LMFDB - Embedded newform 125.2.h.a.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(4,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("125.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.h (of order $50$, degree $20$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			4.2
Character	$\chi$	$=$	125.4
Dual form			125.2.h.a.94.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.48068 - 0.156071i) q^{2} +(-1.52292 - 0.716634i) q^{3} +(4.14517 + 0.523657i) q^{4} +(-0.268080 + 2.21994i) q^{5} +(3.66604 + 2.01542i) q^{6} +(0.423640 - 0.583091i) q^{7} +(-5.31799 - 1.01446i) q^{8} +(-0.106538 - 0.128782i) q^{9} +O(q^{10})$	\(q+(-2.48068 - 0.156071i) q^{2} +(-1.52292 - 0.716634i) q^{3} +(4.14517 + 0.523657i) q^{4} +(-0.268080 + 2.21994i) q^{5} +(3.66604 + 2.01542i) q^{6} +(0.423640 - 0.583091i) q^{7} +(-5.31799 - 1.01446i) q^{8} +(-0.106538 - 0.128782i) q^{9} +(1.01149 - 5.46511i) q^{10} +(0.273623 - 4.34912i) q^{11} +(-5.93751 - 3.76806i) q^{12} +(4.46898 - 3.69706i) q^{13} +(-1.14192 + 1.38034i) q^{14} +(1.99915 - 3.18869i) q^{15} +(4.94018 + 1.26842i) q^{16} +(0.274880 + 2.17590i) q^{17} +(0.244187 + 0.336094i) q^{18} +(-0.866664 - 1.84175i) q^{19} +(-2.27372 + 9.06165i) q^{20} +(-1.06303 + 0.584408i) q^{21} +(-1.35754 + 10.7460i) q^{22} +(3.23134 - 8.16144i) q^{23} +(7.37190 + 5.35600i) q^{24} +(-4.85627 - 1.19024i) q^{25} +(-11.6631 + 8.47374i) q^{26} +(1.32568 + 5.16317i) q^{27} +(2.06140 - 2.19517i) q^{28} +(1.78154 + 1.67298i) q^{29} +(-5.45690 + 7.59809i) q^{30} +(3.64263 - 0.460172i) q^{31} +(-1.75920 - 0.571600i) q^{32} +(-3.53343 + 6.42729i) q^{33} +(-0.342294 - 5.44061i) q^{34} +(1.18086 + 1.09677i) q^{35} +(-0.374179 - 0.589612i) q^{36} +(0.731829 - 2.85029i) q^{37} +(1.86247 + 4.70406i) q^{38} +(-9.45536 + 2.42772i) q^{39} +(3.67769 - 11.5337i) q^{40} +(1.46551 - 0.580238i) q^{41} +(2.72825 - 1.28382i) q^{42} +(3.05674 - 0.993196i) q^{43} +(3.41166 - 17.8845i) q^{44} +(0.314449 - 0.201984i) q^{45} +(-9.28968 + 19.7416i) q^{46} +(-10.4911 + 2.00128i) q^{47} +(-6.61452 - 5.47201i) q^{48} +(2.00260 + 6.16335i) q^{49} +(11.8611 + 3.71053i) q^{50} +(1.14070 - 3.51072i) q^{51} +(20.4607 - 12.9847i) q^{52} +(-1.43707 - 2.61402i) q^{53} +(-2.48276 - 13.0151i) q^{54} +(9.58143 + 1.77334i) q^{55} +(-2.84444 + 2.67110i) q^{56} +3.42593i q^{57} +(-4.15832 - 4.42817i) q^{58} +(6.55255 - 10.3252i) q^{59} +(9.95659 - 12.1708i) q^{60} +(-7.41101 - 2.93423i) q^{61} +(-9.10802 + 0.573028i) q^{62} +(-0.120225 + 0.00756393i) q^{63} +(-5.20969 - 2.06266i) q^{64} +(7.00922 + 10.9120i) q^{65} +(9.76842 - 15.3926i) q^{66} +(0.237099 + 0.252485i) q^{67} +9.16343i q^{68} +(-10.7699 + 10.1136i) q^{69} +(-2.75815 - 2.90503i) q^{70} +(-0.803464 - 4.21190i) q^{71} +(0.435922 + 0.792939i) q^{72} +(-14.2410 + 9.03759i) q^{73} +(-2.26028 + 6.95642i) q^{74} +(6.54276 + 5.29281i) q^{75} +(-2.62802 - 8.08822i) q^{76} +(-2.42001 - 2.00201i) q^{77} +(23.8346 - 4.54669i) q^{78} +(-4.99981 + 10.6251i) q^{79} +(-4.14018 + 10.6269i) q^{80} +(1.58724 - 8.32061i) q^{81} +(-3.72603 + 1.21066i) q^{82} +(4.68650 - 2.20530i) q^{83} +(-4.71249 + 1.86581i) q^{84} +(-4.90406 + 0.0269028i) q^{85} +(-7.73780 + 1.98673i) q^{86} +(-1.51424 - 3.82453i) q^{87} +(-5.86713 + 22.8510i) q^{88} +(3.22583 + 5.08309i) q^{89} +(-0.811570 + 0.451979i) q^{90} +(-0.262483 - 4.17205i) q^{91} +(17.6683 - 32.1384i) q^{92} +(-5.87723 - 1.90963i) q^{93} +(26.3373 - 3.32717i) q^{94} +(4.32092 - 1.43020i) q^{95} +(2.26951 + 2.13121i) q^{96} +(5.66203 - 6.02945i) q^{97} +(-4.00587 - 15.6018i) q^{98} +(-0.589239 + 0.428107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{50}\right)$

Coefficient data

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

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

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

$2$	−2.48068	−	0.156071i	−1.75410	−	0.110359i	−0.847087	−	0.531454i	$-0.821646\pi$
$2$	−2.48068	−	0.156071i	−1.75410	−	0.110359i	−0.907016	+	0.421095i	$0.861646\pi$
$3$	−1.52292	−	0.716634i	−0.879261	−	0.413749i	−0.0674865	−	0.997720i	$-0.521498\pi$
$3$	−1.52292	−	0.716634i	−0.879261	−	0.413749i	−0.811774	+	0.583972i	$0.801498\pi$
$4$	4.14517	+	0.523657i	2.07258	+	0.261828i
$5$	−0.268080	+	2.21994i	−0.119889	+	0.992787i
$5$	−0.268080	+	2.21994i	−0.119889	+	0.992787i
$6$	3.66604	+	2.01542i	1.49665	+	0.822792i
$7$	0.423640	−	0.583091i	0.160121	−	0.220388i	−0.721417	−	0.692501i	$-0.756509\pi$
$7$	0.423640	−	0.583091i	0.160121	−	0.220388i	0.881538	+	0.472114i	$0.156509\pi$
$8$	−5.31799	−	1.01446i	−1.88019	−	0.358666i
$9$	−0.106538	−	0.128782i	−0.0355126	−	0.0429273i
$10$	1.01149	−	5.46511i	0.319860	−	1.72822i
$11$	0.273623	−	4.34912i	0.0825005	−	1.31131i	−0.711196	−	0.702994i	$-0.751846\pi$
$11$	0.273623	−	4.34912i	0.0825005	−	1.31131i	0.793696	−	0.608314i	$-0.208154\pi$
$12$	−5.93751	−	3.76806i	−1.71401	−	1.08774i
$13$	4.46898	−	3.69706i	1.23947	−	1.02538i	0.240978	−	0.970531i	$-0.422532\pi$
$13$	4.46898	−	3.69706i	1.23947	−	1.02538i	0.998495	−	0.0548506i	$-0.0174682\pi$
$14$	−1.14192	+	1.38034i	−0.305190	+	0.368912i
$15$	1.99915	−	3.18869i	0.516178	−	0.823315i
$16$	4.94018	+	1.26842i	1.23504	+	0.317106i
$17$	0.274880	+	2.17590i	0.0666683	+	0.527734i	0.989716	+	0.143048i	$0.0456903\pi$
$17$	0.274880	+	2.17590i	0.0666683	+	0.527734i	−0.923047	+	0.384686i	$0.874310\pi$
$18$	0.244187	+	0.336094i	0.0575553	+	0.0792181i
$19$	−0.866664	−	1.84175i	−0.198826	−	0.422527i	0.780405	−	0.625275i	$-0.215013\pi$
$19$	−0.866664	−	1.84175i	−0.198826	−	0.422527i	−0.979231	+	0.202747i	$0.935013\pi$
$20$	−2.27372	+	9.06165i	−0.508420	+	2.02625i
$21$	−1.06303	+	0.584408i	−0.231973	+	0.127528i
$22$	−1.35754	+	10.7460i	−0.289429	+	2.29107i
$23$	3.23134	−	8.16144i	0.673782	−	1.70178i	−0.0379053	−	0.999281i	$-0.512069\pi$
$23$	3.23134	−	8.16144i	0.673782	−	1.70178i	0.711687	−	0.702497i	$-0.247931\pi$
$24$	7.37190	+	5.35600i	1.50478	+	1.09329i
$25$	−4.85627	−	1.19024i	−0.971253	−	0.238048i
$26$	−11.6631	+	8.47374i	−2.28732	+	1.66184i
$27$	1.32568	+	5.16317i	0.255127	+	0.993653i
$28$	2.06140	−	2.19517i	0.389568	−	0.414848i
$29$	1.78154	+	1.67298i	0.330824	+	0.310664i	0.832103	−	0.554621i	$-0.187137\pi$
$29$	1.78154	+	1.67298i	0.330824	+	0.310664i	−0.501279	+	0.865286i	$0.667137\pi$
$30$	−5.45690	+	7.59809i	−0.996290	+	1.38721i
$31$	3.64263	−	0.460172i	0.654236	−	0.0826493i	0.208794	−	0.977960i	$-0.433046\pi$
$31$	3.64263	−	0.460172i	0.654236	−	0.0826493i	0.445443	+	0.895310i	$0.353046\pi$
$32$	−1.75920	−	0.571600i	−0.310986	−	0.101046i
$33$	−3.53343	+	6.42729i	−0.615092	+	1.11885i
$34$	−0.342294	−	5.44061i	−0.0587030	−	0.933057i
$35$	1.18086	+	1.09677i	0.199601	+	0.185388i
$36$	−0.374179	−	0.589612i	−0.0623632	−	0.0982687i
$37$	0.731829	−	2.85029i	0.120312	−	0.468584i	−0.879663	−	0.475597i	$-0.842232\pi$
$37$	0.731829	−	2.85029i	0.120312	−	0.468584i	0.999975	+	0.00701261i	$0.00223220\pi$
$38$	1.86247	+	4.70406i	0.302132	+	0.763099i
$39$	−9.45536	+	2.42772i	−1.51407	+	0.388747i
$40$	3.67769	−	11.5337i	0.581493	−	1.82363i
$41$	1.46551	−	0.580238i	0.228875	−	0.0906180i	−0.250888	−	0.968016i	$-0.580723\pi$
$41$	1.46551	−	0.580238i	0.228875	−	0.0906180i	0.479763	+	0.877398i	$0.340723\pi$
$42$	2.72825	−	1.28382i	0.420979	−	0.198098i
$43$	3.05674	−	0.993196i	0.466149	−	0.151461i	−0.0665192	−	0.997785i	$-0.521189\pi$
$43$	3.05674	−	0.993196i	0.466149	−	0.151461i	0.532668	+	0.846324i	$0.321189\pi$
$44$	3.41166	−	17.8845i	0.514327	−	2.69620i
$45$	0.314449	−	0.201984i	0.0468753	−	0.0301099i
$46$	−9.28968	+	19.7416i	−1.36969	+	2.91074i
$47$	−10.4911	+	2.00128i	−1.53028	+	0.291916i	−0.882646	−	0.470038i	$-0.844240\pi$
$47$	−10.4911	+	2.00128i	−1.53028	+	0.291916i	−0.647631	+	0.761954i	$0.724240\pi$
$48$	−6.61452	−	5.47201i	−0.954724	−	0.789816i
$49$	2.00260	+	6.16335i	0.286085	+	0.880479i
$50$	11.8611	+	3.71053i	1.67741	+	0.524748i
$51$	1.14070	−	3.51072i	0.159730	−	0.491600i
$52$	20.4607	−	12.9847i	2.83739	−	1.80066i
$53$	−1.43707	−	2.61402i	−0.197397	−	0.359063i	0.759021	−	0.651066i	$-0.225678\pi$
$53$	−1.43707	−	2.61402i	−0.197397	−	0.359063i	−0.956417	+	0.292004i	$0.905678\pi$
$54$	−2.48276	−	13.0151i	−0.337860	−	1.77113i
$55$	9.58143	+	1.77334i	1.29196	+	0.239117i
$56$	−2.84444	+	2.67110i	−0.380104	+	0.356941i
$57$			3.42593i			0.453776i
$58$	−4.15832	−	4.42817i	−0.546015	−	0.581447i
$59$	6.55255	−	10.3252i	0.853069	−	1.34422i	−0.0845000	−	0.996423i	$-0.526929\pi$
$59$	6.55255	−	10.3252i	0.853069	−	1.34422i	0.937569	−	0.347799i	$-0.113071\pi$
$60$	9.95659	−	12.1708i	1.28539	−	1.57124i
$61$	−7.41101	−	2.93423i	−0.948883	−	0.375689i	−0.157850	−	0.987463i	$-0.550456\pi$
$61$	−7.41101	−	2.93423i	−0.948883	−	0.375689i	−0.791033	+	0.611774i	$0.790456\pi$
$62$	−9.10802	+	0.573028i	−1.15672	+	0.0727746i
$63$	−0.120225	+	0.00756393i	−0.0151470	+	0.000952966i
$64$	−5.20969	−	2.06266i	−0.651211	−	0.257833i
$65$	7.00922	+	10.9120i	0.869386	+	1.35346i
$66$	9.76842	−	15.3926i	1.20241	−	1.89469i
$67$	0.237099	+	0.252485i	0.0289663	+	0.0308460i	0.743289	−	0.668971i	$-0.233265\pi$
$67$	0.237099	+	0.252485i	0.0289663	+	0.0308460i	−0.714322	+	0.699817i	$0.753265\pi$
$68$			9.16343i			1.11123i
$69$	−10.7699	+	10.1136i	−1.29654	+	1.21753i
$70$	−2.75815	−	2.90503i	−0.329662	−	0.347218i
$71$	−0.803464	−	4.21190i	−0.0953536	−	0.499861i	−0.997636	−	0.0687161i	$-0.978110\pi$
$71$	−0.803464	−	4.21190i	−0.0953536	−	0.499861i	0.902283	−	0.431145i	$-0.141890\pi$
$72$	0.435922	+	0.792939i	0.0513739	+	0.0934488i
$73$	−14.2410	+	9.03759i	−1.66678	+	1.05777i	−0.747418	+	0.664354i	$0.768707\pi$
$73$	−14.2410	+	9.03759i	−1.66678	+	1.05777i	−0.919361	+	0.393416i	$0.871293\pi$
$74$	−2.26028	+	6.95642i	−0.262752	+	0.808667i
$75$	6.54276	+	5.29281i	0.755493	+	0.611161i
$76$	−2.62802	−	8.08822i	−0.301455	−	0.927782i
$77$	−2.42001	−	2.00201i	−0.275786	−	0.228150i
$78$	23.8346	−	4.54669i	2.69874	−	0.514812i
$79$	−4.99981	+	10.6251i	−0.562523	+	1.19542i	0.398043	+	0.917367i	$0.369690\pi$
$79$	−4.99981	+	10.6251i	−0.562523	+	1.19542i	−0.960565	+	0.278055i	$0.910310\pi$
$80$	−4.14018	+	10.6269i	−0.462886	+	1.18812i
$81$	1.58724	−	8.32061i	0.176360	−	0.924513i
$82$	−3.72603	+	1.21066i	−0.411471	+	0.133695i
$83$	4.68650	−	2.20530i	0.514411	−	0.242063i	−0.151010	−	0.988532i	$-0.548252\pi$
$83$	4.68650	−	2.20530i	0.514411	−	0.242063i	0.665420	+	0.746469i	$0.268252\pi$
$84$	−4.71249	+	1.86581i	−0.514175	+	0.203576i
$85$	−4.90406	+	0.0269028i	−0.531920	+	0.00291801i
$86$	−7.73780	+	1.98673i	−0.834389	+	0.214235i
$87$	−1.51424	−	3.82453i	−0.162344	−	0.410033i
$88$	−5.86713	+	22.8510i	−0.625439	+	2.43592i
$89$	3.22583	+	5.08309i	0.341937	+	0.538806i	0.971163	−	0.238416i	$-0.0766281\pi$
$89$	3.22583	+	5.08309i	0.341937	+	0.538806i	−0.629226	+	0.777222i	$0.716628\pi$
$90$	−0.811570	+	0.451979i	−0.0855470	+	0.0476428i
$91$	−0.262483	−	4.17205i	−0.0275157	−	0.437349i
$92$	17.6683	−	32.1384i	1.84204	−	3.35066i
$93$	−5.87723	−	1.90963i	−0.609440	−	0.198019i
$94$	26.3373	−	3.32717i	2.71648	−	0.343171i
$95$	4.32092	−	1.43020i	0.443317	−	0.146736i
$96$	2.26951	+	2.13121i	0.231630	+	0.217515i
$97$	5.66203	−	6.02945i	0.574892	−	0.612198i	−0.374142	−	0.927371i	$-0.622063\pi$
$97$	5.66203	−	6.02945i	0.574892	−	0.612198i	0.949034	+	0.315174i	$0.102063\pi$
$98$	−4.00587	−	15.6018i	−0.404654	−	1.57602i
$99$	−0.589239	+	0.428107i	−0.0592208	+	0.0430264i
$100$	−19.5068	−	7.47677i	−1.95068	−	0.747677i
$101$	7.75107	+	5.63148i	0.771260	+	0.560354i	0.902343	−	0.431018i	$-0.141845\pi$
$101$	7.75107	+	5.63148i	0.771260	+	0.560354i	−0.131083	+	0.991371i	$0.541845\pi$
$102$	−3.37764	+	8.53094i	−0.334436	+	0.844689i
$103$	−0.704300	+	5.57511i	−0.0693967	+	0.549332i	0.918638	+	0.395100i	$0.129290\pi$
$103$	−0.704300	+	5.57511i	−0.0693967	+	0.549332i	−0.988035	+	0.154231i	$0.950710\pi$
$104$	−27.5165	+	15.1273i	−2.69822	+	1.48336i
$105$	−1.01237	−	2.51654i	−0.0987975	−	0.245589i
$106$	3.15693	+	6.70882i	0.306628	+	0.651618i
$107$	0.709441	+	0.976462i	0.0685843	+	0.0943982i	0.841931	−	0.539585i	$-0.181419\pi$
$107$	0.709441	+	0.976462i	0.0685843	+	0.0943982i	−0.773347	+	0.633983i	$0.781419\pi$
$108$	2.79143	+	22.0964i	0.268605	+	2.12623i
$109$	1.65574	+	0.425121i	0.158591	+	0.0407192i	0.327151	−	0.944972i	$-0.393912\pi$
$109$	1.65574	+	0.425121i	0.158591	+	0.0407192i	−0.168560	+	0.985691i	$0.553912\pi$
$110$	−23.4917	−	5.89446i	−2.23984	−	0.562015i
$111$	−3.15713	+	3.81632i	−0.299662	+	0.362229i
$112$	2.83246	−	2.34322i	0.267643	−	0.221413i
$113$	7.57983	+	4.81030i	0.713050	+	0.452515i	0.842239	−	0.539105i	$-0.181237\pi$
$113$	7.57983	+	4.81030i	0.713050	+	0.452515i	−0.129189	+	0.991620i	$0.541237\pi$
$114$	0.534689	−	8.49863i	0.0500782	−	0.795970i
$115$	17.2517	+	9.36130i	1.60872	+	0.872946i
$116$	6.50872	+	7.86770i	0.604320	+	0.730497i
$117$	−0.952230	−	0.181648i	−0.0880337	−	0.0167933i
$118$	−17.8662	+	24.5907i	−1.64472	+	2.26376i
$119$	1.38520	+	0.761520i	0.126981	+	0.0698084i
$120$	−13.8662	+	14.9293i	−1.26581	+	1.36286i
$121$	−7.92669	−	1.00137i	−0.720608	−	0.0910340i
$122$	17.9264	+	8.43552i	1.62298	+	0.763716i
$123$	−2.64769	−	0.166578i	−0.238734	−	0.0150199i
$124$	15.3403			1.37760
$125$	3.94413	−	10.4615i	0.352774	−	0.935709i
$126$	0.299420			0.0266745
$127$	−0.182756	−	0.0114980i	−0.0162170	−	0.00102029i	0.0546800	−	0.998504i	$-0.482586\pi$
$127$	−0.182756	−	0.0114980i	−0.0162170	−	0.00102029i	−0.0708969	+	0.997484i	$0.522586\pi$
$128$	15.9490	+	7.50504i	1.40971	+	0.663358i
$129$	−5.36695	−	0.678003i	−0.472533	−	0.0596948i
$130$	−15.6846	−	28.1630i	−1.37563	−	2.47006i
$131$	2.88134	+	1.58403i	0.251744	+	0.138397i	0.602630	−	0.798021i	$-0.294120\pi$
$131$	2.88134	+	1.58403i	0.251744	+	0.138397i	−0.350886	+	0.936418i	$0.614120\pi$
$132$	−18.0124	+	24.7919i	−1.56778	+	2.15786i
$133$	−1.44106	−	0.274898i	−0.124956	−	0.0238366i
$134$	−0.548761	−	0.663338i	−0.0474057	−	0.0573037i
$135$	−11.8173	+	1.55878i	−1.01707	+	0.134159i
$136$	0.745556	−	11.8503i	0.0639309	−	1.01615i
$137$	−10.0943	−	6.40607i	−0.862418	−	0.547307i	0.0294685	−	0.999566i	$-0.490619\pi$
$137$	−10.0943	−	6.40607i	−0.862418	−	0.547307i	−0.891887	+	0.452258i	$0.850619\pi$
$138$	28.2950	−	23.4076i	2.40863	−	1.99259i
$139$	3.06502	−	3.70498i	0.259972	−	0.314252i	−0.624336	−	0.781156i	$-0.714630\pi$
$139$	3.06502	−	3.70498i	0.259972	−	0.314252i	0.884308	+	0.466904i	$0.154630\pi$
$140$	4.32052	+	5.16466i	0.365151	+	0.436494i
$141$	17.4113	+	4.47045i	1.46629	+	0.376480i
$142$	1.33578	+	10.5738i	0.112096	+	0.887331i
$143$	−14.8561	−	20.4477i	−1.24233	−	1.70993i
$144$	−0.362965	−	0.771341i	−0.0302471	−	0.0642784i
$145$	−4.19151	+	3.50642i	−0.348086	+	0.291193i
$146$	36.7377	−	20.1967i	3.04044	−	1.67149i
$147$	1.36707	−	10.8214i	0.112754	−	0.892538i
$148$	4.52613	−	11.4317i	0.372045	−	0.939679i
$149$	−10.2789	−	7.46804i	−0.842078	−	0.611805i	0.0808724	−	0.996724i	$-0.474229\pi$
$149$	−10.2789	−	7.46804i	−0.842078	−	0.611805i	−0.922950	+	0.384919i	$0.874229\pi$
$150$	−15.4044	−	14.1509i	−1.25777	−	1.15542i
$151$	0.173129	−	0.125786i	0.0140891	−	0.0102363i	−0.580718	−	0.814104i	$-0.697228\pi$
$151$	0.173129	−	0.125786i	0.0140891	−	0.0102363i	0.594808	+	0.803868i	$0.297228\pi$
$152$	2.74052	+	10.6736i	0.222286	+	0.865745i
$153$	0.250932	−	0.267215i	0.0202866	−	0.0216031i
$154$	5.69081	+	5.34403i	0.458579	+	0.430634i
$155$	0.0450374	+	8.20979i	0.00361749	+	0.659426i
$156$	−40.4654	+	5.11197i	−3.23982	+	0.409285i
$157$	17.8107	+	5.78704i	1.42145	+	0.461856i	0.916061	−	0.401038i	$-0.131351\pi$
$157$	17.8107	+	5.78704i	1.42145	+	0.461856i	0.505385	+	0.862894i	$0.331351\pi$
$158$	14.0612	−	25.5772i	1.11865	−	2.03481i
$159$	0.315253	+	5.01080i	0.0250012	+	0.397382i
$160$	1.74052	−	3.75209i	0.137600	−	0.296629i
$161$	−3.38993	−	5.34168i	−0.267164	−	0.420983i
$162$	−5.23604	+	20.3930i	−0.411382	+	1.60223i
$163$	−6.63250	−	16.7518i	−0.519497	−	1.31210i	−0.918598	−	0.395194i	$-0.870678\pi$
$163$	−6.63250	−	16.7518i	−0.519497	−	1.31210i	0.399100	−	0.916907i	$-0.369322\pi$
$164$	6.37865	−	1.63776i	0.498089	−	0.127888i
$165$	−13.3210	−	9.56703i	−1.03703	−	0.744792i
$166$	−11.9699	+	4.73921i	−0.929043	+	0.367834i
$167$	−1.71785	+	0.808357i	−0.132931	+	0.0625525i	−0.491094	−	0.871106i	$-0.663403\pi$
$167$	−1.71785	+	0.808357i	−0.132931	+	0.0625525i	0.358164	+	0.933659i	$0.383403\pi$
$168$	6.24606	−	2.02947i	0.481894	−	0.156577i
$169$	3.86757	−	20.2745i	0.297505	−	1.55958i
$170$	12.1696	+	0.698645i	0.933365	+	0.0535836i
$171$	−0.144852	+	0.307827i	−0.0110771	+	0.0235401i
$172$	13.1908	−	2.51628i	1.00579	−	0.191865i
$173$	17.6030	+	14.5625i	1.33833	+	1.10716i	0.985166	+	0.171604i	$0.0548951\pi$
$173$	17.6030	+	14.5625i	1.33833	+	1.10716i	0.353166	+	0.935560i	$0.385105\pi$
$174$	3.15944	+	9.72376i	0.239517	+	0.737156i
$175$	−2.75133	+	2.32741i	−0.207981	+	0.175936i
$176$	6.86826	−	21.1383i	0.517715	−	1.59336i
$177$	−17.3784	+	11.0287i	−1.30624	+	0.828965i
$178$	−7.20891	−	13.1130i	−0.540331	−	0.982858i
$179$	2.64141	+	13.8468i	0.197428	+	1.03496i	0.933642	+	0.358207i	$0.116612\pi$
$179$	2.64141	+	13.8468i	0.197428	+	1.03496i	−0.736214	+	0.676749i	$0.763388\pi$
$180$	1.40921	−	0.672593i	0.105037	−	0.0501321i
$181$	11.0549	−	10.3813i	0.821705	−	0.771632i	−0.154613	−	0.987975i	$-0.549413\pi$
$181$	11.0549	−	10.3813i	0.821705	−	0.771632i	0.976317	+	0.216343i	$0.0694129\pi$
$182$			10.3905i			0.770193i
$183$	9.18365	+	9.77959i	0.678875	+	0.722928i
$184$	−25.4637	+	40.1244i	−1.87721	+	2.95801i
$185$	6.13127	+	2.38872i	0.450780	+	0.175622i
$186$	14.2815	+	5.65443i	1.04717	+	0.414603i
$187$	9.53847	−	0.600110i	0.697522	−	0.0438844i
$188$	−44.5352	+	2.80192i	−3.24806	+	0.204351i
$189$	3.57221	+	1.41434i	0.259840	+	0.102878i
$190$	−10.9420	+	2.87351i	−0.793817	+	0.208466i
$191$	−8.17907	+	12.8882i	−0.591817	+	0.932554i	0.407992	+	0.912986i	$0.366229\pi$
$191$	−8.17907	+	12.8882i	−0.591817	+	0.932554i	−0.999809	+	0.0195683i	$0.993771\pi$
$192$	6.45579	+	6.87472i	0.465907	+	0.496140i
$193$			12.7415i			0.917152i	0.888655	+	0.458576i	$0.151640\pi$
$193$			12.7415i			0.917152i	−0.888655	+	0.458576i	$0.848360\pi$
$194$	−14.9867	+	14.0734i	−1.07598	+	1.01041i
$195$	−2.85461	−	21.6412i	−0.204423	−	1.54976i
$196$	5.07361	+	26.5968i	0.362401	+	1.89977i
$197$	−7.99679	−	14.5461i	−0.569748	−	1.03637i	−0.991556	−	0.129682i	$-0.958604\pi$
$197$	−7.99679	−	14.5461i	−0.569748	−	1.03637i	0.421808	−	0.906685i	$-0.361396\pi$
$198$	1.52853	−	0.970033i	0.108628	−	0.0689372i
$199$	1.45887	−	4.48993i	0.103416	−	0.318282i	−0.885939	−	0.463801i	$-0.846485\pi$
$199$	1.45887	−	4.48993i	0.103416	−	0.318282i	0.989355	+	0.145519i	$0.0464851\pi$
$200$	24.6181	+	11.2562i	1.74076	+	0.795932i
$201$	−0.180145	−	0.554429i	−0.0127064	−	0.0391064i
$202$	−18.3490	−	15.1796i	−1.29103	−	1.06803i
$203$	1.73023	−	0.330059i	0.121438	−	0.0231656i
$204$	6.56682	−	13.9552i	0.459769	−	0.977060i
$205$	0.895220	+	3.40890i	0.0625248	+	0.238088i
$206$	2.61725	−	13.7201i	0.182353	−	0.955926i
$207$	−1.39531	+	0.453363i	−0.0969805	+	0.0315109i
$208$	26.7670	−	12.5956i	1.85596	−	0.873348i
$209$	−8.24715	+	3.26528i	−0.570467	+	0.225864i
$210$	2.11861	+	6.40073i	0.146198	+	0.441692i
$211$	−19.6669	+	5.04959i	−1.35392	+	0.347628i	−0.854825	−	0.518917i	$-0.826335\pi$
$211$	−19.6669	+	5.04959i	−1.35392	+	0.347628i	−0.499098	+	0.866545i	$0.666335\pi$
$212$	−4.58804	−	11.5881i	−0.315108	−	0.795872i
$213$	−1.79478	+	6.99020i	−0.122976	+	0.478961i
$214$	−1.60750	−	2.53301i	−0.109886	−	0.173153i
$215$	1.38538	+	7.05204i	0.0944825	+	0.480945i
$216$	−1.81210	−	28.8025i	−0.123298	−	1.95976i
$217$	1.27484	−	2.31893i	0.0865421	−	0.157419i
$218$	−4.04100	−	1.31300i	−0.273691	−	0.0889276i
$219$	28.1645	−	3.55801i	1.90318	−	0.240428i
$220$	38.7880	+	12.3682i	2.61509	+	0.833861i
$221$	9.27289	+	8.70782i	0.623762	+	0.585751i
$222$	8.42744	−	8.97431i	0.565612	−	0.602316i
$223$	0.894444	+	3.48363i	0.0598964	+	0.233281i	0.991483	−	0.130240i	$-0.0415746\pi$
$223$	0.894444	+	3.48363i	0.0598964	+	0.233281i	−0.931586	+	0.363521i	$0.881575\pi$
$224$	−1.07856	+	0.783622i	−0.0720646	+	0.0523580i
$225$	0.364094	+	0.752205i	0.0242729	+	0.0501470i
$226$	−18.0524	−	13.1158i	−1.20082	−	0.872450i
$227$	−2.21315	+	5.58978i	−0.146892	+	0.371007i	−0.984529	−	0.175220i	$-0.943936\pi$
$227$	−2.21315	+	5.58978i	−0.146892	+	0.371007i	0.837637	+	0.546227i	$0.183936\pi$
$228$	−1.79401	+	14.2011i	−0.118811	+	0.940489i
$229$	1.41381	−	0.777248i	0.0934272	−	0.0513620i	−0.434355	−	0.900742i	$-0.643024\pi$
$229$	1.41381	−	0.777248i	0.0934272	−	0.0513620i	0.527782	+	0.849380i	$0.323024\pi$
$230$	−41.3347	−	25.9149i	−2.72553	−	1.70877i
$231$	2.25079	+	4.78317i	0.148091	+	0.314709i
$232$	−7.77704	−	10.7042i	−0.510588	−	0.702764i
$233$	1.91681	+	15.1731i	0.125574	+	0.994023i	0.921432	+	0.388539i	$0.127020\pi$
$233$	1.91681	+	15.1731i	0.125574	+	0.994023i	−0.795858	+	0.605484i	$0.792980\pi$
$234$	2.33383	+	0.599225i	0.152567	+	0.0391725i
$235$	−1.63027	−	23.8260i	−0.106347	−	1.55424i
$236$	32.5683	−	39.3683i	2.12001	−	2.56266i
$237$	15.2287	−	12.5982i	0.989208	−	0.818344i
$238$	−3.31738	−	2.10527i	−0.215034	−	0.136465i
$239$	−1.08564	+	17.2558i	−0.0702245	+	1.11619i	0.792287	+	0.610149i	$0.208890\pi$
$239$	−1.08564	+	17.2558i	−0.0702245	+	1.11619i	−0.862511	+	0.506037i	$0.831110\pi$
$240$	13.9208	−	13.2169i	0.898581	−	0.853148i
$241$	13.1038	+	15.8397i	0.844088	+	1.02033i	0.999473	+	0.0324734i	$0.0103384\pi$
$241$	13.1038	+	15.8397i	0.844088	+	1.02033i	−0.155384	+	0.987854i	$0.549662\pi$
$242$	19.5073	+	3.72121i	1.25397	+	0.239209i
$243$	1.01974	−	1.40355i	0.0654164	−	0.0900380i
$244$	−29.1834	−	16.0437i	−1.86827	−	1.02709i
$245$	−14.2191	+	2.79337i	−0.908427	+	0.178462i
$246$	6.54206	+	0.826454i	0.417106	+	0.0526928i
$247$	−10.6822	−	5.02666i	−0.679692	−	0.319839i
$248$	−19.8383	−	1.24812i	−1.25973	−	0.0792557i
$249$	−8.71758			−0.552454
$250$	−11.4169	+	25.3361i	−0.722065	+	1.60240i
$251$	3.23541			0.204217			0.102109	−	0.994773i	$-0.467441\pi$
$251$	3.23541			0.204217			0.102109	+	0.994773i	$0.467441\pi$
$252$	−0.502315	−	0.0316030i	−0.0316429	−	0.00199080i
$253$	−34.6109	−	16.2867i	−2.17597	−	1.02393i
$254$	0.451565	+	0.0570459i	0.0283337	+	0.00357938i
$255$	7.48780	+	3.47345i	0.468904	+	0.217516i
$256$	−28.5729	−	15.7081i	−1.78580	−	0.981754i
$257$	12.4400	−	17.1222i	0.775985	−	1.06805i	−0.219729	−	0.975561i	$-0.570517\pi$
$257$	12.4400	−	17.1222i	0.775985	−	1.06805i	0.995714	−	0.0924906i	$-0.0294828\pi$
$258$	13.2078	+	2.51953i	0.822284	+	0.156859i
$259$	−1.35194	−	1.63422i	−0.0840056	−	0.101545i
$260$	23.3403	+	48.9024i	1.44750	+	3.03280i
$261$	0.0256482	−	0.407666i	0.00158758	−	0.0252339i
$262$	−6.90045	−	4.37916i	−0.426311	−	0.270545i
$263$	−4.92126	+	4.07122i	−0.303458	+	0.251042i	−0.776672	−	0.629905i	$-0.783094\pi$
$263$	−4.92126	+	4.07122i	−0.303458	+	0.251042i	0.473214	+	0.880947i	$0.343094\pi$
$264$	25.3110	−	30.5957i	1.55778	−	1.88304i
$265$	6.18821	−	2.48944i	0.380139	−	0.152925i
$266$	3.53191	+	0.906840i	0.216555	+	0.0556020i
$267$	−1.26998	−	10.0529i	−0.0777213	−	0.615227i
$268$	0.850601	+	1.17075i	0.0519588	+	0.0715151i
$269$	6.06235	+	12.8832i	0.369628	+	0.785500i	0.999958	+	0.00917251i	$0.00291974\pi$
$269$	6.06235	+	12.8832i	0.369628	+	0.785500i	−0.630330	+	0.776328i	$0.717080\pi$
$270$	29.5582	−	2.02250i	1.79886	−	0.123085i
$271$	−5.00900	+	2.75372i	−0.304275	+	0.167277i	−0.626575	−	0.779361i	$-0.715544\pi$
$271$	−5.00900	+	2.75372i	−0.304275	+	0.167277i	0.322300	+	0.946637i	$0.395544\pi$
$272$	−1.40200	+	11.0980i	−0.0850090	+	0.672916i
$273$	−2.59009	+	6.54182i	−0.156759	+	0.395929i
$274$	24.0410	+	17.4668i	1.45237	+	1.05521i
$275$	−6.50529	+	20.7948i	−0.392284	+	1.25397i
$276$	−49.9389	+	36.2827i	−3.00597	+	2.18396i
$277$	4.66073	+	18.1524i	0.280036	+	1.09067i	0.940495	+	0.339807i	$0.110362\pi$
$277$	4.66073	+	18.1524i	0.280036	+	1.09067i	−0.660459	+	0.750862i	$0.729638\pi$
$278$	−8.18158	+	8.71249i	−0.490698	+	0.522541i
$279$	−0.447340	−	0.420080i	−0.0267815	−	0.0251495i
$280$	−5.16715	−	7.03055i	−0.308797	−	0.420156i
$281$	−9.64456	+	1.21839i	−0.575346	+	0.0726831i	−0.407622	−	0.913151i	$-0.633642\pi$
$281$	−9.64456	+	1.21839i	−0.575346	+	0.0726831i	−0.167724	+	0.985834i	$0.553642\pi$
$282$	−42.4940	−	13.8071i	−2.53048	−	0.822203i
$283$	−5.85802	+	10.6557i	−0.348223	+	0.633415i	−0.991185	−	0.132483i	$-0.957705\pi$
$283$	−5.85802	+	10.6557i	−0.348223	+	0.633415i	0.642962	+	0.765898i	$0.277705\pi$
$284$	−1.12490	−	17.8798i	−0.0667506	−	1.06097i
$285$	−7.60537	−	0.918423i	−0.450503	−	0.0544027i
$286$	33.6620	+	53.0428i	1.99048	+	3.13649i
$287$	0.282519	−	1.10034i	0.0166766	−	0.0649510i
$288$	0.113810	+	0.287451i	0.00670630	+	0.0169382i
$289$	11.8069	−	3.03150i	0.694525	−	0.178324i
$290$	10.9450	−	8.04413i	0.642714	−	0.472368i
$291$	−12.9438	+	5.12479i	−0.758776	+	0.300421i
$292$	−63.7638	+	30.0050i	−3.73149	+	1.75591i
$293$	4.04820	−	1.31534i	0.236499	−	0.0768431i	−0.188370	−	0.982098i	$-0.560320\pi$
$293$	4.04820	−	1.31534i	0.236499	−	0.0768431i	0.424868	+	0.905255i	$0.360320\pi$
$294$	−5.08016	+	26.6312i	−0.296281	+	1.55316i
$295$	21.1646	+	17.3142i	1.23225	+	1.00807i
$296$	−6.78336	+	14.4154i	−0.394275	+	0.837877i
$297$	22.8180	−	4.35276i	1.32403	−	0.252573i
$298$	24.3330	+	20.1300i	1.40957	+	1.16610i
$299$	−15.7326	−	48.4198i	−0.909837	−	2.80019i
$300$	24.3492	+	25.3658i	1.40580	+	1.46449i
$301$	0.715836	−	2.20312i	0.0412601	−	0.126986i
$302$	−0.449110	+	0.285014i	−0.0258434	+	0.0164007i
$303$	−7.76858	−	14.1310i	−0.446293	−	0.811805i
$304$	−1.94535	−	10.1979i	−0.111574	−	0.584889i
$305$	8.50055	−	15.6654i	0.486740	−	0.896998i
$306$	−0.664185	+	0.623712i	−0.0379690	+	0.0356552i
$307$		−	9.96679i		−	0.568835i	−0.958701	−	0.284417i	$-0.908200\pi$
$307$		−	9.96679i		−	0.568835i	0.958701	−	0.284417i	$-0.0918001\pi$
$308$	−8.98300	−	9.56592i	−0.511854	−	0.545069i
$309$	5.06790	−	7.98574i	0.288303	−	0.454293i
$310$	1.16959	−	20.3729i	0.0664281	−	1.15710i
$311$	−4.89012	−	1.93613i	−0.277293	−	0.109788i	0.225362	−	0.974275i	$-0.427643\pi$
$311$	−4.89012	−	1.93613i	−0.277293	−	0.109788i	−0.502655	+	0.864487i	$0.667643\pi$
$312$	52.7463	−	3.31852i	2.98617	−	0.187874i
$313$	16.0366	−	1.00894i	0.906441	−	0.0570285i	0.397278	−	0.917698i	$-0.369955\pi$
$313$	16.0366	−	1.00894i	0.906441	−	0.0570285i	0.509163	+	0.860670i	$0.329955\pi$
$314$	−43.2793	−	17.1355i	−2.44239	−	0.967012i
$315$	0.0154385	−	0.268921i	0.000869859	−	0.0151520i
$316$	−26.2890	+	41.4248i	−1.47887	+	2.33033i
$317$	3.95011	+	4.20644i	0.221860	+	0.236257i	0.830264	−	0.557371i	$-0.188190\pi$
$317$	3.95011	+	4.20644i	0.221860	+	0.236257i	−0.608404	+	0.793628i	$0.708190\pi$
$318$		−	12.4794i		−	0.699809i
$319$	7.76345	−	7.29037i	0.434670	−	0.408182i
$320$	5.97560	−	11.0122i	0.334046	−	0.615603i
$321$	−0.380660	−	1.99549i	−0.0212463	−	0.111377i
$322$	7.57565	+	13.7801i	0.422174	+	0.767932i
$323$	3.76925	−	2.39204i	0.209727	−	0.133097i
$324$	10.9365	−	33.6592i	0.607585	−	1.86995i
$325$	−26.1030	+	12.6348i	−1.44793	+	0.700850i
$326$	13.8386	+	42.5909i	0.766450	+	2.35889i
$327$	−2.21691	−	1.83398i	−0.122595	−	0.101420i
$328$	−8.38222	+	1.59899i	−0.462831	+	0.0882897i
$329$	−3.27751	+	6.96506i	−0.180695	+	0.383996i
$330$	31.5518	+	25.8117i	1.73687	+	1.42089i
$331$	1.24372	−	6.51980i	0.0683610	−	0.358361i	−0.931626	−	0.363418i	$-0.881610\pi$
$331$	1.24372	−	6.51980i	0.0683610	−	0.358361i	0.999987	+	0.00505710i	$0.00160973\pi$
$332$	20.5812	−	6.68723i	1.12954	−	0.367009i
$333$	−0.445033	+	0.209417i	−0.0243876	+	0.0114760i
$334$	4.38758	−	1.73717i	0.240078	−	0.0950535i
$335$	−0.624063	+	0.458660i	−0.0340962	+	0.0250593i
$336$	−5.99286	+	1.53870i	−0.326937	+	0.0839432i
$337$	−0.375180	−	0.947595i	−0.0204373	−	0.0516188i	0.919200	−	0.393792i	$-0.128837\pi$
$337$	−0.375180	−	0.947595i	−0.0204373	−	0.0516188i	−0.939637	+	0.342173i	$0.888837\pi$
$338$	−12.7584	+	49.6909i	−0.693968	+	2.70283i
$339$	−8.09628	−	12.7577i	−0.439729	−	0.692903i
$340$	−20.3423	−	2.45653i	−1.10321	−	0.133224i
$341$	−1.00463	−	15.9682i	−0.0544038	−	0.864724i
$342$	0.407375	−	0.741012i	0.0220283	−	0.0400693i
$343$	9.24043	+	3.00240i	0.498936	+	0.162114i
$344$	−17.2633	+	2.18086i	−0.930774	+	0.117584i
$345$	−19.5643	−	26.6197i	−1.05331	−	1.43315i
$346$	−41.3946	−	38.8721i	−2.22539	−	2.08978i
$347$	−9.20042	+	9.79746i	−0.493905	+	0.525955i	−0.926833	−	0.375473i	$-0.877480\pi$
$347$	−9.20042	+	9.79746i	−0.493905	+	0.525955i	0.432929	+	0.901428i	$0.357480\pi$
$348$	−4.27404	−	16.6463i	−0.229112	−	0.892334i
$349$	5.59314	−	4.06365i	0.299394	−	0.217522i	−0.427938	−	0.903808i	$-0.640760\pi$
$349$	5.59314	−	4.06365i	0.299394	−	0.217522i	0.727332	+	0.686286i	$0.240760\pi$
$350$	7.18840	−	5.34415i	0.384236	−	0.285657i
$351$	25.0130	+	18.1730i	1.33510	+	0.970004i
$352$	−2.96731	+	7.49458i	−0.158158	+	0.399462i
$353$	−0.993365	+	7.86329i	−0.0528715	+	0.418521i	0.943359	+	0.331774i	$0.107647\pi$
$353$	−0.993365	+	7.86329i	−0.0528715	+	0.418521i	−0.996230	+	0.0867468i	$0.972353\pi$
$354$	44.8314	−	24.6463i	2.38276	−	1.30994i
$355$	9.56557	−	0.654515i	0.507688	−	0.0347381i
$356$	10.7098	+	22.7595i	0.567618	+	1.20625i
$357$	−1.56382	−	2.15242i	−0.0827663	−	0.113918i
$358$	−4.39141	−	34.7616i	−0.232093	−	1.83721i
$359$	22.1596	+	5.68961i	1.16954	+	0.300286i	0.783021	−	0.621996i	$-0.213678\pi$
$359$	22.1596	+	5.68961i	1.16954	+	0.300286i	0.386517	+	0.922282i	$0.373678\pi$
$360$	−1.87714	+	0.755150i	−0.0989339	+	0.0397999i
$361$	9.47010	−	11.4474i	0.498426	−	0.602494i
$362$	−29.0439	+	24.0272i	−1.52651	+	1.26284i
$363$	11.3541	+	7.20555i	0.595937	+	0.378193i
$364$	1.09668	−	17.4313i	0.0574819	−	0.913648i
$365$	−16.2452	−	34.0369i	−0.850312	−	1.78157i
$366$	−21.2553	−	25.6933i	−1.11103	−	1.34301i
$367$	−11.7730	−	2.24582i	−0.614545	−	0.117231i	−0.129295	−	0.991606i	$-0.541271\pi$
$367$	−11.7730	−	2.24582i	−0.614545	−	0.117231i	−0.485250	+	0.874375i	$0.661271\pi$
$368$	26.3156	−	36.2203i	1.37179	−	1.88811i
$369$	−0.230857	−	0.126915i	−0.0120179	−	0.00660691i
$370$	−14.8369	−	6.88256i	−0.771334	−	0.357807i
$371$	−2.13301	−	0.269462i	−0.110740	−	0.0139898i
$372$	−23.3621	−	10.9934i	−1.21127	−	0.569980i
$373$	8.44791	+	0.531498i	0.437416	+	0.0275199i	0.279972	−	0.960008i	$-0.409675\pi$
$373$	8.44791	+	0.531498i	0.437416	+	0.0275199i	0.157444	+	0.987528i	$0.449675\pi$
$374$	−23.7555			−1.22837
$375$	−13.5037	+	13.1056i	−0.697328	+	0.676772i
$376$	57.8215			2.98192
$377$	14.1468	+	0.890040i	0.728597	+	0.0458394i
$378$	−8.64076	−	4.06603i	−0.444433	−	0.209134i
$379$	10.4611	+	1.32154i	0.537349	+	0.0678830i	0.389324	−	0.921101i	$-0.372709\pi$
$379$	10.4611	+	1.32154i	0.537349	+	0.0678830i	0.148025	+	0.988984i	$0.452709\pi$
$380$	18.6599	−	3.66576i	0.957232	−	0.188050i
$381$	0.270084	+	0.148480i	0.0138368	+	0.00760686i
$382$	22.3011	−	30.6948i	1.14102	−	1.57048i
$383$	−25.5634	−	4.87648i	−1.30623	−	0.249177i	−0.513152	−	0.858298i	$-0.671522\pi$
$383$	−25.5634	−	4.87648i	−1.30623	−	0.249177i	−0.793077	+	0.609121i	$0.791522\pi$
$384$	−18.9108	−	22.8592i	−0.965037	−	1.16653i
$385$	5.09309	−	4.83558i	0.259568	−	0.246444i
$386$	1.98857	−	31.6075i	0.101216	−	1.60878i
$387$	−0.453564	−	0.287841i	−0.0230560	−	0.0146318i
$388$	26.6274	−	22.0281i	1.35180	−	1.11831i
$389$	4.26633	−	5.15711i	0.216312	−	0.261476i	−0.651185	−	0.758919i	$-0.725728\pi$
$389$	4.26633	−	5.15711i	0.216312	−	0.261476i	0.867497	+	0.497443i	$0.165728\pi$
$390$	3.70381	+	54.1302i	0.187550	+	2.74099i
$391$	18.6467	+	4.78767i	0.943006	+	0.242123i
$392$	−4.39730	−	34.8082i	−0.222097	−	1.75808i
$393$	−3.25289	−	4.47722i	−0.164087	−	0.225846i
$394$	17.5672	+	37.3322i	0.885024	+	1.88077i
$395$	−22.2468	−	13.9477i	−1.11936	−	0.701783i
$396$	−2.66668	+	1.46602i	−0.134006	+	0.0736702i
$397$	0.704988	−	5.58055i	0.0353823	−	0.280080i	−0.964490	−	0.264118i	$-0.914919\pi$
$397$	0.704988	−	5.58055i	0.0353823	−	0.280080i	0.999873	−	0.0159616i	$-0.00508096\pi$
$398$	−4.31972	+	10.9104i	−0.216528	+	0.546887i
$399$	1.99763	+	1.45136i	0.100007	+	0.0726590i
$400$	−22.4811	−	12.0398i	−1.12405	−	0.601990i
$401$	−23.8047	+	17.2951i	−1.18875	+	0.863676i	−0.993131	−	0.117005i	$-0.962671\pi$
$401$	−23.8047	+	17.2951i	−1.18875	+	0.863676i	−0.195616	+	0.980681i	$0.562671\pi$
$402$	0.360351	+	1.40347i	0.0179727	+	0.0699990i
$403$	14.5776	−	15.5235i	0.726161	−	0.773283i
$404$	29.1805	+	27.4024i	1.45179	+	1.36332i
$405$	18.0458	+	5.75417i	0.896701	+	0.285927i
$406$	−4.34366	+	0.548731i	−0.215572	+	0.0272331i
$407$	−12.1960	−	3.96271i	−0.604532	−	0.196424i
$408$	−9.62774	+	17.5128i	−0.476644	+	0.867012i
$409$	−0.0267711	−	0.425514i	−0.00132374	−	0.0210403i	0.997309	−	0.0733072i	$-0.0233554\pi$
$409$	−0.0267711	−	0.425514i	−0.00132374	−	0.0210403i	−0.998633	+	0.0522669i	$0.983355\pi$
$410$	−1.68872	−	8.59611i	−0.0833999	−	0.424532i
$411$	10.7821	+	16.9899i	0.531843	+	0.838050i
$412$	−5.83888	+	22.7410i	−0.287661	+	1.12037i
$413$	−3.24459	−	8.19489i	−0.159656	−	0.403244i
$414$	3.53206	−	0.906879i	0.173591	−	0.0445707i
$415$	3.63928	+	10.9950i	0.178645	+	0.539721i
$416$	−9.97509	+	3.94942i	−0.489069	+	0.193636i
$417$	−7.32291	+	3.44590i	−0.358605	+	0.168747i
$418$	20.9681	−	6.81296i	1.02558	−	0.333233i
$419$	−5.20678	+	27.2949i	−0.254368	+	1.33344i	0.594184	+	0.804329i	$0.297475\pi$
$419$	−5.20678	+	27.2949i	−0.254368	+	1.33344i	−0.848552	+	0.529113i	$0.822525\pi$
$420$	−2.87865	−	10.9616i	−0.140464	−	0.534872i
$421$	9.76409	−	20.7497i	0.475872	−	1.01128i	−0.512424	−	0.858733i	$-0.671252\pi$
$421$	9.76409	−	20.7497i	0.475872	−	1.01128i	0.988296	−	0.152548i	$-0.0487477\pi$
$422$	49.5752	−	9.45698i	2.41328	−	0.460359i
$423$	1.37542	+	1.13785i	0.0668753	+	0.0553240i
$424$	4.99049	+	15.3592i	0.242360	+	0.745907i
$425$	1.25496	−	10.8939i	0.0608744	−	0.528434i
$426$	5.54323	−	17.0603i	0.268571	−	0.826575i
$427$	−4.85053	+	3.07824i	−0.234733	+	0.148966i
$428$	2.42942	+	4.41911i	0.117431	+	0.213606i
$429$	7.97125	+	41.7868i	0.384856	+	2.01748i
$430$	−2.33607	−	17.7101i	−0.112655	−	0.854055i
$431$	−2.46551	+	2.31526i	−0.118759	+	0.111522i	−0.741652	−	0.670785i	$-0.765957\pi$
$431$	−2.46551	+	2.31526i	−0.118759	+	0.111522i	0.622893	+	0.782307i	$0.285957\pi$
$432$			27.1885i			1.30811i
$433$	8.24995	+	8.78531i	0.396467	+	0.422195i	0.895968	−	0.444119i	$-0.146483\pi$
$433$	8.24995	+	8.78531i	0.396467	+	0.422195i	−0.499501	+	0.866314i	$0.666483\pi$
$434$	−3.52439	+	5.55356i	−0.169176	+	0.266579i
$435$	8.89617	−	2.33624i	0.426539	−	0.112014i
$436$	6.64069	+	2.62924i	0.318032	+	0.125918i
$437$	−17.8319	+	1.12189i	−0.853014	+	0.0536671i
$438$	−70.4224	+	4.43060i	−3.36491	+	0.211702i
$439$	−1.30840	−	0.518033i	−0.0624466	−	0.0247244i	0.336694	−	0.941614i	$-0.390691\pi$
$439$	−1.30840	−	0.518033i	−0.0624466	−	0.0247244i	−0.399140	+	0.916890i	$0.630691\pi$
$440$	−49.1549	−	19.1506i	−2.34337	−	0.912967i
$441$	0.580377	−	0.914528i	0.0276370	−	0.0435489i
$442$	−21.6440	−	23.0485i	−1.02950	−	1.09631i
$443$		−	29.7101i		−	1.41157i	−0.708427	−	0.705784i	$-0.750595\pi$
$443$		−	29.7101i		−	1.41157i	0.708427	−	0.705784i	$-0.249405\pi$
$444$	−15.0853	+	14.1660i	−0.715916	+	0.672290i
$445$	−12.1489	+	5.79847i	−0.575915	+	0.274874i
$446$	−1.67513	−	8.78136i	−0.0793199	−	0.415809i
$447$	10.3021	+	18.7394i	0.487272	+	0.886345i
$448$	−3.40975	+	2.16390i	−0.161096	+	0.102234i
$449$	−6.33624	+	19.5009i	−0.299025	+	0.920306i	0.682814	+	0.730592i	$0.260756\pi$
$449$	−6.33624	+	19.5009i	−0.299025	+	0.920306i	−0.981840	+	0.189713i	$0.939244\pi$
$450$	−0.785802	−	1.92280i	−0.0370431	−	0.0906418i
$451$	−2.12253	−	6.53246i	−0.0999458	−	0.307602i
$452$	28.9007	+	23.9088i	1.35938	+	1.12457i
$453$	−0.353805	+	0.0674920i	−0.0166232	+	0.00317105i
$454$	6.36251	−	13.5210i	0.298607	−	0.634573i
$455$	9.33206	+	0.535745i	0.437494	+	0.0251161i
$456$	3.47547	−	18.2191i	0.162754	−	0.853186i
$457$	25.1488	−	8.17135i	1.17641	−	0.382240i	0.345380	−	0.938463i	$-0.387750\pi$
$457$	25.1488	−	8.17135i	1.17641	−	0.382240i	0.831033	+	0.556223i	$0.187750\pi$
$458$	−3.62851	+	1.70745i	−0.169549	+	0.0797838i
$459$	−10.8702	+	4.30380i	−0.507375	+	0.200884i
$460$	66.6089	+	47.8381i	3.10566	+	2.23046i
$461$	−4.03534	+	1.03610i	−0.187945	+	0.0482560i	−0.341489	−	0.939886i	$-0.610931\pi$
$461$	−4.03534	+	1.03610i	−0.187945	+	0.0482560i	0.153544	+	0.988142i	$0.450931\pi$
$462$	−4.83697	−	12.2168i	−0.225036	−	0.568376i
$463$	−7.98574	+	31.1024i	−0.371129	+	1.44545i	0.459277	+	0.888293i	$0.348108\pi$
$463$	−7.98574	+	31.1024i	−0.371129	+	1.44545i	−0.830406	+	0.557159i	$0.811892\pi$
$464$	6.67909	+	10.5246i	0.310069	+	0.488590i
$465$	5.81482	−	12.5352i	0.269656	−	0.581304i
$466$	−2.38690	−	37.9387i	−0.110571	−	1.75748i
$467$	−13.8457	+	25.1851i	−0.640700	+	1.16543i	0.334140	+	0.942524i	$0.391554\pi$
$467$	−13.8457	+	25.1851i	−0.640700	+	1.16543i	−0.974840	+	0.222906i	$0.928446\pi$
$468$	−3.85204	−	1.25160i	−0.178060	−	0.0578553i
$469$	0.247667	−	0.0312876i	0.0114362	−	0.00144473i
$470$	0.325633	+	59.3591i	0.0150203	+	2.73803i
$471$	−22.9771	−	21.5769i	−1.05873	−	0.994213i
$472$	−45.3209	+	48.2618i	−2.08606	+	2.22143i
$473$	−3.48313	−	13.5659i	−0.160155	−	0.623761i
$474$	−39.7436	+	28.8754i	−1.82548	+	1.32629i
$475$	2.01662	+	9.97559i	0.0925288	+	0.457712i
$476$	5.34311	+	3.88200i	0.244901	+	0.177931i
$477$	−0.183536	+	0.463560i	−0.00840355	+	0.0212250i
$478$	5.38626	−	42.6367i	0.246362	−	1.95016i
$479$	−10.9934	+	6.04370i	−0.502303	+	0.276144i	−0.712696	−	0.701473i	$-0.752526\pi$
$479$	−10.9934	+	6.04370i	−0.502303	+	0.276144i	0.210392	+	0.977617i	$0.432526\pi$
$480$	−5.33956	+	4.46683i	−0.243716	+	0.203882i
$481$	−7.26716	−	15.4435i	−0.331354	−	0.704163i
$482$	−30.0341	−	41.3384i	−1.36802	−	1.88291i
$483$	1.33458	+	10.5643i	0.0607257	+	0.480693i
$484$	−32.3331	−	8.30173i	−1.46969	−	0.377351i
$485$	11.8671	+	14.1857i	0.538859	+	0.644141i
$486$	−2.74870	+	3.32261i	−0.124684	+	0.150717i
$487$	−20.7282	+	17.1479i	−0.939285	+	0.777044i	−0.974974	−	0.222319i	$-0.928638\pi$
$487$	−20.7282	+	17.1479i	−0.939285	+	0.777044i	0.0356887	+	0.999363i	$0.488638\pi$
$488$	36.4350	+	23.1224i	1.64934	+	1.04670i
$489$	−1.90410	+	30.2648i	−0.0861063	+	1.36862i
$490$	35.7090	−	4.71026i	1.61317	−	0.212788i
$491$	9.70114	+	11.7267i	0.437806	+	0.529217i	0.942556	−	0.334049i	$-0.108415\pi$
$491$	9.70114	+	11.7267i	0.437806	+	0.529217i	−0.504749	+	0.863266i	$0.668415\pi$
$492$	−10.8879	−	2.07697i	−0.490863	−	0.0936372i
$493$	−3.15053	+	4.33633i	−0.141893	+	0.195298i
$494$	25.7145	+	14.1367i	1.15695	+	0.636040i
$495$	−0.792409	−	1.42284i	−0.0356162	−	0.0639520i
$496$	18.5789	+	2.34707i	0.834219	+	0.105386i
$497$	−2.79630	−	1.31584i	−0.125431	−	0.0590235i
$498$	21.6255	+	1.36056i	0.969062	+	0.0609682i
$499$	30.9705			1.38643			0.693214	−	0.720732i	$-0.256194\pi$
$499$	30.9705			1.38643			0.693214	+	0.720732i	$0.256194\pi$
$500$	21.8273	−	41.2995i	0.976149	−	1.84697i
$501$	3.19545			0.142762
$502$	−8.02600	−	0.504953i	−0.358218	−	0.0225372i
$503$	−6.77484	−	3.18800i	−0.302075	−	0.142146i	0.268768	−	0.963205i	$-0.413384\pi$
$503$	−6.77484	−	3.18800i	−0.302075	−	0.142146i	−0.570843	+	0.821059i	$0.693384\pi$
$504$	0.647030	+	0.0817389i	0.0288210	+	0.00364094i
$505$	−14.5795	+	15.6972i	−0.648777	+	0.698517i
$506$	83.3166	+	45.8037i	3.70387	+	2.03622i
$507$	−20.4194	+	28.1049i	−0.906857	+	1.24818i
$508$	−0.751534	−	0.143363i	−0.0333439	−	0.00636070i
$509$	−5.84873	−	7.06990i	−0.259240	−	0.313368i	0.624794	−	0.780790i	$-0.285183\pi$
$509$	−5.84873	−	7.06990i	−0.259240	−	0.313368i	−0.884034	+	0.467422i	$0.845183\pi$
$510$	−18.0327	−	9.78512i	−0.798501	−	0.433293i
$511$	−0.763310	+	12.1325i	−0.0337668	+	0.536708i
$512$	38.6632	+	24.5364i	1.70869	+	1.08437i
$513$	8.36038	−	6.91631i	0.369120	−	0.305362i
$514$	−33.5319	+	40.5330i	−1.47903	+	1.78784i
$515$	−12.1876	−	3.05808i	−0.537050	−	0.134755i
$516$	−21.8919	−	5.62087i	−0.963735	−	0.247445i
$517$	5.83319	+	46.1744i	0.256543	+	2.03075i
$518$	3.09868	+	4.26497i	0.136148	+	0.187392i
$519$	−16.3721	−	34.7925i	−0.718655	−	1.52722i
$520$	−26.2052	−	65.1404i	−1.14917	−	2.85659i
$521$	20.9559	−	11.5206i	0.918094	−	0.504727i	0.0486824	−	0.998814i	$-0.484498\pi$
$521$	20.9559	−	11.5206i	0.918094	−	0.504727i	0.869412	+	0.494088i	$0.164498\pi$
$522$	−0.127250	+	1.00728i	−0.00556956	+	0.0440876i
$523$	5.48371	−	13.8503i	0.239786	−	0.605630i	−0.759190	−	0.650869i	$-0.774405\pi$
$523$	5.48371	−	13.8503i	0.239786	−	0.605630i	0.998976	+	0.0452386i	$0.0144048\pi$
$524$	11.1142	+	8.07491i	0.485524	+	0.352754i
$525$	5.85797	−	1.57277i	0.255663	−	0.0686415i
$526$	12.8434	−	9.33131i	0.560001	−	0.406865i
$527$	2.00258	+	7.79952i	0.0872336	+	0.339753i
$528$	−25.6083	+	27.2701i	−1.11446	+	1.18678i
$529$	−39.4013	−	37.0002i	−1.71310	−	1.60871i
$530$	−15.7395	+	5.20970i	−0.683679	+	0.226295i
$531$	−2.02779	+	0.256169i	−0.0879985	+	0.0111168i
$532$	−5.82950	−	1.89412i	−0.252741	−	0.0821205i
$533$	4.40418	−	8.01118i	0.190766	−	0.347003i
$534$	1.58143	+	25.1362i	0.0684354	+	1.08775i
$535$	−2.35787	+	1.31315i	−0.101940	+	0.0567723i
$536$	−1.00476	−	1.58324i	−0.0433988	−	0.0683856i
$537$	5.90039	−	22.9805i	0.254621	−	0.991682i
$538$	−13.0281	−	32.9051i	−0.561679	−	1.41864i
$539$	27.3531	−	7.02308i	1.17818	−	0.302506i
$540$	−49.8011	+	0.273199i	−2.14310	+	0.0117566i
$541$	−33.7520	+	13.3634i	−1.45111	+	0.574536i	−0.955758	−	0.294154i	$-0.904962\pi$
$541$	−33.7520	+	13.3634i	−1.45111	+	0.574536i	−0.495355	+	0.868690i	$0.664962\pi$
$542$	12.8555	−	6.04933i	0.552190	−	0.259841i
$543$	−24.2753	+	7.88754i	−1.04175	+	0.338487i
$544$	0.760175	−	3.98498i	0.0325922	−	0.170854i
$545$	−1.38761	+	3.56167i	−0.0594388	+	0.152565i
$546$	7.44616	−	15.8239i	0.318666	−	0.677200i
$547$	2.27362	−	0.433716i	0.0972130	−	0.0185444i	−0.138545	−	0.990356i	$-0.544243\pi$
$547$	2.27362	−	0.433716i	0.0972130	−	0.0185444i	0.235758	+	0.971812i	$0.424243\pi$
$548$	−38.4882	−	31.8402i	−1.64413	−	1.36015i
$549$	0.411677	+	1.26701i	0.0175699	+	0.0540747i
$550$	19.3830	−	50.5699i	0.826493	−	2.15631i
$551$	1.53722	−	4.73107i	0.0654877	−	0.201550i
$552$	67.5338	−	42.8582i	2.87443	−	1.82417i
$553$	4.07730	+	7.41658i	0.173384	+	0.315385i
$554$	−8.72872	−	45.7575i	−0.370848	−	1.94405i
$555$	−7.62563	−	8.03172i	−0.323690	−	0.340927i
$556$	14.6452	−	13.7527i	0.621094	−	0.583246i
$557$			22.4005i			0.949142i	0.880217	+	0.474571i	$0.157397\pi$
$557$			22.4005i			0.949142i	−0.880217	+	0.474571i	$0.842603\pi$
$558$	1.04414	+	1.11190i	0.0442021	+	0.0470704i
$559$	9.98862	−	15.7396i	0.422474	−	0.665712i
$560$	4.44248	+	6.91607i	0.187729	+	0.292257i
$561$	−14.9564	−	5.92167i	−0.631461	−	0.250013i
$562$	24.1152	−	1.51720i	1.01724	−	0.0639992i
$563$	33.3675	−	2.09931i	1.40627	−	0.0884752i	0.658576	−	0.752515i	$-0.271159\pi$
$563$	33.3675	−	2.09931i	1.40627	−	0.0884752i	0.747698	+	0.664039i	$0.231159\pi$
$564$	69.8317	+	27.6483i	2.94044	+	1.16420i
$565$	−12.7106	+	15.5372i	−0.534738	+	0.653656i
$566$	16.1949	−	25.5191i	0.680722	−	1.07265i
$567$	−4.17925	−	4.45045i	−0.175512	−	0.186901i
$568$			23.2139i			0.974035i
$569$	23.7281	−	22.2822i	0.994734	−	0.934117i	−0.00309376	−	0.999995i	$-0.500985\pi$
$569$	23.7281	−	22.2822i	0.994734	−	0.934117i	0.997828	+	0.0658779i	$0.0209848\pi$
$570$	18.7231	+	3.46529i	0.784225	+	0.145145i
$571$	1.44476	+	7.57369i	0.0604612	+	0.316949i	0.999650	−	0.0264522i	$-0.00842099\pi$
$571$	1.44476	+	7.57369i	0.0604612	+	0.316949i	−0.939189	+	0.343401i	$0.888421\pi$
$572$	−50.8737	−	92.5388i	−2.12713	−	3.86924i
$573$	21.6922	−	13.7663i	0.906204	−	0.575095i
$574$	−0.872571	+	2.68550i	−0.0364204	+	0.112090i
$575$	−25.4063	+	35.7881i	−1.05952	+	1.49247i
$576$	0.289395	+	0.890666i	0.0120581	+	0.0371111i
$577$	−8.52484	−	7.05236i	−0.354894	−	0.293594i	0.442843	−	0.896599i	$-0.353970\pi$
$577$	−8.52484	−	7.05236i	−0.354894	−	0.293594i	−0.797737	+	0.603005i	$0.793970\pi$
$578$	−29.7623	+	5.67746i	−1.23795	+	0.236151i
$579$	9.13097	−	19.4043i	0.379470	−	0.806416i
$580$	−19.2107	+	12.3398i	−0.797680	+	0.512383i
$581$	0.699501	−	3.66691i	0.0290202	−	0.152129i
$582$	32.9091	−	10.6928i	1.36413	−	0.443231i
$583$	−11.7619	+	5.53472i	−0.487127	+	0.229225i
$584$	84.9016	−	33.6149i	3.51325	−	1.39099i
$585$	0.658521	−	2.06520i	0.0272265	−	0.0853854i
$586$	−10.2476	+	2.63113i	−0.423323	+	0.108691i
$587$	−4.26235	−	10.7655i	−0.175926	−	0.444339i	0.814880	−	0.579630i	$-0.196803\pi$
$587$	−4.26235	−	10.7655i	−0.175926	−	0.444339i	−0.990806	+	0.135291i	$0.956803\pi$
$588$	11.3334	−	44.1409i	0.467384	−	1.82034i
$589$	−4.00446	−	6.31002i	−0.165001	−	0.260000i
$590$	−49.8004	−	46.2542i	−2.05025	−	1.90426i
$591$	1.75427	+	27.8834i	0.0721612	+	1.14697i
$592$	7.23073	−	13.1526i	0.297181	−	0.540571i
$593$	42.2102	+	13.7149i	1.73336	+	0.563204i	0.993929	−	0.110024i	$-0.0350929\pi$
$593$	42.2102	+	13.7149i	1.73336	+	0.563204i	0.739435	+	0.673228i	$0.235093\pi$
$594$	−57.2834	+	7.23657i	−2.35037	+	0.296920i
$595$	−2.06187	+	2.87091i	−0.0845285	+	0.117696i
$596$	−38.6970	−	36.3389i	−1.58509	−	1.48850i
$597$	−5.43938	+	5.79235i	−0.222619	+	0.237065i
$598$	31.4705	+	122.569i	1.28692	+	5.01223i
$599$	−34.9576	+	25.3982i	−1.42833	+	1.03774i	−0.438006	+	0.898972i	$0.644315\pi$
$599$	−34.9576	+	25.3982i	−1.42833	+	1.03774i	−0.990325	+	0.138771i	$0.955685\pi$
$600$	−29.4250	−	34.7845i	−1.20127	−	1.42007i
$601$	−10.3200	−	7.49795i	−0.420963	−	0.305848i	0.357062	−	0.934081i	$-0.383779\pi$
$601$	−10.3200	−	7.49795i	−0.420963	−	0.305848i	−0.778025	+	0.628233i	$0.783779\pi$
$602$	−2.11960	+	5.35350i	−0.0863885	+	0.218192i
$603$	0.00725551	−	0.0574333i	0.000295467	−	0.00233887i
$604$	0.783519	−	0.430743i	0.0318810	−	0.0175267i
$605$	4.34797	−	17.3283i	0.176770	−	0.704497i
$606$	17.0659	+	36.2669i	0.693255	+	1.47324i
$607$	21.8740	+	30.1070i	0.887839	+	1.22201i	0.974187	+	0.225741i	$0.0724803\pi$
$607$	21.8740	+	30.1070i	0.887839	+	1.22201i	−0.0863480	+	0.996265i	$0.527520\pi$
$608$	0.471891	+	3.73541i	0.0191377	+	0.151491i
$609$	−2.87154	−	0.737287i	−0.116361	−	0.0298764i
$610$	−23.5320	+	37.5341i	−0.952784	+	1.51971i
$611$	−39.4855	+	47.7298i	−1.59741	+	1.93094i
$612$	1.18008	−	0.976251i	0.0477021	−	0.0394626i
$613$	21.9532	+	13.9319i	0.886681	+	0.562705i	0.899357	−	0.437215i	$-0.144035\pi$
$613$	21.9532	+	13.9319i	0.886681	+	0.562705i	−0.0126764	+	0.999920i	$0.504035\pi$
$614$	−1.55553	+	24.7244i	−0.0627759	+	0.997795i
$615$	1.07958	−	5.83305i	0.0435331	−	0.235211i
$616$	10.8386	+	13.1017i	0.436701	+	0.527881i
$617$	35.4558	+	6.76355i	1.42740	+	0.272290i	0.842447	−	0.538780i	$-0.181115\pi$
$617$	35.4558	+	6.76355i	1.42740	+	0.272290i	0.584949	+	0.811070i	$0.301115\pi$
$618$	−13.8182	+	19.0191i	−0.555849	+	0.765060i
$619$	−14.2330	−	7.82466i	−0.572073	−	0.314500i	0.169331	−	0.985559i	$-0.445839\pi$
$619$	−14.2330	−	7.82466i	−0.572073	−	0.314500i	−0.741403	+	0.671060i	$0.765839\pi$
$620$	−4.11242	+	34.0546i	−0.165159	+	1.36766i
$621$	46.4226	+	5.86454i	1.86288	+	0.235336i
$622$	11.8286	+	5.56613i	0.474285	+	0.223181i
$623$	4.33049	+	0.272451i	0.173497	+	0.0109155i
$624$	−49.7906			−1.99322
$625$	22.1667	+	11.5603i	0.886666	+	0.462410i
$626$	−39.9391			−1.59629
$627$	14.8998	+	0.937415i	0.595040	+	0.0374368i
$628$	70.7978	+	33.3149i	2.82514	+	1.32941i
$629$	6.40311	+	0.808901i	0.255309	+	0.0322530i
$630$	−0.0802685	+	0.664696i	−0.00319798	+	0.0264821i
$631$	−36.9075	−	20.2900i	−1.46926	−	0.807734i	−0.471995	−	0.881601i	$-0.656466\pi$
$631$	−36.9075	−	20.2900i	−1.46926	−	0.807734i	−0.997268	+	0.0738673i	$0.976466\pi$
$632$	37.3677	−	51.4323i	1.48641	−	2.04587i
$633$	33.5699	+	6.40379i	1.33428	+	0.254528i
$634$	−9.14244	−	11.0513i	−0.363093	−	0.438904i
$635$	0.0745182	−	0.402625i	0.00295716	−	0.0159777i
$636$	−1.31716	+	20.9357i	−0.0522289	+	0.830155i
$637$	31.7359	+	20.1402i	1.25742	+	0.797984i
$638$	−20.3964	+	16.8734i	−0.807502	+	0.668024i
$639$	−0.456818	+	0.552198i	−0.0180715	+	0.0218446i
$640$	−20.9363	+	33.3939i	−0.827582	+	1.32001i
$641$	−14.9285	−	3.83298i	−0.589640	−	0.151394i	−0.0579305	−	0.998321i	$-0.518450\pi$
$641$	−14.9285	−	3.83298i	−0.589640	−	0.151394i	−0.531709	+	0.846927i	$0.678450\pi$
$642$	0.632856	+	5.00957i	0.0249768	+	0.197712i
$643$	8.07923	+	11.1201i	0.318614	+	0.438534i	0.938043	−	0.346518i	$-0.112636\pi$
$643$	8.07923	+	11.1201i	0.318614	+	0.438534i	−0.619430	+	0.785052i	$0.712636\pi$
$644$	−11.2546	−	23.9173i	−0.443495	−	0.942475i
$645$	2.94390	−	11.7325i	0.115916	−	0.461968i
$646$	−9.72362	+	5.34560i	−0.382571	+	0.210320i
$647$	2.33506	−	18.4839i	0.0918009	−	0.726679i	−0.877288	−	0.479965i	$-0.840649\pi$
$647$	2.33506	−	18.4839i	0.0918009	−	0.726679i	0.969088	−	0.246714i	$-0.0793507\pi$
$648$	−16.8819	+	42.6387i	−0.663182	+	1.67501i
$649$	−43.1124	−	31.3230i	−1.69231	−	1.22954i
$650$	66.7250	−	27.2688i	2.61717	−	1.06957i
$651$	−3.60332	+	2.61796i	−0.141225	+	0.102606i
$652$	−18.7207	−	72.9121i	−0.733157	−	2.85546i
$653$	13.9887	−	14.8964i	0.547418	−	0.582941i	−0.394452	−	0.918916i	$-0.629066\pi$
$653$	13.9887	−	14.8964i	0.547418	−	0.582941i	0.941871	+	0.335975i	$0.109066\pi$
$654$	5.21320	+	4.89552i	0.203852	+	0.191430i
$655$	−4.28888	+	5.97175i	−0.167580	+	0.233336i
$656$	7.97589	−	1.00759i	0.311406	−	0.0393398i
$657$	2.68108	+	0.871135i	0.104599	+	0.0339862i
$658$	9.21748	−	16.7665i	0.359335	−	0.653628i
$659$	0.573115	+	9.10940i	0.0223254	+	0.354852i	0.993292	+	0.115636i	$0.0368905\pi$
$659$	0.573115	+	9.10940i	0.0223254	+	0.354852i	−0.970966	+	0.239216i	$0.923110\pi$
$660$	−50.2078	−	46.6326i	−1.95433	−	1.81517i
$661$	−22.8598	−	36.0213i	−0.889144	−	1.40107i	−0.915892	−	0.401424i	$-0.868515\pi$
$661$	−22.8598	−	36.0213i	−0.889144	−	1.40107i	0.0267482	−	0.999642i	$-0.491485\pi$
$662$	−4.10282	+	15.9794i	−0.159460	+	0.621058i
$663$	−7.88159	−	19.9066i	−0.306095	−	0.773109i
$664$	−27.1600	+	6.97349i	−1.05401	+	0.270624i
$665$	0.996576	−	3.12538i	0.0386456	−	0.121197i
$666$	1.13667	−	0.450038i	0.0440449	−	0.0174386i
$667$	19.4107	−	9.13398i	0.751585	−	0.353669i
$668$	−7.54406	+	2.45122i	−0.291889	+	0.0948404i
$669$	1.13432	−	5.94629i	0.0438552	−	0.229897i
$670$	1.61968	−	1.04039i	0.0625738	−	0.0401938i
$671$	−14.7891	+	31.4285i	−0.570928	+	1.21328i
$672$	2.20414	−	0.420462i	0.0850266	−	0.0162197i
$673$	−17.8913	−	14.8010i	−0.689660	−	0.570536i	0.225198	−	0.974313i	$-0.427697\pi$
$673$	−17.8913	−	14.8010i	−0.689660	−	0.570536i	−0.914858	+	0.403777i	$0.867697\pi$
$674$	0.782807	+	2.40923i	0.0301526	+	0.0928002i
$675$	−0.292420	−	26.6516i	−0.0112553	−	1.02582i
$676$	26.6486	−	82.0159i	1.02495	−	3.15446i
$677$	−39.4921	+	25.0625i	−1.51781	+	0.963229i	−0.524046	+	0.851690i	$0.675578\pi$
$677$	−39.4921	+	25.0625i	−1.51781	+	0.963229i	−0.993760	+	0.111539i	$0.964422\pi$
$678$	18.0931	+	32.9113i	0.694863	+	1.26395i
$679$	−1.11705	−	5.85580i	−0.0428686	−	0.224725i
$680$	26.1070	+	4.83191i	1.00116	+	0.185295i
$681$	7.37628	−	6.92679i	0.282660	−	0.265435i
$682$			39.7686i			1.52282i
$683$	−13.6541	−	14.5402i	−0.522460	−	0.556364i	0.412573	−	0.910925i	$-0.364630\pi$
$683$	−13.6541	−	14.5402i	−0.522460	−	0.556364i	−0.935033	+	0.354561i	$0.884630\pi$
$684$	−0.761633	+	1.20014i	−0.0291218	+	0.0458886i
$685$	16.9272	−	20.6915i	0.646754	−	0.790582i
$686$	−22.4539	−	8.89014i	−0.857295	−	0.339427i
$687$	−2.71013	+	0.170507i	−0.103398	+	0.00650524i
$688$	16.3606	−	1.02932i	0.623744	−	0.0392426i
$689$	−16.0864	−	6.36907i	−0.612844	−	0.242642i
$690$	44.3782	+	69.0882i	1.68945	+	2.63014i
$691$	14.7949	−	23.3130i	0.562823	−	0.886867i	−0.437098	−	0.899414i	$-0.643994\pi$
$691$	14.7949	−	23.3130i	0.562823	−	0.886867i	0.999921	+	0.0125466i	$0.00399380\pi$
$692$	65.3417	+	69.5819i	2.48392	+	2.64511i
$693$			0.524943i			0.0199410i
$694$	24.3524	−	22.8684i	0.924404	−	0.868073i
$695$	7.40316	+	7.79740i	0.280818	+	0.295772i
$696$	4.17287	+	21.8750i	0.158172	+	0.829168i
$697$	1.66538	+	3.02932i	0.0630809	+	0.114744i
$698$	−14.5090	+	9.20768i	−0.549173	+	0.348516i
$699$	7.95440	−	24.4811i	0.300863	−	0.925962i
$700$	−12.6235	+	8.20676i	−0.477123	+	0.310186i
$701$	−13.1363	−	40.4293i	−0.496150	−	1.52699i	−0.815157	−	0.579240i	$-0.803349\pi$
$701$	−13.1363	−	40.4293i	−0.496150	−	1.52699i	0.319007	−	0.947752i	$-0.396651\pi$
$702$	−59.2129	−	48.9852i	−2.23485	−	1.84883i
$703$	−5.88378	+	1.12239i	−0.221911	+	0.0423318i
$704$	−10.3963	+	22.0932i	−0.391824	+	0.832668i
$705$	−14.5917	+	37.4535i	−0.549557	+	1.41058i
$706$	3.69145	−	19.3512i	0.138929	−	0.728294i
$707$	6.56733	−	2.13386i	0.246990	−	0.0802519i
$708$	−77.8116	+	36.6154i	−2.92434	+	1.37609i
$709$	−46.7003	+	18.4899i	−1.75387	+	0.694405i	−0.754596	+	0.656190i	$0.772167\pi$
$709$	−46.7003	+	18.4899i	−1.75387	+	0.694405i	−0.999270	+	0.0382150i	$0.987833\pi$
$710$	−23.8312	+	0.130734i	−0.894370	+	0.00490635i
$711$	1.90099	−	0.488093i	0.0712929	−	0.0183049i
$712$	−11.9983	−	30.3043i	−0.449656	−	1.13570i
$713$	8.01493	−	31.2161i	0.300162	−	1.16905i
$714$	3.54341	+	5.58352i	0.132609	+	0.208958i
$715$	49.3754	−	27.4981i	1.84653	−	1.02837i
$716$	3.69815	+	58.7804i	0.138206	+	2.19673i
$717$	14.0195	−	25.5013i	0.523566	−	0.952363i
$718$	−54.0828	−	17.5726i	−2.01835	−	0.655802i
$719$	18.2431	−	2.30464i	0.680352	−	0.0859485i	0.222441	−	0.974946i	$-0.428598\pi$
$719$	18.2431	−	2.30464i	0.680352	−	0.0859485i	0.457912	+	0.888998i	$0.348598\pi$
$720$	1.80963	−	0.598981i	0.0674411	−	0.0223227i
$721$	2.95242	+	2.77251i	0.109954	+	0.103254i
$722$	−25.2789	+	26.9193i	−0.940782	+	1.00183i
$723$	−8.60476	−	33.5133i	−0.320015	−	1.24637i
$724$	51.2607	−	37.2431i	1.90509	−	1.38413i
$725$	−6.66039	−	10.2449i	−0.247361	−	0.380486i
$726$	−27.0414	−	19.6467i	−1.00360	−	0.729157i
$727$	8.19201	−	20.6907i	0.303825	−	0.767374i	−0.695005	−	0.719005i	$-0.744598\pi$
$727$	8.19201	−	20.6907i	0.303825	−	0.767374i	0.998830	−	0.0483687i	$-0.0154022\pi$
$728$	−2.83650	+	22.4532i	−0.105128	+	0.832170i
$729$	−24.8275	+	13.6490i	−0.919537	+	0.505520i
$730$	34.9869	+	86.9699i	1.29492	+	3.21890i
$731$	3.00134	+	6.37817i	0.111008	+	0.235905i
$732$	32.9466	+	45.3471i	1.21774	+	1.67608i
$733$	−0.344882	−	2.73002i	−0.0127385	−	0.100836i	0.984464	−	0.175589i	$-0.0561830\pi$
$733$	−0.344882	−	2.73002i	−0.0127385	−	0.100836i	−0.997202	+	0.0747535i	$0.976183\pi$
$734$	28.8545	+	7.40857i	1.06504	+	0.273455i
$735$	23.6565	+	5.93582i	0.872583	+	0.218946i
$736$	−10.3497	+	12.5106i	−0.381494	+	0.461147i
$737$	1.16296	−	0.962087i	0.0428383	−	0.0354389i
$738$	0.552873	+	0.350864i	0.0203516	+	0.0129155i
$739$	0.136532	−	2.17011i	0.00502241	−	0.0798289i	−0.994717	−	0.102655i	$-0.967266\pi$
$739$	0.136532	−	2.17011i	0.00502241	−	0.0798289i	0.999739	+	0.0228258i	$0.00726631\pi$
$740$	24.1643	+	13.1123i	0.888297	+	0.482019i
$741$	12.6659	+	15.3104i	0.465293	+	0.562443i
$742$	5.24925	+	1.00135i	0.192706	+	0.0367607i
$743$	29.5169	−	40.6266i	1.08287	−	1.49044i	0.226550	−	0.974000i	$-0.427255\pi$
$743$	29.5169	−	40.6266i	1.08287	−	1.49044i	0.856321	−	0.516444i	$-0.172745\pi$
$744$	29.3178	+	16.1176i	1.07484	+	0.590900i
$745$	19.3342	−	20.8164i	0.708349	−	0.762656i
$746$	−20.8736	−	2.63695i	−0.764236	−	0.0965455i
$747$	−0.783293	−	0.368589i	−0.0286592	−	0.0134860i
$748$	39.8528	+	2.50733i	1.45716	+	0.0916770i
$749$	0.869914			0.0317860
$750$	35.5437	−	30.4033i	1.29787	−	1.11017i
$751$	44.1360			1.61054			0.805272	−	0.592905i	$-0.202019\pi$
$751$	44.1360			1.61054			0.805272	+	0.592905i	$0.202019\pi$
$752$	−54.3661	−	3.42043i	−1.98253	−	0.124730i
$753$	−4.92728	−	2.31860i	−0.179560	−	0.0844945i
$754$	−34.9547	−	4.41580i	−1.27297	−	0.160814i
$755$	0.232825	+	0.418058i	0.00847336	+	0.0152147i
$756$	14.0668	+	7.73328i	0.511604	+	0.281257i
$757$	4.50046	−	6.19435i	0.163572	−	0.225137i	−0.719361	−	0.694636i	$-0.755565\pi$
$757$	4.50046	−	6.19435i	0.163572	−	0.225137i	0.882933	+	0.469499i	$0.155565\pi$
$758$	−25.7443	−	4.91098i	−0.935074	−	0.178375i
$759$	41.0382	+	49.6067i	1.48959	+	1.80061i
$760$	−24.4295	+	3.22241i	−0.886151	+	0.116889i
$761$	1.46061	−	23.2157i	0.0529471	−	0.841570i	−0.878511	−	0.477722i	$-0.841463\pi$
$761$	1.46061	−	23.2157i	0.0529471	−	0.841570i	0.931458	−	0.363848i	$-0.118537\pi$
$762$	−0.646818	−	0.410483i	−0.0234317	−	0.0148702i
$763$	0.949321	−	0.785347i	0.0343677	−	0.0284315i
$764$	−40.6526	+	49.1406i	−1.47076	+	1.77784i
$765$	0.525932	+	0.628689i	0.0190151	+	0.0227303i
$766$	62.6535	+	16.0867i	2.26376	+	0.581235i
$767$	−8.88957	−	70.3682i	−0.320984	−	2.54085i
$768$	32.2574	+	44.3985i	1.16399	+	1.60209i
$769$	−16.1197	−	34.2561i	−0.581290	−	1.23530i	−0.951869	−	0.306504i	$-0.900841\pi$
$769$	−16.1197	−	34.2561i	−0.581290	−	1.23530i	0.370579	−	0.928801i	$-0.379159\pi$
$770$	−13.3890	+	11.2006i	−0.482507	+	0.403643i
$771$	−31.2155	+	17.1609i	−1.12420	+	0.618033i
$772$	−6.67216	+	52.8156i	−0.240136	+	1.90087i
$773$	−6.91856	+	17.4743i	−0.248843	+	0.628506i	−0.999481	−	0.0322074i	$-0.989746\pi$
$773$	−6.91856	+	17.4743i	−0.248843	+	0.628506i	0.750638	+	0.660714i	$0.229746\pi$
$774$	1.08022	+	0.784828i	0.0388278	+	0.0282100i
$775$	−18.2373	−	2.10090i	−0.655104	−	0.0754665i
$776$	−36.2273	+	26.3206i	−1.30048	+	0.944856i
$777$	0.887771	+	3.45764i	0.0318486	+	0.124042i
$778$	−11.3883	+	12.1273i	−0.408289	+	0.434784i
$779$	−2.33877	−	2.19625i	−0.0837950	−	0.0786887i
$780$	−0.500312	−	91.2011i	−0.0179141	−	3.26552i
$781$	−18.5379	+	2.34188i	−0.663339	+	0.0837992i
$782$	−45.5093	−	14.7869i	−1.62741	−	0.528777i
$783$	−6.27613	+	11.4162i	−0.224291	+	0.407983i
$784$	2.07544	+	32.9882i	0.0741229	+	1.17815i
$785$	−17.6216	+	37.9872i	−0.628940	+	1.35582i
$786$	7.37061	+	11.6142i	0.262901	+	0.414266i
$787$	−6.86710	+	26.7456i	−0.244786	+	0.953377i	0.720769	+	0.693176i	$0.243789\pi$
$787$	−6.86710	+	26.7456i	−0.244786	+	0.953377i	−0.965554	+	0.260202i	$0.916211\pi$
$788$	−25.5309	−	64.4836i	−0.909500	−	2.29713i
$789$	10.4123	−	2.67342i	0.370687	−	0.0951762i
$790$	53.0104	+	38.0717i	1.88602	+	1.35453i
$791$	6.01596	−	2.38189i	0.213903	−	0.0846902i
$792$	3.56786	−	1.67891i	0.126779	−	0.0596575i
$793$	−43.9677	+	14.2860i	−1.56134	+	0.507310i
$794$	−2.61981	+	13.7335i	−0.0929736	+	0.487385i
$795$	−11.2082	−	0.643452i	−0.397514	−	0.0228209i
$796$	8.39843	−	17.8476i	0.297674	−	0.632590i
$797$	−35.6511	+	6.80081i	−1.26283	+	0.240897i	−0.774954	−	0.632018i	$-0.782227\pi$
$797$	−35.6511	+	6.80081i	−1.26283	+	0.240897i	−0.487873	+	0.872915i	$0.662227\pi$
$798$	−4.72896	−	3.91214i	−0.167403	−	0.138488i
$799$	−7.23837	−	22.2774i	−0.256075	−	0.788118i
$800$	7.86282	+	4.86972i	0.277993	+	0.172171i
$801$	0.310938	−	0.956969i	0.0109865	−	0.0338128i
$802$	61.7509	−	39.1883i	2.18050	−	1.38379i
$803$	35.4089	+	64.4085i	1.24955	+	2.27293i
$804$	−0.456401	−	2.39254i	−0.0160960	−	0.0843783i
$805$	12.7670	−	6.09345i	0.449977	−	0.214766i
$806$	−38.5850	+	36.2338i	−1.35910	+	1.27628i
$807$		−	23.9646i		−	0.843593i
$808$	−35.5072	−	37.8113i	−1.24914	−	1.33020i
$809$	5.84707	−	9.21351i	0.205572	−	0.323930i	−0.725862	−	0.687841i	$-0.758559\pi$
$809$	5.84707	−	9.21351i	0.205572	−	0.323930i	0.931434	+	0.363911i	$0.118559\pi$
$810$	−43.8676	−	17.0906i	−1.54135	−	0.600504i
$811$	35.1951	+	13.9347i	1.23587	+	0.489314i	0.892994	−	0.450068i	$-0.148600\pi$
$811$	35.1951	+	13.9347i	1.23587	+	0.489314i	0.342872	+	0.939382i	$0.388600\pi$
$812$	7.34494	−	0.462104i	0.257757	−	0.0162167i
$813$	9.60174	−	0.604090i	0.336748	−	0.0211864i
$814$	29.6358	+	11.7337i	1.03873	+	0.411264i
$815$	38.9660	−	10.2329i	1.36492	−	0.358444i
$816$	10.0884	−	15.8967i	0.353163	−	0.556496i
$817$	−4.47839	−	4.76900i	−0.156679	−	0.166846i
$818$			1.05974i			0.0370530i
$819$	−0.509320	+	0.478284i	−0.0177971	+	0.0167126i
$820$	1.92574	+	14.5993i	0.0672498	+	0.509829i
$821$	1.78696	+	9.36759i	0.0623654	+	0.326931i	0.999773	−	0.0213030i	$-0.00678146\pi$
$821$	1.78696	+	9.36759i	0.0623654	+	0.326931i	−0.937408	+	0.348234i	$0.886781\pi$
$822$	−24.0953	−	43.8292i	−0.840421	−	1.52872i
$823$	−25.8292	+	16.3917i	−0.900348	+	0.571378i	−0.903486	−	0.428617i	$-0.859001\pi$
$823$	−25.8292	+	16.3917i	−0.900348	+	0.571378i	0.00313812	+	0.999995i	$0.499001\pi$
$824$	9.40118	−	28.9339i	0.327506	−	1.00796i
$825$	24.8093	−	27.0070i	0.863749	−	0.940263i
$826$	6.76978	+	20.8353i	0.235551	+	0.724951i
$827$	−2.36877	−	1.95962i	−0.0823703	−	0.0681426i	0.595328	−	0.803483i	$-0.297022\pi$
$827$	−2.36877	−	1.95962i	−0.0823703	−	0.0681426i	−0.677698	+	0.735340i	$0.737022\pi$
$828$	−6.02119	+	1.14860i	−0.209251	+	0.0399167i
$829$	−5.27162	+	11.2028i	−0.183091	+	0.389088i	−0.975211	−	0.221278i	$-0.928977\pi$
$829$	−5.27162	+	11.2028i	−0.183091	+	0.389088i	0.792120	+	0.610365i	$0.208977\pi$
$830$	−7.31188	−	27.8429i	−0.253799	−	0.966442i
$831$	5.91065	−	30.9847i	0.205038	−	1.07485i
$832$	−30.9078	+	10.0426i	−1.07154	+	0.348163i
$833$	−12.8604	+	6.05164i	−0.445586	+	0.209677i
$834$	18.7036	−	7.40527i	0.647652	−	0.256424i
$835$	−1.33398	−	4.03022i	−0.0461644	−	0.139471i
$836$	−35.8957	+	9.21645i	−1.24148	+	0.318758i
$837$	7.20490	+	18.1975i	0.249038	+	0.628998i
$838$	17.1763	−	66.8971i	0.593344	−	2.31092i
$839$	−2.36947	−	3.73369i	−0.0818032	−	0.128901i	0.800963	−	0.598714i	$-0.204321\pi$
$839$	−2.36947	−	3.73369i	−0.0818032	−	0.128901i	−0.882766	+	0.469813i	$0.844321\pi$
$840$	2.83086	+	14.4099i	0.0976738	+	0.497190i
$841$	−1.44589	−	22.9818i	−0.0498584	−	0.792476i
$842$	−27.4600	+	49.9495i	−0.946333	+	1.72137i
$843$	15.5611	+	5.05610i	0.535952	+	0.174141i
$844$	−84.1668	+	10.6327i	−2.89714	+	0.365994i
$845$	43.9713	+	14.0209i	1.51266	+	0.482335i
$846$	−3.23439	−	3.03730i	−0.111201	−	0.104424i
$847$	−3.94196	+	4.19776i	−0.135447	+	0.144237i
$848$	−3.78370	−	14.7365i	−0.129933	−	0.506054i
$849$	16.5575	−	12.0298i	0.568254	−	0.412860i
$850$	−4.81337	+	26.8285i	−0.165097	+	0.920209i
$851$	−20.8976	−	15.1830i	−0.716362	−	0.520468i
$852$	−11.1001	+	28.0357i	−0.380284	+	0.960488i
$853$	−2.84160	+	22.4936i	−0.0972945	+	0.770165i	0.865685	+	0.500590i	$0.166883\pi$
$853$	−2.84160	+	22.4936i	−0.0972945	+	0.770165i	−0.962979	+	0.269576i	$0.913117\pi$
$854$	12.5130	−	6.87909i	0.428186	−	0.235397i
$855$	−0.644526	−	0.404086i	−0.0220423	−	0.0138194i
$856$	−2.78222	−	5.91251i	−0.0950943	−	0.202086i
$857$	8.42990	+	11.6028i	0.287960	+	0.396343i	0.928350	−	0.371707i	$-0.121227\pi$
$857$	8.42990	+	11.6028i	0.287960	+	0.396343i	−0.640390	+	0.768050i	$0.721227\pi$
$858$	−13.2524	−	104.904i	−0.452429	−	3.58135i
$859$	28.3951	+	7.29063i	0.968829	+	0.248753i	0.699768	−	0.714370i	$-0.253287\pi$
$859$	28.3951	+	7.29063i	0.968829	+	0.248753i	0.269061	+	0.963123i	$0.413287\pi$
$860$	2.04981	+	29.9574i	0.0698978	+	1.02154i
$861$	−1.21880	+	1.47327i	−0.0415365	+	0.0502090i
$862$	6.47747	−	5.35863i	0.220624	−	0.182516i
$863$	7.09609	+	4.50332i	0.241554	+	0.153295i	0.651093	−	0.758998i	$-0.274311\pi$
$863$	7.09609	+	4.50332i	0.241554	+	0.153295i	−0.409540	+	0.912292i	$0.634311\pi$
$864$	0.619132	−	9.84083i	0.0210633	−	0.334792i
$865$	−37.0468	+	35.1737i	−1.25963	+	1.19594i
$866$	−19.0943	−	23.0811i	−0.648852	−	0.784327i
$867$	−20.1535	−	3.84449i	−0.684450	−	0.130566i
$868$	6.49877	−	8.94479i	0.220583	−	0.303606i
$869$	44.8419	+	24.6520i	1.52116	+	0.836264i
$870$	−22.4331	+	4.40703i	−0.760555	+	0.149412i
$871$	1.99305	+	0.251780i	0.0675318	+	0.00853125i
$872$	−8.37392	−	3.94047i	−0.283577	−	0.133441i
$873$	−1.37970	−	0.0868036i	−0.0466959	−	0.00293786i
$874$	44.4102			1.50220
$875$	−4.42914	−	6.73172i	−0.149732	−	0.227574i
$876$	118.610			4.00746
$877$	−11.0346	−	0.694237i	−0.372611	−	0.0234427i	−0.124619	−	0.992205i	$-0.539771\pi$
$877$	−11.0346	−	0.694237i	−0.372611	−	0.0234427i	−0.247992	+	0.968762i	$0.579771\pi$
$878$	3.16487	+	1.48928i	0.106809	+	0.0502606i
$879$	−7.10773	−	0.897915i	−0.239738	−	0.0302859i
$880$	45.0846	+	20.9139i	1.51980	+	0.705007i
$881$	22.9987	+	12.6437i	0.774846	+	0.425975i	0.819538	−	0.573025i	$-0.194230\pi$
$881$	22.9987	+	12.6437i	0.774846	+	0.425975i	−0.0446912	+	0.999001i	$0.514230\pi$
$882$	−1.58246	+	2.17807i	−0.0532842	+	0.0733394i
$883$	20.2967	+	3.87181i	0.683040	+	0.130297i	0.517211	−	0.855858i	$-0.326970\pi$
$883$	20.2967	+	3.87181i	0.683040	+	0.130297i	0.165829	+	0.986155i	$0.446970\pi$
$884$	33.8778	+	40.9512i	1.13943	+	1.37734i
$885$	−19.8242	−	41.5356i	−0.666383	−	1.39620i
$886$	−4.63688	+	73.7011i	−0.155779	+	2.47604i
$887$	−17.2552	−	10.9505i	−0.579372	−	0.367680i	0.213616	−	0.976918i	$-0.431476\pi$
$887$	−17.2552	−	10.9505i	−0.579372	−	0.367680i	−0.792988	+	0.609237i	$0.791476\pi$
$888$	20.6611	−	17.0923i	0.693341	−	0.573581i
$889$	−0.0841273	+	0.101692i	−0.00282154	+	0.00341065i
$890$	31.0425	−	12.4880i	1.04055	−	0.418600i
$891$	−35.7530	−	9.17981i	−1.19777	−	0.307535i
$892$	1.88340	+	14.9086i	0.0630608	+	0.499177i
$893$	12.7781	+	17.5875i	0.427602	+	0.588544i
$894$	−22.6315	−	48.0944i	−0.756910	−	1.60852i
$895$	−31.4471	+	2.15174i	−1.05116	+	0.0719247i
$896$	11.1328	−	6.12029i	0.371920	−	0.204465i
$897$	−10.7398	+	85.0142i	−0.358591	+	2.83854i
$898$	18.7617	−	47.3866i	0.626085	−	1.58131i
$899$	7.25936	+	5.27423i	0.242113	+	0.175906i
$900$	1.11533	+	3.30868i	0.0371778	+	0.110289i
$901$	5.29283	−	3.84546i	0.176330	−	0.128111i
$902$	4.24577	+	16.5362i	0.141369	+	0.550595i
$903$	−2.66899	+	2.84219i	−0.0888185	+	0.0945821i
$904$	−35.4296	−	33.2706i	−1.17837	−	1.10656i
$905$	20.0822	+	27.3242i	0.667553	+	0.908288i
$906$	0.888210	−	0.112207i	0.0295088	−	0.00372783i
$907$	0.959098	+	0.311630i	0.0318463	+	0.0103475i	0.324897	−	0.945749i	$-0.394670\pi$
$907$	0.959098	+	0.311630i	0.0318463	+	0.0103475i	−0.293051	+	0.956097i	$0.594670\pi$
$908$	−12.1010	+	22.0117i	−0.401586	+	0.730482i
$909$	−0.100548	−	1.59816i	−0.00333496	−	0.0530077i
$910$	−23.0662	−	2.78547i	−0.764638	−	0.0923375i
$911$	−3.24720	−	5.11676i	−0.107584	−	0.169526i	0.786270	−	0.617883i	$-0.212009\pi$
$911$	−3.24720	−	5.11676i	−0.107584	−	0.169526i	−0.893855	+	0.448357i	$0.852009\pi$
$912$	−4.34553	+	16.9247i	−0.143895	+	0.560433i
$913$	−8.30878	−	20.9856i	−0.274980	−	0.694521i
$914$	−63.6614	+	16.3455i	−2.10573	+	0.540660i
$915$	−24.1721	+	17.7654i	−0.799103	+	0.587307i
$916$	6.26749	−	2.48148i	0.207084	−	0.0819903i
$917$	2.14428	−	1.00902i	0.0708105	−	0.0333209i
$918$	27.6370	−	8.97982i	0.912158	−	0.296378i
$919$	−5.32809	+	27.9308i	−0.175758	+	0.921353i	0.779684	+	0.626173i	$0.215380\pi$
$919$	−5.32809	+	27.9308i	−0.175758	+	0.921353i	−0.955442	+	0.295180i	$0.904620\pi$
$920$	−82.2474	−	67.2844i	−2.71162	−	2.21830i
$921$	−7.14254	+	15.1787i	−0.235355	+	0.500154i
$922$	10.1721	−	1.94043i	0.335000	−	0.0639046i
$923$	−19.1623	−	15.8525i	−0.630736	−	0.521791i
$924$	6.82516	+	21.0057i	0.224531	+	0.691036i
$925$	−6.94648	+	12.9707i	−0.228399	+	0.426474i
$926$	24.6642	−	75.9087i	0.810517	−	2.49451i
$927$	0.793008	−	0.503258i	0.0260458	−	0.0165292i
$928$	−2.17782	−	3.96144i	−0.0714904	−	0.130041i
$929$	−1.75869	−	9.21940i	−0.0577009	−	0.302479i	0.941724	−	0.336386i	$-0.109205\pi$
$929$	−1.75869	−	9.21940i	−0.0577009	−	0.302479i	−0.999425	+	0.0339076i	$0.989205\pi$
$930$	−16.3811	+	30.1882i	−0.537157	+	0.989909i
$931$	9.61581	−	9.02985i	0.315145	−	0.295941i
$932$			63.8988i			2.09308i
$933$	6.05978	+	6.45301i	0.198388	+	0.211262i
$934$	38.2773	−	60.3153i	1.25247	−	1.97358i
$935$	−1.22486	+	21.3357i	−0.0400573	+	0.697752i
$936$	4.87968	+	1.93200i	0.159497	+	0.0631494i
$937$	29.2215	−	1.83846i	0.954623	−	0.0600598i	0.422168	−	0.906518i	$-0.361269\pi$
$937$	29.2215	−	1.83846i	0.954623	−	0.0600598i	0.532456	+	0.846458i	$0.321269\pi$
$938$	−0.619264	+	0.0389608i	−0.0202197	+	0.00127211i
$939$	−25.1455	−	9.95582i	−0.820594	−	0.324896i
$940$	5.71889	−	99.6166i	0.186530	−	3.24913i
$941$	−10.4605	+	16.4831i	−0.341003	+	0.537335i	−0.970944	−	0.239309i	$-0.923079\pi$
$941$	−10.4605	+	16.4831i	−0.341003	+	0.537335i	0.629941	+	0.776643i	$0.283079\pi$
$942$	53.6312	+	57.1115i	1.74740	+	1.86079i
$943$		−	13.8357i		−	0.450551i
$944$	45.4674	−	42.6968i	1.47984	−	1.38966i
$945$	−4.09738	+	7.55093i	−0.133288	+	0.245632i
$946$	6.52328	+	34.1962i	0.212090	+	1.11182i
$947$	−14.7301	−	26.7939i	−0.478663	−	0.870685i	−0.999851	−	0.0172432i	$-0.994511\pi$
$947$	−14.7301	−	26.7939i	−0.478663	−	0.870685i	0.521188	−	0.853442i	$-0.325489\pi$
$948$	69.7226	−	44.2473i	2.26448	−	1.43708i
$949$	−30.2301	+	93.0386i	−0.981310	+	3.02016i
$950$	−3.44568	−	25.0610i	−0.111793	−	0.813085i
$951$	−3.00124	−	9.23687i	−0.0973219	−	0.299526i
$952$	−6.59394	−	5.45498i	−0.213711	−	0.176797i
$953$	−26.5432	+	5.06338i	−0.859818	+	0.164019i	−0.598391	−	0.801204i	$-0.704193\pi$
$953$	−26.5432	+	5.06338i	−0.859818	+	0.164019i	−0.261427	+	0.965223i	$0.584193\pi$
$954$	0.527643	−	1.12130i	0.0170831	−	0.0363034i
$955$	−26.4183	−	21.6121i	−0.854875	−	0.699351i
$956$	−13.5363	+	70.9598i	−0.437795	+	2.29500i
$957$	−17.0477	+	5.53912i	−0.551073	+	0.179054i
$958$	28.2144	−	13.2767i	0.911567	−	0.428951i
$959$	−8.01169	+	3.17205i	−0.258711	+	0.102431i
$960$	−16.9921	+	12.4885i	−0.548419	+	0.403064i
$961$	−16.9691	+	4.35691i	−0.547389	+	0.140546i
$962$	15.6172	+	39.4445i	0.503518	+	1.27174i
$963$	0.0501685	−	0.195393i	0.00161666	−	0.00629646i
$964$	46.0228	+	72.5203i	1.48229	+	2.33572i
$965$	−28.2853	−	3.41573i	−0.910537	−	0.109956i
$966$	−1.66189	−	26.4149i	−0.0534704	−	0.849887i
$967$	16.1357	−	29.3506i	0.518888	−	0.943853i	−0.478932	−	0.877852i	$-0.658976\pi$
$967$	16.1357	−	29.3506i	0.518888	−	0.943853i	0.997820	−	0.0660010i	$-0.0210241\pi$
$968$	41.1382	+	13.3666i	1.32223	+	0.429619i
$969$	−7.45450	+	0.941722i	−0.239473	+	0.0302525i
$970$	−27.2246	−	37.0424i	−0.874128	−	1.18936i
$971$	43.2987	+	40.6602i	1.38952	+	1.30485i	0.901999	+	0.431738i	$0.142099\pi$
$971$	43.2987	+	40.6602i	1.38952	+	1.30485i	0.487523	+	0.873110i	$0.337901\pi$
$972$	4.96198	−	5.28397i	0.159156	−	0.169484i
$973$	−0.861871	−	3.35677i	−0.0276303	−	0.107613i
$974$	54.0963	−	39.3033i	1.73336	−	1.25936i
$975$	48.8073	−	0.535512i	1.56309	−	0.0171501i
$976$	−32.8899	−	23.8959i	−1.05278	−	0.764889i
$977$	22.4352	−	56.6648i	0.717765	−	1.81287i	0.151854	−	0.988403i	$-0.451476\pi$
$977$	22.4352	−	56.6648i	0.717765	−	1.81287i	0.565912	−	0.824466i	$-0.308524\pi$
$978$	9.44690	−	74.7799i	0.302079	−	2.39120i
$979$	22.9896	−	12.6386i	0.734751	−	0.403933i
$980$	−60.4035	+	4.13305i	−1.92952	+	0.132026i
$981$	−0.121651	−	0.258521i	−0.00388400	−	0.00825392i
$982$	−22.2352	−	30.6041i	−0.709554	−	0.976617i
$983$	−5.95322	−	47.1246i	−0.189878	−	1.50304i	−0.742634	−	0.669697i	$-0.766424\pi$
$983$	−5.95322	−	47.1246i	−0.189878	−	1.50304i	0.552756	−	0.833343i	$-0.313576\pi$
$984$	13.9114	+	3.57183i	0.443479	+	0.113866i
$985$	34.4353	−	13.8529i	1.09720	−	0.441389i
$986$	8.49222	−	10.2653i	0.270447	−	0.326915i
$987$	9.98279	−	8.25848i	0.317756	−	0.262870i
$988$	−41.6473	−	26.4301i	−1.32498	−	0.840855i
$989$	1.77147	−	28.1568i	0.0563296	−	0.895334i
$990$	1.74365	+	3.65328i	0.0554168	+	0.116109i
$991$	−27.8316	−	33.6427i	−0.884101	−	1.06869i	−0.997175	−	0.0751077i	$-0.976070\pi$
$991$	−27.8316	−	33.6427i	−0.884101	−	1.06869i	0.113075	−	0.993586i	$-0.463930\pi$
$992$	−6.67117	−	1.27259i	−0.211810	−	0.0404049i
$993$	−6.56640	+	9.03787i	−0.208378	+	0.286808i
$994$	6.73136	+	3.70060i	0.213506	+	0.117376i
$995$	9.57628	+	4.44225i	0.303588	+	0.140829i
$996$	−36.1359	−	4.56502i	−1.14501	−	0.144648i
$997$	11.5180	+	5.41994i	0.364778	+	0.171651i	0.599428	−	0.800428i	$-0.295395\pi$
$997$	11.5180	+	5.41994i	0.364778	+	0.171651i	−0.234651	+	0.972080i	$0.575395\pi$
$998$	−76.8277	−	4.83359i	−2.43194	−	0.153005i
$999$	15.6867			0.496305

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.h.a.4.2	✓	240
5.2	odd	4		625.2.g.b.226.23		480
5.3	odd	4		625.2.g.b.226.2		480
5.4	even	2		625.2.h.a.399.11		240
125.17	odd	100		625.2.g.b.401.23		480
125.31	even	25		625.2.h.a.224.11		240
125.94	even	50	inner	125.2.h.a.94.2	yes	240
125.108	odd	100		625.2.g.b.401.2		480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.4.2	✓	240	1.1	even	1	trivial
125.2.h.a.94.2	yes	240	125.94	even	50	inner
625.2.g.b.226.2		480	5.3	odd	4
625.2.g.b.226.23		480	5.2	odd	4
625.2.g.b.401.2		480	125.108	odd	100
625.2.g.b.401.23		480	125.17	odd	100
625.2.h.a.224.11		240	125.31	even	25
625.2.h.a.399.11		240	5.4	even	2

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.48068 - 0.156071i) q^{2} +(-1.52292 - 0.716634i) q^{3} +(4.14517 + 0.523657i) q^{4} +(-0.268080 + 2.21994i) q^{5} +(3.66604 + 2.01542i) q^{6} +(0.423640 - 0.583091i) q^{7} +(-5.31799 - 1.01446i) q^{8} +(-0.106538 - 0.128782i) q^{9} +O(q^{10})\)	\(q+(-2.48068 - 0.156071i) q^{2} +(-1.52292 - 0.716634i) q^{3} +(4.14517 + 0.523657i) q^{4} +(-0.268080 + 2.21994i) q^{5} +(3.66604 + 2.01542i) q^{6} +(0.423640 - 0.583091i) q^{7} +(-5.31799 - 1.01446i) q^{8} +(-0.106538 - 0.128782i) q^{9} +(1.01149 - 5.46511i) q^{10} +(0.273623 - 4.34912i) q^{11} +(-5.93751 - 3.76806i) q^{12} +(4.46898 - 3.69706i) q^{13} +(-1.14192 + 1.38034i) q^{14} +(1.99915 - 3.18869i) q^{15} +(4.94018 + 1.26842i) q^{16} +(0.274880 + 2.17590i) q^{17} +(0.244187 + 0.336094i) q^{18} +(-0.866664 - 1.84175i) q^{19} +(-2.27372 + 9.06165i) q^{20} +(-1.06303 + 0.584408i) q^{21} +(-1.35754 + 10.7460i) q^{22} +(3.23134 - 8.16144i) q^{23} +(7.37190 + 5.35600i) q^{24} +(-4.85627 - 1.19024i) q^{25} +(-11.6631 + 8.47374i) q^{26} +(1.32568 + 5.16317i) q^{27} +(2.06140 - 2.19517i) q^{28} +(1.78154 + 1.67298i) q^{29} +(-5.45690 + 7.59809i) q^{30} +(3.64263 - 0.460172i) q^{31} +(-1.75920 - 0.571600i) q^{32} +(-3.53343 + 6.42729i) q^{33} +(-0.342294 - 5.44061i) q^{34} +(1.18086 + 1.09677i) q^{35} +(-0.374179 - 0.589612i) q^{36} +(0.731829 - 2.85029i) q^{37} +(1.86247 + 4.70406i) q^{38} +(-9.45536 + 2.42772i) q^{39} +(3.67769 - 11.5337i) q^{40} +(1.46551 - 0.580238i) q^{41} +(2.72825 - 1.28382i) q^{42} +(3.05674 - 0.993196i) q^{43} +(3.41166 - 17.8845i) q^{44} +(0.314449 - 0.201984i) q^{45} +(-9.28968 + 19.7416i) q^{46} +(-10.4911 + 2.00128i) q^{47} +(-6.61452 - 5.47201i) q^{48} +(2.00260 + 6.16335i) q^{49} +(11.8611 + 3.71053i) q^{50} +(1.14070 - 3.51072i) q^{51} +(20.4607 - 12.9847i) q^{52} +(-1.43707 - 2.61402i) q^{53} +(-2.48276 - 13.0151i) q^{54} +(9.58143 + 1.77334i) q^{55} +(-2.84444 + 2.67110i) q^{56} +3.42593i q^{57} +(-4.15832 - 4.42817i) q^{58} +(6.55255 - 10.3252i) q^{59} +(9.95659 - 12.1708i) q^{60} +(-7.41101 - 2.93423i) q^{61} +(-9.10802 + 0.573028i) q^{62} +(-0.120225 + 0.00756393i) q^{63} +(-5.20969 - 2.06266i) q^{64} +(7.00922 + 10.9120i) q^{65} +(9.76842 - 15.3926i) q^{66} +(0.237099 + 0.252485i) q^{67} +9.16343i q^{68} +(-10.7699 + 10.1136i) q^{69} +(-2.75815 - 2.90503i) q^{70} +(-0.803464 - 4.21190i) q^{71} +(0.435922 + 0.792939i) q^{72} +(-14.2410 + 9.03759i) q^{73} +(-2.26028 + 6.95642i) q^{74} +(6.54276 + 5.29281i) q^{75} +(-2.62802 - 8.08822i) q^{76} +(-2.42001 - 2.00201i) q^{77} +(23.8346 - 4.54669i) q^{78} +(-4.99981 + 10.6251i) q^{79} +(-4.14018 + 10.6269i) q^{80} +(1.58724 - 8.32061i) q^{81} +(-3.72603 + 1.21066i) q^{82} +(4.68650 - 2.20530i) q^{83} +(-4.71249 + 1.86581i) q^{84} +(-4.90406 + 0.0269028i) q^{85} +(-7.73780 + 1.98673i) q^{86} +(-1.51424 - 3.82453i) q^{87} +(-5.86713 + 22.8510i) q^{88} +(3.22583 + 5.08309i) q^{89} +(-0.811570 + 0.451979i) q^{90} +(-0.262483 - 4.17205i) q^{91} +(17.6683 - 32.1384i) q^{92} +(-5.87723 - 1.90963i) q^{93} +(26.3373 - 3.32717i) q^{94} +(4.32092 - 1.43020i) q^{95} +(2.26951 + 2.13121i) q^{96} +(5.66203 - 6.02945i) q^{97} +(-4.00587 - 15.6018i) q^{98} +(-0.589239 + 0.428107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

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