LMFDB - Embedded newform 225.4.e.d.151.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(76,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.2754297513$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.7
Root			$-2.69252 - 4.66357i$ of defining polynomial
Character	$\chi$	$=$	225.151
Dual form			225.4.e.d.76.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.69252 - 4.66357i) q^{2} +(4.09553 - 3.19791i) q^{3} +(-10.4993 - 18.1853i) q^{4} +(-3.88642 - 27.7102i) q^{6} +(6.28510 - 10.8861i) q^{7} -69.9976 q^{8} +(6.54673 - 26.1943i) q^{9} +O(q^{10})$	\(q+(2.69252 - 4.66357i) q^{2} +(4.09553 - 3.19791i) q^{3} +(-10.4993 - 18.1853i) q^{4} +(-3.88642 - 27.7102i) q^{6} +(6.28510 - 10.8861i) q^{7} -69.9976 q^{8} +(6.54673 - 26.1943i) q^{9} +(-6.41534 + 11.1117i) q^{11} +(-101.155 - 40.9026i) q^{12} +(29.9322 + 51.8442i) q^{13} +(-33.8455 - 58.6220i) q^{14} +(-104.475 + 180.957i) q^{16} +110.011 q^{17} +(-104.532 - 101.060i) q^{18} -12.0872 q^{19} +(-9.07201 - 64.6836i) q^{21} +(34.5468 + 59.8368i) q^{22} +(-33.8608 - 58.6485i) q^{23} +(-286.677 + 223.846i) q^{24} +322.372 q^{26} +(-56.9547 - 128.215i) q^{27} -263.956 q^{28} +(-99.9790 + 173.169i) q^{29} +(-38.3143 - 66.3624i) q^{31} +(282.613 + 489.500i) q^{32} +(9.26000 + 66.0240i) q^{33} +(296.206 - 513.044i) q^{34} +(-545.086 + 155.967i) q^{36} +22.4815 q^{37} +(-32.5449 + 56.3694i) q^{38} +(288.381 + 116.609i) q^{39} +(-43.8807 - 76.0037i) q^{41} +(-326.083 - 131.854i) q^{42} +(59.7050 - 103.412i) q^{43} +269.426 q^{44} -364.682 q^{46} +(121.578 - 210.579i) q^{47} +(150.801 + 1075.22i) q^{48} +(92.4951 + 160.206i) q^{49} +(450.553 - 351.805i) q^{51} +(628.534 - 1088.65i) q^{52} +293.518 q^{53} +(-751.293 - 79.6094i) q^{54} +(-439.942 + 762.002i) q^{56} +(-49.5034 + 38.6537i) q^{57} +(538.390 + 932.519i) q^{58} +(290.692 + 503.493i) q^{59} +(386.847 - 670.038i) q^{61} -412.648 q^{62} +(-244.007 - 235.902i) q^{63} +1372.15 q^{64} +(332.840 + 134.586i) q^{66} +(-115.719 - 200.431i) q^{67} +(-1155.03 - 2000.58i) q^{68} +(-326.231 - 131.913i) q^{69} -744.342 q^{71} +(-458.255 + 1833.54i) q^{72} +264.839 q^{73} +(60.5317 - 104.844i) q^{74} +(126.907 + 219.809i) q^{76} +(80.6421 + 139.676i) q^{77} +(1320.28 - 1030.92i) q^{78} +(-279.858 + 484.729i) q^{79} +(-643.281 - 342.974i) q^{81} -472.598 q^{82} +(-610.443 + 1057.32i) q^{83} +(-1081.04 + 844.108i) q^{84} +(-321.513 - 556.878i) q^{86} +(144.311 + 1028.94i) q^{87} +(449.059 - 777.792i) q^{88} -255.905 q^{89} +752.509 q^{91} +(-711.027 + 1231.53i) q^{92} +(-369.138 - 149.263i) q^{93} +(-654.699 - 1133.97i) q^{94} +(2722.83 + 1100.99i) q^{96} +(524.759 - 908.909i) q^{97} +996.177 q^{98} +(249.064 + 240.791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 + 5 * q^3 - 36 * q^4 - 31 * q^6 + 22 * q^7 + 36 * q^8 + 17 * q^9	\( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9} + 23 q^{11} - 287 q^{12} + 96 q^{13} - 21 q^{14} - 324 q^{16} + 322 q^{17} + 89 q^{18} + 558 q^{19} + 180 q^{21} + 311 q^{22} - 96 q^{23} + 48 q^{24} + 716 q^{26} + 470 q^{27} - 674 q^{28} - 296 q^{29} - 244 q^{31} + 314 q^{32} + 211 q^{33} - 125 q^{34} - 2399 q^{36} - 808 q^{37} - 305 q^{38} + 634 q^{39} - 47 q^{41} - 1941 q^{42} + 525 q^{43} - 110 q^{44} + 1434 q^{46} - 164 q^{47} - 2051 q^{48} - 1225 q^{49} + 1517 q^{51} + 1682 q^{52} + 1012 q^{53} - 4066 q^{54} - 981 q^{56} - 337 q^{57} + 1183 q^{58} - 85 q^{59} - 828 q^{61} - 1572 q^{62} + 828 q^{63} + 4472 q^{64} + 4930 q^{66} + 1093 q^{67} - 2473 q^{68} - 822 q^{69} - 656 q^{71} + 4626 q^{72} - 4170 q^{73} - 1316 q^{74} - 2789 q^{76} - 24 q^{77} + 5314 q^{78} - 2110 q^{79} - 2167 q^{81} + 124 q^{82} - 1290 q^{83} + 5775 q^{84} - 2569 q^{86} - 3604 q^{87} + 2271 q^{88} + 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 696 q^{93} + 517 q^{94} - 593 q^{96} + 1787 q^{97} + 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 5 * q^3 - 36 * q^4 - 31 * q^6 + 22 * q^7 + 36 * q^8 + 17 * q^9 + 23 * q^11 - 287 * q^12 + 96 * q^13 - 21 * q^14 - 324 * q^16 + 322 * q^17 + 89 * q^18 + 558 * q^19 + 180 * q^21 + 311 * q^22 - 96 * q^23 + 48 * q^24 + 716 * q^26 + 470 * q^27 - 674 * q^28 - 296 * q^29 - 244 * q^31 + 314 * q^32 + 211 * q^33 - 125 * q^34 - 2399 * q^36 - 808 * q^37 - 305 * q^38 + 634 * q^39 - 47 * q^41 - 1941 * q^42 + 525 * q^43 - 110 * q^44 + 1434 * q^46 - 164 * q^47 - 2051 * q^48 - 1225 * q^49 + 1517 * q^51 + 1682 * q^52 + 1012 * q^53 - 4066 * q^54 - 981 * q^56 - 337 * q^57 + 1183 * q^58 - 85 * q^59 - 828 * q^61 - 1572 * q^62 + 828 * q^63 + 4472 * q^64 + 4930 * q^66 + 1093 * q^67 - 2473 * q^68 - 822 * q^69 - 656 * q^71 + 4626 * q^72 - 4170 * q^73 - 1316 * q^74 - 2789 * q^76 - 24 * q^77 + 5314 * q^78 - 2110 * q^79 - 2167 * q^81 + 124 * q^82 - 1290 * q^83 + 5775 * q^84 - 2569 * q^86 - 3604 * q^87 + 2271 * q^88 + 6096 * q^89 + 6676 * q^91 - 2763 * q^92 + 696 * q^93 + 517 * q^94 - 593 * q^96 + 1787 * q^97 + 2558 * q^98 + 2320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	0.210745	−	0.977541i	$-0.432411\pi$
$2$	2.69252	−	4.66357i	0.951948	−	1.64882i	0.741203	−	0.671281i	$-0.234256\pi$
$3$	4.09553	−	3.19791i	0.788185	−	0.615438i
$3$	4.09553	−	3.19791i	0.788185	−	0.615438i
$4$	−10.4993	−	18.1853i	−1.31241	−	2.27316i
$5$		0			0
$5$		0			0
$6$	−3.88642	−	27.7102i	−0.264437	−	1.88544i
$7$	6.28510	−	10.8861i	0.339363	−	0.587795i	−0.644950	−	0.764225i	$-0.723122\pi$
$7$	6.28510	−	10.8861i	0.339363	−	0.587795i	0.984313	+	0.176430i	$0.0564550\pi$
$8$	−69.9976			−3.09349
$9$	6.54673	−	26.1943i	0.242471	−	0.970159i
$10$		0			0
$11$	−6.41534	+	11.1117i	−0.175845	+	0.304573i	−0.940454	−	0.339922i	$-0.889599\pi$
$11$	−6.41534	+	11.1117i	−0.175845	+	0.304573i	0.764608	+	0.644495i	$0.222933\pi$
$12$	−101.155	−	40.9026i	−2.43341	−	0.983964i
$13$	29.9322	+	51.8442i	0.638593	+	1.10608i	0.985742	+	0.168266i	$0.0538167\pi$
$13$	29.9322	+	51.8442i	0.638593	+	1.10608i	−0.347148	+	0.937810i	$0.612850\pi$
$14$	−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	$0.212790\pi$
$18$	−104.532	−	101.060i	−1.36880	−	1.32333i
$19$	−12.0872			−0.145947			−0.0729733	−	0.997334i	$-0.523249\pi$
$19$	−12.0872			−0.145947			−0.0729733	+	0.997334i	$0.523249\pi$
$20$		0			0
$21$	−9.07201	−	64.6836i	−0.0942702	−	0.672148i
$22$	34.5468	+	59.8368i	0.334791	+	0.579875i
$23$	−33.8608	−	58.6485i	−0.306976	−	0.531699i	0.670723	−	0.741708i	$-0.265984\pi$
$23$	−33.8608	−	58.6485i	−0.306976	−	0.531699i	−0.977699	+	0.210009i	$0.932651\pi$
$24$	−286.677	+	223.846i	−2.43824	+	1.90385i
$25$		0			0
$26$	322.372			2.43163
$27$	−56.9547	−	128.215i	−0.405960	−	0.913891i
$28$	−263.956			−1.78154
$29$	−99.9790	+	173.169i	−0.640194	+	1.10885i	0.345195	+	0.938531i	$0.387813\pi$
$29$	−99.9790	+	173.169i	−0.640194	+	1.10885i	−0.985389	+	0.170318i	$0.945521\pi$
$30$		0			0
$31$	−38.3143	−	66.3624i	−0.221982	−	0.384485i	0.733427	−	0.679768i	$-0.237919\pi$
$31$	−38.3143	−	66.3624i	−0.221982	−	0.384485i	−0.955410	+	0.295283i	$0.904586\pi$
$32$	282.613	+	489.500i	1.56123	+	2.70413i
$33$	9.26000	+	66.0240i	0.0488473	+	0.348282i
$34$	296.206	−	513.044i	1.49409	−	2.58783i
$35$		0			0
$36$	−545.086	+	155.967i	−2.52355	+	0.722069i
$37$	22.4815			0.0998900			0.0499450	−	0.998752i	$-0.484095\pi$
$37$	22.4815			0.0998900			0.0499450	+	0.998752i	$0.484095\pi$
$38$	−32.5449	+	56.3694i	−0.138934	+	0.240640i
$39$	288.381	+	116.609i	1.18405	+	0.478778i
$40$		0			0
$41$	−43.8807	−	76.0037i	−0.167147	−	0.289507i	0.770269	−	0.637719i	$-0.220122\pi$
$41$	−43.8807	−	76.0037i	−0.167147	−	0.289507i	−0.937416	+	0.348213i	$0.886789\pi$
$42$	−326.083	−	131.854i	−1.19799	−	0.484415i
$43$	59.7050	−	103.412i	0.211743	−	0.366749i	−0.740517	−	0.672037i	$-0.765419\pi$
$43$	59.7050	−	103.412i	0.211743	−	0.366749i	0.952260	+	0.305288i	$0.0987528\pi$
$44$	269.426			0.923124
$45$		0			0
$46$	−364.682			−1.16890
$47$	121.578	−	210.579i	0.377317	−	0.653533i	−0.613354	−	0.789808i	$-0.710180\pi$
$47$	121.578	−	210.579i	0.377317	−	0.653533i	0.990671	+	0.136276i	$0.0435133\pi$
$48$	150.801	+	1075.22i	0.453465	+	3.23321i
$49$	92.4951	+	160.206i	0.269665	+	0.467073i
$50$		0			0
$51$	450.553	−	351.805i	1.23706	−	0.965932i
$52$	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	$0.375801\pi$
$54$	−751.293	−	79.6094i	−1.89330	−	0.200620i
$55$		0			0
$56$	−439.942	+	762.002i	−1.04982	+	1.81834i
$57$	−49.5034	+	38.6537i	−0.115033	+	0.0898212i
$58$	538.390	+	932.519i	1.21886	+	2.11113i
$59$	290.692	+	503.493i	0.641438	+	1.11100i	0.985112	+	0.171914i	$0.0549951\pi$
$59$	290.692	+	503.493i	0.641438	+	1.11100i	−0.343674	+	0.939089i	$0.611672\pi$
$60$		0			0
$61$	386.847	−	670.038i	0.811977	−	1.40639i	−0.0995008	−	0.995037i	$-0.531725\pi$
$61$	386.847	−	670.038i	0.811977	−	1.40639i	0.911478	−	0.411349i	$-0.134942\pi$
$62$	−412.648			−0.845263
$63$	−244.007	−	235.902i	−0.487968	−	0.471760i
$64$	1372.15			2.67998
$65$		0			0
$66$	332.840	+	134.586i	0.620755	+	0.251006i
$67$	−115.719	−	200.431i	−0.211005	−	0.365471i	0.741024	−	0.671478i	$-0.234340\pi$
$67$	−115.719	−	200.431i	−0.211005	−	0.365471i	−0.952029	+	0.306007i	$0.901007\pi$
$68$	−1155.03	−	2000.58i	−2.05983	−	3.56773i
$69$	−326.231	−	131.913i	−0.569182	−	0.230152i
$70$		0			0
$71$	−744.342			−1.24418			−0.622092	−	0.782944i	$-0.713717\pi$
$71$	−744.342			−1.24418			−0.622092	+	0.782944i	$0.713717\pi$
$72$	−458.255	+	1833.54i	−0.750082	+	3.00117i
$73$	264.839			0.424616			0.212308	−	0.977203i	$-0.431902\pi$
$73$	264.839			0.424616			0.212308	+	0.977203i	$0.431902\pi$
$74$	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
$78$	1320.28	−	1030.92i	1.91657	−	1.49652i
$79$	−279.858	+	484.729i	−0.398564	+	0.690333i	−0.993549	−	0.113404i	$-0.963825\pi$
$79$	−279.858	+	484.729i	−0.398564	+	0.690333i	0.594985	+	0.803737i	$0.297158\pi$
$80$		0			0
$81$	−643.281	−	342.974i	−0.882415	−	0.470471i
$82$	−472.598			−0.636460
$83$	−610.443	+	1057.32i	−0.807288	+	1.39826i	0.107448	+	0.994211i	$0.465732\pi$
$83$	−610.443	+	1057.32i	−0.807288	+	1.39826i	−0.914736	+	0.404052i	$0.867601\pi$
$84$	−1081.04	+	844.108i	−1.40418	+	1.09643i
$85$		0			0
$86$	−321.513	−	556.878i	−0.403136	−	0.698252i
$87$	144.311	+	1028.94i	0.177837	+	1.26798i
$88$	449.059	−	777.792i	0.543975	−	0.942193i
$89$	−255.905			−0.304785			−0.152392	−	0.988320i	$-0.548698\pi$
$89$	−255.905			−0.304785			−0.152392	+	0.988320i	$0.548698\pi$
$90$		0			0
$91$	752.509			0.866861
$92$	−711.027	+	1231.53i	−0.805757	+	1.39561i
$93$	−369.138	−	149.263i	−0.411590	−	0.166429i
$94$	−654.699	−	1133.97i	−0.718373	−	1.24426i
$95$		0			0
$96$	2722.83	+	1100.99i	2.89476	+	1.17051i
$97$	524.759	−	908.909i	0.549291	−	0.951400i	−0.449032	−	0.893515i	$-0.648231\pi$
$97$	524.759	−	908.909i	0.549291	−	0.951400i	0.998323	−	0.0578842i	$-0.0184354\pi$
$98$	996.177			1.02683
$99$	249.064	+	240.791i	0.252847	+	0.244448i
$100$		0			0
$101$	−44.3635	+	76.8398i	−0.0437062	+	0.0757014i	−0.887051	−	0.461671i	$-0.847250\pi$
$101$	−44.3635	+	76.8398i	−0.0437062	+	0.0757014i	0.843345	+	0.537373i	$0.180583\pi$
$102$	−427.548	−	3048.43i	−0.415035	−	2.95921i
$103$	−772.035	−	1337.20i	−0.738552	−	1.27921i	−0.953147	−	0.302507i	$-0.902176\pi$
$103$	−772.035	−	1337.20i	−0.738552	−	1.27921i	0.214595	−	0.976703i	$-0.431157\pi$
$104$	−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	$0.414753\pi$
$108$	−1733.65	+	2381.90i	−1.54463	+	2.12221i
$109$	1367.04			1.20127			0.600634	−	0.799524i	$-0.294915\pi$
$109$	1367.04			1.20127			0.600634	+	0.799524i	$0.294915\pi$
$110$		0			0
$111$	92.0735	−	71.8937i	0.0787318	−	0.0614761i
$112$	1313.28	+	2274.66i	1.10797	+	1.91907i
$113$	85.2146	+	147.596i	0.0709408	+	0.122873i	0.899314	−	0.437304i	$-0.144067\pi$
$113$	85.2146	+	147.596i	0.0709408	+	0.122873i	−0.828373	+	0.560177i	$0.810733\pi$
$114$	46.9758	+	334.938i	0.0385937	+	0.275174i
$115$		0			0
$116$	4198.83			3.36079
$117$	1553.98	−	444.644i	1.22791	−	0.351345i
$118$	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
$123$	−422.768	−	170.949i	−0.309916	−	0.125316i
$124$	−804.545	+	1393.51i	−0.582664	+	1.00920i
$125$		0			0
$126$	−1757.14	+	502.775i	−1.24237	+	0.355482i
$127$	−1809.74			−1.26447			−0.632237	−	0.774775i	$-0.717863\pi$
$127$	−1809.74			−1.26447			−0.632237	+	0.774775i	$0.717863\pi$
$128$	1433.63	−	2483.13i	0.989973	−	1.71468i
$129$	−86.1791	−	614.459i	−0.0588190	−	0.419381i
$130$		0			0
$131$	619.147	+	1072.39i	0.412940	+	0.715232i	0.995210	−	0.0977630i	$-0.0311687\pi$
$131$	619.147	+	1072.39i	0.412940	+	0.715232i	−0.582270	+	0.812995i	$0.697835\pi$
$132$	1103.44	−	861.600i	0.727593	−	0.568126i
$133$	−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	−0.776254	−	0.630420i	$-0.782883\pi$
$137$	253.091	−	438.367i	0.157832	−	0.273374i	0.934087	+	0.357046i	$0.116216\pi$
$138$	−1493.57	+	1166.22i	−0.921311	+	0.719387i
$139$	106.840	+	185.052i	0.0651946	+	0.112920i	0.896780	−	0.442476i	$-0.145900\pi$
$139$	106.840	+	185.052i	0.0651946	+	0.112920i	−0.831586	+	0.555396i	$0.812567\pi$
$140$		0			0
$141$	−175.487	−	1251.23i	−0.104813	−	0.747320i
$142$	−2004.15	+	3471.29i	−1.18440	+	2.05144i
$143$	−768.103			−0.449175
$144$	4056.06	+	3921.33i	2.34726	+	2.26929i
$145$		0			0
$146$	713.082	−	1235.09i	0.404213	−	0.700117i
$147$	891.141	+	360.338i	0.500001	+	0.202178i
$148$	−236.039	−	408.832i	−0.131097	−	0.227066i
$149$	452.655	+	784.022i	0.248879	+	0.431071i	0.963215	−	0.268732i	$-0.0866046\pi$
$149$	452.655	+	784.022i	0.248879	+	0.431071i	−0.714336	+	0.699803i	$0.753271\pi$
$150$		0			0
$151$	−679.335	+	1176.64i	−0.366116	+	0.634131i	−0.988955	−	0.148219i	$-0.952646\pi$
$151$	−679.335	+	1176.64i	−0.366116	+	0.634131i	0.622839	+	0.782350i	$0.285979\pi$
$152$	846.073			0.451484
$153$	720.211	−	2881.66i	0.380560	−	1.52267i
$154$	868.521			0.454464
$155$		0			0
$156$	−907.235	−	6468.60i	−0.465622	−	3.31989i
$157$	950.670	+	1646.61i	0.483259	+	0.837030i	0.999815	−	0.0192236i	$-0.00611945\pi$
$157$	950.670	+	1646.61i	0.483259	+	0.837030i	−0.516556	+	0.856254i	$0.672786\pi$
$158$	1507.05	+	2610.28i	0.758824	+	1.31432i
$159$	1202.11	−	938.643i	0.599582	−	0.468172i
$160$		0			0
$161$	−851.273			−0.416706
$162$	−3331.53	+	2076.53i	−1.61574	+	1.00708i
$163$	2325.15			1.11730			0.558649	−	0.829404i	$-0.311320\pi$
$163$	2325.15			1.11730			0.558649	+	0.829404i	$0.311320\pi$
$164$	−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	0.998714	−	0.0507059i	$-0.0161471\pi$
$167$	982.901	+	1702.43i	0.455444	+	0.788853i	−0.543269	+	0.839558i	$0.682814\pi$
$168$	635.019	+	4527.70i	0.291624	+	2.07928i
$169$	−693.379	+	1200.97i	−0.315603	+	0.546640i
$170$		0			0
$171$	−79.1314	+	316.615i	−0.0353879	+	0.141591i
$172$	−2507.44			−1.11157
$173$	−1148.95	+	1990.04i	−0.504932	+	0.874567i	0.495052	+	0.868863i	$0.335149\pi$
$173$	−1148.95	+	1990.04i	−0.504932	+	0.874567i	−0.999984	+	0.00570381i	$0.998184\pi$
$174$	5187.10	+	2097.43i	2.25996	+	0.913828i
$175$		0			0
$176$	−1340.49	−	2321.80i	−0.574110	−	0.994387i
$177$	2800.66	+	1132.46i	1.18933	+	0.480911i
$178$	−689.027	+	1193.43i	−0.290139	+	0.502536i
$179$	−873.696			−0.364822			−0.182411	−	0.983222i	$-0.558390\pi$
$179$	−873.696			−0.364822			−0.182411	+	0.983222i	$0.558390\pi$
$180$		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
$183$	−558.380	−	3981.26i	−0.225555	−	1.60821i
$184$	2370.17	+	4105.26i	0.949627	+	1.64480i
$185$		0			0
$186$	−1690.01	+	1319.61i	−0.666224	+	0.520207i
$187$	−705.758	+	1222.41i	−0.275990	+	0.478028i
$188$	−5105.91			−1.98078
$189$	−1753.73	−	185.831i	−0.674948	−	0.0715196i
$190$		0			0
$191$	−2525.13	+	4373.65i	−0.956607	+	1.65689i	−0.225959	+	0.974137i	$0.572551\pi$
$191$	−2525.13	+	4373.65i	−0.956607	+	1.65689i	−0.730648	+	0.682754i	$0.760782\pi$
$192$	5619.68	−	4388.02i	2.11232	−	1.64936i
$193$	2580.80	+	4470.08i	0.962539	+	1.66717i	0.716087	+	0.698011i	$0.245931\pi$
$193$	2580.80	+	4470.08i	0.962539	+	1.66717i	0.246452	+	0.969155i	$0.420735\pi$
$194$	−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	$0.521545\pi$
$198$	1793.55	−	513.194i	0.643748	−	0.184197i
$199$	603.342			0.214924			0.107462	−	0.994209i	$-0.465728\pi$
$199$	603.342			0.214924			0.107462	+	0.994209i	$0.465728\pi$
$200$		0			0
$201$	−1114.89	−	450.813i	−0.391236	−	0.158198i
$202$	238.899	+	413.785i	0.0832121	+	0.144128i
$203$	1256.76	+	2176.76i	0.434517	+	0.752606i
$204$	−11128.2	−	4499.73i	−3.81925	−	1.54433i
$205$		0			0
$206$	−8314.87			−2.81225
$207$	−1757.93	+	503.002i	−0.590265	+	0.168894i
$208$	−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	0.599452	−	0.800411i	$-0.295385\pi$
$211$	−1205.91	−	2088.69i	−0.393450	−	0.681476i	−0.992902	+	0.118935i	$0.962052\pi$
$212$	−3081.72	−	5337.70i	−0.998366	−	1.72922i
$213$	−3048.47	+	2380.34i	−0.980648	+	0.765719i
$214$	1577.20	−	2731.79i	0.503809	−	0.872623i
$215$		0			0
$216$	3986.69	+	8974.76i	1.25583	+	2.82711i
$217$	−963.237			−0.301331
$218$	3680.76	−	6375.27i	1.14354	−	1.98068i
$219$	1084.65	−	846.930i	0.334676	−	0.261325i
$220$		0			0
$221$	3292.87	+	5703.42i	1.00227	+	1.73599i
$222$	−87.3724	−	622.966i	−0.0264146	−	0.188337i
$223$	2740.64	−	4746.93i	0.822990	−	1.42546i	−0.0804554	−	0.996758i	$-0.525637\pi$
$223$	2740.64	−	4746.93i	0.822990	−	1.42546i	0.903446	−	0.428703i	$-0.141029\pi$
$224$	7105.00			2.11930
$225$		0			0
$226$	917.766			0.270128
$227$	−2736.24	+	4739.30i	−0.800046	+	1.38572i	0.119539	+	0.992830i	$0.461858\pi$
$227$	−2736.24	+	4739.30i	−0.800046	+	1.38572i	−0.919585	+	0.392891i	$0.871475\pi$
$228$	1222.68	+	494.397i	0.355148	+	0.143606i
$229$	−1637.99	−	2837.08i	−0.472670	−	0.818689i	0.526840	−	0.849964i	$-0.323377\pi$
$229$	−1637.99	−	2837.08i	−0.472670	−	0.818689i	−0.999511	+	0.0312750i	$0.990043\pi$
$230$		0			0
$231$	776.945	+	314.162i	0.221295	+	0.0894820i
$232$	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	$0.660992\pi$
$234$	2110.48	−	8444.31i	0.589601	−	2.35907i
$235$		0			0
$236$	6104.11	−	10572.6i	1.68366	−	2.91618i
$237$	403.952	+	2880.18i	0.110715	+	0.789401i
$238$	−3723.37	−	6449.06i	−1.01408	−	1.75643i
$239$	862.406	+	1493.73i	0.233408	+	0.404274i	0.958809	−	0.284053i	$-0.0916790\pi$
$239$	862.406	+	1493.73i	0.233408	+	0.404274i	−0.725401	+	0.688326i	$0.758346\pi$
$240$		0			0
$241$	2787.86	−	4828.71i	0.745152	−	1.29064i	−0.204972	−	0.978768i	$-0.565710\pi$
$241$	2787.86	−	4828.71i	0.745152	−	1.29064i	0.950124	−	0.311873i	$-0.100956\pi$
$242$	6280.96			1.66841
$243$	−3731.37	+	652.496i	−0.985053	+	0.172254i
$244$	−16246.4			−4.26259
$245$		0			0
$246$	−1935.54	+	1511.33i	−0.501649	+	0.391702i
$247$	−361.796	−	626.649i	−0.0932006	−	0.161428i
$248$	2681.91	+	4645.21i	0.686700	+	1.18940i
$249$	881.123	+	6282.42i	0.224253	+	1.59893i
$250$		0			0
$251$	−1356.38			−0.341090			−0.170545	−	0.985350i	$-0.554553\pi$
$251$	−1356.38			−0.341090			−0.170545	+	0.985350i	$0.554553\pi$
$252$	−1728.05	+	6914.14i	−0.431971	+	1.72837i
$253$	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	0.503898	−	0.863763i	$-0.331899\pi$
$257$	−2043.91	−	3540.16i	−0.496092	−	0.859256i	−0.999990	+	0.00450688i	$0.998565\pi$
$258$	−3097.61	−	1252.54i	−0.747476	−	0.302246i
$259$	141.298	−	244.736i	0.0338990	−	0.0587148i
$260$		0			0
$261$	3881.49	+	3752.57i	0.920530	+	0.889954i
$262$	6668.25			1.57239
$263$	−215.130	+	372.616i	−0.0504391	+	0.0873631i	−0.890143	−	0.455682i	$-0.849395\pi$
$263$	−215.130	+	372.616i	−0.0504391	+	0.0873631i	0.839704	+	0.543045i	$0.182729\pi$
$264$	−648.178	−	4621.52i	−0.151108	−	1.07741i
$265$		0			0
$266$	409.096	+	708.575i	0.0942980	+	0.163329i
$267$	−1048.06	+	818.360i	−0.240227	+	0.187576i
$268$	−2429.93	+	4208.76i	−0.553849	+	0.959295i
$269$	3467.85			0.786017			0.393008	−	0.919535i	$-0.371434\pi$
$269$	3467.85			0.786017			0.393008	+	0.919535i	$0.371434\pi$
$270$		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
$273$	3081.92	−	2406.46i	0.683247	−	0.533499i
$274$	−1362.90	−	2360.62i	−0.300497	−	0.520475i
$275$		0			0
$276$	1026.31	+	7317.59i	0.223828	+	1.59589i
$277$	−786.769	+	1362.72i	−0.170658	+	0.295589i	−0.938650	−	0.344871i	$-0.887923\pi$
$277$	−786.769	+	1362.72i	−0.170658	+	0.295589i	0.767992	+	0.640460i	$0.221256\pi$
$278$	1150.67			0.248247
$279$	−1989.15	+	569.160i	−0.426836	+	0.122132i
$280$		0			0
$281$	−4073.23	+	7055.04i	−0.864727	+	1.49775i	0.00259078	+	0.999997i	$0.499175\pi$
$281$	−4073.23	+	7055.04i	−0.864727	+	1.49775i	−0.867318	+	0.497755i	$0.834158\pi$
$282$	−6307.68	−	2550.55i	−1.33198	−	0.538592i
$283$	1549.15	+	2683.21i	0.325398	+	0.563605i	0.981593	−	0.190986i	$-0.0611685\pi$
$283$	1549.15	+	2683.21i	0.325398	+	0.563605i	−0.656195	+	0.754591i	$0.727835\pi$
$284$	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
$288$	14672.3	−	4198.22i	3.00199	−	0.858967i
$289$	7189.39			1.46334
$290$		0			0
$291$	−757.445	−	5400.60i	−0.152585	−	1.08793i
$292$	−2780.61	−	4816.16i	−0.557271	−	0.965221i
$293$	61.0799	+	105.794i	0.0121786	+	0.0210939i	0.872050	−	0.489416i	$-0.162790\pi$
$293$	61.0799	+	105.794i	0.0121786	+	0.0210939i	−0.859872	+	0.510510i	$0.829457\pi$
$294$	4079.87	−	3185.69i	0.809330	−	0.631949i
$295$		0			0
$296$	−1573.65			−0.309008
$297$	1790.07	+	189.682i	0.349733	+	0.0370588i
$298$	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
$303$	64.0349	+	456.570i	0.0121410	+	0.0865652i
$304$	1262.81	−	2187.25i	0.238247	−	0.412657i
$305$		0			0
$306$	−11499.6	−	11117.7i	−2.14833	−	2.07697i
$307$	1928.53			0.358525			0.179263	−	0.983801i	$-0.442629\pi$
$307$	1928.53			0.358525			0.179263	+	0.983801i	$0.442629\pi$
$308$	1693.37	−	2933.00i	0.313275	−	0.542608i
$309$	−7438.15	−	3007.66i	−1.36939	−	0.553721i
$310$		0			0
$311$	−3969.65	−	6875.63i	−0.723788	−	1.25364i	−0.959471	−	0.281807i	$-0.909066\pi$
$311$	−3969.65	−	6875.63i	−0.723788	−	1.25364i	0.235683	−	0.971830i	$-0.424267\pi$
$312$	−20186.0	−	8162.33i	−3.66285	−	1.48109i
$313$	−3379.44	+	5853.37i	−0.610279	+	1.05703i	0.380914	+	0.924611i	$0.375609\pi$
$313$	−3379.44	+	5853.37i	−0.610279	+	1.05703i	−0.991193	+	0.132424i	$0.957724\pi$
$314$	10238.8			1.84015
$315$		0			0
$316$	11753.2			2.09232
$317$	4212.12	−	7295.60i	0.746297	−	1.29262i	−0.203290	−	0.979119i	$-0.565163\pi$
$317$	4212.12	−	7295.60i	0.746297	−	1.29262i	0.949587	−	0.313505i	$-0.101503\pi$
$318$	−1140.73	−	8133.44i	−0.201161	−	1.43428i
$319$	−1282.80	−	2221.87i	−0.225150	−	0.389972i
$320$		0			0
$321$	2399.05	−	1873.25i	0.417139	−	0.325715i
$322$	−2292.06	+	3969.97i	−0.396683	+	0.687074i
$323$	−1329.72			−0.229064
$324$	516.912	+	15299.2i	0.0886337	+	2.62332i
$325$		0			0
$326$	6260.49	−	10843.5i	1.06361	−	1.84222i
$327$	5598.73	−	4371.66i	0.946822	−	0.739307i
$328$	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	−0.876524	−	0.481357i	$-0.840144\pi$
$331$	−128.837	+	223.153i	−0.0213944	+	0.0370562i	0.855130	+	0.518414i	$0.173477\pi$
$332$	25636.9			4.23797
$333$	147.180	−	588.886i	0.0242205	−	0.0969091i
$334$	10585.9			1.73424
$335$		0			0
$336$	12652.7	+	5116.20i	2.05435	+	0.830690i
$337$	−5549.76	−	9612.47i	−0.897077	−	1.55378i	−0.831213	−	0.555954i	$-0.812353\pi$
$337$	−5549.76	−	9612.47i	−0.897077	−	1.55378i	−0.0658636	−	0.997829i	$-0.520980\pi$
$338$	3733.87	+	6467.25i	0.600874	+	1.04075i
$339$	820.997	+	331.975i	0.131535	+	0.0531870i
$340$		0			0
$341$	983.198			0.156138
$342$	1263.49	+	1221.53i	0.199772	+	0.193136i
$343$	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	0.940377	+	0.340134i	$0.110472\pi$
$347$	4943.28	+	8562.02i	0.764753	+	1.32459i	−0.175624	+	0.984457i	$0.556194\pi$
$348$	17196.4	−	13427.5i	2.64892	−	2.06836i
$349$	−3029.60	+	5247.42i	−0.464673	+	0.804837i	−0.999187	−	0.0403230i	$-0.987161\pi$
$349$	−3029.60	+	5247.42i	−0.464673	+	0.804837i	0.534514	+	0.845160i	$0.320495\pi$
$350$		0			0
$351$	4942.43	−	6790.54i	0.751589	−	1.03263i
$352$	−7252.23			−1.09814
$353$	−4548.34	+	7877.96i	−0.685790	+	1.18782i	0.287398	+	0.957811i	$0.407210\pi$
$353$	−4548.34	+	7877.96i	−0.685790	+	1.18782i	−0.973188	+	0.230012i	$0.926123\pi$
$354$	12822.2	−	10011.9i	1.92511	−	1.50318i
$355$		0			0
$356$	2686.81	+	4653.70i	0.400002	+	0.692824i
$357$	−998.020	−	7115.90i	−0.147957	−	1.05494i
$358$	−2352.44	+	4074.55i	−0.347291	+	0.601527i
$359$	−8804.63			−1.29440			−0.647201	−	0.762319i	$-0.724061\pi$
$359$	−8804.63			−1.29440			−0.647201	+	0.762319i	$0.724061\pi$
$360$		0			0
$361$	−6712.90			−0.978700
$362$	4023.17	−	6968.33i	0.584124	−	1.01173i
$363$	5618.70	+	2271.95i	0.812411	+	0.328503i
$364$	−7900.80	−	13684.6i	−1.13768	−	1.97051i
$365$		0			0
$366$	−20070.3	−	8115.56i	−2.86638	−	1.15904i
$367$	4326.18	−	7493.17i	0.615326	−	1.06578i	−0.375001	−	0.927025i	$-0.622358\pi$
$367$	4326.18	−	7493.17i	0.615326	−	1.06578i	0.990327	−	0.138752i	$-0.0443091\pi$
$368$	14150.5			2.00447
$369$	−2278.14	+	651.849i	−0.321396	+	0.0919619i
$370$		0			0
$371$	1844.79	−	3195.27i	0.258158	−	0.447143i
$372$	1161.29	+	8280.04i	0.161855	+	1.15403i
$373$	−5959.31	−	10321.8i	−0.827243	−	1.43283i	−0.900193	−	0.435491i	$-0.856575\pi$
$373$	−5959.31	−	10321.8i	−0.827243	−	1.43283i	0.0729500	−	0.997336i	$-0.476759\pi$
$374$	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
$378$	−5588.59	+	7678.30i	−0.760439	+	1.04479i
$379$	5052.23			0.684738			0.342369	−	0.939566i	$-0.388771\pi$
$379$	5052.23			0.684738			0.342369	+	0.939566i	$0.388771\pi$
$380$		0			0
$381$	−7411.83	+	5787.38i	−0.996640	+	0.778206i
$382$	13597.9	+	23552.2i	1.82128	+	3.15455i
$383$	−2665.19	−	4616.24i	−0.355573	−	0.615871i	0.631642	−	0.775260i	$-0.282381\pi$
$383$	−2665.19	−	4616.24i	−0.355573	−	0.615871i	−0.987216	+	0.159388i	$0.949048\pi$
$384$	−2069.33	−	14754.4i	−0.275000	−	1.96076i
$385$		0			0
$386$	27795.4			3.66515
$387$	−2317.93	−	2240.94i	−0.304463	−	0.294350i
$388$	−22038.4			−2.88358
$389$	−1669.76	+	2892.11i	−0.217635	+	0.376955i	−0.954085	−	0.299537i	$-0.903168\pi$
$389$	−1669.76	+	2892.11i	−0.217635	+	0.376955i	0.736449	+	0.676493i	$0.236501\pi$
$390$		0			0
$391$	−3725.05	−	6451.98i	−0.481800	−	0.834503i
$392$	−6474.43	−	11214.0i	−0.834205	−	1.44488i
$393$	5965.15	+	2412.04i	0.765654	+	0.309597i
$394$	−1007.07	+	1744.29i	−0.128770	+	0.223036i
$395$		0			0
$396$	1763.86	−	7057.42i	0.223831	−	0.895577i
$397$	−9041.65			−1.14304			−0.571520	−	0.820588i	$-0.693646\pi$
$397$	−9041.65			−1.14304			−0.571520	+	0.820588i	$0.693646\pi$
$398$	1624.51	−	2813.73i	0.204596	−	0.354371i
$399$	109.655	+	781.842i	0.0137584	+	0.0980978i
$400$		0			0
$401$	835.978	+	1447.96i	0.104107	+	0.180318i	0.913373	−	0.407124i	$-0.133468\pi$
$401$	835.978	+	1447.96i	0.104107	+	0.180318i	−0.809266	+	0.587442i	$0.800135\pi$
$402$	−5104.26	+	3985.56i	−0.633277	+	0.494482i
$403$	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
$408$	−31537.6	+	24625.5i	−3.82683	+	2.98810i
$409$	−236.363	−	409.393i	−0.0285755	−	0.0494943i	0.851384	−	0.524543i	$-0.175764\pi$
$409$	−236.363	−	409.393i	−0.0285755	−	0.0494943i	−0.879960	+	0.475049i	$0.842430\pi$
$410$		0			0
$411$	−365.316	−	2604.71i	−0.0438436	−	0.312605i
$412$	−16211.6	+	28079.4i	−1.93857	+	3.35770i
$413$	7308.11			0.870722
$414$	−2387.48	+	9552.59i	−0.283425	+	1.13402i
$415$		0			0
$416$	−16918.5	+	29303.7i	−1.99398	+	3.45368i
$417$	1029.35	+	416.222i	0.120881	+	0.0488789i
$418$	−417.573	−	723.258i	−0.0488617	−	0.0846309i
$419$	−6269.65	−	10859.3i	−0.731008	−	1.26614i	−0.956453	−	0.291887i	$-0.905717\pi$
$419$	−6269.65	−	10859.3i	−0.731008	−	1.26614i	0.225445	−	0.974256i	$-0.427616\pi$
$420$		0			0
$421$	3375.88	−	5847.19i	0.390808	−	0.676900i	−0.601748	−	0.798686i	$-0.705529\pi$
$421$	3375.88	−	5847.19i	0.390808	−	0.676900i	0.992556	+	0.121786i	$0.0388623\pi$
$422$	−12987.7			−1.49818
$423$	−4720.02	−	4563.24i	−0.542542	−	0.524521i
$424$	−20545.5			−2.35325
$425$		0			0
$426$	2892.82	+	20625.9i	0.329009	+	2.34584i
$427$	−4862.74	−	8422.51i	−0.551111	−	0.954552i
$428$	−6150.18	−	10652.4i	−0.694580	−	1.20305i
$429$	−3145.79	+	2456.32i	−0.354033	+	0.276439i
$430$		0			0
$431$	7535.06			0.842114			0.421057	−	0.907034i	$-0.361659\pi$
$431$	7535.06			0.842114			0.421057	+	0.907034i	$0.361659\pi$
$432$	29151.8	+	3089.01i	3.24668	+	0.344028i
$433$	5135.13			0.569928			0.284964	−	0.958538i	$-0.408018\pi$
$433$	5135.13			0.569928			0.284964	+	0.958538i	$0.408018\pi$
$434$	−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
$438$	−1029.27	−	7338.74i	−0.112284	−	0.800590i
$439$	−8486.60	+	14699.2i	−0.922650	+	1.59808i	−0.127353	+	0.991857i	$0.540648\pi$
$439$	−8486.60	+	14699.2i	−0.922650	+	1.59808i	−0.795297	+	0.606220i	$0.792685\pi$
$440$		0			0
$441$	4802.02	−	1374.02i	0.518521	−	0.148366i
$442$	35464.4			3.81645
$443$	5676.15	−	9831.39i	0.608763	−	1.05441i	−0.382681	−	0.923880i	$-0.624999\pi$
$443$	5676.15	−	9831.39i	0.608763	−	1.05441i	0.991445	−	0.130529i	$-0.0416675\pi$
$444$	−2274.11	−	919.550i	−0.243073	−	0.0982881i
$445$		0			0
$446$	−14758.4	−	25562.3i	−1.56689	−	2.71393i
$447$	4361.09	+	1763.43i	0.461460	+	0.186594i
$448$	8624.10	−	14937.4i	0.909488	−	1.57528i
$449$	11059.8			1.16246			0.581230	−	0.813740i	$-0.302572\pi$
$449$	11059.8			1.16246			0.581230	+	0.813740i	$0.302572\pi$
$450$		0			0
$451$	1126.04			0.117568
$452$	1789.38	−	3099.30i	0.186207	−	0.322520i
$453$	980.562	+	6991.42i	0.101702	+	0.725134i
$454$	14734.7	+	25521.3i	1.52320	+	2.63827i
$455$		0			0
$456$	3465.12	−	2705.67i	0.355853	−	0.277861i
$457$	178.342	−	308.897i	0.0182549	−	0.0316184i	−0.856754	−	0.515726i	$-0.827522\pi$
$457$	178.342	−	308.897i	0.0182549	−	0.0316184i	0.875009	+	0.484107i	$0.160856\pi$
$458$	−17641.3			−1.79983
$459$	−6265.63	−	14105.1i	−0.637156	−	1.43435i
$460$		0			0
$461$	−5159.88	+	8937.17i	−0.521300	+	0.902918i	0.478393	+	0.878146i	$0.341219\pi$
$461$	−5159.88	+	8937.17i	−0.521300	+	0.902918i	−0.999693	+	0.0247726i	$0.992114\pi$
$462$	3557.05	−	2777.45i	0.358201	−	0.279694i
$463$	−9084.27	−	15734.4i	−0.911839	−	1.57935i	−0.811464	−	0.584403i	$-0.801329\pi$
$463$	−9084.27	−	15734.4i	−0.911839	−	1.57935i	−0.100376	−	0.994950i	$-0.532004\pi$
$464$	−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	$0.560563\pi$
$468$	−24401.6	−	23591.1i	−2.41018	−	2.33013i
$469$	−2909.22			−0.286429
$470$		0			0
$471$	9159.21	+	3703.58i	0.896038	+	0.362318i
$472$	−20347.7	−	35243.3i	−1.98428	−	3.43687i
$473$	766.056	+	1326.85i	0.0744679	+	0.128982i
$474$	14519.6	+	5871.08i	1.40698	+	0.568919i
$475$		0			0
$476$	−29038.0			−2.79613
$477$	1921.58	−	7688.48i	0.184451	−	0.738012i
$478$	9288.17			0.888768
$479$	−1453.28	+	2517.16i	−0.138627	+	0.240109i	−0.926977	−	0.375118i	$-0.877602\pi$
$479$	−1453.28	+	2517.16i	−0.138627	+	0.240109i	0.788350	+	0.615227i	$0.210936\pi$
$480$		0			0
$481$	672.921	+	1165.53i	0.0637891	+	0.110486i
$482$	−15012.7	−	26002.7i	−1.41869	−	2.45725i
$483$	−3486.41	+	2722.29i	−0.328442	+	0.256457i
$484$	12246.1	−	21210.8i	1.15008	−	1.99200i
$485$		0			0
$486$	−7003.82	+	19158.4i	−0.653703	+	1.78815i
$487$	−10411.1			−0.968734			−0.484367	−	0.874865i	$-0.660950\pi$
$487$	−10411.1			−0.968734			−0.484367	+	0.874865i	$0.660950\pi$
$488$	−27078.3	+	46901.0i	−2.51184	+	4.35064i
$489$	9522.70	−	7435.61i	0.880637	−	0.687628i
$490$		0			0
$491$	−7316.26	−	12672.1i	−0.672460	−	1.16474i	−0.977204	−	0.212301i	$-0.931904\pi$
$491$	−7316.26	−	12672.1i	−0.672460	−	1.16474i	0.304744	−	0.952434i	$-0.401429\pi$
$492$	1330.01	+	9482.99i	0.121873	+	0.868956i
$493$	−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
$498$	31671.0	+	12806.3i	2.84982	+	1.15234i
$499$	−4083.42	−	7072.69i	−0.366330	−	0.634503i	0.622658	−	0.782494i	$-0.286053\pi$
$499$	−4083.42	−	7072.69i	−0.366330	−	0.634503i	−0.988989	+	0.147991i	$0.952719\pi$
$500$		0			0
$501$	9469.74	+	3829.14i	0.844464	+	0.341464i
$502$	−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	$0.383412\pi$
$504$	17079.9	+	16512.6i	1.50952	+	1.45938i
$505$		0			0
$506$	2339.56	−	4052.24i	0.205546	−	0.356016i
$507$	1000.83	+	7135.96i	0.0876698	+	0.625087i
$508$	19000.9	+	32910.6i	1.65951	+	2.87435i
$509$	−58.0903	−	100.615i	−0.00505856	−	0.00876169i	0.863485	−	0.504374i	$-0.168277\pi$
$509$	−58.0903	−	100.615i	−0.00505856	−	0.00876169i	−0.868544	+	0.495613i	$0.834944\pi$
$510$		0			0
$511$	1664.54	−	2883.06i	0.144099	−	0.249587i
$512$	−1095.90			−0.0945947
$513$	688.421	+	1549.76i	0.0592486	+	0.133379i
$514$	−22013.0			−1.88901
$515$		0			0
$516$	−10269.3	+	8018.57i	−0.876124	+	0.684104i
$517$	1559.92	+	2701.87i	0.132699	+	0.229841i
$518$	−760.895	−	1317.91i	−0.0645402	−	0.111787i
$519$	1658.41	+	11824.5i	0.140263	+	1.00007i
$520$		0			0
$521$	−14479.3			−1.21756			−0.608780	−	0.793339i	$-0.708341\pi$
$521$	−14479.3			−1.21756			−0.608780	+	0.793339i	$0.708341\pi$
$522$	27951.3	−	7997.79i	2.34367	−	0.670601i
$523$	−6841.05			−0.571966			−0.285983	−	0.958235i	$-0.592320\pi$
$523$	−6841.05			−0.571966			−0.285983	+	0.958235i	$0.592320\pi$
$524$	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
$528$	−12914.9	−	5222.22i	−1.06449	−	0.430432i
$529$	3790.40	−	6565.16i	0.311531	−	0.539588i
$530$		0			0
$531$	15091.7	−	4318.23i	1.23338	−	0.352910i
$532$	3190.48			0.260009
$533$	2626.90	−	4549.92i	0.213478	−	0.369754i
$534$	994.552	+	7091.17i	0.0805964	+	0.574654i
$535$		0			0
$536$	8100.05	+	14029.7i	0.652741	+	1.13058i
$537$	−3578.25	+	2794.00i	−0.287547	+	0.224525i
$538$	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
$543$	6119.56	−	4778.33i	0.483638	−	0.377639i
$544$	31090.5	+	53850.3i	2.45036	+	4.24414i
$545$		0			0
$546$	−2924.56	−	20852.2i	−0.229230	−	1.63442i
$547$	2490.27	−	4313.28i	0.194655	−	0.337152i	−0.752132	−	0.659012i	$-0.770975\pi$
$547$	2490.27	−	4313.28i	0.194655	−	0.337152i	0.946787	+	0.321860i	$0.104308\pi$
$548$	−10629.1			−0.828563
$549$	−15018.6	−	14519.7i	−1.16754	−	1.12876i
$550$		0			0
$551$	1208.46	−	2093.12i	0.0934342	−	0.161833i
$552$	22835.4	+	9233.61i	1.76076	+	0.711972i
$553$	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	$0.492304\pi$
$558$	−2701.49	+	10809.0i	−0.204952	+	0.820039i
$559$	7148.42			0.540869
$560$		0			0
$561$	1018.70	+	7263.36i	0.0766660	+	0.546630i
$562$	21934.4	+	37991.6i	1.64635	+	2.85156i
$563$	−3768.84	−	6527.82i	−0.282127	−	0.488659i	0.689781	−	0.724018i	$-0.257707\pi$
$563$	−3768.84	−	6527.82i	−0.282127	−	0.488659i	−0.971908	+	0.235359i	$0.924373\pi$
$564$	−20911.4	+	16328.2i	−1.56122	+	1.21905i
$565$		0			0
$566$	16684.5			1.23905
$567$	−7776.73	+	4847.20i	−0.576000	+	0.359018i
$568$	52102.2			3.84887
$569$	1129.18	−	1955.79i	0.0831943	−	0.144097i	−0.821426	−	0.570315i	$-0.806821\pi$
$569$	1129.18	−	1955.79i	0.0831943	−	0.144097i	0.904620	+	0.426218i	$0.140154\pi$
$570$		0			0
$571$	−5688.66	−	9853.06i	−0.416923	−	0.722132i	0.578705	−	0.815537i	$-0.303558\pi$
$571$	−5688.66	−	9853.06i	−0.416923	−	0.722132i	−0.995628	+	0.0934047i	$0.970225\pi$
$572$	8064.52	+	13968.2i	0.589501	+	1.02105i
$573$	3644.81	+	25987.5i	0.265731	+	1.89467i
$574$	−2970.33	+	5144.76i	−0.215991	+	0.374108i
$575$		0			0
$576$	8983.10	−	35942.5i	0.649819	−	2.60001i
$577$	25027.9			1.80576			0.902881	−	0.429890i	$-0.141447\pi$
$577$	25027.9			1.80576			0.902881	+	0.429890i	$0.141447\pi$
$578$	19357.5	−	33528.3i	1.39302	−	2.41279i
$579$	24864.6	+	10054.2i	1.78470	+	0.721652i
$580$		0			0
$581$	7673.39	+	13290.7i	0.547928	+	0.949039i
$582$	−27225.5	−	11008.8i	−1.93906	−	0.784071i
$583$	−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	−0.863407	−	0.504507i	$-0.831674\pi$
$587$	74.1295	−	128.396i	0.00521235	−	0.00902806i	0.868620	+	0.495479i	$0.165008\pi$
$588$	−2803.49	−	19988.9i	−0.196622	−	1.40192i
$589$	463.112	+	802.133i	0.0323976	+	0.0561143i
$590$		0			0
$591$	−1531.83	+	1196.10i	−0.106618	+	0.0832503i
$592$	−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	$0.100527\pi$
$594$	5704.40	−	7837.42i	0.394031	−	0.541369i
$595$		0			0
$596$	9505.10	−	16463.3i	0.653262	−	1.13148i
$597$	2471.01	−	1929.43i	0.169400	−	0.132272i
$598$	−10915.8	−	18906.7i	−0.746453	−	1.29289i
$599$	1906.00	+	3301.29i	0.130012	+	0.225187i	0.923681	−	0.383163i	$-0.125165\pi$
$599$	1906.00	+	3301.29i	0.130012	+	0.225187i	−0.793669	+	0.608350i	$0.791832\pi$
$600$		0			0
$601$	−11584.3	+	20064.6i	−0.786247	+	1.36182i	0.142004	+	0.989866i	$0.454646\pi$
$601$	−11584.3	+	20064.6i	−0.786247	+	1.36182i	−0.928251	+	0.371954i	$0.878688\pi$
$602$	−8082.97			−0.547238
$603$	−6007.73	+	1719.01i	−0.405728	+	0.116092i
$604$	28530.1			1.92197
$605$		0			0
$606$	2301.66	+	930.691i	0.154288	+	0.0623873i
$607$	3676.39	+	6367.69i	0.245832	+	0.425794i	0.962365	−	0.271759i	$-0.0876055\pi$
$607$	3676.39	+	6367.69i	0.245832	+	0.425794i	−0.716533	+	0.697553i	$0.754272\pi$
$608$	−3415.99	−	5916.67i	−0.227856	−	0.394659i
$609$	12108.2	+	4896.01i	0.805662	+	0.325774i
$610$		0			0
$611$	14556.4			0.963809
$612$	−59965.4	+	17158.1i	−3.96072	+	1.13329i
$613$	−19902.6			−1.31135			−0.655676	−	0.755043i	$-0.727616\pi$
$613$	−19902.6			−1.31135			−0.655676	+	0.755043i	$0.727616\pi$
$614$	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	0.906868	+	0.421414i	$0.138466\pi$
$617$	12542.6	+	21724.4i	0.818390	+	1.41749i	−0.0884785	+	0.996078i	$0.528200\pi$
$618$	−34053.8	+	26590.2i	−2.21658	+	1.73077i
$619$	1565.52	−	2711.56i	0.101654	−	0.176069i	−0.810712	−	0.585445i	$-0.800920\pi$
$619$	1565.52	−	2711.56i	0.101654	−	0.176069i	0.912366	+	0.409375i	$0.134253\pi$
$620$		0			0
$621$	−5591.11	+	7681.78i	−0.361294	+	0.496391i
$622$	−42753.3			−2.75603
$623$	−1608.39	+	2785.81i	−0.103433	+	0.179151i
$624$	−51229.9	+	40001.8i	−3.28660	+	2.56627i
$625$		0			0
$626$	18198.4	+	31520.6i	1.16191	+	2.01248i
$627$	−111.927	−	798.043i	−0.00712910	−	0.0508306i
$628$	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
$633$	−11618.3	−	4697.92i	−0.729518	−	0.294985i
$634$	−22682.4	−	39287.0i	−1.42087	−	2.46102i
$635$		0			0
$636$	−29690.8	−	12005.6i	−1.85113	−	0.748513i
$637$	−5537.17	+	9590.66i	−0.344412	+	0.596540i
$638$	−13815.8			−0.857325
$639$	−4873.00	+	19497.5i	−0.301679	+	1.20706i
$640$		0			0
$641$	3462.88	−	5997.88i	0.213378	−	0.369582i	−0.739391	−	0.673276i	$-0.764887\pi$
$641$	3462.88	−	5997.88i	0.213378	−	0.369582i	0.952770	+	0.303694i	$0.0982200\pi$
$642$	−2276.55	−	16231.9i	−0.139951	−	0.997852i
$643$	−7482.26	−	12959.7i	−0.458898	−	0.794835i	0.540005	−	0.841662i	$-0.318422\pi$
$643$	−7482.26	−	12959.7i	−0.458898	−	0.794835i	−0.998903	+	0.0468271i	$0.985089\pi$
$644$	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	$0.477043\pi$
$648$	45028.1	+	24007.3i	2.72974	+	1.45540i
$649$	−7459.55			−0.451176
$650$		0			0
$651$	−3944.97	+	3080.35i	−0.237505	+	0.185451i
$652$	−24412.4	−	42283.4i	−1.46635	−	2.53980i
$653$	−7985.85	−	13831.9i	−0.478577	−	0.828919i	0.521122	−	0.853482i	$-0.325514\pi$
$653$	−7985.85	−	13831.9i	−0.478577	−	0.828919i	−0.999698	+	0.0245632i	$0.992180\pi$
$654$	−5312.87	−	37880.9i	−0.317660	−	2.26492i
$655$		0			0
$656$	18337.8			1.09142
$657$	1733.83	−	6937.25i	0.102957	−	0.411945i
$658$	−16459.4			−0.975158
$659$	3421.46	−	5926.15i	0.202248	−	0.350304i	−0.747005	−	0.664819i	$-0.768509\pi$
$659$	3421.46	−	5926.15i	0.202248	−	0.350304i	0.949252	+	0.314515i	$0.101842\pi$
$660$		0			0
$661$	6695.50	+	11597.0i	0.393986	+	0.682404i	0.992971	−	0.118356i	$-0.0377624\pi$
$661$	6695.50	+	11597.0i	0.393986	+	0.682404i	−0.598985	+	0.800760i	$0.704429\pi$
$662$	693.793	+	1201.68i	0.0407327	+	0.0705511i
$663$	31725.1	+	12828.2i	1.85837	+	0.751443i
$664$	42729.6	−	74009.8i	2.49733	−	4.32551i
$665$		0			0
$666$	−2350.03	−	2271.97i	−0.136729	−	0.132188i
$667$	13541.5			0.786098
$668$	20639.5	−	35748.7i	1.19546	−	2.07060i
$669$	−3955.88	−	28205.5i	−0.228615	−	1.63003i
$670$		0			0
$671$	4963.51	+	8597.05i	0.285565	+	0.494613i
$672$	29098.7	−	22721.2i	1.67040	−	1.30430i
$673$	−15951.1	+	27628.1i	−0.913624	+	1.58244i	−0.104720	+	0.994502i	$0.533395\pi$
$673$	−15951.1	+	27628.1i	−0.913624	+	1.58244i	−0.808904	+	0.587941i	$0.799939\pi$
$674$	−59771.3			−3.41588
$675$		0			0
$676$	29119.9			1.65680
$677$	−5930.38	+	10271.7i	−0.336666	+	0.583123i	−0.983803	−	0.179251i	$-0.942633\pi$
$677$	−5930.38	+	10271.7i	−0.336666	+	0.583123i	0.647137	+	0.762373i	$0.275966\pi$
$678$	3758.74	−	2934.93i	0.212911	−	0.166247i
$679$	−6596.33	−	11425.2i	−0.372818	−	0.645741i
$680$		0			0
$681$	3949.53	+	28160.2i	0.222241	+	1.58458i
$682$	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	$0.568646\pi$
$684$	6588.55	−	1885.20i	0.368303	−	0.105384i
$685$		0			0
$686$	17870.1	−	30951.9i	0.994580	−	1.72266i
$687$	−15781.2	−	6381.21i	−0.876405	−	0.354379i
$688$	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	−0.564237	−	0.825613i	$-0.690829\pi$
$691$	7863.00	−	13619.1i	0.432883	−	0.749776i	0.997120	+	0.0758369i	$0.0241628\pi$
$692$	48252.6			2.65071
$693$	4186.66	−	1197.94i	0.229492	−	0.0656652i
$694$	53239.5			2.91202
$695$		0			0
$696$	−10101.4	−	72023.4i	−0.550135	−	3.92247i
$697$	−4827.36	−	8361.23i	−0.262338	−	0.454382i
$698$	16314.5	+	28257.5i	0.884688	+	1.53232i
$699$	−14114.1	+	11020.7i	−0.763724	+	0.596338i
$700$		0			0
$701$	−6338.17			−0.341497			−0.170748	−	0.985315i	$-0.554619\pi$
$701$	−6338.17			−0.341497			−0.170748	+	0.985315i	$0.554619\pi$
$702$	−18360.6	−	41333.0i	−0.987146	−	2.22224i
$703$	−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
$708$	−8810.76	−	62820.9i	−0.467696	−	3.33468i
$709$	−17191.8	+	29777.1i	−0.910651	+	1.57729i	−0.0975047	+	0.995235i	$0.531086\pi$
$709$	−17191.8	+	29777.1i	−0.910651	+	1.57729i	−0.813147	+	0.582059i	$0.802247\pi$
$710$		0			0
$711$	10865.0	+	10504.1i	0.573092	+	0.554056i
$712$	17912.7			0.942847
$713$	−2594.70	+	4494.16i	−0.136287	+	0.236055i
$714$	−35872.7	−	14505.3i	−1.88025	−	0.760292i
$715$		0			0
$716$	9173.18	+	15888.4i	0.478796	+	0.829299i
$717$	8308.83	+	3359.72i	0.432774	+	0.174995i
$718$	−23706.6	+	41061.0i	−1.23220	+	2.13424i
$719$	−988.886			−0.0512924			−0.0256462	−	0.999671i	$-0.508164\pi$
$719$	−988.886			−0.0512924			−0.0256462	+	0.999671i	$0.508164\pi$
$720$		0			0
$721$	−19409.3			−1.00255
$722$	−18074.6	+	31306.1i	−0.931671	+	1.61370i
$723$	−4024.03	−	28691.4i	−0.206992	−	1.47586i
$724$	−15688.1	−	27172.5i	−0.805307	−	1.39483i
$725$		0			0
$726$	25723.8	−	20085.9i	1.31502	−	1.02680i
$727$	−6845.92	+	11857.5i	−0.349245	+	0.604910i	−0.986116	−	0.166061i	$-0.946895\pi$
$727$	−6845.92	+	11857.5i	−0.349245	+	0.604910i	0.636871	+	0.770971i	$0.280229\pi$
$728$	−52673.8			−2.68162
$729$	−13195.3	+	14604.9i	−0.670392	+	0.742007i
$730$		0			0
$731$	6568.20	−	11376.5i	0.332331	−	0.575614i
$732$	−66537.8	+	51954.7i	−3.35971	+	2.62336i
$733$	−1250.97	−	2166.74i	−0.0630363	−	0.109182i	0.832785	−	0.553597i	$-0.186745\pi$
$733$	−1250.97	−	2166.74i	−0.0630363	−	0.109182i	−0.895821	+	0.444415i	$0.853412\pi$
$734$	−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
$738$	−3093.97	+	12379.4i	−0.154323	+	0.617468i
$739$	26453.1			1.31677			0.658384	−	0.752682i	$-0.271240\pi$
$739$	26453.1			1.31677			0.658384	+	0.752682i	$0.271240\pi$
$740$		0			0
$741$	−3485.72	−	1409.47i	−0.172808	−	0.0698760i
$742$	−9934.24	−	17206.6i	−0.491506	−	0.851313i
$743$	−10441.4	−	18085.0i	−0.515555	−	0.892967i	−0.999837	−	0.0180555i	$-0.994252\pi$
$743$	−10441.4	−	18085.0i	−0.515555	−	0.892967i	0.484282	−	0.874912i	$-0.339081\pi$
$744$	25838.8	+	10448.1i	1.27325	+	0.514845i
$745$		0			0
$746$	−64182.2			−3.14997
$747$	23699.3	+	22912.1i	1.16079	+	1.12224i
$748$	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	0.996864	−	0.0791332i	$-0.0252152\pi$
$751$	8847.65	+	15324.6i	0.429901	+	0.744610i	−0.566963	+	0.823743i	$0.691882\pi$
$752$	25403.7	+	44000.6i	1.23189	+	2.13369i
$753$	−5555.08	+	4337.57i	−0.268842	+	0.209920i
$754$	−32230.4	+	55824.8i	−1.55672	+	2.69631i
$755$		0			0
$756$	15033.5	+	33843.2i	0.723233	+	1.62813i
$757$	−7755.61			−0.372368			−0.186184	−	0.982515i	$-0.559612\pi$
$757$	−7755.61			−0.372368			−0.186184	+	0.982515i	$0.559612\pi$
$758$	13603.2	−	23561.4i	0.651835	−	1.12901i
$759$	3558.66	−	2778.71i	0.170186	−	0.132886i
$760$		0			0
$761$	−8527.15	−	14769.5i	−0.406188	−	0.703538i	0.588271	−	0.808664i	$-0.299809\pi$
$761$	−8527.15	−	14769.5i	−0.406188	−	0.703538i	−0.994459	+	0.105126i	$0.966476\pi$
$762$	7033.40	+	50148.2i	0.334374	+	2.38409i
$763$	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
$768$	−21499.9	−	8693.61i	−1.01017	−	0.408468i
$769$	5024.16	+	8702.11i	0.235599	+	0.408070i	0.959447	−	0.281890i	$-0.0909613\pi$
$769$	5024.16	+	8702.11i	0.235599	+	0.408070i	−0.723847	+	0.689960i	$0.757628\pi$
$770$		0			0
$771$	−19692.0	−	7962.57i	−0.919831	−	0.371939i
$772$	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	$0.554272\pi$
$774$	−16691.9	+	4776.09i	−0.775164	+	0.221800i
$775$		0			0
$776$	−36731.9	+	63621.5i	−1.69922	+	2.94314i
$777$	−203.952	−	1454.18i	−0.00941665	−	0.0671409i
$778$	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
$783$	27897.1	+	2956.07i	1.27326	+	0.134919i
$784$	−38653.8			−1.76083
$785$		0			0
$786$	27310.0	−	21324.5i	1.23933	−	0.967708i
$787$	14228.1	+	24643.8i	0.644445	+	1.11621i	0.984429	+	0.175780i	$0.0562448\pi$
$787$	14228.1	+	24643.8i	0.644445	+	1.11621i	−0.339985	+	0.940431i	$0.610422\pi$
$788$	3926.99	+	6801.75i	0.177530	+	0.307490i
$789$	310.522	+	2214.03i	0.0140112	+	0.0999004i
$790$		0			0
$791$	2142.33			0.0962989
$792$	−17433.9	−	16854.8i	−0.782178	−	0.756197i
$793$	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	0.907805	−	0.419392i	$-0.137757\pi$
$797$	2040.73	+	3534.65i	0.0906981	+	0.157094i	−0.817107	+	0.576486i	$0.804424\pi$
$798$	3941.42	+	1593.74i	0.174843	+	0.0706988i
$799$	13374.9	−	23165.9i	0.592201	−	1.02572i
$800$		0			0
$801$	−1675.34	+	6703.24i	−0.0739015	+	0.295689i
$802$	9003.54			0.396416
$803$	−1699.03	+	2942.81i	−0.0746668	+	0.129327i
$804$	3507.40	+	25007.8i	0.153851	+	1.09696i
$805$		0			0
$806$	−12351.5	−	21393.4i	−0.539779	−	0.934925i
$807$	14202.7	−	11089.9i	0.619527	−	0.483745i
$808$	3105.34	−	5378.60i	0.135205	−	0.234181i
$809$	14209.7			0.617536			0.308768	−	0.951137i	$-0.400083\pi$
$809$	14209.7			0.617536			0.308768	+	0.951137i	$0.400083\pi$
$810$		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
$813$	−227.062	+	177.297i	−0.00979511	+	0.00764831i
$814$	776.663	+	1345.22i	0.0334423	+	0.0579237i
$815$		0			0
$816$	16589.8	+	118286.i	0.711714	+	5.07454i
$817$	−721.665	+	1249.96i	−0.0309031	+	0.0535258i
$818$	−2545.64			−0.108810
$819$	4926.47	−	19711.4i	0.210189	−	0.840992i
$820$		0			0
$821$	7259.82	−	12574.4i	0.308611	−	0.534530i	−0.669448	−	0.742859i	$-0.733469\pi$
$821$	7259.82	−	12574.4i	0.308611	−	0.534530i	0.978059	+	0.208329i	$0.0668026\pi$
$822$	−13130.9	−	5309.54i	−0.557167	−	0.225294i
$823$	−19203.2	−	33260.9i	−0.813344	−	1.40875i	−0.910511	−	0.413485i	$-0.864312\pi$
$823$	−19203.2	−	33260.9i	−0.813344	−	1.40875i	0.0971672	−	0.995268i	$-0.469022\pi$
$824$	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	$0.429517\pi$
$828$	27604.3	+	26687.4i	1.15859	+	1.12011i
$829$	−6474.00			−0.271232			−0.135616	−	0.990761i	$-0.543301\pi$
$829$	−6474.00			−0.271232			−0.135616	+	0.990761i	$0.543301\pi$
$830$		0			0
$831$	1135.63	+	8097.09i	0.0474064	+	0.338008i
$832$	41071.6	+	71138.0i	1.71142	+	2.96426i
$833$	10175.5	+	17624.4i	0.423240	+	0.733073i
$834$	4712.61	−	3679.75i	0.195665	−	0.152781i
$835$		0			0
$836$	−3256.60			−0.134727
$837$	−6326.49	+	8692.13i	−0.261261	+	0.358953i
$838$	−67524.5			−2.78353
$839$	−7919.71	+	13717.3i	−0.325886	+	0.564452i	−0.981691	−	0.190478i	$-0.938996\pi$
$839$	−7919.71	+	13717.3i	−0.325886	+	0.564452i	0.655805	+	0.754930i	$0.272329\pi$
$840$		0			0
$841$	−7797.09	−	13505.0i	−0.319697	−	0.553731i
$842$	−18179.2	−	31487.3i	−0.744058	−	1.28875i
$843$	5879.36	+	41919.9i	0.240209	+	1.71269i
$844$	−25322.3	+	43859.5i	−1.03274	+	1.78875i
$845$		0			0
$846$	−33989.7	+	9725.57i	−1.38131	+	0.395239i
$847$	14661.5			0.594778
$848$	−30665.4	+	53114.0i	−1.24181	+	2.15087i
$849$	14925.3	+	6035.12i	0.603338	+	0.243963i
$850$		0			0
$851$	−761.239	−	1318.51i	−0.0306639	−	0.0531114i
$852$	75293.9	+	30445.5i	3.02761	+	1.22423i
$853$	−9420.17	+	16316.2i	−0.378125	+	0.654931i	−0.990789	−	0.135412i	$-0.956764\pi$
$853$	−9420.17	+	16316.2i	−0.378125	+	0.654931i	0.612665	+	0.790343i	$0.290098\pi$
$854$	−52372.0			−2.09852
$855$		0			0
$856$	−41002.6			−1.63720
$857$	4528.11	−	7842.91i	0.180487	−	0.312612i	−0.761560	−	0.648095i	$-0.775566\pi$
$857$	4528.11	−	7842.91i	0.180487	−	0.312612i	0.942046	+	0.335483i	$0.108899\pi$
$858$	2985.17	+	21284.3i	0.118778	+	0.846893i
$859$	−11027.7	−	19100.6i	−0.438022	−	0.758676i	0.559515	−	0.828820i	$-0.310987\pi$
$859$	−11027.7	−	19100.6i	−0.438022	−	0.758676i	−0.997537	+	0.0701440i	$0.977654\pi$
$860$		0			0
$861$	−4518.10	+	3527.87i	−0.178835	+	0.139639i
$862$	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	$0.583219\pi$
$864$	46665.2	−	64114.6i	1.83748	−	2.52456i
$865$		0			0
$866$	13826.4	−	23948.1i	0.542542	−	0.939710i
$867$	29444.4	−	22991.0i	1.15338	−	0.900596i
$868$	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
$873$	−20372.8	−	19696.1i	−0.789821	−	0.763586i
$874$	4407.98			0.170597
$875$		0			0
$876$	−26789.7	−	10832.6i	−1.03327	−	0.417807i
$877$	−18361.1	−	31802.4i	−0.706967	−	1.22450i	−0.965977	−	0.258628i	$-0.916730\pi$
$877$	−18361.1	−	31802.4i	−0.706967	−	1.22450i	0.259010	−	0.965875i	$-0.416604\pi$
$878$	45700.6	+	79155.8i	1.75663	+	3.04257i
$879$	588.473	+	237.952i	0.0225810	+	0.00913076i
$880$		0			0
$881$	36054.4			1.37878			0.689390	−	0.724390i	$-0.257879\pi$
$881$	36054.4			1.37878			0.689390	+	0.724390i	$0.257879\pi$
$882$	6521.70	−	26094.1i	0.248976	−	0.996186i
$883$	−13524.6			−0.515446			−0.257723	−	0.966219i	$-0.582972\pi$
$883$	−13524.6			−0.515446			−0.257723	+	0.966219i	$0.582972\pi$
$884$	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	−0.946863	−	0.321639i	$-0.895766\pi$
$887$	−19865.1	−	34407.4i	−0.751978	−	1.30246i	0.194884	−	0.980826i	$-0.437567\pi$
$888$	−6444.92	+	5032.39i	−0.243556	+	0.190176i
$889$	−11374.4	+	19701.0i	−0.429116	+	0.743251i
$890$		0			0
$891$	7937.89	−	4947.65i	0.298462	−	0.186030i
$892$	−115099.			−4.32040
$893$	−1469.53	+	2545.30i	−0.0550682	+	0.0953810i
$894$	19966.2	−	15590.2i	0.746946	−	0.583238i
$895$		0			0
$896$	−18021.1	−	31213.4i	−0.671921	−	1.16380i
$897$	−2925.88	−	20861.6i	−0.108910	−	0.776532i
$898$	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
$903$	−7230.71	−	2923.78i	−0.266471	−	0.107749i
$904$	−5964.81	−	10331.4i	−0.219454	−	0.380106i
$905$		0			0
$906$	35245.2	+	14251.6i	1.29243	+	0.522602i
$907$	11511.2	−	19938.0i	0.421415	−	0.729912i	−0.574663	−	0.818390i	$-0.694867\pi$
$907$	11511.2	−	19938.0i	0.421415	−	0.729912i	0.996078	+	0.0884783i	$0.0282004\pi$
$908$	114914.			4.19995
$909$	1722.33	+	1665.12i	0.0628449	+	0.0607574i
$910$		0			0
$911$	−15940.1	+	27609.1i	−0.579714	+	1.00409i	0.415798	+	0.909457i	$0.363502\pi$
$911$	−15940.1	+	27609.1i	−0.579714	+	1.00409i	−0.995512	+	0.0946365i	$0.969831\pi$
$912$	−1822.76	−	12996.3i	−0.0661817	−	0.471877i
$913$	−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
$918$	−82650.4	−	8757.89i	−2.97153	−	0.314873i
$919$	38459.6			1.38049			0.690243	−	0.723578i	$-0.257504\pi$
$919$	38459.6			1.38049			0.690243	+	0.723578i	$0.257504\pi$
$920$		0			0
$921$	7898.37	−	6167.28i	0.282584	−	0.220650i
$922$	27786.1	+	48126.9i	0.992501	+	1.71906i
$923$	−22279.8	−	38589.8i	−0.794528	−	1.37616i
$924$	−2444.23	−	17427.4i	−0.0870231	−	0.620477i
$925$		0			0
$926$	−97838.1			−3.47209
$927$	−40081.4	+	11468.6i	−1.42011	+	0.406341i
$928$	−113021.			−3.99796
$929$	18600.5	−	32217.1i	0.656903	−	1.13779i	−0.324509	−	0.945882i	$-0.605199\pi$
$929$	18600.5	−	32217.1i	0.656903	−	1.13779i	0.981413	−	0.191908i	$-0.0614675\pi$
$930$		0			0
$931$	−1118.00	−	1936.44i	−0.0393567	−	0.0681678i
$932$	36182.7	+	62670.3i	1.27168	+	2.20261i
$933$	−38245.5	−	15464.8i	−1.34201	−	0.542651i
$934$	−10277.7	+	17801.5i	−0.360062	+	0.623645i
$935$		0			0
$936$	−108775.	+	31124.0i	−3.79852	+	1.08688i
$937$	23593.7			0.822595			0.411298	−	0.911501i	$-0.365076\pi$
$937$	23593.7			0.822595			0.411298	+	0.911501i	$0.365076\pi$
$938$	−7833.12	+	13567.4i	−0.272666	+	0.472271i
$939$	4877.94	+	34779.8i	0.169527	+	1.20873i
$940$		0			0
$941$	−18285.8	−	31672.0i	−0.633477	−	1.09721i	−0.986836	−	0.161726i	$-0.948294\pi$
$941$	−18285.8	−	31672.0i	−0.633477	−	1.09721i	0.353359	−	0.935488i	$-0.385039\pi$
$942$	41933.2	−	32742.7i	1.45038	−	1.13250i
$943$	−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	−0.432409	−	0.901678i	$-0.642336\pi$
$947$	16455.9	−	28502.4i	0.564671	−	0.978039i	0.997080	−	0.0763615i	$-0.0243303\pi$
$948$	48135.8	−	37585.8i	1.64913	−	1.28769i
$949$	7927.21	+	13730.3i	0.271157	+	0.469658i
$950$		0			0
$951$	−6079.83	−	43349.3i	−0.207310	−	1.47813i
$952$	−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	$0.380557\pi$
$954$	−30681.9	−	29662.8i	−1.04126	−	1.00668i
$955$		0			0
$956$	18109.3	−	31366.2i	0.612653	−	1.06115i
$957$	−12359.1	−	4997.47i	−0.417464	−	0.168804i
$958$	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
$963$	3834.89	−	15343.9i	0.128326	−	0.513447i
$964$	−117082.			−3.91178
$965$		0			0
$966$	3308.40	+	23589.0i	0.110193	+	0.785675i
$967$	14881.9	+	25776.2i	0.494901	+	0.857193i	0.999983	−	0.00587841i	$-0.00187117\pi$
$967$	14881.9	+	25776.2i	0.494901	+	0.857193i	−0.505082	+	0.863071i	$0.668538\pi$
$968$	−40821.7	−	70705.2i	−1.35543	−	2.34768i
$969$	−5445.91	+	4252.33i	−0.180545	+	0.140975i
$970$		0			0
$971$	29812.3			0.985297			0.492648	−	0.870228i	$-0.336029\pi$
$971$	29812.3			0.985297			0.492648	+	0.870228i	$0.336029\pi$
$972$	51042.6	+	61005.4i	1.68435	+	2.01311i
$973$	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	0.815014	−	0.579441i	$-0.196729\pi$
$977$	−2879.87	−	4988.07i	−0.0943041	−	0.163339i	−0.909318	+	0.416102i	$0.863396\pi$
$978$	−9036.49	−	64430.3i	−0.295455	−	2.10660i
$979$	1641.72	−	2843.54i	0.0535950	−	0.0928292i
$980$		0			0
$981$	8949.61	−	35808.5i	0.291273	−	1.16542i
$982$	−78796.5			−2.56059
$983$	−8825.70	+	15286.6i	−0.286364	+	0.495998i	−0.972939	−	0.231062i	$-0.925780\pi$
$983$	−8825.70	+	15286.6i	−0.286364	+	0.495998i	0.686575	+	0.727059i	$0.259113\pi$
$984$	29592.7	+	11966.0i	0.958722	+	0.387665i
$985$		0			0
$986$	59228.7	+	102587.i	1.91301	+	3.31343i
$987$	−14723.9	−	5953.70i	−0.474841	−	0.192005i
$988$	−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
$993$	185.966	+	1325.94i	0.00594305	+	0.0423740i
$994$	25192.6	+	43634.8i	0.803884	+	1.39237i
$995$		0			0
$996$	104996.	−	81984.4i	3.34030	−	2.60821i
$997$	−8055.12	+	13951.9i	−0.255876	+	0.443190i	−0.965133	−	0.261760i	$-0.915697\pi$
$997$	−8055.12	+	13951.9i	−0.255876	+	0.443190i	0.709257	+	0.704950i	$0.249030\pi$
$998$	−43978.6			−1.39491
$999$	−1280.42	−	2882.47i	−0.0405514	−	0.0912885i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.1	✓	14	5.4	even	2
45.4.e.c.31.1	yes	14	45.4	even	6
135.4.e.c.46.7		14	15.14	odd	2
135.4.e.c.91.7		14	45.14	odd	6
225.4.e.d.76.7		14	9.4	even	3	inner
225.4.e.d.151.7		14	1.1	even	1	trivial
225.4.k.d.49.1		28	45.22	odd	12
225.4.k.d.49.14		28	45.13	odd	12
225.4.k.d.124.1		28	5.3	odd	4
225.4.k.d.124.14		28	5.2	odd	4
405.4.a.m.1.7		7	45.34	even	6
405.4.a.n.1.1		7	45.29	odd	6
2025.4.a.ba.1.7		7	9.2	odd	6
2025.4.a.bb.1.1		7	9.7	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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.69252 - 4.66357i) q^{2} +(4.09553 - 3.19791i) q^{3} +(-10.4993 - 18.1853i) q^{4} +(-3.88642 - 27.7102i) q^{6} +(6.28510 - 10.8861i) q^{7} -69.9976 q^{8} +(6.54673 - 26.1943i) q^{9} +O(q^{10})\)	\(q+(2.69252 - 4.66357i) q^{2} +(4.09553 - 3.19791i) q^{3} +(-10.4993 - 18.1853i) q^{4} +(-3.88642 - 27.7102i) q^{6} +(6.28510 - 10.8861i) q^{7} -69.9976 q^{8} +(6.54673 - 26.1943i) q^{9} +(-6.41534 + 11.1117i) q^{11} +(-101.155 - 40.9026i) q^{12} +(29.9322 + 51.8442i) q^{13} +(-33.8455 - 58.6220i) q^{14} +(-104.475 + 180.957i) q^{16} +110.011 q^{17} +(-104.532 - 101.060i) q^{18} -12.0872 q^{19} +(-9.07201 - 64.6836i) q^{21} +(34.5468 + 59.8368i) q^{22} +(-33.8608 - 58.6485i) q^{23} +(-286.677 + 223.846i) q^{24} +322.372 q^{26} +(-56.9547 - 128.215i) q^{27} -263.956 q^{28} +(-99.9790 + 173.169i) q^{29} +(-38.3143 - 66.3624i) q^{31} +(282.613 + 489.500i) q^{32} +(9.26000 + 66.0240i) q^{33} +(296.206 - 513.044i) q^{34} +(-545.086 + 155.967i) q^{36} +22.4815 q^{37} +(-32.5449 + 56.3694i) q^{38} +(288.381 + 116.609i) q^{39} +(-43.8807 - 76.0037i) q^{41} +(-326.083 - 131.854i) q^{42} +(59.7050 - 103.412i) q^{43} +269.426 q^{44} -364.682 q^{46} +(121.578 - 210.579i) q^{47} +(150.801 + 1075.22i) q^{48} +(92.4951 + 160.206i) q^{49} +(450.553 - 351.805i) q^{51} +(628.534 - 1088.65i) q^{52} +293.518 q^{53} +(-751.293 - 79.6094i) q^{54} +(-439.942 + 762.002i) q^{56} +(-49.5034 + 38.6537i) q^{57} +(538.390 + 932.519i) q^{58} +(290.692 + 503.493i) q^{59} +(386.847 - 670.038i) q^{61} -412.648 q^{62} +(-244.007 - 235.902i) q^{63} +1372.15 q^{64} +(332.840 + 134.586i) q^{66} +(-115.719 - 200.431i) q^{67} +(-1155.03 - 2000.58i) q^{68} +(-326.231 - 131.913i) q^{69} -744.342 q^{71} +(-458.255 + 1833.54i) q^{72} +264.839 q^{73} +(60.5317 - 104.844i) q^{74} +(126.907 + 219.809i) q^{76} +(80.6421 + 139.676i) q^{77} +(1320.28 - 1030.92i) q^{78} +(-279.858 + 484.729i) q^{79} +(-643.281 - 342.974i) q^{81} -472.598 q^{82} +(-610.443 + 1057.32i) q^{83} +(-1081.04 + 844.108i) q^{84} +(-321.513 - 556.878i) q^{86} +(144.311 + 1028.94i) q^{87} +(449.059 - 777.792i) q^{88} -255.905 q^{89} +752.509 q^{91} +(-711.027 + 1231.53i) q^{92} +(-369.138 - 149.263i) q^{93} +(-654.699 - 1133.97i) q^{94} +(2722.83 + 1100.99i) q^{96} +(524.759 - 908.909i) q^{97} +996.177 q^{98} +(249.064 + 240.791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 + 5 * q^3 - 36 * q^4 - 31 * q^6 + 22 * q^7 + 36 * q^8 + 17 * q^9	\( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9} + 23 q^{11} - 287 q^{12} + 96 q^{13} - 21 q^{14} - 324 q^{16} + 322 q^{17} + 89 q^{18} + 558 q^{19} + 180 q^{21} + 311 q^{22} - 96 q^{23} + 48 q^{24} + 716 q^{26} + 470 q^{27} - 674 q^{28} - 296 q^{29} - 244 q^{31} + 314 q^{32} + 211 q^{33} - 125 q^{34} - 2399 q^{36} - 808 q^{37} - 305 q^{38} + 634 q^{39} - 47 q^{41} - 1941 q^{42} + 525 q^{43} - 110 q^{44} + 1434 q^{46} - 164 q^{47} - 2051 q^{48} - 1225 q^{49} + 1517 q^{51} + 1682 q^{52} + 1012 q^{53} - 4066 q^{54} - 981 q^{56} - 337 q^{57} + 1183 q^{58} - 85 q^{59} - 828 q^{61} - 1572 q^{62} + 828 q^{63} + 4472 q^{64} + 4930 q^{66} + 1093 q^{67} - 2473 q^{68} - 822 q^{69} - 656 q^{71} + 4626 q^{72} - 4170 q^{73} - 1316 q^{74} - 2789 q^{76} - 24 q^{77} + 5314 q^{78} - 2110 q^{79} - 2167 q^{81} + 124 q^{82} - 1290 q^{83} + 5775 q^{84} - 2569 q^{86} - 3604 q^{87} + 2271 q^{88} + 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 696 q^{93} + 517 q^{94} - 593 q^{96} + 1787 q^{97} + 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 5 * q^3 - 36 * q^4 - 31 * q^6 + 22 * q^7 + 36 * q^8 + 17 * q^9 + 23 * q^11 - 287 * q^12 + 96 * q^13 - 21 * q^14 - 324 * q^16 + 322 * q^17 + 89 * q^18 + 558 * q^19 + 180 * q^21 + 311 * q^22 - 96 * q^23 + 48 * q^24 + 716 * q^26 + 470 * q^27 - 674 * q^28 - 296 * q^29 - 244 * q^31 + 314 * q^32 + 211 * q^33 - 125 * q^34 - 2399 * q^36 - 808 * q^37 - 305 * q^38 + 634 * q^39 - 47 * q^41 - 1941 * q^42 + 525 * q^43 - 110 * q^44 + 1434 * q^46 - 164 * q^47 - 2051 * q^48 - 1225 * q^49 + 1517 * q^51 + 1682 * q^52 + 1012 * q^53 - 4066 * q^54 - 981 * q^56 - 337 * q^57 + 1183 * q^58 - 85 * q^59 - 828 * q^61 - 1572 * q^62 + 828 * q^63 + 4472 * q^64 + 4930 * q^66 + 1093 * q^67 - 2473 * q^68 - 822 * q^69 - 656 * q^71 + 4626 * q^72 - 4170 * q^73 - 1316 * q^74 - 2789 * q^76 - 24 * q^77 + 5314 * q^78 - 2110 * q^79 - 2167 * q^81 + 124 * q^82 - 1290 * q^83 + 5775 * q^84 - 2569 * q^86 - 3604 * q^87 + 2271 * q^88 + 6096 * q^89 + 6676 * q^91 - 2763 * q^92 + 696 * q^93 + 517 * q^94 - 593 * q^96 + 1787 * q^97 + 2558 * q^98 + 2320 * q^99

Introduction

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