LMFDB - Embedded newform 684.3.s.a.445.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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, 1]))

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

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (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			445.1
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.99896 + 0.0790095i) q^{3} +(-2.76024 - 4.78088i) q^{5} +(0.838417 + 1.45218i) q^{7} +(8.98751 - 0.473893i) q^{9} +O(q^{10})$	\(q+(-2.99896 + 0.0790095i) q^{3} +(-2.76024 - 4.78088i) q^{5} +(0.838417 + 1.45218i) q^{7} +(8.98751 - 0.473893i) q^{9} +(0.764365 + 1.32392i) q^{11} +20.7389i q^{13} +(8.65559 + 14.1196i) q^{15} +(9.66839 - 16.7462i) q^{17} +(-16.1509 + 10.0074i) q^{19} +(-2.62911 - 4.28879i) q^{21} +14.7130 q^{23} +(-2.73787 + 4.74213i) q^{25} +(-26.9158 + 2.13128i) q^{27} +(35.3534 + 20.4113i) q^{29} +(-23.1199 - 13.3483i) q^{31} +(-2.39690 - 3.90999i) q^{33} +(4.62847 - 8.01674i) q^{35} -59.7594i q^{37} +(-1.63857 - 62.1953i) q^{39} +(-31.9942 + 18.4719i) q^{41} -4.76215 q^{43} +(-27.0733 - 41.6602i) q^{45} +(27.0304 - 46.8180i) q^{47} +(23.0941 - 40.0002i) q^{49} +(-27.6720 + 50.9849i) q^{51} +(-17.5032 + 10.1055i) q^{53} +(4.21966 - 7.30867i) q^{55} +(47.6452 - 31.2880i) q^{57} +(85.6644 - 49.4583i) q^{59} +(43.6035 - 75.5234i) q^{61} +(8.22346 + 12.6542i) q^{63} +(99.1504 - 57.2445i) q^{65} +86.3585i q^{67} +(-44.1237 + 1.16247i) q^{69} +(-76.0630 - 43.9150i) q^{71} +(30.5689 - 52.9469i) q^{73} +(7.83609 - 14.4378i) q^{75} +(-1.28171 + 2.21999i) q^{77} -36.0178i q^{79} +(80.5509 - 8.51824i) q^{81} +(4.38181 + 7.58953i) q^{83} -106.748 q^{85} +(-107.636 - 58.4194i) q^{87} +(63.7489 - 36.8055i) q^{89} +(-30.1167 + 17.3879i) q^{91} +(70.3903 + 38.2043i) q^{93} +(92.4247 + 49.5925i) q^{95} -48.3262i q^{97} +(7.49713 + 11.5365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−2.99896	+	0.0790095i	−0.999653	+	0.0263365i
$3$	−2.99896	+	0.0790095i	−0.999653	+	0.0263365i
$4$		0			0
$5$	−2.76024	−	4.78088i	−0.552048	−	0.956176i	−0.998127	−	0.0611819i	$-0.980513\pi$
$5$	−2.76024	−	4.78088i	−0.552048	−	0.956176i	0.446078	−	0.894994i	$-0.352820\pi$
$6$		0			0
$7$	0.838417	+	1.45218i	0.119774	+	0.207454i	0.919678	−	0.392673i	$-0.128450\pi$
$7$	0.838417	+	1.45218i	0.119774	+	0.207454i	−0.799904	+	0.600128i	$0.795116\pi$
$8$		0			0
$9$	8.98751	−	0.473893i	0.998613	−	0.0526547i
$10$		0			0
$11$	0.764365	+	1.32392i	0.0694877	+	0.120356i	0.898676	−	0.438613i	$-0.144530\pi$
$11$	0.764365	+	1.32392i	0.0694877	+	0.120356i	−0.829188	+	0.558970i	$0.811197\pi$
$12$		0			0
$13$			20.7389i			1.59530i	0.603118	+	0.797652i	$0.293925\pi$
$13$			20.7389i			1.59530i	−0.603118	+	0.797652i	$0.706075\pi$
$14$		0			0
$15$	8.65559	+	14.1196i	0.577039	+	0.941305i
$16$		0			0
$17$	9.66839	−	16.7462i	0.568729	−	0.985068i	−0.427963	−	0.903796i	$-0.640769\pi$
$17$	9.66839	−	16.7462i	0.568729	−	0.985068i	0.996692	−	0.0812714i	$-0.0258980\pi$
$18$		0			0
$19$	−16.1509	+	10.0074i	−0.850047	+	0.526707i
$19$	−16.1509	+	10.0074i	−0.850047	+	0.526707i
$20$		0			0
$21$	−2.62911	−	4.28879i	−0.125196	−	0.204228i
$22$		0			0
$23$	14.7130			0.639696			0.319848	−	0.947469i	$-0.396368\pi$
$23$	14.7130			0.639696			0.319848	+	0.947469i	$0.396368\pi$
$24$		0			0
$25$	−2.73787	+	4.74213i	−0.109515	+	0.189685i
$26$		0			0
$27$	−26.9158	+	2.13128i	−0.996880	+	0.0789365i
$28$		0			0
$29$	35.3534	+	20.4113i	1.21908	+	0.703838i	0.964722	−	0.263271i	$-0.0848012\pi$
$29$	35.3534	+	20.4113i	1.21908	+	0.703838i	0.254362	+	0.967109i	$0.418135\pi$
$30$		0			0
$31$	−23.1199	−	13.3483i	−0.745803	−	0.430590i	0.0783722	−	0.996924i	$-0.475028\pi$
$31$	−23.1199	−	13.3483i	−0.745803	−	0.430590i	−0.824176	+	0.566334i	$0.808361\pi$
$32$		0			0
$33$	−2.39690	−	3.90999i	−0.0726334	−	0.118484i
$34$		0			0
$35$	4.62847	−	8.01674i	0.132242	−	0.229050i
$36$		0			0
$37$		−	59.7594i		−	1.61512i	−0.589787	−	0.807559i	$-0.700788\pi$
$37$		−	59.7594i		−	1.61512i	0.589787	−	0.807559i	$-0.299212\pi$
$38$		0			0
$39$	−1.63857	−	62.1953i	−0.0420147	−	1.59475i
$40$		0			0
$41$	−31.9942	+	18.4719i	−0.780347	+	0.450534i	−0.836553	−	0.547885i	$-0.815433\pi$
$41$	−31.9942	+	18.4719i	−0.780347	+	0.450534i	0.0562060	+	0.998419i	$0.482100\pi$
$42$		0			0
$43$	−4.76215			−0.110748			−0.0553738	−	0.998466i	$-0.517635\pi$
$43$	−4.76215			−0.110748			−0.0553738	+	0.998466i	$0.517635\pi$
$44$		0			0
$45$	−27.0733	−	41.6602i	−0.601630	−	0.925781i
$46$		0			0
$47$	27.0304	−	46.8180i	0.575114	−	0.996127i	−0.420915	−	0.907100i	$-0.638291\pi$
$47$	27.0304	−	46.8180i	0.575114	−	0.996127i	0.996029	−	0.0890271i	$-0.0283758\pi$
$48$		0			0
$49$	23.0941	−	40.0002i	0.471308	−	0.816330i
$50$		0			0
$51$	−27.6720	+	50.9849i	−0.542589	+	0.999704i
$52$		0			0
$53$	−17.5032	+	10.1055i	−0.330250	+	0.190670i	−0.655952	−	0.754803i	$-0.727733\pi$
$53$	−17.5032	+	10.1055i	−0.330250	+	0.190670i	0.325702	+	0.945472i	$0.394399\pi$
$54$		0			0
$55$	4.21966	−	7.30867i	0.0767211	−	0.132885i
$56$		0			0
$57$	47.6452	−	31.2880i	0.835881	−	0.548911i
$58$		0			0
$59$	85.6644	−	49.4583i	1.45194	−	0.838277i	0.453347	−	0.891334i	$-0.350230\pi$
$59$	85.6644	−	49.4583i	1.45194	−	0.838277i	0.998591	+	0.0530571i	$0.0168965\pi$
$60$		0			0
$61$	43.6035	−	75.5234i	0.714811	−	1.23809i	−0.248222	−	0.968703i	$-0.579846\pi$
$61$	43.6035	−	75.5234i	0.714811	−	1.23809i	0.963032	−	0.269385i	$-0.0868205\pi$
$62$		0			0
$63$	8.22346	+	12.6542i	0.130531	+	0.200860i
$64$		0			0
$65$	99.1504	−	57.2445i	1.52539	−	0.880685i
$66$		0			0
$67$			86.3585i			1.28893i	0.764632	+	0.644467i	$0.222921\pi$
$67$			86.3585i			1.28893i	−0.764632	+	0.644467i	$0.777079\pi$
$68$		0			0
$69$	−44.1237	+	1.16247i	−0.639474	+	0.0168474i
$70$		0			0
$71$	−76.0630	−	43.9150i	−1.07131	−	0.618521i	−0.142771	−	0.989756i	$-0.545601\pi$
$71$	−76.0630	−	43.9150i	−1.07131	−	0.618521i	−0.928539	+	0.371234i	$0.878935\pi$
$72$		0			0
$73$	30.5689	−	52.9469i	0.418752	−	0.725300i	−0.577062	−	0.816700i	$-0.695801\pi$
$73$	30.5689	−	52.9469i	0.418752	−	0.725300i	0.995814	+	0.0914003i	$0.0291343\pi$
$74$		0			0
$75$	7.83609	−	14.4378i	0.104481	−	0.192504i
$76$		0			0
$77$	−1.28171	+	2.21999i	−0.0166456	+	0.0288311i
$78$		0			0
$79$		−	36.0178i		−	0.455922i	−0.973670	−	0.227961i	$-0.926794\pi$
$79$		−	36.0178i		−	0.455922i	0.973670	−	0.227961i	$-0.0732059\pi$
$80$		0			0
$81$	80.5509	−	8.51824i	0.994455	−	0.105163i
$82$		0			0
$83$	4.38181	+	7.58953i	0.0527930	+	0.0914401i	0.891214	−	0.453583i	$-0.149854\pi$
$83$	4.38181	+	7.58953i	0.0527930	+	0.0914401i	−0.838421	+	0.545023i	$0.816521\pi$
$84$		0			0
$85$	−106.748			−1.25586
$86$		0			0
$87$	−107.636	−	58.4194i	−1.23720	−	0.671488i
$88$		0			0
$89$	63.7489	−	36.8055i	0.716280	−	0.413544i	−0.0971020	−	0.995274i	$-0.530957\pi$
$89$	63.7489	−	36.8055i	0.716280	−	0.413544i	0.813382	+	0.581730i	$0.197624\pi$
$90$		0			0
$91$	−30.1167	+	17.3879i	−0.330953	+	0.191076i
$92$		0			0
$93$	70.3903	+	38.2043i	0.756885	+	0.410799i
$94$		0			0
$95$	92.4247	+	49.5925i	0.972891	+	0.522027i
$96$		0			0
$97$		−	48.3262i		−	0.498208i	−0.968477	−	0.249104i	$-0.919864\pi$
$97$		−	48.3262i		−	0.498208i	0.968477	−	0.249104i	$-0.0801361\pi$
$98$		0			0
$99$	7.49713	+	11.5365i	0.0757286	+	0.116530i
$100$		0			0
$101$	14.0538	−	24.3418i	0.139146	−	0.241008i	−0.788028	−	0.615640i	$-0.788898\pi$
$101$	14.0538	−	24.3418i	0.139146	−	0.241008i	0.927174	+	0.374632i	$0.122231\pi$
$102$		0			0
$103$	−76.8268	−	44.3560i	−0.745891	−	0.430641i	0.0783160	−	0.996929i	$-0.475046\pi$
$103$	−76.8268	−	44.3560i	−0.745891	−	0.430641i	−0.824207	+	0.566288i	$0.808379\pi$
$104$		0			0
$105$	−13.2472	+	24.4076i	−0.126164	+	0.232453i
$106$		0			0
$107$			12.6565i			0.118285i	0.998250	+	0.0591424i	$0.0188366\pi$
$107$			12.6565i			0.118285i	−0.998250	+	0.0591424i	$0.981163\pi$
$108$		0			0
$109$	100.232	+	57.8690i	0.919560	+	0.530908i	0.883495	−	0.468442i	$-0.155184\pi$
$109$	100.232	+	57.8690i	0.919560	+	0.530908i	0.0360650	+	0.999349i	$0.488518\pi$
$110$		0			0
$111$	4.72156	+	179.216i	0.0425366	+	1.61456i
$112$		0			0
$113$	−100.398	−	57.9648i	−0.888477	−	0.512963i	−0.0150332	−	0.999887i	$-0.504785\pi$
$113$	−100.398	−	57.9648i	−0.888477	−	0.512963i	−0.873444	+	0.486924i	$0.838119\pi$
$114$		0			0
$115$	−40.6115	−	70.3411i	−0.353143	−	0.611662i
$116$		0			0
$117$	9.82803	+	186.392i	0.0840003	+	1.59309i
$118$		0			0
$119$	32.4246			0.272475
$120$		0			0
$121$	59.3315	−	102.765i	0.490343	−	0.849299i
$122$		0			0
$123$	94.4900	−	57.9243i	0.768211	−	0.470929i
$124$		0			0
$125$	−107.783			−0.862267
$126$		0			0
$127$	93.8993	−	54.2128i	0.739364	−	0.426872i	−0.0824738	−	0.996593i	$-0.526282\pi$
$127$	93.8993	−	54.2128i	0.739364	−	0.426872i	0.821838	+	0.569721i	$0.192949\pi$
$128$		0			0
$129$	14.2815	−	0.376255i	0.110709	−	0.00291671i
$130$		0			0
$131$	80.9125	+	140.145i	0.617653	+	1.06981i	0.989913	+	0.141677i	$0.0452495\pi$
$131$	80.9125	+	140.145i	0.617653	+	1.06981i	−0.372260	+	0.928128i	$0.621417\pi$
$132$		0			0
$133$	−28.0738	−	15.0636i	−0.211081	−	0.113260i
$134$		0			0
$135$	84.4834	+	122.798i	0.625803	+	0.909615i
$136$		0			0
$137$	70.2606	−	121.695i	0.512851	−	0.888284i	−0.487038	−	0.873381i	$-0.661923\pi$
$137$	70.2606	−	121.695i	0.512851	−	0.888284i	0.999889	−	0.0149031i	$-0.00474399\pi$
$138$		0			0
$139$	−195.414			−1.40585			−0.702926	−	0.711263i	$-0.748124\pi$
$139$	−195.414			−1.40585			−0.702926	+	0.711263i	$0.748124\pi$
$140$		0			0
$141$	−77.3639	+	142.541i	−0.548680	+	1.01093i
$142$		0			0
$143$	−27.4567	+	15.8521i	−0.192005	+	0.110854i
$144$		0			0
$145$		−	225.361i		−	1.55421i
$146$		0			0
$147$	−66.0979	+	121.784i	−0.449646	+	0.828460i
$148$		0			0
$149$	31.0000	+	53.6936i	0.208054	+	0.360360i	0.951101	−	0.308879i	$-0.0999538\pi$
$149$	31.0000	+	53.6936i	0.208054	+	0.360360i	−0.743048	+	0.669238i	$0.766620\pi$
$150$		0			0
$151$	−198.836	+	114.798i	−1.31680	+	0.760252i	−0.983212	−	0.182468i	$-0.941591\pi$
$151$	−198.836	+	114.798i	−1.31680	+	0.760252i	−0.333584	+	0.942720i	$0.608258\pi$
$152$		0			0
$153$	78.9590	−	155.088i	0.516072	−	1.01365i
$154$		0			0
$155$			147.378i			0.950826i
$156$		0			0
$157$	−75.7162	−	131.144i	−0.482269	−	0.835314i	0.517524	−	0.855669i	$-0.326854\pi$
$157$	−75.7162	−	131.144i	−0.482269	−	0.835314i	−0.999793	+	0.0203546i	$0.993520\pi$
$158$		0			0
$159$	51.6931	−	31.6889i	0.325114	−	0.199301i
$160$		0			0
$161$	12.3356	+	21.3659i	0.0766188	+	0.132708i
$162$		0			0
$163$	224.865			1.37954			0.689770	−	0.724029i	$-0.257712\pi$
$163$	224.865			1.37954			0.689770	+	0.724029i	$0.257712\pi$
$164$		0			0
$165$	−12.0771	+	22.2518i	−0.0731948	+	0.134859i
$166$		0			0
$167$		−	103.387i		−	0.619084i	−0.950886	−	0.309542i	$-0.899824\pi$
$167$		−	103.387i		−	0.619084i	0.950886	−	0.309542i	$-0.100176\pi$
$168$		0			0
$169$	−261.104			−1.54499
$170$		0			0
$171$	−140.414	+	97.5957i	−0.821134	+	0.570735i
$172$		0			0
$173$		−	236.723i		−	1.36834i	−0.729322	−	0.684170i	$-0.760165\pi$
$173$		−	236.723i		−	1.36834i	0.729322	−	0.684170i	$-0.239835\pi$
$174$		0			0
$175$	−9.18191			−0.0524681
$176$		0			0
$177$	−252.996	+	155.092i	−1.42936	+	0.876225i
$178$		0			0
$179$			165.052i			0.922081i	0.887379	+	0.461040i	$0.152524\pi$
$179$			165.052i			0.922081i	−0.887379	+	0.461040i	$0.847476\pi$
$180$		0			0
$181$	9.86440	−	5.69521i	0.0544994	−	0.0314653i	−0.472503	−	0.881329i	$-0.656649\pi$
$181$	9.86440	−	5.69521i	0.0544994	−	0.0314653i	0.527002	+	0.849864i	$0.323316\pi$
$182$		0			0
$183$	−124.798	+	229.937i	−0.681956	+	1.25648i
$184$		0			0
$185$	−285.702	+	164.950i	−1.54434	+	0.891623i
$186$		0			0
$187$	29.5607			0.158079
$188$		0			0
$189$	−25.6616	−	37.2996i	−0.135776	−	0.197353i
$190$		0			0
$191$	139.076	+	240.886i	0.728146	+	1.26119i	0.957666	+	0.287882i	$0.0929510\pi$
$191$	139.076	+	240.886i	0.728146	+	1.26119i	−0.229520	+	0.973304i	$0.573716\pi$
$192$		0			0
$193$	−253.579	+	146.404i	−1.31388	+	0.758570i	−0.982737	−	0.185010i	$-0.940768\pi$
$193$	−253.579	+	146.404i	−1.31388	+	0.758570i	−0.331145	+	0.943580i	$0.607435\pi$
$194$		0			0
$195$	−292.825	+	179.508i	−1.50167	+	0.920553i
$196$		0			0
$197$	200.140			1.01594			0.507971	−	0.861374i	$-0.330396\pi$
$197$	200.140			1.01594			0.507971	+	0.861374i	$0.330396\pi$
$198$		0			0
$199$	−3.26766	−	5.65976i	−0.0164204	−	0.0284410i	0.857698	−	0.514153i	$-0.171894\pi$
$199$	−3.26766	−	5.65976i	−0.0164204	−	0.0284410i	−0.874119	+	0.485712i	$0.838560\pi$
$200$		0			0
$201$	−6.82315	−	258.986i	−0.0339460	−	1.28849i
$202$		0			0
$203$			68.4528i			0.337206i
$204$		0			0
$205$	176.624	+	101.974i	0.861579	+	0.497433i
$206$		0			0
$207$	132.233	−	6.97239i	0.638809	−	0.0336830i
$208$		0			0
$209$	−25.5942	−	13.7331i	−0.122460	−	0.0657088i
$210$		0			0
$211$	185.229	−	106.942i	0.877863	−	0.506835i	0.00790995	−	0.999969i	$-0.497482\pi$
$211$	185.229	−	106.942i	0.877863	−	0.506835i	0.869953	+	0.493134i	$0.164149\pi$
$212$		0			0
$213$	231.580	+	125.690i	1.08723	+	0.590092i
$214$		0			0
$215$	13.1447	+	22.7673i	0.0611381	+	0.105894i
$216$		0			0
$217$		−	44.7657i		−	0.206294i
$218$		0			0
$219$	−87.4916	+	161.201i	−0.399505	+	0.736077i
$220$		0			0
$221$	347.297	+	200.512i	1.57148	+	0.907295i
$222$		0			0
$223$			347.028i			1.55618i	0.628153	+	0.778090i	$0.283811\pi$
$223$			347.028i			1.55618i	−0.628153	+	0.778090i	$0.716189\pi$
$224$		0			0
$225$	−22.3594	+	43.9174i	−0.0993751	+	0.195189i
$226$		0			0
$227$	324.621	−	187.420i	1.43005	−	0.825640i	0.432926	−	0.901430i	$-0.357481\pi$
$227$	324.621	−	187.420i	1.43005	−	0.825640i	0.997124	+	0.0757900i	$0.0241479\pi$
$228$		0			0
$229$	−15.6607	+	27.1251i	−0.0683872	+	0.118450i	−0.898191	−	0.439604i	$-0.855119\pi$
$229$	−15.6607	+	27.1251i	−0.0683872	+	0.118450i	0.829804	+	0.558054i	$0.188452\pi$
$230$		0			0
$231$	3.66840	−	6.75893i	0.0158805	−	0.0292594i
$232$		0			0
$233$	30.2550	−	52.4032i	0.129850	−	0.224907i	−0.793768	−	0.608220i	$-0.791884\pi$
$233$	30.2550	−	52.4032i	0.129850	−	0.224907i	0.923618	+	0.383314i	$0.125217\pi$
$234$		0			0
$235$	−298.441			−1.26996
$236$		0			0
$237$	2.84575	+	108.016i	0.0120074	+	0.455764i
$238$		0			0
$239$	96.9628	−	167.944i	0.405702	−	0.702696i	−0.588701	−	0.808351i	$-0.700360\pi$
$239$	96.9628	−	167.944i	0.405702	−	0.702696i	0.994403	+	0.105655i	$0.0336938\pi$
$240$		0			0
$241$	169.203	+	97.6893i	0.702087	+	0.405350i	0.808124	−	0.589012i	$-0.200483\pi$
$241$	169.203	+	97.6893i	0.702087	+	0.405350i	−0.106038	+	0.994362i	$0.533816\pi$
$242$		0			0
$243$	−240.896	+	31.9101i	−0.991340	+	0.131317i
$244$		0			0
$245$	−254.981			−1.04074
$246$		0			0
$247$	−207.544	−	334.952i	−0.840257	−	1.35608i
$248$		0			0
$249$	−13.7405	−	22.4145i	−0.0551829	−	0.0900180i
$250$		0			0
$251$	−3.93929	−	6.82305i	−0.0156944	−	0.0271835i	0.858072	−	0.513530i	$-0.171663\pi$
$251$	−3.93929	−	6.82305i	−0.0156944	−	0.0271835i	−0.873766	+	0.486347i	$0.838329\pi$
$252$		0			0
$253$	11.2461	+	19.4788i	0.0444510	+	0.0769914i
$254$		0			0
$255$	320.134	−	8.43414i	1.25543	−	0.0330751i
$256$		0			0
$257$		−	505.708i		−	1.96773i	−0.178902	−	0.983867i	$-0.557255\pi$
$257$		−	505.708i		−	1.96773i	0.178902	−	0.983867i	$-0.442745\pi$
$258$		0			0
$259$	86.7814	−	50.1033i	0.335063	−	0.193449i
$260$		0			0
$261$	327.412	+	166.693i	1.25445	+	0.638671i
$262$		0			0
$263$	265.273			1.00864			0.504321	−	0.863516i	$-0.331743\pi$
$263$	265.273			1.00864			0.504321	+	0.863516i	$0.331743\pi$
$264$		0			0
$265$	96.6264	+	55.7873i	0.364628	+	0.210518i
$266$		0			0
$267$	−188.272	+	115.415i	−0.705140	+	0.432265i
$268$		0			0
$269$	55.3986	+	31.9844i	0.205943	+	0.118901i	0.599424	−	0.800431i	$-0.295396\pi$
$269$	55.3986	+	31.9844i	0.205943	+	0.118901i	−0.393482	+	0.919332i	$0.628730\pi$
$270$		0			0
$271$	−261.759	+	453.380i	−0.965901	+	1.67299i	−0.258726	+	0.965951i	$0.583303\pi$
$271$	−261.759	+	453.380i	−0.965901	+	1.67299i	−0.707175	+	0.707038i	$0.750031\pi$
$272$		0			0
$273$	88.9449	−	54.5251i	0.325806	−	0.199725i
$274$		0			0
$275$	−8.37093			−0.0304397
$276$		0			0
$277$	−38.1732	−	66.1179i	−0.137809	−	0.238693i	0.788858	−	0.614576i	$-0.210673\pi$
$277$	−38.1732	−	66.1179i	−0.137809	−	0.238693i	−0.926667	+	0.375883i	$0.877339\pi$
$278$		0			0
$279$	−214.116	−	109.012i	−0.767441	−	0.390722i
$280$		0			0
$281$	397.504	+	229.499i	1.41460	+	0.816722i	0.995818	−	0.0913621i	$-0.0291221\pi$
$281$	397.504	+	229.499i	1.41460	+	0.816722i	0.418787	+	0.908085i	$0.362455\pi$
$282$		0			0
$283$	−63.3594	−	109.742i	−0.223885	−	0.387780i	0.732099	−	0.681198i	$-0.238541\pi$
$283$	−63.3594	−	109.742i	−0.223885	−	0.387780i	−0.955984	+	0.293418i	$0.905207\pi$
$284$		0			0
$285$	−281.096	−	141.424i	−0.986302	−	0.496223i
$286$		0			0
$287$	−53.6490	−	30.9743i	−0.186930	−	0.107924i
$288$		0			0
$289$	−42.4557	−	73.5354i	−0.146906	−	0.254448i
$290$		0			0
$291$	3.81823	+	144.928i	0.0131211	+	0.498035i
$292$		0			0
$293$	−142.675	−	82.3734i	−0.486945	−	0.281138i	0.236361	−	0.971665i	$-0.424045\pi$
$293$	−142.675	−	82.3734i	−0.486945	−	0.281138i	−0.723306	+	0.690527i	$0.757379\pi$
$294$		0			0
$295$	−472.909	−	273.034i	−1.60308	−	0.925539i
$296$		0			0
$297$	−23.3951	−	34.0052i	−0.0787714	−	0.114496i
$298$		0			0
$299$			305.132i			1.02051i
$300$		0			0
$301$	−3.99267	−	6.91550i	−0.0132647	−	0.0229751i
$302$		0			0
$303$	−40.2234	+	74.1105i	−0.132750	+	0.244589i
$304$		0			0
$305$	−481.424			−1.57844
$306$		0			0
$307$	−143.939	−	83.1031i	−0.468856	−	0.270694i	0.246905	−	0.969040i	$-0.420587\pi$
$307$	−143.939	−	83.1031i	−0.468856	−	0.270694i	−0.715761	+	0.698346i	$0.753920\pi$
$308$		0			0
$309$	233.905	+	126.952i	0.756974	+	0.410847i
$310$		0			0
$311$	129.031	−	223.488i	0.414891	−	0.718612i	−0.580526	−	0.814241i	$-0.697153\pi$
$311$	129.031	−	223.488i	0.414891	−	0.718612i	0.995417	+	0.0956298i	$0.0304865\pi$
$312$		0			0
$313$	−134.027	+	232.142i	−0.428202	+	0.741668i	−0.996713	−	0.0810078i	$-0.974186\pi$
$313$	−134.027	+	232.142i	−0.428202	+	0.741668i	0.568512	+	0.822675i	$0.307519\pi$
$314$		0			0
$315$	37.7993	−	74.2440i	0.119998	−	0.235695i
$316$		0			0
$317$	462.941	+	267.279i	1.46038	+	0.843152i	0.999029	−	0.0440646i	$-0.0140307\pi$
$317$	462.941	+	267.279i	1.46038	+	0.843152i	0.461353	+	0.887217i	$0.347364\pi$
$318$		0			0
$319$			62.4067i			0.195632i
$320$		0			0
$321$	−0.999982	−	37.9563i	−0.00311521	−	0.118244i
$322$		0			0
$323$	11.4327	+	367.221i	0.0353955	+	1.13691i
$324$		0			0
$325$	−98.3468	−	56.7805i	−0.302606	−	0.174709i
$326$		0			0
$327$	−305.164	−	165.627i	−0.933223	−	0.506506i
$328$		0			0
$329$	90.6509			0.275535
$330$		0			0
$331$	255.142	−	147.306i	0.770821	−	0.445034i	−0.0623461	−	0.998055i	$-0.519858\pi$
$331$	255.142	−	147.306i	0.770821	−	0.445034i	0.833168	+	0.553021i	$0.186525\pi$
$332$		0			0
$333$	−28.3195	−	537.088i	−0.0850436	−	1.61288i
$334$		0			0
$335$	412.870	−	238.370i	1.23245	−	0.711554i
$336$		0			0
$337$	203.056	−	117.235i	0.602541	−	0.347877i	−0.167500	−	0.985872i	$-0.553569\pi$
$337$	203.056	−	117.235i	0.602541	−	0.347877i	0.770040	+	0.637995i	$0.220236\pi$
$338$		0			0
$339$	305.669	+	165.902i	0.901679	+	0.489385i
$340$		0			0
$341$		−	40.8118i		−	0.119683i
$342$		0			0
$343$	159.615			0.465349
$344$		0			0
$345$	127.350	+	207.741i	0.369130	+	0.602149i
$346$		0			0
$347$	−294.118	−	509.427i	−0.847602	−	1.46809i	−0.883342	−	0.468728i	$-0.844712\pi$
$347$	−294.118	−	509.427i	−0.847602	−	1.46809i	0.0357404	−	0.999361i	$-0.488621\pi$
$348$		0			0
$349$	230.931	+	399.985i	0.661695	+	1.14609i	0.980170	+	0.198158i	$0.0634958\pi$
$349$	230.931	+	399.985i	0.661695	+	1.14609i	−0.318475	+	0.947931i	$0.603171\pi$
$350$		0			0
$351$	−44.2006	−	558.204i	−0.125928	−	1.59033i
$352$		0			0
$353$	−225.135	−	389.946i	−0.637777	−	1.10466i	−0.985919	−	0.167221i	$-0.946521\pi$
$353$	−225.135	−	389.946i	−0.637777	−	1.10466i	0.348142	−	0.937442i	$-0.386813\pi$
$354$		0			0
$355$			484.864i			1.36581i
$356$		0			0
$357$	−97.2400	+	2.56185i	−0.272381	+	0.00717605i
$358$		0			0
$359$	91.4010	−	158.311i	0.254599	−	0.440978i	−0.710188	−	0.704012i	$-0.751390\pi$
$359$	91.4010	−	158.311i	0.254599	−	0.440978i	0.964786	+	0.263034i	$0.0847232\pi$
$360$		0			0
$361$	160.703	−	323.258i	0.445160	−	0.895451i
$362$		0			0
$363$	−169.813	+	312.876i	−0.467805	+	0.861918i
$364$		0			0
$365$	−337.510			−0.924686
$366$		0			0
$367$	−40.4386	+	70.0417i	−0.110187	+	0.190849i	−0.915846	−	0.401531i	$-0.868478\pi$
$367$	−40.4386	+	70.0417i	−0.110187	+	0.190849i	0.805659	+	0.592380i	$0.201812\pi$
$368$		0			0
$369$	−278.795	+	181.178i	−0.755542	+	0.490998i
$370$		0			0
$371$	−29.3500	−	16.9453i	−0.0791106	−	0.0456745i
$372$		0			0
$373$	−129.659	−	74.8584i	−0.347610	−	0.200693i	0.316022	−	0.948752i	$-0.397653\pi$
$373$	−129.659	−	74.8584i	−0.347610	−	0.200693i	−0.663632	+	0.748059i	$0.730986\pi$
$374$		0			0
$375$	323.238	−	8.51591i	0.861968	−	0.0227091i
$376$		0			0
$377$	−423.309	+	733.193i	−1.12284	+	1.94481i
$378$		0			0
$379$		−	454.252i		−	1.19855i	−0.800542	−	0.599277i	$-0.795455\pi$
$379$		−	454.252i		−	1.19855i	0.800542	−	0.599277i	$-0.204545\pi$
$380$		0			0
$381$	−277.317	+	170.001i	−0.727866	+	0.446196i
$382$		0			0
$383$	−85.1709	+	49.1735i	−0.222378	+	0.128390i	−0.607051	−	0.794663i	$-0.707648\pi$
$383$	−85.1709	+	49.1735i	−0.222378	+	0.128390i	0.384673	+	0.923053i	$0.374314\pi$
$384$		0			0
$385$	14.1513			0.0367567
$386$		0			0
$387$	−42.7999	+	2.25675i	−0.110594	+	0.00583139i
$388$		0			0
$389$	−168.448	+	291.760i	−0.433027	+	0.750025i	−0.997132	−	0.0756780i	$-0.975888\pi$
$389$	−168.448	+	291.760i	−0.433027	+	0.750025i	0.564105	+	0.825703i	$0.309221\pi$
$390$		0			0
$391$	142.251	−	246.386i	0.363814	−	0.630144i
$392$		0			0
$393$	−253.726	−	413.895i	−0.645613	−	1.05317i
$394$		0			0
$395$	−172.197	+	99.4180i	−0.435942	+	0.251691i
$396$		0			0
$397$	−140.690	+	243.683i	−0.354384	+	0.613811i	−0.987012	−	0.160645i	$-0.948643\pi$
$397$	−140.690	+	243.683i	−0.354384	+	0.613811i	0.632628	+	0.774455i	$0.281976\pi$
$398$		0			0
$399$	85.3823	+	42.9571i	0.213991	+	0.107662i
$400$		0			0
$401$	225.514	−	130.200i	0.562378	−	0.324689i	−0.191721	−	0.981449i	$-0.561407\pi$
$401$	225.514	−	130.200i	0.562378	−	0.324689i	0.754099	+	0.656760i	$0.228074\pi$
$402$		0			0
$403$	276.829	−	479.482i	0.686921	−	1.18978i
$404$		0			0
$405$	−263.064	−	361.591i	−0.649542	−	0.892819i
$406$		0			0
$407$	79.1165	−	45.6779i	0.194389	−	0.112231i
$408$		0			0
$409$			185.360i			0.453203i	0.973988	+	0.226601i	$0.0727615\pi$
$409$			185.360i			0.453203i	−0.973988	+	0.226601i	$0.927239\pi$
$410$		0			0
$411$	−201.094	+	370.509i	−0.489279	+	0.901483i
$412$		0			0
$413$	143.645	+	82.9334i	0.347809	+	0.200807i
$414$		0			0
$415$	24.1897	−	41.8979i	0.0582885	−	0.100959i
$416$		0			0
$417$	586.037	−	15.4395i	1.40537	−	0.0370253i
$418$		0			0
$419$	42.6325	−	73.8416i	0.101748	−	0.176233i	−0.810657	−	0.585522i	$-0.800890\pi$
$419$	42.6325	−	73.8416i	0.101748	−	0.176233i	0.912405	+	0.409289i	$0.134223\pi$
$420$		0			0
$421$			608.244i			1.44476i	0.691496	+	0.722381i	$0.256952\pi$
$421$			608.244i			1.44476i	−0.691496	+	0.722381i	$0.743048\pi$
$422$		0			0
$423$	220.749	−	433.587i	0.521866	−	1.02503i
$424$		0			0
$425$	52.9416	+	91.6976i	0.124569	+	0.215759i
$426$		0			0
$427$	146.232			0.342463
$428$		0			0
$429$	81.0890	−	49.7092i	0.189019	−	0.115872i
$430$		0			0
$431$	79.3761	−	45.8278i	0.184167	−	0.106329i	−0.405082	−	0.914280i	$-0.632757\pi$
$431$	79.3761	−	45.8278i	0.184167	−	0.106329i	0.589249	+	0.807951i	$0.299424\pi$
$432$		0			0
$433$	547.653	−	316.188i	1.26479	−	0.730225i	0.290791	−	0.956787i	$-0.406082\pi$
$433$	547.653	−	316.188i	1.26479	−	0.730225i	0.973997	+	0.226561i	$0.0727484\pi$
$434$		0			0
$435$	17.8056	+	675.847i	0.0409325	+	1.55367i
$436$		0			0
$437$	−237.628	+	147.239i	−0.543772	+	0.336932i
$438$		0			0
$439$		−	402.205i		−	0.916185i	−0.888904	−	0.458093i	$-0.848533\pi$
$439$		−	402.205i		−	0.916185i	0.888904	−	0.458093i	$-0.151467\pi$
$440$		0			0
$441$	188.603	−	370.446i	0.427671	−	0.840014i
$442$		0			0
$443$	59.3192	−	102.744i	0.133903	−	0.231927i	−0.791275	−	0.611461i	$-0.790582\pi$
$443$	59.3192	−	102.744i	0.133903	−	0.231927i	0.925178	+	0.379534i	$0.123916\pi$
$444$		0			0
$445$	−351.925	−	203.184i	−0.790842	−	0.456593i
$446$		0			0
$447$	−97.2100	−	158.576i	−0.217472	−	0.354755i
$448$		0			0
$449$		−	217.699i		−	0.484853i	−0.970170	−	0.242426i	$-0.922057\pi$
$449$		−	217.699i		−	0.484853i	0.970170	−	0.242426i	$-0.0779433\pi$
$450$		0			0
$451$	−48.9105	−	28.2385i	−0.108449	−	0.0626131i
$452$		0			0
$453$	587.231	−	359.985i	1.29632	−	0.794668i
$454$		0			0
$455$	166.259	+	95.9895i	0.365404	+	0.210966i
$456$		0			0
$457$	−28.8170	−	49.9125i	−0.0630568	−	0.109218i	0.832774	−	0.553614i	$-0.186752\pi$
$457$	−28.8170	−	49.9125i	−0.0630568	−	0.109218i	−0.895830	+	0.444396i	$0.853418\pi$
$458$		0			0
$459$	−224.541	+	471.341i	−0.489197	+	1.02689i
$460$		0			0
$461$	465.882			1.01059			0.505295	−	0.862946i	$-0.331384\pi$
$461$	465.882			1.01059			0.505295	+	0.862946i	$0.331384\pi$
$462$		0			0
$463$	−46.1604	+	79.9521i	−0.0996984	+	0.172683i	−0.911560	−	0.411168i	$-0.865121\pi$
$463$	−46.1604	+	79.9521i	−0.0996984	+	0.172683i	0.811861	+	0.583850i	$0.198454\pi$
$464$		0			0
$465$	−11.6443	−	441.981i	−0.0250414	−	0.950496i
$466$		0			0
$467$	−601.527			−1.28807			−0.644033	−	0.764998i	$-0.722740\pi$
$467$	−601.527			−1.28807			−0.644033	+	0.764998i	$0.722740\pi$
$468$		0			0
$469$	−125.408	+	72.4045i	−0.267395	+	0.154381i
$470$		0			0
$471$	237.431	+	387.314i	0.504101	+	0.822323i
$472$		0			0
$473$	−3.64002	−	6.30470i	−0.00769560	−	0.0133292i
$474$		0			0
$475$	−3.23749	−	103.989i	−0.00681578	−	0.218924i
$476$		0			0
$477$	−152.522	+	99.1180i	−0.319752	+	0.207795i
$478$		0			0
$479$	186.434	−	322.913i	0.389215	−	0.674140i	−0.603129	−	0.797644i	$-0.706080\pi$
$479$	186.434	−	322.913i	0.389215	−	0.674140i	0.992344	+	0.123503i	$0.0394130\pi$
$480$		0			0
$481$	1239.35			2.57660
$482$		0			0
$483$	−38.6822	−	63.1010i	−0.0800873	−	0.130644i
$484$		0			0
$485$	−231.042	+	133.392i	−0.476374	+	0.275035i
$486$		0			0
$487$			733.353i			1.50586i	0.658102	+	0.752929i	$0.271360\pi$
$487$			733.353i			1.50586i	−0.658102	+	0.752929i	$0.728640\pi$
$488$		0			0
$489$	−674.361	+	17.7665i	−1.37906	+	0.0363323i
$490$		0			0
$491$	22.9680	+	39.7817i	0.0467779	+	0.0810218i	0.888466	−	0.458942i	$-0.151771\pi$
$491$	22.9680	+	39.7817i	0.0467779	+	0.0810218i	−0.841688	+	0.539964i	$0.818438\pi$
$492$		0			0
$493$	683.622	−	394.689i	1.38666	−	0.800587i
$494$		0			0
$495$	34.4608	−	67.6864i	0.0696177	−	0.136740i
$496$		0			0
$497$		−	147.276i		−	0.296331i
$498$		0			0
$499$	−172.909	−	299.487i	−0.346511	−	0.600175i	0.639116	−	0.769111i	$-0.279300\pi$
$499$	−172.909	−	299.487i	−0.346511	−	0.600175i	−0.985627	+	0.168935i	$0.945967\pi$
$500$		0			0
$501$	8.16856	+	310.054i	0.0163045	+	0.618870i
$502$		0			0
$503$	−293.370	−	508.133i	−0.583242	−	1.01020i	−0.995092	−	0.0989526i	$-0.968451\pi$
$503$	−293.370	−	508.133i	−0.583242	−	1.01020i	0.411851	−	0.911251i	$-0.364883\pi$
$504$		0			0
$505$	−155.167			−0.307261
$506$		0			0
$507$	783.040	−	20.6297i	1.54446	−	0.0406897i
$508$		0			0
$509$		−	121.213i		−	0.238140i	−0.992886	−	0.119070i	$-0.962009\pi$
$509$		−	121.213i		−	0.238140i	0.992886	−	0.119070i	$-0.0379913\pi$
$510$		0			0
$511$	102.518			0.200622
$512$		0			0
$513$	413.385	−	303.780i	0.805818	−	0.592163i
$514$		0			0
$515$			489.733i			0.950938i
$516$		0			0
$517$	82.6442			0.159853
$518$		0			0
$519$	18.7034	+	709.922i	0.0360373	+	1.36787i
$520$		0			0
$521$			462.527i			0.887768i	0.896084	+	0.443884i	$0.146400\pi$
$521$			462.527i			0.887768i	−0.896084	+	0.443884i	$0.853600\pi$
$522$		0			0
$523$	−720.329	+	415.882i	−1.37730	+	0.795185i	−0.991834	−	0.127536i	$-0.959293\pi$
$523$	−720.329	+	415.882i	−1.37730	+	0.795185i	−0.385467	+	0.922721i	$0.625960\pi$
$524$		0			0
$525$	27.5362	−	0.725458i	0.0524499	−	0.00138183i
$526$		0			0
$527$	−447.065	+	258.113i	−0.848320	+	0.489778i
$528$		0			0
$529$	−312.527			−0.590789
$530$		0			0
$531$	746.472	−	485.103i	1.40579	−	0.913566i
$532$		0			0
$533$	−383.087	−	663.527i	−0.718738	−	1.24489i
$534$		0			0
$535$	60.5091	−	34.9349i	0.113101	−	0.0652990i
$536$		0			0
$537$	−13.0407	−	494.986i	−0.0242844	−	0.921761i
$538$		0			0
$539$	70.6093			0.131001
$540$		0			0
$541$	−208.868	−	361.769i	−0.386077	−	0.668705i	0.605841	−	0.795586i	$-0.292837\pi$
$541$	−208.868	−	361.769i	−0.386077	−	0.668705i	−0.991918	+	0.126881i	$0.959503\pi$
$542$		0			0
$543$	−29.1330	+	17.8591i	−0.0536519	+	0.0328897i
$544$		0			0
$545$		−	638.929i		−	1.17235i
$546$		0			0
$547$	−445.347	−	257.121i	−0.814162	−	0.470057i	0.0342368	−	0.999414i	$-0.489100\pi$
$547$	−445.347	−	257.121i	−0.814162	−	0.470057i	−0.848399	+	0.529357i	$0.822433\pi$
$548$		0			0
$549$	356.097	−	699.431i	0.648628	−	1.27401i
$550$		0			0
$551$	−775.254	+	24.1361i	−1.40700	+	0.0438042i
$552$		0			0
$553$	52.3044	−	30.1980i	0.0945830	−	0.0546075i
$554$		0			0
$555$	843.777	−	517.252i	1.52032	−	0.931986i
$556$		0			0
$557$	−331.389	−	573.982i	−0.594953	−	1.03049i	−0.993553	−	0.113364i	$-0.963837\pi$
$557$	−331.389	−	573.982i	−0.594953	−	1.03049i	0.398600	−	0.917125i	$-0.369496\pi$
$558$		0			0
$559$		−	98.7620i		−	0.176676i
$560$		0			0
$561$	−88.6514	+	2.33558i	−0.158024	+	0.00416324i
$562$		0			0
$563$	−700.676	−	404.536i	−1.24454	−	0.718536i	−0.274525	−	0.961580i	$-0.588521\pi$
$563$	−700.676	−	404.536i	−1.24454	−	0.718536i	−0.970015	+	0.243044i	$0.921854\pi$
$564$		0			0
$565$			639.987i			1.13272i
$566$		0			0
$567$	79.9052	+	109.833i	0.140926	+	0.193708i
$568$		0			0
$569$	173.823	−	100.357i	0.305488	−	0.176374i	−0.339418	−	0.940636i	$-0.610230\pi$
$569$	173.823	−	100.357i	0.305488	−	0.176374i	0.644906	+	0.764262i	$0.276897\pi$
$570$		0			0
$571$	174.282	−	301.865i	0.305222	−	0.528660i	−0.672089	−	0.740471i	$-0.734603\pi$
$571$	174.282	−	301.865i	0.305222	−	0.528660i	0.977311	+	0.211811i	$0.0679360\pi$
$572$		0			0
$573$	−436.115	−	711.420i	−0.761108	−	1.24157i
$574$		0			0
$575$	−40.2823	+	69.7710i	−0.0700562	+	0.121341i
$576$		0			0
$577$	−102.187			−0.177101			−0.0885503	−	0.996072i	$-0.528223\pi$
$577$	−102.187			−0.177101			−0.0885503	+	0.996072i	$0.528223\pi$
$578$		0			0
$579$	748.906	−	459.095i	1.29345	−	0.792910i
$580$		0			0
$581$	−7.34758	+	12.7264i	−0.0126464	+	0.0219043i
$582$		0			0
$583$	−26.7577	−	15.4486i	−0.0458966	−	0.0264984i
$584$		0			0
$585$	863.988	−	561.472i	1.47690	−	0.959782i
$586$		0			0
$587$	−568.445			−0.968390			−0.484195	−	0.874960i	$-0.660887\pi$
$587$	−568.445			−0.968390			−0.484195	+	0.874960i	$0.660887\pi$
$588$		0			0
$589$	506.989	−	15.7842i	0.860762	−	0.0267982i
$590$		0			0
$591$	−600.213	+	15.8130i	−1.01559	+	0.0267563i
$592$		0			0
$593$	551.047	+	954.441i	0.929252	+	1.60951i	0.784576	+	0.620033i	$0.212881\pi$
$593$	551.047	+	954.441i	0.929252	+	1.60951i	0.144677	+	0.989479i	$0.453786\pi$
$594$		0			0
$595$	−89.4997	−	155.018i	−0.150420	−	0.260534i
$596$		0			0
$597$	10.2468	+	16.7152i	0.0171638	+	0.0279987i
$598$		0			0
$599$		−	582.418i		−	0.972317i	−0.873871	−	0.486159i	$-0.838398\pi$
$599$		−	582.418i		−	0.972317i	0.873871	−	0.486159i	$-0.161602\pi$
$600$		0			0
$601$	462.788	−	267.191i	0.770031	−	0.444577i	−0.0628549	−	0.998023i	$-0.520021\pi$
$601$	462.788	−	267.191i	0.770031	−	0.444577i	0.832886	+	0.553445i	$0.186687\pi$
$602$		0			0
$603$	40.9247	+	776.149i	0.0678685	+	1.28715i
$604$		0			0
$605$	−655.077			−1.08277
$606$		0			0
$607$	549.907	+	317.489i	0.905942	+	0.523046i	0.879123	−	0.476595i	$-0.158129\pi$
$607$	549.907	+	317.489i	0.905942	+	0.523046i	0.0268186	+	0.999640i	$0.491462\pi$
$608$		0			0
$609$	−5.40842	−	205.287i	−0.00888082	−	0.337089i
$610$		0			0
$611$	970.955	+	560.581i	1.58913	+	0.917482i
$612$		0			0
$613$	−73.8570	+	127.924i	−0.120484	+	0.208685i	−0.919959	−	0.392015i	$-0.871778\pi$
$613$	−73.8570	+	127.924i	−0.120484	+	0.208685i	0.799474	+	0.600700i	$0.205111\pi$
$614$		0			0
$615$	−537.744	−	291.860i	−0.874381	−	0.474569i
$616$		0			0
$617$	425.780			0.690080			0.345040	−	0.938588i	$-0.387865\pi$
$617$	425.780			0.690080			0.345040	+	0.938588i	$0.387865\pi$
$618$		0			0
$619$	−294.086	−	509.373i	−0.475099	−	0.822896i	0.524494	−	0.851414i	$-0.324255\pi$
$619$	−294.086	−	509.373i	−0.475099	−	0.822896i	−0.999593	+	0.0285181i	$0.990921\pi$
$620$		0			0
$621$	−396.012	+	31.3576i	−0.637700	+	0.0504953i
$622$		0			0
$623$	106.896	+	61.7166i	0.171583	+	0.0990636i
$624$		0			0
$625$	365.955	+	633.852i	0.585528	+	1.01416i
$626$		0			0
$627$	77.8410	+	39.1629i	0.124148	+	0.0624608i
$628$		0			0
$629$	−1000.74	−	577.777i	−1.59100	−	0.918565i
$630$		0			0
$631$	249.213	+	431.649i	0.394949	+	0.684071i	0.993095	−	0.117316i	$-0.0374290\pi$
$631$	249.213	+	431.649i	0.394949	+	0.684071i	−0.598146	+	0.801387i	$0.704096\pi$
$632$		0			0
$633$	−547.045	+	335.350i	−0.864210	+	0.529779i
$634$		0			0
$635$	−518.369	−	299.281i	−0.816330	−	0.471308i
$636$		0			0
$637$	829.561	+	478.948i	1.30229	+	0.751880i
$638$		0			0
$639$	−704.429	−	358.641i	−1.10239	−	0.561254i
$640$		0			0
$641$		−	483.594i		−	0.754436i	−0.926124	−	0.377218i	$-0.876881\pi$
$641$		−	483.594i		−	0.754436i	0.926124	−	0.377218i	$-0.123119\pi$
$642$		0			0
$643$	−459.770	−	796.345i	−0.715039	−	1.23848i	−0.962944	−	0.269700i	$-0.913076\pi$
$643$	−459.770	−	796.345i	−0.715039	−	1.23848i	0.247905	−	0.968784i	$-0.420258\pi$
$644$		0			0
$645$	−41.2192	−	67.2395i	−0.0639058	−	0.104247i
$646$		0			0
$647$	917.882			1.41867			0.709337	−	0.704869i	$-0.248994\pi$
$647$	917.882			1.41867			0.709337	+	0.704869i	$0.248994\pi$
$648$		0			0
$649$	130.958	+	75.6084i	0.201784	+	0.116500i
$650$		0			0
$651$	3.53692	+	134.251i	0.00543305	+	0.206222i
$652$		0			0
$653$	−188.112	+	325.820i	−0.288074	+	0.498958i	−0.973350	−	0.229325i	$-0.926348\pi$
$653$	−188.112	+	325.820i	−0.288074	+	0.498958i	0.685276	+	0.728283i	$0.259681\pi$
$654$		0			0
$655$	446.676	−	773.666i	0.681948	−	1.18117i
$656$		0			0
$657$	249.647	−	490.347i	0.379981	−	0.746343i
$658$		0			0
$659$	746.538	+	431.014i	1.13283	+	0.654042i	0.944646	−	0.328091i	$-0.106405\pi$
$659$	746.538	+	431.014i	1.13283	+	0.654042i	0.188188	+	0.982133i	$0.439739\pi$
$660$		0			0
$661$			1160.76i			1.75607i	0.478593	+	0.878037i	$0.341147\pi$
$661$			1160.76i			1.75607i	−0.478593	+	0.878037i	$0.658853\pi$
$662$		0			0
$663$	−1057.37	−	573.888i	−1.59483	−	0.865593i
$664$		0			0
$665$	5.47310	+	175.797i	0.00823022	+	0.264356i
$666$		0			0
$667$	520.155	+	300.312i	0.779843	+	0.450243i
$668$		0			0
$669$	−27.4185	−	1040.72i	−0.0409843	−	1.55564i
$670$		0			0
$671$	133.316			0.198682
$672$		0			0
$673$	−793.000	+	457.839i	−1.17831	+	0.680296i	−0.955622	−	0.294595i	$-0.904815\pi$
$673$	−793.000	+	457.839i	−1.17831	+	0.680296i	−0.222685	+	0.974891i	$0.571482\pi$
$674$		0			0
$675$	63.5850	−	133.473i	0.0942000	−	0.197738i
$676$		0			0
$677$	−499.660	+	288.479i	−0.738051	+	0.426114i	−0.821360	−	0.570410i	$-0.806784\pi$
$677$	−499.660	+	288.479i	−0.738051	+	0.426114i	0.0833095	+	0.996524i	$0.473451\pi$
$678$		0			0
$679$	70.1783	−	40.5175i	0.103355	−	0.0596723i
$680$		0			0
$681$	−958.718	+	587.714i	−1.40781	+	0.863016i
$682$		0			0
$683$		−	110.380i		−	0.161611i	−0.996730	−	0.0808054i	$-0.974251\pi$
$683$		−	110.380i		−	0.161611i	0.996730	−	0.0808054i	$-0.0257492\pi$
$684$		0			0
$685$	−775.745			−1.13247
$686$		0			0
$687$	44.8225	−	82.5843i	0.0652439	−	0.120210i
$688$		0			0
$689$	−209.577	−	362.999i	−0.304176	−	0.526849i
$690$		0			0
$691$	316.990	+	549.043i	0.458741	+	0.794564i	0.998895	−	0.0470031i	$-0.0149671\pi$
$691$	316.990	+	549.043i	0.458741	+	0.794564i	−0.540153	+	0.841567i	$0.681634\pi$
$692$		0			0
$693$	−10.4674	+	20.5596i	−0.0151044	+	0.0296675i
$694$		0			0
$695$	539.389	+	934.249i	0.776099	+	1.34424i
$696$		0			0
$697$			714.374i			1.02493i
$698$		0			0
$699$	−86.5932	+	159.546i	−0.123882	+	0.228248i
$700$		0			0
$701$	−314.952	+	545.513i	−0.449290	+	0.778192i	−0.998340	−	0.0575969i	$-0.981656\pi$
$701$	−314.952	+	545.513i	−0.449290	+	0.778192i	0.549050	+	0.835789i	$0.314990\pi$
$702$		0			0
$703$	598.038	+	965.167i	0.850694	+	1.37293i
$704$		0			0
$705$	895.014	−	23.5797i	1.26952	−	0.0334464i
$706$		0			0
$707$	47.1316			0.0666642
$708$		0			0
$709$	−317.429	+	549.804i	−0.447714	+	0.775464i	−0.998237	−	0.0593564i	$-0.981095\pi$
$709$	−317.429	+	549.804i	−0.447714	+	0.775464i	0.550523	+	0.834820i	$0.314429\pi$
$710$		0			0
$711$	−17.0686	−	323.711i	−0.0240065	−	0.455290i
$712$		0			0
$713$	−340.163	−	196.393i	−0.477087	−	0.275447i
$714$		0			0
$715$	151.574	+	87.5113i	0.211992	+	0.122393i
$716$		0			0
$717$	−277.518	+	511.320i	−0.387055	+	0.713137i
$718$		0			0
$719$	−426.697	+	739.061i	−0.593459	+	1.02790i	0.400304	+	0.916383i	$0.368905\pi$
$719$	−426.697	+	739.061i	−0.593459	+	1.02790i	−0.993762	+	0.111518i	$0.964429\pi$
$720$		0			0
$721$		−	148.755i		−	0.206318i
$722$		0			0
$723$	−515.151	−	279.598i	−0.712519	−	0.386719i
$724$		0			0
$725$	−193.586	+	111.767i	−0.267016	+	0.154161i
$726$		0			0
$727$	640.984			0.881683			0.440842	−	0.897585i	$-0.354680\pi$
$727$	640.984			0.881683			0.440842	+	0.897585i	$0.354680\pi$
$728$		0			0
$729$	719.915	−	114.730i	0.987538	−	0.157380i
$730$		0			0
$731$	−46.0423	+	79.7477i	−0.0629854	+	0.109094i
$732$		0			0
$733$	−460.500	+	797.610i	−0.628241	+	1.08814i	0.359664	+	0.933082i	$0.382891\pi$
$733$	−460.500	+	797.610i	−0.628241	+	1.08814i	−0.987905	+	0.155063i	$0.950442\pi$
$734$		0			0
$735$	764.679	−	20.1460i	1.04038	−	0.0274095i
$736$		0			0
$737$	−114.332	+	66.0094i	−0.155131	+	0.0895650i
$738$		0			0
$739$	−21.6756	+	37.5432i	−0.0293310	+	0.0508027i	−0.880318	−	0.474384i	$-0.842671\pi$
$739$	−21.6756	+	37.5432i	−0.0293310	+	0.0508027i	0.850987	+	0.525186i	$0.176004\pi$
$740$		0			0
$741$	648.879	+	988.111i	0.875680	+	1.33348i
$742$		0			0
$743$	−841.417	+	485.793i	−1.13246	+	0.653826i	−0.944552	−	0.328361i	$-0.893504\pi$
$743$	−841.417	+	485.793i	−1.13246	+	0.653826i	−0.187907	+	0.982187i	$0.560170\pi$
$744$		0			0
$745$	171.135	−	296.414i	0.229711	−	0.397872i
$746$		0			0
$747$	42.9782	+	66.1345i	0.0575345	+	0.0885334i
$748$		0			0
$749$	−18.3795	+	10.6114i	−0.0245387	+	0.0141674i
$750$		0			0
$751$			941.805i			1.25407i	0.778992	+	0.627034i	$0.215731\pi$
$751$			941.805i			1.25407i	−0.778992	+	0.627034i	$0.784269\pi$
$752$		0			0
$753$	12.3529	+	20.1508i	0.0164049	+	0.0267607i
$754$		0			0
$755$	1097.67	+	633.741i	1.45387	+	0.839392i
$756$		0			0
$757$	147.926	−	256.215i	0.195411	−	0.338461i	−0.751624	−	0.659591i	$-0.770729\pi$
$757$	147.926	−	256.215i	0.195411	−	0.338461i	0.947035	+	0.321130i	$0.104063\pi$
$758$		0			0
$759$	−35.2656	−	57.5276i	−0.0464633	−	0.0757940i
$760$		0			0
$761$	−47.8819	+	82.9339i	−0.0629198	+	0.108980i	−0.895769	−	0.444519i	$-0.853375\pi$
$761$	−47.8819	+	82.9339i	−0.0629198	+	0.108980i	0.832850	+	0.553499i	$0.186708\pi$
$762$		0			0
$763$			194.073i			0.254356i
$764$		0			0
$765$	−959.403	+	50.5873i	−1.25412	+	0.0661272i
$766$		0			0
$767$	1025.71	+	1776.59i	1.33731	+	2.31628i
$768$		0			0
$769$	−566.429			−0.736578			−0.368289	−	0.929711i	$-0.620056\pi$
$769$	−566.429			−0.736578			−0.368289	+	0.929711i	$0.620056\pi$
$770$		0			0
$771$	39.9557	+	1516.60i	0.0518232	+	1.96705i
$772$		0			0
$773$	−667.545	+	385.407i	−0.863577	+	0.498587i	−0.865209	−	0.501412i	$-0.832814\pi$
$773$	−667.545	+	385.407i	−0.863577	+	0.498587i	0.00163121	+	0.999999i	$0.499481\pi$
$774$		0			0
$775$	126.599	−	73.0917i	0.163353	−	0.0943119i
$776$		0			0
$777$	−256.295	+	157.114i	−0.329852	+	0.202206i
$778$		0			0
$779$	331.879	−	618.518i	0.426033	−	0.793989i
$780$		0			0
$781$		−	134.268i		−	0.171918i
$782$		0			0
$783$	−995.066	−	474.038i	−1.27084	−	0.605412i
$784$		0			0
$785$	−417.990	+	723.980i	−0.532471	+	0.922268i
$786$		0			0
$787$	−536.750	−	309.893i	−0.682020	−	0.393764i	0.118596	−	0.992943i	$-0.462161\pi$
$787$	−536.750	−	309.893i	−0.682020	−	0.393764i	−0.800616	+	0.599178i	$0.795494\pi$
$788$		0			0
$789$	−795.542	+	20.9591i	−1.00829	+	0.0265641i
$790$		0			0
$791$		−	194.395i		−	0.245758i
$792$		0			0
$793$	1566.28	+	904.290i	1.97513	+	1.14034i
$794$		0			0
$795$	−294.186	−	159.669i	−0.370046	−	0.200842i
$796$		0			0
$797$	−323.319	−	186.669i	−0.405670	−	0.234214i	0.283257	−	0.959044i	$-0.408585\pi$
$797$	−323.319	−	186.669i	−0.405670	−	0.234214i	−0.688928	+	0.724830i	$0.741918\pi$
$798$		0			0
$799$	−522.681	−	905.309i	−0.654168	−	1.13305i
$800$		0			0
$801$	555.503	−	361.000i	0.693511	−	0.450686i
$802$		0			0
$803$	93.4632			0.116392
$804$		0			0
$805$	68.0987	−	117.950i	0.0845946	−	0.146522i
$806$		0			0
$807$	−168.665	−	91.5429i	−0.209003	−	0.113436i
$808$		0			0
$809$	−398.989			−0.493188			−0.246594	−	0.969119i	$-0.579311\pi$
$809$	−398.989			−0.493188			−0.246594	+	0.969119i	$0.579311\pi$
$810$		0			0
$811$	−492.099	+	284.113i	−0.606780	+	0.350325i	−0.771704	−	0.635982i	$-0.780595\pi$
$811$	−492.099	+	284.113i	−0.606780	+	0.350325i	0.164924	+	0.986306i	$0.447262\pi$
$812$		0			0
$813$	749.184	−	1380.35i	0.921505	−	1.69785i
$814$		0			0
$815$	−620.682	−	1075.05i	−0.761573	−	1.31908i
$816$		0			0
$817$	76.9130	−	47.6569i	0.0941407	−	0.0583316i
$818$		0			0
$819$	−262.434	+	170.546i	−0.320433	+	0.208237i
$820$		0			0
$821$	−159.565	+	276.375i	−0.194355	+	0.336633i	−0.946689	−	0.322149i	$-0.895595\pi$
$821$	−159.565	+	276.375i	−0.194355	+	0.336633i	0.752334	+	0.658782i	$0.228928\pi$
$822$		0			0
$823$	826.244			1.00394			0.501971	−	0.864885i	$-0.332609\pi$
$823$	826.244			1.00394			0.501971	+	0.864885i	$0.332609\pi$
$824$		0			0
$825$	25.1041	−	0.661383i	0.0304292	−	0.000801676i
$826$		0			0
$827$	−640.947	+	370.051i	−0.775026	+	0.447462i	−0.834665	−	0.550758i	$-0.814339\pi$
$827$	−640.947	+	370.051i	−0.775026	+	0.447462i	0.0596384	+	0.998220i	$0.481005\pi$
$828$		0			0
$829$			1430.53i			1.72561i	0.505539	+	0.862804i	$0.331294\pi$
$829$			1430.53i			1.72561i	−0.505539	+	0.862804i	$0.668706\pi$
$830$		0			0
$831$	119.704	+	195.269i	0.144048	+	0.234981i
$832$		0			0
$833$	−446.566	−	773.475i	−0.536094	−	0.928541i
$834$		0			0
$835$	−494.281	+	285.373i	−0.591953	+	0.341764i
$836$		0			0
$837$	650.739	+	310.004i	0.777465	+	0.370375i
$838$		0			0
$839$			271.541i			0.323649i	0.986820	+	0.161824i	$0.0517378\pi$
$839$			271.541i			0.323649i	−0.986820	+	0.161824i	$0.948262\pi$
$840$		0			0
$841$	412.743	+	714.893i	0.490777	+	0.850051i
$842$		0			0
$843$	−1210.23	−	656.852i	−1.43562	−	0.779183i
$844$		0			0
$845$	720.710	+	1248.31i	0.852911	+	1.47728i
$846$		0			0
$847$	198.978			0.234921
$848$		0			0
$849$	198.683	+	324.105i	0.234020	+	0.381749i
$850$		0			0
$851$		−	879.240i		−	1.03318i
$852$		0			0
$853$	−57.2939			−0.0671675			−0.0335838	−	0.999436i	$-0.510692\pi$
$853$	−57.2939			−0.0671675			−0.0335838	+	0.999436i	$0.510692\pi$
$854$		0			0
$855$	854.170	+	401.914i	0.999029	+	0.470075i
$856$		0			0
$857$		−	549.333i		−	0.640996i	−0.947249	−	0.320498i	$-0.896150\pi$
$857$		−	549.333i		−	0.640996i	0.947249	−	0.320498i	$-0.103850\pi$
$858$		0			0
$859$	−249.807			−0.290811			−0.145406	−	0.989372i	$-0.546449\pi$
$859$	−249.807			−0.290811			−0.145406	+	0.989372i	$0.546449\pi$
$860$		0			0
$861$	163.339	+	88.6518i	0.189708	+	0.102964i
$862$		0			0
$863$			33.3471i			0.0386409i	0.999813	+	0.0193204i	$0.00615027\pi$
$863$			33.3471i			0.0386409i	−0.999813	+	0.0193204i	$0.993850\pi$
$864$		0			0
$865$	−1131.74	+	653.412i	−1.30837	+	0.755390i
$866$		0			0
$867$	133.133	+	217.175i	0.153556	+	0.250491i
$868$		0			0
$869$	47.6847	−	27.5308i	0.0548731	−	0.0316810i
$870$		0			0
$871$	−1790.99			−2.05624
$872$		0			0
$873$	−22.9014	−	434.332i	−0.0262330	−	0.497517i
$874$		0			0
$875$	−90.3674	−	156.521i	−0.103277	−	0.178881i
$876$		0			0
$877$	−775.630	+	447.810i	−0.884413	+	0.510616i	−0.872111	−	0.489308i	$-0.837249\pi$
$877$	−775.630	+	447.810i	−0.884413	+	0.510616i	−0.0123019	+	0.999924i	$0.503916\pi$
$878$		0			0
$879$	434.385	+	235.762i	0.494181	+	0.268216i
$880$		0			0
$881$	−449.443			−0.510151			−0.255075	−	0.966921i	$-0.582100\pi$
$881$	−449.443			−0.510151			−0.255075	+	0.966921i	$0.582100\pi$
$882$		0			0
$883$	−432.651	−	749.374i	−0.489979	−	0.848669i	0.509954	−	0.860201i	$-0.329662\pi$
$883$	−432.651	−	749.374i	−0.489979	−	0.848669i	−0.999933	+	0.0115329i	$0.996329\pi$
$884$		0			0
$885$	1439.81	+	781.454i	1.62690	+	0.882998i
$886$		0			0
$887$		−	931.155i		−	1.04978i	−0.851170	−	0.524890i	$-0.824107\pi$
$887$		−	931.155i		−	1.04978i	0.851170	−	0.524890i	$-0.175893\pi$
$888$		0			0
$889$	157.454	+	90.9058i	0.177113	+	0.102256i
$890$		0			0
$891$	72.8477	+	100.132i	0.0817595	+	0.112381i
$892$		0			0
$893$	31.9630	+	1026.66i	0.0357929	+	1.14967i
$894$		0			0
$895$	789.096	−	455.585i	0.881672	−	0.509033i
$896$		0			0
$897$	−24.1084	−	915.079i	−0.0268766	−	1.02016i
$898$		0			0
$899$	−544.912	−	943.815i	−0.606131	−	1.04985i
$900$		0			0
$901$			390.816i			0.433758i
$902$		0			0
$903$	12.5202	+	20.4239i	0.0138652	+	0.0226178i
$904$		0			0
$905$	−54.4563	−	31.4403i	−0.0601727	−	0.0347407i
$906$		0			0
$907$			250.829i			0.276548i	0.990394	+	0.138274i	$0.0441554\pi$
$907$			250.829i			0.276548i	−0.990394	+	0.138274i	$0.955845\pi$
$908$		0			0
$909$	114.773	−	225.432i	0.126263	−	0.248000i
$910$		0			0
$911$	680.835	−	393.080i	0.747349	−	0.431482i	−0.0773862	−	0.997001i	$-0.524657\pi$
$911$	680.835	−	393.080i	0.747349	−	0.431482i	0.824735	+	0.565519i	$0.191324\pi$
$912$		0			0
$913$	−6.69861	+	11.6023i	−0.00733692	+	0.0127079i
$914$		0			0
$915$	1443.77	−	38.0371i	1.57789	−	0.0415706i
$916$		0			0
$917$	−135.677	+	234.999i	−0.147957	+	0.256269i
$918$		0			0
$919$	668.462			0.727380			0.363690	−	0.931520i	$-0.381517\pi$
$919$	668.462			0.727380			0.363690	+	0.931520i	$0.381517\pi$
$920$		0			0
$921$	438.233	+	237.850i	0.475823	+	0.258252i
$922$		0			0
$923$	910.751	−	1577.47i	0.986729	−	1.70907i
$924$		0			0
$925$	283.387	+	163.613i	0.306364	+	0.176879i
$926$		0			0
$927$	−711.502	−	362.242i	−0.767532	−	0.390768i
$928$		0			0
$929$	−1573.13			−1.69335			−0.846677	−	0.532108i	$-0.821400\pi$
$929$	−1573.13			−1.69335			−0.846677	+	0.532108i	$0.821400\pi$
$930$		0			0
$931$	27.3085	+	877.151i	0.0293324	+	0.942160i
$932$		0			0
$933$	−369.301	+	680.427i	−0.395821	+	0.729289i
$934$		0			0
$935$	−81.5947	−	141.326i	−0.0872671	−	0.151151i
$936$		0			0
$937$	−351.661	−	609.095i	−0.375305	−	0.650048i	0.615067	−	0.788475i	$-0.289129\pi$
$937$	−351.661	−	609.095i	−0.375305	−	0.650048i	−0.990373	+	0.138427i	$0.955795\pi$
$938$		0			0
$939$	383.601	−	706.774i	0.408520	−	0.752688i
$940$		0			0
$941$			1204.37i			1.27989i	0.768422	+	0.639943i	$0.221042\pi$
$941$			1204.37i			1.27989i	−0.768422	+	0.639943i	$0.778958\pi$
$942$		0			0
$943$	−470.731	+	271.777i	−0.499185	+	0.288205i
$944$		0			0
$945$	−107.493	+	225.641i	−0.113749	+	0.238774i
$946$		0			0
$947$	−805.350			−0.850422			−0.425211	−	0.905094i	$-0.639800\pi$
$947$	−805.350			−0.850422			−0.425211	+	0.905094i	$0.639800\pi$
$948$		0			0
$949$	1098.06	+	633.967i	1.15707	+	0.668037i
$950$		0			0
$951$	−1409.46	−	764.983i	−1.48208	−	0.804398i
$952$		0			0
$953$	−19.1016	−	11.0283i	−0.0200437	−	0.0115722i	0.489945	−	0.871754i	$-0.337017\pi$
$953$	−19.1016	−	11.0283i	−0.0200437	−	0.0115722i	−0.509988	+	0.860181i	$0.670350\pi$
$954$		0			0
$955$	767.766	−	1329.81i	0.803943	−	1.39247i
$956$		0			0
$957$	−4.93073	−	187.155i	−0.00515228	−	0.195565i
$958$		0			0
$959$	235.631			0.245705
$960$		0			0
$961$	−124.147	−	215.028i	−0.129185	−	0.223755i
$962$		0			0
$963$	5.99781	+	113.750i	0.00622826	+	0.118121i
$964$		0			0
$965$	1399.88	+	808.221i	1.45065	+	0.837535i
$966$		0			0
$967$	−551.443	−	955.126i	−0.570261	−	0.987721i	−0.996539	−	0.0831289i	$-0.973509\pi$
$967$	−551.443	−	955.126i	−0.570261	−	0.987721i	0.426278	−	0.904592i	$-0.359825\pi$
$968$		0			0
$969$	−63.3003	−	1100.38i	−0.0653254	−	1.13558i
$970$		0			0
$971$	−1145.08	−	661.109i	−1.17927	−	0.680854i	−0.223427	−	0.974721i	$-0.571725\pi$
$971$	−1145.08	−	661.109i	−1.17927	−	0.680854i	−0.955847	+	0.293866i	$0.905058\pi$
$972$		0			0
$973$	−163.838	−	283.776i	−0.168384	−	0.291650i
$974$		0			0
$975$	299.424	+	162.512i	0.307102	+	0.166679i
$976$		0			0
$977$	1364.73	+	787.927i	1.39686	+	0.806476i	0.994062	−	0.108814i	$-0.0347053\pi$
$977$	1364.73	+	787.927i	1.39686	+	0.806476i	0.402795	+	0.915290i	$0.368039\pi$
$978$		0			0
$979$	97.4548	+	56.2656i	0.0995453	+	0.0574725i
$980$		0			0
$981$	928.260	+	472.599i	0.946239	+	0.481752i
$982$		0			0
$983$		−	209.289i		−	0.212909i	−0.994318	−	0.106454i	$-0.966050\pi$
$983$		−	209.289i		−	0.212909i	0.994318	−	0.106454i	$-0.0339498\pi$
$984$		0			0
$985$	−552.436	−	956.847i	−0.560849	−	0.971419i
$986$		0			0
$987$	−271.858	+	7.16228i	−0.275439	+	0.00725662i
$988$		0			0
$989$	−70.0655			−0.0708448
$990$		0			0
$991$	117.245	+	67.6913i	0.118310	+	0.0683061i	0.557987	−	0.829850i	$-0.311574\pi$
$991$	117.245	+	67.6913i	0.118310	+	0.0683061i	−0.439677	+	0.898156i	$0.644907\pi$
$992$		0			0
$993$	−753.522	+	461.924i	−0.758833	+	0.465180i
$994$		0			0
$995$	−18.0391	+	31.2446i	−0.0181297	+	0.0314016i
$996$		0			0
$997$	543.649	−	941.628i	0.545285	−	0.944462i	−0.453304	−	0.891356i	$-0.649755\pi$
$997$	543.649	−	941.628i	0.545285	−	0.944462i	0.998589	−	0.0531055i	$-0.0169120\pi$
$998$		0			0
$999$	127.364	+	1608.47i	0.127492	+	1.61008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.1	✓	80
3.2	odd	2		2052.3.s.a.901.32		80
9.2	odd	6		2052.3.bl.a.1585.9		80
9.7	even	3		684.3.bl.a.673.15	yes	80
19.12	odd	6		684.3.bl.a.373.15	yes	80
57.50	even	6		2052.3.bl.a.145.9		80
171.88	odd	6	inner	684.3.s.a.601.1	yes	80
171.164	even	6		2052.3.s.a.829.32		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.1	✓	80	1.1	even	1	trivial
684.3.s.a.601.1	yes	80	171.88	odd	6	inner
684.3.bl.a.373.15	yes	80	19.12	odd	6
684.3.bl.a.673.15	yes	80	9.7	even	3
2052.3.s.a.829.32		80	171.164	even	6
2052.3.s.a.901.32		80	3.2	odd	2
2052.3.bl.a.145.9		80	57.50	even	6
2052.3.bl.a.1585.9		80	9.2	odd	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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.99896 + 0.0790095i) q^{3} +(-2.76024 - 4.78088i) q^{5} +(0.838417 + 1.45218i) q^{7} +(8.98751 - 0.473893i) q^{9} +O(q^{10})\)	\(q+(-2.99896 + 0.0790095i) q^{3} +(-2.76024 - 4.78088i) q^{5} +(0.838417 + 1.45218i) q^{7} +(8.98751 - 0.473893i) q^{9} +(0.764365 + 1.32392i) q^{11} +20.7389i q^{13} +(8.65559 + 14.1196i) q^{15} +(9.66839 - 16.7462i) q^{17} +(-16.1509 + 10.0074i) q^{19} +(-2.62911 - 4.28879i) q^{21} +14.7130 q^{23} +(-2.73787 + 4.74213i) q^{25} +(-26.9158 + 2.13128i) q^{27} +(35.3534 + 20.4113i) q^{29} +(-23.1199 - 13.3483i) q^{31} +(-2.39690 - 3.90999i) q^{33} +(4.62847 - 8.01674i) q^{35} -59.7594i q^{37} +(-1.63857 - 62.1953i) q^{39} +(-31.9942 + 18.4719i) q^{41} -4.76215 q^{43} +(-27.0733 - 41.6602i) q^{45} +(27.0304 - 46.8180i) q^{47} +(23.0941 - 40.0002i) q^{49} +(-27.6720 + 50.9849i) q^{51} +(-17.5032 + 10.1055i) q^{53} +(4.21966 - 7.30867i) q^{55} +(47.6452 - 31.2880i) q^{57} +(85.6644 - 49.4583i) q^{59} +(43.6035 - 75.5234i) q^{61} +(8.22346 + 12.6542i) q^{63} +(99.1504 - 57.2445i) q^{65} +86.3585i q^{67} +(-44.1237 + 1.16247i) q^{69} +(-76.0630 - 43.9150i) q^{71} +(30.5689 - 52.9469i) q^{73} +(7.83609 - 14.4378i) q^{75} +(-1.28171 + 2.21999i) q^{77} -36.0178i q^{79} +(80.5509 - 8.51824i) q^{81} +(4.38181 + 7.58953i) q^{83} -106.748 q^{85} +(-107.636 - 58.4194i) q^{87} +(63.7489 - 36.8055i) q^{89} +(-30.1167 + 17.3879i) q^{91} +(70.3903 + 38.2043i) q^{93} +(92.4247 + 49.5925i) q^{95} -48.3262i q^{97} +(7.49713 + 11.5365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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