LMFDB - Embedded newform 684.3.m.a.653.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(353,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 4]))

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

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

chi := DirichletCharacter("684.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.m (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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			653.35
Character	$\chi$	$=$	684.653
Dual form			684.3.m.a.353.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.77223 - 1.14661i) q^{3} +6.14879i q^{5} +(-6.67945 - 11.5692i) q^{7} +(6.37056 - 6.35735i) q^{9} +O(q^{10})$	\(q+(2.77223 - 1.14661i) q^{3} +6.14879i q^{5} +(-6.67945 - 11.5692i) q^{7} +(6.37056 - 6.35735i) q^{9} +(0.586623 - 0.338687i) q^{11} +(10.9877 + 19.0312i) q^{13} +(7.05028 + 17.0459i) q^{15} +(10.9425 - 6.31763i) q^{17} +(7.16635 + 17.5967i) q^{19} +(-31.7823 - 24.4137i) q^{21} +(30.1014 - 17.3790i) q^{23} -12.8077 q^{25} +(10.3713 - 24.9286i) q^{27} -38.1321i q^{29} +(19.7392 - 34.1893i) q^{31} +(1.23791 - 1.61155i) q^{33} +(71.1363 - 41.0706i) q^{35} -24.0074 q^{37} +(52.2818 + 40.1603i) q^{39} +1.00016i q^{41} +(5.90752 - 10.2321i) q^{43} +(39.0901 + 39.1713i) q^{45} -36.4056i q^{47} +(-64.7302 + 112.116i) q^{49} +(23.0912 - 30.0607i) q^{51} +(29.2948 + 16.9134i) q^{53} +(2.08251 + 3.60702i) q^{55} +(40.0434 + 40.5651i) q^{57} +61.9016i q^{59} +99.9371 q^{61} +(-116.101 - 31.2383i) q^{63} +(-117.019 + 67.5609i) q^{65} +(15.8247 + 27.4092i) q^{67} +(63.5210 - 82.6933i) q^{69} +(104.178 - 60.1470i) q^{71} +(9.08945 + 15.7434i) q^{73} +(-35.5058 + 14.6854i) q^{75} +(-7.83664 - 4.52448i) q^{77} +(-4.10688 + 7.11332i) q^{79} +(0.168107 - 80.9998i) q^{81} +(-139.075 + 80.2951i) q^{83} +(38.8458 + 67.2829i) q^{85} +(-43.7227 - 105.711i) q^{87} +(-91.8708 - 53.0416i) q^{89} +(146.783 - 254.236i) q^{91} +(15.5198 - 117.414i) q^{93} +(-108.198 + 44.0644i) q^{95} +(-25.7098 + 44.5306i) q^{97} +(1.58396 - 5.88699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	2.77223	−	1.14661i	0.924078	−	0.382204i
$3$	2.77223	−	1.14661i	0.924078	−	0.382204i
$4$		0			0
$5$			6.14879i			1.22976i	0.788621	+	0.614879i	$0.210795\pi$
$5$			6.14879i			1.22976i	−0.788621	+	0.614879i	$0.789205\pi$
$6$		0			0
$7$	−6.67945	−	11.5692i	−0.954208	−	1.65274i	−0.736171	−	0.676795i	$-0.763368\pi$
$7$	−6.67945	−	11.5692i	−0.954208	−	1.65274i	−0.218036	−	0.975941i	$-0.569965\pi$
$8$		0			0
$9$	6.37056	−	6.35735i	0.707840	−	0.706373i
$10$		0			0
$11$	0.586623	−	0.338687i	0.0533293	−	0.0307897i	−0.473098	−	0.881010i	$-0.656864\pi$
$11$	0.586623	−	0.338687i	0.0533293	−	0.0307897i	0.526428	+	0.850220i	$0.323531\pi$
$12$		0			0
$13$	10.9877	+	19.0312i	0.845205	+	1.46394i	0.885443	+	0.464748i	$0.153855\pi$
$13$	10.9877	+	19.0312i	0.845205	+	1.46394i	−0.0402375	+	0.999190i	$0.512811\pi$
$14$		0			0
$15$	7.05028	+	17.0459i	0.470019	+	1.13639i
$16$		0			0
$17$	10.9425	−	6.31763i	0.643674	−	0.371625i	−0.142354	−	0.989816i	$-0.545467\pi$
$17$	10.9425	−	6.31763i	0.643674	−	0.371625i	0.786028	+	0.618190i	$0.212134\pi$
$18$		0			0
$19$	7.16635	+	17.5967i	0.377176	+	0.926141i
$19$	7.16635	+	17.5967i	0.377176	+	0.926141i
$20$		0			0
$21$	−31.7823	−	24.4137i	−1.51344	−	1.16255i
$22$		0			0
$23$	30.1014	−	17.3790i	1.30876	−	0.755610i	0.326867	−	0.945070i	$-0.394007\pi$
$23$	30.1014	−	17.3790i	1.30876	−	0.755610i	0.981888	+	0.189460i	$0.0606738\pi$
$24$		0			0
$25$	−12.8077			−0.512306
$26$		0			0
$27$	10.3713	−	24.9286i	0.384121	−	0.923283i
$28$		0			0
$29$		−	38.1321i		−	1.31490i	−0.753498	−	0.657450i	$-0.771635\pi$
$29$		−	38.1321i		−	1.31490i	0.753498	−	0.657450i	$-0.228365\pi$
$30$		0			0
$31$	19.7392	−	34.1893i	0.636749	−	1.10288i	−0.349393	−	0.936976i	$-0.613612\pi$
$31$	19.7392	−	34.1893i	0.636749	−	1.10288i	0.986142	−	0.165905i	$-0.0530545\pi$
$32$		0			0
$33$	1.23791	−	1.61155i	0.0375125	−	0.0488348i
$34$		0			0
$35$	71.1363	−	41.0706i	2.03247	−	1.17345i
$36$		0			0
$37$	−24.0074			−0.648850			−0.324425	−	0.945911i	$-0.605171\pi$
$37$	−24.0074			−0.648850			−0.324425	+	0.945911i	$0.605171\pi$
$38$		0			0
$39$	52.2818	+	40.1603i	1.34056	+	1.02975i
$40$		0			0
$41$			1.00016i			0.0243941i	0.999926	+	0.0121970i	$0.00388253\pi$
$41$			1.00016i			0.0243941i	−0.999926	+	0.0121970i	$0.996117\pi$
$42$		0			0
$43$	5.90752	−	10.2321i	0.137384	−	0.237956i	−0.789122	−	0.614237i	$-0.789464\pi$
$43$	5.90752	−	10.2321i	0.137384	−	0.237956i	0.926506	+	0.376281i	$0.122797\pi$
$44$		0			0
$45$	39.0901	+	39.1713i	0.868668	+	0.870473i
$46$		0			0
$47$		−	36.4056i		−	0.774588i	−0.921956	−	0.387294i	$-0.873410\pi$
$47$		−	36.4056i		−	0.774588i	0.921956	−	0.387294i	$-0.126590\pi$
$48$		0			0
$49$	−64.7302	+	112.116i	−1.32102	+	2.28808i
$50$		0			0
$51$	23.0912	−	30.0607i	0.452768	−	0.589426i
$52$		0			0
$53$	29.2948	+	16.9134i	0.552732	+	0.319120i	0.750223	−	0.661185i	$-0.229946\pi$
$53$	29.2948	+	16.9134i	0.552732	+	0.319120i	−0.197491	+	0.980305i	$0.563279\pi$
$54$		0			0
$55$	2.08251	+	3.60702i	0.0378639	+	0.0655822i
$56$		0			0
$57$	40.0434	+	40.5651i	0.702515	+	0.711668i
$58$		0			0
$59$			61.9016i			1.04918i	0.851355	+	0.524590i	$0.175781\pi$
$59$			61.9016i			1.04918i	−0.851355	+	0.524590i	$0.824219\pi$
$60$		0			0
$61$	99.9371			1.63831			0.819156	−	0.573570i	$-0.194442\pi$
$61$	99.9371			1.63831			0.819156	+	0.573570i	$0.194442\pi$
$62$		0			0
$63$	−116.101	−	31.2383i	−1.84287	−	0.495847i
$64$		0			0
$65$	−117.019	+	67.5609i	−1.80029	+	1.03940i
$66$		0			0
$67$	15.8247	+	27.4092i	0.236189	+	0.409092i	0.959618	−	0.281308i	$-0.0907681\pi$
$67$	15.8247	+	27.4092i	0.236189	+	0.409092i	−0.723428	+	0.690399i	$0.757435\pi$
$68$		0			0
$69$	63.5210	−	82.6933i	0.920595	−	1.19845i
$70$		0			0
$71$	104.178	−	60.1470i	1.46729	−	0.847141i	0.467961	−	0.883749i	$-0.344989\pi$
$71$	104.178	−	60.1470i	1.46729	−	0.847141i	0.999330	+	0.0366080i	$0.0116553\pi$
$72$		0			0
$73$	9.08945	+	15.7434i	0.124513	+	0.215663i	0.921542	−	0.388278i	$-0.126930\pi$
$73$	9.08945	+	15.7434i	0.124513	+	0.215663i	−0.797030	+	0.603940i	$0.793596\pi$
$74$		0			0
$75$	−35.5058	+	14.6854i	−0.473411	+	0.195806i
$76$		0			0
$77$	−7.83664	−	4.52448i	−0.101774	−	0.0587595i
$78$		0			0
$79$	−4.10688	+	7.11332i	−0.0519858	+	0.0900420i	−0.890847	−	0.454303i	$-0.849888\pi$
$79$	−4.10688	+	7.11332i	−0.0519858	+	0.0900420i	0.838861	+	0.544345i	$0.183222\pi$
$80$		0			0
$81$	0.168107	−	80.9998i	0.00207540	−	0.999998i
$82$		0			0
$83$	−139.075	+	80.2951i	−1.67560	+	0.967410i	−0.711195	+	0.702995i	$0.751846\pi$
$83$	−139.075	+	80.2951i	−1.67560	+	0.967410i	−0.964409	+	0.264416i	$0.914821\pi$
$84$		0			0
$85$	38.8458	+	67.2829i	0.457010	+	0.791564i
$86$		0			0
$87$	−43.7227	−	105.711i	−0.502560	−	1.21507i
$88$		0			0
$89$	−91.8708	−	53.0416i	−1.03226	−	0.595973i	−0.114626	−	0.993409i	$-0.536567\pi$
$89$	−91.8708	−	53.0416i	−1.03226	−	0.595973i	−0.917630	+	0.397436i	$0.869900\pi$
$90$		0			0
$91$	146.783	−	254.236i	1.61300	−	2.79380i
$92$		0			0
$93$	15.5198	−	117.414i	0.166880	−	1.26252i
$94$		0			0
$95$	−108.198	+	44.0644i	−1.13893	+	0.463836i
$96$		0			0
$97$	−25.7098	+	44.5306i	−0.265049	+	0.459078i	−0.967576	−	0.252578i	$-0.918721\pi$
$97$	−25.7098	+	44.5306i	−0.265049	+	0.459078i	0.702527	+	0.711657i	$0.252055\pi$
$98$		0			0
$99$	1.58396	−	5.88699i	0.0159996	−	0.0594646i
$100$		0			0
$101$			2.95928i			0.0292998i	0.999893	+	0.0146499i	$0.00466337\pi$
$101$			2.95928i			0.0292998i	−0.999893	+	0.0146499i	$0.995337\pi$
$102$		0			0
$103$	5.46277	−	9.46179i	0.0530366	−	0.0918620i	−0.838288	−	0.545227i	$-0.816443\pi$
$103$	5.46277	−	9.46179i	0.0530366	−	0.0918620i	0.891325	+	0.453365i	$0.149777\pi$
$104$		0			0
$105$	150.115	−	195.423i	1.42966	−	1.86117i
$106$		0			0
$107$		−	14.7588i		−	0.137933i	−0.997619	−	0.0689664i	$-0.978030\pi$
$107$		−	14.7588i		−	0.137933i	0.997619	−	0.0689664i	$-0.0219701\pi$
$108$		0			0
$109$	16.1494	+	27.9716i	0.148160	+	0.256620i	0.930547	−	0.366172i	$-0.119332\pi$
$109$	16.1494	+	27.9716i	0.148160	+	0.256620i	−0.782388	+	0.622792i	$0.785998\pi$
$110$		0			0
$111$	−66.5542	+	27.5272i	−0.599588	+	0.247993i
$112$		0			0
$113$	−134.566	−	77.6917i	−1.19085	−	0.687537i	−0.232350	−	0.972632i	$-0.574641\pi$
$113$	−134.566	−	77.6917i	−1.19085	−	0.687537i	−0.958499	+	0.285095i	$0.907975\pi$
$114$		0			0
$115$	106.860	+	185.087i	0.929218	+	1.60945i
$116$		0			0
$117$	190.986	+	51.3869i	1.63236	+	0.439205i
$118$		0			0
$119$	−146.179	−	84.3967i	−1.22840	−	0.709216i
$120$		0			0
$121$	−60.2706	+	104.392i	−0.498104	+	0.862741i
$122$		0			0
$123$	1.14679	+	2.77267i	0.00932351	+	0.0225420i
$124$		0			0
$125$			74.9682i			0.599745i
$126$		0			0
$127$	6.01913	−	10.4254i	0.0473947	−	0.0820900i	−0.841355	−	0.540483i	$-0.818241\pi$
$127$	6.01913	−	10.4254i	0.0473947	−	0.0820900i	0.888750	+	0.458393i	$0.151575\pi$
$128$		0			0
$129$	4.64475	−	35.1395i	0.0360058	−	0.272399i
$130$		0			0
$131$		−	10.5931i		−	0.0808632i	−0.999182	−	0.0404316i	$-0.987127\pi$
$131$		−	10.5931i		−	0.0808632i	0.999182	−	0.0404316i	$-0.0128733\pi$
$132$		0			0
$133$	155.711	−	200.445i	1.17076	−	1.50710i
$134$		0			0
$135$	153.281	+	63.7708i	1.13541	+	0.472376i
$136$		0			0
$137$			18.4865i			0.134938i	0.997721	+	0.0674688i	$0.0214923\pi$
$137$			18.4865i			0.134938i	−0.997721	+	0.0674688i	$0.978508\pi$
$138$		0			0
$139$	63.6164	+	110.187i	0.457672	+	0.792711i	0.998837	−	0.0482048i	$-0.0153500\pi$
$139$	63.6164	+	110.187i	0.457672	+	0.792711i	−0.541165	+	0.840916i	$0.682017\pi$
$140$		0			0
$141$	−41.7431	−	100.925i	−0.296051	−	0.715779i
$142$		0			0
$143$	12.8912	+	7.44275i	0.0901484	+	0.0520472i
$144$		0			0
$145$	234.467			1.61701
$146$		0			0
$147$	−50.8937	+	385.032i	−0.346216	+	2.61927i
$148$		0			0
$149$			199.546i			1.33923i	0.742707	+	0.669616i	$0.233541\pi$
$149$			199.546i			1.33923i	−0.742707	+	0.669616i	$0.766459\pi$
$150$		0			0
$151$	−86.0705	−	149.078i	−0.570003	−	0.987274i	−0.996565	−	0.0828158i	$-0.973609\pi$
$151$	−86.0705	−	149.078i	−0.570003	−	0.987274i	0.426562	−	0.904458i	$-0.359725\pi$
$152$		0			0
$153$	29.5462	−	109.812i	0.193112	−	0.717725i
$154$		0			0
$155$	210.223	+	121.372i	1.35628	+	0.783047i
$156$		0			0
$157$	−126.114			−0.803271			−0.401636	−	0.915800i	$-0.631558\pi$
$157$	−126.114			−0.803271			−0.401636	+	0.915800i	$0.631558\pi$
$158$		0			0
$159$	100.605	+	13.2980i	0.632737	+	0.0836354i
$160$		0			0
$161$	−402.121	−	232.165i	−2.49765	−	1.44202i
$162$		0			0
$163$	−130.019			−0.797661			−0.398831	−	0.917025i	$-0.630584\pi$
$163$	−130.019			−0.797661			−0.398831	+	0.917025i	$0.630584\pi$
$164$		0			0
$165$	9.90907	+	7.61167i	0.0600550	+	0.0461313i
$166$		0			0
$167$	−15.1623	+	8.75398i	−0.0907924	+	0.0524190i	−0.544709	−	0.838625i	$-0.683360\pi$
$167$	−15.1623	+	8.75398i	−0.0907924	+	0.0524190i	0.453916	+	0.891044i	$0.350026\pi$
$168$		0			0
$169$	−156.958	+	271.859i	−0.928744	+	1.60863i
$170$		0			0
$171$	157.522	+	66.5417i	0.921182	+	0.389133i
$172$		0			0
$173$	225.015	+	129.913i	1.30067	+	0.750940i	0.980518	−	0.196427i	$-0.0629339\pi$
$173$	225.015	+	129.913i	1.30067	+	0.750940i	0.320148	+	0.947367i	$0.396267\pi$
$174$		0			0
$175$	85.5482	+	148.174i	0.488847	+	0.846707i
$176$		0			0
$177$	70.9772	+	171.606i	0.401001	+	0.969524i
$178$		0			0
$179$		−	120.898i		−	0.675407i	−0.941252	−	0.337704i	$-0.890350\pi$
$179$		−	120.898i		−	0.675407i	0.941252	−	0.337704i	$-0.109650\pi$
$180$		0			0
$181$	−110.148	+	190.783i	−0.608555	+	1.05405i	0.382924	+	0.923780i	$0.374917\pi$
$181$	−110.148	+	190.783i	−0.608555	+	1.05405i	−0.991479	+	0.130268i	$0.958416\pi$
$182$		0			0
$183$	277.049	−	114.589i	1.51393	−	0.626170i
$184$		0			0
$185$		−	147.617i		−	0.797928i
$186$		0			0
$187$	4.27940	−	7.41213i	0.0228845	−	0.0396371i
$188$		0			0
$189$	−357.678	+	46.5229i	−1.89247	+	0.246153i
$190$		0			0
$191$	−87.7696	+	50.6738i	−0.459527	+	0.265308i	−0.711845	−	0.702336i	$-0.752140\pi$
$191$	−87.7696	+	50.6738i	−0.459527	+	0.265308i	0.252319	+	0.967644i	$0.418807\pi$
$192$		0			0
$193$	−319.750			−1.65673			−0.828367	−	0.560185i	$-0.810730\pi$
$193$	−319.750			−1.65673			−0.828367	+	0.560185i	$0.810730\pi$
$194$		0			0
$195$	−246.938	+	321.470i	−1.26635	+	1.64856i
$196$		0			0
$197$		−	362.670i		−	1.84096i	−0.390786	−	0.920482i	$-0.627797\pi$
$197$		−	362.670i		−	1.84096i	0.390786	−	0.920482i	$-0.372203\pi$
$198$		0			0
$199$	−63.0213	+	109.156i	−0.316690	+	0.548523i	−0.979795	−	0.200003i	$-0.935905\pi$
$199$	−63.0213	+	109.156i	−0.316690	+	0.548523i	0.663105	+	0.748526i	$0.269238\pi$
$200$		0			0
$201$	75.2974	+	57.8398i	0.374614	+	0.287760i
$202$		0			0
$203$	−441.156	+	254.702i	−2.17318	+	1.25469i
$204$		0			0
$205$	−6.14976			−0.0299988
$206$		0			0
$207$	81.2780	−	302.079i	0.392647	−	1.45932i
$208$		0			0
$209$	10.1637	+	7.89546i	0.0486302	+	0.0377773i
$210$		0			0
$211$	52.7903			0.250191			0.125095	−	0.992145i	$-0.460076\pi$
$211$	52.7903			0.250191			0.125095	+	0.992145i	$0.460076\pi$
$212$		0			0
$213$	219.840	−	286.193i	1.03211	−	1.34363i
$214$		0			0
$215$	62.9152	+	36.3241i	0.292629	+	0.168949i
$216$		0			0
$217$	−527.389			−2.43036
$218$		0			0
$219$	43.2496	+	33.2223i	0.197487	+	0.151700i
$220$		0			0
$221$	240.464	+	138.832i	1.08807	+	0.628200i
$222$		0			0
$223$	−0.0946169	+	0.163881i	−0.000424291	+	0.000734893i	−0.866237	−	0.499633i	$-0.833468\pi$
$223$	−0.0946169	+	0.163881i	−0.000424291	+	0.000734893i	0.865813	+	0.500367i	$0.166802\pi$
$224$		0			0
$225$	−81.5920	+	81.4228i	−0.362631	+	0.361879i
$226$		0			0
$227$	−17.0193	+	9.82612i	−0.0749751	+	0.0432869i	−0.537019	−	0.843570i	$-0.680450\pi$
$227$	−17.0193	+	9.82612i	−0.0749751	+	0.0432869i	0.462044	+	0.886857i	$0.347116\pi$
$228$		0			0
$229$	175.467	−	303.918i	0.766233	−	1.32715i	−0.173359	−	0.984859i	$-0.555462\pi$
$229$	175.467	−	303.918i	0.766233	−	1.32715i	0.939592	−	0.342296i	$-0.111204\pi$
$230$		0			0
$231$	−26.9128	−	3.55735i	−0.116506	−	0.0153998i
$232$		0			0
$233$	212.611	−	122.751i	0.912494	−	0.526829i	0.0312613	−	0.999511i	$-0.490048\pi$
$233$	212.611	−	122.751i	0.912494	−	0.526829i	0.881233	+	0.472683i	$0.156714\pi$
$234$		0			0
$235$	223.851			0.952556
$236$		0			0
$237$	−3.22901	+	24.4288i	−0.0136245	+	0.103075i
$238$		0			0
$239$	−215.150	−	124.217i	−0.900210	−	0.519736i	−0.0229416	−	0.999737i	$-0.507303\pi$
$239$	−215.150	−	124.217i	−0.900210	−	0.519736i	−0.877268	+	0.480000i	$0.840637\pi$
$240$		0			0
$241$	−14.4503			−0.0599599			−0.0299800	−	0.999550i	$-0.509544\pi$
$241$	−14.4503			−0.0599599			−0.0299800	+	0.999550i	$0.509544\pi$
$242$		0			0
$243$	−92.4093	−	224.743i	−0.380285	−	0.924869i
$244$		0			0
$245$	−689.378	−	398.013i	−2.81379	−	1.62454i
$246$		0			0
$247$	−256.145	+	329.731i	−1.03702	+	1.33494i
$248$		0			0
$249$	−293.481	+	382.062i	−1.17864	+	1.53439i
$250$		0			0
$251$	−39.7299	−	22.9381i	−0.158286	−	0.0913867i	0.418765	−	0.908095i	$-0.362463\pi$
$251$	−39.7299	−	22.9381i	−0.158286	−	0.0913867i	−0.577051	+	0.816708i	$0.695797\pi$
$252$		0			0
$253$	11.7721	−	20.3899i	0.0465300	−	0.0805923i
$254$		0			0
$255$	184.837	+	141.983i	0.724851	+	0.556796i
$256$		0			0
$257$	377.517	−	217.960i	1.46894	−	0.848093i	0.469546	−	0.882908i	$-0.344418\pi$
$257$	377.517	−	217.960i	1.46894	−	0.848093i	0.999394	+	0.0348156i	$0.0110844\pi$
$258$		0			0
$259$	160.357	+	277.746i	0.619137	+	1.07238i
$260$		0			0
$261$	−242.419	−	242.923i	−0.928810	−	0.930739i
$262$		0			0
$263$	−178.922	−	103.300i	−0.680311	−	0.392778i	0.119661	−	0.992815i	$-0.461819\pi$
$263$	−178.922	−	103.300i	−0.680311	−	0.392778i	−0.799972	+	0.600037i	$0.795152\pi$
$264$		0			0
$265$	−103.997	+	180.128i	−0.392441	+	0.679727i
$266$		0			0
$267$	−315.505	−	41.7036i	−1.18167	−	0.156193i
$268$		0			0
$269$	−250.230	+	144.470i	−0.930224	+	0.537065i	−0.886882	−	0.461995i	$-0.847134\pi$
$269$	−250.230	+	144.470i	−0.930224	+	0.537065i	−0.0433415	+	0.999060i	$0.513800\pi$
$270$		0			0
$271$	147.862	+	256.105i	0.545618	+	0.945037i	0.998568	+	0.0535016i	$0.0170382\pi$
$271$	147.862	+	256.105i	0.545618	+	0.945037i	−0.452950	+	0.891536i	$0.649628\pi$
$272$		0			0
$273$	115.407	−	873.105i	0.422738	−	3.19819i
$274$		0			0
$275$	−7.51326	+	4.33778i	−0.0273210	+	0.0157738i
$276$		0			0
$277$	−46.2692	−	80.1406i	−0.167037	−	0.289316i	0.770340	−	0.637633i	$-0.220087\pi$
$277$	−46.2692	−	80.1406i	−0.167037	−	0.289316i	−0.937377	+	0.348317i	$0.886753\pi$
$278$		0			0
$279$	−91.6037	−	343.294i	−0.328329	−	1.23045i
$280$		0			0
$281$		−	52.7052i		−	0.187563i	−0.995593	−	0.0937815i	$-0.970104\pi$
$281$		−	52.7052i		−	0.187563i	0.995593	−	0.0937815i	$-0.0298955\pi$
$282$		0			0
$283$	378.564			1.33768			0.668842	−	0.743405i	$-0.266790\pi$
$283$	378.564			1.33768			0.668842	+	0.743405i	$0.266790\pi$
$284$		0			0
$285$	−249.426	+	246.218i	−0.875180	+	0.863924i
$286$		0			0
$287$	11.5710	−	6.68050i	0.0403170	−	0.0232770i
$288$		0			0
$289$	−64.6750	+	112.020i	−0.223789	+	0.387614i
$290$		0			0
$291$	−20.2141	+	152.928i	−0.0694644	+	0.525527i
$292$		0			0
$293$	−413.513	−	238.742i	−1.41131	−	0.814818i	−0.415795	−	0.909458i	$-0.636497\pi$
$293$	−413.513	−	238.742i	−1.41131	−	0.814818i	−0.995512	+	0.0946404i	$0.969830\pi$
$294$		0			0
$295$	−380.620			−1.29024
$296$		0			0
$297$	−2.35898	−	18.1363i	−0.00794268	−	0.0610650i
$298$		0			0
$299$	661.488	+	381.910i	2.21233	+	1.27729i
$300$		0			0
$301$	−157.836			−0.524372
$302$		0			0
$303$	3.39314	+	8.20381i	0.0111985	+	0.0270753i
$304$		0			0
$305$			614.492i			2.01473i
$306$		0			0
$307$	24.3451	+	42.1669i	0.0792999	+	0.137351i	0.902948	−	0.429750i	$-0.141398\pi$
$307$	24.3451	+	42.1669i	0.0792999	+	0.137351i	−0.823648	+	0.567101i	$0.808065\pi$
$308$		0			0
$309$	4.29507	−	32.4940i	0.0138999	−	0.105158i
$310$		0			0
$311$	58.5917	+	33.8279i	0.188398	+	0.108771i	0.591232	−	0.806501i	$-0.298642\pi$
$311$	58.5917	+	33.8279i	0.188398	+	0.108771i	−0.402835	+	0.915273i	$0.631975\pi$
$312$		0			0
$313$	−2.73622			−0.00874190			−0.00437095	−	0.999990i	$-0.501391\pi$
$313$	−2.73622			−0.00874190			−0.00437095	+	0.999990i	$0.501391\pi$
$314$		0			0
$315$	192.078	−	713.881i	0.609772	−	2.26629i
$316$		0			0
$317$			413.748i			1.30520i	0.757703	+	0.652600i	$0.226322\pi$
$317$			413.748i			1.30520i	−0.757703	+	0.652600i	$0.773678\pi$
$318$		0			0
$319$	−12.9148	−	22.3692i	−0.0404854	−	0.0701228i
$320$		0			0
$321$	−16.9226	−	40.9149i	−0.0527185	−	0.127461i
$322$		0			0
$323$	189.587	+	147.277i	0.586956	+	0.455965i
$324$		0			0
$325$	−140.726	−	243.745i	−0.433004	−	0.749985i
$326$		0			0
$327$	76.8424	+	59.0266i	0.234992	+	0.180510i
$328$		0			0
$329$	−421.182	+	243.170i	−1.28019	+	0.739117i
$330$		0			0
$331$	198.804	+	344.339i	0.600617	+	1.04030i	0.992728	+	0.120382i	$0.0384118\pi$
$331$	198.804	+	344.339i	0.600617	+	1.04030i	−0.392110	+	0.919918i	$0.628255\pi$
$332$		0			0
$333$	−152.941	+	152.624i	−0.459282	+	0.458330i
$334$		0			0
$335$	−168.533	+	97.3027i	−0.503084	+	0.290456i
$336$		0			0
$337$	−34.1929			−0.101463			−0.0507313	−	0.998712i	$-0.516155\pi$
$337$	−34.1929			−0.101463			−0.0507313	+	0.998712i	$0.516155\pi$
$338$		0			0
$339$	−462.130	−	61.0846i	−1.36322	−	0.180190i
$340$		0			0
$341$		−	26.7416i		−	0.0784212i
$342$		0			0
$343$	1074.86			3.13371
$344$		0			0
$345$	508.464	+	390.578i	1.47381	+	1.13211i
$346$		0			0
$347$			119.082i			0.343177i	0.985169	+	0.171588i	$0.0548899\pi$
$347$			119.082i			0.343177i	−0.985169	+	0.171588i	$0.945110\pi$
$348$		0			0
$349$	196.268	+	339.946i	0.562373	+	0.974059i	0.997289	+	0.0735875i	$0.0234448\pi$
$349$	196.268	+	339.946i	0.562373	+	0.974059i	−0.434916	+	0.900471i	$0.643222\pi$
$350$		0			0
$351$	588.378	−	76.5299i	1.67629	−	0.218034i
$352$		0			0
$353$	−285.889	+	165.058i	−0.809884	+	0.467587i	−0.846915	−	0.531728i	$-0.821543\pi$
$353$	−285.889	+	165.058i	−0.809884	+	0.467587i	0.0370318	+	0.999314i	$0.488210\pi$
$354$		0			0
$355$	369.832	+	640.567i	1.04178	+	1.80441i
$356$		0			0
$357$	−502.013	−	66.3563i	−1.40620	−	0.185872i
$358$		0			0
$359$	−85.9500	+	49.6232i	−0.239415	+	0.138226i	−0.614908	−	0.788599i	$-0.710807\pi$
$359$	−85.9500	+	49.6232i	−0.239415	+	0.138226i	0.375493	+	0.926825i	$0.377473\pi$
$360$		0			0
$361$	−258.287	+	252.208i	−0.715476	+	0.698638i
$362$		0			0
$363$	−47.3874	+	358.505i	−0.130544	+	0.987618i
$364$		0			0
$365$	−96.8028	+	55.8891i	−0.265213	+	0.153121i
$366$		0			0
$367$	66.6391			0.181578			0.0907889	−	0.995870i	$-0.471061\pi$
$367$	66.6391			0.181578			0.0907889	+	0.995870i	$0.471061\pi$
$368$		0			0
$369$	6.35835	+	6.37156i	0.0172313	+	0.0172671i
$370$		0			0
$371$		−	451.888i		−	1.21803i
$372$		0			0
$373$	163.975	−	284.013i	0.439611	−	0.761429i	−0.558048	−	0.829809i	$-0.688449\pi$
$373$	163.975	−	284.013i	0.439611	−	0.761429i	0.997659	+	0.0683793i	$0.0217828\pi$
$374$		0			0
$375$	85.9594	+	207.829i	0.229225	+	0.554212i
$376$		0			0
$377$	725.700	−	418.983i	1.92493	−	1.11136i
$378$		0			0
$379$	−588.049			−1.55158			−0.775790	−	0.630991i	$-0.782649\pi$
$379$	−588.049			−1.55158			−0.775790	+	0.630991i	$0.782649\pi$
$380$		0			0
$381$	4.73250	−	35.8033i	0.0124213	−	0.0939720i
$382$		0			0
$383$			363.143i			0.948153i	0.880484	+	0.474076i	$0.157218\pi$
$383$			363.143i			0.948153i	−0.880484	+	0.474076i	$0.842782\pi$
$384$		0			0
$385$	27.8201	−	48.1859i	0.0722600	−	0.125158i
$386$		0			0
$387$	−27.4150	−	102.741i	−0.0708399	−	0.265480i
$388$		0			0
$389$		−	419.346i		−	1.07801i	−0.842302	−	0.539006i	$-0.818800\pi$
$389$		−	419.346i		−	1.07801i	0.842302	−	0.539006i	$-0.181200\pi$
$390$		0			0
$391$	219.589	−	380.339i	0.561608	−	0.972733i
$392$		0			0
$393$	−12.1462	−	29.3665i	−0.0309062	−	0.0747239i
$394$		0			0
$395$	−43.7383	−	25.2523i	−0.110730	−	0.0639300i
$396$		0			0
$397$	18.4059	+	31.8800i	0.0463625	+	0.0803022i	0.888275	−	0.459311i	$-0.151904\pi$
$397$	18.4059	+	31.8800i	0.0463625	+	0.0803022i	−0.841913	+	0.539613i	$0.818570\pi$
$398$		0			0
$399$	201.836	−	734.221i	0.505855	−	1.84015i
$400$		0			0
$401$		−	553.230i		−	1.37963i	−0.723988	−	0.689813i	$-0.757693\pi$
$401$		−	553.230i		−	1.37963i	0.723988	−	0.689813i	$-0.242307\pi$
$402$		0			0
$403$	867.552			2.15273
$404$		0			0
$405$	498.051	+	1.03366i	1.22976	+	0.00255224i
$406$		0			0
$407$	−14.0833	+	8.13100i	−0.0346027	+	0.0199779i
$408$		0			0
$409$	114.062	+	197.561i	0.278880	+	0.483035i	0.971107	−	0.238646i	$-0.0767034\pi$
$409$	114.062	+	197.561i	0.278880	+	0.483035i	−0.692227	+	0.721680i	$0.743370\pi$
$410$		0			0
$411$	21.1968	+	51.2488i	0.0515737	+	0.124693i
$412$		0			0
$413$	716.149	−	413.469i	1.73402	−	1.00114i
$414$		0			0
$415$	−493.718	−	855.144i	−1.18968	−	2.06059i
$416$		0			0
$417$	302.701	+	232.520i	0.725902	+	0.557603i
$418$		0			0
$419$	−427.551	−	246.847i	−1.02041	−	0.589133i	−0.106187	−	0.994346i	$-0.533864\pi$
$419$	−427.551	−	246.847i	−1.02041	−	0.589133i	−0.914222	+	0.405213i	$0.867197\pi$
$420$		0			0
$421$	−87.0805	+	150.828i	−0.206842	+	0.358261i	−0.950718	−	0.310057i	$-0.899652\pi$
$421$	−87.0805	+	150.828i	−0.206842	+	0.358261i	0.743876	+	0.668318i	$0.232985\pi$
$422$		0			0
$423$	−231.443	−	231.924i	−0.547148	−	0.548284i
$424$		0			0
$425$	−140.147	+	80.9141i	−0.329758	+	0.190386i
$426$		0			0
$427$	−667.525	−	1156.19i	−1.56329	−	2.70770i
$428$		0			0
$429$	44.2714	+	5.85182i	0.103197	+	0.0136406i
$430$		0			0
$431$	183.318	+	105.838i	0.425331	+	0.245565i	0.697356	−	0.716725i	$-0.254360\pi$
$431$	183.318	+	105.838i	0.425331	+	0.245565i	−0.272025	+	0.962290i	$0.587693\pi$
$432$		0			0
$433$	98.5927	−	170.768i	0.227697	−	0.394382i	−0.729428	−	0.684057i	$-0.760214\pi$
$433$	98.5927	−	170.768i	0.227697	−	0.394382i	0.957125	+	0.289675i	$0.0935472\pi$
$434$		0			0
$435$	649.996	−	268.842i	1.49424	−	0.618028i
$436$		0			0
$437$	521.530	+	405.140i	1.19343	+	0.927094i
$438$		0			0
$439$	307.405	−	532.441i	0.700239	−	1.21285i	−0.268143	−	0.963379i	$-0.586410\pi$
$439$	307.405	−	532.441i	0.700239	−	1.21285i	0.968382	−	0.249471i	$-0.0802566\pi$
$440$		0			0
$441$	300.393	+	1125.75i	0.681164	+	2.55273i
$442$		0			0
$443$		−	556.406i		−	1.25599i	−0.778216	−	0.627997i	$-0.783875\pi$
$443$		−	556.406i		−	1.25599i	0.778216	−	0.627997i	$-0.216125\pi$
$444$		0			0
$445$	326.142	−	564.894i	0.732903	−	1.26943i
$446$		0			0
$447$	228.802	+	553.187i	0.511860	+	1.23756i
$448$		0			0
$449$		−	257.610i		−	0.573742i	−0.957969	−	0.286871i	$-0.907385\pi$
$449$		−	257.610i		−	0.573742i	0.957969	−	0.286871i	$-0.0926150\pi$
$450$		0			0
$451$	0.338740	+	0.586715i	0.000751086	+	0.00130092i
$452$		0			0
$453$	−409.543	−	314.591i	−0.904067	−	0.694461i
$454$		0			0
$455$	1563.24	+	902.540i	3.43570	+	1.98360i
$456$		0			0
$457$	215.637	+	373.494i	0.471853	+	0.817273i	0.999481	−	0.0322025i	$-0.0102521\pi$
$457$	215.637	+	373.494i	0.471853	+	0.817273i	−0.527629	+	0.849475i	$0.676919\pi$
$458$		0			0
$459$	−44.0028	−	338.302i	−0.0958666	−	0.737042i
$460$		0			0
$461$	131.196	+	75.7463i	0.284591	+	0.164309i	0.635500	−	0.772101i	$-0.280794\pi$
$461$	131.196	+	75.7463i	0.284591	+	0.164309i	−0.350909	+	0.936410i	$0.614127\pi$
$462$		0			0
$463$	−125.351	+	217.114i	−0.270736	+	0.468928i	−0.969050	−	0.246863i	$-0.920600\pi$
$463$	−125.351	+	217.114i	−0.270736	+	0.468928i	0.698315	+	0.715791i	$0.253934\pi$
$464$		0			0
$465$	721.954	+	95.4282i	1.55259	+	0.205222i
$466$		0			0
$467$		−	263.024i		−	0.563220i	−0.959529	−	0.281610i	$-0.909132\pi$
$467$		−	263.024i		−	0.563220i	0.959529	−	0.281610i	$-0.0908685\pi$
$468$		0			0
$469$	211.400	−	366.156i	0.450747	−	0.780717i
$470$		0			0
$471$	−349.616	+	144.603i	−0.742285	+	0.307013i
$472$		0			0
$473$		−	8.00319i		−	0.0169201i
$474$		0			0
$475$	−91.7842	−	225.372i	−0.193230	−	0.474468i
$476$		0			0
$477$	294.149	−	78.4898i	0.616664	−	0.164549i
$478$		0			0
$479$			638.279i			1.33252i	0.745718	+	0.666262i	$0.232107\pi$
$479$			638.279i			1.33252i	−0.745718	+	0.666262i	$0.767893\pi$
$480$		0			0
$481$	−263.786	−	456.890i	−0.548411	−	0.949876i
$482$		0			0
$483$	−1380.98	−	182.538i	−2.85917	−	0.377926i
$484$		0			0
$485$	−273.809	−	158.084i	−0.564556	−	0.325946i
$486$		0			0
$487$	−780.042			−1.60173			−0.800864	−	0.598846i	$-0.795626\pi$
$487$	−780.042			−1.60173			−0.800864	+	0.598846i	$0.795626\pi$
$488$		0			0
$489$	−360.442	+	149.081i	−0.737101	+	0.304869i
$490$		0			0
$491$			580.181i			1.18163i	0.806806	+	0.590816i	$0.201194\pi$
$491$			580.181i			1.18163i	−0.806806	+	0.590816i	$0.798806\pi$
$492$		0			0
$493$	−240.905	−	417.259i	−0.488651	−	0.846368i
$494$		0			0
$495$	36.1979	+	9.73947i	0.0731271	+	0.0196757i
$496$		0			0
$497$	−1391.70	−	803.498i	−2.80020	−	1.61670i
$498$		0			0
$499$	56.5208			0.113268			0.0566341	−	0.998395i	$-0.481963\pi$
$499$	56.5208			0.113268			0.0566341	+	0.998395i	$0.481963\pi$
$500$		0			0
$501$	−31.9961	+	41.6534i	−0.0638645	+	0.0831405i
$502$		0			0
$503$	144.369	+	83.3516i	0.287016	+	0.165709i	0.636596	−	0.771198i	$-0.280342\pi$
$503$	144.369	+	83.3516i	0.287016	+	0.165709i	−0.349579	+	0.936907i	$0.613675\pi$
$504$		0			0
$505$	−18.1960			−0.0360317
$506$		0			0
$507$	−123.407	+	933.626i	−0.243406	+	1.84147i
$508$		0			0
$509$	259.974	−	150.096i	0.510755	−	0.294885i	−0.222389	−	0.974958i	$-0.571385\pi$
$509$	259.974	−	150.096i	0.510755	−	0.294885i	0.733144	+	0.680073i	$0.238052\pi$
$510$		0			0
$511$	121.425	−	210.314i	0.237622	−	0.411574i
$512$		0			0
$513$	512.986	+	3.85256i	0.999972	+	0.00750986i
$514$		0			0
$515$	58.1786	+	33.5894i	0.112968	+	0.0652222i
$516$		0			0
$517$	−12.3301	−	21.3564i	−0.0238493	−	0.0413082i
$518$		0			0
$519$	772.755	+	102.143i	1.48893	+	0.196807i
$520$		0			0
$521$		−	209.742i		−	0.402575i	−0.979532	−	0.201288i	$-0.935487\pi$
$521$		−	209.742i		−	0.402575i	0.979532	−	0.201288i	$-0.0645126\pi$
$522$		0			0
$523$	−492.016	+	852.197i	−0.940758	+	1.62944i	−0.176727	+	0.984260i	$0.556551\pi$
$523$	−492.016	+	852.197i	−0.940758	+	1.62944i	−0.764031	+	0.645180i	$0.776782\pi$
$524$		0			0
$525$	407.057	+	312.682i	0.775347	+	0.595584i
$526$		0			0
$527$		−	498.820i		−	0.946528i
$528$		0			0
$529$	339.562	−	588.138i	0.641893	−	1.11179i
$530$		0			0
$531$	393.531	+	394.348i	0.741112	+	0.742652i
$532$		0			0
$533$	−19.0342	+	10.9894i	−0.0357114	+	0.0206180i
$534$		0			0
$535$	90.7489			0.169624
$536$		0			0
$537$	−138.623	−	335.157i	−0.258143	−	0.624129i
$538$		0			0
$539$			87.6930i			0.162696i
$540$		0			0
$541$	−486.250	+	842.210i	−0.898799	+	1.55677i	−0.0697678	+	0.997563i	$0.522226\pi$
$541$	−486.250	+	842.210i	−0.898799	+	1.55677i	−0.829031	+	0.559202i	$0.811107\pi$
$542$		0			0
$543$	−86.6035	+	655.192i	−0.159491	+	1.20661i
$544$		0			0
$545$	−171.991	+	99.2993i	−0.315580	+	0.182200i
$546$		0			0
$547$	−1062.63			−1.94265			−0.971326	−	0.237753i	$-0.923589\pi$
$547$	−1062.63			−1.94265			−0.971326	+	0.237753i	$0.923589\pi$
$548$		0			0
$549$	636.655	−	635.335i	1.15966	−	1.15726i
$550$		0			0
$551$	670.999	−	273.268i	1.21778	−	0.495950i
$552$		0			0
$553$	109.727			0.198421
$554$		0			0
$555$	−169.259	−	409.228i	−0.304971	−	0.737348i
$556$		0			0
$557$	−719.310	−	415.294i	−1.29140	−	0.745590i	−0.312497	−	0.949919i	$-0.601166\pi$
$557$	−719.310	−	415.294i	−1.29140	−	0.745590i	−0.978902	+	0.204329i	$0.934499\pi$
$558$		0			0
$559$	259.640			0.464471
$560$		0			0
$561$	3.36465	−	25.4550i	0.00599759	−	0.0453743i
$562$		0			0
$563$	530.247	+	306.138i	0.941824	+	0.543762i	0.890532	−	0.454921i	$-0.150333\pi$
$563$	530.247	+	306.138i	0.941824	+	0.543762i	0.0512923	+	0.998684i	$0.483666\pi$
$564$		0			0
$565$	477.710	−	827.418i	0.845505	−	1.46446i
$566$		0			0
$567$	−938.222	+	539.090i	−1.65471	+	0.950775i
$568$		0			0
$569$	177.066	−	102.229i	0.311188	−	0.179665i	−0.336270	−	0.941766i	$-0.609165\pi$
$569$	177.066	−	102.229i	0.311188	−	0.179665i	0.647458	+	0.762101i	$0.275832\pi$
$570$		0			0
$571$	−244.282	+	423.109i	−0.427814	+	0.740996i	−0.996679	−	0.0814355i	$-0.974050\pi$
$571$	−244.282	+	423.109i	−0.427814	+	0.740996i	0.568865	+	0.822431i	$0.307383\pi$
$572$		0			0
$573$	−185.215	+	241.117i	−0.323237	+	0.420798i
$574$		0			0
$575$	−385.528	+	222.585i	−0.670484	+	0.387104i
$576$		0			0
$577$	856.457			1.48433			0.742164	−	0.670219i	$-0.233800\pi$
$577$	856.457			1.48433			0.742164	+	0.670219i	$0.233800\pi$
$578$		0			0
$579$	−886.421	+	366.629i	−1.53095	+	0.633211i
$580$		0			0
$581$	1857.89	+	1072.65i	3.19775	+	1.84622i
$582$		0			0
$583$	22.9133			0.0393024
$584$		0			0
$585$	−315.968	+	1174.33i	−0.540116	+	2.00740i
$586$		0			0
$587$	−508.197	−	293.408i	−0.865753	−	0.499843i	0.000181329	−	1.00000i	$-0.499942\pi$
$587$	−508.197	−	293.408i	−0.865753	−	0.499843i	−0.865935	+	0.500157i	$0.833276\pi$
$588$		0			0
$589$	743.077	+	102.332i	1.26159	+	0.173739i
$590$		0			0
$591$	−415.841	−	1005.41i	−0.703623	−	1.70119i
$592$		0			0
$593$	316.266	+	182.596i	0.533331	+	0.307919i	0.742372	−	0.669988i	$-0.233701\pi$
$593$	316.266	+	182.596i	0.533331	+	0.307919i	−0.209041	+	0.977907i	$0.567034\pi$
$594$		0			0
$595$	518.938	−	898.826i	0.872164	−	1.51063i
$596$		0			0
$597$	−49.5501	+	374.867i	−0.0829985	+	0.627919i
$598$		0			0
$599$	−388.322	+	224.198i	−0.648283	+	0.374287i	−0.787798	−	0.615933i	$-0.788779\pi$
$599$	−388.322	+	224.198i	−0.648283	+	0.374287i	0.139515	+	0.990220i	$0.455446\pi$
$600$		0			0
$601$	323.504	+	560.326i	0.538277	+	0.932323i	0.998997	+	0.0447773i	$0.0142578\pi$
$601$	323.504	+	560.326i	0.538277	+	0.932323i	−0.460720	+	0.887545i	$0.652409\pi$
$602$		0			0
$603$	275.062	+	74.0086i	0.456155	+	0.122734i
$604$		0			0
$605$	−641.883	−	370.591i	−1.06096	−	0.612548i
$606$		0			0
$607$	413.907	−	716.909i	0.681890	−	1.18107i	−0.292513	−	0.956262i	$-0.594491\pi$
$607$	413.907	−	716.909i	0.681890	−	1.18107i	0.974403	−	0.224807i	$-0.0721753\pi$
$608$		0			0
$609$	−930.944	+	1211.93i	−1.52864	+	1.99003i
$610$		0			0
$611$	692.843	−	400.013i	1.13395	−	0.654686i
$612$		0			0
$613$	420.668	+	728.618i	0.686244	+	1.18861i	0.973044	+	0.230619i	$0.0740752\pi$
$613$	420.668	+	728.618i	0.686244	+	1.18861i	−0.286800	+	0.957991i	$0.592591\pi$
$614$		0			0
$615$	−17.0486	+	7.05139i	−0.0277212	+	0.0114657i
$616$		0			0
$617$	870.051	−	502.324i	1.41013	−	0.814139i	0.414731	−	0.909944i	$-0.363876\pi$
$617$	870.051	−	502.324i	1.41013	−	0.814139i	0.995400	+	0.0958048i	$0.0305425\pi$
$618$		0			0
$619$	9.19386	+	15.9242i	0.0148528	+	0.0257257i	0.873356	−	0.487082i	$-0.161939\pi$
$619$	9.19386	+	15.9242i	0.0148528	+	0.0257257i	−0.858503	+	0.512808i	$0.828605\pi$
$620$		0			0
$621$	−121.046	−	930.629i	−0.194921	−	1.49860i
$622$		0			0
$623$			1417.16i			2.27473i
$624$		0			0
$625$	−781.155			−1.24985
$626$		0			0
$627$	37.2292	+	10.2342i	0.0593767	+	0.0163226i
$628$		0			0
$629$	−262.700	+	151.670i	−0.417648	+	0.241129i
$630$		0			0
$631$	511.523	−	885.984i	0.810655	−	1.40410i	−0.101752	−	0.994810i	$-0.532445\pi$
$631$	511.523	−	885.984i	0.810655	−	1.40410i	0.912406	−	0.409285i	$-0.134222\pi$
$632$		0			0
$633$	146.347	−	60.5300i	0.231196	−	0.0956240i
$634$		0			0
$635$	64.1038	+	37.0104i	0.100951	+	0.0582841i
$636$		0			0
$637$	−2844.94			−4.46615
$638$		0			0
$639$	281.294	−	1045.46i	0.440210	−	1.63609i
$640$		0			0
$641$	−475.462	−	274.508i	−0.741750	−	0.428250i	0.0809552	−	0.996718i	$-0.474203\pi$
$641$	−475.462	−	274.508i	−0.741750	−	0.428250i	−0.822705	+	0.568468i	$0.807536\pi$
$642$		0			0
$643$	−550.274			−0.855791			−0.427896	−	0.903828i	$-0.640745\pi$
$643$	−550.274			−0.855791			−0.427896	+	0.903828i	$0.640745\pi$
$644$		0			0
$645$	216.065	+	28.5596i	0.334985	+	0.0442785i
$646$		0			0
$647$		−	246.104i		−	0.380376i	−0.981748	−	0.190188i	$-0.939090\pi$
$647$		−	246.104i		−	0.380376i	0.981748	−	0.190188i	$-0.0609098\pi$
$648$		0			0
$649$	20.9653	+	36.3129i	0.0323039	+	0.0559521i
$650$		0			0
$651$	−1462.04	+	604.710i	−2.24584	+	0.928894i
$652$		0			0
$653$	70.4998	+	40.7031i	0.107963	+	0.0623324i	0.553009	−	0.833175i	$-0.313479\pi$
$653$	70.4998	+	40.7031i	0.107963	+	0.0623324i	−0.445046	+	0.895508i	$0.646813\pi$
$654$		0			0
$655$	65.1347			0.0994422
$656$		0			0
$657$	157.991	+	42.5094i	0.240474	+	0.0647022i
$658$		0			0
$659$			569.031i			0.863477i	0.901999	+	0.431738i	$0.142100\pi$
$659$			569.031i			0.863477i	−0.901999	+	0.431738i	$0.857900\pi$
$660$		0			0
$661$	−91.5566	−	158.581i	−0.138512	−	0.239910i	0.788421	−	0.615136i	$-0.210899\pi$
$661$	−91.5566	−	158.581i	−0.138512	−	0.239910i	−0.926934	+	0.375225i	$0.877565\pi$
$662$		0			0
$663$	825.810	+	109.156i	1.24557	+	0.164639i
$664$		0			0
$665$	1232.49	+	957.437i	1.85337	+	1.43976i
$666$		0			0
$667$	−662.699	−	1147.83i	−0.993552	−	1.72088i
$668$		0			0
$669$	−0.0743919	+	0.562806i	−0.000111199	+	0.000841265i
$670$		0			0
$671$	58.6253	−	33.8474i	0.0873701	−	0.0504431i
$672$		0			0
$673$	120.295	+	208.356i	0.178744	+	0.309593i	0.941451	−	0.337151i	$-0.109463\pi$
$673$	120.295	+	208.356i	0.178744	+	0.309593i	−0.762707	+	0.646744i	$0.776130\pi$
$674$		0			0
$675$	−132.832	+	319.277i	−0.196788	+	0.473004i
$676$		0			0
$677$	497.193	−	287.055i	0.734407	−	0.424010i	−0.0856253	−	0.996327i	$-0.527289\pi$
$677$	497.193	−	287.055i	0.734407	−	0.424010i	0.820032	+	0.572317i	$0.193955\pi$
$678$		0			0
$679$	686.908			1.01165
$680$		0			0
$681$	−35.9148	+	46.7549i	−0.0527384	+	0.0686562i
$682$		0			0
$683$		−	1104.28i		−	1.61681i	−0.588628	−	0.808404i	$-0.700332\pi$
$683$		−	1104.28i		−	1.61681i	0.588628	−	0.808404i	$-0.299668\pi$
$684$		0			0
$685$	−113.669			−0.165941
$686$		0			0
$687$	137.960	−	1043.73i	0.200815	−	1.51925i
$688$		0			0
$689$			743.354i			1.07889i
$690$		0			0
$691$	−182.004	−	315.241i	−0.263393	−	0.456210i	0.703748	−	0.710449i	$-0.251508\pi$
$691$	−182.004	−	315.241i	−0.263393	−	0.456210i	−0.967141	+	0.254239i	$0.918175\pi$
$692$		0			0
$693$	−78.6875	+	20.9968i	−0.113546	+	0.0302984i
$694$		0			0
$695$	−677.516	+	391.164i	−0.974844	+	0.562826i
$696$		0			0
$697$	6.31862	+	10.9442i	0.00906546	+	0.0157018i
$698$		0			0
$699$	448.660	−	584.077i	0.641860	−	0.835590i
$700$		0			0
$701$	629.268	−	363.308i	0.897672	−	0.518271i	0.0212278	−	0.999775i	$-0.493242\pi$
$701$	629.268	−	363.308i	0.897672	−	0.518271i	0.876444	+	0.481503i	$0.159909\pi$
$702$		0			0
$703$	−172.046	−	422.451i	−0.244731	−	0.600927i
$704$		0			0
$705$	620.566	−	256.670i	0.880236	−	0.364071i
$706$		0			0
$707$	34.2363	−	19.7664i	0.0484248	−	0.0279581i
$708$		0			0
$709$	−32.0041			−0.0451398			−0.0225699	−	0.999745i	$-0.507185\pi$
$709$	−32.0041			−0.0451398			−0.0225699	+	0.999745i	$0.507185\pi$
$710$		0			0
$711$	19.0588	+	71.4247i	0.0268056	+	0.100457i
$712$		0			0
$713$		−	1372.19i		−	1.92454i
$714$		0			0
$715$	−45.7640	+	79.2655i	−0.0640055	+	0.110861i
$716$		0			0
$717$	−738.875	−	97.6648i	−1.03051	−	0.136213i
$718$		0			0
$719$	737.472	−	425.780i	1.02569	−	0.592183i	0.109944	−	0.993938i	$-0.464933\pi$
$719$	737.472	−	425.780i	1.02569	−	0.592183i	0.915747	+	0.401755i	$0.131600\pi$
$720$		0			0
$721$	−145.953			−0.202432
$722$		0			0
$723$	−40.0597	+	16.5689i	−0.0554077	+	0.0229169i
$724$		0			0
$725$			488.383i			0.673632i
$726$		0			0
$727$	−286.128	+	495.588i	−0.393574	+	0.681690i	−0.992918	−	0.118802i	$-0.962095\pi$
$727$	−286.128	+	495.588i	−0.393574	+	0.681690i	0.599344	+	0.800491i	$0.295428\pi$
$728$		0			0
$729$	−513.874	−	517.083i	−0.704902	−	0.709305i
$730$		0			0
$731$		−	149.286i		−	0.204222i
$732$		0			0
$733$	−388.675	+	673.206i	−0.530253	+	0.918425i	0.469124	+	0.883132i	$0.344570\pi$
$733$	−388.675	+	673.206i	−0.530253	+	0.918425i	−0.999377	+	0.0352927i	$0.988764\pi$
$734$		0			0
$735$	−2367.48	−	312.935i	−3.22107	−	0.425762i
$736$		0			0
$737$	18.5662	+	10.7192i	0.0251916	+	0.0145444i
$738$		0			0
$739$	186.632	+	323.256i	0.252546	+	0.437423i	0.964226	−	0.265081i	$-0.0853987\pi$
$739$	186.632	+	323.256i	0.252546	+	0.437423i	−0.711680	+	0.702504i	$0.752065\pi$
$740$		0			0
$741$	−332.019	+	1207.79i	−0.448069	+	1.62995i
$742$		0			0
$743$			648.046i			0.872202i	0.899898	+	0.436101i	$0.143641\pi$
$743$			648.046i			0.872202i	−0.899898	+	0.436101i	$0.856359\pi$
$744$		0			0
$745$	−1226.97			−1.64693
$746$		0			0
$747$	−375.523	+	1395.67i	−0.502708	+	1.86837i
$748$		0			0
$749$	−170.747	+	98.5808i	−0.227967	+	0.131617i
$750$		0			0
$751$	202.582	+	350.883i	0.269750	+	0.467221i	0.968797	−	0.247855i	$-0.0797255\pi$
$751$	202.582	+	350.883i	0.269750	+	0.467221i	−0.699047	+	0.715076i	$0.746392\pi$
$752$		0			0
$753$	−136.442	−	18.0349i	−0.181197	−	0.0239507i
$754$		0			0
$755$	916.652	−	529.229i	1.21411	−	0.700966i
$756$		0			0
$757$	473.100	+	819.433i	0.624966	+	1.08247i	0.988547	+	0.150911i	$0.0482207\pi$
$757$	473.100	+	819.433i	0.624966	+	1.08247i	−0.363581	+	0.931563i	$0.618446\pi$
$758$		0			0
$759$	9.25573	−	70.0235i	0.0121946	−	0.0922576i
$760$		0			0
$761$	−646.639	−	373.337i	−0.849722	−	0.490588i	0.0108347	−	0.999941i	$-0.496551\pi$
$761$	−646.639	−	373.337i	−0.849722	−	0.490588i	−0.860557	+	0.509354i	$0.829884\pi$
$762$		0			0
$763$	215.738	−	373.670i	0.282750	−	0.489737i
$764$		0			0
$765$	675.211	+	181.673i	0.882629	+	0.237482i
$766$		0			0
$767$	−1178.06	+	680.155i	−1.53594	+	0.886773i
$768$		0			0
$769$	340.080	+	589.035i	0.442236	+	0.765975i	0.997855	−	0.0654616i	$-0.0208520\pi$
$769$	340.080	+	589.035i	0.442236	+	0.765975i	−0.555619	+	0.831437i	$0.687519\pi$
$770$		0			0
$771$	796.651	−	1037.10i	1.03327	−	1.34514i
$772$		0			0
$773$	−334.968	−	193.394i	−0.433335	−	0.250186i	0.267431	−	0.963577i	$-0.413825\pi$
$773$	−334.968	−	193.394i	−0.433335	−	0.250186i	−0.700766	+	0.713391i	$0.747158\pi$
$774$		0			0
$775$	−252.813	+	437.885i	−0.326210	+	0.565013i
$776$		0			0
$777$	763.012	+	586.109i	0.981998	+	0.754323i
$778$		0			0
$779$	−17.5994	+	7.16748i	−0.0225924	+	0.00920087i
$780$		0			0
$781$	40.7420	−	70.5672i	0.0521664	−	0.0903549i
$782$		0			0
$783$	−950.582	−	395.478i	−1.21403	−	0.505081i
$784$		0			0
$785$		−	775.446i		−	0.987830i
$786$		0			0
$787$	150.489	−	260.655i	0.191219	−	0.331201i	−0.754436	−	0.656374i	$-0.772089\pi$
$787$	150.489	−	260.655i	0.191219	−	0.331201i	0.945654	+	0.325173i	$0.105423\pi$
$788$		0			0
$789$	−614.458	−	81.2193i	−0.778781	−	0.102940i
$790$		0			0
$791$			2075.75i			2.62421i
$792$		0			0
$793$	1098.08	+	1901.92i	1.38471	+	2.39839i
$794$		0			0
$795$	−81.7668	+	618.600i	−0.102851	+	0.778113i
$796$		0			0
$797$	252.290	+	145.660i	0.316550	+	0.182760i	0.649854	−	0.760059i	$-0.274830\pi$
$797$	252.290	+	145.660i	0.316550	+	0.182760i	−0.333304	+	0.942820i	$0.608163\pi$
$798$		0			0
$799$	−229.997	−	398.367i	−0.287856	−	0.498582i
$800$		0			0
$801$	−922.473	+	246.150i	−1.15165	+	0.307304i
$802$		0			0
$803$	10.6641	+	6.15695i	0.0132804	+	0.00766743i
$804$		0			0
$805$	1427.53	−	2472.56i	1.77333	−	3.07150i
$806$		0			0
$807$	−528.045	+	687.423i	−0.654331	+	0.851825i
$808$		0			0
$809$			1049.66i			1.29748i	0.761011	+	0.648739i	$0.224703\pi$
$809$			1049.66i			1.29748i	−0.761011	+	0.648739i	$0.775297\pi$
$810$		0			0
$811$	208.027	−	360.313i	0.256506	−	0.444282i	−0.708797	−	0.705412i	$-0.750762\pi$
$811$	208.027	−	360.313i	0.256506	−	0.444282i	0.965304	+	0.261130i	$0.0840952\pi$
$812$		0			0
$813$	703.562	+	540.443i	0.865390	+	0.664751i
$814$		0			0
$815$		−	799.459i		−	0.980931i
$816$		0			0
$817$	222.387	+	30.6258i	0.272199	+	0.0374856i
$818$		0			0
$819$	−681.177	−	2552.78i	−0.831718	−	3.11695i
$820$		0			0
$821$		−	83.9316i		−	0.102231i	−0.998693	−	0.0511154i	$-0.983722\pi$
$821$		−	83.9316i		−	0.102231i	0.998693	−	0.0511154i	$-0.0162776\pi$
$822$		0			0
$823$	−382.995	−	663.366i	−0.465364	−	0.806034i	0.533854	−	0.845577i	$-0.320743\pi$
$823$	−382.995	−	663.366i	−0.465364	−	0.806034i	−0.999218	+	0.0395426i	$0.987410\pi$
$824$		0			0
$825$	−15.8548	+	20.6401i	−0.0192179	+	0.0250184i
$826$		0			0
$827$	1372.99	+	792.695i	1.66020	+	0.958518i	0.972617	+	0.232415i	$0.0746628\pi$
$827$	1372.99	+	792.695i	1.66020	+	0.958518i	0.687586	+	0.726103i	$0.258671\pi$
$828$		0			0
$829$	−543.934			−0.656133			−0.328067	−	0.944655i	$-0.606397\pi$
$829$	−543.934			−0.656133			−0.328067	+	0.944655i	$0.606397\pi$
$830$		0			0
$831$	−220.159	−	169.116i	−0.264933	−	0.203509i
$832$		0			0
$833$			1635.77i			1.96370i
$834$		0			0
$835$	−53.8264	−	93.2301i	−0.0644628	−	0.111653i
$836$		0			0
$837$	−647.572	−	846.658i	−0.773683	−	1.01154i
$838$		0			0
$839$	−297.919	−	172.003i	−0.355088	−	0.205010i	0.311836	−	0.950136i	$-0.399056\pi$
$839$	−297.919	−	172.003i	−0.355088	−	0.205010i	−0.666924	+	0.745126i	$0.732389\pi$
$840$		0			0
$841$	−613.058			−0.728964
$842$		0			0
$843$	−60.4324	−	146.111i	−0.0716874	−	0.173323i
$844$		0			0
$845$	−1671.60	−	965.101i	−1.97823	−	1.14213i
$846$		0			0
$847$	1610.30			1.90118
$848$		0			0
$849$	1049.47	−	434.066i	1.23612	−	0.511268i
$850$		0			0
$851$	−722.657	+	417.226i	−0.849185	+	0.490277i
$852$		0			0
$853$	291.512	−	504.914i	0.341749	−	0.591927i	−0.643008	−	0.765859i	$-0.722314\pi$
$853$	291.512	−	504.914i	0.341749	−	0.591927i	0.984758	+	0.173932i	$0.0556473\pi$
$854$		0			0
$855$	−409.151	+	968.571i	−0.478540	+	1.13283i
$856$		0			0
$857$	1216.36	+	702.265i	1.41932	+	0.819446i	0.996239	−	0.0866446i	$-0.0276144\pi$
$857$	1216.36	+	702.265i	1.41932	+	0.819446i	0.423083	+	0.906091i	$0.360948\pi$
$858$		0			0
$859$	543.718	+	941.748i	0.632967	+	1.09633i	0.986942	+	0.161076i	$0.0514963\pi$
$859$	543.718	+	941.748i	0.632967	+	1.09633i	−0.353975	+	0.935255i	$0.615170\pi$
$860$		0			0
$861$	24.4175	−	31.7873i	0.0283594	−	0.0369191i
$862$		0			0
$863$		−	1009.86i		−	1.17018i	−0.810970	−	0.585088i	$-0.801060\pi$
$863$		−	1009.86i		−	1.17018i	0.810970	−	0.585088i	$-0.198940\pi$
$864$		0			0
$865$	−798.806	+	1383.57i	−0.923475	+	1.59951i
$866$		0			0
$867$	−50.8503	+	384.704i	−0.0586509	+	0.443719i
$868$		0			0
$869$			5.56378i			0.00640251i
$870$		0			0
$871$	−347.753	+	602.325i	−0.399257	+	0.691533i
$872$		0			0
$873$	119.311	+	447.131i	0.136668	+	0.512177i
$874$		0			0
$875$	867.318	−	500.746i	0.991221	−	0.572282i
$876$		0			0
$877$	−606.932			−0.692055			−0.346028	−	0.938224i	$-0.612470\pi$
$877$	−606.932			−0.692055			−0.346028	+	0.938224i	$0.612470\pi$
$878$		0			0
$879$	−1420.10	−	187.709i	−1.61558	−	0.213548i
$880$		0			0
$881$			1319.04i			1.49721i	0.663015	+	0.748606i	$0.269277\pi$
$881$			1319.04i			1.49721i	−0.663015	+	0.748606i	$0.730723\pi$
$882$		0			0
$883$	632.552	−	1095.61i	0.716367	−	1.24078i	−0.246063	−	0.969254i	$-0.579137\pi$
$883$	632.552	−	1095.61i	0.716367	−	1.24078i	0.962430	−	0.271530i	$-0.0875295\pi$
$884$		0			0
$885$	−1055.17	+	436.424i	−1.19228	+	0.493134i
$886$		0			0
$887$	420.192	−	242.598i	0.473723	−	0.273504i	−0.244074	−	0.969757i	$-0.578484\pi$
$887$	420.192	−	242.598i	0.473723	−	0.273504i	0.717797	+	0.696252i	$0.245151\pi$
$888$		0			0
$889$	−160.818			−0.180898
$890$		0			0
$891$	−27.3349	−	47.5733i	−0.0306790	−	0.0533931i
$892$		0			0
$893$	640.618	−	260.896i	0.717378	−	0.292156i
$894$		0			0
$895$	743.376			0.830588
$896$		0			0
$897$	2271.70	+	300.274i	2.53255	+	0.334754i
$898$		0			0
$899$	−1303.71	−	752.698i	−1.45018	−	0.837261i
$900$		0			0
$901$	427.410			0.474372
$902$		0			0
$903$	−437.558	+	180.977i	−0.484561	+	0.200417i
$904$		0			0
$905$	−1173.08	−	677.280i	−1.29622	−	0.748375i
$906$		0			0
$907$	−221.770	+	384.116i	−0.244509	+	0.423502i	−0.961993	−	0.273072i	$-0.911960\pi$
$907$	−221.770	+	384.116i	−0.244509	+	0.423502i	0.717484	+	0.696575i	$0.245293\pi$
$908$		0			0
$909$	18.8132	+	18.8523i	0.0206966	+	0.0207396i
$910$		0			0
$911$	−162.124	+	93.6021i	−0.177962	+	0.102747i	−0.586335	−	0.810069i	$-0.699430\pi$
$911$	−162.124	+	93.6021i	−0.177962	+	0.102747i	0.408373	+	0.912815i	$0.366096\pi$
$912$		0			0
$913$	−54.3897	+	94.2058i	−0.0595725	+	0.103183i
$914$		0			0
$915$	704.584	+	1703.52i	0.770038	+	1.86177i
$916$		0			0
$917$	−122.553	+	70.7560i	−0.133646	+	0.0771603i
$918$		0			0
$919$	−829.412			−0.902516			−0.451258	−	0.892394i	$-0.649025\pi$
$919$	−829.412			−0.902516			−0.451258	+	0.892394i	$0.649025\pi$
$920$		0			0
$921$	115.839	+	88.9822i	0.125776	+	0.0966147i
$922$		0			0
$923$	2289.34	+	1321.75i	2.48032	+	1.43202i
$924$		0			0
$925$	307.479			0.332410
$926$		0			0
$927$	−25.3511	−	95.0057i	−0.0273474	−	0.102487i
$928$		0			0
$929$	30.9987	+	17.8971i	0.0333678	+	0.0192649i	0.516591	−	0.856232i	$-0.327201\pi$
$929$	30.9987	+	17.8971i	0.0333678	+	0.0192649i	−0.483223	+	0.875497i	$0.660534\pi$
$930$		0			0
$931$	−2436.75	−	335.574i	−2.61735	−	0.360445i
$932$		0			0
$933$	201.217	+	26.5970i	0.215667	+	0.0285070i
$934$		0			0
$935$	45.5757	+	26.3131i	0.0487440	+	0.0281424i
$936$		0			0
$937$	−678.876	+	1175.85i	−0.724521	+	1.25491i	0.234650	+	0.972080i	$0.424606\pi$
$937$	−678.876	+	1175.85i	−0.724521	+	1.25491i	−0.959171	+	0.282827i	$0.908728\pi$
$938$		0			0
$939$	−7.58543	+	3.13738i	−0.00807820	+	0.00334119i
$940$		0			0
$941$	−1013.23	+	584.991i	−1.07676	+	0.621670i	−0.930022	−	0.367505i	$-0.880212\pi$
$941$	−1013.23	+	584.991i	−1.07676	+	0.621670i	−0.146742	+	0.989175i	$0.546879\pi$
$942$		0			0
$943$	17.3818	+	30.1061i	0.0184324	+	0.0319259i
$944$		0			0
$945$	−286.059	−	2199.29i	−0.302708	−	2.32729i
$946$		0			0
$947$	−897.336	−	518.077i	−0.947557	−	0.547072i	−0.0552355	−	0.998473i	$-0.517591\pi$
$947$	−897.336	−	518.077i	−0.947557	−	0.547072i	−0.892321	+	0.451401i	$0.850924\pi$
$948$		0			0
$949$	−199.744	+	345.966i	−0.210478	+	0.364559i
$950$		0			0
$951$	474.409	+	1147.01i	0.498852	+	1.20611i
$952$		0			0
$953$	21.9587	−	12.6779i	0.0230416	−	0.0133031i	−0.488435	−	0.872600i	$-0.662432\pi$
$953$	21.9587	−	12.6779i	0.0230416	−	0.0133031i	0.511477	+	0.859297i	$0.329099\pi$
$954$		0			0
$955$	−311.583	−	539.677i	−0.326265	−	0.565107i
$956$		0			0
$957$	−61.4517	−	47.2042i	−0.0642129	−	0.0493252i
$958$		0			0
$959$	213.873	−	123.479i	0.223016	−	0.128758i
$960$		0			0
$961$	−298.773	−	517.490i	−0.310898	−	0.538491i
$962$		0			0
$963$	−93.8270	−	94.0219i	−0.0974320	−	0.0976344i
$964$		0			0
$965$		−	1966.08i		−	2.03738i
$966$		0			0
$967$	−1194.01			−1.23475			−0.617376	−	0.786668i	$-0.711804\pi$
$967$	−1194.01			−1.23475			−0.617376	+	0.786668i	$0.711804\pi$
$968$		0			0
$969$	694.449	+	190.903i	0.716665	+	0.197010i
$970$		0			0
$971$	−903.364	+	521.557i	−0.930344	+	0.537134i	−0.886920	−	0.461922i	$-0.847160\pi$
$971$	−903.364	+	521.557i	−0.930344	+	0.537134i	−0.0434236	+	0.999057i	$0.513827\pi$
$972$		0			0
$973$	849.846	−	1471.98i	0.873429	−	1.51282i
$974$		0			0
$975$	−669.607	−	514.360i	−0.686777	−	0.527549i
$976$		0			0
$977$	−22.5462	−	13.0171i	−0.0230770	−	0.0133235i	0.488417	−	0.872610i	$-0.337574\pi$
$977$	−22.5462	−	13.0171i	−0.0230770	−	0.0133235i	−0.511494	+	0.859287i	$0.670908\pi$
$978$		0			0
$979$	−71.8579			−0.0733993
$980$		0			0
$981$	280.706	+	75.5272i	0.286143	+	0.0769900i
$982$		0			0
$983$	283.804	+	163.855i	0.288713	+	0.166688i	0.637361	−	0.770565i	$-0.280026\pi$
$983$	283.804	+	163.855i	0.288713	+	0.166688i	−0.348649	+	0.937254i	$0.613359\pi$
$984$		0			0
$985$	2229.98			2.26394
$986$		0			0
$987$	−888.794	+	1157.06i	−0.900501	+	1.17230i
$988$		0			0
$989$		−	410.668i		−	0.415236i
$990$		0			0
$991$	−559.358	−	968.836i	−0.564438	−	0.977635i	−0.997102	−	0.0760795i	$-0.975760\pi$
$991$	−559.358	−	968.836i	−0.564438	−	0.977635i	0.432664	−	0.901555i	$-0.357574\pi$
$992$		0			0
$993$	945.956	+	726.637i	0.952624	+	0.731760i
$994$		0			0
$995$	−671.179	−	387.505i	−0.674551	−	0.389452i
$996$		0			0
$997$	−817.886			−0.820347			−0.410174	−	0.912007i	$-0.634532\pi$
$997$	−817.886			−0.820347			−0.410174	+	0.912007i	$0.634532\pi$
$998$		0			0
$999$	−248.988	+	598.473i	−0.249237	+	0.599072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.653.35	yes	80
3.2	odd	2		2052.3.m.a.881.9		80
9.2	odd	6		684.3.be.a.425.9	yes	80
9.7	even	3		2052.3.be.a.197.9		80
19.11	even	3		684.3.be.a.581.9	yes	80
57.11	odd	6		2052.3.be.a.125.9		80
171.11	odd	6	inner	684.3.m.a.353.35	✓	80
171.106	even	3		2052.3.m.a.1493.32		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.35	✓	80	171.11	odd	6	inner
684.3.m.a.653.35	yes	80	1.1	even	1	trivial
684.3.be.a.425.9	yes	80	9.2	odd	6
684.3.be.a.581.9	yes	80	19.11	even	3
2052.3.m.a.881.9		80	3.2	odd	2
2052.3.m.a.1493.32		80	171.106	even	3
2052.3.be.a.125.9		80	57.11	odd	6
2052.3.be.a.197.9		80	9.7	even	3

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.77223 - 1.14661i) q^{3} +6.14879i q^{5} +(-6.67945 - 11.5692i) q^{7} +(6.37056 - 6.35735i) q^{9} +O(q^{10})\)	\(q+(2.77223 - 1.14661i) q^{3} +6.14879i q^{5} +(-6.67945 - 11.5692i) q^{7} +(6.37056 - 6.35735i) q^{9} +(0.586623 - 0.338687i) q^{11} +(10.9877 + 19.0312i) q^{13} +(7.05028 + 17.0459i) q^{15} +(10.9425 - 6.31763i) q^{17} +(7.16635 + 17.5967i) q^{19} +(-31.7823 - 24.4137i) q^{21} +(30.1014 - 17.3790i) q^{23} -12.8077 q^{25} +(10.3713 - 24.9286i) q^{27} -38.1321i q^{29} +(19.7392 - 34.1893i) q^{31} +(1.23791 - 1.61155i) q^{33} +(71.1363 - 41.0706i) q^{35} -24.0074 q^{37} +(52.2818 + 40.1603i) q^{39} +1.00016i q^{41} +(5.90752 - 10.2321i) q^{43} +(39.0901 + 39.1713i) q^{45} -36.4056i q^{47} +(-64.7302 + 112.116i) q^{49} +(23.0912 - 30.0607i) q^{51} +(29.2948 + 16.9134i) q^{53} +(2.08251 + 3.60702i) q^{55} +(40.0434 + 40.5651i) q^{57} +61.9016i q^{59} +99.9371 q^{61} +(-116.101 - 31.2383i) q^{63} +(-117.019 + 67.5609i) q^{65} +(15.8247 + 27.4092i) q^{67} +(63.5210 - 82.6933i) q^{69} +(104.178 - 60.1470i) q^{71} +(9.08945 + 15.7434i) q^{73} +(-35.5058 + 14.6854i) q^{75} +(-7.83664 - 4.52448i) q^{77} +(-4.10688 + 7.11332i) q^{79} +(0.168107 - 80.9998i) q^{81} +(-139.075 + 80.2951i) q^{83} +(38.8458 + 67.2829i) q^{85} +(-43.7227 - 105.711i) q^{87} +(-91.8708 - 53.0416i) q^{89} +(146.783 - 254.236i) q^{91} +(15.5198 - 117.414i) q^{93} +(-108.198 + 44.0644i) q^{95} +(-25.7098 + 44.5306i) q^{97} +(1.58396 - 5.88699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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