LMFDB - Embedded newform 1380.2.r.c.737.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(737,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))

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

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

chi := DirichletCharacter("1380.737");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.r (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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.6
Character	$\chi$	$=$	1380.737
Dual form			1380.2.r.c.1013.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50371 - 0.859570i) q^{3} +(-0.917834 - 2.03901i) q^{5} +(0.160200 + 0.160200i) q^{7} +(1.52228 + 2.58509i) q^{9} +O(q^{10})$	\(q+(-1.50371 - 0.859570i) q^{3} +(-0.917834 - 2.03901i) q^{5} +(0.160200 + 0.160200i) q^{7} +(1.52228 + 2.58509i) q^{9} +2.32062i q^{11} +(1.06431 - 1.06431i) q^{13} +(-0.372521 + 3.85503i) q^{15} +(2.03624 - 2.03624i) q^{17} +8.28863i q^{19} +(-0.103191 - 0.378597i) q^{21} +(0.707107 + 0.707107i) q^{23} +(-3.31516 + 3.74295i) q^{25} +(-0.0670025 - 5.19572i) q^{27} -1.52725 q^{29} +3.08837 q^{31} +(1.99473 - 3.48953i) q^{33} +(0.179613 - 0.473687i) q^{35} +(5.39723 + 5.39723i) q^{37} +(-2.51526 + 0.685564i) q^{39} -0.592789i q^{41} +(-0.451122 + 0.451122i) q^{43} +(3.87383 - 5.47663i) q^{45} +(3.84716 - 3.84716i) q^{47} -6.94867i q^{49} +(-4.81220 + 1.31162i) q^{51} +(-0.554734 - 0.554734i) q^{53} +(4.73177 - 2.12994i) q^{55} +(7.12465 - 12.4637i) q^{57} +14.2475 q^{59} -6.37914 q^{61} +(-0.170261 + 0.657999i) q^{63} +(-3.14701 - 1.19329i) q^{65} +(5.84533 + 5.84533i) q^{67} +(-0.455475 - 1.67109i) q^{69} +1.93352i q^{71} +(8.21073 - 8.21073i) q^{73} +(8.20237 - 2.77870i) q^{75} +(-0.371763 + 0.371763i) q^{77} -13.4291i q^{79} +(-4.36533 + 7.87044i) q^{81} +(5.09560 + 5.09560i) q^{83} +(-6.02085 - 2.28299i) q^{85} +(2.29654 + 1.31278i) q^{87} -5.90889 q^{89} +0.341005 q^{91} +(-4.64401 - 2.65467i) q^{93} +(16.9006 - 7.60758i) q^{95} +(6.42509 + 6.42509i) q^{97} +(-5.99899 + 3.53263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{3}+O(q^{10}) $ 80 * q + 8 * q^3	$ 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) $ 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$1$

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
$3$	−1.50371	−	0.859570i	−0.868167	−	0.496273i
$3$	−1.50371	−	0.859570i	−0.868167	−	0.496273i
$4$		0			0
$5$	−0.917834	−	2.03901i	−0.410468	−	0.911875i
$5$	−0.917834	−	2.03901i	−0.410468	−	0.911875i
$6$		0			0
$7$	0.160200	+	0.160200i	0.0605499	+	0.0605499i	0.736733	−	0.676183i	$-0.236367\pi$
$7$	0.160200	+	0.160200i	0.0605499	+	0.0605499i	−0.676183	+	0.736733i	$0.736367\pi$
$8$		0			0
$9$	1.52228	+	2.58509i	0.507426	+	0.861695i
$10$		0			0
$11$			2.32062i			0.699693i	0.936807	+	0.349846i	$0.113766\pi$
$11$			2.32062i			0.699693i	−0.936807	+	0.349846i	$0.886234\pi$
$12$		0			0
$13$	1.06431	−	1.06431i	0.295187	−	0.295187i	−0.543938	−	0.839125i	$-0.683067\pi$
$13$	1.06431	−	1.06431i	0.295187	−	0.295187i	0.839125	+	0.543938i	$0.183067\pi$
$14$		0			0
$15$	−0.372521	+	3.85503i	−0.0961846	+	0.995364i
$16$		0			0
$17$	2.03624	−	2.03624i	0.493860	−	0.493860i	−0.415660	−	0.909520i	$-0.636449\pi$
$17$	2.03624	−	2.03624i	0.493860	−	0.493860i	0.909520	+	0.415660i	$0.136449\pi$
$18$		0			0
$19$			8.28863i			1.90154i	0.309896	+	0.950771i	$0.399706\pi$
$19$			8.28863i			1.90154i	−0.309896	+	0.950771i	$0.600294\pi$
$20$		0			0
$21$	−0.103191	−	0.378597i	−0.0225181	−	0.0826166i
$22$		0			0
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	−3.31516	+	3.74295i	−0.663033	+	0.748591i
$26$		0			0
$27$	−0.0670025	−	5.19572i	−0.0128946	−	0.999917i
$28$		0			0
$29$	−1.52725			−0.283604			−0.141802	−	0.989895i	$-0.545290\pi$
$29$	−1.52725			−0.283604			−0.141802	+	0.989895i	$0.545290\pi$
$30$		0			0
$31$	3.08837			0.554688			0.277344	−	0.960771i	$-0.410546\pi$
$31$	3.08837			0.554688			0.277344	+	0.960771i	$0.410546\pi$
$32$		0			0
$33$	1.99473	−	3.48953i	0.347238	−	0.607450i
$34$		0			0
$35$	0.179613	−	0.473687i	0.0303602	−	0.0800677i
$36$		0			0
$37$	5.39723	+	5.39723i	0.887299	+	0.887299i	0.994263	−	0.106964i	$-0.0341130\pi$
$37$	5.39723	+	5.39723i	0.887299	+	0.887299i	−0.106964	+	0.994263i	$0.534113\pi$
$38$		0			0
$39$	−2.51526	+	0.685564i	−0.402765	+	0.109778i
$40$		0			0
$41$		−	0.592789i		−	0.0925781i	−0.998928	−	0.0462890i	$-0.985260\pi$
$41$		−	0.592789i		−	0.0925781i	0.998928	−	0.0462890i	$-0.0147395\pi$
$42$		0			0
$43$	−0.451122	+	0.451122i	−0.0687954	+	0.0687954i	−0.740667	−	0.671872i	$-0.765491\pi$
$43$	−0.451122	+	0.451122i	−0.0687954	+	0.0687954i	0.671872	+	0.740667i	$0.265491\pi$
$44$		0			0
$45$	3.87383	−	5.47663i	0.577476	−	0.816407i
$46$		0			0
$47$	3.84716	−	3.84716i	0.561165	−	0.561165i	−0.368473	−	0.929638i	$-0.620119\pi$
$47$	3.84716	−	3.84716i	0.561165	−	0.561165i	0.929638	+	0.368473i	$0.120119\pi$
$48$		0			0
$49$		−	6.94867i		−	0.992667i
$50$		0			0
$51$	−4.81220	+	1.31162i	−0.673842	+	0.183663i
$52$		0			0
$53$	−0.554734	−	0.554734i	−0.0761986	−	0.0761986i	0.667980	−	0.744179i	$-0.267159\pi$
$53$	−0.554734	−	0.554734i	−0.0761986	−	0.0761986i	−0.744179	+	0.667980i	$0.767159\pi$
$54$		0			0
$55$	4.73177	−	2.12994i	0.638032	−	0.287201i
$56$		0			0
$57$	7.12465	−	12.4637i	0.943683	−	1.65085i
$58$		0			0
$59$	14.2475			1.85487			0.927434	−	0.373986i	$-0.122009\pi$
$59$	14.2475			1.85487			0.927434	+	0.373986i	$0.122009\pi$
$60$		0			0
$61$	−6.37914			−0.816765			−0.408383	−	0.912811i	$-0.633907\pi$
$61$	−6.37914			−0.816765			−0.408383	+	0.912811i	$0.633907\pi$
$62$		0			0
$63$	−0.170261	+	0.657999i	−0.0214509	+	0.0829001i
$64$		0			0
$65$	−3.14701	−	1.19329i	−0.390338	−	0.148009i
$66$		0			0
$67$	5.84533	+	5.84533i	0.714120	+	0.714120i	0.967395	−	0.253274i	$-0.0815075\pi$
$67$	5.84533	+	5.84533i	0.714120	+	0.714120i	−0.253274	+	0.967395i	$0.581507\pi$
$68$		0			0
$69$	−0.455475	−	1.67109i	−0.0548327	−	0.201176i
$70$		0			0
$71$			1.93352i			0.229466i	0.993396	+	0.114733i	$0.0366013\pi$
$71$			1.93352i			0.229466i	−0.993396	+	0.114733i	$0.963399\pi$
$72$		0			0
$73$	8.21073	−	8.21073i	0.960993	−	0.960993i	−0.0382743	−	0.999267i	$-0.512186\pi$
$73$	8.21073	−	8.21073i	0.960993	−	0.960993i	0.999267	+	0.0382743i	$0.0121861\pi$
$74$		0			0
$75$	8.20237	−	2.77870i	0.947128	−	0.320856i
$76$		0			0
$77$	−0.371763	+	0.371763i	−0.0423663	+	0.0423663i
$78$		0			0
$79$		−	13.4291i		−	1.51089i	−0.655210	−	0.755447i	$-0.727420\pi$
$79$		−	13.4291i		−	1.51089i	0.655210	−	0.755447i	$-0.272580\pi$
$80$		0			0
$81$	−4.36533	+	7.87044i	−0.485037	+	0.874494i
$82$		0			0
$83$	5.09560	+	5.09560i	0.559315	+	0.559315i	0.929112	−	0.369798i	$-0.120573\pi$
$83$	5.09560	+	5.09560i	0.559315	+	0.559315i	−0.369798	+	0.929112i	$0.620573\pi$
$84$		0			0
$85$	−6.02085	−	2.28299i	−0.653052	−	0.247625i
$86$		0			0
$87$	2.29654	+	1.31278i	0.246215	+	0.140745i
$88$		0			0
$89$	−5.90889			−0.626341			−0.313170	−	0.949697i	$-0.601391\pi$
$89$	−5.90889			−0.626341			−0.313170	+	0.949697i	$0.601391\pi$
$90$		0			0
$91$	0.341005			0.0357471
$92$		0			0
$93$	−4.64401	−	2.65467i	−0.481561	−	0.275276i
$94$		0			0
$95$	16.9006	−	7.60758i	1.73397	−	0.780521i
$96$		0			0
$97$	6.42509	+	6.42509i	0.652369	+	0.652369i	0.953563	−	0.301194i	$-0.0973852\pi$
$97$	6.42509	+	6.42509i	0.652369	+	0.652369i	−0.301194	+	0.953563i	$0.597385\pi$
$98$		0			0
$99$	−5.99899	+	3.53263i	−0.602922	+	0.355042i
$100$		0			0
$101$		−	18.7417i		−	1.86487i	−0.361341	−	0.932434i	$-0.617681\pi$
$101$		−	18.7417i		−	1.86487i	0.361341	−	0.932434i	$-0.382319\pi$
$102$		0			0
$103$	11.6259	−	11.6259i	1.14554	−	1.14554i	0.158116	−	0.987421i	$-0.449458\pi$
$103$	11.6259	−	11.6259i	1.14554	−	1.14554i	0.987421	−	0.158116i	$-0.0505421\pi$
$104$		0			0
$105$	−0.677253	+	0.557897i	−0.0660931	+	0.0544452i
$106$		0			0
$107$	−6.45574	+	6.45574i	−0.624100	+	0.624100i	−0.946577	−	0.322477i	$-0.895485\pi$
$107$	−6.45574	+	6.45574i	−0.624100	+	0.624100i	0.322477	+	0.946577i	$0.395485\pi$
$108$		0			0
$109$			6.64106i			0.636098i	0.948074	+	0.318049i	$0.103028\pi$
$109$			6.64106i			0.636098i	−0.948074	+	0.318049i	$0.896972\pi$
$110$		0			0
$111$	−3.47656	−	12.7551i	−0.329981	−	1.21067i
$112$		0			0
$113$	−1.55947	−	1.55947i	−0.146703	−	0.146703i	0.629941	−	0.776643i	$-0.283079\pi$
$113$	−1.55947	−	1.55947i	−0.146703	−	0.146703i	−0.776643	+	0.629941i	$0.783079\pi$
$114$		0			0
$115$	0.792795	−	2.09081i	0.0739285	−	0.194969i
$116$		0			0
$117$	4.37152	+	1.13116i	0.404147	+	0.104576i
$118$		0			0
$119$	0.652410			0.0598063
$120$		0			0
$121$	5.61473			0.510430
$122$		0			0
$123$	−0.509544	+	0.891382i	−0.0459440	+	0.0803732i
$124$		0			0
$125$	10.6747	+	3.32426i	0.954775	+	0.297331i
$126$		0			0
$127$	6.05397	+	6.05397i	0.537203	+	0.537203i	0.922706	−	0.385503i	$-0.125972\pi$
$127$	6.05397	+	6.05397i	0.537203	+	0.537203i	−0.385503	+	0.922706i	$0.625972\pi$
$128$		0			0
$129$	1.06613	−	0.290585i	0.0938672	−	0.0255846i
$130$		0			0
$131$			19.9691i			1.74471i	0.488872	+	0.872356i	$0.337409\pi$
$131$			19.9691i			1.74471i	−0.488872	+	0.872356i	$0.662591\pi$
$132$		0			0
$133$	−1.32784	+	1.32784i	−0.115138	+	0.115138i
$134$		0			0
$135$	−10.5327	+	4.90543i	−0.906506	+	0.422192i
$136$		0			0
$137$	8.00668	−	8.00668i	0.684057	−	0.684057i	−0.276855	−	0.960912i	$-0.589292\pi$
$137$	8.00668	−	8.00668i	0.684057	−	0.684057i	0.960912	+	0.276855i	$0.0892921\pi$
$138$		0			0
$139$			15.1813i			1.28766i	0.765168	+	0.643831i	$0.222656\pi$
$139$			15.1813i			1.28766i	−0.765168	+	0.643831i	$0.777344\pi$
$140$		0			0
$141$	−9.09190	+	2.47810i	−0.765676	+	0.208694i
$142$		0			0
$143$	2.46986	+	2.46986i	0.206540	+	0.206540i
$144$		0			0
$145$	1.40176	+	3.11409i	0.116410	+	0.258611i
$146$		0			0
$147$	−5.97287	+	10.4488i	−0.492634	+	0.861801i
$148$		0			0
$149$	−2.20101			−0.180314			−0.0901569	−	0.995928i	$-0.528737\pi$
$149$	−2.20101			−0.180314			−0.0901569	+	0.995928i	$0.528737\pi$
$150$		0			0
$151$	−5.26629			−0.428564			−0.214282	−	0.976772i	$-0.568741\pi$
$151$	−5.26629			−0.428564			−0.214282	+	0.976772i	$0.568741\pi$
$152$		0			0
$153$	8.36357	+	2.16413i	0.676155	+	0.174959i
$154$		0			0
$155$	−2.83461	−	6.29723i	−0.227681	−	0.505806i
$156$		0			0
$157$	2.74984	+	2.74984i	0.219461	+	0.219461i	0.808271	−	0.588810i	$-0.200404\pi$
$157$	2.74984	+	2.74984i	0.219461	+	0.219461i	−0.588810	+	0.808271i	$0.700404\pi$
$158$		0			0
$159$	0.357326	+	1.31099i	0.0283378	+	0.103968i
$160$		0			0
$161$			0.226557i			0.0178552i
$162$		0			0
$163$	8.69604	−	8.69604i	0.681126	−	0.681126i	−0.279128	−	0.960254i	$-0.590045\pi$
$163$	8.69604	−	8.69604i	0.681126	−	0.681126i	0.960254	+	0.279128i	$0.0900453\pi$
$164$		0			0
$165$	−8.94604	−	0.864480i	−0.696448	−	0.0672997i
$166$		0			0
$167$	−9.66029	+	9.66029i	−0.747536	+	0.747536i	−0.974016	−	0.226480i	$-0.927278\pi$
$167$	−9.66029	+	9.66029i	−0.747536	+	0.747536i	0.226480	+	0.974016i	$0.427278\pi$
$168$		0			0
$169$			10.7345i			0.825729i
$170$		0			0
$171$	−21.4268	+	12.6176i	−1.63855	+	0.964892i
$172$		0			0
$173$	−7.12709	−	7.12709i	−0.541863	−	0.541863i	0.382212	−	0.924075i	$-0.375162\pi$
$173$	−7.12709	−	7.12709i	−0.541863	−	0.541863i	−0.924075	+	0.382212i	$0.875162\pi$
$174$		0			0
$175$	−1.13071	+	0.0685319i	−0.0854736	+	0.00518053i
$176$		0			0
$177$	−21.4241	−	12.2467i	−1.61033	−	0.920521i
$178$		0			0
$179$	−4.51319			−0.337332			−0.168666	−	0.985673i	$-0.553946\pi$
$179$	−4.51319			−0.337332			−0.168666	+	0.985673i	$0.553946\pi$
$180$		0			0
$181$	10.9846			0.816478			0.408239	−	0.912875i	$-0.366143\pi$
$181$	10.9846			0.816478			0.408239	+	0.912875i	$0.366143\pi$
$182$		0			0
$183$	9.59237	+	5.48332i	0.709088	+	0.405338i
$184$		0			0
$185$	6.05127	−	15.9588i	0.444898	−	1.17331i
$186$		0			0
$187$	4.72533	+	4.72533i	0.345550	+	0.345550i
$188$		0			0
$189$	0.821620	−	0.843088i	0.0597641	−	0.0613256i
$190$		0			0
$191$			6.74055i			0.487729i	0.969809	+	0.243865i	$0.0784153\pi$
$191$			6.74055i			0.487729i	−0.969809	+	0.243865i	$0.921585\pi$
$192$		0			0
$193$	−3.40754	+	3.40754i	−0.245280	+	0.245280i	−0.819030	−	0.573750i	$-0.805488\pi$
$193$	−3.40754	+	3.40754i	−0.245280	+	0.245280i	0.573750	+	0.819030i	$0.305488\pi$
$194$		0			0
$195$	3.70647	+	4.49943i	0.265426	+	0.322211i
$196$		0			0
$197$	10.0935	−	10.0935i	0.719129	−	0.719129i	−0.249298	−	0.968427i	$-0.580200\pi$
$197$	10.0935	−	10.0935i	0.719129	−	0.719129i	0.968427	+	0.249298i	$0.0801998\pi$
$198$		0			0
$199$			5.10188i			0.361663i	0.983514	+	0.180831i	$0.0578788\pi$
$199$			5.10188i			0.361663i	−0.983514	+	0.180831i	$0.942121\pi$
$200$		0			0
$201$	−3.76520	−	13.8141i	−0.265577	−	0.974374i
$202$		0			0
$203$	−0.244666	−	0.244666i	−0.0171722	−	0.0171722i
$204$		0			0
$205$	−1.20871	+	0.544082i	−0.0844197	+	0.0380003i
$206$		0			0
$207$	−0.751518	+	2.90435i	−0.0522341	+	0.201866i
$208$		0			0
$209$	−19.2347			−1.33049
$210$		0			0
$211$	−9.59739			−0.660711			−0.330356	−	0.943857i	$-0.607169\pi$
$211$	−9.59739			−0.660711			−0.330356	+	0.943857i	$0.607169\pi$
$212$		0			0
$213$	1.66199	−	2.90745i	0.113878	−	0.199215i
$214$		0			0
$215$	1.33390	+	0.505789i	0.0909711	+	0.0344945i
$216$		0			0
$217$	0.494757	+	0.494757i	0.0335863	+	0.0335863i
$218$		0			0
$219$	−19.4042	+	5.28885i	−1.31122	+	0.357387i
$220$		0			0
$221$		−	4.33438i		−	0.291562i
$222$		0			0
$223$	7.49983	−	7.49983i	0.502226	−	0.502226i	−0.409903	−	0.912129i	$-0.634438\pi$
$223$	7.49983	−	7.49983i	0.502226	−	0.502226i	0.912129	+	0.409903i	$0.134438\pi$
$224$		0			0
$225$	−14.7225	−	2.87216i	−0.981497	−	0.191477i
$226$		0			0
$227$	−13.3968	+	13.3968i	−0.889176	+	0.889176i	−0.994444	−	0.105268i	$-0.966430\pi$
$227$	−13.3968	+	13.3968i	−0.889176	+	0.889176i	0.105268	+	0.994444i	$0.466430\pi$
$228$		0			0
$229$		−	0.224039i		−	0.0148049i	−0.999973	−	0.00740247i	$-0.997644\pi$
$229$		−	0.224039i		−	0.0148049i	0.999973	−	0.00740247i	$-0.00235630\pi$
$230$		0			0
$231$	0.878579	−	0.239467i	0.0578062	−	0.0157558i
$232$		0			0
$233$	−17.0106	−	17.0106i	−1.11440	−	1.11440i	−0.992548	−	0.121851i	$-0.961117\pi$
$233$	−17.0106	−	17.0106i	−1.11440	−	1.11440i	−0.121851	−	0.992548i	$-0.538883\pi$
$234$		0			0
$235$	−11.3755	−	4.31336i	−0.742053	−	0.281372i
$236$		0			0
$237$	−11.5433	+	20.1935i	−0.749815	+	1.31171i
$238$		0			0
$239$	27.5881			1.78453			0.892264	−	0.451514i	$-0.149116\pi$
$239$	27.5881			1.78453			0.892264	+	0.451514i	$0.149116\pi$
$240$		0			0
$241$	24.6774			1.58961			0.794806	−	0.606864i	$-0.207573\pi$
$241$	24.6774			1.58961			0.794806	+	0.606864i	$0.207573\pi$
$242$		0			0
$243$	13.3294	−	8.08254i	0.855080	−	0.518495i
$244$		0			0
$245$	−14.1684	+	6.37773i	−0.905189	+	0.407458i
$246$		0			0
$247$	8.82168	+	8.82168i	0.561310	+	0.561310i
$248$		0			0
$249$	−3.28227	−	12.0423i	−0.208006	−	0.763151i
$250$		0			0
$251$			6.61434i			0.417494i	0.977970	+	0.208747i	$0.0669384\pi$
$251$			6.61434i			0.417494i	−0.977970	+	0.208747i	$0.933062\pi$
$252$		0			0
$253$	−1.64092	+	1.64092i	−0.103164	+	0.103164i
$254$		0			0
$255$	7.09121	+	8.60829i	0.444069	+	0.539072i
$256$		0			0
$257$	−6.63141	+	6.63141i	−0.413656	+	0.413656i	−0.883010	−	0.469354i	$-0.844487\pi$
$257$	−6.63141	+	6.63141i	−0.413656	+	0.413656i	0.469354	+	0.883010i	$0.344487\pi$
$258$		0			0
$259$			1.72927i			0.107452i
$260$		0			0
$261$	−2.32490	−	3.94808i	−0.143908	−	0.244380i
$262$		0			0
$263$	−16.3074	−	16.3074i	−1.00556	−	1.00556i	−0.999984	−	0.00557497i	$-0.998225\pi$
$263$	−16.3074	−	16.3074i	−1.00556	−	1.00556i	−0.00557497	−	0.999984i	$-0.501775\pi$
$264$		0			0
$265$	−0.621958	+	1.64027i	−0.0382066	+	0.100761i
$266$		0			0
$267$	8.88525	+	5.07910i	0.543768	+	0.310836i
$268$		0			0
$269$	−27.0433			−1.64886			−0.824430	−	0.565965i	$-0.808504\pi$
$269$	−27.0433			−1.64886			−0.824430	+	0.565965i	$0.808504\pi$
$270$		0			0
$271$	−21.9196			−1.33152			−0.665760	−	0.746166i	$-0.731893\pi$
$271$	−21.9196			−1.33152			−0.665760	+	0.746166i	$0.731893\pi$
$272$		0			0
$273$	−0.512773	−	0.293118i	−0.0310344	−	0.0177403i
$274$		0			0
$275$	−8.68596	−	7.69322i	−0.523783	−	0.463919i
$276$		0			0
$277$	−0.349561	−	0.349561i	−0.0210031	−	0.0210031i	0.696527	−	0.717530i	$-0.254728\pi$
$277$	−0.349561	−	0.349561i	−0.0210031	−	0.0210031i	−0.717530	+	0.696527i	$0.754728\pi$
$278$		0			0
$279$	4.70136	+	7.98370i	0.281463	+	0.477972i
$280$		0			0
$281$			16.5284i			0.986000i	0.870029	+	0.493000i	$0.164100\pi$
$281$			16.5284i			0.986000i	−0.870029	+	0.493000i	$0.835900\pi$
$282$		0			0
$283$	7.99555	−	7.99555i	0.475286	−	0.475286i	−0.428334	−	0.903620i	$-0.640899\pi$
$283$	7.99555	−	7.99555i	0.475286	−	0.475286i	0.903620	+	0.428334i	$0.140899\pi$
$284$		0			0
$285$	−31.9529	−	3.08769i	−1.89272	−	0.182899i
$286$		0			0
$287$	0.0949647	−	0.0949647i	0.00560559	−	0.00560559i
$288$		0			0
$289$			8.70747i			0.512204i
$290$		0			0
$291$	−4.13865	−	15.1843i	−0.242612	−	0.890118i
$292$		0			0
$293$	12.2257	+	12.2257i	0.714232	+	0.714232i	0.967418	−	0.253186i	$-0.0814784\pi$
$293$	12.2257	+	12.2257i	0.714232	+	0.714232i	−0.253186	+	0.967418i	$0.581478\pi$
$294$		0			0
$295$	−13.0769	−	29.0509i	−0.761364	−	1.69141i
$296$		0			0
$297$	12.0573	−	0.155487i	0.699634	−	0.00902228i
$298$		0			0
$299$	1.50516			0.0870459
$300$		0			0
$301$	−0.144539			−0.00833111
$302$		0			0
$303$	−16.1098	+	28.1820i	−0.925483	+	1.61902i
$304$		0			0
$305$	5.85499	+	13.0072i	0.335256	+	0.744788i
$306$		0			0
$307$	0.646841	+	0.646841i	0.0369172	+	0.0369172i	0.725324	−	0.688407i	$-0.241690\pi$
$307$	0.646841	+	0.646841i	0.0369172	+	0.0369172i	−0.688407	+	0.725324i	$0.741690\pi$
$308$		0			0
$309$	−27.4753	+	7.48871i	−1.56302	+	0.426018i
$310$		0			0
$311$			21.0128i			1.19153i	0.803159	+	0.595765i	$0.203151\pi$
$311$			21.0128i			1.19153i	−0.803159	+	0.595765i	$0.796849\pi$
$312$		0			0
$313$	22.1298	−	22.1298i	1.25085	−	1.25085i	0.295514	−	0.955338i	$-0.404509\pi$
$313$	22.1298	−	22.1298i	1.25085	−	1.25085i	0.955338	−	0.295514i	$-0.0954909\pi$
$314$		0			0
$315$	1.49794	−	0.256768i	0.0843995	−	0.0144673i
$316$		0			0
$317$	−9.69442	+	9.69442i	−0.544493	+	0.544493i	−0.924843	−	0.380350i	$-0.875804\pi$
$317$	−9.69442	+	9.69442i	−0.544493	+	0.544493i	0.380350	+	0.924843i	$0.375804\pi$
$318$		0			0
$319$		−	3.54417i		−	0.198435i
$320$		0			0
$321$	15.2567	−	4.15839i	0.851547	−	0.232099i
$322$		0			0
$323$	16.8776	+	16.8776i	0.939095	+	0.939095i
$324$		0			0
$325$	0.455302	+	7.51203i	0.0252556	+	0.416693i
$326$		0			0
$327$	5.70846	−	9.98622i	0.315678	−	0.552239i
$328$		0			0
$329$	1.23263			0.0679570
$330$		0			0
$331$	17.5470			0.964469			0.482235	−	0.876042i	$-0.339825\pi$
$331$	17.5470			0.964469			0.482235	+	0.876042i	$0.339825\pi$
$332$		0			0
$333$	−5.73621	+	22.1684i	−0.314342	+	1.21482i
$334$		0			0
$335$	6.55367	−	17.2837i	0.358065	−	0.944312i
$336$		0			0
$337$	−14.6849	−	14.6849i	−0.799935	−	0.799935i	0.183150	−	0.983085i	$-0.441371\pi$
$337$	−14.6849	−	14.6849i	−0.799935	−	0.799935i	−0.983085	+	0.183150i	$0.941371\pi$
$338$		0			0
$339$	1.00452	+	3.68547i	0.0545578	+	0.200167i
$340$		0			0
$341$			7.16692i			0.388111i
$342$		0			0
$343$	2.23458	−	2.23458i	0.120656	−	0.120656i
$344$		0			0
$345$	−2.98933	+	2.46250i	−0.160940	+	0.132577i
$346$		0			0
$347$	−11.6055	+	11.6055i	−0.623014	+	0.623014i	−0.946301	−	0.323287i	$-0.895212\pi$
$347$	−11.6055	+	11.6055i	−0.623014	+	0.623014i	0.323287	+	0.946301i	$0.395212\pi$
$348$		0			0
$349$			9.75994i			0.522438i	0.965280	+	0.261219i	$0.0841244\pi$
$349$			9.75994i			0.522438i	−0.965280	+	0.261219i	$0.915876\pi$
$350$		0			0
$351$	−5.60118	−	5.45855i	−0.298969	−	0.291356i
$352$		0			0
$353$	−6.09303	−	6.09303i	−0.324299	−	0.324299i	0.526114	−	0.850414i	$-0.323648\pi$
$353$	−6.09303	−	6.09303i	−0.324299	−	0.324299i	−0.850414	+	0.526114i	$0.823648\pi$
$354$		0			0
$355$	3.94247	−	1.77465i	0.209245	−	0.0941885i
$356$		0			0
$357$	−0.981035	−	0.560792i	−0.0519219	−	0.0296803i
$358$		0			0
$359$	16.9746			0.895885			0.447943	−	0.894062i	$-0.352157\pi$
$359$	16.9746			0.895885			0.447943	+	0.894062i	$0.352157\pi$
$360$		0			0
$361$	−49.7013			−2.61586
$362$		0			0
$363$	−8.44292	−	4.82626i	−0.443139	−	0.253313i
$364$		0			0
$365$	−24.2779	−	9.20571i	−1.27076	−	0.481849i
$366$		0			0
$367$	3.46834	+	3.46834i	0.181046	+	0.181046i	0.791811	−	0.610766i	$-0.209138\pi$
$367$	3.46834	+	3.46834i	0.181046	+	0.181046i	−0.610766	+	0.791811i	$0.709138\pi$
$368$		0			0
$369$	1.53241	−	0.902390i	0.0797741	−	0.0469766i
$370$		0			0
$371$		−	0.177737i		−	0.00922763i
$372$		0			0
$373$	14.0107	−	14.0107i	0.725445	−	0.725445i	−0.244264	−	0.969709i	$-0.578546\pi$
$373$	14.0107	−	14.0107i	0.725445	−	0.725445i	0.969709	+	0.244264i	$0.0785462\pi$
$374$		0			0
$375$	−13.1942	−	14.1744i	−0.681346	−	0.731961i
$376$		0			0
$377$	−1.62547	+	1.62547i	−0.0837161	+	0.0837161i
$378$		0			0
$379$			23.1503i			1.18915i	0.804040	+	0.594575i	$0.202680\pi$
$379$			23.1503i			1.18915i	−0.804040	+	0.594575i	$0.797320\pi$
$380$		0			0
$381$	−3.89960	−	14.3072i	−0.199782	−	0.732981i
$382$		0			0
$383$	2.21743	+	2.21743i	0.113305	+	0.113305i	0.761486	−	0.648181i	$-0.224470\pi$
$383$	2.21743	+	2.21743i	0.113305	+	0.113305i	−0.648181	+	0.761486i	$0.724470\pi$
$384$		0			0
$385$	1.09925	+	0.416813i	0.0560228	+	0.0212428i
$386$		0			0
$387$	−1.85292	−	0.479455i	−0.0941893	−	0.0243721i
$388$		0			0
$389$	1.76669			0.0895746			0.0447873	−	0.998997i	$-0.485739\pi$
$389$	1.76669			0.0895746			0.0447873	+	0.998997i	$0.485739\pi$
$390$		0			0
$391$	2.87967			0.145631
$392$		0			0
$393$	17.1649	−	30.0278i	0.865853	−	1.51470i
$394$		0			0
$395$	−27.3822	+	12.3257i	−1.37775	+	0.620173i
$396$		0			0
$397$	21.3465	+	21.3465i	1.07135	+	1.07135i	0.997251	+	0.0741015i	$0.0236089\pi$
$397$	21.3465	+	21.3465i	1.07135	+	1.07135i	0.0741015	+	0.997251i	$0.476391\pi$
$398$		0			0
$399$	3.13805	−	0.855311i	0.157099	−	0.0428191i
$400$		0			0
$401$			26.8871i			1.34268i	0.741150	+	0.671340i	$0.234281\pi$
$401$			26.8871i			1.34268i	−0.741150	+	0.671340i	$0.765719\pi$
$402$		0			0
$403$	3.28699	−	3.28699i	0.163737	−	0.163737i
$404$		0			0
$405$	20.0546	+	1.67722i	0.996521	+	0.0833418i
$406$		0			0
$407$	−12.5249	+	12.5249i	−0.620836	+	0.620836i
$408$		0			0
$409$		−	3.26604i		−	0.161495i	−0.996735	−	0.0807477i	$-0.974269\pi$
$409$		−	3.26604i		−	0.161495i	0.996735	−	0.0807477i	$-0.0257308\pi$
$410$		0			0
$411$	−18.9220	+	5.15741i	−0.933355	+	0.254397i
$412$		0			0
$413$	2.28245	+	2.28245i	0.112312	+	0.112312i
$414$		0			0
$415$	5.71309	−	15.0669i	0.280445	−	0.739606i
$416$		0			0
$417$	13.0494	−	22.8283i	0.639032	−	1.11791i
$418$		0			0
$419$	−7.88774			−0.385341			−0.192671	−	0.981263i	$-0.561715\pi$
$419$	−7.88774			−0.385341			−0.192671	+	0.981263i	$0.561715\pi$
$420$		0			0
$421$	23.1728			1.12937			0.564686	−	0.825306i	$-0.308997\pi$
$421$	23.1728			1.12937			0.564686	+	0.825306i	$0.308997\pi$
$422$		0			0
$423$	15.8017	+	4.08878i	0.768304	+	0.198803i
$424$		0			0
$425$	0.871082	+	14.3720i	0.0422537	+	0.697144i
$426$		0			0
$427$	−1.02194	−	1.02194i	−0.0494550	−	0.0494550i
$428$		0			0
$429$	−1.59093	−	5.83697i	−0.0768109	−	0.281811i
$430$		0			0
$431$		−	26.8355i		−	1.29262i	−0.763074	−	0.646311i	$-0.776311\pi$
$431$		−	26.8355i		−	1.29262i	0.763074	−	0.646311i	$-0.223689\pi$
$432$		0			0
$433$	4.39267	−	4.39267i	0.211098	−	0.211098i	−0.593636	−	0.804734i	$-0.702308\pi$
$433$	4.39267	−	4.39267i	0.211098	−	0.211098i	0.804734	+	0.593636i	$0.202308\pi$
$434$		0			0
$435$	0.568934	−	5.88760i	0.0272783	−	0.282289i
$436$		0			0
$437$	−5.86094	+	5.86094i	−0.280367	+	0.280367i
$438$		0			0
$439$			18.6937i			0.892203i	0.894982	+	0.446101i	$0.147188\pi$
$439$			18.6937i			0.892203i	−0.894982	+	0.446101i	$0.852812\pi$
$440$		0			0
$441$	17.9629	−	10.5778i	0.855377	−	0.503706i
$442$		0			0
$443$	8.70615	+	8.70615i	0.413642	+	0.413642i	0.883005	−	0.469363i	$-0.155517\pi$
$443$	8.70615	+	8.70615i	0.413642	+	0.413642i	−0.469363	+	0.883005i	$0.655517\pi$
$444$		0			0
$445$	5.42338	+	12.0483i	0.257093	+	0.571145i
$446$		0			0
$447$	3.30968	+	1.89192i	0.156542	+	0.0894849i
$448$		0			0
$449$	22.4799			1.06089			0.530446	−	0.847719i	$-0.322024\pi$
$449$	22.4799			1.06089			0.530446	+	0.847719i	$0.322024\pi$
$450$		0			0
$451$	1.37564			0.0647762
$452$		0			0
$453$	7.91896	+	4.52674i	0.372065	+	0.212685i
$454$		0			0
$455$	−0.312986	−	0.695315i	−0.0146730	−	0.0325969i
$456$		0			0
$457$	−13.9338	−	13.9338i	−0.651797	−	0.651797i	0.301629	−	0.953425i	$-0.402470\pi$
$457$	−13.9338	−	13.9338i	−0.651797	−	0.651797i	−0.953425	+	0.301629i	$0.902470\pi$
$458$		0			0
$459$	−10.7162	−	10.4433i	−0.500187	−	0.487451i
$460$		0			0
$461$		−	22.2377i		−	1.03571i	−0.855467	−	0.517857i	$-0.826730\pi$
$461$		−	22.2377i		−	1.03571i	0.855467	−	0.517857i	$-0.173270\pi$
$462$		0			0
$463$	−13.7274	+	13.7274i	−0.637966	+	0.637966i	−0.950053	−	0.312087i	$-0.898972\pi$
$463$	−13.7274	+	13.7274i	−0.637966	+	0.637966i	0.312087	+	0.950053i	$0.398972\pi$
$464$		0			0
$465$	−1.15048	+	11.9057i	−0.0533524	+	0.552116i
$466$		0			0
$467$	−13.5191	+	13.5191i	−0.625591	+	0.625591i	−0.946955	−	0.321365i	$-0.895858\pi$
$467$	−13.5191	+	13.5191i	−0.625591	+	0.625591i	0.321365	+	0.946955i	$0.395858\pi$
$468$		0			0
$469$			1.87284i			0.0864798i
$470$		0			0
$471$	−1.77128	−	6.49863i	−0.0816161	−	0.299441i
$472$		0			0
$473$	−1.04688	−	1.04688i	−0.0481356	−	0.0481356i
$474$		0			0
$475$	−31.0239	−	27.4781i	−1.42348	−	1.26078i
$476$		0			0
$477$	0.589575	−	2.27850i	0.0269948	−	0.104325i
$478$		0			0
$479$	2.63498			0.120395			0.0601977	−	0.998186i	$-0.480827\pi$
$479$	2.63498			0.120395			0.0601977	+	0.998186i	$0.480827\pi$
$480$		0			0
$481$	11.4887			0.523838
$482$		0			0
$483$	0.194741	−	0.340676i	0.00886104	−	0.0155013i
$484$		0			0
$485$	7.20369	−	18.9980i	0.327103	−	0.862655i
$486$		0			0
$487$	−3.37584	−	3.37584i	−0.152974	−	0.152974i	0.626471	−	0.779445i	$-0.284499\pi$
$487$	−3.37584	−	3.37584i	−0.152974	−	0.152974i	−0.779445	+	0.626471i	$0.784499\pi$
$488$		0			0
$489$	−20.5512	+	5.60145i	−0.929355	+	0.253306i
$490$		0			0
$491$		−	14.6816i		−	0.662573i	−0.943530	−	0.331286i	$-0.892517\pi$
$491$		−	14.6816i		−	0.662573i	0.943530	−	0.331286i	$-0.107483\pi$
$492$		0			0
$493$	−3.10985	+	3.10985i	−0.140060	+	0.140060i
$494$		0			0
$495$	12.7092	+	8.98967i	0.571234	+	0.404056i
$496$		0			0
$497$	−0.309749	+	0.309749i	−0.0138942	+	0.0138942i
$498$		0			0
$499$		−	18.2067i		−	0.815042i	−0.913196	−	0.407521i	$-0.866393\pi$
$499$		−	18.2067i		−	0.815042i	0.913196	−	0.407521i	$-0.133607\pi$
$500$		0			0
$501$	22.8300	−	6.22257i	1.01997	−	0.278004i
$502$		0			0
$503$	24.0238	+	24.0238i	1.07117	+	1.07117i	0.997266	+	0.0739006i	$0.0235448\pi$
$503$	24.0238	+	24.0238i	1.07117	+	1.07117i	0.0739006	+	0.997266i	$0.476455\pi$
$504$		0			0
$505$	−38.2146	+	17.2017i	−1.70053	+	0.765468i
$506$		0			0
$507$	9.22704	−	16.1415i	0.409787	−	0.716871i
$508$		0			0
$509$	4.98907			0.221137			0.110568	−	0.993869i	$-0.464733\pi$
$509$	4.98907			0.221137			0.110568	+	0.993869i	$0.464733\pi$
$510$		0			0
$511$	2.63072			0.116376
$512$		0			0
$513$	43.0654	−	0.555359i	1.90138	−	0.0245197i
$514$		0			0
$515$	−34.3761	−	13.0348i	−1.51479	−	0.574381i
$516$		0			0
$517$	8.92778	+	8.92778i	0.392643	+	0.392643i
$518$		0			0
$519$	4.59083	+	16.8433i	0.201515	+	0.739339i
$520$		0			0
$521$		−	14.7307i		−	0.645363i	−0.946508	−	0.322682i	$-0.895416\pi$
$521$		−	14.7307i		−	0.645363i	0.946508	−	0.322682i	$-0.104584\pi$
$522$		0			0
$523$	9.26618	−	9.26618i	0.405182	−	0.405182i	−0.474873	−	0.880055i	$-0.657506\pi$
$523$	9.26618	−	9.26618i	0.405182	−	0.405182i	0.880055	+	0.474873i	$0.157506\pi$
$524$		0			0
$525$	1.75917	+	0.868872i	0.0767763	+	0.0379207i
$526$		0			0
$527$	6.28865	−	6.28865i	0.273938	−	0.273938i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$		0			0
$531$	21.6887	+	36.8310i	0.941209	+	1.59833i
$532$		0			0
$533$	−0.630912	−	0.630912i	−0.0273278	−	0.0273278i
$534$		0			0
$535$	19.0887	+	7.23806i	0.825275	+	0.312929i
$536$		0			0
$537$	6.78653	+	3.87941i	0.292860	+	0.167409i
$538$		0			0
$539$	16.1252			0.694562
$540$		0			0
$541$	22.4091			0.963442			0.481721	−	0.876325i	$-0.340012\pi$
$541$	22.4091			0.963442			0.481721	+	0.876325i	$0.340012\pi$
$542$		0			0
$543$	−16.5176	−	9.44202i	−0.708839	−	0.405196i
$544$		0			0
$545$	13.5412	−	6.09539i	0.580042	−	0.261098i
$546$		0			0
$547$	−20.1655	−	20.1655i	−0.862217	−	0.862217i	0.129379	−	0.991595i	$-0.458702\pi$
$547$	−20.1655	−	20.1655i	−0.862217	−	0.862217i	−0.991595	+	0.129379i	$0.958702\pi$
$548$		0			0
$549$	−9.71083	−	16.4906i	−0.414448	−	0.703803i
$550$		0			0
$551$		−	12.6588i		−	0.539284i
$552$		0			0
$553$	2.15134	−	2.15134i	0.0914844	−	0.0914844i
$554$		0			0
$555$	−22.8170	+	18.7959i	−0.968529	+	0.797840i
$556$		0			0
$557$	7.49536	−	7.49536i	0.317588	−	0.317588i	−0.530252	−	0.847840i	$-0.677903\pi$
$557$	7.49536	−	7.49536i	0.317588	−	0.317588i	0.847840	+	0.530252i	$0.177903\pi$
$558$		0			0
$559$			0.960268i			0.0406150i
$560$		0			0
$561$	−3.04377	−	11.1673i	−0.128508	−	0.471482i
$562$		0			0
$563$	−5.66571	−	5.66571i	−0.238781	−	0.238781i	0.577564	−	0.816345i	$-0.304003\pi$
$563$	−5.66571	−	5.66571i	−0.238781	−	0.238781i	−0.816345	+	0.577564i	$0.804003\pi$
$564$		0			0
$565$	−1.74845	+	4.61112i	−0.0735579	+	0.193991i
$566$		0			0
$567$	−1.96017	+	0.561518i	−0.0823194	+	0.0235816i
$568$		0			0
$569$	24.3269			1.01984			0.509918	−	0.860223i	$-0.329676\pi$
$569$	24.3269			1.01984			0.509918	+	0.860223i	$0.329676\pi$
$570$		0			0
$571$	−20.4910			−0.857523			−0.428762	−	0.903418i	$-0.641050\pi$
$571$	−20.4910			−0.857523			−0.428762	+	0.903418i	$0.641050\pi$
$572$		0			0
$573$	5.79398	−	10.1358i	0.242047	−	0.423430i
$574$		0			0
$575$	−4.99084	+	0.302493i	−0.208132	+	0.0126148i
$576$		0			0
$577$	7.90752	+	7.90752i	0.329194	+	0.329194i	0.852280	−	0.523086i	$-0.175219\pi$
$577$	7.90752	+	7.90752i	0.329194	+	0.329194i	−0.523086	+	0.852280i	$0.675219\pi$
$578$		0			0
$579$	8.05297	−	2.19493i	0.334670	−	0.0912182i
$580$		0			0
$581$			1.63263i			0.0677329i
$582$		0			0
$583$	1.28733	−	1.28733i	0.0533156	−	0.0533156i
$584$		0			0
$585$	−1.70588	−	9.95180i	−0.0705294	−	0.411456i
$586$		0			0
$587$	0.463881	−	0.463881i	0.0191464	−	0.0191464i	−0.697469	−	0.716615i	$-0.745690\pi$
$587$	0.463881	−	0.463881i	0.0191464	−	0.0191464i	0.716615	+	0.697469i	$0.245690\pi$
$588$		0			0
$589$			25.5983i			1.05476i
$590$		0			0
$591$	−23.8537	+	6.50159i	−0.981208	+	0.267440i
$592$		0			0
$593$	13.2382	+	13.2382i	0.543628	+	0.543628i	0.924591	−	0.380962i	$-0.124407\pi$
$593$	13.2382	+	13.2382i	0.543628	+	0.543628i	−0.380962	+	0.924591i	$0.624407\pi$
$594$		0			0
$595$	−0.598804	−	1.33027i	−0.0245486	−	0.0545359i
$596$		0			0
$597$	4.38542	−	7.67174i	0.179483	−	0.313983i
$598$		0			0
$599$	29.4399			1.20288			0.601441	−	0.798917i	$-0.294593\pi$
$599$	29.4399			1.20288			0.601441	+	0.798917i	$0.294593\pi$
$600$		0			0
$601$	−2.16334			−0.0882444			−0.0441222	−	0.999026i	$-0.514049\pi$
$601$	−2.16334			−0.0882444			−0.0441222	+	0.999026i	$0.514049\pi$
$602$		0			0
$603$	−6.21245	+	24.0089i	−0.252991	+	0.977717i
$604$		0			0
$605$	−5.15339	−	11.4485i	−0.209515	−	0.465449i
$606$		0			0
$607$	−17.0993	−	17.0993i	−0.694038	−	0.694038i	0.269080	−	0.963118i	$-0.413281\pi$
$607$	−17.0993	−	17.0993i	−0.694038	−	0.694038i	−0.963118	+	0.269080i	$0.913281\pi$
$608$		0			0
$609$	0.157599	+	0.578213i	0.00638622	+	0.0234304i
$610$		0			0
$611$		−	8.18915i		−	0.331297i
$612$		0			0
$613$	−29.1024	+	29.1024i	−1.17543	+	1.17543i	−0.194539	+	0.980895i	$0.562321\pi$
$613$	−29.1024	+	29.1024i	−1.17543	+	1.17543i	−0.980895	+	0.194539i	$0.937679\pi$
$614$		0			0
$615$	2.28522	+	0.220827i	0.0921488	+	0.00890459i
$616$		0			0
$617$	−24.5147	+	24.5147i	−0.986924	+	0.986924i	−0.999916	−	0.0129915i	$-0.995865\pi$
$617$	−24.5147	+	24.5147i	−0.986924	+	0.986924i	0.0129915	+	0.999916i	$0.495865\pi$
$618$		0			0
$619$		−	28.5313i		−	1.14677i	−0.819287	−	0.573384i	$-0.805630\pi$
$619$		−	28.5313i		−	1.14677i	0.819287	−	0.573384i	$-0.194370\pi$
$620$		0			0
$621$	3.62655	−	3.72131i	0.145528	−	0.149331i
$622$		0			0
$623$	−0.946603	−	0.946603i	−0.0379249	−	0.0379249i
$624$		0			0
$625$	−3.01939	−	24.8170i	−0.120776	−	0.992680i
$626$		0			0
$627$	28.9234	+	16.5336i	1.15509	+	0.660288i
$628$		0			0
$629$	21.9801			0.876403
$630$		0			0
$631$	−5.53607			−0.220388			−0.110194	−	0.993910i	$-0.535147\pi$
$631$	−5.53607			−0.220388			−0.110194	+	0.993910i	$0.535147\pi$
$632$		0			0
$633$	14.4317	+	8.24962i	0.573607	+	0.327893i
$634$		0			0
$635$	6.78760	−	17.9007i	0.269358	−	0.710366i
$636$		0			0
$637$	−7.39555	−	7.39555i	−0.293022	−	0.293022i
$638$		0			0
$639$	−4.99831	+	2.94335i	−0.197730	+	0.116437i
$640$		0			0
$641$		−	9.25545i		−	0.365568i	−0.983153	−	0.182784i	$-0.941489\pi$
$641$		−	9.25545i		−	0.365568i	0.983153	−	0.182784i	$-0.0585109\pi$
$642$		0			0
$643$	9.69460	−	9.69460i	0.382318	−	0.382318i	−0.489619	−	0.871937i	$-0.662864\pi$
$643$	9.69460	−	9.69460i	0.382318	−	0.382318i	0.871937	+	0.489619i	$0.162864\pi$
$644$		0			0
$645$	−1.57103	−	1.90714i	−0.0618594	−	0.0750935i
$646$		0			0
$647$	15.5355	−	15.5355i	0.610765	−	0.610765i	−0.332380	−	0.943146i	$-0.607852\pi$
$647$	15.5355	−	15.5355i	0.610765	−	0.610765i	0.943146	+	0.332380i	$0.107852\pi$
$648$		0			0
$649$			33.0630i			1.29784i
$650$		0			0
$651$	−0.318692	−	1.16925i	−0.0124905	−	0.0458264i
$652$		0			0
$653$	13.4416	+	13.4416i	0.526010	+	0.526010i	0.919380	−	0.393370i	$-0.128691\pi$
$653$	13.4416	+	13.4416i	0.526010	+	0.526010i	−0.393370	+	0.919380i	$0.628691\pi$
$654$		0			0
$655$	40.7174	−	18.3283i	1.59096	−	0.716148i
$656$		0			0
$657$	33.7245	+	8.72641i	1.31572	+	0.340450i
$658$		0			0
$659$	3.36957			0.131260			0.0656298	−	0.997844i	$-0.479094\pi$
$659$	3.36957			0.131260			0.0656298	+	0.997844i	$0.479094\pi$
$660$		0			0
$661$	−16.3326			−0.635266			−0.317633	−	0.948214i	$-0.602888\pi$
$661$	−16.3326			−0.635266			−0.317633	+	0.948214i	$0.602888\pi$
$662$		0			0
$663$	−3.72570	+	6.51765i	−0.144694	+	0.253124i
$664$		0			0
$665$	3.92621	+	1.48875i	0.152252	+	0.0577311i
$666$		0			0
$667$	−1.07993	−	1.07993i	−0.0418151	−	0.0418151i
$668$		0			0
$669$	−17.7242	+	4.83093i	−0.685257	+	0.186775i
$670$		0			0
$671$		−	14.8035i		−	0.571485i
$672$		0			0
$673$	7.55800	−	7.55800i	0.291339	−	0.291339i	−0.546270	−	0.837609i	$-0.683953\pi$
$673$	7.55800	−	7.55800i	0.291339	−	0.291339i	0.837609	+	0.546270i	$0.183953\pi$
$674$		0			0
$675$	19.6695	+	16.9739i	0.757078	+	0.653325i
$676$		0			0
$677$	−13.1910	+	13.1910i	−0.506972	+	0.506972i	−0.913596	−	0.406624i	$-0.866706\pi$
$677$	−13.1910	+	13.1910i	−0.506972	+	0.506972i	0.406624	+	0.913596i	$0.366706\pi$
$678$		0			0
$679$			2.05860i			0.0790017i
$680$		0			0
$681$	31.6603	−	8.62939i	1.21323	−	0.330679i
$682$		0			0
$683$	−34.1337	−	34.1337i	−1.30609	−	1.30609i	−0.924213	−	0.381878i	$-0.875277\pi$
$683$	−34.1337	−	34.1337i	−1.30609	−	1.30609i	−0.381878	−	0.924213i	$-0.624723\pi$
$684$		0			0
$685$	−23.6746	−	8.97694i	−0.904558	−	0.342991i
$686$		0			0
$687$	−0.192578	+	0.336890i	−0.00734729	+	0.0128532i
$688$		0			0
$689$	−1.18082			−0.0449857
$690$		0			0
$691$	−34.5975			−1.31615			−0.658075	−	0.752952i	$-0.728629\pi$
$691$	−34.5975			−1.31615			−0.658075	+	0.752952i	$0.728629\pi$
$692$		0			0
$693$	−1.52697	−	0.395112i	−0.0580046	−	0.0150091i
$694$		0			0
$695$	30.9549	−	13.9339i	1.17419	−	0.528544i
$696$		0			0
$697$	−1.20706	−	1.20706i	−0.0457206	−	0.0457206i
$698$		0			0
$699$	10.9572	+	40.2007i	0.414438	+	1.52053i
$700$		0			0
$701$		−	14.5324i		−	0.548880i	−0.961604	−	0.274440i	$-0.911508\pi$
$701$		−	14.5324i		−	0.548880i	0.961604	−	0.274440i	$-0.0884924\pi$
$702$		0			0
$703$	−44.7356	+	44.7356i	−1.68723	+	1.68723i
$704$		0			0
$705$	13.3977	+	16.2640i	0.504588	+	0.612539i
$706$		0			0
$707$	3.00242	−	3.00242i	0.112917	−	0.112917i
$708$		0			0
$709$			25.4970i			0.957562i	0.877934	+	0.478781i	$0.158921\pi$
$709$			25.4970i			0.957562i	−0.877934	+	0.478781i	$0.841079\pi$
$710$		0			0
$711$	34.7154	−	20.4429i	1.30193	−	0.766667i
$712$		0			0
$713$	2.18381	+	2.18381i	0.0817842	+	0.0817842i
$714$		0			0
$715$	2.76916	−	7.30300i	0.103561	−	0.273117i
$716$		0			0
$717$	−41.4845	−	23.7139i	−1.54927	−	0.885613i
$718$		0			0
$719$	22.1387			0.825633			0.412816	−	0.910814i	$-0.364545\pi$
$719$	22.1387			0.825633			0.412816	+	0.910814i	$0.364545\pi$
$720$		0			0
$721$	3.72495			0.138724
$722$		0			0
$723$	−37.1076	−	21.2120i	−1.38005	−	0.788881i
$724$		0			0
$725$	5.06309	−	5.71643i	0.188038	−	0.212303i
$726$		0			0
$727$	36.4695	+	36.4695i	1.35258	+	1.35258i	0.882765	+	0.469814i	$0.155679\pi$
$727$	36.4695	+	36.4695i	1.35258	+	1.35258i	0.469814	+	0.882765i	$0.344321\pi$
$728$		0			0
$729$	−26.9910	+	0.696253i	−0.999667	+	0.0257871i
$730$		0			0
$731$			1.83718i			0.0679506i
$732$		0			0
$733$	9.34049	−	9.34049i	0.344999	−	0.344999i	−0.513244	−	0.858243i	$-0.671556\pi$
$733$	9.34049	−	9.34049i	0.344999	−	0.344999i	0.858243	+	0.513244i	$0.171556\pi$
$734$		0			0
$735$	26.7873	+	2.58853i	0.988065	+	0.0954793i
$736$		0			0
$737$	−13.5648	+	13.5648i	−0.499665	+	0.499665i
$738$		0			0
$739$		−	39.2051i		−	1.44218i	−0.692839	−	0.721092i	$-0.743640\pi$
$739$		−	39.2051i		−	1.44218i	0.692839	−	0.721092i	$-0.256360\pi$
$740$		0			0
$741$	−5.68239	−	20.8481i	−0.208748	−	0.765874i
$742$		0			0
$743$	−22.1644	−	22.1644i	−0.813134	−	0.813134i	0.171968	−	0.985102i	$-0.444987\pi$
$743$	−22.1644	−	22.1644i	−0.813134	−	0.813134i	−0.985102	+	0.171968i	$0.944987\pi$
$744$		0			0
$745$	2.02016	+	4.48789i	0.0740130	+	0.164424i
$746$		0			0
$747$	−5.41564	+	20.9295i	−0.198148	+	0.765770i
$748$		0			0
$749$	−2.06842			−0.0755784
$750$		0			0
$751$	−39.3915			−1.43741			−0.718707	−	0.695313i	$-0.755266\pi$
$751$	−39.3915			−1.43741			−0.718707	+	0.695313i	$0.755266\pi$
$752$		0			0
$753$	5.68549	−	9.94604i	0.207191	−	0.362454i
$754$		0			0
$755$	4.83357	+	10.7380i	0.175912	+	0.390797i
$756$		0			0
$757$	28.5675	+	28.5675i	1.03831	+	1.03831i	0.999237	+	0.0390687i	$0.0124391\pi$
$757$	28.5675	+	28.5675i	1.03831	+	1.03831i	0.0390687	+	0.999237i	$0.487561\pi$
$758$		0			0
$759$	3.87796	−	1.05698i	0.140761	−	0.0383660i
$760$		0			0
$761$			13.3805i			0.485041i	0.970146	+	0.242521i	$0.0779742\pi$
$761$			13.3805i			0.485041i	−0.970146	+	0.242521i	$0.922026\pi$
$762$		0			0
$763$	−1.06390	+	1.06390i	−0.0385157	+	0.0385157i
$764$		0			0
$765$	−3.26368	−	19.0397i	−0.117999	−	0.688384i
$766$		0			0
$767$	15.1638	−	15.1638i	0.547533	−	0.547533i
$768$		0			0
$769$		−	15.3036i		−	0.551861i	−0.961178	−	0.275931i	$-0.911014\pi$
$769$		−	15.3036i		−	0.551861i	0.961178	−	0.275931i	$-0.0889860\pi$
$770$		0			0
$771$	15.6719	−	4.27155i	0.564409	−	0.153836i
$772$		0			0
$773$	−7.66882	−	7.66882i	−0.275828	−	0.275828i	0.555613	−	0.831441i	$-0.312484\pi$
$773$	−7.66882	−	7.66882i	−0.275828	−	0.275828i	−0.831441	+	0.555613i	$0.812484\pi$
$774$		0			0
$775$	−10.2384	+	11.5596i	−0.367776	+	0.415234i
$776$		0			0
$777$	1.48643	−	2.60032i	0.0533253	−	0.0932859i
$778$		0			0
$779$	4.91341			0.176041
$780$		0			0
$781$	−4.48695			−0.160556
$782$		0			0
$783$	0.102330	+	7.93517i	0.00365696	+	0.283580i
$784$		0			0
$785$	3.08306	−	8.13085i	0.110039	−	0.290202i
$786$		0			0
$787$	26.5017	+	26.5017i	0.944682	+	0.944682i	0.998548	−	0.0538662i	$-0.0171545\pi$
$787$	26.5017	+	26.5017i	0.944682	+	0.944682i	−0.0538662	+	0.998548i	$0.517154\pi$
$788$		0			0
$789$	10.5042	+	38.5390i	0.373961	+	1.37202i
$790$		0			0
$791$		−	0.499655i		−	0.0177657i
$792$		0			0
$793$	−6.78939	+	6.78939i	−0.241098	+	0.241098i
$794$		0			0
$795$	2.34517	−	1.93186i	0.0831745	−	0.0685162i
$796$		0			0
$797$	37.7047	−	37.7047i	1.33557	−	1.33557i	0.435267	−	0.900301i	$-0.356654\pi$
$797$	37.7047	−	37.7047i	1.33557	−	1.33557i	0.900301	−	0.435267i	$-0.143346\pi$
$798$		0			0
$799$		−	15.6674i		−	0.554274i
$800$		0			0
$801$	−8.99498	−	15.2750i	−0.317822	−	0.539715i
$802$		0			0
$803$	19.0540	+	19.0540i	0.672400	+	0.672400i
$804$		0			0
$805$	0.461953	−	0.207942i	0.0162817	−	0.00732898i
$806$		0			0
$807$	40.6652	+	23.2456i	1.43148	+	0.818284i
$808$		0			0
$809$	29.2491			1.02834			0.514172	−	0.857687i	$-0.328099\pi$
$809$	29.2491			1.02834			0.514172	+	0.857687i	$0.328099\pi$
$810$		0			0
$811$	12.9110			0.453368			0.226684	−	0.973968i	$-0.427212\pi$
$811$	12.9110			0.453368			0.226684	+	0.973968i	$0.427212\pi$
$812$		0			0
$813$	32.9607	+	18.8414i	1.15598	+	0.660798i
$814$		0			0
$815$	−25.7129	−	9.74983i	−0.900682	−	0.341522i
$816$		0			0
$817$	−3.73918	−	3.73918i	−0.130817	−	0.130817i
$818$		0			0
$819$	0.519105	+	0.881528i	0.0181390	+	0.0308031i
$820$		0			0
$821$		−	25.2098i		−	0.879829i	−0.898040	−	0.439914i	$-0.855009\pi$
$821$		−	25.2098i		−	0.879829i	0.898040	−	0.439914i	$-0.144991\pi$
$822$		0			0
$823$	−32.8255	+	32.8255i	−1.14422	+	1.14422i	−0.156554	+	0.987669i	$0.550039\pi$
$823$	−32.8255	+	32.8255i	−1.14422	+	1.14422i	−0.987669	+	0.156554i	$0.949961\pi$
$824$		0			0
$825$	6.44829	+	19.0346i	0.224501	+	0.662698i
$826$		0			0
$827$	−34.1924	+	34.1924i	−1.18899	+	1.18899i	−0.211639	+	0.977348i	$0.567880\pi$
$827$	−34.1924	+	34.1924i	−1.18899	+	1.18899i	−0.977348	+	0.211639i	$0.932120\pi$
$828$		0			0
$829$			34.1557i			1.18628i	0.805101	+	0.593138i	$0.202111\pi$
$829$			34.1557i			1.18628i	−0.805101	+	0.593138i	$0.797889\pi$
$830$		0			0
$831$	0.225166	+	0.826110i	0.00781091	+	0.0286574i
$832$		0			0
$833$	−14.1491	−	14.1491i	−0.490239	−	0.490239i
$834$		0			0
$835$	28.5640	+	10.8309i	0.988498	+	0.374820i
$836$		0			0
$837$	−0.206929	−	16.0463i	−0.00715250	−	0.554641i
$838$		0			0
$839$	4.98786			0.172200			0.0861001	−	0.996286i	$-0.472560\pi$
$839$	4.98786			0.172200			0.0861001	+	0.996286i	$0.472560\pi$
$840$		0			0
$841$	−26.6675			−0.919569
$842$		0			0
$843$	14.2073	−	24.8538i	0.489325	−	0.856012i
$844$		0			0
$845$	21.8878	−	9.85247i	0.752962	−	0.338935i
$846$		0			0
$847$	0.899480	+	0.899480i	0.0309065	+	0.0309065i
$848$		0			0
$849$	−18.8957	+	5.15024i	−0.648499	+	0.176756i
$850$		0			0
$851$			7.63283i			0.261650i
$852$		0			0
$853$	9.04202	−	9.04202i	0.309593	−	0.309593i	−0.535159	−	0.844752i	$-0.679748\pi$
$853$	9.04202	−	9.04202i	0.309593	−	0.309593i	0.844752	+	0.535159i	$0.179748\pi$
$854$		0			0
$855$	45.3937	+	32.1087i	1.55243	+	1.09809i
$856$		0			0
$857$	22.4329	−	22.4329i	0.766294	−	0.766294i	−0.211158	−	0.977452i	$-0.567723\pi$
$857$	22.4329	−	22.4329i	0.766294	−	0.766294i	0.977452	+	0.211158i	$0.0677233\pi$
$858$		0			0
$859$		−	51.6998i		−	1.76397i	−0.471273	−	0.881987i	$-0.656205\pi$
$859$		−	51.6998i		−	1.76397i	0.471273	−	0.881987i	$-0.343795\pi$
$860$		0			0
$861$	−0.224428	+	0.0611705i	−0.00764849	+	0.00208468i
$862$		0			0
$863$	−18.0335	−	18.0335i	−0.613867	−	0.613867i	0.330084	−	0.943951i	$-0.392923\pi$
$863$	−18.0335	−	18.0335i	−0.613867	−	0.613867i	−0.943951	+	0.330084i	$0.892923\pi$
$864$		0			0
$865$	−7.99076	+	21.0737i	−0.271694	+	0.716528i
$866$		0			0
$867$	7.48468	−	13.0935i	0.254193	−	0.444679i
$868$		0			0
$869$	31.1638			1.05716
$870$		0			0
$871$	12.4425			0.421598
$872$		0			0
$873$	−6.82862	+	26.3902i	−0.231114	+	0.893172i
$874$		0			0
$875$	1.17754	+	2.24263i	0.0398081	+	0.0758148i
$876$		0			0
$877$	−36.5669	−	36.5669i	−1.23478	−	1.23478i	−0.962108	−	0.272669i	$-0.912094\pi$
$877$	−36.5669	−	36.5669i	−1.23478	−	1.23478i	−0.272669	−	0.962108i	$-0.587906\pi$
$878$		0			0
$879$	−7.87503	−	28.8927i	−0.265618	−	0.974526i
$880$		0			0
$881$			55.7276i			1.87751i	0.344583	+	0.938756i	$0.388020\pi$
$881$			55.7276i			1.87751i	−0.344583	+	0.938756i	$0.611980\pi$
$882$		0			0
$883$	−24.6387	+	24.6387i	−0.829157	+	0.829157i	−0.987400	−	0.158243i	$-0.949417\pi$
$883$	−24.6387	+	24.6387i	−0.829157	+	0.829157i	0.158243	+	0.987400i	$0.449417\pi$
$884$		0			0
$885$	−5.30751	+	54.9246i	−0.178410	+	1.84627i
$886$		0			0
$887$	−4.89561	+	4.89561i	−0.164379	+	0.164379i	−0.784503	−	0.620125i	$-0.787082\pi$
$887$	−4.89561	+	4.89561i	−0.164379	+	0.164379i	0.620125	+	0.784503i	$0.287082\pi$
$888$		0			0
$889$			1.93969i			0.0650551i
$890$		0			0
$891$	−18.2643	−	10.1303i	−0.611877	−	0.339377i
$892$		0			0
$893$	31.8876	+	31.8876i	1.06708	+	1.06708i
$894$		0			0
$895$	4.14236	+	9.20247i	0.138464	+	0.307605i
$896$		0			0
$897$	−2.26333	−	1.29379i	−0.0755703	−	0.0431985i
$898$		0			0
$899$	−4.71672			−0.157311
$900$		0			0
$901$	−2.25914			−0.0752629
$902$		0			0
$903$	0.217345	+	0.124242i	0.00723279	+	0.00413450i
$904$		0			0
$905$	−10.0820	−	22.3977i	−0.335138	−	0.744526i
$906$		0			0
$907$	−35.9848	−	35.9848i	−1.19485	−	1.19485i	−0.975687	−	0.219168i	$-0.929666\pi$
$907$	−35.9848	−	35.9848i	−1.19485	−	1.19485i	−0.219168	−	0.975687i	$-0.570334\pi$
$908$		0			0
$909$	48.4489	−	28.5301i	1.60695	−	0.946283i
$910$		0			0
$911$			43.7088i			1.44814i	0.689727	+	0.724069i	$0.257730\pi$
$911$			43.7088i			1.44814i	−0.689727	+	0.724069i	$0.742270\pi$
$912$		0			0
$913$	−11.8249	+	11.8249i	−0.391348	+	0.391348i
$914$		0			0
$915$	2.37637	−	24.5918i	0.0785603	−	0.812978i
$916$		0			0
$917$	−3.19905	+	3.19905i	−0.105642	+	0.105642i
$918$		0			0
$919$			35.3655i			1.16660i	0.812256	+	0.583300i	$0.198239\pi$
$919$			35.3655i			1.16660i	−0.812256	+	0.583300i	$0.801761\pi$
$920$		0			0
$921$	−0.416656	−	1.52867i	−0.0137293	−	0.0503713i
$922$		0			0
$923$	2.05786	+	2.05786i	0.0677354	+	0.0677354i
$924$		0			0
$925$	−38.0942	+	2.30888i	−1.25253	+	0.0759155i
$926$		0			0
$927$	47.7519	+	12.3561i	1.56838	+	0.405828i
$928$		0			0
$929$	−15.3121			−0.502375			−0.251187	−	0.967939i	$-0.580821\pi$
$929$	−15.3121			−0.502375			−0.251187	+	0.967939i	$0.580821\pi$
$930$		0			0
$931$	57.5949			1.88760
$932$		0			0
$933$	18.0620	−	31.5972i	0.591324	−	1.03445i
$934$		0			0
$935$	5.29795	−	13.9721i	0.173261	−	0.456936i
$936$		0			0
$937$	2.62620	+	2.62620i	0.0857942	+	0.0857942i	0.748702	−	0.662907i	$-0.230678\pi$
$937$	2.62620	+	2.62620i	0.0857942	+	0.0857942i	−0.662907	+	0.748702i	$0.730678\pi$
$938$		0			0
$939$	−52.2990	+	14.2547i	−1.70671	+	0.465184i
$940$		0			0
$941$			37.5332i			1.22355i	0.791032	+	0.611774i	$0.209544\pi$
$941$			37.5332i			1.22355i	−0.791032	+	0.611774i	$0.790456\pi$
$942$		0			0
$943$	0.419165	−	0.419165i	0.0136499	−	0.0136499i
$944$		0			0
$945$	−2.47318	−	0.901481i	−0.0804525	−	0.0293252i
$946$		0			0
$947$	16.9953	−	16.9953i	0.552273	−	0.552273i	−0.374823	−	0.927096i	$-0.622297\pi$
$947$	16.9953	−	16.9953i	0.552273	−	0.552273i	0.927096	+	0.374823i	$0.122297\pi$
$948$		0			0
$949$		−	17.4775i		−	0.567345i
$950$		0			0
$951$	22.9106	−	6.24455i	0.742927	−	0.202493i
$952$		0			0
$953$	4.42100	+	4.42100i	0.143210	+	0.143210i	0.775077	−	0.631867i	$-0.217711\pi$
$953$	4.42100	+	4.42100i	0.143210	+	0.143210i	−0.631867	+	0.775077i	$0.717711\pi$
$954$		0			0
$955$	13.7441	−	6.18671i	0.444748	−	0.200197i
$956$		0			0
$957$	−3.04646	+	5.32939i	−0.0984780	+	0.172275i
$958$		0			0
$959$	2.56534			0.0828392
$960$		0			0
$961$	−21.4620			−0.692322
$962$		0			0
$963$	−26.5161	−	6.86121i	−0.854469	−	0.221099i
$964$		0			0
$965$	10.0756	+	3.82047i	0.324345	+	0.122985i
$966$		0			0
$967$	−11.8444	−	11.8444i	−0.380892	−	0.380892i	0.490532	−	0.871423i	$-0.336803\pi$
$967$	−11.8444	−	11.8444i	−0.380892	−	0.380892i	−0.871423	+	0.490532i	$0.836803\pi$
$968$		0			0
$969$	−10.8715	−	39.8865i	−0.349244	−	1.28134i
$970$		0			0
$971$		−	40.5676i		−	1.30188i	−0.759131	−	0.650938i	$-0.774376\pi$
$971$		−	40.5676i		−	1.30188i	0.759131	−	0.650938i	$-0.225624\pi$
$972$		0			0
$973$	−2.43205	+	2.43205i	−0.0779678	+	0.0779678i
$974$		0			0
$975$	5.77248	−	11.6873i	0.184867	−	0.374292i
$976$		0			0
$977$	19.2038	−	19.2038i	0.614384	−	0.614384i	−0.329701	−	0.944085i	$-0.606948\pi$
$977$	19.2038	−	19.2038i	0.614384	−	0.614384i	0.944085	+	0.329701i	$0.106948\pi$
$978$		0			0
$979$		−	13.7123i		−	0.438246i
$980$		0			0
$981$	−17.1677	+	10.1095i	−0.548123	+	0.322773i
$982$		0			0
$983$	−15.0007	−	15.0007i	−0.478447	−	0.478447i	0.426188	−	0.904635i	$-0.359856\pi$
$983$	−15.0007	−	15.0007i	−0.478447	−	0.478447i	−0.904635	+	0.426188i	$0.859856\pi$
$984$		0			0
$985$	−29.8448	−	11.3166i	−0.950935	−	0.360577i
$986$		0			0
$987$	−1.85351	−	1.05953i	−0.0589980	−	0.0337252i
$988$		0			0
$989$	−0.637983			−0.0202867
$990$		0			0
$991$	13.6191			0.432624			0.216312	−	0.976324i	$-0.430597\pi$
$991$	13.6191			0.432624			0.216312	+	0.976324i	$0.430597\pi$
$992$		0			0
$993$	−26.3855	−	15.0829i	−0.837320	−	0.478640i
$994$		0			0
$995$	10.4028	−	4.68267i	0.329791	−	0.148451i
$996$		0			0
$997$	−35.4985	−	35.4985i	−1.12425	−	1.12425i	−0.991096	−	0.133152i	$-0.957490\pi$
$997$	−35.4985	−	35.4985i	−1.12425	−	1.12425i	−0.133152	−	0.991096i	$-0.542510\pi$
$998$		0			0
$999$	27.6809	−	28.4041i	0.875783	−	0.898666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.r.c.737.6	✓	80
3.2	odd	2	inner	1380.2.r.c.737.26	yes	80
5.3	odd	4	inner	1380.2.r.c.1013.26	yes	80
15.8	even	4	inner	1380.2.r.c.1013.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.r.c.737.6	✓	80	1.1	even	1	trivial
1380.2.r.c.737.26	yes	80	3.2	odd	2	inner
1380.2.r.c.1013.6	yes	80	15.8	even	4	inner
1380.2.r.c.1013.26	yes	80	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50371 - 0.859570i) q^{3} +(-0.917834 - 2.03901i) q^{5} +(0.160200 + 0.160200i) q^{7} +(1.52228 + 2.58509i) q^{9} +O(q^{10})\)	\(q+(-1.50371 - 0.859570i) q^{3} +(-0.917834 - 2.03901i) q^{5} +(0.160200 + 0.160200i) q^{7} +(1.52228 + 2.58509i) q^{9} +2.32062i q^{11} +(1.06431 - 1.06431i) q^{13} +(-0.372521 + 3.85503i) q^{15} +(2.03624 - 2.03624i) q^{17} +8.28863i q^{19} +(-0.103191 - 0.378597i) q^{21} +(0.707107 + 0.707107i) q^{23} +(-3.31516 + 3.74295i) q^{25} +(-0.0670025 - 5.19572i) q^{27} -1.52725 q^{29} +3.08837 q^{31} +(1.99473 - 3.48953i) q^{33} +(0.179613 - 0.473687i) q^{35} +(5.39723 + 5.39723i) q^{37} +(-2.51526 + 0.685564i) q^{39} -0.592789i q^{41} +(-0.451122 + 0.451122i) q^{43} +(3.87383 - 5.47663i) q^{45} +(3.84716 - 3.84716i) q^{47} -6.94867i q^{49} +(-4.81220 + 1.31162i) q^{51} +(-0.554734 - 0.554734i) q^{53} +(4.73177 - 2.12994i) q^{55} +(7.12465 - 12.4637i) q^{57} +14.2475 q^{59} -6.37914 q^{61} +(-0.170261 + 0.657999i) q^{63} +(-3.14701 - 1.19329i) q^{65} +(5.84533 + 5.84533i) q^{67} +(-0.455475 - 1.67109i) q^{69} +1.93352i q^{71} +(8.21073 - 8.21073i) q^{73} +(8.20237 - 2.77870i) q^{75} +(-0.371763 + 0.371763i) q^{77} -13.4291i q^{79} +(-4.36533 + 7.87044i) q^{81} +(5.09560 + 5.09560i) q^{83} +(-6.02085 - 2.28299i) q^{85} +(2.29654 + 1.31278i) q^{87} -5.90889 q^{89} +0.341005 q^{91} +(-4.64401 - 2.65467i) q^{93} +(16.9006 - 7.60758i) q^{95} +(6.42509 + 6.42509i) q^{97} +(-5.99899 + 3.53263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{3}+O(q^{10}) \) 80 * q + 8 * q^3	\( 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) \) 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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