LMFDB - Embedded newform 135.4.e.c.91.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,4,Mod(46,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("135.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	135.e (of order $3$, 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:	$7.96525785077$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 $ x^14 - 2x^13 + 48x^12 - 60x^11 + 1605x^10 - 1800x^9 + 23232x^8 - 2346x^7 + 209529x^6 - 55412x^5 + 765088x^4 + 276096x^3 + 1572480x^2 - 345600*x + 82944
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{13} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			91.7
Root			$-2.69252 + 4.66357i$ of defining polynomial
Character	$\chi$	$=$	135.91
Dual form			135.4.e.c.46.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.69252 + 4.66357i) q^{2} +(-10.4993 + 18.1853i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-6.28510 - 10.8861i) q^{7} -69.9976 q^{8} +O(q^{10})$	\(q+(2.69252 + 4.66357i) q^{2} +(-10.4993 + 18.1853i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-6.28510 - 10.8861i) q^{7} -69.9976 q^{8} -26.9252 q^{10} +(6.41534 + 11.1117i) q^{11} +(-29.9322 + 51.8442i) q^{13} +(33.8455 - 58.6220i) q^{14} +(-104.475 - 180.957i) q^{16} +110.011 q^{17} -12.0872 q^{19} +(-52.4964 - 90.9264i) q^{20} +(-34.5468 + 59.8368i) q^{22} +(-33.8608 + 58.6485i) q^{23} +(-12.5000 - 21.6506i) q^{25} -322.372 q^{26} +263.956 q^{28} +(99.9790 + 173.169i) q^{29} +(-38.3143 + 66.3624i) q^{31} +(282.613 - 489.500i) q^{32} +(296.206 + 513.044i) q^{34} +62.8510 q^{35} -22.4815 q^{37} +(-32.5449 - 56.3694i) q^{38} +(174.994 - 303.099i) q^{40} +(43.8807 - 76.0037i) q^{41} +(-59.7050 - 103.412i) q^{43} -269.426 q^{44} -364.682 q^{46} +(121.578 + 210.579i) q^{47} +(92.4951 - 160.206i) q^{49} +(67.3129 - 116.589i) q^{50} +(-628.534 - 1088.65i) q^{52} +293.518 q^{53} -64.1534 q^{55} +(439.942 + 762.002i) q^{56} +(-538.390 + 932.519i) q^{58} +(-290.692 + 503.493i) q^{59} +(386.847 + 670.038i) q^{61} -412.648 q^{62} +1372.15 q^{64} +(-149.661 - 259.221i) q^{65} +(115.719 - 200.431i) q^{67} +(-1155.03 + 2000.58i) q^{68} +(169.227 + 293.110i) q^{70} +744.342 q^{71} -264.839 q^{73} +(-60.5317 - 104.844i) q^{74} +(126.907 - 219.809i) q^{76} +(80.6421 - 139.676i) q^{77} +(-279.858 - 484.729i) q^{79} +1044.75 q^{80} +472.598 q^{82} +(-610.443 - 1057.32i) q^{83} +(-275.027 + 476.361i) q^{85} +(321.513 - 556.878i) q^{86} +(-449.059 - 777.792i) q^{88} +255.905 q^{89} +752.509 q^{91} +(-711.027 - 1231.53i) q^{92} +(-654.699 + 1133.97i) q^{94} +(30.2179 - 52.3390i) q^{95} +(-524.759 - 908.909i) q^{97} +996.177 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 36 q^{4} - 35 q^{5} - 22 q^{7} + 36 q^{8}+O(q^{10}) $ 14 * q - 2 * q^2 - 36 * q^4 - 35 * q^5 - 22 * q^7 + 36 * q^8	$ 14 q - 2 q^{2} - 36 q^{4} - 35 q^{5} - 22 q^{7} + 36 q^{8} + 20 q^{10} - 23 q^{11} - 96 q^{13} + 21 q^{14} - 324 q^{16} + 322 q^{17} + 558 q^{19} - 180 q^{20} - 311 q^{22} - 96 q^{23} - 175 q^{25} - 716 q^{26} + 674 q^{28} + 296 q^{29} - 244 q^{31} + 314 q^{32} - 125 q^{34} + 220 q^{35} + 808 q^{37} - 305 q^{38} - 90 q^{40} + 47 q^{41} - 525 q^{43} + 110 q^{44} + 1434 q^{46} - 164 q^{47} - 1225 q^{49} - 50 q^{50} - 1682 q^{52} + 1012 q^{53} + 230 q^{55} + 981 q^{56} - 1183 q^{58} + 85 q^{59} - 828 q^{61} - 1572 q^{62} + 4472 q^{64} - 480 q^{65} - 1093 q^{67} - 2473 q^{68} + 105 q^{70} + 656 q^{71} + 4170 q^{73} + 1316 q^{74} - 2789 q^{76} - 24 q^{77} - 2110 q^{79} + 3240 q^{80} - 124 q^{82} - 1290 q^{83} - 805 q^{85} + 2569 q^{86} - 2271 q^{88} - 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 517 q^{94} - 1395 q^{95} - 1787 q^{97} + 2558 q^{98}+O(q^{100}) $ 14 * q - 2 * q^2 - 36 * q^4 - 35 * q^5 - 22 * q^7 + 36 * q^8 + 20 * q^10 - 23 * q^11 - 96 * q^13 + 21 * q^14 - 324 * q^16 + 322 * q^17 + 558 * q^19 - 180 * q^20 - 311 * q^22 - 96 * q^23 - 175 * q^25 - 716 * q^26 + 674 * q^28 + 296 * q^29 - 244 * q^31 + 314 * q^32 - 125 * q^34 + 220 * q^35 + 808 * q^37 - 305 * q^38 - 90 * q^40 + 47 * q^41 - 525 * q^43 + 110 * q^44 + 1434 * q^46 - 164 * q^47 - 1225 * q^49 - 50 * q^50 - 1682 * q^52 + 1012 * q^53 + 230 * q^55 + 981 * q^56 - 1183 * q^58 + 85 * q^59 - 828 * q^61 - 1572 * q^62 + 4472 * q^64 - 480 * q^65 - 1093 * q^67 - 2473 * q^68 + 105 * q^70 + 656 * q^71 + 4170 * q^73 + 1316 * q^74 - 2789 * q^76 - 24 * q^77 - 2110 * q^79 + 3240 * q^80 - 124 * q^82 - 1290 * q^83 - 805 * q^85 + 2569 * q^86 - 2271 * q^88 - 6096 * q^89 + 6676 * q^91 - 2763 * q^92 + 517 * q^94 - 1395 * q^95 - 1787 * q^97 + 2558 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	2.69252	+	4.66357i	0.951948	+	1.64882i	0.741203	+	0.671281i	$0.234256\pi$
$2$	2.69252	+	4.66357i	0.951948	+	1.64882i	0.210745	+	0.977541i	$0.432411\pi$
$3$		0			0
$3$		0			0
$4$	−10.4993	+	18.1853i	−1.31241	+	2.27316i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	−6.28510	−	10.8861i	−0.339363	−	0.587795i	0.644950	−	0.764225i	$-0.276878\pi$
$7$	−6.28510	−	10.8861i	−0.339363	−	0.587795i	−0.984313	+	0.176430i	$0.943545\pi$
$8$	−69.9976			−3.09349
$9$		0			0
$10$	−26.9252			−0.851448
$11$	6.41534	+	11.1117i	0.175845	+	0.304573i	0.940454	−	0.339922i	$-0.110401\pi$
$11$	6.41534	+	11.1117i	0.175845	+	0.304573i	−0.764608	+	0.644495i	$0.777067\pi$
$12$		0			0
$13$	−29.9322	+	51.8442i	−0.638593	+	1.10608i	0.347148	+	0.937810i	$0.387150\pi$
$13$	−29.9322	+	51.8442i	−0.638593	+	1.10608i	−0.985742	+	0.168266i	$0.946183\pi$
$14$	33.8455	−	58.6220i	0.646113	−	1.11910i
$15$		0			0
$16$	−104.475	−	180.957i	−1.63243	−	2.82745i
$17$	110.011			1.56950			0.784752	−	0.619810i	$-0.212790\pi$
$17$	110.011			1.56950			0.784752	+	0.619810i	$0.212790\pi$
$18$		0			0
$19$	−12.0872			−0.145947			−0.0729733	−	0.997334i	$-0.523249\pi$
$19$	−12.0872			−0.145947			−0.0729733	+	0.997334i	$0.523249\pi$
$20$	−52.4964	−	90.9264i	−0.586927	−	1.01659i
$21$		0			0
$22$	−34.5468	+	59.8368i	−0.334791	+	0.579875i
$23$	−33.8608	+	58.6485i	−0.306976	+	0.531699i	−0.977699	−	0.210009i	$-0.932651\pi$
$23$	−33.8608	+	58.6485i	−0.306976	+	0.531699i	0.670723	+	0.741708i	$0.265984\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−322.372			−2.43163
$27$		0			0
$28$	263.956			1.78154
$29$	99.9790	+	173.169i	0.640194	+	1.10885i	0.985389	+	0.170318i	$0.0544794\pi$
$29$	99.9790	+	173.169i	0.640194	+	1.10885i	−0.345195	+	0.938531i	$0.612187\pi$
$30$		0			0
$31$	−38.3143	+	66.3624i	−0.221982	+	0.384485i	−0.955410	−	0.295283i	$-0.904586\pi$
$31$	−38.3143	+	66.3624i	−0.221982	+	0.384485i	0.733427	+	0.679768i	$0.237919\pi$
$32$	282.613	−	489.500i	1.56123	−	2.70413i
$33$		0			0
$34$	296.206	+	513.044i	1.49409	+	2.58783i
$35$	62.8510			0.303536
$36$		0			0
$37$	−22.4815			−0.0998900			−0.0499450	−	0.998752i	$-0.515905\pi$
$37$	−22.4815			−0.0998900			−0.0499450	+	0.998752i	$0.515905\pi$
$38$	−32.5449	−	56.3694i	−0.138934	−	0.240640i
$39$		0			0
$40$	174.994	−	303.099i	0.691725	−	1.19810i
$41$	43.8807	−	76.0037i	0.167147	−	0.289507i	−0.770269	−	0.637719i	$-0.779878\pi$
$41$	43.8807	−	76.0037i	0.167147	−	0.289507i	0.937416	+	0.348213i	$0.113211\pi$
$42$		0			0
$43$	−59.7050	−	103.412i	−0.211743	−	0.366749i	0.740517	−	0.672037i	$-0.234581\pi$
$43$	−59.7050	−	103.412i	−0.211743	−	0.366749i	−0.952260	+	0.305288i	$0.901247\pi$
$44$	−269.426			−0.923124
$45$		0			0
$46$	−364.682			−1.16890
$47$	121.578	+	210.579i	0.377317	+	0.653533i	0.990671	−	0.136276i	$-0.0435133\pi$
$47$	121.578	+	210.579i	0.377317	+	0.653533i	−0.613354	+	0.789808i	$0.710180\pi$
$48$		0			0
$49$	92.4951	−	160.206i	0.269665	−	0.467073i
$50$	67.3129	−	116.589i	0.190390	−	0.329764i
$51$		0			0
$52$	−628.534	−	1088.65i	−1.67619	−	2.90325i
$53$	293.518			0.760712			0.380356	−	0.924840i	$-0.375801\pi$
$53$	293.518			0.760712			0.380356	+	0.924840i	$0.375801\pi$
$54$		0			0
$55$	−64.1534			−0.157281
$56$	439.942	+	762.002i	1.04982	+	1.81834i
$57$		0			0
$58$	−538.390	+	932.519i	−1.21886	+	2.11113i
$59$	−290.692	+	503.493i	−0.641438	+	1.11100i	0.343674	+	0.939089i	$0.388328\pi$
$59$	−290.692	+	503.493i	−0.641438	+	1.11100i	−0.985112	+	0.171914i	$0.945005\pi$
$60$		0			0
$61$	386.847	+	670.038i	0.811977	+	1.40639i	0.911478	+	0.411349i	$0.134942\pi$
$61$	386.847	+	670.038i	0.811977	+	1.40639i	−0.0995008	+	0.995037i	$0.531725\pi$
$62$	−412.648			−0.845263
$63$		0			0
$64$	1372.15			2.67998
$65$	−149.661	−	259.221i	−0.285588	−	0.494652i
$66$		0			0
$67$	115.719	−	200.431i	0.211005	−	0.365471i	−0.741024	−	0.671478i	$-0.765660\pi$
$67$	115.719	−	200.431i	0.211005	−	0.365471i	0.952029	+	0.306007i	$0.0989931\pi$
$68$	−1155.03	+	2000.58i	−2.05983	+	3.56773i
$69$		0			0
$70$	169.227	+	293.110i	0.288950	+	0.500477i
$71$	744.342			1.24418			0.622092	−	0.782944i	$-0.286283\pi$
$71$	744.342			1.24418			0.622092	+	0.782944i	$0.286283\pi$
$72$		0			0
$73$	−264.839			−0.424616			−0.212308	−	0.977203i	$-0.568098\pi$
$73$	−264.839			−0.424616			−0.212308	+	0.977203i	$0.568098\pi$
$74$	−60.5317	−	104.844i	−0.0950901	−	0.164701i
$75$		0			0
$76$	126.907	−	219.809i	0.191542	−	0.331760i
$77$	80.6421	−	139.676i	0.119351	−	0.206722i
$78$		0			0
$79$	−279.858	−	484.729i	−0.398564	−	0.690333i	0.594985	−	0.803737i	$-0.297158\pi$
$79$	−279.858	−	484.729i	−0.398564	−	0.690333i	−0.993549	+	0.113404i	$0.963825\pi$
$80$	1044.75			1.46009
$81$		0			0
$82$	472.598			0.636460
$83$	−610.443	−	1057.32i	−0.807288	−	1.39826i	−0.914736	−	0.404052i	$-0.867601\pi$
$83$	−610.443	−	1057.32i	−0.807288	−	1.39826i	0.107448	−	0.994211i	$-0.465732\pi$
$84$		0			0
$85$	−275.027	+	476.361i	−0.350952	+	0.607866i
$86$	321.513	−	556.878i	0.403136	−	0.698252i
$87$		0			0
$88$	−449.059	−	777.792i	−0.543975	−	0.942193i
$89$	255.905			0.304785			0.152392	−	0.988320i	$-0.451302\pi$
$89$	255.905			0.304785			0.152392	+	0.988320i	$0.451302\pi$
$90$		0			0
$91$	752.509			0.866861
$92$	−711.027	−	1231.53i	−0.805757	−	1.39561i
$93$		0			0
$94$	−654.699	+	1133.97i	−0.718373	+	1.24426i
$95$	30.2179	−	52.3390i	0.0326347	−	0.0565249i
$96$		0			0
$97$	−524.759	−	908.909i	−0.549291	−	0.951400i	−0.998323	−	0.0578842i	$-0.981565\pi$
$97$	−524.759	−	908.909i	−0.549291	−	0.951400i	0.449032	−	0.893515i	$-0.351769\pi$
$98$	996.177			1.02683
$99$		0			0
$100$	524.964			0.524964
$101$	44.3635	+	76.8398i	0.0437062	+	0.0757014i	0.887051	−	0.461671i	$-0.152750\pi$
$101$	44.3635	+	76.8398i	0.0437062	+	0.0757014i	−0.843345	+	0.537373i	$0.819417\pi$
$102$		0			0
$103$	772.035	−	1337.20i	0.738552	−	1.27921i	−0.214595	−	0.976703i	$-0.568843\pi$
$103$	772.035	−	1337.20i	0.738552	−	1.27921i	0.953147	−	0.302507i	$-0.0978236\pi$
$104$	2095.19	−	3628.97i	1.97548	−	3.42163i
$105$		0			0
$106$	790.301	+	1368.84i	0.724158	+	1.25428i
$107$	585.772			0.529240			0.264620	−	0.964353i	$-0.414753\pi$
$107$	585.772			0.529240			0.264620	+	0.964353i	$0.414753\pi$
$108$		0			0
$109$	1367.04			1.20127			0.600634	−	0.799524i	$-0.294915\pi$
$109$	1367.04			1.20127			0.600634	+	0.799524i	$0.294915\pi$
$110$	−172.734	−	299.184i	−0.149723	−	0.259328i
$111$		0			0
$112$	−1313.28	+	2274.66i	−1.10797	+	1.91907i
$113$	85.2146	−	147.596i	0.0709408	−	0.122873i	−0.828373	−	0.560177i	$-0.810733\pi$
$113$	85.2146	−	147.596i	0.0709408	−	0.122873i	0.899314	+	0.437304i	$0.144067\pi$
$114$		0			0
$115$	−169.304	−	293.243i	−0.137284	−	0.237783i
$116$	−4198.83			−3.36079
$117$		0			0
$118$	−3130.77			−2.44246
$119$	−691.429	−	1197.59i	−0.532632	−	0.922546i
$120$		0			0
$121$	583.187	−	1010.11i	0.438157	−	0.758910i
$122$	−2083.18	+	3608.17i	−1.54592	+	2.67761i
$123$		0			0
$124$	−804.545	−	1393.51i	−0.582664	−	1.00920i
$125$	125.000			0.0894427
$126$		0			0
$127$	1809.74			1.26447			0.632237	−	0.774775i	$-0.282137\pi$
$127$	1809.74			1.26447			0.632237	+	0.774775i	$0.282137\pi$
$128$	1433.63	+	2483.13i	0.989973	+	1.71468i
$129$		0			0
$130$	805.930	−	1395.91i	0.543729	−	0.941766i
$131$	−619.147	+	1072.39i	−0.412940	+	0.715232i	−0.995210	−	0.0977630i	$-0.968831\pi$
$131$	−619.147	+	1072.39i	−0.412940	+	0.715232i	0.582270	+	0.812995i	$0.302165\pi$
$132$		0			0
$133$	75.9691	+	131.582i	0.0495290	+	0.0857867i
$134$	1246.30			0.803462
$135$		0			0
$136$	−7700.50			−4.85524
$137$	253.091	+	438.367i	0.157832	+	0.273374i	0.934087	−	0.357046i	$-0.116216\pi$
$137$	253.091	+	438.367i	0.157832	+	0.273374i	−0.776254	+	0.630420i	$0.782883\pi$
$138$		0			0
$139$	106.840	−	185.052i	0.0651946	−	0.112920i	−0.831586	−	0.555396i	$-0.812567\pi$
$139$	106.840	−	185.052i	0.0651946	−	0.112920i	0.896780	+	0.442476i	$0.145900\pi$
$140$	−659.890	+	1142.96i	−0.398363	+	0.689986i
$141$		0			0
$142$	2004.15	+	3471.29i	1.18440	+	2.05144i
$143$	−768.103			−0.449175
$144$		0			0
$145$	−999.790			−0.572607
$146$	−713.082	−	1235.09i	−0.404213	−	0.700117i
$147$		0			0
$148$	236.039	−	408.832i	0.131097	−	0.227066i
$149$	−452.655	+	784.022i	−0.248879	+	0.431071i	−0.963215	−	0.268732i	$-0.913395\pi$
$149$	−452.655	+	784.022i	−0.248879	+	0.431071i	0.714336	+	0.699803i	$0.246729\pi$
$150$		0			0
$151$	−679.335	−	1176.64i	−0.366116	−	0.634131i	0.622839	−	0.782350i	$-0.285979\pi$
$151$	−679.335	−	1176.64i	−0.366116	−	0.634131i	−0.988955	+	0.148219i	$0.952646\pi$
$152$	846.073			0.451484
$153$		0			0
$154$	868.521			0.454464
$155$	−191.572	−	331.812i	−0.0992736	−	0.171947i
$156$		0			0
$157$	−950.670	+	1646.61i	−0.483259	+	0.837030i	−0.999815	−	0.0192236i	$-0.993881\pi$
$157$	−950.670	+	1646.61i	−0.483259	+	0.837030i	0.516556	+	0.856254i	$0.327214\pi$
$158$	1507.05	−	2610.28i	0.758824	−	1.31432i
$159$		0			0
$160$	1413.06	+	2447.50i	0.698203	+	1.20932i
$161$	851.273			0.416706
$162$		0			0
$163$	−2325.15			−1.11730			−0.558649	−	0.829404i	$-0.688680\pi$
$163$	−2325.15			−1.11730			−0.558649	+	0.829404i	$0.688680\pi$
$164$	921.432	+	1595.97i	0.438730	+	0.759903i
$165$		0			0
$166$	3287.26	−	5693.69i	1.53699	−	2.66215i
$167$	982.901	−	1702.43i	0.455444	−	0.788853i	−0.543269	−	0.839558i	$-0.682814\pi$
$167$	982.901	−	1702.43i	0.455444	−	0.788853i	0.998714	+	0.0507059i	$0.0161471\pi$
$168$		0			0
$169$	−693.379	−	1200.97i	−0.315603	−	0.546640i
$170$	−2962.06			−1.33635
$171$		0			0
$172$	2507.44			1.11157
$173$	−1148.95	−	1990.04i	−0.504932	−	0.874567i	−0.999984	−	0.00570381i	$-0.998184\pi$
$173$	−1148.95	−	1990.04i	−0.504932	−	0.874567i	0.495052	−	0.868863i	$-0.335149\pi$
$174$		0			0
$175$	−157.127	+	272.153i	−0.0678727	+	0.117559i
$176$	1340.49	−	2321.80i	0.574110	−	0.994387i
$177$		0			0
$178$	689.027	+	1193.43i	0.290139	+	0.502536i
$179$	873.696			0.364822			0.182411	−	0.983222i	$-0.441610\pi$
$179$	873.696			0.364822			0.182411	+	0.983222i	$0.441610\pi$
$180$		0			0
$181$	1494.20			0.613609			0.306805	−	0.951772i	$-0.400740\pi$
$181$	1494.20			0.613609			0.306805	+	0.951772i	$0.400740\pi$
$182$	2026.14	+	3509.38i	0.825206	+	1.42930i
$183$		0			0
$184$	2370.17	−	4105.26i	0.949627	−	1.64480i
$185$	56.2037	−	97.3476i	0.0223361	−	0.0386872i
$186$		0			0
$187$	705.758	+	1222.41i	0.275990	+	0.478028i
$188$	−5105.91			−1.98078
$189$		0			0
$190$	325.449			0.124266
$191$	2525.13	+	4373.65i	0.956607	+	1.65689i	0.730648	+	0.682754i	$0.239218\pi$
$191$	2525.13	+	4373.65i	0.956607	+	1.65689i	0.225959	+	0.974137i	$0.427449\pi$
$192$		0			0
$193$	−2580.80	+	4470.08i	−0.962539	+	1.66717i	−0.246452	+	0.969155i	$0.579265\pi$
$193$	−2580.80	+	4470.08i	−0.962539	+	1.66717i	−0.716087	+	0.698011i	$0.754069\pi$
$194$	2825.84	−	4894.50i	1.04579	−	1.81137i
$195$		0			0
$196$	1942.26	+	3364.10i	0.707822	+	1.22598i
$197$	−374.025			−0.135270			−0.0676350	−	0.997710i	$-0.521545\pi$
$197$	−374.025			−0.135270			−0.0676350	+	0.997710i	$0.521545\pi$
$198$		0			0
$199$	603.342			0.214924			0.107462	−	0.994209i	$-0.465728\pi$
$199$	603.342			0.214924			0.107462	+	0.994209i	$0.465728\pi$
$200$	874.970	+	1515.49i	0.309349	+	0.535808i
$201$		0			0
$202$	−238.899	+	413.785i	−0.0832121	+	0.144128i
$203$	1256.76	−	2176.76i	0.434517	−	0.752606i
$204$		0			0
$205$	219.404	+	380.018i	0.0747504	+	0.129471i
$206$	8314.87			2.81225
$207$		0			0
$208$	12508.7			4.16983
$209$	−77.5434	−	134.309i	−0.0256640	−	0.0444514i
$210$		0			0
$211$	−1205.91	+	2088.69i	−0.393450	+	0.681476i	−0.992902	−	0.118935i	$-0.962052\pi$
$211$	−1205.91	+	2088.69i	−0.393450	+	0.681476i	0.599452	+	0.800411i	$0.295385\pi$
$212$	−3081.72	+	5337.70i	−0.998366	+	1.72922i
$213$		0			0
$214$	1577.20	+	2731.79i	0.503809	+	0.872623i
$215$	597.050			0.189388
$216$		0			0
$217$	963.237			0.301331
$218$	3680.76	+	6375.27i	1.14354	+	1.98068i
$219$		0			0
$220$	673.565	−	1166.65i	0.206417	−	0.357525i
$221$	−3292.87	+	5703.42i	−1.00227	+	1.73599i
$222$		0			0
$223$	−2740.64	−	4746.93i	−0.822990	−	1.42546i	−0.903446	−	0.428703i	$-0.858971\pi$
$223$	−2740.64	−	4746.93i	−0.822990	−	1.42546i	0.0804554	−	0.996758i	$-0.474363\pi$
$224$	−7105.00			−2.11930
$225$		0			0
$226$	917.766			0.270128
$227$	−2736.24	−	4739.30i	−0.800046	−	1.38572i	−0.919585	−	0.392891i	$-0.871475\pi$
$227$	−2736.24	−	4739.30i	−0.800046	−	1.38572i	0.119539	−	0.992830i	$-0.461858\pi$
$228$		0			0
$229$	−1637.99	+	2837.08i	−0.472670	+	0.818689i	−0.999511	−	0.0312750i	$-0.990043\pi$
$229$	−1637.99	+	2837.08i	−0.472670	+	0.818689i	0.526840	+	0.849964i	$0.323377\pi$
$230$	911.706	−	1579.12i	0.261374	−	0.452714i
$231$		0			0
$232$	−6998.29	−	12121.4i	−1.98043	−	3.43021i
$233$	−3446.21			−0.968965			−0.484483	−	0.874801i	$-0.660992\pi$
$233$	−3446.21			−0.968965			−0.484483	+	0.874801i	$0.660992\pi$
$234$		0			0
$235$	−1215.78			−0.337483
$236$	−6104.11	−	10572.6i	−1.68366	−	2.91618i
$237$		0			0
$238$	3723.37	−	6449.06i	1.01408	−	1.75643i
$239$	−862.406	+	1493.73i	−0.233408	+	0.404274i	−0.958809	−	0.284053i	$-0.908321\pi$
$239$	−862.406	+	1493.73i	−0.233408	+	0.404274i	0.725401	+	0.688326i	$0.241654\pi$
$240$		0			0
$241$	2787.86	+	4828.71i	0.745152	+	1.29064i	0.950124	+	0.311873i	$0.100956\pi$
$241$	2787.86	+	4828.71i	0.745152	+	1.29064i	−0.204972	+	0.978768i	$0.565710\pi$
$242$	6280.96			1.66841
$243$		0			0
$244$	−16246.4			−4.26259
$245$	462.475	+	801.031i	0.120598	+	0.208882i
$246$		0			0
$247$	361.796	−	626.649i	0.0932006	−	0.161428i
$248$	2681.91	−	4645.21i	0.686700	−	1.18940i
$249$		0			0
$250$	336.564	+	582.947i	0.0851448	+	0.147475i
$251$	1356.38			0.341090			0.170545	−	0.985350i	$-0.445447\pi$
$251$	1356.38			0.341090			0.170545	+	0.985350i	$0.445447\pi$
$252$		0			0
$253$	−868.913			−0.215921
$254$	4872.75	+	8439.84i	1.20371	+	2.08489i
$255$		0			0
$256$	−2231.56	+	3865.18i	−0.544815	+	0.943647i
$257$	−2043.91	+	3540.16i	−0.496092	+	0.859256i	−0.999990	−	0.00450688i	$-0.998565\pi$
$257$	−2043.91	+	3540.16i	−0.496092	+	0.859256i	0.503898	+	0.863763i	$0.331899\pi$
$258$		0			0
$259$	141.298	+	244.736i	0.0338990	+	0.0587148i
$260$	6285.34			1.49923
$261$		0			0
$262$	−6668.25			−1.57239
$263$	−215.130	−	372.616i	−0.0504391	−	0.0873631i	0.839704	−	0.543045i	$-0.182729\pi$
$263$	−215.130	−	372.616i	−0.0504391	−	0.0873631i	−0.890143	+	0.455682i	$0.849395\pi$
$264$		0			0
$265$	−733.794	+	1270.97i	−0.170100	+	0.294623i
$266$	−409.096	+	708.575i	−0.0942980	+	0.163329i
$267$		0			0
$268$	2429.93	+	4208.76i	0.553849	+	0.959295i
$269$	−3467.85			−0.786017			−0.393008	−	0.919535i	$-0.628566\pi$
$269$	−3467.85			−0.786017			−0.393008	+	0.919535i	$0.628566\pi$
$270$		0			0
$271$	−55.4415			−0.0124274			−0.00621371	−	0.999981i	$-0.501978\pi$
$271$	−55.4415			−0.0124274			−0.00621371	+	0.999981i	$0.501978\pi$
$272$	−11493.4	−	19907.2i	−2.56210	−	4.43769i
$273$		0			0
$274$	−1362.90	+	2360.62i	−0.300497	+	0.520475i
$275$	160.384	−	277.793i	0.0351691	−	0.0609146i
$276$		0			0
$277$	786.769	+	1362.72i	0.170658	+	0.295589i	0.938650	−	0.344871i	$-0.112077\pi$
$277$	786.769	+	1362.72i	0.170658	+	0.295589i	−0.767992	+	0.640460i	$0.778744\pi$
$278$	1150.67			0.248247
$279$		0			0
$280$	−4399.42			−0.938984
$281$	4073.23	+	7055.04i	0.864727	+	1.49775i	0.867318	+	0.497755i	$0.165842\pi$
$281$	4073.23	+	7055.04i	0.864727	+	1.49775i	−0.00259078	+	0.999997i	$0.500825\pi$
$282$		0			0
$283$	−1549.15	+	2683.21i	−0.325398	+	0.563605i	−0.981593	−	0.190986i	$-0.938832\pi$
$283$	−1549.15	+	2683.21i	−0.325398	+	0.563605i	0.656195	+	0.754591i	$0.272165\pi$
$284$	−7815.05	+	13536.1i	−1.63288	+	2.82823i
$285$		0			0
$286$	−2068.13	−	3582.10i	−0.427591	−	0.740609i
$287$	−1103.18			−0.226894
$288$		0			0
$289$	7189.39			1.46334
$290$	−2691.95	−	4662.59i	−0.545092	−	0.944127i
$291$		0			0
$292$	2780.61	−	4816.16i	0.557271	−	0.965221i
$293$	61.0799	−	105.794i	0.0121786	−	0.0210939i	−0.859872	−	0.510510i	$-0.829457\pi$
$293$	61.0799	−	105.794i	0.0121786	−	0.0210939i	0.872050	+	0.489416i	$0.162790\pi$
$294$		0			0
$295$	−1453.46	−	2517.46i	−0.286860	−	0.496856i
$296$	1573.65			0.309008
$297$		0			0
$298$	−4875.12			−0.947679
$299$	−2027.06	−	3510.97i	−0.392066	−	0.679078i
$300$		0			0
$301$	−750.504	+	1299.91i	−0.143715	+	0.248922i
$302$	3658.24	−	6336.25i	0.697046	−	1.20732i
$303$		0			0
$304$	1262.81	+	2187.25i	0.238247	+	0.412657i
$305$	−3868.47			−0.726255
$306$		0			0
$307$	−1928.53			−0.358525			−0.179263	−	0.983801i	$-0.557371\pi$
$307$	−1928.53			−0.358525			−0.179263	+	0.983801i	$0.557371\pi$
$308$	1693.37	+	2933.00i	0.313275	+	0.542608i
$309$		0			0
$310$	1031.62	−	1786.82i	0.189007	−	0.327369i
$311$	3969.65	−	6875.63i	0.723788	−	1.25364i	−0.235683	−	0.971830i	$-0.575733\pi$
$311$	3969.65	−	6875.63i	0.723788	−	1.25364i	0.959471	−	0.281807i	$-0.0909338\pi$
$312$		0			0
$313$	3379.44	+	5853.37i	0.610279	+	1.05703i	0.991193	+	0.132424i	$0.0422762\pi$
$313$	3379.44	+	5853.37i	0.610279	+	1.05703i	−0.380914	+	0.924611i	$0.624391\pi$
$314$	−10238.8			−1.84015
$315$		0			0
$316$	11753.2			2.09232
$317$	4212.12	+	7295.60i	0.746297	+	1.29262i	0.949587	+	0.313505i	$0.101503\pi$
$317$	4212.12	+	7295.60i	0.746297	+	1.29262i	−0.203290	+	0.979119i	$0.565163\pi$
$318$		0			0
$319$	−1282.80	+	2221.87i	−0.225150	+	0.389972i
$320$	−3430.38	+	5941.59i	−0.599262	+	1.03795i
$321$		0			0
$322$	2292.06	+	3969.97i	0.396683	+	0.687074i
$323$	−1329.72			−0.229064
$324$		0			0
$325$	1496.61			0.255437
$326$	−6260.49	−	10843.5i	−1.06361	−	1.84222i
$327$		0			0
$328$	−3071.55	+	5320.08i	−0.517067	+	0.895586i
$329$	1528.25	−	2647.01i	0.256095	−	0.443570i
$330$		0			0
$331$	−128.837	−	223.153i	−0.0213944	−	0.0370562i	0.855130	−	0.518414i	$-0.173477\pi$
$331$	−128.837	−	223.153i	−0.0213944	−	0.0370562i	−0.876524	+	0.481357i	$0.840144\pi$
$332$	25636.9			4.23797
$333$		0			0
$334$	10585.9			1.73424
$335$	578.595	+	1002.16i	0.0943642	+	0.163444i
$336$		0			0
$337$	5549.76	−	9612.47i	0.897077	−	1.55378i	0.0658636	−	0.997829i	$-0.479020\pi$
$337$	5549.76	−	9612.47i	0.897077	−	1.55378i	0.831213	−	0.555954i	$-0.187647\pi$
$338$	3733.87	−	6467.25i	0.600874	−	1.04075i
$339$		0			0
$340$	−5775.17	−	10002.9i	−0.921184	−	1.59554i
$341$	−983.198			−0.156138
$342$		0			0
$343$	−6636.94			−1.04478
$344$	4179.21	+	7238.60i	0.655023	+	1.13453i
$345$		0			0
$346$	6187.14	−	10716.4i	0.961337	−	1.66508i
$347$	4943.28	−	8562.02i	0.764753	−	1.32459i	−0.175624	−	0.984457i	$-0.556194\pi$
$347$	4943.28	−	8562.02i	0.764753	−	1.32459i	0.940377	−	0.340134i	$-0.110472\pi$
$348$		0			0
$349$	−3029.60	−	5247.42i	−0.464673	−	0.804837i	0.534514	−	0.845160i	$-0.320495\pi$
$349$	−3029.60	−	5247.42i	−0.464673	−	0.804837i	−0.999187	+	0.0403230i	$0.987161\pi$
$350$	−1692.27			−0.258445
$351$		0			0
$352$	7252.23			1.09814
$353$	−4548.34	−	7877.96i	−0.685790	−	1.18782i	−0.973188	−	0.230012i	$-0.926123\pi$
$353$	−4548.34	−	7877.96i	−0.685790	−	1.18782i	0.287398	−	0.957811i	$-0.407210\pi$
$354$		0			0
$355$	−1860.85	+	3223.10i	−0.278208	+	0.481871i
$356$	−2686.81	+	4653.70i	−0.400002	+	0.692824i
$357$		0			0
$358$	2352.44	+	4074.55i	0.347291	+	0.601527i
$359$	8804.63			1.29440			0.647201	−	0.762319i	$-0.275939\pi$
$359$	8804.63			1.29440			0.647201	+	0.762319i	$0.275939\pi$
$360$		0			0
$361$	−6712.90			−0.978700
$362$	4023.17	+	6968.33i	0.584124	+	1.01173i
$363$		0			0
$364$	−7900.80	+	13684.6i	−1.13768	+	1.97051i
$365$	662.096	−	1146.78i	0.0949471	−	0.164453i
$366$		0			0
$367$	−4326.18	−	7493.17i	−0.615326	−	1.06578i	−0.990327	−	0.138752i	$-0.955691\pi$
$367$	−4326.18	−	7493.17i	−0.615326	−	1.06578i	0.375001	−	0.927025i	$-0.377642\pi$
$368$	14150.5			2.00447
$369$		0			0
$370$	605.317			0.0850511
$371$	−1844.79	−	3195.27i	−0.258158	−	0.447143i
$372$		0			0
$373$	5959.31	−	10321.8i	0.827243	−	1.43283i	−0.0729500	−	0.997336i	$-0.523241\pi$
$373$	5959.31	−	10321.8i	0.827243	−	1.43283i	0.900193	−	0.435491i	$-0.143425\pi$
$374$	−3800.53	+	6582.70i	−0.525456	+	0.910116i
$375$		0			0
$376$	−8510.14	−	14740.0i	−1.16723	−	2.02170i
$377$	−11970.4			−1.63529
$378$		0			0
$379$	5052.23			0.684738			0.342369	−	0.939566i	$-0.388771\pi$
$379$	5052.23			0.684738			0.342369	+	0.939566i	$0.388771\pi$
$380$	634.533	+	1099.04i	0.0856601	+	0.148368i
$381$		0			0
$382$	−13597.9	+	23552.2i	−1.82128	+	3.15455i
$383$	−2665.19	+	4616.24i	−0.355573	+	0.615871i	−0.987216	−	0.159388i	$-0.949048\pi$
$383$	−2665.19	+	4616.24i	−0.355573	+	0.615871i	0.631642	+	0.775260i	$0.282381\pi$
$384$		0			0
$385$	403.211	+	698.381i	0.0533754	+	0.0924489i
$386$	−27795.4			−3.66515
$387$		0			0
$388$	22038.4			2.88358
$389$	1669.76	+	2892.11i	0.217635	+	0.376955i	0.954085	−	0.299537i	$-0.0968324\pi$
$389$	1669.76	+	2892.11i	0.217635	+	0.376955i	−0.736449	+	0.676493i	$0.763499\pi$
$390$		0			0
$391$	−3725.05	+	6451.98i	−0.481800	+	0.834503i
$392$	−6474.43	+	11214.0i	−0.834205	+	1.44488i
$393$		0			0
$394$	−1007.07	−	1744.29i	−0.128770	−	0.223036i
$395$	2798.58			0.356486
$396$		0			0
$397$	9041.65			1.14304			0.571520	−	0.820588i	$-0.306354\pi$
$397$	9041.65			1.14304			0.571520	+	0.820588i	$0.306354\pi$
$398$	1624.51	+	2813.73i	0.204596	+	0.354371i
$399$		0			0
$400$	−2611.89	+	4523.92i	−0.326486	+	0.565490i
$401$	−835.978	+	1447.96i	−0.104107	+	0.180318i	−0.913373	−	0.407124i	$-0.866532\pi$
$401$	−835.978	+	1447.96i	−0.104107	+	0.180318i	0.809266	+	0.587442i	$0.199865\pi$
$402$		0			0
$403$	−2293.67	−	3972.75i	−0.283513	−	0.491059i
$404$	−1863.14			−0.229442
$405$		0			0
$406$	13535.3			1.65455
$407$	−144.226	−	249.807i	−0.0175652	−	0.0304238i
$408$		0			0
$409$	−236.363	+	409.393i	−0.0285755	+	0.0494943i	−0.879960	−	0.475049i	$-0.842430\pi$
$409$	−236.363	+	409.393i	−0.0285755	+	0.0494943i	0.851384	+	0.524543i	$0.175764\pi$
$410$	−1181.50	+	2046.41i	−0.142317	+	0.246500i
$411$		0			0
$412$	16211.6	+	28079.4i	1.93857	+	3.35770i
$413$	7308.11			0.870722
$414$		0			0
$415$	6104.43			0.722060
$416$	16918.5	+	29303.7i	1.99398	+	3.45368i
$417$		0			0
$418$	417.573	−	723.258i	0.0488617	−	0.0846309i
$419$	6269.65	−	10859.3i	0.731008	−	1.26614i	−0.225445	−	0.974256i	$-0.572384\pi$
$419$	6269.65	−	10859.3i	0.731008	−	1.26614i	0.956453	−	0.291887i	$-0.0942830\pi$
$420$		0			0
$421$	3375.88	+	5847.19i	0.390808	+	0.676900i	0.992556	−	0.121786i	$-0.0388623\pi$
$421$	3375.88	+	5847.19i	0.390808	+	0.676900i	−0.601748	+	0.798686i	$0.705529\pi$
$422$	−12987.7			−1.49818
$423$		0			0
$424$	−20545.5			−2.35325
$425$	−1375.14	−	2381.81i	−0.156950	−	0.271846i
$426$		0			0
$427$	4862.74	−	8422.51i	0.551111	−	0.954552i
$428$	−6150.18	+	10652.4i	−0.694580	+	1.20305i
$429$		0			0
$430$	1607.57	+	2784.39i	0.180288	+	0.312268i
$431$	−7535.06			−0.842114			−0.421057	−	0.907034i	$-0.638341\pi$
$431$	−7535.06			−0.842114			−0.421057	+	0.907034i	$0.638341\pi$
$432$		0			0
$433$	−5135.13			−0.569928			−0.284964	−	0.958538i	$-0.591982\pi$
$433$	−5135.13			−0.569928			−0.284964	+	0.958538i	$0.591982\pi$
$434$	2593.53	+	4492.13i	0.286851	+	0.496841i
$435$		0			0
$436$	−14352.9	+	24859.9i	−1.57656	+	2.73068i
$437$	409.281	−	708.895i	0.0448022	−	0.0775996i
$438$		0			0
$439$	−8486.60	−	14699.2i	−0.922650	−	1.59808i	−0.795297	−	0.606220i	$-0.792685\pi$
$439$	−8486.60	−	14699.2i	−0.922650	−	1.59808i	−0.127353	−	0.991857i	$-0.540648\pi$
$440$	4490.59			0.486546
$441$		0			0
$442$	−35464.4			−3.81645
$443$	5676.15	+	9831.39i	0.608763	+	1.05441i	0.991445	+	0.130529i	$0.0416675\pi$
$443$	5676.15	+	9831.39i	0.608763	+	1.05441i	−0.382681	+	0.923880i	$0.624999\pi$
$444$		0			0
$445$	−639.762	+	1108.10i	−0.0681519	+	0.118043i
$446$	14758.4	−	25562.3i	1.56689	−	2.71393i
$447$		0			0
$448$	−8624.10	−	14937.4i	−0.909488	−	1.57528i
$449$	−11059.8			−1.16246			−0.581230	−	0.813740i	$-0.697428\pi$
$449$	−11059.8			−1.16246			−0.581230	+	0.813740i	$0.697428\pi$
$450$		0			0
$451$	1126.04			0.117568
$452$	1789.38	+	3099.30i	0.186207	+	0.322520i
$453$		0			0
$454$	14734.7	−	25521.3i	1.52320	−	2.63827i
$455$	−1881.27	+	3258.46i	−0.193836	+	0.335734i
$456$		0			0
$457$	−178.342	−	308.897i	−0.0182549	−	0.0316184i	0.856754	−	0.515726i	$-0.172478\pi$
$457$	−178.342	−	308.897i	−0.0182549	−	0.0316184i	−0.875009	+	0.484107i	$0.839144\pi$
$458$	−17641.3			−1.79983
$459$		0			0
$460$	7110.27			0.720691
$461$	5159.88	+	8937.17i	0.521300	+	0.902918i	0.999693	+	0.0247726i	$0.00788616\pi$
$461$	5159.88	+	8937.17i	0.521300	+	0.902918i	−0.478393	+	0.878146i	$0.658781\pi$
$462$		0			0
$463$	9084.27	−	15734.4i	0.911839	−	1.57935i	0.100376	−	0.994950i	$-0.467996\pi$
$463$	9084.27	−	15734.4i	0.911839	−	1.57935i	0.811464	−	0.584403i	$-0.198671\pi$
$464$	20890.7	−	36183.7i	2.09014	−	3.62023i
$465$		0			0
$466$	−9278.98	−	16071.7i	−0.922404	−	1.59765i
$467$	−3817.15			−0.378237			−0.189118	−	0.981954i	$-0.560563\pi$
$467$	−3817.15			−0.378237			−0.189118	+	0.981954i	$0.560563\pi$
$468$		0			0
$469$	−2909.22			−0.286429
$470$	−3273.50	−	5669.86i	−0.321266	−	0.556449i
$471$		0			0
$472$	20347.7	−	35243.3i	1.98428	−	3.43687i
$473$	766.056	−	1326.85i	0.0744679	−	0.128982i
$474$		0			0
$475$	151.090	+	261.695i	0.0145947	+	0.0252787i
$476$	29038.0			2.79613
$477$		0			0
$478$	−9288.17			−0.888768
$479$	1453.28	+	2517.16i	0.138627	+	0.240109i	0.926977	−	0.375118i	$-0.122398\pi$
$479$	1453.28	+	2517.16i	0.138627	+	0.240109i	−0.788350	+	0.615227i	$0.789064\pi$
$480$		0			0
$481$	672.921	−	1165.53i	0.0637891	−	0.110486i
$482$	−15012.7	+	26002.7i	−1.41869	+	2.45725i
$483$		0			0
$484$	12246.1	+	21210.8i	1.15008	+	1.99200i
$485$	5247.59			0.491301
$486$		0			0
$487$	10411.1			0.968734			0.484367	−	0.874865i	$-0.339050\pi$
$487$	10411.1			0.968734			0.484367	+	0.874865i	$0.339050\pi$
$488$	−27078.3	−	46901.0i	−2.51184	−	4.35064i
$489$		0			0
$490$	−2490.44	+	4313.57i	−0.229606	+	0.397689i
$491$	7316.26	−	12672.1i	0.672460	−	1.16474i	−0.304744	−	0.952434i	$-0.598571\pi$
$491$	7316.26	−	12672.1i	0.672460	−	1.16474i	0.977204	−	0.212301i	$-0.0680958\pi$
$492$		0			0
$493$	10998.8	+	19050.4i	1.00479	+	1.74034i
$494$	3896.57			0.354888
$495$		0			0
$496$	16011.6			1.44948
$497$	−4678.26	−	8102.99i	−0.422231	−	0.731325i
$498$		0			0
$499$	−4083.42	+	7072.69i	−0.366330	+	0.634503i	−0.988989	−	0.147991i	$-0.952719\pi$
$499$	−4083.42	+	7072.69i	−0.366330	+	0.634503i	0.622658	+	0.782494i	$0.286053\pi$
$500$	−1312.41	+	2273.16i	−0.117385	+	0.203318i
$501$		0			0
$502$	3652.06	+	6325.56i	0.324700	+	0.562397i
$503$	8080.38			0.716275			0.358137	−	0.933669i	$-0.383412\pi$
$503$	8080.38			0.716275			0.358137	+	0.933669i	$0.383412\pi$
$504$		0			0
$505$	−443.635			−0.0390921
$506$	−2339.56	−	4052.24i	−0.205546	−	0.356016i
$507$		0			0
$508$	−19000.9	+	32910.6i	−1.65951	+	2.87435i
$509$	58.0903	−	100.615i	0.00505856	−	0.00876169i	−0.863485	−	0.504374i	$-0.831723\pi$
$509$	58.0903	−	100.615i	0.00505856	−	0.00876169i	0.868544	+	0.495613i	$0.165056\pi$
$510$		0			0
$511$	1664.54	+	2883.06i	0.144099	+	0.249587i
$512$	−1095.90			−0.0945947
$513$		0			0
$514$	−22013.0			−1.88901
$515$	3860.18	+	6686.02i	0.330291	+	0.572080i
$516$		0			0
$517$	−1559.92	+	2701.87i	−0.132699	+	0.229841i
$518$	−760.895	+	1317.91i	−0.0645402	+	0.111787i
$519$		0			0
$520$	10475.9	+	18144.8i	0.883461	+	1.53020i
$521$	14479.3			1.21756			0.608780	−	0.793339i	$-0.291659\pi$
$521$	14479.3			1.21756			0.608780	+	0.793339i	$0.291659\pi$
$522$		0			0
$523$	6841.05			0.571966			0.285983	−	0.958235i	$-0.407680\pi$
$523$	6841.05			0.571966			0.285983	+	0.958235i	$0.407680\pi$
$524$	−13001.2	−	22518.7i	−1.08389	−	1.87736i
$525$		0			0
$526$	1158.48	−	2006.55i	0.0960308	−	0.166330i
$527$	−4214.99	+	7300.58i	−0.348402	+	0.603450i
$528$		0			0
$529$	3790.40	+	6565.16i	0.311531	+	0.539588i
$530$	−7903.01			−0.647707
$531$		0			0
$532$	−3190.48			−0.260009
$533$	2626.90	+	4549.92i	0.213478	+	0.369754i
$534$		0			0
$535$	−1464.43	+	2536.47i	−0.118342	+	0.204974i
$536$	−8100.05	+	14029.7i	−0.652741	+	1.13058i
$537$		0			0
$538$	−9337.24	−	16172.6i	−0.748247	−	1.29600i
$539$	2373.55			0.189677
$540$		0			0
$541$	−12746.0			−1.01293			−0.506465	−	0.862261i	$-0.669048\pi$
$541$	−12746.0			−1.01293			−0.506465	+	0.862261i	$0.669048\pi$
$542$	−149.277	−	258.555i	−0.0118303	−	0.0204906i
$543$		0			0
$544$	31090.5	−	53850.3i	2.45036	−	4.24414i
$545$	−3417.59	+	5919.44i	−0.268612	+	0.465249i
$546$		0			0
$547$	−2490.27	−	4313.28i	−0.194655	−	0.337152i	0.752132	−	0.659012i	$-0.229025\pi$
$547$	−2490.27	−	4313.28i	−0.194655	−	0.337152i	−0.946787	+	0.321860i	$0.895692\pi$
$548$	−10629.1			−0.828563
$549$		0			0
$550$	1727.34			0.133916
$551$	−1208.46	−	2093.12i	−0.0934342	−	0.161833i
$552$		0			0
$553$	−3517.88	+	6093.14i	−0.270516	+	0.468547i
$554$	−4236.77	+	7338.31i	−0.324916	+	0.562771i
$555$		0			0
$556$	2243.48	+	3885.83i	0.171124	+	0.296395i
$557$	635.610			0.0483513			0.0241756	−	0.999708i	$-0.492304\pi$
$557$	635.610			0.0483513			0.0241756	+	0.999708i	$0.492304\pi$
$558$		0			0
$559$	7148.42			0.540869
$560$	−6566.38	−	11373.3i	−0.495501	−	0.858232i
$561$		0			0
$562$	−21934.4	+	37991.6i	−1.64635	+	2.85156i
$563$	−3768.84	+	6527.82i	−0.282127	+	0.488659i	−0.971908	−	0.235359i	$-0.924373\pi$
$563$	−3768.84	+	6527.82i	−0.282127	+	0.488659i	0.689781	+	0.724018i	$0.257707\pi$
$564$		0			0
$565$	426.073	+	737.980i	0.0317257	+	0.0549505i
$566$	−16684.5			−1.23905
$567$		0			0
$568$	−52102.2			−3.84887
$569$	−1129.18	−	1955.79i	−0.0831943	−	0.144097i	0.821426	−	0.570315i	$-0.193179\pi$
$569$	−1129.18	−	1955.79i	−0.0831943	−	0.144097i	−0.904620	+	0.426218i	$0.859846\pi$
$570$		0			0
$571$	−5688.66	+	9853.06i	−0.416923	+	0.722132i	−0.995628	−	0.0934047i	$-0.970225\pi$
$571$	−5688.66	+	9853.06i	−0.416923	+	0.722132i	0.578705	+	0.815537i	$0.303558\pi$
$572$	8064.52	−	13968.2i	0.589501	−	1.02105i
$573$		0			0
$574$	−2970.33	−	5144.76i	−0.215991	−	0.374108i
$575$	1693.04			0.122791
$576$		0			0
$577$	−25027.9			−1.80576			−0.902881	−	0.429890i	$-0.858553\pi$
$577$	−25027.9			−1.80576			−0.902881	+	0.429890i	$0.858553\pi$
$578$	19357.5	+	33528.3i	1.39302	+	2.41279i
$579$		0			0
$580$	10497.1	−	18181.5i	0.751495	−	1.30163i
$581$	−7673.39	+	13290.7i	−0.547928	+	0.949039i
$582$		0			0
$583$	1883.02	+	3261.48i	0.133768	+	0.231692i
$584$	18538.1			1.31355
$585$		0			0
$586$	657.835			0.0463736
$587$	74.1295	+	128.396i	0.00521235	+	0.00902806i	0.868620	−	0.495479i	$-0.165008\pi$
$587$	74.1295	+	128.396i	0.00521235	+	0.00902806i	−0.863407	+	0.504507i	$0.831674\pi$
$588$		0			0
$589$	463.112	−	802.133i	0.0323976	−	0.0561143i
$590$	7826.92	−	13556.6i	0.546151	−	0.945961i
$591$		0			0
$592$	2348.76	+	4068.17i	0.163063	+	0.282434i
$593$	27452.6			1.90109			0.950544	−	0.310590i	$-0.100527\pi$
$593$	27452.6			1.90109			0.950544	+	0.310590i	$0.100527\pi$
$594$		0			0
$595$	6914.29			0.476401
$596$	−9505.10	−	16463.3i	−0.653262	−	1.13148i
$597$		0			0
$598$	10915.8	−	18906.7i	0.746453	−	1.29289i
$599$	−1906.00	+	3301.29i	−0.130012	+	0.225187i	−0.923681	−	0.383163i	$-0.874835\pi$
$599$	−1906.00	+	3301.29i	−0.130012	+	0.225187i	0.793669	+	0.608350i	$0.208168\pi$
$600$		0			0
$601$	−11584.3	−	20064.6i	−0.786247	−	1.36182i	−0.928251	−	0.371954i	$-0.878688\pi$
$601$	−11584.3	−	20064.6i	−0.786247	−	1.36182i	0.142004	−	0.989866i	$-0.454646\pi$
$602$	−8082.97			−0.547238
$603$		0			0
$604$	28530.1			1.92197
$605$	2915.93	+	5050.55i	0.195950	+	0.339395i
$606$		0			0
$607$	−3676.39	+	6367.69i	−0.245832	+	0.425794i	−0.962365	−	0.271759i	$-0.912395\pi$
$607$	−3676.39	+	6367.69i	−0.245832	+	0.425794i	0.716533	+	0.697553i	$0.245728\pi$
$608$	−3415.99	+	5916.67i	−0.227856	+	0.394659i
$609$		0			0
$610$	−10415.9	−	18040.9i	−0.691357	−	1.19746i
$611$	−14556.4			−0.963809
$612$		0			0
$613$	19902.6			1.31135			0.655676	−	0.755043i	$-0.272384\pi$
$613$	19902.6			1.31135			0.655676	+	0.755043i	$0.272384\pi$
$614$	−5192.61	−	8993.86i	−0.341297	−	0.591144i
$615$		0			0
$616$	−5644.76	+	9777.01i	−0.369211	+	0.639492i
$617$	12542.6	−	21724.4i	0.818390	−	1.41749i	−0.0884785	−	0.996078i	$-0.528200\pi$
$617$	12542.6	−	21724.4i	0.818390	−	1.41749i	0.906868	−	0.421414i	$-0.138466\pi$
$618$		0			0
$619$	1565.52	+	2711.56i	0.101654	+	0.176069i	0.912366	−	0.409375i	$-0.134253\pi$
$619$	1565.52	+	2711.56i	0.101654	+	0.176069i	−0.810712	+	0.585445i	$0.800920\pi$
$620$	8045.45			0.521150
$621$		0			0
$622$	42753.3			2.75603
$623$	−1608.39	−	2785.81i	−0.103433	−	0.179151i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−18198.4	+	31520.6i	−1.16191	+	2.01248i
$627$		0			0
$628$	−19962.7	−	34576.4i	−1.26847	−	2.19705i
$629$	−2473.21			−0.156778
$630$		0			0
$631$	−22527.2			−1.42123			−0.710614	−	0.703582i	$-0.751583\pi$
$631$	−22527.2			−1.42123			−0.710614	+	0.703582i	$0.751583\pi$
$632$	19589.4	+	33929.9i	1.23295	+	2.13553i
$633$		0			0
$634$	−22682.4	+	39287.0i	−1.42087	+	2.46102i
$635$	−4524.34	+	7836.39i	−0.282745	+	0.489729i
$636$		0			0
$637$	5537.17	+	9590.66i	0.344412	+	0.596540i
$638$	−13815.8			−0.857325
$639$		0			0
$640$	−14336.3			−0.885459
$641$	−3462.88	−	5997.88i	−0.213378	−	0.369582i	0.739391	−	0.673276i	$-0.235113\pi$
$641$	−3462.88	−	5997.88i	−0.213378	−	0.369582i	−0.952770	+	0.303694i	$0.901780\pi$
$642$		0			0
$643$	7482.26	−	12959.7i	0.458898	−	0.794835i	−0.540005	−	0.841662i	$-0.681578\pi$
$643$	7482.26	−	12959.7i	0.458898	−	0.794835i	0.998903	+	0.0468271i	$0.0149110\pi$
$644$	−8937.75	+	15480.6i	−0.546889	+	0.947240i
$645$		0			0
$646$	−3580.29	−	6201.25i	−0.218057	−	0.377685i
$647$	2371.74			0.144115			0.0720577	−	0.997400i	$-0.477043\pi$
$647$	2371.74			0.144115			0.0720577	+	0.997400i	$0.477043\pi$
$648$		0			0
$649$	−7459.55			−0.451176
$650$	4029.65	+	6979.56i	0.243163	+	0.421171i
$651$		0			0
$652$	24412.4	−	42283.4i	1.46635	−	2.53980i
$653$	−7985.85	+	13831.9i	−0.478577	+	0.828919i	−0.999698	−	0.0245632i	$-0.992180\pi$
$653$	−7985.85	+	13831.9i	−0.478577	+	0.828919i	0.521122	+	0.853482i	$0.325514\pi$
$654$		0			0
$655$	−3095.73	−	5361.97i	−0.184672	−	0.319862i
$656$	−18337.8			−1.09142
$657$		0			0
$658$	16459.4			0.975158
$659$	−3421.46	−	5926.15i	−0.202248	−	0.350304i	0.747005	−	0.664819i	$-0.231491\pi$
$659$	−3421.46	−	5926.15i	−0.202248	−	0.350304i	−0.949252	+	0.314515i	$0.898158\pi$
$660$		0			0
$661$	6695.50	−	11597.0i	0.393986	−	0.682404i	−0.598985	−	0.800760i	$-0.704429\pi$
$661$	6695.50	−	11597.0i	0.393986	−	0.682404i	0.992971	+	0.118356i	$0.0377624\pi$
$662$	693.793	−	1201.68i	0.0407327	−	0.0705511i
$663$		0			0
$664$	42729.6	+	74009.8i	2.49733	+	4.32551i
$665$	−759.691			−0.0443001
$666$		0			0
$667$	−13541.5			−0.786098
$668$	20639.5	+	35748.7i	1.19546	+	2.07060i
$669$		0			0
$670$	−3115.75	+	5396.64i	−0.179660	+	0.311180i
$671$	−4963.51	+	8597.05i	−0.285565	+	0.494613i
$672$		0			0
$673$	15951.1	+	27628.1i	0.913624	+	1.58244i	0.808904	+	0.587941i	$0.200061\pi$
$673$	15951.1	+	27628.1i	0.913624	+	1.58244i	0.104720	+	0.994502i	$0.466605\pi$
$674$	59771.3			3.41588
$675$		0			0
$676$	29119.9			1.65680
$677$	−5930.38	−	10271.7i	−0.336666	−	0.583123i	0.647137	−	0.762373i	$-0.275966\pi$
$677$	−5930.38	−	10271.7i	−0.336666	−	0.583123i	−0.983803	+	0.179251i	$0.942633\pi$
$678$		0			0
$679$	−6596.33	+	11425.2i	−0.372818	+	0.645741i
$680$	19251.2	−	33344.1i	1.08566	−	1.88043i
$681$		0			0
$682$	−2647.28	−	4585.22i	−0.148636	−	0.257444i
$683$	−7639.34			−0.427981			−0.213991	−	0.976836i	$-0.568646\pi$
$683$	−7639.34			−0.427981			−0.213991	+	0.976836i	$0.568646\pi$
$684$		0			0
$685$	−2530.91			−0.141170
$686$	−17870.1	−	30951.9i	−0.994580	−	1.72266i
$687$		0			0
$688$	−12475.4	+	21608.0i	−0.691309	+	1.19738i
$689$	−8785.64	+	15217.2i	−0.485786	+	0.841406i
$690$		0			0
$691$	7863.00	+	13619.1i	0.432883	+	0.749776i	0.997120	−	0.0758369i	$-0.0241628\pi$
$691$	7863.00	+	13619.1i	0.432883	+	0.749776i	−0.564237	+	0.825613i	$0.690829\pi$
$692$	48252.6			2.65071
$693$		0			0
$694$	53239.5			2.91202
$695$	534.200	+	925.261i	0.0291559	+	0.0504995i
$696$		0			0
$697$	4827.36	−	8361.23i	0.262338	−	0.454382i
$698$	16314.5	−	28257.5i	0.884688	−	1.53232i
$699$		0			0
$700$	−3299.45	−	5714.81i	−0.178154	−	0.308571i
$701$	6338.17			0.341497			0.170748	−	0.985315i	$-0.445381\pi$
$701$	6338.17			0.341497			0.170748	+	0.985315i	$0.445381\pi$
$702$		0			0
$703$	271.737			0.0145786
$704$	8802.82	+	15246.9i	0.471262	+	0.816250i
$705$		0			0
$706$	24493.0	−	42423.1i	1.30567	−	2.26149i
$707$	557.658	−	965.892i	0.0296646	−	0.0513806i
$708$		0			0
$709$	−17191.8	−	29777.1i	−0.910651	−	1.57729i	−0.813147	−	0.582059i	$-0.802247\pi$
$709$	−17191.8	−	29777.1i	−0.910651	−	1.57729i	−0.0975047	−	0.995235i	$-0.531086\pi$
$710$	−20041.5			−1.05936
$711$		0			0
$712$	−17912.7			−0.942847
$713$	−2594.70	−	4494.16i	−0.136287	−	0.236055i
$714$		0			0
$715$	1920.26	−	3325.98i	0.100438	−	0.173965i
$716$	−9173.18	+	15888.4i	−0.478796	+	0.829299i
$717$		0			0
$718$	23706.6	+	41061.0i	1.23220	+	2.13424i
$719$	988.886			0.0512924			0.0256462	−	0.999671i	$-0.491836\pi$
$719$	988.886			0.0512924			0.0256462	+	0.999671i	$0.491836\pi$
$720$		0			0
$721$	−19409.3			−1.00255
$722$	−18074.6	−	31306.1i	−0.931671	−	1.61370i
$723$		0			0
$724$	−15688.1	+	27172.5i	−0.805307	+	1.39483i
$725$	2499.47	−	4329.22i	0.128039	−	0.221770i
$726$		0			0
$727$	6845.92	+	11857.5i	0.349245	+	0.604910i	0.986116	−	0.166061i	$-0.0531048\pi$
$727$	6845.92	+	11857.5i	0.349245	+	0.604910i	−0.636871	+	0.770971i	$0.719771\pi$
$728$	−52673.8			−2.68162
$729$		0			0
$730$	7130.82			0.361539
$731$	−6568.20	−	11376.5i	−0.332331	−	0.575614i
$732$		0			0
$733$	1250.97	−	2166.74i	0.0630363	−	0.109182i	−0.832785	−	0.553597i	$-0.813255\pi$
$733$	1250.97	−	2166.74i	0.0630363	−	0.109182i	0.895821	+	0.444415i	$0.146588\pi$
$734$	23296.6	−	40350.9i	1.17152	−	2.02913i
$735$		0			0
$736$	19139.0	+	33149.7i	0.958521	+	1.66021i
$737$	2969.51			0.148417
$738$		0			0
$739$	26453.1			1.31677			0.658384	−	0.752682i	$-0.271240\pi$
$739$	26453.1			1.31677			0.658384	+	0.752682i	$0.271240\pi$
$740$	1180.20	+	2044.16i	0.0586282	+	0.101547i
$741$		0			0
$742$	9934.24	−	17206.6i	0.491506	−	0.851313i
$743$	−10441.4	+	18085.0i	−0.515555	+	0.892967i	0.484282	+	0.874912i	$0.339081\pi$
$743$	−10441.4	+	18085.0i	−0.515555	+	0.892967i	−0.999837	+	0.0180555i	$0.994252\pi$
$744$		0			0
$745$	−2263.28	−	3920.11i	−0.111302	−	0.192781i
$746$	64182.2			3.14997
$747$		0			0
$748$	−29639.8			−1.44885
$749$	−3681.64	−	6376.78i	−0.179605	−	0.311085i
$750$		0			0
$751$	8847.65	−	15324.6i	0.429901	−	0.744610i	−0.566963	−	0.823743i	$-0.691882\pi$
$751$	8847.65	−	15324.6i	0.429901	−	0.744610i	0.996864	+	0.0791332i	$0.0252152\pi$
$752$	25403.7	−	44000.6i	1.23189	−	2.13369i
$753$		0			0
$754$	−32230.4	−	55824.8i	−1.55672	−	2.69631i
$755$	6793.35			0.327464
$756$		0			0
$757$	7755.61			0.372368			0.186184	−	0.982515i	$-0.440388\pi$
$757$	7755.61			0.372368			0.186184	+	0.982515i	$0.440388\pi$
$758$	13603.2	+	23561.4i	0.651835	+	1.12901i
$759$		0			0
$760$	−2115.18	+	3663.60i	−0.100955	+	0.174859i
$761$	8527.15	−	14769.5i	0.406188	−	0.703538i	−0.588271	−	0.808664i	$-0.700191\pi$
$761$	8527.15	−	14769.5i	0.406188	−	0.703538i	0.994459	+	0.105126i	$0.0335245\pi$
$762$		0			0
$763$	−8591.95	−	14881.7i	−0.407667	−	0.706099i
$764$	−106048.			−5.02184
$765$		0			0
$766$	−28704.2			−1.35395
$767$	−17402.1	−	30141.3i	−0.819236	−	1.41896i
$768$		0			0
$769$	5024.16	−	8702.11i	0.235599	−	0.408070i	−0.723847	−	0.689960i	$-0.757628\pi$
$769$	5024.16	−	8702.11i	0.235599	−	0.408070i	0.959447	+	0.281890i	$0.0909613\pi$
$770$	−2171.30	+	3760.81i	−0.101621	+	0.176013i
$771$		0			0
$772$	−54193.0	−	93865.1i	−2.52649	−	4.37601i
$773$	−7293.24			−0.339352			−0.169676	−	0.985500i	$-0.554272\pi$
$773$	−7293.24			−0.339352			−0.169676	+	0.985500i	$0.554272\pi$
$774$		0			0
$775$	1915.72			0.0887930
$776$	36731.9	+	63621.5i	1.69922	+	2.94314i
$777$		0			0
$778$	−8991.70	+	15574.1i	−0.414355	+	0.717684i
$779$	−530.394	+	918.670i	−0.0243945	+	0.0422526i
$780$		0			0
$781$	4775.21	+	8270.90i	0.218784	+	0.378945i
$782$	−40119.0			−1.83460
$783$		0			0
$784$	−38653.8			−1.76083
$785$	−4753.35	−	8233.04i	−0.216120	−	0.374331i
$786$		0			0
$787$	−14228.1	+	24643.8i	−0.644445	+	1.11621i	0.339985	+	0.940431i	$0.389578\pi$
$787$	−14228.1	+	24643.8i	−0.644445	+	1.11621i	−0.984429	+	0.175780i	$0.943755\pi$
$788$	3926.99	−	6801.75i	0.177530	−	0.307490i
$789$		0			0
$790$	7535.23	+	13051.4i	0.339356	+	0.587782i
$791$	−2142.33			−0.0962989
$792$		0			0
$793$	−46316.7			−2.07409
$794$	24344.8	+	42166.4i	1.08812	+	1.88467i
$795$		0			0
$796$	−6334.66	+	10971.9i	−0.282068	+	0.488556i
$797$	2040.73	−	3534.65i	0.0906981	−	0.157094i	−0.817107	−	0.576486i	$-0.804424\pi$
$797$	2040.73	−	3534.65i	0.0906981	−	0.157094i	0.907805	+	0.419392i	$0.137757\pi$
$798$		0			0
$799$	13374.9	+	23165.9i	0.592201	+	1.02572i
$800$	−14130.6			−0.624492
$801$		0			0
$802$	−9003.54			−0.396416
$803$	−1699.03	−	2942.81i	−0.0746668	−	0.129327i
$804$		0			0
$805$	−2128.18	+	3686.12i	−0.0931783	+	0.161390i
$806$	12351.5	−	21393.4i	0.539779	−	0.934925i
$807$		0			0
$808$	−3105.34	−	5378.60i	−0.135205	−	0.234181i
$809$	−14209.7			−0.617536			−0.308768	−	0.951137i	$-0.599917\pi$
$809$	−14209.7			−0.617536			−0.308768	+	0.951137i	$0.599917\pi$
$810$		0			0
$811$	4901.79			0.212238			0.106119	−	0.994353i	$-0.466158\pi$
$811$	4901.79			0.212238			0.106119	+	0.994353i	$0.466158\pi$
$812$	26390.0	+	45708.9i	1.14053	+	1.97545i
$813$		0			0
$814$	776.663	−	1345.22i	0.0334423	−	0.0579237i
$815$	5812.87	−	10068.2i	0.249835	−	0.432727i
$816$		0			0
$817$	721.665	+	1249.96i	0.0309031	+	0.0535258i
$818$	−2545.64			−0.108810
$819$		0			0
$820$	−9214.32			−0.392412
$821$	−7259.82	−	12574.4i	−0.308611	−	0.534530i	0.669448	−	0.742859i	$-0.266531\pi$
$821$	−7259.82	−	12574.4i	−0.308611	−	0.534530i	−0.978059	+	0.208329i	$0.933197\pi$
$822$		0			0
$823$	19203.2	−	33260.9i	0.813344	−	1.40875i	−0.0971672	−	0.995268i	$-0.530978\pi$
$823$	19203.2	−	33260.9i	0.813344	−	1.40875i	0.910511	−	0.413485i	$-0.135688\pi$
$824$	−54040.6	+	93601.1i	−2.28470	+	3.95722i
$825$		0			0
$826$	19677.2	+	34081.9i	0.828882	+	1.43567i
$827$	10446.4			0.439248			0.219624	−	0.975585i	$-0.429517\pi$
$827$	10446.4			0.439248			0.219624	+	0.975585i	$0.429517\pi$
$828$		0			0
$829$	−6474.00			−0.271232			−0.135616	−	0.990761i	$-0.543301\pi$
$829$	−6474.00			−0.271232			−0.135616	+	0.990761i	$0.543301\pi$
$830$	16436.3	+	28468.5i	0.687363	+	1.19055i
$831$		0			0
$832$	−41071.6	+	71138.0i	−1.71142	+	2.96426i
$833$	10175.5	−	17624.4i	0.423240	−	0.733073i
$834$		0			0
$835$	4914.51	+	8512.17i	0.203681	+	0.352786i
$836$	3256.60			0.134727
$837$		0			0
$838$	67524.5			2.78353
$839$	7919.71	+	13717.3i	0.325886	+	0.564452i	0.981691	−	0.190478i	$-0.0610039\pi$
$839$	7919.71	+	13717.3i	0.325886	+	0.564452i	−0.655805	+	0.754930i	$0.727671\pi$
$840$		0			0
$841$	−7797.09	+	13505.0i	−0.319697	+	0.553731i
$842$	−18179.2	+	31487.3i	−0.744058	+	1.28875i
$843$		0			0
$844$	−25322.3	−	43859.5i	−1.03274	−	1.78875i
$845$	6933.79			0.282284
$846$		0			0
$847$	−14661.5			−0.594778
$848$	−30665.4	−	53114.0i	−1.24181	−	2.15087i
$849$		0			0
$850$	7405.15	−	12826.1i	0.298817	−	0.517566i
$851$	761.239	−	1318.51i	0.0306639	−	0.0531114i
$852$		0			0
$853$	9420.17	+	16316.2i	0.378125	+	0.654931i	0.990789	−	0.135412i	$-0.0432357\pi$
$853$	9420.17	+	16316.2i	0.378125	+	0.654931i	−0.612665	+	0.790343i	$0.709902\pi$
$854$	52372.0			2.09852
$855$		0			0
$856$	−41002.6			−1.63720
$857$	4528.11	+	7842.91i	0.180487	+	0.312612i	0.942046	−	0.335483i	$-0.108899\pi$
$857$	4528.11	+	7842.91i	0.180487	+	0.312612i	−0.761560	+	0.648095i	$0.775566\pi$
$858$		0			0
$859$	−11027.7	+	19100.6i	−0.438022	+	0.758676i	−0.997537	−	0.0701440i	$-0.977654\pi$
$859$	−11027.7	+	19100.6i	−0.438022	+	0.758676i	0.559515	+	0.828820i	$0.310987\pi$
$860$	−6268.60	+	10857.5i	−0.248555	+	0.430510i
$861$		0			0
$862$	−20288.3	−	35140.3i	−0.801649	−	1.38850i
$863$	−13105.6			−0.516941			−0.258471	−	0.966019i	$-0.583219\pi$
$863$	−13105.6			−0.516941			−0.258471	+	0.966019i	$0.583219\pi$
$864$		0			0
$865$	11489.5			0.451624
$866$	−13826.4	−	23948.1i	−0.542542	−	0.939710i
$867$		0			0
$868$	−10113.3	+	17516.7i	−0.395470	+	0.684973i
$869$	3590.78	−	6219.41i	0.140171	−	0.242784i
$870$		0			0
$871$	6927.46	+	11998.7i	0.269492	+	0.466775i
$872$	−95689.2			−3.71611
$873$		0			0
$874$	4407.98			0.170597
$875$	−785.637	−	1360.76i	−0.0303536	−	0.0525740i
$876$		0			0
$877$	18361.1	−	31802.4i	0.706967	−	1.22450i	−0.259010	−	0.965875i	$-0.583396\pi$
$877$	18361.1	−	31802.4i	0.706967	−	1.22450i	0.965977	−	0.258628i	$-0.0832705\pi$
$878$	45700.6	−	79155.8i	1.75663	−	3.04257i
$879$		0			0
$880$	6702.46	+	11609.0i	0.256750	+	0.444704i
$881$	−36054.4			−1.37878			−0.689390	−	0.724390i	$-0.742121\pi$
$881$	−36054.4			−1.37878			−0.689390	+	0.724390i	$0.742121\pi$
$882$		0			0
$883$	13524.6			0.515446			0.257723	−	0.966219i	$-0.417028\pi$
$883$	13524.6			0.515446			0.257723	+	0.966219i	$0.417028\pi$
$884$	−69145.6	−	119764.i	−2.63079	−	4.55666i
$885$		0			0
$886$	−30566.3	+	52942.3i	−1.15902	+	2.00749i
$887$	−19865.1	+	34407.4i	−0.751978	+	1.30246i	0.194884	+	0.980826i	$0.437567\pi$
$887$	−19865.1	+	34407.4i	−0.751978	+	1.30246i	−0.946863	+	0.321639i	$0.895766\pi$
$888$		0			0
$889$	−11374.4	−	19701.0i	−0.429116	−	0.743251i
$890$	−6890.27			−0.259508
$891$		0			0
$892$	115099.			4.32040
$893$	−1469.53	−	2545.30i	−0.0550682	−	0.0953810i
$894$		0			0
$895$	−2184.24	+	3783.22i	−0.0815767	+	0.141295i
$896$	18021.1	−	31213.4i	0.671921	−	1.16380i
$897$		0			0
$898$	−29778.7	−	51578.2i	−1.10660	−	1.91669i
$899$	−15322.5			−0.568447
$900$		0			0
$901$	32290.1			1.19394
$902$	3031.88	+	5251.37i	0.111919	+	0.193849i
$903$		0			0
$904$	−5964.81	+	10331.4i	−0.219454	+	0.380106i
$905$	−3735.51	+	6470.09i	−0.137207	+	0.237650i
$906$		0			0
$907$	−11511.2	−	19938.0i	−0.421415	−	0.729912i	0.574663	−	0.818390i	$-0.305133\pi$
$907$	−11511.2	−	19938.0i	−0.421415	−	0.729912i	−0.996078	+	0.0884783i	$0.971800\pi$
$908$	114914.			4.19995
$909$		0			0
$910$	−20261.4			−0.738087
$911$	15940.1	+	27609.1i	0.579714	+	1.00409i	0.995512	+	0.0946365i	$0.0301689\pi$
$911$	15940.1	+	27609.1i	0.579714	+	1.00409i	−0.415798	+	0.909457i	$0.636498\pi$
$912$		0			0
$913$	7832.41	−	13566.1i	0.283916	−	0.491756i
$914$	960.376	−	1663.42i	0.0347554	−	0.0601981i
$915$		0			0
$916$	−34395.5	−	59574.7i	−1.24067	−	2.14891i
$917$	15565.6			0.560547
$918$		0			0
$919$	38459.6			1.38049			0.690243	−	0.723578i	$-0.257504\pi$
$919$	38459.6			1.38049			0.690243	+	0.723578i	$0.257504\pi$
$920$	11850.9	+	20526.3i	0.424686	+	0.735578i
$921$		0			0
$922$	−27786.1	+	48126.9i	−0.992501	+	1.71906i
$923$	−22279.8	+	38589.8i	−0.794528	+	1.37616i
$924$		0			0
$925$	281.018	+	486.738i	0.00998900	+	0.0173015i
$926$	97838.1			3.47209
$927$		0			0
$928$	113021.			3.99796
$929$	−18600.5	−	32217.1i	−0.656903	−	1.13779i	−0.981413	−	0.191908i	$-0.938533\pi$
$929$	−18600.5	−	32217.1i	−0.656903	−	1.13779i	0.324509	−	0.945882i	$-0.394801\pi$
$930$		0			0
$931$	−1118.00	+	1936.44i	−0.0393567	+	0.0681678i
$932$	36182.7	−	62670.3i	1.27168	−	2.20261i
$933$		0			0
$934$	−10277.7	−	17801.5i	−0.360062	−	0.623645i
$935$	−7057.58			−0.246853
$936$		0			0
$937$	−23593.7			−0.822595			−0.411298	−	0.911501i	$-0.634924\pi$
$937$	−23593.7			−0.822595			−0.411298	+	0.911501i	$0.634924\pi$
$938$	−7833.12	−	13567.4i	−0.272666	−	0.472271i
$939$		0			0
$940$	12764.8	−	22109.2i	0.442916	−	0.767153i
$941$	18285.8	−	31672.0i	0.633477	−	1.09721i	−0.353359	−	0.935488i	$-0.614961\pi$
$941$	18285.8	−	31672.0i	0.633477	−	1.09721i	0.986836	−	0.161726i	$-0.0517060\pi$
$942$		0			0
$943$	2971.67	+	5147.08i	0.102620	+	0.177744i
$944$	121481.			4.18841
$945$		0			0
$946$	8250.48			0.283558
$947$	16455.9	+	28502.4i	0.564671	+	0.978039i	0.997080	+	0.0763615i	$0.0243303\pi$
$947$	16455.9	+	28502.4i	0.564671	+	0.978039i	−0.432409	+	0.901678i	$0.642336\pi$
$948$		0			0
$949$	7927.21	−	13730.3i	0.271157	−	0.469658i
$950$	−813.622	+	1409.24i	−0.0277867	+	0.0481280i
$951$		0			0
$952$	48398.4	+	83828.5i	1.64769	+	2.85388i
$953$	21564.5			0.732993			0.366497	−	0.930419i	$-0.380557\pi$
$953$	21564.5			0.732993			0.366497	+	0.930419i	$0.380557\pi$
$954$		0			0
$955$	−25251.3			−0.855615
$956$	−18109.3	−	31366.2i	−0.612653	−	1.06115i
$957$		0			0
$958$	−7825.98	+	13555.0i	−0.263931	+	0.457142i
$959$	3181.41	−	5510.36i	0.107125	−	0.185546i
$960$		0			0
$961$	11959.5	+	20714.5i	0.401448	+	0.695328i
$962$	7247.40			0.242895
$963$		0			0
$964$	−117082.			−3.91178
$965$	−12904.0	−	22350.4i	−0.430460	−	0.745579i
$966$		0			0
$967$	−14881.9	+	25776.2i	−0.494901	+	0.857193i	−0.999983	−	0.00587841i	$-0.998129\pi$
$967$	−14881.9	+	25776.2i	−0.494901	+	0.857193i	0.505082	+	0.863071i	$0.331462\pi$
$968$	−40821.7	+	70705.2i	−1.35543	+	2.34768i
$969$		0			0
$970$	14129.2	+	24472.5i	0.467693	+	0.810067i
$971$	−29812.3			−0.985297			−0.492648	−	0.870228i	$-0.663971\pi$
$971$	−29812.3			−0.985297			−0.492648	+	0.870228i	$0.663971\pi$
$972$		0			0
$973$	−2686.00			−0.0884986
$974$	28032.1	+	48553.1i	0.922184	+	1.59727i
$975$		0			0
$976$	80831.9	−	140005.i	2.65099	−	4.59165i
$977$	−2879.87	+	4988.07i	−0.0943041	+	0.163339i	−0.909318	−	0.416102i	$-0.863396\pi$
$977$	−2879.87	+	4988.07i	−0.0943041	+	0.163339i	0.815014	+	0.579441i	$0.196729\pi$
$978$		0			0
$979$	1641.72	+	2843.54i	0.0535950	+	0.0928292i
$980$	−19422.6			−0.633095
$981$		0			0
$982$	78796.5			2.56059
$983$	−8825.70	−	15286.6i	−0.286364	−	0.495998i	0.686575	−	0.727059i	$-0.259113\pi$
$983$	−8825.70	−	15286.6i	−0.286364	−	0.495998i	−0.972939	+	0.231062i	$0.925780\pi$
$984$		0			0
$985$	935.063	−	1619.58i	0.0302473	−	0.0523898i
$986$	−59228.7	+	102587.i	−1.91301	+	3.31343i
$987$		0			0
$988$	7597.20	+	13158.7i	0.244635	+	0.423720i
$989$	8086.63			0.260000
$990$		0			0
$991$	−5186.45			−0.166249			−0.0831246	−	0.996539i	$-0.526490\pi$
$991$	−5186.45			−0.166249			−0.0831246	+	0.996539i	$0.526490\pi$
$992$	21656.2	+	37509.7i	0.693131	+	1.20054i
$993$		0			0
$994$	25192.6	−	43634.8i	0.803884	−	1.39237i
$995$	−1508.36	+	2612.55i	−0.0480584	+	0.0832395i
$996$		0			0
$997$	8055.12	+	13951.9i	0.255876	+	0.443190i	0.965133	−	0.261760i	$-0.0843028\pi$
$997$	8055.12	+	13951.9i	0.255876	+	0.443190i	−0.709257	+	0.704950i	$0.750970\pi$
$998$	−43978.6			−1.39491
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.4.e.c.91.7		14
3.2	odd	2		45.4.e.c.31.1	yes	14
9.2	odd	6		45.4.e.c.16.1	✓	14
9.4	even	3		405.4.a.n.1.1		7
9.5	odd	6		405.4.a.m.1.7		7
9.7	even	3	inner	135.4.e.c.46.7		14
15.2	even	4		225.4.k.d.49.14		28
15.8	even	4		225.4.k.d.49.1		28
15.14	odd	2		225.4.e.d.76.7		14
45.2	even	12		225.4.k.d.124.1		28
45.4	even	6		2025.4.a.ba.1.7		7
45.14	odd	6		2025.4.a.bb.1.1		7
45.29	odd	6		225.4.e.d.151.7		14
45.38	even	12		225.4.k.d.124.14		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.1	✓	14	9.2	odd	6
45.4.e.c.31.1	yes	14	3.2	odd	2
135.4.e.c.46.7		14	9.7	even	3	inner
135.4.e.c.91.7		14	1.1	even	1	trivial
225.4.e.d.76.7		14	15.14	odd	2
225.4.e.d.151.7		14	45.29	odd	6
225.4.k.d.49.1		28	15.8	even	4
225.4.k.d.49.14		28	15.2	even	4
225.4.k.d.124.1		28	45.2	even	12
225.4.k.d.124.14		28	45.38	even	12
405.4.a.m.1.7		7	9.5	odd	6
405.4.a.n.1.1		7	9.4	even	3
2025.4.a.ba.1.7		7	45.4	even	6
2025.4.a.bb.1.1		7	45.14	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	135.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.69252 + 4.66357i) q^{2} +(-10.4993 + 18.1853i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-6.28510 - 10.8861i) q^{7} -69.9976 q^{8} +O(q^{10})\)	\(q+(2.69252 + 4.66357i) q^{2} +(-10.4993 + 18.1853i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-6.28510 - 10.8861i) q^{7} -69.9976 q^{8} -26.9252 q^{10} +(6.41534 + 11.1117i) q^{11} +(-29.9322 + 51.8442i) q^{13} +(33.8455 - 58.6220i) q^{14} +(-104.475 - 180.957i) q^{16} +110.011 q^{17} -12.0872 q^{19} +(-52.4964 - 90.9264i) q^{20} +(-34.5468 + 59.8368i) q^{22} +(-33.8608 + 58.6485i) q^{23} +(-12.5000 - 21.6506i) q^{25} -322.372 q^{26} +263.956 q^{28} +(99.9790 + 173.169i) q^{29} +(-38.3143 + 66.3624i) q^{31} +(282.613 - 489.500i) q^{32} +(296.206 + 513.044i) q^{34} +62.8510 q^{35} -22.4815 q^{37} +(-32.5449 - 56.3694i) q^{38} +(174.994 - 303.099i) q^{40} +(43.8807 - 76.0037i) q^{41} +(-59.7050 - 103.412i) q^{43} -269.426 q^{44} -364.682 q^{46} +(121.578 + 210.579i) q^{47} +(92.4951 - 160.206i) q^{49} +(67.3129 - 116.589i) q^{50} +(-628.534 - 1088.65i) q^{52} +293.518 q^{53} -64.1534 q^{55} +(439.942 + 762.002i) q^{56} +(-538.390 + 932.519i) q^{58} +(-290.692 + 503.493i) q^{59} +(386.847 + 670.038i) q^{61} -412.648 q^{62} +1372.15 q^{64} +(-149.661 - 259.221i) q^{65} +(115.719 - 200.431i) q^{67} +(-1155.03 + 2000.58i) q^{68} +(169.227 + 293.110i) q^{70} +744.342 q^{71} -264.839 q^{73} +(-60.5317 - 104.844i) q^{74} +(126.907 - 219.809i) q^{76} +(80.6421 - 139.676i) q^{77} +(-279.858 - 484.729i) q^{79} +1044.75 q^{80} +472.598 q^{82} +(-610.443 - 1057.32i) q^{83} +(-275.027 + 476.361i) q^{85} +(321.513 - 556.878i) q^{86} +(-449.059 - 777.792i) q^{88} +255.905 q^{89} +752.509 q^{91} +(-711.027 - 1231.53i) q^{92} +(-654.699 + 1133.97i) q^{94} +(30.2179 - 52.3390i) q^{95} +(-524.759 - 908.909i) q^{97} +996.177 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 36 q^{4} - 35 q^{5} - 22 q^{7} + 36 q^{8}+O(q^{10}) \) 14 * q - 2 * q^2 - 36 * q^4 - 35 * q^5 - 22 * q^7 + 36 * q^8	\( 14 q - 2 q^{2} - 36 q^{4} - 35 q^{5} - 22 q^{7} + 36 q^{8} + 20 q^{10} - 23 q^{11} - 96 q^{13} + 21 q^{14} - 324 q^{16} + 322 q^{17} + 558 q^{19} - 180 q^{20} - 311 q^{22} - 96 q^{23} - 175 q^{25} - 716 q^{26} + 674 q^{28} + 296 q^{29} - 244 q^{31} + 314 q^{32} - 125 q^{34} + 220 q^{35} + 808 q^{37} - 305 q^{38} - 90 q^{40} + 47 q^{41} - 525 q^{43} + 110 q^{44} + 1434 q^{46} - 164 q^{47} - 1225 q^{49} - 50 q^{50} - 1682 q^{52} + 1012 q^{53} + 230 q^{55} + 981 q^{56} - 1183 q^{58} + 85 q^{59} - 828 q^{61} - 1572 q^{62} + 4472 q^{64} - 480 q^{65} - 1093 q^{67} - 2473 q^{68} + 105 q^{70} + 656 q^{71} + 4170 q^{73} + 1316 q^{74} - 2789 q^{76} - 24 q^{77} - 2110 q^{79} + 3240 q^{80} - 124 q^{82} - 1290 q^{83} - 805 q^{85} + 2569 q^{86} - 2271 q^{88} - 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 517 q^{94} - 1395 q^{95} - 1787 q^{97} + 2558 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 - 36 * q^4 - 35 * q^5 - 22 * q^7 + 36 * q^8 + 20 * q^10 - 23 * q^11 - 96 * q^13 + 21 * q^14 - 324 * q^16 + 322 * q^17 + 558 * q^19 - 180 * q^20 - 311 * q^22 - 96 * q^23 - 175 * q^25 - 716 * q^26 + 674 * q^28 + 296 * q^29 - 244 * q^31 + 314 * q^32 - 125 * q^34 + 220 * q^35 + 808 * q^37 - 305 * q^38 - 90 * q^40 + 47 * q^41 - 525 * q^43 + 110 * q^44 + 1434 * q^46 - 164 * q^47 - 1225 * q^49 - 50 * q^50 - 1682 * q^52 + 1012 * q^53 + 230 * q^55 + 981 * q^56 - 1183 * q^58 + 85 * q^59 - 828 * q^61 - 1572 * q^62 + 4472 * q^64 - 480 * q^65 - 1093 * q^67 - 2473 * q^68 + 105 * q^70 + 656 * q^71 + 4170 * q^73 + 1316 * q^74 - 2789 * q^76 - 24 * q^77 - 2110 * q^79 + 3240 * q^80 - 124 * q^82 - 1290 * q^83 - 805 * q^85 + 2569 * q^86 - 2271 * q^88 - 6096 * q^89 + 6676 * q^91 - 2763 * q^92 + 517 * q^94 - 1395 * q^95 - 1787 * q^97 + 2558 * q^98

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