LMFDB - Embedded newform 1148.2.ba.a.701.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.7
Character	$\chi$	$=$	1148.701
Dual form			1148.2.ba.a.113.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.48167i q^{3} +(-0.0508728 + 0.156570i) q^{5} +(0.587785 - 0.809017i) q^{7} +0.804648 q^{9} +O(q^{10})$	\(q-1.48167i q^{3} +(-0.0508728 + 0.156570i) q^{5} +(0.587785 - 0.809017i) q^{7} +0.804648 q^{9} +(-2.04392 + 0.664111i) q^{11} +(3.59771 + 4.95183i) q^{13} +(0.231986 + 0.0753767i) q^{15} +(5.92096 - 1.92384i) q^{17} +(-1.77638 + 2.44498i) q^{19} +(-1.19870 - 0.870905i) q^{21} +(3.15951 - 2.29552i) q^{23} +(4.02316 + 2.92300i) q^{25} -5.63724i q^{27} +(-3.99249 - 1.29724i) q^{29} +(1.08076 + 3.32623i) q^{31} +(0.983995 + 3.02843i) q^{33} +(0.0967657 + 0.133187i) q^{35} +(2.70765 - 8.33329i) q^{37} +(7.33698 - 5.33063i) q^{39} +(3.89499 - 5.08223i) q^{41} +(-5.52617 + 4.01500i) q^{43} +(-0.0409347 + 0.125984i) q^{45} +(-3.11819 - 4.29183i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-2.85049 - 8.77292i) q^{51} +(8.19061 + 2.66129i) q^{53} -0.353803i q^{55} +(3.62265 + 2.63201i) q^{57} +(-5.75201 + 4.17908i) q^{59} +(-9.32691 - 6.77640i) q^{61} +(0.472960 - 0.650974i) q^{63} +(-0.958334 + 0.311382i) q^{65} +(2.44934 + 0.795837i) q^{67} +(-3.40121 - 4.68136i) q^{69} +(4.83900 - 1.57229i) q^{71} +6.80054 q^{73} +(4.33092 - 5.96100i) q^{75} +(-0.664111 + 2.04392i) q^{77} +9.73908i q^{79} -5.93860 q^{81} +8.20719 q^{83} +1.02492i q^{85} +(-1.92208 + 5.91556i) q^{87} +(4.69741 - 6.46543i) q^{89} +6.12079 q^{91} +(4.92838 - 1.60133i) q^{93} +(-0.292441 - 0.402511i) q^{95} +(-7.52542 - 2.44516i) q^{97} +(-1.64464 + 0.534376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		−	1.48167i		−	0.855444i	−0.903910	−	0.427722i	$-0.859316\pi$
$3$		−	1.48167i		−	0.855444i	0.903910	−	0.427722i	$-0.140684\pi$
$4$		0			0
$5$	−0.0508728	+	0.156570i	−0.0227510	+	0.0700203i	−0.961787	−	0.273797i	$-0.911720\pi$
$5$	−0.0508728	+	0.156570i	−0.0227510	+	0.0700203i	0.939036	+	0.343818i	$0.111720\pi$
$6$		0			0
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$8$		0			0
$9$	0.804648			0.268216
$10$		0			0
$11$	−2.04392	+	0.664111i	−0.616267	+	0.200237i	−0.600482	−	0.799638i	$-0.705025\pi$
$11$	−2.04392	+	0.664111i	−0.616267	+	0.200237i	−0.0157845	+	0.999875i	$0.505025\pi$
$12$		0			0
$13$	3.59771	+	4.95183i	0.997826	+	1.37339i	0.926650	+	0.375926i	$0.122675\pi$
$13$	3.59771	+	4.95183i	0.997826	+	1.37339i	0.0711761	+	0.997464i	$0.477325\pi$
$14$		0			0
$15$	0.231986	+	0.0753767i	0.0598985	+	0.0194622i
$16$		0			0
$17$	5.92096	−	1.92384i	1.43604	−	0.466599i	0.515382	−	0.856961i	$-0.327650\pi$
$17$	5.92096	−	1.92384i	1.43604	−	0.466599i	0.920661	+	0.390362i	$0.127650\pi$
$18$		0			0
$19$	−1.77638	+	2.44498i	−0.407530	+	0.560916i	−0.962614	−	0.270878i	$-0.912686\pi$
$19$	−1.77638	+	2.44498i	−0.407530	+	0.560916i	0.555084	+	0.831794i	$0.312686\pi$
$20$		0			0
$21$	−1.19870	−	0.870905i	−0.261577	−	0.190047i
$22$		0			0
$23$	3.15951	−	2.29552i	0.658804	−	0.478649i	−0.207455	−	0.978245i	$-0.566518\pi$
$23$	3.15951	−	2.29552i	0.658804	−	0.478649i	0.866259	+	0.499595i	$0.166518\pi$
$24$		0			0
$25$	4.02316	+	2.92300i	0.804632	+	0.584599i
$26$		0			0
$27$		−	5.63724i		−	1.08489i
$28$		0			0
$29$	−3.99249	−	1.29724i	−0.741387	−	0.240891i	−0.0861157	−	0.996285i	$-0.527445\pi$
$29$	−3.99249	−	1.29724i	−0.741387	−	0.240891i	−0.655271	+	0.755394i	$0.727445\pi$
$30$		0			0
$31$	1.08076	+	3.32623i	0.194110	+	0.597409i	0.999986	+	0.00532434i	$0.00169480\pi$
$31$	1.08076	+	3.32623i	0.194110	+	0.597409i	−0.805876	+	0.592084i	$0.798305\pi$
$32$		0			0
$33$	0.983995	+	3.02843i	0.171292	+	0.527181i
$34$		0			0
$35$	0.0967657	+	0.133187i	0.0163564	+	0.0225126i
$36$		0			0
$37$	2.70765	−	8.33329i	0.445135	−	1.36998i	−0.437200	−	0.899364i	$-0.644030\pi$
$37$	2.70765	−	8.33329i	0.445135	−	1.36998i	0.882336	−	0.470621i	$-0.155970\pi$
$38$		0			0
$39$	7.33698	−	5.33063i	1.17486	−	0.853584i
$40$		0			0
$41$	3.89499	−	5.08223i	0.608296	−	0.793711i
$41$	3.89499	−	5.08223i	0.608296	−	0.793711i
$42$		0			0
$43$	−5.52617	+	4.01500i	−0.842733	+	0.612281i	−0.923133	−	0.384481i	$-0.874380\pi$
$43$	−5.52617	+	4.01500i	−0.842733	+	0.612281i	0.0803999	+	0.996763i	$0.474380\pi$
$44$		0			0
$45$	−0.0409347	+	0.125984i	−0.00610218	+	0.0187806i
$46$		0			0
$47$	−3.11819	−	4.29183i	−0.454835	−	0.626027i	0.518592	−	0.855022i	$-0.326456\pi$
$47$	−3.11819	−	4.29183i	−0.454835	−	0.626027i	−0.973428	+	0.228994i	$0.926456\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$		0			0
$51$	−2.85049	−	8.77292i	−0.399149	−	1.22845i
$52$		0			0
$53$	8.19061	+	2.66129i	1.12507	+	0.365556i	0.811699	−	0.584076i	$-0.198543\pi$
$53$	8.19061	+	2.66129i	1.12507	+	0.365556i	0.313367	+	0.949632i	$0.398543\pi$
$54$		0			0
$55$		−	0.353803i		−	0.0477068i
$56$		0			0
$57$	3.62265	+	2.63201i	0.479832	+	0.348619i
$58$		0			0
$59$	−5.75201	+	4.17908i	−0.748848	+	0.544070i	−0.895469	−	0.445123i	$-0.853160\pi$
$59$	−5.75201	+	4.17908i	−0.748848	+	0.544070i	0.146622	+	0.989193i	$0.453160\pi$
$60$		0			0
$61$	−9.32691	−	6.77640i	−1.19419	−	0.867629i	−0.200488	−	0.979696i	$-0.564253\pi$
$61$	−9.32691	−	6.77640i	−1.19419	−	0.867629i	−0.993701	+	0.112067i	$0.964253\pi$
$62$		0			0
$63$	0.472960	−	0.650974i	0.0595874	−	0.0820150i
$64$		0			0
$65$	−0.958334	+	0.311382i	−0.118867	+	0.0386221i
$66$		0			0
$67$	2.44934	+	0.795837i	0.299234	+	0.0972270i	0.454786	−	0.890601i	$-0.349716\pi$
$67$	2.44934	+	0.795837i	0.299234	+	0.0972270i	−0.155552	+	0.987828i	$0.549716\pi$
$68$		0			0
$69$	−3.40121	−	4.68136i	−0.409458	−	0.563570i
$70$		0			0
$71$	4.83900	−	1.57229i	0.574284	−	0.186596i	−0.00745420	−	0.999972i	$-0.502373\pi$
$71$	4.83900	−	1.57229i	0.574284	−	0.186596i	0.581738	+	0.813376i	$0.302373\pi$
$72$		0			0
$73$	6.80054			0.795943			0.397971	−	0.917398i	$-0.369714\pi$
$73$	6.80054			0.795943			0.397971	+	0.917398i	$0.369714\pi$
$74$		0			0
$75$	4.33092	−	5.96100i	0.500092	−	0.688317i
$76$		0			0
$77$	−0.664111	+	2.04392i	−0.0756825	+	0.232927i
$78$		0			0
$79$			9.73908i			1.09573i	0.836566	+	0.547866i	$0.184560\pi$
$79$			9.73908i			1.09573i	−0.836566	+	0.547866i	$0.815440\pi$
$80$		0			0
$81$	−5.93860			−0.659844
$82$		0			0
$83$	8.20719			0.900856			0.450428	−	0.892813i	$-0.351271\pi$
$83$	8.20719			0.900856			0.450428	+	0.892813i	$0.351271\pi$
$84$		0			0
$85$			1.02492i			0.111168i
$86$		0			0
$87$	−1.92208	+	5.91556i	−0.206069	+	0.634214i
$88$		0			0
$89$	4.69741	−	6.46543i	0.497925	−	0.685334i	−0.483900	−	0.875123i	$-0.660780\pi$
$89$	4.69741	−	6.46543i	0.497925	−	0.685334i	0.981825	+	0.189789i	$0.0607803\pi$
$90$		0			0
$91$	6.12079			0.641634
$92$		0			0
$93$	4.92838	−	1.60133i	0.511050	−	0.166050i
$94$		0			0
$95$	−0.292441	−	0.402511i	−0.0300039	−	0.0412968i
$96$		0			0
$97$	−7.52542	−	2.44516i	−0.764091	−	0.248268i	−0.0990574	−	0.995082i	$-0.531583\pi$
$97$	−7.52542	−	2.44516i	−0.764091	−	0.248268i	−0.665033	+	0.746814i	$0.731583\pi$
$98$		0			0
$99$	−1.64464	+	0.534376i	−0.165293	+	0.0537068i
$100$		0			0
$101$	8.73078	−	12.0169i	0.868745	−	1.19572i	−0.110668	−	0.993857i	$-0.535299\pi$
$101$	8.73078	−	12.0169i	0.868745	−	1.19572i	0.979413	−	0.201868i	$-0.0647010\pi$
$102$		0			0
$103$	−14.1197	−	10.2586i	−1.39125	−	1.01081i	−0.995726	−	0.0923517i	$-0.970562\pi$
$103$	−14.1197	−	10.2586i	−1.39125	−	1.01081i	−0.395528	−	0.918454i	$-0.629438\pi$
$104$		0			0
$105$	0.197339	−	0.143375i	0.0192583	−	0.0139920i
$106$		0			0
$107$	4.47795	+	3.25342i	0.432900	+	0.314520i	0.782807	−	0.622264i	$-0.213787\pi$
$107$	4.47795	+	3.25342i	0.432900	+	0.314520i	−0.349908	+	0.936784i	$0.613787\pi$
$108$		0			0
$109$		−	3.31768i		−	0.317776i	−0.987297	−	0.158888i	$-0.949209\pi$
$109$		−	3.31768i		−	0.317776i	0.987297	−	0.158888i	$-0.0507909\pi$
$110$		0			0
$111$	−12.3472	−	4.01185i	−1.17194	−	0.380788i
$112$		0			0
$113$	4.65535	+	14.3277i	0.437939	+	1.34784i	0.890045	+	0.455872i	$0.150673\pi$
$113$	4.65535	+	14.3277i	0.437939	+	1.34784i	−0.452107	+	0.891964i	$0.649327\pi$
$114$		0			0
$115$	0.198677	+	0.611465i	0.0185267	+	0.0570195i
$116$		0			0
$117$	2.89489	+	3.98448i	0.267633	+	0.368365i
$118$		0			0
$119$	1.92384	−	5.92096i	0.176358	−	0.542773i
$120$		0			0
$121$	−5.16260	+	3.75085i	−0.469327	+	0.340986i
$122$		0			0
$123$	−7.53019	−	5.77110i	−0.678975	−	0.520363i
$124$		0			0
$125$	−1.32826	+	0.965035i	−0.118803	+	0.0863153i
$126$		0			0
$127$	5.02260	−	15.4580i	0.445684	−	1.37167i	−0.436049	−	0.899923i	$-0.643622\pi$
$127$	5.02260	−	15.4580i	0.445684	−	1.37167i	0.881732	−	0.471750i	$-0.156378\pi$
$128$		0			0
$129$	5.94891	+	8.18797i	0.523772	+	0.720911i
$130$		0			0
$131$	2.58003	+	7.94052i	0.225419	+	0.693767i	0.998249	+	0.0591542i	$0.0188404\pi$
$131$	2.58003	+	7.94052i	0.225419	+	0.693767i	−0.772830	+	0.634613i	$0.781160\pi$
$132$		0			0
$133$	0.933898	+	2.87424i	0.0809793	+	0.249229i
$134$		0			0
$135$	0.882624	+	0.286782i	0.0759642	+	0.0246823i
$136$		0			0
$137$			7.29628i			0.623363i	0.950187	+	0.311681i	$0.100892\pi$
$137$			7.29628i			0.623363i	−0.950187	+	0.311681i	$0.899108\pi$
$138$		0			0
$139$	−14.7518	−	10.7178i	−1.25123	−	0.909072i	−0.252938	−	0.967483i	$-0.581397\pi$
$139$	−14.7518	−	10.7178i	−1.25123	−	0.909072i	−0.998293	+	0.0584106i	$0.981397\pi$
$140$		0			0
$141$	−6.35908	+	4.62014i	−0.535531	+	0.389086i
$142$		0			0
$143$	−10.6420	−	7.73188i	−0.889930	−	0.646572i
$144$		0			0
$145$	0.406218	−	0.559111i	0.0337346	−	0.0464316i
$146$		0			0
$147$	−1.40915	+	0.457862i	−0.116225	+	0.0377638i
$148$		0			0
$149$	8.30494	+	2.69844i	0.680367	+	0.221065i	0.628756	−	0.777603i	$-0.283564\pi$
$149$	8.30494	+	2.69844i	0.680367	+	0.221065i	0.0516111	+	0.998667i	$0.483564\pi$
$150$		0			0
$151$	5.65924	+	7.78928i	0.460543	+	0.633882i	0.974621	−	0.223861i	$-0.0718660\pi$
$151$	5.65924	+	7.78928i	0.460543	+	0.633882i	−0.514079	+	0.857743i	$0.671866\pi$
$152$		0			0
$153$	4.76429	−	1.54801i	0.385170	−	0.125149i
$154$		0			0
$155$	−0.575770			−0.0462470
$156$		0			0
$157$	−10.6281	+	14.6283i	−0.848216	+	1.16747i	0.136038	+	0.990704i	$0.456563\pi$
$157$	−10.6281	+	14.6283i	−0.848216	+	1.16747i	−0.984253	+	0.176765i	$0.943437\pi$
$158$		0			0
$159$	3.94316	−	12.1358i	0.312713	−	0.962431i
$160$		0			0
$161$		−	3.90537i		−	0.307787i
$162$		0			0
$163$	10.7123			0.839055			0.419528	−	0.907743i	$-0.362196\pi$
$163$	10.7123			0.839055			0.419528	+	0.907743i	$0.362196\pi$
$164$		0			0
$165$	−0.524220			−0.0408105
$166$		0			0
$167$			1.55628i			0.120429i	0.998185	+	0.0602143i	$0.0191784\pi$
$167$			1.55628i			0.120429i	−0.998185	+	0.0602143i	$0.980822\pi$
$168$		0			0
$169$	−7.55983	+	23.2668i	−0.581525	+	1.78975i
$170$		0			0
$171$	−1.42936	+	1.96735i	−0.109306	+	0.150447i
$172$		0			0
$173$	−3.20051			−0.243331			−0.121665	−	0.992571i	$-0.538823\pi$
$173$	−3.20051			−0.243331			−0.121665	+	0.992571i	$0.538823\pi$
$174$		0			0
$175$	4.72951	−	1.53671i	0.357517	−	0.116164i
$176$		0			0
$177$	6.19202	+	8.52259i	0.465421	+	0.640597i
$178$		0			0
$179$	−16.0452	−	5.21339i	−1.19927	−	0.389667i	−0.359780	−	0.933037i	$-0.617148\pi$
$179$	−16.0452	−	5.21339i	−1.19927	−	0.389667i	−0.839493	+	0.543370i	$0.817148\pi$
$180$		0			0
$181$	−13.6442	+	4.43327i	−1.01417	+	0.329522i	−0.768512	−	0.639835i	$-0.779003\pi$
$181$	−13.6442	+	4.43327i	−1.01417	+	0.329522i	−0.245654	+	0.969358i	$0.579003\pi$
$182$		0			0
$183$	−10.0404	+	13.8194i	−0.742208	+	1.02156i
$184$		0			0
$185$	1.16700	+	0.847875i	0.0857995	+	0.0623370i
$186$		0			0
$187$	−10.8244	+	7.86435i	−0.791555	+	0.575098i
$188$		0			0
$189$	−4.56062	−	3.31349i	−0.331737	−	0.241021i
$190$		0			0
$191$		−	5.79551i		−	0.419349i	−0.977771	−	0.209674i	$-0.932760\pi$
$191$		−	5.79551i		−	0.419349i	0.977771	−	0.209674i	$-0.0672404\pi$
$192$		0			0
$193$	−1.26442	−	0.410835i	−0.0910150	−	0.0295726i	0.263156	−	0.964753i	$-0.415237\pi$
$193$	−1.26442	−	0.410835i	−0.0910150	−	0.0295726i	−0.354171	+	0.935181i	$0.615237\pi$
$194$		0			0
$195$	0.461365	+	1.41994i	0.0330391	+	0.101684i
$196$		0			0
$197$	7.35070	+	22.6231i	0.523715	+	1.61183i	0.766842	+	0.641836i	$0.221827\pi$
$197$	7.35070	+	22.6231i	0.523715	+	1.61183i	−0.243127	+	0.969995i	$0.578173\pi$
$198$		0			0
$199$	9.53263	+	13.1205i	0.675750	+	0.930090i	0.999873	−	0.0159249i	$-0.00506926\pi$
$199$	9.53263	+	13.1205i	0.675750	+	0.930090i	−0.324123	+	0.946015i	$0.605069\pi$
$200$		0			0
$201$	1.17917	−	3.62911i	0.0831722	−	0.255978i
$202$		0			0
$203$	−3.39621	+	2.46749i	−0.238367	+	0.173184i
$204$		0			0
$205$	0.597577	+	0.868387i	0.0417366	+	0.0606508i
$206$		0			0
$207$	2.54230	−	1.84709i	0.176702	−	0.128381i
$208$		0			0
$209$	2.00705	−	6.17707i	0.138831	−	0.427277i
$210$		0			0
$211$	12.2597	+	16.8741i	0.843994	+	1.16166i	0.985154	+	0.171672i	$0.0549169\pi$
$211$	12.2597	+	16.8741i	0.843994	+	1.16166i	−0.141160	+	0.989987i	$0.545083\pi$
$212$		0			0
$213$	−2.32961	−	7.16982i	−0.159623	−	0.491268i
$214$		0			0
$215$	−0.347498	−	1.06949i	−0.0236991	−	0.0729384i
$216$		0			0
$217$	3.32623	+	1.08076i	0.225799	+	0.0733666i
$218$		0			0
$219$		−	10.0762i		−	0.680884i
$220$		0			0
$221$	30.8284	+	22.3981i	2.07374	+	1.50666i
$222$		0			0
$223$	10.7940	−	7.84227i	0.722817	−	0.525157i	−0.164466	−	0.986383i	$-0.552590\pi$
$223$	10.7940	−	7.84227i	0.722817	−	0.525157i	0.887283	+	0.461226i	$0.152590\pi$
$224$		0			0
$225$	3.23723	+	2.35198i	0.215815	+	0.156799i
$226$		0			0
$227$	12.5068	−	17.2141i	0.830104	−	1.14254i	−0.157800	−	0.987471i	$-0.550440\pi$
$227$	12.5068	−	17.2141i	0.830104	−	1.14254i	0.987904	−	0.155069i	$-0.0495599\pi$
$228$		0			0
$229$	−12.5263	+	4.07004i	−0.827760	+	0.268956i	−0.692102	−	0.721800i	$-0.743315\pi$
$229$	−12.5263	+	4.07004i	−0.827760	+	0.268956i	−0.135659	+	0.990756i	$0.543315\pi$
$230$		0			0
$231$	3.02843	+	0.983995i	0.199256	+	0.0647421i
$232$		0			0
$233$	−3.30671	−	4.55129i	−0.216630	−	0.298165i	0.686847	−	0.726802i	$-0.258994\pi$
$233$	−3.30671	−	4.55129i	−0.216630	−	0.298165i	−0.903477	+	0.428637i	$0.858994\pi$
$234$		0			0
$235$	0.830603	−	0.269879i	0.0541826	−	0.0176050i
$236$		0			0
$237$	14.4301			0.937337
$238$		0			0
$239$	−4.82031	+	6.63459i	−0.311800	+	0.429156i	−0.935942	−	0.352155i	$-0.885449\pi$
$239$	−4.82031	+	6.63459i	−0.311800	+	0.429156i	0.624141	+	0.781311i	$0.285449\pi$
$240$		0			0
$241$	−2.65228	+	8.16287i	−0.170848	+	0.525817i	−0.999420	−	0.0340668i	$-0.989154\pi$
$241$	−2.65228	+	8.16287i	−0.170848	+	0.525817i	0.828571	+	0.559883i	$0.189154\pi$
$242$		0			0
$243$		−	8.11267i		−	0.520428i
$244$		0			0
$245$	0.164628			0.0105177
$246$		0			0
$247$	−18.4980			−1.17700
$248$		0			0
$249$		−	12.1604i		−	0.770631i
$250$		0			0
$251$	−8.07469	+	24.8513i	−0.509670	+	1.56860i	0.283106	+	0.959089i	$0.408635\pi$
$251$	−8.07469	+	24.8513i	−0.509670	+	1.56860i	−0.792776	+	0.609513i	$0.791365\pi$
$252$		0			0
$253$	−4.93333	+	6.79014i	−0.310156	+	0.426893i
$254$		0			0
$255$	1.51859			0.0950978
$256$		0			0
$257$	−22.5474	+	7.32609i	−1.40647	+	0.456989i	−0.911277	−	0.411795i	$-0.864902\pi$
$257$	−22.5474	+	7.32609i	−1.40647	+	0.456989i	−0.495191	+	0.868784i	$0.664902\pi$
$258$		0			0
$259$	−5.15026	−	7.08872i	−0.320021	−	0.440472i
$260$		0			0
$261$	−3.21255	−	1.04382i	−0.198852	−	0.0646109i
$262$		0			0
$263$	−14.9562	+	4.85958i	−0.922242	+	0.299655i	−0.731386	−	0.681964i	$-0.761126\pi$
$263$	−14.9562	+	4.85958i	−0.922242	+	0.299655i	−0.190856	+	0.981618i	$0.561126\pi$
$264$		0			0
$265$	−0.833358	+	1.14702i	−0.0511928	+	0.0704608i
$266$		0			0
$267$	−9.57965	−	6.96002i	−0.586265	−	0.425946i
$268$		0			0
$269$	−8.47867	+	6.16011i	−0.516954	+	0.375589i	−0.815455	−	0.578820i	$-0.803513\pi$
$269$	−8.47867	+	6.16011i	−0.516954	+	0.375589i	0.298501	+	0.954409i	$0.403513\pi$
$270$		0			0
$271$	−19.5382	−	14.1954i	−1.18686	−	0.862306i	−0.193934	−	0.981015i	$-0.562125\pi$
$271$	−19.5382	−	14.1954i	−1.18686	−	0.862306i	−0.992929	+	0.118708i	$0.962125\pi$
$272$		0			0
$273$		−	9.06901i		−	0.548881i
$274$		0			0
$275$	−10.1642	−	3.30256i	−0.612926	−	0.199152i
$276$		0			0
$277$	−0.0626312	−	0.192759i	−0.00376314	−	0.0115818i	0.949157	−	0.314802i	$-0.101938\pi$
$277$	−0.0626312	−	0.192759i	−0.00376314	−	0.0115818i	−0.952920	+	0.303220i	$0.901938\pi$
$278$		0			0
$279$	0.869630	+	2.67645i	0.0520634	+	0.160235i
$280$		0			0
$281$	−4.76579	−	6.55955i	−0.284303	−	0.391310i	0.642850	−	0.765992i	$-0.277752\pi$
$281$	−4.76579	−	6.55955i	−0.284303	−	0.391310i	−0.927153	+	0.374682i	$0.877752\pi$
$282$		0			0
$283$	−7.29278	+	22.4449i	−0.433511	+	1.33421i	0.461094	+	0.887351i	$0.347457\pi$
$283$	−7.29278	+	22.4449i	−0.433511	+	1.33421i	−0.894605	+	0.446858i	$0.852543\pi$
$284$		0			0
$285$	−0.596389	+	0.433302i	−0.0353271	+	0.0256666i
$286$		0			0
$287$	−1.82219	−	6.13837i	−0.107560	−	0.362337i
$288$		0			0
$289$	17.6033	−	12.7896i	1.03549	−	0.752326i
$290$		0			0
$291$	−3.62292	+	11.1502i	−0.212379	+	0.653637i
$292$		0			0
$293$	−13.4045	−	18.4498i	−0.783101	−	1.07785i	−0.994933	−	0.100540i	$-0.967943\pi$
$293$	−13.4045	−	18.4498i	−0.783101	−	1.07785i	0.211832	−	0.977306i	$-0.432057\pi$
$294$		0			0
$295$	−0.361699	−	1.11319i	−0.0210589	−	0.0648127i
$296$		0			0
$297$	3.74376	+	11.5221i	0.217235	+	0.668580i
$298$		0			0
$299$	22.7340	+	7.38674i	1.31474	+	0.427186i
$300$		0			0
$301$			6.83072i			0.393716i
$302$		0			0
$303$	−17.8051	−	12.9362i	−1.02288	−	0.743162i
$304$		0			0
$305$	1.53547	−	1.11558i	0.0879206	−	0.0638781i
$306$		0			0
$307$	15.4101	+	11.1961i	0.879501	+	0.638995i	0.933120	−	0.359566i	$-0.117075\pi$
$307$	15.4101	+	11.1961i	0.879501	+	0.638995i	−0.0536181	+	0.998562i	$0.517075\pi$
$308$		0			0
$309$	−15.1998	+	20.9208i	−0.864687	+	1.19014i
$310$		0			0
$311$	10.6313	−	3.45431i	0.602844	−	0.195876i	0.00833558	−	0.999965i	$-0.497347\pi$
$311$	10.6313	−	3.45431i	0.602844	−	0.195876i	0.594508	+	0.804089i	$0.297347\pi$
$312$		0			0
$313$	18.3889	+	5.97492i	1.03940	+	0.337722i	0.778501	−	0.627643i	$-0.215980\pi$
$313$	18.3889	+	5.97492i	1.03940	+	0.337722i	0.260901	+	0.965365i	$0.415980\pi$
$314$		0			0
$315$	0.0778624	+	0.107168i	0.00438705	+	0.00603825i
$316$		0			0
$317$	−32.9940	+	10.7204i	−1.85313	+	0.602117i	−0.856882	+	0.515512i	$0.827602\pi$
$317$	−32.9940	+	10.7204i	−1.85313	+	0.602117i	−0.996243	+	0.0866048i	$0.972398\pi$
$318$		0			0
$319$	9.02186			0.505127
$320$		0			0
$321$	4.82050	−	6.63485i	0.269054	−	0.370321i
$322$		0			0
$323$	−5.81414	+	17.8941i	−0.323507	+	0.995653i
$324$		0			0
$325$			30.4381i			1.68840i
$326$		0			0
$327$	−4.91572			−0.271840
$328$		0			0
$329$	−5.30499			−0.292473
$330$		0			0
$331$		−	30.9478i		−	1.70105i	−0.525937	−	0.850524i	$-0.676285\pi$
$331$		−	30.9478i		−	1.70105i	0.525937	−	0.850524i	$-0.323715\pi$
$332$		0			0
$333$	2.17871	−	6.70537i	0.119392	−	0.367452i
$334$		0			0
$335$	−0.249209	+	0.343007i	−0.0136157	+	0.0187405i
$336$		0			0
$337$	−18.4944			−1.00746			−0.503728	−	0.863862i	$-0.668039\pi$
$337$	−18.4944			−1.00746			−0.503728	+	0.863862i	$0.668039\pi$
$338$		0			0
$339$	21.2289	−	6.89770i	1.15300	−	0.374632i
$340$		0			0
$341$	−4.41798	−	6.08082i	−0.239247	−	0.329295i
$342$		0			0
$343$	−0.951057	−	0.309017i	−0.0513522	−	0.0166853i
$344$		0			0
$345$	0.905991	−	0.294374i	0.0487769	−	0.0158486i
$346$		0			0
$347$	−2.26279	+	3.11447i	−0.121473	+	0.167193i	−0.865423	−	0.501042i	$-0.832950\pi$
$347$	−2.26279	+	3.11447i	−0.121473	+	0.167193i	0.743950	+	0.668236i	$0.232950\pi$
$348$		0			0
$349$	−9.75575	−	7.08797i	−0.522213	−	0.379410i	0.295224	−	0.955428i	$-0.404606\pi$
$349$	−9.75575	−	7.08797i	−0.522213	−	0.379410i	−0.817437	+	0.576018i	$0.804606\pi$
$350$		0			0
$351$	27.9146	−	20.2812i	1.48997	−	1.08253i
$352$		0			0
$353$	−8.93723	−	6.49328i	−0.475681	−	0.345602i	0.323970	−	0.946067i	$-0.394982\pi$
$353$	−8.93723	−	6.49328i	−0.475681	−	0.345602i	−0.799651	+	0.600465i	$0.794982\pi$
$354$		0			0
$355$			0.837631i			0.0444568i
$356$		0			0
$357$	−8.77292	−	2.85049i	−0.464312	−	0.150864i
$358$		0			0
$359$	−4.75644	−	14.6388i	−0.251035	−	0.772607i	−0.994585	−	0.103926i	$-0.966859\pi$
$359$	−4.75644	−	14.6388i	−0.251035	−	0.772607i	0.743550	−	0.668681i	$-0.233141\pi$
$360$		0			0
$361$	3.04893	+	9.38365i	0.160470	+	0.493877i
$362$		0			0
$363$	5.55753	+	7.64928i	0.291695	+	0.401483i
$364$		0			0
$365$	−0.345962	+	1.06476i	−0.0181085	+	0.0557322i
$366$		0			0
$367$	−13.4120	+	9.74437i	−0.700100	+	0.508652i	−0.879965	−	0.475039i	$-0.842434\pi$
$367$	−13.4120	+	9.74437i	−0.700100	+	0.508652i	0.179865	+	0.983691i	$0.442434\pi$
$368$		0			0
$369$	3.13410	−	4.08941i	0.163155	−	0.212886i
$370$		0			0
$371$	6.96735	−	5.06207i	0.361727	−	0.262810i
$372$		0			0
$373$	−7.33117	+	22.5630i	−0.379594	+	1.16827i	0.560733	+	0.827996i	$0.310519\pi$
$373$	−7.33117	+	22.5630i	−0.379594	+	1.16827i	−0.940327	+	0.340272i	$0.889481\pi$
$374$		0			0
$375$	1.42986	+	1.96804i	0.0738379	+	0.101629i
$376$		0			0
$377$	−7.94013	−	24.4372i	−0.408937	−	1.25858i
$378$		0			0
$379$	5.07824	+	15.6292i	0.260852	+	0.802818i	0.992620	+	0.121265i	$0.0386952\pi$
$379$	5.07824	+	15.6292i	0.260852	+	0.802818i	−0.731769	+	0.681553i	$0.761305\pi$
$380$		0			0
$381$	−22.9036	−	7.44185i	−1.17339	−	0.381257i
$382$		0			0
$383$		−	36.2821i		−	1.85393i	−0.375149	−	0.926964i	$-0.622409\pi$
$383$		−	36.2821i		−	1.85393i	0.375149	−	0.926964i	$-0.377591\pi$
$384$		0			0
$385$	−0.286233	−	0.207960i	−0.0145878	−	0.0105986i
$386$		0			0
$387$	−4.44662	+	3.23066i	−0.226035	+	0.164224i
$388$		0			0
$389$	−6.88628	−	5.00318i	−0.349149	−	0.253671i	0.399363	−	0.916793i	$-0.369231\pi$
$389$	−6.88628	−	5.00318i	−0.349149	−	0.253671i	−0.748512	+	0.663122i	$0.769231\pi$
$390$		0			0
$391$	14.2911	−	19.6701i	0.722734	−	0.994758i
$392$		0			0
$393$	11.7653	−	3.82276i	0.593478	−	0.192833i
$394$		0			0
$395$	−1.52485	−	0.495454i	−0.0767235	−	0.0249290i
$396$		0			0
$397$	−14.7560	−	20.3098i	−0.740581	−	1.01932i	−0.998585	−	0.0531783i	$-0.983065\pi$
$397$	−14.7560	−	20.3098i	−0.740581	−	1.01932i	0.258004	−	0.966144i	$-0.416935\pi$
$398$		0			0
$399$	4.25869	−	1.38373i	0.213201	−	0.0692732i
$400$		0			0
$401$	35.8171			1.78862			0.894309	−	0.447449i	$-0.147667\pi$
$401$	35.8171			1.78862			0.894309	+	0.447449i	$0.147667\pi$
$402$		0			0
$403$	−12.5827	+	17.3185i	−0.626787	+	0.862698i
$404$		0			0
$405$	0.302113	−	0.929807i	0.0150121	−	0.0462025i
$406$		0			0
$407$			18.8308i			0.933408i
$408$		0			0
$409$	−7.39908			−0.365861			−0.182931	−	0.983126i	$-0.558558\pi$
$409$	−7.39908			−0.365861			−0.182931	+	0.983126i	$0.558558\pi$
$410$		0			0
$411$	10.8107			0.533252
$412$		0			0
$413$			7.10987i			0.349854i
$414$		0			0
$415$	−0.417522	+	1.28500i	−0.0204954	+	0.0630782i
$416$		0			0
$417$	−15.8803	+	21.8573i	−0.777660	+	1.07036i
$418$		0			0
$419$	19.9432			0.974290			0.487145	−	0.873321i	$-0.338038\pi$
$419$	19.9432			0.974290			0.487145	+	0.873321i	$0.338038\pi$
$420$		0			0
$421$	−0.897797	+	0.291712i	−0.0437559	+	0.0142172i	−0.330813	−	0.943696i	$-0.607323\pi$
$421$	−0.897797	+	0.291712i	−0.0437559	+	0.0142172i	0.287057	+	0.957913i	$0.407323\pi$
$422$		0			0
$423$	−2.50905	−	3.45341i	−0.121994	−	0.167911i
$424$		0			0
$425$	29.4443	+	9.56704i	1.42826	+	0.464070i
$426$		0			0
$427$	−10.9644	+	3.56256i	−0.530606	+	0.172405i
$428$		0			0
$429$	−11.4561	+	15.7680i	−0.553106	+	0.761285i
$430$		0			0
$431$	1.89042	+	1.37347i	0.0910584	+	0.0661578i	0.632383	−	0.774656i	$-0.282077\pi$
$431$	1.89042	+	1.37347i	0.0910584	+	0.0661578i	−0.541324	+	0.840814i	$0.682077\pi$
$432$		0			0
$433$	0.458230	−	0.332923i	0.0220211	−	0.0159993i	−0.576720	−	0.816942i	$-0.695668\pi$
$433$	0.458230	−	0.332923i	0.0220211	−	0.0159993i	0.598741	+	0.800942i	$0.295668\pi$
$434$		0			0
$435$	−0.828419	−	0.601882i	−0.0397196	−	0.0288580i
$436$		0			0
$437$			11.8027i			0.564598i
$438$		0			0
$439$	−8.94065	−	2.90499i	−0.426714	−	0.138648i	0.0877836	−	0.996140i	$-0.472022\pi$
$439$	−8.94065	−	2.90499i	−0.426714	−	0.138648i	−0.514498	+	0.857492i	$0.672022\pi$
$440$		0			0
$441$	−0.248650	−	0.765266i	−0.0118405	−	0.0364412i
$442$		0			0
$443$	−10.6864	−	32.8893i	−0.507726	−	1.56262i	−0.796140	−	0.605113i	$-0.793128\pi$
$443$	−10.6864	−	32.8893i	−0.507726	−	1.56262i	0.288414	−	0.957506i	$-0.406872\pi$
$444$		0			0
$445$	0.773324	+	1.06439i	0.0366591	+	0.0504569i
$446$		0			0
$447$	3.99820	−	12.3052i	0.189108	−	0.582016i
$448$		0			0
$449$	26.8676	−	19.5204i	1.26796	−	0.921226i	0.268840	−	0.963185i	$-0.413360\pi$
$449$	26.8676	−	19.5204i	1.26796	−	0.921226i	0.999119	+	0.0419586i	$0.0133597\pi$
$450$		0			0
$451$	−4.58591	+	12.9744i	−0.215942	+	0.610941i
$452$		0			0
$453$	11.5412	−	8.38514i	0.542251	−	0.393968i
$454$		0			0
$455$	−0.311382	+	0.958334i	−0.0145978	+	0.0449274i
$456$		0			0
$457$	−3.92520	−	5.40258i	−0.183613	−	0.252722i	0.707281	−	0.706932i	$-0.249921\pi$
$457$	−3.92520	−	5.40258i	−0.183613	−	0.252722i	−0.890895	+	0.454210i	$0.849921\pi$
$458$		0			0
$459$	−10.8451	−	33.3779i	−0.506207	−	1.55795i
$460$		0			0
$461$	−4.13378	−	12.7225i	−0.192529	−	0.592544i	−0.999997	−	0.00263170i	$-0.999162\pi$
$461$	−4.13378	−	12.7225i	−0.192529	−	0.592544i	0.807467	−	0.589912i	$-0.200838\pi$
$462$		0			0
$463$	−24.8668	−	8.07973i	−1.15566	−	0.375497i	−0.332388	−	0.943143i	$-0.607854\pi$
$463$	−24.8668	−	8.07973i	−1.15566	−	0.375497i	−0.823273	+	0.567646i	$0.807854\pi$
$464$		0			0
$465$			0.853102i			0.0395617i
$466$		0			0
$467$	−20.9608	−	15.2289i	−0.969950	−	0.704710i	−0.0145098	−	0.999895i	$-0.504619\pi$
$467$	−20.9608	−	15.2289i	−0.969950	−	0.704710i	−0.955440	+	0.295185i	$0.904619\pi$
$468$		0			0
$469$	2.08353	−	1.51377i	0.0962084	−	0.0698995i
$470$		0			0
$471$	21.6744	+	15.7474i	0.998704	+	0.725601i
$472$		0			0
$473$	8.62867	−	11.8763i	0.396747	−	0.546075i
$474$		0			0
$475$	−14.2933	+	4.64418i	−0.655822	+	0.213090i
$476$		0			0
$477$	6.59056	+	2.14140i	0.301761	+	0.0980481i
$478$		0			0
$479$	2.98035	+	4.10210i	0.136176	+	0.187430i	0.871659	−	0.490114i	$-0.163045\pi$
$479$	2.98035	+	4.10210i	0.136176	+	0.187430i	−0.735483	+	0.677543i	$0.763045\pi$
$480$		0			0
$481$	51.0064	−	16.5730i	2.32569	−	0.755663i
$482$		0			0
$483$	−5.78648			−0.263294
$484$		0			0
$485$	0.765678	−	1.05387i	0.0347676	−	0.0478536i
$486$		0			0
$487$	−10.1544	+	31.2522i	−0.460142	+	1.41617i	0.404849	+	0.914383i	$0.367324\pi$
$487$	−10.1544	+	31.2522i	−0.460142	+	1.41617i	−0.864991	+	0.501787i	$0.832676\pi$
$488$		0			0
$489$		−	15.8722i		−	0.717764i
$490$		0			0
$491$	32.7495			1.47797			0.738983	−	0.673724i	$-0.235306\pi$
$491$	32.7495			1.47797			0.738983	+	0.673724i	$0.235306\pi$
$492$		0			0
$493$	−26.1350			−1.17706
$494$		0			0
$495$		−	0.284687i		−	0.0127957i
$496$		0			0
$497$	1.57229	−	4.83900i	0.0705267	−	0.217059i
$498$		0			0
$499$	8.34358	−	11.4840i	0.373510	−	0.514093i	−0.580341	−	0.814374i	$-0.697081\pi$
$499$	8.34358	−	11.4840i	0.373510	−	0.514093i	0.953851	+	0.300281i	$0.0970806\pi$
$500$		0			0
$501$	2.30590			0.103020
$502$		0			0
$503$	12.4927	−	4.05914i	0.557024	−	0.180988i	−0.0169576	−	0.999856i	$-0.505398\pi$
$503$	12.4927	−	4.05914i	0.557024	−	0.180988i	0.573982	+	0.818868i	$0.305398\pi$
$504$		0			0
$505$	1.43733	+	1.97831i	0.0639603	+	0.0880338i
$506$		0			0
$507$	34.4737	+	11.2012i	1.53103	+	0.497462i
$508$		0			0
$509$	15.2239	−	4.94654i	0.674786	−	0.219251i	0.0484751	−	0.998824i	$-0.484564\pi$
$509$	15.2239	−	4.94654i	0.674786	−	0.219251i	0.626311	+	0.779573i	$0.284564\pi$
$510$		0			0
$511$	3.99726	−	5.50175i	0.176828	−	0.243383i
$512$		0			0
$513$	13.7829	+	10.0139i	0.608531	+	0.442124i
$514$		0			0
$515$	2.32449	−	1.68884i	0.102429	−	0.0744193i
$516$		0			0
$517$	9.22361	+	6.70134i	0.405654	+	0.294725i
$518$		0			0
$519$			4.74211i			0.208156i
$520$		0			0
$521$	−9.80436	−	3.18563i	−0.429537	−	0.139565i	0.0862663	−	0.996272i	$-0.472506\pi$
$521$	−9.80436	−	3.18563i	−0.429537	−	0.139565i	−0.515803	+	0.856707i	$0.672506\pi$
$522$		0			0
$523$	1.32934	+	4.09128i	0.0581279	+	0.178899i	0.975905	−	0.218197i	$-0.0700177\pi$
$523$	1.32934	+	4.09128i	0.0581279	+	0.178899i	−0.917777	+	0.397097i	$0.870018\pi$
$524$		0			0
$525$	−2.27690	−	7.00758i	−0.0993721	−	0.305836i
$526$		0			0
$527$	12.7982	+	17.6153i	0.557500	+	0.767333i
$528$		0			0
$529$	−2.39428	+	7.36883i	−0.104099	+	0.320384i
$530$		0			0
$531$	−4.62834	+	3.36269i	−0.200853	+	0.145928i
$532$		0			0
$533$	39.1794	+	1.00293i	1.69705	+	0.0434418i
$534$		0			0
$535$	−0.737194	+	0.535603i	−0.0318717	+	0.0231561i
$536$		0			0
$537$	−7.72454	+	23.7737i	−0.333339	+	1.02591i
$538$		0			0
$539$	1.26322	+	1.73867i	0.0544105	+	0.0748897i
$540$		0			0
$541$	−3.29337	−	10.1360i	−0.141593	−	0.435779i	0.854964	−	0.518687i	$-0.173579\pi$
$541$	−3.29337	−	10.1360i	−0.141593	−	0.435779i	−0.996557	+	0.0829084i	$0.973579\pi$
$542$		0			0
$543$	6.56865	+	20.2162i	0.281888	+	0.867562i
$544$		0			0
$545$	0.519450	+	0.168780i	0.0222508	+	0.00722972i
$546$		0			0
$547$			38.1179i			1.62980i	0.579598	+	0.814902i	$0.303210\pi$
$547$			38.1179i			1.62980i	−0.579598	+	0.814902i	$0.696790\pi$
$548$		0			0
$549$	−7.50488	−	5.45262i	−0.320301	−	0.232712i
$550$		0			0
$551$	10.2639	−	7.45716i	0.437257	−	0.317686i
$552$		0			0
$553$	7.87908	+	5.72449i	0.335053	+	0.243430i
$554$		0			0
$555$	1.25627	−	1.72911i	0.0533258	−	0.0733967i
$556$		0			0
$557$	26.6890	−	8.67180i	1.13085	−	0.367436i	0.316952	−	0.948442i	$-0.397341\pi$
$557$	26.6890	−	8.67180i	1.13085	−	0.367436i	0.813899	+	0.581006i	$0.197341\pi$
$558$		0			0
$559$	−39.7631	−	12.9198i	−1.68180	−	0.546450i
$560$		0			0
$561$	11.6524	+	16.0381i	0.491964	+	0.677131i
$562$		0			0
$563$	1.70343	−	0.553477i	0.0717909	−	0.0233263i	−0.272901	−	0.962042i	$-0.587983\pi$
$563$	1.70343	−	0.553477i	0.0717909	−	0.0233263i	0.344692	+	0.938716i	$0.387983\pi$
$564$		0			0
$565$	−2.48012			−0.104339
$566$		0			0
$567$	−3.49062	+	4.80443i	−0.146592	+	0.201767i
$568$		0			0
$569$	−13.1437	+	40.4521i	−0.551012	+	1.69584i	0.155237	+	0.987877i	$0.450386\pi$
$569$	−13.1437	+	40.4521i	−0.551012	+	1.69584i	−0.706249	+	0.707964i	$0.749614\pi$
$570$		0			0
$571$		−	2.63954i		−	0.110462i	−0.998474	−	0.0552308i	$-0.982411\pi$
$571$		−	2.63954i		−	0.110462i	0.998474	−	0.0552308i	$-0.0175894\pi$
$572$		0			0
$573$	−8.58705			−0.358729
$574$		0			0
$575$	19.4210			0.809913
$576$		0			0
$577$		−	27.3681i		−	1.13935i	−0.821871	−	0.569674i	$-0.807069\pi$
$577$		−	27.3681i		−	1.13935i	0.821871	−	0.569674i	$-0.192931\pi$
$578$		0			0
$579$	−0.608723	+	1.87346i	−0.0252977	+	0.0778582i
$580$		0			0
$581$	4.82406	−	6.63975i	0.200136	−	0.275463i
$582$		0			0
$583$	−18.5084			−0.766539
$584$		0			0
$585$	−0.771122	+	0.250553i	−0.0318820	+	0.0103591i
$586$		0			0
$587$	3.92980	+	5.40890i	0.162200	+	0.223249i	0.882379	−	0.470539i	$-0.155940\pi$
$587$	3.92980	+	5.40890i	0.162200	+	0.223249i	−0.720179	+	0.693788i	$0.755940\pi$
$588$		0			0
$589$	−10.0524	−	3.26622i	−0.414202	−	0.134582i
$590$		0			0
$591$	33.5200	−	10.8913i	1.37883	−	0.448009i
$592$		0			0
$593$	10.8035	−	14.8697i	0.443646	−	0.610626i	−0.527372	−	0.849635i	$-0.676822\pi$
$593$	10.8035	−	14.8697i	0.443646	−	0.610626i	0.971017	+	0.239009i	$0.0768224\pi$
$594$		0			0
$595$	0.829175	+	0.602431i	0.0339929	+	0.0246973i
$596$		0			0
$597$	19.4403	−	14.1242i	0.795640	−	0.578066i
$598$		0			0
$599$	−31.0820	−	22.5824i	−1.26998	−	0.922691i	−0.270773	−	0.962643i	$-0.587279\pi$
$599$	−31.0820	−	22.5824i	−1.26998	−	0.922691i	−0.999202	+	0.0399522i	$0.987279\pi$
$600$		0			0
$601$		−	0.134811i		−	0.00549905i	−0.999996	−	0.00274953i	$-0.999125\pi$
$601$		−	0.134811i		−	0.00549905i	0.999996	−	0.00274953i	$-0.000875203\pi$
$602$		0			0
$603$	1.97085	+	0.640369i	0.0802594	+	0.0260778i
$604$		0			0
$605$	−0.324636	−	0.999126i	−0.0131983	−	0.0406202i
$606$		0			0
$607$	12.9545	+	39.8700i	0.525809	+	1.61827i	0.762711	+	0.646740i	$0.223868\pi$
$607$	12.9545	+	39.8700i	0.525809	+	1.61827i	−0.236902	+	0.971534i	$0.576132\pi$
$608$		0			0
$609$	3.65602	+	5.03207i	0.148149	+	0.203910i
$610$		0			0
$611$	10.0340	−	30.8815i	0.405933	−	1.24933i
$612$		0			0
$613$	−10.0530	+	7.30393i	−0.406037	+	0.295003i	−0.771995	−	0.635628i	$-0.780741\pi$
$613$	−10.0530	+	7.30393i	−0.406037	+	0.295003i	0.365959	+	0.930631i	$0.380741\pi$
$614$		0			0
$615$	1.28666	−	0.885413i	0.0518833	−	0.0357033i
$616$		0			0
$617$	−35.3489	+	25.6825i	−1.42309	+	1.03394i	−0.431841	+	0.901950i	$0.642136\pi$
$617$	−35.3489	+	25.6825i	−1.42309	+	1.03394i	−0.991251	+	0.131987i	$0.957864\pi$
$618$		0			0
$619$	1.21533	−	3.74041i	0.0488484	−	0.150340i	−0.923657	−	0.383220i	$-0.874815\pi$
$619$	1.21533	−	3.74041i	0.0488484	−	0.150340i	0.972505	+	0.232880i	$0.0748150\pi$
$620$		0			0
$621$	−12.9404	−	17.8109i	−0.519281	−	0.714729i
$622$		0			0
$623$	−2.46958	−	7.60057i	−0.0989414	−	0.304510i
$624$		0			0
$625$	7.60003	+	23.3905i	0.304001	+	0.935619i
$626$		0			0
$627$	−9.15238	−	2.97379i	−0.365511	−	0.118762i
$628$		0			0
$629$		−	54.5501i		−	2.17506i
$630$		0			0
$631$	10.5711	+	7.68035i	0.420828	+	0.305750i	0.777971	−	0.628300i	$-0.216249\pi$
$631$	10.5711	+	7.68035i	0.420828	+	0.305750i	−0.357143	+	0.934050i	$0.616249\pi$
$632$		0			0
$633$	25.0018	−	18.1649i	0.993734	−	0.721990i
$634$		0			0
$635$	2.16475	+	1.57278i	0.0859053	+	0.0624138i
$636$		0			0
$637$	3.59771	−	4.95183i	0.142547	−	0.196198i
$638$		0			0
$639$	3.89370	−	1.26514i	0.154032	−	0.0500481i
$640$		0			0
$641$	11.8356	+	3.84561i	0.467477	+	0.151892i	0.533277	−	0.845940i	$-0.320960\pi$
$641$	11.8356	+	3.84561i	0.467477	+	0.151892i	−0.0658008	+	0.997833i	$0.520960\pi$
$642$		0			0
$643$	3.24843	+	4.47108i	0.128106	+	0.176322i	0.868252	−	0.496124i	$-0.165244\pi$
$643$	3.24843	+	4.47108i	0.128106	+	0.176322i	−0.740146	+	0.672446i	$0.765244\pi$
$644$		0			0
$645$	−1.58463	+	0.514877i	−0.0623947	+	0.0202733i
$646$		0			0
$647$	−35.3366			−1.38923			−0.694613	−	0.719384i	$-0.744424\pi$
$647$	−35.3366			−1.38923			−0.694613	+	0.719384i	$0.744424\pi$
$648$		0			0
$649$	8.98130	−	12.3617i	0.352547	−	0.485239i
$650$		0			0
$651$	1.60133	−	4.92838i	0.0627610	−	0.193159i
$652$		0			0
$653$		−	25.0020i		−	0.978405i	−0.872170	−	0.489202i	$-0.837288\pi$
$653$		−	25.0020i		−	0.978405i	0.872170	−	0.489202i	$-0.162712\pi$
$654$		0			0
$655$	−1.37450			−0.0537063
$656$		0			0
$657$	5.47204			0.213485
$658$		0			0
$659$		−	30.0961i		−	1.17238i	−0.810175	−	0.586188i	$-0.800628\pi$
$659$		−	30.0961i		−	1.17238i	0.810175	−	0.586188i	$-0.199372\pi$
$660$		0			0
$661$	10.8568	−	33.4139i	0.422281	−	1.29965i	−0.483292	−	0.875459i	$-0.660559\pi$
$661$	10.8568	−	33.4139i	0.422281	−	1.29965i	0.905573	−	0.424189i	$-0.139441\pi$
$662$		0			0
$663$	33.1867	−	45.6776i	1.28886	−	1.77397i
$664$		0			0
$665$	−0.497531			−0.0192934
$666$		0			0
$667$	−15.5922	+	5.06620i	−0.603731	+	0.196164i
$668$		0			0
$669$	−11.6197	−	15.9931i	−0.449242	−	0.618329i
$670$		0			0
$671$	23.5638	+	7.65634i	0.909670	+	0.295570i
$672$		0			0
$673$	30.8489	−	10.0234i	1.18914	−	0.386374i	0.353383	−	0.935479i	$-0.385031\pi$
$673$	30.8489	−	10.0234i	1.18914	−	0.386374i	0.835754	+	0.549105i	$0.185031\pi$
$674$		0			0
$675$	16.4776	−	22.6795i	0.634224	−	0.872935i
$676$		0			0
$677$	20.4388	+	14.8497i	0.785529	+	0.570720i	0.906633	−	0.421920i	$-0.138644\pi$
$677$	20.4388	+	14.8497i	0.785529	+	0.570720i	−0.121105	+	0.992640i	$0.538644\pi$
$678$		0			0
$679$	−6.40151	+	4.65097i	−0.245667	+	0.178488i
$680$		0			0
$681$	−25.5056	−	18.5309i	−0.977379	−	0.710107i
$682$		0			0
$683$			19.1333i			0.732116i	0.930592	+	0.366058i	$0.119293\pi$
$683$			19.1333i			0.732116i	−0.930592	+	0.366058i	$0.880707\pi$
$684$		0			0
$685$	−1.14238	−	0.371182i	−0.0436481	−	0.0141821i
$686$		0			0
$687$	6.03046	+	18.5598i	0.230076	+	0.708102i
$688$		0			0
$689$	16.2892	+	50.1330i	0.620569	+	1.90992i
$690$		0			0
$691$	−0.632753	−	0.870910i	−0.0240711	−	0.0331310i	0.796812	−	0.604228i	$-0.206518\pi$
$691$	−0.632753	−	0.870910i	−0.0240711	−	0.0331310i	−0.820883	+	0.571097i	$0.806518\pi$
$692$		0			0
$693$	−0.534376	+	1.64464i	−0.0202993	+	0.0624747i
$694$		0			0
$695$	2.42855	−	1.76445i	0.0921203	−	0.0669293i
$696$		0			0
$697$	13.2847	−	37.5850i	0.503194	−	1.42363i
$698$		0			0
$699$	−6.74352	+	4.89945i	−0.255063	+	0.185314i
$700$		0			0
$701$	−5.76507	+	17.7431i	−0.217744	+	0.670146i	0.781204	+	0.624276i	$0.214606\pi$
$701$	−5.76507	+	17.7431i	−0.217744	+	0.670146i	−0.998947	+	0.0458699i	$0.985394\pi$
$702$		0			0
$703$	15.5649	+	21.4232i	0.587041	+	0.807993i
$704$		0			0
$705$	−0.399873	−	1.23068i	−0.0150601	−	0.0463502i
$706$		0			0
$707$	−4.59004	−	14.1267i	−0.172626	−	0.531289i
$708$		0			0
$709$	−34.9582	−	11.3586i	−1.31288	−	0.426581i	−0.432837	−	0.901472i	$-0.642487\pi$
$709$	−34.9582	−	11.3586i	−1.31288	−	0.426581i	−0.880044	+	0.474892i	$0.842487\pi$
$710$		0			0
$711$			7.83653i			0.293893i
$712$		0			0
$713$	11.0501	+	8.02837i	0.413830	+	0.300665i
$714$		0			0
$715$	1.75197	−	1.27288i	0.0655200	−	0.0476031i
$716$		0			0
$717$	9.83029	+	7.14212i	0.367119	+	0.266728i
$718$		0			0
$719$	25.1679	−	34.6406i	0.938602	−	1.29188i	−0.0178054	−	0.999841i	$-0.505668\pi$
$719$	25.1679	−	34.6406i	0.938602	−	1.29188i	0.956408	−	0.292034i	$-0.0943321\pi$
$720$		0			0
$721$	−16.5987	+	5.39324i	−0.618168	+	0.200855i
$722$		0			0
$723$	12.0947	+	3.92981i	0.449807	+	0.146151i
$724$		0			0
$725$	−12.2706	−	16.8890i	−0.455718	−	0.627243i
$726$		0			0
$727$	16.8507	−	5.47513i	0.624958	−	0.203061i	0.0206178	−	0.999787i	$-0.493437\pi$
$727$	16.8507	−	5.47513i	0.624958	−	0.203061i	0.604340	+	0.796726i	$0.293437\pi$
$728$		0			0
$729$	−29.8361			−1.10504
$730$		0			0
$731$	−24.9960	+	34.4041i	−0.924511	+	1.27248i
$732$		0			0
$733$	−7.43392	+	22.8792i	−0.274578	+	0.845064i	0.714753	+	0.699377i	$0.246539\pi$
$733$	−7.43392	+	22.8792i	−0.274578	+	0.845064i	−0.989331	+	0.145687i	$0.953461\pi$
$734$		0			0
$735$		−	0.243924i		−	0.00899728i
$736$		0			0
$737$	−5.53478			−0.203876
$738$		0			0
$739$	0.0829569			0.00305162			0.00152581	−	0.999999i	$-0.499514\pi$
$739$	0.0829569			0.00305162			0.00152581	+	0.999999i	$0.499514\pi$
$740$		0			0
$741$			27.4080i			1.00686i
$742$		0			0
$743$	−0.164219	+	0.505413i	−0.00602459	+	0.0185418i	−0.954024	−	0.299731i	$-0.903103\pi$
$743$	−0.164219	+	0.505413i	−0.00602459	+	0.0185418i	0.947999	+	0.318273i	$0.103103\pi$
$744$		0			0
$745$	−0.844990	+	1.16303i	−0.0309581	+	0.0426101i
$746$		0			0
$747$	6.60390			0.241624
$748$		0			0
$749$	5.26414	−	1.71042i	0.192348	−	0.0624975i
$750$		0			0
$751$	14.6520	+	20.1667i	0.534659	+	0.735895i	0.987832	−	0.155528i	$-0.0497078\pi$
$751$	14.6520	+	20.1667i	0.534659	+	0.735895i	−0.453172	+	0.891423i	$0.649708\pi$
$752$		0			0
$753$	36.8215	+	11.9640i	1.34185	+	0.435994i
$754$		0			0
$755$	−1.50747	+	0.489807i	−0.0548625	+	0.0178259i
$756$		0			0
$757$	5.34474	−	7.35640i	0.194258	−	0.267373i	−0.700766	−	0.713391i	$-0.747158\pi$
$757$	5.34474	−	7.35640i	0.194258	−	0.267373i	0.895024	+	0.446018i	$0.147158\pi$
$758$		0			0
$759$	10.0608	+	7.30957i	0.365183	+	0.265321i
$760$		0			0
$761$	−37.8313	+	27.4860i	−1.37138	+	0.996368i	−0.373756	+	0.927527i	$0.621930\pi$
$761$	−37.8313	+	27.4860i	−1.37138	+	0.996368i	−0.997628	+	0.0688410i	$0.978070\pi$
$762$		0			0
$763$	−2.68406	−	1.95008i	−0.0971695	−	0.0705978i
$764$		0			0
$765$			0.824697i			0.0298170i
$766$		0			0
$767$	−41.3881	−	13.4478i	−1.49444	−	0.485573i
$768$		0			0
$769$	−13.6146	−	41.9013i	−0.490954	−	1.51100i	−0.823169	−	0.567797i	$-0.807796\pi$
$769$	−13.6146	−	41.9013i	−0.490954	−	1.51100i	0.332215	−	0.943204i	$-0.392204\pi$
$770$		0			0
$771$	10.8549	+	33.4078i	0.390928	+	1.20315i
$772$		0			0
$773$	−16.5517	−	22.7815i	−0.595323	−	0.819392i	0.399947	−	0.916538i	$-0.369029\pi$
$773$	−16.5517	−	22.7815i	−0.595323	−	0.819392i	−0.995270	+	0.0971460i	$0.969029\pi$
$774$		0			0
$775$	−5.37450	+	16.5410i	−0.193058	+	0.594171i
$776$		0			0
$777$	−10.5032	+	7.63099i	−0.376799	+	0.273760i
$778$		0			0
$779$	5.50695	+	18.5511i	0.197307	+	0.664663i
$780$		0			0
$781$	−8.84639	+	6.42728i	−0.316549	+	0.229986i
$782$		0			0
$783$	−7.31284	+	22.5066i	−0.261340	+	0.804321i
$784$		0			0
$785$	−1.74968	−	2.40823i	−0.0624488	−	0.0859534i
$786$		0			0
$787$	−13.1845	−	40.5778i	−0.469977	−	1.44644i	−0.852613	−	0.522542i	$-0.824984\pi$
$787$	−13.1845	−	40.5778i	−0.469977	−	1.44644i	0.382636	−	0.923899i	$-0.375016\pi$
$788$		0			0
$789$	7.20030	+	22.1603i	0.256338	+	0.788926i
$790$		0			0
$791$	14.3277	+	4.65535i	0.509434	+	0.165525i
$792$		0			0
$793$		−	70.5648i		−	2.50583i
$794$		0			0
$795$	1.69951	+	1.23476i	0.0602752	+	0.0437925i
$796$		0			0
$797$	−24.9938	+	18.1591i	−0.885327	+	0.643228i	−0.934655	−	0.355555i	$-0.884292\pi$
$797$	−24.9938	+	18.1591i	−0.885327	+	0.643228i	0.0493283	+	0.998783i	$0.484292\pi$
$798$		0			0
$799$	−26.7195	−	19.4128i	−0.945267	−	0.686776i
$800$		0			0
$801$	3.77976	−	5.20240i	0.133551	−	0.183818i
$802$		0			0
$803$	−13.8998	+	4.51632i	−0.490513	+	0.159377i
$804$		0			0
$805$	0.611465	+	0.198677i	0.0215513	+	0.00700245i
$806$		0			0
$807$	9.12727	+	12.5626i	0.321295	+	0.442225i
$808$		0			0
$809$	25.3676	−	8.24244i	0.891878	−	0.289789i	0.172997	−	0.984922i	$-0.444655\pi$
$809$	25.3676	−	8.24244i	0.891878	−	0.289789i	0.718881	+	0.695134i	$0.244655\pi$
$810$		0			0
$811$	40.7197			1.42986			0.714931	−	0.699195i	$-0.246458\pi$
$811$	40.7197			1.42986			0.714931	+	0.699195i	$0.246458\pi$
$812$		0			0
$813$	−21.0329	+	28.9492i	−0.737654	+	1.01529i
$814$		0			0
$815$	−0.544966	+	1.67723i	−0.0190893	+	0.0587509i
$816$		0			0
$817$		−	20.6435i		−	0.722225i
$818$		0			0
$819$	4.92509			0.172096
$820$		0			0
$821$	−4.07096			−0.142077			−0.0710387	−	0.997474i	$-0.522631\pi$
$821$	−4.07096			−0.142077			−0.0710387	+	0.997474i	$0.522631\pi$
$822$		0			0
$823$		−	39.3024i		−	1.37000i	−0.728545	−	0.684998i	$-0.759803\pi$
$823$		−	39.3024i		−	1.37000i	0.728545	−	0.684998i	$-0.240197\pi$
$824$		0			0
$825$	−4.89331	+	15.0601i	−0.170363	+	0.524324i
$826$		0			0
$827$	13.2146	−	18.1883i	0.459515	−	0.632468i	−0.514893	−	0.857254i	$-0.672168\pi$
$827$	13.2146	−	18.1883i	0.459515	−	0.632468i	0.974408	+	0.224786i	$0.0721684\pi$
$828$		0			0
$829$	−32.9345			−1.14386			−0.571931	−	0.820302i	$-0.693805\pi$
$829$	−32.9345			−1.14386			−0.571931	+	0.820302i	$0.693805\pi$
$830$		0			0
$831$	−0.285606	+	0.0927989i	−0.00990755	+	0.00321916i
$832$		0			0
$833$	−3.65935	−	5.03667i	−0.126789	−	0.174510i
$834$		0			0
$835$	−0.243667	−	0.0791722i	−0.00843245	−	0.00273987i
$836$		0			0
$837$	18.7508	−	6.09249i	0.648121	−	0.210587i
$838$		0			0
$839$	−12.7705	+	17.5771i	−0.440886	+	0.606827i	−0.970409	−	0.241468i	$-0.922371\pi$
$839$	−12.7705	+	17.5771i	−0.440886	+	0.606827i	0.529523	+	0.848296i	$0.322371\pi$
$840$		0			0
$841$	−9.20435	−	6.68736i	−0.317392	−	0.230598i
$842$		0			0
$843$	−9.71911	+	7.06134i	−0.334744	+	0.243206i
$844$		0			0
$845$	−3.25829	−	2.36729i	−0.112089	−	0.0814372i
$846$		0			0
$847$			6.38133i			0.219265i
$848$		0			0
$849$	33.2559	+	10.8055i	1.14134	+	0.370844i
$850$		0			0
$851$	−10.5744	−	32.5446i	−0.362485	−	1.11562i
$852$		0			0
$853$	0.243035	+	0.747986i	0.00832137	+	0.0256105i	0.955131	−	0.296184i	$-0.0957141\pi$
$853$	0.243035	+	0.747986i	0.00832137	+	0.0256105i	−0.946810	+	0.321794i	$0.895714\pi$
$854$		0			0
$855$	−0.235312	−	0.323880i	−0.00804752	−	0.0110765i
$856$		0			0
$857$	−7.20198	+	22.1654i	−0.246015	+	0.757156i	0.749453	+	0.662058i	$0.230317\pi$
$857$	−7.20198	+	22.1654i	−0.246015	+	0.757156i	−0.995468	+	0.0950986i	$0.969683\pi$
$858$		0			0
$859$	−31.5688	+	22.9361i	−1.07711	+	0.782570i	−0.977178	−	0.212424i	$-0.931864\pi$
$859$	−31.5688	+	22.9361i	−1.07711	+	0.782570i	−0.0999371	+	0.994994i	$0.531864\pi$
$860$		0			0
$861$	−9.09506	+	2.69989i	−0.309959	+	0.0920119i
$862$		0			0
$863$	−24.9362	+	18.1172i	−0.848838	+	0.616717i	−0.924825	−	0.380392i	$-0.875789\pi$
$863$	−24.9362	+	18.1172i	−0.848838	+	0.616717i	0.0759874	+	0.997109i	$0.475789\pi$
$864$		0			0
$865$	0.162819	−	0.501105i	0.00553601	−	0.0170381i
$866$		0			0
$867$	−18.9499	−	26.0823i	−0.643573	−	0.885802i
$868$		0			0
$869$	−6.46783	−	19.9059i	−0.219406	−	0.675263i
$870$		0			0
$871$	4.87116	+	14.9919i	0.165053	+	0.507980i
$872$		0			0
$873$	−6.05532	−	1.96749i	−0.204941	−	0.0665895i
$874$		0			0
$875$			1.64182i			0.0555035i
$876$		0			0
$877$	−35.7086	−	25.9438i	−1.20579	−	0.876061i	−0.210952	−	0.977496i	$-0.567656\pi$
$877$	−35.7086	−	25.9438i	−1.20579	−	0.876061i	−0.994842	+	0.101435i	$0.967656\pi$
$878$		0			0
$879$	−27.3365	+	19.8611i	−0.922037	+	0.669899i
$880$		0			0
$881$	29.1605	+	21.1864i	0.982443	+	0.713786i	0.958253	−	0.285921i	$-0.0922995\pi$
$881$	29.1605	+	21.1864i	0.982443	+	0.713786i	0.0241895	+	0.999707i	$0.492299\pi$
$882$		0			0
$883$	−9.29707	+	12.7963i	−0.312871	+	0.430631i	−0.936274	−	0.351270i	$-0.885750\pi$
$883$	−9.29707	+	12.7963i	−0.312871	+	0.430631i	0.623403	+	0.781901i	$0.285750\pi$
$884$		0			0
$885$	−1.64939	+	0.535919i	−0.0554436	+	0.0180147i
$886$		0			0
$887$	4.71338	+	1.53147i	0.158260	+	0.0514217i	0.387075	−	0.922048i	$-0.373485\pi$
$887$	4.71338	+	1.53147i	0.158260	+	0.0514217i	−0.228816	+	0.973470i	$0.573485\pi$
$888$		0			0
$889$	−9.55355	−	13.1493i	−0.320416	−	0.441015i
$890$		0			0
$891$	12.1380	−	3.94389i	0.406640	−	0.132125i
$892$		0			0
$893$	16.0325			0.536508
$894$		0			0
$895$	1.63253	−	2.24698i	0.0545693	−	0.0751082i
$896$		0			0
$897$	10.9447	−	33.6844i	0.365434	−	1.12469i
$898$		0			0
$899$		−	14.6819i		−	0.489670i
$900$		0			0
$901$	53.6161			1.78621
$902$		0			0
$903$	10.1209			0.336802
$904$		0			0
$905$		−	2.36181i		−	0.0785092i
$906$		0			0
$907$	−17.0737	+	52.5473i	−0.566922	+	1.74481i	0.0952501	+	0.995453i	$0.469635\pi$
$907$	−17.0737	+	52.5473i	−0.566922	+	1.74481i	−0.662172	+	0.749352i	$0.730365\pi$
$908$		0			0
$909$	7.02521	−	9.66937i	0.233011	−	0.320713i
$910$		0			0
$911$	−29.3447			−0.972233			−0.486116	−	0.873894i	$-0.661587\pi$
$911$	−29.3447			−0.972233			−0.486116	+	0.873894i	$0.661587\pi$
$912$		0			0
$913$	−16.7749	+	5.45049i	−0.555167	+	0.180385i
$914$		0			0
$915$	−1.65293	−	2.27506i	−0.0546441	−	0.0752112i
$916$		0			0
$917$	7.94052	+	2.58003i	0.262219	+	0.0852002i
$918$		0			0
$919$	−26.5289	+	8.61975i	−0.875107	+	0.284339i	−0.711924	−	0.702256i	$-0.752176\pi$
$919$	−26.5289	+	8.61975i	−0.875107	+	0.284339i	−0.163183	+	0.986596i	$0.552176\pi$
$920$		0			0
$921$	16.5889	−	22.8327i	0.546624	−	0.752364i
$922$		0			0
$923$	25.1950	+	18.3053i	0.829305	+	0.602525i
$924$		0			0
$925$	35.2515	−	25.6117i	1.15906	−	0.842108i
$926$		0			0
$927$	−11.3614	−	8.25453i	−0.373157	−	0.271114i
$928$		0			0
$929$		−	25.9326i		−	0.850822i	−0.905000	−	0.425411i	$-0.860130\pi$
$929$		−	25.9326i		−	0.850822i	0.905000	−	0.425411i	$-0.139870\pi$
$930$		0			0
$931$	2.87424	+	0.933898i	0.0941995	+	0.0306073i
$932$		0			0
$933$	−5.11815	−	15.7521i	−0.167561	−	0.515699i
$934$		0			0
$935$	−0.680659	−	2.09485i	−0.0222599	−	0.0685090i
$936$		0			0
$937$	−7.77596	−	10.7027i	−0.254030	−	0.349642i	0.662888	−	0.748719i	$-0.269331\pi$
$937$	−7.77596	−	10.7027i	−0.254030	−	0.349642i	−0.916917	+	0.399077i	$0.869331\pi$
$938$		0			0
$939$	8.85287	−	27.2463i	0.288902	−	0.889150i
$940$		0			0
$941$	−4.33059	+	3.14636i	−0.141173	+	0.102568i	−0.656130	−	0.754648i	$-0.727808\pi$
$941$	−4.33059	+	3.14636i	−0.141173	+	0.102568i	0.514957	+	0.857216i	$0.327808\pi$
$942$		0			0
$943$	0.639921	−	24.9984i	0.0208387	−	0.814060i
$944$		0			0
$945$	0.750805	−	0.545492i	0.0244237	−	0.0177448i
$946$		0			0
$947$	−12.0184	+	36.9888i	−0.390546	+	1.20198i	0.541831	+	0.840487i	$0.317731\pi$
$947$	−12.0184	+	36.9888i	−0.390546	+	1.20198i	−0.932377	+	0.361488i	$0.882269\pi$
$948$		0			0
$949$	24.4664	+	33.6751i	0.794212	+	1.09314i
$950$		0			0
$951$	15.8841	+	48.8862i	0.515077	+	1.58524i
$952$		0			0
$953$	−3.38623	−	10.4217i	−0.109691	−	0.337593i	0.881112	−	0.472907i	$-0.156796\pi$
$953$	−3.38623	−	10.4217i	−0.109691	−	0.337593i	−0.990803	+	0.135315i	$0.956796\pi$
$954$		0			0
$955$	0.907405	+	0.294834i	0.0293629	+	0.00954059i
$956$		0			0
$957$		−	13.3674i		−	0.432108i
$958$		0			0
$959$	5.90281	+	4.28864i	0.190612	+	0.138488i
$960$		0			0
$961$	15.1838	−	11.0316i	0.489798	−	0.355859i
$962$		0			0
$963$	3.60317	+	2.61786i	0.116111	+	0.0843593i
$964$		0			0
$965$	0.128649	−	0.177070i	0.00414136	−	0.00570010i
$966$		0			0
$967$	34.5517	−	11.2265i	1.11111	−	0.361021i	0.304740	−	0.952436i	$-0.401430\pi$
$967$	34.5517	−	11.2265i	1.11111	−	0.361021i	0.806368	+	0.591415i	$0.201430\pi$
$968$		0			0
$969$	26.5131	+	8.61464i	0.851725	+	0.276742i
$970$		0			0
$971$	−10.6677	−	14.6828i	−0.342342	−	0.471193i	0.602782	−	0.797906i	$-0.294059\pi$
$971$	−10.6677	−	14.6828i	−0.342342	−	0.471193i	−0.945124	+	0.326713i	$0.894059\pi$
$972$		0			0
$973$	−17.3418	+	5.63468i	−0.555952	+	0.180640i
$974$		0			0
$975$	45.0993			1.44433
$976$		0			0
$977$	−15.6808	+	21.5828i	−0.501673	+	0.690494i	−0.982487	−	0.186329i	$-0.940341\pi$
$977$	−15.6808	+	21.5828i	−0.501673	+	0.690494i	0.480814	+	0.876822i	$0.340341\pi$
$978$		0			0
$979$	−5.30739	+	16.3345i	−0.169625	+	0.522052i
$980$		0			0
$981$		−	2.66957i		−	0.0852327i
$982$		0			0
$983$	−1.48604			−0.0473974			−0.0236987	−	0.999719i	$-0.507544\pi$
$983$	−1.48604			−0.0473974			−0.0236987	+	0.999719i	$0.507544\pi$
$984$		0			0
$985$	−3.91606			−0.124776
$986$		0			0
$987$			7.86025i			0.250195i
$988$		0			0
$989$	−8.24350	+	25.3709i	−0.262128	+	0.806747i
$990$		0			0
$991$	3.25154	−	4.47536i	0.103289	−	0.142165i	−0.754244	−	0.656594i	$-0.771996\pi$
$991$	3.25154	−	4.47536i	0.103289	−	0.142165i	0.857533	+	0.514430i	$0.171996\pi$
$992$		0			0
$993$	−45.8545			−1.45515
$994$		0			0
$995$	−2.53924	+	0.825048i	−0.0804992	+	0.0261558i
$996$		0			0
$997$	−13.7125	−	18.8737i	−0.434281	−	0.597736i	0.534648	−	0.845075i	$-0.320444\pi$
$997$	−13.7125	−	18.8737i	−0.434281	−	0.597736i	−0.968929	+	0.247338i	$0.920444\pi$
$998$		0			0
$999$	−46.9768	−	15.2637i	−1.48628	−	0.482921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.701.7	yes	80
41.31	even	10	inner	1148.2.ba.a.113.14	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.14	✓	80	41.31	even	10	inner
1148.2.ba.a.701.7	yes	80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-1.48167i q^{3} +(-0.0508728 + 0.156570i) q^{5} +(0.587785 - 0.809017i) q^{7} +0.804648 q^{9} +O(q^{10})\)	\(q-1.48167i q^{3} +(-0.0508728 + 0.156570i) q^{5} +(0.587785 - 0.809017i) q^{7} +0.804648 q^{9} +(-2.04392 + 0.664111i) q^{11} +(3.59771 + 4.95183i) q^{13} +(0.231986 + 0.0753767i) q^{15} +(5.92096 - 1.92384i) q^{17} +(-1.77638 + 2.44498i) q^{19} +(-1.19870 - 0.870905i) q^{21} +(3.15951 - 2.29552i) q^{23} +(4.02316 + 2.92300i) q^{25} -5.63724i q^{27} +(-3.99249 - 1.29724i) q^{29} +(1.08076 + 3.32623i) q^{31} +(0.983995 + 3.02843i) q^{33} +(0.0967657 + 0.133187i) q^{35} +(2.70765 - 8.33329i) q^{37} +(7.33698 - 5.33063i) q^{39} +(3.89499 - 5.08223i) q^{41} +(-5.52617 + 4.01500i) q^{43} +(-0.0409347 + 0.125984i) q^{45} +(-3.11819 - 4.29183i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-2.85049 - 8.77292i) q^{51} +(8.19061 + 2.66129i) q^{53} -0.353803i q^{55} +(3.62265 + 2.63201i) q^{57} +(-5.75201 + 4.17908i) q^{59} +(-9.32691 - 6.77640i) q^{61} +(0.472960 - 0.650974i) q^{63} +(-0.958334 + 0.311382i) q^{65} +(2.44934 + 0.795837i) q^{67} +(-3.40121 - 4.68136i) q^{69} +(4.83900 - 1.57229i) q^{71} +6.80054 q^{73} +(4.33092 - 5.96100i) q^{75} +(-0.664111 + 2.04392i) q^{77} +9.73908i q^{79} -5.93860 q^{81} +8.20719 q^{83} +1.02492i q^{85} +(-1.92208 + 5.91556i) q^{87} +(4.69741 - 6.46543i) q^{89} +6.12079 q^{91} +(4.92838 - 1.60133i) q^{93} +(-0.292441 - 0.402511i) q^{95} +(-7.52542 - 2.44516i) q^{97} +(-1.64464 + 0.534376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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