LMFDB - Embedded newform 117.3.p.a.107.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(35,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("117.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.p (of order $6$, degree $2$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
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} - 32 x^{18} + 690 x^{16} - 7984 x^{14} + 66147 x^{12} - 315440 x^{10} + 1074610 x^{8} + \cdots + 1327104 $ x^20 - 32x^18 + 690x^16 - 7984x^14 + 66147x^12 - 315440x^10 + 1074610x^8 - 2130504x^6 + 3043521x^4 - 2471040*x^2 + 1327104
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.4
Root			$-1.02559 - 0.592124i$ of defining polynomial
Character	$\chi$	$=$	117.107
Dual form			117.3.p.a.35.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02559 + 0.592124i) q^{2} +(-1.29878 + 2.24955i) q^{4} -4.21775i q^{5} +(-4.97984 + 8.62533i) q^{7} -7.81314i q^{8} +(2.49743 + 4.32568i) q^{10} +(-16.4265 + 9.48387i) q^{11} +(-4.13369 - 12.3253i) q^{13} -11.7947i q^{14} +(-0.568765 - 0.985130i) q^{16} +(-7.09992 - 4.09914i) q^{17} +(-11.0605 + 19.1573i) q^{19} +(9.48805 + 5.47793i) q^{20} +(11.2313 - 19.4531i) q^{22} +(-17.6145 + 10.1697i) q^{23} +7.21054 q^{25} +(11.5376 + 10.1930i) q^{26} +(-12.9354 - 22.4048i) q^{28} +(9.66183 - 5.57826i) q^{29} +11.3212 q^{31} +(28.2322 + 16.2998i) q^{32} +9.70880 q^{34} +(36.3795 + 21.0037i) q^{35} +(25.2130 + 43.6702i) q^{37} -26.1967i q^{38} -32.9539 q^{40} +(9.23379 - 5.33113i) q^{41} +(30.1139 - 52.1588i) q^{43} -49.2698i q^{44} +(12.0435 - 20.8599i) q^{46} +71.8407i q^{47} +(-25.0975 - 43.4702i) q^{49} +(-7.39505 + 4.26954i) q^{50} +(33.0951 + 6.70886i) q^{52} +12.1630i q^{53} +(40.0006 + 69.2831i) q^{55} +(67.3909 + 38.9082i) q^{56} +(-6.60604 + 11.4420i) q^{58} +(-43.4868 - 25.1071i) q^{59} +(-31.6610 + 54.8384i) q^{61} +(-11.6109 + 6.70355i) q^{62} -34.0560 q^{64} +(-51.9850 + 17.4349i) q^{65} +(-36.7269 - 63.6128i) q^{67} +(18.4425 - 10.6478i) q^{68} -49.7472 q^{70} +(-84.7355 - 48.9220i) q^{71} +9.79592 q^{73} +(-51.7163 - 29.8584i) q^{74} +(-28.7302 - 49.7622i) q^{76} -188.912i q^{77} -17.6643 q^{79} +(-4.15504 + 2.39891i) q^{80} +(-6.31338 + 10.9351i) q^{82} +13.4580i q^{83} +(-17.2892 + 29.9457i) q^{85} +71.3246i q^{86} +(74.0988 + 128.343i) q^{88} +(-143.871 + 83.0642i) q^{89} +(126.895 + 25.7234i) q^{91} -52.8329i q^{92} +(-42.5386 - 73.6790i) q^{94} +(80.8008 + 46.6504i) q^{95} +(-53.9353 + 93.4187i) q^{97} +(51.4795 + 29.7217i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 24 q^{4} - 6 q^{7} + 12 q^{10} - 2 q^{13} - 104 q^{16} - 92 q^{19} + 44 q^{22} - 116 q^{25} + 76 q^{28} - 156 q^{31} + 80 q^{34} + 148 q^{37} + 328 q^{40} + 186 q^{43} + 164 q^{46} + 8 q^{49} + 392 q^{52}+ \cdots - 14 q^{97}+O(q^{100}) $ 20 * q + 24 * q^4 - 6 * q^7 + 12 * q^10 - 2 * q^13 - 104 * q^16 - 92 * q^19 + 44 * q^22 - 116 * q^25 + 76 * q^28 - 156 * q^31 + 80 * q^34 + 148 * q^37 + 328 * q^40 + 186 * q^43 + 164 * q^46 + 8 * q^49 + 392 * q^52 - 208 * q^55 - 236 * q^58 + 210 * q^61 - 1568 * q^64 - 158 * q^67 - 1048 * q^70 + 156 * q^73 + 764 * q^76 - 132 * q^79 + 648 * q^82 + 44 * q^85 + 372 * q^88 + 834 * q^91 - 220 * q^94 - 14 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.02559	+	0.592124i	−0.512794	+	0.296062i	−0.733982	−	0.679169i	$-0.762340\pi$
$2$	−1.02559	+	0.592124i	−0.512794	+	0.296062i	0.221187	+	0.975231i	$0.429007\pi$
$3$		0			0
$3$		0			0
$4$	−1.29878	+	2.24955i	−0.324695	+	0.562388i
$5$		−	4.21775i		−	0.843551i	−0.906700	−	0.421775i	$-0.861407\pi$
$5$		−	4.21775i		−	0.843551i	0.906700	−	0.421775i	$-0.138593\pi$
$6$		0			0
$7$	−4.97984	+	8.62533i	−0.711405	+	1.23219i	0.252925	+	0.967486i	$0.418608\pi$
$7$	−4.97984	+	8.62533i	−0.711405	+	1.23219i	−0.964330	+	0.264704i	$0.914726\pi$
$8$		−	7.81314i		−	0.976643i
$9$		0			0
$10$	2.49743	+	4.32568i	0.249743	+	0.432568i
$11$	−16.4265	+	9.48387i	−1.49332	+	0.862170i	−0.999971	−	0.00766011i	$-0.997562\pi$
$11$	−16.4265	+	9.48387i	−1.49332	+	0.862170i	−0.493351	+	0.869830i	$0.664228\pi$
$12$		0			0
$13$	−4.13369	−	12.3253i	−0.317977	−	0.948099i
$13$	−4.13369	−	12.3253i	−0.317977	−	0.948099i
$14$		−	11.7947i		−	0.842480i
$15$		0			0
$16$	−0.568765	−	0.985130i	−0.0355478	−	0.0615707i
$17$	−7.09992	−	4.09914i	−0.417643	−	0.241126i	0.276426	−	0.961035i	$-0.410850\pi$
$17$	−7.09992	−	4.09914i	−0.417643	−	0.241126i	−0.694068	+	0.719909i	$0.744183\pi$
$18$		0			0
$19$	−11.0605	+	19.1573i	−0.582130	+	1.00828i	0.413096	+	0.910687i	$0.364447\pi$
$19$	−11.0605	+	19.1573i	−0.582130	+	1.00828i	−0.995227	+	0.0975919i	$0.968886\pi$
$20$	9.48805	+	5.47793i	0.474403	+	0.273896i
$21$		0			0
$22$	11.2313	−	19.4531i	0.510511	−	0.884232i
$23$	−17.6145	+	10.1697i	−0.765847	+	0.442162i	−0.831391	−	0.555688i	$-0.812455\pi$
$23$	−17.6145	+	10.1697i	−0.765847	+	0.442162i	0.0655444	+	0.997850i	$0.479122\pi$
$24$		0			0
$25$	7.21054			0.288422
$26$	11.5376	+	10.1930i	0.443752	+	0.392039i
$27$		0			0
$28$	−12.9354	−	22.4048i	−0.461979	−	0.800171i
$29$	9.66183	−	5.57826i	0.333166	−	0.192354i	−0.324080	−	0.946030i	$-0.605055\pi$
$29$	9.66183	−	5.57826i	0.333166	−	0.192354i	0.657246	+	0.753676i	$0.271721\pi$
$30$		0			0
$31$	11.3212			0.365200			0.182600	−	0.983187i	$-0.441549\pi$
$31$	11.3212			0.365200			0.182600	+	0.983187i	$0.441549\pi$
$32$	28.2322	+	16.2998i	0.882255	+	0.509370i
$33$		0			0
$34$	9.70880			0.285553
$35$	36.3795	+	21.0037i	1.03942	+	0.600107i
$36$		0			0
$37$	25.2130	+	43.6702i	0.681432	+	1.18027i	0.974544	+	0.224196i	$0.0719757\pi$
$37$	25.2130	+	43.6702i	0.681432	+	1.18027i	−0.293112	+	0.956078i	$0.594691\pi$
$38$		−	26.1967i		−	0.689387i
$39$		0			0
$40$	−32.9539			−0.823848
$41$	9.23379	−	5.33113i	0.225214	−	0.130028i	−0.383148	−	0.923687i	$-0.625160\pi$
$41$	9.23379	−	5.33113i	0.225214	−	0.130028i	0.608362	+	0.793659i	$0.291827\pi$
$42$		0			0
$43$	30.1139	−	52.1588i	0.700323	−	1.21300i	−0.268030	−	0.963411i	$-0.586373\pi$
$43$	30.1139	−	52.1588i	0.700323	−	1.21300i	0.968353	−	0.249585i	$-0.0802941\pi$
$44$		−	49.2698i		−	1.11977i
$45$		0			0
$46$	12.0435	−	20.8599i	0.261815	−	0.453476i
$47$			71.8407i			1.52852i	0.644906	+	0.764262i	$0.276897\pi$
$47$			71.8407i			1.52852i	−0.644906	+	0.764262i	$0.723103\pi$
$48$		0			0
$49$	−25.0975	−	43.4702i	−0.512195	−	0.887147i
$50$	−7.39505	+	4.26954i	−0.147901	+	0.0853907i
$51$		0			0
$52$	33.0951	+	6.70886i	0.636444	+	0.129016i
$53$			12.1630i			0.229490i	0.993395	+	0.114745i	$0.0366051\pi$
$53$			12.1630i			0.229490i	−0.993395	+	0.114745i	$0.963395\pi$
$54$		0			0
$55$	40.0006	+	69.2831i	0.727284	+	1.25969i
$56$	67.3909	+	38.9082i	1.20341	+	0.694789i
$57$		0			0
$58$	−6.60604	+	11.4420i	−0.113897	+	0.197276i
$59$	−43.4868	−	25.1071i	−0.737064	−	0.425544i	0.0839366	−	0.996471i	$-0.473251\pi$
$59$	−43.4868	−	25.1071i	−0.737064	−	0.425544i	−0.821001	+	0.570927i	$0.806584\pi$
$60$		0			0
$61$	−31.6610	+	54.8384i	−0.519032	+	0.898990i	0.480723	+	0.876872i	$0.340374\pi$
$61$	−31.6610	+	54.8384i	−0.519032	+	0.898990i	−0.999755	+	0.0221175i	$0.992959\pi$
$62$	−11.6109	+	6.70355i	−0.187272	+	0.108122i
$63$		0			0
$64$	−34.0560			−0.532125
$65$	−51.9850	+	17.4349i	−0.799769	+	0.268229i
$66$		0			0
$67$	−36.7269	−	63.6128i	−0.548163	−	0.949445i	−0.998401	−	0.0565367i	$-0.981994\pi$
$67$	−36.7269	−	63.6128i	−0.548163	−	0.949445i	0.450238	−	0.892909i	$-0.351339\pi$
$68$	18.4425	−	10.6478i	0.271213	−	0.156585i
$69$		0			0
$70$	−49.7472			−0.710675
$71$	−84.7355	−	48.9220i	−1.19346	−	0.689043i	−0.234368	−	0.972148i	$-0.575302\pi$
$71$	−84.7355	−	48.9220i	−1.19346	−	0.689043i	−0.959089	+	0.283105i	$0.908635\pi$
$72$		0			0
$73$	9.79592			0.134191			0.0670953	−	0.997747i	$-0.478627\pi$
$73$	9.79592			0.134191			0.0670953	+	0.997747i	$0.478627\pi$
$74$	−51.7163	−	29.8584i	−0.698869	−	0.403492i
$75$		0			0
$76$	−28.7302	−	49.7622i	−0.378029	−	0.654766i
$77$		−	188.912i		−	2.45341i
$78$		0			0
$79$	−17.6643			−0.223599			−0.111799	−	0.993731i	$-0.535661\pi$
$79$	−17.6643			−0.223599			−0.111799	+	0.993731i	$0.535661\pi$
$80$	−4.15504	+	2.39891i	−0.0519380	+	0.0299864i
$81$		0			0
$82$	−6.31338	+	10.9351i	−0.0769924	+	0.133355i
$83$			13.4580i			0.162145i	0.996708	+	0.0810724i	$0.0258345\pi$
$83$			13.4580i			0.162145i	−0.996708	+	0.0810724i	$0.974166\pi$
$84$		0			0
$85$	−17.2892	+	29.9457i	−0.203402	+	0.352303i
$86$			71.3246i			0.829356i
$87$		0			0
$88$	74.0988	+	128.343i	0.842032	+	1.45844i
$89$	−143.871	+	83.0642i	−1.61653	+	0.933305i	−0.628724	+	0.777628i	$0.716423\pi$
$89$	−143.871	+	83.0642i	−1.61653	+	0.933305i	−0.987808	+	0.155677i	$0.950244\pi$
$90$		0			0
$91$	126.895	+	25.7234i	1.39445	+	0.282675i
$92$		−	52.8329i		−	0.574270i
$93$		0			0
$94$	−42.5386	−	73.6790i	−0.452538	−	0.783819i
$95$	80.8008	+	46.6504i	0.850535	+	0.491057i
$96$		0			0
$97$	−53.9353	+	93.4187i	−0.556034	+	0.963079i	0.441788	+	0.897119i	$0.354344\pi$
$97$	−53.9353	+	93.4187i	−0.556034	+	0.963079i	−0.997822	+	0.0659597i	$0.978989\pi$
$98$	51.4795	+	29.7217i	0.525301	+	0.303283i
$99$		0			0
$100$	−9.36490	+	16.2205i	−0.0936490	+	0.162205i
$101$	74.7414	−	43.1520i	0.740014	−	0.427247i	−0.0820604	−	0.996627i	$-0.526150\pi$
$101$	74.7414	−	43.1520i	0.740014	−	0.427247i	0.822074	+	0.569380i	$0.192817\pi$
$102$		0			0
$103$	−35.5732			−0.345371			−0.172686	−	0.984977i	$-0.555244\pi$
$103$	−35.5732			−0.345371			−0.172686	+	0.984977i	$0.555244\pi$
$104$	−96.2992	+	32.2971i	−0.925954	+	0.310549i
$105$		0			0
$106$	−7.20199	−	12.4742i	−0.0679433	−	0.117681i
$107$	91.0758	−	52.5826i	0.851176	−	0.491427i	−0.00987169	−	0.999951i	$-0.503142\pi$
$107$	91.0758	−	52.5826i	0.851176	−	0.491427i	0.861047	+	0.508525i	$0.169809\pi$
$108$		0			0
$109$	−52.4151			−0.480872			−0.240436	−	0.970665i	$-0.577290\pi$
$109$	−52.4151			−0.480872			−0.240436	+	0.970665i	$0.577290\pi$
$110$	−82.0484	−	47.3707i	−0.745895	−	0.430642i
$111$		0			0
$112$	11.3294			0.101156
$113$	131.527	+	75.9374i	1.16396	+	0.672012i	0.952250	−	0.305320i	$-0.0987635\pi$
$113$	131.527	+	75.9374i	1.16396	+	0.672012i	0.211710	+	0.977333i	$0.432097\pi$
$114$		0			0
$115$	42.8934	+	74.2935i	0.372986	+	0.646031i
$116$			28.9797i			0.249825i
$117$		0			0
$118$	59.4661			0.503950
$119$	70.7129	−	40.8261i	0.594226	−	0.343077i
$120$		0			0
$121$	119.388	−	206.785i	0.986674	−	1.70897i
$122$		−	74.9888i		−	0.614663i
$123$		0			0
$124$	−14.7037	+	25.4676i	−0.118578	+	0.205384i
$125$		−	135.856i		−	1.08685i
$126$		0			0
$127$	0.0526860	+	0.0912549i	0.000414851	+	0.000718542i	0.866233	−	0.499641i	$-0.166535\pi$
$127$	0.0526860	+	0.0912549i	0.000414851	+	0.000718542i	−0.865818	+	0.500359i	$0.833201\pi$
$128$	−78.0012	+	45.0340i	−0.609384	+	0.351828i
$129$		0			0
$130$	42.9916	−	48.6626i	0.330705	−	0.374328i
$131$			199.955i			1.52638i	0.646176	+	0.763189i	$0.276367\pi$
$131$			199.955i			1.52638i	−0.646176	+	0.763189i	$0.723633\pi$
$132$		0			0
$133$	−110.159	−	190.801i	−0.828261	−	1.43459i
$134$	75.3334	+	43.4937i	0.562189	+	0.324580i
$135$		0			0
$136$	−32.0272	+	55.4727i	−0.235494	+	0.407888i
$137$	77.1055	+	44.5169i	0.562814	+	0.324941i	0.754274	−	0.656560i	$-0.227989\pi$
$137$	77.1055	+	44.5169i	0.562814	+	0.324941i	−0.191460	+	0.981500i	$0.561322\pi$
$138$		0			0
$139$	51.4076	−	89.0405i	0.369839	−	0.640579i	−0.619701	−	0.784838i	$-0.712746\pi$
$139$	51.4076	−	89.0405i	0.369839	−	0.640579i	0.989540	+	0.144258i	$0.0460796\pi$
$140$	−94.4979	+	54.5584i	−0.674985	+	0.389703i
$141$		0			0
$142$	115.872			0.815997
$143$	184.794	+	163.258i	1.29226	+	1.14167i
$144$		0			0
$145$	−23.5277	−	40.7512i	−0.162260	−	0.281043i
$146$	−10.0466	+	5.80040i	−0.0688122	+	0.0397287i
$147$		0			0
$148$	−130.984			−0.885029
$149$	−113.193	−	65.3518i	−0.759682	−	0.438603i	0.0694993	−	0.997582i	$-0.477860\pi$
$149$	−113.193	−	65.3518i	−0.759682	−	0.438603i	−0.829182	+	0.558979i	$0.811193\pi$
$150$		0			0
$151$	43.2696			0.286554			0.143277	−	0.989683i	$-0.454236\pi$
$151$	43.2696			0.286554			0.143277	+	0.989683i	$0.454236\pi$
$152$	149.679	+	86.4171i	0.984729	+	0.568533i
$153$		0			0
$154$	111.860	+	193.747i	0.726361	+	1.25809i
$155$		−	47.7500i		−	0.308065i
$156$		0			0
$157$	−187.971			−1.19727			−0.598633	−	0.801024i	$-0.704289\pi$
$157$	−187.971			−1.19727			−0.598633	+	0.801024i	$0.704289\pi$
$158$	18.1163	−	10.4594i	0.114660	−	0.0661990i
$159$		0			0
$160$	68.7487	−	119.076i	0.429680	−	0.744227i
$161$		−	202.574i		−	1.25822i
$162$		0			0
$163$	112.682	−	195.171i	0.691301	−	1.19737i	−0.280111	−	0.959968i	$-0.590371\pi$
$163$	112.682	−	195.171i	0.691301	−	1.19737i	0.971412	−	0.237401i	$-0.0762954\pi$
$164$			27.6958i			0.168877i
$165$		0			0
$166$	−7.96881	−	13.8024i	−0.0480049	−	0.0831469i
$167$	−109.448	+	63.1901i	−0.655380	+	0.378384i	−0.790514	−	0.612443i	$-0.790187\pi$
$167$	−109.448	+	63.1901i	−0.655380	+	0.378384i	0.135134	+	0.990827i	$0.456853\pi$
$168$		0			0
$169$	−134.825	+	101.898i	−0.797782	+	0.602946i
$170$		−	40.9493i		−	0.240878i
$171$		0			0
$172$	78.2226	+	135.485i	0.454782	+	0.787706i
$173$	127.224	+	73.4527i	0.735398	+	0.424582i	0.820394	−	0.571799i	$-0.193754\pi$
$173$	127.224	+	73.4527i	0.735398	+	0.424582i	−0.0849956	+	0.996381i	$0.527088\pi$
$174$		0			0
$175$	−35.9073	+	62.1933i	−0.205185	+	0.355390i
$176$	18.6857	+	10.7882i	0.106169	+	0.0612965i
$177$		0			0
$178$	98.3686	−	170.379i	0.552632	−	0.957187i
$179$	−216.513	+	125.004i	−1.20957	+	0.698346i	−0.962666	−	0.270693i	$-0.912747\pi$
$179$	−216.513	+	125.004i	−1.20957	+	0.698346i	−0.246906	+	0.969039i	$0.579414\pi$
$180$		0			0
$181$	−246.457			−1.36164			−0.680821	−	0.732450i	$-0.738377\pi$
$181$	−246.457			−1.36164			−0.680821	+	0.732450i	$0.738377\pi$
$182$	−145.373	+	48.7558i	−0.798754	+	0.267889i
$183$		0			0
$184$	79.4575	+	137.624i	0.431834	+	0.747959i
$185$	184.190	−	106.342i	0.995622	−	0.574822i
$186$		0			0
$187$	155.503			0.831566
$188$	−161.609	−	93.3051i	−0.859623	−	0.496304i
$189$		0			0
$190$	−110.491			−0.581533
$191$	−116.707	−	67.3810i	−0.611033	−	0.352780i	0.162337	−	0.986735i	$-0.448097\pi$
$191$	−116.707	−	67.3810i	−0.611033	−	0.352780i	−0.773370	+	0.633955i	$0.781430\pi$
$192$		0			0
$193$	72.8800	+	126.232i	0.377617	+	0.654051i	0.990715	−	0.135956i	$-0.0434104\pi$
$193$	72.8800	+	126.232i	0.377617	+	0.654051i	−0.613098	+	0.790007i	$0.710077\pi$
$194$		−	127.746i		−	0.658482i
$195$		0			0
$196$	130.385			0.665228
$197$	119.773	−	69.1510i	0.607985	−	0.351020i	−0.164192	−	0.986428i	$-0.552502\pi$
$197$	119.773	−	69.1510i	0.607985	−	0.351020i	0.772176	+	0.635408i	$0.219168\pi$
$198$		0			0
$199$	−134.850	+	233.568i	−0.677640	+	1.17371i	0.298050	+	0.954550i	$0.403664\pi$
$199$	−134.850	+	233.568i	−0.677640	+	1.17371i	−0.975690	+	0.219156i	$0.929670\pi$
$200$		−	56.3370i		−	0.281685i
$201$		0			0
$202$	−51.1026	+	88.5124i	−0.252983	+	0.438180i
$203$			111.115i			0.547366i
$204$		0			0
$205$	−22.4854	−	38.9459i	−0.109685	−	0.189980i
$206$	36.4835	−	21.0638i	0.177104	−	0.102251i
$207$		0			0
$208$	−9.79091	+	11.0824i	−0.0470717	+	0.0532809i
$209$		−	419.584i		−	2.00758i
$210$		0			0
$211$	−18.7716	−	32.5133i	−0.0889647	−	0.154091i	0.818109	−	0.575063i	$-0.195023\pi$
$211$	−18.7716	−	32.5133i	−0.0889647	−	0.154091i	−0.907074	+	0.420972i	$0.861689\pi$
$212$	−27.3612	−	15.7970i	−0.129062	−	0.0745142i
$213$		0			0
$214$	−62.2709	+	107.856i	−0.290985	+	0.504001i
$215$	−219.993	−	127.013i	−1.02322	−	0.590758i
$216$		0			0
$217$	−56.3777	+	97.6491i	−0.259805	+	0.449996i
$218$	53.7563	−	31.0362i	0.246589	−	0.142368i
$219$		0			0
$220$	−207.808			−0.944581
$221$	−21.1742	+	104.453i	−0.0958107	+	0.472639i
$222$		0			0
$223$	−59.4033	−	102.890i	−0.266383	−	0.461388i	0.701542	−	0.712628i	$-0.252495\pi$
$223$	−59.4033	−	102.890i	−0.266383	−	0.461388i	−0.967925	+	0.251239i	$0.919162\pi$
$224$	−281.183	+	162.341i	−1.25528	+	0.724737i
$225$		0			0
$226$	−179.857			−0.795829
$227$	57.6521	+	33.2855i	0.253974	+	0.146632i	0.621583	−	0.783349i	$-0.286490\pi$
$227$	57.6521	+	33.2855i	0.253974	+	0.146632i	−0.367609	+	0.929981i	$0.619823\pi$
$228$		0			0
$229$	251.034			1.09622			0.548108	−	0.836407i	$-0.315348\pi$
$229$	251.034			1.09622			0.548108	+	0.836407i	$0.315348\pi$
$230$	−87.9819	−	50.7964i	−0.382530	−	0.220854i
$231$		0			0
$232$	−43.5837	−	75.4892i	−0.187861	−	0.325385i
$233$			113.740i			0.488152i	0.969756	+	0.244076i	$0.0784847\pi$
$233$			113.740i			0.488152i	−0.969756	+	0.244076i	$0.921515\pi$
$234$		0			0
$235$	303.006			1.28939
$236$	112.959	−	65.2172i	0.478642	−	0.276344i
$237$		0			0
$238$	−48.3482	+	83.7416i	−0.203144	+	0.351855i
$239$			41.0252i			0.171653i	0.996310	+	0.0858267i	$0.0273531\pi$
$239$			41.0252i			0.171653i	−0.996310	+	0.0858267i	$0.972647\pi$
$240$		0			0
$241$	−153.259	+	265.452i	−0.635930	+	1.10146i	0.350388	+	0.936605i	$0.386050\pi$
$241$	−153.259	+	265.452i	−0.635930	+	1.10146i	−0.986317	+	0.164858i	$0.947284\pi$
$242$			282.769i			1.16847i
$243$		0			0
$244$	−82.2411	−	142.446i	−0.337054	−	0.583794i
$245$	−183.347	+	105.855i	−0.748354	+	0.432062i
$246$		0			0
$247$	281.840	+	57.1330i	1.14105	+	0.231308i
$248$		−	88.4541i		−	0.356670i
$249$		0			0
$250$	80.4437	+	139.333i	0.321775	+	0.557330i
$251$	311.446	+	179.814i	1.24082	+	0.716389i	0.969262	−	0.246032i	$-0.0791269\pi$
$251$	311.446	+	179.814i	1.24082	+	0.716389i	0.271561	+	0.962421i	$0.412460\pi$
$252$		0			0
$253$	192.897	−	334.107i	0.762437	−	1.32058i
$254$	−0.108068	−	0.0623933i	−0.000425466	−	0.000245643i
$255$		0			0
$256$	121.443	−	210.346i	0.474388	−	0.821665i
$257$	84.3262	−	48.6857i	0.328117	−	0.189439i	−0.326888	−	0.945063i	$-0.606000\pi$
$257$	84.3262	−	48.6857i	0.328117	−	0.189439i	0.655005	+	0.755625i	$0.272667\pi$
$258$		0			0
$259$	−502.226			−1.93910
$260$	28.2963	−	139.587i	0.108832	−	0.536873i
$261$		0			0
$262$	−118.398	−	205.072i	−0.451902	−	0.782718i
$263$	−1.56065	+	0.901039i	−0.00593401	+	0.00342600i	−0.502964	−	0.864307i	$-0.667757\pi$
$263$	−1.56065	+	0.901039i	−0.00593401	+	0.00342600i	0.497030	+	0.867733i	$0.334424\pi$
$264$		0			0
$265$	51.3005			0.193587
$266$	225.955	+	130.455i	0.849455	+	0.490433i
$267$		0			0
$268$	190.800			0.711942
$269$	−458.960	−	264.981i	−1.70617	−	0.985059i	−0.939195	−	0.343384i	$-0.888427\pi$
$269$	−458.960	−	264.981i	−1.70617	−	0.985059i	−0.766977	−	0.641675i	$-0.778240\pi$
$270$		0			0
$271$	−45.6359	−	79.0437i	−0.168398	−	0.291674i	0.769459	−	0.638697i	$-0.220526\pi$
$271$	−45.6359	−	79.0437i	−0.168398	−	0.291674i	−0.937857	+	0.347022i	$0.887193\pi$
$272$			9.32580i			0.0342860i
$273$		0			0
$274$	−105.438			−0.384811
$275$	−118.444	+	68.3839i	−0.430707	+	0.248669i
$276$		0			0
$277$	134.386	−	232.763i	0.485147	−	0.840299i	−0.514707	−	0.857366i	$-0.672099\pi$
$277$	134.386	−	232.763i	0.485147	−	0.840299i	0.999854	+	0.0170668i	$0.00543278\pi$
$278$			121.759i			0.437981i
$279$		0			0
$280$	164.105	−	284.238i	0.586090	−	1.01514i
$281$		−	144.003i		−	0.512465i	−0.966615	−	0.256233i	$-0.917519\pi$
$281$		−	144.003i		−	0.512465i	0.966615	−	0.256233i	$-0.0824813\pi$
$282$		0			0
$283$	58.3176	+	101.009i	0.206069	+	0.356923i	0.950473	−	0.310807i	$-0.100599\pi$
$283$	58.3176	+	101.009i	0.206069	+	0.356923i	−0.744404	+	0.667730i	$0.767266\pi$
$284$	220.105	−	127.078i	0.775018	−	0.447457i
$285$		0			0
$286$	−286.191	−	58.0152i	−1.00067	−	0.202850i
$287$			106.193i			0.370009i
$288$		0			0
$289$	−110.894	−	192.074i	−0.383716	−	0.664616i
$290$	48.2595	+	27.8627i	0.166412	+	0.0960781i
$291$		0			0
$292$	−12.7227	+	22.0364i	−0.0435710	+	0.0754672i
$293$	134.482	+	77.6432i	0.458983	+	0.264994i	0.711617	−	0.702568i	$-0.247963\pi$
$293$	134.482	+	77.6432i	0.458983	+	0.264994i	−0.252634	+	0.967562i	$0.581297\pi$
$294$		0			0
$295$	−105.896	+	183.417i	−0.358968	+	0.621751i
$296$	341.201	−	196.993i	1.15271	−	0.665515i
$297$		0			0
$298$	154.786			0.519414
$299$	198.158	+	175.065i	0.662734	+	0.585501i
$300$		0			0
$301$	299.925	+	519.485i	0.996427	+	1.72586i
$302$	−44.3768	+	25.6210i	−0.146943	+	0.0848376i
$303$		0			0
$304$	25.1633			0.0827739
$305$	231.295	+	133.538i	0.758344	+	0.437830i
$306$		0			0
$307$	121.197			0.394777			0.197388	−	0.980325i	$-0.436754\pi$
$307$	121.197			0.394777			0.197388	+	0.980325i	$0.436754\pi$
$308$	424.968	+	245.355i	1.37977	+	0.796609i
$309$		0			0
$310$	28.2739	+	48.9719i	0.0912063	+	0.157974i
$311$		−	4.80610i		−	0.0154537i	−0.999970	−	0.00772686i	$-0.997540\pi$
$311$		−	4.80610i		−	0.0154537i	0.999970	−	0.00772686i	$-0.00245956\pi$
$312$		0			0
$313$	−43.5018			−0.138983			−0.0694916	−	0.997583i	$-0.522138\pi$
$313$	−43.5018			−0.138983			−0.0694916	+	0.997583i	$0.522138\pi$
$314$	192.781	−	111.302i	0.613951	−	0.354465i
$315$		0			0
$316$	22.9420	−	39.7367i	0.0726013	−	0.125749i
$317$			498.372i			1.57215i	0.618130	+	0.786076i	$0.287891\pi$
$317$			498.372i			1.57215i	−0.618130	+	0.786076i	$0.712109\pi$
$318$		0			0
$319$	−105.807	+	183.263i	−0.331683	+	0.574492i
$320$			143.640i			0.448874i
$321$		0			0
$322$	119.949	+	207.758i	0.372512	+	0.645210i
$323$	157.057	−	90.6769i	0.486245	−	0.280734i
$324$		0			0
$325$	−29.8062	−	88.8720i	−0.0917114	−	0.273452i
$326$			266.887i			0.818672i
$327$		0			0
$328$	−41.6529	−	72.1449i	−0.126990	−	0.219954i
$329$	−619.649	−	357.755i	−1.88343	−	1.08740i
$330$		0			0
$331$	282.481	−	489.272i	0.853418	−	1.47816i	−0.0246877	−	0.999695i	$-0.507859\pi$
$331$	282.481	−	489.272i	0.853418	−	1.47816i	0.878105	−	0.478467i	$-0.158808\pi$
$332$	−30.2745	−	17.4790i	−0.0911882	−	0.0526475i
$333$		0			0
$334$	74.8327	−	129.614i	0.224050	−	0.388066i
$335$	−268.303	+	154.905i	−0.800906	+	0.462403i
$336$		0			0
$337$	593.567			1.76133			0.880663	−	0.473743i	$-0.157097\pi$
$337$	593.567			1.76133			0.880663	+	0.473743i	$0.157097\pi$
$338$	77.9389	−	184.339i	0.230589	−	0.545380i
$339$		0			0
$340$	−44.9096	−	77.7857i	−0.132087	−	0.228782i
$341$	−185.968	+	107.369i	−0.545361	+	0.314864i
$342$		0			0
$343$	11.9027			0.0347016
$344$	−407.524	−	235.284i	−1.18466	−	0.683966i
$345$		0			0
$346$	−173.972			−0.502811
$347$	285.437	+	164.797i	0.822586	+	0.474920i	0.851307	−	0.524667i	$-0.175810\pi$
$347$	285.437	+	164.797i	0.822586	+	0.474920i	−0.0287216	+	0.999587i	$0.509144\pi$
$348$		0			0
$349$	49.6917	+	86.0685i	0.142383	+	0.246615i	0.928394	−	0.371598i	$-0.121190\pi$
$349$	49.6917	+	86.0685i	0.142383	+	0.246615i	−0.786010	+	0.618213i	$0.787857\pi$
$350$		−	85.0464i		−	0.242990i
$351$		0			0
$352$	−618.342			−1.75665
$353$	121.195	−	69.9722i	0.343330	−	0.198222i	−0.318414	−	0.947952i	$-0.603150\pi$
$353$	121.195	−	69.9722i	0.343330	−	0.198222i	0.661744	+	0.749730i	$0.269817\pi$
$354$		0			0
$355$	−206.341	+	357.393i	−0.581243	+	1.00674i
$356$		−	431.528i		−	1.21216i
$357$		0			0
$358$	148.036	−	256.405i	0.413508	−	0.716216i
$359$		−	477.480i		−	1.33003i	−0.746831	−	0.665014i	$-0.768425\pi$
$359$		−	477.480i		−	1.33003i	0.746831	−	0.665014i	$-0.231575\pi$
$360$		0			0
$361$	−64.1683	−	111.143i	−0.177751	−	0.307874i
$362$	252.764	−	145.933i	0.698242	−	0.403130i
$363$		0			0
$364$	−222.674	+	252.047i	−0.611742	+	0.692437i
$365$		−	41.3168i		−	0.113197i
$366$		0			0
$367$	−85.7664	−	148.552i	−0.233696	−	0.404773i	0.725197	−	0.688541i	$-0.241749\pi$
$367$	−85.7664	−	148.552i	−0.233696	−	0.404773i	−0.958893	+	0.283768i	$0.908415\pi$
$368$	20.0370	+	11.5684i	0.0544484	+	0.0314358i
$369$		0			0
$370$	−125.935	+	218.127i	−0.340366	+	0.589531i
$371$	−104.910	−	60.5696i	−0.282775	−	0.163260i
$372$		0			0
$373$	−236.337	+	409.348i	−0.633612	+	1.09745i	0.353195	+	0.935550i	$0.385095\pi$
$373$	−236.337	+	409.348i	−0.633612	+	1.09745i	−0.986807	+	0.161899i	$0.948238\pi$
$374$	−159.482	+	92.0770i	−0.426423	+	0.246195i
$375$		0			0
$376$	561.301			1.49282
$377$	−108.693	−	96.0259i	−0.288309	−	0.254711i
$378$		0			0
$379$	60.5549	+	104.884i	0.159775	+	0.276739i	0.934788	−	0.355207i	$-0.115590\pi$
$379$	60.5549	+	104.884i	0.159775	+	0.276739i	−0.775012	+	0.631946i	$0.782256\pi$
$380$	−209.885	+	121.177i	−0.552328	+	0.318887i
$381$		0			0
$382$	159.592			0.417779
$383$	−42.1280	−	24.3226i	−0.109995	−	0.0635056i	0.443993	−	0.896030i	$-0.353561\pi$
$383$	−42.1280	−	24.3226i	−0.109995	−	0.0635056i	−0.553988	+	0.832525i	$0.686895\pi$
$384$		0			0
$385$	−796.786			−2.06958
$386$	−149.490	−	86.3080i	−0.387279	−	0.223596i
$387$		0			0
$388$	−140.100	−	242.660i	−0.361082	−	0.625413i
$389$			685.925i			1.76330i	0.471900	+	0.881652i	$0.343568\pi$
$389$			685.925i			1.76330i	−0.471900	+	0.881652i	$0.656432\pi$
$390$		0			0
$391$	166.749			0.426467
$392$	−339.639	+	196.091i	−0.866426	+	0.500231i
$393$		0			0
$394$	−81.8919	+	141.841i	−0.207847	+	0.360002i
$395$			74.5036i			0.188617i
$396$		0			0
$397$	−67.8419	+	117.506i	−0.170886	+	0.295984i	−0.938730	−	0.344653i	$-0.887996\pi$
$397$	−67.8419	+	117.506i	−0.170886	+	0.295984i	0.767844	+	0.640637i	$0.221330\pi$
$398$		−	319.392i		−	0.802493i
$399$		0			0
$400$	−4.10111	−	7.10333i	−0.0102528	−	0.0177583i
$401$	−458.427	+	264.673i	−1.14321	+	0.660033i	−0.947224	−	0.320573i	$-0.896124\pi$
$401$	−458.427	+	264.673i	−1.14321	+	0.660033i	−0.195987	+	0.980606i	$0.562791\pi$
$402$		0			0
$403$	−46.7984	−	139.537i	−0.116125	−	0.346246i
$404$			224.179i			0.554900i
$405$		0			0
$406$	−65.7940	−	113.959i	−0.162054	−	0.280686i
$407$	−828.324	−	478.233i	−2.03519	−	1.17502i
$408$		0			0
$409$	−95.6888	+	165.738i	−0.233958	+	0.405227i	−0.958969	−	0.283510i	$-0.908501\pi$
$409$	−95.6888	+	165.738i	−0.233958	+	0.405227i	0.725011	+	0.688737i	$0.241834\pi$
$410$	46.1215	+	26.6283i	0.112492	+	0.0649470i
$411$		0			0
$412$	46.2017	−	80.0237i	0.112140	−	0.194232i
$413$	433.114	−	250.059i	1.04870	−	0.605469i
$414$		0			0
$415$	56.7626			0.136777
$416$	84.1970	−	415.348i	0.202397	−	0.998432i
$417$		0			0
$418$	248.446	+	430.321i	0.594368	+	1.02948i
$419$	447.490	−	258.359i	1.06800	−	0.616608i	0.140363	−	0.990100i	$-0.455173\pi$
$419$	447.490	−	258.359i	1.06800	−	0.616608i	0.927633	+	0.373492i	$0.121840\pi$
$420$		0			0
$421$	−197.347			−0.468759			−0.234379	−	0.972145i	$-0.575306\pi$
$421$	−197.347			−0.468759			−0.234379	+	0.972145i	$0.575306\pi$
$422$	38.5038	+	22.2302i	0.0912412	+	0.0526781i
$423$		0			0
$424$	95.0311			0.224130
$425$	−51.1943	−	29.5570i	−0.120457	−	0.0695460i
$426$		0			0
$427$	−315.333	−	546.172i	−0.738484	−	1.27909i
$428$			273.173i			0.638254i
$429$		0			0
$430$	300.830			0.699604
$431$	−651.926	+	376.390i	−1.51259	+	0.873294i	−0.512697	+	0.858569i	$0.671354\pi$
$431$	−651.926	+	376.390i	−1.51259	+	0.873294i	−0.999892	+	0.0147244i	$0.995313\pi$
$432$		0			0
$433$	−55.5839	+	96.2742i	−0.128369	+	0.222342i	−0.923045	−	0.384692i	$-0.874308\pi$
$433$	−55.5839	+	96.2742i	−0.128369	+	0.222342i	0.794676	+	0.607034i	$0.207641\pi$
$434$		−	133.530i		−	0.307674i
$435$		0			0
$436$	68.0756	−	117.910i	0.156137	−	0.270437i
$437$		−	449.928i		−	1.02958i
$438$		0			0
$439$	175.861	+	304.600i	0.400594	+	0.693849i	0.993798	−	0.111203i	$-0.0354705\pi$
$439$	175.861	+	304.600i	0.400594	+	0.693849i	−0.593204	+	0.805052i	$0.702137\pi$
$440$	541.319	−	312.531i	1.23027	−	0.710297i
$441$		0			0
$442$	−40.1332	−	119.664i	−0.0907991	−	0.270732i
$443$			260.221i			0.587407i	0.955897	+	0.293704i	$0.0948878\pi$
$443$			260.221i			0.587407i	−0.955897	+	0.293704i	$0.905112\pi$
$444$		0			0
$445$	350.344	+	606.814i	0.787291	+	1.36363i
$446$	121.847	+	70.3483i	0.273199	+	0.157732i
$447$		0			0
$448$	169.593	−	293.744i	0.378556	−	0.655679i
$449$	−9.46292	−	5.46342i	−0.0210755	−	0.0121680i	0.489425	−	0.872045i	$-0.337207\pi$
$449$	−9.46292	−	5.46342i	−0.0210755	−	0.0121680i	−0.510501	+	0.859877i	$0.670540\pi$
$450$		0			0
$451$	−101.119	+	175.144i	−0.224212	+	0.388346i
$452$	−341.650	+	197.252i	−0.755863	+	0.436398i
$453$		0			0
$454$	−78.8365			−0.173649
$455$	108.495	−	535.211i	0.238451	−	1.17629i
$456$		0			0
$457$	−345.420	−	598.285i	−0.755842	−	1.30916i	−0.944955	−	0.327202i	$-0.893894\pi$
$457$	−345.420	−	598.285i	−0.755842	−	1.30916i	0.189112	−	0.981955i	$-0.439439\pi$
$458$	−257.457	+	148.643i	−0.562134	+	0.324548i
$459$		0			0
$460$	−222.836			−0.484426
$461$	537.813	+	310.507i	1.16662	+	0.673550i	0.952882	−	0.303340i	$-0.0981018\pi$
$461$	537.813	+	310.507i	1.16662	+	0.673550i	0.213741	+	0.976890i	$0.431435\pi$
$462$		0			0
$463$	−18.7384			−0.0404716			−0.0202358	−	0.999795i	$-0.506442\pi$
$463$	−18.7384			−0.0404716			−0.0202358	+	0.999795i	$0.506442\pi$
$464$	−10.9906	−	6.34544i	−0.0236867	−	0.0136755i
$465$		0			0
$466$	−67.3479	−	116.650i	−0.144523	−	0.250322i
$467$		−	75.9065i		−	0.162541i	−0.996692	−	0.0812704i	$-0.974102\pi$
$467$		−	75.9065i		−	0.162541i	0.996692	−	0.0812704i	$-0.0258977\pi$
$468$		0			0
$469$	731.576			1.55986
$470$	−310.760	+	179.417i	−0.661191	+	0.381739i
$471$		0			0
$472$	−196.165	+	339.769i	−0.415605	+	0.719849i
$473$			1142.39i			2.41519i
$474$		0			0
$475$	−79.7521	+	138.135i	−0.167899	+	0.290810i
$476$			212.096i			0.445581i
$477$		0			0
$478$	−24.2920	−	42.0750i	−0.0508201	−	0.0880229i
$479$	556.926	−	321.541i	1.16268	−	0.671276i	0.210739	−	0.977542i	$-0.432413\pi$
$479$	556.926	−	321.541i	1.16268	−	0.671276i	0.951946	+	0.306266i	$0.0990797\pi$
$480$		0			0
$481$	434.024	−	491.276i	0.902337	−	1.02136i
$482$		−	362.993i		−	0.753098i
$483$		0			0
$484$	310.116	+	537.137i	0.640736	+	1.10979i
$485$	394.017	+	227.486i	0.812406	+	0.469043i
$486$		0			0
$487$	−237.526	+	411.407i	−0.487733	+	0.844778i	−0.999900	−	0.0141074i	$-0.995509\pi$
$487$	−237.526	+	411.407i	−0.487733	+	0.844778i	0.512168	+	0.858886i	$0.328843\pi$
$488$	428.460	+	247.372i	0.877992	+	0.506909i
$489$		0			0
$490$	125.359	−	217.128i	0.255834	−	0.443118i
$491$	644.512	−	372.109i	1.31265	−	0.757860i	0.330117	−	0.943940i	$-0.392912\pi$
$491$	644.512	−	372.109i	1.31265	−	0.757860i	0.982535	+	0.186080i	$0.0595785\pi$
$492$		0			0
$493$	−91.4643			−0.185526
$494$	−322.882	+	108.289i	−0.653606	+	0.219209i
$495$		0			0
$496$	−6.43911	−	11.1529i	−0.0129821	−	0.0224856i
$497$	843.937	−	487.248i	1.69806	−	0.980377i
$498$		0			0
$499$	933.109			1.86996			0.934979	−	0.354704i	$-0.115418\pi$
$499$	933.109			1.86996			0.934979	+	0.354704i	$0.115418\pi$
$500$	305.615	+	176.447i	0.611231	+	0.352894i
$501$		0			0
$502$	−425.888			−0.848382
$503$	−796.938	−	460.112i	−1.58437	−	0.914736i	−0.994211	−	0.107449i	$-0.965732\pi$
$503$	−796.938	−	460.112i	−1.58437	−	0.914736i	−0.590159	−	0.807287i	$-0.700935\pi$
$504$		0			0
$505$	−182.004	−	315.241i	−0.360405	−	0.624240i
$506$			456.875i			0.902915i
$507$		0			0
$508$	−0.273710			−0.000538799
$509$	71.9132	−	41.5191i	0.141283	−	0.0815700i	−0.427692	−	0.903924i	$-0.640673\pi$
$509$	71.9132	−	41.5191i	0.141283	−	0.0815700i	0.568975	+	0.822354i	$0.307340\pi$
$510$		0			0
$511$	−48.7821	+	84.4930i	−0.0954639	+	0.165348i
$512$		−	72.6339i		−	0.141863i
$513$		0			0
$514$	−57.6560	+	99.8631i	−0.112171	+	0.194286i
$515$			150.039i			0.291338i
$516$		0			0
$517$	−681.327	−	1180.09i	−1.31785	−	2.28258i
$518$	515.077	−	297.380i	0.994358	−	0.574093i
$519$		0			0
$520$	136.221	+	406.166i	0.261964	+	0.781089i
$521$			455.389i			0.874067i	0.899445	+	0.437033i	$0.143971\pi$
$521$			455.389i			0.874067i	−0.899445	+	0.437033i	$0.856029\pi$
$522$		0			0
$523$	−238.853	−	413.706i	−0.456699	−	0.791025i	0.542086	−	0.840323i	$-0.317635\pi$
$523$	−238.853	−	413.706i	−0.456699	−	0.791025i	−0.998784	+	0.0492983i	$0.984302\pi$
$524$	−449.810	−	259.698i	−0.858416	−	0.495607i
$525$		0			0
$526$	1.06705	−	1.84819i	0.00202862	−	0.00351367i
$527$	−80.3796	−	46.4072i	−0.152523	−	0.0880592i
$528$		0			0
$529$	−57.6536	+	99.8590i	−0.108986	+	0.188769i
$530$	−52.6132	+	30.3762i	−0.0992701	+	0.0573136i
$531$		0			0
$532$	572.287			1.07573
$533$	−103.877	−	91.7718i	−0.194892	−	0.172180i
$534$		0			0
$535$	−221.781	−	384.135i	−0.414543	−	0.718010i
$536$	−497.016	+	286.952i	−0.927269	+	0.535359i
$537$		0			0
$538$	627.606			1.16655
$539$	824.532	+	476.044i	1.52974	+	0.883198i
$540$		0			0
$541$	399.422			0.738304			0.369152	−	0.929369i	$-0.379648\pi$
$541$	399.422			0.738304			0.369152	+	0.929369i	$0.379648\pi$
$542$	93.6074	+	54.0442i	0.172707	+	0.0997126i
$543$		0			0
$544$	−133.631	−	231.455i	−0.245645	−	0.425469i
$545$			221.074i			0.405640i
$546$		0			0
$547$	−348.652			−0.637389			−0.318695	−	0.947857i	$-0.603244\pi$
$547$	−348.652			−0.637389			−0.318695	+	0.947857i	$0.603244\pi$
$548$	−200.286	+	115.635i	−0.365485	+	0.211013i
$549$		0			0
$550$	80.9834	−	140.267i	0.147243	−	0.255032i
$551$			246.793i			0.447900i
$552$		0			0
$553$	87.9653	−	152.360i	0.159069	−	0.275516i
$554$			318.292i			0.574534i
$555$		0			0
$556$	133.534	+	231.288i	0.240169	+	0.415985i
$557$	209.574	−	120.998i	0.376255	−	0.217231i	−0.299932	−	0.953960i	$-0.596964\pi$
$557$	209.574	−	120.998i	0.376255	−	0.217231i	0.676188	+	0.736729i	$0.263631\pi$
$558$		0			0
$559$	−767.354	−	155.554i	−1.37273	−	0.278271i
$560$		−	47.7848i		−	0.0853299i
$561$		0			0
$562$	85.2675	+	147.688i	0.151721	+	0.262789i
$563$	−245.890	−	141.965i	−0.436750	−	0.252158i	0.265468	−	0.964120i	$-0.414474\pi$
$563$	−245.890	−	141.965i	−0.436750	−	0.252158i	−0.702218	+	0.711962i	$0.747807\pi$
$564$		0			0
$565$	320.285	−	554.750i	0.566877	−	0.981859i
$566$	−119.620	−	69.0625i	−0.211342	−	0.122019i
$567$		0			0
$568$	−382.235	+	662.050i	−0.672949	+	1.16558i
$569$	111.778	−	64.5353i	0.196447	−	0.113419i	−0.398550	−	0.917147i	$-0.630486\pi$
$569$	111.778	−	64.5353i	0.196447	−	0.113419i	0.594997	+	0.803728i	$0.297153\pi$
$570$		0			0
$571$	392.417			0.687245			0.343623	−	0.939108i	$-0.388346\pi$
$571$	392.417			0.687245			0.343623	+	0.939108i	$0.388346\pi$
$572$	−607.264	+	203.666i	−1.06165	+	0.356060i
$573$		0			0
$574$	−62.8792	−	108.910i	−0.109546	−	0.189739i
$575$	−127.010	+	73.3292i	−0.220887	+	0.127529i
$576$		0			0
$577$	929.471			1.61087			0.805434	−	0.592685i	$-0.201932\pi$
$577$	929.471			1.61087			0.805434	+	0.592685i	$0.201932\pi$
$578$	227.463	+	131.326i	0.393535	+	0.227208i
$579$		0			0
$580$	122.229			0.210740
$581$	−116.080	−	67.0187i	−0.199793	−	0.115351i
$582$		0			0
$583$	−115.352	−	199.796i	−0.197860	−	0.342703i
$584$		−	76.5369i		−	0.131056i
$585$		0			0
$586$	−183.898			−0.313819
$587$	136.435	−	78.7705i	0.232427	−	0.134192i	−0.379264	−	0.925288i	$-0.623823\pi$
$587$	136.435	−	78.7705i	0.232427	−	0.134192i	0.611691	+	0.791097i	$0.290490\pi$
$588$		0			0
$589$	−125.218	+	216.884i	−0.212594	+	0.368224i
$590$		−	250.813i		−	0.425107i
$591$		0			0
$592$	28.6805	−	49.6761i	0.0484468	−	0.0839124i
$593$			209.697i			0.353621i	0.984245	+	0.176811i	$0.0565780\pi$
$593$			209.697i			0.353621i	−0.984245	+	0.176811i	$0.943422\pi$
$594$		0			0
$595$	−172.195	−	298.250i	−0.289403	−	0.501260i
$596$	294.024	−	169.755i	0.493330	−	0.284824i
$597$		0			0
$598$	−306.888	−	62.2107i	−0.513191	−	0.104031i
$599$			210.660i			0.351687i	0.984418	+	0.175843i	$0.0562653\pi$
$599$			210.660i			0.351687i	−0.984418	+	0.175843i	$0.943735\pi$
$600$		0			0
$601$	397.607	+	688.675i	0.661576	+	1.14588i	0.980202	+	0.198002i	$0.0634453\pi$
$601$	397.607	+	688.675i	0.661576	+	1.14588i	−0.318626	+	0.947881i	$0.603221\pi$
$602$	−615.199	−	355.185i	−1.02192	−	0.590008i
$603$		0			0
$604$	−56.1976	+	97.3372i	−0.0930424	+	0.161154i
$605$	−872.170	−	503.547i	−1.44160	−	0.832310i
$606$		0			0
$607$	−83.2043	+	144.114i	−0.137075	+	0.237420i	−0.926388	−	0.376570i	$-0.877103\pi$
$607$	−83.2043	+	144.114i	−0.137075	+	0.237420i	0.789313	+	0.613990i	$0.210437\pi$
$608$	−624.522	+	360.568i	−1.02717	+	0.593040i
$609$		0			0
$610$	−316.285			−0.518499
$611$	885.456	−	296.967i	1.44919	−	0.486035i
$612$		0			0
$613$	345.888	+	599.096i	0.564255	+	0.977318i	0.997119	+	0.0758585i	$0.0241697\pi$
$613$	345.888	+	599.096i	0.564255	+	0.977318i	−0.432864	+	0.901459i	$0.642497\pi$
$614$	−124.298	+	71.7634i	−0.202439	+	0.116878i
$615$		0			0
$616$	−1476.00			−2.39610
$617$	40.2231	+	23.2228i	0.0651914	+	0.0376383i	0.532241	−	0.846593i	$-0.321350\pi$
$617$	40.2231	+	23.2228i	0.0651914	+	0.0376383i	−0.467050	+	0.884231i	$0.654683\pi$
$618$		0			0
$619$	−603.722			−0.975319			−0.487659	−	0.873034i	$-0.662149\pi$
$619$	−603.722			−0.975319			−0.487659	+	0.873034i	$0.662149\pi$
$620$	107.416	+	62.0167i	0.173252	+	0.100027i
$621$		0			0
$622$	2.84581	+	4.92909i	0.00457526	+	0.00792458i
$623$		−	1654.58i		−	2.65583i
$624$		0			0
$625$	−392.744			−0.628391
$626$	44.6149	−	25.7584i	0.0712698	−	0.0411477i
$627$		0			0
$628$	244.132	−	422.850i	0.388746	−	0.673327i
$629$		−	413.406i		−	0.657244i
$630$		0			0
$631$	−454.672	+	787.515i	−0.720558	+	1.24804i	0.240219	+	0.970719i	$0.422781\pi$
$631$	−454.672	+	787.515i	−0.720558	+	1.24804i	−0.960776	+	0.277324i	$0.910552\pi$
$632$			138.014i			0.218376i
$633$		0			0
$634$	−295.098	−	511.125i	−0.465454	−	0.806191i
$635$	0.384891	−	0.222217i	0.000606127	−	0.000349948i
$636$		0			0
$637$	−432.037	+	489.027i	−0.678237	+	0.767703i
$638$		−	250.603i		−	0.392795i
$639$		0			0
$640$	189.942	+	328.990i	0.296785	+	0.514047i
$641$	−506.403	−	292.372i	−0.790021	−	0.456119i	0.0499491	−	0.998752i	$-0.484094\pi$
$641$	−506.403	−	292.372i	−0.790021	−	0.456119i	−0.839970	+	0.542633i	$0.817427\pi$
$642$		0			0
$643$	−313.719	+	543.377i	−0.487898	+	0.845065i	−0.999903	−	0.0139178i	$-0.995570\pi$
$643$	−313.719	+	543.377i	−0.487898	+	0.845065i	0.512005	+	0.858983i	$0.328903\pi$
$644$	455.701	+	263.099i	0.707610	+	0.408539i
$645$		0			0
$646$	−107.384	+	185.994i	−0.166229	+	0.287917i
$647$	232.943	−	134.490i	0.360035	−	0.207866i	−0.309061	−	0.951042i	$-0.600015\pi$
$647$	232.943	−	134.490i	0.360035	−	0.207866i	0.669096	+	0.743176i	$0.266681\pi$
$648$		0			0
$649$	952.450			1.46757
$650$	83.1921	+	73.4972i	0.127988	+	0.113073i
$651$		0			0
$652$	292.698	+	506.968i	0.448923	+	0.777558i
$653$	−496.584	+	286.703i	−0.760465	+	0.439055i	−0.829463	−	0.558562i	$-0.811353\pi$
$653$	−496.584	+	286.703i	−0.760465	+	0.439055i	0.0689977	+	0.997617i	$0.478020\pi$
$654$		0			0
$655$	843.363			1.28758
$656$	−10.5037	−	6.06432i	−0.0160118	−	0.00924440i
$657$		0			0
$658$	847.340			1.28775
$659$	−95.2083	−	54.9685i	−0.144474	−	0.0834120i	0.426021	−	0.904713i	$-0.359915\pi$
$659$	−95.2083	−	54.9685i	−0.144474	−	0.0834120i	−0.570495	+	0.821301i	$0.693248\pi$
$660$		0			0
$661$	246.116	+	426.285i	0.372338	+	0.644909i	0.989925	−	0.141594i	$-0.0452228\pi$
$661$	246.116	+	426.285i	0.372338	+	0.644909i	−0.617586	+	0.786503i	$0.711889\pi$
$662$			669.056i			1.01066i
$663$		0			0
$664$	105.149			0.158358
$665$	−804.750	+	464.622i	−1.21015	+	0.698680i
$666$		0			0
$667$	−113.459	+	196.516i	−0.170103	+	0.294627i
$668$		−	328.280i		−	0.491437i
$669$		0			0
$670$	183.446	−	317.738i	0.273800	−	0.474235i
$671$		−	1201.07i		−	1.78998i
$672$		0			0
$673$	474.953	+	822.642i	0.705725	+	1.22235i	0.966429	+	0.256932i	$0.0827118\pi$
$673$	474.953	+	822.642i	0.705725	+	1.22235i	−0.260705	+	0.965419i	$0.583955\pi$
$674$	−608.756	+	351.465i	−0.903198	+	0.521462i
$675$		0			0
$676$	−54.1165	−	435.639i	−0.0800540	−	0.644436i
$677$			93.7981i			0.138550i	0.997598	+	0.0692748i	$0.0220685\pi$
$677$			93.7981i			0.138550i	−0.997598	+	0.0692748i	$0.977931\pi$
$678$		0			0
$679$	−537.178	−	930.419i	−0.791131	−	1.37028i
$680$	233.970	+	135.083i	0.344074	+	0.198651i
$681$		0			0
$682$	127.151	−	220.232i	0.186439	−	0.322921i
$683$	384.711	+	222.113i	0.563266	+	0.325202i	0.754455	−	0.656351i	$-0.227901\pi$
$683$	384.711	+	222.113i	0.563266	+	0.325202i	−0.191189	+	0.981553i	$0.561234\pi$
$684$		0			0
$685$	187.761	−	325.212i	0.274104	−	0.474762i
$686$	−12.2072	+	7.04785i	−0.0177948	+	0.0102738i
$687$		0			0
$688$	−68.5110			−0.0995799
$689$	149.912	−	50.2780i	0.217579	−	0.0729725i
$690$		0			0
$691$	−230.253	−	398.810i	−0.333217	−	0.577148i	0.649924	−	0.759999i	$-0.274801\pi$
$691$	−230.253	−	398.810i	−0.333217	−	0.577148i	−0.983141	+	0.182851i	$0.941467\pi$
$692$	−330.471	+	190.798i	−0.477560	+	0.275719i
$693$		0			0
$694$	−390.322			−0.562423
$695$	−375.551	−	216.825i	−0.540361	−	0.311978i
$696$		0			0
$697$	−87.4122			−0.125412
$698$	−101.926	−	58.8473i	−0.146026	−	0.0843084i
$699$		0			0
$700$	−93.2714	−	161.551i	−0.133245	−	0.230787i
$701$			817.244i			1.16583i	0.812535	+	0.582913i	$0.198087\pi$
$701$			817.244i			1.16583i	−0.812535	+	0.582913i	$0.801913\pi$
$702$		0			0
$703$	−1115.47			−1.58673
$704$	559.422	−	322.983i	0.794634	−	0.458782i
$705$		0			0
$706$	−82.8645	+	143.525i	−0.117372	+	0.203294i
$707$			859.559i			1.21578i
$708$		0			0
$709$	0.0790417	−	0.136904i	0.000111483	−	0.000193095i	−0.865970	−	0.500097i	$-0.833298\pi$
$709$	0.0790417	−	0.136904i	0.000111483	−	0.000193095i	0.866081	+	0.499903i	$0.166631\pi$
$710$		−	488.718i		−	0.688335i
$711$		0			0
$712$	648.992	+	1124.09i	0.911506	+	1.57877i
$713$	−199.417	+	115.133i	−0.279687	+	0.161477i
$714$		0			0
$715$	688.584	−	779.414i	0.963054	−	1.09009i
$716$		−	649.410i		−	0.906997i
$717$		0			0
$718$	282.727	+	489.698i	0.393771	+	0.682031i
$719$	68.0663	+	39.2981i	0.0946681	+	0.0546566i	0.546587	−	0.837403i	$-0.315927\pi$
$719$	68.0663	+	39.2981i	0.0946681	+	0.0546566i	−0.451919	+	0.892059i	$0.649260\pi$
$720$		0			0
$721$	177.149	−	306.831i	0.245699	−	0.425563i
$722$	131.620	+	75.9911i	0.182300	+	0.105251i
$723$		0			0
$724$	320.093	−	554.418i	0.442118	−	0.765771i
$725$	69.6670	−	40.2223i	0.0960925	−	0.0554790i
$726$		0			0
$727$	−655.351			−0.901445			−0.450723	−	0.892664i	$-0.648834\pi$
$727$	−655.351			−0.901445			−0.450723	+	0.892664i	$0.648834\pi$
$728$	200.981	−	991.447i	0.276072	−	1.36188i
$729$		0			0
$730$	24.4647	+	42.3740i	0.0335132	+	0.0580466i
$731$	−427.613	+	246.882i	−0.584970	+	0.337732i
$732$		0			0
$733$	−790.442			−1.07837			−0.539183	−	0.842189i	$-0.681267\pi$
$733$	−790.442			−1.07837			−0.539183	+	0.842189i	$0.681267\pi$
$734$	175.922	+	101.569i	0.239676	+	0.138377i
$735$		0			0
$736$	−663.059			−0.900896
$737$	1206.59	+	696.626i	1.63717	+	0.945218i
$738$		0			0
$739$	288.669	+	499.989i	0.390621	+	0.676575i	0.992532	−	0.121988i	$-0.0389270\pi$
$739$	288.669	+	499.989i	0.390621	+	0.676575i	−0.601911	+	0.798564i	$0.705594\pi$
$740$			552.460i			0.746567i
$741$		0			0
$742$	143.459			0.193341
$743$	558.106	−	322.223i	0.751152	−	0.433678i	−0.0749578	−	0.997187i	$-0.523882\pi$
$743$	558.106	−	322.223i	0.751152	−	0.433678i	0.826110	+	0.563509i	$0.190549\pi$
$744$		0			0
$745$	−275.638	+	477.419i	−0.369984	+	0.640831i
$746$		−	559.764i		−	0.750354i
$747$		0			0
$748$	−201.964	+	349.812i	−0.270005	+	0.467663i
$749$			1047.41i			1.39841i
$750$		0			0
$751$	151.686	+	262.728i	0.201979	+	0.349837i	0.949166	−	0.314776i	$-0.101929\pi$
$751$	151.686	+	262.728i	0.201979	+	0.349837i	−0.747187	+	0.664614i	$0.768596\pi$
$752$	70.7724	−	40.8605i	0.0941123	−	0.0543357i
$753$		0			0
$754$	168.333	+	34.1236i	0.223254	+	0.0452567i
$755$		−	182.501i		−	0.241723i
$756$		0			0
$757$	−571.558	−	989.968i	−0.755030	−	1.30775i	−0.945359	−	0.326031i	$-0.894289\pi$
$757$	−571.558	−	989.968i	−0.755030	−	1.30775i	0.190329	−	0.981720i	$-0.439045\pi$
$758$	−124.209	−	71.7120i	−0.163864	−	0.0946068i
$759$		0			0
$760$	364.486	−	631.308i	0.479587	−	0.830669i
$761$	−442.623	−	255.549i	−0.581634	−	0.335806i	0.180149	−	0.983639i	$-0.442342\pi$
$761$	−442.623	−	255.549i	−0.581634	−	0.335806i	−0.761782	+	0.647833i	$0.775675\pi$
$762$		0			0
$763$	261.018	−	452.097i	0.342095	−	0.592526i
$764$	303.154	−	175.026i	0.396798	−	0.229092i
$765$		0			0
$766$	57.6080			0.0752063
$767$	−129.691	+	639.772i	−0.169089	+	0.834123i
$768$		0			0
$769$	−373.414	−	646.772i	−0.485584	−	0.841056i	0.514279	−	0.857623i	$-0.328060\pi$
$769$	−373.414	−	646.772i	−0.485584	−	0.841056i	−0.999863	+	0.0165667i	$0.994726\pi$
$770$	817.175	−	471.796i	1.06127	−	0.612723i
$771$		0			0
$772$	−378.620			−0.490440
$773$	−219.390	−	126.665i	−0.283816	−	0.163861i	0.351334	−	0.936250i	$-0.385728\pi$
$773$	−219.390	−	126.665i	−0.283816	−	0.163861i	−0.635150	+	0.772389i	$0.719062\pi$
$774$		0			0
$775$	81.6320			0.105332
$776$	729.893	+	421.404i	0.940584	+	0.543047i
$777$		0			0
$778$	−406.153	−	703.477i	−0.522047	−	0.904213i
$779$			235.859i			0.302772i
$780$		0			0
$781$	1855.88			2.37629
$782$	−171.015	+	98.7358i	−0.218690	+	0.126261i
$783$		0			0
$784$	−28.5492	+	49.4487i	−0.0364148	+	0.0630723i
$785$			792.814i			1.00995i
$786$		0			0
$787$	586.543	−	1015.92i	0.745290	−	1.29088i	−0.204770	−	0.978810i	$-0.565645\pi$
$787$	586.543	−	1015.92i	0.745290	−	1.29088i	0.950059	−	0.312069i	$-0.101022\pi$
$788$			359.247i			0.455897i
$789$		0			0
$790$	−44.1154	−	76.4101i	−0.0558423	−	0.0967216i
$791$	−1309.97	+	756.312i	−1.65609	+	0.956146i
$792$		0			0
$793$	806.775	+	163.545i	1.01737	+	0.206236i
$794$		−	160.683i		−	0.202372i
$795$		0			0
$796$	−350.281	−	606.705i	−0.440052	−	0.762192i
$797$	389.097	+	224.645i	0.488203	+	0.281864i	0.723828	−	0.689980i	$-0.242381\pi$
$797$	389.097	+	224.645i	0.488203	+	0.281864i	−0.235626	+	0.971844i	$0.575714\pi$
$798$		0			0
$799$	294.485	−	510.063i	0.368567	−	0.638377i
$800$	203.569	+	117.531i	0.254462	+	0.146913i
$801$		0			0
$802$	313.439	−	542.892i	0.390821	−	0.676922i
$803$	−160.913	+	92.9032i	−0.200390	+	0.115695i
$804$		0			0
$805$	−854.408			−1.06138
$806$	130.619	+	115.397i	0.162058	+	0.143173i
$807$		0			0
$808$	−337.153	−	583.965i	−0.417268	−	0.722729i
$809$	1003.93	−	579.621i	1.24096	−	0.716466i	0.271667	−	0.962391i	$-0.412425\pi$
$809$	1003.93	−	579.621i	1.24096	−	0.716466i	0.969289	+	0.245925i	$0.0790918\pi$
$810$		0			0
$811$	−278.983			−0.343999			−0.171999	−	0.985097i	$-0.555023\pi$
$811$	−278.983			−0.343999			−0.171999	+	0.985097i	$0.555023\pi$
$812$	−249.959	−	144.314i	−0.307832	−	0.177727i
$813$		0			0
$814$	1132.69			1.39151
$815$	−823.183	−	475.265i	−1.01004	−	0.583147i
$816$		0			0
$817$	666.148	+	1153.80i	0.815359	+	1.41224i
$818$		−	226.638i		−	0.277064i
$819$		0			0
$820$	116.814			0.142456
$821$	429.565	−	248.010i	0.523222	−	0.302082i	−0.215030	−	0.976607i	$-0.568985\pi$
$821$	429.565	−	248.010i	0.523222	−	0.302082i	0.738252	+	0.674525i	$0.235652\pi$
$822$		0			0
$823$	7.30758	−	12.6571i	0.00887920	−	0.0153792i	−0.861552	−	0.507670i	$-0.830507\pi$
$823$	7.30758	−	12.6571i	0.00887920	−	0.0153792i	0.870431	+	0.492291i	$0.163840\pi$
$824$			277.939i			0.337304i
$825$		0			0
$826$	−296.131	+	512.915i	−0.358513	+	0.620962i
$827$		−	531.778i		−	0.643021i	−0.946906	−	0.321510i	$-0.895810\pi$
$827$		−	531.778i		−	0.643021i	0.946906	−	0.321510i	$-0.104190\pi$
$828$		0			0
$829$	−185.562	−	321.403i	−0.223839	−	0.387700i	0.732132	−	0.681163i	$-0.238526\pi$
$829$	−185.562	−	321.403i	−0.223839	−	0.387700i	−0.955970	+	0.293463i	$0.905192\pi$
$830$	−58.2151	+	33.6105i	−0.0701387	+	0.0404946i
$831$		0			0
$832$	140.777	+	419.750i	0.169203	+	0.504507i
$833$			411.514i			0.494014i
$834$		0			0
$835$	266.520	+	461.627i	0.319186	+	0.552846i
$836$	943.876	+	544.947i	1.12904	+	0.651851i
$837$		0			0
$838$	−305.961	+	529.940i	−0.365108	+	0.632386i
$839$	567.195	+	327.470i	0.676037	+	0.390310i	0.798360	−	0.602180i	$-0.205701\pi$
$839$	567.195	+	327.470i	0.676037	+	0.390310i	−0.122323	+	0.992490i	$0.539034\pi$
$840$		0			0
$841$	−358.266	+	620.535i	−0.426000	+	0.737854i
$842$	202.397	−	116.854i	0.240377	−	0.138782i
$843$		0			0
$844$	97.5204			0.115545
$845$	429.780	+	568.659i	0.508616	+	0.672970i
$846$		0			0
$847$	1189.06	+	2059.51i	1.40385	+	2.43154i
$848$	11.9821	−	6.91788i	0.0141299	−	0.00815788i
$849$		0			0
$850$	70.0057			0.0823597
$851$	−888.226	−	512.818i	−1.04374	−	0.602606i
$852$		0			0
$853$	−1463.35			−1.71553			−0.857766	−	0.514040i	$-0.828148\pi$
$853$	−1463.35			−1.71553			−0.857766	+	0.514040i	$0.828148\pi$
$854$	646.803	+	373.432i	0.757381	+	0.437274i
$855$		0			0
$856$	−410.836	−	711.588i	−0.479948	−	0.831295i
$857$		−	535.499i		−	0.624853i	−0.949942	−	0.312427i	$-0.898858\pi$
$857$		−	535.499i		−	0.624853i	0.949942	−	0.312427i	$-0.101142\pi$
$858$		0			0
$859$	−724.656			−0.843604			−0.421802	−	0.906688i	$-0.638602\pi$
$859$	−724.656			−0.843604			−0.421802	+	0.906688i	$0.638602\pi$
$860$	571.444	−	329.924i	0.664470	−	0.383632i
$861$		0			0
$862$	445.739	−	772.042i	0.517098	−	0.895640i
$863$		−	479.621i		−	0.555760i	−0.960616	−	0.277880i	$-0.910368\pi$
$863$		−	479.621i		−	0.555760i	0.960616	−	0.277880i	$-0.0896318\pi$
$864$		0			0
$865$	309.806	−	536.599i	0.358157	−	0.620346i
$866$		−	131.650i		−	0.152021i
$867$		0			0
$868$	−146.444	−	253.649i	−0.168715	−	0.292222i
$869$	290.163	−	167.526i	0.333905	−	0.192780i
$870$		0			0
$871$	−632.228	+	715.625i	−0.725865	+	0.821613i
$872$			409.526i			0.469640i
$873$		0			0
$874$	266.413	+	461.441i	0.304820	+	0.527964i
$875$	1171.80	+	676.542i	1.33920	+	0.773190i
$876$		0			0
$877$	222.767	−	385.844i	0.254011	−	0.439959i	−0.710616	−	0.703580i	$-0.751583\pi$
$877$	222.767	−	385.844i	0.254011	−	0.439959i	0.964626	+	0.263621i	$0.0849168\pi$
$878$	−360.722	−	208.263i	−0.410845	−	0.237201i
$879$		0			0
$880$	45.5019	−	78.8117i	0.0517068	−	0.0895587i
$881$	−625.341	+	361.041i	−0.709808	+	0.409808i	−0.810990	−	0.585060i	$-0.801071\pi$
$881$	−625.341	+	361.041i	−0.709808	+	0.409808i	0.101182	+	0.994868i	$0.467738\pi$
$882$		0			0
$883$	−611.701			−0.692754			−0.346377	−	0.938095i	$-0.612588\pi$
$883$	−611.701			−0.692754			−0.346377	+	0.938095i	$0.612588\pi$
$884$	−207.472	−	183.294i	−0.234697	−	0.207346i
$885$		0			0
$886$	−154.083	−	266.880i	−0.173909	−	0.301219i
$887$	−826.163	+	476.986i	−0.931413	+	0.537751i	−0.887258	−	0.461273i	$-0.847393\pi$
$887$	−826.163	+	476.986i	−0.931413	+	0.537751i	−0.0441547	+	0.999025i	$0.514059\pi$
$888$		0			0
$889$	−1.04947			−0.00118051
$890$	−718.618	−	414.894i	−0.807436	−	0.466174i
$891$		0			0
$892$	308.607			0.345972
$893$	−1376.27	−	794.592i	−1.54118	−	0.889800i
$894$		0			0
$895$	527.236	+	913.200i	0.589091	+	1.02034i
$896$		−	897.048i		−	1.00117i
$897$		0			0
$898$	12.9401			0.0144099
$899$	109.383	−	63.1526i	0.121672	−	0.0702476i
$900$		0			0
$901$	49.8578	−	86.3562i	0.0553360	−	0.0958448i
$902$		−	239.501i		−	0.265522i
$903$		0			0
$904$	593.310	−	1027.64i	0.656316	−	1.13677i
$905$			1039.50i			1.14861i
$906$		0			0
$907$	196.565	+	340.460i	0.216720	+	0.375369i	0.953803	−	0.300432i	$-0.0971309\pi$
$907$	196.565	+	340.460i	0.216720	+	0.375369i	−0.737084	+	0.675802i	$0.763798\pi$
$908$	−149.755	+	86.4609i	−0.164928	+	0.0952212i
$909$		0			0
$910$	205.640	+	613.149i	0.225978	+	0.673790i
$911$		−	578.215i		−	0.634704i	−0.948308	−	0.317352i	$-0.897206\pi$
$911$		−	578.215i		−	0.634704i	0.948308	−	0.317352i	$-0.102794\pi$
$912$		0			0
$913$	−127.634	−	221.069i	−0.139796	−	0.242134i
$914$	708.517	+	409.063i	0.775183	+	0.447552i
$915$		0			0
$916$	−326.037	+	564.713i	−0.355936	+	0.616499i
$917$	−1724.68	−	995.746i	−1.88079	−	1.08587i
$918$		0			0
$919$	−538.208	+	932.204i	−0.585645	+	1.01437i	0.409149	+	0.912467i	$0.365826\pi$
$919$	−538.208	+	932.204i	−0.585645	+	1.01437i	−0.994795	+	0.101900i	$0.967508\pi$
$920$	580.466	−	335.132i	0.630941	−	0.364274i
$921$		0			0
$922$	−735.434			−0.797651
$923$	−252.707	+	1246.62i	−0.273789	+	1.35061i
$924$		0			0
$925$	181.799	+	314.886i	0.196540	+	0.340417i
$926$	19.2179	−	11.0954i	0.0207536	−	0.0119821i
$927$		0			0
$928$	363.699			0.391917
$929$	6.97990	+	4.02985i	0.00751335	+	0.00433783i	0.503752	−	0.863848i	$-0.331953\pi$
$929$	6.97990	+	4.02985i	0.00751335	+	0.00433783i	−0.496239	+	0.868186i	$0.665286\pi$
$930$		0			0
$931$	1110.36			1.19266
$932$	−255.863	−	147.722i	−0.274531	−	0.158500i
$933$		0			0
$934$	44.9461	+	77.8489i	0.0481221	+	0.0833500i
$935$		−	655.873i		−	0.701469i
$936$		0			0
$937$	−307.794			−0.328489			−0.164245	−	0.986420i	$-0.552519\pi$
$937$	−307.794			−0.328489			−0.164245	+	0.986420i	$0.552519\pi$
$938$	−750.296	+	433.183i	−0.799889	+	0.461816i
$939$		0			0
$940$	−393.538	+	681.628i	−0.418657	+	0.725136i
$941$		−	1630.11i		−	1.73232i	−0.499767	−	0.866160i	$-0.666581\pi$
$941$		−	1630.11i		−	1.73232i	0.499767	−	0.866160i	$-0.333419\pi$
$942$		0			0
$943$	−108.432	+	187.810i	−0.114986	+	0.199162i
$944$			57.1202i			0.0605087i
$945$		0			0
$946$	−676.434	−	1171.62i	−0.715046	−	1.23850i
$947$	676.707	−	390.697i	0.714580	−	0.412563i	−0.0981744	−	0.995169i	$-0.531300\pi$
$947$	676.707	−	390.697i	0.714580	−	0.412563i	0.812755	+	0.582606i	$0.197967\pi$
$948$		0			0
$949$	−40.4933	−	120.737i	−0.0426695	−	0.127226i
$950$		−	188.892i		−	0.198834i
$951$		0			0
$952$	−318.980	−	552.490i	−0.335063	−	0.580347i
$953$	−500.074	−	288.718i	−0.524737	−	0.302957i	0.214134	−	0.976804i	$-0.431307\pi$
$953$	−500.074	−	288.718i	−0.524737	−	0.302957i	−0.738871	+	0.673847i	$0.764641\pi$
$954$		0			0
$955$	−284.197	+	492.243i	−0.297588	+	0.515438i
$956$	−92.2882	−	53.2826i	−0.0965358	−	0.0557350i
$957$		0			0
$958$	−380.785	+	659.538i	−0.397479	+	0.688453i
$959$	−767.946	+	443.374i	−0.800778	+	0.462329i
$960$		0			0
$961$	−832.830			−0.866629
$962$	−154.234	+	760.843i	−0.160326	+	0.790897i
$963$		0			0
$964$	−398.099	−	689.528i	−0.412966	−	0.715278i
$965$	532.415	−	307.390i	0.551725	−	0.318539i
$966$		0			0
$967$	−773.361			−0.799753			−0.399876	−	0.916569i	$-0.630947\pi$
$967$	−773.361			−0.799753			−0.399876	+	0.916569i	$0.630947\pi$
$968$	−1615.64	−	932.792i	−1.66905	−	0.963628i
$969$		0			0
$970$	−538.799			−0.555463
$971$	−808.128	−	466.573i	−0.832263	−	0.480507i	0.0223637	−	0.999750i	$-0.492881\pi$
$971$	−808.128	−	466.573i	−0.832263	−	0.480507i	−0.854627	+	0.519243i	$0.826214\pi$
$972$		0			0
$973$	512.003	+	886.814i	0.526210	+	0.911423i
$974$		−	562.579i		−	0.577597i
$975$		0			0
$976$	72.0306			0.0738019
$977$	1595.54	−	921.184i	1.63310	−	0.942870i	0.649969	−	0.759961i	$-0.274782\pi$
$977$	1595.54	−	921.184i	1.63310	−	0.942870i	0.983130	−	0.182909i	$-0.0585513\pi$
$978$		0			0
$979$	1575.54	−	2728.91i	1.60934	−	2.78745i
$980$		−	549.930i		−	0.561153i
$981$		0			0
$982$	−440.669	+	763.262i	−0.448747	+	0.777252i
$983$			759.313i			0.772445i	0.922406	+	0.386222i	$0.126220\pi$
$983$			759.313i			0.772445i	−0.922406	+	0.386222i	$0.873780\pi$
$984$		0			0
$985$	−291.662	−	505.173i	−0.296103	−	0.512866i
$986$	93.8048	−	54.1582i	0.0951367	−	0.0549272i
$987$		0			0
$988$	−494.571	+	559.810i	−0.500578	+	0.566609i
$989$			1225.00i			1.23862i
$990$		0			0
$991$	−308.172	−	533.770i	−0.310971	−	0.538617i	0.667602	−	0.744518i	$-0.267321\pi$
$991$	−308.172	−	533.770i	−0.310971	−	0.538617i	−0.978573	+	0.205901i	$0.933988\pi$
$992$	319.622	+	184.534i	0.322199	+	0.186022i
$993$		0			0
$994$	−577.022	+	999.431i	−0.580505	+	1.00546i
$995$	985.131	+	568.765i	0.990081	+	0.571624i
$996$		0			0
$997$	892.908	−	1546.56i	0.895595	−	1.55122i	0.0625282	−	0.998043i	$-0.480084\pi$
$997$	892.908	−	1546.56i	0.895595	−	1.55122i	0.833067	−	0.553173i	$-0.186583\pi$
$998$	−956.986	+	552.516i	−0.958904	+	0.553623i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.p.a.107.4	yes	20
3.2	odd	2	inner	117.3.p.a.107.7	yes	20
13.9	even	3	inner	117.3.p.a.35.7	yes	20
39.35	odd	6	inner	117.3.p.a.35.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.p.a.35.4	✓	20	39.35	odd	6	inner
117.3.p.a.35.7	yes	20	13.9	even	3	inner
117.3.p.a.107.4	yes	20	1.1	even	1	trivial
117.3.p.a.107.7	yes	20	3.2	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02559 + 0.592124i) q^{2} +(-1.29878 + 2.24955i) q^{4} -4.21775i q^{5} +(-4.97984 + 8.62533i) q^{7} -7.81314i q^{8} +(2.49743 + 4.32568i) q^{10} +(-16.4265 + 9.48387i) q^{11} +(-4.13369 - 12.3253i) q^{13} -11.7947i q^{14} +(-0.568765 - 0.985130i) q^{16} +(-7.09992 - 4.09914i) q^{17} +(-11.0605 + 19.1573i) q^{19} +(9.48805 + 5.47793i) q^{20} +(11.2313 - 19.4531i) q^{22} +(-17.6145 + 10.1697i) q^{23} +7.21054 q^{25} +(11.5376 + 10.1930i) q^{26} +(-12.9354 - 22.4048i) q^{28} +(9.66183 - 5.57826i) q^{29} +11.3212 q^{31} +(28.2322 + 16.2998i) q^{32} +9.70880 q^{34} +(36.3795 + 21.0037i) q^{35} +(25.2130 + 43.6702i) q^{37} -26.1967i q^{38} -32.9539 q^{40} +(9.23379 - 5.33113i) q^{41} +(30.1139 - 52.1588i) q^{43} -49.2698i q^{44} +(12.0435 - 20.8599i) q^{46} +71.8407i q^{47} +(-25.0975 - 43.4702i) q^{49} +(-7.39505 + 4.26954i) q^{50} +(33.0951 + 6.70886i) q^{52} +12.1630i q^{53} +(40.0006 + 69.2831i) q^{55} +(67.3909 + 38.9082i) q^{56} +(-6.60604 + 11.4420i) q^{58} +(-43.4868 - 25.1071i) q^{59} +(-31.6610 + 54.8384i) q^{61} +(-11.6109 + 6.70355i) q^{62} -34.0560 q^{64} +(-51.9850 + 17.4349i) q^{65} +(-36.7269 - 63.6128i) q^{67} +(18.4425 - 10.6478i) q^{68} -49.7472 q^{70} +(-84.7355 - 48.9220i) q^{71} +9.79592 q^{73} +(-51.7163 - 29.8584i) q^{74} +(-28.7302 - 49.7622i) q^{76} -188.912i q^{77} -17.6643 q^{79} +(-4.15504 + 2.39891i) q^{80} +(-6.31338 + 10.9351i) q^{82} +13.4580i q^{83} +(-17.2892 + 29.9457i) q^{85} +71.3246i q^{86} +(74.0988 + 128.343i) q^{88} +(-143.871 + 83.0642i) q^{89} +(126.895 + 25.7234i) q^{91} -52.8329i q^{92} +(-42.5386 - 73.6790i) q^{94} +(80.8008 + 46.6504i) q^{95} +(-53.9353 + 93.4187i) q^{97} +(51.4795 + 29.7217i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 24 q^{4} - 6 q^{7} + 12 q^{10} - 2 q^{13} - 104 q^{16} - 92 q^{19} + 44 q^{22} - 116 q^{25} + 76 q^{28} - 156 q^{31} + 80 q^{34} + 148 q^{37} + 328 q^{40} + 186 q^{43} + 164 q^{46} + 8 q^{49} + 392 q^{52}+ \cdots - 14 q^{97}+O(q^{100}) \) 20 * q + 24 * q^4 - 6 * q^7 + 12 * q^10 - 2 * q^13 - 104 * q^16 - 92 * q^19 + 44 * q^22 - 116 * q^25 + 76 * q^28 - 156 * q^31 + 80 * q^34 + 148 * q^37 + 328 * q^40 + 186 * q^43 + 164 * q^46 + 8 * q^49 + 392 * q^52 - 208 * q^55 - 236 * q^58 + 210 * q^61 - 1568 * q^64 - 158 * q^67 - 1048 * q^70 + 156 * q^73 + 764 * q^76 - 132 * q^79 + 648 * q^82 + 44 * q^85 + 372 * q^88 + 834 * q^91 - 220 * q^94 - 14 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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