LMFDB - Embedded newform 684.3.bl.a.373.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(373,684)]

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, 2, 5]))

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

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

chi := DirichletCharacter("684.373");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.bl (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			373.17
Character	$\chi$	$=$	684.373
Dual form			684.3.bl.a.673.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.981973 - 2.83474i) q^{3} +0.638534 q^{5} +(-1.11619 - 1.93329i) q^{7} +(-7.07146 + 5.56727i) q^{9} +O(q^{10})$	\(q+(-0.981973 - 2.83474i) q^{3} +0.638534 q^{5} +(-1.11619 - 1.93329i) q^{7} +(-7.07146 + 5.56727i) q^{9} +(1.89002 + 3.27360i) q^{11} +(-8.35812 + 4.82556i) q^{13} +(-0.627024 - 1.81008i) q^{15} +(11.4559 + 19.8422i) q^{17} +(7.12829 + 17.6121i) q^{19} +(-4.38431 + 5.06253i) q^{21} +(-3.96509 - 6.86774i) q^{23} -24.5923 q^{25} +(22.7257 + 14.5788i) q^{27} -30.4204i q^{29} +(50.4054 + 29.1016i) q^{31} +(7.42386 - 8.57229i) q^{33} +(-0.712723 - 1.23447i) q^{35} -12.8801i q^{37} +(21.8867 + 18.9545i) q^{39} +57.9407i q^{41} +(-14.6011 + 25.2898i) q^{43} +(-4.51537 + 3.55489i) q^{45} -44.5207 q^{47} +(22.0083 - 38.1194i) q^{49} +(44.9981 - 51.9590i) q^{51} +(-15.1786 - 8.76336i) q^{53} +(1.20684 + 2.09031i) q^{55} +(42.9260 - 37.5015i) q^{57} +47.6628i q^{59} +69.9915 q^{61} +(18.6562 + 7.45708i) q^{63} +(-5.33695 + 3.08129i) q^{65} +(18.0367 - 10.4135i) q^{67} +(-15.5746 + 17.9839i) q^{69} +(99.8380 - 57.6415i) q^{71} +(66.8138 + 115.725i) q^{73} +(24.1490 + 69.7126i) q^{75} +(4.21922 - 7.30790i) q^{77} +(13.6901 + 7.90398i) q^{79} +(19.0110 - 78.7374i) q^{81} +(47.6602 + 82.5498i) q^{83} +(7.31500 + 12.6699i) q^{85} +(-86.2339 + 29.8721i) q^{87} +(-70.8072 - 40.8805i) q^{89} +(18.6584 + 10.7725i) q^{91} +(32.9985 - 171.463i) q^{93} +(4.55166 + 11.2460i) q^{95} +(39.1925 + 22.6278i) q^{97} +(-31.5902 - 12.6269i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{3} - q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 6 * q^3 - q^7 - 2 * q^9	$ 80 q - 6 q^{3} - q^{7} - 2 q^{9} - 6 q^{11} - 15 q^{13} + 24 q^{15} - 21 q^{17} - 20 q^{19} + 24 q^{23} + 400 q^{25} + 63 q^{27} + 24 q^{31} + 30 q^{33} - 54 q^{35} - 81 q^{39} + 76 q^{43} + 188 q^{45} + 24 q^{47} - 267 q^{49} - 243 q^{51} - 36 q^{53} + 72 q^{57} + 14 q^{61} + 284 q^{63} + 288 q^{65} - 21 q^{67} - 48 q^{69} - 81 q^{71} + 55 q^{73} - 165 q^{75} + 30 q^{77} - 51 q^{79} - 110 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 204 q^{93} - 432 q^{95} + 90 q^{97} + 260 q^{99}+O(q^{100}) $ 80 * q - 6 * q^3 - q^7 - 2 * q^9 - 6 * q^11 - 15 * q^13 + 24 * q^15 - 21 * q^17 - 20 * q^19 + 24 * q^23 + 400 * q^25 + 63 * q^27 + 24 * q^31 + 30 * q^33 - 54 * q^35 - 81 * q^39 + 76 * q^43 + 188 * q^45 + 24 * q^47 - 267 * q^49 - 243 * q^51 - 36 * q^53 + 72 * q^57 + 14 * q^61 + 284 * q^63 + 288 * q^65 - 21 * q^67 - 48 * q^69 - 81 * q^71 + 55 * q^73 - 165 * q^75 + 30 * q^77 - 51 * q^79 - 110 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 204 * q^93 - 432 * q^95 + 90 * q^97 + 260 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.981973	−	2.83474i	−0.327324	−	0.944912i
$3$	−0.981973	−	2.83474i	−0.327324	−	0.944912i
$4$		0			0
$5$	0.638534			0.127707			0.0638534	−	0.997959i	$-0.479661\pi$
$5$	0.638534			0.127707			0.0638534	+	0.997959i	$0.479661\pi$
$6$		0			0
$7$	−1.11619	−	1.93329i	−0.159455	−	0.276185i	0.775217	−	0.631695i	$-0.217640\pi$
$7$	−1.11619	−	1.93329i	−0.159455	−	0.276185i	−0.934672	+	0.355510i	$0.884307\pi$
$8$		0			0
$9$	−7.07146	+	5.56727i	−0.785717	+	0.618586i
$10$		0			0
$11$	1.89002	+	3.27360i	0.171820	+	0.297600i	0.939056	−	0.343764i	$-0.111702\pi$
$11$	1.89002	+	3.27360i	0.171820	+	0.297600i	−0.767236	+	0.641364i	$0.778369\pi$
$12$		0			0
$13$	−8.35812	+	4.82556i	−0.642932	+	0.371197i	−0.785743	−	0.618553i	$-0.787719\pi$
$13$	−8.35812	+	4.82556i	−0.642932	+	0.371197i	0.142811	+	0.989750i	$0.454386\pi$
$14$		0			0
$15$	−0.627024	−	1.81008i	−0.0418016	−	0.120672i
$16$		0			0
$17$	11.4559	+	19.8422i	0.673877	+	1.16719i	0.976796	+	0.214173i	$0.0687057\pi$
$17$	11.4559	+	19.8422i	0.673877	+	1.16719i	−0.302918	+	0.953017i	$0.597961\pi$
$18$		0			0
$19$	7.12829	+	17.6121i	0.375173	+	0.926955i
$19$	7.12829	+	17.6121i	0.375173	+	0.926955i
$20$		0			0
$21$	−4.38431	+	5.06253i	−0.208776	+	0.241073i
$22$		0			0
$23$	−3.96509	−	6.86774i	−0.172395	−	0.298597i	0.766862	−	0.641813i	$-0.221817\pi$
$23$	−3.96509	−	6.86774i	−0.172395	−	0.298597i	−0.939257	+	0.343215i	$0.888484\pi$
$24$		0			0
$25$	−24.5923			−0.983691
$26$		0			0
$27$	22.7257	+	14.5788i	0.841693	+	0.539956i
$28$		0			0
$29$		−	30.4204i		−	1.04898i	−0.851416	−	0.524490i	$-0.824256\pi$
$29$		−	30.4204i		−	1.04898i	0.851416	−	0.524490i	$-0.175744\pi$
$30$		0			0
$31$	50.4054	+	29.1016i	1.62598	+	0.938761i	0.985275	+	0.170976i	$0.0546920\pi$
$31$	50.4054	+	29.1016i	1.62598	+	0.938761i	0.640707	+	0.767785i	$0.278641\pi$
$32$		0			0
$33$	7.42386	−	8.57229i	0.224965	−	0.259766i
$34$		0			0
$35$	−0.712723	−	1.23447i	−0.0203635	−	0.0352707i
$36$		0			0
$37$		−	12.8801i		−	0.348112i	−0.984736	−	0.174056i	$-0.944313\pi$
$37$		−	12.8801i		−	0.348112i	0.984736	−	0.174056i	$-0.0556873\pi$
$38$		0			0
$39$	21.8867	+	18.9545i	0.561196	+	0.486013i
$40$		0			0
$41$			57.9407i			1.41319i	0.707620	+	0.706594i	$0.249769\pi$
$41$			57.9407i			1.41319i	−0.707620	+	0.706594i	$0.750231\pi$
$42$		0			0
$43$	−14.6011	+	25.2898i	−0.339560	+	0.588135i	−0.984350	−	0.176225i	$-0.943611\pi$
$43$	−14.6011	+	25.2898i	−0.339560	+	0.588135i	0.644790	+	0.764360i	$0.276945\pi$
$44$		0			0
$45$	−4.51537	+	3.55489i	−0.100342	+	0.0789976i
$46$		0			0
$47$	−44.5207			−0.947249			−0.473624	−	0.880727i	$-0.657055\pi$
$47$	−44.5207			−0.947249			−0.473624	+	0.880727i	$0.657055\pi$
$48$		0			0
$49$	22.0083	−	38.1194i	0.449148	−	0.777947i
$50$		0			0
$51$	44.9981	−	51.9590i	0.882315	−	1.01880i
$52$		0			0
$53$	−15.1786	−	8.76336i	−0.286389	−	0.165346i	0.349924	−	0.936778i	$-0.386208\pi$
$53$	−15.1786	−	8.76336i	−0.286389	−	0.165346i	−0.636312	+	0.771432i	$0.719541\pi$
$54$		0			0
$55$	1.20684	+	2.09031i	0.0219425	+	0.0380056i
$56$		0			0
$57$	42.9260	−	37.5015i	0.753087	−	0.657920i
$58$		0			0
$59$			47.6628i			0.807844i	0.914794	+	0.403922i	$0.132353\pi$
$59$			47.6628i			0.807844i	−0.914794	+	0.403922i	$0.867647\pi$
$60$		0			0
$61$	69.9915			1.14740			0.573700	−	0.819065i	$-0.305507\pi$
$61$	69.9915			1.14740			0.573700	+	0.819065i	$0.305507\pi$
$62$		0			0
$63$	18.6562	+	7.45708i	0.296130	+	0.118366i
$64$		0			0
$65$	−5.33695	+	3.08129i	−0.0821069	+	0.0474044i
$66$		0			0
$67$	18.0367	−	10.4135i	0.269205	−	0.155425i	−0.359322	−	0.933214i	$-0.616992\pi$
$67$	18.0367	−	10.4135i	0.269205	−	0.155425i	0.628526	+	0.777789i	$0.283659\pi$
$68$		0			0
$69$	−15.5746	+	17.9839i	−0.225719	+	0.260637i
$70$		0			0
$71$	99.8380	−	57.6415i	1.40617	−	0.811852i	0.411153	−	0.911566i	$-0.365126\pi$
$71$	99.8380	−	57.6415i	1.40617	−	0.811852i	0.995016	+	0.0997140i	$0.0317928\pi$
$72$		0			0
$73$	66.8138	+	115.725i	0.915257	+	1.58527i	0.806524	+	0.591201i	$0.201346\pi$
$73$	66.8138	+	115.725i	0.915257	+	1.58527i	0.108733	+	0.994071i	$0.465321\pi$
$74$		0			0
$75$	24.1490	+	69.7126i	0.321986	+	0.929501i
$76$		0			0
$77$	4.21922	−	7.30790i	0.0547951	−	0.0949078i
$78$		0			0
$79$	13.6901	+	7.90398i	0.173292	+	0.100050i	0.584137	−	0.811655i	$-0.301433\pi$
$79$	13.6901	+	7.90398i	0.173292	+	0.100050i	−0.410845	+	0.911705i	$0.634766\pi$
$80$		0			0
$81$	19.0110	−	78.7374i	0.234704	−	0.972067i
$82$		0			0
$83$	47.6602	+	82.5498i	0.574219	+	0.994576i	0.996126	+	0.0879370i	$0.0280274\pi$
$83$	47.6602	+	82.5498i	0.574219	+	0.994576i	−0.421907	+	0.906639i	$0.638639\pi$
$84$		0			0
$85$	7.31500	+	12.6699i	0.0860588	+	0.149058i
$86$		0			0
$87$	−86.2339	+	29.8721i	−0.991194	+	0.343357i
$88$		0			0
$89$	−70.8072	−	40.8805i	−0.795586	−	0.459332i	0.0463393	−	0.998926i	$-0.485244\pi$
$89$	−70.8072	−	40.8805i	−0.795586	−	0.459332i	−0.841925	+	0.539594i	$0.818578\pi$
$90$		0			0
$91$	18.6584	+	10.7725i	0.205038	+	0.118379i
$92$		0			0
$93$	32.9985	−	171.463i	0.354823	−	1.84369i
$94$		0			0
$95$	4.55166	+	11.2460i	0.0479122	+	0.118379i
$96$		0			0
$97$	39.1925	+	22.6278i	0.404046	+	0.233276i	0.688228	−	0.725494i	$-0.258389\pi$
$97$	39.1925	+	22.6278i	0.404046	+	0.233276i	−0.284182	+	0.958770i	$0.591722\pi$
$98$		0			0
$99$	−31.5902	−	12.6269i	−0.319093	−	0.127545i
$100$		0			0
$101$	37.3898			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$101$	37.3898			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$102$		0			0
$103$	95.1351	+	54.9263i	0.923642	+	0.533265i	0.884795	−	0.465980i	$-0.154298\pi$
$103$	95.1351	+	54.9263i	0.923642	+	0.533265i	0.0388467	+	0.999245i	$0.487632\pi$
$104$		0			0
$105$	−2.79953	+	3.23260i	−0.0266622	+	0.0307867i
$106$		0			0
$107$			199.591i			1.86533i	0.360738	+	0.932667i	$0.382525\pi$
$107$			199.591i			1.86533i	−0.360738	+	0.932667i	$0.617475\pi$
$108$		0			0
$109$	−106.877	+	61.7056i	−0.980526	+	0.566107i	−0.902429	−	0.430839i	$-0.858218\pi$
$109$	−106.877	+	61.7056i	−0.980526	+	0.566107i	−0.0780969	+	0.996946i	$0.524884\pi$
$110$		0			0
$111$	−36.5118	+	12.6479i	−0.328935	+	0.113945i
$112$		0			0
$113$	−141.848	−	81.8961i	−1.25529	−	0.724744i	−0.283138	−	0.959079i	$-0.591375\pi$
$113$	−141.848	−	81.8961i	−1.25529	−	0.724744i	−0.972156	+	0.234335i	$0.924709\pi$
$114$		0			0
$115$	−2.53185	−	4.38529i	−0.0220161	−	0.0381329i
$116$		0			0
$117$	32.2389	−	80.6557i	0.275546	−	0.689365i
$118$		0			0
$119$	25.5739	−	44.2953i	0.214907	−	0.372229i
$120$		0			0
$121$	53.3557	−	92.4147i	0.440956	−	0.763758i
$122$		0			0
$123$	164.247	−	56.8962i	1.33534	−	0.462571i
$124$		0			0
$125$	−31.6664			−0.253331
$126$		0			0
$127$	200.120	+	115.539i	1.57575	+	0.909758i	0.995443	+	0.0953582i	$0.0303996\pi$
$127$	200.120	+	115.539i	1.57575	+	0.909758i	0.580304	+	0.814400i	$0.302934\pi$
$128$		0			0
$129$	86.0277	+	16.5563i	0.666882	+	0.128343i
$130$		0			0
$131$	−135.791			−1.03657			−0.518286	−	0.855208i	$-0.673430\pi$
$131$	−135.791			−1.03657			−0.518286	+	0.855208i	$0.673430\pi$
$132$		0			0
$133$	26.0929	−	33.4395i	0.196187	−	0.251425i
$134$		0			0
$135$	14.5112	+	9.30907i	0.107490	+	0.0689561i
$136$		0			0
$137$	−99.5734			−0.726813			−0.363407	−	0.931631i	$-0.618386\pi$
$137$	−99.5734			−0.726813			−0.363407	+	0.931631i	$0.618386\pi$
$138$		0			0
$139$	−90.6517	−	157.013i	−0.652171	−	1.12959i	−0.982595	−	0.185760i	$-0.940525\pi$
$139$	−90.6517	−	157.013i	−0.652171	−	1.12959i	0.330424	−	0.943833i	$-0.392808\pi$
$140$		0			0
$141$	43.7181	+	126.204i	0.310058	+	0.895067i
$142$		0			0
$143$	−31.5940	−	18.2408i	−0.220937	−	0.127558i
$144$		0			0
$145$		−	19.4245i		−	0.133962i
$146$		0			0
$147$	−129.670	−	24.9553i	−0.882109	−	0.169764i
$148$		0			0
$149$	−52.4987			−0.352340			−0.176170	−	0.984360i	$-0.556371\pi$
$149$	−52.4987			−0.352340			−0.176170	+	0.984360i	$0.556371\pi$
$150$		0			0
$151$	−222.845	+	128.660i	−1.47579	+	0.852050i	−0.999627	−	0.0273044i	$-0.991308\pi$
$151$	−222.845	+	128.660i	−1.47579	+	0.852050i	−0.476167	+	0.879355i	$0.657974\pi$
$152$		0			0
$153$	−191.477	−	76.5353i	−1.25148	−	0.500231i
$154$		0			0
$155$	32.1856	+	18.5824i	0.207649	+	0.119886i
$156$		0			0
$157$	−40.2480			−0.256357			−0.128178	−	0.991751i	$-0.540913\pi$
$157$	−40.2480			−0.256357			−0.128178	+	0.991751i	$0.540913\pi$
$158$		0			0
$159$	−9.93685	+	51.6327i	−0.0624959	+	0.324734i
$160$		0			0
$161$	−8.85156	+	15.3314i	−0.0549786	+	0.0952258i
$162$		0			0
$163$	−14.8179			−0.0909071			−0.0454536	−	0.998966i	$-0.514473\pi$
$163$	−14.8179			−0.0909071			−0.0454536	+	0.998966i	$0.514473\pi$
$164$		0			0
$165$	4.74039	−	5.47370i	0.0287296	−	0.0331739i
$166$		0			0
$167$	−283.221	+	163.518i	−1.69593	+	0.979148i	−0.746392	+	0.665507i	$0.768215\pi$
$167$	−283.221	+	163.518i	−1.69593	+	0.979148i	−0.949542	+	0.313641i	$0.898451\pi$
$168$		0			0
$169$	−37.9279	+	65.6930i	−0.224425	+	0.388716i
$170$		0			0
$171$	−148.459	−	84.8584i	−0.868181	−	0.496248i
$172$		0			0
$173$	−148.923	−	85.9805i	−0.860824	−	0.496997i	0.00346391	−	0.999994i	$-0.498897\pi$
$173$	−148.923	−	85.9805i	−0.860824	−	0.496997i	−0.864288	+	0.502997i	$0.832231\pi$
$174$		0			0
$175$	27.4496	+	47.5440i	0.156855	+	0.271680i
$176$		0			0
$177$	135.111	−	46.8036i	0.763341	−	0.264427i
$178$		0			0
$179$		−	253.843i		−	1.41812i	−0.705151	−	0.709058i	$-0.749121\pi$
$179$		−	253.843i		−	1.41812i	0.705151	−	0.709058i	$-0.250879\pi$
$180$		0			0
$181$	193.550	+	111.746i	1.06934	+	0.617383i	0.928001	−	0.372578i	$-0.121526\pi$
$181$	193.550	+	111.746i	1.06934	+	0.617383i	0.141338	+	0.989961i	$0.454860\pi$
$182$		0			0
$183$	−68.7297	−	198.407i	−0.375572	−	1.08419i
$184$		0			0
$185$		−	8.22441i		−	0.0444562i
$186$		0			0
$187$	−43.3037	+	75.0043i	−0.231571	+	0.401092i
$188$		0			0
$189$	2.81893	−	60.2081i	0.0149150	−	0.318561i
$190$		0			0
$191$	61.3902	+	106.331i	0.321414	+	0.556706i	0.980780	−	0.195116i	$-0.0625084\pi$
$191$	61.3902	+	106.331i	0.321414	+	0.556706i	−0.659366	+	0.751822i	$0.729175\pi$
$192$		0			0
$193$			207.815i			1.07676i	0.842701	+	0.538381i	$0.180964\pi$
$193$			207.815i			1.07676i	−0.842701	+	0.538381i	$0.819036\pi$
$194$		0			0
$195$	13.9754	+	12.1031i	0.0716686	+	0.0620672i
$196$		0			0
$197$	−72.7857			−0.369471			−0.184735	−	0.982788i	$-0.559143\pi$
$197$	−72.7857			−0.369471			−0.184735	+	0.982788i	$0.559143\pi$
$198$		0			0
$199$	28.4841	−	49.3359i	0.143136	−	0.247919i	−0.785540	−	0.618811i	$-0.787615\pi$
$199$	28.4841	−	49.3359i	0.143136	−	0.247919i	0.928676	+	0.370892i	$0.120948\pi$
$200$		0			0
$201$	−47.2311	−	40.9035i	−0.234980	−	0.203500i
$202$		0			0
$203$	−58.8116	+	33.9549i	−0.289712	+	0.167265i
$204$		0			0
$205$			36.9971i			0.180474i
$206$		0			0
$207$	66.2735	+	26.4902i	0.320162	+	0.127972i
$208$		0			0
$209$	−44.1826	+	56.6224i	−0.211400	+	0.270921i
$210$		0			0
$211$			34.3761i			0.162920i	0.996677	+	0.0814600i	$0.0259583\pi$
$211$			34.3761i			0.162920i	−0.996677	+	0.0814600i	$0.974042\pi$
$212$		0			0
$213$	−261.437	−	226.412i	−1.22740	−	1.06297i
$214$		0			0
$215$	−9.32328	+	16.1484i	−0.0433641	+	0.0751088i
$216$		0			0
$217$		−	129.931i		−	0.598761i
$218$		0			0
$219$	262.440	−	303.038i	1.19836	−	1.38374i
$220$		0			0
$221$	−191.500	−	110.563i	−0.866515	−	0.500283i
$222$		0			0
$223$	234.207	+	135.219i	1.05025	+	0.606364i	0.922720	−	0.385470i	$-0.125961\pi$
$223$	234.207	+	135.219i	1.05025	+	0.606364i	0.127534	+	0.991834i	$0.459294\pi$
$224$		0			0
$225$	173.903	−	136.912i	0.772903	−	0.608497i
$226$		0			0
$227$	−115.627	+	66.7570i	−0.509368	+	0.294084i	−0.732574	−	0.680688i	$-0.761681\pi$
$227$	−115.627	+	66.7570i	−0.509368	+	0.294084i	0.223206	+	0.974771i	$0.428348\pi$
$228$		0			0
$229$	67.7204	−	117.295i	0.295722	−	0.512206i	−0.679430	−	0.733740i	$-0.737773\pi$
$229$	67.7204	−	117.295i	0.295722	−	0.512206i	0.975153	+	0.221534i	$0.0711064\pi$
$230$		0			0
$231$	−24.8591	−	4.78421i	−0.107615	−	0.0207109i
$232$		0			0
$233$	−49.8017	−	86.2591i	−0.213741	−	0.370211i	0.739141	−	0.673550i	$-0.235232\pi$
$233$	−49.8017	−	86.2591i	−0.213741	−	0.370211i	−0.952882	+	0.303340i	$0.901898\pi$
$234$		0			0
$235$	−28.4280			−0.120970
$236$		0			0
$237$	8.96239	−	46.5693i	0.0378160	−	0.196495i
$238$		0			0
$239$	−195.201	+	338.098i	−0.816740	+	1.41464i	0.0913311	+	0.995821i	$0.470888\pi$
$239$	−195.201	+	338.098i	−0.816740	+	1.41464i	−0.908071	+	0.418815i	$0.862445\pi$
$240$		0			0
$241$		−	44.4356i		−	0.184380i	−0.995741	−	0.0921900i	$-0.970613\pi$
$241$		−	44.4356i		−	0.184380i	0.995741	−	0.0921900i	$-0.0293867\pi$
$242$		0			0
$243$	−241.868	+	23.4269i	−0.995342	+	0.0964068i
$244$		0			0
$245$	14.0530	−	24.3406i	0.0573593	−	0.0993492i
$246$		0			0
$247$	−144.568	−	112.806i	−0.585294	−	0.456706i
$248$		0			0
$249$	187.206	−	216.166i	0.751831	−	0.868135i
$250$		0			0
$251$	216.564	−	375.100i	0.862805	−	1.49442i	−0.00640431	−	0.999979i	$-0.502039\pi$
$251$	216.564	−	375.100i	0.862805	−	1.49442i	0.869210	−	0.494443i	$-0.164628\pi$
$252$		0			0
$253$	14.9882	−	25.9603i	0.0592418	−	0.102610i
$254$		0			0
$255$	28.7328	−	33.1776i	0.112678	−	0.130108i
$256$		0			0
$257$	−85.1943	+	49.1869i	−0.331495	+	0.191389i	−0.656505	−	0.754322i	$-0.727966\pi$
$257$	−85.1943	+	49.1869i	−0.331495	+	0.191389i	0.325009	+	0.945711i	$0.394633\pi$
$258$		0			0
$259$	−24.9010	+	14.3766i	−0.0961430	+	0.0555082i
$260$		0			0
$261$	169.359	+	215.117i	0.648884	+	0.824202i
$262$		0			0
$263$	−64.0831	+	110.995i	−0.243662	+	0.422035i	−0.961755	−	0.273912i	$-0.911682\pi$
$263$	−64.0831	+	110.995i	−0.243662	+	0.422035i	0.718092	+	0.695948i	$0.245015\pi$
$264$		0			0
$265$	−9.69205	−	5.59571i	−0.0365738	−	0.0211159i
$266$		0			0
$267$	−46.3548	+	240.863i	−0.173613	+	0.902109i
$268$		0			0
$269$	255.028	−	147.241i	0.948061	−	0.547363i	0.0555826	−	0.998454i	$-0.482298\pi$
$269$	255.028	−	147.241i	0.948061	−	0.547363i	0.892478	+	0.451091i	$0.148965\pi$
$270$		0			0
$271$	35.9512	+	62.2693i	0.132661	+	0.229776i	0.924702	−	0.380693i	$-0.124314\pi$
$271$	35.9512	+	62.2693i	0.132661	+	0.229776i	−0.792040	+	0.610469i	$0.790981\pi$
$272$		0			0
$273$	12.2150	−	63.4700i	0.0447435	−	0.232491i
$274$		0			0
$275$	−46.4798	−	80.5054i	−0.169017	−	0.292747i
$276$		0			0
$277$	−198.459	−	343.741i	−0.716458	−	1.24094i	−0.962394	−	0.271656i	$-0.912429\pi$
$277$	−198.459	−	343.741i	−0.716458	−	1.24094i	0.245936	−	0.969286i	$-0.420905\pi$
$278$		0			0
$279$	−518.456	+	74.8300i	−1.85827	+	0.268208i
$280$		0			0
$281$		−	469.708i		−	1.67156i	−0.549064	−	0.835780i	$-0.685016\pi$
$281$		−	469.708i		−	1.67156i	0.549064	−	0.835780i	$-0.314984\pi$
$282$		0			0
$283$	−57.0929			−0.201742			−0.100871	−	0.994900i	$-0.532163\pi$
$283$	−57.0929			−0.201742			−0.100871	+	0.994900i	$0.532163\pi$
$284$		0			0
$285$	27.4097	−	23.9460i	0.0961744	−	0.0840210i
$286$		0			0
$287$	112.016	−	64.6726i	0.390300	−	0.225340i
$288$		0			0
$289$	−117.976	+	204.340i	−0.408221	+	0.707060i
$290$		0			0
$291$	25.6578	−	133.320i	0.0881712	−	0.458145i
$292$		0			0
$293$	15.2683	+	8.81513i	0.0521101	+	0.0300858i	0.525829	−	0.850590i	$-0.323755\pi$
$293$	15.2683	+	8.81513i	0.0521101	+	0.0300858i	−0.473719	+	0.880676i	$0.657089\pi$
$294$		0			0
$295$			30.4343i			0.103167i
$296$		0			0
$297$	−4.77324	+	101.949i	−0.0160715	+	0.343263i
$298$		0			0
$299$	66.2814	+	38.2676i	0.221677	+	0.127985i
$300$		0			0
$301$	65.1900			0.216578
$302$		0			0
$303$	−36.7157	−	105.990i	−0.121174	−	0.349802i
$304$		0			0
$305$	44.6920			0.146531
$306$		0			0
$307$	439.762	−	253.897i	1.43245	−	0.827024i	0.435141	−	0.900362i	$-0.356698\pi$
$307$	439.762	−	253.897i	1.43245	−	0.827024i	0.997307	+	0.0733377i	$0.0233651\pi$
$308$		0			0
$309$	62.2814	−	323.619i	0.201558	−	1.04731i
$310$		0			0
$311$	−54.6499	+	94.6565i	−0.175723	+	0.304362i	−0.940411	−	0.340039i	$-0.889560\pi$
$311$	−54.6499	+	94.6565i	−0.175723	+	0.304362i	0.764688	+	0.644401i	$0.222893\pi$
$312$		0			0
$313$	−404.104			−1.29107			−0.645534	−	0.763732i	$-0.723365\pi$
$313$	−404.104			−1.29107			−0.645534	+	0.763732i	$0.723365\pi$
$314$		0			0
$315$	11.9126	+	4.76160i	0.0378179	+	0.0151162i
$316$		0			0
$317$			222.527i			0.701978i	0.936380	+	0.350989i	$0.114155\pi$
$317$			222.527i			0.701978i	−0.936380	+	0.350989i	$0.885845\pi$
$318$		0			0
$319$	99.5844	−	57.4951i	0.312177	−	0.180235i
$320$		0			0
$321$	565.787	−	195.993i	1.76258	−	0.610570i
$322$		0			0
$323$	−267.803	+	343.204i	−0.829112	+	1.06255i
$324$		0			0
$325$	205.545	−	118.672i	0.632447	−	0.365143i
$326$		0			0
$327$	279.870	+	242.376i	0.855871	+	0.741210i
$328$		0			0
$329$	49.6934	+	86.0715i	0.151044	+	0.261615i
$330$		0			0
$331$	114.801	−	66.2803i	0.346830	−	0.200243i	−0.316458	−	0.948607i	$-0.602494\pi$
$331$	114.801	−	66.2803i	0.346830	−	0.200243i	0.663288	+	0.748364i	$0.269160\pi$
$332$		0			0
$333$	71.7072	+	91.0813i	0.215337	+	0.273517i
$334$		0			0
$335$	11.5171	−	6.64938i	0.0343793	−	0.0198489i
$336$		0			0
$337$			190.456i			0.565151i	0.959245	+	0.282576i	$0.0911888\pi$
$337$			190.456i			0.565151i	−0.959245	+	0.282576i	$0.908811\pi$
$338$		0			0
$339$	−92.8626	+	482.522i	−0.273931	+	1.42337i
$340$		0			0
$341$			220.010i			0.645190i
$342$		0			0
$343$	−207.648			−0.605386
$344$		0			0
$345$	−9.94493	+	11.4834i	−0.0288259	+	0.0332851i
$346$		0			0
$347$	−514.114			−1.48160			−0.740799	−	0.671727i	$-0.765553\pi$
$347$	−514.114			−1.48160			−0.740799	+	0.671727i	$0.765553\pi$
$348$		0			0
$349$	280.971	+	486.656i	0.805074	+	1.39443i	0.916241	+	0.400628i	$0.131208\pi$
$349$	280.971	+	486.656i	0.805074	+	1.39443i	−0.111166	+	0.993802i	$0.535459\pi$
$350$		0			0
$351$	−260.295	−	12.1870i	−0.741582	−	0.0347208i
$352$		0			0
$353$	−240.672	−	416.856i	−0.681790	−	1.18090i	−0.974434	−	0.224674i	$-0.927868\pi$
$353$	−240.672	−	416.856i	−0.681790	−	1.18090i	0.292644	−	0.956221i	$-0.405465\pi$
$354$		0			0
$355$	63.7500	−	36.8061i	0.179577	−	0.103679i
$356$		0			0
$357$	−150.678	−	28.9984i	−0.422068	−	0.0812281i
$358$		0			0
$359$	128.660	+	222.846i	0.358386	+	0.620742i	0.987691	−	0.156416i	$-0.0499940\pi$
$359$	128.660	+	222.846i	0.358386	+	0.620742i	−0.629306	+	0.777158i	$0.716661\pi$
$360$		0			0
$361$	−259.375	+	251.089i	−0.718490	+	0.695537i
$362$		0			0
$363$	−314.365	−	60.5005i	−0.866020	−	0.166668i
$364$		0			0
$365$	42.6629	+	73.8943i	0.116885	+	0.202450i
$366$		0			0
$367$	525.453			1.43175			0.715876	−	0.698227i	$-0.246027\pi$
$367$	525.453			1.43175			0.715876	+	0.698227i	$0.246027\pi$
$368$		0			0
$369$	−322.571	−	409.725i	−0.874177	−	1.11037i
$370$		0			0
$371$			39.1262i			0.105461i
$372$		0			0
$373$	221.645	+	127.967i	0.594223	+	0.343075i	0.766766	−	0.641927i	$-0.221865\pi$
$373$	221.645	+	127.967i	0.594223	+	0.343075i	−0.172542	+	0.985002i	$0.555198\pi$
$374$		0			0
$375$	31.0955	+	89.7658i	0.0829214	+	0.239375i
$376$		0			0
$377$	146.796	+	254.258i	0.389379	+	0.674424i
$378$		0			0
$379$			308.432i			0.813806i	0.913471	+	0.406903i	$0.133391\pi$
$379$			308.432i			0.813806i	−0.913471	+	0.406903i	$0.866609\pi$
$380$		0			0
$381$	131.011	−	680.744i	0.343861	−	1.78673i
$382$		0			0
$383$			310.573i			0.810896i	0.914118	+	0.405448i	$0.132885\pi$
$383$			310.573i			0.810896i	−0.914118	+	0.405448i	$0.867115\pi$
$384$		0			0
$385$	2.69412	−	4.66635i	0.00699771	−	0.0121204i
$386$		0			0
$387$	−37.5443	−	260.124i	−0.0970136	−	0.672154i
$388$		0			0
$389$	255.602			0.657075			0.328537	−	0.944491i	$-0.393444\pi$
$389$	255.602			0.657075			0.328537	+	0.944491i	$0.393444\pi$
$390$		0			0
$391$	90.8475	−	157.352i	0.232347	−	0.402436i
$392$		0			0
$393$	133.343	+	384.931i	0.339295	+	0.979469i
$394$		0			0
$395$	8.74160	+	5.04697i	0.0221306	+	0.0127771i
$396$		0			0
$397$	38.6713	+	66.9806i	0.0974087	+	0.168717i	0.910611	−	0.413264i	$-0.135611\pi$
$397$	38.6713	+	66.9806i	0.0974087	+	0.168717i	−0.813203	+	0.581981i	$0.802278\pi$
$398$		0			0
$399$	−120.415	−	41.1298i	−0.301791	−	0.103082i
$400$		0			0
$401$			205.468i			0.512388i	0.966625	+	0.256194i	$0.0824686\pi$
$401$			205.468i			0.512388i	−0.966625	+	0.256194i	$0.917531\pi$
$402$		0			0
$403$	−561.727			−1.39386
$404$		0			0
$405$	12.1392	−	50.2766i	0.0299733	−	0.124140i
$406$		0			0
$407$	42.1644	−	24.3436i	0.103598	−	0.0598124i
$408$		0			0
$409$	117.824	−	68.0258i	0.288079	−	0.166322i	−0.348996	−	0.937124i	$-0.613477\pi$
$409$	117.824	−	68.0258i	0.288079	−	0.166322i	0.637075	+	0.770802i	$0.280144\pi$
$410$		0			0
$411$	97.7785	+	282.264i	0.237904	+	0.686775i
$412$		0			0
$413$	92.1460	−	53.2005i	0.223114	−	0.128815i
$414$		0			0
$415$	30.4326	+	52.7109i	0.0733317	+	0.127014i
$416$		0			0
$417$	−356.074	+	411.157i	−0.853895	+	0.985987i
$418$		0			0
$419$	237.137	−	410.733i	0.565959	−	0.980269i	−0.431001	−	0.902351i	$-0.641839\pi$
$419$	237.137	−	410.733i	0.565959	−	0.980269i	0.996960	−	0.0779180i	$-0.0248272\pi$
$420$		0			0
$421$	−49.9585	−	28.8435i	−0.118666	−	0.0685120i	0.439492	−	0.898246i	$-0.355158\pi$
$421$	−49.9585	−	28.8435i	−0.118666	−	0.0685120i	−0.558158	+	0.829735i	$0.688492\pi$
$422$		0			0
$423$	314.826	−	247.859i	0.744270	−	0.585954i
$424$		0			0
$425$	−281.727	−	487.966i	−0.662887	−	1.14815i
$426$		0			0
$427$	−78.1235	−	135.314i	−0.182959	−	0.316894i
$428$		0			0
$429$	−20.6834	+	107.473i	−0.0482130	+	0.250519i
$430$		0			0
$431$	419.316	+	242.092i	0.972892	+	0.561699i	0.900117	−	0.435649i	$-0.143481\pi$
$431$	419.316	+	242.092i	0.972892	+	0.561699i	0.0727750	+	0.997348i	$0.476815\pi$
$432$		0			0
$433$	−356.336	−	205.731i	−0.822948	−	0.475129i	0.0284841	−	0.999594i	$-0.490932\pi$
$433$	−356.336	−	205.731i	−0.822948	−	0.475129i	−0.851432	+	0.524465i	$0.824265\pi$
$434$		0			0
$435$	−55.0633	+	19.0743i	−0.126582	+	0.0438490i
$436$		0			0
$437$	92.6913	−	118.789i	0.212108	−	0.271828i
$438$		0			0
$439$	−203.451	−	117.462i	−0.463441	−	0.267568i	0.250049	−	0.968233i	$-0.419553\pi$
$439$	−203.451	−	117.462i	−0.463441	−	0.267568i	−0.713490	+	0.700665i	$0.752887\pi$
$440$		0			0
$441$	56.5907	+	392.086i	0.128323	+	0.889083i
$442$		0			0
$443$	403.611			0.911085			0.455542	−	0.890214i	$-0.349445\pi$
$443$	403.611			0.911085			0.455542	+	0.890214i	$0.349445\pi$
$444$		0			0
$445$	−45.2128	−	26.1036i	−0.101602	−	0.0586598i
$446$		0			0
$447$	51.5523	+	148.820i	0.115329	+	0.332930i
$448$		0			0
$449$			300.202i			0.668601i	0.942467	+	0.334300i	$0.108500\pi$
$449$			300.202i			0.668601i	−0.942467	+	0.334300i	$0.891500\pi$
$450$		0			0
$451$	−189.675	+	109.509i	−0.420565	+	0.242813i
$452$		0			0
$453$	583.544	+	505.366i	1.28818	+	1.11560i
$454$		0			0
$455$	11.9141	+	6.87859i	0.0261847	+	0.0151178i
$456$		0			0
$457$	259.933	+	450.217i	0.568781	+	0.985157i	0.996687	+	0.0813338i	$0.0259180\pi$
$457$	259.933	+	450.217i	0.568781	+	0.985157i	−0.427906	+	0.903823i	$0.640749\pi$
$458$		0			0
$459$	−28.9320	+	617.943i	−0.0630326	+	1.34628i
$460$		0			0
$461$	288.327	−	499.397i	0.625438	−	1.08329i	−0.363018	−	0.931782i	$-0.618254\pi$
$461$	288.327	−	499.397i	0.625438	−	1.08329i	0.988456	−	0.151508i	$-0.0484130\pi$
$462$		0			0
$463$	−181.919	+	315.092i	−0.392913	+	0.680545i	−0.992832	−	0.119516i	$-0.961866\pi$
$463$	−181.919	+	315.092i	−0.392913	+	0.680545i	0.599920	+	0.800060i	$0.295199\pi$
$464$		0			0
$465$	21.0707	−	109.485i	0.0453134	−	0.235452i
$466$		0			0
$467$	405.084			0.867419			0.433709	−	0.901053i	$-0.357204\pi$
$467$	405.084			0.867419			0.433709	+	0.901053i	$0.357204\pi$
$468$		0			0
$469$	−40.2646	−	23.2468i	−0.0858521	−	0.0495667i
$470$		0			0
$471$	39.5225	+	114.093i	0.0839119	+	0.242235i
$472$		0			0
$473$	−110.385			−0.233372
$474$		0			0
$475$	−175.301	−	433.123i	−0.369054	−	0.911837i
$476$		0			0
$477$	156.123	−	22.5336i	0.327301	−	0.0472402i
$478$		0			0
$479$	−658.757			−1.37528			−0.687638	−	0.726054i	$-0.741352\pi$
$479$	−658.757			−1.37528			−0.687638	+	0.726054i	$0.741352\pi$
$480$		0			0
$481$	62.1539	+	107.654i	0.129218	+	0.223812i
$482$		0			0
$483$	52.1523	+	10.0369i	0.107976	+	0.0207803i
$484$		0			0
$485$	25.0257	+	14.4486i	0.0515995	+	0.0297910i
$486$		0			0
$487$			176.762i			0.362961i	0.983395	+	0.181480i	$0.0580889\pi$
$487$			176.762i			0.362961i	−0.983395	+	0.181480i	$0.941911\pi$
$488$		0			0
$489$	14.5507	+	42.0047i	0.0297561	+	0.0858992i
$490$		0			0
$491$	600.529			1.22307			0.611537	−	0.791216i	$-0.290552\pi$
$491$	600.529			1.22307			0.611537	+	0.791216i	$0.290552\pi$
$492$		0			0
$493$	603.609	−	348.494i	1.22436	−	0.706884i
$494$		0			0
$495$	−20.1714	−	8.06272i	−0.0407504	−	0.0162883i
$496$		0			0
$497$	−222.876	−	128.677i	−0.448442	−	0.258908i
$498$		0			0
$499$	4.14047			0.00829753			0.00414876	−	0.999991i	$-0.498679\pi$
$499$	4.14047			0.00829753			0.00414876	+	0.999991i	$0.498679\pi$
$500$		0			0
$501$	741.645	+	642.286i	1.48033	+	1.28201i
$502$		0			0
$503$	199.290	−	345.180i	0.396203	−	0.686243i	−0.597051	−	0.802203i	$-0.703661\pi$
$503$	199.290	−	345.180i	0.396203	−	0.686243i	0.993254	+	0.115960i	$0.0369944\pi$
$504$		0			0
$505$	23.8746			0.0472765
$506$		0			0
$507$	223.466	+	43.0067i	0.440762	+	0.0848259i
$508$		0			0
$509$	299.105	−	172.688i	0.587633	−	0.339270i	−0.176528	−	0.984296i	$-0.556487\pi$
$509$	299.105	−	172.688i	0.587633	−	0.339270i	0.764161	+	0.645026i	$0.223153\pi$
$510$		0			0
$511$	149.153	−	258.341i	0.291885	−	0.505560i
$512$		0			0
$513$	−94.7685	+	504.171i	−0.184734	+	0.982789i
$514$		0			0
$515$	60.7470	+	35.0723i	0.117955	+	0.0681016i
$516$		0			0
$517$	−84.1448	−	145.743i	−0.162756	−	0.281902i
$518$		0			0
$519$	−97.4940	+	506.587i	−0.187850	+	0.976083i
$520$		0			0
$521$			828.985i			1.59114i	0.605861	+	0.795571i	$0.292829\pi$
$521$			828.985i			1.59114i	−0.605861	+	0.795571i	$0.707171\pi$
$522$		0			0
$523$	16.3065	+	9.41456i	0.0311788	+	0.0180011i	0.515508	−	0.856885i	$-0.327603\pi$
$523$	16.3065	+	9.41456i	0.0311788	+	0.0180011i	−0.484330	+	0.874886i	$0.660936\pi$
$524$		0			0
$525$	107.820	−	124.499i	0.205372	−	0.237141i
$526$		0			0
$527$			1333.54i			2.53044i
$528$		0			0
$529$	233.056	−	403.665i	0.440560	−	0.763072i
$530$		0			0
$531$	−265.352	−	337.045i	−0.499720	−	0.634737i
$532$		0			0
$533$	−279.596	−	484.275i	−0.524571	−	0.908584i
$534$		0			0
$535$			127.446i			0.238216i
$536$		0			0
$537$	−719.577	+	249.267i	−1.33999	+	0.464184i
$538$		0			0
$539$	166.384			0.308690
$540$		0			0
$541$	267.260	−	462.908i	0.494011	−	0.855652i	−0.505965	−	0.862554i	$-0.668864\pi$
$541$	267.260	−	462.908i	0.494011	−	0.855652i	0.999976	+	0.00690205i	$0.00219701\pi$
$542$		0			0
$543$	126.710	−	658.396i	0.233352	−	1.21252i
$544$		0			0
$545$	−68.2448	+	39.4012i	−0.125220	+	0.0722957i
$546$		0			0
$547$			229.299i			0.419195i	0.977788	+	0.209597i	$0.0672153\pi$
$547$			229.299i			0.419195i	−0.977788	+	0.209597i	$0.932785\pi$
$548$		0			0
$549$	−494.942	+	389.661i	−0.901533	+	0.709766i
$550$		0			0
$551$	535.769	−	216.846i	0.972357	−	0.393549i
$552$		0			0
$553$		−	35.2893i		−	0.0638142i
$554$		0			0
$555$	−23.3140	+	8.07615i	−0.0420072	+	0.0145516i
$556$		0			0
$557$	5.22291	−	9.04635i	0.00937686	−	0.0162412i	−0.861299	−	0.508099i	$-0.830349\pi$
$557$	5.22291	−	9.04635i	0.00937686	−	0.0162412i	0.870676	+	0.491857i	$0.163682\pi$
$558$		0			0
$559$		−	281.833i		−	0.504174i
$560$		0			0
$561$	255.140	+	49.1025i	0.454796	+	0.0875267i
$562$		0			0
$563$	542.443	+	313.179i	0.963486	+	0.556269i	0.897244	−	0.441535i	$-0.145566\pi$
$563$	542.443	+	313.179i	0.963486	+	0.556269i	0.0662420	+	0.997804i	$0.478899\pi$
$564$		0			0
$565$	−90.5749	−	52.2935i	−0.160310	−	0.0925548i
$566$		0			0
$567$	−173.442	+	51.1318i	−0.305895	+	0.0901796i
$568$		0			0
$569$	−358.551	+	207.010i	−0.630143	+	0.363813i	−0.780807	−	0.624772i	$-0.785192\pi$
$569$	−358.551	+	207.010i	−0.630143	+	0.363813i	0.150665	+	0.988585i	$0.451859\pi$
$570$		0			0
$571$	472.543	−	818.468i	0.827571	−	1.43339i	−0.0723676	−	0.997378i	$-0.523055\pi$
$571$	472.543	−	818.468i	0.827571	−	1.43339i	0.899939	−	0.436017i	$-0.143611\pi$
$572$		0			0
$573$	241.136	−	278.439i	0.420832	−	0.485932i
$574$		0			0
$575$	97.5106	+	168.893i	0.169584	+	0.293728i
$576$		0			0
$577$	−789.998			−1.36915			−0.684573	−	0.728944i	$-0.740012\pi$
$577$	−789.998			−1.36915			−0.684573	+	0.728944i	$0.740012\pi$
$578$		0			0
$579$	589.101	−	204.069i	1.01745	−	0.352451i
$580$		0			0
$581$	106.395	−	184.282i	0.183124	−	0.317181i
$582$		0			0
$583$		−	66.2516i		−	0.113639i
$584$		0			0
$585$	20.5856	−	51.5014i	0.0351891	−	0.0880366i
$586$		0			0
$587$	570.696	−	988.475i	0.972225	−	1.68394i	0.283422	−	0.958995i	$-0.408530\pi$
$587$	570.696	−	988.475i	0.972225	−	1.68394i	0.688803	−	0.724948i	$-0.258136\pi$
$588$		0			0
$589$	−153.237	+	1095.19i	−0.260165	+	1.85941i
$590$		0			0
$591$	71.4736	+	206.328i	0.120937	+	0.349117i
$592$		0			0
$593$	168.444	−	291.754i	0.284054	−	0.491996i	−0.688325	−	0.725402i	$-0.741654\pi$
$593$	168.444	−	291.754i	0.284054	−	0.491996i	0.972379	+	0.233406i	$0.0749872\pi$
$594$		0			0
$595$	16.3298	−	28.2840i	0.0274450	−	0.0475362i
$596$		0			0
$597$	−167.825	−	32.2984i	−0.281114	−	0.0541011i
$598$		0			0
$599$	173.985	−	100.450i	0.290458	−	0.167696i	−0.347690	−	0.937609i	$-0.613034\pi$
$599$	173.985	−	100.450i	0.290458	−	0.167696i	0.638149	+	0.769913i	$0.279701\pi$
$600$		0			0
$601$	−185.853	+	107.302i	−0.309239	+	0.178539i	−0.646586	−	0.762841i	$-0.723804\pi$
$601$	−185.853	+	107.302i	−0.309239	+	0.178539i	0.337347	+	0.941380i	$0.390471\pi$
$602$		0			0
$603$	−69.5710	+	174.054i	−0.115375	+	0.288646i
$604$		0			0
$605$	34.0694	−	59.0100i	0.0563131	−	0.0975372i
$606$		0			0
$607$	−467.695	−	270.024i	−0.770502	−	0.444850i	0.0625515	−	0.998042i	$-0.480076\pi$
$607$	−467.695	−	270.024i	−0.770502	−	0.444850i	−0.833054	+	0.553192i	$0.813410\pi$
$608$		0			0
$609$	154.004	+	133.372i	0.252881	+	0.219002i
$610$		0			0
$611$	372.109	−	214.837i	0.609017	−	0.351616i
$612$		0			0
$613$	−411.679	−	713.048i	−0.671580	−	1.16321i	−0.977456	−	0.211139i	$-0.932283\pi$
$613$	−411.679	−	713.048i	−0.671580	−	1.16321i	0.305876	−	0.952071i	$-0.401051\pi$
$614$		0			0
$615$	104.877	−	36.3302i	0.170532	−	0.0590735i
$616$		0			0
$617$	−387.197	−	670.644i	−0.627547	−	1.08694i	−0.988042	−	0.154182i	$-0.950726\pi$
$617$	−387.197	−	670.644i	−0.627547	−	1.08694i	0.360495	−	0.932761i	$-0.382608\pi$
$618$		0			0
$619$	−187.199	−	324.238i	−0.302421	−	0.523809i	0.674263	−	0.738492i	$-0.264462\pi$
$619$	−187.199	−	324.238i	−0.302421	−	0.523809i	−0.976684	+	0.214683i	$0.931128\pi$
$620$		0			0
$621$	10.0139	−	213.881i	0.0161254	−	0.344413i
$622$		0			0
$623$			182.521i			0.292971i
$624$		0			0
$625$	594.587			0.951339
$626$		0			0
$627$	203.896	+	69.6443i	0.325193	+	0.111075i
$628$		0			0
$629$	255.570	−	147.554i	0.406312	−	0.234585i
$630$		0			0
$631$	501.168	−	868.048i	0.794243	−	1.37567i	−0.129075	−	0.991635i	$-0.541201\pi$
$631$	501.168	−	868.048i	0.794243	−	1.37567i	0.923318	−	0.384035i	$-0.125466\pi$
$632$		0			0
$633$	97.4472	−	33.7564i	0.153945	−	0.0533277i
$634$		0			0
$635$	127.783	+	73.7758i	0.201234	+	0.116182i
$636$		0			0
$637$			424.809i			0.666890i
$638$		0			0
$639$	−385.094	+	963.435i	−0.602652	+	1.50772i
$640$		0			0
$641$	−171.882	−	99.2360i	−0.268146	−	0.154814i	0.359899	−	0.932991i	$-0.382811\pi$
$641$	−171.882	−	99.2360i	−0.268146	−	0.154814i	−0.628045	+	0.778177i	$0.716145\pi$
$642$		0			0
$643$	−118.658			−0.184539			−0.0922693	−	0.995734i	$-0.529412\pi$
$643$	−118.658			−0.184539			−0.0922693	+	0.995734i	$0.529412\pi$
$644$		0			0
$645$	54.9317	+	10.5717i	0.0851654	+	0.0163903i
$646$		0			0
$647$	736.989			1.13909			0.569543	−	0.821962i	$-0.307120\pi$
$647$	736.989			1.13909			0.569543	+	0.821962i	$0.307120\pi$
$648$		0			0
$649$	−156.029	+	90.0834i	−0.240415	+	0.138803i
$650$		0			0
$651$	−368.321	+	127.589i	−0.565777	+	0.195989i
$652$		0			0
$653$	5.46359	−	9.46322i	0.00836691	−	0.0144919i	−0.861812	−	0.507228i	$-0.830670\pi$
$653$	5.46359	−	9.46322i	0.00836691	−	0.0144919i	0.870179	+	0.492737i	$0.164003\pi$
$654$		0			0
$655$	−86.7071			−0.132377
$656$		0			0
$657$	−1116.74	−	446.373i	−1.69976	−	0.679411i
$658$		0			0
$659$		−	208.467i		−	0.316338i	−0.987412	−	0.158169i	$-0.949441\pi$
$659$		−	208.467i		−	0.316338i	0.987412	−	0.158169i	$-0.0505590\pi$
$660$		0			0
$661$	−1078.93	+	622.922i	−1.63227	+	0.942394i	−0.648885	+	0.760887i	$0.724764\pi$
$661$	−1078.93	+	622.922i	−1.63227	+	0.942394i	−0.983390	+	0.181507i	$0.941902\pi$
$662$		0			0
$663$	−125.368	+	651.421i	−0.189092	+	0.982536i
$664$		0			0
$665$	16.6612	−	21.3523i	0.0250545	−	0.0321087i
$666$		0			0
$667$	−208.920	+	120.620i	−0.313223	+	0.180839i
$668$		0			0
$669$	153.326	−	796.696i	0.229187	−	1.19088i
$670$		0			0
$671$	132.285	+	229.124i	0.197146	+	0.341467i
$672$		0			0
$673$	139.585	−	80.5897i	0.207408	−	0.119747i	−0.392698	−	0.919667i	$-0.628458\pi$
$673$	139.585	−	80.5897i	0.207408	−	0.119747i	0.600106	+	0.799920i	$0.295125\pi$
$674$		0			0
$675$	−558.877	−	358.526i	−0.827966	−	0.531150i
$676$		0			0
$677$	429.929	−	248.220i	0.635050	−	0.366646i	−0.147655	−	0.989039i	$-0.547173\pi$
$677$	429.929	−	248.220i	0.635050	−	0.366646i	0.782705	+	0.622393i	$0.213839\pi$
$678$		0			0
$679$		−	101.027i		−	0.148788i
$680$		0			0
$681$	302.781	+	262.217i	0.444612	+	0.385047i
$682$		0			0
$683$			207.417i			0.303685i	0.988405	+	0.151842i	$0.0485206\pi$
$683$			207.417i			0.303685i	−0.988405	+	0.151842i	$0.951479\pi$
$684$		0			0
$685$	−63.5811			−0.0928191
$686$		0			0
$687$	−399.000	−	76.7887i	−0.580787	−	0.111774i
$688$		0			0
$689$	169.153			0.245505
$690$		0			0
$691$	−204.703	−	354.556i	−0.296241	−	0.513105i	0.679032	−	0.734109i	$-0.262400\pi$
$691$	−204.703	−	354.556i	−0.296241	−	0.513105i	−0.975273	+	0.221004i	$0.929067\pi$
$692$		0			0
$693$	10.8490	+	75.1671i	0.0156552	+	0.108466i
$694$		0			0
$695$	−57.8843	−	100.258i	−0.0832867	−	0.144257i
$696$		0			0
$697$	−1149.67	+	663.764i	−1.64946	+	0.952315i
$698$		0			0
$699$	−195.618	+	225.879i	−0.279854	+	0.323146i
$700$		0			0
$701$	92.2392	+	159.763i	0.131582	+	0.227907i	0.924287	−	0.381699i	$-0.124661\pi$
$701$	92.2392	+	159.763i	0.131582	+	0.227907i	−0.792704	+	0.609606i	$0.791328\pi$
$702$		0			0
$703$	226.847	−	91.8133i	0.322684	−	0.130602i
$704$		0			0
$705$	27.9155	+	80.5859i	0.0395965	+	0.114306i
$706$		0			0
$707$	−41.7339	−	72.2853i	−0.0590296	−	0.102242i
$708$		0			0
$709$	−344.376			−0.485721			−0.242860	−	0.970061i	$-0.578086\pi$
$709$	−344.376			−0.485721			−0.242860	+	0.970061i	$0.578086\pi$
$710$		0			0
$711$	−140.813	+	20.3238i	−0.198049	+	0.0285848i
$712$		0			0
$713$		−	461.562i		−	0.647352i
$714$		0			0
$715$	−20.1738	−	11.6474i	−0.0282152	−	0.0162900i
$716$		0			0
$717$	1150.10	+	221.340i	1.60405	+	0.308703i
$718$		0			0
$719$	497.985	+	862.536i	0.692608	+	1.19963i	0.970980	+	0.239159i	$0.0768717\pi$
$719$	497.985	+	862.536i	0.692608	+	1.19963i	−0.278372	+	0.960473i	$0.589795\pi$
$720$		0			0
$721$		−	245.232i		−	0.340127i
$722$		0			0
$723$	−125.963	+	43.6345i	−0.174223	+	0.0603520i
$724$		0			0
$725$			748.108i			1.03187i
$726$		0			0
$727$	360.574	−	624.532i	0.495975	−	0.859054i	−0.504014	−	0.863695i	$-0.668144\pi$
$727$	360.574	−	624.532i	0.495975	−	0.859054i	0.999989	+	0.00464126i	$0.00147737\pi$
$728$		0			0
$729$	303.917	+	662.628i	0.416896	+	0.908954i
$730$		0			0
$731$	−669.074			−0.915286
$732$		0			0
$733$	−345.666	+	598.710i	−0.471576	+	0.816794i	−0.999471	−	0.0325154i	$-0.989648\pi$
$733$	−345.666	+	598.710i	−0.471576	+	0.816794i	0.527895	+	0.849310i	$0.322982\pi$
$734$		0			0
$735$	−82.7988	−	15.9348i	−0.112651	−	0.0216801i
$736$		0			0
$737$	68.1793	+	39.3633i	0.0925092	+	0.0534102i
$738$		0			0
$739$	64.0868	+	111.002i	0.0867210	+	0.150205i	0.906123	−	0.423014i	$-0.139028\pi$
$739$	64.0868	+	111.002i	0.0867210	+	0.150205i	−0.819402	+	0.573219i	$0.805694\pi$
$740$		0			0
$741$	−177.815	+	520.584i	−0.239966	+	0.702542i
$742$		0			0
$743$		−	1191.99i		−	1.60430i	−0.597124	−	0.802149i	$-0.703690\pi$
$743$		−	1191.99i		−	1.60430i	0.597124	−	0.802149i	$-0.296310\pi$
$744$		0			0
$745$	−33.5222			−0.0449962
$746$		0			0
$747$	−796.604	−	318.410i	−1.06640	−	0.426252i
$748$		0			0
$749$	385.867	−	222.781i	0.515176	−	0.297437i
$750$		0			0
$751$	935.070	−	539.863i	1.24510	−	0.718859i	0.274972	−	0.961452i	$-0.411331\pi$
$751$	935.070	−	539.863i	1.24510	−	0.718859i	0.970128	+	0.242594i	$0.0779982\pi$
$752$		0			0
$753$	−1275.97	−	245.564i	−1.69452	−	0.326114i
$754$		0			0
$755$	−142.294	+	82.1536i	−0.188469	+	0.108813i
$756$		0			0
$757$	197.525	+	342.123i	0.260931	+	0.451946i	0.966490	−	0.256706i	$-0.0826371\pi$
$757$	197.525	+	342.123i	0.260931	+	0.451946i	−0.705558	+	0.708652i	$0.749304\pi$
$758$		0			0
$759$	−88.3085	−	16.9952i	−0.116348	−	0.0223916i
$760$		0			0
$761$	−234.981	+	407.000i	−0.308780	+	0.534822i	−0.978096	−	0.208156i	$-0.933254\pi$
$761$	−234.981	+	407.000i	−0.308780	+	0.534822i	0.669316	+	0.742978i	$0.266587\pi$
$762$		0			0
$763$	238.590	+	137.750i	0.312700	+	0.180537i
$764$		0			0
$765$	−122.265	−	48.8704i	−0.159823	−	0.0638829i
$766$		0			0
$767$	−230.000	−	398.371i	−0.299869	−	0.519389i
$768$		0			0
$769$	−111.660	−	193.400i	−0.145201	−	0.251496i	0.784247	−	0.620449i	$-0.213050\pi$
$769$	−111.660	−	193.400i	−0.145201	−	0.251496i	−0.929448	+	0.368953i	$0.879716\pi$
$770$		0			0
$771$	223.091	+	193.203i	0.289352	+	0.250588i
$772$		0			0
$773$	−691.069	−	398.989i	−0.894009	−	0.516156i	−0.0187574	−	0.999824i	$-0.505971\pi$
$773$	−691.069	−	398.989i	−0.894009	−	0.516156i	−0.875252	+	0.483668i	$0.839304\pi$
$774$		0			0
$775$	−1239.58	−	715.675i	−1.59946	−	0.923451i
$776$		0			0
$777$	65.2061	+	56.4704i	0.0839203	+	0.0726775i
$778$		0			0
$779$	−1020.46	+	413.018i	−1.30996	+	0.530190i
$780$		0			0
$781$	377.391	+	217.887i	0.483215	+	0.278984i
$782$		0			0
$783$	443.493	−	691.326i	0.566403	−	0.882920i
$784$		0			0
$785$	−25.6998			−0.0327386
$786$		0			0
$787$	−712.779	−	411.523i	−0.905691	−	0.522901i	−0.0266488	−	0.999645i	$-0.508484\pi$
$787$	−712.779	−	411.523i	−0.905691	−	0.522901i	−0.879042	+	0.476744i	$0.841817\pi$
$788$		0			0
$789$	377.570	+	72.6644i	0.478543	+	0.0920969i
$790$		0			0
$791$			365.645i			0.462257i
$792$		0			0
$793$	−584.997	+	337.748i	−0.737701	+	0.425912i
$794$		0			0
$795$	−6.34502	+	32.9692i	−0.00798116	+	0.0414708i
$796$		0			0
$797$	−1071.45	−	618.604i	−1.34436	−	0.776166i	−0.356915	−	0.934137i	$-0.616171\pi$
$797$	−1071.45	−	618.604i	−1.34436	−	0.776166i	−0.987444	+	0.157971i	$0.949505\pi$
$798$		0			0
$799$	−510.025	−	883.390i	−0.638330	−	1.10562i
$800$		0			0
$801$	728.303	−	105.118i	0.909242	−	0.131233i
$802$		0			0
$803$	−252.558	+	437.444i	−0.314518	+	0.544762i
$804$		0			0
$805$	−5.65203	+	9.78960i	−0.00702115	+	0.0121610i
$806$		0			0
$807$	−667.819	−	578.351i	−0.827533	−	0.716669i
$808$		0			0
$809$	−676.586			−0.836323			−0.418162	−	0.908373i	$-0.637325\pi$
$809$	−676.586			−0.836323			−0.418162	+	0.908373i	$0.637325\pi$
$810$		0			0
$811$	367.503	+	212.178i	0.453148	+	0.261625i	0.709159	−	0.705049i	$-0.249075\pi$
$811$	367.503	+	212.178i	0.453148	+	0.261625i	−0.256011	+	0.966674i	$0.582408\pi$
$812$		0			0
$813$	141.214	−	163.059i	0.173695	−	0.200564i
$814$		0			0
$815$	−9.46171			−0.0116095
$816$		0			0
$817$	−549.488	−	76.8832i	−0.672568	−	0.0941042i
$818$		0			0
$819$	−191.916	+	27.6996i	−0.234329	+	0.0338213i
$820$		0			0
$821$	−902.886			−1.09974			−0.549869	−	0.835251i	$-0.685323\pi$
$821$	−902.886			−1.09974			−0.549869	+	0.835251i	$0.685323\pi$
$822$		0			0
$823$	−384.377	−	665.761i	−0.467044	−	0.808944i	0.532247	−	0.846589i	$-0.321348\pi$
$823$	−384.377	−	665.761i	−0.467044	−	0.808944i	−0.999291	+	0.0376449i	$0.988014\pi$
$824$		0			0
$825$	−182.570	+	210.812i	−0.221296	+	0.255530i
$826$		0			0
$827$	843.004	+	486.708i	1.01935	+	0.588523i	0.913916	−	0.405903i	$-0.133043\pi$
$827$	843.004	+	486.708i	1.01935	+	0.588523i	0.105435	+	0.994426i	$0.466376\pi$
$828$		0			0
$829$		−	961.753i		−	1.16014i	−0.814568	−	0.580068i	$-0.803026\pi$
$829$		−	961.753i		−	1.16014i	0.814568	−	0.580068i	$-0.196974\pi$
$830$		0			0
$831$	−779.533	+	900.123i	−0.938067	+	1.08318i
$832$		0			0
$833$	1008.50			1.21068
$834$		0			0
$835$	−180.846	+	104.412i	−0.216582	+	0.125044i
$836$		0			0
$837$	721.234	+	1396.21i	0.861689	+	1.66811i
$838$		0			0
$839$	−35.0787	−	20.2527i	−0.0418102	−	0.0241391i	0.478949	−	0.877843i	$-0.341018\pi$
$839$	−35.0787	−	20.2527i	−0.0418102	−	0.0241391i	−0.520759	+	0.853703i	$0.674351\pi$
$840$		0			0
$841$	−84.4027			−0.100360
$842$		0			0
$843$	−1331.50	+	461.241i	−1.57948	+	0.547142i
$844$		0			0
$845$	−24.2182	+	41.9472i	−0.0286606	+	0.0496417i
$846$		0			0
$847$	−238.220			−0.281251
$848$		0			0
$849$	56.0637	+	161.843i	0.0660349	+	0.190628i
$850$		0			0
$851$	−88.4574	+	51.0709i	−0.103945	+	0.0600128i
$852$		0			0
$853$	−21.8810	+	37.8991i	−0.0256519	+	0.0444303i	−0.878566	−	0.477620i	$-0.841499\pi$
$853$	−21.8810	+	37.8991i	−0.0256519	+	0.0444303i	0.852914	+	0.522051i	$0.174833\pi$
$854$		0			0
$855$	−94.7961	−	54.1850i	−0.110873	−	0.0633743i
$856$		0			0
$857$	487.922	+	281.702i	0.569338	+	0.328707i	0.756885	−	0.653548i	$-0.226720\pi$
$857$	487.922	+	281.702i	0.569338	+	0.328707i	−0.187547	+	0.982256i	$0.560054\pi$
$858$		0			0
$859$	−178.202	−	308.654i	−0.207452	−	0.359318i	0.743459	−	0.668782i	$-0.233184\pi$
$859$	−178.202	−	308.654i	−0.207452	−	0.359318i	−0.950911	+	0.309464i	$0.899851\pi$
$860$		0			0
$861$	−293.327	−	254.030i	−0.340681	−	0.295040i
$862$		0			0
$863$		−	633.593i		−	0.734175i	−0.930186	−	0.367088i	$-0.880355\pi$
$863$		−	633.593i		−	0.734175i	0.930186	−	0.367088i	$-0.119645\pi$
$864$		0			0
$865$	−95.0922	−	54.9015i	−0.109933	−	0.0634700i
$866$		0			0
$867$	695.100	+	133.774i	0.801731	+	0.154295i
$868$		0			0
$869$			59.7546i			0.0687625i
$870$		0			0
$871$	−100.502	+	174.075i	−0.115387	+	0.199856i
$872$		0			0
$873$	−403.123	+	58.1837i	−0.461767	+	0.0666480i
$874$		0			0
$875$	35.3456	+	61.2203i	0.0403949	+	0.0699661i
$876$		0			0
$877$		−	751.503i		−	0.856903i	−0.903565	−	0.428451i	$-0.859059\pi$
$877$		−	751.503i		−	0.856903i	0.903565	−	0.428451i	$-0.140941\pi$
$878$		0			0
$879$	9.99555	−	51.9377i	0.0113715	−	0.0590872i
$880$		0			0
$881$	1433.27			1.62687			0.813436	−	0.581655i	$-0.197595\pi$
$881$	1433.27			1.62687			0.813436	+	0.581655i	$0.197595\pi$
$882$		0			0
$883$	280.948	−	486.617i	0.318175	−	0.551095i	−0.661932	−	0.749564i	$-0.730263\pi$
$883$	280.948	−	486.617i	0.318175	−	0.551095i	0.980107	+	0.198468i	$0.0635967\pi$
$884$		0			0
$885$	86.2733	−	29.8857i	0.0974839	−	0.0337691i
$886$		0			0
$887$	−366.194	+	211.422i	−0.412845	+	0.238356i	−0.692012	−	0.721886i	$-0.743275\pi$
$887$	−366.194	+	211.422i	−0.412845	+	0.238356i	0.279166	+	0.960243i	$0.409942\pi$
$888$		0			0
$889$		−	515.853i		−	0.580263i
$890$		0			0
$891$	293.686	−	86.5805i	0.329614	−	0.0971723i
$892$		0			0
$893$	−317.356	−	784.105i	−0.355382	−	0.878057i
$894$		0			0
$895$		−	162.087i		−	0.181103i
$896$		0			0
$897$	43.3920	−	225.468i	0.0483745	−	0.251358i
$898$		0			0
$899$	885.283	−	1533.36i	0.984742	−	1.70562i
$900$		0			0
$901$		−	401.569i		−	0.445693i
$902$		0			0
$903$	−64.0149	−	184.797i	−0.0708913	−	0.204647i
$904$		0			0
$905$	123.589	+	71.3539i	0.136562	+	0.0788441i
$906$		0			0
$907$	604.129	+	348.794i	0.666074	+	0.384558i	0.794587	−	0.607150i	$-0.207687\pi$
$907$	604.129	+	348.794i	0.666074	+	0.384558i	−0.128514	+	0.991708i	$0.541021\pi$
$908$		0			0
$909$	−264.400	+	208.159i	−0.290869	+	0.228998i
$910$		0			0
$911$	1344.62	−	776.316i	1.47598	−	0.852158i	0.476348	−	0.879257i	$-0.341960\pi$
$911$	1344.62	−	776.316i	1.47598	−	0.852158i	0.999633	+	0.0270991i	$0.00862697\pi$
$912$		0			0
$913$	−180.157	+	312.041i	−0.197324	+	0.341775i
$914$		0			0
$915$	−43.8863	−	126.690i	−0.0479632	−	0.138459i
$916$		0			0
$917$	151.568	+	262.523i	0.165287	+	0.286285i
$918$		0			0
$919$	−747.802			−0.813713			−0.406857	−	0.913492i	$-0.633375\pi$
$919$	−747.802			−0.813713			−0.406857	+	0.913492i	$0.633375\pi$
$920$		0			0
$921$	−1151.56	−	997.289i	−1.25034	−	1.08283i
$922$		0			0
$923$	−556.306	+	963.550i	−0.602715	+	1.04393i
$924$		0			0
$925$			316.752i			0.342434i
$926$		0			0
$927$	−978.533	+	141.234i	−1.05559	+	0.152356i
$928$		0			0
$929$	−314.783	+	545.221i	−0.338841	+	0.586890i	−0.984215	−	0.176977i	$-0.943368\pi$
$929$	−314.783	+	545.221i	−0.338841	+	0.586890i	0.645374	+	0.763867i	$0.276702\pi$
$930$		0			0
$931$	828.246	+	115.886i	0.889630	+	0.124475i
$932$		0			0
$933$	321.991	+	61.9680i	0.345113	+	0.0664180i
$934$		0			0
$935$	−27.6509	+	47.8928i	−0.0295732	+	0.0512222i
$936$		0			0
$937$	−277.515	+	480.671i	−0.296174	+	0.512989i	−0.975257	−	0.221073i	$-0.929044\pi$
$937$	−277.515	+	480.671i	−0.296174	+	0.512989i	0.679083	+	0.734061i	$0.262378\pi$
$938$		0			0
$939$	396.819	+	1145.53i	0.422598	+	1.21995i
$940$		0			0
$941$	826.899	−	477.410i	0.878745	−	0.507344i	0.00850049	−	0.999964i	$-0.497294\pi$
$941$	826.899	−	477.410i	0.878745	−	0.507344i	0.870244	+	0.492620i	$0.163961\pi$
$942$		0			0
$943$	397.922	−	229.740i	0.421974	−	0.243627i
$944$		0			0
$945$	1.79999	−	38.4450i	0.00190475	−	0.0406825i
$946$		0			0
$947$	459.107	−	795.196i	0.484801	−	0.839700i	−0.515046	−	0.857162i	$-0.672225\pi$
$947$	459.107	−	795.196i	0.484801	−	0.839700i	0.999848	+	0.0174621i	$0.00555865\pi$
$948$		0			0
$949$	−1116.88	−	644.828i	−1.17690	−	0.679482i
$950$		0			0
$951$	630.806	−	218.516i	0.663308	−	0.229775i
$952$		0			0
$953$	−1540.87	+	889.619i	−1.61686	+	0.933493i	−0.629131	+	0.777299i	$0.716589\pi$
$953$	−1540.87	+	889.619i	−1.61686	+	0.933493i	−0.987726	+	0.156194i	$0.950077\pi$
$954$		0			0
$955$	39.1997	+	67.8959i	0.0410468	+	0.0710952i
$956$		0			0
$957$	−260.773	−	225.837i	−0.272490	−	0.235984i
$958$		0			0
$959$	111.143	+	192.505i	0.115894	+	0.200735i
$960$		0			0
$961$	1213.31	+	2101.51i	1.26255	+	2.18679i
$962$		0			0
$963$	−1111.18	−	1411.40i	−1.15387	−	1.46563i
$964$		0			0
$965$			132.697i			0.137510i
$966$		0			0
$967$	953.581			0.986123			0.493061	−	0.869995i	$-0.335878\pi$
$967$	953.581			0.986123			0.493061	+	0.869995i	$0.335878\pi$
$968$		0			0
$969$	1235.87	+	422.134i	1.27541	+	0.435638i
$970$		0			0
$971$	170.348	−	98.3506i	0.175436	−	0.101288i	−0.409711	−	0.912216i	$-0.634370\pi$
$971$	170.348	−	98.3506i	0.175436	−	0.101288i	0.585146	+	0.810928i	$0.301037\pi$
$972$		0			0
$973$	−202.368	+	350.512i	−0.207984	+	0.360239i
$974$		0			0
$975$	−538.243	−	466.134i	−0.552044	−	0.478086i
$976$		0			0
$977$	675.011	+	389.718i	0.690901	+	0.398892i	0.803950	−	0.594697i	$-0.202728\pi$
$977$	675.011	+	389.718i	0.690901	+	0.398892i	−0.113048	+	0.993589i	$0.536061\pi$
$978$		0			0
$979$		−	309.059i		−	0.315689i
$980$		0			0
$981$	412.246	−	1031.36i	0.420231	−	1.05134i
$982$		0			0
$983$	−913.504	−	527.412i	−0.929302	−	0.536533i	−0.0427115	−	0.999087i	$-0.513600\pi$
$983$	−913.504	−	527.412i	−0.929302	−	0.536533i	−0.886591	+	0.462555i	$0.846933\pi$
$984$		0			0
$985$	−46.4762			−0.0471839
$986$		0			0
$987$	195.192	−	225.388i	0.197763	−	0.228356i
$988$		0			0
$989$	231.578			0.234154
$990$		0			0
$991$	377.160	−	217.754i	0.380585	−	0.219731i	−0.297487	−	0.954726i	$-0.596149\pi$
$991$	377.160	−	217.754i	0.380585	−	0.219731i	0.678073	+	0.734995i	$0.262815\pi$
$992$		0			0
$993$	−300.618	−	260.345i	−0.302738	−	0.262180i
$994$		0			0
$995$	18.1881	−	31.5027i	0.0182795	−	0.0316610i
$996$		0			0
$997$	1275.02			1.27885			0.639426	−	0.768852i	$-0.279172\pi$
$997$	1275.02			1.27885			0.639426	+	0.768852i	$0.279172\pi$
$998$		0			0
$999$	187.777	−	292.710i	0.187965	−	0.293003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.bl.a.373.17	yes	80
3.2	odd	2		2052.3.bl.a.145.18		80
9.2	odd	6		2052.3.s.a.829.23		80
9.7	even	3		684.3.s.a.601.30	yes	80
19.8	odd	6		684.3.s.a.445.30	✓	80
57.8	even	6		2052.3.s.a.901.23		80
171.65	even	6		2052.3.bl.a.1585.18		80
171.160	odd	6	inner	684.3.bl.a.673.17	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.30	✓	80	19.8	odd	6
684.3.s.a.601.30	yes	80	9.7	even	3
684.3.bl.a.373.17	yes	80	1.1	even	1	trivial
684.3.bl.a.673.17	yes	80	171.160	odd	6	inner
2052.3.s.a.829.23		80	9.2	odd	6
2052.3.s.a.901.23		80	57.8	even	6
2052.3.bl.a.145.18		80	3.2	odd	2
2052.3.bl.a.1585.18		80	171.65	even	6

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.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.981973 - 2.83474i) q^{3} +0.638534 q^{5} +(-1.11619 - 1.93329i) q^{7} +(-7.07146 + 5.56727i) q^{9} +O(q^{10})\)	\(q+(-0.981973 - 2.83474i) q^{3} +0.638534 q^{5} +(-1.11619 - 1.93329i) q^{7} +(-7.07146 + 5.56727i) q^{9} +(1.89002 + 3.27360i) q^{11} +(-8.35812 + 4.82556i) q^{13} +(-0.627024 - 1.81008i) q^{15} +(11.4559 + 19.8422i) q^{17} +(7.12829 + 17.6121i) q^{19} +(-4.38431 + 5.06253i) q^{21} +(-3.96509 - 6.86774i) q^{23} -24.5923 q^{25} +(22.7257 + 14.5788i) q^{27} -30.4204i q^{29} +(50.4054 + 29.1016i) q^{31} +(7.42386 - 8.57229i) q^{33} +(-0.712723 - 1.23447i) q^{35} -12.8801i q^{37} +(21.8867 + 18.9545i) q^{39} +57.9407i q^{41} +(-14.6011 + 25.2898i) q^{43} +(-4.51537 + 3.55489i) q^{45} -44.5207 q^{47} +(22.0083 - 38.1194i) q^{49} +(44.9981 - 51.9590i) q^{51} +(-15.1786 - 8.76336i) q^{53} +(1.20684 + 2.09031i) q^{55} +(42.9260 - 37.5015i) q^{57} +47.6628i q^{59} +69.9915 q^{61} +(18.6562 + 7.45708i) q^{63} +(-5.33695 + 3.08129i) q^{65} +(18.0367 - 10.4135i) q^{67} +(-15.5746 + 17.9839i) q^{69} +(99.8380 - 57.6415i) q^{71} +(66.8138 + 115.725i) q^{73} +(24.1490 + 69.7126i) q^{75} +(4.21922 - 7.30790i) q^{77} +(13.6901 + 7.90398i) q^{79} +(19.0110 - 78.7374i) q^{81} +(47.6602 + 82.5498i) q^{83} +(7.31500 + 12.6699i) q^{85} +(-86.2339 + 29.8721i) q^{87} +(-70.8072 - 40.8805i) q^{89} +(18.6584 + 10.7725i) q^{91} +(32.9985 - 171.463i) q^{93} +(4.55166 + 11.2460i) q^{95} +(39.1925 + 22.6278i) q^{97} +(-31.5902 - 12.6269i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{3} - q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 6 * q^3 - q^7 - 2 * q^9	\( 80 q - 6 q^{3} - q^{7} - 2 q^{9} - 6 q^{11} - 15 q^{13} + 24 q^{15} - 21 q^{17} - 20 q^{19} + 24 q^{23} + 400 q^{25} + 63 q^{27} + 24 q^{31} + 30 q^{33} - 54 q^{35} - 81 q^{39} + 76 q^{43} + 188 q^{45} + 24 q^{47} - 267 q^{49} - 243 q^{51} - 36 q^{53} + 72 q^{57} + 14 q^{61} + 284 q^{63} + 288 q^{65} - 21 q^{67} - 48 q^{69} - 81 q^{71} + 55 q^{73} - 165 q^{75} + 30 q^{77} - 51 q^{79} - 110 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 204 q^{93} - 432 q^{95} + 90 q^{97} + 260 q^{99}+O(q^{100}) \) 80 * q - 6 * q^3 - q^7 - 2 * q^9 - 6 * q^11 - 15 * q^13 + 24 * q^15 - 21 * q^17 - 20 * q^19 + 24 * q^23 + 400 * q^25 + 63 * q^27 + 24 * q^31 + 30 * q^33 - 54 * q^35 - 81 * q^39 + 76 * q^43 + 188 * q^45 + 24 * q^47 - 267 * q^49 - 243 * q^51 - 36 * q^53 + 72 * q^57 + 14 * q^61 + 284 * q^63 + 288 * q^65 - 21 * q^67 - 48 * q^69 - 81 * q^71 + 55 * q^73 - 165 * q^75 + 30 * q^77 - 51 * q^79 - 110 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 204 * q^93 - 432 * q^95 + 90 * q^97 + 260 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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