LMFDB - Embedded newform 100.4.e.e.43.2

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			43.2
Root			$-1.83244 + 0.801352i$ of defining polynomial
Character	$\chi$	$=$	100.43
Dual form			100.4.e.e.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03109 - 2.63379i) q^{2} +(-5.55970 + 5.55970i) q^{3} +(-5.87372 + 5.43134i) q^{4} +(20.3756 + 8.91056i) q^{6} +(1.14202 + 1.14202i) q^{7} +(20.3613 + 9.86997i) q^{8} -34.8205i q^{9} +O(q^{10})$	\(q+(-1.03109 - 2.63379i) 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} +(20.3613 + 9.86997i) q^{8} -34.8205i q^{9} -27.0350i q^{11} +(2.45951 - 62.8527i) 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} +(-91.7099 + 35.9029i) q^{18} +56.8829 q^{19} -12.6985 q^{21} +(-71.2046 + 27.8754i) 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} +(-12.9106 - 0.505208i) q^{28} +57.1173i q^{29} -190.845i q^{31} +(-173.204 + 52.6158i) 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} +(-58.6513 - 149.818i) q^{38} +450.088 q^{39} -71.5197 q^{41} +(13.0933 + 33.4453i) 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} +(326.928 + 382.538i) q^{48} -340.392i q^{49} +403.339i q^{51} +(457.603 + 17.9066i) 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} +(150.435 - 58.8929i) q^{58} -738.207 q^{59} -187.952 q^{61} +(-502.645 + 196.777i) 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} +(-16.0468 + 410.074i) q^{68} +611.387i q^{69} -157.380i q^{71} +(343.677 - 708.991i) 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} +(-464.080 - 1185.44i) q^{78} -55.6778 q^{79} +456.687 q^{81} +(73.7430 + 188.368i) 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} +(266.835 - 550.468i) q^{88} -158.689i q^{89} -92.4525i q^{91} +(-24.3239 + 621.596i) 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} +(-896.521 + 350.973i) 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 $

$2$	−1.03109	−	2.63379i	−0.364544	−	0.931186i
$2$	−1.03109	−	2.63379i	−0.364544	−	0.931186i
$3$	−5.55970	+	5.55970i	−1.06996	+	1.06996i	−0.0726035	+	0.997361i	$0.523131\pi$
$3$	−5.55970	+	5.55970i	−1.06996	+	1.06996i	−0.997361	+	0.0726035i	$0.976869\pi$
$4$	−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	0.737266	−	0.675603i	$-0.236117\pi$
$7$	1.14202	+	1.14202i	0.0616631	+	0.0616631i	−0.675603	+	0.737266i	$0.736117\pi$
$8$	20.3613	+	9.86997i	0.899852	+	0.436195i
$9$		−	34.8205i		−	1.28965i
$10$		0			0
$11$		−	27.0350i		−	0.741033i	−0.928826	−	0.370516i	$-0.879181\pi$
$11$		−	27.0350i		−	0.741033i	0.928826	−	0.370516i	$-0.120819\pi$
$12$	2.45951	−	62.8527i	0.0591667	−	1.51200i
$13$	−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	$0.130750\pi$
$18$	−91.7099	+	35.9029i	−1.20090	+	0.470134i
$19$	56.8829			0.686834			0.343417	−	0.939183i	$-0.388416\pi$
$19$	56.8829			0.686834			0.343417	+	0.939183i	$0.388416\pi$
$20$		0			0
$21$	−12.6985			−0.131955
$22$	−71.2046	+	27.8754i	−0.690039	+	0.270139i
$23$	54.9839	−	54.9839i	0.498475	−	0.498475i	−0.412488	−	0.910963i	$-0.635340\pi$
$23$	54.9839	−	54.9839i	0.498475	−	0.498475i	0.910963	+	0.412488i	$0.135340\pi$
$24$	−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
$28$	−12.9106	−	0.505208i	−0.0871381	−	0.00340983i
$29$			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	$-0.813540\pi$
$31$		−	190.845i		−	1.10570i	0.833281	−	0.552850i	$-0.186460\pi$
$32$	−173.204	+	52.6158i	−0.956825	+	0.290664i
$33$	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	$0.199322\pi$
$38$	−58.6513	−	149.818i	−0.250381	−	0.639570i
$39$	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	$0.543493\pi$
$42$	13.0933	+	33.4453i	0.0481033	+	0.122874i
$43$	66.9381	−	66.9381i	0.237394	−	0.237394i	−0.578376	−	0.815770i	$-0.696313\pi$
$43$	66.9381	−	66.9381i	0.237394	−	0.237394i	0.815770	+	0.578376i	$0.196313\pi$
$44$	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	$0.0212762\pi$
$47$	343.017	+	343.017i	1.06456	+	1.06456i	0.0667913	+	0.997767i	$0.478724\pi$
$48$	326.928	+	382.538i	0.983082	+	1.15030i
$49$		−	340.392i		−	0.992395i
$50$		0			0
$51$			403.339i			1.10743i
$52$	457.603	+	17.9066i	1.22035	+	0.0477539i
$53$	−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
$58$	150.435	−	58.8929i	0.340571	−	0.133328i
$59$	−738.207			−1.62892			−0.814461	−	0.580218i	$-0.802967\pi$
$59$	−738.207			−1.62892			−0.814461	+	0.580218i	$0.802967\pi$
$60$		0			0
$61$	−187.952			−0.394506			−0.197253	−	0.980353i	$-0.563202\pi$
$61$	−187.952			−0.394506			−0.197253	+	0.980353i	$0.563202\pi$
$62$	−502.645	+	196.777i	−1.02961	+	0.403077i
$63$	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	$-0.983293\pi$
$67$	−576.434	−	576.434i	−1.05108	−	1.05108i	−0.0524612	−	0.998623i	$-0.516707\pi$
$68$	−16.0468	+	410.074i	−0.0286170	+	0.731305i
$69$			611.387i			1.06670i
$70$		0			0
$71$		−	157.380i		−	0.263064i	−0.991312	−	0.131532i	$-0.958010\pi$
$71$		−	157.380i		−	0.263064i	0.991312	−	0.131532i	$-0.0419896\pi$
$72$	343.677	−	708.991i	0.562538	−	1.16049i
$73$	−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
$78$	−464.080	−	1185.44i	−0.673676	−	1.72083i
$79$	−55.6778			−0.0792942			−0.0396471	−	0.999214i	$-0.512623\pi$
$79$	−55.6778			−0.0792942			−0.0396471	+	0.999214i	$0.512623\pi$
$80$		0			0
$81$	456.687			0.626457
$82$	73.7430	+	188.368i	0.0993116	+	0.253680i
$83$	−858.601	+	858.601i	−1.13547	+	1.13547i	−0.146213	+	0.989253i	$0.546708\pi$
$83$	−858.601	+	858.601i	−1.13547	+	1.13547i	−0.989253	+	0.146213i	$0.953292\pi$
$84$	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
$88$	266.835	−	550.468i	0.323235	−	0.666820i
$89$		−	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
$92$	−24.3239	+	621.596i	−0.0275646	+	0.704411i
$93$	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	$-0.0598720\pi$
$98$	−896.521	+	350.973i	−0.924105	+	0.361772i
$99$	−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	$0.373147\pi$
$102$	1062.31	−	415.878i	1.03122	−	0.403706i
$103$	522.455	−	522.455i	0.499796	−	0.499796i	−0.411578	−	0.911374i	$-0.635022\pi$
$103$	522.455	−	522.455i	0.499796	−	0.499796i	0.911374	+	0.411578i	$0.135022\pi$
$104$	−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	0.372240	−	0.928137i	$-0.378590\pi$
$107$	−615.276	−	615.276i	−0.555897	−	0.555897i	−0.928137	+	0.372240i	$0.878590\pi$
$108$	−491.538	−	19.2346i	−0.437947	−	0.0171375i
$109$			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
$112$	78.5770	−	67.1542i	0.0662931	−	0.0566560i
$113$	−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
$118$	761.156	+	1944.28i	0.593814	+	1.51683i
$119$	82.8499			0.0638221
$120$		0			0
$121$	600.109			0.450871
$122$	193.795	+	495.028i	0.143815	+	0.367358i
$123$	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	0.859512	−	0.511116i	$-0.170768\pi$
$127$	498.629	+	498.629i	0.348395	+	0.348395i	−0.511116	+	0.859512i	$0.670768\pi$
$128$	731.577	−	1249.78i	0.505179	−	0.863015i
$129$			744.311i			0.508007i
$130$		0			0
$131$			1747.61i			1.16557i	0.812626	+	0.582785i	$0.198037\pi$
$131$			1747.61i			1.16557i	−0.812626	+	0.582785i	$0.801963\pi$
$132$	−1699.22	−	66.4929i	−1.12044	−	0.0438444i
$133$	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	$0.267454\pi$
$138$	1610.27	−	630.394i	0.993297	−	0.388860i
$139$	−9.83873			−0.00600367			−0.00300184	−	0.999995i	$-0.500956\pi$
$139$	−9.83873			−0.00600367			−0.00300184	+	0.999995i	$0.500956\pi$
$140$		0			0
$141$	−3814.15			−2.27808
$142$	−414.506	+	162.272i	−0.244962	+	0.0958985i
$143$	−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
$148$	−22.3229	+	570.459i	−0.0123982	+	0.316834i
$149$		−	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	$-0.712611\pi$
$151$		−	2913.54i		−	1.57020i	0.619368	−	0.785101i	$-0.287389\pi$
$152$	1158.21	+	561.433i	0.618049	+	0.299594i
$153$	−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	$0.441184\pi$
$158$	57.4087	+	146.644i	0.0289063	+	0.0738377i
$159$	2670.30			1.33188
$160$		0			0
$161$	125.585			0.0614751
$162$	−470.884	−	1202.82i	−0.228371	−	0.583348i
$163$	1457.19	−	1457.19i	0.700222	−	0.700222i	−0.264236	−	0.964458i	$-0.585120\pi$
$163$	1457.19	−	1457.19i	0.700222	−	0.700222i	0.964458	+	0.264236i	$0.0851199\pi$
$164$	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	0.867939	−	0.496671i	$-0.165444\pi$
$167$	801.239	+	801.239i	0.371268	+	0.371268i	−0.496671	+	0.867939i	$0.665444\pi$
$168$	−258.559	−	125.334i	−0.118740	−	0.0575580i
$169$			1079.90i			0.491532i
$170$		0			0
$171$		−	1980.69i		−	0.885773i
$172$	−29.6122	+	756.739i	−0.0131274	+	0.335470i
$173$	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
$178$	−417.953	+	163.622i	−0.175994	+	0.0688987i
$179$	3724.41			1.55517			0.777585	−	0.628778i	$-0.216445\pi$
$179$	3724.41			1.55517			0.777585	+	0.628778i	$0.216445\pi$
$180$		0			0
$181$	545.856			0.224161			0.112081	−	0.993699i	$-0.464249\pi$
$181$	545.856			0.224161			0.112081	+	0.993699i	$0.464249\pi$
$182$	−243.501	+	95.3266i	−0.0991729	+	0.0388246i
$183$	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
$188$	−3877.83	−	151.745i	−1.50436	−	0.0588677i
$189$			99.3087i			0.0382203i
$190$		0			0
$191$			3668.60i			1.38980i	0.719109	+	0.694898i	$0.244550\pi$
$191$			3668.60i			1.38980i	−0.719109	+	0.694898i	$0.755450\pi$
$192$	−3997.97	−	471.264i	−1.50275	−	0.177138i
$193$	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	$0.272239\pi$
$198$	970.636	+	2479.38i	0.348384	+	0.889907i
$199$	−4554.16			−1.62229			−0.811146	−	0.584844i	$-0.801156\pi$
$199$	−4554.16			−1.62229			−0.811146	+	0.584844i	$0.801156\pi$
$200$		0			0
$201$	6409.60			2.24925
$202$	−812.269	−	2074.85i	−0.282926	−	0.722702i
$203$	−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
$208$	−2785.09	+	2380.22i	−0.928419	+	0.793454i
$209$		−	1537.83i		−	0.508966i
$210$		0			0
$211$		−	4250.89i		−	1.38694i	−0.720487	−	0.693468i	$-0.756082\pi$
$211$		−	4250.89i		−	1.38694i	0.720487	−	0.693468i	$-0.243918\pi$
$212$	2714.89	+	106.237i	0.879525	+	0.0344170i
$213$	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
$218$	1050.56	−	411.276i	0.326389	−	0.127776i
$219$	2008.31			0.619675
$220$		0			0
$221$	−2936.54			−0.893814
$222$	1477.80	−	578.533i	0.446771	−	0.174904i
$223$	−258.746	+	258.746i	−0.0776991	+	0.0776991i	−0.744888	−	0.667189i	$-0.767497\pi$
$223$	−258.746	+	258.746i	−0.0776991	+	0.0776991i	0.667189	+	0.744888i	$0.267497\pi$
$224$	−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	0.946063	−	0.323983i	$-0.105022\pi$
$227$	2127.58	+	2127.58i	0.622080	+	0.622080i	−0.323983	+	0.946063i	$0.605022\pi$
$228$	139.904	−	3575.25i	0.0406377	−	1.03849i
$229$			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
$232$	−563.746	+	1162.98i	−0.159533	+	0.329111i
$233$	−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
$238$	−85.4254	−	218.209i	−0.0232660	−	0.0594303i
$239$	−1434.32			−0.388195			−0.194098	−	0.980982i	$-0.562178\pi$
$239$	−1434.32			−0.388195			−0.194098	+	0.980982i	$0.562178\pi$
$240$		0			0
$241$	−6438.62			−1.72094			−0.860472	−	0.509497i	$-0.829831\pi$
$241$	−6438.62			−1.72094			−0.860472	+	0.509497i	$0.829831\pi$
$242$	−618.764	−	1580.56i	−0.164362	−	0.419845i
$243$	−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
$248$	1883.63	−	3885.85i	0.482301	−	0.994966i
$249$		−	9547.12i		−	2.42982i
$250$		0			0
$251$		−	1877.58i		−	0.472159i	−0.971734	−	0.236079i	$-0.924137\pi$
$251$		−	1877.58i		−	0.472159i	0.971734	−	0.236079i	$-0.0758626\pi$
$252$	−17.5916	+	449.552i	−0.00439748	+	0.112377i
$253$	−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	$0.358066\pi$
$258$	1960.36	−	767.449i	0.473049	−	0.185191i
$259$	115.254			0.0276506
$260$		0			0
$261$	1988.85			0.471674
$262$	4602.85	−	1801.94i	1.08536	−	0.424902i
$263$	−1004.94	+	1004.94i	−0.235616	+	0.235616i	−0.815032	−	0.579416i	$-0.803281\pi$
$263$	−1004.94	+	1004.94i	−0.235616	+	0.235616i	0.579416	+	0.815032i	$0.303281\pi$
$264$	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
$268$	6516.62	+	255.004i	1.48532	+	0.0581227i
$269$			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	$0.180026\pi$
$271$			4781.49i			1.07179i	−0.844285	+	0.535895i	$0.819974\pi$
$272$	−2133.00	−	2495.81i	−0.475485	−	0.556364i
$273$	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	$0.931324\pi$
$278$	10.1446	+	25.9132i	0.00218860	+	0.00559053i
$279$	−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	$0.395189\pi$
$282$	3932.72	+	10045.7i	0.830461	+	2.12132i
$283$	5858.21	−	5858.21i	1.23051	−	1.23051i	0.266743	−	0.963768i	$-0.414053\pi$
$283$	5858.21	−	5858.21i	1.23051	−	1.23051i	0.963768	−	0.266743i	$-0.0859474\pi$
$284$	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
$288$	1832.11	+	6031.04i	0.374854	+	1.23397i
$289$			2281.47i			0.464374i
$290$		0			0
$291$			12421.8i			2.50232i
$292$	2041.84	+	79.9000i	0.409211	+	0.0160130i
$293$	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
$298$	−7481.04	+	2928.71i	−1.45425	+	0.569314i
$299$	−4451.25			−0.860944
$300$		0			0
$301$	152.889			0.0292770
$302$	−7673.66	+	3004.11i	−1.46215	+	0.572408i
$303$	−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	0.557722	−	0.830028i	$-0.311676\pi$
$307$	−1464.75	−	1464.75i	−0.272306	−	0.272306i	−0.830028	+	0.557722i	$0.811676\pi$
$308$	−13.6583	+	349.037i	−0.00252680	+	0.0645722i
$309$			5809.38i			1.06953i
$310$		0			0
$311$		−	1381.23i		−	0.251840i	−0.992040	−	0.125920i	$-0.959812\pi$
$311$		−	1381.23i		−	0.251840i	0.992040	−	0.125920i	$-0.0401882\pi$
$312$	9164.39	+	4442.36i	1.66292	+	0.806086i
$313$	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	$0.166131\pi$
$318$	−2753.31	−	7033.02i	−0.485529	−	1.24023i
$319$	1544.17			0.271024
$320$		0			0
$321$	6841.49			1.18958
$322$	−129.489	−	330.765i	−0.0224104	−	0.0572447i
$323$	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
$328$	−1456.24	−	705.898i	−0.245144	−	0.118831i
$329$			783.463i			0.131288i
$330$		0			0
$331$		−	8633.95i		−	1.43373i	−0.697211	−	0.716866i	$-0.745576\pi$
$331$		−	8633.95i		−	1.43373i	0.697211	−	0.716866i	$-0.254424\pi$
$332$	379.830	−	9706.53i	0.0627888	−	1.60456i
$333$	−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	$0.134124\pi$
$338$	2844.22	−	1113.47i	0.457708	−	0.179185i
$339$	7704.49			1.23437
$340$		0			0
$341$	−5159.48			−0.819360
$342$	−5216.73	+	2042.26i	−0.824820	+	0.322904i
$343$	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	0.755379	−	0.655288i	$-0.227453\pi$
$347$	646.980	+	646.980i	0.100091	+	0.100091i	−0.655288	+	0.755379i	$0.727453\pi$
$348$	3589.98	+	140.481i	0.552997	+	0.0216395i
$349$		−	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
$352$	1422.47	+	4682.57i	0.215391	+	0.709039i
$353$	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
$358$	−3840.19	−	9809.32i	−0.566928	−	1.44815i
$359$	5598.06			0.822992			0.411496	−	0.911411i	$-0.365006\pi$
$359$	5598.06			0.822992			0.411496	+	0.911411i	$0.365006\pi$
$360$		0			0
$361$	−3623.33			−0.528259
$362$	−562.825	−	1437.67i	−0.0817167	−	0.208736i
$363$	−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	0.918463	−	0.395506i	$-0.129431\pi$
$367$	3676.76	+	3676.76i	0.522957	+	0.522957i	−0.395506	+	0.918463i	$0.629431\pi$
$368$	−3233.22	−	3783.19i	−0.457999	−	0.535903i
$369$			2490.35i			0.351335i
$370$		0			0
$371$		−	548.506i		−	0.0767575i
$372$	−11995.1	−	469.385i	−1.67182	−	0.0654206i
$373$	−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
$378$	261.558	−	102.396i	0.0355902	−	0.0139330i
$379$	−9992.48			−1.35430			−0.677150	−	0.735845i	$-0.736785\pi$
$379$	−9992.48			−1.35430			−0.677150	+	0.735845i	$0.736785\pi$
$380$		0			0
$381$	−5544.46			−0.745541
$382$	9662.34	−	3782.65i	1.29416	−	0.506642i
$383$	1910.84	−	1910.84i	0.254932	−	0.254932i	−0.568057	−	0.822989i	$-0.692305\pi$
$383$	1910.84	−	1910.84i	0.254932	−	0.254932i	0.822989	+	0.568057i	$0.192305\pi$
$384$	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
$388$	−494.196	+	12629.2i	−0.0646624	+	1.65244i
$389$		−	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
$392$	3359.66	−	6930.82i	0.432878	−	0.893009i
$393$	−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	$0.361030\pi$
$398$	4695.74	+	11994.7i	0.591397	+	1.51065i
$399$	−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	$0.261463\pi$
$402$	−6608.85	−	16881.6i	−0.819949	−	2.09447i
$403$	−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
$408$	−3980.95	+	8212.52i	−0.483055	+	0.996521i
$409$		−	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
$412$	−231.125	+	5906.38i	−0.0276376	+	0.706278i
$413$	−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
$418$	−4050.32	+	1585.64i	−0.473942	+	0.185541i
$419$	2828.22			0.329755			0.164878	−	0.986314i	$-0.447277\pi$
$419$	2828.22			0.329755			0.164878	+	0.986314i	$0.447277\pi$
$420$		0			0
$421$	739.946			0.0856597			0.0428299	−	0.999082i	$-0.486363\pi$
$421$	739.946			0.0856597			0.0428299	+	0.999082i	$0.486363\pi$
$422$	−11196.0	+	4383.04i	−1.29150	+	0.505600i
$423$	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
$428$	6955.73	+	272.187i	0.785555	+	0.0307399i
$429$		−	12168.1i		−	1.36942i
$430$		0			0
$431$			7074.45i			0.790636i	0.918544	+	0.395318i	$0.129366\pi$
$431$			7074.45i			0.790636i	−0.918544	+	0.395318i	$0.870634\pi$
$432$	2991.63	−	2556.73i	0.333182	−	0.284747i
$433$	−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
$438$	−2070.74	−	5289.46i	−0.225899	−	0.577033i
$439$	12903.4			1.40284			0.701419	−	0.712750i	$-0.252550\pi$
$439$	12903.4			1.40284			0.701419	+	0.712750i	$0.252550\pi$
$440$		0			0
$441$	−11852.6			−1.27984
$442$	3027.83	+	7734.23i	0.325835	+	0.832307i
$443$	2108.72	−	2108.72i	0.226159	−	0.226159i	−0.584927	−	0.811086i	$-0.698877\pi$
$443$	2108.72	−	2108.72i	0.226159	−	0.226159i	0.811086	+	0.584927i	$0.198877\pi$
$444$	−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
$448$	−96.8022	+	821.223i	−0.0102087	+	0.0866052i
$449$		−	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
$452$	7833.13	+	306.521i	0.815132	+	0.0318972i
$453$	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	$0.0898828\pi$
$458$	12260.3	−	4799.69i	1.25084	−	0.489683i
$459$	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	$0.339639\pi$
$462$	904.194	−	353.977i	0.0910539	−	0.0356461i
$463$	−914.613	+	914.613i	−0.0918049	+	0.0918049i	−0.751518	−	0.659713i	$-0.770678\pi$
$463$	−914.613	+	914.613i	−0.0918049	+	0.0918049i	0.659713	+	0.751518i	$0.270678\pi$
$464$	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	0.679753	−	0.733441i	$-0.262087\pi$
$467$	−541.819	−	541.819i	−0.0536882	−	0.0536882i	−0.733441	+	0.679753i	$0.762087\pi$
$468$	623.518	−	15934.0i	0.0615857	−	1.57382i
$469$		−	1316.59i		−	0.129626i
$470$		0			0
$471$		−	17482.9i		−	1.71034i
$472$	−15030.9	−	7286.09i	−1.46579	−	0.710528i
$473$	−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
$478$	1478.91	+	3777.71i	0.141514	+	0.361482i
$479$	19357.9			1.84652			0.923260	−	0.384176i	$-0.125514\pi$
$479$	19357.9			1.84652			0.923260	+	0.384176i	$0.125514\pi$
$480$		0			0
$481$	−4085.06			−0.387240
$482$	6638.77	+	16958.0i	0.627361	+	1.60252i
$483$	−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	0.700509	−	0.713644i	$-0.252956\pi$
$487$	−141.166	−	141.166i	−0.0131352	−	0.0131352i	−0.713644	+	0.700509i	$0.752956\pi$
$488$	−3826.96	−	1855.09i	−0.354997	−	0.172082i
$489$			16203.1i			1.49842i
$490$		0			0
$491$			929.849i			0.0854654i	0.999087	+	0.0427327i	$0.0136064\pi$
$491$			929.849i			0.0854654i	−0.999087	+	0.0427327i	$0.986394\pi$
$492$	−175.904	+	4495.21i	−0.0161186	+	0.411910i
$493$	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
$498$	−25145.1	+	9843.91i	−2.26261	+	0.885776i
$499$	−13526.6			−1.21349			−0.606747	−	0.794895i	$-0.707526\pi$
$499$	−13526.6			−1.21349			−0.606747	+	0.794895i	$0.707526\pi$
$500$		0			0
$501$	−8909.29			−0.794487
$502$	−4945.16	+	1935.95i	−0.439668	+	0.172123i
$503$	−4770.81	+	4770.81i	−0.422902	+	0.422902i	−0.886202	−	0.463300i	$-0.846665\pi$
$503$	−4770.81	+	4770.81i	−0.422902	+	0.422902i	0.463300	+	0.886202i	$0.346665\pi$
$504$	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
$508$	−5637.03	−	220.585i	−0.492328	−	0.0192655i
$509$			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
$512$	2490.89	+	11314.3i	0.215006	+	0.976613i
$513$	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
$518$	−118.836	−	303.554i	−0.0100799	−	0.0257479i
$519$	−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	$0.573809\pi$
$522$	−2050.68	−	5238.22i	−0.171946	−	0.439216i
$523$	9877.72	−	9877.72i	0.825856	−	0.825856i	−0.161085	−	0.986941i	$-0.551499\pi$
$523$	9877.72	−	9877.72i	0.825856	−	0.825856i	0.986941	+	0.161085i	$0.0514993\pi$
$524$	−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
$528$	10341.9	−	8838.49i	0.852412	−	0.728496i
$529$			6120.55i			0.503045i
$530$		0			0
$531$			25704.7i			2.10073i
$532$	−734.391	−	28.7377i	−0.0598494	−	0.00234199i
$533$	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
$538$	17369.7	−	6799.95i	1.39193	−	0.544920i
$539$	−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	$0.295651\pi$
$542$	12593.5	−	4930.13i	0.998035	−	0.390715i
$543$	−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	0.862875	−	0.505418i	$-0.168662\pi$
$547$	4573.04	+	4573.04i	0.357457	+	0.357457i	−0.505418	+	0.862875i	$0.668662\pi$
$548$	54.9835	−	1405.10i	0.00428609	−	0.109531i
$549$			6544.60i			0.508773i
$550$		0			0
$551$			3249.00i			0.251202i
$552$	−6034.38	+	12448.7i	−0.465290	+	0.959873i
$553$	−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	$0.282858\pi$
$558$	6851.88	+	17502.3i	0.519827	+	1.32784i
$559$	−5419.00			−0.410017
$560$		0			0
$561$	10904.3			0.820640
$562$	−3140.99	−	8023.30i	−0.235756	−	0.602211i
$563$	1561.15	−	1561.15i	0.116864	−	0.116864i	−0.646256	−	0.763120i	$-0.723666\pi$
$563$	1561.15	−	1561.15i	0.116864	−	0.116864i	0.763120	+	0.646256i	$0.223666\pi$
$564$	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
$568$	1553.33	−	3204.46i	0.114747	−	0.236719i
$569$		−	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	$0.0652312\pi$
$571$			5553.22i			0.406997i	−0.979075	+	0.203498i	$0.934769\pi$
$572$	484.106	−	12371.3i	0.0353872	−	0.904318i
$573$	−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	$0.262386\pi$
$578$	6008.91	−	2352.39i	0.432418	−	0.169285i
$579$	−7950.68			−0.570672
$580$		0			0
$581$	−1961.07			−0.140033
$582$	32716.3	−	12807.9i	2.33013	−	0.912208i
$583$	−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	$-0.978762\pi$
$587$	−15138.4	−	15138.4i	−1.06445	−	1.06445i	−0.0666722	−	0.997775i	$-0.521238\pi$
$588$	−21394.5	−	837.198i	−1.50050	−	0.0587167i
$589$		−	10855.8i		−	0.759432i
$590$		0			0
$591$		−	3035.33i		−	0.211264i
$592$	−2967.24	−	3471.96i	−0.206001	−	0.241042i
$593$	−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
$598$	4589.62	+	11723.7i	0.313852	+	0.801699i
$599$	−10193.4			−0.695312			−0.347656	−	0.937622i	$-0.613022\pi$
$599$	−10193.4			−0.695312			−0.347656	+	0.937622i	$0.613022\pi$
$600$		0			0
$601$	−10688.6			−0.725454			−0.362727	−	0.931895i	$-0.618154\pi$
$601$	−10688.6			−0.725454			−0.362727	+	0.931895i	$0.618154\pi$
$602$	−157.642	−	402.677i	−0.0106727	−	0.0272623i
$603$	−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	0.178230	−	0.983989i	$-0.442963\pi$
$607$	−12050.0	−	12050.0i	−0.805759	−	0.805759i	−0.983989	+	0.178230i	$0.942963\pi$
$608$	−9852.35	+	2992.94i	−0.657180	+	0.199638i
$609$		−	725.306i		−	0.0482609i
$610$		0			0
$611$		−	27769.1i		−	1.83866i
$612$	14279.0	+	558.756i	0.943126	+	0.0369058i
$613$	−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	$0.312233\pi$
$618$	15300.7	−	5989.98i	0.995930	−	0.389890i
$619$	6990.42			0.453907			0.226954	−	0.973906i	$-0.427123\pi$
$619$	6990.42			0.453907			0.226954	+	0.973906i	$0.427123\pi$
$620$		0			0
$621$	4781.34			0.308967
$622$	−3637.86	+	1424.16i	−0.234510	+	0.0918068i
$623$	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
$628$	695.553	−	17774.8i	0.0441968	−	1.12945i
$629$		−	3660.76i		−	0.232057i
$630$		0			0
$631$			16801.3i			1.05998i	0.848003	+	0.529991i	$0.177805\pi$
$631$			16801.3i			1.05998i	−0.848003	+	0.529991i	$0.822195\pi$
$632$	−1133.67	−	549.539i	−0.0713531	−	0.0345878i
$633$	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
$638$	−1592.17	−	4067.01i	−0.0988003	−	0.252374i
$639$	−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	$0.424393\pi$
$642$	−7054.17	−	18019.1i	−0.433654	−	1.10772i
$643$	−13378.3	+	13378.3i	−0.820509	+	0.820509i	−0.986181	−	0.165672i	$-0.947021\pi$
$643$	−13378.3	+	13378.3i	−0.820509	+	0.820509i	0.165672	+	0.986181i	$0.447021\pi$
$644$	−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	0.934096	−	0.357023i	$-0.116208\pi$
$647$	9497.02	+	9497.02i	0.577073	+	0.577073i	−0.357023	+	0.934096i	$0.616208\pi$
$648$	9298.76	+	4507.49i	0.563719	+	0.273258i
$649$			19957.4i			1.20708i
$650$		0			0
$651$			2423.45i			0.145902i
$652$	−644.636	+	16473.6i	−0.0387207	+	0.989506i
$653$	−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
$658$	2063.48	−	807.819i	0.122254	−	0.0478603i
$659$	−5899.85			−0.348749			−0.174374	−	0.984679i	$-0.555790\pi$
$659$	−5899.85			−0.348749			−0.174374	+	0.984679i	$0.555790\pi$
$660$		0			0
$661$	25892.6			1.52361			0.761804	−	0.647808i	$-0.224314\pi$
$661$	25892.6			1.52361			0.761804	+	0.647808i	$0.224314\pi$
$662$	−22740.0	+	8902.36i	−1.33507	+	0.522658i
$663$	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
$668$	−9058.05	−	354.454i	−0.524650	−	0.0205303i
$669$		−	2877.10i		−	0.166270i
$670$		0			0
$671$			5081.29i			0.292342i
$672$	2199.44	−	668.143i	0.126258	−	0.0383544i
$673$	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	$-0.00356878\pi$
$678$	−7944.00	−	20292.0i	−0.449982	−	1.14943i
$679$	2551.55			0.144211
$680$		0			0
$681$	−23657.4			−1.33121
$682$	5319.88	+	13589.0i	0.298693	+	0.762976i
$683$	13579.6	−	13579.6i	0.760775	−	0.760775i	−0.215687	−	0.976463i	$-0.569199\pi$
$683$	13579.6	−	13579.6i	0.760775	−	0.760775i	0.976463	+	0.215687i	$0.0691991\pi$
$684$	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
$688$	−3936.17	−	4605.70i	−0.218118	−	0.255219i
$689$			19441.3i			1.07497i
$690$		0			0
$691$		−	12840.8i		−	0.706928i	−0.935448	−	0.353464i	$-0.885004\pi$
$691$		−	12840.8i		−	0.706928i	0.935448	−	0.353464i	$-0.114996\pi$
$692$	−13346.7	−	522.274i	−0.733186	−	0.0286906i
$693$	−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
$698$	−25315.4	+	9910.56i	−1.37278	+	0.537422i
$699$	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	$0.721399\pi$
$702$	−9270.70	+	3629.33i	−0.498433	+	0.195128i
$703$	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
$708$	−1815.63	+	46398.3i	−0.0963779	+	2.46293i
$709$			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
$712$	1566.25	−	3231.11i	0.0824408	−	0.170072i
$713$	−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
$718$	−5772.09	−	14744.1i	−0.300017	−	0.766359i
$719$	−22553.8			−1.16984			−0.584921	−	0.811090i	$-0.698874\pi$
$719$	−22553.8			−1.16984			−0.584921	+	0.811090i	$0.698874\pi$
$720$		0			0
$721$	1193.30			0.0616380
$722$	3735.97	+	9543.10i	0.192574	+	0.491908i
$723$	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	$0.00314935\pi$
$727$	19795.0	+	19795.0i	1.00984	+	1.00984i	0.00989382	+	0.999951i	$0.496851\pi$
$728$	912.504	−	1882.46i	0.0464556	−	0.0958358i
$729$		−	28955.6i		−	1.47110i
$730$		0			0
$731$		−	4856.16i		−	0.245706i
$732$	−462.272	+	11813.3i	−0.0233416	+	0.596493i
$733$	−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
$738$	6559.06	−	2567.77i	0.327158	−	0.128077i
$739$	28579.3			1.42261			0.711304	−	0.702885i	$-0.248105\pi$
$739$	28579.3			1.42261			0.711304	+	0.702885i	$0.248105\pi$
$740$		0			0
$741$	25602.3			1.26926
$742$	−1444.65	+	565.558i	−0.0714755	+	0.0279815i
$743$	−20848.1	+	20848.1i	−1.02940	+	1.02940i	−0.0298445	+	0.999555i	$0.509501\pi$
$743$	−20848.1	+	20848.1i	−1.02940	+	1.02940i	−0.999555	+	0.0298445i	$0.990499\pi$
$744$	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
$748$	11086.3	+	433.824i	0.541921	+	0.0212061i
$749$		−	1405.31i		−	0.0685566i
$750$		0			0
$751$			13588.4i			0.660252i	0.943937	+	0.330126i	$0.107091\pi$
$751$			13588.4i			0.660252i	−0.943937	+	0.330126i	$0.892909\pi$
$752$	23601.5	−	20170.5i	1.14449	−	0.978115i
$753$	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	$0.232374\pi$
$758$	10303.1	+	26318.1i	0.493702	+	1.26110i
$759$	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	$0.793919\pi$
$762$	5716.82	+	14602.9i	0.271783	+	0.694237i
$763$	−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
$768$	26042.6	−	18946.3i	1.22361	−	0.890188i
$769$		−	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
$772$	−8083.43	−	316.316i	−0.376851	−	0.0147467i
$773$	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
$778$	−402.902	+	157.729i	−0.0185665	+	0.00726848i
$779$	−4068.25			−0.187112
$780$		0			0
$781$	−4254.76			−0.194939
$782$	−10506.0	+	4112.92i	−0.480425	+	0.188079i
$783$	−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	0.396180	−	0.918173i	$-0.370336\pi$
$787$	−11524.6	−	11524.6i	−0.521993	−	0.521993i	−0.918173	+	0.396180i	$0.870336\pi$
$788$	120.760	−	3086.01i	0.00545925	−	0.139511i
$789$		−	11174.3i		−	0.504202i
$790$		0			0
$791$		−	1582.58i		−	0.0711378i
$792$	−19167.6	−	9291.31i	−0.859962	−	0.416859i
$793$	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	$0.256571\pi$
$798$	744.785	+	1902.47i	0.0330390	+	0.0843942i
$799$	24884.9			1.10183
$800$		0			0
$801$	−5525.62			−0.243743
$802$	−11280.0	−	28813.5i	−0.496648	−	1.26863i
$803$	−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
$808$	16040.2	+	7775.37i	0.698383	+	0.338535i
$809$		−	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	$0.219309\pi$
$811$			29366.2i			1.27150i	−0.771896	+	0.635749i	$0.780691\pi$
$812$	28.8561	−	737.417i	0.00124711	−	0.0318698i
$813$	−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
$818$	−7855.67	+	3075.37i	−0.335779	+	0.131452i
$819$	−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	$0.439796\pi$
$822$	−3639.96	+	1424.99i	−0.154450	+	0.0604649i
$823$	−16257.0	+	16257.0i	−0.688559	+	0.688559i	−0.961913	−	0.273355i	$-0.911867\pi$
$823$	−16257.0	+	16257.0i	−0.688559	+	0.688559i	0.273355	+	0.961913i	$0.411867\pi$
$824$	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	0.984119	−	0.177507i	$-0.0568034\pi$
$827$	19183.3	+	19183.3i	0.806612	+	0.806612i	−0.177507	+	0.984119i	$0.556803\pi$
$828$	21644.3	+	846.970i	0.908442	+	0.0355486i
$829$		−	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
$832$	3431.07	−	29107.5i	0.142970	−	1.21289i
$833$	−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
$838$	−2916.14	−	7448.93i	−0.120210	−	0.307063i
$839$	−13726.1			−0.564814			−0.282407	−	0.959295i	$-0.591133\pi$
$839$	−13726.1			−0.564814			−0.282407	+	0.959295i	$0.591133\pi$
$840$		0			0
$841$	21126.6			0.866235
$842$	−762.948	−	1948.86i	−0.0312268	−	0.0797651i
$843$	−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
$848$	−16523.5	+	14121.5i	−0.669127	+	0.571855i
$849$			65139.8i			2.63320i
$850$		0			0
$851$		−	5549.03i		−	0.223523i
$852$	−9891.74	−	387.078i	−0.397753	−	0.0155646i
$853$	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	$0.988067\pi$
$858$	−32048.3	+	12546.4i	−1.27519	+	0.499216i
$859$	4857.84			0.192954			0.0964769	−	0.995335i	$-0.469243\pi$
$859$	4857.84			0.192954			0.0964769	+	0.995335i	$0.469243\pi$
$860$		0			0
$861$	908.196			0.0359480
$862$	18632.6	−	7294.37i	0.736229	−	0.288222i
$863$	23423.0	−	23423.0i	0.923904	−	0.923904i	−0.0733988	−	0.997303i	$-0.523385\pi$
$863$	23423.0	−	23423.0i	0.923904	−	0.923904i	0.997303	+	0.0733988i	$0.0233846\pi$
$864$	−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
$868$	−96.4163	+	2463.91i	−0.00377025	+	0.0963486i
$869$			1505.25i			0.0587596i
$870$		0			0
$871$			46665.5i			1.81539i
$872$	−3936.90	+	8121.66i	−0.152890	+	0.315406i
$873$	−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	$0.0763046\pi$
$878$	−13304.5	−	33984.9i	−0.511396	−	1.30630i
$879$	−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	$0.539902\pi$
$882$	12221.1	+	31217.3i	0.466558	+	1.19177i
$883$	23546.4	−	23546.4i	0.897395	−	0.897395i	−0.0978097	−	0.995205i	$-0.531184\pi$
$883$	23546.4	−	23546.4i	0.897395	−	0.897395i	0.995205	+	0.0978097i	$0.0311836\pi$
$884$	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	0.405162	−	0.914245i	$-0.367215\pi$
$887$	−13448.5	−	13448.5i	−0.509082	−	0.509082i	−0.914245	+	0.405162i	$0.867215\pi$
$888$	−5537.95	+	11424.5i	−0.209281	+	0.431737i
$889$			1138.89i			0.0429663i
$890$		0			0
$891$		−	12346.5i		−	0.464225i
$892$	114.465	−	2925.13i	0.00429659	−	0.109799i
$893$	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
$898$	−358.531	+	140.359i	−0.0133233	+	0.00521585i
$899$	10900.5			0.404397
$900$		0			0
$901$	−17422.0			−0.644186
$902$	5092.53	−	1993.64i	0.187985	−	0.0735932i
$903$	−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	0.710763	−	0.703431i	$-0.248350\pi$
$907$	200.288	+	200.288i	0.00733237	+	0.00733237i	−0.703431	+	0.710763i	$0.748350\pi$
$908$	−24052.4	−	941.202i	−0.879081	−	0.0343997i
$909$		−	27430.9i		−	1.00091i
$910$		0			0
$911$			7662.84i			0.278684i	0.990244	+	0.139342i	$0.0444987\pi$
$911$			7662.84i			0.278684i	−0.990244	+	0.139342i	$0.955501\pi$
$912$	18596.6	+	21759.9i	0.675214	+	0.790067i
$913$	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
$918$	−3252.37	−	8307.79i	−0.116933	−	0.298691i
$919$	17176.1			0.616527			0.308263	−	0.951301i	$-0.400252\pi$
$919$	17176.1			0.616527			0.308263	+	0.951301i	$0.400252\pi$
$920$		0			0
$921$	16287.2			0.582715
$922$	−9853.62	−	25169.9i	−0.351965	−	0.899054i
$923$	−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
$928$	−3005.27	−	9892.94i	−0.106307	−	0.349948i
$929$			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
$932$	38352.7	+	1500.80i	1.34795	+	0.0527470i
$933$	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	$0.218558\pi$
$938$	−3467.64	+	1357.52i	−0.120706	+	0.0472545i
$939$	−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	$0.271621\pi$
$942$	−46046.3	+	18026.4i	−1.59264	+	0.623495i
$943$	−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	0.435070	−	0.900397i	$-0.356724\pi$
$947$	−13560.7	−	13560.7i	−0.465327	−	0.465327i	−0.900397	+	0.435070i	$0.856724\pi$
$948$	−136.940	+	3499.50i	−0.00469158	+	0.119893i
$949$			14621.6i			0.500145i
$950$		0			0
$951$			23115.4i			0.788189i
$952$	1686.93	+	817.726i	0.0574305	+	0.0278389i
$953$	−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
$958$	−19959.6	−	50984.6i	−0.673138	−	1.71945i
$959$	−283.881			−0.00955892
$960$		0			0
$961$	−6630.66			−0.222573
$962$	4212.05	+	10759.2i	0.141166	+	0.360593i
$963$	−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	0.908917	−	0.416978i	$-0.136911\pi$
$967$	14792.8	+	14792.8i	0.491939	+	0.491939i	−0.416978	+	0.908917i	$0.636911\pi$
$968$	12219.0	+	5923.06i	0.405717	+	0.196668i
$969$			22943.1i			0.760619i
$970$		0			0
$971$			14139.9i			0.467322i	0.972318	+	0.233661i	$0.0750706\pi$
$971$			14139.9i			0.467322i	−0.972318	+	0.233661i	$0.924929\pi$
$972$	1642.56	−	41975.6i	0.0542029	−	1.38515i
$973$	−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	$0.266877\pi$
$978$	42675.6	−	16706.8i	1.39531	−	0.546242i
$979$	−4290.15			−0.140055
$980$		0			0
$981$	13889.1			0.452033
$982$	2449.03	−	958.755i	0.0795842	−	0.0311559i
$983$	−6757.28	+	6757.28i	−0.219251	+	0.219251i	−0.808183	−	0.588932i	$-0.799549\pi$
$983$	−6757.28	+	6757.28i	−0.219251	+	0.219251i	0.588932	+	0.808183i	$0.299549\pi$
$984$	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
$988$	26029.8	+	1018.58i	0.838177	+	0.0327990i
$989$		−	7361.03i		−	0.236670i
$990$		0			0
$991$		−	18118.1i		−	0.580767i	−0.956910	−	0.290384i	$-0.906217\pi$
$991$		−	18118.1i		−	0.580767i	0.956910	−	0.290384i	$-0.0937829\pi$
$992$	10041.4	+	33055.0i	0.321387	+	1.05796i
$993$	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	$0.384142\pi$
$998$	13947.1	+	35626.2i	0.442372	+	1.12999i
$999$	4388.00			0.138969

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.03109 - 2.63379i) q^{2} +(-5.55970 + 5.55970i) q^{3} +(-5.87372 + 5.43134i) q^{4} +(20.3756 + 8.91056i) q^{6} +(1.14202 + 1.14202i) q^{7} +(20.3613 + 9.86997i) q^{8} -34.8205i q^{9} +O(q^{10})\)	\(q+(-1.03109 - 2.63379i) 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} +(20.3613 + 9.86997i) q^{8} -34.8205i q^{9} -27.0350i q^{11} +(2.45951 - 62.8527i) 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} +(-91.7099 + 35.9029i) q^{18} +56.8829 q^{19} -12.6985 q^{21} +(-71.2046 + 27.8754i) 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} +(-12.9106 - 0.505208i) q^{28} +57.1173i q^{29} -190.845i q^{31} +(-173.204 + 52.6158i) 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} +(-58.6513 - 149.818i) q^{38} +450.088 q^{39} -71.5197 q^{41} +(13.0933 + 33.4453i) 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} +(326.928 + 382.538i) q^{48} -340.392i q^{49} +403.339i q^{51} +(457.603 + 17.9066i) 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} +(150.435 - 58.8929i) q^{58} -738.207 q^{59} -187.952 q^{61} +(-502.645 + 196.777i) 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} +(-16.0468 + 410.074i) q^{68} +611.387i q^{69} -157.380i q^{71} +(343.677 - 708.991i) 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} +(-464.080 - 1185.44i) q^{78} -55.6778 q^{79} +456.687 q^{81} +(73.7430 + 188.368i) 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} +(266.835 - 550.468i) q^{88} -158.689i q^{89} -92.4525i q^{91} +(-24.3239 + 621.596i) 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} +(-896.521 + 350.973i) 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

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Representations

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Database

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