LMFDB - Embedded newform 225.4.e.d.151.6

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			151.6
Root			$-1.52087 - 2.63422i$ of defining polynomial
Character	$\chi$	$=$	225.151
Dual form			225.4.e.d.76.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52087 - 2.63422i) q^{2} +(-4.01867 - 3.29398i) q^{3} +(-0.626094 - 1.08443i) q^{4} +(-14.7890 + 5.57636i) q^{6} +(-6.85611 + 11.8751i) q^{7} +20.5251 q^{8} +(5.29939 + 26.4748i) q^{9} +O(q^{10})$	\(q+(1.52087 - 2.63422i) q^{2} +(-4.01867 - 3.29398i) q^{3} +(-0.626094 - 1.08443i) q^{4} +(-14.7890 + 5.57636i) q^{6} +(-6.85611 + 11.8751i) q^{7} +20.5251 q^{8} +(5.29939 + 26.4748i) q^{9} +(-15.9034 + 27.5455i) q^{11} +(-1.05602 + 6.42029i) q^{12} +(29.1216 + 50.4401i) q^{13} +(20.8545 + 36.1211i) q^{14} +(36.2248 - 62.7431i) q^{16} -109.055 q^{17} +(77.8003 + 26.3050i) q^{18} +129.695 q^{19} +(66.6689 - 25.1383i) q^{21} +(48.3740 + 83.7863i) q^{22} +(39.8342 + 68.9949i) q^{23} +(-82.4836 - 67.6093i) q^{24} +177.161 q^{26} +(65.9111 - 123.850i) q^{27} +17.1703 q^{28} +(-4.51769 + 7.82486i) q^{29} +(16.6904 + 28.9087i) q^{31} +(-28.0860 - 48.6463i) q^{32} +(154.645 - 58.3108i) q^{33} +(-165.858 + 287.275i) q^{34} +(25.3921 - 22.3225i) q^{36} +22.1645 q^{37} +(197.250 - 341.647i) q^{38} +(49.1186 - 298.628i) q^{39} +(-60.8698 - 105.430i) q^{41} +(35.1747 - 213.853i) q^{42} +(5.07086 - 8.78298i) q^{43} +39.8281 q^{44} +242.331 q^{46} +(-220.746 + 382.343i) q^{47} +(-352.250 + 132.820i) q^{48} +(77.4875 + 134.212i) q^{49} +(438.255 + 359.225i) q^{51} +(36.4657 - 63.1604i) q^{52} +593.610 q^{53} +(-226.006 - 361.984i) q^{54} +(-140.722 + 243.738i) q^{56} +(-521.202 - 427.214i) q^{57} +(13.7416 + 23.8012i) q^{58} +(-221.230 - 383.182i) q^{59} +(-72.2881 + 125.207i) q^{61} +101.536 q^{62} +(-350.725 - 118.583i) q^{63} +408.736 q^{64} +(81.5912 - 496.052i) q^{66} +(431.360 + 747.138i) q^{67} +(68.2786 + 118.262i) q^{68} +(67.1873 - 408.481i) q^{69} -818.541 q^{71} +(108.771 + 543.398i) q^{72} -495.052 q^{73} +(33.7093 - 58.3863i) q^{74} +(-81.2014 - 140.645i) q^{76} +(-218.071 - 377.710i) q^{77} +(-711.950 - 583.563i) q^{78} +(-585.263 + 1013.71i) q^{79} +(-672.833 + 280.601i) q^{81} -370.300 q^{82} +(-212.022 + 367.232i) q^{83} +(-69.0017 - 56.5586i) q^{84} +(-15.4242 - 26.7156i) q^{86} +(43.9300 - 16.5644i) q^{87} +(-326.419 + 565.374i) q^{88} +1031.37 q^{89} -798.643 q^{91} +(49.8799 - 86.3945i) q^{92} +(28.1513 - 171.152i) q^{93} +(671.452 + 1162.99i) q^{94} +(-47.3718 + 288.008i) q^{96} +(799.356 - 1384.53i) q^{97} +471.394 q^{98} +(-813.541 - 275.066i) 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 $

$2$	1.52087	−	2.63422i	0.537709	−	0.931339i	−0.461318	−	0.887235i	$-0.652623\pi$
$2$	1.52087	−	2.63422i	0.537709	−	0.931339i	0.999027	−	0.0441043i	$-0.0140434\pi$
$3$	−4.01867	−	3.29398i	−0.773393	−	0.633927i
$3$	−4.01867	−	3.29398i	−0.773393	−	0.633927i
$4$	−0.626094	−	1.08443i	−0.0782617	−	0.135553i
$5$		0			0
$5$		0			0
$6$	−14.7890	+	5.57636i	−1.00626	+	0.379423i
$7$	−6.85611	+	11.8751i	−0.370195	+	0.641197i	−0.989595	−	0.143879i	$-0.954043\pi$
$7$	−6.85611	+	11.8751i	−0.370195	+	0.641197i	0.619400	+	0.785075i	$0.287376\pi$
$8$	20.5251			0.907090
$9$	5.29939	+	26.4748i	0.196274	+	0.980549i
$10$		0			0
$11$	−15.9034	+	27.5455i	−0.435914	+	0.755026i	−0.997370	−	0.0724812i	$-0.976908\pi$
$11$	−15.9034	+	27.5455i	−0.435914	+	0.755026i	0.561455	+	0.827507i	$0.310242\pi$
$12$	−1.05602	+	6.42029i	−0.0254038	+	0.154448i
$13$	29.1216	+	50.4401i	0.621298	+	1.07612i	0.989244	+	0.146272i	$0.0467276\pi$
$13$	29.1216	+	50.4401i	0.621298	+	1.07612i	−0.367946	+	0.929847i	$0.619939\pi$
$14$	20.8545	+	36.1211i	0.398115	+	0.689555i
$15$		0			0
$16$	36.2248	−	62.7431i	0.566012	−	0.980361i
$17$	−109.055			−1.55586			−0.777932	−	0.628348i	$-0.783731\pi$
$17$	−109.055			−1.55586			−0.777932	+	0.628348i	$0.783731\pi$
$18$	77.8003	+	26.3050i	1.01876	+	0.344453i
$19$	129.695			1.56601			0.783004	−	0.622017i	$-0.213687\pi$
$19$	129.695			1.56601			0.783004	+	0.622017i	$0.213687\pi$
$20$		0			0
$21$	66.6689	−	25.1383i	0.692778	−	0.261221i
$22$	48.3740	+	83.7863i	0.468790	+	0.811968i
$23$	39.8342	+	68.9949i	0.361131	+	0.625497i	0.988147	−	0.153509i	$-0.0490575\pi$
$23$	39.8342	+	68.9949i	0.361131	+	0.625497i	−0.627017	+	0.779006i	$0.715724\pi$
$24$	−82.4836	−	67.6093i	−0.701537	−	0.575028i
$25$		0			0
$26$	177.161			1.33631
$27$	65.9111	−	123.850i	0.469800	−	0.882773i
$28$	17.1703			0.115888
$29$	−4.51769	+	7.82486i	−0.0289280	+	0.0501048i	−0.880127	−	0.474738i	$-0.842543\pi$
$29$	−4.51769	+	7.82486i	−0.0289280	+	0.0501048i	0.851199	+	0.524843i	$0.175876\pi$
$30$		0			0
$31$	16.6904	+	28.9087i	0.0966998	+	0.167489i	0.910317	−	0.413912i	$-0.135838\pi$
$31$	16.6904	+	28.9087i	0.0966998	+	0.167489i	−0.813617	+	0.581401i	$0.802505\pi$
$32$	−28.0860	−	48.6463i	−0.155154	−	0.268735i
$33$	154.645	−	58.3108i	0.815764	−	0.307594i
$34$	−165.858	+	287.275i	−0.836602	+	1.44904i
$35$		0			0
$36$	25.3921	−	22.3225i	0.117556	−	0.103345i
$37$	22.1645			0.0984817			0.0492408	−	0.998787i	$-0.484320\pi$
$37$	22.1645			0.0984817			0.0492408	+	0.998787i	$0.484320\pi$
$38$	197.250	−	341.647i	0.842056	−	1.45848i
$39$	49.1186	−	298.628i	0.201673	−	1.22612i
$40$		0			0
$41$	−60.8698	−	105.430i	−0.231860	−	0.401593i	0.726495	−	0.687171i	$-0.241148\pi$
$41$	−60.8698	−	105.430i	−0.231860	−	0.401593i	−0.958356	+	0.285578i	$0.907814\pi$
$42$	35.1747	−	213.853i	0.129228	−	0.785672i
$43$	5.07086	−	8.78298i	0.0179837	−	0.0311487i	−0.856894	−	0.515493i	$-0.827609\pi$
$43$	5.07086	−	8.78298i	0.0179837	−	0.0311487i	0.874877	+	0.484345i	$0.160942\pi$
$44$	39.8281			0.136462
$45$		0			0
$46$	242.331			0.776733
$47$	−220.746	+	382.343i	−0.685088	+	1.18661i	0.288321	+	0.957534i	$0.406903\pi$
$47$	−220.746	+	382.343i	−0.685088	+	1.18661i	−0.973409	+	0.229073i	$0.926430\pi$
$48$	−352.250	+	132.820i	−1.05923	+	0.399395i
$49$	77.4875	+	134.212i	0.225911	+	0.391289i
$50$		0			0
$51$	438.255	+	359.225i	1.20329	+	0.986304i
$52$	36.4657	−	63.1604i	0.0972477	−	0.168438i
$53$	593.610			1.53846			0.769232	−	0.638969i	$-0.220639\pi$
$53$	593.610			1.53846			0.769232	+	0.638969i	$0.220639\pi$
$54$	−226.006	−	361.984i	−0.569546	−	0.912218i
$55$		0			0
$56$	−140.722	+	243.738i	−0.335800	+	0.581623i
$57$	−521.202	−	427.214i	−1.21114	−	0.992734i
$58$	13.7416	+	23.8012i	0.0311097	+	0.0538836i
$59$	−221.230	−	383.182i	−0.488164	−	0.845525i	0.511743	−	0.859139i	$-0.329000\pi$
$59$	−221.230	−	383.182i	−0.488164	−	0.845525i	−0.999907	+	0.0136133i	$0.995667\pi$
$60$		0			0
$61$	−72.2881	+	125.207i	−0.151730	+	0.262804i	−0.931864	−	0.362809i	$-0.881818\pi$
$61$	−72.2881	+	125.207i	−0.151730	+	0.262804i	0.780133	+	0.625613i	$0.215151\pi$
$62$	101.536			0.207985
$63$	−350.725	−	118.583i	−0.701385	−	0.237145i
$64$	408.736			0.798312
$65$		0			0
$66$	81.5912	−	496.052i	0.152169	−	0.925149i
$67$	431.360	+	747.138i	0.786553	+	1.36235i	0.928067	+	0.372414i	$0.121470\pi$
$67$	431.360	+	747.138i	0.786553	+	1.36235i	−0.141514	+	0.989936i	$0.545197\pi$
$68$	68.2786	+	118.262i	0.121765	+	0.210902i
$69$	67.1873	−	408.481i	0.117223	−	0.712685i
$70$		0			0
$71$	−818.541			−1.36821			−0.684105	−	0.729384i	$-0.739807\pi$
$71$	−818.541			−1.36821			−0.684105	+	0.729384i	$0.739807\pi$
$72$	108.771	+	543.398i	0.178038	+	0.889446i
$73$	−495.052			−0.793719			−0.396859	−	0.917879i	$-0.629900\pi$
$73$	−495.052			−0.793719			−0.396859	+	0.917879i	$0.629900\pi$
$74$	33.7093	−	58.3863i	0.0529545	−	0.0917198i
$75$		0			0
$76$	−81.2014	−	140.645i	−0.122558	−	0.212277i
$77$	−218.071	−	377.710i	−0.322747	−	0.559014i
$78$	−711.950	−	583.563i	−1.03349	−	0.847122i
$79$	−585.263	+	1013.71i	−0.833510	+	1.44368i	0.0617284	+	0.998093i	$0.480339\pi$
$79$	−585.263	+	1013.71i	−0.833510	+	1.44368i	−0.895238	+	0.445588i	$0.852995\pi$
$80$		0			0
$81$	−672.833	+	280.601i	−0.922953	+	0.384912i
$82$	−370.300			−0.498693
$83$	−212.022	+	367.232i	−0.280390	+	0.485651i	−0.971481	−	0.237118i	$-0.923797\pi$
$83$	−212.022	+	367.232i	−0.280390	+	0.485651i	0.691090	+	0.722768i	$0.257131\pi$
$84$	−69.0017	−	56.5586i	−0.0896273	−	0.0734648i
$85$		0			0
$86$	−15.4242	−	26.7156i	−0.0193400	−	0.0334978i
$87$	43.9300	−	16.5644i	0.0541355	−	0.0204125i
$88$	−326.419	+	565.374i	−0.395413	+	0.684876i
$89$	1031.37			1.22837			0.614183	−	0.789163i	$-0.289486\pi$
$89$	1031.37			1.22837			0.614183	+	0.789163i	$0.289486\pi$
$90$		0			0
$91$	−798.643			−0.920006
$92$	49.8799	−	86.3945i	0.0565254	−	0.0979049i
$93$	28.1513	−	171.152i	0.0313888	−	0.190835i
$94$	671.452	+	1162.99i	0.736756	+	1.27610i
$95$		0			0
$96$	−47.3718	+	288.008i	−0.0503632	+	0.306195i
$97$	799.356	−	1384.53i	0.836725	−	1.44925i	−0.0558930	−	0.998437i	$-0.517801\pi$
$97$	799.356	−	1384.53i	0.836725	−	1.44925i	0.892618	−	0.450814i	$-0.148866\pi$
$98$	471.394			0.485897
$99$	−813.541	−	275.066i	−0.825898	−	0.279244i
$100$		0			0
$101$	107.000	−	185.330i	0.105415	−	0.182584i	−0.808493	−	0.588506i	$-0.799716\pi$
$101$	107.000	−	185.330i	0.105415	−	0.182584i	0.913908	+	0.405922i	$0.133050\pi$
$102$	1612.81	−	608.129i	1.56561	−	0.590331i
$103$	836.160	+	1448.27i	0.799897	+	1.38546i	0.919683	+	0.392662i	$0.128446\pi$
$103$	836.160	+	1448.27i	0.799897	+	1.38546i	−0.119786	+	0.992800i	$0.538221\pi$
$104$	597.723	+	1035.29i	0.563573	+	0.976137i
$105$		0			0
$106$	902.804	−	1563.70i	0.827246	−	1.43283i
$107$	600.699			0.542727			0.271363	−	0.962477i	$-0.412525\pi$
$107$	600.699			0.542727			0.271363	+	0.962477i	$0.412525\pi$
$108$	−175.572	+	6.06581i	−0.156430	+	0.00540447i
$109$	−771.570			−0.678009			−0.339005	−	0.940785i	$-0.610090\pi$
$109$	−771.570			−0.678009			−0.339005	+	0.940785i	$0.610090\pi$
$110$		0			0
$111$	−89.0718	−	73.0094i	−0.0761650	−	0.0624302i
$112$	496.722	+	860.348i	0.419070	+	0.725850i
$113$	−583.338	−	1010.37i	−0.485627	−	0.841131i	0.514237	−	0.857648i	$-0.328075\pi$
$113$	−583.338	−	1010.37i	−0.485627	−	0.841131i	−0.999864	+	0.0165177i	$0.994742\pi$
$114$	−1918.06	+	723.228i	−1.57581	+	0.594180i
$115$		0			0
$116$	11.3140			0.00905583
$117$	−1181.06	+	1038.29i	−0.933244	+	0.820427i
$118$	−1345.85			−1.04996
$119$	747.692	−	1295.04i	0.575973	−	0.997615i
$120$		0			0
$121$	159.663	+	276.545i	0.119957	+	0.207772i
$122$	219.882	+	380.846i	0.163173	+	0.282624i
$123$	−102.667	+	624.190i	−0.0752618	+	0.457572i
$124$	20.8996	−	36.1991i	0.0151358	−	0.0262159i
$125$		0			0
$126$	−845.783	+	743.539i	−0.598003	+	0.525712i
$127$	−1630.10			−1.13896			−0.569479	−	0.822006i	$-0.692855\pi$
$127$	−1630.10			−1.13896			−0.569479	+	0.822006i	$0.692855\pi$
$128$	846.322	−	1465.87i	0.584414	−	1.01223i
$129$	−49.3091	+	18.5926i	−0.0336544	+	0.0126898i
$130$		0			0
$131$	−129.412	−	224.149i	−0.0863115	−	0.149496i	0.819638	−	0.572882i	$-0.194175\pi$
$131$	−129.412	−	224.149i	−0.0863115	−	0.149496i	−0.905949	+	0.423386i	$0.860841\pi$
$132$	−160.056	−	131.193i	−0.105538	−	0.0865067i
$133$	−889.206	+	1540.15i	−0.579729	+	1.00412i
$134$	2624.17			1.69175
$135$		0			0
$136$	−2238.36			−1.41131
$137$	526.385	−	911.726i	0.328264	−	0.568569i	−0.653904	−	0.756578i	$-0.726870\pi$
$137$	526.385	−	911.726i	0.328264	−	0.568569i	0.982167	+	0.188009i	$0.0602033\pi$
$138$	−973.847	−	798.232i	−0.600720	−	0.492392i
$139$	−1192.25	−	2065.03i	−0.727519	−	1.26010i	−0.957929	−	0.287006i	$-0.907340\pi$
$139$	−1192.25	−	2065.03i	−0.727519	−	1.26010i	0.230410	−	0.973094i	$-0.425993\pi$
$140$		0			0
$141$	2146.54	−	809.378i	1.28206	−	0.483418i
$142$	−1244.89	+	2156.22i	−0.735699	+	1.27427i
$143$	−1852.53			−1.08333
$144$	1853.08	+	626.544i	1.07239	+	0.362583i
$145$		0			0
$146$	−752.910	+	1304.08i	−0.426790	+	0.739221i
$147$	130.696	−	794.597i	0.0733308	−	0.445831i
$148$	−13.8771	−	24.0358i	−0.00770735	−	0.0133495i
$149$	−573.144	−	992.715i	−0.315126	−	0.545815i	0.664338	−	0.747432i	$-0.268714\pi$
$149$	−573.144	−	992.715i	−0.315126	−	0.545815i	−0.979464	+	0.201617i	$0.935380\pi$
$150$		0			0
$151$	583.058	−	1009.89i	0.314229	−	0.544261i	−0.665044	−	0.746804i	$-0.731587\pi$
$151$	583.058	−	1009.89i	0.314229	−	0.544261i	0.979273	+	0.202543i	$0.0649207\pi$
$152$	2662.01			1.42051
$153$	−577.924	−	2887.21i	−0.305375	−	1.52560i
$154$	−1326.63			−0.694175
$155$		0			0
$156$	−354.593	+	133.704i	−0.181988	+	0.0686208i
$157$	−1737.81	−	3009.97i	−0.883390	−	1.53008i	−0.847548	−	0.530719i	$-0.821922\pi$
$157$	−1737.81	−	3009.97i	−0.883390	−	1.53008i	−0.0358423	−	0.999357i	$-0.511411\pi$
$158$	1780.22	+	3083.43i	0.896371	+	1.55256i
$159$	−2385.52	−	1955.34i	−1.18984	−	0.975274i
$160$		0			0
$161$	−1092.43			−0.534755
$162$	−284.126	+	2199.15i	−0.137796	+	1.06655i
$163$	2223.32			1.06837			0.534183	−	0.845369i	$-0.320619\pi$
$163$	2223.32			1.06837			0.534183	+	0.845369i	$0.320619\pi$
$164$	−76.2204	+	132.018i	−0.0362915	+	0.0628588i
$165$		0			0
$166$	644.915	+	1117.03i	0.301537	+	0.522277i
$167$	−793.991	−	1375.23i	−0.367909	−	0.637238i	0.621329	−	0.783550i	$-0.286593\pi$
$167$	−793.991	−	1375.23i	−0.367909	−	0.637238i	−0.989239	+	0.146312i	$0.953260\pi$
$168$	1368.39	−	515.967i	0.628412	−	0.236951i
$169$	−597.632	+	1035.13i	−0.272022	+	0.471156i
$170$		0			0
$171$	687.306	+	3433.66i	0.307366	+	1.53555i
$172$	−12.6993			−0.00562974
$173$	753.898	−	1305.79i	0.331317	−	0.573857i	−0.651454	−	0.758689i	$-0.725840\pi$
$173$	753.898	−	1305.79i	0.331317	−	0.573857i	0.982770	+	0.184831i	$0.0591738\pi$
$174$	23.1776	−	140.914i	0.0100982	−	0.0613945i
$175$		0			0
$176$	1152.19	+	1995.66i	0.493465	+	0.854707i
$177$	−373.143	+	2268.61i	−0.158458	+	0.963384i
$178$	1568.58	−	2716.85i	0.660504	−	1.14403i
$179$	1572.66			0.656683			0.328341	−	0.944559i	$-0.393510\pi$
$179$	1572.66			0.656683			0.328341	+	0.944559i	$0.393510\pi$
$180$		0			0
$181$	1984.41			0.814918			0.407459	−	0.913223i	$-0.366415\pi$
$181$	1984.41			0.814918			0.407459	+	0.913223i	$0.366415\pi$
$182$	−1214.63	+	2103.81i	−0.494695	+	0.856838i
$183$	702.930	−	265.048i	0.283946	−	0.107065i
$184$	817.601	+	1416.13i	0.327578	+	0.567382i
$185$		0			0
$186$	−408.040	−	334.458i	−0.160854	−	0.131847i
$187$	1734.34	−	3003.97i	0.678223	−	1.17472i
$188$	552.831			0.214465
$189$	1018.84	+	1631.83i	0.392114	+	0.628032i
$190$		0			0
$191$	1174.18	−	2033.73i	0.444819	−	0.770450i	−0.553220	−	0.833035i	$-0.686601\pi$
$191$	1174.18	−	2033.73i	0.444819	−	0.770450i	0.998040	+	0.0625853i	$0.0199345\pi$
$192$	−1642.57	−	1346.37i	−0.617409	−	0.506071i
$193$	−117.085	−	202.797i	−0.0436681	−	0.0756354i	0.843365	−	0.537341i	$-0.180571\pi$
$193$	−117.085	−	202.797i	−0.0436681	−	0.0756354i	−0.887033	+	0.461705i	$0.847238\pi$
$194$	−2431.43	−	4211.37i	−0.899829	−	1.55855i
$195$		0			0
$196$	97.0288	−	168.059i	0.0353604	−	0.0612460i
$197$	717.846			0.259616			0.129808	−	0.991539i	$-0.458564\pi$
$197$	717.846			0.259616			0.129808	+	0.991539i	$0.458564\pi$
$198$	−1961.87	+	1724.71i	−0.704163	+	0.619040i
$199$	1701.45			0.606094			0.303047	−	0.952976i	$-0.401996\pi$
$199$	1701.45			0.606094			0.303047	+	0.952976i	$0.401996\pi$
$200$		0			0
$201$	727.564	−	4423.39i	0.255315	−	1.55225i
$202$	−325.467	−	563.725i	−0.113365	−	0.196354i
$203$	−61.9475	−	107.296i	−0.0214180	−	0.0370971i
$204$	115.164	−	700.164i	0.0395248	−	0.240300i
$205$		0			0
$206$	5086.77			1.72045
$207$	−1615.53	+	1420.23i	−0.542450	+	0.476875i
$208$	4219.69			1.40665
$209$	−2062.60	+	3572.52i	−0.682645	+	1.18238i
$210$		0			0
$211$	2469.33	+	4277.01i	0.805667	+	1.39546i	0.915840	+	0.401544i	$0.131526\pi$
$211$	2469.33	+	4277.01i	0.805667	+	1.39546i	−0.110172	+	0.993912i	$0.535140\pi$
$212$	−371.656	−	643.727i	−0.120403	−	0.208544i
$213$	3289.44	+	2696.26i	1.05816	+	0.867345i
$214$	913.585	−	1582.38i	0.291829	−	0.505463i
$215$		0			0
$216$	1352.83	−	2542.03i	0.426150	−	0.800754i
$217$	−457.726			−0.143191
$218$	−1173.46	+	2032.49i	−0.364572	+	0.631456i
$219$	1989.45	+	1630.69i	0.613857	+	0.503160i
$220$		0			0
$221$	−3175.85	−	5500.73i	−0.966655	−	1.67430i
$222$	−327.790	+	123.597i	−0.0990983	+	0.0373662i
$223$	−1526.57	+	2644.10i	−0.458416	+	0.794001i	−0.998877	−	0.0473684i	$-0.984917\pi$
$223$	−1526.57	+	2644.10i	−0.458416	+	0.794001i	0.540461	+	0.841369i	$0.318250\pi$
$224$	770.242			0.229750
$225$		0			0
$226$	−3548.73			−1.04450
$227$	−419.976	+	727.420i	−0.122797	+	0.212690i	−0.920869	−	0.389871i	$-0.872520\pi$
$227$	−419.976	+	727.420i	−0.122797	+	0.212690i	0.798073	+	0.602561i	$0.205853\pi$
$228$	−136.960	+	832.682i	−0.0397825	+	0.241867i
$229$	−700.753	−	1213.74i	−0.202214	−	0.350245i	0.747027	−	0.664793i	$-0.231480\pi$
$229$	−700.753	−	1213.74i	−0.202214	−	0.350245i	−0.949242	+	0.314548i	$0.898147\pi$
$230$		0			0
$231$	−367.814	+	2236.21i	−0.104764	+	0.636935i
$232$	−92.7259	+	160.606i	−0.0262403	+	0.0454496i
$233$	2856.99			0.803295			0.401647	−	0.915794i	$-0.368438\pi$
$233$	2856.99			0.803295			0.401647	+	0.915794i	$0.368438\pi$
$234$	938.843	+	4690.30i	0.262282	+	1.31032i
$235$		0			0
$236$	−277.021	+	479.815i	−0.0764092	+	0.132345i
$237$	5691.11	−	2145.90i	1.55982	−	0.588149i
$238$	−2274.29	−	3939.18i	−0.619412	−	1.07285i
$239$	854.917	+	1480.76i	0.231381	+	0.400763i	0.958215	−	0.286050i	$-0.0923424\pi$
$239$	854.917	+	1480.76i	0.231381	+	0.400763i	−0.726834	+	0.686813i	$0.759009\pi$
$240$		0			0
$241$	2166.23	−	3752.02i	0.579000	−	1.00286i	−0.416594	−	0.909092i	$-0.636776\pi$
$241$	2166.23	−	3752.02i	0.579000	−	1.00286i	0.995594	−	0.0937648i	$-0.0298902\pi$
$242$	971.309			0.258009
$243$	3628.19	+	1088.66i	0.957812	+	0.287396i
$244$	181.036			0.0474987
$245$		0			0
$246$	1488.11	+	1219.76i	0.385686	+	0.316135i
$247$	3776.93	+	6541.84i	0.972957	+	1.68521i
$248$	342.573	+	593.354i	0.0877154	+	0.151927i
$249$	2061.70	−	777.390i	0.524719	−	0.197852i
$250$		0			0
$251$	−1724.73			−0.433722			−0.216861	−	0.976202i	$-0.569582\pi$
$251$	−1724.73			−0.433722			−0.216861	+	0.976202i	$0.569582\pi$
$252$	90.9920	+	454.580i	0.0227459	+	0.113634i
$253$	−2534.00			−0.629688
$254$	−2479.16	+	4294.04i	−0.612428	+	1.06076i
$255$		0			0
$256$	−939.349	−	1627.00i	−0.229333	−	0.397217i
$257$	−2926.63	−	5069.07i	−0.710342	−	1.23035i	−0.964729	−	0.263246i	$-0.915207\pi$
$257$	−2926.63	−	5069.07i	−0.710342	−	1.23035i	0.254386	−	0.967103i	$-0.418127\pi$
$258$	−26.0156	+	158.168i	−0.00627776	+	0.0381671i
$259$	−151.962	+	263.206i	−0.0364574	+	0.0631462i
$260$		0			0
$261$	−231.103	−	78.1380i	−0.0548081	−	0.0185311i
$262$	−787.277			−0.185642
$263$	196.180	−	339.794i	0.0459962	−	0.0796677i	−0.842111	−	0.539305i	$-0.818687\pi$
$263$	196.180	−	339.794i	0.0459962	−	0.0796677i	0.888107	+	0.459637i	$0.152020\pi$
$264$	3174.10	−	1196.83i	0.739971	−	0.279015i
$265$		0			0
$266$	2704.73	+	4684.73i	0.623450	+	1.07985i
$267$	−4144.72	−	3397.30i	−0.950010	−	0.778695i
$268$	540.144	−	935.557i	0.123114	−	0.213240i
$269$	−4610.33			−1.04497			−0.522485	−	0.852648i	$-0.674995\pi$
$269$	−4610.33			−1.04497			−0.522485	+	0.852648i	$0.674995\pi$
$270$		0			0
$271$	−1155.72			−0.259058			−0.129529	−	0.991576i	$-0.541347\pi$
$271$	−1155.72			−0.259058			−0.129529	+	0.991576i	$0.541347\pi$
$272$	−3950.49	+	6842.44i	−0.880638	+	1.52531i
$273$	3209.48	+	2630.71i	0.711526	+	0.583216i
$274$	−1601.13	−	2773.23i	−0.353020	−	0.611449i
$275$		0			0
$276$	−485.033	+	182.888i	−0.105781	+	0.0398860i
$277$	−304.205	+	526.898i	−0.0659852	+	0.114290i	−0.897131	−	0.441765i	$-0.854352\pi$
$277$	−304.205	+	526.898i	−0.0659852	+	0.114290i	0.831145	+	0.556055i	$0.187686\pi$
$278$	−7253.02			−1.56477
$279$	−676.904	+	595.075i	−0.145251	+	0.127693i
$280$		0			0
$281$	−1374.62	+	2380.91i	−0.291825	+	0.505456i	−0.974241	−	0.225508i	$-0.927596\pi$
$281$	−1374.62	+	2380.91i	−0.291825	+	0.505456i	0.682416	+	0.730964i	$0.260929\pi$
$282$	1132.52	−	6885.42i	0.239151	−	1.45397i
$283$	510.780	+	884.697i	0.107289	+	0.185830i	0.914671	−	0.404199i	$-0.132450\pi$
$283$	510.780	+	884.697i	0.107289	+	0.185830i	−0.807382	+	0.590029i	$0.799116\pi$
$284$	512.483	+	887.647i	0.107078	+	0.185465i
$285$		0			0
$286$	−2817.46	+	4879.98i	−0.582516	+	1.00895i
$287$	1669.32			0.343334
$288$	1139.06	−	1001.37i	0.233056	−	0.204882i
$289$	6979.96			1.42071
$290$		0			0
$291$	−7772.95	+	2930.89i	−1.56584	+	0.590418i
$292$	309.949	+	536.848i	0.0621178	+	0.107591i
$293$	−2616.25	−	4531.47i	−0.521648	−	0.903521i	−0.999683	−	0.0251800i	$-0.991984\pi$
$293$	−2616.25	−	4531.47i	−0.521648	−	0.903521i	0.478035	−	0.878341i	$-0.341349\pi$
$294$	−1894.37	−	1552.76i	−0.375790	−	0.308023i
$295$		0			0
$296$	454.929			0.0893317
$297$	2363.29	+	3785.18i	0.461724	+	0.739524i
$298$	−3486.71			−0.677785
$299$	−2320.07	+	4018.48i	−0.448739	+	0.777240i
$300$		0			0
$301$	69.5327	+	120.434i	0.0133149	+	0.0230622i
$302$	−1773.51	−	3071.81i	−0.337927	−	0.585307i
$303$	−1040.47	+	392.322i	−0.197272	+	0.0743839i
$304$	4698.18	−	8137.49i	0.886379	−	1.53525i
$305$		0			0
$306$	−8484.50	−	2868.69i	−1.58506	−	0.535921i
$307$	4912.68			0.913296			0.456648	−	0.889648i	$-0.349050\pi$
$307$	4912.68			0.913296			0.456648	+	0.889648i	$0.349050\pi$
$308$	−273.066	+	472.964i	−0.0505174	+	0.0874988i
$309$	1410.33	−	8574.42i	0.259647	−	1.57858i
$310$		0			0
$311$	414.430	+	717.813i	0.0755632	+	0.130879i	0.901331	−	0.433131i	$-0.142591\pi$
$311$	414.430	+	717.813i	0.0755632	+	0.130879i	−0.825768	+	0.564010i	$0.809258\pi$
$312$	1008.16	−	6129.36i	0.182936	−	1.11220i
$313$	4618.60	−	7999.66i	0.834054	−	1.44462i	−0.0607442	−	0.998153i	$-0.519347\pi$
$313$	4618.60	−	7999.66i	0.834054	−	1.44462i	0.894798	−	0.446471i	$-0.147319\pi$
$314$	−10571.9			−1.90003
$315$		0			0
$316$	1465.72			0.260928
$317$	−4549.20	+	7879.45i	−0.806021	+	1.39607i	0.109578	+	0.993978i	$0.465050\pi$
$317$	−4549.20	+	7879.45i	−0.806021	+	1.39607i	−0.915599	+	0.402091i	$0.868283\pi$
$318$	−8778.88	+	3310.18i	−1.54810	+	0.583729i
$319$	−143.693	−	248.884i	−0.0252203	−	0.0436828i
$320$		0			0
$321$	−2414.01	−	1978.69i	−0.419741	−	0.344049i
$322$	−1661.45	+	2877.71i	−0.287543	+	0.498039i
$323$	−14143.9			−2.43649
$324$	725.548	+	553.955i	0.124408	+	0.0949855i
$325$		0			0
$326$	3381.38	−	5856.72i	0.574470	−	0.995011i
$327$	3100.68	+	2541.54i	0.524368	+	0.429808i
$328$	−1249.36	−	2163.95i	−0.210318	−	0.364281i
$329$	−3026.92	−	5242.78i	−0.507233	−	0.878553i
$330$		0			0
$331$	−2981.73	+	5164.50i	−0.495137	+	0.857603i	−0.999984	−	0.00560570i	$-0.998216\pi$
$331$	−2981.73	+	5164.50i	−0.495137	+	0.857603i	0.504847	+	0.863209i	$0.331549\pi$
$332$	530.982			0.0877754
$333$	117.458	+	586.801i	0.0193294	+	0.0965661i
$334$	−4830.23			−0.791313
$335$		0			0
$336$	837.807	−	5093.65i	0.136030	−	0.827027i
$337$	298.427	+	516.890i	0.0482384	+	0.0835514i	0.889136	−	0.457642i	$-0.151306\pi$
$337$	298.427	+	516.890i	0.0482384	+	0.0835514i	−0.840898	+	0.541194i	$0.817973\pi$
$338$	1817.84	+	3148.60i	0.292537	+	0.506690i
$339$	−983.901	+	5981.85i	−0.157635	+	0.958377i
$340$		0			0
$341$	−1061.74			−0.168611
$342$	10090.3	+	3411.63i	1.59539	+	0.539415i
$343$	−6828.34			−1.07492
$344$	104.080	−	180.272i	0.0163128	−	0.0282546i
$345$		0			0
$346$	−2293.16	−	3971.87i	−0.356304	−	0.617137i
$347$	−2281.05	−	3950.90i	−0.352891	−	0.611226i	0.633863	−	0.773445i	$-0.281468\pi$
$347$	−2281.05	−	3950.90i	−0.352891	−	0.611226i	−0.986755	+	0.162219i	$0.948135\pi$
$348$	−45.4671	−	37.2680i	−0.00700372	−	0.00574074i
$349$	−337.633	+	584.798i	−0.0517854	+	0.0896949i	−0.890756	−	0.454482i	$-0.849825\pi$
$349$	−337.633	+	584.798i	−0.0517854	+	0.0896949i	0.838971	+	0.544177i	$0.183158\pi$
$350$		0			0
$351$	8166.42	−	282.140i	1.24185	−	0.0429046i
$352$	1786.65			0.270536
$353$	−1680.91	+	2911.43i	−0.253445	+	0.438979i	−0.964472	−	0.264185i	$-0.914897\pi$
$353$	−1680.91	+	2911.43i	−0.253445	+	0.438979i	0.711027	+	0.703165i	$0.248230\pi$
$354$	5408.52	+	4433.20i	0.812033	+	0.665598i
$355$		0			0
$356$	−645.732	−	1118.44i	−0.0961341	−	0.166509i
$357$	−7270.57	+	2741.46i	−1.07787	+	0.406424i
$358$	2391.81	−	4142.74i	0.353104	−	0.611594i
$359$	7701.61			1.13224			0.566122	−	0.824322i	$-0.308443\pi$
$359$	7701.61			1.13224			0.566122	+	0.824322i	$0.308443\pi$
$360$		0			0
$361$	9961.87			1.45238
$362$	3018.03	−	5227.39i	0.438189	−	0.758965i
$363$	269.300	−	1637.27i	0.0389382	−	0.236734i
$364$	500.026	+	866.070i	0.0720013	+	0.124710i
$365$		0			0
$366$	370.868	−	2254.78i	0.0529661	−	0.322020i
$367$	2954.75	−	5117.77i	0.420263	−	0.727917i	−0.575702	−	0.817660i	$-0.695271\pi$
$367$	2954.75	−	5117.77i	0.420263	−	0.727917i	0.995965	+	0.0897425i	$0.0286044\pi$
$368$	5771.94			0.817617
$369$	2468.66	−	2170.23i	0.348274	−	0.306172i
$370$		0			0
$371$	−4069.86	+	7049.20i	−0.569532	+	0.986459i
$372$	−203.228	+	76.6295i	−0.0283249	+	0.0106803i
$373$	−4212.19	−	7295.73i	−0.584716	−	1.01276i	−0.994911	−	0.100760i	$-0.967873\pi$
$373$	−4212.19	−	7295.73i	−0.584716	−	1.01276i	0.410195	−	0.911998i	$-0.365461\pi$
$374$	−5275.42	−	9137.30i	−0.729374	−	1.26331i
$375$		0			0
$376$	−4530.84	+	7847.64i	−0.621436	+	1.07636i
$377$	−526.249			−0.0718917
$378$	5848.13	−	202.046i	0.795754	−	0.0274923i
$379$	−3510.24			−0.475749			−0.237875	−	0.971296i	$-0.576451\pi$
$379$	−3510.24			−0.475749			−0.237875	+	0.971296i	$0.576451\pi$
$380$		0			0
$381$	6550.81	+	5369.50i	0.880862	+	0.722016i
$382$	−3571.54	−	6186.09i	−0.478367	−	0.828555i
$383$	2866.01	+	4964.08i	0.382367	+	0.662279i	0.991400	−	0.130866i	$-0.0417758\pi$
$383$	2866.01	+	4964.08i	0.382367	+	0.662279i	−0.609033	+	0.793145i	$0.708442\pi$
$384$	−8229.64	+	3103.09i	−1.09366	+	0.412380i
$385$		0			0
$386$	−712.283			−0.0939229
$387$	259.400	+	87.7056i	0.0340725	+	0.0115202i
$388$	−2001.89			−0.261934
$389$	−7183.60	+	12442.4i	−0.936306	+	1.62173i	−0.164019	+	0.986457i	$0.552446\pi$
$389$	−7183.60	+	12442.4i	−0.936306	+	1.62173i	−0.772288	+	0.635273i	$0.780888\pi$
$390$		0			0
$391$	−4344.11	−	7524.23i	−0.561870	−	0.973188i
$392$	1590.44	+	2754.72i	0.204922	+	0.354934i
$393$	−218.276	+	1327.06i	−0.0280167	+	0.170334i
$394$	1091.75	−	1890.97i	0.139598	−	0.241791i
$395$		0			0
$396$	211.065	+	1054.44i	0.0267838	+	0.133807i
$397$	9014.42			1.13960			0.569800	−	0.821784i	$-0.307021\pi$
$397$	9014.42			1.13960			0.569800	+	0.821784i	$0.307021\pi$
$398$	2587.69	−	4482.01i	0.325902	−	0.564479i
$399$	8646.64	−	3260.32i	1.08490	−	0.409073i
$400$		0			0
$401$	−5255.55	−	9102.87i	−0.654487	−	1.13361i	−0.982022	−	0.188766i	$-0.939551\pi$
$401$	−5255.55	−	9102.87i	−0.654487	−	1.13361i	0.327535	−	0.944839i	$-0.393782\pi$
$402$	−10545.7	−	8643.97i	−1.30839	−	1.07244i
$403$	−972.104	+	1683.73i	−0.120159	+	0.208121i
$404$	−267.969			−0.0329998
$405$		0			0
$406$	−376.857			−0.0460667
$407$	−352.491	+	610.533i	−0.0429296	+	0.0743562i
$408$	8995.23	+	7373.12i	1.09150	+	0.894666i
$409$	−1659.10	−	2873.65i	−0.200580	−	0.347415i	0.748135	−	0.663546i	$-0.230949\pi$
$409$	−1659.10	−	2873.65i	−0.200580	−	0.347415i	−0.948715	+	0.316131i	$0.897616\pi$
$410$		0			0
$411$	−5118.57	+	1930.02i	−0.614308	+	0.231632i
$412$	1047.03	−	1813.51i	0.125203	−	0.216857i
$413$	6067.11			0.722864
$414$	1284.20	+	6415.66i	0.152452	+	0.761625i
$415$		0			0
$416$	1635.81	−	2833.31i	0.192794	−	0.333929i
$417$	−2010.93	+	12225.9i	−0.236153	+	1.43575i
$418$	6273.89	+	10866.7i	0.734129	+	1.27155i
$419$	243.069	+	421.008i	0.0283406	+	0.0490873i	0.879848	−	0.475255i	$-0.157644\pi$
$419$	243.069	+	421.008i	0.0283406	+	0.0490873i	−0.851507	+	0.524343i	$0.824311\pi$
$420$		0			0
$421$	−2525.96	+	4375.10i	−0.292418	+	0.506482i	−0.974381	−	0.224904i	$-0.927793\pi$
$421$	−2525.96	+	4375.10i	−0.292418	+	0.506482i	0.681963	+	0.731387i	$0.261126\pi$
$422$	15022.1			1.73286
$423$	−11292.3	−	3818.03i	−1.29799	−	0.438863i
$424$	12183.9			1.39553
$425$		0			0
$426$	12105.4	−	4564.48i	1.37678	−	0.519130i
$427$	−991.230	−	1716.86i	−0.112340	−	0.194578i
$428$	−376.094	−	651.414i	−0.0424747	−	0.0735684i
$429$	7444.70	+	6102.19i	0.837840	+	0.686752i
$430$		0			0
$431$	6944.24			0.776084			0.388042	−	0.921642i	$-0.373152\pi$
$431$	6944.24			0.776084			0.388042	+	0.921642i	$0.373152\pi$
$432$	−5383.10	−	8621.89i	−0.599525	−	0.960234i
$433$	13738.3			1.52476			0.762378	−	0.647131i	$-0.224032\pi$
$433$	13738.3			1.52476			0.762378	+	0.647131i	$0.224032\pi$
$434$	−696.142	+	1205.75i	−0.0769952	+	0.133360i
$435$		0			0
$436$	483.075	+	836.711i	0.0530622	+	0.0919064i
$437$	5166.31	+	8948.31i	0.565533	+	0.979533i
$438$	7321.31	−	2760.59i	0.798688	−	0.301155i
$439$	−4240.92	+	7345.48i	−0.461066	+	0.798589i	−0.999014	−	0.0443883i	$-0.985866\pi$
$439$	−4240.92	+	7345.48i	−0.461066	+	0.798589i	0.537949	+	0.842978i	$0.319199\pi$
$440$		0			0
$441$	−3142.61	+	2762.71i	−0.339338	+	0.298317i
$442$	−19320.2			−2.07912
$443$	−279.098	+	483.411i	−0.0299330	+	0.0518455i	−0.880604	−	0.473853i	$-0.842863\pi$
$443$	−279.098	+	483.411i	−0.0299330	+	0.0518455i	0.850671	+	0.525699i	$0.176196\pi$
$444$	−23.4061	+	142.303i	−0.00250181	+	0.0152103i
$445$		0			0
$446$	4643.44	+	8042.67i	0.492989	+	0.853882i
$447$	−966.707	+	5877.32i	−0.102290	+	0.621896i
$448$	−2802.34	+	4853.79i	−0.295531	+	0.511875i
$449$	14775.0			1.55295			0.776476	−	0.630147i	$-0.217005\pi$
$449$	14775.0			1.55295			0.776476	+	0.630147i	$0.217005\pi$
$450$		0			0
$451$	3872.15			0.404285
$452$	−730.449	+	1265.17i	−0.0760120	+	0.131657i
$453$	−5669.66	+	2137.82i	−0.588044	+	0.221729i
$454$	1277.46	+	2212.62i	0.132058	+	0.228730i
$455$		0			0
$456$	−10697.7	−	8768.60i	−1.09861	−	0.900499i
$457$	−7103.97	+	12304.4i	−0.727154	+	1.25947i	0.230927	+	0.972971i	$0.425824\pi$
$457$	−7103.97	+	12304.4i	−0.727154	+	1.25947i	−0.958081	+	0.286497i	$0.907509\pi$
$458$	−4263.02			−0.434930
$459$	−7187.92	+	13506.4i	−0.730944	+	1.37347i
$460$		0			0
$461$	3851.26	−	6670.57i	0.389091	−	0.673925i	−0.603237	−	0.797562i	$-0.706123\pi$
$461$	3851.26	−	6670.57i	0.389091	−	0.673925i	0.992328	+	0.123637i	$0.0394558\pi$
$462$	5331.29	+	4369.90i	0.536870	+	0.440056i
$463$	3954.53	+	6849.45i	0.396939	+	0.687518i	0.993347	−	0.115163i	$-0.0367391\pi$
$463$	3954.53	+	6849.45i	0.396939	+	0.687518i	−0.596408	+	0.802682i	$0.703406\pi$
$464$	327.304	+	566.908i	0.0327472	+	0.0567199i
$465$		0			0
$466$	4345.11	−	7525.96i	0.431939	−	0.748140i
$467$	−11639.8			−1.15337			−0.576685	−	0.816967i	$-0.695654\pi$
$467$	−11639.8			−1.15337			−0.576685	+	0.816967i	$0.695654\pi$
$468$	1865.41	+	630.711i	0.184249	+	0.0622962i
$469$	−11829.8			−1.16471
$470$		0			0
$471$	−2931.11	+	17820.4i	−0.286749	+	1.74336i
$472$	−4540.77	−	7864.84i	−0.442809	−	0.766967i
$473$	161.288	+	279.359i	0.0156787	+	0.0271563i
$474$	3002.65	−	18255.3i	0.290962	−	1.76897i
$475$		0			0
$476$	−1872.50			−0.180307
$477$	3145.77	+	15715.7i	0.301960	+	1.50854i
$478$	5200.87			0.497662
$479$	9347.93	−	16191.1i	0.891687	−	1.54445i	0.0538341	−	0.998550i	$-0.482856\pi$
$479$	9347.93	−	16191.1i	0.891687	−	1.54445i	0.837853	−	0.545897i	$-0.183811\pi$
$480$		0			0
$481$	645.465	+	1117.98i	0.0611865	+	0.105978i
$482$	−6589.10	−	11412.7i	−0.622667	−	1.07849i
$483$	4390.12	+	3598.45i	0.413576	+	0.338996i
$484$	199.928	−	346.286i	0.0187761	−	0.0325212i
$485$		0			0
$486$	8385.77	−	7901.75i	0.782687	−	0.737512i
$487$	2249.54			0.209315			0.104658	−	0.994508i	$-0.466625\pi$
$487$	2249.54			0.209315			0.104658	+	0.994508i	$0.466625\pi$
$488$	−1483.72	+	2569.88i	−0.137633	+	0.238387i
$489$	−8934.78	−	7323.57i	−0.826267	−	0.677266i
$490$		0			0
$491$	−994.175	−	1721.96i	−0.0913778	−	0.158271i	0.816713	−	0.577044i	$-0.195794\pi$
$491$	−994.175	−	1721.96i	−0.0913778	−	0.158271i	−0.908091	+	0.418773i	$0.862460\pi$
$492$	741.168	−	279.466i	0.0679155	−	0.0256084i
$493$	492.676	−	853.339i	0.0450081	−	0.0779563i
$494$	22976.9			2.09267
$495$		0			0
$496$	2418.43			0.218933
$497$	5612.01	−	9720.28i	0.506505	−	0.877292i
$498$	1087.76	−	6613.29i	0.0978790	−	0.595078i
$499$	−1206.95	−	2090.50i	−0.108278	−	0.187543i	0.806795	−	0.590832i	$-0.201200\pi$
$499$	−1206.95	−	2090.50i	−0.108278	−	0.187543i	−0.915073	+	0.403289i	$0.867867\pi$
$500$		0			0
$501$	−1339.20	+	8142.00i	−0.119423	+	0.726063i
$502$	−2623.10	+	4543.34i	−0.233216	+	0.403942i
$503$	8758.56			0.776391			0.388196	−	0.921577i	$-0.373098\pi$
$503$	8758.56			0.776391			0.388196	+	0.921577i	$0.373098\pi$
$504$	−7198.67	−	2433.94i	−0.636219	−	0.215111i
$505$		0			0
$506$	−3853.88	+	6675.12i	−0.338589	+	0.586453i
$507$	5811.38	−	2191.25i	0.509058	−	0.191947i
$508$	1020.59	+	1767.72i	0.0891368	+	0.154389i
$509$	5924.01	+	10260.7i	0.515869	+	0.893511i	0.999830	+	0.0184220i	$0.00586422\pi$
$509$	5924.01	+	10260.7i	0.515869	+	0.893511i	−0.483961	+	0.875089i	$0.660802\pi$
$510$		0			0
$511$	3394.13	−	5878.81i	0.293831	−	0.508930i
$512$	7826.64			0.675570
$513$	8548.36	−	16062.7i	0.735710	−	1.38243i
$514$	−17804.1			−1.52783
$515$		0			0
$516$	51.0344	+	41.8313i	0.00435400	+	0.00356884i
$517$	−7021.23	−	12161.1i	−0.597279	−	1.03452i
$518$	462.230	+	800.606i	0.0392070	+	0.0679085i
$519$	−7330.91	+	2764.21i	−0.620022	+	0.233787i
$520$		0			0
$521$	3816.55			0.320933			0.160466	−	0.987041i	$-0.448700\pi$
$521$	3816.55			0.320933			0.160466	+	0.987041i	$0.448700\pi$
$522$	−557.310	+	489.939i	−0.0467295	+	0.0410806i
$523$	12158.9			1.01658			0.508288	−	0.861187i	$-0.330278\pi$
$523$	12158.9			1.01658			0.508288	+	0.861187i	$0.330278\pi$
$524$	−162.049	+	280.676i	−0.0135098	+	0.0233996i
$525$		0			0
$526$	−596.729	−	1033.57i	−0.0494651	−	0.0856761i
$527$	−1820.17	−	3152.63i	−0.150452	−	0.260590i
$528$	1943.37	−	11815.2i	0.160179	−	0.973846i
$529$	2909.97	−	5040.22i	0.239169	−	0.414253i
$530$		0			0
$531$	8972.28	−	7887.65i	0.733265	−	0.644623i
$532$	2226.90			0.181482
$533$	3545.25	−	6140.55i	0.288108	−	0.499018i
$534$	−15252.8	+	5751.27i	−1.23606	+	0.466071i
$535$		0			0
$536$	8853.71	+	15335.1i	0.713474	+	1.23577i
$537$	−6320.00	−	5180.31i	−0.507874	−	0.416289i
$538$	−7011.72	+	12144.7i	−0.561890	+	0.973222i
$539$	−4929.26			−0.393911
$540$		0			0
$541$	14919.8			1.18568			0.592840	−	0.805321i	$-0.298007\pi$
$541$	14919.8			1.18568			0.592840	+	0.805321i	$0.298007\pi$
$542$	−1757.69	+	3044.42i	−0.139298	+	0.241271i
$543$	−7974.69	−	6536.61i	−0.630252	−	0.516598i
$544$	3062.91	+	5305.12i	0.241399	+	0.418116i
$545$		0			0
$546$	11811.1	−	4453.52i	0.925766	−	0.349072i
$547$	−513.578	+	889.543i	−0.0401444	+	0.0695322i	−0.885400	−	0.464831i	$-0.846115\pi$
$547$	−513.578	+	889.543i	−0.0401444	+	0.0695322i	0.845255	+	0.534363i	$0.179448\pi$
$548$	−1318.27			−0.102762
$549$	−3697.91	−	1250.30i	−0.287473	−	0.0971973i
$550$		0			0
$551$	−585.923	+	1014.85i	−0.0453015	+	0.0784646i
$552$	1379.02	−	8384.10i	0.106332	−	0.646469i
$553$	−8025.26	−	13900.2i	−0.617123	−	1.06889i
$554$	925.313	+	1602.69i	0.0709617	+	0.122909i
$555$		0			0
$556$	−1492.92	+	2585.81i	−0.113874	+	0.197235i
$557$	10590.8			0.805648			0.402824	−	0.915277i	$-0.368029\pi$
$557$	10590.8			0.805648			0.402824	+	0.915277i	$0.368029\pi$
$558$	538.079	+	2688.15i	0.0408220	+	0.203940i
$559$	590.685			0.0446929
$560$		0			0
$561$	−16864.8	+	6359.07i	−1.26922	+	0.478574i
$562$	4181.23	+	7242.11i	0.313834	+	0.543576i
$563$	−1096.03	−	1898.38i	−0.0820467	−	0.142109i	0.822082	−	0.569369i	$-0.192812\pi$
$563$	−1096.03	−	1898.38i	−0.0820467	−	0.142109i	−0.904129	+	0.427260i	$0.859479\pi$
$564$	−2221.64	−	1821.01i	−0.165865	−	0.135955i
$565$		0			0
$566$	3107.32			0.230761
$567$	1280.84	−	9913.81i	0.0948684	−	0.734287i
$568$	−16800.6			−1.24109
$569$	8284.89	−	14349.8i	0.610405	−	1.05725i	−0.380767	−	0.924671i	$-0.624340\pi$
$569$	8284.89	−	14349.8i	0.610405	−	1.05725i	0.991172	−	0.132582i	$-0.0423267\pi$
$570$		0			0
$571$	−3639.66	−	6304.08i	−0.266752	−	0.462027i	0.701269	−	0.712896i	$-0.252617\pi$
$571$	−3639.66	−	6304.08i	−0.266752	−	0.462027i	−0.968021	+	0.250869i	$0.919284\pi$
$572$	1159.86	+	2008.93i	0.0847833	+	0.146849i
$573$	−11417.7	+	4305.19i	−0.832429	+	0.313878i
$574$	2538.82	−	4397.36i	0.184614	−	0.319760i
$575$		0			0
$576$	2166.05	+	10821.2i	0.156688	+	0.782784i
$577$	17938.0			1.29422			0.647112	−	0.762395i	$-0.275976\pi$
$577$	17938.0			1.29422			0.647112	+	0.762395i	$0.275976\pi$
$578$	10615.6	−	18386.8i	0.763930	−	1.32317i
$579$	−197.484	+	1200.65i	−0.0141747	+	0.0861782i
$580$		0			0
$581$	−2907.29	−	5035.57i	−0.207598	−	0.359571i
$582$	−4101.03	+	24933.2i	−0.292085	+	1.77580i
$583$	−9440.42	+	16351.3i	−0.670639	+	1.16158i
$584$	−10161.0			−0.719974
$585$		0			0
$586$	−15915.9			−1.12198
$587$	5754.83	−	9967.67i	0.404646	−	0.700868i	−0.589634	−	0.807671i	$-0.700728\pi$
$587$	5754.83	−	9967.67i	0.404646	−	0.700868i	0.994280	+	0.106803i	$0.0340613\pi$
$588$	−943.509	+	355.762i	−0.0661729	+	0.0249513i
$589$	2164.67	+	3749.32i	0.151433	+	0.262289i
$590$		0			0
$591$	−2884.79	−	2364.57i	−0.200785	−	0.164578i
$592$	802.904	−	1390.67i	0.0557418	−	0.0965476i
$593$	9612.80			0.665684			0.332842	−	0.942983i	$-0.391992\pi$
$593$	9612.80			0.665684			0.332842	+	0.942983i	$0.391992\pi$
$594$	13565.3	−	468.664i	0.937021	−	0.0323729i
$595$		0			0
$596$	−717.684	+	1243.07i	−0.0493247	+	0.0854328i
$597$	−6837.57	−	5604.55i	−0.468749	−	0.384219i
$598$	7057.05	+	12223.2i	0.482582	+	0.835857i
$599$	−3686.00	−	6384.33i	−0.251429	−	0.435487i	0.712491	−	0.701681i	$-0.247567\pi$
$599$	−3686.00	−	6384.33i	−0.251429	−	0.435487i	−0.963919	+	0.266194i	$0.914234\pi$
$600$		0			0
$601$	12095.3	−	20949.7i	0.820927	−	1.42189i	−0.0840654	−	0.996460i	$-0.526790\pi$
$601$	12095.3	−	20949.7i	0.820927	−	1.42189i	0.904993	−	0.425427i	$-0.139876\pi$
$602$	423.001			0.0286383
$603$	−17494.4	+	15379.6i	−1.18147	+	1.03865i
$604$	−1460.20			−0.0983684
$605$		0			0
$606$	−548.956	+	3337.50i	−0.0367984	+	0.223724i
$607$	−658.866	−	1141.19i	−0.0440569	−	0.0763088i	0.843156	−	0.537669i	$-0.180695\pi$
$607$	−658.866	−	1141.19i	−0.0440569	−	0.0763088i	−0.887213	+	0.461360i	$0.847362\pi$
$608$	−3642.62	−	6309.20i	−0.242973	−	0.420842i
$609$	−104.485	+	635.242i	−0.00695230	+	0.0422681i
$610$		0			0
$611$	−25713.9			−1.70257
$612$	−2769.13	+	2434.38i	−0.182901	+	0.160791i
$613$	4137.52			0.272615			0.136307	−	0.990667i	$-0.456477\pi$
$613$	4137.52			0.272615			0.136307	+	0.990667i	$0.456477\pi$
$614$	7471.56	−	12941.1i	0.491087	−	0.850588i
$615$		0			0
$616$	−4475.93	−	7752.54i	−0.292760	−	0.507076i
$617$	−3895.81	−	6747.74i	−0.254197	−	0.440281i	0.710480	−	0.703717i	$-0.248478\pi$
$617$	−3895.81	−	6747.74i	−0.254197	−	0.440281i	−0.964677	+	0.263436i	$0.915144\pi$
$618$	−20442.0	−	16755.7i	−1.33058	−	1.09064i
$619$	−10978.2	+	19014.8i	−0.712844	+	1.23468i	0.250941	+	0.968002i	$0.419260\pi$
$619$	−10978.2	+	19014.8i	−0.712844	+	1.23468i	−0.963785	+	0.266680i	$0.914073\pi$
$620$		0			0
$621$	11170.5	−	385.927i	0.721831	−	0.0249384i
$622$	2521.18			0.162524
$623$	−7071.17	+	12247.6i	−0.454736	+	0.787625i
$624$	−16957.5	−	13899.6i	−1.08789	−	0.891712i
$625$		0			0
$626$	−14048.6	−	24332.9i	−0.896957	−	1.55357i
$627$	20056.7	−	7562.63i	1.27749	−	0.481694i
$628$	−2176.06	+	3769.05i	−0.138271	+	0.239493i
$629$	−2417.15			−0.153224
$630$		0			0
$631$	−11152.7			−0.703618			−0.351809	−	0.936072i	$-0.614433\pi$
$631$	−11152.7			−0.703618			−0.351809	+	0.936072i	$0.614433\pi$
$632$	−12012.6	+	20806.4i	−0.756068	+	1.30955i
$633$	4164.95	−	25321.8i	0.261520	−	1.58997i
$634$	13837.5	+	23967.2i	0.866810	+	1.50136i
$635$		0			0
$636$	−626.861	+	3811.15i	−0.0390828	+	0.237613i
$637$	−4513.11	+	7816.94i	−0.280716	+	0.486214i
$638$	−874.155			−0.0542447
$639$	−4337.77	−	21670.7i	−0.268544	−	1.34160i
$640$		0			0
$641$	−2404.72	+	4165.10i	−0.148176	+	0.256648i	−0.930553	−	0.366156i	$-0.880674\pi$
$641$	−2404.72	+	4165.10i	−0.148176	+	0.256648i	0.782377	+	0.622805i	$0.214007\pi$
$642$	−8883.71	+	3349.71i	−0.546125	+	0.205923i
$643$	−1276.51	−	2210.98i	−0.0782904	−	0.135603i	0.824222	−	0.566267i	$-0.191613\pi$
$643$	−1276.51	−	2210.98i	−0.0782904	−	0.135603i	−0.902512	+	0.430664i	$0.858279\pi$
$644$	683.964	+	1184.66i	0.0418509	+	0.0724879i
$645$		0			0
$646$	−21511.0	+	37258.2i	−1.31013	+	2.26920i
$647$	−8446.00			−0.513210			−0.256605	−	0.966516i	$-0.582604\pi$
$647$	−8446.00			−0.513210			−0.256605	+	0.966516i	$0.582604\pi$
$648$	−13810.0	+	5759.36i	−0.837201	+	0.349150i
$649$	14073.2			0.851191
$650$		0			0
$651$	1839.45	+	1507.74i	0.110743	+	0.0907727i
$652$	−1392.01	−	2411.02i	−0.0836122	−	0.144821i
$653$	4047.44	+	7010.37i	0.242555	+	0.420118i	0.961441	−	0.275010i	$-0.0886812\pi$
$653$	4047.44	+	7010.37i	0.242555	+	0.420118i	−0.718886	+	0.695128i	$0.755348\pi$
$654$	11410.7	−	4302.55i	0.682254	−	0.257252i
$655$		0			0
$656$	−8819.97			−0.524942
$657$	−2623.47	−	13106.4i	−0.155786	−	0.778280i
$658$	−18414.2			−1.09097
$659$	−1087.67	+	1883.89i	−0.0642936	+	0.111360i	−0.896380	−	0.443286i	$-0.853813\pi$
$659$	−1087.67	+	1883.89i	−0.0642936	+	0.111360i	0.832087	+	0.554645i	$0.187146\pi$
$660$		0			0
$661$	4438.47	+	7687.66i	0.261175	+	0.452368i	0.966554	−	0.256462i	$-0.0825567\pi$
$661$	4438.47	+	7687.66i	0.261175	+	0.452368i	−0.705379	+	0.708830i	$0.749223\pi$
$662$	9069.64	+	15709.1i	0.532480	+	0.922282i
$663$	−5356.62	+	32566.8i	−0.313776	+	1.90768i
$664$	−4351.77	+	7537.48i	−0.254339	+	0.440529i
$665$		0			0
$666$	1724.41	+	583.037i	0.100329	+	0.0339223i
$667$	−719.834			−0.0417872
$668$	−994.226	+	1722.05i	−0.0575865	+	0.0997427i
$669$	14844.4	−	5597.27i	0.857874	−	0.323472i
$670$		0			0
$671$	−2299.25	−	3982.42i	−0.132283	−	0.229120i
$672$	−3095.35	−	2537.16i	−0.177687	−	0.145645i
$673$	−4583.96	+	7939.65i	−0.262554	+	0.454757i	−0.966920	−	0.255080i	$-0.917898\pi$
$673$	−4583.96	+	7939.65i	−0.262554	+	0.454757i	0.704366	+	0.709837i	$0.251231\pi$
$674$	1815.47			0.103753
$675$		0			0
$676$	1496.70			0.0851557
$677$	−9438.93	+	16348.7i	−0.535846	+	0.928112i	0.463276	+	0.886214i	$0.346674\pi$
$677$	−9438.93	+	16348.7i	−0.535846	+	0.928112i	−0.999122	+	0.0418983i	$0.986659\pi$
$678$	14261.2	+	11689.4i	0.807812	+	0.662139i
$679$	10961.0	+	18984.9i	0.619503	+	1.07301i
$680$		0			0
$681$	4083.85	−	1539.87i	0.229800	−	0.0866488i
$682$	−1614.77	+	2796.86i	−0.0906638	+	0.157034i
$683$	27207.5			1.52426			0.762128	−	0.647426i	$-0.224155\pi$
$683$	27207.5			1.52426			0.762128	+	0.647426i	$0.224155\pi$
$684$	3293.23	−	2895.13i	0.184094	−	0.161839i
$685$		0			0
$686$	−10385.0	+	17987.4i	−0.577991	+	1.00111i
$687$	−1181.94	+	7185.89i	−0.0656388	+	0.399067i
$688$	−367.381	−	636.323i	−0.0203580	−	0.0352610i
$689$	17286.9	+	29941.7i	0.955845	+	1.65557i
$690$		0			0
$691$	8703.62	−	15075.1i	0.479162	−	0.829934i	−0.520552	−	0.853830i	$-0.674274\pi$
$691$	8703.62	−	15075.1i	0.479162	−	0.829934i	0.999714	+	0.0238963i	$0.00760715\pi$
$692$	−1888.04			−0.103718
$693$	8844.17	−	7775.03i	0.484794	−	0.426189i
$694$	−13876.7			−0.759011
$695$		0			0
$696$	901.668	−	339.985i	0.0491058	−	0.0185159i
$697$	6638.15	+	11497.6i	0.360743	+	0.624825i
$698$	1026.99	+	1778.80i	0.0556909	+	0.0964595i
$699$	−11481.3	−	9410.87i	−0.621263	−	0.509230i
$700$		0			0
$701$	18543.0			0.999086			0.499543	−	0.866289i	$-0.333501\pi$
$701$	18543.0			0.999086			0.499543	+	0.866289i	$0.333501\pi$
$702$	11676.8	−	21941.3i	0.627798	−	1.17966i
$703$	2874.63			0.154223
$704$	−6500.29	+	11258.8i	−0.347996	+	0.602746i
$705$		0			0
$706$	5112.91	+	8855.81i	0.272559	+	0.472086i
$707$	1467.21	+	2541.28i	0.0780482	+	0.135184i
$708$	2693.76	−	1015.72i	0.142991	−	0.0539165i
$709$	−13116.9	+	22719.1i	−0.694803	+	1.20343i	0.275444	+	0.961317i	$0.411175\pi$
$709$	−13116.9	+	22719.1i	−0.694803	+	1.20343i	−0.970247	+	0.242117i	$0.922158\pi$
$710$		0			0
$711$	−29939.2	−	10122.7i	−1.57920	−	0.533941i
$712$	21168.9			1.11424
$713$	−1329.70	+	2303.11i	−0.0698425	+	0.120971i
$714$	−3835.98	+	23321.7i	−0.201061	+	1.22240i
$715$		0			0
$716$	−984.633	−	1705.43i	−0.0513931	−	0.0890155i
$717$	1441.96	−	8766.76i	0.0751062	−	0.456626i
$718$	11713.2	−	20287.8i	0.608817	−	1.05450i
$719$	−3043.06			−0.157840			−0.0789199	−	0.996881i	$-0.525147\pi$
$719$	−3043.06			−0.157840			−0.0789199	+	0.996881i	$0.525147\pi$
$720$		0			0
$721$	−22931.2			−1.18447
$722$	15150.7	−	26241.8i	0.780958	−	1.35266i
$723$	−21064.4	+	7942.60i	−1.08353	+	0.408559i
$724$	−1242.43	−	2151.95i	−0.0637769	−	0.110465i
$725$		0			0
$726$	−3903.37	−	3199.47i	−0.199542	−	0.163559i
$727$	10971.2	−	19002.7i	0.559698	−	0.969426i	−0.437823	−	0.899061i	$-0.644250\pi$
$727$	10971.2	−	19002.7i	0.559698	−	0.969426i	0.997521	−	0.0703647i	$-0.0224163\pi$
$728$	−16392.2			−0.834528
$729$	−10994.5	−	16326.1i	−0.558577	−	0.829453i
$730$		0			0
$731$	−553.002	+	957.827i	−0.0279802	+	0.0484631i
$732$	−727.525	−	596.330i	−0.0367351	−	0.0301107i
$733$	−13288.4	−	23016.2i	−0.669604	−	1.15979i	−0.978015	−	0.208535i	$-0.933131\pi$
$733$	−13288.4	−	23016.2i	−0.669604	−	1.15979i	0.308411	−	0.951253i	$-0.400203\pi$
$734$	−8987.58	−	15566.9i	−0.451959	−	0.782815i
$735$		0			0
$736$	2237.56	−	3875.57i	0.112062	−	0.194097i
$737$	−27440.4			−1.37148
$738$	−1962.37	−	9803.63i	−0.0978803	−	0.488993i
$739$	28787.7			1.43298			0.716489	−	0.697598i	$-0.245748\pi$
$739$	28787.7			1.43298			0.716489	+	0.697598i	$0.245748\pi$
$740$		0			0
$741$	6370.45	−	38730.6i	0.315822	−	1.92011i
$742$	12379.5	+	21441.8i	0.612485	+	1.06086i
$743$	−2251.51	−	3899.73i	−0.111171	−	0.192553i	0.805072	−	0.593177i	$-0.202127\pi$
$743$	−2251.51	−	3899.73i	−0.111171	−	0.192553i	−0.916243	+	0.400624i	$0.868793\pi$
$744$	577.808	−	3512.92i	0.0284724	−	0.173105i
$745$		0			0
$746$	−25624.8			−1.25763
$747$	−10846.0	−	3667.13i	−0.531238	−	0.179616i
$748$	−4343.45			−0.212316
$749$	−4118.46	+	7133.38i	−0.200915	+	0.347995i
$750$		0			0
$751$	−2852.83	−	4941.24i	−0.138617	−	0.240091i	0.788357	−	0.615219i	$-0.210932\pi$
$751$	−2852.83	−	4941.24i	−0.138617	−	0.240091i	−0.926973	+	0.375128i	$0.877599\pi$
$752$	15993.0	+	27700.6i	0.775536	+	1.34327i
$753$	6931.13	+	5681.24i	0.335438	+	0.274948i
$754$	−800.356	+	1386.26i	−0.0386568	+	0.0669556i
$755$		0			0
$756$	1131.71	−	2126.53i	0.0544444	−	0.102303i
$757$	−17397.6			−0.835305			−0.417652	−	0.908607i	$-0.637147\pi$
$757$	−17397.6			−0.835305			−0.417652	+	0.908607i	$0.637147\pi$
$758$	−5338.62	+	9246.77i	−0.255815	+	0.443084i
$759$	10183.3	+	8346.94i	0.486996	+	0.399176i
$760$		0			0
$761$	17757.2	+	30756.3i	0.845857	+	1.46507i	0.884875	+	0.465829i	$0.154244\pi$
$761$	17757.2	+	30756.3i	0.845857	+	1.46507i	−0.0390179	+	0.999239i	$0.512423\pi$
$762$	24107.4	−	9090.00i	1.14609	−	0.432147i
$763$	5289.97	−	9162.50i	0.250996	−	0.434737i
$764$	−2940.58			−0.139249
$765$		0			0
$766$	17435.3			0.822408
$767$	12885.1	−	22317.7i	0.606591	−	1.05065i
$768$	−1584.37	+	9632.57i	−0.0744416	+	0.452585i
$769$	−15631.8	−	27075.1i	−0.733027	−	1.26964i	−0.955583	−	0.294721i	$-0.904773\pi$
$769$	−15631.8	−	27075.1i	−0.733027	−	1.26964i	0.222556	−	0.974920i	$-0.428560\pi$
$770$		0			0
$771$	−4936.26	+	30011.2i	−0.230577	+	1.40185i
$772$	−146.612	+	253.940i	−0.00683508	+	0.0118387i
$773$	6676.47			0.310654			0.155327	−	0.987863i	$-0.450357\pi$
$773$	6676.47			0.310654			0.155327	+	0.987863i	$0.450357\pi$
$774$	625.551	−	549.930i	0.0290503	−	0.0255385i
$775$		0			0
$776$	16406.9	−	28417.5i	0.758985	−	1.31460i
$777$	1477.68	−	557.179i	0.0682260	−	0.0257254i
$778$	21850.7	+	37846.5i	1.00692	+	1.74404i
$779$	−7894.53	−	13673.7i	−0.363095	−	0.628898i
$780$		0			0
$781$	13017.6	−	22547.1i	0.596422	−	1.03303i
$782$	−26427.3			−1.20849
$783$	671.341	+	1075.26i	0.0306408	+	0.0490761i
$784$	11227.9			0.511473
$785$		0			0
$786$	3163.81	+	2593.28i	0.143574	+	0.117683i
$787$	4716.91	+	8169.93i	0.213646	+	0.370047i	0.952853	−	0.303432i	$-0.0981326\pi$
$787$	4716.91	+	8169.93i	0.213646	+	0.370047i	−0.739207	+	0.673479i	$0.764799\pi$
$788$	−449.439	−	778.451i	−0.0203180	−	0.0351919i
$789$	−1907.66	+	719.306i	−0.0860766	+	0.0324562i
$790$		0			0
$791$	15997.7			0.719107
$792$	−16698.0	−	5645.75i	−0.749164	−	0.253299i
$793$	−8420.57			−0.377078
$794$	13709.8	−	23746.0i	0.612773	−	1.06135i
$795$		0			0
$796$	−1065.27	−	1845.10i	−0.0474340	−	0.0821580i
$797$	−11738.1	−	20331.1i	−0.521689	−	0.903592i	−0.999682	−	0.0252283i	$-0.991969\pi$
$797$	−11738.1	−	20331.1i	−0.521689	−	0.903592i	0.477992	−	0.878364i	$-0.341365\pi$
$798$	4562.00	−	27735.7i	0.202372	−	1.23037i
$799$	24073.4	−	41696.4i	1.06590	−	1.84620i
$800$		0			0
$801$	5465.61	+	27305.3i	0.241096	+	1.20447i
$802$	−31972.0			−1.40769
$803$	7873.02	−	13636.5i	0.345993	−	0.599278i
$804$	−5252.37	+	1980.47i	−0.230394	+	0.0868729i
$805$		0			0
$806$	2956.89	+	5121.48i	0.129221	+	0.223817i
$807$	18527.4	+	15186.3i	0.808173	+	0.662435i
$808$	2196.19	−	3803.91i	0.0956208	−	0.165620i
$809$	−33269.8			−1.44586			−0.722932	−	0.690919i	$-0.757206\pi$
$809$	−33269.8			−1.44586			−0.722932	+	0.690919i	$0.757206\pi$
$810$		0			0
$811$	27892.8			1.20771			0.603853	−	0.797096i	$-0.293631\pi$
$811$	27892.8			1.20771			0.603853	+	0.797096i	$0.293631\pi$
$812$	−77.5699	+	134.355i	−0.00335243	+	0.00580657i
$813$	4644.44	+	3806.91i	0.200354	+	0.164224i
$814$	1072.19	+	1857.08i	0.0461672	+	0.0799640i
$815$		0			0
$816$	38414.6	−	14484.7i	1.64801	−	0.621404i
$817$	657.666	−	1139.11i	0.0281626	−	0.0487790i
$818$	−10093.1			−0.431415
$819$	−4232.32	−	21143.9i	−0.180573	−	0.902111i
$820$		0			0
$821$	1848.66	−	3201.98i	0.0785856	−	0.136114i	−0.824054	−	0.566511i	$-0.808293\pi$
$821$	1848.66	−	3201.98i	0.0785856	−	0.136114i	0.902640	+	0.430397i	$0.141626\pi$
$822$	−2700.58	+	16418.8i	−0.114591	+	0.696680i
$823$	3572.25	+	6187.32i	0.151301	+	0.262061i	0.931706	−	0.363213i	$-0.118320\pi$
$823$	3572.25	+	6187.32i	0.151301	+	0.262061i	−0.780405	+	0.625275i	$0.784987\pi$
$824$	17162.3	+	29725.9i	0.725578	+	1.25674i
$825$		0			0
$826$	9227.29	−	15982.1i	0.388691	−	0.673232i
$827$	−19866.9			−0.835357			−0.417679	−	0.908595i	$-0.637156\pi$
$827$	−19866.9			−0.835357			−0.417679	+	0.908595i	$0.637156\pi$
$828$	2551.61	+	862.723i	0.107095	+	0.0362098i
$829$	−36736.5			−1.53910			−0.769548	−	0.638589i	$-0.779518\pi$
$829$	−36736.5			−1.53910			−0.769548	+	0.638589i	$0.779518\pi$
$830$		0			0
$831$	2958.09	−	1115.39i	0.123484	−	0.0465611i
$832$	11903.0	+	20616.7i	0.495990	+	0.859079i
$833$	−8450.38	−	14636.5i	−0.351487	−	0.608793i
$834$	29147.5	+	23891.3i	1.21018	+	0.991952i
$835$		0			0
$836$	5165.52			0.213700
$837$	4680.42	−	161.703i	0.193284	−	0.00667773i
$838$	1478.71			0.0609560
$839$	−15006.1	+	25991.4i	−0.617485	+	1.06951i	0.372458	+	0.928049i	$0.378515\pi$
$839$	−15006.1	+	25991.4i	−0.617485	+	1.06951i	−0.989943	+	0.141466i	$0.954818\pi$
$840$		0			0
$841$	12153.7	+	21050.8i	0.498326	+	0.863127i
$842$	7683.32	+	13307.9i	0.314471	+	0.544680i
$843$	13366.8	−	5040.12i	0.546117	−	0.205920i
$844$	3092.07	−	5355.62i	0.126106	−	0.218422i
$845$		0			0
$846$	−27231.7	+	23939.7i	−1.10667	+	0.972890i
$847$	−4378.68			−0.177631
$848$	21503.4	−	37245.0i	0.870789	−	1.50825i
$849$	861.519	−	5237.80i	0.0348260	−	0.211733i
$850$		0			0
$851$	882.905	+	1529.24i	0.0355648	+	0.0616000i
$852$	864.391	−	5255.27i	0.0347577	−	0.211318i
$853$	−2690.51	+	4660.10i	−0.107997	+	0.187056i	−0.914959	−	0.403548i	$-0.867777\pi$
$853$	−2690.51	+	4660.10i	−0.107997	+	0.187056i	0.806962	+	0.590604i	$0.201110\pi$
$854$	−6030.13			−0.241624
$855$		0			0
$856$	12329.4			0.492302
$857$	7319.88	−	12678.4i	0.291765	−	0.505352i	−0.682462	−	0.730921i	$-0.739091\pi$
$857$	7319.88	−	12678.4i	0.291765	−	0.505352i	0.974227	+	0.225569i	$0.0724242\pi$
$858$	27397.0	−	10330.4i	1.09011	−	0.411041i
$859$	−14770.0	−	25582.4i	−0.586667	−	1.01614i	−0.994665	−	0.103154i	$-0.967107\pi$
$859$	−14770.0	−	25582.4i	−0.586667	−	1.01614i	0.407999	−	0.912983i	$-0.366227\pi$
$860$		0			0
$861$	−6708.44	−	5498.71i	−0.265532	−	0.217649i
$862$	10561.3	−	18292.7i	0.417307	−	0.722797i
$863$	−3387.63			−0.133622			−0.0668112	−	0.997766i	$-0.521283\pi$
$863$	−3387.63			−0.133622			−0.0668112	+	0.997766i	$0.521283\pi$
$864$	−7876.00	+	272.106i	−0.310124	+	0.0107144i
$865$		0			0
$866$	20894.1	−	36189.7i	0.819875	−	1.42007i
$867$	−28050.2	−	22991.9i	−1.09877	−	0.900628i
$868$	286.580	+	496.370i	0.0112064	+	0.0194100i
$869$	−18615.4	−	32242.8i	−0.726678	−	1.25864i
$870$		0			0
$871$	−25123.8	+	43515.7i	−0.977368	+	1.69285i
$872$	−15836.5			−0.615015
$873$	40891.2	+	13825.7i	1.58529	+	0.536000i
$874$	31429.2			1.21637
$875$		0			0
$876$	522.783	−	3178.38i	0.0201635	−	0.122588i
$877$	−122.052	−	211.400i	−0.00469944	−	0.00813967i	0.863666	−	0.504064i	$-0.168163\pi$
$877$	−122.052	−	211.400i	−0.00469944	−	0.00813967i	−0.868366	+	0.495925i	$0.834829\pi$
$878$	12899.8	+	22343.1i	0.495838	+	0.858817i
$879$	−4412.75	+	26828.4i	−0.169327	+	1.02946i
$880$		0			0
$881$	13910.2			0.531948			0.265974	−	0.963980i	$-0.414307\pi$
$881$	13910.2			0.531948			0.265974	+	0.963980i	$0.414307\pi$
$882$	2498.10	+	12480.1i	0.0953689	+	0.476446i
$883$	8805.87			0.335607			0.167803	−	0.985820i	$-0.446333\pi$
$883$	8805.87			0.335607			0.167803	+	0.985820i	$0.446333\pi$
$884$	−3976.76	+	6887.95i	−0.151304	+	0.262067i
$885$		0			0
$886$	848.943	+	1470.41i	0.0321905	+	0.0557556i
$887$	6640.41	+	11501.5i	0.251368	+	0.435381i	0.963903	−	0.266255i	$-0.0857864\pi$
$887$	6640.41	+	11501.5i	0.251368	+	0.435381i	−0.712535	+	0.701637i	$0.752453\pi$
$888$	−1828.21	−	1498.53i	−0.0690885	−	0.0566298i
$889$	11176.1	−	19357.6i	0.421637	−	0.730296i
$890$		0			0
$891$	2971.04	−	22996.0i	0.111710	−	0.864642i
$892$	3823.11			0.143506
$893$	−28629.7	+	49588.2i	−1.07285	+	1.85824i
$894$	14011.9	+	11485.2i	0.524194	+	0.429666i
$895$		0			0
$896$	11605.0	+	20100.4i	0.432695	+	0.749449i
$897$	22560.4	−	8506.67i	0.839765	−	0.316644i
$898$	22470.9	−	38920.7i	0.835036	−	1.44633i
$899$	−301.609			−0.0111893
$900$		0			0
$901$	−64736.1			−2.39364
$902$	5889.04	−	10200.1i	0.217387	−	0.376526i
$903$	117.279	−	713.025i	0.00432204	−	0.0262768i
$904$	−11973.1	−	20738.0i	−0.440507	−	0.762981i
$905$		0			0
$906$	−2991.33	+	18186.5i	−0.109691	+	0.666894i
$907$	−542.122	+	938.982i	−0.0198466	+	0.0343753i	−0.875778	−	0.482714i	$-0.839651\pi$
$907$	−542.122	+	938.982i	−0.0198466	+	0.0343753i	0.855932	+	0.517089i	$0.172984\pi$
$908$	1051.78			0.0384411
$909$	5473.61	+	1850.68i	0.199723	+	0.0675281i
$910$		0			0
$911$	−25094.4	+	43464.7i	−0.912638	+	1.58073i	−0.102314	+	0.994752i	$0.532625\pi$
$911$	−25094.4	+	43464.7i	−0.912638	+	1.58073i	−0.810324	+	0.585983i	$0.800709\pi$
$912$	−45685.2	+	17226.2i	−1.65876	+	0.625455i
$913$	−6743.74	−	11680.5i	−0.244452	−	0.423404i
$914$	21608.4	+	37426.9i	0.781995	+	1.35445i
$915$		0			0
$916$	−877.475	+	1519.83i	−0.0316513	+	0.0548216i
$917$	3549.06			0.127808
$918$	24647.0	+	39476.1i	0.886136	+	1.41929i
$919$	30376.1			1.09033			0.545166	−	0.838328i	$-0.316467\pi$
$919$	30376.1			1.09033			0.545166	+	0.838328i	$0.316467\pi$
$920$		0			0
$921$	−19742.5	−	16182.3i	−0.706336	−	0.578962i
$922$	−11714.5	−	20290.2i	−0.418435	−	0.724751i
$923$	−23837.2	−	41287.2i	−0.850066	−	1.47236i
$924$	2655.30	−	1001.21i	0.0945377	−	0.0356466i
$925$		0			0
$926$	24057.3			0.853750
$927$	−33911.6	+	29812.2i	−1.20151	+	1.05627i
$928$	507.534			0.0179533
$929$	23098.8	−	40008.3i	0.815766	−	1.41295i	−0.0930102	−	0.995665i	$-0.529649\pi$
$929$	23098.8	−	40008.3i	0.815766	−	1.41295i	0.908776	−	0.417283i	$-0.137018\pi$
$930$		0			0
$931$	10049.8	+	17406.7i	0.353778	+	0.612762i
$932$	−1788.74	−	3098.20i	−0.0628672	−	0.108889i
$933$	699.007	−	4249.78i	0.0245278	−	0.149123i
$934$	−17702.6	+	30661.7i	−0.620177	+	1.07418i
$935$		0			0
$936$	−24241.5	+	21311.0i	−0.846536	+	0.744201i
$937$	−37004.7			−1.29017			−0.645085	−	0.764111i	$-0.723178\pi$
$937$	−37004.7			−1.29017			−0.645085	+	0.764111i	$0.723178\pi$
$938$	−17991.6	+	31162.4i	−0.626277	+	1.08474i
$939$	−44911.3	+	16934.4i	−1.56084	+	0.588533i
$940$		0			0
$941$	−21907.2	−	37944.4i	−0.758932	−	1.31451i	−0.943396	−	0.331669i	$-0.892388\pi$
$941$	−21907.2	−	37944.4i	−0.758932	−	1.31451i	0.184464	−	0.982839i	$-0.440945\pi$
$942$	42485.1	+	34823.7i	1.46947	+	1.20448i
$943$	4849.40	−	8399.41i	0.167464	−	0.290055i
$944$	−32056.0			−1.10523
$945$		0			0
$946$	981.191			0.0337223
$947$	2304.86	−	3992.14i	0.0790898	−	0.136988i	−0.823768	−	0.566928i	$-0.808132\pi$
$947$	2304.86	−	3992.14i	0.0790898	−	0.136988i	0.902857	+	0.429940i	$0.141465\pi$
$948$	−5890.24	−	4828.05i	−0.201800	−	0.165409i
$949$	−14416.7	−	24970.5i	−0.493136	−	0.854136i
$950$		0			0
$951$	44236.5	−	16679.9i	1.50838	−	0.568752i
$952$	15346.5	−	26580.8i	0.522460	−	0.904927i
$953$	−4281.80			−0.145542			−0.0727708	−	0.997349i	$-0.523184\pi$
$953$	−4281.80			−0.145542			−0.0727708	+	0.997349i	$0.523184\pi$
$954$	46183.1	+	15614.9i	1.56733	+	0.529928i
$955$		0			0
$956$	1070.52	−	1854.19i	0.0362165	−	0.0627288i
$957$	−242.363	+	1473.50i	−0.00818651	+	0.0497718i
$958$	−28434.0	−	49249.1i	−0.958936	−	1.66093i
$959$	7217.91	+	12501.8i	0.243043	+	0.420963i
$960$		0			0
$961$	14338.4	−	24834.8i	0.481298	−	0.833633i
$962$	3926.68			0.131602
$963$	3183.34	+	15903.4i	0.106523	+	0.532170i
$964$	−5425.05			−0.181254
$965$		0			0
$966$	16155.9	−	6091.79i	0.538104	−	0.202899i
$967$	−18114.9	−	31375.9i	−0.602416	−	1.04341i	−0.992454	−	0.122616i	$-0.960872\pi$
$967$	−18114.9	−	31375.9i	−0.602416	−	1.04341i	0.390038	−	0.920799i	$-0.372462\pi$
$968$	3277.10	+	5676.11i	0.108812	+	0.188468i
$969$	56839.7	+	46589.7i	1.88437	+	1.54456i
$970$		0			0
$971$	844.928			0.0279249			0.0139624	−	0.999903i	$-0.495555\pi$
$971$	844.928			0.0279249			0.0139624	+	0.999903i	$0.495555\pi$
$972$	−1091.02	−	4616.10i	−0.0360025	−	0.152327i
$973$	32696.7			1.07730
$974$	3421.26	−	5925.80i	0.112551	−	0.194943i
$975$		0			0
$976$	5237.24	+	9071.16i	0.171762	+	0.297501i
$977$	22922.5	+	39702.9i	0.750619	+	1.30011i	0.947523	+	0.319687i	$0.103578\pi$
$977$	22922.5	+	39702.9i	0.750619	+	1.30011i	−0.196904	+	0.980423i	$0.563089\pi$
$978$	−32880.6	+	12398.0i	−1.07506	+	0.405363i
$979$	−16402.2	+	28409.5i	−0.535463	+	0.927449i
$980$		0			0
$981$	−4088.85	−	20427.2i	−0.133075	−	0.664821i
$982$	−6048.05			−0.196539
$983$	−20101.0	+	34815.9i	−0.652210	+	1.12966i	0.330376	+	0.943849i	$0.392824\pi$
$983$	−20101.0	+	34815.9i	−0.652210	+	1.12966i	−0.982586	+	0.185811i	$0.940509\pi$
$984$	−2107.26	+	12811.6i	−0.0682692	+	0.415059i
$985$		0			0
$986$	−1498.59	−	2595.64i	−0.0484025	−	0.0838356i
$987$	−5105.42	+	31039.6i	−0.164648	+	1.00101i
$988$	4729.43	−	8191.61i	0.152291	−	0.263775i
$989$	807.974			0.0259778
$990$		0			0
$991$	1797.91			0.0576313			0.0288157	−	0.999585i	$-0.490826\pi$
$991$	1797.91			0.0576313			0.0288157	+	0.999585i	$0.490826\pi$
$992$	937.534	−	1623.86i	0.0300068	−	0.0519733i
$993$	28994.3	−	10932.7i	0.926594	−	0.349384i
$994$	−17070.3	−	29566.6i	−0.544704	−	0.943455i
$995$		0			0
$996$	−2133.84	−	1749.04i	−0.0678849	−	0.0556432i
$997$	4566.04	−	7908.61i	0.145043	−	0.251222i	−0.784346	−	0.620324i	$-0.787001\pi$
$997$	4566.04	−	7908.61i	0.145043	−	0.251222i	0.929389	+	0.369102i	$0.120335\pi$
$998$	−7342.47			−0.232888
$999$	1460.89	−	2745.07i	0.0462667	−	0.0869370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.d.151.6		14
5.2	odd	4		225.4.k.d.124.11		28
5.3	odd	4		225.4.k.d.124.4		28
5.4	even	2		45.4.e.c.16.2	✓	14
9.2	odd	6		2025.4.a.ba.1.6		7
9.4	even	3	inner	225.4.e.d.76.6		14
9.7	even	3		2025.4.a.bb.1.2		7
15.14	odd	2		135.4.e.c.46.6		14
45.4	even	6		45.4.e.c.31.2	yes	14
45.13	odd	12		225.4.k.d.49.11		28
45.14	odd	6		135.4.e.c.91.6		14
45.22	odd	12		225.4.k.d.49.4		28
45.29	odd	6		405.4.a.n.1.2		7
45.34	even	6		405.4.a.m.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.c.16.2	✓	14	5.4	even	2
45.4.e.c.31.2	yes	14	45.4	even	6
135.4.e.c.46.6		14	15.14	odd	2
135.4.e.c.91.6		14	45.14	odd	6
225.4.e.d.76.6		14	9.4	even	3	inner
225.4.e.d.151.6		14	1.1	even	1	trivial
225.4.k.d.49.4		28	45.22	odd	12
225.4.k.d.49.11		28	45.13	odd	12
225.4.k.d.124.4		28	5.3	odd	4
225.4.k.d.124.11		28	5.2	odd	4
405.4.a.m.1.6		7	45.34	even	6
405.4.a.n.1.2		7	45.29	odd	6
2025.4.a.ba.1.6		7	9.2	odd	6
2025.4.a.bb.1.2		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)

\(f(q)\)	\(=\)	\(q+(1.52087 - 2.63422i) q^{2} +(-4.01867 - 3.29398i) q^{3} +(-0.626094 - 1.08443i) q^{4} +(-14.7890 + 5.57636i) q^{6} +(-6.85611 + 11.8751i) q^{7} +20.5251 q^{8} +(5.29939 + 26.4748i) q^{9} +O(q^{10})\)	\(q+(1.52087 - 2.63422i) q^{2} +(-4.01867 - 3.29398i) q^{3} +(-0.626094 - 1.08443i) q^{4} +(-14.7890 + 5.57636i) q^{6} +(-6.85611 + 11.8751i) q^{7} +20.5251 q^{8} +(5.29939 + 26.4748i) q^{9} +(-15.9034 + 27.5455i) q^{11} +(-1.05602 + 6.42029i) q^{12} +(29.1216 + 50.4401i) q^{13} +(20.8545 + 36.1211i) q^{14} +(36.2248 - 62.7431i) q^{16} -109.055 q^{17} +(77.8003 + 26.3050i) q^{18} +129.695 q^{19} +(66.6689 - 25.1383i) q^{21} +(48.3740 + 83.7863i) q^{22} +(39.8342 + 68.9949i) q^{23} +(-82.4836 - 67.6093i) q^{24} +177.161 q^{26} +(65.9111 - 123.850i) q^{27} +17.1703 q^{28} +(-4.51769 + 7.82486i) q^{29} +(16.6904 + 28.9087i) q^{31} +(-28.0860 - 48.6463i) q^{32} +(154.645 - 58.3108i) q^{33} +(-165.858 + 287.275i) q^{34} +(25.3921 - 22.3225i) q^{36} +22.1645 q^{37} +(197.250 - 341.647i) q^{38} +(49.1186 - 298.628i) q^{39} +(-60.8698 - 105.430i) q^{41} +(35.1747 - 213.853i) q^{42} +(5.07086 - 8.78298i) q^{43} +39.8281 q^{44} +242.331 q^{46} +(-220.746 + 382.343i) q^{47} +(-352.250 + 132.820i) q^{48} +(77.4875 + 134.212i) q^{49} +(438.255 + 359.225i) q^{51} +(36.4657 - 63.1604i) q^{52} +593.610 q^{53} +(-226.006 - 361.984i) q^{54} +(-140.722 + 243.738i) q^{56} +(-521.202 - 427.214i) q^{57} +(13.7416 + 23.8012i) q^{58} +(-221.230 - 383.182i) q^{59} +(-72.2881 + 125.207i) q^{61} +101.536 q^{62} +(-350.725 - 118.583i) q^{63} +408.736 q^{64} +(81.5912 - 496.052i) q^{66} +(431.360 + 747.138i) q^{67} +(68.2786 + 118.262i) q^{68} +(67.1873 - 408.481i) q^{69} -818.541 q^{71} +(108.771 + 543.398i) q^{72} -495.052 q^{73} +(33.7093 - 58.3863i) q^{74} +(-81.2014 - 140.645i) q^{76} +(-218.071 - 377.710i) q^{77} +(-711.950 - 583.563i) q^{78} +(-585.263 + 1013.71i) q^{79} +(-672.833 + 280.601i) q^{81} -370.300 q^{82} +(-212.022 + 367.232i) q^{83} +(-69.0017 - 56.5586i) q^{84} +(-15.4242 - 26.7156i) q^{86} +(43.9300 - 16.5644i) q^{87} +(-326.419 + 565.374i) q^{88} +1031.37 q^{89} -798.643 q^{91} +(49.8799 - 86.3945i) q^{92} +(28.1513 - 171.152i) q^{93} +(671.452 + 1162.99i) q^{94} +(-47.3718 + 288.008i) q^{96} +(799.356 - 1384.53i) q^{97} +471.394 q^{98} +(-813.541 - 275.066i) 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

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