LMFDB - Embedded newform 684.3.s.a.445.30

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			445.30
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.96397 - 2.26778i) q^{3} +(-0.319267 - 0.552987i) q^{5} +(-1.11619 - 1.93329i) q^{7} +(-1.28567 - 8.90770i) q^{9} +O(q^{10})$	\(q+(1.96397 - 2.26778i) q^{3} +(-0.319267 - 0.552987i) q^{5} +(-1.11619 - 1.93329i) q^{7} +(-1.28567 - 8.90770i) q^{9} +(1.89002 + 3.27360i) q^{11} +9.65113i q^{13} +(-1.88108 - 0.362020i) q^{15} +(11.4559 - 19.8422i) q^{17} +(7.12829 - 17.6121i) q^{19} +(-6.57644 - 1.26565i) q^{21} +7.93018 q^{23} +(12.2961 - 21.2975i) q^{25} +(-22.7257 - 14.5788i) q^{27} +(-26.3449 - 15.2102i) q^{29} +(-50.4054 - 29.1016i) q^{31} +(11.1357 + 2.14310i) q^{33} +(-0.712723 + 1.23447i) q^{35} +12.8801i q^{37} +(21.8867 + 18.9545i) q^{39} +(-50.1781 + 28.9703i) q^{41} +29.2021 q^{43} +(-4.51537 + 3.55489i) q^{45} +(22.2603 - 38.5561i) q^{47} +(22.0083 - 38.1194i) q^{49} +(-22.4988 - 64.9490i) q^{51} +(-15.1786 + 8.76336i) q^{53} +(1.20684 - 2.09031i) q^{55} +(-25.9408 - 50.7551i) q^{57} +(-41.2772 + 23.8314i) q^{59} +(-34.9957 + 60.6144i) q^{61} +(-15.7861 + 12.4282i) q^{63} +(5.33695 - 3.08129i) q^{65} -20.8270i q^{67} +(15.5746 - 17.9839i) q^{69} +(99.8380 + 57.6415i) q^{71} +(66.8138 - 115.725i) q^{73} +(-24.1490 - 69.7126i) q^{75} +(4.21922 - 7.30790i) q^{77} +15.8080i q^{79} +(-77.6941 + 22.9047i) q^{81} +(47.6602 + 82.5498i) q^{83} -14.6300 q^{85} +(-86.2339 + 29.8721i) q^{87} +(-70.8072 + 40.8805i) q^{89} +(18.6584 - 10.7725i) q^{91} +(-164.991 + 57.1540i) q^{93} +(-12.0151 + 1.68113i) q^{95} +45.2556i q^{97} +(26.7303 - 21.0445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.96397	−	2.26778i	0.654656	−	0.755927i
$3$	1.96397	−	2.26778i	0.654656	−	0.755927i
$4$		0			0
$5$	−0.319267	−	0.552987i	−0.0638534	−	0.110597i	0.832331	−	0.554278i	$-0.187006\pi$
$5$	−0.319267	−	0.552987i	−0.0638534	−	0.110597i	−0.896185	+	0.443681i	$0.853672\pi$
$6$		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
$9$	−1.28567	−	8.90770i	−0.142852	−	0.989744i
$10$		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
$13$			9.65113i			0.742394i	0.928554	+	0.371197i	$0.121053\pi$
$13$			9.65113i			0.742394i	−0.928554	+	0.371197i	$0.878947\pi$
$14$		0			0
$15$	−1.88108	−	0.362020i	−0.125406	−	0.0241347i
$16$		0			0
$17$	11.4559	−	19.8422i	0.673877	−	1.16719i	−0.302918	−	0.953017i	$-0.597961\pi$
$17$	11.4559	−	19.8422i	0.673877	−	1.16719i	0.976796	−	0.214173i	$-0.0687057\pi$
$18$		0			0
$19$	7.12829	−	17.6121i	0.375173	−	0.926955i
$19$	7.12829	−	17.6121i	0.375173	−	0.926955i
$20$		0			0
$21$	−6.57644	−	1.26565i	−0.313164	−	0.0602692i
$22$		0			0
$23$	7.93018			0.344791			0.172395	−	0.985028i	$-0.444849\pi$
$23$	7.93018			0.344791			0.172395	+	0.985028i	$0.444849\pi$
$24$		0			0
$25$	12.2961	−	21.2975i	0.491845	−	0.851901i
$26$		0			0
$27$	−22.7257	−	14.5788i	−0.841693	−	0.539956i
$28$		0			0
$29$	−26.3449	−	15.2102i	−0.908444	−	0.524490i	−0.0285136	−	0.999593i	$-0.509077\pi$
$29$	−26.3449	−	15.2102i	−0.908444	−	0.524490i	−0.879930	+	0.475103i	$0.842411\pi$
$30$		0			0
$31$	−50.4054	−	29.1016i	−1.62598	−	0.938761i	−0.985275	−	0.170976i	$-0.945308\pi$
$31$	−50.4054	−	29.1016i	−1.62598	−	0.938761i	−0.640707	−	0.767785i	$-0.721359\pi$
$32$		0			0
$33$	11.1357	+	2.14310i	0.337447	+	0.0649426i
$34$		0			0
$35$	−0.712723	+	1.23447i	−0.0203635	+	0.0352707i
$36$		0			0
$37$			12.8801i			0.348112i	0.984736	+	0.174056i	$0.0556873\pi$
$37$			12.8801i			0.348112i	−0.984736	+	0.174056i	$0.944313\pi$
$38$		0			0
$39$	21.8867	+	18.9545i	0.561196	+	0.486013i
$40$		0			0
$41$	−50.1781	+	28.9703i	−1.22386	+	0.706594i	−0.965738	−	0.259520i	$-0.916436\pi$
$41$	−50.1781	+	28.9703i	−1.22386	+	0.706594i	−0.258118	+	0.966113i	$0.583102\pi$
$42$		0			0
$43$	29.2021			0.679119			0.339560	−	0.940585i	$-0.389722\pi$
$43$	29.2021			0.679119			0.339560	+	0.940585i	$0.389722\pi$
$44$		0			0
$45$	−4.51537	+	3.55489i	−0.100342	+	0.0789976i
$46$		0			0
$47$	22.2603	−	38.5561i	0.473624	−	0.820342i	−0.525920	−	0.850534i	$-0.676279\pi$
$47$	22.2603	−	38.5561i	0.473624	−	0.820342i	0.999544	+	0.0301927i	$0.00961208\pi$
$48$		0			0
$49$	22.0083	−	38.1194i	0.449148	−	0.777947i
$50$		0			0
$51$	−22.4988	−	64.9490i	−0.441153	−	1.27351i
$52$		0			0
$53$	−15.1786	+	8.76336i	−0.286389	+	0.165346i	−0.636312	−	0.771432i	$-0.719541\pi$
$53$	−15.1786	+	8.76336i	−0.286389	+	0.165346i	0.349924	+	0.936778i	$0.386208\pi$
$54$		0			0
$55$	1.20684	−	2.09031i	0.0219425	−	0.0380056i
$56$		0			0
$57$	−25.9408	−	50.7551i	−0.455101	−	0.890440i
$58$		0			0
$59$	−41.2772	+	23.8314i	−0.699613	+	0.403922i	−0.807203	−	0.590274i	$-0.799020\pi$
$59$	−41.2772	+	23.8314i	−0.699613	+	0.403922i	0.107590	+	0.994195i	$0.465687\pi$
$60$		0			0
$61$	−34.9957	+	60.6144i	−0.573700	+	0.993678i	0.422481	+	0.906372i	$0.361159\pi$
$61$	−34.9957	+	60.6144i	−0.573700	+	0.993678i	−0.996181	+	0.0873066i	$0.972174\pi$
$62$		0			0
$63$	−15.7861	+	12.4282i	−0.250573	+	0.197273i
$64$		0			0
$65$	5.33695	−	3.08129i	0.0821069	−	0.0474044i
$66$		0			0
$67$		−	20.8270i		−	0.310851i	−0.987848	−	0.155425i	$-0.950325\pi$
$67$		−	20.8270i		−	0.310851i	0.987848	−	0.155425i	$-0.0496748\pi$
$68$		0			0
$69$	15.5746	−	17.9839i	0.225719	−	0.260637i
$70$		0			0
$71$	99.8380	+	57.6415i	1.40617	+	0.811852i	0.995016	−	0.0997140i	$-0.0317928\pi$
$71$	99.8380	+	57.6415i	1.40617	+	0.811852i	0.411153	+	0.911566i	$0.365126\pi$
$72$		0			0
$73$	66.8138	−	115.725i	0.915257	−	1.58527i	0.108733	−	0.994071i	$-0.465321\pi$
$73$	66.8138	−	115.725i	0.915257	−	1.58527i	0.806524	−	0.591201i	$-0.201346\pi$
$74$		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
$79$			15.8080i			0.200101i	0.994982	+	0.100050i	$0.0319004\pi$
$79$			15.8080i			0.200101i	−0.994982	+	0.100050i	$0.968100\pi$
$80$		0			0
$81$	−77.6941	+	22.9047i	−0.959187	+	0.282774i
$82$		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
$85$	−14.6300			−0.172118
$86$		0			0
$87$	−86.2339	+	29.8721i	−0.991194	+	0.343357i
$88$		0			0
$89$	−70.8072	+	40.8805i	−0.795586	+	0.459332i	−0.841925	−	0.539594i	$-0.818578\pi$
$89$	−70.8072	+	40.8805i	−0.795586	+	0.459332i	0.0463393	+	0.998926i	$0.485244\pi$
$90$		0			0
$91$	18.6584	−	10.7725i	0.205038	−	0.118379i
$92$		0			0
$93$	−164.991	+	57.1540i	−1.77409	+	0.614559i
$94$		0			0
$95$	−12.0151	+	1.68113i	−0.126475	+	0.0176961i
$96$		0			0
$97$			45.2556i			0.466552i	0.972411	+	0.233276i	$0.0749446\pi$
$97$			45.2556i			0.466552i	−0.972411	+	0.233276i	$0.925055\pi$
$98$		0			0
$99$	26.7303	−	21.0445i	0.270003	−	0.212570i
$100$		0			0
$101$	−18.6949	+	32.3805i	−0.185098	+	0.320599i	−0.943609	−	0.331061i	$-0.892594\pi$
$101$	−18.6949	+	32.3805i	−0.185098	+	0.320599i	0.758512	+	0.651659i	$0.225927\pi$
$102$		0			0
$103$	−95.1351	−	54.9263i	−0.923642	−	0.533265i	−0.0388467	−	0.999245i	$-0.512368\pi$
$103$	−95.1351	−	54.9263i	−0.923642	−	0.533265i	−0.884795	+	0.465980i	$0.845702\pi$
$104$		0			0
$105$	1.39975	+	4.04077i	0.0133310	+	0.0384835i
$106$		0			0
$107$		−	199.591i		−	1.86533i	−0.360738	−	0.932667i	$-0.617475\pi$
$107$		−	199.591i		−	1.86533i	0.360738	−	0.932667i	$-0.382525\pi$
$108$		0			0
$109$	−106.877	−	61.7056i	−0.980526	−	0.566107i	−0.0780969	−	0.996946i	$-0.524884\pi$
$109$	−106.877	−	61.7056i	−0.980526	−	0.566107i	−0.902429	+	0.430839i	$0.858218\pi$
$110$		0			0
$111$	29.2093	+	25.2961i	0.263147	+	0.227893i
$112$		0			0
$113$	141.848	+	81.8961i	1.25529	+	0.724744i	0.972156	−	0.234335i	$-0.0752913\pi$
$113$	141.848	+	81.8961i	1.25529	+	0.724744i	0.283138	+	0.959079i	$0.408625\pi$
$114$		0			0
$115$	−2.53185	−	4.38529i	−0.0220161	−	0.0381329i
$116$		0			0
$117$	85.9693	−	12.4082i	0.734781	−	0.106053i
$118$		0			0
$119$	−51.1478			−0.429813
$120$		0			0
$121$	53.3557	−	92.4147i	0.440956	−	0.763758i
$122$		0			0
$123$	−32.8497	+	170.690i	−0.267071	+	1.38772i
$124$		0			0
$125$	−31.6664			−0.253331
$126$		0			0
$127$	200.120	−	115.539i	1.57575	−	0.909758i	0.580304	−	0.814400i	$-0.302934\pi$
$127$	200.120	−	115.539i	1.57575	−	0.909758i	0.995443	−	0.0953582i	$-0.0303996\pi$
$128$		0			0
$129$	57.3520	−	66.2241i	0.444589	−	0.513365i
$130$		0			0
$131$	67.8954	+	117.598i	0.518286	+	0.897697i	0.999774	+	0.0212447i	$0.00676291\pi$
$131$	67.8954	+	117.598i	0.518286	+	0.897697i	−0.481489	+	0.876452i	$0.659904\pi$
$132$		0			0
$133$	−42.0059	+	5.87737i	−0.315834	+	0.0441908i
$134$		0			0
$135$	−0.806311	+	17.2216i	−0.00597267	+	0.127567i
$136$		0			0
$137$	49.7867	−	86.2331i	0.363407	−	0.629439i	−0.625112	−	0.780535i	$-0.714947\pi$
$137$	49.7867	−	86.2331i	0.363407	−	0.629439i	0.988519	+	0.151096i	$0.0482802\pi$
$138$		0			0
$139$	181.303			1.30434			0.652171	−	0.758072i	$-0.273858\pi$
$139$	181.303			1.30434			0.652171	+	0.758072i	$0.273858\pi$
$140$		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
$147$	−43.2230	−	124.775i	−0.294034	−	0.848811i
$148$		0			0
$149$	26.2493	+	45.4652i	0.176170	+	0.305135i	0.940566	−	0.339612i	$-0.110296\pi$
$149$	26.2493	+	45.4652i	0.176170	+	0.305135i	−0.764396	+	0.644748i	$0.776962\pi$
$150$		0			0
$151$	222.845	−	128.660i	1.47579	−	0.852050i	0.476167	−	0.879355i	$-0.342026\pi$
$151$	222.845	−	128.660i	1.47579	−	0.852050i	0.999627	+	0.0273044i	$0.00869233\pi$
$152$		0			0
$153$	−191.477	−	76.5353i	−1.25148	−	0.500231i
$154$		0			0
$155$			37.1647i			0.239773i
$156$		0			0
$157$	20.1240	+	34.8558i	0.128178	+	0.222012i	0.922971	−	0.384870i	$-0.125754\pi$
$157$	20.1240	+	34.8558i	0.128178	+	0.222012i	−0.794792	+	0.606881i	$0.792420\pi$
$158$		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
$165$	−2.37017	−	6.84215i	−0.0143647	−	0.0414676i
$166$		0			0
$167$			327.035i			1.95830i	0.203150	+	0.979148i	$0.434882\pi$
$167$			327.035i			1.95830i	−0.203150	+	0.979148i	$0.565118\pi$
$168$		0			0
$169$	75.8557			0.448850
$170$		0			0
$171$	−166.048	−	40.8532i	−0.971042	−	0.238908i
$172$		0			0
$173$		−	171.961i		−	0.993994i	−0.867752	−	0.496997i	$-0.834436\pi$
$173$		−	171.961i		−	0.993994i	0.867752	−	0.496997i	$-0.165564\pi$
$174$		0			0
$175$	−54.8991			−0.313709
$176$		0			0
$177$	−27.0226	+	140.412i	−0.152670	+	0.793286i
$178$		0			0
$179$			253.843i			1.41812i	0.705151	+	0.709058i	$0.250879\pi$
$179$			253.843i			1.41812i	−0.705151	+	0.709058i	$0.749121\pi$
$180$		0			0
$181$	193.550	−	111.746i	1.06934	−	0.617383i	0.141338	−	0.989961i	$-0.454860\pi$
$181$	193.550	−	111.746i	1.06934	−	0.617383i	0.928001	+	0.372578i	$0.121526\pi$
$182$		0			0
$183$	68.7297	+	198.407i	0.375572	+	1.08419i
$184$		0			0
$185$	7.12254	−	4.11220i	0.0385002	−	0.0222281i
$186$		0			0
$187$	86.6074			0.463141
$188$		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
$193$	−179.973	+	103.908i	−0.932504	+	0.538381i	−0.887603	−	0.460610i	$-0.847631\pi$
$193$	−179.973	+	103.908i	−0.932504	+	0.538381i	−0.0449012	+	0.998991i	$0.514297\pi$
$194$		0			0
$195$	3.49390	−	18.1546i	0.0179174	−	0.0931004i
$196$		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	0.928676	−	0.370892i	$-0.120948\pi$
$199$	28.4841	+	49.3359i	0.143136	+	0.247919i	−0.785540	+	0.618811i	$0.787615\pi$
$200$		0			0
$201$	−47.2311	−	40.9035i	−0.234980	−	0.203500i
$202$		0			0
$203$			67.9097i			0.334531i
$204$		0			0
$205$	32.0404	+	18.4986i	0.156295	+	0.0902369i
$206$		0			0
$207$	−10.1956	−	70.6397i	−0.0492541	−	0.341254i
$208$		0			0
$209$	71.1277	−	9.95204i	0.340324	−	0.0476174i
$210$		0			0
$211$	−29.7706	+	17.1881i	−0.141093	+	0.0814600i	−0.568885	−	0.822417i	$-0.692625\pi$
$211$	−29.7706	+	17.1881i	−0.141093	+	0.0814600i	0.427792	+	0.903877i	$0.359292\pi$
$212$		0			0
$213$	326.797	−	113.205i	1.53426	−	0.531478i
$214$		0			0
$215$	−9.32328	−	16.1484i	−0.0433641	−	0.0751088i
$216$		0			0
$217$			129.931i			0.598761i
$218$		0			0
$219$	−131.219	−	378.799i	−0.599172	−	1.72968i
$220$		0			0
$221$	191.500	+	110.563i	0.866515	+	0.500283i
$222$		0			0
$223$			270.439i			1.21273i	0.795187	+	0.606364i	$0.207373\pi$
$223$			270.439i			1.21273i	−0.795187	+	0.606364i	$0.792627\pi$
$224$		0			0
$225$	−205.521	−	82.1487i	−0.913425	−	0.365105i
$226$		0			0
$227$	115.627	−	66.7570i	0.509368	−	0.294084i	−0.223206	−	0.974771i	$-0.571652\pi$
$227$	115.627	−	66.7570i	0.509368	−	0.294084i	0.732574	+	0.680688i	$0.238319\pi$
$228$		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
$231$	−8.28632	−	23.9208i	−0.0358715	−	0.103553i
$232$		0			0
$233$	−49.8017	+	86.2591i	−0.213741	+	0.370211i	−0.952882	−	0.303340i	$-0.901898\pi$
$233$	−49.8017	+	86.2591i	−0.213741	+	0.370211i	0.739141	+	0.673550i	$0.235232\pi$
$234$		0			0
$235$	−28.4280			−0.120970
$236$		0			0
$237$	35.8490	+	31.0463i	0.151262	+	0.130997i
$238$		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
$241$	−38.4823	−	22.2178i	−0.159678	−	0.0921900i	0.418032	−	0.908432i	$-0.362720\pi$
$241$	−38.4823	−	22.2178i	−0.159678	−	0.0921900i	−0.577710	+	0.816242i	$0.696053\pi$
$242$		0			0
$243$	−100.646	+	221.177i	−0.414180	+	0.910195i
$244$		0			0
$245$	−28.1061			−0.114719
$246$		0			0
$247$	169.977	+	68.7960i	0.688166	+	0.278526i
$248$		0			0
$249$	280.808	+	54.0423i	1.12774	+	0.217037i
$250$		0			0
$251$	216.564	+	375.100i	0.862805	+	1.49442i	0.869210	+	0.494443i	$0.164628\pi$
$251$	216.564	+	375.100i	0.862805	+	1.49442i	−0.00640431	+	0.999979i	$0.502039\pi$
$252$		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
$257$			98.3739i			0.382778i	0.981514	+	0.191389i	$0.0612992\pi$
$257$			98.3739i			0.382778i	−0.981514	+	0.191389i	$0.938701\pi$
$258$		0			0
$259$	24.9010	−	14.3766i	0.0961430	−	0.0555082i
$260$		0			0
$261$	−101.617	+	254.227i	−0.389338	+	0.974051i
$262$		0			0
$263$	128.166			0.487324			0.243662	−	0.969860i	$-0.421651\pi$
$263$	128.166			0.487324			0.243662	+	0.969860i	$0.421651\pi$
$264$		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	0.892478	−	0.451091i	$-0.148965\pi$
$269$	255.028	+	147.241i	0.948061	+	0.547363i	0.0555826	+	0.998454i	$0.482298\pi$
$270$		0			0
$271$	35.9512	−	62.2693i	0.132661	−	0.229776i	−0.792040	−	0.610469i	$-0.790981\pi$
$271$	35.9512	−	62.2693i	0.132661	−	0.229776i	0.924702	+	0.380693i	$0.124314\pi$
$272$		0			0
$273$	12.2150	−	63.4700i	0.0447435	−	0.232491i
$274$		0			0
$275$	92.9596			0.338035
$276$		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
$279$	−194.423	+	486.411i	−0.696858	+	1.74341i
$280$		0			0
$281$	−406.779	−	234.854i	−1.44761	−	0.835780i	−0.449275	−	0.893394i	$-0.648317\pi$
$281$	−406.779	−	234.854i	−1.44761	−	0.835780i	−0.998339	+	0.0576137i	$0.981651\pi$
$282$		0			0
$283$	28.5464	+	49.4439i	0.100871	+	0.174713i	0.912044	−	0.410093i	$-0.134504\pi$
$283$	28.5464	+	49.4439i	0.100871	+	0.174713i	−0.811173	+	0.584806i	$0.801170\pi$
$284$		0			0
$285$	−19.7849	+	30.5493i	−0.0694205	+	0.107191i
$286$		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
$291$	102.630	+	88.8804i	0.352680	+	0.305431i
$292$		0			0
$293$	−15.2683	−	8.81513i	−0.0521101	−	0.0300858i	0.473719	−	0.880676i	$-0.342911\pi$
$293$	−15.2683	−	8.81513i	−0.0521101	−	0.0300858i	−0.525829	+	0.850590i	$0.676245\pi$
$294$		0			0
$295$	26.3569	+	15.2172i	0.0893454	+	0.0515836i
$296$		0			0
$297$	4.77324	−	101.949i	0.0160715	−	0.343263i
$298$		0			0
$299$			76.5352i			0.255971i
$300$		0			0
$301$	−32.5950	−	56.4562i	−0.108289	−	0.187562i
$302$		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	0.997307	−	0.0733377i	$-0.0233651\pi$
$307$	439.762	+	253.897i	1.43245	+	0.827024i	0.435141	+	0.900362i	$0.356698\pi$
$308$		0			0
$309$	−311.403	+	107.872i	−1.00778	+	0.349101i
$310$		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
$313$	202.052	−	349.964i	0.645534	−	1.11810i	−0.338644	−	0.940914i	$-0.609968\pi$
$313$	202.052	−	349.964i	0.645534	−	1.11810i	0.984178	−	0.177183i	$-0.0566983\pi$
$314$		0			0
$315$	11.9126	+	4.76160i	0.0378179	+	0.0151162i
$316$		0			0
$317$	192.714	+	111.264i	0.607931	+	0.350989i	0.772155	−	0.635434i	$-0.219179\pi$
$317$	192.714	+	111.264i	0.607931	+	0.350989i	−0.164224	+	0.986423i	$0.552512\pi$
$318$		0			0
$319$		−	114.990i		−	0.360471i
$320$		0			0
$321$	−452.628	−	391.990i	−1.41006	−	1.22115i
$322$		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
$327$	−349.838	+	121.187i	−1.06984	+	0.370601i
$328$		0			0
$329$	−99.3868			−0.302088
$330$		0			0
$331$	−114.801	+	66.2803i	−0.346830	+	0.200243i	−0.663288	−	0.748364i	$-0.730840\pi$
$331$	−114.801	+	66.2803i	−0.346830	+	0.200243i	0.316458	+	0.948607i	$0.397506\pi$
$332$		0			0
$333$	114.732	−	16.5596i	0.344541	−	0.0497285i
$334$		0			0
$335$	−11.5171	+	6.64938i	−0.0343793	+	0.0198489i
$336$		0			0
$337$	−164.940	+	95.2280i	−0.489435	+	0.282576i	−0.724340	−	0.689443i	$-0.757855\pi$
$337$	−164.940	+	95.2280i	−0.489435	+	0.282576i	0.234905	+	0.972018i	$0.424522\pi$
$338$		0			0
$339$	464.308	−	160.840i	1.36964	−	0.474453i
$340$		0			0
$341$		−	220.010i		−	0.645190i
$342$		0			0
$343$	−207.648			−0.605386
$344$		0			0
$345$	−14.9173	−	2.87088i	−0.0432387	−	0.00832140i
$346$		0			0
$347$	257.057	+	445.236i	0.740799	+	1.28310i	0.952132	+	0.305687i	$0.0988862\pi$
$347$	257.057	+	445.236i	0.740799	+	1.28310i	−0.211333	+	0.977414i	$0.567780\pi$
$348$		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
$351$	140.702	−	219.329i	0.400860	−	0.624869i
$352$		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
$355$		−	73.6122i		−	0.207358i
$356$		0			0
$357$	−100.452	+	115.992i	−0.281380	+	0.324907i
$358$		0			0
$359$	128.660	−	222.846i	0.358386	−	0.620742i	−0.629306	−	0.777158i	$-0.716661\pi$
$359$	128.660	−	222.846i	0.358386	−	0.620742i	0.987691	+	0.156416i	$0.0499940\pi$
$360$		0			0
$361$	−259.375	−	251.089i	−0.718490	−	0.695537i
$362$		0			0
$363$	−104.788	−	302.499i	−0.288671	−	0.833329i
$364$		0			0
$365$	−85.3258			−0.233769
$366$		0			0
$367$	−262.727	+	455.056i	−0.715876	+	1.23993i	0.246744	+	0.969081i	$0.420639\pi$
$367$	−262.727	+	455.056i	−0.715876	+	1.23993i	−0.962621	+	0.270853i	$0.912694\pi$
$368$		0			0
$369$	322.571	+	409.725i	0.874177	+	1.11037i
$370$		0			0
$371$	33.8843	+	19.5631i	0.0913323	+	0.0527307i
$372$		0			0
$373$	−221.645	−	127.967i	−0.594223	−	0.343075i	0.172542	−	0.985002i	$-0.444802\pi$
$373$	−221.645	−	127.967i	−0.594223	−	0.343075i	−0.766766	+	0.641927i	$0.778135\pi$
$374$		0			0
$375$	−62.1917	+	71.8124i	−0.165845	+	0.191500i
$376$		0			0
$377$	146.796	−	254.258i	0.389379	−	0.674424i
$378$		0			0
$379$		−	308.432i		−	0.813806i	−0.913471	−	0.406903i	$-0.866609\pi$
$379$		−	308.432i		−	0.813806i	0.913471	−	0.406903i	$-0.133391\pi$
$380$		0			0
$381$	131.011	−	680.744i	0.343861	−	1.78673i
$382$		0			0
$383$	−268.964	+	155.287i	−0.702257	+	0.405448i	−0.808187	−	0.588925i	$-0.799551\pi$
$383$	−268.964	+	155.287i	−0.702257	+	0.405448i	0.105931	+	0.994374i	$0.466218\pi$
$384$		0			0
$385$	−5.38823			−0.0139954
$386$		0			0
$387$	−37.5443	−	260.124i	−0.0970136	−	0.672154i
$388$		0			0
$389$	−127.801	+	221.358i	−0.328537	+	0.569043i	−0.982222	−	0.187724i	$-0.939889\pi$
$389$	−127.801	+	221.358i	−0.328537	+	0.569043i	0.653685	+	0.756767i	$0.273222\pi$
$390$		0			0
$391$	90.8475	−	157.352i	0.232347	−	0.402436i
$392$		0			0
$393$	400.032	+	76.9872i	1.01789	+	0.195896i
$394$		0			0
$395$	8.74160	−	5.04697i	0.0221306	−	0.0127771i
$396$		0			0
$397$	38.6713	−	66.9806i	0.0974087	−	0.168717i	−0.813203	−	0.581981i	$-0.802278\pi$
$397$	38.6713	−	66.9806i	0.0974087	−	0.168717i	0.910611	+	0.413264i	$0.135611\pi$
$398$		0			0
$399$	−69.1696	+	106.803i	−0.173357	+	0.267677i
$400$		0			0
$401$	−177.940	+	102.734i	−0.443741	+	0.256194i	−0.705183	−	0.709025i	$-0.749135\pi$
$401$	−177.940	+	102.734i	−0.443741	+	0.256194i	0.261442	+	0.965219i	$0.415802\pi$
$402$		0			0
$403$	280.863	−	486.469i	0.696931	−	1.20712i
$404$		0			0
$405$	37.4712	+	35.6511i	0.0925214	+	0.0880274i
$406$		0			0
$407$	−42.1644	+	24.3436i	−0.103598	+	0.0598124i
$408$		0			0
$409$		−	136.052i		−	0.332644i	−0.986071	−	0.166322i	$-0.946811\pi$
$409$		−	136.052i		−	0.332644i	0.986071	−	0.166322i	$-0.0531892\pi$
$410$		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
$421$		−	57.6871i		−	0.137024i	−0.997650	−	0.0685120i	$-0.978175\pi$
$421$		−	57.6871i		−	0.137024i	0.997650	−	0.0685120i	$-0.0218251\pi$
$422$		0			0
$423$	−372.065	−	148.718i	−0.879586	−	0.351579i
$424$		0			0
$425$	−281.727	−	487.966i	−0.662887	−	1.14815i
$426$		0			0
$427$	156.247			0.365918
$428$		0			0
$429$	−20.6834	+	107.473i	−0.0482130	+	0.250519i
$430$		0			0
$431$	419.316	−	242.092i	0.972892	−	0.561699i	0.0727750	−	0.997348i	$-0.476815\pi$
$431$	419.316	−	242.092i	0.972892	−	0.561699i	0.900117	+	0.435649i	$0.143481\pi$
$432$		0			0
$433$	−356.336	+	205.731i	−0.822948	+	0.475129i	−0.851432	−	0.524465i	$-0.824265\pi$
$433$	−356.336	+	205.731i	−0.822948	+	0.475129i	0.0284841	+	0.999594i	$0.490932\pi$
$434$		0			0
$435$	44.0505	+	38.1491i	0.101266	+	0.0876990i
$436$		0			0
$437$	56.5286	−	139.668i	0.129356	−	0.319605i
$438$		0			0
$439$		−	234.925i		−	0.535136i	−0.963539	−	0.267568i	$-0.913780\pi$
$439$		−	234.925i		−	0.535136i	0.963539	−	0.267568i	$-0.0862200\pi$
$440$		0			0
$441$	−367.852	−	147.034i	−0.834130	−	0.333410i
$442$		0			0
$443$	−201.805	+	349.537i	−0.455542	+	0.789023i	−0.998719	−	0.0505957i	$-0.983888\pi$
$443$	−201.805	+	349.537i	−0.455542	+	0.789023i	0.543177	+	0.839618i	$0.317221\pi$
$444$		0			0
$445$	45.2128	+	26.1036i	0.101602	+	0.0586598i
$446$		0			0
$447$	154.658	+	29.7643i	0.345991	+	0.0665869i
$448$		0			0
$449$		−	300.202i		−	0.668601i	−0.942467	−	0.334300i	$-0.891500\pi$
$449$		−	300.202i		−	0.668601i	0.942467	−	0.334300i	$-0.108500\pi$
$450$		0			0
$451$	−189.675	−	109.509i	−0.420565	−	0.242813i
$452$		0			0
$453$	145.888	−	758.047i	0.322049	−	1.67339i
$454$		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
$459$	−549.620	+	283.915i	−1.19743	+	0.618552i
$460$		0			0
$461$	−576.654			−1.25088			−0.625438	−	0.780274i	$-0.715080\pi$
$461$	−576.654			−1.25088			−0.625438	+	0.780274i	$0.715080\pi$
$462$		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
$465$	84.2815	+	72.9903i	0.181251	+	0.156968i
$466$		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
$471$	118.568	+	22.8188i	0.251737	+	0.0484476i
$472$		0			0
$473$	55.1925	+	95.5962i	0.116686	+	0.202106i
$474$		0			0
$475$	−287.445	−	368.376i	−0.605147	−	0.775529i
$476$		0			0
$477$	97.5760	+	123.940i	0.204562	+	0.259831i
$478$		0			0
$479$	329.378	−	570.500i	0.687638	−	1.19102i	−0.284962	−	0.958539i	$-0.591981\pi$
$479$	329.378	−	570.500i	0.687638	−	1.19102i	0.972600	−	0.232485i	$-0.0746856\pi$
$480$		0			0
$481$	−124.308			−0.258436
$482$		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	$-0.941911\pi$
$487$		−	176.762i		−	0.362961i	0.983395	−	0.181480i	$-0.0580889\pi$
$488$		0			0
$489$	−29.1018	+	33.6037i	−0.0595128	+	0.0687192i
$490$		0			0
$491$	−300.265	−	520.073i	−0.611537	−	1.05921i	−0.990982	−	0.133998i	$-0.957218\pi$
$491$	−300.265	−	520.073i	−0.611537	−	1.05921i	0.379445	−	0.925214i	$-0.376115\pi$
$492$		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
$497$		−	257.355i		−	0.517816i
$498$		0			0
$499$	−2.07023	−	3.58575i	−0.00414876	−	0.00718587i	0.863944	−	0.503589i	$-0.167987\pi$
$499$	−2.07023	−	3.58575i	−0.00414876	−	0.00718587i	−0.868092	+	0.496403i	$0.834654\pi$
$500$		0			0
$501$	741.645	+	642.286i	1.48033	+	1.28201i
$502$		0			0
$503$	199.290	+	345.180i	0.396203	+	0.686243i	0.993254	−	0.115960i	$-0.0369944\pi$
$503$	199.290	+	345.180i	0.396203	+	0.686243i	−0.597051	+	0.802203i	$0.703661\pi$
$504$		0			0
$505$	23.8746			0.0472765
$506$		0			0
$507$	148.978	−	172.024i	0.293842	−	0.339298i
$508$		0			0
$509$		−	345.377i		−	0.678540i	−0.940689	−	0.339270i	$-0.889820\pi$
$509$		−	345.377i		−	0.678540i	0.940689	−	0.339270i	$-0.110180\pi$
$510$		0			0
$511$	−298.307			−0.583770
$512$		0			0
$513$	−418.759	+	296.327i	−0.816295	+	0.577635i
$514$		0			0
$515$			70.1446i			0.136203i
$516$		0			0
$517$	168.290			0.325512
$518$		0			0
$519$	−389.970	−	337.726i	−0.751387	−	0.650724i
$520$		0			0
$521$		−	828.985i		−	1.59114i	−0.605861	−	0.795571i	$-0.707171\pi$
$521$		−	828.985i		−	1.59114i	0.605861	−	0.795571i	$-0.292829\pi$
$522$		0			0
$523$	16.3065	−	9.41456i	0.0311788	−	0.0180011i	−0.484330	−	0.874886i	$-0.660936\pi$
$523$	16.3065	−	9.41456i	0.0311788	−	0.0180011i	0.515508	+	0.856885i	$0.327603\pi$
$524$		0			0
$525$	−107.820	+	124.499i	−0.205372	+	0.237141i
$526$		0			0
$527$	−1154.88	+	666.771i	−2.19143	+	1.26522i
$528$		0			0
$529$	−466.112			−0.881119
$530$		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
$535$	−110.371	+	63.7228i	−0.206301	+	0.119108i
$536$		0			0
$537$	575.660	+	498.538i	1.07199	+	0.928377i
$538$		0			0
$539$	166.384			0.308690
$540$		0			0
$541$	267.260	+	462.908i	0.494011	+	0.855652i	0.999976	−	0.00690205i	$-0.00219701\pi$
$541$	267.260	+	462.908i	0.494011	+	0.855652i	−0.505965	+	0.862554i	$0.668864\pi$
$542$		0			0
$543$	126.710	−	658.396i	0.233352	−	1.21252i
$544$		0			0
$545$			78.8023i			0.144591i
$546$		0			0
$547$	198.579	+	114.650i	0.363033	+	0.209597i	0.670410	−	0.741990i	$-0.266118\pi$
$547$	198.579	+	114.650i	0.363033	+	0.209597i	−0.307377	+	0.951588i	$0.599451\pi$
$548$		0			0
$549$	584.927	+	233.801i	1.06544	+	0.425868i
$550$		0			0
$551$	−455.678	+	355.567i	−0.827002	+	0.645312i
$552$		0			0
$553$	30.5614	−	17.6446i	0.0552648	−	0.0319071i
$554$		0			0
$555$	4.66286	−	24.2286i	0.00840155	−	0.0436551i
$556$		0			0
$557$	5.22291	+	9.04635i	0.00937686	+	0.0162412i	0.870676	−	0.491857i	$-0.163682\pi$
$557$	5.22291	+	9.04635i	0.00937686	+	0.0162412i	−0.861299	+	0.508099i	$0.830349\pi$
$558$		0			0
$559$			281.833i			0.504174i
$560$		0			0
$561$	170.094	−	196.407i	0.303198	−	0.350101i
$562$		0			0
$563$	−542.443	−	313.179i	−0.963486	−	0.556269i	−0.0662420	−	0.997804i	$-0.521101\pi$
$563$	−542.443	−	313.179i	−0.963486	−	0.556269i	−0.897244	+	0.441535i	$0.854434\pi$
$564$		0			0
$565$		−	104.587i		−	0.185110i
$566$		0			0
$567$	131.003	+	124.639i	0.231045	+	0.219823i
$568$		0			0
$569$	358.551	−	207.010i	0.630143	−	0.363813i	−0.150665	−	0.988585i	$-0.548141\pi$
$569$	358.551	−	207.010i	0.630143	−	0.363813i	0.780807	+	0.624772i	$0.214808\pi$
$570$		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
$573$	361.703	+	69.6108i	0.631245	+	0.121485i
$574$		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
$579$	−117.822	+	612.211i	−0.203492	+	1.05736i
$580$		0			0
$581$	106.395	−	184.282i	0.183124	−	0.317181i
$582$		0			0
$583$	−57.3756	−	33.1258i	−0.0984143	−	0.0568195i
$584$		0			0
$585$	−34.3087	−	43.5784i	−0.0586474	−	0.0744930i
$586$		0			0
$587$	−1141.39			−1.94445			−0.972225	−	0.234047i	$-0.924803\pi$
$587$	−1141.39			−1.94445			−0.972225	+	0.234047i	$0.924803\pi$
$588$		0			0
$589$	−871.846	+	680.303i	−1.48021	+	1.15501i
$590$		0			0
$591$	−142.949	+	165.062i	−0.241876	+	0.279293i
$592$		0			0
$593$	168.444	+	291.754i	0.284054	+	0.491996i	0.972379	−	0.233406i	$-0.0749872\pi$
$593$	168.444	+	291.754i	0.284054	+	0.491996i	−0.688325	+	0.725402i	$0.741654\pi$
$594$		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
$599$		−	200.900i		−	0.335392i	−0.985839	−	0.167696i	$-0.946367\pi$
$599$		−	200.900i		−	0.335392i	0.985839	−	0.167696i	$-0.0536328\pi$
$600$		0			0
$601$	185.853	−	107.302i	0.309239	−	0.178539i	−0.337347	−	0.941380i	$-0.609529\pi$
$601$	185.853	−	107.302i	0.309239	−	0.178539i	0.646586	+	0.762841i	$0.276196\pi$
$602$		0			0
$603$	−185.521	+	26.7766i	−0.307663	+	0.0444057i
$604$		0			0
$605$	−68.1389			−0.112626
$606$		0			0
$607$	467.695	+	270.024i	0.770502	+	0.444850i	0.833054	−	0.553192i	$-0.186590\pi$
$607$	467.695	+	270.024i	0.770502	+	0.444850i	−0.0625515	+	0.998042i	$0.519924\pi$
$608$		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	0.305876	+	0.952071i	$0.401051\pi$
$613$	−411.679	+	713.048i	−0.671580	+	1.16321i	−0.977456	+	0.211139i	$0.932283\pi$
$614$		0			0
$615$	104.877	−	36.3302i	0.170532	−	0.0590735i
$616$		0			0
$617$	774.393			1.25509			0.627547	−	0.778579i	$-0.284059\pi$
$617$	774.393			1.25509			0.627547	+	0.778579i	$0.284059\pi$
$618$		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
$621$	−180.219	−	115.613i	−0.290208	−	0.186172i
$622$		0			0
$623$	158.068	+	91.2606i	0.253721	+	0.146486i
$624$		0			0
$625$	−297.293	−	514.927i	−0.475669	−	0.823884i
$626$		0			0
$627$	117.123	−	180.848i	0.186800	−	0.288433i
$628$		0			0
$629$	255.570	+	147.554i	0.406312	+	0.234585i
$630$		0			0
$631$	501.168	+	868.048i	0.794243	+	1.37567i	0.923318	+	0.384035i	$0.125466\pi$
$631$	501.168	+	868.048i	0.794243	+	1.37567i	−0.129075	+	0.991635i	$0.541201\pi$
$632$		0			0
$633$	−19.4897	+	101.270i	−0.0307894	+	0.159984i
$634$		0			0
$635$	−127.783	−	73.7758i	−0.201234	−	0.116182i
$636$		0			0
$637$	367.895	+	212.404i	0.577544	+	0.333445i
$638$		0			0
$639$	385.094	−	963.435i	0.602652	−	1.50772i
$640$		0			0
$641$		−	198.472i		−	0.309629i	−0.987944	−	0.154814i	$-0.950522\pi$
$641$		−	198.472i		−	0.309629i	0.987944	−	0.154814i	$-0.0494779\pi$
$642$		0			0
$643$	59.3292	+	102.761i	0.0922693	+	0.159815i	0.908466	−	0.417959i	$-0.137255\pi$
$643$	59.3292	+	102.761i	0.0922693	+	0.159815i	−0.816196	+	0.577775i	$0.803921\pi$
$644$		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
$651$	294.656	+	255.181i	0.452620	+	0.391983i
$652$		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
$655$	43.3536	−	75.0906i	0.0661886	−	0.114642i
$656$		0			0
$657$	−1116.74	−	446.373i	−1.69976	−	0.679411i
$658$		0			0
$659$	−180.537	−	104.233i	−0.273956	−	0.158169i	0.356728	−	0.934208i	$-0.383892\pi$
$659$	−180.537	−	104.233i	−0.273956	−	0.158169i	−0.630684	+	0.776040i	$0.717226\pi$
$660$		0			0
$661$			1245.84i			1.88479i	0.334505	+	0.942394i	$0.391431\pi$
$661$			1245.84i			1.88479i	−0.334505	+	0.942394i	$0.608569\pi$
$662$		0			0
$663$	626.831	−	217.139i	0.945447	−	0.327510i
$664$		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
$669$	613.296	+	531.132i	0.916735	+	0.793920i
$670$		0			0
$671$	−264.570			−0.394292
$672$		0			0
$673$	−139.585	+	80.5897i	−0.207408	+	0.119747i	−0.600106	−	0.799920i	$-0.704875\pi$
$673$	−139.585	+	80.5897i	−0.207408	+	0.119747i	0.392698	+	0.919667i	$0.371542\pi$
$674$		0			0
$675$	−589.931	+	304.739i	−0.873972	+	0.451465i
$676$		0			0
$677$	−429.929	+	248.220i	−0.635050	+	0.366646i	−0.782705	−	0.622393i	$-0.786161\pi$
$677$	−429.929	+	248.220i	−0.635050	+	0.366646i	0.147655	+	0.989039i	$0.452827\pi$
$678$		0			0
$679$	87.4922	−	50.5136i	0.128854	−	0.0743942i
$680$		0			0
$681$	75.6963	−	393.324i	0.111155	−	0.577569i
$682$		0			0
$683$		−	207.417i		−	0.303685i	−0.988405	−	0.151842i	$-0.951479\pi$
$683$		−	207.417i		−	0.303685i	0.988405	−	0.151842i	$-0.0485206\pi$
$684$		0			0
$685$	−63.5811			−0.0928191
$686$		0			0
$687$	−132.999	−	383.939i	−0.193594	−	0.558863i
$688$		0			0
$689$	−84.5764	−	146.491i	−0.122752	−	0.212613i
$690$		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
$693$	−70.5211	−	28.1880i	−0.101762	−	0.0406753i
$694$		0			0
$695$	−57.8843	−	100.258i	−0.0832867	−	0.144257i
$696$		0			0
$697$			1327.53i			1.90463i
$698$		0			0
$699$	97.8079	+	282.349i	0.139925	+	0.403933i
$700$		0			0
$701$	92.2392	−	159.763i	0.131582	−	0.227907i	−0.792704	−	0.609606i	$-0.791328\pi$
$701$	92.2392	−	159.763i	0.131582	−	0.227907i	0.924287	+	0.381699i	$0.124661\pi$
$702$		0			0
$703$	226.847	+	91.8133i	0.322684	+	0.130602i
$704$		0			0
$705$	−55.8316	+	64.4685i	−0.0791938	+	0.0914447i
$706$		0			0
$707$	83.4679			0.118059
$708$		0			0
$709$	172.188	−	298.238i	0.242860	−	0.420646i	−0.718668	−	0.695354i	$-0.755248\pi$
$709$	172.188	−	298.238i	0.242860	−	0.420646i	0.961528	+	0.274707i	$0.0885810\pi$
$710$		0			0
$711$	140.813	−	20.3238i	0.198049	−	0.0285848i
$712$		0			0
$713$	−399.724	−	230.781i	−0.560623	−	0.323676i
$714$		0			0
$715$	20.1738	+	11.6474i	0.0282152	+	0.0162900i
$716$		0			0
$717$	383.364	+	1106.69i	0.534678	+	1.54350i
$718$		0			0
$719$	497.985	−	862.536i	0.692608	−	1.19963i	−0.278372	−	0.960473i	$-0.589795\pi$
$719$	497.985	−	862.536i	0.692608	−	1.19963i	0.970980	−	0.239159i	$-0.0768717\pi$
$720$		0			0
$721$			245.232i			0.340127i
$722$		0			0
$723$	−125.963	+	43.6345i	−0.174223	+	0.0603520i
$724$		0			0
$725$	−647.880	+	374.054i	−0.893628	+	0.515936i
$726$		0			0
$727$	−721.148			−0.991950			−0.495975	−	0.868337i	$-0.665189\pi$
$727$	−721.148			−0.991950			−0.495975	+	0.868337i	$0.665189\pi$
$728$		0			0
$729$	303.917	+	662.628i	0.416896	+	0.908954i
$730$		0			0
$731$	334.537	−	579.435i	0.457643	−	0.792661i
$732$		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
$735$	−55.1994	+	63.7384i	−0.0751012	+	0.0867189i
$736$		0			0
$737$	68.1793	−	39.3633i	0.0925092	−	0.0534102i
$738$		0			0
$739$	64.0868	−	111.002i	0.0867210	−	0.150205i	−0.819402	−	0.573219i	$-0.805694\pi$
$739$	64.0868	−	111.002i	0.0867210	−	0.150205i	0.906123	+	0.423014i	$0.139028\pi$
$740$		0			0
$741$	489.844	−	250.358i	0.661057	−	0.337865i
$742$		0			0
$743$	1032.30	−	595.997i	1.38936	−	0.802149i	0.396120	−	0.918199i	$-0.370357\pi$
$743$	1032.30	−	595.997i	1.38936	−	0.802149i	0.993243	+	0.116050i	$0.0370232\pi$
$744$		0			0
$745$	16.7611	−	29.0311i	0.0224981	−	0.0389679i
$746$		0			0
$747$	674.053	−	530.674i	0.902347	−	0.710407i
$748$		0			0
$749$	−385.867	+	222.781i	−0.515176	+	0.297437i
$750$		0			0
$751$		−	1079.73i		−	1.43772i	−0.695156	−	0.718859i	$-0.744665\pi$
$751$		−	1079.73i		−	1.43772i	0.695156	−	0.718859i	$-0.255335\pi$
$752$		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	−0.705558	−	0.708652i	$-0.749304\pi$
$757$	197.525	−	342.123i	0.260931	−	0.451946i	0.966490	+	0.256706i	$0.0826371\pi$
$758$		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
$763$			275.500i			0.361075i
$764$		0			0
$765$	18.8093	+	130.320i	0.0245874	+	0.170352i
$766$		0			0
$767$	−230.000	−	398.371i	−0.299869	−	0.519389i
$768$		0			0
$769$	223.319			0.290402			0.145201	−	0.989402i	$-0.453617\pi$
$769$	223.319			0.290402			0.145201	+	0.989402i	$0.453617\pi$
$770$		0			0
$771$	223.091	+	193.203i	0.289352	+	0.250588i
$772$		0			0
$773$	−691.069	+	398.989i	−0.894009	+	0.516156i	−0.875252	−	0.483668i	$-0.839304\pi$
$773$	−691.069	+	398.989i	−0.894009	+	0.516156i	−0.0187574	+	0.999824i	$0.505971\pi$
$774$		0			0
$775$	−1239.58	+	715.675i	−1.59946	+	0.923451i
$776$		0			0
$777$	16.3018	−	84.7054i	0.0209804	−	0.109016i
$778$		0			0
$779$	152.546	+	1090.25i	0.195823	+	1.39955i
$780$		0			0
$781$			435.773i			0.557969i
$782$		0			0
$783$	376.959	+	729.740i	0.481430	+	0.931979i
$784$		0			0
$785$	12.8499	−	22.2566i	0.0163693	−	0.0283524i
$786$		0			0
$787$	712.779	+	411.523i	0.905691	+	0.522901i	0.879042	−	0.476744i	$-0.158183\pi$
$787$	712.779	+	411.523i	0.905691	+	0.522901i	0.0266488	+	0.999645i	$0.491516\pi$
$788$		0			0
$789$	251.714	−	290.653i	0.319030	−	0.368382i
$790$		0			0
$791$		−	365.645i		−	0.462257i
$792$		0			0
$793$	−584.997	−	337.748i	−0.737701	−	0.425912i
$794$		0			0
$795$	31.7247	−	10.9897i	0.0399053	−	0.0138235i
$796$		0			0
$797$	1071.45	+	618.604i	1.34436	+	0.776166i	0.987444	−	0.157971i	$-0.0504954\pi$
$797$	1071.45	+	618.604i	1.34436	+	0.776166i	0.356915	+	0.934137i	$0.383829\pi$
$798$		0			0
$799$	−510.025	−	883.390i	−0.638330	−	1.10562i
$800$		0			0
$801$	455.186	+	578.170i	0.568272	+	0.721810i
$802$		0			0
$803$	505.116			0.629037
$804$		0			0
$805$	−5.65203	+	9.78960i	−0.00702115	+	0.0121610i
$806$		0			0
$807$	834.777	−	289.173i	1.03442	−	0.358331i
$808$		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	−0.256011	−	0.966674i	$-0.582408\pi$
$811$	367.503	−	212.178i	0.453148	−	0.261625i	0.709159	+	0.705049i	$0.249075\pi$
$812$		0			0
$813$	−70.6062	−	203.824i	−0.0868465	−	0.250706i
$814$		0			0
$815$	4.73086	+	8.19408i	0.00580473	+	0.0100541i
$816$		0			0
$817$	208.161	−	514.312i	0.254787	−	0.629513i
$818$		0			0
$819$	−119.946	−	152.354i	−0.146455	−	0.186024i
$820$		0			0
$821$	451.443	−	781.922i	0.549869	−	0.952402i	−0.448414	−	0.893826i	$-0.648011\pi$
$821$	451.443	−	781.922i	0.549869	−	0.952402i	0.998283	−	0.0585756i	$-0.0186559\pi$
$822$		0			0
$823$	768.755			0.934088			0.467044	−	0.884234i	$-0.345319\pi$
$823$	768.755			0.934088			0.467044	+	0.884234i	$0.345319\pi$
$824$		0			0
$825$	182.570	−	210.812i	0.221296	−	0.255530i
$826$		0			0
$827$	843.004	−	486.708i	1.01935	−	0.588523i	0.105435	−	0.994426i	$-0.466376\pi$
$827$	843.004	−	486.708i	1.01935	−	0.588523i	0.913916	+	0.405903i	$0.133043\pi$
$828$		0			0
$829$			961.753i			1.16014i	0.814568	+	0.580068i	$0.196974\pi$
$829$			961.753i			1.16014i	−0.814568	+	0.580068i	$0.803026\pi$
$830$		0			0
$831$	−1169.30	−	225.034i	−1.40710	−	0.270799i
$832$		0			0
$833$	−504.249	−	873.386i	−0.605341	−	1.04848i
$834$		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
$839$		−	40.5054i		−	0.0482782i	−0.999709	−	0.0241391i	$-0.992316\pi$
$839$		−	40.5054i		−	0.0482782i	0.999709	−	0.0241391i	$-0.00768446\pi$
$840$		0			0
$841$	42.2013	+	73.0949i	0.0501800	+	0.0869142i
$842$		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
$849$	168.192	+	32.3690i	0.198106	+	0.0381261i
$850$		0			0
$851$			102.142i			0.120026i
$852$		0			0
$853$	43.7621			0.0513037			0.0256519	−	0.999671i	$-0.491834\pi$
$853$	43.7621			0.0513037			0.0256519	+	0.999671i	$0.491834\pi$
$854$		0			0
$855$	30.4224	+	104.866i	0.0355818	+	0.122650i
$856$		0			0
$857$			563.404i			0.657414i	0.944432	+	0.328707i	$0.106613\pi$
$857$			563.404i			0.657414i	−0.944432	+	0.328707i	$0.893387\pi$
$858$		0			0
$859$	356.403			0.414905			0.207452	−	0.978245i	$-0.433483\pi$
$859$	356.403			0.414905			0.207452	+	0.978245i	$0.433483\pi$
$860$		0			0
$861$	366.660	−	127.014i	0.425853	−	0.147519i
$862$		0			0
$863$			633.593i			0.734175i	0.930186	+	0.367088i	$0.119645\pi$
$863$			633.593i			0.734175i	−0.930186	+	0.367088i	$0.880355\pi$
$864$		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
$869$	−51.7490	+	29.8773i	−0.0595501	+	0.0343813i
$870$		0			0
$871$	201.004			0.230774
$872$		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
$877$	650.821	−	375.752i	0.742099	−	0.428451i	−0.0807328	−	0.996736i	$-0.525726\pi$
$877$	650.821	−	375.752i	0.742099	−	0.428451i	0.822832	+	0.568285i	$0.192393\pi$
$878$		0			0
$879$	−49.9771	+	17.3124i	−0.0568568	+	0.0196956i
$880$		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	0.980107	−	0.198468i	$-0.0635967\pi$
$883$	280.948	+	486.617i	0.318175	+	0.551095i	−0.661932	+	0.749564i	$0.730263\pi$
$884$		0			0
$885$	86.2733	−	29.8857i	0.0974839	−	0.0337691i
$886$		0			0
$887$			422.844i			0.476713i	0.971178	+	0.238356i	$0.0766086\pi$
$887$			422.844i			0.476713i	−0.971178	+	0.238356i	$0.923391\pi$
$888$		0			0
$889$	−446.742	−	257.927i	−0.502522	−	0.290131i
$890$		0			0
$891$	−221.824	−	211.049i	−0.248961	−	0.236868i
$892$		0			0
$893$	−520.377	−	666.891i	−0.582728	−	0.746798i
$894$		0			0
$895$	140.372	−	81.0436i	0.156840	−	0.0905515i
$896$		0			0
$897$	173.565	+	150.313i	0.193495	+	0.167573i
$898$		0			0
$899$	885.283	+	1533.36i	0.984742	+	1.70562i
$900$		0			0
$901$			401.569i			0.445693i
$902$		0			0
$903$	−192.046	−	36.9598i	−0.212675	−	0.0409300i
$904$		0			0
$905$	−123.589	−	71.3539i	−0.136562	−	0.0788441i
$906$		0			0
$907$			697.588i			0.769116i	0.923101	+	0.384558i	$0.125646\pi$
$907$			697.588i			0.769116i	−0.923101	+	0.384558i	$0.874354\pi$
$908$		0			0
$909$	312.471	+	124.898i	0.343752	+	0.137401i
$910$		0			0
$911$	−1344.62	+	776.316i	−1.47598	+	0.852158i	−0.999633	−	0.0270991i	$-0.991373\pi$
$911$	−1344.62	+	776.316i	−1.47598	+	0.852158i	−0.476348	+	0.879257i	$0.658040\pi$
$912$		0			0
$913$	−180.157	+	312.041i	−0.197324	+	0.341775i
$914$		0			0
$915$	87.7735	−	101.352i	0.0959273	−	0.110767i
$916$		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
$921$	1439.46	−	498.639i	1.56293	−	0.541411i
$922$		0			0
$923$	−556.306	+	963.550i	−0.602715	+	1.04393i
$924$		0			0
$925$	274.315	+	158.376i	0.296557	+	0.171217i
$926$		0			0
$927$	−366.954	+	918.052i	−0.395852	+	0.990347i
$928$		0			0
$929$	629.567			0.677682			0.338841	−	0.940844i	$-0.389965\pi$
$929$	629.567			0.677682			0.338841	+	0.940844i	$0.389965\pi$
$930$		0			0
$931$	−514.483	−	659.339i	−0.552614	−	0.708205i
$932$		0			0
$933$	107.330	+	309.836i	0.115037	+	0.332086i
$934$		0			0
$935$	−27.6509	−	47.8928i	−0.0295732	−	0.0512222i
$936$		0			0
$937$	−277.515	−	480.671i	−0.296174	−	0.512989i	0.679083	−	0.734061i	$-0.262378\pi$
$937$	−277.515	−	480.671i	−0.296174	−	0.512989i	−0.975257	+	0.221073i	$0.929044\pi$
$938$		0			0
$939$	−396.819	−	1145.53i	−0.422598	−	1.21995i
$940$		0			0
$941$		−	954.821i		−	1.01469i	−0.861744	−	0.507344i	$-0.830628\pi$
$941$		−	954.821i		−	1.01469i	0.861744	−	0.507344i	$-0.169372\pi$
$942$		0			0
$943$	−397.922	+	229.740i	−0.421974	+	0.243627i
$944$		0			0
$945$	34.1943	−	17.6636i	0.0361844	−	0.0186917i
$946$		0			0
$947$	−918.213			−0.969602			−0.484801	−	0.874624i	$-0.661108\pi$
$947$	−918.213			−0.969602			−0.484801	+	0.874624i	$0.661108\pi$
$948$		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	−0.987726	−	0.156194i	$-0.950077\pi$
$953$	−1540.87	−	889.619i	−1.61686	−	0.933493i	−0.629131	−	0.777299i	$-0.716589\pi$
$954$		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
$959$	−222.285			−0.231788
$960$		0			0
$961$	1213.31	+	2101.51i	1.26255	+	2.18679i
$962$		0			0
$963$	−1777.89	+	256.608i	−1.84620	+	0.266467i
$964$		0			0
$965$	114.919	+	66.3486i	0.119087	+	0.0687550i
$966$		0			0
$967$	−476.790	−	825.825i	−0.493061	−	0.854007i	0.506907	−	0.862001i	$-0.330789\pi$
$967$	−476.790	−	825.825i	−0.493061	−	0.854007i	−0.999968	+	0.00799354i	$0.997456\pi$
$968$		0			0
$969$	−1304.27	−	66.7229i	−1.34599	−	0.0688575i
$970$		0			0
$971$	170.348	+	98.3506i	0.175436	+	0.101288i	0.585146	−	0.810928i	$-0.301037\pi$
$971$	170.348	+	98.3506i	0.175436	+	0.101288i	−0.409711	+	0.912216i	$0.634370\pi$
$972$		0			0
$973$	−202.368	−	350.512i	−0.207984	−	0.360239i
$974$		0			0
$975$	672.805	−	233.065i	0.690057	−	0.239041i
$976$		0			0
$977$	−675.011	−	389.718i	−0.690901	−	0.398892i	0.113048	−	0.993589i	$-0.463939\pi$
$977$	−675.011	−	389.718i	−0.690901	−	0.398892i	−0.803950	+	0.594697i	$0.797272\pi$
$978$		0			0
$979$	−267.653	−	154.530i	−0.273395	−	0.157844i
$980$		0			0
$981$	−412.246	+	1031.36i	−0.420231	+	1.05134i
$982$		0			0
$983$		−	1054.82i		−	1.07307i	−0.843879	−	0.536533i	$-0.819734\pi$
$983$		−	1054.82i		−	1.07307i	0.843879	−	0.536533i	$-0.180266\pi$
$984$		0			0
$985$	23.2381	+	40.2495i	0.0235920	+	0.0408625i
$986$		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	0.678073	−	0.734995i	$-0.262815\pi$
$991$	377.160	+	217.754i	0.380585	+	0.219731i	−0.297487	+	0.954726i	$0.596149\pi$
$992$		0			0
$993$	−75.1558	+	390.516i	−0.0756856	+	0.393268i
$994$		0			0
$995$	18.1881	−	31.5027i	0.0182795	−	0.0316610i
$996$		0			0
$997$	−637.508	+	1104.20i	−0.639426	+	1.10752i	0.346133	+	0.938186i	$0.387495\pi$
$997$	−637.508	+	1104.20i	−0.639426	+	1.10752i	−0.985559	+	0.169333i	$0.945839\pi$
$998$		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.s.a.445.30	✓	80
3.2	odd	2		2052.3.s.a.901.23		80
9.2	odd	6		2052.3.bl.a.1585.18		80
9.7	even	3		684.3.bl.a.673.17	yes	80
19.12	odd	6		684.3.bl.a.373.17	yes	80
57.50	even	6		2052.3.bl.a.145.18		80
171.88	odd	6	inner	684.3.s.a.601.30	yes	80
171.164	even	6		2052.3.s.a.829.23		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.30	✓	80	1.1	even	1	trivial
684.3.s.a.601.30	yes	80	171.88	odd	6	inner
684.3.bl.a.373.17	yes	80	19.12	odd	6
684.3.bl.a.673.17	yes	80	9.7	even	3
2052.3.s.a.829.23		80	171.164	even	6
2052.3.s.a.901.23		80	3.2	odd	2
2052.3.bl.a.145.18		80	57.50	even	6
2052.3.bl.a.1585.18		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)

\(f(q)\)	\(=\)	\(q+(1.96397 - 2.26778i) q^{3} +(-0.319267 - 0.552987i) q^{5} +(-1.11619 - 1.93329i) q^{7} +(-1.28567 - 8.90770i) q^{9} +O(q^{10})\)	\(q+(1.96397 - 2.26778i) q^{3} +(-0.319267 - 0.552987i) q^{5} +(-1.11619 - 1.93329i) q^{7} +(-1.28567 - 8.90770i) q^{9} +(1.89002 + 3.27360i) q^{11} +9.65113i q^{13} +(-1.88108 - 0.362020i) q^{15} +(11.4559 - 19.8422i) q^{17} +(7.12829 - 17.6121i) q^{19} +(-6.57644 - 1.26565i) q^{21} +7.93018 q^{23} +(12.2961 - 21.2975i) q^{25} +(-22.7257 - 14.5788i) q^{27} +(-26.3449 - 15.2102i) q^{29} +(-50.4054 - 29.1016i) q^{31} +(11.1357 + 2.14310i) q^{33} +(-0.712723 + 1.23447i) q^{35} +12.8801i q^{37} +(21.8867 + 18.9545i) q^{39} +(-50.1781 + 28.9703i) q^{41} +29.2021 q^{43} +(-4.51537 + 3.55489i) q^{45} +(22.2603 - 38.5561i) q^{47} +(22.0083 - 38.1194i) q^{49} +(-22.4988 - 64.9490i) q^{51} +(-15.1786 + 8.76336i) q^{53} +(1.20684 - 2.09031i) q^{55} +(-25.9408 - 50.7551i) q^{57} +(-41.2772 + 23.8314i) q^{59} +(-34.9957 + 60.6144i) q^{61} +(-15.7861 + 12.4282i) q^{63} +(5.33695 - 3.08129i) q^{65} -20.8270i q^{67} +(15.5746 - 17.9839i) q^{69} +(99.8380 + 57.6415i) q^{71} +(66.8138 - 115.725i) q^{73} +(-24.1490 - 69.7126i) q^{75} +(4.21922 - 7.30790i) q^{77} +15.8080i q^{79} +(-77.6941 + 22.9047i) q^{81} +(47.6602 + 82.5498i) q^{83} -14.6300 q^{85} +(-86.2339 + 29.8721i) q^{87} +(-70.8072 + 40.8805i) q^{89} +(18.6584 - 10.7725i) q^{91} +(-164.991 + 57.1540i) q^{93} +(-12.0151 + 1.68113i) q^{95} +45.2556i q^{97} +(26.7303 - 21.0445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 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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