LMFDB - Embedded newform 975.2.bc.m.751.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(751,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.751"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,-8,10,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} + 26x^{14} + 269x^{12} + 1420x^{10} + 4080x^{8} + 6272x^{6} + 4672x^{4} + 1308x^{2} + 100 $ x^16 + 26x^14 + 269x^12 + 1420x^10 + 4080x^8 + 6272x^6 + 4672x^4 + 1308*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.5
Root			$0.592086i$ of defining polynomial
Character	$\chi$	$=$	975.751
Dual form			975.2.bc.m.901.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.512762 - 0.296043i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.824717 + 1.42845i) q^{4} +(-0.512762 - 0.296043i) q^{6} +(-1.43536 - 0.828705i) q^{7} +2.16078i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.22336 + 0.706307i) q^{11} +1.64943 q^{12} +(3.60552 + 0.0145731i) q^{13} -0.981329 q^{14} +(-1.00975 - 1.74894i) q^{16} +(1.63925 - 2.83926i) q^{17} +0.592086i q^{18} +(-7.29219 - 4.21015i) q^{19} +1.65741i q^{21} +(-0.418195 + 0.724334i) q^{22} +(-3.29099 - 5.70016i) q^{23} +(1.87129 - 1.08039i) q^{24} +(1.85309 - 1.05992i) q^{26} +1.00000 q^{27} +(2.36753 - 1.36689i) q^{28} +(-0.252903 - 0.438041i) q^{29} -0.791382i q^{31} +(-4.77810 - 2.75864i) q^{32} +(1.22336 + 0.706307i) q^{33} -1.94115i q^{34} +(-0.824717 - 1.42845i) q^{36} +(-4.12017 + 2.37878i) q^{37} -4.98554 q^{38} +(-1.79014 - 3.12976i) q^{39} +(-7.67224 + 4.42957i) q^{41} +(0.490665 + 0.849856i) q^{42} +(1.11596 - 1.93289i) q^{43} -2.33001i q^{44} +(-3.37499 - 1.94855i) q^{46} -3.43727i q^{47} +(-1.00975 + 1.74894i) q^{48} +(-2.12650 - 3.68320i) q^{49} -3.27850 q^{51} +(-2.99435 + 5.13830i) q^{52} -0.422128 q^{53} +(0.512762 - 0.296043i) q^{54} +(1.79065 - 3.10149i) q^{56} +8.42030i q^{57} +(-0.259358 - 0.149740i) q^{58} +(-11.3443 - 6.54963i) q^{59} +(-0.463750 + 0.803239i) q^{61} +(-0.234283 - 0.405790i) q^{62} +(1.43536 - 0.828705i) q^{63} +0.772299 q^{64} +0.836389 q^{66} +(10.7587 - 6.21154i) q^{67} +(2.70384 + 4.68318i) q^{68} +(-3.29099 + 5.70016i) q^{69} +(0.947838 + 0.547235i) q^{71} +(-1.87129 - 1.08039i) q^{72} +11.2130i q^{73} +(-1.40844 + 2.43950i) q^{74} +(12.0280 - 6.94436i) q^{76} +2.34128 q^{77} +(-1.84446 - 1.07486i) q^{78} +9.25299 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-2.62269 + 4.54263i) q^{82} +4.02601i q^{83} +(-2.36753 - 1.36689i) q^{84} -1.32149i q^{86} +(-0.252903 + 0.438041i) q^{87} +(-1.52617 - 2.64341i) q^{88} +(0.517890 - 0.299004i) q^{89} +(-5.16314 - 3.00883i) q^{91} +10.8565 q^{92} +(-0.685357 + 0.395691i) q^{93} +(-1.01758 - 1.76250i) q^{94} +5.51728i q^{96} +(2.73609 + 1.57968i) q^{97} +(-2.18077 - 1.25907i) q^{98} -1.41261i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 10 q^{4} - 6 q^{7} - 8 q^{9} - 6 q^{11} - 20 q^{12} - 4 q^{14} - 14 q^{16} + 10 q^{17} - 2 q^{22} + 12 q^{23} + 26 q^{26} + 16 q^{27} - 24 q^{28} + 12 q^{29} - 30 q^{32} + 6 q^{33} + 10 q^{36}+ \cdots + 24 q^{98}+O(q^{100}) $ 16 * q - 8 * q^3 + 10 * q^4 - 6 * q^7 - 8 * q^9 - 6 * q^11 - 20 * q^12 - 4 * q^14 - 14 * q^16 + 10 * q^17 - 2 * q^22 + 12 * q^23 + 26 * q^26 + 16 * q^27 - 24 * q^28 + 12 * q^29 - 30 * q^32 + 6 * q^33 + 10 * q^36 - 6 * q^37 + 16 * q^38 - 18 * q^41 + 2 * q^42 + 16 * q^43 - 24 * q^46 - 14 * q^48 + 14 * q^49 - 20 * q^51 - 24 * q^52 + 40 * q^53 - 28 * q^56 - 72 * q^58 - 42 * q^59 - 16 * q^61 + 34 * q^62 + 6 * q^63 - 68 * q^64 + 4 * q^66 + 18 * q^67 - 28 * q^68 + 12 * q^69 + 6 * q^71 - 20 * q^74 + 24 * q^76 - 48 * q^77 - 16 * q^78 + 52 * q^79 - 8 * q^81 + 28 * q^82 + 24 * q^84 + 12 * q^87 + 68 * q^88 + 24 * q^89 + 6 * q^91 + 108 * q^92 - 6 * q^93 + 4 * q^94 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	0.512762	−	0.296043i	0.362577	−	0.209334i	−0.307633	−	0.951505i	$-0.599537\pi$
$2$	0.512762	−	0.296043i	0.362577	−	0.209334i	0.670211	+	0.742171i	$0.266204\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.824717	+	1.42845i	−0.412359	+	0.714226i
$5$		0			0
$5$		0			0
$6$	−0.512762	−	0.296043i	−0.209334	−	0.120859i
$7$	−1.43536	−	0.828705i	−0.542515	−	0.313221i	0.203583	−	0.979058i	$-0.434741\pi$
$7$	−1.43536	−	0.828705i	−0.542515	−	0.313221i	−0.746097	+	0.665837i	$0.768075\pi$
$8$			2.16078i			0.763951i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−1.22336	+	0.706307i	−0.368857	+	0.212960i	−0.672959	−	0.739680i	$-0.734977\pi$
$11$	−1.22336	+	0.706307i	−0.368857	+	0.212960i	0.304102	+	0.952639i	$0.401644\pi$
$12$	1.64943			0.476151
$13$	3.60552	+	0.0145731i	0.999992	+	0.00404184i
$13$	3.60552	+	0.0145731i	0.999992	+	0.00404184i
$14$	−0.981329			−0.262271
$15$		0			0
$16$	−1.00975	−	1.74894i	−0.252438	−	0.437235i
$17$	1.63925	−	2.83926i	0.397577	−	0.688623i	−0.595850	−	0.803096i	$-0.703185\pi$
$17$	1.63925	−	2.83926i	0.397577	−	0.688623i	0.993426	+	0.114473i	$0.0365180\pi$
$18$			0.592086i			0.139556i
$19$	−7.29219	−	4.21015i	−1.67294	−	0.965875i	−0.965977	−	0.258628i	$-0.916730\pi$
$19$	−7.29219	−	4.21015i	−1.67294	−	0.965875i	−0.706967	−	0.707247i	$-0.749937\pi$
$20$		0			0
$21$			1.65741i			0.361676i
$22$	−0.418195	+	0.724334i	−0.0891594	+	0.154429i
$23$	−3.29099	−	5.70016i	−0.686219	−	1.18857i	−0.973052	−	0.230585i	$-0.925936\pi$
$23$	−3.29099	−	5.70016i	−0.686219	−	1.18857i	0.286834	−	0.957980i	$-0.407397\pi$
$24$	1.87129	−	1.08039i	0.381975	−	0.220534i
$25$		0			0
$26$	1.85309	−	1.05992i	0.363420	−	0.207867i
$27$	1.00000			0.192450
$28$	2.36753	−	1.36689i	0.447421	−	0.258319i
$29$	−0.252903	−	0.438041i	−0.0469629	−	0.0813422i	0.841588	−	0.540119i	$-0.181621\pi$
$29$	−0.252903	−	0.438041i	−0.0469629	−	0.0813422i	−0.888551	+	0.458777i	$0.848288\pi$
$30$		0			0
$31$		−	0.791382i		−	0.142136i	−0.997471	−	0.0710682i	$-0.977359\pi$
$31$		−	0.791382i		−	0.142136i	0.997471	−	0.0710682i	$-0.0226408\pi$
$32$	−4.77810	−	2.75864i	−0.844657	−	0.487663i
$33$	1.22336	+	0.706307i	0.212960	+	0.122952i
$34$		−	1.94115i		−	0.332905i
$35$		0			0
$36$	−0.824717	−	1.42845i	−0.137453	−	0.238075i
$37$	−4.12017	+	2.37878i	−0.677352	+	0.391069i	−0.798857	−	0.601521i	$-0.794561\pi$
$37$	−4.12017	+	2.37878i	−0.677352	+	0.391069i	0.121504	+	0.992591i	$0.461228\pi$
$38$	−4.98554			−0.808762
$39$	−1.79014	−	3.12976i	−0.286652	−	0.501163i
$40$		0			0
$41$	−7.67224	+	4.42957i	−1.19820	+	0.691782i	−0.960154	−	0.279471i	$-0.909841\pi$
$41$	−7.67224	+	4.42957i	−1.19820	+	0.691782i	−0.238048	+	0.971253i	$0.576508\pi$
$42$	0.490665	+	0.849856i	0.0757112	+	0.131136i
$43$	1.11596	−	1.93289i	0.170182	−	0.294764i	−0.768301	−	0.640088i	$-0.778898\pi$
$43$	1.11596	−	1.93289i	0.170182	−	0.294764i	0.938483	+	0.345325i	$0.112231\pi$
$44$		−	2.33001i		−	0.351263i
$45$		0			0
$46$	−3.37499	−	1.94855i	−0.497614	−	0.287298i
$47$		−	3.43727i		−	0.501377i	−0.968068	−	0.250688i	$-0.919343\pi$
$47$		−	3.43727i		−	0.501377i	0.968068	−	0.250688i	$-0.0806570\pi$
$48$	−1.00975	+	1.74894i	−0.145745	+	0.252438i
$49$	−2.12650	−	3.68320i	−0.303785	−	0.526172i
$50$		0			0
$51$	−3.27850			−0.459082
$52$	−2.99435	+	5.13830i	−0.415242	+	0.712553i
$53$	−0.422128			−0.0579838			−0.0289919	−	0.999580i	$-0.509230\pi$
$53$	−0.422128			−0.0579838			−0.0289919	+	0.999580i	$0.509230\pi$
$54$	0.512762	−	0.296043i	0.0697780	−	0.0402864i
$55$		0			0
$56$	1.79065	−	3.10149i	0.239285	−	0.414454i
$57$			8.42030i			1.11530i
$58$	−0.259358	−	0.149740i	−0.0340554	−	0.0196619i
$59$	−11.3443	−	6.54963i	−1.47690	−	0.852689i	−0.477241	−	0.878772i	$-0.658363\pi$
$59$	−11.3443	−	6.54963i	−1.47690	−	0.852689i	−0.999660	+	0.0260834i	$0.991696\pi$
$60$		0			0
$61$	−0.463750	+	0.803239i	−0.0593771	+	0.102844i	−0.894186	−	0.447696i	$-0.852245\pi$
$61$	−0.463750	+	0.803239i	−0.0593771	+	0.102844i	0.834809	+	0.550540i	$0.185578\pi$
$62$	−0.234283	−	0.405790i	−0.0297540	−	0.0515354i
$63$	1.43536	−	0.828705i	0.180838	−	0.104407i
$64$	0.772299			0.0965374
$65$		0			0
$66$	0.836389			0.102952
$67$	10.7587	−	6.21154i	1.31439	−	0.758861i	0.331567	−	0.943432i	$-0.392423\pi$
$67$	10.7587	−	6.21154i	1.31439	−	0.758861i	0.982819	+	0.184571i	$0.0590895\pi$
$68$	2.70384	+	4.68318i	0.327888	+	0.567919i
$69$	−3.29099	+	5.70016i	−0.396188	+	0.686219i
$70$		0			0
$71$	0.947838	+	0.547235i	0.112488	+	0.0649448i	0.555188	−	0.831725i	$-0.312646\pi$
$71$	0.947838	+	0.547235i	0.112488	+	0.0649448i	−0.442701	+	0.896670i	$0.645980\pi$
$72$	−1.87129	−	1.08039i	−0.220534	−	0.127325i
$73$			11.2130i			1.31239i	0.754593	+	0.656193i	$0.227834\pi$
$73$			11.2130i			1.31239i	−0.754593	+	0.656193i	$0.772166\pi$
$74$	−1.40844	+	2.43950i	−0.163728	+	0.283586i
$75$		0			0
$76$	12.0280	−	6.94436i	1.37971	−	0.796573i
$77$	2.34128			0.266814
$78$	−1.84446	−	1.07486i	−0.208844	−	0.121704i
$79$	9.25299			1.04104			0.520522	−	0.853849i	$-0.325738\pi$
$79$	9.25299			1.04104			0.520522	+	0.853849i	$0.325738\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.62269	+	4.54263i	−0.289627	+	0.501649i
$83$			4.02601i			0.441912i	0.975284	+	0.220956i	$0.0709178\pi$
$83$			4.02601i			0.441912i	−0.975284	+	0.220956i	$0.929082\pi$
$84$	−2.36753	−	1.36689i	−0.258319	−	0.149140i
$85$		0			0
$86$		−	1.32149i		−	0.142499i
$87$	−0.252903	+	0.438041i	−0.0271141	+	0.0469629i
$88$	−1.52617	−	2.64341i	−0.162691	−	0.281789i
$89$	0.517890	−	0.299004i	0.0548962	−	0.0316943i	−0.472301	−	0.881437i	$-0.656576\pi$
$89$	0.517890	−	0.299004i	0.0548962	−	0.0316943i	0.527197	+	0.849743i	$0.323243\pi$
$90$		0			0
$91$	−5.16314	−	3.00883i	−0.541244	−	0.315411i
$92$	10.8565			1.13187
$93$	−0.685357	+	0.395691i	−0.0710682	+	0.0410312i
$94$	−1.01758	−	1.76250i	−0.104955	−	0.181788i
$95$		0			0
$96$			5.51728i			0.563105i
$97$	2.73609	+	1.57968i	0.277808	+	0.160392i	0.632431	−	0.774617i	$-0.282057\pi$
$97$	2.73609	+	1.57968i	0.277808	+	0.160392i	−0.354623	+	0.935009i	$0.615391\pi$
$98$	−2.18077	−	1.25907i	−0.220291	−	0.127185i
$99$		−	1.41261i		−	0.141973i
$100$		0			0
$101$	−4.47142	−	7.74473i	−0.444923	−	0.770629i	0.553124	−	0.833099i	$-0.313436\pi$
$101$	−4.47142	−	7.74473i	−0.444923	−	0.770629i	−0.998047	+	0.0624697i	$0.980102\pi$
$102$	−1.68109	+	0.970577i	−0.166453	+	0.0961015i
$103$	−15.0296			−1.48091			−0.740457	−	0.672103i	$-0.765391\pi$
$103$	−15.0296			−1.48091			−0.740457	+	0.672103i	$0.765391\pi$
$104$	−0.0314892	+	7.79074i	−0.00308777	+	0.763945i
$105$		0			0
$106$	−0.216451	+	0.124968i	−0.0210236	+	0.0121380i
$107$	−9.44308	−	16.3559i	−0.912897	−	1.58118i	−0.809951	−	0.586498i	$-0.800506\pi$
$107$	−9.44308	−	16.3559i	−0.912897	−	1.58118i	−0.102946	−	0.994687i	$-0.532827\pi$
$108$	−0.824717	+	1.42845i	−0.0793584	+	0.137453i
$109$			6.71317i			0.643005i	0.946909	+	0.321502i	$0.104188\pi$
$109$			6.71317i			0.643005i	−0.946909	+	0.321502i	$0.895812\pi$
$110$		0			0
$111$	4.12017	+	2.37878i	0.391069	+	0.225784i
$112$			3.34714i			0.316275i
$113$	9.80892	−	16.9895i	0.922745	−	1.59824i	0.127598	−	0.991826i	$-0.459273\pi$
$113$	9.80892	−	16.9895i	0.922745	−	1.59824i	0.795148	−	0.606416i	$-0.207393\pi$
$114$	2.49277	+	4.31761i	0.233469	+	0.404381i
$115$		0			0
$116$	0.834294			0.0774623
$117$	−1.81538	+	3.11519i	−0.167832	+	0.287999i
$118$	−7.75589			−0.713987
$119$	−4.70582	+	2.71691i	−0.431382	+	0.249059i
$120$		0			0
$121$	−4.50226	+	7.79814i	−0.409296	+	0.708922i
$122$			0.549160i			0.0497186i
$123$	7.67224	+	4.42957i	0.691782	+	0.399401i
$124$	1.13045	+	0.652666i	0.101518	+	0.0586112i
$125$		0			0
$126$	0.490665	−	0.849856i	0.0437119	−	0.0757112i
$127$	8.22136	+	14.2398i	0.729527	+	1.26358i	0.957083	+	0.289813i	$0.0935932\pi$
$127$	8.22136	+	14.2398i	0.729527	+	1.26358i	−0.227556	+	0.973765i	$0.573073\pi$
$128$	9.95221	−	5.74591i	0.879659	−	0.507872i
$129$	−2.23191			−0.196509
$130$		0			0
$131$	6.11561			0.534323			0.267162	−	0.963652i	$-0.413914\pi$
$131$	6.11561			0.534323			0.267162	+	0.963652i	$0.413914\pi$
$132$	−2.01785	+	1.16501i	−0.175631	+	0.101401i
$133$	6.97794	+	12.0861i	0.605064	+	1.04800i
$134$	3.67777	−	6.37008i	0.317711	−	0.550291i
$135$		0			0
$136$	6.13502	+	3.54206i	0.526074	+	0.303729i
$137$	−11.2142	−	6.47453i	−0.958095	−	0.553156i	−0.0625088	−	0.998044i	$-0.519910\pi$
$137$	−11.2142	−	6.47453i	−0.958095	−	0.553156i	−0.895586	+	0.444888i	$0.853243\pi$
$138$			3.89710i			0.331743i
$139$	−5.62458	+	9.74205i	−0.477070	+	0.826310i	−0.999655	−	0.0262776i	$-0.991635\pi$
$139$	−5.62458	+	9.74205i	−0.477070	+	0.826310i	0.522584	+	0.852588i	$0.324968\pi$
$140$		0			0
$141$	−2.97676	+	1.71863i	−0.250688	+	0.144735i
$142$	0.648020			0.0543806
$143$	−4.42114	+	2.52878i	−0.369715	+	0.211467i
$144$	2.01950			0.168292
$145$		0			0
$146$	3.31954	+	5.74961i	0.274727	+	0.475841i
$147$	−2.12650	+	3.68320i	−0.175391	+	0.303785i
$148$		−	7.84729i		−	0.645043i
$149$	17.0840	+	9.86345i	1.39958	+	0.808045i	0.994348	−	0.106171i	$-0.0338590\pi$
$149$	17.0840	+	9.86345i	1.39958	+	0.808045i	0.405228	+	0.914216i	$0.367192\pi$
$150$		0			0
$151$			3.42805i			0.278971i	0.990224	+	0.139485i	$0.0445448\pi$
$151$			3.42805i			0.278971i	−0.990224	+	0.139485i	$0.955455\pi$
$152$	9.09720	−	15.7568i	0.737881	−	1.27805i
$153$	1.63925	+	2.83926i	0.132526	+	0.229541i
$154$	1.20052	−	0.693120i	0.0967405	−	0.0558532i
$155$		0			0
$156$	5.94707	+	0.0240373i	0.476147	+	0.00192453i
$157$	3.96627			0.316543			0.158271	−	0.987396i	$-0.449408\pi$
$157$	3.96627			0.316543			0.158271	+	0.987396i	$0.449408\pi$
$158$	4.74458	−	2.73928i	0.377459	−	0.217926i
$159$	0.211064	+	0.365574i	0.0167385	+	0.0289919i
$160$		0			0
$161$			10.9090i			0.859752i
$162$	−0.512762	−	0.296043i	−0.0402864	−	0.0232593i
$163$	1.72740	+	0.997316i	0.135301	+	0.0781158i	0.566122	−	0.824321i	$-0.308443\pi$
$163$	1.72740	+	0.997316i	0.135301	+	0.0781158i	−0.430822	+	0.902437i	$0.641776\pi$
$164$		−	14.6126i		−	1.14105i
$165$		0			0
$166$	1.19187	+	2.06439i	0.0925073	+	0.160227i
$167$	−9.94672	+	5.74274i	−0.769701	+	0.444387i	−0.832768	−	0.553622i	$-0.813245\pi$
$167$	−9.94672	+	5.74274i	−0.769701	+	0.444387i	0.0630672	+	0.998009i	$0.479912\pi$
$168$	−3.58130			−0.276303
$169$	12.9996	+	0.105087i	0.999967	+	0.00808362i
$170$		0			0
$171$	7.29219	−	4.21015i	0.557648	−	0.321958i
$172$	1.84070	+	3.18818i	0.140352	+	0.243097i
$173$	6.33521	−	10.9729i	0.481657	−	0.834254i	−0.518122	−	0.855307i	$-0.673369\pi$
$173$	6.33521	−	10.9729i	0.481657	−	0.834254i	0.999778	+	0.0210530i	$0.00670186\pi$
$174$			0.299481i			0.0227036i
$175$		0			0
$176$	2.47058	+	1.42639i	0.186227	+	0.107518i
$177$			13.0993i			0.984601i
$178$	0.177036	−	0.306635i	0.0132694	−	0.0229833i
$179$	4.28745	+	7.42609i	0.320459	+	0.555052i	0.980583	−	0.196105i	$-0.0628294\pi$
$179$	4.28745	+	7.42609i	0.320459	+	0.555052i	−0.660124	+	0.751157i	$0.729496\pi$
$180$		0			0
$181$	−22.9517			−1.70599			−0.852994	−	0.521921i	$-0.825215\pi$
$181$	−22.9517			−1.70599			−0.852994	+	0.521921i	$0.825215\pi$
$182$	−3.53820	−	0.0143010i	−0.262269	−	0.00106006i
$183$	0.927500			0.0685628
$184$	12.3168	−	7.11110i	0.908005	−	0.524237i
$185$		0			0
$186$	−0.234283	+	0.405790i	−0.0171785	+	0.0297540i
$187$			4.63126i			0.338671i
$188$	4.90997	+	2.83477i	0.358096	+	0.206747i
$189$	−1.43536	−	0.828705i	−0.104407	−	0.0602794i
$190$		0			0
$191$	−2.14865	+	3.72158i	−0.155471	+	0.269284i	−0.933230	−	0.359278i	$-0.883023\pi$
$191$	−2.14865	+	3.72158i	−0.155471	+	0.269284i	0.777759	+	0.628562i	$0.216356\pi$
$192$	−0.386149	−	0.668830i	−0.0278679	−	0.0482687i
$193$	−5.48344	+	3.16587i	−0.394707	+	0.227884i	−0.684198	−	0.729297i	$-0.739847\pi$
$193$	−5.48344	+	3.16587i	−0.394707	+	0.227884i	0.289491	+	0.957181i	$0.406514\pi$
$194$	1.87062			0.134302
$195$		0			0
$196$	7.01503			0.501074
$197$	19.2617	−	11.1207i	1.37234	−	0.792320i	0.381116	−	0.924527i	$-0.375540\pi$
$197$	19.2617	−	11.1207i	1.37234	−	0.792320i	0.991222	+	0.132207i	$0.0422065\pi$
$198$	−0.418195	−	0.724334i	−0.0297198	−	0.0514762i
$199$	2.19713	−	3.80554i	0.155750	−	0.269768i	−0.777582	−	0.628782i	$-0.783554\pi$
$199$	2.19713	−	3.80554i	0.155750	−	0.269768i	0.933332	+	0.359014i	$0.116887\pi$
$200$		0			0
$201$	−10.7587	−	6.21154i	−0.758861	−	0.438129i
$202$	−4.58555	−	2.64747i	−0.322638	−	0.186275i
$203$			0.838328i			0.0588391i
$204$	2.70384	−	4.68318i	0.189306	−	0.327888i
$205$		0			0
$206$	−7.70662	+	4.44942i	−0.536946	+	0.310006i
$207$	6.58198			0.457479
$208$	−3.61519	−	6.32055i	−0.250668	−	0.438251i
$209$	11.8946			0.822769
$210$		0			0
$211$	3.35237	+	5.80648i	0.230787	+	0.399734i	0.958040	−	0.286635i	$-0.0925367\pi$
$211$	3.35237	+	5.80648i	0.230787	+	0.399734i	−0.727253	+	0.686369i	$0.759203\pi$
$212$	0.348136	−	0.602990i	0.0239101	−	0.0414135i
$213$		−	1.09447i		−	0.0749918i
$214$	−9.68410	−	5.59112i	−0.661991	−	0.382201i
$215$		0			0
$216$			2.16078i			0.147022i
$217$	−0.655822	+	1.13592i	−0.0445201	+	0.0771111i
$218$	1.98739	+	3.44225i	0.134603	+	0.233139i
$219$	9.71077	−	5.60652i	0.656193	−	0.378853i
$220$		0			0
$221$	5.95173	−	10.2131i	0.400357	−	0.687010i
$222$	2.81689			0.189057
$223$	11.7532	−	6.78573i	0.787055	−	0.454406i	−0.0518698	−	0.998654i	$-0.516518\pi$
$223$	11.7532	−	6.78573i	0.787055	−	0.454406i	0.838925	+	0.544248i	$0.183185\pi$
$224$	4.57219	+	7.91927i	0.305493	+	0.529129i
$225$		0			0
$226$		−	11.6154i		−	0.772648i
$227$	−0.257216	−	0.148503i	−0.0170720	−	0.00985652i	0.491440	−	0.870912i	$-0.336471\pi$
$227$	−0.257216	−	0.148503i	−0.0170720	−	0.00985652i	−0.508512	+	0.861055i	$0.669804\pi$
$228$	−12.0280	−	6.94436i	−0.796573	−	0.459902i
$229$			14.3158i			0.946014i	0.881059	+	0.473007i	$0.156832\pi$
$229$			14.3158i			0.946014i	−0.881059	+	0.473007i	$0.843168\pi$
$230$		0			0
$231$	−1.17064	−	2.02761i	−0.0770225	−	0.133407i
$232$	0.946510	−	0.546468i	0.0621414	−	0.0358774i
$233$	−12.9800			−0.850345			−0.425173	−	0.905112i	$-0.639787\pi$
$233$	−12.9800			−0.850345			−0.425173	+	0.905112i	$0.639787\pi$
$234$	−0.00862852	+	2.13478i	−0.000564064	+	0.139555i
$235$		0			0
$236$	18.7117	−	10.8032i	1.21803	−	0.703227i
$237$	−4.62650	−	8.01333i	−0.300523	−	0.520522i
$238$	−1.60864	+	2.78625i	−0.104273	+	0.180606i
$239$			13.6665i			0.884015i	0.897011	+	0.442007i	$0.145734\pi$
$239$			13.6665i			0.884015i	−0.897011	+	0.442007i	$0.854266\pi$
$240$		0			0
$241$	10.5045	+	6.06478i	0.676655	+	0.390667i	0.798594	−	0.601871i	$-0.205578\pi$
$241$	10.5045	+	6.06478i	0.676655	+	0.390667i	−0.121939	+	0.992538i	$0.538911\pi$
$242$			5.33145i			0.342719i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−0.764925	−	1.32489i	−0.0489693	−	0.0848173i
$245$		0			0
$246$	5.24537			0.334433
$247$	−26.2308	−	15.2861i	−1.66903	−	0.972628i
$248$	1.71000			0.108585
$249$	3.48663	−	2.01301i	0.220956	−	0.127569i
$250$		0			0
$251$	−6.88951	+	11.9330i	−0.434862	+	0.753203i	−0.997284	−	0.0736468i	$-0.976536\pi$
$251$	−6.88951	+	11.9330i	−0.434862	+	0.753203i	0.562422	+	0.826850i	$0.309870\pi$
$252$			2.73379i			0.172212i
$253$	8.05213	+	4.64890i	0.506233	+	0.292274i
$254$	8.43119	+	4.86775i	0.529020	+	0.305430i
$255$		0			0
$256$	2.62977	−	4.55490i	0.164361	−	0.284681i
$257$	−2.80002	−	4.84978i	−0.174661	−	0.302521i	0.765383	−	0.643575i	$-0.222550\pi$
$257$	−2.80002	−	4.84978i	−0.174661	−	0.302521i	−0.940044	+	0.341054i	$0.889216\pi$
$258$	−1.14444	+	0.660743i	−0.0712497	+	0.0411360i
$259$	7.88523			0.489965
$260$		0			0
$261$	0.505806			0.0313086
$262$	3.13585	−	1.81048i	0.193733	−	0.111852i
$263$	−4.49001	−	7.77693i	−0.276866	−	0.479546i	0.693738	−	0.720227i	$-0.255962\pi$
$263$	−4.49001	−	7.77693i	−0.276866	−	0.479546i	−0.970604	+	0.240681i	$0.922629\pi$
$264$	−1.52617	+	2.64341i	−0.0939295	+	0.162691i
$265$		0			0
$266$	7.15604	+	4.13154i	0.438765	+	0.253321i
$267$	−0.517890	−	0.299004i	−0.0316943	−	0.0182987i
$268$			20.4911i			1.25169i
$269$	−2.03862	+	3.53099i	−0.124297	+	0.215288i	−0.921458	−	0.388478i	$-0.873001\pi$
$269$	−2.03862	+	3.53099i	−0.124297	+	0.215288i	0.797161	+	0.603767i	$0.206334\pi$
$270$		0			0
$271$	17.1435	−	9.89780i	1.04139	−	0.601249i	0.121166	−	0.992632i	$-0.461337\pi$
$271$	17.1435	−	9.89780i	1.04139	−	0.601249i	0.920228	+	0.391384i	$0.128003\pi$
$272$	−6.62093			−0.401453
$273$	−0.0241536	+	5.97583i	−0.00146184	+	0.361673i
$274$	−7.66696			−0.463178
$275$		0			0
$276$	−5.42827	−	9.40204i	−0.326743	−	0.565936i
$277$	7.26380	−	12.5813i	0.436439	−	0.755935i	−0.560972	−	0.827834i	$-0.689573\pi$
$277$	7.26380	−	12.5813i	0.436439	−	0.755935i	0.997412	+	0.0718991i	$0.0229060\pi$
$278$			6.66047i			0.399468i
$279$	0.685357	+	0.395691i	0.0410312	+	0.0236894i
$280$		0			0
$281$		−	11.7874i		−	0.703176i	−0.936155	−	0.351588i	$-0.885642\pi$
$281$		−	11.7874i		−	0.703176i	0.936155	−	0.351588i	$-0.114358\pi$
$282$	−1.01758	+	1.76250i	−0.0605959	+	0.104955i
$283$	−11.5509	−	20.0067i	−0.686630	−	1.18928i	−0.972922	−	0.231135i	$-0.925756\pi$
$283$	−11.5509	−	20.0067i	−0.686630	−	1.18928i	0.286292	−	0.958142i	$-0.407577\pi$
$284$	−1.56340	+	0.902628i	−0.0927705	+	0.0535611i
$285$		0			0
$286$	−1.51837	+	2.60551i	−0.0897828	+	0.154067i
$287$	14.6832			0.866723
$288$	4.77810	−	2.75864i	0.281552	−	0.162554i
$289$	3.12572	+	5.41390i	0.183866	+	0.318465i
$290$		0			0
$291$		−	3.15936i		−	0.185205i
$292$	−16.0173	−	9.24758i	−0.937340	−	0.541174i
$293$	−8.30075	−	4.79244i	−0.484935	−	0.279977i	0.237536	−	0.971379i	$-0.423660\pi$
$293$	−8.30075	−	4.79244i	−0.484935	−	0.279977i	−0.722471	+	0.691401i	$0.756994\pi$
$294$			2.51814i			0.146861i
$295$		0			0
$296$	−5.14002	−	8.90278i	−0.298758	−	0.517464i
$297$	−1.22336	+	0.706307i	−0.0709865	+	0.0409841i
$298$	11.6800			0.676606
$299$	−11.7827	−	20.6000i	−0.681409	−	1.19133i
$300$		0			0
$301$	−3.20360	+	1.84960i	−0.184652	+	0.106609i
$302$	1.01485	+	1.75777i	0.0583980	+	0.101148i
$303$	−4.47142	+	7.74473i	−0.256876	+	0.444923i
$304$			17.0048i			0.975292i
$305$		0			0
$306$	1.68109	+	0.970577i	0.0961015	+	0.0554842i
$307$			25.2144i			1.43906i	0.694461	+	0.719530i	$0.255643\pi$
$307$			25.2144i			1.43906i	−0.694461	+	0.719530i	$0.744357\pi$
$308$	−1.93089	+	3.34441i	−0.110023	+	0.190565i
$309$	7.51482	+	13.0161i	0.427503	+	0.740457i
$310$		0			0
$311$	1.70269			0.0965509			0.0482755	−	0.998834i	$-0.484627\pi$
$311$	1.70269			0.0965509			0.0482755	+	0.998834i	$0.484627\pi$
$312$	6.76272	−	3.86810i	0.382864	−	0.218988i
$313$	25.1073			1.41915			0.709573	−	0.704632i	$-0.248888\pi$
$313$	25.1073			1.41915			0.709573	+	0.704632i	$0.248888\pi$
$314$	2.03375	−	1.17419i	0.114771	−	0.0662632i
$315$		0			0
$316$	−7.63110	+	13.2175i	−0.429283	+	0.743540i
$317$		−	1.89871i		−	0.106642i	−0.998577	−	0.0533210i	$-0.983019\pi$
$317$		−	1.89871i		−	0.106642i	0.998577	−	0.0533210i	$-0.0169807\pi$
$318$	0.216451	+	0.124968i	0.0121380	+	0.00700787i
$319$	0.618783	+	0.357255i	0.0346452	+	0.0200024i
$320$		0			0
$321$	−9.44308	+	16.3559i	−0.527061	+	0.912897i
$322$	3.22954	+	5.59373i	0.179975	+	0.311727i
$323$	−23.9075	+	13.8030i	−1.33025	+	0.768018i
$324$	1.64943			0.0916352
$325$		0			0
$326$	1.18099			0.0654092
$327$	5.81377	−	3.35658i	0.321502	−	0.185620i
$328$	−9.57132	−	16.5780i	−0.528488	−	0.915368i
$329$	−2.84848	+	4.93371i	−0.157042	+	0.272004i
$330$		0			0
$331$	−17.5641	−	10.1406i	−0.965410	−	0.557380i	−0.0675763	−	0.997714i	$-0.521527\pi$
$331$	−17.5641	−	10.1406i	−0.965410	−	0.557380i	−0.897834	+	0.440334i	$0.854860\pi$
$332$	−5.75097	−	3.32032i	−0.315625	−	0.182226i
$333$		−	4.75757i		−	0.260713i
$334$	−3.40020	+	5.88932i	−0.186051	+	0.322249i
$335$		0			0
$336$	2.89871	−	1.67357i	0.158137	−	0.0913007i
$337$	−16.8233			−0.916421			−0.458211	−	0.888844i	$-0.651509\pi$
$337$	−16.8233			−0.916421			−0.458211	+	0.888844i	$0.651509\pi$
$338$	6.69679	−	3.79455i	0.364258	−	0.206396i
$339$	−19.6178			−1.06549
$340$		0			0
$341$	0.558959	+	0.968145i	0.0302693	+	0.0524280i
$342$	2.49277	−	4.31761i	0.134794	−	0.233469i
$343$			18.6508i			1.00705i
$344$	4.17656	+	2.41134i	0.225185	+	0.130011i
$345$		0			0
$346$		−	7.50197i		−	0.403309i
$347$	−4.07853	+	7.06423i	−0.218947	+	0.379228i	−0.954486	−	0.298255i	$-0.903596\pi$
$347$	−4.07853	+	7.06423i	−0.218947	+	0.379228i	0.735539	+	0.677482i	$0.236929\pi$
$348$	−0.417147	−	0.722520i	−0.0223614	−	0.0387311i
$349$	−12.7740	+	7.37508i	−0.683777	+	0.394779i	−0.801277	−	0.598294i	$-0.795845\pi$
$349$	−12.7740	+	7.37508i	−0.683777	+	0.394779i	0.117500	+	0.993073i	$0.462512\pi$
$350$		0			0
$351$	3.60552	+	0.0145731i	0.192449	+	0.000777853i
$352$	7.79378			0.415410
$353$	−13.5328	+	7.81315i	−0.720277	+	0.415852i	−0.814854	−	0.579666i	$-0.803183\pi$
$353$	−13.5328	+	7.81315i	−0.720277	+	0.415852i	0.0945779	+	0.995517i	$0.469850\pi$
$354$	3.87794	+	6.71680i	0.206110	+	0.356994i
$355$		0			0
$356$			0.986374i			0.0522777i
$357$	4.70582	+	2.71691i	0.249059	+	0.143794i
$358$	4.39688	+	2.53854i	0.232382	+	0.134166i
$359$		−	23.5802i		−	1.24452i	−0.782812	−	0.622258i	$-0.786215\pi$
$359$		−	23.5802i		−	1.24452i	0.782812	−	0.622258i	$-0.213785\pi$
$360$		0			0
$361$	25.9507	+	44.9480i	1.36583	+	2.36568i
$362$	−11.7688	+	6.79469i	−0.618552	+	0.357121i
$363$	9.00452			0.472615
$364$	8.55610	−	4.89386i	0.448461	−	0.256508i
$365$		0			0
$366$	0.475586	−	0.274580i	0.0248593	−	0.0143525i
$367$	7.20758	+	12.4839i	0.376233	+	0.651654i	0.990511	−	0.137435i	$-0.0438859\pi$
$367$	7.20758	+	12.4839i	0.376233	+	0.651654i	−0.614278	+	0.789090i	$0.710553\pi$
$368$	−6.64615	+	11.5115i	−0.346455	+	0.600077i
$369$		−	8.85914i		−	0.461188i
$370$		0			0
$371$	0.605906	+	0.349820i	0.0314571	+	0.0181617i
$372$		−	1.30533i		−	0.0676783i
$373$	−5.19893	+	9.00480i	−0.269190	+	0.466251i	−0.968653	−	0.248418i	$-0.920089\pi$
$373$	−5.19893	+	9.00480i	−0.269190	+	0.466251i	0.699463	+	0.714669i	$0.253423\pi$
$374$	1.37105	+	2.37473i	0.0708954	+	0.122794i
$375$		0			0
$376$	7.42717			0.383027
$377$	−0.905464	−	1.58305i	−0.0466338	−	0.0815313i
$378$	−0.981329			−0.0504741
$379$	3.38172	−	1.95244i	0.173708	−	0.100290i	−0.410625	−	0.911804i	$-0.634690\pi$
$379$	3.38172	−	1.95244i	0.173708	−	0.100290i	0.584333	+	0.811514i	$0.301356\pi$
$380$		0			0
$381$	8.22136	−	14.2398i	0.421193	−	0.729527i
$382$			2.54437i			0.130182i
$383$	−28.1639	−	16.2604i	−1.43911	−	0.830869i	−0.441320	−	0.897350i	$-0.645490\pi$
$383$	−28.1639	−	16.2604i	−1.43911	−	0.830869i	−0.997788	+	0.0664805i	$0.978823\pi$
$384$	−9.95221	−	5.74591i	−0.507872	−	0.293220i
$385$		0			0
$386$	−1.87447	+	3.24667i	−0.0954078	+	0.165251i
$387$	1.11596	+	1.93289i	0.0567273	+	0.0982545i
$388$	−4.51300	+	2.60558i	−0.229113	+	0.132278i
$389$	−36.5188			−1.85158			−0.925789	−	0.378042i	$-0.876598\pi$
$389$	−36.5188			−1.85158			−0.925789	+	0.378042i	$0.876598\pi$
$390$		0			0
$391$	−21.5790			−1.09130
$392$	7.95858	−	4.59489i	0.401969	−	0.232077i
$393$	−3.05780	−	5.29627i	−0.154246	−	0.267162i
$394$	6.58443	−	11.4046i	0.331719	−	0.574554i
$395$		0			0
$396$	2.01785	+	1.16501i	0.101401	+	0.0585438i
$397$	−8.93103	−	5.15633i	−0.448235	−	0.258789i	0.258849	−	0.965918i	$-0.416657\pi$
$397$	−8.93103	−	5.15633i	−0.448235	−	0.258789i	−0.707085	+	0.707129i	$0.749990\pi$
$398$		−	2.60178i		−	0.130415i
$399$	6.97794	−	12.0861i	0.349334	−	0.605064i
$400$		0			0
$401$	−18.0710	+	10.4333i	−0.902421	+	0.521013i	−0.877985	−	0.478689i	$-0.841112\pi$
$401$	−18.0710	+	10.4333i	−0.902421	+	0.521013i	−0.0244360	+	0.999701i	$0.507779\pi$
$402$	−7.35554			−0.366861
$403$	0.0115329	−	2.85335i	0.000574493	−	0.142135i
$404$	14.7506			0.733871
$405$		0			0
$406$	0.248181	+	0.429862i	0.0123170	+	0.0213337i
$407$	3.36030	−	5.82021i	0.166564	−	0.288497i
$408$		−	7.08412i		−	0.350716i
$409$	−3.35024	−	1.93426i	−0.165659	−	0.0956432i	0.414878	−	0.909877i	$-0.363824\pi$
$409$	−3.35024	−	1.93426i	−0.165659	−	0.0956432i	−0.580537	+	0.814234i	$0.697157\pi$
$410$		0			0
$411$			12.9491i			0.638730i
$412$	12.3952	−	21.4691i	0.610668	−	1.05771i
$413$	10.8554	+	18.8021i	0.534160	+	0.925192i
$414$	3.37499	−	1.94855i	0.165871	−	0.0957659i
$415$		0			0
$416$	−17.1873	−	10.0160i	−0.842679	−	0.491073i
$417$	11.2492			0.550873
$418$	6.09911	−	3.52132i	0.298317	−	0.172234i
$419$	−10.8008	−	18.7076i	−0.527656	−	0.913926i	−0.999480	−	0.0322339i	$-0.989738\pi$
$419$	−10.8008	−	18.7076i	−0.527656	−	0.913926i	0.471825	−	0.881692i	$-0.343595\pi$
$420$		0			0
$421$			11.8818i			0.579085i	0.957165	+	0.289542i	$0.0935031\pi$
$421$			11.8818i			0.579085i	−0.957165	+	0.289542i	$0.906497\pi$
$422$	3.43793	+	1.98489i	0.167356	+	0.0966230i
$423$	2.97676	+	1.71863i	0.144735	+	0.0835628i
$424$		−	0.912126i		−	0.0442968i
$425$		0			0
$426$	−0.324010	−	0.561202i	−0.0156983	−	0.0271903i
$427$	1.33130	−	0.768624i	0.0644259	−	0.0371963i
$428$	31.1515			1.50576
$429$	4.40056	+	2.56443i	0.212461	+	0.123812i
$430$		0			0
$431$	−9.43023	+	5.44454i	−0.454238	+	0.262254i	−0.709618	−	0.704586i	$-0.751133\pi$
$431$	−9.43023	+	5.44454i	−0.454238	+	0.262254i	0.255380	+	0.966841i	$0.417799\pi$
$432$	−1.00975	−	1.74894i	−0.0485816	−	0.0841459i
$433$	16.0280	−	27.7614i	0.770258	−	1.33413i	−0.167163	−	0.985929i	$-0.553461\pi$
$433$	16.0280	−	27.7614i	0.770258	−	1.33413i	0.937421	−	0.348197i	$-0.113206\pi$
$434$			0.776606i			0.0372783i
$435$		0			0
$436$	−9.58944	−	5.53646i	−0.459251	−	0.265149i
$437$			55.4222i			2.65120i
$438$	3.31954	−	5.74961i	0.158614	−	0.274727i
$439$	−12.5421	−	21.7235i	−0.598600	−	1.03681i	−0.993028	−	0.117879i	$-0.962390\pi$
$439$	−12.5421	−	21.7235i	−0.598600	−	1.03681i	0.394427	−	0.918927i	$-0.370943\pi$
$440$		0			0
$441$	4.25299			0.202524
$442$	0.0282886	−	6.99888i	0.00134555	−	0.332903i
$443$	32.0707			1.52373			0.761863	−	0.647738i	$-0.224285\pi$
$443$	32.0707			1.52373			0.761863	+	0.647738i	$0.224285\pi$
$444$	−6.79595	+	3.92365i	−0.322522	+	0.186208i
$445$		0			0
$446$	4.01774	−	6.95893i	0.190245	−	0.329515i
$447$		−	19.7269i		−	0.933050i
$448$	−1.10853	−	0.640008i	−0.0523729	−	0.0302375i
$449$	20.8143	+	12.0171i	0.982286	+	0.567123i	0.902960	−	0.429725i	$-0.141390\pi$
$449$	20.8143	+	12.0171i	0.982286	+	0.567123i	0.0793266	+	0.996849i	$0.474723\pi$
$450$		0			0
$451$	6.25727	−	10.8379i	0.294643	−	0.510337i
$452$	16.1792	+	28.0231i	0.761004	+	1.31810i
$453$	2.96878	−	1.71402i	0.139485	−	0.0805319i
$454$	−0.175854			−0.00825322
$455$		0			0
$456$	−18.1944			−0.852031
$457$	−3.73789	+	2.15807i	−0.174851	+	0.100950i	−0.584871	−	0.811126i	$-0.698855\pi$
$457$	−3.73789	+	2.15807i	−0.174851	+	0.100950i	0.410020	+	0.912077i	$0.365522\pi$
$458$	4.23809	+	7.34059i	0.198033	+	0.343003i
$459$	1.63925	−	2.83926i	0.0765137	−	0.132526i
$460$		0			0
$461$	−0.533988	−	0.308298i	−0.0248703	−	0.0143589i	0.487513	−	0.873116i	$-0.337904\pi$
$461$	−0.533988	−	0.308298i	−0.0248703	−	0.0143589i	−0.512384	+	0.858757i	$0.671237\pi$
$462$	−1.20052	−	0.693120i	−0.0558532	−	0.0322468i
$463$		−	13.3637i		−	0.621062i	−0.950563	−	0.310531i	$-0.899493\pi$
$463$		−	13.3637i		−	0.621062i	0.950563	−	0.310531i	$-0.100507\pi$
$464$	−0.510738	+	0.884624i	−0.0237104	+	0.0410676i
$465$		0			0
$466$	−6.65562	+	3.84263i	−0.308316	+	0.178006i
$467$	−26.1210			−1.20873			−0.604367	−	0.796706i	$-0.706574\pi$
$467$	−26.1210			−1.20873			−0.604367	+	0.796706i	$0.706574\pi$
$468$	−2.95272	−	5.16233i	−0.136489	−	0.238629i
$469$	−20.5901			−0.950765
$470$		0			0
$471$	−1.98314	−	3.43489i	−0.0913781	−	0.158271i
$472$	14.1523	−	24.5125i	0.651412	−	1.12828i
$473$			3.15283i			0.144967i
$474$	−4.74458	−	2.73928i	−0.217926	−	0.125820i
$475$		0			0
$476$		−	8.96272i		−	0.410806i
$477$	0.211064	−	0.365574i	0.00966397	−	0.0167385i
$478$	4.04588	+	7.00768i	0.185054	+	0.320524i
$479$	7.51515	−	4.33887i	0.343376	−	0.198248i	−0.318388	−	0.947960i	$-0.603141\pi$
$479$	7.51515	−	4.33887i	0.343376	−	0.198248i	0.661764	+	0.749712i	$0.269808\pi$
$480$		0			0
$481$	−14.8900	+	8.51671i	−0.678927	+	0.388329i
$482$	7.18175			0.327120
$483$	9.44750	−	5.45452i	0.429876	−	0.248189i
$484$	−7.42618	−	12.8625i	−0.337554	−	0.584660i
$485$		0			0
$486$			0.592086i			0.0268576i
$487$	24.6955	+	14.2580i	1.11906	+	0.646090i	0.941161	−	0.337959i	$-0.109737\pi$
$487$	24.6955	+	14.2580i	1.11906	+	0.646090i	0.177899	+	0.984049i	$0.443070\pi$
$488$	−1.73562	−	1.00206i	−0.0785679	−	0.0453612i
$489$		−	1.99463i		−	0.0902004i
$490$		0			0
$491$	−16.2907	−	28.2163i	−0.735189	−	1.27338i	−0.954641	−	0.297761i	$-0.903760\pi$
$491$	−16.2907	−	28.2163i	−0.735189	−	1.27338i	0.219452	−	0.975623i	$-0.429573\pi$
$492$	−12.6548	+	7.30628i	−0.570525	+	0.329393i
$493$	−1.65829			−0.0746854
$494$	−17.9755	−	0.0726547i	−0.808755	−	0.00326889i
$495$		0			0
$496$	−1.38408	+	0.799098i	−0.0621470	+	0.0358806i
$497$	−0.906992	−	1.57096i	−0.0406842	−	0.0704670i
$498$	1.19187	−	2.06439i	0.0534091	−	0.0925073i
$499$		−	28.2348i		−	1.26396i	−0.774983	−	0.631982i	$-0.782242\pi$
$499$		−	28.2348i		−	1.26396i	0.774983	−	0.631982i	$-0.217758\pi$
$500$		0			0
$501$	9.94672	+	5.74274i	0.444387	+	0.256567i
$502$			8.15837i			0.364126i
$503$	2.50973	−	4.34699i	0.111903	−	0.193823i	−0.804634	−	0.593771i	$-0.797639\pi$
$503$	2.50973	−	4.34699i	0.111903	−	0.193823i	0.916538	+	0.399948i	$0.130972\pi$
$504$	1.79065	+	3.10149i	0.0797618	+	0.138151i
$505$		0			0
$506$	5.50510			0.244731
$507$	−6.40878	−	11.3105i	−0.284624	−	0.502317i
$508$	−27.1212			−1.20331
$509$	−19.8608	+	11.4666i	−0.880313	+	0.508249i	−0.870762	−	0.491705i	$-0.836374\pi$
$509$	−19.8608	+	11.4666i	−0.880313	+	0.508249i	−0.00955142	+	0.999954i	$0.503040\pi$
$510$		0			0
$511$	9.29229	−	16.0947i	0.411067	−	0.711989i
$512$			19.8695i			0.878118i
$513$	−7.29219	−	4.21015i	−0.321958	−	0.185883i
$514$	−2.87149	−	1.65786i	−0.126656	−	0.0731249i
$515$		0			0
$516$	1.84070	−	3.18818i	0.0810322	−	0.140352i
$517$	2.42777	+	4.20501i	0.106773	+	0.184936i
$518$	4.04325	−	2.33437i	0.177650	−	0.102566i
$519$	−12.6704			−0.556169
$520$		0			0
$521$	42.3619			1.85591			0.927955	−	0.372692i	$-0.121565\pi$
$521$	42.3619			1.85591			0.927955	+	0.372692i	$0.121565\pi$
$522$	0.259358	−	0.149740i	0.0113518	−	0.00655396i
$523$	0.760610	+	1.31741i	0.0332591	+	0.0576065i	0.882176	−	0.470920i	$-0.156078\pi$
$523$	0.760610	+	1.31741i	0.0332591	+	0.0576065i	−0.848917	+	0.528527i	$0.822745\pi$
$524$	−5.04365	+	8.73585i	−0.220333	+	0.381627i
$525$		0			0
$526$	−4.60461	−	2.65847i	−0.200771	−	0.115915i
$527$	−2.24694	−	1.29727i	−0.0978784	−	0.0565101i
$528$		−	2.85278i		−	0.124151i
$529$	−10.1612	+	17.5997i	−0.441792	+	0.765206i
$530$		0			0
$531$	11.3443	−	6.54963i	0.492300	−	0.284230i
$532$	−23.0193			−0.998014
$533$	−27.7270	+	15.8591i	−1.20099	+	0.686934i
$534$	−0.354072			−0.0153222
$535$		0			0
$536$	13.4218	+	23.2472i	0.579732	+	1.00413i
$537$	4.28745	−	7.42609i	0.185017	−	0.320459i
$538$			2.41408i			0.104078i
$539$	5.20294	+	3.00392i	0.224107	+	0.129388i
$540$		0			0
$541$		−	38.8503i		−	1.67030i	−0.550019	−	0.835152i	$-0.685380\pi$
$541$		−	38.8503i		−	1.67030i	0.550019	−	0.835152i	$-0.314620\pi$
$542$	5.86035	−	10.1504i	0.251724	−	0.435998i
$543$	11.4759	+	19.8768i	0.492476	+	0.852994i
$544$	−15.6650	+	9.04420i	−0.671632	+	0.387767i
$545$		0			0
$546$	1.75672	+	3.07132i	0.0751805	+	0.131441i
$547$	25.8936			1.10713			0.553565	−	0.832806i	$-0.313267\pi$
$547$	25.8936			1.10713			0.553565	+	0.832806i	$0.313267\pi$
$548$	18.4971	−	10.6793i	0.790157	−	0.456198i
$549$	−0.463750	−	0.803239i	−0.0197924	−	0.0342814i
$550$		0			0
$551$			4.25904i			0.181441i
$552$	−12.3168	−	7.11110i	−0.524237	−	0.302668i
$553$	−13.2814	−	7.66800i	−0.564781	−	0.326077i
$554$		−	8.60159i		−	0.365447i
$555$		0			0
$556$	−9.27737	−	16.0689i	−0.393448	−	0.681472i
$557$	1.12489	−	0.649455i	0.0476631	−	0.0275183i	−0.475979	−	0.879457i	$-0.657906\pi$
$557$	1.12489	−	0.649455i	0.0476631	−	0.0275183i	0.523642	+	0.851938i	$0.324573\pi$
$558$	0.468566			0.0198360
$559$	4.05178	−	6.95283i	0.171372	−	0.294073i
$560$		0			0
$561$	4.01079	−	2.31563i	0.169336	−	0.0977659i
$562$	−3.48957	−	6.04411i	−0.147199	−	0.254955i
$563$	−11.0683	+	19.1708i	−0.466473	+	0.807955i	−0.999267	−	0.0382903i	$-0.987809\pi$
$563$	−11.0683	+	19.1708i	−0.466473	+	0.807955i	0.532794	+	0.846245i	$0.321142\pi$
$564$		−	5.66955i		−	0.238731i
$565$		0			0
$566$	−11.8457	−	6.83913i	−0.497913	−	0.287470i
$567$			1.65741i			0.0696047i
$568$	−1.18245	+	2.04807i	−0.0496146	+	0.0859351i
$569$	−18.6123	−	32.2374i	−0.780267	−	1.35146i	−0.931786	−	0.363008i	$-0.881750\pi$
$569$	−18.6123	−	32.2374i	−0.780267	−	1.35146i	0.151519	−	0.988454i	$-0.451584\pi$
$570$		0			0
$571$	−2.36985			−0.0991752			−0.0495876	−	0.998770i	$-0.515791\pi$
$571$	−2.36985			−0.0991752			−0.0495876	+	0.998770i	$0.515791\pi$
$572$	0.0339555	−	8.40092i	0.00141975	−	0.351260i
$573$	4.29731			0.179523
$574$	7.52899	−	4.34686i	0.314254	−	0.181435i
$575$		0			0
$576$	−0.386149	+	0.668830i	−0.0160896	+	0.0278679i
$577$		−	18.2135i		−	0.758238i	−0.925348	−	0.379119i	$-0.876227\pi$
$577$		−	18.2135i		−	0.758238i	0.925348	−	0.379119i	$-0.123773\pi$
$578$	3.20550	+	1.85069i	0.133331	+	0.0769787i
$579$	5.48344	+	3.16587i	0.227884	+	0.131569i
$580$		0			0
$581$	3.33638	−	5.77877i	0.138416	−	0.239744i
$582$	−0.935308	−	1.62000i	−0.0387698	−	0.0671512i
$583$	0.516415	−	0.298152i	0.0213877	−	0.0123482i
$584$	−24.2289			−1.00260
$585$		0			0
$586$	−5.67508			−0.234435
$587$	−22.6115	+	13.0547i	−0.933275	+	0.538827i	−0.887846	−	0.460141i	$-0.847799\pi$
$587$	−22.6115	+	13.0547i	−0.933275	+	0.538827i	−0.0454293	+	0.998968i	$0.514466\pi$
$588$	−3.50752	−	6.07520i	−0.144648	−	0.250537i
$589$	−3.33184	+	5.77091i	−0.137286	+	0.237786i
$590$		0			0
$591$	−19.2617	−	11.1207i	−0.792320	−	0.457446i
$592$	8.32069	+	4.80395i	0.341978	+	0.197441i
$593$		−	24.8984i		−	1.02245i	−0.859446	−	0.511226i	$-0.829191\pi$
$593$		−	24.8984i		−	1.02245i	0.859446	−	0.511226i	$-0.170809\pi$
$594$	−0.418195	+	0.724334i	−0.0171587	+	0.0297198i
$595$		0			0
$596$	−28.1789	+	16.2691i	−1.15425	+	0.666409i
$597$	−4.39426			−0.179845
$598$	−12.1402	−	7.07472i	−0.496449	−	0.289307i
$599$	6.57002			0.268444			0.134222	−	0.990951i	$-0.457147\pi$
$599$	6.57002			0.268444			0.134222	+	0.990951i	$0.457147\pi$
$600$		0			0
$601$	−12.8209	−	22.2064i	−0.522975	−	0.905819i	−0.999643	−	0.0267356i	$-0.991489\pi$
$601$	−12.8209	−	22.2064i	−0.522975	−	0.905819i	0.476668	−	0.879084i	$-0.341845\pi$
$602$	−1.09512	+	1.89681i	−0.0446338	+	0.0773080i
$603$			12.4231i			0.505907i
$604$	−4.89680	−	2.82717i	−0.199248	−	0.115036i
$605$		0			0
$606$			5.29493i			0.215092i
$607$	19.9118	−	34.4882i	0.808195	−	1.39983i	−0.105918	−	0.994375i	$-0.533778\pi$
$607$	19.9118	−	34.4882i	0.808195	−	1.39983i	0.914113	−	0.405460i	$-0.132889\pi$
$608$	23.2286	+	40.2330i	0.942043	+	1.63167i
$609$	0.726013	−	0.419164i	0.0294195	−	0.0169854i
$610$		0			0
$611$	0.0500916	−	12.3931i	0.00202649	−	0.501373i
$612$	−5.40767			−0.218592
$613$	−30.7228	+	17.7378i	−1.24088	+	0.716423i	−0.969274	−	0.245985i	$-0.920889\pi$
$613$	−30.7228	+	17.7378i	−1.24088	+	0.716423i	−0.271608	+	0.962408i	$0.587555\pi$
$614$	7.46454	+	12.9290i	0.301244	+	0.521771i
$615$		0			0
$616$			5.05899i			0.203833i
$617$	−9.67668	−	5.58683i	−0.389568	−	0.224917i	0.292405	−	0.956295i	$-0.405545\pi$
$617$	−9.67668	−	5.58683i	−0.389568	−	0.224917i	−0.681973	+	0.731377i	$0.738878\pi$
$618$	7.70662	+	4.44942i	0.310006	+	0.178982i
$619$			35.2047i			1.41500i	0.706715	+	0.707498i	$0.250176\pi$
$619$			35.2047i			1.41500i	−0.706715	+	0.707498i	$0.749824\pi$
$620$		0			0
$621$	−3.29099	−	5.70016i	−0.132063	−	0.228740i
$622$	0.873076	−	0.504071i	0.0350072	−	0.0202114i
$623$	−0.991143			−0.0397093
$624$	−3.66616	+	6.29112i	−0.146764	+	0.251846i
$625$		0			0
$626$	12.8740	−	7.43283i	0.514550	−	0.297076i
$627$	−5.94732	−	10.3011i	−0.237513	−	0.411385i
$628$	−3.27105	+	5.66563i	−0.130529	+	0.226083i
$629$			15.5977i			0.621920i
$630$		0			0
$631$	4.83806	+	2.79326i	0.192600	+	0.111198i	0.593199	−	0.805056i	$-0.297865\pi$
$631$	4.83806	+	2.79326i	0.192600	+	0.111198i	−0.400599	+	0.916253i	$0.631198\pi$
$632$			19.9937i			0.795306i
$633$	3.35237	−	5.80648i	0.133245	−	0.230787i
$634$	−0.562099	−	0.973584i	−0.0223238	−	0.0386659i
$635$		0			0
$636$	−0.696273			−0.0276090
$637$	−7.61346	−	13.3109i	−0.301656	−	0.527395i
$638$	0.423051			0.0167487
$639$	−0.947838	+	0.547235i	−0.0374959	+	0.0216483i
$640$		0			0
$641$	−10.8579	+	18.8064i	−0.428861	+	0.742809i	−0.996772	−	0.0802807i	$-0.974418\pi$
$641$	−10.8579	+	18.8064i	−0.428861	+	0.742809i	0.567911	+	0.823090i	$0.307752\pi$
$642$			11.1822i			0.441328i
$643$	−13.8777	−	8.01232i	−0.547285	−	0.315975i	0.200741	−	0.979644i	$-0.435665\pi$
$643$	−13.8777	−	8.01232i	−0.547285	−	0.315975i	−0.748026	+	0.663669i	$0.768998\pi$
$644$	−15.5830	−	8.99686i	−0.614057	−	0.354526i
$645$		0			0
$646$	−8.17255	+	14.1553i	−0.321545	+	0.556932i
$647$	5.53356	+	9.58441i	0.217547	+	0.376802i	0.954057	−	0.299624i	$-0.0968612\pi$
$647$	5.53356	+	9.58441i	0.217547	+	0.376802i	−0.736511	+	0.676426i	$0.763528\pi$
$648$	1.87129	−	1.08039i	0.0735112	−	0.0424417i
$649$	18.5042			0.726353
$650$		0			0
$651$	1.31164			0.0514074
$652$	−2.84924	+	1.64501i	−0.111585	+	0.0644234i
$653$	−14.2069	−	24.6070i	−0.555957	−	0.962946i	−0.997828	−	0.0658676i	$-0.979019\pi$
$653$	−14.2069	−	24.6070i	−0.555957	−	0.962946i	0.441871	−	0.897079i	$-0.354315\pi$
$654$	1.98739	−	3.44225i	0.0777130	−	0.134603i
$655$		0			0
$656$	15.4941	+	8.94552i	0.604943	+	0.349264i
$657$	−9.71077	−	5.60652i	−0.378853	−	0.218731i
$658$			3.37309i			0.131497i
$659$	13.1876	−	22.8416i	0.513717	−	0.889783i	−0.486157	−	0.873872i	$-0.661602\pi$
$659$	13.1876	−	22.8416i	0.513717	−	0.889783i	0.999873	−	0.0159116i	$-0.00506504\pi$
$660$		0			0
$661$	25.3928	−	14.6606i	0.987667	−	0.570230i	0.0830907	−	0.996542i	$-0.473521\pi$
$661$	25.3928	−	14.6606i	0.987667	−	0.570230i	0.904576	+	0.426312i	$0.140188\pi$
$662$	−12.0083			−0.466714
$663$	−11.8207	−	0.0477778i	−0.459078	−	0.00185554i
$664$	−8.69933			−0.337599
$665$		0			0
$666$	−1.40844	−	2.43950i	−0.0545761	−	0.0945286i
$667$	−1.66460	+	2.88318i	−0.0644537	+	0.111637i
$668$		−	18.9446i		−	0.732987i
$669$	−11.7532	−	6.78573i	−0.454406	−	0.262352i
$670$		0			0
$671$		−	1.31020i		−	0.0505797i
$672$	4.57219	−	7.91927i	0.176376	−	0.305493i
$673$	20.4358	+	35.3958i	0.787741	+	1.36441i	0.927348	+	0.374200i	$0.122083\pi$
$673$	20.4358	+	35.3958i	0.787741	+	1.36441i	−0.139607	+	0.990207i	$0.544584\pi$
$674$	−8.62632	+	4.98041i	−0.332274	+	0.191838i
$675$		0			0
$676$	−10.8711	+	18.4826i	−0.418119	+	0.710869i
$677$	33.8996			1.30287			0.651435	−	0.758705i	$-0.274167\pi$
$677$	33.8996			1.30287			0.651435	+	0.758705i	$0.274167\pi$
$678$	−10.0593	+	5.80772i	−0.386324	+	0.223044i
$679$	−2.61818	−	4.53482i	−0.100477	−	0.174030i
$680$		0			0
$681$			0.297007i			0.0113813i
$682$	0.573225	+	0.330952i	0.0219499	+	0.0126728i
$683$	9.15608	+	5.28626i	0.350347	+	0.202273i	0.664838	−	0.746987i	$-0.268500\pi$
$683$	9.15608	+	5.28626i	0.350347	+	0.202273i	−0.314491	+	0.949261i	$0.601834\pi$
$684$			13.8887i			0.531049i
$685$		0			0
$686$	5.52145	+	9.56342i	0.210810	+	0.365133i
$687$	12.3978	−	7.15790i	0.473007	−	0.273091i
$688$	−4.50735			−0.171841
$689$	−1.52199	−	0.00615171i	−0.0579833	−	0.000234361i
$690$		0			0
$691$	8.65326	−	4.99596i	0.329186	−	0.190055i	−0.326294	−	0.945268i	$-0.605800\pi$
$691$	8.65326	−	4.99596i	0.329186	−	0.190055i	0.655479	+	0.755213i	$0.272467\pi$
$692$	10.4495	+	18.0991i	0.397231	+	0.688024i
$693$	−1.17064	+	2.02761i	−0.0444689	+	0.0770225i
$694$			4.82968i			0.183332i
$695$		0			0
$696$	−0.946510	−	0.546468i	−0.0358774	−	0.0207138i
$697$			29.0447i			1.10015i
$698$	−4.36668	+	7.56331i	−0.165281	+	0.286276i
$699$	6.48998	+	11.2410i	0.245473	+	0.425173i
$700$		0			0
$701$	30.4957			1.15181			0.575903	−	0.817518i	$-0.304651\pi$
$701$	30.4957			1.15181			0.575903	+	0.817518i	$0.304651\pi$
$702$	1.85309	−	1.05992i	0.0699403	−	0.0400040i
$703$	40.0601			1.51090
$704$	−0.944799	+	0.545480i	−0.0356085	+	0.0205586i
$705$		0			0
$706$	−4.62606	+	8.01256i	−0.174104	+	0.301557i
$707$			14.8220i			0.557437i
$708$	−18.7117	−	10.8032i	−0.703227	−	0.406008i
$709$	9.17071	+	5.29471i	0.344413	+	0.198847i	0.662222	−	0.749308i	$-0.269614\pi$
$709$	9.17071	+	5.29471i	0.344413	+	0.198847i	−0.317809	+	0.948155i	$0.602947\pi$
$710$		0			0
$711$	−4.62650	+	8.01333i	−0.173507	+	0.300523i
$712$	0.646081	+	1.11905i	0.0242129	+	0.0419380i
$713$	−4.51100	+	2.60443i	−0.168938	+	0.0975366i
$714$	3.21729			0.120404
$715$		0			0
$716$	−14.1437			−0.528576
$717$	11.8356	−	6.83327i	0.442007	−	0.255193i
$718$	−6.98076	−	12.0910i	−0.260520	−	0.451233i
$719$	3.68101	−	6.37570i	0.137279	−	0.237774i	−0.789187	−	0.614153i	$-0.789498\pi$
$719$	3.68101	−	6.37570i	0.137279	−	0.237774i	0.926466	+	0.376379i	$0.122831\pi$
$720$		0			0
$721$	21.5729	+	12.4551i	0.803418	+	0.463854i
$722$	26.6131	+	15.3651i	0.990436	+	0.571828i
$723$		−	12.1296i		−	0.451103i
$724$	18.9287	−	32.7854i	0.703478	−	1.21846i
$725$		0			0
$726$	4.61717	−	2.66573i	0.171359	−	0.0989344i
$727$	−30.8420			−1.14387			−0.571934	−	0.820300i	$-0.693807\pi$
$727$	−30.8420			−1.14387			−0.571934	+	0.820300i	$0.693807\pi$
$728$	6.50142	−	11.1564i	0.240959	−	0.413484i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−3.65867	−	6.33700i	−0.135321	−	0.234382i
$732$	−0.764925	+	1.32489i	−0.0282724	+	0.0489693i
$733$		−	30.7552i		−	1.13597i	−0.823039	−	0.567985i	$-0.807723\pi$
$733$		−	30.7552i		−	1.13597i	0.823039	−	0.567985i	$-0.192277\pi$
$734$	7.39154	+	4.26751i	0.272827	+	0.157517i
$735$		0			0
$736$			36.3146i			1.33857i
$737$	−8.77452	+	15.1979i	−0.323213	+	0.559822i
$738$	−2.62269	−	4.54263i	−0.0965424	−	0.167216i
$739$	31.3327	−	18.0899i	1.15259	−	0.665449i	0.203074	−	0.979163i	$-0.434907\pi$
$739$	31.3327	−	18.0899i	1.15259	−	0.665449i	0.949517	+	0.313715i	$0.101574\pi$
$740$		0			0
$741$	−0.122710	+	30.3596i	−0.00450785	+	1.11529i
$742$	0.414247			0.0152075
$743$	12.5084	−	7.22170i	0.458887	−	0.264938i	−0.252689	−	0.967547i	$-0.581315\pi$
$743$	12.5084	−	7.22170i	0.458887	−	0.264938i	0.711576	+	0.702609i	$0.247982\pi$
$744$	−0.855001	−	1.48091i	−0.0313459	−	0.0542926i
$745$		0			0
$746$			6.15642i			0.225403i
$747$	−3.48663	−	2.01301i	−0.127569	−	0.0736521i
$748$	−6.61553	−	3.81948i	−0.241888	−	0.139654i
$749$			31.3021i			1.14375i
$750$		0			0
$751$	−0.691642	−	1.19796i	−0.0252384	−	0.0437142i	0.853130	−	0.521698i	$-0.174701\pi$
$751$	−0.691642	−	1.19796i	−0.0252384	−	0.0437142i	−0.878369	+	0.477984i	$0.841368\pi$
$752$	−6.01157	+	3.47078i	−0.219219	+	0.126566i
$753$	13.7790			0.502136
$754$	−0.932939	−	0.543672i	−0.0339756	−	0.0197994i
$755$		0			0
$756$	2.36753	−	1.36689i	0.0861062	−	0.0497134i
$757$	−25.5168	−	44.1964i	−0.927424	−	1.60635i	−0.787616	−	0.616167i	$-0.788685\pi$
$757$	−25.5168	−	44.1964i	−0.927424	−	1.60635i	−0.139808	−	0.990179i	$-0.544649\pi$
$758$	1.15601	−	2.00227i	0.0419883	−	0.0727258i
$759$		−	9.29780i		−	0.337489i
$760$		0			0
$761$	−2.32993	−	1.34518i	−0.0844598	−	0.0487629i	0.457175	−	0.889377i	$-0.348861\pi$
$761$	−2.32993	−	1.34518i	−0.0844598	−	0.0487629i	−0.541635	+	0.840614i	$0.682195\pi$
$762$		−	9.73550i		−	0.352680i
$763$	5.56323	−	9.63580i	0.201403	−	0.348840i
$764$	−3.54406	−	6.13849i	−0.128220	−	0.222083i
$765$		0			0
$766$	−19.2552			−0.695717
$767$	−40.8066	−	23.7802i	−1.47344	−	0.858651i
$768$	−5.25955			−0.189788
$769$	−8.85248	+	5.11098i	−0.319228	+	0.184307i	−0.651049	−	0.759036i	$-0.725671\pi$
$769$	−8.85248	+	5.11098i	−0.319228	+	0.184307i	0.331820	+	0.943343i	$0.392337\pi$
$770$		0			0
$771$	−2.80002	+	4.84978i	−0.100840	+	0.174661i
$772$		−	10.4438i		−	0.375880i
$773$	16.3925	+	9.46421i	0.589597	+	0.340404i	0.764938	−	0.644104i	$-0.222770\pi$
$773$	16.3925	+	9.46421i	0.589597	+	0.340404i	−0.175341	+	0.984508i	$0.556103\pi$
$774$	1.14444	+	0.660743i	0.0411360	+	0.0237499i
$775$		0			0
$776$	−3.41334	+	5.91208i	−0.122532	+	0.212231i
$777$	−3.94262	−	6.82881i	−0.141441	−	0.244982i
$778$	−18.7254	+	10.8111i	−0.671340	+	0.387598i
$779$	74.5966			2.67270
$780$		0			0
$781$	−1.54606			−0.0553225
$782$	−11.0649	+	6.38832i	−0.395680	+	0.228446i
$783$	−0.252903	−	0.438041i	−0.00903802	−	0.0156543i
$784$	−4.29446	+	7.43823i	−0.153374	+	0.265651i
$785$		0			0
$786$	−3.13585	−	1.81048i	−0.111852	−	0.0645778i
$787$	−18.9030	−	10.9136i	−0.673818	−	0.389029i	0.123703	−	0.992319i	$-0.460523\pi$
$787$	−18.9030	−	10.9136i	−0.673818	−	0.389029i	−0.797522	+	0.603290i	$0.793856\pi$
$788$			36.6858i			1.30688i
$789$	−4.49001	+	7.77693i	−0.159849	+	0.276866i
$790$		0			0
$791$	−28.1586	+	16.2574i	−1.00121	+	0.578046i
$792$	3.05235			0.108460
$793$	−1.68377	+	2.88934i	−0.0597923	+	0.102603i
$794$	−6.10598			−0.216693
$795$		0			0
$796$	3.62402	+	6.27699i	0.128450	+	0.222482i
$797$	19.3519	−	33.5184i	0.685478	−	1.18728i	−0.287809	−	0.957688i	$-0.592927\pi$
$797$	19.3519	−	33.5184i	0.685478	−	1.18728i	0.973286	−	0.229594i	$-0.0737400\pi$
$798$		−	8.26308i		−	0.292510i
$799$	−9.75931	−	5.63454i	−0.345260	−	0.199336i
$800$		0			0
$801$			0.598008i			0.0211296i
$802$	−6.17740	+	10.6996i	−0.218131	+	0.377815i
$803$	−7.91985	−	13.7176i	−0.279485	−	0.484083i
$804$	17.7458	−	10.2455i	0.625846	−	0.361332i
$805$		0			0
$806$	−0.838799	−	1.46650i	−0.0295454	−	0.0516553i
$807$	4.07724			0.143526
$808$	16.7347	−	9.66175i	0.588723	−	0.339899i
$809$	21.3022	+	36.8965i	0.748946	+	1.29721i	0.948328	+	0.317291i	$0.102773\pi$
$809$	21.3022	+	36.8965i	0.748946	+	1.29721i	−0.199383	+	0.979922i	$0.563894\pi$
$810$		0			0
$811$		−	9.60428i		−	0.337252i	−0.985680	−	0.168626i	$-0.946067\pi$
$811$		−	9.60428i		−	0.337252i	0.985680	−	0.168626i	$-0.0539330\pi$
$812$	−1.19751	−	0.691383i	−0.0420244	−	0.0242628i
$813$	−17.1435	−	9.89780i	−0.601249	−	0.347131i
$814$		−	3.97918i		−	0.139470i
$815$		0			0
$816$	3.31047	+	5.73390i	0.115890	+	0.200727i
$817$	−16.2755	+	9.39669i	−0.569409	+	0.328749i
$818$	−2.29050			−0.0800855
$819$	5.18729	−	2.96700i	0.181259	−	0.103675i
$820$		0			0
$821$	−29.9683	+	17.3022i	−1.04590	+	0.603851i	−0.921499	−	0.388381i	$-0.873035\pi$
$821$	−29.9683	+	17.3022i	−1.04590	+	0.603851i	−0.124402	+	0.992232i	$0.539701\pi$
$822$	3.83348	+	6.63978i	0.133708	+	0.231589i
$823$	13.8808	−	24.0422i	0.483853	−	0.838057i	−0.515975	−	0.856603i	$-0.672570\pi$
$823$	13.8808	−	24.0422i	0.483853	−	0.838057i	0.999828	+	0.0185460i	$0.00590371\pi$
$824$		−	32.4757i		−	1.13135i
$825$		0			0
$826$	11.1325	+	6.42734i	0.387349	+	0.223636i
$827$			27.8932i			0.969943i	0.874530	+	0.484971i	$0.161170\pi$
$827$			27.8932i			0.969943i	−0.874530	+	0.484971i	$0.838830\pi$
$828$	−5.42827	+	9.40204i	−0.188645	+	0.326743i
$829$	7.47706	+	12.9507i	0.259689	+	0.449795i	0.966159	−	0.257949i	$-0.0830466\pi$
$829$	7.47706	+	12.9507i	0.259689	+	0.449795i	−0.706469	+	0.707744i	$0.749713\pi$
$830$		0			0
$831$	−14.5276			−0.503957
$832$	2.78454	+	0.0112548i	0.0965366	+	0.000390189i
$833$	−13.9434			−0.483112
$834$	5.76813	−	3.33023i	0.199734	−	0.115317i
$835$		0			0
$836$	−9.80971	+	16.9909i	−0.339276	+	0.587643i
$837$		−	0.791382i		−	0.0273542i
$838$	−11.0765	−	6.39503i	−0.382632	−	0.220913i
$839$	−20.9723	−	12.1084i	−0.724044	−	0.418027i	0.0921951	−	0.995741i	$-0.470612\pi$
$839$	−20.9723	−	12.1084i	−0.724044	−	0.418027i	−0.816239	+	0.577714i	$0.803945\pi$
$840$		0			0
$841$	14.3721	−	24.8932i	0.495589	−	0.858385i
$842$	3.51753	+	6.09254i	0.121222	+	0.209963i
$843$	−10.2082	+	5.89369i	−0.351588	+	0.202989i
$844$	−11.0590			−0.380667
$845$		0			0
$846$	2.03516			0.0699702
$847$	12.9247	−	7.46209i	0.444099	−	0.256400i
$848$	0.426244	+	0.738277i	0.0146373	+	0.0253525i
$849$	−11.5509	+	20.0067i	−0.396426	+	0.686630i
$850$		0			0
$851$	27.1189	+	15.6571i	0.929623	+	0.536718i
$852$	1.56340	+	0.902628i	0.0535611	+	0.0309235i
$853$			25.6140i			0.877008i	0.898729	+	0.438504i	$0.144492\pi$
$853$			25.6140i			0.877008i	−0.898729	+	0.438504i	$0.855508\pi$
$854$	0.455091	−	0.788242i	0.0155729	−	0.0269731i
$855$		0			0
$856$	35.3415	−	20.4044i	1.20795	−	0.697409i
$857$	38.9380			1.33010			0.665049	−	0.746800i	$-0.268411\pi$
$857$	38.9380			1.33010			0.665049	+	0.746800i	$0.268411\pi$
$858$	3.01562	+	0.0121888i	0.102952	+	0.000416118i
$859$	32.9648			1.12474			0.562372	−	0.826885i	$-0.309889\pi$
$859$	32.9648			1.12474			0.562372	+	0.826885i	$0.309889\pi$
$860$		0			0
$861$	−7.34161	−	12.7160i	−0.250201	−	0.433361i
$862$	−3.22364	+	5.58351i	−0.109798	+	0.190175i
$863$			12.9022i			0.439197i	0.975590	+	0.219598i	$0.0704747\pi$
$863$			12.9022i			0.439197i	−0.975590	+	0.219598i	$0.929525\pi$
$864$	−4.77810	−	2.75864i	−0.162554	−	0.0938508i
$865$		0			0
$866$		−	18.9799i		−	0.644965i
$867$	3.12572	−	5.41390i	0.106155	−	0.183866i
$868$	−1.08174	−	1.87362i	−0.0367165	−	0.0635948i
$869$	−11.3197	+	6.53546i	−0.383996	+	0.221700i
$870$		0			0
$871$	38.8813	−	22.2391i	1.31744	−	0.753542i
$872$	−14.5057			−0.491224
$873$	−2.73609	+	1.57968i	−0.0926026	+	0.0534641i
$874$	16.4074	+	28.4184i	0.554987	+	0.961266i
$875$		0			0
$876$			18.4952i			0.624894i
$877$	−9.94043	−	5.73911i	−0.335664	−	0.193796i	0.322689	−	0.946505i	$-0.395413\pi$
$877$	−9.94043	−	5.73911i	−0.335664	−	0.193796i	−0.658353	+	0.752709i	$0.728747\pi$
$878$	−12.8622	−	7.42599i	−0.434078	−	0.250615i
$879$			9.58488i			0.323290i
$880$		0			0
$881$	0.584497	+	1.01238i	0.0196922	+	0.0341079i	0.875704	−	0.482849i	$-0.160398\pi$
$881$	0.584497	+	1.01238i	0.0196922	+	0.0341079i	−0.856011	+	0.516957i	$0.827065\pi$
$882$	2.18077	−	1.25907i	0.0734304	−	0.0423951i
$883$	−1.40478			−0.0472746			−0.0236373	−	0.999721i	$-0.507525\pi$
$883$	−1.40478			−0.0472746			−0.0236373	+	0.999721i	$0.507525\pi$
$884$	9.68049	+	16.9247i	0.325590	+	0.569240i
$885$		0			0
$886$	16.4446	−	9.49431i	0.552468	−	0.318968i
$887$	8.68394	+	15.0410i	0.291578	+	0.505028i	0.974183	−	0.225759i	$-0.0724863\pi$
$887$	8.68394	+	15.0410i	0.291578	+	0.505028i	−0.682605	+	0.730788i	$0.739153\pi$
$888$	−5.14002	+	8.90278i	−0.172488	+	0.298758i
$889$		−	27.2523i		−	0.914013i
$890$		0			0
$891$	1.22336	+	0.706307i	0.0409841	+	0.0236622i
$892$			22.3852i			0.749513i
$893$	−14.4714	+	25.0652i	−0.484267	+	0.838775i
$894$	−5.84001	−	10.1152i	−0.195319	−	0.338303i
$895$		0			0
$896$	−19.0467			−0.636304
$897$	−11.9488	+	20.5041i	−0.398959	+	0.684612i
$898$	14.2303			0.474873
$899$	−0.346658	+	0.200143i	−0.0115617	+	0.00667514i
$900$		0			0
$901$	−0.691974	+	1.19853i	−0.0230530	+	0.0399290i
$902$		−	7.40969i		−	0.246716i
$903$	3.20360	+	1.84960i	0.106609	+	0.0615508i
$904$	36.7107	+	21.1949i	1.22098	+	0.704932i
$905$		0			0
$906$	1.01485	−	1.75777i	0.0337161	−	0.0583980i
$907$	4.58028	+	7.93327i	0.152086	+	0.263420i	0.931994	−	0.362474i	$-0.118068\pi$
$907$	4.58028	+	7.93327i	0.152086	+	0.263420i	−0.779908	+	0.625894i	$0.784734\pi$
$908$	0.424260	−	0.244947i	0.0140796	−	0.00812884i
$909$	8.94284			0.296615
$910$		0			0
$911$	46.2229			1.53143			0.765717	−	0.643177i	$-0.222384\pi$
$911$	46.2229			1.53143			0.765717	+	0.643177i	$0.222384\pi$
$912$	14.7266	−	8.50240i	0.487646	−	0.281543i
$913$	−2.84360	−	4.92526i	−0.0941095	−	0.163002i
$914$	−1.27777	+	2.21316i	−0.0422647	+	0.0732047i
$915$		0			0
$916$	−20.4494	−	11.8065i	−0.675668	−	0.390097i
$917$	−8.77809	−	5.06803i	−0.289878	−	0.167361i
$918$		−	1.94115i		−	0.0640676i
$919$	6.81590	−	11.8055i	0.224836	−	0.389427i	−0.731434	−	0.681912i	$-0.761149\pi$
$919$	6.81590	−	11.8055i	0.224836	−	0.389427i	0.956270	+	0.292485i	$0.0944820\pi$
$920$		0			0
$921$	21.8363	−	12.6072i	0.719530	−	0.415421i
$922$	−0.365078			−0.0120232
$923$	3.40948	+	1.98688i	0.112224	+	0.0653989i
$924$	3.86179			0.127043
$925$		0			0
$926$	−3.95622	−	6.85238i	−0.130010	−	0.225183i
$927$	7.51482	−	13.0161i	0.246819	−	0.427503i
$928$			2.79067i			0.0916083i
$929$	37.6193	+	21.7195i	1.23425	+	0.712594i	0.967913	−	0.251286i	$-0.0808534\pi$
$929$	37.6193	+	21.7195i	1.23425	+	0.712594i	0.266336	+	0.963880i	$0.414187\pi$
$930$		0			0
$931$			35.8115i			1.17367i
$932$	10.7048	−	18.5412i	0.350647	−	0.607338i
$933$	−0.851347	−	1.47458i	−0.0278719	−	0.0482755i
$934$	−13.3938	+	7.73293i	−0.438260	+	0.253029i
$935$		0			0
$936$	−6.73123	−	3.92264i	−0.220017	−	0.128215i
$937$	30.4186			0.993731			0.496865	−	0.867828i	$-0.334484\pi$
$937$	30.4186			0.993731			0.496865	+	0.867828i	$0.334484\pi$
$938$	−10.5578	+	6.09557i	−0.344726	+	0.199027i
$939$	−12.5536	−	21.7435i	−0.409672	−	0.709573i
$940$		0			0
$941$		−	55.9477i		−	1.82384i	−0.410363	−	0.911922i	$-0.634598\pi$
$941$		−	55.9477i		−	1.82384i	0.410363	−	0.911922i	$-0.365402\pi$
$942$	−2.03375	−	1.17419i	−0.0662632	−	0.0382571i
$943$	50.4985	+	29.1553i	1.64446	+	0.949428i
$944$			26.4540i			0.861003i
$945$		0			0
$946$	0.933375	+	1.61665i	0.0303466	+	0.0525619i
$947$	−20.9804	+	12.1131i	−0.681773	+	0.393622i	−0.800523	−	0.599303i	$-0.795445\pi$
$947$	−20.9804	+	12.1131i	−0.681773	+	0.393622i	0.118750	+	0.992924i	$0.462111\pi$
$948$	15.2622			0.495693
$949$	−0.163408	+	40.4288i	−0.00530446	+	1.31238i
$950$		0			0
$951$	−1.64433	+	0.949353i	−0.0533210	+	0.0307849i
$952$	−5.87064	−	10.1682i	−0.190269	−	0.329555i
$953$	19.1935	−	33.2441i	0.621739	−	1.07688i	−0.367423	−	0.930054i	$-0.619760\pi$
$953$	19.1935	−	33.2441i	0.621739	−	1.07688i	0.989162	−	0.146830i	$-0.0469069\pi$
$954$		−	0.249936i		−	0.00809199i
$955$		0			0
$956$	−19.5220	−	11.2710i	−0.631386	−	0.364531i
$957$		−	0.714509i		−	0.0230968i
$958$	2.56899	−	4.44961i	0.0830002	−	0.143760i
$959$	10.7309	+	18.5865i	0.346520	+	0.600191i
$960$		0			0
$961$	30.3737			0.979797
$962$	−5.11373	+	8.77513i	−0.164873	+	0.282922i
$963$	18.8862			0.608598
$964$	−17.3265	+	10.0035i	−0.558049	+	0.322190i
$965$		0			0
$966$	3.22954	−	5.59373i	0.103909	−	0.179975i
$967$			2.66874i			0.0858209i	0.999079	+	0.0429104i	$0.0136630\pi$
$967$			2.66874i			0.0858209i	−0.999079	+	0.0429104i	$0.986337\pi$
$968$	−16.8501	−	9.72839i	−0.541582	−	0.312682i
$969$	23.9075	+	13.8030i	0.768018	+	0.443416i
$970$		0			0
$971$	20.4823	−	35.4763i	0.657307	−	1.13849i	−0.324003	−	0.946056i	$-0.605029\pi$
$971$	20.4823	−	35.4763i	0.657307	−	1.13849i	0.981310	−	0.192433i	$-0.0616380\pi$
$972$	−0.824717	−	1.42845i	−0.0264528	−	0.0458176i
$973$	16.1466	−	9.32222i	0.517635	−	0.298857i
$974$	16.8839			0.540994
$975$		0			0
$976$	1.87309			0.0599561
$977$	37.6377	−	21.7302i	1.20414	−	0.695209i	0.242665	−	0.970110i	$-0.421978\pi$
$977$	37.6377	−	21.7302i	1.20414	−	0.695209i	0.961473	+	0.274901i	$0.0886449\pi$
$978$	−0.590497	−	1.02277i	−0.0188820	−	0.0327046i
$979$	−0.422377	+	0.731578i	−0.0134992	+	0.0233813i
$980$		0			0
$981$	−5.81377	−	3.35658i	−0.185620	−	0.107167i
$982$	−16.7065	−	9.64549i	−0.533125	−	0.307800i
$983$			22.1143i			0.705337i	0.935748	+	0.352669i	$0.114726\pi$
$983$			22.1143i			0.705337i	−0.935748	+	0.352669i	$0.885274\pi$
$984$	−9.57132	+	16.5780i	−0.305123	+	0.528488i
$985$		0			0
$986$	−0.850305	+	0.490924i	−0.0270792	+	0.0156342i
$987$	5.69696			0.181336
$988$	43.4684	−	24.8628i	1.38291	−	0.790990i
$989$	−14.6904			−0.467128
$990$		0			0
$991$	−21.4294	−	37.1168i	−0.680727	−	1.17905i	−0.974759	−	0.223258i	$-0.928331\pi$
$991$	−21.4294	−	37.1168i	−0.680727	−	1.17905i	0.294033	−	0.955795i	$-0.405003\pi$
$992$	−2.18314	+	3.78130i	−0.0693147	+	0.120057i
$993$			20.2813i			0.643607i
$994$	−0.930141	−	0.537017i	−0.0295023	−	0.0170332i
$995$		0			0
$996$			6.64065i			0.210417i
$997$	−13.0699	+	22.6378i	−0.413929	+	0.716946i	−0.995315	−	0.0966819i	$-0.969177\pi$
$997$	−13.0699	+	22.6378i	−0.413929	+	0.716946i	0.581387	+	0.813627i	$0.302510\pi$
$998$	−8.35872	−	14.4777i	−0.264591	−	0.458285i
$999$	−4.12017	+	2.37878i	−0.130356	+	0.0752614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bc.m.751.5		16
5.2	odd	4		195.2.v.a.49.10	yes	32
5.3	odd	4		195.2.v.a.49.7	yes	32
5.4	even	2		975.2.bc.n.751.4		16
13.4	even	6	inner	975.2.bc.m.901.5		16
15.2	even	4		585.2.bf.c.244.7		32
15.8	even	4		585.2.bf.c.244.10		32
65.4	even	6		975.2.bc.n.901.4		16
65.17	odd	12		195.2.v.a.4.7	✓	32
65.43	odd	12		195.2.v.a.4.10	yes	32
195.17	even	12		585.2.bf.c.199.10		32
195.173	even	12		585.2.bf.c.199.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.v.a.4.7	✓	32	65.17	odd	12
195.2.v.a.4.10	yes	32	65.43	odd	12
195.2.v.a.49.7	yes	32	5.3	odd	4
195.2.v.a.49.10	yes	32	5.2	odd	4
585.2.bf.c.199.7		32	195.173	even	12
585.2.bf.c.199.10		32	195.17	even	12
585.2.bf.c.244.7		32	15.2	even	4
585.2.bf.c.244.10		32	15.8	even	4
975.2.bc.m.751.5		16	1.1	even	1	trivial
975.2.bc.m.901.5		16	13.4	even	6	inner
975.2.bc.n.751.4		16	5.4	even	2
975.2.bc.n.901.4		16	65.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.512762 - 0.296043i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.824717 + 1.42845i) q^{4} +(-0.512762 - 0.296043i) q^{6} +(-1.43536 - 0.828705i) q^{7} +2.16078i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.22336 + 0.706307i) q^{11} +1.64943 q^{12} +(3.60552 + 0.0145731i) q^{13} -0.981329 q^{14} +(-1.00975 - 1.74894i) q^{16} +(1.63925 - 2.83926i) q^{17} +0.592086i q^{18} +(-7.29219 - 4.21015i) q^{19} +1.65741i q^{21} +(-0.418195 + 0.724334i) q^{22} +(-3.29099 - 5.70016i) q^{23} +(1.87129 - 1.08039i) q^{24} +(1.85309 - 1.05992i) q^{26} +1.00000 q^{27} +(2.36753 - 1.36689i) q^{28} +(-0.252903 - 0.438041i) q^{29} -0.791382i q^{31} +(-4.77810 - 2.75864i) q^{32} +(1.22336 + 0.706307i) q^{33} -1.94115i q^{34} +(-0.824717 - 1.42845i) q^{36} +(-4.12017 + 2.37878i) q^{37} -4.98554 q^{38} +(-1.79014 - 3.12976i) q^{39} +(-7.67224 + 4.42957i) q^{41} +(0.490665 + 0.849856i) q^{42} +(1.11596 - 1.93289i) q^{43} -2.33001i q^{44} +(-3.37499 - 1.94855i) q^{46} -3.43727i q^{47} +(-1.00975 + 1.74894i) q^{48} +(-2.12650 - 3.68320i) q^{49} -3.27850 q^{51} +(-2.99435 + 5.13830i) q^{52} -0.422128 q^{53} +(0.512762 - 0.296043i) q^{54} +(1.79065 - 3.10149i) q^{56} +8.42030i q^{57} +(-0.259358 - 0.149740i) q^{58} +(-11.3443 - 6.54963i) q^{59} +(-0.463750 + 0.803239i) q^{61} +(-0.234283 - 0.405790i) q^{62} +(1.43536 - 0.828705i) q^{63} +0.772299 q^{64} +0.836389 q^{66} +(10.7587 - 6.21154i) q^{67} +(2.70384 + 4.68318i) q^{68} +(-3.29099 + 5.70016i) q^{69} +(0.947838 + 0.547235i) q^{71} +(-1.87129 - 1.08039i) q^{72} +11.2130i q^{73} +(-1.40844 + 2.43950i) q^{74} +(12.0280 - 6.94436i) q^{76} +2.34128 q^{77} +(-1.84446 - 1.07486i) q^{78} +9.25299 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-2.62269 + 4.54263i) q^{82} +4.02601i q^{83} +(-2.36753 - 1.36689i) q^{84} -1.32149i q^{86} +(-0.252903 + 0.438041i) q^{87} +(-1.52617 - 2.64341i) q^{88} +(0.517890 - 0.299004i) q^{89} +(-5.16314 - 3.00883i) q^{91} +10.8565 q^{92} +(-0.685357 + 0.395691i) q^{93} +(-1.01758 - 1.76250i) q^{94} +5.51728i q^{96} +(2.73609 + 1.57968i) q^{97} +(-2.18077 - 1.25907i) q^{98} -1.41261i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 10 q^{4} - 6 q^{7} - 8 q^{9} - 6 q^{11} - 20 q^{12} - 4 q^{14} - 14 q^{16} + 10 q^{17} - 2 q^{22} + 12 q^{23} + 26 q^{26} + 16 q^{27} - 24 q^{28} + 12 q^{29} - 30 q^{32} + 6 q^{33} + 10 q^{36}+ \cdots + 24 q^{98}+O(q^{100}) \) 16 * q - 8 * q^3 + 10 * q^4 - 6 * q^7 - 8 * q^9 - 6 * q^11 - 20 * q^12 - 4 * q^14 - 14 * q^16 + 10 * q^17 - 2 * q^22 + 12 * q^23 + 26 * q^26 + 16 * q^27 - 24 * q^28 + 12 * q^29 - 30 * q^32 + 6 * q^33 + 10 * q^36 - 6 * q^37 + 16 * q^38 - 18 * q^41 + 2 * q^42 + 16 * q^43 - 24 * q^46 - 14 * q^48 + 14 * q^49 - 20 * q^51 - 24 * q^52 + 40 * q^53 - 28 * q^56 - 72 * q^58 - 42 * q^59 - 16 * q^61 + 34 * q^62 + 6 * q^63 - 68 * q^64 + 4 * q^66 + 18 * q^67 - 28 * q^68 + 12 * q^69 + 6 * q^71 - 20 * q^74 + 24 * q^76 - 48 * q^77 - 16 * q^78 + 52 * q^79 - 8 * q^81 + 28 * q^82 + 24 * q^84 + 12 * q^87 + 68 * q^88 + 24 * q^89 + 6 * q^91 + 108 * q^92 - 6 * q^93 + 4 * q^94 + 24 * q^98

Introduction

L-functions

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