LMFDB - Embedded newform 616.2.r.d.113.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [616,2,Mod(113,616)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(616, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 8]))

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

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

chi := DirichletCharacter("616.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.r (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} - 2 x^{15} + 5 x^{14} + 7 x^{13} + 31 x^{12} + x^{11} + 487 x^{10} + 402 x^{9} + 1095 x^{8} + \cdots + 16 $ x^16 - 2x^15 + 5x^14 + 7x^13 + 31x^12 + x^11 + 487x^10 + 402x^9 + 1095x^8 + 498x^7 + 752x^6 + 225x^5 + 219x^4 + 14x^3 + 12x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			113.4
Root			$-1.97859 - 1.43753i$ of defining polynomial
Character	$\chi$	$=$	616.113
Dual form			616.2.r.d.169.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.768256 + 2.36445i) q^{3} +(1.50334 + 1.09224i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-2.57335 + 1.86964i) q^{9} +(2.66041 + 1.98046i) q^{11} +(-5.08555 + 3.69487i) q^{13} +(-1.42760 + 4.39369i) q^{15} +(4.30386 + 3.12693i) q^{17} +(-2.26664 - 6.97601i) q^{19} +2.48613 q^{21} +2.03148 q^{23} +(-0.478044 - 1.47127i) q^{25} +(-0.363706 - 0.264248i) q^{27} +(-1.23552 + 3.80255i) q^{29} +(4.99042 - 3.62575i) q^{31} +(-2.63882 + 7.81190i) q^{33} +(1.50334 - 1.09224i) q^{35} +(-3.03530 + 9.34170i) q^{37} +(-12.6433 - 9.18591i) q^{39} +(-3.72176 - 11.4544i) q^{41} -4.70559 q^{43} -5.91071 q^{45} +(-0.0441697 - 0.135940i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-4.08701 + 12.5785i) q^{51} +(-6.22136 + 4.52008i) q^{53} +(1.83636 + 5.88311i) q^{55} +(14.7531 - 10.7187i) q^{57} +(1.51314 - 4.65696i) q^{59} +(7.92048 + 5.75456i) q^{61} +(0.982930 + 3.02515i) q^{63} -11.6810 q^{65} +3.97261 q^{67} +(1.56069 + 4.80332i) q^{69} +(-0.0826955 - 0.0600818i) q^{71} +(4.32558 - 13.3128i) q^{73} +(3.11147 - 2.26062i) q^{75} +(2.70564 - 1.91820i) q^{77} +(4.13711 - 3.00579i) q^{79} +(-2.60341 + 8.01247i) q^{81} +(-7.67093 - 5.57326i) q^{83} +(3.05479 + 9.40169i) q^{85} -9.94014 q^{87} +14.2422 q^{89} +(1.94251 + 5.97842i) q^{91} +(12.4068 + 9.01408i) q^{93} +(4.21195 - 12.9630i) q^{95} +(1.14934 - 0.835042i) q^{97} +(-10.5489 - 0.122391i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{3} + 6 q^{5} - 4 q^{7} - q^{9} - 2 q^{11} + 4 q^{13} + 22 q^{15} - 6 q^{17} - 10 q^{19} + 4 q^{21} + 14 q^{23} + 8 q^{25} + 29 q^{27} - 4 q^{29} - 8 q^{31} - 51 q^{33} + 6 q^{35} + 11 q^{37}+ \cdots - 12 q^{99}+O(q^{100}) $ 16 * q - q^3 + 6 * q^5 - 4 * q^7 - q^9 - 2 * q^11 + 4 * q^13 + 22 * q^15 - 6 * q^17 - 10 * q^19 + 4 * q^21 + 14 * q^23 + 8 * q^25 + 29 * q^27 - 4 * q^29 - 8 * q^31 - 51 * q^33 + 6 * q^35 + 11 * q^37 - 38 * q^39 + 6 * q^41 - 36 * q^43 - 70 * q^45 - 9 * q^47 - 4 * q^49 - 4 * q^51 - 4 * q^53 - 13 * q^55 + 24 * q^57 + 17 * q^59 + 25 * q^61 - 11 * q^63 + 26 * q^65 - 20 * q^67 + 45 * q^69 + 18 * q^71 + 48 * q^73 + 8 * q^75 + 3 * q^77 + 21 * q^79 - 30 * q^81 - 8 * q^83 - 38 * q^85 + 8 * q^87 - 16 * q^89 + 4 * q^91 + 85 * q^93 + 16 * q^95 - 44 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	0.768256	+	2.36445i	0.443553	+	1.36511i	0.884063	+	0.467367i	$0.154797\pi$
$3$	0.768256	+	2.36445i	0.443553	+	1.36511i	−0.440511	+	0.897747i	$0.645203\pi$
$4$		0			0
$5$	1.50334	+	1.09224i	0.672314	+	0.488465i	0.870799	−	0.491639i	$-0.163602\pi$
$5$	1.50334	+	1.09224i	0.672314	+	0.488465i	−0.198485	+	0.980104i	$0.563602\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$		0			0
$9$	−2.57335	+	1.86964i	−0.857782	+	0.623215i
$10$		0			0
$11$	2.66041	+	1.98046i	0.802143	+	0.597131i
$11$	2.66041	+	1.98046i	0.802143	+	0.597131i
$12$		0			0
$13$	−5.08555	+	3.69487i	−1.41048	+	1.02477i	−0.417224	+	0.908804i	$0.636997\pi$
$13$	−5.08555	+	3.69487i	−1.41048	+	1.02477i	−0.993253	+	0.115967i	$0.963003\pi$
$14$		0			0
$15$	−1.42760	+	4.39369i	−0.368604	+	1.13445i
$16$		0			0
$17$	4.30386	+	3.12693i	1.04384	+	0.758393i	0.971031	−	0.238953i	$-0.0768042\pi$
$17$	4.30386	+	3.12693i	1.04384	+	0.758393i	0.0728074	+	0.997346i	$0.476804\pi$
$18$		0			0
$19$	−2.26664	−	6.97601i	−0.520004	−	1.60041i	−0.773989	−	0.633199i	$-0.781741\pi$
$19$	−2.26664	−	6.97601i	−0.520004	−	1.60041i	0.253985	−	0.967208i	$-0.418259\pi$
$20$		0			0
$21$	2.48613			0.542517
$22$		0			0
$23$	2.03148			0.423592			0.211796	−	0.977314i	$-0.432069\pi$
$23$	2.03148			0.423592			0.211796	+	0.977314i	$0.432069\pi$
$24$		0			0
$25$	−0.478044	−	1.47127i	−0.0956087	−	0.294253i
$26$		0			0
$27$	−0.363706	−	0.264248i	−0.0699953	−	0.0508546i
$28$		0			0
$29$	−1.23552	+	3.80255i	−0.229431	+	0.706116i	0.768380	+	0.639993i	$0.221063\pi$
$29$	−1.23552	+	3.80255i	−0.229431	+	0.706116i	−0.997811	+	0.0661230i	$0.978937\pi$
$30$		0			0
$31$	4.99042	−	3.62575i	0.896306	−	0.651204i	−0.0412085	−	0.999151i	$-0.513121\pi$
$31$	4.99042	−	3.62575i	0.896306	−	0.651204i	0.937515	+	0.347946i	$0.113121\pi$
$32$		0			0
$33$	−2.63882	+	7.81190i	−0.459360	+	1.35988i
$34$		0			0
$35$	1.50334	−	1.09224i	0.254111	−	0.184622i
$36$		0			0
$37$	−3.03530	+	9.34170i	−0.499001	+	1.53577i	0.311627	+	0.950204i	$0.399126\pi$
$37$	−3.03530	+	9.34170i	−0.499001	+	1.53577i	−0.810628	+	0.585562i	$0.800874\pi$
$38$		0			0
$39$	−12.6433	−	9.18591i	−2.02455	−	1.47092i
$40$		0			0
$41$	−3.72176	−	11.4544i	−0.581242	−	1.78888i	−0.613866	−	0.789411i	$-0.710386\pi$
$41$	−3.72176	−	11.4544i	−0.581242	−	1.78888i	0.0326238	−	0.999468i	$-0.489614\pi$
$42$		0			0
$43$	−4.70559			−0.717596			−0.358798	−	0.933415i	$-0.616813\pi$
$43$	−4.70559			−0.717596			−0.358798	+	0.933415i	$0.616813\pi$
$44$		0			0
$45$	−5.91071			−0.881117
$46$		0			0
$47$	−0.0441697	−	0.135940i	−0.00644281	−	0.0198289i	0.947783	−	0.318915i	$-0.103318\pi$
$47$	−0.0441697	−	0.135940i	−0.00644281	−	0.0198289i	−0.954226	+	0.299086i	$0.903318\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	−4.08701	+	12.5785i	−0.572296	+	1.76135i
$52$		0			0
$53$	−6.22136	+	4.52008i	−0.854570	+	0.620881i	−0.926402	−	0.376535i	$-0.877115\pi$
$53$	−6.22136	+	4.52008i	−0.854570	+	0.620881i	0.0718324	+	0.997417i	$0.477115\pi$
$54$		0			0
$55$	1.83636	+	5.88311i	0.247615	+	0.793278i
$56$		0			0
$57$	14.7531	−	10.7187i	1.95409	−	1.41973i
$58$		0			0
$59$	1.51314	−	4.65696i	0.196994	−	0.606284i	−0.802954	−	0.596041i	$-0.796739\pi$
$59$	1.51314	−	4.65696i	0.196994	−	0.606284i	0.999948	−	0.0102431i	$-0.00326054\pi$
$60$		0			0
$61$	7.92048	+	5.75456i	1.01411	+	0.736796i	0.965068	−	0.262000i	$-0.0843821\pi$
$61$	7.92048	+	5.75456i	1.01411	+	0.736796i	0.0490455	+	0.998797i	$0.484382\pi$
$62$		0			0
$63$	0.982930	+	3.02515i	0.123838	+	0.381133i
$64$		0			0
$65$	−11.6810			−1.44885
$66$		0			0
$67$	3.97261			0.485331			0.242666	−	0.970110i	$-0.421978\pi$
$67$	3.97261			0.485331			0.242666	+	0.970110i	$0.421978\pi$
$68$		0			0
$69$	1.56069	+	4.80332i	0.187885	+	0.578251i
$70$		0			0
$71$	−0.0826955	−	0.0600818i	−0.00981415	−	0.00713039i	0.582867	−	0.812567i	$-0.301931\pi$
$71$	−0.0826955	−	0.0600818i	−0.00981415	−	0.00713039i	−0.592682	+	0.805437i	$0.701931\pi$
$72$		0			0
$73$	4.32558	−	13.3128i	0.506271	−	1.55814i	−0.292352	−	0.956311i	$-0.594438\pi$
$73$	4.32558	−	13.3128i	0.506271	−	1.55814i	0.798623	−	0.601832i	$-0.205562\pi$
$74$		0			0
$75$	3.11147	−	2.26062i	0.359282	−	0.261034i
$76$		0			0
$77$	2.70564	−	1.91820i	0.308337	−	0.218599i
$78$		0			0
$79$	4.13711	−	3.00579i	0.465461	−	0.338177i	−0.330208	−	0.943908i	$-0.607119\pi$
$79$	4.13711	−	3.00579i	0.465461	−	0.338177i	0.795670	+	0.605731i	$0.207119\pi$
$80$		0			0
$81$	−2.60341	+	8.01247i	−0.289268	+	0.890275i
$82$		0			0
$83$	−7.67093	−	5.57326i	−0.841994	−	0.611745i	0.0809327	−	0.996720i	$-0.474210\pi$
$83$	−7.67093	−	5.57326i	−0.841994	−	0.611745i	−0.922927	+	0.384975i	$0.874210\pi$
$84$		0			0
$85$	3.05479	+	9.40169i	0.331339	+	1.01976i
$86$		0			0
$87$	−9.94014			−1.06569
$88$		0			0
$89$	14.2422			1.50967			0.754836	−	0.655914i	$-0.227717\pi$
$89$	14.2422			1.50967			0.754836	+	0.655914i	$0.227717\pi$
$90$		0			0
$91$	1.94251	+	5.97842i	0.203630	+	0.626708i
$92$		0			0
$93$	12.4068	+	9.01408i	1.28653	+	0.934717i
$94$		0			0
$95$	4.21195	−	12.9630i	0.432137	−	1.32998i
$96$		0			0
$97$	1.14934	−	0.835042i	0.116697	−	0.0847857i	−0.527906	−	0.849303i	$-0.677023\pi$
$97$	1.14934	−	0.835042i	0.116697	−	0.0847857i	0.644603	+	0.764517i	$0.277023\pi$
$98$		0			0
$99$	−10.5489	−	0.122391i	−1.06021	−	0.0123008i
$100$		0			0
$101$	9.89133	−	7.18647i	0.984224	−	0.715081i	0.0255753	−	0.999673i	$-0.491858\pi$
$101$	9.89133	−	7.18647i	0.984224	−	0.715081i	0.958649	+	0.284592i	$0.0918582\pi$
$102$		0			0
$103$	0.0977572	−	0.300866i	0.00963231	−	0.0296452i	−0.946125	−	0.323802i	$-0.895039\pi$
$103$	0.0977572	−	0.300866i	0.00963231	−	0.0296452i	0.955757	+	0.294157i	$0.0950388\pi$
$104$		0			0
$105$	3.73749	+	2.71545i	0.364742	+	0.265001i
$106$		0			0
$107$	−4.79866	−	14.7688i	−0.463904	−	1.42775i	−0.860355	−	0.509695i	$-0.829758\pi$
$107$	−4.79866	−	14.7688i	−0.463904	−	1.42775i	0.396451	−	0.918056i	$-0.370242\pi$
$108$		0			0
$109$	−0.981379			−0.0939991			−0.0469995	−	0.998895i	$-0.514966\pi$
$109$	−0.981379			−0.0939991			−0.0469995	+	0.998895i	$0.514966\pi$
$110$		0			0
$111$	−24.4199			−2.31783
$112$		0			0
$113$	3.09296	+	9.51915i	0.290961	+	0.895486i	0.984548	+	0.175114i	$0.0560293\pi$
$113$	3.09296	+	9.51915i	0.290961	+	0.895486i	−0.693587	+	0.720373i	$0.743971\pi$
$114$		0			0
$115$	3.05400	+	2.21886i	0.284787	+	0.206910i
$116$		0			0
$117$	6.17878	−	19.0163i	0.571228	−	1.75806i
$118$		0			0
$119$	4.30386	−	3.12693i	0.394534	−	0.286646i
$120$		0			0
$121$	3.15555	+	10.5377i	0.286868	+	0.957970i
$122$		0			0
$123$	24.2241	−	17.5998i	2.18421	−	1.58692i
$124$		0			0
$125$	3.75944	−	11.5704i	0.336254	−	1.03488i
$126$		0			0
$127$	9.70891	+	7.05394i	0.861527	+	0.625936i	0.928300	−	0.371832i	$-0.121270\pi$
$127$	9.70891	+	7.05394i	0.861527	+	0.625936i	−0.0667732	+	0.997768i	$0.521270\pi$
$128$		0			0
$129$	−3.61510	−	11.1261i	−0.318292	−	0.979601i
$130$		0			0
$131$	19.5613			1.70908			0.854538	−	0.519388i	$-0.173840\pi$
$131$	19.5613			1.70908			0.854538	+	0.519388i	$0.173840\pi$
$132$		0			0
$133$	−7.33501			−0.636026
$134$		0			0
$135$	−0.258152	−	0.794509i	−0.0222182	−	0.0683804i
$136$		0			0
$137$	−1.64110	−	1.19233i	−0.140209	−	0.101868i	0.515470	−	0.856908i	$-0.327617\pi$
$137$	−1.64110	−	1.19233i	−0.140209	−	0.101868i	−0.655679	+	0.755040i	$0.727617\pi$
$138$		0			0
$139$	−2.76573	+	8.51205i	−0.234586	+	0.721983i	0.762590	+	0.646883i	$0.223928\pi$
$139$	−2.76573	+	8.51205i	−0.234586	+	0.721983i	−0.997176	+	0.0751000i	$0.976072\pi$
$140$		0			0
$141$	0.287490	−	0.208874i	0.0242111	−	0.0175904i
$142$		0			0
$143$	−20.8472	−	0.241874i	−1.74333	−	0.0202265i
$144$		0			0
$145$	−6.01071	+	4.36704i	−0.499163	+	0.362663i
$146$		0			0
$147$	0.768256	−	2.36445i	0.0633647	−	0.195016i
$148$		0			0
$149$	−5.26071	−	3.82213i	−0.430974	−	0.313121i	0.351064	−	0.936351i	$-0.385820\pi$
$149$	−5.26071	−	3.82213i	−0.430974	−	0.313121i	−0.782038	+	0.623231i	$0.785820\pi$
$150$		0			0
$151$	−1.98127	−	6.09771i	−0.161233	−	0.496225i	0.837506	−	0.546428i	$-0.184013\pi$
$151$	−1.98127	−	6.09771i	−0.161233	−	0.496225i	−0.998739	+	0.0502037i	$0.984013\pi$
$152$		0			0
$153$	−16.9216			−1.36803
$154$		0			0
$155$	11.4625			0.920689
$156$		0			0
$157$	−0.728782	−	2.24296i	−0.0581632	−	0.179008i	0.917754	−	0.397149i	$-0.130001\pi$
$157$	−0.728782	−	2.24296i	−0.0581632	−	0.179008i	−0.975917	+	0.218142i	$0.930001\pi$
$158$		0			0
$159$	−15.4671	−	11.2375i	−1.22662	−	0.891192i
$160$		0			0
$161$	0.627760	−	1.93205i	0.0494745	−	0.152267i
$162$		0			0
$163$	6.68530	−	4.85715i	0.523633	−	0.380441i	−0.294338	−	0.955701i	$-0.595099\pi$
$163$	6.68530	−	4.85715i	0.523633	−	0.380441i	0.817971	+	0.575260i	$0.195099\pi$
$164$		0			0
$165$	−12.4995	+	8.86171i	−0.973086	+	0.689883i
$166$		0			0
$167$	−3.52447	+	2.56068i	−0.272732	+	0.198151i	−0.715741	−	0.698366i	$-0.753911\pi$
$167$	−3.52447	+	2.56068i	−0.272732	+	0.198151i	0.443009	+	0.896517i	$0.353911\pi$
$168$		0			0
$169$	8.19353	−	25.2171i	0.630271	−	1.93978i
$170$		0			0
$171$	18.8755	+	13.7139i	1.44345	+	1.04873i
$172$		0			0
$173$	−1.32705	−	4.08424i	−0.100894	−	0.310519i	0.887851	−	0.460131i	$-0.152197\pi$
$173$	−1.32705	−	4.08424i	−0.100894	−	0.310519i	−0.988745	+	0.149612i	$0.952197\pi$
$174$		0			0
$175$	−1.54698			−0.116941
$176$		0			0
$177$	12.1736			0.915025
$178$		0			0
$179$	2.40082	+	7.38898i	0.179446	+	0.552278i	0.999809	−	0.0195656i	$-0.00622833\pi$
$179$	2.40082	+	7.38898i	0.179446	+	0.552278i	−0.820363	+	0.571844i	$0.806228\pi$
$180$		0			0
$181$	−13.4859	−	9.79808i	−1.00240	−	0.728285i	−0.0397974	−	0.999208i	$-0.512671\pi$
$181$	−13.4859	−	9.79808i	−1.00240	−	0.728285i	−0.962601	+	0.270923i	$0.912671\pi$
$182$		0			0
$183$	−7.52141	+	23.1485i	−0.555999	+	1.71119i
$184$		0			0
$185$	−14.7665	+	10.7285i	−1.08565	+	0.788773i
$186$		0			0
$187$	5.25724	+	16.8425i	0.384448	+	1.23165i
$188$		0			0
$189$	−0.363706	+	0.264248i	−0.0264557	+	0.0192212i
$190$		0			0
$191$	−1.18897	+	3.65928i	−0.0860310	+	0.264776i	−0.984813	−	0.173620i	$-0.944453\pi$
$191$	−1.18897	+	3.65928i	−0.0860310	+	0.264776i	0.898782	+	0.438397i	$0.144453\pi$
$192$		0			0
$193$	8.14829	+	5.92008i	0.586527	+	0.426137i	0.841071	−	0.540924i	$-0.181926\pi$
$193$	8.14829	+	5.92008i	0.586527	+	0.426137i	−0.254544	+	0.967061i	$0.581926\pi$
$194$		0			0
$195$	−8.97398	−	27.6191i	−0.642640	−	1.97784i
$196$		0			0
$197$	−5.76160			−0.410497			−0.205249	−	0.978710i	$-0.565800\pi$
$197$	−5.76160			−0.410497			−0.205249	+	0.978710i	$0.565800\pi$
$198$		0			0
$199$	11.7863			0.835509			0.417754	−	0.908560i	$-0.362817\pi$
$199$	11.7863			0.835509			0.417754	+	0.908560i	$0.362817\pi$
$200$		0			0
$201$	3.05198	+	9.39302i	0.215270	+	0.662533i
$202$		0			0
$203$	3.23465	+	2.35011i	0.227028	+	0.164945i
$204$		0			0
$205$	6.91589	−	21.2849i	0.483027	−	1.48660i
$206$		0			0
$207$	−5.22769	+	3.79814i	−0.363349	+	0.263989i
$208$		0			0
$209$	7.78552	−	23.0480i	0.538536	−	1.59427i
$210$		0			0
$211$	−0.205646	+	0.149411i	−0.0141573	+	0.0102859i	−0.594841	−	0.803843i	$-0.702785\pi$
$211$	−0.205646	+	0.149411i	−0.0141573	+	0.0102859i	0.580684	+	0.814129i	$0.302785\pi$
$212$		0			0
$213$	0.0785290	−	0.241687i	0.00538072	−	0.0165601i
$214$		0			0
$215$	−7.07410	−	5.13964i	−0.482450	−	0.350520i
$216$		0			0
$217$	−1.90617	−	5.86659i	−0.129399	−	0.398250i
$218$		0			0
$219$	34.8005			2.35160
$220$		0			0
$221$	−33.4411			−2.24949
$222$		0			0
$223$	−5.92655	−	18.2400i	−0.396871	−	1.22144i	−0.927495	−	0.373836i	$-0.878042\pi$
$223$	−5.92655	−	18.2400i	−0.396871	−	1.22144i	0.530624	−	0.847607i	$-0.321958\pi$
$224$		0			0
$225$	3.98092	+	2.89231i	0.265395	+	0.192820i
$226$		0			0
$227$	1.32844	−	4.08853i	0.0881720	−	0.271365i	−0.897242	−	0.441539i	$-0.854433\pi$
$227$	1.32844	−	4.08853i	0.0881720	−	0.271365i	0.985414	+	0.170173i	$0.0544328\pi$
$228$		0			0
$229$	−10.6837	+	7.76215i	−0.705998	+	0.512937i	−0.881880	−	0.471474i	$-0.843722\pi$
$229$	−10.6837	+	7.76215i	−0.705998	+	0.512937i	0.175882	+	0.984411i	$0.443722\pi$
$230$		0			0
$231$	6.61411	+	4.92368i	0.435177	+	0.323954i
$232$		0			0
$233$	−8.41998	+	6.11747i	−0.551611	+	0.400769i	−0.828379	−	0.560168i	$-0.810737\pi$
$233$	−8.41998	+	6.11747i	−0.551611	+	0.400769i	0.276768	+	0.960937i	$0.410737\pi$
$234$		0			0
$235$	0.0820775	−	0.252608i	0.00535414	−	0.0164784i
$236$		0			0
$237$	10.2854	+	7.47277i	0.668108	+	0.485409i
$238$		0			0
$239$	−6.75164	−	20.7794i	−0.436727	−	1.34411i	−0.891306	−	0.453402i	$-0.850210\pi$
$239$	−6.75164	−	20.7794i	−0.436727	−	1.34411i	0.454579	−	0.890706i	$-0.349790\pi$
$240$		0			0
$241$	−28.9328			−1.86372			−0.931861	−	0.362815i	$-0.881816\pi$
$241$	−28.9328			−1.86372			−0.931861	+	0.362815i	$0.881816\pi$
$242$		0			0
$243$	−22.2939			−1.43015
$244$		0			0
$245$	−0.574225	−	1.76728i	−0.0366859	−	0.112907i
$246$		0			0
$247$	37.3026	+	27.1019i	2.37350	+	1.72445i
$248$		0			0
$249$	7.28444	−	22.4192i	0.461633	−	1.42076i
$250$		0			0
$251$	3.48686	−	2.53335i	0.220089	−	0.159904i	−0.472278	−	0.881450i	$-0.656568\pi$
$251$	3.48686	−	2.53335i	0.220089	−	0.159904i	0.692367	+	0.721546i	$0.256568\pi$
$252$		0			0
$253$	5.40455	+	4.02326i	0.339781	+	0.252940i
$254$		0			0
$255$	−19.8829	+	14.4458i	−1.24512	+	0.904631i
$256$		0			0
$257$	−2.75175	+	8.46903i	−0.171650	+	0.528283i	−0.999465	−	0.0327179i	$-0.989584\pi$
$257$	−2.75175	+	8.46903i	−0.171650	+	0.528283i	0.827815	+	0.561001i	$0.189584\pi$
$258$		0			0
$259$	7.94653	+	5.77349i	0.493773	+	0.358747i
$260$		0			0
$261$	−3.92999	−	12.0953i	−0.243260	−	0.748679i
$262$		0			0
$263$	−0.672809			−0.0414872			−0.0207436	−	0.999785i	$-0.506603\pi$
$263$	−0.672809			−0.0414872			−0.0207436	+	0.999785i	$0.506603\pi$
$264$		0			0
$265$	−14.2898			−0.877818
$266$		0			0
$267$	10.9417	+	33.6750i	0.669619	+	2.06087i
$268$		0			0
$269$	−1.15241	−	0.837272i	−0.0702634	−	0.0510494i	0.552099	−	0.833779i	$-0.313827\pi$
$269$	−1.15241	−	0.837272i	−0.0702634	−	0.0510494i	−0.622362	+	0.782729i	$0.713827\pi$
$270$		0			0
$271$	−8.59531	+	26.4537i	−0.522128	+	1.60695i	0.247798	+	0.968812i	$0.420293\pi$
$271$	−8.59531	+	26.4537i	−0.522128	+	1.60695i	−0.769926	+	0.638133i	$0.779707\pi$
$272$		0			0
$273$	−12.6433	+	9.18591i	−0.765208	+	0.555956i
$274$		0			0
$275$	1.64200	−	4.86092i	0.0990161	−	0.293124i
$276$		0			0
$277$	3.32383	−	2.41491i	0.199710	−	0.145098i	−0.483436	−	0.875380i	$-0.660611\pi$
$277$	3.32383	−	2.41491i	0.199710	−	0.145098i	0.683146	+	0.730282i	$0.260611\pi$
$278$		0			0
$279$	−6.06321	+	18.6606i	−0.362995	+	1.11718i
$280$		0			0
$281$	−9.00204	−	6.54037i	−0.537017	−	0.390166i	0.285959	−	0.958242i	$-0.407688\pi$
$281$	−9.00204	−	6.54037i	−0.537017	−	0.390166i	−0.822976	+	0.568076i	$0.807688\pi$
$282$		0			0
$283$	4.72864	+	14.5533i	0.281088	+	0.865101i	0.987544	+	0.157344i	$0.0502930\pi$
$283$	4.72864	+	14.5533i	0.281088	+	0.865101i	−0.706456	+	0.707757i	$0.749707\pi$
$284$		0			0
$285$	33.8863			2.00725
$286$		0			0
$287$	−12.0439			−0.710928
$288$		0			0
$289$	3.49217	+	10.7478i	0.205422	+	0.632223i
$290$		0			0
$291$	2.85740	+	2.07602i	0.167504	+	0.121698i
$292$		0			0
$293$	−7.46261	+	22.9675i	−0.435970	+	1.34178i	0.456119	+	0.889919i	$0.349239\pi$
$293$	−7.46261	+	22.9675i	−0.435970	+	1.34178i	−0.892089	+	0.451859i	$0.850761\pi$
$294$		0			0
$295$	7.36128	−	5.34828i	0.428590	−	0.311389i
$296$		0			0
$297$	−0.444274	−	1.42331i	−0.0257794	−	0.0825890i
$298$		0			0
$299$	−10.3312	+	7.50603i	−0.597467	+	0.434085i
$300$		0			0
$301$	−1.45411	+	4.47528i	−0.0838134	+	0.257951i
$302$		0			0
$303$	24.5911	+	17.8665i	1.41272	+	1.02640i
$304$		0			0
$305$	5.62180	+	17.3021i	0.321903	+	0.990717i
$306$		0			0
$307$	13.8792			0.792126			0.396063	−	0.918223i	$-0.370376\pi$
$307$	13.8792			0.792126			0.396063	+	0.918223i	$0.370376\pi$
$308$		0			0
$309$	0.786484			0.0447415
$310$		0			0
$311$	−0.852395	−	2.62340i	−0.0483349	−	0.148759i	0.923976	−	0.382450i	$-0.124920\pi$
$311$	−0.852395	−	2.62340i	−0.0483349	−	0.148759i	−0.972311	+	0.233691i	$0.924920\pi$
$312$		0			0
$313$	10.7197	+	7.78830i	0.605912	+	0.440221i	0.847972	−	0.530040i	$-0.177823\pi$
$313$	10.7197	+	7.78830i	0.605912	+	0.440221i	−0.242061	+	0.970261i	$0.577823\pi$
$314$		0			0
$315$	−1.82651	+	5.62142i	−0.102912	+	0.316731i
$316$		0			0
$317$	8.47338	−	6.15627i	0.475912	−	0.345771i	−0.323829	−	0.946116i	$-0.604970\pi$
$317$	8.47338	−	6.15627i	0.475912	−	0.345771i	0.799741	+	0.600345i	$0.204970\pi$
$318$		0			0
$319$	−10.8178	+	7.66944i	−0.605681	+	0.429406i
$320$		0			0
$321$	31.2334	−	22.6924i	1.74328	−	1.26657i
$322$		0			0
$323$	12.0582	−	37.1114i	0.670938	−	2.06493i
$324$		0			0
$325$	7.86725	+	5.71589i	0.436396	+	0.317060i
$326$		0			0
$327$	−0.753950	−	2.32042i	−0.0416935	−	0.128320i
$328$		0			0
$329$	−0.142936			−0.00788033
$330$		0			0
$331$	−25.0809			−1.37857			−0.689286	−	0.724490i	$-0.742075\pi$
$331$	−25.0809			−1.37857			−0.689286	+	0.724490i	$0.742075\pi$
$332$		0			0
$333$	−9.65478	−	29.7144i	−0.529079	−	1.62834i
$334$		0			0
$335$	5.97218	+	4.33904i	0.326295	+	0.237067i
$336$		0			0
$337$	−5.56934	+	17.1407i	−0.303382	+	0.933712i	0.676895	+	0.736080i	$0.263325\pi$
$337$	−5.56934	+	17.1407i	−0.303382	+	0.933712i	−0.980276	+	0.197632i	$0.936675\pi$
$338$		0			0
$339$	−20.1314	+	14.6263i	−1.09338	+	0.794391i
$340$		0			0
$341$	20.4572	+	0.237350i	1.10782	+	0.0128532i
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$		0			0
$345$	−2.90013	+	8.92567i	−0.156138	+	0.480542i
$346$		0			0
$347$	−12.1956	−	8.86063i	−0.654695	−	0.475664i	0.210172	−	0.977664i	$-0.432597\pi$
$347$	−12.1956	−	8.86063i	−0.654695	−	0.475664i	−0.864867	+	0.502001i	$0.832597\pi$
$348$		0			0
$349$	−1.31797	−	4.05631i	−0.0705495	−	0.217129i	0.909565	−	0.415562i	$-0.136415\pi$
$349$	−1.31797	−	4.05631i	−0.0705495	−	0.217129i	−0.980115	+	0.198433i	$0.936415\pi$
$350$		0			0
$351$	2.82601			0.150841
$352$		0			0
$353$	−6.01751			−0.320280			−0.160140	−	0.987094i	$-0.551195\pi$
$353$	−6.01751			−0.320280			−0.160140	+	0.987094i	$0.551195\pi$
$354$		0			0
$355$	−0.0586956	−	0.180647i	−0.00311524	−	0.00958773i
$356$		0			0
$357$	10.6999	+	7.77396i	0.566301	+	0.411441i
$358$		0			0
$359$	−0.817594	+	2.51629i	−0.0431509	+	0.132805i	−0.970311	−	0.241860i	$-0.922242\pi$
$359$	−0.817594	+	2.51629i	−0.0431509	+	0.132805i	0.927160	+	0.374665i	$0.122242\pi$
$360$		0			0
$361$	−28.1558	+	20.4564i	−1.48188	+	1.07665i
$362$		0			0
$363$	−22.4915	+	15.5568i	−1.18050	+	0.816518i
$364$		0			0
$365$	21.0436	−	15.2890i	1.10147	−	0.800265i
$366$		0			0
$367$	7.33138	−	22.5637i	0.382695	−	1.17781i	−0.555444	−	0.831554i	$-0.687452\pi$
$367$	7.33138	−	22.5637i	0.382695	−	1.17781i	0.938139	−	0.346259i	$-0.112548\pi$
$368$		0			0
$369$	30.9931	+	22.5178i	1.61343	+	1.17223i
$370$		0			0
$371$	2.37635	+	7.31365i	0.123374	+	0.379706i
$372$		0			0
$373$	1.58576			0.0821076			0.0410538	−	0.999157i	$-0.486928\pi$
$373$	1.58576			0.0821076			0.0410538	+	0.999157i	$0.486928\pi$
$374$		0			0
$375$	30.2457			1.56188
$376$		0			0
$377$	−7.76661	−	23.9032i	−0.400001	−	1.23108i
$378$		0			0
$379$	3.71774	+	2.70110i	0.190968	+	0.138746i	0.679161	−	0.733989i	$-0.262344\pi$
$379$	3.71774	+	2.70110i	0.190968	+	0.138746i	−0.488193	+	0.872736i	$0.662344\pi$
$380$		0			0
$381$	−9.21974	+	28.3754i	−0.472342	+	1.45372i
$382$		0			0
$383$	−19.3061	+	14.0267i	−0.986495	+	0.716730i	−0.959151	−	0.282896i	$-0.908705\pi$
$383$	−19.3061	+	14.0267i	−0.986495	+	0.716730i	−0.0273442	+	0.999626i	$0.508705\pi$
$384$		0			0
$385$	6.16264	+	0.0715005i	0.314077	+	0.00364400i
$386$		0			0
$387$	12.1091	−	8.79779i	0.615541	−	0.447217i
$388$		0			0
$389$	2.89749	−	8.91757i	0.146909	−	0.452139i	−0.850343	−	0.526229i	$-0.823605\pi$
$389$	2.89749	−	8.91757i	0.146909	−	0.452139i	0.997252	+	0.0740905i	$0.0236054\pi$
$390$		0			0
$391$	8.74318	+	6.35229i	0.442162	+	0.321249i
$392$		0			0
$393$	15.0281	+	46.2516i	0.758066	+	2.33309i
$394$		0			0
$395$	9.50252			0.478124
$396$		0			0
$397$	−17.6151			−0.884075			−0.442037	−	0.896997i	$-0.645744\pi$
$397$	−17.6151			−0.884075			−0.442037	+	0.896997i	$0.645744\pi$
$398$		0			0
$399$	−5.63517	−	17.3433i	−0.282111	−	0.868249i
$400$		0			0
$401$	−1.20316	−	0.874147i	−0.0600829	−	0.0436528i	0.557338	−	0.830285i	$-0.311823\pi$
$401$	−1.20316	−	0.874147i	−0.0600829	−	0.0436528i	−0.617421	+	0.786633i	$0.711823\pi$
$402$		0			0
$403$	−11.9823	+	36.8779i	−0.596883	+	1.83702i
$404$		0			0
$405$	−12.6654	+	9.20192i	−0.629346	+	0.457247i
$406$		0			0
$407$	−26.5760	+	18.8414i	−1.31732	+	0.933936i
$408$		0			0
$409$	−7.47926	+	5.43400i	−0.369826	+	0.268694i	−0.757139	−	0.653254i	$-0.773403\pi$
$409$	−7.47926	+	5.43400i	−0.369826	+	0.268694i	0.387313	+	0.921948i	$0.373403\pi$
$410$		0			0
$411$	1.55842	−	4.79632i	0.0768711	−	0.236585i
$412$		0			0
$413$	−3.96145	−	2.87816i	−0.194930	−	0.141625i
$414$		0			0
$415$	−5.44468	−	16.7570i	−0.267269	−	0.822569i
$416$		0			0
$417$	−22.2511			−1.08964
$418$		0			0
$419$	−10.2513			−0.500810			−0.250405	−	0.968141i	$-0.580564\pi$
$419$	−10.2513			−0.500810			−0.250405	+	0.968141i	$0.580564\pi$
$420$		0			0
$421$	−6.63979	−	20.4352i	−0.323604	−	0.995949i	−0.972067	−	0.234704i	$-0.924588\pi$
$421$	−6.63979	−	20.4352i	−0.323604	−	0.995949i	0.648463	−	0.761246i	$-0.275412\pi$
$422$		0			0
$423$	0.367824	+	0.267240i	0.0178842	+	0.0129936i
$424$		0			0
$425$	2.54312	−	7.82693i	0.123360	−	0.379662i
$426$		0			0
$427$	7.92048	−	5.75456i	0.383299	−	0.278483i
$428$		0			0
$429$	−15.4441	−	49.4779i	−0.745646	−	2.38881i
$430$		0			0
$431$	−24.0434	+	17.4686i	−1.15813	+	0.841431i	−0.989540	−	0.144256i	$-0.953921\pi$
$431$	−24.0434	+	17.4686i	−1.15813	+	0.841431i	−0.168589	+	0.985686i	$0.553921\pi$
$432$		0			0
$433$	−2.49337	+	7.67380i	−0.119824	+	0.368779i	−0.992923	−	0.118764i	$-0.962107\pi$
$433$	−2.49337	+	7.67380i	−0.119824	+	0.368779i	0.873099	+	0.487543i	$0.162107\pi$
$434$		0			0
$435$	−14.9434	−	10.8570i	−0.716481	−	0.520554i
$436$		0			0
$437$	−4.60463	−	14.1716i	−0.220269	−	0.677920i
$438$		0			0
$439$	−39.2659			−1.87406			−0.937030	−	0.349248i	$-0.886437\pi$
$439$	−39.2659			−1.87406			−0.937030	+	0.349248i	$0.886437\pi$
$440$		0			0
$441$	3.18083			0.151468
$442$		0			0
$443$	−6.03892	−	18.5859i	−0.286918	−	0.883042i	−0.985817	−	0.167822i	$-0.946327\pi$
$443$	−6.03892	−	18.5859i	−0.286918	−	0.883042i	0.698900	−	0.715220i	$-0.253673\pi$
$444$		0			0
$445$	21.4109	+	15.5559i	1.01497	+	0.737421i
$446$		0			0
$447$	4.99565	−	15.3750i	0.236286	−	0.727214i
$448$		0			0
$449$	−9.02781	+	6.55909i	−0.426049	+	0.309542i	−0.780067	−	0.625696i	$-0.784815\pi$
$449$	−9.02781	+	6.55909i	−0.426049	+	0.309542i	0.354018	+	0.935238i	$0.384815\pi$
$450$		0			0
$451$	12.7836	−	37.8442i	0.601956	−	1.78201i
$452$		0			0
$453$	12.8956	−	9.36920i	0.605888	−	0.440204i
$454$		0			0
$455$	−3.60962	+	11.1093i	−0.169222	+	0.520811i
$456$		0			0
$457$	−7.17118	−	5.21017i	−0.335454	−	0.243721i	0.407288	−	0.913300i	$-0.366475\pi$
$457$	−7.17118	−	5.21017i	−0.335454	−	0.243721i	−0.742741	+	0.669579i	$0.766475\pi$
$458$		0			0
$459$	−0.739053	−	2.27457i	−0.0344960	−	0.106168i
$460$		0			0
$461$	41.2827			1.92273			0.961363	−	0.275284i	$-0.0887720\pi$
$461$	41.2827			1.92273			0.961363	+	0.275284i	$0.0887720\pi$
$462$		0			0
$463$	5.00452			0.232580			0.116290	−	0.993215i	$-0.462900\pi$
$463$	5.00452			0.232580			0.116290	+	0.993215i	$0.462900\pi$
$464$		0			0
$465$	8.80612	+	27.1025i	0.408374	+	1.25685i
$466$		0			0
$467$	−13.2945	−	9.65904i	−0.615197	−	0.446967i	0.236043	−	0.971743i	$-0.424149\pi$
$467$	−13.2945	−	9.65904i	−0.615197	−	0.446967i	−0.851241	+	0.524776i	$0.824149\pi$
$468$		0			0
$469$	1.22760	−	3.77817i	0.0566855	−	0.174460i
$470$		0			0
$471$	4.74347	−	3.44634i	0.218568	−	0.158799i
$472$		0			0
$473$	−12.5188	−	9.31924i	−0.575615	−	0.428499i
$474$		0			0
$475$	−9.18002	+	6.66968i	−0.421208	+	0.306026i
$476$		0			0
$477$	7.55876	−	23.2635i	0.346092	−	1.06516i
$478$		0			0
$479$	−23.3765	−	16.9840i	−1.06810	−	0.776018i	−0.0925284	−	0.995710i	$-0.529495\pi$
$479$	−23.3765	−	16.9840i	−1.06810	−	0.776018i	−0.975569	+	0.219692i	$0.929495\pi$
$480$		0			0
$481$	−19.0802	−	58.7227i	−0.869980	−	2.67752i
$482$		0			0
$483$	5.05051			0.229806
$484$		0			0
$485$	2.63991			0.119872
$486$		0			0
$487$	2.32603	+	7.15879i	0.105403	+	0.324396i	0.989825	−	0.142292i	$-0.0454472\pi$
$487$	2.32603	+	7.15879i	0.105403	+	0.324396i	−0.884422	+	0.466688i	$0.845447\pi$
$488$		0			0
$489$	16.6205	+	12.0755i	0.751605	+	0.546073i
$490$		0			0
$491$	5.55887	−	17.1084i	0.250868	−	0.772093i	−0.743747	−	0.668461i	$-0.766954\pi$
$491$	5.55887	−	17.1084i	0.250868	−	0.772093i	0.994616	−	0.103632i	$-0.0330465\pi$
$492$		0			0
$493$	−17.2079	+	12.5022i	−0.775003	+	0.563073i
$494$		0			0
$495$	−15.7249	−	11.7059i	−0.706782	−	0.526143i
$496$		0			0
$497$	−0.0826955	+	0.0600818i	−0.00370940	+	0.00269504i
$498$		0			0
$499$	−6.37964	+	19.6345i	−0.285592	+	0.878962i	0.700629	+	0.713526i	$0.252903\pi$
$499$	−6.37964	+	19.6345i	−0.285592	+	0.878962i	−0.986221	+	0.165436i	$0.947097\pi$
$500$		0			0
$501$	−8.76228	−	6.36617i	−0.391470	−	0.284420i
$502$		0			0
$503$	−3.68481	−	11.3407i	−0.164297	−	0.505656i	0.834686	−	0.550726i	$-0.185649\pi$
$503$	−3.68481	−	11.3407i	−0.164297	−	0.505656i	−0.998984	+	0.0450700i	$0.985649\pi$
$504$		0			0
$505$	22.7194			1.01100
$506$		0			0
$507$	65.9192			2.92757
$508$		0			0
$509$	−9.95912	−	30.6510i	−0.441430	−	1.35858i	−0.886351	−	0.463013i	$-0.846768\pi$
$509$	−9.95912	−	30.6510i	−0.441430	−	1.35858i	0.444921	−	0.895570i	$-0.353232\pi$
$510$		0			0
$511$	−11.3245	−	8.22775i	−0.500967	−	0.363974i
$512$		0			0
$513$	−1.01901	+	3.13618i	−0.0449902	+	0.138466i
$514$		0			0
$515$	0.475580	−	0.345529i	0.0209566	−	0.0152258i
$516$		0			0
$517$	0.151715	−	0.449133i	0.00667243	−	0.0197529i
$518$		0			0
$519$	8.63745	−	6.27547i	0.379142	−	0.275463i
$520$		0			0
$521$	11.9314	−	36.7210i	0.522723	−	1.60878i	−0.246051	−	0.969257i	$-0.579133\pi$
$521$	11.9314	−	36.7210i	0.522723	−	1.60878i	0.768774	−	0.639520i	$-0.220867\pi$
$522$		0			0
$523$	12.1295	+	8.81257i	0.530384	+	0.385347i	0.820502	−	0.571644i	$-0.193694\pi$
$523$	12.1295	+	8.81257i	0.530384	+	0.385347i	−0.290117	+	0.956991i	$0.593694\pi$
$524$		0			0
$525$	−1.18848	−	3.65776i	−0.0518694	−	0.159638i
$526$		0			0
$527$	32.8155			1.42947
$528$		0			0
$529$	−18.8731			−0.820570
$530$		0			0
$531$	4.81303	+	14.8130i	0.208868	+	0.642829i
$532$		0			0
$533$	61.2497	+	44.5005i	2.65302	+	1.92753i
$534$		0			0
$535$	8.91702	−	27.4438i	0.385516	−	1.18650i
$536$		0			0
$537$	−15.6264	+	11.3532i	−0.674329	+	0.489929i
$538$		0			0
$539$	−0.988230	−	3.16598i	−0.0425661	−	0.136368i
$540$		0			0
$541$	−8.73119	+	6.34358i	−0.375383	+	0.272732i	−0.759440	−	0.650578i	$-0.774527\pi$
$541$	−8.73119	+	6.34358i	−0.375383	+	0.272732i	0.384056	+	0.923310i	$0.374527\pi$
$542$		0			0
$543$	12.8064	−	39.4141i	0.549576	−	1.69142i
$544$		0			0
$545$	−1.47535	−	1.07190i	−0.0631969	−	0.0459152i
$546$		0			0
$547$	6.65797	+	20.4911i	0.284674	+	0.876137i	0.986496	+	0.163785i	$0.0523703\pi$
$547$	6.65797	+	20.4911i	0.284674	+	0.876137i	−0.701822	+	0.712353i	$0.747630\pi$
$548$		0			0
$549$	−31.1411			−1.32907
$550$		0			0
$551$	29.3272			1.24938
$552$		0			0
$553$	−1.58024	−	4.86347i	−0.0671985	−	0.206816i
$554$		0			0
$555$	−36.7113	−	26.6723i	−1.55831	−	1.13218i
$556$		0			0
$557$	−4.99317	+	15.3674i	−0.211567	+	0.651138i	0.787812	+	0.615916i	$0.211214\pi$
$557$	−4.99317	+	15.3674i	−0.211567	+	0.651138i	−0.999380	+	0.0352220i	$0.988786\pi$
$558$		0			0
$559$	23.9305	−	17.3865i	1.01215	−	0.735372i
$560$		0			0
$561$	−35.7844	+	25.3699i	−1.51082	+	1.07112i
$562$		0			0
$563$	−1.01463	+	0.737174i	−0.0427617	+	0.0310682i	−0.608961	−	0.793200i	$-0.708413\pi$
$563$	−1.01463	+	0.737174i	−0.0427617	+	0.0310682i	0.566199	+	0.824269i	$0.308413\pi$
$564$		0			0
$565$	−5.74743	+	17.6888i	−0.241796	+	0.744172i
$566$		0			0
$567$	6.81582	+	4.95198i	0.286237	+	0.207964i
$568$		0			0
$569$	9.56512	+	29.4384i	0.400991	+	1.23412i	0.924197	+	0.381916i	$0.124736\pi$
$569$	9.56512	+	29.4384i	0.400991	+	1.23412i	−0.523206	+	0.852206i	$0.675264\pi$
$570$		0			0
$571$	9.43699			0.394926			0.197463	−	0.980310i	$-0.436730\pi$
$571$	9.43699			0.394926			0.197463	+	0.980310i	$0.436730\pi$
$572$		0			0
$573$	−9.56561			−0.399609
$574$		0			0
$575$	−0.971134	−	2.98884i	−0.0404991	−	0.124643i
$576$		0			0
$577$	23.9914	+	17.4308i	0.998776	+	0.725653i	0.961825	−	0.273664i	$-0.0882356\pi$
$577$	23.9914	+	17.4308i	0.998776	+	0.725653i	0.0369506	+	0.999317i	$0.488236\pi$
$578$		0			0
$579$	−7.73775	+	23.8143i	−0.321570	+	0.989690i
$580$		0			0
$581$	−7.67093	+	5.57326i	−0.318244	+	0.231218i
$582$		0			0
$583$	−25.5032	−	0.295895i	−1.05624	−	0.0122547i
$584$		0			0
$585$	30.0592	−	21.8393i	1.24279	−	0.902943i
$586$		0			0
$587$	10.0865	−	31.0429i	0.416313	−	1.28128i	−0.494759	−	0.869030i	$-0.664744\pi$
$587$	10.0865	−	31.0429i	0.416313	−	1.28128i	0.911071	−	0.412249i	$-0.135256\pi$
$588$		0			0
$589$	−36.6048	−	26.5950i	−1.50827	−	1.09583i
$590$		0			0
$591$	−4.42638	−	13.6230i	−0.182077	−	0.560376i
$592$		0			0
$593$	32.5670			1.33737			0.668684	−	0.743547i	$-0.266858\pi$
$593$	32.5670			1.33737			0.668684	+	0.743547i	$0.266858\pi$
$594$		0			0
$595$	9.88552			0.405267
$596$		0			0
$597$	9.05489	+	27.8681i	0.370592	+	1.14057i
$598$		0			0
$599$	7.23079	+	5.25348i	0.295442	+	0.214651i	0.725625	−	0.688091i	$-0.241551\pi$
$599$	7.23079	+	5.25348i	0.295442	+	0.214651i	−0.430183	+	0.902742i	$0.641551\pi$
$600$		0			0
$601$	7.83327	−	24.1083i	0.319526	−	0.983399i	−0.654326	−	0.756213i	$-0.727047\pi$
$601$	7.83327	−	24.1083i	0.319526	−	0.983399i	0.973851	−	0.227186i	$-0.0729525\pi$
$602$		0			0
$603$	−10.2229	+	7.42737i	−0.416308	+	0.302466i
$604$		0			0
$605$	−6.76581	+	19.2883i	−0.275069	+	0.784181i
$606$		0			0
$607$	−6.26471	+	4.55158i	−0.254277	+	0.184743i	−0.707620	−	0.706593i	$-0.750231\pi$
$607$	−6.26471	+	4.55158i	−0.254277	+	0.184743i	0.453343	+	0.891336i	$0.350231\pi$
$608$		0			0
$609$	−3.07167	+	9.45363i	−0.124470	+	0.383081i
$610$		0			0
$611$	0.726908	+	0.528130i	0.0294076	+	0.0213658i
$612$		0			0
$613$	−0.691197	−	2.12729i	−0.0279172	−	0.0859203i	0.936127	−	0.351662i	$-0.114383\pi$
$613$	−0.691197	−	2.12729i	−0.0279172	−	0.0859203i	−0.964044	+	0.265741i	$0.914383\pi$
$614$		0			0
$615$	55.6403			2.24363
$616$		0			0
$617$	−18.7427			−0.754551			−0.377275	−	0.926101i	$-0.623139\pi$
$617$	−18.7427			−0.754551			−0.377275	+	0.926101i	$0.623139\pi$
$618$		0			0
$619$	12.0980	+	37.2338i	0.486260	+	1.49655i	0.830148	+	0.557543i	$0.188256\pi$
$619$	12.0980	+	37.2338i	0.486260	+	1.49655i	−0.343888	+	0.939011i	$0.611744\pi$
$620$		0			0
$621$	−0.738860	−	0.536813i	−0.0296494	−	0.0215416i
$622$		0			0
$623$	4.40108	−	13.5451i	0.176326	−	0.542675i
$624$		0			0
$625$	12.0317	−	8.74151i	0.481266	−	0.349660i
$626$		0			0
$627$	60.4772	+	0.701672i	2.41523	+	0.0280221i
$628$		0			0
$629$	−42.2744	+	30.7141i	−1.68559	+	1.22465i
$630$		0			0
$631$	13.9126	−	42.8186i	0.553852	−	1.70458i	−0.145102	−	0.989417i	$-0.546351\pi$
$631$	13.9126	−	42.8186i	0.553852	−	1.70458i	0.698955	−	0.715166i	$-0.253649\pi$
$632$		0			0
$633$	−0.511263	−	0.371454i	−0.0203209	−	0.0147640i
$634$		0			0
$635$	6.89120	+	21.2089i	0.273469	+	0.841651i
$636$		0			0
$637$	6.28608			0.249064
$638$		0			0
$639$	0.325136			0.0128622
$640$		0			0
$641$	−1.28520	−	3.95543i	−0.0507623	−	0.156230i	0.922462	−	0.386088i	$-0.126174\pi$
$641$	−1.28520	−	3.95543i	−0.0507623	−	0.156230i	−0.973224	+	0.229858i	$0.926174\pi$
$642$		0			0
$643$	−15.9966	−	11.6222i	−0.630842	−	0.458334i	0.225850	−	0.974162i	$-0.427484\pi$
$643$	−15.9966	−	11.6222i	−0.630842	−	0.458334i	−0.856692	+	0.515828i	$0.827484\pi$
$644$		0			0
$645$	6.71768	−	20.6749i	0.264509	−	0.814073i
$646$		0			0
$647$	−24.4564	+	17.7686i	−0.961480	+	0.698556i	−0.953494	−	0.301412i	$-0.902542\pi$
$647$	−24.4564	+	17.7686i	−0.961480	+	0.698556i	−0.00798632	+	0.999968i	$0.502542\pi$
$648$		0			0
$649$	13.2485	−	9.39270i	0.520049	−	0.368696i
$650$		0			0
$651$	12.4068	−	9.01408i	0.486262	−	0.353290i
$652$		0			0
$653$	−13.9380	+	42.8968i	−0.545437	+	1.67868i	0.174513	+	0.984655i	$0.444165\pi$
$653$	−13.9380	+	42.8968i	−0.545437	+	1.67868i	−0.719950	+	0.694026i	$0.755835\pi$
$654$		0			0
$655$	29.4072	+	21.3656i	1.14904	+	0.834824i
$656$		0			0
$657$	13.7589	+	42.3457i	0.536788	+	1.65206i
$658$		0			0
$659$	−40.2148			−1.56655			−0.783273	−	0.621678i	$-0.786451\pi$
$659$	−40.2148			−1.56655			−0.783273	+	0.621678i	$0.786451\pi$
$660$		0			0
$661$	18.8542			0.733343			0.366672	−	0.930350i	$-0.380497\pi$
$661$	18.8542			0.733343			0.366672	+	0.930350i	$0.380497\pi$
$662$		0			0
$663$	−25.6913	−	79.0696i	−0.997767	−	3.07081i
$664$		0			0
$665$	−11.0270	−	8.01160i	−0.427609	−	0.310676i
$666$		0			0
$667$	−2.50994	+	7.72479i	−0.0971852	+	0.299105i
$668$		0			0
$669$	38.5745	−	28.0260i	1.49138	−	1.08355i
$670$		0			0
$671$	9.67502	+	30.9957i	0.373500	+	1.19658i
$672$		0			0
$673$	−30.6219	+	22.2481i	−1.18039	+	0.857602i	−0.992215	−	0.124534i	$-0.960257\pi$
$673$	−30.6219	+	22.2481i	−1.18039	+	0.857602i	−0.188173	+	0.982136i	$0.560257\pi$
$674$		0			0
$675$	−0.214912	+	0.661431i	−0.00827197	+	0.0254585i
$676$		0			0
$677$	18.3326	+	13.3194i	0.704579	+	0.511907i	0.881420	−	0.472333i	$-0.156588\pi$
$677$	18.3326	+	13.3194i	0.704579	+	0.511907i	−0.176841	+	0.984239i	$0.556588\pi$
$678$		0			0
$679$	−0.439008	−	1.35113i	−0.0168476	−	0.0518515i
$680$		0			0
$681$	10.6877			0.409554
$682$		0			0
$683$	−24.2740			−0.928818			−0.464409	−	0.885621i	$-0.653733\pi$
$683$	−24.2740			−0.928818			−0.464409	+	0.885621i	$0.653733\pi$
$684$		0			0
$685$	−1.16482	−	3.58496i	−0.0445056	−	0.136974i
$686$		0			0
$687$	−26.5610	−	19.2977i	−1.01337	−	0.736253i
$688$		0			0
$689$	14.9379	−	45.9742i	0.569089	−	1.75148i
$690$		0			0
$691$	−1.83268	+	1.33152i	−0.0697182	+	0.0506533i	−0.622098	−	0.782939i	$-0.713720\pi$
$691$	−1.83268	+	1.33152i	−0.0697182	+	0.0506533i	0.552380	+	0.833592i	$0.313720\pi$
$692$		0			0
$693$	−3.37619	+	9.99479i	−0.128251	+	0.379671i
$694$		0			0
$695$	−13.4550	+	9.77566i	−0.510379	+	0.370812i
$696$		0			0
$697$	19.7993	−	60.9358i	0.749950	−	2.30811i
$698$		0			0
$699$	−20.9331	−	15.2088i	−0.791764	−	0.575250i
$700$		0			0
$701$	3.24984	+	10.0020i	0.122745	+	0.377769i	0.993483	−	0.113977i	$-0.0363589\pi$
$701$	3.24984	+	10.0020i	0.122745	+	0.377769i	−0.870739	+	0.491746i	$0.836359\pi$
$702$		0			0
$703$	72.0478			2.71733
$704$		0			0
$705$	0.660336			0.0248697
$706$		0			0
$707$	−3.77815	−	11.6280i	−0.142092	−	0.437314i
$708$		0			0
$709$	−30.2759	−	21.9968i	−1.13704	−	0.826105i	−0.150333	−	0.988635i	$-0.548035\pi$
$709$	−30.2759	−	21.9968i	−1.13704	−	0.826105i	−0.986704	+	0.162530i	$0.948035\pi$
$710$		0			0
$711$	−5.02646	+	15.4699i	−0.188507	+	0.580165i
$712$		0			0
$713$	10.1379	−	7.36563i	0.379668	−	0.275845i
$714$		0			0
$715$	−31.0762	−	23.1337i	−1.16218	−	0.865152i
$716$		0			0
$717$	43.9448	−	31.9278i	1.64115	−	1.19237i
$718$		0			0
$719$	−7.73655	+	23.8107i	−0.288525	+	0.887988i	0.696795	+	0.717270i	$0.254609\pi$
$719$	−7.73655	+	23.8107i	−0.288525	+	0.887988i	−0.985320	+	0.170718i	$0.945391\pi$
$720$		0			0
$721$	−0.255932	−	0.185945i	−0.00953140	−	0.00692497i
$722$		0			0
$723$	−22.2277	−	68.4100i	−0.826659	−	2.54419i
$724$		0			0
$725$	6.18521			0.229713
$726$		0			0
$727$	−25.0023			−0.927284			−0.463642	−	0.886023i	$-0.653458\pi$
$727$	−25.0023			−0.927284			−0.463642	+	0.886023i	$0.653458\pi$
$728$		0			0
$729$	−9.31715	−	28.6752i	−0.345080	−	1.06205i
$730$		0			0
$731$	−20.2522	−	14.7141i	−0.749054	−	0.544220i
$732$		0			0
$733$	1.33492	−	4.10846i	0.0493064	−	0.151749i	−0.923372	−	0.383907i	$-0.874578\pi$
$733$	1.33492	−	4.10846i	0.0493064	−	0.151749i	0.972678	+	0.232157i	$0.0745784\pi$
$734$		0			0
$735$	3.73749	−	2.71545i	0.137860	−	0.100161i
$736$		0			0
$737$	10.5688	+	7.86760i	0.389305	+	0.289807i
$738$		0			0
$739$	−10.2192	+	7.42468i	−0.375919	+	0.273121i	−0.759661	−	0.650319i	$-0.774635\pi$
$739$	−10.2192	+	7.42468i	−0.375919	+	0.273121i	0.383742	+	0.923440i	$0.374635\pi$
$740$		0			0
$741$	−35.4231	+	109.021i	−1.30130	+	4.00499i
$742$		0			0
$743$	−2.81947	−	2.04847i	−0.103436	−	0.0751510i	0.534865	−	0.844938i	$-0.320363\pi$
$743$	−2.81947	−	2.04847i	−0.103436	−	0.0751510i	−0.638301	+	0.769787i	$0.720363\pi$
$744$		0			0
$745$	−3.73395	−	11.4919i	−0.136801	−	0.421031i
$746$		0			0
$747$	30.1600			1.10350
$748$		0			0
$749$	−15.5288			−0.567410
$750$		0			0
$751$	14.6943	+	45.2244i	0.536202	+	1.65026i	0.741036	+	0.671465i	$0.234335\pi$
$751$	14.6943	+	45.2244i	0.536202	+	1.65026i	−0.204834	+	0.978797i	$0.565665\pi$
$752$		0			0
$753$	8.66878	+	6.29824i	0.315908	+	0.229521i
$754$		0			0
$755$	3.68165	−	11.3309i	0.133989	−	0.412375i
$756$		0			0
$757$	37.9690	−	27.5861i	1.38001	−	1.00263i	0.383127	−	0.923696i	$-0.374847\pi$
$757$	37.9690	−	27.5861i	1.38001	−	1.00263i	0.996880	−	0.0789381i	$-0.0251529\pi$
$758$		0			0
$759$	−5.36070	+	15.8697i	−0.194581	+	0.576033i
$760$		0			0
$761$	11.8043	−	8.57629i	0.427904	−	0.310890i	−0.352906	−	0.935659i	$-0.614807\pi$
$761$	11.8043	−	8.57629i	0.427904	−	0.310890i	0.780810	+	0.624768i	$0.214807\pi$
$762$		0			0
$763$	−0.303263	+	0.933347i	−0.0109789	+	0.0337894i
$764$		0			0
$765$	−25.4389	−	18.4824i	−0.919744	−	0.668233i
$766$		0			0
$767$	9.51170	+	29.2740i	0.343448	+	1.05702i
$768$		0			0
$769$	−4.34485			−0.156679			−0.0783397	−	0.996927i	$-0.524962\pi$
$769$	−4.34485			−0.156679			−0.0783397	+	0.996927i	$0.524962\pi$
$770$		0			0
$771$	−22.1386			−0.797303
$772$		0			0
$773$	9.08036	+	27.9465i	0.326598	+	1.00517i	0.970714	+	0.240238i	$0.0772253\pi$
$773$	9.08036	+	27.9465i	0.326598	+	1.00517i	−0.644116	+	0.764928i	$0.722775\pi$
$774$		0			0
$775$	−7.72009	−	5.60897i	−0.277314	−	0.201480i
$776$		0			0
$777$	−7.54615	+	23.2247i	−0.270717	+	0.833180i
$778$		0			0
$779$	−71.4702	+	51.9261i	−2.56069	+	1.86045i
$780$		0			0
$781$	−0.101014	−	0.323617i	−0.00361457	−	0.0115799i
$782$		0			0
$783$	1.45419	−	1.05653i	0.0519683	−	0.0377572i
$784$		0			0
$785$	1.35425	−	4.16794i	0.0483351	−	0.148760i
$786$		0			0
$787$	−40.7033	−	29.5727i	−1.45092	−	1.05415i	−0.985616	−	0.168999i	$-0.945947\pi$
$787$	−40.7033	−	29.5727i	−1.45092	−	1.05415i	−0.465299	−	0.885153i	$-0.654053\pi$
$788$		0			0
$789$	−0.516889	−	1.59082i	−0.0184017	−	0.0566348i
$790$		0			0
$791$	10.0090			0.355880
$792$		0			0
$793$	−61.5423			−2.18543
$794$		0			0
$795$	−10.9782	−	33.7876i	−0.389358	−	1.19832i
$796$		0			0
$797$	32.8148	+	23.8414i	1.16236	+	0.844505i	0.990075	−	0.140542i	$-0.0448846\pi$
$797$	32.8148	+	23.8414i	1.16236	+	0.844505i	0.172286	+	0.985047i	$0.444885\pi$
$798$		0			0
$799$	0.234977	−	0.723184i	0.00831288	−	0.0255844i
$800$		0			0
$801$	−36.6501	+	26.6279i	−1.29497	+	0.940850i
$802$		0			0
$803$	37.8733	−	26.8508i	1.33652	−	0.947543i
$804$		0			0
$805$	3.05400	−	2.21886i	0.107639	−	0.0782045i
$806$		0			0
$807$	1.09434	−	3.36804i	0.0385227	−	0.118561i
$808$		0			0
$809$	15.5784	+	11.3184i	0.547709	+	0.397934i	0.826940	−	0.562290i	$-0.190080\pi$
$809$	15.5784	+	11.3184i	0.547709	+	0.397934i	−0.279231	+	0.960224i	$0.590080\pi$
$810$		0			0
$811$	1.25343	+	3.85767i	0.0440140	+	0.135461i	0.970649	−	0.240502i	$-0.0773120\pi$
$811$	1.25343	+	3.85767i	0.0440140	+	0.135461i	−0.926635	+	0.375963i	$0.877312\pi$
$812$		0			0
$813$	−69.1517			−2.42526
$814$		0			0
$815$	15.3554			0.537878
$816$		0			0
$817$	10.6659	+	32.8263i	0.373153	+	1.14845i
$818$		0			0
$819$	−16.1763	−	11.7527i	−0.565244	−	0.410674i
$820$		0			0
$821$	0.571685	−	1.75947i	0.0199519	−	0.0614058i	−0.940585	−	0.339559i	$-0.889722\pi$
$821$	0.571685	−	1.75947i	0.0199519	−	0.0614058i	0.960537	+	0.278153i	$0.0897222\pi$
$822$		0			0
$823$	18.0171	−	13.0902i	0.628037	−	0.456296i	−0.227682	−	0.973735i	$-0.573115\pi$
$823$	18.0171	−	13.0902i	0.628037	−	0.456296i	0.855720	+	0.517440i	$0.173115\pi$
$824$		0			0
$825$	12.7549	+	0.147985i	0.444067	+	0.00515218i
$826$		0			0
$827$	30.7192	−	22.3188i	1.06821	−	0.776100i	0.0926203	−	0.995701i	$-0.470476\pi$
$827$	30.7192	−	22.3188i	1.06821	−	0.776100i	0.975590	+	0.219602i	$0.0704757\pi$
$828$		0			0
$829$	−16.6820	+	51.3418i	−0.579388	+	1.78317i	0.0413368	+	0.999145i	$0.486838\pi$
$829$	−16.6820	+	51.3418i	−0.579388	+	1.78317i	−0.620725	+	0.784028i	$0.713162\pi$
$830$		0			0
$831$	8.26347	+	6.00376i	0.286657	+	0.208268i
$832$		0			0
$833$	−1.64393	−	5.05949i	−0.0569587	−	0.175301i
$834$		0			0
$835$	−8.09535			−0.280151
$836$		0			0
$837$	−2.77315			−0.0958539
$838$		0			0
$839$	−3.15489	−	9.70975i	−0.108919	−	0.335218i	0.881711	−	0.471789i	$-0.156392\pi$
$839$	−3.15489	−	9.70975i	−0.108919	−	0.335218i	−0.990630	+	0.136571i	$0.956392\pi$
$840$		0			0
$841$	10.5286	+	7.64948i	0.363055	+	0.263775i
$842$		0			0
$843$	8.54848	−	26.3095i	0.294425	−	0.906148i
$844$		0			0
$845$	39.8608	−	28.9605i	1.37125	−	0.996273i
$846$		0			0
$847$	10.9970	+	0.255215i	0.377863	+	0.00876930i
$848$		0			0
$849$	−30.7776	+	22.3612i	−1.05628	+	0.767436i
$850$		0			0
$851$	−6.16614	+	18.9774i	−0.211373	+	0.650538i
$852$		0			0
$853$	8.64513	+	6.28105i	0.296004	+	0.215059i	0.725868	−	0.687834i	$-0.241439\pi$
$853$	8.64513	+	6.28105i	0.296004	+	0.215059i	−0.429864	+	0.902894i	$0.641439\pi$
$854$		0			0
$855$	13.3975	+	41.2332i	0.458184	+	1.41015i
$856$		0			0
$857$	−1.03083			−0.0352124			−0.0176062	−	0.999845i	$-0.505605\pi$
$857$	−1.03083			−0.0352124			−0.0176062	+	0.999845i	$0.505605\pi$
$858$		0			0
$859$	−9.74857			−0.332617			−0.166309	−	0.986074i	$-0.553185\pi$
$859$	−9.74857			−0.332617			−0.166309	+	0.986074i	$0.553185\pi$
$860$		0			0
$861$	−9.25278	−	28.4771i	−0.315334	−	0.970498i
$862$		0			0
$863$	2.45885	+	1.78646i	0.0837001	+	0.0608117i	0.628848	−	0.777528i	$-0.283527\pi$
$863$	2.45885	+	1.78646i	0.0837001	+	0.0608117i	−0.545148	+	0.838340i	$0.683527\pi$
$864$		0			0
$865$	2.46596	−	7.58945i	0.0838452	−	0.258049i
$866$		0			0
$867$	−22.7297	+	16.5141i	−0.771942	+	0.560849i
$868$		0			0
$869$	16.9593	+	0.196766i	0.575303	+	0.00667481i
$870$		0			0
$871$	−20.2029	+	14.6783i	−0.684549	+	0.497354i
$872$		0			0
$873$	−1.39641	+	4.29770i	−0.0472613	+	0.145455i
$874$		0			0
$875$	−9.84234	−	7.15088i	−0.332732	−	0.241744i
$876$		0			0
$877$	−6.57322	−	20.2303i	−0.221962	−	0.683128i	−0.998586	−	0.0531637i	$-0.983069\pi$
$877$	−6.57322	−	20.2303i	−0.221962	−	0.683128i	0.776624	−	0.629964i	$-0.216931\pi$
$878$		0			0
$879$	−60.0387			−2.02506
$880$		0			0
$881$	36.0834			1.21568			0.607840	−	0.794059i	$-0.292036\pi$
$881$	36.0834			1.21568			0.607840	+	0.794059i	$0.292036\pi$
$882$		0			0
$883$	2.80942	+	8.64650i	0.0945445	+	0.290978i	0.987135	−	0.159891i	$-0.0511142\pi$
$883$	2.80942	+	8.64650i	0.0945445	+	0.290978i	−0.892590	+	0.450869i	$0.851114\pi$
$884$		0			0
$885$	18.3011	+	13.2965i	0.615184	+	0.446957i
$886$		0			0
$887$	10.7401	−	33.0545i	0.360616	−	1.10986i	−0.592064	−	0.805891i	$-0.701687\pi$
$887$	10.7401	−	33.0545i	0.360616	−	1.10986i	0.952681	−	0.303972i	$-0.0983131\pi$
$888$		0			0
$889$	9.70891	−	7.05394i	0.325626	−	0.236581i
$890$		0			0
$891$	−22.7945	+	16.1605i	−0.763645	+	0.541397i
$892$		0			0
$893$	−0.848205	+	0.616257i	−0.0283841	+	0.0206223i
$894$		0			0
$895$	−4.46128	+	13.7304i	−0.149124	+	0.458957i
$896$		0			0
$897$	−25.6846	−	18.6609i	−0.857583	−	0.623071i
$898$		0			0
$899$	7.62133	+	23.4560i	0.254186	+	0.782303i
$900$		0			0
$901$	−40.9099			−1.36290
$902$		0			0
$903$	−11.6987			−0.389308
$904$		0			0
$905$	−9.57203	−	29.4597i	−0.318185	−	0.979272i
$906$		0			0
$907$	5.62375	+	4.08589i	0.186733	+	0.135670i	0.677224	−	0.735776i	$-0.263183\pi$
$907$	5.62375	+	4.08589i	0.186733	+	0.135670i	−0.490491	+	0.871446i	$0.663183\pi$
$908$		0			0
$909$	−12.0177	+	36.9865i	−0.398600	+	1.22677i
$910$		0			0
$911$	−3.07901	+	2.23703i	−0.102012	+	0.0741161i	−0.637622	−	0.770349i	$-0.720082\pi$
$911$	−3.07901	+	2.23703i	−0.102012	+	0.0741161i	0.535610	+	0.844466i	$0.320082\pi$
$912$		0			0
$913$	−9.37019	−	30.0191i	−0.310108	−	0.993488i
$914$		0			0
$915$	−36.5910	+	26.5849i	−1.20966	+	0.878870i
$916$		0			0
$917$	6.04477	−	18.6039i	0.199616	−	0.614354i
$918$		0			0
$919$	38.8532	+	28.2285i	1.28165	+	0.931171i	0.999601	−	0.0282295i	$-0.00898692\pi$
$919$	38.8532	+	28.2285i	1.28165	+	0.931171i	0.282046	+	0.959401i	$0.408987\pi$
$920$		0			0
$921$	10.6627	+	32.8166i	0.351349	+	1.08134i
$922$		0			0
$923$	0.642546			0.0211496
$924$		0			0
$925$	15.1951			0.499613
$926$		0			0
$927$	0.310949	+	0.957003i	0.0102129	+	0.0314321i
$928$		0			0
$929$	4.95356	+	3.59897i	0.162521	+	0.118078i	0.666073	−	0.745886i	$-0.267974\pi$
$929$	4.95356	+	3.59897i	0.162521	+	0.118078i	−0.503552	+	0.863965i	$0.667974\pi$
$930$		0			0
$931$	−2.26664	+	6.97601i	−0.0742863	+	0.228630i
$932$		0			0
$933$	5.54804	−	4.03089i	0.181635	−	0.131965i
$934$		0			0
$935$	−10.4927	+	31.0622i	−0.343147	+	1.01584i
$936$		0			0
$937$	32.2497	−	23.4308i	1.05355	−	0.765450i	0.0806672	−	0.996741i	$-0.474295\pi$
$937$	32.2497	−	23.4308i	1.05355	−	0.765450i	0.972885	+	0.231291i	$0.0742949\pi$
$938$		0			0
$939$	−10.1796	+	31.3295i	−0.332198	+	1.02240i
$940$		0			0
$941$	−0.638752	−	0.464081i	−0.0208227	−	0.0151286i	0.577325	−	0.816514i	$-0.304096\pi$
$941$	−0.638752	−	0.464081i	−0.0208227	−	0.0151286i	−0.598148	+	0.801386i	$0.704096\pi$
$942$		0			0
$943$	−7.56067	−	23.2694i	−0.246209	−	0.757754i
$944$		0			0
$945$	−0.835396			−0.0271754
$946$		0			0
$947$	32.7556			1.06441			0.532206	−	0.846615i	$-0.321363\pi$
$947$	32.7556			1.06441			0.532206	+	0.846615i	$0.321363\pi$
$948$		0			0
$949$	27.1910	+	83.6852i	0.882656	+	2.71654i
$950$		0			0
$951$	21.0659	+	15.3053i	0.683109	+	0.496308i
$952$		0			0
$953$	−0.989526	+	3.04545i	−0.0320539	+	0.0986518i	−0.965803	−	0.259275i	$-0.916516\pi$
$953$	−0.989526	+	3.04545i	−0.0320539	+	0.0986518i	0.933750	+	0.357927i	$0.116516\pi$
$954$		0			0
$955$	−5.78424	+	4.20250i	−0.187174	+	0.135990i
$956$		0			0
$957$	−26.4448	−	19.6861i	−0.854840	−	0.636360i
$958$		0			0
$959$	−1.64110	+	1.19233i	−0.0529940	+	0.0385024i
$960$		0			0
$961$	2.17869	−	6.70532i	0.0702803	−	0.216301i
$962$		0			0
$963$	39.9610	+	29.0333i	1.28772	+	0.935587i
$964$		0			0
$965$	5.78350	+	17.7998i	0.186177	+	0.572995i
$966$		0			0
$967$	−46.4013			−1.49217			−0.746083	−	0.665853i	$-0.768068\pi$
$967$	−46.4013			−1.49217			−0.746083	+	0.665853i	$0.768068\pi$
$968$		0			0
$969$	97.0118			3.11647
$970$		0			0
$971$	15.2213	+	46.8463i	0.488474	+	1.50337i	0.826885	+	0.562371i	$0.190111\pi$
$971$	15.2213	+	46.8463i	0.488474	+	1.50337i	−0.338411	+	0.940999i	$0.609889\pi$
$972$		0			0
$973$	7.24078	+	5.26074i	0.232129	+	0.168651i
$974$		0			0
$975$	−7.47086	+	22.9930i	−0.239259	+	0.736364i
$976$		0			0
$977$	17.5794	−	12.7722i	0.562414	−	0.408618i	−0.269927	−	0.962881i	$-0.587000\pi$
$977$	17.5794	−	12.7722i	0.562414	−	0.408618i	0.832342	+	0.554263i	$0.187000\pi$
$978$		0			0
$979$	37.8901	+	28.2061i	1.21097	+	0.901472i
$980$		0			0
$981$	2.52543	−	1.83483i	0.0806307	−	0.0585816i
$982$		0			0
$983$	3.10432	−	9.55410i	0.0990123	−	0.304729i	−0.889266	−	0.457390i	$-0.848784\pi$
$983$	3.10432	−	9.55410i	0.0990123	−	0.304729i	0.988279	+	0.152661i	$0.0487844\pi$
$984$		0			0
$985$	−8.66165	−	6.29305i	−0.275983	−	0.200513i
$986$		0			0
$987$	−0.109812	−	0.337965i	−0.00349534	−	0.0107575i
$988$		0			0
$989$	−9.55930			−0.303968
$990$		0			0
$991$	15.7681			0.500889			0.250444	−	0.968131i	$-0.419423\pi$
$991$	15.7681			0.500889			0.250444	+	0.968131i	$0.419423\pi$
$992$		0			0
$993$	−19.2685	−	59.3025i	−0.611469	−	1.88191i
$994$		0			0
$995$	17.7188	+	12.8735i	0.561724	+	0.408117i
$996$		0			0
$997$	−6.45712	+	19.8730i	−0.204499	+	0.629384i	0.795234	+	0.606302i	$0.207348\pi$
$997$	−6.45712	+	19.8730i	−0.204499	+	0.629384i	−0.999734	+	0.0230817i	$0.992652\pi$
$998$		0			0
$999$	3.57248	−	2.59556i	0.113028	−	0.0821199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.r.d.113.4	✓	16
11.2	odd	10		6776.2.a.bk.1.7		8
11.4	even	5	inner	616.2.r.d.169.4	yes	16
11.9	even	5		6776.2.a.bl.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.r.d.113.4	✓	16	1.1	even	1	trivial
616.2.r.d.169.4	yes	16	11.4	even	5	inner
6776.2.a.bk.1.7		8	11.2	odd	10
6776.2.a.bl.1.7		8	11.9	even	5

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:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.r (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.768256 + 2.36445i) q^{3} +(1.50334 + 1.09224i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-2.57335 + 1.86964i) q^{9} +(2.66041 + 1.98046i) q^{11} +(-5.08555 + 3.69487i) q^{13} +(-1.42760 + 4.39369i) q^{15} +(4.30386 + 3.12693i) q^{17} +(-2.26664 - 6.97601i) q^{19} +2.48613 q^{21} +2.03148 q^{23} +(-0.478044 - 1.47127i) q^{25} +(-0.363706 - 0.264248i) q^{27} +(-1.23552 + 3.80255i) q^{29} +(4.99042 - 3.62575i) q^{31} +(-2.63882 + 7.81190i) q^{33} +(1.50334 - 1.09224i) q^{35} +(-3.03530 + 9.34170i) q^{37} +(-12.6433 - 9.18591i) q^{39} +(-3.72176 - 11.4544i) q^{41} -4.70559 q^{43} -5.91071 q^{45} +(-0.0441697 - 0.135940i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-4.08701 + 12.5785i) q^{51} +(-6.22136 + 4.52008i) q^{53} +(1.83636 + 5.88311i) q^{55} +(14.7531 - 10.7187i) q^{57} +(1.51314 - 4.65696i) q^{59} +(7.92048 + 5.75456i) q^{61} +(0.982930 + 3.02515i) q^{63} -11.6810 q^{65} +3.97261 q^{67} +(1.56069 + 4.80332i) q^{69} +(-0.0826955 - 0.0600818i) q^{71} +(4.32558 - 13.3128i) q^{73} +(3.11147 - 2.26062i) q^{75} +(2.70564 - 1.91820i) q^{77} +(4.13711 - 3.00579i) q^{79} +(-2.60341 + 8.01247i) q^{81} +(-7.67093 - 5.57326i) q^{83} +(3.05479 + 9.40169i) q^{85} -9.94014 q^{87} +14.2422 q^{89} +(1.94251 + 5.97842i) q^{91} +(12.4068 + 9.01408i) q^{93} +(4.21195 - 12.9630i) q^{95} +(1.14934 - 0.835042i) q^{97} +(-10.5489 - 0.122391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{3} + 6 q^{5} - 4 q^{7} - q^{9} - 2 q^{11} + 4 q^{13} + 22 q^{15} - 6 q^{17} - 10 q^{19} + 4 q^{21} + 14 q^{23} + 8 q^{25} + 29 q^{27} - 4 q^{29} - 8 q^{31} - 51 q^{33} + 6 q^{35} + 11 q^{37}+ \cdots - 12 q^{99}+O(q^{100}) \) 16 * q - q^3 + 6 * q^5 - 4 * q^7 - q^9 - 2 * q^11 + 4 * q^13 + 22 * q^15 - 6 * q^17 - 10 * q^19 + 4 * q^21 + 14 * q^23 + 8 * q^25 + 29 * q^27 - 4 * q^29 - 8 * q^31 - 51 * q^33 + 6 * q^35 + 11 * q^37 - 38 * q^39 + 6 * q^41 - 36 * q^43 - 70 * q^45 - 9 * q^47 - 4 * q^49 - 4 * q^51 - 4 * q^53 - 13 * q^55 + 24 * q^57 + 17 * q^59 + 25 * q^61 - 11 * q^63 + 26 * q^65 - 20 * q^67 + 45 * q^69 + 18 * q^71 + 48 * q^73 + 8 * q^75 + 3 * q^77 + 21 * q^79 - 30 * q^81 - 8 * q^83 - 38 * q^85 + 8 * q^87 - 16 * q^89 + 4 * q^91 + 85 * q^93 + 16 * q^95 - 44 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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