LMFDB - Embedded newform 252.2.i.b.121.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(25,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 4]))

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

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.i (of order $3$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.5
Root			$-1.73040 + 0.0755709i$ of defining polynomial
Character	$\chi$	$=$	252.121
Dual form			252.2.i.b.25.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.799754 - 1.53636i) q^{3} +(-0.483929 - 0.838189i) q^{5} +(-1.52054 - 2.16517i) q^{7} +(-1.72079 - 2.45742i) q^{9} +O(q^{10})$	\(q+(0.799754 - 1.53636i) q^{3} +(-0.483929 - 0.838189i) q^{5} +(-1.52054 - 2.16517i) q^{7} +(-1.72079 - 2.45742i) q^{9} +(-0.364122 + 0.630678i) q^{11} +(1.81066 - 3.13615i) q^{13} +(-1.67478 + 0.0731419i) q^{15} +(3.49948 + 6.06128i) q^{17} +(-0.348050 + 0.602841i) q^{19} +(-4.54253 + 0.604489i) q^{21} +(-3.21898 - 5.57544i) q^{23} +(2.03163 - 3.51888i) q^{25} +(-5.15168 + 0.678412i) q^{27} +(3.34727 + 5.79764i) q^{29} +9.16620 q^{31} +(0.677738 + 1.06381i) q^{33} +(-1.07899 + 2.32229i) q^{35} +(0.854506 - 1.48005i) q^{37} +(-3.37017 - 5.28997i) q^{39} +(-3.62444 + 6.27771i) q^{41} +(-0.348050 - 0.602841i) q^{43} +(-1.22704 + 2.63156i) q^{45} +7.66240 q^{47} +(-2.37591 + 6.58445i) q^{49} +(12.1110 - 0.528918i) q^{51} +(2.05637 + 3.56174i) q^{53} +0.704836 q^{55} +(0.647824 + 1.01685i) q^{57} -4.77618 q^{59} +4.92574 q^{61} +(-2.70420 + 7.46239i) q^{63} -3.50492 q^{65} -5.82070 q^{67} +(-11.1403 + 0.486523i) q^{69} +0.304424 q^{71} +(5.33879 + 9.24705i) q^{73} +(-3.78145 - 5.93554i) q^{75} +(1.91919 - 0.170585i) q^{77} -3.23890 q^{79} +(-3.07779 + 8.45738i) q^{81} +(0.618759 + 1.07172i) q^{83} +(3.38700 - 5.86646i) q^{85} +(11.5842 - 0.505913i) q^{87} +(-5.78679 + 10.0230i) q^{89} +(-9.54349 + 0.848265i) q^{91} +(7.33071 - 14.0826i) q^{93} +0.673726 q^{95} +(1.32933 + 2.30247i) q^{97} +(2.17641 - 0.190462i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9	$ 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) $ 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 11 * q^21 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 4 * q^33 - 19 * q^35 + 10 * q^37 - 2 * q^39 - 33 * q^41 + 7 * q^43 - 10 * q^45 + 6 * q^47 - 4 * q^49 - 13 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 + 28 * q^59 + 20 * q^61 + 33 * q^63 - 30 * q^65 - 12 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 - 44 * q^75 - 47 * q^77 + 20 * q^79 - 29 * q^81 - 25 * q^83 + 8 * q^85 + 28 * q^87 - 6 * q^89 + 2 * q^91 + 22 * q^93 + 56 * q^95 - 18 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	0.799754	−	1.53636i	0.461738	−	0.887016i
$3$	0.799754	−	1.53636i	0.461738	−	0.887016i
$4$		0			0
$5$	−0.483929	−	0.838189i	−0.216419	−	0.374850i	0.737291	−	0.675575i	$-0.236105\pi$
$5$	−0.483929	−	0.838189i	−0.216419	−	0.374850i	−0.953711	+	0.300725i	$0.902771\pi$
$6$		0			0
$7$	−1.52054	−	2.16517i	−0.574710	−	0.818357i
$7$	−1.52054	−	2.16517i	−0.574710	−	0.818357i
$8$		0			0
$9$	−1.72079	−	2.45742i	−0.573595	−	0.819139i
$10$		0			0
$11$	−0.364122	+	0.630678i	−0.109787	+	0.190156i	−0.915684	−	0.401899i	$-0.868350\pi$
$11$	−0.364122	+	0.630678i	−0.109787	+	0.190156i	0.805897	+	0.592056i	$0.201683\pi$
$12$		0			0
$13$	1.81066	−	3.13615i	0.502187	−	0.869813i	−0.497810	−	0.867286i	$-0.665862\pi$
$13$	1.81066	−	3.13615i	0.502187	−	0.869813i	0.999997	−	0.00252677i	$-0.000804296\pi$
$14$		0			0
$15$	−1.67478	+	0.0731419i	−0.432427	+	0.0188851i
$16$		0			0
$17$	3.49948	+	6.06128i	0.848749	+	1.47008i	0.882325	+	0.470641i	$0.155977\pi$
$17$	3.49948	+	6.06128i	0.848749	+	1.47008i	−0.0335755	+	0.999436i	$0.510689\pi$
$18$		0			0
$19$	−0.348050	+	0.602841i	−0.0798483	+	0.138301i	−0.903184	−	0.429253i	$-0.858777\pi$
$19$	−0.348050	+	0.602841i	−0.0798483	+	0.138301i	0.823336	+	0.567554i	$0.192110\pi$
$20$		0			0
$21$	−4.54253	+	0.604489i	−0.991262	+	0.131910i
$22$		0			0
$23$	−3.21898	−	5.57544i	−0.671204	−	1.16256i	−0.977563	−	0.210643i	$-0.932444\pi$
$23$	−3.21898	−	5.57544i	−0.671204	−	1.16256i	0.306359	−	0.951916i	$-0.400889\pi$
$24$		0			0
$25$	2.03163	−	3.51888i	0.406325	−	0.703776i
$26$		0			0
$27$	−5.15168	+	0.678412i	−0.991440	+	0.130560i
$28$		0			0
$29$	3.34727	+	5.79764i	0.621573	+	1.07660i	0.989193	+	0.146619i	$0.0468393\pi$
$29$	3.34727	+	5.79764i	0.621573	+	1.07660i	−0.367620	+	0.929976i	$0.619827\pi$
$30$		0			0
$31$	9.16620			1.64630			0.823149	−	0.567825i	$-0.192215\pi$
$31$	9.16620			1.64630			0.823149	+	0.567825i	$0.192215\pi$
$32$		0			0
$33$	0.677738	+	1.06381i	0.117979	+	0.185185i
$34$		0			0
$35$	−1.07899	+	2.32229i	−0.182382	+	0.392538i
$36$		0			0
$37$	0.854506	−	1.48005i	0.140480	−	0.243318i	−0.787197	−	0.616701i	$-0.788469\pi$
$37$	0.854506	−	1.48005i	0.140480	−	0.243318i	0.927677	+	0.373383i	$0.121802\pi$
$38$		0			0
$39$	−3.37017	−	5.28997i	−0.539659	−	0.847074i
$40$		0			0
$41$	−3.62444	+	6.27771i	−0.566042	+	0.980413i	0.430910	+	0.902395i	$0.358193\pi$
$41$	−3.62444	+	6.27771i	−0.566042	+	0.980413i	−0.996952	+	0.0780185i	$0.975141\pi$
$42$		0			0
$43$	−0.348050	−	0.602841i	−0.0530772	−	0.0919324i	0.838266	−	0.545261i	$-0.183570\pi$
$43$	−0.348050	−	0.602841i	−0.0530772	−	0.0919324i	−0.891343	+	0.453329i	$0.850236\pi$
$44$		0			0
$45$	−1.22704	+	2.63156i	−0.182917	+	0.392289i
$46$		0			0
$47$	7.66240			1.11768			0.558838	−	0.829277i	$-0.311247\pi$
$47$	7.66240			1.11768			0.558838	+	0.829277i	$0.311247\pi$
$48$		0			0
$49$	−2.37591	+	6.58445i	−0.339416	+	0.940636i
$50$		0			0
$51$	12.1110	−	0.528918i	1.69588	−	0.0740634i
$52$		0			0
$53$	2.05637	+	3.56174i	0.282465	+	0.489243i	0.971991	−	0.235017i	$-0.0755147\pi$
$53$	2.05637	+	3.56174i	0.282465	+	0.489243i	−0.689527	+	0.724260i	$0.742181\pi$
$54$		0			0
$55$	0.704836			0.0950401
$56$		0			0
$57$	0.647824	+	1.01685i	0.0858064	+	0.134686i
$58$		0			0
$59$	−4.77618			−0.621806			−0.310903	−	0.950442i	$-0.600631\pi$
$59$	−4.77618			−0.621806			−0.310903	+	0.950442i	$0.600631\pi$
$60$		0			0
$61$	4.92574			0.630677			0.315338	−	0.948979i	$-0.397882\pi$
$61$	4.92574			0.630677			0.315338	+	0.948979i	$0.397882\pi$
$62$		0			0
$63$	−2.70420	+	7.46239i	−0.340697	+	0.940173i
$64$		0			0
$65$	−3.50492			−0.434732
$66$		0			0
$67$	−5.82070			−0.711111			−0.355556	−	0.934655i	$-0.615708\pi$
$67$	−5.82070			−0.711111			−0.355556	+	0.934655i	$0.615708\pi$
$68$		0			0
$69$	−11.1403	+	0.486523i	−1.34113	+	0.0585704i
$70$		0			0
$71$	0.304424			0.0361285			0.0180642	−	0.999837i	$-0.494250\pi$
$71$	0.304424			0.0361285			0.0180642	+	0.999837i	$0.494250\pi$
$72$		0			0
$73$	5.33879	+	9.24705i	0.624858	+	1.08229i	0.988568	+	0.150773i	$0.0481763\pi$
$73$	5.33879	+	9.24705i	0.624858	+	1.08229i	−0.363711	+	0.931512i	$0.618490\pi$
$74$		0			0
$75$	−3.78145	−	5.93554i	−0.436645	−	0.685377i
$76$		0			0
$77$	1.91919	−	0.170585i	0.218711	−	0.0194400i
$78$		0			0
$79$	−3.23890			−0.364405			−0.182203	−	0.983261i	$-0.558323\pi$
$79$	−3.23890			−0.364405			−0.182203	+	0.983261i	$0.558323\pi$
$80$		0			0
$81$	−3.07779	+	8.45738i	−0.341977	+	0.939708i
$82$		0			0
$83$	0.618759	+	1.07172i	0.0679176	+	0.117637i	0.897985	−	0.440027i	$-0.145031\pi$
$83$	0.618759	+	1.07172i	0.0679176	+	0.117637i	−0.830067	+	0.557664i	$0.811698\pi$
$84$		0			0
$85$	3.38700	−	5.86646i	0.367372	−	0.636307i
$86$		0			0
$87$	11.5842	−	0.505913i	1.24196	−	0.0542395i
$88$		0			0
$89$	−5.78679	+	10.0230i	−0.613399	+	1.06244i	0.377264	+	0.926106i	$0.376865\pi$
$89$	−5.78679	+	10.0230i	−0.613399	+	1.06244i	−0.990663	+	0.136333i	$0.956468\pi$
$90$		0			0
$91$	−9.54349	+	0.848265i	−1.00043	+	0.0889223i
$92$		0			0
$93$	7.33071	−	14.0826i	0.760159	−	1.46029i
$94$		0			0
$95$	0.673726			0.0691229
$96$		0			0
$97$	1.32933	+	2.30247i	0.134973	+	0.233780i	0.925587	−	0.378534i	$-0.123572\pi$
$97$	1.32933	+	2.30247i	0.134973	+	0.233780i	−0.790614	+	0.612315i	$0.790238\pi$
$98$		0			0
$99$	2.17641	−	0.190462i	0.218738	−	0.0191422i
$100$		0			0
$101$	−0.806969	+	1.39771i	−0.0802964	+	0.139077i	−0.903377	−	0.428847i	$-0.858920\pi$
$101$	−0.806969	+	1.39771i	−0.0802964	+	0.139077i	0.823081	+	0.567924i	$0.192253\pi$
$102$		0			0
$103$	−5.42007	−	9.38783i	−0.534055	−	0.925010i	−0.999208	−	0.0397803i	$-0.987334\pi$
$103$	−5.42007	−	9.38783i	−0.534055	−	0.925010i	0.465153	−	0.885230i	$-0.345999\pi$
$104$		0			0
$105$	2.70494	+	3.51497i	0.263975	+	0.343026i
$106$		0			0
$107$	4.97630	−	8.61920i	0.481077	−	0.833249i	−0.518688	−	0.854964i	$-0.673579\pi$
$107$	4.97630	−	8.61920i	0.481077	−	0.833249i	0.999764	+	0.0217146i	$0.00691252\pi$
$108$		0			0
$109$	−9.27835	−	16.0706i	−0.888705	−	1.53928i	−0.841407	−	0.540401i	$-0.818272\pi$
$109$	−9.27835	−	16.0706i	−0.888705	−	1.53928i	−0.0472974	−	0.998881i	$-0.515061\pi$
$110$		0			0
$111$	−1.59049	−	2.49650i	−0.150962	−	0.236957i
$112$		0			0
$113$	5.75824	−	9.97356i	0.541689	−	0.938234i	−0.457118	−	0.889406i	$-0.651118\pi$
$113$	5.75824	−	9.97356i	0.541689	−	0.938234i	0.998807	−	0.0488275i	$-0.0155485\pi$
$114$		0			0
$115$	−3.11551	+	5.39623i	−0.290523	+	0.503201i
$116$		0			0
$117$	−10.8226	+	0.947106i	−1.00055	+	0.0875599i
$118$		0			0
$119$	7.80260	−	16.7934i	0.715263	−	1.53945i
$120$		0			0
$121$	5.23483	+	9.06699i	0.475894	+	0.824272i
$122$		0			0
$123$	6.74614	+	10.5891i	0.608279	+	0.954783i
$124$		0			0
$125$	−8.77193			−0.784586
$126$		0			0
$127$	9.06977			0.804812			0.402406	−	0.915461i	$-0.368174\pi$
$127$	9.06977			0.804812			0.402406	+	0.915461i	$0.368174\pi$
$128$		0			0
$129$	−1.20453	+	0.0526050i	−0.106053	+	0.00463161i
$130$		0			0
$131$	−6.54255	−	11.3320i	−0.571625	−	0.990084i	−0.996399	−	0.0847847i	$-0.972980\pi$
$131$	−6.54255	−	11.3320i	−0.571625	−	0.990084i	0.424774	−	0.905299i	$-0.360354\pi$
$132$		0			0
$133$	1.83448	−	0.163056i	0.159069	−	0.0141388i
$134$		0			0
$135$	3.06168	+	3.98977i	0.263508	+	0.343385i
$136$		0			0
$137$	10.0382	−	17.3867i	0.857623	−	1.48545i	−0.0165668	−	0.999863i	$-0.505274\pi$
$137$	10.0382	−	17.3867i	0.857623	−	1.48545i	0.874190	−	0.485584i	$-0.161393\pi$
$138$		0			0
$139$	0.337832	−	0.585143i	0.0286546	−	0.0496312i	−0.851343	−	0.524610i	$-0.824211\pi$
$139$	0.337832	−	0.585143i	0.0286546	−	0.0496312i	0.879997	+	0.474979i	$0.157544\pi$
$140$		0			0
$141$	6.12804	−	11.7722i	0.516074	−	0.991397i
$142$		0			0
$143$	1.31860	+	2.28388i	0.110267	+	0.190988i
$144$		0			0
$145$	3.23968	−	5.61129i	0.269041	−	0.465992i
$146$		0			0
$147$	8.21592	+	8.91620i	0.677638	+	0.735396i
$148$		0			0
$149$	−10.7544	−	18.6271i	−0.881034	−	1.52599i	−0.850193	−	0.526471i	$-0.823515\pi$
$149$	−10.7544	−	18.6271i	−0.881034	−	1.52599i	−0.0308402	−	0.999524i	$-0.509818\pi$
$150$		0			0
$151$	−7.08523	+	12.2720i	−0.576588	+	0.998680i	0.419279	+	0.907857i	$0.362283\pi$
$151$	−7.08523	+	12.2720i	−0.576588	+	0.998680i	−0.995867	+	0.0908223i	$0.971050\pi$
$152$		0			0
$153$	8.87324	−	19.0299i	0.717359	−	1.53847i
$154$		0			0
$155$	−4.43579	−	7.68301i	−0.356291	−	0.617114i
$156$		0			0
$157$	−15.9969			−1.27669			−0.638346	−	0.769750i	$-0.720381\pi$
$157$	−15.9969			−1.27669			−0.638346	+	0.769750i	$0.720381\pi$
$158$		0			0
$159$	7.11670	−	0.310804i	0.564391	−	0.0246484i
$160$		0			0
$161$	−7.17717	+	15.4473i	−0.565641	+	1.21742i
$162$		0			0
$163$	−10.0904	+	17.4771i	−0.790340	+	1.36891i	0.135417	+	0.990789i	$0.456763\pi$
$163$	−10.0904	+	17.4771i	−0.790340	+	1.36891i	−0.925757	+	0.378120i	$0.876571\pi$
$164$		0			0
$165$	0.563696	−	1.08288i	0.0438836	−	0.0843021i
$166$		0			0
$167$	−12.2299	+	21.1828i	−0.946378	+	1.63917i	−0.193410	+	0.981118i	$0.561955\pi$
$167$	−12.2299	+	21.1828i	−0.946378	+	1.63917i	−0.752968	+	0.658057i	$0.771379\pi$
$168$		0			0
$169$	−0.0569772	−	0.0986874i	−0.00438286	−	0.00759134i
$170$		0			0
$171$	2.08035	−	0.182055i	0.159088	−	0.0139221i
$172$		0			0
$173$	19.7560			1.50202			0.751010	−	0.660290i	$-0.229567\pi$
$173$	19.7560			1.50202			0.751010	+	0.660290i	$0.229567\pi$
$174$		0			0
$175$	−10.7081	+	0.951784i	−0.809459	+	0.0719481i
$176$		0			0
$177$	−3.81977	+	7.33792i	−0.287112	+	0.551552i
$178$		0			0
$179$	−6.32439	−	10.9542i	−0.472707	−	0.818753i	0.526805	−	0.849986i	$-0.323390\pi$
$179$	−6.32439	−	10.9542i	−0.472707	−	0.818753i	−0.999512	+	0.0312332i	$0.990057\pi$
$180$		0			0
$181$	12.5654			0.933975			0.466988	−	0.884264i	$-0.345339\pi$
$181$	12.5654			0.933975			0.466988	+	0.884264i	$0.345339\pi$
$182$		0			0
$183$	3.93938	−	7.56770i	0.291208	−	0.559421i
$184$		0			0
$185$	−1.65408			−0.121610
$186$		0			0
$187$	−5.09695			−0.372726
$188$		0			0
$189$	9.30221	+	10.1227i	0.676636	+	0.736318i
$190$		0			0
$191$	−7.40632			−0.535903			−0.267951	−	0.963432i	$-0.586347\pi$
$191$	−7.40632			−0.535903			−0.267951	+	0.963432i	$0.586347\pi$
$192$		0			0
$193$	−1.62787			−0.117177			−0.0585885	−	0.998282i	$-0.518660\pi$
$193$	−1.62787			−0.117177			−0.0585885	+	0.998282i	$0.518660\pi$
$194$		0			0
$195$	−2.80308	+	5.38481i	−0.200732	+	0.385614i
$196$		0			0
$197$	−8.27125			−0.589302			−0.294651	−	0.955605i	$-0.595203\pi$
$197$	−8.27125			−0.589302			−0.294651	+	0.955605i	$0.595203\pi$
$198$		0			0
$199$	5.34411	+	9.25627i	0.378834	+	0.656159i	0.990893	−	0.134653i	$-0.0429919\pi$
$199$	5.34411	+	9.25627i	0.378834	+	0.656159i	−0.612059	+	0.790812i	$0.709659\pi$
$200$		0			0
$201$	−4.65513	+	8.94267i	−0.328347	+	0.630767i
$202$		0			0
$203$	7.46322	−	16.0630i	0.523815	−	1.12740i
$204$		0			0
$205$	7.01587			0.490010
$206$		0			0
$207$	−8.16199	+	17.5045i	−0.567298	+	1.21665i
$208$		0			0
$209$	−0.253466	−	0.439015i	−0.0175326	−	0.0303673i
$210$		0			0
$211$	−11.2725	+	19.5246i	−0.776034	+	1.34413i	0.158178	+	0.987411i	$0.449438\pi$
$211$	−11.2725	+	19.5246i	−0.776034	+	1.34413i	−0.934211	+	0.356720i	$0.883895\pi$
$212$		0			0
$213$	0.243465	−	0.467704i	0.0166819	−	0.0320466i
$214$		0			0
$215$	−0.336863	+	0.583464i	−0.0229739	+	0.0397919i
$216$		0			0
$217$	−13.9376	−	19.8464i	−0.946145	−	1.34726i
$218$		0			0
$219$	18.4765	−	0.806914i	1.24853	−	0.0545262i
$220$		0			0
$221$	25.3455			1.70492
$222$		0			0
$223$	3.70093	+	6.41020i	0.247832	+	0.429258i	0.962924	−	0.269772i	$-0.0869484\pi$
$223$	3.70093	+	6.41020i	0.247832	+	0.429258i	−0.715092	+	0.699031i	$0.753615\pi$
$224$		0			0
$225$	−12.1433	+	1.06269i	−0.809556	+	0.0708458i
$226$		0			0
$227$	0.299086	−	0.518033i	0.0198511	−	0.0343831i	−0.855929	−	0.517093i	$-0.827014\pi$
$227$	0.299086	−	0.518033i	0.0198511	−	0.0343831i	0.875780	+	0.482710i	$0.160347\pi$
$228$		0			0
$229$	2.01858	+	3.49629i	0.133392	+	0.231041i	0.924982	−	0.380011i	$-0.124080\pi$
$229$	2.01858	+	3.49629i	0.133392	+	0.231041i	−0.791590	+	0.611052i	$0.790747\pi$
$230$		0			0
$231$	1.27280	−	3.08498i	0.0837439	−	0.202977i
$232$		0			0
$233$	−5.59754	+	9.69523i	−0.366707	+	0.635155i	−0.989049	−	0.147591i	$-0.952848\pi$
$233$	−5.59754	+	9.69523i	−0.366707	+	0.635155i	0.622341	+	0.782746i	$0.286182\pi$
$234$		0			0
$235$	−3.70805	−	6.42254i	−0.241887	−	0.418960i
$236$		0			0
$237$	−2.59033	+	4.97611i	−0.168260	+	0.323233i
$238$		0			0
$239$	−12.8171	+	22.1999i	−0.829069	+	1.43599i	0.0697006	+	0.997568i	$0.477796\pi$
$239$	−12.8171	+	22.1999i	−0.829069	+	1.43599i	−0.898769	+	0.438421i	$0.855538\pi$
$240$		0			0
$241$	3.29590	−	5.70866i	0.212307	−	0.367727i	−0.740129	−	0.672465i	$-0.765236\pi$
$241$	3.29590	−	5.70866i	0.212307	−	0.367727i	0.952436	+	0.304738i	$0.0985688\pi$
$242$		0			0
$243$	10.5321	+	11.4924i	0.675633	+	0.737238i
$244$		0			0
$245$	6.66879	−	1.19494i	0.426053	−	0.0763419i
$246$		0			0
$247$	1.26040	+	2.18308i	0.0801975	+	0.138906i
$248$		0			0
$249$	2.14140	−	0.0935204i	0.135706	−	0.00592661i
$250$		0			0
$251$	25.0438			1.58075			0.790374	−	0.612624i	$-0.209886\pi$
$251$	25.0438			1.58075			0.790374	+	0.612624i	$0.209886\pi$
$252$		0			0
$253$	4.68840			0.294757
$254$		0			0
$255$	−6.30420	−	9.89537i	−0.394785	−	0.619672i
$256$		0			0
$257$	9.07036	+	15.7103i	0.565794	+	0.979984i	0.996975	+	0.0777184i	$0.0247635\pi$
$257$	9.07036	+	15.7103i	0.565794	+	0.979984i	−0.431182	+	0.902265i	$0.641903\pi$
$258$		0			0
$259$	−4.50387	+	0.400322i	−0.279857	+	0.0248748i
$260$		0			0
$261$	8.48729	−	18.2021i	0.525350	−	1.12668i
$262$		0			0
$263$	−6.40438	+	11.0927i	−0.394911	+	0.684006i	−0.993090	−	0.117357i	$-0.962558\pi$
$263$	−6.40438	+	11.0927i	−0.394911	+	0.684006i	0.598179	+	0.801363i	$0.295891\pi$
$264$		0			0
$265$	1.99028	−	3.44726i	0.122262	−	0.211763i
$266$		0			0
$267$	10.7709	+	16.9065i	0.659170	+	1.03466i
$268$		0			0
$269$	−14.4412	−	25.0129i	−0.880497	−	1.52507i	−0.850789	−	0.525507i	$-0.823876\pi$
$269$	−14.4412	−	25.0129i	−0.880497	−	1.52507i	−0.0297079	−	0.999559i	$-0.509458\pi$
$270$		0			0
$271$	4.59579	−	7.96015i	0.279175	−	0.483544i	−0.692005	−	0.721892i	$-0.743273\pi$
$271$	4.59579	−	7.96015i	0.279175	−	0.483544i	0.971180	+	0.238348i	$0.0766059\pi$
$272$		0			0
$273$	−6.32921	+	15.3406i	−0.383061	+	0.928456i
$274$		0			0
$275$	1.47952	+	2.56260i	0.0892183	+	0.154531i
$276$		0			0
$277$	1.95778	−	3.39098i	0.117632	−	0.203744i	−0.801197	−	0.598401i	$-0.795803\pi$
$277$	1.95778	−	3.39098i	0.117632	−	0.203744i	0.918829	+	0.394656i	$0.129136\pi$
$278$		0			0
$279$	−15.7731	−	22.5252i	−0.944309	−	1.34855i
$280$		0			0
$281$	7.64654	+	13.2442i	0.456154	+	0.790082i	0.998754	−	0.0499093i	$-0.0158932\pi$
$281$	7.64654	+	13.2442i	0.456154	+	0.790082i	−0.542600	+	0.839991i	$0.682560\pi$
$282$		0			0
$283$	24.9779			1.48478			0.742392	−	0.669966i	$-0.233691\pi$
$283$	24.9779			1.48478			0.742392	+	0.669966i	$0.233691\pi$
$284$		0			0
$285$	0.538816	−	1.03508i	0.0319167	−	0.0613131i
$286$		0			0
$287$	19.1034	−	1.69799i	1.12764	−	0.100229i
$288$		0			0
$289$	−15.9928	+	27.7003i	−0.940751	+	1.62943i
$290$		0			0
$291$	4.60056	−	0.200918i	0.269689	−	0.0117780i
$292$		0			0
$293$	−4.08092	+	7.06835i	−0.238410	+	0.412938i	−0.960258	−	0.279114i	$-0.909959\pi$
$293$	−4.08092	+	7.06835i	−0.238410	+	0.412938i	0.721848	+	0.692051i	$0.243293\pi$
$294$		0			0
$295$	2.31133	+	4.00334i	0.134571	+	0.233084i
$296$		0			0
$297$	1.44798	−	3.49607i	0.0840202	−	0.202863i
$298$		0			0
$299$	−23.3139			−1.34828
$300$		0			0
$301$	−0.776028	+	1.67023i	−0.0447295	+	0.0962706i
$302$		0			0
$303$	1.50201	+	2.35762i	0.0862880	+	0.135442i
$304$		0			0
$305$	−2.38371	−	4.12870i	−0.136491	−	0.236409i
$306$		0			0
$307$	18.0692			1.03126			0.515631	−	0.856811i	$-0.327558\pi$
$307$	18.0692			1.03126			0.515631	+	0.856811i	$0.327558\pi$
$308$		0			0
$309$	−18.7578	+	0.819199i	−1.06709	+	0.0466026i
$310$		0			0
$311$	−10.0077			−0.567484			−0.283742	−	0.958901i	$-0.591576\pi$
$311$	−10.0077			−0.567484			−0.283742	+	0.958901i	$0.591576\pi$
$312$		0			0
$313$	2.99065			0.169041			0.0845207	−	0.996422i	$-0.473064\pi$
$313$	2.99065			0.169041			0.0845207	+	0.996422i	$0.473064\pi$
$314$		0			0
$315$	7.56353	−	1.34464i	0.426157	−	0.0757617i
$316$		0			0
$317$	−23.8492			−1.33951			−0.669754	−	0.742583i	$-0.733600\pi$
$317$	−23.8492			−1.33951			−0.669754	+	0.742583i	$0.733600\pi$
$318$		0			0
$319$	−4.87526			−0.272962
$320$		0			0
$321$	−9.26235	−	14.5386i	−0.516974	−	0.811466i
$322$		0			0
$323$	−4.87199			−0.271085
$324$		0			0
$325$	−7.35717	−	12.7430i	−0.408102	−	0.706854i
$326$		0			0
$327$	−32.1105	+	1.40235i	−1.77572	+	0.0775500i
$328$		0			0
$329$	−11.6510	−	16.5904i	−0.642340	−	0.914658i
$330$		0			0
$331$	−16.0377			−0.881513			−0.440757	−	0.897627i	$-0.645290\pi$
$331$	−16.0377			−0.881513			−0.440757	+	0.897627i	$0.645290\pi$
$332$		0			0
$333$	−5.10752	+	0.446968i	−0.279890	+	0.0244937i
$334$		0			0
$335$	2.81680	+	4.87884i	0.153898	+	0.266560i
$336$		0			0
$337$	16.8985	−	29.2691i	0.920520	−	1.59439i	0.121907	−	0.992542i	$-0.461099\pi$
$337$	16.8985	−	29.2691i	0.920520	−	1.59439i	0.798613	−	0.601845i	$-0.205568\pi$
$338$		0			0
$339$	−10.7178	−	16.8231i	−0.582110	−	0.913706i
$340$		0			0
$341$	−3.33761	+	5.78092i	−0.180742	+	0.313054i
$342$		0			0
$343$	17.8691	−	4.86767i	0.964842	−	0.262829i
$344$		0			0
$345$	5.79889	+	9.10220i	0.312201	+	0.490046i
$346$		0			0
$347$	35.3274			1.89647			0.948237	−	0.317562i	$-0.102864\pi$
$347$	35.3274			1.89647			0.948237	+	0.317562i	$0.102864\pi$
$348$		0			0
$349$	−5.75344	−	9.96526i	−0.307975	−	0.533428i	0.669944	−	0.742411i	$-0.266318\pi$
$349$	−5.75344	−	9.96526i	−0.307975	−	0.533428i	−0.977919	+	0.208983i	$0.932985\pi$
$350$		0			0
$351$	−7.20033	+	17.3848i	−0.384325	+	0.927933i
$352$		0			0
$353$	−12.4432	+	21.5522i	−0.662283	+	1.14711i	0.317732	+	0.948181i	$0.397079\pi$
$353$	−12.4432	+	21.5522i	−0.662283	+	1.14711i	−0.980014	+	0.198926i	$0.936254\pi$
$354$		0			0
$355$	−0.147320	−	0.255165i	−0.00781891	−	0.0135427i
$356$		0			0
$357$	−19.5605	−	25.4182i	−1.03525	−	1.34527i
$358$		0			0
$359$	9.22681	−	15.9813i	0.486972	−	0.843461i	−0.512916	−	0.858439i	$-0.671435\pi$
$359$	9.22681	−	15.9813i	0.486972	−	0.843461i	0.999888	+	0.0149785i	$0.00476798\pi$
$360$		0			0
$361$	9.25772	+	16.0348i	0.487249	+	0.843939i
$362$		0			0
$363$	18.1167	−	0.791202i	0.950881	−	0.0415273i
$364$		0			0
$365$	5.16718	−	8.94982i	0.270463	−	0.468455i
$366$		0			0
$367$	9.10688	−	15.7736i	0.475375	−	0.823374i	−0.524227	−	0.851579i	$-0.675646\pi$
$367$	9.10688	−	15.7736i	0.475375	−	0.823374i	0.999602	+	0.0282046i	$0.00897899\pi$
$368$		0			0
$369$	21.6638	−	1.89584i	1.12777	−	0.0986936i
$370$		0			0
$371$	4.58498	−	9.86817i	0.238040	−	0.512330i
$372$		0			0
$373$	9.09995	+	15.7616i	0.471177	+	0.816103i	0.999456	−	0.0329676i	$-0.0104958\pi$
$373$	9.09995	+	15.7616i	0.471177	+	0.816103i	−0.528279	+	0.849071i	$0.677162\pi$
$374$		0			0
$375$	−7.01539	+	13.4768i	−0.362273	+	0.695940i
$376$		0			0
$377$	24.2431			1.24858
$378$		0			0
$379$	−24.1061			−1.23825			−0.619124	−	0.785293i	$-0.712512\pi$
$379$	−24.1061			−1.23825			−0.619124	+	0.785293i	$0.712512\pi$
$380$		0			0
$381$	7.25359	−	13.9344i	0.371613	−	0.713882i
$382$		0			0
$383$	3.21847	+	5.57455i	0.164456	+	0.284846i	0.936462	−	0.350769i	$-0.114080\pi$
$383$	3.21847	+	5.57455i	0.164456	+	0.284846i	−0.772006	+	0.635615i	$0.780746\pi$
$384$		0			0
$385$	−1.07173	−	1.52609i	−0.0546205	−	0.0777767i
$386$		0			0
$387$	−0.882511	+	1.89267i	−0.0448606	+	0.0962096i
$388$		0			0
$389$	−16.9299	+	29.3234i	−0.858379	+	1.48676i	0.0150964	+	0.999886i	$0.495194\pi$
$389$	−16.9299	+	29.3234i	−0.858379	+	1.48676i	−0.873475	+	0.486869i	$0.838139\pi$
$390$		0			0
$391$	22.5295	−	39.0223i	1.13937	−	1.97344i
$392$		0			0
$393$	−22.6425	+	0.988853i	−1.14216	+	0.0498810i
$394$		0			0
$395$	1.56740	+	2.71481i	0.0788643	+	0.136597i
$396$		0			0
$397$	−0.808630	+	1.40059i	−0.0405840	+	0.0702935i	−0.885604	−	0.464441i	$-0.846255\pi$
$397$	−0.808630	+	1.40059i	−0.0405840	+	0.0702935i	0.845020	+	0.534735i	$0.179588\pi$
$398$		0			0
$399$	1.21662	−	2.94882i	0.0609071	−	0.147626i
$400$		0			0
$401$	−2.87691	−	4.98296i	−0.143666	−	0.248837i	0.785208	−	0.619232i	$-0.212556\pi$
$401$	−2.87691	−	4.98296i	−0.143666	−	0.248837i	−0.928874	+	0.370395i	$0.879222\pi$
$402$		0			0
$403$	16.5969	−	28.7466i	0.826749	−	1.43197i
$404$		0			0
$405$	8.57831	−	1.51300i	0.426260	−	0.0751813i
$406$		0			0
$407$	0.622289	+	1.07784i	0.0308457	+	0.0534263i
$408$		0			0
$409$	−5.77262			−0.285438			−0.142719	−	0.989763i	$-0.545584\pi$
$409$	−5.77262			−0.285438			−0.142719	+	0.989763i	$0.545584\pi$
$410$		0			0
$411$	−18.6841	−	29.3274i	−0.921618	−	1.44661i
$412$		0			0
$413$	7.26237	+	10.3412i	0.357358	+	0.508859i
$414$		0			0
$415$	0.598871	−	1.03727i	0.0293974	−	0.0509178i
$416$		0			0
$417$	−0.628806	−	0.987002i	−0.0307927	−	0.0483337i
$418$		0			0
$419$	−9.29032	+	16.0913i	−0.453862	+	0.786111i	−0.998622	−	0.0524804i	$-0.983287\pi$
$419$	−9.29032	+	16.0913i	−0.453862	+	0.786111i	0.544760	+	0.838592i	$0.316621\pi$
$420$		0			0
$421$	−8.05788	−	13.9567i	−0.392717	−	0.680206i	0.600090	−	0.799933i	$-0.295131\pi$
$421$	−8.05788	−	13.9567i	−0.392717	−	0.680206i	−0.992807	+	0.119727i	$0.961798\pi$
$422$		0			0
$423$	−13.1854	−	18.8297i	−0.641094	−	0.915532i
$424$		0			0
$425$	28.4386			1.37947
$426$		0			0
$427$	−7.48979	−	10.6651i	−0.362456	−	0.516119i
$428$		0			0
$429$	4.56342	−	0.199296i	0.220324	−	0.00962210i
$430$		0			0
$431$	1.82664	+	3.16383i	0.0879860	+	0.152396i	0.906660	−	0.421863i	$-0.138624\pi$
$431$	1.82664	+	3.16383i	0.0879860	+	0.152396i	−0.818674	+	0.574259i	$0.805290\pi$
$432$		0			0
$433$	12.6697			0.608865			0.304432	−	0.952534i	$-0.401533\pi$
$433$	12.6697			0.608865			0.304432	+	0.952534i	$0.401533\pi$
$434$		0			0
$435$	−6.03000	−	9.46496i	−0.289116	−	0.453810i
$436$		0			0
$437$	4.48147			0.214378
$438$		0			0
$439$	11.7162			0.559183			0.279592	−	0.960119i	$-0.409801\pi$
$439$	11.7162			0.559183			0.279592	+	0.960119i	$0.409801\pi$
$440$		0			0
$441$	20.2692	−	5.49182i	0.965199	−	0.261515i
$442$		0			0
$443$	−29.7470			−1.41332			−0.706661	−	0.707552i	$-0.749799\pi$
$443$	−29.7470			−1.41332			−0.706661	+	0.707552i	$0.749799\pi$
$444$		0			0
$445$	11.2016			0.531006
$446$		0			0
$447$	−37.2188	+	1.62544i	−1.76039	+	0.0768806i
$448$		0			0
$449$	11.0193			0.520034			0.260017	−	0.965604i	$-0.416272\pi$
$449$	11.0193			0.520034			0.260017	+	0.965604i	$0.416272\pi$
$450$		0			0
$451$	−2.63947	−	4.57170i	−0.124288	−	0.215273i
$452$		0			0
$453$	13.1877	+	20.7000i	0.619612	+	0.972572i
$454$		0			0
$455$	5.32937	+	7.58875i	0.249845	+	0.355766i
$456$		0			0
$457$	0.516448			0.0241584			0.0120792	−	0.999927i	$-0.496155\pi$
$457$	0.516448			0.0241584			0.0120792	+	0.999927i	$0.496155\pi$
$458$		0			0
$459$	−22.1402	−	28.8517i	−1.03342	−	1.34668i
$460$		0			0
$461$	−3.54962	−	6.14813i	−0.165322	−	0.286347i	0.771447	−	0.636293i	$-0.219533\pi$
$461$	−3.54962	−	6.14813i	−0.165322	−	0.286347i	−0.936770	+	0.349946i	$0.886200\pi$
$462$		0			0
$463$	−4.91148	+	8.50693i	−0.228256	+	0.395351i	−0.957291	−	0.289125i	$-0.906636\pi$
$463$	−4.91148	+	8.50693i	−0.228256	+	0.395351i	0.729035	+	0.684476i	$0.239969\pi$
$464$		0			0
$465$	−15.3514	+	0.670433i	−0.711904	+	0.0310906i
$466$		0			0
$467$	−4.79604	+	8.30698i	−0.221934	+	0.384401i	−0.955395	−	0.295330i	$-0.904570\pi$
$467$	−4.79604	+	8.30698i	−0.221934	+	0.384401i	0.733461	+	0.679731i	$0.237904\pi$
$468$		0			0
$469$	8.85061	+	12.6028i	0.408683	+	0.581943i
$470$		0			0
$471$	−12.7936	+	24.5770i	−0.589498	+	1.13245i
$472$		0			0
$473$	0.506931			0.0233087
$474$		0			0
$475$	1.41422	+	2.44950i	0.0648887	+	0.112391i
$476$		0			0
$477$	5.21411	−	11.1824i	0.238738	−	0.512005i
$478$		0			0
$479$	−8.13621	+	14.0923i	−0.371753	+	0.643895i	−0.989835	−	0.142218i	$-0.954576\pi$
$479$	−8.13621	+	14.0923i	−0.371753	+	0.643895i	0.618082	+	0.786113i	$0.287910\pi$
$480$		0			0
$481$	−3.09444	−	5.35973i	−0.141094	−	0.244383i
$482$		0			0
$483$	17.9926	+	23.3808i	0.818692	+	1.06386i
$484$		0			0
$485$	1.28660	−	2.22846i	0.0584217	−	0.101189i
$486$		0			0
$487$	−9.50511	−	16.4633i	−0.430718	−	0.746025i	0.566217	−	0.824256i	$-0.308406\pi$
$487$	−9.50511	−	16.4633i	−0.430718	−	0.746025i	−0.996935	+	0.0782307i	$0.975073\pi$
$488$		0			0
$489$	18.7812	+	29.4798i	0.849314	+	1.33312i
$490$		0			0
$491$	2.55413	−	4.42387i	0.115266	−	0.199647i	−0.802620	−	0.596491i	$-0.796561\pi$
$491$	2.55413	−	4.42387i	0.115266	−	0.199647i	0.917886	+	0.396844i	$0.129895\pi$
$492$		0			0
$493$	−23.4274	+	40.5775i	−1.05512	+	1.82752i
$494$		0			0
$495$	−1.21287	−	1.73208i	−0.0545145	−	0.0778510i
$496$		0			0
$497$	−0.462889	−	0.659130i	−0.0207634	−	0.0295660i
$498$		0			0
$499$	14.2638	+	24.7056i	0.638536	+	1.10598i	0.985754	+	0.168192i	$0.0537928\pi$
$499$	14.2638	+	24.7056i	0.638536	+	1.10598i	−0.347219	+	0.937784i	$0.612874\pi$
$500$		0			0
$501$	22.7634	+	35.7305i	1.01700	+	1.59632i
$502$		0			0
$503$	4.05885			0.180975			0.0904877	−	0.995898i	$-0.471157\pi$
$503$	4.05885			0.180975			0.0904877	+	0.995898i	$0.471157\pi$
$504$		0			0
$505$	1.56206			0.0695108
$506$		0			0
$507$	−0.197187	+	0.00861164i	−0.00875738	+	0.000382456i
$508$		0			0
$509$	−8.63023	−	14.9480i	−0.382528	−	0.662558i	0.608895	−	0.793251i	$-0.291613\pi$
$509$	−8.63023	−	14.9480i	−0.382528	−	0.662558i	−0.991423	+	0.130693i	$0.958280\pi$
$510$		0			0
$511$	11.9036	−	25.6199i	0.526584	−	1.13336i
$512$		0			0
$513$	1.38407	−	3.34176i	0.0611081	−	0.147542i
$514$		0			0
$515$	−5.24585	+	9.08608i	−0.231160	+	0.400380i
$516$		0			0
$517$	−2.79005	+	4.83250i	−0.122706	+	0.212533i
$518$		0			0
$519$	15.7999	−	30.3523i	0.693541	−	1.33232i
$520$		0			0
$521$	−17.0525	−	29.5358i	−0.747083	−	1.29399i	−0.949215	−	0.314628i	$-0.898120\pi$
$521$	−17.0525	−	29.5358i	−0.747083	−	1.29399i	0.202132	−	0.979358i	$-0.435213\pi$
$522$		0			0
$523$	−9.44847	+	16.3652i	−0.413153	+	0.715602i	−0.995233	−	0.0975299i	$-0.968906\pi$
$523$	−9.44847	+	16.3652i	−0.413153	+	0.715602i	0.582080	+	0.813132i	$0.302239\pi$
$524$		0			0
$525$	−7.10160	+	17.2127i	−0.309939	+	0.751225i
$526$		0			0
$527$	32.0770	+	55.5589i	1.39729	+	2.42019i
$528$		0			0
$529$	−9.22366	+	15.9758i	−0.401029	+	0.694602i
$530$		0			0
$531$	8.21878	+	11.7371i	0.356665	+	0.509345i
$532$		0			0
$533$	13.1252	+	22.7336i	0.568517	+	0.984701i
$534$		0			0
$535$	−9.63269			−0.416457
$536$		0			0
$537$	−21.8875	+	0.955880i	−0.944514	+	0.0412493i
$538$		0			0
$539$	−3.28754	−	3.89598i	−0.141605	−	0.167812i
$540$		0			0
$541$	0.564117	−	0.977080i	0.0242533	−	0.0420080i	−0.853644	−	0.520857i	$-0.825613\pi$
$541$	0.564117	−	0.977080i	0.0242533	−	0.0420080i	0.877897	+	0.478849i	$0.158946\pi$
$542$		0			0
$543$	10.0492	−	19.3049i	0.431252	−	0.828451i
$544$		0			0
$545$	−8.98012	+	15.5540i	−0.384666	+	0.666261i
$546$		0			0
$547$	15.8427	+	27.4404i	0.677386	+	1.17327i	0.975765	+	0.218819i	$0.0702205\pi$
$547$	15.8427	+	27.4404i	0.677386	+	1.17327i	−0.298380	+	0.954447i	$0.596446\pi$
$548$		0			0
$549$	−8.47615	−	12.1046i	−0.361753	−	0.516612i
$550$		0			0
$551$	−4.66008			−0.198526
$552$		0			0
$553$	4.92488	+	7.01277i	0.209427	+	0.298213i
$554$		0			0
$555$	−1.32286	+	2.54126i	−0.0561522	+	0.107870i
$556$		0			0
$557$	−13.8135	−	23.9257i	−0.585298	−	1.01377i	−0.994838	−	0.101474i	$-0.967644\pi$
$557$	−13.8135	−	23.9257i	−0.585298	−	1.01377i	0.409540	−	0.912292i	$-0.365689\pi$
$558$		0			0
$559$	−2.52080			−0.106619
$560$		0			0
$561$	−4.07631	+	7.83074i	−0.172102	+	0.330614i
$562$		0			0
$563$	1.84137			0.0776045			0.0388022	−	0.999247i	$-0.487646\pi$
$563$	1.84137			0.0776045			0.0388022	+	0.999247i	$0.487646\pi$
$564$		0			0
$565$	−11.1463			−0.468929
$566$		0			0
$567$	22.9916	−	6.19584i	0.965555	−	0.260201i
$568$		0			0
$569$	−11.5105			−0.482545			−0.241272	−	0.970457i	$-0.577565\pi$
$569$	−11.5105			−0.482545			−0.241272	+	0.970457i	$0.577565\pi$
$570$		0			0
$571$	−8.70524			−0.364303			−0.182152	−	0.983270i	$-0.558306\pi$
$571$	−8.70524			−0.364303			−0.182152	+	0.983270i	$0.558306\pi$
$572$		0			0
$573$	−5.92324	+	11.3788i	−0.247447	+	0.475354i
$574$		0			0
$575$	−26.1591			−1.09091
$576$		0			0
$577$	−7.24358	−	12.5462i	−0.301554	−	0.522307i	0.674934	−	0.737878i	$-0.264172\pi$
$577$	−7.24358	−	12.5462i	−0.301554	−	0.522307i	−0.976488	+	0.215571i	$0.930839\pi$
$578$		0			0
$579$	−1.30190	+	2.50100i	−0.0541051	+	0.103938i
$580$		0			0
$581$	1.37961	−	2.96932i	0.0572359	−	0.123188i
$582$		0			0
$583$	−2.99508			−0.124044
$584$		0			0
$585$	6.03122	+	8.61305i	0.249360	+	0.356106i
$586$		0			0
$587$	−14.3695	−	24.8886i	−0.593091	−	1.02726i	−0.993813	−	0.111065i	$-0.964574\pi$
$587$	−14.3695	−	24.8886i	−0.593091	−	1.02726i	0.400722	−	0.916200i	$-0.368759\pi$
$588$		0			0
$589$	−3.19030	+	5.52576i	−0.131454	+	0.227685i
$590$		0			0
$591$	−6.61497	+	12.7076i	−0.272103	+	0.522720i
$592$		0			0
$593$	6.82328	−	11.8183i	0.280199	−	0.485318i	−0.691235	−	0.722630i	$-0.742933\pi$
$593$	6.82328	−	11.8183i	0.280199	−	0.485318i	0.971434	+	0.237312i	$0.0762663\pi$
$594$		0			0
$595$	−17.8519	+	1.58676i	−0.731858	+	0.0650506i
$596$		0			0
$597$	18.4949	−	0.807718i	0.756946	−	0.0330577i
$598$		0			0
$599$	5.29170			0.216213			0.108106	−	0.994139i	$-0.465521\pi$
$599$	5.29170			0.216213			0.108106	+	0.994139i	$0.465521\pi$
$600$		0			0
$601$	17.0522	+	29.5353i	0.695574	+	1.20477i	0.969987	+	0.243158i	$0.0781834\pi$
$601$	17.0522	+	29.5353i	0.695574	+	1.20477i	−0.274412	+	0.961612i	$0.588483\pi$
$602$		0			0
$603$	10.0162	+	14.3039i	0.407890	+	0.582499i
$604$		0			0
$605$	5.06657	−	8.77555i	0.205985	−	0.356777i
$606$		0			0
$607$	4.52232	+	7.83289i	0.183555	+	0.317927i	0.943089	−	0.332541i	$-0.107906\pi$
$607$	4.52232	+	7.83289i	0.183555	+	0.317927i	−0.759533	+	0.650468i	$0.774573\pi$
$608$		0			0
$609$	−18.7097	−	24.3126i	−0.758155	−	0.985196i
$610$		0			0
$611$	13.8740	−	24.0305i	0.561282	−	0.972169i
$612$		0			0
$613$	5.97889	+	10.3557i	0.241485	+	0.418264i	0.961137	−	0.276070i	$-0.0890322\pi$
$613$	5.97889	+	10.3557i	0.241485	+	0.418264i	−0.719653	+	0.694334i	$0.755699\pi$
$614$		0			0
$615$	5.61098	−	10.7789i	0.226256	−	0.434647i
$616$		0			0
$617$	5.13220	−	8.88923i	0.206615	−	0.357867i	−0.744031	−	0.668145i	$-0.767089\pi$
$617$	5.13220	−	8.88923i	0.206615	−	0.357867i	0.950646	+	0.310278i	$0.100422\pi$
$618$		0			0
$619$	21.7803	−	37.7245i	0.875423	−	1.51628i	0.0191114	−	0.999817i	$-0.493916\pi$
$619$	21.7803	−	37.7245i	0.875423	−	1.51628i	0.856312	−	0.516460i	$-0.172750\pi$
$620$		0			0
$621$	20.3656	+	26.5390i	0.817243	+	1.06498i
$622$		0			0
$623$	30.5006	−	2.71102i	1.22198	−	0.108615i
$624$		0			0
$625$	−5.91314	−	10.2419i	−0.236526	−	0.409674i
$626$		0			0
$627$	−0.877194	+	0.0383093i	−0.0350318	+	0.00152992i
$628$		0			0
$629$	11.9613			0.476929
$630$		0			0
$631$	19.3703			0.771119			0.385559	−	0.922683i	$-0.374008\pi$
$631$	19.3703			0.771119			0.385559	+	0.922683i	$0.374008\pi$
$632$		0			0
$633$	20.9815	+	32.9336i	0.833941	+	1.30899i
$634$		0			0
$635$	−4.38912	−	7.60218i	−0.174177	−	0.301684i
$636$		0			0
$637$	16.3479	+	19.3734i	0.647727	+	0.767604i
$638$		0			0
$639$	−0.523849	−	0.748097i	−0.0207231	−	0.0295943i
$640$		0			0
$641$	−2.25008	+	3.89725i	−0.0888728	+	0.153932i	−0.907035	−	0.421055i	$-0.861660\pi$
$641$	−2.25008	+	3.89725i	−0.0888728	+	0.153932i	0.818162	+	0.574988i	$0.194993\pi$
$642$		0			0
$643$	−20.9045	+	36.2077i	−0.824394	+	1.42789i	0.0779869	+	0.996954i	$0.475151\pi$
$643$	−20.9045	+	36.2077i	−0.824394	+	1.42789i	−0.902381	+	0.430939i	$0.858183\pi$
$644$		0			0
$645$	0.627001	+	0.984170i	0.0246882	+	0.0387517i
$646$		0			0
$647$	11.9381	+	20.6773i	0.469334	+	0.812910i	0.999385	−	0.0350555i	$-0.0111608\pi$
$647$	11.9381	+	20.6773i	0.469334	+	0.812910i	−0.530052	+	0.847965i	$0.677827\pi$
$648$		0			0
$649$	1.73911	−	3.01223i	0.0682661	−	0.118240i
$650$		0			0
$651$	−41.6378	+	5.54087i	−1.63191	+	0.217164i
$652$		0			0
$653$	4.16674	+	7.21700i	0.163057	+	0.282423i	0.935964	−	0.352097i	$-0.114531\pi$
$653$	4.16674	+	7.21700i	0.163057	+	0.282423i	−0.772907	+	0.634520i	$0.781198\pi$
$654$		0			0
$655$	−6.33226	+	10.9678i	−0.247422	+	0.428547i
$656$		0			0
$657$	13.5369	−	29.0318i	0.528126	−	1.13264i
$658$		0			0
$659$	−20.2488	−	35.0719i	−0.788781	−	1.36621i	−0.926714	−	0.375767i	$-0.877379\pi$
$659$	−20.2488	−	35.0719i	−0.788781	−	1.36621i	0.137933	−	0.990442i	$-0.455954\pi$
$660$		0			0
$661$	−7.77118			−0.302264			−0.151132	−	0.988514i	$-0.548292\pi$
$661$	−7.77118			−0.302264			−0.151132	+	0.988514i	$0.548292\pi$
$662$		0			0
$663$	20.2702	−	38.9397i	0.787228	−	1.51229i
$664$		0			0
$665$	−1.02443	−	1.45873i	−0.0397256	−	0.0565672i
$666$		0			0
$667$	21.5496	−	37.3250i	0.834404	−	1.44523i
$668$		0			0
$669$	12.8082	−	0.559365i	0.495193	−	0.0216263i
$670$		0			0
$671$	−1.79357	+	3.10656i	−0.0692400	+	0.119927i
$672$		0			0
$673$	−22.7830	−	39.4614i	−0.878221	−	1.52112i	−0.853291	−	0.521435i	$-0.825397\pi$
$673$	−22.7830	−	39.4614i	−0.878221	−	1.52112i	−0.0249302	−	0.999689i	$-0.507936\pi$
$674$		0			0
$675$	−8.07903	+	19.5064i	−0.310962	+	0.750802i
$676$		0			0
$677$	13.0904			0.503106			0.251553	−	0.967844i	$-0.419059\pi$
$677$	13.0904			0.503106			0.251553	+	0.967844i	$0.419059\pi$
$678$		0			0
$679$	2.96394	−	6.37923i	0.113745	−	0.244812i
$680$		0			0
$681$	−0.556688	−	0.873803i	−0.0213323	−	0.0334842i
$682$		0			0
$683$	−12.6506	−	21.9114i	−0.484060	−	0.838417i	0.515772	−	0.856726i	$-0.327505\pi$
$683$	−12.6506	−	21.9114i	−0.484060	−	0.838417i	−0.999832	+	0.0183087i	$0.994172\pi$
$684$		0			0
$685$	−19.4311			−0.742425
$686$		0			0
$687$	6.98592	−	0.305092i	0.266529	−	0.0116400i
$688$		0			0
$689$	14.8936			0.567400
$690$		0			0
$691$	−24.4031			−0.928339			−0.464170	−	0.885746i	$-0.653647\pi$
$691$	−24.4031			−0.928339			−0.464170	+	0.885746i	$0.653647\pi$
$692$		0			0
$693$	−3.72171	−	4.42270i	−0.141376	−	0.168004i
$694$		0			0
$695$	−0.653947			−0.0248056
$696$		0			0
$697$	−50.7346			−1.92171
$698$		0			0
$699$	10.4187	+	16.3536i	0.394070	+	0.618551i
$700$		0			0
$701$	−18.4137			−0.695476			−0.347738	−	0.937592i	$-0.613050\pi$
$701$	−18.4137			−0.695476			−0.347738	+	0.937592i	$0.613050\pi$
$702$		0			0
$703$	0.594823	+	1.03026i	0.0224342	+	0.0388571i
$704$		0			0
$705$	−12.8328	+	0.560442i	−0.483313	+	0.0211075i
$706$		0			0
$707$	4.25331	−	0.378052i	0.159962	−	0.0142181i
$708$		0			0
$709$	−13.3300			−0.500619			−0.250310	−	0.968166i	$-0.580532\pi$
$709$	−13.3300			−0.500619			−0.250310	+	0.968166i	$0.580532\pi$
$710$		0			0
$711$	5.57346	+	7.95933i	0.209021	+	0.298498i
$712$		0			0
$713$	−29.5058	−	51.1056i	−1.10500	−	1.91392i
$714$		0			0
$715$	1.27622	−	2.21047i	0.0477278	−	0.0826671i
$716$		0			0
$717$	23.8564	+	37.4461i	0.890933	+	1.39845i
$718$		0			0
$719$	−7.84705	+	13.5915i	−0.292646	+	0.506877i	−0.974434	−	0.224672i	$-0.927869\pi$
$719$	−7.84705	+	13.5915i	−0.292646	+	0.506877i	0.681789	+	0.731549i	$0.261202\pi$
$720$		0			0
$721$	−12.0848	+	26.0099i	−0.450062	+	0.968660i
$722$		0			0
$723$	−6.13463	−	9.62920i	−0.228150	−	0.358114i
$724$		0			0
$725$	27.2016			1.01024
$726$		0			0
$727$	−12.8388	−	22.2374i	−0.476163	−	0.824739i	0.523464	−	0.852048i	$-0.324640\pi$
$727$	−12.8388	−	22.2374i	−0.476163	−	0.824739i	−0.999627	+	0.0273090i	$0.991306\pi$
$728$		0			0
$729$	26.0795	−	6.98992i	0.965908	−	0.258886i
$730$		0			0
$731$	2.43599	−	4.21926i	0.0900985	−	0.156055i
$732$		0			0
$733$	−0.586541	−	1.01592i	−0.0216644	−	0.0375238i	0.854990	−	0.518645i	$-0.173563\pi$
$733$	−0.586541	−	1.01592i	−0.0216644	−	0.0375238i	−0.876654	+	0.481121i	$0.840230\pi$
$734$		0			0
$735$	3.49754	−	11.2013i	0.129009	−	0.413166i
$736$		0			0
$737$	2.11944	−	3.67098i	0.0780707	−	0.135222i
$738$		0			0
$739$	11.6114	+	20.1116i	0.427133	+	0.739816i	0.996617	−	0.0821861i	$-0.0261902\pi$
$739$	11.6114	+	20.1116i	0.427133	+	0.739816i	−0.569484	+	0.822003i	$0.692857\pi$
$740$		0			0
$741$	4.36200	−	0.190499i	0.160242	−	0.00699817i
$742$		0			0
$743$	11.7846	−	20.4115i	0.432335	−	0.748826i	−0.564739	−	0.825269i	$-0.691023\pi$
$743$	11.7846	−	20.4115i	0.432335	−	0.748826i	0.997074	+	0.0764439i	$0.0243566\pi$
$744$		0			0
$745$	−10.4087	+	18.0284i	−0.381346	+	0.660510i
$746$		0			0
$747$	1.56892	−	3.36475i	0.0574036	−	0.123110i
$748$		0			0
$749$	−26.2287	+	2.33131i	−0.958375	+	0.0851844i
$750$		0			0
$751$	−22.0531	−	38.1971i	−0.804728	−	1.39383i	−0.916474	−	0.400093i	$-0.868978\pi$
$751$	−22.0531	−	38.1971i	−0.804728	−	1.39383i	0.111746	−	0.993737i	$-0.464356\pi$
$752$		0			0
$753$	20.0289	−	38.4762i	0.729892	−	1.40215i
$754$		0			0
$755$	13.7150			0.499139
$756$		0			0
$757$	−2.71020			−0.0985040			−0.0492520	−	0.998786i	$-0.515684\pi$
$757$	−2.71020			−0.0985040			−0.0492520	+	0.998786i	$0.515684\pi$
$758$		0			0
$759$	3.74957	−	7.20306i	0.136101	−	0.261455i
$760$		0			0
$761$	−14.5248	−	25.1577i	−0.526524	−	0.911966i	−0.999522	−	0.0309029i	$-0.990162\pi$
$761$	−14.5248	−	25.1577i	−0.526524	−	0.911966i	0.472999	−	0.881063i	$-0.343172\pi$
$762$		0			0
$763$	−20.6874	+	44.5252i	−0.748934	+	1.61192i
$764$		0			0
$765$	−20.2446	+	1.77165i	−0.731946	+	0.0640540i
$766$		0			0
$767$	−8.64804	+	14.9788i	−0.312263	+	0.540855i
$768$		0			0
$769$	−5.25175	+	9.09629i	−0.189383	+	0.328021i	−0.945045	−	0.326941i	$-0.893982\pi$
$769$	−5.25175	+	9.09629i	−0.189383	+	0.328021i	0.755662	+	0.654962i	$0.227315\pi$
$770$		0			0
$771$	31.3907	−	1.37091i	1.13051	−	0.0493722i
$772$		0			0
$773$	−11.9230	−	20.6513i	−0.428841	−	0.742774i	0.567930	−	0.823077i	$-0.307745\pi$
$773$	−11.9230	−	20.6513i	−0.428841	−	0.742774i	−0.996771	+	0.0803029i	$0.974411\pi$
$774$		0			0
$775$	18.6223	−	32.2548i	0.668933	−	1.15863i
$776$		0			0
$777$	−2.98695	+	7.23971i	−0.107156	+	0.259723i
$778$		0			0
$779$	−2.52297	−	4.36992i	−0.0903949	−	0.156569i
$780$		0			0
$781$	−0.110847	+	0.191993i	−0.00396643	+	0.00687007i
$782$		0			0
$783$	−21.1772	−	27.5968i	−0.756813	−	0.986227i
$784$		0			0
$785$	7.74136	+	13.4084i	0.276301	+	0.478567i
$786$		0			0
$787$	−4.39576			−0.156692			−0.0783460	−	0.996926i	$-0.524964\pi$
$787$	−4.39576			−0.156692			−0.0783460	+	0.996926i	$0.524964\pi$
$788$		0			0
$789$	11.9204	+	18.7109i	0.424379	+	0.666124i
$790$		0			0
$791$	−30.3501	+	2.69764i	−1.07912	+	0.0959171i
$792$		0			0
$793$	8.91885	−	15.4479i	0.316717	−	0.548571i
$794$		0			0
$795$	−3.70449	−	5.81474i	−0.131385	−	0.206227i
$796$		0			0
$797$	−2.56236	+	4.43813i	−0.0907633	+	0.157207i	−0.907833	−	0.419333i	$-0.862264\pi$
$797$	−2.56236	+	4.43813i	−0.0907633	+	0.157207i	0.817069	+	0.576540i	$0.195597\pi$
$798$		0			0
$799$	26.8144	+	46.4440i	0.948627	+	1.64307i
$800$		0			0
$801$	34.5886	−	3.02691i	1.22213	−	0.106951i
$802$		0			0
$803$	−7.77587			−0.274405
$804$		0			0
$805$	16.4210	−	1.45957i	0.578764	−	0.0514430i
$806$		0			0
$807$	−49.9782	+	2.18267i	−1.75932	+	0.0768338i
$808$		0			0
$809$	−16.4612	−	28.5116i	−0.578744	−	1.00241i	−0.995624	−	0.0934519i	$-0.970210\pi$
$809$	−16.4612	−	28.5116i	−0.578744	−	1.00241i	0.416880	−	0.908961i	$-0.363123\pi$
$810$		0			0
$811$	−31.8830			−1.11956			−0.559781	−	0.828640i	$-0.689115\pi$
$811$	−31.8830			−1.11956			−0.559781	+	0.828640i	$0.689115\pi$
$812$		0			0
$813$	−8.55412	−	13.4269i	−0.300006	−	0.470903i
$814$		0			0
$815$	19.5321			0.684179
$816$		0			0
$817$	0.484556			0.0169525
$818$		0			0
$819$	18.5068	+	21.9926i	0.646681	+	0.768485i
$820$		0			0
$821$	34.2277			1.19456			0.597278	−	0.802034i	$-0.296249\pi$
$821$	34.2277			1.19456			0.597278	+	0.802034i	$0.296249\pi$
$822$		0			0
$823$	38.3732			1.33760			0.668802	−	0.743440i	$-0.266807\pi$
$823$	38.3732			1.33760			0.668802	+	0.743440i	$0.266807\pi$
$824$		0			0
$825$	5.12032	−	0.223617i	0.178267	−	0.00778535i
$826$		0			0
$827$	9.23903			0.321273			0.160636	−	0.987014i	$-0.448645\pi$
$827$	9.23903			0.321273			0.160636	+	0.987014i	$0.448645\pi$
$828$		0			0
$829$	20.8224	+	36.0654i	0.723191	+	1.25260i	0.959714	+	0.280978i	$0.0906589\pi$
$829$	20.8224	+	36.0654i	0.723191	+	1.25260i	−0.236523	+	0.971626i	$0.576008\pi$
$830$		0			0
$831$	−3.64401	−	5.71981i	−0.126409	−	0.198418i
$832$		0			0
$833$	−48.2247	+	8.64110i	−1.67089	+	0.299396i
$834$		0			0
$835$	23.6736			0.819259
$836$		0			0
$837$	−47.2213	+	6.21846i	−1.63221	+	0.214941i
$838$		0			0
$839$	−15.4241	−	26.7154i	−0.532500	−	0.922318i	−0.999280	−	0.0379439i	$-0.987919\pi$
$839$	−15.4241	−	26.7154i	−0.532500	−	0.922318i	0.466780	−	0.884374i	$-0.345414\pi$
$840$		0			0
$841$	−7.90845	+	13.6978i	−0.272705	+	0.472339i
$842$		0			0
$843$	26.4632	−	1.15571i	0.911439	−	0.0398048i
$844$		0			0
$845$	−0.0551458	+	0.0955153i	−0.00189707	+	0.00328583i
$846$		0			0
$847$	11.6718	−	25.1210i	0.401048	−	0.863168i
$848$		0			0
$849$	19.9762	−	38.3750i	0.685582	−	1.31703i
$850$		0			0
$851$	−11.0026			−0.377163
$852$		0			0
$853$	−11.4171	−	19.7750i	−0.390913	−	0.677082i	0.601657	−	0.798755i	$-0.294507\pi$
$853$	−11.4171	−	19.7750i	−0.390913	−	0.677082i	−0.992570	+	0.121673i	$0.961174\pi$
$854$		0			0
$855$	−1.15934	−	1.65563i	−0.0396485	−	0.0566212i
$856$		0			0
$857$	26.6720	−	46.1973i	0.911100	−	1.57807i	0.0985862	−	0.995129i	$-0.468568\pi$
$857$	26.6720	−	46.1973i	0.911100	−	1.57807i	0.812513	−	0.582942i	$-0.198099\pi$
$858$		0			0
$859$	11.5878	+	20.0707i	0.395372	+	0.684804i	0.993149	−	0.116859i	$-0.0372825\pi$
$859$	11.5878	+	20.0707i	0.395372	+	0.684804i	−0.597777	+	0.801663i	$0.703949\pi$
$860$		0			0
$861$	12.6693	−	30.7076i	0.431769	−	1.04651i
$862$		0			0
$863$	4.58456	−	7.94069i	0.156060	−	0.270304i	−0.777384	−	0.629026i	$-0.783454\pi$
$863$	4.58456	−	7.94069i	0.156060	−	0.270304i	0.933445	+	0.358722i	$0.116787\pi$
$864$		0			0
$865$	−9.56049	−	16.5593i	−0.325067	−	0.563032i
$866$		0			0
$867$	29.7672	+	46.7240i	1.01095	+	1.58683i
$868$		0			0
$869$	1.17936	−	2.04270i	0.0400069	−	0.0692940i
$870$		0			0
$871$	−10.5393	+	18.2546i	−0.357111	+	0.618534i
$872$		0			0
$873$	3.37063	−	7.22878i	0.114079	−	0.244657i
$874$		0			0
$875$	13.3381	+	18.9927i	0.450909	+	0.642071i
$876$		0			0
$877$	−18.6190	−	32.2490i	−0.628718	−	1.08897i	−0.987809	−	0.155670i	$-0.950247\pi$
$877$	−18.6190	−	32.2490i	−0.628718	−	1.08897i	0.359091	−	0.933303i	$-0.383087\pi$
$878$		0			0
$879$	7.59578	+	11.9227i	0.256199	+	0.402142i
$880$		0			0
$881$	7.15345			0.241006			0.120503	−	0.992713i	$-0.461549\pi$
$881$	7.15345			0.241006			0.120503	+	0.992713i	$0.461549\pi$
$882$		0			0
$883$	−39.8688			−1.34169			−0.670846	−	0.741596i	$-0.734069\pi$
$883$	−39.8688			−1.34169			−0.670846	+	0.741596i	$0.734069\pi$
$884$		0			0
$885$	7.99906	−	0.349339i	0.268885	−	0.0117429i
$886$		0			0
$887$	10.6755	+	18.4904i	0.358447	+	0.620848i	0.987702	−	0.156351i	$-0.0499731\pi$
$887$	10.6755	+	18.4904i	0.358447	+	0.620848i	−0.629255	+	0.777199i	$0.716640\pi$
$888$		0			0
$889$	−13.7910	−	19.6376i	−0.462534	−	0.658624i
$890$		0			0
$891$	−4.21319	−	5.02061i	−0.141147	−	0.168197i
$892$		0			0
$893$	−2.66690	+	4.61921i	−0.0892445	+	0.154576i
$894$		0			0
$895$	−6.12111	+	10.6021i	−0.204606	+	0.354388i
$896$		0			0
$897$	−18.6454	+	35.8185i	−0.622552	+	1.19594i
$898$		0			0
$899$	30.6818	+	53.1424i	1.02329	+	1.77240i
$900$		0			0
$901$	−14.3925	+	24.9285i	−0.479483	+	0.830490i
$902$		0			0
$903$	1.94544	+	2.52803i	0.0647402	+	0.0841276i
$904$		0			0
$905$	−6.08073	−	10.5321i	−0.202130	−	0.350100i
$906$		0			0
$907$	11.3012	−	19.5742i	0.375250	−	0.649951i	−0.615115	−	0.788438i	$-0.710890\pi$
$907$	11.3012	−	19.5742i	0.375250	−	0.649951i	0.990364	+	0.138486i	$0.0442237\pi$
$908$		0			0
$909$	4.82338	−	0.422103i	0.159981	−	0.0140003i
$910$		0			0
$911$	12.7594	+	22.0999i	0.422738	+	0.732203i	0.996206	−	0.0870243i	$-0.0277358\pi$
$911$	12.7594	+	22.0999i	0.422738	+	0.732203i	−0.573468	+	0.819228i	$0.694402\pi$
$912$		0			0
$913$	−0.901215			−0.0298259
$914$		0			0
$915$	−8.24954	+	0.360278i	−0.272722	+	0.0119104i
$916$		0			0
$917$	−14.5876	+	31.3965i	−0.481723	+	1.03681i
$918$		0			0
$919$	5.71326	−	9.89566i	0.188463	−	0.326428i	−0.756275	−	0.654254i	$-0.772983\pi$
$919$	5.71326	−	9.89566i	0.188463	−	0.326428i	0.944738	+	0.327826i	$0.106316\pi$
$920$		0			0
$921$	14.4509	−	27.7607i	0.476173	−	0.914745i
$922$		0			0
$923$	0.551208	−	0.954721i	0.0181432	−	0.0314250i
$924$		0			0
$925$	−3.47207	−	6.01381i	−0.114161	−	0.197733i
$926$		0			0
$927$	−13.7430	+	29.4738i	−0.451380	+	0.968047i
$928$		0			0
$929$	13.5970			0.446104			0.223052	−	0.974807i	$-0.428398\pi$
$929$	13.5970			0.446104			0.223052	+	0.974807i	$0.428398\pi$
$930$		0			0
$931$	−3.14244	−	3.72402i	−0.102989	−	0.122050i
$932$		0			0
$933$	−8.00369	+	15.3754i	−0.262029	+	0.503367i
$934$		0			0
$935$	2.46656	+	4.27221i	0.0806652	+	0.139716i
$936$		0			0
$937$	−11.1455			−0.364109			−0.182054	−	0.983288i	$-0.558275\pi$
$937$	−11.1455			−0.364109			−0.182054	+	0.983288i	$0.558275\pi$
$938$		0			0
$939$	2.39178	−	4.59470i	0.0780529	−	0.149942i
$940$		0			0
$941$	41.4621			1.35163			0.675813	−	0.737073i	$-0.263793\pi$
$941$	41.4621			1.35163			0.675813	+	0.737073i	$0.263793\pi$
$942$		0			0
$943$	46.6680			1.51972
$944$		0			0
$945$	3.98313	−	12.6957i	0.129571	−	0.412990i
$946$		0			0
$947$	42.5567			1.38291			0.691454	−	0.722421i	$-0.256971\pi$
$947$	42.5567			1.38291			0.691454	+	0.722421i	$0.256971\pi$
$948$		0			0
$949$	38.6669			1.25518
$950$		0			0
$951$	−19.0735	+	36.6410i	−0.618502	+	1.18816i
$952$		0			0
$953$	21.2114			0.687106			0.343553	−	0.939133i	$-0.388370\pi$
$953$	21.2114			0.687106			0.343553	+	0.939133i	$0.388370\pi$
$954$		0			0
$955$	3.58413	+	6.20790i	0.115980	+	0.200883i
$956$		0			0
$957$	−3.89901	+	7.49014i	−0.126037	+	0.242122i
$958$		0			0
$959$	−52.9087	+	4.70275i	−1.70851	+	0.151860i
$960$		0			0
$961$	53.0193			1.71030
$962$		0			0
$963$	−29.7441	+	2.60296i	−0.958490	+	0.0838793i
$964$		0			0
$965$	0.787775	+	1.36447i	0.0253594	+	0.0439237i
$966$		0			0
$967$	−9.83257	+	17.0305i	−0.316194	+	0.547664i	−0.979691	−	0.200515i	$-0.935738\pi$
$967$	−9.83257	+	17.0305i	−0.316194	+	0.547664i	0.663496	+	0.748179i	$0.269072\pi$
$968$		0			0
$969$	−3.89639	+	7.48511i	−0.125170	+	0.240456i
$970$		0			0
$971$	−12.2892	+	21.2855i	−0.394379	+	0.683084i	−0.993022	−	0.117932i	$-0.962374\pi$
$971$	−12.2892	+	21.2855i	−0.394379	+	0.683084i	0.598643	+	0.801016i	$0.295707\pi$
$972$		0			0
$973$	−1.78062	+	0.158269i	−0.0570841	+	0.00507387i
$974$		0			0
$975$	−25.4617	+	1.11198i	−0.815427	+	0.0356117i
$976$		0			0
$977$	−47.4718			−1.51876			−0.759378	−	0.650650i	$-0.774497\pi$
$977$	−47.4718			−1.51876			−0.759378	+	0.650650i	$0.774497\pi$
$978$		0			0
$979$	−4.21420	−	7.29920i	−0.134686	−	0.233284i
$980$		0			0
$981$	−23.5260	+	50.4548i	−0.751129	+	1.61090i
$982$		0			0
$983$	−13.7720	+	23.8538i	−0.439258	+	0.760817i	−0.997632	−	0.0687719i	$-0.978092\pi$
$983$	−13.7720	+	23.8538i	−0.439258	+	0.760817i	0.558374	+	0.829589i	$0.311425\pi$
$984$		0			0
$985$	4.00269	+	6.93287i	0.127536	+	0.220900i
$986$		0			0
$987$	−34.8067	+	4.63184i	−1.10791	+	0.147433i
$988$		0			0
$989$	−2.24073	+	3.88107i	−0.0712512	+	0.123411i
$990$		0			0
$991$	19.2335	+	33.3135i	0.610973	+	1.05824i	0.991077	+	0.133293i	$0.0425551\pi$
$991$	19.2335	+	33.3135i	0.610973	+	1.05824i	−0.380103	+	0.924944i	$0.624112\pi$
$992$		0			0
$993$	−12.8262	+	24.6397i	−0.407029	+	0.781917i
$994$		0			0
$995$	5.17233	−	8.95874i	0.163974	−	0.284011i
$996$		0			0
$997$	16.2272	−	28.1064i	0.513921	−	0.890138i	−0.485948	−	0.873988i	$-0.661526\pi$
$997$	16.2272	−	28.1064i	0.513921	−	0.890138i	0.999870	−	0.0161503i	$-0.00514103\pi$
$998$		0			0
$999$	−3.39806	+	8.20444i	−0.107510	+	0.259577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.i.b.121.5	yes	14
3.2	odd	2		756.2.i.b.37.5		14
4.3	odd	2		1008.2.q.j.625.3		14
7.2	even	3		1764.2.j.g.589.6		14
7.3	odd	6		1764.2.l.i.949.7		14
7.4	even	3		252.2.l.b.193.1	yes	14
7.5	odd	6		1764.2.j.h.589.2		14
7.6	odd	2		1764.2.i.i.373.3		14
9.2	odd	6		756.2.l.b.289.3		14
9.4	even	3		2268.2.k.e.1297.3		14
9.5	odd	6		2268.2.k.f.1297.5		14
9.7	even	3		252.2.l.b.205.1	yes	14
12.11	even	2		3024.2.q.j.2305.5		14
21.2	odd	6		5292.2.j.h.1765.5		14
21.5	even	6		5292.2.j.g.1765.3		14
21.11	odd	6		756.2.l.b.361.3		14
21.17	even	6		5292.2.l.i.361.5		14
21.20	even	2		5292.2.i.i.1549.3		14
28.11	odd	6		1008.2.t.j.193.7		14
36.7	odd	6		1008.2.t.j.961.7		14
36.11	even	6		3024.2.t.j.289.3		14
63.2	odd	6		5292.2.j.h.3529.5		14
63.4	even	3		2268.2.k.e.1621.3		14
63.11	odd	6		756.2.i.b.613.5		14
63.16	even	3		1764.2.j.g.1177.6		14
63.20	even	6		5292.2.l.i.3313.5		14
63.25	even	3	inner	252.2.i.b.25.5	✓	14
63.32	odd	6		2268.2.k.f.1621.5		14
63.34	odd	6		1764.2.l.i.961.7		14
63.38	even	6		5292.2.i.i.2125.3		14
63.47	even	6		5292.2.j.g.3529.3		14
63.52	odd	6		1764.2.i.i.1537.3		14
63.61	odd	6		1764.2.j.h.1177.2		14
84.11	even	6		3024.2.t.j.1873.3		14
252.11	even	6		3024.2.q.j.2881.5		14
252.151	odd	6		1008.2.q.j.529.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.5	✓	14	63.25	even	3	inner
252.2.i.b.121.5	yes	14	1.1	even	1	trivial
252.2.l.b.193.1	yes	14	7.4	even	3
252.2.l.b.205.1	yes	14	9.7	even	3
756.2.i.b.37.5		14	3.2	odd	2
756.2.i.b.613.5		14	63.11	odd	6
756.2.l.b.289.3		14	9.2	odd	6
756.2.l.b.361.3		14	21.11	odd	6
1008.2.q.j.529.3		14	252.151	odd	6
1008.2.q.j.625.3		14	4.3	odd	2
1008.2.t.j.193.7		14	28.11	odd	6
1008.2.t.j.961.7		14	36.7	odd	6
1764.2.i.i.373.3		14	7.6	odd	2
1764.2.i.i.1537.3		14	63.52	odd	6
1764.2.j.g.589.6		14	7.2	even	3
1764.2.j.g.1177.6		14	63.16	even	3
1764.2.j.h.589.2		14	7.5	odd	6
1764.2.j.h.1177.2		14	63.61	odd	6
1764.2.l.i.949.7		14	7.3	odd	6
1764.2.l.i.961.7		14	63.34	odd	6
2268.2.k.e.1297.3		14	9.4	even	3
2268.2.k.e.1621.3		14	63.4	even	3
2268.2.k.f.1297.5		14	9.5	odd	6
2268.2.k.f.1621.5		14	63.32	odd	6
3024.2.q.j.2305.5		14	12.11	even	2
3024.2.q.j.2881.5		14	252.11	even	6
3024.2.t.j.289.3		14	36.11	even	6
3024.2.t.j.1873.3		14	84.11	even	6
5292.2.i.i.1549.3		14	21.20	even	2
5292.2.i.i.2125.3		14	63.38	even	6
5292.2.j.g.1765.3		14	21.5	even	6
5292.2.j.g.3529.3		14	63.47	even	6
5292.2.j.h.1765.5		14	21.2	odd	6
5292.2.j.h.3529.5		14	63.2	odd	6
5292.2.l.i.361.5		14	21.17	even	6
5292.2.l.i.3313.5		14	63.20	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.799754 - 1.53636i) q^{3} +(-0.483929 - 0.838189i) q^{5} +(-1.52054 - 2.16517i) q^{7} +(-1.72079 - 2.45742i) q^{9} +O(q^{10})\)	\(q+(0.799754 - 1.53636i) q^{3} +(-0.483929 - 0.838189i) q^{5} +(-1.52054 - 2.16517i) q^{7} +(-1.72079 - 2.45742i) q^{9} +(-0.364122 + 0.630678i) q^{11} +(1.81066 - 3.13615i) q^{13} +(-1.67478 + 0.0731419i) q^{15} +(3.49948 + 6.06128i) q^{17} +(-0.348050 + 0.602841i) q^{19} +(-4.54253 + 0.604489i) q^{21} +(-3.21898 - 5.57544i) q^{23} +(2.03163 - 3.51888i) q^{25} +(-5.15168 + 0.678412i) q^{27} +(3.34727 + 5.79764i) q^{29} +9.16620 q^{31} +(0.677738 + 1.06381i) q^{33} +(-1.07899 + 2.32229i) q^{35} +(0.854506 - 1.48005i) q^{37} +(-3.37017 - 5.28997i) q^{39} +(-3.62444 + 6.27771i) q^{41} +(-0.348050 - 0.602841i) q^{43} +(-1.22704 + 2.63156i) q^{45} +7.66240 q^{47} +(-2.37591 + 6.58445i) q^{49} +(12.1110 - 0.528918i) q^{51} +(2.05637 + 3.56174i) q^{53} +0.704836 q^{55} +(0.647824 + 1.01685i) q^{57} -4.77618 q^{59} +4.92574 q^{61} +(-2.70420 + 7.46239i) q^{63} -3.50492 q^{65} -5.82070 q^{67} +(-11.1403 + 0.486523i) q^{69} +0.304424 q^{71} +(5.33879 + 9.24705i) q^{73} +(-3.78145 - 5.93554i) q^{75} +(1.91919 - 0.170585i) q^{77} -3.23890 q^{79} +(-3.07779 + 8.45738i) q^{81} +(0.618759 + 1.07172i) q^{83} +(3.38700 - 5.86646i) q^{85} +(11.5842 - 0.505913i) q^{87} +(-5.78679 + 10.0230i) q^{89} +(-9.54349 + 0.848265i) q^{91} +(7.33071 - 14.0826i) q^{93} +0.673726 q^{95} +(1.32933 + 2.30247i) q^{97} +(2.17641 - 0.190462i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9	\( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) \) 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 11 * q^21 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 4 * q^33 - 19 * q^35 + 10 * q^37 - 2 * q^39 - 33 * q^41 + 7 * q^43 - 10 * q^45 + 6 * q^47 - 4 * q^49 - 13 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 + 28 * q^59 + 20 * q^61 + 33 * q^63 - 30 * q^65 - 12 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 - 44 * q^75 - 47 * q^77 + 20 * q^79 - 29 * q^81 - 25 * q^83 + 8 * q^85 + 28 * q^87 - 6 * q^89 + 2 * q^91 + 22 * q^93 + 56 * q^95 - 18 * q^97 + 7 * q^99

Introduction

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