LMFDB - Embedded newform 140.2.m.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(13,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("140.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.m (of order $4$, degree $2$, 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:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.11574317056.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 45x^{4} + 4 $ x^8 + 45*x^4 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.3
Root			$0.386289 - 0.386289i$ of defining polynomial
Character	$\chi$	$=$	140.13
Dual form			140.2.m.a.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.386289 - 0.386289i) q^{3} +(0.386289 - 2.20245i) q^{5} +(0.0564123 - 2.64515i) q^{7} +2.70156i q^{9} +O(q^{10})$	\(q+(0.386289 - 0.386289i) q^{3} +(0.386289 - 2.20245i) q^{5} +(0.0564123 - 2.64515i) q^{7} +2.70156i q^{9} +1.70156 q^{11} +(0.386289 - 0.386289i) q^{13} +(-0.701562 - 1.00000i) q^{15} +(4.79119 + 4.79119i) q^{17} -5.95005 q^{19} +(-1.00000 - 1.04358i) q^{21} +(-2.70156 - 2.70156i) q^{23} +(-4.70156 - 1.70156i) q^{25} +(2.20245 + 2.20245i) q^{27} +5.70156i q^{29} +8.03722i q^{31} +(0.657294 - 0.657294i) q^{33} +(-5.80402 - 1.14604i) q^{35} +(2.70156 - 2.70156i) q^{37} -0.298438i q^{39} +5.95005i q^{41} +(-5.00000 - 5.00000i) q^{43} +(5.95005 + 1.04358i) q^{45} +(-3.24603 - 3.24603i) q^{47} +(-6.99364 - 0.298438i) q^{49} +3.70156 q^{51} +(5.00000 + 5.00000i) q^{53} +(0.657294 - 3.74760i) q^{55} +(-2.29844 + 2.29844i) q^{57} +5.95005 q^{59} -11.9001i q^{61} +(7.14604 + 0.152401i) q^{63} +(-0.701562 - 1.00000i) q^{65} +(5.00000 - 5.00000i) q^{67} -2.08717 q^{69} +7.40312 q^{71} +(-1.81616 + 1.81616i) q^{73} +(-2.47345 + 1.15887i) q^{75} +(0.0959890 - 4.50089i) q^{77} +0.298438i q^{79} -6.40312 q^{81} +(4.13389 - 4.13389i) q^{83} +(12.4031 - 8.70156i) q^{85} +(2.20245 + 2.20245i) q^{87} +2.08717 q^{89} +(-1.00000 - 1.04358i) q^{91} +(3.10469 + 3.10469i) q^{93} +(-2.29844 + 13.1047i) q^{95} +(-1.15887 - 1.15887i) q^{97} +4.59688i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{7}+O(q^{10}) $ 8 * q - 2 * q^7	$ 8 q - 2 q^{7} - 12 q^{11} + 20 q^{15} - 8 q^{21} + 4 q^{23} - 12 q^{25} - 14 q^{35} - 4 q^{37} - 40 q^{43} + 4 q^{51} + 40 q^{53} - 44 q^{57} + 42 q^{63} + 20 q^{65} + 40 q^{67} + 8 q^{71} + 44 q^{77} + 48 q^{85} - 8 q^{91} - 52 q^{93} - 44 q^{95}+O(q^{100}) $ 8 * q - 2 * q^7 - 12 * q^11 + 20 * q^15 - 8 * q^21 + 4 * q^23 - 12 * q^25 - 14 * q^35 - 4 * q^37 - 40 * q^43 + 4 * q^51 + 40 * q^53 - 44 * q^57 + 42 * q^63 + 20 * q^65 + 40 * q^67 + 8 * q^71 + 44 * q^77 + 48 * q^85 - 8 * q^91 - 52 * q^93 - 44 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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
$3$	0.386289	−	0.386289i	0.223024	−	0.223024i	−0.586747	−	0.809771i	$-0.699592\pi$
$3$	0.386289	−	0.386289i	0.223024	−	0.223024i	0.809771	+	0.586747i	$0.199592\pi$
$4$		0			0
$5$	0.386289	−	2.20245i	0.172754	−	0.984965i
$5$	0.386289	−	2.20245i	0.172754	−	0.984965i
$6$		0			0
$7$	0.0564123	−	2.64515i	0.0213218	−	0.999773i
$7$	0.0564123	−	2.64515i	0.0213218	−	0.999773i
$8$		0			0
$9$			2.70156i			0.900521i
$10$		0			0
$11$	1.70156			0.513040			0.256520	−	0.966539i	$-0.417424\pi$
$11$	1.70156			0.513040			0.256520	+	0.966539i	$0.417424\pi$
$12$		0			0
$13$	0.386289	−	0.386289i	0.107137	−	0.107137i	−0.651506	−	0.758643i	$-0.725863\pi$
$13$	0.386289	−	0.386289i	0.107137	−	0.107137i	0.758643	+	0.651506i	$0.225863\pi$
$14$		0			0
$15$	−0.701562	−	1.00000i	−0.181143	−	0.258199i
$16$		0			0
$17$	4.79119	+	4.79119i	1.16203	+	1.16203i	0.984030	+	0.178004i	$0.0569639\pi$
$17$	4.79119	+	4.79119i	1.16203	+	1.16203i	0.178004	+	0.984030i	$0.443036\pi$
$18$		0			0
$19$	−5.95005			−1.36504			−0.682518	−	0.730869i	$-0.739115\pi$
$19$	−5.95005			−1.36504			−0.682518	+	0.730869i	$0.739115\pi$
$20$		0			0
$21$	−1.00000	−	1.04358i	−0.218218	−	0.227728i
$22$		0			0
$23$	−2.70156	−	2.70156i	−0.563315	−	0.563315i	0.366933	−	0.930247i	$-0.380408\pi$
$23$	−2.70156	−	2.70156i	−0.563315	−	0.563315i	−0.930247	+	0.366933i	$0.880408\pi$
$24$		0			0
$25$	−4.70156	−	1.70156i	−0.940312	−	0.340312i
$26$		0			0
$27$	2.20245	+	2.20245i	0.423861	+	0.423861i
$28$		0			0
$29$			5.70156i			1.05875i	0.848387	+	0.529377i	$0.177574\pi$
$29$			5.70156i			1.05875i	−0.848387	+	0.529377i	$0.822426\pi$
$30$		0			0
$31$			8.03722i			1.44353i	0.692140	+	0.721763i	$0.256668\pi$
$31$			8.03722i			1.44353i	−0.692140	+	0.721763i	$0.743332\pi$
$32$		0			0
$33$	0.657294	−	0.657294i	0.114420	−	0.114420i
$34$		0			0
$35$	−5.80402	−	1.14604i	−0.981058	−	0.193716i
$36$		0			0
$37$	2.70156	−	2.70156i	0.444134	−	0.444134i	−0.449265	−	0.893399i	$-0.648314\pi$
$37$	2.70156	−	2.70156i	0.444134	−	0.444134i	0.893399	+	0.449265i	$0.148314\pi$
$38$		0			0
$39$		−	0.298438i		−	0.0477883i
$40$		0			0
$41$			5.95005i			0.929242i	0.885510	+	0.464621i	$0.153809\pi$
$41$			5.95005i			0.929242i	−0.885510	+	0.464621i	$0.846191\pi$
$42$		0			0
$43$	−5.00000	−	5.00000i	−0.762493	−	0.762493i	0.214280	−	0.976772i	$-0.431260\pi$
$43$	−5.00000	−	5.00000i	−0.762493	−	0.762493i	−0.976772	+	0.214280i	$0.931260\pi$
$44$		0			0
$45$	5.95005	+	1.04358i	0.886981	+	0.155568i
$46$		0			0
$47$	−3.24603	−	3.24603i	−0.473482	−	0.473482i	0.429557	−	0.903040i	$-0.358670\pi$
$47$	−3.24603	−	3.24603i	−0.473482	−	0.473482i	−0.903040	+	0.429557i	$0.858670\pi$
$48$		0			0
$49$	−6.99364	−	0.298438i	−0.999091	−	0.0426340i
$50$		0			0
$51$	3.70156			0.518322
$52$		0			0
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	−0.274721	+	0.961524i	$0.588586\pi$
$54$		0			0
$55$	0.657294	−	3.74760i	0.0886295	−	0.505327i
$56$		0			0
$57$	−2.29844	+	2.29844i	−0.304436	+	0.304436i
$58$		0			0
$59$	5.95005			0.774631			0.387315	−	0.921947i	$-0.373402\pi$
$59$	5.95005			0.774631			0.387315	+	0.921947i	$0.373402\pi$
$60$		0			0
$61$		−	11.9001i		−	1.52365i	−0.647782	−	0.761826i	$-0.724303\pi$
$61$		−	11.9001i		−	1.52365i	0.647782	−	0.761826i	$-0.275697\pi$
$62$		0			0
$63$	7.14604	+	0.152401i	0.900316	+	0.0192008i
$64$		0			0
$65$	−0.701562	−	1.00000i	−0.0870181	−	0.124035i
$66$		0			0
$67$	5.00000	−	5.00000i	0.610847	−	0.610847i	−0.332320	−	0.943167i	$-0.607831\pi$
$67$	5.00000	−	5.00000i	0.610847	−	0.610847i	0.943167	+	0.332320i	$0.107831\pi$
$68$		0			0
$69$	−2.08717			−0.251265
$70$		0			0
$71$	7.40312			0.878589			0.439295	−	0.898343i	$-0.355228\pi$
$71$	7.40312			0.878589			0.439295	+	0.898343i	$0.355228\pi$
$72$		0			0
$73$	−1.81616	+	1.81616i	−0.212565	+	0.212565i	−0.805356	−	0.592791i	$-0.798026\pi$
$73$	−1.81616	+	1.81616i	−0.212565	+	0.212565i	0.592791	+	0.805356i	$0.298026\pi$
$74$		0			0
$75$	−2.47345	+	1.15887i	−0.285610	+	0.133814i
$76$		0			0
$77$	0.0959890	−	4.50089i	0.0109390	−	0.512924i
$78$		0			0
$79$			0.298438i			0.0335769i	0.999859	+	0.0167884i	$0.00534418\pi$
$79$			0.298438i			0.0335769i	−0.999859	+	0.0167884i	$0.994656\pi$
$80$		0			0
$81$	−6.40312			−0.711458
$82$		0			0
$83$	4.13389	−	4.13389i	0.453754	−	0.453754i	−0.442845	−	0.896598i	$-0.646031\pi$
$83$	4.13389	−	4.13389i	0.453754	−	0.453754i	0.896598	+	0.442845i	$0.146031\pi$
$84$		0			0
$85$	12.4031	−	8.70156i	1.34531	−	0.943817i
$86$		0			0
$87$	2.20245	+	2.20245i	0.236127	+	0.236127i
$88$		0			0
$89$	2.08717			0.221239			0.110620	−	0.993863i	$-0.464716\pi$
$89$	2.08717			0.221239			0.110620	+	0.993863i	$0.464716\pi$
$90$		0			0
$91$	−1.00000	−	1.04358i	−0.104828	−	0.109397i
$92$		0			0
$93$	3.10469	+	3.10469i	0.321941	+	0.321941i
$94$		0			0
$95$	−2.29844	+	13.1047i	−0.235815	+	1.34451i
$96$		0			0
$97$	−1.15887	−	1.15887i	−0.117665	−	0.117665i	0.645823	−	0.763488i	$-0.276515\pi$
$97$	−1.15887	−	1.15887i	−0.117665	−	0.117665i	−0.763488	+	0.645823i	$0.776515\pi$
$98$		0			0
$99$			4.59688i			0.462003i
$100$		0			0
$101$		−	5.95005i		−	0.592052i	−0.955180	−	0.296026i	$-0.904338\pi$
$101$		−	5.95005i		−	0.592052i	0.955180	−	0.296026i	$-0.0956616\pi$
$102$		0			0
$103$	−5.56376	+	5.56376i	−0.548214	+	0.548214i	−0.925924	−	0.377710i	$-0.876712\pi$
$103$	−5.56376	+	5.56376i	−0.548214	+	0.548214i	0.377710	+	0.925924i	$0.376712\pi$
$104$		0			0
$105$	−2.68473	+	1.79932i	−0.262002	+	0.175596i
$106$		0			0
$107$	−10.4031	+	10.4031i	−1.00571	+	1.00571i	−0.00572436	+	0.999984i	$0.501822\pi$
$107$	−10.4031	+	10.4031i	−1.00571	+	1.00571i	−0.999984	+	0.00572436i	$0.998178\pi$
$108$		0			0
$109$		−	9.70156i		−	0.929241i	−0.885510	−	0.464621i	$-0.846191\pi$
$109$		−	9.70156i		−	0.929241i	0.885510	−	0.464621i	$-0.153809\pi$
$110$		0			0
$111$		−	2.08717i		−	0.198105i
$112$		0			0
$113$	−12.7016	−	12.7016i	−1.19486	−	1.19486i	−0.975685	−	0.219177i	$-0.929663\pi$
$113$	−12.7016	−	12.7016i	−1.19486	−	1.19486i	−0.219177	−	0.975685i	$-0.570337\pi$
$114$		0			0
$115$	−6.99364	+	4.90647i	−0.652160	+	0.457531i
$116$		0			0
$117$	1.04358	+	1.04358i	0.0964793	+	0.0964793i
$118$		0			0
$119$	12.9437	−	12.4031i	1.18655	−	1.13699i
$120$		0			0
$121$	−8.10469			−0.736790
$122$		0			0
$123$	2.29844	+	2.29844i	0.207243	+	0.207243i
$124$		0			0
$125$	−5.56376	+	9.69766i	−0.497638	+	0.867385i
$126$		0			0
$127$	−10.4031	+	10.4031i	−0.923128	+	0.923128i	−0.997249	−	0.0741212i	$-0.976385\pi$
$127$	−10.4031	+	10.4031i	−0.923128	+	0.923128i	0.0741212	+	0.997249i	$0.476385\pi$
$128$		0			0
$129$	−3.86289			−0.340108
$130$		0			0
$131$			13.9873i			1.22207i	0.791602	+	0.611037i	$0.209247\pi$
$131$			13.9873i			1.22207i	−0.791602	+	0.611037i	$0.790753\pi$
$132$		0			0
$133$	−0.335656	+	15.7388i	−0.0291051	+	1.36473i
$134$		0			0
$135$	5.70156	−	4.00000i	0.490712	−	0.344265i
$136$		0			0
$137$	2.70156	−	2.70156i	0.230810	−	0.230810i	−0.582221	−	0.813031i	$-0.697816\pi$
$137$	2.70156	−	2.70156i	0.230810	−	0.230810i	0.813031	+	0.582221i	$0.197816\pi$
$138$		0			0
$139$	16.0744			1.36342			0.681708	−	0.731624i	$-0.261237\pi$
$139$	16.0744			1.36342			0.681708	+	0.731624i	$0.261237\pi$
$140$		0			0
$141$	−2.50781			−0.211196
$142$		0			0
$143$	0.657294	−	0.657294i	0.0549657	−	0.0549657i
$144$		0			0
$145$	12.5574	+	2.20245i	1.04284	+	0.182903i
$146$		0			0
$147$	−2.81685	+	2.58628i	−0.232329	+	0.213313i
$148$		0			0
$149$		−	6.80625i		−	0.557590i	−0.960351	−	0.278795i	$-0.910065\pi$
$149$		−	6.80625i		−	0.557590i	0.960351	−	0.278795i	$-0.0899349\pi$
$150$		0			0
$151$	−13.7016			−1.11502			−0.557509	−	0.830171i	$-0.688243\pi$
$151$	−13.7016			−1.11502			−0.557509	+	0.830171i	$0.688243\pi$
$152$		0			0
$153$	−12.9437	+	12.9437i	−1.04644	+	1.04644i
$154$		0			0
$155$	17.7016	+	3.10469i	1.42182	+	0.249374i
$156$		0			0
$157$	−10.6260	−	10.6260i	−0.848044	−	0.848044i	0.141845	−	0.989889i	$-0.454696\pi$
$157$	−10.6260	−	10.6260i	−0.848044	−	0.848044i	−0.989889	+	0.141845i	$0.954696\pi$
$158$		0			0
$159$	3.86289			0.306347
$160$		0			0
$161$	−7.29844	+	6.99364i	−0.575197	+	0.551176i
$162$		0			0
$163$	−2.70156	−	2.70156i	−0.211603	−	0.211603i	0.593345	−	0.804948i	$-0.297807\pi$
$163$	−2.70156	−	2.70156i	−0.211603	−	0.211603i	−0.804948	+	0.593345i	$0.797807\pi$
$164$		0			0
$165$	−1.19375	−	1.70156i	−0.0929334	−	0.132466i
$166$		0			0
$167$	−9.19608	−	9.19608i	−0.711614	−	0.711614i	0.255258	−	0.966873i	$-0.417839\pi$
$167$	−9.19608	−	9.19608i	−0.711614	−	0.711614i	−0.966873	+	0.255258i	$0.917839\pi$
$168$		0			0
$169$			12.7016i			0.977043i
$170$		0			0
$171$		−	16.0744i		−	1.22924i
$172$		0			0
$173$	6.33634	−	6.33634i	0.481743	−	0.481743i	−0.423945	−	0.905688i	$-0.639355\pi$
$173$	6.33634	−	6.33634i	0.481743	−	0.481743i	0.905688	+	0.423945i	$0.139355\pi$
$174$		0			0
$175$	−4.76611	+	12.3403i	−0.360284	+	0.932843i
$176$		0			0
$177$	2.29844	−	2.29844i	0.172761	−	0.172761i
$178$		0			0
$179$		−	16.8062i		−	1.25616i	−0.778150	−	0.628079i	$-0.783841\pi$
$179$		−	16.8062i		−	1.25616i	0.778150	−	0.628079i	$-0.216159\pi$
$180$		0			0
$181$		−	17.8502i		−	1.32679i	−0.748269	−	0.663396i	$-0.769115\pi$
$181$		−	17.8502i		−	1.32679i	0.748269	−	0.663396i	$-0.230885\pi$
$182$		0			0
$183$	−4.59688	−	4.59688i	−0.339811	−	0.339811i
$184$		0			0
$185$	−4.90647	−	6.99364i	−0.360731	−	0.514182i
$186$		0			0
$187$	8.15250	+	8.15250i	0.596170	+	0.596170i
$188$		0			0
$189$	5.95005	−	5.70156i	0.432803	−	0.414728i
$190$		0			0
$191$	17.1047			1.23765			0.618826	−	0.785528i	$-0.287609\pi$
$191$	17.1047			1.23765			0.618826	+	0.785528i	$0.287609\pi$
$192$		0			0
$193$	18.1047	+	18.1047i	1.30320	+	1.30320i	0.926220	+	0.376984i	$0.123039\pi$
$193$	18.1047	+	18.1047i	1.30320	+	1.30320i	0.376984	+	0.926220i	$0.376961\pi$
$194$		0			0
$195$	−0.657294	−	0.115283i	−0.0470698	−	0.00825560i
$196$		0			0
$197$	−10.4031	+	10.4031i	−0.741192	+	0.741192i	−0.972807	−	0.231615i	$-0.925599\pi$
$197$	−10.4031	+	10.4031i	−0.741192	+	0.741192i	0.231615	+	0.972807i	$0.425599\pi$
$198$		0			0
$199$	−10.1244			−0.717699			−0.358849	−	0.933396i	$-0.616831\pi$
$199$	−10.1244			−0.717699			−0.358849	+	0.933396i	$0.616831\pi$
$200$		0			0
$201$		−	3.86289i		−	0.272467i
$202$		0			0
$203$	15.0815	+	0.321638i	1.05851	+	0.0225746i
$204$		0			0
$205$	13.1047	+	2.29844i	0.915271	+	0.160530i
$206$		0			0
$207$	7.29844	−	7.29844i	0.507276	−	0.507276i
$208$		0			0
$209$	−10.1244			−0.700318
$210$		0			0
$211$	6.29844			0.433602			0.216801	−	0.976216i	$-0.430438\pi$
$211$	6.29844			0.433602			0.216801	+	0.976216i	$0.430438\pi$
$212$		0			0
$213$	2.85974	−	2.85974i	0.195946	−	0.195946i
$214$		0			0
$215$	−12.9437	+	9.08080i	−0.882752	+	0.619305i
$216$		0			0
$217$	21.2596	+	0.453398i	1.44320	+	0.0307786i
$218$		0			0
$219$			1.40312i			0.0948143i
$220$		0			0
$221$	3.70156			0.248994
$222$		0			0
$223$	16.4607	−	16.4607i	1.10229	−	1.10229i	0.108158	−	0.994134i	$-0.465505\pi$
$223$	16.4607	−	16.4607i	1.10229	−	1.10229i	0.994134	−	0.108158i	$-0.0344952\pi$
$224$		0			0
$225$	4.59688	−	12.7016i	0.306458	−	0.846771i
$226$		0			0
$227$	−21.0962	−	21.0962i	−1.40020	−	1.40020i	−0.799388	−	0.600816i	$-0.794843\pi$
$227$	−21.0962	−	21.0962i	−1.40020	−	1.40020i	−0.600816	−	0.799388i	$-0.705157\pi$
$228$		0			0
$229$	19.9373			1.31750			0.658748	−	0.752364i	$-0.271086\pi$
$229$	19.9373			1.31750			0.658748	+	0.752364i	$0.271086\pi$
$230$		0			0
$231$	−1.70156	−	1.77572i	−0.111955	−	0.116834i
$232$		0			0
$233$	−8.10469	−	8.10469i	−0.530956	−	0.530956i	0.389901	−	0.920857i	$-0.372509\pi$
$233$	−8.10469	−	8.10469i	−0.530956	−	0.530956i	−0.920857	+	0.389901i	$0.872509\pi$
$234$		0			0
$235$	−8.40312	+	5.89531i	−0.548159	+	0.384568i
$236$		0			0
$237$	0.115283	+	0.115283i	0.00748845	+	0.00748845i
$238$		0			0
$239$			4.89531i			0.316652i	0.987387	+	0.158326i	$0.0506096\pi$
$239$			4.89531i			0.316652i	−0.987387	+	0.158326i	$0.949390\pi$
$240$		0			0
$241$		−	4.17433i		−	0.268892i	−0.990921	−	0.134446i	$-0.957074\pi$
$241$		−	4.17433i		−	0.268892i	0.990921	−	0.134446i	$-0.0429255\pi$
$242$		0			0
$243$	−9.08080	+	9.08080i	−0.582534	+	0.582534i
$244$		0			0
$245$	−3.35886	+	15.2878i	−0.214589	+	0.976704i
$246$		0			0
$247$	−2.29844	+	2.29844i	−0.146246	+	0.146246i
$248$		0			0
$249$		−	3.19375i		−	0.202396i
$250$		0			0
$251$			13.9873i			0.882869i	0.897294	+	0.441434i	$0.145530\pi$
$251$			13.9873i			0.882869i	−0.897294	+	0.441434i	$0.854470\pi$
$252$		0			0
$253$	−4.59688	−	4.59688i	−0.289003	−	0.289003i
$254$		0			0
$255$	1.42987	−	8.15250i	0.0895420	−	0.510529i
$256$		0			0
$257$	5.44848	+	5.44848i	0.339867	+	0.339867i	0.856317	−	0.516450i	$-0.172747\pi$
$257$	5.44848	+	5.44848i	0.339867	+	0.339867i	−0.516450	+	0.856317i	$0.672747\pi$
$258$		0			0
$259$	−6.99364	−	7.29844i	−0.434563	−	0.453503i
$260$		0			0
$261$	−15.4031			−0.953429
$262$		0			0
$263$	−0.403124	−	0.403124i	−0.0248577	−	0.0248577i	0.694569	−	0.719426i	$-0.255595\pi$
$263$	−0.403124	−	0.403124i	−0.0248577	−	0.0248577i	−0.719426	+	0.694569i	$0.755595\pi$
$264$		0			0
$265$	12.9437	−	9.08080i	0.795124	−	0.557829i
$266$		0			0
$267$	0.806248	−	0.806248i	0.0493416	−	0.0493416i
$268$		0			0
$269$	2.08717			0.127257			0.0636284	−	0.997974i	$-0.479733\pi$
$269$	2.08717			0.127257			0.0636284	+	0.997974i	$0.479733\pi$
$270$		0			0
$271$			9.81294i			0.596094i	0.954551	+	0.298047i	$0.0963352\pi$
$271$			9.81294i			0.596094i	−0.954551	+	0.298047i	$0.903665\pi$
$272$		0			0
$273$	−0.789413	−	0.0168356i	−0.0477774	−	0.00101893i
$274$		0			0
$275$	−8.00000	−	2.89531i	−0.482418	−	0.174594i
$276$		0			0
$277$	−8.10469	+	8.10469i	−0.486963	+	0.486963i	−0.907347	−	0.420383i	$-0.861896\pi$
$277$	−8.10469	+	8.10469i	−0.486963	+	0.486963i	0.420383	+	0.907347i	$0.361896\pi$
$278$		0			0
$279$	−21.7130			−1.29993
$280$		0			0
$281$	17.9109			1.06848			0.534238	−	0.845334i	$-0.320598\pi$
$281$	17.9109			1.06848			0.534238	+	0.845334i	$0.320598\pi$
$282$		0			0
$283$	−11.5138	+	11.5138i	−0.684425	+	0.684425i	−0.960994	−	0.276569i	$-0.910803\pi$
$283$	−11.5138	+	11.5138i	−0.684425	+	0.684425i	0.276569	+	0.960994i	$0.410803\pi$
$284$		0			0
$285$	4.17433	+	5.95005i	0.247266	+	0.352451i
$286$		0			0
$287$	15.7388	+	0.335656i	0.929031	+	0.0198131i
$288$		0			0
$289$			28.9109i			1.70064i
$290$		0			0
$291$	−0.895314			−0.0524842
$292$		0			0
$293$	−11.5138	+	11.5138i	−0.672644	+	0.672644i	−0.958325	−	0.285681i	$-0.907780\pi$
$293$	−11.5138	+	11.5138i	−0.672644	+	0.672644i	0.285681	+	0.958325i	$0.407780\pi$
$294$		0			0
$295$	2.29844	−	13.1047i	0.133820	−	0.762984i
$296$		0			0
$297$	3.74760	+	3.74760i	0.217458	+	0.217458i
$298$		0			0
$299$	−2.08717			−0.120704
$300$		0			0
$301$	−13.5078	+	12.9437i	−0.778577	+	0.746062i
$302$		0			0
$303$	−2.29844	−	2.29844i	−0.132042	−	0.132042i
$304$		0			0
$305$	−26.2094	−	4.59688i	−1.50074	−	0.263216i
$306$		0			0
$307$	12.8284	+	12.8284i	0.732156	+	0.732156i	0.971046	−	0.238891i	$-0.0767838\pi$
$307$	12.8284	+	12.8284i	0.732156	+	0.732156i	−0.238891	+	0.971046i	$0.576784\pi$
$308$		0			0
$309$			4.29844i			0.244530i
$310$		0			0
$311$			8.03722i			0.455749i	0.973691	+	0.227874i	$0.0731776\pi$
$311$			8.03722i			0.455749i	−0.973691	+	0.227874i	$0.926822\pi$
$312$		0			0
$313$	12.2864	−	12.2864i	0.694468	−	0.694468i	−0.268744	−	0.963212i	$-0.586608\pi$
$313$	12.2864	−	12.2864i	0.694468	−	0.694468i	0.963212	+	0.268744i	$0.0866085\pi$
$314$		0			0
$315$	3.09609	−	15.6799i	0.174445	−	0.883463i
$316$		0			0
$317$	0.403124	−	0.403124i	0.0226417	−	0.0226417i	−0.695695	−	0.718337i	$-0.744904\pi$
$317$	0.403124	−	0.403124i	0.0226417	−	0.0226417i	0.718337	+	0.695695i	$0.244904\pi$
$318$		0			0
$319$			9.70156i			0.543183i
$320$		0			0
$321$			8.03722i			0.448594i
$322$		0			0
$323$	−28.5078	−	28.5078i	−1.58622	−	1.58622i
$324$		0			0
$325$	−2.47345	+	1.15887i	−0.137203	+	0.0642823i
$326$		0			0
$327$	−3.74760	−	3.74760i	−0.207243	−	0.207243i
$328$		0			0
$329$	−8.76936	+	8.40312i	−0.483470	+	0.463279i
$330$		0			0
$331$	−3.40312			−0.187053			−0.0935263	−	0.995617i	$-0.529814\pi$
$331$	−3.40312			−0.187053			−0.0935263	+	0.995617i	$0.529814\pi$
$332$		0			0
$333$	7.29844	+	7.29844i	0.399952	+	0.399952i
$334$		0			0
$335$	−9.08080	−	12.9437i	−0.496137	−	0.707189i
$336$		0			0
$337$	−1.89531	+	1.89531i	−0.103244	+	0.103244i	−0.756842	−	0.653598i	$-0.773259\pi$
$337$	−1.89531	+	1.89531i	−0.103244	+	0.103244i	0.653598	+	0.756842i	$0.273259\pi$
$338$		0			0
$339$	−9.81294			−0.532966
$340$		0			0
$341$			13.6758i			0.740587i
$342$		0			0
$343$	−1.18394	+	18.4824i	−0.0639267	+	0.997955i
$344$		0			0
$345$	−0.806248	+	4.59688i	−0.0434070	+	0.247487i
$346$		0			0
$347$	7.29844	−	7.29844i	0.391801	−	0.391801i	−0.483528	−	0.875329i	$-0.660645\pi$
$347$	7.29844	−	7.29844i	0.391801	−	0.391801i	0.875329	+	0.483528i	$0.160645\pi$
$348$		0			0
$349$	8.03722			0.430222			0.215111	−	0.976590i	$-0.430989\pi$
$349$	8.03722			0.430222			0.215111	+	0.976590i	$0.430989\pi$
$350$		0			0
$351$	1.70156			0.0908227
$352$		0			0
$353$	18.2364	−	18.2364i	0.970628	−	0.970628i	−0.0289527	−	0.999581i	$-0.509217\pi$
$353$	18.2364	−	18.2364i	0.970628	−	0.970628i	0.999581	+	0.0289527i	$0.00921722\pi$
$354$		0			0
$355$	2.85974	−	16.3050i	0.151779	−	0.865380i
$356$		0			0
$357$	0.208814	−	9.79119i	0.0110516	−	0.518205i
$358$		0			0
$359$		−	6.00000i		−	0.316668i	−0.987386	−	0.158334i	$-0.949388\pi$
$359$		−	6.00000i		−	0.316668i	0.987386	−	0.158334i	$-0.0506123\pi$
$360$		0			0
$361$	16.4031			0.863322
$362$		0			0
$363$	−3.13075	+	3.13075i	−0.164322	+	0.164322i
$364$		0			0
$365$	3.29844	+	4.70156i	0.172648	+	0.246091i
$366$		0			0
$367$	24.7285	+	24.7285i	1.29082	+	1.29082i	0.934282	+	0.356536i	$0.116042\pi$
$367$	24.7285	+	24.7285i	1.29082	+	1.29082i	0.356536	+	0.934282i	$0.383958\pi$
$368$		0			0
$369$	−16.0744			−0.836802
$370$		0			0
$371$	13.5078	−	12.9437i	0.701291	−	0.672003i
$372$		0			0
$373$	−12.7016	−	12.7016i	−0.657662	−	0.657662i	0.297164	−	0.954826i	$-0.403959\pi$
$373$	−12.7016	−	12.7016i	−0.657662	−	0.657662i	−0.954826	+	0.297164i	$0.903959\pi$
$374$		0			0
$375$	1.59688	+	5.89531i	0.0824623	+	0.304433i
$376$		0			0
$377$	2.20245	+	2.20245i	0.113432	+	0.113432i
$378$		0			0
$379$			31.0156i			1.59317i	0.604530	+	0.796583i	$0.293361\pi$
$379$			31.0156i			1.59317i	−0.604530	+	0.796583i	$0.706639\pi$
$380$		0			0
$381$			8.03722i			0.411759i
$382$		0			0
$383$	4.13389	−	4.13389i	0.211232	−	0.211232i	−0.593559	−	0.804791i	$-0.702278\pi$
$383$	4.13389	−	4.13389i	0.211232	−	0.211232i	0.804791	+	0.593559i	$0.202278\pi$
$384$		0			0
$385$	−9.87589	−	1.95005i	−0.503322	−	0.0993839i
$386$		0			0
$387$	13.5078	−	13.5078i	0.686641	−	0.686641i
$388$		0			0
$389$		−	14.2984i		−	0.724960i	−0.931992	−	0.362480i	$-0.881930\pi$
$389$		−	14.2984i		−	0.724960i	0.931992	−	0.362480i	$-0.118070\pi$
$390$		0			0
$391$		−	25.8874i		−	1.30918i
$392$		0			0
$393$	5.40312	+	5.40312i	0.272552	+	0.272552i
$394$		0			0
$395$	0.657294	+	0.115283i	0.0330721	+	0.00580053i
$396$		0			0
$397$	−7.10892	−	7.10892i	−0.356786	−	0.356786i	0.505841	−	0.862627i	$-0.331182\pi$
$397$	−7.10892	−	7.10892i	−0.356786	−	0.356786i	−0.862627	+	0.505841i	$0.831182\pi$
$398$		0			0
$399$	5.95005	+	6.20937i	0.297875	+	0.310857i
$400$		0			0
$401$	33.3141			1.66362			0.831812	−	0.555057i	$-0.187304\pi$
$401$	33.3141			1.66362			0.831812	+	0.555057i	$0.187304\pi$
$402$		0			0
$403$	3.10469	+	3.10469i	0.154655	+	0.154655i
$404$		0			0
$405$	−2.47345	+	14.1026i	−0.122907	+	0.700762i
$406$		0			0
$407$	4.59688	−	4.59688i	0.227859	−	0.227859i
$408$		0			0
$409$	−12.2115			−0.603822			−0.301911	−	0.953336i	$-0.597625\pi$
$409$	−12.2115			−0.603822			−0.301911	+	0.953336i	$0.597625\pi$
$410$		0			0
$411$		−	2.08717i		−	0.102952i
$412$		0			0
$413$	0.335656	−	15.7388i	0.0165166	−	0.774455i
$414$		0			0
$415$	−7.50781	−	10.7016i	−0.368544	−	0.525319i
$416$		0			0
$417$	6.20937	−	6.20937i	0.304074	−	0.304074i
$418$		0			0
$419$	5.95005			0.290679			0.145340	−	0.989382i	$-0.453573\pi$
$419$	5.95005			0.290679			0.145340	+	0.989382i	$0.453573\pi$
$420$		0			0
$421$	11.7016			0.570299			0.285150	−	0.958483i	$-0.407957\pi$
$421$	11.7016			0.570299			0.285150	+	0.958483i	$0.407957\pi$
$422$		0			0
$423$	8.76936	−	8.76936i	0.426381	−	0.426381i
$424$		0			0
$425$	−14.3736	−	30.6786i	−0.697220	−	1.48813i
$426$		0			0
$427$	−31.4776	−	0.671312i	−1.52331	−	0.0324871i
$428$		0			0
$429$		−	0.507811i		−	0.0245173i
$430$		0			0
$431$	−13.7016			−0.659981			−0.329991	−	0.943984i	$-0.607046\pi$
$431$	−13.7016			−0.659981			−0.329991	+	0.943984i	$0.607046\pi$
$432$		0			0
$433$	20.2083	−	20.2083i	0.971150	−	0.971150i	−0.0284451	−	0.999595i	$-0.509056\pi$
$433$	20.2083	−	20.2083i	0.971150	−	0.971150i	0.999595	+	0.0284451i	$0.00905557\pi$
$434$		0			0
$435$	5.70156	−	4.00000i	0.273369	−	0.191785i
$436$		0			0
$437$	16.0744	+	16.0744i	0.768945	+	0.768945i
$438$		0			0
$439$	−23.8002			−1.13592			−0.567961	−	0.823055i	$-0.692268\pi$
$439$	−23.8002			−1.13592			−0.567961	+	0.823055i	$0.692268\pi$
$440$		0			0
$441$	0.806248	−	18.8937i	0.0383928	−	0.899702i
$442$		0			0
$443$	25.8062	+	25.8062i	1.22609	+	1.22609i	0.965430	+	0.260662i	$0.0839407\pi$
$443$	25.8062	+	25.8062i	1.22609	+	1.22609i	0.260662	+	0.965430i	$0.416059\pi$
$444$		0			0
$445$	0.806248	−	4.59688i	0.0382198	−	0.217913i
$446$		0			0
$447$	−2.62918	−	2.62918i	−0.124356	−	0.124356i
$448$		0			0
$449$			5.70156i			0.269073i	0.990909	+	0.134537i	$0.0429546\pi$
$449$			5.70156i			0.269073i	−0.990909	+	0.134537i	$0.957045\pi$
$450$		0			0
$451$			10.1244i			0.476739i
$452$		0			0
$453$	−5.29276	+	5.29276i	−0.248675	+	0.248675i
$454$		0			0
$455$	−2.68473	+	1.79932i	−0.125862	+	0.0843536i
$456$		0			0
$457$	9.59688	−	9.59688i	0.448923	−	0.448923i	−0.446073	−	0.894996i	$-0.647178\pi$
$457$	9.59688	−	9.59688i	0.448923	−	0.448923i	0.894996	+	0.446073i	$0.147178\pi$
$458$		0			0
$459$			21.1047i			0.985082i
$460$		0			0
$461$			16.0744i			0.748661i	0.927295	+	0.374331i	$0.122127\pi$
$461$			16.0744i			0.748661i	−0.927295	+	0.374331i	$0.877873\pi$
$462$		0			0
$463$	1.89531	+	1.89531i	0.0880827	+	0.0880827i	0.749775	−	0.661693i	$-0.230162\pi$
$463$	1.89531	+	1.89531i	0.0880827	+	0.0880827i	−0.661693	+	0.749775i	$0.730162\pi$
$464$		0			0
$465$	8.03722	−	5.63861i	0.372717	−	0.261484i
$466$		0			0
$467$	−3.24603	−	3.24603i	−0.150208	−	0.150208i	0.628003	−	0.778211i	$-0.283873\pi$
$467$	−3.24603	−	3.24603i	−0.150208	−	0.150208i	−0.778211	+	0.628003i	$0.783873\pi$
$468$		0			0
$469$	−12.9437	−	13.5078i	−0.597684	−	0.623733i
$470$		0			0
$471$	−8.20937			−0.378268
$472$		0			0
$473$	−8.50781	−	8.50781i	−0.391190	−	0.391190i
$474$		0			0
$475$	27.9745	+	10.1244i	1.28356	+	0.464539i
$476$		0			0
$477$	−13.5078	+	13.5078i	−0.618480	+	0.618480i
$478$		0			0
$479$	35.7003			1.63119			0.815595	−	0.578624i	$-0.196410\pi$
$479$	35.7003			1.63119			0.815595	+	0.578624i	$0.196410\pi$
$480$		0			0
$481$		−	2.08717i		−	0.0951666i
$482$		0			0
$483$	−0.117742	+	5.52087i	−0.00535744	+	0.251208i
$484$		0			0
$485$	−3.00000	+	2.10469i	−0.136223	+	0.0955689i
$486$		0			0
$487$	28.9109	−	28.9109i	1.31008	−	1.31008i	0.388726	−	0.921353i	$-0.372915\pi$
$487$	28.9109	−	28.9109i	1.31008	−	1.31008i	0.921353	−	0.388726i	$-0.127085\pi$
$488$		0			0
$489$	−2.08717			−0.0943849
$490$		0			0
$491$	−19.9109			−0.898568			−0.449284	−	0.893389i	$-0.648321\pi$
$491$	−19.9109			−0.898568			−0.449284	+	0.893389i	$0.648321\pi$
$492$		0			0
$493$	−27.3172	+	27.3172i	−1.23031	+	1.23031i
$494$		0			0
$495$	10.1244	+	1.77572i	0.455057	+	0.0798127i
$496$		0			0
$497$	0.417627	−	19.5824i	0.0187331	−	0.878389i
$498$		0			0
$499$		−	15.1047i		−	0.676179i	−0.941114	−	0.338089i	$-0.890219\pi$
$499$		−	15.1047i		−	0.676179i	0.941114	−	0.338089i	$-0.109781\pi$
$500$		0			0
$501$	−7.10469			−0.317414
$502$		0			0
$503$	−23.4139	+	23.4139i	−1.04398	+	1.04398i	−0.0449876	+	0.998988i	$0.514325\pi$
$503$	−23.4139	+	23.4139i	−1.04398	+	1.04398i	−0.998988	+	0.0449876i	$0.985675\pi$
$504$		0			0
$505$	−13.1047	−	2.29844i	−0.583151	−	0.102279i
$506$		0			0
$507$	4.90647	+	4.90647i	0.217904	+	0.217904i
$508$		0			0
$509$	−2.08717			−0.0925120			−0.0462560	−	0.998930i	$-0.514729\pi$
$509$	−2.08717			−0.0925120			−0.0462560	+	0.998930i	$0.514729\pi$
$510$		0			0
$511$	4.70156	+	4.90647i	0.207985	+	0.217049i
$512$		0			0
$513$	−13.1047	−	13.1047i	−0.578586	−	0.578586i
$514$		0			0
$515$	10.1047	+	14.4031i	0.445266	+	0.634677i
$516$		0			0
$517$	−5.52332	−	5.52332i	−0.242916	−	0.242916i
$518$		0			0
$519$		−	4.89531i		−	0.214880i
$520$		0			0
$521$			33.9246i			1.48626i	0.669145	+	0.743132i	$0.266660\pi$
$521$			33.9246i			1.48626i	−0.669145	+	0.743132i	$0.733340\pi$
$522$		0			0
$523$	14.2583	−	14.2583i	0.623471	−	0.623471i	−0.322946	−	0.946417i	$-0.604673\pi$
$523$	14.2583	−	14.2583i	0.623471	−	0.623471i	0.946417	+	0.322946i	$0.104673\pi$
$524$		0			0
$525$	2.92584	+	6.60803i	0.127694	+	0.288398i
$526$		0			0
$527$	−38.5078	+	38.5078i	−1.67743	+	1.67743i
$528$		0			0
$529$		−	8.40312i		−	0.365353i
$530$		0			0
$531$			16.0744i			0.697571i
$532$		0			0
$533$	2.29844	+	2.29844i	0.0995564	+	0.0995564i
$534$		0			0
$535$	18.8937	+	26.9310i	0.816848	+	1.16433i
$536$		0			0
$537$	−6.49206	−	6.49206i	−0.280153	−	0.280153i
$538$		0			0
$539$	−11.9001	−	0.507811i	−0.512574	−	0.0218730i
$540$		0			0
$541$	−12.8953			−0.554413			−0.277206	−	0.960810i	$-0.589409\pi$
$541$	−12.8953			−0.554413			−0.277206	+	0.960810i	$0.589409\pi$
$542$		0			0
$543$	−6.89531	−	6.89531i	−0.295906	−	0.295906i
$544$		0			0
$545$	−21.3672	−	3.74760i	−0.915270	−	0.160530i
$546$		0			0
$547$	2.70156	−	2.70156i	0.115510	−	0.115510i	−0.646989	−	0.762499i	$-0.723972\pi$
$547$	2.70156	−	2.70156i	0.115510	−	0.115510i	0.762499	+	0.646989i	$0.223972\pi$
$548$		0			0
$549$	32.1489			1.37208
$550$		0			0
$551$		−	33.9246i		−	1.44524i
$552$		0			0
$553$	0.789413	+	0.0168356i	0.0335693	+	0.000715921i
$554$		0			0
$555$	−4.59688	−	0.806248i	−0.195127	−	0.0342233i
$556$		0			0
$557$	−28.1047	+	28.1047i	−1.19083	+	1.19083i	−0.214000	+	0.976834i	$0.568649\pi$
$557$	−28.1047	+	28.1047i	−1.19083	+	1.19083i	−0.976834	+	0.214000i	$0.931351\pi$
$558$		0			0
$559$	−3.86289			−0.163383
$560$		0			0
$561$	6.29844			0.265920
$562$		0			0
$563$	8.30822	−	8.30822i	0.350150	−	0.350150i	−0.510015	−	0.860165i	$-0.670360\pi$
$563$	8.30822	−	8.30822i	0.350150	−	0.350150i	0.860165	+	0.510015i	$0.170360\pi$
$564$		0			0
$565$	−32.8810	+	23.0681i	−1.38331	+	0.970481i
$566$		0			0
$567$	−0.361215	+	16.9372i	−0.0151696	+	0.711297i
$568$		0			0
$569$		−	5.19375i		−	0.217733i	−0.994056	−	0.108867i	$-0.965278\pi$
$569$		−	5.19375i		−	0.217733i	0.994056	−	0.108867i	$-0.0347222\pi$
$570$		0			0
$571$	−34.2094			−1.43162			−0.715809	−	0.698296i	$-0.753942\pi$
$571$	−34.2094			−1.43162			−0.715809	+	0.698296i	$0.753942\pi$
$572$		0			0
$573$	6.60735	−	6.60735i	0.276026	−	0.276026i
$574$		0			0
$575$	8.10469	+	17.2984i	0.337989	+	0.721395i
$576$		0			0
$577$	−7.10892	−	7.10892i	−0.295948	−	0.295948i	0.543476	−	0.839424i	$-0.317108\pi$
$577$	−7.10892	−	7.10892i	−0.295948	−	0.295948i	−0.839424	+	0.543476i	$0.817108\pi$
$578$		0			0
$579$	13.9873			0.581291
$580$		0			0
$581$	−10.7016	−	11.1680i	−0.443976	−	0.463325i
$582$		0			0
$583$	8.50781	+	8.50781i	0.352358	+	0.352358i
$584$		0			0
$585$	2.70156	−	1.89531i	0.111696	−	0.0783616i
$586$		0			0
$587$	21.2115	+	21.2115i	0.875491	+	0.875491i	0.993064	−	0.117573i	$-0.0375114\pi$
$587$	21.2115	+	21.2115i	0.875491	+	0.875491i	−0.117573	+	0.993064i	$0.537511\pi$
$588$		0			0
$589$		−	47.8219i		−	1.97047i
$590$		0			0
$591$			8.03722i			0.330607i
$592$		0			0
$593$	−17.4639	+	17.4639i	−0.717155	+	0.717155i	−0.968022	−	0.250867i	$-0.919284\pi$
$593$	−17.4639	+	17.4639i	−0.717155	+	0.717155i	0.250867	+	0.968022i	$0.419284\pi$
$594$		0			0
$595$	−22.3172	−	33.2990i	−0.914918	−	1.36513i
$596$		0			0
$597$	−3.91093	+	3.91093i	−0.160064	+	0.160064i
$598$		0			0
$599$			0.298438i			0.0121938i	0.999981	+	0.00609692i	$0.00194072\pi$
$599$			0.298438i			0.0121938i	−0.999981	+	0.00609692i	$0.998059\pi$
$600$		0			0
$601$		−	5.95005i		−	0.242708i	−0.992609	−	0.121354i	$-0.961276\pi$
$601$		−	5.95005i		−	0.242708i	0.992609	−	0.121354i	$-0.0387236\pi$
$602$		0			0
$603$	13.5078	+	13.5078i	0.550081	+	0.550081i
$604$		0			0
$605$	−3.13075	+	17.8502i	−0.127283	+	0.725712i
$606$		0			0
$607$	−15.1461	−	15.1461i	−0.614763	−	0.614763i	0.329421	−	0.944183i	$-0.393147\pi$
$607$	−15.1461	−	15.1461i	−0.614763	−	0.614763i	−0.944183	+	0.329421i	$0.893147\pi$
$608$		0			0
$609$	5.95005	−	5.70156i	0.241108	−	0.231039i
$610$		0			0
$611$	−2.50781			−0.101455
$612$		0			0
$613$	−5.80625	−	5.80625i	−0.234512	−	0.234512i	0.580061	−	0.814573i	$-0.303029\pi$
$613$	−5.80625	−	5.80625i	−0.234512	−	0.234512i	−0.814573	+	0.580061i	$0.803029\pi$
$614$		0			0
$615$	5.95005	−	4.17433i	0.239929	−	0.168325i
$616$		0			0
$617$	18.1047	−	18.1047i	0.728867	−	0.728867i	−0.241527	−	0.970394i	$-0.577648\pi$
$617$	18.1047	−	18.1047i	0.728867	−	0.728867i	0.970394	+	0.241527i	$0.0776482\pi$
$618$		0			0
$619$	−4.17433			−0.167781			−0.0838903	−	0.996475i	$-0.526735\pi$
$619$	−4.17433			−0.167781			−0.0838903	+	0.996475i	$0.526735\pi$
$620$		0			0
$621$		−	11.9001i		−	0.477535i
$622$		0			0
$623$	0.117742	−	5.52087i	0.00471722	−	0.221189i
$624$		0			0
$625$	19.2094	+	16.0000i	0.768375	+	0.640000i
$626$		0			0
$627$	−3.91093	+	3.91093i	−0.156188	+	0.156188i
$628$		0			0
$629$	25.8874			1.03220
$630$		0			0
$631$	−13.7016			−0.545451			−0.272725	−	0.962092i	$-0.587925\pi$
$631$	−13.7016			−0.545451			−0.272725	+	0.962092i	$0.587925\pi$
$632$		0			0
$633$	2.43302	−	2.43302i	0.0967037	−	0.0967037i
$634$		0			0
$635$	18.8937	+	26.9310i	0.749775	+	1.06872i
$636$		0			0
$637$	−2.81685	+	2.58628i	−0.111607	+	0.102472i
$638$		0			0
$639$			20.0000i			0.791188i
$640$		0			0
$641$	48.2094			1.90416			0.952078	−	0.305856i	$-0.0989425\pi$
$641$	48.2094			1.90416			0.952078	+	0.305856i	$0.0989425\pi$
$642$		0			0
$643$	−9.73810	+	9.73810i	−0.384033	+	0.384033i	−0.872553	−	0.488520i	$-0.837537\pi$
$643$	−9.73810	+	9.73810i	−0.384033	+	0.384033i	0.488520	+	0.872553i	$0.337537\pi$
$644$		0			0
$645$	−1.49219	+	8.50781i	−0.0587549	+	0.334995i
$646$		0			0
$647$	−4.36446	−	4.36446i	−0.171585	−	0.171585i	0.616091	−	0.787675i	$-0.288715\pi$
$647$	−4.36446	−	4.36446i	−0.171585	−	0.171585i	−0.787675	+	0.616091i	$0.788715\pi$
$648$		0			0
$649$	10.1244			0.397417
$650$		0			0
$651$	8.38750	−	8.03722i	0.328732	−	0.315003i
$652$		0			0
$653$	5.00000	+	5.00000i	0.195665	+	0.195665i	0.798139	−	0.602474i	$-0.205818\pi$
$653$	5.00000	+	5.00000i	0.195665	+	0.195665i	−0.602474	+	0.798139i	$0.705818\pi$
$654$		0			0
$655$	30.8062	+	5.40312i	1.20370	+	0.211118i
$656$		0			0
$657$	−4.90647	−	4.90647i	−0.191420	−	0.191420i
$658$		0			0
$659$		−	5.91093i		−	0.230257i	−0.993351	−	0.115129i	$-0.963272\pi$
$659$		−	5.91093i		−	0.230257i	0.993351	−	0.115129i	$-0.0367280\pi$
$660$		0			0
$661$		−	23.8002i		−	0.925721i	−0.886431	−	0.462860i	$-0.846823\pi$
$661$		−	23.8002i		−	0.925721i	0.886431	−	0.462860i	$-0.153177\pi$
$662$		0			0
$663$	1.42987	−	1.42987i	0.0555316	−	0.0555316i
$664$		0			0
$665$	34.5342	+	6.81898i	1.33918	+	0.264429i
$666$		0			0
$667$	15.4031	−	15.4031i	0.596411	−	0.596411i
$668$		0			0
$669$		−	12.7172i		−	0.491675i
$670$		0			0
$671$		−	20.2488i		−	0.781695i
$672$		0			0
$673$	7.29844	+	7.29844i	0.281334	+	0.281334i	0.833641	−	0.552307i	$-0.186252\pi$
$673$	7.29844	+	7.29844i	0.281334	+	0.281334i	−0.552307	+	0.833641i	$0.686252\pi$
$674$		0			0
$675$	−6.60735	−	14.1026i	−0.254317	−	0.542808i
$676$		0			0
$677$	−17.2333	−	17.2333i	−0.662330	−	0.662330i	0.293599	−	0.955929i	$-0.405147\pi$
$677$	−17.2333	−	17.2333i	−0.662330	−	0.662330i	−0.955929	+	0.293599i	$0.905147\pi$
$678$		0			0
$679$	−3.13075	+	3.00000i	−0.120147	+	0.115129i
$680$		0			0
$681$	−16.2984			−0.624557
$682$		0			0
$683$	3.50781	+	3.50781i	0.134223	+	0.134223i	0.771026	−	0.636803i	$-0.219744\pi$
$683$	3.50781	+	3.50781i	0.134223	+	0.134223i	−0.636803	+	0.771026i	$0.719744\pi$
$684$		0			0
$685$	−4.90647	−	6.99364i	−0.187467	−	0.267213i
$686$		0			0
$687$	7.70156	−	7.70156i	0.293833	−	0.293833i
$688$		0			0
$689$	3.86289			0.147164
$690$		0			0
$691$		−	21.7130i		−	0.826003i	−0.910730	−	0.413002i	$-0.864480\pi$
$691$		−	21.7130i		−	0.826003i	0.910730	−	0.413002i	$-0.135520\pi$
$692$		0			0
$693$	12.1594	+	0.259320i	0.461898	+	0.00985076i
$694$		0			0
$695$	6.20937	−	35.4031i	0.235535	−	1.34292i
$696$		0			0
$697$	−28.5078	+	28.5078i	−1.07981	+	1.07981i
$698$		0			0
$699$	−6.26150			−0.236832
$700$		0			0
$701$	−28.2984			−1.06882			−0.534409	−	0.845226i	$-0.679466\pi$
$701$	−28.2984			−1.06882			−0.534409	+	0.845226i	$0.679466\pi$
$702$		0			0
$703$	−16.0744	+	16.0744i	−0.606259	+	0.606259i
$704$		0			0
$705$	−0.968739	+	5.52332i	−0.0364848	+	0.208020i
$706$		0			0
$707$	−15.7388	−	0.335656i	−0.591918	−	0.0126236i
$708$		0			0
$709$		−	20.5078i		−	0.770187i	−0.922878	−	0.385093i	$-0.874169\pi$
$709$		−	20.5078i		−	0.770187i	0.922878	−	0.385093i	$-0.125831\pi$
$710$		0			0
$711$	−0.806248			−0.0302367
$712$		0			0
$713$	21.7130	−	21.7130i	0.813160	−	0.813160i
$714$		0			0
$715$	−1.19375	−	1.70156i	−0.0446438	−	0.0636348i
$716$		0			0
$717$	1.89100	+	1.89100i	0.0706208	+	0.0706208i
$718$		0			0
$719$	20.2488			0.755152			0.377576	−	0.925979i	$-0.376758\pi$
$719$	20.2488			0.755152			0.377576	+	0.925979i	$0.376758\pi$
$720$		0			0
$721$	14.4031	+	15.0309i	0.536400	+	0.559778i
$722$		0			0
$723$	−1.61250	−	1.61250i	−0.0599694	−	0.0599694i
$724$		0			0
$725$	9.70156	−	26.8062i	0.360307	−	0.995559i
$726$		0			0
$727$	−26.3889	−	26.3889i	−0.978712	−	0.978712i	0.0210662	−	0.999778i	$-0.493294\pi$
$727$	−26.3889	−	26.3889i	−0.978712	−	0.978712i	−0.999778	+	0.0210662i	$0.993294\pi$
$728$		0			0
$729$		−	12.1938i		−	0.451620i
$730$		0			0
$731$		−	47.9119i		−	1.77208i
$732$		0			0
$733$	−15.6881	+	15.6881i	−0.579455	+	0.579455i	−0.934753	−	0.355298i	$-0.884379\pi$
$733$	−15.6881	+	15.6881i	−0.579455	+	0.579455i	0.355298	+	0.934753i	$0.384379\pi$
$734$		0			0
$735$	4.60803	+	7.20301i	0.169970	+	0.265687i
$736$		0			0
$737$	8.50781	−	8.50781i	0.313389	−	0.313389i
$738$		0			0
$739$			6.50781i			0.239394i	0.992810	+	0.119697i	$0.0381923\pi$
$739$			6.50781i			0.239394i	−0.992810	+	0.119697i	$0.961808\pi$
$740$		0			0
$741$			1.77572i			0.0652327i
$742$		0			0
$743$	32.0156	+	32.0156i	1.17454	+	1.17454i	0.981115	+	0.193424i	$0.0619593\pi$
$743$	32.0156	+	32.0156i	1.17454	+	1.17454i	0.193424	+	0.981115i	$0.438041\pi$
$744$		0			0
$745$	−14.9904	−	2.62918i	−0.549206	−	0.0963256i
$746$		0			0
$747$	11.1680	+	11.1680i	0.408615	+	0.408615i
$748$		0			0
$749$	26.9310	+	28.1047i	0.984036	+	1.02692i
$750$		0			0
$751$	17.1047			0.624159			0.312079	−	0.950056i	$-0.398974\pi$
$751$	17.1047			0.624159			0.312079	+	0.950056i	$0.398974\pi$
$752$		0			0
$753$	5.40312	+	5.40312i	0.196901	+	0.196901i
$754$		0			0
$755$	−5.29276	+	30.1770i	−0.192623	+	1.09825i
$756$		0			0
$757$	−12.7016	+	12.7016i	−0.461646	+	0.461646i	−0.899195	−	0.437549i	$-0.855847\pi$
$757$	−12.7016	+	12.7016i	−0.461646	+	0.461646i	0.437549	+	0.899195i	$0.355847\pi$
$758$		0			0
$759$	−3.55144			−0.128909
$760$		0			0
$761$			32.1489i			1.16540i	0.812689	+	0.582698i	$0.198003\pi$
$761$			32.1489i			1.16540i	−0.812689	+	0.582698i	$0.801997\pi$
$762$		0			0
$763$	−25.6621	−	0.547287i	−0.929030	−	0.0198131i
$764$		0			0
$765$	23.5078	+	33.5078i	0.849927	+	1.21148i
$766$		0			0
$767$	2.29844	−	2.29844i	0.0829918	−	0.0829918i
$768$		0			0
$769$	24.1117			0.869488			0.434744	−	0.900554i	$-0.356839\pi$
$769$	24.1117			0.869488			0.434744	+	0.900554i	$0.356839\pi$
$770$		0			0
$771$	4.20937			0.151597
$772$		0			0
$773$	10.5107	−	10.5107i	0.378043	−	0.378043i	−0.492353	−	0.870396i	$-0.663863\pi$
$773$	10.5107	−	10.5107i	0.378043	−	0.378043i	0.870396	+	0.492353i	$0.163863\pi$
$774$		0			0
$775$	13.6758	−	37.7875i	0.491250	−	1.35737i
$776$		0			0
$777$	−5.52087	−	0.117742i	−0.198060	−	0.00422396i
$778$		0			0
$779$		−	35.4031i		−	1.26845i
$780$		0			0
$781$	12.5969			0.450752
$782$		0			0
$783$	−12.5574	+	12.5574i	−0.448765	+	0.448765i
$784$		0			0
$785$	−27.5078	+	19.2984i	−0.981796	+	0.688791i
$786$		0			0
$787$	−9.19608	−	9.19608i	−0.327805	−	0.327805i	0.523946	−	0.851751i	$-0.324459\pi$
$787$	−9.19608	−	9.19608i	−0.327805	−	0.327805i	−0.851751	+	0.523946i	$0.824459\pi$
$788$		0			0
$789$	−0.311445			−0.0110877
$790$		0			0
$791$	−34.3141	+	32.8810i	−1.22007	+	1.16911i
$792$		0			0
$793$	−4.59688	−	4.59688i	−0.163240	−	0.163240i
$794$		0			0
$795$	1.49219	−	8.50781i	0.0529225	−	0.301741i
$796$		0			0
$797$	−11.2832	−	11.2832i	−0.399673	−	0.399673i	0.478445	−	0.878118i	$-0.341201\pi$
$797$	−11.2832	−	11.2832i	−0.399673	−	0.399673i	−0.878118	+	0.478445i	$0.841201\pi$
$798$		0			0
$799$		−	31.1047i		−	1.10040i
$800$		0			0
$801$			5.63861i			0.199230i
$802$		0			0
$803$	−3.09031	+	3.09031i	−0.109055	+	0.109055i
$804$		0			0
$805$	12.5838	+	18.7760i	0.443521	+	0.661767i
$806$		0			0
$807$	0.806248	−	0.806248i	0.0283813	−	0.0283813i
$808$		0			0
$809$			25.7016i			0.903619i	0.892114	+	0.451809i	$0.149221\pi$
$809$			25.7016i			0.903619i	−0.892114	+	0.451809i	$0.850779\pi$
$810$		0			0
$811$			13.9873i			0.491160i	0.969376	+	0.245580i	$0.0789783\pi$
$811$			13.9873i			0.491160i	−0.969376	+	0.245580i	$0.921022\pi$
$812$		0			0
$813$	3.79063	+	3.79063i	0.132943	+	0.132943i
$814$		0			0
$815$	−6.99364	+	4.90647i	−0.244976	+	0.171866i
$816$		0			0
$817$	29.7503	+	29.7503i	1.04083	+	1.04083i
$818$		0			0
$819$	2.81930	−	2.70156i	0.0985145	−	0.0944002i
$820$		0			0
$821$	−5.31406			−0.185462			−0.0927310	−	0.995691i	$-0.529560\pi$
$821$	−5.31406			−0.185462			−0.0927310	+	0.995691i	$0.529560\pi$
$822$		0			0
$823$	−35.8062	−	35.8062i	−1.24813	−	1.24813i	−0.956546	−	0.291581i	$-0.905819\pi$
$823$	−35.8062	−	35.8062i	−1.24813	−	1.24813i	−0.291581	−	0.956546i	$-0.594181\pi$
$824$		0			0
$825$	−4.20874	+	1.97188i	−0.146529	+	0.0686521i
$826$		0			0
$827$	11.8953	−	11.8953i	0.413641	−	0.413641i	−0.469364	−	0.883005i	$-0.655517\pi$
$827$	11.8953	−	11.8953i	0.413641	−	0.413641i	0.883005	+	0.469364i	$0.155517\pi$
$828$		0			0
$829$	−31.8374			−1.10576			−0.552880	−	0.833261i	$-0.686471\pi$
$829$	−31.8374			−1.10576			−0.552880	+	0.833261i	$0.686471\pi$
$830$		0			0
$831$			6.26150i			0.217209i
$832$		0			0
$833$	−32.0779	−	34.9377i	−1.11143	−	1.21052i
$834$		0			0
$835$	−23.8062	+	16.7016i	−0.823849	+	0.577981i
$836$		0			0
$837$	−17.7016	+	17.7016i	−0.611855	+	0.611855i
$838$		0			0
$839$	−32.1489			−1.10990			−0.554951	−	0.831883i	$-0.687263\pi$
$839$	−32.1489			−1.10990			−0.554951	+	0.831883i	$0.687263\pi$
$840$		0			0
$841$	−3.50781			−0.120959
$842$		0			0
$843$	6.91879	−	6.91879i	0.238296	−	0.238296i
$844$		0			0
$845$	27.9745	+	4.90647i	0.962353	+	0.168788i
$846$		0			0
$847$	−0.457204	+	21.4381i	−0.0157097	+	0.736622i
$848$		0			0
$849$			8.89531i			0.305286i
$850$		0			0
$851$	−14.5969			−0.500374
$852$		0			0
$853$	2.35817	−	2.35817i	0.0807422	−	0.0807422i	−0.665582	−	0.746325i	$-0.731817\pi$
$853$	2.35817	−	2.35817i	0.0807422	−	0.0807422i	0.746325	+	0.665582i	$0.231817\pi$
$854$		0			0
$855$	−35.4031	−	6.20937i	−1.21076	−	0.212356i
$856$		0			0
$857$	−10.6260	−	10.6260i	−0.362976	−	0.362976i	0.501932	−	0.864907i	$-0.332623\pi$
$857$	−10.6260	−	10.6260i	−0.362976	−	0.362976i	−0.864907	+	0.501932i	$0.832623\pi$
$858$		0			0
$859$	4.17433			0.142426			0.0712132	−	0.997461i	$-0.477313\pi$
$859$	4.17433			0.142426			0.0712132	+	0.997461i	$0.477313\pi$
$860$		0			0
$861$	6.20937	−	5.95005i	0.211615	−	0.202777i
$862$		0			0
$863$	−0.403124	−	0.403124i	−0.0137225	−	0.0137225i	0.700212	−	0.713935i	$-0.253089\pi$
$863$	−0.403124	−	0.403124i	−0.0137225	−	0.0137225i	−0.713935	+	0.700212i	$0.753089\pi$
$864$		0			0
$865$	−11.5078	−	16.4031i	−0.391277	−	0.557723i
$866$		0			0
$867$	11.1680	+	11.1680i	0.379284	+	0.379284i
$868$		0			0
$869$			0.507811i			0.0172263i
$870$		0			0
$871$		−	3.86289i		−	0.130889i
$872$		0			0
$873$	3.13075	−	3.13075i	0.105960	−	0.105960i
$874$		0			0
$875$	25.3379	+	15.2641i	0.856577	+	0.516019i
$876$		0			0
$877$	14.1938	−	14.1938i	0.479289	−	0.479289i	−0.425615	−	0.904904i	$-0.639942\pi$
$877$	14.1938	−	14.1938i	0.479289	−	0.479289i	0.904904	+	0.425615i	$0.139942\pi$
$878$		0			0
$879$			8.89531i			0.300031i
$880$		0			0
$881$		−	4.17433i		−	0.140637i	−0.997525	−	0.0703184i	$-0.977598\pi$
$881$		−	4.17433i		−	0.140637i	0.997525	−	0.0703184i	$-0.0224015\pi$
$882$		0			0
$883$	17.2984	+	17.2984i	0.582139	+	0.582139i	0.935491	−	0.353352i	$-0.114958\pi$
$883$	17.2984	+	17.2984i	0.582139	+	0.582139i	−0.353352	+	0.935491i	$0.614958\pi$
$884$		0			0
$885$	−4.17433	−	5.95005i	−0.140319	−	0.200009i
$886$		0			0
$887$	37.2859	+	37.2859i	1.25194	+	1.25194i	0.954850	+	0.297088i	$0.0960156\pi$
$887$	37.2859	+	37.2859i	1.25194	+	1.25194i	0.297088	+	0.954850i	$0.403984\pi$
$888$		0			0
$889$	26.9310	+	28.1047i	0.903235	+	0.942601i
$890$		0			0
$891$	−10.8953			−0.365007
$892$		0			0
$893$	19.3141	+	19.3141i	0.646320	+	0.646320i
$894$		0			0
$895$	−37.0149	−	6.49206i	−1.23727	−	0.217006i
$896$		0			0
$897$	−0.806248	+	0.806248i	−0.0269199	+	0.0269199i
$898$		0			0
$899$	−45.8247			−1.52834
$900$		0			0
$901$			47.9119i			1.59618i
$902$		0			0
$903$	−0.217914	+	10.2179i	−0.00725173	+	0.340031i
$904$		0			0
$905$	−39.3141	−	6.89531i	−1.30684	−	0.229208i
$906$		0			0
$907$	13.5078	−	13.5078i	0.448519	−	0.448519i	−0.446343	−	0.894862i	$-0.647274\pi$
$907$	13.5078	−	13.5078i	0.448519	−	0.448519i	0.894862	+	0.446343i	$0.147274\pi$
$908$		0			0
$909$	16.0744			0.533155
$910$		0			0
$911$	−23.4031			−0.775380			−0.387690	−	0.921790i	$-0.626727\pi$
$911$	−23.4031			−0.775380			−0.387690	+	0.921790i	$0.626727\pi$
$912$		0			0
$913$	7.03407	−	7.03407i	0.232794	−	0.232794i
$914$		0			0
$915$	−11.9001	+	8.34866i	−0.393405	+	0.275998i
$916$		0			0
$917$	36.9984	+	0.789054i	1.22180	+	0.0260569i
$918$		0			0
$919$			21.9109i			0.722775i	0.932416	+	0.361388i	$0.117697\pi$
$919$			21.9109i			0.722775i	−0.932416	+	0.361388i	$0.882303\pi$
$920$		0			0
$921$	9.91093			0.326576
$922$		0			0
$923$	2.85974	−	2.85974i	0.0941296	−	0.0941296i
$924$		0			0
$925$	−17.2984	+	8.10469i	−0.568769	+	0.266480i
$926$		0			0
$927$	−15.0309	−	15.0309i	−0.493678	−	0.493678i
$928$		0			0
$929$	−59.8120			−1.96237			−0.981184	−	0.193077i	$-0.938153\pi$
$929$	−59.8120			−1.96237			−0.981184	+	0.193077i	$0.938153\pi$
$930$		0			0
$931$	41.6125	+	1.77572i	1.36379	+	0.0581969i
$932$		0			0
$933$	3.10469	+	3.10469i	0.101643	+	0.101643i
$934$		0			0
$935$	21.1047	−	14.8062i	0.690197	−	0.484216i
$936$		0			0
$937$	18.4670	+	18.4670i	0.603291	+	0.603291i	0.941184	−	0.337893i	$-0.109714\pi$
$937$	18.4670	+	18.4670i	0.603291	+	0.603291i	−0.337893	+	0.941184i	$0.609714\pi$
$938$		0			0
$939$		−	9.49219i		−	0.309766i
$940$		0			0
$941$		−	19.6259i		−	0.639785i	−0.947454	−	0.319893i	$-0.896353\pi$
$941$		−	19.6259i		−	0.639785i	0.947454	−	0.319893i	$-0.103647\pi$
$942$		0			0
$943$	16.0744	−	16.0744i	0.523456	−	0.523456i
$944$		0			0
$945$	−10.2590	−	15.3071i	−0.333724	−	0.497941i
$946$		0			0
$947$	−15.0000	+	15.0000i	−0.487435	+	0.487435i	−0.907496	−	0.420061i	$-0.862009\pi$
$947$	−15.0000	+	15.0000i	−0.487435	+	0.487435i	0.420061	+	0.907496i	$0.362009\pi$
$948$		0			0
$949$			1.40312i			0.0455473i
$950$		0			0
$951$		−	0.311445i		−	0.0100993i
$952$		0			0
$953$	14.1938	+	14.1938i	0.459781	+	0.459781i	0.898583	−	0.438803i	$-0.144597\pi$
$953$	14.1938	+	14.1938i	0.459781	+	0.459781i	−0.438803	+	0.898583i	$0.644597\pi$
$954$		0			0
$955$	6.60735	−	37.6722i	0.213809	−	1.21904i
$956$		0			0
$957$	3.74760	+	3.74760i	0.121143	+	0.121143i
$958$		0			0
$959$	−6.99364	−	7.29844i	−0.225836	−	0.235679i
$960$		0			0
$961$	−33.5969			−1.08377
$962$		0			0
$963$	−28.1047	−	28.1047i	−0.905661	−	0.905661i
$964$		0			0
$965$	46.8683	−	32.8810i	1.50874	−	1.05848i
$966$		0			0
$967$	25.0000	−	25.0000i	0.803946	−	0.803946i	−0.179764	−	0.983710i	$-0.557533\pi$
$967$	25.0000	−	25.0000i	0.803946	−	0.803946i	0.983710	+	0.179764i	$0.0575334\pi$
$968$		0			0
$969$	−22.0245			−0.707529
$970$		0			0
$971$		−	11.5887i		−	0.371898i	−0.982559	−	0.185949i	$-0.940464\pi$
$971$		−	11.5887i		−	0.371898i	0.982559	−	0.185949i	$-0.0595359\pi$
$972$		0			0
$973$	0.906796	−	42.5193i	0.0290705	−	1.36311i
$974$		0			0
$975$	−0.507811	+	1.40312i	−0.0162630	+	0.0449359i
$976$		0			0
$977$	−19.5969	+	19.5969i	−0.626960	+	0.626960i	−0.947302	−	0.320342i	$-0.896202\pi$
$977$	−19.5969	+	19.5969i	−0.626960	+	0.626960i	0.320342	+	0.947302i	$0.396202\pi$
$978$		0			0
$979$	3.55144			0.113505
$980$		0			0
$981$	26.2094			0.836801
$982$		0			0
$983$	−17.4639	+	17.4639i	−0.557011	+	0.557011i	−0.928455	−	0.371444i	$-0.878863\pi$
$983$	−17.4639	+	17.4639i	−0.557011	+	0.557011i	0.371444	+	0.928455i	$0.378863\pi$
$984$		0			0
$985$	18.8937	+	26.9310i	0.602005	+	0.858092i
$986$		0			0
$987$	−0.141471	+	6.63353i	−0.00450308	+	0.211148i
$988$		0			0
$989$			27.0156i			0.859047i
$990$		0			0
$991$	33.6125			1.06774			0.533868	−	0.845568i	$-0.320738\pi$
$991$	33.6125			1.06774			0.533868	+	0.845568i	$0.320738\pi$
$992$		0			0
$993$	−1.31459	+	1.31459i	−0.0417172	+	0.0417172i
$994$		0			0
$995$	−3.91093	+	22.2984i	−0.123985	+	0.706908i
$996$		0			0
$997$	−35.0835	−	35.0835i	−1.11110	−	1.11110i	−0.993001	−	0.118103i	$-0.962319\pi$
$997$	−35.0835	−	35.0835i	−1.11110	−	1.11110i	−0.118103	−	0.993001i	$-0.537681\pi$
$998$		0			0
$999$	11.9001			0.376503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.m.a.13.3	yes	8
3.2	odd	2		1260.2.ba.a.433.2		8
4.3	odd	2		560.2.bj.b.433.2		8
5.2	odd	4	inner	140.2.m.a.97.2	yes	8
5.3	odd	4		700.2.m.c.657.3		8
5.4	even	2		700.2.m.c.293.2		8
7.2	even	3		980.2.v.b.913.3		16
7.3	odd	6		980.2.v.b.313.3		16
7.4	even	3		980.2.v.b.313.2		16
7.5	odd	6		980.2.v.b.913.2		16
7.6	odd	2	inner	140.2.m.a.13.2	✓	8
15.2	even	4		1260.2.ba.a.937.3		8
20.7	even	4		560.2.bj.b.97.3		8
21.20	even	2		1260.2.ba.a.433.3		8
28.27	even	2		560.2.bj.b.433.3		8
35.2	odd	12		980.2.v.b.717.3		16
35.12	even	12		980.2.v.b.717.2		16
35.13	even	4		700.2.m.c.657.2		8
35.17	even	12		980.2.v.b.117.3		16
35.27	even	4	inner	140.2.m.a.97.3	yes	8
35.32	odd	12		980.2.v.b.117.2		16
35.34	odd	2		700.2.m.c.293.3		8
105.62	odd	4		1260.2.ba.a.937.2		8
140.27	odd	4		560.2.bj.b.97.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.m.a.13.2	✓	8	7.6	odd	2	inner
140.2.m.a.13.3	yes	8	1.1	even	1	trivial
140.2.m.a.97.2	yes	8	5.2	odd	4	inner
140.2.m.a.97.3	yes	8	35.27	even	4	inner
560.2.bj.b.97.2		8	140.27	odd	4
560.2.bj.b.97.3		8	20.7	even	4
560.2.bj.b.433.2		8	4.3	odd	2
560.2.bj.b.433.3		8	28.27	even	2
700.2.m.c.293.2		8	5.4	even	2
700.2.m.c.293.3		8	35.34	odd	2
700.2.m.c.657.2		8	35.13	even	4
700.2.m.c.657.3		8	5.3	odd	4
980.2.v.b.117.2		16	35.32	odd	12
980.2.v.b.117.3		16	35.17	even	12
980.2.v.b.313.2		16	7.4	even	3
980.2.v.b.313.3		16	7.3	odd	6
980.2.v.b.717.2		16	35.12	even	12
980.2.v.b.717.3		16	35.2	odd	12
980.2.v.b.913.2		16	7.5	odd	6
980.2.v.b.913.3		16	7.2	even	3
1260.2.ba.a.433.2		8	3.2	odd	2
1260.2.ba.a.433.3		8	21.20	even	2
1260.2.ba.a.937.2		8	105.62	odd	4
1260.2.ba.a.937.3		8	15.2	even	4

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.386289 - 0.386289i) q^{3} +(0.386289 - 2.20245i) q^{5} +(0.0564123 - 2.64515i) q^{7} +2.70156i q^{9} +O(q^{10})\)	\(q+(0.386289 - 0.386289i) q^{3} +(0.386289 - 2.20245i) q^{5} +(0.0564123 - 2.64515i) q^{7} +2.70156i q^{9} +1.70156 q^{11} +(0.386289 - 0.386289i) q^{13} +(-0.701562 - 1.00000i) q^{15} +(4.79119 + 4.79119i) q^{17} -5.95005 q^{19} +(-1.00000 - 1.04358i) q^{21} +(-2.70156 - 2.70156i) q^{23} +(-4.70156 - 1.70156i) q^{25} +(2.20245 + 2.20245i) q^{27} +5.70156i q^{29} +8.03722i q^{31} +(0.657294 - 0.657294i) q^{33} +(-5.80402 - 1.14604i) q^{35} +(2.70156 - 2.70156i) q^{37} -0.298438i q^{39} +5.95005i q^{41} +(-5.00000 - 5.00000i) q^{43} +(5.95005 + 1.04358i) q^{45} +(-3.24603 - 3.24603i) q^{47} +(-6.99364 - 0.298438i) q^{49} +3.70156 q^{51} +(5.00000 + 5.00000i) q^{53} +(0.657294 - 3.74760i) q^{55} +(-2.29844 + 2.29844i) q^{57} +5.95005 q^{59} -11.9001i q^{61} +(7.14604 + 0.152401i) q^{63} +(-0.701562 - 1.00000i) q^{65} +(5.00000 - 5.00000i) q^{67} -2.08717 q^{69} +7.40312 q^{71} +(-1.81616 + 1.81616i) q^{73} +(-2.47345 + 1.15887i) q^{75} +(0.0959890 - 4.50089i) q^{77} +0.298438i q^{79} -6.40312 q^{81} +(4.13389 - 4.13389i) q^{83} +(12.4031 - 8.70156i) q^{85} +(2.20245 + 2.20245i) q^{87} +2.08717 q^{89} +(-1.00000 - 1.04358i) q^{91} +(3.10469 + 3.10469i) q^{93} +(-2.29844 + 13.1047i) q^{95} +(-1.15887 - 1.15887i) q^{97} +4.59688i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{7}+O(q^{10}) \) 8 * q - 2 * q^7	\( 8 q - 2 q^{7} - 12 q^{11} + 20 q^{15} - 8 q^{21} + 4 q^{23} - 12 q^{25} - 14 q^{35} - 4 q^{37} - 40 q^{43} + 4 q^{51} + 40 q^{53} - 44 q^{57} + 42 q^{63} + 20 q^{65} + 40 q^{67} + 8 q^{71} + 44 q^{77} + 48 q^{85} - 8 q^{91} - 52 q^{93} - 44 q^{95}+O(q^{100}) \) 8 * q - 2 * q^7 - 12 * q^11 + 20 * q^15 - 8 * q^21 + 4 * q^23 - 12 * q^25 - 14 * q^35 - 4 * q^37 - 40 * q^43 + 4 * q^51 + 40 * q^53 - 44 * q^57 + 42 * q^63 + 20 * q^65 + 40 * q^67 + 8 * q^71 + 44 * q^77 + 48 * q^85 - 8 * q^91 - 52 * q^93 - 44 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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