LMFDB - Embedded newform 75.2.i.a.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,2,Mod(4,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("75.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.i (of order $10$, degree $4$, 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:	$0.598878015160$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.1
Root			$-1.53767i$ of defining polynomial
Character	$\chi$	$=$	75.64
Dual form			75.2.i.a.34.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.903822 - 1.24400i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.112618 + 0.346603i) q^{4} +(-1.93338 - 1.12340i) q^{5} +(0.475167 + 1.46241i) q^{6} -1.68601i q^{7} +(-2.39187 + 0.777165i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.903822 - 1.24400i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.112618 + 0.346603i) q^{4} +(-1.93338 - 1.12340i) q^{5} +(0.475167 + 1.46241i) q^{6} -1.68601i q^{7} +(-2.39187 + 0.777165i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.349919 + 3.42049i) q^{10} +(2.40891 - 1.75017i) q^{11} +(0.214212 - 0.294838i) q^{12} +(0.136890 - 0.188414i) q^{13} +(-2.09740 + 1.52385i) q^{14} +(1.49161 + 1.66587i) q^{15} +(3.71829 + 2.70150i) q^{16} +(7.09394 - 2.30496i) q^{17} -1.53767i q^{18} +(-0.232853 - 0.716646i) q^{19} +(0.607107 - 0.543601i) q^{20} +(-0.521005 + 1.60349i) q^{21} +(-4.35444 - 1.41484i) q^{22} +(-0.512972 - 0.706046i) q^{23} +2.51496 q^{24} +(2.47594 + 4.34393i) q^{25} -0.358112 q^{26} +(-0.587785 - 0.809017i) q^{27} +(0.584375 + 0.189875i) q^{28} +(-2.12444 + 6.53835i) q^{29} +(0.724197 - 3.36121i) q^{30} +(-3.03433 - 9.33870i) q^{31} -2.03733i q^{32} +(-2.83184 + 0.920120i) q^{33} +(-9.27904 - 6.74162i) q^{34} +(-1.89406 + 3.25970i) q^{35} +(-0.294838 + 0.214212i) q^{36} +(-5.95259 + 8.19304i) q^{37} +(-0.681054 + 0.937390i) q^{38} +(-0.188414 + 0.136890i) q^{39} +(5.49746 + 1.18447i) q^{40} +(-3.07210 - 2.23201i) q^{41} +(2.46564 - 0.801135i) q^{42} -5.27322i q^{43} +(0.335328 + 1.03203i) q^{44} +(-0.903822 - 2.04526i) q^{45} +(-0.414688 + 1.27628i) q^{46} +(8.14814 + 2.64749i) q^{47} +(-2.70150 - 3.71829i) q^{48} +4.15738 q^{49} +(3.16605 - 7.00622i) q^{50} -7.45901 q^{51} +(0.0498883 + 0.0686654i) q^{52} +(5.68614 + 1.84754i) q^{53} +(-0.475167 + 1.46241i) q^{54} +(-6.62348 + 0.677588i) q^{55} +(1.31031 + 4.03270i) q^{56} +0.753527i q^{57} +(10.0538 - 3.26669i) q^{58} +(-3.11564 - 2.26365i) q^{59} +(-0.745375 + 0.329388i) q^{60} +(3.55679 - 2.58416i) q^{61} +(-8.87488 + 12.2152i) q^{62} +(0.991010 - 1.36401i) q^{63} +(4.90214 - 3.56161i) q^{64} +(-0.476326 + 0.210493i) q^{65} +(3.70411 + 2.69119i) q^{66} +(1.70508 - 0.554013i) q^{67} +2.71836i q^{68} +(0.269686 + 0.830007i) q^{69} +(5.76697 - 0.589966i) q^{70} +(-1.35179 + 4.16039i) q^{71} +(-2.39187 - 0.777165i) q^{72} +(8.84783 + 12.1780i) q^{73} +15.5723 q^{74} +(-1.01241 - 4.89643i) q^{75} +0.274615 q^{76} +(-2.95080 - 4.06143i) q^{77} +(0.340585 + 0.110663i) q^{78} +(-2.27926 + 7.01484i) q^{79} +(-4.15402 - 9.40016i) q^{80} +(0.309017 + 0.951057i) q^{81} +5.83904i q^{82} +(-4.13188 + 1.34253i) q^{83} +(-0.497099 - 0.361163i) q^{84} +(-16.3047 - 3.51297i) q^{85} +(-6.55991 + 4.76605i) q^{86} +(4.04092 - 5.56185i) q^{87} +(-4.40161 + 6.05830i) q^{88} +(9.79170 - 7.11409i) q^{89} +(-1.72742 + 2.97291i) q^{90} +(-0.317667 - 0.230798i) q^{91} +(0.302487 - 0.0982841i) q^{92} +9.81929i q^{93} +(-4.07098 - 12.5292i) q^{94} +(-0.354888 + 1.64714i) q^{95} +(-0.629569 + 1.93761i) q^{96} +(-9.01055 - 2.92771i) q^{97} +(-3.75753 - 5.17180i) q^{98} +2.97757 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9	$ 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} + 10 q^{17} - 2 q^{19} + 20 q^{20} + 4 q^{21} - 30 q^{22} - 20 q^{23} + 24 q^{24} - 10 q^{25} + 12 q^{26} + 30 q^{28} + 16 q^{29} - 20 q^{30} + 6 q^{31} + 10 q^{33} - 36 q^{34} + 10 q^{35} - 2 q^{36} - 10 q^{37} + 30 q^{38} - 8 q^{39} + 10 q^{40} - 14 q^{41} - 10 q^{42} + 26 q^{44} + 16 q^{46} + 40 q^{47} + 20 q^{50} - 32 q^{51} + 40 q^{52} + 10 q^{53} - 2 q^{54} + 10 q^{55} + 10 q^{58} + 12 q^{59} - 30 q^{60} - 10 q^{62} - 10 q^{63} + 8 q^{64} - 70 q^{65} + 16 q^{66} - 40 q^{67} - 12 q^{69} + 30 q^{70} - 8 q^{71} - 30 q^{72} - 20 q^{73} - 52 q^{74} - 32 q^{76} - 40 q^{77} - 20 q^{79} - 4 q^{81} + 10 q^{83} + 12 q^{84} - 20 q^{85} - 36 q^{86} + 40 q^{87} - 40 q^{88} + 18 q^{89} + 30 q^{90} + 26 q^{91} + 10 q^{92} - 38 q^{94} - 40 q^{95} - 26 q^{96} + 40 q^{97} + 60 q^{98} - 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 + 10 * q^17 - 2 * q^19 + 20 * q^20 + 4 * q^21 - 30 * q^22 - 20 * q^23 + 24 * q^24 - 10 * q^25 + 12 * q^26 + 30 * q^28 + 16 * q^29 - 20 * q^30 + 6 * q^31 + 10 * q^33 - 36 * q^34 + 10 * q^35 - 2 * q^36 - 10 * q^37 + 30 * q^38 - 8 * q^39 + 10 * q^40 - 14 * q^41 - 10 * q^42 + 26 * q^44 + 16 * q^46 + 40 * q^47 + 20 * q^50 - 32 * q^51 + 40 * q^52 + 10 * q^53 - 2 * q^54 + 10 * q^55 + 10 * q^58 + 12 * q^59 - 30 * q^60 - 10 * q^62 - 10 * q^63 + 8 * q^64 - 70 * q^65 + 16 * q^66 - 40 * q^67 - 12 * q^69 + 30 * q^70 - 8 * q^71 - 30 * q^72 - 20 * q^73 - 52 * q^74 - 32 * q^76 - 40 * q^77 - 20 * q^79 - 4 * q^81 + 10 * q^83 + 12 * q^84 - 20 * q^85 - 36 * q^86 + 40 * q^87 - 40 * q^88 + 18 * q^89 + 30 * q^90 + 26 * q^91 + 10 * q^92 - 38 * q^94 - 40 * q^95 - 26 * q^96 + 40 * q^97 + 60 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.903822	−	1.24400i	−0.639099	−	0.879644i	0.359469	−	0.933157i	$-0.382958\pi$
$2$	−0.903822	−	1.24400i	−0.639099	−	0.879644i	−0.998567	+	0.0535136i	$0.982958\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−0.112618	+	0.346603i	−0.0563090	+	0.173301i
$5$	−1.93338	−	1.12340i	−0.864635	−	0.502400i
$5$	−1.93338	−	1.12340i	−0.864635	−	0.502400i
$6$	0.475167	+	1.46241i	0.193986	+	0.597028i
$7$		−	1.68601i		−	0.637251i	−0.947881	−	0.318625i	$-0.896779\pi$
$7$		−	1.68601i		−	0.637251i	0.947881	−	0.318625i	$-0.103221\pi$
$8$	−2.39187	+	0.777165i	−0.845653	+	0.274769i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	0.349919	+	3.42049i	0.110654	+	1.08165i
$11$	2.40891	−	1.75017i	0.726312	−	0.527697i	−0.162082	−	0.986777i	$-0.551821\pi$
$11$	2.40891	−	1.75017i	0.726312	−	0.527697i	0.888395	+	0.459080i	$0.151821\pi$
$12$	0.214212	−	0.294838i	0.0618377	−	0.0851123i
$13$	0.136890	−	0.188414i	0.0379666	−	0.0522565i	−0.789612	−	0.613607i	$-0.789718\pi$
$13$	0.136890	−	0.188414i	0.0379666	−	0.0522565i	0.827578	+	0.561350i	$0.189718\pi$
$14$	−2.09740	+	1.52385i	−0.560554	+	0.407266i
$15$	1.49161	+	1.66587i	0.385131	+	0.430125i
$16$	3.71829	+	2.70150i	0.929573	+	0.675375i
$17$	7.09394	−	2.30496i	1.72053	−	0.559035i	0.728505	−	0.685041i	$-0.240216\pi$
$17$	7.09394	−	2.30496i	1.72053	−	0.559035i	0.992030	+	0.126005i	$0.0402156\pi$
$18$		−	1.53767i		−	0.362433i
$19$	−0.232853	−	0.716646i	−0.0534200	−	0.164410i	0.920787	−	0.390065i	$-0.127548\pi$
$19$	−0.232853	−	0.716646i	−0.0534200	−	0.164410i	−0.974207	+	0.225656i	$0.927548\pi$
$20$	0.607107	−	0.543601i	0.135753	−	0.121553i
$21$	−0.521005	+	1.60349i	−0.113693	+	0.349910i
$22$	−4.35444	−	1.41484i	−0.928370	−	0.301646i
$23$	−0.512972	−	0.706046i	−0.106962	−	0.147221i	0.752180	−	0.658958i	$-0.229002\pi$
$23$	−0.512972	−	0.706046i	−0.106962	−	0.147221i	−0.859142	+	0.511737i	$0.829002\pi$
$24$	2.51496			0.513364
$25$	2.47594	+	4.34393i	0.495189	+	0.868786i
$26$	−0.358112			−0.0702315
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	0.584375	+	0.189875i	0.110436	+	0.0358830i
$29$	−2.12444	+	6.53835i	−0.394498	+	1.21414i	0.534854	+	0.844945i	$0.320367\pi$
$29$	−2.12444	+	6.53835i	−0.394498	+	1.21414i	−0.929352	+	0.369195i	$0.879633\pi$
$30$	0.724197	−	3.36121i	0.132220	−	0.613670i
$31$	−3.03433	−	9.33870i	−0.544981	−	1.67728i	−0.721035	−	0.692899i	$-0.756333\pi$
$31$	−3.03433	−	9.33870i	−0.544981	−	1.67728i	0.176054	−	0.984381i	$-0.443667\pi$
$32$		−	2.03733i		−	0.360152i
$33$	−2.83184	+	0.920120i	−0.492960	+	0.160172i
$34$	−9.27904	−	6.74162i	−1.59134	−	1.15618i
$35$	−1.89406	+	3.25970i	−0.320155	+	0.550990i
$36$	−0.294838	+	0.214212i	−0.0491396	+	0.0357020i
$37$	−5.95259	+	8.19304i	−0.978600	+	1.34693i	−0.0410198	+	0.999158i	$0.513061\pi$
$37$	−5.95259	+	8.19304i	−0.978600	+	1.34693i	−0.937580	+	0.347769i	$0.886939\pi$
$38$	−0.681054	+	0.937390i	−0.110482	+	0.152065i
$39$	−0.188414	+	0.136890i	−0.0301703	+	0.0219200i
$40$	5.49746	+	1.18447i	0.869225	+	0.187281i
$41$	−3.07210	−	2.23201i	−0.479781	−	0.348581i	0.321460	−	0.946923i	$-0.395826\pi$
$41$	−3.07210	−	2.23201i	−0.479781	−	0.348581i	−0.801241	+	0.598342i	$0.795826\pi$
$42$	2.46564	−	0.801135i	0.380457	−	0.123618i
$43$		−	5.27322i		−	0.804159i	−0.915605	−	0.402079i	$-0.868288\pi$
$43$		−	5.27322i		−	0.804159i	0.915605	−	0.402079i	$-0.131712\pi$
$44$	0.335328	+	1.03203i	0.0505526	+	0.155585i
$45$	−0.903822	−	2.04526i	−0.134734	−	0.304890i
$46$	−0.414688	+	1.27628i	−0.0611425	+	0.188177i
$47$	8.14814	+	2.64749i	1.18853	+	0.386176i	0.835529	−	0.549447i	$-0.185161\pi$
$47$	8.14814	+	2.64749i	1.18853	+	0.386176i	0.353000	+	0.935623i	$0.385161\pi$
$48$	−2.70150	−	3.71829i	−0.389928	−	0.536689i
$49$	4.15738			0.593911
$50$	3.16605	−	7.00622i	0.447747	−	0.990829i
$51$	−7.45901			−1.04447
$52$	0.0498883	+	0.0686654i	0.00691826	+	0.00952217i
$53$	5.68614	+	1.84754i	0.781051	+	0.253779i	0.672289	−	0.740289i	$-0.265311\pi$
$53$	5.68614	+	1.84754i	0.781051	+	0.253779i	0.108762	+	0.994068i	$0.465311\pi$
$54$	−0.475167	+	1.46241i	−0.0646621	+	0.199009i
$55$	−6.62348	+	0.677588i	−0.893110	+	0.0913660i
$56$	1.31031	+	4.03270i	0.175097	+	0.538893i
$57$			0.753527i			0.0998070i
$58$	10.0538	−	3.26669i	1.32013	−	0.428937i
$59$	−3.11564	−	2.26365i	−0.405622	−	0.294702i	0.366205	−	0.930534i	$-0.380657\pi$
$59$	−3.11564	−	2.26365i	−0.405622	−	0.294702i	−0.771827	+	0.635833i	$0.780657\pi$
$60$	−0.745375	+	0.329388i	−0.0962275	+	0.0425239i
$61$	3.55679	−	2.58416i	0.455400	−	0.330867i	−0.336324	−	0.941746i	$-0.609184\pi$
$61$	3.55679	−	2.58416i	0.455400	−	0.330867i	0.791724	+	0.610879i	$0.209184\pi$
$62$	−8.87488	+	12.2152i	−1.12711	+	1.55134i
$63$	0.991010	−	1.36401i	0.124856	−	0.171849i
$64$	4.90214	−	3.56161i	0.612768	−	0.445202i
$65$	−0.476326	+	0.210493i	−0.0590809	+	0.0261084i
$66$	3.70411	+	2.69119i	0.455944	+	0.331263i
$67$	1.70508	−	0.554013i	0.208308	−	0.0676835i	−0.203004	−	0.979178i	$-0.565070\pi$
$67$	1.70508	−	0.554013i	0.208308	−	0.0676835i	0.411312	+	0.911494i	$0.365070\pi$
$68$			2.71836i			0.329650i
$69$	0.269686	+	0.830007i	0.0324663	+	0.0999211i
$70$	5.76697	−	0.589966i	0.689285	−	0.0705145i
$71$	−1.35179	+	4.16039i	−0.160428	+	0.493748i	−0.998670	−	0.0515506i	$-0.983584\pi$
$71$	−1.35179	+	4.16039i	−0.160428	+	0.493748i	0.838242	+	0.545298i	$0.183584\pi$
$72$	−2.39187	−	0.777165i	−0.281884	−	0.0915897i
$73$	8.84783	+	12.1780i	1.03556	+	1.42533i	0.900690	+	0.434463i	$0.143062\pi$
$73$	8.84783	+	12.1780i	1.03556	+	1.42533i	0.134870	+	0.990863i	$0.456938\pi$
$74$	15.5723			1.81024
$75$	−1.01241	−	4.89643i	−0.116903	−	0.565391i
$76$	0.274615			0.0315005
$77$	−2.95080	−	4.06143i	−0.336275	−	0.462843i
$78$	0.340585	+	0.110663i	0.0385636	+	0.0125301i
$79$	−2.27926	+	7.01484i	−0.256437	+	0.789232i	0.737106	+	0.675777i	$0.236192\pi$
$79$	−2.27926	+	7.01484i	−0.256437	+	0.789232i	−0.993543	+	0.113455i	$0.963808\pi$
$80$	−4.15402	−	9.40016i	−0.464434	−	1.05097i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$			5.83904i			0.644814i
$83$	−4.13188	+	1.34253i	−0.453532	+	0.147362i	−0.526871	−	0.849946i	$-0.676635\pi$
$83$	−4.13188	+	1.34253i	−0.453532	+	0.147362i	0.0733383	+	0.997307i	$0.476635\pi$
$84$	−0.497099	−	0.361163i	−0.0542379	−	0.0394061i
$85$	−16.3047	−	3.51297i	−1.76849	−	0.381035i
$86$	−6.55991	+	4.76605i	−0.707373	+	0.513937i
$87$	4.04092	−	5.56185i	0.433232	−	0.596293i
$88$	−4.40161	+	6.05830i	−0.469213	+	0.645817i
$89$	9.79170	−	7.11409i	1.03792	−	0.754092i	0.0680399	−	0.997683i	$-0.478325\pi$
$89$	9.79170	−	7.11409i	1.03792	−	0.754092i	0.969878	+	0.243591i	$0.0783255\pi$
$90$	−1.72742	+	2.97291i	−0.182086	+	0.313372i
$91$	−0.317667	−	0.230798i	−0.0333005	−	0.0241942i
$92$	0.302487	−	0.0982841i	0.0315365	−	0.0102468i
$93$			9.81929i			1.01821i
$94$	−4.07098	−	12.5292i	−0.419889	−	1.29229i
$95$	−0.354888	+	1.64714i	−0.0364107	+	0.168993i
$96$	−0.629569	+	1.93761i	−0.0642551	+	0.197757i
$97$	−9.01055	−	2.92771i	−0.914883	−	0.297264i	−0.186517	−	0.982452i	$-0.559720\pi$
$97$	−9.01055	−	2.92771i	−0.914883	−	0.297264i	−0.728366	+	0.685188i	$0.759720\pi$
$98$	−3.75753	−	5.17180i	−0.379568	−	0.522430i
$99$	2.97757			0.299257
$100$	−1.78445	+	0.368964i	−0.178445	+	0.0368964i
$101$	−6.54468			−0.651220			−0.325610	−	0.945504i	$-0.605570\pi$
$101$	−6.54468			−0.651220			−0.325610	+	0.945504i	$0.605570\pi$
$102$	6.74162	+	9.27904i	0.667520	+	0.918762i
$103$	−0.666504	−	0.216560i	−0.0656726	−	0.0213383i	0.275996	−	0.961159i	$-0.410992\pi$
$103$	−0.666504	−	0.216560i	−0.0656726	−	0.0213383i	−0.341669	+	0.939820i	$0.610992\pi$
$104$	−0.180995	+	0.557047i	−0.0177481	+	0.0546229i
$105$	2.80866	−	2.51486i	0.274097	−	0.245425i
$106$	−2.84091	−	8.74342i	−0.275934	−	0.849236i
$107$		−	12.5288i		−	1.21120i	−0.795768	−	0.605602i	$-0.792933\pi$
$107$		−	12.5288i		−	1.21120i	0.795768	−	0.605602i	$-0.207067\pi$
$108$	0.346603	−	0.112618i	0.0333519	−	0.0108367i
$109$	3.46541	+	2.51776i	0.331926	+	0.241158i	0.741247	−	0.671232i	$-0.234235\pi$
$109$	3.46541	+	2.51776i	0.331926	+	0.241158i	−0.409322	+	0.912390i	$0.634235\pi$
$110$	6.82937	+	7.62722i	0.651155	+	0.727227i
$111$	8.19304	−	5.95259i	0.777649	−	0.564995i
$112$	4.55474	−	6.26907i	0.430383	−	0.592371i
$113$	4.83607	−	6.65628i	0.454939	−	0.626170i	−0.518511	−	0.855071i	$-0.673513\pi$
$113$	4.83607	−	6.65628i	0.454939	−	0.626170i	0.973450	+	0.228901i	$0.0735133\pi$
$114$	0.937390	−	0.681054i	0.0877946	−	0.0637865i
$115$	0.198600	+	1.94133i	0.0185195	+	0.181030i
$116$	−2.02696	−	1.47267i	−0.188198	−	0.136734i
$117$	0.221493	−	0.0719676i	0.0204771	−	0.00665340i
$118$			5.92180i			0.545146i
$119$	−3.88618	−	11.9604i	−0.356246	−	1.09641i
$120$	−4.86238	−	2.82530i	−0.443872	−	0.257914i
$121$	−0.659464	+	2.02962i	−0.0599512	+	0.184511i
$122$	−6.42940	−	2.08904i	−0.582091	−	0.189133i
$123$	2.23201	+	3.07210i	0.201253	+	0.277002i
$124$	3.57854			0.321362
$125$	0.0930242	−	11.1800i	0.00832034	−	0.999965i
$126$	−2.59253			−0.230961
$127$	7.02296	+	9.66627i	0.623187	+	0.857743i	0.997580	−	0.0695269i	$-0.0221490\pi$
$127$	7.02296	+	9.66627i	0.623187	+	0.857743i	−0.374393	+	0.927270i	$0.622149\pi$
$128$	−12.7366	−	4.13836i	−1.12576	−	0.365783i
$129$	−1.62951	+	5.01513i	−0.143471	+	0.441558i
$130$	0.692367	+	0.402303i	0.0607246	+	0.0352843i
$131$	6.63068	+	20.4071i	0.579326	+	1.78298i	0.620953	+	0.783848i	$0.286746\pi$
$131$	6.63068	+	20.4071i	0.579326	+	1.78298i	−0.0416276	+	0.999133i	$0.513254\pi$
$132$		−	1.08514i		−	0.0944497i
$133$	−1.20827	+	0.392591i	−0.104770	+	0.0340420i
$134$	−2.23028	−	1.62039i	−0.192667	−	0.139981i
$135$	0.227564	+	2.22446i	0.0195856	+	0.191451i
$136$	−15.1764	+	11.0263i	−1.30137	+	0.945500i
$137$	−5.88914	+	8.10570i	−0.503143	+	0.692517i	−0.982744	−	0.184970i	$-0.940781\pi$
$137$	−5.88914	+	8.10570i	−0.503143	+	0.692517i	0.479601	+	0.877487i	$0.340781\pi$
$138$	0.788784	−	1.08567i	0.0671458	−	0.0924182i
$139$	−5.31902	+	3.86450i	−0.451154	+	0.327782i	−0.790051	−	0.613041i	$-0.789946\pi$
$139$	−5.31902	+	3.86450i	−0.451154	+	0.327782i	0.338897	+	0.940823i	$0.389946\pi$
$140$	−0.916515	−	1.02359i	−0.0774596	−	0.0865089i
$141$	−6.93123	−	5.03583i	−0.583714	−	0.424093i
$142$	6.39733	−	2.07862i	0.536852	−	0.174434i
$143$		−	0.693452i		−	0.0579894i
$144$	1.42026	+	4.37112i	0.118355	+	0.364260i
$145$	11.4525	−	10.2545i	0.951081	−	0.851593i
$146$	7.15261	−	22.0135i	0.591954	−	1.82185i
$147$	−3.95390	−	1.28470i	−0.326112	−	0.105960i
$148$	−2.16936	−	2.98587i	−0.178320	−	0.245437i
$149$	−10.9143			−0.894132			−0.447066	−	0.894501i	$-0.647531\pi$
$149$	−10.9143			−0.894132			−0.447066	+	0.894501i	$0.647531\pi$
$150$	−5.17614	+	5.68495i	−0.422630	+	0.464174i
$151$	20.4128			1.66117			0.830584	−	0.556894i	$-0.188007\pi$
$151$	20.4128			1.66117			0.830584	+	0.556894i	$0.188007\pi$
$152$	1.11390	+	1.53316i	0.0903496	+	0.124356i
$153$	7.09394	+	2.30496i	0.573511	+	0.186345i
$154$	−2.38544	+	7.34162i	−0.192224	+	0.591605i
$155$	−4.62458	+	21.4640i	−0.371455	+	1.72403i
$156$	−0.0262278	−	0.0807210i	−0.00209991	−	0.00646285i
$157$		−	3.49944i		−	0.279286i	−0.990202	−	0.139643i	$-0.955405\pi$
$157$		−	3.49944i		−	0.279286i	0.990202	−	0.139643i	$-0.0445954\pi$
$158$	10.7865	−	3.50476i	0.858131	−	0.278824i
$159$	−4.83692	−	3.51423i	−0.383592	−	0.278696i
$160$	−2.28874	+	3.93894i	−0.180940	+	0.311400i
$161$	−1.19040	+	0.864875i	−0.0938165	+	0.0681617i
$162$	0.903822	−	1.24400i	0.0710109	−	0.0977382i
$163$	3.51118	−	4.83272i	0.275017	−	0.378528i	−0.649059	−	0.760738i	$-0.724837\pi$
$163$	3.51118	−	4.83272i	0.275017	−	0.378528i	0.924075	+	0.382210i	$0.124837\pi$
$164$	1.11959	−	0.813432i	0.0874256	−	0.0635184i
$165$	6.50869	+	1.40234i	0.506701	+	0.109172i
$166$	5.40459	+	3.92666i	0.419477	+	0.304768i
$167$	−2.22326	+	0.722381i	−0.172041	+	0.0558995i	−0.393771	−	0.919209i	$-0.628830\pi$
$167$	−2.22326	+	0.722381i	−0.172041	+	0.0558995i	0.221730	+	0.975108i	$0.428830\pi$
$168$		−	4.24024i		−	0.327141i
$169$	4.00046	+	12.3122i	0.307728	+	0.947089i
$170$	10.3664	+	23.4582i	0.795067	+	1.79916i
$171$	0.232853	−	0.716646i	0.0178067	−	0.0548033i
$172$	1.82771	+	0.593860i	0.139362	+	0.0452814i
$173$	−3.56844	−	4.91154i	−0.271303	−	0.373417i	0.651526	−	0.758626i	$-0.274129\pi$
$173$	−3.56844	−	4.91154i	−0.271303	−	0.373417i	−0.922829	+	0.385209i	$0.874129\pi$
$174$	−10.5712			−0.801403
$175$	7.32389	−	4.17446i	0.553634	−	0.315559i
$176$	13.6851			1.03155
$177$	2.26365	+	3.11564i	0.170146	+	0.234186i
$178$	−17.6999	−	5.75105i	−1.32666	−	0.431059i
$179$	−3.53007	+	10.8644i	−0.263850	+	0.812045i	0.728107	+	0.685464i	$0.240401\pi$
$179$	−3.53007	+	10.8644i	−0.263850	+	0.812045i	−0.991956	+	0.126581i	$0.959599\pi$
$180$	0.810681	−	0.0829334i	0.0604246	−	0.00618149i
$181$	−2.42581	−	7.46586i	−0.180309	−	0.554933i	0.819527	−	0.573040i	$-0.194236\pi$
$181$	−2.42581	−	7.46586i	−0.180309	−	0.554933i	−0.999836	+	0.0181070i	$0.994236\pi$
$182$			0.603779i			0.0447551i
$183$	−4.18125	+	1.35857i	−0.309087	+	0.100428i
$184$	1.77568	+	1.29010i	0.130905	+	0.0951077i
$185$	20.7127	−	9.15314i	1.52283	−	0.672952i
$186$	12.2152	−	8.87488i	0.895664	−	0.650738i
$187$	13.0546	−	17.9681i	0.954644	−	1.31395i
$188$	−1.83526	+	2.52601i	−0.133850	+	0.184228i
$189$	−1.36401	+	0.991010i	−0.0992170	+	0.0720854i
$190$	2.36980	−	1.04724i	0.171924	−	0.0759747i
$191$	−10.1646	−	7.38502i	−0.735485	−	0.534361i	0.155809	−	0.987787i	$-0.450202\pi$
$191$	−10.1646	−	7.38502i	−0.735485	−	0.534361i	−0.891294	+	0.453426i	$0.850202\pi$
$192$	−5.76281	+	1.87245i	−0.415895	+	0.135133i
$193$		−	10.1437i		−	0.730161i	−0.930976	−	0.365081i	$-0.881041\pi$
$193$		−	10.1437i		−	0.730161i	0.930976	−	0.365081i	$-0.118959\pi$
$194$	4.50186	+	13.8553i	0.323214	+	0.994752i
$195$	0.518058	−	0.0529979i	0.0370989	−	0.00379526i
$196$	−0.468196	+	1.44096i	−0.0334426	+	0.102926i
$197$	1.94684	+	0.632566i	0.138706	+	0.0450685i	0.377547	−	0.925990i	$-0.376767\pi$
$197$	1.94684	+	0.632566i	0.138706	+	0.0450685i	−0.238841	+	0.971059i	$0.576767\pi$
$198$	−2.69119	−	3.70411i	−0.191255	−	0.263240i
$199$	−3.57125			−0.253159			−0.126580	−	0.991956i	$-0.540400\pi$
$199$	−3.57125			−0.253159			−0.126580	+	0.991956i	$0.540400\pi$
$200$	−9.29807	−	8.46588i	−0.657473	−	0.598628i
$201$	−1.79282			−0.126456
$202$	5.91522	+	8.14161i	0.416194	+	0.572842i
$203$	11.0237	+	3.58182i	0.773712	+	0.251394i
$204$	0.840020	−	2.58531i	0.0588131	−	0.181008i
$205$	3.43210	+	7.76652i	0.239708	+	0.542437i
$206$	0.332999	+	1.02487i	0.0232011	+	0.0714058i
$207$		−	0.872721i		−	0.0606583i
$208$	1.01800	−	0.330767i	0.0705854	−	0.0229346i
$209$	−1.81517	−	1.31880i	−0.125558	−	0.0912234i
$210$	−5.66702	−	1.22100i	−0.391062	−	0.0842570i
$211$	−3.01474	+	2.19034i	−0.207543	+	0.150789i	−0.686701	−	0.726940i	$-0.740942\pi$
$211$	−3.01474	+	2.19034i	−0.207543	+	0.150789i	0.479158	+	0.877729i	$0.340942\pi$
$212$	−1.28072	+	1.76276i	−0.0879604	+	0.121067i
$213$	2.57126	−	3.53904i	0.176180	−	0.242491i
$214$	−15.5859	+	11.3238i	−1.06543	+	0.774078i
$215$	−5.92394	+	10.1952i	−0.404009	+	0.695304i
$216$	2.03464	+	1.47826i	0.138440	+	0.100583i
$217$	−15.7451	+	5.11590i	−1.06885	+	0.347290i
$218$		−	6.58659i		−	0.446100i
$219$	−4.65158	−	14.3161i	−0.314325	−	0.967391i
$220$	0.511070	−	2.37203i	0.0344563	−	0.159922i
$221$	0.536807	−	1.65212i	0.0361096	−	0.111134i
$222$	−14.8101	−	4.81209i	−0.993988	−	0.322966i
$223$	−15.4287	−	21.2357i	−1.03318	−	1.42205i	−0.902533	−	0.430622i	$-0.858294\pi$
$223$	−15.4287	−	21.2357i	−1.03318	−	1.42205i	−0.130647	−	0.991429i	$-0.541706\pi$
$224$	−3.43495			−0.229507
$225$	−0.550217	+	4.96963i	−0.0366811	+	0.331309i
$226$	−12.6514			−0.841557
$227$	−2.63981	−	3.63338i	−0.175210	−	0.241156i	0.712376	−	0.701798i	$-0.247619\pi$
$227$	−2.63981	−	3.63338i	−0.175210	−	0.241156i	−0.887586	+	0.460642i	$0.847619\pi$
$228$	−0.261174	−	0.0848607i	−0.0172967	−	0.00562004i
$229$	2.32979	−	7.17035i	0.153957	−	0.473830i	−0.844097	−	0.536191i	$-0.819863\pi$
$229$	2.32979	−	7.17035i	0.153957	−	0.473830i	0.998054	+	0.0623605i	$0.0198629\pi$
$230$	2.23552	−	2.00168i	0.147406	−	0.131987i
$231$	1.55133	+	4.77450i	0.102070	+	0.314139i
$232$		−	17.2899i		−	1.13514i
$233$	−9.85679	+	3.20266i	−0.645740	+	0.209814i	−0.613535	−	0.789668i	$-0.710253\pi$
$233$	−9.85679	+	3.20266i	−0.645740	+	0.209814i	−0.0322049	+	0.999481i	$0.510253\pi$
$234$	−0.289719	−	0.210493i	−0.0189395	−	0.0137603i
$235$	−12.7793	−	14.2722i	−0.833629	−	0.931019i
$236$	1.13546	−	0.824962i	0.0739124	−	0.0537005i
$237$	4.33541	−	5.96718i	0.281615	−	0.387610i
$238$	−11.3664	+	15.6445i	−0.736775	+	1.01408i
$239$	−15.0265	+	10.9174i	−0.971985	+	0.706188i	−0.955903	−	0.293683i	$-0.905119\pi$
$239$	−15.0265	+	10.9174i	−0.971985	+	0.706188i	−0.0160815	+	0.999871i	$0.505119\pi$
$240$	1.04590	+	10.2238i	0.0675125	+	0.659940i
$241$	4.39735	+	3.19486i	0.283258	+	0.205799i	0.720337	−	0.693624i	$-0.243987\pi$
$241$	4.39735	+	3.19486i	0.283258	+	0.205799i	−0.437079	+	0.899423i	$0.643987\pi$
$242$	3.12089	−	1.01404i	0.200619	−	0.0651849i
$243$		−	1.00000i		−	0.0641500i
$244$	0.495117	+	1.52381i	0.0316966	+	0.0975522i
$245$	−8.03781	−	4.67040i	−0.513517	−	0.298381i
$246$	1.80436	−	5.55325i	0.115042	−	0.354063i
$247$	−0.166901	−	0.0542295i	−0.0106197	−	0.00345054i
$248$	14.5154	+	19.9787i	0.921729	+	1.26865i
$249$	4.34451			0.275322
$250$	−13.9920	+	9.98896i	−0.884931	+	0.631757i
$251$	23.3577			1.47432			0.737162	−	0.675716i	$-0.236166\pi$
$251$	23.3577			1.47432			0.737162	+	0.675716i	$0.236166\pi$
$252$	0.361163	+	0.497099i	0.0227511	+	0.0313143i
$253$	−2.47140	−	0.803008i	−0.155376	−	0.0504847i
$254$	5.67738	−	17.4732i	0.356230	−	1.09636i
$255$	14.4211	+	8.37946i	0.903087	+	0.524742i
$256$	2.61854	+	8.05903i	0.163659	+	0.503690i
$257$		−	4.48380i		−	0.279692i	−0.990173	−	0.139846i	$-0.955339\pi$
$257$		−	4.48380i		−	0.279692i	0.990173	−	0.139846i	$-0.0446607\pi$
$258$	7.71163	−	2.50566i	0.480105	−	0.155996i
$259$	13.8135	+	10.0361i	0.858330	+	0.623614i
$260$	−0.0193145	−	0.188801i	−0.00119784	−	0.0117089i
$261$	−5.56185	+	4.04092i	−0.344270	+	0.250127i
$262$	19.3936	−	26.6930i	1.19814	−	1.64910i
$263$	−4.54093	+	6.25006i	−0.280006	+	0.385395i	−0.925736	−	0.378171i	$-0.876553\pi$
$263$	−4.54093	+	6.25006i	−0.280006	+	0.385395i	0.645730	+	0.763566i	$0.276553\pi$
$264$	6.05830	−	4.40161i	0.372862	−	0.270900i
$265$	−8.91796	−	9.95981i	−0.547826	−	0.611826i
$266$	1.58045	+	1.14826i	0.0969034	+	0.0704044i
$267$	−11.5108	+	3.74010i	−0.704451	+	0.228890i
$268$			0.653376i			0.0399113i
$269$	−3.31865	−	10.2138i	−0.202342	−	0.622743i	−0.999812	−	0.0193855i	$-0.993829\pi$
$269$	−3.31865	−	10.2138i	−0.202342	−	0.622743i	0.797470	−	0.603358i	$-0.206171\pi$
$270$	2.56156	−	2.29360i	0.155891	−	0.139584i
$271$	−7.94563	+	24.4541i	−0.482662	+	1.48548i	0.352676	+	0.935746i	$0.385272\pi$
$271$	−7.94563	+	24.4541i	−0.482662	+	1.48548i	−0.835338	+	0.549737i	$0.814728\pi$
$272$	32.6042	+	10.5938i	1.97692	+	0.642341i
$273$	0.230798	+	0.317667i	0.0139685	+	0.0192261i
$274$	15.4063			0.930726
$275$	13.5669	+	6.13079i	0.818117	+	0.369700i
$276$	−0.318054			−0.0191446
$277$	5.65712	+	7.78635i	0.339903	+	0.467837i	0.944413	−	0.328761i	$-0.106631\pi$
$277$	5.65712	+	7.78635i	0.339903	+	0.467837i	−0.604510	+	0.796598i	$0.706631\pi$
$278$	9.61490	+	3.12407i	0.576663	+	0.187369i
$279$	3.03433	−	9.33870i	0.181660	−	0.559093i
$280$	1.99702	−	9.26876i	0.119345	−	0.553914i
$281$	−0.875368	−	2.69411i	−0.0522201	−	0.160717i	0.921545	−	0.388270i	$-0.126927\pi$
$281$	−0.875368	−	2.69411i	−0.0522201	−	0.160717i	−0.973766	+	0.227553i	$0.926927\pi$
$282$			13.1740i			0.784498i
$283$	−22.5052	+	7.31238i	−1.33780	+	0.434676i	−0.888569	−	0.458742i	$-0.848300\pi$
$283$	−22.5052	+	7.31238i	−1.33780	+	0.434676i	−0.449226	+	0.893418i	$0.648300\pi$
$284$	−1.28977	−	0.937071i	−0.0765336	−	0.0556049i
$285$	0.846512	−	1.45686i	0.0501431	−	0.0862967i
$286$	−0.862658	+	0.626757i	−0.0510100	+	0.0370609i
$287$	−3.76318	+	5.17958i	−0.222134	+	0.305741i
$288$	1.19751	−	1.64823i	0.0705640	−	0.0971231i
$289$	31.2579	−	22.7102i	1.83870	−	1.33589i
$290$	−23.1077	−	4.97872i	−1.35693	−	0.292361i
$291$	7.66483	+	5.56883i	0.449321	+	0.326450i
$292$	−5.21735	+	1.69522i	−0.305322	+	0.0992052i
$293$			23.2376i			1.35755i	0.734345	+	0.678777i	$0.237490\pi$
$293$			23.2376i			1.35755i	−0.734345	+	0.678777i	$0.762510\pi$
$294$	1.97545	+	6.07981i	0.115211	+	0.354582i
$295$	3.48075	+	7.87661i	0.202657	+	0.458594i
$296$	7.87047	−	24.2228i	0.457462	−	1.40792i
$297$	−2.83184	−	0.920120i	−0.164320	−	0.0533908i
$298$	9.86455	+	13.5774i	0.571438	+	0.786517i
$299$	−0.203250			−0.0117542
$300$	1.81113	+	0.200521i	0.104566	+	0.0115771i
$301$	−8.89069			−0.512451
$302$	−18.4495	−	25.3936i	−1.06165	−	1.46124i
$303$	6.22436	+	2.02242i	0.357580	+	0.116185i
$304$	1.07020	−	3.29375i	0.0613805	−	0.188910i
$305$	−9.77967	+	1.00047i	−0.559982	+	0.0572867i
$306$	−3.54428	−	10.9082i	−0.202613	−	0.623579i
$307$			21.8131i			1.24494i	0.782643	+	0.622470i	$0.213871\pi$
$307$			21.8131i			1.24494i	−0.782643	+	0.622470i	$0.786129\pi$
$308$	1.74002	−	0.565366i	0.0991467	−	0.0322147i
$309$	0.566962	+	0.411922i	0.0322533	+	0.0234334i
$310$	30.8811	−	13.6467i	1.75393	−	0.775079i
$311$	−8.12364	+	5.90217i	−0.460649	+	0.334681i	−0.793786	−	0.608197i	$-0.791893\pi$
$311$	−8.12364	+	5.90217i	−0.460649	+	0.334681i	0.333137	+	0.942879i	$0.391893\pi$
$312$	0.344274	−	0.473852i	0.0194907	−	0.0268266i
$313$	3.55825	−	4.89752i	0.201124	−	0.276824i	−0.696527	−	0.717531i	$-0.745272\pi$
$313$	3.55825	−	4.89752i	0.201124	−	0.276824i	0.897651	+	0.440707i	$0.145272\pi$
$314$	−4.35332	+	3.16287i	−0.245672	+	0.178491i
$315$	−3.44833	+	1.52385i	−0.194291	+	0.0858592i
$316$	−2.17468	−	1.58000i	−0.122335	−	0.0888817i
$317$	−8.08309	+	2.62636i	−0.453992	+	0.147511i	−0.527082	−	0.849814i	$-0.676714\pi$
$317$	−8.08309	+	2.62636i	−0.453992	+	0.147511i	0.0730902	+	0.997325i	$0.476714\pi$
$318$			9.19338i			0.515539i
$319$	6.32566	+	19.4684i	0.354169	+	1.09002i
$320$	−13.4788	+	1.37890i	−0.753490	+	0.0770827i
$321$	−3.87161	+	11.9156i	−0.216092	+	0.665063i
$322$	2.15182	+	0.699167i	0.119916	+	0.0389631i
$323$	−3.30369	−	4.54713i	−0.183822	−	0.253009i
$324$	−0.364440			−0.0202466
$325$	1.15739	+	0.128141i	0.0642003	+	0.00710799i
$326$	−9.18540			−0.508733
$327$	−2.51776	−	3.46541i	−0.139233	−	0.191637i
$328$	9.08268	+	2.95114i	0.501507	+	0.162950i
$329$	4.46369	−	13.7378i	0.246091	−	0.757391i
$330$	−4.13818	−	9.36431i	−0.227799	−	0.515488i
$331$	5.03526	+	15.4969i	0.276763	+	0.851789i	0.988748	+	0.149594i	$0.0477966\pi$
$331$	5.03526	+	15.4969i	0.276763	+	0.851789i	−0.711984	+	0.702195i	$0.752203\pi$
$332$		−	1.58331i		−	0.0868955i
$333$	−9.63150	+	3.12946i	−0.527803	+	0.171493i
$334$	2.90808	+	2.11284i	0.159123	+	0.115610i
$335$	−3.91895	−	0.844365i	−0.214115	−	0.0461326i
$336$	−6.26907	+	4.55474i	−0.342006	+	0.248482i
$337$	−14.5161	+	19.9796i	−0.790740	+	1.08836i	0.203275	+	0.979122i	$0.434841\pi$
$337$	−14.5161	+	19.9796i	−0.790740	+	1.08836i	−0.994015	+	0.109239i	$0.965159\pi$
$338$	11.7007	−	16.1046i	0.636432	−	0.875974i
$339$	−6.65628	+	4.83607i	−0.361519	+	0.262659i
$340$	3.05381	−	5.25563i	0.165616	−	0.285027i
$341$	−23.6537	−	17.1854i	−1.28092	−	0.930644i
$342$	−1.10197	+	0.358051i	−0.0595876	+	0.0193612i
$343$		−	18.8114i		−	1.01572i
$344$	4.09816	+	12.6128i	0.220958	+	0.680039i
$345$	0.411024	−	1.90769i	0.0221288	−	0.102706i
$346$	−2.88474	+	8.87831i	−0.155084	+	0.477301i
$347$	13.2640	+	4.30975i	0.712051	+	0.231359i	0.642573	−	0.766224i	$-0.277867\pi$
$347$	13.2640	+	4.30975i	0.712051	+	0.231359i	0.0694775	+	0.997584i	$0.477867\pi$
$348$	1.47267	+	2.02696i	0.0789435	+	0.108656i
$349$	−18.4966			−0.990099			−0.495049	−	0.868865i	$-0.664850\pi$
$349$	−18.4966			−0.990099			−0.495049	+	0.868865i	$0.664850\pi$
$350$	−11.8125	−	5.33799i	−0.631407	−	0.285327i
$351$	−0.232892			−0.0124309
$352$	−3.56568	−	4.90773i	−0.190051	−	0.261583i
$353$	−0.420113	−	0.136503i	−0.0223604	−	0.00726532i	0.297815	−	0.954623i	$-0.403742\pi$
$353$	−0.420113	−	0.136503i	−0.0223604	−	0.00726532i	−0.320176	+	0.947358i	$0.603742\pi$
$354$	1.82994	−	5.63197i	0.0972601	−	0.299336i
$355$	7.28732	−	6.52503i	0.386771	−	0.346313i
$356$	1.36304	+	4.19500i	0.0722409	+	0.222335i
$357$			12.5760i			0.665590i
$358$	16.7059	−	5.42809i	0.882936	−	0.286883i
$359$	3.73869	+	2.71631i	0.197320	+	0.143362i	0.682058	−	0.731298i	$-0.261085\pi$
$359$	3.73869	+	2.71631i	0.197320	+	0.143362i	−0.484738	+	0.874659i	$0.661085\pi$
$360$	3.75133	+	4.18958i	0.197712	+	0.220810i
$361$	14.9120	−	10.8342i	0.784840	−	0.570220i
$362$	−7.09506	+	9.76552i	−0.372908	+	0.513264i
$363$	1.25437	−	1.72650i	0.0658376	−	0.0906176i
$364$	0.115770	−	0.0841120i	0.00606801	−	0.00440867i
$365$	−3.42548	−	33.4844i	−0.179298	−	1.75265i
$366$	5.46917	+	3.97359i	0.285878	+	0.207703i
$367$	8.34738	−	2.71223i	0.435730	−	0.141577i	−0.0829348	−	0.996555i	$-0.526429\pi$
$367$	8.34738	−	2.71223i	0.435730	−	0.141577i	0.518665	+	0.854978i	$0.326429\pi$
$368$		−	4.01108i		−	0.209092i
$369$	−1.17344	−	3.61147i	−0.0610867	−	0.188005i
$370$	−30.1071	−	17.4939i	−1.56520	−	0.909463i
$371$	3.11496	−	9.58687i	0.161721	−	0.497725i
$372$	−3.40339	−	1.10583i	−0.176458	−	0.0573345i
$373$	9.10804	+	12.5361i	0.471596	+	0.649097i	0.976863	−	0.213867i	$-0.0686058\pi$
$373$	9.10804	+	12.5361i	0.471596	+	0.649097i	−0.505266	+	0.862963i	$0.668606\pi$
$374$	−34.1513			−1.76592
$375$	−3.54327	+	10.6040i	−0.182974	+	0.547589i
$376$	−21.5468			−1.11119
$377$	0.941098	+	1.29531i	0.0484690	+	0.0667118i
$378$	2.46564	+	0.801135i	0.126819	+	0.0412060i
$379$	8.43404	−	25.9573i	0.433227	−	1.33334i	−0.461665	−	0.887054i	$-0.652748\pi$
$379$	8.43404	−	25.9573i	0.433227	−	1.33334i	0.894892	−	0.446282i	$-0.147252\pi$
$380$	−0.530936	−	0.308503i	−0.0272364	−	0.0158258i
$381$	−3.69219	−	11.3634i	−0.189157	−	0.582164i
$382$			19.3196i			0.988474i
$383$	12.4628	−	4.04941i	0.636820	−	0.206915i	0.0272261	−	0.999629i	$-0.491333\pi$
$383$	12.4628	−	4.04941i	0.636820	−	0.206915i	0.609594	+	0.792714i	$0.291333\pi$
$384$	10.8344	+	7.87162i	0.552889	+	0.401697i
$385$	1.14242	+	11.1672i	0.0582231	+	0.569135i
$386$	−12.6188	+	9.16812i	−0.642282	+	0.466645i
$387$	3.09952	−	4.26612i	0.157558	−	0.216859i
$388$	2.02950	−	2.79337i	0.103032	−	0.141812i
$389$	13.6769	−	9.93685i	0.693447	−	0.503818i	−0.184345	−	0.982862i	$-0.559016\pi$
$389$	13.6769	−	9.93685i	0.693447	−	0.503818i	0.877791	+	0.479043i	$0.159016\pi$
$390$	−0.534162	−	0.596566i	−0.0270483	−	0.0302083i
$391$	−5.26641	−	3.82627i	−0.266334	−	0.193503i
$392$	−9.94390	+	3.23097i	−0.502243	+	0.163189i
$393$		−	21.4573i		−	1.08238i
$394$	−0.972680	−	2.99360i	−0.0490029	−	0.150815i
$395$	12.2872	−	11.0019i	0.618234	−	0.553564i
$396$	−0.335328	+	1.03203i	−0.0168509	+	0.0518617i
$397$	−9.89842	−	3.21619i	−0.496787	−	0.161416i	0.0498977	−	0.998754i	$-0.484110\pi$
$397$	−9.89842	−	3.21619i	−0.496787	−	0.161416i	−0.546685	+	0.837338i	$0.684110\pi$
$398$	3.22778	+	4.44265i	0.161794	+	0.222690i
$399$	1.27045			0.0636021
$400$	−2.52883	+	22.8408i	−0.126442	+	1.14204i
$401$	−0.694800			−0.0346967			−0.0173483	−	0.999850i	$-0.505522\pi$
$401$	−0.694800			−0.0346967			−0.0173483	+	0.999850i	$0.505522\pi$
$402$	1.62039	+	2.23028i	0.0808179	+	0.111236i
$403$	−2.17491	−	0.706670i	−0.108340	−	0.0352017i
$404$	0.737049	−	2.26840i	0.0366696	−	0.112857i
$405$	0.470969	−	2.18591i	0.0234026	−	0.108619i
$406$	−5.50766	−	16.9508i	−0.273341	−	0.841256i
$407$			30.1543i			1.49469i
$408$	17.8410	−	5.79688i	0.883260	−	0.286988i
$409$	−0.962002	−	0.698936i	−0.0475680	−	0.0345601i	0.563747	−	0.825947i	$-0.309359\pi$
$409$	−0.962002	−	0.698936i	−0.0475680	−	0.0345601i	−0.611315	+	0.791387i	$0.709359\pi$
$410$	6.55958	−	11.2891i	0.323954	−	0.557529i
$411$	8.10570	−	5.88914i	0.399825	−	0.290490i
$412$	0.150121	−	0.206623i	0.00739592	−	0.0101796i
$413$	−3.81652	+	5.25299i	−0.187799	+	0.258483i
$414$	−1.08567	+	0.788784i	−0.0533577	+	0.0387666i
$415$	9.49670	+	2.04613i	0.466174	+	0.100441i
$416$	−0.383860	−	0.278891i	−0.0188203	−	0.0136737i
$417$	6.25289	−	2.03169i	0.306205	−	0.0994921i
$418$			3.45005i			0.168747i
$419$	−0.611361	−	1.88158i	−0.0298670	−	0.0919210i	0.935012	−	0.354616i	$-0.115389\pi$
$419$	−0.611361	−	1.88158i	−0.0298670	−	0.0919210i	−0.964879	+	0.262695i	$0.915389\pi$
$420$	0.555351	+	1.25671i	0.0270984	+	0.0613211i
$421$	3.42467	−	10.5400i	0.166908	−	0.513690i	−0.832264	−	0.554380i	$-0.812955\pi$
$421$	3.42467	−	10.5400i	0.166908	−	0.513690i	0.999172	+	0.0406895i	$0.0129554\pi$
$422$	5.44958	+	1.77068i	0.265281	+	0.0861951i
$423$	5.03583	+	6.93123i	0.244850	+	0.337008i
$424$	−15.0363			−0.730229
$425$	27.5768	+	25.1086i	1.33767	+	1.21795i
$426$	−6.72655			−0.325902
$427$	−4.35690	−	5.99677i	−0.210845	−	0.290204i
$428$	4.34251	+	1.41097i	0.209903	+	0.0682017i
$429$	−0.214289	+	0.659512i	−0.0103460	+	0.0318416i
$430$	18.0370	−	1.84520i	0.869821	−	0.0889835i
$431$	−3.21800	−	9.90398i	−0.155005	−	0.477058i	0.843156	−	0.537669i	$-0.180695\pi$
$431$	−3.21800	−	9.90398i	−0.155005	−	0.477058i	−0.998161	+	0.0606112i	$0.980695\pi$
$432$		−	4.59606i		−	0.221128i
$433$	−9.76195	+	3.17185i	−0.469129	+	0.152429i	−0.534035	−	0.845462i	$-0.679325\pi$
$433$	−9.76195	+	3.17185i	−0.469129	+	0.152429i	0.0649063	+	0.997891i	$0.479325\pi$
$434$	20.5950	+	14.9631i	0.988590	+	0.718253i
$435$	−14.0608	+	6.21361i	−0.674165	+	0.297920i
$436$	−1.26293	+	0.917573i	−0.0604834	+	0.0439438i
$437$	−0.386538	+	0.532024i	−0.0184906	+	0.0254502i
$438$	−13.6051	+	18.7258i	−0.650075	+	0.894752i
$439$	−19.9920	+	14.5251i	−0.954168	+	0.693244i	−0.951789	−	0.306753i	$-0.900757\pi$
$439$	−19.9920	+	14.5251i	−0.954168	+	0.693244i	−0.00237925	+	0.999997i	$0.500757\pi$
$440$	15.3159	−	6.76824i	0.730157	−	0.322663i
$441$	3.36339	+	2.44365i	0.160161	+	0.116364i
$442$	−2.54043	+	0.825434i	−0.120836	+	0.0392619i
$443$		−	7.52935i		−	0.357730i	−0.983874	−	0.178865i	$-0.942757\pi$
$443$		−	7.52935i		−	0.357730i	0.983874	−	0.178865i	$-0.0572426\pi$
$444$	1.14050	+	3.51010i	0.0541257	+	0.166582i
$445$	−26.9231	+	2.75426i	−1.27628	+	0.130564i
$446$	−12.4726	+	38.3867i	−0.590594	+	1.81766i
$447$	10.3801	+	3.37269i	0.490961	+	0.159523i
$448$	−6.00491	−	8.26505i	−0.283705	−	0.390487i
$449$	31.6627			1.49426			0.747128	−	0.664681i	$-0.231432\pi$
$449$	31.6627			1.49426			0.747128	+	0.664681i	$0.231432\pi$
$450$	6.67954	−	3.80719i	0.314877	−	0.179473i
$451$	−11.3068			−0.532416
$452$	1.76245	+	2.42581i	0.0828989	+	0.114101i
$453$	−19.4137	−	6.30789i	−0.912135	−	0.296371i
$454$	−2.13403	+	6.56786i	−0.100155	+	0.308245i
$455$	0.354892	+	0.803088i	0.0166376	+	0.0376494i
$456$	−0.585614	−	1.80234i	−0.0274239	−	0.0844021i
$457$			2.95742i			0.138342i	0.997605	+	0.0691712i	$0.0220355\pi$
$457$			2.95742i			0.138342i	−0.997605	+	0.0691712i	$0.977965\pi$
$458$	−11.0257	+	3.58245i	−0.515195	+	0.167397i
$459$	−6.03447	−	4.38430i	−0.281665	−	0.204642i
$460$	−0.695236	−	0.149794i	−0.0324156	−	0.00698416i
$461$	14.2396	−	10.3457i	0.663204	−	0.481846i	−0.204539	−	0.978858i	$-0.565570\pi$
$461$	14.2396	−	10.3457i	0.663204	−	0.481846i	0.867743	+	0.497012i	$0.165570\pi$
$462$	4.53737	−	6.24516i	0.211098	−	0.290551i
$463$	15.4835	−	21.3112i	0.719578	−	0.990414i	−0.279960	−	0.960012i	$-0.590321\pi$
$463$	15.4835	−	21.3112i	0.719578	−	0.990414i	0.999538	−	0.0304024i	$-0.00967889\pi$
$464$	−25.5626	+	18.5723i	−1.18671	+	0.862198i
$465$	11.0310	−	18.9844i	0.511550	−	0.880383i
$466$	12.8929	+	9.36724i	0.597252	+	0.433929i
$467$	6.99888	−	2.27408i	0.323870	−	0.105232i	−0.142570	−	0.989785i	$-0.545537\pi$
$467$	6.99888	−	2.27408i	0.323870	−	0.105232i	0.466439	+	0.884553i	$0.345537\pi$
$468$			0.0848751i			0.00392335i
$469$	−0.934070	−	2.87477i	−0.0431313	−	0.132745i
$470$	−6.20453	+	28.7971i	−0.286194	+	1.32831i
$471$	−1.08139	+	3.32816i	−0.0498276	+	0.153354i
$472$	9.21143	+	2.99297i	0.423990	+	0.137763i
$473$	−9.22905	−	12.7027i	−0.424352	−	0.584070i
$474$	−11.3416			−0.520939
$475$	2.53653	−	2.78587i	0.116384	−	0.127824i
$476$	4.58317			0.210069
$477$	3.51423	+	4.83692i	0.160905	+	0.221467i
$478$	27.1626	+	8.82566i	1.24239	+	0.403676i
$479$	8.79679	−	27.0737i	0.401936	−	1.23703i	−0.521491	−	0.853257i	$-0.674624\pi$
$479$	8.79679	−	27.0737i	0.401936	−	1.23703i	0.923427	−	0.383774i	$-0.125376\pi$
$480$	3.39392	−	3.03889i	0.154910	−	0.138706i
$481$	0.728827	+	2.24310i	0.0332316	+	0.102276i
$482$		−	8.35791i		−	0.380692i
$483$	1.39940	−	0.454692i	0.0636748	−	0.0206892i
$484$	−0.629204	−	0.457144i	−0.0286002	−	0.0207793i
$485$	14.1319	+	15.7828i	0.641695	+	0.716662i
$486$	−1.24400	+	0.903822i	−0.0564292	+	0.0409982i
$487$	−1.40132	+	1.92875i	−0.0634998	+	0.0873999i	−0.839586	−	0.543227i	$-0.817202\pi$
$487$	−1.40132	+	1.92875i	−0.0634998	+	0.0873999i	0.776086	+	0.630627i	$0.217202\pi$
$488$	−6.49904	+	8.94516i	−0.294198	+	0.404929i
$489$	−4.83272	+	3.51118i	−0.218543	+	0.158781i
$490$	1.45475	+	14.2203i	0.0657188	+	0.642407i
$491$	20.8105	+	15.1197i	0.939163	+	0.682342i	0.948219	−	0.317617i	$-0.102883\pi$
$491$	20.8105	+	15.1197i	0.939163	+	0.682342i	−0.00905626	+	0.999959i	$0.502883\pi$
$492$	−1.31616	+	0.427647i	−0.0593371	+	0.0192798i
$493$			51.2794i			2.30951i
$494$	0.0833872	+	0.256640i	0.00375177	+	0.0115468i
$495$	−5.75679	−	3.34501i	−0.258748	−	0.150347i
$496$	13.9460	−	42.9212i	0.626192	−	1.92722i
$497$	7.01445	+	2.27913i	0.314641	+	0.102233i
$498$	−3.92666	−	5.40459i	−0.175958	−	0.242185i
$499$	−29.9989			−1.34293			−0.671467	−	0.741035i	$-0.734335\pi$
$499$	−29.9989			−1.34293			−0.671467	+	0.741035i	$0.734335\pi$
$500$	3.86453	+	1.29131i	0.172827	+	0.0577490i
$501$	2.33767			0.104440
$502$	−21.1112	−	29.0570i	−0.942238	−	1.29688i
$503$	−13.1483	−	4.27216i	−0.586256	−	0.190486i	0.000845408	−	1.00000i	$-0.499731\pi$
$503$	−13.1483	−	4.27216i	−0.586256	−	0.190486i	−0.587101	+	0.809514i	$0.699731\pi$
$504$	−1.31031	+	4.03270i	−0.0583656	+	0.179631i
$505$	12.6534	+	7.35230i	0.563068	+	0.327173i
$506$	1.23476	+	3.80021i	0.0548920	+	0.168940i
$507$		−	12.9458i		−	0.574941i
$508$	−4.14127	+	1.34558i	−0.183739	+	0.0597004i
$509$	25.8511	+	18.7819i	1.14583	+	0.832493i	0.987921	−	0.154960i	$-0.0495250\pi$
$509$	25.8511	+	18.7819i	1.14583	+	0.832493i	0.157908	+	0.987454i	$0.449525\pi$
$510$	−2.61005	−	25.5135i	−0.115575	−	1.12976i
$511$	20.5322	−	14.9175i	0.908290	−	0.659911i
$512$	−8.08447	+	11.1273i	−0.357286	+	0.491763i
$513$	−0.442912	+	0.609616i	−0.0195550	+	0.0269152i
$514$	−5.57787	+	4.05256i	−0.246029	+	0.178751i
$515$	1.04532	+	1.16744i	0.0460625	+	0.0514438i
$516$	−1.55474	−	1.12959i	−0.0684438	−	0.0497273i
$517$	24.2617	−	7.88310i	1.06703	−	0.346698i
$518$		−	26.2549i		−	1.15358i
$519$	1.87604	+	5.77386i	0.0823490	+	0.253444i
$520$	0.975720	−	0.873654i	0.0427881	−	0.0383123i
$521$	−11.9889	+	36.8979i	−0.525242	+	1.61653i	0.238595	+	0.971119i	$0.423313\pi$
$521$	−11.9889	+	36.8979i	−0.525242	+	1.61653i	−0.763837	+	0.645409i	$0.776687\pi$
$522$	10.0538	+	3.26669i	0.440045	+	0.142979i
$523$	−13.9389	−	19.1853i	−0.609507	−	0.838914i	0.387030	−	0.922067i	$-0.373501\pi$
$523$	−13.9389	−	19.1853i	−0.609507	−	0.838914i	−0.996537	+	0.0831532i	$0.973501\pi$
$524$	−7.81991			−0.341614
$525$	−8.25541	+	1.70694i	−0.360296	+	0.0744968i
$526$	11.8793			0.517962
$527$	−43.0507	−	59.2542i	−1.87532	−	2.58115i
$528$	−13.0153	−	4.22893i	−0.566419	−	0.184041i
$529$	6.87203	−	21.1499i	0.298784	−	0.919562i
$530$	−4.32980	+	20.0959i	−0.188074	+	0.872909i
$531$	−1.19007	−	3.66266i	−0.0516446	−	0.158946i
$532$		−	0.463003i		−	0.0200737i
$533$	−0.841081	+	0.273284i	−0.0364313	+	0.0118372i
$534$	15.0564	+	10.9391i	0.651556	+	0.473383i
$535$	−14.0748	+	24.2229i	−0.608509	+	1.04725i
$536$	−3.64776	+	2.65025i	−0.157559	+	0.114473i
$537$	6.71458	−	9.24183i	0.289756	−	0.398815i
$538$	−9.70648	+	13.3598i	−0.418476	+	0.575983i
$539$	10.0147	−	7.27613i	0.431365	−	0.313405i
$540$	−0.796631	−	0.171640i	−0.0342815	−	0.00738620i
$541$	−2.27953	−	1.65618i	−0.0980046	−	0.0712045i	0.537704	−	0.843134i	$-0.319292\pi$
$541$	−2.27953	−	1.65618i	−0.0980046	−	0.0712045i	−0.635708	+	0.771929i	$0.719292\pi$
$542$	37.6025	−	12.2178i	1.61516	−	0.524799i
$543$			7.85007i			0.336879i
$544$	−4.69597	−	14.4527i	−0.201338	−	0.619654i
$545$	−3.87150	−	8.76084i	−0.165837	−	0.375273i
$546$	0.186578	−	0.574228i	0.00798480	−	0.0245747i
$547$	4.20728	+	1.36703i	0.179890	+	0.0584499i	0.397577	−	0.917569i	$-0.369851\pi$
$547$	4.20728	+	1.36703i	0.179890	+	0.0584499i	−0.217687	+	0.976019i	$0.569851\pi$
$548$	−2.14623	−	2.95404i	−0.0916826	−	0.126190i
$549$	4.39643			0.187635
$550$	−4.63537	−	22.4185i	−0.197653	−	0.955926i
$551$	5.18036			0.220691
$552$	−1.29010	−	1.77568i	−0.0549105	−	0.0755778i
$553$	11.8271	+	3.84285i	0.502938	+	0.163415i
$554$	4.57323	−	14.0749i	0.194298	−	0.597987i
$555$	−22.5274	+	2.30458i	−0.956236	+	0.0978238i
$556$	−0.740427	−	2.27880i	−0.0314011	−	0.0966426i
$557$		−	7.20182i		−	0.305151i	−0.988292	−	0.152575i	$-0.951243\pi$
$557$		−	7.20182i		−	0.305151i	0.988292	−	0.152575i	$-0.0487567\pi$
$558$	−14.3599	+	4.66580i	−0.607902	+	0.197519i
$559$	−0.993546	−	0.721854i	−0.0420225	−	0.0305312i
$560$	−15.8487	+	7.00371i	−0.669732	+	0.295961i
$561$	−17.9681	+	13.0546i	−0.758612	+	0.551164i
$562$	−2.56030	+	3.52395i	−0.108000	+	0.148649i
$563$	−13.6665	+	18.8103i	−0.575975	+	0.792761i	−0.993247	−	0.116020i	$-0.962986\pi$
$563$	−13.6665	+	18.8103i	−0.575975	+	0.792761i	0.417272	+	0.908782i	$0.362986\pi$
$564$	2.52601	−	1.83526i	0.106364	−	0.0772782i
$565$	−16.8276	+	7.43629i	−0.707944	+	0.312847i
$566$	29.4373	+	21.3875i	1.23734	+	0.898982i
$567$	1.60349	−	0.521005i	0.0673402	−	0.0218801i
$568$		−	11.0017i		−	0.461620i
$569$	6.37307	+	19.6143i	0.267173	+	0.822273i	0.991185	+	0.132486i	$0.0422960\pi$
$569$	6.37307	+	19.6143i	0.267173	+	0.822273i	−0.724012	+	0.689787i	$0.757704\pi$
$570$	−2.57743	+	0.263674i	−0.107957	+	0.0110441i
$571$	0.557381	−	1.71544i	0.0233257	−	0.0717890i	−0.938716	−	0.344691i	$-0.887984\pi$
$571$	0.557381	−	1.71544i	0.0233257	−	0.0717890i	0.962042	+	0.272902i	$0.0879836\pi$
$572$	0.240352	+	0.0780952i	0.0100496	+	0.00326533i
$573$	7.38502	+	10.1646i	0.308514	+	0.424633i
$574$	9.84466			0.410908
$575$	1.79692	−	3.97644i	0.0749368	−	0.165829i
$576$	6.05938			0.252474
$577$	−9.69043	−	13.3377i	−0.403418	−	0.555257i	0.558180	−	0.829720i	$-0.311500\pi$
$577$	−9.69043	−	13.3377i	−0.403418	−	0.555257i	−0.961598	+	0.274463i	$0.911500\pi$
$578$	−56.5032	−	18.3590i	−2.35022	−	0.763633i
$579$	−3.13458	+	9.64725i	−0.130269	+	0.400926i
$580$	2.26449	+	5.12432i	0.0940277	+	0.212776i
$581$	2.26351	+	6.96637i	0.0939063	+	0.289014i
$582$		−	14.5683i		−	0.603876i
$583$	16.9309	−	5.50118i	0.701205	−	0.227835i
$584$	−30.6271	−	22.2519i	−1.26736	−	0.920791i
$585$	−0.509080	−	0.109685i	−0.0210479	−	0.00453491i
$586$	28.9076	−	21.0026i	1.19416	−	0.867610i
$587$	4.27415	−	5.88286i	0.176413	−	0.242811i	−0.711649	−	0.702535i	$-0.752051\pi$
$587$	4.27415	−	5.88286i	0.176413	−	0.242811i	0.888062	+	0.459723i	$0.152051\pi$
$588$	0.890562	−	1.22575i	0.0367261	−	0.0505492i
$589$	−5.98599	+	4.34908i	−0.246649	+	0.179201i
$590$	6.65256	−	11.4491i	0.273881	−	0.471353i
$591$	−1.65608	−	1.20321i	−0.0681220	−	0.0494935i
$592$	−44.2670	+	14.3832i	−1.81936	+	0.591146i
$593$			2.47898i			0.101800i	0.998704	+	0.0508998i	$0.0162089\pi$
$593$			2.47898i			0.101800i	−0.998704	+	0.0508998i	$0.983791\pi$
$594$	1.41484	+	4.35444i	0.0580518	+	0.178665i
$595$	−5.92288	+	27.4899i	−0.242815	+	1.12697i
$596$	1.22914	−	3.78291i	0.0503477	−	0.154954i
$597$	3.39646	+	1.10358i	0.139008	+	0.0451664i
$598$	0.183701	+	0.252843i	0.00751211	+	0.0103395i
$599$	−30.2951			−1.23782			−0.618912	−	0.785460i	$-0.712426\pi$
$599$	−30.2951			−1.23782			−0.618912	+	0.785460i	$0.712426\pi$
$600$	6.22689	+	10.9248i	0.254212	+	0.446003i
$601$	4.46130			0.181980			0.0909900	−	0.995852i	$-0.470997\pi$
$601$	4.46130			0.181980			0.0909900	+	0.995852i	$0.470997\pi$
$602$	8.03560	+	11.0600i	0.327506	+	0.450774i
$603$	1.70508	+	0.554013i	0.0694361	+	0.0225612i
$604$	−2.29885	+	7.07512i	−0.0935387	+	0.287882i
$605$	3.55507	−	3.18319i	0.144534	−	0.129415i
$606$	−3.10982	−	9.57103i	−0.126328	−	0.388797i
$607$		−	17.2931i		−	0.701906i	−0.936393	−	0.350953i	$-0.885858\pi$
$607$		−	17.2931i		−	0.701906i	0.936393	−	0.350953i	$-0.114142\pi$
$608$	−1.46004	+	0.474397i	−0.0592126	+	0.0192393i
$609$	−9.37732	−	6.81302i	−0.379988	−	0.276077i
$610$	10.0837	+	11.2617i	0.408276	+	0.455973i
$611$	1.61423	−	1.17280i	0.0653046	−	0.0474466i
$612$	−1.59781	+	2.19920i	−0.0645877	+	0.0888974i
$613$	8.41293	−	11.5794i	0.339795	−	0.467688i	−0.604587	−	0.796539i	$-0.706662\pi$
$613$	8.41293	−	11.5794i	0.339795	−	0.467688i	0.944382	+	0.328852i	$0.106662\pi$
$614$	27.1356	−	19.7152i	1.09510	−	0.795640i
$615$	−0.864134	−	8.44698i	−0.0348452	−	0.340615i
$616$	10.2143	+	7.42115i	0.411547	+	0.299006i
$617$	−25.0669	+	8.14472i	−1.00915	+	0.327894i	−0.766518	−	0.642223i	$-0.778012\pi$
$617$	−25.0669	+	8.14472i	−1.00915	+	0.327894i	−0.242637	+	0.970117i	$0.578012\pi$
$618$		−	1.07761i		−	0.0433477i
$619$	0.864708	+	2.66130i	0.0347555	+	0.106967i	0.966929	−	0.255045i	$-0.0820902\pi$
$619$	0.864708	+	2.66130i	0.0347555	+	0.106967i	−0.932174	+	0.362011i	$0.882090\pi$
$620$	−6.91868	−	4.02013i	−0.277861	−	0.161452i
$621$	−0.269686	+	0.830007i	−0.0108221	+	0.0333070i
$622$	14.6846	+	4.77133i	0.588800	+	0.191313i
$623$	−11.9944	−	16.5089i	−0.480545	−	0.661414i
$624$	−1.07039			−0.0428497
$625$	−12.7394	+	21.5106i	−0.509577	+	0.860425i
$626$	−9.30856			−0.372045
$627$	1.31880	+	1.81517i	0.0526679	+	0.0724911i
$628$	1.21291	+	0.394100i	0.0484006	+	0.0157263i
$629$	−23.3427	+	71.8415i	−0.930735	+	2.86451i
$630$	5.01235	+	2.91245i	0.199697	+	0.116035i
$631$	10.9403	+	33.6707i	0.435526	+	1.34041i	0.892547	+	0.450955i	$0.148916\pi$
$631$	10.9403	+	33.6707i	0.435526	+	1.34041i	−0.457021	+	0.889456i	$0.651084\pi$
$632$		−	18.5499i		−	0.737877i
$633$	3.54404	−	1.15153i	0.140863	−	0.0457692i
$634$	10.5729	+	7.68164i	0.419902	+	0.305077i
$635$	−2.71898	−	26.5782i	−0.107899	−	1.05472i
$636$	1.76276	−	1.28072i	0.0698981	−	0.0507840i
$637$	0.569106	−	0.783307i	0.0225488	−	0.0310357i
$638$	18.5015	−	25.4651i	0.732481	−	1.00817i
$639$	−3.53904	+	2.57126i	−0.140002	+	0.101718i
$640$	19.9756	+	22.3093i	0.789605	+	0.881852i
$641$	−13.6994	−	9.95321i	−0.541094	−	0.393128i	0.283397	−	0.959003i	$-0.408539\pi$
$641$	−13.6994	−	9.95321i	−0.541094	−	0.393128i	−0.824491	+	0.565875i	$0.808539\pi$
$642$	18.3223	−	5.95327i	0.723122	−	0.234957i
$643$			25.9118i			1.02186i	0.859622	+	0.510931i	$0.170699\pi$
$643$			25.9118i			1.02186i	−0.859622	+	0.510931i	$0.829301\pi$
$644$	−0.165708	−	0.509996i	−0.00652980	−	0.0200966i
$645$	8.78448	−	7.86557i	0.345888	−	0.309707i
$646$	−2.67071	+	8.21960i	−0.105078	+	0.323396i
$647$	−10.3911	−	3.37629i	−0.408518	−	0.132736i	0.0975468	−	0.995231i	$-0.468900\pi$
$647$	−10.3911	−	3.37629i	−0.408518	−	0.132736i	−0.506065	+	0.862495i	$0.668900\pi$
$648$	−1.47826	−	2.03464i	−0.0580713	−	0.0799283i
$649$	−11.4671			−0.450121
$650$	−0.886664	−	1.55561i	−0.0347778	−	0.0610161i
$651$	16.5554			0.648857
$652$	1.27961	+	1.76124i	0.0501135	+	0.0689753i
$653$	13.5602	+	4.40596i	0.530650	+	0.172419i	0.562073	−	0.827088i	$-0.310004\pi$
$653$	13.5602	+	4.40596i	0.530650	+	0.172419i	−0.0314233	+	0.999506i	$0.510004\pi$
$654$	−2.03537	+	6.26422i	−0.0795892	+	0.244950i
$655$	10.1057	−	46.9038i	0.394864	−	1.83268i
$656$	−5.39319	−	16.5985i	−0.210569	−	0.648063i
$657$			15.0528i			0.587267i
$658$	−21.1243	+	6.86370i	−0.823511	+	0.267575i
$659$	18.5179	+	13.4540i	0.721355	+	0.524095i	0.886817	−	0.462121i	$-0.152912\pi$
$659$	18.5179	+	13.4540i	0.721355	+	0.524095i	−0.165462	+	0.986216i	$0.552912\pi$
$660$	−1.21905	+	2.09800i	−0.0474515	+	0.0816646i
$661$	32.2838	−	23.4556i	1.25570	−	0.912316i	0.257158	−	0.966369i	$-0.417214\pi$
$661$	32.2838	−	23.4556i	1.25570	−	0.912316i	0.998538	+	0.0540529i	$0.0172140\pi$
$662$	14.7273	−	20.2704i	0.572392	−	0.787830i
$663$	−1.02107	+	1.40538i	−0.0396550	+	0.0545804i
$664$	8.83953	−	6.42230i	0.343040	−	0.249233i
$665$	2.77709	+	0.598343i	0.107691	+	0.0232028i
$666$	12.5982	+	9.15314i	0.488171	+	0.354677i
$667$	5.70615	−	1.85404i	0.220943	−	0.0717887i
$668$		−	0.851941i		−	0.0329626i
$669$	8.11133	+	24.9641i	0.313602	+	0.965168i
$670$	2.49164	+	5.63834i	0.0962603	+	0.217828i
$671$	4.04524	−	12.4500i	0.156165	−	0.480626i
$672$	3.26683	+	1.06146i	0.126021	+	0.0409466i
$673$	1.26872	+	1.74624i	0.0489054	+	0.0673126i	0.832769	−	0.553620i	$-0.186754\pi$
$673$	1.26872	+	1.74624i	0.0489054	+	0.0673126i	−0.783864	+	0.620933i	$0.786754\pi$
$674$	37.9747			1.46273
$675$	2.05899	−	4.55638i	0.0792505	−	0.175375i
$676$	−4.71795			−0.181460
$677$	24.6717	+	33.9577i	0.948210	+	1.30510i	0.952318	+	0.305108i	$0.0986926\pi$
$677$	24.6717	+	33.9577i	0.948210	+	1.30510i	−0.00410738	+	0.999992i	$0.501307\pi$
$678$	12.0322	+	3.90949i	0.462093	+	0.150143i
$679$	−4.93613	+	15.1919i	−0.189431	+	0.583010i
$680$	41.7289	−	4.26890i	1.60023	−	0.163705i
$681$	1.38783	+	4.27129i	0.0531817	+	0.163676i
$682$			44.9579i			1.72153i
$683$	27.7767	−	9.02521i	1.06285	−	0.345340i	0.275149	−	0.961401i	$-0.411273\pi$
$683$	27.7767	−	9.02521i	1.06285	−	0.345340i	0.787698	+	0.616061i	$0.211273\pi$
$684$	0.222168	+	0.161415i	0.00849481	+	0.00617184i
$685$	20.4919	−	9.05557i	0.782956	−	0.345996i
$686$	−23.4015	+	17.0022i	−0.893473	+	0.649146i
$687$	−4.43152	+	6.09946i	−0.169073	+	0.232709i
$688$	14.2456	−	19.6074i	0.543108	−	0.747524i
$689$	1.12648	−	0.818435i	0.0429154	−	0.0311799i
$690$	−2.74466	+	1.21289i	−0.104488	+	0.0461740i
$691$	−36.0221	−	26.1716i	−1.37034	−	0.995614i	−0.997710	−	0.0676353i	$-0.978455\pi$
$691$	−36.0221	−	26.1716i	−1.37034	−	0.995614i	−0.372634	−	0.927978i	$-0.621545\pi$
$692$	2.10422	−	0.683703i	0.0799905	−	0.0259905i
$693$		−	5.02021i		−	0.190702i
$694$	−6.62698	−	20.3958i	−0.251557	−	0.774212i
$695$	14.6251	−	1.49616i	0.554761	−	0.0567526i
$696$	−5.34287	+	16.4437i	−0.202521	+	0.623295i
$697$	−26.9380	−	8.75268i	−1.02035	−	0.331531i
$698$	16.7176	+	23.0098i	0.632771	+	0.870934i
$699$	10.3640			0.392004
$700$	0.622075	+	3.00860i	0.0235122	+	0.113714i
$701$	−4.50567			−0.170177			−0.0850884	−	0.996373i	$-0.527117\pi$
$701$	−4.50567			−0.170177			−0.0850884	+	0.996373i	$0.527117\pi$
$702$	0.210493	+	0.289719i	0.00794454	+	0.0109347i
$703$	7.25759	+	2.35813i	0.273725	+	0.0889387i
$704$	5.57536	−	17.1592i	0.210129	−	0.646711i
$705$	7.74346	+	17.5227i	0.291636	+	0.659944i
$706$	0.209897	+	0.645997i	0.00789958	+	0.0243124i
$707$			11.0344i			0.414990i
$708$	−1.33482	+	0.433708i	−0.0501655	+	0.0162998i
$709$	−41.4788	−	30.1361i	−1.55777	−	1.13178i	−0.937809	−	0.347151i	$-0.887149\pi$
$709$	−41.4788	−	30.1361i	−1.55777	−	1.13178i	−0.619959	−	0.784634i	$-0.712851\pi$
$710$	−14.7036	−	3.16800i	−0.551816	−	0.118893i
$711$	−5.96718	+	4.33541i	−0.223787	+	0.162591i
$712$	−17.8916	+	24.6257i	−0.670517	+	0.922887i
$713$	−5.03702	+	6.93287i	−0.188638	+	0.259638i
$714$	15.6445	−	11.3664i	0.585482	−	0.425378i
$715$	−0.779025	+	1.34071i	−0.0291339	+	0.0501397i
$716$	−3.36809	−	2.44706i	−0.125871	−	0.0914509i
$717$	17.6647	−	5.73962i	0.659701	−	0.214350i
$718$		−	7.10600i		−	0.265194i
$719$	−10.8976	−	33.5393i	−0.406411	−	1.25080i	−0.919712	−	0.392595i	$-0.871578\pi$
$719$	−10.8976	−	33.5393i	−0.406411	−	1.25080i	0.513301	−	0.858209i	$-0.328422\pi$
$720$	2.16460	−	10.0466i	0.0806700	−	0.374413i
$721$	−0.365122	+	1.12373i	−0.0135979	+	0.0418499i
$722$	−26.9555	−	8.75838i	−1.00318	−	0.325953i
$723$	−3.19486	−	4.39735i	−0.118818	−	0.163539i
$724$	2.86088			0.106324
$725$	−33.6621	+	6.96017i	−1.25018	+	0.258494i
$726$	−3.28150			−0.121788
$727$	25.8648	+	35.5998i	0.959271	+	1.32032i	0.947284	+	0.320396i	$0.103816\pi$
$727$	25.8648	+	35.5998i	0.959271	+	1.32032i	0.0119876	+	0.999928i	$0.496184\pi$
$728$	0.939184	+	0.305160i	0.0348085	+	0.0113100i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−38.5587	+	34.5252i	−1.42712	+	1.27784i
$731$	−12.1546	−	37.4079i	−0.449553	−	1.38358i
$732$		−	1.60223i		−	0.0592202i
$733$	26.5098	−	8.61356i	0.979162	−	0.318149i	0.224653	−	0.974439i	$-0.427875\pi$
$733$	26.5098	−	8.61356i	0.979162	−	0.318149i	0.754509	+	0.656290i	$0.227875\pi$
$734$	−10.9186	−	7.93281i	−0.403012	−	0.292805i
$735$	6.20118	+	6.92564i	0.228734	+	0.255456i
$736$	−1.43845	+	1.04509i	−0.0530219	+	0.0385226i
$737$	3.13775	−	4.31874i	0.115581	−	0.159083i
$738$	−3.43210	+	4.72388i	−0.126337	+	0.173888i
$739$	−26.2456	+	19.0685i	−0.965459	+	0.701447i	−0.954412	−	0.298492i	$-0.903516\pi$
$739$	−26.2456	+	19.0685i	−0.965459	+	0.701447i	−0.0110469	+	0.999939i	$0.503516\pi$
$740$	0.839879	+	8.20989i	0.0308746	+	0.301801i
$741$	0.141975	+	0.103151i	0.00521557	+	0.00378933i
$742$	−14.7415	+	4.78979i	−0.541176	+	0.175839i
$743$			9.09256i			0.333574i	0.985993	+	0.166787i	$0.0533392\pi$
$743$			9.09256i			0.333574i	−0.985993	+	0.166787i	$0.946661\pi$
$744$	−7.63120	−	23.4864i	−0.279773	−	0.861054i
$745$	21.1015	+	12.2611i	0.773098	+	0.449212i
$746$	7.36297	−	22.6609i	0.269577	−	0.829674i
$747$	−4.13188	−	1.34253i	−0.151177	−	0.0491205i
$748$	4.75760	+	6.54827i	0.173955	+	0.239429i
$749$	−21.1236			−0.771840
$750$	16.3939	−	5.17631i	0.598622	−	0.189012i
$751$	−49.8861			−1.82037			−0.910185	−	0.414202i	$-0.864061\pi$
$751$	−49.8861			−1.82037			−0.910185	+	0.414202i	$0.864061\pi$
$752$	23.1450	+	31.8563i	0.844011	+	1.16168i
$753$	−22.2145	−	7.21792i	−0.809540	−	0.263036i
$754$	0.760786	−	2.34146i	0.0277062	−	0.0852709i
$755$	−39.4657	−	22.9317i	−1.43630	−	0.834570i
$756$	−0.189875	−	0.584375i	−0.00690568	−	0.0212535i
$757$		−	31.1239i		−	1.13122i	−0.824674	−	0.565608i	$-0.808642\pi$
$757$		−	31.1239i		−	1.13122i	0.824674	−	0.565608i	$-0.191358\pi$
$758$	−39.9138	+	12.9688i	−1.44974	+	0.471048i
$759$	2.10230	+	1.52741i	0.0763087	+	0.0554415i
$760$	−0.431254	−	4.21554i	−0.0156432	−	0.152914i
$761$	−31.6544	+	22.9982i	−1.14747	+	0.833686i	−0.988142	−	0.153540i	$-0.950933\pi$
$761$	−31.6544	+	22.9982i	−1.14747	+	0.833686i	−0.159327	+	0.987226i	$0.550933\pi$
$762$	−10.7990	+	14.8636i	−0.391207	+	0.538450i
$763$	4.24497	−	5.84270i	0.153678	−	0.211520i
$764$	3.70438	−	2.69139i	0.134020	−	0.0973712i
$765$	−11.1259	−	12.4257i	−0.402258	−	0.449253i
$766$	−16.3016	−	11.8438i	−0.589002	−	0.427935i
$767$	−0.853003	+	0.277158i	−0.0308002	+	0.0100076i
$768$		−	8.47377i		−	0.305771i
$769$	−4.43076	−	13.6365i	−0.159777	−	0.491744i	0.838836	−	0.544384i	$-0.183236\pi$
$769$	−4.43076	−	13.6365i	−0.159777	−	0.491744i	−0.998614	+	0.0526398i	$0.983236\pi$
$770$	12.8595	−	11.5144i	0.463426	−	0.414949i
$771$	−1.38557	+	4.26435i	−0.0499001	+	0.153577i
$772$	3.51584	+	1.14237i	0.126538	+	0.0411146i
$773$	2.49807	+	3.43830i	0.0898493	+	0.123667i	0.851575	−	0.524232i	$-0.175648\pi$
$773$	2.49807	+	3.43830i	0.0898493	+	0.123667i	−0.761726	+	0.647899i	$0.775648\pi$
$774$	−8.10849			−0.291454
$775$	33.0538	−	36.3030i	1.18733	−	1.30404i
$776$	23.8274			0.855352
$777$	−10.0361	−	13.8135i	−0.360043	−	0.495557i
$778$	−24.7230	−	8.03298i	−0.886361	−	0.287996i
$779$	−0.884215	+	2.72134i	−0.0316803	+	0.0975020i
$780$	−0.0399735	+	0.185529i	−0.00143128	+	0.00664300i
$781$	4.02506	+	12.3879i	0.144028	+	0.443273i
$782$			10.0097i			0.357946i
$783$	6.53835	−	2.12444i	0.233661	−	0.0759212i
$784$	15.4584	+	11.2312i	0.552084	+	0.401113i
$785$	−3.93127	+	6.76576i	−0.140313	+	0.241480i
$786$	−26.6930	+	19.3936i	−0.952109	+	0.691747i
$787$	15.9464	−	21.9483i	0.568428	−	0.782374i	−0.423940	−	0.905690i	$-0.639353\pi$
$787$	15.9464	−	21.9483i	0.568428	−	0.782374i	0.992367	+	0.123317i	$0.0393531\pi$
$788$	−0.438498	+	0.603541i	−0.0156208	+	0.0215002i
$789$	6.25006	−	4.54093i	0.222508	−	0.161662i
$790$	−24.7918	−	5.34156i	−0.882051	−	0.190044i
$791$	−11.2225	−	8.15364i	−0.399027	−	0.289910i
$792$	−7.12195	+	2.31406i	−0.253068	+	0.0822267i
$793$		−	1.02389i		−	0.0363595i
$794$	4.94545	+	15.2205i	0.175507	+	0.540156i
$795$	5.40373	+	12.2281i	0.191651	+	0.433687i
$796$	0.402187	−	1.23781i	0.0142552	−	0.0438729i
$797$	12.0000	+	3.89902i	0.425060	+	0.138111i	0.513733	−	0.857950i	$-0.328262\pi$
$797$	12.0000	+	3.89902i	0.425060	+	0.138111i	−0.0886722	+	0.996061i	$0.528262\pi$
$798$	−1.14826	−	1.58045i	−0.0406480	−	0.0559472i
$799$	63.9049			2.26079
$800$	8.85001	−	5.04431i	0.312895	−	0.178343i
$801$	12.1032			0.427646
$802$	0.627976	+	0.864334i	0.0221746	+	0.0305207i
$803$	42.6272	+	13.8504i	1.50428	+	0.488770i
$804$	0.201904	−	0.621398i	0.00712062	−	0.0219150i
$805$	3.27310	−	0.334841i	0.115362	−	0.0118016i
$806$	1.08663	+	3.34430i	0.0382748	+	0.117798i
$807$			10.7394i			0.378044i
$808$	15.6540	−	5.08629i	0.550706	−	0.178935i
$809$	−30.2684	−	21.9913i	−1.06418	−	0.773172i	−0.0893229	−	0.996003i	$-0.528470\pi$
$809$	−30.2684	−	21.9913i	−1.06418	−	0.773172i	−0.974857	+	0.222831i	$0.928470\pi$
$810$	−3.14495	+	1.38978i	−0.110502	+	0.0488320i
$811$	−30.0948	+	21.8651i	−1.05677	+	0.767789i	−0.973488	−	0.228737i	$-0.926540\pi$
$811$	−30.0948	+	21.8651i	−1.05677	+	0.767789i	−0.0832825	+	0.996526i	$0.526540\pi$
$812$	−2.48293	+	3.41747i	−0.0871339	+	0.119930i
$813$	15.1135	−	20.8019i	0.530053	−	0.729555i
$814$	37.5121	−	27.2541i	1.31480	−	0.955257i
$815$	−12.2175	+	5.39905i	−0.427962	+	0.189120i
$816$	−27.7348	−	20.1505i	−0.970912	−	0.705409i
$817$	−3.77903	+	1.22788i	−0.132212	+	0.0429582i
$818$			1.82845i			0.0639302i
$819$	−0.121338	−	0.373439i	−0.00423989	−	0.0130490i
$820$	−3.07841	+	0.314925i	−0.107503	+	0.0109976i
$821$	8.48994	−	26.1294i	0.296301	−	0.911921i	−0.686480	−	0.727148i	$-0.740845\pi$
$821$	8.48994	−	26.1294i	0.296301	−	0.911921i	0.982781	−	0.184772i	$-0.0591548\pi$
$822$	−14.6522	−	4.76080i	−0.511055	−	0.166052i
$823$	13.7698	+	18.9526i	0.479987	+	0.660645i	0.978502	−	0.206236i	$-0.0661214\pi$
$823$	13.7698	+	18.9526i	0.479987	+	0.660645i	−0.498516	+	0.866881i	$0.666121\pi$
$824$	1.76249			0.0613993
$825$	−11.0084	−	10.0231i	−0.383263	−	0.348961i
$826$	9.98420			0.347395
$827$	19.0778	+	26.2583i	0.663399	+	0.913090i	0.999588	−	0.0287047i	$-0.00913823\pi$
$827$	19.0778	+	26.2583i	0.663399	+	0.913090i	−0.336189	+	0.941794i	$0.609138\pi$
$828$	0.302487	+	0.0982841i	0.0105122	+	0.00341561i
$829$	0.0476213	−	0.146563i	0.00165395	−	0.00509035i	−0.950226	−	0.311561i	$-0.899148\pi$
$829$	0.0476213	−	0.146563i	0.00165395	−	0.00509035i	0.951880	+	0.306471i	$0.0991482\pi$
$830$	−6.03793	−	13.6633i	−0.209579	−	0.474259i
$831$	−2.97412	−	9.15340i	−0.103171	−	0.317528i
$832$		−	1.41118i		−	0.0489239i
$833$	29.4922	−	9.58260i	1.02185	−	0.332018i
$834$	−8.17892	−	5.94233i	−0.283213	−	0.205766i
$835$	5.10994	+	1.10097i	0.176837	+	0.0381007i
$836$	0.661522	−	0.480624i	0.0228792	−	0.0166227i
$837$	−5.77163	+	7.94397i	−0.199497	+	0.274584i
$838$	−1.78813	+	2.46115i	−0.0617698	+	0.0850189i
$839$	−28.6568	+	20.8204i	−0.989342	+	0.718799i	−0.959777	−	0.280764i	$-0.909412\pi$
$839$	−28.6568	+	20.8204i	−0.989342	+	0.718799i	−0.0295652	+	0.999563i	$0.509412\pi$
$840$	−4.76348	+	8.19800i	−0.164356	+	0.282858i
$841$	−14.7752	−	10.7348i	−0.509491	−	0.370167i
$842$	−16.2072	+	5.26602i	−0.558535	+	0.181479i
$843$			2.83275i			0.0975651i
$844$	−0.419663	−	1.29159i	−0.0144454	−	0.0444583i
$845$	6.09705	−	28.2982i	0.209745	−	0.973489i
$846$	4.07098	−	12.5292i	0.139963	−	0.430762i
$847$	3.42195	+	1.11186i	0.117580	+	0.0382040i
$848$	16.1516	+	22.2308i	0.554648	+	0.763408i
$849$	23.6634			0.812125
$850$	6.31073	−	56.9994i	0.216456	−	1.95506i
$851$	8.83818			0.302969
$852$	0.937071	+	1.28977i	0.0321035	+	0.0441867i
$853$	34.8150	+	11.3121i	1.19204	+	0.387318i	0.836828	−	0.547467i	$-0.184408\pi$
$853$	34.8150	+	11.3121i	1.19204	+	0.387318i	0.355215	+	0.934785i	$0.384408\pi$
$854$	−3.52213	+	10.8400i	−0.120525	+	0.370938i
$855$	−1.25527	+	1.12397i	−0.0429295	+	0.0384388i
$856$	9.73693	+	29.9672i	0.332801	+	1.02426i
$857$		−	2.04867i		−	0.0699813i	−0.999388	−	0.0349907i	$-0.988860\pi$
$857$		−	2.04867i		−	0.0699813i	0.999388	−	0.0349907i	$-0.0111402\pi$
$858$	1.01411	−	0.329506i	0.0346213	−	0.0112491i
$859$	11.4736	+	8.33605i	0.391474	+	0.284422i	0.766059	−	0.642770i	$-0.222215\pi$
$859$	11.4736	+	8.33605i	0.391474	+	0.284422i	−0.374585	+	0.927192i	$0.622215\pi$
$860$	−2.86653	−	3.20141i	−0.0977477	−	0.109167i
$861$	5.17958	−	3.76318i	0.176519	−	0.128249i
$862$	−9.41209	+	12.9546i	−0.320577	+	0.441237i
$863$	−25.3546	+	34.8976i	−0.863081	+	1.18793i	0.117745	+	0.993044i	$0.462433\pi$
$863$	−25.3546	+	34.8976i	−0.863081	+	1.18793i	−0.980826	+	0.194885i	$0.937567\pi$
$864$	−1.64823	+	1.19751i	−0.0560740	+	0.0407402i
$865$	1.38154	+	13.5047i	0.0469738	+	0.459172i
$866$	12.7689	+	9.27711i	0.433903	+	0.315249i
$867$	−36.7459	+	11.9395i	−1.24796	+	0.405485i
$868$		−	6.03344i		−	0.204788i
$869$	6.78666	+	20.8872i	0.230222	+	0.708550i
$870$	20.4382	+	11.8757i	0.692921	+	0.402625i
$871$	0.129025	−	0.397099i	0.00437185	−	0.0134552i
$872$	−10.2455	−	3.32897i	−0.346957	−	0.112733i
$873$	−5.56883	−	7.66483i	−0.188476	−	0.259415i
$874$	1.01120			0.0342044
$875$	−18.8495	−	0.156840i	−0.637229	−	0.00530214i
$876$	5.48584			0.185350
$877$	3.96567	+	5.45827i	0.133911	+	0.184313i	0.870707	−	0.491803i	$-0.163662\pi$
$877$	3.96567	+	5.45827i	0.133911	+	0.184313i	−0.736795	+	0.676116i	$0.763662\pi$
$878$	36.1385	+	11.7421i	1.21962	+	0.396277i
$879$	7.18080	−	22.1002i	0.242202	−	0.745423i
$880$	−26.4586	−	15.3739i	−0.891918	−	0.518253i
$881$	5.30839	+	16.3375i	0.178844	+	0.550426i	0.999788	−	0.0205829i	$-0.00655221\pi$
$881$	5.30839	+	16.3375i	0.178844	+	0.550426i	−0.820944	+	0.571009i	$0.806552\pi$
$882$		−	6.39269i		−	0.215253i
$883$	−54.0787	+	17.5712i	−1.81989	+	0.591319i	−0.820075	+	0.572257i	$0.806068\pi$
$883$	−54.0787	+	17.5712i	−1.81989	+	0.591319i	−0.999818	+	0.0190624i	$0.993932\pi$
$884$	0.512176	+	0.372118i	0.0172263	+	0.0125157i
$885$	−0.876382	−	8.56671i	−0.0294593	−	0.287967i
$886$	−9.36654	+	6.80519i	−0.314675	+	0.228625i
$887$	21.7067	−	29.8768i	0.728841	−	1.00316i	−0.270342	−	0.962764i	$-0.587137\pi$
$887$	21.7067	−	29.8768i	0.728841	−	1.00316i	0.999184	−	0.0403995i	$-0.0128631\pi$
$888$	−14.9705	+	20.6051i	−0.502378	+	0.691463i
$889$	16.2974	−	11.8408i	0.546597	−	0.397126i
$890$	27.7600	+	31.0031i	0.930516	+	1.03922i
$891$	2.40891	+	1.75017i	0.0807014	+	0.0586330i
$892$	9.09791	−	2.95609i	0.304621	−	0.0989772i
$893$		−	6.45581i		−	0.216036i
$894$	−5.18610	−	15.9612i	−0.173449	−	0.533822i
$895$	19.0301	−	17.0394i	0.636105	−	0.569565i
$896$	−6.97730	+	21.4739i	−0.233095	+	0.717393i
$897$	0.193302	+	0.0628076i	0.00645416	+	0.00209708i
$898$	−28.6174	−	39.3885i	−0.954976	−	1.31441i
$899$	67.5058			2.25145
$900$	−1.66052	−	0.750377i	−0.0553508	−	0.0250126i
$901$	44.5956			1.48570
$902$	10.2193	+	14.0657i	0.340266	+	0.468336i
$903$	8.45555	+	2.74737i	0.281383	+	0.0914269i
$904$	−6.39421	+	19.6793i	−0.212668	+	0.654525i
$905$	−3.69714	+	17.1595i	−0.122897	+	0.570402i
$906$	9.69948	+	29.8519i	0.322244	+	0.991764i
$907$		−	25.7833i		−	0.856120i	−0.903750	−	0.428060i	$-0.859197\pi$
$907$		−	25.7833i		−	0.856120i	0.903750	−	0.428060i	$-0.140803\pi$
$908$	1.55663	−	0.505779i	0.0516585	−	0.0167849i
$909$	−5.29476	−	3.84687i	−0.175616	−	0.127593i
$910$	0.678286	−	1.16734i	0.0224849	−	0.0386968i
$911$	21.8488	−	15.8741i	0.723882	−	0.525931i	−0.163740	−	0.986504i	$-0.552356\pi$
$911$	21.8488	−	15.8741i	0.723882	−	0.525931i	0.887622	+	0.460572i	$0.152356\pi$
$912$	−2.03565	+	2.80183i	−0.0674071	+	0.0927780i
$913$	−7.60364	+	10.4655i	−0.251644	+	0.346358i
$914$	3.67905	−	2.67298i	0.121692	−	0.0884145i
$915$	9.61018	+	2.07058i	0.317703	+	0.0684513i
$916$	2.22289	+	1.61502i	0.0734462	+	0.0533618i
$917$	34.4066	−	11.1794i	1.13621	−	0.369176i
$918$			11.4695i			0.378551i
$919$	8.01412	+	24.6649i	0.264362	+	0.813621i	0.991840	+	0.127490i	$0.0406922\pi$
$919$	8.01412	+	24.6649i	0.264362	+	0.813621i	−0.727478	+	0.686131i	$0.759308\pi$
$920$	−1.98376	−	4.48906i	−0.0654026	−	0.148000i
$921$	6.74062	−	20.7455i	0.222111	−	0.683588i
$922$	−25.7401	−	8.36347i	−0.847705	−	0.275436i
$923$	0.598827	+	0.824214i	0.0197106	+	0.0271293i
$924$	−1.82956			−0.0601882
$925$	−50.3282	−	5.57213i	−1.65478	−	0.183211i
$926$	−40.5055			−1.33109
$927$	−0.411922	−	0.566962i	−0.0135293	−	0.0186215i
$928$	13.3208	+	4.32818i	0.437275	+	0.142079i
$929$	−4.66201	+	14.3482i	−0.152955	+	0.470749i	−0.997948	−	0.0640296i	$-0.979605\pi$
$929$	−4.66201	+	14.3482i	−0.152955	+	0.470749i	0.844993	+	0.534778i	$0.179605\pi$
$930$	−33.5868	+	3.43596i	−1.10135	+	0.112670i
$931$	−0.968057	−	2.97937i	−0.0317268	−	0.0976450i
$932$		−	3.77707i		−	0.123722i
$933$	9.54991	−	3.10295i	0.312650	−	0.101586i
$934$	−9.15470	−	6.65128i	−0.299551	−	0.217637i
$935$	−45.4248	+	20.0737i	−1.48555	+	0.656479i
$936$	−0.473852	+	0.344274i	−0.0154883	+	0.0112529i
$937$	0.385330	−	0.530361i	0.0125882	−	0.0173262i	−0.802677	−	0.596415i	$-0.796591\pi$
$937$	0.385330	−	0.530361i	0.0125882	−	0.0173262i	0.815265	+	0.579088i	$0.196591\pi$
$938$	−2.73199	+	3.76027i	−0.0892028	+	0.122777i
$939$	−4.89752	+	3.55825i	−0.159824	+	0.116119i
$940$	6.38598	−	2.82202i	0.208288	−	0.0920443i
$941$	29.4596	+	21.4036i	0.960354	+	0.697738i	0.953233	−	0.302237i	$-0.0977333\pi$
$941$	29.4596	+	21.4036i	0.960354	+	0.697738i	0.00712112	+	0.999975i	$0.497733\pi$
$942$	5.11763	−	1.66282i	0.166741	−	0.0541776i
$943$			3.31400i			0.107919i
$944$	−5.46963	−	16.8338i	−0.178021	−	0.547893i
$945$	3.75045	−	0.383675i	0.122002	−	0.0124809i
$946$	−7.46079	+	22.9619i	−0.242571	+	0.746557i
$947$	−43.1901	−	14.0333i	−1.40349	−	0.456021i	−0.493171	−	0.869932i	$-0.664162\pi$
$947$	−43.1901	−	14.0333i	−1.40349	−	0.456021i	−0.910317	+	0.413911i	$0.864162\pi$
$948$	1.58000	+	2.17468i	0.0513159	+	0.0706302i
$949$	3.50568			0.113799
$950$	−5.75820	−	0.637524i	−0.186821	−	0.0206840i
$951$	8.49907			0.275601
$952$	18.5905	+	25.5876i	0.602520	+	0.829298i
$953$	−43.9898	−	14.2932i	−1.42497	−	0.463001i	−0.507793	−	0.861479i	$-0.669538\pi$
$953$	−43.9898	−	14.2932i	−1.42497	−	0.463001i	−0.917178	+	0.398478i	$0.869538\pi$
$954$	2.84091	−	8.74342i	0.0919779	−	0.283079i
$955$	11.3557	+	25.6970i	0.367463	+	0.831535i
$956$	−2.09174	−	6.43773i	−0.0676518	−	0.208211i
$957$		−	20.4703i		−	0.661710i
$958$	−41.6306	+	13.5266i	−1.34502	+	0.437024i
$959$	13.6663	+	9.92913i	0.441307	+	0.320628i
$960$	13.2452	+	2.85378i	0.427488	+	0.0921054i
$961$	−52.9246	+	38.4520i	−1.70724	+	1.24039i
$962$	2.13169	−	2.93402i	0.0687285	−	0.0945967i
$963$	7.36423	−	10.1360i	0.237309	−	0.326628i
$964$	−1.60257	+	1.16433i	−0.0516153	+	0.0375007i
$965$	−11.3955	+	19.6117i	−0.366833	+	0.631323i
$966$	−1.83044	−	1.32990i	−0.0588936	−	0.0427887i
$967$	−2.77461	+	0.901526i	−0.0892255	+	0.0289911i	−0.353290	−	0.935514i	$-0.614937\pi$
$967$	−2.77461	+	0.901526i	−0.0892255	+	0.0289911i	0.264064	+	0.964505i	$0.414937\pi$
$968$		−	5.36709i		−	0.172505i
$969$	1.73685	+	5.34548i	0.0557957	+	0.171721i
$970$	6.86122	−	31.8450i	0.220301	−	1.02248i
$971$	−0.376445	+	1.15858i	−0.0120807	+	0.0371806i	−0.956915	−	0.290368i	$-0.906222\pi$
$971$	−0.376445	+	1.15858i	−0.0120807	+	0.0371806i	0.944834	+	0.327548i	$0.106222\pi$
$972$	0.346603	+	0.112618i	0.0111173	+	0.00361222i
$973$	6.51557	+	8.96791i	0.208879	+	0.287498i
$974$	3.66591			0.117463
$975$	−1.06114	−	0.479522i	−0.0339838	−	0.0153570i
$976$	20.2063			0.646787
$977$	26.2575	+	36.1404i	0.840053	+	1.15623i	0.985968	+	0.166936i	$0.0533873\pi$
$977$	26.2575	+	36.1404i	0.840053	+	1.15623i	−0.145915	+	0.989297i	$0.546613\pi$
$978$	8.73584	+	2.83845i	0.279341	+	0.0907635i
$979$	11.1364	−	34.2743i	0.355921	−	1.09541i
$980$	2.52398	−	2.25995i	0.0806255	−	0.0721916i
$981$	1.32367	+	4.07383i	0.0422614	+	0.130067i
$982$		−	39.5538i		−	1.26221i
$983$	34.3627	−	11.1651i	1.09600	−	0.356112i	0.295437	−	0.955362i	$-0.404535\pi$
$983$	34.3627	−	11.1651i	1.09600	−	0.356112i	0.800561	+	0.599251i	$0.204535\pi$
$984$	−7.72619	−	5.61341i	−0.246302	−	0.178949i
$985$	−3.05336	−	3.41007i	−0.0972881	−	0.108654i
$986$	63.7918	−	46.3474i	2.03154	−	1.47600i
$987$	−8.49044	+	11.6861i	−0.270254	+	0.371972i
$988$	0.0375922	−	0.0517412i	0.00119597	−	0.00164611i
$989$	−3.72314	+	2.70502i	−0.118389	+	0.0860145i
$990$	1.04191	+	10.1848i	0.0331141	+	0.323693i
$991$	32.3765	+	23.5229i	1.02847	+	0.747229i	0.968002	−	0.250941i	$-0.0807399\pi$
$991$	32.3765	+	23.5229i	1.02847	+	0.747229i	0.0604705	+	0.998170i	$0.480740\pi$
$992$	−19.0260	+	6.18192i	−0.604076	+	0.196276i
$993$		−	16.2945i		−	0.517089i
$994$	−3.50456	−	10.7859i	−0.111158	−	0.342109i
$995$	6.90460	+	4.01195i	0.218891	+	0.127187i
$996$	−0.489270	+	1.50582i	−0.0155031	+	0.0477137i
$997$	−3.08464	−	1.00226i	−0.0976915	−	0.0317419i	0.259763	−	0.965672i	$-0.416355\pi$
$997$	−3.08464	−	1.00226i	−0.0976915	−	0.0317419i	−0.357455	+	0.933930i	$0.616355\pi$
$998$	27.1136	+	37.3187i	0.858267	+	1.18130i
$999$	10.1272			0.320409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.i.a.64.1	yes	16
3.2	odd	2		225.2.m.b.64.4		16
5.2	odd	4		375.2.g.d.301.4		16
5.3	odd	4		375.2.g.e.301.1		16
5.4	even	2		375.2.i.c.199.4		16
25.3	odd	20		1875.2.a.m.1.8		8
25.4	even	10		1875.2.b.h.1249.3		16
25.9	even	10	inner	75.2.i.a.34.1	✓	16
25.12	odd	20		375.2.g.d.76.4		16
25.13	odd	20		375.2.g.e.76.1		16
25.16	even	5		375.2.i.c.49.4		16
25.21	even	5		1875.2.b.h.1249.14		16
25.22	odd	20		1875.2.a.p.1.1		8
75.47	even	20		5625.2.a.t.1.8		8
75.53	even	20		5625.2.a.bd.1.1		8
75.59	odd	10		225.2.m.b.109.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.34.1	✓	16	25.9	even	10	inner
75.2.i.a.64.1	yes	16	1.1	even	1	trivial
225.2.m.b.64.4		16	3.2	odd	2
225.2.m.b.109.4		16	75.59	odd	10
375.2.g.d.76.4		16	25.12	odd	20
375.2.g.d.301.4		16	5.2	odd	4
375.2.g.e.76.1		16	25.13	odd	20
375.2.g.e.301.1		16	5.3	odd	4
375.2.i.c.49.4		16	25.16	even	5
375.2.i.c.199.4		16	5.4	even	2
1875.2.a.m.1.8		8	25.3	odd	20
1875.2.a.p.1.1		8	25.22	odd	20
1875.2.b.h.1249.3		16	25.4	even	10
1875.2.b.h.1249.14		16	25.21	even	5
5625.2.a.t.1.8		8	75.47	even	20
5625.2.a.bd.1.1		8	75.53	even	20

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.903822 - 1.24400i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.112618 + 0.346603i) q^{4} +(-1.93338 - 1.12340i) q^{5} +(0.475167 + 1.46241i) q^{6} -1.68601i q^{7} +(-2.39187 + 0.777165i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.903822 - 1.24400i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.112618 + 0.346603i) q^{4} +(-1.93338 - 1.12340i) q^{5} +(0.475167 + 1.46241i) q^{6} -1.68601i q^{7} +(-2.39187 + 0.777165i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.349919 + 3.42049i) q^{10} +(2.40891 - 1.75017i) q^{11} +(0.214212 - 0.294838i) q^{12} +(0.136890 - 0.188414i) q^{13} +(-2.09740 + 1.52385i) q^{14} +(1.49161 + 1.66587i) q^{15} +(3.71829 + 2.70150i) q^{16} +(7.09394 - 2.30496i) q^{17} -1.53767i q^{18} +(-0.232853 - 0.716646i) q^{19} +(0.607107 - 0.543601i) q^{20} +(-0.521005 + 1.60349i) q^{21} +(-4.35444 - 1.41484i) q^{22} +(-0.512972 - 0.706046i) q^{23} +2.51496 q^{24} +(2.47594 + 4.34393i) q^{25} -0.358112 q^{26} +(-0.587785 - 0.809017i) q^{27} +(0.584375 + 0.189875i) q^{28} +(-2.12444 + 6.53835i) q^{29} +(0.724197 - 3.36121i) q^{30} +(-3.03433 - 9.33870i) q^{31} -2.03733i q^{32} +(-2.83184 + 0.920120i) q^{33} +(-9.27904 - 6.74162i) q^{34} +(-1.89406 + 3.25970i) q^{35} +(-0.294838 + 0.214212i) q^{36} +(-5.95259 + 8.19304i) q^{37} +(-0.681054 + 0.937390i) q^{38} +(-0.188414 + 0.136890i) q^{39} +(5.49746 + 1.18447i) q^{40} +(-3.07210 - 2.23201i) q^{41} +(2.46564 - 0.801135i) q^{42} -5.27322i q^{43} +(0.335328 + 1.03203i) q^{44} +(-0.903822 - 2.04526i) q^{45} +(-0.414688 + 1.27628i) q^{46} +(8.14814 + 2.64749i) q^{47} +(-2.70150 - 3.71829i) q^{48} +4.15738 q^{49} +(3.16605 - 7.00622i) q^{50} -7.45901 q^{51} +(0.0498883 + 0.0686654i) q^{52} +(5.68614 + 1.84754i) q^{53} +(-0.475167 + 1.46241i) q^{54} +(-6.62348 + 0.677588i) q^{55} +(1.31031 + 4.03270i) q^{56} +0.753527i q^{57} +(10.0538 - 3.26669i) q^{58} +(-3.11564 - 2.26365i) q^{59} +(-0.745375 + 0.329388i) q^{60} +(3.55679 - 2.58416i) q^{61} +(-8.87488 + 12.2152i) q^{62} +(0.991010 - 1.36401i) q^{63} +(4.90214 - 3.56161i) q^{64} +(-0.476326 + 0.210493i) q^{65} +(3.70411 + 2.69119i) q^{66} +(1.70508 - 0.554013i) q^{67} +2.71836i q^{68} +(0.269686 + 0.830007i) q^{69} +(5.76697 - 0.589966i) q^{70} +(-1.35179 + 4.16039i) q^{71} +(-2.39187 - 0.777165i) q^{72} +(8.84783 + 12.1780i) q^{73} +15.5723 q^{74} +(-1.01241 - 4.89643i) q^{75} +0.274615 q^{76} +(-2.95080 - 4.06143i) q^{77} +(0.340585 + 0.110663i) q^{78} +(-2.27926 + 7.01484i) q^{79} +(-4.15402 - 9.40016i) q^{80} +(0.309017 + 0.951057i) q^{81} +5.83904i q^{82} +(-4.13188 + 1.34253i) q^{83} +(-0.497099 - 0.361163i) q^{84} +(-16.3047 - 3.51297i) q^{85} +(-6.55991 + 4.76605i) q^{86} +(4.04092 - 5.56185i) q^{87} +(-4.40161 + 6.05830i) q^{88} +(9.79170 - 7.11409i) q^{89} +(-1.72742 + 2.97291i) q^{90} +(-0.317667 - 0.230798i) q^{91} +(0.302487 - 0.0982841i) q^{92} +9.81929i q^{93} +(-4.07098 - 12.5292i) q^{94} +(-0.354888 + 1.64714i) q^{95} +(-0.629569 + 1.93761i) q^{96} +(-9.01055 - 2.92771i) q^{97} +(-3.75753 - 5.17180i) q^{98} +2.97757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9	\( 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} + 10 q^{17} - 2 q^{19} + 20 q^{20} + 4 q^{21} - 30 q^{22} - 20 q^{23} + 24 q^{24} - 10 q^{25} + 12 q^{26} + 30 q^{28} + 16 q^{29} - 20 q^{30} + 6 q^{31} + 10 q^{33} - 36 q^{34} + 10 q^{35} - 2 q^{36} - 10 q^{37} + 30 q^{38} - 8 q^{39} + 10 q^{40} - 14 q^{41} - 10 q^{42} + 26 q^{44} + 16 q^{46} + 40 q^{47} + 20 q^{50} - 32 q^{51} + 40 q^{52} + 10 q^{53} - 2 q^{54} + 10 q^{55} + 10 q^{58} + 12 q^{59} - 30 q^{60} - 10 q^{62} - 10 q^{63} + 8 q^{64} - 70 q^{65} + 16 q^{66} - 40 q^{67} - 12 q^{69} + 30 q^{70} - 8 q^{71} - 30 q^{72} - 20 q^{73} - 52 q^{74} - 32 q^{76} - 40 q^{77} - 20 q^{79} - 4 q^{81} + 10 q^{83} + 12 q^{84} - 20 q^{85} - 36 q^{86} + 40 q^{87} - 40 q^{88} + 18 q^{89} + 30 q^{90} + 26 q^{91} + 10 q^{92} - 38 q^{94} - 40 q^{95} - 26 q^{96} + 40 q^{97} + 60 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 + 10 * q^17 - 2 * q^19 + 20 * q^20 + 4 * q^21 - 30 * q^22 - 20 * q^23 + 24 * q^24 - 10 * q^25 + 12 * q^26 + 30 * q^28 + 16 * q^29 - 20 * q^30 + 6 * q^31 + 10 * q^33 - 36 * q^34 + 10 * q^35 - 2 * q^36 - 10 * q^37 + 30 * q^38 - 8 * q^39 + 10 * q^40 - 14 * q^41 - 10 * q^42 + 26 * q^44 + 16 * q^46 + 40 * q^47 + 20 * q^50 - 32 * q^51 + 40 * q^52 + 10 * q^53 - 2 * q^54 + 10 * q^55 + 10 * q^58 + 12 * q^59 - 30 * q^60 - 10 * q^62 - 10 * q^63 + 8 * q^64 - 70 * q^65 + 16 * q^66 - 40 * q^67 - 12 * q^69 + 30 * q^70 - 8 * q^71 - 30 * q^72 - 20 * q^73 - 52 * q^74 - 32 * q^76 - 40 * q^77 - 20 * q^79 - 4 * q^81 + 10 * q^83 + 12 * q^84 - 20 * q^85 - 36 * q^86 + 40 * q^87 - 40 * q^88 + 18 * q^89 + 30 * q^90 + 26 * q^91 + 10 * q^92 - 38 * q^94 - 40 * q^95 - 26 * q^96 + 40 * q^97 + 60 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more