LMFDB - Embedded newform 525.3.o.l.451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(376,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("525.376");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.o (of order $6$, 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:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.523596960000.16
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} - 2x^{5} + 91x^{4} - 50x^{3} + 190x^{2} + 100x + 100 $ x^8 - 2x^7 + 13x^6 - 2x^5 + 91x^4 - 50x^3 + 190x^2 + 100*x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.2
Root			$0.836732 + 1.44926i$ of defining polynomial
Character	$\chi$	$=$	525.451
Dual form			525.3.o.l.376.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.836732 - 1.44926i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.599760 - 1.03881i) q^{4} -2.89852i q^{6} +(-4.76104 - 5.13152i) q^{7} -8.70121 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.836732 - 1.44926i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.599760 - 1.03881i) q^{4} -2.89852i q^{6} +(-4.76104 - 5.13152i) q^{7} -8.70121 q^{8} +(1.50000 + 2.59808i) q^{9} +(6.91411 - 11.9756i) q^{11} +(1.79928 - 1.03881i) q^{12} -6.12052i q^{13} +(-3.45321 + 11.1937i) q^{14} +(4.88154 + 8.45507i) q^{16} +(2.14655 + 1.23931i) q^{17} +(2.51020 - 4.34779i) q^{18} +(-24.2290 + 13.9886i) q^{19} +(-2.69753 - 11.8205i) q^{21} -23.1410 q^{22} +(6.62020 + 11.4665i) q^{23} +(-13.0518 - 7.53547i) q^{24} +(-8.87024 + 5.12123i) q^{26} +5.19615i q^{27} +(-8.18618 + 1.86816i) q^{28} -27.6516 q^{29} +(-16.2122 - 9.36010i) q^{31} +(-9.23334 + 15.9926i) q^{32} +(20.7423 - 11.9756i) q^{33} -4.14789i q^{34} +3.59856 q^{36} +(-20.5067 - 35.5187i) q^{37} +(40.5463 + 23.4094i) q^{38} +(5.30052 - 9.18078i) q^{39} -22.5351i q^{41} +(-14.8738 + 13.8000i) q^{42} -7.60485 q^{43} +(-8.29361 - 14.3650i) q^{44} +(11.0787 - 19.1888i) q^{46} +(11.9214 - 6.88283i) q^{47} +16.9101i q^{48} +(-3.66502 + 48.8627i) q^{49} +(2.14655 + 3.71794i) q^{51} +(-6.35808 - 3.67084i) q^{52} +(46.2995 - 80.1930i) q^{53} +(7.53059 - 4.34779i) q^{54} +(41.4268 + 44.6504i) q^{56} -48.4579 q^{57} +(23.1370 + 40.0744i) q^{58} +(-61.5680 - 35.5463i) q^{59} +(-100.214 + 57.8584i) q^{61} +31.3276i q^{62} +(6.19052 - 20.0668i) q^{63} +69.9556 q^{64} +(-34.7115 - 20.0407i) q^{66} +(-5.70227 + 9.87662i) q^{67} +(2.57483 - 1.48658i) q^{68} +22.9330i q^{69} +99.4924 q^{71} +(-13.0518 - 22.6064i) q^{72} +(-90.1276 - 52.0352i) q^{73} +(-34.3172 + 59.4392i) q^{74} +33.5592i q^{76} +(-94.3714 + 21.5364i) q^{77} -17.7405 q^{78} +(-64.4982 - 111.714i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-32.6592 + 18.8558i) q^{82} +30.3382i q^{83} +(-13.8971 - 4.28721i) q^{84} +(6.36322 + 11.0214i) q^{86} +(-41.4774 - 23.9470i) q^{87} +(-60.1611 + 104.202i) q^{88} +(93.9587 - 54.2471i) q^{89} +(-31.4076 + 29.1400i) q^{91} +15.8821 q^{92} +(-16.2122 - 28.0803i) q^{93} +(-19.9501 - 11.5182i) q^{94} +(-27.7000 + 15.9926i) q^{96} +153.154i q^{97} +(73.8816 - 35.5734i) q^{98} +41.4847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 12 q^{3} - 6 q^{4} + 16 q^{7} + 32 q^{8} + 12 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 12 * q^3 - 6 * q^4 + 16 * q^7 + 32 * q^8 + 12 * q^9	$ 8 q - 2 q^{2} + 12 q^{3} - 6 q^{4} + 16 q^{7} + 32 q^{8} + 12 q^{9} + 20 q^{11} - 18 q^{12} - 16 q^{14} - 2 q^{16} + 18 q^{17} + 6 q^{18} + 48 q^{21} + 16 q^{22} - 62 q^{23} + 48 q^{24} + 120 q^{26} + 120 q^{28} - 100 q^{29} - 126 q^{31} - 36 q^{32} + 60 q^{33} - 36 q^{36} + 80 q^{37} - 114 q^{38} - 12 q^{39} - 90 q^{42} - 352 q^{43} - 18 q^{44} - 82 q^{46} + 72 q^{47} + 38 q^{49} + 18 q^{51} + 48 q^{52} + 76 q^{53} + 18 q^{54} + 196 q^{56} + 40 q^{58} - 54 q^{59} - 396 q^{61} + 96 q^{63} - 4 q^{64} + 24 q^{66} - 184 q^{67} + 312 q^{68} + 164 q^{71} + 48 q^{72} - 348 q^{73} - 140 q^{74} - 152 q^{77} + 240 q^{78} - 206 q^{79} - 36 q^{81} - 204 q^{82} + 132 q^{84} + 178 q^{86} - 150 q^{87} - 124 q^{88} + 282 q^{89} - 114 q^{91} + 288 q^{92} - 126 q^{93} + 30 q^{94} - 108 q^{96} + 592 q^{98} + 120 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 12 * q^3 - 6 * q^4 + 16 * q^7 + 32 * q^8 + 12 * q^9 + 20 * q^11 - 18 * q^12 - 16 * q^14 - 2 * q^16 + 18 * q^17 + 6 * q^18 + 48 * q^21 + 16 * q^22 - 62 * q^23 + 48 * q^24 + 120 * q^26 + 120 * q^28 - 100 * q^29 - 126 * q^31 - 36 * q^32 + 60 * q^33 - 36 * q^36 + 80 * q^37 - 114 * q^38 - 12 * q^39 - 90 * q^42 - 352 * q^43 - 18 * q^44 - 82 * q^46 + 72 * q^47 + 38 * q^49 + 18 * q^51 + 48 * q^52 + 76 * q^53 + 18 * q^54 + 196 * q^56 + 40 * q^58 - 54 * q^59 - 396 * q^61 + 96 * q^63 - 4 * q^64 + 24 * q^66 - 184 * q^67 + 312 * q^68 + 164 * q^71 + 48 * q^72 - 348 * q^73 - 140 * q^74 - 152 * q^77 + 240 * q^78 - 206 * q^79 - 36 * q^81 - 204 * q^82 + 132 * q^84 + 178 * q^86 - 150 * q^87 - 124 * q^88 + 282 * q^89 - 114 * q^91 + 288 * q^92 - 126 * q^93 + 30 * q^94 - 108 * q^96 + 592 * q^98 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.836732	−	1.44926i	−0.418366	−	0.724631i	0.577409	−	0.816455i	$-0.304064\pi$
$2$	−0.836732	−	1.44926i	−0.418366	−	0.724631i	−0.995775	+	0.0918238i	$0.970730\pi$
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$	0.599760	−	1.03881i	0.149940	−	0.259704i
$5$		0			0
$5$		0			0
$6$		−	2.89852i		−	0.483087i
$7$	−4.76104	−	5.13152i	−0.680148	−	0.733074i
$7$	−4.76104	−	5.13152i	−0.680148	−	0.733074i
$8$	−8.70121			−1.08765
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	6.91411	−	11.9756i	0.628556	−	1.08869i	−0.359286	−	0.933227i	$-0.616980\pi$
$11$	6.91411	−	11.9756i	0.628556	−	1.08869i	0.987842	−	0.155463i	$-0.0496869\pi$
$12$	1.79928	−	1.03881i	0.149940	−	0.0865679i
$13$		−	6.12052i		−	0.470809i	−0.971897	−	0.235405i	$-0.924358\pi$
$13$		−	6.12052i		−	0.470809i	0.971897	−	0.235405i	$-0.0756415\pi$
$14$	−3.45321	+	11.1937i	−0.246658	+	0.799550i
$15$		0			0
$16$	4.88154	+	8.45507i	0.305096	+	0.528442i
$17$	2.14655	+	1.23931i	0.126268	+	0.0729008i	0.561804	−	0.827271i	$-0.310108\pi$
$17$	2.14655	+	1.23931i	0.126268	+	0.0729008i	−0.435536	+	0.900171i	$0.643441\pi$
$18$	2.51020	−	4.34779i	0.139455	−	0.241544i
$19$	−24.2290	+	13.9886i	−1.27521	+	0.736242i	−0.975963	−	0.217935i	$-0.930068\pi$
$19$	−24.2290	+	13.9886i	−1.27521	+	0.736242i	−0.299245	+	0.954176i	$0.596735\pi$
$20$		0			0
$21$	−2.69753	−	11.8205i	−0.128454	−	0.562879i
$22$	−23.1410			−1.05186
$23$	6.62020	+	11.4665i	0.287835	+	0.498544i	0.973293	−	0.229568i	$-0.0737313\pi$
$23$	6.62020	+	11.4665i	0.287835	+	0.498544i	−0.685458	+	0.728112i	$0.740398\pi$
$24$	−13.0518	−	7.53547i	−0.543825	−	0.313978i
$25$		0			0
$26$	−8.87024	+	5.12123i	−0.341163	+	0.196970i
$27$			5.19615i			0.192450i
$28$	−8.18618	+	1.86816i	−0.292364	+	0.0667199i
$29$	−27.6516			−0.953503			−0.476751	−	0.879038i	$-0.658186\pi$
$29$	−27.6516			−0.953503			−0.476751	+	0.879038i	$0.658186\pi$
$30$		0			0
$31$	−16.2122	−	9.36010i	−0.522973	−	0.301939i	0.215177	−	0.976575i	$-0.430967\pi$
$31$	−16.2122	−	9.36010i	−0.522973	−	0.301939i	−0.738150	+	0.674636i	$0.764300\pi$
$32$	−9.23334	+	15.9926i	−0.288542	+	0.499769i
$33$	20.7423	−	11.9756i	0.628556	−	0.362897i
$34$		−	4.14789i		−	0.121997i
$35$		0			0
$36$	3.59856			0.0999600
$37$	−20.5067	−	35.5187i	−0.554235	−	0.959964i	−0.997963	−	0.0638017i	$-0.979677\pi$
$37$	−20.5067	−	35.5187i	−0.554235	−	0.959964i	0.443727	−	0.896162i	$-0.353656\pi$
$38$	40.5463	+	23.4094i	1.06701	+	0.616037i
$39$	5.30052	−	9.18078i	0.135911	−	0.235405i
$40$		0			0
$41$		−	22.5351i		−	0.549636i	−0.961496	−	0.274818i	$-0.911382\pi$
$41$		−	22.5351i		−	0.549636i	0.961496	−	0.274818i	$-0.0886176\pi$
$42$	−14.8738	+	13.8000i	−0.354139	+	0.328571i
$43$	−7.60485			−0.176857			−0.0884285	−	0.996083i	$-0.528184\pi$
$43$	−7.60485			−0.176857			−0.0884285	+	0.996083i	$0.528184\pi$
$44$	−8.29361	−	14.3650i	−0.188491	−	0.326476i
$45$		0			0
$46$	11.0787	−	19.1888i	0.240840	−	0.417148i
$47$	11.9214	−	6.88283i	0.253647	−	0.146443i	−0.367786	−	0.929910i	$-0.619884\pi$
$47$	11.9214	−	6.88283i	0.253647	−	0.146443i	0.621433	+	0.783467i	$0.286551\pi$
$48$			16.9101i			0.352295i
$49$	−3.66502	+	48.8627i	−0.0747963	+	0.997199i
$50$		0			0
$51$	2.14655	+	3.71794i	0.0420893	+	0.0729008i
$52$	−6.35808	−	3.67084i	−0.122271	−	0.0705931i
$53$	46.2995	−	80.1930i	0.873575	−	1.51308i	0.0153016	−	0.999883i	$-0.495129\pi$
$53$	46.2995	−	80.1930i	0.873575	−	1.51308i	0.858273	−	0.513193i	$-0.171537\pi$
$54$	7.53059	−	4.34779i	0.139455	−	0.0805146i
$55$		0			0
$56$	41.4268	+	44.6504i	0.739764	+	0.797329i
$57$	−48.4579			−0.850139
$58$	23.1370	+	40.0744i	0.398913	+	0.690938i
$59$	−61.5680	−	35.5463i	−1.04352	−	0.602479i	−0.122695	−	0.992444i	$-0.539154\pi$
$59$	−61.5680	−	35.5463i	−1.04352	−	0.602479i	−0.920830	+	0.389965i	$0.872487\pi$
$60$		0			0
$61$	−100.214	+	57.8584i	−1.64285	+	0.948498i	−0.663031	+	0.748592i	$0.730730\pi$
$61$	−100.214	+	57.8584i	−1.64285	+	0.948498i	−0.979815	+	0.199906i	$0.935936\pi$
$62$			31.3276i			0.505283i
$63$	6.19052	−	20.0668i	0.0982623	−	0.318521i
$64$	69.9556			1.09306
$65$		0			0
$66$	−34.7115	−	20.0407i	−0.525932	−	0.303647i
$67$	−5.70227	+	9.87662i	−0.0851085	+	0.147412i	−0.905437	−	0.424480i	$-0.860457\pi$
$67$	−5.70227	+	9.87662i	−0.0851085	+	0.147412i	0.820329	+	0.571892i	$0.193790\pi$
$68$	2.57483	−	1.48658i	0.0378652	−	0.0218615i
$69$			22.9330i			0.332363i
$70$		0			0
$71$	99.4924			1.40130			0.700651	−	0.713504i	$-0.252893\pi$
$71$	99.4924			1.40130			0.700651	+	0.713504i	$0.252893\pi$
$72$	−13.0518	−	22.6064i	−0.181275	−	0.313978i
$73$	−90.1276	−	52.0352i	−1.23462	−	0.712811i	−0.266634	−	0.963798i	$-0.585912\pi$
$73$	−90.1276	−	52.0352i	−1.23462	−	0.712811i	−0.967991	+	0.250987i	$0.919245\pi$
$74$	−34.3172	+	59.4392i	−0.463746	+	0.803232i
$75$		0			0
$76$			33.5592i			0.441568i
$77$	−94.3714	+	21.5364i	−1.22560	+	0.279693i
$78$	−17.7405			−0.227442
$79$	−64.4982	−	111.714i	−0.816433	−	1.41410i	−0.908294	−	0.418331i	$-0.862615\pi$
$79$	−64.4982	−	111.714i	−0.816433	−	1.41410i	0.0918616	−	0.995772i	$-0.470718\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−32.6592	+	18.8558i	−0.398283	+	0.229949i
$83$			30.3382i			0.365520i	0.983158	+	0.182760i	$0.0585032\pi$
$83$			30.3382i			0.365520i	−0.983158	+	0.182760i	$0.941497\pi$
$84$	−13.8971	−	4.28721i	−0.165442	−	0.0510382i
$85$		0			0
$86$	6.36322	+	11.0214i	0.0739909	+	0.128156i
$87$	−41.4774	−	23.9470i	−0.476751	−	0.275253i
$88$	−60.1611	+	104.202i	−0.683649	+	1.18411i
$89$	93.9587	−	54.2471i	1.05572	−	0.609518i	0.131472	−	0.991320i	$-0.458030\pi$
$89$	93.9587	−	54.2471i	1.05572	−	0.609518i	0.924244	+	0.381802i	$0.124696\pi$
$90$		0			0
$91$	−31.4076	+	29.1400i	−0.345138	+	0.320220i
$92$	15.8821			0.172632
$93$	−16.2122	−	28.0803i	−0.174324	−	0.301939i
$94$	−19.9501	−	11.5182i	−0.212235	−	0.122534i
$95$		0			0
$96$	−27.7000	+	15.9926i	−0.288542	+	0.166590i
$97$			153.154i			1.57890i	0.613812	+	0.789452i	$0.289635\pi$
$97$			153.154i			1.57890i	−0.613812	+	0.789452i	$0.710365\pi$
$98$	73.8816	−	35.5734i	0.753893	−	0.362994i
$99$	41.4847			0.419037
$100$		0			0
$101$	98.9544	+	57.1314i	0.979747	+	0.565657i	0.902194	−	0.431331i	$-0.141956\pi$
$101$	98.9544	+	57.1314i	0.979747	+	0.565657i	0.0775531	+	0.996988i	$0.475289\pi$
$102$	3.59218	−	6.22184i	0.0352174	−	0.0609984i
$103$	48.4794	−	27.9896i	0.470674	−	0.271744i	−0.245848	−	0.969308i	$-0.579066\pi$
$103$	48.4794	−	27.9896i	0.470674	−	0.271744i	0.716522	+	0.697565i	$0.245733\pi$
$104$			53.2559i			0.512076i
$105$		0			0
$106$	−154.961			−1.46190
$107$	49.3529	+	85.4817i	0.461242	+	0.798895i	0.999023	−	0.0441897i	$-0.0140706\pi$
$107$	49.3529	+	85.4817i	0.461242	+	0.798895i	−0.537781	+	0.843085i	$0.680737\pi$
$108$	5.39784	+	3.11644i	0.0499800	+	0.0288560i
$109$	−26.3791	+	45.6900i	−0.242010	+	0.419174i	−0.961287	−	0.275550i	$-0.911140\pi$
$109$	−26.3791	+	45.6900i	−0.242010	+	0.419174i	0.719276	+	0.694724i	$0.244473\pi$
$110$		0			0
$111$		−	71.0373i		−	0.639976i
$112$	20.1462	−	65.3046i	0.179877	−	0.583077i
$113$	−106.206			−0.939875			−0.469937	−	0.882700i	$-0.655724\pi$
$113$	−106.206			−0.939875			−0.469937	+	0.882700i	$0.655724\pi$
$114$	40.5463	+	70.2282i	0.355669	+	0.616037i
$115$		0			0
$116$	−16.5843	+	28.7249i	−0.142968	+	0.247628i
$117$	15.9016	−	9.18078i	0.135911	−	0.0784682i
$118$			118.971i			1.00823i
$119$	−3.86026	−	16.9155i	−0.0324392	−	0.142147i
$120$		0			0
$121$	−35.1099	−	60.8121i	−0.290164	−	0.502579i
$122$	167.704	+	96.8239i	1.37462	+	0.793638i
$123$	19.5160	−	33.8026i	0.158666	−	0.274818i
$124$	−19.4468	+	11.2276i	−0.156829	+	0.0905453i
$125$		0			0
$126$	−34.2619	+	7.81886i	−0.271920	+	0.0620544i
$127$	197.402			1.55434			0.777172	−	0.629288i	$-0.216653\pi$
$127$	197.402			1.55434			0.777172	+	0.629288i	$0.216653\pi$
$128$	−21.6007	−	37.4135i	−0.168756	−	0.292293i
$129$	−11.4073	−	6.58599i	−0.0884285	−	0.0510542i
$130$		0			0
$131$	127.379	−	73.5423i	0.972358	−	0.561391i	0.0724040	−	0.997375i	$-0.476933\pi$
$131$	127.379	−	73.5423i	0.972358	−	0.561391i	0.899954	+	0.435984i	$0.143600\pi$
$132$		−	28.7299i		−	0.217651i
$133$	187.138	+	57.7311i	1.40705	+	0.434069i
$134$	19.0851			0.142426
$135$		0			0
$136$	−18.6776	−	10.7835i	−0.137335	−	0.0792906i
$137$	124.296	−	215.287i	0.907270	−	1.57144i	0.0894293	−	0.995993i	$-0.471496\pi$
$137$	124.296	−	215.287i	0.907270	−	1.57144i	0.817841	−	0.575445i	$-0.195171\pi$
$138$	33.2360	−	19.1888i	0.240840	−	0.139049i
$139$		−	15.7344i		−	0.113197i	−0.998397	−	0.0565985i	$-0.981974\pi$
$139$		−	15.7344i		−	0.113197i	0.998397	−	0.0565985i	$-0.0180255\pi$
$140$		0			0
$141$	23.8428			0.169098
$142$	−83.2485	−	144.191i	−0.586257	−	1.01543i
$143$	−73.2968	−	42.3180i	−0.512565	−	0.295930i
$144$	−14.6446	+	25.3652i	−0.101699	+	0.176147i
$145$		0			0
$146$			174.158i			1.19286i
$147$	−47.8139	+	70.1201i	−0.325265	+	0.477008i
$148$	−49.1964			−0.332408
$149$	−92.1029	−	159.527i	−0.618140	−	1.07065i	−0.989825	−	0.142291i	$-0.954553\pi$
$149$	−92.1029	−	159.527i	−0.618140	−	1.07065i	0.371684	−	0.928359i	$-0.378780\pi$
$150$		0			0
$151$	131.625	−	227.982i	0.871690	−	1.50981i	0.0114426	−	0.999935i	$-0.496358\pi$
$151$	131.625	−	227.982i	0.871690	−	1.50981i	0.860247	−	0.509877i	$-0.170309\pi$
$152$	210.821	−	121.718i	1.38698	−	0.800774i
$153$			7.43588i			0.0486005i
$154$	110.175	+	118.749i	0.715424	+	0.771095i
$155$		0			0
$156$	−6.35808	−	11.0125i	−0.0407570	−	0.0705931i
$157$	−187.600	−	108.311i	−1.19490	−	0.689878i	−0.235489	−	0.971877i	$-0.575669\pi$
$157$	−187.600	−	108.311i	−1.19490	−	0.689878i	−0.959415	+	0.281999i	$0.909003\pi$
$158$	−107.935	+	186.950i	−0.683135	+	1.18323i
$159$	138.898	−	80.1930i	0.873575	−	0.504359i
$160$		0			0
$161$	27.3217	−	88.5642i	0.169700	−	0.550088i
$162$	15.0612			0.0929702
$163$	−86.2901	−	149.459i	−0.529387	−	0.916926i	−0.999413	−	0.0342728i	$-0.989088\pi$
$163$	−86.2901	−	149.459i	−0.529387	−	0.916926i	0.470025	−	0.882653i	$-0.344245\pi$
$164$	−23.4098	−	13.5156i	−0.142743	−	0.0824124i
$165$		0			0
$166$	43.9680	−	25.3849i	0.264867	−	0.152921i
$167$			156.923i			0.939658i	0.882758	+	0.469829i	$0.155684\pi$
$167$			156.923i			0.939658i	−0.882758	+	0.469829i	$0.844316\pi$
$168$	23.4718	+	102.852i	0.139713	+	0.612216i
$169$	131.539			0.778339
$170$		0			0
$171$	−72.6869	−	41.9658i	−0.425069	−	0.245414i
$172$	−4.56108	+	7.90003i	−0.0265179	+	0.0459304i
$173$	41.2245	−	23.8010i	0.238292	−	0.137578i	−0.376100	−	0.926579i	$-0.622735\pi$
$173$	41.2245	−	23.8010i	0.238292	−	0.137578i	0.614391	+	0.789001i	$0.289402\pi$
$174$			80.1488i			0.460625i
$175$		0			0
$176$	135.006			0.767079
$177$	−61.5680	−	106.639i	−0.347842	−	0.602479i
$178$	−157.237	−	90.7805i	−0.883351	−	0.510003i
$179$	−14.7747	+	25.5905i	−0.0825402	+	0.142964i	−0.904340	−	0.426812i	$-0.859637\pi$
$179$	−14.7747	+	25.5905i	−0.0825402	+	0.142964i	0.821800	+	0.569776i	$0.192970\pi$
$180$		0			0
$181$		−	10.3249i		−	0.0570439i	−0.999593	−	0.0285219i	$-0.990920\pi$
$181$		−	10.3249i		−	0.0570439i	0.999593	−	0.0285219i	$-0.00908005\pi$
$182$	68.5112	+	21.1354i	0.376435	+	0.116129i
$183$	−200.427			−1.09523
$184$	−57.6037	−	99.7725i	−0.313064	−	0.542242i
$185$		0			0
$186$	−27.1305	+	46.9913i	−0.145863	+	0.252642i
$187$	29.6830	−	17.1375i	0.158733	−	0.0916444i
$188$		−	16.5122i		−	0.0878308i
$189$	26.6642	−	24.7391i	0.141080	−	0.130895i
$190$		0			0
$191$	59.5045	+	103.065i	0.311542	+	0.539607i	0.978696	−	0.205313i	$-0.0658212\pi$
$191$	59.5045	+	103.065i	0.311542	+	0.539607i	−0.667154	+	0.744920i	$0.732488\pi$
$192$	104.933	+	60.5833i	0.546528	+	0.315538i
$193$	4.95254	−	8.57805i	0.0256608	−	0.0444459i	−0.852910	−	0.522058i	$-0.825164\pi$
$193$	4.95254	−	8.57805i	0.0256608	−	0.0444459i	0.878571	+	0.477612i	$0.158498\pi$
$194$	221.960	−	128.149i	1.14412	−	0.660560i
$195$		0			0
$196$	48.5612	+	33.1132i	0.247761	+	0.168945i
$197$	290.342			1.47382			0.736908	−	0.675994i	$-0.236285\pi$
$197$	290.342			1.47382			0.736908	+	0.675994i	$0.236285\pi$
$198$	−34.7115	−	60.1222i	−0.175311	−	0.303647i
$199$	294.002	+	169.742i	1.47740	+	0.852977i	0.999674	−	0.0255322i	$-0.00812803\pi$
$199$	294.002	+	169.742i	1.47740	+	0.852977i	0.477725	+	0.878509i	$0.341461\pi$
$200$		0			0
$201$	−17.1068	+	9.87662i	−0.0851085	+	0.0491374i
$202$		−	191.215i		−	0.946607i
$203$	131.650	+	141.895i	0.648523	+	0.698989i
$204$	5.14967			0.0252435
$205$		0			0
$206$	−81.1285	−	46.8396i	−0.393828	−	0.227377i
$207$	−19.8606	+	34.3995i	−0.0959449	+	0.166181i
$208$	51.7494	−	29.8775i	0.248795	−	0.143642i
$209$			386.875i			1.85108i
$210$		0			0
$211$	11.1098			0.0526531			0.0263265	−	0.999653i	$-0.491619\pi$
$211$	11.1098			0.0526531			0.0263265	+	0.999653i	$0.491619\pi$
$212$	−55.5371	−	96.1931i	−0.261968	−	0.453741i
$213$	149.239	+	86.1630i	0.700651	+	0.404521i
$214$	82.5903	−	143.051i	0.385936	−	0.668461i
$215$		0			0
$216$		−	45.2128i		−	0.209319i
$217$	29.1552	+	127.757i	0.134356	+	0.588741i
$218$	88.2890			0.404996
$219$	−90.1276	−	156.106i	−0.411542	−	0.712811i
$220$		0			0
$221$	7.58524	−	13.1380i	0.0343224	−	0.0594481i
$222$	−102.952	+	59.4392i	−0.463746	+	0.267744i
$223$		−	359.376i		−	1.61155i	−0.592220	−	0.805776i	$-0.701748\pi$
$223$		−	359.376i		−	1.61155i	0.592220	−	0.805776i	$-0.298252\pi$
$224$	126.027	−	28.7604i	0.562619	−	0.128395i
$225$		0			0
$226$	88.8658	+	153.920i	0.393212	+	0.681062i
$227$	64.3040	+	37.1259i	0.283277	+	0.163550i	0.634906	−	0.772589i	$-0.281039\pi$
$227$	64.3040	+	37.1259i	0.283277	+	0.163550i	−0.351629	+	0.936140i	$0.614372\pi$
$228$	−29.0631	+	50.3388i	−0.127470	+	0.220784i
$229$	288.608	−	166.628i	1.26030	−	0.727633i	0.287165	−	0.957881i	$-0.407287\pi$
$229$	288.608	−	166.628i	1.26030	−	0.727633i	0.973132	+	0.230248i	$0.0739538\pi$
$230$		0			0
$231$	−160.208	−	49.4235i	−0.693541	−	0.213954i
$232$	240.602			1.03708
$233$	−132.338	−	229.216i	−0.567975	−	0.983761i	−0.996766	−	0.0803575i	$-0.974394\pi$
$233$	−132.338	−	229.216i	−0.567975	−	0.983761i	0.428791	−	0.903404i	$-0.358940\pi$
$234$	−26.6107	−	15.3637i	−0.113721	−	0.0656568i
$235$		0			0
$236$	−73.8520	+	42.6385i	−0.312932	+	0.180671i
$237$		−	223.428i		−	0.942735i
$238$	−21.2850	+	19.7483i	−0.0894328	+	0.0829759i
$239$	−266.197			−1.11380			−0.556898	−	0.830581i	$-0.688009\pi$
$239$	−266.197			−1.11380			−0.556898	+	0.830581i	$0.688009\pi$
$240$		0			0
$241$	−29.4197	−	16.9855i	−0.122074	−	0.0704792i	0.437720	−	0.899111i	$-0.355786\pi$
$241$	−29.4197	−	16.9855i	−0.122074	−	0.0704792i	−0.559793	+	0.828632i	$0.689120\pi$
$242$	−58.7551	+	101.767i	−0.242790	+	0.420524i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$			138.805i			0.568871i
$245$		0			0
$246$	−65.3185			−0.265522
$247$	85.6174	+	148.294i	0.346629	+	0.600380i
$248$	141.065	+	81.4441i	0.568812	+	0.328404i
$249$	−26.2736	+	45.5073i	−0.105517	+	0.182760i
$250$		0			0
$251$		−	84.6771i		−	0.337359i	−0.985671	−	0.168680i	$-0.946050\pi$
$251$		−	84.6771i		−	0.337359i	0.985671	−	0.168680i	$-0.0539503\pi$
$252$	−17.1329	−	18.4661i	−0.0679876	−	0.0732781i
$253$	183.091			0.723680
$254$	−165.172	−	286.087i	−0.650285	−	1.12633i
$255$		0			0
$256$	103.763	−	179.723i	0.405325	−	0.702044i
$257$	−27.6440	+	15.9603i	−0.107564	+	0.0621022i	−0.552817	−	0.833303i	$-0.686447\pi$
$257$	−27.6440	+	15.9603i	−0.107564	+	0.0621022i	0.445253	+	0.895405i	$0.353114\pi$
$258$			22.0428i			0.0854374i
$259$	−84.6315	+	274.336i	−0.326763	+	1.05921i
$260$		0			0
$261$	−41.4774	−	71.8409i	−0.158917	−	0.275253i
$262$	−213.164	−	123.070i	−0.813603	−	0.469734i
$263$	−74.0405	+	128.242i	−0.281523	+	0.487612i	−0.971760	−	0.235971i	$-0.924173\pi$
$263$	−74.0405	+	128.242i	−0.281523	+	0.487612i	0.690237	+	0.723583i	$0.257506\pi$
$264$	−180.483	+	104.202i	−0.683649	+	0.394705i
$265$		0			0
$266$	−72.9165	−	319.517i	−0.274122	−	1.20119i
$267$	187.917			0.703811
$268$	6.83998	+	11.8472i	0.0255223	+	0.0442060i
$269$	−78.8909	−	45.5477i	−0.293275	−	0.169322i	0.346143	−	0.938182i	$-0.387491\pi$
$269$	−78.8909	−	45.5477i	−0.293275	−	0.169322i	−0.639418	+	0.768859i	$0.720825\pi$
$270$		0			0
$271$	−108.045	+	62.3797i	−0.398689	+	0.230183i	−0.685918	−	0.727679i	$-0.740599\pi$
$271$	−108.045	+	62.3797i	−0.398689	+	0.230183i	0.287229	+	0.957862i	$0.407266\pi$
$272$			24.1990i			0.0889670i
$273$	−72.3474	+	16.5103i	−0.265009	+	0.0604772i
$274$	−416.010			−1.51828
$275$		0			0
$276$	23.8232	+	13.7543i	0.0863158	+	0.0498345i
$277$	−61.9619	+	107.321i	−0.223689	+	0.387441i	−0.955925	−	0.293610i	$-0.905143\pi$
$277$	−61.9619	+	107.321i	−0.223689	+	0.387441i	0.732236	+	0.681051i	$0.238477\pi$
$278$	−22.8033	+	13.1655i	−0.0820261	+	0.0473578i
$279$		−	56.1606i		−	0.201292i
$280$		0			0
$281$	−17.8049			−0.0633627			−0.0316814	−	0.999498i	$-0.510086\pi$
$281$	−17.8049			−0.0633627			−0.0316814	+	0.999498i	$0.510086\pi$
$282$	−19.9501	−	34.5545i	−0.0707449	−	0.122534i
$283$	96.2623	+	55.5770i	0.340149	+	0.196385i	0.660338	−	0.750968i	$-0.270413\pi$
$283$	96.2623	+	55.5770i	0.340149	+	0.196385i	−0.320189	+	0.947354i	$0.603746\pi$
$284$	59.6716	−	103.354i	0.210111	−	0.363923i
$285$		0			0
$286$			141.635i			0.495228i
$287$	−115.639	+	107.290i	−0.402924	+	0.373834i
$288$	−55.4000			−0.192361
$289$	−141.428	−	244.961i	−0.489371	−	0.847615i
$290$		0			0
$291$	−132.635	+	229.731i	−0.455791	+	0.789452i
$292$	−108.110	+	62.4173i	−0.370239	+	0.213758i
$293$			76.6488i			0.261600i	0.991409	+	0.130800i	$0.0417546\pi$
$293$			76.6488i			0.261600i	−0.991409	+	0.130800i	$0.958245\pi$
$294$	141.630	+	10.6231i	0.481734	+	0.0361332i
$295$		0			0
$296$	178.433	+	309.055i	0.602814	+	1.04411i
$297$	62.2270	+	35.9268i	0.209519	+	0.120966i
$298$	−154.131	+	266.963i	−0.517218	+	0.895847i
$299$	70.1810	−	40.5190i	0.234719	−	0.135515i
$300$		0			0
$301$	36.2070	+	39.0244i	0.120289	+	0.129649i
$302$	−440.540			−1.45874
$303$	98.9544	+	171.394i	0.326582	+	0.565657i
$304$	−236.549	−	136.572i	−0.778122	−	0.449249i
$305$		0			0
$306$	10.7765	−	6.22184i	0.0352174	−	0.0203328i
$307$			357.562i			1.16470i	0.812939	+	0.582349i	$0.197866\pi$
$307$			357.562i			1.16470i	−0.812939	+	0.582349i	$0.802134\pi$
$308$	−34.2279	+	110.951i	−0.111129	+	0.360230i
$309$	96.9588			0.313783
$310$		0			0
$311$	272.856	+	157.533i	0.877349	+	0.506538i	0.869784	−	0.493434i	$-0.164258\pi$
$311$	272.856	+	157.533i	0.877349	+	0.506538i	0.00756579	+	0.999971i	$0.497592\pi$
$312$	−46.1210	+	79.8839i	−0.147824	+	0.256038i
$313$	227.260	−	131.209i	0.726070	−	0.419197i	−0.0909126	−	0.995859i	$-0.528978\pi$
$313$	227.260	−	131.209i	0.726070	−	0.419197i	0.816983	+	0.576662i	$0.195645\pi$
$314$			362.508i			1.15449i
$315$		0			0
$316$	−154.734			−0.489664
$317$	−154.797	−	268.117i	−0.488320	−	0.845795i	0.511590	−	0.859230i	$-0.329057\pi$
$317$	−154.797	−	268.117i	−0.488320	−	0.845795i	−0.999910	+	0.0134349i	$0.995723\pi$
$318$	−232.441	−	134.200i	−0.730948	−	0.422013i
$319$	−191.186	+	331.144i	−0.599330	+	1.03807i
$320$		0			0
$321$			170.963i			0.532597i
$322$	−151.214	+	34.5082i	−0.469607	+	0.107168i
$323$	−69.3450			−0.214690
$324$	5.39784	+	9.34933i	0.0166600	+	0.0288560i
$325$		0			0
$326$	−144.403	+	250.114i	−0.442955	+	0.767221i
$327$	−79.1374	+	45.6900i	−0.242010	+	0.139725i
$328$			196.082i			0.597812i
$329$	−92.0778	−	28.4056i	−0.279872	−	0.0863391i
$330$		0			0
$331$	43.4062	+	75.1818i	0.131137	+	0.227135i	0.924115	−	0.382115i	$-0.124804\pi$
$331$	43.4062	+	75.1818i	0.131137	+	0.227135i	−0.792978	+	0.609250i	$0.791471\pi$
$332$	31.5157	+	18.1956i	0.0949269	+	0.0548061i
$333$	61.5201	−	106.556i	0.184745	−	0.319988i
$334$	227.422	−	131.302i	0.680905	−	0.393121i
$335$		0			0
$336$	86.7747	−	80.5098i	0.258258	−	0.239613i
$337$	−373.915			−1.10954			−0.554770	−	0.832004i	$-0.687194\pi$
$337$	−373.915			−1.10954			−0.554770	+	0.832004i	$0.687194\pi$
$338$	−110.063	−	190.635i	−0.325630	−	0.564008i
$339$	−159.309	−	91.9770i	−0.469937	−	0.271318i
$340$		0			0
$341$	−224.185	+	129.433i	−0.657435	+	0.379570i
$342$			140.456i			0.410691i
$343$	268.190	−	213.830i	0.781894	−	0.623412i
$344$	66.1714			0.192359
$345$		0			0
$346$	−68.9877	−	39.8301i	−0.199386	−	0.115116i
$347$	−165.439	+	286.549i	−0.476770	+	0.825790i	−0.999646	−	0.0266188i	$-0.991526\pi$
$347$	−165.439	+	286.549i	−0.476770	+	0.825790i	0.522875	+	0.852409i	$0.324859\pi$
$348$	−49.7529	+	28.7249i	−0.142968	+	0.0825427i
$349$		−	250.907i		−	0.718932i	−0.933158	−	0.359466i	$-0.882959\pi$
$349$		−	250.907i		−	0.718932i	0.933158	−	0.359466i	$-0.117041\pi$
$350$		0			0
$351$	31.8031			0.0906073
$352$	127.681	+	221.149i	0.362729	+	0.628265i
$353$	108.875	+	62.8589i	0.308427	+	0.178071i	0.646222	−	0.763149i	$-0.276348\pi$
$353$	108.875	+	62.8589i	0.308427	+	0.178071i	−0.337795	+	0.941220i	$0.609681\pi$
$354$	−103.032	+	178.456i	−0.291050	+	0.504114i
$355$		0			0
$356$		−	130.141i		−	0.365564i
$357$	8.85886	−	28.7163i	0.0248147	−	0.0804379i
$358$	49.4498			0.138128
$359$	178.790	+	309.674i	0.498023	+	0.862601i	0.999997	−	0.00228149i	$-0.000726221\pi$
$359$	178.790	+	309.674i	0.498023	+	0.862601i	−0.501975	+	0.864882i	$0.667393\pi$
$360$		0			0
$361$	210.861	−	365.223i	0.584103	−	1.01170i
$362$	−14.9636	+	8.63921i	−0.0413358	+	0.0238652i
$363$		−	121.624i		−	0.335053i
$364$	11.4341	+	50.1037i	0.0314123	+	0.137647i
$365$		0			0
$366$	167.704	+	290.472i	0.458207	+	0.793638i
$367$	−603.879	−	348.650i	−1.64545	−	0.949999i	−0.978850	−	0.204582i	$-0.934417\pi$
$367$	−603.879	−	348.650i	−1.64545	−	0.949999i	−0.666598	−	0.745418i	$-0.732250\pi$
$368$	−64.6334	+	111.948i	−0.175634	+	0.304208i
$369$	58.5479	−	33.8026i	0.158666	−	0.0916060i
$370$		0			0
$371$	−631.946	+	144.215i	−1.70336	+	0.388721i
$372$	−38.8936			−0.104553
$373$	−72.6433	−	125.822i	−0.194754	−	0.337324i	0.752066	−	0.659088i	$-0.229058\pi$
$373$	−72.6433	−	125.822i	−0.194754	−	0.337324i	−0.946820	+	0.321764i	$0.895724\pi$
$374$	−49.6735	−	28.6790i	−0.132817	−	0.0766818i
$375$		0			0
$376$	−103.731	+	59.8890i	−0.275880	+	0.159279i
$377$			169.242i			0.448918i
$378$	−58.1642	−	17.9434i	−0.153873	−	0.0474693i
$379$	−222.630			−0.587415			−0.293708	−	0.955895i	$-0.594889\pi$
$379$	−222.630			−0.587415			−0.293708	+	0.955895i	$0.594889\pi$
$380$		0			0
$381$	296.103	+	170.955i	0.777172	+	0.448701i
$382$	99.5787	−	172.475i	0.260677	−	0.451506i
$383$	30.1012	−	17.3789i	0.0785932	−	0.0453758i	−0.460188	−	0.887821i	$-0.652218\pi$
$383$	30.1012	−	17.3789i	0.0785932	−	0.0453758i	0.538782	+	0.842445i	$0.318885\pi$
$384$		−	74.8271i		−	0.194862i
$385$		0			0
$386$	−16.5758			−0.0429425
$387$	−11.4073	−	19.7580i	−0.0294762	−	0.0510542i
$388$	159.098	+	91.8555i	0.410047	+	0.236741i
$389$	−276.283	+	478.537i	−0.710240	+	1.23017i	0.254528	+	0.967066i	$0.418080\pi$
$389$	−276.283	+	478.537i	−0.710240	+	1.23017i	−0.964767	+	0.263105i	$0.915253\pi$
$390$		0			0
$391$			32.8180i			0.0839335i
$392$	31.8901	−	425.165i	0.0813523	−	1.08460i
$393$	254.758			0.648239
$394$	−242.938	−	420.781i	−0.616594	−	1.06797i
$395$		0			0
$396$	24.8808	−	43.0949i	0.0628304	−	0.108825i
$397$	−49.9274	+	28.8256i	−0.125762	+	0.0726085i	−0.561561	−	0.827435i	$-0.689799\pi$
$397$	−49.9274	+	28.8256i	−0.125762	+	0.0726085i	0.435799	+	0.900044i	$0.356466\pi$
$398$		−	568.115i		−	1.42743i
$399$	230.710	+	248.663i	0.578220	+	0.623215i
$400$		0			0
$401$	−281.160	−	486.983i	−0.701146	−	1.21442i	−0.968064	−	0.250701i	$-0.919339\pi$
$401$	−281.160	−	486.983i	−0.701146	−	1.21442i	0.266918	−	0.963719i	$-0.413995\pi$
$402$	28.6276	+	16.5282i	0.0712130	+	0.0411148i
$403$	−57.2886	+	99.2268i	−0.142155	+	0.246220i
$404$	118.698	−	68.5302i	0.293806	−	0.169629i
$405$		0			0
$406$	95.4866	−	309.524i	0.235189	−	0.762373i
$407$	−567.143			−1.39347
$408$	−18.6776	−	32.3506i	−0.0457785	−	0.0792906i
$409$	−174.709	−	100.869i	−0.427163	−	0.246622i	0.270975	−	0.962587i	$-0.412654\pi$
$409$	−174.709	−	100.869i	−0.427163	−	0.246622i	−0.698137	+	0.715964i	$0.745987\pi$
$410$		0			0
$411$	372.888	−	215.287i	0.907270	−	0.523813i
$412$		−	67.1482i		−	0.162981i
$413$	110.721	+	485.175i	0.268090	+	1.17476i
$414$	66.4719			0.160560
$415$		0			0
$416$	97.8831	+	56.5128i	0.235296	+	0.135848i
$417$	13.6264	−	23.6016i	0.0326772	−	0.0565985i
$418$	560.683	−	323.710i	1.34135	−	0.774427i
$419$		−	304.381i		−	0.726447i	−0.931702	−	0.363223i	$-0.881676\pi$
$419$		−	304.381i		−	0.726447i	0.931702	−	0.363223i	$-0.118324\pi$
$420$		0			0
$421$	556.622			1.32214			0.661071	−	0.750323i	$-0.270102\pi$
$421$	556.622			1.32214			0.661071	+	0.750323i	$0.270102\pi$
$422$	−9.29592	−	16.1010i	−0.0220283	−	0.0381541i
$423$	35.7643	+	20.6485i	0.0845491	+	0.0488144i
$424$	−402.861	+	697.776i	−0.950144	+	1.64570i
$425$		0			0
$426$		−	288.381i		−	0.676951i
$427$	774.022	+	238.782i	1.81270	+	0.559209i
$428$	118.400			0.276635
$429$	−73.2968	−	126.954i	−0.170855	−	0.295930i
$430$		0			0
$431$	90.2225	−	156.270i	0.209333	−	0.362575i	−0.742172	−	0.670210i	$-0.766204\pi$
$431$	90.2225	−	156.270i	0.209333	−	0.362575i	0.951505	+	0.307634i	$0.0995374\pi$
$432$	−43.9338	+	25.3652i	−0.101699	+	0.0587158i
$433$			724.048i			1.67217i	0.548603	+	0.836083i	$0.315160\pi$
$433$			724.048i			1.67217i	−0.548603	+	0.836083i	$0.684840\pi$
$434$	160.758	−	149.152i	0.370410	−	0.343668i
$435$		0			0
$436$	31.6423	+	54.8061i	0.0725741	+	0.125702i
$437$	−320.801	−	185.214i	−0.734098	−	0.423832i
$438$	−150.825	+	261.237i	−0.344350	+	0.596432i
$439$	354.272	−	204.539i	0.806997	−	0.465920i	−0.0389147	−	0.999243i	$-0.512390\pi$
$439$	354.272	−	204.539i	0.806997	−	0.465920i	0.845912	+	0.533322i	$0.179057\pi$
$440$		0			0
$441$	−132.447	+	63.7721i	−0.300333	+	0.144608i
$442$	−25.3873			−0.0574372
$443$	−199.400	−	345.370i	−0.450112	−	0.779617i	0.548280	−	0.836295i	$-0.315283\pi$
$443$	−199.400	−	345.370i	−0.450112	−	0.779617i	−0.998393	+	0.0566775i	$0.981949\pi$
$444$	−73.7946	−	42.6053i	−0.166204	−	0.0959579i
$445$		0			0
$446$	−520.830	+	300.702i	−1.16778	+	0.674219i
$447$		−	319.054i		−	0.713767i
$448$	−333.061	−	358.979i	−0.743441	−	0.801292i
$449$	−519.843			−1.15778			−0.578889	−	0.815406i	$-0.696514\pi$
$449$	−519.843			−1.15778			−0.578889	+	0.815406i	$0.696514\pi$
$450$		0			0
$451$	−269.871	−	155.810i	−0.598384	−	0.345477i
$452$	−63.6980	+	110.328i	−0.140925	+	0.244089i
$453$	394.876	−	227.982i	0.871690	−	0.503270i
$454$		−	124.258i		−	0.273695i
$455$		0			0
$456$	421.642			0.924654
$457$	116.891	+	202.462i	0.255780	+	0.443024i	0.965107	−	0.261856i	$-0.0843344\pi$
$457$	116.891	+	202.462i	0.255780	+	0.443024i	−0.709327	+	0.704880i	$0.751001\pi$
$458$	−482.975	−	278.846i	−1.05453	−	0.608834i
$459$	−6.43966	+	11.1538i	−0.0140298	+	0.0243003i
$460$		0			0
$461$		−	745.085i		−	1.61624i	−0.589021	−	0.808118i	$-0.700486\pi$
$461$		−	745.085i		−	1.61624i	0.589021	−	0.808118i	$-0.299514\pi$
$462$	62.4236	+	273.538i	0.135116	+	0.592073i
$463$	−742.448			−1.60356			−0.801779	−	0.597620i	$-0.796113\pi$
$463$	−742.448			−1.60356			−0.801779	+	0.597620i	$0.796113\pi$
$464$	−134.982	−	233.796i	−0.290910	−	0.503871i
$465$		0			0
$466$	−221.463	+	383.585i	−0.475242	+	0.823144i
$467$	524.404	−	302.765i	1.12292	−	0.648318i	0.180776	−	0.983524i	$-0.442139\pi$
$467$	524.404	−	302.765i	1.12292	−	0.648318i	0.942145	+	0.335206i	$0.108806\pi$
$468$		−	22.0251i		−	0.0470621i
$469$	77.8308	−	17.7617i	0.165951	−	0.0378713i
$470$		0			0
$471$	−187.600	−	324.933i	−0.398301	−	0.689878i
$472$	535.716	+	309.296i	1.13499	+	0.655287i
$473$	−52.5808	+	91.0726i	−0.111164	+	0.192542i
$474$	−323.806	+	186.950i	−0.683135	+	0.394408i
$475$		0			0
$476$	−19.8873	−	6.13515i	−0.0417801	−	0.0128890i
$477$	277.797			0.582383
$478$	222.736	+	385.790i	0.465974	+	0.807091i
$479$	260.542	+	150.424i	0.543930	+	0.314038i	0.746670	−	0.665194i	$-0.231651\pi$
$479$	260.542	+	150.424i	0.543930	+	0.314038i	−0.202740	+	0.979233i	$0.564985\pi$
$480$		0			0
$481$	−217.393	+	125.512i	−0.451960	+	0.260939i
$482$			56.8492i			0.117944i
$483$	117.681	−	109.185i	0.243647	−	0.226056i
$484$	−84.2300			−0.174029
$485$		0			0
$486$	22.5918	+	13.0434i	0.0464851	+	0.0268382i
$487$	295.602	−	511.998i	0.606986	−	1.05133i	−0.384748	−	0.923021i	$-0.625712\pi$
$487$	295.602	−	511.998i	0.606986	−	1.05133i	0.991734	−	0.128309i	$-0.0409549\pi$
$488$	871.979	−	503.438i	1.78684	−	1.03163i
$489$		−	298.918i		−	0.611284i
$490$		0			0
$491$	−308.637			−0.628589			−0.314295	−	0.949325i	$-0.601768\pi$
$491$	−308.637			−0.628589			−0.314295	+	0.949325i	$0.601768\pi$
$492$	−23.4098	−	40.5469i	−0.0475808	−	0.0824124i
$493$	−59.3556	−	34.2690i	−0.120397	−	0.0695111i
$494$	143.278	−	248.164i	0.290036	−	0.502357i
$495$		0			0
$496$		−	182.767i		−	0.368481i
$497$	−473.687	−	510.548i	−0.953093	−	1.02726i
$498$	87.9359			0.176578
$499$	447.344	+	774.822i	0.896480	+	1.55275i	0.831962	+	0.554833i	$0.187218\pi$
$499$	447.344	+	774.822i	0.896480	+	1.55275i	0.0645183	+	0.997917i	$0.479449\pi$
$500$		0			0
$501$	−135.899	+	235.384i	−0.271256	+	0.469829i
$502$	−122.719	+	70.8520i	−0.244461	+	0.141140i
$503$			609.546i			1.21182i	0.795533	+	0.605911i	$0.207191\pi$
$503$			609.546i			1.21182i	−0.795533	+	0.605911i	$0.792809\pi$
$504$	−53.8650	+	174.606i	−0.106875	+	0.346440i
$505$		0			0
$506$	−153.198	−	265.347i	−0.302763	−	0.524401i
$507$	197.309	+	113.916i	0.389169	+	0.224687i
$508$	118.394	−	205.064i	0.233058	−	0.403669i
$509$	205.570	−	118.686i	0.403871	−	0.233175i	−0.284282	−	0.958741i	$-0.591755\pi$
$509$	205.570	−	118.686i	0.403871	−	0.233175i	0.688153	+	0.725566i	$0.258422\pi$
$510$		0			0
$511$	162.081	+	710.233i	0.317185	+	1.38989i
$512$	−520.094			−1.01581
$513$	−72.6869	−	125.897i	−0.141690	−	0.245414i
$514$	46.2612	+	26.7089i	0.0900023	+	0.0519629i
$515$		0			0
$516$	−13.6833	+	7.90003i	−0.0265179	+	0.0153101i
$517$		−	190.355i		−	0.368191i
$518$	468.399	−	106.893i	0.904245	−	0.206356i
$519$	82.4490			0.158861
$520$		0			0
$521$	−32.6670	−	18.8603i	−0.0627006	−	0.0362002i	0.468322	−	0.883558i	$-0.344859\pi$
$521$	−32.6670	−	18.8603i	−0.0627006	−	0.0362002i	−0.531023	+	0.847358i	$0.678192\pi$
$522$	−69.4109	+	120.223i	−0.132971	+	0.230313i
$523$	−40.5068	+	23.3866i	−0.0774509	+	0.0447163i	−0.538225	−	0.842801i	$-0.680905\pi$
$523$	−40.5068	+	23.3866i	−0.0774509	+	0.0447163i	0.460774	+	0.887517i	$0.347572\pi$
$524$		−	176.431i		−	0.336700i
$525$		0			0
$526$	247.808			0.471118
$527$	−23.2002	−	40.1839i	−0.0440231	−	0.0762503i
$528$	202.509	+	116.919i	0.383540	+	0.221437i
$529$	176.846	−	306.306i	0.334303	−	0.579029i
$530$		0			0
$531$		−	213.278i		−	0.401653i
$532$	172.210	−	159.777i	0.323702	−	0.300332i
$533$	−137.926			−0.258774
$534$	−157.237	−	272.342i	−0.294450	−	0.510003i
$535$		0			0
$536$	49.6166	−	85.9385i	0.0925683	−	0.160333i
$537$	−44.3241	+	25.5905i	−0.0825402	+	0.0476546i
$538$			152.445i			0.283355i
$539$	559.820	+	381.733i	1.03863	+	0.708225i
$540$		0			0
$541$	195.629	+	338.839i	0.361606	+	0.626320i	0.988225	−	0.153005i	$-0.0488951\pi$
$541$	195.629	+	338.839i	0.361606	+	0.626320i	−0.626619	+	0.779326i	$0.715562\pi$
$542$	180.809	+	104.390i	0.333596	+	0.192602i
$543$	8.94167	−	15.4874i	0.0164672	−	0.0285219i
$544$	−39.6397	+	22.8860i	−0.0728671	+	0.0420699i
$545$		0			0
$546$	84.4631	+	91.0356i	0.154694	+	0.166732i
$547$	389.827			0.712664			0.356332	−	0.934359i	$-0.384027\pi$
$547$	389.827			0.712664			0.356332	+	0.934359i	$0.384027\pi$
$548$	−149.096	−	258.241i	−0.272072	−	0.471243i
$549$	−300.641	−	173.575i	−0.547615	−	0.316166i
$550$		0			0
$551$	669.969	−	386.807i	1.21591	−	0.702009i
$552$		−	199.545i		−	0.361495i
$553$	−266.185	+	862.849i	−0.481347	+	1.56031i
$554$	207.382			0.374336
$555$		0			0
$556$	−16.3451	−	9.43686i	−0.0293977	−	0.0169728i
$557$	89.4085	−	154.860i	0.160518	−	0.278025i	−0.774537	−	0.632529i	$-0.782017\pi$
$557$	89.4085	−	154.860i	0.160518	−	0.278025i	0.935055	+	0.354504i	$0.115350\pi$
$558$	−81.3914	+	46.9913i	−0.145863	+	0.0842139i
$559$			46.5456i			0.0832659i
$560$		0			0
$561$	59.3661			0.105822
$562$	14.8979	+	25.8040i	0.0265088	+	0.0459146i
$563$	139.571	+	80.5815i	0.247906	+	0.143129i	0.618805	−	0.785545i	$-0.287617\pi$
$563$	139.571	+	80.5815i	0.247906	+	0.143129i	−0.370899	+	0.928673i	$0.620950\pi$
$564$	14.3000	−	24.7683i	0.0253546	−	0.0439154i
$565$		0			0
$566$		−	186.012i		−	0.328644i
$567$	61.4209	−	14.0168i	0.108326	−	0.0247210i
$568$	−865.704			−1.52413
$569$	−6.24946	−	10.8244i	−0.0109832	−	0.0190235i	0.860482	−	0.509482i	$-0.170163\pi$
$569$	−6.24946	−	10.8244i	−0.0109832	−	0.0190235i	−0.871465	+	0.490458i	$0.836829\pi$
$570$		0			0
$571$	−61.6982	+	106.864i	−0.108053	+	0.187153i	−0.914981	−	0.403496i	$-0.867795\pi$
$571$	−61.6982	+	106.864i	−0.108053	+	0.187153i	0.806929	+	0.590649i	$0.201128\pi$
$572$	−87.9210	+	50.7612i	−0.153708	+	0.0887434i
$573$			206.130i			0.359738i
$574$	252.251	+	77.8183i	0.439462	+	0.135572i
$575$		0			0
$576$	104.933	+	181.750i	0.182176	+	0.315538i
$577$	143.692	+	82.9608i	0.249033	+	0.143779i	0.619322	−	0.785137i	$-0.287408\pi$
$577$	143.692	+	82.9608i	0.249033	+	0.143779i	−0.370288	+	0.928917i	$0.620741\pi$
$578$	−236.675	+	409.933i	−0.409472	+	0.709227i
$579$	14.8576	−	8.57805i	0.0256608	−	0.0148153i
$580$		0			0
$581$	155.681	−	144.441i	0.267954	−	0.248608i
$582$	443.920			0.762749
$583$	−640.239	−	1108.93i	−1.09818	−	1.90210i
$584$	784.219	+	452.769i	1.34284	+	0.775290i
$585$		0			0
$586$	111.084	−	64.1345i	0.189564	−	0.109445i
$587$			186.037i			0.316929i	0.987365	+	0.158465i	$0.0506544\pi$
$587$			186.037i			0.316929i	−0.987365	+	0.158465i	$0.949346\pi$
$588$	44.1649	+	91.7250i	0.0751104	+	0.155995i
$589$	523.738			0.889199
$590$		0			0
$591$	435.512	+	251.443i	0.736908	+	0.425454i
$592$	200.208	−	346.771i	0.338190	−	0.585762i
$593$	−494.838	+	285.695i	−0.834465	+	0.481779i	−0.855379	−	0.518003i	$-0.826676\pi$
$593$	−494.838	+	285.695i	−0.834465	+	0.481779i	0.0209140	+	0.999781i	$0.493342\pi$
$594$		−	120.244i		−	0.202431i
$595$		0			0
$596$	−220.959			−0.370736
$597$	294.002	+	509.227i	0.492466	+	0.852977i
$598$	−117.445	−	67.8071i	−0.196397	−	0.113390i
$599$	−87.2619	+	151.142i	−0.145679	+	0.252324i	−0.929626	−	0.368504i	$-0.879870\pi$
$599$	−87.2619	+	151.142i	−0.145679	+	0.252324i	0.783947	+	0.620828i	$0.213203\pi$
$600$		0			0
$601$			667.415i			1.11051i	0.831681	+	0.555254i	$0.187379\pi$
$601$			667.415i			1.11051i	−0.831681	+	0.555254i	$0.812621\pi$
$602$	26.2611	−	85.1264i	0.0436231	−	0.141406i
$603$	−34.2136			−0.0567390
$604$	−157.887	−	273.468i	−0.261402	−	0.452762i
$605$		0			0
$606$	165.597	−	286.822i	0.273262	−	0.473303i
$607$	−23.3123	+	13.4594i	−0.0384057	+	0.0221736i	−0.519080	−	0.854726i	$-0.673725\pi$
$607$	−23.3123	+	13.4594i	−0.0384057	+	0.0221736i	0.480674	+	0.876899i	$0.340392\pi$
$608$		−	516.646i		−	0.849746i
$609$	74.5910	+	326.855i	0.122481	+	0.536707i
$610$		0			0
$611$	−42.1265	−	72.9653i	−0.0689468	−	0.119419i
$612$	7.72450	+	4.45974i	0.0126217	+	0.00728716i
$613$	−32.7197	+	56.6723i	−0.0533764	+	0.0924507i	−0.891479	−	0.453062i	$-0.850332\pi$
$613$	−32.7197	+	56.6723i	−0.0533764	+	0.0924507i	0.838103	+	0.545513i	$0.183665\pi$
$614$	518.201	−	299.183i	0.843976	−	0.487270i
$615$		0			0
$616$	821.145	−	187.392i	1.33303	−	0.304208i
$617$	−1059.51			−1.71720			−0.858601	−	0.512644i	$-0.828666\pi$
$617$	−1059.51			−1.71720			−0.858601	+	0.512644i	$0.828666\pi$
$618$	−81.1285	−	140.519i	−0.131276	−	0.227377i
$619$	139.355	+	80.4565i	0.225129	+	0.129978i	0.608323	−	0.793690i	$-0.291843\pi$
$619$	139.355	+	80.4565i	0.225129	+	0.129978i	−0.383194	+	0.923668i	$0.625176\pi$
$620$		0			0
$621$	−59.5818	+	34.3995i	−0.0959449	+	0.0553938i
$622$		−	527.252i		−	0.847673i
$623$	−725.711	−	223.879i	−1.16487	−	0.359356i
$624$	103.499			0.165863
$625$		0			0
$626$	−380.311	−	219.573i	−0.607526	−	0.350755i
$627$	−335.043	+	580.312i	−0.534359	+	0.925538i
$628$	−225.030	+	129.921i	−0.358328	+	0.206881i
$629$		−	101.657i		−	0.161617i
$630$		0			0
$631$	−45.2151			−0.0716562			−0.0358281	−	0.999358i	$-0.511407\pi$
$631$	−45.2151			−0.0716562			−0.0358281	+	0.999358i	$0.511407\pi$
$632$	561.212	+	972.048i	0.887994	+	1.53805i
$633$	16.6647	+	9.62137i	0.0263265	+	0.0151996i
$634$	−259.048	+	448.684i	−0.408593	+	0.707703i
$635$		0			0
$636$		−	192.386i		−	0.302494i
$637$	299.065	+	22.4318i	0.469490	+	0.0352148i
$638$	639.886			1.00296
$639$	149.239	+	258.489i	0.233550	+	0.404521i
$640$		0			0
$641$	−161.675	+	280.030i	−0.252224	+	0.436865i	−0.964138	−	0.265402i	$-0.914495\pi$
$641$	−161.675	+	280.030i	−0.252224	+	0.436865i	0.711914	+	0.702267i	$0.247829\pi$
$642$	247.771	−	143.051i	0.385936	−	0.222820i
$643$			363.744i			0.565698i	0.959164	+	0.282849i	$0.0912795\pi$
$643$			363.744i			0.565698i	−0.959164	+	0.282849i	$0.908720\pi$
$644$	−75.6153	−	81.4994i	−0.117415	−	0.126552i
$645$		0			0
$646$	58.0232	+	100.499i	0.0898191	+	0.155571i
$647$	1114.98	+	643.737i	1.72331	+	0.994956i	0.911812	+	0.410608i	$0.134683\pi$
$647$	1114.98	+	643.737i	1.72331	+	0.994956i	0.811503	+	0.584348i	$0.198650\pi$
$648$	39.1554	−	67.8192i	0.0604250	−	0.104659i
$649$	−851.376	+	491.542i	−1.31183	+	0.757384i
$650$		0			0
$651$	−66.9079	+	216.884i	−0.102777	+	0.333156i
$652$	−207.013			−0.317505
$653$	308.886	+	535.007i	0.473026	+	0.819306i	0.999523	−	0.0308714i	$-0.00982823\pi$
$653$	308.886	+	535.007i	0.473026	+	0.819306i	−0.526497	+	0.850177i	$0.676495\pi$
$654$	132.434	+	76.4606i	0.202498	+	0.116912i
$655$		0			0
$656$	190.536	−	110.006i	0.290451	−	0.167692i
$657$		−	312.211i		−	0.475207i
$658$	35.8773	+	157.213i	0.0545247	+	0.238925i
$659$	−1229.62			−1.86589			−0.932945	−	0.360019i	$-0.882770\pi$
$659$	−1229.62			−1.86589			−0.932945	+	0.360019i	$0.882770\pi$
$660$		0			0
$661$	−606.437	−	350.127i	−0.917454	−	0.529692i	−0.0346322	−	0.999400i	$-0.511026\pi$
$661$	−606.437	−	350.127i	−0.917454	−	0.529692i	−0.882822	+	0.469708i	$0.844359\pi$
$662$	72.6387	−	125.814i	0.109726	−	0.190051i
$663$	22.7557	−	13.1380i	0.0343224	−	0.0198160i
$664$		−	263.979i		−	0.397558i
$665$		0			0
$666$	−205.903			−0.309164
$667$	−183.059	−	317.067i	−0.274451	−	0.475363i
$668$	163.014	+	94.1160i	0.244032	+	0.140892i
$669$	311.229	−	539.064i	0.465215	−	0.805776i
$670$		0			0
$671$			1600.16i			2.38473i
$672$	213.947	+	66.0018i	0.318374	+	0.0982169i
$673$	121.032			0.179840			0.0899201	−	0.995949i	$-0.471339\pi$
$673$	121.032			0.179840			0.0899201	+	0.995949i	$0.471339\pi$
$674$	312.867	+	541.901i	0.464194	+	0.804007i
$675$		0			0
$676$	78.8920	−	136.645i	0.116704	−	0.202137i
$677$	851.854	−	491.818i	1.25828	−	0.726467i	0.285538	−	0.958367i	$-0.407828\pi$
$677$	851.854	−	491.818i	1.25828	−	0.726467i	0.972739	+	0.231901i	$0.0744944\pi$
$678$			307.840i			0.454042i
$679$	785.912	−	729.171i	1.15745	−	1.07389i
$680$		0			0
$681$	64.3040	+	111.378i	0.0944258	+	0.163550i
$682$	375.166	+	216.602i	0.550097	+	0.317599i
$683$	56.5263	−	97.9064i	0.0827618	−	0.143348i	−0.821674	−	0.569958i	$-0.806959\pi$
$683$	56.5263	−	97.9064i	0.0827618	−	0.143348i	0.904435	+	0.426611i	$0.140293\pi$
$684$	−87.1893	+	50.3388i	−0.127470	+	0.0735947i
$685$		0			0
$686$	−534.299	−	209.758i	−0.778861	−	0.305770i
$687$	577.216			0.840198
$688$	−37.1234	−	64.2995i	−0.0539584	−	0.0934586i
$689$	−490.823	−	283.377i	−0.712370	−	0.411287i
$690$		0			0
$691$	−771.062	+	445.173i	−1.11586	+	0.644244i	−0.940342	−	0.340231i	$-0.889495\pi$
$691$	−771.062	+	445.173i	−1.11586	+	0.644244i	−0.175522	+	0.984475i	$0.556161\pi$
$692$		−	57.0995i		−	0.0825137i
$693$	−197.510	−	212.879i	−0.285007	−	0.307185i
$694$	553.713			0.797858
$695$		0			0
$696$	360.903	+	208.368i	0.518539	+	0.299379i
$697$	27.9280	−	48.3728i	0.0400689	−	0.0694014i
$698$	−363.630	+	209.942i	−0.520960	+	0.300776i
$699$		−	458.433i		−	0.655841i
$700$		0			0
$701$	−730.892			−1.04264			−0.521321	−	0.853361i	$-0.674560\pi$
$701$	−730.892			−1.04264			−0.521321	+	0.853361i	$0.674560\pi$
$702$	−26.6107	−	46.0911i	−0.0379070	−	0.0656568i
$703$	993.712	+	573.720i	1.41353	+	0.816102i
$704$	483.681	−	837.760i	0.687047	−	1.19000i
$705$		0			0
$706$		−	210.384i		−	0.297995i
$707$	−177.955	−	779.791i	−0.251704	−	1.10296i
$708$	−147.704			−0.208621
$709$	−576.325	−	998.224i	−0.812870	−	1.40793i	−0.910847	−	0.412744i	$-0.864570\pi$
$709$	−576.325	−	998.224i	−0.812870	−	1.40793i	0.0979765	−	0.995189i	$-0.468763\pi$
$710$		0			0
$711$	193.495	−	335.142i	0.272144	−	0.471368i
$712$	−817.554	+	472.015i	−1.14825	+	0.662943i
$713$		−	247.863i		−	0.347633i
$714$	−49.0300	+	11.1891i	−0.0686695	+	0.0156710i
$715$		0			0
$716$	17.7225	+	30.6963i	0.0247521	+	0.0428720i
$717$	−399.296	−	230.534i	−0.556898	−	0.321525i
$718$	299.199	−	518.228i	0.416712	−	0.721766i
$719$	688.275	−	397.376i	0.957267	−	0.552678i	0.0619361	−	0.998080i	$-0.480273\pi$
$719$	688.275	−	397.376i	0.957267	−	0.552678i	0.895331	+	0.445402i	$0.146939\pi$
$720$		0			0
$721$	−374.442	−	115.514i	−0.519336	−	0.160213i
$722$	−705.738			−0.977476
$723$	−29.4197	−	50.9565i	−0.0406912	−	0.0704792i
$724$	−10.7257	−	6.19249i	−0.0148145	−	0.00855316i
$725$		0			0
$726$	−176.265	+	101.767i	−0.242790	+	0.140175i
$727$			312.108i			0.429310i	0.976690	+	0.214655i	$0.0688626\pi$
$727$			312.108i			0.429310i	−0.976690	+	0.214655i	$0.931137\pi$
$728$	273.284	−	253.553i	0.375390	−	0.348288i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−16.3242	−	9.42479i	−0.0223314	−	0.0128930i
$732$	−120.208	+	208.207i	−0.164219	+	0.284435i
$733$	−215.629	+	124.493i	−0.294173	+	0.169841i	−0.639822	−	0.768523i	$-0.720992\pi$
$733$	−215.629	+	124.493i	−0.294173	+	0.169841i	0.345649	+	0.938364i	$0.387659\pi$
$734$			1166.91i			1.58979i
$735$		0			0
$736$	−244.506			−0.332209
$737$	78.8522	+	136.576i	0.106991	+	0.185314i
$738$	−97.9777	−	56.5675i	−0.132761	−	0.0766497i
$739$	−152.219	+	263.652i	−0.205980	+	0.356768i	−0.950445	−	0.310894i	$-0.899372\pi$
$739$	−152.219	+	263.652i	−0.205980	+	0.356768i	0.744464	+	0.667662i	$0.232705\pi$
$740$		0			0
$741$			296.588i			0.400253i
$742$	737.775	+	795.185i	0.994306	+	1.07168i
$743$	235.455			0.316898			0.158449	−	0.987367i	$-0.449351\pi$
$743$	235.455			0.316898			0.158449	+	0.987367i	$0.449351\pi$
$744$	141.065	+	244.332i	0.189604	+	0.328404i
$745$		0			0
$746$	−121.566	+	210.558i	−0.162957	+	0.282250i
$747$	−78.8209	+	45.5073i	−0.105517	+	0.0609200i
$748$		−	41.1136i		−	0.0549646i
$749$	203.680	−	660.237i	0.271936	−	0.881492i
$750$		0			0
$751$	387.921	+	671.900i	0.516540	+	0.894673i	0.999816	+	0.0192050i	$0.00611351\pi$
$751$	387.921	+	671.900i	0.516540	+	0.894673i	−0.483276	+	0.875468i	$0.660553\pi$
$752$	116.390	+	67.1976i	0.154774	+	0.0893585i
$753$	73.3325	−	127.016i	0.0973872	−	0.168680i
$754$	245.276	−	141.610i	0.325300	−	0.187812i
$755$		0			0
$756$	−9.70722	−	42.5366i	−0.0128402	−	0.0562654i
$757$	194.342			0.256727			0.128363	−	0.991727i	$-0.459028\pi$
$757$	194.342			0.256727			0.128363	+	0.991727i	$0.459028\pi$
$758$	186.282	+	322.650i	0.245755	+	0.425659i
$759$	274.637	+	158.562i	0.361840	+	0.208908i
$760$		0			0
$761$	−441.278	+	254.772i	−0.579866	+	0.334786i	−0.761080	−	0.648658i	$-0.775331\pi$
$761$	−441.278	+	254.772i	−0.579866	+	0.334786i	0.181214	+	0.983444i	$0.441997\pi$
$762$		−	572.174i		−	0.750884i
$763$	360.051	−	82.1668i	0.471889	−	0.107689i
$764$	142.754			0.186850
$765$		0			0
$766$	−50.3732	−	29.0830i	−0.0657614	−	0.0379674i
$767$	−217.562	+	376.828i	−0.283653	+	0.491301i
$768$	311.290	−	179.723i	0.405325	−	0.234015i
$769$		−	1174.80i		−	1.52769i	−0.645398	−	0.763846i	$-0.723308\pi$
$769$		−	1174.80i		−	1.52769i	0.645398	−	0.763846i	$-0.276692\pi$
$770$		0			0
$771$	−55.2880			−0.0717094
$772$	−5.94067	−	10.2895i	−0.00769517	−	0.0133284i
$773$	−996.623	−	575.401i	−1.28929	−	0.744373i	−0.310764	−	0.950487i	$-0.600585\pi$
$773$	−996.623	−	575.401i	−1.28929	−	0.744373i	−0.978528	+	0.206114i	$0.933918\pi$
$774$	−19.0897	+	33.0643i	−0.0246636	+	0.0427187i
$775$		0			0
$776$		−	1332.62i		−	1.71730i
$777$	−364.529	+	338.211i	−0.469150	+	0.435278i
$778$	924.700			1.18856
$779$	315.234	+	546.001i	0.404665	+	0.700900i
$780$		0			0
$781$	687.902	−	1191.48i	0.880796	−	1.52558i
$782$	47.5619	−	27.4599i	0.0608208	−	0.0351149i
$783$		−	143.682i		−	0.183502i
$784$	−431.029	+	207.537i	−0.549782	+	0.264716i
$785$		0			0
$786$	−213.164	−	369.211i	−0.271201	−	0.469734i
$787$	199.749	+	115.325i	0.253810	+	0.146538i	0.621508	−	0.783408i	$-0.286520\pi$
$787$	199.749	+	115.325i	0.253810	+	0.146538i	−0.367697	+	0.929946i	$0.619854\pi$
$788$	174.135	−	301.611i	0.220984	−	0.382755i
$789$	−222.121	+	128.242i	−0.281523	+	0.162537i
$790$		0			0
$791$	505.650	+	544.998i	0.639254	+	0.688998i
$792$	−360.967			−0.455766
$793$	354.123	+	613.359i	0.446561	+	0.773467i
$794$	83.5517	+	48.2386i	0.105229	+	0.0607539i
$795$		0			0
$796$	352.662	−	203.609i	0.443042	−	0.255791i
$797$		−	246.018i		−	0.308680i	−0.988018	−	0.154340i	$-0.950675\pi$
$797$		−	246.018i		−	0.308680i	0.988018	−	0.154340i	$-0.0493251\pi$
$798$	167.335	−	542.423i	0.209693	−	0.679728i
$799$	34.1200			0.0427033
$800$		0			0
$801$	281.876	+	162.741i	0.351905	+	0.203173i
$802$	−470.510	+	814.948i	−0.586671	+	1.01614i
$803$	−1246.30	+	719.554i	−1.55206	+	0.896083i
$804$			23.6944i			0.0294706i
$805$		0			0
$806$	191.741			0.237892
$807$	−78.8909	−	136.643i	−0.0977583	−	0.169322i
$808$	−861.023	−	497.112i	−1.06562	−	0.615237i
$809$	−120.772	+	209.183i	−0.149285	+	0.258569i	−0.930963	−	0.365112i	$-0.881031\pi$
$809$	−120.772	+	209.183i	−0.149285	+	0.258569i	0.781678	+	0.623682i	$0.214364\pi$
$810$		0			0
$811$			626.619i			0.772650i	0.922363	+	0.386325i	$0.126256\pi$
$811$			626.619i			0.772650i	−0.922363	+	0.386325i	$0.873744\pi$
$812$	226.361	−	51.6575i	0.278770	−	0.0636176i
$813$	−216.090			−0.265793
$814$	474.546	+	821.938i	0.582981	+	1.00975i
$815$		0			0
$816$	−20.9570	+	36.2985i	−0.0256826	+	0.0444835i
$817$	184.258	−	106.381i	0.225529	−	0.130209i
$818$			337.600i			0.412714i
$819$	−122.819	−	37.8892i	−0.149963	−	0.0462628i
$820$		0			0
$821$	49.3857	+	85.5386i	0.0601532	+	0.104188i	0.894534	−	0.447000i	$-0.147508\pi$
$821$	49.3857	+	85.5386i	0.0601532	+	0.104188i	−0.834381	+	0.551189i	$0.814174\pi$
$822$	−624.014	−	360.275i	−0.759142	−	0.438291i
$823$	391.560	−	678.202i	0.475772	−	0.824061i	−0.523843	−	0.851815i	$-0.675502\pi$
$823$	391.560	−	678.202i	0.475772	−	0.824061i	0.999615	+	0.0277542i	$0.00883556\pi$
$824$	−421.829	+	243.543i	−0.511929	+	0.295562i
$825$		0			0
$826$	610.501	−	566.425i	0.739106	−	0.685744i
$827$	1131.53			1.36823			0.684116	−	0.729373i	$-0.260188\pi$
$827$	1131.53			1.36823			0.684116	+	0.729373i	$0.260188\pi$
$828$	23.8232	+	41.2629i	0.0287719	+	0.0498345i
$829$	164.501	+	94.9749i	0.198434	+	0.114566i	0.595925	−	0.803040i	$-0.296786\pi$
$829$	164.501	+	94.9749i	0.198434	+	0.114566i	−0.397491	+	0.917606i	$0.630119\pi$
$830$		0			0
$831$	−185.886	+	107.321i	−0.223689	+	0.129147i
$832$		−	428.165i		−	0.514621i
$833$	−68.4234	+	100.344i	−0.0821410	+	0.120461i
$834$	−45.6065			−0.0546841
$835$		0			0
$836$	401.891	+	232.032i	0.480731	+	0.277550i
$837$	48.6365	−	84.2409i	0.0581081	−	0.100646i
$838$	−441.128	+	254.685i	−0.526406	+	0.303921i
$839$			1431.33i			1.70599i	0.521919	+	0.852995i	$0.325216\pi$
$839$			1431.33i			1.70599i	−0.521919	+	0.852995i	$0.674784\pi$
$840$		0			0
$841$	−76.3899			−0.0908322
$842$	−465.743	−	806.691i	−0.553139	−	0.958065i
$843$	−26.7074	−	15.4195i	−0.0316814	−	0.0182912i
$844$	6.66321	−	11.5410i	0.00789480	−	0.0136742i
$845$		0			0
$846$		−	69.1090i		−	0.0816892i
$847$	−144.899	+	469.696i	−0.171073	+	0.554541i
$848$	904.050			1.06610
$849$	96.2623	+	166.731i	0.113383	+	0.196385i
$850$		0			0
$851$	271.517	−	470.281i	0.319056	−	0.552621i
$852$	179.015	−	103.354i	0.210111	−	0.121308i
$853$		−	1123.73i		−	1.31739i	−0.752412	−	0.658693i	$-0.771110\pi$
$853$		−	1123.73i		−	1.31739i	0.752412	−	0.658693i	$-0.228890\pi$
$854$	−301.591	−	1321.56i	−0.353151	−	1.54749i
$855$		0			0
$856$	−429.430	−	743.794i	−0.501670	−	0.868919i
$857$	−1300.05	−	750.584i	−1.51698	−	0.875827i	−0.999801	−	0.0199480i	$-0.993650\pi$
$857$	−1300.05	−	750.584i	−1.51698	−	0.875827i	−0.517176	−	0.855879i	$-0.673017\pi$
$858$	−122.660	+	212.453i	−0.142960	+	0.247614i
$859$	−1203.93	+	695.091i	−1.40155	+	0.809186i	−0.994552	−	0.104242i	$-0.966758\pi$
$859$	−1203.93	+	695.091i	−1.40155	+	0.809186i	−0.407000	+	0.913428i	$0.633425\pi$
$860$		0			0
$861$	−266.375	+	60.7891i	−0.309379	+	0.0706029i
$862$	−301.968			−0.350311
$863$	133.534	+	231.288i	0.154732	+	0.268004i	0.932962	−	0.359976i	$-0.117215\pi$
$863$	133.534	+	231.288i	0.154732	+	0.268004i	−0.778229	+	0.627980i	$0.783882\pi$
$864$	−83.1001	−	47.9778i	−0.0961806	−	0.0555299i
$865$		0			0
$866$	1049.33	−	605.834i	1.21170	−	0.699577i
$867$		−	489.922i		−	0.565077i
$868$	150.202	+	46.3366i	0.173044	+	0.0533832i
$869$	−1783.79			−2.05269
$870$		0			0
$871$	60.4500	+	34.9008i	0.0694030	+	0.0400699i
$872$	229.530	−	397.558i	0.263223	−	0.455915i
$873$	−397.905	+	229.731i	−0.455791	+	0.263151i
$874$			619.899i			0.709267i
$875$		0			0
$876$	−216.220			−0.246826
$877$	−499.609	−	865.348i	−0.569679	−	0.986714i	−0.996597	−	0.0824232i	$-0.973734\pi$
$877$	−499.609	−	865.348i	−0.569679	−	0.986714i	0.426918	−	0.904290i	$-0.359599\pi$
$878$	−592.861	−	342.288i	−0.675240	−	0.389850i
$879$	−66.3798	+	114.973i	−0.0755175	+	0.130800i
$880$		0			0
$881$			94.1956i			0.106919i	0.998570	+	0.0534595i	$0.0170248\pi$
$881$			94.1956i			0.106919i	−0.998570	+	0.0534595i	$0.982975\pi$
$882$	203.245	+	138.590i	0.230436	+	0.157131i
$883$	389.465			0.441070			0.220535	−	0.975379i	$-0.429220\pi$
$883$	389.465			0.441070			0.220535	+	0.975379i	$0.429220\pi$
$884$	−9.09865	−	15.7593i	−0.0102926	−	0.0178273i
$885$		0			0
$886$	−333.688	+	577.965i	−0.376623	+	0.652330i
$887$	−638.869	+	368.851i	−0.720258	+	0.415841i	−0.814848	−	0.579675i	$-0.803179\pi$
$887$	−638.869	+	368.851i	−0.720258	+	0.415841i	0.0945896	+	0.995516i	$0.469846\pi$
$888$			618.110i			0.696070i
$889$	−939.837	−	1012.97i	−1.05718	−	1.13945i
$890$		0			0
$891$	62.2270	+	107.780i	0.0698395	+	0.120966i
$892$	−373.325	−	215.539i	−0.418526	−	0.241636i
$893$	−192.562	+	333.528i	−0.215635	+	0.373491i
$894$	−462.393	+	266.963i	−0.517218	+	0.298616i
$895$		0			0
$896$	−89.1465	+	288.972i	−0.0994939	+	0.322513i
$897$	140.362			0.156479
$898$	434.969	+	753.388i	0.484375	+	0.838962i
$899$	448.292	+	258.821i	0.498656	+	0.287899i
$900$		0			0
$901$	198.769	−	114.759i	0.220609	−	0.127369i
$902$			521.485i			0.578143i
$903$	20.5143	+	89.8928i	0.0227180	+	0.0995491i
$904$	924.119			1.02226
$905$		0			0
$906$	−660.810	−	381.519i	−0.729371	−	0.421102i
$907$	64.2146	−	111.223i	0.0707989	−	0.122627i	−0.828453	−	0.560059i	$-0.810778\pi$
$907$	64.2146	−	111.223i	0.0707989	−	0.122627i	0.899252	+	0.437432i	$0.144112\pi$
$908$	77.1339	−	44.5333i	0.0849492	−	0.0490454i
$909$			342.788i			0.377105i
$910$		0			0
$911$	851.535			0.934725			0.467363	−	0.884066i	$-0.345204\pi$
$911$	851.535			0.934725			0.467363	+	0.884066i	$0.345204\pi$
$912$	−236.549	−	409.715i	−0.259374	−	0.449249i
$913$	363.318	+	209.762i	0.397938	+	0.229750i
$914$	195.614	−	338.813i	0.214019	−	0.370692i
$915$		0			0
$916$		−	399.747i		−	0.436405i
$917$	−983.840	−	303.510i	−1.07289	−	0.330982i
$918$	21.5531			0.0234783
$919$	755.722	+	1308.95i	0.822330	+	1.42432i	0.903943	+	0.427654i	$0.140660\pi$
$919$	755.722	+	1308.95i	0.822330	+	1.42432i	−0.0816123	+	0.996664i	$0.526007\pi$
$920$		0			0
$921$	−309.658	+	536.343i	−0.336219	+	0.582349i
$922$	−1079.82	+	623.436i	−1.17117	+	0.676178i
$923$		−	608.945i		−	0.659746i
$924$	−147.428	+	136.784i	−0.159554	+	0.148035i
$925$		0			0
$926$	621.230	+	1076.00i	0.670874	+	1.16199i
$927$	145.438	+	83.9688i	0.156891	+	0.0905812i
$928$	255.316	−	442.221i	0.275126	−	0.476531i
$929$	−44.6801	+	25.7961i	−0.0480949	+	0.0277676i	−0.523855	−	0.851808i	$-0.675506\pi$
$929$	−44.6801	+	25.7961i	−0.0480949	+	0.0277676i	0.475760	+	0.879575i	$0.342173\pi$
$930$		0			0
$931$	−594.721	−	1235.16i	−0.638798	−	1.32670i
$932$	−317.484			−0.340648
$933$	272.856	+	472.600i	0.292450	+	0.506538i
$934$	−877.571	−	506.666i	−0.939583	−	0.542469i
$935$		0			0
$936$	−138.363	+	79.8839i	−0.147824	+	0.0853460i
$937$		−	1321.41i		−	1.41026i	−0.709080	−	0.705128i	$-0.750890\pi$
$937$		−	1321.41i		−	1.41026i	0.709080	−	0.705128i	$-0.249110\pi$
$938$	−90.8648	−	97.9355i	−0.0968708	−	0.104409i
$939$	454.520			0.484047
$940$		0			0
$941$	708.633	+	409.129i	0.753063	+	0.434781i	0.826800	−	0.562496i	$-0.190159\pi$
$941$	708.633	+	409.129i	0.753063	+	0.434781i	−0.0737363	+	0.997278i	$0.523492\pi$
$942$	−313.942	+	543.763i	−0.333271	+	0.577243i
$943$	258.399	−	149.187i	0.274018	−	0.158204i
$944$		−	694.082i		−	0.735256i
$945$		0			0
$946$	175.984			0.186030
$947$	716.084	+	1240.29i	0.756160	+	1.30971i	0.944796	+	0.327661i	$0.106260\pi$
$947$	716.084	+	1240.29i	0.756160	+	1.30971i	−0.188635	+	0.982047i	$0.560406\pi$
$948$	−232.101	−	134.003i	−0.244832	−	0.141354i
$949$	−318.482	+	551.628i	−0.335598	+	0.581273i
$950$		0			0
$951$		−	536.234i		−	0.563863i
$952$	33.5889	+	147.185i	0.0352825	+	0.154606i
$953$	864.220			0.906841			0.453421	−	0.891297i	$-0.350204\pi$
$953$	864.220			0.906841			0.453421	+	0.891297i	$0.350204\pi$
$954$	−232.441	−	402.600i	−0.243649	−	0.422013i
$955$		0			0
$956$	−159.654	+	276.530i	−0.167003	+	0.289257i
$957$	−573.558	+	331.144i	−0.599330	+	0.346023i
$958$		−	503.459i		−	0.525531i
$959$	−1696.53	+	387.162i	−1.76906	+	0.403714i
$960$		0			0
$961$	−305.277	−	528.756i	−0.317666	−	0.550214i
$962$	363.799	+	210.039i	0.378169	+	0.218336i
$963$	−148.059	+	256.445i	−0.153747	+	0.266298i
$964$	−35.2895	+	20.3744i	−0.0366074	+	0.0211353i
$965$		0			0
$966$	−256.705	−	79.1925i	−0.265741	−	0.0819798i
$967$	247.825			0.256282			0.128141	−	0.991756i	$-0.459099\pi$
$967$	247.825			0.256282			0.128141	+	0.991756i	$0.459099\pi$
$968$	305.498	+	529.139i	0.315597	+	0.546631i
$969$	−104.017	−	60.0545i	−0.107345	−	0.0619758i
$970$		0			0
$971$	119.734	−	69.1286i	0.123310	−	0.0711932i	−0.437076	−	0.899424i	$-0.643986\pi$
$971$	119.734	−	69.1286i	0.123310	−	0.0711932i	0.560386	+	0.828231i	$0.310653\pi$
$972$			18.6987i			0.0192373i
$973$	−80.7414	+	74.9120i	−0.0829819	+	0.0769908i
$974$	−989.359			−1.01577
$975$		0			0
$976$	−978.393	−	564.875i	−1.00245	−	0.578766i
$977$	89.6857	−	155.340i	0.0917971	−	0.158997i	−0.816470	−	0.577387i	$-0.804072\pi$
$977$	89.6857	−	155.340i	0.0917971	−	0.158997i	0.908267	+	0.418390i	$0.137406\pi$
$978$	−433.210	+	250.114i	−0.442955	+	0.255740i
$979$		−	1500.28i		−	1.53246i
$980$		0			0
$981$	−158.275			−0.161340
$982$	258.247	+	447.296i	0.262980	+	0.455495i
$983$	670.259	+	386.974i	0.681850	+	0.393666i	0.800552	−	0.599264i	$-0.204540\pi$
$983$	670.259	+	386.974i	0.681850	+	0.393666i	−0.118702	+	0.992930i	$0.537873\pi$
$984$	−169.812	+	294.124i	−0.172574	+	0.298906i
$985$		0			0
$986$			114.696i			0.116324i
$987$	−113.517	−	122.350i	−0.115012	−	0.123962i
$988$	205.400			0.207894
$989$	−50.3456	−	87.2011i	−0.0509055	−	0.0881710i
$990$		0			0
$991$	314.025	−	543.907i	0.316877	−	0.548847i	−0.662958	−	0.748657i	$-0.730699\pi$
$991$	314.025	−	543.907i	0.316877	−	0.548847i	0.979835	+	0.199810i	$0.0640324\pi$
$992$	299.385	−	172.850i	0.301799	−	0.174244i
$993$			150.364i			0.151423i
$994$	−343.568	+	1113.69i	−0.345642	+	1.12041i
$995$		0			0
$996$	31.5157	+	54.5869i	0.0316423	+	0.0548061i
$997$	−1245.49	−	719.086i	−1.24924	−	0.721250i	−0.278283	−	0.960499i	$-0.589765\pi$
$997$	−1245.49	−	719.086i	−1.24924	−	0.721250i	−0.970958	+	0.239250i	$0.923099\pi$
$998$	748.613	−	1296.64i	0.750113	−	1.29923i
$999$	184.560	−	106.556i	0.184745	−	0.106663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.o.l.451.2		8
5.2	odd	4		525.3.s.h.199.6		16
5.3	odd	4		525.3.s.h.199.3		16
5.4	even	2		105.3.n.a.31.3	✓	8
7.5	odd	6	inner	525.3.o.l.376.2		8
15.14	odd	2		315.3.w.a.136.2		8
35.4	even	6		735.3.h.a.391.4		8
35.12	even	12		525.3.s.h.124.3		16
35.19	odd	6		105.3.n.a.61.3	yes	8
35.24	odd	6		735.3.h.a.391.3		8
35.33	even	12		525.3.s.h.124.6		16
105.89	even	6		315.3.w.a.271.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.a.31.3	✓	8	5.4	even	2
105.3.n.a.61.3	yes	8	35.19	odd	6
315.3.w.a.136.2		8	15.14	odd	2
315.3.w.a.271.2		8	105.89	even	6
525.3.o.l.376.2		8	7.5	odd	6	inner
525.3.o.l.451.2		8	1.1	even	1	trivial
525.3.s.h.124.3		16	35.12	even	12
525.3.s.h.124.6		16	35.33	even	12
525.3.s.h.199.3		16	5.3	odd	4
525.3.s.h.199.6		16	5.2	odd	4
735.3.h.a.391.3		8	35.24	odd	6
735.3.h.a.391.4		8	35.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.836732 - 1.44926i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.599760 - 1.03881i) q^{4} -2.89852i q^{6} +(-4.76104 - 5.13152i) q^{7} -8.70121 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.836732 - 1.44926i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.599760 - 1.03881i) q^{4} -2.89852i q^{6} +(-4.76104 - 5.13152i) q^{7} -8.70121 q^{8} +(1.50000 + 2.59808i) q^{9} +(6.91411 - 11.9756i) q^{11} +(1.79928 - 1.03881i) q^{12} -6.12052i q^{13} +(-3.45321 + 11.1937i) q^{14} +(4.88154 + 8.45507i) q^{16} +(2.14655 + 1.23931i) q^{17} +(2.51020 - 4.34779i) q^{18} +(-24.2290 + 13.9886i) q^{19} +(-2.69753 - 11.8205i) q^{21} -23.1410 q^{22} +(6.62020 + 11.4665i) q^{23} +(-13.0518 - 7.53547i) q^{24} +(-8.87024 + 5.12123i) q^{26} +5.19615i q^{27} +(-8.18618 + 1.86816i) q^{28} -27.6516 q^{29} +(-16.2122 - 9.36010i) q^{31} +(-9.23334 + 15.9926i) q^{32} +(20.7423 - 11.9756i) q^{33} -4.14789i q^{34} +3.59856 q^{36} +(-20.5067 - 35.5187i) q^{37} +(40.5463 + 23.4094i) q^{38} +(5.30052 - 9.18078i) q^{39} -22.5351i q^{41} +(-14.8738 + 13.8000i) q^{42} -7.60485 q^{43} +(-8.29361 - 14.3650i) q^{44} +(11.0787 - 19.1888i) q^{46} +(11.9214 - 6.88283i) q^{47} +16.9101i q^{48} +(-3.66502 + 48.8627i) q^{49} +(2.14655 + 3.71794i) q^{51} +(-6.35808 - 3.67084i) q^{52} +(46.2995 - 80.1930i) q^{53} +(7.53059 - 4.34779i) q^{54} +(41.4268 + 44.6504i) q^{56} -48.4579 q^{57} +(23.1370 + 40.0744i) q^{58} +(-61.5680 - 35.5463i) q^{59} +(-100.214 + 57.8584i) q^{61} +31.3276i q^{62} +(6.19052 - 20.0668i) q^{63} +69.9556 q^{64} +(-34.7115 - 20.0407i) q^{66} +(-5.70227 + 9.87662i) q^{67} +(2.57483 - 1.48658i) q^{68} +22.9330i q^{69} +99.4924 q^{71} +(-13.0518 - 22.6064i) q^{72} +(-90.1276 - 52.0352i) q^{73} +(-34.3172 + 59.4392i) q^{74} +33.5592i q^{76} +(-94.3714 + 21.5364i) q^{77} -17.7405 q^{78} +(-64.4982 - 111.714i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-32.6592 + 18.8558i) q^{82} +30.3382i q^{83} +(-13.8971 - 4.28721i) q^{84} +(6.36322 + 11.0214i) q^{86} +(-41.4774 - 23.9470i) q^{87} +(-60.1611 + 104.202i) q^{88} +(93.9587 - 54.2471i) q^{89} +(-31.4076 + 29.1400i) q^{91} +15.8821 q^{92} +(-16.2122 - 28.0803i) q^{93} +(-19.9501 - 11.5182i) q^{94} +(-27.7000 + 15.9926i) q^{96} +153.154i q^{97} +(73.8816 - 35.5734i) q^{98} +41.4847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 12 q^{3} - 6 q^{4} + 16 q^{7} + 32 q^{8} + 12 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 12 * q^3 - 6 * q^4 + 16 * q^7 + 32 * q^8 + 12 * q^9	\( 8 q - 2 q^{2} + 12 q^{3} - 6 q^{4} + 16 q^{7} + 32 q^{8} + 12 q^{9} + 20 q^{11} - 18 q^{12} - 16 q^{14} - 2 q^{16} + 18 q^{17} + 6 q^{18} + 48 q^{21} + 16 q^{22} - 62 q^{23} + 48 q^{24} + 120 q^{26} + 120 q^{28} - 100 q^{29} - 126 q^{31} - 36 q^{32} + 60 q^{33} - 36 q^{36} + 80 q^{37} - 114 q^{38} - 12 q^{39} - 90 q^{42} - 352 q^{43} - 18 q^{44} - 82 q^{46} + 72 q^{47} + 38 q^{49} + 18 q^{51} + 48 q^{52} + 76 q^{53} + 18 q^{54} + 196 q^{56} + 40 q^{58} - 54 q^{59} - 396 q^{61} + 96 q^{63} - 4 q^{64} + 24 q^{66} - 184 q^{67} + 312 q^{68} + 164 q^{71} + 48 q^{72} - 348 q^{73} - 140 q^{74} - 152 q^{77} + 240 q^{78} - 206 q^{79} - 36 q^{81} - 204 q^{82} + 132 q^{84} + 178 q^{86} - 150 q^{87} - 124 q^{88} + 282 q^{89} - 114 q^{91} + 288 q^{92} - 126 q^{93} + 30 q^{94} - 108 q^{96} + 592 q^{98} + 120 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 12 * q^3 - 6 * q^4 + 16 * q^7 + 32 * q^8 + 12 * q^9 + 20 * q^11 - 18 * q^12 - 16 * q^14 - 2 * q^16 + 18 * q^17 + 6 * q^18 + 48 * q^21 + 16 * q^22 - 62 * q^23 + 48 * q^24 + 120 * q^26 + 120 * q^28 - 100 * q^29 - 126 * q^31 - 36 * q^32 + 60 * q^33 - 36 * q^36 + 80 * q^37 - 114 * q^38 - 12 * q^39 - 90 * q^42 - 352 * q^43 - 18 * q^44 - 82 * q^46 + 72 * q^47 + 38 * q^49 + 18 * q^51 + 48 * q^52 + 76 * q^53 + 18 * q^54 + 196 * q^56 + 40 * q^58 - 54 * q^59 - 396 * q^61 + 96 * q^63 - 4 * q^64 + 24 * q^66 - 184 * q^67 + 312 * q^68 + 164 * q^71 + 48 * q^72 - 348 * q^73 - 140 * q^74 - 152 * q^77 + 240 * q^78 - 206 * q^79 - 36 * q^81 - 204 * q^82 + 132 * q^84 + 178 * q^86 - 150 * q^87 - 124 * q^88 + 282 * q^89 - 114 * q^91 + 288 * q^92 - 126 * q^93 + 30 * q^94 - 108 * q^96 + 592 * q^98 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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