LMFDB - Embedded newform 115.3.c.c.114.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,3,Mod(114,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("115.114");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.13352304014$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 6 x^{18} - 827 x^{16} - 12720 x^{14} + 346250 x^{12} + 9668500 x^{10} + 216406250 x^{8} + \cdots + 95367431640625 $ x^20 + 6x^18 - 827x^16 - 12720x^14 + 346250x^12 + 9668500x^10 + 216406250x^8 - 4968750000x^6 - 201904296875x^4 + 915527343750*x^2 + 95367431640625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			114.2
Root			$-3.24366 + 3.80508i$ of defining polynomial
Character	$\chi$	$=$	115.114
Dual form			115.3.c.c.114.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.64975i q^{2} -3.06547i q^{3} -9.32065 q^{4} +(3.24366 + 3.80508i) q^{5} -11.1882 q^{6} -12.1877 q^{7} +19.4190i q^{8} -0.397130 q^{9} +(13.8876 - 11.8385i) q^{10} -10.9113i q^{11} +28.5722i q^{12} -17.9696i q^{13} +44.4819i q^{14} +(11.6644 - 9.94336i) q^{15} +33.5919 q^{16} -0.374070 q^{17} +1.44942i q^{18} -10.3828i q^{19} +(-30.2330 - 35.4658i) q^{20} +37.3610i q^{21} -39.8234 q^{22} +(22.9432 + 1.61605i) q^{23} +59.5285 q^{24} +(-3.95733 + 24.6848i) q^{25} -65.5844 q^{26} -26.3719i q^{27} +113.597 q^{28} -11.7286 q^{29} +(-36.2907 - 42.5720i) q^{30} +32.5811 q^{31} -44.9257i q^{32} -33.4483 q^{33} +1.36526i q^{34} +(-39.5327 - 46.3752i) q^{35} +3.70151 q^{36} -25.4631 q^{37} -37.8947 q^{38} -55.0853 q^{39} +(-73.8910 + 62.9887i) q^{40} +13.8789 q^{41} +136.358 q^{42} -14.5797 q^{43} +101.700i q^{44} +(-1.28815 - 1.51111i) q^{45} +(5.89818 - 83.7367i) q^{46} -41.7513i q^{47} -102.975i q^{48} +99.5396 q^{49} +(90.0933 + 14.4432i) q^{50} +1.14670i q^{51} +167.488i q^{52} +68.2269 q^{53} -96.2506 q^{54} +(41.5184 - 35.3925i) q^{55} -236.673i q^{56} -31.8283 q^{57} +42.8063i q^{58} +9.15737 q^{59} +(-108.720 + 92.6785i) q^{60} +63.7896i q^{61} -118.913i q^{62} +4.84009 q^{63} -29.6001 q^{64} +(68.3758 - 58.2872i) q^{65} +122.078i q^{66} -4.06489 q^{67} +3.48658 q^{68} +(4.95396 - 70.3316i) q^{69} +(-169.258 + 144.284i) q^{70} +47.2503 q^{71} -7.71187i q^{72} +80.6273i q^{73} +92.9338i q^{74} +(75.6706 + 12.1311i) q^{75} +96.7746i q^{76} +132.983i q^{77} +201.047i q^{78} -74.1335i q^{79} +(108.961 + 127.820i) q^{80} -84.4165 q^{81} -50.6546i q^{82} -151.130 q^{83} -348.229i q^{84} +(-1.21336 - 1.42337i) q^{85} +53.2123i q^{86} +35.9536i q^{87} +211.886 q^{88} -84.2652i q^{89} +(-5.51518 + 4.70144i) q^{90} +219.008i q^{91} +(-213.845 - 15.0626i) q^{92} -99.8764i q^{93} -152.382 q^{94} +(39.5075 - 33.6784i) q^{95} -137.719 q^{96} +36.3451 q^{97} -363.294i q^{98} +4.33320i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 56 q^{4} - 8 q^{6} - 72 q^{9} + 88 q^{16} + 44 q^{24} - 12 q^{25} - 56 q^{26} + 236 q^{31} + 92 q^{35} - 32 q^{36} - 168 q^{39} + 124 q^{41} - 248 q^{46} + 88 q^{49} + 200 q^{50} - 196 q^{54} + 268 q^{55}+ \cdots - 264 q^{96}+O(q^{100}) $ 20 * q - 56 * q^4 - 8 * q^6 - 72 * q^9 + 88 * q^16 + 44 * q^24 - 12 * q^25 - 56 * q^26 + 236 * q^31 + 92 * q^35 - 32 * q^36 - 168 * q^39 + 124 * q^41 - 248 * q^46 + 88 * q^49 + 200 * q^50 - 196 * q^54 + 268 * q^55 + 56 * q^59 - 28 * q^64 + 376 * q^69 - 636 * q^70 - 196 * q^71 + 428 * q^75 - 988 * q^81 - 284 * q^85 + 276 * q^94 + 184 * q^95 - 264 * q^96

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 $

$2$		−	3.64975i		−	1.82487i	−0.409218	−	0.912437i	$-0.634199\pi$
$2$		−	3.64975i		−	1.82487i	0.409218	−	0.912437i	$-0.365801\pi$
$3$		−	3.06547i		−	1.02182i	−0.859633	−	0.510912i	$-0.829308\pi$
$3$		−	3.06547i		−	1.02182i	0.859633	−	0.510912i	$-0.170692\pi$
$4$	−9.32065			−2.33016
$5$	3.24366	+	3.80508i	0.648732	+	0.761017i
$5$	3.24366	+	3.80508i	0.648732	+	0.761017i
$6$	−11.1882			−1.86470
$7$	−12.1877			−1.74110			−0.870549	−	0.492082i	$-0.836236\pi$
$7$	−12.1877			−1.74110			−0.870549	+	0.492082i	$0.836236\pi$
$8$			19.4190i			2.42738i
$9$	−0.397130			−0.0441255
$10$	13.8876	−	11.8385i	1.38876	−	1.18385i
$11$		−	10.9113i		−	0.991935i	−0.868341	−	0.495968i	$-0.834813\pi$
$11$		−	10.9113i		−	0.991935i	0.868341	−	0.495968i	$-0.165187\pi$
$12$			28.5722i			2.38102i
$13$		−	17.9696i		−	1.38228i	−0.722723	−	0.691138i	$-0.757110\pi$
$13$		−	17.9696i		−	1.38228i	0.722723	−	0.691138i	$-0.242890\pi$
$14$			44.4819i			3.17728i
$15$	11.6644	−	9.94336i	0.777626	−	0.662891i
$16$	33.5919			2.09949
$17$	−0.374070			−0.0220041			−0.0110021	−	0.999939i	$-0.503502\pi$
$17$	−0.374070			−0.0220041			−0.0110021	+	0.999939i	$0.503502\pi$
$18$			1.44942i			0.0805235i
$19$		−	10.3828i		−	0.546464i	−0.961948	−	0.273232i	$-0.911907\pi$
$19$		−	10.3828i		−	0.546464i	0.961948	−	0.273232i	$-0.0880927\pi$
$20$	−30.2330	−	35.4658i	−1.51165	−	1.77329i
$21$			37.3610i			1.77910i
$22$	−39.8234			−1.81016
$23$	22.9432	+	1.61605i	0.997528	+	0.0702631i
$23$	22.9432	+	1.61605i	0.997528	+	0.0702631i
$24$	59.5285			2.48035
$25$	−3.95733	+	24.6848i	−0.158293	+	0.987392i
$26$	−65.5844			−2.52248
$27$		−	26.3719i		−	0.976736i
$28$	113.597			4.05704
$29$	−11.7286			−0.404433			−0.202217	−	0.979341i	$-0.564814\pi$
$29$	−11.7286			−0.404433			−0.202217	+	0.979341i	$0.564814\pi$
$30$	−36.2907	−	42.5720i	−1.20969	−	1.41907i
$31$	32.5811			1.05100			0.525501	−	0.850793i	$-0.323878\pi$
$31$	32.5811			1.05100			0.525501	+	0.850793i	$0.323878\pi$
$32$		−	44.9257i		−	1.40393i
$33$	−33.4483			−1.01358
$34$			1.36526i			0.0401548i
$35$	−39.5327	−	46.3752i	−1.12951	−	1.32500i
$36$	3.70151			0.102820
$37$	−25.4631			−0.688192			−0.344096	−	0.938935i	$-0.611815\pi$
$37$	−25.4631			−0.688192			−0.344096	+	0.938935i	$0.611815\pi$
$38$	−37.8947			−0.997228
$39$	−55.0853			−1.41244
$40$	−73.8910	+	62.9887i	−1.84727	+	1.57472i
$41$	13.8789			0.338510			0.169255	−	0.985572i	$-0.445864\pi$
$41$	13.8789			0.338510			0.169255	+	0.985572i	$0.445864\pi$
$42$	136.358			3.24662
$43$	−14.5797			−0.339063			−0.169532	−	0.985525i	$-0.554226\pi$
$43$	−14.5797			−0.339063			−0.169532	+	0.985525i	$0.554226\pi$
$44$			101.700i			2.31137i
$45$	−1.28815	−	1.51111i	−0.0286257	−	0.0335803i
$46$	5.89818	−	83.7367i	0.128221	−	1.82036i
$47$		−	41.7513i		−	0.888325i	−0.895946	−	0.444163i	$-0.853501\pi$
$47$		−	41.7513i		−	0.888325i	0.895946	−	0.444163i	$-0.146499\pi$
$48$		−	102.975i		−	2.14531i
$49$	99.5396			2.03142
$50$	90.0933	+	14.4432i	1.80187	+	0.288865i
$51$			1.14670i			0.0224844i
$52$			167.488i			3.22093i
$53$	68.2269			1.28730			0.643650	−	0.765320i	$-0.277419\pi$
$53$	68.2269			1.28730			0.643650	+	0.765320i	$0.277419\pi$
$54$	−96.2506			−1.78242
$55$	41.5184	−	35.3925i	0.754879	−	0.643500i
$56$		−	236.673i		−	4.22630i
$57$	−31.8283			−0.558391
$58$			42.8063i			0.738039i
$59$	9.15737			0.155210			0.0776049	−	0.996984i	$-0.475273\pi$
$59$	9.15737			0.155210			0.0776049	+	0.996984i	$0.475273\pi$
$60$	−108.720	+	92.6785i	−1.81199	+	1.54464i
$61$			63.7896i			1.04573i	0.852415	+	0.522866i	$0.175137\pi$
$61$			63.7896i			1.04573i	−0.852415	+	0.522866i	$0.824863\pi$
$62$		−	118.913i		−	1.91795i
$63$	4.84009			0.0768268
$64$	−29.6001			−0.462501
$65$	68.3758	−	58.2872i	1.05194	−	0.896727i
$66$			122.078i			1.84966i
$67$	−4.06489			−0.0606700			−0.0303350	−	0.999540i	$-0.509657\pi$
$67$	−4.06489			−0.0606700			−0.0303350	+	0.999540i	$0.509657\pi$
$68$	3.48658			0.0512732
$69$	4.95396	−	70.3316i	0.0717966	−	1.01930i
$70$	−169.258	+	144.284i	−2.41796	+	2.06121i
$71$	47.2503			0.665497			0.332748	−	0.943016i	$-0.392024\pi$
$71$	47.2503			0.665497			0.332748	+	0.943016i	$0.392024\pi$
$72$		−	7.71187i		−	0.107109i
$73$			80.6273i			1.10448i	0.833684	+	0.552241i	$0.186227\pi$
$73$			80.6273i			1.10448i	−0.833684	+	0.552241i	$0.813773\pi$
$74$			92.9338i			1.25586i
$75$	75.6706	+	12.1311i	1.00894	+	0.161748i
$76$			96.7746i			1.27335i
$77$			132.983i			1.72706i
$78$			201.047i			2.57753i
$79$		−	74.1335i		−	0.938398i	−0.883092	−	0.469199i	$-0.844543\pi$
$79$		−	74.1335i		−	0.938398i	0.883092	−	0.469199i	$-0.155457\pi$
$80$	108.961	+	127.820i	1.36201	+	1.59775i
$81$	−84.4165			−1.04218
$82$		−	50.6546i		−	0.617738i
$83$	−151.130			−1.82084			−0.910420	−	0.413686i	$-0.864241\pi$
$83$	−151.130			−1.82084			−0.910420	+	0.413686i	$0.864241\pi$
$84$		−	348.229i		−	4.14558i
$85$	−1.21336	−	1.42337i	−0.0142748	−	0.0167455i
$86$			53.2123i			0.618748i
$87$			35.9536i			0.413260i
$88$	211.886			2.40780
$89$		−	84.2652i		−	0.946799i	−0.880848	−	0.473400i	$-0.843027\pi$
$89$		−	84.2652i		−	0.946799i	0.880848	−	0.473400i	$-0.156973\pi$
$90$	−5.51518	+	4.70144i	−0.0612797	+	0.0522382i
$91$			219.008i			2.40668i
$92$	−213.845	−	15.0626i	−2.32440	−	0.163724i
$93$		−	99.8764i		−	1.07394i
$94$	−152.382			−1.62108
$95$	39.5075	−	33.6784i	0.415869	−	0.354509i
$96$	−137.719			−1.43457
$97$	36.3451			0.374692			0.187346	−	0.982294i	$-0.440011\pi$
$97$	36.3451			0.374692			0.187346	+	0.982294i	$0.440011\pi$
$98$		−	363.294i		−	3.70708i
$99$			4.33320i			0.0437697i
$100$	36.8848	−	230.078i	0.368848	−	2.30078i
$101$	64.5806			0.639412			0.319706	−	0.947517i	$-0.396416\pi$
$101$	64.5806			0.639412			0.319706	+	0.947517i	$0.396416\pi$
$102$	4.18518			0.0410311
$103$	170.756			1.65782			0.828912	−	0.559379i	$-0.188961\pi$
$103$	170.756			1.65782			0.828912	+	0.559379i	$0.188961\pi$
$104$	348.951			3.35530
$105$	−142.162	+	121.186i	−1.35392	+	1.15416i
$106$		−	249.011i		−	2.34916i
$107$	−71.3921			−0.667216			−0.333608	−	0.942712i	$-0.608266\pi$
$107$	−71.3921			−0.667216			−0.333608	+	0.942712i	$0.608266\pi$
$108$			245.803i			2.27595i
$109$		−	35.8133i		−	0.328562i	−0.986414	−	0.164281i	$-0.947470\pi$
$109$		−	35.8133i		−	0.328562i	0.986414	−	0.164281i	$-0.0525304\pi$
$110$	−129.174	−	151.531i	−1.17431	−	1.37756i
$111$			78.0564i			0.703211i
$112$	−409.407			−3.65542
$113$	76.6774			0.678561			0.339280	−	0.940685i	$-0.389816\pi$
$113$	76.6774			0.678561			0.339280	+	0.940685i	$0.389816\pi$
$114$			116.165i			1.01899i
$115$	68.2706	+	92.5426i	0.593657	+	0.804718i
$116$	109.318			0.942394
$117$			7.13626i			0.0609936i
$118$		−	33.4221i		−	0.283238i
$119$	4.55905			0.0383114
$120$	193.090	+	226.511i	1.60908	+	1.88759i
$121$	1.94383			0.0160647
$122$	232.816			1.90833
$123$		−	42.5455i		−	0.345898i
$124$	−303.677			−2.44901
$125$	−106.764	+	65.0112i	−0.854112	+	0.520089i
$126$		−	17.6651i		−	0.140199i
$127$			1.19072i			0.00937579i	0.999989	+	0.00468789i	$0.00149221\pi$
$127$			1.19072i			0.00937579i	−0.999989	+	0.00468789i	$0.998508\pi$
$128$		−	71.6702i		−	0.559923i
$129$			44.6938i			0.346463i
$130$	−212.734	−	249.554i	−1.63641	−	1.91965i
$131$	−168.759			−1.28824			−0.644120	−	0.764924i	$-0.722776\pi$
$131$	−168.759			−1.28824			−0.644120	+	0.764924i	$0.722776\pi$
$132$	311.759			2.36181
$133$			126.543i			0.951448i
$134$			14.8358i			0.110715i
$135$	100.347	−	85.5414i	0.743313	−	0.633640i
$136$		−	7.26408i		−	0.0534123i
$137$	−45.0248			−0.328648			−0.164324	−	0.986406i	$-0.552544\pi$
$137$	−45.0248			−0.328648			−0.164324	+	0.986406i	$0.552544\pi$
$138$	−256.693	−	18.0807i	−1.86009	−	0.131020i
$139$	−17.7031			−0.127361			−0.0636804	−	0.997970i	$-0.520284\pi$
$139$	−17.7031			−0.127361			−0.0636804	+	0.997970i	$0.520284\pi$
$140$	368.470	+	432.246i	2.63193	+	3.08747i
$141$	−127.987			−0.907712
$142$		−	172.452i		−	1.21445i
$143$	−196.071			−1.37113
$144$	−13.3403			−0.0926412
$145$	−38.0435	−	44.6281i	−0.262369	−	0.307780i
$146$	294.269			2.01554
$147$		−	305.136i		−	2.07576i
$148$	237.332			1.60360
$149$			20.2199i			0.135704i	0.997695	+	0.0678520i	$0.0216146\pi$
$149$			20.2199i			0.135704i	−0.997695	+	0.0678520i	$0.978385\pi$
$150$	44.2754	−	276.179i	0.295169	−	1.84119i
$151$	220.693			1.46154			0.730771	−	0.682622i	$-0.239161\pi$
$151$	220.693			1.46154			0.730771	+	0.682622i	$0.239161\pi$
$152$	201.624			1.32647
$153$	0.148554			0.000970944
$154$	485.355			3.15166
$155$	105.682	+	123.974i	0.681819	+	0.799831i
$156$	513.431			3.29122
$157$	23.3995			0.149042			0.0745208	−	0.997219i	$-0.476257\pi$
$157$	23.3995			0.149042			0.0745208	+	0.997219i	$0.476257\pi$
$158$	−270.568			−1.71246
$159$		−	209.148i		−	1.31540i
$160$	170.946	−	145.724i	1.06841	−	0.910774i
$161$	−279.624	−	19.6959i	−1.73679	−	0.122335i
$162$			308.099i			1.90184i
$163$		−	210.152i		−	1.28928i	−0.764487	−	0.644639i	$-0.777008\pi$
$163$		−	210.152i		−	1.28928i	0.764487	−	0.644639i	$-0.222992\pi$
$164$	−129.361			−0.788784
$165$	−108.495	−	127.273i	−0.657544	−	0.771354i
$166$			551.585i			3.32280i
$167$			219.460i			1.31413i	0.753833	+	0.657066i	$0.228203\pi$
$167$			219.460i			1.31413i	−0.753833	+	0.657066i	$0.771797\pi$
$168$	−725.514			−4.31854
$169$	−153.906			−0.910686
$170$	−5.19494	+	4.42845i	−0.0305585	+	0.0260497i
$171$			4.12333i			0.0241130i
$172$	135.892			0.790072
$173$			178.252i			1.03036i	0.857082	+	0.515179i	$0.172275\pi$
$173$			178.252i			1.03036i	−0.857082	+	0.515179i	$0.827725\pi$
$174$	131.221			0.754146
$175$	48.2306	−	300.851i	0.275604	−	1.71915i
$176$		−	366.530i		−	2.08256i
$177$		−	28.0717i		−	0.158597i
$178$	−307.546			−1.72779
$179$	−259.957			−1.45227			−0.726137	−	0.687550i	$-0.758686\pi$
$179$	−259.957			−1.45227			−0.726137	+	0.687550i	$0.758686\pi$
$180$	12.0064	+	14.0845i	0.0667024	+	0.0782474i
$181$		−	81.7698i		−	0.451767i	−0.974154	−	0.225883i	$-0.927473\pi$
$181$		−	81.7698i		−	0.451767i	0.974154	−	0.225883i	$-0.0725269\pi$
$182$	799.322			4.39188
$183$	195.545			1.06855
$184$	−31.3821	+	445.533i	−0.170555	+	2.42138i
$185$	−82.5936	−	96.8892i	−0.446452	−	0.523725i
$186$	−364.524			−1.95980
$187$			4.08159i			0.0218267i
$188$			389.149i			2.06994i
$189$			321.412i			1.70059i
$190$	−122.917	−	144.192i	−0.646934	−	0.758907i
$191$			151.168i			0.791453i	0.918368	+	0.395727i	$0.129507\pi$
$191$			151.168i			0.791453i	−0.918368	+	0.395727i	$0.870493\pi$
$192$			90.7382i			0.472595i
$193$			203.305i			1.05340i	0.850053	+	0.526698i	$0.176570\pi$
$193$			203.305i			1.05340i	−0.850053	+	0.526698i	$0.823430\pi$
$194$		−	132.650i		−	0.683765i
$195$	−178.678	−	209.604i	−0.916298	−	1.07489i
$196$	−927.773			−4.73354
$197$			28.3927i			0.144125i	0.997400	+	0.0720626i	$0.0229582\pi$
$197$			28.3927i			0.144125i	−0.997400	+	0.0720626i	$0.977042\pi$
$198$	15.8151			0.0798741
$199$			273.697i			1.37536i	0.726014	+	0.687680i	$0.241371\pi$
$199$			273.697i			1.37536i	−0.726014	+	0.687680i	$0.758629\pi$
$200$	−479.354	−	76.8473i	−2.39677	−	0.384237i
$201$			12.4608i			0.0619941i
$202$		−	235.703i		−	1.16685i
$203$	142.944			0.704157
$204$		−	10.6880i		−	0.0523922i
$205$	45.0185	+	52.8105i	0.219603	+	0.257612i
$206$		−	623.215i		−	3.02532i
$207$	−9.11141	−	0.641782i	−0.0440165	−	0.00310040i
$208$		−	603.632i		−	2.90208i
$209$	−113.290			−0.542057
$210$	442.300	+	518.855i	2.10619	+	2.47074i
$211$	40.1001			0.190048			0.0950238	−	0.995475i	$-0.469707\pi$
$211$	40.1001			0.190048			0.0950238	+	0.995475i	$0.469707\pi$
$212$	−635.919			−2.99962
$213$		−	144.844i		−	0.680021i
$214$			260.563i			1.21758i
$215$	−47.2917	−	55.4771i	−0.219961	−	0.258033i
$216$	512.116			2.37091
$217$	−397.088			−1.82990
$218$	−130.709			−0.599584
$219$	247.161			1.12859
$220$	−386.978	+	329.881i	−1.75899	+	1.49946i
$221$			6.72189i			0.0304158i
$222$	284.886			1.28327
$223$			131.579i			0.590041i	0.955491	+	0.295021i	$0.0953265\pi$
$223$			131.579i			0.590041i	−0.955491	+	0.295021i	$0.904673\pi$
$224$			547.541i			2.44438i
$225$	1.57157	−	9.80307i	0.00698476	−	0.0435692i
$226$		−	279.853i		−	1.23829i
$227$	113.610			0.500486			0.250243	−	0.968183i	$-0.419489\pi$
$227$	113.610			0.500486			0.250243	+	0.968183i	$0.419489\pi$
$228$	296.660			1.30114
$229$		−	86.3794i		−	0.377203i	−0.982054	−	0.188601i	$-0.939605\pi$
$229$		−	86.3794i		−	0.377203i	0.982054	−	0.188601i	$-0.0603954\pi$
$230$	337.757	−	249.170i	1.46851	−	1.08335i
$231$	407.657			1.76475
$232$		−	227.757i		−	0.981711i
$233$			14.6508i			0.0628790i	0.999506	+	0.0314395i	$0.0100092\pi$
$233$			14.6508i			0.0628790i	−0.999506	+	0.0314395i	$0.989991\pi$
$234$	26.0455			0.111306
$235$	158.867	−	135.427i	0.676030	−	0.576285i
$236$	−85.3526			−0.361664
$237$	−227.254			−0.958878
$238$		−	16.6394i		−	0.0699134i
$239$	56.1742			0.235039			0.117519	−	0.993071i	$-0.462506\pi$
$239$	56.1742			0.235039			0.117519	+	0.993071i	$0.462506\pi$
$240$	391.828	−	334.016i	1.63262	−	1.39173i
$241$		−	437.008i		−	1.81331i	−0.421871	−	0.906656i	$-0.638627\pi$
$241$		−	437.008i		−	1.81331i	0.421871	−	0.906656i	$-0.361373\pi$
$242$		−	7.09449i		−	0.0293161i
$243$			21.4296i			0.0881875i
$244$		−	594.561i		−	2.43672i
$245$	322.873	+	378.757i	1.31785	+	1.54595i
$246$	−155.280			−0.631220
$247$	−186.575			−0.755365
$248$			632.692i			2.55118i
$249$			463.284i			1.86058i
$250$	237.274	+	389.661i	0.949097	+	1.55865i
$251$			64.4696i			0.256851i	0.991719	+	0.128425i	$0.0409923\pi$
$251$			64.4696i			0.256851i	−0.991719	+	0.128425i	$0.959008\pi$
$252$	−45.1128			−0.179019
$253$	17.6332	−	250.339i	0.0696964	−	0.989484i
$254$	4.34584			0.0171096
$255$	−4.36330	+	3.71952i	−0.0171110	+	0.0145863i
$256$	−379.978			−1.48429
$257$			167.595i			0.652120i	0.945349	+	0.326060i	$0.105721\pi$
$257$			167.595i			0.652120i	−0.945349	+	0.326060i	$0.894279\pi$
$258$	163.121			0.632251
$259$	310.336			1.19821
$260$	−637.306	+	543.275i	−2.45118	+	2.08952i
$261$	4.65776			0.0178458
$262$			615.929i			2.35087i
$263$	−451.846			−1.71805			−0.859023	−	0.511937i	$-0.828928\pi$
$263$	−451.846			−1.71805			−0.859023	+	0.511937i	$0.828928\pi$
$264$		−	649.532i		−	2.46035i
$265$	221.305	+	259.609i	0.835113	+	0.979657i
$266$	461.848			1.73627
$267$	−258.313			−0.967463
$268$	37.8874			0.141371
$269$	447.061			1.66194			0.830968	−	0.556320i	$-0.187787\pi$
$269$	447.061			1.66194			0.830968	+	0.556320i	$0.187787\pi$
$270$	−312.204	−	366.242i	−1.15631	−	1.35645i
$271$	382.640			1.41196			0.705979	−	0.708233i	$-0.250507\pi$
$271$	382.640			1.41196			0.705979	+	0.708233i	$0.250507\pi$
$272$	−12.5657			−0.0461975
$273$	671.362			2.45920
$274$			164.329i			0.599741i
$275$	269.343	+	43.1795i	0.979429	+	0.157016i
$276$	−46.1741	+	655.536i	−0.167298	+	2.37513i
$277$			210.611i			0.760327i	0.924919	+	0.380164i	$0.124132\pi$
$277$			210.611i			0.760327i	−0.924919	+	0.380164i	$0.875868\pi$
$278$			64.6120i			0.232417i
$279$	−12.9389			−0.0463760
$280$	900.559	−	767.686i	3.21628	−	2.74174i
$281$		−	410.892i		−	1.46225i	−0.682243	−	0.731125i	$-0.738995\pi$
$281$		−	410.892i		−	1.46225i	0.682243	−	0.731125i	$-0.261005\pi$
$282$			467.122i			1.65646i
$283$	141.513			0.500047			0.250024	−	0.968240i	$-0.419562\pi$
$283$	141.513			0.500047			0.250024	+	0.968240i	$0.419562\pi$
$284$	−440.403			−1.55072
$285$	−103.240	−	121.109i	−0.362246	−	0.424945i
$286$			715.610i			2.50213i
$287$	−169.152			−0.589380
$288$			17.8413i			0.0619491i
$289$	−288.860			−0.999516
$290$	−162.881	+	138.849i	−0.561660	+	0.478790i
$291$		−	111.415i		−	0.382869i
$292$		−	751.498i		−	2.57362i
$293$	286.076			0.976367			0.488184	−	0.872741i	$-0.337660\pi$
$293$	286.076			0.976367			0.488184	+	0.872741i	$0.337660\pi$
$294$	−1113.67			−3.78799
$295$	29.7034	+	34.8446i	0.100690	+	0.118117i
$296$		−	494.468i		−	1.67050i
$297$	−287.751			−0.968859
$298$	73.7975			0.247643
$299$	29.0398	−	412.279i	0.0971230	−	1.37886i
$300$	−705.299	−	113.069i	−2.35100	−	0.376898i
$301$	177.693			0.590342
$302$		−	805.473i		−	2.66713i
$303$		−	197.970i		−	0.653367i
$304$		−	348.778i		−	1.14730i
$305$	−242.725	+	206.912i	−0.795819	+	0.678400i
$306$		−	0.542186i		−	0.00177185i
$307$			225.226i			0.733634i	0.930293	+	0.366817i	$0.119553\pi$
$307$			225.226i			0.733634i	−0.930293	+	0.366817i	$0.880447\pi$
$308$		−	1239.49i		−	4.02432i
$309$		−	523.447i		−	1.69400i
$310$	452.473	−	385.712i	1.45959	−	1.24423i
$311$	217.119			0.698131			0.349065	−	0.937098i	$-0.386499\pi$
$311$	217.119			0.698131			0.349065	+	0.937098i	$0.386499\pi$
$312$		−	1069.70i		−	3.42853i
$313$	−215.119			−0.687280			−0.343640	−	0.939102i	$-0.611660\pi$
$313$	−215.119			−0.687280			−0.343640	+	0.939102i	$0.611660\pi$
$314$		−	85.4023i		−	0.271982i
$315$	15.6996	+	18.4170i	0.0498400	+	0.0584665i
$316$			690.972i			2.18662i
$317$		−	403.874i		−	1.27405i	−0.770843	−	0.637025i	$-0.780165\pi$
$317$		−	403.874i		−	1.27405i	0.770843	−	0.637025i	$-0.219835\pi$
$318$	−763.336			−2.40043
$319$			127.974i			0.401171i
$320$	−96.0126	−	112.631i	−0.300039	−	0.351971i
$321$			218.851i			0.681778i
$322$	−71.8851	+	1020.56i	−0.223246	+	3.16943i
$323$			3.88391i			0.0120245i
$324$	786.816			2.42844
$325$	443.576	+	71.1115i	1.36485	+	0.218805i
$326$	−767.002			−2.35277
$327$	−109.785			−0.335733
$328$			269.515i			0.821692i
$329$			508.851i			1.54666i
$330$	−464.516	+	395.979i	−1.40762	+	1.19994i
$331$	−475.088			−1.43531			−0.717655	−	0.696399i	$-0.754784\pi$
$331$	−475.088			−1.43531			−0.717655	+	0.696399i	$0.754784\pi$
$332$	1408.63			4.24285
$333$	10.1122			0.0303668
$334$	800.973			2.39812
$335$	−13.1851	−	15.4673i	−0.0393586	−	0.0461709i
$336$			1255.03i			3.73520i
$337$	515.422			1.52944			0.764720	−	0.644362i	$-0.222877\pi$
$337$	515.422			1.52944			0.764720	+	0.644362i	$0.222877\pi$
$338$			561.718i			1.66189i
$339$		−	235.052i		−	0.693370i
$340$	11.3093	+	13.2667i	0.0332626	+	0.0390198i
$341$		−	355.501i		−	1.04253i
$342$	15.0491			0.0440032
$343$	−615.961			−1.79580
$344$		−	283.124i		−	0.823034i
$345$	283.687	−	209.282i	0.822280	−	0.606614i
$346$	650.575			1.88027
$347$		−	415.425i		−	1.19719i	−0.801051	−	0.598596i	$-0.795726\pi$
$347$		−	415.425i		−	1.19719i	0.801051	−	0.598596i	$-0.204274\pi$
$348$		−	335.111i		−	0.962962i
$349$	−291.133			−0.834193			−0.417096	−	0.908862i	$-0.636952\pi$
$349$	−291.133			−0.834193			−0.417096	+	0.908862i	$0.636952\pi$
$350$	−1098.03	−	176.030i	−3.13722	−	0.502942i
$351$	−473.892			−1.35012
$352$	−490.198			−1.39261
$353$		−	143.579i		−	0.406740i	−0.979102	−	0.203370i	$-0.934811\pi$
$353$		−	143.579i		−	0.406740i	0.979102	−	0.203370i	$-0.0651895\pi$
$354$	−102.455			−0.289420
$355$	153.264	+	179.791i	0.431729	+	0.506454i
$356$			785.406i			2.20620i
$357$		−	13.9757i		−	0.0391475i
$358$			948.777i			2.65022i
$359$			458.518i			1.27721i	0.769536	+	0.638604i	$0.220488\pi$
$359$			458.518i			1.27721i	−0.769536	+	0.638604i	$0.779512\pi$
$360$	29.3443	−	25.0147i	0.0815119	−	0.0694852i
$361$	253.197			0.701377
$362$	−298.439			−0.824417
$363$		−	5.95876i		−	0.0164153i
$364$		−	2041.29i		−	5.60795i
$365$	−306.793	+	261.527i	−0.840530	+	0.716514i
$366$		−	713.691i		−	1.94998i
$367$	540.344			1.47233			0.736164	−	0.676803i	$-0.236635\pi$
$367$	540.344			1.47233			0.736164	+	0.676803i	$0.236635\pi$
$368$	770.703	+	54.2862i	2.09430	+	0.147517i
$369$	−5.51173			−0.0149369
$370$	−353.621	+	301.446i	−0.955732	+	0.814718i
$371$	−831.528			−2.24132
$372$			930.913i			2.50245i
$373$	−153.140			−0.410563			−0.205282	−	0.978703i	$-0.565811\pi$
$373$	−153.140			−0.410563			−0.205282	+	0.978703i	$0.565811\pi$
$374$	14.8968			0.0398309
$375$	199.290	+	327.282i	0.531440	+	0.872752i
$376$	810.768			2.15630
$377$			210.757i			0.559038i
$378$	1173.07			3.10337
$379$			389.555i			1.02785i	0.857835	+	0.513925i	$0.171809\pi$
$379$			389.555i			1.02785i	−0.857835	+	0.513925i	$0.828191\pi$
$380$	−368.236	+	313.904i	−0.969041	+	0.826063i
$381$	3.65014			0.00958041
$382$	551.723			1.44430
$383$	−57.2079			−0.149368			−0.0746840	−	0.997207i	$-0.523795\pi$
$383$	−57.2079			−0.149368			−0.0746840	+	0.997207i	$0.523795\pi$
$384$	−219.703			−0.572144
$385$	−506.013	+	431.353i	−1.31432	+	1.12040i
$386$	742.013			1.92231
$387$	5.79004			0.0149613
$388$	−338.760			−0.873092
$389$		−	507.440i		−	1.30447i	−0.758015	−	0.652237i	$-0.773831\pi$
$389$		−	507.440i		−	1.30447i	0.758015	−	0.652237i	$-0.226169\pi$
$390$	−765.002	+	652.129i	−1.96154	+	1.67213i
$391$	−8.58236	−	0.604517i	−0.0219498	−	0.00154608i
$392$			1932.96i			4.93102i
$393$			517.328i			1.31636i
$394$	103.626			0.263010
$395$	282.084	−	240.464i	0.714137	−	0.608769i
$396$		−	40.3882i		−	0.101990i
$397$		−	453.820i		−	1.14312i	−0.820559	−	0.571561i	$-0.806338\pi$
$397$		−	453.820i		−	1.14312i	0.820559	−	0.571561i	$-0.193662\pi$
$398$	998.923			2.50986
$399$	387.913			0.972213
$400$	−132.934	+	829.209i	−0.332335	+	2.07302i
$401$		−	518.111i		−	1.29205i	−0.763318	−	0.646023i	$-0.776431\pi$
$401$		−	518.111i		−	1.29205i	0.763318	−	0.646023i	$-0.223569\pi$
$402$	45.4788			0.113131
$403$		−	585.468i		−	1.45278i
$404$	−601.933			−1.48993
$405$	−273.818	−	321.212i	−0.676095	−	0.793115i
$406$		−	521.709i		−	1.28500i
$407$			277.835i			0.682641i
$408$	−22.2678			−0.0545780
$409$	255.249			0.624080			0.312040	−	0.950069i	$-0.398988\pi$
$409$	255.249			0.624080			0.312040	+	0.950069i	$0.398988\pi$
$410$	192.745	−	164.306i	0.470109	−	0.400747i
$411$			138.022i			0.335821i
$412$	−1591.55			−3.86300
$413$	−111.607			−0.270235
$414$	−2.34234	+	33.2543i	−0.00565783	+	0.0803245i
$415$	−490.213	−	575.061i	−1.18124	−	1.38569i
$416$	−807.297			−1.94062
$417$			54.2685i			0.130140i
$418$			413.480i			0.989186i
$419$		−	443.006i		−	1.05729i	−0.848842	−	0.528647i	$-0.822700\pi$
$419$		−	443.006i		−	1.05729i	0.848842	−	0.528647i	$-0.177300\pi$
$420$	1325.04	−	1129.54i	3.15486	−	2.68937i
$421$		−	460.877i		−	1.09472i	−0.836897	−	0.547360i	$-0.815633\pi$
$421$		−	460.877i		−	1.09472i	0.836897	−	0.547360i	$-0.184367\pi$
$422$		−	146.355i		−	0.346813i
$423$			16.5807i			0.0391978i
$424$			1324.90i			3.12476i
$425$	1.48032	−	9.23386i	0.00348310	−	0.0217267i
$426$	−528.646			−1.24095
$427$		−	777.448i		−	1.82072i
$428$	665.421			1.55472
$429$			601.051i			1.40105i
$430$	−202.477	+	172.603i	−0.470877	+	0.401401i
$431$			61.7007i			0.143157i	0.997435	+	0.0715785i	$0.0228037\pi$
$431$			61.7007i			0.143157i	−0.997435	+	0.0715785i	$0.977196\pi$
$432$		−	885.880i		−	2.05065i
$433$	560.427			1.29429			0.647144	−	0.762368i	$-0.275963\pi$
$433$	560.427			1.29429			0.647144	+	0.762368i	$0.275963\pi$
$434$			1449.27i			3.33933i
$435$	−136.806	+	116.621i	−0.314497	+	0.268095i
$436$			333.803i			0.765603i
$437$	16.7792	−	238.215i	0.0383963	−	0.545114i
$438$		−	902.074i		−	2.05953i
$439$	−213.637			−0.486644			−0.243322	−	0.969946i	$-0.578237\pi$
$439$	−213.637			−0.486644			−0.243322	+	0.969946i	$0.578237\pi$
$440$	687.287	+	806.245i	1.56202	+	1.83238i
$441$	−39.5301			−0.0896375
$442$	24.5332			0.0555050
$443$			387.430i			0.874559i	0.899326	+	0.437280i	$0.144058\pi$
$443$			387.430i			0.874559i	−0.899326	+	0.437280i	$0.855942\pi$
$444$		−	727.536i		−	1.63860i
$445$	320.636	−	273.328i	0.720530	−	0.614219i
$446$	480.231			1.07675
$447$	61.9836			0.138666
$448$	360.756			0.805259
$449$	−440.505			−0.981079			−0.490540	−	0.871419i	$-0.663200\pi$
$449$	−440.505			−0.981079			−0.490540	+	0.871419i	$0.663200\pi$
$450$	−35.7787	−	5.73584i	−0.0795083	−	0.0127463i
$451$		−	151.437i		−	0.335780i
$452$	−714.683			−1.58116
$453$		−	676.528i		−	1.49344i
$454$		−	414.649i		−	0.913324i
$455$	−833.342	+	710.386i	−1.83152	+	1.56129i
$456$		−	618.074i		−	1.35542i
$457$	109.473			0.239547			0.119774	−	0.992801i	$-0.461783\pi$
$457$	109.473			0.239547			0.119774	+	0.992801i	$0.461783\pi$
$458$	−315.263			−0.688347
$459$			9.86494i			0.0214922i
$460$	−636.326	−	862.556i	−1.38332	−	1.87512i
$461$	−120.723			−0.261871			−0.130936	−	0.991391i	$-0.541798\pi$
$461$	−120.723			−0.261871			−0.130936	+	0.991391i	$0.541798\pi$
$462$		−	1487.84i		−	3.22044i
$463$			110.321i			0.238275i	0.992878	+	0.119138i	$0.0380130\pi$
$463$			110.321i			0.238275i	−0.992878	+	0.119138i	$0.961987\pi$
$464$	−393.984			−0.849104
$465$	380.038	−	323.965i	0.817287	−	0.696700i
$466$	53.4717			0.114746
$467$	614.180			1.31516			0.657580	−	0.753385i	$-0.271580\pi$
$467$	614.180			1.31516			0.657580	+	0.753385i	$0.271580\pi$
$468$		−	66.5145i		−	0.142125i
$469$	49.5416			0.105632
$470$	−494.274	−	579.825i	−1.05165	−	1.23367i
$471$		−	71.7306i		−	0.152294i
$472$			177.827i			0.376752i
$473$			159.084i			0.336329i
$474$			829.420i			1.74983i
$475$	256.298	+	41.0882i	0.539575	+	0.0865015i
$476$	−42.4933			−0.0892717
$477$	−27.0949			−0.0568028
$478$		−	205.022i		−	0.428915i
$479$			326.931i			0.682528i	0.939968	+	0.341264i	$0.110855\pi$
$479$			326.931i			0.682528i	−0.939968	+	0.341264i	$0.889145\pi$
$480$	−446.713	−	524.031i	−0.930651	−	1.09173i
$481$			457.561i			0.951271i
$482$	−1594.97			−3.30906
$483$	−60.3773	+	857.180i	−0.125005	+	1.77470i
$484$	−18.1178			−0.0374334
$485$	117.891	+	138.296i	0.243075	+	0.285147i
$486$	78.2125			0.160931
$487$			509.809i			1.04684i	0.852076	+	0.523418i	$0.175343\pi$
$487$			509.809i			1.04684i	−0.852076	+	0.523418i	$0.824657\pi$
$488$	−1238.73			−2.53838
$489$	−644.216			−1.31742
$490$	1382.37	−	1178.40i	2.82115	−	2.40491i
$491$	−60.2356			−0.122679			−0.0613397	−	0.998117i	$-0.519537\pi$
$491$	−60.2356			−0.122679			−0.0613397	+	0.998117i	$0.519537\pi$
$492$			396.551i			0.805999i
$493$	4.38731			0.00889920
$494$			680.952i			1.37844i
$495$	−16.4882	+	14.0554i	−0.0333094	+	0.0283948i
$496$	1094.46			2.20657
$497$	−575.871			−1.15869
$498$	1690.87			3.39532
$499$	−628.018			−1.25855			−0.629276	−	0.777182i	$-0.716649\pi$
$499$	−628.018			−1.25855			−0.629276	+	0.777182i	$0.716649\pi$
$500$	995.109	−	605.946i	1.99022	−	1.21189i
$501$	672.749			1.34281
$502$	235.298			0.468720
$503$	408.012			0.811157			0.405578	−	0.914060i	$-0.367070\pi$
$503$	408.012			0.811157			0.405578	+	0.914060i	$0.367070\pi$
$504$			93.9898i			0.186488i
$505$	209.478	+	245.735i	0.414807	+	0.486603i
$506$	−913.675	−	64.3567i	−1.80568	−	0.127187i
$507$			471.795i			0.930562i
$508$		−	11.0983i		−	0.0218471i
$509$	168.871			0.331769			0.165885	−	0.986145i	$-0.446952\pi$
$509$	168.871			0.331769			0.165885	+	0.986145i	$0.446952\pi$
$510$	13.5753	+	15.9249i	0.0266182	+	0.0312254i
$511$		−	982.659i		−	1.92301i
$512$			1100.14i			2.14872i
$513$	−273.815			−0.533752
$514$	611.679			1.19004
$515$	553.874	+	649.740i	1.07548	+	1.26163i
$516$		−	416.575i		−	0.807315i
$517$	−455.560			−0.881161
$518$		−	1132.65i		−	2.18658i
$519$	546.427			1.05285
$520$	1131.88	+	1327.79i	2.17669	+	2.55344i
$521$			816.261i			1.56672i	0.621569	+	0.783360i	$0.286496\pi$
$521$			816.261i			1.56672i	−0.621569	+	0.783360i	$0.713504\pi$
$522$		−	16.9996i		−	0.0325664i
$523$	−918.460			−1.75614			−0.878069	−	0.478534i	$-0.841168\pi$
$523$	−918.460			−1.75614			−0.878069	+	0.478534i	$0.841168\pi$
$524$	1572.95			3.00181
$525$	−922.250	−	147.850i	−1.75667	−	0.281619i
$526$			1649.12i			3.13521i
$527$	−12.1876			−0.0231264
$528$	−1123.59			−2.12801
$529$	523.777	+	74.1546i	0.990126	+	0.140179i
$530$	947.507	−	807.707i	1.78775	−	1.52398i
$531$	−3.63667			−0.00684871
$532$		−	1179.46i		−	2.21703i
$533$		−	249.399i		−	0.467915i
$534$			942.775i			1.76550i
$535$	−231.572	−	271.653i	−0.432845	−	0.507763i
$536$		−	78.9362i		−	0.147269i
$537$			796.892i			1.48397i
$538$		−	1631.66i		−	3.03282i
$539$		−	1086.11i		−	2.01504i
$540$	−935.301	+	797.301i	−1.73204	+	1.47648i
$541$	−749.196			−1.38484			−0.692418	−	0.721497i	$-0.743455\pi$
$541$	−749.196			−1.38484			−0.692418	+	0.721497i	$0.743455\pi$
$542$		−	1396.54i		−	2.57664i
$543$	−250.663			−0.461627
$544$			16.8054i			0.0308923i
$545$	136.273	−	116.166i	0.250041	−	0.213149i
$546$		−	2450.30i		−	4.48773i
$547$			420.350i			0.768464i	0.923237	+	0.384232i	$0.125534\pi$
$547$			420.350i			0.768464i	−0.923237	+	0.384232i	$0.874466\pi$
$548$	419.660			0.765803
$549$		−	25.3328i		−	0.0461435i
$550$	157.594	−	983.033i	0.286535	−	1.78733i
$551$			121.776i			0.221008i
$552$	1365.77	+	96.2010i	2.47422	+	0.174277i
$553$			903.515i			1.63384i
$554$	768.676			1.38750
$555$	−297.011	+	253.189i	−0.535155	+	0.456196i
$556$	165.005			0.296771
$557$	454.071			0.815209			0.407604	−	0.913159i	$-0.366364\pi$
$557$	454.071			0.815209			0.407604	+	0.913159i	$0.366364\pi$
$558$			47.2238i			0.0846304i
$559$			261.992i			0.468679i
$560$	−1327.98	−	1557.83i	−2.37139	−	2.78184i
$561$	12.5120			0.0223030
$562$	−1499.65			−2.66842
$563$	−291.886			−0.518448			−0.259224	−	0.965817i	$-0.583467\pi$
$563$	−291.886			−0.518448			−0.259224	+	0.965817i	$0.583467\pi$
$564$	1192.93			2.11512
$565$	248.715	+	291.764i	0.440204	+	0.516396i
$566$		−	516.488i		−	0.912523i
$567$	1028.84			1.81453
$568$			917.554i			1.61541i
$569$		−	22.8719i		−	0.0401966i	−0.999798	−	0.0200983i	$-0.993602\pi$
$569$		−	22.8719i		−	0.0401966i	0.999798	−	0.0200983i	$-0.00639792\pi$
$570$	−442.018	+	376.800i	−0.775470	+	0.661053i
$571$			330.897i			0.579504i	0.957102	+	0.289752i	$0.0935728\pi$
$571$			330.897i			0.579504i	−0.957102	+	0.289752i	$0.906427\pi$
$572$	1827.51			3.19495
$573$	463.400			0.808726
$574$			617.362i			1.07554i
$575$	−130.685	+	559.952i	−0.227279	+	0.973830i
$576$	11.7551			0.0204081
$577$			674.901i			1.16967i	0.811151	+	0.584836i	$0.198841\pi$
$577$			674.901i			1.16967i	−0.811151	+	0.584836i	$0.801159\pi$
$578$			1054.27i			1.82399i
$579$	623.227			1.07639
$580$	354.590	+	415.963i	0.611362	+	0.717178i
$581$	1841.92			3.17026
$582$	−406.636			−0.698688
$583$		−	744.443i		−	1.27692i
$584$	−1565.70			−2.68100
$585$	−27.1541	+	23.1476i	−0.0464172	+	0.0395685i
$586$		−	1044.10i		−	1.78175i
$587$			337.351i			0.574703i	0.957825	+	0.287352i	$0.0927748\pi$
$587$			337.351i			0.574703i	−0.957825	+	0.287352i	$0.907225\pi$
$588$			2844.07i			4.83685i
$589$		−	338.284i		−	0.574336i
$590$	127.174	−	108.410i	0.215549	−	0.183746i
$591$	87.0370			0.147271
$592$	−855.353			−1.44485
$593$		−	1052.75i		−	1.77530i	−0.460520	−	0.887650i	$-0.652337\pi$
$593$		−	1052.75i		−	1.77530i	0.460520	−	0.887650i	$-0.347663\pi$
$594$			1050.22i			1.76804i
$595$	14.7880	+	17.3476i	0.0248538	+	0.0291556i
$596$		−	188.463i		−	0.316212i
$597$	839.010			1.40538
$598$	−1504.71	−	105.988i	−2.51624	−	0.177237i
$599$	−825.344			−1.37787			−0.688935	−	0.724823i	$-0.741921\pi$
$599$	−825.344			−1.37787			−0.688935	+	0.724823i	$0.741921\pi$
$600$	−235.574	+	1469.45i	−0.392623	+	2.44908i
$601$	148.497			0.247083			0.123542	−	0.992339i	$-0.460575\pi$
$601$	148.497			0.247083			0.123542	+	0.992339i	$0.460575\pi$
$602$		−	648.534i		−	1.07730i
$603$	1.61429			0.00267710
$604$	−2057.00			−3.40563
$605$	6.30513	+	7.39644i	0.0104217	+	0.0122255i
$606$	−722.541			−1.19231
$607$			0.574338i			0.000946190i	1.00000		0.000473095i	$0.000150591\pi$
$607$			0.574338i			0.000946190i	−1.00000		0.000473095i	$0.999849\pi$
$608$	−466.456			−0.767197
$609$		−	438.191i		−	0.719525i
$610$	755.176	+	885.884i	1.23799	+	1.45227i
$611$	−750.253			−1.22791
$612$	−1.38462			−0.00226246
$613$	847.151			1.38198			0.690988	−	0.722866i	$-0.257176\pi$
$613$	847.151			1.38198			0.690988	+	0.722866i	$0.257176\pi$
$614$	822.017			1.33879
$615$	161.889	−	138.003i	0.263234	−	0.224395i
$616$	−2582.40			−4.19221
$617$	−192.343			−0.311738			−0.155869	−	0.987778i	$-0.549818\pi$
$617$	−192.343			−0.311738			−0.155869	+	0.987778i	$0.549818\pi$
$618$	−1910.45			−3.09134
$619$			934.813i			1.51020i	0.655611	+	0.755099i	$0.272411\pi$
$619$			934.813i			1.51020i	−0.655611	+	0.755099i	$0.727589\pi$
$620$	−985.024	−	1155.52i	−1.58875	−	1.86373i
$621$	42.6183	−	605.054i	0.0686285	−	0.974322i
$622$		−	792.428i		−	1.27400i
$623$			1027.00i			1.64847i
$624$	−1850.42			−2.96541
$625$	−593.679	−	195.372i	−0.949887	−	0.312595i
$626$			785.128i			1.25420i
$627$			347.287i			0.553887i
$628$	−218.099			−0.347291
$629$	9.52499			0.0151431
$630$	67.2172	−	57.2996i	0.106694	−	0.0909518i
$631$		−	555.181i		−	0.879844i	−0.898036	−	0.439922i	$-0.855006\pi$
$631$		−	555.181i		−	0.879844i	0.898036	−	0.439922i	$-0.144994\pi$
$632$	1439.60			2.27785
$633$		−	122.926i		−	0.194195i
$634$	−1474.04			−2.32498
$635$	−4.53081	+	3.86231i	−0.00713513	+	0.00608238i
$636$			1949.39i			3.06508i
$637$		−	1788.69i		−	2.80798i
$638$	467.071			0.732087
$639$	−18.7645			−0.0293654
$640$	272.711	−	232.474i	0.426111	−	0.363240i
$641$			748.031i			1.16698i	0.812122	+	0.583488i	$0.198312\pi$
$641$			748.031i			1.16698i	−0.812122	+	0.583488i	$0.801688\pi$
$642$	798.750			1.24416
$643$	−229.224			−0.356492			−0.178246	−	0.983986i	$-0.557042\pi$
$643$	−229.224			−0.356492			−0.178246	+	0.983986i	$0.557042\pi$
$644$	2606.28	+	183.579i	4.04701	+	0.285060i
$645$	−170.064	+	144.971i	−0.263664	+	0.224762i
$646$	14.1753			0.0219432
$647$		−	527.882i		−	0.815892i	−0.913006	−	0.407946i	$-0.866245\pi$
$647$		−	527.882i		−	0.815892i	0.913006	−	0.407946i	$-0.133755\pi$
$648$		−	1639.28i		−	2.52976i
$649$		−	99.9187i		−	0.153958i
$650$	259.539	−	1618.94i	0.399291	−	2.49067i
$651$			1217.26i			1.86983i
$652$			1958.75i			3.00422i
$653$			302.572i			0.463356i	0.972792	+	0.231678i	$0.0744216\pi$
$653$			302.572i			0.463356i	−0.972792	+	0.231678i	$0.925578\pi$
$654$			400.686i			0.612670i
$655$	−547.398	−	642.144i	−0.835723	−	0.980372i
$656$	466.219			0.710700
$657$		−	32.0195i		−	0.0487359i
$658$	1857.18			2.82246
$659$		−	530.234i		−	0.804604i	−0.915507	−	0.402302i	$-0.868210\pi$
$659$		−	530.234i		−	0.804604i	0.915507	−	0.402302i	$-0.131790\pi$
$660$	1011.24	+	1186.27i	1.53218	+	1.79738i
$661$			632.276i			0.956545i	0.878211	+	0.478273i	$0.158737\pi$
$661$			632.276i			0.956545i	−0.878211	+	0.478273i	$0.841263\pi$
$662$			1733.95i			2.61926i
$663$	20.6058			0.0310796
$664$		−	2934.79i		−	4.41986i
$665$	−481.505	+	410.461i	−0.724068	+	0.617235i
$666$		−	36.9068i		−	0.0554156i
$667$	−269.090	−	18.9539i	−0.403433	−	0.0284167i
$668$		−	2045.51i		−	3.06214i
$669$	403.353			0.602919
$670$	−56.4516	+	48.1224i	−0.0842560	+	0.0718245i
$671$	696.027			1.03730
$672$	1678.47			2.49772
$673$		−	1249.04i		−	1.85593i	−0.372673	−	0.927963i	$-0.621559\pi$
$673$		−	1249.04i		−	1.85593i	0.372673	−	0.927963i	$-0.378441\pi$
$674$		−	1881.16i		−	2.79104i
$675$	650.985	+	104.362i	0.964422	+	0.154611i
$676$	1434.50			2.12205
$677$	61.8524			0.0913625			0.0456812	−	0.998956i	$-0.485454\pi$
$677$	61.8524			0.0913625			0.0456812	+	0.998956i	$0.485454\pi$
$678$	−857.882			−1.26531
$679$	−442.962			−0.652375
$680$	27.6404	−	23.5622i	0.0406477	−	0.0346503i
$681$		−	348.270i		−	0.511409i
$682$	−1297.49			−1.90248
$683$			1191.39i			1.74434i	0.489200	+	0.872172i	$0.337289\pi$
$683$			1191.39i			1.74434i	−0.489200	+	0.872172i	$0.662711\pi$
$684$		−	38.4321i		−	0.0561873i
$685$	−146.045	−	171.323i	−0.213205	−	0.250107i
$686$			2248.10i			3.27711i
$687$	−264.794			−0.385435
$688$	−489.760			−0.711860
$689$		−	1226.01i		−	1.77940i
$690$	−763.825	−	1035.38i	−1.10699	−	1.50056i
$691$	435.751			0.630609			0.315304	−	0.948991i	$-0.397893\pi$
$691$	435.751			0.630609			0.315304	+	0.948991i	$0.397893\pi$
$692$		−	1661.42i		−	2.40090i
$693$		−	52.8116i		−	0.0762072i
$694$	−1516.20			−2.18472
$695$	−57.4230	−	67.3620i	−0.0826230	−	0.0969237i
$696$	−698.183			−1.00314
$697$	−5.19170			−0.00744863
$698$			1062.56i			1.52230i
$699$	44.9117			0.0642513
$700$	−449.541	+	2804.12i	−0.642201	+	4.00589i
$701$			676.541i			0.965108i	0.875866	+	0.482554i	$0.160291\pi$
$701$			676.541i			0.965108i	−0.875866	+	0.482554i	$0.839709\pi$
$702$			1729.58i			2.46379i
$703$			264.379i			0.376072i
$704$			322.975i			0.458771i
$705$	−415.148	−	487.003i	−0.588862	−	0.690784i
$706$	−524.028			−0.742249
$707$	−787.088			−1.11328
$708$			261.646i			0.369557i
$709$		−	336.510i		−	0.474627i	−0.971433	−	0.237313i	$-0.923733\pi$
$709$		−	336.510i		−	0.474627i	0.971433	−	0.237313i	$-0.0762668\pi$
$710$	656.193	−	559.374i	0.924215	−	0.787851i
$711$			29.4406i			0.0414073i
$712$	1636.35			2.29824
$713$	747.513	+	52.6527i	1.04840	+	0.0738467i
$714$	−51.0076			−0.0714392
$715$	−635.989	−	746.068i	−0.889495	−	1.04345i
$716$	2422.97			3.38403
$717$		−	172.201i		−	0.240168i
$718$	1673.47			2.33074
$719$	−560.437			−0.779468			−0.389734	−	0.920927i	$-0.627433\pi$
$719$	−560.437			−0.779468			−0.389734	+	0.920927i	$0.627433\pi$
$720$	−43.2715	−	50.7611i	−0.0600993	−	0.0705015i
$721$	−2081.12			−2.88643
$722$		−	924.105i		−	1.27992i
$723$	−1339.64			−1.85289
$724$			762.148i			1.05269i
$725$	46.4137	−	289.517i	0.0640189	−	0.399334i
$726$	−21.7480			−0.0299559
$727$	206.877			0.284563			0.142281	−	0.989826i	$-0.454556\pi$
$727$	206.877			0.284563			0.142281	+	0.989826i	$0.454556\pi$
$728$	−4252.91			−5.84191
$729$	−694.056			−0.952066
$730$	954.509	+	1119.72i	1.30755	+	1.53386i
$731$	5.45384			0.00746080
$732$	−1822.61			−2.48990
$733$	816.371			1.11374			0.556869	−	0.830600i	$-0.312002\pi$
$733$	816.371			1.11374			0.556869	+	0.830600i	$0.312002\pi$
$734$		−	1972.12i		−	2.68681i
$735$	1161.07	−	989.758i	1.57968	−	1.34661i
$736$	72.6023	−	1030.74i	0.0986444	−	1.40046i
$737$			44.3532i			0.0601807i
$738$			20.1164i			0.0272580i
$739$	486.014			0.657664			0.328832	−	0.944388i	$-0.393345\pi$
$739$	486.014			0.657664			0.328832	+	0.944388i	$0.393345\pi$
$740$	769.826	+	903.070i	1.04031	+	1.22036i
$741$			571.941i			0.771850i
$742$			3034.87i			4.09012i
$743$	−549.254			−0.739238			−0.369619	−	0.929183i	$-0.620512\pi$
$743$	−549.254			−0.739238			−0.369619	+	0.929183i	$0.620512\pi$
$744$	1939.50			2.60686
$745$	−76.9384	+	65.5865i	−0.103273	+	0.0880356i
$746$			558.922i			0.749226i
$747$	60.0181			0.0803455
$748$		−	38.0431i		−	0.0508597i
$749$	870.105			1.16169
$750$	1194.50	−	727.358i	1.59266	−	0.969811i
$751$			435.216i			0.579515i	0.957100	+	0.289757i	$0.0935746\pi$
$751$			435.216i			0.579515i	−0.957100	+	0.289757i	$0.906425\pi$
$752$		−	1402.50i		−	1.86503i
$753$	197.630			0.262457
$754$	769.211			1.02017
$755$	715.853	+	839.755i	0.948150	+	1.11226i
$756$		−	2995.77i		−	3.96266i
$757$	−651.064			−0.860058			−0.430029	−	0.902815i	$-0.641497\pi$
$757$	−651.064			−0.860058			−0.430029	+	0.902815i	$0.641497\pi$
$758$	1421.78			1.87569
$759$	−767.409	−	54.0541i	−1.01108	−	0.0712175i
$760$	654.000	+	767.197i	0.860527	+	1.00947i
$761$	−107.717			−0.141547			−0.0707736	−	0.997492i	$-0.522547\pi$
$761$	−107.717			−0.141547			−0.0707736	+	0.997492i	$0.522547\pi$
$762$		−	13.3221i		−	0.0174830i
$763$			436.481i			0.572059i
$764$		−	1408.98i		−	1.84421i
$765$	0.481860	+	0.565262i	0.000629883	+	0.000738905i
$766$			208.794i			0.272578i
$767$		−	164.554i		−	0.214543i
$768$			1164.81i			1.51668i
$769$			913.047i			1.18732i	0.804717	+	0.593659i	$0.202317\pi$
$769$			913.047i			1.18732i	−0.804717	+	0.593659i	$0.797683\pi$
$770$	1574.33	+	1846.82i	2.04458	+	2.39846i
$771$	513.758			0.666352
$772$		−	1894.94i		−	2.45458i
$773$	−1303.84			−1.68672			−0.843362	−	0.537345i	$-0.819427\pi$
$773$	−1303.84			−1.68672			−0.843362	+	0.537345i	$0.819427\pi$
$774$		−	21.1322i		−	0.0273026i
$775$	−128.934	+	804.258i	−0.166366	+	1.03775i
$776$			705.786i			0.909518i
$777$		−	951.327i		−	1.22436i
$778$	−1852.03			−2.38050
$779$		−	144.102i		−	0.184984i
$780$	1665.39	+	1953.65i	2.13512	+	2.50467i
$781$		−	515.561i		−	0.660130i
$782$	−2.20633	+	31.3234i	−0.00282140	+	0.0400555i
$783$			309.304i			0.395024i
$784$	3343.72			4.26495
$785$	75.9001	+	89.0371i	0.0966880	+	0.113423i
$786$	1888.11			2.40218
$787$	1106.36			1.40579			0.702895	−	0.711294i	$-0.251891\pi$
$787$	1106.36			1.40579			0.702895	+	0.711294i	$0.251891\pi$
$788$		−	264.638i		−	0.335835i
$789$			1385.12i			1.75554i
$790$	−877.632	−	1029.54i	−1.11093	−	1.30321i
$791$	−934.520			−1.18144
$792$	−84.1464			−0.106245
$793$	1146.27			1.44549
$794$	−1656.33			−2.08605
$795$	795.825	−	678.405i	1.00104	−	0.853339i
$796$		−	2551.03i		−	3.20481i
$797$	−514.580			−0.645646			−0.322823	−	0.946459i	$-0.604632\pi$
$797$	−514.580			−0.645646			−0.322823	+	0.946459i	$0.604632\pi$
$798$		−	1415.78i		−	1.77416i
$799$			15.6179i			0.0195468i
$800$	1108.98	+	177.786i	1.38623	+	0.222232i
$801$			33.4642i			0.0417780i
$802$	−1890.97			−2.35782
$803$	879.747			1.09558
$804$		−	116.143i		−	0.144456i
$805$	−832.061	−	1127.88i	−1.03362	−	1.40109i
$806$	−2136.81			−2.65113
$807$		−	1370.45i		−	1.69821i
$808$			1254.09i			1.55209i
$809$	455.926			0.563568			0.281784	−	0.959478i	$-0.409074\pi$
$809$	455.926			0.563568			0.281784	+	0.959478i	$0.409074\pi$
$810$	−1172.34	+	999.368i	−1.44733	+	1.23379i
$811$	429.150			0.529162			0.264581	−	0.964364i	$-0.414766\pi$
$811$	429.150			0.529162			0.264581	+	0.964364i	$0.414766\pi$
$812$	−1332.33			−1.64080
$813$		−	1172.97i		−	1.44277i
$814$	1014.03			1.24573
$815$	799.647	−	681.663i	0.981162	−	0.836396i
$816$			38.5199i			0.0472057i
$817$			151.379i			0.185286i
$818$		−	931.594i		−	1.13887i
$819$		−	86.9744i		−	0.106196i
$820$	−419.602	−	492.228i	−0.511709	−	0.600278i
$821$	355.911			0.433509			0.216754	−	0.976226i	$-0.430453\pi$
$821$	355.911			0.433509			0.216754	+	0.976226i	$0.430453\pi$
$822$	503.746			0.612830
$823$		−	64.3646i		−	0.0782073i	−0.999235	−	0.0391036i	$-0.987550\pi$
$823$		−	64.3646i		−	0.0782073i	0.999235	−	0.0391036i	$-0.0124503\pi$
$824$			3315.91i			4.02416i
$825$	132.366	−	825.664i	0.160443	−	1.00080i
$826$			407.338i			0.493145i
$827$	1333.98			1.61304			0.806518	−	0.591209i	$-0.201349\pi$
$827$	1333.98			1.61304			0.806518	+	0.591209i	$0.201349\pi$
$828$	84.9242	+	5.98182i	0.102565	+	0.00722442i
$829$	843.007			1.01690			0.508448	−	0.861093i	$-0.330219\pi$
$829$	843.007			1.01690			0.508448	+	0.861093i	$0.330219\pi$
$830$	−2098.83	+	1789.15i	−2.52871	+	2.15561i
$831$	645.622			0.776921
$832$			531.901i			0.639304i
$833$	−37.2348			−0.0446997
$834$	198.066			0.237490
$835$	−835.064	+	711.854i	−1.00008	+	0.852520i
$836$	1055.94			1.26308
$837$		−	859.224i		−	1.02655i
$838$	−1616.86			−1.92943
$839$		−	466.892i		−	0.556486i	−0.960511	−	0.278243i	$-0.910248\pi$
$839$		−	466.892i		−	0.556486i	0.960511	−	0.278243i	$-0.0897520\pi$
$840$	−2353.32	−	2760.64i	−2.80157	−	3.28648i
$841$	−703.441			−0.836434
$842$	−1682.08			−1.99772
$843$	−1259.58			−1.49416
$844$	−373.758			−0.442842
$845$	−499.219	−	585.625i	−0.590791	−	0.693047i
$846$	60.5153			0.0715310
$847$	−23.6908			−0.0279702
$848$	2291.87			2.70268
$849$		−	433.806i		−	0.510961i
$850$	−33.7012	−	5.40279i	−0.0396485	−	0.00635622i
$851$	−584.204	−	41.1497i	−0.686491	−	0.0483545i
$852$			1350.04i			1.58456i
$853$		−	912.358i		−	1.06959i	−0.844983	−	0.534794i	$-0.820389\pi$
$853$		−	912.358i		−	1.06959i	0.844983	−	0.534794i	$-0.179611\pi$
$854$	−2837.49			−3.32258
$855$	−15.6896	+	13.3747i	−0.0183504	+	0.0156429i
$856$		−	1386.36i		−	1.61958i
$857$			1218.75i			1.42211i	0.703136	+	0.711055i	$0.251782\pi$
$857$			1218.75i			1.42211i	−0.703136	+	0.711055i	$0.748218\pi$
$858$	2193.68			2.55674
$859$	660.884			0.769365			0.384682	−	0.923049i	$-0.374311\pi$
$859$	660.884			0.769365			0.384682	+	0.923049i	$0.374311\pi$
$860$	440.789	+	517.082i	0.512545	+	0.601258i
$861$			518.531i			0.602243i
$862$	225.192			0.261244
$863$		−	1280.50i		−	1.48378i	−0.670524	−	0.741888i	$-0.733931\pi$
$863$		−	1280.50i		−	1.48378i	0.670524	−	0.741888i	$-0.266069\pi$
$864$	−1184.78			−1.37127
$865$	−678.264	+	578.189i	−0.784120	+	0.668427i
$866$		−	2045.41i		−	2.36191i
$867$			885.493i			1.02133i
$868$	3701.12			4.26396
$869$	−808.891			−0.930830
$870$	425.638	+	499.309i	0.489239	+	0.573918i
$871$			73.0444i			0.0838627i
$872$	695.458			0.797544
$873$	−14.4337			−0.0165335
$874$	−869.423	−	61.2397i	−0.994764	−	0.0700683i
$875$	1301.21	−	792.336i	1.48709	−	0.905526i
$876$	−2303.70			−2.62979
$877$		−	83.1670i		−	0.0948313i	−0.998875	−	0.0474156i	$-0.984901\pi$
$877$		−	83.1670i		−	0.0948313i	0.998875	−	0.0474156i	$-0.0150985\pi$
$878$			779.719i			0.888063i
$879$		−	876.957i		−	0.997676i
$880$	1394.68	−	1188.90i	1.58486	−	1.35102i
$881$			625.318i			0.709782i	0.934908	+	0.354891i	$0.115482\pi$
$881$			625.318i			0.709782i	−0.934908	+	0.354891i	$0.884518\pi$
$882$			144.275i			0.163577i
$883$		−	227.584i		−	0.257739i	−0.991662	−	0.128870i	$-0.958865\pi$
$883$		−	227.584i		−	0.257739i	0.991662	−	0.128870i	$-0.0411349\pi$
$884$		−	62.6524i		−	0.0708737i
$885$	106.815	−	91.0550i	0.120695	−	0.102887i
$886$	1414.02			1.59596
$887$			1473.82i			1.66158i	0.556590	+	0.830788i	$0.312110\pi$
$887$			1473.82i			1.66158i	−0.556590	+	0.830788i	$0.687890\pi$
$888$	−1515.78			−1.70696
$889$		−	14.5122i		−	0.0163242i
$890$	−997.576	−	1170.24i	−1.12087	−	1.31488i
$891$			921.092i			1.03377i
$892$		−	1226.40i		−	1.37489i
$893$	−433.496			−0.485438
$894$		−	226.224i		−	0.253047i
$895$	−843.213	−	989.158i	−0.942137	−	1.10520i
$896$			873.494i			0.974881i
$897$	−1263.83	−	89.0206i	−1.40895	−	0.0992426i
$898$			1607.73i			1.79035i
$899$	−382.129			−0.425060
$900$	−14.6481	+	91.3709i	−0.0162756	+	0.101523i
$901$	−25.5217			−0.0283259
$902$	−552.706			−0.612756
$903$		−	544.713i		−	0.603226i
$904$			1489.00i			1.64712i
$905$	311.141	−	265.234i	0.343802	−	0.293076i
$906$	−2469.16			−2.72534
$907$	997.272			1.09953			0.549764	−	0.835320i	$-0.314718\pi$
$907$	997.272			1.09953			0.549764	+	0.835320i	$0.314718\pi$
$908$	−1058.92			−1.16621
$909$	−25.6469			−0.0282144
$910$	2592.73	+	3041.49i	2.84915	+	3.34229i
$911$			261.725i			0.287294i	0.989629	+	0.143647i	$0.0458830\pi$
$911$			261.725i			0.287294i	−0.989629	+	0.143647i	$0.954117\pi$
$912$	−1069.17			−1.17234
$913$			1649.02i			1.80615i
$914$		−	399.549i		−	0.437143i
$915$	634.283	+	744.067i	0.693206	+	0.813188i
$916$			805.112i			0.878943i
$917$	2056.79			2.24295
$918$	36.0045			0.0392206
$919$			1615.07i			1.75743i	0.477351	+	0.878713i	$0.341597\pi$
$919$			1615.07i			1.75743i	−0.477351	+	0.878713i	$0.658403\pi$
$920$	−1797.08	+	1325.75i	−1.95335	+	1.44103i
$921$	690.424			0.749646
$922$			440.607i			0.477882i
$923$		−	849.068i		−	0.919900i
$924$	−3799.62			−4.11215
$925$	100.766	−	628.551i	0.108936	−	0.679515i
$926$	402.645			0.434822
$927$	−67.8122			−0.0731523
$928$			526.914i			0.567795i
$929$	1085.56			1.16853			0.584265	−	0.811563i	$-0.301383\pi$
$929$	1085.56			1.16853			0.584265	+	0.811563i	$0.301383\pi$
$930$	−1182.39	−	1387.04i	−1.27139	−	1.49144i
$931$		−	1033.50i		−	1.11010i
$932$		−	136.555i		−	0.146518i
$933$		−	665.572i		−	0.713367i
$934$		−	2241.60i		−	2.40000i
$935$	−15.5308	+	13.2393i	−0.0166105	+	0.0141597i
$936$	−138.579			−0.148055
$937$	847.610			0.904600			0.452300	−	0.891866i	$-0.350604\pi$
$937$	847.610			0.904600			0.452300	+	0.891866i	$0.350604\pi$
$938$		−	180.814i		−	0.192766i
$939$			659.440i			0.702279i
$940$	−1480.74	+	1262.27i	−1.57526	+	1.34284i
$941$			562.777i			0.598063i	0.954243	+	0.299031i	$0.0966635\pi$
$941$			562.777i			0.598063i	−0.954243	+	0.299031i	$0.903336\pi$
$942$	−261.799			−0.277918
$943$	318.426	+	22.4291i	0.337674	+	0.0237848i
$944$	307.613			0.325861
$945$	−1223.00	+	1042.55i	−1.29418	+	1.10323i
$946$	580.614			0.613757
$947$			463.167i			0.489089i	0.969638	+	0.244545i	$0.0786384\pi$
$947$			463.167i			0.489089i	−0.969638	+	0.244545i	$0.921362\pi$
$948$	2118.16			2.23434
$949$	1448.84			1.52670
$950$	149.962	−	935.423i	0.157854	−	0.984655i
$951$	−1238.07			−1.30186
$952$			88.5323i			0.0929961i
$953$	−373.393			−0.391808			−0.195904	−	0.980623i	$-0.562764\pi$
$953$	−373.393			−0.391808			−0.195904	+	0.980623i	$0.562764\pi$
$954$			98.8896i			0.103658i
$955$	−575.205	+	490.336i	−0.602309	+	0.513441i
$956$	−523.580			−0.547678
$957$	392.300			0.409927
$958$	1193.21			1.24553
$959$	548.748			0.572208
$960$	−345.267	+	294.324i	−0.359653	+	0.306588i
$961$	100.527			0.104606
$962$	1669.98			1.73595
$963$	28.3519			0.0294413
$964$			4073.20i			4.22531i
$965$	−773.594	+	659.454i	−0.801652	+	0.683372i
$966$	3128.49	+	220.362i	3.23860	+	0.228118i
$967$		−	1005.98i		−	1.04031i	−0.854071	−	0.520156i	$-0.825874\pi$
$967$		−	1005.98i		−	1.04031i	0.854071	−	0.520156i	$-0.174126\pi$
$968$			37.7473i			0.0389951i
$969$	11.9060			0.0122869
$970$	504.746	−	430.273i	0.520356	−	0.443580i
$971$			621.178i			0.639730i	0.947463	+	0.319865i	$0.103638\pi$
$971$			621.178i			0.639730i	−0.947463	+	0.319865i	$0.896362\pi$
$972$		−	199.737i		−	0.205491i
$973$	215.760			0.221748
$974$	1860.67			1.91034
$975$	217.990	−	1359.77i	0.223580	−	1.39464i
$976$			2142.81i			2.19550i
$977$	676.931			0.692866			0.346433	−	0.938075i	$-0.387393\pi$
$977$	676.931			0.692866			0.346433	+	0.938075i	$0.387393\pi$
$978$			2351.23i			2.40412i
$979$	−919.441			−0.939164
$980$	−3009.38	−	3530.26i	−3.07080	−	3.60230i
$981$			14.2225i			0.0144980i
$982$			219.845i			0.223874i
$983$	−1520.24			−1.54653			−0.773266	−	0.634081i	$-0.781378\pi$
$983$	−1520.24			−1.54653			−0.773266	+	0.634081i	$0.781378\pi$
$984$	826.191			0.839625
$985$	−108.037	+	92.0962i	−0.109682	+	0.0934987i
$986$		−	16.0126i		−	0.0162399i
$987$	1559.87			1.58042
$988$	1739.00			1.76012
$989$	−334.505	−	23.5616i	−0.338225	−	0.0238236i
$990$	51.2987	+	60.1777i	0.0518169	+	0.0607855i
$991$	1736.62			1.75239			0.876196	−	0.481956i	$-0.160073\pi$
$991$	1736.62			1.75239			0.876196	+	0.481956i	$0.160073\pi$
$992$		−	1463.73i		−	1.47553i
$993$			1456.37i			1.46663i
$994$			2101.78i			2.11447i
$995$	−1041.44	+	887.779i	−1.04667	+	0.892240i
$996$		−	4318.11i		−	4.33545i
$997$			1589.28i			1.59406i	0.603937	+	0.797032i	$0.293598\pi$
$997$			1589.28i			1.59406i	−0.603937	+	0.797032i	$0.706402\pi$
$998$			2292.11i			2.29670i
$999$			671.509i			0.672182i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.c.c.114.2	yes	20
5.2	odd	4		575.3.d.i.551.19		20
5.3	odd	4		575.3.d.i.551.2		20
5.4	even	2	inner	115.3.c.c.114.19	yes	20
23.22	odd	2	inner	115.3.c.c.114.1	✓	20
115.22	even	4		575.3.d.i.551.20		20
115.68	even	4		575.3.d.i.551.1		20
115.114	odd	2	inner	115.3.c.c.114.20	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.c.c.114.1	✓	20	23.22	odd	2	inner
115.3.c.c.114.2	yes	20	1.1	even	1	trivial
115.3.c.c.114.19	yes	20	5.4	even	2	inner
115.3.c.c.114.20	yes	20	115.114	odd	2	inner
575.3.d.i.551.1		20	115.68	even	4
575.3.d.i.551.2		20	5.3	odd	4
575.3.d.i.551.19		20	5.2	odd	4
575.3.d.i.551.20		20	115.22	even	4

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.64975i q^{2} -3.06547i q^{3} -9.32065 q^{4} +(3.24366 + 3.80508i) q^{5} -11.1882 q^{6} -12.1877 q^{7} +19.4190i q^{8} -0.397130 q^{9} +(13.8876 - 11.8385i) q^{10} -10.9113i q^{11} +28.5722i q^{12} -17.9696i q^{13} +44.4819i q^{14} +(11.6644 - 9.94336i) q^{15} +33.5919 q^{16} -0.374070 q^{17} +1.44942i q^{18} -10.3828i q^{19} +(-30.2330 - 35.4658i) q^{20} +37.3610i q^{21} -39.8234 q^{22} +(22.9432 + 1.61605i) q^{23} +59.5285 q^{24} +(-3.95733 + 24.6848i) q^{25} -65.5844 q^{26} -26.3719i q^{27} +113.597 q^{28} -11.7286 q^{29} +(-36.2907 - 42.5720i) q^{30} +32.5811 q^{31} -44.9257i q^{32} -33.4483 q^{33} +1.36526i q^{34} +(-39.5327 - 46.3752i) q^{35} +3.70151 q^{36} -25.4631 q^{37} -37.8947 q^{38} -55.0853 q^{39} +(-73.8910 + 62.9887i) q^{40} +13.8789 q^{41} +136.358 q^{42} -14.5797 q^{43} +101.700i q^{44} +(-1.28815 - 1.51111i) q^{45} +(5.89818 - 83.7367i) q^{46} -41.7513i q^{47} -102.975i q^{48} +99.5396 q^{49} +(90.0933 + 14.4432i) q^{50} +1.14670i q^{51} +167.488i q^{52} +68.2269 q^{53} -96.2506 q^{54} +(41.5184 - 35.3925i) q^{55} -236.673i q^{56} -31.8283 q^{57} +42.8063i q^{58} +9.15737 q^{59} +(-108.720 + 92.6785i) q^{60} +63.7896i q^{61} -118.913i q^{62} +4.84009 q^{63} -29.6001 q^{64} +(68.3758 - 58.2872i) q^{65} +122.078i q^{66} -4.06489 q^{67} +3.48658 q^{68} +(4.95396 - 70.3316i) q^{69} +(-169.258 + 144.284i) q^{70} +47.2503 q^{71} -7.71187i q^{72} +80.6273i q^{73} +92.9338i q^{74} +(75.6706 + 12.1311i) q^{75} +96.7746i q^{76} +132.983i q^{77} +201.047i q^{78} -74.1335i q^{79} +(108.961 + 127.820i) q^{80} -84.4165 q^{81} -50.6546i q^{82} -151.130 q^{83} -348.229i q^{84} +(-1.21336 - 1.42337i) q^{85} +53.2123i q^{86} +35.9536i q^{87} +211.886 q^{88} -84.2652i q^{89} +(-5.51518 + 4.70144i) q^{90} +219.008i q^{91} +(-213.845 - 15.0626i) q^{92} -99.8764i q^{93} -152.382 q^{94} +(39.5075 - 33.6784i) q^{95} -137.719 q^{96} +36.3451 q^{97} -363.294i q^{98} +4.33320i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 56 q^{4} - 8 q^{6} - 72 q^{9} + 88 q^{16} + 44 q^{24} - 12 q^{25} - 56 q^{26} + 236 q^{31} + 92 q^{35} - 32 q^{36} - 168 q^{39} + 124 q^{41} - 248 q^{46} + 88 q^{49} + 200 q^{50} - 196 q^{54} + 268 q^{55}+ \cdots - 264 q^{96}+O(q^{100}) \) 20 * q - 56 * q^4 - 8 * q^6 - 72 * q^9 + 88 * q^16 + 44 * q^24 - 12 * q^25 - 56 * q^26 + 236 * q^31 + 92 * q^35 - 32 * q^36 - 168 * q^39 + 124 * q^41 - 248 * q^46 + 88 * q^49 + 200 * q^50 - 196 * q^54 + 268 * q^55 + 56 * q^59 - 28 * q^64 + 376 * q^69 - 636 * q^70 - 196 * q^71 + 428 * q^75 - 988 * q^81 - 284 * q^85 + 276 * q^94 + 184 * q^95 - 264 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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