LMFDB - Embedded newform 1274.2.v.e.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(361,1274)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("1274.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.v (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.1729412175$
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			361.3
Root			$0.500000 + 3.15681i$ of defining polynomial
Character	$\chi$	$=$	1274.361
Dual form			1274.2.v.e.667.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +2.29079 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.781015 + 0.450919i) q^{5} +(-1.98388 - 1.14539i) q^{6} -1.00000i q^{8} +2.24770 q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +2.29079 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.781015 + 0.450919i) q^{5} +(-1.98388 - 1.14539i) q^{6} -1.00000i q^{8} +2.24770 q^{9} +0.901839 q^{10} -4.33716i q^{11} +(1.14539 + 1.98388i) q^{12} +(-0.426876 - 3.58019i) q^{13} +(-1.78914 + 1.03296i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.53296 + 4.38722i) q^{17} +(-1.94657 - 1.12385i) q^{18} -6.17238i q^{19} +(-0.781015 - 0.450919i) q^{20} +(-2.16858 + 3.75609i) q^{22} +(4.22559 - 7.31893i) q^{23} -2.29079i q^{24} +(-2.09334 + 3.62578i) q^{25} +(-1.42041 + 3.31398i) q^{26} -1.72335 q^{27} +(1.09643 + 1.89907i) q^{29} +2.06592 q^{30} +(0.756094 + 0.436531i) q^{31} +(0.866025 - 0.500000i) q^{32} -9.93552i q^{33} -5.06592i q^{34} +(1.12385 + 1.94657i) q^{36} +(-0.124973 - 0.0721531i) q^{37} +(-3.08619 + 5.34544i) q^{38} +(-0.977882 - 8.20146i) q^{39} +(0.450919 + 0.781015i) q^{40} +(-3.46110 + 1.99827i) q^{41} +(3.85426 - 6.67577i) q^{43} +(3.75609 - 2.16858i) q^{44} +(-1.75549 + 1.01353i) q^{45} +(-7.31893 + 4.22559i) q^{46} +(2.52979 - 1.46057i) q^{47} +(-1.14539 + 1.98388i) q^{48} +(3.62578 - 2.09334i) q^{50} +(5.80247 + 10.0502i) q^{51} +(2.88710 - 2.15978i) q^{52} +(-0.848493 + 1.46963i) q^{53} +(1.49246 + 0.861675i) q^{54} +(1.95571 + 3.38739i) q^{55} -14.1396i q^{57} -2.19286i q^{58} +(7.40394 - 4.27467i) q^{59} +(-1.78914 - 1.03296i) q^{60} +8.33440 q^{61} +(-0.436531 - 0.756094i) q^{62} -1.00000 q^{64} +(1.94777 + 2.60370i) q^{65} +(-4.96776 + 8.60441i) q^{66} -10.3828i q^{67} +(-2.53296 + 4.38722i) q^{68} +(9.67992 - 16.7661i) q^{69} +(-2.83932 - 1.63928i) q^{71} -2.24770i q^{72} +(0.466808 + 0.269511i) q^{73} +(0.0721531 + 0.124973i) q^{74} +(-4.79540 + 8.30588i) q^{75} +(5.34544 - 3.08619i) q^{76} +(-3.25386 + 7.59161i) q^{78} +(-3.26674 - 5.65817i) q^{79} -0.901839i q^{80} -10.6909 q^{81} +3.99654 q^{82} +13.2348i q^{83} +(-3.95656 - 2.28432i) q^{85} +(-6.67577 + 3.85426i) q^{86} +(2.51168 + 4.35037i) q^{87} -4.33716 q^{88} +(6.74790 + 3.89590i) q^{89} +2.02707 q^{90} +8.45117 q^{92} +(1.73205 + 1.00000i) q^{93} -2.92115 q^{94} +(2.78325 + 4.82072i) q^{95} +(1.98388 - 1.14539i) q^{96} +(10.1378 + 5.85305i) q^{97} -9.74866i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9	$ 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9} + 4 q^{10} + 2 q^{12} - 8 q^{13} - 6 q^{15} - 6 q^{16} + 4 q^{17} - 2 q^{22} - 6 q^{23} + 12 q^{25} + 16 q^{26} + 40 q^{27} - 10 q^{29} - 28 q^{30} - 18 q^{31} + 6 q^{36} + 6 q^{37} - 4 q^{38} + 30 q^{39} + 2 q^{40} - 24 q^{41} + 26 q^{43} + 18 q^{44} - 72 q^{45} + 6 q^{46} - 48 q^{47} - 2 q^{48} - 12 q^{50} + 18 q^{51} - 4 q^{52} - 18 q^{53} + 36 q^{54} - 6 q^{55} - 6 q^{59} - 6 q^{60} + 56 q^{61} - 2 q^{62} - 12 q^{64} + 38 q^{65} - 4 q^{68} + 32 q^{69} + 48 q^{71} + 48 q^{73} - 48 q^{75} + 12 q^{76} - 8 q^{78} - 22 q^{79} + 68 q^{81} - 12 q^{82} + 54 q^{85} - 6 q^{86} + 2 q^{87} - 4 q^{88} - 12 q^{89} + 12 q^{90} - 12 q^{92} - 16 q^{94} + 32 q^{95} - 6 q^{96} + 60 q^{97}+O(q^{100}) $ 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9 + 4 * q^10 + 2 * q^12 - 8 * q^13 - 6 * q^15 - 6 * q^16 + 4 * q^17 - 2 * q^22 - 6 * q^23 + 12 * q^25 + 16 * q^26 + 40 * q^27 - 10 * q^29 - 28 * q^30 - 18 * q^31 + 6 * q^36 + 6 * q^37 - 4 * q^38 + 30 * q^39 + 2 * q^40 - 24 * q^41 + 26 * q^43 + 18 * q^44 - 72 * q^45 + 6 * q^46 - 48 * q^47 - 2 * q^48 - 12 * q^50 + 18 * q^51 - 4 * q^52 - 18 * q^53 + 36 * q^54 - 6 * q^55 - 6 * q^59 - 6 * q^60 + 56 * q^61 - 2 * q^62 - 12 * q^64 + 38 * q^65 - 4 * q^68 + 32 * q^69 + 48 * q^71 + 48 * q^73 - 48 * q^75 + 12 * q^76 - 8 * q^78 - 22 * q^79 + 68 * q^81 - 12 * q^82 + 54 * q^85 - 6 * q^86 + 2 * q^87 - 4 * q^88 - 12 * q^89 + 12 * q^90 - 12 * q^92 - 16 * q^94 + 32 * q^95 - 6 * q^96 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	2.29079			1.32259			0.661293	−	0.750128i	$-0.270008\pi$
$3$	2.29079			1.32259			0.661293	+	0.750128i	$0.270008\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.781015	+	0.450919i	−0.349281	+	0.201657i	−0.664368	−	0.747405i	$-0.731299\pi$
$5$	−0.781015	+	0.450919i	−0.349281	+	0.201657i	0.315088	+	0.949063i	$0.397966\pi$
$6$	−1.98388	−	1.14539i	−0.809915	−	0.467605i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	2.24770			0.749235
$10$	0.901839			0.285186
$11$		−	4.33716i		−	1.30770i	−0.756622	−	0.653852i	$-0.773152\pi$
$11$		−	4.33716i		−	1.30770i	0.756622	−	0.653852i	$-0.226848\pi$
$12$	1.14539	+	1.98388i	0.330647	+	0.572697i
$13$	−0.426876	−	3.58019i	−0.118394	−	0.992967i
$13$	−0.426876	−	3.58019i	−0.118394	−	0.992967i
$14$		0			0
$15$	−1.78914	+	1.03296i	−0.461954	+	0.266709i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.53296	+	4.38722i	0.614333	+	1.06406i	0.990501	+	0.137505i	$0.0439082\pi$
$17$	2.53296	+	4.38722i	0.614333	+	1.06406i	−0.376168	+	0.926551i	$0.622758\pi$
$18$	−1.94657	−	1.12385i	−0.458811	−	0.264894i
$19$		−	6.17238i		−	1.41604i	−0.706192	−	0.708021i	$-0.749588\pi$
$19$		−	6.17238i		−	1.41604i	0.706192	−	0.708021i	$-0.250412\pi$
$20$	−0.781015	−	0.450919i	−0.174640	−	0.100829i
$21$		0			0
$22$	−2.16858	+	3.75609i	−0.462343	+	0.800802i
$23$	4.22559	−	7.31893i	0.881096	−	1.52610i	0.0309711	−	0.999520i	$-0.490140\pi$
$23$	4.22559	−	7.31893i	0.881096	−	1.52610i	0.850124	−	0.526582i	$-0.176527\pi$
$24$		−	2.29079i		−	0.467605i
$25$	−2.09334	+	3.62578i	−0.418669	+	0.725155i
$26$	−1.42041	+	3.31398i	−0.278565	+	0.649924i
$27$	−1.72335			−0.331659
$28$		0			0
$29$	1.09643	+	1.89907i	0.203602	+	0.352649i	0.949686	−	0.313203i	$-0.101402\pi$
$29$	1.09643	+	1.89907i	0.203602	+	0.352649i	−0.746085	+	0.665851i	$0.768069\pi$
$30$	2.06592			0.377184
$31$	0.756094	+	0.436531i	0.135799	+	0.0784033i	0.566360	−	0.824158i	$-0.308351\pi$
$31$	0.756094	+	0.436531i	0.135799	+	0.0784033i	−0.430562	+	0.902561i	$0.641684\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		−	9.93552i		−	1.72955i
$34$		−	5.06592i		−	0.868798i
$35$		0			0
$36$	1.12385	+	1.94657i	0.187309	+	0.324428i
$37$	−0.124973	−	0.0721531i	−0.0205454	−	0.0118619i	0.489692	−	0.871895i	$-0.337109\pi$
$37$	−0.124973	−	0.0721531i	−0.0205454	−	0.0118619i	−0.510238	+	0.860034i	$0.670443\pi$
$38$	−3.08619	+	5.34544i	−0.500646	+	0.867145i
$39$	−0.977882	−	8.20146i	−0.156586	−	1.31328i
$40$	0.450919	+	0.781015i	0.0712966	+	0.123489i
$41$	−3.46110	+	1.99827i	−0.540533	+	0.312077i	−0.745295	−	0.666735i	$-0.767691\pi$
$41$	−3.46110	+	1.99827i	−0.540533	+	0.312077i	0.204762	+	0.978812i	$0.434358\pi$
$42$		0			0
$43$	3.85426	−	6.67577i	0.587768	−	1.01804i	−0.406756	−	0.913537i	$-0.633340\pi$
$43$	3.85426	−	6.67577i	0.587768	−	1.01804i	0.994524	−	0.104508i	$-0.0333267\pi$
$44$	3.75609	−	2.16858i	0.566253	−	0.326926i
$45$	−1.75549	+	1.01353i	−0.261693	+	0.151089i
$46$	−7.31893	+	4.22559i	−1.07912	+	0.623029i
$47$	2.52979	−	1.46057i	0.369008	−	0.213047i	−0.304017	−	0.952667i	$-0.598328\pi$
$47$	2.52979	−	1.46057i	0.369008	−	0.213047i	0.673025	+	0.739620i	$0.264995\pi$
$48$	−1.14539	+	1.98388i	−0.165323	+	0.286348i
$49$		0			0
$50$	3.62578	−	2.09334i	0.512762	−	0.296043i
$51$	5.80247	+	10.0502i	0.812509	+	1.40731i
$52$	2.88710	−	2.15978i	0.400369	−	0.299508i
$53$	−0.848493	+	1.46963i	−0.116549	+	0.201870i	−0.918398	−	0.395658i	$-0.870517\pi$
$53$	−0.848493	+	1.46963i	−0.116549	+	0.201870i	0.801849	+	0.597527i	$0.203850\pi$
$54$	1.49246	+	0.861675i	0.203099	+	0.117259i
$55$	1.95571	+	3.38739i	0.263708	+	0.456756i
$56$		0			0
$57$		−	14.1396i		−	1.87284i
$58$		−	2.19286i		−	0.287936i
$59$	7.40394	−	4.27467i	0.963911	−	0.556514i	0.0665363	−	0.997784i	$-0.478805\pi$
$59$	7.40394	−	4.27467i	0.963911	−	0.556514i	0.897374	+	0.441270i	$0.145472\pi$
$60$	−1.78914	−	1.03296i	−0.230977	−	0.133355i
$61$	8.33440			1.06711			0.533555	−	0.845765i	$-0.320856\pi$
$61$	8.33440			1.06711			0.533555	+	0.845765i	$0.320856\pi$
$62$	−0.436531	−	0.756094i	−0.0554395	−	0.0960241i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.94777	+	2.60370i	0.241592	+	0.322949i
$66$	−4.96776	+	8.60441i	−0.611489	+	1.05913i
$67$		−	10.3828i		−	1.26847i	−0.773142	−	0.634233i	$-0.781316\pi$
$67$		−	10.3828i		−	1.26847i	0.773142	−	0.634233i	$-0.218684\pi$
$68$	−2.53296	+	4.38722i	−0.307167	+	0.532028i
$69$	9.67992	−	16.7661i	1.16532	−	2.01840i
$70$		0			0
$71$	−2.83932	−	1.63928i	−0.336965	−	0.194547i	0.321964	−	0.946752i	$-0.395657\pi$
$71$	−2.83932	−	1.63928i	−0.336965	−	0.194547i	−0.658929	+	0.752205i	$0.728990\pi$
$72$		−	2.24770i		−	0.264894i
$73$	0.466808	+	0.269511i	0.0546357	+	0.0315439i	0.527069	−	0.849822i	$-0.323291\pi$
$73$	0.466808	+	0.269511i	0.0546357	+	0.0315439i	−0.472433	+	0.881366i	$0.656624\pi$
$74$	0.0721531	+	0.124973i	0.00838763	+	0.0145278i
$75$	−4.79540	+	8.30588i	−0.553725	+	0.959081i
$76$	5.34544	−	3.08619i	0.613164	−	0.354010i
$77$		0			0
$78$	−3.25386	+	7.59161i	−0.368427	+	0.859581i
$79$	−3.26674	−	5.65817i	−0.367537	−	0.636593i	0.621643	−	0.783301i	$-0.286466\pi$
$79$	−3.26674	−	5.65817i	−0.367537	−	0.636593i	−0.989180	+	0.146708i	$0.953132\pi$
$80$		−	0.901839i		−	0.100829i
$81$	−10.6909			−1.18788
$82$	3.99654			0.441343
$83$			13.2348i			1.45271i	0.687319	+	0.726356i	$0.258788\pi$
$83$			13.2348i			1.45271i	−0.687319	+	0.726356i	$0.741212\pi$
$84$		0			0
$85$	−3.95656	−	2.28432i	−0.429149	−	0.247769i
$86$	−6.67577	+	3.85426i	−0.719866	+	0.415615i
$87$	2.51168	+	4.35037i	0.269281	+	0.466408i
$88$	−4.33716			−0.462343
$89$	6.74790	+	3.89590i	0.715276	+	0.412965i	0.813011	−	0.582248i	$-0.197827\pi$
$89$	6.74790	+	3.89590i	0.715276	+	0.412965i	−0.0977357	+	0.995212i	$0.531160\pi$
$90$	2.02707			0.213672
$91$		0			0
$92$	8.45117			0.881096
$93$	1.73205	+	1.00000i	0.179605	+	0.103695i
$94$	−2.92115			−0.301294
$95$	2.78325	+	4.82072i	0.285555	+	0.494596i
$96$	1.98388	−	1.14539i	0.202479	−	0.116901i
$97$	10.1378	+	5.85305i	1.02934	+	0.594287i	0.916794	−	0.399360i	$-0.130768\pi$
$97$	10.1378	+	5.85305i	1.02934	+	0.594287i	0.112541	+	0.993647i	$0.464101\pi$
$98$		0			0
$99$		−	9.74866i		−	0.979777i
$100$	−4.18669			−0.418669
$101$	10.7429			1.06896			0.534479	−	0.845182i	$-0.320508\pi$
$101$	10.7429			1.06896			0.534479	+	0.845182i	$0.320508\pi$
$102$		−	11.6049i		−	1.14906i
$103$	−2.40550	−	4.16644i	−0.237021	−	0.410532i	0.722837	−	0.691018i	$-0.242838\pi$
$103$	−2.40550	−	4.16644i	−0.237021	−	0.410532i	−0.959858	+	0.280486i	$0.909504\pi$
$104$	−3.58019	+	0.426876i	−0.351067	+	0.0418586i
$105$		0			0
$106$	1.46963	−	0.848493i	0.142743	−	0.0824129i
$107$	−6.82652	+	11.8239i	−0.659944	+	1.14306i	0.320686	+	0.947186i	$0.396087\pi$
$107$	−6.82652	+	11.8239i	−0.659944	+	1.14306i	−0.980630	+	0.195871i	$0.937247\pi$
$108$	−0.861675	−	1.49246i	−0.0829147	−	0.143612i
$109$	4.43186	+	2.55874i	0.424495	+	0.245082i	0.696999	−	0.717072i	$-0.254518\pi$
$109$	4.43186	+	2.55874i	0.424495	+	0.245082i	−0.272503	+	0.962155i	$0.587852\pi$
$110$		−	3.91142i		−	0.372940i
$111$	−0.286286	−	0.165287i	−0.0271731	−	0.0156884i
$112$		0			0
$113$	−8.96603	+	15.5296i	−0.843453	+	1.46090i	0.0435052	+	0.999053i	$0.486147\pi$
$113$	−8.96603	+	15.5296i	−0.843453	+	1.46090i	−0.886958	+	0.461850i	$0.847186\pi$
$114$	−7.06980	+	12.2453i	−0.662148	+	1.14687i
$115$			7.62159i			0.710717i
$116$	−1.09643	+	1.89907i	−0.101801	+	0.176324i
$117$	−0.959491	−	8.04721i	−0.0887049	−	0.743965i
$118$	−8.54933			−0.787030
$119$		0			0
$120$	1.03296	+	1.78914i	0.0942959	+	0.163325i
$121$	−7.81099			−0.710090
$122$	−7.21780	−	4.16720i	−0.653469	−	0.377281i
$123$	−7.92864	+	4.57761i	−0.714902	+	0.412749i
$124$			0.873062i			0.0784033i
$125$		−	8.28491i		−	0.741025i
$126$		0			0
$127$	−9.75681	−	16.8993i	−0.865777	−	1.49957i	−0.866273	−	0.499570i	$-0.833491\pi$
$127$	−9.75681	−	16.8993i	−0.865777	−	1.49957i	0.000496195	−	1.00000i	$-0.499842\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	8.82928	−	15.2928i	0.777375	−	1.34645i
$130$	−0.384973	−	3.22876i	−0.0337644	−	0.283181i
$131$	10.3248	+	17.8831i	0.902083	+	1.56245i	0.824785	+	0.565446i	$0.191296\pi$
$131$	10.3248	+	17.8831i	0.902083	+	1.56245i	0.0772984	+	0.997008i	$0.475371\pi$
$132$	8.60441	−	4.96776i	0.748918	−	0.432388i
$133$		0			0
$134$	−5.19142	+	8.99180i	−0.448470	+	0.776773i
$135$	1.34596	−	0.777092i	0.115842	−	0.0668814i
$136$	4.38722	−	2.53296i	0.376201	−	0.217200i
$137$	−2.76224	+	1.59478i	−0.235994	+	0.136251i	−0.613334	−	0.789823i	$-0.710172\pi$
$137$	−2.76224	+	1.59478i	−0.235994	+	0.136251i	0.377340	+	0.926075i	$0.376839\pi$
$138$	−16.7661	+	9.67992i	−1.42723	+	0.824009i
$139$	0.297855	−	0.515900i	0.0252637	−	0.0437581i	−0.853117	−	0.521719i	$-0.825291\pi$
$139$	0.297855	−	0.515900i	0.0252637	−	0.0437581i	0.878381	+	0.477961i	$0.158624\pi$
$140$		0			0
$141$	5.79521	−	3.34587i	0.488045	−	0.281773i
$142$	1.63928	+	2.83932i	0.137565	+	0.238270i
$143$	−15.5279	+	1.85143i	−1.29851	+	0.154824i
$144$	−1.12385	+	1.94657i	−0.0936543	+	0.162214i
$145$	−1.71266	−	0.988802i	−0.142228	−	0.0821155i
$146$	−0.269511	−	0.466808i	−0.0223049	−	0.0386333i
$147$		0			0
$148$		−	0.144306i		−	0.0118619i
$149$		−	11.2096i		−	0.918329i	−0.888351	−	0.459165i	$-0.848149\pi$
$149$		−	11.2096i		−	0.918329i	0.888351	−	0.459165i	$-0.151851\pi$
$150$	8.30588	−	4.79540i	0.678172	−	0.391543i
$151$	−11.3216	−	6.53653i	−0.921339	−	0.531935i	−0.0372772	−	0.999305i	$-0.511868\pi$
$151$	−11.3216	−	6.53653i	−0.921339	−	0.531935i	−0.884062	+	0.467369i	$0.845202\pi$
$152$	−6.17238			−0.500646
$153$	5.69334	+	9.86116i	0.460280	+	0.797228i
$154$		0			0
$155$	−0.787362			−0.0632424
$156$	6.61373	−	4.94760i	0.529522	−	0.396125i
$157$	−8.96225	+	15.5231i	−0.715266	+	1.23888i	0.247591	+	0.968865i	$0.420361\pi$
$157$	−8.96225	+	15.5231i	−0.715266	+	1.23888i	−0.962857	+	0.270012i	$0.912972\pi$
$158$			6.53349i			0.519776i
$159$	−1.94372	+	3.36661i	−0.154147	+	0.266990i
$160$	−0.450919	+	0.781015i	−0.0356483	+	0.0617447i
$161$		0			0
$162$	9.25862	+	5.34547i	0.727426	+	0.419980i
$163$		−	20.3179i		−	1.59142i	−0.605678	−	0.795710i	$-0.707098\pi$
$163$		−	20.3179i		−	1.59142i	0.605678	−	0.795710i	$-0.292902\pi$
$164$	−3.46110	−	1.99827i	−0.270267	−	0.156038i
$165$	4.48012	+	7.75979i	0.348777	+	0.604099i
$166$	6.61742	−	11.4617i	0.513611	−	0.889601i
$167$	−2.79770	+	1.61525i	−0.216493	+	0.124992i	−0.604325	−	0.796738i	$-0.706557\pi$
$167$	−2.79770	+	1.61525i	−0.216493	+	0.124992i	0.387833	+	0.921730i	$0.373224\pi$
$168$		0			0
$169$	−12.6356	+	3.05660i	−0.971966	+	0.235123i
$170$	2.28432	+	3.95656i	0.175199	+	0.303454i
$171$		−	13.8737i		−	1.06095i
$172$	7.70851			0.587768
$173$	9.17044			0.697216			0.348608	−	0.937269i	$-0.386655\pi$
$173$	9.17044			0.697216			0.348608	+	0.937269i	$0.386655\pi$
$174$		−	5.02337i		−	0.380821i
$175$		0			0
$176$	3.75609	+	2.16858i	0.283126	+	0.163463i
$177$	16.9608	−	9.79235i	1.27486	−	0.736038i
$178$	−3.89590	−	6.74790i	−0.292010	−	0.505776i
$179$	16.9549			1.26727			0.633636	−	0.773631i	$-0.281562\pi$
$179$	16.9549			1.26727			0.633636	+	0.773631i	$0.281562\pi$
$180$	−1.75549	−	1.01353i	−0.130847	−	0.0755443i
$181$	−2.65743			−0.197525			−0.0987626	−	0.995111i	$-0.531488\pi$
$181$	−2.65743			−0.197525			−0.0987626	+	0.995111i	$0.531488\pi$
$182$		0			0
$183$	19.0923			1.41135
$184$	−7.31893	−	4.22559i	−0.539559	−	0.311514i
$185$	0.130141			0.00956816
$186$	−1.00000	−	1.73205i	−0.0733236	−	0.127000i
$187$	19.0281	−	10.9859i	1.39147	−	0.803366i
$188$	2.52979	+	1.46057i	0.184504	+	0.106523i
$189$		0			0
$190$		−	5.56649i		−	0.403836i
$191$	−24.4861			−1.77175			−0.885875	−	0.463924i	$-0.846441\pi$
$191$	−24.4861			−1.77175			−0.885875	+	0.463924i	$0.846441\pi$
$192$	−2.29079			−0.165323
$193$			12.2409i			0.881120i	0.897723	+	0.440560i	$0.145220\pi$
$193$			12.2409i			0.881120i	−0.897723	+	0.440560i	$0.854780\pi$
$194$	−5.85305	−	10.1378i	−0.420224	−	0.727850i
$195$	4.46194	+	5.96452i	0.319526	+	0.427128i
$196$		0			0
$197$	4.72634	−	2.72876i	0.336738	−	0.194416i	−0.322091	−	0.946709i	$-0.604386\pi$
$197$	4.72634	−	2.72876i	0.336738	−	0.194416i	0.658829	+	0.752293i	$0.271052\pi$
$198$	−4.87433	+	8.44259i	−0.346404	+	0.599989i
$199$	−6.40832	−	11.0995i	−0.454274	−	0.786825i	0.544372	−	0.838844i	$-0.316768\pi$
$199$	−6.40832	−	11.0995i	−0.454274	−	0.786825i	−0.998646	+	0.0520184i	$0.983435\pi$
$200$	3.62578	+	2.09334i	0.256381	+	0.148022i
$201$		−	23.7849i		−	1.67766i
$202$	−9.30362	−	5.37145i	−0.654600	−	0.377934i
$203$		0			0
$204$	−5.80247	+	10.0502i	−0.406254	+	0.703653i
$205$	1.80212	−	3.12136i	0.125865	−	0.218005i
$206$			4.81099i			0.335198i
$207$	9.49787	−	16.4508i	0.660147	−	1.14341i
$208$	3.31398	+	1.42041i	0.229783	+	0.0984878i
$209$	−26.7706			−1.85176
$210$		0			0
$211$	9.65552	+	16.7239i	0.664713	+	1.15132i	0.979363	+	0.202110i	$0.0647797\pi$
$211$	9.65552	+	16.7239i	0.664713	+	1.15132i	−0.314649	+	0.949208i	$0.601887\pi$
$212$	−1.69699			−0.116549
$213$	−6.50427	−	3.75524i	−0.445665	−	0.257305i
$214$	11.8239	−	6.82652i	0.808263	−	0.466651i
$215$			6.95183i			0.474111i
$216$			1.72335i			0.117259i
$217$		0			0
$218$	−2.55874	−	4.43186i	−0.173299	−	0.300163i
$219$	1.06936	+	0.617393i	0.0722604	+	0.0417196i
$220$	−1.95571	+	3.38739i	−0.131854	+	0.228378i
$221$	14.6258	−	10.9413i	0.983839	−	0.735990i
$222$	0.165287	+	0.286286i	0.0110934	+	0.0192143i
$223$	−9.21079	+	5.31785i	−0.616800	+	0.356110i	−0.775622	−	0.631197i	$-0.782564\pi$
$223$	−9.21079	+	5.31785i	−0.616800	+	0.356110i	0.158822	+	0.987307i	$0.449230\pi$
$224$		0			0
$225$	−4.70522	+	8.14967i	−0.313681	+	0.543312i
$226$	15.5296	−	8.96603i	1.03301	−	0.596411i
$227$	−19.6776	+	11.3609i	−1.30605	+	0.754047i	−0.981434	−	0.191800i	$-0.938567\pi$
$227$	−19.6776	+	11.3609i	−1.30605	+	0.754047i	−0.324613	+	0.945847i	$0.605234\pi$
$228$	12.2453	−	7.06980i	0.810962	−	0.468209i
$229$	−17.5885	+	10.1547i	−1.16228	+	0.671042i	−0.951849	−	0.306567i	$-0.900820\pi$
$229$	−17.5885	+	10.1547i	−1.16228	+	0.671042i	−0.210429	+	0.977609i	$0.567486\pi$
$230$	3.81080	−	6.60049i	0.251277	−	0.435224i
$231$		0			0
$232$	1.89907	−	1.09643i	0.124680	−	0.0719841i
$233$	−5.32231	−	9.21851i	−0.348676	−	0.603925i	0.637338	−	0.770584i	$-0.280035\pi$
$233$	−5.32231	−	9.21851i	−0.348676	−	0.603925i	−0.986015	+	0.166659i	$0.946702\pi$
$234$	−3.19266	+	7.44884i	−0.208711	+	0.486946i
$235$	−1.31720	+	2.28146i	−0.0859248	+	0.148826i
$236$	7.40394	+	4.27467i	0.481955	+	0.278257i
$237$	−7.48341	−	12.9617i	−0.486100	−	0.841950i
$238$		0			0
$239$			0.311564i			0.0201534i	0.999949	+	0.0100767i	$0.00320757\pi$
$239$			0.311564i			0.0201534i	−0.999949	+	0.0100767i	$0.996792\pi$
$240$		−	2.06592i		−	0.133355i
$241$	21.9100	−	12.6498i	1.41135	−	0.814843i	0.415833	−	0.909441i	$-0.363490\pi$
$241$	21.9100	−	12.6498i	1.41135	−	0.814843i	0.995516	+	0.0945983i	$0.0301567\pi$
$242$	6.76452	+	3.90550i	0.434840	+	0.251055i
$243$	−19.3206			−1.23942
$244$	4.16720	+	7.21780i	0.266778	+	0.462073i
$245$		0			0
$246$	9.15521			0.583715
$247$	−22.0983	+	2.63484i	−1.40608	+	0.167651i
$248$	0.436531	−	0.756094i	0.0277198	−	0.0480120i
$249$			30.3182i			1.92134i
$250$	−4.14246	+	7.17494i	−0.261992	+	0.453783i
$251$	4.02015	−	6.96311i	0.253750	−	0.439507i	−0.710805	−	0.703389i	$-0.751669\pi$
$251$	4.02015	−	6.96311i	0.253750	−	0.439507i	0.964555	+	0.263881i	$0.0850027\pi$
$252$		0			0
$253$	−31.7434	−	18.3271i	−1.99569	−	1.15221i
$254$			19.5136i			1.22439i
$255$	−9.06364	−	5.23289i	−0.567587	−	0.327697i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.46634	+	14.6641i	−0.528116	+	0.914723i	0.471347	+	0.881948i	$0.343768\pi$
$257$	−8.46634	+	14.6641i	−0.528116	+	0.914723i	−0.999463	+	0.0327753i	$0.989565\pi$
$258$	−15.2928	+	8.82928i	−0.952085	+	0.549687i
$259$		0			0
$260$	−1.28098	+	2.98867i	−0.0794431	+	0.185350i
$261$	2.46445	+	4.26855i	0.152545	+	0.264217i
$262$		−	20.6496i		−	1.27574i
$263$	10.3209			0.636414			0.318207	−	0.948021i	$-0.396919\pi$
$263$	10.3209			0.636414			0.318207	+	0.948021i	$0.396919\pi$
$264$	−9.93552			−0.611489
$265$		−	1.53041i		−	0.0940122i
$266$		0			0
$267$	15.4580	+	8.92468i	0.946014	+	0.546181i
$268$	8.99180	−	5.19142i	0.549262	−	0.317116i
$269$	3.06999	+	5.31738i	0.187181	+	0.324207i	0.944309	−	0.329059i	$-0.106732\pi$
$269$	3.06999	+	5.31738i	0.187181	+	0.324207i	−0.757128	+	0.653266i	$0.773398\pi$
$270$	−1.55418			−0.0945846
$271$	−9.24673	−	5.33860i	−0.561699	−	0.324297i	0.192128	−	0.981370i	$-0.438461\pi$
$271$	−9.24673	−	5.33860i	−0.561699	−	0.324297i	−0.753827	+	0.657073i	$0.771794\pi$
$272$	−5.06592			−0.307167
$273$		0			0
$274$	3.18956			0.192689
$275$	15.7256	+	9.07917i	0.948289	+	0.547495i
$276$	19.3598			1.16532
$277$	10.9545	+	18.9737i	0.658191	+	1.14002i	0.981084	+	0.193585i	$0.0620114\pi$
$277$	10.9545	+	18.9737i	0.658191	+	1.14002i	−0.322892	+	0.946436i	$0.604655\pi$
$278$	−0.515900	+	0.297855i	−0.0309416	+	0.0178642i
$279$	1.69948	+	0.981193i	0.101745	+	0.0587425i
$280$		0			0
$281$			25.7719i			1.53743i	0.639594	+	0.768713i	$0.279102\pi$
$281$			25.7719i			1.53743i	−0.639594	+	0.768713i	$0.720898\pi$
$282$	−6.69173			−0.398487
$283$	11.3269			0.673314			0.336657	−	0.941627i	$-0.390704\pi$
$283$	11.3269			0.673314			0.336657	+	0.941627i	$0.390704\pi$
$284$		−	3.27856i		−	0.194547i
$285$	6.37582	+	11.0432i	0.377671	+	0.654146i
$286$	14.3733	+	6.16055i	0.849908	+	0.364281i
$287$		0			0
$288$	1.94657	−	1.12385i	0.114703	−	0.0662236i
$289$	−4.33177	+	7.50285i	−0.254810	+	0.441344i
$290$	0.988802	+	1.71266i	0.0580645	+	0.100571i
$291$	23.2235	+	13.4081i	1.36139	+	0.785996i
$292$			0.539023i			0.0315439i
$293$	20.5646	+	11.8730i	1.20140	+	0.693626i	0.960865	−	0.277016i	$-0.0893454\pi$
$293$	20.5646	+	11.8730i	1.20140	+	0.693626i	0.240530	+	0.970642i	$0.422679\pi$
$294$		0			0
$295$	−3.85506	+	6.67716i	−0.224450	+	0.388759i
$296$	−0.0721531	+	0.124973i	−0.00419382	+	0.00726390i
$297$			7.47445i			0.433712i
$298$	−5.60482	+	9.70783i	−0.324678	+	0.562360i
$299$	−28.0070	−	12.0041i	−1.61969	−	0.694217i
$300$	−9.59081			−0.553725
$301$		0			0
$302$	6.53653	+	11.3216i	0.376135	+	0.651485i
$303$	24.6097			1.41379
$304$	5.34544	+	3.08619i	0.306582	+	0.177005i
$305$	−6.50930	+	3.75814i	−0.372721	+	0.215191i
$306$		−	11.3867i		−	0.650934i
$307$			6.68810i			0.381710i	0.981618	+	0.190855i	$0.0611261\pi$
$307$			6.68810i			0.381710i	−0.981618	+	0.190855i	$0.938874\pi$
$308$		0			0
$309$	−5.51048	−	9.54443i	−0.313480	−	0.542964i
$310$	0.681875	+	0.393681i	0.0387279	+	0.0223596i
$311$	−4.59362	+	7.95639i	−0.260480	+	0.451165i	−0.966370	−	0.257157i	$-0.917214\pi$
$311$	−4.59362	+	7.95639i	−0.260480	+	0.451165i	0.705889	+	0.708322i	$0.250548\pi$
$312$	−8.20146	+	0.977882i	−0.464316	+	0.0553616i
$313$	8.58157	+	14.8637i	0.485059	+	0.840147i	0.999853	−	0.0171671i	$-0.00546471\pi$
$313$	8.58157	+	14.8637i	0.485059	+	0.840147i	−0.514793	+	0.857314i	$0.672131\pi$
$314$	15.5231	−	8.96225i	0.876018	−	0.505769i
$315$		0			0
$316$	3.26674	−	5.65817i	0.183769	−	0.318297i
$317$	3.25840	−	1.88124i	0.183010	−	0.105661i	−0.405696	−	0.914008i	$-0.632971\pi$
$317$	3.25840	−	1.88124i	0.183010	−	0.105661i	0.588706	+	0.808347i	$0.299638\pi$
$318$	3.36661	−	1.94372i	0.188790	−	0.108998i
$319$	8.23658	−	4.75539i	0.461160	−	0.266251i
$320$	0.781015	−	0.450919i	0.0436601	−	0.0252072i
$321$	−15.6381	+	27.0860i	−0.872833	+	1.51179i
$322$		0			0
$323$	27.0796	−	15.6344i	1.50675	−	0.869921i
$324$	−5.34547	−	9.25862i	−0.296971	−	0.514368i
$325$	13.8746	+	5.94682i	0.769623	+	0.329870i
$326$	−10.1589	+	17.5958i	−0.562652	+	0.974542i
$327$	10.1524	+	5.86152i	0.561432	+	0.324143i
$328$	1.99827	+	3.46110i	0.110336	+	0.191107i
$329$		0			0
$330$		−	8.96024i		−	0.493245i
$331$			32.2257i			1.77129i	0.464367	+	0.885643i	$0.346282\pi$
$331$			32.2257i			1.77129i	−0.464367	+	0.885643i	$0.653718\pi$
$332$	−11.4617	+	6.61742i	−0.629043	+	0.363178i
$333$	−0.280902	−	0.162179i	−0.0153933	−	0.00888735i
$334$	3.23051			0.176765
$335$	4.68182	+	8.10916i	0.255795	+	0.443051i
$336$		0			0
$337$	−3.01703			−0.164348			−0.0821740	−	0.996618i	$-0.526186\pi$
$337$	−3.01703			−0.164348			−0.0821740	+	0.996618i	$0.526186\pi$
$338$	12.4710	+	3.67069i	0.678333	+	0.199659i
$339$	−20.5393	+	35.5750i	−1.11554	+	1.93217i
$340$		−	4.56864i		−	0.247769i
$341$	1.89331	−	3.27931i	0.102528	−	0.177584i
$342$	−6.93684	+	12.0150i	−0.375101	+	0.649695i
$343$		0			0
$344$	−6.67577	−	3.85426i	−0.359933	−	0.207808i
$345$			17.4594i			0.939985i
$346$	−7.94183	−	4.58522i	−0.426956	−	0.246503i
$347$	−0.234270	−	0.405768i	−0.0125763	−	0.0217828i	0.859669	−	0.510852i	$-0.170670\pi$
$347$	−0.234270	−	0.405768i	−0.0125763	−	0.0217828i	−0.872245	+	0.489069i	$0.837337\pi$
$348$	−2.51168	+	4.35037i	−0.134640	+	0.233204i
$349$	−27.9044	+	16.1106i	−1.49369	+	0.862380i	−0.999974	−	0.00724565i	$-0.997694\pi$
$349$	−27.9044	+	16.1106i	−1.49369	+	0.862380i	−0.493712	+	0.869625i	$0.664360\pi$
$350$		0			0
$351$	0.735656	+	6.16992i	0.0392664	+	0.329326i
$352$	−2.16858	−	3.75609i	−0.115586	−	0.200200i
$353$		−	13.1154i		−	0.698063i	−0.937111	−	0.349031i	$-0.886511\pi$
$353$		−	13.1154i		−	0.698063i	0.937111	−	0.349031i	$-0.113489\pi$
$354$	−19.5847			−1.04091
$355$	2.95673			0.156927
$356$			7.79180i			0.412965i
$357$		0			0
$358$	−14.6834	−	8.47747i	−0.776043	−	0.448048i
$359$	−3.79302	+	2.18990i	−0.200188	+	0.115579i	−0.596743	−	0.802432i	$-0.703539\pi$
$359$	−3.79302	+	2.18990i	−0.200188	+	0.115579i	0.396555	+	0.918011i	$0.370206\pi$
$360$	1.01353	+	1.75549i	0.0534179	+	0.0925225i
$361$	−19.0983			−1.00517
$362$	2.30140	+	1.32871i	0.120959	+	0.0698357i
$363$	−17.8933			−0.939156
$364$		0			0
$365$	−0.486112			−0.0254443
$366$	−16.5344	−	9.54617i	−0.864269	−	0.498986i
$367$	25.8188			1.34773			0.673865	−	0.738854i	$-0.264633\pi$
$367$	25.8188			1.34773			0.673865	+	0.738854i	$0.264633\pi$
$368$	4.22559	+	7.31893i	0.220274	+	0.381526i
$369$	−7.77953	+	4.49151i	−0.404986	+	0.233819i
$370$	−0.112705	−	0.0650705i	−0.00585928	−	0.00338285i
$371$		0			0
$372$			2.00000i			0.103695i
$373$	30.6285			1.58588			0.792942	−	0.609297i	$-0.208548\pi$
$373$	30.6285			1.58588			0.792942	+	0.609297i	$0.208548\pi$
$374$	−21.9717			−1.13613
$375$		−	18.9790i		−	0.980069i
$376$	−1.46057	−	2.52979i	−0.0753234	−	0.130464i
$377$	6.33100	−	4.73609i	0.326063	−	0.243921i
$378$		0			0
$379$	−33.0409	+	19.0762i	−1.69720	+	0.979877i	−0.748796	+	0.662801i	$0.769368\pi$
$379$	−33.0409	+	19.0762i	−1.69720	+	0.979877i	−0.948400	+	0.317076i	$0.897299\pi$
$380$	−2.78325	+	4.82072i	−0.142778	+	0.247298i
$381$	−22.3508	−	38.7127i	−1.14507	−	1.98331i
$382$	21.2056	+	12.2430i	1.08497	+	0.626408i
$383$			31.9602i			1.63309i	0.577283	+	0.816544i	$0.304113\pi$
$383$			31.9602i			1.63309i	−0.577283	+	0.816544i	$0.695887\pi$
$384$	1.98388	+	1.14539i	0.101239	+	0.0584506i
$385$		0			0
$386$	6.12046	−	10.6009i	0.311523	−	0.539574i
$387$	8.66323	−	15.0051i	0.440377	−	0.762754i
$388$			11.7061i			0.594287i
$389$	−2.62292	+	4.54304i	−0.132988	+	0.230341i	−0.924827	−	0.380388i	$-0.875790\pi$
$389$	−2.62292	+	4.54304i	−0.132988	+	0.230341i	0.791839	+	0.610729i	$0.209124\pi$
$390$	−0.881892	−	7.39639i	−0.0446563	−	0.374531i
$391$	42.8130			2.16514
$392$		0			0
$393$	23.6520	+	40.9664i	1.19308	+	2.06648i
$394$	−5.45751			−0.274946
$395$	5.10275	+	2.94608i	0.256747	+	0.148233i
$396$	8.44259	−	4.87433i	0.424256	−	0.244944i
$397$		−	24.5296i		−	1.23110i	−0.788096	−	0.615552i	$-0.788933\pi$
$397$		−	24.5296i		−	1.23110i	0.788096	−	0.615552i	$-0.211067\pi$
$398$			12.8166i			0.642440i
$399$		0			0
$400$	−2.09334	−	3.62578i	−0.104667	−	0.181289i
$401$	−3.69916	−	2.13571i	−0.184727	−	0.106652i	0.404784	−	0.914412i	$-0.367347\pi$
$401$	−3.69916	−	2.13571i	−0.184727	−	0.106652i	−0.589512	+	0.807760i	$0.700680\pi$
$402$	−11.8924	+	20.5983i	−0.593141	+	1.02735i
$403$	1.24011	−	2.89331i	0.0617741	−	0.144126i
$404$	5.37145	+	9.30362i	0.267239	+	0.462872i
$405$	8.34979	−	4.82075i	0.414904	−	0.239545i
$406$		0			0
$407$	−0.312940	+	0.542028i	−0.0155119	+	0.0268673i
$408$	10.0502	−	5.80247i	0.497558	−	0.287265i
$409$	1.39990	−	0.808235i	0.0692208	−	0.0399646i	−0.464990	−	0.885316i	$-0.653942\pi$
$409$	1.39990	−	0.808235i	0.0692208	−	0.0399646i	0.534211	+	0.845351i	$0.320609\pi$
$410$	−3.12136	+	1.80212i	−0.154153	+	0.0890001i
$411$	−6.32771	+	3.65330i	−0.312123	+	0.180204i
$412$	2.40550	−	4.16644i	0.118510	−	0.205266i
$413$		0			0
$414$	−16.4508	+	9.49787i	−0.808512	+	0.466795i
$415$	−5.96784	−	10.3366i	−0.292950	−	0.507404i
$416$	−2.15978	−	2.88710i	−0.105892	−	0.141552i
$417$	0.682322	−	1.18182i	0.0334135	−	0.0578738i
$418$	23.1840	+	13.3853i	1.13397	+	0.654697i
$419$	13.0156	+	22.5437i	0.635854	+	1.10133i	0.986334	+	0.164761i	$0.0526851\pi$
$419$	13.0156	+	22.5437i	0.635854	+	1.10133i	−0.350480	+	0.936570i	$0.613982\pi$
$420$		0			0
$421$		−	37.5391i		−	1.82954i	−0.403971	−	0.914772i	$-0.632370\pi$
$421$		−	37.5391i		−	1.82954i	0.403971	−	0.914772i	$-0.367630\pi$
$422$		−	19.3110i		−	0.940047i
$423$	5.68622	−	3.28294i	0.276473	−	0.159622i
$424$	1.46963	+	0.848493i	0.0713717	+	0.0412064i
$425$	−21.2094			−1.02881
$426$	3.75524	+	6.50427i	0.181942	+	0.315133i
$427$		0			0
$428$	−13.6530			−0.659944
$429$	−35.5711	+	4.24123i	−1.71739	+	0.204769i
$430$	3.47592	−	6.02046i	0.167624	−	0.290333i
$431$			21.5538i			1.03821i	0.854710	+	0.519106i	$0.173735\pi$
$431$			21.5538i			1.03821i	−0.854710	+	0.519106i	$0.826265\pi$
$432$	0.861675	−	1.49246i	0.0414573	−	0.0718062i
$433$	1.59958	−	2.77056i	0.0768710	−	0.133145i	−0.825027	−	0.565093i	$-0.808840\pi$
$433$	1.59958	−	2.77056i	0.0768710	−	0.133145i	0.901898	+	0.431948i	$0.142174\pi$
$434$		0			0
$435$	−3.92333	−	2.26513i	−0.188109	−	0.108605i
$436$			5.11747i			0.245082i
$437$	−45.1752	−	26.0819i	−2.16102	−	1.24767i
$438$	−0.617393	−	1.06936i	−0.0295002	−	0.0510958i
$439$	13.3114	−	23.0560i	0.635317	−	1.10040i	−0.351131	−	0.936326i	$-0.614203\pi$
$439$	13.3114	−	23.0560i	0.635317	−	1.10040i	0.986448	−	0.164075i	$-0.0524638\pi$
$440$	3.38739	−	1.95571i	0.161488	−	0.0932349i
$441$		0			0
$442$	−18.1370	+	2.16252i	−0.862688	+	0.102861i
$443$	−4.54933	−	7.87968i	−0.216145	−	0.374375i	0.737481	−	0.675368i	$-0.236015\pi$
$443$	−4.54933	−	7.87968i	−0.216145	−	0.374375i	−0.953626	+	0.300993i	$0.902682\pi$
$444$		−	0.330575i		−	0.0156884i
$445$	−7.02695			−0.333109
$446$	10.6357			0.503615
$447$		−	25.6789i		−	1.21457i
$448$		0			0
$449$	6.08550	+	3.51346i	0.287192	+	0.165811i	0.636675	−	0.771132i	$-0.280309\pi$
$449$	6.08550	+	3.51346i	0.287192	+	0.165811i	−0.349483	+	0.936943i	$0.613643\pi$
$450$	8.14967	−	4.70522i	0.384179	−	0.221806i
$451$	8.66681	+	15.0114i	0.408104	+	0.706858i
$452$	−17.9321			−0.843453
$453$	−25.9354	−	14.9738i	−1.21855	−	0.703531i
$454$	22.7217			1.06638
$455$		0			0
$456$	−14.1396			−0.662148
$457$	16.5853	+	9.57556i	0.775830	+	0.447926i	0.834950	−	0.550325i	$-0.185496\pi$
$457$	16.5853	+	9.57556i	0.775830	+	0.447926i	−0.0591204	+	0.998251i	$0.518830\pi$
$458$	20.3094			0.948996
$459$	−4.36518	−	7.56071i	−0.203749	−	0.352904i
$460$	−6.60049	+	3.81080i	−0.307750	+	0.177679i
$461$	−2.82026	−	1.62828i	−0.131353	−	0.0758365i	0.432884	−	0.901450i	$-0.357496\pi$
$461$	−2.82026	−	1.62828i	−0.131353	−	0.0758365i	−0.564236	+	0.825613i	$0.690829\pi$
$462$		0			0
$463$		−	21.2761i		−	0.988786i	−0.869238	−	0.494393i	$-0.835390\pi$
$463$		−	21.2761i		−	0.988786i	0.869238	−	0.494393i	$-0.164610\pi$
$464$	−2.19286			−0.101801
$465$	−1.80368			−0.0836435
$466$			10.6446i			0.493102i
$467$	1.66586	+	2.88535i	0.0770866	+	0.133518i	0.901992	−	0.431753i	$-0.142105\pi$
$467$	1.66586	+	2.88535i	0.0770866	+	0.133518i	−0.824905	+	0.565271i	$0.808772\pi$
$468$	6.48935	−	4.85455i	0.299970	−	0.224402i
$469$		0			0
$470$	2.28146	−	1.31720i	0.105236	−	0.0607580i
$471$	−20.5306	+	35.5601i	−0.946001	+	1.63852i
$472$	−4.27467	−	7.40394i	−0.196757	−	0.340794i
$473$	−28.9539	−	16.7165i	−1.33130	−	0.768627i
$474$			14.9668i			0.687449i
$475$	22.3797	+	12.9209i	1.02685	+	0.592852i
$476$		0			0
$477$	−1.90716	+	3.30330i	−0.0873229	+	0.151248i
$478$	0.155782	−	0.269822i	0.00712530	−	0.0123414i
$479$		−	0.185216i		−	0.00846273i	−0.999991	−	0.00423136i	$-0.998653\pi$
$479$		−	0.185216i		−	0.00846273i	0.999991	−	0.00423136i	$-0.00134689\pi$
$480$	−1.03296	+	1.78914i	−0.0471480	+	0.0816627i
$481$	−0.204974	+	0.478227i	−0.00934602	+	0.0218053i
$482$	−25.2995			−1.15236
$483$		0			0
$484$	−3.90550	−	6.76452i	−0.177523	−	0.307478i
$485$	−10.5570			−0.479369
$486$	16.7321	+	9.66031i	0.758985	+	0.438200i
$487$	27.0466	−	15.6154i	1.22560	−	0.707601i	0.259494	−	0.965745i	$-0.416444\pi$
$487$	27.0466	−	15.6154i	1.22560	−	0.707601i	0.966106	+	0.258144i	$0.0831110\pi$
$488$		−	8.33440i		−	0.377281i
$489$		−	46.5440i		−	2.10479i
$490$		0			0
$491$	13.4236	+	23.2504i	0.605799	+	1.04927i	0.991925	+	0.126829i	$0.0404798\pi$
$491$	13.4236	+	23.2504i	0.605799	+	1.04927i	−0.386126	+	0.922446i	$0.626187\pi$
$492$	−7.92864	−	4.57761i	−0.357451	−	0.206374i
$493$	−5.55442	+	9.62054i	−0.250159	+	0.433287i
$494$	20.4551	+	8.76732i	0.920319	+	0.394460i
$495$	4.39586	+	7.61385i	0.197579	+	0.342217i
$496$	−0.756094	+	0.436531i	−0.0339496	+	0.0196008i
$497$		0			0
$498$	15.1591	−	26.2563i	0.679295	−	1.17657i
$499$	13.2389	−	7.64346i	0.592653	−	0.342168i	−0.173493	−	0.984835i	$-0.555505\pi$
$499$	13.2389	−	7.64346i	0.592653	−	0.342168i	0.766146	+	0.642667i	$0.222172\pi$
$500$	7.17494	−	4.14246i	0.320873	−	0.185256i
$501$	−6.40893	+	3.70020i	−0.286330	+	0.165313i
$502$	−6.96311	+	4.02015i	−0.310779	+	0.179428i
$503$	13.0551	−	22.6121i	0.582097	−	1.00822i	−0.413133	−	0.910671i	$-0.635566\pi$
$503$	13.0551	−	22.6121i	0.582097	−	1.00822i	0.995230	−	0.0975513i	$-0.0311010\pi$
$504$		0			0
$505$	−8.39036	+	4.84418i	−0.373366	+	0.215563i
$506$	18.3271	+	31.7434i	0.814737	+	1.41117i
$507$	−28.9454	+	7.00201i	−1.28551	+	0.310970i
$508$	9.75681	−	16.8993i	0.432889	−	0.749785i
$509$	−14.7459	−	8.51357i	−0.653602	−	0.377357i	0.136233	−	0.990677i	$-0.456500\pi$
$509$	−14.7459	−	8.51357i	−0.653602	−	0.377357i	−0.789835	+	0.613320i	$0.789834\pi$
$510$	5.23289	+	9.06364i	0.231716	+	0.401345i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$			10.6372i			0.469643i
$514$	14.6641	−	8.46634i	0.646807	−	0.373434i
$515$	3.75746	+	2.16937i	0.165573	+	0.0955939i
$516$	17.6586			0.777375
$517$	−6.33475	−	10.9721i	−0.278602	−	0.482553i
$518$		0			0
$519$	21.0075			0.922128
$520$	2.60370	−	1.94777i	0.114180	−	0.0854156i
$521$	9.38802	−	16.2605i	0.411297	−	0.712387i	−0.583735	−	0.811944i	$-0.698409\pi$
$521$	9.38802	−	16.2605i	0.411297	−	0.712387i	0.995032	+	0.0995575i	$0.0317427\pi$
$522$		−	4.92890i		−	0.215732i
$523$	1.51624	−	2.62620i	0.0663004	−	0.114836i	−0.830970	−	0.556318i	$-0.812214\pi$
$523$	1.51624	−	2.62620i	0.0663004	−	0.114836i	0.897270	+	0.441482i	$0.145547\pi$
$524$	−10.3248	+	17.8831i	−0.451042	+	0.781227i
$525$		0			0
$526$	−8.93817	−	5.16045i	−0.389723	−	0.225006i
$527$			4.42286i			0.192663i
$528$	8.60441	+	4.96776i	0.374459	+	0.216194i
$529$	−24.2111	−	41.9349i	−1.05266	−	1.82326i
$530$	−0.765204	+	1.32537i	−0.0332383	+	0.0575705i
$531$	16.6419	−	9.60818i	0.722195	−	0.416960i
$532$		0			0
$533$	8.63164	+	11.5384i	0.373878	+	0.499783i
$534$	−8.92468	−	15.4580i	−0.386209	−	0.668933i
$535$		−	12.3128i		−	0.532330i
$536$	−10.3828			−0.448470
$537$	38.8402			1.67608
$538$		−	6.13999i		−	0.264714i
$539$		0			0
$540$	1.34596	+	0.777092i	0.0579210	+	0.0334407i
$541$	−5.29873	+	3.05922i	−0.227810	+	0.131526i	−0.609561	−	0.792739i	$-0.708654\pi$
$541$	−5.29873	+	3.05922i	−0.227810	+	0.131526i	0.381751	+	0.924265i	$0.375321\pi$
$542$	5.33860	+	9.24673i	0.229313	+	0.397181i
$543$	−6.08760			−0.261244
$544$	4.38722	+	2.53296i	0.188100	+	0.108600i
$545$	−4.61513			−0.197691
$546$		0			0
$547$	−37.4754			−1.60233			−0.801166	−	0.598442i	$-0.795786\pi$
$547$	−37.4754			−1.60233			−0.801166	+	0.598442i	$0.795786\pi$
$548$	−2.76224	−	1.59478i	−0.117997	−	0.0681257i
$549$	18.7333			0.799516
$550$	−9.07917	−	15.7256i	−0.387137	−	0.670541i
$551$	11.7218	−	6.76758i	0.499365	−	0.288308i
$552$	−16.7661	−	9.67992i	−0.713613	−	0.412005i
$553$		0			0
$554$		−	21.9090i		−	0.930823i
$555$	0.298125			0.0126547
$556$	0.595710			0.0252637
$557$		−	8.89051i		−	0.376703i	−0.982102	−	0.188352i	$-0.939686\pi$
$557$		−	8.89051i		−	0.376703i	0.982102	−	0.188352i	$-0.0603144\pi$
$558$	−0.981193	−	1.69948i	−0.0415372	−	0.0719446i
$559$	−25.5458	−	10.9493i	−1.08047	−	0.463104i
$560$		0			0
$561$	43.5893	−	25.1663i	1.84034	−	1.06252i
$562$	12.8860	−	22.3192i	0.543562	−	0.941477i
$563$	8.89598	+	15.4083i	0.374921	+	0.649382i	0.990315	−	0.138838i	$-0.0443366\pi$
$563$	8.89598	+	15.4083i	0.374921	+	0.649382i	−0.615394	+	0.788219i	$0.711003\pi$
$564$	5.79521	+	3.34587i	0.244022	+	0.140886i
$565$		−	16.1718i		−	0.680354i
$566$	−9.80937	−	5.66344i	−0.412319	−	0.238052i
$567$		0			0
$568$	−1.63928	+	2.83932i	−0.0687826	+	0.119135i
$569$	5.58684	−	9.67669i	0.234212	−	0.405668i	−0.724831	−	0.688927i	$-0.758082\pi$
$569$	5.58684	−	9.67669i	0.234212	−	0.405668i	0.959044	+	0.283259i	$0.0914155\pi$
$570$		−	12.7516i		−	0.534108i
$571$	8.36194	−	14.4833i	0.349936	−	0.606108i	−0.636301	−	0.771441i	$-0.719537\pi$
$571$	8.36194	−	14.4833i	0.349936	−	0.606108i	0.986238	+	0.165333i	$0.0528698\pi$
$572$	−9.36733	−	12.5218i	−0.391668	−	0.523564i
$573$	−56.0924			−2.34329
$574$		0			0
$575$	17.6912	+	30.6421i	0.737774	+	1.27786i
$576$	−2.24770			−0.0936543
$577$	0.691857	+	0.399444i	0.0288024	+	0.0166291i	0.514332	−	0.857591i	$-0.328040\pi$
$577$	0.691857	+	0.399444i	0.0288024	+	0.0166291i	−0.485530	+	0.874220i	$0.661373\pi$
$578$	7.50285	−	4.33177i	0.312078	−	0.180178i
$579$			28.0413i			1.16536i
$580$		−	1.97760i		−	0.0821155i
$581$		0			0
$582$	−13.4081	−	23.2235i	−0.555783	−	0.962645i
$583$	6.37404	+	3.68005i	0.263986	+	0.152412i
$584$	0.269511	−	0.466808i	0.0111525	−	0.0193166i
$585$	4.37802	+	5.85234i	0.181009	+	0.241965i
$586$	−11.8730	−	20.5646i	−0.490468	−	0.849515i
$587$	6.94921	−	4.01213i	0.286825	−	0.165598i	−0.349684	−	0.936868i	$-0.613711\pi$
$587$	6.94921	−	4.01213i	0.286825	−	0.165598i	0.636509	+	0.771269i	$0.280378\pi$
$588$		0			0
$589$	2.69444	−	4.66690i	0.111022	−	0.192296i
$590$	6.67716	−	3.85506i	0.274894	−	0.158710i
$591$	10.8270	−	6.25100i	0.445365	−	0.257132i
$592$	0.124973	−	0.0721531i	0.00513635	−	0.00296548i
$593$	4.27055	−	2.46560i	0.175370	−	0.101250i	−0.409745	−	0.912200i	$-0.634382\pi$
$593$	4.27055	−	2.46560i	0.175370	−	0.101250i	0.585116	+	0.810950i	$0.301049\pi$
$594$	3.73723	−	6.47306i	0.153340	−	0.265593i
$595$		0			0
$596$	9.70783	−	5.60482i	0.397648	−	0.229582i
$597$	−14.6801	−	25.4267i	−0.600816	−	1.04064i
$598$	18.2527	+	24.3994i	0.746408	+	0.997765i
$599$	8.91246	−	15.4368i	0.364153	−	0.630732i	−0.624487	−	0.781035i	$-0.714692\pi$
$599$	8.91246	−	15.4368i	0.364153	−	0.630732i	0.988640	+	0.150304i	$0.0480251\pi$
$600$	8.30588	+	4.79540i	0.339086	+	0.195772i
$601$	0.0809165	+	0.140152i	0.00330065	+	0.00571690i	0.867671	−	0.497139i	$-0.165616\pi$
$601$	0.0809165	+	0.140152i	0.00330065	+	0.00571690i	−0.864370	+	0.502856i	$0.832283\pi$
$602$		0			0
$603$		−	23.3375i		−	0.950378i
$604$		−	13.0731i		−	0.531935i
$605$	6.10050	−	3.52213i	0.248021	−	0.143195i
$606$	−21.3126	−	12.3048i	−0.865765	−	0.499850i
$607$	6.18846			0.251182			0.125591	−	0.992082i	$-0.459917\pi$
$607$	6.18846			0.251182			0.125591	+	0.992082i	$0.459917\pi$
$608$	−3.08619	−	5.34544i	−0.125162	−	0.216786i
$609$		0			0
$610$	7.51629			0.304326
$611$	−6.30904	−	8.43365i	−0.255237	−	0.341189i
$612$	−5.69334	+	9.86116i	−0.230140	+	0.398614i
$613$			37.2124i			1.50299i	0.659736	+	0.751497i	$0.270668\pi$
$613$			37.2124i			1.50299i	−0.659736	+	0.751497i	$0.729332\pi$
$614$	3.34405	−	5.79207i	0.134955	−	0.233749i
$615$	4.12826	−	7.15036i	0.166468	−	0.288330i
$616$		0			0
$617$	−5.78536	−	3.34018i	−0.232910	−	0.134471i	0.379004	−	0.925395i	$-0.376267\pi$
$617$	−5.78536	−	3.34018i	−0.232910	−	0.134471i	−0.611914	+	0.790924i	$0.709600\pi$
$618$			11.0210i			0.443328i
$619$	−20.5546	−	11.8672i	−0.826158	−	0.476982i	0.0263776	−	0.999652i	$-0.491603\pi$
$619$	−20.5546	−	11.8672i	−0.826158	−	0.476982i	−0.852535	+	0.522670i	$0.824936\pi$
$620$	−0.393681	−	0.681875i	−0.0158106	−	0.0273848i
$621$	−7.28216	+	12.6131i	−0.292223	+	0.506145i
$622$	7.95639	−	4.59362i	0.319022	−	0.184187i
$623$		0			0
$624$	7.59161	+	3.25386i	0.303908	+	0.130259i
$625$	−6.73089	−	11.6582i	−0.269236	−	0.466330i
$626$		−	17.1631i		−	0.685977i
$627$	−61.3258			−2.44912
$628$	−17.9245			−0.715266
$629$		−	0.731044i		−	0.0291486i
$630$		0			0
$631$	19.9348	+	11.5093i	0.793590	+	0.458180i	0.841225	−	0.540685i	$-0.181835\pi$
$631$	19.9348	+	11.5093i	0.793590	+	0.458180i	−0.0476346	+	0.998865i	$0.515168\pi$
$632$	−5.65817	+	3.26674i	−0.225070	+	0.129944i
$633$	22.1187	+	38.3108i	0.879141	+	1.52272i
$634$	−3.76247			−0.149427
$635$	15.2404	+	8.79907i	0.604798	+	0.349181i
$636$	−3.88743			−0.154147
$637$		0			0
$638$	−9.51078			−0.376536
$639$	−6.38194	−	3.68461i	−0.252466	−	0.145761i
$640$	−0.901839			−0.0356483
$641$	6.32539	+	10.9559i	0.249838	+	0.432732i	0.963481	−	0.267778i	$-0.0862893\pi$
$641$	6.32539	+	10.9559i	0.249838	+	0.432732i	−0.713643	+	0.700510i	$0.752956\pi$
$642$	27.0860	−	15.6381i	1.06900	−	0.617186i
$643$	−13.1971	−	7.61938i	−0.520445	−	0.300479i	0.216672	−	0.976244i	$-0.430480\pi$
$643$	−13.1971	−	7.61938i	−0.520445	−	0.300479i	−0.737117	+	0.675766i	$0.763813\pi$
$644$		0			0
$645$			15.9252i			0.627053i
$646$	−31.2688			−1.23025
$647$	29.3642			1.15443			0.577213	−	0.816594i	$-0.304140\pi$
$647$	29.3642			1.15443			0.577213	+	0.816594i	$0.304140\pi$
$648$			10.6909i			0.419980i
$649$	−18.5399	−	32.1121i	−0.727756	−	1.26051i
$650$	−9.04233	−	12.0874i	−0.354669	−	0.474106i
$651$		0			0
$652$	17.5958	−	10.1589i	0.689105	−	0.397855i
$653$	14.5106	−	25.1330i	0.567842	−	0.983532i	−0.428937	−	0.903335i	$-0.641112\pi$
$653$	14.5106	−	25.1330i	0.567842	−	0.983532i	0.996779	−	0.0801974i	$-0.0255551\pi$
$654$	−5.86152	−	10.1524i	−0.229204	−	0.396992i
$655$	−16.1277	−	9.31132i	−0.630161	−	0.363823i
$656$		−	3.99654i		−	0.156038i
$657$	1.04925	+	0.605782i	0.0409350	+	0.0236338i
$658$		0			0
$659$	−3.98651	+	6.90484i	−0.155293	+	0.268975i	−0.933166	−	0.359447i	$-0.882965\pi$
$659$	−3.98651	+	6.90484i	−0.155293	+	0.268975i	0.777873	+	0.628422i	$0.216299\pi$
$660$	−4.48012	+	7.75979i	−0.174388	+	0.302049i
$661$			3.93370i			0.153003i	0.997069	+	0.0765015i	$0.0243750\pi$
$661$			3.93370i			0.153003i	−0.997069	+	0.0765015i	$0.975625\pi$
$662$	16.1129	−	27.9083i	0.626244	−	1.08469i
$663$	33.5046	−	25.0641i	1.30121	−	0.973411i
$664$	13.2348			0.513611
$665$		0			0
$666$	0.162179	+	0.280902i	0.00628430	+	0.0108847i
$667$	18.5322			0.717570
$668$	−2.79770	−	1.61525i	−0.108246	−	0.0624960i
$669$	−21.1000	+	12.1821i	−0.815772	+	0.470986i
$670$		−	9.36365i		−	0.361749i
$671$		−	36.1477i		−	1.39547i
$672$		0			0
$673$	18.1599	+	31.4539i	0.700014	+	1.21246i	0.968461	+	0.249166i	$0.0801563\pi$
$673$	18.1599	+	31.4539i	0.700014	+	1.21246i	−0.268447	+	0.963295i	$0.586510\pi$
$674$	2.61282	+	1.50851i	0.100642	+	0.0581058i
$675$	3.60756	−	6.24848i	0.138855	−	0.240504i
$676$	−8.96487	−	9.41441i	−0.344803	−	0.362093i
$677$	10.5534	+	18.2790i	0.405600	+	0.702520i	0.994391	−	0.105765i	$-0.0337292\pi$
$677$	10.5534	+	18.2790i	0.405600	+	0.702520i	−0.588791	+	0.808285i	$0.700396\pi$
$678$	35.5750	−	20.5393i	1.36625	−	0.788805i
$679$		0			0
$680$	−2.28432	+	3.95656i	−0.0875997	+	0.151727i
$681$	−45.0771	+	26.0253i	−1.72736	+	0.997292i
$682$	−3.27931	+	1.89331i	−0.125571	+	0.0724985i
$683$	22.8854	−	13.2129i	0.875685	−	0.505577i	0.00645161	−	0.999979i	$-0.497946\pi$
$683$	22.8854	−	13.2129i	0.875685	−	0.505577i	0.869233	+	0.494402i	$0.164613\pi$
$684$	12.0150	−	6.93684i	0.459404	−	0.265237i
$685$	1.43824	−	2.49110i	0.0549522	−	0.0951799i
$686$		0			0
$687$	−40.2914	+	23.2623i	−1.53721	+	0.887511i
$688$	3.85426	+	6.67577i	0.146942	+	0.254511i
$689$	5.62377	+	2.41042i	0.214248	+	0.0918295i
$690$	8.72972	−	15.1203i	0.332335	−	0.575621i
$691$	−0.675291	−	0.389880i	−0.0256893	−	0.0148317i	0.487100	−	0.873346i	$-0.338055\pi$
$691$	−0.675291	−	0.389880i	−0.0256893	−	0.0148317i	−0.512790	+	0.858514i	$0.671388\pi$
$692$	4.58522	+	7.94183i	0.174304	+	0.301903i
$693$		0			0
$694$			0.468540i			0.0177855i
$695$			0.537234i			0.0203785i
$696$	4.35037	−	2.51168i	0.164900	−	0.0952052i
$697$	−17.5337	−	10.1231i	−0.664135	−	0.383438i
$698$	32.2212			1.21959
$699$	−12.1923	−	21.1176i	−0.461154	−	0.798742i
$700$		0			0
$701$	21.5491			0.813899			0.406950	−	0.913451i	$-0.366592\pi$
$701$	21.5491			0.813899			0.406950	+	0.913451i	$0.366592\pi$
$702$	2.44786	−	5.71114i	0.0923887	−	0.215553i
$703$	−0.445357	+	0.771380i	−0.0167969	+	0.0290932i
$704$			4.33716i			0.163463i
$705$	−3.01743	+	5.22634i	−0.113643	+	0.196835i
$706$	−6.55771	+	11.3583i	−0.246803	+	0.427474i
$707$		0			0
$708$	16.9608	+	9.79235i	0.637428	+	0.368019i
$709$			4.53742i			0.170406i	0.996364	+	0.0852031i	$0.0271539\pi$
$709$			4.53742i			0.170406i	−0.996364	+	0.0852031i	$0.972846\pi$
$710$	−2.56060	−	1.47837i	−0.0960978	−	0.0554821i
$711$	−7.34267	−	12.7179i	−0.275372	−	0.476958i
$712$	3.89590	−	6.74790i	0.146005	−	0.252888i
$713$	6.38988	−	3.68920i	0.239303	−	0.138162i
$714$		0			0
$715$	11.2927	−	8.44782i	0.422322	−	0.315931i
$716$	8.47747	+	14.6834i	0.316818	+	0.548745i
$717$			0.713727i			0.0266546i
$718$	4.37981			0.163453
$719$	14.6007			0.544515			0.272258	−	0.962224i	$-0.412230\pi$
$719$	14.6007			0.544515			0.272258	+	0.962224i	$0.412230\pi$
$720$		−	2.02707i		−	0.0755443i
$721$		0			0
$722$	16.5396	+	9.54914i	0.615540	+	0.355382i
$723$	50.1912	−	28.9779i	1.86663	−	1.07770i
$724$	−1.32871	−	2.30140i	−0.0493813	−	0.0855309i
$725$	−9.18081			−0.340967
$726$	15.4961	+	8.94666i	0.575113	+	0.332042i
$727$	30.6315			1.13606			0.568030	−	0.823008i	$-0.307706\pi$
$727$	30.6315			1.13606			0.568030	+	0.823008i	$0.307706\pi$
$728$		0			0
$729$	−12.1866			−0.451355
$730$	0.420985	+	0.243056i	0.0155814	+	0.00899590i
$731$	39.0507			1.44434
$732$	9.54617	+	16.5344i	0.352837	+	0.611131i
$733$	−15.3455	+	8.85973i	−0.566799	+	0.327242i	−0.755870	−	0.654722i	$-0.772786\pi$
$733$	−15.3455	+	8.85973i	−0.566799	+	0.327242i	0.189071	+	0.981963i	$0.439452\pi$
$734$	−22.3597	−	12.9094i	−0.825313	−	0.476495i
$735$		0			0
$736$		−	8.45117i		−	0.311514i
$737$	−45.0321			−1.65878
$738$	8.98303			0.330670
$739$		−	10.4502i		−	0.384417i	−0.981354	−	0.192208i	$-0.938435\pi$
$739$		−	10.4502i		−	0.384417i	0.981354	−	0.192208i	$-0.0615649\pi$
$740$	0.0650705	+	0.112705i	0.00239204	+	0.00414313i
$741$	−50.6225	+	6.03586i	−1.85966	+	0.221733i
$742$		0			0
$743$	42.0103	−	24.2547i	1.54121	−	0.889818i	0.542447	−	0.840090i	$-0.317498\pi$
$743$	42.0103	−	24.2547i	1.54121	−	0.889818i	0.998763	−	0.0497278i	$-0.0158354\pi$
$744$	1.00000	−	1.73205i	0.0366618	−	0.0635001i
$745$	5.05464	+	8.75490i	0.185188	+	0.320755i
$746$	−26.5251	−	15.3143i	−0.971152	−	0.560695i
$747$			29.7480i			1.08842i
$748$	19.0281	+	10.9859i	0.695735	+	0.401683i
$749$		0			0
$750$	−9.48948	+	16.4363i	−0.346507	+	0.600168i
$751$	15.7278	−	27.2413i	0.573914	−	0.994049i	−0.422244	−	0.906482i	$-0.638758\pi$
$751$	15.7278	−	27.2413i	0.573914	−	0.994049i	0.996159	−	0.0875667i	$-0.0279091\pi$
$752$			2.92115i			0.106523i
$753$	9.20931	−	15.9510i	0.335606	−	0.581286i
$754$	−7.85085	+	0.936078i	−0.285911	+	0.0340900i
$755$	11.7898			0.429075
$756$		0			0
$757$	−24.3442	−	42.1654i	−0.884805	−	1.53253i	−0.845937	−	0.533283i	$-0.820958\pi$
$757$	−24.3442	−	42.1654i	−0.884805	−	1.53253i	−0.0388676	−	0.999244i	$-0.512375\pi$
$758$	38.1523			1.38575
$759$	−72.7174	−	41.9834i	−2.63947	−	1.52390i
$760$	4.82072	−	2.78325i	0.174866	−	0.100959i
$761$			46.5749i			1.68834i	0.536077	+	0.844169i	$0.319906\pi$
$761$			46.5749i			1.68834i	−0.536077	+	0.844169i	$0.680094\pi$
$762$			44.7016i			1.61937i
$763$		0			0
$764$	−12.2430	−	21.2056i	−0.442937	−	0.767190i
$765$	−8.89318	−	5.13448i	−0.321534	−	0.185637i
$766$	15.9801	−	27.6783i	0.577384	−	1.00006i
$767$	−18.4647	−	24.6828i	−0.666721	−	0.891243i
$768$	−1.14539	−	1.98388i	−0.0413308	−	0.0715871i
$769$	−24.1069	+	13.9181i	−0.869315	+	0.501899i	−0.867121	−	0.498098i	$-0.834032\pi$
$769$	−24.1069	+	13.9181i	−0.869315	+	0.501899i	−0.00219468	+	0.999998i	$0.500699\pi$
$770$		0			0
$771$	−19.3946	+	33.5924i	−0.698479	+	1.20980i
$772$	−10.6009	+	6.12046i	−0.381536	+	0.220280i
$773$	−24.6578	+	14.2362i	−0.886880	+	0.512040i	−0.872921	−	0.487862i	$-0.837777\pi$
$773$	−24.6578	+	14.2362i	−0.886880	+	0.512040i	−0.0139594	+	0.999903i	$0.504444\pi$
$774$	−15.0051	+	8.66323i	−0.539349	+	0.311393i
$775$	−3.16553	+	1.82762i	−0.113709	+	0.0656500i
$776$	5.85305	−	10.1378i	0.210112	−	0.363925i
$777$		0			0
$778$	4.54304	−	2.62292i	0.162876	−	0.0940364i
$779$	12.3341	+	21.3632i	0.441914	+	0.765417i
$780$	−2.93446	+	6.84641i	−0.105070	+	0.245141i
$781$	−7.10982	+	12.3146i	−0.254409	+	0.440650i
$782$	−37.0771	−	21.4065i	−1.32587	−	0.765494i
$783$	−1.88953	−	3.27276i	−0.0675263	−	0.116959i
$784$		0			0
$785$		−	16.1650i		−	0.576954i
$786$		−	47.3039i		−	1.68727i
$787$	−13.1046	+	7.56594i	−0.467128	+	0.269697i	−0.715037	−	0.699087i	$-0.753590\pi$
$787$	−13.1046	+	7.56594i	−0.467128	+	0.269697i	0.247908	+	0.968783i	$0.420257\pi$
$788$	4.72634	+	2.72876i	0.168369	+	0.0972079i
$789$	23.6430			0.841713
$790$	−2.94608	−	5.10275i	−0.104817	−	0.181548i
$791$		0			0
$792$	−9.74866			−0.346404
$793$	−3.55776	−	29.8388i	−0.126340	−	1.05961i
$794$	−12.2648	+	21.2432i	−0.435261	+	0.753894i
$795$		−	3.50584i		−	0.124339i
$796$	6.40832	−	11.0995i	0.227137	−	0.393413i
$797$	6.97234	−	12.0764i	0.246973	−	0.427770i	−0.715712	−	0.698396i	$-0.753897\pi$
$797$	6.97234	−	12.0764i	0.246973	−	0.427770i	0.962684	+	0.270626i	$0.0872308\pi$
$798$		0			0
$799$	12.8157	+	7.39916i	0.453387	+	0.261763i
$800$			4.18669i			0.148022i
$801$	15.1673	+	8.75683i	0.535909	+	0.309407i
$802$	2.13571	+	3.69916i	0.0754147	+	0.130622i
$803$	1.16892	−	2.02462i	0.0412501	−	0.0714473i
$804$	20.5983	−	11.8924i	0.726446	−	0.419414i
$805$		0			0
$806$	−2.52062	+	1.88562i	−0.0887850	+	0.0664183i
$807$	7.03270	+	12.1810i	0.247563	+	0.428791i
$808$		−	10.7429i		−	0.377934i
$809$	−21.7429			−0.764440			−0.382220	−	0.924071i	$-0.624840\pi$
$809$	−21.7429			−0.764440			−0.382220	+	0.924071i	$0.624840\pi$
$810$	−9.64150			−0.338768
$811$		−	21.1256i		−	0.741819i	−0.928669	−	0.370910i	$-0.879046\pi$
$811$		−	21.1256i		−	0.741819i	0.928669	−	0.370910i	$-0.120954\pi$
$812$		0			0
$813$	−21.1823	−	12.2296i	−0.742895	−	0.428911i
$814$	0.542028	−	0.312940i	0.0189981	−	0.0109685i
$815$	9.16173	+	15.8686i	0.320921	+	0.555852i
$816$	−11.6049			−0.406254
$817$	−41.2054	−	23.7899i	−1.44159	−	0.832304i
$818$	−1.61647			−0.0565185
$819$		0			0
$820$	3.60423			0.125865
$821$	14.0933	+	8.13678i	0.491860	+	0.283976i	0.725346	−	0.688385i	$-0.241680\pi$
$821$	14.0933	+	8.13678i	0.491860	+	0.283976i	−0.233486	+	0.972360i	$0.575013\pi$
$822$	7.30661			0.254847
$823$	9.32713	+	16.1551i	0.325123	+	0.563130i	0.981537	−	0.191271i	$-0.0612609\pi$
$823$	9.32713	+	16.1551i	0.325123	+	0.563130i	−0.656414	+	0.754401i	$0.727928\pi$
$824$	−4.16644	+	2.40550i	−0.145145	+	0.0837994i
$825$	36.0240	+	20.7985i	1.25419	+	0.724109i
$826$		0			0
$827$		−	47.3361i		−	1.64604i	−0.568015	−	0.823018i	$-0.692288\pi$
$827$		−	47.3361i		−	1.64604i	0.568015	−	0.823018i	$-0.307712\pi$
$828$	18.9957			0.660147
$829$	−0.921975			−0.0320215			−0.0160108	−	0.999872i	$-0.505097\pi$
$829$	−0.921975			−0.0320215			−0.0160108	+	0.999872i	$0.505097\pi$
$830$			11.9357i			0.414294i
$831$	25.0944	+	43.4647i	0.870515	+	1.50778i
$832$	0.426876	+	3.58019i	0.0147993	+	0.124121i
$833$		0			0
$834$	−1.18182	+	0.682322i	−0.0409230	+	0.0236269i
$835$	1.45670	−	2.52307i	0.0504111	−	0.0873146i
$836$	−13.3853	−	23.1840i	−0.462941	−	0.801837i
$837$	−1.30301	−	0.752296i	−0.0450388	−	0.0260032i
$838$		−	26.0312i		−	0.899233i
$839$	−14.3894	−	8.30775i	−0.496779	−	0.286815i	0.230604	−	0.973048i	$-0.425930\pi$
$839$	−14.3894	−	8.30775i	−0.496779	−	0.286815i	−0.727382	+	0.686232i	$0.759263\pi$
$840$		0			0
$841$	12.0957	−	20.9503i	0.417093	−	0.722426i
$842$	−18.7696	+	32.5098i	−0.646841	+	1.12036i
$843$			59.0380i			2.03338i
$844$	−9.65552	+	16.7239i	−0.332357	+	0.575659i
$845$	8.49028	−	8.08486i	0.292075	−	0.278128i
$846$	−6.56588			−0.225740
$847$		0			0
$848$	−0.848493	−	1.46963i	−0.0291374	−	0.0504674i
$849$	25.9475			0.890515
$850$	18.3679	+	10.6047i	0.630014	+	0.363739i
$851$	−1.05617	+	0.609779i	−0.0362050	+	0.0209029i
$852$		−	7.51048i		−	0.257305i
$853$			26.3277i			0.901445i	0.892664	+	0.450722i	$0.148834\pi$
$853$			26.3277i			0.901445i	−0.892664	+	0.450722i	$0.851166\pi$
$854$		0			0
$855$	6.25591	+	10.8356i	0.213948	+	0.370568i
$856$	11.8239	+	6.82652i	0.404132	+	0.233325i
$857$	−7.05290	+	12.2160i	−0.240923	+	0.417290i	−0.960977	−	0.276627i	$-0.910783\pi$
$857$	−7.05290	+	12.2160i	−0.240923	+	0.417290i	0.720055	+	0.693917i	$0.244117\pi$
$858$	32.9261	+	14.1125i	1.12408	+	0.481793i
$859$	−11.7359	−	20.3272i	−0.400425	−	0.693557i	0.593352	−	0.804943i	$-0.297804\pi$
$859$	−11.7359	−	20.3272i	−0.400425	−	0.693557i	−0.993777	+	0.111386i	$0.964471\pi$
$860$	−6.02046	+	3.47592i	−0.205296	+	0.118528i
$861$		0			0
$862$	10.7769	−	18.6662i	0.367063	−	0.635772i
$863$	−10.3476	+	5.97418i	−0.352236	+	0.203364i	−0.665670	−	0.746247i	$-0.731854\pi$
$863$	−10.3476	+	5.97418i	−0.352236	+	0.203364i	0.313434	+	0.949610i	$0.398521\pi$
$864$	−1.49246	+	0.861675i	−0.0507747	+	0.0293148i
$865$	−7.16225	+	4.13513i	−0.243524	+	0.140599i
$866$	−2.77056	+	1.59958i	−0.0941474	+	0.0543560i
$867$	−9.92317	+	17.1874i	−0.337009	+	0.583716i
$868$		0			0
$869$	−24.5404	+	14.1684i	−0.832476	+	0.480630i
$870$	2.26513	+	3.92333i	0.0767953	+	0.133013i
$871$	−37.1726	+	4.43218i	−1.25954	+	0.150179i
$872$	2.55874	−	4.43186i	0.0866497	−	0.150082i
$873$	22.7867	+	13.1559i	0.771214	+	0.445261i
$874$	26.0819	+	45.1752i	0.882234	+	1.52807i
$875$		0			0
$876$			1.23479i			0.0417196i
$877$			32.7341i			1.10535i	0.833396	+	0.552677i	$0.186394\pi$
$877$			32.7341i			1.10535i	−0.833396	+	0.552677i	$0.813606\pi$
$878$	−23.0560	+	13.3114i	−0.778101	+	0.449237i
$879$	47.1091	+	27.1984i	1.58895	+	0.917380i
$880$	−3.91142			−0.131854
$881$	−5.29540	−	9.17190i	−0.178407	−	0.309009i	0.762928	−	0.646483i	$-0.223761\pi$
$881$	−5.29540	−	9.17190i	−0.178407	−	0.309009i	−0.941335	+	0.337474i	$0.890428\pi$
$882$		0			0
$883$	−38.6713			−1.30139			−0.650696	−	0.759338i	$-0.725523\pi$
$883$	−38.6713			−1.30139			−0.650696	+	0.759338i	$0.725523\pi$
$884$	16.7883	+	7.19569i	0.564653	+	0.242017i
$885$	−8.83112	+	15.2959i	−0.296855	+	0.514168i
$886$			9.09867i			0.305676i
$887$	−2.36082	+	4.08906i	−0.0792685	+	0.137297i	−0.902935	−	0.429778i	$-0.858592\pi$
$887$	−2.36082	+	4.08906i	−0.0792685	+	0.137297i	0.823666	+	0.567075i	$0.191925\pi$
$888$	−0.165287	+	0.286286i	−0.00554668	+	0.00960714i
$889$		0			0
$890$	6.08551	+	3.51347i	0.203987	+	0.117772i
$891$			46.3684i			1.55340i
$892$	−9.21079	−	5.31785i	−0.308400	−	0.178055i
$893$	−9.01522	−	15.6148i	−0.301683	−	0.522530i
$894$	−12.8394	+	22.2386i	−0.429415	+	0.743769i
$895$	−13.2421	+	7.64531i	−0.442634	+	0.255555i
$896$		0			0
$897$	−64.1580	−	27.4989i	−2.14217	−	0.918162i
$898$	−3.51346	−	6.08550i	−0.117246	−	0.203076i
$899$			1.91450i			0.0638522i
$900$	−9.41043			−0.313681
$901$	−8.59679			−0.286401
$902$		−	17.3336i		−	0.577147i
$903$		0			0
$904$	15.5296	+	8.96603i	0.516507	+	0.298206i
$905$	2.07549	−	1.19829i	0.0689917	−	0.0398324i
$906$	14.9738	+	25.9354i	0.497471	+	0.861646i
$907$	41.9309			1.39229			0.696146	−	0.717900i	$-0.254896\pi$
$907$	41.9309			1.39229			0.696146	+	0.717900i	$0.254896\pi$
$908$	−19.6776	−	11.3609i	−0.653023	−	0.377023i
$909$	24.1468			0.800900
$910$		0			0
$911$	−54.1425			−1.79382			−0.896910	−	0.442213i	$-0.854194\pi$
$911$	−54.1425			−1.79382			−0.896910	+	0.442213i	$0.854194\pi$
$912$	12.2453	+	7.06980i	0.405481	+	0.234105i
$913$	57.4017			1.89972
$914$	−9.57556	−	16.5853i	−0.316731	−	0.548595i
$915$	−14.9114	+	8.60910i	−0.492956	+	0.284608i
$916$	−17.5885	−	10.1547i	−0.581139	−	0.335521i
$917$		0			0
$918$			8.73035i			0.288145i
$919$	−25.8233			−0.851832			−0.425916	−	0.904763i	$-0.640048\pi$
$919$	−25.8233			−0.851832			−0.425916	+	0.904763i	$0.640048\pi$
$920$	7.62159			0.251277
$921$			15.3210i			0.504845i
$922$	1.62828	+	2.82026i	0.0536245	+	0.0928804i
$923$	−4.65690	+	10.8651i	−0.153284	+	0.357628i
$924$		0			0
$925$	0.523222	−	0.302083i	0.0172034	−	0.00993241i
$926$	−10.6381	+	18.4257i	−0.349589	+	0.605506i
$927$	−5.40684	−	9.36493i	−0.177584	−	0.307585i
$928$	1.89907	+	1.09643i	0.0623400	+	0.0359920i
$929$		−	16.0322i		−	0.525999i	−0.964796	−	0.263000i	$-0.915288\pi$
$929$		−	16.0322i		−	0.525999i	0.964796	−	0.263000i	$-0.0847118\pi$
$930$	1.56203	+	0.901839i	0.0512210	+	0.0295725i
$931$		0			0
$932$	5.32231	−	9.21851i	0.174338	−	0.301962i
$933$	−10.5230	+	18.2264i	−0.344508	+	0.596705i
$934$		−	3.33171i		−	0.109017i
$935$	−9.90748	+	17.1603i	−0.324009	+	0.561200i
$936$	−8.04721	+	0.959491i	−0.263031	+	0.0313619i
$937$	47.0232			1.53618			0.768091	−	0.640340i	$-0.221207\pi$
$937$	47.0232			1.53618			0.768091	+	0.640340i	$0.221207\pi$
$938$		0			0
$939$	19.6586	+	34.0496i	0.641533	+	1.11117i
$940$	−2.63441			−0.0859248
$941$	−45.7754	−	26.4284i	−1.49224	−	0.861542i	−0.492275	−	0.870440i	$-0.663835\pi$
$941$	−45.7754	−	26.4284i	−1.49224	−	0.861542i	−0.999960	+	0.00889731i	$0.997168\pi$
$942$	35.5601	−	20.5306i	1.15861	−	0.668923i
$943$			33.7754i			1.09988i
$944$			8.54933i			0.278257i
$945$		0			0
$946$	16.7165	+	28.9539i	0.543502	+	0.941372i
$947$	33.4029	+	19.2852i	1.08545	+	0.626684i	0.932361	−	0.361528i	$-0.117745\pi$
$947$	33.4029	+	19.2852i	1.08545	+	0.626684i	0.153088	+	0.988213i	$0.451078\pi$
$948$	7.48341	−	12.9617i	0.243050	−	0.420975i
$949$	0.765634	−	1.78631i	0.0248535	−	0.0579860i
$950$	−12.9209	−	22.3797i	−0.419210	−	0.726093i
$951$	7.46430	−	4.30951i	0.242046	−	0.139746i
$952$		0			0
$953$	13.6505	−	23.6433i	0.442182	−	0.765882i	−0.555669	−	0.831404i	$-0.687538\pi$
$953$	13.6505	−	23.6433i	0.442182	−	0.765882i	0.997851	+	0.0655217i	$0.0208711\pi$
$954$	3.30330	−	1.90716i	0.106948	−	0.0617466i
$955$	19.1240	−	11.0412i	0.618838	−	0.357286i
$956$	−0.269822	+	0.155782i	−0.00872668	+	0.00503835i
$957$	18.8683	−	10.8936i	0.609924	−	0.352140i
$958$	−0.0926079	+	0.160402i	−0.00299203	+	0.00518234i
$959$		0			0
$960$	1.78914	−	1.03296i	0.0577442	−	0.0333386i
$961$	−15.1189	−	26.1867i	−0.487706	−	0.844731i
$962$	0.416627	−	0.311670i	0.0134326	−	0.0100486i
$963$	−15.3440	+	26.5766i	−0.494453	+	0.856418i
$964$	21.9100	+	12.6498i	0.705674	+	0.407421i
$965$	−5.51966	−	9.56034i	−0.177684	−	0.307758i
$966$		0			0
$967$			25.2494i			0.811966i	0.913881	+	0.405983i	$0.133071\pi$
$967$			25.2494i			0.811966i	−0.913881	+	0.405983i	$0.866929\pi$
$968$			7.81099i			0.251055i
$969$	62.0335	−	35.8151i	1.99280	−	1.15055i
$970$	9.14264	+	5.27851i	0.293553	+	0.169483i
$971$	−6.57364			−0.210958			−0.105479	−	0.994422i	$-0.533638\pi$
$971$	−6.57364			−0.210958			−0.105479	+	0.994422i	$0.533638\pi$
$972$	−9.66031	−	16.7321i	−0.309854	−	0.536684i
$973$		0			0
$974$	−31.2308			−1.00070
$975$	31.7837	+	13.6229i	1.01789	+	0.436281i
$976$	−4.16720	+	7.21780i	−0.133389	+	0.231036i
$977$			13.9457i			0.446163i	0.974800	+	0.223081i	$0.0716116\pi$
$977$			13.9457i			0.446163i	−0.974800	+	0.223081i	$0.928388\pi$
$978$	−23.2720	+	40.3083i	−0.744156	+	1.28892i
$979$	16.8972	−	29.2667i	0.540036	−	0.935369i
$980$		0			0
$981$	9.96151	+	5.75128i	0.318047	+	0.183624i
$982$		−	26.8472i		−	0.856729i
$983$	40.8235	+	23.5695i	1.30207	+	0.751750i	0.980759	−	0.195224i	$-0.0625435\pi$
$983$	40.8235	+	23.5695i	1.30207	+	0.751750i	0.321310	+	0.946974i	$0.395877\pi$
$984$	4.57761	+	7.92864i	0.145929	+	0.252756i
$985$	−2.46090	+	4.26240i	−0.0784107	+	0.135811i
$986$	9.62054	−	5.55442i	0.306380	−	0.176889i
$987$		0			0
$988$	−13.3310	−	17.8203i	−0.424115	−	0.566939i
$989$	−32.5730	−	56.4180i	−1.03576	−	1.79399i
$990$		−	8.79172i		−	0.279419i
$991$	9.41609			0.299112			0.149556	−	0.988753i	$-0.452216\pi$
$991$	9.41609			0.299112			0.149556	+	0.988753i	$0.452216\pi$
$992$	0.873062			0.0277198
$993$			73.8223i			2.34268i
$994$		0			0
$995$	10.0100	+	5.77927i	0.317338	+	0.183215i
$996$	−26.2563	+	15.1591i	−0.831963	+	0.480334i
$997$	−20.2607	−	35.0926i	−0.641664	−	1.11139i	−0.985061	−	0.172204i	$-0.944911\pi$
$997$	−20.2607	−	35.0926i	−0.641664	−	1.11139i	0.343398	−	0.939190i	$-0.388422\pi$
$998$	−15.2869			−0.483899
$999$	0.215372	+	0.124345i	0.00681407	+	0.00393410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.v.e.361.3		12
7.2	even	3		1274.2.o.d.569.4		12
7.3	odd	6		1274.2.m.c.491.6		12
7.4	even	3		182.2.m.b.127.4	yes	12
7.5	odd	6		1274.2.o.e.569.6		12
7.6	odd	2		1274.2.v.d.361.1		12
13.4	even	6		1274.2.o.d.459.1		12
21.11	odd	6		1638.2.bj.g.127.2		12
28.11	odd	6		1456.2.cc.d.673.5		12
91.4	even	6		182.2.m.b.43.4	✓	12
91.11	odd	12		2366.2.a.bf.1.5		6
91.17	odd	6		1274.2.m.c.589.6		12
91.30	even	6	inner	1274.2.v.e.667.3		12
91.67	odd	12		2366.2.a.bh.1.5		6
91.69	odd	6		1274.2.o.e.459.3		12
91.81	even	3		2366.2.d.r.337.11		12
91.82	odd	6		1274.2.v.d.667.1		12
91.88	even	6		2366.2.d.r.337.5		12
273.95	odd	6		1638.2.bj.g.1135.2		12
364.95	odd	6		1456.2.cc.d.225.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.4	✓	12	91.4	even	6
182.2.m.b.127.4	yes	12	7.4	even	3
1274.2.m.c.491.6		12	7.3	odd	6
1274.2.m.c.589.6		12	91.17	odd	6
1274.2.o.d.459.1		12	13.4	even	6
1274.2.o.d.569.4		12	7.2	even	3
1274.2.o.e.459.3		12	91.69	odd	6
1274.2.o.e.569.6		12	7.5	odd	6
1274.2.v.d.361.1		12	7.6	odd	2
1274.2.v.d.667.1		12	91.82	odd	6
1274.2.v.e.361.3		12	1.1	even	1	trivial
1274.2.v.e.667.3		12	91.30	even	6	inner
1456.2.cc.d.225.5		12	364.95	odd	6
1456.2.cc.d.673.5		12	28.11	odd	6
1638.2.bj.g.127.2		12	21.11	odd	6
1638.2.bj.g.1135.2		12	273.95	odd	6
2366.2.a.bf.1.5		6	91.11	odd	12
2366.2.a.bh.1.5		6	91.67	odd	12
2366.2.d.r.337.5		12	91.88	even	6
2366.2.d.r.337.11		12	91.81	even	3

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:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.v (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +2.29079 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.781015 + 0.450919i) q^{5} +(-1.98388 - 1.14539i) q^{6} -1.00000i q^{8} +2.24770 q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +2.29079 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.781015 + 0.450919i) q^{5} +(-1.98388 - 1.14539i) q^{6} -1.00000i q^{8} +2.24770 q^{9} +0.901839 q^{10} -4.33716i q^{11} +(1.14539 + 1.98388i) q^{12} +(-0.426876 - 3.58019i) q^{13} +(-1.78914 + 1.03296i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.53296 + 4.38722i) q^{17} +(-1.94657 - 1.12385i) q^{18} -6.17238i q^{19} +(-0.781015 - 0.450919i) q^{20} +(-2.16858 + 3.75609i) q^{22} +(4.22559 - 7.31893i) q^{23} -2.29079i q^{24} +(-2.09334 + 3.62578i) q^{25} +(-1.42041 + 3.31398i) q^{26} -1.72335 q^{27} +(1.09643 + 1.89907i) q^{29} +2.06592 q^{30} +(0.756094 + 0.436531i) q^{31} +(0.866025 - 0.500000i) q^{32} -9.93552i q^{33} -5.06592i q^{34} +(1.12385 + 1.94657i) q^{36} +(-0.124973 - 0.0721531i) q^{37} +(-3.08619 + 5.34544i) q^{38} +(-0.977882 - 8.20146i) q^{39} +(0.450919 + 0.781015i) q^{40} +(-3.46110 + 1.99827i) q^{41} +(3.85426 - 6.67577i) q^{43} +(3.75609 - 2.16858i) q^{44} +(-1.75549 + 1.01353i) q^{45} +(-7.31893 + 4.22559i) q^{46} +(2.52979 - 1.46057i) q^{47} +(-1.14539 + 1.98388i) q^{48} +(3.62578 - 2.09334i) q^{50} +(5.80247 + 10.0502i) q^{51} +(2.88710 - 2.15978i) q^{52} +(-0.848493 + 1.46963i) q^{53} +(1.49246 + 0.861675i) q^{54} +(1.95571 + 3.38739i) q^{55} -14.1396i q^{57} -2.19286i q^{58} +(7.40394 - 4.27467i) q^{59} +(-1.78914 - 1.03296i) q^{60} +8.33440 q^{61} +(-0.436531 - 0.756094i) q^{62} -1.00000 q^{64} +(1.94777 + 2.60370i) q^{65} +(-4.96776 + 8.60441i) q^{66} -10.3828i q^{67} +(-2.53296 + 4.38722i) q^{68} +(9.67992 - 16.7661i) q^{69} +(-2.83932 - 1.63928i) q^{71} -2.24770i q^{72} +(0.466808 + 0.269511i) q^{73} +(0.0721531 + 0.124973i) q^{74} +(-4.79540 + 8.30588i) q^{75} +(5.34544 - 3.08619i) q^{76} +(-3.25386 + 7.59161i) q^{78} +(-3.26674 - 5.65817i) q^{79} -0.901839i q^{80} -10.6909 q^{81} +3.99654 q^{82} +13.2348i q^{83} +(-3.95656 - 2.28432i) q^{85} +(-6.67577 + 3.85426i) q^{86} +(2.51168 + 4.35037i) q^{87} -4.33716 q^{88} +(6.74790 + 3.89590i) q^{89} +2.02707 q^{90} +8.45117 q^{92} +(1.73205 + 1.00000i) q^{93} -2.92115 q^{94} +(2.78325 + 4.82072i) q^{95} +(1.98388 - 1.14539i) q^{96} +(10.1378 + 5.85305i) q^{97} -9.74866i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9	\( 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9} + 4 q^{10} + 2 q^{12} - 8 q^{13} - 6 q^{15} - 6 q^{16} + 4 q^{17} - 2 q^{22} - 6 q^{23} + 12 q^{25} + 16 q^{26} + 40 q^{27} - 10 q^{29} - 28 q^{30} - 18 q^{31} + 6 q^{36} + 6 q^{37} - 4 q^{38} + 30 q^{39} + 2 q^{40} - 24 q^{41} + 26 q^{43} + 18 q^{44} - 72 q^{45} + 6 q^{46} - 48 q^{47} - 2 q^{48} - 12 q^{50} + 18 q^{51} - 4 q^{52} - 18 q^{53} + 36 q^{54} - 6 q^{55} - 6 q^{59} - 6 q^{60} + 56 q^{61} - 2 q^{62} - 12 q^{64} + 38 q^{65} - 4 q^{68} + 32 q^{69} + 48 q^{71} + 48 q^{73} - 48 q^{75} + 12 q^{76} - 8 q^{78} - 22 q^{79} + 68 q^{81} - 12 q^{82} + 54 q^{85} - 6 q^{86} + 2 q^{87} - 4 q^{88} - 12 q^{89} + 12 q^{90} - 12 q^{92} - 16 q^{94} + 32 q^{95} - 6 q^{96} + 60 q^{97}+O(q^{100}) \) 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9 + 4 * q^10 + 2 * q^12 - 8 * q^13 - 6 * q^15 - 6 * q^16 + 4 * q^17 - 2 * q^22 - 6 * q^23 + 12 * q^25 + 16 * q^26 + 40 * q^27 - 10 * q^29 - 28 * q^30 - 18 * q^31 + 6 * q^36 + 6 * q^37 - 4 * q^38 + 30 * q^39 + 2 * q^40 - 24 * q^41 + 26 * q^43 + 18 * q^44 - 72 * q^45 + 6 * q^46 - 48 * q^47 - 2 * q^48 - 12 * q^50 + 18 * q^51 - 4 * q^52 - 18 * q^53 + 36 * q^54 - 6 * q^55 - 6 * q^59 - 6 * q^60 + 56 * q^61 - 2 * q^62 - 12 * q^64 + 38 * q^65 - 4 * q^68 + 32 * q^69 + 48 * q^71 + 48 * q^73 - 48 * q^75 + 12 * q^76 - 8 * q^78 - 22 * q^79 + 68 * q^81 - 12 * q^82 + 54 * q^85 - 6 * q^86 + 2 * q^87 - 4 * q^88 - 12 * q^89 + 12 * q^90 - 12 * q^92 - 16 * q^94 + 32 * q^95 - 6 * q^96 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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