LMFDB - Embedded newform 1274.2.v.e.667.3

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			667.3
Root			$0.500000 - 3.15681i$ of defining polynomial
Character	$\chi$	$=$	1274.667
Dual form			1274.2.v.e.361.3

$q$-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 $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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	0.315088	−	0.949063i	$-0.397966\pi$
$5$	−0.781015	−	0.450919i	−0.349281	−	0.201657i	−0.664368	+	0.747405i	$0.731299\pi$
$6$	−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	$0.226848\pi$
$11$			4.33716i			1.30770i	−0.756622	+	0.653852i	$0.773152\pi$
$12$	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	−0.376168	−	0.926551i	$-0.622758\pi$
$17$	2.53296	−	4.38722i	0.614333	−	1.06406i	0.990501	−	0.137505i	$-0.0439082\pi$
$18$	−1.94657	+	1.12385i	−0.458811	+	0.264894i
$19$			6.17238i			1.41604i	0.706192	+	0.708021i	$0.250412\pi$
$19$			6.17238i			1.41604i	−0.706192	+	0.708021i	$0.749588\pi$
$20$	−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	0.850124	+	0.526582i	$0.176527\pi$
$23$	4.22559	+	7.31893i	0.881096	+	1.52610i	0.0309711	+	0.999520i	$0.490140\pi$
$24$			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	−0.746085	−	0.665851i	$-0.768069\pi$
$29$	1.09643	−	1.89907i	0.203602	−	0.352649i	0.949686	+	0.313203i	$0.101402\pi$
$30$	2.06592			0.377184
$31$	0.756094	−	0.436531i	0.135799	−	0.0784033i	−0.430562	−	0.902561i	$-0.641684\pi$
$31$	0.756094	−	0.436531i	0.135799	−	0.0784033i	0.566360	+	0.824158i	$0.308351\pi$
$32$	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	−0.510238	−	0.860034i	$-0.670443\pi$
$37$	−0.124973	+	0.0721531i	−0.0205454	+	0.0118619i	0.489692	+	0.871895i	$0.337109\pi$
$38$	−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	0.204762	−	0.978812i	$-0.434358\pi$
$41$	−3.46110	−	1.99827i	−0.540533	−	0.312077i	−0.745295	+	0.666735i	$0.767691\pi$
$42$		0			0
$43$	3.85426	+	6.67577i	0.587768	+	1.01804i	0.994524	+	0.104508i	$0.0333267\pi$
$43$	3.85426	+	6.67577i	0.587768	+	1.01804i	−0.406756	+	0.913537i	$0.633340\pi$
$44$	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	0.673025	−	0.739620i	$-0.264995\pi$
$47$	2.52979	+	1.46057i	0.369008	+	0.213047i	−0.304017	+	0.952667i	$0.598328\pi$
$48$	−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	0.801849	−	0.597527i	$-0.203850\pi$
$53$	−0.848493	−	1.46963i	−0.116549	−	0.201870i	−0.918398	+	0.395658i	$0.870517\pi$
$54$	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	0.897374	−	0.441270i	$-0.145472\pi$
$59$	7.40394	+	4.27467i	0.963911	+	0.556514i	0.0665363	+	0.997784i	$0.478805\pi$
$60$	−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	$0.218684\pi$
$67$			10.3828i			1.26847i	−0.773142	+	0.634233i	$0.781316\pi$
$68$	−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	−0.658929	−	0.752205i	$-0.728990\pi$
$71$	−2.83932	+	1.63928i	−0.336965	+	0.194547i	0.321964	+	0.946752i	$0.395657\pi$
$72$			2.24770i			0.264894i
$73$	0.466808	−	0.269511i	0.0546357	−	0.0315439i	−0.472433	−	0.881366i	$-0.656624\pi$
$73$	0.466808	−	0.269511i	0.0546357	−	0.0315439i	0.527069	+	0.849822i	$0.323291\pi$
$74$	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	−0.989180	−	0.146708i	$-0.953132\pi$
$79$	−3.26674	+	5.65817i	−0.367537	+	0.636593i	0.621643	+	0.783301i	$0.286466\pi$
$80$			0.901839i			0.100829i
$81$	−10.6909			−1.18788
$82$	3.99654			0.441343
$83$		−	13.2348i		−	1.45271i	−0.687319	−	0.726356i	$-0.741212\pi$
$83$		−	13.2348i		−	1.45271i	0.687319	−	0.726356i	$-0.258788\pi$
$84$		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	−0.0977357	−	0.995212i	$-0.531160\pi$
$89$	6.74790	−	3.89590i	0.715276	−	0.412965i	0.813011	+	0.582248i	$0.197827\pi$
$90$	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	0.112541	−	0.993647i	$-0.464101\pi$
$97$	10.1378	−	5.85305i	1.02934	−	0.594287i	0.916794	+	0.399360i	$0.130768\pi$
$98$		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	−0.959858	−	0.280486i	$-0.909504\pi$
$103$	−2.40550	+	4.16644i	−0.237021	+	0.410532i	0.722837	+	0.691018i	$0.242838\pi$
$104$	−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	−0.980630	−	0.195871i	$-0.937247\pi$
$107$	−6.82652	−	11.8239i	−0.659944	−	1.14306i	0.320686	−	0.947186i	$-0.396087\pi$
$108$	−0.861675	+	1.49246i	−0.0829147	+	0.143612i
$109$	4.43186	−	2.55874i	0.424495	−	0.245082i	−0.272503	−	0.962155i	$-0.587852\pi$
$109$	4.43186	−	2.55874i	0.424495	−	0.245082i	0.696999	+	0.717072i	$0.254518\pi$
$110$			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	−0.886958	−	0.461850i	$-0.847186\pi$
$113$	−8.96603	−	15.5296i	−0.843453	−	1.46090i	0.0435052	−	0.999053i	$-0.486147\pi$
$114$	−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	0.000496195		1.00000i	$0.499842\pi$
$127$	−9.75681	+	16.8993i	−0.865777	+	1.49957i	−0.866273	+	0.499570i	$0.833491\pi$
$128$	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	0.0772984	−	0.997008i	$-0.475371\pi$
$131$	10.3248	−	17.8831i	0.902083	−	1.56245i	0.824785	−	0.565446i	$-0.191296\pi$
$132$	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	0.377340	−	0.926075i	$-0.376839\pi$
$137$	−2.76224	−	1.59478i	−0.235994	−	0.136251i	−0.613334	+	0.789823i	$0.710172\pi$
$138$	−16.7661	−	9.67992i	−1.42723	−	0.824009i
$139$	0.297855	+	0.515900i	0.0252637	+	0.0437581i	0.878381	−	0.477961i	$-0.158624\pi$
$139$	0.297855	+	0.515900i	0.0252637	+	0.0437581i	−0.853117	+	0.521719i	$0.825291\pi$
$140$		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	$0.151851\pi$
$149$			11.2096i			0.918329i	−0.888351	+	0.459165i	$0.848149\pi$
$150$	8.30588	+	4.79540i	0.678172	+	0.391543i
$151$	−11.3216	+	6.53653i	−0.921339	+	0.531935i	−0.884062	−	0.467369i	$-0.845202\pi$
$151$	−11.3216	+	6.53653i	−0.921339	+	0.531935i	−0.0372772	+	0.999305i	$0.511868\pi$
$152$	−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	−0.962857	−	0.270012i	$-0.912972\pi$
$157$	−8.96225	−	15.5231i	−0.715266	−	1.23888i	0.247591	−	0.968865i	$-0.420361\pi$
$158$		−	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	$0.292902\pi$
$163$			20.3179i			1.59142i	−0.605678	+	0.795710i	$0.707098\pi$
$164$	−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	0.387833	−	0.921730i	$-0.373224\pi$
$167$	−2.79770	−	1.61525i	−0.216493	−	0.124992i	−0.604325	+	0.796738i	$0.706557\pi$
$168$		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	$-0.854780\pi$
$193$		−	12.2409i		−	0.881120i	0.897723	−	0.440560i	$-0.145220\pi$
$194$	−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	0.658829	−	0.752293i	$-0.271052\pi$
$197$	4.72634	+	2.72876i	0.336738	+	0.194416i	−0.322091	+	0.946709i	$0.604386\pi$
$198$	−4.87433	−	8.44259i	−0.346404	−	0.599989i
$199$	−6.40832	+	11.0995i	−0.454274	+	0.786825i	−0.998646	−	0.0520184i	$-0.983435\pi$
$199$	−6.40832	+	11.0995i	−0.454274	+	0.786825i	0.544372	+	0.838844i	$0.316768\pi$
$200$	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	−0.314649	−	0.949208i	$-0.601887\pi$
$211$	9.65552	−	16.7239i	0.664713	−	1.15132i	0.979363	−	0.202110i	$-0.0647797\pi$
$212$	−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	0.158822	−	0.987307i	$-0.449230\pi$
$223$	−9.21079	−	5.31785i	−0.616800	−	0.356110i	−0.775622	+	0.631197i	$0.782564\pi$
$224$		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	−0.324613	−	0.945847i	$-0.605234\pi$
$227$	−19.6776	−	11.3609i	−1.30605	−	0.754047i	−0.981434	+	0.191800i	$0.938567\pi$
$228$	12.2453	+	7.06980i	0.810962	+	0.468209i
$229$	−17.5885	−	10.1547i	−1.16228	−	0.671042i	−0.210429	−	0.977609i	$-0.567486\pi$
$229$	−17.5885	−	10.1547i	−1.16228	−	0.671042i	−0.951849	+	0.306567i	$0.900820\pi$
$230$	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	−0.986015	−	0.166659i	$-0.946702\pi$
$233$	−5.32231	+	9.21851i	−0.348676	+	0.603925i	0.637338	+	0.770584i	$0.280035\pi$
$234$	−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	$-0.996792\pi$
$239$		−	0.311564i		−	0.0201534i	0.999949	−	0.0100767i	$-0.00320757\pi$
$240$			2.06592i			0.133355i
$241$	21.9100	+	12.6498i	1.41135	+	0.814843i	0.995516	−	0.0945983i	$-0.0301567\pi$
$241$	21.9100	+	12.6498i	1.41135	+	0.814843i	0.415833	+	0.909441i	$0.363490\pi$
$242$	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	0.964555	−	0.263881i	$-0.0850027\pi$
$251$	4.02015	+	6.96311i	0.253750	+	0.439507i	−0.710805	+	0.703389i	$0.751669\pi$
$252$		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	−0.999463	−	0.0327753i	$-0.989565\pi$
$257$	−8.46634	−	14.6641i	−0.528116	−	0.914723i	0.471347	−	0.881948i	$-0.343768\pi$
$258$	−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	−0.757128	−	0.653266i	$-0.773398\pi$
$269$	3.06999	−	5.31738i	0.187181	−	0.324207i	0.944309	+	0.329059i	$0.106732\pi$
$270$	−1.55418			−0.0945846
$271$	−9.24673	+	5.33860i	−0.561699	+	0.324297i	−0.753827	−	0.657073i	$-0.771794\pi$
$271$	−9.24673	+	5.33860i	−0.561699	+	0.324297i	0.192128	+	0.981370i	$0.438461\pi$
$272$	−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	−0.322892	−	0.946436i	$-0.604655\pi$
$277$	10.9545	−	18.9737i	0.658191	−	1.14002i	0.981084	−	0.193585i	$-0.0620114\pi$
$278$	−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	$-0.720898\pi$
$281$		−	25.7719i		−	1.53743i	0.639594	−	0.768713i	$-0.279102\pi$
$282$	−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	0.240530	−	0.970642i	$-0.422679\pi$
$293$	20.5646	−	11.8730i	1.20140	−	0.693626i	0.960865	+	0.277016i	$0.0893454\pi$
$294$		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	$-0.938874\pi$
$307$		−	6.68810i		−	0.381710i	0.981618	−	0.190855i	$-0.0611261\pi$
$308$		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	0.705889	−	0.708322i	$-0.250548\pi$
$311$	−4.59362	−	7.95639i	−0.260480	−	0.451165i	−0.966370	+	0.257157i	$0.917214\pi$
$312$	−8.20146	−	0.977882i	−0.464316	−	0.0553616i
$313$	8.58157	−	14.8637i	0.485059	−	0.840147i	−0.514793	−	0.857314i	$-0.672131\pi$
$313$	8.58157	−	14.8637i	0.485059	−	0.840147i	0.999853	+	0.0171671i	$0.00546471\pi$
$314$	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	0.588706	−	0.808347i	$-0.299638\pi$
$317$	3.25840	+	1.88124i	0.183010	+	0.105661i	−0.405696	+	0.914008i	$0.632971\pi$
$318$	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	$-0.653718\pi$
$331$		−	32.2257i		−	1.77129i	0.464367	−	0.885643i	$-0.346282\pi$
$332$	−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	−0.872245	−	0.489069i	$-0.837337\pi$
$347$	−0.234270	+	0.405768i	−0.0125763	+	0.0217828i	0.859669	+	0.510852i	$0.170670\pi$
$348$	−2.51168	−	4.35037i	−0.134640	−	0.233204i
$349$	−27.9044	−	16.1106i	−1.49369	−	0.862380i	−0.493712	−	0.869625i	$-0.664360\pi$
$349$	−27.9044	−	16.1106i	−1.49369	−	0.862380i	−0.999974	+	0.00724565i	$0.997694\pi$
$350$		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	$0.113489\pi$
$353$			13.1154i			0.698063i	−0.937111	+	0.349031i	$0.886511\pi$
$354$	−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	0.396555	−	0.918011i	$-0.370206\pi$
$359$	−3.79302	−	2.18990i	−0.200188	−	0.115579i	−0.596743	+	0.802432i	$0.703539\pi$
$360$	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	−0.948400	−	0.317076i	$-0.897299\pi$
$379$	−33.0409	−	19.0762i	−1.69720	−	0.979877i	−0.748796	−	0.662801i	$-0.769368\pi$
$380$	−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	$-0.695887\pi$
$383$		−	31.9602i		−	1.63309i	0.577283	−	0.816544i	$-0.304113\pi$
$384$	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	0.791839	−	0.610729i	$-0.209124\pi$
$389$	−2.62292	−	4.54304i	−0.132988	−	0.230341i	−0.924827	+	0.380388i	$0.875790\pi$
$390$	−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	$0.211067\pi$
$397$			24.5296i			1.23110i	−0.788096	+	0.615552i	$0.788933\pi$
$398$		−	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	−0.589512	−	0.807760i	$-0.700680\pi$
$401$	−3.69916	+	2.13571i	−0.184727	+	0.106652i	0.404784	+	0.914412i	$0.367347\pi$
$402$	−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	0.534211	−	0.845351i	$-0.320609\pi$
$409$	1.39990	+	0.808235i	0.0692208	+	0.0399646i	−0.464990	+	0.885316i	$0.653942\pi$
$410$	−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	−0.350480	−	0.936570i	$-0.613982\pi$
$419$	13.0156	−	22.5437i	0.635854	−	1.10133i	0.986334	−	0.164761i	$-0.0526851\pi$
$420$		0			0
$421$			37.5391i			1.82954i	0.403971	+	0.914772i	$0.367630\pi$
$421$			37.5391i			1.82954i	−0.403971	+	0.914772i	$0.632370\pi$
$422$			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	$-0.826265\pi$
$431$		−	21.5538i		−	1.03821i	0.854710	−	0.519106i	$-0.173735\pi$
$432$	0.861675	+	1.49246i	0.0414573	+	0.0718062i
$433$	1.59958	+	2.77056i	0.0768710	+	0.133145i	0.901898	−	0.431948i	$-0.142174\pi$
$433$	1.59958	+	2.77056i	0.0768710	+	0.133145i	−0.825027	+	0.565093i	$0.808840\pi$
$434$		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	0.986448	+	0.164075i	$0.0524638\pi$
$439$	13.3114	+	23.0560i	0.635317	+	1.10040i	−0.351131	+	0.936326i	$0.614203\pi$
$440$	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	−0.953626	−	0.300993i	$-0.902682\pi$
$443$	−4.54933	+	7.87968i	−0.216145	+	0.374375i	0.737481	+	0.675368i	$0.236015\pi$
$444$			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	−0.349483	−	0.936943i	$-0.613643\pi$
$449$	6.08550	−	3.51346i	0.287192	−	0.165811i	0.636675	+	0.771132i	$0.280309\pi$
$450$	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	−0.0591204	−	0.998251i	$-0.518830\pi$
$457$	16.5853	−	9.57556i	0.775830	−	0.447926i	0.834950	+	0.550325i	$0.185496\pi$
$458$	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	−0.564236	−	0.825613i	$-0.690829\pi$
$461$	−2.82026	+	1.62828i	−0.131353	+	0.0758365i	0.432884	+	0.901450i	$0.357496\pi$
$462$		0			0
$463$			21.2761i			0.988786i	0.869238	+	0.494393i	$0.164610\pi$
$463$			21.2761i			0.988786i	−0.869238	+	0.494393i	$0.835390\pi$
$464$	−2.19286			−0.101801
$465$	−1.80368			−0.0836435
$466$		−	10.6446i		−	0.493102i
$467$	1.66586	−	2.88535i	0.0770866	−	0.133518i	−0.824905	−	0.565271i	$-0.808772\pi$
$467$	1.66586	−	2.88535i	0.0770866	−	0.133518i	0.901992	+	0.431753i	$0.142105\pi$
$468$	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	$0.00134689\pi$
$479$			0.185216i			0.00846273i	−0.999991	+	0.00423136i	$0.998653\pi$
$480$	−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	0.966106	−	0.258144i	$-0.0831110\pi$
$487$	27.0466	+	15.6154i	1.22560	+	0.707601i	0.259494	+	0.965745i	$0.416444\pi$
$488$			8.33440i			0.377281i
$489$			46.5440i			2.10479i
$490$		0			0
$491$	13.4236	−	23.2504i	0.605799	−	1.04927i	−0.386126	−	0.922446i	$-0.626187\pi$
$491$	13.4236	−	23.2504i	0.605799	−	1.04927i	0.991925	−	0.126829i	$-0.0404798\pi$
$492$	−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	0.766146	−	0.642667i	$-0.222172\pi$
$499$	13.2389	+	7.64346i	0.592653	+	0.342168i	−0.173493	+	0.984835i	$0.555505\pi$
$500$	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	0.995230	+	0.0975513i	$0.0311010\pi$
$503$	13.0551	+	22.6121i	0.582097	+	1.00822i	−0.413133	+	0.910671i	$0.635566\pi$
$504$		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	−0.789835	−	0.613320i	$-0.789834\pi$
$509$	−14.7459	+	8.51357i	−0.653602	+	0.377357i	0.136233	+	0.990677i	$0.456500\pi$
$510$	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	0.995032	−	0.0995575i	$-0.0317427\pi$
$521$	9.38802	+	16.2605i	0.411297	+	0.712387i	−0.583735	+	0.811944i	$0.698409\pi$
$522$			4.92890i			0.215732i
$523$	1.51624	+	2.62620i	0.0663004	+	0.114836i	0.897270	−	0.441482i	$-0.145547\pi$
$523$	1.51624	+	2.62620i	0.0663004	+	0.114836i	−0.830970	+	0.556318i	$0.812214\pi$
$524$	−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	0.381751	−	0.924265i	$-0.375321\pi$
$541$	−5.29873	−	3.05922i	−0.227810	−	0.131526i	−0.609561	+	0.792739i	$0.708654\pi$
$542$	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	$0.0603144\pi$
$557$			8.89051i			0.376703i	−0.982102	+	0.188352i	$0.939686\pi$
$558$	−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	−0.615394	−	0.788219i	$-0.711003\pi$
$563$	8.89598	−	15.4083i	0.374921	−	0.649382i	0.990315	+	0.138838i	$0.0443366\pi$
$564$	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	0.959044	−	0.283259i	$-0.0914155\pi$
$569$	5.58684	+	9.67669i	0.234212	+	0.405668i	−0.724831	+	0.688927i	$0.758082\pi$
$570$			12.7516i			0.534108i
$571$	8.36194	+	14.4833i	0.349936	+	0.606108i	0.986238	−	0.165333i	$-0.0528698\pi$
$571$	8.36194	+	14.4833i	0.349936	+	0.606108i	−0.636301	+	0.771441i	$0.719537\pi$
$572$	−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	−0.485530	−	0.874220i	$-0.661373\pi$
$577$	0.691857	−	0.399444i	0.0288024	−	0.0166291i	0.514332	+	0.857591i	$0.328040\pi$
$578$	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	0.636509	−	0.771269i	$-0.280378\pi$
$587$	6.94921	+	4.01213i	0.286825	+	0.165598i	−0.349684	+	0.936868i	$0.613711\pi$
$588$		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	0.585116	−	0.810950i	$-0.301049\pi$
$593$	4.27055	+	2.46560i	0.175370	+	0.101250i	−0.409745	+	0.912200i	$0.634382\pi$
$594$	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	0.988640	−	0.150304i	$-0.0480251\pi$
$599$	8.91246	+	15.4368i	0.364153	+	0.630732i	−0.624487	+	0.781035i	$0.714692\pi$
$600$	8.30588	−	4.79540i	0.339086	−	0.195772i
$601$	0.0809165	−	0.140152i	0.00330065	−	0.00571690i	−0.864370	−	0.502856i	$-0.832283\pi$
$601$	0.0809165	−	0.140152i	0.00330065	−	0.00571690i	0.867671	+	0.497139i	$0.165616\pi$
$602$		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	$-0.729332\pi$
$613$		−	37.2124i		−	1.50299i	0.659736	−	0.751497i	$-0.270668\pi$
$614$	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	−0.611914	−	0.790924i	$-0.709600\pi$
$617$	−5.78536	+	3.34018i	−0.232910	+	0.134471i	0.379004	+	0.925395i	$0.376267\pi$
$618$		−	11.0210i		−	0.443328i
$619$	−20.5546	+	11.8672i	−0.826158	+	0.476982i	−0.852535	−	0.522670i	$-0.824936\pi$
$619$	−20.5546	+	11.8672i	−0.826158	+	0.476982i	0.0263776	+	0.999652i	$0.491603\pi$
$620$	−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	−0.0476346	−	0.998865i	$-0.515168\pi$
$631$	19.9348	−	11.5093i	0.793590	−	0.458180i	0.841225	+	0.540685i	$0.181835\pi$
$632$	−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	−0.713643	−	0.700510i	$-0.752956\pi$
$641$	6.32539	−	10.9559i	0.249838	−	0.432732i	0.963481	+	0.267778i	$0.0862893\pi$
$642$	27.0860	+	15.6381i	1.06900	+	0.617186i
$643$	−13.1971	+	7.61938i	−0.520445	+	0.300479i	−0.737117	−	0.675766i	$-0.763813\pi$
$643$	−13.1971	+	7.61938i	−0.520445	+	0.300479i	0.216672	+	0.976244i	$0.430480\pi$
$644$		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	0.996779	+	0.0801974i	$0.0255551\pi$
$653$	14.5106	+	25.1330i	0.567842	+	0.983532i	−0.428937	+	0.903335i	$0.641112\pi$
$654$	−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	0.777873	−	0.628422i	$-0.216299\pi$
$659$	−3.98651	−	6.90484i	−0.155293	−	0.268975i	−0.933166	+	0.359447i	$0.882965\pi$
$660$	−4.48012	−	7.75979i	−0.174388	−	0.302049i
$661$		−	3.93370i		−	0.153003i	−0.997069	−	0.0765015i	$-0.975625\pi$
$661$		−	3.93370i		−	0.153003i	0.997069	−	0.0765015i	$-0.0243750\pi$
$662$	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	−0.268447	−	0.963295i	$-0.586510\pi$
$673$	18.1599	−	31.4539i	0.700014	−	1.21246i	0.968461	−	0.249166i	$-0.0801563\pi$
$674$	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	−0.588791	−	0.808285i	$-0.700396\pi$
$677$	10.5534	−	18.2790i	0.405600	−	0.702520i	0.994391	+	0.105765i	$0.0337292\pi$
$678$	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	0.869233	−	0.494402i	$-0.164613\pi$
$683$	22.8854	+	13.2129i	0.875685	+	0.505577i	0.00645161	+	0.999979i	$0.497946\pi$
$684$	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	−0.512790	−	0.858514i	$-0.671388\pi$
$691$	−0.675291	+	0.389880i	−0.0256893	+	0.0148317i	0.487100	+	0.873346i	$0.338055\pi$
$692$	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	$-0.972846\pi$
$709$		−	4.53742i		−	0.170406i	0.996364	−	0.0852031i	$-0.0271539\pi$
$710$	−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	0.189071	−	0.981963i	$-0.439452\pi$
$733$	−15.3455	−	8.85973i	−0.566799	−	0.327242i	−0.755870	+	0.654722i	$0.772786\pi$
$734$	−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	$0.0615649\pi$
$739$			10.4502i			0.384417i	−0.981354	+	0.192208i	$0.938435\pi$
$740$	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	0.998763	+	0.0497278i	$0.0158354\pi$
$743$	42.0103	+	24.2547i	1.54121	+	0.889818i	0.542447	+	0.840090i	$0.317498\pi$
$744$	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	0.996159	+	0.0875667i	$0.0279091\pi$
$751$	15.7278	+	27.2413i	0.573914	+	0.994049i	−0.422244	+	0.906482i	$0.638758\pi$
$752$		−	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	−0.0388676	+	0.999244i	$0.512375\pi$
$757$	−24.3442	+	42.1654i	−0.884805	+	1.53253i	−0.845937	+	0.533283i	$0.820958\pi$
$758$	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	$-0.680094\pi$
$761$		−	46.5749i		−	1.68834i	0.536077	−	0.844169i	$-0.319906\pi$
$762$		−	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	−0.00219468	−	0.999998i	$-0.500699\pi$
$769$	−24.1069	−	13.9181i	−0.869315	−	0.501899i	−0.867121	+	0.498098i	$0.834032\pi$
$770$		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	−0.0139594	−	0.999903i	$-0.504444\pi$
$773$	−24.6578	−	14.2362i	−0.886880	−	0.512040i	−0.872921	+	0.487862i	$0.837777\pi$
$774$	−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	0.247908	−	0.968783i	$-0.420257\pi$
$787$	−13.1046	−	7.56594i	−0.467128	−	0.269697i	−0.715037	+	0.699087i	$0.753590\pi$
$788$	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	0.962684	−	0.270626i	$-0.0872308\pi$
$797$	6.97234	+	12.0764i	0.246973	+	0.427770i	−0.715712	+	0.698396i	$0.753897\pi$
$798$		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	$0.120954\pi$
$811$			21.1256i			0.741819i	−0.928669	+	0.370910i	$0.879046\pi$
$812$		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	−0.233486	−	0.972360i	$-0.575013\pi$
$821$	14.0933	−	8.13678i	0.491860	−	0.283976i	0.725346	+	0.688385i	$0.241680\pi$
$822$	7.30661			0.254847
$823$	9.32713	−	16.1551i	0.325123	−	0.563130i	−0.656414	−	0.754401i	$-0.727928\pi$
$823$	9.32713	−	16.1551i	0.325123	−	0.563130i	0.981537	+	0.191271i	$0.0612609\pi$
$824$	−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	$0.307712\pi$
$827$			47.3361i			1.64604i	−0.568015	+	0.823018i	$0.692288\pi$
$828$	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	−0.727382	−	0.686232i	$-0.759263\pi$
$839$	−14.3894	+	8.30775i	−0.496779	+	0.286815i	0.230604	+	0.973048i	$0.425930\pi$
$840$		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	$-0.851166\pi$
$853$		−	26.3277i		−	0.901445i	0.892664	−	0.450722i	$-0.148834\pi$
$854$		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	0.720055	−	0.693917i	$-0.244117\pi$
$857$	−7.05290	−	12.2160i	−0.240923	−	0.417290i	−0.960977	+	0.276627i	$0.910783\pi$
$858$	32.9261	−	14.1125i	1.12408	−	0.481793i
$859$	−11.7359	+	20.3272i	−0.400425	+	0.693557i	−0.993777	−	0.111386i	$-0.964471\pi$
$859$	−11.7359	+	20.3272i	−0.400425	+	0.693557i	0.593352	+	0.804943i	$0.297804\pi$
$860$	−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	0.313434	−	0.949610i	$-0.398521\pi$
$863$	−10.3476	−	5.97418i	−0.352236	−	0.203364i	−0.665670	+	0.746247i	$0.731854\pi$
$864$	−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	$-0.813606\pi$
$877$		−	32.7341i		−	1.10535i	0.833396	−	0.552677i	$-0.186394\pi$
$878$	−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	−0.941335	−	0.337474i	$-0.890428\pi$
$881$	−5.29540	+	9.17190i	−0.178407	+	0.309009i	0.762928	+	0.646483i	$0.223761\pi$
$882$		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	0.823666	−	0.567075i	$-0.191925\pi$
$887$	−2.36082	−	4.08906i	−0.0792685	−	0.137297i	−0.902935	+	0.429778i	$0.858592\pi$
$888$	−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	$0.0847118\pi$
$929$			16.0322i			0.525999i	−0.964796	+	0.263000i	$0.915288\pi$
$930$	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	−0.999960	−	0.00889731i	$-0.997168\pi$
$941$	−45.7754	+	26.4284i	−1.49224	+	0.861542i	−0.492275	+	0.870440i	$0.663835\pi$
$942$	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	0.153088	−	0.988213i	$-0.451078\pi$
$947$	33.4029	−	19.2852i	1.08545	−	0.626684i	0.932361	+	0.361528i	$0.117745\pi$
$948$	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	0.997851	−	0.0655217i	$-0.0208711\pi$
$953$	13.6505	+	23.6433i	0.442182	+	0.765882i	−0.555669	+	0.831404i	$0.687538\pi$
$954$	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	$-0.866929\pi$
$967$		−	25.2494i		−	0.811966i	0.913881	−	0.405983i	$-0.133071\pi$
$968$		−	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	$-0.928388\pi$
$977$		−	13.9457i		−	0.446163i	0.974800	−	0.223081i	$-0.0716116\pi$
$978$	−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	0.321310	−	0.946974i	$-0.395877\pi$
$983$	40.8235	−	23.5695i	1.30207	−	0.751750i	0.980759	+	0.195224i	$0.0625435\pi$
$984$	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	0.343398	+	0.939190i	$0.388422\pi$
$997$	−20.2607	+	35.0926i	−0.641664	+	1.11139i	−0.985061	+	0.172204i	$0.944911\pi$
$998$	−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.667.3		12
7.2	even	3		182.2.m.b.43.4	✓	12
7.3	odd	6		1274.2.o.e.459.3		12
7.4	even	3		1274.2.o.d.459.1		12
7.5	odd	6		1274.2.m.c.589.6		12
7.6	odd	2		1274.2.v.d.667.1		12
13.10	even	6		1274.2.o.d.569.4		12
21.2	odd	6		1638.2.bj.g.1135.2		12
28.23	odd	6		1456.2.cc.d.225.5		12
91.9	even	3		2366.2.d.r.337.5		12
91.10	odd	6		1274.2.v.d.361.1		12
91.23	even	6		182.2.m.b.127.4	yes	12
91.30	even	6		2366.2.d.r.337.11		12
91.58	odd	12		2366.2.a.bf.1.5		6
91.62	odd	6		1274.2.o.e.569.6		12
91.72	odd	12		2366.2.a.bh.1.5		6
91.75	odd	6		1274.2.m.c.491.6		12
91.88	even	6	inner	1274.2.v.e.361.3		12
273.23	odd	6		1638.2.bj.g.127.2		12
364.23	odd	6		1456.2.cc.d.673.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.4	✓	12	7.2	even	3
182.2.m.b.127.4	yes	12	91.23	even	6
1274.2.m.c.491.6		12	91.75	odd	6
1274.2.m.c.589.6		12	7.5	odd	6
1274.2.o.d.459.1		12	7.4	even	3
1274.2.o.d.569.4		12	13.10	even	6
1274.2.o.e.459.3		12	7.3	odd	6
1274.2.o.e.569.6		12	91.62	odd	6
1274.2.v.d.361.1		12	91.10	odd	6
1274.2.v.d.667.1		12	7.6	odd	2
1274.2.v.e.361.3		12	91.88	even	6	inner
1274.2.v.e.667.3		12	1.1	even	1	trivial
1456.2.cc.d.225.5		12	28.23	odd	6
1456.2.cc.d.673.5		12	364.23	odd	6
1638.2.bj.g.127.2		12	273.23	odd	6
1638.2.bj.g.1135.2		12	21.2	odd	6
2366.2.a.bf.1.5		6	91.58	odd	12
2366.2.a.bh.1.5		6	91.72	odd	12
2366.2.d.r.337.5		12	91.9	even	3
2366.2.d.r.337.11		12	91.30	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
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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