LMFDB - Embedded newform 1100.2.cb.a.949.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1100,2,Mod(49,1100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("1100.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.cb (of order $10$, degree $4$, not 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:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			949.1
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	1100.949
Dual form			1100.2.cb.a.1049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.48990 + 0.809017i) q^{3} +(-3.66547 - 1.19098i) q^{7} +(3.11803 - 2.26538i) q^{9} +O(q^{10})$	\(q+(-2.48990 + 0.809017i) q^{3} +(-3.66547 - 1.19098i) q^{7} +(3.11803 - 2.26538i) q^{9} +(1.23607 - 3.07768i) q^{11} +(1.40008 + 1.92705i) q^{13} +(1.40008 - 1.92705i) q^{17} +(-1.19098 - 3.66547i) q^{19} +10.0902 q^{21} +2.47214i q^{23} +(-1.31433 + 1.80902i) q^{27} +(-2.66312 + 8.19624i) q^{29} +(-0.690983 + 0.502029i) q^{31} +(-0.587785 + 8.66312i) q^{33} +(-1.76336 - 0.572949i) q^{37} +(-5.04508 - 3.66547i) q^{39} +(2.66312 + 8.19624i) q^{41} +(-1.31433 + 0.427051i) q^{47} +(6.35410 + 4.61653i) q^{49} +(-1.92705 + 5.93085i) q^{51} +(-2.40414 - 3.30902i) q^{53} +(5.93085 + 8.16312i) q^{57} +(-0.336881 + 1.03681i) q^{59} +(-1.92705 - 1.40008i) q^{61} +(-14.1271 + 4.59017i) q^{63} +12.9443i q^{67} +(-2.00000 - 6.15537i) q^{69} +(5.16312 + 3.75123i) q^{71} +(0.865300 + 0.281153i) q^{73} +(-8.19624 + 9.80902i) q^{77} +(-5.78115 + 4.20025i) q^{79} +(-1.76393 + 5.42882i) q^{81} +(-7.66145 + 10.5451i) q^{83} -22.5623i q^{87} -0.472136 q^{89} +(-2.83688 - 8.73102i) q^{91} +(1.31433 - 1.80902i) q^{93} +(8.55951 + 11.7812i) q^{97} +(-3.11803 - 12.3965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{9}+O(q^{10}) $ 8 * q + 16 * q^9	$ 8 q + 16 q^{9} - 8 q^{11} - 14 q^{19} + 36 q^{21} + 10 q^{29} - 10 q^{31} - 18 q^{39} - 10 q^{41} + 24 q^{49} - 2 q^{51} - 34 q^{59} - 2 q^{61} - 16 q^{69} + 10 q^{71} - 6 q^{79} - 32 q^{81} + 32 q^{89} - 54 q^{91} - 16 q^{99}+O(q^{100}) $ 8 * q + 16 * q^9 - 8 * q^11 - 14 * q^19 + 36 * q^21 + 10 * q^29 - 10 * q^31 - 18 * q^39 - 10 * q^41 + 24 * q^49 - 2 * q^51 - 34 * q^59 - 2 * q^61 - 16 * q^69 + 10 * q^71 - 6 * q^79 - 32 * q^81 + 32 * q^89 - 54 * q^91 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$	$1$

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
$3$	−2.48990	+	0.809017i	−1.43754	+	0.467086i	−0.921131	−	0.389254i	$-0.872733\pi$
$3$	−2.48990	+	0.809017i	−1.43754	+	0.467086i	−0.516413	+	0.856340i	$0.672733\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.66547	−	1.19098i	−1.38542	−	0.450149i	−0.480971	−	0.876737i	$-0.659716\pi$
$7$	−3.66547	−	1.19098i	−1.38542	−	0.450149i	−0.904446	+	0.426587i	$0.859716\pi$
$8$		0			0
$9$	3.11803	−	2.26538i	1.03934	−	0.755128i
$10$		0			0
$11$	1.23607	−	3.07768i	0.372689	−	0.927957i
$11$	1.23607	−	3.07768i	0.372689	−	0.927957i
$12$		0			0
$13$	1.40008	+	1.92705i	0.388314	+	0.534468i	0.957763	−	0.287559i	$-0.0928436\pi$
$13$	1.40008	+	1.92705i	0.388314	+	0.534468i	−0.569449	+	0.822026i	$0.692844\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.40008	−	1.92705i	0.339570	−	0.467379i	−0.604746	−	0.796419i	$-0.706725\pi$
$17$	1.40008	−	1.92705i	0.339570	−	0.467379i	0.944316	+	0.329040i	$0.106725\pi$
$18$		0			0
$19$	−1.19098	−	3.66547i	−0.273230	−	0.840916i	−0.989682	−	0.143280i	$-0.954235\pi$
$19$	−1.19098	−	3.66547i	−0.273230	−	0.840916i	0.716452	−	0.697636i	$-0.245765\pi$
$20$		0			0
$21$	10.0902			2.20186
$22$		0			0
$23$			2.47214i			0.515476i	0.966215	+	0.257738i	$0.0829771\pi$
$23$			2.47214i			0.515476i	−0.966215	+	0.257738i	$0.917023\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.31433	+	1.80902i	−0.252942	+	0.348145i
$28$		0			0
$29$	−2.66312	+	8.19624i	−0.494529	+	1.52200i	0.323161	+	0.946344i	$0.395254\pi$
$29$	−2.66312	+	8.19624i	−0.494529	+	1.52200i	−0.817690	+	0.575659i	$0.804746\pi$
$30$		0			0
$31$	−0.690983	+	0.502029i	−0.124104	+	0.0901670i	−0.648106	−	0.761550i	$-0.724439\pi$
$31$	−0.690983	+	0.502029i	−0.124104	+	0.0901670i	0.524002	+	0.851717i	$0.324439\pi$
$32$		0			0
$33$	−0.587785	+	8.66312i	−0.102320	+	1.50806i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.76336	−	0.572949i	−0.289894	−	0.0941922i	0.160460	−	0.987042i	$-0.448702\pi$
$37$	−1.76336	−	0.572949i	−0.289894	−	0.0941922i	−0.450354	+	0.892850i	$0.648702\pi$
$38$		0			0
$39$	−5.04508	−	3.66547i	−0.807860	−	0.586945i
$40$		0			0
$41$	2.66312	+	8.19624i	0.415909	+	1.28004i	0.911435	+	0.411444i	$0.134975\pi$
$41$	2.66312	+	8.19624i	0.415909	+	1.28004i	−0.495526	+	0.868593i	$0.665025\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.31433	+	0.427051i	−0.191714	+	0.0622918i	−0.403301	−	0.915068i	$-0.632137\pi$
$47$	−1.31433	+	0.427051i	−0.191714	+	0.0622918i	0.211586	+	0.977359i	$0.432137\pi$
$48$		0			0
$49$	6.35410	+	4.61653i	0.907729	+	0.659504i
$50$		0			0
$51$	−1.92705	+	5.93085i	−0.269841	+	0.830486i
$52$		0			0
$53$	−2.40414	−	3.30902i	−0.330234	−	0.454528i	0.611323	−	0.791381i	$-0.290638\pi$
$53$	−2.40414	−	3.30902i	−0.330234	−	0.454528i	−0.941557	+	0.336853i	$0.890638\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	5.93085	+	8.16312i	0.785561	+	1.08123i
$58$		0			0
$59$	−0.336881	+	1.03681i	−0.0438582	+	0.134982i	−0.970588	−	0.240747i	$-0.922608\pi$
$59$	−0.336881	+	1.03681i	−0.0438582	+	0.134982i	0.926730	+	0.375729i	$0.122608\pi$
$60$		0			0
$61$	−1.92705	−	1.40008i	−0.246734	−	0.179262i	0.457544	−	0.889187i	$-0.348729\pi$
$61$	−1.92705	−	1.40008i	−0.246734	−	0.179262i	−0.704278	+	0.709924i	$0.748729\pi$
$62$		0			0
$63$	−14.1271	+	4.59017i	−1.77985	+	0.578307i
$64$		0			0
$65$		0			0
$66$		0			0
$67$			12.9443i			1.58139i	0.612207	+	0.790697i	$0.290282\pi$
$67$			12.9443i			1.58139i	−0.612207	+	0.790697i	$0.709718\pi$
$68$		0			0
$69$	−2.00000	−	6.15537i	−0.240772	−	0.741019i
$70$		0			0
$71$	5.16312	+	3.75123i	0.612749	+	0.445189i	0.850381	−	0.526167i	$-0.176371\pi$
$71$	5.16312	+	3.75123i	0.612749	+	0.445189i	−0.237632	+	0.971355i	$0.576371\pi$
$72$		0			0
$73$	0.865300	+	0.281153i	0.101276	+	0.0329065i	0.359217	−	0.933254i	$-0.383044\pi$
$73$	0.865300	+	0.281153i	0.101276	+	0.0329065i	−0.257941	+	0.966161i	$0.583044\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8.19624	+	9.80902i	−0.934048	+	1.11784i
$78$		0			0
$79$	−5.78115	+	4.20025i	−0.650431	+	0.472565i	−0.863418	−	0.504490i	$-0.831681\pi$
$79$	−5.78115	+	4.20025i	−0.650431	+	0.472565i	0.212987	+	0.977055i	$0.431681\pi$
$80$		0			0
$81$	−1.76393	+	5.42882i	−0.195992	+	0.603203i
$82$		0			0
$83$	−7.66145	+	10.5451i	−0.840954	+	1.15747i	0.144830	+	0.989456i	$0.453736\pi$
$83$	−7.66145	+	10.5451i	−0.840954	+	1.15747i	−0.985784	+	0.168017i	$0.946264\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	22.5623i		−	2.41893i
$88$		0			0
$89$	−0.472136			−0.0500463			−0.0250232	−	0.999687i	$-0.507966\pi$
$89$	−0.472136			−0.0500463			−0.0250232	+	0.999687i	$0.507966\pi$
$90$		0			0
$91$	−2.83688	−	8.73102i	−0.297386	−	0.915260i
$92$		0			0
$93$	1.31433	−	1.80902i	0.136289	−	0.187586i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	8.55951	+	11.7812i	0.869086	+	1.19619i	0.979326	+	0.202290i	$0.0648383\pi$
$97$	8.55951	+	11.7812i	0.869086	+	1.19619i	−0.110239	+	0.993905i	$0.535162\pi$
$98$		0			0
$99$	−3.11803	−	12.3965i	−0.313374	−	1.24589i
$100$		0			0
$101$	−14.3992	+	10.4616i	−1.43277	+	1.04097i	−0.443281	+	0.896383i	$0.646185\pi$
$101$	−14.3992	+	10.4616i	−1.43277	+	1.04097i	−0.989492	+	0.144587i	$0.953815\pi$
$102$		0			0
$103$	7.46969	+	2.42705i	0.736011	+	0.239144i	0.652951	−	0.757400i	$-0.273531\pi$
$103$	7.46969	+	2.42705i	0.736011	+	0.239144i	0.0830599	+	0.996545i	$0.473531\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.9964	−	3.57295i	1.06306	−	0.345410i	0.275281	−	0.961364i	$-0.411229\pi$
$107$	10.9964	−	3.57295i	1.06306	−	0.345410i	0.787782	+	0.615954i	$0.211229\pi$
$108$		0			0
$109$	12.4721			1.19461			0.597307	−	0.802013i	$-0.296237\pi$
$109$	12.4721			1.19461			0.597307	+	0.802013i	$0.296237\pi$
$110$		0			0
$111$	4.85410			0.460731
$112$		0			0
$113$	16.7027	−	5.42705i	1.57126	−	0.510534i	0.611475	−	0.791264i	$-0.290576\pi$
$113$	16.7027	−	5.42705i	1.57126	−	0.510534i	0.959787	+	0.280730i	$0.0905764\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	8.73102	+	2.83688i	0.807183	+	0.262270i
$118$		0			0
$119$	−7.42705	+	5.39607i	−0.680837	+	0.494657i
$120$		0			0
$121$	−7.94427	−	7.60845i	−0.722207	−	0.691677i
$122$		0			0
$123$	−13.2618	−	18.2533i	−1.19578	−	1.64584i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−1.40008	+	1.92705i	−0.124237	+	0.170998i	−0.866605	−	0.498995i	$-0.833703\pi$
$127$	−1.40008	+	1.92705i	−0.124237	+	0.170998i	0.742368	+	0.669993i	$0.233703\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.52786			0.832453			0.416227	−	0.909261i	$-0.363352\pi$
$131$	9.52786			0.832453			0.416227	+	0.909261i	$0.363352\pi$
$132$		0			0
$133$			14.8541i			1.28801i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.11048	−	11.1631i	0.692925	−	0.953730i	−0.307073	−	0.951686i	$-0.599350\pi$
$137$	8.11048	−	11.1631i	0.692925	−	0.953730i	0.999998	−	0.00204358i	$-0.000650494\pi$
$138$		0			0
$139$	−3.57295	+	10.9964i	−0.303054	+	0.932703i	0.677343	+	0.735668i	$0.263131\pi$
$139$	−3.57295	+	10.9964i	−0.303054	+	0.932703i	−0.980396	+	0.197035i	$0.936869\pi$
$140$		0			0
$141$	2.92705	−	2.12663i	0.246502	−	0.179094i
$142$		0			0
$143$	7.66145	−	1.92705i	0.640683	−	0.161148i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−19.5559	−	6.35410i	−1.61294	−	0.524077i
$148$		0			0
$149$	1.92705	+	1.40008i	0.157870	+	0.114699i	0.663916	−	0.747807i	$-0.268893\pi$
$149$	1.92705	+	1.40008i	0.157870	+	0.114699i	−0.506046	+	0.862507i	$0.668893\pi$
$150$		0			0
$151$	5.95492	+	18.3273i	0.484604	+	1.49146i	0.832553	+	0.553945i	$0.186878\pi$
$151$	5.95492	+	18.3273i	0.484604	+	1.49146i	−0.347949	+	0.937513i	$0.613122\pi$
$152$		0			0
$153$		−	9.18034i		−	0.742186i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−16.7027	+	5.42705i	−1.33302	+	0.433126i	−0.886948	−	0.461869i	$-0.847179\pi$
$157$	−16.7027	+	5.42705i	−1.33302	+	0.433126i	−0.446076	+	0.894995i	$0.647179\pi$
$158$		0			0
$159$	8.66312	+	6.29412i	0.687030	+	0.499157i
$160$		0			0
$161$	2.94427	−	9.06154i	0.232041	−	0.714149i
$162$		0			0
$163$	6.65740	+	9.16312i	0.521447	+	0.717711i	0.985797	−	0.167941i	$-0.0537119\pi$
$163$	6.65740	+	9.16312i	0.521447	+	0.717711i	−0.464350	+	0.885652i	$0.653712\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.4616	−	14.3992i	−0.809545	−	1.11424i	−0.991393	−	0.130916i	$-0.958208\pi$
$167$	−10.4616	−	14.3992i	−0.809545	−	1.11424i	0.181849	−	0.983326i	$-0.441792\pi$
$168$		0			0
$169$	2.26393	−	6.96767i	0.174149	−	0.535974i
$170$		0			0
$171$	−12.0172	−	8.73102i	−0.918980	−	0.667678i
$172$		0			0
$173$	−6.46564	+	2.10081i	−0.491573	+	0.159722i	−0.544306	−	0.838887i	$-0.683207\pi$
$173$	−6.46564	+	2.10081i	−0.491573	+	0.159722i	0.0527326	+	0.998609i	$0.483207\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	2.85410i		−	0.214527i
$178$		0			0
$179$	0.809017	+	2.48990i	0.0604688	+	0.186104i	0.976728	−	0.214482i	$-0.0688065\pi$
$179$	0.809017	+	2.48990i	0.0604688	+	0.186104i	−0.916259	+	0.400586i	$0.868806\pi$
$180$		0			0
$181$	1.30902	+	0.951057i	0.0972985	+	0.0706915i	0.635371	−	0.772207i	$-0.280847\pi$
$181$	1.30902	+	0.951057i	0.0972985	+	0.0706915i	−0.538072	+	0.842899i	$0.680847\pi$
$182$		0			0
$183$	5.93085	+	1.92705i	0.438421	+	0.142452i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−4.20025	−	6.69098i	−0.307153	−	0.489293i
$188$		0			0
$189$	6.97214	−	5.06555i	0.507148	−	0.368465i
$190$		0			0
$191$	8.04508	−	24.7602i	0.582122	−	1.79159i	−0.0284112	−	0.999596i	$-0.509045\pi$
$191$	8.04508	−	24.7602i	0.582122	−	1.79159i	0.610533	−	0.791991i	$-0.290955\pi$
$192$		0			0
$193$	13.2618	−	18.2533i	0.954605	−	1.31390i	0.00515308	−	0.999987i	$-0.498360\pi$
$193$	13.2618	−	18.2533i	0.954605	−	1.31390i	0.949451	−	0.313914i	$-0.101640\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	2.94427i		−	0.209771i	−0.994484	−	0.104885i	$-0.966552\pi$
$197$		−	2.94427i		−	0.209771i	0.994484	−	0.104885i	$-0.0334476\pi$
$198$		0			0
$199$	0.944272			0.0669377			0.0334688	−	0.999440i	$-0.489345\pi$
$199$	0.944272			0.0669377			0.0334688	+	0.999440i	$0.489345\pi$
$200$		0			0
$201$	−10.4721	−	32.2299i	−0.738648	−	2.27332i
$202$		0			0
$203$	19.5232	−	26.8713i	1.37026	−	1.88600i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	5.60034	+	7.70820i	0.389250	+	0.535757i
$208$		0			0
$209$	−12.7533	−	0.865300i	−0.882163	−	0.0598540i
$210$		0			0
$211$	−9.63525	+	7.00042i	−0.663318	+	0.481929i	−0.867782	−	0.496945i	$-0.834455\pi$
$211$	−9.63525	+	7.00042i	−0.663318	+	0.481929i	0.204464	+	0.978874i	$0.434455\pi$
$212$		0			0
$213$	−15.8904	−	5.16312i	−1.08880	−	0.353771i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	3.13068	−	1.01722i	0.212525	−	0.0690535i
$218$		0			0
$219$	−2.38197			−0.160958
$220$		0			0
$221$	5.67376			0.381659
$222$		0			0
$223$	−11.5514	+	3.75329i	−0.773541	+	0.251339i	−0.669080	−	0.743190i	$-0.733312\pi$
$223$	−11.5514	+	3.75329i	−0.773541	+	0.251339i	−0.104461	+	0.994529i	$0.533312\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.39607	+	1.75329i	0.358150	+	0.116370i	0.482565	−	0.875860i	$-0.339705\pi$
$227$	5.39607	+	1.75329i	0.358150	+	0.116370i	−0.124415	+	0.992230i	$0.539705\pi$
$228$		0			0
$229$	13.1631	−	9.56357i	0.869843	−	0.631978i	−0.0607015	−	0.998156i	$-0.519334\pi$
$229$	13.1631	−	9.56357i	0.869843	−	0.631978i	0.930545	+	0.366178i	$0.119334\pi$
$230$		0			0
$231$	12.4721	−	31.0543i	0.820606	−	2.04323i
$232$		0			0
$233$	1.40008	+	1.92705i	0.0917226	+	0.126245i	0.852412	−	0.522871i	$-0.175139\pi$
$233$	1.40008	+	1.92705i	0.0917226	+	0.126245i	−0.760689	+	0.649116i	$0.775139\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	10.9964	−	15.1353i	0.714293	−	0.983140i
$238$		0			0
$239$	3.57295	+	10.9964i	0.231115	+	0.711298i	0.997613	+	0.0690519i	$0.0219974\pi$
$239$	3.57295	+	10.9964i	0.231115	+	0.711298i	−0.766498	+	0.642246i	$0.778003\pi$
$240$		0			0
$241$	12.4721			0.803401			0.401700	−	0.915771i	$-0.368419\pi$
$241$	12.4721			0.803401			0.401700	+	0.915771i	$0.368419\pi$
$242$		0			0
$243$		−	21.6525i		−	1.38901i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	5.39607	−	7.42705i	0.343344	−	0.472572i
$248$		0			0
$249$	10.5451	−	32.4544i	0.668268	−	2.05672i
$250$		0			0
$251$	−20.8713	+	15.1639i	−1.31739	+	0.957137i	−0.317425	+	0.948283i	$0.602818\pi$
$251$	−20.8713	+	15.1639i	−1.31739	+	0.957137i	−0.999961	+	0.00885387i	$0.997182\pi$
$252$		0			0
$253$	7.60845	+	3.05573i	0.478339	+	0.192112i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.66953	−	1.51722i	−0.291277	−	0.0946416i	0.159734	−	0.987160i	$-0.448936\pi$
$257$	−4.66953	−	1.51722i	−0.291277	−	0.0946416i	−0.451011	+	0.892518i	$0.648936\pi$
$258$		0			0
$259$	5.78115	+	4.20025i	0.359223	+	0.260991i
$260$		0			0
$261$	10.2639	+	31.5891i	0.635321	+	1.95532i
$262$		0			0
$263$		−	5.88854i		−	0.363103i	−0.983381	−	0.181552i	$-0.941888\pi$
$263$		−	5.88854i		−	0.363103i	0.983381	−	0.181552i	$-0.0581119\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.17557	−	0.381966i	0.0719437	−	0.0233759i
$268$		0			0
$269$	−19.4894	−	14.1598i	−1.18829	−	0.863341i	−0.195205	−	0.980762i	$-0.562537\pi$
$269$	−19.4894	−	14.1598i	−1.18829	−	0.863341i	−0.993082	+	0.117421i	$0.962537\pi$
$270$		0			0
$271$	−5.95492	+	18.3273i	−0.361735	+	1.11331i	0.590265	+	0.807210i	$0.299023\pi$
$271$	−5.95492	+	18.3273i	−0.361735	+	1.11331i	−0.952000	+	0.306097i	$0.900977\pi$
$272$		0			0
$273$	14.1271	+	19.4443i	0.855010	+	1.17682i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	13.2618	+	18.2533i	0.796824	+	1.09673i	0.993225	+	0.116210i	$0.0370746\pi$
$277$	13.2618	+	18.2533i	0.796824	+	1.09673i	−0.196401	+	0.980524i	$0.562925\pi$
$278$		0			0
$279$	−1.01722	+	3.13068i	−0.0608994	+	0.187429i
$280$		0			0
$281$	−22.1074	−	16.0620i	−1.31882	−	0.958176i	−0.999946	−	0.0103778i	$-0.996697\pi$
$281$	−22.1074	−	16.0620i	−1.31882	−	0.958176i	−0.318870	−	0.947798i	$-0.603303\pi$
$282$		0			0
$283$	−10.9964	+	3.57295i	−0.653669	+	0.212390i	−0.617031	−	0.786939i	$-0.711665\pi$
$283$	−10.9964	+	3.57295i	−0.653669	+	0.212390i	−0.0366375	+	0.999329i	$0.511665\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	33.2148i		−	1.96061i
$288$		0			0
$289$	3.50000	+	10.7719i	0.205882	+	0.633641i
$290$		0			0
$291$	−30.8435	−	22.4091i	−1.80808	−	1.31364i
$292$		0			0
$293$	−8.19624	−	2.66312i	−0.478829	−	0.155581i	0.0596508	−	0.998219i	$-0.481001\pi$
$293$	−8.19624	−	2.66312i	−0.478829	−	0.155581i	−0.538480	+	0.842638i	$0.681001\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.94298	+	6.28115i	0.228795	+	0.364469i
$298$		0			0
$299$	−4.76393	+	3.46120i	−0.275505	+	0.200166i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	27.3889	−	37.6976i	1.57345	−	2.16567i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			9.52786i			0.543784i	0.962328	+	0.271892i	$0.0876493\pi$
$307$			9.52786i			0.543784i	−0.962328	+	0.271892i	$0.912351\pi$
$308$		0			0
$309$	−20.5623			−1.16975
$310$		0			0
$311$	5.19098	+	15.9762i	0.294354	+	0.905927i	0.983438	+	0.181246i	$0.0580130\pi$
$311$	5.19098	+	15.9762i	0.294354	+	0.905927i	−0.689084	+	0.724681i	$0.741987\pi$
$312$		0			0
$313$	4.41226	−	6.07295i	0.249395	−	0.343263i	−0.665904	−	0.746037i	$-0.731954\pi$
$313$	4.41226	−	6.07295i	0.249395	−	0.343263i	0.915299	+	0.402774i	$0.131954\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.55951	+	11.7812i	0.480750	+	0.661695i	0.978649	−	0.205540i	$-0.0658949\pi$
$317$	8.55951	+	11.7812i	0.480750	+	0.661695i	−0.497899	+	0.867235i	$0.665895\pi$
$318$		0			0
$319$	21.9336	+	18.3273i	1.22805	+	1.02613i
$320$		0			0
$321$	−24.4894	+	17.7926i	−1.36686	+	0.993084i
$322$		0			0
$323$	−8.73102	−	2.83688i	−0.485807	−	0.157848i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−31.0543	+	10.0902i	−1.71731	+	0.557988i
$328$		0			0
$329$	5.32624			0.293645
$330$		0			0
$331$	−12.0000			−0.659580			−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000			−0.659580			−0.329790	+	0.944054i	$0.606978\pi$
$332$		0			0
$333$	−6.79615	+	2.20820i	−0.372427	+	0.121009i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	22.8581	+	7.42705i	1.24516	+	0.404577i	0.856184	−	0.516670i	$-0.172829\pi$
$337$	22.8581	+	7.42705i	1.24516	+	0.404577i	0.388976	+	0.921248i	$0.372829\pi$
$338$		0			0
$339$	−37.1976	+	27.0256i	−2.02029	+	1.46783i
$340$		0			0
$341$	0.690983	+	2.74717i	0.0374188	+	0.148768i
$342$		0			0
$343$	−1.93487	−	2.66312i	−0.104473	−	0.143795i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.4616	+	14.3992i	−0.561609	+	0.772989i	−0.991530	−	0.129878i	$-0.958542\pi$
$347$	−10.4616	+	14.3992i	−0.561609	+	0.772989i	0.429921	+	0.902867i	$0.358542\pi$
$348$		0			0
$349$	5.04508	+	15.5272i	0.270057	+	0.831151i	0.990485	+	0.137621i	$0.0439455\pi$
$349$	5.04508	+	15.5272i	0.270057	+	0.831151i	−0.720428	+	0.693530i	$0.756055\pi$
$350$		0			0
$351$	−5.32624			−0.284294
$352$		0			0
$353$			14.9443i			0.795403i	0.917515	+	0.397702i	$0.130192\pi$
$353$			14.9443i			0.795403i	−0.917515	+	0.397702i	$0.869808\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	14.1271	−	19.4443i	0.747685	−	1.02910i
$358$		0			0
$359$	−3.57295	+	10.9964i	−0.188573	+	0.580368i	−0.999992	−	0.00409736i	$-0.998696\pi$
$359$	−3.57295	+	10.9964i	−0.188573	+	0.580368i	0.811419	+	0.584465i	$0.198696\pi$
$360$		0			0
$361$	3.35410	−	2.43690i	0.176532	−	0.128258i
$362$		0			0
$363$	25.9358	+	12.5172i	1.36128	+	0.656984i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	19.1599	+	6.22542i	1.00014	+	0.324965i	0.762921	−	0.646492i	$-0.223765\pi$
$367$	19.1599	+	6.22542i	1.00014	+	0.324965i	0.237217	+	0.971457i	$0.423765\pi$
$368$		0			0
$369$	26.8713	+	19.5232i	1.39887	+	1.01634i
$370$		0			0
$371$	4.87132	+	14.9924i	0.252906	+	0.778366i
$372$		0			0
$373$			6.58359i			0.340885i	0.985368	+	0.170443i	$0.0545198\pi$
$373$			6.58359i			0.340885i	−0.985368	+	0.170443i	$0.945480\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−19.5232	+	6.34346i	−1.00549	+	0.326705i
$378$		0			0
$379$	2.54508	+	1.84911i	0.130732	+	0.0949825i	0.651230	−	0.758881i	$-0.274253\pi$
$379$	2.54508	+	1.84911i	0.130732	+	0.0949825i	−0.520497	+	0.853863i	$0.674253\pi$
$380$		0			0
$381$	1.92705	−	5.93085i	0.0987258	−	0.303847i
$382$		0			0
$383$	11.7027	+	16.1074i	0.597980	+	0.823049i	0.995522	−	0.0945351i	$-0.0301364\pi$
$383$	11.7027	+	16.1074i	0.597980	+	0.823049i	−0.397541	+	0.917584i	$0.630136\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.28115	−	25.4868i	0.419871	−	1.29223i	−0.487950	−	0.872872i	$-0.662255\pi$
$389$	8.28115	−	25.4868i	0.419871	−	1.29223i	0.907821	−	0.419359i	$-0.137745\pi$
$390$		0			0
$391$	4.76393	+	3.46120i	0.240922	+	0.175040i
$392$		0			0
$393$	−23.7234	+	7.70820i	−1.19669	+	0.388827i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			32.8328i			1.64783i	0.566712	+	0.823916i	$0.308215\pi$
$397$			32.8328i			1.64783i	−0.566712	+	0.823916i	$0.691785\pi$
$398$		0			0
$399$	−12.0172	−	36.9852i	−0.601614	−	1.85158i
$400$		0			0
$401$	−5.45492	−	3.96323i	−0.272405	−	0.197914i	0.443193	−	0.896426i	$-0.353846\pi$
$401$	−5.45492	−	3.96323i	−0.272405	−	0.197914i	−0.715598	+	0.698512i	$0.753846\pi$
$402$		0			0
$403$	−1.93487	−	0.628677i	−0.0963827	−	0.0313166i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.94298	+	4.71885i	−0.195446	+	0.233905i
$408$		0			0
$409$	−5.78115	+	4.20025i	−0.285860	+	0.207689i	−0.721469	−	0.692447i	$-0.756533\pi$
$409$	−5.78115	+	4.20025i	−0.285860	+	0.207689i	0.435610	+	0.900136i	$0.356533\pi$
$410$		0			0
$411$	−11.1631	+	34.3565i	−0.550636	+	1.69468i
$412$		0			0
$413$	2.46965	−	3.39919i	0.121524	−	0.167263i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	30.2705i		−	1.48235i
$418$		0			0
$419$	4.58359			0.223923			0.111962	−	0.993713i	$-0.464287\pi$
$419$	4.58359			0.223923			0.111962	+	0.993713i	$0.464287\pi$
$420$		0			0
$421$	−2.86475	−	8.81678i	−0.139619	−	0.429704i	0.856661	−	0.515880i	$-0.172535\pi$
$421$	−2.86475	−	8.81678i	−0.139619	−	0.429704i	−0.996280	+	0.0861767i	$0.972535\pi$
$422$		0			0
$423$	−3.13068	+	4.30902i	−0.152219	+	0.209512i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	5.39607	+	7.42705i	0.261134	+	0.359420i
$428$		0			0
$429$	−17.5172	+	10.9964i	−0.845739	+	0.530912i
$430$		0			0
$431$	13.4894	−	9.80059i	0.649759	−	0.472078i	−0.213430	−	0.976958i	$-0.568463\pi$
$431$	13.4894	−	9.80059i	0.649759	−	0.472078i	0.863189	+	0.504881i	$0.168463\pi$
$432$		0			0
$433$	−18.4989	−	6.01064i	−0.888998	−	0.288853i	−0.171310	−	0.985217i	$-0.554800\pi$
$433$	−18.4989	−	6.01064i	−0.888998	−	0.288853i	−0.717689	+	0.696364i	$0.754800\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	9.06154	−	2.94427i	0.433472	−	0.140844i
$438$		0			0
$439$	15.4164			0.735785			0.367893	−	0.929868i	$-0.380079\pi$
$439$	15.4164			0.735785			0.367893	+	0.929868i	$0.380079\pi$
$440$		0			0
$441$	30.2705			1.44145
$442$		0			0
$443$	3.11044	−	1.01064i	0.147781	−	0.0480171i	−0.234192	−	0.972190i	$-0.575245\pi$
$443$	3.11044	−	1.01064i	0.147781	−	0.0480171i	0.381974	+	0.924173i	$0.375245\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−5.93085	−	1.92705i	−0.280520	−	0.0911464i
$448$		0			0
$449$	−11.7812	+	8.55951i	−0.555987	+	0.403948i	−0.829988	−	0.557781i	$-0.811653\pi$
$449$	−11.7812	+	8.55951i	−0.555987	+	0.403948i	0.274001	+	0.961729i	$0.411653\pi$
$450$		0			0
$451$	28.5172	+	1.93487i	1.34282	+	0.0911094i
$452$		0			0
$453$	−29.6543	−	40.8156i	−1.39328	−	1.91768i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.20025	+	5.78115i	−0.196480	+	0.270431i	−0.895877	−	0.444302i	$-0.853452\pi$
$457$	−4.20025	+	5.78115i	−0.196480	+	0.270431i	0.699398	+	0.714733i	$0.253452\pi$
$458$		0			0
$459$	1.64590	+	5.06555i	0.0768239	+	0.236440i
$460$		0			0
$461$	−33.7771			−1.57316			−0.786578	−	0.617491i	$-0.788149\pi$
$461$	−33.7771			−1.57316			−0.786578	+	0.617491i	$0.788149\pi$
$462$		0			0
$463$			12.0000i			0.557687i	0.960337	+	0.278844i	$0.0899511\pi$
$463$			12.0000i			0.557687i	−0.960337	+	0.278844i	$0.910049\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.44945	−	10.2533i	0.344719	−	0.474466i	−0.601093	−	0.799179i	$-0.705268\pi$
$467$	7.44945	−	10.2533i	0.344719	−	0.474466i	0.945812	+	0.324713i	$0.105268\pi$
$468$		0			0
$469$	15.4164	−	47.4468i	0.711864	−	2.19089i
$470$		0			0
$471$	37.1976	−	27.0256i	1.71397	−	1.24527i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−14.9924	−	4.87132i	−0.686454	−	0.223043i
$478$		0			0
$479$	−22.1074	−	16.0620i	−1.01011	−	0.733890i	−0.0458798	−	0.998947i	$-0.514609\pi$
$479$	−22.1074	−	16.0620i	−1.01011	−	0.733890i	−0.964233	+	0.265057i	$0.914609\pi$
$480$		0			0
$481$	−1.36475	−	4.20025i	−0.0622270	−	0.191515i
$482$		0			0
$483$			24.9443i			1.13500i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	17.1518	−	5.57295i	0.777221	−	0.252534i	0.106568	−	0.994305i	$-0.466014\pi$
$487$	17.1518	−	5.57295i	0.777221	−	0.252534i	0.670653	+	0.741771i	$0.266014\pi$
$488$		0			0
$489$	−23.9894	−	17.4293i	−1.08484	−	0.788180i
$490$		0			0
$491$	3.57295	−	10.9964i	0.161245	−	0.496261i	−0.837495	−	0.546445i	$-0.815981\pi$
$491$	3.57295	−	10.9964i	0.161245	−	0.496261i	0.998740	+	0.0501840i	$0.0159808\pi$
$492$		0			0
$493$	12.0660	+	16.6074i	0.543424	+	0.747959i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−14.4576	−	19.8992i	−0.648512	−	0.892601i
$498$		0			0
$499$	7.19098	−	22.1316i	0.321913	−	0.990745i	−0.650902	−	0.759161i	$-0.725609\pi$
$499$	7.19098	−	22.1316i	0.321913	−	0.990745i	0.972815	−	0.231584i	$-0.0743907\pi$
$500$		0			0
$501$	37.6976	+	27.3889i	1.68420	+	1.22364i
$502$		0			0
$503$	−34.7198	+	11.2812i	−1.54808	+	0.503002i	−0.953592	−	0.301102i	$-0.902645\pi$
$503$	−34.7198	+	11.2812i	−1.54808	+	0.503002i	−0.594488	+	0.804104i	$0.702645\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			19.1803i			0.851829i
$508$		0			0
$509$	8.86475	+	27.2829i	0.392923	+	1.20929i	0.930567	+	0.366121i	$0.119314\pi$
$509$	8.86475	+	27.2829i	0.392923	+	1.20929i	−0.537644	+	0.843172i	$0.680686\pi$
$510$		0			0
$511$	−2.83688	−	2.06111i	−0.125496	−	0.0911783i
$512$		0			0
$513$	8.19624	+	2.66312i	0.361873	+	0.117580i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−0.310271	+	4.57295i	−0.0136457	+	0.201118i
$518$		0			0
$519$	14.3992	−	10.4616i	0.632054	−	0.459214i
$520$		0			0
$521$	2.37132	−	7.29818i	0.103890	−	0.319739i	−0.885579	−	0.464489i	$-0.846238\pi$
$521$	2.37132	−	7.29818i	0.103890	−	0.319739i	0.989468	+	0.144750i	$0.0462379\pi$
$522$		0			0
$523$	−16.7230	+	23.0172i	−0.731245	+	1.00647i	0.267830	+	0.963466i	$0.413694\pi$
$523$	−16.7230	+	23.0172i	−0.731245	+	1.00647i	−0.999075	+	0.0430065i	$0.986306\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			2.03444i			0.0886217i
$528$		0			0
$529$	16.8885			0.734285
$530$		0			0
$531$	1.29837	+	3.99598i	0.0563446	+	0.173411i
$532$		0			0
$533$	−12.0660	+	16.6074i	−0.522635	+	0.719346i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−4.02874	−	5.54508i	−0.173853	−	0.239288i
$538$		0			0
$539$	22.0623	−	13.8496i	0.950291	−	0.596543i
$540$		0			0
$541$	−6.69098	+	4.86128i	−0.287668	+	0.209003i	−0.722255	−	0.691627i	$-0.756894\pi$
$541$	−6.69098	+	4.86128i	−0.287668	+	0.209003i	0.434587	+	0.900630i	$0.356894\pi$
$542$		0			0
$543$	−4.02874	−	1.30902i	−0.172890	−	0.0561753i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−36.4504	+	11.8435i	−1.55851	+	0.506390i	−0.956409	−	0.292032i	$-0.905669\pi$
$547$	−36.4504	+	11.8435i	−1.55851	+	0.506390i	−0.602099	+	0.798422i	$0.705669\pi$
$548$		0			0
$549$	−9.18034			−0.391807
$550$		0			0
$551$	33.2148			1.41500
$552$		0			0
$553$	26.1931	−	8.51064i	1.11384	−	0.361909i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−30.1891	−	9.80902i	−1.27915	−	0.415621i	−0.410870	−	0.911694i	$-0.634775\pi$
$557$	−30.1891	−	9.80902i	−1.27915	−	0.415621i	−0.868281	+	0.496073i	$0.834775\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	15.8713	+	13.2618i	0.670088	+	0.559913i
$562$		0			0
$563$	−7.66145	−	10.5451i	−0.322892	−	0.444422i	0.616456	−	0.787390i	$-0.288568\pi$
$563$	−7.66145	−	10.5451i	−0.322892	−	0.444422i	−0.939347	+	0.342967i	$0.888568\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	12.9313	−	17.7984i	0.543063	−	0.747461i
$568$		0			0
$569$	−9.24671	−	28.4585i	−0.387642	−	1.19304i	−0.934545	−	0.355844i	$-0.884193\pi$
$569$	−9.24671	−	28.4585i	−0.387642	−	1.19304i	0.546903	−	0.837196i	$-0.315807\pi$
$570$		0			0
$571$	9.52786			0.398729			0.199364	−	0.979925i	$-0.436112\pi$
$571$	9.52786			0.398729			0.199364	+	0.979925i	$0.436112\pi$
$572$		0			0
$573$			68.1591i			2.84739i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−21.2133	+	29.1976i	−0.883120	+	1.21551i	0.0924270	+	0.995719i	$0.470538\pi$
$577$	−21.2133	+	29.1976i	−0.883120	+	1.21551i	−0.975547	+	0.219791i	$0.929462\pi$
$578$		0			0
$579$	−18.2533	+	56.1778i	−0.758581	+	2.33467i
$580$		0			0
$581$	40.6418	−	29.5280i	1.68611	−	1.22503i
$582$		0			0
$583$	−13.1558	+	3.30902i	−0.544857	+	0.137045i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.46969	−	2.42705i	−0.308307	−	0.100175i	0.150777	−	0.988568i	$-0.451822\pi$
$587$	−7.46969	−	2.42705i	−0.308307	−	0.100175i	−0.459084	+	0.888393i	$0.651822\pi$
$588$		0			0
$589$	2.66312	+	1.93487i	0.109732	+	0.0797249i
$590$		0			0
$591$	2.38197	+	7.33094i	0.0979810	+	0.301554i
$592$		0			0
$593$		−	37.4164i		−	1.53651i	−0.640145	−	0.768254i	$-0.721126\pi$
$593$		−	37.4164i		−	1.53651i	0.640145	−	0.768254i	$-0.278874\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.35114	+	0.763932i	−0.0962258	+	0.0312657i
$598$		0			0
$599$	37.1976	+	27.0256i	1.51985	+	1.10424i	0.961561	+	0.274591i	$0.0885423\pi$
$599$	37.1976	+	27.0256i	1.51985	+	1.10424i	0.558290	+	0.829646i	$0.311458\pi$
$600$		0			0
$601$	10.3713	−	31.9196i	0.423055	−	1.30203i	−0.481789	−	0.876287i	$-0.660013\pi$
$601$	10.3713	−	31.9196i	0.423055	−	1.30203i	0.904844	−	0.425743i	$-0.139987\pi$
$602$		0			0
$603$	29.3238	+	40.3607i	1.19416	+	1.64361i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−12.6008	−	17.3435i	−0.511449	−	0.703949i	0.472714	−	0.881216i	$-0.343274\pi$
$607$	−12.6008	−	17.3435i	−0.511449	−	0.703949i	−0.984163	+	0.177267i	$0.943274\pi$
$608$		0			0
$609$	−26.8713	+	82.7014i	−1.08888	+	3.35123i
$610$		0			0
$611$	−2.66312	−	1.93487i	−0.107738	−	0.0782764i
$612$		0			0
$613$	−9.92684	+	3.22542i	−0.400941	+	0.130274i	−0.502545	−	0.864551i	$-0.667603\pi$
$613$	−9.92684	+	3.22542i	−0.400941	+	0.130274i	0.101603	+	0.994825i	$0.467603\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	7.52786i		−	0.303060i	−0.988453	−	0.151530i	$-0.951580\pi$
$617$		−	7.52786i		−	0.303060i	0.988453	−	0.151530i	$-0.0484201\pi$
$618$		0			0
$619$	−6.89919	−	21.2335i	−0.277302	−	0.853447i	−0.988601	−	0.150558i	$-0.951893\pi$
$619$	−6.89919	−	21.2335i	−0.277302	−	0.853447i	0.711299	−	0.702889i	$-0.248107\pi$
$620$		0			0
$621$	−4.47214	−	3.24920i	−0.179461	−	0.130386i
$622$		0			0
$623$	1.73060	+	0.562306i	0.0693350	+	0.0225283i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	32.4544	−	8.16312i	1.29611	−	0.326004i
$628$		0			0
$629$	−3.57295	+	2.59590i	−0.142463	+	0.103505i
$630$		0			0
$631$	−7.37132	+	22.6866i	−0.293448	+	0.903139i	0.690291	+	0.723532i	$0.257483\pi$
$631$	−7.37132	+	22.6866i	−0.293448	+	0.903139i	−0.983738	+	0.179607i	$0.942517\pi$
$632$		0			0
$633$	18.3273	−	25.2254i	0.728447	−	1.00262i
$634$		0			0
$635$		0			0
$636$		0			0
$637$			18.7082i			0.741246i
$638$		0			0
$639$	24.5967			0.973032
$640$		0			0
$641$	8.37132	+	25.7643i	0.330647	+	1.01763i	0.968827	+	0.247740i	$0.0796879\pi$
$641$	8.37132	+	25.7643i	0.330647	+	1.01763i	−0.638179	+	0.769888i	$0.720312\pi$
$642$		0			0
$643$	7.21242	−	9.92705i	0.284430	−	0.391485i	−0.642765	−	0.766064i	$-0.722213\pi$
$643$	7.21242	−	9.92705i	0.284430	−	0.391485i	0.927195	+	0.374579i	$0.122213\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−3.96323	−	5.45492i	−0.155811	−	0.214455i	0.723974	−	0.689827i	$-0.242313\pi$
$647$	−3.96323	−	5.45492i	−0.155811	−	0.214455i	−0.879785	+	0.475372i	$0.842313\pi$
$648$		0			0
$649$	2.77458	+	2.31838i	0.108912	+	0.0910046i
$650$		0			0
$651$	−6.97214	+	5.06555i	−0.273260	+	0.198535i
$652$		0			0
$653$	−7.29818	−	2.37132i	−0.285600	−	0.0927970i	0.162714	−	0.986673i	$-0.447975\pi$
$653$	−7.29818	−	2.37132i	−0.285600	−	0.0927970i	−0.448314	+	0.893876i	$0.647975\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	3.33495	−	1.08359i	0.130109	−	0.0422750i
$658$		0			0
$659$	−40.3607			−1.57223			−0.786114	−	0.618081i	$-0.787910\pi$
$659$	−40.3607			−1.57223			−0.786114	+	0.618081i	$0.787910\pi$
$660$		0			0
$661$	−30.3607			−1.18089			−0.590447	−	0.807077i	$-0.701048\pi$
$661$	−30.3607			−1.18089			−0.590447	+	0.807077i	$0.701048\pi$
$662$		0			0
$663$	−14.1271	+	4.59017i	−0.548651	+	0.178267i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−20.2622	−	6.58359i	−0.784556	−	0.254918i
$668$		0			0
$669$	25.7254	−	18.6906i	0.994602	−	0.722621i
$670$		0			0
$671$	−6.69098	+	4.20025i	−0.258303	+	0.162149i
$672$		0			0
$673$	21.6623	+	29.8156i	0.835020	+	1.14931i	0.986968	+	0.160918i	$0.0514455\pi$
$673$	21.6623	+	29.8156i	0.835020	+	1.14931i	−0.151948	+	0.988389i	$0.548554\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.06111	+	2.83688i	−0.0792151	+	0.109030i	−0.846786	−	0.531934i	$-0.821465\pi$
$677$	−2.06111	+	2.83688i	−0.0792151	+	0.109030i	0.767571	+	0.640964i	$0.221465\pi$
$678$		0			0
$679$	−17.3435	−	53.3777i	−0.665581	−	2.04845i
$680$		0			0
$681$	−14.8541			−0.569210
$682$		0			0
$683$			0.944272i			0.0361316i	0.999837	+	0.0180658i	$0.00575083\pi$
$683$			0.944272i			0.0361316i	−0.999837	+	0.0180658i	$0.994249\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−25.0377	+	34.4615i	−0.955249	+	1.31479i
$688$		0			0
$689$	3.01064	−	9.26581i	0.114696	−	0.352999i
$690$		0			0
$691$	19.4894	−	14.1598i	0.741410	−	0.538666i	−0.151742	−	0.988420i	$-0.548488\pi$
$691$	19.4894	−	14.1598i	0.741410	−	0.538666i	0.893152	+	0.449754i	$0.148488\pi$
$692$		0			0
$693$	−3.33495	+	49.1525i	−0.126684	+	1.86715i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	19.5232	+	6.34346i	0.739492	+	0.240276i
$698$		0			0
$699$	−5.04508	−	3.66547i	−0.190823	−	0.138641i
$700$		0			0
$701$	15.1353	+	46.5815i	0.571651	+	1.75936i	0.647311	+	0.762226i	$0.275894\pi$
$701$	15.1353	+	46.5815i	0.571651	+	1.75936i	−0.0756600	+	0.997134i	$0.524106\pi$
$702$		0			0
$703$			7.14590i			0.269513i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	65.2394	−	21.1976i	2.45358	−	0.797216i
$708$		0			0
$709$	18.8713	+	13.7108i	0.708727	+	0.514921i	0.882763	−	0.469819i	$-0.155681\pi$
$709$	18.8713	+	13.7108i	0.708727	+	0.514921i	−0.174035	+	0.984739i	$0.555681\pi$
$710$		0			0
$711$	−8.51064	+	26.1931i	−0.319174	+	0.982317i
$712$		0			0
$713$	−1.24108	−	1.70820i	−0.0464789	−	0.0639727i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−17.7926	−	24.4894i	−0.664475	−	0.914572i
$718$		0			0
$719$	12.1353	−	37.3485i	0.452569	−	1.39286i	−0.421397	−	0.906876i	$-0.638460\pi$
$719$	12.1353	−	37.3485i	0.452569	−	1.39286i	0.873966	−	0.485987i	$-0.161540\pi$
$720$		0			0
$721$	−24.4894	−	17.7926i	−0.912031	−	0.662630i
$722$		0			0
$723$	−31.0543	+	10.0902i	−1.15492	+	0.375257i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			32.0000i			1.18681i	0.804902	+	0.593407i	$0.202218\pi$
$727$			32.0000i			1.18681i	−0.804902	+	0.593407i	$0.797782\pi$
$728$		0			0
$729$	12.2254	+	37.6260i	0.452794	+	1.39356i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−31.9196	−	10.3713i	−1.17898	−	0.383074i	−0.346992	−	0.937868i	$-0.612797\pi$
$733$	−31.9196	−	10.3713i	−1.17898	−	0.383074i	−0.831987	+	0.554795i	$0.812797\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	39.8384	+	16.0000i	1.46747	+	0.589368i
$738$		0			0
$739$	19.1631	−	13.9228i	0.704927	−	0.512159i	−0.176606	−	0.984282i	$-0.556512\pi$
$739$	19.1631	−	13.9228i	0.704927	−	0.512159i	0.881533	+	0.472122i	$0.156512\pi$
$740$		0			0
$741$	−7.42705	+	22.8581i	−0.272840	+	0.839714i
$742$		0			0
$743$	−2.06111	+	2.83688i	−0.0756150	+	0.104075i	−0.845149	−	0.534531i	$-0.820488\pi$
$743$	−2.06111	+	2.83688i	−0.0756150	+	0.104075i	0.769534	+	0.638606i	$0.220488\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			50.2361i			1.83804i
$748$		0			0
$749$	−44.5623			−1.62827
$750$		0			0
$751$	2.13525	+	6.57164i	0.0779166	+	0.239803i	0.982426	−	0.186650i	$-0.0597631\pi$
$751$	2.13525	+	6.57164i	0.0779166	+	0.239803i	−0.904510	+	0.426453i	$0.859763\pi$
$752$		0			0
$753$	39.6996	−	54.6418i	1.44673	−	1.99126i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−15.7189	−	21.6353i	−0.571314	−	0.786347i	0.421395	−	0.906877i	$-0.361540\pi$
$757$	−15.7189	−	21.6353i	−0.571314	−	0.786347i	−0.992710	+	0.120530i	$0.961540\pi$
$758$		0			0
$759$	−21.4164	−	1.45309i	−0.777366	−	0.0527436i
$760$		0			0
$761$	15.3090	−	11.1227i	0.554951	−	0.403196i	−0.274656	−	0.961542i	$-0.588564\pi$
$761$	15.3090	−	11.1227i	0.554951	−	0.403196i	0.829608	+	0.558347i	$0.188564\pi$
$762$		0			0
$763$	−45.7162	−	14.8541i	−1.65504	−	0.537755i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.46965	+	0.802439i	−0.0891740	+	0.0289744i
$768$		0			0
$769$	−37.4164			−1.34927			−0.674635	−	0.738151i	$-0.735699\pi$
$769$	−37.4164			−1.34927			−0.674635	+	0.738151i	$0.735699\pi$
$770$		0			0
$771$	12.8541			0.462929
$772$		0			0
$773$	−26.9399	+	8.75329i	−0.968959	+	0.314834i	−0.750396	−	0.660989i	$-0.770137\pi$
$773$	−26.9399	+	8.75329i	−0.968959	+	0.314834i	−0.218563	+	0.975823i	$0.570137\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−17.7926	−	5.78115i	−0.638305	−	0.207398i
$778$		0			0
$779$	26.8713	−	19.5232i	0.962765	−	0.699490i
$780$		0			0
$781$	17.9271	−	11.2537i	0.641480	−	0.402688i
$782$		0			0
$783$	−11.3269	−	15.5902i	−0.404791	−	0.557147i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	9.80059	−	13.4894i	0.349353	−	0.480844i	−0.597791	−	0.801652i	$-0.703955\pi$
$787$	9.80059	−	13.4894i	0.349353	−	0.480844i	0.947144	+	0.320809i	$0.103955\pi$
$788$		0			0
$789$	4.76393	+	14.6619i	0.169600	+	0.521977i
$790$		0			0
$791$	−67.6869			−2.40667
$792$		0			0
$793$		−	5.67376i		−	0.201481i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.11048	−	11.1631i	0.287288	−	0.395418i	−0.640843	−	0.767672i	$-0.721415\pi$
$797$	8.11048	−	11.1631i	0.287288	−	0.395418i	0.928131	+	0.372254i	$0.121415\pi$
$798$		0			0
$799$	−1.01722	+	3.13068i	−0.0359867	+	0.110756i
$800$		0			0
$801$	−1.47214	+	1.06957i	−0.0520154	+	0.0377914i
$802$		0			0
$803$	1.93487	−	2.31559i	0.0682801	−	0.0817156i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	59.9821	+	19.4894i	2.11147	+	0.686058i
$808$		0			0
$809$	−15.3090	−	11.1227i	−0.538236	−	0.391052i	0.285193	−	0.958470i	$-0.407942\pi$
$809$	−15.3090	−	11.1227i	−0.538236	−	0.391052i	−0.823430	+	0.567418i	$0.807942\pi$
$810$		0			0
$811$	−9.46149	−	29.1195i	−0.332238	−	1.02252i	−0.968067	−	0.250693i	$-0.919342\pi$
$811$	−9.46149	−	29.1195i	−0.332238	−	1.02252i	0.635829	−	0.771830i	$-0.280658\pi$
$812$		0			0
$813$		−	50.4508i		−	1.76939i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−28.6246	−	20.7970i	−1.00022	−	0.726706i
$820$		0			0
$821$	−7.98936	+	24.5887i	−0.278830	+	0.858152i	0.709350	+	0.704857i	$0.248989\pi$
$821$	−7.98936	+	24.5887i	−0.278830	+	0.858152i	−0.988180	+	0.153295i	$0.951011\pi$
$822$		0			0
$823$	−23.2214	−	31.9615i	−0.809447	−	1.11411i	−0.991409	−	0.130802i	$-0.958245\pi$
$823$	−23.2214	−	31.9615i	−0.809447	−	1.11411i	0.181962	−	0.983306i	$-0.441755\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	7.66145	+	10.5451i	0.266415	+	0.366689i	0.921175	−	0.389148i	$-0.127231\pi$
$827$	7.66145	+	10.5451i	0.266415	+	0.366689i	−0.654760	+	0.755836i	$0.727231\pi$
$828$		0			0
$829$	−10.7746	+	33.1607i	−0.374216	+	1.15172i	0.569789	+	0.821791i	$0.307025\pi$
$829$	−10.7746	+	33.1607i	−0.374216	+	1.15172i	−0.944006	+	0.329929i	$0.892975\pi$
$830$		0			0
$831$	−47.7877	−	34.7198i	−1.65774	−	1.20442i
$832$		0			0
$833$	17.7926	−	5.78115i	0.616476	−	0.200305i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	1.90983i		−	0.0660134i
$838$		0			0
$839$	0.809017	+	2.48990i	0.0279304	+	0.0859608i	0.964050	−	0.265721i	$-0.0856099\pi$
$839$	0.809017	+	2.48990i	0.0279304	+	0.0859608i	−0.936120	+	0.351682i	$0.885610\pi$
$840$		0			0
$841$	−36.6246	−	26.6093i	−1.26292	−	0.917563i
$842$		0			0
$843$	68.0396	+	22.1074i	2.34341	+	0.761419i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	20.0579	+	37.3500i	0.689199	+	1.28336i
$848$		0			0
$849$	24.4894	−	17.7926i	0.840473	−	0.610639i
$850$		0			0
$851$	1.41641	−	4.35926i	0.0485538	−	0.149433i
$852$		0			0
$853$	−10.4616	+	14.3992i	−0.358199	+	0.493019i	−0.949646	−	0.313325i	$-0.898557\pi$
$853$	−10.4616	+	14.3992i	−0.358199	+	0.493019i	0.591447	+	0.806344i	$0.298557\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			2.94427i			0.100574i	0.998735	+	0.0502872i	$0.0160137\pi$
$857$			2.94427i			0.100574i	−0.998735	+	0.0502872i	$0.983986\pi$
$858$		0			0
$859$	31.0557			1.05961			0.529804	−	0.848120i	$-0.322266\pi$
$859$	31.0557			1.05961			0.529804	+	0.848120i	$0.322266\pi$
$860$		0			0
$861$	26.8713	+	82.7014i	0.915772	+	2.81846i
$862$		0			0
$863$	14.8209	−	20.3992i	0.504509	−	0.694396i	−0.478473	−	0.878102i	$-0.658809\pi$
$863$	14.8209	−	20.3992i	0.504509	−	0.694396i	0.982981	+	0.183706i	$0.0588094\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−17.4293	−	23.9894i	−0.591930	−	0.814721i
$868$		0			0
$869$	5.78115	+	22.9844i	0.196112	+	0.779691i
$870$		0			0
$871$	−24.9443	+	18.1231i	−0.845204	+	0.614077i
$872$		0			0
$873$	53.3777	+	17.3435i	1.80656	+	0.586987i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−26.3193	+	8.55166i	−0.888740	+	0.288769i	−0.717582	−	0.696474i	$-0.754751\pi$
$877$	−26.3193	+	8.55166i	−0.888740	+	0.288769i	−0.171158	+	0.985244i	$0.554751\pi$
$878$		0			0
$879$	22.5623			0.761008
$880$		0			0
$881$	15.8885			0.535299			0.267649	−	0.963516i	$-0.413753\pi$
$881$	15.8885			0.535299			0.267649	+	0.963516i	$0.413753\pi$
$882$		0			0
$883$	4.77553	−	1.55166i	0.160709	−	0.0522176i	−0.227557	−	0.973765i	$-0.573074\pi$
$883$	4.77553	−	1.55166i	0.160709	−	0.0522176i	0.388267	+	0.921547i	$0.373074\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.93487	+	0.628677i	0.0649665	+	0.0211089i	0.341320	−	0.939947i	$-0.389126\pi$
$887$	1.93487	+	0.628677i	0.0649665	+	0.0211089i	−0.276353	+	0.961056i	$0.589126\pi$
$888$		0			0
$889$	7.42705	−	5.39607i	0.249095	−	0.180978i
$890$		0			0
$891$	14.5279	+	12.1392i	0.486702	+	0.406679i
$892$		0			0
$893$	3.13068	+	4.30902i	0.104764	+	0.144196i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	9.06154	−	12.4721i	0.302556	−	0.416432i
$898$		0			0
$899$	−2.27458	−	7.00042i	−0.0758613	−	0.233477i
$900$		0			0
$901$	−9.74265			−0.324575
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.16306	−	1.60081i	0.0386187	−	0.0531541i	−0.789271	−	0.614045i	$-0.789541\pi$
$907$	1.16306	−	1.60081i	0.0386187	−	0.0531541i	0.827890	+	0.560891i	$0.189541\pi$
$908$		0			0
$909$	−21.1976	+	65.2394i	−0.703079	+	2.16385i
$910$		0			0
$911$	15.7812	−	11.4657i	0.522853	−	0.379875i	−0.294825	−	0.955551i	$-0.595261\pi$
$911$	15.7812	−	11.4657i	0.522853	−	0.379875i	0.817678	+	0.575676i	$0.195261\pi$
$912$		0			0
$913$	22.9844	+	36.6140i	0.760671	+	1.21175i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−34.9241	−	11.3475i	−1.15330	−	0.374728i
$918$		0			0
$919$	−17.3435	−	12.6008i	−0.572108	−	0.415661i	0.263762	−	0.964588i	$-0.415037\pi$
$919$	−17.3435	−	12.6008i	−0.572108	−	0.415661i	−0.835870	+	0.548927i	$0.815037\pi$
$920$		0			0
$921$	−7.70820	−	23.7234i	−0.253994	−	0.781713i
$922$		0			0
$923$			15.2016i			0.500368i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	28.7890	−	9.35410i	0.945554	−	0.307229i
$928$		0			0
$929$	16.1074	+	11.7027i	0.528466	+	0.383953i	0.819784	−	0.572673i	$-0.194094\pi$
$929$	16.1074	+	11.7027i	0.528466	+	0.383953i	−0.291317	+	0.956626i	$0.594094\pi$
$930$		0			0
$931$	9.35410	−	28.7890i	0.306568	−	0.943520i
$932$		0			0
$933$	−25.8500	−	35.5795i	−0.846292	−	1.16482i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	4.20025	+	5.78115i	0.137216	+	0.188862i	0.872095	−	0.489336i	$-0.162761\pi$
$937$	4.20025	+	5.78115i	0.137216	+	0.188862i	−0.734879	+	0.678198i	$0.762761\pi$
$938$		0			0
$939$	−6.07295	+	18.6906i	−0.198183	+	0.609945i
$940$		0			0
$941$	−9.63525	−	7.00042i	−0.314100	−	0.228207i	0.419554	−	0.907731i	$-0.362187\pi$
$941$	−9.63525	−	7.00042i	−0.314100	−	0.228207i	−0.733654	+	0.679523i	$0.762187\pi$
$942$		0			0
$943$	−20.2622	+	6.58359i	−0.659828	+	0.214391i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	23.7771i		−	0.772652i	−0.922362	−	0.386326i	$-0.873744\pi$
$947$		−	23.7771i		−	0.772652i	0.922362	−	0.386326i	$-0.126256\pi$
$948$		0			0
$949$	0.669697	+	2.06111i	0.0217393	+	0.0669066i
$950$		0			0
$951$	−30.8435	−	22.4091i	−1.00017	−	0.726664i
$952$		0			0
$953$	−43.1203	−	14.0106i	−1.39680	−	0.453849i	−0.488648	−	0.872481i	$-0.662510\pi$
$953$	−43.1203	−	14.0106i	−1.39680	−	0.453849i	−0.908156	+	0.418632i	$0.862510\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−69.4396	−	27.8885i	−2.24466	−	0.901509i
$958$		0			0
$959$	−43.0238	+	31.2586i	−1.38931	+	1.00939i
$960$		0			0
$961$	−9.35410	+	28.7890i	−0.301745	+	0.928676i
$962$		0			0
$963$	26.1931	−	36.0517i	0.844060	−	1.16175i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			44.0000i			1.41494i	0.706741	+	0.707472i	$0.250165\pi$
$967$			44.0000i			1.41494i	−0.706741	+	0.707472i	$0.749835\pi$
$968$		0			0
$969$	24.0344			0.772098
$970$		0			0
$971$	2.13525	+	6.57164i	0.0685236	+	0.210894i	0.979455	−	0.201665i	$-0.0646352\pi$
$971$	2.13525	+	6.57164i	0.0685236	+	0.210894i	−0.910931	+	0.412559i	$0.864635\pi$
$972$		0			0
$973$	26.1931	−	36.0517i	0.839711	−	1.15576i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	12.0207	+	16.5451i	0.384577	+	0.529324i	0.956790	−	0.290781i	$-0.0939150\pi$
$977$	12.0207	+	16.5451i	0.384577	+	0.529324i	−0.572213	+	0.820105i	$0.693915\pi$
$978$		0			0
$979$	−0.583592	+	1.45309i	−0.0186517	+	0.0464408i
$980$		0			0
$981$	38.8885	−	28.2542i	1.24162	−	0.902087i
$982$		0			0
$983$	37.3485	+	12.1353i	1.19123	+	0.387055i	0.836528	−	0.547924i	$-0.184582\pi$
$983$	37.3485	+	12.1353i	1.19123	+	0.387055i	0.354703	+	0.934979i	$0.384582\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−13.2618	+	4.30902i	−0.422127	+	0.137158i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	24.0000			0.762385			0.381193	−	0.924496i	$-0.375513\pi$
$991$	24.0000			0.762385			0.381193	+	0.924496i	$0.375513\pi$
$992$		0			0
$993$	29.8788	−	9.70820i	0.948174	−	0.308081i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	28.4585	+	9.24671i	0.901288	+	0.292846i	0.722769	−	0.691090i	$-0.242869\pi$
$997$	28.4585	+	9.24671i	0.901288	+	0.292846i	0.178520	+	0.983936i	$0.442869\pi$
$998$		0			0
$999$	3.35410	−	2.43690i	0.106119	−	0.0771000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.cb.a.949.1		8
5.2	odd	4		1100.2.n.a.201.1		4
5.3	odd	4		44.2.e.a.25.1	✓	4
5.4	even	2	inner	1100.2.cb.a.949.2		8
11.4	even	5	inner	1100.2.cb.a.1049.2		8
15.8	even	4		396.2.j.a.289.1		4
20.3	even	4		176.2.m.b.113.1		4
40.3	even	4		704.2.m.d.641.1		4
40.13	odd	4		704.2.m.e.641.1		4
55.3	odd	20		484.2.e.e.269.1		4
55.4	even	10	inner	1100.2.cb.a.1049.1		8
55.8	even	20		484.2.e.d.269.1		4
55.13	even	20		484.2.a.c.1.1		2
55.18	even	20		484.2.e.c.81.1		4
55.28	even	20		484.2.e.d.9.1		4
55.37	odd	20		1100.2.n.a.301.1		4
55.38	odd	20		484.2.e.e.9.1		4
55.43	even	4		484.2.e.c.245.1		4
55.48	odd	20		44.2.e.a.37.1	yes	4
55.53	odd	20		484.2.a.b.1.1		2
165.53	even	20		4356.2.a.t.1.2		2
165.68	odd	20		4356.2.a.u.1.2		2
165.158	even	20		396.2.j.a.37.1		4
220.103	even	20		176.2.m.b.81.1		4
220.123	odd	20		1936.2.a.z.1.2		2
220.163	even	20		1936.2.a.ba.1.2		2
440.13	even	20		7744.2.a.db.1.2		2
440.53	odd	20		7744.2.a.da.1.2		2
440.123	odd	20		7744.2.a.bo.1.1		2
440.163	even	20		7744.2.a.bp.1.1		2
440.213	odd	20		704.2.m.e.257.1		4
440.323	even	20		704.2.m.d.257.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.e.a.25.1	✓	4	5.3	odd	4
44.2.e.a.37.1	yes	4	55.48	odd	20
176.2.m.b.81.1		4	220.103	even	20
176.2.m.b.113.1		4	20.3	even	4
396.2.j.a.37.1		4	165.158	even	20
396.2.j.a.289.1		4	15.8	even	4
484.2.a.b.1.1		2	55.53	odd	20
484.2.a.c.1.1		2	55.13	even	20
484.2.e.c.81.1		4	55.18	even	20
484.2.e.c.245.1		4	55.43	even	4
484.2.e.d.9.1		4	55.28	even	20
484.2.e.d.269.1		4	55.8	even	20
484.2.e.e.9.1		4	55.38	odd	20
484.2.e.e.269.1		4	55.3	odd	20
704.2.m.d.257.1		4	440.323	even	20
704.2.m.d.641.1		4	40.3	even	4
704.2.m.e.257.1		4	440.213	odd	20
704.2.m.e.641.1		4	40.13	odd	4
1100.2.n.a.201.1		4	5.2	odd	4
1100.2.n.a.301.1		4	55.37	odd	20
1100.2.cb.a.949.1		8	1.1	even	1	trivial
1100.2.cb.a.949.2		8	5.4	even	2	inner
1100.2.cb.a.1049.1		8	55.4	even	10	inner
1100.2.cb.a.1049.2		8	11.4	even	5	inner
1936.2.a.z.1.2		2	220.123	odd	20
1936.2.a.ba.1.2		2	220.163	even	20
4356.2.a.t.1.2		2	165.53	even	20
4356.2.a.u.1.2		2	165.68	odd	20
7744.2.a.bo.1.1		2	440.123	odd	20
7744.2.a.bp.1.1		2	440.163	even	20
7744.2.a.da.1.2		2	440.53	odd	20
7744.2.a.db.1.2		2	440.13	even	20

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:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.cb (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.48990 + 0.809017i) q^{3} +(-3.66547 - 1.19098i) q^{7} +(3.11803 - 2.26538i) q^{9} +O(q^{10})\)	\(q+(-2.48990 + 0.809017i) q^{3} +(-3.66547 - 1.19098i) q^{7} +(3.11803 - 2.26538i) q^{9} +(1.23607 - 3.07768i) q^{11} +(1.40008 + 1.92705i) q^{13} +(1.40008 - 1.92705i) q^{17} +(-1.19098 - 3.66547i) q^{19} +10.0902 q^{21} +2.47214i q^{23} +(-1.31433 + 1.80902i) q^{27} +(-2.66312 + 8.19624i) q^{29} +(-0.690983 + 0.502029i) q^{31} +(-0.587785 + 8.66312i) q^{33} +(-1.76336 - 0.572949i) q^{37} +(-5.04508 - 3.66547i) q^{39} +(2.66312 + 8.19624i) q^{41} +(-1.31433 + 0.427051i) q^{47} +(6.35410 + 4.61653i) q^{49} +(-1.92705 + 5.93085i) q^{51} +(-2.40414 - 3.30902i) q^{53} +(5.93085 + 8.16312i) q^{57} +(-0.336881 + 1.03681i) q^{59} +(-1.92705 - 1.40008i) q^{61} +(-14.1271 + 4.59017i) q^{63} +12.9443i q^{67} +(-2.00000 - 6.15537i) q^{69} +(5.16312 + 3.75123i) q^{71} +(0.865300 + 0.281153i) q^{73} +(-8.19624 + 9.80902i) q^{77} +(-5.78115 + 4.20025i) q^{79} +(-1.76393 + 5.42882i) q^{81} +(-7.66145 + 10.5451i) q^{83} -22.5623i q^{87} -0.472136 q^{89} +(-2.83688 - 8.73102i) q^{91} +(1.31433 - 1.80902i) q^{93} +(8.55951 + 11.7812i) q^{97} +(-3.11803 - 12.3965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{9}+O(q^{10}) \) 8 * q + 16 * q^9	\( 8 q + 16 q^{9} - 8 q^{11} - 14 q^{19} + 36 q^{21} + 10 q^{29} - 10 q^{31} - 18 q^{39} - 10 q^{41} + 24 q^{49} - 2 q^{51} - 34 q^{59} - 2 q^{61} - 16 q^{69} + 10 q^{71} - 6 q^{79} - 32 q^{81} + 32 q^{89} - 54 q^{91} - 16 q^{99}+O(q^{100}) \) 8 * q + 16 * q^9 - 8 * q^11 - 14 * q^19 + 36 * q^21 + 10 * q^29 - 10 * q^31 - 18 * q^39 - 10 * q^41 + 24 * q^49 - 2 * q^51 - 34 * q^59 - 2 * q^61 - 16 * q^69 + 10 * q^71 - 6 * q^79 - 32 * q^81 + 32 * q^89 - 54 * q^91 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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