LMFDB - Embedded newform 712.2.u.a.25.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [712,2,Mod(25,712)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(712, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("712.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 712 = 2^{3} \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	712.u (of order $22$, 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:	$5.68534862392$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			25.10
Character	$\chi$	$=$	712.25
Dual form			712.2.u.a.57.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.703549 - 2.39607i) q^{3} +(-1.32830 - 2.90857i) q^{5} +(-0.192082 + 0.0877207i) q^{7} +(-2.72241 - 1.74958i) q^{9} +O(q^{10})$	\(q+(0.703549 - 2.39607i) q^{3} +(-1.32830 - 2.90857i) q^{5} +(-0.192082 + 0.0877207i) q^{7} +(-2.72241 - 1.74958i) q^{9} +(1.07347 - 2.35057i) q^{11} +(0.935804 - 3.18706i) q^{13} +(-7.90366 + 1.13638i) q^{15} +(-0.622296 + 4.32816i) q^{17} +(-1.92165 + 2.99015i) q^{19} +(0.0750460 + 0.521957i) q^{21} +(0.106110 - 0.165110i) q^{23} +(-3.42110 + 3.94816i) q^{25} +(-0.445641 + 0.386150i) q^{27} +(3.88668 - 1.77499i) q^{29} +(-2.53028 - 3.93720i) q^{31} +(-4.87690 - 4.22586i) q^{33} +(0.510284 + 0.442164i) q^{35} +1.85202i q^{37} +(-6.97802 - 4.48450i) q^{39} +(2.90051 + 9.87823i) q^{41} +(-10.4324 - 4.76433i) q^{43} +(-1.47262 + 10.2423i) q^{45} +(3.06589 - 0.900228i) q^{47} +(-4.55482 + 5.25655i) q^{49} +(9.93276 + 4.53614i) q^{51} +(6.56760 + 1.92842i) q^{53} -8.26270 q^{55} +(5.81263 + 6.70813i) q^{57} +(-0.653933 - 2.22709i) q^{59} +(4.06895 - 3.52576i) q^{61} +(0.676399 + 0.0972514i) q^{63} +(-10.5128 + 1.51151i) q^{65} +(4.86751 + 1.42923i) q^{67} +(-0.320961 - 0.370409i) q^{69} +(5.65175 - 12.3756i) q^{71} +(-3.83710 + 2.46596i) q^{73} +(7.05316 + 10.9749i) q^{75} +0.545667i q^{77} +(3.34082 - 2.14702i) q^{79} +(-3.42130 - 7.49160i) q^{81} +(-7.22513 - 1.03882i) q^{83} +(13.4154 - 3.93911i) q^{85} +(-1.51852 - 10.5616i) q^{87} +(4.25931 - 8.41774i) q^{89} +(0.0998201 + 0.694264i) q^{91} +(-11.2140 + 3.29272i) q^{93} +(11.2496 + 1.61745i) q^{95} +(-5.27727 - 11.5556i) q^{97} +(-7.03495 + 4.52109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 10 q^{9}+O(q^{10}) $ 100 * q + 10 * q^9	$ 100 q + 10 q^{9} + 14 q^{11} + 22 q^{13} - 8 q^{17} - 11 q^{19} - 34 q^{21} + 33 q^{23} + 24 q^{25} - 66 q^{27} - 22 q^{33} + 33 q^{35} - 36 q^{39} + 55 q^{41} + 8 q^{45} - 40 q^{47} - 30 q^{49} + 22 q^{51} - 38 q^{53} + 42 q^{55} + 54 q^{57} + 22 q^{59} + 11 q^{61} + 11 q^{63} - 33 q^{65} + 2 q^{67} + 17 q^{69} - 13 q^{71} + 20 q^{73} - 12 q^{79} - 38 q^{81} + 11 q^{83} + 35 q^{85} - 50 q^{87} + 47 q^{89} + 26 q^{91} - 2 q^{93} + 44 q^{95} + 36 q^{97} - 38 q^{99}+O(q^{100}) $ 100 * q + 10 * q^9 + 14 * q^11 + 22 * q^13 - 8 * q^17 - 11 * q^19 - 34 * q^21 + 33 * q^23 + 24 * q^25 - 66 * q^27 - 22 * q^33 + 33 * q^35 - 36 * q^39 + 55 * q^41 + 8 * q^45 - 40 * q^47 - 30 * q^49 + 22 * q^51 - 38 * q^53 + 42 * q^55 + 54 * q^57 + 22 * q^59 + 11 * q^61 + 11 * q^63 - 33 * q^65 + 2 * q^67 + 17 * q^69 - 13 * q^71 + 20 * q^73 - 12 * q^79 - 38 * q^81 + 11 * q^83 + 35 * q^85 - 50 * q^87 + 47 * q^89 + 26 * q^91 - 2 * q^93 + 44 * q^95 + 36 * q^97 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/712\mathbb{Z}\right)^\times$.

$n$	$357$	$535$	$537$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{22}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.703549	−	2.39607i	0.406194	−	1.38337i	−0.461882	−	0.886941i	$-0.652826\pi$
$3$	0.703549	−	2.39607i	0.406194	−	1.38337i	0.868077	−	0.496430i	$-0.165356\pi$
$4$		0			0
$5$	−1.32830	−	2.90857i	−0.594034	−	1.30075i	−0.932974	−	0.359945i	$-0.882796\pi$
$5$	−1.32830	−	2.90857i	−0.594034	−	1.30075i	0.338940	−	0.940808i	$-0.389932\pi$
$6$		0			0
$7$	−0.192082	+	0.0877207i	−0.0726000	+	0.0331553i	−0.451384	−	0.892330i	$-0.649070\pi$
$7$	−0.192082	+	0.0877207i	−0.0726000	+	0.0331553i	0.378784	+	0.925485i	$0.376342\pi$
$8$		0			0
$9$	−2.72241	−	1.74958i	−0.907468	−	0.583195i
$10$		0			0
$11$	1.07347	−	2.35057i	0.323664	−	0.708725i	−0.675938	−	0.736959i	$-0.736261\pi$
$11$	1.07347	−	2.35057i	0.323664	−	0.708725i	0.999601	+	0.0282342i	$0.00898843\pi$
$12$		0			0
$13$	0.935804	−	3.18706i	0.259545	−	0.883930i	−0.721869	−	0.692030i	$-0.756717\pi$
$13$	0.935804	−	3.18706i	0.259545	−	0.883930i	0.981414	−	0.191901i	$-0.0614651\pi$
$14$		0			0
$15$	−7.90366	+	1.13638i	−2.04072	+	0.293411i
$16$		0			0
$17$	−0.622296	+	4.32816i	−0.150929	+	1.04973i	0.763738	+	0.645526i	$0.223362\pi$
$17$	−0.622296	+	4.32816i	−0.150929	+	1.04973i	−0.914667	+	0.404208i	$0.867547\pi$
$18$		0			0
$19$	−1.92165	+	2.99015i	−0.440858	+	0.685988i	−0.988584	−	0.150670i	$-0.951857\pi$
$19$	−1.92165	+	2.99015i	−0.440858	+	0.685988i	0.547727	+	0.836657i	$0.315493\pi$
$20$		0			0
$21$	0.0750460	+	0.521957i	0.0163764	+	0.113900i
$22$		0			0
$23$	0.106110	−	0.165110i	0.0221254	−	0.0344278i	−0.830015	−	0.557742i	$-0.811668\pi$
$23$	0.106110	−	0.165110i	0.0221254	−	0.0344278i	0.852140	+	0.523314i	$0.175304\pi$
$24$		0			0
$25$	−3.42110	+	3.94816i	−0.684221	+	0.789633i
$26$		0			0
$27$	−0.445641	+	0.386150i	−0.0857636	+	0.0743146i
$28$		0			0
$29$	3.88668	−	1.77499i	0.721739	−	0.329607i	−0.0204565	−	0.999791i	$-0.506512\pi$
$29$	3.88668	−	1.77499i	0.721739	−	0.329607i	0.742195	+	0.670184i	$0.233785\pi$
$30$		0			0
$31$	−2.53028	−	3.93720i	−0.454452	−	0.707141i	0.536119	−	0.844143i	$-0.319890\pi$
$31$	−2.53028	−	3.93720i	−0.454452	−	0.707141i	−0.990571	+	0.137001i	$0.956254\pi$
$32$		0			0
$33$	−4.87690	−	4.22586i	−0.848959	−	0.735627i
$34$		0			0
$35$	0.510284	+	0.442164i	0.0862537	+	0.0747393i
$36$		0			0
$37$			1.85202i			0.304470i	0.988344	+	0.152235i	$0.0486471\pi$
$37$			1.85202i			0.304470i	−0.988344	+	0.152235i	$0.951353\pi$
$38$		0			0
$39$	−6.97802	−	4.48450i	−1.11738	−	0.718095i
$40$		0			0
$41$	2.90051	+	9.87823i	0.452984	+	1.54272i	0.797132	+	0.603806i	$0.206350\pi$
$41$	2.90051	+	9.87823i	0.452984	+	1.54272i	−0.344148	+	0.938915i	$0.611832\pi$
$42$		0			0
$43$	−10.4324	−	4.76433i	−1.59093	−	0.726554i	−0.593972	−	0.804486i	$-0.702441\pi$
$43$	−10.4324	−	4.76433i	−1.59093	−	0.726554i	−0.996959	+	0.0779321i	$0.975168\pi$
$44$		0			0
$45$	−1.47262	+	10.2423i	−0.219525	+	1.52683i
$46$		0			0
$47$	3.06589	−	0.900228i	0.447207	−	0.131312i	−0.0503721	−	0.998731i	$-0.516041\pi$
$47$	3.06589	−	0.900228i	0.447207	−	0.131312i	0.497579	+	0.867419i	$0.334223\pi$
$48$		0			0
$49$	−4.55482	+	5.25655i	−0.650689	+	0.750935i
$50$		0			0
$51$	9.93276	+	4.53614i	1.39087	+	0.635187i
$52$		0			0
$53$	6.56760	+	1.92842i	0.902130	+	0.264889i	0.699725	−	0.714413i	$-0.253306\pi$
$53$	6.56760	+	1.92842i	0.902130	+	0.264889i	0.202405	+	0.979302i	$0.435124\pi$
$54$		0			0
$55$	−8.26270			−1.11414
$56$		0			0
$57$	5.81263	+	6.70813i	0.769902	+	0.888514i
$58$		0			0
$59$	−0.653933	−	2.22709i	−0.0851349	−	0.289943i	0.905910	−	0.423470i	$-0.139188\pi$
$59$	−0.653933	−	2.22709i	−0.0851349	−	0.289943i	−0.991045	+	0.133527i	$0.957370\pi$
$60$		0			0
$61$	4.06895	−	3.52576i	0.520975	−	0.451427i	−0.354245	−	0.935153i	$-0.615262\pi$
$61$	4.06895	−	3.52576i	0.520975	−	0.451427i	0.875220	+	0.483725i	$0.160717\pi$
$62$		0			0
$63$	0.676399	+	0.0972514i	0.0852182	+	0.0122525i
$64$		0			0
$65$	−10.5128	+	1.51151i	−1.30395	+	0.187480i
$66$		0			0
$67$	4.86751	+	1.42923i	0.594661	+	0.174608i	0.565195	−	0.824958i	$-0.308801\pi$
$67$	4.86751	+	1.42923i	0.594661	+	0.174608i	0.0294664	+	0.999566i	$0.490619\pi$
$68$		0			0
$69$	−0.320961	−	0.370409i	−0.0386392	−	0.0445920i
$70$		0			0
$71$	5.65175	−	12.3756i	0.670739	−	1.46871i	−0.201427	−	0.979504i	$-0.564558\pi$
$71$	5.65175	−	12.3756i	0.670739	−	1.46871i	0.872166	−	0.489210i	$-0.162715\pi$
$72$		0			0
$73$	−3.83710	+	2.46596i	−0.449099	+	0.288618i	−0.745575	−	0.666422i	$-0.767825\pi$
$73$	−3.83710	+	2.46596i	−0.449099	+	0.288618i	0.296476	+	0.955040i	$0.404189\pi$
$74$		0			0
$75$	7.05316	+	10.9749i	0.814429	+	1.26728i
$76$		0			0
$77$			0.545667i			0.0621846i
$78$		0			0
$79$	3.34082	−	2.14702i	0.375872	−	0.241558i	−0.339041	−	0.940771i	$-0.610103\pi$
$79$	3.34082	−	2.14702i	0.375872	−	0.241558i	0.714913	+	0.699213i	$0.246466\pi$
$80$		0			0
$81$	−3.42130	−	7.49160i	−0.380144	−	0.832400i
$82$		0			0
$83$	−7.22513	−	1.03882i	−0.793061	−	0.114025i	−0.266134	−	0.963936i	$-0.585747\pi$
$83$	−7.22513	−	1.03882i	−0.793061	−	0.114025i	−0.526926	+	0.849911i	$0.676656\pi$
$84$		0			0
$85$	13.4154	−	3.93911i	1.45510	−	0.427256i
$86$		0			0
$87$	−1.51852	−	10.5616i	−0.162803	−	1.13232i
$88$		0			0
$89$	4.25931	−	8.41774i	0.451486	−	0.892278i
$89$	4.25931	−	8.41774i	0.451486	−	0.892278i
$90$		0			0
$91$	0.0998201	+	0.694264i	0.0104640	+	0.0727787i
$92$		0			0
$93$	−11.2140	+	3.29272i	−1.16283	+	0.341439i
$94$		0			0
$95$	11.2496	+	1.61745i	1.15418	+	0.165947i
$96$		0			0
$97$	−5.27727	−	11.5556i	−0.535825	−	1.17329i	−0.963093	−	0.269169i	$-0.913251\pi$
$97$	−5.27727	−	11.5556i	−0.535825	−	1.17329i	0.427268	−	0.904125i	$-0.359476\pi$
$98$		0			0
$99$	−7.03495	+	4.52109i	−0.707039	+	0.454386i
$100$		0			0
$101$			8.50200i			0.845981i	0.906134	+	0.422991i	$0.139020\pi$
$101$			8.50200i			0.845981i	−0.906134	+	0.422991i	$0.860980\pi$
$102$		0			0
$103$	−4.79892	−	7.46726i	−0.472851	−	0.735771i	0.520124	−	0.854091i	$-0.325886\pi$
$103$	−4.79892	−	7.46726i	−0.472851	−	0.735771i	−0.992976	+	0.118319i	$0.962249\pi$
$104$		0			0
$105$	1.41846	−	0.911592i	0.138428	−	0.0889622i
$106$		0			0
$107$	5.31174	−	11.6311i	0.513505	−	1.12442i	−0.458336	−	0.888779i	$-0.651554\pi$
$107$	5.31174	−	11.6311i	0.513505	−	1.12442i	0.971840	−	0.235640i	$-0.0757185\pi$
$108$		0			0
$109$	−3.23336	−	3.73150i	−0.309700	−	0.357412i	0.579467	−	0.814996i	$-0.303261\pi$
$109$	−3.23336	−	3.73150i	−0.309700	−	0.357412i	−0.889167	+	0.457583i	$0.848715\pi$
$110$		0			0
$111$	4.43757	+	1.30299i	0.421196	+	0.123674i
$112$		0			0
$113$	10.0090	−	1.43908i	0.941569	−	0.135377i	0.345598	−	0.938383i	$-0.387676\pi$
$113$	10.0090	−	1.43908i	0.941569	−	0.135377i	0.595971	+	0.803006i	$0.296767\pi$
$114$		0			0
$115$	−0.621180	−	0.0893121i	−0.0579253	−	0.00832840i
$116$		0			0
$117$	−8.12366	+	7.03919i	−0.751033	+	0.650773i
$118$		0			0
$119$	−0.260138	−	0.885949i	−0.0238468	−	0.0812148i
$120$		0			0
$121$	2.83061	+	3.26670i	0.257328	+	0.296973i
$122$		0			0
$123$	25.7096			2.31816
$124$		0			0
$125$	0.687751	+	0.201942i	0.0615143	+	0.0180622i
$126$		0			0
$127$	1.98021	+	0.904330i	0.175715	+	0.0802463i	0.501330	−	0.865256i	$-0.332844\pi$
$127$	1.98021	+	0.904330i	0.175715	+	0.0802463i	−0.325615	+	0.945502i	$0.605571\pi$
$128$		0			0
$129$	−18.7554	+	21.6449i	−1.65132	+	1.90573i
$130$		0			0
$131$	16.4291	−	4.82402i	1.43542	−	0.421476i	0.530726	−	0.847544i	$-0.321919\pi$
$131$	16.4291	−	4.82402i	1.43542	−	0.421476i	0.904691	+	0.426067i	$0.140101\pi$
$132$		0			0
$133$	0.106816	−	0.742922i	0.00926212	−	0.0644195i
$134$		0			0
$135$	1.71509	+	0.783255i	0.147611	+	0.0674119i
$136$		0			0
$137$	5.66055	+	19.2781i	0.483614	+	1.64704i	0.734193	+	0.678941i	$0.237561\pi$
$137$	5.66055	+	19.2781i	0.483614	+	1.64704i	−0.250580	+	0.968096i	$0.580621\pi$
$138$		0			0
$139$	1.71133	+	1.09981i	0.145153	+	0.0932843i	0.611202	−	0.791475i	$-0.290686\pi$
$139$	1.71133	+	1.09981i	0.145153	+	0.0932843i	−0.466049	+	0.884759i	$0.654323\pi$
$140$		0			0
$141$		−	7.97945i		−	0.671991i
$142$		0			0
$143$	−6.48685	−	5.62089i	−0.542458	−	0.470042i
$144$		0			0
$145$	−10.3254	−	8.94698i	−0.857475	−	0.743006i
$146$		0			0
$147$	9.39051	+	14.6119i	0.774516	+	1.20517i
$148$		0			0
$149$	18.1798	−	8.30242i	1.48934	−	0.680161i	0.506103	−	0.862473i	$-0.331085\pi$
$149$	18.1798	−	8.30242i	1.48934	−	0.680161i	0.983241	+	0.182312i	$0.0583582\pi$
$150$		0			0
$151$	−4.09623	+	3.54940i	−0.333347	+	0.288846i	−0.805410	−	0.592718i	$-0.798055\pi$
$151$	−4.09623	+	3.54940i	−0.333347	+	0.288846i	0.472063	+	0.881565i	$0.343509\pi$
$152$		0			0
$153$	9.26663	−	10.6943i	0.749162	−	0.864579i
$154$		0			0
$155$	−8.09064	+	12.5893i	−0.649856	+	1.01120i
$156$		0			0
$157$	−0.980700	−	6.82092i	−0.0782684	−	0.544369i	−0.990797	−	0.135356i	$-0.956782\pi$
$157$	−0.980700	−	6.82092i	−0.0782684	−	0.544369i	0.912529	−	0.409013i	$-0.134127\pi$
$158$		0			0
$159$	9.24127	−	14.3797i	0.732880	−	1.14038i
$160$		0			0
$161$	−0.00589816	+	0.0410226i	−0.000464840	+	0.00323303i
$162$		0			0
$163$	−5.56816	+	0.800581i	−0.436132	+	0.0627063i	−0.356884	−	0.934149i	$-0.616161\pi$
$163$	−5.56816	+	0.800581i	−0.436132	+	0.0627063i	−0.0792479	+	0.996855i	$0.525252\pi$
$164$		0			0
$165$	−5.81322	+	19.7980i	−0.452559	+	1.54127i
$166$		0			0
$167$	4.59780	−	10.0678i	0.355788	−	0.779067i	−0.644112	−	0.764931i	$-0.722773\pi$
$167$	4.59780	−	10.0678i	0.355788	−	0.779067i	0.999900	−	0.0141361i	$-0.00449980\pi$
$168$		0			0
$169$	1.65470	+	1.06341i	0.127284	+	0.0818008i
$170$		0			0
$171$	10.4630	−	4.77831i	0.800129	−	0.365406i
$172$		0			0
$173$	2.60917	+	5.71329i	0.198372	+	0.434374i	0.982509	−	0.186213i	$-0.0596216\pi$
$173$	2.60917	+	5.71329i	0.198372	+	0.434374i	−0.784138	+	0.620587i	$0.786894\pi$
$174$		0			0
$175$	0.310795	−	1.05847i	0.0234939	−	0.0800129i
$176$		0			0
$177$	−5.79634			−0.435680
$178$		0			0
$179$	−25.9576			−1.94016			−0.970080	−	0.242785i	$-0.921939\pi$
$179$	−25.9576			−1.94016			−0.970080	+	0.242785i	$0.921939\pi$
$180$		0			0
$181$	4.94442	−	16.8392i	0.367516	−	1.25164i	−0.543548	−	0.839378i	$-0.682919\pi$
$181$	4.94442	−	16.8392i	0.367516	−	1.25164i	0.911064	−	0.412266i	$-0.135263\pi$
$182$		0			0
$183$	−5.58526	−	12.2300i	−0.412875	−	0.904069i
$184$		0			0
$185$	5.38674	−	2.46004i	0.396041	−	0.180866i
$186$		0			0
$187$	9.50565	+	6.10891i	0.695122	+	0.446728i
$188$		0			0
$189$	0.0517261	−	0.113264i	0.00376252	−	0.00823876i
$190$		0			0
$191$	−0.931620	+	3.17280i	−0.0674096	+	0.229576i	−0.986307	−	0.164921i	$-0.947263\pi$
$191$	−0.931620	+	3.17280i	−0.0674096	+	0.229576i	0.918897	+	0.394497i	$0.129081\pi$
$192$		0			0
$193$	−2.78445	+	0.400344i	−0.200429	+	0.0288174i	−0.241798	−	0.970327i	$-0.577737\pi$
$193$	−2.78445	+	0.400344i	−0.200429	+	0.0288174i	0.0413689	+	0.999144i	$0.486828\pi$
$194$		0			0
$195$	−3.77459	+	26.2528i	−0.270304	+	1.88001i
$196$		0			0
$197$	−5.44762	+	8.47666i	−0.388127	+	0.603937i	−0.979253	−	0.202642i	$-0.935047\pi$
$197$	−5.44762	+	8.47666i	−0.388127	+	0.603937i	0.591126	+	0.806579i	$0.298684\pi$
$198$		0			0
$199$	3.20612	+	22.2991i	0.227276	+	1.58074i	0.709509	+	0.704696i	$0.248917\pi$
$199$	3.20612	+	22.2991i	0.227276	+	1.58074i	−0.482233	+	0.876043i	$0.660174\pi$
$200$		0			0
$201$	6.84907	−	10.6574i	0.483096	−	0.751712i
$202$		0			0
$203$	−0.590857	+	0.681885i	−0.0414700	+	0.0478589i
$204$		0			0
$205$	24.8788	−	21.5576i	1.73761	−	1.50565i
$206$		0			0
$207$	−0.577747	+	0.263848i	−0.0401562	+	0.0183387i
$208$		0			0
$209$	4.96573	+	7.72683i	0.343487	+	0.534476i
$210$		0			0
$211$	16.0103	+	13.8730i	1.10219	+	0.955056i	0.999215	−	0.0396276i	$-0.0126172\pi$
$211$	16.0103	+	13.8730i	1.10219	+	0.955056i	0.102979	+	0.994684i	$0.467163\pi$
$212$		0			0
$213$	−25.6765	−	22.2488i	−1.75933	−	1.52446i
$214$		0			0
$215$			36.6719i			2.50100i
$216$		0			0
$217$	0.831394	+	0.534304i	0.0564387	+	0.0362710i
$218$		0			0
$219$	3.20901	+	10.9289i	0.216845	+	0.738506i
$220$		0			0
$221$	13.2118	+	6.03361i	0.888719	+	0.405864i
$222$		0			0
$223$	3.48411	−	24.2325i	0.233313	−	1.62273i	−0.450295	−	0.892880i	$-0.648681\pi$
$223$	3.48411	−	24.2325i	0.233313	−	1.62273i	0.683608	−	0.729849i	$-0.260410\pi$
$224$		0			0
$225$	16.2213	−	4.76299i	1.08142	−	0.317533i
$226$		0			0
$227$	3.65005	−	4.21238i	0.242262	−	0.279586i	−0.621577	−	0.783353i	$-0.713508\pi$
$227$	3.65005	−	4.21238i	0.242262	−	0.279586i	0.863839	+	0.503767i	$0.168053\pi$
$228$		0			0
$229$	16.0853	+	7.34590i	1.06295	+	0.485431i	0.868606	−	0.495503i	$-0.165016\pi$
$229$	16.0853	+	7.34590i	1.06295	+	0.485431i	0.194339	+	0.980934i	$0.437744\pi$
$230$		0			0
$231$	1.30746	+	0.383904i	0.0860244	+	0.0252590i
$232$		0			0
$233$	24.3786			1.59709			0.798546	−	0.601934i	$-0.205603\pi$
$233$	24.3786			1.59709			0.798546	+	0.601934i	$0.205603\pi$
$234$		0			0
$235$	−6.69080	−	7.72160i	−0.436460	−	0.503702i
$236$		0			0
$237$	−2.79396	−	9.51537i	−0.181487	−	0.618090i
$238$		0			0
$239$	−3.83989	+	3.32729i	−0.248382	+	0.215224i	−0.770149	−	0.637864i	$-0.779818\pi$
$239$	−3.83989	+	3.32729i	−0.248382	+	0.215224i	0.521767	+	0.853088i	$0.325273\pi$
$240$		0			0
$241$	8.70193	+	1.25115i	0.560540	+	0.0805935i	0.416761	−	0.909016i	$-0.363165\pi$
$241$	8.70193	+	1.25115i	0.560540	+	0.0805935i	0.143780	+	0.989610i	$0.454074\pi$
$242$		0			0
$243$	−22.1084	+	3.17871i	−1.41826	+	0.203915i
$244$		0			0
$245$	21.3392	+	6.26576i	1.36331	+	0.400305i
$246$		0			0
$247$	7.73149	+	8.92261i	0.491943	+	0.567732i
$248$		0			0
$249$	−7.57231	+	16.5810i	−0.479876	+	1.05078i
$250$		0			0
$251$	−15.6468	+	10.0556i	−0.987615	+	0.634702i	−0.931507	−	0.363723i	$-0.881505\pi$
$251$	−15.6468	+	10.0556i	−0.987615	+	0.634702i	−0.0561078	+	0.998425i	$0.517869\pi$
$252$		0			0
$253$	−0.274197	−	0.426659i	−0.0172386	−	0.0268238i
$254$		0			0
$255$		−	34.9155i		−	2.18649i
$256$		0			0
$257$	−6.48068	+	4.16488i	−0.404254	+	0.259798i	−0.726930	−	0.686711i	$-0.759054\pi$
$257$	−6.48068	+	4.16488i	−0.404254	+	0.259798i	0.322677	+	0.946509i	$0.395417\pi$
$258$		0			0
$259$	−0.162461	−	0.355739i	−0.0100948	−	0.0221046i
$260$		0			0
$261$	−13.6866	−	1.96784i	−0.847180	−	0.121806i
$262$		0			0
$263$	0.100578	−	0.0295325i	0.00620193	−	0.00182105i	−0.278630	−	0.960398i	$-0.589880\pi$
$263$	0.100578	−	0.0295325i	0.00620193	−	0.00182105i	0.284832	+	0.958577i	$0.408062\pi$
$264$		0			0
$265$	−3.11479	−	21.6639i	−0.191340	−	1.33080i
$266$		0			0
$267$	−17.1728	−	16.1279i	−1.05096	−	0.987011i
$268$		0			0
$269$	2.23679	+	15.5572i	0.136379	+	0.948540i	0.936990	+	0.349355i	$0.113599\pi$
$269$	2.23679	+	15.5572i	0.136379	+	0.948540i	−0.800611	+	0.599185i	$0.795492\pi$
$270$		0			0
$271$	−21.5415	+	6.32517i	−1.30856	+	0.384227i	−0.860350	−	0.509704i	$-0.829755\pi$
$271$	−21.5415	+	6.32517i	−1.30856	+	0.384227i	−0.448206	+	0.893930i	$0.647937\pi$
$272$		0			0
$273$	1.73373	+	0.249273i	0.104930	+	0.0150867i
$274$		0			0
$275$	5.60799	+	12.2798i	0.338175	+	0.740499i
$276$		0			0
$277$	−11.6245	+	7.47062i	−0.698449	+	0.448866i	−0.841080	−	0.540910i	$-0.818080\pi$
$277$	−11.6245	+	7.47062i	−0.698449	+	0.448866i	0.142632	+	0.989776i	$0.454444\pi$
$278$		0			0
$279$			15.1456i			0.906742i
$280$		0			0
$281$	9.02257	+	14.0394i	0.538241	+	0.837520i	0.998742	−	0.0501393i	$-0.0159665\pi$
$281$	9.02257	+	14.0394i	0.538241	+	0.837520i	−0.460501	+	0.887659i	$0.652330\pi$
$282$		0			0
$283$	−6.93246	+	4.45522i	−0.412092	+	0.264835i	−0.730220	−	0.683212i	$-0.760582\pi$
$283$	−6.93246	+	4.45522i	−0.412092	+	0.264835i	0.318128	+	0.948048i	$0.396946\pi$
$284$		0			0
$285$	11.7902	−	25.8169i	0.698389	−	1.52926i
$286$		0			0
$287$	−1.42366	−	1.64299i	−0.0840360	−	0.0969827i
$288$		0			0
$289$	−2.03437	−	0.597345i	−0.119669	−	0.0351379i
$290$		0			0
$291$	−31.4009	+	4.51476i	−1.84075	+	0.264660i
$292$		0			0
$293$	−16.3798	−	2.35507i	−0.956920	−	0.137584i	−0.353876	−	0.935292i	$-0.615137\pi$
$293$	−16.3798	−	2.35507i	−0.956920	−	0.137584i	−0.603044	+	0.797708i	$0.706046\pi$
$294$		0			0
$295$	−5.60904	+	4.86026i	−0.326571	+	0.282975i
$296$		0			0
$297$	0.429292	+	1.46203i	0.0249100	+	0.0848357i
$298$		0			0
$299$	−0.426917	−	0.492688i	−0.0246892	−	0.0284929i
$300$		0			0
$301$	2.42181			0.139591
$302$		0			0
$303$	20.3714	+	5.98158i	1.17031	+	0.343633i
$304$		0			0
$305$	−15.6597	−	7.15155i	−0.896672	−	0.409497i
$306$		0			0
$307$	2.06786	−	2.38644i	0.118019	−	0.136201i	−0.693666	−	0.720297i	$-0.744005\pi$
$307$	2.06786	−	2.38644i	0.118019	−	0.136201i	0.811685	+	0.584096i	$0.198551\pi$
$308$		0			0
$309$	−21.2684	+	6.24495i	−1.20991	+	0.355263i
$310$		0			0
$311$	−3.38025	+	23.5102i	−0.191676	+	1.33314i	0.635894	+	0.771777i	$0.280632\pi$
$311$	−3.38025	+	23.5102i	−0.191676	+	1.33314i	−0.827570	+	0.561362i	$0.810277\pi$
$312$		0			0
$313$	−5.05901	−	2.31037i	−0.285952	−	0.130590i	0.267275	−	0.963620i	$-0.413877\pi$
$313$	−5.05901	−	2.31037i	−0.285952	−	0.130590i	−0.553228	+	0.833030i	$0.686604\pi$
$314$		0			0
$315$	−0.615597	−	2.09653i	−0.0346850	−	0.118126i
$316$		0			0
$317$	−15.3595	−	9.87093i	−0.862674	−	0.554407i	0.0328300	−	0.999461i	$-0.489548\pi$
$317$	−15.3595	−	9.87093i	−0.862674	−	0.554407i	−0.895504	+	0.445054i	$0.853184\pi$
$318$		0			0
$319$		−	11.0413i		−	0.618196i
$320$		0			0
$321$	−24.1318	−	20.9103i	−1.34691	−	1.16710i
$322$		0			0
$323$	−11.7460	−	10.1780i	−0.653566	−	0.566319i
$324$		0			0
$325$	9.38154	+	14.5980i	0.520394	+	0.809749i
$326$		0			0
$327$	−11.2158	+	5.12206i	−0.620232	+	0.283251i
$328$		0			0
$329$	−0.509933	+	0.441860i	−0.0281135	+	0.0243605i
$330$		0			0
$331$	−10.1768	+	11.7447i	−0.559369	+	0.645547i	−0.963040	−	0.269358i	$-0.913189\pi$
$331$	−10.1768	+	11.7447i	−0.559369	+	0.645547i	0.403671	+	0.914904i	$0.367734\pi$
$332$		0			0
$333$	3.24027	−	5.04195i	0.177565	−	0.276297i
$334$		0			0
$335$	−2.30850	−	16.0560i	−0.126127	−	0.877230i
$336$		0			0
$337$	17.6132	−	27.4067i	0.959453	−	1.49294i	0.0917945	−	0.995778i	$-0.470740\pi$
$337$	17.6132	−	27.4067i	0.959453	−	1.49294i	0.867659	−	0.497160i	$-0.165624\pi$
$338$		0			0
$339$	3.59370	−	24.9948i	0.195183	−	1.35753i
$340$		0			0
$341$	−11.9708	+	1.72115i	−0.648258	+	0.0932054i
$342$		0			0
$343$	0.830232	−	2.82751i	0.0448283	−	0.152671i
$344$		0			0
$345$	−0.651029	+	1.42555i	−0.0350502	+	0.0767492i
$346$		0			0
$347$	29.5216	+	18.9724i	1.58480	+	1.01849i	0.973954	+	0.226745i	$0.0728085\pi$
$347$	29.5216	+	18.9724i	1.58480	+	1.01849i	0.610850	+	0.791746i	$0.290828\pi$
$348$		0			0
$349$	−14.8017	+	6.75969i	−0.792315	+	0.361838i	−0.770107	−	0.637915i	$-0.779797\pi$
$349$	−14.8017	+	6.75969i	−0.792315	+	0.361838i	−0.0222084	+	0.999753i	$0.507070\pi$
$350$		0			0
$351$	0.813649	+	1.78164i	0.0434294	+	0.0950971i
$352$		0			0
$353$	−3.80821	+	12.9696i	−0.202691	+	0.690302i	0.793919	+	0.608024i	$0.208038\pi$
$353$	−3.80821	+	12.9696i	−0.202691	+	0.690302i	−0.996609	+	0.0822775i	$0.973781\pi$
$354$		0			0
$355$	−43.5025			−2.30888
$356$		0			0
$357$	−2.30581			−0.122037
$358$		0			0
$359$	6.90191	−	23.5057i	0.364269	−	1.24059i	−0.549893	−	0.835235i	$-0.685331\pi$
$359$	6.90191	−	23.5057i	0.364269	−	1.24059i	0.914161	−	0.405350i	$-0.132850\pi$
$360$		0			0
$361$	2.64463	+	5.79094i	0.139191	+	0.304786i
$362$		0			0
$363$	9.81872	−	4.48406i	0.515349	−	0.235352i
$364$		0			0
$365$	12.2692	+	7.88496i	0.642201	+	0.412718i
$366$		0			0
$367$	6.60929	−	14.4723i	0.345002	−	0.755450i	−0.654998	−	0.755631i	$-0.727330\pi$
$367$	6.60929	−	14.4723i	0.345002	−	0.755450i	1.00000		0.000181110i	$5.76490e-5\pi$
$368$		0			0
$369$	9.38643	−	31.9672i	0.488638	−	1.66415i
$370$		0			0
$371$	−1.43068	+	0.205700i	−0.0742771	+	0.0106794i
$372$		0			0
$373$	−3.99217	+	27.7661i	−0.206707	+	1.43768i	0.577101	+	0.816673i	$0.304184\pi$
$373$	−3.99217	+	27.7661i	−0.206707	+	1.43768i	−0.783808	+	0.621004i	$0.786725\pi$
$374$		0			0
$375$	0.967734	−	1.50582i	0.0499736	−	0.0777604i
$376$		0			0
$377$	−2.01981	−	14.0481i	−0.104026	−	0.723515i
$378$		0			0
$379$	−1.32154	+	2.05636i	−0.0678830	+	0.105628i	−0.873536	−	0.486760i	$-0.838179\pi$
$379$	−1.32154	+	2.05636i	−0.0678830	+	0.105628i	0.805653	+	0.592388i	$0.201815\pi$
$380$		0			0
$381$	3.56001	−	4.10847i	0.182385	−	0.210483i
$382$		0			0
$383$	10.9105	−	9.45404i	0.557503	−	0.483079i	−0.329937	−	0.944003i	$-0.607027\pi$
$383$	10.9105	−	9.45404i	0.557503	−	0.483079i	0.887440	+	0.460924i	$0.152482\pi$
$384$		0			0
$385$	1.58711	−	0.724810i	0.0808868	−	0.0369397i
$386$		0			0
$387$	20.0657	+	31.2228i	1.02000	+	1.58715i
$388$		0			0
$389$	−23.7469	−	20.5768i	−1.20401	−	1.04328i	−0.997901	−	0.0647553i	$-0.979373\pi$
$389$	−23.7469	−	20.5768i	−1.20401	−	1.04328i	−0.206112	−	0.978528i	$-0.566081\pi$
$390$		0			0
$391$	0.648591	+	0.562007i	0.0328007	+	0.0284219i
$392$		0			0
$393$		−	42.7592i		−	2.15692i
$394$		0			0
$395$	−10.6824	−	6.86514i	−0.537488	−	0.345422i
$396$		0			0
$397$	−8.10007	−	27.5863i	−0.406531	−	1.38452i	−0.867649	−	0.497178i	$-0.834370\pi$
$397$	−8.10007	−	27.5863i	−0.406531	−	1.38452i	0.461118	−	0.887339i	$-0.347448\pi$
$398$		0			0
$399$	−1.70494	−	0.778621i	−0.0853538	−	0.0389798i
$400$		0			0
$401$	2.32721	−	16.1861i	0.116215	−	0.808296i	−0.845447	−	0.534060i	$-0.820666\pi$
$401$	2.32721	−	16.1861i	0.116215	−	0.808296i	0.961662	−	0.274237i	$-0.0884251\pi$
$402$		0			0
$403$	−14.9159	+	4.37971i	−0.743014	+	0.218169i
$404$		0			0
$405$	−17.2453	+	19.9022i	−0.856928	+	0.988947i
$406$		0			0
$407$	4.35331	+	1.98809i	0.215786	+	0.0985460i
$408$		0			0
$409$	−0.668073	−	0.196164i	−0.0330341	−	0.00969969i	0.265174	−	0.964201i	$-0.414571\pi$
$409$	−0.668073	−	0.196164i	−0.0330341	−	0.00969969i	−0.298208	+	0.954501i	$0.596389\pi$
$410$		0			0
$411$	50.1741			2.47490
$412$		0			0
$413$	0.320971	+	0.370420i	0.0157939	+	0.0182272i
$414$		0			0
$415$	6.57566	+	22.3947i	0.322787	+	1.09931i
$416$		0			0
$417$	3.83922	−	3.32670i	0.188007	−	0.162909i
$418$		0			0
$419$	0.240090	+	0.0345198i	0.0117292	+	0.00168640i	0.148177	−	0.988961i	$-0.452659\pi$
$419$	0.240090	+	0.0345198i	0.0117292	+	0.00168640i	−0.136448	+	0.990647i	$0.543569\pi$
$420$		0			0
$421$	6.23732	−	0.896791i	0.303988	−	0.0437069i	0.0113673	−	0.999935i	$-0.496382\pi$
$421$	6.23732	−	0.896791i	0.303988	−	0.0437069i	0.292621	+	0.956228i	$0.405473\pi$
$422$		0			0
$423$	−9.92163	−	2.91325i	−0.482406	−	0.141647i
$424$		0			0
$425$	−14.9594	−	17.2640i	−0.725636	−	0.837428i
$426$		0			0
$427$	−0.472287	+	1.03416i	−0.0228556	+	0.0500467i
$428$		0			0
$429$	−18.0319	+	11.5884i	−0.870586	+	0.559492i
$430$		0			0
$431$	8.07405	+	12.5635i	0.388913	+	0.605161i	0.979411	−	0.201879i	$-0.0647047\pi$
$431$	8.07405	+	12.5635i	0.388913	+	0.605161i	−0.590497	+	0.807040i	$0.701068\pi$
$432$		0			0
$433$		−	37.5217i		−	1.80318i	−0.432595	−	0.901588i	$-0.642402\pi$
$433$		−	37.5217i		−	1.80318i	0.432595	−	0.901588i	$-0.357598\pi$
$434$		0			0
$435$	−28.7020	+	18.4456i	−1.37615	+	0.884401i
$436$		0			0
$437$	0.289798	+	0.634568i	0.0138629	+	0.0303555i
$438$		0			0
$439$	−33.6989	−	4.84517i	−1.60836	−	0.231247i	−0.721207	−	0.692720i	$-0.756412\pi$
$439$	−33.6989	−	4.84517i	−1.60836	−	0.231247i	−0.887155	+	0.461472i	$0.847321\pi$
$440$		0			0
$441$	21.5968	−	6.34141i	1.02842	−	0.301972i
$442$		0			0
$443$	−0.540053	−	3.75615i	−0.0256587	−	0.178460i	0.972962	−	0.230965i	$-0.0741884\pi$
$443$	−0.540053	−	3.75615i	−0.0256587	−	0.178460i	−0.998621	+	0.0525054i	$0.983279\pi$
$444$		0			0
$445$	−30.1412	−	1.20722i	−1.42883	−	0.0572279i
$446$		0			0
$447$	−7.10281	−	49.4011i	−0.335951	−	2.33659i
$448$		0			0
$449$	−32.6675	+	9.59205i	−1.54168	+	0.452677i	−0.938600	−	0.345007i	$-0.887877\pi$
$449$	−32.6675	+	9.59205i	−1.54168	+	0.452677i	−0.603076	+	0.797684i	$0.706058\pi$
$450$		0			0
$451$	26.3331	+	3.78613i	1.23998	+	0.178282i
$452$		0			0
$453$	5.62272	+	12.3120i	0.264178	+	0.578470i
$454$		0			0
$455$	1.88673	−	1.21253i	0.0884511	−	0.0568441i
$456$		0			0
$457$			40.9887i			1.91737i	0.284468	+	0.958686i	$0.408183\pi$
$457$			40.9887i			1.91737i	−0.284468	+	0.958686i	$0.591817\pi$
$458$		0			0
$459$	−1.39400	−	2.16911i	−0.0650664	−	0.101245i
$460$		0			0
$461$	18.0233	−	11.5829i	0.839429	−	0.539468i	−0.0488324	−	0.998807i	$-0.515550\pi$
$461$	18.0233	−	11.5829i	0.839429	−	0.539468i	0.888261	+	0.459339i	$0.151914\pi$
$462$		0			0
$463$	0.0300517	−	0.0658041i	0.00139662	−	0.00305817i	−0.908932	−	0.416944i	$-0.863101\pi$
$463$	0.0300517	−	0.0658041i	0.00139662	−	0.00305817i	0.910329	+	0.413885i	$0.135829\pi$
$464$		0			0
$465$	24.4726	+	28.2429i	1.13489	+	1.30973i
$466$		0			0
$467$	22.1086	+	6.49168i	1.02307	+	0.300399i	0.749888	−	0.661564i	$-0.230107\pi$
$467$	22.1086	+	6.49168i	1.02307	+	0.300399i	0.273178	+	0.961964i	$0.411925\pi$
$468$		0			0
$469$	−1.06033	+	0.152453i	−0.0489616	+	0.00703961i
$470$		0			0
$471$	−17.0334	−	2.44903i	−0.784856	−	0.112845i
$472$		0			0
$473$	−22.3978	+	19.4078i	−1.02985	+	0.892373i
$474$		0			0
$475$	−5.23143	−	17.8166i	−0.240035	−	0.817482i
$476$		0			0
$477$	−14.5057	−	16.7405i	−0.664172	−	0.766496i
$478$		0			0
$479$	38.5935			1.76338			0.881691	−	0.471827i	$-0.156405\pi$
$479$	38.5935			1.76338			0.881691	+	0.471827i	$0.156405\pi$
$480$		0			0
$481$	5.90250	+	1.73313i	0.269131	+	0.0790239i
$482$		0			0
$483$	0.0941433	+	0.0429938i	0.00428367	+	0.00195629i
$484$		0			0
$485$	−26.6005	+	30.6986i	−1.20787	+	1.39395i
$486$		0			0
$487$	−15.3536	+	4.50824i	−0.695740	+	0.204288i	−0.610434	−	0.792067i	$-0.709005\pi$
$487$	−15.3536	+	4.50824i	−0.695740	+	0.204288i	−0.0853060	+	0.996355i	$0.527187\pi$
$488$		0			0
$489$	−1.99923	+	13.9050i	−0.0904083	+	0.628804i
$490$		0			0
$491$	31.4307	+	14.3539i	1.41845	+	0.647784i	0.969347	−	0.245697i	$-0.0790167\pi$
$491$	31.4307	+	14.3539i	1.41845	+	0.647784i	0.449102	+	0.893481i	$0.351744\pi$
$492$		0			0
$493$	5.26377	+	17.9268i	0.237068	+	0.807381i
$494$		0			0
$495$	22.4944	+	14.4563i	1.01105	+	0.649762i
$496$		0			0
$497$			2.87290i			0.128867i
$498$		0			0
$499$	28.4909	+	24.6875i	1.27543	+	1.10517i	0.989133	+	0.147025i	$0.0469698\pi$
$499$	28.4909	+	24.6875i	1.27543	+	1.10517i	0.286297	+	0.958141i	$0.407576\pi$
$500$		0			0
$501$	−20.8883	−	18.0998i	−0.933220	−	0.808640i
$502$		0			0
$503$	10.5438	+	16.4065i	0.470125	+	0.731529i	0.992640	−	0.121101i	$-0.0386425\pi$
$503$	10.5438	+	16.4065i	0.470125	+	0.731529i	−0.522515	+	0.852630i	$0.675006\pi$
$504$		0			0
$505$	24.7287	−	11.2932i	1.10041	−	0.502541i
$506$		0			0
$507$	3.71217	−	3.21661i	0.164863	−	0.142855i
$508$		0			0
$509$	−19.5794	+	22.5958i	−0.867841	+	1.00154i	0.132106	+	0.991236i	$0.457826\pi$
$509$	−19.5794	+	22.5958i	−0.867841	+	1.00154i	−0.999947	+	0.0103063i	$0.996719\pi$
$510$		0			0
$511$	0.520722	−	0.810259i	0.0230354	−	0.0358437i
$512$		0			0
$513$	−0.298280	−	2.07458i	−0.0131694	−	0.0915950i
$514$		0			0
$515$	−15.3447	+	23.8768i	−0.676167	+	1.05214i
$516$		0			0
$517$	1.17510	−	8.17298i	0.0516807	−	0.359447i
$518$		0			0
$519$	15.5251	−	2.23218i	0.681478	−	0.0979817i
$520$		0			0
$521$	4.13948	−	14.0978i	0.181354	−	0.617635i	−0.817761	−	0.575559i	$-0.804785\pi$
$521$	4.13948	−	14.0978i	0.181354	−	0.617635i	0.999114	−	0.0420760i	$-0.0133972\pi$
$522$		0			0
$523$	9.50352	−	20.8098i	0.415560	−	0.909949i	−0.579893	−	0.814693i	$-0.696906\pi$
$523$	9.50352	−	20.8098i	0.415560	−	0.909949i	0.995453	−	0.0952564i	$-0.0303671\pi$
$524$		0			0
$525$	−2.31751	−	1.48937i	−0.101144	−	0.0650016i
$526$		0			0
$527$	18.6154	−	8.50137i	0.810900	−	0.370326i
$528$		0			0
$529$	9.53854	+	20.8865i	0.414719	+	0.908109i
$530$		0			0
$531$	−2.11621	+	7.20716i	−0.0918358	+	0.312764i
$532$		0			0
$533$	34.1968			1.48123
$534$		0			0
$535$	−40.8854			−1.76763
$536$		0			0
$537$	−18.2624	+	62.1961i	−0.788082	+	2.68396i
$538$		0			0
$539$	7.46643	+	16.3492i	0.321602	+	0.704210i
$540$		0			0
$541$	−24.0899	+	11.0015i	−1.03570	+	0.472990i	−0.859378	−	0.511341i	$-0.829149\pi$
$541$	−24.0899	+	11.0015i	−1.03570	+	0.472990i	−0.176327	+	0.984332i	$0.556422\pi$
$542$		0			0
$543$	−36.8691	−	23.6943i	−1.58221	−	1.01682i
$544$		0			0
$545$	−6.55845	+	14.3610i	−0.280933	+	0.615158i
$546$		0			0
$547$	9.45790	−	32.2106i	0.404391	−	1.37723i	−0.465965	−	0.884803i	$-0.654293\pi$
$547$	9.45790	−	32.2106i	0.404391	−	1.37723i	0.870355	−	0.492424i	$-0.163889\pi$
$548$		0			0
$549$	−17.2459	+	2.47959i	−0.736038	+	0.105826i
$550$		0			0
$551$	−2.16137	+	15.0327i	−0.0920776	+	0.640414i
$552$		0			0
$553$	−0.453372	+	0.705461i	−0.0192794	+	0.0299993i
$554$		0			0
$555$	−2.10459	−	14.6378i	−0.0893349	−	0.621338i
$556$		0			0
$557$	−7.06183	+	10.9884i	−0.299219	+	0.465595i	−0.958011	−	0.286731i	$-0.907431\pi$
$557$	−7.06183	+	10.9884i	−0.299219	+	0.465595i	0.658792	+	0.752325i	$0.271068\pi$
$558$		0			0
$559$	−24.9469	+	28.7903i	−1.05514	+	1.21770i
$560$		0			0
$561$	21.3251	−	18.4783i	0.900345	−	0.780153i
$562$		0			0
$563$	19.5117	−	8.91070i	0.822321	−	0.375541i	0.0406043	−	0.999175i	$-0.487072\pi$
$563$	19.5117	−	8.91070i	0.822321	−	0.375541i	0.781716	+	0.623634i	$0.214344\pi$
$564$		0			0
$565$	−17.4806	−	27.2004i	−0.735416	−	1.14433i
$566$		0			0
$567$	1.31434	+	1.13888i	0.0551969	+	0.0478284i
$568$		0			0
$569$	27.1738	+	23.5463i	1.13919	+	0.987110i	0.999995	−	0.00315536i	$-0.00100438\pi$
$569$	27.1738	+	23.5463i	1.13919	+	0.987110i	0.139191	+	0.990266i	$0.455550\pi$
$570$		0			0
$571$			36.4608i			1.52584i	0.646495	+	0.762918i	$0.276234\pi$
$571$			36.4608i			1.52584i	−0.646495	+	0.762918i	$0.723766\pi$
$572$		0			0
$573$	6.94682	+	4.46445i	0.290208	+	0.186505i
$574$		0			0
$575$	0.288869	+	0.983797i	0.0120467	+	0.0410272i
$576$		0			0
$577$	−7.13100	−	3.25662i	−0.296867	−	0.135575i	0.261413	−	0.965227i	$-0.415811\pi$
$577$	−7.13100	−	3.25662i	−0.296867	−	0.135575i	−0.558281	+	0.829652i	$0.688539\pi$
$578$		0			0
$579$	−0.999749	+	6.95341i	−0.0415481	+	0.288974i
$580$		0			0
$581$	1.47894	−	0.434256i	0.0613567	−	0.0180160i
$582$		0			0
$583$	11.5830	−	13.3675i	0.479720	−	0.553626i
$584$		0			0
$585$	31.2646	+	14.2781i	1.29263	+	0.590326i
$586$		0			0
$587$	−19.6681	−	5.77508i	−0.811791	−	0.238363i	−0.150613	−	0.988593i	$-0.548125\pi$
$587$	−19.6681	−	5.77508i	−0.811791	−	0.238363i	−0.661177	+	0.750230i	$0.729943\pi$
$588$		0			0
$589$	16.6351			0.685439
$590$		0			0
$591$	16.4780	+	19.0166i	0.677814	+	0.782239i
$592$		0			0
$593$	−8.91673	−	30.3676i	−0.366166	−	1.24705i	−0.912360	−	0.409389i	$-0.865742\pi$
$593$	−8.91673	−	30.3676i	−0.366166	−	1.24705i	0.546194	−	0.837659i	$-0.316076\pi$
$594$		0			0
$595$	−2.23130	+	1.93344i	−0.0914745	+	0.0792631i
$596$		0			0
$597$	55.6858	+	8.00641i	2.27907	+	0.327680i
$598$		0			0
$599$	−4.91324	+	0.706417i	−0.200749	+	0.0288634i	−0.241956	−	0.970287i	$-0.577789\pi$
$599$	−4.91324	+	0.706417i	−0.200749	+	0.0288634i	0.0412065	+	0.999151i	$0.486880\pi$
$600$		0			0
$601$	−3.71498	−	1.09082i	−0.151537	−	0.0444953i	0.205084	−	0.978744i	$-0.434253\pi$
$601$	−3.71498	−	1.09082i	−0.151537	−	0.0444953i	−0.356621	+	0.934249i	$0.616071\pi$
$602$		0			0
$603$	−10.7508	−	12.4071i	−0.437806	−	0.505255i
$604$		0			0
$605$	5.74153	−	12.5722i	0.233426	−	0.511132i
$606$		0			0
$607$	−30.4107	+	19.5438i	−1.23433	+	0.793257i	−0.984560	−	0.175048i	$-0.943992\pi$
$607$	−30.4107	+	19.5438i	−1.23433	+	0.793257i	−0.249772	+	0.968305i	$0.580356\pi$
$608$		0			0
$609$	1.21815	+	1.89547i	0.0493618	+	0.0768085i
$610$		0			0
$611$		−	10.6136i		−	0.429381i
$612$		0			0
$613$	12.9298	−	8.30950i	0.522231	−	0.335618i	−0.252823	−	0.967513i	$-0.581359\pi$
$613$	12.9298	−	8.30950i	0.522231	−	0.335618i	0.775054	+	0.631895i	$0.217723\pi$
$614$		0			0
$615$	−34.1500	−	74.7782i	−1.37706	−	3.01535i
$616$		0			0
$617$	5.74197	+	0.825571i	0.231163	+	0.0332362i	0.256923	−	0.966432i	$-0.417291\pi$
$617$	5.74197	+	0.825571i	0.231163	+	0.0332362i	−0.0257597	+	0.999668i	$0.508200\pi$
$618$		0			0
$619$	29.8159	−	8.75475i	1.19840	−	0.351883i	0.379161	−	0.925331i	$-0.376213\pi$
$619$	29.8159	−	8.75475i	1.19840	−	0.351883i	0.819242	+	0.573447i	$0.194394\pi$
$620$		0			0
$621$	0.0164704	+	0.114554i	0.000660934	+	0.00459689i
$622$		0			0
$623$	−0.0797248	+	1.99052i	−0.00319411	+	0.0797486i
$624$		0			0
$625$	3.39121	+	23.5864i	0.135648	+	0.943454i
$626$		0			0
$627$	22.0077	−	6.46203i	0.878901	−	0.258069i
$628$		0			0
$629$	−8.01585	−	1.15251i	−0.319613	−	0.0459534i
$630$		0			0
$631$	14.0969	+	30.8680i	0.561190	+	1.22884i	0.951357	+	0.308091i	$0.0996902\pi$
$631$	14.0969	+	30.8680i	0.561190	+	1.22884i	−0.390167	+	0.920744i	$0.627583\pi$
$632$		0			0
$633$	44.5047	−	28.6014i	1.76890	−	1.13680i
$634$		0			0
$635$		−	6.96079i		−	0.276231i
$636$		0			0
$637$	12.4905	+	19.4356i	0.494891	+	0.770066i
$638$		0			0
$639$	−37.0385	+	23.8032i	−1.46522	+	0.941640i
$640$		0			0
$641$	−3.30398	+	7.23472i	−0.130500	+	0.285754i	−0.963591	−	0.267381i	$-0.913842\pi$
$641$	−3.30398	+	7.23472i	−0.130500	+	0.285754i	0.833091	+	0.553136i	$0.186569\pi$
$642$		0			0
$643$	−5.72626	−	6.60846i	−0.225822	−	0.260612i	0.631520	−	0.775359i	$-0.282431\pi$
$643$	−5.72626	−	6.60846i	−0.225822	−	0.260612i	−0.857342	+	0.514747i	$0.827886\pi$
$644$		0			0
$645$	87.8685	+	25.8005i	3.45982	+	1.01589i
$646$		0			0
$647$	−0.506485	+	0.0728215i	−0.0199120	+	0.00286291i	−0.152264	−	0.988340i	$-0.548656\pi$
$647$	−0.506485	+	0.0728215i	−0.0199120	+	0.00286291i	0.132352	+	0.991203i	$0.457747\pi$
$648$		0			0
$649$	−5.93692	−	0.853601i	−0.233045	−	0.0335068i
$650$		0			0
$651$	1.86516	−	1.61617i	0.0731013	−	0.0633426i
$652$		0			0
$653$	7.74886	+	26.3902i	0.303236	+	1.03273i	0.960318	+	0.278908i	$0.0899725\pi$
$653$	7.74886	+	26.3902i	0.303236	+	1.03273i	−0.657082	+	0.753820i	$0.728209\pi$
$654$		0			0
$655$	−35.8538	−	41.3775i	−1.40092	−	1.61675i
$656$		0			0
$657$	14.7606			0.575864
$658$		0			0
$659$	−3.96991	−	1.16567i	−0.154646	−	0.0454081i	0.203493	−	0.979076i	$-0.434770\pi$
$659$	−3.96991	−	1.16567i	−0.154646	−	0.0454081i	−0.358139	+	0.933668i	$0.616589\pi$
$660$		0			0
$661$	20.2253	+	9.23659i	0.786673	+	0.359262i	0.767906	−	0.640562i	$-0.221299\pi$
$661$	20.2253	+	9.23659i	0.786673	+	0.359262i	0.0187671	+	0.999824i	$0.494026\pi$
$662$		0			0
$663$	23.7521	−	27.4113i	0.922454	−	1.06457i
$664$		0			0
$665$	−2.30272	+	0.676141i	−0.0892958	+	0.0262196i
$666$		0			0
$667$	0.119347	−	0.830073i	0.00462112	−	0.0321406i
$668$		0			0
$669$	−55.6115	−	25.3969i	−2.15007	−	0.981902i
$670$		0			0
$671$	−3.91967	−	13.3492i	−0.151317	−	0.515338i
$672$		0			0
$673$	27.8635	+	17.9068i	1.07406	+	0.690256i	0.953178	−	0.302411i	$-0.0977915\pi$
$673$	27.8635	+	17.9068i	1.07406	+	0.690256i	0.120882	+	0.992667i	$0.461428\pi$
$674$		0			0
$675$		−	3.08052i		−	0.118569i
$676$		0			0
$677$	14.1937	+	12.2989i	0.545508	+	0.472685i	0.883479	−	0.468472i	$-0.155195\pi$
$677$	14.1937	+	12.2989i	0.545508	+	0.472685i	−0.337971	+	0.941157i	$0.609741\pi$
$678$		0			0
$679$	2.02733	+	1.75669i	0.0778019	+	0.0674157i
$680$		0			0
$681$	−7.52517	−	11.7094i	−0.288365	−	0.448705i
$682$		0			0
$683$	−13.4255	+	6.13123i	−0.513713	+	0.234605i	−0.655366	−	0.755311i	$-0.727486\pi$
$683$	−13.4255	+	6.13123i	−0.513713	+	0.234605i	0.141653	+	0.989916i	$0.454758\pi$
$684$		0			0
$685$	48.5527	−	42.0712i	1.85510	−	1.60746i
$686$		0			0
$687$	28.9181	−	33.3732i	1.10329	−	1.27327i
$688$		0			0
$689$	12.2920	−	19.1267i	0.468287	−	0.728669i
$690$		0			0
$691$	−0.212758	−	1.47977i	−0.00809371	−	0.0562930i	0.985374	−	0.170404i	$-0.0545072\pi$
$691$	−0.212758	−	1.47977i	−0.00809371	−	0.0562930i	−0.993468	+	0.114111i	$0.963598\pi$
$692$		0			0
$693$	0.954691	−	1.48553i	0.0362657	−	0.0564305i
$694$		0			0
$695$	0.925702	−	6.43840i	0.0351139	−	0.244222i
$696$		0			0
$697$	−44.5596	+	6.40670i	−1.68781	+	0.242671i
$698$		0			0
$699$	17.1515	−	58.4127i	0.648730	−	2.20937i
$700$		0			0
$701$	18.5065	−	40.5236i	0.698981	−	1.53055i	−0.142222	−	0.989835i	$-0.545425\pi$
$701$	18.5065	−	40.5236i	0.698981	−	1.53055i	0.841203	−	0.540720i	$-0.181848\pi$
$702$		0			0
$703$	−5.53782	−	3.55894i	−0.208863	−	0.134228i
$704$		0			0
$705$	−23.2088	+	10.5991i	−0.874094	+	0.399185i
$706$		0			0
$707$	−0.745802	−	1.63308i	−0.0280488	−	0.0614182i
$708$		0			0
$709$	−5.77782	+	19.6775i	−0.216991	+	0.739002i	0.776996	+	0.629505i	$0.216742\pi$
$709$	−5.77782	+	19.6775i	−0.216991	+	0.739002i	−0.993987	+	0.109497i	$0.965076\pi$
$710$		0			0
$711$	−12.8514			−0.481967
$712$		0			0
$713$	−0.918557			−0.0344002
$714$		0			0
$715$	−7.73227	+	26.3337i	−0.289171	+	0.984824i
$716$		0			0
$717$	5.27085	+	11.5416i	0.196844	+	0.431027i
$718$		0			0
$719$	−39.2349	+	17.9180i	−1.46321	+	0.668227i	−0.978462	−	0.206425i	$-0.933817\pi$
$719$	−39.2349	+	17.9180i	−1.46321	+	0.668227i	−0.484751	+	0.874652i	$0.661090\pi$
$720$		0			0
$721$	1.57682	+	1.01336i	0.0587237	+	0.0377395i
$722$		0			0
$723$	9.12007	−	19.9702i	0.339179	−	0.742699i
$724$		0			0
$725$	−6.28880	+	21.4177i	−0.233560	+	0.795432i
$726$		0			0
$727$	−31.6976	+	4.55742i	−1.17560	+	0.169025i	−0.702303	−	0.711878i	$-0.747845\pi$
$727$	−31.6976	+	4.55742i	−1.17560	+	0.169025i	−0.473295	+	0.880904i	$0.656936\pi$
$728$		0			0
$729$	−4.42171	+	30.7536i	−0.163767	+	1.13902i
$730$		0			0
$731$	27.1129	−	42.1884i	1.00281	−	1.56040i
$732$		0			0
$733$	−0.876724	−	6.09775i	−0.0323825	−	0.225225i	0.967203	−	0.254003i	$-0.0817475\pi$
$733$	−0.876724	−	6.09775i	−0.0323825	−	0.225225i	−0.999586	+	0.0287781i	$0.990838\pi$
$734$		0			0
$735$	30.0264	−	46.7220i	1.10754	−	1.72337i
$736$		0			0
$737$	8.58464	−	9.90721i	0.316219	−	0.364937i
$738$		0			0
$739$	23.9397	−	20.7439i	0.880638	−	0.763077i	−0.0919134	−	0.995767i	$-0.529298\pi$
$739$	23.9397	−	20.7439i	0.880638	−	0.763077i	0.972551	+	0.232690i	$0.0747528\pi$
$740$		0			0
$741$	26.8187	−	12.2477i	0.985209	−	0.449930i
$742$		0			0
$743$	10.0035	+	15.5658i	0.366994	+	0.571053i	0.974813	−	0.223022i	$-0.0715921\pi$
$743$	10.0035	+	15.5658i	0.366994	+	0.571053i	−0.607820	+	0.794075i	$0.707956\pi$
$744$		0			0
$745$	−48.2963	−	41.8490i	−1.76944	−	1.53323i
$746$		0			0
$747$	17.8522	+	15.4690i	0.653179	+	0.565983i
$748$		0			0
$749$			2.70007i			0.0986582i
$750$		0			0
$751$	31.0053	+	19.9259i	1.13140	+	0.727106i	0.965852	−	0.259096i	$-0.0834246\pi$
$751$	31.0053	+	19.9259i	1.13140	+	0.727106i	0.165547	+	0.986202i	$0.447061\pi$
$752$		0			0
$753$	13.0856	+	44.5653i	0.476864	+	1.62405i
$754$		0			0
$755$	15.7647	+	7.19951i	0.573737	+	0.262017i
$756$		0			0
$757$	−1.01386	+	7.05157i	−0.0368494	+	0.256294i	−0.999916	−	0.0129704i	$-0.995871\pi$
$757$	−1.01386	+	7.05157i	−0.0368494	+	0.256294i	0.963066	+	0.269264i	$0.0867804\pi$
$758$		0			0
$759$	−1.21522	+	0.356820i	−0.0441096	+	0.0129517i
$760$		0			0
$761$	18.2480	−	21.0593i	0.661490	−	0.763400i	−0.321530	−	0.946899i	$-0.604197\pi$
$761$	18.2480	−	21.0593i	0.661490	−	0.763400i	0.983020	+	0.183499i	$0.0587426\pi$
$762$		0			0
$763$	0.948398	+	0.433119i	0.0343343	+	0.0156800i
$764$		0			0
$765$	−43.4139	−	12.7475i	−1.56963	−	0.460885i
$766$		0			0
$767$	−7.70982			−0.278386
$768$		0			0
$769$	−13.1506	−	15.1766i	−0.474223	−	0.547282i	0.467359	−	0.884068i	$-0.345206\pi$
$769$	−13.1506	−	15.1766i	−0.474223	−	0.547282i	−0.941581	+	0.336785i	$0.890660\pi$
$770$		0			0
$771$	5.41986	+	18.4584i	0.195192	+	0.664762i
$772$		0			0
$773$	22.2937	−	19.3176i	0.801847	−	0.694805i	−0.154193	−	0.988041i	$-0.549278\pi$
$773$	22.2937	−	19.3176i	0.801847	−	0.694805i	0.956040	+	0.293236i	$0.0947322\pi$
$774$		0			0
$775$	24.2010	+	3.47958i	0.869327	+	0.124990i
$776$		0			0
$777$	−0.966675	+	0.138987i	−0.0346793	+	0.00498613i
$778$		0			0
$779$	−35.1112	−	10.3096i	−1.25799	−	0.369379i
$780$		0			0
$781$	−23.0228	−	26.5697i	−0.823820	−	0.950739i
$782$		0			0
$783$	−1.04665	+	2.29185i	−0.0374043	+	0.0819040i
$784$		0			0
$785$	−18.5365	+	11.9127i	−0.661595	+	0.425181i
$786$		0			0
$787$	7.48421	+	11.6457i	0.266783	+	0.415123i	0.948637	−	0.316365i	$-0.102463\pi$
$787$	7.48421	+	11.6457i	0.266783	+	0.415123i	−0.681854	+	0.731488i	$0.738826\pi$
$788$		0			0
$789$		−	0.261770i		−	0.00931928i
$790$		0			0
$791$	−1.79631	+	1.15442i	−0.0638694	+	0.0410464i
$792$		0			0
$793$	−7.42906	−	16.2674i	−0.263814	−	0.577672i
$794$		0			0
$795$	−54.0995	−	7.77834i	−1.91871	−	0.275869i
$796$		0			0
$797$	11.8123	−	3.46841i	0.418414	−	0.122858i	−0.0657469	−	0.997836i	$-0.520943\pi$
$797$	11.8123	−	3.46841i	0.418414	−	0.122858i	0.484161	+	0.874979i	$0.339125\pi$
$798$		0			0
$799$	1.98844	+	13.8299i	0.0703459	+	0.489267i
$800$		0			0
$801$	−26.3231	+	15.4645i	−0.930081	+	0.546410i
$802$		0			0
$803$	1.67739	+	11.6665i	0.0591939	+	0.411703i
$804$		0			0
$805$	0.127152	−	0.0373351i	0.00448151	−	0.00131589i
$806$		0			0
$807$	38.8498	+	5.58576i	1.36758	+	0.196628i
$808$		0			0
$809$	21.8849	+	47.9213i	0.769433	+	1.68482i	0.727897	+	0.685687i	$0.240498\pi$
$809$	21.8849	+	47.9213i	0.769433	+	1.68482i	0.0415362	+	0.999137i	$0.486775\pi$
$810$		0			0
$811$	−17.9341	+	11.5256i	−0.629753	+	0.404718i	−0.816218	−	0.577744i	$-0.803933\pi$
$811$	−17.9341	+	11.5256i	−0.629753	+	0.404718i	0.186465	+	0.982462i	$0.440297\pi$
$812$		0			0
$813$			56.0651i			1.96629i
$814$		0			0
$815$	9.72474	+	15.1320i	0.340643	+	0.530050i
$816$		0			0
$817$	34.2936	−	22.0391i	1.19978	−	0.771052i
$818$		0			0
$819$	0.942922	−	2.06471i	0.0329484	−	0.0721469i
$820$		0			0
$821$	−18.1053	−	20.8947i	−0.631881	−	0.729229i	0.346037	−	0.938221i	$-0.387527\pi$
$821$	−18.1053	−	20.8947i	−0.631881	−	0.729229i	−0.977917	+	0.208992i	$0.932982\pi$
$822$		0			0
$823$	37.1339	+	10.9035i	1.29441	+	0.380072i	0.855192	−	0.518311i	$-0.173439\pi$
$823$	37.1339	+	10.9035i	1.29441	+	0.380072i	0.439213	+	0.898383i	$0.355257\pi$
$824$		0			0
$825$	33.3687	−	4.79770i	1.16175	−	0.167034i
$826$		0			0
$827$	−14.2862	−	2.05405i	−0.496781	−	0.0714263i	−0.110629	−	0.993862i	$-0.535287\pi$
$827$	−14.2862	−	2.05405i	−0.496781	−	0.0714263i	−0.386151	+	0.922435i	$0.626196\pi$
$828$		0			0
$829$	6.65378	−	5.76553i	0.231095	−	0.200245i	−0.531614	−	0.846987i	$-0.678414\pi$
$829$	6.65378	−	5.76553i	0.231095	−	0.200245i	0.762709	+	0.646742i	$0.223869\pi$
$830$		0			0
$831$	9.72170	+	33.1091i	0.337242	+	1.14854i
$832$		0			0
$833$	−19.9168	−	22.9852i	−0.690075	−	0.796388i
$834$		0			0
$835$	−35.3901			−1.22472
$836$		0			0
$837$	2.64795	+	0.777507i	0.0915264	+	0.0268746i
$838$		0			0
$839$	43.9583	+	20.0751i	1.51761	+	0.693068i	0.987897	−	0.155110i	$-0.0495731\pi$
$839$	43.9583	+	20.0751i	1.51761	+	0.693068i	0.529711	+	0.848178i	$0.322300\pi$
$840$		0			0
$841$	−7.03525	+	8.11911i	−0.242595	+	0.279969i
$842$		0			0
$843$	39.9872	−	11.7413i	1.37723	−	0.404392i
$844$		0			0
$845$	0.895068	−	6.22533i	0.0307913	−	0.214158i
$846$		0			0
$847$	−0.830266	−	0.379170i	−0.0285283	−	0.0130284i
$848$		0			0
$849$	5.79769	+	19.7451i	0.198976	+	0.677651i
$850$		0			0
$851$	0.305787	+	0.196517i	0.0104822	+	0.00673653i
$852$		0			0
$853$			12.4008i			0.424596i	0.977205	+	0.212298i	$0.0680947\pi$
$853$			12.4008i			0.424596i	−0.977205	+	0.212298i	$0.931905\pi$
$854$		0			0
$855$	−27.7961	−	24.0855i	−0.950607	−	0.823706i
$856$		0			0
$857$	2.13371	+	1.84887i	0.0728861	+	0.0631562i	0.690542	−	0.723292i	$-0.257372\pi$
$857$	2.13371	+	1.84887i	0.0728861	+	0.0631562i	−0.617656	+	0.786449i	$0.711918\pi$
$858$		0			0
$859$	0.0970186	+	0.150964i	0.00331023	+	0.00515082i	0.842905	−	0.538063i	$-0.180844\pi$
$859$	0.0970186	+	0.150964i	0.00331023	+	0.00515082i	−0.839594	+	0.543214i	$0.817207\pi$
$860$		0			0
$861$	−4.93834	+	2.25526i	−0.168298	+	0.0768592i
$862$		0			0
$863$	38.2969	−	33.1844i	1.30364	−	1.12961i	0.320404	−	0.947281i	$-0.396181\pi$
$863$	38.2969	−	33.1844i	1.30364	−	1.12961i	0.983237	−	0.182331i	$-0.0583642\pi$
$864$		0			0
$865$	13.1518	−	15.1779i	0.447173	−	0.516065i
$866$		0			0
$867$	−2.86256	+	4.45423i	−0.0972176	+	0.151274i
$868$		0			0
$869$	−1.46044	−	10.1576i	−0.0495421	−	0.344573i
$870$		0			0
$871$	9.11007	−	14.1756i	0.308683	−	0.480320i
$872$		0			0
$873$	−5.85064	+	40.6921i	−0.198014	+	1.37722i
$874$		0			0
$875$	−0.149819	+	0.0215407i	−0.00506480	+	0.000728208i
$876$		0			0
$877$	−15.6884	+	53.4299i	−0.529760	+	1.80420i	0.0619901	+	0.998077i	$0.480255\pi$
$877$	−15.6884	+	53.4299i	−0.529760	+	1.80420i	−0.591750	+	0.806121i	$0.701563\pi$
$878$		0			0
$879$	−17.1669	+	37.5903i	−0.579026	+	1.26789i
$880$		0			0
$881$	−31.6040	−	20.3107i	−1.06477	−	0.684284i	−0.113777	−	0.993506i	$-0.536295\pi$
$881$	−31.6040	−	20.3107i	−1.06477	−	0.684284i	−0.950990	+	0.309222i	$0.899931\pi$
$882$		0			0
$883$	−11.1160	+	5.07652i	−0.374084	+	0.170839i	−0.593580	−	0.804775i	$-0.702286\pi$
$883$	−11.1160	+	5.07652i	−0.374084	+	0.170839i	0.219496	+	0.975613i	$0.429559\pi$
$884$		0			0
$885$	7.69928	+	16.8591i	0.258809	+	0.566712i
$886$		0			0
$887$	−1.51068	+	5.14490i	−0.0507237	+	0.172749i	−0.980959	−	0.194214i	$-0.937784\pi$
$887$	−1.51068	+	5.14490i	−0.0507237	+	0.172749i	0.930235	+	0.366963i	$0.119602\pi$
$888$		0			0
$889$	−0.459689			−0.0154175
$890$		0			0
$891$	−21.2822			−0.712981
$892$		0			0
$893$	−3.19977	+	10.8974i	−0.107076	+	0.364668i
$894$		0			0
$895$	34.4794	+	75.4995i	1.15252	+	2.52367i
$896$		0			0
$897$	−1.48087	+	0.676292i	−0.0494449	+	0.0225807i
$898$		0			0
$899$	−16.8229	−	10.8114i	−0.561074	−	0.360581i
$900$		0			0
$901$	−12.4335	+	27.2256i	−0.414221	+	0.907017i
$902$		0			0
$903$	1.70386	−	5.80282i	0.0567010	−	0.193106i
$904$		0			0
$905$	−55.5456	+	7.98624i	−1.84640	+	0.265472i
$906$		0			0
$907$	3.54309	−	24.6427i	0.117646	−	0.818249i	−0.842489	−	0.538713i	$-0.818911\pi$
$907$	3.54309	−	24.6427i	0.117646	−	0.818249i	0.960135	−	0.279535i	$-0.0901804\pi$
$908$		0			0
$909$	14.8750	−	23.1459i	0.493372	−	0.767701i
$910$		0			0
$911$	2.18295	+	15.1828i	0.0723245	+	0.503028i	0.993496	+	0.113870i	$0.0363248\pi$
$911$	2.18295	+	15.1828i	0.0723245	+	0.503028i	−0.921171	+	0.389158i	$0.872766\pi$
$912$		0			0
$913$	−10.1978	+	15.8681i	−0.337497	+	0.525156i
$914$		0			0
$915$	−28.1530	+	32.4903i	−0.930709	+	1.07410i
$916$		0			0
$917$	−2.73256	+	2.36778i	−0.0902371	+	0.0781909i
$918$		0			0
$919$	−35.1144	+	16.0362i	−1.15832	+	0.528985i	−0.899491	−	0.436939i	$-0.856062\pi$
$919$	−35.1144	+	16.0362i	−1.15832	+	0.528985i	−0.258825	+	0.965924i	$0.583335\pi$
$920$		0			0
$921$	−4.26322	−	6.63371i	−0.140478	−	0.218588i
$922$		0			0
$923$	−34.1528	−	29.5936i	−1.12415	−	0.974085i
$924$		0			0
$925$	−7.31208	−	6.33596i	−0.240420	−	0.208325i
$926$		0			0
$927$			28.7250i			0.943453i
$928$		0			0
$929$	−42.9561	−	27.6062i	−1.40934	−	0.905730i	−0.409365	−	0.912371i	$-0.634250\pi$
$929$	−42.9561	−	27.6062i	−1.40934	−	0.905730i	−0.999978	+	0.00664066i	$0.997886\pi$
$930$		0			0
$931$	−6.96508	−	23.7209i	−0.228271	−	0.777420i
$932$		0			0
$933$	53.9538	+	24.6399i	1.76637	+	0.806673i
$934$		0			0
$935$	5.14185	−	35.7623i	0.168156	−	1.16955i
$936$		0			0
$937$	−47.4818	+	13.9419i	−1.55116	+	0.455462i	−0.941448	−	0.337159i	$-0.890534\pi$
$937$	−47.4818	+	13.9419i	−1.55116	+	0.455462i	−0.609714	+	0.792621i	$0.708716\pi$
$938$		0			0
$939$	−9.09508	+	10.4963i	−0.296807	+	0.342533i
$940$		0			0
$941$	−4.01973	−	1.83575i	−0.131039	−	0.0598437i	0.348816	−	0.937191i	$-0.386584\pi$
$941$	−4.01973	−	1.83575i	−0.131039	−	0.0598437i	−0.479856	+	0.877347i	$0.659311\pi$
$942$		0			0
$943$	1.93877	+	0.569273i	0.0631349	+	0.0185381i
$944$		0			0
$945$	−0.398145			−0.0129517
$946$		0			0
$947$	−15.7167	−	18.1380i	−0.510724	−	0.589407i	0.440560	−	0.897723i	$-0.354780\pi$
$947$	−15.7167	−	18.1380i	−0.510724	−	0.589407i	−0.951284	+	0.308317i	$0.900234\pi$
$948$		0			0
$949$	4.26837	+	14.5367i	0.138557	+	0.471882i
$950$		0			0
$951$	−34.4576	+	29.8577i	−1.11736	+	0.968201i
$952$		0			0
$953$	−9.70645	−	1.39558i	−0.314423	−	0.0452072i	−0.0167030	−	0.999860i	$-0.505317\pi$
$953$	−9.70645	−	1.39558i	−0.314423	−	0.0452072i	−0.297720	+	0.954653i	$0.596226\pi$
$954$		0			0
$955$	10.4658	−	1.50475i	0.338665	−	0.0486927i
$956$		0			0
$957$	−26.4558	−	7.76812i	−0.855194	−	0.251108i
$958$		0			0
$959$	−2.77837	−	3.20641i	−0.0897184	−	0.103541i
$960$		0			0
$961$	3.77869	−	8.27417i	0.121893	−	0.266909i
$962$		0			0
$963$	−34.8102	+	22.3712i	−1.12174	+	0.720901i
$964$		0			0
$965$	4.86302	+	7.56701i	0.156546	+	0.243591i
$966$		0			0
$967$		−	37.0068i		−	1.19006i	−0.803704	−	0.595029i	$-0.797141\pi$
$967$		−	37.0068i		−	1.19006i	0.803704	−	0.595029i	$-0.202859\pi$
$968$		0			0
$969$	−32.6511	+	20.9836i	−1.04890	+	0.674089i
$970$		0			0
$971$	3.04403	+	6.66549i	0.0976875	+	0.213906i	0.952166	−	0.305581i	$-0.0988506\pi$
$971$	3.04403	+	6.66549i	0.0976875	+	0.213906i	−0.854479	+	0.519486i	$0.826123\pi$
$972$		0			0
$973$	−0.425191	−	0.0611332i	−0.0136310	−	0.00195984i
$974$		0			0
$975$	41.5781	−	12.2084i	1.33156	−	0.390983i
$976$		0			0
$977$	2.33813	+	16.2620i	0.0748033	+	0.520269i	0.992429	+	0.122822i	$0.0391945\pi$
$977$	2.33813	+	16.2620i	0.0748033	+	0.520269i	−0.917625	+	0.397446i	$0.869896\pi$
$978$		0			0
$979$	−15.2143	−	19.0480i	−0.486250	−	0.608777i
$980$		0			0
$981$	2.27395	+	15.8157i	0.0726017	+	0.504956i
$982$		0			0
$983$	34.9851	−	10.2725i	1.11585	−	0.327643i	0.328719	−	0.944428i	$-0.393383\pi$
$983$	34.9851	−	10.2725i	1.11585	−	0.327643i	0.787132	+	0.616785i	$0.211565\pi$
$984$		0			0
$985$	31.8910	+	4.58524i	1.01613	+	0.146098i
$986$		0			0
$987$	0.699963	+	1.53271i	0.0222801	+	0.0487865i
$988$		0			0
$989$	−1.89362	+	1.21696i	−0.0602136	+	0.0386969i
$990$		0			0
$991$			23.3850i			0.742848i	0.928463	+	0.371424i	$0.121130\pi$
$991$			23.3850i			0.742848i	−0.928463	+	0.371424i	$0.878870\pi$
$992$		0			0
$993$	20.9812	+	32.6474i	0.665818	+	1.03603i
$994$		0			0
$995$	60.5998	−	38.9451i	1.92114	−	1.23464i
$996$		0			0
$997$	14.6038	−	31.9779i	0.462508	−	1.01275i	−0.524401	−	0.851472i	$-0.675711\pi$
$997$	14.6038	−	31.9779i	0.462508	−	1.01275i	0.986909	−	0.161280i	$-0.0515621\pi$
$998$		0			0
$999$	−0.715158	−	0.825337i	−0.0226266	−	0.0261125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	712.2.u.a.25.10	✓	100
89.57	even	22	inner	712.2.u.a.57.10	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
712.2.u.a.25.10	✓	100	1.1	even	1	trivial
712.2.u.a.57.10	yes	100	89.57	even	22	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:	\( N \)	\(=\)	\( 712 = 2^{3} \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	712.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.703549 - 2.39607i) q^{3} +(-1.32830 - 2.90857i) q^{5} +(-0.192082 + 0.0877207i) q^{7} +(-2.72241 - 1.74958i) q^{9} +O(q^{10})\)	\(q+(0.703549 - 2.39607i) q^{3} +(-1.32830 - 2.90857i) q^{5} +(-0.192082 + 0.0877207i) q^{7} +(-2.72241 - 1.74958i) q^{9} +(1.07347 - 2.35057i) q^{11} +(0.935804 - 3.18706i) q^{13} +(-7.90366 + 1.13638i) q^{15} +(-0.622296 + 4.32816i) q^{17} +(-1.92165 + 2.99015i) q^{19} +(0.0750460 + 0.521957i) q^{21} +(0.106110 - 0.165110i) q^{23} +(-3.42110 + 3.94816i) q^{25} +(-0.445641 + 0.386150i) q^{27} +(3.88668 - 1.77499i) q^{29} +(-2.53028 - 3.93720i) q^{31} +(-4.87690 - 4.22586i) q^{33} +(0.510284 + 0.442164i) q^{35} +1.85202i q^{37} +(-6.97802 - 4.48450i) q^{39} +(2.90051 + 9.87823i) q^{41} +(-10.4324 - 4.76433i) q^{43} +(-1.47262 + 10.2423i) q^{45} +(3.06589 - 0.900228i) q^{47} +(-4.55482 + 5.25655i) q^{49} +(9.93276 + 4.53614i) q^{51} +(6.56760 + 1.92842i) q^{53} -8.26270 q^{55} +(5.81263 + 6.70813i) q^{57} +(-0.653933 - 2.22709i) q^{59} +(4.06895 - 3.52576i) q^{61} +(0.676399 + 0.0972514i) q^{63} +(-10.5128 + 1.51151i) q^{65} +(4.86751 + 1.42923i) q^{67} +(-0.320961 - 0.370409i) q^{69} +(5.65175 - 12.3756i) q^{71} +(-3.83710 + 2.46596i) q^{73} +(7.05316 + 10.9749i) q^{75} +0.545667i q^{77} +(3.34082 - 2.14702i) q^{79} +(-3.42130 - 7.49160i) q^{81} +(-7.22513 - 1.03882i) q^{83} +(13.4154 - 3.93911i) q^{85} +(-1.51852 - 10.5616i) q^{87} +(4.25931 - 8.41774i) q^{89} +(0.0998201 + 0.694264i) q^{91} +(-11.2140 + 3.29272i) q^{93} +(11.2496 + 1.61745i) q^{95} +(-5.27727 - 11.5556i) q^{97} +(-7.03495 + 4.52109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 10 q^{9}+O(q^{10}) \) 100 * q + 10 * q^9	\( 100 q + 10 q^{9} + 14 q^{11} + 22 q^{13} - 8 q^{17} - 11 q^{19} - 34 q^{21} + 33 q^{23} + 24 q^{25} - 66 q^{27} - 22 q^{33} + 33 q^{35} - 36 q^{39} + 55 q^{41} + 8 q^{45} - 40 q^{47} - 30 q^{49} + 22 q^{51} - 38 q^{53} + 42 q^{55} + 54 q^{57} + 22 q^{59} + 11 q^{61} + 11 q^{63} - 33 q^{65} + 2 q^{67} + 17 q^{69} - 13 q^{71} + 20 q^{73} - 12 q^{79} - 38 q^{81} + 11 q^{83} + 35 q^{85} - 50 q^{87} + 47 q^{89} + 26 q^{91} - 2 q^{93} + 44 q^{95} + 36 q^{97} - 38 q^{99}+O(q^{100}) \) 100 * q + 10 * q^9 + 14 * q^11 + 22 * q^13 - 8 * q^17 - 11 * q^19 - 34 * q^21 + 33 * q^23 + 24 * q^25 - 66 * q^27 - 22 * q^33 + 33 * q^35 - 36 * q^39 + 55 * q^41 + 8 * q^45 - 40 * q^47 - 30 * q^49 + 22 * q^51 - 38 * q^53 + 42 * q^55 + 54 * q^57 + 22 * q^59 + 11 * q^61 + 11 * q^63 - 33 * q^65 + 2 * q^67 + 17 * q^69 - 13 * q^71 + 20 * q^73 - 12 * q^79 - 38 * q^81 + 11 * q^83 + 35 * q^85 - 50 * q^87 + 47 * q^89 + 26 * q^91 - 2 * q^93 + 44 * q^95 + 36 * q^97 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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