LMFDB - Embedded newform 1020.3.bm.a.217.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1020,3,Mod(217,1020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1020, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1020.217");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1020.bm (of order $4$, 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:	$27.7929869648$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			217.11
Character	$\chi$	$=$	1020.217
Dual form			1020.3.bm.a.973.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205 q^{3} +(-2.43367 - 4.36775i) q^{5} +1.56608 q^{7} +3.00000 q^{9} +O(q^{10})$	\(q-1.73205 q^{3} +(-2.43367 - 4.36775i) q^{5} +1.56608 q^{7} +3.00000 q^{9} +(-8.90102 + 8.90102i) q^{11} +(0.110765 - 0.110765i) q^{13} +(4.21525 + 7.56516i) q^{15} +(13.2142 + 10.6951i) q^{17} +27.5906 q^{19} -2.71253 q^{21} -31.5827i q^{23} +(-13.1545 + 21.2594i) q^{25} -5.19615 q^{27} +(36.7872 - 36.7872i) q^{29} +(-5.58894 - 5.58894i) q^{31} +(15.4170 - 15.4170i) q^{33} +(-3.81133 - 6.84024i) q^{35} +41.6141i q^{37} +(-0.191850 + 0.191850i) q^{39} +(-16.1149 + 16.1149i) q^{41} +(-15.5861 - 15.5861i) q^{43} +(-7.30102 - 13.1032i) q^{45} +(-57.5178 - 57.5178i) q^{47} -46.5474 q^{49} +(-22.8877 - 18.5244i) q^{51} +(16.8076 + 16.8076i) q^{53} +(60.5396 + 17.2152i) q^{55} -47.7884 q^{57} -98.0403 q^{59} +(79.3726 - 79.3726i) q^{61} +4.69824 q^{63} +(-0.753356 - 0.214227i) q^{65} +(-19.3303 - 19.3303i) q^{67} +54.7028i q^{69} +(33.2117 + 33.2117i) q^{71} +10.7283 q^{73} +(22.7842 - 36.8223i) q^{75} +(-13.9397 + 13.9397i) q^{77} +(-37.4383 - 37.4383i) q^{79} +9.00000 q^{81} +(-59.5176 - 59.5176i) q^{83} +(14.5542 - 83.7447i) q^{85} +(-63.7172 + 63.7172i) q^{87} -132.233i q^{89} +(0.173466 - 0.173466i) q^{91} +(9.68033 + 9.68033i) q^{93} +(-67.1466 - 120.509i) q^{95} -63.1364i q^{97} +(-26.7030 + 26.7030i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{5} - 24 q^{7} + 216 q^{9}+O(q^{10}) $ 72 * q - 8 * q^5 - 24 * q^7 + 216 * q^9	$ 72 q - 8 q^{5} - 24 q^{7} + 216 q^{9} + 4 q^{13} - 12 q^{15} - 16 q^{17} - 28 q^{25} + 72 q^{29} + 8 q^{31} + 36 q^{33} - 88 q^{35} - 48 q^{39} + 216 q^{41} + 60 q^{43} - 24 q^{45} + 360 q^{49} - 32 q^{55} - 144 q^{57} + 184 q^{61} - 72 q^{63} + 104 q^{65} + 48 q^{67} - 72 q^{71} + 112 q^{73} + 48 q^{75} + 136 q^{77} + 120 q^{79} + 648 q^{81} + 224 q^{83} + 344 q^{85} + 96 q^{87} + 56 q^{91} - 48 q^{95}+O(q^{100}) $ 72 * q - 8 * q^5 - 24 * q^7 + 216 * q^9 + 4 * q^13 - 12 * q^15 - 16 * q^17 - 28 * q^25 + 72 * q^29 + 8 * q^31 + 36 * q^33 - 88 * q^35 - 48 * q^39 + 216 * q^41 + 60 * q^43 - 24 * q^45 + 360 * q^49 - 32 * q^55 - 144 * q^57 + 184 * q^61 - 72 * q^63 + 104 * q^65 + 48 * q^67 - 72 * q^71 + 112 * q^73 + 48 * q^75 + 136 * q^77 + 120 * q^79 + 648 * q^81 + 224 * q^83 + 344 * q^85 + 96 * q^87 + 56 * q^91 - 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1020\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$		0			0
$5$	−2.43367	−	4.36775i	−0.486735	−	0.873550i
$5$	−2.43367	−	4.36775i	−0.486735	−	0.873550i
$6$		0			0
$7$	1.56608			0.223726			0.111863	−	0.993724i	$-0.464318\pi$
$7$	1.56608			0.223726			0.111863	+	0.993724i	$0.464318\pi$
$8$		0			0
$9$	3.00000			0.333333
$10$		0			0
$11$	−8.90102	+	8.90102i	−0.809183	+	0.809183i	−0.984510	−	0.175327i	$-0.943902\pi$
$11$	−8.90102	+	8.90102i	−0.809183	+	0.809183i	0.175327	+	0.984510i	$0.443902\pi$
$12$		0			0
$13$	0.110765	−	0.110765i	0.00852035	−	0.00852035i	−0.702834	−	0.711354i	$-0.748082\pi$
$13$	0.110765	−	0.110765i	0.00852035	−	0.00852035i	0.711354	+	0.702834i	$0.248082\pi$
$14$		0			0
$15$	4.21525	+	7.56516i	0.281017	+	0.504344i
$16$		0			0
$17$	13.2142	+	10.6951i	0.777308	+	0.629121i
$17$	13.2142	+	10.6951i	0.777308	+	0.629121i
$18$		0			0
$19$	27.5906			1.45214			0.726069	−	0.687622i	$-0.241345\pi$
$19$	27.5906			1.45214			0.726069	+	0.687622i	$0.241345\pi$
$20$		0			0
$21$	−2.71253			−0.129168
$22$		0			0
$23$		−	31.5827i		−	1.37316i	−0.727055	−	0.686580i	$-0.759111\pi$
$23$		−	31.5827i		−	1.37316i	0.727055	−	0.686580i	$-0.240889\pi$
$24$		0			0
$25$	−13.1545	+	21.2594i	−0.526178	+	0.850374i
$26$		0			0
$27$	−5.19615			−0.192450
$28$		0			0
$29$	36.7872	−	36.7872i	1.26852	−	1.26852i	0.321671	−	0.946851i	$-0.395755\pi$
$29$	36.7872	−	36.7872i	1.26852	−	1.26852i	0.946851	−	0.321671i	$-0.104245\pi$
$30$		0			0
$31$	−5.58894	−	5.58894i	−0.180288	−	0.180288i	0.611193	−	0.791482i	$-0.290690\pi$
$31$	−5.58894	−	5.58894i	−0.180288	−	0.180288i	−0.791482	+	0.611193i	$0.790690\pi$
$32$		0			0
$33$	15.4170	−	15.4170i	0.467182	−	0.467182i
$34$		0			0
$35$	−3.81133	−	6.84024i	−0.108895	−	0.195436i
$36$		0			0
$37$			41.6141i			1.12471i	0.826898	+	0.562353i	$0.190104\pi$
$37$			41.6141i			1.12471i	−0.826898	+	0.562353i	$0.809896\pi$
$38$		0			0
$39$	−0.191850	+	0.191850i	−0.00491923	+	0.00491923i
$40$		0			0
$41$	−16.1149	+	16.1149i	−0.393047	+	0.393047i	−0.875772	−	0.482725i	$-0.839647\pi$
$41$	−16.1149	+	16.1149i	−0.393047	+	0.393047i	0.482725	+	0.875772i	$0.339647\pi$
$42$		0			0
$43$	−15.5861	−	15.5861i	−0.362468	−	0.362468i	0.502253	−	0.864721i	$-0.332505\pi$
$43$	−15.5861	−	15.5861i	−0.362468	−	0.362468i	−0.864721	+	0.502253i	$0.832505\pi$
$44$		0			0
$45$	−7.30102	−	13.1032i	−0.162245	−	0.291183i
$46$		0			0
$47$	−57.5178	−	57.5178i	−1.22378	−	1.22378i	−0.966277	−	0.257507i	$-0.917099\pi$
$47$	−57.5178	−	57.5178i	−1.22378	−	1.22378i	−0.257507	−	0.966277i	$-0.582901\pi$
$48$		0			0
$49$	−46.5474			−0.949947
$50$		0			0
$51$	−22.8877	−	18.5244i	−0.448779	−	0.363223i
$52$		0			0
$53$	16.8076	+	16.8076i	0.317125	+	0.317125i	0.847662	−	0.530537i	$-0.178010\pi$
$53$	16.8076	+	16.8076i	0.317125	+	0.317125i	−0.530537	+	0.847662i	$0.678010\pi$
$54$		0			0
$55$	60.5396	+	17.2152i	1.10072	+	0.313004i
$56$		0			0
$57$	−47.7884			−0.838392
$58$		0			0
$59$	−98.0403			−1.66170			−0.830850	−	0.556497i	$-0.812145\pi$
$59$	−98.0403			−1.66170			−0.830850	+	0.556497i	$0.812145\pi$
$60$		0			0
$61$	79.3726	−	79.3726i	1.30119	−	1.30119i	0.373601	−	0.927590i	$-0.378123\pi$
$61$	79.3726	−	79.3726i	1.30119	−	1.30119i	0.927590	−	0.373601i	$-0.121877\pi$
$62$		0			0
$63$	4.69824			0.0745752
$64$		0			0
$65$	−0.753356	−	0.214227i	−0.0115901	−	0.00329580i
$66$		0			0
$67$	−19.3303	−	19.3303i	−0.288512	−	0.288512i	0.547980	−	0.836491i	$-0.315397\pi$
$67$	−19.3303	−	19.3303i	−0.288512	−	0.288512i	−0.836491	+	0.547980i	$0.815397\pi$
$68$		0			0
$69$			54.7028i			0.792794i
$70$		0			0
$71$	33.2117	+	33.2117i	0.467771	+	0.467771i	0.901192	−	0.433421i	$-0.142694\pi$
$71$	33.2117	+	33.2117i	0.467771	+	0.467771i	−0.433421	+	0.901192i	$0.642694\pi$
$72$		0			0
$73$	10.7283			0.146963			0.0734813	−	0.997297i	$-0.476589\pi$
$73$	10.7283			0.146963			0.0734813	+	0.997297i	$0.476589\pi$
$74$		0			0
$75$	22.7842	−	36.8223i	0.303789	−	0.490964i
$76$		0			0
$77$	−13.9397	+	13.9397i	−0.181035	+	0.181035i
$78$		0			0
$79$	−37.4383	−	37.4383i	−0.473903	−	0.473903i	0.429272	−	0.903175i	$-0.358770\pi$
$79$	−37.4383	−	37.4383i	−0.473903	−	0.473903i	−0.903175	+	0.429272i	$0.858770\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		0			0
$83$	−59.5176	−	59.5176i	−0.717079	−	0.717079i	0.250927	−	0.968006i	$-0.419265\pi$
$83$	−59.5176	−	59.5176i	−0.717079	−	0.717079i	−0.968006	+	0.250927i	$0.919265\pi$
$84$		0			0
$85$	14.5542	−	83.7447i	0.171226	−	0.985232i
$86$		0			0
$87$	−63.7172	+	63.7172i	−0.732382	+	0.732382i
$88$		0			0
$89$		−	132.233i		−	1.48576i	−0.669423	−	0.742881i	$-0.733459\pi$
$89$		−	132.233i		−	1.48576i	0.669423	−	0.742881i	$-0.266541\pi$
$90$		0			0
$91$	0.173466	−	0.173466i	0.00190622	−	0.00190622i
$92$		0			0
$93$	9.68033	+	9.68033i	0.104090	+	0.104090i
$94$		0			0
$95$	−67.1466	−	120.509i	−0.706806	−	1.26851i
$96$		0			0
$97$		−	63.1364i		−	0.650891i	−0.945561	−	0.325445i	$-0.894486\pi$
$97$		−	63.1364i		−	0.650891i	0.945561	−	0.325445i	$-0.105514\pi$
$98$		0			0
$99$	−26.7030	+	26.7030i	−0.269728	+	0.269728i
$100$		0			0
$101$	−92.5882			−0.916715			−0.458358	−	0.888768i	$-0.651562\pi$
$101$	−92.5882			−0.916715			−0.458358	+	0.888768i	$0.651562\pi$
$102$		0			0
$103$	127.530	−	127.530i	1.23816	−	1.23816i	0.277402	−	0.960754i	$-0.410527\pi$
$103$	127.530	−	127.530i	1.23816	−	1.23816i	0.960754	−	0.277402i	$-0.0894735\pi$
$104$		0			0
$105$	6.60142	+	11.8476i	0.0628706	+	0.112835i
$106$		0			0
$107$		−	149.868i		−	1.40064i	−0.713830	−	0.700319i	$-0.753041\pi$
$107$		−	149.868i		−	1.40064i	0.713830	−	0.700319i	$-0.246959\pi$
$108$		0			0
$109$	31.2530	+	31.2530i	0.286725	+	0.286725i	0.835784	−	0.549059i	$-0.185014\pi$
$109$	31.2530	+	31.2530i	0.286725	+	0.286725i	−0.549059	+	0.835784i	$0.685014\pi$
$110$		0			0
$111$		−	72.0777i		−	0.649349i
$112$		0			0
$113$		−	191.302i		−	1.69294i	−0.532436	−	0.846470i	$-0.678723\pi$
$113$		−	191.302i		−	1.69294i	0.532436	−	0.846470i	$-0.321277\pi$
$114$		0			0
$115$	−137.945	+	76.8619i	−1.19952	+	0.668365i
$116$		0			0
$117$	0.332294	−	0.332294i	0.00284012	−	0.00284012i
$118$		0			0
$119$	20.6945	+	16.7493i	0.173904	+	0.140751i
$120$		0			0
$121$		−	37.4562i		−	0.309555i
$122$		0			0
$123$	27.9119	−	27.9119i	0.226926	−	0.226926i
$124$		0			0
$125$	124.869	+	5.71698i	0.998954	+	0.0457358i
$126$		0			0
$127$	−31.5695	+	31.5695i	−0.248579	+	0.248579i	−0.820387	−	0.571808i	$-0.806242\pi$
$127$	−31.5695	+	31.5695i	−0.248579	+	0.248579i	0.571808	+	0.820387i	$0.306242\pi$
$128$		0			0
$129$	26.9959	+	26.9959i	0.209271	+	0.209271i
$130$		0			0
$131$	162.984	+	162.984i	1.24416	+	1.24416i	0.958261	+	0.285895i	$0.0922909\pi$
$131$	162.984	+	162.984i	1.24416	+	1.24416i	0.285895	+	0.958261i	$0.407709\pi$
$132$		0			0
$133$	43.2091			0.324881
$134$		0			0
$135$	12.6457	+	22.6955i	0.0936722	+	0.168115i
$136$		0			0
$137$	−104.986	−	104.986i	−0.766319	−	0.766319i	0.211137	−	0.977456i	$-0.432283\pi$
$137$	−104.986	−	104.986i	−0.766319	−	0.766319i	−0.977456	+	0.211137i	$0.932283\pi$
$138$		0			0
$139$	−8.48818	+	8.48818i	−0.0610661	+	0.0610661i	−0.736980	−	0.675914i	$-0.763749\pi$
$139$	−8.48818	+	8.48818i	−0.0610661	+	0.0610661i	0.675914	+	0.736980i	$0.263749\pi$
$140$		0			0
$141$	99.6238	+	99.6238i	0.706552	+	0.706552i
$142$		0			0
$143$			1.97183i			0.0137890i
$144$		0			0
$145$	−250.205	−	71.1491i	−1.72555	−	0.490683i
$146$		0			0
$147$	80.6225			0.548452
$148$		0			0
$149$			40.2764i			0.270311i	0.990824	+	0.135156i	$0.0431534\pi$
$149$			40.2764i			0.270311i	−0.990824	+	0.135156i	$0.956847\pi$
$150$		0			0
$151$			129.688i			0.858861i	0.903100	+	0.429431i	$0.141286\pi$
$151$			129.688i			0.858861i	−0.903100	+	0.429431i	$0.858714\pi$
$152$		0			0
$153$	39.6427	+	32.0852i	0.259103	+	0.209707i
$154$		0			0
$155$	−10.8094	+	38.0128i	−0.0697382	+	0.245244i
$156$		0			0
$157$	28.7061	+	28.7061i	0.182842	+	0.182842i	0.792593	−	0.609751i	$-0.208731\pi$
$157$	28.7061	+	28.7061i	0.182842	+	0.182842i	−0.609751	+	0.792593i	$0.708731\pi$
$158$		0			0
$159$	−29.1117	−	29.1117i	−0.183092	−	0.183092i
$160$		0			0
$161$		−	49.4610i		−	0.307211i
$162$		0			0
$163$			158.513i			0.972473i	0.873827	+	0.486237i	$0.161631\pi$
$163$			158.513i			0.972473i	−0.873827	+	0.486237i	$0.838369\pi$
$164$		0			0
$165$	−104.858	−	29.8176i	−0.635501	−	0.180713i
$166$		0			0
$167$		−	263.902i		−	1.58025i	−0.612946	−	0.790125i	$-0.710016\pi$
$167$		−	263.902i		−	1.58025i	0.612946	−	0.790125i	$-0.289984\pi$
$168$		0			0
$169$			168.975i			0.999855i
$170$		0			0
$171$	82.7719			0.484046
$172$		0			0
$173$	149.219			0.862537			0.431268	−	0.902224i	$-0.358066\pi$
$173$	149.219			0.862537			0.431268	+	0.902224i	$0.358066\pi$
$174$		0			0
$175$	−20.6009	+	33.2939i	−0.117720	+	0.190251i
$176$		0			0
$177$	169.811			0.959383
$178$		0			0
$179$	199.112			1.11236			0.556179	−	0.831063i	$-0.312267\pi$
$179$	199.112			1.11236			0.556179	+	0.831063i	$0.312267\pi$
$180$		0			0
$181$	172.868	−	172.868i	0.955072	−	0.955072i	−0.0439617	−	0.999033i	$-0.513998\pi$
$181$	172.868	−	172.868i	0.955072	−	0.955072i	0.999033	+	0.0439617i	$0.0139979\pi$
$182$		0			0
$183$	−137.477	+	137.477i	−0.751243	+	0.751243i
$184$		0			0
$185$	181.760	−	101.275i	0.982486	−	0.547433i
$186$		0			0
$187$	−212.817	+	22.4232i	−1.13806	+	0.119910i
$188$		0			0
$189$	−8.13759			−0.0430560
$190$		0			0
$191$	−301.976			−1.58102			−0.790512	−	0.612446i	$-0.790186\pi$
$191$	−301.976			−1.58102			−0.790512	+	0.612446i	$0.790186\pi$
$192$		0			0
$193$		−	192.740i		−	0.998653i	−0.866414	−	0.499327i	$-0.833581\pi$
$193$		−	192.740i		−	0.998653i	0.866414	−	0.499327i	$-0.166419\pi$
$194$		0			0
$195$	1.30485	+	0.371052i	0.00669155	+	0.00190283i
$196$		0			0
$197$	−228.794			−1.16139			−0.580696	−	0.814120i	$-0.697220\pi$
$197$	−228.794			−1.16139			−0.580696	+	0.814120i	$0.697220\pi$
$198$		0			0
$199$	19.7399	−	19.7399i	0.0991954	−	0.0991954i	−0.655768	−	0.754963i	$-0.727655\pi$
$199$	19.7399	−	19.7399i	0.0991954	−	0.0991954i	0.754963	+	0.655768i	$0.227655\pi$
$200$		0			0
$201$	33.4810	+	33.4810i	0.166572	+	0.166572i
$202$		0			0
$203$	57.6116	−	57.6116i	0.283801	−	0.283801i
$204$		0			0
$205$	109.604	+	31.1675i	0.534656	+	0.152036i
$206$		0			0
$207$		−	94.7480i		−	0.457720i
$208$		0			0
$209$	−245.585	+	245.585i	−1.17505	+	1.17505i
$210$		0			0
$211$	−214.980	+	214.980i	−1.01886	+	1.01886i	−0.0190437	+	0.999819i	$0.506062\pi$
$211$	−214.980	+	214.980i	−1.01886	+	1.01886i	−0.999819	+	0.0190437i	$0.993938\pi$
$212$		0			0
$213$	−57.5244	−	57.5244i	−0.270068	−	0.270068i
$214$		0			0
$215$	−30.1447	+	106.008i	−0.140208	+	0.493059i
$216$		0			0
$217$	−8.75273	−	8.75273i	−0.0403352	−	0.0403352i
$218$		0			0
$219$	−18.5819			−0.0848489
$220$		0			0
$221$	2.64830	−	0.279035i	0.0119833	−	0.00126260i
$222$		0			0
$223$	−152.674	−	152.674i	−0.684635	−	0.684635i	0.276406	−	0.961041i	$-0.410857\pi$
$223$	−152.674	−	152.674i	−0.684635	−	0.684635i	−0.961041	+	0.276406i	$0.910857\pi$
$224$		0			0
$225$	−39.4634	+	63.7781i	−0.175393	+	0.283458i
$226$		0			0
$227$	−327.931			−1.44463			−0.722314	−	0.691565i	$-0.756922\pi$
$227$	−327.931			−1.44463			−0.722314	+	0.691565i	$0.756922\pi$
$228$		0			0
$229$	158.280			0.691181			0.345591	−	0.938385i	$-0.387679\pi$
$229$	158.280			0.691181			0.345591	+	0.938385i	$0.387679\pi$
$230$		0			0
$231$	24.1443	−	24.1443i	0.104521	−	0.104521i
$232$		0			0
$233$	357.513			1.53439			0.767196	−	0.641412i	$-0.221651\pi$
$233$	357.513			1.53439			0.767196	+	0.641412i	$0.221651\pi$
$234$		0			0
$235$	−111.244	+	391.203i	−0.473377	+	1.66469i
$236$		0			0
$237$	64.8451	+	64.8451i	0.273608	+	0.273608i
$238$		0			0
$239$		−	273.497i		−	1.14434i	−0.820135	−	0.572170i	$-0.806102\pi$
$239$		−	273.497i		−	1.14434i	0.820135	−	0.572170i	$-0.193898\pi$
$240$		0			0
$241$	242.881	+	242.881i	1.00780	+	1.00780i	0.999969	+	0.00783517i	$0.00249404\pi$
$241$	242.881	+	242.881i	1.00780	+	1.00780i	0.00783517	+	0.999969i	$0.497506\pi$
$242$		0			0
$243$	−15.5885			−0.0641500
$244$		0			0
$245$	113.281	+	203.307i	0.462372	+	0.829826i
$246$		0			0
$247$	3.05606	−	3.05606i	0.0123727	−	0.0123727i
$248$		0			0
$249$	103.087	+	103.087i	0.414006	+	0.414006i
$250$		0			0
$251$	130.533			0.520051			0.260026	−	0.965602i	$-0.416269\pi$
$251$	130.533			0.520051			0.260026	+	0.965602i	$0.416269\pi$
$252$		0			0
$253$	281.118	+	281.118i	1.11114	+	1.11114i
$254$		0			0
$255$	−25.2086	+	145.050i	−0.0988571	+	0.568824i
$256$		0			0
$257$	170.186	−	170.186i	0.662203	−	0.662203i	−0.293696	−	0.955899i	$-0.594885\pi$
$257$	170.186	−	170.186i	0.662203	−	0.662203i	0.955899	+	0.293696i	$0.0948853\pi$
$258$		0			0
$259$			65.1710i			0.251625i
$260$		0			0
$261$	110.361	−	110.361i	0.422841	−	0.422841i
$262$		0			0
$263$	−169.670	−	169.670i	−0.645135	−	0.645135i	0.306678	−	0.951813i	$-0.400782\pi$
$263$	−169.670	−	169.670i	−0.645135	−	0.645135i	−0.951813	+	0.306678i	$0.900782\pi$
$264$		0			0
$265$	32.5072	−	114.316i	0.122669	−	0.431381i
$266$		0			0
$267$			229.034i			0.857805i
$268$		0			0
$269$	−83.0205	+	83.0205i	−0.308626	+	0.308626i	−0.844377	−	0.535750i	$-0.820029\pi$
$269$	−83.0205	+	83.0205i	−0.308626	+	0.308626i	0.535750	+	0.844377i	$0.320029\pi$
$270$		0			0
$271$	−382.296			−1.41069			−0.705344	−	0.708865i	$-0.749207\pi$
$271$	−382.296			−1.41069			−0.705344	+	0.708865i	$0.749207\pi$
$272$		0			0
$273$	−0.300452	+	0.300452i	−0.00110056	+	0.00110056i
$274$		0			0
$275$	−72.1419	−	306.318i	−0.262334	−	1.11388i
$276$		0			0
$277$		−	333.085i		−	1.20247i	−0.799071	−	0.601237i	$-0.794675\pi$
$277$		−	333.085i		−	1.20247i	0.799071	−	0.601237i	$-0.205325\pi$
$278$		0			0
$279$	−16.7668	−	16.7668i	−0.0600962	−	0.0600962i
$280$		0			0
$281$		−	396.583i		−	1.41133i	−0.708548	−	0.705663i	$-0.750649\pi$
$281$		−	396.583i		−	1.41133i	0.708548	−	0.705663i	$-0.249351\pi$
$282$		0			0
$283$			477.217i			1.68628i	0.537693	+	0.843140i	$0.319296\pi$
$283$			477.217i			1.68628i	−0.537693	+	0.843140i	$0.680704\pi$
$284$		0			0
$285$	116.301	+	208.728i	0.408075	+	0.732377i
$286$		0			0
$287$	−25.2373	+	25.2373i	−0.0879348	+	0.0879348i
$288$		0			0
$289$	60.2316	+	282.654i	0.208414	+	0.978041i
$290$		0			0
$291$			109.355i			0.375792i
$292$		0			0
$293$	−179.460	+	179.460i	−0.612491	+	0.612491i	−0.943595	−	0.331103i	$-0.892579\pi$
$293$	−179.460	+	179.460i	−0.612491	+	0.612491i	0.331103	+	0.943595i	$0.392579\pi$
$294$		0			0
$295$	238.598	+	428.215i	0.808807	+	1.45158i
$296$		0			0
$297$	46.2510	−	46.2510i	0.155727	−	0.155727i
$298$		0			0
$299$	−3.49824	−	3.49824i	−0.0116998	−	0.0116998i
$300$		0			0
$301$	−24.4091	−	24.4091i	−0.0810934	−	0.0810934i
$302$		0			0
$303$	160.368			0.529266
$304$		0			0
$305$	−539.847	−	153.512i	−1.76999	−	0.503320i
$306$		0			0
$307$	−100.685	−	100.685i	−0.327964	−	0.327964i	0.523848	−	0.851812i	$-0.324496\pi$
$307$	−100.685	−	100.685i	−0.327964	−	0.327964i	−0.851812	+	0.523848i	$0.824496\pi$
$308$		0			0
$309$	−220.889	+	220.889i	−0.714850	+	0.714850i
$310$		0			0
$311$	214.158	+	214.158i	0.688610	+	0.688610i	0.961925	−	0.273315i	$-0.0881201\pi$
$311$	214.158	+	214.158i	0.688610	+	0.688610i	−0.273315	+	0.961925i	$0.588120\pi$
$312$		0			0
$313$		−	603.120i		−	1.92690i	−0.267885	−	0.963451i	$-0.586325\pi$
$313$		−	603.120i		−	1.92690i	0.267885	−	0.963451i	$-0.413675\pi$
$314$		0			0
$315$	−11.4340	−	20.5207i	−0.0362984	−	0.0651452i
$316$		0			0
$317$	315.099			0.994004			0.497002	−	0.867749i	$-0.334434\pi$
$317$	315.099			0.994004			0.497002	+	0.867749i	$0.334434\pi$
$318$		0			0
$319$			654.886i			2.05293i
$320$		0			0
$321$			259.579i			0.808659i
$322$		0			0
$323$	364.589	+	295.083i	1.12876	+	0.913570i
$324$		0			0
$325$	0.897736	+	3.81183i	0.00276226	+	0.0117287i
$326$		0			0
$327$	−54.1318	−	54.1318i	−0.165541	−	0.165541i
$328$		0			0
$329$	−90.0775	−	90.0775i	−0.273792	−	0.273792i
$330$		0			0
$331$		−	101.021i		−	0.305200i	−0.988288	−	0.152600i	$-0.951235\pi$
$331$		−	101.021i		−	0.305200i	0.988288	−	0.152600i	$-0.0487646\pi$
$332$		0			0
$333$			124.842i			0.374902i
$334$		0			0
$335$	−37.3862	+	131.473i	−0.111601	+	0.392458i
$336$		0			0
$337$			213.468i			0.633435i	0.948520	+	0.316718i	$0.102581\pi$
$337$			213.468i			0.633435i	−0.948520	+	0.316718i	$0.897419\pi$
$338$		0			0
$339$			331.345i			0.977420i
$340$		0			0
$341$	99.4945			0.291773
$342$		0			0
$343$	−149.635			−0.436253
$344$		0			0
$345$	238.928	−	133.129i	0.692545	−	0.385880i
$346$		0			0
$347$	−273.469			−0.788094			−0.394047	−	0.919090i	$-0.628925\pi$
$347$	−273.469			−0.788094			−0.394047	+	0.919090i	$0.628925\pi$
$348$		0			0
$349$	125.545			0.359728			0.179864	−	0.983691i	$-0.442434\pi$
$349$	125.545			0.359728			0.179864	+	0.983691i	$0.442434\pi$
$350$		0			0
$351$	−0.575549	+	0.575549i	−0.00163974	+	0.00163974i
$352$		0			0
$353$	−246.504	+	246.504i	−0.698311	+	0.698311i	−0.964046	−	0.265735i	$-0.914385\pi$
$353$	−246.504	+	246.504i	−0.698311	+	0.698311i	0.265735	+	0.964046i	$0.414385\pi$
$354$		0			0
$355$	64.2340	−	225.887i	0.180941	−	0.636302i
$356$		0			0
$357$	−35.8440	−	29.0107i	−0.100403	−	0.0812623i
$358$		0			0
$359$	398.635			1.11040			0.555202	−	0.831715i	$-0.312641\pi$
$359$	398.635			1.11040			0.555202	+	0.831715i	$0.312641\pi$
$360$		0			0
$361$	400.243			1.10871
$362$		0			0
$363$			64.8760i			0.178722i
$364$		0			0
$365$	−26.1091	−	46.8584i	−0.0715318	−	0.128379i
$366$		0			0
$367$	164.926			0.449390			0.224695	−	0.974429i	$-0.427861\pi$
$367$	164.926			0.449390			0.224695	+	0.974429i	$0.427861\pi$
$368$		0			0
$369$	−48.3448	+	48.3448i	−0.131016	+	0.131016i
$370$		0			0
$371$	26.3221	+	26.3221i	0.0709491	+	0.0709491i
$372$		0			0
$373$	−131.124	+	131.124i	−0.351540	+	0.351540i	−0.860682	−	0.509143i	$-0.829963\pi$
$373$	−131.124	+	131.124i	−0.351540	+	0.351540i	0.509143	+	0.860682i	$0.329963\pi$
$374$		0			0
$375$	−216.280	−	9.90209i	−0.576746	−	0.0264056i
$376$		0			0
$377$		−	8.14943i		−	0.0216165i
$378$		0			0
$379$	339.317	−	339.317i	0.895297	−	0.895297i	−0.0997190	−	0.995016i	$-0.531794\pi$
$379$	339.317	−	339.317i	0.895297	−	0.895297i	0.995016	+	0.0997190i	$0.0317944\pi$
$380$		0			0
$381$	54.6800	−	54.6800i	0.143517	−	0.143517i
$382$		0			0
$383$	98.8805	+	98.8805i	0.258174	+	0.258174i	0.824311	−	0.566137i	$-0.191563\pi$
$383$	98.8805	+	98.8805i	0.258174	+	0.258174i	−0.566137	+	0.824311i	$0.691563\pi$
$384$		0			0
$385$	94.8098	+	26.9604i	0.246259	+	0.0700270i
$386$		0			0
$387$	−46.7583	−	46.7583i	−0.120823	−	0.120823i
$388$		0			0
$389$	660.164			1.69708			0.848540	−	0.529132i	$-0.177482\pi$
$389$	660.164			1.69708			0.848540	+	0.529132i	$0.177482\pi$
$390$		0			0
$391$	337.778	−	417.340i	0.863883	−	1.06737i
$392$		0			0
$393$	−282.297	−	282.297i	−0.718314	−	0.718314i
$394$		0			0
$395$	−72.4085	+	254.634i	−0.183313	+	0.644643i
$396$		0			0
$397$	277.688			0.699465			0.349732	−	0.936850i	$-0.386272\pi$
$397$	277.688			0.699465			0.349732	+	0.936850i	$0.386272\pi$
$398$		0			0
$399$	−74.8404			−0.187570
$400$		0			0
$401$	200.677	−	200.677i	0.500440	−	0.500440i	−0.411134	−	0.911575i	$-0.634867\pi$
$401$	200.677	−	200.677i	0.500440	−	0.500440i	0.911575	+	0.411134i	$0.134867\pi$
$402$		0			0
$403$	−1.23811			−0.00307224
$404$		0			0
$405$	−21.9031	−	39.3097i	−0.0540817	−	0.0970611i
$406$		0			0
$407$	−370.408	−	370.408i	−0.910093	−	0.910093i
$408$		0			0
$409$			699.246i			1.70965i	0.518917	+	0.854824i	$0.326335\pi$
$409$			699.246i			1.70965i	−0.518917	+	0.854824i	$0.673665\pi$
$410$		0			0
$411$	181.841	+	181.841i	0.442435	+	0.442435i
$412$		0			0
$413$	−153.539			−0.371765
$414$		0			0
$415$	−115.111	+	404.804i	−0.277377	+	0.975432i
$416$		0			0
$417$	14.7020	−	14.7020i	0.0352565	−	0.0352565i
$418$		0			0
$419$	−158.165	−	158.165i	−0.377482	−	0.377482i	0.492711	−	0.870193i	$-0.336006\pi$
$419$	−158.165	−	158.165i	−0.377482	−	0.377482i	−0.870193	+	0.492711i	$0.836006\pi$
$420$		0			0
$421$	259.013			0.615233			0.307616	−	0.951510i	$-0.400469\pi$
$421$	259.013			0.615233			0.307616	+	0.951510i	$0.400469\pi$
$422$		0			0
$423$	−172.553	−	172.553i	−0.407928	−	0.407928i
$424$		0			0
$425$	−401.196	+	140.238i	−0.943990	+	0.329973i
$426$		0			0
$427$	124.304	−	124.304i	0.291110	−	0.291110i
$428$		0			0
$429$		−	3.41532i		−	0.00796111i
$430$		0			0
$431$	−296.381	+	296.381i	−0.687658	+	0.687658i	−0.961714	−	0.274056i	$-0.911635\pi$
$431$	−296.381	+	296.381i	−0.687658	+	0.687658i	0.274056	+	0.961714i	$0.411635\pi$
$432$		0			0
$433$	243.290	+	243.290i	0.561872	+	0.561872i	0.929839	−	0.367967i	$-0.119946\pi$
$433$	243.290	+	243.290i	0.561872	+	0.561872i	−0.367967	+	0.929839i	$0.619946\pi$
$434$		0			0
$435$	433.368	+	123.234i	0.996248	+	0.283296i
$436$		0			0
$437$		−	871.385i		−	1.99402i
$438$		0			0
$439$	136.529	−	136.529i	0.311000	−	0.311000i	−0.534297	−	0.845297i	$-0.679424\pi$
$439$	136.529	−	136.529i	0.311000	−	0.311000i	0.845297	+	0.534297i	$0.179424\pi$
$440$		0			0
$441$	−139.642			−0.316649
$442$		0			0
$443$	106.745	−	106.745i	0.240959	−	0.240959i	−0.576288	−	0.817247i	$-0.695499\pi$
$443$	106.745	−	106.745i	0.240959	−	0.240959i	0.817247	+	0.576288i	$0.195499\pi$
$444$		0			0
$445$	−577.560	+	321.812i	−1.29789	+	0.723172i
$446$		0			0
$447$		−	69.7607i		−	0.156064i
$448$		0			0
$449$	−457.083	−	457.083i	−1.01800	−	1.01800i	−0.999835	−	0.0181671i	$-0.994217\pi$
$449$	−457.083	−	457.083i	−1.01800	−	1.01800i	−0.0181671	−	0.999835i	$-0.505783\pi$
$450$		0			0
$451$		−	286.879i		−	0.636094i
$452$		0			0
$453$		−	224.626i		−	0.495864i
$454$		0			0
$455$	−1.17982	−	0.335496i	−0.00259300	−	0.000737354i
$456$		0			0
$457$	−371.740	+	371.740i	−0.813435	+	0.813435i	−0.985147	−	0.171712i	$-0.945070\pi$
$457$	−371.740	+	371.740i	−0.813435	+	0.813435i	0.171712	+	0.985147i	$0.445070\pi$
$458$		0			0
$459$	−68.6631	−	55.5731i	−0.149593	−	0.121074i
$460$		0			0
$461$			183.216i			0.397431i	0.980057	+	0.198716i	$0.0636770\pi$
$461$			183.216i			0.397431i	−0.980057	+	0.198716i	$0.936323\pi$
$462$		0			0
$463$	250.829	−	250.829i	0.541746	−	0.541746i	−0.382294	−	0.924041i	$-0.624866\pi$
$463$	250.829	−	250.829i	0.541746	−	0.541746i	0.924041	+	0.382294i	$0.124866\pi$
$464$		0			0
$465$	18.7225	−	65.8400i	0.0402634	−	0.141591i
$466$		0			0
$467$	51.3054	−	51.3054i	0.109862	−	0.109862i	−0.650039	−	0.759901i	$-0.725247\pi$
$467$	51.3054	−	51.3054i	0.109862	−	0.109862i	0.759901	+	0.650039i	$0.225247\pi$
$468$		0			0
$469$	−30.2728	−	30.2728i	−0.0645475	−	0.0645475i
$470$		0			0
$471$	−49.7205	−	49.7205i	−0.105564	−	0.105564i
$472$		0			0
$473$	277.465			0.586606
$474$		0			0
$475$	−362.940	+	586.559i	−0.764083	+	1.23486i
$476$		0			0
$477$	50.4229	+	50.4229i	0.105708	+	0.105708i
$478$		0			0
$479$	−174.253	+	174.253i	−0.363785	+	0.363785i	−0.865204	−	0.501420i	$-0.832811\pi$
$479$	−174.253	+	174.253i	−0.363785	+	0.363785i	0.501420	+	0.865204i	$0.332811\pi$
$480$		0			0
$481$	4.60936	+	4.60936i	0.00958288	+	0.00958288i
$482$		0			0
$483$			85.6689i			0.177368i
$484$		0			0
$485$	−275.764	+	153.654i	−0.568586	+	0.316811i
$486$		0			0
$487$	−185.321			−0.380537			−0.190268	−	0.981732i	$-0.560936\pi$
$487$	−185.321			−0.380537			−0.190268	+	0.981732i	$0.560936\pi$
$488$		0			0
$489$		−	274.553i		−	0.561458i
$490$		0			0
$491$			691.260i			1.40786i	0.710269	+	0.703930i	$0.248573\pi$
$491$			691.260i			1.40786i	−0.710269	+	0.703930i	$0.751427\pi$
$492$		0			0
$493$	879.555	−	92.6732i	1.78409	−	0.187978i
$494$		0			0
$495$	181.619	+	51.6457i	0.366907	+	0.104335i
$496$		0			0
$497$	52.0123	+	52.0123i	0.104652	+	0.104652i
$498$		0			0
$499$	−573.760	−	573.760i	−1.14982	−	1.14982i	−0.986588	−	0.163231i	$-0.947808\pi$
$499$	−573.760	−	573.760i	−1.14982	−	1.14982i	−0.163231	−	0.986588i	$-0.552192\pi$
$500$		0			0
$501$			457.091i			0.912357i
$502$		0			0
$503$		−	728.398i		−	1.44811i	−0.689743	−	0.724054i	$-0.742277\pi$
$503$		−	728.398i		−	1.44811i	0.689743	−	0.724054i	$-0.257723\pi$
$504$		0			0
$505$	225.330	+	404.402i	0.446197	+	0.800796i
$506$		0			0
$507$		−	292.674i		−	0.577266i
$508$		0			0
$509$			911.157i			1.79009i	0.445973	+	0.895046i	$0.352858\pi$
$509$			911.157i			1.79009i	−0.445973	+	0.895046i	$0.647142\pi$
$510$		0			0
$511$	16.8013			0.0328793
$512$		0			0
$513$	−143.365			−0.279464
$514$		0			0
$515$	−867.386	−	246.653i	−1.68424	−	0.478937i
$516$		0			0
$517$	1023.93			1.98053
$518$		0			0
$519$	−258.455			−0.497986
$520$		0			0
$521$	85.7397	−	85.7397i	0.164568	−	0.164568i	−0.620019	−	0.784587i	$-0.712875\pi$
$521$	85.7397	−	85.7397i	0.164568	−	0.164568i	0.784587	+	0.620019i	$0.212875\pi$
$522$		0			0
$523$	34.2680	−	34.2680i	0.0655221	−	0.0655221i	−0.673586	−	0.739108i	$-0.735247\pi$
$523$	34.2680	−	34.2680i	0.0655221	−	0.0655221i	0.739108	+	0.673586i	$0.235247\pi$
$524$		0			0
$525$	35.6819	−	57.6667i	0.0679654	−	0.109841i
$526$		0			0
$527$	−14.0795	−	133.628i	−0.0267163	−	0.253563i
$528$		0			0
$529$	−468.464			−0.885566
$530$		0			0
$531$	−294.121			−0.553900
$532$		0			0
$533$			3.56993i			0.00669780i
$534$		0			0
$535$	−654.587	+	364.731i	−1.22353	+	0.681739i
$536$		0			0
$537$	−344.872			−0.642220
$538$		0			0
$539$	414.319	−	414.319i	0.768681	−	0.768681i
$540$		0			0
$541$	−115.539	−	115.539i	−0.213565	−	0.213565i	0.592215	−	0.805780i	$-0.298254\pi$
$541$	−115.539	−	115.539i	−0.213565	−	0.213565i	−0.805780	+	0.592215i	$0.798254\pi$
$542$		0			0
$543$	−299.416	+	299.416i	−0.551411	+	0.551411i
$544$		0			0
$545$	60.4457	−	212.565i	0.110909	−	0.390028i
$546$		0			0
$547$			251.288i			0.459393i	0.973262	+	0.229696i	$0.0737733\pi$
$547$			251.288i			0.459393i	−0.973262	+	0.229696i	$0.926227\pi$
$548$		0			0
$549$	238.118	−	238.118i	0.433730	−	0.433730i
$550$		0			0
$551$	1014.98	−	1014.98i	1.84207	−	1.84207i
$552$		0			0
$553$	−58.6314	−	58.6314i	−0.106024	−	0.106024i
$554$		0			0
$555$	−314.817	+	175.414i	−0.567238	+	0.316061i
$556$		0			0
$557$	−566.808	−	566.808i	−1.01761	−	1.01761i	−0.999842	−	0.0177667i	$-0.994344\pi$
$557$	−566.808	−	566.808i	−1.01761	−	1.01761i	−0.0177667	−	0.999842i	$-0.505656\pi$
$558$		0			0
$559$	−3.45278			−0.00617670
$560$		0			0
$561$	368.610	−	38.8381i	0.657058	−	0.0692302i
$562$		0			0
$563$	212.248	+	212.248i	0.376994	+	0.376994i	0.870017	−	0.493023i	$-0.164108\pi$
$563$	212.248	+	212.248i	0.376994	+	0.376994i	−0.493023	+	0.870017i	$0.664108\pi$
$564$		0			0
$565$	−835.560	+	465.567i	−1.47887	+	0.824013i
$566$		0			0
$567$	14.0947			0.0248584
$568$		0			0
$569$	−499.889			−0.878540			−0.439270	−	0.898355i	$-0.644763\pi$
$569$	−499.889			−0.878540			−0.439270	+	0.898355i	$0.644763\pi$
$570$		0			0
$571$	−107.615	+	107.615i	−0.188468	+	0.188468i	−0.795034	−	0.606565i	$-0.792547\pi$
$571$	−107.615	+	107.615i	−0.188468	+	0.188468i	0.606565	+	0.795034i	$0.292547\pi$
$572$		0			0
$573$	523.037			0.912805
$574$		0			0
$575$	671.427	+	415.453i	1.16770	+	0.722526i
$576$		0			0
$577$	−585.001	−	585.001i	−1.01387	−	1.01387i	−0.999903	−	0.0139637i	$-0.995555\pi$
$577$	−585.001	−	585.001i	−1.01387	−	1.01387i	−0.0139637	−	0.999903i	$-0.504445\pi$
$578$		0			0
$579$			333.836i			0.576573i
$580$		0			0
$581$	−93.2093	−	93.2093i	−0.160429	−	0.160429i
$582$		0			0
$583$	−299.210			−0.513225
$584$		0			0
$585$	−2.26007	−	0.642680i	−0.00386337	−	0.00109860i
$586$		0			0
$587$	312.139	−	312.139i	0.531753	−	0.531753i	−0.389341	−	0.921094i	$-0.627297\pi$
$587$	312.139	−	312.139i	0.531753	−	0.531753i	0.921094	+	0.389341i	$0.127297\pi$
$588$		0			0
$589$	−154.202	−	154.202i	−0.261804	−	0.261804i
$590$		0			0
$591$	396.283			0.670530
$592$		0			0
$593$	259.082	+	259.082i	0.436901	+	0.436901i	0.890968	−	0.454067i	$-0.150027\pi$
$593$	259.082	+	259.082i	0.436901	+	0.436901i	−0.454067	+	0.890968i	$0.650027\pi$
$594$		0			0
$595$	22.7930	−	131.151i	0.0383076	−	0.220422i
$596$		0			0
$597$	−34.1905	+	34.1905i	−0.0572705	+	0.0572705i
$598$		0			0
$599$			424.610i			0.708865i	0.935082	+	0.354432i	$0.115326\pi$
$599$			424.610i			0.708865i	−0.935082	+	0.354432i	$0.884674\pi$
$600$		0			0
$601$	33.3717	−	33.3717i	0.0555269	−	0.0555269i	−0.678798	−	0.734325i	$-0.737499\pi$
$601$	33.3717	−	33.3717i	0.0555269	−	0.0555269i	0.734325	+	0.678798i	$0.237499\pi$
$602$		0			0
$603$	−57.9908	−	57.9908i	−0.0961705	−	0.0961705i
$604$		0			0
$605$	−163.599	+	91.1562i	−0.270412	+	0.150671i
$606$		0			0
$607$			56.5351i			0.0931385i	0.998915	+	0.0465693i	$0.0148288\pi$
$607$			56.5351i			0.0931385i	−0.998915	+	0.0465693i	$0.985171\pi$
$608$		0			0
$609$	−99.7863	+	99.7863i	−0.163853	+	0.163853i
$610$		0			0
$611$	−12.7419			−0.0208541
$612$		0			0
$613$	362.205	−	362.205i	0.590873	−	0.590873i	−0.346994	−	0.937867i	$-0.612798\pi$
$613$	362.205	−	362.205i	0.590873	−	0.590873i	0.937867	+	0.346994i	$0.112798\pi$
$614$		0			0
$615$	−189.841	−	53.9836i	−0.308684	−	0.0877783i
$616$		0			0
$617$			228.053i			0.369616i	0.982775	+	0.184808i	$0.0591663\pi$
$617$			228.053i			0.369616i	−0.982775	+	0.184808i	$0.940834\pi$
$618$		0			0
$619$	−408.330	−	408.330i	−0.659660	−	0.659660i	0.295639	−	0.955300i	$-0.404467\pi$
$619$	−408.330	−	408.330i	−0.659660	−	0.659660i	−0.955300	+	0.295639i	$0.904467\pi$
$620$		0			0
$621$			164.108i			0.264265i
$622$		0			0
$623$		−	207.087i		−	0.332403i
$624$		0			0
$625$	−278.921	−	559.311i	−0.446273	−	0.894897i
$626$		0			0
$627$	425.365	−	425.365i	0.678413	−	0.678413i
$628$		0			0
$629$	−445.065	+	549.898i	−0.707575	+	0.874242i
$630$		0			0
$631$			232.298i			0.368143i	0.982913	+	0.184071i	$0.0589278\pi$
$631$			232.298i			0.368143i	−0.982913	+	0.184071i	$0.941072\pi$
$632$		0			0
$633$	372.356	−	372.356i	0.588240	−	0.588240i
$634$		0			0
$635$	214.718	+	61.0578i	0.338138	+	0.0961540i
$636$		0			0
$637$	−5.15580	+	5.15580i	−0.00809388	+	0.00809388i
$638$		0			0
$639$	99.6352	+	99.6352i	0.155924	+	0.155924i
$640$		0			0
$641$	119.723	+	119.723i	0.186775	+	0.186775i	0.794300	−	0.607525i	$-0.207838\pi$
$641$	119.723	+	119.723i	0.186775	+	0.186775i	−0.607525	+	0.794300i	$0.707838\pi$
$642$		0			0
$643$	933.945			1.45248			0.726240	−	0.687441i	$-0.241266\pi$
$643$	933.945			1.45248			0.726240	+	0.687441i	$0.241266\pi$
$644$		0			0
$645$	52.2121	−	183.611i	0.0809491	−	0.284668i
$646$		0			0
$647$	−318.132	−	318.132i	−0.491704	−	0.491704i	0.417139	−	0.908843i	$-0.363033\pi$
$647$	−318.132	−	318.132i	−0.491704	−	0.491704i	−0.908843	+	0.417139i	$0.863033\pi$
$648$		0			0
$649$	872.658	−	872.658i	1.34462	−	1.34462i
$650$		0			0
$651$	15.1602	+	15.1602i	0.0232875	+	0.0232875i
$652$		0			0
$653$		−	401.500i		−	0.614855i	−0.951572	−	0.307427i	$-0.900532\pi$
$653$		−	401.500i		−	0.614855i	0.951572	−	0.307427i	$-0.0994682\pi$
$654$		0			0
$655$	315.224	−	1108.53i	0.481258	−	1.69241i
$656$		0			0
$657$	32.1848			0.0489875
$658$		0			0
$659$		−	812.152i		−	1.23240i	−0.787590	−	0.616200i	$-0.788671\pi$
$659$		−	812.152i		−	1.23240i	0.787590	−	0.616200i	$-0.211329\pi$
$660$		0			0
$661$		−	608.447i		−	0.920495i	−0.887791	−	0.460248i	$-0.847761\pi$
$661$		−	608.447i		−	0.920495i	0.887791	−	0.460248i	$-0.152239\pi$
$662$		0			0
$663$	−4.58699	+	0.483303i	−0.00691854	+	0.000728964i
$664$		0			0
$665$	−105.157	−	188.727i	−0.158131	−	0.283799i
$666$		0			0
$667$	−1161.84	−	1161.84i	−1.74188	−	1.74188i
$668$		0			0
$669$	264.439	+	264.439i	0.395274	+	0.395274i
$670$		0			0
$671$			1412.99i			2.10580i
$672$		0			0
$673$		−	264.768i		−	0.393415i	−0.980462	−	0.196708i	$-0.936975\pi$
$673$		−	264.768i		−	0.393415i	0.980462	−	0.196708i	$-0.0630250\pi$
$674$		0			0
$675$	68.3525	−	110.467i	0.101263	−	0.163655i
$676$		0			0
$677$			790.423i			1.16754i	0.811920	+	0.583769i	$0.198423\pi$
$677$			790.423i			1.16754i	−0.811920	+	0.583769i	$0.801577\pi$
$678$		0			0
$679$		−	98.8767i		−	0.145621i
$680$		0			0
$681$	567.993			0.834057
$682$		0			0
$683$	1056.42			1.54674			0.773369	−	0.633956i	$-0.218570\pi$
$683$	1056.42			1.54674			0.773369	+	0.633956i	$0.218570\pi$
$684$		0			0
$685$	−203.050	+	714.052i	−0.296424	+	1.04241i
$686$		0			0
$687$	−274.150			−0.399054
$688$		0			0
$689$	3.72338			0.00540404
$690$		0			0
$691$	232.433	−	232.433i	0.336372	−	0.336372i	−0.518628	−	0.855000i	$-0.673557\pi$
$691$	232.433	−	232.433i	0.336372	−	0.336372i	0.855000	+	0.518628i	$0.173557\pi$
$692$		0			0
$693$	−41.8191	+	41.8191i	−0.0603450	+	0.0603450i
$694$		0			0
$695$	57.7317	+	16.4168i	0.0830672	+	0.0236213i
$696$		0			0
$697$	−385.297	+	40.5963i	−0.552793	+	0.0582444i
$698$		0			0
$699$	−619.232			−0.885882
$700$		0			0
$701$	791.759			1.12947			0.564735	−	0.825272i	$-0.308978\pi$
$701$	791.759			1.12947			0.564735	+	0.825272i	$0.308978\pi$
$702$		0			0
$703$			1148.16i			1.63323i
$704$		0			0
$705$	192.680	−	677.583i	0.273305	−	0.961111i
$706$		0			0
$707$	−145.001			−0.205093
$708$		0			0
$709$	221.900	−	221.900i	0.312975	−	0.312975i	−0.533086	−	0.846061i	$-0.678968\pi$
$709$	221.900	−	221.900i	0.312975	−	0.312975i	0.846061	+	0.533086i	$0.178968\pi$
$710$		0			0
$711$	−112.315	−	112.315i	−0.157968	−	0.157968i
$712$		0			0
$713$	−176.514	+	176.514i	−0.247565	+	0.247565i
$714$		0			0
$715$	8.61247	−	4.79880i	0.0120454	−	0.00671161i
$716$		0			0
$717$			473.711i			0.660685i
$718$		0			0
$719$	−538.494	+	538.494i	−0.748949	+	0.748949i	−0.974282	−	0.225333i	$-0.927653\pi$
$719$	−538.494	+	538.494i	−0.748949	+	0.748949i	0.225333	+	0.974282i	$0.427653\pi$
$720$		0			0
$721$	199.722	−	199.722i	0.277007	−	0.277007i
$722$		0			0
$723$	−420.682	−	420.682i	−0.581856	−	0.581856i
$724$		0			0
$725$	298.156	+	1265.99i	0.411250	+	1.74619i
$726$		0			0
$727$	382.087	+	382.087i	0.525566	+	0.525566i	0.919247	−	0.393681i	$-0.128799\pi$
$727$	382.087	+	382.087i	0.525566	+	0.525566i	−0.393681	+	0.919247i	$0.628799\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$		0			0
$731$	−39.2641	−	372.653i	−0.0537129	−	0.509785i
$732$		0			0
$733$	528.567	+	528.567i	0.721100	+	0.721100i	0.968829	−	0.247729i	$-0.0796842\pi$
$733$	528.567	+	528.567i	0.721100	+	0.721100i	−0.247729	+	0.968829i	$0.579684\pi$
$734$		0			0
$735$	−196.209	−	352.139i	−0.266951	−	0.479100i
$736$		0			0
$737$	344.118			0.466917
$738$		0			0
$739$	−285.527			−0.386370			−0.193185	−	0.981162i	$-0.561882\pi$
$739$	−285.527			−0.386370			−0.193185	+	0.981162i	$0.561882\pi$
$740$		0			0
$741$	−5.29326	+	5.29326i	−0.00714340	+	0.00714340i
$742$		0			0
$743$	−1281.28			−1.72447			−0.862233	−	0.506512i	$-0.830935\pi$
$743$	−1281.28			−1.72447			−0.862233	+	0.506512i	$0.830935\pi$
$744$		0			0
$745$	175.917	−	98.0196i	0.236130	−	0.131570i
$746$		0			0
$747$	−178.553	−	178.553i	−0.239026	−	0.239026i
$748$		0			0
$749$		−	234.706i		−	0.313359i
$750$		0			0
$751$	−476.855	−	476.855i	−0.634960	−	0.634960i	0.314348	−	0.949308i	$-0.398214\pi$
$751$	−476.855	−	476.855i	−0.634960	−	0.634960i	−0.949308	+	0.314348i	$0.898214\pi$
$752$		0			0
$753$	−226.090			−0.300252
$754$		0			0
$755$	566.445	−	315.618i	0.750258	−	0.418038i
$756$		0			0
$757$	−628.711	+	628.711i	−0.830530	+	0.830530i	−0.987589	−	0.157059i	$-0.949799\pi$
$757$	−628.711	+	628.711i	−0.830530	+	0.830530i	0.157059	+	0.987589i	$0.449799\pi$
$758$		0			0
$759$	−486.910	−	486.910i	−0.641515	−	0.641515i
$760$		0			0
$761$	430.029			0.565085			0.282542	−	0.959255i	$-0.408822\pi$
$761$	430.029			0.565085			0.282542	+	0.959255i	$0.408822\pi$
$762$		0			0
$763$	48.9447	+	48.9447i	0.0641478	+	0.0641478i
$764$		0			0
$765$	43.6625	−	251.234i	0.0570752	−	0.328411i
$766$		0			0
$767$	−10.8594	+	10.8594i	−0.0141583	+	0.0141583i
$768$		0			0
$769$		−	1328.86i		−	1.72803i	−0.503463	−	0.864017i	$-0.667941\pi$
$769$		−	1328.86i		−	1.72803i	0.503463	−	0.864017i	$-0.332059\pi$
$770$		0			0
$771$	−294.771	+	294.771i	−0.382323	+	0.382323i
$772$		0			0
$773$	−1037.38	−	1037.38i	−1.34201	−	1.34201i	−0.894053	−	0.447961i	$-0.852150\pi$
$773$	−1037.38	−	1037.38i	−1.34201	−	1.34201i	−0.447961	−	0.894053i	$-0.647850\pi$
$774$		0			0
$775$	192.337	−	45.2978i	0.248177	−	0.0584488i
$776$		0			0
$777$		−	112.879i		−	0.145276i
$778$		0			0
$779$	−444.621	+	444.621i	−0.570759	+	0.570759i
$780$		0			0
$781$	−591.237			−0.757025
$782$		0			0
$783$	−191.152	+	191.152i	−0.244127	+	0.244127i
$784$		0			0
$785$	55.5198	−	195.243i	0.0707258	−	0.248717i
$786$		0			0
$787$			140.873i			0.179000i	0.995987	+	0.0895002i	$0.0285270\pi$
$787$			140.873i			0.179000i	−0.995987	+	0.0895002i	$0.971473\pi$
$788$		0			0
$789$	293.878	+	293.878i	0.372469	+	0.372469i
$790$		0			0
$791$		−	299.595i		−	0.378754i
$792$		0			0
$793$		−	17.5833i		−	0.0221732i
$794$		0			0
$795$	−56.3042	+	198.001i	−0.0708228	+	0.249058i
$796$		0			0
$797$	−194.132	+	194.132i	−0.243578	+	0.243578i	−0.818329	−	0.574751i	$-0.805099\pi$
$797$	−194.132	+	194.132i	−0.243578	+	0.243578i	0.574751	+	0.818329i	$0.305099\pi$
$798$		0			0
$799$	−144.897	−	1375.21i	−0.181348	−	1.72116i
$800$		0			0
$801$		−	396.698i		−	0.495254i
$802$		0			0
$803$	−95.4925	+	95.4925i	−0.118920	+	0.118920i
$804$		0			0
$805$	−216.033	+	120.372i	−0.268364	+	0.149530i
$806$		0			0
$807$	143.796	−	143.796i	0.178185	−	0.178185i
$808$		0			0
$809$	586.892	+	586.892i	0.725454	+	0.725454i	0.969711	−	0.244257i	$-0.0785439\pi$
$809$	586.892	+	586.892i	0.725454	+	0.725454i	−0.244257	+	0.969711i	$0.578544\pi$
$810$		0			0
$811$	653.251	+	653.251i	0.805488	+	0.805488i	0.983947	−	0.178459i	$-0.0571112\pi$
$811$	653.251	+	653.251i	0.805488	+	0.805488i	−0.178459	+	0.983947i	$0.557111\pi$
$812$		0			0
$813$	662.157			0.814461
$814$		0			0
$815$	692.346	−	385.769i	0.849504	−	0.473337i
$816$		0			0
$817$	−430.031	−	430.031i	−0.526353	−	0.526353i
$818$		0			0
$819$	0.520398	−	0.520398i	0.000635407	−	0.000635407i
$820$		0			0
$821$	−506.504	−	506.504i	−0.616936	−	0.616936i	0.327808	−	0.944744i	$-0.393690\pi$
$821$	−506.504	−	506.504i	−0.616936	−	0.616936i	−0.944744	+	0.327808i	$0.893690\pi$
$822$		0			0
$823$		−	1485.30i		−	1.80474i	−0.430964	−	0.902369i	$-0.641826\pi$
$823$		−	1485.30i		−	1.80474i	0.430964	−	0.902369i	$-0.358174\pi$
$824$		0			0
$825$	124.953	+	530.558i	0.151459	+	0.643101i
$826$		0			0
$827$	998.059			1.20684			0.603421	−	0.797423i	$-0.293804\pi$
$827$	998.059			1.20684			0.603421	+	0.797423i	$0.293804\pi$
$828$		0			0
$829$			1038.19i			1.25234i	0.779688	+	0.626168i	$0.215378\pi$
$829$			1038.19i			1.25234i	−0.779688	+	0.626168i	$0.784622\pi$
$830$		0			0
$831$			576.921i			0.694249i
$832$		0			0
$833$	−615.088	−	497.827i	−0.738401	−	0.597631i
$834$		0			0
$835$	−1152.66	+	642.251i	−1.38043	+	0.769163i
$836$		0			0
$837$	29.0410	+	29.0410i	0.0346965	+	0.0346965i
$838$		0			0
$839$	−507.856	−	507.856i	−0.605311	−	0.605311i	0.336406	−	0.941717i	$-0.390788\pi$
$839$	−507.856	−	507.856i	−0.605311	−	0.605311i	−0.941717	+	0.336406i	$0.890788\pi$
$840$		0			0
$841$		−	1865.59i		−	2.21830i
$842$		0			0
$843$			686.901i			0.814830i
$844$		0			0
$845$	738.042	−	411.231i	0.873423	−	0.486664i
$846$		0			0
$847$		−	58.6594i		−	0.0692555i
$848$		0			0
$849$		−	826.565i		−	0.973575i
$850$		0			0
$851$	1314.28			1.54440
$852$		0			0
$853$	−10.7675			−0.0126231			−0.00631154	−	0.999980i	$-0.502009\pi$
$853$	−10.7675			−0.0126231			−0.00631154	+	0.999980i	$0.502009\pi$
$854$		0			0
$855$	−201.440	−	361.527i	−0.235602	−	0.422838i
$856$		0			0
$857$	−636.725			−0.742970			−0.371485	−	0.928439i	$-0.621151\pi$
$857$	−636.725			−0.742970			−0.371485	+	0.928439i	$0.621151\pi$
$858$		0			0
$859$	181.997			0.211871			0.105935	−	0.994373i	$-0.466216\pi$
$859$	181.997			0.211871			0.105935	+	0.994373i	$0.466216\pi$
$860$		0			0
$861$	43.7122	−	43.7122i	0.0507692	−	0.0507692i
$862$		0			0
$863$	152.369	−	152.369i	0.176558	−	0.176558i	−0.613296	−	0.789853i	$-0.710157\pi$
$863$	152.369	−	152.369i	0.176558	−	0.176558i	0.789853	+	0.613296i	$0.210157\pi$
$864$		0			0
$865$	−363.150	−	651.751i	−0.419827	−	0.753469i
$866$		0			0
$867$	−104.324	−	489.571i	−0.120328	−	0.564672i
$868$		0			0
$869$	666.478			0.766948
$870$		0			0
$871$	−4.28222			−0.00491644
$872$		0			0
$873$		−	189.409i		−	0.216964i
$874$		0			0
$875$	195.555	+	8.95324i	0.223492	+	0.0102323i
$876$		0			0
$877$	−411.143			−0.468807			−0.234403	−	0.972139i	$-0.575314\pi$
$877$	−411.143			−0.468807			−0.234403	+	0.972139i	$0.575314\pi$
$878$		0			0
$879$	310.834	−	310.834i	0.353622	−	0.353622i
$880$		0			0
$881$	1184.77	+	1184.77i	1.34481	+	1.34481i	0.891205	+	0.453601i	$0.149861\pi$
$881$	1184.77	+	1184.77i	1.34481	+	1.34481i	0.453601	+	0.891205i	$0.350139\pi$
$882$		0			0
$883$	90.6253	−	90.6253i	0.102633	−	0.102633i	−0.653925	−	0.756559i	$-0.726879\pi$
$883$	90.6253	−	90.6253i	0.102633	−	0.102633i	0.756559	+	0.653925i	$0.226879\pi$
$884$		0			0
$885$	−413.264	−	741.690i	−0.466965	−	0.838068i
$886$		0			0
$887$			245.305i			0.276556i	0.990393	+	0.138278i	$0.0441568\pi$
$887$			245.305i			0.276556i	−0.990393	+	0.138278i	$0.955843\pi$
$888$		0			0
$889$	−49.4404	+	49.4404i	−0.0556135	+	0.0556135i
$890$		0			0
$891$	−80.1091	+	80.1091i	−0.0899093	+	0.0899093i
$892$		0			0
$893$	−1586.95	−	1586.95i	−1.77710	−	1.77710i
$894$		0			0
$895$	−484.574	−	869.671i	−0.541423	−	0.971700i
$896$		0			0
$897$	6.05913	+	6.05913i	0.00675488	+	0.00675488i
$898$		0			0
$899$	−411.203			−0.457400
$900$		0			0
$901$	42.3414	+	401.859i	0.0469937	+	0.446014i
$902$		0			0
$903$	42.2778	+	42.2778i	0.0468193	+	0.0468193i
$904$		0			0
$905$	−1175.75	−	334.339i	−1.29917	−	0.369436i
$906$		0			0
$907$	−299.114			−0.329784			−0.164892	−	0.986312i	$-0.552728\pi$
$907$	−299.114			−0.329784			−0.164892	+	0.986312i	$0.552728\pi$
$908$		0			0
$909$	−277.765			−0.305572
$910$		0			0
$911$	−942.098	+	942.098i	−1.03414	+	1.03414i	−0.0347402	+	0.999396i	$0.511060\pi$
$911$	−942.098	+	942.098i	−1.03414	+	1.03414i	−0.999396	+	0.0347402i	$0.988940\pi$
$912$		0			0
$913$	1059.53			1.16050
$914$		0			0
$915$	935.042	+	265.891i	1.02190	+	0.290592i
$916$		0			0
$917$	255.247	+	255.247i	0.278350	+	0.278350i
$918$		0			0
$919$			1142.25i			1.24293i	0.783442	+	0.621465i	$0.213462\pi$
$919$			1142.25i			1.24293i	−0.783442	+	0.621465i	$0.786538\pi$
$920$		0			0
$921$	174.391	+	174.391i	0.189350	+	0.189350i
$922$		0			0
$923$	7.35737			0.00797115
$924$		0			0
$925$	−884.689	−	547.411i	−0.956420	−	0.591795i
$926$		0			0
$927$	382.590	−	382.590i	0.412719	−	0.412719i
$928$		0			0
$929$	51.8357	+	51.8357i	0.0557973	+	0.0557973i	0.734455	−	0.678658i	$-0.237438\pi$
$929$	51.8357	+	51.8357i	0.0557973	+	0.0557973i	−0.678658	+	0.734455i	$0.737438\pi$
$930$		0			0
$931$	−1284.27			−1.37945
$932$		0			0
$933$	−370.932	−	370.932i	−0.397569	−	0.397569i
$934$		0			0
$935$	615.866	+	874.960i	0.658680	+	0.935786i
$936$		0			0
$937$	−287.594	+	287.594i	−0.306930	+	0.306930i	−0.843718	−	0.536787i	$-0.819638\pi$
$937$	−287.594	+	287.594i	−0.306930	+	0.306930i	0.536787	+	0.843718i	$0.319638\pi$
$938$		0			0
$939$			1044.63i			1.11250i
$940$		0			0
$941$	−135.540	+	135.540i	−0.144039	+	0.144039i	−0.775449	−	0.631410i	$-0.782476\pi$
$941$	−135.540	+	135.540i	−0.144039	+	0.144039i	0.631410	+	0.775449i	$0.282476\pi$
$942$		0			0
$943$	508.952	+	508.952i	0.539716	+	0.539716i
$944$		0			0
$945$	19.8042	+	35.5429i	0.0209569	+	0.0376116i
$946$		0			0
$947$			1181.02i			1.24712i	0.781775	+	0.623561i	$0.214315\pi$
$947$			1181.02i			1.24712i	−0.781775	+	0.623561i	$0.785685\pi$
$948$		0			0
$949$	1.18831	−	1.18831i	0.00125217	−	0.00125217i
$950$		0			0
$951$	−545.768			−0.573889
$952$		0			0
$953$	−503.282	+	503.282i	−0.528103	+	0.528103i	−0.920006	−	0.391903i	$-0.871817\pi$
$953$	−503.282	+	503.282i	−0.528103	+	0.528103i	0.391903	+	0.920006i	$0.371817\pi$
$954$		0			0
$955$	734.911	+	1318.95i	0.769540	+	1.38110i
$956$		0			0
$957$		−	1134.30i		−	1.18526i
$958$		0			0
$959$	−164.416	−	164.416i	−0.171445	−	0.171445i
$960$		0			0
$961$		−	898.527i		−	0.934992i
$962$		0			0
$963$		−	449.605i		−	0.466879i
$964$		0			0
$965$	−841.840	+	469.067i	−0.872373	+	0.486079i
$966$		0			0
$967$	−187.795	+	187.795i	−0.194203	+	0.194203i	−0.797510	−	0.603306i	$-0.793850\pi$
$967$	−187.795	+	187.795i	−0.194203	+	0.194203i	0.603306	+	0.797510i	$0.293850\pi$
$968$		0			0
$969$	−631.486	−	511.099i	−0.651689	−	0.527450i
$970$		0			0
$971$		−	305.635i		−	0.314763i	−0.987538	−	0.157381i	$-0.949695\pi$
$971$		−	305.635i		−	0.314763i	0.987538	−	0.157381i	$-0.0503052\pi$
$972$		0			0
$973$	−13.2932	+	13.2932i	−0.0136621	+	0.0136621i
$974$		0			0
$975$	−1.55492	−	6.60228i	−0.00159479	−	0.00677157i
$976$		0			0
$977$	325.536	−	325.536i	0.333200	−	0.333200i	−0.520601	−	0.853800i	$-0.674292\pi$
$977$	325.536	−	325.536i	0.333200	−	0.333200i	0.853800	+	0.520601i	$0.174292\pi$
$978$		0			0
$979$	1177.01	+	1177.01i	1.20225	+	1.20225i
$980$		0			0
$981$	93.7591	+	93.7591i	0.0955750	+	0.0955750i
$982$		0			0
$983$	876.090			0.891241			0.445621	−	0.895222i	$-0.352983\pi$
$983$	876.090			0.891241			0.445621	+	0.895222i	$0.352983\pi$
$984$		0			0
$985$	556.811	+	999.316i	0.565290	+	1.01453i
$986$		0			0
$987$	156.019	+	156.019i	0.158074	+	0.158074i
$988$		0			0
$989$	−492.251	+	492.251i	−0.497726	+	0.497726i
$990$		0			0
$991$	−1214.30	−	1214.30i	−1.22532	−	1.22532i	−0.965714	−	0.259610i	$-0.916406\pi$
$991$	−1214.30	−	1214.30i	−1.22532	−	1.22532i	−0.259610	−	0.965714i	$-0.583594\pi$
$992$		0			0
$993$			174.974i			0.176207i
$994$		0			0
$995$	−134.259	−	38.1784i	−0.134934	−	0.0383702i
$996$		0			0
$997$	1158.21			1.16169			0.580847	−	0.814013i	$-0.302721\pi$
$997$	1158.21			1.16169			0.580847	+	0.814013i	$0.302721\pi$
$998$		0			0
$999$		−	216.233i		−	0.216450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1020.3.bm.a.217.11	yes	72
5.3	odd	4		1020.3.t.a.13.11	✓	72
17.4	even	4		1020.3.t.a.157.26	yes	72
85.38	odd	4	inner	1020.3.bm.a.973.11	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1020.3.t.a.13.11	✓	72	5.3	odd	4
1020.3.t.a.157.26	yes	72	17.4	even	4
1020.3.bm.a.217.11	yes	72	1.1	even	1	trivial
1020.3.bm.a.973.11	yes	72	85.38	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1020.bm (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.73205 q^{3} +(-2.43367 - 4.36775i) q^{5} +1.56608 q^{7} +3.00000 q^{9} +O(q^{10})\)	\(q-1.73205 q^{3} +(-2.43367 - 4.36775i) q^{5} +1.56608 q^{7} +3.00000 q^{9} +(-8.90102 + 8.90102i) q^{11} +(0.110765 - 0.110765i) q^{13} +(4.21525 + 7.56516i) q^{15} +(13.2142 + 10.6951i) q^{17} +27.5906 q^{19} -2.71253 q^{21} -31.5827i q^{23} +(-13.1545 + 21.2594i) q^{25} -5.19615 q^{27} +(36.7872 - 36.7872i) q^{29} +(-5.58894 - 5.58894i) q^{31} +(15.4170 - 15.4170i) q^{33} +(-3.81133 - 6.84024i) q^{35} +41.6141i q^{37} +(-0.191850 + 0.191850i) q^{39} +(-16.1149 + 16.1149i) q^{41} +(-15.5861 - 15.5861i) q^{43} +(-7.30102 - 13.1032i) q^{45} +(-57.5178 - 57.5178i) q^{47} -46.5474 q^{49} +(-22.8877 - 18.5244i) q^{51} +(16.8076 + 16.8076i) q^{53} +(60.5396 + 17.2152i) q^{55} -47.7884 q^{57} -98.0403 q^{59} +(79.3726 - 79.3726i) q^{61} +4.69824 q^{63} +(-0.753356 - 0.214227i) q^{65} +(-19.3303 - 19.3303i) q^{67} +54.7028i q^{69} +(33.2117 + 33.2117i) q^{71} +10.7283 q^{73} +(22.7842 - 36.8223i) q^{75} +(-13.9397 + 13.9397i) q^{77} +(-37.4383 - 37.4383i) q^{79} +9.00000 q^{81} +(-59.5176 - 59.5176i) q^{83} +(14.5542 - 83.7447i) q^{85} +(-63.7172 + 63.7172i) q^{87} -132.233i q^{89} +(0.173466 - 0.173466i) q^{91} +(9.68033 + 9.68033i) q^{93} +(-67.1466 - 120.509i) q^{95} -63.1364i q^{97} +(-26.7030 + 26.7030i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{5} - 24 q^{7} + 216 q^{9}+O(q^{10}) \) 72 * q - 8 * q^5 - 24 * q^7 + 216 * q^9	\( 72 q - 8 q^{5} - 24 q^{7} + 216 q^{9} + 4 q^{13} - 12 q^{15} - 16 q^{17} - 28 q^{25} + 72 q^{29} + 8 q^{31} + 36 q^{33} - 88 q^{35} - 48 q^{39} + 216 q^{41} + 60 q^{43} - 24 q^{45} + 360 q^{49} - 32 q^{55} - 144 q^{57} + 184 q^{61} - 72 q^{63} + 104 q^{65} + 48 q^{67} - 72 q^{71} + 112 q^{73} + 48 q^{75} + 136 q^{77} + 120 q^{79} + 648 q^{81} + 224 q^{83} + 344 q^{85} + 96 q^{87} + 56 q^{91} - 48 q^{95}+O(q^{100}) \) 72 * q - 8 * q^5 - 24 * q^7 + 216 * q^9 + 4 * q^13 - 12 * q^15 - 16 * q^17 - 28 * q^25 + 72 * q^29 + 8 * q^31 + 36 * q^33 - 88 * q^35 - 48 * q^39 + 216 * q^41 + 60 * q^43 - 24 * q^45 + 360 * q^49 - 32 * q^55 - 144 * q^57 + 184 * q^61 - 72 * q^63 + 104 * q^65 + 48 * q^67 - 72 * q^71 + 112 * q^73 + 48 * q^75 + 136 * q^77 + 120 * q^79 + 648 * q^81 + 224 * q^83 + 344 * q^85 + 96 * q^87 + 56 * q^91 - 48 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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