LMFDB - Embedded newform 441.3.n.f.128.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,3,Mod(128,441)] 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("441.128"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [22,-6,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			128.1
Character	$\chi$	$=$	441.128
Dual form			441.3.n.f.410.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.19625 + 1.84536i) q^{2} +(-2.96329 - 0.467854i) q^{3} +(4.81069 - 8.33236i) q^{4} +5.83234i q^{5} +(10.3348 - 3.97296i) q^{6} +20.7469i q^{8} +(8.56223 + 2.77278i) q^{9} +(-10.7628 - 18.6416i) q^{10} +3.36449i q^{11} +(-18.1538 + 22.4405i) q^{12} +(-0.158134 - 0.273895i) q^{13} +(2.72868 - 17.2829i) q^{15} +(-19.0428 - 32.9830i) q^{16} +(-2.99912 + 1.73154i) q^{17} +(-32.4838 + 6.93788i) q^{18} +(12.0337 - 20.8430i) q^{19} +(48.5972 + 28.0576i) q^{20} +(-6.20870 - 10.7538i) q^{22} -34.0258i q^{23} +(9.70653 - 61.4793i) q^{24} -9.01621 q^{25} +(1.01087 + 0.583626i) q^{26} +(-24.0751 - 12.2224i) q^{27} +(31.6161 + 18.2536i) q^{29} +(23.1717 + 60.2761i) q^{30} +(12.0916 - 20.9433i) q^{31} +(49.8615 + 28.7875i) q^{32} +(1.57409 - 9.96999i) q^{33} +(6.39064 - 11.0689i) q^{34} +(64.2940 - 58.0046i) q^{36} +(4.23403 - 7.33356i) q^{37} +88.8260i q^{38} +(0.340453 + 0.885616i) q^{39} -121.003 q^{40} +(39.9308 - 23.0541i) q^{41} +(-26.4994 + 45.8984i) q^{43} +(28.0342 + 16.1855i) q^{44} +(-16.1718 + 49.9378i) q^{45} +(62.7897 + 108.755i) q^{46} +(17.2703 - 9.97104i) q^{47} +(40.9981 + 106.648i) q^{48} +(28.8181 - 16.6381i) q^{50} +(9.69739 - 3.72792i) q^{51} -3.04293 q^{52} +(-29.2909 + 16.9111i) q^{53} +(99.5050 - 5.36130i) q^{54} -19.6229 q^{55} +(-45.4109 + 56.1339i) q^{57} -134.738 q^{58} +(-31.5660 - 18.2246i) q^{59} +(-130.881 - 105.879i) q^{60} +(6.02138 + 10.4293i) q^{61} +89.2535i q^{62} -60.1511 q^{64} +(1.59745 - 0.922289i) q^{65} +(13.3670 + 34.7714i) q^{66} +(17.4628 - 30.2465i) q^{67} +33.3197i q^{68} +(-15.9191 + 100.828i) q^{69} +85.7413i q^{71} +(-57.5266 + 177.640i) q^{72} +(35.3783 + 61.2770i) q^{73} +31.2532i q^{74} +(26.7177 + 4.21827i) q^{75} +(-115.781 - 200.539i) q^{76} +(-2.72245 - 2.20240i) q^{78} +(50.7030 + 87.8201i) q^{79} +(192.368 - 111.064i) q^{80} +(65.6234 + 47.4823i) q^{81} +(-85.0860 + 147.373i) q^{82} +(-26.0171 - 15.0210i) q^{83} +(-10.0990 - 17.4919i) q^{85} -195.604i q^{86} +(-85.1479 - 68.8825i) q^{87} -69.8030 q^{88} +(46.5438 + 26.8721i) q^{89} +(-40.4641 - 189.457i) q^{90} +(-283.515 - 163.688i) q^{92} +(-45.6294 + 56.4041i) q^{93} +(-36.8003 + 63.7400i) q^{94} +(121.563 + 70.1847i) q^{95} +(-134.286 - 108.634i) q^{96} +(3.60974 - 6.25225i) q^{97} +(-9.32899 + 28.8076i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 6 q^{2} - 8 q^{3} + 12 q^{4} + 8 q^{6} + 20 q^{9} - 25 q^{10} + 20 q^{12} + 18 q^{13} + 53 q^{15} + 12 q^{16} - 6 q^{17} - 56 q^{18} - 3 q^{19} + 39 q^{20} - 59 q^{22} - 15 q^{24} - 114 q^{25} + 3 q^{26}+ \cdots - 103 q^{99}+O(q^{100}) $ 22 * q - 6 * q^2 - 8 * q^3 + 12 * q^4 + 8 * q^6 + 20 * q^9 - 25 * q^10 + 20 * q^12 + 18 * q^13 + 53 * q^15 + 12 * q^16 - 6 * q^17 - 56 * q^18 - 3 * q^19 + 39 * q^20 - 59 * q^22 - 15 * q^24 - 114 * q^25 + 3 * q^26 + 97 * q^27 - 63 * q^29 - 20 * q^30 + 29 * q^31 + 246 * q^32 - 77 * q^33 + 99 * q^34 + 76 * q^36 - 20 * q^37 + 200 * q^39 - 210 * q^40 + 51 * q^41 + 65 * q^43 + 54 * q^44 - 71 * q^45 + 75 * q^46 - 261 * q^47 + 113 * q^48 + 63 * q^50 - 78 * q^51 - 92 * q^52 - 63 * q^53 + 485 * q^54 + 100 * q^55 + 224 * q^57 - 80 * q^58 + 102 * q^59 + 103 * q^60 - 78 * q^61 + 106 * q^64 - 225 * q^65 + 401 * q^66 - 132 * q^67 + 297 * q^69 - 66 * q^72 - q^73 + 245 * q^75 - 233 * q^76 - 440 * q^78 + 140 * q^79 - 96 * q^80 + 104 * q^81 + 157 * q^82 - 255 * q^83 + 102 * q^85 + 136 * q^87 - 816 * q^88 + 720 * q^89 - 418 * q^90 - 1239 * q^92 + 210 * q^93 - 261 * q^94 + 642 * q^95 - 539 * q^96 - 178 * q^97 - 103 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−3.19625	+	1.84536i	−1.59813	+	0.922679i	−0.606279	+	0.795252i	$0.707339\pi$
$2$	−3.19625	+	1.84536i	−1.59813	+	0.922679i	−0.991848	+	0.127427i	$0.959328\pi$
$3$	−2.96329	−	0.467854i	−0.987765	−	0.155951i
$3$	−2.96329	−	0.467854i	−0.987765	−	0.155951i
$4$	4.81069	−	8.33236i	1.20267	−	2.08309i
$5$			5.83234i			1.16647i	0.812304	+	0.583234i	$0.198213\pi$
$5$			5.83234i			1.16647i	−0.812304	+	0.583234i	$0.801787\pi$
$6$	10.3348	−	3.97296i	1.72247	−	0.662160i
$7$		0			0
$7$		0			0
$8$			20.7469i			2.59337i
$9$	8.56223	+	2.77278i	0.951358	+	0.308086i
$10$	−10.7628	−	18.6416i	−1.07628	−	1.86416i
$11$			3.36449i			0.305863i	0.988237	+	0.152932i	$0.0488714\pi$
$11$			3.36449i			0.305863i	−0.988237	+	0.152932i	$0.951129\pi$
$12$	−18.1538	+	22.4405i	−1.51282	+	1.87005i
$13$	−0.158134	−	0.273895i	−0.0121641	−	0.0210689i	0.859879	−	0.510497i	$-0.170539\pi$
$13$	−0.158134	−	0.273895i	−0.0121641	−	0.0210689i	−0.872043	+	0.489429i	$0.837205\pi$
$14$		0			0
$15$	2.72868	−	17.2829i	0.181912	−	1.15220i
$16$	−19.0428	−	32.9830i	−1.19017	−	2.06144i
$17$	−2.99912	+	1.73154i	−0.176419	+	0.101856i	−0.585609	−	0.810594i	$-0.699145\pi$
$17$	−2.99912	+	1.73154i	−0.176419	+	0.101856i	0.409190	+	0.912449i	$0.365811\pi$
$18$	−32.4838	+	6.93788i	−1.80466	+	0.385438i
$19$	12.0337	−	20.8430i	0.633353	−	1.09700i	−0.353508	−	0.935431i	$-0.615011\pi$
$19$	12.0337	−	20.8430i	0.633353	−	1.09700i	0.986861	−	0.161569i	$-0.0516553\pi$
$20$	48.5972	+	28.0576i	2.42986	+	1.40288i
$21$		0			0
$22$	−6.20870	−	10.7538i	−0.282214	−	0.488808i
$23$		−	34.0258i		−	1.47938i	−0.672947	−	0.739691i	$-0.734972\pi$
$23$		−	34.0258i		−	1.47938i	0.672947	−	0.739691i	$-0.265028\pi$
$24$	9.70653	−	61.4793i	0.404439	−	2.56164i
$25$	−9.01621			−0.360648
$26$	1.01087	+	0.583626i	0.0388796	+	0.0224472i
$27$	−24.0751	−	12.2224i	−0.891672	−	0.452682i
$28$		0			0
$29$	31.6161	+	18.2536i	1.09021	+	0.629434i	0.933633	−	0.358231i	$-0.116620\pi$
$29$	31.6161	+	18.2536i	1.09021	+	0.629434i	0.156579	+	0.987665i	$0.449953\pi$
$30$	23.1717	+	60.2761i	0.772389	+	2.00920i
$31$	12.0916	−	20.9433i	0.390052	−	0.675591i	−0.602404	−	0.798192i	$-0.705790\pi$
$31$	12.0916	−	20.9433i	0.390052	−	0.675591i	0.992456	+	0.122601i	$0.0391235\pi$
$32$	49.8615	+	28.7875i	1.55817	+	0.899610i
$33$	1.57409	−	9.96999i	0.0476997	−	0.302121i
$34$	6.39064	−	11.0689i	0.187960	−	0.325556i
$35$		0			0
$36$	64.2940	−	58.0046i	1.78594	−	1.61124i
$37$	4.23403	−	7.33356i	0.114433	−	0.198204i	−0.803120	−	0.595818i	$-0.796828\pi$
$37$	4.23403	−	7.33356i	0.114433	−	0.198204i	0.917553	+	0.397613i	$0.130161\pi$
$38$			88.8260i			2.33753i
$39$	0.340453	+	0.885616i	0.00872958	+	0.0227081i
$40$	−121.003			−3.02508
$41$	39.9308	−	23.0541i	0.973922	−	0.562294i	0.0734924	−	0.997296i	$-0.476586\pi$
$41$	39.9308	−	23.0541i	0.973922	−	0.562294i	0.900430	+	0.435002i	$0.143252\pi$
$42$		0			0
$43$	−26.4994	+	45.8984i	−0.616266	+	1.06740i	0.373895	+	0.927471i	$0.378022\pi$
$43$	−26.4994	+	45.8984i	−0.616266	+	1.06740i	−0.990161	+	0.139933i	$0.955311\pi$
$44$	28.0342	+	16.1855i	0.637141	+	0.367853i
$45$	−16.1718	+	49.9378i	−0.359373	+	1.10973i
$46$	62.7897	+	108.755i	1.36499	+	2.36424i
$47$	17.2703	−	9.97104i	0.367454	−	0.212150i	−0.304891	−	0.952387i	$-0.598620\pi$
$47$	17.2703	−	9.97104i	0.367454	−	0.212150i	0.672346	+	0.740237i	$0.265287\pi$
$48$	40.9981	+	106.648i	0.854126	+	2.22182i
$49$		0			0
$50$	28.8181	−	16.6381i	0.576362	−	0.332763i
$51$	9.69739	−	3.72792i	0.190145	−	0.0730966i
$52$	−3.04293			−0.0585179
$53$	−29.2909	+	16.9111i	−0.552659	+	0.319078i	−0.750194	−	0.661218i	$-0.770040\pi$
$53$	−29.2909	+	16.9111i	−0.552659	+	0.319078i	0.197535	+	0.980296i	$0.436706\pi$
$54$	99.5050	−	5.36130i	1.84269	−	0.0992834i
$55$	−19.6229			−0.356780
$56$		0			0
$57$	−45.4109	+	56.1339i	−0.796682	+	0.984806i
$58$	−134.738			−2.32306
$59$	−31.5660	−	18.2246i	−0.535017	−	0.308892i	0.208040	−	0.978120i	$-0.433292\pi$
$59$	−31.5660	−	18.2246i	−0.535017	−	0.308892i	−0.743057	+	0.669228i	$0.766625\pi$
$60$	−130.881	−	105.879i	−2.18135	−	1.76465i
$61$	6.02138	+	10.4293i	0.0987111	+	0.170973i	0.911151	−	0.412072i	$-0.135195\pi$
$61$	6.02138	+	10.4293i	0.0987111	+	0.170973i	−0.812440	+	0.583044i	$0.801861\pi$
$62$			89.2535i			1.43957i
$63$		0			0
$64$	−60.1511			−0.939861
$65$	1.59745	−	0.922289i	0.0245762	−	0.0141891i
$66$	13.3670	+	34.7714i	0.202530	+	0.526839i
$67$	17.4628	−	30.2465i	0.260639	−	0.451440i	−0.705773	−	0.708438i	$-0.749400\pi$
$67$	17.4628	−	30.2465i	0.260639	−	0.451440i	0.966412	+	0.256998i	$0.0827334\pi$
$68$			33.3197i			0.489996i
$69$	−15.9191	+	100.828i	−0.230711	+	1.46128i
$70$		0			0
$71$			85.7413i			1.20762i	0.797127	+	0.603812i	$0.206352\pi$
$71$			85.7413i			1.20762i	−0.797127	+	0.603812i	$0.793648\pi$
$72$	−57.5266	+	177.640i	−0.798981	+	2.46722i
$73$	35.3783	+	61.2770i	0.484634	+	0.839411i	0.999844	−	0.0176532i	$-0.00561948\pi$
$73$	35.3783	+	61.2770i	0.484634	+	0.839411i	−0.515210	+	0.857064i	$0.672286\pi$
$74$			31.2532i			0.422341i
$75$	26.7177	+	4.21827i	0.356236	+	0.0562435i
$76$	−115.781	−	200.539i	−1.52343	−	2.63866i
$77$		0			0
$78$	−2.72245	−	2.20240i	−0.0349033	−	0.0282358i
$79$	50.7030	+	87.8201i	0.641810	+	1.11165i	0.985029	+	0.172392i	$0.0551494\pi$
$79$	50.7030	+	87.8201i	0.641810	+	1.11165i	−0.343219	+	0.939255i	$0.611517\pi$
$80$	192.368	−	111.064i	2.40460	−	1.38830i
$81$	65.6234	+	47.4823i	0.810166	+	0.586201i
$82$	−85.0860	+	147.373i	−1.03763	+	1.79723i
$83$	−26.0171	−	15.0210i	−0.313459	−	0.180976i	0.335014	−	0.942213i	$-0.391259\pi$
$83$	−26.0171	−	15.0210i	−0.313459	−	0.180976i	−0.648473	+	0.761237i	$0.724592\pi$
$84$		0			0
$85$	−10.0990	−	17.4919i	−0.118811	−	0.205787i
$86$		−	195.604i		−	2.27446i
$87$	−85.1479	−	68.8825i	−0.978712	−	0.791753i
$88$	−69.8030			−0.793215
$89$	46.5438	+	26.8721i	0.522964	+	0.301933i	0.738146	−	0.674641i	$-0.235701\pi$
$89$	46.5438	+	26.8721i	0.522964	+	0.301933i	−0.215183	+	0.976574i	$0.569035\pi$
$90$	−40.4641	−	189.457i	−0.449601	−	2.10507i
$91$		0			0
$92$	−283.515	−	163.688i	−3.08169	−	1.77921i
$93$	−45.6294	+	56.4041i	−0.490639	+	0.606495i
$94$	−36.8003	+	63.7400i	−0.391492	+	0.678085i
$95$	121.563	+	70.1847i	1.27962	+	0.738786i
$96$	−134.286	−	108.634i	−1.39881	−	1.13160i
$97$	3.60974	−	6.25225i	0.0372138	−	0.0644561i	−0.846819	−	0.531882i	$-0.821485\pi$
$97$	3.60974	−	6.25225i	0.0372138	−	0.0644561i	0.884032	+	0.467426i	$0.154818\pi$
$98$		0			0
$99$	−9.32899	+	28.8076i	−0.0942322	+	0.290986i
$100$	−43.3742	+	75.1263i	−0.433742	+	0.751263i
$101$			60.4957i			0.598967i	0.954101	+	0.299484i	$0.0968144\pi$
$101$			60.4957i			0.598967i	−0.954101	+	0.299484i	$0.903186\pi$
$102$	−24.1160	+	29.8106i	−0.236431	+	0.292260i
$103$	163.244			1.58489			0.792447	−	0.609941i	$-0.208807\pi$
$103$	163.244			1.58489			0.792447	+	0.609941i	$0.208807\pi$
$104$	5.68249	−	3.28079i	0.0546393	−	0.0315460i
$105$		0			0
$106$	62.4142	−	108.105i	0.588813	−	1.01985i
$107$	97.8099	+	56.4706i	0.914111	+	0.527762i	0.881752	−	0.471714i	$-0.156364\pi$
$107$	97.8099	+	56.4706i	0.914111	+	0.527762i	0.0323597	+	0.999476i	$0.489698\pi$
$108$	−217.660	+	141.805i	−2.01537	+	1.31300i
$109$	−62.6322	−	108.482i	−0.574607	−	0.995248i	−0.996084	−	0.0884094i	$-0.971822\pi$
$109$	−62.6322	−	108.482i	−0.574607	−	0.995248i	0.421477	−	0.906839i	$-0.361512\pi$
$110$	62.7197	−	36.2112i	0.570179	−	0.329193i
$111$	−15.9777	+	19.7506i	−0.143943	+	0.177933i
$112$		0			0
$113$	−29.6935	+	17.1435i	−0.262774	+	0.151713i	−0.625599	−	0.780144i	$-0.715146\pi$
$113$	−29.6935	+	17.1435i	−0.262774	+	0.151713i	0.362825	+	0.931857i	$0.381812\pi$
$114$	41.5576	−	263.218i	0.364540	−	2.30893i
$115$	198.450			1.72565
$116$	304.191	−	175.625i	2.62234	−	1.51401i
$117$	−0.594525	−	2.78362i	−0.00508141	−	0.0237917i
$118$	134.524			1.14003
$119$		0			0
$120$	358.568	+	56.6118i	2.98807	+	0.471765i
$121$	109.680			0.906448
$122$	−38.4917	−	22.2232i	−0.315506	−	0.182157i
$123$	−129.113	+	49.6342i	−1.04970	+	0.403530i
$124$	−116.338	−	201.504i	−0.938211	−	1.62503i
$125$			93.2229i			0.745784i
$126$		0			0
$127$	216.982			1.70852			0.854259	−	0.519847i	$-0.174011\pi$
$127$	216.982			1.70852			0.854259	+	0.519847i	$0.174011\pi$
$128$	−7.18756	+	4.14974i	−0.0561528	+	0.0324199i
$129$	99.9993	−	123.612i	0.775188	−	0.958236i
$130$	−3.40391	+	5.89574i	−0.0261839	+	0.0453519i
$131$		−	124.360i		−	0.949310i	−0.880172	−	0.474655i	$-0.842573\pi$
$131$		−	124.360i		−	0.949310i	0.880172	−	0.474655i	$-0.157427\pi$
$132$	−75.5011	−	61.0784i	−0.571978	−	0.462716i
$133$		0			0
$134$			128.901i			0.961944i
$135$	71.2853	−	140.414i	0.528039	−	1.04011i
$136$	−35.9242	−	62.2226i	−0.264149	−	0.457519i
$137$		−	6.67088i		−	0.0486925i	−0.999704	−	0.0243463i	$-0.992250\pi$
$137$		−	6.67088i		−	0.0486925i	0.999704	−	0.0243463i	$-0.00775042\pi$
$138$	−135.183	−	351.649i	−0.979587	−	2.54818i
$139$	8.80202	+	15.2455i	0.0633239	+	0.109680i	0.895949	−	0.444156i	$-0.146497\pi$
$139$	8.80202	+	15.2455i	0.0633239	+	0.109680i	−0.832625	+	0.553837i	$0.813163\pi$
$140$		0			0
$141$	−55.8421	+	21.4671i	−0.396043	+	0.152249i
$142$	−158.223	−	274.051i	−1.11425	−	1.92994i
$143$	0.921520	−	0.532040i	0.00644419	−	0.00372056i
$144$	−71.5938	−	335.209i	−0.497179	−	2.32784i
$145$	−106.461	+	184.396i	−0.734215	+	1.27170i
$146$	−226.156	−	130.571i	−1.54901	−	0.894323i
$147$		0			0
$148$	−40.7373	−	70.5590i	−0.275252	−	0.476750i
$149$			29.6949i			0.199294i	0.995023	+	0.0996472i	$0.0317714\pi$
$149$			29.6949i			0.199294i	−0.995023	+	0.0996472i	$0.968229\pi$
$150$	−93.1807	+	35.8210i	−0.621205	+	0.238807i
$151$	−69.9591			−0.463306			−0.231653	−	0.972799i	$-0.574413\pi$
$151$	−69.9591			−0.463306			−0.231653	+	0.972799i	$0.574413\pi$
$152$	432.428	+	249.663i	2.84492	+	1.64252i
$153$	−30.4803	+	6.50998i	−0.199218	+	0.0425489i
$154$		0			0
$155$	122.149	+	70.5225i	0.788055	+	0.454984i
$156$	9.01709	+	1.42365i	0.0578019	+	0.00912593i
$157$	−98.3195	+	170.294i	−0.626239	+	1.08468i	0.362061	+	0.932155i	$0.382073\pi$
$157$	−98.3195	+	170.294i	−0.626239	+	1.08468i	−0.988300	+	0.152523i	$0.951260\pi$
$158$	−324.119	−	187.130i	−2.05139	−	1.18437i
$159$	94.7096	−	36.4088i	0.595658	−	0.228986i
$160$	−167.899	+	290.809i	−1.04937	+	1.81756i
$161$		0			0
$162$	−297.371	−	30.6667i	−1.83562	−	0.189300i
$163$	−4.64174	+	8.03973i	−0.0284769	+	0.0493235i	−0.879913	−	0.475135i	$-0.842399\pi$
$163$	−4.64174	+	8.03973i	−0.0284769	+	0.0493235i	0.851436	+	0.524459i	$0.175732\pi$
$164$		−	443.624i		−	2.70502i
$165$	58.1484	+	9.18064i	0.352414	+	0.0556402i
$166$	110.876			0.667931
$167$	91.5268	−	52.8430i	0.548065	−	0.316425i	−0.200276	−	0.979739i	$-0.564184\pi$
$167$	91.5268	−	52.8430i	0.548065	−	0.316425i	0.748341	+	0.663314i	$0.230851\pi$
$168$		0			0
$169$	84.4500	−	146.272i	0.499704	−	0.865513i
$170$	64.5577	+	37.2724i	0.379751	+	0.219249i
$171$	160.828	−	145.096i	0.940516	−	0.848513i
$172$	254.961	+	441.606i	1.48233	+	2.56748i
$173$	−166.778	+	96.2891i	−0.964033	+	0.556585i	−0.897412	−	0.441194i	$-0.854555\pi$
$173$	−166.778	+	96.2891i	−0.964033	+	0.556585i	−0.0666210	+	0.997778i	$0.521222\pi$
$174$	399.267	+	63.0375i	2.29464	+	0.362284i
$175$		0			0
$176$	110.971	−	64.0692i	0.630518	−	0.364030i
$177$	85.0129	+	68.7733i	0.480299	+	0.388550i
$178$	−198.354			−1.11435
$179$	46.3963	−	26.7869i	0.259197	−	0.149648i	−0.364771	−	0.931097i	$-0.618853\pi$
$179$	46.3963	−	26.7869i	0.259197	−	0.149648i	0.623968	+	0.781450i	$0.285519\pi$
$180$	338.303	+	374.985i	1.87946	+	2.08325i
$181$	113.509			0.627124			0.313562	−	0.949568i	$-0.398478\pi$
$181$	113.509			0.627124			0.313562	+	0.949568i	$0.398478\pi$
$182$		0			0
$183$	−12.9637	−	33.7223i	−0.0708400	−	0.184275i
$184$	705.930			3.83658
$185$	42.7718	+	24.6943i	0.231199	+	0.133483i
$186$	41.7576	−	264.484i	0.224503	−	1.42196i
$187$	−5.82577	−	10.0905i	−0.0311539	−	0.0539601i
$188$		−	191.870i		−	1.02059i
$189$		0			0
$190$	−518.064			−2.72665
$191$	−149.464	+	86.2931i	−0.782535	+	0.451797i	−0.837328	−	0.546701i	$-0.815883\pi$
$191$	−149.464	+	86.2931i	−0.782535	+	0.451797i	0.0547932	+	0.998498i	$0.482550\pi$
$192$	178.245	+	28.1419i	0.928362	+	0.146572i
$193$	−95.1620	+	164.825i	−0.493068	+	0.854018i	−0.999968	−	0.00798645i	$-0.997458\pi$
$193$	−95.1620	+	164.825i	−0.493068	+	0.854018i	0.506901	+	0.862005i	$0.330791\pi$
$194$			26.6450i			0.137345i
$195$	−5.16522	+	1.98564i	−0.0264883	+	0.0101828i
$196$		0			0
$197$			98.0156i			0.497541i	0.968562	+	0.248770i	$0.0800265\pi$
$197$			98.0156i			0.497541i	−0.968562	+	0.248770i	$0.919974\pi$
$198$	−23.3425	−	109.292i	−0.117891	−	0.551978i
$199$	−128.149	−	221.961i	−0.643965	−	1.11538i	−0.984540	−	0.175162i	$-0.943955\pi$
$199$	−128.149	−	221.961i	−0.643965	−	1.11538i	0.340575	−	0.940217i	$-0.389378\pi$
$200$		−	187.059i		−	0.935293i
$201$	−65.8984	+	81.4592i	−0.327853	+	0.405270i
$202$	−111.636	−	193.360i	−0.552655	−	0.957226i
$203$		0			0
$204$	15.5887	−	98.7361i	0.0764154	−	0.484000i
$205$	134.459	+	232.890i	0.655898	+	1.13605i
$206$	−521.769	+	301.244i	−2.53286	+	1.46235i
$207$	94.3458	−	291.336i	0.455777	−	1.40742i
$208$	−6.02260	+	10.4314i	−0.0289548	+	0.0501512i
$209$	70.1262	+	40.4874i	0.335532	+	0.193719i
$210$		0			0
$211$	−130.914	−	226.750i	−0.620447	−	1.07465i	−0.989402	−	0.145199i	$-0.953618\pi$
$211$	−130.914	−	226.750i	−0.620447	−	1.07465i	0.368955	−	0.929447i	$-0.379716\pi$
$212$			325.417i			1.53499i
$213$	40.1144	−	254.077i	0.188330	−	1.19285i
$214$	−416.834			−1.94782
$215$	−267.695	−	154.554i	−1.24509	−	0.718854i
$216$	253.578	−	499.485i	1.17397	−	2.31243i
$217$		0			0
$218$	400.377	+	231.157i	1.83659	+	1.06036i
$219$	−76.1676	−	198.134i	−0.347797	−	0.904719i
$220$	−94.3997	+	163.505i	−0.429089	+	0.743205i
$221$	0.948524	+	0.547631i	0.00429196	+	0.00247797i
$222$	14.6219	−	92.6125i	0.0658646	−	0.417173i
$223$	−179.709	+	311.266i	−0.805872	+	1.39581i	0.109829	+	0.993950i	$0.464970\pi$
$223$	−179.709	+	311.266i	−0.805872	+	1.39581i	−0.915701	+	0.401860i	$0.868364\pi$
$224$		0			0
$225$	−77.1988	−	24.9999i	−0.343106	−	0.111111i
$226$	63.2719	−	109.590i	0.279964	−	0.484912i
$227$			407.746i			1.79624i	0.439754	+	0.898118i	$0.355066\pi$
$227$			407.746i			1.79624i	−0.439754	+	0.898118i	$0.644934\pi$
$228$	249.270	+	648.423i	1.09329	+	2.84396i
$229$	−77.5928			−0.338833			−0.169417	−	0.985545i	$-0.554188\pi$
$229$	−77.5928			−0.338833			−0.169417	+	0.985545i	$0.554188\pi$
$230$	−634.296	+	366.211i	−2.75781	+	1.59222i
$231$		0			0
$232$	−378.706	+	655.938i	−1.63235	+	2.82732i
$233$	−393.484	−	227.178i	−1.68877	−	0.975013i	−0.955460	−	0.295121i	$-0.904640\pi$
$233$	−393.484	−	227.178i	−1.68877	−	0.975013i	−0.733312	−	0.679892i	$-0.762027\pi$
$234$	7.03703	+	7.80006i	0.0300728	+	0.0333336i
$235$	58.1545	+	100.727i	0.247466	+	0.428624i
$236$	−303.709	+	175.346i	−1.28690	+	0.742993i
$237$	−109.161	−	283.958i	−0.460594	−	1.19814i
$238$		0			0
$239$	−44.0684	+	25.4429i	−0.184387	+	0.106456i	−0.589352	−	0.807876i	$-0.700617\pi$
$239$	−44.0684	+	25.4429i	−0.184387	+	0.106456i	0.404965	+	0.914332i	$0.367284\pi$
$240$	−622.005	+	239.115i	−2.59169	+	0.996311i
$241$	191.564			0.794873			0.397436	−	0.917630i	$-0.369900\pi$
$241$	191.564			0.794873			0.397436	+	0.917630i	$0.369900\pi$
$242$	−350.566	+	202.399i	−1.44862	+	0.836360i
$243$	−172.247	−	171.406i	−0.708834	−	0.705375i
$244$	115.868			0.474869
$245$		0			0
$246$	321.084	−	396.903i	1.30522	−	1.61342i
$247$	−7.61174			−0.0308167
$248$	434.509	+	250.864i	1.75205	+	1.01155i
$249$	70.0688	+	56.6839i	0.281401	+	0.227646i
$250$	−172.030	−	297.964i	−0.688119	−	1.19186i
$251$			262.216i			1.04469i	0.852735	+	0.522343i	$0.174942\pi$
$251$			262.216i			1.04469i	−0.852735	+	0.522343i	$0.825058\pi$
$252$		0			0
$253$	114.480			0.452488
$254$	−693.529	+	400.409i	−2.73043	+	1.57641i
$255$	21.7425	+	56.5585i	0.0852648	+	0.221798i
$256$	135.618	−	234.897i	0.529757	−	0.917566i
$257$			141.472i			0.550474i	0.961376	+	0.275237i	$0.0887563\pi$
$257$			141.472i			0.550474i	−0.961376	+	0.275237i	$0.911244\pi$
$258$	−91.5139	+	579.631i	−0.354705	+	2.24663i
$259$		0			0
$260$		−	17.7474i		−	0.0682592i
$261$	220.091	+	243.956i	0.843262	+	0.934697i
$262$	229.488	+	397.485i	0.875908	+	1.51712i
$263$		−	441.499i		−	1.67870i	−0.543588	−	0.839352i	$-0.682935\pi$
$263$		−	441.499i		−	1.67870i	0.543588	−	0.839352i	$-0.317065\pi$
$264$	206.847	+	32.6576i	0.783510	+	0.123703i
$265$	−98.6315	−	170.835i	−0.372194	−	0.644659i
$266$		0			0
$267$	−125.351	−	101.405i	−0.469478	−	0.379796i
$268$	−168.016	−	291.013i	−0.626927	−	1.08587i
$269$	88.6239	−	51.1670i	0.329457	−	0.190212i	−0.326143	−	0.945320i	$-0.605749\pi$
$269$	88.6239	−	51.1670i	0.329457	−	0.190212i	0.655600	+	0.755108i	$0.272416\pi$
$270$	31.2689	+	580.347i	0.115811	+	2.14943i
$271$	160.403	−	277.826i	0.591893	−	1.02519i	−0.402084	−	0.915603i	$-0.631714\pi$
$271$	160.403	−	277.826i	0.591893	−	1.02519i	0.993977	−	0.109586i	$-0.0349526\pi$
$272$	114.223	+	65.9467i	0.419938	+	0.242451i
$273$		0			0
$274$	12.3102	+	21.3218i	0.0449276	+	0.0778168i
$275$		−	30.3350i		−	0.110309i
$276$	763.557	+	617.698i	2.76651	+	2.23804i
$277$	204.414			0.737958			0.368979	−	0.929438i	$-0.379707\pi$
$277$	204.414			0.737958			0.368979	+	0.929438i	$0.379707\pi$
$278$	−56.2670	−	32.4857i	−0.202399	−	0.116855i
$279$	161.602	−	145.794i	0.579220	−	0.522559i
$280$		0			0
$281$	−10.0933	−	5.82736i	−0.0359191	−	0.0207379i	0.481933	−	0.876208i	$-0.339935\pi$
$281$	−10.0933	−	5.82736i	−0.0359191	−	0.0207379i	−0.517852	+	0.855470i	$0.673268\pi$
$282$	138.871	−	171.663i	0.492450	−	0.608734i
$283$	173.123	−	299.857i	0.611740	−	1.05957i	−0.379207	−	0.925312i	$-0.623803\pi$
$283$	173.123	−	299.857i	0.611740	−	1.05957i	0.990947	−	0.134254i	$-0.0428637\pi$
$284$	714.428	+	412.475i	2.51559	+	1.45238i
$285$	−327.392	−	264.852i	−1.14874	−	0.929305i
$286$	−1.96361	+	3.40107i	−0.00686576	+	0.0118918i
$287$		0			0
$288$	347.104	+	384.740i	1.20522	+	1.33590i
$289$	−138.504	+	239.895i	−0.479251	+	0.830087i
$290$		−	785.836i		−	2.70978i
$291$	−13.6218	+	16.8384i	−0.0468105	+	0.0578640i
$292$	680.776			2.33142
$293$	81.5708	−	47.0949i	0.278399	−	0.160734i	−0.354300	−	0.935132i	$-0.615281\pi$
$293$	81.5708	−	47.0949i	0.278399	−	0.160734i	0.632698	+	0.774398i	$0.281947\pi$
$294$		0			0
$295$	106.292	−	184.104i	0.360313	−	0.624081i
$296$	152.149	+	87.8432i	0.514016	+	0.296768i
$297$	41.1223	−	81.0007i	0.138459	−	0.272730i
$298$	−54.7976	−	94.9123i	−0.183885	−	0.318498i
$299$	−9.31950	+	5.38062i	−0.0311689	+	0.0179954i
$300$	163.679	−	202.329i	0.545595	−	0.674429i
$301$		0			0
$302$	223.607	−	129.100i	0.740421	−	0.427482i
$303$	28.3031	−	179.267i	0.0934097	−	0.591639i
$304$	−916.620			−3.01520
$305$	−60.8274	+	35.1187i	−0.199434	+	0.115143i
$306$	85.4097	−	77.0547i	0.279117	−	0.251813i
$307$	503.730			1.64081			0.820407	−	0.571781i	$-0.193747\pi$
$307$	503.730			1.64081			0.820407	+	0.571781i	$0.193747\pi$
$308$		0			0
$309$	−483.740	−	76.3743i	−1.56550	−	0.247166i
$310$	−520.557			−1.67922
$311$	238.993	+	137.983i	0.768467	+	0.443675i	0.832328	−	0.554284i	$-0.187008\pi$
$311$	238.993	+	137.983i	0.768467	+	0.443675i	−0.0638603	+	0.997959i	$0.520341\pi$
$312$	−18.3738	+	7.06337i	−0.0588905	+	0.0226390i
$313$	190.541	+	330.028i	0.608759	+	1.05440i	0.991445	+	0.130523i	$0.0416656\pi$
$313$	190.541	+	330.028i	0.608759	+	1.05440i	−0.382687	+	0.923878i	$0.625001\pi$
$314$		−	725.739i		−	2.31127i
$315$		0			0
$316$	975.665			3.08755
$317$	527.735	−	304.688i	1.66478	−	0.961160i	0.694394	−	0.719595i	$-0.255672\pi$
$317$	527.735	−	304.688i	1.66478	−	0.961160i	0.970384	−	0.241566i	$-0.0776610\pi$
$318$	−235.529	+	291.145i	−0.740656	+	0.915550i
$319$	−61.4141	+	106.372i	−0.192521	+	0.333456i
$320$		−	350.822i		−	1.09632i
$321$	−263.420	−	213.100i	−0.820622	−	0.663862i
$322$		0			0
$323$			83.3476i			0.258042i
$324$	711.334	−	318.376i	2.19547	−	0.982641i
$325$	1.42577	+	2.46950i	0.00438697	+	0.00759846i
$326$		−	34.2627i		−	0.105100i
$327$	134.844	+	350.767i	0.412366	+	1.07268i
$328$	478.301	+	828.442i	1.45824	+	2.52574i
$329$		0			0
$330$	−202.799	+	77.9609i	−0.614541	+	0.236245i
$331$	255.442	+	442.438i	0.771727	+	1.33667i	0.936616	+	0.350358i	$0.113940\pi$
$331$	255.442	+	442.438i	0.771727	+	1.33667i	−0.164889	+	0.986312i	$0.552727\pi$
$332$	−250.321	+	144.523i	−0.753979	+	0.435310i
$333$	56.5871	−	51.0516i	0.169931	−	0.153308i
$334$	−195.029	+	337.799i	−0.583918	+	1.01138i
$335$	176.408	+	101.849i	0.526590	+	0.304027i
$336$		0			0
$337$	−72.9765	−	126.399i	−0.216547	−	0.375071i	0.737203	−	0.675672i	$-0.236146\pi$
$337$	−72.9765	−	126.399i	−0.216547	−	0.375071i	−0.953750	+	0.300600i	$0.902813\pi$
$338$			623.362i			1.84427i
$339$	96.0112	−	36.9091i	0.283219	−	0.108877i
$340$	−194.332			−0.571564
$341$	70.4637	+	40.6822i	0.206638	+	0.119303i
$342$	−246.295	+	760.548i	−0.720160	+	2.22383i
$343$		0			0
$344$	−952.250	−	549.782i	−2.76817	−	1.59820i
$345$	−588.065	−	92.8455i	−1.70454	−	0.269117i
$346$	355.376	−	615.529i	1.02710	−	1.77899i
$347$	238.896	+	137.927i	0.688461	+	0.397483i	0.803035	−	0.595931i	$-0.203217\pi$
$347$	238.896	+	137.927i	0.688461	+	0.397483i	−0.114574	+	0.993415i	$0.536550\pi$
$348$	−983.574	+	378.111i	−2.82636	+	1.08653i
$349$	−119.986	+	207.822i	−0.343800	+	0.595480i	−0.985135	−	0.171782i	$-0.945048\pi$
$349$	−119.986	+	207.822i	−0.343800	+	0.595480i	0.641335	+	0.767261i	$0.278381\pi$
$350$		0			0
$351$	0.459424	+	8.52685i	0.00130890	+	0.0242930i
$352$	−96.8555	+	167.759i	−0.275158	+	0.476587i
$353$		−	541.837i		−	1.53495i	−0.641080	−	0.767474i	$-0.721513\pi$
$353$		−	541.837i		−	1.53495i	0.641080	−	0.767474i	$-0.278487\pi$
$354$	−398.634	−	62.9375i	−1.12609	−	0.177790i
$355$	−500.073			−1.40866
$356$	447.815	−	258.546i	1.25791	−	0.726254i
$357$		0			0
$358$	−98.8629	+	171.236i	−0.276153	+	0.478312i
$359$	−383.110	−	221.189i	−1.06716	−	0.616124i	−0.139754	−	0.990186i	$-0.544631\pi$
$359$	−383.110	−	221.189i	−1.06716	−	0.616124i	−0.927404	+	0.374062i	$0.877965\pi$
$360$	−1036.06	−	335.515i	−2.87794	−	0.931985i
$361$	−109.120	−	189.002i	−0.302273	−	0.523551i
$362$	−362.805	+	209.466i	−1.00222	+	0.578634i
$363$	−325.015	−	51.3143i	−0.895357	−	0.141362i
$364$		0			0
$365$	−357.388	+	206.338i	−0.979146	+	0.565310i
$366$	103.665	+	83.8624i	0.283238	+	0.229132i
$367$	306.189			0.834303			0.417151	−	0.908837i	$-0.363029\pi$
$367$	306.189			0.834303			0.417151	+	0.908837i	$0.363029\pi$
$368$	−1122.27	+	647.944i	−3.04965	+	1.76072i
$369$	405.820	−	86.6749i	1.09978	−	0.234891i
$370$	−182.279			−0.492647
$371$		0			0
$372$	250.470	+	651.544i	0.673307	+	1.75146i
$373$	218.629			0.586138			0.293069	−	0.956091i	$-0.405323\pi$
$373$	218.629			0.586138			0.293069	+	0.956091i	$0.405323\pi$
$374$	37.2413	+	21.5013i	0.0995756	+	0.0574900i
$375$	43.6147	−	276.247i	0.116306	−	0.736659i
$376$	206.869	+	358.307i	0.550182	+	0.952944i
$377$		−	11.5460i		−	0.0306261i
$378$		0			0
$379$	254.498			0.671500			0.335750	−	0.941951i	$-0.391010\pi$
$379$	254.498			0.671500			0.335750	+	0.941951i	$0.391010\pi$
$380$	1169.61	−	675.274i	3.07792	−	1.77704i
$381$	−642.981	−	101.516i	−1.68761	−	0.266445i
$382$	318.483	−	551.630i	0.833726	−	1.44406i
$383$		−	567.515i		−	1.48176i	−0.671637	−	0.740881i	$-0.734408\pi$
$383$		−	567.515i		−	1.48176i	0.671637	−	0.740881i	$-0.265592\pi$
$384$	23.2403	−	8.93418i	0.0605217	−	0.0232661i
$385$		0			0
$386$		−	702.432i		−	1.81977i
$387$	−354.160	+	319.515i	−0.915142	+	0.825620i
$388$	−34.7307	−	60.1553i	−0.0895120	−	0.155039i
$389$			290.720i			0.747352i	0.927559	+	0.373676i	$0.121903\pi$
$389$			290.720i			0.747352i	−0.927559	+	0.373676i	$0.878097\pi$
$390$	12.8451	−	15.8783i	0.0329362	−	0.0407135i
$391$	58.9171	+	102.047i	0.150683	+	0.260991i
$392$		0			0
$393$	−58.1821	+	368.514i	−0.148046	+	0.937695i
$394$	−180.874	−	313.283i	−0.459071	−	0.795134i
$395$	−512.197	+	295.717i	−1.29670	+	0.748651i
$396$	195.156	+	216.317i	0.492819	+	0.546255i
$397$	−229.543	+	397.580i	−0.578194	+	1.00146i	0.417493	+	0.908680i	$0.362909\pi$
$397$	−229.543	+	397.580i	−0.578194	+	1.00146i	−0.995687	+	0.0927809i	$0.970424\pi$
$398$	819.194	+	472.962i	2.05828	+	1.18835i
$399$		0			0
$400$	171.693	+	297.382i	0.429234	+	0.743454i
$401$		−	459.987i		−	1.14710i	−0.819170	−	0.573550i	$-0.805566\pi$
$401$		−	459.987i		−	1.14710i	0.819170	−	0.573550i	$-0.194434\pi$
$402$	60.3066	−	381.970i	0.150016	−	0.950175i
$403$	−7.64837			−0.0189786
$404$	504.072	+	291.026i	1.24770	+	0.720362i
$405$	−276.933	+	382.738i	−0.683785	+	0.945033i
$406$		0			0
$407$	24.6737	+	14.2454i	0.0606234	+	0.0350009i
$408$	77.3430	+	201.191i	0.189566	+	0.493116i
$409$	−291.920	+	505.621i	−0.713741	+	1.23624i	0.249702	+	0.968323i	$0.419667\pi$
$409$	−291.920	+	505.621i	−0.713741	+	1.23624i	−0.963443	+	0.267913i	$0.913666\pi$
$410$	−859.531	−	496.251i	−2.09642	−	1.21037i
$411$	−3.12099	+	19.7678i	−0.00759366	+	0.0480968i
$412$	785.317	−	1360.21i	1.90611	−	3.30148i
$413$		0			0
$414$	236.067	+	1105.29i	0.570209	+	2.66977i
$415$	87.6076	−	151.741i	0.211103	−	0.365641i
$416$		−	18.2091i		−	0.0437719i
$417$	−18.9503	−	49.2951i	−0.0454443	−	0.118214i
$418$	−298.855			−0.714963
$419$	−125.878	+	72.6756i	−0.300424	+	0.173450i	−0.642634	−	0.766174i	$-0.722158\pi$
$419$	−125.878	+	72.6756i	−0.300424	+	0.173450i	0.342209	+	0.939624i	$0.388825\pi$
$420$		0			0
$421$	23.2429	−	40.2578i	0.0552087	−	0.0956243i	−0.837100	−	0.547050i	$-0.815751\pi$
$421$	23.2429	−	40.2578i	0.0552087	−	0.0956243i	0.892309	+	0.451425i	$0.149084\pi$
$422$	836.871	+	483.168i	1.98311	+	1.14495i
$423$	175.520	−	37.4875i	0.414941	−	0.0886229i
$424$	−350.854	−	607.697i	−0.827486	−	1.43325i
$425$	27.0407	−	15.6120i	0.0636252	−	0.0367340i
$426$	340.647	+	886.119i	0.799640	+	2.08009i
$427$		0			0
$428$	941.067	−	543.325i	2.19875	−	1.26945i
$429$	−2.97965	+	1.14545i	−0.00694557	+	0.00267006i
$430$	1140.83			2.65309
$431$	217.312	−	125.465i	0.504204	−	0.291103i	−0.226244	−	0.974071i	$-0.572645\pi$
$431$	217.312	−	125.465i	0.504204	−	0.291103i	0.730448	+	0.682968i	$0.239311\pi$
$432$	55.3247	+	1026.82i	0.128067	+	2.37690i
$433$	−158.357			−0.365720			−0.182860	−	0.983139i	$-0.558536\pi$
$433$	−158.357			−0.365720			−0.182860	+	0.983139i	$0.558536\pi$
$434$		0			0
$435$	401.746	−	496.612i	0.923554	−	1.14164i
$436$	−1205.22			−2.76426
$437$	−709.199	−	409.456i	−1.62288	−	0.936971i
$438$	609.078	+	492.729i	1.39059	+	1.12495i
$439$	167.384	+	289.917i	0.381284	+	0.660403i	0.991246	−	0.132027i	$-0.0421487\pi$
$439$	167.384	+	289.917i	0.381284	+	0.660403i	−0.609962	+	0.792431i	$0.708815\pi$
$440$		−	407.115i		−	0.925261i
$441$		0			0
$442$	−4.04230			−0.00914547
$443$	18.5652	−	10.7187i	0.0419080	−	0.0241956i	−0.478900	−	0.877870i	$-0.658964\pi$
$443$	18.5652	−	10.7187i	0.0419080	−	0.0241956i	0.520808	+	0.853674i	$0.325631\pi$
$444$	87.7052	+	228.146i	0.197534	+	0.513843i
$445$	−156.727	+	271.459i	−0.352196	+	0.610021i
$446$		−	1326.51i		−	2.97424i
$447$	13.8928	−	87.9946i	0.0310802	−	0.196856i
$448$		0			0
$449$			113.632i			0.253078i	0.991962	+	0.126539i	$0.0403868\pi$
$449$			113.632i			0.253078i	−0.991962	+	0.126539i	$0.959613\pi$
$450$	292.881	−	62.5533i	0.650846	−	0.139007i
$451$	77.5653	+	134.347i	0.171985	+	0.297887i
$452$			329.889i			0.729843i
$453$	207.309	+	32.7306i	0.457637	+	0.0722531i
$454$	−752.437	−	1303.26i	−1.65735	−	2.87061i
$455$		0			0
$456$	−1164.61	−	942.137i	−2.55396	−	2.06609i
$457$	−55.7498	−	96.5615i	−0.121991	−	0.211294i	0.798562	−	0.601913i	$-0.205595\pi$
$457$	−55.7498	−	96.5615i	−0.121991	−	0.211294i	−0.920553	+	0.390618i	$0.872261\pi$
$458$	248.006	−	143.186i	0.541498	−	0.312634i
$459$	93.3680	−	5.03064i	0.203416	−	0.0109600i
$460$	954.681	−	1653.56i	2.07539	−	3.59469i
$461$	143.867	+	83.0619i	0.312077	+	0.180178i	0.647855	−	0.761763i	$-0.275666\pi$
$461$	143.867	+	83.0619i	0.312077	+	0.180178i	−0.335779	+	0.941941i	$0.608999\pi$
$462$		0			0
$463$	121.635	+	210.678i	0.262711	+	0.455028i	0.966961	−	0.254923i	$-0.0820502\pi$
$463$	121.635	+	210.678i	0.262711	+	0.455028i	−0.704251	+	0.709951i	$0.748717\pi$
$464$		−	1390.39i		−	2.99654i
$465$	−328.968	−	266.127i	−0.707458	−	0.572315i
$466$	1676.90			3.59850
$467$	−300.050	−	173.234i	−0.642505	−	0.370950i	0.143074	−	0.989712i	$-0.454301\pi$
$467$	−300.050	−	173.234i	−0.642505	−	0.370950i	−0.785579	+	0.618762i	$0.787635\pi$
$468$	−26.0542	−	8.43736i	−0.0556715	−	0.0180285i
$469$		0			0
$470$	−371.753	−	214.632i	−0.790964	−	0.456663i
$471$	371.023	−	458.633i	0.787734	−	0.973744i
$472$	378.106	−	654.898i	0.801071	−	1.38750i
$473$	−154.425	−	89.1572i	−0.326479	−	0.188493i
$474$	872.911	+	706.162i	1.84158	+	1.48979i
$475$	−108.498	+	187.925i	−0.228418	+	0.395631i
$476$		0			0
$477$	−297.686	+	63.5797i	−0.624080	+	0.133291i
$478$	93.9026	−	162.644i	0.196449	−	0.340260i
$479$			557.565i			1.16402i	0.813182	+	0.582009i	$0.197733\pi$
$479$			557.565i			1.16402i	−0.813182	+	0.582009i	$0.802267\pi$
$480$	633.589	−	783.201i	1.31998	−	1.63167i
$481$	−2.67817			−0.00556792
$482$	−612.288	+	353.505i	−1.27031	+	0.733412i
$483$		0			0
$484$	527.638	−	913.895i	1.09016	−	1.88821i
$485$	36.4652	+	21.0532i	0.0751860	+	0.0434087i
$486$	866.850	+	230.000i	1.78364	+	0.473252i
$487$	−190.990	−	330.804i	−0.392176	−	0.679269i	0.600560	−	0.799580i	$-0.294944\pi$
$487$	−190.990	−	330.804i	−0.392176	−	0.679269i	−0.992736	+	0.120310i	$0.961611\pi$
$488$	−216.377	+	124.925i	−0.443395	+	0.255994i
$489$	17.5163	−	21.6524i	0.0358206	−	0.0442790i
$490$		0			0
$491$	448.359	−	258.860i	0.913155	−	0.527210i	0.0317099	−	0.999497i	$-0.489905\pi$
$491$	448.359	−	258.860i	0.913155	−	0.527210i	0.881445	+	0.472287i	$0.156571\pi$
$492$	−207.551	+	1314.59i	−0.421852	+	2.67193i
$493$	−126.428			−0.256445
$494$	24.3290	−	14.0464i	0.0492491	−	0.0284340i
$495$	−168.016	−	54.4099i	−0.339425	−	0.109919i
$496$	−921.031			−1.85692
$497$		0			0
$498$	−328.560	−	51.8740i	−0.659758	−	0.104165i
$499$	−62.2576			−0.124765			−0.0623824	−	0.998052i	$-0.519870\pi$
$499$	−62.2576			−0.124765			−0.0623824	+	0.998052i	$0.519870\pi$
$500$	776.767	+	448.467i	1.55353	+	0.896934i
$501$	−295.944	+	113.768i	−0.590706	+	0.227082i
$502$	−483.883	−	838.110i	−0.963911	−	1.66954i
$503$		−	608.089i		−	1.20892i	−0.796634	−	0.604462i	$-0.793388\pi$
$503$		−	608.089i		−	1.20892i	0.796634	−	0.604462i	$-0.206612\pi$
$504$		0			0
$505$	−352.832			−0.698677
$506$	−365.906	+	211.256i	−0.723134	+	0.417501i
$507$	−318.684	+	393.936i	−0.628568	+	0.776994i
$508$	1043.83	−	1807.97i	2.05479	−	3.55900i
$509$			387.658i			0.761608i	0.924656	+	0.380804i	$0.124353\pi$
$509$			387.658i			0.761608i	−0.924656	+	0.380804i	$0.875647\pi$
$510$	−173.865	−	140.653i	−0.340912	−	0.275789i
$511$		0			0
$512$			967.855i			1.89034i
$513$	−544.465	+	354.717i	−1.06134	+	0.691456i
$514$	−261.066	−	452.180i	−0.507911	−	0.879727i
$515$			952.095i			1.84873i
$516$	−548.918	−	1427.89i	−1.06379	−	2.76723i
$517$	33.5475	+	58.1060i	0.0648888	+	0.112391i
$518$		0			0
$519$	539.261	−	207.306i	1.03904	−	0.399433i
$520$	19.1347	+	33.1422i	0.0367974	+	0.0637351i
$521$	457.542	−	264.162i	0.878200	−	0.507029i	0.00813547	−	0.999967i	$-0.497410\pi$
$521$	457.542	−	264.162i	0.878200	−	0.507029i	0.870064	+	0.492938i	$0.164077\pi$
$522$	−1153.65	−	373.597i	−2.21006	−	0.715703i
$523$	179.837	−	311.487i	0.343856	−	0.595577i	−0.641289	−	0.767300i	$-0.721600\pi$
$523$	179.837	−	311.487i	0.343856	−	0.595577i	0.985145	+	0.171723i	$0.0549333\pi$
$524$	−1036.21	−	598.256i	−1.97750	−	1.14171i
$525$		0			0
$526$	814.724	+	1411.14i	1.54890	+	2.68278i
$527$			83.7487i			0.158916i
$528$	−358.815	+	137.938i	−0.679574	+	0.261246i
$529$	−628.753			−1.18857
$530$	630.502	+	364.021i	1.18963	+	0.686832i
$531$	−219.742	−	243.569i	−0.413828	−	0.458699i
$532$		0			0
$533$	−12.6288	−	7.29124i	−0.0236938	−	0.0136796i
$534$	587.782	+	92.8008i	1.10072	+	0.173784i
$535$	−329.356	+	570.461i	−0.615618	+	1.06628i
$536$	627.522	+	362.300i	1.17075	+	0.675932i
$537$	−150.018	+	57.6708i	−0.279364	+	0.107394i
$538$	−188.843	+	327.086i	−0.351009	+	0.607966i
$539$		0			0
$540$	−827.052	−	1269.47i	−1.53158	−	2.35086i
$541$	35.5347	−	61.5479i	0.0656834	−	0.113767i	−0.831314	−	0.555804i	$-0.812411\pi$
$541$	35.5347	−	61.5479i	0.0656834	−	0.113767i	0.896997	+	0.442037i	$0.145744\pi$
$542$			1184.00i			2.18451i
$543$	−336.362	−	53.1058i	−0.619451	−	0.0978008i
$544$	−199.387			−0.366521
$545$	632.705	−	365.292i	1.16093	−	0.670261i
$546$		0			0
$547$	−180.236	+	312.177i	−0.329498	+	0.570708i	−0.982412	−	0.186724i	$-0.940213\pi$
$547$	−180.236	+	312.177i	−0.329498	+	0.570708i	0.652914	+	0.757432i	$0.273546\pi$
$548$	−55.5842	−	32.0915i	−0.101431	−	0.0585612i
$549$	22.6382	+	105.994i	0.0412353	+	0.193068i
$550$	55.9789	+	96.9583i	0.101780	+	0.176288i
$551$	760.919	−	439.317i	1.38098	−	0.797308i
$552$	−2091.88	−	330.272i	−3.78964	−	0.598319i
$553$		0			0
$554$	−653.361	+	377.218i	−1.17935	+	0.680899i
$555$	−115.192	−	93.1875i	−0.207553	−	0.167905i
$556$	169.375			0.304632
$557$	−133.574	+	77.1188i	−0.239809	+	0.138454i	−0.615089	−	0.788458i	$-0.710880\pi$
$557$	−133.574	+	77.1188i	−0.239809	+	0.138454i	0.375280	+	0.926912i	$0.377547\pi$
$558$	−247.480	+	764.209i	−0.443513	+	1.36955i
$559$	16.7618			0.0299853
$560$		0			0
$561$	12.5426	+	32.6268i	0.0223575	+	0.0581583i
$562$	43.0142			0.0765378
$563$	686.120	+	396.131i	1.21869	+	0.703608i	0.964637	−	0.263583i	$-0.0849044\pi$
$563$	686.120	+	396.131i	1.21869	+	0.703608i	0.254049	+	0.967191i	$0.418238\pi$
$564$	−89.7673	+	568.569i	−0.159162	+	1.00810i
$565$	−99.9870	−	173.183i	−0.176968	−	0.306518i
$566$			1277.89i			2.25776i
$567$		0			0
$568$	−1778.87			−3.13181
$569$	223.053	−	128.780i	0.392009	−	0.226327i	−0.291021	−	0.956717i	$-0.593995\pi$
$569$	223.053	−	128.780i	0.392009	−	0.226327i	0.683030	+	0.730390i	$0.260662\pi$
$570$	1535.18	+	242.378i	2.69329	+	0.425224i
$571$	−336.677	+	583.142i	−0.589627	+	1.02126i	0.404654	+	0.914470i	$0.367392\pi$
$571$	−336.677	+	583.142i	−0.589627	+	1.02126i	−0.994281	+	0.106794i	$0.965941\pi$
$572$		−	10.2379i		−	0.0178985i
$573$	483.279	−	185.785i	0.843418	−	0.324232i
$574$		0			0
$575$			306.783i			0.533536i
$576$	−515.027	−	166.786i	−0.894145	−	0.289558i
$577$	−424.944	−	736.025i	−0.736472	−	1.27561i	−0.954075	−	0.299569i	$-0.903157\pi$
$577$	−424.944	−	736.025i	−0.736472	−	1.27561i	0.217603	−	0.976037i	$-0.430176\pi$
$578$		−	1022.35i		−	1.76878i
$579$	359.107	−	443.905i	0.620220	−	0.766675i
$580$	1024.30	+	1774.15i	1.76604	+	3.05887i
$581$		0			0
$582$	12.4660	−	78.9570i	0.0214192	−	0.135665i
$583$	−56.8974	−	98.5492i	−0.0975942	−	0.169038i
$584$	−1271.31	+	733.991i	−2.17690	+	1.25683i
$585$	16.2350	−	3.46747i	0.0277522	−	0.00592730i
$586$	−173.814	+	301.055i	−0.296611	+	0.513745i
$587$	−181.073	−	104.543i	−0.308472	−	0.178097i	0.337770	−	0.941229i	$-0.390327\pi$
$587$	−181.073	−	104.543i	−0.308472	−	0.178097i	−0.646243	+	0.763132i	$0.723661\pi$
$588$		0			0
$589$	−291.014	−	504.051i	−0.494082	−	0.855775i
$590$			784.590i			1.32981i
$591$	45.8569	−	290.449i	0.0775921	−	0.491453i
$592$	−322.511			−0.544781
$593$	123.884	+	71.5246i	0.208911	+	0.120615i	0.600805	−	0.799395i	$-0.294847\pi$
$593$	123.884	+	71.5246i	0.208911	+	0.120615i	−0.391894	+	0.920010i	$0.628180\pi$
$594$	18.0381	+	334.784i	0.0303671	+	0.563610i
$595$		0			0
$596$	247.428	+	142.853i	0.415148	+	0.239686i
$597$	275.898	+	717.690i	0.462141	+	1.20216i
$598$	19.8583	−	34.3956i	0.0332079	−	0.0575178i
$599$	567.489	+	327.640i	0.947394	+	0.546978i	0.892270	−	0.451501i	$-0.149111\pi$
$599$	567.489	+	327.640i	0.947394	+	0.546978i	0.0551235	+	0.998480i	$0.482445\pi$
$600$	−87.5161	+	554.310i	−0.145860	+	0.923850i
$601$	403.102	−	698.192i	0.670718	−	1.16172i	−0.306983	−	0.951715i	$-0.599319\pi$
$601$	403.102	−	698.192i	0.670718	−	1.16172i	0.977701	−	0.210003i	$-0.0673473\pi$
$602$		0			0
$603$	233.387	−	210.557i	0.387044	−	0.349182i
$604$	−336.552	+	582.925i	−0.557205	+	0.965107i
$605$			639.692i			1.05734i
$606$	240.347	+	625.211i	0.396612	+	1.03170i
$607$	1186.66			1.95497			0.977483	−	0.211016i	$-0.0676771\pi$
$607$	1186.66			1.95497			0.977483	+	0.211016i	$0.0676771\pi$
$608$	1200.04	−	692.841i	1.97374	−	1.13954i
$609$		0			0
$610$	129.613	−	224.497i	0.212481	−	0.368028i
$611$	−5.46205	−	3.15351i	−0.00893952	−	0.00516123i
$612$	−92.3881	+	285.291i	−0.150961	+	0.466161i
$613$	−175.369	−	303.748i	−0.286083	−	0.495510i	0.686788	−	0.726858i	$-0.259020\pi$
$613$	−175.369	−	303.748i	−0.286083	−	0.495510i	−0.972871	+	0.231347i	$0.925687\pi$
$614$	−1610.05	+	929.562i	−2.62223	+	1.51394i
$615$	−289.484	−	753.029i	−0.470705	−	1.22444i
$616$		0			0
$617$	−161.583	+	93.2899i	−0.261885	+	0.151199i	−0.625194	−	0.780469i	$-0.714980\pi$
$617$	−161.583	+	93.2899i	−0.261885	+	0.151199i	0.363309	+	0.931669i	$0.381647\pi$
$618$	1687.09	−	648.562i	2.72993	−	1.04945i
$619$	−543.077			−0.877346			−0.438673	−	0.898647i	$-0.644551\pi$
$619$	−543.077			−0.877346			−0.438673	+	0.898647i	$0.644551\pi$
$620$	1175.24	−	678.524i	1.89555	−	1.09439i
$621$	−415.877	+	819.175i	−0.669690	+	1.31912i
$622$	−1018.51			−1.63748
$623$		0			0
$624$	22.7271	−	28.0937i	0.0364217	−	0.0450220i
$625$	−769.113			−1.23058
$626$	−1218.04	−	703.235i	−1.94575	−	1.12338i
$627$	−188.862	−	152.785i	−0.301216	−	0.243676i
$628$	945.970	+	1638.47i	1.50632	+	2.60903i
$629$			29.3257i			0.0466227i
$630$		0			0
$631$	−181.605			−0.287805			−0.143902	−	0.989592i	$-0.545965\pi$
$631$	−181.605			−0.287805			−0.143902	+	0.989592i	$0.545965\pi$
$632$	−1822.00	+	1051.93i	−2.88291	+	1.66445i
$633$	281.852	+	733.177i	0.445264	+	1.15826i
$634$	−1124.52	+	1947.72i	−1.77369	+	3.07211i
$635$			1265.51i			1.99293i
$636$	152.247	−	964.306i	0.239383	−	1.51620i
$637$		0			0
$638$		−	453.324i		−	0.710539i
$639$	−237.741	+	734.137i	−0.372052	+	1.14888i
$640$	−24.2027	−	41.9203i	−0.0378167	−	0.0655005i
$641$		−	331.090i		−	0.516521i	−0.966075	−	0.258260i	$-0.916851\pi$
$641$		−	331.090i		−	0.516521i	0.966075	−	0.258260i	$-0.0831492\pi$
$642$	1235.20	+	195.017i	1.92399	+	0.303765i
$643$	−457.251	−	791.983i	−0.711122	−	1.23170i	−0.964436	−	0.264315i	$-0.914854\pi$
$643$	−457.251	−	791.983i	−0.711122	−	1.23170i	0.253314	−	0.967384i	$-0.418479\pi$
$644$		0			0
$645$	720.950	+	583.230i	1.11775	+	0.904233i
$646$	−153.806	−	266.400i	−0.238090	−	0.412384i
$647$	364.736	−	210.580i	0.563733	−	0.325472i	−0.190909	−	0.981608i	$-0.561144\pi$
$647$	364.736	−	210.580i	0.563733	−	0.325472i	0.754643	+	0.656136i	$0.227810\pi$
$648$	−985.112	+	1361.48i	−1.52023	+	2.10106i
$649$	61.3167	−	106.204i	0.0944788	−	0.163642i
$650$	−9.11422	−	5.26209i	−0.0140219	−	0.00809553i
$651$		0			0
$652$	44.6600	+	77.3533i	0.0684969	+	0.118640i
$653$			283.329i			0.433888i	0.976184	+	0.216944i	$0.0696089\pi$
$653$			283.329i			0.433888i	−0.976184	+	0.216944i	$0.930391\pi$
$654$	−1078.29	−	872.305i	−1.64875	−	1.33380i
$655$	725.307			1.10734
$656$	−1520.78	−	878.026i	−2.31827	−	1.33845i
$657$	133.009	+	622.763i	0.202450	+	0.947889i
$658$		0			0
$659$	98.1069	+	56.6421i	0.148872	+	0.0859515i	0.572586	−	0.819845i	$-0.305940\pi$
$659$	98.1069	+	56.6421i	0.148872	+	0.0859515i	−0.423713	+	0.905796i	$0.639274\pi$
$660$	356.230	−	440.348i	0.539743	−	0.667194i
$661$	−534.002	+	924.918i	−0.807869	+	1.39927i	0.106468	+	0.994316i	$0.466046\pi$
$661$	−534.002	+	924.918i	−0.807869	+	1.39927i	−0.914337	+	0.404954i	$0.867287\pi$
$662$	−1632.91	−	942.762i	−2.46664	−	1.42411i
$663$	−2.55454	−	2.06656i	−0.00385301	−	0.00311699i
$664$	311.640	−	539.776i	0.469337	−	0.812915i
$665$		0			0
$666$	−86.6582	+	267.597i	−0.130117	+	0.401798i
$667$	621.092	−	1075.76i	0.931173	−	1.61284i
$668$		−	1016.85i		−	1.52222i
$669$	678.159	−	838.294i	1.01369	−	1.25306i
$670$	−751.792			−1.12208
$671$	−35.0894	+	20.2589i	−0.0522943	+	0.0301921i
$672$		0			0
$673$	−438.286	+	759.133i	−0.651242	+	1.12798i	0.331580	+	0.943427i	$0.392418\pi$
$673$	−438.286	+	759.133i	−0.651242	+	1.12798i	−0.982822	+	0.184557i	$0.940915\pi$
$674$	466.503	+	269.335i	0.692140	+	0.399607i
$675$	217.066	+	110.200i	0.321580	+	0.163259i
$676$	−812.526	−	1407.34i	−1.20196	−	2.08186i
$677$	1029.66	−	594.477i	1.52092	−	0.878104i	0.521226	−	0.853419i	$-0.325475\pi$
$677$	1029.66	−	594.477i	1.52092	−	0.878104i	0.999695	−	0.0246857i	$-0.00785851\pi$
$678$	−238.766	+	295.146i	−0.352162	+	0.435319i
$679$		0			0
$680$	362.903	−	209.522i	0.533681	−	0.308121i
$681$	190.765	−	1208.27i	0.280125	−	1.77426i
$682$	−300.293			−0.440312
$683$	−604.484	+	348.999i	−0.885043	+	0.510980i	−0.872318	−	0.488939i	$-0.837384\pi$
$683$	−604.484	+	348.999i	−0.885043	+	0.510980i	−0.0127252	+	0.999919i	$0.504051\pi$
$684$	−435.294	−	2038.09i	−0.636395	−	2.97966i
$685$	38.9068			0.0567983
$686$		0			0
$687$	229.930	+	36.3021i	0.334687	+	0.0528414i
$688$	2018.49			2.93385
$689$	9.26376	+	5.34844i	0.0134452	+	0.00776261i
$690$	2050.94	−	788.434i	2.97238	−	1.14266i
$691$	−506.608	−	877.470i	−0.733151	−	1.26986i	−0.955530	−	0.294895i	$-0.904715\pi$
$691$	−506.608	−	877.470i	−0.733151	−	1.26986i	0.222378	−	0.974960i	$-0.428618\pi$
$692$			1852.87i			2.67756i
$693$		0			0
$694$	−1018.10			−1.46700
$695$	−88.9172	+	51.3364i	−0.127938	+	0.0738653i
$696$	1429.10	−	1766.56i	2.05330	−	2.53816i
$697$	−79.8382	+	138.284i	−0.114546	+	0.198399i
$698$		−	885.671i		−	1.26887i
$699$	1059.72	+	857.288i	1.51606	+	1.22645i
$700$		0			0
$701$		−	910.897i		−	1.29942i	−0.760180	−	0.649712i	$-0.774889\pi$
$701$		−	910.897i		−	1.29942i	0.760180	−	0.649712i	$-0.225111\pi$
$702$	−17.2035	−	26.4062i	−0.0245064	−	0.0376156i
$703$	−101.902	−	176.500i	−0.144953	−	0.251067i
$704$		−	202.378i		−	0.287469i
$705$	−125.204	−	325.690i	−0.177594	−	0.461972i
$706$	999.883	+	1731.85i	1.41626	+	2.45304i
$707$		0			0
$708$	982.015	−	377.512i	1.38703	−	0.533208i
$709$	469.175	+	812.635i	0.661742	+	1.14617i	0.980158	+	0.198219i	$0.0635159\pi$
$709$	469.175	+	812.635i	0.661742	+	1.14617i	−0.318416	+	0.947951i	$0.603151\pi$
$710$	1598.36	−	922.813i	2.25121	−	1.29974i
$711$	190.625	+	892.524i	0.268108	+	1.25531i
$712$	−557.513	+	965.640i	−0.783024	+	1.35624i
$713$	−712.612	−	411.427i	−0.999456	−	0.577036i
$714$		0			0
$715$	3.10304	+	5.37462i	0.00433991	+	0.00751695i
$716$		−	515.454i		−	0.719908i
$717$	142.491	−	54.7773i	0.198733	−	0.0763979i
$718$	1632.69			2.27394
$719$	−268.462	−	154.996i	−0.373382	−	0.215572i	0.301553	−	0.953449i	$-0.402495\pi$
$719$	−268.462	−	154.996i	−0.373382	−	0.215572i	−0.674935	+	0.737877i	$0.735828\pi$
$720$	1955.06	−	417.560i	2.71535	−	0.579944i
$721$		0			0
$722$	697.553	+	402.732i	0.966140	+	0.557801i
$723$	−567.661	−	89.6240i	−0.785147	−	0.123961i
$724$	546.059	−	945.802i	0.754225	−	1.30636i
$725$	−285.058	−	164.578i	−0.393183	−	0.227004i
$726$	1133.52	−	435.755i	1.56133	−	0.600213i
$727$	−712.724	+	1234.47i	−0.980363	+	1.69804i	−0.319400	+	0.947620i	$0.603481\pi$
$727$	−712.724	+	1234.47i	−0.980363	+	1.69804i	−0.660963	+	0.750418i	$0.729852\pi$
$728$		0			0
$729$	430.225	+	588.513i	0.590158	+	0.807288i
$730$	761.536	−	1319.02i	1.04320	−	1.80687i
$731$		−	183.540i		−	0.251080i
$732$	−343.351	−	54.2093i	−0.469059	−	0.0740564i
$733$	940.447			1.28301			0.641506	−	0.767118i	$-0.278310\pi$
$733$	940.447			1.28301			0.641506	+	0.767118i	$0.278310\pi$
$734$	−978.658	+	565.028i	−1.33332	+	0.769793i
$735$		0			0
$736$	979.518	−	1696.57i	1.33087	−	2.30513i
$737$	101.764	+	58.7535i	0.138079	+	0.0797199i
$738$	−1137.16	+	1025.92i	−1.54087	+	1.39013i
$739$	488.765	+	846.566i	0.661387	+	1.14556i	0.980251	+	0.197756i	$0.0633654\pi$
$739$	488.765	+	846.566i	0.661387	+	1.14556i	−0.318864	+	0.947801i	$0.603301\pi$
$740$	411.524	−	237.594i	0.556114	−	0.321072i
$741$	22.5558	+	3.56118i	0.0304397	+	0.00480591i
$742$		0			0
$743$	626.132	−	361.497i	0.842707	−	0.486537i	−0.0154762	−	0.999880i	$-0.504926\pi$
$743$	626.132	−	361.497i	0.842707	−	0.486537i	0.858184	+	0.513343i	$0.171593\pi$
$744$	−1170.21	−	946.671i	−1.57287	−	1.27241i
$745$	−173.191			−0.232471
$746$	−698.795	+	403.449i	−0.936722	+	0.540817i
$747$	−181.115	−	200.753i	−0.242456	−	0.268745i
$748$	−112.104			−0.149872
$749$		0			0
$750$	370.371	+	963.440i	0.493828	+	1.28459i
$751$	−231.592			−0.308379			−0.154189	−	0.988041i	$-0.549277\pi$
$751$	−231.592			−0.308379			−0.154189	+	0.988041i	$0.549277\pi$
$752$	−657.750	−	379.752i	−0.874668	−	0.504990i
$753$	122.679	−	777.024i	0.162920	−	1.03190i
$754$	21.3065	+	36.9040i	0.0282580	+	0.0489443i
$755$		−	408.026i		−	0.540431i
$756$		0			0
$757$	1088.59			1.43804			0.719018	−	0.694992i	$-0.244592\pi$
$757$	1088.59			1.43804			0.719018	+	0.694992i	$0.244592\pi$
$758$	−813.442	+	469.641i	−1.07314	+	0.619579i
$759$	−339.237	−	53.5597i	−0.446952	−	0.0705661i
$760$	−1456.12	+	2522.07i	−1.91594	+	3.31851i
$761$		−	136.067i		−	0.178801i	−0.995996	−	0.0894004i	$-0.971505\pi$
$761$		−	136.067i		−	0.178801i	0.995996	−	0.0894004i	$-0.0284951\pi$
$762$	2242.46	−	862.060i	2.94287	−	1.13131i
$763$		0			0
$764$			1660.52i			2.17345i
$765$	−37.9684	−	177.772i	−0.0496319	−	0.232381i
$766$	1047.27	+	1813.92i	1.36719	+	2.36804i
$767$			11.5277i			0.0150296i
$768$	−511.773	+	632.619i	−0.666371	+	0.823723i
$769$	402.392	+	696.964i	0.523267	+	0.906325i	0.999633	+	0.0270779i	$0.00862021\pi$
$769$	402.392	+	696.964i	0.523267	+	0.906325i	−0.476367	+	0.879247i	$0.658046\pi$
$770$		0			0
$771$	66.1881	−	419.222i	0.0858470	−	0.543739i
$772$	915.591	+	1585.85i	1.18600	+	2.05421i
$773$	−299.560	+	172.951i	−0.387529	+	0.223740i	−0.681089	−	0.732201i	$-0.738493\pi$
$773$	−299.560	+	172.951i	−0.387529	+	0.223740i	0.293560	+	0.955941i	$0.405160\pi$
$774$	542.365	−	1674.80i	0.700730	−	2.16383i
$775$	−109.021	+	188.829i	−0.140672	+	0.243651i
$776$	129.715	+	74.8910i	0.167158	+	0.0965090i
$777$		0			0
$778$	−536.483	−	929.215i	−0.689566	−	1.19436i
$779$		−	1109.70i		−	1.42452i
$780$	−8.30318	+	52.5908i	−0.0106451	+	0.0674241i
$781$	−288.476			−0.369368
$782$	−376.628	−	217.446i	−0.481622	−	0.278064i
$783$	−538.060	−	825.883i	−0.687178	−	1.05477i
$784$		0			0
$785$	−993.215	−	573.433i	−1.26524	−	0.730488i
$786$	−494.076	−	1285.23i	−0.628595	−	1.63515i
$787$	18.6416	−	32.2883i	0.0236870	−	0.0410270i	−0.853939	−	0.520373i	$-0.825793\pi$
$787$	18.6416	−	32.2883i	0.0236870	−	0.0410270i	0.877626	+	0.479346i	$0.159126\pi$
$788$	816.701	+	471.523i	1.03642	+	0.598379i
$789$	−206.557	+	1308.29i	−0.261796	+	1.65816i
$790$	1091.41	−	1890.37i	1.38153	−	2.39288i
$791$		0			0
$792$	−597.669	−	193.548i	−0.754632	−	0.244379i
$793$	1.90436	−	3.29846i	0.00240147	−	0.00415947i
$794$		−	1694.36i		−	2.13395i
$795$	212.348	+	552.379i	0.267105	+	0.694816i
$796$	−2465.94			−3.09792
$797$	1009.32	−	582.728i	1.26639	−	0.731152i	0.292089	−	0.956391i	$-0.405650\pi$
$797$	1009.32	−	582.728i	1.26639	−	0.731152i	0.974304	+	0.225239i	$0.0723162\pi$
$798$		0			0
$799$	−34.5306	+	59.8087i	−0.0432173	+	0.0748545i
$800$	−449.561	−	259.554i	−0.561951	−	0.324443i
$801$	324.008	+	359.140i	0.404504	+	0.448365i
$802$	848.841	+	1470.24i	1.05841	+	1.83321i
$803$	−206.166	+	119.030i	−0.256745	+	0.148232i
$804$	361.731	+	940.964i	0.449914	+	1.17035i
$805$		0			0
$806$	24.4461	−	14.1140i	0.0303302	−	0.0175111i
$807$	−286.557	+	110.160i	−0.355090	+	0.136506i
$808$	−1255.10			−1.55334
$809$	865.722	−	499.825i	1.07011	−	0.617830i	0.141901	−	0.989881i	$-0.454679\pi$
$809$	865.722	−	499.825i	1.07011	−	0.617830i	0.928212	+	0.372051i	$0.121345\pi$
$810$	178.858	−	1734.37i	0.220813	−	2.14120i
$811$	−634.194			−0.781990			−0.390995	−	0.920393i	$-0.627869\pi$
$811$	−634.194			−0.781990			−0.390995	+	0.920393i	$0.627869\pi$
$812$		0			0
$813$	−605.304	+	748.236i	−0.744531	+	0.920339i
$814$	−105.151			−0.129179
$815$	−46.8905	−	27.0722i	−0.0575343	−	0.0332174i
$816$	−307.623	−	248.859i	−0.376989	−	0.304975i
$817$	637.773	+	1104.66i	0.780628	+	1.35209i
$818$		−	2154.79i		−	2.63422i
$819$		0			0
$820$	2587.37			3.15532
$821$	263.766	−	152.285i	0.321274	−	0.185488i	−0.330686	−	0.943741i	$-0.607280\pi$
$821$	263.766	−	152.285i	0.321274	−	0.185488i	0.651960	+	0.758253i	$0.273947\pi$
$822$	−26.5031	−	68.9421i	−0.0322422	−	0.0838712i
$823$	425.387	−	736.793i	0.516874	−	0.895252i	−0.482934	−	0.875657i	$-0.660429\pi$
$823$	425.387	−	736.793i	0.516874	−	0.895252i	0.999808	−	0.0195954i	$-0.00623780\pi$
$824$			3386.81i			4.11021i
$825$	−14.1923	+	89.8915i	−0.0172028	+	0.108959i
$826$		0			0
$827$		−	0.427608i		−	0.000517059i	−1.00000		0.000258530i	$-0.999918\pi$
$827$		−	0.427608i		−	0.000517059i	1.00000		0.000258530i	$-8.22925e-5\pi$
$828$	−1973.65	−	2187.65i	−2.38364	−	2.64209i
$829$	−224.677	−	389.151i	−0.271021	−	0.469422i	0.698102	−	0.715998i	$-0.254028\pi$
$829$	−224.677	−	389.151i	−0.271021	−	0.469422i	−0.969124	+	0.246575i	$0.920695\pi$
$830$			646.670i			0.779120i
$831$	−605.740	−	95.6361i	−0.728929	−	0.115086i
$832$	9.51191	+	16.4751i	0.0114326	+	0.0198018i
$833$		0			0
$834$	151.537	+	122.590i	0.181699	+	0.146990i
$835$	308.199	+	533.816i	0.369100	+	0.639300i
$836$	674.711	−	389.544i	0.807070	−	0.465962i
$837$	−547.085	+	356.424i	−0.653627	+	0.425835i
$838$	268.225	−	464.579i	0.320078	−	0.554390i
$839$	185.989	+	107.381i	0.221680	+	0.127987i	0.606728	−	0.794910i	$-0.292482\pi$
$839$	185.989	+	107.381i	0.221680	+	0.127987i	−0.385048	+	0.922897i	$0.625815\pi$
$840$		0			0
$841$	245.887	+	425.889i	0.292374	+	0.506407i
$842$			171.566i			0.203760i
$843$	27.1830	+	21.9904i	0.0322456	+	0.0260858i
$844$	−2519.16			−2.98478
$845$	853.106	+	492.541i	1.00959	+	0.582889i
$846$	−491.829	+	443.717i	−0.581358	+	0.524488i
$847$		0			0
$848$	1115.56	+	644.069i	1.31552	+	0.759515i
$849$	−653.302	+	807.569i	−0.769496	+	0.951200i
$850$	−57.6193	+	99.7996i	−0.0677874	+	0.117411i
$851$	−249.530	−	144.066i	−0.293220	−	0.169291i
$852$	−1924.08	−	1556.53i	−2.25831	−	1.82692i
$853$	−192.842	+	334.012i	−0.226075	+	0.391573i	−0.956641	−	0.291269i	$-0.905923\pi$
$853$	−192.842	+	334.012i	−0.226075	+	0.391573i	0.730567	+	0.682841i	$0.239256\pi$
$854$		0			0
$855$	846.248	+	938.006i	0.989763	+	1.09708i
$856$	−1171.59	+	2029.26i	−1.36868	+	2.37063i
$857$		−	1305.56i		−	1.52341i	−0.647922	−	0.761707i	$-0.724362\pi$
$857$		−	1305.56i		−	1.52341i	0.647922	−	0.761707i	$-0.275638\pi$
$858$	7.40995	−	9.15968i	0.00863630	−	0.0106756i
$859$	−1181.22			−1.37511			−0.687554	−	0.726133i	$-0.741315\pi$
$859$	−1181.22			−1.37511			−0.687554	+	0.726133i	$0.741315\pi$
$860$	−2575.60	+	1487.02i	−2.99488	+	1.72909i
$861$		0			0
$862$	−463.056	+	802.037i	−0.537188	+	0.930438i
$863$	782.044	+	451.514i	0.906193	+	0.523191i	0.879204	−	0.476445i	$-0.158075\pi$
$863$	782.044	+	451.514i	0.906193	+	0.523191i	0.0269886	+	0.999636i	$0.491408\pi$
$864$	−848.568	−	1302.49i	−0.982139	−	1.50751i
$865$	−561.591	−	972.704i	−0.649238	−	1.12451i
$866$	506.148	−	292.225i	0.584467	−	0.337442i
$867$	522.662	−	646.080i	0.602840	−	0.745191i
$868$		0			0
$869$	−295.470	+	170.590i	−0.340012	+	0.196306i
$870$	−367.656	+	2328.66i	−0.422593	+	2.67662i
$871$	−11.0458			−0.0126818
$872$	2250.67	−	1299.43i	2.58104	−	1.49017i
$873$	48.2435	−	43.5242i	0.0552617	−	0.0498558i
$874$	3022.37			3.45809
$875$		0			0
$876$	−2017.34	−	318.504i	−2.30290	−	0.363589i
$877$	−554.211			−0.631940			−0.315970	−	0.948769i	$-0.602330\pi$
$877$	−554.211			−0.631940			−0.315970	+	0.948769i	$0.602330\pi$
$878$	−1070.00	−	617.766i	−1.21868	−	0.703606i
$879$	−263.752	+	101.393i	−0.300059	+	0.115350i
$880$	373.674	+	647.222i	0.424629	+	0.735479i
$881$			750.603i			0.851990i	0.904726	+	0.425995i	$0.140076\pi$
$881$			750.603i			0.851990i	−0.904726	+	0.425995i	$0.859924\pi$
$882$		0			0
$883$	−1042.83			−1.18101			−0.590504	−	0.807035i	$-0.701071\pi$
$883$	−1042.83			−1.18101			−0.590504	+	0.807035i	$0.701071\pi$
$884$	9.12611	−	5.26896i	0.0103237	−	0.00596037i
$885$	−401.109	+	495.824i	−0.453231	+	0.560254i
$886$	−39.5595	+	68.5191i	−0.0446495	+	0.0773353i
$887$			85.1498i			0.0959975i	0.998847	+	0.0479987i	$0.0152843\pi$
$887$			85.1498i			0.0959975i	−0.998847	+	0.0479987i	$0.984716\pi$
$888$	−409.764	−	331.489i	−0.461446	−	0.373298i
$889$		0			0
$890$		−	1156.87i		−	1.29985i
$891$	−159.754	+	220.790i	−0.179297	+	0.247800i
$892$	1729.05	+	2994.81i	1.93840	+	3.35741i
$893$		−	479.954i		−	0.537463i
$894$	117.976	+	306.890i	0.131965	+	0.343278i
$895$	156.230	+	270.599i	0.174559	+	0.302345i
$896$		0			0
$897$	30.1338	−	11.5842i	0.0335939	−	0.0129144i
$898$	−209.691	−	363.196i	−0.233509	−	0.404450i
$899$	764.581	−	441.431i	0.850479	−	0.491025i
$900$	−579.688	+	522.982i	−0.644098	+	0.581091i
$901$	58.5647	−	101.437i	0.0649997	−	0.112583i
$902$	−495.837	−	286.271i	−0.549708	−	0.317374i
$903$		0			0
$904$	−355.676	−	616.049i	−0.393447	−	0.681470i
$905$			662.026i			0.731520i
$906$	−723.013	+	277.945i	−0.798028	+	0.306782i
$907$	−860.153			−0.948349			−0.474175	−	0.880431i	$-0.657253\pi$
$907$	−860.153			−0.948349			−0.474175	+	0.880431i	$0.657253\pi$
$908$	3397.48	+	1961.54i	3.74172	+	2.16029i
$909$	−167.741	+	517.978i	−0.184534	+	0.569833i
$910$		0			0
$911$	−1335.63	−	771.127i	−1.46612	−	0.846462i	−0.466833	−	0.884345i	$-0.654605\pi$
$911$	−1335.63	−	771.127i	−1.46612	−	0.846462i	−0.999282	+	0.0378830i	$0.987939\pi$
$912$	2716.21	+	428.844i	2.97831	+	0.470224i
$913$	50.5381	−	87.5345i	0.0553539	−	0.0958757i
$914$	356.381	+	205.757i	0.389914	+	0.225117i
$915$	196.680	−	75.6088i	0.214951	−	0.0826326i
$916$	−373.275	+	646.531i	−0.407505	+	0.705820i
$917$		0			0
$918$	−289.144	+	188.376i	−0.314972	+	0.205203i
$919$	838.124	−	1451.67i	0.911995	−	1.57962i	0.100753	−	0.994911i	$-0.467875\pi$
$919$	838.124	−	1451.67i	0.911995	−	1.57962i	0.811242	−	0.584711i	$-0.198792\pi$
$920$			4117.23i			4.47525i
$921$	−1492.70	−	235.672i	−1.62074	−	0.255887i
$922$	−613.116			−0.664985
$923$	23.4842	−	13.5586i	0.0254433	−	0.0146897i
$924$		0			0
$925$	−38.1749	+	66.1209i	−0.0412702	+	0.0714820i
$926$	−777.553	−	448.920i	−0.839690	−	0.484795i
$927$	1397.73	+	452.639i	1.50780	+	0.488284i
$928$	1050.95	+	1820.30i	1.13249	+	1.96153i
$929$	−1270.20	+	733.353i	−1.36728	+	0.789400i	−0.990580	−	0.136935i	$-0.956275\pi$
$929$	−1270.20	+	733.353i	−1.36728	+	0.789400i	−0.376701	+	0.926335i	$0.622942\pi$
$930$	1542.56	+	243.544i	1.65867	+	0.261876i
$931$		0			0
$932$	−3785.86	+	2185.77i	−4.06208	+	2.34524i
$933$	−643.652	−	520.698i	−0.689873	−	0.558090i
$934$	1278.71			1.36907
$935$	58.8514	−	33.9779i	0.0629427	−	0.0363400i
$936$	57.7517	−	12.3346i	0.0617005	−	0.0131780i
$937$	−322.074			−0.343729			−0.171864	−	0.985121i	$-0.554979\pi$
$937$	−322.074			−0.343729			−0.171864	+	0.985121i	$0.554979\pi$
$938$		0			0
$939$	−410.226	−	1067.11i	−0.436875	−	1.13644i
$940$	1119.05			1.19048
$941$	−324.300	−	187.235i	−0.344633	−	0.198974i	0.317686	−	0.948196i	$-0.397094\pi$
$941$	−324.300	−	187.235i	−0.344633	−	0.198974i	−0.662319	+	0.749222i	$0.730428\pi$
$942$	−339.540	+	2150.58i	−0.360445	+	2.28299i
$943$	−784.432	−	1358.68i	−0.831847	−	1.44080i
$944$			1388.19i			1.47054i
$945$		0			0
$946$	658.108			0.695674
$947$	−142.844	+	82.4709i	−0.150838	+	0.0870865i	−0.573519	−	0.819192i	$-0.694422\pi$
$947$	−142.844	+	82.4709i	−0.150838	+	0.0870865i	0.422681	+	0.906278i	$0.361089\pi$
$948$	−2891.18	−	456.469i	−3.04977	−	0.481507i
$949$	11.1890	−	19.3799i	0.0117903	−	0.0204214i
$950$		−	800.874i		−	0.843025i
$951$	−1706.38	+	655.977i	−1.79430	+	0.689776i
$952$		0			0
$953$		−	1354.42i		−	1.42122i	−0.703586	−	0.710610i	$-0.748419\pi$
$953$		−	1354.42i		−	1.42122i	0.703586	−	0.710610i	$-0.251581\pi$
$954$	834.154	−	752.555i	0.874375	−	0.788842i
$955$	−503.291	−	871.726i	−0.527006	−	0.912802i
$956$			489.592i			0.512126i
$957$	231.755	−	286.480i	0.242168	−	0.299352i
$958$	−1028.91	−	1782.12i	−1.07402	−	1.86025i
$959$		0			0
$960$	−164.133	+	1039.59i	−0.170972	+	1.08290i
$961$	188.085	+	325.773i	0.195718	+	0.338994i
$962$	8.56012	−	4.94218i	0.00889825	−	0.00513741i
$963$	680.890	+	754.719i	0.707051	+	0.783716i
$964$	921.557	−	1596.18i	0.955972	−	1.65579i
$965$	−961.319	−	555.018i	−0.996185	−	0.575148i
$966$		0			0
$967$	−344.963	−	597.493i	−0.356735	−	0.617883i	0.630678	−	0.776044i	$-0.282777\pi$
$967$	−344.963	−	597.493i	−0.356735	−	0.617883i	−0.987413	+	0.158161i	$0.949443\pi$
$968$			2275.53i			2.35075i
$969$	38.9945	−	246.983i	0.0402420	−	0.254885i
$970$	−155.403			−0.160209
$971$	−665.293	−	384.107i	−0.685163	−	0.395579i	0.116634	−	0.993175i	$-0.462789\pi$
$971$	−665.293	−	384.107i	−0.685163	−	0.395579i	−0.801797	+	0.597596i	$0.796123\pi$
$972$	−2256.84	+	610.641i	−2.32186	+	0.628231i
$973$		0			0
$974$	1220.90	+	704.889i	1.25350	+	0.723706i
$975$	−3.06960	−	7.98490i	−0.00314831	−	0.00818964i
$976$	229.327	−	397.207i	0.234966	−	0.406974i
$977$	1200.33	+	693.012i	1.22859	+	0.709326i	0.966735	−	0.255781i	$-0.0823327\pi$
$977$	1200.33	+	693.012i	1.22859	+	0.709326i	0.261854	+	0.965107i	$0.415666\pi$
$978$	−16.0299	+	101.530i	−0.0163905	+	0.103814i
$979$	−90.4109	+	156.596i	−0.0923502	+	0.159955i
$980$		0			0
$981$	−235.474	−	1102.51i	−0.240035	−	1.12387i
$982$	−955.379	+	1654.77i	−0.972891	+	1.68510i
$983$		−	525.350i		−	0.534435i	−0.963636	−	0.267217i	$-0.913896\pi$
$983$		−	525.350i		−	0.534435i	0.963636	−	0.267217i	$-0.0861042\pi$
$984$	−1029.76	−	2678.69i	−1.04650	−	2.72225i
$985$	−571.660			−0.580366
$986$	404.095	−	233.304i	0.409832	−	0.236617i
$987$		0			0
$988$	−36.6177	+	63.4238i	−0.0370625	+	0.0641941i
$989$	1561.73	+	901.663i	1.57910	+	0.911692i
$990$	637.426	−	136.141i	0.643865	−	0.137516i
$991$	214.326	+	371.223i	0.216272	+	0.374594i	0.953665	−	0.300869i	$-0.0972768\pi$
$991$	214.326	+	371.223i	0.216272	+	0.374594i	−0.737393	+	0.675464i	$0.763943\pi$
$992$	1205.81	−	696.176i	1.21554	−	0.701790i
$993$	−549.953	−	1430.58i	−0.553829	−	1.44067i
$994$		0			0
$995$	1294.55	−	747.409i	1.30106	−	0.751165i
$996$	809.390	−	311.150i	0.812640	−	0.312400i
$997$	1196.77			1.20037			0.600184	−	0.799862i	$-0.295094\pi$
$997$	1196.77			1.20037			0.600184	+	0.799862i	$0.295094\pi$
$998$	198.991	−	114.888i	0.199390	−	0.115118i
$999$	−191.569	+	124.806i	−0.191761	+	0.124931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.n.f.128.1		22
7.2	even	3		441.3.r.f.344.11		22
7.3	odd	6		63.3.j.b.11.1	✓	22
7.4	even	3		441.3.j.f.263.1		22
7.5	odd	6		441.3.r.g.344.11		22
7.6	odd	2		63.3.n.b.2.1	yes	22
9.5	odd	6		441.3.j.f.275.11		22
21.17	even	6		189.3.j.b.116.11		22
21.20	even	2		189.3.n.b.170.11		22
63.5	even	6		441.3.r.g.50.11		22
63.13	odd	6		189.3.j.b.44.1		22
63.23	odd	6		441.3.r.f.50.11		22
63.31	odd	6		189.3.n.b.179.11		22
63.32	odd	6	inner	441.3.n.f.410.1		22
63.41	even	6		63.3.j.b.23.11	yes	22
63.59	even	6		63.3.n.b.32.1	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.1	✓	22	7.3	odd	6
63.3.j.b.23.11	yes	22	63.41	even	6
63.3.n.b.2.1	yes	22	7.6	odd	2
63.3.n.b.32.1	yes	22	63.59	even	6
189.3.j.b.44.1		22	63.13	odd	6
189.3.j.b.116.11		22	21.17	even	6
189.3.n.b.170.11		22	21.20	even	2
189.3.n.b.179.11		22	63.31	odd	6
441.3.j.f.263.1		22	7.4	even	3
441.3.j.f.275.11		22	9.5	odd	6
441.3.n.f.128.1		22	1.1	even	1	trivial
441.3.n.f.410.1		22	63.32	odd	6	inner
441.3.r.f.50.11		22	63.23	odd	6
441.3.r.f.344.11		22	7.2	even	3
441.3.r.g.50.11		22	63.5	even	6
441.3.r.g.344.11		22	7.5	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.19625 + 1.84536i) q^{2} +(-2.96329 - 0.467854i) q^{3} +(4.81069 - 8.33236i) q^{4} +5.83234i q^{5} +(10.3348 - 3.97296i) q^{6} +20.7469i q^{8} +(8.56223 + 2.77278i) q^{9} +(-10.7628 - 18.6416i) q^{10} +3.36449i q^{11} +(-18.1538 + 22.4405i) q^{12} +(-0.158134 - 0.273895i) q^{13} +(2.72868 - 17.2829i) q^{15} +(-19.0428 - 32.9830i) q^{16} +(-2.99912 + 1.73154i) q^{17} +(-32.4838 + 6.93788i) q^{18} +(12.0337 - 20.8430i) q^{19} +(48.5972 + 28.0576i) q^{20} +(-6.20870 - 10.7538i) q^{22} -34.0258i q^{23} +(9.70653 - 61.4793i) q^{24} -9.01621 q^{25} +(1.01087 + 0.583626i) q^{26} +(-24.0751 - 12.2224i) q^{27} +(31.6161 + 18.2536i) q^{29} +(23.1717 + 60.2761i) q^{30} +(12.0916 - 20.9433i) q^{31} +(49.8615 + 28.7875i) q^{32} +(1.57409 - 9.96999i) q^{33} +(6.39064 - 11.0689i) q^{34} +(64.2940 - 58.0046i) q^{36} +(4.23403 - 7.33356i) q^{37} +88.8260i q^{38} +(0.340453 + 0.885616i) q^{39} -121.003 q^{40} +(39.9308 - 23.0541i) q^{41} +(-26.4994 + 45.8984i) q^{43} +(28.0342 + 16.1855i) q^{44} +(-16.1718 + 49.9378i) q^{45} +(62.7897 + 108.755i) q^{46} +(17.2703 - 9.97104i) q^{47} +(40.9981 + 106.648i) q^{48} +(28.8181 - 16.6381i) q^{50} +(9.69739 - 3.72792i) q^{51} -3.04293 q^{52} +(-29.2909 + 16.9111i) q^{53} +(99.5050 - 5.36130i) q^{54} -19.6229 q^{55} +(-45.4109 + 56.1339i) q^{57} -134.738 q^{58} +(-31.5660 - 18.2246i) q^{59} +(-130.881 - 105.879i) q^{60} +(6.02138 + 10.4293i) q^{61} +89.2535i q^{62} -60.1511 q^{64} +(1.59745 - 0.922289i) q^{65} +(13.3670 + 34.7714i) q^{66} +(17.4628 - 30.2465i) q^{67} +33.3197i q^{68} +(-15.9191 + 100.828i) q^{69} +85.7413i q^{71} +(-57.5266 + 177.640i) q^{72} +(35.3783 + 61.2770i) q^{73} +31.2532i q^{74} +(26.7177 + 4.21827i) q^{75} +(-115.781 - 200.539i) q^{76} +(-2.72245 - 2.20240i) q^{78} +(50.7030 + 87.8201i) q^{79} +(192.368 - 111.064i) q^{80} +(65.6234 + 47.4823i) q^{81} +(-85.0860 + 147.373i) q^{82} +(-26.0171 - 15.0210i) q^{83} +(-10.0990 - 17.4919i) q^{85} -195.604i q^{86} +(-85.1479 - 68.8825i) q^{87} -69.8030 q^{88} +(46.5438 + 26.8721i) q^{89} +(-40.4641 - 189.457i) q^{90} +(-283.515 - 163.688i) q^{92} +(-45.6294 + 56.4041i) q^{93} +(-36.8003 + 63.7400i) q^{94} +(121.563 + 70.1847i) q^{95} +(-134.286 - 108.634i) q^{96} +(3.60974 - 6.25225i) q^{97} +(-9.32899 + 28.8076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 6 q^{2} - 8 q^{3} + 12 q^{4} + 8 q^{6} + 20 q^{9} - 25 q^{10} + 20 q^{12} + 18 q^{13} + 53 q^{15} + 12 q^{16} - 6 q^{17} - 56 q^{18} - 3 q^{19} + 39 q^{20} - 59 q^{22} - 15 q^{24} - 114 q^{25} + 3 q^{26}+ \cdots - 103 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 - 8 * q^3 + 12 * q^4 + 8 * q^6 + 20 * q^9 - 25 * q^10 + 20 * q^12 + 18 * q^13 + 53 * q^15 + 12 * q^16 - 6 * q^17 - 56 * q^18 - 3 * q^19 + 39 * q^20 - 59 * q^22 - 15 * q^24 - 114 * q^25 + 3 * q^26 + 97 * q^27 - 63 * q^29 - 20 * q^30 + 29 * q^31 + 246 * q^32 - 77 * q^33 + 99 * q^34 + 76 * q^36 - 20 * q^37 + 200 * q^39 - 210 * q^40 + 51 * q^41 + 65 * q^43 + 54 * q^44 - 71 * q^45 + 75 * q^46 - 261 * q^47 + 113 * q^48 + 63 * q^50 - 78 * q^51 - 92 * q^52 - 63 * q^53 + 485 * q^54 + 100 * q^55 + 224 * q^57 - 80 * q^58 + 102 * q^59 + 103 * q^60 - 78 * q^61 + 106 * q^64 - 225 * q^65 + 401 * q^66 - 132 * q^67 + 297 * q^69 - 66 * q^72 - q^73 + 245 * q^75 - 233 * q^76 - 440 * q^78 + 140 * q^79 - 96 * q^80 + 104 * q^81 + 157 * q^82 - 255 * q^83 + 102 * q^85 + 136 * q^87 - 816 * q^88 + 720 * q^89 - 418 * q^90 - 1239 * q^92 + 210 * q^93 - 261 * q^94 + 642 * q^95 - 539 * q^96 - 178 * q^97 - 103 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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