LMFDB - Embedded newform 780.2.r.a.577.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [780,2,Mod(73,780)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(780, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("780.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	780.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:	$6.22833135766$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.4
Character	$\chi$	$=$	780.577
Dual form			780.2.r.a.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(0.136841 + 2.23188i) q^{5} +4.69969i q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(0.136841 + 2.23188i) q^{5} +4.69969i q^{7} -1.00000i q^{9} +(0.315352 + 0.315352i) q^{11} +(2.87788 + 2.17205i) q^{13} +(-1.67494 - 1.48141i) q^{15} +(1.07992 - 1.07992i) q^{17} +(-3.49017 - 3.49017i) q^{19} +(-3.32318 - 3.32318i) q^{21} +(-3.48094 - 3.48094i) q^{23} +(-4.96255 + 0.610824i) q^{25} +(0.707107 + 0.707107i) q^{27} +2.87828i q^{29} +(-1.13365 + 1.13365i) q^{31} -0.445975 q^{33} +(-10.4891 + 0.643109i) q^{35} +8.92799i q^{37} +(-3.57084 + 0.499101i) q^{39} +(6.10267 - 6.10267i) q^{41} +(-0.557675 - 0.557675i) q^{43} +(2.23188 - 0.136841i) q^{45} +6.16002i q^{47} -15.0871 q^{49} +1.52723i q^{51} +(8.42127 - 8.42127i) q^{53} +(-0.660673 + 0.746979i) q^{55} +4.93584 q^{57} +(-1.44238 + 1.44238i) q^{59} -5.80499 q^{61} +4.69969 q^{63} +(-4.45393 + 6.72031i) q^{65} +4.05741 q^{67} +4.92280 q^{69} +(-6.68803 + 6.68803i) q^{71} +0.734212 q^{73} +(3.07713 - 3.94097i) q^{75} +(-1.48205 + 1.48205i) q^{77} +12.9137i q^{79} -1.00000 q^{81} +1.05600i q^{83} +(2.55801 + 2.26246i) q^{85} +(-2.03525 - 2.03525i) q^{87} +(5.36534 - 5.36534i) q^{89} +(-10.2079 + 13.5251i) q^{91} -1.60322i q^{93} +(7.31203 - 8.26723i) q^{95} -4.56277 q^{97} +(0.315352 - 0.315352i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q + 8 q^{11} - 4 q^{13} - 4 q^{15} - 4 q^{17} - 16 q^{19} + 8 q^{21} - 8 q^{23} + 12 q^{25} - 8 q^{33} + 8 q^{39} + 12 q^{41} + 16 q^{43} + 4 q^{45} - 36 q^{49} + 36 q^{53} + 40 q^{55} + 16 q^{59} + 8 q^{61} - 40 q^{65} + 48 q^{67} - 8 q^{69} + 8 q^{71} + 48 q^{73} - 48 q^{77} - 28 q^{81} - 4 q^{85} - 24 q^{87} - 36 q^{89} - 24 q^{91} + 72 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) $ 28 * q + 8 * q^11 - 4 * q^13 - 4 * q^15 - 4 * q^17 - 16 * q^19 + 8 * q^21 - 8 * q^23 + 12 * q^25 - 8 * q^33 + 8 * q^39 + 12 * q^41 + 16 * q^43 + 4 * q^45 - 36 * q^49 + 36 * q^53 + 40 * q^55 + 16 * q^59 + 8 * q^61 - 40 * q^65 + 48 * q^67 - 8 * q^69 + 8 * q^71 + 48 * q^73 - 48 * q^77 - 28 * q^81 - 4 * q^85 - 24 * q^87 - 36 * q^89 - 24 * q^91 + 72 * q^95 - 72 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/780\mathbb{Z}\right)^\times$.

$n$	$157$	$301$	$391$	$521$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	0.136841	+	2.23188i	0.0611971	+	0.998126i
$5$	0.136841	+	2.23188i	0.0611971	+	0.998126i
$6$		0			0
$7$			4.69969i			1.77631i	0.459539	+	0.888157i	$0.348014\pi$
$7$			4.69969i			1.77631i	−0.459539	+	0.888157i	$0.651986\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	0.315352	+	0.315352i	0.0950822	+	0.0950822i	0.753048	−	0.657966i	$-0.228583\pi$
$11$	0.315352	+	0.315352i	0.0950822	+	0.0950822i	−0.657966	+	0.753048i	$0.728583\pi$
$12$		0			0
$13$	2.87788	+	2.17205i	0.798181	+	0.602418i
$13$	2.87788	+	2.17205i	0.798181	+	0.602418i
$14$		0			0
$15$	−1.67494	−	1.48141i	−0.432467	−	0.382500i
$16$		0			0
$17$	1.07992	−	1.07992i	0.261918	−	0.261918i	−0.563915	−	0.825833i	$-0.690705\pi$
$17$	1.07992	−	1.07992i	0.261918	−	0.261918i	0.825833	+	0.563915i	$0.190705\pi$
$18$		0			0
$19$	−3.49017	−	3.49017i	−0.800700	−	0.800700i	0.182505	−	0.983205i	$-0.441579\pi$
$19$	−3.49017	−	3.49017i	−0.800700	−	0.800700i	−0.983205	+	0.182505i	$0.941579\pi$
$20$		0			0
$21$	−3.32318	−	3.32318i	−0.725177	−	0.725177i
$22$		0			0
$23$	−3.48094	−	3.48094i	−0.725827	−	0.725827i	0.243959	−	0.969786i	$-0.421554\pi$
$23$	−3.48094	−	3.48094i	−0.725827	−	0.725827i	−0.969786	+	0.243959i	$0.921554\pi$
$24$		0			0
$25$	−4.96255	+	0.610824i	−0.992510	+	0.122165i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$			2.87828i			0.534483i	0.963630	+	0.267241i	$0.0861121\pi$
$29$			2.87828i			0.534483i	−0.963630	+	0.267241i	$0.913888\pi$
$30$		0			0
$31$	−1.13365	+	1.13365i	−0.203610	+	0.203610i	−0.801545	−	0.597935i	$-0.795988\pi$
$31$	−1.13365	+	1.13365i	−0.203610	+	0.203610i	0.597935	+	0.801545i	$0.295988\pi$
$32$		0			0
$33$	−0.445975			−0.0776343
$34$		0			0
$35$	−10.4891	+	0.643109i	−1.77299	+	0.108705i
$36$		0			0
$37$			8.92799i			1.46775i	0.679283	+	0.733876i	$0.262291\pi$
$37$			8.92799i			1.46775i	−0.679283	+	0.733876i	$0.737709\pi$
$38$		0			0
$39$	−3.57084	+	0.499101i	−0.571792	+	0.0799202i
$40$		0			0
$41$	6.10267	−	6.10267i	0.953078	−	0.953078i	−0.0458697	−	0.998947i	$-0.514606\pi$
$41$	6.10267	−	6.10267i	0.953078	−	0.953078i	0.998947	+	0.0458697i	$0.0146059\pi$
$42$		0			0
$43$	−0.557675	−	0.557675i	−0.0850447	−	0.0850447i	0.663305	−	0.748349i	$-0.269153\pi$
$43$	−0.557675	−	0.557675i	−0.0850447	−	0.0850447i	−0.748349	+	0.663305i	$0.769153\pi$
$44$		0			0
$45$	2.23188	−	0.136841i	0.332709	−	0.0203990i
$46$		0			0
$47$			6.16002i			0.898531i	0.893398	+	0.449265i	$0.148314\pi$
$47$			6.16002i			0.898531i	−0.893398	+	0.449265i	$0.851686\pi$
$48$		0			0
$49$	−15.0871			−2.15529
$50$		0			0
$51$			1.52723i			0.213855i
$52$		0			0
$53$	8.42127	−	8.42127i	1.15675	−	1.15675i	0.171581	−	0.985170i	$-0.445113\pi$
$53$	8.42127	−	8.42127i	1.15675	−	1.15675i	0.985170	−	0.171581i	$-0.0548874\pi$
$54$		0			0
$55$	−0.660673	+	0.746979i	−0.0890852	+	0.100723i
$56$		0			0
$57$	4.93584			0.653769
$58$		0			0
$59$	−1.44238	+	1.44238i	−0.187782	+	0.187782i	−0.794736	−	0.606955i	$-0.792391\pi$
$59$	−1.44238	+	1.44238i	−0.187782	+	0.187782i	0.606955	+	0.794736i	$0.292391\pi$
$60$		0			0
$61$	−5.80499			−0.743253			−0.371626	−	0.928382i	$-0.621200\pi$
$61$	−5.80499			−0.743253			−0.371626	+	0.928382i	$0.621200\pi$
$62$		0			0
$63$	4.69969			0.592105
$64$		0			0
$65$	−4.45393	+	6.72031i	−0.552442	+	0.833551i
$66$		0			0
$67$	4.05741			0.495691			0.247846	−	0.968800i	$-0.420277\pi$
$67$	4.05741			0.495691			0.247846	+	0.968800i	$0.420277\pi$
$68$		0			0
$69$	4.92280			0.592635
$70$		0			0
$71$	−6.68803	+	6.68803i	−0.793723	+	0.793723i	−0.982097	−	0.188374i	$-0.939678\pi$
$71$	−6.68803	+	6.68803i	−0.793723	+	0.793723i	0.188374	+	0.982097i	$0.439678\pi$
$72$		0			0
$73$	0.734212			0.0859330			0.0429665	−	0.999077i	$-0.486319\pi$
$73$	0.734212			0.0859330			0.0429665	+	0.999077i	$0.486319\pi$
$74$		0			0
$75$	3.07713	−	3.94097i	0.355317	−	0.455064i
$76$		0			0
$77$	−1.48205	+	1.48205i	−0.168896	+	0.168896i
$78$		0			0
$79$			12.9137i			1.45290i	0.687218	+	0.726451i	$0.258832\pi$
$79$			12.9137i			1.45290i	−0.687218	+	0.726451i	$0.741168\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$			1.05600i			0.115911i	0.998319	+	0.0579553i	$0.0184581\pi$
$83$			1.05600i			0.115911i	−0.998319	+	0.0579553i	$0.981542\pi$
$84$		0			0
$85$	2.55801	+	2.26246i	0.277456	+	0.245398i
$86$		0			0
$87$	−2.03525	−	2.03525i	−0.218202	−	0.218202i
$88$		0			0
$89$	5.36534	−	5.36534i	0.568725	−	0.568725i	−0.363046	−	0.931771i	$-0.618263\pi$
$89$	5.36534	−	5.36534i	0.568725	−	0.568725i	0.931771	+	0.363046i	$0.118263\pi$
$90$		0			0
$91$	−10.2079	+	13.5251i	−1.07008	+	1.41782i
$92$		0			0
$93$		−	1.60322i		−	0.166246i
$94$		0			0
$95$	7.31203	−	8.26723i	0.750199	−	0.848200i
$96$		0			0
$97$	−4.56277			−0.463279			−0.231640	−	0.972802i	$-0.574409\pi$
$97$	−4.56277			−0.463279			−0.231640	+	0.972802i	$0.574409\pi$
$98$		0			0
$99$	0.315352	−	0.315352i	0.0316941	−	0.0316941i
$100$		0			0
$101$		−	8.68921i		−	0.864609i	−0.901728	−	0.432304i	$-0.857701\pi$
$101$		−	8.68921i		−	0.864609i	0.901728	−	0.432304i	$-0.142299\pi$
$102$		0			0
$103$	3.72580	+	3.72580i	0.367114	+	0.367114i	0.866424	−	0.499310i	$-0.166413\pi$
$103$	3.72580	+	3.72580i	0.367114	+	0.367114i	−0.499310	+	0.866424i	$0.666413\pi$
$104$		0			0
$105$	6.96218	−	7.87168i	0.679440	−	0.768197i
$106$		0			0
$107$	−12.4478	−	12.4478i	−1.20337	−	1.20337i	−0.973134	−	0.230240i	$-0.926049\pi$
$107$	−12.4478	−	12.4478i	−1.20337	−	1.20337i	−0.230240	−	0.973134i	$-0.573951\pi$
$108$		0			0
$109$	12.0020	+	12.0020i	1.14958	+	1.14958i	0.986635	+	0.162949i	$0.0521006\pi$
$109$	12.0020	+	12.0020i	1.14958	+	1.14958i	0.162949	+	0.986635i	$0.447899\pi$
$110$		0			0
$111$	−6.31304	−	6.31304i	−0.599207	−	0.599207i
$112$		0			0
$113$	11.3426	−	11.3426i	1.06702	−	1.06702i	0.0694367	−	0.997586i	$-0.477880\pi$
$113$	11.3426	−	11.3426i	1.06702	−	1.06702i	0.997586	−	0.0694367i	$-0.0221202\pi$
$114$		0			0
$115$	7.29270	−	8.24537i	0.680048	−	0.768885i
$116$		0			0
$117$	2.17205	−	2.87788i	0.200806	−	0.266060i
$118$		0			0
$119$	5.07526	+	5.07526i	0.465249	+	0.465249i
$120$		0			0
$121$		−	10.8011i		−	0.981919i
$122$		0			0
$123$			8.63049i			0.778185i
$124$		0			0
$125$	−2.04236	−	10.9922i	−0.182674	−	0.983173i
$126$		0			0
$127$	−6.73937	+	6.73937i	−0.598022	+	0.598022i	−0.939786	−	0.341764i	$-0.888976\pi$
$127$	−6.73937	+	6.73937i	−0.598022	+	0.598022i	0.341764	+	0.939786i	$0.388976\pi$
$128$		0			0
$129$	0.788672			0.0694387
$130$		0			0
$131$	−5.18022			−0.452598			−0.226299	−	0.974058i	$-0.572663\pi$
$131$	−5.18022			−0.452598			−0.226299	+	0.974058i	$0.572663\pi$
$132$		0			0
$133$	16.4027	−	16.4027i	1.42229	−	1.42229i
$134$		0			0
$135$	−1.48141	+	1.67494i	−0.127500	+	0.144156i
$136$		0			0
$137$			16.8964i			1.44356i	0.692124	+	0.721778i	$0.256675\pi$
$137$			16.8964i			1.44356i	−0.692124	+	0.721778i	$0.743325\pi$
$138$		0			0
$139$		−	3.05422i		−	0.259056i	−0.991576	−	0.129528i	$-0.958654\pi$
$139$		−	3.05422i		−	0.259056i	0.991576	−	0.129528i	$-0.0413462\pi$
$140$		0			0
$141$	−4.35579	−	4.35579i	−0.366824	−	0.366824i
$142$		0			0
$143$	0.222587	+	1.59250i	0.0186136	+	0.133172i
$144$		0			0
$145$	−6.42396	+	0.393866i	−0.533481	+	0.0327088i
$146$		0			0
$147$	10.6682	−	10.6682i	0.879895	−	0.879895i
$148$		0			0
$149$	−0.623594	−	0.623594i	−0.0510868	−	0.0510868i	0.681102	−	0.732189i	$-0.261501\pi$
$149$	−0.623594	−	0.623594i	−0.0510868	−	0.0510868i	−0.732189	+	0.681102i	$0.761501\pi$
$150$		0			0
$151$	5.84579	+	5.84579i	0.475724	+	0.475724i	0.903761	−	0.428037i	$-0.140795\pi$
$151$	5.84579	+	5.84579i	0.475724	+	0.475724i	−0.428037	+	0.903761i	$0.640795\pi$
$152$		0			0
$153$	−1.07992	−	1.07992i	−0.0873060	−	0.0873060i
$154$		0			0
$155$	−2.68530	−	2.37504i	−0.215688	−	0.190768i
$156$		0			0
$157$	10.2125	+	10.2125i	0.815046	+	0.815046i	0.985385	−	0.170339i	$-0.0544864\pi$
$157$	10.2125	+	10.2125i	0.815046	+	0.815046i	−0.170339	+	0.985385i	$0.554486\pi$
$158$		0			0
$159$			11.9095i			0.944483i
$160$		0			0
$161$	16.3593	−	16.3593i	1.28930	−	1.28930i
$162$		0			0
$163$	23.2373			1.82009			0.910044	−	0.414511i	$-0.136047\pi$
$163$	23.2373			1.82009			0.910044	+	0.414511i	$0.136047\pi$
$164$		0			0
$165$	−0.0610276	−	0.995361i	−0.00475099	−	0.0774887i
$166$		0			0
$167$		−	12.5054i		−	0.967697i	−0.875152	−	0.483848i	$-0.839239\pi$
$167$		−	12.5054i		−	0.967697i	0.875152	−	0.483848i	$-0.160761\pi$
$168$		0			0
$169$	3.56442	+	12.5018i	0.274186	+	0.961677i
$170$		0			0
$171$	−3.49017	+	3.49017i	−0.266900	+	0.266900i
$172$		0			0
$173$	18.3381	+	18.3381i	1.39422	+	1.39422i	0.815599	+	0.578618i	$0.196408\pi$
$173$	18.3381	+	18.3381i	1.39422	+	1.39422i	0.578618	+	0.815599i	$0.303592\pi$
$174$		0			0
$175$	−2.87068	−	23.3224i	−0.217003	−	1.76301i
$176$		0			0
$177$		−	2.03983i		−	0.153323i
$178$		0			0
$179$	13.9880			1.04552			0.522758	−	0.852481i	$-0.324903\pi$
$179$	13.9880			1.04552			0.522758	+	0.852481i	$0.324903\pi$
$180$		0			0
$181$			14.6342i			1.08775i	0.839165	+	0.543877i	$0.183044\pi$
$181$			14.6342i			1.08775i	−0.839165	+	0.543877i	$0.816956\pi$
$182$		0			0
$183$	4.10475	−	4.10475i	0.303432	−	0.303432i
$184$		0			0
$185$	−19.9262	+	1.22171i	−1.46500	+	0.0898221i
$186$		0			0
$187$	0.681107			0.0498074
$188$		0			0
$189$	−3.32318	+	3.32318i	−0.241726	+	0.241726i
$190$		0			0
$191$	−13.6896			−0.990548			−0.495274	−	0.868737i	$-0.664932\pi$
$191$	−13.6896			−0.990548			−0.495274	+	0.868737i	$0.664932\pi$
$192$		0			0
$193$	−11.3452			−0.816647			−0.408323	−	0.912837i	$-0.633886\pi$
$193$	−11.3452			−0.816647			−0.408323	+	0.912837i	$0.633886\pi$
$194$		0			0
$195$	−1.60257	−	7.90138i	−0.114762	−	0.565829i
$196$		0			0
$197$	12.7625			0.909294			0.454647	−	0.890672i	$-0.349766\pi$
$197$	12.7625			0.909294			0.454647	+	0.890672i	$0.349766\pi$
$198$		0			0
$199$	−2.52762			−0.179178			−0.0895892	−	0.995979i	$-0.528555\pi$
$199$	−2.52762			−0.179178			−0.0895892	+	0.995979i	$0.528555\pi$
$200$		0			0
$201$	−2.86902	+	2.86902i	−0.202365	+	0.202365i
$202$		0			0
$203$	−13.5270			−0.949409
$204$		0			0
$205$	14.4555	+	12.7853i	1.00962	+	0.892966i
$206$		0			0
$207$	−3.48094	+	3.48094i	−0.241942	+	0.241942i
$208$		0			0
$209$		−	2.20126i		−	0.152265i
$210$		0			0
$211$	10.4839			0.721738			0.360869	−	0.932616i	$-0.382480\pi$
$211$	10.4839			0.721738			0.360869	+	0.932616i	$0.382480\pi$
$212$		0			0
$213$		−	9.45830i		−	0.648072i
$214$		0			0
$215$	1.16835	−	1.32098i	0.0796808	−	0.0900898i
$216$		0			0
$217$	−5.32780	−	5.32780i	−0.361675	−	0.361675i
$218$		0			0
$219$	−0.519166	+	0.519166i	−0.0350820	+	0.0350820i
$220$		0			0
$221$	5.45350	−	0.762243i	0.366842	−	0.0512740i
$222$		0			0
$223$		−	1.90938i		−	0.127861i	−0.997954	−	0.0639306i	$-0.979636\pi$
$223$		−	1.90938i		−	0.127861i	0.997954	−	0.0639306i	$-0.0203636\pi$
$224$		0			0
$225$	0.610824	+	4.96255i	0.0407216	+	0.330837i
$226$		0			0
$227$	28.0353			1.86077			0.930385	−	0.366584i	$-0.119473\pi$
$227$	28.0353			1.86077			0.930385	+	0.366584i	$0.119473\pi$
$228$		0			0
$229$	5.80903	−	5.80903i	0.383871	−	0.383871i	−0.488623	−	0.872495i	$-0.662501\pi$
$229$	5.80903	−	5.80903i	0.383871	−	0.383871i	0.872495	+	0.488623i	$0.162501\pi$
$230$		0			0
$231$		−	2.09594i		−	0.137903i
$232$		0			0
$233$	10.4654	+	10.4654i	0.685613	+	0.685613i	0.961259	−	0.275646i	$-0.0888919\pi$
$233$	10.4654	+	10.4654i	0.685613	+	0.685613i	−0.275646	+	0.961259i	$0.588892\pi$
$234$		0			0
$235$	−13.7484	+	0.842942i	−0.896847	+	0.0549875i
$236$		0			0
$237$	−9.13135	−	9.13135i	−0.593145	−	0.593145i
$238$		0			0
$239$	0.358095	+	0.358095i	0.0231633	+	0.0231633i	0.718594	−	0.695430i	$-0.244786\pi$
$239$	0.358095	+	0.358095i	0.0231633	+	0.0231633i	−0.695430	+	0.718594i	$0.744786\pi$
$240$		0			0
$241$	−8.96339	−	8.96339i	−0.577383	−	0.577383i	0.356799	−	0.934181i	$-0.383868\pi$
$241$	−8.96339	−	8.96339i	−0.577383	−	0.577383i	−0.934181	+	0.356799i	$0.883868\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−2.06453	−	33.6725i	−0.131898	−	2.15125i
$246$		0			0
$247$	−2.46349	−	17.6251i	−0.156748	−	1.12146i
$248$		0			0
$249$	−0.746702	−	0.746702i	−0.0473203	−	0.0473203i
$250$		0			0
$251$			10.3022i			0.650272i	0.945667	+	0.325136i	$0.105410\pi$
$251$			10.3022i			0.650272i	−0.945667	+	0.325136i	$0.894590\pi$
$252$		0			0
$253$		−	2.19544i		−	0.138026i
$254$		0			0
$255$	−3.40859	+	0.208988i	−0.213454	+	0.0130873i
$256$		0			0
$257$	−20.2281	+	20.2281i	−1.26179	+	1.26179i	−0.311572	+	0.950222i	$0.600856\pi$
$257$	−20.2281	+	20.2281i	−1.26179	+	1.26179i	−0.950222	+	0.311572i	$0.899144\pi$
$258$		0			0
$259$	−41.9587			−2.60719
$260$		0			0
$261$	2.87828			0.178161
$262$		0			0
$263$	−5.83060	+	5.83060i	−0.359530	+	0.359530i	−0.863640	−	0.504110i	$-0.831821\pi$
$263$	−5.83060	+	5.83060i	−0.359530	+	0.359530i	0.504110	+	0.863640i	$0.331821\pi$
$264$		0			0
$265$	19.9476	+	17.6429i	1.22537	+	1.08379i
$266$		0			0
$267$			7.58774i			0.464362i
$268$		0			0
$269$		−	26.2933i		−	1.60313i	−0.597906	−	0.801566i	$-0.704001\pi$
$269$		−	26.2933i		−	1.60313i	0.597906	−	0.801566i	$-0.295999\pi$
$270$		0			0
$271$	−21.5497	−	21.5497i	−1.30905	−	1.30905i	−0.922100	−	0.386953i	$-0.873528\pi$
$271$	−21.5497	−	21.5497i	−1.30905	−	1.30905i	−0.386953	−	0.922100i	$-0.626472\pi$
$272$		0			0
$273$	−2.34562	−	16.7818i	−0.141963	−	1.01568i
$274$		0			0
$275$	−1.75757	−	1.37232i	−0.105986	−	0.0827543i
$276$		0			0
$277$	11.0701	−	11.0701i	0.665137	−	0.665137i	−0.291449	−	0.956586i	$-0.594137\pi$
$277$	11.0701	−	11.0701i	0.665137	−	0.665137i	0.956586	+	0.291449i	$0.0941375\pi$
$278$		0			0
$279$	1.13365	+	1.13365i	0.0678698	+	0.0678698i
$280$		0			0
$281$	13.6165	+	13.6165i	0.812291	+	0.812291i	0.984977	−	0.172686i	$-0.0552446\pi$
$281$	13.6165	+	13.6165i	0.812291	+	0.812291i	−0.172686	+	0.984977i	$0.555245\pi$
$282$		0			0
$283$	12.6708	+	12.6708i	0.753204	+	0.753204i	0.975076	−	0.221872i	$-0.0712168\pi$
$283$	12.6708	+	12.6708i	0.753204	+	0.753204i	−0.221872	+	0.975076i	$0.571217\pi$
$284$		0			0
$285$	0.675425	+	11.0162i	0.0400087	+	0.652543i
$286$		0			0
$287$	28.6807	+	28.6807i	1.69297	+	1.69297i
$288$		0			0
$289$			14.6676i			0.862798i
$290$		0			0
$291$	3.22637	−	3.22637i	0.189133	−	0.189133i
$292$		0			0
$293$	−31.1560			−1.82015			−0.910077	−	0.414439i	$-0.863978\pi$
$293$	−31.1560			−1.82015			−0.910077	+	0.414439i	$0.863978\pi$
$294$		0			0
$295$	−3.41659	−	3.02184i	−0.198921	−	0.175938i
$296$		0			0
$297$			0.445975i			0.0258781i
$298$		0			0
$299$	−2.45697	−	17.5785i	−0.142090	−	1.01659i
$300$		0			0
$301$	2.62090	−	2.62090i	0.151066	−	0.151066i
$302$		0			0
$303$	6.14420	+	6.14420i	0.352975	+	0.352975i
$304$		0			0
$305$	−0.794359	−	12.9560i	−0.0454849	−	0.741860i
$306$		0			0
$307$			28.0732i			1.60222i	0.598517	+	0.801110i	$0.295757\pi$
$307$			28.0732i			1.60222i	−0.598517	+	0.801110i	$0.704243\pi$
$308$		0			0
$309$	−5.26907			−0.299747
$310$		0			0
$311$			12.7252i			0.721579i	0.932647	+	0.360789i	$0.117493\pi$
$311$			12.7252i			0.721579i	−0.932647	+	0.360789i	$0.882507\pi$
$312$		0			0
$313$	−14.1806	+	14.1806i	−0.801534	+	0.801534i	−0.983335	−	0.181801i	$-0.941807\pi$
$313$	−14.1806	+	14.1806i	−0.801534	+	0.801534i	0.181801	+	0.983335i	$0.441807\pi$
$314$		0			0
$315$	0.643109	+	10.4891i	0.0362351	+	0.590995i
$316$		0			0
$317$	7.64077			0.429148			0.214574	−	0.976708i	$-0.431164\pi$
$317$	7.64077			0.429148			0.214574	+	0.976708i	$0.431164\pi$
$318$		0			0
$319$	−0.907670	+	0.907670i	−0.0508198	+	0.0508198i
$320$		0			0
$321$	17.6038			0.982551
$322$		0			0
$323$	−7.53817			−0.419435
$324$		0			0
$325$	−15.6084	−	9.02101i	−0.865797	−	0.500396i
$326$		0			0
$327$	−16.9734			−0.938631
$328$		0			0
$329$	−28.9502			−1.59607
$330$		0			0
$331$	15.0162	−	15.0162i	0.825365	−	0.825365i	−0.161507	−	0.986872i	$-0.551635\pi$
$331$	15.0162	−	15.0162i	0.825365	−	0.825365i	0.986872	+	0.161507i	$0.0516354\pi$
$332$		0			0
$333$	8.92799			0.489251
$334$		0			0
$335$	0.555219	+	9.05564i	0.0303349	+	0.494762i
$336$		0			0
$337$	−9.44617	+	9.44617i	−0.514566	+	0.514566i	−0.915922	−	0.401356i	$-0.868539\pi$
$337$	−9.44617	+	9.44617i	−0.514566	+	0.514566i	0.401356	+	0.915922i	$0.368539\pi$
$338$		0			0
$339$			16.0409i			0.871221i
$340$		0			0
$341$	−0.714997			−0.0387193
$342$		0			0
$343$		−	38.0066i		−	2.05217i
$344$		0			0
$345$	0.673640	+	10.9871i	0.0362675	+	0.591524i
$346$		0			0
$347$	20.5249	+	20.5249i	1.10183	+	1.10183i	0.994190	+	0.107642i	$0.0343302\pi$
$347$	20.5249	+	20.5249i	1.10183	+	1.10183i	0.107642	+	0.994190i	$0.465670\pi$
$348$		0			0
$349$	−1.54929	+	1.54929i	−0.0829316	+	0.0829316i	−0.747356	−	0.664424i	$-0.768677\pi$
$349$	−1.54929	+	1.54929i	−0.0829316	+	0.0829316i	0.664424	+	0.747356i	$0.268677\pi$
$350$		0			0
$351$	0.499101	+	3.57084i	0.0266401	+	0.190597i
$352$		0			0
$353$		−	9.75270i		−	0.519084i	−0.965732	−	0.259542i	$-0.916428\pi$
$353$		−	9.75270i		−	0.519084i	0.965732	−	0.259542i	$-0.0835716\pi$
$354$		0			0
$355$	−15.8421	−	14.0117i	−0.840809	−	0.743662i
$356$		0			0
$357$	−7.17751			−0.379874
$358$		0			0
$359$	2.81152	−	2.81152i	0.148387	−	0.148387i	−0.629010	−	0.777397i	$-0.716540\pi$
$359$	2.81152	−	2.81152i	0.148387	−	0.148387i	0.777397	+	0.629010i	$0.216540\pi$
$360$		0			0
$361$			5.36257i			0.282240i
$362$		0			0
$363$	7.63754	+	7.63754i	0.400867	+	0.400867i
$364$		0			0
$365$	0.100470	+	1.63867i	0.00525885	+	0.0857719i
$366$		0			0
$367$	−23.2265	−	23.2265i	−1.21241	−	1.21241i	−0.970230	−	0.242184i	$-0.922136\pi$
$367$	−23.2265	−	23.2265i	−1.21241	−	1.21241i	−0.242184	−	0.970230i	$-0.577864\pi$
$368$		0			0
$369$	−6.10267	−	6.10267i	−0.317693	−	0.317693i
$370$		0			0
$371$	39.5773	+	39.5773i	2.05475	+	2.05475i
$372$		0			0
$373$	−3.06758	+	3.06758i	−0.158833	+	0.158833i	−0.782050	−	0.623216i	$-0.785826\pi$
$373$	−3.06758	+	3.06758i	−0.158833	+	0.158833i	0.623216	+	0.782050i	$0.285826\pi$
$374$		0			0
$375$	9.21684	+	6.32850i	0.475955	+	0.326802i
$376$		0			0
$377$	−6.25175	+	8.28334i	−0.321982	+	0.426614i
$378$		0			0
$379$	16.7416	+	16.7416i	0.859959	+	0.859959i	0.991333	−	0.131374i	$-0.0419387\pi$
$379$	16.7416	+	16.7416i	0.859959	+	0.859959i	−0.131374	+	0.991333i	$0.541939\pi$
$380$		0			0
$381$		−	9.53091i		−	0.488283i
$382$		0			0
$383$			5.16648i			0.263995i	0.991250	+	0.131997i	$0.0421390\pi$
$383$			5.16648i			0.263995i	−0.991250	+	0.131997i	$0.957861\pi$
$384$		0			0
$385$	−3.51057	−	3.10496i	−0.178915	−	0.158243i
$386$		0			0
$387$	−0.557675	+	0.557675i	−0.0283482	+	0.0283482i
$388$		0			0
$389$	−4.92391			−0.249652			−0.124826	−	0.992179i	$-0.539837\pi$
$389$	−4.92391			−0.249652			−0.124826	+	0.992179i	$0.539837\pi$
$390$		0			0
$391$	−7.51825			−0.380214
$392$		0			0
$393$	3.66297	−	3.66297i	0.184772	−	0.184772i
$394$		0			0
$395$	−28.8217	+	1.76712i	−1.45018	+	0.0889134i
$396$		0			0
$397$		−	26.9445i		−	1.35231i	−0.736760	−	0.676154i	$-0.763645\pi$
$397$		−	26.9445i		−	1.35231i	0.736760	−	0.676154i	$-0.236355\pi$
$398$		0			0
$399$			23.1969i			1.16130i
$400$		0			0
$401$	−25.1188	−	25.1188i	−1.25437	−	1.25437i	−0.953739	−	0.300635i	$-0.902801\pi$
$401$	−25.1188	−	25.1188i	−1.25437	−	1.25437i	−0.300635	−	0.953739i	$-0.597199\pi$
$402$		0			0
$403$	−5.72485	+	0.800171i	−0.285175	+	0.0398593i
$404$		0			0
$405$	−0.136841	−	2.23188i	−0.00679967	−	0.110903i
$406$		0			0
$407$	−2.81546	+	2.81546i	−0.139557	+	0.139557i
$408$		0			0
$409$	0.765296	+	0.765296i	0.0378414	+	0.0378414i	0.725774	−	0.687933i	$-0.241482\pi$
$409$	0.765296	+	0.765296i	0.0378414	+	0.0378414i	−0.687933	+	0.725774i	$0.741482\pi$
$410$		0			0
$411$	−11.9476	−	11.9476i	−0.589330	−	0.589330i
$412$		0			0
$413$	−6.77873	−	6.77873i	−0.333559	−	0.333559i
$414$		0			0
$415$	−2.35685	+	0.144503i	−0.115693	+	0.00709340i
$416$		0			0
$417$	2.15966	+	2.15966i	0.105759	+	0.105759i
$418$		0			0
$419$		−	6.89257i		−	0.336724i	−0.985725	−	0.168362i	$-0.946152\pi$
$419$		−	6.89257i		−	0.336724i	0.985725	−	0.168362i	$-0.0538477\pi$
$420$		0			0
$421$	19.8483	−	19.8483i	0.967349	−	0.967349i	−0.0321346	−	0.999484i	$-0.510231\pi$
$421$	19.8483	−	19.8483i	0.967349	−	0.967349i	0.999484	+	0.0321346i	$0.0102305\pi$
$422$		0			0
$423$	6.16002			0.299510
$424$		0			0
$425$	−4.69949	+	6.01877i	−0.227959	+	0.291953i
$426$		0			0
$427$		−	27.2816i		−	1.32025i
$428$		0			0
$429$	−1.28346	−	0.968678i	−0.0619662	−	0.0467682i
$430$		0			0
$431$	−18.3880	+	18.3880i	−0.885718	+	0.885718i	−0.994108	−	0.108391i	$-0.965430\pi$
$431$	−18.3880	+	18.3880i	−0.885718	+	0.885718i	0.108391	+	0.994108i	$0.465430\pi$
$432$		0			0
$433$	6.17848	+	6.17848i	0.296919	+	0.296919i	0.839806	−	0.542887i	$-0.182669\pi$
$433$	6.17848	+	6.17848i	0.296919	+	0.296919i	−0.542887	+	0.839806i	$0.682669\pi$
$434$		0			0
$435$	4.26392	−	4.82093i	0.204439	−	0.231146i
$436$		0			0
$437$			24.2982i			1.16234i
$438$		0			0
$439$	15.7983			0.754013			0.377006	−	0.926211i	$-0.376954\pi$
$439$	15.7983			0.754013			0.377006	+	0.926211i	$0.376954\pi$
$440$		0			0
$441$			15.0871i			0.718431i
$442$		0			0
$443$	−7.28734	+	7.28734i	−0.346232	+	0.346232i	−0.858704	−	0.512472i	$-0.828730\pi$
$443$	−7.28734	+	7.28734i	−0.346232	+	0.346232i	0.512472	+	0.858704i	$0.328730\pi$
$444$		0			0
$445$	12.7090	+	11.2406i	0.602463	+	0.532855i
$446$		0			0
$447$	0.881895			0.0417122
$448$		0			0
$449$	−11.9047	+	11.9047i	−0.561819	+	0.561819i	−0.929824	−	0.368005i	$-0.880041\pi$
$449$	−11.9047	+	11.9047i	−0.561819	+	0.561819i	0.368005	+	0.929824i	$0.380041\pi$
$450$		0			0
$451$	3.84898			0.181241
$452$		0			0
$453$	−8.26719			−0.388427
$454$		0			0
$455$	−31.5833	−	20.9321i	−1.48065	−	0.981311i
$456$		0			0
$457$	−10.4884			−0.490628			−0.245314	−	0.969444i	$-0.578891\pi$
$457$	−10.4884			−0.490628			−0.245314	+	0.969444i	$0.578891\pi$
$458$		0			0
$459$	1.52723			0.0712850
$460$		0			0
$461$	−17.4899	+	17.4899i	−0.814587	+	0.814587i	−0.985318	−	0.170731i	$-0.945387\pi$
$461$	−17.4899	+	17.4899i	−0.814587	+	0.814587i	0.170731	+	0.985318i	$0.445387\pi$
$462$		0			0
$463$	16.3159			0.758266			0.379133	−	0.925342i	$-0.376222\pi$
$463$	16.3159			0.758266			0.379133	+	0.925342i	$0.376222\pi$
$464$		0			0
$465$	3.57820	−	0.219386i	0.165935	−	0.0101738i
$466$		0			0
$467$	−13.5684	+	13.5684i	−0.627870	+	0.627870i	−0.947532	−	0.319662i	$-0.896431\pi$
$467$	−13.5684	+	13.5684i	−0.627870	+	0.627870i	0.319662	+	0.947532i	$0.396431\pi$
$468$		0			0
$469$			19.0686i			0.880504i
$470$		0			0
$471$	−14.4427			−0.665482
$472$		0			0
$473$		−	0.351728i		−	0.0161725i
$474$		0			0
$475$	19.4520	+	15.1883i	0.892520	+	0.696885i
$476$		0			0
$477$	−8.42127	−	8.42127i	−0.385584	−	0.385584i
$478$		0			0
$479$	17.7533	−	17.7533i	0.811171	−	0.811171i	−0.173639	−	0.984809i	$-0.555552\pi$
$479$	17.7533	−	17.7533i	0.811171	−	0.811171i	0.984809	+	0.173639i	$0.0555524\pi$
$480$		0			0
$481$	−19.3920	+	25.6937i	−0.884200	+	1.17153i
$482$		0			0
$483$			23.1356i			1.05271i
$484$		0			0
$485$	−0.624374	−	10.1835i	−0.0283513	−	0.462411i
$486$		0			0
$487$	33.7675			1.53015			0.765075	−	0.643941i	$-0.222702\pi$
$487$	33.7675			1.53015			0.765075	+	0.643941i	$0.222702\pi$
$488$		0			0
$489$	−16.4313	+	16.4313i	−0.743048	+	0.743048i
$490$		0			0
$491$		−	22.9938i		−	1.03770i	−0.854866	−	0.518849i	$-0.826361\pi$
$491$		−	22.9938i		−	1.03770i	0.854866	−	0.518849i	$-0.173639\pi$
$492$		0			0
$493$	3.10830	+	3.10830i	0.139991	+	0.139991i
$494$		0			0
$495$	0.746979	+	0.660673i	0.0335742	+	0.0296951i
$496$		0			0
$497$	−31.4317	−	31.4317i	−1.40990	−	1.40990i
$498$		0			0
$499$	−6.02065	−	6.02065i	−0.269521	−	0.269521i	0.559386	−	0.828907i	$-0.311037\pi$
$499$	−6.02065	−	6.02065i	−0.269521	−	0.269521i	−0.828907	+	0.559386i	$0.811037\pi$
$500$		0			0
$501$	8.84265	+	8.84265i	0.395060	+	0.395060i
$502$		0			0
$503$	−10.3721	+	10.3721i	−0.462470	+	0.462470i	−0.899464	−	0.436995i	$-0.856043\pi$
$503$	−10.3721	+	10.3721i	−0.462470	+	0.462470i	0.436995	+	0.899464i	$0.356043\pi$
$504$		0			0
$505$	19.3932	−	1.18904i	0.862988	−	0.0529115i
$506$		0			0
$507$	−11.3605	−	6.31968i	−0.504539	−	0.280667i
$508$		0			0
$509$	5.39148	+	5.39148i	0.238973	+	0.238973i	0.816425	−	0.577452i	$-0.195953\pi$
$509$	5.39148	+	5.39148i	0.238973	+	0.238973i	−0.577452	+	0.816425i	$0.695953\pi$
$510$		0			0
$511$			3.45057i			0.152644i
$512$		0			0
$513$		−	4.93584i		−	0.217923i
$514$		0			0
$515$	−7.80568	+	8.82536i	−0.343959	+	0.388892i
$516$		0			0
$517$	−1.94257	+	1.94257i	−0.0854343	+	0.0854343i
$518$		0			0
$519$	−25.9339			−1.13837
$520$		0			0
$521$	42.1874			1.84826			0.924131	−	0.382076i	$-0.124791\pi$
$521$	42.1874			1.84826			0.924131	+	0.382076i	$0.124791\pi$
$522$		0			0
$523$	11.3298	−	11.3298i	0.495417	−	0.495417i	−0.414591	−	0.910008i	$-0.636075\pi$
$523$	11.3298	−	11.3298i	0.495417	−	0.495417i	0.910008	+	0.414591i	$0.136075\pi$
$524$		0			0
$525$	18.5213	+	14.4616i	0.808337	+	0.631155i
$526$		0			0
$527$			2.44849i			0.106658i
$528$		0			0
$529$			1.23393i			0.0536492i
$530$		0			0
$531$	1.44238	+	1.44238i	0.0625939	+	0.0625939i
$532$		0			0
$533$	30.8181	−	4.30749i	1.33488	−	0.186578i
$534$		0			0
$535$	26.0786	−	29.4853i	1.12748	−	1.27476i
$536$		0			0
$537$	−9.89104	+	9.89104i	−0.426830	+	0.426830i
$538$		0			0
$539$	−4.75773	−	4.75773i	−0.204930	−	0.204930i
$540$		0			0
$541$	−11.3903	−	11.3903i	−0.489709	−	0.489709i	0.418506	−	0.908214i	$-0.362554\pi$
$541$	−11.3903	−	11.3903i	−0.489709	−	0.489709i	−0.908214	+	0.418506i	$0.862554\pi$
$542$		0			0
$543$	−10.3480	−	10.3480i	−0.444074	−	0.444074i
$544$		0			0
$545$	−25.1446	+	28.4294i	−1.07708	+	1.21778i
$546$		0			0
$547$	11.3855	+	11.3855i	0.486809	+	0.486809i	0.907298	−	0.420489i	$-0.138141\pi$
$547$	11.3855	+	11.3855i	0.486809	+	0.486809i	−0.420489	+	0.907298i	$0.638141\pi$
$548$		0			0
$549$			5.80499i			0.247751i
$550$		0			0
$551$	10.0457	−	10.0457i	0.427960	−	0.427960i
$552$		0			0
$553$	−60.6902			−2.58081
$554$		0			0
$555$	13.2260	−	14.9538i	0.561414	−	0.634754i
$556$		0			0
$557$			34.1016i			1.44493i	0.691408	+	0.722465i	$0.256991\pi$
$557$			34.1016i			1.44493i	−0.691408	+	0.722465i	$0.743009\pi$
$558$		0			0
$559$	−0.393627	−	2.81622i	−0.0166487	−	0.119113i
$560$		0			0
$561$	−0.481615	+	0.481615i	−0.0203338	+	0.0203338i
$562$		0			0
$563$	−25.7769	−	25.7769i	−1.08637	−	1.08637i	−0.995899	−	0.0904666i	$-0.971164\pi$
$563$	−25.7769	−	25.7769i	−1.08637	−	1.08637i	−0.0904666	−	0.995899i	$-0.528836\pi$
$564$		0			0
$565$	26.8674	+	23.7632i	1.13032	+	0.999724i
$566$		0			0
$567$		−	4.69969i		−	0.197368i
$568$		0			0
$569$	26.2934			1.10228			0.551138	−	0.834414i	$-0.314194\pi$
$569$	26.2934			1.10228			0.551138	+	0.834414i	$0.314194\pi$
$570$		0			0
$571$		−	14.6838i		−	0.614496i	−0.951629	−	0.307248i	$-0.900592\pi$
$571$		−	14.6838i		−	0.614496i	0.951629	−	0.307248i	$-0.0994082\pi$
$572$		0			0
$573$	9.68004	−	9.68004i	0.404389	−	0.404389i
$574$		0			0
$575$	19.4006	+	15.1481i	0.809061	+	0.631720i
$576$		0			0
$577$	23.1978			0.965735			0.482868	−	0.875693i	$-0.339595\pi$
$577$	23.1978			0.965735			0.482868	+	0.875693i	$0.339595\pi$
$578$		0			0
$579$	8.02228	−	8.02228i	0.333395	−	0.333395i
$580$		0			0
$581$	−4.96285			−0.205894
$582$		0			0
$583$	5.31133			0.219973
$584$		0			0
$585$	6.72031	+	4.45393i	0.277850	+	0.184147i
$586$		0			0
$587$	7.91675			0.326759			0.163380	−	0.986563i	$-0.447760\pi$
$587$	7.91675			0.326759			0.163380	+	0.986563i	$0.447760\pi$
$588$		0			0
$589$	7.91326			0.326060
$590$		0			0
$591$	−9.02448	+	9.02448i	−0.371218	+	0.371218i
$592$		0			0
$593$	−43.6618			−1.79297			−0.896487	−	0.443071i	$-0.853889\pi$
$593$	−43.6618			−1.79297			−0.896487	+	0.443071i	$0.853889\pi$
$594$		0			0
$595$	−10.6329	+	12.0219i	−0.435905	+	0.492849i
$596$		0			0
$597$	1.78730	−	1.78730i	0.0731492	−	0.0731492i
$598$		0			0
$599$		−	15.5444i		−	0.635126i	−0.948237	−	0.317563i	$-0.897136\pi$
$599$		−	15.5444i		−	0.635126i	0.948237	−	0.317563i	$-0.102864\pi$
$600$		0			0
$601$	−7.39443			−0.301625			−0.150813	−	0.988562i	$-0.548189\pi$
$601$	−7.39443			−0.301625			−0.150813	+	0.988562i	$0.548189\pi$
$602$		0			0
$603$		−	4.05741i		−	0.165230i
$604$		0			0
$605$	24.1067	−	1.47803i	0.980078	−	0.0600906i
$606$		0			0
$607$	−29.2174	−	29.2174i	−1.18590	−	1.18590i	−0.978192	−	0.207705i	$-0.933401\pi$
$607$	−29.2174	−	29.2174i	−1.18590	−	1.18590i	−0.207705	−	0.978192i	$-0.566599\pi$
$608$		0			0
$609$	9.56503	−	9.56503i	0.387595	−	0.387595i
$610$		0			0
$611$	−13.3798	+	17.7278i	−0.541291	+	0.717190i
$612$		0			0
$613$		−	39.5039i		−	1.59555i	−0.602957	−	0.797774i	$-0.706011\pi$
$613$		−	39.5039i		−	1.59555i	0.602957	−	0.797774i	$-0.293989\pi$
$614$		0			0
$615$	−19.2622	+	1.18100i	−0.776726	+	0.0476226i
$616$		0			0
$617$	2.88852			0.116288			0.0581438	−	0.998308i	$-0.481482\pi$
$617$	2.88852			0.116288			0.0581438	+	0.998308i	$0.481482\pi$
$618$		0			0
$619$	13.1526	−	13.1526i	0.528649	−	0.528649i	−0.391520	−	0.920169i	$-0.628051\pi$
$619$	13.1526	−	13.1526i	0.528649	−	0.528649i	0.920169	+	0.391520i	$0.128051\pi$
$620$		0			0
$621$		−	4.92280i		−	0.197545i
$622$		0			0
$623$	25.2154	+	25.2154i	1.01023	+	1.01023i
$624$		0			0
$625$	24.2538	−	6.06249i	0.970152	−	0.242499i
$626$		0			0
$627$	1.55653	+	1.55653i	0.0621617	+	0.0621617i
$628$		0			0
$629$	9.64147	+	9.64147i	0.384431	+	0.384431i
$630$		0			0
$631$	−26.9044	−	26.9044i	−1.07105	−	1.07105i	−0.997275	−	0.0737713i	$-0.976497\pi$
$631$	−26.9044	−	26.9044i	−1.07105	−	1.07105i	−0.0737713	−	0.997275i	$-0.523503\pi$
$632$		0			0
$633$	−7.41320	+	7.41320i	−0.294648	+	0.294648i
$634$		0			0
$635$	−15.9637	−	14.1192i	−0.633499	−	0.560304i
$636$		0			0
$637$	−43.4188	−	32.7698i	−1.72032	−	1.29839i
$638$		0			0
$639$	6.68803	+	6.68803i	0.264574	+	0.264574i
$640$		0			0
$641$			7.72592i			0.305156i	0.988291	+	0.152578i	$0.0487575\pi$
$641$			7.72592i			0.305156i	−0.988291	+	0.152578i	$0.951243\pi$
$642$		0			0
$643$			17.3325i			0.683528i	0.939786	+	0.341764i	$0.111024\pi$
$643$			17.3325i			0.683528i	−0.939786	+	0.341764i	$0.888976\pi$
$644$		0			0
$645$	0.107923	+	1.76022i	0.00424945	+	0.0693086i
$646$		0			0
$647$	11.2911	−	11.2911i	0.443898	−	0.443898i	−0.449421	−	0.893320i	$-0.648370\pi$
$647$	11.2911	−	11.2911i	0.443898	−	0.443898i	0.893320	+	0.449421i	$0.148370\pi$
$648$		0			0
$649$	−0.909714			−0.0357094
$650$		0			0
$651$	7.53465			0.295306
$652$		0			0
$653$	−19.3452	+	19.3452i	−0.757037	+	0.757037i	−0.975782	−	0.218745i	$-0.929804\pi$
$653$	−19.3452	+	19.3452i	−0.757037	+	0.757037i	0.218745	+	0.975782i	$0.429804\pi$
$654$		0			0
$655$	−0.708866	−	11.5616i	−0.0276977	−	0.451750i
$656$		0			0
$657$		−	0.734212i		−	0.0286443i
$658$		0			0
$659$		−	41.8280i		−	1.62939i	−0.579890	−	0.814695i	$-0.696905\pi$
$659$		−	41.8280i		−	1.62939i	0.579890	−	0.814695i	$-0.303095\pi$
$660$		0			0
$661$	−14.9894	−	14.9894i	−0.583022	−	0.583022i	0.352711	−	0.935732i	$-0.385260\pi$
$661$	−14.9894	−	14.9894i	−0.583022	−	0.583022i	−0.935732	+	0.352711i	$0.885260\pi$
$662$		0			0
$663$	−3.31722	+	4.39519i	−0.128830	+	0.170695i
$664$		0			0
$665$	38.8534	+	34.3643i	1.50667	+	1.33259i
$666$		0			0
$667$	10.0191	−	10.0191i	0.387942	−	0.387942i
$668$		0			0
$669$	1.35013	+	1.35013i	0.0521991	+	0.0521991i
$670$		0			0
$671$	−1.83061	−	1.83061i	−0.0706701	−	0.0706701i
$672$		0			0
$673$	11.3096	+	11.3096i	0.435952	+	0.435952i	0.890647	−	0.454695i	$-0.150252\pi$
$673$	11.3096	+	11.3096i	0.435952	+	0.435952i	−0.454695	+	0.890647i	$0.650252\pi$
$674$		0			0
$675$	−3.94097	−	3.07713i	−0.151688	−	0.118439i
$676$		0			0
$677$	−14.2625	−	14.2625i	−0.548153	−	0.548153i	0.377753	−	0.925906i	$-0.376697\pi$
$677$	−14.2625	−	14.2625i	−0.548153	−	0.548153i	−0.925906	+	0.377753i	$0.876697\pi$
$678$		0			0
$679$		−	21.4436i		−	0.822930i
$680$		0			0
$681$	−19.8240	+	19.8240i	−0.759656	+	0.759656i
$682$		0			0
$683$	24.2502			0.927910			0.463955	−	0.885859i	$-0.346430\pi$
$683$	24.2502			0.927910			0.463955	+	0.885859i	$0.346430\pi$
$684$		0			0
$685$	−37.7107	+	2.31212i	−1.44085	+	0.0883415i
$686$		0			0
$687$			8.21520i			0.313430i
$688$		0			0
$689$	42.5268	−	5.94404i	1.62014	−	0.226450i
$690$		0			0
$691$	18.8507	−	18.8507i	0.717116	−	0.717116i	−0.250898	−	0.968014i	$-0.580726\pi$
$691$	18.8507	−	18.8507i	0.717116	−	0.717116i	0.968014	+	0.250898i	$0.0807257\pi$
$692$		0			0
$693$	1.48205	+	1.48205i	0.0562986	+	0.0562986i
$694$		0			0
$695$	6.81665	−	0.417942i	0.258570	−	0.0158535i
$696$		0			0
$697$		−	13.1807i		−	0.499256i
$698$		0			0
$699$	−14.8003			−0.559800
$700$		0			0
$701$		−	23.7436i		−	0.896783i	−0.893837	−	0.448392i	$-0.851997\pi$
$701$		−	23.7436i		−	0.896783i	0.893837	−	0.448392i	$-0.148003\pi$
$702$		0			0
$703$	31.1602	−	31.1602i	1.17523	−	1.17523i
$704$		0			0
$705$	9.12554	−	10.3176i	0.343688	−	0.388585i
$706$		0			0
$707$	40.8366			1.53582
$708$		0			0
$709$	6.02523	−	6.02523i	0.226282	−	0.226282i	−0.584855	−	0.811138i	$-0.698849\pi$
$709$	6.02523	−	6.02523i	0.226282	−	0.226282i	0.811138	+	0.584855i	$0.198849\pi$
$710$		0			0
$711$	12.9137			0.484301
$712$		0			0
$713$	7.89234			0.295571
$714$		0			0
$715$	−3.52382	+	0.714706i	−0.131783	+	0.0267285i
$716$		0			0
$717$	−0.506423			−0.0189127
$718$		0			0
$719$	5.39301			0.201125			0.100563	−	0.994931i	$-0.467936\pi$
$719$	5.39301			0.201125			0.100563	+	0.994931i	$0.467936\pi$
$720$		0			0
$721$	−17.5101	+	17.5101i	−0.652109	+	0.652109i
$722$		0			0
$723$	12.6761			0.471431
$724$		0			0
$725$	−1.75812	−	14.2836i	−0.0652949	−	0.530479i
$726$		0			0
$727$	27.4677	−	27.4677i	1.01872	−	1.01872i	0.0188979	−	0.999821i	$-0.493984\pi$
$727$	27.4677	−	27.4677i	1.01872	−	1.01872i	0.999821	−	0.0188979i	$-0.00601576\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−1.20448			−0.0445495
$732$		0			0
$733$			40.5951i			1.49941i	0.661770	+	0.749707i	$0.269806\pi$
$733$			40.5951i			1.49941i	−0.661770	+	0.749707i	$0.730194\pi$
$734$		0			0
$735$	25.2699	+	22.3502i	0.932093	+	0.824399i
$736$		0			0
$737$	1.27951	+	1.27951i	0.0471314	+	0.0471314i
$738$		0			0
$739$	19.5815	−	19.5815i	0.720315	−	0.720315i	−0.248354	−	0.968669i	$-0.579890\pi$
$739$	19.5815	−	19.5815i	0.720315	−	0.720315i	0.968669	+	0.248354i	$0.0798896\pi$
$740$		0			0
$741$	14.2048	+	10.7209i	0.521826	+	0.393842i
$742$		0			0
$743$		−	33.1542i		−	1.21631i	−0.793818	−	0.608155i	$-0.791910\pi$
$743$		−	33.1542i		−	1.21631i	0.793818	−	0.608155i	$-0.208090\pi$
$744$		0			0
$745$	1.30645	−	1.47712i	0.0478647	−	0.0541174i
$746$		0			0
$747$	1.05600			0.0386369
$748$		0			0
$749$	58.5008	−	58.5008i	2.13757	−	2.13757i
$750$		0			0
$751$			9.49285i			0.346399i	0.984887	+	0.173200i	$0.0554105\pi$
$751$			9.49285i			0.346399i	−0.984887	+	0.173200i	$0.944589\pi$
$752$		0			0
$753$	−7.28479	−	7.28479i	−0.265472	−	0.265472i
$754$		0			0
$755$	−12.2471	+	13.8470i	−0.445719	+	0.503945i
$756$		0			0
$757$	2.84463	+	2.84463i	0.103390	+	0.103390i	0.756909	−	0.653520i	$-0.226708\pi$
$757$	2.84463	+	2.84463i	0.103390	+	0.103390i	−0.653520	+	0.756909i	$0.726708\pi$
$758$		0			0
$759$	1.55241	+	1.55241i	0.0563490	+	0.0563490i
$760$		0			0
$761$	33.6477	+	33.6477i	1.21973	+	1.21973i	0.967727	+	0.252002i	$0.0810888\pi$
$761$	33.6477	+	33.6477i	1.21973	+	1.21973i	0.252002	+	0.967727i	$0.418911\pi$
$762$		0			0
$763$	−56.4057	+	56.4057i	−2.04202	+	2.04202i
$764$		0			0
$765$	2.26246	−	2.55801i	0.0817995	−	0.0924852i
$766$		0			0
$767$	−7.28391	+	1.01808i	−0.263007	+	0.0367608i
$768$		0			0
$769$	−2.09238	−	2.09238i	−0.0754532	−	0.0754532i	0.668373	−	0.743826i	$-0.266991\pi$
$769$	−2.09238	−	2.09238i	−0.0754532	−	0.0754532i	−0.743826	+	0.668373i	$0.766991\pi$
$770$		0			0
$771$		−	28.6069i		−	1.03025i
$772$		0			0
$773$			33.8949i			1.21911i	0.792742	+	0.609557i	$0.208653\pi$
$773$			33.8949i			1.21911i	−0.792742	+	0.609557i	$0.791347\pi$
$774$		0			0
$775$	4.93333	−	6.31825i	0.177211	−	0.226958i
$776$		0			0
$777$	29.6693	−	29.6693i	1.06438	−	1.06438i
$778$		0			0
$779$	−42.5987			−1.52626
$780$		0			0
$781$	−4.21817			−0.150938
$782$		0			0
$783$	−2.03525	+	2.03525i	−0.0727339	+	0.0727339i
$784$		0			0
$785$	−21.3956	+	24.1905i	−0.763640	+	0.863397i
$786$		0			0
$787$			13.3356i			0.475363i	0.971343	+	0.237682i	$0.0763875\pi$
$787$			13.3356i			0.475363i	−0.971343	+	0.237682i	$0.923612\pi$
$788$		0			0
$789$		−	8.24571i		−	0.293555i
$790$		0			0
$791$	53.3067	+	53.3067i	1.89537	+	1.89537i
$792$		0			0
$793$	−16.7061	−	12.6087i	−0.593250	−	0.447748i
$794$		0			0
$795$	−26.5805	+	1.62970i	−0.942713	+	0.0577996i
$796$		0			0
$797$	−2.21618	+	2.21618i	−0.0785012	+	0.0785012i	−0.745267	−	0.666766i	$-0.767678\pi$
$797$	−2.21618	+	2.21618i	−0.0785012	+	0.0785012i	0.666766	+	0.745267i	$0.267678\pi$
$798$		0			0
$799$	6.65230	+	6.65230i	0.235341	+	0.235341i
$800$		0			0
$801$	−5.36534	−	5.36534i	−0.189575	−	0.189575i
$802$		0			0
$803$	0.231535	+	0.231535i	0.00817069	+	0.00817069i
$804$		0			0
$805$	38.7507	+	34.2734i	1.36578	+	1.20798i
$806$		0			0
$807$	18.5922	+	18.5922i	0.654476	+	0.654476i
$808$		0			0
$809$		−	10.3854i		−	0.365131i	−0.983194	−	0.182565i	$-0.941560\pi$
$809$		−	10.3854i		−	0.365131i	0.983194	−	0.182565i	$-0.0584401\pi$
$810$		0			0
$811$	−2.72201	+	2.72201i	−0.0955825	+	0.0955825i	−0.753281	−	0.657699i	$-0.771530\pi$
$811$	−2.72201	+	2.72201i	−0.0955825	+	0.0955825i	0.657699	+	0.753281i	$0.271530\pi$
$812$		0			0
$813$	30.4759			1.06884
$814$		0			0
$815$	3.17982	+	51.8629i	0.111384	+	1.81668i
$816$		0			0
$817$			3.89276i			0.136191i
$818$		0			0
$819$	13.5251	+	10.2079i	0.472607	+	0.356694i
$820$		0			0
$821$	3.79821	−	3.79821i	0.132558	−	0.132558i	−0.637714	−	0.770273i	$-0.720120\pi$
$821$	3.79821	−	3.79821i	0.132558	−	0.132558i	0.770273	+	0.637714i	$0.220120\pi$
$822$		0			0
$823$	36.2441	+	36.2441i	1.26339	+	1.26339i	0.949439	+	0.313951i	$0.101653\pi$
$823$	36.2441	+	36.2441i	1.26339	+	1.26339i	0.313951	+	0.949439i	$0.398347\pi$
$824$		0			0
$825$	2.21317	−	0.272412i	0.0770528	−	0.00948417i
$826$		0			0
$827$		−	36.2770i		−	1.26147i	−0.775996	−	0.630737i	$-0.782753\pi$
$827$		−	36.2770i		−	1.26147i	0.775996	−	0.630737i	$-0.217247\pi$
$828$		0			0
$829$	11.4935			0.399185			0.199592	−	0.979879i	$-0.436038\pi$
$829$	11.4935			0.399185			0.199592	+	0.979879i	$0.436038\pi$
$830$		0			0
$831$			15.6555i			0.543082i
$832$		0			0
$833$	−16.2927	+	16.2927i	−0.564510	+	0.564510i
$834$		0			0
$835$	27.9105	−	1.71125i	0.965883	−	0.0592202i
$836$		0			0
$837$	−1.60322			−0.0554155
$838$		0			0
$839$	20.5056	−	20.5056i	0.707931	−	0.707931i	−0.258169	−	0.966100i	$-0.583119\pi$
$839$	20.5056	−	20.5056i	0.707931	−	0.707931i	0.966100	+	0.258169i	$0.0831191\pi$
$840$		0			0
$841$	20.7155			0.714328
$842$		0			0
$843$	−19.2566			−0.663233
$844$		0			0
$845$	−27.4147	+	9.66611i	−0.943095	+	0.332524i
$846$		0			0
$847$	50.7618			1.74420
$848$		0			0
$849$	−17.9193			−0.614988
$850$		0			0
$851$	31.0778	−	31.0778i	1.06533	−	1.06533i
$852$		0			0
$853$	−10.6968			−0.366253			−0.183126	−	0.983089i	$-0.558622\pi$
$853$	−10.6968			−0.366253			−0.183126	+	0.983089i	$0.558622\pi$
$854$		0			0
$855$	−8.26723	−	7.31203i	−0.282733	−	0.250066i
$856$		0			0
$857$	−20.4311	+	20.4311i	−0.697912	+	0.697912i	−0.963960	−	0.266048i	$-0.914282\pi$
$857$	−20.4311	+	20.4311i	−0.697912	+	0.697912i	0.266048	+	0.963960i	$0.414282\pi$
$858$		0			0
$859$		−	31.0854i		−	1.06062i	−0.847803	−	0.530311i	$-0.822075\pi$
$859$		−	31.0854i		−	1.06062i	0.847803	−	0.530311i	$-0.177925\pi$
$860$		0			0
$861$	−40.5606			−1.38230
$862$		0			0
$863$			32.6466i			1.11130i	0.831415	+	0.555651i	$0.187531\pi$
$863$			32.6466i			1.11130i	−0.831415	+	0.555651i	$0.812469\pi$
$864$		0			0
$865$	−38.4189	+	43.4377i	−1.30628	+	1.47693i
$866$		0			0
$867$	−10.3715	−	10.3715i	−0.352236	−	0.352236i
$868$		0			0
$869$	−4.07235	+	4.07235i	−0.138145	+	0.138145i
$870$		0			0
$871$	11.6768	+	8.81289i	0.395652	+	0.298613i
$872$		0			0
$873$			4.56277i			0.154426i
$874$		0			0
$875$	51.6600	−	9.59847i	1.74643	−	0.324487i
$876$		0			0
$877$	−24.8946			−0.840629			−0.420315	−	0.907378i	$-0.638080\pi$
$877$	−24.8946			−0.840629			−0.420315	+	0.907378i	$0.638080\pi$
$878$		0			0
$879$	22.0306	−	22.0306i	0.743075	−	0.743075i
$880$		0			0
$881$		−	57.1910i		−	1.92681i	−0.268046	−	0.963406i	$-0.586378\pi$
$881$		−	57.1910i		−	1.92681i	0.268046	−	0.963406i	$-0.413622\pi$
$882$		0			0
$883$	−18.8928	−	18.8928i	−0.635793	−	0.635793i	0.313722	−	0.949515i	$-0.398424\pi$
$883$	−18.8928	−	18.8928i	−0.635793	−	0.635793i	−0.949515	+	0.313722i	$0.898424\pi$
$884$		0			0
$885$	4.55265	−	0.279132i	0.153036	−	0.00938293i
$886$		0			0
$887$	−14.5287	−	14.5287i	−0.487826	−	0.487826i	0.419794	−	0.907620i	$-0.362102\pi$
$887$	−14.5287	−	14.5287i	−0.487826	−	0.487826i	−0.907620	+	0.419794i	$0.862102\pi$
$888$		0			0
$889$	−31.6729	−	31.6729i	−1.06228	−	1.06228i
$890$		0			0
$891$	−0.315352	−	0.315352i	−0.0105647	−	0.0105647i
$892$		0			0
$893$	21.4995	−	21.4995i	0.719454	−	0.719454i
$894$		0			0
$895$	1.91414	+	31.2196i	0.0639825	+	1.04356i
$896$		0			0
$897$	14.1672	+	10.6925i	0.473030	+	0.357014i
$898$		0			0
$899$	−3.26296	−	3.26296i	−0.108826	−	0.108826i
$900$		0			0
$901$		−	18.1885i		−	0.605948i
$902$		0			0
$903$			3.70651i			0.123345i
$904$		0			0
$905$	−32.6618	+	2.00256i	−1.08572	+	0.0665673i
$906$		0			0
$907$	−14.2325	+	14.2325i	−0.472583	+	0.472583i	−0.902750	−	0.430166i	$-0.858455\pi$
$907$	−14.2325	+	14.2325i	−0.472583	+	0.472583i	0.430166	+	0.902750i	$0.358455\pi$
$908$		0			0
$909$	−8.68921			−0.288203
$910$		0			0
$911$	32.2436			1.06828			0.534139	−	0.845397i	$-0.320636\pi$
$911$	32.2436			1.06828			0.534139	+	0.845397i	$0.320636\pi$
$912$		0			0
$913$	−0.333010	+	0.333010i	−0.0110210	+	0.0110210i
$914$		0			0
$915$	9.72299	+	8.59959i	0.321432	+	0.284294i
$916$		0			0
$917$		−	24.3454i		−	0.803956i
$918$		0			0
$919$			9.73620i			0.321168i	0.987022	+	0.160584i	$0.0513377\pi$
$919$			9.73620i			0.321168i	−0.987022	+	0.160584i	$0.948662\pi$
$920$		0			0
$921$	−19.8507	−	19.8507i	−0.654103	−	0.654103i
$922$		0			0
$923$	−33.7741	+	4.72065i	−1.11169	+	0.155382i
$924$		0			0
$925$	−5.45343	−	44.3056i	−0.179308	−	1.45676i
$926$		0			0
$927$	3.72580	−	3.72580i	0.122371	−	0.122371i
$928$		0			0
$929$	9.82032	+	9.82032i	0.322194	+	0.322194i	0.849608	−	0.527414i	$-0.176838\pi$
$929$	9.82032	+	9.82032i	0.322194	+	0.322194i	−0.527414	+	0.849608i	$0.676838\pi$
$930$		0			0
$931$	52.6564	+	52.6564i	1.72574	+	1.72574i
$932$		0			0
$933$	−8.99806	−	8.99806i	−0.294583	−	0.294583i
$934$		0			0
$935$	0.0932032	+	1.52015i	0.00304807	+	0.0497141i
$936$		0			0
$937$	−6.29485	−	6.29485i	−0.205644	−	0.205644i	0.596769	−	0.802413i	$-0.296451\pi$
$937$	−6.29485	−	6.29485i	−0.205644	−	0.205644i	−0.802413	+	0.596769i	$0.796451\pi$
$938$		0			0
$939$		−	20.0544i		−	0.654450i
$940$		0			0
$941$	32.4276	−	32.4276i	1.05711	−	1.05711i	0.0588409	−	0.998267i	$-0.481260\pi$
$941$	32.4276	−	32.4276i	1.05711	−	1.05711i	0.998267	−	0.0588409i	$-0.0187405\pi$
$942$		0			0
$943$	−42.4861			−1.38354
$944$		0			0
$945$	−7.87168	−	6.96218i	−0.256066	−	0.226480i
$946$		0			0
$947$		−	41.1923i		−	1.33857i	−0.743006	−	0.669285i	$-0.766601\pi$
$947$		−	41.1923i		−	1.33857i	0.743006	−	0.669285i	$-0.233399\pi$
$948$		0			0
$949$	2.11298	+	1.59474i	0.0685901	+	0.0517675i
$950$		0			0
$951$	−5.40284	+	5.40284i	−0.175199	+	0.175199i
$952$		0			0
$953$	−33.0574	−	33.0574i	−1.07083	−	1.07083i	−0.997292	−	0.0735423i	$-0.976570\pi$
$953$	−33.0574	−	33.0574i	−1.07083	−	1.07083i	−0.0735423	−	0.997292i	$-0.523430\pi$
$954$		0			0
$955$	−1.87330	−	30.5536i	−0.0606186	−	0.988691i
$956$		0			0
$957$		−	1.28364i		−	0.0414942i
$958$		0			0
$959$	−79.4078			−2.56421
$960$		0			0
$961$			28.4297i			0.917086i
$962$		0			0
$963$	−12.4478	+	12.4478i	−0.401125	+	0.401125i
$964$		0			0
$965$	−1.55249	−	25.3211i	−0.0499764	−	0.815116i
$966$		0			0
$967$	54.2975			1.74609			0.873045	−	0.487640i	$-0.162142\pi$
$967$	54.2975			1.74609			0.873045	+	0.487640i	$0.162142\pi$
$968$		0			0
$969$	5.33029	−	5.33029i	0.171234	−	0.171234i
$970$		0			0
$971$	−48.8468			−1.56757			−0.783785	−	0.621033i	$-0.786713\pi$
$971$	−48.8468			−1.56757			−0.783785	+	0.621033i	$0.786713\pi$
$972$		0			0
$973$	14.3539			0.460165
$974$		0			0
$975$	17.4156	−	4.65797i	0.557746	−	0.149174i
$976$		0			0
$977$	−56.8534			−1.81890			−0.909451	−	0.415811i	$-0.863498\pi$
$977$	−56.8534			−1.81890			−0.909451	+	0.415811i	$0.863498\pi$
$978$		0			0
$979$	3.38394			0.108151
$980$		0			0
$981$	12.0020	−	12.0020i	0.383194	−	0.383194i
$982$		0			0
$983$	−15.7995			−0.503924			−0.251962	−	0.967737i	$-0.581076\pi$
$983$	−15.7995			−0.503924			−0.251962	+	0.967737i	$0.581076\pi$
$984$		0			0
$985$	1.74644	+	28.4844i	0.0556461	+	0.907589i
$986$		0			0
$987$	20.4709	−	20.4709i	0.651594	−	0.651594i
$988$		0			0
$989$			3.88247i			0.123455i
$990$		0			0
$991$	−17.8662			−0.567538			−0.283769	−	0.958893i	$-0.591585\pi$
$991$	−17.8662			−0.567538			−0.283769	+	0.958893i	$0.591585\pi$
$992$		0			0
$993$			21.2361i			0.673907i
$994$		0			0
$995$	−0.345882	−	5.64134i	−0.0109652	−	0.178842i
$996$		0			0
$997$	5.03661	+	5.03661i	0.159511	+	0.159511i	0.782350	−	0.622839i	$-0.214021\pi$
$997$	5.03661	+	5.03661i	0.159511	+	0.159511i	−0.622839	+	0.782350i	$0.714021\pi$
$998$		0			0
$999$	−6.31304	+	6.31304i	−0.199736	+	0.199736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.r.a.577.4	yes	28
3.2	odd	2		2340.2.u.i.577.7		28
5.2	odd	4		3900.2.bm.b.2293.8		28
5.3	odd	4		780.2.bm.a.733.1	yes	28
5.4	even	2		3900.2.r.b.1357.8		28
13.8	odd	4		780.2.bm.a.697.1	yes	28
15.8	even	4		2340.2.bp.i.1513.14		28
39.8	even	4		2340.2.bp.i.1477.14		28
65.8	even	4	inner	780.2.r.a.73.4	✓	28
65.34	odd	4		3900.2.bm.b.2257.8		28
65.47	even	4		3900.2.r.b.3193.8		28
195.8	odd	4		2340.2.u.i.73.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.r.a.73.4	✓	28	65.8	even	4	inner
780.2.r.a.577.4	yes	28	1.1	even	1	trivial
780.2.bm.a.697.1	yes	28	13.8	odd	4
780.2.bm.a.733.1	yes	28	5.3	odd	4
2340.2.u.i.73.7		28	195.8	odd	4
2340.2.u.i.577.7		28	3.2	odd	2
2340.2.bp.i.1477.14		28	39.8	even	4
2340.2.bp.i.1513.14		28	15.8	even	4
3900.2.r.b.1357.8		28	5.4	even	2
3900.2.r.b.3193.8		28	65.47	even	4
3900.2.bm.b.2257.8		28	65.34	odd	4
3900.2.bm.b.2293.8		28	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	780.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(0.136841 + 2.23188i) q^{5} +4.69969i q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(0.136841 + 2.23188i) q^{5} +4.69969i q^{7} -1.00000i q^{9} +(0.315352 + 0.315352i) q^{11} +(2.87788 + 2.17205i) q^{13} +(-1.67494 - 1.48141i) q^{15} +(1.07992 - 1.07992i) q^{17} +(-3.49017 - 3.49017i) q^{19} +(-3.32318 - 3.32318i) q^{21} +(-3.48094 - 3.48094i) q^{23} +(-4.96255 + 0.610824i) q^{25} +(0.707107 + 0.707107i) q^{27} +2.87828i q^{29} +(-1.13365 + 1.13365i) q^{31} -0.445975 q^{33} +(-10.4891 + 0.643109i) q^{35} +8.92799i q^{37} +(-3.57084 + 0.499101i) q^{39} +(6.10267 - 6.10267i) q^{41} +(-0.557675 - 0.557675i) q^{43} +(2.23188 - 0.136841i) q^{45} +6.16002i q^{47} -15.0871 q^{49} +1.52723i q^{51} +(8.42127 - 8.42127i) q^{53} +(-0.660673 + 0.746979i) q^{55} +4.93584 q^{57} +(-1.44238 + 1.44238i) q^{59} -5.80499 q^{61} +4.69969 q^{63} +(-4.45393 + 6.72031i) q^{65} +4.05741 q^{67} +4.92280 q^{69} +(-6.68803 + 6.68803i) q^{71} +0.734212 q^{73} +(3.07713 - 3.94097i) q^{75} +(-1.48205 + 1.48205i) q^{77} +12.9137i q^{79} -1.00000 q^{81} +1.05600i q^{83} +(2.55801 + 2.26246i) q^{85} +(-2.03525 - 2.03525i) q^{87} +(5.36534 - 5.36534i) q^{89} +(-10.2079 + 13.5251i) q^{91} -1.60322i q^{93} +(7.31203 - 8.26723i) q^{95} -4.56277 q^{97} +(0.315352 - 0.315352i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q + 8 q^{11} - 4 q^{13} - 4 q^{15} - 4 q^{17} - 16 q^{19} + 8 q^{21} - 8 q^{23} + 12 q^{25} - 8 q^{33} + 8 q^{39} + 12 q^{41} + 16 q^{43} + 4 q^{45} - 36 q^{49} + 36 q^{53} + 40 q^{55} + 16 q^{59} + 8 q^{61} - 40 q^{65} + 48 q^{67} - 8 q^{69} + 8 q^{71} + 48 q^{73} - 48 q^{77} - 28 q^{81} - 4 q^{85} - 24 q^{87} - 36 q^{89} - 24 q^{91} + 72 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) \) 28 * q + 8 * q^11 - 4 * q^13 - 4 * q^15 - 4 * q^17 - 16 * q^19 + 8 * q^21 - 8 * q^23 + 12 * q^25 - 8 * q^33 + 8 * q^39 + 12 * q^41 + 16 * q^43 + 4 * q^45 - 36 * q^49 + 36 * q^53 + 40 * q^55 + 16 * q^59 + 8 * q^61 - 40 * q^65 + 48 * q^67 - 8 * q^69 + 8 * q^71 + 48 * q^73 - 48 * q^77 - 28 * q^81 - 4 * q^85 - 24 * q^87 - 36 * q^89 - 24 * q^91 + 72 * q^95 - 72 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more