LMFDB - Embedded newform 1890.2.bk.b.341.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(341,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1890.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bk (of order $6$, degree $2$, not 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.6
Character	$\chi$	$=$	1890.341
Dual form			1890.2.bk.b.521.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.323069 - 2.62595i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.323069 - 2.62595i) q^{7} +1.00000i q^{8} +(0.866025 - 0.500000i) q^{10} +(-0.664943 - 0.383905i) q^{11} +(3.78024 + 2.18252i) q^{13} +(-2.62595 + 0.323069i) q^{14} +1.00000 q^{16} +(-1.15157 - 1.99457i) q^{17} +(4.19206 + 2.42029i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.383905 + 0.664943i) q^{22} +(-4.84784 + 2.79890i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(2.18252 - 3.78024i) q^{26} +(0.323069 + 2.62595i) q^{28} +(9.12141 - 5.26625i) q^{29} -8.05924i q^{31} -1.00000i q^{32} +(-1.99457 + 1.15157i) q^{34} +(2.11261 - 1.59276i) q^{35} +(4.15617 - 7.19869i) q^{37} +(2.42029 - 4.19206i) q^{38} +(-0.866025 + 0.500000i) q^{40} +(-2.65381 + 4.59654i) q^{41} +(5.94724 + 10.3009i) q^{43} +(0.664943 + 0.383905i) q^{44} +(2.79890 + 4.84784i) q^{46} -6.46146 q^{47} +(-6.79125 + 1.69673i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-3.78024 - 2.18252i) q^{52} +(6.48067 - 3.74161i) q^{53} -0.767810i q^{55} +(2.62595 - 0.323069i) q^{56} +(-5.26625 - 9.12141i) q^{58} -11.4347 q^{59} -9.49997i q^{61} -8.05924 q^{62} -1.00000 q^{64} +4.36505i q^{65} +13.7047 q^{67} +(1.15157 + 1.99457i) q^{68} +(-1.59276 - 2.11261i) q^{70} -7.50583i q^{71} +(10.1185 - 5.84190i) q^{73} +(-7.19869 - 4.15617i) q^{74} +(-4.19206 - 2.42029i) q^{76} +(-0.793294 + 1.87014i) q^{77} -1.11044 q^{79} +(0.500000 + 0.866025i) q^{80} +(4.59654 + 2.65381i) q^{82} +(-0.254578 - 0.440942i) q^{83} +(1.15157 - 1.99457i) q^{85} +(10.3009 - 5.94724i) q^{86} +(0.383905 - 0.664943i) q^{88} +(2.80167 - 4.85263i) q^{89} +(4.50993 - 10.6318i) q^{91} +(4.84784 - 2.79890i) q^{92} +6.46146i q^{94} +4.84057i q^{95} +(7.61423 - 4.39608i) q^{97} +(1.69673 + 6.79125i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7}+O(q^{10}) $ 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7	$ 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7} + 28 q^{16} - 6 q^{17} - 6 q^{19} - 14 q^{20} - 6 q^{22} - 30 q^{23} - 14 q^{25} + 12 q^{26} - 8 q^{28} + 4 q^{35} + 4 q^{37} + 6 q^{38} + 18 q^{41} + 28 q^{43} - 18 q^{46} - 60 q^{47} - 20 q^{49} - 42 q^{53} + 6 q^{58} + 48 q^{59} - 12 q^{62} - 28 q^{64} + 80 q^{67} + 6 q^{68} + 6 q^{70} + 6 q^{73} + 6 q^{76} + 18 q^{77} - 4 q^{79} + 14 q^{80} + 24 q^{82} - 18 q^{83} + 6 q^{85} + 96 q^{86} + 6 q^{88} + 6 q^{89} + 66 q^{91} + 30 q^{92} + 72 q^{97} - 24 q^{98}+O(q^{100}) $ 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7 + 28 * q^16 - 6 * q^17 - 6 * q^19 - 14 * q^20 - 6 * q^22 - 30 * q^23 - 14 * q^25 + 12 * q^26 - 8 * q^28 + 4 * q^35 + 4 * q^37 + 6 * q^38 + 18 * q^41 + 28 * q^43 - 18 * q^46 - 60 * q^47 - 20 * q^49 - 42 * q^53 + 6 * q^58 + 48 * q^59 - 12 * q^62 - 28 * q^64 + 80 * q^67 + 6 * q^68 + 6 * q^70 + 6 * q^73 + 6 * q^76 + 18 * q^77 - 4 * q^79 + 14 * q^80 + 24 * q^82 - 18 * q^83 + 6 * q^85 + 96 * q^86 + 6 * q^88 + 6 * q^89 + 66 * q^91 + 30 * q^92 + 72 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.323069	−	2.62595i	−0.122108	−	0.992517i
$7$	−0.323069	−	2.62595i	−0.122108	−	0.992517i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$	−0.664943	−	0.383905i	−0.200488	−	0.115752i	0.396395	−	0.918080i	$-0.370261\pi$
$11$	−0.664943	−	0.383905i	−0.200488	−	0.115752i	−0.596883	+	0.802328i	$0.703594\pi$
$12$		0			0
$13$	3.78024	+	2.18252i	1.04845	+	0.605323i	0.922215	−	0.386677i	$-0.126377\pi$
$13$	3.78024	+	2.18252i	1.04845	+	0.605323i	0.126236	+	0.992000i	$0.459710\pi$
$14$	−2.62595	+	0.323069i	−0.701815	+	0.0863437i
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.15157	−	1.99457i	−0.279296	−	0.483755i	0.691914	−	0.721980i	$-0.256768\pi$
$17$	−1.15157	−	1.99457i	−0.279296	−	0.483755i	−0.971210	+	0.238225i	$0.923434\pi$
$18$		0			0
$19$	4.19206	+	2.42029i	0.961725	+	0.555252i	0.896703	−	0.442632i	$-0.145955\pi$
$19$	4.19206	+	2.42029i	0.961725	+	0.555252i	0.0650212	+	0.997884i	$0.479288\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	−0.383905	+	0.664943i	−0.0818489	+	0.141766i
$23$	−4.84784	+	2.79890i	−1.01084	+	0.583611i	−0.911439	−	0.411436i	$-0.865027\pi$
$23$	−4.84784	+	2.79890i	−1.01084	+	0.583611i	−0.0994054	+	0.995047i	$0.531694\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.18252	−	3.78024i	0.428028	−	0.741367i
$27$		0			0
$28$	0.323069	+	2.62595i	0.0610542	+	0.496258i
$29$	9.12141	−	5.26625i	1.69380	−	0.977918i	0.742407	−	0.669949i	$-0.233684\pi$
$29$	9.12141	−	5.26625i	1.69380	−	0.977918i	0.951397	−	0.307968i	$-0.0996491\pi$
$30$		0			0
$31$		−	8.05924i		−	1.44748i	−0.690072	−	0.723741i	$-0.742421\pi$
$31$		−	8.05924i		−	1.44748i	0.690072	−	0.723741i	$-0.257579\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−1.99457	+	1.15157i	−0.342066	+	0.197492i
$35$	2.11261	−	1.59276i	0.357096	−	0.269226i
$36$		0			0
$37$	4.15617	−	7.19869i	0.683269	−	1.18346i	−0.290708	−	0.956812i	$-0.593891\pi$
$37$	4.15617	−	7.19869i	0.683269	−	1.18346i	0.973977	−	0.226645i	$-0.0727759\pi$
$38$	2.42029	−	4.19206i	0.392622	−	0.680042i
$39$		0			0
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	−2.65381	+	4.59654i	−0.414456	+	0.717859i	−0.995371	−	0.0961053i	$-0.969361\pi$
$41$	−2.65381	+	4.59654i	−0.414456	+	0.717859i	0.580915	+	0.813964i	$0.302695\pi$
$42$		0			0
$43$	5.94724	+	10.3009i	0.906945	+	1.57087i	0.818285	+	0.574813i	$0.194925\pi$
$43$	5.94724	+	10.3009i	0.906945	+	1.57087i	0.0886598	+	0.996062i	$0.471742\pi$
$44$	0.664943	+	0.383905i	0.100244	+	0.0578759i
$45$		0			0
$46$	2.79890	+	4.84784i	0.412675	+	0.714775i
$47$	−6.46146			−0.942500			−0.471250	−	0.882000i	$-0.656197\pi$
$47$	−6.46146			−0.942500			−0.471250	+	0.882000i	$0.656197\pi$
$48$		0			0
$49$	−6.79125	+	1.69673i	−0.970179	+	0.242389i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$	−3.78024	−	2.18252i	−0.524225	−	0.302662i
$53$	6.48067	−	3.74161i	0.890188	−	0.513950i	0.0161839	−	0.999869i	$-0.494848\pi$
$53$	6.48067	−	3.74161i	0.890188	−	0.513950i	0.874004	+	0.485919i	$0.161515\pi$
$54$		0			0
$55$		−	0.767810i		−	0.103532i
$56$	2.62595	−	0.323069i	0.350908	−	0.0431719i
$57$		0			0
$58$	−5.26625	−	9.12141i	−0.691492	−	1.19770i
$59$	−11.4347			−1.48867			−0.744337	−	0.667804i	$-0.767234\pi$
$59$	−11.4347			−1.48867			−0.744337	+	0.667804i	$0.767234\pi$
$60$		0			0
$61$		−	9.49997i		−	1.21635i	−0.793804	−	0.608174i	$-0.791902\pi$
$61$		−	9.49997i		−	1.21635i	0.793804	−	0.608174i	$-0.208098\pi$
$62$	−8.05924			−1.02352
$63$		0			0
$64$	−1.00000			−0.125000
$65$			4.36505i			0.541418i
$66$		0			0
$67$	13.7047			1.67430			0.837151	−	0.546972i	$-0.184220\pi$
$67$	13.7047			1.67430			0.837151	+	0.546972i	$0.184220\pi$
$68$	1.15157	+	1.99457i	0.139648	+	0.241877i
$69$		0			0
$70$	−1.59276	−	2.11261i	−0.190371	−	0.252505i
$71$		−	7.50583i		−	0.890779i	−0.895337	−	0.445389i	$-0.853065\pi$
$71$		−	7.50583i		−	0.890779i	0.895337	−	0.445389i	$-0.146935\pi$
$72$		0			0
$73$	10.1185	−	5.84190i	1.18428	−	0.683742i	0.227277	−	0.973830i	$-0.427018\pi$
$73$	10.1185	−	5.84190i	1.18428	−	0.683742i	0.957000	+	0.290088i	$0.0936845\pi$
$74$	−7.19869	−	4.15617i	−0.836831	−	0.483144i
$75$		0			0
$76$	−4.19206	−	2.42029i	−0.480862	−	0.277626i
$77$	−0.793294	+	1.87014i	−0.0904043	+	0.213122i
$78$		0			0
$79$	−1.11044			−0.124934			−0.0624669	−	0.998047i	$-0.519897\pi$
$79$	−1.11044			−0.124934			−0.0624669	+	0.998047i	$0.519897\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	4.59654	+	2.65381i	0.507603	+	0.293065i
$83$	−0.254578	−	0.440942i	−0.0279435	−	0.0483996i	0.851715	−	0.524005i	$-0.175563\pi$
$83$	−0.254578	−	0.440942i	−0.0279435	−	0.0483996i	−0.879659	+	0.475605i	$0.842229\pi$
$84$		0			0
$85$	1.15157	−	1.99457i	0.124905	−	0.216342i
$86$	10.3009	−	5.94724i	1.11078	−	0.641307i
$87$		0			0
$88$	0.383905	−	0.664943i	0.0409244	−	0.0708832i
$89$	2.80167	−	4.85263i	0.296976	−	0.514378i	−0.678467	−	0.734631i	$-0.737355\pi$
$89$	2.80167	−	4.85263i	0.296976	−	0.514378i	0.975443	+	0.220254i	$0.0706885\pi$
$90$		0			0
$91$	4.50993	−	10.6318i	0.472769	−	1.11452i
$92$	4.84784	−	2.79890i	0.505422	−	0.291806i
$93$		0			0
$94$			6.46146i			0.666448i
$95$			4.84057i			0.496632i
$96$		0			0
$97$	7.61423	−	4.39608i	0.773107	−	0.446354i	−0.0608745	−	0.998145i	$-0.519389\pi$
$97$	7.61423	−	4.39608i	0.773107	−	0.446354i	0.833982	+	0.551792i	$0.186056\pi$
$98$	1.69673	+	6.79125i	0.171395	+	0.686020i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	5.92574	−	10.2637i	0.589633	−	1.02127i	−0.404648	−	0.914473i	$-0.632606\pi$
$101$	5.92574	−	10.2637i	0.589633	−	1.02127i	0.994280	−	0.106801i	$-0.0340609\pi$
$102$		0			0
$103$	−0.760480	+	0.439063i	−0.0749323	+	0.0432622i	−0.536998	−	0.843584i	$-0.680442\pi$
$103$	−0.760480	+	0.439063i	−0.0749323	+	0.0432622i	0.462066	+	0.886846i	$0.347108\pi$
$104$	−2.18252	+	3.78024i	−0.214014	+	0.370683i
$105$		0			0
$106$	−3.74161	−	6.48067i	−0.363418	−	0.629458i
$107$	5.55184	+	3.20536i	0.536717	+	0.309874i	0.743747	−	0.668461i	$-0.233047\pi$
$107$	5.55184	+	3.20536i	0.536717	+	0.309874i	−0.207031	+	0.978334i	$0.566380\pi$
$108$		0			0
$109$	−4.36380	−	7.55832i	−0.417976	−	0.723955i	0.577760	−	0.816207i	$-0.303927\pi$
$109$	−4.36380	−	7.55832i	−0.417976	−	0.723955i	−0.995736	+	0.0922513i	$0.970594\pi$
$110$	−0.767810			−0.0732078
$111$		0			0
$112$	−0.323069	−	2.62595i	−0.0305271	−	0.248129i
$113$	0.697613	+	0.402767i	0.0656259	+	0.0378891i	0.532454	−	0.846459i	$-0.321270\pi$
$113$	0.697613	+	0.402767i	0.0656259	+	0.0378891i	−0.466828	+	0.884348i	$0.654603\pi$
$114$		0			0
$115$	−4.84784	−	2.79890i	−0.452063	−	0.260999i
$116$	−9.12141	+	5.26625i	−0.846902	+	0.488959i
$117$		0			0
$118$			11.4347i			1.05265i
$119$	−4.86562	+	3.66834i	−0.446031	+	0.336277i
$120$		0			0
$121$	−5.20523	−	9.01573i	−0.473203	−	0.819612i
$122$	−9.49997			−0.860087
$123$		0			0
$124$			8.05924i			0.723741i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−12.6479			−1.12232			−0.561162	−	0.827706i	$-0.689645\pi$
$127$	−12.6479			−1.12232			−0.561162	+	0.827706i	$0.689645\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	4.36505			0.382840
$131$	4.96301	+	8.59619i	0.433620	+	0.751053i	0.997182	−	0.0750215i	$-0.0239025\pi$
$131$	4.96301	+	8.59619i	0.433620	+	0.751053i	−0.563561	+	0.826074i	$0.690569\pi$
$132$		0			0
$133$	5.00124	−	11.7901i	0.433662	−	1.02233i
$134$		−	13.7047i		−	1.18391i
$135$		0			0
$136$	1.99457	−	1.15157i	0.171033	−	0.0987461i
$137$	−12.4651	−	7.19674i	−1.06497	−	0.614859i	−0.138165	−	0.990409i	$-0.544120\pi$
$137$	−12.4651	−	7.19674i	−1.06497	−	0.614859i	−0.926802	+	0.375550i	$0.877454\pi$
$138$		0			0
$139$	8.82052	+	5.09253i	0.748147	+	0.431943i	0.825024	−	0.565098i	$-0.191162\pi$
$139$	8.82052	+	5.09253i	0.748147	+	0.431943i	−0.0768772	+	0.997041i	$0.524495\pi$
$140$	−2.11261	+	1.59276i	−0.178548	+	0.134613i
$141$		0			0
$142$	−7.50583			−0.629876
$143$	−1.67576	−	2.90251i	−0.140135	−	0.242720i
$144$		0			0
$145$	9.12141	+	5.26625i	0.757492	+	0.437338i
$146$	−5.84190	−	10.1185i	−0.483479	−	0.837410i
$147$		0			0
$148$	−4.15617	+	7.19869i	−0.341635	+	0.591729i
$149$	7.75355	−	4.47651i	0.635196	−	0.366730i	−0.147566	−	0.989052i	$-0.547144\pi$
$149$	7.75355	−	4.47651i	0.635196	−	0.366730i	0.782761	+	0.622322i	$0.213810\pi$
$150$		0			0
$151$	2.50359	−	4.33635i	0.203739	−	0.352887i	−0.745991	−	0.665956i	$-0.768024\pi$
$151$	2.50359	−	4.33635i	0.203739	−	0.352887i	0.949730	+	0.313069i	$0.101357\pi$
$152$	−2.42029	+	4.19206i	−0.196311	+	0.340021i
$153$		0			0
$154$	1.87014	+	0.793294i	0.150700	+	0.0639255i
$155$	6.97950	−	4.02962i	0.560607	−	0.323667i
$156$		0			0
$157$			3.25327i			0.259639i	0.991538	+	0.129819i	$0.0414398\pi$
$157$			3.25327i			0.259639i	−0.991538	+	0.129819i	$0.958560\pi$
$158$			1.11044i			0.0883415i
$159$		0			0
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	8.91596	+	11.8260i	0.702676	+	0.932016i
$162$		0			0
$163$	2.40931	−	4.17306i	0.188712	−	0.326859i	−0.756109	−	0.654446i	$-0.772902\pi$
$163$	2.40931	−	4.17306i	0.188712	−	0.326859i	0.944821	+	0.327587i	$0.106235\pi$
$164$	2.65381	−	4.59654i	0.207228	−	0.358929i
$165$		0			0
$166$	−0.440942	+	0.254578i	−0.0342237	+	0.0197591i
$167$	−4.97259	+	8.61278i	−0.384791	+	0.666477i	−0.991740	−	0.128263i	$-0.959060\pi$
$167$	−4.97259	+	8.61278i	−0.384791	+	0.666477i	0.606949	+	0.794740i	$0.292393\pi$
$168$		0			0
$169$	3.02683	+	5.24262i	0.232833	+	0.403278i
$170$	−1.99457	−	1.15157i	−0.152977	−	0.0883212i
$171$		0			0
$172$	−5.94724	−	10.3009i	−0.453472	−	0.785437i
$173$	16.6263			1.26408			0.632039	−	0.774937i	$-0.282218\pi$
$173$	16.6263			1.26408			0.632039	+	0.774937i	$0.282218\pi$
$174$		0			0
$175$	2.43568	+	1.03319i	0.184120	+	0.0781019i
$176$	−0.664943	−	0.383905i	−0.0501220	−	0.0289379i
$177$		0			0
$178$	−4.85263	−	2.80167i	−0.363720	−	0.209994i
$179$	4.07453	−	2.35243i	0.304545	−	0.175829i	−0.339938	−	0.940448i	$-0.610406\pi$
$179$	4.07453	−	2.35243i	0.304545	−	0.175829i	0.644483	+	0.764619i	$0.277073\pi$
$180$		0			0
$181$			8.33408i			0.619467i	0.950823	+	0.309734i	$0.100240\pi$
$181$			8.33408i			0.619467i	−0.950823	+	0.309734i	$0.899760\pi$
$182$	−10.6318	−	4.50993i	−0.788085	−	0.334298i
$183$		0			0
$184$	−2.79890	−	4.84784i	−0.206338	−	0.357387i
$185$	8.31233			0.611135
$186$		0			0
$187$			1.76837i			0.129316i
$188$	6.46146			0.471250
$189$		0			0
$190$	4.84057			0.351172
$191$			3.79290i			0.274444i	0.990540	+	0.137222i	$0.0438174\pi$
$191$			3.79290i			0.274444i	−0.990540	+	0.137222i	$0.956183\pi$
$192$		0			0
$193$	−21.4959			−1.54731			−0.773656	−	0.633606i	$-0.781574\pi$
$193$	−21.4959			−1.54731			−0.773656	+	0.633606i	$0.781574\pi$
$194$	−4.39608	−	7.61423i	−0.315620	−	0.546670i
$195$		0			0
$196$	6.79125	−	1.69673i	0.485090	−	0.121195i
$197$			13.3908i			0.954054i	0.878889	+	0.477027i	$0.158286\pi$
$197$			13.3908i			0.954054i	−0.878889	+	0.477027i	$0.841714\pi$
$198$		0			0
$199$	0.485507	−	0.280308i	0.0344167	−	0.0198705i	−0.482693	−	0.875790i	$-0.660341\pi$
$199$	0.485507	−	0.280308i	0.0344167	−	0.0198705i	0.517110	+	0.855919i	$0.327008\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$		0			0
$202$	−10.2637	−	5.92574i	−0.722150	−	0.416933i
$203$	−16.7758	−	22.2510i	−1.17743	−	1.56172i
$204$		0			0
$205$	−5.30763			−0.370701
$206$	0.439063	+	0.760480i	0.0305910	+	0.0529851i
$207$		0			0
$208$	3.78024	+	2.18252i	0.262113	+	0.151331i
$209$	−1.85832	−	3.21871i	−0.128543	−	0.222643i
$210$		0			0
$211$	1.76537	−	3.05771i	0.121533	−	0.210501i	−0.798839	−	0.601544i	$-0.794552\pi$
$211$	1.76537	−	3.05771i	0.121533	−	0.210501i	0.920372	+	0.391043i	$0.127886\pi$
$212$	−6.48067	+	3.74161i	−0.445094	+	0.256975i
$213$		0			0
$214$	3.20536	−	5.55184i	0.219114	−	0.379516i
$215$	−5.94724	+	10.3009i	−0.405598	+	0.702516i
$216$		0			0
$217$	−21.1632	+	2.60369i	−1.43665	+	0.176750i
$218$	−7.55832	+	4.36380i	−0.511914	+	0.295554i
$219$		0			0
$220$			0.767810i			0.0517658i
$221$		−	10.0533i		−	0.676258i
$222$		0			0
$223$	−22.1791	+	12.8051i	−1.48522	+	0.857495i	−0.999859	−	0.0168159i	$-0.994647\pi$
$223$	−22.1791	+	12.8051i	−1.48522	+	0.857495i	−0.485366	+	0.874311i	$0.661314\pi$
$224$	−2.62595	+	0.323069i	−0.175454	+	0.0215859i
$225$		0			0
$226$	0.402767	−	0.697613i	0.0267917	−	0.0464045i
$227$	−5.56930	+	9.64631i	−0.369647	+	0.640248i	−0.989510	−	0.144462i	$-0.953855\pi$
$227$	−5.56930	+	9.64631i	−0.369647	+	0.640248i	0.619863	+	0.784710i	$0.287188\pi$
$228$		0			0
$229$	−3.29819	+	1.90421i	−0.217951	+	0.125834i	−0.605001	−	0.796225i	$-0.706827\pi$
$229$	−3.29819	+	1.90421i	−0.217951	+	0.125834i	0.387050	+	0.922059i	$0.373494\pi$
$230$	−2.79890	+	4.84784i	−0.184554	+	0.319657i
$231$		0			0
$232$	5.26625	+	9.12141i	0.345746	+	0.598850i
$233$	2.04230	+	1.17912i	0.133795	+	0.0772468i	0.565404	−	0.824814i	$-0.308720\pi$
$233$	2.04230	+	1.17912i	0.133795	+	0.0772468i	−0.431608	+	0.902061i	$0.642054\pi$
$234$		0			0
$235$	−3.23073	−	5.59578i	−0.210749	−	0.365029i
$236$	11.4347			0.744337
$237$		0			0
$238$	3.66834	+	4.86562i	0.237783	+	0.315391i
$239$	−10.1968	−	5.88712i	−0.659576	−	0.380806i	0.132540	−	0.991178i	$-0.457687\pi$
$239$	−10.1968	−	5.88712i	−0.659576	−	0.380806i	−0.792115	+	0.610372i	$0.791020\pi$
$240$		0			0
$241$	16.2931	+	9.40683i	1.04953	+	0.605947i	0.922518	−	0.385954i	$-0.126128\pi$
$241$	16.2931	+	9.40683i	1.04953	+	0.605947i	0.127013	+	0.991901i	$0.459461\pi$
$242$	−9.01573	+	5.20523i	−0.579553	+	0.334605i
$243$		0			0
$244$			9.49997i			0.608174i
$245$	−4.86503	−	5.03304i	−0.310816	−	0.321549i
$246$		0			0
$247$	10.5647	+	18.2986i	0.672214	+	1.16431i
$248$	8.05924			0.511762
$249$		0			0
$250$			1.00000i			0.0632456i
$251$	−3.35759			−0.211929			−0.105965	−	0.994370i	$-0.533793\pi$
$251$	−3.35759			−0.211929			−0.105965	+	0.994370i	$0.533793\pi$
$252$		0			0
$253$	4.29805			0.270216
$254$			12.6479i			0.793602i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−5.66810	−	9.81743i	−0.353566	−	0.612394i	0.633305	−	0.773902i	$-0.281698\pi$
$257$	−5.66810	−	9.81743i	−0.353566	−	0.612394i	−0.986871	+	0.161508i	$0.948364\pi$
$258$		0			0
$259$	−20.2461	−	8.58822i	−1.25803	−	0.533646i
$260$		−	4.36505i		−	0.270709i
$261$		0			0
$262$	8.59619	−	4.96301i	0.531074	−	0.306616i
$263$	22.3278	+	12.8910i	1.37679	+	0.794892i	0.991772	−	0.128015i	$-0.0408606\pi$
$263$	22.3278	+	12.8910i	1.37679	+	0.794892i	0.385022	+	0.922908i	$0.374194\pi$
$264$		0			0
$265$	6.48067	+	3.74161i	0.398104	+	0.229846i
$266$	−11.7901	−	5.00124i	−0.722896	−	0.306645i
$267$		0			0
$268$	−13.7047			−0.837151
$269$	2.94884	+	5.10754i	0.179794	+	0.311412i	0.941810	−	0.336146i	$-0.109124\pi$
$269$	2.94884	+	5.10754i	0.179794	+	0.311412i	−0.762016	+	0.647558i	$0.775790\pi$
$270$		0			0
$271$	−8.76680	−	5.06151i	−0.532545	−	0.307465i	0.209507	−	0.977807i	$-0.432814\pi$
$271$	−8.76680	−	5.06151i	−0.532545	−	0.307465i	−0.742052	+	0.670342i	$0.766147\pi$
$272$	−1.15157	−	1.99457i	−0.0698240	−	0.120939i
$273$		0			0
$274$	−7.19674	+	12.4651i	−0.434771	+	0.753045i
$275$	0.664943	−	0.383905i	0.0400976	−	0.0231504i
$276$		0			0
$277$	−5.19502	+	8.99804i	−0.312139	+	0.540640i	−0.978825	−	0.204698i	$-0.934379\pi$
$277$	−5.19502	+	8.99804i	−0.312139	+	0.540640i	0.666686	+	0.745338i	$0.267712\pi$
$278$	5.09253	−	8.82052i	0.305430	−	0.529020i
$279$		0			0
$280$	1.59276	+	2.11261i	0.0951857	+	0.126252i
$281$	14.3149	−	8.26473i	0.853957	−	0.493032i	−0.00802696	−	0.999968i	$-0.502555\pi$
$281$	14.3149	−	8.26473i	0.853957	−	0.493032i	0.861984	+	0.506935i	$0.169222\pi$
$282$		0			0
$283$			10.3924i			0.617765i	0.951100	+	0.308882i	$0.0999550\pi$
$283$			10.3924i			0.617765i	−0.951100	+	0.308882i	$0.900045\pi$
$284$			7.50583i			0.445389i
$285$		0			0
$286$	−2.90251	+	1.67576i	−0.171629	+	0.0990901i
$287$	12.9277	+	5.48379i	0.763095	+	0.323698i
$288$		0			0
$289$	5.84779	−	10.1287i	0.343987	−	0.595804i
$290$	5.26625	−	9.12141i	0.309245	−	0.535628i
$291$		0			0
$292$	−10.1185	+	5.84190i	−0.592138	+	0.341871i
$293$	−12.7786	+	22.1332i	−0.746533	+	1.29303i	0.202942	+	0.979191i	$0.434950\pi$
$293$	−12.7786	+	22.1332i	−0.746533	+	1.29303i	−0.949475	+	0.313843i	$0.898384\pi$
$294$		0			0
$295$	−5.71736	−	9.90276i	−0.332878	−	0.576561i
$296$	7.19869	+	4.15617i	0.418415	+	0.241572i
$297$		0			0
$298$	−4.47651	−	7.75355i	−0.259318	−	0.449151i
$299$	−24.4347			−1.41309
$300$		0			0
$301$	25.1283	−	18.9451i	1.44837	−	1.09198i
$302$	−4.33635	−	2.50359i	−0.249529	−	0.144065i
$303$		0			0
$304$	4.19206	+	2.42029i	0.240431	+	0.138813i
$305$	8.22722	−	4.74999i	0.471089	−	0.271983i
$306$		0			0
$307$			9.33336i			0.532683i	0.963879	+	0.266342i	$0.0858149\pi$
$307$			9.33336i			0.532683i	−0.963879	+	0.266342i	$0.914185\pi$
$308$	0.793294	−	1.87014i	0.0452021	−	0.106561i
$309$		0			0
$310$	−4.02962	−	6.97950i	−0.228867	−	0.396409i
$311$	5.36577			0.304265			0.152132	−	0.988360i	$-0.451386\pi$
$311$	5.36577			0.304265			0.152132	+	0.988360i	$0.451386\pi$
$312$		0			0
$313$			25.4559i			1.43885i	0.694568	+	0.719427i	$0.255596\pi$
$313$			25.4559i			1.43885i	−0.694568	+	0.719427i	$0.744404\pi$
$314$	3.25327			0.183592
$315$		0			0
$316$	1.11044			0.0624669
$317$			7.48676i			0.420498i	0.977648	+	0.210249i	$0.0674275\pi$
$317$			7.48676i			0.420498i	−0.977648	+	0.210249i	$0.932572\pi$
$318$		0			0
$319$	−8.08696			−0.452783
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	11.8260	−	8.91596i	0.659035	−	0.496867i
$323$		−	11.1485i		−	0.620319i
$324$		0			0
$325$	−3.78024	+	2.18252i	−0.209690	+	0.121065i
$326$	−4.17306	−	2.40931i	−0.231124	−	0.133440i
$327$		0			0
$328$	−4.59654	−	2.65381i	−0.253801	−	0.146532i
$329$	2.08749	+	16.9675i	0.115087	+	0.935447i
$330$		0			0
$331$	7.42867			0.408317			0.204158	−	0.978938i	$-0.434554\pi$
$331$	7.42867			0.408317			0.204158	+	0.978938i	$0.434554\pi$
$332$	0.254578	+	0.440942i	0.0139718	+	0.0241998i
$333$		0			0
$334$	8.61278	+	4.97259i	0.471270	+	0.272088i
$335$	6.85237	+	11.8687i	0.374385	+	0.648454i
$336$		0			0
$337$	−12.9171	+	22.3731i	−0.703641	+	1.21874i	0.263539	+	0.964649i	$0.415110\pi$
$337$	−12.9171	+	22.3731i	−0.703641	+	1.21874i	−0.967180	+	0.254093i	$0.918223\pi$
$338$	5.24262	−	3.02683i	0.285161	−	0.164638i
$339$		0			0
$340$	−1.15157	+	1.99457i	−0.0624525	+	0.108171i
$341$	−3.09398	+	5.35894i	−0.167549	+	0.290203i
$342$		0			0
$343$	6.64956	+	17.2854i	0.359043	+	0.933321i
$344$	−10.3009	+	5.94724i	−0.555388	+	0.320653i
$345$		0			0
$346$		−	16.6263i		−	0.893838i
$347$		−	18.4244i		−	0.989073i	−0.869157	−	0.494537i	$-0.835338\pi$
$347$		−	18.4244i		−	0.989073i	0.869157	−	0.494537i	$-0.164662\pi$
$348$		0			0
$349$	1.37452	−	0.793577i	0.0735761	−	0.0424792i	−0.462761	−	0.886483i	$-0.653141\pi$
$349$	1.37452	−	0.793577i	0.0735761	−	0.0424792i	0.536337	+	0.844004i	$0.319808\pi$
$350$	1.03319	−	2.43568i	0.0552264	−	0.130192i
$351$		0			0
$352$	−0.383905	+	0.664943i	−0.0204622	+	0.0354416i
$353$	4.60268	−	7.97208i	0.244976	−	0.424311i	−0.717149	−	0.696920i	$-0.754553\pi$
$353$	4.60268	−	7.97208i	0.244976	−	0.424311i	0.962125	+	0.272609i	$0.0878865\pi$
$354$		0			0
$355$	6.50024	−	3.75292i	0.344997	−	0.199184i
$356$	−2.80167	+	4.85263i	−0.148488	+	0.257189i
$357$		0			0
$358$	−2.35243	−	4.07453i	−0.124330	−	0.215346i
$359$	22.3751	+	12.9183i	1.18091	+	0.681801i	0.956226	−	0.292629i	$-0.0945302\pi$
$359$	22.3751	+	12.9183i	1.18091	+	0.681801i	0.224689	+	0.974431i	$0.427864\pi$
$360$		0			0
$361$	2.21558	+	3.83750i	0.116610	+	0.201974i
$362$	8.33408			0.438029
$363$		0			0
$364$	−4.50993	+	10.6318i	−0.236384	+	0.557260i
$365$	10.1185	+	5.84190i	0.529625	+	0.305779i
$366$		0			0
$367$	19.2746	+	11.1282i	1.00613	+	0.580888i	0.910055	−	0.414487i	$-0.136039\pi$
$367$	19.2746	+	11.1282i	1.00613	+	0.580888i	0.0960716	+	0.995374i	$0.469372\pi$
$368$	−4.84784	+	2.79890i	−0.252711	+	0.145903i
$369$		0			0
$370$		−	8.31233i		−	0.432137i
$371$	−11.9190	−	15.8091i	−0.618804	−	0.820769i
$372$		0			0
$373$	16.3900	+	28.3884i	0.848644	+	1.46989i	0.882419	+	0.470465i	$0.155914\pi$
$373$	16.3900	+	28.3884i	0.848644	+	1.46989i	−0.0337752	+	0.999429i	$0.510753\pi$
$374$	1.76837			0.0914403
$375$		0			0
$376$		−	6.46146i		−	0.333224i
$377$	45.9749			2.36783
$378$		0			0
$379$	−26.7133			−1.37217			−0.686085	−	0.727522i	$-0.740672\pi$
$379$	−26.7133			−1.37217			−0.686085	+	0.727522i	$0.740672\pi$
$380$		−	4.84057i		−	0.248316i
$381$		0			0
$382$	3.79290			0.194061
$383$	0.908668	+	1.57386i	0.0464307	+	0.0804204i	0.888307	−	0.459251i	$-0.151882\pi$
$383$	0.908668	+	1.57386i	0.0464307	+	0.0804204i	−0.841876	+	0.539671i	$0.818549\pi$
$384$		0			0
$385$	−2.01623	+	0.248055i	−0.102757	+	0.0126421i
$386$			21.4959i			1.09411i
$387$		0			0
$388$	−7.61423	+	4.39608i	−0.386554	+	0.223177i
$389$	−25.9543	−	14.9847i	−1.31593	−	0.759755i	−0.332863	−	0.942975i	$-0.608015\pi$
$389$	−25.9543	−	14.9847i	−1.31593	−	0.759755i	−0.983072	+	0.183220i	$0.941348\pi$
$390$		0			0
$391$	11.1652	+	6.44624i	0.564650	+	0.326001i
$392$	−1.69673	−	6.79125i	−0.0856976	−	0.343010i
$393$		0			0
$394$	13.3908			0.674618
$395$	−0.555218	−	0.961666i	−0.0279360	−	0.0483867i
$396$		0			0
$397$	0.811242	+	0.468371i	0.0407151	+	0.0235069i	0.520219	−	0.854033i	$-0.325850\pi$
$397$	0.811242	+	0.468371i	0.0407151	+	0.0235069i	−0.479504	+	0.877540i	$0.659184\pi$
$398$	−0.280308	−	0.485507i	−0.0140506	−	0.0243363i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	5.03054	−	2.90439i	0.251213	−	0.145038i	−0.369106	−	0.929387i	$-0.620336\pi$
$401$	5.03054	−	2.90439i	0.251213	−	0.145038i	0.620320	+	0.784349i	$0.287003\pi$
$402$		0			0
$403$	17.5895	−	30.4659i	0.876195	−	1.51761i
$404$	−5.92574	+	10.2637i	−0.294816	+	0.510637i
$405$		0			0
$406$	−22.2510	+	16.7758i	−1.10430	+	0.832567i
$407$	−5.52723	+	3.19115i	−0.273975	+	0.158179i
$408$		0			0
$409$			21.8817i			1.08198i	0.841029	+	0.540990i	$0.181950\pi$
$409$			21.8817i			1.08198i	−0.841029	+	0.540990i	$0.818050\pi$
$410$			5.30763i			0.262125i
$411$		0			0
$412$	0.760480	−	0.439063i	0.0374661	−	0.0216311i
$413$	3.69420	+	30.0270i	0.181780	+	1.47753i
$414$		0			0
$415$	0.254578	−	0.440942i	0.0124967	−	0.0216450i
$416$	2.18252	−	3.78024i	0.107007	−	0.185342i
$417$		0			0
$418$	−3.21871	+	1.85832i	−0.157432	+	0.0908935i
$419$	−7.97218	+	13.8082i	−0.389467	+	0.674576i	−0.992378	−	0.123232i	$-0.960674\pi$
$419$	−7.97218	+	13.8082i	−0.389467	+	0.674576i	0.602911	+	0.797808i	$0.294007\pi$
$420$		0			0
$421$	8.26978	+	14.3237i	0.403044	+	0.698093i	0.994092	−	0.108544i	$-0.0346187\pi$
$421$	8.26978	+	14.3237i	0.403044	+	0.698093i	−0.591047	+	0.806637i	$0.701285\pi$
$422$	−3.05771	−	1.76537i	−0.148847	−	0.0859368i
$423$		0			0
$424$	3.74161	+	6.48067i	0.181709	+	0.314729i
$425$	2.30313			0.111718
$426$		0			0
$427$	−24.9465	+	3.06914i	−1.20724	+	0.148526i
$428$	−5.55184	−	3.20536i	−0.268358	−	0.154937i
$429$		0			0
$430$	10.3009	+	5.94724i	0.496754	+	0.286801i
$431$	−10.5417	+	6.08623i	−0.507774	+	0.293163i	−0.731918	−	0.681393i	$-0.761375\pi$
$431$	−10.5417	+	6.08623i	−0.507774	+	0.293163i	0.224144	+	0.974556i	$0.428041\pi$
$432$		0			0
$433$			8.54538i			0.410665i	0.978692	+	0.205332i	$0.0658276\pi$
$433$			8.54538i			0.410665i	−0.978692	+	0.205332i	$0.934172\pi$
$434$	2.60369	+	21.1632i	0.124981	+	1.01586i
$435$		0			0
$436$	4.36380	+	7.55832i	0.208988	+	0.361978i
$437$	−27.0966			−1.29620
$438$		0			0
$439$			6.58176i			0.314130i	0.987588	+	0.157065i	$0.0502032\pi$
$439$			6.58176i			0.314130i	−0.987588	+	0.157065i	$0.949797\pi$
$440$	0.767810			0.0366039
$441$		0			0
$442$	−10.0533			−0.478186
$443$		−	27.0738i		−	1.28631i	−0.765734	−	0.643157i	$-0.777624\pi$
$443$		−	27.0738i		−	1.28631i	0.765734	−	0.643157i	$-0.222376\pi$
$444$		0			0
$445$	5.60333			0.265623
$446$	12.8051	+	22.1791i	0.606341	+	1.05021i
$447$		0			0
$448$	0.323069	+	2.62595i	0.0152636	+	0.124065i
$449$		−	17.9654i		−	0.847841i	−0.905700	−	0.423920i	$-0.860654\pi$
$449$		−	17.9654i		−	0.847841i	0.905700	−	0.423920i	$-0.139346\pi$
$450$		0			0
$451$	3.52927	−	2.03763i	0.166187	−	0.0959480i
$452$	−0.697613	−	0.402767i	−0.0328130	−	0.0189446i
$453$		0			0
$454$	9.64631	+	5.56930i	0.452724	+	0.261380i
$455$	11.4624	−	1.41021i	0.537366	−	0.0661117i
$456$		0			0
$457$	−5.14932			−0.240875			−0.120438	−	0.992721i	$-0.538430\pi$
$457$	−5.14932			−0.240875			−0.120438	+	0.992721i	$0.538430\pi$
$458$	1.90421	+	3.29819i	0.0889780	+	0.154114i
$459$		0			0
$460$	4.84784	+	2.79890i	0.226032	+	0.130499i
$461$	5.46051	+	9.45788i	0.254321	+	0.440498i	0.964711	−	0.263311i	$-0.0848146\pi$
$461$	5.46051	+	9.45788i	0.254321	+	0.440498i	−0.710390	+	0.703809i	$0.751481\pi$
$462$		0			0
$463$	14.8704	−	25.7563i	0.691088	−	1.19700i	−0.280394	−	0.959885i	$-0.590465\pi$
$463$	14.8704	−	25.7563i	0.691088	−	1.19700i	0.971482	−	0.237114i	$-0.0762015\pi$
$464$	9.12141	−	5.26625i	0.423451	−	0.244479i
$465$		0			0
$466$	1.17912	−	2.04230i	0.0546217	−	0.0946076i
$467$	−4.55724	+	7.89337i	−0.210884	+	0.365262i	−0.951991	−	0.306125i	$-0.900968\pi$
$467$	−4.55724	+	7.89337i	−0.210884	+	0.365262i	0.741107	+	0.671386i	$0.234301\pi$
$468$		0			0
$469$	−4.42757	−	35.9880i	−0.204446	−	1.66177i
$470$	−5.59578	+	3.23073i	−0.258114	+	0.149022i
$471$		0			0
$472$		−	11.4347i		−	0.526326i
$473$		−	9.13270i		−	0.419922i
$474$		0			0
$475$	−4.19206	+	2.42029i	−0.192345	+	0.111050i
$476$	4.86562	−	3.66834i	0.223015	−	0.168138i
$477$		0			0
$478$	−5.88712	+	10.1968i	−0.269271	+	0.466390i
$479$	18.6486	−	32.3003i	0.852076	−	1.47584i	−0.0272561	−	0.999628i	$-0.508677\pi$
$479$	18.6486	−	32.3003i	0.852076	−	1.47584i	0.879332	−	0.476210i	$-0.157990\pi$
$480$		0			0
$481$	31.4226	−	18.1419i	1.43275	−	0.827198i
$482$	9.40683	−	16.2931i	0.428469	−	0.742130i
$483$		0			0
$484$	5.20523	+	9.01573i	0.236602	+	0.409806i
$485$	7.61423	+	4.39608i	0.345744	+	0.199615i
$486$		0			0
$487$	−9.44574	−	16.3605i	−0.428027	−	0.741365i	0.568671	−	0.822565i	$-0.307458\pi$
$487$	−9.44574	−	16.3605i	−0.428027	−	0.741365i	−0.996698	+	0.0812005i	$0.974125\pi$
$488$	9.49997			0.430044
$489$		0			0
$490$	−5.03304	+	4.86503i	−0.227369	+	0.219780i
$491$	30.1458	+	17.4047i	1.36046	+	0.785462i	0.989685	−	0.143260i	$-0.0457586\pi$
$491$	30.1458	+	17.4047i	1.36046	+	0.785462i	0.370776	+	0.928723i	$0.379092\pi$
$492$		0			0
$493$	−21.0078	−	12.1289i	−0.946145	−	0.546257i
$494$	18.2986	−	10.5647i	0.823291	−	0.475327i
$495$		0			0
$496$		−	8.05924i		−	0.361870i
$497$	−19.7100	+	2.42490i	−0.884113	+	0.108772i
$498$		0			0
$499$	−12.2163	−	21.1593i	−0.546878	−	0.947220i	−0.998486	−	0.0550038i	$-0.982483\pi$
$499$	−12.2163	−	21.1593i	−0.546878	−	0.947220i	0.451608	−	0.892216i	$-0.350850\pi$
$500$	1.00000			0.0447214
$501$		0			0
$502$			3.35759i			0.149857i
$503$	−13.5009			−0.601977			−0.300988	−	0.953628i	$-0.597317\pi$
$503$	−13.5009			−0.601977			−0.300988	+	0.953628i	$0.597317\pi$
$504$		0			0
$505$	11.8515			0.527384
$506$		−	4.29805i		−	0.191072i
$507$		0			0
$508$	12.6479			0.561162
$509$	13.6722	+	23.6809i	0.606008	+	1.04964i	0.991891	+	0.127089i	$0.0405634\pi$
$509$	13.6722	+	23.6809i	0.606008	+	1.04964i	−0.385883	+	0.922548i	$0.626103\pi$
$510$		0			0
$511$	−18.6095	−	24.6833i	−0.823236	−	1.09192i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−9.81743	+	5.66810i	−0.433028	+	0.250009i
$515$	−0.760480	−	0.439063i	−0.0335107	−	0.0193474i
$516$		0			0
$517$	4.29650	+	2.48059i	0.188960	+	0.109096i
$518$	−8.58822	+	20.2461i	−0.377345	+	0.889564i
$519$		0			0
$520$	−4.36505			−0.191420
$521$	5.24997	+	9.09321i	0.230005	+	0.398381i	0.957809	−	0.287404i	$-0.0927923\pi$
$521$	5.24997	+	9.09321i	0.230005	+	0.398381i	−0.727804	+	0.685785i	$0.759459\pi$
$522$		0			0
$523$	−15.4653	−	8.92889i	−0.676250	−	0.390433i	0.122191	−	0.992507i	$-0.461008\pi$
$523$	−15.4653	−	8.92889i	−0.676250	−	0.390433i	−0.798441	+	0.602074i	$0.794341\pi$
$524$	−4.96301	−	8.59619i	−0.216810	−	0.375526i
$525$		0			0
$526$	12.8910	−	22.3278i	0.562074	−	0.973540i
$527$	−16.0747	+	9.28075i	−0.700226	+	0.404276i
$528$		0			0
$529$	4.16769	−	7.21865i	0.181204	−	0.313854i
$530$	3.74161	−	6.48067i	0.162525	−	0.281502i
$531$		0			0
$532$	−5.00124	+	11.7901i	−0.216831	+	0.511164i
$533$	−20.0641	+	11.5840i	−0.869074	+	0.501760i
$534$		0			0
$535$			6.41071i			0.277159i
$536$			13.7047i			0.591955i
$537$		0			0
$538$	5.10754	−	2.94884i	0.220202	−	0.127134i
$539$	5.16718	+	1.47897i	0.222566	+	0.0637038i
$540$		0			0
$541$	4.16365	−	7.21166i	0.179009	−	0.310053i	−0.762532	−	0.646950i	$-0.776044\pi$
$541$	4.16365	−	7.21166i	0.179009	−	0.310053i	0.941542	+	0.336897i	$0.109377\pi$
$542$	−5.06151	+	8.76680i	−0.217411	+	0.376566i
$543$		0			0
$544$	−1.99457	+	1.15157i	−0.0855166	+	0.0493730i
$545$	4.36380	−	7.55832i	0.186924	−	0.323763i
$546$		0			0
$547$	15.3348	+	26.5606i	0.655667	+	1.13565i	0.981726	+	0.190299i	$0.0609459\pi$
$547$	15.3348	+	26.5606i	0.655667	+	1.13565i	−0.326059	+	0.945349i	$0.605721\pi$
$548$	12.4651	+	7.19674i	0.532483	+	0.307429i
$549$		0			0
$550$	−0.383905	−	0.664943i	−0.0163698	−	0.0283533i
$551$	50.9833			2.17196
$552$		0			0
$553$	0.358747	+	2.91595i	0.0152555	+	0.123999i
$554$	8.99804	+	5.19502i	0.382290	+	0.220715i
$555$		0			0
$556$	−8.82052	−	5.09253i	−0.374073	−	0.215971i
$557$	−1.82492	+	1.05362i	−0.0773242	+	0.0446432i	−0.538164	−	0.842840i	$-0.680882\pi$
$557$	−1.82492	+	1.05362i	−0.0773242	+	0.0446432i	0.460839	+	0.887484i	$0.347548\pi$
$558$		0			0
$559$			51.9199i			2.19598i
$560$	2.11261	−	1.59276i	0.0892740	−	0.0673065i
$561$		0			0
$562$	−8.26473	−	14.3149i	−0.348627	−	0.603839i
$563$	−11.4883			−0.484174			−0.242087	−	0.970255i	$-0.577832\pi$
$563$	−11.4883			−0.484174			−0.242087	+	0.970255i	$0.577832\pi$
$564$		0			0
$565$			0.805534i			0.0338891i
$566$	10.3924			0.436826
$567$		0			0
$568$	7.50583			0.314938
$569$			45.8657i			1.92279i	0.275172	+	0.961395i	$0.411265\pi$
$569$			45.8657i			1.92279i	−0.275172	+	0.961395i	$0.588735\pi$
$570$		0			0
$571$	−13.5859			−0.568552			−0.284276	−	0.958742i	$-0.591753\pi$
$571$	−13.5859			−0.568552			−0.284276	+	0.958742i	$0.591753\pi$
$572$	1.67576	+	2.90251i	0.0700673	+	0.121360i
$573$		0			0
$574$	5.48379	−	12.9277i	0.228889	−	0.539590i
$575$		−	5.59780i		−	0.233444i
$576$		0			0
$577$	−17.2122	+	9.93748i	−0.716554	+	0.413703i	−0.813483	−	0.581589i	$-0.802431\pi$
$577$	−17.2122	+	9.93748i	−0.716554	+	0.413703i	0.0969291	+	0.995291i	$0.469098\pi$
$578$	−10.1287	−	5.84779i	−0.421297	−	0.243236i
$579$		0			0
$580$	−9.12141	−	5.26625i	−0.378746	−	0.218669i
$581$	−1.07565	+	0.810964i	−0.0446253	+	0.0336444i
$582$		0			0
$583$	−5.74570			−0.237963
$584$	5.84190	+	10.1185i	0.241739	+	0.418705i
$585$		0			0
$586$	22.1332	+	12.7786i	0.914313	+	0.527879i
$587$	11.8126	+	20.4600i	0.487558	+	0.844475i	0.999898	−	0.0143079i	$-0.00455451\pi$
$587$	11.8126	+	20.4600i	0.487558	+	0.844475i	−0.512340	+	0.858783i	$0.671221\pi$
$588$		0			0
$589$	19.5057	−	33.7848i	0.803717	−	1.39208i
$590$	−9.90276	+	5.71736i	−0.407690	+	0.235380i
$591$		0			0
$592$	4.15617	−	7.19869i	0.170817	−	0.295864i
$593$	−23.9443	+	41.4727i	−0.983274	+	1.70308i	−0.333907	+	0.942606i	$0.608367\pi$
$593$	−23.9443	+	41.4727i	−0.983274	+	1.70308i	−0.649367	+	0.760475i	$0.724966\pi$
$594$		0			0
$595$	−5.60969	−	2.37958i	−0.229975	−	0.0975531i
$596$	−7.75355	+	4.47651i	−0.317598	+	0.183365i
$597$		0			0
$598$			24.4347i			0.999208i
$599$		−	14.8968i		−	0.608669i	−0.952565	−	0.304334i	$-0.901566\pi$
$599$		−	14.8968i		−	0.608669i	0.952565	−	0.304334i	$-0.0984340\pi$
$600$		0			0
$601$	−13.3073	+	7.68296i	−0.542815	+	0.313394i	−0.746219	−	0.665700i	$-0.768133\pi$
$601$	−13.3073	+	7.68296i	−0.542815	+	0.313394i	0.203404	+	0.979095i	$0.434800\pi$
$602$	−18.9451	−	25.1283i	−0.772143	−	1.02415i
$603$		0			0
$604$	−2.50359	+	4.33635i	−0.101870	+	0.176443i
$605$	5.20523	−	9.01573i	0.211623	−	0.366542i
$606$		0			0
$607$	−7.76159	+	4.48116i	−0.315033	+	0.181885i	−0.649177	−	0.760638i	$-0.724886\pi$
$607$	−7.76159	+	4.48116i	−0.315033	+	0.181885i	0.334143	+	0.942522i	$0.391553\pi$
$608$	2.42029	−	4.19206i	0.0981556	−	0.170011i
$609$		0			0
$610$	−4.74999	−	8.22722i	−0.192321	−	0.333110i
$611$	−24.4259	−	14.1023i	−0.988165	−	0.570517i
$612$		0			0
$613$	−10.8226	−	18.7452i	−0.437119	−	0.757113i	0.560347	−	0.828258i	$-0.310668\pi$
$613$	−10.8226	−	18.7452i	−0.437119	−	0.757113i	−0.997466	+	0.0711452i	$0.977335\pi$
$614$	9.33336			0.376664
$615$		0			0
$616$	−1.87014	−	0.793294i	−0.0753500	−	0.0319627i
$617$	28.3642	+	16.3761i	1.14190	+	0.659277i	0.946901	−	0.321527i	$-0.104196\pi$
$617$	28.3642	+	16.3761i	1.14190	+	0.659277i	0.195000	+	0.980803i	$0.437529\pi$
$618$		0			0
$619$	11.3946	+	6.57868i	0.457988	+	0.264420i	0.711198	−	0.702992i	$-0.248153\pi$
$619$	11.3946	+	6.57868i	0.457988	+	0.264420i	−0.253210	+	0.967411i	$0.581486\pi$
$620$	−6.97950	+	4.02962i	−0.280304	+	0.161833i
$621$		0			0
$622$		−	5.36577i		−	0.215148i
$623$	−13.6479	−	5.78931i	−0.546792	−	0.231944i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	25.4559			1.01742
$627$		0			0
$628$		−	3.25327i		−	0.129819i
$629$	−19.1444			−0.763338
$630$		0			0
$631$	−32.3439			−1.28759			−0.643795	−	0.765198i	$-0.722641\pi$
$631$	−32.3439			−1.28759			−0.643795	+	0.765198i	$0.722641\pi$
$632$		−	1.11044i		−	0.0441708i
$633$		0			0
$634$	7.48676			0.297337
$635$	−6.32397	−	10.9534i	−0.250959	−	0.434674i
$636$		0			0
$637$	−29.3757	−	8.40804i	−1.16391	−	0.333139i
$638$			8.08696i			0.320166i
$639$		0			0
$640$	−0.866025	+	0.500000i	−0.0342327	+	0.0197642i
$641$	−24.2747	−	14.0150i	−0.958793	−	0.553559i	−0.0629917	−	0.998014i	$-0.520064\pi$
$641$	−24.2747	−	14.0150i	−0.958793	−	0.553559i	−0.895801	+	0.444455i	$0.853397\pi$
$642$		0			0
$643$	11.6003	+	6.69742i	0.457470	+	0.264121i	0.710980	−	0.703212i	$-0.248252\pi$
$643$	11.6003	+	6.69742i	0.457470	+	0.264121i	−0.253510	+	0.967333i	$0.581585\pi$
$644$	−8.91596	−	11.8260i	−0.351338	−	0.466008i
$645$		0			0
$646$	−11.1485			−0.438632
$647$	−10.5813	−	18.3274i	−0.415995	−	0.720524i	0.579537	−	0.814946i	$-0.303233\pi$
$647$	−10.5813	−	18.3274i	−0.415995	−	0.720524i	−0.995532	+	0.0944214i	$0.969900\pi$
$648$		0			0
$649$	7.60344	+	4.38985i	0.298461	+	0.172317i
$650$	2.18252	+	3.78024i	0.0856057	+	0.148273i
$651$		0			0
$652$	−2.40931	+	4.17306i	−0.0943560	+	0.163429i
$653$	18.2718	−	10.5492i	0.715030	−	0.412823i	−0.0978908	−	0.995197i	$-0.531210\pi$
$653$	18.2718	−	10.5492i	0.715030	−	0.412823i	0.812921	+	0.582374i	$0.197876\pi$
$654$		0			0
$655$	−4.96301	+	8.59619i	−0.193921	+	0.335881i
$656$	−2.65381	+	4.59654i	−0.103614	+	0.179465i
$657$		0			0
$658$	16.9675	−	2.08749i	0.661461	−	0.0813790i
$659$	−24.0800	+	13.9026i	−0.938025	+	0.541569i	−0.889341	−	0.457245i	$-0.848836\pi$
$659$	−24.0800	+	13.9026i	−0.938025	+	0.541569i	−0.0486845	+	0.998814i	$0.515503\pi$
$660$		0			0
$661$		−	10.1692i		−	0.395534i	−0.980249	−	0.197767i	$-0.936631\pi$
$661$		−	10.1692i		−	0.395534i	0.980249	−	0.197767i	$-0.0633690\pi$
$662$		−	7.42867i		−	0.288723i
$663$		0			0
$664$	0.440942	−	0.254578i	0.0171119	−	0.00987953i
$665$	12.7111	−	1.56384i	0.492916	−	0.0606430i
$666$		0			0
$667$	−29.4794	+	51.0598i	−1.14145	+	1.97704i
$668$	4.97259	−	8.61278i	0.192395	−	0.333238i
$669$		0			0
$670$	11.8687	−	6.85237i	0.458526	−	0.264730i
$671$	−3.64709	+	6.31694i	−0.140794	+	0.243863i
$672$		0			0
$673$	−5.29232	−	9.16657i	−0.204004	−	0.353345i	0.745811	−	0.666158i	$-0.232062\pi$
$673$	−5.29232	−	9.16657i	−0.204004	−	0.353345i	−0.949815	+	0.312812i	$0.898729\pi$
$674$	22.3731	+	12.9171i	0.861781	+	0.497549i
$675$		0			0
$676$	−3.02683	−	5.24262i	−0.116416	−	0.201639i
$677$	33.1306			1.27331			0.636657	−	0.771147i	$-0.280317\pi$
$677$	33.1306			1.27331			0.636657	+	0.771147i	$0.280317\pi$
$678$		0			0
$679$	−14.0038	−	18.5744i	−0.537417	−	0.712819i
$680$	1.99457	+	1.15157i	0.0764884	+	0.0441606i
$681$		0			0
$682$	5.35894	+	3.09398i	0.205204	+	0.118475i
$683$	−15.1376	+	8.73972i	−0.579225	+	0.334416i	−0.760826	−	0.648957i	$-0.775206\pi$
$683$	−15.1376	+	8.73972i	−0.579225	+	0.334416i	0.181600	+	0.983372i	$0.441872\pi$
$684$		0			0
$685$		−	14.3935i		−	0.549947i
$686$	17.2854	−	6.64956i	0.659958	−	0.253881i
$687$		0			0
$688$	5.94724	+	10.3009i	0.226736	+	0.392719i
$689$	32.6647			1.24442
$690$		0			0
$691$			19.0857i			0.726054i	0.931779	+	0.363027i	$0.118257\pi$
$691$			19.0857i			0.726054i	−0.931779	+	0.363027i	$0.881743\pi$
$692$	−16.6263			−0.632039
$693$		0			0
$694$	−18.4244			−0.699380
$695$			10.1851i			0.386341i
$696$		0			0
$697$	12.2242			0.463024
$698$	−0.793577	−	1.37452i	−0.0300373	−	0.0520262i
$699$		0			0
$700$	−2.43568	−	1.03319i	−0.0920599	−	0.0390509i
$701$		−	14.4247i		−	0.544815i	−0.962182	−	0.272407i	$-0.912180\pi$
$701$		−	14.4247i		−	0.544815i	0.962182	−	0.272407i	$-0.0878198\pi$
$702$		0			0
$703$	34.8458	−	20.1182i	1.31423	−	0.758773i
$704$	0.664943	+	0.383905i	0.0250610	+	0.0144690i
$705$		0			0
$706$	−7.97208	−	4.60268i	−0.300033	−	0.173224i
$707$	−28.8663	−	12.2448i	−1.08563	−	0.460514i
$708$		0			0
$709$	23.9438			0.899229			0.449615	−	0.893223i	$-0.351561\pi$
$709$	23.9438			0.899229			0.449615	+	0.893223i	$0.351561\pi$
$710$	−3.75292	−	6.50024i	−0.140844	−	0.243950i
$711$		0			0
$712$	4.85263	+	2.80167i	0.181860	+	0.104997i
$713$	22.5570	+	39.0699i	0.844766	+	1.46318i
$714$		0			0
$715$	1.67576	−	2.90251i	0.0626701	−	0.108548i
$716$	−4.07453	+	2.35243i	−0.152272	+	0.0879145i
$717$		0			0
$718$	12.9183	−	22.3751i	0.482106	−	0.835033i
$719$	−7.04096	+	12.1953i	−0.262584	+	0.454808i	−0.966928	−	0.255051i	$-0.917908\pi$
$719$	−7.04096	+	12.1953i	−0.262584	+	0.454808i	0.704344	+	0.709859i	$0.251241\pi$
$720$		0			0
$721$	1.39865	+	1.85514i	0.0520883	+	0.0690889i
$722$	3.83750	−	2.21558i	0.142817	−	0.0824554i
$723$		0			0
$724$		−	8.33408i		−	0.309734i
$725$			10.5325i			0.391167i
$726$		0			0
$727$	−10.6031	+	6.12171i	−0.393248	+	0.227042i	−0.683566	−	0.729888i	$-0.739572\pi$
$727$	−10.6031	+	6.12171i	−0.393248	+	0.227042i	0.290319	+	0.956930i	$0.406239\pi$
$728$	10.6318	+	4.50993i	0.394042	+	0.167149i
$729$		0			0
$730$	5.84190	−	10.1185i	0.216218	−	0.374501i
$731$	13.6973	−	23.7244i	0.506612	−	0.877478i
$732$		0			0
$733$	−27.7009	+	15.9931i	−1.02316	+	0.590720i	−0.915017	−	0.403416i	$-0.867823\pi$
$733$	−27.7009	+	15.9931i	−1.02316	+	0.590720i	−0.108140	+	0.994136i	$0.534489\pi$
$734$	11.1282	−	19.2746i	0.410750	−	0.711439i
$735$		0			0
$736$	2.79890	+	4.84784i	0.103169	+	0.178694i
$737$	−9.11288	−	5.26132i	−0.335677	−	0.193803i
$738$		0			0
$739$	−17.7732	−	30.7841i	−0.653798	−	1.13241i	−0.982194	−	0.187871i	$-0.939841\pi$
$739$	−17.7732	−	30.7841i	−0.653798	−	1.13241i	0.328396	−	0.944540i	$-0.393492\pi$
$740$	−8.31233			−0.305567
$741$		0			0
$742$	−15.8091	+	11.9190i	−0.580371	+	0.437560i
$743$	−19.6903	−	11.3682i	−0.722366	−	0.417058i	0.0932570	−	0.995642i	$-0.470272\pi$
$743$	−19.6903	−	11.3682i	−0.722366	−	0.417058i	−0.815623	+	0.578584i	$0.803606\pi$
$744$		0			0
$745$	7.75355	+	4.47651i	0.284068	+	0.164007i
$746$	28.3884	−	16.3900i	1.03937	−	0.600082i
$747$		0			0
$748$		−	1.76837i		−	0.0646580i
$749$	6.62349	−	15.6144i	0.242017	−	0.570539i
$750$		0			0
$751$	−7.22595	−	12.5157i	−0.263678	−	0.456705i	0.703538	−	0.710658i	$-0.251602\pi$
$751$	−7.22595	−	12.5157i	−0.263678	−	0.456705i	−0.967217	+	0.253953i	$0.918269\pi$
$752$	−6.46146			−0.235625
$753$		0			0
$754$		−	45.9749i		−	1.67431i
$755$	5.00718			0.182230
$756$		0			0
$757$	29.2971			1.06482			0.532410	−	0.846487i	$-0.321287\pi$
$757$	29.2971			1.06482			0.532410	+	0.846487i	$0.321287\pi$
$758$			26.7133i			0.970270i
$759$		0			0
$760$	−4.84057			−0.175586
$761$	−24.4664	−	42.3770i	−0.886906	−	1.53617i	−0.843513	−	0.537109i	$-0.819516\pi$
$761$	−24.4664	−	42.3770i	−0.886906	−	1.53617i	−0.0433933	−	0.999058i	$-0.513817\pi$
$762$		0			0
$763$	−18.4380	+	13.9010i	−0.667500	+	0.503249i
$764$		−	3.79290i		−	0.137222i
$765$		0			0
$766$	1.57386	−	0.908668i	0.0568658	−	0.0328315i
$767$	−43.2260	−	24.9566i	−1.56080	−	0.901129i
$768$		0			0
$769$	−44.0886	−	25.4546i	−1.58988	−	0.917915i	−0.993326	−	0.115339i	$-0.963205\pi$
$769$	−44.0886	−	25.4546i	−1.58988	−	0.917915i	−0.596549	−	0.802577i	$-0.703462\pi$
$770$	0.248055	+	2.01623i	0.00893930	+	0.0726600i
$771$		0			0
$772$	21.4959			0.773656
$773$	−10.7757	−	18.6640i	−0.387574	−	0.671297i	0.604549	−	0.796568i	$-0.293353\pi$
$773$	−10.7757	−	18.6640i	−0.387574	−	0.671297i	−0.992123	+	0.125271i	$0.960020\pi$
$774$		0			0
$775$	6.97950	+	4.02962i	0.250711	+	0.144748i
$776$	4.39608	+	7.61423i	0.157810	+	0.273335i
$777$		0			0
$778$	−14.9847	+	25.9543i	−0.537228	+	0.930507i
$779$	−22.2499	+	12.8460i	−0.797185	+	0.460255i
$780$		0			0
$781$	−2.88153	+	4.99095i	−0.103109	+	0.178590i
$782$	6.44624	−	11.1652i	0.230517	−	0.399268i
$783$		0			0
$784$	−6.79125	+	1.69673i	−0.242545	+	0.0605973i
$785$	−2.81741	+	1.62663i	−0.100558	+	0.0580570i
$786$		0			0
$787$			24.6504i			0.878693i	0.898318	+	0.439347i	$0.144790\pi$
$787$			24.6504i			0.878693i	−0.898318	+	0.439347i	$0.855210\pi$
$788$		−	13.3908i		−	0.477027i
$789$		0			0
$790$	−0.961666	+	0.555218i	−0.0342145	+	0.0197538i
$791$	0.832270	−	1.96202i	0.0295921	−	0.0697614i
$792$		0			0
$793$	20.7339	−	35.9122i	0.736283	−	1.27528i
$794$	0.468371	−	0.811242i	0.0166219	−	0.0287899i
$795$		0			0
$796$	−0.485507	+	0.280308i	−0.0172083	+	0.00993524i
$797$	1.27405	−	2.20672i	0.0451293	−	0.0781662i	−0.842578	−	0.538574i	$-0.818963\pi$
$797$	1.27405	−	2.20672i	0.0451293	−	0.0781662i	0.887708	+	0.460407i	$0.152297\pi$
$798$		0			0
$799$	7.44080	+	12.8878i	0.263237	+	0.455939i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	−2.90439	−	5.03054i	−0.102557	−	0.177635i
$803$	−8.97094			−0.316578
$804$		0			0
$805$	−5.78360	+	13.6344i	−0.203845	+	0.480550i
$806$	−30.4659	−	17.5895i	−1.07311	−	0.619563i
$807$		0			0
$808$	10.2637	+	5.92574i	0.361075	+	0.208467i
$809$	−3.56339	+	2.05733i	−0.125282	+	0.0723318i	−0.561331	−	0.827591i	$-0.689711\pi$
$809$	−3.56339	+	2.05733i	−0.125282	+	0.0723318i	0.436049	+	0.899923i	$0.356377\pi$
$810$		0			0
$811$			36.4586i			1.28024i	0.768277	+	0.640118i	$0.221115\pi$
$811$			36.4586i			1.28024i	−0.768277	+	0.640118i	$0.778885\pi$
$812$	16.7758	+	22.2510i	0.588714	+	0.780858i
$813$		0			0
$814$	3.19115	+	5.52723i	0.111850	+	0.193729i
$815$	4.81863			0.168789
$816$		0			0
$817$			57.5761i			2.01433i
$818$	21.8817			0.765076
$819$		0			0
$820$	5.30763			0.185350
$821$			32.3659i			1.12958i	0.825236	+	0.564789i	$0.191042\pi$
$821$			32.3659i			1.12958i	−0.825236	+	0.564789i	$0.808958\pi$
$822$		0			0
$823$	−7.68356			−0.267832			−0.133916	−	0.990993i	$-0.542755\pi$
$823$	−7.68356			−0.267832			−0.133916	+	0.990993i	$0.542755\pi$
$824$	−0.439063	−	0.760480i	−0.0152955	−	0.0264926i
$825$		0			0
$826$	30.0270	−	3.69420i	1.04477	−	0.128538i
$827$		−	8.88863i		−	0.309088i	−0.987986	−	0.154544i	$-0.950609\pi$
$827$		−	8.88863i		−	0.309088i	0.987986	−	0.154544i	$-0.0493908\pi$
$828$		0			0
$829$	15.5068	−	8.95287i	0.538574	−	0.310946i	−0.205927	−	0.978567i	$-0.566021\pi$
$829$	15.5068	−	8.95287i	0.538574	−	0.310946i	0.744501	+	0.667621i	$0.232688\pi$
$830$	−0.440942	−	0.254578i	−0.0153053	−	0.00883652i
$831$		0			0
$832$	−3.78024	−	2.18252i	−0.131056	−	0.0756654i
$833$	11.2048	+	11.5918i	0.388224	+	0.401631i
$834$		0			0
$835$	−9.94518			−0.344167
$836$	1.85832	+	3.21871i	0.0642714	+	0.111321i
$837$		0			0
$838$	13.8082	+	7.97218i	0.476997	+	0.275395i
$839$	−15.0745	−	26.1098i	−0.520430	−	0.901412i	−0.999718	−	0.0237538i	$-0.992438\pi$
$839$	−15.0745	−	26.1098i	−0.520430	−	0.901412i	0.479287	−	0.877658i	$-0.340895\pi$
$840$		0			0
$841$	40.9667	−	70.9565i	1.41265	−	2.44678i
$842$	14.3237	−	8.26978i	0.493627	−	0.284995i
$843$		0			0
$844$	−1.76537	+	3.05771i	−0.0607665	+	0.105251i
$845$	−3.02683	+	5.24262i	−0.104126	+	0.180352i
$846$		0			0
$847$	−21.9932	+	16.5814i	−0.755696	+	0.569743i
$848$	6.48067	−	3.74161i	0.222547	−	0.128488i
$849$		0			0
$850$		−	2.30313i		−	0.0789969i
$851$			46.5308i			1.59505i
$852$		0			0
$853$	11.2347	−	6.48634i	0.384668	−	0.222088i	−0.295180	−	0.955442i	$-0.595379\pi$
$853$	11.2347	−	6.48634i	0.384668	−	0.222088i	0.679847	+	0.733354i	$0.262046\pi$
$854$	3.06914	+	24.9465i	0.105024	+	0.853651i
$855$		0			0
$856$	−3.20536	+	5.55184i	−0.109557	+	0.189758i
$857$	13.2292	−	22.9136i	0.451900	−	0.782714i	−0.546604	−	0.837391i	$-0.684080\pi$
$857$	13.2292	−	22.9136i	0.451900	−	0.782714i	0.998504	+	0.0546774i	$0.0174130\pi$
$858$		0			0
$859$	26.4968	−	15.2980i	0.904060	−	0.521959i	0.0255448	−	0.999674i	$-0.491868\pi$
$859$	26.4968	−	15.2980i	0.904060	−	0.521959i	0.878515	+	0.477714i	$0.158535\pi$
$860$	5.94724	−	10.3009i	0.202799	−	0.351258i
$861$		0			0
$862$	6.08623	+	10.5417i	0.207298	+	0.359050i
$863$	−42.9051	−	24.7713i	−1.46051	−	0.843223i	−0.461471	−	0.887155i	$-0.652678\pi$
$863$	−42.9051	−	24.7713i	−1.46051	−	0.843223i	−0.999035	+	0.0439320i	$0.986012\pi$
$864$		0			0
$865$	8.31317	+	14.3988i	0.282656	+	0.489575i
$866$	8.54538			0.290384
$867$		0			0
$868$	21.1632	−	2.60369i	0.718325	−	0.0883749i
$869$	0.738377	+	0.426302i	0.0250477	+	0.0144613i
$870$		0			0
$871$	51.8073	+	29.9109i	1.75542	+	1.01349i
$872$	7.55832	−	4.36380i	0.255957	−	0.147777i
$873$		0			0
$874$			27.0966i			0.916555i
$875$	0.323069	+	2.62595i	0.0109217	+	0.0887734i
$876$		0			0
$877$	22.0621	+	38.2126i	0.744983	+	1.29035i	0.950203	+	0.311633i	$0.100876\pi$
$877$	22.0621	+	38.2126i	0.744983	+	1.29035i	−0.205219	+	0.978716i	$0.565791\pi$
$878$	6.58176			0.222124
$879$		0			0
$880$		−	0.767810i		−	0.0258829i
$881$	14.2789			0.481068			0.240534	−	0.970641i	$-0.422677\pi$
$881$	14.2789			0.481068			0.240534	+	0.970641i	$0.422677\pi$
$882$		0			0
$883$	−2.99831			−0.100901			−0.0504505	−	0.998727i	$-0.516066\pi$
$883$	−2.99831			−0.100901			−0.0504505	+	0.998727i	$0.516066\pi$
$884$			10.0533i			0.338129i
$885$		0			0
$886$	−27.0738			−0.909561
$887$	−18.0122	−	31.1981i	−0.604791	−	1.04753i	−0.992084	−	0.125572i	$-0.959923\pi$
$887$	−18.0122	−	31.1981i	−0.604791	−	1.04753i	0.387293	−	0.921957i	$-0.373410\pi$
$888$		0			0
$889$	4.08615	+	33.2129i	0.137045	+	1.11392i
$890$		−	5.60333i		−	0.187824i
$891$		0			0
$892$	22.1791	−	12.8051i	0.742612	−	0.428748i
$893$	−27.0868	−	15.6386i	−0.906426	−	0.523325i
$894$		0			0
$895$	4.07453	+	2.35243i	0.136197	+	0.0786331i
$896$	2.62595	−	0.323069i	0.0877269	−	0.0107930i
$897$		0			0
$898$	−17.9654			−0.599514
$899$	−42.4419	−	73.5116i	−1.41552	−	2.45175i
$900$		0			0
$901$	−14.9258	−	8.61744i	−0.497252	−	0.287089i
$902$	−2.03763	−	3.52927i	−0.0678455	−	0.117512i
$903$		0			0
$904$	−0.402767	+	0.697613i	−0.0133958	+	0.0232023i
$905$	−7.21752	+	4.16704i	−0.239919	+	0.138517i
$906$		0			0
$907$	−10.5464	+	18.2670i	−0.350189	+	0.606545i	−0.986282	−	0.165067i	$-0.947216\pi$
$907$	−10.5464	+	18.2670i	−0.350189	+	0.606545i	0.636093	+	0.771612i	$0.280549\pi$
$908$	5.56930	−	9.64631i	0.184824	−	0.320124i
$909$		0			0
$910$	−1.41021	−	11.4624i	−0.0467480	−	0.379975i
$911$	23.7590	−	13.7172i	0.787169	−	0.454472i	−0.0517958	−	0.998658i	$-0.516495\pi$
$911$	23.7590	−	13.7172i	0.787169	−	0.454472i	0.838965	+	0.544185i	$0.183161\pi$
$912$		0			0
$913$			0.390935i			0.0129381i
$914$			5.14932i			0.170324i
$915$		0			0
$916$	3.29819	−	1.90421i	0.108975	−	0.0629169i
$917$	20.9698	−	15.8098i	0.692484	−	0.522085i
$918$		0			0
$919$	2.13518	−	3.69824i	0.0704332	−	0.121994i	−0.828658	−	0.559755i	$-0.810895\pi$
$919$	2.13518	−	3.69824i	0.0704332	−	0.121994i	0.899091	+	0.437761i	$0.144229\pi$
$920$	2.79890	−	4.84784i	0.0922770	−	0.159828i
$921$		0			0
$922$	9.45788	−	5.46051i	0.311479	−	0.179832i
$923$	16.3817	−	28.3739i	0.539209	−	0.933938i
$924$		0			0
$925$	4.15617	+	7.19869i	0.136654	+	0.236691i
$926$	−25.7563	−	14.8704i	−0.846406	−	0.488673i
$927$		0			0
$928$	−5.26625	−	9.12141i	−0.172873	−	0.299425i
$929$	−11.8008			−0.387171			−0.193585	−	0.981083i	$-0.562012\pi$
$929$	−11.8008			−0.387171			−0.193585	+	0.981083i	$0.562012\pi$
$930$		0			0
$931$	−32.5759	−	9.32401i	−1.06763	−	0.305582i
$932$	−2.04230	−	1.17912i	−0.0668977	−	0.0386234i
$933$		0			0
$934$	7.89337	+	4.55724i	0.258279	+	0.149117i
$935$	−1.53145	+	0.884185i	−0.0500839	+	0.0289159i
$936$		0			0
$937$		−	52.8223i		−	1.72563i	−0.505520	−	0.862815i	$-0.668699\pi$
$937$		−	52.8223i		−	1.72563i	0.505520	−	0.862815i	$-0.331301\pi$
$938$	−35.9880	+	4.42757i	−1.17505	+	0.144565i
$939$		0			0
$940$	3.23073	+	5.59578i	0.105375	+	0.182514i
$941$	41.3578			1.34823			0.674113	−	0.738629i	$-0.264526\pi$
$941$	41.3578			1.34823			0.674113	+	0.738629i	$0.264526\pi$
$942$		0			0
$943$		−	29.7110i		−	0.967524i
$944$	−11.4347			−0.372168
$945$		0			0
$946$	−9.13270			−0.296930
$947$			19.1358i			0.621829i	0.950438	+	0.310914i	$0.100635\pi$
$947$			19.1358i			0.621829i	−0.950438	+	0.310914i	$0.899365\pi$
$948$		0			0
$949$	51.0003			1.65554
$950$	2.42029	+	4.19206i	0.0785245	+	0.136008i
$951$		0			0
$952$	−3.66834	−	4.86562i	−0.118892	−	0.157696i
$953$		−	16.1271i		−	0.522407i	−0.965284	−	0.261203i	$-0.915881\pi$
$953$		−	16.1271i		−	0.522407i	0.965284	−	0.261203i	$-0.0841193\pi$
$954$		0			0
$955$	−3.28474	+	1.89645i	−0.106292	+	0.0613676i
$956$	10.1968	+	5.88712i	0.329788	+	0.190403i
$957$		0			0
$958$	−32.3003	−	18.6486i	−1.04358	−	0.602508i
$959$	−14.8712	+	35.0578i	−0.480216	+	1.13208i
$960$		0			0
$961$	−33.9513			−1.09520
$962$	−18.1419	−	31.4226i	−0.584917	−	1.01311i
$963$		0			0
$964$	−16.2931	−	9.40683i	−0.524765	−	0.302973i
$965$	−10.7480	−	18.6160i	−0.345989	−	0.599271i
$966$		0			0
$967$	23.6109	−	40.8952i	0.759274	−	1.31510i	−0.183948	−	0.982936i	$-0.558888\pi$
$967$	23.6109	−	40.8952i	0.759274	−	1.31510i	0.943221	−	0.332165i	$-0.107779\pi$
$968$	9.01573	−	5.20523i	0.289777	−	0.167303i
$969$		0			0
$970$	4.39608	−	7.61423i	0.141149	−	0.244478i
$971$	12.0076	−	20.7978i	0.385343	−	0.667434i	−0.606474	−	0.795104i	$-0.707416\pi$
$971$	12.0076	−	20.7978i	0.385343	−	0.667434i	0.991817	+	0.127670i	$0.0407497\pi$
$972$		0			0
$973$	10.5231	−	24.8075i	0.337355	−	0.795292i
$974$	−16.3605	+	9.44574i	−0.524224	+	0.302661i
$975$		0			0
$976$		−	9.49997i		−	0.304087i
$977$		−	10.7320i		−	0.343348i	−0.985154	−	0.171674i	$-0.945082\pi$
$977$		−	10.7320i		−	0.343348i	0.985154	−	0.171674i	$-0.0549176\pi$
$978$		0			0
$979$	−3.72590	+	2.15115i	−0.119080	+	0.0687510i
$980$	4.86503	+	5.03304i	0.155408	+	0.160774i
$981$		0			0
$982$	17.4047	−	30.1458i	0.555406	−	0.961991i
$983$	−27.1880	+	47.0910i	−0.867162	+	1.50197i	−0.00227708	+	0.999997i	$0.500725\pi$
$983$	−27.1880	+	47.0910i	−0.867162	+	1.50197i	−0.864885	+	0.501971i	$0.832609\pi$
$984$		0			0
$985$	−11.5968	+	6.69540i	−0.369504	+	0.213333i
$986$	−12.1289	+	21.0078i	−0.386262	+	0.669026i
$987$		0			0
$988$	−10.5647	−	18.2986i	−0.336107	−	0.582154i
$989$	−57.6625	−	33.2914i	−1.83356	−	1.05861i
$990$		0			0
$991$	1.44414	+	2.50132i	0.0458746	+	0.0794571i	0.888051	−	0.459745i	$-0.152059\pi$
$991$	1.44414	+	2.50132i	0.0458746	+	0.0794571i	−0.842176	+	0.539202i	$0.818726\pi$
$992$	−8.05924			−0.255881
$993$		0			0
$994$	2.42490	+	19.7100i	0.0769131	+	0.625162i
$995$	0.485507	+	0.280308i	0.0153916	+	0.00888635i
$996$		0			0
$997$	−8.67758	−	5.01001i	−0.274822	−	0.158668i	0.356255	−	0.934389i	$-0.384053\pi$
$997$	−8.67758	−	5.01001i	−0.274822	−	0.158668i	−0.631077	+	0.775720i	$0.717387\pi$
$998$	−21.1593	+	12.2163i	−0.669786	+	0.386701i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bk.b.341.6		28
3.2	odd	2		630.2.bk.b.131.10	yes	28
7.3	odd	6		1890.2.t.b.1151.11		28
9.2	odd	6		1890.2.t.b.1601.11		28
9.7	even	3		630.2.t.b.551.1	yes	28
21.17	even	6		630.2.t.b.311.1	✓	28
63.38	even	6	inner	1890.2.bk.b.521.6		28
63.52	odd	6		630.2.bk.b.101.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.1	✓	28	21.17	even	6
630.2.t.b.551.1	yes	28	9.7	even	3
630.2.bk.b.101.3	yes	28	63.52	odd	6
630.2.bk.b.131.10	yes	28	3.2	odd	2
1890.2.t.b.1151.11		28	7.3	odd	6
1890.2.t.b.1601.11		28	9.2	odd	6
1890.2.bk.b.341.6		28	1.1	even	1	trivial
1890.2.bk.b.521.6		28	63.38	even	6	inner

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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bk (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.323069 - 2.62595i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.323069 - 2.62595i) q^{7} +1.00000i q^{8} +(0.866025 - 0.500000i) q^{10} +(-0.664943 - 0.383905i) q^{11} +(3.78024 + 2.18252i) q^{13} +(-2.62595 + 0.323069i) q^{14} +1.00000 q^{16} +(-1.15157 - 1.99457i) q^{17} +(4.19206 + 2.42029i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.383905 + 0.664943i) q^{22} +(-4.84784 + 2.79890i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(2.18252 - 3.78024i) q^{26} +(0.323069 + 2.62595i) q^{28} +(9.12141 - 5.26625i) q^{29} -8.05924i q^{31} -1.00000i q^{32} +(-1.99457 + 1.15157i) q^{34} +(2.11261 - 1.59276i) q^{35} +(4.15617 - 7.19869i) q^{37} +(2.42029 - 4.19206i) q^{38} +(-0.866025 + 0.500000i) q^{40} +(-2.65381 + 4.59654i) q^{41} +(5.94724 + 10.3009i) q^{43} +(0.664943 + 0.383905i) q^{44} +(2.79890 + 4.84784i) q^{46} -6.46146 q^{47} +(-6.79125 + 1.69673i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-3.78024 - 2.18252i) q^{52} +(6.48067 - 3.74161i) q^{53} -0.767810i q^{55} +(2.62595 - 0.323069i) q^{56} +(-5.26625 - 9.12141i) q^{58} -11.4347 q^{59} -9.49997i q^{61} -8.05924 q^{62} -1.00000 q^{64} +4.36505i q^{65} +13.7047 q^{67} +(1.15157 + 1.99457i) q^{68} +(-1.59276 - 2.11261i) q^{70} -7.50583i q^{71} +(10.1185 - 5.84190i) q^{73} +(-7.19869 - 4.15617i) q^{74} +(-4.19206 - 2.42029i) q^{76} +(-0.793294 + 1.87014i) q^{77} -1.11044 q^{79} +(0.500000 + 0.866025i) q^{80} +(4.59654 + 2.65381i) q^{82} +(-0.254578 - 0.440942i) q^{83} +(1.15157 - 1.99457i) q^{85} +(10.3009 - 5.94724i) q^{86} +(0.383905 - 0.664943i) q^{88} +(2.80167 - 4.85263i) q^{89} +(4.50993 - 10.6318i) q^{91} +(4.84784 - 2.79890i) q^{92} +6.46146i q^{94} +4.84057i q^{95} +(7.61423 - 4.39608i) q^{97} +(1.69673 + 6.79125i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7}+O(q^{10}) \) 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7	\( 28 q - 28 q^{4} + 14 q^{5} + 8 q^{7} + 28 q^{16} - 6 q^{17} - 6 q^{19} - 14 q^{20} - 6 q^{22} - 30 q^{23} - 14 q^{25} + 12 q^{26} - 8 q^{28} + 4 q^{35} + 4 q^{37} + 6 q^{38} + 18 q^{41} + 28 q^{43} - 18 q^{46} - 60 q^{47} - 20 q^{49} - 42 q^{53} + 6 q^{58} + 48 q^{59} - 12 q^{62} - 28 q^{64} + 80 q^{67} + 6 q^{68} + 6 q^{70} + 6 q^{73} + 6 q^{76} + 18 q^{77} - 4 q^{79} + 14 q^{80} + 24 q^{82} - 18 q^{83} + 6 q^{85} + 96 q^{86} + 6 q^{88} + 6 q^{89} + 66 q^{91} + 30 q^{92} + 72 q^{97} - 24 q^{98}+O(q^{100}) \) 28 * q - 28 * q^4 + 14 * q^5 + 8 * q^7 + 28 * q^16 - 6 * q^17 - 6 * q^19 - 14 * q^20 - 6 * q^22 - 30 * q^23 - 14 * q^25 + 12 * q^26 - 8 * q^28 + 4 * q^35 + 4 * q^37 + 6 * q^38 + 18 * q^41 + 28 * q^43 - 18 * q^46 - 60 * q^47 - 20 * q^49 - 42 * q^53 + 6 * q^58 + 48 * q^59 - 12 * q^62 - 28 * q^64 + 80 * q^67 + 6 * q^68 + 6 * q^70 + 6 * q^73 + 6 * q^76 + 18 * q^77 - 4 * q^79 + 14 * q^80 + 24 * q^82 - 18 * q^83 + 6 * q^85 + 96 * q^86 + 6 * q^88 + 6 * q^89 + 66 * q^91 + 30 * q^92 + 72 * q^97 - 24 * q^98

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