LMFDB - Embedded newform 968.2.q.b.89.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(89,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("968.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.q (of order $11$, degree $10$, 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$170$
Relative dimension:	$17$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			89.16
Character	$\chi$	$=$	968.89
Dual form			968.2.q.b.881.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.05084 q^{3} +(1.06220 + 2.32589i) q^{5} +(0.403770 - 0.259487i) q^{7} +6.30765 q^{9} +(2.36007 - 2.33025i) q^{11} +(-4.56000 - 1.33894i) q^{13} +(3.24060 + 7.09593i) q^{15} +(0.632909 - 0.730416i) q^{17} +(0.816943 + 0.942802i) q^{19} +(1.23184 - 0.791654i) q^{21} +(1.65302 + 1.06233i) q^{23} +(-1.00720 + 1.16237i) q^{25} +10.0911 q^{27} +(-3.62654 - 4.18525i) q^{29} +(-4.72110 + 1.38624i) q^{31} +(7.20021 - 7.10922i) q^{33} +(1.03242 + 0.663498i) q^{35} +(-3.35408 + 0.984847i) q^{37} +(-13.9119 - 4.08489i) q^{39} +(-1.64647 + 11.4515i) q^{41} +(2.03055 - 4.44629i) q^{43} +(6.69998 + 14.6709i) q^{45} +(0.753286 + 5.23922i) q^{47} +(-2.81221 + 6.15788i) q^{49} +(1.93091 - 2.22838i) q^{51} +(2.00897 - 1.29109i) q^{53} +(7.92677 + 3.01409i) q^{55} +(2.49236 + 2.87634i) q^{57} +(-0.179816 - 1.25065i) q^{59} +(-0.771525 - 5.36608i) q^{61} +(2.54684 - 1.63675i) q^{63} +(-1.72941 - 12.0283i) q^{65} +(-1.33999 + 9.31985i) q^{67} +(5.04311 + 3.24101i) q^{69} +(-7.83397 - 9.04089i) q^{71} +(-7.48670 - 4.81141i) q^{73} +(-3.07282 + 3.54622i) q^{75} +(0.348257 - 1.55329i) q^{77} +(0.0532924 + 0.116694i) q^{79} +11.8635 q^{81} +(-11.8744 + 7.63120i) q^{83} +(2.37114 + 0.696230i) q^{85} +(-11.0640 - 12.7686i) q^{87} +(8.15680 - 9.41345i) q^{89} +(-2.18863 + 0.642639i) q^{91} +(-14.4033 + 4.22920i) q^{93} +(-1.32510 + 2.90156i) q^{95} +(6.21189 - 13.6021i) q^{97} +(14.8865 - 14.6984i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 170 q + 10 q^{3} - 3 q^{5} + 2 q^{7} + 180 q^{9} + 2 q^{11} + 3 q^{13} + 10 q^{15} - 6 q^{17} + 9 q^{19} + 16 q^{21} + 23 q^{23} - 18 q^{25} - 26 q^{27} + q^{29} - 38 q^{31} + q^{33} - 10 q^{35} - 24 q^{37}+ \cdots - 74 q^{99}+O(q^{100}) $ 170 * q + 10 * q^3 - 3 * q^5 + 2 * q^7 + 180 * q^9 + 2 * q^11 + 3 * q^13 + 10 * q^15 - 6 * q^17 + 9 * q^19 + 16 * q^21 + 23 * q^23 - 18 * q^25 - 26 * q^27 + q^29 - 38 * q^31 + q^33 - 10 * q^35 - 24 * q^37 + 79 * q^39 - 4 * q^41 + 3 * q^43 - 37 * q^45 - 25 * q^47 - 39 * q^49 + 9 * q^51 + 17 * q^53 + 69 * q^55 + 63 * q^57 - 28 * q^59 + 34 * q^61 + 22 * q^63 + 84 * q^65 - 19 * q^67 - 12 * q^69 + 15 * q^71 - 46 * q^73 + 23 * q^75 + 108 * q^77 + 47 * q^79 + 226 * q^81 - 9 * q^83 - 8 * q^85 - 91 * q^87 - 100 * q^89 - 16 * q^91 - 6 * q^93 + 45 * q^95 + 18 * q^97 - 74 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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
$3$	3.05084			1.76141			0.880703	−	0.473669i	$-0.157071\pi$
$3$	3.05084			1.76141			0.880703	+	0.473669i	$0.157071\pi$
$4$		0			0
$5$	1.06220	+	2.32589i	0.475030	+	1.04017i	0.983800	+	0.179268i	$0.0573730\pi$
$5$	1.06220	+	2.32589i	0.475030	+	1.04017i	−0.508770	+	0.860902i	$0.669900\pi$
$6$		0			0
$7$	0.403770	−	0.259487i	0.152611	−	0.0980769i	−0.462107	−	0.886824i	$-0.652906\pi$
$7$	0.403770	−	0.259487i	0.152611	−	0.0980769i	0.614718	+	0.788747i	$0.289270\pi$
$8$		0			0
$9$	6.30765			2.10255
$10$		0			0
$11$	2.36007	−	2.33025i	0.711589	−	0.702596i
$11$	2.36007	−	2.33025i	0.711589	−	0.702596i
$12$		0			0
$13$	−4.56000	−	1.33894i	−1.26472	−	0.371354i	−0.420469	−	0.907307i	$-0.638134\pi$
$13$	−4.56000	−	1.33894i	−1.26472	−	0.371354i	−0.844248	+	0.535953i	$0.819953\pi$
$14$		0			0
$15$	3.24060	+	7.09593i	0.836721	+	1.83216i
$16$		0			0
$17$	0.632909	−	0.730416i	0.153503	−	0.177152i	−0.673789	−	0.738923i	$-0.735335\pi$
$17$	0.632909	−	0.730416i	0.153503	−	0.177152i	0.827292	+	0.561772i	$0.189880\pi$
$18$		0			0
$19$	0.816943	+	0.942802i	0.187419	+	0.216294i	0.841681	−	0.539974i	$-0.181566\pi$
$19$	0.816943	+	0.942802i	0.187419	+	0.216294i	−0.654262	+	0.756268i	$0.727021\pi$
$20$		0			0
$21$	1.23184	−	0.791654i	0.268809	−	0.172753i
$22$		0			0
$23$	1.65302	+	1.06233i	0.344679	+	0.221511i	0.701514	−	0.712656i	$-0.252508\pi$
$23$	1.65302	+	1.06233i	0.344679	+	0.221511i	−0.356835	+	0.934167i	$0.616144\pi$
$24$		0			0
$25$	−1.00720	+	1.16237i	−0.201441	+	0.232475i
$26$		0			0
$27$	10.0911			1.94204
$28$		0			0
$29$	−3.62654	−	4.18525i	−0.673432	−	0.777182i	0.311477	−	0.950254i	$-0.399176\pi$
$29$	−3.62654	−	4.18525i	−0.673432	−	0.777182i	−0.984909	+	0.173072i	$0.944631\pi$
$30$		0			0
$31$	−4.72110	+	1.38624i	−0.847935	+	0.248976i	−0.676704	−	0.736255i	$-0.736592\pi$
$31$	−4.72110	+	1.38624i	−0.847935	+	0.248976i	−0.171231	+	0.985231i	$0.554774\pi$
$32$		0			0
$33$	7.20021	−	7.10922i	1.25340	−	1.23756i
$34$		0			0
$35$	1.03242	+	0.663498i	0.174511	+	0.112152i
$36$		0			0
$37$	−3.35408	+	0.984847i	−0.551407	+	0.161908i	−0.545555	−	0.838075i	$-0.683681\pi$
$37$	−3.35408	+	0.984847i	−0.551407	+	0.161908i	−0.00585236	+	0.999983i	$0.501863\pi$
$38$		0			0
$39$	−13.9119	−	4.08489i	−2.22768	−	0.654106i
$40$		0			0
$41$	−1.64647	+	11.4515i	−0.257136	+	1.78842i	0.295854	+	0.955233i	$0.404396\pi$
$41$	−1.64647	+	11.4515i	−0.257136	+	1.78842i	−0.552990	+	0.833188i	$0.686513\pi$
$42$		0			0
$43$	2.03055	−	4.44629i	0.309657	−	0.678053i	−0.689264	−	0.724511i	$-0.742066\pi$
$43$	2.03055	−	4.44629i	0.309657	−	0.678053i	0.998920	+	0.0464572i	$0.0147931\pi$
$44$		0			0
$45$	6.69998	+	14.6709i	0.998774	+	2.18701i
$46$		0			0
$47$	0.753286	+	5.23922i	0.109878	+	0.764219i	0.968032	+	0.250826i	$0.0807023\pi$
$47$	0.753286	+	5.23922i	0.109878	+	0.764219i	−0.858154	+	0.513392i	$0.828389\pi$
$48$		0			0
$49$	−2.81221	+	6.15788i	−0.401744	+	0.879697i
$50$		0			0
$51$	1.93091	−	2.22838i	0.270381	−	0.312036i
$52$		0			0
$53$	2.00897	−	1.29109i	0.275953	−	0.177345i	−0.395343	−	0.918534i	$-0.629374\pi$
$53$	2.00897	−	1.29109i	0.275953	−	0.177345i	0.671296	+	0.741189i	$0.265738\pi$
$54$		0			0
$55$	7.92677	+	3.01409i	1.06885	+	0.406419i
$56$		0			0
$57$	2.49236	+	2.87634i	0.330122	+	0.380981i
$58$		0			0
$59$	−0.179816	−	1.25065i	−0.0234101	−	0.162821i	0.974763	−	0.223243i	$-0.0716644\pi$
$59$	−0.179816	−	1.25065i	−0.0234101	−	0.162821i	−0.998173	+	0.0604222i	$0.980755\pi$
$60$		0			0
$61$	−0.771525	−	5.36608i	−0.0987837	−	0.687056i	−0.977689	−	0.210059i	$-0.932634\pi$
$61$	−0.771525	−	5.36608i	−0.0987837	−	0.687056i	0.878905	−	0.476997i	$-0.158275\pi$
$62$		0			0
$63$	2.54684	−	1.63675i	0.320871	−	0.206212i
$64$		0			0
$65$	−1.72941	−	12.0283i	−0.214507	−	1.49193i
$66$		0			0
$67$	−1.33999	+	9.31985i	−0.163706	+	1.13860i	0.727865	+	0.685720i	$0.240513\pi$
$67$	−1.33999	+	9.31985i	−0.163706	+	1.13860i	−0.891571	+	0.452880i	$0.850396\pi$
$68$		0			0
$69$	5.04311	+	3.24101i	0.607119	+	0.390172i
$70$		0			0
$71$	−7.83397	−	9.04089i	−0.929722	−	1.07296i	−0.997166	−	0.0752330i	$-0.976030\pi$
$71$	−7.83397	−	9.04089i	−0.929722	−	1.07296i	0.0674443	−	0.997723i	$-0.478516\pi$
$72$		0			0
$73$	−7.48670	−	4.81141i	−0.876252	−	0.563133i	0.0234074	−	0.999726i	$-0.492549\pi$
$73$	−7.48670	−	4.81141i	−0.876252	−	0.563133i	−0.899659	+	0.436593i	$0.856185\pi$
$74$		0			0
$75$	−3.07282	+	3.54622i	−0.354819	+	0.409482i
$76$		0			0
$77$	0.348257	−	1.55329i	0.0396875	−	0.177014i
$78$		0			0
$79$	0.0532924	+	0.116694i	0.00599586	+	0.0131291i	0.912606	−	0.408840i	$-0.134066\pi$
$79$	0.0532924	+	0.116694i	0.00599586	+	0.0131291i	−0.906610	+	0.421969i	$0.861339\pi$
$80$		0			0
$81$	11.8635			1.31817
$82$		0			0
$83$	−11.8744	+	7.63120i	−1.30338	+	0.837633i	−0.993576	−	0.113167i	$-0.963901\pi$
$83$	−11.8744	+	7.63120i	−1.30338	+	0.837633i	−0.309806	+	0.950800i	$0.600264\pi$
$84$		0			0
$85$	2.37114	+	0.696230i	0.257187	+	0.0755168i
$86$		0			0
$87$	−11.0640	−	12.7686i	−1.18619	−	1.36893i
$88$		0			0
$89$	8.15680	−	9.41345i	0.864619	−	0.997823i	−0.135357	−	0.990797i	$-0.543218\pi$
$89$	8.15680	−	9.41345i	0.864619	−	0.997823i	0.999975	−	0.00702626i	$-0.00223655\pi$
$90$		0			0
$91$	−2.18863	+	0.642639i	−0.229430	+	0.0673669i
$92$		0			0
$93$	−14.4033	+	4.22920i	−1.49356	+	0.438548i
$94$		0			0
$95$	−1.32510	+	2.90156i	−0.135952	+	0.297694i
$96$		0			0
$97$	6.21189	−	13.6021i	0.630722	−	1.38109i	−0.276736	−	0.960946i	$-0.589253\pi$
$97$	6.21189	−	13.6021i	0.630722	−	1.38109i	0.907458	−	0.420142i	$-0.138020\pi$
$98$		0			0
$99$	14.8865	−	14.6984i	1.49615	−	1.47724i
$100$		0			0
$101$	−0.331438	−	2.30520i	−0.0329793	−	0.229376i	0.966665	−	0.256044i	$-0.0824193\pi$
$101$	−0.331438	−	2.30520i	−0.0329793	−	0.229376i	−0.999644	+	0.0266683i	$0.991510\pi$
$102$		0			0
$103$	−2.15712	+	15.0031i	−0.212548	+	1.47830i	0.552060	+	0.833805i	$0.313842\pi$
$103$	−2.15712	+	15.0031i	−0.212548	+	1.47830i	−0.764607	+	0.644496i	$0.777067\pi$
$104$		0			0
$105$	3.14976	+	2.02423i	0.307385	+	0.197544i
$106$		0			0
$107$	−6.86894	−	15.0409i	−0.664045	−	1.45406i	−0.878704	−	0.477367i	$-0.841591\pi$
$107$	−6.86894	−	15.0409i	−0.664045	−	1.45406i	0.214659	−	0.976689i	$-0.431136\pi$
$108$		0			0
$109$	6.36885	+	1.87006i	0.610025	+	0.179120i	0.572131	−	0.820162i	$-0.306117\pi$
$109$	6.36885	+	1.87006i	0.610025	+	0.179120i	0.0378941	+	0.999282i	$0.487935\pi$
$110$		0			0
$111$	−10.2328	+	3.00461i	−0.971252	+	0.285185i
$112$		0			0
$113$	5.77880	−	12.6538i	0.543624	−	1.19037i	−0.416073	−	0.909331i	$-0.636594\pi$
$113$	5.77880	−	12.6538i	0.543624	−	1.19037i	0.959697	−	0.281038i	$-0.0906788\pi$
$114$		0			0
$115$	−0.715032	+	4.97315i	−0.0666770	+	0.463749i
$116$		0			0
$117$	−28.7629	−	8.44555i	−2.65913	−	0.780791i
$118$		0			0
$119$	0.0660160	−	0.459151i	0.00605167	−	0.0420903i
$120$		0			0
$121$	0.139887	−	10.9991i	0.0127170	−	0.999919i
$122$		0			0
$123$	−5.02314	+	34.9367i	−0.452921	+	3.15013i
$124$		0			0
$125$	8.49352	+	2.49392i	0.759683	+	0.223063i
$126$		0			0
$127$	0.0814098	−	0.566217i	0.00722395	−	0.0502437i	−0.985891	−	0.167391i	$-0.946466\pi$
$127$	0.0814098	−	0.566217i	0.00722395	−	0.0502437i	0.993115	+	0.117147i	$0.0373749\pi$
$128$		0			0
$129$	6.19490	−	13.5649i	0.545431	−	1.19433i
$130$		0			0
$131$	18.1469	−	5.32842i	1.58551	−	0.465546i	0.634039	−	0.773301i	$-0.281396\pi$
$131$	18.1469	−	5.32842i	1.58551	−	0.465546i	0.951466	+	0.307754i	$0.0995775\pi$
$132$		0			0
$133$	0.574501	+	0.168689i	0.0498156	+	0.0146272i
$134$		0			0
$135$	10.7188	+	23.4709i	0.922526	+	2.02005i
$136$		0			0
$137$	−11.4633	−	7.36699i	−0.979373	−	0.629405i	−0.0500787	−	0.998745i	$-0.515947\pi$
$137$	−11.4633	−	7.36699i	−0.979373	−	0.629405i	−0.929294	+	0.369341i	$0.879584\pi$
$138$		0			0
$139$	−1.74133	+	12.1112i	−0.147698	+	1.02726i	0.772278	+	0.635285i	$0.219117\pi$
$139$	−1.74133	+	12.1112i	−0.147698	+	1.02726i	−0.919975	+	0.391976i	$0.871792\pi$
$140$		0			0
$141$	2.29816	+	15.9840i	0.193540	+	1.34610i
$142$		0			0
$143$	−13.8820	+	7.46595i	−1.16087	+	0.624334i
$144$		0			0
$145$	5.88233	−	12.8805i	0.488501	−	1.06967i
$146$		0			0
$147$	−8.57961	+	18.7867i	−0.707634	+	1.54950i
$148$		0			0
$149$	4.29895	−	1.26229i	0.352184	−	0.103411i	−0.100855	−	0.994901i	$-0.532158\pi$
$149$	4.29895	−	1.26229i	0.352184	−	0.103411i	0.453039	+	0.891491i	$0.350340\pi$
$150$		0			0
$151$	6.62705	−	1.94588i	0.539301	−	0.158353i	−0.000727433	−	1.00000i	$-0.500232\pi$
$151$	6.62705	−	1.94588i	0.539301	−	0.158353i	0.540029	+	0.841647i	$0.318413\pi$
$152$		0			0
$153$	3.99217	−	4.60721i	0.322748	−	0.372471i
$154$		0			0
$155$	−8.23900	−	9.50831i	−0.661772	−	0.763726i
$156$		0			0
$157$	19.9578	+	5.86013i	1.59280	+	0.467689i	0.953532	−	0.301293i	$-0.0974182\pi$
$157$	19.9578	+	5.86013i	1.59280	+	0.467689i	0.639271	+	0.768982i	$0.279236\pi$
$158$		0			0
$159$	6.12906	−	3.93891i	0.486066	−	0.312376i
$160$		0			0
$161$	0.943100			0.0743267
$162$		0			0
$163$	3.44967	+	7.55372i	0.270199	+	0.591653i	0.995284	−	0.0970064i	$-0.0309267\pi$
$163$	3.44967	+	7.55372i	0.270199	+	0.591653i	−0.725085	+	0.688660i	$0.758199\pi$
$164$		0			0
$165$	24.1834	+	9.19551i	1.88267	+	0.715869i
$166$		0			0
$167$	−0.195776	+	0.225937i	−0.0151496	+	0.0174835i	−0.763274	−	0.646075i	$-0.776409\pi$
$167$	−0.195776	+	0.225937i	−0.0151496	+	0.0174835i	0.748124	+	0.663559i	$0.230955\pi$
$168$		0			0
$169$	8.06456	+	5.18278i	0.620351	+	0.398675i
$170$		0			0
$171$	5.15299	+	5.94687i	0.394059	+	0.454768i
$172$		0			0
$173$	−7.57371	−	4.86733i	−0.575819	−	0.370056i	0.220084	−	0.975481i	$-0.429367\pi$
$173$	−7.57371	−	4.86733i	−0.575819	−	0.370056i	−0.795903	+	0.605425i	$0.793003\pi$
$174$		0			0
$175$	−0.105057	+	0.730687i	−0.00794156	+	0.0552348i
$176$		0			0
$177$	−0.548592	−	3.81554i	−0.0412347	−	0.286794i
$178$		0			0
$179$	−14.1208	+	9.07489i	−1.05544	+	0.678289i	−0.948758	−	0.316004i	$-0.897659\pi$
$179$	−14.1208	+	9.07489i	−1.05544	+	0.678289i	−0.106681	+	0.994293i	$0.534022\pi$
$180$		0			0
$181$	−2.20560	−	15.3403i	−0.163941	−	1.14023i	−0.891114	−	0.453780i	$-0.850075\pi$
$181$	−2.20560	−	15.3403i	−0.163941	−	1.14023i	0.727173	−	0.686454i	$-0.240834\pi$
$182$		0			0
$183$	−2.35380	−	16.3711i	−0.173998	−	1.21018i
$184$		0			0
$185$	−5.85335	−	6.75512i	−0.430347	−	0.496647i
$186$		0			0
$187$	−0.208339	−	3.19867i	−0.0152353	−	0.233910i
$188$		0			0
$189$	4.07449	−	2.61852i	0.296376	−	0.190469i
$190$		0			0
$191$	−14.7894	+	17.0679i	−1.07012	+	1.23499i	−0.0993349	+	0.995054i	$0.531671\pi$
$191$	−14.7894	+	17.0679i	−1.07012	+	1.23499i	−0.970789	+	0.239935i	$0.922874\pi$
$192$		0			0
$193$	−7.15738	+	15.6725i	−0.515200	+	1.12813i	0.456025	+	0.889967i	$0.349273\pi$
$193$	−7.15738	+	15.6725i	−0.515200	+	1.12813i	−0.971225	+	0.238163i	$0.923455\pi$
$194$		0			0
$195$	−5.27615	−	36.6964i	−0.377833	−	2.62789i
$196$		0			0
$197$	5.70939	+	12.5018i	0.406777	+	0.890718i	0.996538	+	0.0831401i	$0.0264949\pi$
$197$	5.70939	+	12.5018i	0.406777	+	0.890718i	−0.589760	+	0.807578i	$0.700778\pi$
$198$		0			0
$199$	10.7570	−	23.5544i	0.762540	−	1.66973i	0.0201184	−	0.999798i	$-0.493596\pi$
$199$	10.7570	−	23.5544i	0.762540	−	1.66973i	0.742422	−	0.669933i	$-0.233677\pi$
$200$		0			0
$201$	−4.08811	+	28.4334i	−0.288353	+	2.00554i
$202$		0			0
$203$	−2.55031	−	0.748837i	−0.178996	−	0.0525581i
$204$		0			0
$205$	−28.3838	+	8.33423i	−1.98241	+	0.582088i
$206$		0			0
$207$	10.4267	+	6.70082i	0.724704	+	0.465739i
$208$		0			0
$209$	4.12501	+	0.321402i	0.285333	+	0.0222319i
$210$		0			0
$211$	17.3544	−	5.09571i	1.19473	−	0.350803i	0.376891	−	0.926257i	$-0.376993\pi$
$211$	17.3544	−	5.09571i	1.19473	−	0.350803i	0.817834	+	0.575454i	$0.195175\pi$
$212$		0			0
$213$	−23.9002	−	27.5823i	−1.63762	−	1.88991i
$214$		0			0
$215$	12.4985			0.852387
$216$		0			0
$217$	−1.54653	+	1.78479i	−0.104985	+	0.121159i
$218$		0			0
$219$	−22.8407	−	14.6789i	−1.54343	−	0.991905i
$220$		0			0
$221$	−3.86405	+	2.48327i	−0.259924	+	0.167043i
$222$		0			0
$223$	3.69089	+	4.25951i	0.247160	+	0.285238i	0.865751	−	0.500475i	$-0.166841\pi$
$223$	3.69089	+	4.25951i	0.247160	+	0.285238i	−0.618591	+	0.785714i	$0.712296\pi$
$224$		0			0
$225$	−6.35308	+	7.33185i	−0.423539	+	0.488790i
$226$		0			0
$227$	−0.0332066	−	0.0727122i	−0.00220400	−	0.00482608i	0.908527	−	0.417827i	$-0.137208\pi$
$227$	−0.0332066	−	0.0727122i	−0.00220400	−	0.00482608i	−0.910731	+	0.413001i	$0.864481\pi$
$228$		0			0
$229$	−19.1568	−	5.62494i	−1.26592	−	0.371706i	−0.421222	−	0.906957i	$-0.638399\pi$
$229$	−19.1568	−	5.62494i	−1.26592	−	0.371706i	−0.844693	+	0.535251i	$0.820217\pi$
$230$		0			0
$231$	1.06248	−	4.73885i	0.0699058	−	0.311793i
$232$		0			0
$233$	−21.3554			−1.39904			−0.699518	−	0.714615i	$-0.746602\pi$
$233$	−21.3554			−1.39904			−0.699518	+	0.714615i	$0.746602\pi$
$234$		0			0
$235$	−11.3857	+	7.31716i	−0.742723	+	0.477319i
$236$		0			0
$237$	0.162587	+	0.356015i	0.0105611	+	0.0231257i
$238$		0			0
$239$	−24.6801			−1.59642			−0.798211	−	0.602378i	$-0.794220\pi$
$239$	−24.6801			−1.59642			−0.798211	+	0.602378i	$0.794220\pi$
$240$		0			0
$241$	20.7408			1.33603			0.668016	−	0.744147i	$-0.267144\pi$
$241$	20.7408			1.33603			0.668016	+	0.744147i	$0.267144\pi$
$242$		0			0
$243$	5.92033			0.379789
$244$		0			0
$245$	−17.3097			−1.10588
$246$		0			0
$247$	−2.46291	−	5.39301i	−0.156711	−	0.343149i
$248$		0			0
$249$	−36.2269	+	23.2816i	−2.29578	+	1.47541i
$250$		0			0
$251$	−1.41393			−0.0892463			−0.0446232	−	0.999004i	$-0.514209\pi$
$251$	−1.41393			−0.0892463			−0.0446232	+	0.999004i	$0.514209\pi$
$252$		0			0
$253$	6.37674	−	1.34477i	0.400902	−	0.0845448i
$254$		0			0
$255$	7.23399	+	2.12409i	0.453010	+	0.133016i
$256$		0			0
$257$	−5.22467	−	11.4404i	−0.325906	−	0.713635i	0.673774	−	0.738938i	$-0.264672\pi$
$257$	−5.22467	−	11.4404i	−0.325906	−	0.713635i	−0.999680	+	0.0253028i	$0.991945\pi$
$258$		0			0
$259$	−1.09872	+	1.26799i	−0.0682712	+	0.0787891i
$260$		0			0
$261$	−22.8750	−	26.3991i	−1.41592	−	1.63406i
$262$		0			0
$263$	−6.84921	+	4.40172i	−0.422341	+	0.271422i	−0.734501	−	0.678608i	$-0.762584\pi$
$263$	−6.84921	+	4.40172i	−0.422341	+	0.271422i	0.312160	+	0.950029i	$0.398947\pi$
$264$		0			0
$265$	5.13686	+	3.30126i	0.315555	+	0.202795i
$266$		0			0
$267$	24.8851	−	28.7190i	1.52294	−	1.75757i
$268$		0			0
$269$	−2.46795			−0.150474			−0.0752369	−	0.997166i	$-0.523971\pi$
$269$	−2.46795			−0.150474			−0.0752369	+	0.997166i	$0.523971\pi$
$270$		0			0
$271$	2.70901	+	3.12637i	0.164561	+	0.189913i	0.832041	−	0.554714i	$-0.187172\pi$
$271$	2.70901	+	3.12637i	0.164561	+	0.189913i	−0.667480	+	0.744628i	$0.732627\pi$
$272$		0			0
$273$	−6.67716	+	1.96059i	−0.404120	+	0.118660i
$274$		0			0
$275$	0.331548	+	5.09032i	0.0199931	+	0.306958i
$276$		0			0
$277$	19.0805	+	12.2623i	1.14644	+	0.736770i	0.968926	−	0.247349i	$-0.0795595\pi$
$277$	19.0805	+	12.2623i	1.14644	+	0.736770i	0.177510	+	0.984119i	$0.443196\pi$
$278$		0			0
$279$	−29.7791	+	8.74392i	−1.78283	+	0.523485i
$280$		0			0
$281$	8.53435	+	2.50591i	0.509117	+	0.149490i	0.526195	−	0.850364i	$-0.323618\pi$
$281$	8.53435	+	2.50591i	0.509117	+	0.149490i	−0.0170781	+	0.999854i	$0.505436\pi$
$282$		0			0
$283$	−1.77024	+	12.3123i	−0.105230	+	0.731889i	0.867076	+	0.498176i	$0.165997\pi$
$283$	−1.77024	+	12.3123i	−0.105230	+	0.731889i	−0.972306	+	0.233713i	$0.924912\pi$
$284$		0			0
$285$	−4.04267	+	8.85222i	−0.239467	+	0.524360i
$286$		0			0
$287$	2.30671	+	5.05100i	0.136161	+	0.298151i
$288$		0			0
$289$	2.28642	+	15.9024i	0.134495	+	0.935435i
$290$		0			0
$291$	18.9515	−	41.4980i	1.11096	−	2.43266i
$292$		0			0
$293$	19.0329	−	21.9652i	1.11192	−	1.28322i	0.156590	−	0.987664i	$-0.449950\pi$
$293$	19.0329	−	21.9652i	1.11192	−	1.28322i	0.955326	−	0.295555i	$-0.0955046\pi$
$294$		0			0
$295$	2.71788	−	1.74667i	0.158241	−	0.101695i
$296$		0			0
$297$	23.8158	−	23.5148i	1.38193	−	1.36447i
$298$		0			0
$299$	−6.11538	−	7.05752i	−0.353661	−	0.408147i
$300$		0			0
$301$	−0.333879	−	2.32218i	−0.0192445	−	0.133848i
$302$		0			0
$303$	−1.01116	−	7.03280i	−0.0580899	−	0.404024i
$304$		0			0
$305$	11.6614	−	7.49433i	0.667730	−	0.429124i
$306$		0			0
$307$	−1.93778	−	13.4776i	−0.110595	−	0.769206i	−0.967343	−	0.253471i	$-0.918428\pi$
$307$	−1.93778	−	13.4776i	−0.110595	−	0.769206i	0.856748	−	0.515736i	$-0.172481\pi$
$308$		0			0
$309$	−6.58104	+	45.7722i	−0.374383	+	2.60389i
$310$		0			0
$311$	21.1191	+	13.5724i	1.19755	+	0.769621i	0.978531	−	0.206099i	$-0.0660769\pi$
$311$	21.1191	+	13.5724i	1.19755	+	0.769621i	0.219022	+	0.975720i	$0.429713\pi$
$312$		0			0
$313$	−2.38207	−	2.74906i	−0.134643	−	0.155386i	0.684424	−	0.729084i	$-0.260054\pi$
$313$	−2.38207	−	2.74906i	−0.134643	−	0.155386i	−0.819067	+	0.573698i	$0.805508\pi$
$314$		0			0
$315$	6.51216	+	4.18511i	0.366919	+	0.235804i
$316$		0			0
$317$	17.3979	−	20.0782i	0.977163	−	1.12771i	−0.0146357	−	0.999893i	$-0.504659\pi$
$317$	17.3979	−	20.0782i	0.977163	−	1.12771i	0.991798	−	0.127813i	$-0.0407957\pi$
$318$		0			0
$319$	−18.3116	−	1.42676i	−1.02525	−	0.0798831i
$320$		0			0
$321$	−20.9561	−	45.8874i	−1.16965	−	2.56118i
$322$		0			0
$323$	1.20569			0.0670862
$324$		0			0
$325$	6.14919	−	3.95185i	0.341096	−	0.219209i
$326$		0			0
$327$	19.4304	+	5.70527i	1.07450	+	0.315502i
$328$		0			0
$329$	1.66366	+	1.91997i	0.0917207	+	0.105851i
$330$		0			0
$331$	−2.70347	+	3.11997i	−0.148596	+	0.171489i	−0.825168	−	0.564888i	$-0.808920\pi$
$331$	−2.70347	+	3.11997i	−0.148596	+	0.171489i	0.676572	+	0.736377i	$0.263465\pi$
$332$		0			0
$333$	−21.1564	+	6.21207i	−1.15936	+	0.340419i
$334$		0			0
$335$	−23.1003	+	6.78286i	−1.26210	+	0.370587i
$336$		0			0
$337$	−10.2525	+	22.4497i	−0.558487	+	1.22292i	0.394218	+	0.919017i	$0.371015\pi$
$337$	−10.2525	+	22.4497i	−0.558487	+	1.22292i	−0.952705	+	0.303898i	$0.901712\pi$
$338$		0			0
$339$	17.6302	−	38.6048i	0.957542	−	2.09672i
$340$		0			0
$341$	−7.91186	+	14.2730i	−0.428451	+	0.772925i
$342$		0			0
$343$	0.940545	+	6.54163i	0.0507846	+	0.353215i
$344$		0			0
$345$	−2.18145	+	15.1723i	−0.117445	+	0.816850i
$346$		0			0
$347$	4.00443	+	2.57349i	0.214969	+	0.138152i	0.643694	−	0.765283i	$-0.277401\pi$
$347$	4.00443	+	2.57349i	0.214969	+	0.138152i	−0.428725	+	0.903435i	$0.641037\pi$
$348$		0			0
$349$	4.58438	+	10.0384i	0.245396	+	0.537342i	0.991747	−	0.128210i	$-0.0409232\pi$
$349$	4.58438	+	10.0384i	0.245396	+	0.537342i	−0.746351	+	0.665553i	$0.768196\pi$
$350$		0			0
$351$	−46.0156	−	13.5114i	−2.45613	−	0.721184i
$352$		0			0
$353$	−17.7629	+	5.21565i	−0.945421	+	0.277601i	−0.717879	−	0.696167i	$-0.754887\pi$
$353$	−17.7629	+	5.21565i	−0.945421	+	0.277601i	−0.227542	+	0.973768i	$0.573069\pi$
$354$		0			0
$355$	12.7069	−	27.8242i	0.674412	−	1.47676i
$356$		0			0
$357$	0.201404	−	1.40080i	0.0106595	−	0.0741381i
$358$		0			0
$359$	−21.8030	−	6.40194i	−1.15072	−	0.337882i	−0.349899	−	0.936787i	$-0.613784\pi$
$359$	−21.8030	−	6.40194i	−1.15072	−	0.337882i	−0.800820	+	0.598906i	$0.795602\pi$
$360$		0			0
$361$	2.48250	−	17.2662i	0.130658	−	0.908746i
$362$		0			0
$363$	0.426774	−	33.5566i	0.0223998	−	1.76126i
$364$		0			0
$365$	3.23845	−	22.5239i	0.169508	−	1.17896i
$366$		0			0
$367$	2.28230	+	0.670144i	0.119135	+	0.0349812i	0.340757	−	0.940152i	$-0.389317\pi$
$367$	2.28230	+	0.670144i	0.119135	+	0.0349812i	−0.221622	+	0.975133i	$0.571135\pi$
$368$		0			0
$369$	−10.3854	+	72.2319i	−0.540642	+	3.76024i
$370$		0			0
$371$	0.476141	−	1.04260i	0.0247200	−	0.0541293i
$372$		0			0
$373$	−24.3301	+	7.14395i	−1.25976	+	0.369900i	−0.842406	−	0.538843i	$-0.818862\pi$
$373$	−24.3301	+	7.14395i	−1.25976	+	0.369900i	−0.417357	+	0.908743i	$0.637043\pi$
$374$		0			0
$375$	25.9124	+	7.60857i	1.33811	+	0.392905i
$376$		0			0
$377$	10.9332	+	23.9405i	0.563091	+	1.23300i
$378$		0			0
$379$	11.0263	+	7.08620i	0.566385	+	0.363994i	0.792280	−	0.610158i	$-0.208894\pi$
$379$	11.0263	+	7.08620i	0.566385	+	0.363994i	−0.225894	+	0.974152i	$0.572530\pi$
$380$		0			0
$381$	0.248369	−	1.72744i	0.0127243	−	0.0884995i
$382$		0			0
$383$	4.81306	+	33.4756i	0.245936	+	1.71052i	0.621240	+	0.783620i	$0.286629\pi$
$383$	4.81306	+	33.4756i	0.245936	+	1.71052i	−0.375304	+	0.926902i	$0.622462\pi$
$384$		0			0
$385$	3.98271	−	0.839898i	0.202978	−	0.0428052i
$386$		0			0
$387$	12.8080	−	28.0457i	0.651069	−	1.42564i
$388$		0			0
$389$	−11.6157	+	25.4349i	−0.588940	+	1.28960i	0.347141	+	0.937813i	$0.387153\pi$
$389$	−11.6157	+	25.4349i	−0.588940	+	1.28960i	−0.936081	+	0.351785i	$0.885575\pi$
$390$		0			0
$391$	1.82215	−	0.535033i	0.0921503	−	0.0270578i
$392$		0			0
$393$	55.3635	−	16.2562i	2.79272	−	0.820016i
$394$		0			0
$395$	−0.214811	+	0.247905i	−0.0108083	+	0.0124734i
$396$		0			0
$397$	−0.688528	−	0.794604i	−0.0345562	−	0.0398800i	0.738208	−	0.674573i	$-0.235672\pi$
$397$	−0.688528	−	0.794604i	−0.0345562	−	0.0398800i	−0.772765	+	0.634693i	$0.781127\pi$
$398$		0			0
$399$	1.75271	+	0.514643i	0.0877455	+	0.0257644i
$400$		0			0
$401$	−17.0807	+	10.9771i	−0.852970	+	0.548170i	−0.892500	−	0.451048i	$-0.851050\pi$
$401$	−17.0807	+	10.9771i	−0.852970	+	0.548170i	0.0395301	+	0.999218i	$0.487414\pi$
$402$		0			0
$403$	23.3843			1.16486
$404$		0			0
$405$	12.6014	+	27.5932i	0.626169	+	1.37112i
$406$		0			0
$407$	−5.62093	+	10.1401i	−0.278619	+	0.502628i
$408$		0			0
$409$	3.44017	−	3.97017i	0.170105	−	0.196312i	−0.664296	−	0.747470i	$-0.731268\pi$
$409$	3.44017	−	3.97017i	0.170105	−	0.196312i	0.834401	+	0.551158i	$0.185814\pi$
$410$		0			0
$411$	−34.9726	−	22.4755i	−1.72507	−	1.10864i
$412$		0			0
$413$	−0.397132	−	0.458315i	−0.0195416	−	0.0225522i
$414$		0			0
$415$	−30.3623	−	19.5127i	−1.49043	−	0.957839i
$416$		0			0
$417$	−5.31253	+	36.9495i	−0.260156	+	1.80942i
$418$		0			0
$419$	2.62344	+	18.2464i	0.128163	+	0.891396i	0.947880	+	0.318627i	$0.103222\pi$
$419$	2.62344	+	18.2464i	0.128163	+	0.891396i	−0.819717	+	0.572769i	$0.805869\pi$
$420$		0			0
$421$	32.8625	−	21.1194i	1.60162	−	1.02930i	0.635193	−	0.772353i	$-0.280920\pi$
$421$	32.8625	−	21.1194i	1.60162	−	1.02930i	0.966426	−	0.256945i	$-0.0827160\pi$
$422$		0			0
$423$	4.75147	+	33.0472i	0.231024	+	1.60681i
$424$		0			0
$425$	0.211549	+	1.47135i	0.0102616	+	0.0713711i
$426$		0			0
$427$	−1.70395	−	1.96646i	−0.0824597	−	0.0951636i
$428$		0			0
$429$	−42.3518	+	22.7774i	−2.04476	+	1.09970i
$430$		0			0
$431$	−17.2618	+	11.0935i	−0.831470	+	0.534353i	−0.885745	−	0.464173i	$-0.846352\pi$
$431$	−17.2618	+	11.0935i	−0.831470	+	0.534353i	0.0542746	+	0.998526i	$0.482715\pi$
$432$		0			0
$433$	−8.56162	+	9.88064i	−0.411445	+	0.474833i	−0.923212	−	0.384291i	$-0.874446\pi$
$433$	−8.56162	+	9.88064i	−0.411445	+	0.474833i	0.511767	+	0.859125i	$0.328991\pi$
$434$		0			0
$435$	17.9461	−	39.2964i	0.860449	−	1.88412i
$436$		0			0
$437$	0.348854	+	2.42633i	0.0166880	+	0.116067i
$438$		0			0
$439$	−9.43003	−	20.6489i	−0.450071	−	0.985518i	−0.989639	−	0.143576i	$-0.954140\pi$
$439$	−9.43003	−	20.6489i	−0.450071	−	0.985518i	0.539568	−	0.841942i	$-0.318587\pi$
$440$		0			0
$441$	−17.7384	+	38.8417i	−0.844687	+	1.84961i
$442$		0			0
$443$	−0.0255541	+	0.177733i	−0.00121411	+	0.00844433i	−0.990419	−	0.138091i	$-0.955903\pi$
$443$	−0.0255541	+	0.177733i	−0.00121411	+	0.00844433i	0.989205	+	0.146536i	$0.0468123\pi$
$444$		0			0
$445$	30.5588	+	8.97287i	1.44863	+	0.425355i
$446$		0			0
$447$	13.1154	−	3.85104i	0.620339	−	0.182148i
$448$		0			0
$449$	−19.2523	−	12.3727i	−0.908572	−	0.583903i	0.000749057	−	1.00000i	$-0.499762\pi$
$449$	−19.2523	−	12.3727i	−0.908572	−	0.583903i	−0.909321	+	0.416096i	$0.863398\pi$
$450$		0			0
$451$	22.7990	+	30.8630i	1.07356	+	1.45328i
$452$		0			0
$453$	20.2181	−	5.93656i	0.949928	−	0.278924i
$454$		0			0
$455$	−3.81947	−	4.40790i	−0.179059	−	0.206646i
$456$		0			0
$457$	11.8547			0.554541			0.277271	−	0.960792i	$-0.410570\pi$
$457$	11.8547			0.554541			0.277271	+	0.960792i	$0.410570\pi$
$458$		0			0
$459$	6.38676	−	7.37072i	0.298109	−	0.344036i
$460$		0			0
$461$	21.3906	+	13.7469i	0.996261	+	0.640258i	0.933802	−	0.357789i	$-0.116469\pi$
$461$	21.3906	+	13.7469i	0.996261	+	0.640258i	0.0624588	+	0.998048i	$0.480106\pi$
$462$		0			0
$463$	18.4635	−	11.8658i	0.858072	−	0.551449i	−0.0360106	−	0.999351i	$-0.511465\pi$
$463$	18.4635	−	11.8658i	0.858072	−	0.551449i	0.894083	+	0.447902i	$0.147829\pi$
$464$		0			0
$465$	−25.1359	−	29.0084i	−1.16565	−	1.34523i
$466$		0			0
$467$	26.1037	−	30.1252i	1.20793	−	1.39403i	0.311858	−	0.950129i	$-0.399049\pi$
$467$	26.1037	−	30.1252i	1.20793	−	1.39403i	0.896076	−	0.443901i	$-0.146406\pi$
$468$		0			0
$469$	1.87733	+	4.11078i	0.0866871	+	0.189818i
$470$		0			0
$471$	60.8880	+	17.8783i	2.80557	+	0.823790i
$472$		0			0
$473$	−5.56871	−	15.2253i	−0.256050	−	0.700059i
$474$		0			0
$475$	−1.91872			−0.0880367
$476$		0			0
$477$	12.6719	−	8.14373i	0.580206	−	0.372876i
$478$		0			0
$479$	6.58966	+	14.4293i	0.301089	+	0.659293i	0.998344	−	0.0575304i	$-0.0183226\pi$
$479$	6.58966	+	14.4293i	0.301089	+	0.659293i	−0.697255	+	0.716823i	$0.745595\pi$
$480$		0			0
$481$	16.6133			0.757499
$482$		0			0
$483$	2.87725			0.130920
$484$		0			0
$485$	38.2354			1.73618
$486$		0			0
$487$	8.25996			0.374295			0.187147	−	0.982332i	$-0.440076\pi$
$487$	8.25996			0.374295			0.187147	+	0.982332i	$0.440076\pi$
$488$		0			0
$489$	10.5244	+	23.0452i	0.475930	+	1.04214i
$490$		0			0
$491$	20.0659	−	12.8956i	0.905562	−	0.581970i	−0.00287264	−	0.999996i	$-0.500914\pi$
$491$	20.0659	−	12.8956i	0.905562	−	0.581970i	0.908435	+	0.418026i	$0.137278\pi$
$492$		0			0
$493$	−5.35224			−0.241053
$494$		0			0
$495$	49.9993	+	19.0118i	2.24730	+	0.854517i
$496$		0			0
$497$	−5.50911	−	1.61762i	−0.247118	−	0.0725603i
$498$		0			0
$499$	17.7262	+	38.8150i	0.793535	+	1.73760i	0.666243	+	0.745735i	$0.267901\pi$
$499$	17.7262	+	38.8150i	0.793535	+	1.73760i	0.127293	+	0.991865i	$0.459371\pi$
$500$		0			0
$501$	−0.597281	+	0.689299i	−0.0266845	+	0.0307956i
$502$		0			0
$503$	23.9349	+	27.6223i	1.06720	+	1.23162i	0.971707	+	0.236188i	$0.0758981\pi$
$503$	23.9349	+	27.6223i	1.06720	+	1.23162i	0.0954955	+	0.995430i	$0.469556\pi$
$504$		0			0
$505$	5.00959	−	3.21947i	0.222924	−	0.143265i
$506$		0			0
$507$	24.6037	+	15.8119i	1.09269	+	0.702229i
$508$		0			0
$509$	−1.06659	+	1.23091i	−0.0472756	+	0.0545590i	−0.778895	−	0.627154i	$-0.784219\pi$
$509$	−1.06659	+	1.23091i	−0.0472756	+	0.0545590i	0.731619	+	0.681713i	$0.238765\pi$
$510$		0			0
$511$	−4.27140			−0.188956
$512$		0			0
$513$	8.24387	+	9.51393i	0.363976	+	0.420050i
$514$		0			0
$515$	−37.1869	+	10.9191i	−1.63865	+	0.481152i
$516$		0			0
$517$	13.9865	+	10.6096i	0.615125	+	0.466610i
$518$		0			0
$519$	−23.1062	−	14.8495i	−1.01425	−	0.651819i
$520$		0			0
$521$	16.2584	−	4.77391i	0.712295	−	0.209149i	0.0945420	−	0.995521i	$-0.469861\pi$
$521$	16.2584	−	4.77391i	0.712295	−	0.209149i	0.617753	+	0.786372i	$0.288043\pi$
$522$		0			0
$523$	23.9464	+	7.03131i	1.04710	+	0.307458i	0.759647	−	0.650336i	$-0.225372\pi$
$523$	23.9464	+	7.03131i	1.04710	+	0.307458i	0.287458	+	0.957793i	$0.407190\pi$
$524$		0			0
$525$	−0.320513	+	2.22921i	−0.0139883	+	0.0972909i
$526$		0			0
$527$	−1.97549	+	4.32573i	−0.0860539	+	0.188432i
$528$		0			0
$529$	−7.95062	−	17.4094i	−0.345679	−	0.756932i
$530$		0			0
$531$	−1.13422	−	7.88867i	−0.0492209	−	0.342339i
$532$		0			0
$533$	22.8407	−	50.0142i	0.989342	−	2.16636i
$534$		0			0
$535$	27.6873	−	31.9528i	1.19703	−	1.38144i
$536$		0			0
$537$	−43.0804	+	27.6861i	−1.85906	+	1.19474i
$538$		0			0
$539$	7.71237	+	21.0862i	0.332195	+	0.908246i
$540$		0			0
$541$	13.2227	+	15.2598i	0.568489	+	0.656072i	0.965090	−	0.261920i	$-0.0843556\pi$
$541$	13.2227	+	15.2598i	0.568489	+	0.656072i	−0.396600	+	0.917991i	$0.629810\pi$
$542$		0			0
$543$	−6.72894	−	46.8008i	−0.288767	−	2.00842i
$544$		0			0
$545$	2.41542	+	16.7996i	0.103465	+	0.719617i
$546$		0			0
$547$	0.423733	−	0.272317i	0.0181175	−	0.0116434i	−0.531551	−	0.847026i	$-0.678391\pi$
$547$	0.423733	−	0.272317i	0.0181175	−	0.0116434i	0.549668	+	0.835383i	$0.314754\pi$
$548$		0			0
$549$	−4.86651	−	33.8473i	−0.207698	−	1.44457i
$550$		0			0
$551$	0.983188	−	6.83822i	0.0418852	−	0.291318i
$552$		0			0
$553$	0.0517984	+	0.0332888i	0.00220269	+	0.00141558i
$554$		0			0
$555$	−17.8577	−	20.6088i	−0.758015	−	0.874796i
$556$		0			0
$557$	−31.9209	−	20.5143i	−1.35253	−	0.869220i	−0.354698	−	0.934981i	$-0.615416\pi$
$557$	−31.9209	−	20.5143i	−1.35253	−	0.869220i	−0.997835	+	0.0657605i	$0.979053\pi$
$558$		0			0
$559$	−15.2126	+	17.5563i	−0.643426	+	0.742553i
$560$		0			0
$561$	−0.635610	−	9.75864i	−0.0268355	−	0.412010i
$562$		0			0
$563$	−1.02755	−	2.25002i	−0.0433061	−	0.0948272i	0.886742	−	0.462264i	$-0.152963\pi$
$563$	−1.02755	−	2.25002i	−0.0433061	−	0.0948272i	−0.930049	+	0.367437i	$0.880235\pi$
$564$		0			0
$565$	35.5696			1.49642
$566$		0			0
$567$	4.79012	−	3.07843i	0.201166	−	0.129282i
$568$		0			0
$569$	25.0995	+	7.36989i	1.05223	+	0.308962i	0.761717	−	0.647910i	$-0.224357\pi$
$569$	25.0995	+	7.36989i	1.05223	+	0.308962i	0.290510	+	0.956872i	$0.406175\pi$
$570$		0			0
$571$	8.15545	+	9.41189i	0.341295	+	0.393876i	0.900286	−	0.435298i	$-0.143357\pi$
$571$	8.15545	+	9.41189i	0.341295	+	0.393876i	−0.558991	+	0.829173i	$0.688812\pi$
$572$		0			0
$573$	−45.1202	+	52.0715i	−1.88492	+	2.17532i
$574$		0			0
$575$	−2.89975	+	0.851444i	−0.120928	+	0.0355077i
$576$		0			0
$577$	3.82990	−	1.12456i	0.159441	−	0.0468161i	−0.201038	−	0.979583i	$-0.564431\pi$
$577$	3.82990	−	1.12456i	0.159441	−	0.0468161i	0.360479	+	0.932767i	$0.382613\pi$
$578$		0			0
$579$	−21.8361	+	47.8143i	−0.907476	+	1.98710i
$580$		0			0
$581$	−2.81432	+	6.16249i	−0.116758	+	0.255663i
$582$		0			0
$583$	1.73276	−	7.72846i	0.0717638	−	0.320080i
$584$		0			0
$585$	−10.9085	−	75.8702i	−0.451011	−	3.13685i
$586$		0			0
$587$	−1.60113	+	11.1361i	−0.0660858	+	0.459637i	0.929729	+	0.368244i	$0.120041\pi$
$587$	−1.60113	+	11.1361i	−0.0660858	+	0.459637i	−0.995815	+	0.0913927i	$0.970868\pi$
$588$		0			0
$589$	−5.16382	−	3.31859i	−0.212771	−	0.136740i
$590$		0			0
$591$	17.4185	+	38.1411i	0.716500	+	1.56892i
$592$		0			0
$593$	−28.4381	−	8.35017i	−1.16781	−	0.342900i	−0.360348	−	0.932818i	$-0.617342\pi$
$593$	−28.4381	−	8.35017i	−1.16781	−	0.342900i	−0.807463	+	0.589918i	$0.799160\pi$
$594$		0			0
$595$	1.13806	−	0.334164i	0.0466558	−	0.0136994i
$596$		0			0
$597$	32.8178	−	71.8609i	1.34314	−	2.94107i
$598$		0			0
$599$	0.302659	−	2.10504i	0.0123663	−	0.0860096i	−0.982704	−	0.185185i	$-0.940711\pi$
$599$	0.302659	−	2.10504i	0.0123663	−	0.0860096i	0.995070	+	0.0991757i	$0.0316206\pi$
$600$		0			0
$601$	19.0371	+	5.58979i	0.776538	+	0.228012i	0.645904	−	0.763419i	$-0.276481\pi$
$601$	19.0371	+	5.58979i	0.776538	+	0.228012i	0.130634	+	0.991431i	$0.458299\pi$
$602$		0			0
$603$	−8.45220	+	58.7863i	−0.344200	+	2.39397i
$604$		0			0
$605$	25.7313	−	11.3579i	1.04613	−	0.461764i
$606$		0			0
$607$	−3.76741	+	26.2029i	−0.152914	+	1.06354i	0.758387	+	0.651804i	$0.225988\pi$
$607$	−3.76741	+	26.2029i	−0.152914	+	1.06354i	−0.911302	+	0.411739i	$0.864922\pi$
$608$		0			0
$609$	−7.78059	−	2.28459i	−0.315285	−	0.0925761i
$610$		0			0
$611$	3.58000	−	24.8995i	0.144831	−	1.00732i
$612$		0			0
$613$	3.88839	−	8.51438i	0.157051	−	0.343893i	−0.814708	−	0.579872i	$-0.803103\pi$
$613$	3.88839	−	8.51438i	0.157051	−	0.343893i	0.971758	+	0.235979i	$0.0758298\pi$
$614$		0			0
$615$	−86.5945	+	25.4264i	−3.49183	+	1.02529i
$616$		0			0
$617$	1.00373	+	0.294722i	0.0404086	+	0.0118650i	0.301874	−	0.953348i	$-0.402388\pi$
$617$	1.00373	+	0.294722i	0.0404086	+	0.0118650i	−0.261466	+	0.965213i	$0.584206\pi$
$618$		0			0
$619$	6.97651	+	15.2764i	0.280410	+	0.614012i	0.996463	−	0.0840340i	$-0.0267804\pi$
$619$	6.97651	+	15.2764i	0.280410	+	0.614012i	−0.716053	+	0.698046i	$0.754053\pi$
$620$		0			0
$621$	16.6808	+	10.7201i	0.669379	+	0.430184i
$622$		0			0
$623$	0.850800	−	5.91745i	0.0340866	−	0.237077i
$624$		0			0
$625$	4.31565	+	30.0160i	0.172626	+	1.20064i
$626$		0			0
$627$	12.5848	+	0.980549i	0.502587	+	0.0391593i
$628$		0			0
$629$	−1.40348	+	3.07319i	−0.0559604	+	0.122536i
$630$		0			0
$631$	3.28047	−	7.18323i	0.130593	−	0.285960i	−0.833028	−	0.553231i	$-0.813395\pi$
$631$	3.28047	−	7.18323i	0.130593	−	0.285960i	0.963621	+	0.267271i	$0.0861220\pi$
$632$		0			0
$633$	52.9455	−	15.5462i	2.10440	−	0.617906i
$634$		0			0
$635$	1.40343	−	0.412085i	0.0556936	−	0.0163531i
$636$		0			0
$637$	21.0687	−	24.3146i	0.834772	−	0.963378i
$638$		0			0
$639$	−49.4140	−	57.0268i	−1.95479	−	2.25594i
$640$		0			0
$641$	−40.2522	−	11.8191i	−1.58987	−	0.466827i	−0.637164	−	0.770729i	$-0.719892\pi$
$641$	−40.2522	−	11.8191i	−1.58987	−	0.466827i	−0.952703	+	0.303901i	$0.901711\pi$
$642$		0			0
$643$	−4.75758	+	3.05751i	−0.187621	+	0.120576i	−0.631079	−	0.775718i	$-0.717388\pi$
$643$	−4.75758	+	3.05751i	−0.187621	+	0.120576i	0.443459	+	0.896295i	$0.353751\pi$
$644$		0			0
$645$	38.1308			1.50140
$646$		0			0
$647$	19.4497	+	42.5889i	0.764647	+	1.67434i	0.738096	+	0.674696i	$0.235725\pi$
$647$	19.4497	+	42.5889i	0.764647	+	1.67434i	0.0265506	+	0.999647i	$0.491548\pi$
$648$		0			0
$649$	−3.33871	−	2.53261i	−0.131056	−	0.0994137i
$650$		0			0
$651$	−4.71821	+	5.44511i	−0.184921	+	0.213411i
$652$		0			0
$653$	5.70297	+	3.66507i	0.223174	+	0.143425i	0.647451	−	0.762107i	$-0.275835\pi$
$653$	5.70297	+	3.66507i	0.223174	+	0.143425i	−0.424276	+	0.905533i	$0.639472\pi$
$654$		0			0
$655$	31.6690	+	36.5480i	1.23741	+	1.42805i
$656$		0			0
$657$	−47.2235	−	30.3487i	−1.84236	−	1.18401i
$658$		0			0
$659$	4.96147	−	34.5078i	0.193272	−	1.34423i	−0.630004	−	0.776592i	$-0.716947\pi$
$659$	4.96147	−	34.5078i	0.193272	−	1.34423i	0.823276	−	0.567642i	$-0.192144\pi$
$660$		0			0
$661$	1.93134	+	13.4328i	0.0751206	+	0.522475i	0.992286	+	0.123969i	$0.0395622\pi$
$661$	1.93134	+	13.4328i	0.0751206	+	0.522475i	−0.917166	+	0.398506i	$0.869529\pi$
$662$		0			0
$663$	−11.7886	+	7.57607i	−0.457831	+	0.294230i
$664$		0			0
$665$	0.217883	+	1.51541i	0.00844914	+	0.0587651i
$666$		0			0
$667$	−1.54862	−	10.7709i	−0.0599628	−	0.417051i
$668$		0			0
$669$	11.2603	+	12.9951i	0.435349	+	0.502420i
$670$		0			0
$671$	−14.3251	−	10.8665i	−0.553016	−	0.419496i
$672$		0			0
$673$	−24.6364	+	15.8329i	−0.949665	+	0.610313i	−0.921120	−	0.389280i	$-0.872724\pi$
$673$	−24.6364	+	15.8329i	−0.949665	+	0.610313i	−0.0285455	+	0.999592i	$0.509088\pi$
$674$		0			0
$675$	−10.1638	+	11.7297i	−0.391205	+	0.451475i
$676$		0			0
$677$	20.9918	−	45.9656i	0.806780	−	1.76660i	0.186112	−	0.982529i	$-0.440411\pi$
$677$	20.9918	−	45.9656i	0.806780	−	1.76660i	0.620668	−	0.784073i	$-0.286861\pi$
$678$		0			0
$679$	−1.02141	−	7.10404i	−0.0391980	−	0.272628i
$680$		0			0
$681$	−0.101308	−	0.221834i	−0.00388213	−	0.00850069i
$682$		0			0
$683$	−0.817910	+	1.79097i	−0.0312965	+	0.0685297i	−0.924635	−	0.380855i	$-0.875630\pi$
$683$	−0.817910	+	1.79097i	−0.0312965	+	0.0685297i	0.893338	+	0.449385i	$0.148357\pi$
$684$		0			0
$685$	4.95856	−	34.4875i	0.189457	−	1.31770i
$686$		0			0
$687$	−58.4443	−	17.1608i	−2.22979	−	0.654726i
$688$		0			0
$689$	−10.8896	+	3.19747i	−0.414861	+	0.121814i
$690$		0			0
$691$	−7.93629	−	5.10034i	−0.301911	−	0.194026i	0.380910	−	0.924612i	$-0.375611\pi$
$691$	−7.93629	−	5.10034i	−0.301911	−	0.194026i	−0.682821	+	0.730586i	$0.739247\pi$
$692$		0			0
$693$	2.19668	−	9.79762i	0.0834450	−	0.372181i
$694$		0			0
$695$	−30.0191	+	8.81439i	−1.13869	+	0.334349i
$696$		0			0
$697$	7.32227	+	8.45035i	0.277351	+	0.320080i
$698$		0			0
$699$	−65.1519			−2.46427
$700$		0			0
$701$	19.4558	−	22.4532i	0.734835	−	0.848045i	−0.258172	−	0.966099i	$-0.583120\pi$
$701$	19.4558	−	22.4532i	0.734835	−	0.848045i	0.993007	+	0.118054i	$0.0376655\pi$
$702$		0			0
$703$	−3.66861	−	2.35767i	−0.138364	−	0.0889212i
$704$		0			0
$705$	−34.7361	+	22.3235i	−1.30824	+	0.840752i
$706$		0			0
$707$	−0.731994	−	0.844766i	−0.0275295	−	0.0317707i
$708$		0			0
$709$	−0.945176	+	1.09079i	−0.0354968	+	0.0409655i	−0.773220	−	0.634137i	$-0.781355\pi$
$709$	−0.945176	+	1.09079i	−0.0354968	+	0.0409655i	0.737724	+	0.675103i	$0.235901\pi$
$710$		0			0
$711$	0.336150	+	0.736065i	0.0126066	+	0.0276046i
$712$		0			0
$713$	−9.27672	−	2.72389i	−0.347416	−	0.102011i
$714$		0			0
$715$	−32.1104	−	24.3577i	−1.20086	−	0.910926i
$716$		0			0
$717$	−75.2951			−2.81195
$718$		0			0
$719$	29.1358	−	18.7244i	1.08658	−	0.698303i	0.130512	−	0.991447i	$-0.458338\pi$
$719$	29.1358	−	18.7244i	1.08658	−	0.698303i	0.956068	+	0.293144i	$0.0947016\pi$
$720$		0			0
$721$	3.02213	+	6.61755i	0.112550	+	0.246450i
$722$		0			0
$723$	63.2769			2.35329
$724$		0			0
$725$	8.51749			0.316332
$726$		0			0
$727$	23.7731			0.881695			0.440848	−	0.897582i	$-0.354678\pi$
$727$	23.7731			0.881695			0.440848	+	0.897582i	$0.354678\pi$
$728$		0			0
$729$	−17.5285			−0.649205
$730$		0			0
$731$	−1.96249	−	4.29725i	−0.0725852	−	0.158939i
$732$		0			0
$733$	−37.9742	+	24.4045i	−1.40261	+	0.901403i	−0.999903	−	0.0139264i	$-0.995567\pi$
$733$	−37.9742	+	24.4045i	−1.40261	+	0.901403i	−0.402707	+	0.915329i	$0.631931\pi$
$734$		0			0
$735$	−52.8092			−1.94790
$736$		0			0
$737$	18.5551	+	25.1180i	0.683485	+	0.925235i
$738$		0			0
$739$	22.4565	+	6.59383i	0.826076	+	0.242558i	0.667330	−	0.744762i	$-0.267437\pi$
$739$	22.4565	+	6.59383i	0.826076	+	0.242558i	0.158746	+	0.987320i	$0.449255\pi$
$740$		0			0
$741$	−7.51394	−	16.4532i	−0.276032	−	0.604425i
$742$		0			0
$743$	−0.0640747	+	0.0739461i	−0.00235067	+	0.00271282i	−0.756924	−	0.653503i	$-0.773299\pi$
$743$	−0.0640747	+	0.0739461i	−0.00235067	+	0.00271282i	0.754573	+	0.656216i	$0.227844\pi$
$744$		0			0
$745$	7.50229	+	8.65810i	0.274863	+	0.317208i
$746$		0			0
$747$	−74.8994	+	48.1349i	−2.74043	+	1.76117i
$748$		0			0
$749$	−6.67638	−	4.29065i	−0.243950	−	0.156777i
$750$		0			0
$751$	31.5119	−	36.3667i	1.14989	−	1.32704i	0.213142	−	0.977021i	$-0.431630\pi$
$751$	31.5119	−	36.3667i	1.14989	−	1.32704i	0.936743	−	0.350017i	$-0.113824\pi$
$752$		0			0
$753$	−4.31367			−0.157199
$754$		0			0
$755$	11.5651	+	13.3469i	0.420899	+	0.485743i
$756$		0			0
$757$	−20.0557	+	5.88888i	−0.728937	+	0.214035i	−0.625084	−	0.780558i	$-0.714935\pi$
$757$	−20.0557	+	5.88888i	−0.728937	+	0.214035i	−0.103853	+	0.994593i	$0.533117\pi$
$758$		0			0
$759$	19.4545	−	4.10268i	0.706152	−	0.148918i
$760$		0			0
$761$	−7.55249	−	4.85369i	−0.273778	−	0.175946i	0.396547	−	0.918015i	$-0.370209\pi$
$761$	−7.55249	−	4.85369i	−0.273778	−	0.175946i	−0.670324	+	0.742068i	$0.733845\pi$
$762$		0			0
$763$	3.05680	−	0.897559i	0.110664	−	0.0324938i
$764$		0			0
$765$	14.9563	+	4.39158i	0.540748	+	0.158778i
$766$		0			0
$767$	−0.854580	+	5.94373i	−0.0308571	+	0.214616i
$768$		0			0
$769$	−18.6969	+	40.9406i	−0.674229	+	1.47636i	0.194416	+	0.980919i	$0.437719\pi$
$769$	−18.6969	+	40.9406i	−0.674229	+	1.47636i	−0.868645	+	0.495436i	$0.835008\pi$
$770$		0			0
$771$	−15.9397	−	34.9030i	−0.574053	−	1.25700i
$772$		0			0
$773$	−3.52873	−	24.5429i	−0.126920	−	0.882745i	−0.949426	−	0.313990i	$-0.898334\pi$
$773$	−3.52873	−	24.5429i	−0.126920	−	0.882745i	0.822507	−	0.568755i	$-0.192575\pi$
$774$		0			0
$775$	3.14378	−	6.88391i	0.112928	−	0.247277i
$776$		0			0
$777$	−3.35203	+	3.86844i	−0.120253	+	0.138780i
$778$		0			0
$779$	−12.1416	+	7.80290i	−0.435016	+	0.279568i
$780$		0			0
$781$	−39.5563	−	3.08205i	−1.41543	−	0.110284i
$782$		0			0
$783$	−36.5959	−	42.2339i	−1.30783	−	1.50932i
$784$		0			0
$785$	7.56909	+	52.6442i	0.270153	+	1.87895i
$786$		0			0
$787$	5.92311	+	41.1962i	0.211136	+	1.46848i	0.769371	+	0.638802i	$0.220570\pi$
$787$	5.92311	+	41.1962i	0.211136	+	1.46848i	−0.558235	+	0.829683i	$0.688521\pi$
$788$		0			0
$789$	−20.8959	+	13.4290i	−0.743913	+	0.478084i
$790$		0			0
$791$	−0.950194	−	6.60874i	−0.0337850	−	0.234980i
$792$		0			0
$793$	−3.66668	+	25.5023i	−0.130208	+	0.905615i
$794$		0			0
$795$	15.6718	+	10.0716i	0.555820	+	0.357204i
$796$		0			0
$797$	−5.84645	−	6.74716i	−0.207092	−	0.238997i	0.642696	−	0.766121i	$-0.277816\pi$
$797$	−5.84645	−	6.74716i	−0.207092	−	0.238997i	−0.849788	+	0.527124i	$0.823270\pi$
$798$		0			0
$799$	4.30357	+	2.76574i	0.152249	+	0.0978447i
$800$		0			0
$801$	51.4502	−	59.3767i	1.81790	−	2.09797i
$802$		0			0
$803$	−28.8809	+	6.09059i	−1.01919	+	0.214932i
$804$		0			0
$805$	1.00176	+	2.19355i	0.0353074	+	0.0773125i
$806$		0			0
$807$	−7.52934			−0.265045
$808$		0			0
$809$	3.82308	−	2.45694i	0.134412	−	0.0863815i	−0.471707	−	0.881756i	$-0.656362\pi$
$809$	3.82308	−	2.45694i	0.134412	−	0.0863815i	0.606119	+	0.795374i	$0.292726\pi$
$810$		0			0
$811$	39.8706	+	11.7071i	1.40005	+	0.411091i	0.892700	−	0.450652i	$-0.148808\pi$
$811$	39.8706	+	11.7071i	1.40005	+	0.411091i	0.507346	+	0.861742i	$0.330627\pi$
$812$		0			0
$813$	8.26478	+	9.53806i	0.289858	+	0.334514i
$814$		0			0
$815$	−13.9049	+	16.0471i	−0.487068	+	0.562106i
$816$		0			0
$817$	5.85082	−	1.71796i	0.204694	−	0.0601037i
$818$		0			0
$819$	−13.8051	+	4.05354i	−0.482389	+	0.141642i
$820$		0			0
$821$	8.37900	−	18.3475i	0.292429	−	0.640331i	−0.705210	−	0.708998i	$-0.749147\pi$
$821$	8.37900	−	18.3475i	0.292429	−	0.640331i	0.997640	+	0.0686675i	$0.0218747\pi$
$822$		0			0
$823$	16.3482	−	35.7975i	0.569861	−	1.24782i	−0.377010	−	0.926209i	$-0.623048\pi$
$823$	16.3482	−	35.7975i	0.569861	−	1.24782i	0.946871	−	0.321613i	$-0.104225\pi$
$824$		0			0
$825$	1.01150	+	15.5298i	0.0352159	+	0.540677i
$826$		0			0
$827$	−2.12186	−	14.7579i	−0.0737844	−	0.513182i	−0.992877	−	0.119141i	$-0.961986\pi$
$827$	−2.12186	−	14.7579i	−0.0737844	−	0.513182i	0.919093	−	0.394041i	$-0.128923\pi$
$828$		0			0
$829$	3.51786	−	24.4672i	0.122180	−	0.849783i	−0.832897	−	0.553427i	$-0.813320\pi$
$829$	3.51786	−	24.4672i	0.122180	−	0.849783i	0.955078	−	0.296355i	$-0.0957713\pi$
$830$		0			0
$831$	58.2116	+	37.4103i	2.01934	+	1.29775i
$832$		0			0
$833$	2.71794	+	5.95146i	0.0941710	+	0.206206i
$834$		0			0
$835$	−0.733458	−	0.215363i	−0.0253824	−	0.00745293i
$836$		0			0
$837$	−47.6412	+	13.9887i	−1.64672	+	0.483521i
$838$		0			0
$839$	10.7371	−	23.5110i	0.370686	−	0.811690i	−0.628733	−	0.777621i	$-0.716426\pi$
$839$	10.7371	−	23.5110i	0.370686	−	0.811690i	0.999419	−	0.0340688i	$-0.0108465\pi$
$840$		0			0
$841$	−0.237400	+	1.65115i	−0.00818622	+	0.0569364i
$842$		0			0
$843$	26.0370	+	7.64515i	0.896761	+	0.263313i
$844$		0			0
$845$	−3.48841	+	24.2624i	−0.120005	+	0.834654i
$846$		0			0
$847$	−2.79764	−	4.47741i	−0.0961282	−	0.153845i
$848$		0			0
$849$	−5.40072	+	37.5628i	−0.185352	+	1.28915i
$850$		0			0
$851$	−6.59059	−	1.93517i	−0.225923	−	0.0663369i
$852$		0			0
$853$	−4.32114	+	30.0542i	−0.147953	+	1.02904i	0.771611	+	0.636095i	$0.219451\pi$
$853$	−4.32114	+	30.0542i	−0.147953	+	1.02904i	−0.919564	+	0.392940i	$0.871458\pi$
$854$		0			0
$855$	−8.35827	+	18.3021i	−0.285847	+	0.625917i
$856$		0			0
$857$	−10.7497	+	3.15638i	−0.367201	+	0.107820i	−0.460127	−	0.887853i	$-0.652196\pi$
$857$	−10.7497	+	3.15638i	−0.367201	+	0.107820i	0.0929260	+	0.995673i	$0.470378\pi$
$858$		0			0
$859$	−50.5596	−	14.8456i	−1.72507	−	0.506527i	−0.739122	−	0.673571i	$-0.764759\pi$
$859$	−50.5596	−	14.8456i	−1.72507	−	0.506527i	−0.985949	+	0.167044i	$0.946578\pi$
$860$		0			0
$861$	7.03742	+	15.4098i	0.239835	+	0.525165i
$862$		0			0
$863$	−30.7414	−	19.7563i	−1.04645	−	0.672511i	−0.0998747	−	0.995000i	$-0.531844\pi$
$863$	−30.7414	−	19.7563i	−1.04645	−	0.672511i	−0.946573	+	0.322489i	$0.895481\pi$
$864$		0			0
$865$	3.27609	−	22.7857i	0.111390	−	0.774738i
$866$		0			0
$867$	6.97551	+	48.5157i	0.236901	+	1.64768i
$868$		0			0
$869$	0.397700	+	0.151222i	0.0134910	+	0.00512985i
$870$		0			0
$871$	18.5891	−	40.7044i	0.629866	−	1.37921i
$872$		0			0
$873$	39.1824	−	85.7976i	1.32612	−	2.90381i
$874$		0			0
$875$	4.07656	−	1.19699i	0.137813	−	0.0404656i
$876$		0			0
$877$	11.2387	−	3.29997i	0.379503	−	0.111432i	−0.0864169	−	0.996259i	$-0.527542\pi$
$877$	11.2387	−	3.29997i	0.379503	−	0.111432i	0.465920	+	0.884827i	$0.345724\pi$
$878$		0			0
$879$	58.0665	−	67.0123i	1.95853	−	2.26027i
$880$		0			0
$881$	−17.6227	−	20.3377i	−0.593725	−	0.685195i	0.376772	−	0.926306i	$-0.377034\pi$
$881$	−17.6227	−	20.3377i	−0.593725	−	0.685195i	−0.970498	+	0.241110i	$0.922488\pi$
$882$		0			0
$883$	−38.9345	−	11.4322i	−1.31025	−	0.384724i	−0.449286	−	0.893388i	$-0.648322\pi$
$883$	−38.9345	−	11.4322i	−1.31025	−	0.384724i	−0.860965	+	0.508664i	$0.830140\pi$
$884$		0			0
$885$	8.29182	−	5.32883i	0.278727	−	0.179127i
$886$		0			0
$887$	−17.9996			−0.604368			−0.302184	−	0.953250i	$-0.597716\pi$
$887$	−17.9996			−0.604368			−0.302184	+	0.953250i	$0.597716\pi$
$888$		0			0
$889$	−0.114055	−	0.249746i	−0.00382529	−	0.00837622i
$890$		0			0
$891$	27.9987	−	27.6449i	0.937993	−	0.926139i
$892$		0			0
$893$	−4.32416	+	4.99034i	−0.144702	+	0.166995i
$894$		0			0
$895$	−36.1063	−	23.2041i	−1.20690	−	0.775628i
$896$		0			0
$897$	−18.6571	−	21.5314i	−0.622941	−	0.718913i
$898$		0			0
$899$	22.9230	+	14.7317i	0.764526	+	0.491331i
$900$		0			0
$901$	0.328465	−	2.28452i	0.0109428	−	0.0761085i
$902$		0			0
$903$	−1.01861	−	7.08461i	−0.0338973	−	0.235761i
$904$		0			0
$905$	33.3371	−	21.4244i	1.10816	−	0.712172i
$906$		0			0
$907$	−0.497282	−	3.45867i	−0.0165120	−	0.114843i	0.979898	−	0.199497i	$-0.0639307\pi$
$907$	−0.497282	−	3.45867i	−0.0165120	−	0.114843i	−0.996410	+	0.0846536i	$0.973022\pi$
$908$		0			0
$909$	−2.09059	−	14.5404i	−0.0693406	−	0.482274i
$910$		0			0
$911$	14.4933	+	16.7262i	0.480184	+	0.554162i	0.943216	−	0.332179i	$-0.107784\pi$
$911$	14.4933	+	16.7262i	0.480184	+	0.554162i	−0.463032	+	0.886342i	$0.653238\pi$
$912$		0			0
$913$	−10.2418	+	45.6804i	−0.338954	+	1.51180i
$914$		0			0
$915$	35.5771	−	22.8640i	1.17614	−	0.755861i
$916$		0			0
$917$	5.94453	−	6.86035i	0.196306	−	0.226549i
$918$		0			0
$919$	−5.50575	+	12.0559i	−0.181618	+	0.397688i	−0.978441	−	0.206524i	$-0.933785\pi$
$919$	−5.50575	+	12.0559i	−0.181618	+	0.397688i	0.796824	+	0.604212i	$0.206512\pi$
$920$		0			0
$921$	−5.91188	−	41.1180i	−0.194803	−	1.35488i
$922$		0			0
$923$	23.6178	+	51.7157i	0.777388	+	1.70224i
$924$		0			0
$925$	2.23348	−	4.89064i	0.0734363	−	0.160803i
$926$		0			0
$927$	−13.6064	+	94.6344i	−0.446892	+	3.10820i
$928$		0			0
$929$	27.3522	+	8.03134i	0.897398	+	0.263500i	0.697727	−	0.716363i	$-0.254195\pi$
$929$	27.3522	+	8.03134i	0.897398	+	0.263500i	0.199670	+	0.979863i	$0.436013\pi$
$930$		0			0
$931$	−8.10307	+	2.37928i	−0.265567	+	0.0779776i
$932$		0			0
$933$	64.4310	+	41.4073i	2.10938	+	1.35561i
$934$		0			0
$935$	7.21846	−	3.88220i	0.236069	−	0.126961i
$936$		0			0
$937$	−21.8577	+	6.41799i	−0.714059	+	0.209667i	−0.618531	−	0.785760i	$-0.712272\pi$
$937$	−21.8577	+	6.41799i	−0.714059	+	0.209667i	−0.0955278	+	0.995427i	$0.530454\pi$
$938$		0			0
$939$	−7.26733	−	8.38695i	−0.237160	−	0.273698i
$940$		0			0
$941$	10.5607			0.344268			0.172134	−	0.985074i	$-0.444934\pi$
$941$	10.5607			0.344268			0.172134	+	0.985074i	$0.444934\pi$
$942$		0			0
$943$	−14.8869	+	17.1804i	−0.484785	+	0.559472i
$944$		0			0
$945$	10.4183	+	6.69544i	0.338908	+	0.217803i
$946$		0			0
$947$	−6.93113	+	4.45437i	−0.225231	+	0.144747i	−0.648390	−	0.761308i	$-0.724558\pi$
$947$	−6.93113	+	4.45437i	−0.225231	+	0.144747i	0.423159	+	0.906055i	$0.360921\pi$
$948$		0			0
$949$	27.6972	+	31.9642i	0.899088	+	1.03760i
$950$		0			0
$951$	53.0782	−	61.2556i	1.72118	−	1.98635i
$952$		0			0
$953$	8.73587	+	19.1289i	0.282983	+	0.619645i	0.996734	−	0.0807536i	$-0.0257327\pi$
$953$	8.73587	+	19.1289i	0.282983	+	0.619645i	−0.713752	+	0.700399i	$0.753005\pi$
$954$		0			0
$955$	−55.4074	−	16.2691i	−1.79294	−	0.526455i
$956$		0			0
$957$	−55.8658	−	4.35282i	−1.80588	−	0.140707i
$958$		0			0
$959$	−6.54016			−0.211193
$960$		0			0
$961$	−5.71172	+	3.67070i	−0.184249	+	0.118410i
$962$		0			0
$963$	−43.3269	−	94.8726i	−1.39619	−	3.05723i
$964$		0			0
$965$	−44.0551			−1.41818
$966$		0			0
$967$	31.2016			1.00338			0.501689	−	0.865048i	$-0.332712\pi$
$967$	31.2016			1.00338			0.501689	+	0.865048i	$0.332712\pi$
$968$		0			0
$969$	3.67836			0.118166
$970$		0			0
$971$	−11.1431			−0.357598			−0.178799	−	0.983886i	$-0.557221\pi$
$971$	−11.1431			−0.357598			−0.178799	+	0.983886i	$0.557221\pi$
$972$		0			0
$973$	2.43961	+	5.34200i	0.0782103	+	0.171257i
$974$		0			0
$975$	18.7602	−	12.0565i	0.600808	−	0.386116i
$976$		0			0
$977$	39.1185			1.25151			0.625756	−	0.780019i	$-0.284791\pi$
$977$	39.1185			1.25151			0.625756	+	0.780019i	$0.284791\pi$
$978$		0			0
$979$	−2.68503	−	41.2238i	−0.0858139	−	1.31752i
$980$		0			0
$981$	40.1725	+	11.7957i	1.28261	+	0.376608i
$982$		0			0
$983$	−11.2830	−	24.7062i	−0.359870	−	0.788006i	−0.999808	−	0.0195796i	$-0.993767\pi$
$983$	−11.2830	−	24.7062i	−0.359870	−	0.788006i	0.639938	−	0.768427i	$-0.278960\pi$
$984$		0			0
$985$	−23.0134	+	26.5589i	−0.733267	+	0.846236i
$986$		0			0
$987$	5.07558	+	5.85753i	0.161557	+	0.186447i
$988$		0			0
$989$	8.07998	−	5.19269i	0.256929	−	0.165118i
$990$		0			0
$991$	13.5494	+	8.70769i	0.430412	+	0.276609i	0.737857	−	0.674957i	$-0.235838\pi$
$991$	13.5494	+	8.70769i	0.430412	+	0.276609i	−0.307445	+	0.951566i	$0.599474\pi$
$992$		0			0
$993$	−8.24787	+	9.51855i	−0.261738	+	0.302062i
$994$		0			0
$995$	66.2111			2.09903
$996$		0			0
$997$	9.73293	+	11.2324i	0.308245	+	0.355734i	0.888643	−	0.458599i	$-0.151649\pi$
$997$	9.73293	+	11.2324i	0.308245	+	0.355734i	−0.580398	+	0.814333i	$0.697103\pi$
$998$		0			0
$999$	−33.8464	+	9.93821i	−1.07085	+	0.314431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.q.b.89.16	✓	170
121.34	even	11	inner	968.2.q.b.881.16	yes	170

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
968.2.q.b.89.16	✓	170	1.1	even	1	trivial
968.2.q.b.881.16	yes	170	121.34	even	11	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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+3.05084 q^{3} +(1.06220 + 2.32589i) q^{5} +(0.403770 - 0.259487i) q^{7} +6.30765 q^{9} +(2.36007 - 2.33025i) q^{11} +(-4.56000 - 1.33894i) q^{13} +(3.24060 + 7.09593i) q^{15} +(0.632909 - 0.730416i) q^{17} +(0.816943 + 0.942802i) q^{19} +(1.23184 - 0.791654i) q^{21} +(1.65302 + 1.06233i) q^{23} +(-1.00720 + 1.16237i) q^{25} +10.0911 q^{27} +(-3.62654 - 4.18525i) q^{29} +(-4.72110 + 1.38624i) q^{31} +(7.20021 - 7.10922i) q^{33} +(1.03242 + 0.663498i) q^{35} +(-3.35408 + 0.984847i) q^{37} +(-13.9119 - 4.08489i) q^{39} +(-1.64647 + 11.4515i) q^{41} +(2.03055 - 4.44629i) q^{43} +(6.69998 + 14.6709i) q^{45} +(0.753286 + 5.23922i) q^{47} +(-2.81221 + 6.15788i) q^{49} +(1.93091 - 2.22838i) q^{51} +(2.00897 - 1.29109i) q^{53} +(7.92677 + 3.01409i) q^{55} +(2.49236 + 2.87634i) q^{57} +(-0.179816 - 1.25065i) q^{59} +(-0.771525 - 5.36608i) q^{61} +(2.54684 - 1.63675i) q^{63} +(-1.72941 - 12.0283i) q^{65} +(-1.33999 + 9.31985i) q^{67} +(5.04311 + 3.24101i) q^{69} +(-7.83397 - 9.04089i) q^{71} +(-7.48670 - 4.81141i) q^{73} +(-3.07282 + 3.54622i) q^{75} +(0.348257 - 1.55329i) q^{77} +(0.0532924 + 0.116694i) q^{79} +11.8635 q^{81} +(-11.8744 + 7.63120i) q^{83} +(2.37114 + 0.696230i) q^{85} +(-11.0640 - 12.7686i) q^{87} +(8.15680 - 9.41345i) q^{89} +(-2.18863 + 0.642639i) q^{91} +(-14.4033 + 4.22920i) q^{93} +(-1.32510 + 2.90156i) q^{95} +(6.21189 - 13.6021i) q^{97} +(14.8865 - 14.6984i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 170 q + 10 q^{3} - 3 q^{5} + 2 q^{7} + 180 q^{9} + 2 q^{11} + 3 q^{13} + 10 q^{15} - 6 q^{17} + 9 q^{19} + 16 q^{21} + 23 q^{23} - 18 q^{25} - 26 q^{27} + q^{29} - 38 q^{31} + q^{33} - 10 q^{35} - 24 q^{37}+ \cdots - 74 q^{99}+O(q^{100}) \) 170 * q + 10 * q^3 - 3 * q^5 + 2 * q^7 + 180 * q^9 + 2 * q^11 + 3 * q^13 + 10 * q^15 - 6 * q^17 + 9 * q^19 + 16 * q^21 + 23 * q^23 - 18 * q^25 - 26 * q^27 + q^29 - 38 * q^31 + q^33 - 10 * q^35 - 24 * q^37 + 79 * q^39 - 4 * q^41 + 3 * q^43 - 37 * q^45 - 25 * q^47 - 39 * q^49 + 9 * q^51 + 17 * q^53 + 69 * q^55 + 63 * q^57 - 28 * q^59 + 34 * q^61 + 22 * q^63 + 84 * q^65 - 19 * q^67 - 12 * q^69 + 15 * q^71 - 46 * q^73 + 23 * q^75 + 108 * q^77 + 47 * q^79 + 226 * q^81 - 9 * q^83 - 8 * q^85 - 91 * q^87 - 100 * q^89 - 16 * q^91 - 6 * q^93 + 45 * q^95 + 18 * q^97 - 74 * q^99

Introduction

L-functions

Modular forms

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Database

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