LMFDB - Embedded newform 1380.2.r.c.737.20

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			737.20
Character	$\chi$	$=$	1380.737
Dual form			1380.2.r.c.1013.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.251606 + 1.71368i) q^{3} +(-0.257544 + 2.22119i) q^{5} +(-2.77975 - 2.77975i) q^{7} +(-2.87339 + 0.862345i) q^{9} +O(q^{10})$	\(q+(0.251606 + 1.71368i) q^{3} +(-0.257544 + 2.22119i) q^{5} +(-2.77975 - 2.77975i) q^{7} +(-2.87339 + 0.862345i) q^{9} +2.09128i q^{11} +(-1.42129 + 1.42129i) q^{13} +(-3.87120 + 0.117517i) q^{15} +(-1.02464 + 1.02464i) q^{17} -8.29259i q^{19} +(4.06419 - 5.46299i) q^{21} +(0.707107 + 0.707107i) q^{23} +(-4.86734 - 1.14411i) q^{25} +(-2.20074 - 4.70709i) q^{27} -1.95646 q^{29} +5.12381 q^{31} +(-3.58379 + 0.526180i) q^{33} +(6.89024 - 5.45843i) q^{35} +(-0.798227 - 0.798227i) q^{37} +(-2.79325 - 2.07804i) q^{39} -6.20653i q^{41} +(-2.81616 + 2.81616i) q^{43} +(-1.17540 - 6.60442i) q^{45} +(4.38422 - 4.38422i) q^{47} +8.45397i q^{49} +(-2.01372 - 1.49810i) q^{51} +(-5.35588 - 5.35588i) q^{53} +(-4.64513 - 0.538597i) q^{55} +(14.2108 - 2.08647i) q^{57} -5.93912 q^{59} -10.8418 q^{61} +(10.3844 + 5.59019i) q^{63} +(-2.79091 - 3.52301i) q^{65} +(-0.857707 - 0.857707i) q^{67} +(-1.03384 + 1.38967i) q^{69} +4.49470i q^{71} +(-7.08026 + 7.08026i) q^{73} +(0.735977 - 8.62892i) q^{75} +(5.81324 - 5.81324i) q^{77} -0.306144i q^{79} +(7.51272 - 4.95570i) q^{81} +(3.25756 + 3.25756i) q^{83} +(-2.01203 - 2.53982i) q^{85} +(-0.492259 - 3.35275i) q^{87} +15.9451 q^{89} +7.90167 q^{91} +(1.28918 + 8.78056i) q^{93} +(18.4194 + 2.13571i) q^{95} +(-4.29414 - 4.29414i) q^{97} +(-1.80341 - 6.00907i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.251606	+	1.71368i	0.145265	+	0.989393i
$3$	0.251606	+	1.71368i	0.145265	+	0.989393i
$4$		0			0
$5$	−0.257544	+	2.22119i	−0.115177	+	0.993345i
$5$	−0.257544	+	2.22119i	−0.115177	+	0.993345i
$6$		0			0
$7$	−2.77975	−	2.77975i	−1.05064	−	1.05064i	−0.998647	−	0.0519977i	$-0.983441\pi$
$7$	−2.77975	−	2.77975i	−1.05064	−	1.05064i	−0.0519977	−	0.998647i	$-0.516559\pi$
$8$		0			0
$9$	−2.87339	+	0.862345i	−0.957796	+	0.287448i
$10$		0			0
$11$			2.09128i			0.630546i	0.949001	+	0.315273i	$0.102096\pi$
$11$			2.09128i			0.630546i	−0.949001	+	0.315273i	$0.897904\pi$
$12$		0			0
$13$	−1.42129	+	1.42129i	−0.394196	+	0.394196i	−0.876180	−	0.481984i	$-0.839916\pi$
$13$	−1.42129	+	1.42129i	−0.394196	+	0.394196i	0.481984	+	0.876180i	$0.339916\pi$
$14$		0			0
$15$	−3.87120	+	0.117517i	−0.999540	+	0.0303428i
$16$		0			0
$17$	−1.02464	+	1.02464i	−0.248513	+	0.248513i	−0.820360	−	0.571847i	$-0.806227\pi$
$17$	−1.02464	+	1.02464i	−0.248513	+	0.248513i	0.571847	+	0.820360i	$0.306227\pi$
$18$		0			0
$19$		−	8.29259i		−	1.90245i	−0.308496	−	0.951226i	$-0.599826\pi$
$19$		−	8.29259i		−	1.90245i	0.308496	−	0.951226i	$-0.400174\pi$
$20$		0			0
$21$	4.06419	−	5.46299i	0.886879	−	1.19212i
$22$		0			0
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	−4.86734	−	1.14411i	−0.973468	−	0.228821i
$26$		0			0
$27$	−2.20074	−	4.70709i	−0.423533	−	0.905880i
$28$		0			0
$29$	−1.95646			−0.363306			−0.181653	−	0.983363i	$-0.558145\pi$
$29$	−1.95646			−0.363306			−0.181653	+	0.983363i	$0.558145\pi$
$30$		0			0
$31$	5.12381			0.920264			0.460132	−	0.887851i	$-0.347802\pi$
$31$	5.12381			0.920264			0.460132	+	0.887851i	$0.347802\pi$
$32$		0			0
$33$	−3.58379	+	0.526180i	−0.623857	+	0.0915962i
$34$		0			0
$35$	6.89024	−	5.45843i	1.16466	−	0.922642i
$36$		0			0
$37$	−0.798227	−	0.798227i	−0.131228	−	0.131228i	0.638442	−	0.769670i	$-0.279579\pi$
$37$	−0.798227	−	0.798227i	−0.131228	−	0.131228i	−0.769670	+	0.638442i	$0.779579\pi$
$38$		0			0
$39$	−2.79325	−	2.07804i	−0.447278	−	0.332752i
$40$		0			0
$41$		−	6.20653i		−	0.969297i	−0.874709	−	0.484648i	$-0.838948\pi$
$41$		−	6.20653i		−	0.969297i	0.874709	−	0.484648i	$-0.161052\pi$
$42$		0			0
$43$	−2.81616	+	2.81616i	−0.429461	+	0.429461i	−0.888445	−	0.458984i	$-0.848214\pi$
$43$	−2.81616	+	2.81616i	−0.429461	+	0.429461i	0.458984	+	0.888445i	$0.348214\pi$
$44$		0			0
$45$	−1.17540	−	6.60442i	−0.175219	−	0.984529i
$46$		0			0
$47$	4.38422	−	4.38422i	0.639505	−	0.639505i	−0.310929	−	0.950433i	$-0.600640\pi$
$47$	4.38422	−	4.38422i	0.639505	−	0.639505i	0.950433	+	0.310929i	$0.100640\pi$
$48$		0			0
$49$			8.45397i			1.20771i
$50$		0			0
$51$	−2.01372	−	1.49810i	−0.281977	−	0.209776i
$52$		0			0
$53$	−5.35588	−	5.35588i	−0.735686	−	0.735686i	0.236054	−	0.971740i	$-0.424146\pi$
$53$	−5.35588	−	5.35588i	−0.735686	−	0.735686i	−0.971740	+	0.236054i	$0.924146\pi$
$54$		0			0
$55$	−4.64513	−	0.538597i	−0.626349	−	0.0726245i
$56$		0			0
$57$	14.2108	−	2.08647i	1.88227	−	0.276360i
$58$		0			0
$59$	−5.93912			−0.773208			−0.386604	−	0.922246i	$-0.626352\pi$
$59$	−5.93912			−0.773208			−0.386604	+	0.922246i	$0.626352\pi$
$60$		0			0
$61$	−10.8418			−1.38815			−0.694074	−	0.719904i	$-0.744186\pi$
$61$	−10.8418			−1.38815			−0.694074	+	0.719904i	$0.744186\pi$
$62$		0			0
$63$	10.3844	+	5.59019i	1.30831	+	0.704298i
$64$		0			0
$65$	−2.79091	−	3.52301i	−0.346170	−	0.436975i
$66$		0			0
$67$	−0.857707	−	0.857707i	−0.104786	−	0.104786i	0.652770	−	0.757556i	$-0.273607\pi$
$67$	−0.857707	−	0.857707i	−0.104786	−	0.104786i	−0.757556	+	0.652770i	$0.773607\pi$
$68$		0			0
$69$	−1.03384	+	1.38967i	−0.124460	+	0.167296i
$70$		0			0
$71$			4.49470i			0.533423i	0.963776	+	0.266711i	$0.0859370\pi$
$71$			4.49470i			0.533423i	−0.963776	+	0.266711i	$0.914063\pi$
$72$		0			0
$73$	−7.08026	+	7.08026i	−0.828682	+	0.828682i	−0.987335	−	0.158652i	$-0.949285\pi$
$73$	−7.08026	+	7.08026i	−0.828682	+	0.828682i	0.158652	+	0.987335i	$0.449285\pi$
$74$		0			0
$75$	0.735977	−	8.62892i	0.0849833	−	0.996382i
$76$		0			0
$77$	5.81324	−	5.81324i	0.662480	−	0.662480i
$78$		0			0
$79$		−	0.306144i		−	0.0344438i	−0.999852	−	0.0172219i	$-0.994518\pi$
$79$		−	0.306144i		−	0.0344438i	0.999852	−	0.0172219i	$-0.00548218\pi$
$80$		0			0
$81$	7.51272	−	4.95570i	0.834747	−	0.550634i
$82$		0			0
$83$	3.25756	+	3.25756i	0.357563	+	0.357563i	0.862914	−	0.505351i	$-0.168637\pi$
$83$	3.25756	+	3.25756i	0.357563	+	0.357563i	−0.505351	+	0.862914i	$0.668637\pi$
$84$		0			0
$85$	−2.01203	−	2.53982i	−0.218236	−	0.275482i
$86$		0			0
$87$	−0.492259	−	3.35275i	−0.0527757	−	0.359453i
$88$		0			0
$89$	15.9451			1.69018			0.845091	−	0.534623i	$-0.179546\pi$
$89$	15.9451			1.69018			0.845091	+	0.534623i	$0.179546\pi$
$90$		0			0
$91$	7.90167			0.828320
$92$		0			0
$93$	1.28918	+	8.78056i	0.133682	+	0.910502i
$94$		0			0
$95$	18.4194	+	2.13571i	1.88979	+	0.219119i
$96$		0			0
$97$	−4.29414	−	4.29414i	−0.436004	−	0.436004i	0.454661	−	0.890665i	$-0.349760\pi$
$97$	−4.29414	−	4.29414i	−0.436004	−	0.436004i	−0.890665	+	0.454661i	$0.849760\pi$
$98$		0			0
$99$	−1.80341	−	6.00907i	−0.181249	−	0.603934i
$100$		0			0
$101$		−	6.43677i		−	0.640483i	−0.947336	−	0.320241i	$-0.896236\pi$
$101$		−	6.43677i		−	0.640483i	0.947336	−	0.320241i	$-0.103764\pi$
$102$		0			0
$103$	−7.32336	+	7.32336i	−0.721592	+	0.721592i	−0.968929	−	0.247337i	$-0.920444\pi$
$103$	−7.32336	+	7.32336i	−0.721592	+	0.721592i	0.247337	+	0.968929i	$0.420444\pi$
$104$		0			0
$105$	11.0876	+	10.4343i	1.08204	+	1.01828i
$106$		0			0
$107$	0.578291	−	0.578291i	0.0559055	−	0.0559055i	−0.678601	−	0.734507i	$-0.737414\pi$
$107$	0.578291	−	0.578291i	0.0559055	−	0.0559055i	0.734507	+	0.678601i	$0.237414\pi$
$108$		0			0
$109$		−	16.4177i		−	1.57253i	−0.617890	−	0.786265i	$-0.712012\pi$
$109$		−	16.4177i		−	1.57253i	0.617890	−	0.786265i	$-0.287988\pi$
$110$		0			0
$111$	1.16707	−	1.56874i	0.110773	−	0.148898i
$112$		0			0
$113$	−2.10597	−	2.10597i	−0.198113	−	0.198113i	0.601078	−	0.799191i	$-0.294738\pi$
$113$	−2.10597	−	2.10597i	−0.198113	−	0.198113i	−0.799191	+	0.601078i	$0.794738\pi$
$114$		0			0
$115$	−1.75273	+	1.38851i	−0.163443	+	0.129479i
$116$		0			0
$117$	2.85829	−	5.30958i	0.264249	−	0.490871i
$118$		0			0
$119$	5.69650			0.522197
$120$		0			0
$121$	6.62653			0.602412
$122$		0			0
$123$	10.6360	−	1.56160i	0.959015	−	0.140805i
$124$		0			0
$125$	3.79483	−	10.5166i	0.339420	−	0.940635i
$126$		0			0
$127$	−3.21125	−	3.21125i	−0.284952	−	0.284952i	0.550128	−	0.835080i	$-0.314579\pi$
$127$	−3.21125	−	3.21125i	−0.284952	−	0.284952i	−0.835080	+	0.550128i	$0.814579\pi$
$128$		0			0
$129$	−5.53456	−	4.11743i	−0.487291	−	0.362520i
$130$		0			0
$131$			0.0593050i			0.00518150i	0.999997	+	0.00259075i	$0.000824662\pi$
$131$			0.0593050i			0.00518150i	−0.999997	+	0.00259075i	$0.999175\pi$
$132$		0			0
$133$	−23.0513	+	23.0513i	−1.99880	+	1.99880i
$134$		0			0
$135$	11.0221	−	3.67598i	0.948633	−	0.316378i
$136$		0			0
$137$	−15.4409	+	15.4409i	−1.31921	+	1.31921i	−0.404803	+	0.914404i	$0.632660\pi$
$137$	−15.4409	+	15.4409i	−1.31921	+	1.31921i	−0.914404	+	0.404803i	$0.867340\pi$
$138$		0			0
$139$			14.0946i			1.19549i	0.801687	+	0.597744i	$0.203936\pi$
$139$			14.0946i			1.19549i	−0.801687	+	0.597744i	$0.796064\pi$
$140$		0			0
$141$	8.61625	+	6.41005i	0.725619	+	0.539824i
$142$		0			0
$143$	−2.97233	−	2.97233i	−0.248559	−	0.248559i
$144$		0			0
$145$	0.503876	−	4.34567i	0.0418446	−	0.360889i
$146$		0			0
$147$	−14.4874	+	2.12707i	−1.19490	+	0.175438i
$148$		0			0
$149$	−20.8627			−1.70914			−0.854570	−	0.519337i	$-0.826179\pi$
$149$	−20.8627			−1.70914			−0.854570	+	0.519337i	$0.826179\pi$
$150$		0			0
$151$	1.82129			0.148214			0.0741072	−	0.997250i	$-0.476389\pi$
$151$	1.82129			0.148214			0.0741072	+	0.997250i	$0.476389\pi$
$152$		0			0
$153$	2.06060	−	3.82780i	0.166590	−	0.309459i
$154$		0			0
$155$	−1.31961	+	11.3809i	−0.105993	+	0.914139i
$156$		0			0
$157$	−10.3558	−	10.3558i	−0.826481	−	0.826481i	0.160547	−	0.987028i	$-0.448674\pi$
$157$	−10.3558	−	10.3558i	−0.826481	−	0.826481i	−0.987028	+	0.160547i	$0.948674\pi$
$158$		0			0
$159$	7.83068	−	10.5258i	0.621013	−	0.834752i
$160$		0			0
$161$		−	3.93115i		−	0.309818i
$162$		0			0
$163$	−4.22981	+	4.22981i	−0.331305	+	0.331305i	−0.853082	−	0.521777i	$-0.825269\pi$
$163$	−4.22981	+	4.22981i	−0.331305	+	0.331305i	0.521777	+	0.853082i	$0.325269\pi$
$164$		0			0
$165$	−0.245761	−	8.09578i	−0.0191325	−	0.630255i
$166$		0			0
$167$	−5.36323	+	5.36323i	−0.415020	+	0.415020i	−0.883483	−	0.468463i	$-0.844808\pi$
$167$	−5.36323	+	5.36323i	−0.415020	+	0.415020i	0.468463	+	0.883483i	$0.344808\pi$
$168$		0			0
$169$			8.95984i			0.689219i
$170$		0			0
$171$	7.15107	+	23.8278i	0.546856	+	1.82216i
$172$		0			0
$173$	−13.1383	−	13.1383i	−0.998887	−	0.998887i	0.00111218	−	0.999999i	$-0.499646\pi$
$173$	−13.1383	−	13.1383i	−0.998887	−	0.998887i	−0.999999	+	0.00111218i	$0.999646\pi$
$174$		0			0
$175$	10.3496	+	16.7103i	0.782360	+	1.26318i
$176$		0			0
$177$	−1.49432	−	10.1777i	−0.112320	−	0.765006i
$178$		0			0
$179$	6.12624			0.457897			0.228948	−	0.973439i	$-0.426471\pi$
$179$	6.12624			0.457897			0.228948	+	0.973439i	$0.426471\pi$
$180$		0			0
$181$	−25.1218			−1.86729			−0.933646	−	0.358198i	$-0.883391\pi$
$181$	−25.1218			−1.86729			−0.933646	+	0.358198i	$0.883391\pi$
$182$		0			0
$183$	−2.72786	−	18.5793i	−0.201649	−	1.37342i
$184$		0			0
$185$	1.97859	−	1.56743i	0.145469	−	0.115240i
$186$		0			0
$187$	−2.14282	−	2.14282i	−0.156699	−	0.156699i
$188$		0			0
$189$	−6.96701	+	19.2020i	−0.506775	+	1.39674i
$190$		0			0
$191$		−	25.3875i		−	1.83698i	−0.395448	−	0.918488i	$-0.629411\pi$
$191$		−	25.3875i		−	1.83698i	0.395448	−	0.918488i	$-0.370589\pi$
$192$		0			0
$193$	4.85000	−	4.85000i	0.349111	−	0.349111i	−0.510668	−	0.859778i	$-0.670602\pi$
$193$	4.85000	−	4.85000i	0.349111	−	0.349111i	0.859778	+	0.510668i	$0.170602\pi$
$194$		0			0
$195$	5.33509	−	5.66914i	0.382054	−	0.405976i
$196$		0			0
$197$	−14.3028	+	14.3028i	−1.01903	+	1.01903i	−0.0192140	+	0.999815i	$0.506116\pi$
$197$	−14.3028	+	14.3028i	−1.01903	+	1.01903i	−0.999815	+	0.0192140i	$0.993884\pi$
$198$		0			0
$199$		−	5.73774i		−	0.406737i	−0.979102	−	0.203369i	$-0.934811\pi$
$199$		−	5.73774i		−	0.406737i	0.979102	−	0.203369i	$-0.0651890\pi$
$200$		0			0
$201$	1.25403	−	1.68564i	0.0884524	−	0.118896i
$202$		0			0
$203$	5.43847	+	5.43847i	0.381706	+	0.381706i
$204$		0			0
$205$	13.7859	+	1.59845i	0.962846	+	0.111641i
$206$		0			0
$207$	−2.64156	−	1.42202i	−0.183601	−	0.0988374i
$208$		0			0
$209$	17.3422			1.19958
$210$		0			0
$211$	−4.34237			−0.298941			−0.149471	−	0.988766i	$-0.547757\pi$
$211$	−4.34237			−0.298941			−0.149471	+	0.988766i	$0.547757\pi$
$212$		0			0
$213$	−7.70247	+	1.13089i	−0.527764	+	0.0774876i
$214$		0			0
$215$	−5.52994	−	6.98051i	−0.377138	−	0.476067i
$216$		0			0
$217$	−14.2429	−	14.2429i	−0.966870	−	0.966870i
$218$		0			0
$219$	−13.9147	−	10.3519i	−0.940271	−	0.699514i
$220$		0			0
$221$		−	2.91264i		−	0.195925i
$222$		0			0
$223$	−17.5922	+	17.5922i	−1.17806	+	1.17806i	−0.197822	+	0.980238i	$0.563387\pi$
$223$	−17.5922	+	17.5922i	−1.17806	+	1.17806i	−0.980238	+	0.197822i	$0.936613\pi$
$224$		0			0
$225$	14.9724	−	0.909864i	0.998159	−	0.0606576i
$226$		0			0
$227$	−18.0869	+	18.0869i	−1.20047	+	1.20047i	−0.226447	+	0.974024i	$0.572711\pi$
$227$	−18.0869	+	18.0869i	−1.20047	+	1.20047i	−0.974024	+	0.226447i	$0.927289\pi$
$228$		0			0
$229$		−	1.22073i		−	0.0806682i	−0.999186	−	0.0403341i	$-0.987158\pi$
$229$		−	1.22073i		−	0.0806682i	0.999186	−	0.0403341i	$-0.0128422\pi$
$230$		0			0
$231$	11.4247	+	8.49937i	0.751688	+	0.559217i
$232$		0			0
$233$	9.13076	+	9.13076i	0.598176	+	0.598176i	0.939827	−	0.341651i	$-0.110986\pi$
$233$	9.13076	+	9.13076i	0.598176	+	0.598176i	−0.341651	+	0.939827i	$0.610986\pi$
$234$		0			0
$235$	8.60905	+	10.8673i	0.561592	+	0.708905i
$236$		0			0
$237$	0.524632	−	0.0770277i	0.0340785	−	0.00500348i
$238$		0			0
$239$	20.8677			1.34982			0.674910	−	0.737900i	$-0.264182\pi$
$239$	20.8677			1.34982			0.674910	+	0.737900i	$0.264182\pi$
$240$		0			0
$241$	29.5939			1.90631			0.953156	−	0.302478i	$-0.0978140\pi$
$241$	29.5939			1.90631			0.953156	+	0.302478i	$0.0978140\pi$
$242$		0			0
$243$	10.3827	+	11.6275i	0.666052	+	0.745905i
$244$		0			0
$245$	−18.7778	−	2.17727i	−1.19967	−	0.139101i
$246$		0			0
$247$	11.7862	+	11.7862i	0.749939	+	0.749939i
$248$		0			0
$249$	−4.76278	+	6.40203i	−0.301829	+	0.405712i
$250$		0			0
$251$			22.2104i			1.40191i	0.713205	+	0.700955i	$0.247243\pi$
$251$			22.2104i			1.40191i	−0.713205	+	0.700955i	$0.752757\pi$
$252$		0			0
$253$	−1.47876	+	1.47876i	−0.0929689	+	0.0929689i
$254$		0			0
$255$	3.84619	−	4.08702i	0.240858	−	0.255939i
$256$		0			0
$257$	−11.8431	+	11.8431i	−0.738751	+	0.738751i	−0.972336	−	0.233585i	$-0.924954\pi$
$257$	−11.8431	+	11.8431i	−0.738751	+	0.738751i	0.233585	+	0.972336i	$0.424954\pi$
$258$		0			0
$259$			4.43773i			0.275747i
$260$		0			0
$261$	5.62168	−	1.68715i	0.347973	−	0.104432i
$262$		0			0
$263$	−3.05584	−	3.05584i	−0.188431	−	0.188431i	0.606586	−	0.795018i	$-0.292538\pi$
$263$	−3.05584	−	3.05584i	−0.188431	−	0.188431i	−0.795018	+	0.606586i	$0.792538\pi$
$264$		0			0
$265$	13.2758	−	10.5170i	0.815525	−	0.646056i
$266$		0			0
$267$	4.01190	+	27.3249i	0.245524	+	1.67225i
$268$		0			0
$269$	−17.5857			−1.07222			−0.536109	−	0.844148i	$-0.680107\pi$
$269$	−17.5857			−1.07222			−0.536109	+	0.844148i	$0.680107\pi$
$270$		0			0
$271$	−7.02949			−0.427011			−0.213506	−	0.976942i	$-0.568488\pi$
$271$	−7.02949			−0.427011			−0.213506	+	0.976942i	$0.568488\pi$
$272$		0			0
$273$	1.98811	+	13.5409i	0.120326	+	0.819534i
$274$		0			0
$275$	2.39265	−	10.1790i	0.144282	−	0.613816i
$276$		0			0
$277$	6.15251	+	6.15251i	0.369669	+	0.369669i	0.867356	−	0.497688i	$-0.165817\pi$
$277$	6.15251	+	6.15251i	0.369669	+	0.369669i	−0.497688	+	0.867356i	$0.665817\pi$
$278$		0			0
$279$	−14.7227	+	4.41849i	−0.881425	+	0.264528i
$280$		0			0
$281$			16.0747i			0.958939i	0.877558	+	0.479470i	$0.159171\pi$
$281$			16.0747i			0.958939i	−0.877558	+	0.479470i	$0.840829\pi$
$282$		0			0
$283$	20.1014	−	20.1014i	1.19490	−	1.19490i	0.219232	−	0.975673i	$-0.429645\pi$
$283$	20.1014	−	20.1014i	1.19490	−	1.19490i	0.975673	−	0.219232i	$-0.0703552\pi$
$284$		0			0
$285$	0.974521	+	32.1023i	0.0577256	+	1.90158i
$286$		0			0
$287$	−17.2526	+	17.2526i	−1.01839	+	1.01839i
$288$		0			0
$289$			14.9002i			0.876483i
$290$		0			0
$291$	6.27834	−	8.43920i	0.368043	−	0.494715i
$292$		0			0
$293$	9.71216	+	9.71216i	0.567391	+	0.567391i	0.931397	−	0.364006i	$-0.118591\pi$
$293$	9.71216	+	9.71216i	0.567391	+	0.567391i	−0.364006	+	0.931397i	$0.618591\pi$
$294$		0			0
$295$	1.52958	−	13.1919i	0.0890559	−	0.768062i
$296$		0			0
$297$	9.84387	−	4.60238i	0.571199	−	0.267057i
$298$		0			0
$299$	−2.01001			−0.116242
$300$		0			0
$301$	15.6564			0.902421
$302$		0			0
$303$	11.0306	−	1.61953i	0.633689	−	0.0930397i
$304$		0			0
$305$	2.79223	−	24.0816i	0.159883	−	1.37891i
$306$		0			0
$307$	−12.5938	−	12.5938i	−0.718767	−	0.718767i	0.249585	−	0.968353i	$-0.419706\pi$
$307$	−12.5938	−	12.5938i	−0.718767	−	0.718767i	−0.968353	+	0.249585i	$0.919706\pi$
$308$		0			0
$309$	−14.3925	−	10.7073i	−0.818760	−	0.609116i
$310$		0			0
$311$		−	11.8865i		−	0.674024i	−0.941500	−	0.337012i	$-0.890584\pi$
$311$		−	11.8865i		−	0.674024i	0.941500	−	0.337012i	$-0.109416\pi$
$312$		0			0
$313$	7.73018	−	7.73018i	0.436935	−	0.436935i	−0.454044	−	0.890979i	$-0.650019\pi$
$313$	7.73018	−	7.73018i	0.436935	−	0.436935i	0.890979	+	0.454044i	$0.150019\pi$
$314$		0			0
$315$	−15.0913	+	21.6259i	−0.850298	+	1.21848i
$316$		0			0
$317$	−9.07064	+	9.07064i	−0.509458	+	0.509458i	−0.914360	−	0.404902i	$-0.867306\pi$
$317$	−9.07064	+	9.07064i	−0.509458	+	0.509458i	0.404902	+	0.914360i	$0.367306\pi$
$318$		0			0
$319$		−	4.09152i		−	0.229081i
$320$		0			0
$321$	1.13651	+	0.845503i	0.0634336	+	0.0471914i
$322$		0			0
$323$	8.49696	+	8.49696i	0.472783	+	0.472783i
$324$		0			0
$325$	8.54404	−	5.29181i	0.473938	−	0.293537i
$326$		0			0
$327$	28.1346	−	4.13079i	1.55585	−	0.228433i
$328$		0			0
$329$	−24.3740			−1.34378
$330$		0			0
$331$	5.17208			0.284283			0.142141	−	0.989846i	$-0.454601\pi$
$331$	5.17208			0.284283			0.142141	+	0.989846i	$0.454601\pi$
$332$		0			0
$333$	2.98196	+	1.60527i	0.163410	+	0.0879682i
$334$		0			0
$335$	2.12602	−	1.68423i	0.116157	−	0.0920193i
$336$		0			0
$337$	−0.182777	−	0.182777i	−0.00995649	−	0.00995649i	0.702111	−	0.712067i	$-0.252241\pi$
$337$	−0.182777	−	0.182777i	−0.00995649	−	0.00995649i	−0.712067	+	0.702111i	$0.752241\pi$
$338$		0			0
$339$	3.07908	−	4.13883i	0.167233	−	0.224790i
$340$		0			0
$341$			10.7153i			0.580268i
$342$		0			0
$343$	4.04165	−	4.04165i	0.218229	−	0.218229i
$344$		0			0
$345$	−2.82045	−	2.65425i	−0.151848	−	0.142900i
$346$		0			0
$347$	10.3939	−	10.3939i	0.557974	−	0.557974i	−0.370756	−	0.928730i	$-0.620901\pi$
$347$	10.3939	−	10.3939i	0.557974	−	0.557974i	0.928730	+	0.370756i	$0.120901\pi$
$348$		0			0
$349$		−	21.6823i		−	1.16063i	−0.814393	−	0.580314i	$-0.802930\pi$
$349$		−	21.6823i		−	1.16063i	0.814393	−	0.580314i	$-0.197070\pi$
$350$		0			0
$351$	9.81807	+	3.56226i	0.524050	+	0.190139i
$352$		0			0
$353$	23.6650	+	23.6650i	1.25956	+	1.25956i	0.951303	+	0.308258i	$0.0997459\pi$
$353$	23.6650	+	23.6650i	1.25956	+	1.25956i	0.308258	+	0.951303i	$0.400254\pi$
$354$		0			0
$355$	−9.98357	−	1.15758i	−0.529873	−	0.0614381i
$356$		0			0
$357$	1.43327	+	9.76197i	0.0758570	+	0.516658i
$358$		0			0
$359$	28.5631			1.50750			0.753751	−	0.657161i	$-0.228243\pi$
$359$	28.5631			1.50750			0.753751	+	0.657161i	$0.228243\pi$
$360$		0			0
$361$	−49.7671			−2.61932
$362$		0			0
$363$	1.66728	+	11.3557i	0.0875094	+	0.596022i
$364$		0			0
$365$	−13.9031	−	17.5501i	−0.727722	−	0.918612i
$366$		0			0
$367$	−7.91391	−	7.91391i	−0.413103	−	0.413103i	0.469715	−	0.882818i	$-0.344357\pi$
$367$	−7.91391	−	7.91391i	−0.413103	−	0.413103i	−0.882818	+	0.469715i	$0.844357\pi$
$368$		0			0
$369$	5.35217	+	17.8338i	0.278623	+	0.928389i
$370$		0			0
$371$			29.7760i			1.54589i
$372$		0			0
$373$	−7.00835	+	7.00835i	−0.362879	+	0.362879i	−0.864872	−	0.501993i	$-0.832600\pi$
$373$	−7.00835	+	7.00835i	−0.362879	+	0.362879i	0.501993	+	0.864872i	$0.332600\pi$
$374$		0			0
$375$	18.9769	+	3.85707i	0.979963	+	0.199178i
$376$		0			0
$377$	2.78071	−	2.78071i	0.143214	−	0.143214i
$378$		0			0
$379$		−	33.0607i		−	1.69822i	−0.528220	−	0.849108i	$-0.677140\pi$
$379$		−	33.0607i		−	1.69822i	0.528220	−	0.849108i	$-0.322860\pi$
$380$		0			0
$381$	4.69508	−	6.31102i	0.240536	−	0.323323i
$382$		0			0
$383$	16.0312	+	16.0312i	0.819154	+	0.819154i	0.985985	−	0.166832i	$-0.0533536\pi$
$383$	16.0312	+	16.0312i	0.819154	+	0.819154i	−0.166832	+	0.985985i	$0.553354\pi$
$384$		0			0
$385$	11.4151	+	14.4094i	0.581768	+	0.734373i
$386$		0			0
$387$	5.66342	−	10.5204i	0.287888	−	0.534783i
$388$		0			0
$389$	−26.1493			−1.32582			−0.662910	−	0.748699i	$-0.730679\pi$
$389$	−26.1493			−1.32582			−0.662910	+	0.748699i	$0.730679\pi$
$390$		0			0
$391$	−1.44907			−0.0732824
$392$		0			0
$393$	−0.101630	+	0.0149215i	−0.00512654	+	0.000752691i
$394$		0			0
$395$	0.680002	+	0.0788454i	0.0342146	+	0.00396714i
$396$		0			0
$397$	11.4361	+	11.4361i	0.573964	+	0.573964i	0.933234	−	0.359270i	$-0.116974\pi$
$397$	11.4361	+	11.4361i	0.573964	+	0.573964i	−0.359270	+	0.933234i	$0.616974\pi$
$398$		0			0
$399$	−45.3024	−	33.7027i	−2.26795	−	1.68724i
$400$		0			0
$401$			3.90238i			0.194875i	0.995242	+	0.0974377i	$0.0310647\pi$
$401$			3.90238i			0.194875i	−0.995242	+	0.0974377i	$0.968935\pi$
$402$		0			0
$403$	−7.28244	+	7.28244i	−0.362764	+	0.362764i
$404$		0			0
$405$	9.07269	+	17.9635i	0.450825	+	0.892612i
$406$		0			0
$407$	1.66932	−	1.66932i	0.0827450	−	0.0827450i
$408$		0			0
$409$			8.57872i			0.424191i	0.977249	+	0.212095i	$0.0680287\pi$
$409$			8.57872i			0.424191i	−0.977249	+	0.212095i	$0.931971\pi$
$410$		0			0
$411$	−30.3458	−	22.5757i	−1.49685	−	1.11358i
$412$		0			0
$413$	16.5092	+	16.5092i	0.812367	+	0.812367i
$414$		0			0
$415$	−8.07461	+	6.39668i	−0.396367	+	0.314001i
$416$		0			0
$417$	−24.1536	+	3.54629i	−1.18281	+	0.173663i
$418$		0			0
$419$	1.06570			0.0520627			0.0260313	−	0.999661i	$-0.491713\pi$
$419$	1.06570			0.0520627			0.0260313	+	0.999661i	$0.491713\pi$
$420$		0			0
$421$	−8.18730			−0.399025			−0.199512	−	0.979895i	$-0.563936\pi$
$421$	−8.18730			−0.399025			−0.199512	+	0.979895i	$0.563936\pi$
$422$		0			0
$423$	−8.81686	+	16.3783i	−0.428691	+	0.796340i
$424$		0			0
$425$	6.15959	−	3.81499i	0.298784	−	0.185054i
$426$		0			0
$427$	30.1374	+	30.1374i	1.45845	+	1.45845i
$428$		0			0
$429$	4.34576	−	5.84147i	0.209815	−	0.282029i
$430$		0			0
$431$		−	26.7826i		−	1.29007i	−0.764153	−	0.645035i	$-0.776843\pi$
$431$		−	26.7826i		−	1.29007i	0.764153	−	0.645035i	$-0.223157\pi$
$432$		0			0
$433$	−14.4098	+	14.4098i	−0.692492	+	0.692492i	−0.962780	−	0.270288i	$-0.912881\pi$
$433$	−14.4098	+	14.4098i	−0.692492	+	0.692492i	0.270288	+	0.962780i	$0.412881\pi$
$434$		0			0
$435$	7.57387	−	0.229918i	0.363139	−	0.0110237i
$436$		0			0
$437$	5.86375	−	5.86375i	0.280501	−	0.280501i
$438$		0			0
$439$			9.26396i			0.442145i	0.975257	+	0.221072i	$0.0709557\pi$
$439$			9.26396i			0.442145i	−0.975257	+	0.221072i	$0.929044\pi$
$440$		0			0
$441$	−7.29023	−	24.2915i	−0.347154	−	1.15674i
$442$		0			0
$443$	−24.0899	−	24.0899i	−1.14455	−	1.14455i	−0.987608	−	0.156939i	$-0.949837\pi$
$443$	−24.0899	−	24.0899i	−1.14455	−	1.14455i	−0.156939	−	0.987608i	$-0.550163\pi$
$444$		0			0
$445$	−4.10658	+	35.4171i	−0.194670	+	1.67893i
$446$		0			0
$447$	−5.24919	−	35.7520i	−0.248278	−	1.69101i
$448$		0			0
$449$	−8.43935			−0.398277			−0.199139	−	0.979971i	$-0.563814\pi$
$449$	−8.43935			−0.398277			−0.199139	+	0.979971i	$0.563814\pi$
$450$		0			0
$451$	12.9796			0.611186
$452$		0			0
$453$	0.458248	+	3.12110i	0.0215303	+	0.146642i
$454$		0			0
$455$	−2.03503	+	17.5511i	−0.0954036	+	0.822808i
$456$		0			0
$457$	−7.15431	−	7.15431i	−0.334664	−	0.334664i	0.519690	−	0.854355i	$-0.326047\pi$
$457$	−7.15431	−	7.15431i	−0.334664	−	0.334664i	−0.854355	+	0.519690i	$0.826047\pi$
$458$		0			0
$459$	7.07807	+	2.56812i	0.330376	+	0.119869i
$460$		0			0
$461$			32.3930i			1.50869i	0.656476	+	0.754347i	$0.272046\pi$
$461$			32.3930i			1.50869i	−0.656476	+	0.754347i	$0.727954\pi$
$462$		0			0
$463$	−16.0338	+	16.0338i	−0.745155	+	0.745155i	−0.973565	−	0.228410i	$-0.926647\pi$
$463$	−16.0338	+	16.0338i	−0.745155	+	0.745155i	0.228410	+	0.973565i	$0.426647\pi$
$464$		0			0
$465$	−19.8353	+	0.602135i	−0.919840	+	0.0279233i
$466$		0			0
$467$	19.7811	−	19.7811i	0.915358	−	0.915358i	−0.0813294	−	0.996687i	$-0.525917\pi$
$467$	19.7811	−	19.7811i	0.915358	−	0.915358i	0.996687	+	0.0813294i	$0.0259166\pi$
$468$		0			0
$469$			4.76841i			0.220185i
$470$		0			0
$471$	15.1409	−	20.3520i	0.697655	−	0.937773i
$472$		0			0
$473$	−5.88939	−	5.88939i	−0.270795	−	0.270795i
$474$		0			0
$475$	−9.48761	+	40.3629i	−0.435321	+	1.85198i
$476$		0			0
$477$	20.0081	+	10.7709i	0.916109	+	0.493166i
$478$		0			0
$479$	24.9210			1.13867			0.569335	−	0.822105i	$-0.307201\pi$
$479$	24.9210			1.13867			0.569335	+	0.822105i	$0.307201\pi$
$480$		0			0
$481$	2.26903			0.103459
$482$		0			0
$483$	6.73673	−	0.989103i	0.306532	−	0.0450057i
$484$		0			0
$485$	10.6440	−	8.43215i	0.483320	−	0.382884i
$486$		0			0
$487$	−16.7969	−	16.7969i	−0.761139	−	0.761139i	0.215389	−	0.976528i	$-0.430898\pi$
$487$	−16.7969	−	16.7969i	−0.761139	−	0.761139i	−0.976528	+	0.215389i	$0.930898\pi$
$488$		0			0
$489$	−8.31279	−	6.18429i	−0.375917	−	0.279663i
$490$		0			0
$491$		−	8.95545i		−	0.404154i	−0.979370	−	0.202077i	$-0.935231\pi$
$491$		−	8.95545i		−	0.404154i	0.979370	−	0.202077i	$-0.0647691\pi$
$492$		0			0
$493$	2.00468	−	2.00468i	0.0902862	−	0.0902862i
$494$		0			0
$495$	13.8117	−	2.45810i	0.620791	−	0.110484i
$496$		0			0
$497$	12.4941	−	12.4941i	0.560438	−	0.560438i
$498$		0			0
$499$		−	29.9823i		−	1.34219i	−0.741370	−	0.671097i	$-0.765823\pi$
$499$		−	29.9823i		−	1.34219i	0.741370	−	0.671097i	$-0.234177\pi$
$500$		0			0
$501$	−10.5403	−	7.84144i	−0.470905	−	0.350330i
$502$		0			0
$503$	−0.996614	−	0.996614i	−0.0444368	−	0.0444368i	0.684539	−	0.728976i	$-0.260003\pi$
$503$	−0.996614	−	0.996614i	−0.0444368	−	0.0444368i	−0.728976	+	0.684539i	$0.760003\pi$
$504$		0			0
$505$	14.2973	+	1.65775i	0.636220	+	0.0737690i
$506$		0			0
$507$	−15.3543	+	2.25435i	−0.681908	+	0.100119i
$508$		0			0
$509$	19.4160			0.860601			0.430300	−	0.902686i	$-0.358408\pi$
$509$	19.4160			0.860601			0.430300	+	0.902686i	$0.358408\pi$
$510$		0			0
$511$	39.3627			1.74130
$512$		0			0
$513$	−39.0340	+	18.2499i	−1.72339	+	0.805752i
$514$		0			0
$515$	−14.3805	−	18.1526i	−0.633679	−	0.799901i
$516$		0			0
$517$	9.16865	+	9.16865i	0.403237	+	0.403237i
$518$		0			0
$519$	19.2092	−	25.8205i	0.843188	−	1.13340i
$520$		0			0
$521$			20.7736i			0.910108i	0.890464	+	0.455054i	$0.150380\pi$
$521$			20.7736i			0.910108i	−0.890464	+	0.455054i	$0.849620\pi$
$522$		0			0
$523$	30.2848	−	30.2848i	1.32426	−	1.32426i	0.413969	−	0.910291i	$-0.364142\pi$
$523$	30.2848	−	30.2848i	1.32426	−	1.32426i	0.910291	−	0.413969i	$-0.135858\pi$
$524$		0			0
$525$	−26.0320	+	21.9404i	−1.13613	+	0.957557i
$526$		0			0
$527$	−5.25008	+	5.25008i	−0.228697	+	0.228697i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$		0			0
$531$	17.0654	−	5.12157i	0.740575	−	0.222257i
$532$		0			0
$533$	8.82130	+	8.82130i	0.382093	+	0.382093i
$534$		0			0
$535$	1.13556	+	1.43343i	0.0490944	+	0.0619725i
$536$		0			0
$537$	1.54140	+	10.4984i	0.0665164	+	0.453040i
$538$		0			0
$539$	−17.6796			−0.761516
$540$		0			0
$541$	6.50731			0.279771			0.139886	−	0.990168i	$-0.455327\pi$
$541$	6.50731			0.279771			0.139886	+	0.990168i	$0.455327\pi$
$542$		0			0
$543$	−6.32081	−	43.0508i	−0.271252	−	1.84748i
$544$		0			0
$545$	36.4668	+	4.22828i	1.56206	+	0.181120i
$546$		0			0
$547$	8.14576	+	8.14576i	0.348287	+	0.348287i	0.859471	−	0.511184i	$-0.170793\pi$
$547$	8.14576	+	8.14576i	0.348287	+	0.348287i	−0.511184	+	0.859471i	$0.670793\pi$
$548$		0			0
$549$	31.1526	−	9.34935i	1.32956	−	0.399020i
$550$		0			0
$551$			16.2242i			0.691173i
$552$		0			0
$553$	−0.851001	+	0.851001i	−0.0361882	+	0.0361882i
$554$		0			0
$555$	3.18390	+	2.99629i	0.135149	+	0.127185i
$556$		0			0
$557$	6.62439	−	6.62439i	0.280684	−	0.280684i	−0.552697	−	0.833382i	$-0.686402\pi$
$557$	6.62439	−	6.62439i	0.280684	−	0.280684i	0.833382	+	0.552697i	$0.186402\pi$
$558$		0			0
$559$		−	8.00519i		−	0.338583i
$560$		0			0
$561$	3.13296	−	4.21125i	0.132274	−	0.177799i
$562$		0			0
$563$	10.1294	+	10.1294i	0.426903	+	0.426903i	0.887572	−	0.460669i	$-0.152390\pi$
$563$	10.1294	+	10.1294i	0.426903	+	0.426903i	−0.460669	+	0.887572i	$0.652390\pi$
$564$		0			0
$565$	5.22013	−	4.13537i	0.219613	−	0.173976i
$566$		0			0
$567$	−34.6590	−	7.10786i	−1.45554	−	0.298502i
$568$		0			0
$569$	−8.21656			−0.344456			−0.172228	−	0.985057i	$-0.555097\pi$
$569$	−8.21656			−0.344456			−0.172228	+	0.985057i	$0.555097\pi$
$570$		0			0
$571$	22.9584			0.960779			0.480389	−	0.877055i	$-0.340495\pi$
$571$	22.9584			0.960779			0.480389	+	0.877055i	$0.340495\pi$
$572$		0			0
$573$	43.5061	−	6.38766i	1.81749	−	0.266848i
$574$		0			0
$575$	−2.63273	−	4.25074i	−0.109792	−	0.177268i
$576$		0			0
$577$	−18.7367	−	18.7367i	−0.780017	−	0.780017i	0.199816	−	0.979833i	$-0.435966\pi$
$577$	−18.7367	−	18.7367i	−0.780017	−	0.780017i	−0.979833	+	0.199816i	$0.935966\pi$
$578$		0			0
$579$	9.53163	+	7.09105i	0.396121	+	0.294694i
$580$		0			0
$581$		−	18.1104i		−	0.751344i
$582$		0			0
$583$	11.2007	−	11.2007i	0.463884	−	0.463884i
$584$		0			0
$585$	11.0574	+	7.71624i	0.457168	+	0.319027i
$586$		0			0
$587$	−19.7253	+	19.7253i	−0.814152	+	0.814152i	−0.985253	−	0.171102i	$-0.945267\pi$
$587$	−19.7253	+	19.7253i	−0.814152	+	0.814152i	0.171102	+	0.985253i	$0.445267\pi$
$588$		0			0
$589$		−	42.4897i		−	1.75076i
$590$		0			0
$591$	−28.1090	−	20.9117i	−1.15625	−	0.860191i
$592$		0			0
$593$	−10.7006	−	10.7006i	−0.439420	−	0.439420i	0.452397	−	0.891817i	$-0.350569\pi$
$593$	−10.7006	−	10.7006i	−0.439420	−	0.439420i	−0.891817	+	0.452397i	$0.850569\pi$
$594$		0			0
$595$	−1.46710	+	12.6530i	−0.0601452	+	0.518722i
$596$		0			0
$597$	9.83264	−	1.44365i	0.402423	−	0.0590847i
$598$		0			0
$599$	−23.6720			−0.967213			−0.483607	−	0.875285i	$-0.660673\pi$
$599$	−23.6720			−0.967213			−0.483607	+	0.875285i	$0.660673\pi$
$600$		0			0
$601$	−29.8896			−1.21922			−0.609612	−	0.792700i	$-0.708675\pi$
$601$	−29.8896			−1.21922			−0.609612	+	0.792700i	$0.708675\pi$
$602$		0			0
$603$	3.20416	+	1.72489i	0.130484	+	0.0702428i
$604$		0			0
$605$	−1.70662	+	14.7188i	−0.0693841	+	0.598403i
$606$		0			0
$607$	−1.62565	−	1.62565i	−0.0659830	−	0.0659830i	0.673345	−	0.739328i	$-0.264857\pi$
$607$	−1.62565	−	1.62565i	−0.0659830	−	0.0659830i	−0.739328	+	0.673345i	$0.764857\pi$
$608$		0			0
$609$	−7.95144	+	10.6881i	−0.322209	+	0.433106i
$610$		0			0
$611$			12.4625i			0.504181i
$612$		0			0
$613$	−25.9485	+	25.9485i	−1.04805	+	1.04805i	−0.0492648	+	0.998786i	$0.515688\pi$
$613$	−25.9485	+	25.9485i	−1.04805	+	1.04805i	−0.998786	+	0.0492648i	$0.984312\pi$
$614$		0			0
$615$	0.729373	+	24.0267i	0.0294111	+	0.968850i
$616$		0			0
$617$	3.18087	−	3.18087i	0.128057	−	0.128057i	−0.640173	−	0.768230i	$-0.721138\pi$
$617$	3.18087	−	3.18087i	0.128057	−	0.128057i	0.768230	+	0.640173i	$0.221138\pi$
$618$		0			0
$619$		−	0.688855i		−	0.0276874i	−0.999904	−	0.0138437i	$-0.995593\pi$
$619$		−	0.688855i		−	0.0276874i	0.999904	−	0.0138437i	$-0.00440673\pi$
$620$		0			0
$621$	1.77226	−	4.88458i	0.0711182	−	0.196011i
$622$		0			0
$623$	−44.3234	−	44.3234i	−1.77578	−	1.77578i
$624$		0			0
$625$	22.3820	+	11.1375i	0.895282	+	0.445501i
$626$		0			0
$627$	4.36340	+	29.7189i	0.174257	+	1.18686i
$628$		0			0
$629$	1.63580			0.0652235
$630$		0			0
$631$	−35.3086			−1.40562			−0.702808	−	0.711380i	$-0.748070\pi$
$631$	−35.3086			−1.40562			−0.702808	+	0.711380i	$0.748070\pi$
$632$		0			0
$633$	−1.09257	−	7.44143i	−0.0434257	−	0.295770i
$634$		0			0
$635$	7.95982	−	6.30575i	0.315876	−	0.250236i
$636$		0			0
$637$	−12.0156	−	12.0156i	−0.476074	−	0.476074i
$638$		0			0
$639$	−3.87598	−	12.9150i	−0.153331	−	0.510910i
$640$		0			0
$641$		−	5.05249i		−	0.199561i	−0.995009	−	0.0997807i	$-0.968186\pi$
$641$		−	5.05249i		−	0.199561i	0.995009	−	0.0997807i	$-0.0318141\pi$
$642$		0			0
$643$	−13.7611	+	13.7611i	−0.542684	+	0.542684i	−0.924315	−	0.381631i	$-0.875363\pi$
$643$	−13.7611	+	13.7611i	−0.542684	+	0.542684i	0.381631	+	0.924315i	$0.375363\pi$
$644$		0			0
$645$	10.5710	−	11.2329i	0.416232	−	0.442294i
$646$		0			0
$647$	−10.0395	+	10.0395i	−0.394695	+	0.394695i	−0.876357	−	0.481662i	$-0.840033\pi$
$647$	−10.0395	+	10.0395i	−0.394695	+	0.394695i	0.481662	+	0.876357i	$0.340033\pi$
$648$		0			0
$649$		−	12.4204i		−	0.487543i
$650$		0			0
$651$	20.8241	−	27.9913i	0.816162	−	1.09707i
$652$		0			0
$653$	30.5242	+	30.5242i	1.19451	+	1.19451i	0.975788	+	0.218718i	$0.0701874\pi$
$653$	30.5242	+	30.5242i	1.19451	+	1.19451i	0.218718	+	0.975788i	$0.429813\pi$
$654$		0			0
$655$	−0.131727	−	0.0152736i	−0.00514702	−	0.000596791i
$656$		0			0
$657$	14.2387	−	26.4500i	0.555505	−	1.03191i
$658$		0			0
$659$	34.4272			1.34109			0.670547	−	0.741867i	$-0.266059\pi$
$659$	34.4272			1.34109			0.670547	+	0.741867i	$0.266059\pi$
$660$		0			0
$661$	−48.1199			−1.87165			−0.935824	−	0.352468i	$-0.885343\pi$
$661$	−48.1199			−1.87165			−0.935824	+	0.352468i	$0.885343\pi$
$662$		0			0
$663$	4.99133	−	0.732839i	0.193847	−	0.0284611i
$664$		0			0
$665$	−45.2645	−	57.1380i	−1.75528	−	2.21572i
$666$		0			0
$667$	−1.38343	−	1.38343i	−0.0535666	−	0.0535666i
$668$		0			0
$669$	−34.5737	−	25.7210i	−1.33669	−	0.994433i
$670$		0			0
$671$		−	22.6732i		−	0.875290i
$672$		0			0
$673$	35.8488	−	35.8488i	1.38187	−	1.38187i	0.540568	−	0.841300i	$-0.318209\pi$
$673$	35.8488	−	35.8488i	1.38187	−	1.38187i	0.841300	−	0.540568i	$-0.181791\pi$
$674$		0			0
$675$	5.32636	+	25.4289i	0.205012	+	0.978760i
$676$		0			0
$677$	25.2413	−	25.2413i	0.970101	−	0.970101i	−0.0294652	−	0.999566i	$-0.509380\pi$
$677$	25.2413	−	25.2413i	0.970101	−	0.970101i	0.999566	+	0.0294652i	$0.00938041\pi$
$678$		0			0
$679$			23.8732i			0.916170i
$680$		0			0
$681$	−35.5459	−	26.4444i	−1.36212	−	1.01335i
$682$		0			0
$683$	−0.208044	−	0.208044i	−0.00796059	−	0.00796059i	0.703115	−	0.711076i	$-0.251792\pi$
$683$	−0.208044	−	0.208044i	−0.00796059	−	0.00796059i	−0.711076	+	0.703115i	$0.751792\pi$
$684$		0			0
$685$	−30.3205	−	38.2739i	−1.15848	−	1.46237i
$686$		0			0
$687$	2.09194	−	0.307144i	0.0798125	−	0.0117183i
$688$		0			0
$689$	15.2246			0.580010
$690$		0			0
$691$	38.8358			1.47738			0.738692	−	0.674043i	$-0.235444\pi$
$691$	38.8358			1.47738			0.738692	+	0.674043i	$0.235444\pi$
$692$		0			0
$693$	−11.6907	+	21.7167i	−0.444092	+	0.824949i
$694$		0			0
$695$	−31.3068	−	3.62998i	−1.18753	−	0.137693i
$696$		0			0
$697$	6.35948	+	6.35948i	0.240883	+	0.240883i
$698$		0			0
$699$	−13.3498	+	17.9446i	−0.504937	+	0.678725i
$700$		0			0
$701$		−	41.5266i		−	1.56844i	−0.620483	−	0.784220i	$-0.713064\pi$
$701$		−	41.5266i		−	1.56844i	0.620483	−	0.784220i	$-0.286936\pi$
$702$		0			0
$703$	−6.61937	+	6.61937i	−0.249654	+	0.249654i
$704$		0			0
$705$	−16.4570	+	17.4874i	−0.619806	+	0.658615i
$706$		0			0
$707$	−17.8926	+	17.8926i	−0.672920	+	0.672920i
$708$		0			0
$709$			2.94124i			0.110460i	0.998474	+	0.0552302i	$0.0175893\pi$
$709$			2.94124i			0.110460i	−0.998474	+	0.0552302i	$0.982411\pi$
$710$		0			0
$711$	0.264001	+	0.879669i	0.00990082	+	0.0329902i
$712$		0			0
$713$	3.62308	+	3.62308i	0.135685	+	0.135685i
$714$		0			0
$715$	7.36760	−	5.83659i	0.275533	−	0.218276i
$716$		0			0
$717$	5.25045	+	35.7605i	0.196082	+	1.33550i
$718$		0			0
$719$	40.9970			1.52893			0.764466	−	0.644664i	$-0.223003\pi$
$719$	40.9970			1.52893			0.764466	+	0.644664i	$0.223003\pi$
$720$		0			0
$721$	40.7141			1.51627
$722$		0			0
$723$	7.44602	+	50.7145i	0.276920	+	1.88609i
$724$		0			0
$725$	9.52278	+	2.23840i	0.353667	+	0.0831322i
$726$		0			0
$727$	25.2906	+	25.2906i	0.937978	+	0.937978i	0.998186	−	0.0602077i	$-0.0191763\pi$
$727$	25.2906	+	25.2906i	0.937978	+	0.937978i	−0.0602077	+	0.998186i	$0.519176\pi$
$728$		0			0
$729$	−17.3134	+	20.7182i	−0.641239	+	0.767341i
$730$		0			0
$731$		−	5.77113i		−	0.213453i
$732$		0			0
$733$	27.6448	−	27.6448i	1.02109	−	1.02109i	0.0213126	−	0.999773i	$-0.493215\pi$
$733$	27.6448	−	27.6448i	1.02109	−	1.02109i	0.999773	−	0.0213126i	$-0.00678451\pi$
$734$		0			0
$735$	−0.993485	−	32.7270i	−0.0366452	−	1.20715i
$736$		0			0
$737$	1.79371	−	1.79371i	0.0660721	−	0.0660721i
$738$		0			0
$739$		−	20.3261i		−	0.747708i	−0.927488	−	0.373854i	$-0.878036\pi$
$739$		−	20.3261i		−	0.747708i	0.927488	−	0.373854i	$-0.121964\pi$
$740$		0			0
$741$	−17.2323	+	23.1633i	−0.633044	+	0.850924i
$742$		0			0
$743$	−13.9856	−	13.9856i	−0.513081	−	0.513081i	0.402388	−	0.915469i	$-0.368180\pi$
$743$	−13.9856	−	13.9856i	−0.513081	−	0.513081i	−0.915469	+	0.402388i	$0.868180\pi$
$744$		0			0
$745$	5.37307	−	46.3400i	0.196854	−	1.69777i
$746$		0			0
$747$	−12.1694	−	6.55109i	−0.445254	−	0.239692i
$748$		0			0
$749$	−3.21500			−0.117474
$750$		0			0
$751$	−44.1289			−1.61029			−0.805143	−	0.593081i	$-0.797911\pi$
$751$	−44.1289			−1.61029			−0.805143	+	0.593081i	$0.797911\pi$
$752$		0			0
$753$	−38.0616	+	5.58829i	−1.38704	+	0.203649i
$754$		0			0
$755$	−0.469062	+	4.04542i	−0.0170709	+	0.147228i
$756$		0			0
$757$	2.21865	+	2.21865i	0.0806384	+	0.0806384i	0.746276	−	0.665637i	$-0.231840\pi$
$757$	2.21865	+	2.21865i	0.0806384	+	0.0806384i	−0.665637	+	0.746276i	$0.731840\pi$
$758$		0			0
$759$	−2.90619	−	2.16206i	−0.105488	−	0.0784776i
$760$		0			0
$761$			15.2538i			0.552948i	0.961021	+	0.276474i	$0.0891660\pi$
$761$			15.2538i			0.552948i	−0.961021	+	0.276474i	$0.910834\pi$
$762$		0			0
$763$	−45.6370	+	45.6370i	−1.65217	+	1.65217i
$764$		0			0
$765$	7.97156	+	5.56281i	0.288212	+	0.201124i
$766$		0			0
$767$	8.44124	−	8.44124i	0.304795	−	0.304795i
$768$		0			0
$769$			19.5114i			0.703598i	0.936076	+	0.351799i	$0.114430\pi$
$769$			19.5114i			0.703598i	−0.936076	+	0.351799i	$0.885570\pi$
$770$		0			0
$771$	−23.2750	−	17.3154i	−0.838230	−	0.623601i
$772$		0			0
$773$	−31.3087	−	31.3087i	−1.12610	−	1.12610i	−0.990806	−	0.135290i	$-0.956803\pi$
$773$	−31.3087	−	31.3087i	−1.12610	−	1.12610i	−0.135290	−	0.990806i	$-0.543197\pi$
$774$		0			0
$775$	−24.9393	−	5.86219i	−0.895848	−	0.210576i
$776$		0			0
$777$	−7.60485	+	1.11656i	−0.272822	+	0.0400564i
$778$		0			0
$779$	−51.4682			−1.84404
$780$		0			0
$781$	−9.39969			−0.336347
$782$		0			0
$783$	4.30568	+	9.20926i	0.153872	+	0.329112i
$784$		0			0
$785$	25.6692	−	20.3350i	0.916172	−	0.725789i
$786$		0			0
$787$	−29.9558	−	29.9558i	−1.06781	−	1.06781i	−0.997527	−	0.0702815i	$-0.977610\pi$
$787$	−29.9558	−	29.9558i	−1.06781	−	1.06781i	−0.0702815	−	0.997527i	$-0.522390\pi$
$788$		0			0
$789$	4.46786	−	6.00559i	0.159060	−	0.213805i
$790$		0			0
$791$			11.7081i			0.416293i
$792$		0			0
$793$	15.4094	−	15.4094i	0.547202	−	0.547202i
$794$		0			0
$795$	21.3631	+	20.1043i	0.757670	+	0.713025i
$796$		0			0
$797$	25.4553	−	25.4553i	0.901675	−	0.901675i	−0.0939063	−	0.995581i	$-0.529935\pi$
$797$	25.4553	−	25.4553i	0.901675	−	0.901675i	0.995581	+	0.0939063i	$0.0299354\pi$
$798$		0			0
$799$			8.98454i			0.317850i
$800$		0			0
$801$	−45.8166	+	13.7502i	−1.61885	+	0.485840i
$802$		0			0
$803$	−14.8068	−	14.8068i	−0.522522	−	0.522522i
$804$		0			0
$805$	8.73183	+	1.01244i	0.307756	+	0.0356840i
$806$		0			0
$807$	−4.42467	−	30.1362i	−0.155756	−	1.06085i
$808$		0			0
$809$	16.4039			0.576732			0.288366	−	0.957520i	$-0.406888\pi$
$809$	16.4039			0.576732			0.288366	+	0.957520i	$0.406888\pi$
$810$		0			0
$811$	22.3570			0.785061			0.392531	−	0.919739i	$-0.371600\pi$
$811$	22.3570			0.785061			0.392531	+	0.919739i	$0.371600\pi$
$812$		0			0
$813$	−1.76866	−	12.0463i	−0.0620298	−	0.422482i
$814$		0			0
$815$	−8.30584	−	10.4846i	−0.290941	−	0.367258i
$816$		0			0
$817$	23.3533	+	23.3533i	0.817028	+	0.817028i
$818$		0			0
$819$	−22.7046	+	6.81397i	−0.793362	+	0.238099i
$820$		0			0
$821$			38.8774i			1.35683i	0.734679	+	0.678415i	$0.237333\pi$
$821$			38.8774i			1.35683i	−0.734679	+	0.678415i	$0.762667\pi$
$822$		0			0
$823$	−8.92056	+	8.92056i	−0.310951	+	0.310951i	−0.845278	−	0.534327i	$-0.820565\pi$
$823$	−8.92056	+	8.92056i	−0.310951	+	0.310951i	0.534327	+	0.845278i	$0.320565\pi$
$824$		0			0
$825$	18.0455	+	1.53914i	0.628265	+	0.0535859i
$826$		0			0
$827$	10.3439	−	10.3439i	0.359691	−	0.359691i	−0.504008	−	0.863699i	$-0.668142\pi$
$827$	10.3439	−	10.3439i	0.359691	−	0.359691i	0.863699	+	0.504008i	$0.168142\pi$
$828$		0			0
$829$		−	38.6554i		−	1.34256i	−0.741205	−	0.671279i	$-0.765745\pi$
$829$		−	38.6554i		−	1.34256i	0.741205	−	0.671279i	$-0.234255\pi$
$830$		0			0
$831$	−8.99542	+	12.0914i	−0.312048	+	0.419447i
$832$		0			0
$833$	−8.66230	−	8.66230i	−0.300131	−	0.300131i
$834$		0			0
$835$	−10.5315	−	13.2940i	−0.364457	−	0.460058i
$836$		0			0
$837$	−11.2762	−	24.1183i	−0.389762	−	0.833649i
$838$		0			0
$839$	40.8408			1.40998			0.704991	−	0.709216i	$-0.250951\pi$
$839$	40.8408			1.40998			0.704991	+	0.709216i	$0.250951\pi$
$840$		0			0
$841$	−25.1722			−0.868008
$842$		0			0
$843$	−27.5470	+	4.04451i	−0.948768	+	0.139300i
$844$		0			0
$845$	−19.9015	−	2.30755i	−0.684632	−	0.0793823i
$846$		0			0
$847$	−18.4201	−	18.4201i	−0.632921	−	0.632921i
$848$		0			0
$849$	39.5050	+	29.3897i	1.35581	+	1.00865i
$850$		0			0
$851$		−	1.12886i		−	0.0386969i
$852$		0			0
$853$	38.7603	−	38.7603i	1.32713	−	1.32713i	0.419264	−	0.907865i	$-0.362288\pi$
$853$	38.7603	−	38.7603i	1.32713	−	1.32713i	0.907865	−	0.419264i	$-0.137712\pi$
$854$		0			0
$855$	−54.7678	+	9.74715i	−1.87302	+	0.333346i
$856$		0			0
$857$	−1.67353	+	1.67353i	−0.0571666	+	0.0571666i	−0.735112	−	0.677946i	$-0.762871\pi$
$857$	−1.67353	+	1.67353i	−0.0571666	+	0.0571666i	0.677946	+	0.735112i	$0.262871\pi$
$858$		0			0
$859$			31.6190i			1.07883i	0.842041	+	0.539413i	$0.181354\pi$
$859$			31.6190i			1.07883i	−0.842041	+	0.539413i	$0.818646\pi$
$860$		0			0
$861$	−33.9062	−	25.2245i	−1.15552	−	0.859648i
$862$		0			0
$863$	5.95130	+	5.95130i	0.202585	+	0.202585i	0.801106	−	0.598522i	$-0.204245\pi$
$863$	5.95130	+	5.95130i	0.202585	+	0.202585i	−0.598522	+	0.801106i	$0.704245\pi$
$864$		0			0
$865$	32.5663	−	25.7989i	1.10729	−	0.877191i
$866$		0			0
$867$	−25.5342	+	3.74899i	−0.867186	+	0.127322i
$868$		0			0
$869$	0.640233			0.0217184
$870$		0			0
$871$	2.43811			0.0826121
$872$		0			0
$873$	16.0418	+	8.63570i	0.542931	+	0.292274i
$874$		0			0
$875$	−39.7822	+	18.6849i	−1.34488	+	0.631664i
$876$		0			0
$877$	25.6773	+	25.6773i	0.867060	+	0.867060i	0.992146	−	0.125086i	$-0.0399206\pi$
$877$	25.6773	+	25.6773i	0.867060	+	0.867060i	−0.125086	+	0.992146i	$0.539921\pi$
$878$		0			0
$879$	−14.1999	+	19.0872i	−0.478950	+	0.643794i
$880$		0			0
$881$			22.4391i			0.755993i	0.925807	+	0.377997i	$0.123387\pi$
$881$			22.4391i			0.755993i	−0.925807	+	0.377997i	$0.876613\pi$
$882$		0			0
$883$	22.9171	−	22.9171i	0.771221	−	0.771221i	−0.207099	−	0.978320i	$-0.566402\pi$
$883$	22.9171	−	22.9171i	0.771221	−	0.771221i	0.978320	+	0.207099i	$0.0664022\pi$
$884$		0			0
$885$	22.9915	−	0.697948i	0.772851	−	0.0234613i
$886$		0			0
$887$	−14.9858	+	14.9858i	−0.503173	+	0.503173i	−0.912423	−	0.409249i	$-0.865791\pi$
$887$	−14.9858	+	14.9858i	−0.503173	+	0.503173i	0.409249	+	0.912423i	$0.365791\pi$
$888$		0			0
$889$			17.8529i			0.598767i
$890$		0			0
$891$	10.3638	+	15.7112i	0.347200	+	0.526346i
$892$		0			0
$893$	−36.3566	−	36.3566i	−1.21663	−	1.21663i
$894$		0			0
$895$	−1.57778	+	13.6075i	−0.0527393	+	0.454850i
$896$		0			0
$897$	−0.505732	−	3.44452i	−0.0168859	−	0.115009i
$898$		0			0
$899$	−10.0246			−0.334338
$900$		0			0
$901$	10.9757			0.365655
$902$		0			0
$903$	3.93925	+	26.8301i	0.131090	+	0.892849i
$904$		0			0
$905$	6.46998	−	55.8003i	0.215069	−	1.85486i
$906$		0			0
$907$	−29.2604	−	29.2604i	−0.971577	−	0.971577i	0.0280300	−	0.999607i	$-0.491077\pi$
$907$	−29.2604	−	29.2604i	−0.971577	−	0.971577i	−0.999607	+	0.0280300i	$0.991077\pi$
$908$		0			0
$909$	5.55072	+	18.4954i	0.184106	+	0.613452i
$910$		0			0
$911$		−	51.2630i		−	1.69842i	−0.528056	−	0.849209i	$-0.677079\pi$
$911$		−	51.2630i		−	1.69842i	0.528056	−	0.849209i	$-0.322921\pi$
$912$		0			0
$913$	−6.81247	+	6.81247i	−0.225460	+	0.225460i
$914$		0			0
$915$	41.9707	−	1.27409i	1.38751	−	0.0421202i
$916$		0			0
$917$	0.164853	−	0.164853i	0.00544392	−	0.00544392i
$918$		0			0
$919$			27.8803i			0.919687i	0.888000	+	0.459844i	$0.152095\pi$
$919$			27.8803i			0.919687i	−0.888000	+	0.459844i	$0.847905\pi$
$920$		0			0
$921$	18.4131	−	24.7504i	0.606732	−	0.815555i
$922$		0			0
$923$	−6.38829	−	6.38829i	−0.210273	−	0.210273i
$924$		0			0
$925$	2.97199	+	4.79850i	0.0977183	+	0.157774i
$926$		0			0
$927$	14.7276	−	27.3581i	0.483718	−	0.898558i
$928$		0			0
$929$	29.8262			0.978566			0.489283	−	0.872125i	$-0.337259\pi$
$929$	29.8262			0.978566			0.489283	+	0.872125i	$0.337259\pi$
$930$		0			0
$931$	70.1053			2.29761
$932$		0			0
$933$	20.3697	−	2.99073i	0.666874	−	0.0979120i
$934$		0			0
$935$	5.31148	−	4.20774i	0.173704	−	0.137608i
$936$		0			0
$937$	4.84312	+	4.84312i	0.158218	+	0.158218i	0.781777	−	0.623559i	$-0.214314\pi$
$937$	4.84312	+	4.84312i	0.158218	+	0.158218i	−0.623559	+	0.781777i	$0.714314\pi$
$938$		0			0
$939$	15.1920	+	11.3021i	0.495772	+	0.368829i
$940$		0			0
$941$			7.01236i			0.228596i	0.993446	+	0.114298i	$0.0364619\pi$
$941$			7.01236i			0.228596i	−0.993446	+	0.114298i	$0.963538\pi$
$942$		0			0
$943$	4.38868	−	4.38868i	0.142915	−	0.142915i
$944$		0			0
$945$	−40.8570	−	20.4204i	−1.32908	−	0.664276i
$946$		0			0
$947$	−24.3843	+	24.3843i	−0.792382	+	0.792382i	−0.981881	−	0.189499i	$-0.939314\pi$
$947$	−24.3843	+	24.3843i	−0.792382	+	0.792382i	0.189499	+	0.981881i	$0.439314\pi$
$948$		0			0
$949$		−	20.1263i		−	0.653327i
$950$		0			0
$951$	−17.8264	−	13.2619i	−0.578060	−	0.430048i
$952$		0			0
$953$	34.1950	+	34.1950i	1.10768	+	1.10768i	0.993454	+	0.114231i	$0.0364403\pi$
$953$	34.1950	+	34.1950i	1.10768	+	1.10768i	0.114231	+	0.993454i	$0.463560\pi$
$954$		0			0
$955$	56.3904	+	6.53840i	1.82475	+	0.211578i
$956$		0			0
$957$	7.01155	−	1.02945i	0.226651	−	0.0332775i
$958$		0			0
$959$	85.8436			2.77204
$960$		0			0
$961$	−4.74657			−0.153115
$962$		0			0
$963$	−1.16297	+	2.16034i	−0.0374761	+	0.0696160i
$964$		0			0
$965$	9.52367	+	12.0218i	0.306578	+	0.386997i
$966$		0			0
$967$	−15.4360	−	15.4360i	−0.496388	−	0.496388i	0.413923	−	0.910312i	$-0.364158\pi$
$967$	−15.4360	−	15.4360i	−0.496388	−	0.496388i	−0.910312	+	0.413923i	$0.864158\pi$
$968$		0			0
$969$	−12.4232	+	16.6989i	−0.399090	+	0.536447i
$970$		0			0
$971$			54.6394i			1.75346i	0.480982	+	0.876730i	$0.340280\pi$
$971$			54.6394i			1.75346i	−0.480982	+	0.876730i	$0.659720\pi$
$972$		0			0
$973$	39.1794	−	39.1794i	1.25603	−	1.25603i
$974$		0			0
$975$	11.2182	+	13.3103i	0.359270	+	0.426270i
$976$		0			0
$977$	18.6586	−	18.6586i	0.596940	−	0.596940i	−0.342557	−	0.939497i	$-0.611293\pi$
$977$	18.6586	−	18.6586i	0.596940	−	0.596940i	0.939497	+	0.342557i	$0.111293\pi$
$978$		0			0
$979$			33.3458i			1.06574i
$980$		0			0
$981$	14.1577	+	47.1744i	0.452021	+	1.50616i
$982$		0			0
$983$	−16.0140	−	16.0140i	−0.510767	−	0.510767i	0.403994	−	0.914761i	$-0.367621\pi$
$983$	−16.0140	−	16.0140i	−0.510767	−	0.510767i	−0.914761	+	0.403994i	$0.867621\pi$
$984$		0			0
$985$	−28.0855	−	35.4527i	−0.894879	−	1.12962i
$986$		0			0
$987$	−6.13266	−	41.7693i	−0.195205	−	1.32953i
$988$		0			0
$989$	−3.98265			−0.126641
$990$		0			0
$991$	33.3244			1.05858			0.529292	−	0.848440i	$-0.322458\pi$
$991$	33.3244			1.05858			0.529292	+	0.848440i	$0.322458\pi$
$992$		0			0
$993$	1.30133	+	8.86328i	0.0412964	+	0.281268i
$994$		0			0
$995$	12.7446	+	1.47772i	0.404030	+	0.0468469i
$996$		0			0
$997$	26.0246	+	26.0246i	0.824208	+	0.824208i	0.986708	−	0.162501i	$-0.0519560\pi$
$997$	26.0246	+	26.0246i	0.824208	+	0.824208i	−0.162501	+	0.986708i	$0.551956\pi$
$998$		0			0
$999$	−2.00063	+	5.51402i	−0.0632973	+	0.174456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.r.c.737.20	yes	80
3.2	odd	2	inner	1380.2.r.c.737.2	✓	80
5.3	odd	4	inner	1380.2.r.c.1013.2	yes	80
15.8	even	4	inner	1380.2.r.c.1013.20	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.r.c.737.2	✓	80	3.2	odd	2	inner
1380.2.r.c.737.20	yes	80	1.1	even	1	trivial
1380.2.r.c.1013.2	yes	80	5.3	odd	4	inner
1380.2.r.c.1013.20	yes	80	15.8	even	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)

\(f(q)\)	\(=\)	\(q+(0.251606 + 1.71368i) q^{3} +(-0.257544 + 2.22119i) q^{5} +(-2.77975 - 2.77975i) q^{7} +(-2.87339 + 0.862345i) q^{9} +O(q^{10})\)	\(q+(0.251606 + 1.71368i) q^{3} +(-0.257544 + 2.22119i) q^{5} +(-2.77975 - 2.77975i) q^{7} +(-2.87339 + 0.862345i) q^{9} +2.09128i q^{11} +(-1.42129 + 1.42129i) q^{13} +(-3.87120 + 0.117517i) q^{15} +(-1.02464 + 1.02464i) q^{17} -8.29259i q^{19} +(4.06419 - 5.46299i) q^{21} +(0.707107 + 0.707107i) q^{23} +(-4.86734 - 1.14411i) q^{25} +(-2.20074 - 4.70709i) q^{27} -1.95646 q^{29} +5.12381 q^{31} +(-3.58379 + 0.526180i) q^{33} +(6.89024 - 5.45843i) q^{35} +(-0.798227 - 0.798227i) q^{37} +(-2.79325 - 2.07804i) q^{39} -6.20653i q^{41} +(-2.81616 + 2.81616i) q^{43} +(-1.17540 - 6.60442i) q^{45} +(4.38422 - 4.38422i) q^{47} +8.45397i q^{49} +(-2.01372 - 1.49810i) q^{51} +(-5.35588 - 5.35588i) q^{53} +(-4.64513 - 0.538597i) q^{55} +(14.2108 - 2.08647i) q^{57} -5.93912 q^{59} -10.8418 q^{61} +(10.3844 + 5.59019i) q^{63} +(-2.79091 - 3.52301i) q^{65} +(-0.857707 - 0.857707i) q^{67} +(-1.03384 + 1.38967i) q^{69} +4.49470i q^{71} +(-7.08026 + 7.08026i) q^{73} +(0.735977 - 8.62892i) q^{75} +(5.81324 - 5.81324i) q^{77} -0.306144i q^{79} +(7.51272 - 4.95570i) q^{81} +(3.25756 + 3.25756i) q^{83} +(-2.01203 - 2.53982i) q^{85} +(-0.492259 - 3.35275i) q^{87} +15.9451 q^{89} +7.90167 q^{91} +(1.28918 + 8.78056i) q^{93} +(18.4194 + 2.13571i) q^{95} +(-4.29414 - 4.29414i) q^{97} +(-1.80341 - 6.00907i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{3}+O(q^{10}) \) 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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