$912$			6.81005e7i			0.0897771i
$913$	5.11360e7			0.0671915
$914$			5.26268e7i			0.0689237i
$915$	5.16550e7			0.0674294
$916$			1.29081e7i			0.0167948i
$917$			2.28165e8i			0.295897i
$918$			3.45758e8i			0.446935i
$919$			1.50351e9i			1.93714i	0.248745	+	0.968569i	$0.419982\pi$
$919$			1.50351e9i			1.93714i	−0.248745	+	0.968569i	$0.580018\pi$
$920$	−2.38808e8	+	2.46635e8i	−0.306680	+	0.316732i
$921$	1.71220e8			0.219167
$922$	−1.31222e8			−0.167423
$923$	−3.81654e8			−0.485360
$924$	−322379.			−0.000408650
$925$		−	1.19922e8i		−	0.151522i
$926$	2.65051e8			0.333808
$927$		−	6.64455e8i		−	0.834116i
$928$	−3.43996e7			−0.0430437
$929$	1.38687e8			0.172978			0.0864888	−	0.996253i	$-0.472435\pi$
$929$	1.38687e8			0.172978			0.0864888	+	0.996253i	$0.472435\pi$
$930$		−	4.45508e7i		−	0.0553868i
$931$			3.88583e8i			0.481542i
$932$	4.12790e7			0.0509896
$933$	−9.27975e7			−0.114259
$934$			7.72073e7i			0.0947585i
$935$			1.34701e8i			0.164792i
$936$	6.82816e8			0.832676
$937$		−	1.73865e8i		−	0.211346i	−0.994401	−	0.105673i	$-0.966300\pi$
$937$		−	1.73865e8i		−	0.211346i	0.994401	−	0.105673i	$-0.0336997\pi$
$938$	4.61276e8			0.558924
$939$		−	2.21573e8i		−	0.267621i
$940$		−	1.89886e7i		−	0.0228617i
$941$		−	9.82458e7i		−	0.117909i	−0.998261	−	0.0589543i	$-0.981223\pi$
$941$		−	9.82458e7i		−	0.117909i	0.998261	−	0.0589543i	$-0.0187766\pi$
$942$			1.29065e7i			0.0154403i
$943$	−6.78009e7	−	6.56492e7i	−0.0808538	−	0.0782879i
$944$	−7.63806e8			−0.907961
$945$	4.27321e7			0.0506359
$946$	−2.84425e8			−0.335965
$947$	−1.43079e9			−1.68472			−0.842359	−	0.538917i	$-0.818834\pi$
$947$	−1.43079e9			−1.68472			−0.842359	+	0.538917i	$0.818834\pi$
$948$			594866.i			0.000698223i
$949$	1.05690e9			1.23662
$950$			9.64660e7i			0.112513i
$951$	−4.38152e7			−0.0509428
$952$	4.38471e8			0.508194
$953$			4.20569e7i			0.0485913i	0.999705	+	0.0242957i	$0.00773431\pi$
$953$			4.20569e7i			0.0485913i	−0.999705	+	0.0242957i	$0.992266\pi$
$954$			1.59804e9i			1.84053i
$955$	2.29494e7			0.0263488
$956$	−2.65468e7			−0.0303836
$957$		−	2.82063e7i		−	0.0321818i
$958$			8.69413e8i			0.988849i
$959$	−4.20218e8			−0.476452
$960$			6.05388e7i			0.0684259i
$961$	−3.53760e8			−0.398602
$962$			5.92153e8i			0.665133i
$963$			4.84945e8i			0.543017i
$964$		−	3.84212e7i		−	0.0428884i
$965$			2.07112e7i			0.0230475i
$966$	3.64343e7	−	3.76284e7i	0.0404184	−	0.0417431i
$967$	1.25705e8			0.139019			0.0695095	−	0.997581i	$-0.477857\pi$
$967$	1.25705e8			0.139019			0.0695095	+	0.997581i	$0.477857\pi$
$968$	8.33705e8			0.919150
$969$	−1.12730e8			−0.123899
$970$	7.53477e8			0.825572
$971$		−	8.73080e8i		−	0.953666i	−0.878994	−	0.476833i	$-0.841785\pi$
$971$		−	8.73080e8i		−	0.953666i	0.878994	−	0.476833i	$-0.158215\pi$
$972$	−1.15068e7			−0.0125301
$973$			3.33144e7i			0.0361654i
$974$	7.64362e8			0.827222
$975$	−2.52973e7			−0.0272935
$976$			9.13423e8i			0.982477i
$977$			1.54679e9i			1.65862i	0.558786	+	0.829312i	$0.311267\pi$
$977$			1.54679e9i			1.65862i	−0.558786	+	0.829312i	$0.688733\pi$
$978$	−9.11777e7			−0.0974702
$979$	−1.68404e8			−0.179475
$980$		−	1.00103e7i		−	0.0106358i
$981$		−	1.11324e9i		−	1.17918i
$982$	6.81537e8			0.719706
$983$		−	3.45780e8i		−	0.364031i	−0.983296	−	0.182016i	$-0.941738\pi$
$983$		−	3.45780e8i		−	0.364031i	0.983296	−	0.182016i	$-0.0582622\pi$
$984$	−1.66552e7			−0.0174810
$985$			4.77261e8i			0.499399i
$986$		−	1.08121e9i		−	1.12793i
$987$		−	1.02793e8i		−	0.106908i
$988$		−	1.27082e7i		−	0.0131769i
$989$	8.57606e8	−	8.85714e8i	0.886541	−	0.915598i
$990$	−1.11550e8			−0.114964
$991$	1.62273e9			1.66734			0.833672	−	0.552261i	$-0.186235\pi$
$991$	1.62273e9			1.66734			0.833672	+	0.552261i	$0.186235\pi$
$992$	4.14903e7			0.0425022
$993$	−2.22601e8			−0.227342
$994$		−	2.02957e8i		−	0.206654i
$995$	−5.70094e7			−0.0578732
$996$		−	1.10245e6i		−	0.00111579i
$997$	−1.79395e8			−0.181019			−0.0905095	−	0.995896i	$-0.528850\pi$
$997$	−1.79395e8			−0.181019			−0.0905095	+	0.995896i	$0.528850\pi$
$998$	4.04344e8			0.406780
$999$			2.35063e8i			0.235770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.7.d.a.91.13	✓	48
23.22	odd	2	inner	115.7.d.a.91.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.7.d.a.91.13	✓	48	1.1	even	1	trivial
115.7.d.a.91.14	yes	48	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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8.10890 q^{2} -4.25404 q^{3} +1.75429 q^{4} -55.9017i q^{5} +34.4956 q^{6} +124.794i q^{7} +504.744 q^{8} -710.903 q^{9} +O(q^{10})\)	\(q-8.10890 q^{2} -4.25404 q^{3} +1.75429 q^{4} -55.9017i q^{5} +34.4956 q^{6} +124.794i q^{7} +504.744 q^{8} -710.903 q^{9} +453.301i q^{10} -346.155i q^{11} -7.46283 q^{12} -1902.93 q^{13} -1011.94i q^{14} +237.808i q^{15} -4205.20 q^{16} -6961.06i q^{17} +5764.64 q^{18} +3806.82i q^{19} -98.0678i q^{20} -530.879i q^{21} +2806.93i q^{22} +(-8740.95 - 8463.55i) q^{23} -2147.20 q^{24} -3125.00 q^{25} +15430.6 q^{26} +6125.41 q^{27} +218.925i q^{28} -19154.6 q^{29} -1928.36i q^{30} +23102.9 q^{31} +1795.89 q^{32} +1472.56i q^{33} +56446.5i q^{34} +6976.20 q^{35} -1247.13 q^{36} +38375.1i q^{37} -30869.1i q^{38} +8095.13 q^{39} -28216.1i q^{40} +7756.70 q^{41} +4304.85i q^{42} +101329. i q^{43} -607.256i q^{44} +39740.7i q^{45} +(70879.5 + 68630.1i) q^{46} +193627. q^{47} +17889.1 q^{48} +102075. q^{49} +25340.3 q^{50} +29612.6i q^{51} -3338.29 q^{52} +277214. i q^{53} -49670.4 q^{54} -19350.6 q^{55} +62989.1i q^{56} -16194.4i q^{57} +155323. q^{58} +181634. q^{59} +417.185i q^{60} -217213. i q^{61} -187339. q^{62} -88716.4i q^{63} +254570. q^{64} +106377. i q^{65} -11940.8i q^{66} +455833. i q^{67} -12211.7i q^{68} +(37184.4 + 36004.3i) q^{69} -56569.3 q^{70} +200562. q^{71} -358824. q^{72} -555408. q^{73} -311180. i q^{74} +13293.9 q^{75} +6678.26i q^{76} +43198.0 q^{77} -65642.6 q^{78} -79710.6i q^{79} +235078. i q^{80} +492191. q^{81} -62898.3 q^{82} +147726. i q^{83} -931.316i q^{84} -389135. q^{85} -821670. i q^{86} +81484.6 q^{87} -174720. i q^{88} -486500. i q^{89} -322253. i q^{90} -237474. i q^{91} +(-15334.2 - 14847.5i) q^{92} -98280.7 q^{93} -1.57010e6 q^{94} +212808. q^{95} -7639.80 q^{96} -1.66220e6i q^{97} -827720. q^{98} +246082. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9}+O(q^{10}) \) 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

Properties

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