LMFDB - Embedded newform 920.2.bv.a.617.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			617.12
Character	$\chi$	$=$	920.617
Dual form			920.2.bv.a.753.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.663302 + 1.21475i) q^{3} +(-2.23606 - 0.00503036i) q^{5} +(-0.273851 - 0.205002i) q^{7} +(0.586283 + 0.912274i) q^{9} +(0.437876 + 0.199971i) q^{11} +(1.09003 + 1.45611i) q^{13} +(1.48929 - 2.71291i) q^{15} +(-5.99978 - 0.429113i) q^{17} +(-2.24436 + 2.59013i) q^{19} +(0.430671 - 0.196681i) q^{21} +(-0.477794 - 4.77197i) q^{23} +(4.99995 + 0.0224964i) q^{25} +(-5.63862 + 0.403282i) q^{27} +(7.06351 - 6.12056i) q^{29} +(-8.81071 - 2.58706i) q^{31} +(-0.533358 + 0.399267i) q^{33} +(0.611316 + 0.459775i) q^{35} +(-0.982790 + 4.51781i) q^{37} +(-2.49182 + 0.358270i) q^{39} +(-5.19934 - 3.34142i) q^{41} +(-4.89997 - 2.67559i) q^{43} +(-1.30638 - 2.04285i) q^{45} +(-6.66836 - 6.66836i) q^{47} +(-1.93916 - 6.60417i) q^{49} +(4.50093 - 7.00358i) q^{51} +(8.08702 - 10.8030i) q^{53} +(-0.978111 - 0.449350i) q^{55} +(-1.65766 - 4.44437i) q^{57} +(5.21327 + 0.749555i) q^{59} +(-4.23334 + 14.4174i) q^{61} +(0.0264641 - 0.370016i) q^{63} +(-2.43005 - 3.26143i) q^{65} +(-6.31343 - 2.35479i) q^{67} +(6.11366 + 2.58486i) q^{69} +(5.71261 + 12.5089i) q^{71} +(-0.232710 - 3.25371i) q^{73} +(-3.34380 + 6.05875i) q^{75} +(-0.0789181 - 0.144528i) q^{77} +(1.00791 - 7.01019i) q^{79} +(1.89876 - 4.15771i) q^{81} +(-7.55568 - 1.64364i) q^{83} +(13.4137 + 0.989704i) q^{85} +(2.74970 + 12.6402i) q^{87} +(-0.505952 + 0.148561i) q^{89} -0.622215i q^{91} +(8.98678 - 8.98678i) q^{93} +(5.03156 - 5.78041i) q^{95} +(2.54782 - 0.554245i) q^{97} +(0.0742905 + 0.516702i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{15}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.663302	+	1.21475i	−0.382957	+	0.701334i	−0.996061	−	0.0886682i	$-0.971739\pi$
$3$	−0.663302	+	1.21475i	−0.382957	+	0.701334i	0.613104	+	0.790002i	$0.289921\pi$
$4$		0			0
$5$	−2.23606	−	0.00503036i	−0.999997	−	0.00224964i
$5$	−2.23606	−	0.00503036i	−0.999997	−	0.00224964i
$6$		0			0
$7$	−0.273851	−	0.205002i	−0.103506	−	0.0774835i	0.546271	−	0.837608i	$-0.316047\pi$
$7$	−0.273851	−	0.205002i	−0.103506	−	0.0774835i	−0.649777	+	0.760125i	$0.725138\pi$
$8$		0			0
$9$	0.586283	+	0.912274i	0.195428	+	0.304091i
$10$		0			0
$11$	0.437876	+	0.199971i	0.132024	+	0.0602935i	0.480332	−	0.877087i	$-0.340516\pi$
$11$	0.437876	+	0.199971i	0.132024	+	0.0602935i	−0.348307	+	0.937380i	$0.613243\pi$
$12$		0			0
$13$	1.09003	+	1.45611i	0.302320	+	0.403852i	0.925816	−	0.377974i	$-0.123379\pi$
$13$	1.09003	+	1.45611i	0.302320	+	0.403852i	−0.623496	+	0.781826i	$0.714288\pi$
$14$		0			0
$15$	1.48929	−	2.71291i	0.384534	−	0.700471i
$16$		0			0
$17$	−5.99978	−	0.429113i	−1.45516	−	0.104075i	−0.678781	−	0.734341i	$-0.737491\pi$
$17$	−5.99978	−	0.429113i	−1.45516	−	0.104075i	−0.776379	+	0.630266i	$0.782946\pi$
$18$		0			0
$19$	−2.24436	+	2.59013i	−0.514892	+	0.594217i	−0.952345	−	0.305024i	$-0.901335\pi$
$19$	−2.24436	+	2.59013i	−0.514892	+	0.594217i	0.437452	+	0.899242i	$0.355881\pi$
$20$		0			0
$21$	0.430671	−	0.196681i	0.0939802	−	0.0429193i
$22$		0			0
$23$	−0.477794	−	4.77197i	−0.0996270	−	0.995025i
$23$	−0.477794	−	4.77197i	−0.0996270	−	0.995025i
$24$		0			0
$25$	4.99995	+	0.0224964i	0.999990	+	0.00449928i
$26$		0			0
$27$	−5.63862	+	0.403282i	−1.08515	+	0.0776116i
$28$		0			0
$29$	7.06351	−	6.12056i	1.31166	−	1.13656i	0.330407	−	0.943838i	$-0.392814\pi$
$29$	7.06351	−	6.12056i	1.31166	−	1.13656i	0.981253	−	0.192722i	$-0.0617315\pi$
$30$		0			0
$31$	−8.81071	−	2.58706i	−1.58245	−	0.464649i	−0.631856	−	0.775086i	$-0.717707\pi$
$31$	−8.81071	−	2.58706i	−1.58245	−	0.464649i	−0.950594	+	0.310436i	$0.899525\pi$
$32$		0			0
$33$	−0.533358	+	0.399267i	−0.0928457	+	0.0695034i
$34$		0			0
$35$	0.611316	+	0.459775i	0.103331	+	0.0777162i
$36$		0			0
$37$	−0.982790	+	4.51781i	−0.161570	+	0.742724i	0.823044	+	0.567978i	$0.192274\pi$
$37$	−0.982790	+	4.51781i	−0.161570	+	0.742724i	−0.984614	+	0.174746i	$0.944090\pi$
$38$		0			0
$39$	−2.49182	+	0.358270i	−0.399011	+	0.0573691i
$40$		0			0
$41$	−5.19934	−	3.34142i	−0.812001	−	0.521841i	0.0675106	−	0.997719i	$-0.478494\pi$
$41$	−5.19934	−	3.34142i	−0.812001	−	0.521841i	−0.879512	+	0.475877i	$0.842131\pi$
$42$		0			0
$43$	−4.89997	−	2.67559i	−0.747239	−	0.408023i	0.0600382	−	0.998196i	$-0.480878\pi$
$43$	−4.89997	−	2.67559i	−0.747239	−	0.408023i	−0.807277	+	0.590173i	$0.799060\pi$
$44$		0			0
$45$	−1.30638	−	2.04285i	−0.194743	−	0.304530i
$46$		0			0
$47$	−6.66836	−	6.66836i	−0.972680	−	0.972680i	0.0269569	−	0.999637i	$-0.491418\pi$
$47$	−6.66836	−	6.66836i	−0.972680	−	0.972680i	−0.999637	+	0.0269569i	$0.991418\pi$
$48$		0			0
$49$	−1.93916	−	6.60417i	−0.277023	−	0.943453i
$50$		0			0
$51$	4.50093	−	7.00358i	0.630256	−	0.980697i
$52$		0			0
$53$	8.08702	−	10.8030i	1.11084	−	1.48390i	0.254798	−	0.966994i	$-0.417991\pi$
$53$	8.08702	−	10.8030i	1.11084	−	1.48390i	0.856039	−	0.516911i	$-0.172918\pi$
$54$		0			0
$55$	−0.978111	−	0.449350i	−0.131888	−	0.0605904i
$56$		0			0
$57$	−1.65766	−	4.44437i	−0.219563	−	0.588671i
$58$		0			0
$59$	5.21327	+	0.749555i	0.678710	+	0.0975838i	0.473045	−	0.881039i	$-0.343155\pi$
$59$	5.21327	+	0.749555i	0.678710	+	0.0975838i	0.205666	+	0.978622i	$0.434064\pi$
$60$		0			0
$61$	−4.23334	+	14.4174i	−0.542024	+	1.84596i	−0.00884702	+	0.999961i	$0.502816\pi$
$61$	−4.23334	+	14.4174i	−0.542024	+	1.84596i	−0.533177	+	0.846004i	$0.679002\pi$
$62$		0			0
$63$	0.0264641	−	0.370016i	0.00333416	−	0.0466177i
$64$		0			0
$65$	−2.43005	−	3.26143i	−0.301411	−	0.404531i
$66$		0			0
$67$	−6.31343	−	2.35479i	−0.771308	−	0.287683i	−0.0671659	−	0.997742i	$-0.521396\pi$
$67$	−6.31343	−	2.35479i	−0.771308	−	0.287683i	−0.704143	+	0.710059i	$0.748668\pi$
$68$		0			0
$69$	6.11366	+	2.58486i	0.735998	+	0.311180i
$70$		0			0
$71$	5.71261	+	12.5089i	0.677962	+	1.48453i	0.864789	+	0.502136i	$0.167452\pi$
$71$	5.71261	+	12.5089i	0.677962	+	1.48453i	−0.186827	+	0.982393i	$0.559820\pi$
$72$		0			0
$73$	−0.232710	−	3.25371i	−0.0272367	−	0.380818i	−0.992728	−	0.120382i	$-0.961588\pi$
$73$	−0.232710	−	3.25371i	−0.0272367	−	0.380818i	0.965491	−	0.260436i	$-0.0838664\pi$
$74$		0			0
$75$	−3.34380	+	6.05875i	−0.386109	+	0.699604i
$76$		0			0
$77$	−0.0789181	−	0.144528i	−0.00899355	−	0.0164705i
$78$		0			0
$79$	1.00791	−	7.01019i	0.113399	−	0.788708i	−0.851172	−	0.524886i	$-0.824108\pi$
$79$	1.00791	−	7.01019i	0.113399	−	0.788708i	0.964571	−	0.263822i	$-0.0849831\pi$
$80$		0			0
$81$	1.89876	−	4.15771i	0.210974	−	0.461968i
$82$		0			0
$83$	−7.55568	−	1.64364i	−0.829344	−	0.180413i	−0.222196	−	0.975002i	$-0.571323\pi$
$83$	−7.55568	−	1.64364i	−0.829344	−	0.180413i	−0.607147	+	0.794589i	$0.707686\pi$
$84$		0			0
$85$	13.4137	+	0.989704i	1.45492	+	0.107348i
$86$		0			0
$87$	2.74970	+	12.6402i	0.294798	+	1.35517i
$88$		0			0
$89$	−0.505952	+	0.148561i	−0.0536308	+	0.0157474i	−0.308438	−	0.951244i	$-0.599806\pi$
$89$	−0.505952	+	0.148561i	−0.0536308	+	0.0157474i	0.254807	+	0.966992i	$0.417988\pi$
$90$		0			0
$91$		−	0.622215i		−	0.0652259i
$92$		0			0
$93$	8.98678	−	8.98678i	0.931885	−	0.931885i
$94$		0			0
$95$	5.03156	−	5.78041i	0.516228	−	0.593057i
$96$		0			0
$97$	2.54782	−	0.554245i	0.258692	−	0.0562750i	−0.0813487	−	0.996686i	$-0.525923\pi$
$97$	2.54782	−	0.554245i	0.258692	−	0.0562750i	0.340041	+	0.940411i	$0.389559\pi$
$98$		0			0
$99$	0.0742905	+	0.516702i	0.00746648	+	0.0519305i
$100$		0			0
$101$	13.8433	−	8.89658i	1.37746	−	0.885243i	0.378283	−	0.925690i	$-0.376515\pi$
$101$	13.8433	−	8.89658i	1.37746	−	0.885243i	0.999182	+	0.0404471i	$0.0128782\pi$
$102$		0			0
$103$	−11.9101	+	4.44225i	−1.17354	+	0.437708i	−0.859218	−	0.511609i	$-0.829050\pi$
$103$	−11.9101	+	4.44225i	−1.17354	+	0.437708i	−0.314321	+	0.949317i	$0.601777\pi$
$104$		0			0
$105$	−0.963998	+	0.437625i	−0.0940765	+	0.0427078i
$106$		0			0
$107$	−11.1321	+	6.07858i	−1.07618	+	0.587638i	−0.916705	−	0.399564i	$-0.869162\pi$
$107$	−11.1321	+	6.07858i	−1.07618	+	0.587638i	−0.159474	+	0.987202i	$0.550980\pi$
$108$		0			0
$109$	4.75520	+	5.48779i	0.455465	+	0.525635i	0.936312	−	0.351170i	$-0.114216\pi$
$109$	4.75520	+	5.48779i	0.455465	+	0.525635i	−0.480847	+	0.876805i	$0.659671\pi$
$110$		0			0
$111$	−4.83611	−	4.19051i	−0.459023	−	0.397746i
$112$		0			0
$113$	−3.92314	+	10.5184i	−0.369058	+	0.989483i	0.611150	+	0.791515i	$0.290707\pi$
$113$	−3.92314	+	10.5184i	−0.369058	+	0.989483i	−0.980208	+	0.197969i	$0.936566\pi$
$114$		0			0
$115$	1.04437	+	10.6728i	0.0973882	+	0.995246i
$116$		0			0
$117$	−0.689305	+	1.84810i	−0.0637262	+	0.170857i
$118$		0			0
$119$	1.55508	+	1.34748i	0.142554	+	0.123523i
$120$		0			0
$121$	−7.05172	−	8.13812i	−0.641066	−	0.739829i
$122$		0			0
$123$	7.50771	−	4.09952i	0.676947	−	0.369641i
$124$		0			0
$125$	−11.1801	−	0.0754549i	−0.999977	−	0.00674889i
$126$		0			0
$127$	−10.1810	+	3.79731i	−0.903417	+	0.336957i	−0.757879	−	0.652396i	$-0.773764\pi$
$127$	−10.1810	+	3.79731i	−0.903417	+	0.336957i	−0.145538	+	0.989353i	$0.546491\pi$
$128$		0			0
$129$	6.50032	−	4.17750i	0.572321	−	0.367808i
$130$		0			0
$131$	−0.730718	−	5.08226i	−0.0638432	−	0.444039i	−0.996522	−	0.0833309i	$-0.973444\pi$
$131$	−0.730718	−	5.08226i	−0.0638432	−	0.444039i	0.932679	−	0.360708i	$-0.117465\pi$
$132$		0			0
$133$	1.14560	−	0.249211i	0.0993364	−	0.0216093i
$134$		0			0
$135$	12.6103	−	0.873399i	1.08532	−	0.0751702i
$136$		0			0
$137$	−5.18289	+	5.18289i	−0.442804	+	0.442804i	−0.892953	−	0.450149i	$-0.851371\pi$
$137$	−5.18289	+	5.18289i	−0.442804	+	0.442804i	0.450149	+	0.892953i	$0.351371\pi$
$138$		0			0
$139$			20.3063i			1.72236i	0.508302	+	0.861179i	$0.330273\pi$
$139$			20.3063i			1.72236i	−0.508302	+	0.861179i	$0.669727\pi$
$140$		0			0
$141$	12.5235	−	3.67723i	1.05467	−	0.309679i
$142$		0			0
$143$	0.186118	+	0.855569i	0.0155639	+	0.0715463i
$144$		0			0
$145$	−15.8252	+	13.6504i	−1.31421	+	1.13361i
$146$		0			0
$147$	9.30864	+	2.02497i	0.767764	+	0.167017i
$148$		0			0
$149$	−7.20474	+	15.7762i	−0.590235	+	1.29243i	0.345065	+	0.938579i	$0.387857\pi$
$149$	−7.20474	+	15.7762i	−0.590235	+	1.29243i	−0.935300	+	0.353856i	$0.884870\pi$
$150$		0			0
$151$	1.43401	−	9.97378i	0.116698	−	0.811655i	−0.844452	−	0.535631i	$-0.820074\pi$
$151$	1.43401	−	9.97378i	0.116698	−	0.811655i	0.961151	−	0.276024i	$-0.0890170\pi$
$152$		0			0
$153$	−3.12610	−	5.72502i	−0.252730	−	0.462841i
$154$		0			0
$155$	19.6883	+	5.82914i	1.58140	+	0.468208i
$156$		0			0
$157$	0.983567	+	13.7521i	0.0784972	+	1.09753i	0.872174	+	0.489195i	$0.162709\pi$
$157$	0.983567	+	13.7521i	0.0784972	+	1.09753i	−0.793677	+	0.608339i	$0.791836\pi$
$158$		0			0
$159$	7.75876	+	16.9893i	0.615310	+	1.34734i
$160$		0			0
$161$	−0.847420	+	1.40476i	−0.0667861	+	0.110710i
$162$		0			0
$163$	1.62553	+	0.606290i	0.127321	+	0.0474883i	0.412317	−	0.911040i	$-0.364720\pi$
$163$	1.62553	+	0.606290i	0.127321	+	0.0474883i	−0.284996	+	0.958529i	$0.591992\pi$
$164$		0			0
$165$	1.19463	−	0.890102i	0.0930018	−	0.0692944i
$166$		0			0
$167$	0.679565	−	9.50157i	0.0525863	−	0.735253i	−0.900940	−	0.433944i	$-0.857122\pi$
$167$	0.679565	−	9.50157i	0.0525863	−	0.735253i	0.953526	−	0.301310i	$-0.0974238\pi$
$168$		0			0
$169$	2.73043	−	9.29900i	0.210033	−	0.715308i
$170$		0			0
$171$	−3.67874	−	0.528923i	−0.281320	−	0.0404478i
$172$		0			0
$173$	−0.0290287	−	0.0778291i	−0.00220701	−	0.00591723i	0.935842	−	0.352421i	$-0.114641\pi$
$173$	−0.0290287	−	0.0778291i	−0.00220701	−	0.00591723i	−0.938049	+	0.346504i	$0.887369\pi$
$174$		0			0
$175$	−1.36463	−	1.03116i	−0.103156	−	0.0779485i
$176$		0			0
$177$	−4.36849	+	5.83562i	−0.328356	+	0.438632i
$178$		0			0
$179$	−4.07713	+	6.34413i	−0.304739	+	0.474183i	−0.959522	−	0.281634i	$-0.909124\pi$
$179$	−4.07713	+	6.34413i	−0.304739	+	0.474183i	0.654783	+	0.755817i	$0.272760\pi$
$180$		0			0
$181$	0.155884	+	0.530891i	0.0115867	+	0.0394608i	0.965083	−	0.261943i	$-0.0843631\pi$
$181$	0.155884	+	0.530891i	0.0115867	+	0.0394608i	−0.953497	+	0.301403i	$0.902545\pi$
$182$		0			0
$183$	−14.7056	−	14.7056i	−1.08707	−	1.08707i
$184$		0			0
$185$	2.22031	−	10.0972i	0.163240	−	0.742359i
$186$		0			0
$187$	−2.54135	−	1.38768i	−0.185842	−	0.101477i
$188$		0			0
$189$	1.62681	+	1.04549i	0.118333	+	0.0760482i
$190$		0			0
$191$	−6.89106	+	0.990785i	−0.498619	+	0.0716907i	−0.387036	−	0.922064i	$-0.626501\pi$
$191$	−6.89106	+	0.990785i	−0.498619	+	0.0716907i	−0.111583	+	0.993755i	$0.535592\pi$
$192$		0			0
$193$	−2.97621	+	13.6814i	−0.214232	+	0.984808i	0.736895	+	0.676007i	$0.236291\pi$
$193$	−2.97621	+	13.6814i	−0.214232	+	0.984808i	−0.951127	+	0.308801i	$0.900072\pi$
$194$		0			0
$195$	5.57367	−	0.788579i	0.399139	−	0.0564713i
$196$		0			0
$197$	7.05460	−	5.28101i	0.502619	−	0.376256i	−0.317673	−	0.948200i	$-0.602901\pi$
$197$	7.05460	−	5.28101i	0.502619	−	0.376256i	0.820293	+	0.571944i	$0.193811\pi$
$198$		0			0
$199$	16.6566	+	4.89080i	1.18075	+	0.346700i	0.812464	−	0.583012i	$-0.198126\pi$
$199$	16.6566	+	4.89080i	1.18075	+	0.346700i	0.368288	+	0.929712i	$0.379944\pi$
$200$		0			0
$201$	7.04818	−	6.10728i	0.497140	−	0.430775i
$202$		0			0
$203$	−3.18908	+	0.228087i	−0.223829	+	0.0160086i
$204$		0			0
$205$	11.6092	+	7.49777i	0.810825	+	0.523667i
$206$		0			0
$207$	4.07322	−	3.23360i	0.283109	−	0.224751i
$208$		0			0
$209$	−1.50070	+	0.685348i	−0.103806	+	0.0474065i
$210$		0			0
$211$	−4.14939	+	4.78865i	−0.285656	+	0.329664i	−0.880383	−	0.474263i	$-0.842715\pi$
$211$	−4.14939	+	4.78865i	−0.285656	+	0.329664i	0.594727	+	0.803927i	$0.297260\pi$
$212$		0			0
$213$	−18.9843	−	1.35778i	−1.30078	−	0.0930337i
$214$		0			0
$215$	10.9432	+	6.00743i	0.746319	+	0.409703i
$216$		0			0
$217$	1.88247	+	2.51468i	0.127790	+	0.170708i
$218$		0			0
$219$	4.10679	+	1.87551i	0.277511	+	0.126735i
$220$		0			0
$221$	−5.91510	−	9.20408i	−0.397893	−	0.619134i
$222$		0			0
$223$	11.2501	+	8.42173i	0.753364	+	0.563961i	0.905474	−	0.424403i	$-0.139516\pi$
$223$	11.2501	+	8.42173i	0.753364	+	0.563961i	−0.152110	+	0.988364i	$0.548607\pi$
$224$		0			0
$225$	2.91086	+	4.57451i	0.194057	+	0.304967i
$226$		0			0
$227$	−3.94905	+	7.23215i	−0.262108	+	0.480015i	−0.975280	−	0.220975i	$-0.929076\pi$
$227$	−3.94905	+	7.23215i	−0.262108	+	0.480015i	0.713172	+	0.700989i	$0.247258\pi$
$228$		0			0
$229$	−12.9303			−0.854461			−0.427230	−	0.904143i	$-0.640511\pi$
$229$	−12.9303			−0.854461			−0.427230	+	0.904143i	$0.640511\pi$
$230$		0			0
$231$	0.227911			0.0149954
$232$		0			0
$233$	0.573767	−	1.05078i	0.0375887	−	0.0688386i	−0.858209	−	0.513300i	$-0.828423\pi$
$233$	0.573767	−	1.05078i	0.0375887	−	0.0688386i	0.895798	+	0.444461i	$0.146605\pi$
$234$		0			0
$235$	14.8773	+	14.9444i	0.970489	+	0.974865i
$236$		0			0
$237$	7.84706	+	5.87423i	0.509721	+	0.381572i
$238$		0			0
$239$	−6.67177	−	10.3815i	−0.431561	−	0.671522i	0.555564	−	0.831474i	$-0.312503\pi$
$239$	−6.67177	−	10.3815i	−0.431561	−	0.671522i	−0.987125	+	0.159952i	$0.948866\pi$
$240$		0			0
$241$	11.5578	+	5.27826i	0.744502	+	0.340003i	0.751288	−	0.659974i	$-0.229433\pi$
$241$	11.5578	+	5.27826i	0.744502	+	0.340003i	−0.00678624	+	0.999977i	$0.502160\pi$
$242$		0			0
$243$	−6.37207	−	8.51209i	−0.408769	−	0.546051i
$244$		0			0
$245$	4.30286	+	14.7771i	0.274900	+	0.944074i
$246$		0			0
$247$	−6.21794	−	0.444716i	−0.395638	−	0.0282966i
$248$		0			0
$249$	7.00830	−	8.08801i	0.444133	−	0.512557i
$250$		0			0
$251$	22.1458	−	10.1136i	1.39783	−	0.638366i	0.433035	−	0.901377i	$-0.357443\pi$
$251$	22.1458	−	10.1136i	1.39783	−	0.638366i	0.964793	+	0.263011i	$0.0847155\pi$
$252$		0			0
$253$	0.745042	−	2.18507i	0.0468404	−	0.137374i
$254$		0			0
$255$	−10.0996	+	15.6378i	−0.632461	+	0.979277i
$256$		0			0
$257$	0.735075	−	0.0525736i	0.0458527	−	0.00327945i	−0.0483940	−	0.998828i	$-0.515410\pi$
$257$	0.735075	−	0.0525736i	0.0458527	−	0.00327945i	0.0942467	+	0.995549i	$0.469956\pi$
$258$		0			0
$259$	1.19530	−	1.03573i	0.0742723	−	0.0643573i
$260$		0			0
$261$	9.72484	+	2.85547i	0.601953	+	0.176749i
$262$		0			0
$263$	14.6624	−	10.9762i	0.904125	−	0.676820i	−0.0425205	−	0.999096i	$-0.513539\pi$
$263$	14.6624	−	10.9762i	0.904125	−	0.676820i	0.946646	+	0.322276i	$0.104448\pi$
$264$		0			0
$265$	−18.1374	+	24.1155i	−1.11417	+	1.48140i
$266$		0			0
$267$	0.155135	−	0.713144i	0.00949410	−	0.0436437i
$268$		0			0
$269$	−16.0708	+	2.31063i	−0.979855	+	0.140882i	−0.613586	−	0.789628i	$-0.710274\pi$
$269$	−16.0708	+	2.31063i	−0.979855	+	0.140882i	−0.366268	+	0.930509i	$0.619365\pi$
$270$		0			0
$271$	2.55320	+	1.64084i	0.155096	+	0.0996740i	0.615887	−	0.787835i	$-0.288798\pi$
$271$	2.55320	+	1.64084i	0.155096	+	0.0996740i	−0.460791	+	0.887509i	$0.652434\pi$
$272$		0			0
$273$	0.755834	+	0.412717i	0.0457451	+	0.0249787i
$274$		0			0
$275$	2.18486	+	1.00970i	0.131752	+	0.0608870i
$276$		0			0
$277$	11.0723	+	11.0723i	0.665268	+	0.665268i	0.956617	−	0.291349i	$-0.0941041\pi$
$277$	11.0723	+	11.0723i	0.665268	+	0.665268i	−0.291349	+	0.956617i	$0.594104\pi$
$278$		0			0
$279$	−2.80546	−	9.55453i	−0.167959	−	0.572015i
$280$		0			0
$281$	2.41198	−	3.75311i	0.143887	−	0.223892i	−0.761829	−	0.647779i	$-0.775698\pi$
$281$	2.41198	−	3.75311i	0.143887	−	0.223892i	0.905715	+	0.423887i	$0.139335\pi$
$282$		0			0
$283$	1.28430	−	1.71562i	0.0763435	−	0.101983i	−0.760744	−	0.649052i	$-0.775166\pi$
$283$	1.28430	−	1.71562i	0.0763435	−	0.101983i	0.837087	+	0.547069i	$0.184257\pi$
$284$		0			0
$285$	3.68429	+	9.94623i	0.218238	+	0.589164i
$286$		0			0
$287$	0.738847	+	1.98093i	0.0436128	+	0.116930i
$288$		0			0
$289$	18.9863	+	2.72981i	1.11684	+	0.160577i
$290$		0			0
$291$	−1.01671	+	3.46259i	−0.0596005	+	0.202981i
$292$		0			0
$293$	0.972299	−	13.5945i	0.0568023	−	0.794200i	−0.886597	−	0.462542i	$-0.846937\pi$
$293$	0.972299	−	13.5945i	0.0568023	−	0.794200i	0.943400	−	0.331658i	$-0.107608\pi$
$294$		0			0
$295$	−11.6534	−	1.70228i	−0.678489	−	0.0991104i
$296$		0			0
$297$	−2.54966	−	0.950973i	−0.147946	−	0.0551811i
$298$		0			0
$299$	6.42770	−	5.89731i	0.371724	−	0.341050i
$300$		0			0
$301$	0.793360	+	1.73722i	0.0457285	+	0.100131i
$302$		0			0
$303$	1.62477	+	22.7173i	0.0933407	+	1.30507i
$304$		0			0
$305$	9.53854	−	32.2170i	0.546175	−	1.84474i
$306$		0			0
$307$	−15.6557	−	28.6713i	−0.893519	−	1.63636i	−0.764412	−	0.644728i	$-0.776971\pi$
$307$	−15.6557	−	28.6713i	−0.893519	−	1.63636i	−0.129108	−	0.991631i	$-0.541211\pi$
$308$		0			0
$309$	2.50380	−	17.4143i	0.142436	−	0.990667i
$310$		0			0
$311$	14.3216	−	31.3600i	0.812105	−	1.77826i	0.214020	−	0.976829i	$-0.431344\pi$
$311$	14.3216	−	31.3600i	0.812105	−	1.77826i	0.598085	−	0.801433i	$-0.295929\pi$
$312$		0			0
$313$	1.84619	+	0.401614i	0.104353	+	0.0227005i	0.264438	−	0.964403i	$-0.414813\pi$
$313$	1.84619	+	0.401614i	0.104353	+	0.0227005i	−0.160086	+	0.987103i	$0.551177\pi$
$314$		0			0
$315$	−0.0610367	+	0.827246i	−0.00343903	+	0.0466100i
$316$		0			0
$317$	6.45016	+	29.6509i	0.362277	+	1.66536i	0.692470	+	0.721446i	$0.256522\pi$
$317$	6.45016	+	29.6509i	0.362277	+	1.66536i	−0.330193	+	0.943913i	$0.607114\pi$
$318$		0			0
$319$	4.31687	−	1.26755i	0.241699	−	0.0709691i
$320$		0			0
$321$		−	17.5546i		−	0.979802i
$322$		0			0
$323$	14.5771	−	14.5771i	0.811094	−	0.811094i
$324$		0			0
$325$	5.41734	+	7.30500i	0.300500	+	0.405208i
$326$		0			0
$327$	−9.82040	+	2.13630i	−0.543069	+	0.118138i
$328$		0			0
$329$	0.459107	+	3.19316i	0.0253114	+	0.176045i
$330$		0			0
$331$	−11.0838	+	7.12312i	−0.609220	+	0.391522i	−0.808565	−	0.588407i	$-0.799755\pi$
$331$	−11.0838	+	7.12312i	−0.609220	+	0.391522i	0.199344	+	0.979930i	$0.436119\pi$
$332$		0			0
$333$	−4.69768	+	1.75214i	−0.257431	+	0.0960168i
$334$		0			0
$335$	14.1054	+	5.29721i	0.770659	+	0.289418i
$336$		0			0
$337$	−25.4751	+	13.9104i	−1.38772	+	0.757750i	−0.987343	−	0.158602i	$-0.949301\pi$
$337$	−25.4751	+	13.9104i	−1.38772	+	0.757750i	−0.400373	+	0.916352i	$0.631119\pi$
$338$		0			0
$339$	−10.1749	−	11.7425i	−0.552625	−	0.637763i
$340$		0			0
$341$	−3.34066	−	2.89470i	−0.180907	−	0.156757i
$342$		0			0
$343$	−1.65965	+	4.44969i	−0.0896125	+	0.240260i
$344$		0			0
$345$	−13.6575	−	5.81066i	−0.735296	−	0.312835i
$346$		0			0
$347$	−7.69921	+	20.6424i	−0.413315	+	1.10814i	0.548909	+	0.835882i	$0.315043\pi$
$347$	−7.69921	+	20.6424i	−0.413315	+	1.10814i	−0.962224	+	0.272258i	$0.912229\pi$
$348$		0			0
$349$	−9.46026	−	8.19736i	−0.506396	−	0.438795i	0.363817	−	0.931470i	$-0.381473\pi$
$349$	−9.46026	−	8.19736i	−0.506396	−	0.438795i	−0.870213	+	0.492676i	$0.836019\pi$
$350$		0			0
$351$	−6.73348	−	7.77085i	−0.359407	−	0.414778i
$352$		0			0
$353$	−26.8895	+	14.6828i	−1.43118	+	0.781485i	−0.993080	−	0.117439i	$-0.962532\pi$
$353$	−26.8895	+	14.6828i	−1.43118	+	0.781485i	−0.438104	+	0.898924i	$0.644350\pi$
$354$		0			0
$355$	−12.7108	−	27.9993i	−0.674620	−	1.48605i
$356$		0			0
$357$	−2.66833	+	0.995236i	−0.141223	+	0.0526735i
$358$		0			0
$359$	−27.5733	+	17.7203i	−1.45526	+	0.935240i	−0.456293	+	0.889830i	$0.650823\pi$
$359$	−27.5733	+	17.7203i	−1.45526	+	0.935240i	−0.998968	+	0.0454098i	$0.985541\pi$
$360$		0			0
$361$	1.03236	+	7.18021i	0.0543347	+	0.377906i
$362$		0			0
$363$	14.5632	−	3.16802i	0.764368	−	0.166278i
$364$		0			0
$365$	0.503987	+	7.27667i	0.0263799	+	0.380878i
$366$		0			0
$367$	16.9996	−	16.9996i	0.887373	−	0.887373i	−0.106897	−	0.994270i	$-0.534091\pi$
$367$	16.9996	−	16.9996i	0.887373	−	0.887373i	0.994270	+	0.106897i	$0.0340914\pi$
$368$		0			0
$369$		−	6.70224i		−	0.348905i
$370$		0			0
$371$	−4.42927	+	1.30055i	−0.229956	+	0.0675213i
$372$		0			0
$373$	−0.814532	−	3.74434i	−0.0421749	−	0.193875i	0.951239	−	0.308454i	$-0.0998116\pi$
$373$	−0.814532	−	3.74434i	−0.0421749	−	0.193875i	−0.993414	+	0.114579i	$0.963448\pi$
$374$		0			0
$375$	7.50743	−	13.5309i	0.387682	−	0.698734i
$376$		0			0
$377$	16.6116	+	3.61364i	0.855543	+	0.186112i
$378$		0			0
$379$	−3.26503	+	7.14942i	−0.167713	+	0.367241i	−0.974763	−	0.223243i	$-0.928336\pi$
$379$	−3.26503	+	7.14942i	−0.167713	+	0.367241i	0.807050	+	0.590484i	$0.201063\pi$
$380$		0			0
$381$	2.14030	−	14.8861i	0.109651	−	0.762637i
$382$		0			0
$383$	11.0063	+	20.1566i	0.562398	+	1.02995i	0.991916	+	0.126896i	$0.0405015\pi$
$383$	11.0063	+	20.1566i	0.562398	+	1.02995i	−0.429519	+	0.903058i	$0.641317\pi$
$384$		0			0
$385$	0.175739	+	0.323570i	0.00895648	+	0.0164907i
$386$		0			0
$387$	−0.431901	−	6.03877i	−0.0219548	−	0.306968i
$388$		0			0
$389$	−9.91792	−	21.7172i	−0.502859	−	1.10111i	−0.975530	−	0.219868i	$-0.929437\pi$
$389$	−9.91792	−	21.7172i	−0.502859	−	1.10111i	0.472671	−	0.881239i	$-0.343290\pi$
$390$		0			0
$391$	0.818945	+	28.8358i	0.0414159	+	1.45829i
$392$		0			0
$393$	6.65834	+	2.48343i	0.335869	+	0.125273i
$394$		0			0
$395$	−2.28902	+	15.6702i	−0.115173	+	0.788451i
$396$		0			0
$397$	2.13857	−	29.9011i	0.107332	−	1.50069i	−0.603519	−	0.797348i	$-0.706235\pi$
$397$	2.13857	−	29.9011i	0.107332	−	1.50069i	0.710851	−	0.703343i	$-0.248310\pi$
$398$		0			0
$399$	−0.457153	+	1.55692i	−0.0228863	+	0.0779435i
$400$		0			0
$401$	−18.2622	−	2.62571i	−0.911971	−	0.131122i	−0.329671	−	0.944096i	$-0.606938\pi$
$401$	−18.2622	−	2.62571i	−0.911971	−	0.131122i	−0.582300	+	0.812974i	$0.697847\pi$
$402$		0			0
$403$	−5.83690	−	15.6493i	−0.290757	−	0.779549i
$404$		0			0
$405$	−4.26667	+	9.28735i	−0.212012	+	0.461492i
$406$		0			0
$407$	−1.33377	+	1.78171i	−0.0661126	+	0.0883161i
$408$		0			0
$409$	−3.32710	+	5.17708i	−0.164515	+	0.255990i	−0.913717	−	0.406352i	$-0.866801\pi$
$409$	−3.32710	+	5.17708i	−0.164515	+	0.255990i	0.749202	+	0.662341i	$0.230437\pi$
$410$		0			0
$411$	−2.85807	−	9.73371i	−0.140978	−	0.480128i
$412$		0			0
$413$	−1.27400	−	1.27400i	−0.0626894	−	0.0626894i
$414$		0			0
$415$	16.8867	+	3.71328i	0.828936	+	0.182278i
$416$		0			0
$417$	−24.6670	−	13.4692i	−1.20795	−	0.659590i
$418$		0			0
$419$	16.3546	+	10.5104i	0.798973	+	0.513469i	0.875281	−	0.483615i	$-0.160677\pi$
$419$	16.3546	+	10.5104i	0.798973	+	0.513469i	−0.0763072	+	0.997084i	$0.524313\pi$
$420$		0			0
$421$	22.8972	−	3.29212i	1.11594	−	0.160448i	0.440423	−	0.897790i	$-0.354829\pi$
$421$	22.8972	−	3.29212i	1.11594	−	0.160448i	0.675520	+	0.737342i	$0.263919\pi$
$422$		0			0
$423$	2.17382	−	9.99291i	0.105695	−	0.485872i
$424$		0			0
$425$	−29.9889	−	2.28052i	−1.45468	−	0.110621i
$426$		0			0
$427$	4.11491	−	3.08038i	0.199135	−	0.149070i
$428$		0			0
$429$	−1.16275	−	0.341415i	−0.0561382	−	0.0164837i
$430$		0			0
$431$	−5.28791	+	4.58200i	−0.254710	+	0.220707i	−0.772851	−	0.634588i	$-0.781170\pi$
$431$	−5.28791	+	4.58200i	−0.254710	+	0.220707i	0.518141	+	0.855295i	$0.326624\pi$
$432$		0			0
$433$	−4.97304	+	0.355679i	−0.238989	+	0.0170928i	−0.190320	−	0.981722i	$-0.560953\pi$
$433$	−4.97304	+	0.355679i	−0.238989	+	0.0170928i	−0.0486692	+	0.998815i	$0.515498\pi$
$434$		0			0
$435$	−6.08491	−	28.2780i	−0.291749	−	1.35583i
$436$		0			0
$437$	13.4324	+	9.47249i	0.642558	+	0.453130i
$438$		0			0
$439$	2.42656	−	1.10817i	0.115813	−	0.0528901i	−0.356666	−	0.934232i	$-0.616087\pi$
$439$	2.42656	−	1.10817i	0.115813	−	0.0528901i	0.472479	+	0.881342i	$0.343359\pi$
$440$		0			0
$441$	4.88792	−	5.64096i	0.232758	−	0.268617i
$442$		0			0
$443$	−15.3419	−	1.09727i	−0.728916	−	0.0521331i	−0.298052	−	0.954550i	$-0.596337\pi$
$443$	−15.3419	−	1.09727i	−0.728916	−	0.0521331i	−0.430864	+	0.902417i	$0.641791\pi$
$444$		0			0
$445$	1.13209	−	0.329646i	0.0536661	−	0.0156267i
$446$		0			0
$447$	−14.3851	−	19.2163i	−0.680394	−	0.908900i
$448$		0			0
$449$	−11.7182	−	5.35152i	−0.553016	−	0.252554i	0.119249	−	0.992864i	$-0.461951\pi$
$449$	−11.7182	−	5.35152i	−0.553016	−	0.252554i	−0.672265	+	0.740311i	$0.734678\pi$
$450$		0			0
$451$	−1.60848	−	2.50284i	−0.0757403	−	0.117854i
$452$		0			0
$453$	11.1644	+	8.35759i	0.524551	+	0.392674i
$454$		0			0
$455$	−0.00312997	+	1.39131i	−0.000146735	+	0.0652257i
$456$		0			0
$457$	3.57426	−	6.54577i	0.167197	−	0.306198i	−0.780624	−	0.625000i	$-0.785099\pi$
$457$	3.57426	−	6.54577i	0.167197	−	0.306198i	0.947821	+	0.318802i	$0.103281\pi$
$458$		0			0
$459$	34.0035			1.58715
$460$		0			0
$461$	1.78272			0.0830295			0.0415147	−	0.999138i	$-0.486782\pi$
$461$	1.78272			0.0830295			0.0415147	+	0.999138i	$0.486782\pi$
$462$		0			0
$463$	8.42465	−	15.4286i	0.391527	−	0.717028i	−0.605354	−	0.795957i	$-0.706968\pi$
$463$	8.42465	−	15.4286i	0.391527	−	0.717028i	0.996880	+	0.0789291i	$0.0251501\pi$
$464$		0			0
$465$	−20.1402	+	20.0498i	−0.933980	+	0.929787i
$466$		0			0
$467$	−31.3812	−	23.4916i	−1.45215	−	1.08706i	−0.978476	−	0.206362i	$-0.933838\pi$
$467$	−31.3812	−	23.4916i	−1.45215	−	1.08706i	−0.473671	−	0.880702i	$-0.657071\pi$
$468$		0			0
$469$	1.24620	+	1.93913i	0.0575443	+	0.0895406i
$470$		0			0
$471$	−17.3577	−	7.92699i	−0.799800	−	0.365256i
$472$		0			0
$473$	−1.61054	−	2.15143i	−0.0740526	−	0.0989227i
$474$		0			0
$475$	−11.2800	+	12.9000i	−0.517560	+	0.591895i
$476$		0			0
$477$	14.5966	+	1.04397i	0.668331	+	0.0478000i
$478$		0			0
$479$	−2.50775	+	2.89410i	−0.114582	+	0.132235i	−0.810143	−	0.586232i	$-0.800611\pi$
$479$	−2.50775	+	2.89410i	−0.114582	+	0.132235i	0.695561	+	0.718467i	$0.255156\pi$
$480$		0			0
$481$	−7.64970	+	3.49350i	−0.348796	+	0.159290i
$482$		0			0
$483$	−1.14433	−	1.96118i	−0.0520688	−	0.0892367i
$484$		0			0
$485$	−5.69988	+	1.22651i	−0.258818	+	0.0556929i
$486$		0			0
$487$	−38.1241	+	2.72669i	−1.72757	+	0.123558i	−0.899458	−	0.437006i	$-0.856039\pi$
$487$	−38.1241	+	2.72669i	−1.72757	+	0.123558i	−0.828111	+	0.560564i	$0.810584\pi$
$488$		0			0
$489$	−1.81470	+	1.57245i	−0.0820638	+	0.0711087i
$490$		0			0
$491$	−14.5271	−	4.26553i	−0.655598	−	0.192501i	−0.0630177	−	0.998012i	$-0.520072\pi$
$491$	−14.5271	−	4.26553i	−0.655598	−	0.192501i	−0.592580	+	0.805512i	$0.701891\pi$
$492$		0			0
$493$	−45.0059	+	33.6910i	−2.02696	+	1.51737i
$494$		0			0
$495$	−0.163519	−	1.15575i	−0.00734964	−	0.0519472i
$496$		0			0
$497$	0.999942	−	4.59666i	0.0448535	−	0.206188i
$498$		0			0
$499$	21.1033	−	3.03420i	0.944714	−	0.135829i	0.347293	−	0.937757i	$-0.387101\pi$
$499$	21.1033	−	3.03420i	0.944714	−	0.135829i	0.597422	+	0.801927i	$0.296192\pi$
$500$		0			0
$501$	11.0912	+	7.12790i	0.495520	+	0.318451i
$502$		0			0
$503$	−1.33739	−	0.730270i	−0.0596312	−	0.0325611i	0.449157	−	0.893453i	$-0.351724\pi$
$503$	−1.33739	−	0.730270i	−0.0596312	−	0.0325611i	−0.508788	+	0.860892i	$0.669906\pi$
$504$		0			0
$505$	−30.9993	+	19.8237i	−1.37945	+	0.882142i
$506$		0			0
$507$	9.48483	+	9.48483i	0.421236	+	0.421236i
$508$		0			0
$509$	−3.13431	−	10.6745i	−0.138926	−	0.473138i	0.860409	−	0.509604i	$-0.170208\pi$
$509$	−3.13431	−	10.6745i	−0.138926	−	0.473138i	−0.999335	+	0.0364663i	$0.988390\pi$
$510$		0			0
$511$	−0.603290	+	0.938738i	−0.0266880	+	0.0415273i
$512$		0			0
$513$	11.6105	−	15.5099i	0.512618	−	0.684778i
$514$		0			0
$515$	26.6541	−	9.87323i	1.17452	−	0.435067i
$516$		0			0
$517$	−1.58643	−	4.25339i	−0.0697712	−	0.187064i
$518$		0			0
$519$	0.113797	+	0.0163616i	0.00499515	+	0.000718194i
$520$		0			0
$521$	1.21793	−	4.14789i	0.0533586	−	0.181723i	−0.928502	−	0.371328i	$-0.878903\pi$
$521$	1.21793	−	4.14789i	0.0533586	−	0.181723i	0.981860	+	0.189605i	$0.0607208\pi$
$522$		0			0
$523$	−1.00394	+	14.0370i	−0.0438994	+	0.613793i	0.927116	+	0.374775i	$0.122280\pi$
$523$	−1.00394	+	14.0370i	−0.0438994	+	0.613793i	−0.971015	+	0.239018i	$0.923174\pi$
$524$		0			0
$525$	2.15776	−	0.973707i	0.0941724	−	0.0424960i
$526$		0			0
$527$	51.7522	+	19.3026i	2.25436	+	0.840833i
$528$		0			0
$529$	−22.5434	+	4.56004i	−0.980149	+	0.198263i
$530$		0			0
$531$	2.37265	+	5.19538i	0.102964	+	0.225460i
$532$		0			0
$533$	−0.801974	−	11.2131i	−0.0347373	−	0.485691i
$534$		0			0
$535$	24.9226	−	13.5361i	1.07750	−	0.585216i
$536$		0			0
$537$	−5.00215	−	9.16075i	−0.215859	−	0.395315i
$538$		0			0
$539$	0.471533	−	3.27958i	0.0203103	−	0.141262i
$540$		0			0
$541$	−15.8761	+	34.7639i	−0.682568	+	1.49462i	0.177330	+	0.984151i	$0.443254\pi$
$541$	−15.8761	+	34.7639i	−0.682568	+	1.49462i	−0.859899	+	0.510465i	$0.829473\pi$
$542$		0			0
$543$	−0.748296	−	0.162782i	−0.0321125	−	0.00698564i
$544$		0			0
$545$	−10.6053	−	12.2950i	−0.454282	−	0.526658i
$546$		0			0
$547$	2.60970	+	11.9966i	0.111583	+	0.512937i	0.998680	+	0.0513554i	$0.0163541\pi$
$547$	2.60970	+	11.9966i	0.111583	+	0.512937i	−0.887098	+	0.461581i	$0.847282\pi$
$548$		0			0
$549$	−15.6346	+	4.59073i	−0.667268	+	0.195928i
$550$		0			0
$551$			32.0322i			1.36462i
$552$		0			0
$553$	−1.71312	+	1.71312i	−0.0728494	+	0.0728494i
$554$		0			0
$555$	10.7928	+	9.39458i	0.458127	+	0.398778i
$556$		0			0
$557$	−15.8125	+	3.43979i	−0.669995	+	0.145749i	−0.534681	−	0.845054i	$-0.679568\pi$
$557$	−15.8125	+	3.43979i	−0.669995	+	0.145749i	−0.135315	+	0.990803i	$0.543204\pi$
$558$		0			0
$559$	−1.44517	−	10.0514i	−0.0611241	−	0.425127i
$560$		0			0
$561$	3.37136	−	2.16664i	0.142339	−	0.0914757i
$562$		0			0
$563$	42.4186	−	15.8213i	1.78773	−	0.666789i	0.789113	−	0.614248i	$-0.210541\pi$
$563$	42.4186	−	15.8213i	1.78773	−	0.666789i	0.998619	−	0.0525413i	$-0.0167321\pi$
$564$		0			0
$565$	8.82530	−	23.5000i	0.371283	−	0.988651i
$566$		0			0
$567$	−1.37232	+	0.749342i	−0.0576320	+	0.0314694i
$568$		0			0
$569$	−14.6434	−	16.8994i	−0.613883	−	0.708459i	0.360650	−	0.932701i	$-0.382555\pi$
$569$	−14.6434	−	16.8994i	−0.613883	−	0.708459i	−0.974533	+	0.224242i	$0.928009\pi$
$570$		0			0
$571$	−3.23046	−	2.79921i	−0.135190	−	0.117143i	0.584641	−	0.811292i	$-0.301235\pi$
$571$	−3.23046	−	2.79921i	−0.135190	−	0.117143i	−0.719831	+	0.694149i	$0.755781\pi$
$572$		0			0
$573$	3.36730	−	9.02808i	0.140671	−	0.377153i
$574$		0			0
$575$	−2.28159	−	23.8704i	−0.0951490	−	0.995463i
$576$		0			0
$577$	−2.60111	+	6.97385i	−0.108286	+	0.290325i	−0.979779	−	0.200082i	$-0.935879\pi$
$577$	−2.60111	+	6.97385i	−0.108286	+	0.290325i	0.871493	+	0.490407i	$0.163152\pi$
$578$		0			0
$579$	−14.6453	−	12.6902i	−0.608638	−	0.527388i
$580$		0			0
$581$	1.73218	+	1.99904i	0.0718629	+	0.0829343i
$582$		0			0
$583$	5.70139	−	3.11320i	0.236128	−	0.128935i
$584$		0			0
$585$	1.55062	−	4.12899i	0.0641105	−	0.170713i
$586$		0			0
$587$	−7.31666	+	2.72897i	−0.301991	+	0.112637i	−0.495892	−	0.868384i	$-0.665159\pi$
$587$	−7.31666	+	2.72897i	−0.301991	+	0.112637i	0.193901	+	0.981021i	$0.437886\pi$
$588$		0			0
$589$	26.4753	−	17.0146i	1.09089	−	0.701075i
$590$		0			0
$591$	1.73576	+	12.0725i	0.0713995	+	0.496594i
$592$		0			0
$593$	3.36052	−	0.731036i	0.138000	−	0.0300201i	−0.143035	−	0.989718i	$-0.545686\pi$
$593$	3.36052	−	0.731036i	0.138000	−	0.0300201i	0.281035	+	0.959698i	$0.409322\pi$
$594$		0			0
$595$	−3.47047	−	3.02087i	−0.142275	−	0.123844i
$596$		0			0
$597$	−16.9894	+	16.9894i	−0.695330	+	0.695330i
$598$		0			0
$599$			9.17302i			0.374799i	0.982284	+	0.187400i	$0.0600060\pi$
$599$			9.17302i			0.374799i	−0.982284	+	0.187400i	$0.939994\pi$
$600$		0			0
$601$	−1.24243	+	0.364811i	−0.0506799	+	0.0148810i	−0.306974	−	0.951718i	$-0.599317\pi$
$601$	−1.24243	+	0.364811i	−0.0506799	+	0.0148810i	0.256294	+	0.966599i	$0.417498\pi$
$602$		0			0
$603$	−1.55324	−	7.14015i	−0.0632530	−	0.290769i
$604$		0			0
$605$	15.7272	+	18.2328i	0.639400	+	0.741269i
$606$		0			0
$607$	20.1460	+	4.38250i	0.817702	+	0.177880i	0.601915	−	0.798560i	$-0.294405\pi$
$607$	20.1460	+	4.38250i	0.817702	+	0.177880i	0.215787	+	0.976440i	$0.430768\pi$
$608$		0			0
$609$	1.83825	−	4.02521i	0.0744897	−	0.163110i
$610$		0			0
$611$	2.44115	−	16.9786i	0.0987583	−	0.686879i
$612$		0			0
$613$	−8.59214	−	15.7353i	−0.347033	−	0.635544i	0.644616	−	0.764506i	$-0.277017\pi$
$613$	−8.59214	−	15.7353i	−0.347033	−	0.635544i	−0.991649	+	0.128962i	$0.958835\pi$
$614$		0			0
$615$	−16.8083	+	9.12901i	−0.677777	+	0.368117i
$616$		0			0
$617$	−1.91170	−	26.7290i	−0.0769620	−	1.07607i	−0.878379	−	0.477964i	$-0.841375\pi$
$617$	−1.91170	−	26.7290i	−0.0769620	−	1.07607i	0.801417	−	0.598106i	$-0.204080\pi$
$618$		0			0
$619$	7.48869	+	16.3979i	0.300996	+	0.659089i	0.998337	−	0.0576506i	$-0.0183609\pi$
$619$	7.48869	+	16.3979i	0.300996	+	0.659089i	−0.697341	+	0.716740i	$0.745634\pi$
$620$		0			0
$621$	4.61855	+	26.7146i	0.185336	+	1.07202i
$622$		0			0
$623$	0.169011	+	0.0630377i	0.00677127	+	0.00252555i
$624$		0			0
$625$	24.9990	+	0.224962i	0.999960	+	0.00899846i
$626$		0			0
$627$	0.162895	−	2.27757i	0.00650539	−	0.0909573i
$628$		0			0
$629$	7.83518	−	26.6842i	0.312409	−	1.06397i
$630$		0			0
$631$	−19.3844	−	2.78705i	−0.771680	−	0.110951i	−0.254783	−	0.966998i	$-0.582004\pi$
$631$	−19.3844	−	2.78705i	−0.771680	−	0.110951i	−0.516897	+	0.856048i	$0.672913\pi$
$632$		0			0
$633$	−3.06470	−	8.21678i	−0.121811	−	0.326588i
$634$		0			0
$635$	22.7844	−	8.43982i	0.904173	−	0.334924i
$636$		0			0
$637$	7.50265	−	10.0224i	0.297266	−	0.397101i
$638$		0			0
$639$	−8.06230	+	12.5452i	−0.318940	+	0.496280i
$640$		0			0
$641$	−6.91160	−	23.5387i	−0.272992	−	0.929724i	−0.975859	−	0.218403i	$-0.929915\pi$
$641$	−6.91160	−	23.5387i	−0.272992	−	0.929724i	0.702867	−	0.711321i	$-0.251903\pi$
$642$		0			0
$643$	22.6055	+	22.6055i	0.891474	+	0.891474i	0.994662	−	0.103188i	$-0.0329043\pi$
$643$	22.6055	+	22.6055i	0.891474	+	0.891474i	−0.103188	+	0.994662i	$0.532904\pi$
$644$		0			0
$645$	−14.5561	+	9.30845i	−0.573147	+	0.366520i
$646$		0			0
$647$	31.5544	+	17.2300i	1.24053	+	0.677381i	0.959335	−	0.282270i	$-0.0910873\pi$
$647$	31.5544	+	17.2300i	1.24053	+	0.677381i	0.281195	+	0.959651i	$0.409269\pi$
$648$		0			0
$649$	2.13288	+	1.37072i	0.0837227	+	0.0538053i
$650$		0			0
$651$	−4.30335	+	0.618728i	−0.168661	+	0.0242499i
$652$		0			0
$653$	1.38923	−	6.38617i	0.0543646	−	0.249910i	−0.941942	−	0.335775i	$-0.891002\pi$
$653$	1.38923	−	6.38617i	0.0543646	−	0.249910i	0.996307	+	0.0858650i	$0.0273654\pi$
$654$		0			0
$655$	1.60837	+	11.3679i	0.0628441	+	0.444181i
$656$		0			0
$657$	2.83184	−	2.11989i	0.110481	−	0.0827048i
$658$		0			0
$659$	−42.0499	−	12.3470i	−1.63803	−	0.480970i	−0.672250	−	0.740324i	$-0.734672\pi$
$659$	−42.0499	−	12.3470i	−1.63803	−	0.480970i	−0.965782	+	0.259355i	$0.916490\pi$
$660$		0			0
$661$	3.70631	−	3.21154i	0.144159	−	0.124914i	−0.579796	−	0.814762i	$-0.696868\pi$
$661$	3.70631	−	3.21154i	0.144159	−	0.124914i	0.723955	+	0.689847i	$0.242322\pi$
$662$		0			0
$663$	15.1041	−	1.08027i	0.586596	−	0.0419541i
$664$		0			0
$665$	−2.56289	+	0.551488i	−0.0993848	+	0.0213858i
$666$		0			0
$667$	−32.5821	−	30.7825i	−1.26158	−	1.19190i
$668$		0			0
$669$	−17.6925	+	8.07989i	−0.684031	+	0.312387i
$670$		0			0
$671$	−4.73675	+	5.46650i	−0.182860	+	0.211032i
$672$		0			0
$673$	24.3510	+	1.74162i	0.938661	+	0.0671344i	0.532279	−	0.846569i	$-0.321336\pi$
$673$	24.3510	+	1.74162i	0.938661	+	0.0671344i	0.406382	+	0.913703i	$0.366790\pi$
$674$		0			0
$675$	−28.2019	+	1.88954i	−1.08549	+	0.0727284i
$676$		0			0
$677$	−12.2056	−	16.3048i	−0.469101	−	0.626646i	0.502128	−	0.864793i	$-0.332551\pi$
$677$	−12.2056	−	16.3048i	−0.469101	−	0.626646i	−0.971229	+	0.238148i	$0.923460\pi$
$678$		0			0
$679$	−0.811345	−	0.370529i	−0.0311366	−	0.0142196i
$680$		0			0
$681$	−6.16581	−	9.59419i	−0.236275	−	0.367650i
$682$		0			0
$683$	−4.23779	−	3.17237i	−0.162155	−	0.121387i	0.515119	−	0.857119i	$-0.327748\pi$
$683$	−4.23779	−	3.17237i	−0.162155	−	0.121387i	−0.677274	+	0.735731i	$0.736839\pi$
$684$		0			0
$685$	11.6153	−	11.5632i	0.443799	−	0.441807i
$686$		0			0
$687$	8.57672	−	15.7071i	0.327222	−	0.599263i
$688$		0			0
$689$	24.5454			0.935106
$690$		0			0
$691$	−19.3261			−0.735198			−0.367599	−	0.929984i	$-0.619820\pi$
$691$	−19.3261			−0.735198			−0.367599	+	0.929984i	$0.619820\pi$
$692$		0			0
$693$	0.0855805	−	0.156729i	0.00325094	−	0.00595364i
$694$		0			0
$695$	0.102148	−	45.4061i	0.00387469	−	1.72235i
$696$		0			0
$697$	29.7611	+	22.2789i	1.12728	+	0.843872i
$698$		0			0
$699$	0.895845	+	1.39396i	0.0338840	+	0.0527245i
$700$		0			0
$701$	−9.11833	−	4.16420i	−0.344395	−	0.157280i	0.235706	−	0.971824i	$-0.424260\pi$
$701$	−9.11833	−	4.16420i	−0.344395	−	0.157280i	−0.580101	+	0.814545i	$0.696987\pi$
$702$		0			0
$703$	−9.49600	−	12.6852i	−0.358148	−	0.478430i
$704$		0			0
$705$	−28.0218	+	8.15952i	−1.05536	+	0.307305i
$706$		0			0
$707$	−5.61483	−	0.401581i	−0.211167	−	0.0151030i
$708$		0			0
$709$	9.38474	−	10.8306i	0.352451	−	0.406750i	−0.551645	−	0.834079i	$-0.686000\pi$
$709$	9.38474	−	10.8306i	0.352451	−	0.406750i	0.904096	+	0.427328i	$0.140545\pi$
$710$		0			0
$711$	6.98614	−	3.19046i	0.262001	−	0.119652i
$712$		0			0
$713$	−8.13566	+	43.2805i	−0.304683	+	1.62087i
$714$		0			0
$715$	−0.411867	−	1.91404i	−0.0154030	−	0.0715811i
$716$		0			0
$717$	17.0363	−	1.21846i	0.636231	−	0.0455041i
$718$		0			0
$719$	−16.3929	+	14.2045i	−0.611352	+	0.529739i	−0.904580	−	0.426303i	$-0.859816\pi$
$719$	−16.3929	+	14.2045i	−0.611352	+	0.529739i	0.293229	+	0.956042i	$0.405270\pi$
$720$		0			0
$721$	4.17227	+	1.22509i	0.155383	+	0.0456247i
$722$		0			0
$723$	−14.0780	+	10.5387i	−0.523568	+	0.391938i
$724$		0			0
$725$	35.4549	−	30.4436i	1.31676	−	1.13065i
$726$		0			0
$727$	−2.64100	+	12.1405i	−0.0979494	+	0.450266i	0.901883	+	0.431980i	$0.142185\pi$
$727$	−2.64100	+	12.1405i	−0.0979494	+	0.450266i	−0.999833	+	0.0182865i	$0.994179\pi$
$728$		0			0
$729$	28.1394	−	4.04583i	1.04220	−	0.149846i
$730$		0			0
$731$	28.2506	+	18.1556i	1.04489	+	0.671508i
$732$		0			0
$733$	−12.6497	−	6.90727i	−0.467228	−	0.255126i	0.228346	−	0.973580i	$-0.426668\pi$
$733$	−12.6497	−	6.90727i	−0.467228	−	0.255126i	−0.695574	+	0.718454i	$0.744850\pi$
$734$		0			0
$735$	−20.8045	−	4.57479i	−0.767386	−	0.168744i
$736$		0			0
$737$	−2.29361	−	2.29361i	−0.0844861	−	0.0844861i
$738$		0			0
$739$	9.19622	+	31.3194i	0.338288	+	1.15210i	0.936471	+	0.350745i	$0.114071\pi$
$739$	9.19622	+	31.3194i	0.338288	+	1.15210i	−0.598183	+	0.801360i	$0.704110\pi$
$740$		0			0
$741$	4.66459	−	7.25824i	0.171358	−	0.266638i
$742$		0			0
$743$	19.3814	−	25.8905i	0.711035	−	0.949832i	−0.288936	−	0.957348i	$-0.593302\pi$
$743$	19.3814	−	25.8905i	0.711035	−	0.949832i	0.999972	+	0.00751631i	$0.00239254\pi$
$744$		0			0
$745$	16.1896	−	35.2403i	0.593141	−	1.29110i
$746$		0			0
$747$	−2.93032	−	7.85649i	−0.107215	−	0.287454i
$748$		0			0
$749$	4.29465	+	0.617478i	0.156923	+	0.0225622i
$750$		0			0
$751$	−7.87817	+	26.8306i	−0.287479	+	0.979062i	0.681480	+	0.731837i	$0.261337\pi$
$751$	−7.87817	+	26.8306i	−0.287479	+	0.979062i	−0.968958	+	0.247225i	$0.920481\pi$
$752$		0			0
$753$	−2.40382	+	33.6099i	−0.0876002	+	1.22481i
$754$		0			0
$755$	−3.25671	+	22.2948i	−0.118524	+	0.811390i
$756$		0			0
$757$	23.4398	+	8.74260i	0.851935	+	0.317755i	0.737228	−	0.675644i	$-0.236134\pi$
$757$	23.4398	+	8.74260i	0.851935	+	0.317755i	0.114707	+	0.993399i	$0.463407\pi$
$758$		0			0
$759$	2.16012	+	2.35440i	0.0784075	+	0.0854593i
$760$		0			0
$761$	14.0409	+	30.7452i	0.508981	+	1.11451i	0.973445	+	0.228921i	$0.0735198\pi$
$761$	14.0409	+	30.7452i	0.508981	+	1.11451i	−0.464464	+	0.885592i	$0.653753\pi$
$762$		0			0
$763$	−0.177206	−	2.47766i	−0.00641528	−	0.0896974i
$764$		0			0
$765$	6.96135	+	12.8172i	0.251688	+	0.463408i
$766$		0			0
$767$	4.59119	+	8.40813i	0.165778	+	0.303600i
$768$		0			0
$769$	−3.25665	+	22.6505i	−0.117438	+	0.816798i	0.842922	+	0.538035i	$0.180833\pi$
$769$	−3.25665	+	22.6505i	−0.117438	+	0.816798i	−0.960360	+	0.278762i	$0.910076\pi$
$770$		0			0
$771$	−0.423713	+	0.927802i	−0.0152597	+	0.0334140i
$772$		0			0
$773$	14.4255	+	3.13807i	0.518848	+	0.112868i	0.464361	−	0.885646i	$-0.346284\pi$
$773$	14.4255	+	3.13807i	0.518848	+	0.112868i	0.0544868	+	0.998514i	$0.482648\pi$
$774$		0			0
$775$	−43.9949	−	13.1334i	−1.58034	−	0.471764i
$776$		0			0
$777$	0.465309	+	2.13899i	0.0166929	+	0.0767358i
$778$		0			0
$779$	20.3239	−	5.96764i	0.728180	−	0.213813i
$780$		0			0
$781$			6.61968i			0.236871i
$782$		0			0
$783$	−37.3601	+	37.3601i	−1.33514	+	1.33514i
$784$		0			0
$785$	−2.13014	−	30.7554i	−0.0760280	−	1.09771i
$786$		0			0
$787$	−2.11720	+	0.460569i	−0.0754702	+	0.0164175i	−0.250142	−	0.968209i	$-0.580477\pi$
$787$	−2.11720	+	0.460569i	−0.0754702	+	0.0164175i	0.174672	+	0.984627i	$0.444114\pi$
$788$		0			0
$789$	3.60764	+	25.0917i	0.128435	+	0.893287i
$790$		0			0
$791$	3.23064	−	2.07621i	0.114868	−	0.0738214i
$792$		0			0
$793$	−25.6078	+	9.55123i	−0.909361	+	0.339174i
$794$		0			0
$795$	−17.2636	−	38.0282i	−0.612277	−	1.34872i
$796$		0			0
$797$	−31.2174	+	17.0460i	−1.10578	+	0.603800i	−0.925093	−	0.379741i	$-0.876013\pi$
$797$	−31.2174	+	17.0460i	−1.10578	+	0.603800i	−0.180684	+	0.983541i	$0.557831\pi$
$798$		0			0
$799$	37.1472	+	42.8701i	1.31417	+	1.51664i
$800$		0			0
$801$	−0.432159	−	0.374468i	−0.0152696	−	0.0132312i
$802$		0			0
$803$	0.548750	−	1.47126i	0.0193650	−	0.0519195i
$804$		0			0
$805$	1.90195	−	3.13686i	0.0670350	−	0.110560i
$806$		0			0
$807$	7.85296	−	21.0546i	0.276437	−	0.741157i
$808$		0			0
$809$	−8.63341	−	7.48089i	−0.303535	−	0.263014i	0.489753	−	0.871861i	$-0.337087\pi$
$809$	−8.63341	−	7.48089i	−0.303535	−	0.263014i	−0.793288	+	0.608847i	$0.791632\pi$
$810$		0			0
$811$	5.12440	+	5.91387i	0.179942	+	0.207664i	0.838554	−	0.544819i	$-0.183402\pi$
$811$	5.12440	+	5.91387i	0.179942	+	0.207664i	−0.658612	+	0.752483i	$0.728856\pi$
$812$		0			0
$813$	−3.68675	+	2.01312i	−0.129300	+	0.0706031i
$814$		0			0
$815$	−3.63173	−	1.36388i	−0.127214	−	0.0477746i
$816$		0			0
$817$	17.9274	−	6.68659i	0.627202	−	0.233934i
$818$		0			0
$819$	0.567631	−	0.364794i	0.0198346	−	0.0127469i
$820$		0			0
$821$	5.49638	+	38.2282i	0.191825	+	1.33417i	0.827174	+	0.561946i	$0.189947\pi$
$821$	5.49638	+	38.2282i	0.191825	+	1.33417i	−0.635349	+	0.772225i	$0.719144\pi$
$822$		0			0
$823$	−17.5392	+	3.81542i	−0.611377	+	0.132997i	−0.507585	−	0.861602i	$-0.669462\pi$
$823$	−17.5392	+	3.81542i	−0.611377	+	0.132997i	−0.103793	+	0.994599i	$0.533098\pi$
$824$		0			0
$825$	−2.67574	+	1.98431i	−0.0931574	+	0.0690850i
$826$		0			0
$827$	21.8354	−	21.8354i	0.759291	−	0.759291i	−0.216902	−	0.976193i	$-0.569595\pi$
$827$	21.8354	−	21.8354i	0.759291	−	0.759291i	0.976193	+	0.216902i	$0.0695953\pi$
$828$		0			0
$829$		−	37.2747i		−	1.29460i	−0.762234	−	0.647302i	$-0.775897\pi$
$829$		−	37.2747i		−	1.29460i	0.762234	−	0.647302i	$-0.224103\pi$
$830$		0			0
$831$	−20.7942	+	6.10574i	−0.721344	+	0.211806i
$832$		0			0
$833$	8.80060	+	40.4557i	0.304923	+	1.40171i
$834$		0			0
$835$	−1.56735	+	21.2427i	−0.0542403	+	0.735133i
$836$		0			0
$837$	50.7235	+	11.0342i	1.75326	+	0.381399i
$838$		0			0
$839$	−3.22273	+	7.05680i	−0.111261	+	0.243628i	−0.957069	−	0.289859i	$-0.906391\pi$
$839$	−3.22273	+	7.05680i	−0.111261	+	0.243628i	0.845808	+	0.533487i	$0.179119\pi$
$840$		0			0
$841$	8.30471	−	57.7605i	0.286369	−	1.99174i
$842$		0			0
$843$	2.95921	+	5.41939i	0.101921	+	0.186654i
$844$		0			0
$845$	−6.15220	+	20.7794i	−0.211642	+	0.714834i
$846$		0			0
$847$	0.262788	+	3.67425i	0.00902949	+	0.126249i
$848$		0			0
$849$	1.23217	+	2.69807i	0.0422878	+	0.0925974i
$850$		0			0
$851$	22.0284	+	2.53126i	0.755126	+	0.0867706i
$852$		0			0
$853$	9.64922	+	3.59897i	0.330383	+	0.123226i	0.509181	−	0.860659i	$-0.329948\pi$
$853$	9.64922	+	3.59897i	0.330383	+	0.123226i	−0.178798	+	0.983886i	$0.557221\pi$
$854$		0			0
$855$	8.22323	+	1.20121i	0.281229	+	0.0410805i
$856$		0			0
$857$	2.46588	−	34.4775i	0.0842329	−	1.17773i	−0.762961	−	0.646445i	$-0.776255\pi$
$857$	2.46588	−	34.4775i	0.0842329	−	1.17773i	0.847193	−	0.531284i	$-0.178290\pi$
$858$		0			0
$859$	−5.50305	+	18.7417i	−0.187762	+	0.639458i	0.810774	+	0.585360i	$0.199047\pi$
$859$	−5.50305	+	18.7417i	−0.187762	+	0.639458i	−0.998536	+	0.0540983i	$0.982772\pi$
$860$		0			0
$861$	−2.89640	−	0.416440i	−0.0987091	−	0.0141922i
$862$		0			0
$863$	0.361310	+	0.968710i	0.0122991	+	0.0329753i	0.942954	−	0.332922i	$-0.108035\pi$
$863$	0.361310	+	0.968710i	0.0122991	+	0.0329753i	−0.930655	+	0.365898i	$0.880762\pi$
$864$		0			0
$865$	0.0645186	+	0.174177i	0.00219370	+	0.00592218i
$866$		0			0
$867$	−15.9096	+	21.2528i	−0.540320	+	0.721783i
$868$		0			0
$869$	1.84318	−	2.86804i	0.0625255	−	0.0972916i
$870$		0			0
$871$	−3.45300	−	11.7598i	−0.117000	−	0.398467i
$872$		0			0
$873$	1.99937	+	1.99937i	0.0676683	+	0.0676683i
$874$		0			0
$875$	3.04621	+	2.31261i	0.102981	+	0.0781803i
$876$		0			0
$877$	28.6705	+	15.6553i	0.968134	+	0.528641i	0.883835	−	0.467799i	$-0.154953\pi$
$877$	28.6705	+	15.6553i	0.968134	+	0.528641i	0.0842994	+	0.996440i	$0.473135\pi$
$878$		0			0
$879$	15.8690	+	10.1984i	0.535247	+	0.343982i
$880$		0			0
$881$	16.4824	−	2.36981i	0.555306	−	0.0798410i	0.141052	−	0.990002i	$-0.454952\pi$
$881$	16.4824	−	2.36981i	0.555306	−	0.0798410i	0.414254	+	0.910161i	$0.364042\pi$
$882$		0			0
$883$	5.62741	−	25.8688i	0.189377	−	0.870554i	−0.780154	−	0.625587i	$-0.784859\pi$
$883$	5.62741	−	25.8688i	0.189377	−	0.870554i	0.969532	−	0.244967i	$-0.0787770\pi$
$884$		0			0
$885$	9.79758	−	13.0268i	0.329342	−	0.437892i
$886$		0			0
$887$	−1.90218	+	1.42395i	−0.0638688	+	0.0478116i	−0.630735	−	0.775998i	$-0.717247\pi$
$887$	−1.90218	+	1.42395i	−0.0638688	+	0.0478116i	0.566866	+	0.823810i	$0.308156\pi$
$888$		0			0
$889$	3.56653	+	1.04723i	0.119618	+	0.0351229i
$890$		0			0
$891$	1.66284	−	1.44086i	0.0557074	−	0.0482707i
$892$		0			0
$893$	32.2381	−	2.30572i	1.07881	−	0.0771579i
$894$		0			0
$895$	9.14862	−	14.1654i	0.305805	−	0.473496i
$896$		0			0
$897$	2.90023	+	11.7197i	0.0968359	+	0.391310i
$898$		0			0
$899$	−78.0688	+	35.6528i	−2.60374	+	1.18909i
$900$		0			0
$901$	−53.1560	+	61.3453i	−1.77088	+	2.04371i
$902$		0			0
$903$	−2.63651	−	0.188567i	−0.0877377	−	0.00627513i
$904$		0			0
$905$	−0.345895	−	1.18789i	−0.0114979	−	0.0394868i
$906$		0			0
$907$	8.36505	+	11.1744i	0.277757	+	0.371040i	0.917627	−	0.397444i	$-0.130103\pi$
$907$	8.36505	+	11.1744i	0.277757	+	0.371040i	−0.639870	+	0.768483i	$0.721012\pi$
$908$		0			0
$909$	16.2322	+	7.41301i	0.538389	+	0.245874i
$910$		0			0
$911$	−4.12898	−	6.42481i	−0.136799	−	0.212864i	0.766094	−	0.642728i	$-0.222198\pi$
$911$	−4.12898	−	6.42481i	−0.136799	−	0.212864i	−0.902893	+	0.429865i	$0.858561\pi$
$912$		0			0
$913$	−2.97977	−	2.23063i	−0.0986159	−	0.0738230i
$914$		0			0
$915$	32.8086	+	32.9565i	1.08462	+	1.08951i
$916$		0			0
$917$	−0.841766	+	1.54158i	−0.0277976	+	0.0509074i
$918$		0			0
$919$	−19.5874			−0.646130			−0.323065	−	0.946377i	$-0.604713\pi$
$919$	−19.5874			−0.646130			−0.323065	+	0.946377i	$0.604713\pi$
$920$		0			0
$921$	45.2129			1.48981
$922$		0			0
$923$	−11.9874	+	21.9532i	−0.394569	+	0.722599i
$924$		0			0
$925$	−5.01554	+	22.5667i	−0.164910	+	0.741989i
$926$		0			0
$927$	−11.0352	−	8.26088i	−0.362445	−	0.271323i
$928$		0			0
$929$	17.0422	+	26.5181i	0.559135	+	0.870031i	0.999615	−	0.0277309i	$-0.00882815\pi$
$929$	17.0422	+	26.5181i	0.559135	+	0.870031i	−0.440480	+	0.897762i	$0.645192\pi$
$930$		0			0
$931$	21.4579	+	9.79947i	0.703253	+	0.321165i
$932$		0			0
$933$	28.5949	+	38.1983i	0.936154	+	1.25056i
$934$		0			0
$935$	5.67563	+	3.11572i	0.185613	+	0.101895i
$936$		0			0
$937$	−17.9541	−	1.28410i	−0.586535	−	0.0419498i	−0.225081	−	0.974340i	$-0.572265\pi$
$937$	−17.9541	−	1.28410i	−0.586535	−	0.0419498i	−0.361453	+	0.932390i	$0.617719\pi$
$938$		0			0
$939$	−1.71244	+	1.97626i	−0.0558833	+	0.0644928i
$940$		0			0
$941$	45.7808	−	20.9074i	1.49241	−	0.681562i	0.508639	−	0.860980i	$-0.330149\pi$
$941$	45.7808	−	20.9074i	1.49241	−	0.681562i	0.983773	+	0.179418i	$0.0574214\pi$
$942$		0			0
$943$	−13.4609	+	26.4076i	−0.438348	+	0.859951i
$944$		0			0
$945$	−3.63240	−	2.34596i	−0.118162	−	0.0763142i
$946$		0			0
$947$	42.1691	−	3.01599i	1.37031	−	0.0980065i	0.633310	−	0.773898i	$-0.281696\pi$
$947$	42.1691	−	3.01599i	1.37031	−	0.0980065i	0.737001	+	0.675892i	$0.236241\pi$
$948$		0			0
$949$	4.48410	−	3.88549i	0.145560	−	0.126128i
$950$		0			0
$951$	−40.2967	−	11.8322i	−1.30671	−	0.383685i
$952$		0			0
$953$	−7.28903	+	5.45650i	−0.236115	+	0.176753i	−0.710783	−	0.703412i	$-0.751659\pi$
$953$	−7.28903	+	5.45650i	−0.236115	+	0.176753i	0.474668	+	0.880165i	$0.342568\pi$
$954$		0			0
$955$	15.4138	−	2.18079i	0.498779	−	0.0705688i
$956$		0			0
$957$	−1.32364	+	6.08467i	−0.0427872	+	0.196690i
$958$		0			0
$959$	2.48184	−	0.356835i	0.0801428	−	0.0115228i
$960$		0			0
$961$	44.8569	+	28.8278i	1.44700	+	0.929928i
$962$		0			0
$963$	−12.0719	−	6.59174i	−0.389011	−	0.212416i
$964$		0			0
$965$	6.72380	−	30.5775i	0.216447	−	0.984324i
$966$		0			0
$967$	38.9774	+	38.9774i	1.25343	+	1.25343i	0.954174	+	0.299254i	$0.0967376\pi$
$967$	38.9774	+	38.9774i	1.25343	+	1.25343i	0.299254	+	0.954174i	$0.403262\pi$
$968$		0			0
$969$	8.03849	+	27.3766i	0.258233	+	0.879462i
$970$		0			0
$971$	−26.1330	+	40.6638i	−0.838649	+	1.30496i	0.111689	+	0.993743i	$0.464374\pi$
$971$	−26.1330	+	40.6638i	−0.838649	+	1.30496i	−0.950338	+	0.311219i	$0.899263\pi$
$972$		0			0
$973$	4.16284	−	5.56090i	0.133454	−	0.178274i
$974$		0			0
$975$	−12.4670	+	1.73527i	−0.399265	+	0.0555733i
$976$		0			0
$977$	−3.09764	−	8.30510i	−0.0991023	−	0.265704i	0.877932	−	0.478785i	$-0.158923\pi$
$977$	−3.09764	−	8.30510i	−0.0991023	−	0.265704i	−0.977034	+	0.213082i	$0.931650\pi$
$978$		0			0
$979$	−0.251252	−	0.0361245i	−0.00803004	−	0.00115455i
$980$		0			0
$981$	−2.21848	+	7.55544i	−0.0708305	+	0.241227i
$982$		0			0
$983$	2.80039	−	39.1545i	0.0893184	−	1.24883i	−0.733167	−	0.680049i	$-0.761959\pi$
$983$	2.80039	−	39.1545i	0.0893184	−	1.24883i	0.822486	−	0.568786i	$-0.192587\pi$
$984$		0			0
$985$	−15.8011	+	11.7732i	−0.503465	+	0.375125i
$986$		0			0
$987$	−4.18341	−	1.56033i	−0.133159	−	0.0496659i
$988$		0			0
$989$	−10.4266	+	24.6609i	−0.331548	+	0.784171i
$990$		0			0
$991$	16.1771	+	35.4229i	0.513883	+	1.12525i	0.971704	+	0.236202i	$0.0759028\pi$
$991$	16.1771	+	35.4229i	0.513883	+	1.12525i	−0.457821	+	0.889044i	$0.651370\pi$
$992$		0			0
$993$	−1.30089	−	18.1888i	−0.0412824	−	0.577203i
$994$		0			0
$995$	−37.2205	−	11.0199i	−1.17997	−	0.349355i
$996$		0			0
$997$	15.9122	+	29.1410i	0.503944	+	0.922905i	0.998552	+	0.0537891i	$0.0171299\pi$
$997$	15.9122	+	29.1410i	0.503944	+	0.922905i	−0.494608	+	0.869116i	$0.664688\pi$
$998$		0			0
$999$	3.71963	−	25.8706i	0.117684	−	0.818508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.617.12	yes	720
5.3	odd	4	inner	920.2.bv.a.433.12	yes	720
23.17	odd	22	inner	920.2.bv.a.17.12	✓	720
115.63	even	44	inner	920.2.bv.a.753.12	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.12	✓	720	23.17	odd	22	inner
920.2.bv.a.433.12	yes	720	5.3	odd	4	inner
920.2.bv.a.617.12	yes	720	1.1	even	1	trivial
920.2.bv.a.753.12	yes	720	115.63	even	44	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.663302 + 1.21475i) q^{3} +(-2.23606 - 0.00503036i) q^{5} +(-0.273851 - 0.205002i) q^{7} +(0.586283 + 0.912274i) q^{9} +(0.437876 + 0.199971i) q^{11} +(1.09003 + 1.45611i) q^{13} +(1.48929 - 2.71291i) q^{15} +(-5.99978 - 0.429113i) q^{17} +(-2.24436 + 2.59013i) q^{19} +(0.430671 - 0.196681i) q^{21} +(-0.477794 - 4.77197i) q^{23} +(4.99995 + 0.0224964i) q^{25} +(-5.63862 + 0.403282i) q^{27} +(7.06351 - 6.12056i) q^{29} +(-8.81071 - 2.58706i) q^{31} +(-0.533358 + 0.399267i) q^{33} +(0.611316 + 0.459775i) q^{35} +(-0.982790 + 4.51781i) q^{37} +(-2.49182 + 0.358270i) q^{39} +(-5.19934 - 3.34142i) q^{41} +(-4.89997 - 2.67559i) q^{43} +(-1.30638 - 2.04285i) q^{45} +(-6.66836 - 6.66836i) q^{47} +(-1.93916 - 6.60417i) q^{49} +(4.50093 - 7.00358i) q^{51} +(8.08702 - 10.8030i) q^{53} +(-0.978111 - 0.449350i) q^{55} +(-1.65766 - 4.44437i) q^{57} +(5.21327 + 0.749555i) q^{59} +(-4.23334 + 14.4174i) q^{61} +(0.0264641 - 0.370016i) q^{63} +(-2.43005 - 3.26143i) q^{65} +(-6.31343 - 2.35479i) q^{67} +(6.11366 + 2.58486i) q^{69} +(5.71261 + 12.5089i) q^{71} +(-0.232710 - 3.25371i) q^{73} +(-3.34380 + 6.05875i) q^{75} +(-0.0789181 - 0.144528i) q^{77} +(1.00791 - 7.01019i) q^{79} +(1.89876 - 4.15771i) q^{81} +(-7.55568 - 1.64364i) q^{83} +(13.4137 + 0.989704i) q^{85} +(2.74970 + 12.6402i) q^{87} +(-0.505952 + 0.148561i) q^{89} -0.622215i q^{91} +(8.98678 - 8.98678i) q^{93} +(5.03156 - 5.78041i) q^{95} +(2.54782 - 0.554245i) q^{97} +(0.0742905 + 0.516702i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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