LMFDB - Embedded newform 441.3.k.a.313.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(31,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("441.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			313.6
Character	$\chi$	$=$	441.313
Dual form			441.3.k.a.31.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.952438 - 1.64967i) q^{2} +(1.69506 - 2.47523i) q^{3} +(0.185723 - 0.321682i) q^{4} +8.23162i q^{5} +(-5.69776 - 0.438798i) q^{6} -8.32706 q^{8} +(-3.25351 - 8.39135i) q^{9} +O(q^{10})$	\(q+(-0.952438 - 1.64967i) q^{2} +(1.69506 - 2.47523i) q^{3} +(0.185723 - 0.321682i) q^{4} +8.23162i q^{5} +(-5.69776 - 0.438798i) q^{6} -8.32706 q^{8} +(-3.25351 - 8.39135i) q^{9} +(13.5795 - 7.84010i) q^{10} -11.9301 q^{11} +(-0.481424 - 1.00498i) q^{12} +(1.37508 - 0.793905i) q^{13} +(20.3751 + 13.9531i) q^{15} +(7.18812 + 12.4502i) q^{16} +(-16.8893 + 9.75102i) q^{17} +(-10.7442 + 13.3595i) q^{18} +(-5.79843 - 3.34773i) q^{19} +(2.64796 + 1.52880i) q^{20} +(11.3626 + 19.6807i) q^{22} -28.1484 q^{23} +(-14.1149 + 20.6114i) q^{24} -42.7595 q^{25} +(-2.61936 - 1.51229i) q^{26} +(-26.2854 - 6.17070i) q^{27} +(5.48400 - 9.49857i) q^{29} +(3.61202 - 46.9017i) q^{30} +(-27.4600 - 15.8540i) q^{31} +(-2.96165 + 5.12973i) q^{32} +(-20.2222 + 29.5296i) q^{33} +(32.1720 + 18.5745i) q^{34} +(-3.30360 - 0.511872i) q^{36} +(3.44395 - 5.96510i) q^{37} +12.7540i q^{38} +(0.365760 - 4.74937i) q^{39} -68.5452i q^{40} +(1.35364 - 0.781523i) q^{41} +(-32.5242 + 56.3336i) q^{43} +(-2.21569 + 3.83769i) q^{44} +(69.0743 - 26.7816i) q^{45} +(26.8096 + 46.4357i) q^{46} +(47.8835 - 27.6455i) q^{47} +(43.0014 + 3.31164i) q^{48} +(40.7258 + 70.5391i) q^{50} +(-4.49240 + 58.3334i) q^{51} -0.589787i q^{52} +(16.9628 + 29.3805i) q^{53} +(14.8556 + 49.2395i) q^{54} -98.2037i q^{55} +(-18.1151 + 8.67783i) q^{57} -20.8927 q^{58} +(-5.69639 - 3.28881i) q^{59} +(8.27261 - 3.96290i) q^{60} +(65.9734 - 38.0898i) q^{61} +60.3999i q^{62} +68.7881 q^{64} +(6.53512 + 11.3192i) q^{65} +(67.9746 + 5.23489i) q^{66} +(11.8586 - 20.5396i) q^{67} +7.24397i q^{68} +(-47.7134 + 69.6738i) q^{69} -14.0551 q^{71} +(27.0922 + 69.8753i) q^{72} +(34.8385 - 20.1140i) q^{73} -13.1206 q^{74} +(-72.4801 + 105.840i) q^{75} +(-2.15381 + 1.24350i) q^{76} +(-8.18326 + 3.92009i) q^{78} +(-31.8645 - 55.1909i) q^{79} +(-102.485 + 59.1698i) q^{80} +(-59.8293 + 54.6026i) q^{81} +(-2.57851 - 1.48870i) q^{82} +(1.94261 + 1.12157i) q^{83} +(-80.2667 - 139.026i) q^{85} +123.909 q^{86} +(-14.2154 - 29.6749i) q^{87} +99.3424 q^{88} +(-50.5972 - 29.2123i) q^{89} +(-109.970 - 88.4421i) q^{90} +(-5.22782 + 9.05485i) q^{92} +(-85.7887 + 41.0961i) q^{93} +(-91.2121 - 52.6613i) q^{94} +(27.5572 - 47.7305i) q^{95} +(7.67706 + 16.0260i) q^{96} +(111.760 + 64.5247i) q^{97} +(38.8146 + 100.109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 12 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 12 * q^9	$ 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 12 q^{9} - 8 q^{11} - 54 q^{15} - 42 q^{16} - 138 q^{18} + 14 q^{22} - 8 q^{23} - 56 q^{25} - 38 q^{29} - 294 q^{30} - 168 q^{32} + 234 q^{36} - 18 q^{37} + 84 q^{39} - 66 q^{43} - 54 q^{44} + 20 q^{46} + 196 q^{50} + 318 q^{51} - 260 q^{53} - 198 q^{57} + 68 q^{58} + 366 q^{60} + 72 q^{64} - 102 q^{65} + 68 q^{67} - 332 q^{71} + 714 q^{72} + 1232 q^{74} - 168 q^{78} + 146 q^{79} - 516 q^{81} + 78 q^{85} + 680 q^{86} + 148 q^{88} + 606 q^{92} - 1146 q^{93} - 360 q^{95} + 900 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 12 * q^9 - 8 * q^11 - 54 * q^15 - 42 * q^16 - 138 * q^18 + 14 * q^22 - 8 * q^23 - 56 * q^25 - 38 * q^29 - 294 * q^30 - 168 * q^32 + 234 * q^36 - 18 * q^37 + 84 * q^39 - 66 * q^43 - 54 * q^44 + 20 * q^46 + 196 * q^50 + 318 * q^51 - 260 * q^53 - 198 * q^57 + 68 * q^58 + 366 * q^60 + 72 * q^64 - 102 * q^65 + 68 * q^67 - 332 * q^71 + 714 * q^72 + 1232 * q^74 - 168 * q^78 + 146 * q^79 - 516 * q^81 + 78 * q^85 + 680 * q^86 + 148 * q^88 + 606 * q^92 - 1146 * q^93 - 360 * q^95 + 900 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.952438	−	1.64967i	−0.476219	−	0.824836i	0.523410	−	0.852081i	$-0.324660\pi$
$2$	−0.952438	−	1.64967i	−0.476219	−	0.824836i	−0.999629	+	0.0272455i	$0.991326\pi$
$3$	1.69506	−	2.47523i	0.565022	−	0.825076i
$3$	1.69506	−	2.47523i	0.565022	−	0.825076i
$4$	0.185723	−	0.321682i	0.0464308	−	0.0804206i
$5$			8.23162i			1.64632i	0.567807	+	0.823162i	$0.307792\pi$
$5$			8.23162i			1.64632i	−0.567807	+	0.823162i	$0.692208\pi$
$6$	−5.69776	−	0.438798i	−0.949626	−	0.0731330i
$7$		0			0
$7$		0			0
$8$	−8.32706			−1.04088
$9$	−3.25351	−	8.39135i	−0.361501	−	0.932372i
$10$	13.5795	−	7.84010i	1.35795	−	0.784010i
$11$	−11.9301			−1.08455			−0.542276	−	0.840201i	$-0.682437\pi$
$11$	−11.9301			−1.08455			−0.542276	+	0.840201i	$0.682437\pi$
$12$	−0.481424	−	1.00498i	−0.0401187	−	0.0837483i
$13$	1.37508	−	0.793905i	0.105776	−	0.0610696i	−0.446179	−	0.894944i	$-0.647216\pi$
$13$	1.37508	−	0.793905i	0.105776	−	0.0610696i	0.551955	+	0.833874i	$0.313882\pi$
$14$		0			0
$15$	20.3751	+	13.9531i	1.35834	+	0.930208i
$16$	7.18812	+	12.4502i	0.449258	+	0.778137i
$17$	−16.8893	+	9.75102i	−0.993486	+	0.573590i	−0.906315	−	0.422604i	$-0.861116\pi$
$17$	−16.8893	+	9.75102i	−0.993486	+	0.573590i	−0.0871718	+	0.996193i	$0.527783\pi$
$18$	−10.7442	+	13.3595i	−0.596900	+	0.742192i
$19$	−5.79843	−	3.34773i	−0.305181	−	0.176196i	0.339587	−	0.940575i	$-0.389713\pi$
$19$	−5.79843	−	3.34773i	−0.305181	−	0.176196i	−0.644768	+	0.764378i	$0.723046\pi$
$20$	2.64796	+	1.52880i	0.132398	+	0.0764401i
$21$		0			0
$22$	11.3626	+	19.6807i	0.516484	+	0.894576i
$23$	−28.1484			−1.22384			−0.611922	−	0.790918i	$-0.709604\pi$
$23$	−28.1484			−1.22384			−0.611922	+	0.790918i	$0.709604\pi$
$24$	−14.1149	+	20.6114i	−0.588121	+	0.858808i
$25$	−42.7595			−1.71038
$26$	−2.61936	−	1.51229i	−0.100745	−	0.0581650i
$27$	−26.2854	−	6.17070i	−0.973534	−	0.228544i
$28$		0			0
$29$	5.48400	−	9.49857i	0.189104	−	0.327537i	−0.755848	−	0.654747i	$-0.772775\pi$
$29$	5.48400	−	9.49857i	0.189104	−	0.327537i	0.944952	+	0.327210i	$0.106108\pi$
$30$	3.61202	−	46.9017i	0.120401	−	1.56339i
$31$	−27.4600	−	15.8540i	−0.885805	−	0.511420i	−0.0132371	−	0.999912i	$-0.504214\pi$
$31$	−27.4600	−	15.8540i	−0.885805	−	0.511420i	−0.872568	+	0.488493i	$0.837547\pi$
$32$	−2.96165	+	5.12973i	−0.0925516	+	0.160304i
$33$	−20.2222	+	29.5296i	−0.612795	+	0.894837i
$34$	32.1720	+	18.5745i	0.946234	+	0.546309i
$35$		0			0
$36$	−3.30360	−	0.511872i	−0.0917666	−	0.0142187i
$37$	3.44395	−	5.96510i	0.0930798	−	0.161219i	−0.815726	−	0.578439i	$-0.803662\pi$
$37$	3.44395	−	5.96510i	0.0930798	−	0.161219i	0.908806	+	0.417220i	$0.136995\pi$
$38$			12.7540i			0.335632i
$39$	0.365760	−	4.74937i	0.00937847	−	0.121779i
$40$		−	68.5452i		−	1.71363i
$41$	1.35364	−	0.781523i	0.0330155	−	0.0190615i	−0.483401	−	0.875399i	$-0.660599\pi$
$41$	1.35364	−	0.781523i	0.0330155	−	0.0190615i	0.516417	+	0.856337i	$0.327265\pi$
$42$		0			0
$43$	−32.5242	+	56.3336i	−0.756377	+	1.31008i	0.188310	+	0.982110i	$0.439699\pi$
$43$	−32.5242	+	56.3336i	−0.756377	+	1.31008i	−0.944687	+	0.327973i	$0.893634\pi$
$44$	−2.21569	+	3.83769i	−0.0503566	+	0.0872202i
$45$	69.0743	−	26.7816i	1.53499	−	0.595148i
$46$	26.8096	+	46.4357i	0.582818	+	1.00947i
$47$	47.8835	−	27.6455i	1.01880	−	0.588203i	0.105042	−	0.994468i	$-0.466502\pi$
$47$	47.8835	−	27.6455i	1.01880	−	0.588203i	0.913755	+	0.406265i	$0.133169\pi$
$48$	43.0014	+	3.31164i	0.895862	+	0.0689925i
$49$		0			0
$50$	40.7258	+	70.5391i	0.814516	+	1.41078i
$51$	−4.49240	+	58.3334i	−0.0880862	+	1.14379i
$52$		−	0.589787i		−	0.0113420i
$53$	16.9628	+	29.3805i	0.320053	+	0.554348i	0.980499	−	0.196526i	$-0.0629659\pi$
$53$	16.9628	+	29.3805i	0.320053	+	0.554348i	−0.660445	+	0.750874i	$0.729633\pi$
$54$	14.8556	+	49.2395i	0.275104	+	0.911842i
$55$		−	98.2037i		−	1.78552i
$56$		0			0
$57$	−18.1151	+	8.67783i	−0.317809	+	0.152243i
$58$	−20.8927			−0.360219
$59$	−5.69639	−	3.28881i	−0.0965490	−	0.0557426i	0.450948	−	0.892550i	$-0.351086\pi$
$59$	−5.69639	−	3.28881i	−0.0965490	−	0.0557426i	−0.547497	+	0.836808i	$0.684419\pi$
$60$	8.27261	−	3.96290i	0.137877	−	0.0660483i
$61$	65.9734	−	38.0898i	1.08153	−	0.624422i	0.150222	−	0.988652i	$-0.452001\pi$
$61$	65.9734	−	38.0898i	1.08153	−	0.624422i	0.931309	+	0.364230i	$0.118668\pi$
$62$			60.3999i			0.974192i
$63$		0			0
$64$	68.7881			1.07481
$65$	6.53512	+	11.3192i	0.100540	+	0.174141i
$66$	67.9746	+	5.23489i	1.02992	+	0.0793165i
$67$	11.8586	−	20.5396i	0.176993	−	0.306562i	−0.763856	−	0.645387i	$-0.776696\pi$
$67$	11.8586	−	20.5396i	0.176993	−	0.306562i	0.940849	+	0.338825i	$0.110030\pi$
$68$			7.24397i			0.106529i
$69$	−47.7134	+	69.6738i	−0.691499	+	1.00977i
$70$		0			0
$71$	−14.0551			−0.197960			−0.0989798	−	0.995089i	$-0.531558\pi$
$71$	−14.0551			−0.197960			−0.0989798	+	0.995089i	$0.531558\pi$
$72$	27.0922	+	69.8753i	0.376280	+	0.970490i
$73$	34.8385	−	20.1140i	0.477240	−	0.275535i	−0.242025	−	0.970270i	$-0.577812\pi$
$73$	34.8385	−	20.1140i	0.477240	−	0.275535i	0.719266	+	0.694735i	$0.244478\pi$
$74$	−13.1206			−0.177305
$75$	−72.4801	+	105.840i	−0.966402	+	1.41119i
$76$	−2.15381	+	1.24350i	−0.0283396	+	0.0163619i
$77$		0			0
$78$	−8.18326	+	3.92009i	−0.104914	+	0.0502576i
$79$	−31.8645	−	55.1909i	−0.403348	−	0.698618i	0.590780	−	0.806833i	$-0.298820\pi$
$79$	−31.8645	−	55.1909i	−0.403348	−	0.698618i	−0.994128	+	0.108214i	$0.965487\pi$
$80$	−102.485	+	59.1698i	−1.28106	+	0.739623i
$81$	−59.8293	+	54.6026i	−0.738634	+	0.674107i
$82$	−2.57851	−	1.48870i	−0.0314453	−	0.0181549i
$83$	1.94261	+	1.12157i	0.0234050	+	0.0135129i	0.511657	−	0.859190i	$-0.329032\pi$
$83$	1.94261	+	1.12157i	0.0234050	+	0.0135129i	−0.488252	+	0.872703i	$0.662365\pi$
$84$		0			0
$85$	−80.2667	−	139.026i	−0.944314	−	1.63560i
$86$	123.909			1.44080
$87$	−14.2154	−	29.6749i	−0.163395	−	0.341090i
$88$	99.3424			1.12889
$89$	−50.5972	−	29.2123i	−0.568507	−	0.328228i	0.188046	−	0.982160i	$-0.439785\pi$
$89$	−50.5972	−	29.2123i	−0.568507	−	0.328228i	−0.756553	+	0.653932i	$0.773118\pi$
$90$	−109.970	−	88.4421i	−1.22189	−	0.982690i
$91$		0			0
$92$	−5.22782	+	9.05485i	−0.0568241	+	0.0984223i
$93$	−85.7887	+	41.0961i	−0.922459	+	0.441893i
$94$	−91.2121	−	52.6613i	−0.970342	−	0.560227i
$95$	27.5572	−	47.7305i	0.290076	−	0.502426i
$96$	7.67706	+	16.0260i	0.0799694	+	0.166937i
$97$	111.760	+	64.5247i	1.15217	+	0.665203i	0.949414	−	0.314027i	$-0.101678\pi$
$97$	111.760	+	64.5247i	1.15217	+	0.665203i	0.202751	+	0.979230i	$0.435012\pi$
$98$		0			0
$99$	38.8146	+	100.109i	0.392066	+	1.01120i
$100$	−7.94144	+	13.7550i	−0.0794144	+	0.137550i
$101$			194.507i			1.92581i	0.269844	+	0.962904i	$0.413028\pi$
$101$			194.507i			1.92581i	−0.269844	+	0.962904i	$0.586972\pi$
$102$	100.510	−	48.1480i	0.985389	−	0.472039i
$103$		−	95.2765i		−	0.925015i	−0.886615	−	0.462507i	$-0.846950\pi$
$103$		−	95.2765i		−	0.925015i	0.886615	−	0.462507i	$-0.153050\pi$
$104$	−11.4504	+	6.61090i	−0.110100	+	0.0635663i
$105$		0			0
$106$	32.3121	−	55.9662i	0.304831	−	0.527983i
$107$	5.02536	−	8.70417i	0.0469660	−	0.0813474i	−0.841587	−	0.540122i	$-0.818378\pi$
$107$	5.02536	−	8.70417i	0.0469660	−	0.0813474i	0.888553	+	0.458775i	$0.151711\pi$
$108$	−6.86682	+	7.30950i	−0.0635816	+	0.0676806i
$109$	−35.4984	−	61.4850i	−0.325673	−	0.564082i	0.655975	−	0.754782i	$-0.272258\pi$
$109$	−35.4984	−	61.4850i	−0.325673	−	0.564082i	−0.981648	+	0.190700i	$0.938924\pi$
$110$	−162.004	+	93.5329i	−1.47276	+	0.850299i
$111$	−8.92726	−	18.6358i	−0.0804258	−	0.167890i
$112$		0			0
$113$	−27.0133	−	46.7883i	−0.239055	−	0.414056i	0.721388	−	0.692531i	$-0.243504\pi$
$113$	−27.0133	−	46.7883i	−0.239055	−	0.414056i	−0.960444	+	0.278475i	$0.910171\pi$
$114$	31.5691	+	21.6189i	0.276922	+	0.189639i
$115$		−	231.707i		−	2.01484i
$116$	−2.03701	−	3.52821i	−0.0175605	−	0.0304156i
$117$	−11.1358	−	8.95582i	−0.0951776	−	0.0765455i
$118$			12.5296i			0.106183i
$119$		0			0
$120$	−169.665	−	116.189i	−1.41388	−	0.968238i
$121$	21.3264			0.176251
$122$	−125.671	−	72.5563i	−1.03009	−	0.594724i
$123$	0.360056	−	4.67529i	0.00292728	−	0.0380105i
$124$	−10.1999	+	5.88892i	−0.0822573	+	0.0474913i
$125$		−	146.189i		−	1.16952i
$126$		0			0
$127$	50.2162			0.395403			0.197701	−	0.980262i	$-0.436652\pi$
$127$	50.2162			0.395403			0.197701	+	0.980262i	$0.436652\pi$
$128$	−53.6698	−	92.9589i	−0.419296	−	0.726241i
$129$	84.3078	+	175.994i	0.653549	+	1.36429i
$130$	12.4486	−	21.5616i	0.0957584	−	0.165858i
$131$		−	45.7188i		−	0.348999i	−0.984657	−	0.174499i	$-0.944169\pi$
$131$		−	45.7188i		−	0.348999i	0.984657	−	0.174499i	$-0.0558307\pi$
$132$	5.74342	+	11.9895i	0.0435107	+	0.0908293i
$133$		0			0
$134$	−45.1782			−0.337151
$135$	50.7948	−	216.371i	0.376258	−	1.60275i
$136$	140.638	−	81.1974i	1.03410	−	0.597040i
$137$	31.4485			0.229551			0.114776	−	0.993391i	$-0.463385\pi$
$137$	31.4485			0.229551			0.114776	+	0.993391i	$0.463385\pi$
$138$	160.383	+	12.3515i	1.16220	+	0.0895035i
$139$	−103.269	+	59.6226i	−0.742945	+	0.428939i	−0.823139	−	0.567840i	$-0.807779\pi$
$139$	−103.269	+	59.6226i	−0.742945	+	0.428939i	0.0801942	+	0.996779i	$0.474446\pi$
$140$		0			0
$141$	12.7366	−	165.384i	0.0903304	−	1.17293i
$142$	13.3866	+	23.1863i	0.0942721	+	0.163284i
$143$	−16.4048	+	9.47133i	−0.114719	+	0.0662331i
$144$	81.0872	−	100.825i	0.563106	−	0.700172i
$145$	78.1886	+	45.1422i	0.539232	+	0.311326i
$146$	−66.3631	−	38.3148i	−0.454542	−	0.262430i
$147$		0			0
$148$	−1.27924	−	2.21572i	−0.00864354	−	0.0149711i
$149$	60.1447			0.403656			0.201828	−	0.979421i	$-0.435312\pi$
$149$	60.1447			0.403656			0.201828	+	0.979421i	$0.435312\pi$
$150$	243.633	+	18.7628i	1.62422	+	0.125085i
$151$	−207.625			−1.37500			−0.687499	−	0.726185i	$-0.741292\pi$
$151$	−207.625			−1.37500			−0.687499	+	0.726185i	$0.741292\pi$
$152$	48.2839	+	27.8767i	0.317657	+	0.183400i
$153$	136.774	+	109.999i	0.893945	+	0.718945i
$154$		0			0
$155$	130.504	−	226.040i	0.841962	−	1.45832i
$156$	−1.45986	−	0.999726i	−0.00935805	−	0.00640850i
$157$	−91.7198	−	52.9544i	−0.584202	−	0.337289i	0.178599	−	0.983922i	$-0.442843\pi$
$157$	−91.7198	−	52.9544i	−0.584202	−	0.337289i	−0.762802	+	0.646632i	$0.776177\pi$
$158$	−60.6978	+	105.132i	−0.384164	+	0.665391i
$159$	101.476	+	7.81495i	0.638217	+	0.0491506i
$160$	−42.2259	−	24.3792i	−0.263912	−	0.152370i
$161$		0			0
$162$	147.060	+	46.6931i	0.907779	+	0.288229i
$163$	−28.1435	+	48.7460i	−0.172660	+	0.299055i	−0.939349	−	0.342963i	$-0.888569\pi$
$163$	−28.1435	+	48.7460i	−0.172660	+	0.299055i	0.766689	+	0.642018i	$0.221903\pi$
$164$		−	0.580588i		−	0.00354017i
$165$	−243.077	−	166.462i	−1.47319	−	1.00886i
$166$		−	4.27289i		−	0.0257403i
$167$	147.343	−	85.0687i	0.882296	−	0.509394i	0.0108810	−	0.999941i	$-0.496536\pi$
$167$	147.343	−	85.0687i	0.882296	−	0.509394i	0.871415	+	0.490547i	$0.163203\pi$
$168$		0			0
$169$	−83.2394	+	144.175i	−0.492541	+	0.853106i
$170$	−152.898	+	264.827i	−0.899401	+	1.55781i
$171$	−9.22667	+	59.5485i	−0.0539572	+	0.348237i
$172$	12.0810	+	20.9249i	0.0702384	+	0.121656i
$173$	−82.8923	+	47.8579i	−0.479146	+	0.276635i	−0.720061	−	0.693911i	$-0.755886\pi$
$173$	−82.8923	+	47.8579i	−0.479146	+	0.276635i	0.240914	+	0.970546i	$0.422553\pi$
$174$	−35.4145	+	51.7142i	−0.203532	+	0.297208i
$175$		0			0
$176$	−85.7547	−	148.532i	−0.487243	−	0.843929i
$177$	−17.7963	+	8.52512i	−0.100544	+	0.0481645i
$178$			111.292i			0.625233i
$179$	−143.028	−	247.732i	−0.799040	−	1.38398i	−0.920242	−	0.391351i	$-0.872008\pi$
$179$	−143.028	−	247.732i	−0.799040	−	1.38398i	0.121201	−	0.992628i	$-0.461325\pi$
$180$	4.21354	−	27.1940i	0.0234085	−	0.151078i
$181$			246.704i			1.36300i	0.731816	+	0.681502i	$0.238673\pi$
$181$			246.704i			1.36300i	−0.731816	+	0.681502i	$0.761327\pi$
$182$		0			0
$183$	17.5484	−	227.864i	0.0958926	−	1.24516i
$184$	234.394			1.27388
$185$	49.1024	+	28.3493i	0.265418	+	0.153239i
$186$	149.503	+	102.382i	0.803782	+	0.550439i
$187$	201.490	−	116.330i	1.07749	−	0.622087i
$188$		−	20.5377i		−	0.109243i
$189$		0			0
$190$	−104.986			−0.552558
$191$	−135.755	−	235.134i	−0.710758	−	1.23107i	−0.964573	−	0.263816i	$-0.915019\pi$
$191$	−135.755	−	235.134i	−0.710758	−	1.23107i	0.253815	−	0.967253i	$-0.418314\pi$
$192$	116.600	−	170.266i	0.607293	−	0.886804i
$193$	96.3189	−	166.829i	0.499062	−	0.864400i	−0.500938	−	0.865483i	$-0.667011\pi$
$193$	96.3189	−	166.829i	0.499062	−	0.864400i	0.999999	+	0.00108311i	$0.000344764\pi$
$194$		−	245.823i		−	1.26713i
$195$	39.0950	+	3.01080i	0.200487	+	0.0154400i
$196$		0			0
$197$	−163.463			−0.829763			−0.414882	−	0.909875i	$-0.636177\pi$
$197$	−163.463			−0.829763			−0.414882	+	0.909875i	$0.636177\pi$
$198$	128.179	−	159.379i	0.647368	−	0.804945i
$199$	−257.404	+	148.612i	−1.29349	+	0.746796i	−0.979271	−	0.202555i	$-0.935076\pi$
$199$	−257.404	+	148.612i	−1.29349	+	0.746796i	−0.314218	+	0.949351i	$0.601742\pi$
$200$	356.061			1.78031
$201$	−30.7392	−	64.1687i	−0.152932	−	0.319247i
$202$	320.872	−	185.255i	1.58847	−	0.917106i
$203$		0			0
$204$	17.9305	+	12.2790i	0.0878945	+	0.0601912i
$205$	6.43319	+	11.1426i	0.0313814	+	0.0543542i
$206$	−157.175	+	90.7450i	−0.762985	+	0.440510i
$207$	91.5812	+	236.203i	0.442421	+	1.14108i
$208$	19.7685	+	11.4134i	0.0950410	+	0.0548720i
$209$	69.1757	+	39.9386i	0.330984	+	0.191094i
$210$		0			0
$211$	−43.4986	−	75.3418i	−0.206155	−	0.357070i	0.744345	−	0.667795i	$-0.232762\pi$
$211$	−43.4986	−	75.3418i	−0.206155	−	0.357070i	−0.950500	+	0.310725i	$0.899428\pi$
$212$	12.6016			0.0594413
$213$	−23.8244	+	34.7897i	−0.111851	+	0.163332i
$214$	−19.1454			−0.0894643
$215$	−463.716	−	267.727i	−2.15682	−	1.24524i
$216$	218.880	+	51.3838i	1.01333	+	0.237888i
$217$		0			0
$218$	−67.6200	+	117.121i	−0.310183	+	0.537253i
$219$	9.26675	−	120.328i	0.0423139	−	0.549443i
$220$	−31.5904	−	18.2387i	−0.143593	−	0.0829032i
$221$	−15.4828	+	26.8169i	−0.0700578	+	0.121344i
$222$	−22.2403	+	32.4765i	−0.100181	+	0.146291i
$223$	−318.293	−	183.766i	−1.42732	−	0.824065i	−0.430413	−	0.902632i	$-0.641632\pi$
$223$	−318.293	−	183.766i	−1.42732	−	0.824065i	−0.996909	+	0.0785674i	$0.974965\pi$
$224$		0			0
$225$	139.118	+	358.810i	0.618304	+	1.59471i
$226$	−51.4569	+	89.1260i	−0.227685	+	0.394363i
$227$		−	167.443i		−	0.737633i	−0.929502	−	0.368817i	$-0.879763\pi$
$227$		−	167.443i		−	0.737633i	0.929502	−	0.368817i	$-0.120237\pi$
$228$	−0.572894	+	7.43898i	−0.00251269	+	0.0326271i
$229$			437.899i			1.91222i	0.293001	+	0.956112i	$0.405346\pi$
$229$			437.899i			1.91222i	−0.293001	+	0.956112i	$0.594654\pi$
$230$	−382.241	+	220.687i	−1.66192	+	0.959507i
$231$		0			0
$232$	−45.6657	+	79.0952i	−0.196835	+	0.340928i
$233$	−113.790	+	197.091i	−0.488370	+	0.845882i	−0.999911	−	0.0133773i	$-0.995742\pi$
$233$	−113.790	+	197.091i	−0.488370	+	0.845882i	0.511540	+	0.859259i	$0.329075\pi$
$234$	−4.16803	+	26.9002i	−0.0178121	+	0.114958i
$235$	227.568	+	394.159i	0.968373	+	1.67727i
$236$	−2.11591	+	1.22162i	−0.00896570	+	0.00517635i
$237$	−190.622	−	14.6803i	−0.804313	−	0.0619421i
$238$		0			0
$239$	177.645	+	307.690i	0.743285	+	1.28741i	0.950992	+	0.309216i	$0.100067\pi$
$239$	177.645	+	307.690i	0.743285	+	1.28741i	−0.207707	+	0.978191i	$0.566600\pi$
$240$	−27.2602	+	353.971i	−0.113584	+	1.47488i
$241$		−	255.935i		−	1.06197i	−0.847381	−	0.530985i	$-0.821822\pi$
$241$		−	255.935i		−	1.06197i	0.847381	−	0.530985i	$-0.178178\pi$
$242$	−20.3120	−	35.1815i	−0.0839341	−	0.145378i
$243$	33.7394	+	240.646i	0.138845	+	0.990314i
$244$		−	28.2966i		−	0.115970i
$245$		0			0
$246$	−8.05563	+	3.85895i	−0.0327464	+	0.0156868i
$247$	−10.6311			−0.0430409
$248$	228.661	+	132.017i	0.922020	+	0.532328i
$249$	6.06899	−	2.90728i	0.0243734	−	0.0116758i
$250$	−241.164	+	139.236i	−0.964658	+	0.556945i
$251$		−	200.521i		−	0.798889i	−0.916757	−	0.399444i	$-0.869203\pi$
$251$		−	200.521i		−	0.798889i	0.916757	−	0.399444i	$-0.130797\pi$
$252$		0			0
$253$	335.813			1.32732
$254$	−47.8278	−	82.8402i	−0.188298	−	0.326142i
$255$	−480.178	−	36.9797i	−1.88305	−	0.145018i
$256$	35.3419	−	61.2139i	0.138054	−	0.239117i
$257$			151.654i			0.590092i	0.955483	+	0.295046i	$0.0953349\pi$
$257$			151.654i			0.590092i	−0.955483	+	0.295046i	$0.904665\pi$
$258$	210.034	−	306.703i	0.814085	−	1.18877i
$259$		0			0
$260$	4.85490			0.0186727
$261$	−97.5481	−	15.1145i	−0.373747	−	0.0579099i
$262$	−75.4210	+	43.5444i	−0.287867	+	0.166200i
$263$	−356.262			−1.35461			−0.677305	−	0.735702i	$-0.736852\pi$
$263$	−356.262			−1.35461			−0.677305	+	0.735702i	$0.736852\pi$
$264$	168.392	−	245.895i	0.637848	−	0.931421i
$265$	−241.849	+	139.631i	−0.912637	+	0.526911i
$266$		0			0
$267$	−158.073	+	75.7228i	−0.592032	+	0.283606i
$268$	−4.40482	−	7.62938i	−0.0164359	−	0.0284678i
$269$	172.949	−	99.8522i	0.642933	−	0.371198i	−0.142810	−	0.989750i	$-0.545614\pi$
$269$	172.949	−	99.8522i	0.642933	−	0.371198i	0.785744	+	0.618552i	$0.212281\pi$
$270$	−405.320	+	122.286i	−1.50119	+	0.452910i
$271$	131.489	+	75.9155i	0.485201	+	0.280131i	0.722581	−	0.691286i	$-0.242955\pi$
$271$	131.489	+	75.9155i	0.485201	+	0.280131i	−0.237380	+	0.971417i	$0.576289\pi$
$272$	−242.804	−	140.183i	−0.892663	−	0.515379i
$273$		0			0
$274$	−29.9528	−	51.8797i	−0.109317	−	0.189342i
$275$	510.123			1.85499
$276$	13.5513	+	28.2886i	0.0490990	+	0.102495i
$277$	−61.4847			−0.221966			−0.110983	−	0.993822i	$-0.535400\pi$
$277$	−61.4847			−0.221966			−0.110983	+	0.993822i	$0.535400\pi$
$278$	196.715	+	113.574i	0.707609	+	0.408538i
$279$	−43.6953	+	282.007i	−0.156614	+	1.01078i
$280$		0			0
$281$	−60.9222	+	105.520i	−0.216805	+	0.375517i	−0.953829	−	0.300349i	$-0.902897\pi$
$281$	−60.9222	+	105.520i	−0.216805	+	0.375517i	0.737024	+	0.675866i	$0.236230\pi$
$282$	−284.959	+	136.506i	−1.01049	+	0.484065i
$283$	440.287	+	254.200i	1.55578	+	0.898232i	0.997653	+	0.0684790i	$0.0218146\pi$
$283$	440.287	+	254.200i	1.55578	+	0.898232i	0.558131	+	0.829753i	$0.311519\pi$
$284$	−2.61037	+	4.52128i	−0.00919143	+	0.0159200i
$285$	−71.4326	−	149.117i	−0.250641	−	0.523216i
$286$	31.2492	+	18.0417i	0.109263	+	0.0630829i
$287$		0			0
$288$	52.6811	+	8.16261i	0.182920	+	0.0283424i
$289$	45.6650	−	79.0940i	0.158010	−	0.273682i
$290$		−	171.981i		−	0.593037i
$291$	349.154	−	167.258i	1.19984	−	0.574770i
$292$		−	14.9426i		−	0.0511732i
$293$	383.226	−	221.256i	1.30794	−	0.755139i	0.326187	−	0.945305i	$-0.394236\pi$
$293$	383.226	−	221.256i	1.30794	−	0.755139i	0.981752	+	0.190166i	$0.0609028\pi$
$294$		0			0
$295$	27.0722	−	46.8905i	0.0917703	−	0.158951i
$296$	−28.6780	+	49.6718i	−0.0968852	+	0.167810i
$297$	313.586	+	73.6168i	1.05585	+	0.247868i
$298$	−57.2841	−	99.2190i	−0.192229	−	0.332950i
$299$	−38.7064	+	22.3472i	−0.129453	+	0.0747397i
$300$	20.5854	+	42.9724i	0.0686181	+	0.143241i
$301$		0			0
$302$	197.750	+	342.513i	0.654801	+	1.13415i
$303$	481.448	+	329.701i	1.58894	+	1.08812i
$304$		−	96.2554i		−	0.316630i
$305$	313.540	+	543.068i	1.02800	+	1.78055i
$306$	51.1932	−	330.398i	0.167298	−	1.07973i
$307$			378.900i			1.23420i	0.786884	+	0.617101i	$0.211693\pi$
$307$			378.900i			1.23420i	−0.786884	+	0.617101i	$0.788307\pi$
$308$		0			0
$309$	−235.831	−	161.500i	−0.763208	−	0.522653i
$310$	−497.189			−1.60383
$311$	66.5780	+	38.4388i	0.214077	+	0.123597i	0.603205	−	0.797586i	$-0.293890\pi$
$311$	66.5780	+	38.4388i	0.214077	+	0.123597i	−0.389128	+	0.921184i	$0.627224\pi$
$312$	−3.04571	+	39.5483i	−0.00976189	+	0.126757i
$313$	124.343	−	71.7896i	0.397263	−	0.229360i	−0.288040	−	0.957619i	$-0.593003\pi$
$313$	124.343	−	71.7896i	0.397263	−	0.229360i	0.685302	+	0.728259i	$0.259670\pi$
$314$			201.743i			0.642495i
$315$		0			0
$316$	−23.6719			−0.0749110
$317$	−47.3918	−	82.0850i	−0.149501	−	0.258943i	0.781542	−	0.623852i	$-0.214433\pi$
$317$	−47.3918	−	82.0850i	−0.149501	−	0.258943i	−0.931043	+	0.364909i	$0.881100\pi$
$318$	−83.7579	−	174.846i	−0.263390	−	0.549830i
$319$	−65.4245	+	113.319i	−0.205093	+	0.355231i
$320$			566.237i			1.76949i
$321$	−13.0265	−	27.1930i	−0.0405810	−	0.0847135i
$322$		0			0
$323$	130.575			0.404257
$324$	6.45299	+	29.3870i	0.0199167	+	0.0907007i
$325$	−58.7979	+	33.9470i	−0.180917	+	0.104452i
$326$	107.220			0.328895
$327$	−212.361	−	16.3545i	−0.649423	−	0.0500136i
$328$	−11.2718	+	6.50779i	−0.0343653	+	0.0198408i
$329$		0			0
$330$	−43.0916	+	559.541i	−0.130581	+	1.69558i
$331$	−234.166	−	405.588i	−0.707451	−	1.22534i	−0.965800	−	0.259289i	$-0.916512\pi$
$331$	−234.166	−	405.588i	−0.707451	−	1.22534i	0.258349	−	0.966052i	$-0.416822\pi$
$332$	0.721576	−	0.416602i	0.00217342	−	0.00125483i
$333$	−61.2602	−	9.49188i	−0.183964	−	0.0285041i
$334$	−280.671	−	162.045i	−0.840332	−	0.485166i
$335$	169.074	+	97.6151i	0.504700	+	0.291388i
$336$		0			0
$337$	165.656	+	286.924i	0.491560	+	0.851406i	0.999953	−	0.00971895i	$-0.00309369\pi$
$337$	165.656	+	286.924i	0.491560	+	0.851406i	−0.508393	+	0.861125i	$0.669760\pi$
$338$	317.122			0.938230
$339$	−161.601	−	12.4453i	−0.476699	−	0.0367118i
$340$	−59.6296			−0.175381
$341$	327.599	+	189.139i	0.960701	+	0.554661i
$342$	107.023	−	41.4953i	0.312934	−	0.121331i
$343$		0			0
$344$	270.831	−	469.093i	0.787300	−	1.36364i
$345$	−573.528	−	392.759i	−1.66240	−	1.13843i
$346$	157.900	+	91.1634i	0.456357	+	0.263478i
$347$	−186.025	+	322.204i	−0.536094	+	0.928542i	0.463016	+	0.886350i	$0.346767\pi$
$347$	−186.025	+	322.204i	−0.536094	+	0.928542i	−0.999110	+	0.0421915i	$0.986566\pi$
$348$	−12.1860	−	0.938474i	−0.0350173	−	0.00269676i
$349$	−6.77897	−	3.91384i	−0.0194240	−	0.0112144i	0.490257	−	0.871578i	$-0.336903\pi$
$349$	−6.77897	−	3.91384i	−0.0194240	−	0.0112144i	−0.509681	+	0.860364i	$0.670236\pi$
$350$		0			0
$351$	−41.0436	+	12.3829i	−0.116933	+	0.0352789i
$352$	35.3327	−	61.1980i	0.100377	−	0.173858i
$353$		−	78.2312i		−	0.221618i	−0.993842	−	0.110809i	$-0.964656\pi$
$353$		−	78.2312i		−	0.221618i	0.993842	−	0.110809i	$-0.0353442\pi$
$354$	31.0135	+	21.2384i	0.0876089	+	0.0599956i
$355$		−	115.696i		−	0.325905i
$356$	−18.7941	+	10.8508i	−0.0527925	+	0.0304798i
$357$		0			0
$358$	−272.451	+	471.899i	−0.761036	+	1.31815i
$359$	132.717	−	229.872i	0.369685	−	0.640313i	−0.619831	−	0.784735i	$-0.712799\pi$
$359$	132.717	−	229.872i	0.369685	−	0.640313i	0.989516	+	0.144422i	$0.0461323\pi$
$360$	−575.186	+	223.012i	−1.59774	+	0.619479i
$361$	−158.085	−	273.812i	−0.437910	−	0.758482i
$362$	406.980	−	234.970i	1.12425	−	0.649089i
$363$	36.1496	−	52.7876i	0.0995856	−	0.145420i
$364$		0			0
$365$	165.571	+	286.777i	0.453619	+	0.785692i
$366$	−392.614	+	188.077i	−1.07272	+	0.513872i
$367$			440.261i			1.19962i	0.800142	+	0.599811i	$0.204757\pi$
$367$			440.261i			1.19962i	−0.800142	+	0.599811i	$0.795243\pi$
$368$	−202.334	−	350.453i	−0.549822	−	0.952319i
$369$	−10.9621	−	8.81614i	−0.0297076	−	0.0238920i
$370$		−	108.004i		−	0.291902i
$371$		0			0
$372$	−2.71309	+	35.2292i	−0.00729324	+	0.0947022i
$373$	150.712			0.404053			0.202026	−	0.979380i	$-0.435247\pi$
$373$	150.712			0.404053			0.202026	+	0.979380i	$0.435247\pi$
$374$	−383.814	−	221.595i	−1.02624	−	0.592500i
$375$	−361.852	−	247.801i	−0.964939	−	0.660801i
$376$	−398.729	+	230.206i	−1.06045	+	0.612251i
$377$		−	17.4151i		−	0.0461939i
$378$		0			0
$379$	313.660			0.827599			0.413800	−	0.910368i	$-0.364201\pi$
$379$	313.660			0.827599			0.413800	+	0.910368i	$0.364201\pi$
$380$	−10.2360	−	17.7293i	−0.0269369	−	0.0466561i
$381$	85.1197	−	124.296i	0.223411	−	0.326237i
$382$	−258.596	+	447.901i	−0.676953	+	1.17252i
$383$		−	647.602i		−	1.69087i	−0.534081	−	0.845434i	$-0.679342\pi$
$383$		−	647.602i		−	1.69087i	0.534081	−	0.845434i	$-0.320658\pi$
$384$	−321.068	−	24.7262i	−0.836115	−	0.0643913i
$385$		0			0
$386$	−366.951			−0.950651
$387$	578.532	+	89.6400i	1.49492	+	0.231628i
$388$	41.5129	−	23.9675i	0.106992	−	0.0617718i
$389$	−203.760			−0.523806			−0.261903	−	0.965094i	$-0.584350\pi$
$389$	−203.760			−0.523806			−0.261903	+	0.965094i	$0.584350\pi$
$390$	−32.2687	−	67.3614i	−0.0827403	−	0.172722i
$391$	475.407	−	274.476i	1.21587	−	0.701985i
$392$		0			0
$393$	−113.165	−	77.4964i	−0.287950	−	0.197192i
$394$	155.689	+	269.661i	0.395149	+	0.684418i
$395$	454.310	−	262.296i	1.15015	−	0.664040i
$396$	39.4121	+	6.10667i	0.0995256	+	0.0154209i
$397$	−245.589	−	141.791i	−0.618613	−	0.357156i	0.157716	−	0.987485i	$-0.449587\pi$
$397$	−245.589	−	141.791i	−0.618613	−	0.357156i	−0.776329	+	0.630328i	$0.782920\pi$
$398$	490.323	+	283.088i	1.23197	+	0.711277i
$399$		0			0
$400$	−307.360	−	532.364i	−0.768401	−	1.33091i
$401$	−624.239			−1.55671			−0.778353	−	0.627827i	$-0.783945\pi$
$401$	−624.239			−1.55671			−0.778353	+	0.627827i	$0.783945\pi$
$402$	−76.5800	+	111.826i	−0.190497	+	0.278175i
$403$	−50.3463			−0.124929
$404$	62.5693	+	36.1244i	0.154875	+	0.0894169i
$405$	−449.468	−	492.492i	−1.10980	−	1.21603i
$406$		0			0
$407$	−41.0866	+	71.1640i	−0.100950	+	0.174850i
$408$	37.4085	−	485.746i	0.0916875	−	1.19055i
$409$	−25.9439	−	14.9787i	−0.0634326	−	0.0366228i	0.467948	−	0.883756i	$-0.344993\pi$
$409$	−25.9439	−	14.9787i	−0.0634326	−	0.0366228i	−0.531381	+	0.847133i	$0.678327\pi$
$410$	12.2544	−	21.2253i	0.0298889	−	0.0517691i
$411$	53.3073	−	77.8423i	0.129701	−	0.189397i
$412$	−30.6488	−	17.6951i	−0.0743902	−	0.0429492i
$413$		0			0
$414$	302.432	−	376.048i	0.730513	−	0.908328i
$415$	−9.23231	+	15.9908i	−0.0222465	+	0.0385321i
$416$			9.40507i			0.0226083i
$417$	−27.4687	+	356.679i	−0.0658723	+	0.855346i
$418$		−	152.156i		−	0.364010i
$419$	−66.7511	+	38.5388i	−0.159310	+	0.0919779i	−0.577536	−	0.816365i	$-0.695986\pi$
$419$	−66.7511	+	38.5388i	−0.159310	+	0.0919779i	0.418225	+	0.908343i	$0.362652\pi$
$420$		0			0
$421$	296.758	−	514.000i	0.704888	−	1.22090i	−0.261844	−	0.965110i	$-0.584330\pi$
$421$	296.758	−	514.000i	0.704888	−	1.22090i	0.966732	−	0.255792i	$-0.0823362\pi$
$422$	−82.8595	+	143.517i	−0.196349	+	0.340087i
$423$	−387.773	−	311.862i	−0.916720	−	0.737262i
$424$	−141.251	−	244.653i	−0.333138	−	0.577012i
$425$	722.177	−	416.949i	1.69924	−	0.981056i
$426$	80.0827	+	6.16736i	0.187988	+	0.0144774i
$427$		0			0
$428$	−1.86665	−	3.23314i	−0.00436134	−	0.00755406i
$429$	−4.36354	+	56.6602i	−0.0101714	+	0.132075i
$430$			1019.97i			2.37203i
$431$	−210.140	−	363.973i	−0.487564	−	0.844485i	0.512334	−	0.858786i	$-0.328781\pi$
$431$	−210.140	−	363.973i	−0.487564	−	0.844485i	−0.999898	+	0.0143010i	$0.995448\pi$
$432$	−112.116	−	371.614i	−0.259529	−	0.860218i
$433$		−	686.056i		−	1.58442i	−0.610246	−	0.792212i	$-0.708929\pi$
$433$		−	686.056i		−	1.58442i	0.610246	−	0.792212i	$-0.291071\pi$
$434$		0			0
$435$	244.272	−	117.016i	0.561545	−	0.269002i
$436$	−26.3715			−0.0604851
$437$	163.217	+	94.2333i	0.373494	+	0.215637i
$438$	−207.328	+	99.3178i	−0.473351	+	0.226753i
$439$	−71.8544	+	41.4852i	−0.163677	+	0.0944992i	−0.579601	−	0.814900i	$-0.696792\pi$
$439$	−71.8544	+	41.4852i	−0.163677	+	0.0944992i	0.415924	+	0.909399i	$0.363458\pi$
$440$			817.748i			1.85852i
$441$		0			0
$442$	58.9855			0.133451
$443$	−131.882	−	228.427i	−0.297703	−	0.515636i	0.677907	−	0.735147i	$-0.262887\pi$
$443$	−131.882	−	228.427i	−0.297703	−	0.515636i	−0.975610	+	0.219511i	$0.929554\pi$
$444$	−7.65281	−	0.589361i	−0.0172361	−	0.00132739i
$445$	240.464	−	416.496i	0.540369	−	0.935947i
$446$			700.105i			1.56974i
$447$	101.949	−	148.872i	0.228074	−	0.333047i
$448$		0			0
$449$	−781.684			−1.74095			−0.870473	−	0.492217i	$-0.836187\pi$
$449$	−781.684			−1.74095			−0.870473	+	0.492217i	$0.836187\pi$
$450$	459.416	−	571.244i	1.02093	−	1.26943i
$451$	−16.1490	+	9.32361i	−0.0358070	+	0.0206732i
$452$	−20.0680			−0.0443982
$453$	−351.938	+	513.919i	−0.776904	+	1.13448i
$454$	−276.225	+	159.479i	−0.608426	+	0.351275i
$455$		0			0
$456$	150.846	−	72.2609i	0.330802	−	0.158467i
$457$	427.972	+	741.269i	0.936481	+	1.62203i	0.771971	+	0.635657i	$0.219271\pi$
$457$	427.972	+	741.269i	0.936481	+	1.62203i	0.164510	+	0.986375i	$0.447396\pi$
$458$	722.390	−	417.072i	1.57727	−	0.910638i
$459$	504.112	−	152.091i	1.09828	−	0.331353i
$460$	−74.5361	−	43.0334i	−0.162035	−	0.0935509i
$461$	−381.518	−	220.269i	−0.827587	−	0.477808i	0.0254388	−	0.999676i	$-0.491902\pi$
$461$	−381.518	−	220.269i	−0.827587	−	0.477808i	−0.853026	+	0.521869i	$0.825235\pi$
$462$		0			0
$463$	117.785	+	204.010i	0.254396	+	0.440626i	0.964731	−	0.263237i	$-0.0847901\pi$
$463$	117.785	+	204.010i	0.254396	+	0.440626i	−0.710336	+	0.703863i	$0.751457\pi$
$464$	157.679			0.339825
$465$	−338.287	−	706.180i	−0.727499	−	1.51867i
$466$	433.513			0.930285
$467$	804.753	+	464.624i	1.72324	+	0.994913i	0.911988	+	0.410217i	$0.134547\pi$
$467$	804.753	+	464.624i	1.72324	+	0.994913i	0.811252	+	0.584696i	$0.198786\pi$
$468$	−4.94910	+	1.91888i	−0.0105750	+	0.00410016i
$469$		0			0
$470$	433.488	−	750.823i	0.922315	−	1.59750i
$471$	−286.545	+	137.266i	−0.608376	+	0.291436i
$472$	47.4342	+	27.3862i	0.100496	+	0.0580215i
$473$	388.016	−	672.063i	0.820329	−	1.42085i
$474$	157.338	+	328.446i	0.331937	+	0.692924i
$475$	247.938	+	143.147i	0.521975	+	0.301362i
$476$		0			0
$477$	191.353	−	237.931i	0.401159	−	0.498806i
$478$	338.392	−	586.112i	0.707933	−	1.22618i
$479$			26.6452i			0.0556267i	0.999613	+	0.0278134i	$0.00885441\pi$
$479$			26.6452i			0.0556267i	−0.999613	+	0.0278134i	$0.991146\pi$
$480$	−131.920	+	63.1946i	−0.274833	+	0.131655i
$481$		−	10.9367i		−	0.0227374i
$482$	−422.208	+	243.762i	−0.875951	+	0.505730i
$483$		0			0
$484$	3.96080	−	6.86031i	0.00818348	−	0.0141742i
$485$	−531.142	+	919.966i	−1.09514	+	1.89684i
$486$	364.853	−	284.860i	0.750726	−	0.586131i
$487$	356.247	+	617.038i	0.731513	+	1.26702i	0.956236	+	0.292596i	$0.0945189\pi$
$487$	356.247	+	617.038i	0.731513	+	1.26702i	−0.224723	+	0.974423i	$0.572148\pi$
$488$	−549.365	+	317.176i	−1.12575	+	0.649951i
$489$	72.9524	+	152.289i	0.149187	+	0.311430i
$490$		0			0
$491$	−177.716	−	307.813i	−0.361946	−	0.626909i	0.626335	−	0.779554i	$-0.284554\pi$
$491$	−177.716	−	307.813i	−0.361946	−	0.626909i	−0.988281	+	0.152645i	$0.951221\pi$
$492$	−1.43709	−	0.984134i	−0.00292091	−	0.00200027i
$493$			213.899i			0.433872i
$494$	10.1255	+	17.5378i	0.0204969	+	0.0355017i
$495$	−824.061	+	319.507i	−1.66477	+	0.645468i
$496$		−	455.842i		−	0.919037i
$497$		0			0
$498$	−10.5764	−	7.24283i	−0.0212377	−	0.0145438i
$499$	236.886			0.474722			0.237361	−	0.971422i	$-0.423718\pi$
$499$	236.886			0.474722			0.237361	+	0.971422i	$0.423718\pi$
$500$	−47.0265	−	27.1508i	−0.0940531	−	0.0543016i
$501$	39.1920	−	508.906i	0.0782276	−	1.01578i
$502$	−330.794	+	190.984i	−0.658952	+	0.380446i
$503$			471.038i			0.936457i	0.883608	+	0.468228i	$0.155108\pi$
$503$			471.038i			0.936457i	−0.883608	+	0.468228i	$0.844892\pi$
$504$		0			0
$505$	−1601.10			−3.17050
$506$	−319.841	−	553.980i	−0.632096	−	1.09482i
$507$	215.770	+	450.422i	0.425581	+	0.888407i
$508$	9.32631	−	16.1536i	0.0183589	−	0.0317985i
$509$		−	477.868i		−	0.938837i	−0.882976	−	0.469418i	$-0.844464\pi$
$509$		−	477.868i		−	0.938837i	0.882976	−	0.469418i	$-0.155536\pi$
$510$	396.336	+	827.357i	0.777129	+	1.62227i
$511$		0			0
$512$	−564.002			−1.10157
$513$	131.756	+	123.777i	0.256835	+	0.241280i
$514$	250.178	−	144.441i	0.486729	−	0.281013i
$515$	784.280			1.52287
$516$	72.2720	+	5.56584i	0.140062	+	0.0107865i
$517$	−571.253	+	329.813i	−1.10494	+	0.637936i
$518$		0			0
$519$	−22.0486	+	286.300i	−0.0424829	+	0.551637i
$520$	−54.4184	−	94.2554i	−0.104651	−	0.181260i
$521$	74.1810	−	42.8284i	0.142382	−	0.0822042i	−0.427117	−	0.904196i	$-0.640471\pi$
$521$	74.1810	−	42.8284i	0.142382	−	0.0822042i	0.569499	+	0.821992i	$0.307137\pi$
$522$	67.9746	+	175.318i	0.130220	+	0.335858i
$523$	498.721	+	287.937i	0.953578	+	0.550548i	0.894191	−	0.447687i	$-0.147752\pi$
$523$	498.721	+	287.937i	0.953578	+	0.550548i	0.0593872	+	0.998235i	$0.481085\pi$
$524$	−14.7069	−	8.49105i	−0.0280667	−	0.0162043i
$525$		0			0
$526$	339.318	+	587.716i	0.645091	+	1.11733i
$527$	618.372			1.17338
$528$	−513.009	−	39.5081i	−0.971608	−	0.0748259i
$529$	263.334			0.497797
$530$	460.692	+	265.981i	0.869230	+	0.501850i
$531$	−9.06430	+	58.5006i	−0.0170702	+	0.110171i
$532$		0			0
$533$	1.24091	−	2.14932i	0.00232816	−	0.00403249i
$534$	275.472	+	188.646i	0.515865	+	0.353270i
$535$	71.6494	+	41.3668i	0.133924	+	0.0773211i
$536$	−98.7470	+	171.035i	−0.184230	+	0.319095i
$537$	−855.636	−	65.8946i	−1.59336	−	0.122709i
$538$	−329.447	−	190.206i	−0.612354	−	0.353543i
$539$		0			0
$540$	−60.1690	−	56.5250i	−0.111424	−	0.104676i
$541$	−399.314	+	691.633i	−0.738104	+	1.27843i	0.215244	+	0.976560i	$0.430945\pi$
$541$	−399.314	+	691.633i	−0.738104	+	1.27843i	−0.953348	+	0.301874i	$0.902388\pi$
$542$		−	289.219i		−	0.533615i
$543$	610.648	+	418.179i	1.12458	+	0.770127i
$544$		−	115.516i		−	0.212346i
$545$	506.121	−	292.209i	0.928662	−	0.536163i
$546$		0			0
$547$	136.742	−	236.844i	0.249986	−	0.432988i	−0.713536	−	0.700619i	$-0.752907\pi$
$547$	136.742	−	236.844i	0.249986	−	0.432988i	0.963521	+	0.267631i	$0.0862408\pi$
$548$	5.84072	−	10.1164i	0.0106583	−	0.0184606i
$549$	−534.270	−	429.680i	−0.973169	−	0.782660i
$550$	−485.861	−	841.536i	−0.883384	−	1.53007i
$551$	−63.5973	+	36.7179i	−0.115422	+	0.0666386i
$552$	397.313	−	580.178i	0.719770	−	1.05105i
$553$		0			0
$554$	58.5604	+	101.430i	0.105705	+	0.183086i
$555$	153.403	−	73.4858i	0.276401	−	0.132407i
$556$			44.2932i			0.0796641i
$557$	263.054	+	455.623i	0.472269	+	0.817994i	0.999496	−	0.0317304i	$-0.0101018\pi$
$557$	263.054	+	455.623i	0.472269	+	0.817994i	−0.527228	+	0.849724i	$0.676768\pi$
$558$	506.836	−	196.512i	0.908309	−	0.352171i
$559$			103.284i			0.184767i
$560$		0			0
$561$	53.5946	−	695.921i	0.0955340	−	1.24050i
$562$	232.099			0.412987
$563$	334.915	+	193.363i	0.594876	+	0.343452i	0.767023	−	0.641619i	$-0.221737\pi$
$563$	334.915	+	193.363i	0.594876	+	0.343452i	−0.172147	+	0.985071i	$0.555070\pi$
$564$	−50.8355	−	34.8127i	−0.0901338	−	0.0617247i
$565$	385.144	−	222.363i	0.681670	−	0.393562i
$566$		−	968.438i		−	1.71102i
$567$		0			0
$568$	117.038			0.206053
$569$	177.346	+	307.172i	0.311680	+	0.539845i	0.978726	−	0.205171i	$-0.0657751\pi$
$569$	177.346	+	307.172i	0.311680	+	0.539845i	−0.667046	+	0.745016i	$0.732442\pi$
$570$	−177.958	+	259.865i	−0.312207	+	0.455903i
$571$	−78.2068	+	135.458i	−0.136965	+	0.237230i	−0.926346	−	0.376673i	$-0.877068\pi$
$571$	−78.2068	+	135.458i	−0.136965	+	0.237230i	0.789382	+	0.613903i	$0.210401\pi$
$572$			7.03619i			0.0123010i
$573$	−812.124	−	62.5436i	−1.41732	−	0.109151i
$574$		0			0
$575$	1203.61			2.09324
$576$	−223.803	−	577.225i	−0.388547	−	1.00213i
$577$	−172.608	+	99.6551i	−0.299147	+	0.172713i	−0.642060	−	0.766655i	$-0.721920\pi$
$577$	−172.608	+	99.6551i	−0.299147	+	0.172713i	0.342913	+	0.939367i	$0.388586\pi$
$578$	−173.972			−0.300990
$579$	−249.674	−	521.198i	−0.431215	−	0.900169i
$580$	29.0429	−	16.7679i	0.0500740	−	0.0289102i
$581$		0			0
$582$	−608.468	−	416.686i	−1.04548	−	0.715955i
$583$	−202.368	−	350.511i	−0.347114	−	0.601219i
$584$	−290.103	+	167.491i	−0.496751	+	0.286800i
$585$	73.7209	−	91.6654i	0.126019	−	0.156693i
$586$	−729.998	−	421.465i	−1.24573	−	0.719223i
$587$	124.893	+	72.1071i	0.212765	+	0.122840i	0.602596	−	0.798046i	$-0.294133\pi$
$587$	124.893	+	72.1071i	0.212765	+	0.122840i	−0.389831	+	0.920887i	$0.627466\pi$
$588$		0			0
$589$	106.150	+	183.857i	0.180220	+	0.312151i
$590$	−103.139			−0.174811
$591$	−277.081	+	404.609i	−0.468834	+	0.684618i
$592$	99.0222			0.167267
$593$	−644.186	−	371.921i	−1.08632	−	0.627185i	−0.153723	−	0.988114i	$-0.549126\pi$
$593$	−644.186	−	371.921i	−1.08632	−	0.627185i	−0.932593	+	0.360929i	$0.882460\pi$
$594$	−177.228	−	587.430i	−0.298364	−	0.988939i
$595$		0			0
$596$	11.1703	−	19.3475i	0.0187421	−	0.0324622i
$597$	−68.4673	+	889.042i	−0.114686	+	1.48918i
$598$	73.7310	+	42.5686i	0.123296	+	0.0711850i
$599$	85.4229	−	147.957i	0.142609	−	0.247006i	−0.785869	−	0.618393i	$-0.787784\pi$
$599$	85.4229	−	147.957i	0.142609	−	0.247006i	0.928478	+	0.371386i	$0.121117\pi$
$600$	603.547	−	881.333i	1.00591	−	1.46889i
$601$	1021.76	+	589.915i	1.70010	+	0.981555i	0.945641	+	0.325212i	$0.105436\pi$
$601$	1021.76	+	589.915i	1.70010	+	0.981555i	0.754462	+	0.656343i	$0.227898\pi$
$602$		0			0
$603$	−210.937	−	32.6834i	−0.349813	−	0.0542013i
$604$	−38.5608	+	66.7892i	−0.0638423	+	0.110578i
$605$			175.550i			0.290166i
$606$	85.3491	−	1108.25i	0.140840	−	1.82880i
$607$			484.623i			0.798390i	0.916866	+	0.399195i	$0.130710\pi$
$607$			484.623i			0.798390i	−0.916866	+	0.399195i	$0.869290\pi$
$608$	34.3459	−	19.8296i	0.0564899	−	0.0326145i
$609$		0			0
$610$	597.256	−	1034.48i	0.979108	−	1.69586i
$611$	43.8959	−	76.0299i	0.0718427	−	0.124435i
$612$	60.7867	−	23.5683i	0.0993246	−	0.0385103i
$613$	100.974	+	174.892i	0.164721	+	0.285305i	0.936556	−	0.350517i	$-0.113994\pi$
$613$	100.974	+	174.892i	0.164721	+	0.285305i	−0.771835	+	0.635823i	$0.780661\pi$
$614$	625.060	−	360.879i	1.01801	−	0.587750i
$615$	38.4852	+	2.96384i	0.0625776	+	0.00481925i
$616$		0			0
$617$	−484.279	−	838.795i	−0.784893	−	1.35947i	−0.929063	−	0.369921i	$-0.879385\pi$
$617$	−484.279	−	838.795i	−0.784893	−	1.35947i	0.144171	−	0.989553i	$-0.453949\pi$
$618$	−41.8072	+	542.863i	−0.0676491	+	0.878418i
$619$			28.0026i			0.0452385i	0.999744	+	0.0226193i	$0.00720055\pi$
$619$			28.0026i			0.0452385i	−0.999744	+	0.0226193i	$0.992799\pi$
$620$	−48.4753	−	83.9617i	−0.0781860	−	0.135422i
$621$	739.893	+	173.695i	1.19145	+	0.279703i
$622$		−	146.442i		−	0.235438i
$623$		0			0
$624$	61.7596	−	29.5852i	0.0989738	−	0.0474122i
$625$	134.387			0.215020
$626$	−236.858	−	136.750i	−0.378368	−	0.218451i
$627$	216.114	−	103.527i	0.344680	−	0.165115i
$628$	−34.0690	+	19.6697i	−0.0542500	+	0.0313213i
$629$			134.328i			0.213558i
$630$		0			0
$631$	−322.046			−0.510373			−0.255187	−	0.966892i	$-0.582137\pi$
$631$	−322.046			−0.510373			−0.255187	+	0.966892i	$0.582137\pi$
$632$	265.337	+	459.578i	0.419838	+	0.727180i
$633$	−260.221	−	20.0403i	−0.411092	−	0.0316592i
$634$	−90.2755	+	156.362i	−0.142390	+	0.246627i
$635$			413.360i			0.650961i
$636$	21.3605	−	31.1917i	0.0335856	−	0.0490436i
$637$		0			0
$638$	249.251			0.390676
$639$	45.7285	+	117.941i	0.0715626	+	0.184572i
$640$	765.202	−	441.789i	1.19563	−	0.690296i
$641$	467.164			0.728804			0.364402	−	0.931242i	$-0.381273\pi$
$641$	467.164			0.728804			0.364402	+	0.931242i	$0.381273\pi$
$642$	−32.4526	+	47.3892i	−0.0505493	+	0.0738149i
$643$	127.403	−	73.5564i	0.198139	−	0.114396i	−0.397648	−	0.917538i	$-0.630173\pi$
$643$	127.403	−	73.5564i	0.198139	−	0.114396i	0.595787	+	0.803142i	$0.296840\pi$
$644$		0			0
$645$	−1448.71	+	693.989i	−2.24607	+	1.07595i
$646$	−124.365	−	215.406i	−0.192515	−	0.333446i
$647$	−596.401	+	344.332i	−0.921795	+	0.532198i	−0.884207	−	0.467095i	$-0.845301\pi$
$647$	−596.401	+	344.332i	−0.921795	+	0.532198i	−0.0375875	+	0.999293i	$0.511967\pi$
$648$	498.203	−	454.680i	0.768832	−	0.701666i
$649$	67.9583	+	39.2357i	0.104712	+	0.0604557i
$650$	112.003	+	64.6648i	0.172312	+	0.0994843i
$651$		0			0
$652$	10.4538	+	18.1065i	0.0160335	+	0.0277708i
$653$	1170.28			1.79216			0.896081	−	0.443890i	$-0.146402\pi$
$653$	1170.28			1.79216			0.896081	+	0.443890i	$0.146402\pi$
$654$	175.282	+	365.903i	0.268015	+	0.559485i
$655$	376.340			0.574565
$656$	19.4602	+	11.2354i	0.0296650	+	0.0171271i
$657$	−282.131	−	226.901i	−0.429424	−	0.345359i
$658$		0			0
$659$	−505.251	+	875.121i	−0.766694	+	1.32795i	0.172652	+	0.984983i	$0.444766\pi$
$659$	−505.251	+	875.121i	−0.766694	+	1.32795i	−0.939346	+	0.342970i	$0.888567\pi$
$660$	−98.6927	+	47.2776i	−0.149534	+	0.0716327i
$661$	−479.449	−	276.810i	−0.725338	−	0.418774i	0.0913760	−	0.995816i	$-0.470873\pi$
$661$	−479.449	−	276.810i	−0.725338	−	0.418774i	−0.816714	+	0.577042i	$0.804207\pi$
$662$	−446.058	+	772.595i	−0.673803	+	1.16706i
$663$	40.1338	+	83.7799i	0.0605336	+	0.126365i
$664$	−16.1763	−	9.33936i	−0.0243618	−	0.0140653i
$665$		0			0
$666$	42.6880	+	110.100i	0.0640961	+	0.165315i
$667$	−154.366	+	267.370i	−0.231433	+	0.400855i
$668$		−	63.1970i		−	0.0946063i
$669$	−994.391	+	476.351i	−1.48638	+	0.712035i
$670$		−	371.890i		−	0.555059i
$671$	−787.067	+	454.413i	−1.17298	+	0.677218i
$672$		0			0
$673$	77.7290	−	134.631i	0.115496	−	0.200046i	−0.802482	−	0.596677i	$-0.796487\pi$
$673$	77.7290	−	134.631i	0.115496	−	0.200046i	0.917978	+	0.396631i	$0.129821\pi$
$674$	315.553	−	546.554i	0.468180	−	0.810912i
$675$	1123.95	+	263.856i	1.66511	+	0.390898i
$676$	30.9190	+	53.5533i	0.0457382	+	0.0792208i
$677$	−768.208	+	443.525i	−1.13472	+	0.655133i	−0.945119	−	0.326727i	$-0.894054\pi$
$677$	−768.208	+	443.525i	−1.13472	+	0.655133i	−0.189605	+	0.981860i	$0.560721\pi$
$678$	133.384	+	278.442i	0.196732	+	0.410681i
$679$		0			0
$680$	668.386	+	1157.68i	0.982920	+	1.70247i
$681$	−414.459	−	283.826i	−0.608603	−	0.416779i
$682$		−	720.574i		−	1.05656i
$683$	−220.278	−	381.532i	−0.322515	−	0.558612i	0.658491	−	0.752588i	$-0.271195\pi$
$683$	−220.278	−	381.532i	−0.322515	−	0.558612i	−0.981006	+	0.193976i	$0.937862\pi$
$684$	17.4421	+	14.0276i	0.0255001	+	0.0205082i
$685$			258.872i			0.377915i
$686$		0			0
$687$	1083.90	+	742.268i	1.57773	+	1.08045i
$688$	−935.151			−1.35923
$689$	46.6506	+	26.9337i	0.0677077	+	0.0390910i
$690$	−101.673	+	1320.21i	−0.147352	+	1.91335i
$691$	−356.503	+	205.827i	−0.515923	+	0.297868i	−0.735265	−	0.677780i	$-0.762942\pi$
$691$	−356.503	+	205.827i	−0.515923	+	0.297868i	0.219342	+	0.975648i	$0.429609\pi$
$692$			35.5533i			0.0513776i
$693$		0			0
$694$	708.707			1.02119
$695$	−490.790	−	850.074i	−0.706173	−	1.22313i
$696$	118.373	+	247.105i	0.170075	+	0.355035i
$697$	−15.2413	+	26.3987i	−0.0218670	+	0.0378747i
$698$			14.9108i			0.0213621i
$699$	294.962	+	615.738i	0.421977	+	0.880884i
$700$		0			0
$701$	−61.6807			−0.0879895			−0.0439948	−	0.999032i	$-0.514008\pi$
$701$	−61.6807			−0.0879895			−0.0439948	+	0.999032i	$0.514008\pi$
$702$	59.5192	+	55.9145i	0.0847851	+	0.0796502i
$703$	−39.9391	+	23.0588i	−0.0568123	+	0.0328006i
$704$	−820.646			−1.16569
$705$	1361.37	+	104.843i	1.93103	+	0.148713i
$706$	−129.056	+	74.5104i	−0.182798	+	0.105539i
$707$		0			0
$708$	−0.562812	+	7.30807i	−0.000794933	+	0.0103221i
$709$	−547.216	−	947.806i	−0.771814	−	1.33682i	−0.936568	−	0.350486i	$-0.886017\pi$
$709$	−547.216	−	947.806i	−0.771814	−	1.33682i	0.164755	−	0.986335i	$-0.447317\pi$
$710$	−190.861	+	110.194i	−0.268818	+	0.155202i
$711$	−359.454	+	446.950i	−0.505562	+	0.628621i
$712$	421.326	+	243.253i	0.591750	+	0.341647i
$713$	772.955	+	446.266i	1.08409	+	0.625899i
$714$		0			0
$715$	−77.9644	−	135.038i	−0.109041	−	0.188865i
$716$	−106.255			−0.148400
$717$	1062.72	+	81.8429i	1.48218	+	0.114146i
$718$	−505.619			−0.704204
$719$	−499.999	−	288.675i	−0.695409	−	0.401495i	0.110226	−	0.993907i	$-0.464843\pi$
$719$	−499.999	−	288.675i	−0.695409	−	0.401495i	−0.805635	+	0.592412i	$0.798176\pi$
$720$	829.951	+	667.479i	1.15271	+	0.927054i
$721$		0			0
$722$	−301.133	+	521.578i	−0.417082	+	0.722407i
$723$	−633.497	−	433.826i	−0.876206	−	0.600036i
$724$	79.3602	+	45.8186i	0.109614	+	0.0632854i
$725$	−234.493	+	406.154i	−0.323439	+	0.560213i
$726$	−121.512	−	9.35797i	−0.167373	−	0.0128898i
$727$	77.5777	+	44.7895i	0.106709	+	0.0616087i	0.552405	−	0.833576i	$-0.313710\pi$
$727$	77.5777	+	44.7895i	0.106709	+	0.0616087i	−0.445696	+	0.895185i	$0.647044\pi$
$728$		0			0
$729$	652.845	+	324.398i	0.895535	+	0.444991i
$730$	315.392	−	546.276i	0.432044	−	0.748323i
$731$		−	1268.58i		−	1.73540i
$732$	−70.0406	−	47.9646i	−0.0956839	−	0.0655255i
$733$			191.799i			0.261663i	0.991405	+	0.130832i	$0.0417648\pi$
$733$			191.799i			0.261663i	−0.991405	+	0.130832i	$0.958235\pi$
$734$	726.286	−	419.321i	0.989490	−	0.571283i
$735$		0			0
$736$	83.3658	−	144.394i	0.113269	−	0.196187i
$737$	−141.473	+	245.039i	−0.191958	+	0.332482i
$738$	−4.10302	+	26.4807i	−0.00555965	+	0.0358817i
$739$	−502.465	−	870.296i	−0.679926	−	1.17767i	−0.975003	−	0.222193i	$-0.928679\pi$
$739$	−502.465	−	870.296i	−0.679926	−	1.17767i	0.295077	−	0.955474i	$-0.404655\pi$
$740$	18.2389	−	10.5302i	0.0246472	−	0.0142301i
$741$	−18.0204	+	26.3144i	−0.0243190	+	0.0355120i
$742$		0			0
$743$	−159.690	−	276.590i	−0.214925	−	0.372262i	0.738324	−	0.674446i	$-0.235617\pi$
$743$	−159.690	−	276.590i	−0.214925	−	0.372262i	−0.953249	+	0.302184i	$0.902284\pi$
$744$	714.368	−	342.210i	0.960172	−	0.459959i
$745$			495.088i			0.664548i
$746$	−143.544	−	248.625i	−0.192418	−	0.333277i
$747$	3.09115	−	19.9502i	0.00413809	−	0.0267070i
$748$		−	86.4210i		−	0.115536i
$749$		0			0
$750$	−64.1476	+	832.952i	−0.0855302	+	1.11060i
$751$	328.885			0.437930			0.218965	−	0.975733i	$-0.429732\pi$
$751$	328.885			0.437930			0.218965	+	0.975733i	$0.429732\pi$
$752$	688.385	+	397.439i	0.915405	+	0.528509i
$753$	−496.335	−	339.896i	−0.659144	−	0.451389i
$754$	−28.7292	+	16.5868i	−0.0381024	+	0.0219984i
$755$		−	1709.09i		−	2.26369i
$756$		0			0
$757$	−314.963			−0.416068			−0.208034	−	0.978122i	$-0.566706\pi$
$757$	−314.963			−0.416068			−0.208034	+	0.978122i	$0.566706\pi$
$758$	−298.742	−	517.436i	−0.394119	−	0.682633i
$759$	569.224	−	831.213i	0.749966	−	1.09514i
$760$	−229.471	+	397.455i	−0.301935	+	0.522967i
$761$		−	1077.49i		−	1.41589i	−0.706267	−	0.707946i	$-0.749622\pi$
$761$		−	1077.49i		−	1.41589i	0.706267	−	0.707946i	$-0.250378\pi$
$762$	−286.120	−	22.0348i	−0.375485	−	0.0289170i
$763$		0			0
$764$	−100.851			−0.132004
$765$	−905.467	+	1125.87i	−1.18362	+	1.47172i
$766$	−1068.33	+	616.801i	−1.39469	+	0.805223i
$767$	−10.4440			−0.0136167
$768$	−91.6116	−	191.241i	−0.119286	−	0.249011i
$769$	−878.320	+	507.098i	−1.14216	+	0.659426i	−0.946964	−	0.321339i	$-0.895867\pi$
$769$	−878.320	+	507.098i	−1.14216	+	0.659426i	−0.195194	+	0.980765i	$0.562534\pi$
$770$		0			0
$771$	375.377	+	257.063i	0.486870	+	0.333415i
$772$	−35.7773	−	61.9682i	−0.0463437	−	0.0802696i
$773$	−633.766	+	365.905i	−0.819878	+	0.473357i	−0.850375	−	0.526178i	$-0.823625\pi$
$773$	−633.766	+	365.905i	−0.819878	+	0.473357i	0.0304961	+	0.999535i	$0.490291\pi$
$774$	−403.140	−	1039.76i	−0.520852	−	1.34336i
$775$	1174.17	+	677.910i	1.51506	+	0.874722i
$776$	−930.633	−	537.301i	−1.19927	−	0.692398i
$777$		0			0
$778$	194.069	+	336.138i	0.249446	+	0.432054i
$779$	−10.4653			−0.0134343
$780$	8.22936	−	12.0170i	0.0105505	−	0.0154064i
$781$	167.679			0.214697
$782$	−905.591	−	522.843i	−1.15804	−	0.668597i
$783$	−202.762	+	215.834i	−0.258955	+	0.275650i
$784$		0			0
$785$	435.901	−	755.002i	0.555287	−	0.961786i
$786$	−20.0613	+	260.495i	−0.0255233	+	0.331418i
$787$	−130.853	−	75.5479i	−0.166268	−	0.0959947i	0.414557	−	0.910023i	$-0.363937\pi$
$787$	−130.853	−	75.5479i	−0.166268	−	0.0959947i	−0.580825	+	0.814029i	$0.697270\pi$
$788$	−30.3590	+	52.5833i	−0.0385266	+	0.0667300i
$789$	−603.888	+	881.831i	−0.765384	+	1.11766i
$790$	−865.404	−	499.641i	−1.09545	−	0.632457i
$791$		0			0
$792$	−323.211	−	833.616i	−0.408095	−	1.05255i
$793$	60.4793	−	104.753i	0.0762665	−	0.132097i
$794$			540.189i			0.680338i
$795$	−64.3296	+	835.315i	−0.0809178	+	1.05071i
$796$			110.403i			0.138697i
$797$	−136.019	+	78.5308i	−0.170664	+	0.0985330i	−0.582899	−	0.812545i	$-0.698082\pi$
$797$	−136.019	+	78.5308i	−0.170664	+	0.0985330i	0.412235	+	0.911078i	$0.364748\pi$
$798$		0			0
$799$	−539.145	+	933.826i	−0.674775	+	1.16874i
$800$	126.639	−	219.345i	0.158298	−	0.274181i
$801$	−80.5120	+	519.621i	−0.100514	+	0.648715i
$802$	594.549	+	1029.79i	0.741333	+	1.28403i
$803$	−415.626	+	239.962i	−0.517591	+	0.298832i
$804$	−26.3509	−	2.02935i	−0.0327748	−	0.00252406i
$805$		0			0
$806$	47.9518	+	83.0549i	0.0594935	+	0.103046i
$807$	46.0029	−	597.344i	0.0570049	−	0.740204i
$808$		−	1619.67i		−	2.00454i
$809$	−214.097	−	370.827i	−0.264644	−	0.458377i	0.702826	−	0.711361i	$-0.251921\pi$
$809$	−214.097	−	370.827i	−0.264644	−	0.458377i	−0.967470	+	0.252985i	$0.918588\pi$
$810$	−384.360	+	1210.54i	−0.474518	+	1.49450i
$811$			1167.08i			1.43906i	0.694459	+	0.719532i	$0.255644\pi$
$811$			1167.08i			1.43906i	−0.694459	+	0.719532i	$0.744356\pi$
$812$		0			0
$813$	410.791	−	196.785i	0.505278	−	0.242048i
$814$	156.530			0.192297
$815$	−401.258	−	231.667i	−0.492342	−	0.284254i
$816$	−758.554	+	363.376i	−0.929601	+	0.445314i
$817$	377.179	−	217.764i	0.461663	−	0.266541i
$818$			57.0653i			0.0697620i
$819$		0			0
$820$	4.77918			0.00582826
$821$	431.425	+	747.250i	0.525487	+	0.910170i	0.999559	+	0.0296842i	$0.00945017\pi$
$821$	431.425	+	747.250i	0.525487	+	0.910170i	−0.474072	+	0.880486i	$0.657216\pi$
$822$	−179.186	−	13.7995i	−0.217988	−	0.0167878i
$823$	−276.715	+	479.284i	−0.336227	+	0.582363i	−0.983720	−	0.179709i	$-0.942484\pi$
$823$	−276.715	+	479.284i	−0.336227	+	0.582363i	0.647493	+	0.762072i	$0.275818\pi$
$824$			793.374i			0.962832i
$825$	864.692	−	1262.67i	1.04811	−	1.53051i
$826$		0			0
$827$	726.434			0.878396			0.439198	−	0.898390i	$-0.355263\pi$
$827$	726.434			0.878396			0.439198	+	0.898390i	$0.355263\pi$
$828$	92.9911	+	14.4084i	0.112308	+	0.0174015i
$829$	−132.793	+	76.6682i	−0.160185	+	0.0924828i	−0.577950	−	0.816072i	$-0.696147\pi$
$829$	−132.793	+	76.6682i	−0.160185	+	0.0924828i	0.417765	+	0.908555i	$0.362814\pi$
$830$	35.1728			0.0423769
$831$	−104.221	+	152.189i	−0.125416	+	0.183139i
$832$	94.5894	−	54.6112i	0.113689	−	0.0656385i
$833$		0			0
$834$	614.566	−	294.401i	0.736890	−	0.352998i
$835$	700.253	+	1212.87i	0.838627	+	1.45254i
$836$	25.6951	−	14.8351i	0.0307357	−	0.0177453i
$837$	623.966	+	586.176i	0.745479	+	0.700330i
$838$	127.153	+	73.4116i	0.151733	+	0.0876033i
$839$	−1358.20	−	784.159i	−1.61884	−	0.934635i	−0.987222	−	0.159352i	$-0.949059\pi$
$839$	−1358.20	−	784.159i	−1.61884	−	0.934635i	−0.631614	−	0.775283i	$-0.717607\pi$
$840$		0			0
$841$	360.351	+	624.147i	0.428480	+	0.742149i
$842$	−1130.57			−1.34272
$843$	157.920	+	329.660i	0.187331	+	0.391056i
$844$	−32.3148			−0.0382877
$845$	−1186.79	−	685.195i	−1.40449	−	0.810882i
$846$	−145.140	+	936.727i	−0.171560	+	1.10724i
$847$		0			0
$848$	−243.862	+	422.381i	−0.287573	+	0.498090i
$849$	1375.52	−	658.925i	1.62016	−	0.776119i
$850$	−1375.66	−	794.236i	−1.61842	−	0.934395i
$851$	−96.9419	+	167.908i	−0.113915	+	0.197307i
$852$	6.76647	+	14.1251i	0.00794187	+	0.0165788i
$853$	−807.491	−	466.205i	−0.946649	−	0.546548i	−0.0546104	−	0.998508i	$-0.517392\pi$
$853$	−807.491	−	466.205i	−0.946649	−	0.546548i	−0.892038	+	0.451960i	$0.850725\pi$
$854$		0			0
$855$	−490.180	−	75.9504i	−0.573310	−	0.0888309i
$856$	−41.8465	+	72.4802i	−0.0488861	+	0.0846732i
$857$			1058.31i			1.23490i	0.786609	+	0.617451i	$0.211835\pi$
$857$			1058.31i			1.23490i	−0.786609	+	0.617451i	$0.788165\pi$
$858$	97.6267	−	46.7670i	0.113784	−	0.0545069i
$859$			64.7528i			0.0753816i	0.999289	+	0.0376908i	$0.0120002\pi$
$859$			64.7528i			0.0753816i	−0.999289	+	0.0376908i	$0.988000\pi$
$860$	−172.246	+	99.4462i	−0.200286	+	0.115635i
$861$		0			0
$862$	−400.291	+	693.324i	−0.464374	+	0.804320i
$863$	−605.330	+	1048.46i	−0.701425	+	1.21490i	0.266541	+	0.963824i	$0.414119\pi$
$863$	−605.330	+	1048.46i	−0.701425	+	1.21490i	−0.967966	+	0.251080i	$0.919214\pi$
$864$	109.502	−	116.562i	0.126739	−	0.134909i
$865$	−393.948	−	682.338i	−0.455431	−	0.788830i
$866$	−1131.77	+	653.426i	−1.30689	+	0.754533i
$867$	−118.371	−	247.101i	−0.136529	−	0.285007i
$868$		0			0
$869$	380.145	+	658.430i	0.437451	+	0.757687i
$870$	−425.691	−	291.518i	−0.489300	−	0.335079i
$871$		−	37.6583i		−	0.0432357i
$872$	295.597	+	511.989i	0.338988	+	0.587144i
$873$	177.837	−	1147.75i	0.203707	−	1.31472i
$874$		−	359.005i		−	0.410761i
$875$		0			0
$876$	−36.9863	−	25.3287i	−0.0422218	−	0.0289140i
$877$	−834.997			−0.952106			−0.476053	−	0.879416i	$-0.657933\pi$
$877$	−834.997			−0.952106			−0.476053	+	0.879416i	$0.657933\pi$
$878$	136.874	+	79.0241i	0.155893	+	0.0900047i
$879$	101.935	−	1323.61i	0.115967	−	1.50582i
$880$	1222.65	−	705.900i	1.38938	−	0.802159i
$881$			955.525i			1.08459i	0.840188	+	0.542296i	$0.182445\pi$
$881$			955.525i			1.08459i	−0.840188	+	0.542296i	$0.817555\pi$
$882$		0			0
$883$	513.712			0.581780			0.290890	−	0.956757i	$-0.406049\pi$
$883$	513.712			0.581780			0.290890	+	0.956757i	$0.406049\pi$
$884$	5.75102	+	9.96106i	0.00650568	+	0.0112682i
$885$	−70.1755	−	146.492i	−0.0792943	−	0.165528i
$886$	−251.219	+	435.125i	−0.283543	+	0.491111i
$887$		−	816.561i		−	0.920587i	−0.887767	−	0.460294i	$-0.847744\pi$
$887$		−	816.561i		−	0.920587i	0.887767	−	0.460294i	$-0.152256\pi$
$888$	74.3379	+	155.182i	0.0837138	+	0.174754i
$889$		0			0
$890$	−916.109			−1.02934
$891$	713.768	−	651.413i	0.801086	−	0.731103i
$892$	−118.229	+	68.2594i	−0.132543	+	0.0765240i
$893$	−370.199			−0.414556
$894$	−342.690	−	26.3914i	−0.383322	−	0.0295206i
$895$	2039.24	−	1177.35i	2.27848	−	1.31548i
$896$		0			0
$897$	−10.2956	+	133.687i	−0.0114778	+	0.149038i
$898$	744.506	+	1289.52i	0.829071	+	1.43599i
$899$	−301.181	+	173.887i	−0.335018	+	0.193423i
$900$	141.260	+	21.8874i	0.156956	+	0.0243193i
$901$	−572.979	−	330.810i	−0.635937	−	0.367158i
$902$	30.7618	+	17.7603i	0.0341040	+	0.0196899i
$903$		0			0
$904$	224.941	+	389.610i	0.248829	+	0.430984i
$905$	−2030.77			−2.24395
$906$	1183.00	+	91.1054i	1.30573	+	0.100558i
$907$	−1001.84			−1.10456			−0.552280	−	0.833659i	$-0.686242\pi$
$907$	−1001.84			−1.10456			−0.552280	+	0.833659i	$0.686242\pi$
$908$	−53.8633	−	31.0980i	−0.0593209	−	0.0342489i
$909$	1632.17	−	632.829i	1.79557	−	0.696182i
$910$		0			0
$911$	−121.663	+	210.727i	−0.133549	+	0.231314i	−0.925042	−	0.379864i	$-0.875971\pi$
$911$	−121.663	+	210.727i	−0.133549	+	0.231314i	0.791493	+	0.611178i	$0.209304\pi$
$912$	−238.254	−	163.159i	−0.261244	−	0.178903i
$913$	−23.1755	−	13.3804i	−0.0253839	−	0.0146554i
$914$	815.233	−	1412.03i	0.891940	−	1.54489i
$915$	1875.69	+	144.451i	2.04993	+	0.157870i
$916$	140.864	+	81.3281i	0.153782	+	0.0887862i
$917$		0			0
$918$	−731.036	−	686.762i	−0.796335	−	0.748106i
$919$	652.582	−	1130.30i	0.710100	−	1.22993i	−0.254719	−	0.967015i	$-0.581983\pi$
$919$	652.582	−	1130.30i	0.710100	−	1.22993i	0.964819	−	0.262914i	$-0.0846836\pi$
$920$			1929.44i			2.09722i
$921$	937.863	+	642.260i	1.01831	+	0.697350i
$922$			839.171i			0.910164i
$923$	−19.3270	+	11.1584i	−0.0209393	+	0.0120893i
$924$		0			0
$925$	−147.262	+	255.065i	−0.159202	+	0.275746i
$926$	224.366	−	388.614i	0.242296	−	0.419669i
$927$	−799.498	+	309.983i	−0.862458	+	0.334394i
$928$	32.4834	+	56.2629i	0.0350037	+	0.0606281i
$929$	−78.7831	+	45.4854i	−0.0848042	+	0.0489617i	−0.541802	−	0.840506i	$-0.682258\pi$
$929$	−78.7831	+	45.4854i	−0.0848042	+	0.0489617i	0.456998	+	0.889468i	$0.348925\pi$
$930$	−842.767	+	1230.66i	−0.906201	+	1.32329i
$931$		0			0
$932$	42.2670	+	73.2086i	0.0453509	+	0.0785500i
$933$	207.999	−	99.6394i	0.222936	−	0.106795i
$934$		−	1770.10i		−	1.89519i
$935$	957.587	+	1658.59i	1.02416	+	1.77389i
$936$	92.7283	+	74.5757i	0.0990687	+	0.0796749i
$937$			1324.34i			1.41338i	0.707523	+	0.706690i	$0.249812\pi$
$937$			1324.34i			1.41338i	−0.707523	+	0.706690i	$0.750188\pi$
$938$		0			0
$939$	33.0742	−	429.466i	0.0352228	−	0.457365i
$940$	169.058			0.179849
$941$	−937.976	−	541.541i	−0.996786	−	0.575495i	−0.0894904	−	0.995988i	$-0.528524\pi$
$941$	−937.976	−	541.541i	−0.996786	−	0.575495i	−0.907296	+	0.420493i	$0.861857\pi$
$942$	499.361	+	341.968i	0.530107	+	0.363023i
$943$	−38.1028	+	21.9986i	−0.0404059	+	0.0233284i
$944$		−	94.5616i		−	0.100171i
$945$		0			0
$946$	−1478.24			−1.56263
$947$	59.8439	+	103.653i	0.0631931	+	0.109454i	0.895891	−	0.444274i	$-0.146538\pi$
$947$	59.8439	+	103.653i	0.0631931	+	0.109454i	−0.832698	+	0.553728i	$0.813205\pi$
$948$	−40.1254	+	58.5933i	−0.0423264	+	0.0618073i
$949$	31.9373	−	55.3170i	0.0336536	−	0.0582897i
$950$		−	545.355i		−	0.574058i
$951$	−283.511	−	21.8339i	−0.298119	−	0.0229589i
$952$		0			0
$953$	463.471			0.486329			0.243164	−	0.969985i	$-0.421815\pi$
$953$	463.471			0.486329			0.243164	+	0.969985i	$0.421815\pi$
$954$	−574.759	−	89.0553i	−0.602473	−	0.0933494i
$955$	1935.53	−	1117.48i	2.02674	−	1.17014i
$956$	131.971			0.138045
$957$	169.591	+	354.023i	0.177211	+	0.369930i
$958$	43.9558	−	25.3779i	0.0458829	−	0.0264905i
$959$		0			0
$960$	1401.57	+	959.809i	1.45997	+	0.999801i
$961$	22.1996	+	38.4509i	0.0231005	+	0.0400113i
$962$	−18.0419	+	10.4165i	−0.0187546	+	0.0108280i
$963$	−89.3898	−	13.8504i	−0.0928243	−	0.0143825i
$964$	−82.3296	−	47.5330i	−0.0854042	−	0.0493081i
$965$	1373.27	+	792.860i	1.42308	+	0.821617i
$966$		0			0
$967$	259.963	+	450.270i	0.268835	+	0.465636i	0.968561	−	0.248775i	$-0.0800281\pi$
$967$	259.963	+	450.270i	0.268835	+	0.465636i	−0.699726	+	0.714411i	$0.746695\pi$
$968$	−177.586			−0.183457
$969$	221.333	−	323.203i	0.228414	−	0.333543i
$970$	2023.52			2.08610
$971$	−43.8932	−	25.3417i	−0.0452041	−	0.0260986i	0.477228	−	0.878780i	$-0.341642\pi$
$971$	−43.8932	−	25.3417i	−0.0452041	−	0.0260986i	−0.522432	+	0.852681i	$0.674975\pi$
$972$	83.6778	+	33.8403i	0.0860883	+	0.0348151i
$973$		0			0
$974$	678.606	−	1175.38i	0.696721	−	1.20676i
$975$	−15.6397	+	203.081i	−0.0160407	+	0.208288i
$976$	948.450	+	547.588i	0.971772	+	0.561053i
$977$	246.559	−	427.052i	0.252363	−	0.437105i	−0.711813	−	0.702369i	$-0.752126\pi$
$977$	246.559	−	427.052i	0.252363	−	0.437105i	0.964176	+	0.265264i	$0.0854590\pi$
$978$	181.745	−	265.394i	0.185833	−	0.271364i
$979$	603.627	+	348.504i	0.616575	+	0.355980i
$980$		0			0
$981$	−400.447	+	497.921i	−0.408203	+	0.507565i
$982$	−338.526	+	586.345i	−0.344731	+	0.597092i
$983$			808.577i			0.822561i	0.911509	+	0.411281i	$0.134918\pi$
$983$			808.577i			0.822561i	−0.911509	+	0.411281i	$0.865082\pi$
$984$	−2.99821	+	38.9315i	−0.00304696	+	0.0395645i
$985$		−	1345.57i		−	1.36606i
$986$	352.862	−	203.725i	0.357873	−	0.206618i
$987$		0			0
$988$	−1.97444	+	3.41984i	−0.00199843	+	0.00346137i
$989$	915.505	−	1585.70i	0.925688	−	1.60334i
$990$	1311.95	+	1055.12i	1.32520	+	1.06578i
$991$	294.478	+	510.051i	0.297152	+	0.514683i	0.975483	−	0.220074i	$-0.0706298\pi$
$991$	294.478	+	510.051i	0.297152	+	0.514683i	−0.678331	+	0.734756i	$0.737296\pi$
$992$	162.654	−	93.9081i	0.163965	−	0.0946654i
$993$	−1400.85	−	107.883i	−1.41072	−	0.108643i
$994$		0			0
$995$	−1223.32	−	2118.85i	−1.22947	−	2.12950i
$996$	0.191933	−	2.49223i	0.000192704	−	0.00250224i
$997$		−	539.626i		−	0.541250i	−0.962685	−	0.270625i	$-0.912770\pi$
$997$		−	539.626i		−	0.541250i	0.962685	−	0.270625i	$-0.0872304\pi$
$998$	−225.620	−	390.784i	−0.226072	−	0.391568i
$999$	−127.335	+	135.544i	−0.127462	+	0.135679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.k.a.313.6		28
7.2	even	3		63.3.l.a.34.6	yes	28
7.3	odd	6		441.3.t.b.178.10		28
7.4	even	3		441.3.t.b.178.9		28
7.5	odd	6		63.3.l.a.34.5	yes	28
7.6	odd	2	inner	441.3.k.a.313.5		28
9.4	even	3		441.3.t.b.166.10		28
21.2	odd	6		189.3.l.a.181.9		28
21.5	even	6		189.3.l.a.181.10		28
63.2	odd	6		567.3.d.g.244.5		14
63.4	even	3	inner	441.3.k.a.31.5		28
63.5	even	6		189.3.l.a.118.9		28
63.13	odd	6		441.3.t.b.166.9		28
63.16	even	3		567.3.d.h.244.10		14
63.23	odd	6		189.3.l.a.118.10		28
63.31	odd	6	inner	441.3.k.a.31.6		28
63.40	odd	6		63.3.l.a.13.6	yes	28
63.47	even	6		567.3.d.g.244.6		14
63.58	even	3		63.3.l.a.13.5	✓	28
63.61	odd	6		567.3.d.h.244.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.l.a.13.5	✓	28	63.58	even	3
63.3.l.a.13.6	yes	28	63.40	odd	6
63.3.l.a.34.5	yes	28	7.5	odd	6
63.3.l.a.34.6	yes	28	7.2	even	3
189.3.l.a.118.9		28	63.5	even	6
189.3.l.a.118.10		28	63.23	odd	6
189.3.l.a.181.9		28	21.2	odd	6
189.3.l.a.181.10		28	21.5	even	6
441.3.k.a.31.5		28	63.4	even	3	inner
441.3.k.a.31.6		28	63.31	odd	6	inner
441.3.k.a.313.5		28	7.6	odd	2	inner
441.3.k.a.313.6		28	1.1	even	1	trivial
441.3.t.b.166.9		28	63.13	odd	6
441.3.t.b.166.10		28	9.4	even	3
441.3.t.b.178.9		28	7.4	even	3
441.3.t.b.178.10		28	7.3	odd	6
567.3.d.g.244.5		14	63.2	odd	6
567.3.d.g.244.6		14	63.47	even	6
567.3.d.h.244.9		14	63.61	odd	6
567.3.d.h.244.10		14	63.16	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.952438 - 1.64967i) q^{2} +(1.69506 - 2.47523i) q^{3} +(0.185723 - 0.321682i) q^{4} +8.23162i q^{5} +(-5.69776 - 0.438798i) q^{6} -8.32706 q^{8} +(-3.25351 - 8.39135i) q^{9} +O(q^{10})\)	\(q+(-0.952438 - 1.64967i) q^{2} +(1.69506 - 2.47523i) q^{3} +(0.185723 - 0.321682i) q^{4} +8.23162i q^{5} +(-5.69776 - 0.438798i) q^{6} -8.32706 q^{8} +(-3.25351 - 8.39135i) q^{9} +(13.5795 - 7.84010i) q^{10} -11.9301 q^{11} +(-0.481424 - 1.00498i) q^{12} +(1.37508 - 0.793905i) q^{13} +(20.3751 + 13.9531i) q^{15} +(7.18812 + 12.4502i) q^{16} +(-16.8893 + 9.75102i) q^{17} +(-10.7442 + 13.3595i) q^{18} +(-5.79843 - 3.34773i) q^{19} +(2.64796 + 1.52880i) q^{20} +(11.3626 + 19.6807i) q^{22} -28.1484 q^{23} +(-14.1149 + 20.6114i) q^{24} -42.7595 q^{25} +(-2.61936 - 1.51229i) q^{26} +(-26.2854 - 6.17070i) q^{27} +(5.48400 - 9.49857i) q^{29} +(3.61202 - 46.9017i) q^{30} +(-27.4600 - 15.8540i) q^{31} +(-2.96165 + 5.12973i) q^{32} +(-20.2222 + 29.5296i) q^{33} +(32.1720 + 18.5745i) q^{34} +(-3.30360 - 0.511872i) q^{36} +(3.44395 - 5.96510i) q^{37} +12.7540i q^{38} +(0.365760 - 4.74937i) q^{39} -68.5452i q^{40} +(1.35364 - 0.781523i) q^{41} +(-32.5242 + 56.3336i) q^{43} +(-2.21569 + 3.83769i) q^{44} +(69.0743 - 26.7816i) q^{45} +(26.8096 + 46.4357i) q^{46} +(47.8835 - 27.6455i) q^{47} +(43.0014 + 3.31164i) q^{48} +(40.7258 + 70.5391i) q^{50} +(-4.49240 + 58.3334i) q^{51} -0.589787i q^{52} +(16.9628 + 29.3805i) q^{53} +(14.8556 + 49.2395i) q^{54} -98.2037i q^{55} +(-18.1151 + 8.67783i) q^{57} -20.8927 q^{58} +(-5.69639 - 3.28881i) q^{59} +(8.27261 - 3.96290i) q^{60} +(65.9734 - 38.0898i) q^{61} +60.3999i q^{62} +68.7881 q^{64} +(6.53512 + 11.3192i) q^{65} +(67.9746 + 5.23489i) q^{66} +(11.8586 - 20.5396i) q^{67} +7.24397i q^{68} +(-47.7134 + 69.6738i) q^{69} -14.0551 q^{71} +(27.0922 + 69.8753i) q^{72} +(34.8385 - 20.1140i) q^{73} -13.1206 q^{74} +(-72.4801 + 105.840i) q^{75} +(-2.15381 + 1.24350i) q^{76} +(-8.18326 + 3.92009i) q^{78} +(-31.8645 - 55.1909i) q^{79} +(-102.485 + 59.1698i) q^{80} +(-59.8293 + 54.6026i) q^{81} +(-2.57851 - 1.48870i) q^{82} +(1.94261 + 1.12157i) q^{83} +(-80.2667 - 139.026i) q^{85} +123.909 q^{86} +(-14.2154 - 29.6749i) q^{87} +99.3424 q^{88} +(-50.5972 - 29.2123i) q^{89} +(-109.970 - 88.4421i) q^{90} +(-5.22782 + 9.05485i) q^{92} +(-85.7887 + 41.0961i) q^{93} +(-91.2121 - 52.6613i) q^{94} +(27.5572 - 47.7305i) q^{95} +(7.67706 + 16.0260i) q^{96} +(111.760 + 64.5247i) q^{97} +(38.8146 + 100.109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 12 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 12 * q^9	\( 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 12 q^{9} - 8 q^{11} - 54 q^{15} - 42 q^{16} - 138 q^{18} + 14 q^{22} - 8 q^{23} - 56 q^{25} - 38 q^{29} - 294 q^{30} - 168 q^{32} + 234 q^{36} - 18 q^{37} + 84 q^{39} - 66 q^{43} - 54 q^{44} + 20 q^{46} + 196 q^{50} + 318 q^{51} - 260 q^{53} - 198 q^{57} + 68 q^{58} + 366 q^{60} + 72 q^{64} - 102 q^{65} + 68 q^{67} - 332 q^{71} + 714 q^{72} + 1232 q^{74} - 168 q^{78} + 146 q^{79} - 516 q^{81} + 78 q^{85} + 680 q^{86} + 148 q^{88} + 606 q^{92} - 1146 q^{93} - 360 q^{95} + 900 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 12 * q^9 - 8 * q^11 - 54 * q^15 - 42 * q^16 - 138 * q^18 + 14 * q^22 - 8 * q^23 - 56 * q^25 - 38 * q^29 - 294 * q^30 - 168 * q^32 + 234 * q^36 - 18 * q^37 + 84 * q^39 - 66 * q^43 - 54 * q^44 + 20 * q^46 + 196 * q^50 + 318 * q^51 - 260 * q^53 - 198 * q^57 + 68 * q^58 + 366 * q^60 + 72 * q^64 - 102 * q^65 + 68 * q^67 - 332 * q^71 + 714 * q^72 + 1232 * q^74 - 168 * q^78 + 146 * q^79 - 516 * q^81 + 78 * q^85 + 680 * q^86 + 148 * q^88 + 606 * q^92 - 1146 * q^93 - 360 * q^95 + 900 * q^99

Introduction

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