LMFDB - Embedded newform 1274.2.m.c.491.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(491,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1274.491"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,2,6,0,-6,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.1
Root			$0.500000 - 1.73154i$ of defining polynomial
Character	$\chi$	$=$	1274.491
Dual form			1274.2.m.c.589.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.432757 - 0.749558i) q^{3} +(0.500000 - 0.866025i) q^{4} -3.71131i q^{5} +(0.749558 + 0.432757i) q^{6} +1.00000i q^{8} +(1.12544 - 1.94932i) q^{9} +(1.85566 + 3.21409i) q^{10} +(-5.00118 + 2.88743i) q^{11} -0.865515 q^{12} +(-2.87757 - 2.17246i) q^{13} +(-2.78184 + 1.60610i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.106098 - 0.183768i) q^{17} +2.25088i q^{18} +(-1.85081 - 1.06857i) q^{19} +(-3.21409 - 1.85566i) q^{20} +(2.88743 - 5.00118i) q^{22} +(1.23970 + 2.14722i) q^{23} +(0.749558 - 0.432757i) q^{24} -8.77384 q^{25} +(3.57828 + 0.442616i) q^{26} -4.54472 q^{27} +(0.0492830 + 0.0853606i) q^{29} +(1.60610 - 2.78184i) q^{30} +2.31076i q^{31} +(0.866025 + 0.500000i) q^{32} +(4.32860 + 2.49912i) q^{33} +0.212197i q^{34} +(-1.12544 - 1.94932i) q^{36} +(6.81859 - 3.93672i) q^{37} +2.13714 q^{38} +(-0.383091 + 3.09706i) q^{39} +3.71131 q^{40} +(-6.51354 + 3.76060i) q^{41} +(2.28987 - 3.96617i) q^{43} +5.77486i q^{44} +(-7.23455 - 4.17687i) q^{45} +(-2.14722 - 1.23970i) q^{46} +9.15570i q^{47} +(-0.432757 + 0.749558i) q^{48} +(7.59837 - 4.38692i) q^{50} -0.183660 q^{51} +(-3.32019 + 1.40582i) q^{52} +12.0948 q^{53} +(3.93584 - 2.27236i) q^{54} +(10.7162 + 18.5609i) q^{55} +1.84972i q^{57} +(-0.0853606 - 0.0492830i) q^{58} +(0.200843 + 0.115957i) q^{59} +3.21220i q^{60} +(4.01605 - 6.95601i) q^{61} +(-1.15538 - 2.00118i) q^{62} -1.00000 q^{64} +(-8.06267 + 10.6796i) q^{65} -4.99823 q^{66} +(-11.2323 + 6.48500i) q^{67} +(-0.106098 - 0.183768i) q^{68} +(1.07298 - 1.85845i) q^{69} +(6.37721 + 3.68188i) q^{71} +(1.94932 + 1.12544i) q^{72} +5.60414i q^{73} +(-3.93672 + 6.81859i) q^{74} +(3.79695 + 6.57650i) q^{75} +(-1.85081 + 1.06857i) q^{76} +(-1.21676 - 2.87367i) q^{78} -9.19749 q^{79} +(-3.21409 + 1.85566i) q^{80} +(-1.40956 - 2.44144i) q^{81} +(3.76060 - 6.51354i) q^{82} +3.17186i q^{83} +(-0.682021 - 0.393765i) q^{85} +4.57973i q^{86} +(0.0426552 - 0.0738809i) q^{87} +(-2.88743 - 5.00118i) q^{88} +(10.2335 - 5.90833i) q^{89} +8.35373 q^{90} +2.47940 q^{92} +(1.73205 - 1.00000i) q^{93} +(-4.57785 - 7.92907i) q^{94} +(-3.96579 + 6.86895i) q^{95} -0.865515i q^{96} +(-12.1952 - 7.04093i) q^{97} +12.9985i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} + 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} - 18 q^{11} + 4 q^{12} + 8 q^{13} - 6 q^{15} - 6 q^{16} - 4 q^{17} - 12 q^{19} - 2 q^{22} - 6 q^{23} - 6 q^{24} - 24 q^{25} + 14 q^{26} - 40 q^{27}+ \cdots - 60 q^{97}+O(q^{100}) $ 12 * q + 2 * q^3 + 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 - 18 * q^11 + 4 * q^12 + 8 * q^13 - 6 * q^15 - 6 * q^16 - 4 * q^17 - 12 * q^19 - 2 * q^22 - 6 * q^23 - 6 * q^24 - 24 * q^25 + 14 * q^26 - 40 * q^27 - 10 * q^29 + 14 * q^30 - 12 * q^33 + 6 * q^36 - 6 * q^37 - 8 * q^38 - 54 * q^39 + 4 * q^40 + 24 * q^41 + 26 * q^43 - 72 * q^45 - 6 * q^46 + 2 * q^48 - 12 * q^50 - 36 * q^51 + 4 * q^52 + 36 * q^53 + 36 * q^54 + 6 * q^55 + 24 * q^58 - 6 * q^59 + 28 * q^61 + 2 * q^62 - 12 * q^64 - 34 * q^65 - 42 * q^67 + 4 * q^68 - 32 * q^69 + 48 * q^71 + 48 * q^75 - 12 * q^76 - 8 * q^78 + 44 * q^79 - 34 * q^81 - 6 * q^82 + 54 * q^85 - 2 * q^87 + 2 * q^88 - 12 * q^89 - 12 * q^90 - 12 * q^92 - 8 * q^94 + 32 * q^95 - 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.432757	−	0.749558i	−0.249853	−	0.432757i	0.713632	−	0.700521i	$-0.247049\pi$
$3$	−0.432757	−	0.749558i	−0.249853	−	0.432757i	−0.963485	+	0.267763i	$0.913716\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	3.71131i		−	1.65975i	−0.557950	−	0.829875i	$-0.688412\pi$
$5$		−	3.71131i		−	1.65975i	0.557950	−	0.829875i	$-0.311588\pi$
$6$	0.749558	+	0.432757i	0.306006	+	0.176673i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	1.12544	−	1.94932i	0.375147	−	0.649774i
$10$	1.85566	+	3.21409i	0.586810	+	1.01638i
$11$	−5.00118	+	2.88743i	−1.50791	+	0.870594i	−0.507955	+	0.861384i	$0.669598\pi$
$11$	−5.00118	+	2.88743i	−1.50791	+	0.870594i	−0.999958	+	0.00920984i	$0.997068\pi$
$12$	−0.865515			−0.249853
$13$	−2.87757	−	2.17246i	−0.798095	−	0.602531i
$13$	−2.87757	−	2.17246i	−0.798095	−	0.602531i
$14$		0			0
$15$	−2.78184	+	1.60610i	−0.718269	+	0.414693i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.106098	−	0.183768i	0.0257327	−	0.0445703i	−0.852872	−	0.522120i	$-0.825141\pi$
$17$	0.106098	−	0.183768i	0.0257327	−	0.0445703i	0.878605	+	0.477549i	$0.158475\pi$
$18$			2.25088i			0.530538i
$19$	−1.85081	−	1.06857i	−0.424606	−	0.245146i	0.272440	−	0.962173i	$-0.412169\pi$
$19$	−1.85081	−	1.06857i	−0.424606	−	0.245146i	−0.697046	+	0.717026i	$0.745503\pi$
$20$	−3.21409	−	1.85566i	−0.718693	−	0.414937i
$21$		0			0
$22$	2.88743	−	5.00118i	0.615603	−	1.06626i
$23$	1.23970	+	2.14722i	0.258495	+	0.447727i	0.965839	−	0.259143i	$-0.0834400\pi$
$23$	1.23970	+	2.14722i	0.258495	+	0.447727i	−0.707344	+	0.706870i	$0.750107\pi$
$24$	0.749558	−	0.432757i	0.153003	−	0.0883363i
$25$	−8.77384			−1.75477
$26$	3.57828	+	0.442616i	0.701759	+	0.0868041i
$27$	−4.54472			−0.874632
$28$		0			0
$29$	0.0492830	+	0.0853606i	0.00915162	+	0.0158511i	0.870565	−	0.492054i	$-0.163754\pi$
$29$	0.0492830	+	0.0853606i	0.00915162	+	0.0158511i	−0.861413	+	0.507905i	$0.830420\pi$
$30$	1.60610	−	2.78184i	0.293232	−	0.507893i
$31$			2.31076i			0.415025i	0.978232	+	0.207513i	$0.0665368\pi$
$31$			2.31076i			0.415025i	−0.978232	+	0.207513i	$0.933463\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	4.32860	+	2.49912i	0.753512	+	0.435040i
$34$			0.212197i			0.0363915i
$35$		0			0
$36$	−1.12544	−	1.94932i	−0.187574	−	0.324887i
$37$	6.81859	−	3.93672i	1.12097	−	0.647192i	0.179321	−	0.983791i	$-0.442610\pi$
$37$	6.81859	−	3.93672i	1.12097	−	0.647192i	0.941648	+	0.336599i	$0.109277\pi$
$38$	2.13714			0.346689
$39$	−0.383091	+	3.09706i	−0.0613436	+	0.495926i
$40$	3.71131			0.586810
$41$	−6.51354	+	3.76060i	−1.01724	+	0.587306i	−0.913305	−	0.407277i	$-0.866478\pi$
$41$	−6.51354	+	3.76060i	−1.01724	+	0.587306i	−0.103940	+	0.994584i	$0.533145\pi$
$42$		0			0
$43$	2.28987	−	3.96617i	0.349201	−	0.604835i	−0.636906	−	0.770941i	$-0.719786\pi$
$43$	2.28987	−	3.96617i	0.349201	−	0.604835i	0.986108	+	0.166107i	$0.0531196\pi$
$44$			5.77486i			0.870594i
$45$	−7.23455	−	4.17687i	−1.07846	−	0.622651i
$46$	−2.14722	−	1.23970i	−0.316591	−	0.182784i
$47$			9.15570i			1.33550i	0.744388	+	0.667748i	$0.232742\pi$
$47$			9.15570i			1.33550i	−0.744388	+	0.667748i	$0.767258\pi$
$48$	−0.432757	+	0.749558i	−0.0624632	+	0.108189i
$49$		0			0
$50$	7.59837	−	4.38692i	1.07457	−	0.620404i
$51$	−0.183660			−0.0257175
$52$	−3.32019	+	1.40582i	−0.460427	+	0.194953i
$53$	12.0948			1.66135			0.830674	−	0.556759i	$-0.187955\pi$
$53$	12.0948			1.66135			0.830674	+	0.556759i	$0.187955\pi$
$54$	3.93584	−	2.27236i	0.535600	−	0.309229i
$55$	10.7162	+	18.5609i	1.44497	+	2.50276i
$56$		0			0
$57$			1.84972i			0.245002i
$58$	−0.0853606	−	0.0492830i	−0.0112084	−	0.00647117i
$59$	0.200843	+	0.115957i	0.0261476	+	0.0150963i	0.513017	−	0.858379i	$-0.328528\pi$
$59$	0.200843	+	0.115957i	0.0261476	+	0.0150963i	−0.486869	+	0.873475i	$0.661861\pi$
$60$			3.21220i			0.414693i
$61$	4.01605	−	6.95601i	0.514203	−	0.890626i	−0.485661	−	0.874147i	$-0.661421\pi$
$61$	4.01605	−	6.95601i	0.514203	−	0.890626i	0.999864	−	0.0164787i	$-0.00524558\pi$
$62$	−1.15538	−	2.00118i	−0.146734	−	0.254150i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−8.06267	+	10.6796i	−1.00005	+	1.32464i
$66$	−4.99823			−0.615240
$67$	−11.2323	+	6.48500i	−1.37225	+	0.792269i	−0.991211	−	0.132291i	$-0.957767\pi$
$67$	−11.2323	+	6.48500i	−1.37225	+	0.792269i	−0.381039	+	0.924559i	$0.624433\pi$
$68$	−0.106098	−	0.183768i	−0.0128663	−	0.0222851i
$69$	1.07298	−	1.85845i	0.129171	−	0.223731i
$70$		0			0
$71$	6.37721	+	3.68188i	0.756836	+	0.436959i	0.828158	−	0.560494i	$-0.189389\pi$
$71$	6.37721	+	3.68188i	0.756836	+	0.436959i	−0.0713229	+	0.997453i	$0.522722\pi$
$72$	1.94932	+	1.12544i	0.229730	+	0.132635i
$73$			5.60414i			0.655915i	0.944692	+	0.327958i	$0.106360\pi$
$73$			5.60414i			0.655915i	−0.944692	+	0.327958i	$0.893640\pi$
$74$	−3.93672	+	6.81859i	−0.457634	+	0.792645i
$75$	3.79695	+	6.57650i	0.438434	+	0.759389i
$76$	−1.85081	+	1.06857i	−0.212303	+	0.122573i
$77$		0			0
$78$	−1.21676	−	2.87367i	−0.137771	−	0.325380i
$79$	−9.19749			−1.03480			−0.517399	−	0.855744i	$-0.673100\pi$
$79$	−9.19749			−1.03480			−0.517399	+	0.855744i	$0.673100\pi$
$80$	−3.21409	+	1.85566i	−0.359346	+	0.207469i
$81$	−1.40956	−	2.44144i	−0.156618	−	0.271271i
$82$	3.76060	−	6.51354i	0.415288	−	0.719301i
$83$			3.17186i			0.348157i	0.984732	+	0.174078i	$0.0556946\pi$
$83$			3.17186i			0.348157i	−0.984732	+	0.174078i	$0.944305\pi$
$84$		0			0
$85$	−0.682021	−	0.393765i	−0.0739755	−	0.0427098i
$86$			4.57973i			0.493845i
$87$	0.0426552	−	0.0738809i	0.00457311	−	0.00792087i
$88$	−2.88743	−	5.00118i	−0.307801	−	0.533128i
$89$	10.2335	−	5.90833i	1.08475	−	0.626282i	0.152577	−	0.988292i	$-0.451243\pi$
$89$	10.2335	−	5.90833i	1.08475	−	0.626282i	0.932174	+	0.362010i	$0.117909\pi$
$90$	8.35373			0.880561
$91$		0			0
$92$	2.47940			0.258495
$93$	1.73205	−	1.00000i	0.179605	−	0.103695i
$94$	−4.57785	−	7.92907i	−0.472169	−	0.817821i
$95$	−3.96579	+	6.86895i	−0.406882	+	0.704740i
$96$		−	0.865515i		−	0.0883363i
$97$	−12.1952	−	7.04093i	−1.23824	−	0.714898i	−0.269506	−	0.962999i	$-0.586860\pi$
$97$	−12.1952	−	7.04093i	−1.23824	−	0.714898i	−0.968734	+	0.248101i	$0.920194\pi$
$98$		0			0
$99$			12.9985i			1.30640i
$100$	−4.38692	+	7.59837i	−0.438692	+	0.759837i
$101$	3.07622	+	5.32816i	0.306095	+	0.530172i	0.977505	−	0.210914i	$-0.0676441\pi$
$101$	3.07622	+	5.32816i	0.306095	+	0.530172i	−0.671410	+	0.741087i	$0.734311\pi$
$102$	0.159054	−	0.0918298i	0.0157487	−	0.00909251i
$103$	−19.3491			−1.90652			−0.953260	−	0.302152i	$-0.902295\pi$
$103$	−19.3491			−1.90652			−0.953260	+	0.302152i	$0.902295\pi$
$104$	2.17246	−	2.87757i	0.213027	−	0.282169i
$105$		0			0
$106$	−10.4744	+	6.04740i	−1.01736	+	0.587375i
$107$	−5.82506	−	10.0893i	−0.563130	−	0.975369i	−0.997221	−	0.0745005i	$-0.976264\pi$
$107$	−5.82506	−	10.0893i	−0.563130	−	0.975369i	0.434091	−	0.900869i	$-0.357070\pi$
$108$	−2.27236	+	3.93584i	−0.218658	+	0.378727i
$109$			5.73307i			0.549129i	0.961569	+	0.274564i	$0.0885336\pi$
$109$			5.73307i			0.549129i	−0.961569	+	0.274564i	$0.911466\pi$
$110$	−18.5609	−	10.7162i	−1.76972	−	1.02175i
$111$	−5.90159	−	3.40729i	−0.560154	−	0.323405i
$112$		0			0
$113$	−8.25971	+	14.3062i	−0.777008	+	1.34582i	0.156650	+	0.987654i	$0.449930\pi$
$113$	−8.25971	+	14.3062i	−0.777008	+	1.34582i	−0.933659	+	0.358164i	$0.883403\pi$
$114$	−0.924862	−	1.60191i	−0.0866213	−	0.150032i
$115$	7.96901	−	4.60091i	0.743114	−	0.429037i
$116$	0.0985660			0.00915162
$117$	−7.47336	+	3.16435i	−0.690913	+	0.292544i
$118$	−0.231914			−0.0213494
$119$		0			0
$120$	−1.60610	−	2.78184i	−0.146616	−	0.253946i
$121$	11.1745	−	19.3549i	1.01587	−	1.75953i
$122$			8.03211i			0.727193i
$123$	5.63757	+	3.25485i	0.508323	+	0.293480i
$124$	2.00118	+	1.15538i	0.179711	+	0.103756i
$125$			14.0059i			1.25273i
$126$		0			0
$127$	−5.89420	−	10.2090i	−0.523025	−	0.905907i	−0.999641	−	0.0267947i	$-0.991470\pi$
$127$	−5.89420	−	10.2090i	−0.523025	−	0.905907i	0.476616	−	0.879112i	$-0.341863\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−3.96383			−0.348996
$130$	1.64269	−	13.2801i	0.144073	−	1.16474i
$131$	5.12859			0.448087			0.224043	−	0.974579i	$-0.428074\pi$
$131$	5.12859			0.448087			0.224043	+	0.974579i	$0.428074\pi$
$132$	4.32860	−	2.49912i	0.376756	−	0.217520i
$133$		0			0
$134$	6.48500	−	11.2323i	0.560219	−	0.970327i
$135$			16.8669i			1.45167i
$136$	0.183768	+	0.106098i	0.0157580	+	0.00909787i
$137$	−8.13482	−	4.69664i	−0.695005	−	0.401261i	0.110479	−	0.993878i	$-0.464761\pi$
$137$	−8.13482	−	4.69664i	−0.695005	−	0.401261i	−0.805484	+	0.592617i	$0.798095\pi$
$138$			2.14596i			0.182676i
$139$	7.57063	−	13.1127i	0.642133	−	1.11221i	−0.342823	−	0.939400i	$-0.611383\pi$
$139$	7.57063	−	13.1127i	0.642133	−	1.11221i	0.984956	−	0.172806i	$-0.0552835\pi$
$140$		0			0
$141$	6.86273	−	3.96220i	0.577946	−	0.333677i
$142$	−7.36377			−0.617954
$143$	20.6641	+	2.55605i	1.72802	+	0.213747i
$144$	−2.25088			−0.187574
$145$	0.316800	−	0.182905i	0.0263088	−	0.0151894i
$146$	−2.80207	−	4.85333i	−0.231901	−	0.401664i
$147$		0			0
$148$		−	7.87343i		−	0.647192i
$149$	−17.8425	−	10.3013i	−1.46171	−	0.843919i	−0.462620	−	0.886557i	$-0.653091\pi$
$149$	−17.8425	−	10.3013i	−1.46171	−	0.843919i	−0.999091	+	0.0426374i	$0.986424\pi$
$150$	−6.57650	−	3.79695i	−0.536969	−	0.310019i
$151$		−	11.9407i		−	0.971721i	−0.874036	−	0.485861i	$-0.838506\pi$
$151$		−	11.9407i		−	0.971721i	0.874036	−	0.485861i	$-0.161494\pi$
$152$	1.06857	−	1.85081i	0.0866723	−	0.150121i
$153$	−0.238815	−	0.413640i	−0.0193071	−	0.0334408i
$154$		0			0
$155$	8.57596			0.688838
$156$	2.49058	+	1.88029i	0.199406	+	0.150544i
$157$	−9.34022			−0.745431			−0.372715	−	0.927946i	$-0.621573\pi$
$157$	−9.34022			−0.745431			−0.372715	+	0.927946i	$0.621573\pi$
$158$	7.96526	−	4.59875i	0.633682	−	0.365857i
$159$	−5.23411	−	9.06575i	−0.415092	−	0.718961i
$160$	1.85566	−	3.21409i	0.146703	−	0.254096i
$161$		0			0
$162$	2.44144	+	1.40956i	0.191817	+	0.110746i
$163$	3.87746	+	2.23865i	0.303706	+	0.175345i	0.644106	−	0.764936i	$-0.277229\pi$
$163$	3.87746	+	2.23865i	0.303706	+	0.175345i	−0.340401	+	0.940280i	$0.610563\pi$
$164$			7.52119i			0.587306i
$165$	9.27500	−	16.0648i	0.722058	−	1.25064i
$166$	−1.58593	−	2.74691i	−0.123092	−	0.213202i
$167$	−12.7365	+	7.35342i	−0.985579	+	0.569025i	−0.903950	−	0.427638i	$-0.859346\pi$
$167$	−12.7365	+	7.35342i	−0.985579	+	0.569025i	−0.0816295	+	0.996663i	$0.526012\pi$
$168$		0			0
$169$	3.56086	+	12.5028i	0.273912	+	0.961755i
$170$	0.787529			0.0604008
$171$	−4.16597	+	2.40522i	−0.318580	+	0.183932i
$172$	−2.28987	−	3.96617i	−0.174601	−	0.302417i
$173$	−6.88286	+	11.9215i	−0.523294	+	0.906372i	0.476339	+	0.879262i	$0.341964\pi$
$173$	−6.88286	+	11.9215i	−0.523294	+	0.906372i	−0.999632	+	0.0271097i	$0.991370\pi$
$174$			0.0853103i			0.00646736i
$175$		0			0
$176$	5.00118	+	2.88743i	0.376978	+	0.217648i
$177$		−	0.200725i		−	0.0150874i
$178$	−5.90833	+	10.2335i	−0.442848	+	0.767035i
$179$	7.63936	+	13.2318i	0.570992	+	0.988988i	0.996464	+	0.0840164i	$0.0267748\pi$
$179$	7.63936	+	13.2318i	0.570992	+	0.988988i	−0.425472	+	0.904972i	$0.639892\pi$
$180$	−7.23455	+	4.17687i	−0.539231	+	0.311325i
$181$	1.66748			0.123943			0.0619713	−	0.998078i	$-0.480261\pi$
$181$	1.66748			0.123943			0.0619713	+	0.998078i	$0.480261\pi$
$182$		0			0
$183$	−6.95191			−0.513900
$184$	−2.14722	+	1.23970i	−0.158295	+	0.0913919i
$185$	−14.6104	−	25.3059i	−1.07418	−	1.86053i
$186$	−1.00000	+	1.73205i	−0.0733236	+	0.127000i
$187$			1.22541i			0.0896108i
$188$	7.92907	+	4.57785i	0.578287	+	0.333874i
$189$		0			0
$190$		−	7.93158i		−	0.575418i
$191$	−0.0604880	+	0.104768i	−0.00437676	+	0.00758076i	−0.868205	−	0.496205i	$-0.834727\pi$
$191$	−0.0604880	+	0.104768i	−0.00437676	+	0.00758076i	0.863829	+	0.503786i	$0.168060\pi$
$192$	0.432757	+	0.749558i	0.0312316	+	0.0540947i
$193$	−2.38633	+	1.37775i	−0.171772	+	0.0991725i	−0.583421	−	0.812170i	$-0.698286\pi$
$193$	−2.38633	+	1.37775i	−0.171772	+	0.0991725i	0.411649	+	0.911342i	$0.364953\pi$
$194$	14.0819			1.01102
$195$	11.4941	+	1.42177i	0.823113	+	0.101815i
$196$		0			0
$197$	−13.0989	+	7.56267i	−0.933260	+	0.538818i	−0.887841	−	0.460150i	$-0.847796\pi$
$197$	−13.0989	+	7.56267i	−0.933260	+	0.538818i	−0.0454187	+	0.998968i	$0.514462\pi$
$198$	−6.49927	−	11.2571i	−0.461883	−	0.800005i
$199$	−2.65320	+	4.59548i	−0.188080	+	0.325765i	−0.944610	−	0.328194i	$-0.893560\pi$
$199$	−2.65320	+	4.59548i	−0.188080	+	0.325765i	0.756530	+	0.653959i	$0.226893\pi$
$200$		−	8.77384i		−	0.620404i
$201$	9.72176	+	5.61286i	0.685720	+	0.395901i
$202$	−5.32816	−	3.07622i	−0.374888	−	0.216442i
$203$		0			0
$204$	−0.0918298	+	0.159054i	−0.00642937	+	0.0111360i
$205$	13.9567	+	24.1738i	0.974782	+	1.68837i
$206$	16.7568	−	9.67453i	1.16750	−	0.674056i
$207$	5.58084			0.387895
$208$	−0.442616	+	3.57828i	−0.0306899	+	0.248109i
$209$	12.3417			0.853691
$210$		0			0
$211$	−8.94910	−	15.5003i	−0.616081	−	1.06708i	−0.990194	−	0.139701i	$-0.955386\pi$
$211$	−8.94910	−	15.5003i	−0.616081	−	1.06708i	0.374112	−	0.927383i	$-0.377947\pi$
$212$	6.04740	−	10.4744i	0.415337	−	0.719385i
$213$		−	6.37345i		−	0.436702i
$214$	10.0893	+	5.82506i	0.689690	+	0.398193i
$215$	−14.7197	−	8.49841i	−1.00387	−	0.579587i
$216$		−	4.54472i		−	0.309229i
$217$		0			0
$218$	−2.86654	−	4.96499i	−0.194146	−	0.336271i
$219$	4.20063	−	2.42524i	0.283852	−	0.163882i
$220$	21.4323			1.44497
$221$	−0.704534	+	0.298312i	−0.0473921	+	0.0200666i
$222$	6.81457			0.457364
$223$	14.2362	−	8.21925i	0.953324	−	0.550402i	0.0592118	−	0.998245i	$-0.481141\pi$
$223$	14.2362	−	8.21925i	0.953324	−	0.550402i	0.894112	+	0.447844i	$0.147808\pi$
$224$		0			0
$225$	−9.87445	+	17.1031i	−0.658297	+	1.14020i
$226$		−	16.5194i		−	1.09886i
$227$	4.87655	+	2.81547i	0.323668	+	0.186870i	0.653026	−	0.757335i	$-0.273499\pi$
$227$	4.87655	+	2.81547i	0.323668	+	0.186870i	−0.329359	+	0.944205i	$0.606832\pi$
$228$	1.60191	+	0.924862i	0.106089	+	0.0612505i
$229$			27.7225i			1.83196i	0.401228	+	0.915978i	$0.368584\pi$
$229$			27.7225i			1.83196i	−0.401228	+	0.915978i	$0.631416\pi$
$230$	−4.60091	+	7.96901i	−0.303375	+	0.525461i
$231$		0			0
$232$	−0.0853606	+	0.0492830i	−0.00560420	+	0.00323559i
$233$	−20.1104			−1.31747			−0.658737	−	0.752374i	$-0.728909\pi$
$233$	−20.1104			−1.31747			−0.658737	+	0.752374i	$0.728909\pi$
$234$	4.88995	−	6.47708i	0.319666	−	0.423420i
$235$	33.9797			2.21659
$236$	0.200843	−	0.115957i	0.0130738	−	0.00754816i
$237$	3.98028	+	6.89405i	0.258547	+	0.447817i
$238$		0			0
$239$		−	6.62968i		−	0.428838i	−0.976742	−	0.214419i	$-0.931214\pi$
$239$		−	6.62968i		−	0.428838i	0.976742	−	0.214419i	$-0.0687858\pi$
$240$	2.78184	+	1.60610i	0.179567	+	0.103673i
$241$	−1.40025	−	0.808433i	−0.0901978	−	0.0520757i	0.454223	−	0.890888i	$-0.349917\pi$
$241$	−1.40025	−	0.808433i	−0.0901978	−	0.0520757i	−0.544420	+	0.838812i	$0.683250\pi$
$242$			22.3491i			1.43665i
$243$	−8.03708	+	13.9206i	−0.515579	+	0.893009i
$244$	−4.01605	−	6.95601i	−0.257102	−	0.445313i
$245$		0			0
$246$	−6.50970			−0.415044
$247$	3.00444	+	7.09570i	0.191168	+	0.451489i
$248$	−2.31076			−0.146734
$249$	2.37749	−	1.37265i	0.150667	−	0.0869879i
$250$	−7.00296	−	12.1295i	−0.442906	−	0.767136i
$251$	−0.253506	+	0.439085i	−0.0160011	+	0.0277148i	−0.873915	−	0.486079i	$-0.838427\pi$
$251$	−0.253506	+	0.439085i	−0.0160011	+	0.0277148i	0.857914	+	0.513793i	$0.171760\pi$
$252$		0			0
$253$	−12.3999	−	7.15910i	−0.779576	−	0.450089i
$254$	10.2090	+	5.89420i	0.640573	+	0.369835i
$255$			0.681619i			0.0426846i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.82032	+	8.34903i	0.300683	+	0.520798i	0.976291	−	0.216463i	$-0.0694520\pi$
$257$	4.82032	+	8.34903i	0.300683	+	0.520798i	−0.675608	+	0.737261i	$0.736119\pi$
$258$	3.43278	−	1.98191i	0.213715	−	0.123389i
$259$		0			0
$260$	5.21745	+	12.3223i	0.323573	+	0.764194i
$261$	0.221861			0.0137328
$262$	−4.44149	+	2.56429i	−0.274396	+	0.158423i
$263$	3.67309	+	6.36197i	0.226492	+	0.392296i	0.956766	−	0.290858i	$-0.0939409\pi$
$263$	3.67309	+	6.36197i	0.226492	+	0.392296i	−0.730274	+	0.683155i	$0.760608\pi$
$264$	−2.49912	+	4.32860i	−0.153810	+	0.266407i
$265$		−	44.8876i		−	2.75742i
$266$		0			0
$267$	−8.85727	−	5.11375i	−0.542056	−	0.312956i
$268$			12.9700i			0.792269i
$269$	11.1770	−	19.3592i	0.681476	−	1.18035i	−0.293055	−	0.956096i	$-0.594672\pi$
$269$	11.1770	−	19.3592i	0.681476	−	1.18035i	0.974530	−	0.224255i	$-0.0719949\pi$
$270$	−8.43344	−	14.6071i	−0.513243	−	0.888962i
$271$	8.32891	−	4.80870i	0.505945	−	0.292108i	−0.225220	−	0.974308i	$-0.572310\pi$
$271$	8.32891	−	4.80870i	0.505945	−	0.292108i	0.731165	+	0.682200i	$0.238977\pi$
$272$	−0.212197			−0.0128663
$273$		0			0
$274$	9.39328			0.567469
$275$	43.8796	−	25.3339i	2.64604	−	1.52769i
$276$	−1.07298	−	1.85845i	−0.0645857	−	0.111866i
$277$	5.08945	−	8.81518i	0.305795	−	0.529653i	−0.671643	−	0.740875i	$-0.734411\pi$
$277$	5.08945	−	8.81518i	0.305795	−	0.529653i	0.977438	+	0.211222i	$0.0677444\pi$
$278$			15.1413i			0.908113i
$279$	4.50442	+	2.60063i	0.269673	+	0.155696i
$280$		0			0
$281$		−	14.1692i		−	0.845265i	−0.906301	−	0.422633i	$-0.861106\pi$
$281$		−	14.1692i		−	0.845265i	0.906301	−	0.422633i	$-0.138894\pi$
$282$	−3.96220	+	6.86273i	−0.235945	+	0.408669i
$283$	−9.46631	−	16.3961i	−0.562714	−	0.974649i	−0.997258	−	0.0739986i	$-0.976424\pi$
$283$	−9.46631	−	16.3961i	−0.562714	−	0.974649i	0.434545	−	0.900650i	$-0.356909\pi$
$284$	6.37721	−	3.68188i	0.378418	−	0.218480i
$285$	6.86490			0.406642
$286$	−19.1736	+	8.11844i	−1.13376	+	0.480053i
$287$		0			0
$288$	1.94932	−	1.12544i	0.114865	−	0.0663173i
$289$	8.47749	+	14.6834i	0.498676	+	0.863732i
$290$	−0.182905	+	0.316800i	−0.0107405	+	0.0186031i
$291$			12.1881i			0.714477i
$292$	4.85333	+	2.80207i	0.284020	+	0.163979i
$293$	−3.16950	−	1.82991i	−0.185164	−	0.106905i	0.404553	−	0.914515i	$-0.367427\pi$
$293$	−3.16950	−	1.82991i	−0.185164	−	0.106905i	−0.589717	+	0.807610i	$0.700761\pi$
$294$		0			0
$295$	0.430353	−	0.745393i	0.0250561	−	0.0433985i
$296$	3.93672	+	6.81859i	0.228817	+	0.396323i
$297$	22.7290	−	13.1226i	1.31887	−	0.761449i
$298$	20.6027			1.19348
$299$	1.09742	−	8.87198i	0.0634655	−	0.513080i
$300$	7.59389			0.438434
$301$		0			0
$302$	5.97036	+	10.3410i	0.343555	+	0.595055i
$303$	2.66251	−	4.61161i	0.152957	−	0.264930i
$304$			2.13714i			0.122573i
$305$	−25.8159	−	14.9048i	−1.47822	−	0.853448i
$306$	0.413640	+	0.238815i	0.0236462	+	0.0136522i
$307$		−	19.6987i		−	1.12426i	−0.827048	−	0.562132i	$-0.809981\pi$
$307$		−	19.6987i		−	1.12426i	0.827048	−	0.562132i	$-0.190019\pi$
$308$		0			0
$309$	8.37345	+	14.5032i	0.476349	+	0.825061i
$310$	−7.42700	+	4.28798i	−0.421825	+	0.243541i
$311$	−16.9685			−0.962195			−0.481098	−	0.876667i	$-0.659762\pi$
$311$	−16.9685			−0.962195			−0.481098	+	0.876667i	$0.659762\pi$
$312$	−3.09706	−	0.383091i	−0.175336	−	0.0216882i
$313$	4.53794			0.256500			0.128250	−	0.991742i	$-0.459064\pi$
$313$	4.53794			0.256500			0.128250	+	0.991742i	$0.459064\pi$
$314$	8.08887	−	4.67011i	0.456481	−	0.263550i
$315$		0			0
$316$	−4.59875	+	7.96526i	−0.258700	+	0.448081i
$317$		−	29.1866i		−	1.63928i	−0.572877	−	0.819641i	$-0.694173\pi$
$317$		−	29.1866i		−	1.63928i	0.572877	−	0.819641i	$-0.305827\pi$
$318$	9.06575	+	5.23411i	0.508382	+	0.293515i
$319$	−0.492946	−	0.284603i	−0.0275997	−	0.0159347i
$320$			3.71131i			0.207469i
$321$	−5.04168	+	8.73244i	−0.281399	+	0.487397i
$322$		0			0
$323$	−0.392737	+	0.226747i	−0.0218525	+	0.0126165i
$324$	−2.81913			−0.156618
$325$	25.2474	+	19.0608i	1.40047	+	1.05730i
$326$	−4.47730			−0.247975
$327$	4.29727	−	2.48103i	0.237640	−	0.137201i
$328$	−3.76060	−	6.51354i	−0.207644	−	0.359650i
$329$		0			0
$330$			18.5500i			1.02114i
$331$	4.16161	+	2.40271i	0.228743	+	0.132065i	0.609992	−	0.792408i	$-0.291173\pi$
$331$	4.16161	+	2.40271i	0.228743	+	0.132065i	−0.381249	+	0.924472i	$0.624506\pi$
$332$	2.74691	+	1.58593i	0.150756	+	0.0870392i
$333$		−	17.7222i		−	0.971169i
$334$	7.35342	−	12.7365i	0.402361	−	0.696910i
$335$	24.0679	+	41.6868i	1.31497	+	2.27759i
$336$		0			0
$337$	17.7312			0.965883			0.482941	−	0.875653i	$-0.339568\pi$
$337$	17.7312			0.965883			0.482941	+	0.875653i	$0.339568\pi$
$338$	−9.33520	−	9.04732i	−0.507768	−	0.492109i
$339$	14.2978			0.776550
$340$	−0.682021	+	0.393765i	−0.0369878	+	0.0213549i
$341$	−6.67217	−	11.5565i	−0.361318	−	0.625822i
$342$	2.40522	−	4.16597i	0.130060	−	0.225270i
$343$		0			0
$344$	3.96617	+	2.28987i	0.213841	+	0.123461i
$345$	−6.89730	−	3.98216i	−0.371338	−	0.214392i
$346$		−	13.7657i		−	0.740049i
$347$	8.35240	−	14.4668i	0.448380	−	0.776617i	−0.549901	−	0.835230i	$-0.685334\pi$
$347$	8.35240	−	14.4668i	0.448380	−	0.776617i	0.998281	+	0.0586128i	$0.0186677\pi$
$348$	−0.0426552	−	0.0738809i	−0.00228656	−	0.00396043i
$349$	−0.0173616	+	0.0100237i	−0.000929347	+	0.000536559i	−0.500465	−	0.865757i	$-0.666837\pi$
$349$	−0.0173616	+	0.0100237i	−0.000929347	+	0.000536559i	0.499535	+	0.866294i	$0.333504\pi$
$350$		0			0
$351$	13.0778	+	9.87321i	0.698039	+	0.526993i
$352$	−5.77486			−0.307801
$353$	−25.8299	+	14.9129i	−1.37479	+	0.793734i	−0.991526	−	0.129905i	$-0.958533\pi$
$353$	−25.8299	+	14.9129i	−1.37479	+	0.793734i	−0.383262	+	0.923640i	$0.625199\pi$
$354$	0.100363	+	0.173833i	0.00533421	+	0.00923912i
$355$	13.6646	−	23.6678i	0.725243	−	1.25616i
$356$		−	11.8167i		−	0.626282i
$357$		0			0
$358$	−13.2318	−	7.63936i	−0.699320	−	0.403753i
$359$			18.3351i			0.967687i	0.875154	+	0.483844i	$0.160760\pi$
$359$			18.3351i			0.967687i	−0.875154	+	0.483844i	$0.839240\pi$
$360$	4.17687	−	7.23455i	0.220140	−	0.381294i
$361$	−7.21632	−	12.4990i	−0.379806	−	0.657844i
$362$	−1.44408	+	0.833739i	−0.0758991	+	0.0438204i
$363$	−19.3434			−1.01527
$364$		0			0
$365$	20.7987			1.08866
$366$	6.02053	−	3.47596i	0.314698	−	0.181691i
$367$	0.672426	+	1.16468i	0.0351004	+	0.0607956i	0.883042	−	0.469294i	$-0.155492\pi$
$367$	0.672426	+	1.16468i	0.0351004	+	0.0607956i	−0.847942	+	0.530090i	$0.822158\pi$
$368$	1.23970	−	2.14722i	0.0646238	−	0.111932i
$369$			16.9293i			0.881306i
$370$	25.3059	+	14.6104i	1.31559	+	0.759558i
$371$		0			0
$372$		−	2.00000i		−	0.103695i
$373$	5.53575	−	9.58821i	0.286630	−	0.496458i	−0.686373	−	0.727250i	$-0.740798\pi$
$373$	5.53575	−	9.58821i	0.286630	−	0.496458i	0.973003	+	0.230791i	$0.0741315\pi$
$374$	−0.612704	−	1.06124i	−0.0316822	−	0.0548752i
$375$	10.4982	−	6.06116i	0.542127	−	0.312997i
$376$	−9.15570			−0.472169
$377$	0.0436269	−	0.352697i	0.00224690	−	0.0181648i
$378$		0			0
$379$	14.5583	−	8.40523i	0.747808	−	0.431747i	−0.0770930	−	0.997024i	$-0.524564\pi$
$379$	14.5583	−	8.40523i	0.747808	−	0.431747i	0.824902	+	0.565276i	$0.191231\pi$
$380$	3.96579	+	6.86895i	0.203441	+	0.352370i
$381$	−5.10152	+	8.83608i	−0.261359	+	0.452686i
$382$		−	0.120976i		−	0.00618967i
$383$	−14.3562	−	8.28855i	−0.733567	−	0.423525i	0.0861585	−	0.996281i	$-0.472541\pi$
$383$	−14.3562	−	8.28855i	−0.733567	−	0.423525i	−0.819726	+	0.572756i	$0.805874\pi$
$384$	−0.749558	−	0.432757i	−0.0382507	−	0.0220841i
$385$		0			0
$386$	1.37775	−	2.38633i	0.0701256	−	0.121461i
$387$	−5.15422	−	8.92738i	−0.262004	−	0.453804i
$388$	−12.1952	+	7.04093i	−0.619120	+	0.357449i
$389$	−1.17013			−0.0593280			−0.0296640	−	0.999560i	$-0.509444\pi$
$389$	−1.17013			−0.0593280			−0.0296640	+	0.999560i	$0.509444\pi$
$390$	−10.6651	+	4.51578i	−0.540049	+	0.228666i
$391$	0.526121			0.0266071
$392$		0			0
$393$	−2.21944	−	3.84418i	−0.111956	−	0.193913i
$394$	7.56267	−	13.0989i	0.381002	−	0.659914i
$395$			34.1348i			1.71751i
$396$	11.2571	+	6.49927i	0.565689	+	0.326601i
$397$	−22.6877	−	13.0987i	−1.13866	−	0.657406i	−0.192562	−	0.981285i	$-0.561680\pi$
$397$	−22.6877	−	13.0987i	−1.13866	−	0.657406i	−0.946099	+	0.323878i	$0.895013\pi$
$398$		−	5.30640i		−	0.265986i
$399$		0			0
$400$	4.38692	+	7.59837i	0.219346	+	0.379919i
$401$	−9.84559	+	5.68436i	−0.491665	+	0.283863i	−0.725265	−	0.688470i	$-0.758283\pi$
$401$	−9.84559	+	5.68436i	−0.491665	+	0.283863i	0.233600	+	0.972333i	$0.424949\pi$
$402$	−11.2257			−0.559888
$403$	5.02003	−	6.64939i	0.250066	−	0.331230i
$404$	6.15243			0.306095
$405$	−9.06094	+	5.23134i	−0.450242	+	0.259947i
$406$		0			0
$407$	−22.7340	+	39.3764i	−1.12688	+	1.95182i
$408$		−	0.183660i		−	0.00909251i
$409$	20.2056	+	11.6657i	0.999102	+	0.576832i	0.907982	−	0.419008i	$-0.137622\pi$
$409$	20.2056	+	11.6657i	0.999102	+	0.576832i	0.0911196	+	0.995840i	$0.470955\pi$
$410$	−24.1738	−	13.9567i	−1.19386	−	0.689275i
$411$			8.13003i			0.401025i
$412$	−9.67453	+	16.7568i	−0.476630	+	0.825547i
$413$		0			0
$414$	−4.83315	+	2.79042i	−0.237536	+	0.137142i
$415$	11.7718			0.577853
$416$	−1.40582	−	3.32019i	−0.0689262	−	0.162786i
$417$	−13.1050			−0.641754
$418$	−10.6882	+	6.17084i	−0.522777	+	0.301826i
$419$	−6.33402	−	10.9709i	−0.309437	−	0.535961i	0.668802	−	0.743441i	$-0.266807\pi$
$419$	−6.33402	−	10.9709i	−0.309437	−	0.535961i	−0.978239	+	0.207479i	$0.933474\pi$
$420$		0			0
$421$		−	27.6625i		−	1.34819i	−0.738646	−	0.674094i	$-0.764534\pi$
$421$		−	27.6625i		−	1.34819i	0.738646	−	0.674094i	$-0.235466\pi$
$422$	15.5003	+	8.94910i	0.754543	+	0.435635i
$423$	17.8474	+	10.3042i	0.867771	+	0.501008i
$424$			12.0948i			0.587375i
$425$	−0.930892	+	1.61235i	−0.0451549	+	0.0782105i
$426$	3.18673	+	5.51957i	0.154397	+	0.267424i
$427$		0			0
$428$	−11.6501			−0.563130
$429$	−7.02663	−	16.5951i	−0.339249	−	0.801218i
$430$	16.9968			0.819660
$431$	5.55462	−	3.20696i	0.267557	−	0.154474i	−0.360220	−	0.932867i	$-0.617298\pi$
$431$	5.55462	−	3.20696i	0.267557	−	0.154474i	0.627777	+	0.778393i	$0.283965\pi$
$432$	2.27236	+	3.93584i	0.109329	+	0.189363i
$433$	0.0325135	−	0.0563150i	0.00156250	−	0.00270633i	−0.865243	−	0.501353i	$-0.832836\pi$
$433$	0.0325135	−	0.0563150i	0.00156250	−	0.00270633i	0.866806	+	0.498646i	$0.166169\pi$
$434$		0			0
$435$	−0.274195	−	0.158307i	−0.0131467	−	0.00759022i
$436$	4.96499	+	2.86654i	0.237780	+	0.137282i
$437$		−	5.29881i		−	0.253477i
$438$	−2.42524	+	4.20063i	−0.115882	+	0.200714i
$439$	−18.3889	−	31.8505i	−0.877655	−	1.52014i	−0.853908	−	0.520424i	$-0.825774\pi$
$439$	−18.3889	−	31.8505i	−0.877655	−	1.52014i	−0.0237469	−	0.999718i	$-0.507560\pi$
$440$	−18.5609	+	10.7162i	−0.884858	+	0.510873i
$441$		0			0
$442$	0.460989	−	0.610613i	0.0219270	−	0.0290439i
$443$	−8.46383			−0.402129			−0.201064	−	0.979578i	$-0.564440\pi$
$443$	−8.46383			−0.402129			−0.201064	+	0.979578i	$0.564440\pi$
$444$	−5.90159	+	3.40729i	−0.280077	+	0.161703i
$445$	−21.9277	−	37.9798i	−1.03947	−	1.80042i
$446$	−8.21925	+	14.2362i	−0.389193	+	0.674102i
$447$			17.8319i			0.843422i
$448$		0			0
$449$	−19.5984	−	11.3152i	−0.924907	−	0.533995i	−0.0397096	−	0.999211i	$-0.512643\pi$
$449$	−19.5984	−	11.3152i	−0.924907	−	0.533995i	−0.885197	+	0.465216i	$0.845977\pi$
$450$		−	19.7489i		−	0.930972i
$451$	21.7169	−	37.6148i	1.02261	−	1.77121i
$452$	8.25971	+	14.3062i	0.388504	+	0.672909i
$453$	−8.95026	+	5.16743i	−0.420520	+	0.242787i
$454$	−5.63095			−0.264274
$455$		0			0
$456$	−1.84972			−0.0866213
$457$	−14.1310	+	8.15851i	−0.661018	+	0.381639i	−0.792665	−	0.609658i	$-0.791307\pi$
$457$	−14.1310	+	8.15851i	−0.661018	+	0.381639i	0.131647	+	0.991297i	$0.457974\pi$
$458$	−13.8613	−	24.0084i	−0.647694	−	1.12184i
$459$	−0.482188	+	0.835174i	−0.0225066	+	0.0389826i
$460$		−	9.20183i		−	0.429037i
$461$	−16.6951	−	9.63892i	−0.777568	−	0.448929i	0.0579996	−	0.998317i	$-0.481528\pi$
$461$	−16.6951	−	9.63892i	−0.777568	−	0.448929i	−0.835568	+	0.549387i	$0.814861\pi$
$462$		0			0
$463$			2.70218i			0.125581i	0.998027	+	0.0627904i	$0.0200000\pi$
$463$			2.70218i			0.125581i	−0.998027	+	0.0627904i	$0.980000\pi$
$464$	0.0492830	−	0.0853606i	0.00228791	−	0.00396277i
$465$	−3.71131	−	6.42818i	−0.172108	−	0.298100i
$466$	17.4161	−	10.0552i	0.806784	−	0.465797i
$467$	18.3906			0.851014			0.425507	−	0.904955i	$-0.360096\pi$
$467$	18.3906			0.851014			0.425507	+	0.904955i	$0.360096\pi$
$468$	−0.996277	+	8.05429i	−0.0460529	+	0.372310i
$469$		0			0
$470$	−29.4272	+	16.9898i	−1.35738	+	0.783682i
$471$	4.04205	+	7.00104i	0.186248	+	0.322591i
$472$	−0.115957	+	0.200843i	−0.00533735	+	0.00924457i
$473$			26.4473i			1.21605i
$474$	−6.89405	−	3.98028i	−0.316654	−	0.182820i
$475$	16.2388	+	9.37545i	0.745085	+	0.430175i
$476$		0			0
$477$	13.6120	−	23.5767i	0.623250	−	1.07950i
$478$	3.31484	+	5.74147i	0.151617	+	0.262609i
$479$	−35.3951	+	20.4354i	−1.61725	+	0.933717i	−0.629617	+	0.776906i	$0.716788\pi$
$479$	−35.3951	+	20.4354i	−1.61725	+	0.933717i	−0.987629	+	0.156811i	$0.949879\pi$
$480$	−3.21220			−0.146616
$481$	−28.1733	−	3.48491i	−1.28459	−	0.158898i
$482$	1.61687			0.0736462
$483$		0			0
$484$	−11.1745	−	19.3549i	−0.507933	−	0.879766i
$485$	−26.1311	+	45.2604i	−1.18655	+	2.05517i
$486$		−	16.0742i		−	0.729138i
$487$	15.2674	+	8.81466i	0.691834	+	0.399430i	0.804299	−	0.594225i	$-0.202541\pi$
$487$	15.2674	+	8.81466i	0.691834	+	0.399430i	−0.112465	+	0.993656i	$0.535875\pi$
$488$	6.95601	+	4.01605i	0.314884	+	0.181798i
$489$		−	3.87517i		−	0.175241i
$490$		0			0
$491$	−9.42997	−	16.3332i	−0.425569	−	0.737106i	0.570905	−	0.821016i	$-0.306593\pi$
$491$	−9.42997	−	16.3332i	−0.425569	−	0.737106i	−0.996473	+	0.0839098i	$0.973259\pi$
$492$	5.63757	−	3.25485i	0.254161	−	0.146740i
$493$	0.0209154			0.000941982
$494$	−6.14977	−	4.64284i	−0.276691	−	0.208891i
$495$	48.2417			2.16830
$496$	2.00118	−	1.15538i	0.0898556	−	0.0518782i
$497$		0			0
$498$	−1.37265	+	2.37749i	−0.0615097	+	0.106538i
$499$		−	2.10742i		−	0.0943410i	−0.998887	−	0.0471705i	$-0.984980\pi$
$499$		−	2.10742i		−	0.0943410i	0.998887	−	0.0471705i	$-0.0150204\pi$
$500$	12.1295	+	7.00296i	0.542447	+	0.313182i
$501$	11.0236	+	6.36449i	0.492499	+	0.284345i
$502$		−	0.507011i		−	0.0226290i
$503$	10.8942	−	18.8693i	0.485749	−	0.841342i	−0.514117	−	0.857720i	$-0.671880\pi$
$503$	10.8942	−	18.8693i	0.485749	−	0.841342i	0.999866	+	0.0163784i	$0.00521363\pi$
$504$		0			0
$505$	19.7745	−	11.4168i	0.879953	−	0.508041i
$506$	14.3182			0.636521
$507$	7.83059	−	8.07976i	0.347769	−	0.358835i
$508$	−11.7884			−0.523025
$509$	10.5636	−	6.09887i	0.468221	−	0.270328i	−0.247273	−	0.968946i	$-0.579535\pi$
$509$	10.5636	−	6.09887i	0.468221	−	0.270328i	0.715495	+	0.698618i	$0.246201\pi$
$510$	−0.340809	−	0.590299i	−0.0150913	−	0.0261389i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	8.41143	+	4.85634i	0.371374	+	0.214413i
$514$	−8.34903	−	4.82032i	−0.368260	−	0.212615i
$515$			71.8104i			3.16435i
$516$	−1.98191	+	3.43278i	−0.0872489	+	0.151120i
$517$	−26.4365	−	45.7893i	−1.16267	−	2.01381i
$518$		0			0
$519$	11.9144			0.522986
$520$	−10.6796	−	8.06267i	−0.468330	−	0.353571i
$521$	26.9765			1.18186			0.590932	−	0.806722i	$-0.298760\pi$
$521$	26.9765			1.18186			0.590932	+	0.806722i	$0.298760\pi$
$522$	−0.192137	+	0.110930i	−0.00840960	+	0.00485529i
$523$	−1.87683	−	3.25076i	−0.0820679	−	0.142146i	0.822070	−	0.569386i	$-0.192819\pi$
$523$	−1.87683	−	3.25076i	−0.0820679	−	0.142146i	−0.904138	+	0.427241i	$0.859486\pi$
$524$	2.56429	−	4.44149i	0.112022	−	0.194027i
$525$		0			0
$526$	−6.36197	−	3.67309i	−0.277395	−	0.160154i
$527$	0.424644	+	0.245168i	0.0184978	+	0.0106797i
$528$		−	4.99823i		−	0.217520i
$529$	8.42629	−	14.5948i	0.366360	−	0.634555i
$530$	22.4438	+	38.8738i	0.974896	+	1.68857i
$531$	0.452075	−	0.261006i	0.0196184	−	0.0113267i
$532$		0			0
$533$	26.9129	+	3.32900i	1.16573	+	0.144195i
$534$	10.2275			0.442587
$535$	−37.4445	+	21.6186i	−1.61887	+	0.934654i
$536$	−6.48500	−	11.2323i	−0.280109	−	0.485163i
$537$	6.61198	−	11.4523i	0.285328	−	0.494203i
$538$			22.3541i			0.963752i
$539$		0			0
$540$	14.6071	+	8.43344i	0.628591	+	0.362917i
$541$			0.0135705i			0.000583440i	1.00000		0.000291720i	$9.28574e-5\pi$
$541$			0.0135705i			0.000583440i	−1.00000		0.000291720i	$0.999907\pi$
$542$	−4.80870	+	8.32891i	−0.206551	+	0.357757i
$543$	−0.721614	−	1.24987i	−0.0309674	−	0.0536371i
$544$	0.183768	−	0.106098i	0.00787899	−	0.00454894i
$545$	21.2772			0.911416
$546$		0			0
$547$	−9.66115			−0.413081			−0.206540	−	0.978438i	$-0.566220\pi$
$547$	−9.66115			−0.413081			−0.206540	+	0.978438i	$0.566220\pi$
$548$	−8.13482	+	4.69664i	−0.347502	+	0.200631i
$549$	−9.03967	−	15.6572i	−0.385804	−	0.668232i
$550$	−25.3339	+	43.8796i	−1.08024	+	1.87103i
$551$		−	0.210649i		−	0.00897395i
$552$	1.85845	+	1.07298i	0.0791010	+	0.0456690i
$553$		0			0
$554$			10.1789i			0.432460i
$555$	−12.6455	+	21.9027i	−0.536772	+	0.929716i
$556$	−7.57063	−	13.1127i	−0.321066	−	0.556103i
$557$	−21.6145	+	12.4791i	−0.915834	+	0.528757i	−0.882304	−	0.470680i	$-0.844008\pi$
$557$	−21.6145	+	12.4791i	−0.915834	+	0.528757i	−0.0335307	+	0.999438i	$0.510675\pi$
$558$	−5.20126			−0.220187
$559$	−15.2056	+	6.43830i	−0.643128	+	0.272311i
$560$		0			0
$561$	0.918515	−	0.530305i	0.0387797	−	0.0223895i
$562$	7.08461	+	12.2709i	0.298846	+	0.517617i
$563$	−7.94970	+	13.7693i	−0.335040	+	0.580306i	−0.983492	−	0.180949i	$-0.942083\pi$
$563$	−7.94970	+	13.7693i	−0.335040	+	0.580306i	0.648453	+	0.761255i	$0.275416\pi$
$564$		−	7.92439i		−	0.333677i
$565$	53.0949	+	30.6544i	2.23372	+	1.28964i
$566$	16.3961	+	9.46631i	0.689181	+	0.397899i
$567$		0			0
$568$	−3.68188	+	6.37721i	−0.154488	+	0.267582i
$569$	−8.95465	−	15.5099i	−0.375398	−	0.650209i	0.614988	−	0.788536i	$-0.289161\pi$
$569$	−8.95465	−	15.5099i	−0.375398	−	0.650209i	−0.990387	+	0.138327i	$0.955827\pi$
$570$	−5.94518	+	3.43245i	−0.249016	+	0.143770i
$571$	−12.5123			−0.523623			−0.261812	−	0.965119i	$-0.584320\pi$
$571$	−12.5123			−0.523623			−0.261812	+	0.965119i	$0.584320\pi$
$572$	12.5456	−	16.6176i	0.524560	−	0.694817i
$573$	0.104707			0.00437418
$574$		0			0
$575$	−10.8769	−	18.8394i	−0.453599	−	0.785657i
$576$	−1.12544	+	1.94932i	−0.0468934	+	0.0812218i
$577$			22.0910i			0.919662i	0.888007	+	0.459831i	$0.152090\pi$
$577$			22.0910i			0.919662i	−0.888007	+	0.459831i	$0.847910\pi$
$578$	−14.6834	−	8.47749i	−0.610750	−	0.352617i
$579$	2.06540	+	1.19246i	0.0858353	+	0.0495570i
$580$		−	0.365809i		−	0.0151894i
$581$		0			0
$582$	−6.09403	−	10.5552i	−0.252606	−	0.437526i
$583$	−60.4883	+	34.9229i	−2.50517	+	1.44636i
$584$	−5.60414			−0.231901
$585$	11.7439	+	27.7360i	0.485550	+	1.14674i
$586$	3.65982			0.151186
$587$	18.3007	−	10.5659i	0.755352	−	0.436102i	−0.0722727	−	0.997385i	$-0.523025\pi$
$587$	18.3007	−	10.5659i	0.755352	−	0.436102i	0.827624	+	0.561282i	$0.189692\pi$
$588$		0			0
$589$	2.46921	−	4.27679i	0.101742	−	0.176222i
$590$			0.860706i			0.0354347i
$591$	11.3373	+	6.54560i	0.466355	+	0.269250i
$592$	−6.81859	−	3.93672i	−0.280242	−	0.161798i
$593$		−	8.95493i		−	0.367735i	−0.982951	−	0.183867i	$-0.941138\pi$
$593$		−	8.95493i		−	0.367735i	0.982951	−	0.183867i	$-0.0588617\pi$
$594$	−13.1226	+	22.7290i	−0.538425	+	0.932580i
$595$		0			0
$596$	−17.8425	+	10.3013i	−0.730855	+	0.421960i
$597$	4.59277			0.187970
$598$	3.48560	+	8.23207i	0.142537	+	0.336635i
$599$	41.7996			1.70788			0.853942	−	0.520368i	$-0.174205\pi$
$599$	41.7996			1.70788			0.853942	+	0.520368i	$0.174205\pi$
$600$	−6.57650	+	3.79695i	−0.268485	+	0.155010i
$601$	7.64481	+	13.2412i	0.311838	+	0.540120i	0.978760	−	0.205008i	$-0.0657220\pi$
$601$	7.64481	+	13.2412i	0.311838	+	0.540120i	−0.666922	+	0.745127i	$0.732389\pi$
$602$		0			0
$603$			29.1940i			1.18887i
$604$	−10.3410	−	5.97036i	−0.420768	−	0.242930i
$605$	−71.8319	−	41.4722i	−2.92038	−	1.68608i
$606$			5.32502i			0.216314i
$607$	7.30434	−	12.6515i	0.296474	−	0.513508i	−0.678853	−	0.734275i	$-0.737522\pi$
$607$	7.30434	−	12.6515i	0.296474	−	0.513508i	0.975327	+	0.220766i	$0.0708558\pi$
$608$	−1.06857	−	1.85081i	−0.0433362	−	0.0750604i
$609$		0			0
$610$	29.8097			1.20696
$611$	19.8904	−	26.3462i	0.804678	−	1.06585i
$612$	−0.477631			−0.0193071
$613$	−33.9623	+	19.6081i	−1.37172	+	0.791965i	−0.991145	−	0.132783i	$-0.957609\pi$
$613$	−33.9623	+	19.6081i	−1.37172	+	0.791965i	−0.380579	+	0.924748i	$0.624275\pi$
$614$	9.84935	+	17.0596i	0.397487	+	0.688468i
$615$	12.0798	−	20.9228i	0.487104	−	0.843688i
$616$		0			0
$617$	8.10486	+	4.67934i	0.326289	+	0.188383i	0.654192	−	0.756328i	$-0.273009\pi$
$617$	8.10486	+	4.67934i	0.326289	+	0.188383i	−0.327903	+	0.944711i	$0.606342\pi$
$618$	−14.5032	−	8.37345i	−0.583406	−	0.336830i
$619$			43.7075i			1.75675i	0.477970	+	0.878376i	$0.341373\pi$
$619$			43.7075i			1.75675i	−0.477970	+	0.878376i	$0.658627\pi$
$620$	4.28798	−	7.42700i	0.172210	−	0.298276i
$621$	−5.63409	−	9.75852i	−0.226088	−	0.391596i
$622$	14.6952	−	8.48425i	0.589222	−	0.340187i
$623$		0			0
$624$	2.87367	−	1.21676i	0.115039	−	0.0487094i
$625$	8.11112			0.324445
$626$	−3.92997	+	2.26897i	−0.157073	+	0.0906863i
$627$	−5.34095	−	9.25080i	−0.213297	−	0.369441i
$628$	−4.67011	+	8.08887i	−0.186358	+	0.322781i
$629$		−	1.67072i		−	0.0666159i
$630$		0			0
$631$	−18.0096	−	10.3978i	−0.716951	−	0.413932i	0.0966785	−	0.995316i	$-0.469178\pi$
$631$	−18.0096	−	10.3978i	−0.716951	−	0.413932i	−0.813629	+	0.581384i	$0.802511\pi$
$632$		−	9.19749i		−	0.365857i
$633$	−7.74558	+	13.4157i	−0.307859	+	0.533228i
$634$	14.5933	+	25.2763i	0.579574	+	1.00385i
$635$	−37.8890	+	21.8752i	−1.50358	+	0.868091i
$636$	−10.4682			−0.415092
$637$		0			0
$638$	0.569205			0.0225350
$639$	14.3544	−	8.28749i	0.567850	−	0.327848i
$640$	−1.85566	−	3.21409i	−0.0733513	−	0.127048i
$641$	−3.61897	+	6.26824i	−0.142941	+	0.247581i	−0.928603	−	0.371075i	$-0.878989\pi$
$641$	−3.61897	+	6.26824i	−0.142941	+	0.247581i	0.785662	+	0.618656i	$0.212323\pi$
$642$		−	10.0834i		−	0.397958i
$643$	−34.7898	−	20.0859i	−1.37198	−	0.792111i	−0.380800	−	0.924658i	$-0.624351\pi$
$643$	−34.7898	−	20.0859i	−1.37198	−	0.792111i	−0.991177	+	0.132547i	$0.957685\pi$
$644$		0			0
$645$			14.7110i			0.579245i
$646$	0.226747	−	0.392737i	0.00892124	−	0.0154520i
$647$	−7.27561	−	12.6017i	−0.286034	−	0.495425i	0.686826	−	0.726822i	$-0.259004\pi$
$647$	−7.27561	−	12.6017i	−0.286034	−	0.495425i	−0.972859	+	0.231397i	$0.925670\pi$
$648$	2.44144	−	1.40956i	0.0959087	−	0.0553729i
$649$	−1.33927			−0.0525710
$650$	−31.3953	−	3.88344i	−1.23142	−	0.152321i
$651$		0			0
$652$	3.87746	−	2.23865i	0.151853	−	0.0876723i
$653$	24.8634	+	43.0646i	0.972978	+	1.68525i	0.686451	+	0.727176i	$0.259168\pi$
$653$	24.8634	+	43.0646i	0.972978	+	1.68525i	0.286527	+	0.958072i	$0.407499\pi$
$654$	−2.48103	+	4.29727i	−0.0970159	+	0.168037i
$655$		−	19.0338i		−	0.743712i
$656$	6.51354	+	3.76060i	0.254311	+	0.146827i
$657$	10.9243	+	6.30714i	0.426197	+	0.246065i
$658$		0			0
$659$	15.7988	−	27.3644i	0.615436	−	1.06597i	−0.374872	−	0.927076i	$-0.622313\pi$
$659$	15.7988	−	27.3644i	0.615436	−	1.06597i	0.990308	−	0.138889i	$-0.0443532\pi$
$660$	−9.27500	−	16.0648i	−0.361029	−	0.625320i
$661$	21.5391	−	12.4356i	0.837775	−	0.483689i	−0.0187325	−	0.999825i	$-0.505963\pi$
$661$	21.5391	−	12.4356i	0.837775	−	0.483689i	0.856507	+	0.516135i	$0.172630\pi$
$662$	−4.80542			−0.186768
$663$	0.528494	+	0.398993i	0.0205250	+	0.0154956i
$664$	−3.17186			−0.123092
$665$		0			0
$666$	8.86109	+	15.3479i	0.343360	+	0.594717i
$667$	−0.122192	+	0.211643i	−0.00473130	+	0.00819485i
$668$			14.7068i			0.569025i
$669$	−12.3216	−	7.11388i	−0.476381	−	0.275039i
$670$	−41.6868	−	24.0679i	−1.61050	−	0.929822i
$671$			46.3843i			1.79065i
$672$		0			0
$673$	−10.8245	−	18.7486i	−0.417254	−	0.722705i	0.578408	−	0.815748i	$-0.303674\pi$
$673$	−10.8245	−	18.7486i	−0.417254	−	0.722705i	−0.995662	+	0.0930423i	$0.970341\pi$
$674$	−15.3557	+	8.86562i	−0.591480	+	0.341491i
$675$	39.8747			1.53478
$676$	12.6082	+	3.16761i	0.484930	+	0.121831i
$677$	−14.3935			−0.553187			−0.276594	−	0.960987i	$-0.589206\pi$
$677$	−14.3935			−0.553187			−0.276594	+	0.960987i	$0.589206\pi$
$678$	−12.3823	+	7.14890i	−0.475538	+	0.274552i
$679$		0			0
$680$	0.393765	−	0.682021i	0.0151002	−	0.0261543i
$681$		−	4.87367i		−	0.186759i
$682$	11.5565	+	6.67217i	0.442523	+	0.255491i
$683$	−36.6968	−	21.1869i	−1.40416	−	0.810694i	−0.409346	−	0.912379i	$-0.634243\pi$
$683$	−36.6968	−	21.1869i	−1.40416	−	0.810694i	−0.994817	+	0.101686i	$0.967576\pi$
$684$			4.81045i			0.183932i
$685$	−17.4307	+	30.1909i	−0.665993	+	1.15353i
$686$		0			0
$687$	20.7796	−	11.9971i	0.792793	−	0.457719i
$688$	−4.57973			−0.174601
$689$	−34.8037	−	26.2754i	−1.32591	−	1.00101i
$690$	7.96432			0.303196
$691$	19.8651	−	11.4691i	0.755703	−	0.436305i	−0.0720480	−	0.997401i	$-0.522953\pi$
$691$	19.8651	−	11.4691i	0.755703	−	0.436305i	0.827751	+	0.561096i	$0.189620\pi$
$692$	6.88286	+	11.9215i	0.261647	+	0.453186i
$693$		0			0
$694$			16.7048i			0.634105i
$695$	−48.6654	−	28.0970i	−1.84598	−	1.06578i
$696$	0.0738809	+	0.0426552i	0.00280045	+	0.00161684i
$697$			1.59597i			0.0604518i
$698$	0.0100237	−	0.0173616i	0.000379404	−	0.000657147i
$699$	8.70291	+	15.0739i	0.329174	+	0.570146i
$700$		0			0
$701$	1.70699			0.0644723			0.0322361	−	0.999480i	$-0.489737\pi$
$701$	1.70699			0.0644723			0.0322361	+	0.999480i	$0.489737\pi$
$702$	−16.2623	−	2.01157i	−0.613780	−	0.0759216i
$703$	−16.8266			−0.634627
$704$	5.00118	−	2.88743i	0.188489	−	0.108824i
$705$	−14.7050	−	25.4697i	−0.553821	−	0.959245i
$706$	14.9129	−	25.8299i	0.561255	−	0.972122i
$707$		0			0
$708$	−0.173833	−	0.100363i	−0.00653304	−	0.00377186i
$709$	−15.7730	−	9.10657i	−0.592369	−	0.342005i	0.173665	−	0.984805i	$-0.444439\pi$
$709$	−15.7730	−	9.10657i	−0.592369	−	0.342005i	−0.766034	+	0.642800i	$0.777772\pi$
$710$			27.3292i			1.02565i
$711$	−10.3512	+	17.9289i	−0.388202	+	0.672385i
$712$	5.90833	+	10.2335i	0.221424	+	0.383518i
$713$	−4.96172	+	2.86465i	−0.185818	+	0.107282i
$714$		0			0
$715$	9.48629	−	76.6909i	0.354767	−	2.86808i
$716$	15.2787			0.570992
$717$	−4.96933	+	2.86904i	−0.185583	+	0.107146i
$718$	−9.16753	−	15.8786i	−0.342129	−	0.592585i
$719$	−1.79107	+	3.10222i	−0.0667956	+	0.115693i	−0.897489	−	0.441037i	$-0.854611\pi$
$719$	−1.79107	+	3.10222i	−0.0667956	+	0.115693i	0.830694	+	0.556730i	$0.187944\pi$
$720$			8.35373i			0.311325i
$721$		0			0
$722$	12.4990	+	7.21632i	0.465166	+	0.268564i
$723$			1.39942i			0.0520450i
$724$	0.833739	−	1.44408i	0.0309857	−	0.0536688i
$725$	−0.432401	−	0.748941i	−0.0160590	−	0.0278150i
$726$	16.7519	−	9.67172i	0.621722	−	0.358951i
$727$	−3.21747			−0.119329			−0.0596647	−	0.998218i	$-0.519003\pi$
$727$	−3.21747			−0.119329			−0.0596647	+	0.998218i	$0.519003\pi$
$728$		0			0
$729$	5.45503			0.202038
$730$	−18.0122	+	10.3994i	−0.666662	+	0.384898i
$731$	−0.485903	−	0.841608i	−0.0179718	−	0.0311280i
$732$	−3.47596	+	6.02053i	−0.128475	+	0.222525i
$733$		−	4.79233i		−	0.177009i	−0.996076	−	0.0885043i	$-0.971791\pi$
$733$		−	4.79233i		−	0.177009i	0.996076	−	0.0885043i	$-0.0282087\pi$
$734$	−1.16468	−	0.672426i	−0.0429890	−	0.0248197i
$735$		0			0
$736$			2.47940i			0.0913919i
$737$	37.4500	−	64.8653i	1.37949	−	2.38934i
$738$	−8.46466	−	14.6612i	−0.311589	−	0.539687i
$739$	9.69853	−	5.59945i	0.356766	−	0.205979i	−0.310895	−	0.950444i	$-0.600629\pi$
$739$	9.69853	−	5.59945i	0.356766	−	0.205979i	0.667661	+	0.744465i	$0.267295\pi$
$740$	−29.2208			−1.07418
$741$	4.01845	−	5.32272i	0.147621	−	0.195535i
$742$		0			0
$743$	−33.1315	+	19.1285i	−1.21548	+	0.701757i	−0.963947	−	0.266093i	$-0.914267\pi$
$743$	−33.1315	+	19.1285i	−1.21548	+	0.701757i	−0.251531	+	0.967849i	$0.580934\pi$
$744$	1.00000	+	1.73205i	0.0366618	+	0.0635001i
$745$	−38.2315	+	66.2189i	−1.40069	+	2.42607i
$746$			11.0715i			0.405357i
$747$	6.18297	+	3.56974i	0.226223	+	0.130610i
$748$	1.06124	+	0.612704i	0.0388026	+	0.0224027i
$749$		0			0
$750$	−6.06116	+	10.4982i	−0.221322	+	0.383342i
$751$	−0.920125	−	1.59370i	−0.0335758	−	0.0581551i	0.848749	−	0.528796i	$-0.177356\pi$
$751$	−0.920125	−	1.59370i	−0.0335758	−	0.0581551i	−0.882325	+	0.470641i	$0.844023\pi$
$752$	7.92907	−	4.57785i	0.289143	−	0.166937i
$753$	0.438826			0.0159917
$754$	0.138566	+	0.327258i	0.00504629	+	0.0119180i
$755$	−44.3157			−1.61281
$756$		0			0
$757$	10.5961	+	18.3529i	0.385120	+	0.667048i	0.991786	−	0.127909i	$-0.0408266\pi$
$757$	10.5961	+	18.3529i	0.385120	+	0.667048i	−0.606666	+	0.794957i	$0.707493\pi$
$758$	−8.40523	+	14.5583i	−0.305292	+	0.528780i
$759$			12.3926i			0.449823i
$760$	−6.86895	−	3.96579i	−0.249163	−	0.143854i
$761$	12.2381	+	7.06566i	0.443630	+	0.256130i	0.705136	−	0.709072i	$-0.250886\pi$
$761$	12.2381	+	7.06566i	0.443630	+	0.256130i	−0.261506	+	0.965202i	$0.584219\pi$
$762$		−	10.2030i		−	0.369617i
$763$		0			0
$764$	0.0604880	+	0.104768i	0.00218838	+	0.00379038i
$765$	−1.53515	+	0.886319i	−0.0555034	+	0.0320449i
$766$	16.5771			0.598955
$767$	−0.326030	−	0.769999i	−0.0117723	−	0.0278030i
$768$	0.865515			0.0312316
$769$	26.5219	−	15.3124i	0.956405	−	0.552181i	0.0613401	−	0.998117i	$-0.480463\pi$
$769$	26.5219	−	15.3124i	0.956405	−	0.552181i	0.895065	+	0.445936i	$0.147129\pi$
$770$		0			0
$771$	4.17206	−	7.22621i	0.150253	−	0.260246i
$772$			2.75550i			0.0991725i
$773$	8.48254	+	4.89740i	0.305096	+	0.176147i	0.644730	−	0.764411i	$-0.276970\pi$
$773$	8.48254	+	4.89740i	0.305096	+	0.176147i	−0.339634	+	0.940558i	$0.610303\pi$
$774$	8.92738	+	5.15422i	0.320888	+	0.185265i
$775$		−	20.2743i		−	0.728273i
$776$	7.04093	−	12.1952i	0.252755	−	0.437784i
$777$		0			0
$778$	1.01336	−	0.585065i	0.0363308	−	0.0209756i
$779$	16.0738			0.575904
$780$	6.97836	−	9.24333i	0.249865	−	0.330964i
$781$	−42.5248			−1.52166
$782$	−0.455634	+	0.263061i	−0.0162934	+	0.00940702i
$783$	−0.223977	−	0.387940i	−0.00800430	−	0.0138638i
$784$		0			0
$785$			34.6645i			1.23723i
$786$	3.84418	+	2.21944i	0.137117	+	0.0791647i
$787$	−17.8665	−	10.3152i	−0.636873	−	0.367699i	0.146536	−	0.989205i	$-0.453188\pi$
$787$	−17.8665	−	10.3152i	−0.636873	−	0.367699i	−0.783409	+	0.621507i	$0.786521\pi$
$788$			15.1253i			0.538818i
$789$	3.17911	−	5.50638i	0.113179	−	0.196032i
$790$	−17.0674	−	29.5616i	−0.607230	−	1.05175i
$791$		0			0
$792$	−12.9985			−0.461883
$793$	−26.6681	+	11.2917i	−0.947013	+	0.400981i
$794$	26.1975			0.929713
$795$	−33.6458	+	19.4254i	−1.19330	+	0.688949i
$796$	2.65320	+	4.59548i	0.0940402	+	0.162882i
$797$	−3.88584	+	6.73047i	−0.137643	+	0.238405i	−0.926604	−	0.376038i	$-0.877286\pi$
$797$	−3.88584	+	6.73047i	−0.137643	+	0.238405i	0.788961	+	0.614444i	$0.210619\pi$
$798$		0			0
$799$	1.68252	+	0.971406i	0.0595234	+	0.0343659i
$800$	−7.59837	−	4.38692i	−0.268643	−	0.155101i
$801$		−	26.5979i		−	0.939791i
$802$	5.68436	−	9.84559i	0.200722	−	0.347660i
$803$	−16.1816	−	28.0273i	−0.571036	−	0.989063i
$804$	9.72176	−	5.61286i	0.342860	−	0.197950i
$805$		0			0
$806$	−1.02278	+	8.26856i	−0.0360259	+	0.291248i
$807$	−19.3478			−0.681074
$808$	−5.32816	+	3.07622i	−0.187444	+	0.108221i
$809$	−21.2715	−	36.8433i	−0.747866	−	1.29534i	−0.948844	−	0.315746i	$-0.897745\pi$
$809$	−21.2715	−	36.8433i	−0.747866	−	1.29534i	0.200977	−	0.979596i	$-0.435588\pi$
$810$	5.23134	−	9.06094i	0.183810	−	0.318369i
$811$			22.1131i			0.776494i	0.921555	+	0.388247i	$0.126919\pi$
$811$			22.1131i			0.776494i	−0.921555	+	0.388247i	$0.873081\pi$
$812$		0			0
$813$	−7.20880	−	4.16200i	−0.252824	−	0.145968i
$814$		−	45.4680i		−	1.59365i
$815$	8.30833	−	14.3905i	0.291028	−	0.504076i
$816$	0.0918298	+	0.159054i	0.00321469	+	0.00556800i
$817$	−8.47624	+	4.89376i	−0.296546	+	0.171211i
$818$	−23.3314			−0.815763
$819$		0			0
$820$	27.9135			0.974782
$821$	21.0920	−	12.1775i	0.736115	−	0.424996i	−0.0845401	−	0.996420i	$-0.526942\pi$
$821$	21.0920	−	12.1775i	0.736115	−	0.424996i	0.820655	+	0.571424i	$0.193609\pi$
$822$	−4.06501	−	7.04081i	−0.141784	−	0.245576i
$823$	−2.37957	+	4.12153i	−0.0829465	+	0.143668i	−0.904514	−	0.426443i	$-0.859766\pi$
$823$	−2.37957	+	4.12153i	−0.0829465	+	0.143668i	0.821568	+	0.570111i	$0.193100\pi$
$824$		−	19.3491i		−	0.674056i
$825$	−37.9784	−	21.9269i	−1.32224	−	0.763395i
$826$		0			0
$827$			7.00333i			0.243530i	0.992559	+	0.121765i	$0.0388554\pi$
$827$			7.00333i			0.243530i	−0.992559	+	0.121765i	$0.961145\pi$
$828$	2.79042	−	4.83315i	0.0969738	−	0.167964i
$829$	2.87619	+	4.98170i	0.0998941	+	0.173022i	0.911641	−	0.410988i	$-0.134816\pi$
$829$	2.87619	+	4.98170i	0.0998941	+	0.173022i	−0.811747	+	0.584010i	$0.801483\pi$
$830$	−10.1946	+	5.88588i	−0.353861	+	0.204302i
$831$	−8.80998			−0.305615
$832$	2.87757	+	2.17246i	0.0997619	+	0.0753164i
$833$		0			0
$834$	11.3493	−	6.55250i	0.392993	−	0.226894i
$835$	27.2908	+	47.2691i	0.944438	+	1.63582i
$836$	6.17084	−	10.6882i	0.213423	−	0.369659i
$837$		−	10.5018i		−	0.362994i
$838$	10.9709	+	6.33402i	0.378982	+	0.218805i
$839$	35.6863	+	20.6035i	1.23203	+	0.711311i	0.967452	−	0.253054i	$-0.0814350\pi$
$839$	35.6863	+	20.6035i	1.23203	+	0.711311i	0.264575	+	0.964365i	$0.414768\pi$
$840$		0			0
$841$	14.4951	−	25.1063i	0.499832	−	0.865735i
$842$	13.8312	+	23.9564i	0.476656	+	0.825593i
$843$	−10.6207	+	6.13184i	−0.365795	+	0.211192i
$844$	−17.8982			−0.616081
$845$	46.4018	−	13.2155i	1.59627	−	0.454626i
$846$	−20.6084			−0.708532
$847$		0			0
$848$	−6.04740	−	10.4744i	−0.207669	−	0.359692i
$849$	−8.19323	+	14.1911i	−0.281191	+	0.487037i
$850$		−	1.86178i		−	0.0638586i
$851$	16.9060	+	9.76069i	0.579530	+	0.334592i
$852$	−5.51957	−	3.18673i	−0.189097	−	0.109175i
$853$			2.38939i			0.0818113i	0.999163	+	0.0409056i	$0.0130243\pi$
$853$			2.38939i			0.0818113i	−0.999163	+	0.0409056i	$0.986976\pi$
$854$		0			0
$855$	8.92654	+	15.4612i	0.305281	+	0.528762i
$856$	10.0893	−	5.82506i	0.344845	−	0.199096i
$857$	13.8037			0.471526			0.235763	−	0.971811i	$-0.424241\pi$
$857$	13.8037			0.471526			0.235763	+	0.971811i	$0.424241\pi$
$858$	14.3828	+	10.8584i	0.491020	+	0.370701i
$859$	37.7276			1.28725			0.643624	−	0.765342i	$-0.277430\pi$
$859$	37.7276			1.28725			0.643624	+	0.765342i	$0.277430\pi$
$860$	−14.7197	+	8.49841i	−0.501937	+	0.289793i
$861$		0			0
$862$	−3.20696	+	5.55462i	−0.109230	+	0.189191i
$863$			25.5180i			0.868643i	0.900758	+	0.434322i	$0.143012\pi$
$863$			25.5180i			0.868643i	−0.900758	+	0.434322i	$0.856988\pi$
$864$	−3.93584	−	2.27236i	−0.133900	−	0.0773072i
$865$	44.2443	+	25.5444i	1.50435	+	0.868537i
$866$			0.0650270i			0.00220971i
$867$	7.33739	−	12.7087i	0.249191	−	0.431611i
$868$		0			0
$869$	45.9983	−	26.5571i	1.56039	−	0.900889i
$870$	0.316613			0.0107342
$871$	46.4103	+	5.74073i	1.57255	+	0.194517i
$872$	−5.73307			−0.194146
$873$	−27.4501	+	15.8483i	−0.929045	+	0.536384i
$874$	2.64941	+	4.58891i	0.0896175	+	0.155222i
$875$		0			0
$876$		−	4.85047i		−	0.163882i
$877$	10.7726	+	6.21955i	0.363764	+	0.210019i	0.670731	−	0.741701i	$-0.265981\pi$
$877$	10.7726	+	6.21955i	0.363764	+	0.210019i	−0.306966	+	0.951720i	$0.599314\pi$
$878$	31.8505	+	18.3889i	1.07490	+	0.620596i
$879$			3.16763i			0.106842i
$880$	10.7162	−	18.5609i	0.361242	−	0.625689i
$881$	11.2710	+	19.5219i	0.379728	+	0.657709i	0.991023	−	0.133694i	$-0.0426841\pi$
$881$	11.2710	+	19.5219i	0.379728	+	0.657709i	−0.611294	+	0.791404i	$0.709351\pi$
$882$		0			0
$883$	−15.1548			−0.509998			−0.254999	−	0.966941i	$-0.582075\pi$
$883$	−15.1548			−0.509998			−0.254999	+	0.966941i	$0.582075\pi$
$884$	−0.0939218	+	0.759300i	−0.00315893	+	0.0255380i
$885$	−0.744954			−0.0250413
$886$	7.32989	−	4.23191i	0.246252	−	0.142174i
$887$	20.8875	+	36.1781i	0.701332	+	1.21474i	0.967999	+	0.250954i	$0.0807443\pi$
$887$	20.8875	+	36.1781i	0.701332	+	1.21474i	−0.266667	+	0.963789i	$0.585922\pi$
$888$	3.40729	−	5.90159i	0.114341	−	0.198044i
$889$		0			0
$890$	37.9798	+	21.9277i	1.27309	+	0.735017i
$891$	14.0990	+	8.14004i	0.472333	+	0.272702i
$892$		−	16.4385i		−	0.550402i
$893$	9.78349	−	16.9455i	0.327392	−	0.567060i
$894$	−8.91597	−	15.4429i	−0.298195	−	0.516488i
$895$	49.1072	−	28.3521i	1.64147	−	0.947705i
$896$		0			0
$897$	−7.12498	+	3.01684i	−0.237896	+	0.100729i
$898$	22.6303			0.755183
$899$	−0.197248	+	0.113881i	−0.00657860	+	0.00379815i
$900$	9.87445	+	17.1031i	0.329148	+	0.570102i
$901$	1.28324	−	2.22264i	0.0427509	−	0.0740468i
$902$			43.4339i			1.44619i
$903$		0			0
$904$	−14.3062	−	8.25971i	−0.475818	−	0.274714i
$905$		−	6.18853i		−	0.205714i
$906$	5.16743	−	8.95026i	0.171676	−	0.297352i
$907$	2.14376	+	3.71310i	0.0711823	+	0.123291i	0.899420	−	0.437086i	$-0.143989\pi$
$907$	2.14376	+	3.71310i	0.0711823	+	0.123291i	−0.828237	+	0.560377i	$0.810656\pi$
$908$	4.87655	−	2.81547i	0.161834	−	0.0934348i
$909$	13.8484			0.459323
$910$		0			0
$911$	−3.87618			−0.128423			−0.0642117	−	0.997936i	$-0.520453\pi$
$911$	−3.87618			−0.128423			−0.0642117	+	0.997936i	$0.520453\pi$
$912$	1.60191	−	0.924862i	0.0530445	−	0.0306252i
$913$	−9.15853	−	15.8630i	−0.303103	−	0.524990i
$914$	8.15851	−	14.1310i	0.269859	−	0.467410i
$915$			25.8007i			0.852945i
$916$	24.0084	+	13.8613i	0.793260	+	0.457989i
$917$		0			0
$918$		−	0.964376i		−	0.0318291i
$919$	−22.9524	+	39.7547i	−0.757129	+	1.31139i	0.187180	+	0.982326i	$0.440065\pi$
$919$	−22.9524	+	39.7547i	−0.757129	+	1.31139i	−0.944309	+	0.329060i	$0.893268\pi$
$920$	4.60091	+	7.96901i	0.151688	+	0.262731i
$921$	−14.7653	+	8.52476i	−0.486534	+	0.280900i
$922$	19.2778			0.634882
$923$	−10.3522	−	24.4491i	−0.340745	−	0.804752i
$924$		0			0
$925$	−59.8253	+	34.5401i	−1.96704	+	1.13567i
$926$	−1.35109	−	2.34015i	−0.0443995	−	0.0769022i
$927$	−21.7762	+	37.7176i	−0.715226	+	1.23881i
$928$			0.0985660i			0.00323559i
$929$	−8.51833	−	4.91806i	−0.279477	−	0.161356i	0.353709	−	0.935355i	$-0.384920\pi$
$929$	−8.51833	−	4.91806i	−0.279477	−	0.161356i	−0.633187	+	0.773999i	$0.718254\pi$
$930$	6.42818	+	3.71131i	0.210788	+	0.121699i
$931$		0			0
$932$	−10.0552	+	17.4161i	−0.329368	+	0.570483i
$933$	7.34325	+	12.7189i	0.240407	+	0.416397i
$934$	−15.9267	+	9.19528i	−0.521137	+	0.300879i
$935$	4.54788			0.148731
$936$	−3.16435	−	7.47336i	−0.103430	−	0.244274i
$937$	−21.5135			−0.702815			−0.351407	−	0.936223i	$-0.614297\pi$
$937$	−21.5135			−0.702815			−0.351407	+	0.936223i	$0.614297\pi$
$938$		0			0
$939$	−1.96383	−	3.40145i	−0.0640871	−	0.111002i
$940$	16.9898	−	29.4272i	0.554147	−	0.959811i
$941$		−	6.41845i		−	0.209236i	−0.994513	−	0.104618i	$-0.966638\pi$
$941$		−	6.41845i		−	0.209236i	0.994513	−	0.104618i	$-0.0333619\pi$
$942$	−7.00104	−	4.04205i	−0.228106	−	0.131697i
$943$	−16.1497	−	9.32402i	−0.525906	−	0.303632i
$944$		−	0.231914i		−	0.00754816i
$945$		0			0
$946$	−13.2237	−	22.9041i	−0.429939	−	0.744675i
$947$	6.55812	−	3.78633i	0.213110	−	0.123039i	−0.389646	−	0.920965i	$-0.627403\pi$
$947$	6.55812	−	3.78633i	0.213110	−	0.123039i	0.602756	+	0.797926i	$0.294069\pi$
$948$	7.96057			0.258547
$949$	12.1748	−	16.1263i	0.395209	−	0.523483i
$950$	−18.7509			−0.608360
$951$	−21.8770	+	12.6307i	−0.709412	+	0.409579i
$952$		0			0
$953$	−17.9022	+	31.0075i	−0.579909	+	1.00443i	0.415580	+	0.909557i	$0.363579\pi$
$953$	−17.9022	+	31.0075i	−0.579909	+	1.00443i	−0.995489	+	0.0948754i	$0.969755\pi$
$954$			27.2240i			0.881409i
$955$	0.388828	+	0.224490i	0.0125822	+	0.00726432i
$956$	−5.74147	−	3.31484i	−0.185692	−	0.107210i
$957$			0.492656i			0.0159253i
$958$	20.4354	−	35.3951i	0.660238	−	1.14357i
$959$		0			0
$960$	2.78184	−	1.60610i	0.0897836	−	0.0518366i
$961$	25.6604			0.827754
$962$	26.1413	−	11.0687i	0.842829	−	0.356868i
$963$	−26.2231			−0.845027
$964$	−1.40025	+	0.808433i	−0.0450989	+	0.0260379i
$965$	5.11326	+	8.85642i	0.164602	+	0.285098i
$966$		0			0
$967$		−	32.3876i		−	1.04152i	−0.853704	−	0.520758i	$-0.825649\pi$
$967$		−	32.3876i		−	1.04152i	0.853704	−	0.520758i	$-0.174351\pi$
$968$	19.3549	+	11.1745i	0.622089	+	0.359163i
$969$	0.339920	+	0.196253i	0.0109198	+	0.00630455i
$970$		−	52.2622i		−	1.67804i
$971$	17.2033	−	29.7969i	0.552079	−	0.956229i	−0.446045	−	0.895010i	$-0.647168\pi$
$971$	17.2033	−	29.7969i	0.552079	−	0.956229i	0.998124	−	0.0612186i	$-0.0194987\pi$
$972$	8.03708	+	13.9206i	0.257789	+	0.446504i
$973$		0			0
$974$	−17.6293			−0.564880
$975$	3.36118	−	27.1731i	0.107644	−	0.870235i
$976$	−8.03211			−0.257102
$977$	20.0471	−	11.5742i	0.641364	−	0.370291i	−0.143776	−	0.989610i	$-0.545924\pi$
$977$	20.0471	−	11.5742i	0.641364	−	0.370291i	0.785140	+	0.619319i	$0.212591\pi$
$978$	1.93759	+	3.35600i	0.0619571	+	0.107313i
$979$	−34.1198	+	59.0972i	−1.09047	+	1.88876i
$980$		0			0
$981$	11.1756	+	6.45224i	0.356810	+	0.206004i
$982$	16.3332	+	9.42997i	0.521213	+	0.300922i
$983$		−	47.0579i		−	1.50092i	−0.660919	−	0.750458i	$-0.729833\pi$
$983$		−	47.0579i		−	1.50092i	0.660919	−	0.750458i	$-0.270167\pi$
$984$	−3.25485	+	5.63757i	−0.103761	+	0.179719i
$985$	28.0674	+	48.6142i	0.894303	+	1.54898i
$986$	−0.0181133	+	0.0104577i	−0.000576844	+	0.000333041i
$987$		0			0
$988$	7.64727	+	0.945931i	0.243292	+	0.0300941i
$989$	11.3550			0.361068
$990$	−41.7785	+	24.1208i	−1.32781	+	0.766611i
$991$	5.95052	+	10.3066i	0.189025	+	0.327400i	0.944925	−	0.327286i	$-0.106134\pi$
$991$	5.95052	+	10.3066i	0.189025	+	0.327400i	−0.755901	+	0.654686i	$0.772801\pi$
$992$	−1.15538	+	2.00118i	−0.0366834	+	0.0635375i
$993$		−	4.15916i		−	0.131987i
$994$		0			0
$995$	17.0553	+	9.84686i	0.540688	+	0.312167i
$996$		−	2.74529i		−	0.0869879i
$997$	6.50714	−	11.2707i	0.206083	−	0.356946i	−0.744394	−	0.667740i	$-0.767262\pi$
$997$	6.50714	−	11.2707i	0.206083	−	0.356946i	0.950477	+	0.310794i	$0.100595\pi$
$998$	1.05371	+	1.82508i	0.0333546	+	0.0577718i
$999$	−30.9886	+	17.8913i	−0.980435	+	0.566055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.m.c.491.1		12
7.2	even	3		1274.2.v.d.361.6		12
7.3	odd	6		1274.2.o.d.569.3		12
7.4	even	3		1274.2.o.e.569.1		12
7.5	odd	6		1274.2.v.e.361.4		12
7.6	odd	2		182.2.m.b.127.3	yes	12
13.4	even	6	inner	1274.2.m.c.589.1		12
21.20	even	2		1638.2.bj.g.127.4		12
28.27	even	2		1456.2.cc.d.673.2		12
91.4	even	6		1274.2.v.d.667.6		12
91.17	odd	6		1274.2.v.e.667.4		12
91.30	even	6		1274.2.o.e.459.4		12
91.41	even	12		2366.2.a.bf.1.2		6
91.55	odd	6		2366.2.d.r.337.2		12
91.62	odd	6		2366.2.d.r.337.8		12
91.69	odd	6		182.2.m.b.43.3	✓	12
91.76	even	12		2366.2.a.bh.1.2		6
91.82	odd	6		1274.2.o.d.459.6		12
273.251	even	6		1638.2.bj.g.1135.6		12
364.251	even	6		1456.2.cc.d.225.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.3	✓	12	91.69	odd	6
182.2.m.b.127.3	yes	12	7.6	odd	2
1274.2.m.c.491.1		12	1.1	even	1	trivial
1274.2.m.c.589.1		12	13.4	even	6	inner
1274.2.o.d.459.6		12	91.82	odd	6
1274.2.o.d.569.3		12	7.3	odd	6
1274.2.o.e.459.4		12	91.30	even	6
1274.2.o.e.569.1		12	7.4	even	3
1274.2.v.d.361.6		12	7.2	even	3
1274.2.v.d.667.6		12	91.4	even	6
1274.2.v.e.361.4		12	7.5	odd	6
1274.2.v.e.667.4		12	91.17	odd	6
1456.2.cc.d.225.2		12	364.251	even	6
1456.2.cc.d.673.2		12	28.27	even	2
1638.2.bj.g.127.4		12	21.20	even	2
1638.2.bj.g.1135.6		12	273.251	even	6
2366.2.a.bf.1.2		6	91.41	even	12
2366.2.a.bh.1.2		6	91.76	even	12
2366.2.d.r.337.2		12	91.55	odd	6
2366.2.d.r.337.8		12	91.62	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.432757 - 0.749558i) q^{3} +(0.500000 - 0.866025i) q^{4} -3.71131i q^{5} +(0.749558 + 0.432757i) q^{6} +1.00000i q^{8} +(1.12544 - 1.94932i) q^{9} +(1.85566 + 3.21409i) q^{10} +(-5.00118 + 2.88743i) q^{11} -0.865515 q^{12} +(-2.87757 - 2.17246i) q^{13} +(-2.78184 + 1.60610i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.106098 - 0.183768i) q^{17} +2.25088i q^{18} +(-1.85081 - 1.06857i) q^{19} +(-3.21409 - 1.85566i) q^{20} +(2.88743 - 5.00118i) q^{22} +(1.23970 + 2.14722i) q^{23} +(0.749558 - 0.432757i) q^{24} -8.77384 q^{25} +(3.57828 + 0.442616i) q^{26} -4.54472 q^{27} +(0.0492830 + 0.0853606i) q^{29} +(1.60610 - 2.78184i) q^{30} +2.31076i q^{31} +(0.866025 + 0.500000i) q^{32} +(4.32860 + 2.49912i) q^{33} +0.212197i q^{34} +(-1.12544 - 1.94932i) q^{36} +(6.81859 - 3.93672i) q^{37} +2.13714 q^{38} +(-0.383091 + 3.09706i) q^{39} +3.71131 q^{40} +(-6.51354 + 3.76060i) q^{41} +(2.28987 - 3.96617i) q^{43} +5.77486i q^{44} +(-7.23455 - 4.17687i) q^{45} +(-2.14722 - 1.23970i) q^{46} +9.15570i q^{47} +(-0.432757 + 0.749558i) q^{48} +(7.59837 - 4.38692i) q^{50} -0.183660 q^{51} +(-3.32019 + 1.40582i) q^{52} +12.0948 q^{53} +(3.93584 - 2.27236i) q^{54} +(10.7162 + 18.5609i) q^{55} +1.84972i q^{57} +(-0.0853606 - 0.0492830i) q^{58} +(0.200843 + 0.115957i) q^{59} +3.21220i q^{60} +(4.01605 - 6.95601i) q^{61} +(-1.15538 - 2.00118i) q^{62} -1.00000 q^{64} +(-8.06267 + 10.6796i) q^{65} -4.99823 q^{66} +(-11.2323 + 6.48500i) q^{67} +(-0.106098 - 0.183768i) q^{68} +(1.07298 - 1.85845i) q^{69} +(6.37721 + 3.68188i) q^{71} +(1.94932 + 1.12544i) q^{72} +5.60414i q^{73} +(-3.93672 + 6.81859i) q^{74} +(3.79695 + 6.57650i) q^{75} +(-1.85081 + 1.06857i) q^{76} +(-1.21676 - 2.87367i) q^{78} -9.19749 q^{79} +(-3.21409 + 1.85566i) q^{80} +(-1.40956 - 2.44144i) q^{81} +(3.76060 - 6.51354i) q^{82} +3.17186i q^{83} +(-0.682021 - 0.393765i) q^{85} +4.57973i q^{86} +(0.0426552 - 0.0738809i) q^{87} +(-2.88743 - 5.00118i) q^{88} +(10.2335 - 5.90833i) q^{89} +8.35373 q^{90} +2.47940 q^{92} +(1.73205 - 1.00000i) q^{93} +(-4.57785 - 7.92907i) q^{94} +(-3.96579 + 6.86895i) q^{95} -0.865515i q^{96} +(-12.1952 - 7.04093i) q^{97} +12.9985i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} + 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} - 18 q^{11} + 4 q^{12} + 8 q^{13} - 6 q^{15} - 6 q^{16} - 4 q^{17} - 12 q^{19} - 2 q^{22} - 6 q^{23} - 6 q^{24} - 24 q^{25} + 14 q^{26} - 40 q^{27}+ \cdots - 60 q^{97}+O(q^{100}) \) 12 * q + 2 * q^3 + 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 - 18 * q^11 + 4 * q^12 + 8 * q^13 - 6 * q^15 - 6 * q^16 - 4 * q^17 - 12 * q^19 - 2 * q^22 - 6 * q^23 - 6 * q^24 - 24 * q^25 + 14 * q^26 - 40 * q^27 - 10 * q^29 + 14 * q^30 - 12 * q^33 + 6 * q^36 - 6 * q^37 - 8 * q^38 - 54 * q^39 + 4 * q^40 + 24 * q^41 + 26 * q^43 - 72 * q^45 - 6 * q^46 + 2 * q^48 - 12 * q^50 - 36 * q^51 + 4 * q^52 + 36 * q^53 + 36 * q^54 + 6 * q^55 + 24 * q^58 - 6 * q^59 + 28 * q^61 + 2 * q^62 - 12 * q^64 - 34 * q^65 - 42 * q^67 + 4 * q^68 - 32 * q^69 + 48 * q^71 + 48 * q^75 - 12 * q^76 - 8 * q^78 + 44 * q^79 - 34 * q^81 - 6 * q^82 + 54 * q^85 - 2 * q^87 + 2 * q^88 - 12 * q^89 - 12 * q^90 - 12 * q^92 - 8 * q^94 + 32 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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