LMFDB - Embedded newform 980.4.i.c.961.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,4,Mod(361,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.361"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	980.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-5,0,-5,0,0,0,2,0,-15] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$57.8218718056$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	980.961
Dual form			980.4.i.c.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.50000 - 4.33013i) q^{3} +(-2.50000 + 4.33013i) q^{5} +(1.00000 - 1.73205i) q^{9} +(-7.50000 - 12.9904i) q^{11} -17.0000 q^{13} +25.0000 q^{15} +(61.5000 + 106.521i) q^{17} +(43.0000 - 74.4782i) q^{19} +(-27.0000 + 46.7654i) q^{23} +(-12.5000 - 21.6506i) q^{25} -145.000 q^{27} -177.000 q^{29} +(106.000 + 183.597i) q^{31} +(-37.5000 + 64.9519i) q^{33} +(-37.0000 + 64.0859i) q^{37} +(42.5000 + 73.6122i) q^{39} +444.000 q^{41} -46.0000 q^{43} +(5.00000 + 8.66025i) q^{45} +(235.500 - 407.898i) q^{47} +(307.500 - 532.606i) q^{51} +(90.0000 + 155.885i) q^{53} +75.0000 q^{55} -430.000 q^{57} +(72.0000 + 124.708i) q^{59} +(-188.000 + 325.626i) q^{61} +(42.5000 - 73.6122i) q^{65} +(-178.000 - 308.305i) q^{67} +270.000 q^{69} -48.0000 q^{71} +(409.000 + 708.409i) q^{73} +(-62.5000 + 108.253i) q^{75} +(-44.5000 + 77.0763i) q^{79} +(335.500 + 581.103i) q^{81} +780.000 q^{83} -615.000 q^{85} +(442.500 + 766.432i) q^{87} +(570.000 - 987.269i) q^{89} +(530.000 - 917.987i) q^{93} +(215.000 + 372.391i) q^{95} +169.000 q^{97} -30.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 5 q^{3} - 5 q^{5} + 2 q^{9} - 15 q^{11} - 34 q^{13} + 50 q^{15} + 123 q^{17} + 86 q^{19} - 54 q^{23} - 25 q^{25} - 290 q^{27} - 354 q^{29} + 212 q^{31} - 75 q^{33} - 74 q^{37} + 85 q^{39} + 888 q^{41}+ \cdots - 60 q^{99}+O(q^{100}) $ 2 * q - 5 * q^3 - 5 * q^5 + 2 * q^9 - 15 * q^11 - 34 * q^13 + 50 * q^15 + 123 * q^17 + 86 * q^19 - 54 * q^23 - 25 * q^25 - 290 * q^27 - 354 * q^29 + 212 * q^31 - 75 * q^33 - 74 * q^37 + 85 * q^39 + 888 * q^41 - 92 * q^43 + 10 * q^45 + 471 * q^47 + 615 * q^51 + 180 * q^53 + 150 * q^55 - 860 * q^57 + 144 * q^59 - 376 * q^61 + 85 * q^65 - 356 * q^67 + 540 * q^69 - 96 * q^71 + 818 * q^73 - 125 * q^75 - 89 * q^79 + 671 * q^81 + 1560 * q^83 - 1230 * q^85 + 885 * q^87 + 1140 * q^89 + 1060 * q^93 + 430 * q^95 + 338 * q^97 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.50000	−	4.33013i	−0.481125	−	0.833333i	0.518640	−	0.854993i	$-0.326438\pi$
$3$	−2.50000	−	4.33013i	−0.481125	−	0.833333i	−0.999765	+	0.0216593i	$0.993105\pi$
$4$		0			0
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.00000	−	1.73205i	0.0370370	−	0.0641500i
$10$		0			0
$11$	−7.50000	−	12.9904i	−0.205576	−	0.356068i	0.744740	−	0.667355i	$-0.232573\pi$
$11$	−7.50000	−	12.9904i	−0.205576	−	0.356068i	−0.950316	+	0.311287i	$0.899240\pi$
$12$		0			0
$13$	−17.0000			−0.362689			−0.181344	−	0.983420i	$-0.558045\pi$
$13$	−17.0000			−0.362689			−0.181344	+	0.983420i	$0.558045\pi$
$14$		0			0
$15$	25.0000			0.430331
$16$		0			0
$17$	61.5000	+	106.521i	0.877408	+	1.51972i	0.854175	+	0.519986i	$0.174063\pi$
$17$	61.5000	+	106.521i	0.877408	+	1.51972i	0.0232333	+	0.999730i	$0.492604\pi$
$18$		0			0
$19$	43.0000	−	74.4782i	0.519204	−	0.899288i	−0.480547	−	0.876969i	$-0.659562\pi$
$19$	43.0000	−	74.4782i	0.519204	−	0.899288i	0.999751	−	0.0223187i	$-0.00710486\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−27.0000	+	46.7654i	−0.244778	+	0.423968i	−0.962069	−	0.272806i	$-0.912048\pi$
$23$	−27.0000	+	46.7654i	−0.244778	+	0.423968i	0.717291	+	0.696773i	$0.245382\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$		0			0
$27$	−145.000			−1.03353
$28$		0			0
$29$	−177.000			−1.13338			−0.566691	−	0.823930i	$-0.691777\pi$
$29$	−177.000			−1.13338			−0.566691	+	0.823930i	$0.691777\pi$
$30$		0			0
$31$	106.000	+	183.597i	0.614134	+	1.06371i	0.990536	+	0.137255i	$0.0438280\pi$
$31$	106.000	+	183.597i	0.614134	+	1.06371i	−0.376401	+	0.926457i	$0.622839\pi$
$32$		0			0
$33$	−37.5000	+	64.9519i	−0.197816	+	0.342627i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−37.0000	+	64.0859i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−37.0000	+	64.0859i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$		0			0
$39$	42.5000	+	73.6122i	0.174499	+	0.302240i
$40$		0			0
$41$	444.000			1.69125			0.845624	−	0.533779i	$-0.179229\pi$
$41$	444.000			1.69125			0.845624	+	0.533779i	$0.179229\pi$
$42$		0			0
$43$	−46.0000			−0.163138			−0.0815690	−	0.996668i	$-0.525993\pi$
$43$	−46.0000			−0.163138			−0.0815690	+	0.996668i	$0.525993\pi$
$44$		0			0
$45$	5.00000	+	8.66025i	0.0165635	+	0.0286888i
$46$		0			0
$47$	235.500	−	407.898i	0.730877	−	1.26592i	−0.225632	−	0.974213i	$-0.572445\pi$
$47$	235.500	−	407.898i	0.730877	−	1.26592i	0.956509	−	0.291703i	$-0.0942219\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	307.500	−	532.606i	0.844287	−	1.46235i
$52$		0			0
$53$	90.0000	+	155.885i	0.233254	+	0.404007i	0.958764	−	0.284204i	$-0.0917294\pi$
$53$	90.0000	+	155.885i	0.233254	+	0.404007i	−0.725510	+	0.688212i	$0.758396\pi$
$54$		0			0
$55$	75.0000			0.183873
$56$		0			0
$57$	−430.000			−0.999209
$58$		0			0
$59$	72.0000	+	124.708i	0.158875	+	0.275179i	0.934463	−	0.356060i	$-0.115880\pi$
$59$	72.0000	+	124.708i	0.158875	+	0.275179i	−0.775589	+	0.631239i	$0.782547\pi$
$60$		0			0
$61$	−188.000	+	325.626i	−0.394605	+	0.683477i	−0.993051	−	0.117687i	$-0.962452\pi$
$61$	−188.000	+	325.626i	−0.394605	+	0.683477i	0.598445	+	0.801164i	$0.295785\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	42.5000	−	73.6122i	0.0810996	−	0.140469i
$66$		0			0
$67$	−178.000	−	308.305i	−0.324570	−	0.562171i	0.656856	−	0.754016i	$-0.271886\pi$
$67$	−178.000	−	308.305i	−0.324570	−	0.562171i	−0.981425	+	0.191845i	$0.938553\pi$
$68$		0			0
$69$	270.000			0.471075
$70$		0			0
$71$	−48.0000			−0.0802331			−0.0401166	−	0.999195i	$-0.512773\pi$
$71$	−48.0000			−0.0802331			−0.0401166	+	0.999195i	$0.512773\pi$
$72$		0			0
$73$	409.000	+	708.409i	0.655751	+	1.13579i	0.981705	+	0.190409i	$0.0609813\pi$
$73$	409.000	+	708.409i	0.655751	+	1.13579i	−0.325954	+	0.945386i	$0.605685\pi$
$74$		0			0
$75$	−62.5000	+	108.253i	−0.0962250	+	0.166667i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−44.5000	+	77.0763i	−0.0633752	+	0.109769i	−0.895972	−	0.444110i	$-0.853520\pi$
$79$	−44.5000	+	77.0763i	−0.0633752	+	0.109769i	0.832597	+	0.553879i	$0.186853\pi$
$80$		0			0
$81$	335.500	+	581.103i	0.460219	+	0.797124i
$82$		0			0
$83$	780.000			1.03152			0.515760	−	0.856733i	$-0.327510\pi$
$83$	780.000			1.03152			0.515760	+	0.856733i	$0.327510\pi$
$84$		0			0
$85$	−615.000			−0.784778
$86$		0			0
$87$	442.500	+	766.432i	0.545299	+	0.944485i
$88$		0			0
$89$	570.000	−	987.269i	0.678875	−	1.17585i	−0.296445	−	0.955050i	$-0.595801\pi$
$89$	570.000	−	987.269i	0.678875	−	1.17585i	0.975320	−	0.220796i	$-0.0708655\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	530.000	−	917.987i	0.590951	−	1.02356i
$94$		0			0
$95$	215.000	+	372.391i	0.232195	+	0.402174i
$96$		0			0
$97$	169.000			0.176901			0.0884503	−	0.996081i	$-0.471809\pi$
$97$	169.000			0.176901			0.0884503	+	0.996081i	$0.471809\pi$
$98$		0			0
$99$	−30.0000			−0.0304557
$100$		0			0
$101$	−369.000	−	639.127i	−0.363533	−	0.629658i	0.625006	−	0.780620i	$-0.285096\pi$
$101$	−369.000	−	639.127i	−0.363533	−	0.629658i	−0.988540	+	0.150961i	$0.951763\pi$
$102$		0			0
$103$	425.500	−	736.988i	0.407046	−	0.705025i	−0.587511	−	0.809216i	$-0.699892\pi$
$103$	425.500	−	736.988i	0.407046	−	0.705025i	0.994557	+	0.104191i	$0.0332255\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	447.000	−	774.227i	0.403861	−	0.699508i	−0.590327	−	0.807164i	$-0.701001\pi$
$107$	447.000	−	774.227i	0.403861	−	0.699508i	0.994188	+	0.107656i	$0.0343346\pi$
$108$		0			0
$109$	−830.500	−	1438.47i	−0.729793	−	1.26404i	−0.956970	−	0.290186i	$-0.906283\pi$
$109$	−830.500	−	1438.47i	−0.729793	−	1.26404i	0.227177	−	0.973853i	$-0.427050\pi$
$110$		0			0
$111$	370.000			0.316386
$112$		0			0
$113$	1302.00			1.08391			0.541955	−	0.840407i	$-0.317684\pi$
$113$	1302.00			1.08391			0.541955	+	0.840407i	$0.317684\pi$
$114$		0			0
$115$	−135.000	−	233.827i	−0.109468	−	0.189604i
$116$		0			0
$117$	−17.0000	+	29.4449i	−0.0134329	+	0.0232665i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	553.000	−	957.824i	0.415477	−	0.719627i
$122$		0			0
$123$	−1110.00	−	1922.58i	−0.813702	−	1.40937i
$124$		0			0
$125$	125.000			0.0894427
$126$		0			0
$127$	2624.00			1.83340			0.916702	−	0.399571i	$-0.130841\pi$
$127$	2624.00			1.83340			0.916702	+	0.399571i	$0.130841\pi$
$128$		0			0
$129$	115.000	+	199.186i	0.0784898	+	0.135948i
$130$		0			0
$131$	423.000	−	732.657i	0.282120	−	0.488646i	−0.689787	−	0.724012i	$-0.742296\pi$
$131$	423.000	−	732.657i	0.282120	−	0.488646i	0.971907	+	0.235367i	$0.0756291\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	362.500	−	627.868i	0.231104	−	0.400284i
$136$		0			0
$137$	−522.000	−	904.131i	−0.325529	−	0.563833i	0.656090	−	0.754682i	$-0.272209\pi$
$137$	−522.000	−	904.131i	−0.325529	−	0.563833i	−0.981619	+	0.190850i	$0.938876\pi$
$138$		0			0
$139$	−1946.00			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−1946.00			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$		0			0
$141$	−2355.00			−1.40657
$142$		0			0
$143$	127.500	+	220.836i	0.0745600	+	0.129142i
$144$		0			0
$145$	442.500	−	766.432i	0.253432	−	0.438957i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	783.000	−	1356.20i	0.430509	−	0.745664i	−0.566408	−	0.824125i	$-0.691667\pi$
$149$	783.000	−	1356.20i	0.430509	−	0.745664i	0.996917	+	0.0784613i	$0.0250007\pi$
$150$		0			0
$151$	−608.500	−	1053.95i	−0.327941	−	0.568010i	0.654162	−	0.756354i	$-0.273021\pi$
$151$	−608.500	−	1053.95i	−0.327941	−	0.568010i	−0.982103	+	0.188344i	$0.939688\pi$
$152$		0			0
$153$	246.000			0.129986
$154$		0			0
$155$	−1060.00			−0.549298
$156$		0			0
$157$	1243.00	+	2152.94i	0.631861	+	1.09442i	0.987171	+	0.159667i	$0.0510420\pi$
$157$	1243.00	+	2152.94i	0.631861	+	1.09442i	−0.355310	+	0.934749i	$0.615625\pi$
$158$		0			0
$159$	450.000	−	779.423i	0.224449	−	0.388756i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1781.00	−	3084.78i	0.855820	−	1.48232i	−0.0200619	−	0.999799i	$-0.506386\pi$
$163$	1781.00	−	3084.78i	0.855820	−	1.48232i	0.875882	−	0.482525i	$-0.160280\pi$
$164$		0			0
$165$	−187.500	−	324.760i	−0.0884658	−	0.153227i
$166$		0			0
$167$	1557.00			0.721463			0.360731	−	0.932670i	$-0.382527\pi$
$167$	1557.00			0.721463			0.360731	+	0.932670i	$0.382527\pi$
$168$		0			0
$169$	−1908.00			−0.868457
$170$		0			0
$171$	−86.0000	−	148.956i	−0.0384596	−	0.0666139i
$172$		0			0
$173$	−1234.50	+	2138.22i	−0.542528	+	0.939686i	0.456230	+	0.889862i	$0.349199\pi$
$173$	−1234.50	+	2138.22i	−0.542528	+	0.939686i	−0.998758	+	0.0498238i	$0.984134\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	360.000	−	623.538i	0.152877	−	0.264791i
$178$		0			0
$179$	1326.00	+	2296.70i	0.553687	+	0.959013i	0.998004	+	0.0631440i	$0.0201128\pi$
$179$	1326.00	+	2296.70i	0.553687	+	0.959013i	−0.444318	+	0.895869i	$0.646554\pi$
$180$		0			0
$181$	1996.00			0.819677			0.409838	−	0.912158i	$-0.365585\pi$
$181$	1996.00			0.819677			0.409838	+	0.912158i	$0.365585\pi$
$182$		0			0
$183$	1880.00			0.759419
$184$		0			0
$185$	−185.000	−	320.429i	−0.0735215	−	0.127343i
$186$		0			0
$187$	922.500	−	1597.82i	0.360748	−	0.624834i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1792.50	−	3104.70i	0.679062	−	1.17617i	−0.296202	−	0.955125i	$-0.595720\pi$
$191$	1792.50	−	3104.70i	0.679062	−	1.17617i	0.975264	−	0.221044i	$-0.0709464\pi$
$192$		0			0
$193$	−286.000	−	495.367i	−0.106667	−	0.184753i	0.807751	−	0.589524i	$-0.200685\pi$
$193$	−286.000	−	495.367i	−0.106667	−	0.184753i	−0.914418	+	0.404771i	$0.867351\pi$
$194$		0			0
$195$	−425.000			−0.156076
$196$		0			0
$197$	−3408.00			−1.23254			−0.616269	−	0.787536i	$-0.711357\pi$
$197$	−3408.00			−1.23254			−0.616269	+	0.787536i	$0.711357\pi$
$198$		0			0
$199$	−1808.00	−	3131.55i	−0.644049	−	1.11553i	−0.984520	−	0.175270i	$-0.943920\pi$
$199$	−1808.00	−	3131.55i	−0.644049	−	1.11553i	0.340471	−	0.940255i	$-0.389413\pi$
$200$		0			0
$201$	−890.000	+	1541.53i	−0.312317	+	0.540949i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−1110.00	+	1922.58i	−0.378174	+	0.655017i
$206$		0			0
$207$	54.0000	+	93.5307i	0.0181317	+	0.0314050i
$208$		0			0
$209$	−1290.00			−0.426943
$210$		0			0
$211$	4889.00			1.59513			0.797565	−	0.603232i	$-0.206121\pi$
$211$	4889.00			1.59513			0.797565	+	0.603232i	$0.206121\pi$
$212$		0			0
$213$	120.000	+	207.846i	0.0386022	+	0.0668609i
$214$		0			0
$215$	115.000	−	199.186i	0.0364788	−	0.0631831i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	2045.00	−	3542.04i	0.630997	−	1.09292i
$220$		0			0
$221$	−1045.50	−	1810.86i	−0.318226	−	0.551184i
$222$		0			0
$223$	3229.00			0.969641			0.484820	−	0.874614i	$-0.338885\pi$
$223$	3229.00			0.969641			0.484820	+	0.874614i	$0.338885\pi$
$224$		0			0
$225$	−50.0000			−0.0148148
$226$		0			0
$227$	607.500	+	1052.22i	0.177626	+	0.307658i	0.941067	−	0.338220i	$-0.109825\pi$
$227$	607.500	+	1052.22i	0.177626	+	0.307658i	−0.763441	+	0.645878i	$0.776491\pi$
$228$		0			0
$229$	1102.00	−	1908.72i	0.318001	−	0.550794i	−0.662070	−	0.749442i	$-0.730322\pi$
$229$	1102.00	−	1908.72i	0.318001	−	0.550794i	0.980071	+	0.198648i	$0.0636552\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−108.000	+	187.061i	−0.0303662	+	0.0525957i	−0.880809	−	0.473472i	$-0.843001\pi$
$233$	−108.000	+	187.061i	−0.0303662	+	0.0525957i	0.850443	+	0.526067i	$0.176334\pi$
$234$		0			0
$235$	1177.50	+	2039.49i	0.326858	+	0.566135i
$236$		0			0
$237$	445.000			0.121966
$238$		0			0
$239$	−5235.00			−1.41684			−0.708418	−	0.705793i	$-0.750591\pi$
$239$	−5235.00			−1.41684			−0.708418	+	0.705793i	$0.750591\pi$
$240$		0			0
$241$	2971.00	+	5145.92i	0.794103	+	1.37543i	0.923407	+	0.383822i	$0.125393\pi$
$241$	2971.00	+	5145.92i	0.794103	+	1.37543i	−0.129303	+	0.991605i	$0.541274\pi$
$242$		0			0
$243$	−280.000	+	484.974i	−0.0739177	+	0.128029i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−731.000	+	1266.13i	−0.188309	+	0.326161i
$248$		0			0
$249$	−1950.00	−	3377.50i	−0.496290	−	0.859600i
$250$		0			0
$251$	954.000			0.239904			0.119952	−	0.992780i	$-0.461726\pi$
$251$	954.000			0.239904			0.119952	+	0.992780i	$0.461726\pi$
$252$		0			0
$253$	810.000			0.201282
$254$		0			0
$255$	1537.50	+	2663.03i	0.377576	+	0.653982i
$256$		0			0
$257$	1743.00	−	3018.96i	0.423056	−	0.732754i	−0.573181	−	0.819429i	$-0.694291\pi$
$257$	1743.00	−	3018.96i	0.423056	−	0.732754i	0.996237	+	0.0866747i	$0.0276241\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−177.000	+	306.573i	−0.0419771	+	0.0727065i
$262$		0			0
$263$	339.000	+	587.165i	0.0794815	+	0.137666i	0.903026	−	0.429585i	$-0.141340\pi$
$263$	339.000	+	587.165i	0.0794815	+	0.137666i	−0.823545	+	0.567251i	$0.808007\pi$
$264$		0			0
$265$	−900.000			−0.208629
$266$		0			0
$267$	−5700.00			−1.30650
$268$		0			0
$269$	−1695.00	−	2935.83i	−0.384186	−	0.665429i	0.607470	−	0.794343i	$-0.292184\pi$
$269$	−1695.00	−	2935.83i	−0.384186	−	0.665429i	−0.991656	+	0.128913i	$0.958851\pi$
$270$		0			0
$271$	280.000	−	484.974i	0.0627631	−	0.108709i	−0.832936	−	0.553369i	$-0.813342\pi$
$271$	280.000	−	484.974i	0.0627631	−	0.108709i	0.895700	+	0.444660i	$0.146675\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−187.500	+	324.760i	−0.0411152	+	0.0712136i
$276$		0			0
$277$	3929.00	+	6805.23i	0.852241	+	1.47612i	0.879181	+	0.476488i	$0.158090\pi$
$277$	3929.00	+	6805.23i	0.852241	+	1.47612i	−0.0269403	+	0.999637i	$0.508576\pi$
$278$		0			0
$279$	424.000			0.0909829
$280$		0			0
$281$	6171.00			1.31007			0.655037	−	0.755596i	$-0.272653\pi$
$281$	6171.00			1.31007			0.655037	+	0.755596i	$0.272653\pi$
$282$		0			0
$283$	2060.50	+	3568.89i	0.432806	+	0.749641i	0.997114	−	0.0759229i	$-0.0241903\pi$
$283$	2060.50	+	3568.89i	0.432806	+	0.749641i	−0.564308	+	0.825564i	$0.690857\pi$
$284$		0			0
$285$	1075.00	−	1861.95i	0.223430	−	0.386992i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−5108.00	+	8847.32i	−1.03969	+	1.80080i
$290$		0			0
$291$	−422.500	−	731.791i	−0.0851113	−	0.147417i
$292$		0			0
$293$	9.00000			0.00179449			0.000897245	−	1.00000i	$-0.499714\pi$
$293$	9.00000			0.00179449			0.000897245		1.00000i	$0.499714\pi$
$294$		0			0
$295$	−720.000			−0.142102
$296$		0			0
$297$	1087.50	+	1883.61i	0.212469	+	0.368006i
$298$		0			0
$299$	459.000	−	795.011i	0.0887781	−	0.153768i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−1845.00	+	3195.63i	−0.349810	+	0.605889i
$304$		0			0
$305$	−940.000	−	1628.13i	−0.176473	−	0.305660i
$306$		0			0
$307$	6487.00			1.20597			0.602985	−	0.797753i	$-0.293978\pi$
$307$	6487.00			1.20597			0.602985	+	0.797753i	$0.293978\pi$
$308$		0			0
$309$	−4255.00			−0.783361
$310$		0			0
$311$	2703.00	+	4681.73i	0.492839	+	0.853623i	0.999966	−	0.00824865i	$-0.00262566\pi$
$311$	2703.00	+	4681.73i	0.492839	+	0.853623i	−0.507127	+	0.861872i	$0.669292\pi$
$312$		0			0
$313$	−633.500	+	1097.25i	−0.114401	+	0.198148i	−0.917540	−	0.397643i	$-0.869828\pi$
$313$	−633.500	+	1097.25i	−0.114401	+	0.198148i	0.803139	+	0.595792i	$0.203162\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1731.00	+	2998.18i	−0.306696	+	0.531213i	−0.977638	−	0.210297i	$-0.932557\pi$
$317$	−1731.00	+	2998.18i	−0.306696	+	0.531213i	0.670941	+	0.741510i	$0.265890\pi$
$318$		0			0
$319$	1327.50	+	2299.30i	0.232996	+	0.403561i
$320$		0			0
$321$	−4470.00			−0.777231
$322$		0			0
$323$	10578.0			1.82222
$324$		0			0
$325$	212.500	+	368.061i	0.0362689	+	0.0628195i
$326$		0			0
$327$	−4152.50	+	7192.34i	−0.702244	+	1.21632i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−4102.00	+	7104.87i	−0.681167	+	1.17982i	0.293458	+	0.955972i	$0.405194\pi$
$331$	−4102.00	+	7104.87i	−0.681167	+	1.17982i	−0.974625	+	0.223844i	$0.928139\pi$
$332$		0			0
$333$	74.0000	+	128.172i	0.0121777	+	0.0210924i
$334$		0			0
$335$	1780.00			0.290304
$336$		0			0
$337$	−4066.00			−0.657238			−0.328619	−	0.944463i	$-0.606583\pi$
$337$	−4066.00			−0.657238			−0.328619	+	0.944463i	$0.606583\pi$
$338$		0			0
$339$	−3255.00	−	5637.83i	−0.521497	−	0.903259i
$340$		0			0
$341$	1590.00	−	2753.96i	0.252502	−	0.437347i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−675.000	+	1169.13i	−0.105336	+	0.182447i
$346$		0			0
$347$	1611.00	+	2790.33i	0.249231	+	0.431680i	0.963313	−	0.268382i	$-0.0864890\pi$
$347$	1611.00	+	2790.33i	0.249231	+	0.431680i	−0.714082	+	0.700062i	$0.753156\pi$
$348$		0			0
$349$	−11666.0			−1.78930			−0.894651	−	0.446765i	$-0.852576\pi$
$349$	−11666.0			−1.78930			−0.894651	+	0.446765i	$0.852576\pi$
$350$		0			0
$351$	2465.00			0.374849
$352$		0			0
$353$	−4300.50	−	7448.68i	−0.648421	−	1.12310i	−0.983500	−	0.180908i	$-0.942096\pi$
$353$	−4300.50	−	7448.68i	−0.648421	−	1.12310i	0.335079	−	0.942190i	$-0.391237\pi$
$354$		0			0
$355$	120.000	−	207.846i	0.0179407	−	0.0310742i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2340.00	−	4053.00i	0.344012	−	0.595847i	−0.641161	−	0.767406i	$-0.721547\pi$
$359$	2340.00	−	4053.00i	0.344012	−	0.595847i	0.985174	+	0.171559i	$0.0548804\pi$
$360$		0			0
$361$	−268.500	−	465.056i	−0.0391456	−	0.0678023i
$362$		0			0
$363$	−5530.00			−0.799586
$364$		0			0
$365$	−4090.00			−0.586522
$366$		0			0
$367$	2879.50	+	4987.44i	0.409560	+	0.709379i	0.994840	−	0.101452i	$-0.0323488\pi$
$367$	2879.50	+	4987.44i	0.409560	+	0.709379i	−0.585280	+	0.810831i	$0.699015\pi$
$368$		0			0
$369$	444.000	−	769.031i	0.0626388	−	0.108494i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	6122.00	−	10603.6i	0.849826	−	1.47194i	−0.0315370	−	0.999503i	$-0.510040\pi$
$373$	6122.00	−	10603.6i	0.849826	−	1.47194i	0.881363	−	0.472439i	$-0.156626\pi$
$374$		0			0
$375$	−312.500	−	541.266i	−0.0430331	−	0.0745356i
$376$		0			0
$377$	3009.00			0.411065
$378$		0			0
$379$	9308.00			1.26153			0.630765	−	0.775974i	$-0.282741\pi$
$379$	9308.00			1.26153			0.630765	+	0.775974i	$0.282741\pi$
$380$		0			0
$381$	−6560.00	−	11362.3i	−0.882097	−	1.52784i
$382$		0			0
$383$	−2934.00	+	5081.84i	−0.391437	+	0.677989i	−0.992639	−	0.121108i	$-0.961355\pi$
$383$	−2934.00	+	5081.84i	−0.391437	+	0.677989i	0.601202	+	0.799097i	$0.294689\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−46.0000	+	79.6743i	−0.00604215	+	0.0104653i
$388$		0			0
$389$	1675.50	+	2902.05i	0.218384	+	0.378251i	0.954314	−	0.298806i	$-0.0965883\pi$
$389$	1675.50	+	2902.05i	0.218384	+	0.378251i	−0.735930	+	0.677057i	$0.763255\pi$
$390$		0			0
$391$	−6642.00			−0.859080
$392$		0			0
$393$	−4230.00			−0.542940
$394$		0			0
$395$	−222.500	−	385.381i	−0.0283423	−	0.0490902i
$396$		0			0
$397$	−4434.50	+	7680.78i	−0.560607	+	0.971001i	0.436836	+	0.899541i	$0.356099\pi$
$397$	−4434.50	+	7680.78i	−0.560607	+	0.971001i	−0.997444	+	0.0714595i	$0.977234\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7336.50	+	12707.2i	−0.913634	+	1.58246i	−0.104746	+	0.994499i	$0.533403\pi$
$401$	−7336.50	+	12707.2i	−0.913634	+	1.58246i	−0.808889	+	0.587962i	$0.799931\pi$
$402$		0			0
$403$	−1802.00	−	3121.16i	−0.222739	−	0.385796i
$404$		0			0
$405$	−3355.00			−0.411633
$406$		0			0
$407$	1110.00			0.135186
$408$		0			0
$409$	−7145.00	−	12375.5i	−0.863808	−	1.49616i	−0.868226	−	0.496169i	$-0.834740\pi$
$409$	−7145.00	−	12375.5i	−0.863808	−	1.49616i	0.00441771	−	0.999990i	$-0.498594\pi$
$410$		0			0
$411$	−2610.00	+	4520.65i	−0.313240	+	0.542548i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1950.00	+	3377.50i	−0.230655	+	0.399506i
$416$		0			0
$417$	4865.00	+	8426.43i	0.571319	+	0.989554i
$418$		0			0
$419$	10452.0			1.21865			0.609324	−	0.792921i	$-0.291441\pi$
$419$	10452.0			1.21865			0.609324	+	0.792921i	$0.291441\pi$
$420$		0			0
$421$	−13795.0			−1.59698			−0.798488	−	0.602010i	$-0.794367\pi$
$421$	−13795.0			−1.59698			−0.798488	+	0.602010i	$0.794367\pi$
$422$		0			0
$423$	−471.000	−	815.796i	−0.0541390	−	0.0937715i
$424$		0			0
$425$	1537.50	−	2663.03i	0.175482	−	0.303943i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	637.500	−	1104.18i	0.0717454	−	0.124267i
$430$		0			0
$431$	1582.50	+	2740.97i	0.176859	+	0.306329i	0.940803	−	0.338953i	$-0.110073\pi$
$431$	1582.50	+	2740.97i	0.176859	+	0.306329i	−0.763944	+	0.645283i	$0.776740\pi$
$432$		0			0
$433$	6526.00			0.724295			0.362147	−	0.932121i	$-0.382044\pi$
$433$	6526.00			0.724295			0.362147	+	0.932121i	$0.382044\pi$
$434$		0			0
$435$	−4425.00			−0.487730
$436$		0			0
$437$	2322.00	+	4021.82i	0.254179	+	0.440251i
$438$		0			0
$439$	−8909.00	+	15430.8i	−0.968573	+	1.67762i	−0.268879	+	0.963174i	$0.586653\pi$
$439$	−8909.00	+	15430.8i	−0.968573	+	1.67762i	−0.699694	+	0.714443i	$0.746680\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5901.00	+	10220.8i	−0.632878	+	1.09618i	0.354082	+	0.935214i	$0.384793\pi$
$443$	−5901.00	+	10220.8i	−0.632878	+	1.09618i	−0.986960	+	0.160963i	$0.948540\pi$
$444$		0			0
$445$	2850.00	+	4936.34i	0.303602	+	0.525854i
$446$		0			0
$447$	−7830.00			−0.828515
$448$		0			0
$449$	10743.0			1.12916			0.564581	−	0.825378i	$-0.309038\pi$
$449$	10743.0			1.12916			0.564581	+	0.825378i	$0.309038\pi$
$450$		0			0
$451$	−3330.00	−	5767.73i	−0.347680	−	0.602199i
$452$		0			0
$453$	−3042.50	+	5269.76i	−0.315561	+	0.546568i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3964.00	+	6865.85i	−0.405751	+	0.702781i	−0.994409	−	0.105601i	$-0.966323\pi$
$457$	−3964.00	+	6865.85i	−0.405751	+	0.702781i	0.588658	+	0.808382i	$0.299657\pi$
$458$		0			0
$459$	−8917.50	−	15445.6i	−0.906826	−	1.57067i
$460$		0			0
$461$	−4104.00			−0.414625			−0.207313	−	0.978275i	$-0.566472\pi$
$461$	−4104.00			−0.414625			−0.207313	+	0.978275i	$0.566472\pi$
$462$		0			0
$463$	12416.0			1.24626			0.623132	−	0.782116i	$-0.285860\pi$
$463$	12416.0			1.24626			0.623132	+	0.782116i	$0.285860\pi$
$464$		0			0
$465$	2650.00	+	4589.93i	0.264281	+	0.457749i
$466$		0			0
$467$	4618.50	−	7999.48i	0.457642	−	0.792659i	−0.541194	−	0.840898i	$-0.682028\pi$
$467$	4618.50	−	7999.48i	0.457642	−	0.792659i	0.998836	+	0.0482390i	$0.0153609\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	6215.00	−	10764.7i	0.608009	−	1.05310i
$472$		0			0
$473$	345.000	+	597.558i	0.0335372	+	0.0580882i
$474$		0			0
$475$	−2150.00			−0.207682
$476$		0			0
$477$	360.000			0.0345561
$478$		0			0
$479$	−9945.00	−	17225.2i	−0.948640	−	1.64309i	−0.748293	−	0.663368i	$-0.769126\pi$
$479$	−9945.00	−	17225.2i	−0.948640	−	1.64309i	−0.200347	−	0.979725i	$-0.564207\pi$
$480$		0			0
$481$	629.000	−	1089.46i	0.0596256	−	0.103275i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−422.500	+	731.791i	−0.0395562	+	0.0685133i
$486$		0			0
$487$	−997.000	−	1726.85i	−0.0927688	−	0.160680i	0.815906	−	0.578184i	$-0.196238\pi$
$487$	−997.000	−	1726.85i	−0.0927688	−	0.160680i	−0.908675	+	0.417504i	$0.862905\pi$
$488$		0			0
$489$	−17810.0			−1.64703
$490$		0			0
$491$	18885.0			1.73578			0.867890	−	0.496756i	$-0.165476\pi$
$491$	18885.0			1.73578			0.867890	+	0.496756i	$0.165476\pi$
$492$		0			0
$493$	−10885.5	−	18854.2i	−0.994439	−	1.72242i
$494$		0			0
$495$	75.0000	−	129.904i	0.00681010	−	0.0117954i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1121.50	+	1942.49i	−0.100612	+	0.174265i	−0.911937	−	0.410331i	$-0.865413\pi$
$499$	−1121.50	+	1942.49i	−0.100612	+	0.174265i	0.811325	+	0.584595i	$0.198747\pi$
$500$		0			0
$501$	−3892.50	−	6742.01i	−0.347114	−	0.601219i
$502$		0			0
$503$	−10461.0			−0.927302			−0.463651	−	0.886018i	$-0.653461\pi$
$503$	−10461.0			−0.927302			−0.463651	+	0.886018i	$0.653461\pi$
$504$		0			0
$505$	3690.00			0.325154
$506$		0			0
$507$	4770.00	+	8261.88i	0.417837	+	0.723714i
$508$		0			0
$509$	−399.000	+	691.088i	−0.0347453	+	0.0601806i	−0.882875	−	0.469608i	$-0.844395\pi$
$509$	−399.000	+	691.088i	−0.0347453	+	0.0601806i	0.848130	+	0.529788i	$0.177729\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−6235.00	+	10799.3i	−0.536612	+	0.929439i
$514$		0			0
$515$	2127.50	+	3684.94i	0.182037	+	0.315297i
$516$		0			0
$517$	−7065.00			−0.601003
$518$		0			0
$519$	12345.0			1.04410
$520$		0			0
$521$	−7413.00	−	12839.7i	−0.623358	−	1.07969i	−0.988856	−	0.148875i	$-0.952435\pi$
$521$	−7413.00	−	12839.7i	−0.623358	−	1.07969i	0.365498	−	0.930812i	$-0.380899\pi$
$522$		0			0
$523$	−3098.00	+	5365.89i	−0.259017	+	0.448631i	−0.965979	−	0.258621i	$-0.916732\pi$
$523$	−3098.00	+	5365.89i	−0.259017	+	0.448631i	0.706962	+	0.707252i	$0.250065\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−13038.0	+	22582.5i	−1.07769	+	1.86662i
$528$		0			0
$529$	4625.50	+	8011.60i	0.380168	+	0.658470i
$530$		0			0
$531$	288.000			0.0235370
$532$		0			0
$533$	−7548.00			−0.613396
$534$		0			0
$535$	2235.00	+	3871.13i	0.180612	+	0.312829i
$536$		0			0
$537$	6630.00	−	11483.5i	0.532785	−	0.922811i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	5340.50	−	9250.02i	0.424410	−	0.735100i	−0.571955	−	0.820285i	$-0.693815\pi$
$541$	5340.50	−	9250.02i	0.424410	−	0.735100i	0.996365	+	0.0851848i	$0.0271481\pi$
$542$		0			0
$543$	−4990.00	−	8642.93i	−0.394367	−	0.683064i
$544$		0			0
$545$	8305.00			0.652747
$546$		0			0
$547$	−6856.00			−0.535907			−0.267954	−	0.963432i	$-0.586347\pi$
$547$	−6856.00			−0.535907			−0.267954	+	0.963432i	$0.586347\pi$
$548$		0			0
$549$	376.000	+	651.251i	0.0292300	+	0.0506279i
$550$		0			0
$551$	−7611.00	+	13182.6i	−0.588456	+	1.01924i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−925.000	+	1602.15i	−0.0707461	+	0.122536i
$556$		0			0
$557$	−1284.00	−	2223.95i	−0.0976747	−	0.169178i	0.813047	−	0.582198i	$-0.197807\pi$
$557$	−1284.00	−	2223.95i	−0.0976747	−	0.169178i	−0.910722	+	0.413020i	$0.864474\pi$
$558$		0			0
$559$	782.000			0.0591683
$560$		0			0
$561$	−9225.00			−0.694260
$562$		0			0
$563$	126.000	+	218.238i	0.00943209	+	0.0163369i	0.870703	−	0.491809i	$-0.163664\pi$
$563$	126.000	+	218.238i	0.00943209	+	0.0163369i	−0.861271	+	0.508146i	$0.830331\pi$
$564$		0			0
$565$	−3255.00	+	5637.83i	−0.242370	+	0.419797i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	6351.00	−	11000.3i	0.467922	−	0.810465i	−0.531406	−	0.847117i	$-0.678336\pi$
$569$	6351.00	−	11000.3i	0.467922	−	0.810465i	0.999328	+	0.0366522i	$0.0116694\pi$
$570$		0			0
$571$	10790.0	+	18688.8i	0.790801	+	1.36971i	0.925471	+	0.378817i	$0.123669\pi$
$571$	10790.0	+	18688.8i	0.790801	+	1.36971i	−0.134670	+	0.990890i	$0.542998\pi$
$572$		0			0
$573$	−17925.0			−1.30685
$574$		0			0
$575$	1350.00			0.0979111
$576$		0			0
$577$	10568.5	+	18305.2i	0.762517	+	1.32072i	0.941549	+	0.336875i	$0.109370\pi$
$577$	10568.5	+	18305.2i	0.762517	+	1.32072i	−0.179032	+	0.983843i	$0.557297\pi$
$578$		0			0
$579$	−1430.00	+	2476.83i	−0.102640	+	0.177778i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1350.00	−	2338.27i	0.0959027	−	0.166108i
$584$		0			0
$585$	−85.0000	−	147.224i	−0.00600738	−	0.0104051i
$586$		0			0
$587$	22104.0			1.55422			0.777112	−	0.629362i	$-0.216684\pi$
$587$	22104.0			1.55422			0.777112	+	0.629362i	$0.216684\pi$
$588$		0			0
$589$	18232.0			1.27544
$590$		0			0
$591$	8520.00	+	14757.1i	0.593005	+	1.02711i
$592$		0			0
$593$	11608.5	−	20106.5i	0.803885	−	1.39237i	−0.113156	−	0.993577i	$-0.536096\pi$
$593$	11608.5	−	20106.5i	0.803885	−	1.39237i	0.917041	−	0.398793i	$-0.130571\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−9040.00	+	15657.7i	−0.619736	+	1.07341i
$598$		0			0
$599$	−7705.50	−	13346.3i	−0.525606	−	0.910377i	−0.999555	−	0.0298245i	$-0.990505\pi$
$599$	−7705.50	−	13346.3i	−0.525606	−	0.910377i	0.473949	−	0.880552i	$-0.342828\pi$
$600$		0			0
$601$	19210.0			1.30381			0.651907	−	0.758299i	$-0.273969\pi$
$601$	19210.0			1.30381			0.651907	+	0.758299i	$0.273969\pi$
$602$		0			0
$603$	−712.000			−0.0480844
$604$		0			0
$605$	2765.00	+	4789.12i	0.185807	+	0.321827i
$606$		0			0
$607$	5702.50	−	9877.02i	0.381314	−	0.660454i	−0.609937	−	0.792450i	$-0.708805\pi$
$607$	5702.50	−	9877.02i	0.381314	−	0.660454i	0.991250	+	0.131996i	$0.0421385\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4003.50	+	6934.27i	−0.265081	+	0.459133i
$612$		0			0
$613$	12131.0	+	21011.5i	0.799293	+	1.38442i	0.920077	+	0.391737i	$0.128126\pi$
$613$	12131.0	+	21011.5i	0.799293	+	1.38442i	−0.120784	+	0.992679i	$0.538541\pi$
$614$		0			0
$615$	11100.0			0.727797
$616$		0			0
$617$	−22614.0			−1.47554			−0.737768	−	0.675055i	$-0.764120\pi$
$617$	−22614.0			−1.47554			−0.737768	+	0.675055i	$0.764120\pi$
$618$		0			0
$619$	223.000	+	386.247i	0.0144800	+	0.0250801i	0.873175	−	0.487408i	$-0.162057\pi$
$619$	223.000	+	386.247i	0.0144800	+	0.0250801i	−0.858695	+	0.512488i	$0.828724\pi$
$620$		0			0
$621$	3915.00	−	6780.98i	0.252985	−	0.438182i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	3225.00	+	5585.86i	0.205413	+	0.355786i
$628$		0			0
$629$	−9102.00			−0.576980
$630$		0			0
$631$	2819.00			0.177849			0.0889244	−	0.996038i	$-0.471657\pi$
$631$	2819.00			0.177849			0.0889244	+	0.996038i	$0.471657\pi$
$632$		0			0
$633$	−12222.5	−	21170.0i	−0.767458	−	1.32928i
$634$		0			0
$635$	−6560.00	+	11362.3i	−0.409962	+	0.710074i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−48.0000	+	83.1384i	−0.00297160	+	0.00514696i
$640$		0			0
$641$	−2769.00	−	4796.05i	−0.170622	−	0.295527i	0.768015	−	0.640432i	$-0.221244\pi$
$641$	−2769.00	−	4796.05i	−0.170622	−	0.295527i	−0.938638	+	0.344905i	$0.887911\pi$
$642$		0			0
$643$	2077.00			0.127386			0.0636928	−	0.997970i	$-0.479712\pi$
$643$	2077.00			0.127386			0.0636928	+	0.997970i	$0.479712\pi$
$644$		0			0
$645$	−1150.00			−0.0702034
$646$		0			0
$647$	11244.0	+	19475.2i	0.683226	+	1.18338i	0.973991	+	0.226588i	$0.0727570\pi$
$647$	11244.0	+	19475.2i	0.683226	+	1.18338i	−0.290765	+	0.956795i	$0.593910\pi$
$648$		0			0
$649$	1080.00	−	1870.61i	0.0653216	−	0.113140i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−849.000	+	1470.51i	−0.0508789	+	0.0881249i	−0.890343	−	0.455290i	$-0.849536\pi$
$653$	−849.000	+	1470.51i	−0.0508789	+	0.0881249i	0.839464	+	0.543415i	$0.182869\pi$
$654$		0			0
$655$	2115.00	+	3663.29i	0.126168	+	0.218529i
$656$		0			0
$657$	1636.00			0.0971483
$658$		0			0
$659$	2691.00			0.159069			0.0795345	−	0.996832i	$-0.474657\pi$
$659$	2691.00			0.159069			0.0795345	+	0.996832i	$0.474657\pi$
$660$		0			0
$661$	−5648.00	−	9782.62i	−0.332348	−	0.575643i	0.650624	−	0.759400i	$-0.274507\pi$
$661$	−5648.00	−	9782.62i	−0.332348	−	0.575643i	−0.982972	+	0.183757i	$0.941174\pi$
$662$		0			0
$663$	−5227.50	+	9054.30i	−0.306213	+	0.530377i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4779.00	−	8277.47i	0.277427	−	0.480517i
$668$		0			0
$669$	−8072.50	−	13982.0i	−0.466519	−	0.808034i
$670$		0			0
$671$	5640.00			0.324486
$672$		0			0
$673$	−12316.0			−0.705419			−0.352709	−	0.935733i	$-0.614740\pi$
$673$	−12316.0			−0.705419			−0.352709	+	0.935733i	$0.614740\pi$
$674$		0			0
$675$	1812.50	+	3139.34i	0.103353	+	0.179012i
$676$		0			0
$677$	5896.50	−	10213.0i	0.334743	−	0.579792i	−0.648693	−	0.761051i	$-0.724684\pi$
$677$	5896.50	−	10213.0i	0.334743	−	0.579792i	0.983435	+	0.181259i	$0.0580172\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	3037.50	−	5261.10i	0.170921	−	0.296044i
$682$		0			0
$683$	−15948.0	−	27622.7i	−0.893460	−	1.54752i	−0.835699	−	0.549188i	$-0.814937\pi$
$683$	−15948.0	−	27622.7i	−0.893460	−	1.54752i	−0.0577612	−	0.998330i	$-0.518396\pi$
$684$		0			0
$685$	5220.00			0.291162
$686$		0			0
$687$	−11020.0			−0.611993
$688$		0			0
$689$	−1530.00	−	2650.04i	−0.0845985	−	0.146529i
$690$		0			0
$691$	−10346.0	+	17919.8i	−0.569581	+	0.986543i	0.427026	+	0.904239i	$0.359561\pi$
$691$	−10346.0	+	17919.8i	−0.569581	+	0.986543i	−0.996607	+	0.0823039i	$0.973772\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4865.00	−	8426.43i	0.265525	−	0.459903i
$696$		0			0
$697$	27306.0	+	47295.4i	1.48391	+	2.57022i
$698$		0			0
$699$	1080.00			0.0584397
$700$		0			0
$701$	−28173.0			−1.51795			−0.758973	−	0.651123i	$-0.774298\pi$
$701$	−28173.0			−1.51795			−0.758973	+	0.651123i	$0.774298\pi$
$702$		0			0
$703$	3182.00	+	5511.39i	0.170713	+	0.295684i
$704$		0			0
$705$	5887.50	−	10197.4i	0.314519	−	0.544763i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	5124.50	−	8875.89i	0.271445	−	0.470157i	−0.697787	−	0.716305i	$-0.745832\pi$
$709$	5124.50	−	8875.89i	0.271445	−	0.470157i	0.969232	+	0.246149i	$0.0791651\pi$
$710$		0			0
$711$	89.0000	+	154.153i	0.00469446	+	0.00813104i
$712$		0			0
$713$	−11448.0			−0.601306
$714$		0			0
$715$	−1275.00			−0.0666885
$716$		0			0
$717$	13087.5	+	22668.2i	0.681676	+	1.18070i
$718$		0			0
$719$	−14601.0	+	25289.7i	−0.757337	+	1.31175i	0.186867	+	0.982385i	$0.440167\pi$
$719$	−14601.0	+	25289.7i	−0.757337	+	1.31175i	−0.944204	+	0.329361i	$0.893167\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	14855.0	−	25729.6i	0.764126	−	1.32351i
$724$		0			0
$725$	2212.50	+	3832.16i	0.113338	+	0.196308i
$726$		0			0
$727$	6856.00			0.349759			0.174880	−	0.984590i	$-0.444046\pi$
$727$	6856.00			0.349759			0.174880	+	0.984590i	$0.444046\pi$
$728$		0			0
$729$	20917.0			1.06269
$730$		0			0
$731$	−2829.00	−	4899.97i	−0.143139	−	0.247923i
$732$		0			0
$733$	12062.5	−	20892.9i	0.607829	−	1.05279i	−0.383769	−	0.923429i	$-0.625374\pi$
$733$	12062.5	−	20892.9i	0.607829	−	1.05279i	0.991598	−	0.129361i	$-0.0412927\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2670.00	+	4624.58i	−0.133447	+	0.231138i
$738$		0			0
$739$	−11711.5	−	20284.9i	−0.582970	−	1.00973i	−0.995125	−	0.0986194i	$-0.968557\pi$
$739$	−11711.5	−	20284.9i	−0.582970	−	1.00973i	0.412156	−	0.911113i	$-0.364776\pi$
$740$		0			0
$741$	7310.00			0.362402
$742$		0			0
$743$	−13572.0			−0.670132			−0.335066	−	0.942195i	$-0.608759\pi$
$743$	−13572.0			−0.670132			−0.335066	+	0.942195i	$0.608759\pi$
$744$		0			0
$745$	3915.00	+	6780.98i	0.192530	+	0.333471i
$746$		0			0
$747$	780.000	−	1351.00i	0.0382044	−	0.0661720i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	8247.50	−	14285.1i	0.400740	−	0.694102i	−0.593076	−	0.805147i	$-0.702086\pi$
$751$	8247.50	−	14285.1i	0.400740	−	0.694102i	0.993815	+	0.111045i	$0.0354198\pi$
$752$		0			0
$753$	−2385.00	−	4130.94i	−0.115424	−	0.199920i
$754$		0			0
$755$	6085.00			0.293319
$756$		0			0
$757$	−22768.0			−1.09315			−0.546577	−	0.837409i	$-0.684069\pi$
$757$	−22768.0			−1.09315			−0.546577	+	0.837409i	$0.684069\pi$
$758$		0			0
$759$	−2025.00	−	3507.40i	−0.0968417	−	0.167735i
$760$		0			0
$761$	12135.0	−	21018.4i	0.578047	−	1.00121i	−0.417657	−	0.908605i	$-0.637149\pi$
$761$	12135.0	−	21018.4i	0.578047	−	1.00121i	0.995703	−	0.0926011i	$-0.0295181\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−615.000	+	1065.21i	−0.0290658	+	0.0503435i
$766$		0			0
$767$	−1224.00	−	2120.03i	−0.0576220	−	0.0998042i
$768$		0			0
$769$	13378.0			0.627338			0.313669	−	0.949532i	$-0.398442\pi$
$769$	13378.0			0.627338			0.313669	+	0.949532i	$0.398442\pi$
$770$		0			0
$771$	−17430.0			−0.814171
$772$		0			0
$773$	16636.5	+	28815.3i	0.774092	+	1.34077i	0.935303	+	0.353847i	$0.115127\pi$
$773$	16636.5	+	28815.3i	0.774092	+	1.34077i	−0.161211	+	0.986920i	$0.551540\pi$
$774$		0			0
$775$	2650.00	−	4589.93i	0.122827	−	0.212742i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	19092.0	−	33068.3i	0.878103	−	1.52092i
$780$		0			0
$781$	360.000	+	623.538i	0.0164940	+	0.0285684i
$782$		0			0
$783$	25665.0			1.17138
$784$		0			0
$785$	−12430.0			−0.565154
$786$		0			0
$787$	19499.5	+	33774.1i	0.883205	+	1.52976i	0.847758	+	0.530384i	$0.177952\pi$
$787$	19499.5	+	33774.1i	0.883205	+	1.52976i	0.0354471	+	0.999372i	$0.488714\pi$
$788$		0			0
$789$	1695.00	−	2935.83i	0.0764811	−	0.132469i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	3196.00	−	5535.63i	0.143119	−	0.247889i
$794$		0			0
$795$	2250.00	+	3897.11i	0.100376	+	0.173857i
$796$		0			0
$797$	−9651.00			−0.428928			−0.214464	−	0.976732i	$-0.568801\pi$
$797$	−9651.00			−0.428928			−0.214464	+	0.976732i	$0.568801\pi$
$798$		0			0
$799$	57933.0			2.56511
$800$		0			0
$801$	−1140.00	−	1974.54i	−0.0502870	−	0.0870997i
$802$		0			0
$803$	6135.00	−	10626.1i	0.269613	−	0.466984i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−8475.00	+	14679.1i	−0.369683	+	0.640310i
$808$		0			0
$809$	−8260.50	−	14307.6i	−0.358991	−	0.621791i	0.628802	−	0.777566i	$-0.283546\pi$
$809$	−8260.50	−	14307.6i	−0.358991	−	0.621791i	−0.987793	+	0.155775i	$0.950212\pi$
$810$		0			0
$811$	−44534.0			−1.92824			−0.964119	−	0.265472i	$-0.914472\pi$
$811$	−44534.0			−1.92824			−0.964119	+	0.265472i	$0.914472\pi$
$812$		0			0
$813$	−2800.00			−0.120788
$814$		0			0
$815$	8905.00	+	15423.9i	0.382734	+	0.662915i
$816$		0			0
$817$	−1978.00	+	3426.00i	−0.0847019	+	0.146708i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4864.50	+	8425.56i	−0.206787	+	0.358166i	−0.950701	−	0.310110i	$-0.899634\pi$
$821$	−4864.50	+	8425.56i	−0.206787	+	0.358166i	0.743914	+	0.668276i	$0.232967\pi$
$822$		0			0
$823$	15974.0	+	27667.8i	0.676572	+	1.17186i	0.976007	+	0.217740i	$0.0698685\pi$
$823$	15974.0	+	27667.8i	0.676572	+	1.17186i	−0.299435	+	0.954117i	$0.596798\pi$
$824$		0			0
$825$	1875.00			0.0791262
$826$		0			0
$827$	1506.00			0.0633238			0.0316619	−	0.999499i	$-0.489920\pi$
$827$	1506.00			0.0633238			0.0316619	+	0.999499i	$0.489920\pi$
$828$		0			0
$829$	3094.00	+	5358.97i	0.129625	+	0.224517i	0.923531	−	0.383523i	$-0.125289\pi$
$829$	3094.00	+	5358.97i	0.129625	+	0.224517i	−0.793906	+	0.608040i	$0.791956\pi$
$830$		0			0
$831$	19645.0	−	34026.1i	0.820069	−	1.42040i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−3892.50	+	6742.01i	−0.161324	+	0.279421i
$836$		0			0
$837$	−15370.0	−	26621.6i	−0.634725	−	1.09938i
$838$		0			0
$839$	27414.0			1.12805			0.564026	−	0.825757i	$-0.309252\pi$
$839$	27414.0			1.12805			0.564026	+	0.825757i	$0.309252\pi$
$840$		0			0
$841$	6940.00			0.284555
$842$		0			0
$843$	−15427.5	−	26721.2i	−0.630310	−	1.09173i
$844$		0			0
$845$	4770.00	−	8261.88i	0.194193	−	0.336352i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	10302.5	−	17844.5i	0.416467	−	0.721343i
$850$		0			0
$851$	−1998.00	−	3460.64i	−0.0804824	−	0.139400i
$852$		0			0
$853$	−34478.0			−1.38394			−0.691972	−	0.721924i	$-0.743258\pi$
$853$	−34478.0			−1.38394			−0.691972	+	0.721924i	$0.743258\pi$
$854$		0			0
$855$	860.000			0.0343993
$856$		0			0
$857$	8553.00	+	14814.2i	0.340916	+	0.590484i	0.984603	−	0.174805i	$-0.0559295\pi$
$857$	8553.00	+	14814.2i	0.340916	+	0.590484i	−0.643687	+	0.765289i	$0.722596\pi$
$858$		0			0
$859$	6922.00	−	11989.3i	0.274942	−	0.476214i	−0.695178	−	0.718838i	$-0.744675\pi$
$859$	6922.00	−	11989.3i	0.274942	−	0.476214i	0.970121	+	0.242623i	$0.0780079\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	852.000	−	1475.71i	0.0336065	−	0.0582082i	−0.848733	−	0.528822i	$-0.822634\pi$
$863$	852.000	−	1475.71i	0.0336065	−	0.0582082i	0.882339	+	0.470613i	$0.155967\pi$
$864$		0			0
$865$	−6172.50	−	10691.1i	−0.242626	−	0.420240i
$866$		0			0
$867$	51080.0			2.00089
$868$		0			0
$869$	1335.00			0.0521137
$870$		0			0
$871$	3026.00	+	5241.19i	0.117718	+	0.203893i
$872$		0			0
$873$	169.000	−	292.717i	0.00655187	−	0.0113482i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	8675.00	−	15025.5i	0.334018	−	0.578536i	−0.649278	−	0.760552i	$-0.724929\pi$
$877$	8675.00	−	15025.5i	0.334018	−	0.578536i	0.983296	+	0.182015i	$0.0582620\pi$
$878$		0			0
$879$	−22.5000	−	38.9711i	−0.000863374	−	0.00149541i
$880$		0			0
$881$	−13632.0			−0.521310			−0.260655	−	0.965432i	$-0.583938\pi$
$881$	−13632.0			−0.521310			−0.260655	+	0.965432i	$0.583938\pi$
$882$		0			0
$883$	−7204.00			−0.274557			−0.137279	−	0.990532i	$-0.543836\pi$
$883$	−7204.00			−0.274557			−0.137279	+	0.990532i	$0.543836\pi$
$884$		0			0
$885$	1800.00	+	3117.69i	0.0683687	+	0.118418i
$886$		0			0
$887$	7356.00	−	12741.0i	0.278456	−	0.482300i	−0.692545	−	0.721374i	$-0.743511\pi$
$887$	7356.00	−	12741.0i	0.278456	−	0.482300i	0.971001	+	0.239075i	$0.0768441\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	5032.50	−	8716.55i	0.189220	−	0.327739i
$892$		0			0
$893$	−20253.0	−	35079.2i	−0.758948	−	1.31454i
$894$		0			0
$895$	−13260.0			−0.495232
$896$		0			0
$897$	−4590.00			−0.170854
$898$		0			0
$899$	−18762.0	−	32496.7i	−0.696049	−	1.20559i
$900$		0			0
$901$	−11070.0	+	19173.8i	−0.409318	+	0.708959i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4990.00	+	8642.93i	−0.183285	+	0.317459i
$906$		0			0
$907$	−18823.0	−	32602.4i	−0.689093	−	1.19354i	−0.972132	−	0.234436i	$-0.924676\pi$
$907$	−18823.0	−	32602.4i	−0.689093	−	1.19354i	0.283039	−	0.959109i	$-0.408658\pi$
$908$		0			0
$909$	−1476.00			−0.0538568
$910$		0			0
$911$	12552.0			0.456494			0.228247	−	0.973603i	$-0.426701\pi$
$911$	12552.0			0.456494			0.228247	+	0.973603i	$0.426701\pi$
$912$		0			0
$913$	−5850.00	−	10132.5i	−0.212056	−	0.367291i
$914$		0			0
$915$	−4700.00	+	8140.64i	−0.169811	+	0.294122i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	26445.5	−	45804.9i	0.949245	−	1.64414i	0.202226	−	0.979339i	$-0.435182\pi$
$919$	26445.5	−	45804.9i	0.949245	−	1.64414i	0.747019	−	0.664802i	$-0.231484\pi$
$920$		0			0
$921$	−16217.5	−	28089.5i	−0.580222	−	1.00497i
$922$		0			0
$923$	816.000			0.0290996
$924$		0			0
$925$	1850.00			0.0657596
$926$		0			0
$927$	−851.000	−	1473.98i	−0.0301516	−	0.0522241i
$928$		0			0
$929$	−19110.0	+	33099.5i	−0.674896	+	1.16895i	0.301603	+	0.953434i	$0.402478\pi$
$929$	−19110.0	+	33099.5i	−0.674896	+	1.16895i	−0.976499	+	0.215521i	$0.930855\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	13515.0	−	23408.7i	0.474235	−	0.821399i
$934$		0			0
$935$	4612.50	+	7989.08i	0.161331	+	0.279434i
$936$		0			0
$937$	10897.0			0.379925			0.189962	−	0.981791i	$-0.439163\pi$
$937$	10897.0			0.379925			0.189962	+	0.981791i	$0.439163\pi$
$938$		0			0
$939$	6335.00			0.220165
$940$		0			0
$941$	384.000	+	665.108i	0.0133029	+	0.0230413i	0.872600	−	0.488435i	$-0.162432\pi$
$941$	384.000	+	665.108i	0.0133029	+	0.0230413i	−0.859297	+	0.511476i	$0.829099\pi$
$942$		0			0
$943$	−11988.0	+	20763.8i	−0.413980	+	0.717034i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	22056.0	−	38202.1i	0.756836	−	1.31088i	−0.187620	−	0.982242i	$-0.560077\pi$
$947$	22056.0	−	38202.1i	0.756836	−	1.31088i	0.944456	−	0.328637i	$-0.106589\pi$
$948$		0			0
$949$	−6953.00	−	12042.9i	−0.237833	−	0.411940i
$950$		0			0
$951$	17310.0			0.590237
$952$		0			0
$953$	24720.0			0.840251			0.420126	−	0.907466i	$-0.361986\pi$
$953$	24720.0			0.840251			0.420126	+	0.907466i	$0.361986\pi$
$954$		0			0
$955$	8962.50	+	15523.5i	0.303686	+	0.525999i
$956$		0			0
$957$	6637.50	−	11496.5i	0.224201	−	0.388327i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−7576.50	+	13122.9i	−0.254322	+	0.440498i
$962$		0			0
$963$	−894.000	−	1548.45i	−0.0299156	−	0.0518154i
$964$		0			0
$965$	2860.00			0.0954059
$966$		0			0
$967$	−5098.00			−0.169535			−0.0847676	−	0.996401i	$-0.527015\pi$
$967$	−5098.00			−0.169535			−0.0847676	+	0.996401i	$0.527015\pi$
$968$		0			0
$969$	−26445.0	−	45804.1i	−0.876714	−	1.51851i
$970$		0			0
$971$	16320.0	−	28267.1i	0.539376	−	0.934226i	−0.459562	−	0.888146i	$-0.651994\pi$
$971$	16320.0	−	28267.1i	0.539376	−	0.934226i	0.998938	−	0.0460803i	$-0.0146730\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1062.50	−	1840.30i	0.0348997	−	0.0604481i
$976$		0			0
$977$	29589.0	+	51249.7i	0.968921	+	1.67822i	0.698689	+	0.715425i	$0.253767\pi$
$977$	29589.0	+	51249.7i	0.968921	+	1.67822i	0.270232	+	0.962795i	$0.412900\pi$
$978$		0			0
$979$	−17100.0			−0.558241
$980$		0			0
$981$	−3322.00			−0.108118
$982$		0			0
$983$	−25537.5	−	44232.2i	−0.828606	−	1.43519i	−0.899132	−	0.437678i	$-0.855801\pi$
$983$	−25537.5	−	44232.2i	−0.828606	−	1.43519i	0.0705258	−	0.997510i	$-0.477532\pi$
$984$		0			0
$985$	8520.00	−	14757.1i	0.275604	−	0.477360i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1242.00	−	2151.21i	0.0399326	−	0.0691652i
$990$		0			0
$991$	13268.0	+	22980.9i	0.425300	+	0.736641i	0.996448	−	0.0842060i	$-0.0268354\pi$
$991$	13268.0	+	22980.9i	0.425300	+	0.736641i	−0.571149	+	0.820847i	$0.693502\pi$
$992$		0			0
$993$	41020.0			1.31091
$994$		0			0
$995$	18080.0			0.576055
$996$		0			0
$997$	20435.5	+	35395.3i	0.649146	+	1.12435i	0.983327	+	0.181845i	$0.0582070\pi$
$997$	20435.5	+	35395.3i	0.649146	+	1.12435i	−0.334181	+	0.942509i	$0.608460\pi$
$998$		0			0
$999$	5365.00	−	9292.45i	0.169911	−	0.294294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.4.i.c.961.1		2
7.2	even	3		980.4.a.m.1.1		1
7.3	odd	6		980.4.i.p.361.1		2
7.4	even	3	inner	980.4.i.c.361.1		2
7.5	odd	6		140.4.a.a.1.1	✓	1
7.6	odd	2		980.4.i.p.961.1		2
21.5	even	6		1260.4.a.k.1.1		1
28.19	even	6		560.4.a.n.1.1		1
35.12	even	12		700.4.e.e.449.2		2
35.19	odd	6		700.4.a.k.1.1		1
35.33	even	12		700.4.e.e.449.1		2
56.5	odd	6		2240.4.a.bf.1.1		1
56.19	even	6		2240.4.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.4.a.a.1.1	✓	1	7.5	odd	6
560.4.a.n.1.1		1	28.19	even	6
700.4.a.k.1.1		1	35.19	odd	6
700.4.e.e.449.1		2	35.33	even	12
700.4.e.e.449.2		2	35.12	even	12
980.4.a.m.1.1		1	7.2	even	3
980.4.i.c.361.1		2	7.4	even	3	inner
980.4.i.c.961.1		2	1.1	even	1	trivial
980.4.i.p.361.1		2	7.3	odd	6
980.4.i.p.961.1		2	7.6	odd	2
1260.4.a.k.1.1		1	21.5	even	6
2240.4.a.i.1.1		1	56.19	even	6
2240.4.a.bf.1.1		1	56.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	980.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.50000 - 4.33013i) q^{3} +(-2.50000 + 4.33013i) q^{5} +(1.00000 - 1.73205i) q^{9} +(-7.50000 - 12.9904i) q^{11} -17.0000 q^{13} +25.0000 q^{15} +(61.5000 + 106.521i) q^{17} +(43.0000 - 74.4782i) q^{19} +(-27.0000 + 46.7654i) q^{23} +(-12.5000 - 21.6506i) q^{25} -145.000 q^{27} -177.000 q^{29} +(106.000 + 183.597i) q^{31} +(-37.5000 + 64.9519i) q^{33} +(-37.0000 + 64.0859i) q^{37} +(42.5000 + 73.6122i) q^{39} +444.000 q^{41} -46.0000 q^{43} +(5.00000 + 8.66025i) q^{45} +(235.500 - 407.898i) q^{47} +(307.500 - 532.606i) q^{51} +(90.0000 + 155.885i) q^{53} +75.0000 q^{55} -430.000 q^{57} +(72.0000 + 124.708i) q^{59} +(-188.000 + 325.626i) q^{61} +(42.5000 - 73.6122i) q^{65} +(-178.000 - 308.305i) q^{67} +270.000 q^{69} -48.0000 q^{71} +(409.000 + 708.409i) q^{73} +(-62.5000 + 108.253i) q^{75} +(-44.5000 + 77.0763i) q^{79} +(335.500 + 581.103i) q^{81} +780.000 q^{83} -615.000 q^{85} +(442.500 + 766.432i) q^{87} +(570.000 - 987.269i) q^{89} +(530.000 - 917.987i) q^{93} +(215.000 + 372.391i) q^{95} +169.000 q^{97} -30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 5 q^{3} - 5 q^{5} + 2 q^{9} - 15 q^{11} - 34 q^{13} + 50 q^{15} + 123 q^{17} + 86 q^{19} - 54 q^{23} - 25 q^{25} - 290 q^{27} - 354 q^{29} + 212 q^{31} - 75 q^{33} - 74 q^{37} + 85 q^{39} + 888 q^{41}+ \cdots - 60 q^{99}+O(q^{100}) \) 2 * q - 5 * q^3 - 5 * q^5 + 2 * q^9 - 15 * q^11 - 34 * q^13 + 50 * q^15 + 123 * q^17 + 86 * q^19 - 54 * q^23 - 25 * q^25 - 290 * q^27 - 354 * q^29 + 212 * q^31 - 75 * q^33 - 74 * q^37 + 85 * q^39 + 888 * q^41 - 92 * q^43 + 10 * q^45 + 471 * q^47 + 615 * q^51 + 180 * q^53 + 150 * q^55 - 860 * q^57 + 144 * q^59 - 376 * q^61 + 85 * q^65 - 356 * q^67 + 540 * q^69 - 96 * q^71 + 818 * q^73 - 125 * q^75 - 89 * q^79 + 671 * q^81 + 1560 * q^83 - 1230 * q^85 + 885 * q^87 + 1140 * q^89 + 1060 * q^93 + 430 * q^95 + 338 * q^97 - 60 * q^99

Introduction

L-functions

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