LMFDB - Embedded newform 100.4.e.e.43.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,4,Mod(7,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("100.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	100.e (of order $4$, 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:	$5.90019100057$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 44x^{8} - 156x^{6} + 704x^{4} - 1792x^{2} + 4096 $ x^12 - 7x^10 + 44x^8 - 156x^6 + 704x^4 - 1792*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.5
Root			$1.83244 + 0.801352i$ of defining polynomial
Character	$\chi$	$=$	100.43
Dual form			100.4.e.e.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.63379 + 1.03109i) q^{2} +(5.55970 - 5.55970i) q^{3} +(5.87372 + 5.43134i) q^{4} +(20.3756 - 8.91056i) q^{6} +(-1.14202 - 1.14202i) q^{7} +(9.86997 + 20.3613i) q^{8} -34.8205i q^{9} +O(q^{10})$	\(q+(2.63379 + 1.03109i) q^{2} +(5.55970 - 5.55970i) q^{3} +(5.87372 + 5.43134i) q^{4} +(20.3756 - 8.91056i) q^{6} +(-1.14202 - 1.14202i) q^{7} +(9.86997 + 20.3613i) q^{8} -34.8205i q^{9} +27.0350i q^{11} +(62.8527 - 2.45951i) q^{12} +(-40.4777 - 40.4777i) q^{13} +(-1.83032 - 4.18535i) q^{14} +(5.00116 + 63.8043i) q^{16} +(36.2735 - 36.2735i) q^{17} +(35.9029 - 91.7099i) q^{18} -56.8829 q^{19} -12.6985 q^{21} +(-27.8754 + 71.2046i) q^{22} +(-54.9839 + 54.9839i) q^{23} +(168.077 + 58.3288i) q^{24} +(-64.8739 - 148.346i) q^{26} +(-43.4795 - 43.4795i) q^{27} +(-0.505208 - 12.9106i) q^{28} +57.1173i q^{29} +190.845i q^{31} +(-52.6158 + 173.204i) q^{32} +(150.306 + 150.306i) q^{33} +(132.938 - 58.1357i) q^{34} +(189.122 - 204.526i) q^{36} +(50.4605 - 50.4605i) q^{37} +(-149.818 - 58.6513i) q^{38} -450.088 q^{39} -71.5197 q^{41} +(-33.4453 - 13.0933i) q^{42} +(-66.9381 + 66.9381i) q^{43} +(-146.836 + 158.796i) q^{44} +(-201.509 + 88.1229i) q^{46} +(-343.017 - 343.017i) q^{47} +(382.538 + 326.928i) q^{48} -340.392i q^{49} -403.339i q^{51} +(-17.9066 - 457.603i) q^{52} +(-240.148 - 240.148i) q^{53} +(-69.6848 - 159.347i) q^{54} +(11.9813 - 34.5247i) q^{56} +(-316.252 + 316.252i) q^{57} +(-58.8929 + 150.435i) q^{58} +738.207 q^{59} -187.952 q^{61} +(-196.777 + 502.645i) q^{62} +(-39.7656 + 39.7656i) q^{63} +(-317.167 + 401.932i) q^{64} +(240.897 + 550.855i) q^{66} +(576.434 + 576.434i) q^{67} +(410.074 - 16.0468i) q^{68} +611.387i q^{69} +157.380i q^{71} +(708.991 - 343.677i) q^{72} +(-180.613 - 180.613i) q^{73} +(184.932 - 80.8733i) q^{74} +(-334.114 - 308.950i) q^{76} +(30.8744 - 30.8744i) q^{77} +(-1185.44 - 464.080i) q^{78} +55.6778 q^{79} +456.687 q^{81} +(-188.368 - 73.7430i) q^{82} +(858.601 - 858.601i) q^{83} +(-74.5876 - 68.9700i) q^{84} +(-245.320 + 107.282i) q^{86} +(317.555 + 317.555i) q^{87} +(-550.468 + 266.835i) q^{88} -158.689i q^{89} +92.4525i q^{91} +(-621.596 + 24.3239i) q^{92} +(1061.04 + 1061.04i) q^{93} +(-549.756 - 1257.12i) q^{94} +(670.433 + 1255.49i) q^{96} +(1117.12 - 1117.12i) q^{97} +(350.973 - 896.521i) q^{98} +941.372 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 8 q^{6} + 12 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 + 8 * q^6 + 12 * q^8	$ 12 q + 6 q^{2} + 8 q^{6} + 12 q^{8} + 80 q^{12} - 116 q^{13} + 312 q^{16} + 332 q^{17} - 198 q^{18} - 144 q^{21} - 360 q^{22} - 164 q^{26} + 880 q^{28} + 376 q^{32} - 80 q^{33} + 460 q^{36} - 508 q^{37} - 1600 q^{38} - 656 q^{41} - 1160 q^{42} - 1432 q^{46} + 2720 q^{48} + 932 q^{52} + 644 q^{53} + 2048 q^{56} + 960 q^{57} - 1576 q^{58} - 896 q^{61} - 2440 q^{62} - 1680 q^{66} + 844 q^{68} + 3036 q^{72} - 1436 q^{73} + 800 q^{76} - 3120 q^{77} - 3720 q^{78} + 5988 q^{81} + 1352 q^{82} - 2552 q^{86} + 2400 q^{88} + 1840 q^{92} + 3280 q^{93} + 1088 q^{96} + 4772 q^{97} - 1698 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 + 8 * q^6 + 12 * q^8 + 80 * q^12 - 116 * q^13 + 312 * q^16 + 332 * q^17 - 198 * q^18 - 144 * q^21 - 360 * q^22 - 164 * q^26 + 880 * q^28 + 376 * q^32 - 80 * q^33 + 460 * q^36 - 508 * q^37 - 1600 * q^38 - 656 * q^41 - 1160 * q^42 - 1432 * q^46 + 2720 * q^48 + 932 * q^52 + 644 * q^53 + 2048 * q^56 + 960 * q^57 - 1576 * q^58 - 896 * q^61 - 2440 * q^62 - 1680 * q^66 + 844 * q^68 + 3036 * q^72 - 1436 * q^73 + 800 * q^76 - 3120 * q^77 - 3720 * q^78 + 5988 * q^81 + 1352 * q^82 - 2552 * q^86 + 2400 * q^88 + 1840 * q^92 + 3280 * q^93 + 1088 * q^96 + 4772 * q^97 - 1698 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	2.63379	+	1.03109i	0.931186	+	0.364544i
$2$	2.63379	+	1.03109i	0.931186	+	0.364544i
$3$	5.55970	−	5.55970i	1.06996	−	1.06996i	0.0726035	−	0.997361i	$-0.476869\pi$
$3$	5.55970	−	5.55970i	1.06996	−	1.06996i	0.997361	−	0.0726035i	$-0.0231308\pi$
$4$	5.87372	+	5.43134i	0.734215	+	0.678917i
$5$		0			0
$5$		0			0
$6$	20.3756	−	8.91056i	1.38639	−	0.606286i
$7$	−1.14202	−	1.14202i	−0.0616631	−	0.0616631i	0.675603	−	0.737266i	$-0.263883\pi$
$7$	−1.14202	−	1.14202i	−0.0616631	−	0.0616631i	−0.737266	+	0.675603i	$0.763883\pi$
$8$	9.86997	+	20.3613i	0.436195	+	0.899852i
$9$		−	34.8205i		−	1.28965i
$10$		0			0
$11$			27.0350i			0.741033i	0.928826	+	0.370516i	$0.120819\pi$
$11$			27.0350i			0.741033i	−0.928826	+	0.370516i	$0.879181\pi$
$12$	62.8527	−	2.45951i	1.51200	−	0.0591667i
$13$	−40.4777	−	40.4777i	−0.863577	−	0.863577i	0.128174	−	0.991752i	$-0.459088\pi$
$13$	−40.4777	−	40.4777i	−0.863577	−	0.863577i	−0.991752	+	0.128174i	$0.959088\pi$
$14$	−1.83032	−	4.18535i	−0.0349409	−	0.0798988i
$15$		0			0
$16$	5.00116	+	63.8043i	0.0781431	+	0.996942i
$17$	36.2735	−	36.2735i	0.517507	−	0.517507i	−0.399309	−	0.916816i	$-0.630750\pi$
$17$	36.2735	−	36.2735i	0.517507	−	0.517507i	0.916816	+	0.399309i	$0.130750\pi$
$18$	35.9029	−	91.7099i	0.470134	−	1.20090i
$19$	−56.8829			−0.686834			−0.343417	−	0.939183i	$-0.611584\pi$
$19$	−56.8829			−0.686834			−0.343417	+	0.939183i	$0.611584\pi$
$20$		0			0
$21$	−12.6985			−0.131955
$22$	−27.8754	+	71.2046i	−0.270139	+	0.690039i
$23$	−54.9839	+	54.9839i	−0.498475	+	0.498475i	−0.910963	−	0.412488i	$-0.864660\pi$
$23$	−54.9839	+	54.9839i	−0.498475	+	0.498475i	0.412488	+	0.910963i	$0.364660\pi$
$24$	168.077	+	58.3288i	1.42952	+	0.496096i
$25$		0			0
$26$	−64.8739	−	148.346i	−0.489339	−	1.11896i
$27$	−43.4795	−	43.4795i	−0.309912	−	0.309912i
$28$	−0.505208	−	12.9106i	−0.00340983	−	0.0871381i
$29$			57.1173i			0.365739i	0.983137	+	0.182869i	$0.0585385\pi$
$29$			57.1173i			0.365739i	−0.983137	+	0.182869i	$0.941461\pi$
$30$		0			0
$31$			190.845i			1.10570i	0.833281	+	0.552850i	$0.186460\pi$
$31$			190.845i			1.10570i	−0.833281	+	0.552850i	$0.813540\pi$
$32$	−52.6158	+	173.204i	−0.290664	+	0.956825i
$33$	150.306	+	150.306i	0.792878	+	0.792878i
$34$	132.938	−	58.1357i	0.670549	−	0.293241i
$35$		0			0
$36$	189.122	−	204.526i	0.875564	−	0.946878i
$37$	50.4605	−	50.4605i	0.224207	−	0.224207i	−0.586060	−	0.810267i	$-0.699322\pi$
$37$	50.4605	−	50.4605i	0.224207	−	0.224207i	0.810267	+	0.586060i	$0.199322\pi$
$38$	−149.818	−	58.6513i	−0.639570	−	0.250381i
$39$	−450.088			−1.84799
$40$		0			0
$41$	−71.5197			−0.272427			−0.136213	−	0.990680i	$-0.543493\pi$
$41$	−71.5197			−0.272427			−0.136213	+	0.990680i	$0.543493\pi$
$42$	−33.4453	−	13.0933i	−0.122874	−	0.0481033i
$43$	−66.9381	+	66.9381i	−0.237394	+	0.237394i	−0.815770	−	0.578376i	$-0.803687\pi$
$43$	−66.9381	+	66.9381i	−0.237394	+	0.237394i	0.578376	+	0.815770i	$0.303687\pi$
$44$	−146.836	+	158.796i	−0.503100	+	0.544077i
$45$		0			0
$46$	−201.509	+	88.1229i	−0.645889	+	0.282457i
$47$	−343.017	−	343.017i	−1.06456	−	1.06456i	−0.997767	−	0.0667913i	$-0.978724\pi$
$47$	−343.017	−	343.017i	−1.06456	−	1.06456i	−0.0667913	−	0.997767i	$-0.521276\pi$
$48$	382.538	+	326.928i	1.15030	+	0.983082i
$49$		−	340.392i		−	0.992395i
$50$		0			0
$51$		−	403.339i		−	1.10743i
$52$	−17.9066	−	457.603i	−0.0477539	−	1.22035i
$53$	−240.148	−	240.148i	−0.622394	−	0.622394i	0.323749	−	0.946143i	$-0.395057\pi$
$53$	−240.148	−	240.148i	−0.622394	−	0.622394i	−0.946143	+	0.323749i	$0.895057\pi$
$54$	−69.6848	−	159.347i	−0.175609	−	0.401563i
$55$		0			0
$56$	11.9813	−	34.5247i	0.0285905	−	0.0823848i
$57$	−316.252	+	316.252i	−0.734888	+	0.734888i
$58$	−58.8929	+	150.435i	−0.133328	+	0.340571i
$59$	738.207			1.62892			0.814461	−	0.580218i	$-0.197033\pi$
$59$	738.207			1.62892			0.814461	+	0.580218i	$0.197033\pi$
$60$		0			0
$61$	−187.952			−0.394506			−0.197253	−	0.980353i	$-0.563202\pi$
$61$	−187.952			−0.394506			−0.197253	+	0.980353i	$0.563202\pi$
$62$	−196.777	+	502.645i	−0.403077	+	1.02961i
$63$	−39.7656	+	39.7656i	−0.0795237	+	0.0795237i
$64$	−317.167	+	401.932i	−0.619467	+	0.785022i
$65$		0			0
$66$	240.897	+	550.855i	0.449278	+	1.02736i
$67$	576.434	+	576.434i	1.05108	+	1.05108i	0.998623	+	0.0524612i	$0.0167066\pi$
$67$	576.434	+	576.434i	1.05108	+	1.05108i	0.0524612	+	0.998623i	$0.483293\pi$
$68$	410.074	−	16.0468i	0.731305	−	0.0286170i
$69$			611.387i			1.06670i
$70$		0			0
$71$			157.380i			0.263064i	0.991312	+	0.131532i	$0.0419896\pi$
$71$			157.380i			0.263064i	−0.991312	+	0.131532i	$0.958010\pi$
$72$	708.991	−	343.677i	1.16049	−	0.562538i
$73$	−180.613	−	180.613i	−0.289577	−	0.289577i	0.547336	−	0.836913i	$-0.315642\pi$
$73$	−180.613	−	180.613i	−0.289577	−	0.289577i	−0.836913	+	0.547336i	$0.815642\pi$
$74$	184.932	−	80.8733i	0.290512	−	0.127045i
$75$		0			0
$76$	−334.114	−	308.950i	−0.504284	−	0.466303i
$77$	30.8744	−	30.8744i	0.0456944	−	0.0456944i
$78$	−1185.44	−	464.080i	−1.72083	−	0.673676i
$79$	55.6778			0.0792942			0.0396471	−	0.999214i	$-0.487377\pi$
$79$	55.6778			0.0792942			0.0396471	+	0.999214i	$0.487377\pi$
$80$		0			0
$81$	456.687			0.626457
$82$	−188.368	−	73.7430i	−0.253680	−	0.0993116i
$83$	858.601	−	858.601i	1.13547	−	1.13547i	0.146213	−	0.989253i	$-0.453292\pi$
$83$	858.601	−	858.601i	1.13547	−	1.13547i	0.989253	−	0.146213i	$-0.0467085\pi$
$84$	−74.5876	−	68.9700i	−0.0968831	−	0.0895863i
$85$		0			0
$86$	−245.320	+	107.282i	−0.307599	+	0.134518i
$87$	317.555	+	317.555i	0.391327	+	0.391327i
$88$	−550.468	+	266.835i	−0.666820	+	0.323235i
$89$		−	158.689i		−	0.189000i	−0.995525	−	0.0944998i	$-0.969875\pi$
$89$		−	158.689i		−	0.189000i	0.995525	−	0.0944998i	$-0.0301252\pi$
$90$		0			0
$91$			92.4525i			0.106502i
$92$	−621.596	+	24.3239i	−0.704411	+	0.0275646i
$93$	1061.04	+	1061.04i	1.18306	+	1.18306i
$94$	−549.756	−	1257.12i	−0.603223	−	1.37938i
$95$		0			0
$96$	670.433	+	1255.49i	0.712769	+	1.33477i
$97$	1117.12	−	1117.12i	1.16935	−	1.16935i	0.186986	−	0.982363i	$-0.440128\pi$
$97$	1117.12	−	1117.12i	1.16935	−	1.16935i	0.982363	−	0.186986i	$-0.0598720\pi$
$98$	350.973	−	896.521i	0.361772	−	0.924105i
$99$	941.372			0.955671
$100$		0			0
$101$	787.780			0.776109			0.388055	−	0.921636i	$-0.373147\pi$
$101$	787.780			0.776109			0.388055	+	0.921636i	$0.373147\pi$
$102$	415.878	−	1062.31i	0.403706	−	1.03122i
$103$	−522.455	+	522.455i	−0.499796	+	0.499796i	−0.911374	−	0.411578i	$-0.864978\pi$
$103$	−522.455	+	522.455i	−0.499796	+	0.499796i	0.411578	+	0.911374i	$0.364978\pi$
$104$	424.666	−	1223.69i	0.400403	−	1.15378i
$105$		0			0
$106$	−384.887	−	880.114i	−0.352674	−	0.806455i
$107$	615.276	+	615.276i	0.555897	+	0.555897i	0.928137	−	0.372240i	$-0.121410\pi$
$107$	615.276	+	615.276i	0.555897	+	0.555897i	−0.372240	+	0.928137i	$0.621410\pi$
$108$	−19.2346	−	491.538i	−0.0171375	−	0.437947i
$109$			398.877i			0.350509i	0.984523	+	0.175254i	$0.0560748\pi$
$109$			398.877i			0.350509i	−0.984523	+	0.175254i	$0.943925\pi$
$110$		0			0
$111$		−	561.091i		−	0.479787i
$112$	67.1542	−	78.5770i	0.0566560	−	0.0662931i
$113$	−692.888	−	692.888i	−0.576826	−	0.576826i	0.357201	−	0.934028i	$-0.383731\pi$
$113$	−692.888	−	692.888i	−0.576826	−	0.576826i	−0.934028	+	0.357201i	$0.883731\pi$
$114$	−1159.03	+	506.859i	−0.952216	+	0.416418i
$115$		0			0
$116$	−310.223	+	335.491i	−0.248306	+	0.268531i
$117$	−1409.45	+	1409.45i	−1.11371	+	1.11371i
$118$	1944.28	+	761.156i	1.51683	+	0.593814i
$119$	−82.8499			−0.0638221
$120$		0			0
$121$	600.109			0.450871
$122$	−495.028	−	193.795i	−0.367358	−	0.143815i
$123$	−397.628	+	397.628i	−0.291487	+	0.291487i
$124$	−1036.54	+	1120.97i	−0.750679	+	0.811821i
$125$		0			0
$126$	−145.736	+	63.7325i	−0.103041	+	0.0450614i
$127$	−498.629	−	498.629i	−0.348395	−	0.348395i	0.511116	−	0.859512i	$-0.329232\pi$
$127$	−498.629	−	498.629i	−0.348395	−	0.348395i	−0.859512	+	0.511116i	$0.829232\pi$
$128$	−1249.78	+	731.577i	−0.863015	+	0.505179i
$129$			744.311i			0.508007i
$130$		0			0
$131$		−	1747.61i		−	1.16557i	−0.812626	−	0.582785i	$-0.801963\pi$
$131$		−	1747.61i		−	1.16557i	0.812626	−	0.582785i	$-0.198037\pi$
$132$	66.4929	+	1699.22i	0.0438444	+	1.12044i
$133$	64.9613	+	64.9613i	0.0423523	+	0.0423523i
$134$	923.854	+	2112.56i	0.595588	+	1.36192i
$135$		0			0
$136$	1096.59	+	380.558i	0.691413	+	0.239945i
$137$	−124.289	+	124.289i	−0.0775092	+	0.0775092i	−0.744799	−	0.667289i	$-0.767454\pi$
$137$	−124.289	+	124.289i	−0.0775092	+	0.0775092i	0.667289	+	0.744799i	$0.267454\pi$
$138$	−630.394	+	1610.27i	−0.388860	+	0.993297i
$139$	9.83873			0.00600367			0.00300184	−	0.999995i	$-0.499044\pi$
$139$	9.83873			0.00600367			0.00300184	+	0.999995i	$0.499044\pi$
$140$		0			0
$141$	−3814.15			−2.27808
$142$	−162.272	+	414.506i	−0.0958985	+	0.244962i
$143$	1094.32	−	1094.32i	0.639939	−	0.639939i
$144$	2221.70	−	174.143i	1.28570	−	0.100777i
$145$		0			0
$146$	−289.469	−	661.925i	−0.164087	−	0.375214i
$147$	−1892.47	−	1892.47i	−1.06183	−	1.06183i
$148$	570.459	−	22.3229i	0.316834	−	0.0123982i
$149$		−	2840.41i		−	1.56171i	−0.624711	−	0.780856i	$-0.714783\pi$
$149$		−	2840.41i		−	1.56171i	0.624711	−	0.780856i	$-0.285217\pi$
$150$		0			0
$151$			2913.54i			1.57020i	0.619368	+	0.785101i	$0.287389\pi$
$151$			2913.54i			1.57020i	−0.619368	+	0.785101i	$0.712611\pi$
$152$	−561.433	−	1158.21i	−0.299594	−	0.618049i
$153$	−1263.06	−	1263.06i	−0.667401	−	0.667401i
$154$	113.151	−	49.4826i	0.0592076	−	0.0258923i
$155$		0			0
$156$	−2643.69	−	2444.58i	−1.35682	−	1.25463i
$157$	−1572.29	+	1572.29i	−0.799251	+	0.799251i	−0.982977	−	0.183727i	$-0.941184\pi$
$157$	−1572.29	+	1572.29i	−0.799251	+	0.799251i	0.183727	+	0.982977i	$0.441184\pi$
$158$	146.644	+	57.4087i	0.0738377	+	0.0289063i
$159$	−2670.30			−1.33188
$160$		0			0
$161$	125.585			0.0614751
$162$	1202.82	+	470.884i	0.583348	+	0.228371i
$163$	−1457.19	+	1457.19i	−0.700222	+	0.700222i	−0.964458	−	0.264236i	$-0.914880\pi$
$163$	−1457.19	+	1457.19i	−0.700222	+	0.700222i	0.264236	+	0.964458i	$0.414880\pi$
$164$	−420.087	−	388.448i	−0.200020	−	0.184955i
$165$		0			0
$166$	3146.67	−	1376.08i	1.47126	−	0.643402i
$167$	−801.239	−	801.239i	−0.371268	−	0.371268i	0.496671	−	0.867939i	$-0.334556\pi$
$167$	−801.239	−	801.239i	−0.371268	−	0.371268i	−0.867939	+	0.496671i	$0.834556\pi$
$168$	−125.334	−	258.559i	−0.0575580	−	0.118740i
$169$			1079.90i			0.491532i
$170$		0			0
$171$			1980.69i			0.885773i
$172$	−756.739	+	29.6122i	−0.335470	+	0.0131274i
$173$	1180.59	+	1180.59i	0.518837	+	0.518837i	0.917220	−	0.398382i	$-0.130428\pi$
$173$	1180.59	+	1180.59i	0.518837	+	0.518837i	−0.398382	+	0.917220i	$0.630428\pi$
$174$	508.947	+	1163.80i	0.221742	+	0.507055i
$175$		0			0
$176$	−1724.95	+	135.206i	−0.738767	+	0.0579066i
$177$	4104.21	−	4104.21i	1.74289	−	1.74289i
$178$	163.622	−	417.953i	0.0688987	−	0.175994i
$179$	−3724.41			−1.55517			−0.777585	−	0.628778i	$-0.783555\pi$
$179$	−3724.41			−1.55517			−0.777585	+	0.628778i	$0.783555\pi$
$180$		0			0
$181$	545.856			0.224161			0.112081	−	0.993699i	$-0.464249\pi$
$181$	545.856			0.224161			0.112081	+	0.993699i	$0.464249\pi$
$182$	−95.3266	+	243.501i	−0.0388246	+	0.0991729i
$183$	−1044.96	+	1044.96i	−0.422107	+	0.422107i
$184$	−1662.23	−	576.855i	−0.665986	−	0.231121i
$185$		0			0
$186$	1700.53	+	3888.58i	0.670371	+	1.53293i
$187$	980.654	+	980.654i	0.383489	+	0.383489i
$188$	−151.745	−	3877.83i	−0.0588677	−	1.50436i
$189$			99.3087i			0.0382203i
$190$		0			0
$191$		−	3668.60i		−	1.38980i	−0.719109	−	0.694898i	$-0.755450\pi$
$191$		−	3668.60i		−	1.38980i	0.719109	−	0.694898i	$-0.244550\pi$
$192$	471.264	+	3997.97i	0.177138	+	1.50275i
$193$	715.028	+	715.028i	0.266678	+	0.266678i	0.827760	−	0.561082i	$-0.189615\pi$
$193$	715.028	+	715.028i	0.266678	+	0.266678i	−0.561082	+	0.827760i	$0.689615\pi$
$194$	4094.13	−	1790.42i	1.51516	−	0.662602i
$195$		0			0
$196$	1848.78	−	1999.36i	0.673754	−	0.728631i
$197$	−272.976	+	272.976i	−0.0987246	+	0.0987246i	−0.754744	−	0.656019i	$-0.772239\pi$
$197$	−272.976	+	272.976i	−0.0987246	+	0.0987246i	0.656019	+	0.754744i	$0.272239\pi$
$198$	2479.38	+	970.636i	0.889907	+	0.348384i
$199$	4554.16			1.62229			0.811146	−	0.584844i	$-0.198844\pi$
$199$	4554.16			1.62229			0.811146	+	0.584844i	$0.198844\pi$
$200$		0			0
$201$	6409.60			2.24925
$202$	2074.85	+	812.269i	0.722702	+	0.282926i
$203$	65.2289	−	65.2289i	0.0225526	−	0.0225526i
$204$	2190.67	−	2369.10i	0.751851	−	0.813090i
$205$		0			0
$206$	−1914.73	+	837.341i	−0.647601	+	0.283205i
$207$	1914.56	+	1914.56i	0.642857	+	0.642857i
$208$	2380.22	−	2785.09i	0.793454	−	0.928419i
$209$		−	1537.83i		−	0.508966i
$210$		0			0
$211$			4250.89i			1.38694i	0.720487	+	0.693468i	$0.243918\pi$
$211$			4250.89i			1.38694i	−0.720487	+	0.693468i	$0.756082\pi$
$212$	−106.237	−	2714.89i	−0.0344170	−	0.879525i
$213$	874.984	+	874.984i	0.281469	+	0.281469i
$214$	986.105	+	2254.91i	0.314994	+	0.720292i
$215$		0			0
$216$	456.159	−	1314.44i	0.143693	−	0.414058i
$217$	217.948	−	217.948i	0.0681809	−	0.0681809i
$218$	−411.276	+	1050.56i	−0.127776	+	0.326389i
$219$	−2008.31			−0.619675
$220$		0			0
$221$	−2936.54			−0.893814
$222$	578.533	−	1477.80i	0.174904	−	0.446771i
$223$	258.746	−	258.746i	0.0776991	−	0.0776991i	−0.667189	−	0.744888i	$-0.732503\pi$
$223$	258.746	−	258.746i	0.0776991	−	0.0776991i	0.744888	+	0.667189i	$0.232503\pi$
$224$	257.890	−	137.714i	0.0769241	−	0.0410776i
$225$		0			0
$226$	−1110.49	−	2539.35i	−0.326854	−	0.747412i
$227$	−2127.58	−	2127.58i	−0.622080	−	0.622080i	0.323983	−	0.946063i	$-0.394978\pi$
$227$	−2127.58	−	2127.58i	−0.622080	−	0.622080i	−0.946063	+	0.323983i	$0.894978\pi$
$228$	−3575.25	+	139.904i	−1.03849	+	0.0406377i
$229$			4654.98i			1.34328i	0.740880	+	0.671638i	$0.234409\pi$
$229$			4654.98i			1.34328i	−0.740880	+	0.671638i	$0.765591\pi$
$230$		0			0
$231$		−	343.305i		−	0.0977827i
$232$	−1162.98	+	563.746i	−0.329111	+	0.159533i
$233$	−3392.53	−	3392.53i	−0.953871	−	0.953871i	0.0451108	−	0.998982i	$-0.485636\pi$
$233$	−3392.53	−	3392.53i	−0.953871	−	0.953871i	−0.998982	+	0.0451108i	$0.985636\pi$
$234$	−5165.48	+	2258.94i	−1.44307	+	0.631075i
$235$		0			0
$236$	4336.02	+	4009.45i	1.19598	+	1.10590i
$237$	309.552	−	309.552i	0.0848420	−	0.0848420i
$238$	−218.209	−	85.4254i	−0.0594303	−	0.0232660i
$239$	1434.32			0.388195			0.194098	−	0.980982i	$-0.437822\pi$
$239$	1434.32			0.388195			0.194098	+	0.980982i	$0.437822\pi$
$240$		0			0
$241$	−6438.62			−1.72094			−0.860472	−	0.509497i	$-0.829831\pi$
$241$	−6438.62			−1.72094			−0.860472	+	0.509497i	$0.829831\pi$
$242$	1580.56	+	618.764i	0.419845	+	0.164362i
$243$	3712.99	−	3712.99i	0.980199	−	0.980199i
$244$	−1103.98	−	1020.83i	−0.289652	−	0.267837i
$245$		0			0
$246$	−1457.26	+	637.280i	−0.377689	+	0.165169i
$247$	2302.49	+	2302.49i	0.593134	+	0.593134i
$248$	−3885.85	+	1883.63i	−0.994966	+	0.482301i
$249$		−	9547.12i		−	2.42982i
$250$		0			0
$251$			1877.58i			0.472159i	0.971734	+	0.236079i	$0.0758626\pi$
$251$			1877.58i			0.472159i	−0.971734	+	0.236079i	$0.924137\pi$
$252$	−449.552	+	17.5916i	−0.112377	+	0.00439748i
$253$	−1486.49	−	1486.49i	−0.369386	−	0.369386i
$254$	−799.156	−	1827.42i	−0.197415	−	0.451426i
$255$		0			0
$256$	−4045.98	+	638.191i	−0.987787	+	0.155808i
$257$	−1940.33	+	1940.33i	−0.470952	+	0.470952i	−0.902223	−	0.431270i	$-0.858066\pi$
$257$	−1940.33	+	1940.33i	−0.470952	+	0.470952i	0.431270	+	0.902223i	$0.358066\pi$
$258$	−767.449	+	1960.36i	−0.185191	+	0.473049i
$259$	−115.254			−0.0276506
$260$		0			0
$261$	1988.85			0.471674
$262$	1801.94	−	4602.85i	0.424902	−	1.08536i
$263$	1004.94	−	1004.94i	0.235616	−	0.235616i	−0.579416	−	0.815032i	$-0.696719\pi$
$263$	1004.94	−	1004.94i	0.235616	−	0.235616i	0.815032	+	0.579416i	$0.196719\pi$
$264$	−1576.92	+	4543.96i	−0.367623	+	1.05932i
$265$		0			0
$266$	104.114	+	238.075i	0.0239986	+	0.0548772i
$267$	−882.261	−	882.261i	−0.202223	−	0.202223i
$268$	255.004	+	6516.62i	0.0581227	+	1.48532i
$269$			6594.94i			1.49480i	0.664376	+	0.747398i	$0.268697\pi$
$269$			6594.94i			1.49480i	−0.664376	+	0.747398i	$0.731303\pi$
$270$		0			0
$271$		−	4781.49i		−	1.07179i	−0.844285	−	0.535895i	$-0.819974\pi$
$271$		−	4781.49i		−	1.07179i	0.844285	−	0.535895i	$-0.180026\pi$
$272$	2495.81	+	2133.00i	0.556364	+	0.475485i
$273$	514.008	+	514.008i	0.113953	+	0.113953i
$274$	−455.506	+	199.199i	−0.100431	+	0.0439200i
$275$		0			0
$276$	−3320.65	+	3591.12i	−0.724202	+	0.783188i
$277$	−5490.27	+	5490.27i	−1.19090	+	1.19090i	−0.214082	+	0.976816i	$0.568676\pi$
$277$	−5490.27	+	5490.27i	−1.19090	+	1.19090i	−0.976816	+	0.214082i	$0.931324\pi$
$278$	25.9132	+	10.1446i	0.00559053	+	0.00218860i
$279$	6645.30			1.42596
$280$		0			0
$281$	3046.29			0.646714			0.323357	−	0.946277i	$-0.395189\pi$
$281$	3046.29			0.646714			0.323357	+	0.946277i	$0.395189\pi$
$282$	−10045.7	−	3932.72i	−2.12132	−	0.830461i
$283$	−5858.21	+	5858.21i	−1.23051	+	1.23051i	−0.266743	+	0.963768i	$0.585947\pi$
$283$	−5858.21	+	5858.21i	−1.23051	+	1.23051i	−0.963768	+	0.266743i	$0.914053\pi$
$284$	−854.783	+	924.405i	−0.178599	+	0.193146i
$285$		0			0
$286$	4010.53	−	1753.87i	0.829188	−	0.362616i
$287$	81.6767	+	81.6767i	0.0167987	+	0.0167987i
$288$	6031.04	+	1832.11i	1.23397	+	0.374854i
$289$			2281.47i			0.464374i
$290$		0			0
$291$		−	12421.8i		−	2.50232i
$292$	−79.9000	−	2041.84i	−0.0160130	−	0.409211i
$293$	5371.12	+	5371.12i	1.07094	+	1.07094i	0.997284	+	0.0736515i	$0.0234653\pi$
$293$	5371.12	+	5371.12i	1.07094	+	1.07094i	0.0736515	+	0.997284i	$0.476535\pi$
$294$	−3033.08	−	6935.69i	−0.601676	−	1.37584i
$295$		0			0
$296$	1525.49	+	529.399i	0.299551	+	0.103955i
$297$	1175.47	−	1175.47i	0.229655	−	0.229655i
$298$	2928.71	−	7481.04i	0.569314	−	1.45425i
$299$	4451.25			0.860944
$300$		0			0
$301$	152.889			0.0292770
$302$	−3004.11	+	7673.66i	−0.572408	+	1.46215i
$303$	4379.82	−	4379.82i	0.830409	−	0.830409i
$304$	−284.481	−	3629.38i	−0.0536713	−	0.684734i
$305$		0			0
$306$	−2024.31	−	4628.96i	−0.378177	−	0.864772i
$307$	1464.75	+	1464.75i	0.272306	+	0.272306i	0.830028	−	0.557722i	$-0.188324\pi$
$307$	1464.75	+	1464.75i	0.272306	+	0.272306i	−0.557722	+	0.830028i	$0.688324\pi$
$308$	349.037	−	13.6583i	0.0645722	−	0.00252680i
$309$			5809.38i			1.06953i
$310$		0			0
$311$			1381.23i			0.251840i	0.992040	+	0.125920i	$0.0401882\pi$
$311$			1381.23i			0.251840i	−0.992040	+	0.125920i	$0.959812\pi$
$312$	−4442.36	−	9164.39i	−0.806086	−	1.66292i
$313$	1989.95	+	1989.95i	0.359356	+	0.359356i	0.863575	−	0.504220i	$-0.168220\pi$
$313$	1989.95	+	1989.95i	0.359356	+	0.359356i	−0.504220	+	0.863575i	$0.668220\pi$
$314$	−5762.25	+	2519.92i	−1.03561	+	0.452889i
$315$		0			0
$316$	327.036	+	302.405i	0.0582190	+	0.0538342i
$317$	2078.83	−	2078.83i	0.368325	−	0.368325i	−0.498541	−	0.866866i	$-0.666131\pi$
$317$	2078.83	−	2078.83i	0.368325	−	0.368325i	0.866866	+	0.498541i	$0.166131\pi$
$318$	−7033.02	−	2753.31i	−1.24023	−	0.485529i
$319$	−1544.17			−0.271024
$320$		0			0
$321$	6841.49			1.18958
$322$	330.765	+	129.489i	0.0572447	+	0.0224104i
$323$	−2063.34	+	2063.34i	−0.355441	+	0.355441i
$324$	2682.45	+	2480.42i	0.459954	+	0.425312i
$325$		0			0
$326$	−5340.43	+	2335.45i	−0.907298	+	0.396775i
$327$	2217.63	+	2217.63i	0.375032	+	0.375032i
$328$	−705.898	−	1456.24i	−0.118831	−	0.245144i
$329$			783.463i			0.131288i
$330$		0			0
$331$			8633.95i			1.43373i	0.697211	+	0.716866i	$0.254424\pi$
$331$			8633.95i			1.43373i	−0.697211	+	0.716866i	$0.745576\pi$
$332$	9706.53	−	379.830i	1.60456	−	0.0627888i
$333$	−1757.06	−	1757.06i	−0.289148	−	0.289148i
$334$	−1284.15	−	2936.44i	−0.210376	−	0.481063i
$335$		0			0
$336$	−63.5074	−	810.221i	−0.0103113	−	0.131551i
$337$	3115.08	−	3115.08i	0.503528	−	0.503528i	−0.409004	−	0.912532i	$-0.634124\pi$
$337$	3115.08	−	3115.08i	0.503528	−	0.503528i	0.912532	+	0.409004i	$0.134124\pi$
$338$	−1113.47	+	2844.22i	−0.179185	+	0.457708i
$339$	−7704.49			−1.23437
$340$		0			0
$341$	−5159.48			−0.819360
$342$	−2042.26	+	5216.73i	−0.322904	+	0.824820i
$343$	−780.445	+	780.445i	−0.122857	+	0.122857i
$344$	−2023.62	−	702.271i	−0.317170	−	0.110070i
$345$		0			0
$346$	1892.14	+	4326.73i	0.293995	+	0.672273i
$347$	−646.980	−	646.980i	−0.100091	−	0.100091i	0.655288	−	0.755379i	$-0.272547\pi$
$347$	−646.980	−	646.980i	−0.100091	−	0.100091i	−0.755379	+	0.655288i	$0.772547\pi$
$348$	140.481	+	3589.98i	0.0216395	+	0.552997i
$349$		−	9611.76i		−	1.47423i	−0.675768	−	0.737114i	$-0.736188\pi$
$349$		−	9611.76i		−	1.47423i	0.675768	−	0.737114i	$-0.263812\pi$
$350$		0			0
$351$			3519.90i			0.535267i
$352$	−4682.57	−	1422.47i	−0.709039	−	0.215391i
$353$	5085.16	+	5085.16i	0.766730	+	0.766730i	0.977529	−	0.210799i	$-0.0676066\pi$
$353$	5085.16	+	5085.16i	0.766730	+	0.766730i	−0.210799	+	0.977529i	$0.567607\pi$
$354$	15041.4	−	6577.84i	2.25831	−	0.987593i
$355$		0			0
$356$	861.892	−	932.093i	0.128315	−	0.138766i
$357$	−460.620	+	460.620i	−0.0682874	+	0.0682874i
$358$	−9809.32	−	3840.19i	−1.44815	−	0.566928i
$359$	−5598.06			−0.822992			−0.411496	−	0.911411i	$-0.634994\pi$
$359$	−5598.06			−0.822992			−0.411496	+	0.911411i	$0.634994\pi$
$360$		0			0
$361$	−3623.33			−0.528259
$362$	1437.67	+	562.825i	0.208736	+	0.0817167i
$363$	3336.42	−	3336.42i	0.482416	−	0.482416i
$364$	−502.141	+	543.040i	−0.0723059	+	0.0781952i
$365$		0			0
$366$	−3829.65	+	1674.76i	−0.546937	+	0.239183i
$367$	−3676.76	−	3676.76i	−0.522957	−	0.522957i	0.395506	−	0.918463i	$-0.370569\pi$
$367$	−3676.76	−	3676.76i	−0.522957	−	0.522957i	−0.918463	+	0.395506i	$0.870569\pi$
$368$	−3783.19	−	3233.22i	−0.535903	−	0.457999i
$369$			2490.35i			0.351335i
$370$		0			0
$371$			548.506i			0.0767575i
$372$	469.385	+	11995.1i	0.0654206	+	1.67182i
$373$	−6801.10	−	6801.10i	−0.944096	−	0.944096i	0.0544219	−	0.998518i	$-0.482668\pi$
$373$	−6801.10	−	6801.10i	−0.944096	−	0.944096i	−0.998518	+	0.0544219i	$0.982668\pi$
$374$	1571.70	+	3593.98i	0.217301	+	0.496899i
$375$		0			0
$376$	3598.72	−	10369.9i	0.493590	−	1.42230i
$377$	2311.98	−	2311.98i	0.315844	−	0.315844i
$378$	−102.396	+	261.558i	−0.0139330	+	0.0355902i
$379$	9992.48			1.35430			0.677150	−	0.735845i	$-0.263215\pi$
$379$	9992.48			1.35430			0.677150	+	0.735845i	$0.263215\pi$
$380$		0			0
$381$	−5544.46			−0.745541
$382$	3782.65	−	9662.34i	0.506642	−	1.29416i
$383$	−1910.84	+	1910.84i	−0.254932	+	0.254932i	−0.822989	−	0.568057i	$-0.807695\pi$
$383$	−1910.84	+	1910.84i	−0.254932	+	0.254932i	0.568057	+	0.822989i	$0.307695\pi$
$384$	−2881.05	+	11015.7i	−0.382872	+	1.46392i
$385$		0			0
$386$	1145.98	+	2620.49i	0.151111	+	0.345543i
$387$	2330.82	+	2330.82i	0.306155	+	0.306155i
$388$	12629.2	−	494.196i	1.65244	−	0.0646624i
$389$		−	152.974i		−	0.0199385i	−0.999950	−	0.00996927i	$-0.996827\pi$
$389$		−	152.974i		−	0.0199385i	0.999950	−	0.00996927i	$-0.00317337\pi$
$390$		0			0
$391$			3988.91i			0.515929i
$392$	6930.82	−	3359.66i	0.893009	−	0.432878i
$393$	−9716.21	−	9716.21i	−1.24712	−	1.24712i
$394$	−1000.42	+	437.500i	−0.127920	+	0.0559415i
$395$		0			0
$396$	5529.35	+	5112.91i	0.701668	+	0.648821i
$397$	−3823.37	+	3823.37i	−0.483349	+	0.483349i	−0.906199	−	0.422850i	$-0.861030\pi$
$397$	−3823.37	+	3823.37i	−0.483349	+	0.483349i	0.422850	+	0.906199i	$0.361030\pi$
$398$	11994.7	+	4695.74i	1.51065	+	0.591397i
$399$	722.330			0.0906309
$400$		0			0
$401$	10939.9			1.36238			0.681190	−	0.732106i	$-0.261463\pi$
$401$	10939.9			1.36238			0.681190	+	0.732106i	$0.261463\pi$
$402$	16881.6	+	6608.85i	2.09447	+	0.819949i
$403$	7724.96	−	7724.96i	0.954858	−	0.954858i
$404$	4627.20	+	4278.70i	0.569831	+	0.526914i
$405$		0			0
$406$	239.056	−	104.543i	0.0292221	−	0.0127792i
$407$	1364.20	+	1364.20i	0.166145	+	0.166145i
$408$	8212.52	−	3980.95i	0.996521	−	0.483055i
$409$		−	2982.65i		−	0.360593i	−0.983612	−	0.180296i	$-0.942294\pi$
$409$		−	2982.65i		−	0.360593i	0.983612	−	0.180296i	$-0.0577057\pi$
$410$		0			0
$411$			1382.02i			0.165864i
$412$	−5906.38	+	231.125i	−0.706278	+	0.0276376i
$413$	−843.045	−	843.045i	−0.100444	−	0.100444i
$414$	3068.48	+	7016.65i	0.364270	+	0.832970i
$415$		0			0
$416$	9140.67	−	4881.13i	1.07730	−	0.575282i
$417$	54.7004	−	54.7004i	0.00642371	−	0.00642371i
$418$	1585.64	−	4050.32i	0.185541	−	0.473942i
$419$	−2828.22			−0.329755			−0.164878	−	0.986314i	$-0.552723\pi$
$419$	−2828.22			−0.329755			−0.164878	+	0.986314i	$0.552723\pi$
$420$		0			0
$421$	739.946			0.0856597			0.0428299	−	0.999082i	$-0.486363\pi$
$421$	739.946			0.0856597			0.0428299	+	0.999082i	$0.486363\pi$
$422$	−4383.04	+	11196.0i	−0.505600	+	1.29150i
$423$	−11944.0	+	11944.0i	−1.37290	+	1.37290i
$424$	2519.48	−	7259.99i	0.288577	−	0.831548i
$425$		0			0
$426$	1402.34	+	3206.71i	0.159492	+	0.364708i
$427$	214.645	+	214.645i	0.0243265	+	0.0243265i
$428$	272.187	+	6955.73i	0.0307399	+	0.785555i
$429$		−	12168.1i		−	1.36942i
$430$		0			0
$431$		−	7074.45i		−	0.790636i	−0.918544	−	0.395318i	$-0.870634\pi$
$431$		−	7074.45i		−	0.790636i	0.918544	−	0.395318i	$-0.129366\pi$
$432$	2556.73	−	2991.63i	0.284747	−	0.333182i
$433$	−2645.06	−	2645.06i	−0.293564	−	0.293564i	0.544922	−	0.838487i	$-0.316559\pi$
$433$	−2645.06	−	2645.06i	−0.293564	−	0.293564i	−0.838487	+	0.544922i	$0.816559\pi$
$434$	798.752	−	349.306i	0.0883441	−	0.0386341i
$435$		0			0
$436$	−2166.43	+	2342.89i	−0.237966	+	0.257349i
$437$	3127.64	−	3127.64i	0.342370	−	0.342370i
$438$	−5289.46	−	2070.74i	−0.577033	−	0.225899i
$439$	−12903.4			−1.40284			−0.701419	−	0.712750i	$-0.747450\pi$
$439$	−12903.4			−1.40284			−0.701419	+	0.712750i	$0.747450\pi$
$440$		0			0
$441$	−11852.6			−1.27984
$442$	−7734.23	−	3027.83i	−0.832307	−	0.325835i
$443$	−2108.72	+	2108.72i	−0.226159	+	0.226159i	−0.811086	−	0.584927i	$-0.801123\pi$
$443$	−2108.72	+	2108.72i	−0.226159	+	0.226159i	0.584927	+	0.811086i	$0.301123\pi$
$444$	3047.47	−	3295.69i	0.325736	−	0.352267i
$445$		0			0
$446$	948.272	−	414.693i	0.100677	−	0.0440275i
$447$	−15791.8	−	15791.8i	−1.67098	−	1.67098i
$448$	821.223	−	96.8022i	0.0866052	−	0.0102087i
$449$		−	136.127i		−	0.0143079i	−0.999974	−	0.00715394i	$-0.997723\pi$
$449$		−	136.127i		−	0.0143079i	0.999974	−	0.00715394i	$-0.00227719\pi$
$450$		0			0
$451$		−	1933.53i		−	0.201877i
$452$	−306.521	−	7833.13i	−0.0318972	−	0.815132i
$453$	16198.4	+	16198.4i	1.68006	+	1.68006i
$454$	−3409.88	−	7797.31i	−0.352497	−	0.806048i
$455$		0			0
$456$	−9560.71	−	3317.91i	−0.981845	−	0.340736i
$457$	6660.47	−	6660.47i	0.681759	−	0.681759i	−0.278638	−	0.960396i	$-0.589883\pi$
$457$	6660.47	−	6660.47i	0.681759	−	0.681759i	0.960396	+	0.278638i	$0.0898828\pi$
$458$	−4799.69	+	12260.3i	−0.489683	+	1.25084i
$459$	−3154.31			−0.320764
$460$		0			0
$461$	9556.54			0.965493			0.482747	−	0.875760i	$-0.339639\pi$
$461$	9556.54			0.965493			0.482747	+	0.875760i	$0.339639\pi$
$462$	353.977	−	904.194i	0.0356461	−	0.0910539i
$463$	914.613	−	914.613i	0.0918049	−	0.0918049i	−0.659713	−	0.751518i	$-0.729322\pi$
$463$	914.613	−	914.613i	0.0918049	−	0.0918049i	0.751518	+	0.659713i	$0.229322\pi$
$464$	−3644.33	+	285.653i	−0.364620	+	0.0285799i
$465$		0			0
$466$	−5437.22	−	12433.2i	−0.540503	−	1.23596i
$467$	541.819	+	541.819i	0.0536882	+	0.0536882i	0.733441	−	0.679753i	$-0.237913\pi$
$467$	541.819	+	541.819i	0.0536882	+	0.0536882i	−0.679753	+	0.733441i	$0.737913\pi$
$468$	−15934.0	+	623.518i	−1.57382	+	0.0615857i
$469$		−	1316.59i		−	0.129626i
$470$		0			0
$471$			17482.9i			1.71034i
$472$	7286.09	+	15030.9i	0.710528	+	1.46579i
$473$	−1809.67	−	1809.67i	−0.175917	−	0.175917i
$474$	1134.47	−	496.120i	0.109932	−	0.0480750i
$475$		0			0
$476$	−486.637	−	449.986i	−0.0468592	−	0.0433299i
$477$	−8362.07	+	8362.07i	−0.802669	+	0.802669i
$478$	3777.71	+	1478.91i	0.361482	+	0.141514i
$479$	−19357.9			−1.84652			−0.923260	−	0.384176i	$-0.874486\pi$
$479$	−19357.9			−1.84652			−0.923260	+	0.384176i	$0.874486\pi$
$480$		0			0
$481$	−4085.06			−0.387240
$482$	−16958.0	−	6638.77i	−1.60252	−	0.627361i
$483$	698.215	−	698.215i	0.0657761	−	0.0657761i
$484$	3524.87	+	3259.39i	0.331036	+	0.306104i
$485$		0			0
$486$	13607.7	−	5950.83i	1.27007	−	0.555422i
$487$	141.166	+	141.166i	0.0131352	+	0.0131352i	0.713644	−	0.700509i	$-0.247044\pi$
$487$	141.166	+	141.166i	0.0131352	+	0.0131352i	−0.700509	+	0.713644i	$0.747044\pi$
$488$	−1855.09	−	3826.96i	−0.172082	−	0.354997i
$489$			16203.1i			1.49842i
$490$		0			0
$491$		−	929.849i		−	0.0854654i	−0.999087	−	0.0427327i	$-0.986394\pi$
$491$		−	929.849i		−	0.0854654i	0.999087	−	0.0427327i	$-0.0136064\pi$
$492$	−4495.21	+	175.904i	−0.411910	+	0.0161186i
$493$	2071.84	+	2071.84i	0.189272	+	0.189272i
$494$	3690.22	+	8438.36i	0.336095	+	0.768542i
$495$		0			0
$496$	−12176.7	+	954.444i	−1.10232	+	0.0864028i
$497$	179.730	−	179.730i	0.0162213	−	0.0162213i
$498$	9843.91	−	25145.1i	0.885776	−	2.26261i
$499$	13526.6			1.21349			0.606747	−	0.794895i	$-0.292474\pi$
$499$	13526.6			1.21349			0.606747	+	0.794895i	$0.292474\pi$
$500$		0			0
$501$	−8909.29			−0.794487
$502$	−1935.95	+	4945.16i	−0.172123	+	0.439668i
$503$	4770.81	−	4770.81i	0.422902	−	0.422902i	−0.463300	−	0.886202i	$-0.653335\pi$
$503$	4770.81	−	4770.81i	0.422902	−	0.422902i	0.886202	+	0.463300i	$0.153335\pi$
$504$	−1202.16	−	417.195i	−0.106247	−	0.0368717i
$505$		0			0
$506$	−2382.40	−	5447.80i	−0.209310	−	0.478625i
$507$	6003.89	+	6003.89i	0.525922	+	0.525922i
$508$	−220.585	−	5637.03i	−0.0192655	−	0.492328i
$509$			8188.23i			0.713039i	0.934288	+	0.356520i	$0.116037\pi$
$509$			8188.23i			0.713039i	−0.934288	+	0.356520i	$0.883963\pi$
$510$		0			0
$511$			412.526i			0.0357125i
$512$	−11314.3	−	2490.89i	−0.976613	−	0.215006i
$513$	2473.24	+	2473.24i	0.212858	+	0.212858i
$514$	−7111.09	+	3109.78i	−0.610227	+	0.266861i
$515$		0			0
$516$	−4042.60	+	4371.87i	−0.344895	+	0.372986i
$517$	9273.48	−	9273.48i	0.788872	−	0.788872i
$518$	−303.554	−	118.836i	−0.0257479	−	0.0100799i
$519$	13127.5			1.11028
$520$		0			0
$521$	−5465.70			−0.459610			−0.229805	−	0.973237i	$-0.573809\pi$
$521$	−5465.70			−0.459610			−0.229805	+	0.973237i	$0.573809\pi$
$522$	5238.22	+	2050.68i	0.439216	+	0.171946i
$523$	−9877.72	+	9877.72i	−0.825856	+	0.825856i	−0.986941	−	0.161085i	$-0.948501\pi$
$523$	−9877.72	+	9877.72i	−0.825856	+	0.825856i	0.161085	+	0.986941i	$0.448501\pi$
$524$	9491.88	−	10265.0i	0.791326	−	0.855780i
$525$		0			0
$526$	3682.97	−	1610.62i	0.305295	−	0.133510i
$527$	6922.60	+	6922.60i	0.572207	+	0.572207i
$528$	−8838.49	+	10341.9i	−0.728496	+	0.852412i
$529$			6120.55i			0.503045i
$530$		0			0
$531$		−	25704.7i		−	2.10073i
$532$	28.7377	+	734.391i	0.00234199	+	0.0598494i
$533$	2894.96	+	2894.96i	0.235262	+	0.235262i
$534$	−1414.00	−	3233.38i	−0.114588	−	0.262026i
$535$		0			0
$536$	−6047.57	+	17426.4i	−0.487342	+	1.40430i
$537$	−20706.6	+	20706.6i	−1.66398	+	1.66398i
$538$	−6799.95	+	17369.7i	−0.544920	+	1.39193i
$539$	9202.49			0.735397
$540$		0			0
$541$	15069.4			1.19757			0.598784	−	0.800910i	$-0.295651\pi$
$541$	15069.4			1.19757			0.598784	+	0.800910i	$0.295651\pi$
$542$	4930.13	−	12593.5i	0.390715	−	0.998035i
$543$	3034.80	−	3034.80i	0.239845	−	0.239845i
$544$	4374.15	+	8191.27i	0.344743	+	0.645584i
$545$		0			0
$546$	823.803	+	1883.78i	0.0645706	+	0.147652i
$547$	−4573.04	−	4573.04i	−0.357457	−	0.357457i	0.505418	−	0.862875i	$-0.331338\pi$
$547$	−4573.04	−	4573.04i	−0.357457	−	0.357457i	−0.862875	+	0.505418i	$0.831338\pi$
$548$	−1405.10	+	54.9835i	−0.109531	+	0.00428609i
$549$			6544.60i			0.508773i
$550$		0			0
$551$		−	3249.00i		−	0.251202i
$552$	−12448.7	+	6034.38i	−0.959873	+	0.465290i
$553$	−63.5850	−	63.5850i	−0.00488953	−	0.00488953i
$554$	−20121.2	+	8799.29i	−1.54308	+	0.674812i
$555$		0			0
$556$	57.7899	+	53.4375i	0.00440798	+	0.00407599i
$557$	−1915.65	+	1915.65i	−0.145725	+	0.145725i	−0.776205	−	0.630480i	$-0.782858\pi$
$557$	−1915.65	+	1915.65i	−0.145725	+	0.145725i	0.630480	+	0.776205i	$0.282858\pi$
$558$	17502.3	+	6851.88i	1.32784	+	0.519827i
$559$	5419.00			0.410017
$560$		0			0
$561$	10904.3			0.820640
$562$	8023.30	+	3140.99i	0.602211	+	0.235756i
$563$	−1561.15	+	1561.15i	−0.116864	+	0.116864i	−0.763120	−	0.646256i	$-0.776334\pi$
$563$	−1561.15	+	1561.15i	−0.116864	+	0.116864i	0.646256	+	0.763120i	$0.276334\pi$
$564$	−22403.2	−	20715.9i	−1.67260	−	1.54663i
$565$		0			0
$566$	−21469.6	+	9388.98i	−1.59441	+	0.697259i
$567$	−521.544	−	521.544i	−0.0386293	−	0.0386293i
$568$	−3204.46	+	1553.33i	−0.236719	+	0.114747i
$569$		−	21457.5i		−	1.58093i	−0.612510	−	0.790463i	$-0.709840\pi$
$569$		−	21457.5i		−	1.58093i	0.612510	−	0.790463i	$-0.290160\pi$
$570$		0			0
$571$		−	5553.22i		−	0.406997i	−0.979075	−	0.203498i	$-0.934769\pi$
$571$		−	5553.22i		−	0.406997i	0.979075	−	0.203498i	$-0.0652312\pi$
$572$	12371.3	−	484.106i	0.904318	−	0.0353872i
$573$	−20396.3	−	20396.3i	−1.48703	−	1.48703i
$574$	130.904	+	299.335i	0.00951884	+	0.0217666i
$575$		0			0
$576$	13995.4	+	11043.9i	1.01240	+	0.798894i
$577$	−762.522	+	762.522i	−0.0550160	+	0.0550160i	−0.734079	−	0.679064i	$-0.762386\pi$
$577$	−762.522	+	762.522i	−0.0550160	+	0.0550160i	0.679064	+	0.734079i	$0.262386\pi$
$578$	−2352.39	+	6008.91i	−0.169285	+	0.432418i
$579$	7950.68			0.570672
$580$		0			0
$581$	−1961.07			−0.140033
$582$	12807.9	−	32716.3i	0.912208	−	2.33013i
$583$	6492.40	−	6492.40i	0.461214	−	0.461214i
$584$	1894.87	−	5460.17i	0.134265	−	0.386889i
$585$		0			0
$586$	8608.32	+	19684.5i	0.606837	+	1.38764i
$587$	15138.4	+	15138.4i	1.06445	+	1.06445i	0.997775	+	0.0666722i	$0.0212382\pi$
$587$	15138.4	+	15138.4i	1.06445	+	1.06445i	0.0666722	+	0.997775i	$0.478762\pi$
$588$	−837.198	−	21394.5i	−0.0587167	−	1.50050i
$589$		−	10855.8i		−	0.759432i
$590$		0			0
$591$			3035.33i			0.211264i
$592$	3471.96	+	2967.24i	0.241042	+	0.206001i
$593$	−1637.51	−	1637.51i	−0.113397	−	0.113397i	0.648131	−	0.761529i	$-0.275551\pi$
$593$	−1637.51	−	1637.51i	−0.113397	−	0.113397i	−0.761529	+	0.648131i	$0.775551\pi$
$594$	4307.95	−	1883.93i	0.297571	−	0.130132i
$595$		0			0
$596$	15427.2	−	16683.8i	1.06027	−	1.14663i
$597$	25319.8	−	25319.8i	1.73579	−	1.73579i
$598$	11723.7	+	4589.62i	0.801699	+	0.313852i
$599$	10193.4			0.695312			0.347656	−	0.937622i	$-0.386978\pi$
$599$	10193.4			0.695312			0.347656	+	0.937622i	$0.386978\pi$
$600$		0			0
$601$	−10688.6			−0.725454			−0.362727	−	0.931895i	$-0.618154\pi$
$601$	−10688.6			−0.725454			−0.362727	+	0.931895i	$0.618154\pi$
$602$	402.677	+	157.642i	0.0272623	+	0.0106727i
$603$	20071.7	−	20071.7i	1.35553	−	1.35553i
$604$	−15824.4	+	17113.3i	−1.06604	+	1.15287i
$605$		0			0
$606$	16051.5	−	7019.56i	1.07599	−	0.470544i
$607$	12050.0	+	12050.0i	0.805759	+	0.805759i	0.983989	−	0.178230i	$-0.0570372\pi$
$607$	12050.0	+	12050.0i	0.805759	+	0.805759i	−0.178230	+	0.983989i	$0.557037\pi$
$608$	2992.94	−	9852.35i	0.199638	−	0.657180i
$609$		−	725.306i		−	0.0482609i
$610$		0			0
$611$			27769.1i			1.83866i
$612$	−558.756	−	14279.0i	−0.0369058	−	0.943126i
$613$	−3893.39	−	3893.39i	−0.256529	−	0.256529i	0.567112	−	0.823641i	$-0.308061\pi$
$613$	−3893.39	−	3893.39i	−0.256529	−	0.256529i	−0.823641	+	0.567112i	$0.808061\pi$
$614$	2347.57	+	5368.15i	0.154300	+	0.352835i
$615$		0			0
$616$	933.374	+	323.914i	0.0610498	+	0.0211865i
$617$	−4210.58	+	4210.58i	−0.274735	+	0.274735i	−0.831003	−	0.556268i	$-0.812233\pi$
$617$	−4210.58	+	4210.58i	−0.274735	+	0.274735i	0.556268	+	0.831003i	$0.312233\pi$
$618$	−5989.98	+	15300.7i	−0.389890	+	0.995930i
$619$	−6990.42			−0.453907			−0.226954	−	0.973906i	$-0.572877\pi$
$619$	−6990.42			−0.453907			−0.226954	+	0.973906i	$0.572877\pi$
$620$		0			0
$621$	4781.34			0.308967
$622$	−1424.16	+	3637.86i	−0.0918068	+	0.234510i
$623$	−181.225	+	181.225i	−0.0116543	+	0.0116543i
$624$	−2250.96	−	28717.6i	−0.144408	−	1.84234i
$625$		0			0
$626$	3189.30	+	7292.91i	0.203626	+	0.465628i
$627$	−8549.87	−	8549.87i	−0.544576	−	0.544576i
$628$	−17774.8	+	695.553i	−1.12945	+	0.0441968i
$629$		−	3660.76i		−	0.232057i
$630$		0			0
$631$		−	16801.3i		−	1.05998i	−0.848003	−	0.529991i	$-0.822195\pi$
$631$		−	16801.3i		−	1.05998i	0.848003	−	0.529991i	$-0.177805\pi$
$632$	549.539	+	1133.67i	0.0345878	+	0.0713531i
$633$	23633.7	+	23633.7i	1.48397	+	1.48397i
$634$	7618.67	−	3331.76i	0.477249	−	0.208708i
$635$		0			0
$636$	−15684.6	−	14503.3i	−0.977885	−	0.904235i
$637$	−13778.3	+	13778.3i	−0.857010	+	0.857010i
$638$	−4067.01	−	1592.17i	−0.252374	−	0.0988003i
$639$	5480.04			0.339260
$640$		0			0
$641$	7637.22			0.470596			0.235298	−	0.971923i	$-0.424393\pi$
$641$	7637.22			0.470596			0.235298	+	0.971923i	$0.424393\pi$
$642$	18019.1	+	7054.17i	1.10772	+	0.433654i
$643$	13378.3	−	13378.3i	0.820509	−	0.820509i	−0.165672	−	0.986181i	$-0.552979\pi$
$643$	13378.3	−	13378.3i	0.820509	−	0.820509i	0.986181	+	0.165672i	$0.0529793\pi$
$644$	737.651	+	682.094i	0.0451359	+	0.0417365i
$645$		0			0
$646$	−7561.90	+	3306.93i	−0.460556	+	0.201408i
$647$	−9497.02	−	9497.02i	−0.577073	−	0.577073i	0.357023	−	0.934096i	$-0.383792\pi$
$647$	−9497.02	−	9497.02i	−0.577073	−	0.577073i	−0.934096	+	0.357023i	$0.883792\pi$
$648$	4507.49	+	9298.76i	0.273258	+	0.563719i
$649$			19957.4i			1.20708i
$650$		0			0
$651$		−	2423.45i		−	0.145902i
$652$	−16473.6	+	644.636i	−0.989506	+	0.0387207i
$653$	−12420.7	−	12420.7i	−0.744346	−	0.744346i	0.229065	−	0.973411i	$-0.426433\pi$
$653$	−12420.7	−	12420.7i	−0.744346	−	0.744346i	−0.973411	+	0.229065i	$0.926433\pi$
$654$	3554.21	+	8127.36i	0.212509	+	0.485940i
$655$		0			0
$656$	−357.681	−	4563.26i	−0.0212883	−	0.271594i
$657$	−6289.03	+	6289.03i	−0.373453	+	0.373453i
$658$	−807.819	+	2063.48i	−0.0478603	+	0.122254i
$659$	5899.85			0.348749			0.174374	−	0.984679i	$-0.444210\pi$
$659$	5899.85			0.348749			0.174374	+	0.984679i	$0.444210\pi$
$660$		0			0
$661$	25892.6			1.52361			0.761804	−	0.647808i	$-0.224314\pi$
$661$	25892.6			1.52361			0.761804	+	0.647808i	$0.224314\pi$
$662$	−8902.36	+	22740.0i	−0.522658	+	1.33507i
$663$	−16326.3	+	16326.3i	−0.956349	+	0.956349i
$664$	25956.6	+	9007.88i	1.51704	+	0.526466i
$665$		0			0
$666$	−2816.05	−	6439.41i	−0.163843	−	0.374658i
$667$	−3140.53	−	3140.53i	−0.182312	−	0.182312i
$668$	−354.454	−	9058.05i	−0.0205303	−	0.524650i
$669$		−	2877.10i		−	0.166270i
$670$		0			0
$671$		−	5081.29i		−	0.292342i
$672$	668.143	−	2199.44i	0.0383544	−	0.126258i
$673$	19481.3	+	19481.3i	1.11582	+	1.11582i	0.992348	+	0.123475i	$0.0394040\pi$
$673$	19481.3	+	19481.3i	1.11582	+	1.11582i	0.123475	+	0.992348i	$0.460596\pi$
$674$	11416.4	−	4992.55i	0.652437	−	0.285320i
$675$		0			0
$676$	−5865.28	+	6343.00i	−0.333709	+	0.360890i
$677$	17811.4	−	17811.4i	1.01115	−	1.01115i	0.0112114	−	0.999937i	$-0.496431\pi$
$677$	17811.4	−	17811.4i	1.01115	−	1.01115i	0.999937	−	0.0112114i	$-0.00356878\pi$
$678$	−20292.0	−	7944.00i	−1.14943	−	0.449982i
$679$	−2551.55			−0.144211
$680$		0			0
$681$	−23657.4			−1.33121
$682$	−13589.0	−	5319.88i	−0.762976	−	0.298693i
$683$	−13579.6	+	13579.6i	−0.760775	+	0.760775i	−0.976463	−	0.215687i	$-0.930801\pi$
$683$	−13579.6	+	13579.6i	−0.760775	+	0.760775i	0.215687	+	0.976463i	$0.430801\pi$
$684$	−10757.8	+	11634.0i	−0.601367	+	0.650348i
$685$		0			0
$686$	−2860.24	+	1250.82i	−0.159190	+	0.0696161i
$687$	25880.3	+	25880.3i	1.43726	+	1.43726i
$688$	−4605.70	−	3936.17i	−0.255219	−	0.218118i
$689$			19441.3i			1.07497i
$690$		0			0
$691$			12840.8i			0.706928i	0.935448	+	0.353464i	$0.114996\pi$
$691$			12840.8i			0.706928i	−0.935448	+	0.353464i	$0.885004\pi$
$692$	522.274	+	13346.7i	0.0286906	+	0.733186i
$693$	−1075.06	−	1075.06i	−0.0589296	−	0.0589296i
$694$	−1036.92	−	2371.10i	−0.0567159	−	0.129691i
$695$		0			0
$696$	−3331.58	+	9600.10i	−0.181441	+	0.522832i
$697$	−2594.27	+	2594.27i	−0.140983	+	0.140983i
$698$	9910.56	−	25315.4i	0.537422	−	1.37278i
$699$	−37722.9			−2.04122
$700$		0			0
$701$	−23786.6			−1.28161			−0.640805	−	0.767704i	$-0.721399\pi$
$701$	−23786.6			−1.28161			−0.640805	+	0.767704i	$0.721399\pi$
$702$	−3629.33	+	9270.70i	−0.195128	+	0.498433i
$703$	−2870.34	+	2870.34i	−0.153993	+	0.153993i
$704$	−10866.2	−	8574.62i	−0.581727	−	0.459045i
$705$		0			0
$706$	8150.01	+	18636.5i	0.434461	+	0.993476i
$707$	−899.658	−	899.658i	−0.0478573	−	0.0478573i
$708$	46398.3	−	1815.63i	2.46293	−	0.0963779i
$709$			21270.0i			1.12667i	0.826227	+	0.563337i	$0.190483\pi$
$709$			21270.0i			1.12667i	−0.826227	+	0.563337i	$0.809517\pi$
$710$		0			0
$711$		−	1938.73i		−	0.102262i
$712$	3231.11	−	1566.25i	0.170072	−	0.0824408i
$713$	−10493.4	−	10493.4i	−0.551164	−	0.551164i
$714$	−1688.12	+	738.238i	−0.0884821	+	0.0386945i
$715$		0			0
$716$	−21876.1	−	20228.5i	−1.14183	−	1.05583i
$717$	7974.40	−	7974.40i	0.415355	−	0.415355i
$718$	−14744.1	−	5772.09i	−0.766359	−	0.300017i
$719$	22553.8			1.16984			0.584921	−	0.811090i	$-0.301126\pi$
$719$	22553.8			1.16984			0.584921	+	0.811090i	$0.301126\pi$
$720$		0			0
$721$	1193.30			0.0616380
$722$	−9543.10	−	3735.97i	−0.491908	−	0.192574i
$723$	−35796.8	+	35796.8i	−1.84135	+	1.84135i
$724$	3206.21	+	2964.73i	0.164583	+	0.152187i
$725$		0			0
$726$	12227.6	−	5347.30i	0.625081	−	0.273357i
$727$	−19795.0	−	19795.0i	−1.00984	−	1.00984i	−0.999951	−	0.00989382i	$-0.996851\pi$
$727$	−19795.0	−	19795.0i	−1.00984	−	1.00984i	−0.00989382	−	0.999951i	$-0.503149\pi$
$728$	−1882.46	+	912.504i	−0.0958358	+	0.0464556i
$729$		−	28955.6i		−	1.47110i
$730$		0			0
$731$			4856.16i			0.245706i
$732$	−11813.3	+	462.272i	−0.596493	+	0.0233416i
$733$	−10191.1	−	10191.1i	−0.513528	−	0.513528i	0.402078	−	0.915606i	$-0.368288\pi$
$733$	−10191.1	−	10191.1i	−0.513528	−	0.513528i	−0.915606	+	0.402078i	$0.868288\pi$
$734$	−5892.76	−	13474.9i	−0.296329	−	0.677612i
$735$		0			0
$736$	−6630.40	−	12416.4i	−0.332065	−	0.621842i
$737$	−15583.9	+	15583.9i	−0.778888	+	0.778888i
$738$	−2567.77	+	6559.06i	−0.128077	+	0.327158i
$739$	−28579.3			−1.42261			−0.711304	−	0.702885i	$-0.751895\pi$
$739$	−28579.3			−1.42261			−0.711304	+	0.702885i	$0.751895\pi$
$740$		0			0
$741$	25602.3			1.26926
$742$	−565.558	+	1444.65i	−0.0279815	+	0.0714755i
$743$	20848.1	−	20848.1i	1.02940	−	1.02940i	0.0298445	−	0.999555i	$-0.490499\pi$
$743$	20848.1	−	20848.1i	1.02940	−	1.02940i	0.999555	−	0.0298445i	$-0.00950122\pi$
$744$	−11131.7	+	32076.6i	−0.548533	+	1.58062i
$745$		0			0
$746$	−10900.2	−	24925.2i	−0.534964	−	1.22329i
$747$	−29896.9	−	29896.9i	−1.46435	−	1.46435i
$748$	433.824	+	11086.3i	0.0212061	+	0.541921i
$749$		−	1405.31i		−	0.0685566i
$750$		0			0
$751$		−	13588.4i		−	0.660252i	−0.943937	−	0.330126i	$-0.892909\pi$
$751$		−	13588.4i		−	0.660252i	0.943937	−	0.330126i	$-0.107091\pi$
$752$	20170.5	−	23601.5i	0.978115	−	1.14449i
$753$	10438.8	+	10438.8i	0.505193	+	0.505193i
$754$	8473.13	−	3705.42i	0.409248	−	0.178970i
$755$		0			0
$756$	−539.379	+	583.311i	−0.0259484	+	0.0280619i
$757$	1630.23	−	1630.23i	0.0782719	−	0.0782719i	−0.666887	−	0.745159i	$-0.732374\pi$
$757$	1630.23	−	1630.23i	0.0782719	−	0.0782719i	0.745159	+	0.666887i	$0.232374\pi$
$758$	26318.1	+	10303.1i	1.26110	+	0.493702i
$759$	−16528.9			−0.790461
$760$		0			0
$761$	−33489.9			−1.59528			−0.797640	−	0.603134i	$-0.793919\pi$
$761$	−33489.9			−1.59528			−0.797640	+	0.603134i	$0.793919\pi$
$762$	−14602.9	−	5716.82i	−0.694237	−	0.271783i
$763$	455.524	−	455.524i	0.0216135	−	0.0216135i
$764$	19925.4	−	21548.4i	0.943556	−	1.02041i
$765$		0			0
$766$	−7002.98	+	3062.51i	−0.330324	+	0.144455i
$767$	−29881.0	−	29881.0i	−1.40670	−	1.40670i
$768$	−18946.3	+	26042.6i	−0.890188	+	1.22361i
$769$		−	26755.6i		−	1.25466i	−0.778755	−	0.627328i	$-0.784149\pi$
$769$		−	26755.6i		−	1.25466i	0.778755	−	0.627328i	$-0.215851\pi$
$770$		0			0
$771$			21575.4i			1.00780i
$772$	316.316	+	8083.43i	0.0147467	+	0.376851i
$773$	6155.27	+	6155.27i	0.286403	+	0.286403i	0.835656	−	0.549253i	$-0.185088\pi$
$773$	6155.27	+	6155.27i	0.286403	+	0.286403i	−0.549253	+	0.835656i	$0.685088\pi$
$774$	3735.61	+	8542.16i	0.173480	+	0.396694i
$775$		0			0
$776$	33772.1	+	11720.1i	1.56231	+	0.542176i
$777$	−640.775	+	640.775i	−0.0295852	+	0.0295852i
$778$	157.729	−	402.902i	0.00726848	−	0.0185665i
$779$	4068.25			0.187112
$780$		0			0
$781$	−4254.76			−0.194939
$782$	−4112.92	+	10506.0i	−0.188079	+	0.480425i
$783$	2483.43	−	2483.43i	0.113347	−	0.113347i
$784$	21718.4	−	1702.35i	0.989361	−	0.0775489i
$785$		0			0
$786$	−15572.2	−	35608.7i	−0.706670	−	1.61593i
$787$	11524.6	+	11524.6i	0.521993	+	0.521993i	0.918173	−	0.396180i	$-0.129664\pi$
$787$	11524.6	+	11524.6i	0.521993	+	0.521993i	−0.396180	+	0.918173i	$0.629664\pi$
$788$	−3086.01	+	120.760i	−0.139511	+	0.00545925i
$789$		−	11174.3i		−	0.504202i
$790$		0			0
$791$			1582.58i			0.0711378i
$792$	9291.31	+	19167.6i	0.416859	+	0.859962i
$793$	7607.89	+	7607.89i	0.340686	+	0.340686i
$794$	−14012.2	+	6127.74i	−0.626290	+	0.273886i
$795$		0			0
$796$	26749.9	+	24735.2i	1.19111	+	1.10140i
$797$	−656.794	+	656.794i	−0.0291905	+	0.0291905i	−0.721551	−	0.692361i	$-0.756571\pi$
$797$	−656.794	+	656.794i	−0.0291905	+	0.0291905i	0.692361	+	0.721551i	$0.256571\pi$
$798$	1902.47	+	744.785i	0.0843942	+	0.0330390i
$799$	−24884.9			−1.10183
$800$		0			0
$801$	−5525.62			−0.243743
$802$	28813.5	+	11280.0i	1.26863	+	0.496648i
$803$	4882.87	−	4882.87i	0.214586	−	0.214586i
$804$	37648.2	+	34812.7i	1.65143	+	1.52705i
$805$		0			0
$806$	28311.0	−	12380.8i	1.23724	−	0.541062i
$807$	36665.9	+	36665.9i	1.59938	+	1.59938i
$808$	7775.37	+	16040.2i	0.338535	+	0.698383i
$809$		−	14179.8i		−	0.616238i	−0.951348	−	0.308119i	$-0.900301\pi$
$809$		−	14179.8i		−	0.616238i	0.951348	−	0.308119i	$-0.0996994\pi$
$810$		0			0
$811$		−	29366.2i		−	1.27150i	−0.771896	−	0.635749i	$-0.780691\pi$
$811$		−	29366.2i		−	1.27150i	0.771896	−	0.635749i	$-0.219309\pi$
$812$	737.417	−	28.8561i	0.0318698	−	0.00124711i
$813$	−26583.7	−	26583.7i	−1.14678	−	1.14678i
$814$	2186.41	+	4999.63i	0.0941445	+	0.215279i
$815$		0			0
$816$	25734.8	−	2017.16i	1.10404	−	0.0865378i
$817$	3807.63	−	3807.63i	0.163050	−	0.163050i
$818$	3075.37	−	7855.67i	0.131452	−	0.335779i
$819$	3219.24			0.137350
$820$		0			0
$821$	8845.67			0.376025			0.188012	−	0.982167i	$-0.439796\pi$
$821$	8845.67			0.376025			0.188012	+	0.982167i	$0.439796\pi$
$822$	−1424.99	+	3639.96i	−0.0604649	+	0.154450i
$823$	16257.0	−	16257.0i	0.688559	−	0.688559i	−0.273355	−	0.961913i	$-0.588133\pi$
$823$	16257.0	−	16257.0i	0.688559	−	0.688559i	0.961913	+	0.273355i	$0.0881332\pi$
$824$	−15794.5	−	5481.26i	−0.667751	−	0.231734i
$825$		0			0
$826$	−1351.15	−	3089.66i	−0.0569160	−	0.130149i
$827$	−19183.3	−	19183.3i	−0.806612	−	0.806612i	0.177507	−	0.984119i	$-0.443197\pi$
$827$	−19183.3	−	19183.3i	−0.806612	−	0.806612i	−0.984119	+	0.177507i	$0.943197\pi$
$828$	846.970	+	21644.3i	0.0355486	+	0.908442i
$829$		−	27097.5i		−	1.13527i	−0.823282	−	0.567633i	$-0.807859\pi$
$829$		−	27097.5i		−	1.13527i	0.823282	−	0.567633i	$-0.192141\pi$
$830$		0			0
$831$			61048.5i			2.54844i
$832$	29107.5	−	3431.07i	1.21289	−	0.142970i
$833$	−12347.2	−	12347.2i	−0.513571	−	0.513571i
$834$	200.470	−	87.6685i	0.00832340	−	0.00363994i
$835$		0			0
$836$	8352.47	−	9032.78i	0.345546	−	0.373691i
$837$	8297.83	−	8297.83i	0.342670	−	0.342670i
$838$	−7448.93	−	2916.14i	−0.307063	−	0.120210i
$839$	13726.1			0.564814			0.282407	−	0.959295i	$-0.408867\pi$
$839$	13726.1			0.564814			0.282407	+	0.959295i	$0.408867\pi$
$840$		0			0
$841$	21126.6			0.866235
$842$	1948.86	+	762.948i	0.0797651	+	0.0312268i
$843$	16936.5	−	16936.5i	0.691961	−	0.691961i
$844$	−23088.0	+	24968.6i	−0.941615	+	1.01831i
$845$		0			0
$846$	−43773.4	+	19142.8i	−1.77891	+	0.777945i
$847$	−685.334	−	685.334i	−0.0278021	−	0.0278021i
$848$	14121.5	−	16523.5i	0.571855	−	0.669127i
$849$			65139.8i			2.63320i
$850$		0			0
$851$			5549.03i			0.223523i
$852$	387.078	+	9891.74i	0.0155646	+	0.397753i
$853$	20720.5	+	20720.5i	0.831720	+	0.831720i	0.987752	−	0.156032i	$-0.0498703\pi$
$853$	20720.5	+	20720.5i	0.831720	+	0.831720i	−0.156032	+	0.987752i	$0.549870\pi$
$854$	344.012	+	786.648i	0.0137844	+	0.0315205i
$855$		0			0
$856$	−6455.07	+	18600.6i	−0.257745	+	0.742704i
$857$	−26011.0	+	26011.0i	−1.03678	+	1.03678i	−0.0374797	+	0.999297i	$0.511933\pi$
$857$	−26011.0	+	26011.0i	−1.03678	+	1.03678i	−0.999297	+	0.0374797i	$0.988067\pi$
$858$	12546.4	−	32048.3i	0.499216	−	1.27519i
$859$	−4857.84			−0.192954			−0.0964769	−	0.995335i	$-0.530757\pi$
$859$	−4857.84			−0.192954			−0.0964769	+	0.995335i	$0.530757\pi$
$860$		0			0
$861$	908.196			0.0359480
$862$	7294.37	−	18632.6i	0.288222	−	0.736229i
$863$	−23423.0	+	23423.0i	−0.923904	+	0.923904i	−0.997303	−	0.0733988i	$-0.976615\pi$
$863$	−23423.0	+	23423.0i	−0.923904	+	0.923904i	0.0733988	+	0.997303i	$0.476615\pi$
$864$	9818.53	−	5243.11i	0.386612	−	0.206452i
$865$		0			0
$866$	−4239.25	−	9693.81i	−0.166346	−	0.380380i
$867$	12684.3	+	12684.3i	0.496863	+	0.496863i
$868$	2463.91	−	96.4163i	0.0963486	−	0.00377025i
$869$			1505.25i			0.0587596i
$870$		0			0
$871$		−	46665.5i		−	1.81539i
$872$	−8121.66	+	3936.90i	−0.315406	+	0.152890i
$873$	−38898.8	−	38898.8i	−1.50805	−	1.50805i
$874$	11462.4	−	5012.69i	0.443619	−	0.194001i
$875$		0			0
$876$	−11796.2	−	10907.8i	−0.454975	−	0.420708i
$877$	19062.6	−	19062.6i	0.733976	−	0.733976i	−0.237429	−	0.971405i	$-0.576305\pi$
$877$	19062.6	−	19062.6i	0.733976	−	0.733976i	0.971405	+	0.237429i	$0.0763046\pi$
$878$	−33984.9	−	13304.5i	−1.30630	−	0.511396i
$879$	59723.6			2.29173
$880$		0			0
$881$	−6538.78			−0.250053			−0.125027	−	0.992153i	$-0.539902\pi$
$881$	−6538.78			−0.250053			−0.125027	+	0.992153i	$0.539902\pi$
$882$	−31217.3	−	12221.1i	−1.19177	−	0.466558i
$883$	−23546.4	+	23546.4i	−0.897395	+	0.897395i	−0.995205	−	0.0978097i	$-0.968816\pi$
$883$	−23546.4	+	23546.4i	−0.897395	+	0.897395i	0.0978097	+	0.995205i	$0.468816\pi$
$884$	−17248.4	−	15949.3i	−0.656252	−	0.606826i
$885$		0			0
$886$	−7728.22	+	3379.66i	−0.293041	+	0.128151i
$887$	13448.5	+	13448.5i	0.509082	+	0.509082i	0.914245	−	0.405162i	$-0.132785\pi$
$887$	13448.5	+	13448.5i	0.509082	+	0.509082i	−0.405162	+	0.914245i	$0.632785\pi$
$888$	11424.5	−	5537.95i	0.431737	−	0.209281i
$889$			1138.89i			0.0429663i
$890$		0			0
$891$			12346.5i			0.464225i
$892$	2925.13	−	114.465i	0.109799	−	0.00429659i
$893$	19511.8	+	19511.8i	0.731175	+	0.731175i
$894$	−25309.6	−	57875.1i	−0.946845	−	2.16514i
$895$		0			0
$896$	2262.74	+	591.795i	0.0843671	+	0.0220653i
$897$	24747.6	−	24747.6i	0.921179	−	0.921179i
$898$	140.359	−	358.531i	0.00521585	−	0.0133233i
$899$	−10900.5			−0.404397
$900$		0			0
$901$	−17422.0			−0.644186
$902$	1993.64	−	5092.53i	0.0735932	−	0.187985i
$903$	850.016	−	850.016i	0.0313253	−	0.0313253i
$904$	7269.33	−	20946.9i	0.267449	−	0.770667i
$905$		0			0
$906$	25961.3	+	59365.2i	0.951992	+	2.17690i
$907$	−200.288	−	200.288i	−0.00733237	−	0.00733237i	0.703431	−	0.710763i	$-0.251650\pi$
$907$	−200.288	−	200.288i	−0.00733237	−	0.00733237i	−0.710763	+	0.703431i	$0.751650\pi$
$908$	−941.202	−	24052.4i	−0.0343997	−	0.879081i
$909$		−	27430.9i		−	1.00091i
$910$		0			0
$911$		−	7662.84i		−	0.278684i	−0.990244	−	0.139342i	$-0.955501\pi$
$911$		−	7662.84i		−	0.278684i	0.990244	−	0.139342i	$-0.0444987\pi$
$912$	−21759.9	−	18596.6i	−0.790067	−	0.675214i
$913$	23212.3	+	23212.3i	0.841417	+	0.841417i
$914$	24409.8	−	10674.8i	0.883375	−	0.386313i
$915$		0			0
$916$	−25282.8	+	27342.1i	−0.911973	+	0.986253i
$917$	−1995.81	+	1995.81i	−0.0718727	+	0.0718727i
$918$	−8307.79	−	3252.37i	−0.298691	−	0.116933i
$919$	−17176.1			−0.616527			−0.308263	−	0.951301i	$-0.599748\pi$
$919$	−17176.1			−0.616527			−0.308263	+	0.951301i	$0.599748\pi$
$920$		0			0
$921$	16287.2			0.582715
$922$	25169.9	+	9853.62i	0.899054	+	0.351965i
$923$	6370.38	−	6370.38i	0.227176	−	0.227176i
$924$	1864.60	−	2016.48i	0.0663863	−	0.0717935i
$925$		0			0
$926$	3351.95	−	1465.85i	0.118954	−	0.0520205i
$927$	18192.1	+	18192.1i	0.644561	+	0.644561i
$928$	−9892.94	−	3005.27i	−0.349948	−	0.106307i
$929$			27097.0i			0.956968i	0.878096	+	0.478484i	$0.158814\pi$
$929$			27097.0i			0.956968i	−0.878096	+	0.478484i	$0.841186\pi$
$930$		0			0
$931$			19362.5i			0.681611i
$932$	−1500.80	−	38352.7i	−0.0527470	−	1.34795i
$933$	7679.20	+	7679.20i	0.269460	+	0.269460i
$934$	868.376	+	1985.70i	0.0304220	+	0.0695654i
$935$		0			0
$936$	−42609.6	−	14787.1i	−1.48797	−	0.516379i
$937$	4000.15	−	4000.15i	0.139465	−	0.139465i	−0.633927	−	0.773393i	$-0.718558\pi$
$937$	4000.15	−	4000.15i	0.139465	−	0.139465i	0.773393	+	0.633927i	$0.218558\pi$
$938$	1357.52	−	3467.64i	0.0472545	−	0.120706i
$939$	22127.0			0.768996
$940$		0			0
$941$	37957.6			1.31496			0.657482	−	0.753470i	$-0.271621\pi$
$941$	37957.6			1.31496			0.657482	+	0.753470i	$0.271621\pi$
$942$	−18026.4	+	46046.3i	−0.623495	+	1.59264i
$943$	3932.43	−	3932.43i	0.135798	−	0.135798i
$944$	3691.89	+	47100.8i	0.127289	+	1.62394i
$945$		0			0
$946$	−2900.37	−	6632.22i	−0.0996819	−	0.227941i
$947$	13560.7	+	13560.7i	0.465327	+	0.465327i	0.900397	−	0.435070i	$-0.143276\pi$
$947$	13560.7	+	13560.7i	0.465327	+	0.465327i	−0.435070	+	0.900397i	$0.643276\pi$
$948$	3499.50	−	136.940i	0.119893	−	0.00469158i
$949$			14621.6i			0.500145i
$950$		0			0
$951$		−	23115.4i		−	0.788189i
$952$	−817.726	−	1686.93i	−0.0278389	−	0.0574305i
$953$	−15366.0	−	15366.0i	−0.522302	−	0.522302i	0.395964	−	0.918266i	$-0.370411\pi$
$953$	−15366.0	−	15366.0i	−0.522302	−	0.522302i	−0.918266	+	0.395964i	$0.870411\pi$
$954$	−30646.0	+	13401.9i	−1.04004	+	0.454826i
$955$		0			0
$956$	8424.81	+	7790.29i	0.285019	+	0.263552i
$957$	−8585.10	+	8585.10i	−0.289986	+	0.289986i
$958$	−50984.6	−	19959.6i	−1.71945	−	0.673138i
$959$	283.881			0.00955892
$960$		0			0
$961$	−6630.66			−0.222573
$962$	−10759.2	−	4212.05i	−0.360593	−	0.141166i
$963$	21424.2	−	21424.2i	0.716911	−	0.716911i
$964$	−37818.6	−	34970.3i	−1.26354	−	1.16838i
$965$		0			0
$966$	2558.87	−	1119.03i	0.0852281	−	0.0372715i
$967$	−14792.8	−	14792.8i	−0.491939	−	0.491939i	0.416978	−	0.908917i	$-0.363089\pi$
$967$	−14792.8	−	14792.8i	−0.491939	−	0.491939i	−0.908917	+	0.416978i	$0.863089\pi$
$968$	5923.06	+	12219.0i	0.196668	+	0.405717i
$969$			22943.1i			0.760619i
$970$		0			0
$971$		−	14139.9i		−	0.467322i	−0.972318	−	0.233661i	$-0.924929\pi$
$971$		−	14139.9i		−	0.467322i	0.972318	−	0.233661i	$-0.0750706\pi$
$972$	41975.6	−	1642.56i	1.38515	−	0.0542029i
$973$	−11.2360	−	11.2360i	−0.000370205	−	0.000370205i
$974$	226.247	+	517.355i	0.00744294	+	0.0170196i
$975$		0			0
$976$	−939.980	−	11992.2i	−0.0308279	−	0.393299i
$977$	−2288.77	+	2288.77i	−0.0749481	+	0.0749481i	−0.743587	−	0.668639i	$-0.766877\pi$
$977$	−2288.77	+	2288.77i	−0.0749481	+	0.0749481i	0.668639	+	0.743587i	$0.266877\pi$
$978$	−16706.8	+	42675.6i	−0.546242	+	1.39531i
$979$	4290.15			0.140055
$980$		0			0
$981$	13889.1			0.452033
$982$	958.755	−	2449.03i	0.0311559	−	0.0795842i
$983$	6757.28	−	6757.28i	0.219251	−	0.219251i	−0.588932	−	0.808183i	$-0.700451\pi$
$983$	6757.28	−	6757.28i	0.219251	−	0.219251i	0.808183	+	0.588932i	$0.200451\pi$
$984$	−12020.8	−	4171.65i	−0.389440	−	0.135150i
$985$		0			0
$986$	3320.56	+	7593.06i	0.107250	+	0.245246i
$987$	4355.82	+	4355.82i	0.140473	+	0.140473i
$988$	1018.58	+	26029.8i	0.0327990	+	0.838177i
$989$		−	7361.03i		−	0.236670i
$990$		0			0
$991$			18118.1i			0.580767i	0.956910	+	0.290384i	$0.0937829\pi$
$991$			18118.1i			0.580767i	−0.956910	+	0.290384i	$0.906217\pi$
$992$	−33055.0	−	10041.4i	−1.05796	−	0.321387i
$993$	48002.2	+	48002.2i	1.53404	+	1.53404i
$994$	658.690	−	288.055i	0.0210185	−	0.00919169i
$995$		0			0
$996$	51853.6	−	56077.1i	1.64964	−	1.78401i
$997$	−18211.2	+	18211.2i	−0.578491	+	0.578491i	−0.934487	−	0.355996i	$-0.884142\pi$
$997$	−18211.2	+	18211.2i	−0.578491	+	0.578491i	0.355996	+	0.934487i	$0.384142\pi$
$998$	35626.2	+	13947.1i	1.12999	+	0.442372i
$999$	−4388.00			−0.138969

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.e.e.43.5		12
4.3	odd	2	inner	100.4.e.e.43.2		12
5.2	odd	4	inner	100.4.e.e.7.2		12
5.3	odd	4		20.4.e.b.7.5	yes	12
5.4	even	2		20.4.e.b.3.2	✓	12
15.8	even	4		180.4.k.e.127.2		12
15.14	odd	2		180.4.k.e.163.5		12
20.3	even	4		20.4.e.b.7.2	yes	12
20.7	even	4	inner	100.4.e.e.7.5		12
20.19	odd	2		20.4.e.b.3.5	yes	12
40.3	even	4		320.4.n.k.127.6		12
40.13	odd	4		320.4.n.k.127.1		12
40.19	odd	2		320.4.n.k.63.1		12
40.29	even	2		320.4.n.k.63.6		12
60.23	odd	4		180.4.k.e.127.5		12
60.59	even	2		180.4.k.e.163.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.4.e.b.3.2	✓	12	5.4	even	2
20.4.e.b.3.5	yes	12	20.19	odd	2
20.4.e.b.7.2	yes	12	20.3	even	4
20.4.e.b.7.5	yes	12	5.3	odd	4
100.4.e.e.7.2		12	5.2	odd	4	inner
100.4.e.e.7.5		12	20.7	even	4	inner
100.4.e.e.43.2		12	4.3	odd	2	inner
100.4.e.e.43.5		12	1.1	even	1	trivial
180.4.k.e.127.2		12	15.8	even	4
180.4.k.e.127.5		12	60.23	odd	4
180.4.k.e.163.2		12	60.59	even	2
180.4.k.e.163.5		12	15.14	odd	2
320.4.n.k.63.1		12	40.19	odd	2
320.4.n.k.63.6		12	40.29	even	2
320.4.n.k.127.1		12	40.13	odd	4
320.4.n.k.127.6		12	40.3	even	4

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.63379 + 1.03109i) q^{2} +(5.55970 - 5.55970i) q^{3} +(5.87372 + 5.43134i) q^{4} +(20.3756 - 8.91056i) q^{6} +(-1.14202 - 1.14202i) q^{7} +(9.86997 + 20.3613i) q^{8} -34.8205i q^{9} +O(q^{10})\)	\(q+(2.63379 + 1.03109i) q^{2} +(5.55970 - 5.55970i) q^{3} +(5.87372 + 5.43134i) q^{4} +(20.3756 - 8.91056i) q^{6} +(-1.14202 - 1.14202i) q^{7} +(9.86997 + 20.3613i) q^{8} -34.8205i q^{9} +27.0350i q^{11} +(62.8527 - 2.45951i) q^{12} +(-40.4777 - 40.4777i) q^{13} +(-1.83032 - 4.18535i) q^{14} +(5.00116 + 63.8043i) q^{16} +(36.2735 - 36.2735i) q^{17} +(35.9029 - 91.7099i) q^{18} -56.8829 q^{19} -12.6985 q^{21} +(-27.8754 + 71.2046i) q^{22} +(-54.9839 + 54.9839i) q^{23} +(168.077 + 58.3288i) q^{24} +(-64.8739 - 148.346i) q^{26} +(-43.4795 - 43.4795i) q^{27} +(-0.505208 - 12.9106i) q^{28} +57.1173i q^{29} +190.845i q^{31} +(-52.6158 + 173.204i) q^{32} +(150.306 + 150.306i) q^{33} +(132.938 - 58.1357i) q^{34} +(189.122 - 204.526i) q^{36} +(50.4605 - 50.4605i) q^{37} +(-149.818 - 58.6513i) q^{38} -450.088 q^{39} -71.5197 q^{41} +(-33.4453 - 13.0933i) q^{42} +(-66.9381 + 66.9381i) q^{43} +(-146.836 + 158.796i) q^{44} +(-201.509 + 88.1229i) q^{46} +(-343.017 - 343.017i) q^{47} +(382.538 + 326.928i) q^{48} -340.392i q^{49} -403.339i q^{51} +(-17.9066 - 457.603i) q^{52} +(-240.148 - 240.148i) q^{53} +(-69.6848 - 159.347i) q^{54} +(11.9813 - 34.5247i) q^{56} +(-316.252 + 316.252i) q^{57} +(-58.8929 + 150.435i) q^{58} +738.207 q^{59} -187.952 q^{61} +(-196.777 + 502.645i) q^{62} +(-39.7656 + 39.7656i) q^{63} +(-317.167 + 401.932i) q^{64} +(240.897 + 550.855i) q^{66} +(576.434 + 576.434i) q^{67} +(410.074 - 16.0468i) q^{68} +611.387i q^{69} +157.380i q^{71} +(708.991 - 343.677i) q^{72} +(-180.613 - 180.613i) q^{73} +(184.932 - 80.8733i) q^{74} +(-334.114 - 308.950i) q^{76} +(30.8744 - 30.8744i) q^{77} +(-1185.44 - 464.080i) q^{78} +55.6778 q^{79} +456.687 q^{81} +(-188.368 - 73.7430i) q^{82} +(858.601 - 858.601i) q^{83} +(-74.5876 - 68.9700i) q^{84} +(-245.320 + 107.282i) q^{86} +(317.555 + 317.555i) q^{87} +(-550.468 + 266.835i) q^{88} -158.689i q^{89} +92.4525i q^{91} +(-621.596 + 24.3239i) q^{92} +(1061.04 + 1061.04i) q^{93} +(-549.756 - 1257.12i) q^{94} +(670.433 + 1255.49i) q^{96} +(1117.12 - 1117.12i) q^{97} +(350.973 - 896.521i) q^{98} +941.372 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 8 q^{6} + 12 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 + 8 * q^6 + 12 * q^8	\( 12 q + 6 q^{2} + 8 q^{6} + 12 q^{8} + 80 q^{12} - 116 q^{13} + 312 q^{16} + 332 q^{17} - 198 q^{18} - 144 q^{21} - 360 q^{22} - 164 q^{26} + 880 q^{28} + 376 q^{32} - 80 q^{33} + 460 q^{36} - 508 q^{37} - 1600 q^{38} - 656 q^{41} - 1160 q^{42} - 1432 q^{46} + 2720 q^{48} + 932 q^{52} + 644 q^{53} + 2048 q^{56} + 960 q^{57} - 1576 q^{58} - 896 q^{61} - 2440 q^{62} - 1680 q^{66} + 844 q^{68} + 3036 q^{72} - 1436 q^{73} + 800 q^{76} - 3120 q^{77} - 3720 q^{78} + 5988 q^{81} + 1352 q^{82} - 2552 q^{86} + 2400 q^{88} + 1840 q^{92} + 3280 q^{93} + 1088 q^{96} + 4772 q^{97} - 1698 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 + 8 * q^6 + 12 * q^8 + 80 * q^12 - 116 * q^13 + 312 * q^16 + 332 * q^17 - 198 * q^18 - 144 * q^21 - 360 * q^22 - 164 * q^26 + 880 * q^28 + 376 * q^32 - 80 * q^33 + 460 * q^36 - 508 * q^37 - 1600 * q^38 - 656 * q^41 - 1160 * q^42 - 1432 * q^46 + 2720 * q^48 + 932 * q^52 + 644 * q^53 + 2048 * q^56 + 960 * q^57 - 1576 * q^58 - 896 * q^61 - 2440 * q^62 - 1680 * q^66 + 844 * q^68 + 3036 * q^72 - 1436 * q^73 + 800 * q^76 - 3120 * q^77 - 3720 * q^78 + 5988 * q^81 + 1352 * q^82 - 2552 * q^86 + 2400 * q^88 + 1840 * q^92 + 3280 * q^93 + 1088 * q^96 + 4772 * q^97 - 1698 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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