LMFDB - Embedded newform 1014.2.g.b.437.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(239,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("1014.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.58498535041007616.52
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 12x^{9} + 72x^{6} - 324x^{3} + 729 $ x^12 - 12x^9 + 72x^6 - 324*x^3 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.2
Root			$-0.949550 + 1.44857i$ of defining polynomial
Character	$\chi$	$=$	1014.437
Dual form			1014.2.g.b.239.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.352860 + 1.69573i) q^{3} -1.00000i q^{4} +(0.499019 - 0.499019i) q^{5} +(-1.44857 - 0.949550i) q^{6} +(-1.39812 + 1.39812i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.75098 + 1.19671i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.352860 + 1.69573i) q^{3} -1.00000i q^{4} +(0.499019 - 0.499019i) q^{5} +(-1.44857 - 0.949550i) q^{6} +(-1.39812 + 1.39812i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.75098 + 1.19671i) q^{9} +0.705720i q^{10} +(3.39145 + 3.39145i) q^{11} +(1.69573 - 0.352860i) q^{12} -1.97724i q^{14} +(1.02228 + 0.670116i) q^{15} -1.00000 q^{16} +4.38949 q^{17} +(1.09904 - 2.79144i) q^{18} +(1.70572 + 1.70572i) q^{19} +(-0.499019 - 0.499019i) q^{20} +(-2.86417 - 1.87749i) q^{21} -4.79624 q^{22} -0.998038 q^{23} +(-0.949550 + 1.44857i) q^{24} +4.50196i q^{25} +(-3.00000 - 4.24264i) q^{27} +(1.39812 + 1.39812i) q^{28} +0.998038i q^{29} +(-1.19671 + 0.249020i) q^{30} +(-6.50196 - 6.50196i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.55427 + 6.94769i) q^{33} +(-3.10384 + 3.10384i) q^{34} +1.39538i q^{35} +(1.19671 + 2.75098i) q^{36} +(-4.10384 + 4.10384i) q^{37} -2.41225 q^{38} +0.705720 q^{40} +(-5.24068 + 5.24068i) q^{41} +(3.35286 - 0.697689i) q^{42} -8.88676i q^{43} +(3.39145 - 3.39145i) q^{44} +(-0.775612 + 1.96997i) q^{45} +(0.705720 - 0.705720i) q^{46} +(0.352168 + 0.352168i) q^{47} +(-0.352860 - 1.69573i) q^{48} +3.09052i q^{49} +(-3.18337 - 3.18337i) q^{50} +(1.54888 + 7.44338i) q^{51} +14.2702i q^{53} +(5.12132 + 0.878680i) q^{54} +3.38480 q^{55} -1.97724 q^{56} +(-2.29055 + 3.49431i) q^{57} +(-0.705720 - 0.705720i) q^{58} +(-0.998038 - 0.998038i) q^{59} +(0.670116 - 1.02228i) q^{60} -9.59248 q^{61} +9.19516 q^{62} +(2.17306 - 5.51934i) q^{63} +1.00000i q^{64} +(-1.69240 - 8.13311i) q^{66} +(5.79624 + 5.79624i) q^{67} -4.38949i q^{68} +(-0.352168 - 1.69240i) q^{69} +(-0.986681 - 0.986681i) q^{70} +(7.13508 - 7.13508i) q^{71} +(-2.79144 - 1.09904i) q^{72} +(1.70572 - 1.70572i) q^{73} -5.80371i q^{74} +(-7.63409 + 1.58856i) q^{75} +(1.70572 - 1.70572i) q^{76} -9.48332 q^{77} -0.207679 q^{79} +(-0.499019 + 0.499019i) q^{80} +(6.13578 - 6.58424i) q^{81} -7.41144i q^{82} +(-9.17632 + 9.17632i) q^{83} +(-1.87749 + 2.86417i) q^{84} +(2.19044 - 2.19044i) q^{85} +(6.28389 + 6.28389i) q^{86} +(-1.69240 + 0.352168i) q^{87} +4.79624i q^{88} +(-2.54027 - 2.54027i) q^{89} +(-0.844540 - 1.94142i) q^{90} +0.998038i q^{92} +(8.73127 - 13.3198i) q^{93} -0.498040 q^{94} +1.70237 q^{95} +(1.44857 + 0.949550i) q^{96} +(3.58856 + 3.58856i) q^{97} +(-2.18533 - 2.18533i) q^{98} +(-13.3884 - 5.27124i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{7}+O(q^{10}) $ 12 * q + 12 * q^7	$ 12 q + 12 q^{7} - 12 q^{16} + 12 q^{19} - 36 q^{27} - 12 q^{28} - 12 q^{31} - 36 q^{33} - 12 q^{37} + 36 q^{42} - 36 q^{45} + 36 q^{54} + 36 q^{57} + 36 q^{63} + 12 q^{67} + 12 q^{73} + 12 q^{76} + 72 q^{79} + 72 q^{85} - 36 q^{93} - 72 q^{94} + 60 q^{97} - 36 q^{99}+O(q^{100}) $ 12 * q + 12 * q^7 - 12 * q^16 + 12 * q^19 - 36 * q^27 - 12 * q^28 - 12 * q^31 - 36 * q^33 - 12 * q^37 + 36 * q^42 - 36 * q^45 + 36 * q^54 + 36 * q^57 + 36 * q^63 + 12 * q^67 + 12 * q^73 + 12 * q^76 + 72 * q^79 + 72 * q^85 - 36 * q^93 - 72 * q^94 + 60 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.352860	+	1.69573i	0.203724	+	0.979028i
$3$	0.352860	+	1.69573i	0.203724	+	0.979028i
$4$		−	1.00000i		−	0.500000i
$5$	0.499019	−	0.499019i	0.223168	−	0.223168i	−0.586663	−	0.809831i	$-0.699559\pi$
$5$	0.499019	−	0.499019i	0.223168	−	0.223168i	0.809831	+	0.586663i	$0.199559\pi$
$6$	−1.44857	−	0.949550i	−0.591376	−	0.387652i
$7$	−1.39812	+	1.39812i	−0.528440	+	0.528440i	−0.920107	−	0.391667i	$-0.871898\pi$
$7$	−1.39812	+	1.39812i	−0.528440	+	0.528440i	0.391667	+	0.920107i	$0.371898\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.75098	+	1.19671i	−0.916993	+	0.398903i
$10$			0.705720i			0.223168i
$11$	3.39145	+	3.39145i	1.02256	+	1.02256i	0.999740	+	0.0228223i	$0.00726519\pi$
$11$	3.39145	+	3.39145i	1.02256	+	1.02256i	0.0228223	+	0.999740i	$0.492735\pi$
$12$	1.69573	−	0.352860i	0.489514	−	0.101862i
$13$		0			0
$13$		0			0
$14$		−	1.97724i		−	0.528440i
$15$	1.02228	+	0.670116i	0.263953	+	0.173023i
$16$	−1.00000			−0.250000
$17$	4.38949			1.06461			0.532304	−	0.846553i	$-0.321326\pi$
$17$	4.38949			1.06461			0.532304	+	0.846553i	$0.321326\pi$
$18$	1.09904	−	2.79144i	0.259045	−	0.657948i
$19$	1.70572	+	1.70572i	0.391319	+	0.391319i	0.875157	−	0.483838i	$-0.160758\pi$
$19$	1.70572	+	1.70572i	0.391319	+	0.391319i	−0.483838	+	0.875157i	$0.660758\pi$
$20$	−0.499019	−	0.499019i	−0.111584	−	0.111584i
$21$	−2.86417	−	1.87749i	−0.625013	−	0.409702i
$22$	−4.79624			−1.02256
$23$	−0.998038			−0.208105			−0.104053	−	0.994572i	$-0.533181\pi$
$23$	−0.998038			−0.208105			−0.104053	+	0.994572i	$0.533181\pi$
$24$	−0.949550	+	1.44857i	−0.193826	+	0.295688i
$25$			4.50196i			0.900392i
$26$		0			0
$27$	−3.00000	−	4.24264i	−0.577350	−	0.816497i
$28$	1.39812	+	1.39812i	0.264220	+	0.264220i
$29$			0.998038i			0.185331i	0.995697	+	0.0926655i	$0.0295387\pi$
$29$			0.998038i			0.185331i	−0.995697	+	0.0926655i	$0.970461\pi$
$30$	−1.19671	+	0.249020i	−0.218488	+	0.0454646i
$31$	−6.50196	−	6.50196i	−1.16779	−	1.16779i	−0.982727	−	0.185059i	$-0.940752\pi$
$31$	−6.50196	−	6.50196i	−1.16779	−	1.16779i	−0.185059	−	0.982727i	$-0.559248\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−4.55427	+	6.94769i	−0.792797	+	1.20944i
$34$	−3.10384	+	3.10384i	−0.532304	+	0.532304i
$35$			1.39538i			0.235862i
$36$	1.19671	+	2.75098i	0.199451	+	0.458497i
$37$	−4.10384	+	4.10384i	−0.674667	+	0.674667i	−0.958788	−	0.284121i	$-0.908298\pi$
$37$	−4.10384	+	4.10384i	−0.674667	+	0.674667i	0.284121	+	0.958788i	$0.408298\pi$
$38$	−2.41225			−0.391319
$39$		0			0
$40$	0.705720			0.111584
$41$	−5.24068	+	5.24068i	−0.818457	+	0.818457i	−0.985884	−	0.167428i	$-0.946454\pi$
$41$	−5.24068	+	5.24068i	−0.818457	+	0.818457i	0.167428	+	0.985884i	$0.446454\pi$
$42$	3.35286	−	0.697689i	0.517358	−	0.107656i
$43$		−	8.88676i		−	1.35522i	−0.735422	−	0.677609i	$-0.763016\pi$
$43$		−	8.88676i		−	1.35522i	0.735422	−	0.677609i	$-0.236984\pi$
$44$	3.39145	−	3.39145i	0.511281	−	0.511281i
$45$	−0.775612	+	1.96997i	−0.115621	+	0.293666i
$46$	0.705720	−	0.705720i	0.104053	−	0.104053i
$47$	0.352168	+	0.352168i	0.0513689	+	0.0513689i	0.732325	−	0.680956i	$-0.238435\pi$
$47$	0.352168	+	0.352168i	0.0513689	+	0.0513689i	−0.680956	+	0.732325i	$0.738435\pi$
$48$	−0.352860	−	1.69573i	−0.0509309	−	0.244757i
$49$			3.09052i			0.441503i
$50$	−3.18337	−	3.18337i	−0.450196	−	0.450196i
$51$	1.54888	+	7.44338i	0.216886	+	1.04228i
$52$		0			0
$53$			14.2702i			1.96016i	0.198613	+	0.980078i	$0.436356\pi$
$53$			14.2702i			1.96016i	−0.198613	+	0.980078i	$0.563644\pi$
$54$	5.12132	+	0.878680i	0.696923	+	0.119573i
$55$	3.38480			0.456406
$56$	−1.97724			−0.264220
$57$	−2.29055	+	3.49431i	−0.303391	+	0.462833i
$58$	−0.705720	−	0.705720i	−0.0926655	−	0.0926655i
$59$	−0.998038	−	0.998038i	−0.129934	−	0.129934i	0.639149	−	0.769083i	$-0.279287\pi$
$59$	−0.998038	−	0.998038i	−0.129934	−	0.129934i	−0.769083	+	0.639149i	$0.779287\pi$
$60$	0.670116	−	1.02228i	0.0865117	−	0.131976i
$61$	−9.59248			−1.22819			−0.614096	−	0.789232i	$-0.710479\pi$
$61$	−9.59248			−1.22819			−0.614096	+	0.789232i	$0.710479\pi$
$62$	9.19516			1.16779
$63$	2.17306	−	5.51934i	0.273780	−	0.695372i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−1.69240	−	8.13311i	−0.208320	−	1.00112i
$67$	5.79624	+	5.79624i	0.708123	+	0.708123i	0.966140	−	0.258017i	$-0.0830690\pi$
$67$	5.79624	+	5.79624i	0.708123	+	0.708123i	−0.258017	+	0.966140i	$0.583069\pi$
$68$		−	4.38949i		−	0.532304i
$69$	−0.352168	−	1.69240i	−0.0423960	−	0.203741i
$70$	−0.986681	−	0.986681i	−0.117931	−	0.117931i
$71$	7.13508	−	7.13508i	0.846778	−	0.846778i	−0.142952	−	0.989730i	$-0.545659\pi$
$71$	7.13508	−	7.13508i	0.846778	−	0.846778i	0.989730	+	0.142952i	$0.0456594\pi$
$72$	−2.79144	−	1.09904i	−0.328974	−	0.129523i
$73$	1.70572	−	1.70572i	0.199639	−	0.199639i	−0.600206	−	0.799845i	$-0.704915\pi$
$73$	1.70572	−	1.70572i	0.199639	−	0.199639i	0.799845	+	0.600206i	$0.204915\pi$
$74$		−	5.80371i		−	0.674667i
$75$	−7.63409	+	1.58856i	−0.881509	+	0.183431i
$76$	1.70572	−	1.70572i	0.195659	−	0.195659i
$77$	−9.48332			−1.08072
$78$		0			0
$79$	−0.207679			−0.0233658			−0.0116829	−	0.999932i	$-0.503719\pi$
$79$	−0.207679			−0.0233658			−0.0116829	+	0.999932i	$0.503719\pi$
$80$	−0.499019	+	0.499019i	−0.0557920	+	0.0557920i
$81$	6.13578	−	6.58424i	0.681753	−	0.731582i
$82$		−	7.41144i		−	0.818457i
$83$	−9.17632	+	9.17632i	−1.00723	+	1.00723i	−0.00725871	+	0.999974i	$0.502311\pi$
$83$	−9.17632	+	9.17632i	−1.00723	+	1.00723i	−0.999974	+	0.00725871i	$0.997689\pi$
$84$	−1.87749	+	2.86417i	−0.204851	+	0.312507i
$85$	2.19044	−	2.19044i	0.237587	−	0.237587i
$86$	6.28389	+	6.28389i	0.677609	+	0.677609i
$87$	−1.69240	+	0.352168i	−0.181444	+	0.0377563i
$88$			4.79624i			0.511281i
$89$	−2.54027	−	2.54027i	−0.269268	−	0.269268i	0.559537	−	0.828805i	$-0.310979\pi$
$89$	−2.54027	−	2.54027i	−0.269268	−	0.269268i	−0.828805	+	0.559537i	$0.810979\pi$
$90$	−0.844540	−	1.94142i	−0.0890224	−	0.204644i
$91$		0			0
$92$			0.998038i			0.104053i
$93$	8.73127	−	13.3198i	0.905390	−	1.38120i
$94$	−0.498040			−0.0513689
$95$	1.70237			0.174660
$96$	1.44857	+	0.949550i	0.147844	+	0.0969131i
$97$	3.58856	+	3.58856i	0.364363	+	0.364363i	0.865416	−	0.501053i	$-0.167054\pi$
$97$	3.58856	+	3.58856i	0.364363	+	0.364363i	−0.501053	+	0.865416i	$0.667054\pi$
$98$	−2.18533	−	2.18533i	−0.220751	−	0.220751i
$99$	−13.3884	−	5.27124i	−1.34558	−	0.529780i
$100$	4.50196			0.450196
$101$	−5.08053			−0.505532			−0.252766	−	0.967527i	$-0.581340\pi$
$101$	−5.08053			−0.505532			−0.252766	+	0.967527i	$0.581340\pi$
$102$	−6.35849	−	4.16804i	−0.629584	−	0.412698i
$103$		−	12.2077i		−	1.20286i	−0.798926	−	0.601429i	$-0.794598\pi$
$103$		−	12.2077i		−	1.20286i	0.798926	−	0.601429i	$-0.205402\pi$
$104$		0			0
$105$	−2.36618	+	0.492373i	−0.230915	+	0.0480506i
$106$	−10.0905	−	10.0905i	−0.980078	−	0.980078i
$107$			6.78291i			0.655728i	0.944725	+	0.327864i	$0.106329\pi$
$107$			6.78291i			0.655728i	−0.944725	+	0.327864i	$0.893671\pi$
$108$	−4.24264	+	3.00000i	−0.408248	+	0.288675i
$109$	−3.30760	−	3.30760i	−0.316811	−	0.316811i	0.530730	−	0.847541i	$-0.321918\pi$
$109$	−3.30760	−	3.30760i	−0.316811	−	0.316811i	−0.847541	+	0.530730i	$0.821918\pi$
$110$	−2.39342	+	2.39342i	−0.228203	+	0.228203i
$111$	−8.40707	−	5.51091i	−0.797964	−	0.523073i
$112$	1.39812	−	1.39812i	0.132110	−	0.132110i
$113$		−	13.2721i		−	1.24854i	−0.781211	−	0.624268i	$-0.785397\pi$
$113$		−	13.2721i		−	1.24854i	0.781211	−	0.624268i	$-0.214603\pi$
$114$	−0.851187	−	4.09052i	−0.0797209	−	0.383112i
$115$	−0.498040	+	0.498040i	−0.0464425	+	0.0464425i
$116$	0.998038			0.0926655
$117$		0			0
$118$	1.41144			0.129934
$119$	−6.13704	+	6.13704i	−0.562581	+	0.562581i
$120$	0.249020	+	1.19671i	0.0227323	+	0.109244i
$121$			12.0039i			1.09127i
$122$	6.78291	−	6.78291i	0.614096	−	0.614096i
$123$	−10.7360	−	7.03754i	−0.968031	−	0.634553i
$124$	−6.50196	+	6.50196i	−0.583893	+	0.583893i
$125$	4.74166	+	4.74166i	0.424107	+	0.424107i
$126$	2.36618	+	5.43935i	0.210796	+	0.484576i
$127$		−	11.6191i		−	1.03103i	−0.856881	−	0.515515i	$-0.827601\pi$
$127$		−	11.6191i		−	1.03103i	0.856881	−	0.515515i	$-0.172399\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	15.0695	−	3.13578i	1.32680	−	0.276090i
$130$		0			0
$131$			7.08990i			0.619448i	0.950827	+	0.309724i	$0.100237\pi$
$131$			7.08990i			0.619448i	−0.950827	+	0.309724i	$0.899763\pi$
$132$	6.94769	+	4.55427i	0.604719	+	0.396399i
$133$	−4.76960			−0.413577
$134$	−8.19712			−0.708123
$135$	−3.61422	−	0.620101i	−0.311062	−	0.0533698i
$136$	3.10384	+	3.10384i	0.266152	+	0.266152i
$137$	15.4150	+	15.4150i	1.31700	+	1.31700i	0.916142	+	0.400854i	$0.131286\pi$
$137$	15.4150	+	15.4150i	1.31700	+	1.31700i	0.400854	+	0.916142i	$0.368714\pi$
$138$	1.44573	+	0.947688i	0.123069	+	0.0806725i
$139$	10.8868			0.923403			0.461701	−	0.887035i	$-0.347239\pi$
$139$	10.8868			0.923403			0.461701	+	0.887035i	$0.347239\pi$
$140$	1.39538			0.117931
$141$	−0.472914	+	0.721446i	−0.0398266	+	0.0607567i
$142$			10.0905i			0.846778i
$143$		0			0
$144$	2.75098	−	1.19671i	0.229248	−	0.0997257i
$145$	0.498040	+	0.498040i	0.0413600	+	0.0413600i
$146$			2.41225i			0.199639i
$147$	−5.24068	+	1.09052i	−0.432244	+	0.0899446i
$148$	4.10384	+	4.10384i	0.337334	+	0.337334i
$149$	−2.54027	+	2.54027i	−0.208107	+	0.208107i	−0.803462	−	0.595356i	$-0.797011\pi$
$149$	−2.54027	+	2.54027i	−0.208107	+	0.208107i	0.595356	+	0.803462i	$0.297011\pi$
$150$	4.27484	−	6.52140i	0.349039	−	0.532470i
$151$	4.01332	−	4.01332i	0.326599	−	0.326599i	−0.524693	−	0.851292i	$-0.675820\pi$
$151$	4.01332	−	4.01332i	0.326599	−	0.326599i	0.851292	+	0.524693i	$0.175820\pi$
$152$			2.41225i			0.195659i
$153$	−12.0754	+	5.25294i	−0.976239	+	0.424675i
$154$	6.70572	−	6.70572i	0.540362	−	0.540362i
$155$	−6.48920			−0.521225
$156$		0			0
$157$	4.76960			0.380656			0.190328	−	0.981721i	$-0.439045\pi$
$157$	4.76960			0.380656			0.190328	+	0.981721i	$0.439045\pi$
$158$	0.146852	−	0.146852i	0.0116829	−	0.0116829i
$159$	−24.1983	+	5.03536i	−1.91905	+	0.399330i
$160$		−	0.705720i		−	0.0557920i
$161$	1.39538	−	1.39538i	0.109971	−	0.109971i
$162$	0.317107	+	8.99441i	0.0249143	+	0.706668i
$163$	11.4154	−	11.4154i	0.894120	−	0.894120i	−0.100788	−	0.994908i	$-0.532136\pi$
$163$	11.4154	−	11.4154i	0.894120	−	0.894120i	0.994908	+	0.100788i	$0.0321364\pi$
$164$	5.24068	+	5.24068i	0.409228	+	0.409228i
$165$	1.19436	+	5.73970i	0.0929808	+	0.446835i
$166$		−	12.9773i		−	1.00723i
$167$	7.78095	+	7.78095i	0.602108	+	0.602108i	0.940871	−	0.338764i	$-0.110009\pi$
$167$	7.78095	+	7.78095i	0.602108	+	0.602108i	−0.338764	+	0.940871i	$0.610009\pi$
$168$	−0.697689	−	3.35286i	−0.0538279	−	0.258679i
$169$		0			0
$170$			3.09775i			0.237587i
$171$	−6.73365	−	2.65115i	−0.514935	−	0.202739i
$172$	−8.88676			−0.677609
$173$	19.3507			1.47121			0.735603	−	0.677413i	$-0.236899\pi$
$173$	19.3507			1.47121			0.735603	+	0.677413i	$0.236899\pi$
$174$	0.947688	−	1.44573i	0.0718440	−	0.109600i
$175$	−6.29428	−	6.29428i	−0.475803	−	0.475803i
$176$	−3.39145	−	3.39145i	−0.255640	−	0.255640i
$177$	1.34023	−	2.04457i	0.100738	−	0.153679i
$178$	3.59248			0.269268
$179$	7.08990			0.529924			0.264962	−	0.964259i	$-0.414641\pi$
$179$	7.08990			0.529924			0.264962	+	0.964259i	$0.414641\pi$
$180$	1.96997	+	0.775612i	0.146833	+	0.0578107i
$181$		−	6.20768i		−	0.461413i	−0.973023	−	0.230707i	$-0.925896\pi$
$181$		−	6.20768i		−	0.461413i	0.973023	−	0.230707i	$-0.0741038\pi$
$182$		0			0
$183$	−3.38480	−	16.2662i	−0.250212	−	1.20243i
$184$	−0.705720	−	0.705720i	−0.0520263	−	0.0520263i
$185$			4.09579i			0.301128i
$186$	3.24460	+	15.5925i	0.237906	+	1.14330i
$187$	14.8868	+	14.8868i	1.08863	+	1.08863i
$188$	0.352168	−	0.352168i	0.0256845	−	0.0256845i
$189$	10.1261	+	1.73736i	0.736564	+	0.126374i
$190$	−1.20376	+	1.20376i	−0.0873299	+	0.0873299i
$191$			9.77702i			0.707441i	0.935351	+	0.353720i	$0.115084\pi$
$191$			9.77702i			0.707441i	−0.935351	+	0.353720i	$0.884916\pi$
$192$	−1.69573	+	0.352860i	−0.122379	+	0.0254655i
$193$	−3.79624	+	3.79624i	−0.273259	+	0.273259i	−0.830411	−	0.557152i	$-0.811894\pi$
$193$	−3.79624	+	3.79624i	−0.273259	+	0.273259i	0.557152	+	0.830411i	$0.311894\pi$
$194$	−5.07499			−0.364363
$195$		0			0
$196$	3.09052			0.220751
$197$	7.28193	−	7.28193i	0.518816	−	0.518816i	−0.398397	−	0.917213i	$-0.630433\pi$
$197$	7.28193	−	7.28193i	0.518816	−	0.518816i	0.917213	+	0.398397i	$0.130433\pi$
$198$	13.1944	−	5.73970i	0.937682	−	0.407903i
$199$			18.1544i			1.28693i	0.765475	+	0.643466i	$0.222504\pi$
$199$			18.1544i			1.28693i	−0.765475	+	0.643466i	$0.777496\pi$
$200$	−3.18337	+	3.18337i	−0.225098	+	0.225098i
$201$	−7.78358	+	11.8741i	−0.549011	+	0.837535i
$202$	3.59248	−	3.59248i	0.252766	−	0.252766i
$203$	−1.39538	−	1.39538i	−0.0979363	−	0.0979363i
$204$	7.44338	−	1.54888i	0.521141	−	0.108443i
$205$			5.23040i			0.365307i
$206$	8.63213	+	8.63213i	0.601429	+	0.601429i
$207$	2.74558	−	1.19436i	0.190831	−	0.0830138i
$208$		0			0
$209$			11.5697i			0.800296i
$210$	1.32498	−	2.02130i	0.0914324	−	0.139483i
$211$	11.2943			0.777530			0.388765	−	0.921337i	$-0.372902\pi$
$211$	11.2943			0.777530			0.388765	+	0.921337i	$0.372902\pi$
$212$	14.2702			0.980078
$213$	14.6168	+	9.58146i	1.00153	+	0.656511i
$214$	−4.79624	−	4.79624i	−0.327864	−	0.327864i
$215$	−4.43466	−	4.43466i	−0.302442	−	0.302442i
$216$	0.878680	−	5.12132i	0.0597866	−	0.348462i
$217$	18.1810			1.23421
$218$	4.67765			0.316811
$219$	3.49431	+	2.29055i	0.236124	+	0.154781i
$220$		−	3.38480i		−	0.228203i
$221$		0			0
$222$	9.84150	−	2.04789i	0.660518	−	0.137446i
$223$	−6.19436	−	6.19436i	−0.414805	−	0.414805i	0.468604	−	0.883409i	$-0.344757\pi$
$223$	−6.19436	−	6.19436i	−0.414805	−	0.414805i	−0.883409	+	0.468604i	$0.844757\pi$
$224$			1.97724i			0.132110i
$225$	−5.38753	−	12.3848i	−0.359169	−	0.825653i
$226$	9.38480	+	9.38480i	0.624268	+	0.624268i
$227$	13.5658	−	13.5658i	0.900395	−	0.900395i	−0.0950753	−	0.995470i	$-0.530309\pi$
$227$	13.5658	−	13.5658i	0.900395	−	0.900395i	0.995470	+	0.0950753i	$0.0303092\pi$
$228$	3.49431	+	2.29055i	0.231417	+	0.151696i
$229$	−3.30760	+	3.30760i	−0.218572	+	0.218572i	−0.807897	−	0.589324i	$-0.799394\pi$
$229$	−3.30760	+	3.30760i	−0.218572	+	0.218572i	0.589324	+	0.807897i	$0.299394\pi$
$230$		−	0.704335i		−	0.0464425i
$231$	−3.34628	−	16.0811i	−0.220169	−	1.05806i
$232$	−0.705720	+	0.705720i	−0.0463328	+	0.0463328i
$233$	10.8787			0.712687			0.356344	−	0.934355i	$-0.384023\pi$
$233$	10.8787			0.712687			0.356344	+	0.934355i	$0.384023\pi$
$234$		0			0
$235$	0.351477			0.0229278
$236$	−0.998038	+	0.998038i	−0.0649668	+	0.0649668i
$237$	−0.0732817	−	0.352168i	−0.00476016	−	0.0228757i
$238$		−	8.67908i		−	0.562581i
$239$	5.13900	−	5.13900i	0.332414	−	0.332414i	−0.521088	−	0.853503i	$-0.674474\pi$
$239$	5.13900	−	5.13900i	0.332414	−	0.332414i	0.853503	+	0.521088i	$0.174474\pi$
$240$	−1.02228	−	0.670116i	−0.0659881	−	0.0432558i
$241$	5.06388	−	5.06388i	0.326193	−	0.326193i	−0.524944	−	0.851137i	$-0.675914\pi$
$241$	5.06388	−	5.06388i	0.326193	−	0.326193i	0.851137	+	0.524944i	$0.175914\pi$
$242$	−8.48805	−	8.48805i	−0.545633	−	0.545633i
$243$	13.3301	+	8.08130i	0.855129	+	0.518415i
$244$			9.59248i			0.614096i
$245$	1.54223	+	1.54223i	0.0985294	+	0.0985294i
$246$	12.5678	−	2.61520i	0.801292	−	0.166739i
$247$		0			0
$248$		−	9.19516i		−	0.583893i
$249$	−18.7985	−	12.3226i	−1.19131	−	0.780912i
$250$	−6.70572			−0.424107
$251$	−19.2603			−1.21570			−0.607851	−	0.794051i	$-0.707968\pi$
$251$	−19.2603			−1.21570			−0.607851	+	0.794051i	$0.707968\pi$
$252$	−5.51934	−	2.17306i	−0.347686	−	0.136890i
$253$	−3.38480	−	3.38480i	−0.212801	−	0.212801i
$254$	8.21596	+	8.21596i	0.515515	+	0.515515i
$255$	4.48731	+	2.94147i	0.281006	+	0.184202i
$256$	1.00000			0.0625000
$257$	18.2490			1.13834			0.569171	−	0.822219i	$-0.307264\pi$
$257$	18.2490			1.13834			0.569171	+	0.822219i	$0.307264\pi$
$258$	−8.43843	+	12.8731i	−0.525354	+	0.801444i
$259$		−	11.4753i		−	0.713042i
$260$		0			0
$261$	−1.19436	−	2.74558i	−0.0739290	−	0.169947i
$262$	−5.01332	−	5.01332i	−0.309724	−	0.309724i
$263$		−	3.99215i		−	0.246167i	−0.992396	−	0.123083i	$-0.960722\pi$
$263$		−	3.99215i		−	0.246167i	0.992396	−	0.123083i	$-0.0392783\pi$
$264$	−8.13311	+	1.69240i	−0.500559	+	0.104160i
$265$	7.12108	+	7.12108i	0.437444	+	0.437444i
$266$	3.37262	−	3.37262i	0.206788	−	0.206788i
$267$	3.41124	−	5.20396i	0.208765	−	0.318477i
$268$	5.79624	−	5.79624i	0.354062	−	0.354062i
$269$			10.4814i			0.639060i	0.947576	+	0.319530i	$0.103525\pi$
$269$			10.4814i			0.639060i	−0.947576	+	0.319530i	$0.896475\pi$
$270$	2.99411	−	2.11716i	0.182216	−	0.128846i
$271$	3.37148	−	3.37148i	0.204803	−	0.204803i	−0.597251	−	0.802054i	$-0.703740\pi$
$271$	3.37148	−	3.37148i	0.204803	−	0.204803i	0.802054	+	0.597251i	$0.203740\pi$
$272$	−4.38949			−0.266152
$273$		0			0
$274$	−21.8002			−1.31700
$275$	−15.2682	+	15.2682i	−0.920706	+	0.920706i
$276$	−1.69240	+	0.352168i	−0.101871	+	0.0211980i
$277$			27.2382i			1.63659i	0.574801	+	0.818294i	$0.305080\pi$
$277$			27.2382i			1.63659i	−0.574801	+	0.818294i	$0.694920\pi$
$278$	−7.69810	+	7.69810i	−0.461701	+	0.461701i
$279$	25.6677	+	10.1058i	1.53669	+	0.605019i
$280$	−0.986681	+	0.986681i	−0.0589655	+	0.0589655i
$281$	2.24656	+	2.24656i	0.134019	+	0.134019i	0.770934	−	0.636915i	$-0.219790\pi$
$281$	2.24656	+	2.24656i	0.134019	+	0.134019i	−0.636915	+	0.770934i	$0.719790\pi$
$282$	−0.175738	−	0.844540i	−0.0104651	−	0.0502916i
$283$			3.00392i			0.178564i	0.996006	+	0.0892822i	$0.0284573\pi$
$283$			3.00392i			0.178564i	−0.996006	+	0.0892822i	$0.971543\pi$
$284$	−7.13508	−	7.13508i	−0.423389	−	0.423389i
$285$	0.600699	+	2.88676i	0.0355824	+	0.170997i
$286$		0			0
$287$		−	14.6542i		−	0.865010i
$288$	−1.09904	+	2.79144i	−0.0647613	+	0.164487i
$289$	2.26764			0.133391
$290$	−0.704335			−0.0413600
$291$	−4.81896	+	7.35148i	−0.282492	+	0.430951i
$292$	−1.70572	−	1.70572i	−0.0998197	−	0.0998197i
$293$	−6.98822	−	6.98822i	−0.408256	−	0.408256i	0.472874	−	0.881130i	$-0.343217\pi$
$293$	−6.98822	−	6.98822i	−0.408256	−	0.408256i	−0.881130	+	0.472874i	$0.843217\pi$
$294$	2.93461	−	4.47683i	0.171150	−	0.261094i
$295$	−0.996080			−0.0579940
$296$	−5.80371			−0.337334
$297$	4.21436	−	24.5631i	0.244542	−	1.42529i
$298$		−	3.59248i		−	0.208107i
$299$		0			0
$300$	1.58856	+	7.63409i	0.0917156	+	0.440755i
$301$	12.4248	+	12.4248i	0.716151	+	0.716151i
$302$			5.67569i			0.326599i
$303$	−1.79272	−	8.61520i	−0.102989	−	0.494930i
$304$	−1.70572	−	1.70572i	−0.0978297	−	0.0978297i
$305$	−4.78683	+	4.78683i	−0.274093	+	0.274093i
$306$	4.82421	−	12.2530i	0.275782	−	0.700457i
$307$	8.88284	−	8.88284i	0.506971	−	0.506971i	−0.406625	−	0.913595i	$-0.633294\pi$
$307$	8.88284	−	8.88284i	0.506971	−	0.506971i	0.913595	+	0.406625i	$0.133294\pi$
$308$			9.48332i			0.540362i
$309$	20.7009	−	4.30760i	1.17763	−	0.245051i
$310$	4.58856	−	4.58856i	0.260613	−	0.260613i
$311$	−13.2721			−0.752592			−0.376296	−	0.926499i	$-0.622803\pi$
$311$	−13.2721			−0.752592			−0.376296	+	0.926499i	$0.622803\pi$
$312$		0			0
$313$	−0.913399			−0.0516284			−0.0258142	−	0.999667i	$-0.508218\pi$
$313$	−0.913399			−0.0516284			−0.0258142	+	0.999667i	$0.508218\pi$
$314$	−3.37262	+	3.37262i	−0.190328	+	0.190328i
$315$	−1.66986	−	3.83866i	−0.0940859	−	0.216284i
$316$			0.207679i			0.0116829i
$317$	0.544191	−	0.544191i	0.0305648	−	0.0305648i	−0.691659	−	0.722224i	$-0.743120\pi$
$317$	0.544191	−	0.544191i	0.0305648	−	0.0305648i	0.722224	+	0.691659i	$0.243120\pi$
$318$	13.5502	−	20.6713i	0.759859	−	1.15919i
$319$	−3.38480	+	3.38480i	−0.189512	+	0.189512i
$320$	0.499019	+	0.499019i	0.0278960	+	0.0278960i
$321$	−11.5020	+	2.39342i	−0.641977	+	0.133587i
$322$			1.97336i			0.109971i
$323$	7.48724	+	7.48724i	0.416601	+	0.416601i
$324$	−6.58424	−	6.13578i	−0.365791	−	0.340877i
$325$		0			0
$326$			16.1438i			0.894120i
$327$	4.44167	−	6.77590i	0.245625	−	0.374708i
$328$	−7.41144			−0.409228
$329$	−0.984745			−0.0542908
$330$	−4.90312	−	3.21404i	−0.269908	−	0.176927i
$331$	10.5925	+	10.5925i	0.582215	+	0.582215i	0.935512	−	0.353296i	$-0.114939\pi$
$331$	10.5925	+	10.5925i	0.582215	+	0.582215i	−0.353296	+	0.935512i	$0.614939\pi$
$332$	9.17632	+	9.17632i	0.503616	+	0.503616i
$333$	6.37848	−	16.2007i	0.349539	−	0.887792i
$334$	−11.0039			−0.602108
$335$	5.78487			0.316061
$336$	2.86417	+	1.87749i	0.156253	+	0.102425i
$337$			13.7363i			0.748263i	0.927376	+	0.374131i	$0.122059\pi$
$337$			13.7363i			0.748263i	−0.927376	+	0.374131i	$0.877941\pi$
$338$		0			0
$339$	22.5059	−	4.68320i	1.22235	−	0.254356i
$340$	−2.19044	−	2.19044i	−0.118793	−	0.118793i
$341$		−	44.1022i		−	2.38827i
$342$	6.63606	−	2.88676i	0.358837	−	0.156098i
$343$	−14.1078	−	14.1078i	−0.761747	−	0.761747i
$344$	6.28389	−	6.28389i	0.338805	−	0.338805i
$345$	−1.02028	−	0.668802i	−0.0549300	−	0.0360071i
$346$	−13.6830	+	13.6830i	−0.735603	+	0.735603i
$347$		−	24.3542i		−	1.30740i	−0.756754	−	0.653700i	$-0.773216\pi$
$347$		−	24.3542i		−	1.30740i	0.756754	−	0.653700i	$-0.226784\pi$
$348$	0.352168	+	1.69240i	0.0188782	+	0.0907222i
$349$	−6.48472	+	6.48472i	−0.347119	+	0.347119i	−0.859035	−	0.511916i	$-0.828936\pi$
$349$	−6.48472	+	6.48472i	−0.347119	+	0.347119i	0.511916	+	0.859035i	$0.328936\pi$
$350$	8.90146			0.475803
$351$		0			0
$352$	4.79624			0.255640
$353$	8.63213	−	8.63213i	0.459442	−	0.459442i	−0.439030	−	0.898472i	$-0.644678\pi$
$353$	8.63213	−	8.63213i	0.459442	−	0.459442i	0.898472	+	0.439030i	$0.144678\pi$
$354$	0.498040	+	2.39342i	0.0264705	+	0.127209i
$355$		−	7.12108i		−	0.377948i
$356$	−2.54027	+	2.54027i	−0.134634	+	0.134634i
$357$	−12.5723	−	8.24123i	−0.665394	−	0.436172i
$358$	−5.01332	+	5.01332i	−0.264962	+	0.264962i
$359$	12.5678	+	12.5678i	0.663302	+	0.663302i	0.956157	−	0.292855i	$-0.0946053\pi$
$359$	12.5678	+	12.5678i	0.663302	+	0.663302i	−0.292855	+	0.956157i	$0.594605\pi$
$360$	−1.94142	+	0.844540i	−0.102322	+	0.0445112i
$361$		−	13.1810i		−	0.693739i
$362$	4.38949	+	4.38949i	0.230707	+	0.230707i
$363$	−20.3554	+	4.23570i	−1.06838	+	0.222317i
$364$		0			0
$365$		−	1.70237i		−	0.0891063i
$366$	13.8954	+	9.10854i	0.726323	+	0.476111i
$367$	19.3848			1.01188			0.505939	−	0.862569i	$-0.331146\pi$
$367$	19.3848			1.01188			0.505939	+	0.862569i	$0.331146\pi$
$368$	0.998038			0.0520263
$369$	8.14544	−	20.6886i	0.424035	−	1.07700i
$370$	−2.89616	−	2.89616i	−0.150564	−	0.150564i
$371$	−19.9514	−	19.9514i	−1.03582	−	1.03582i
$372$	−13.3198	−	8.73127i	−0.690601	−	0.452695i
$373$	24.4154			1.26418			0.632090	−	0.774895i	$-0.282197\pi$
$373$	24.4154			1.26418			0.632090	+	0.774895i	$0.282197\pi$
$374$	−21.0531			−1.08863
$375$	−6.36742	+	9.71370i	−0.328812	+	0.501613i
$376$			0.498040i			0.0256845i
$377$		0			0
$378$	−8.38872	+	5.93172i	−0.431469	+	0.305095i
$379$	2.17712	+	2.17712i	0.111831	+	0.111831i	0.760808	−	0.648977i	$-0.224803\pi$
$379$	2.17712	+	2.17712i	0.111831	+	0.111831i	−0.648977	+	0.760808i	$0.724803\pi$
$380$		−	1.70237i		−	0.0873299i
$381$	19.7029	−	4.09992i	1.00941	−	0.210045i
$382$	−6.91340	−	6.91340i	−0.353720	−	0.353720i
$383$	−4.14096	+	4.14096i	−0.211593	+	0.211593i	−0.804944	−	0.593351i	$-0.797805\pi$
$383$	−4.14096	+	4.14096i	−0.211593	+	0.211593i	0.593351	+	0.804944i	$0.297805\pi$
$384$	0.949550	−	1.44857i	0.0484565	−	0.0739220i
$385$	−4.73236	+	4.73236i	−0.241183	+	0.241183i
$386$		−	5.36869i		−	0.273259i
$387$	10.6349	+	24.4473i	0.540600	+	1.24273i
$388$	3.58856	−	3.58856i	0.182182	−	0.182182i
$389$	6.78291			0.343907			0.171954	−	0.985105i	$-0.444992\pi$
$389$	6.78291			0.343907			0.171954	+	0.985105i	$0.444992\pi$
$390$		0			0
$391$	−4.38088			−0.221551
$392$	−2.18533	+	2.18533i	−0.110376	+	0.110376i
$393$	−12.0225	+	2.50174i	−0.606457	+	0.126196i
$394$			10.2982i			0.518816i
$395$	−0.103636	+	0.103636i	−0.00521449	+	0.00521449i
$396$	−5.27124	+	13.3884i	−0.264890	+	0.672792i
$397$	−17.2716	+	17.2716i	−0.866835	+	0.866835i	−0.992121	−	0.125286i	$-0.960015\pi$
$397$	−17.2716	+	17.2716i	−0.866835	+	0.866835i	0.125286	+	0.992121i	$0.460015\pi$
$398$	−12.8371	−	12.8371i	−0.643466	−	0.643466i
$399$	−1.68300	−	8.08794i	−0.0842554	−	0.404904i
$400$		−	4.50196i		−	0.225098i
$401$	−22.1979	−	22.1979i	−1.10851	−	1.10851i	−0.993346	−	0.115166i	$-0.963260\pi$
$401$	−22.1979	−	22.1979i	−1.10851	−	1.10851i	−0.115166	−	0.993346i	$-0.536740\pi$
$402$	−2.89243	−	13.9001i	−0.144262	−	0.693273i
$403$		0			0
$404$			5.08053i			0.252766i
$405$	−0.223789	−	6.34753i	−0.0111202	−	0.315411i
$406$	1.97336			0.0979363
$407$	−27.8360			−1.37978
$408$	−4.16804	+	6.35849i	−0.206349	+	0.314792i
$409$	−3.02664	−	3.02664i	−0.149658	−	0.149658i	0.628307	−	0.777965i	$-0.283748\pi$
$409$	−3.02664	−	3.02664i	−0.149658	−	0.149658i	−0.777965	+	0.628307i	$0.783748\pi$
$410$	−3.69845	−	3.69845i	−0.182653	−	0.182653i
$411$	−20.7004	+	31.5790i	−1.02107	+	1.55768i
$412$	−12.2077			−0.601429
$413$	2.79075			0.137324
$414$	−1.09688	+	2.78596i	−0.0539087	+	0.136923i
$415$			9.15832i			0.449564i
$416$		0			0
$417$	3.84150	+	18.4610i	0.188119	+	0.904038i
$418$	−8.18104	−	8.18104i	−0.400148	−	0.400148i
$419$			34.2215i			1.67183i	0.548858	+	0.835916i	$0.315063\pi$
$419$			34.2215i			1.67183i	−0.548858	+	0.835916i	$0.684937\pi$
$420$	0.492373	+	2.36618i	0.0240253	+	0.115458i
$421$	−2.87344	−	2.87344i	−0.140043	−	0.140043i	0.633610	−	0.773653i	$-0.281572\pi$
$421$	−2.87344	−	2.87344i	−0.140043	−	0.140043i	−0.773653	+	0.633610i	$0.781572\pi$
$422$	−7.98626	+	7.98626i	−0.388765	+	0.388765i
$423$	−1.39025	−	0.547364i	−0.0675962	−	0.0266138i
$424$	−10.0905	+	10.0905i	−0.490039	+	0.490039i
$425$			19.7613i			0.958565i
$426$	−17.1108	+	3.56054i	−0.829019	+	0.172509i
$427$	13.4114	−	13.4114i	0.649025	−	0.649025i
$428$	6.78291			0.327864
$429$		0			0
$430$	6.27156			0.302442
$431$	6.84137	−	6.84137i	0.329537	−	0.329537i	−0.522873	−	0.852410i	$-0.675140\pi$
$431$	6.84137	−	6.84137i	0.329537	−	0.329537i	0.852410	+	0.522873i	$0.175140\pi$
$432$	3.00000	+	4.24264i	0.144338	+	0.204124i
$433$		−	29.2833i		−	1.40727i	−0.710563	−	0.703633i	$-0.751560\pi$
$433$		−	29.2833i		−	1.40727i	0.710563	−	0.703633i	$-0.248440\pi$
$434$	−12.8559	+	12.8559i	−0.617105	+	0.617105i
$435$	−0.668802	+	1.02028i	−0.0320666	+	0.0489186i
$436$	−3.30760	+	3.30760i	−0.158405	+	0.158405i
$437$	−1.70237	−	1.70237i	−0.0814356	−	0.0814356i
$438$	−4.09052	+	0.851187i	−0.195453	+	0.0406713i
$439$			18.0000i			0.859093i	0.903045	+	0.429547i	$0.141327\pi$
$439$			18.0000i			0.859093i	−0.903045	+	0.429547i	$0.858673\pi$
$440$	2.39342	+	2.39342i	0.114102	+	0.114102i
$441$	−3.69845	−	8.50196i	−0.176117	−	0.404855i
$442$		0			0
$443$		−	26.6439i		−	1.26589i	−0.774196	−	0.632946i	$-0.781845\pi$
$443$		−	26.6439i		−	1.26589i	0.774196	−	0.632946i	$-0.218155\pi$
$444$	−5.51091	+	8.40707i	−0.261536	+	0.398982i
$445$	−2.53528			−0.120184
$446$	8.76015			0.414805
$447$	−5.20396	−	3.41124i	−0.246139	−	0.161346i
$448$	−1.39812	−	1.39812i	−0.0660550	−	0.0660550i
$449$	25.9867	+	25.9867i	1.22639	+	1.22639i	0.965320	+	0.261070i	$0.0840755\pi$
$449$	25.9867	+	25.9867i	1.22639	+	1.22639i	0.261070	+	0.965320i	$0.415925\pi$
$450$	12.5669	+	4.94782i	0.592411	+	0.233242i
$451$	−35.5470			−1.67384
$452$	−13.2721			−0.624268
$453$	8.22163	+	5.38935i	0.386286	+	0.253214i
$454$			19.1850i			0.900395i
$455$		0			0
$456$	−4.09052	+	0.851187i	−0.191556	+	0.0398605i
$457$	18.8907	+	18.8907i	0.883669	+	0.883669i	0.993905	−	0.110237i	$-0.0351609\pi$
$457$	18.8907	+	18.8907i	0.883669	+	0.883669i	−0.110237	+	0.993905i	$0.535161\pi$
$458$		−	4.67765i		−	0.218572i
$459$	−13.1685	−	18.6230i	−0.614652	−	0.869249i
$460$	0.498040	+	0.498040i	0.0232212	+	0.0232212i
$461$	−24.8399	+	24.8399i	−1.15691	+	1.15691i	−0.171773	+	0.985137i	$0.554949\pi$
$461$	−24.8399	+	24.8399i	−1.15691	+	1.15691i	−0.985137	+	0.171773i	$0.945051\pi$
$462$	13.7372	+	9.00489i	0.639115	+	0.418945i
$463$	14.0944	−	14.0944i	0.655024	−	0.655024i	−0.299174	−	0.954198i	$-0.596711\pi$
$463$	14.0944	−	14.0944i	0.655024	−	0.655024i	0.954198	+	0.299174i	$0.0967112\pi$
$464$		−	0.998038i		−	0.0463328i
$465$	−2.28978	−	11.0039i	−0.106186	−	0.510295i
$466$	−7.69240	+	7.69240i	−0.356344	+	0.356344i
$467$	16.6769			0.771713			0.385857	−	0.922559i	$-0.373906\pi$
$467$	16.6769			0.771713			0.385857	+	0.922559i	$0.373906\pi$
$468$		0			0
$469$	−16.2077			−0.748401
$470$	−0.248532	+	0.248532i	−0.0114639	+	0.0114639i
$471$	1.68300	+	8.08794i	0.0775486	+	0.372673i
$472$		−	1.41144i		−	0.0649668i
$473$	30.1390	−	30.1390i	1.38579	−	1.38579i
$474$	0.300838	+	0.197202i	0.0138180	+	0.00905779i
$475$	−7.67908	+	7.67908i	−0.352340	+	0.352340i
$476$	6.13704	+	6.13704i	0.281291	+	0.281291i
$477$	−17.0772	−	39.2569i	−0.781911	−	1.79745i
$478$			7.26764i			0.332414i
$479$	−26.4858	−	26.4858i	−1.21017	−	1.21017i	−0.970972	−	0.239193i	$-0.923117\pi$
$479$	−26.4858	−	26.4858i	−1.21017	−	1.21017i	−0.239193	−	0.970972i	$-0.576883\pi$
$480$	1.19671	−	0.249020i	0.0546220	−	0.0113662i
$481$		0			0
$482$			7.16141i			0.326193i
$483$	2.85855	+	1.87381i	0.130069	+	0.0852611i
$484$	12.0039			0.545633
$485$	3.58152			0.162628
$486$	−15.1402	+	3.71149i	−0.686772	+	0.168357i
$487$	−3.67908	−	3.67908i	−0.166715	−	0.166715i	0.618819	−	0.785534i	$-0.287612\pi$
$487$	−3.67908	−	3.67908i	−0.166715	−	0.166715i	−0.785534	+	0.618819i	$0.787612\pi$
$488$	−6.78291	−	6.78291i	−0.307048	−	0.307048i
$489$	23.3854	+	15.3293i	1.05752	+	0.693215i
$490$	−2.18104			−0.0985294
$491$	−40.7107			−1.83725			−0.918625	−	0.395131i	$-0.870699\pi$
$491$	−40.7107			−1.83725			−0.918625	+	0.395131i	$0.870699\pi$
$492$	−7.03754	+	10.7360i	−0.317277	+	0.484016i
$493$			4.38088i			0.197305i
$494$		0			0
$495$	−9.31152	+	4.05062i	−0.418522	+	0.182062i
$496$	6.50196	+	6.50196i	0.291947	+	0.291947i
$497$			19.9514i			0.894942i
$498$	22.0059	−	4.57916i	0.986109	−	0.205197i
$499$	10.5020	+	10.5020i	0.470132	+	0.470132i	0.901957	−	0.431825i	$-0.142130\pi$
$499$	10.5020	+	10.5020i	0.470132	+	0.470132i	−0.431825	+	0.901957i	$0.642130\pi$
$500$	4.74166	−	4.74166i	0.212053	−	0.212053i
$501$	−10.4488	+	15.9399i	−0.466817	+	0.712144i
$502$	13.6191	−	13.6191i	0.607851	−	0.607851i
$503$		−	1.38208i		−	0.0616241i	−0.999525	−	0.0308120i	$-0.990191\pi$
$503$		−	1.38208i		−	0.0616241i	0.999525	−	0.0308120i	$-0.00980933\pi$
$504$	5.43935	−	2.36618i	0.242288	−	0.105398i
$505$	−2.53528	+	2.53528i	−0.112819	+	0.112819i
$506$	4.78683			0.212801
$507$		0			0
$508$	−11.6191			−0.515515
$509$	7.32710	−	7.32710i	0.324768	−	0.324768i	−0.525825	−	0.850593i	$-0.676243\pi$
$509$	7.32710	−	7.32710i	0.324768	−	0.324768i	0.850593	+	0.525825i	$0.176243\pi$
$510$	−5.25294	+	1.09307i	−0.232604	+	0.0484020i
$511$			4.76960i			0.210995i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	2.11960	−	12.3539i	0.0935825	−	0.545439i
$514$	−12.9040	+	12.9040i	−0.569171	+	0.569171i
$515$	−6.09187	−	6.09187i	−0.268440	−	0.268440i
$516$	−3.13578	−	15.0695i	−0.138045	−	0.663399i
$517$			2.38872i			0.105056i
$518$	8.11428	+	8.11428i	0.356521	+	0.356521i
$519$	6.82808	+	32.8135i	0.299719	+	1.44035i
$520$		0			0
$521$		−	2.09971i		−	0.0919901i	−0.998942	−	0.0459950i	$-0.985354\pi$
$521$		−	2.09971i		−	0.0919901i	0.998942	−	0.0459950i	$-0.0146458\pi$
$522$	2.78596	+	1.09688i	0.121938	+	0.0480091i
$523$	−2.76960			−0.121106			−0.0605531	−	0.998165i	$-0.519286\pi$
$523$	−2.76960			−0.121106			−0.0605531	+	0.998165i	$0.519286\pi$
$524$	7.08990			0.309724
$525$	8.45238	−	12.8944i	0.368892	−	0.562757i
$526$	2.82288	+	2.82288i	0.123083	+	0.123083i
$527$	−28.5403	−	28.5403i	−1.24324	−	1.24324i
$528$	4.55427	−	6.94769i	0.198199	−	0.302359i
$529$	−22.0039			−0.956692
$530$	−10.0707			−0.437444
$531$	3.93994	+	1.55122i	0.170979	+	0.0673173i
$532$			4.76960i			0.206788i
$533$		0			0
$534$	1.26764	+	6.09187i	0.0548562	+	0.263621i
$535$	3.38480	+	3.38480i	0.146338	+	0.146338i
$536$			8.19712i			0.354062i
$537$	2.50174	+	12.0225i	0.107958	+	0.518811i
$538$	−7.41144	−	7.41144i	−0.319530	−	0.319530i
$539$	−10.4814	+	10.4814i	−0.451464	+	0.451464i
$540$	−0.620101	+	3.61422i	−0.0266849	+	0.155531i
$541$	−23.0545	+	23.0545i	−0.991190	+	0.991190i	−0.999962	−	0.00877191i	$-0.997208\pi$
$541$	−23.0545	+	23.0545i	−0.991190	+	0.991190i	0.00877191	+	0.999962i	$0.497208\pi$
$542$			4.76800i			0.204803i
$543$	10.5265	−	2.19044i	0.451737	−	0.0940008i
$544$	3.10384	−	3.10384i	0.133076	−	0.133076i
$545$	−3.30111			−0.141404
$546$		0			0
$547$	28.1172			1.20220			0.601101	−	0.799173i	$-0.294729\pi$
$547$	28.1172			1.20220			0.601101	+	0.799173i	$0.294729\pi$
$548$	15.4150	−	15.4150i	0.658498	−	0.658498i
$549$	26.3887	−	11.4794i	1.12624	−	0.489929i
$550$		−	21.5925i		−	0.920706i
$551$	−1.70237	+	1.70237i	−0.0725235	+	0.0725235i
$552$	0.947688	−	1.44573i	0.0403363	−	0.0615343i
$553$	0.290361	−	0.290361i	0.0123474	−	0.0123474i
$554$	−19.2603	−	19.2603i	−0.818294	−	0.818294i
$555$	−6.94534	+	1.44524i	−0.294813	+	0.0613470i
$556$		−	10.8868i		−	0.461701i
$557$	14.0648	+	14.0648i	0.595946	+	0.595946i	0.939231	−	0.343285i	$-0.111540\pi$
$557$	14.0648	+	14.0648i	0.595946	+	0.595946i	−0.343285	+	0.939231i	$0.611540\pi$
$558$	−25.2957	+	11.0039i	−1.07085	+	0.465833i
$559$		0			0
$560$		−	1.39538i		−	0.0589655i
$561$	−19.9909	+	30.4968i	−0.844018	+	1.28758i
$562$	−3.17712			−0.134019
$563$	28.6400			1.20703			0.603517	−	0.797350i	$-0.293766\pi$
$563$	28.6400			1.20703			0.603517	+	0.797350i	$0.293766\pi$
$564$	0.721446	+	0.472914i	0.0303784	+	0.0199133i
$565$	−6.62304	−	6.62304i	−0.278633	−	0.278633i
$566$	−2.12409	−	2.12409i	−0.0892822	−	0.0892822i
$567$	0.626998	+	17.7841i	0.0263314	+	0.746863i
$568$	10.0905			0.423389
$569$	3.48180			0.145965			0.0729823	−	0.997333i	$-0.476748\pi$
$569$	3.48180			0.145965			0.0729823	+	0.997333i	$0.476748\pi$
$570$	−2.46601	−	1.61649i	−0.103290	−	0.0677073i
$571$		−	5.34756i		−	0.223788i	−0.993720	−	0.111894i	$-0.964308\pi$
$571$		−	5.34756i		−	0.223788i	0.993720	−	0.111894i	$-0.0356918\pi$
$572$		0			0
$573$	−16.5792	+	3.44992i	−0.692604	+	0.144122i
$574$	10.3621	+	10.3621i	0.432505	+	0.432505i
$575$		−	4.49313i		−	0.187376i
$576$	−1.19671	−	2.75098i	−0.0498628	−	0.114624i
$577$	−26.4753	−	26.4753i	−1.10218	−	1.10218i	−0.994147	−	0.108035i	$-0.965544\pi$
$577$	−26.4753	−	26.4753i	−1.10218	−	1.10218i	−0.108035	−	0.994147i	$-0.534456\pi$
$578$	−1.60347	+	1.60347i	−0.0666954	+	0.0666954i
$579$	−7.77693	−	5.09785i	−0.323198	−	0.211859i
$580$	0.498040	−	0.498040i	0.0206800	−	0.0206800i
$581$		−	25.6592i		−	1.06452i
$582$	−1.79076	−	8.60580i	−0.0742294	−	0.356722i
$583$	−48.3966	+	48.3966i	−2.00438	+	2.00438i
$584$	2.41225			0.0998197
$585$		0			0
$586$	9.88284			0.408256
$587$	19.3640	−	19.3640i	0.799237	−	0.799237i	−0.183738	−	0.982975i	$-0.558820\pi$
$587$	19.3640	−	19.3640i	0.799237	−	0.799237i	0.982975	+	0.183738i	$0.0588199\pi$
$588$	1.09052	+	5.24068i	0.0449723	+	0.216122i
$589$		−	22.1810i		−	0.913954i
$590$	0.704335	−	0.704335i	0.0289970	−	0.0289970i
$591$	14.9177	+	9.77866i	0.613631	+	0.402240i
$592$	4.10384	−	4.10384i	0.168667	−	0.168667i
$593$	3.14097	+	3.14097i	0.128984	+	0.128984i	0.768652	−	0.639668i	$-0.220928\pi$
$593$	3.14097	+	3.14097i	0.128984	+	0.128984i	−0.639668	+	0.768652i	$0.720928\pi$
$594$	14.3887	+	20.3487i	0.590376	+	0.834918i
$595$			6.12500i			0.251100i
$596$	2.54027	+	2.54027i	0.104053	+	0.104053i
$597$	−30.7849	+	6.40596i	−1.25994	+	0.262178i
$598$		0			0
$599$		−	38.7280i		−	1.58238i	−0.611570	−	0.791191i	$-0.709462\pi$
$599$		−	38.7280i		−	1.58238i	0.611570	−	0.791191i	$-0.290538\pi$
$600$	−6.52140	−	4.27484i	−0.266235	−	0.174520i
$601$	16.2794			0.664051			0.332025	−	0.943270i	$-0.392268\pi$
$601$	16.2794			0.664051			0.332025	+	0.943270i	$0.392268\pi$
$602$	−17.5713			−0.716151
$603$	−22.8817	−	9.00893i	−0.931817	−	0.366872i
$604$	−4.01332	−	4.01332i	−0.163300	−	0.163300i
$605$	5.99019	+	5.99019i	0.243536	+	0.243536i
$606$	7.35951	+	4.82422i	0.298960	+	0.195971i
$607$	−29.0118			−1.17755			−0.588775	−	0.808297i	$-0.700390\pi$
$607$	−29.0118			−1.17755			−0.588775	+	0.808297i	$0.700390\pi$
$608$	2.41225			0.0978297
$609$	1.87381	−	2.85855i	0.0759305	−	0.115834i
$610$		−	6.76960i		−	0.274093i
$611$		0			0
$612$	5.25294	+	12.0754i	0.212338	+	0.488119i
$613$	9.94004	+	9.94004i	0.401474	+	0.401474i	0.878752	−	0.477278i	$-0.158377\pi$
$613$	9.94004	+	9.94004i	0.401474	+	0.401474i	−0.477278	+	0.878752i	$0.658377\pi$
$614$			12.5622i			0.506971i
$615$	−8.86933	+	1.84560i	−0.357646	+	0.0744217i
$616$	−6.70572	−	6.70572i	−0.270181	−	0.270181i
$617$	−2.15622	+	2.15622i	−0.0868062	+	0.0868062i	−0.749177	−	0.662370i	$-0.769551\pi$
$617$	−2.15622	+	2.15622i	−0.0868062	+	0.0868062i	0.662370	+	0.749177i	$0.269551\pi$
$618$	−11.5918	+	17.6837i	−0.466291	+	0.711342i
$619$	−0.683001	+	0.683001i	−0.0274521	+	0.0274521i	−0.720700	−	0.693247i	$-0.756179\pi$
$619$	−0.683001	+	0.683001i	−0.0274521	+	0.0274521i	0.693247	+	0.720700i	$0.256179\pi$
$620$			6.48920i			0.260613i
$621$	2.99411	+	4.23432i	0.120150	+	0.169917i
$622$	9.38480	−	9.38480i	0.376296	−	0.376296i
$623$	7.10320			0.284584
$624$		0			0
$625$	−17.7774			−0.711098
$626$	0.645871	−	0.645871i	0.0258142	−	0.0258142i
$627$	−19.6191	+	4.08250i	−0.783512	+	0.163039i
$628$		−	4.76960i		−	0.190328i
$629$	−18.0138	+	18.0138i	−0.718256	+	0.718256i
$630$	3.89511	+	1.53357i	0.155185	+	0.0610989i
$631$	7.98668	−	7.98668i	0.317945	−	0.317945i	−0.530033	−	0.847977i	$-0.677820\pi$
$631$	7.98668	−	7.98668i	0.317945	−	0.317945i	0.847977	+	0.530033i	$0.177820\pi$
$632$	−0.146852	−	0.146852i	−0.00584144	−	0.00584144i
$633$	3.98530	+	19.1520i	0.158401	+	0.761224i
$634$			0.769602i			0.0305648i
$635$	−5.79816	−	5.79816i	−0.230093	−	0.230093i
$636$	5.03536	+	24.1983i	0.199665	+	0.959524i
$637$		0			0
$638$		−	4.78683i		−	0.189512i
$639$	−11.0898	+	28.1670i	−0.438708	+	1.11427i
$640$	−0.705720			−0.0278960
$641$	−29.7417			−1.17473			−0.587363	−	0.809323i	$-0.699834\pi$
$641$	−29.7417			−1.17473			−0.587363	+	0.809323i	$0.699834\pi$
$642$	6.44071	−	9.82551i	0.254195	−	0.387782i
$643$	−13.3887	−	13.3887i	−0.528000	−	0.528000i	0.391976	−	0.919975i	$-0.371792\pi$
$643$	−13.3887	−	13.3887i	−0.528000	−	0.528000i	−0.919975	+	0.391976i	$0.871792\pi$
$644$	−1.39538	−	1.39538i	−0.0549856	−	0.0549856i
$645$	5.95516	−	9.08479i	0.234484	−	0.357713i
$646$	−10.5886			−0.416601
$647$	8.77898			0.345137			0.172569	−	0.984997i	$-0.444793\pi$
$647$	8.77898			0.345137			0.172569	+	0.984997i	$0.444793\pi$
$648$	8.99441	−	0.317107i	0.353334	−	0.0124572i
$649$		−	6.76960i		−	0.265730i
$650$		0			0
$651$	6.41536	+	30.8301i	0.251438	+	1.20833i
$652$	−11.4154	−	11.4154i	−0.447060	−	0.447060i
$653$		−	30.2161i		−	1.18245i	−0.806508	−	0.591223i	$-0.798645\pi$
$653$		−	30.2161i		−	1.18245i	0.806508	−	0.591223i	$-0.201355\pi$
$654$	1.65056	+	7.93202i	0.0645418	+	0.310167i
$655$	3.53800	+	3.53800i	0.138241	+	0.138241i
$656$	5.24068	−	5.24068i	0.204614	−	0.204614i
$657$	−2.65115	+	6.73365i	−0.103431	+	0.262705i
$658$	0.696320	−	0.696320i	0.0271454	−	0.0271454i
$659$			5.10712i			0.198945i	0.995040	+	0.0994726i	$0.0317156\pi$
$659$			5.10712i			0.198945i	−0.995040	+	0.0994726i	$0.968284\pi$
$660$	5.73970	−	1.19436i	0.223417	−	0.0464904i
$661$	30.2488	−	30.2488i	1.17654	−	1.17654i	0.195925	−	0.980619i	$-0.437229\pi$
$661$	30.2488	−	30.2488i	1.17654	−	1.17654i	0.980619	−	0.195925i	$-0.0627708\pi$
$662$	−14.9800			−0.582215
$663$		0			0
$664$	−12.9773			−0.503616
$665$	−2.38012	+	2.38012i	−0.0922972	+	0.0922972i
$666$	6.94534	+	15.9659i	0.269126	+	0.618665i
$667$		−	0.996080i		−	0.0385684i
$668$	7.78095	−	7.78095i	0.301054	−	0.301054i
$669$	8.31820	−	12.6897i	0.321600	−	0.490612i
$670$	−4.09052	+	4.09052i	−0.158031	+	0.158031i
$671$	−32.5325	−	32.5325i	−1.25590	−	1.25590i
$672$	−3.35286	+	0.697689i	−0.129339	+	0.0269139i
$673$			40.8601i			1.57504i	0.616288	+	0.787521i	$0.288636\pi$
$673$			40.8601i			1.57504i	−0.616288	+	0.787521i	$0.711364\pi$
$674$	−9.71302	−	9.71302i	−0.374131	−	0.374131i
$675$	19.1002	−	13.5059i	0.735167	−	0.519842i
$676$		0			0
$677$		−	25.8399i		−	0.993108i	−0.868006	−	0.496554i	$-0.834599\pi$
$677$		−	25.8399i		−	0.993108i	0.868006	−	0.496554i	$-0.165401\pi$
$678$	−12.6025	+	19.2256i	−0.483998	+	0.738354i
$679$	−10.0345			−0.385088
$680$	3.09775			0.118793
$681$	27.7908	+	18.2171i	1.06494	+	0.698080i
$682$	31.1850	+	31.1850i	1.19413	+	1.19413i
$683$	2.09971	+	2.09971i	0.0803433	+	0.0803433i	0.746136	−	0.665793i	$-0.231907\pi$
$683$	2.09971	+	2.09971i	0.0803433	+	0.0803433i	−0.665793	+	0.746136i	$0.731907\pi$
$684$	−2.65115	+	6.73365i	−0.101369	+	0.257467i
$685$	15.3848			0.587823
$686$	19.9514			0.761747
$687$	−6.77590	−	4.44167i	−0.258517	−	0.169460i
$688$			8.88676i			0.338805i
$689$		0			0
$690$	1.19436	−	0.248532i	0.0454685	−	0.00946144i
$691$	−24.5020	−	24.5020i	−0.932098	−	0.932098i	0.0657384	−	0.997837i	$-0.479060\pi$
$691$	−24.5020	−	24.5020i	−0.932098	−	0.932098i	−0.997837	+	0.0657384i	$0.979060\pi$
$692$		−	19.3507i		−	0.735603i
$693$	26.0884	−	11.3488i	0.991017	−	0.431104i
$694$	17.2210	+	17.2210i	0.653700	+	0.653700i
$695$	5.43270	−	5.43270i	0.206074	−	0.206074i
$696$	−1.44573	−	0.947688i	−0.0548002	−	0.0359220i
$697$	−23.0039	+	23.0039i	−0.871336	+	0.871336i
$698$		−	9.17078i		−	0.347119i
$699$	3.83866	+	18.4473i	0.145191	+	0.697741i
$700$	−6.29428	+	6.29428i	−0.237901	+	0.237901i
$701$	19.6710			0.742962			0.371481	−	0.928440i	$-0.378850\pi$
$701$	19.6710			0.742962			0.371481	+	0.928440i	$0.378850\pi$
$702$		0			0
$703$	−14.0000			−0.528020
$704$	−3.39145	+	3.39145i	−0.127820	+	0.127820i
$705$	0.124022	+	0.596009i	0.00467094	+	0.0224470i
$706$			12.2077i			0.459442i
$707$	7.10320	−	7.10320i	0.267143	−	0.267143i
$708$	−2.04457	−	1.34023i	−0.0768396	−	0.0503690i
$709$	26.0944	−	26.0944i	0.979997	−	0.979997i	−0.0198066	−	0.999804i	$-0.506305\pi$
$709$	26.0944	−	26.0944i	0.979997	−	0.979997i	0.999804	+	0.0198066i	$0.00630504\pi$
$710$	5.03536	+	5.03536i	0.188974	+	0.188974i
$711$	0.571322	−	0.248532i	0.0214262	−	0.00932066i
$712$		−	3.59248i		−	0.134634i
$713$	6.48920	+	6.48920i	0.243023	+	0.243023i
$714$	14.7174	−	3.06250i	0.550783	−	0.114611i
$715$		0			0
$716$		−	7.08990i		−	0.264962i
$717$	10.5277	+	6.90099i	0.393164	+	0.257722i
$718$	−17.7735			−0.663302
$719$	−28.7437			−1.07196			−0.535979	−	0.844231i	$-0.680057\pi$
$719$	−28.7437			−1.07196			−0.535979	+	0.844231i	$0.680057\pi$
$720$	0.775612	−	1.96997i	0.0289053	−	0.0734165i
$721$	17.0678	+	17.0678i	0.635638	+	0.635638i
$722$	9.32040	+	9.32040i	0.346870	+	0.346870i
$723$	10.3738	+	6.80012i	0.385806	+	0.252899i
$724$	−6.20768			−0.230707
$725$	−4.49313			−0.166871
$726$	11.3983	−	17.3885i	0.423032	−	0.645348i
$727$		−	11.3848i		−	0.422239i	−0.977460	−	0.211119i	$-0.932289\pi$
$727$		−	11.3848i		−	0.422239i	0.977460	−	0.211119i	$-0.0677109\pi$
$728$		0			0
$729$	−9.00000	+	25.4558i	−0.333333	+	0.942809i
$730$	1.20376	+	1.20376i	0.0445532	+	0.0445532i
$731$		−	39.0084i		−	1.44278i
$732$	−16.2662	+	3.38480i	−0.601217	+	0.125106i
$733$	−27.3154	−	27.3154i	−1.00892	−	1.00892i	−0.999960	−	0.00895888i	$-0.997148\pi$
$733$	−27.3154	−	27.3154i	−1.00892	−	1.00892i	−0.00895888	−	0.999960i	$-0.502852\pi$
$734$	−13.7071	+	13.7071i	−0.505939	+	0.505939i
$735$	−2.07101	+	3.15939i	−0.0763903	+	0.116536i
$736$	−0.705720	+	0.705720i	−0.0260132	+	0.0260132i
$737$			39.3154i			1.44820i
$738$	8.86933	+	20.3887i	0.326484	+	0.750519i
$739$	2.26764	−	2.26764i	0.0834166	−	0.0834166i	−0.664167	−	0.747584i	$-0.731214\pi$
$739$	2.26764	−	2.26764i	0.0834166	−	0.0834166i	0.747584	+	0.664167i	$0.231214\pi$
$740$	4.09579			0.150564
$741$		0			0
$742$	28.2155			1.03582
$743$	0.645871	−	0.645871i	0.0236947	−	0.0236947i	−0.695160	−	0.718855i	$-0.744667\pi$
$743$	0.645871	−	0.645871i	0.0236947	−	0.0236947i	0.718855	+	0.695160i	$0.244667\pi$
$744$	15.5925	−	3.24460i	0.571648	−	0.118953i
$745$			2.53528i			0.0928856i
$746$	−17.2643	+	17.2643i	−0.632090	+	0.632090i
$747$	14.2625	−	36.2253i	0.521838	−	1.32541i
$748$	14.8868	−	14.8868i	0.544314	−	0.544314i
$749$	−9.48332	−	9.48332i	−0.346513	−	0.346513i
$750$	−2.36618	−	11.3711i	−0.0864006	−	0.415213i
$751$		−	26.5964i		−	0.970516i	−0.874371	−	0.485258i	$-0.838726\pi$
$751$		−	26.5964i		−	0.970516i	0.874371	−	0.485258i	$-0.161274\pi$
$752$	−0.352168	−	0.352168i	−0.0128422	−	0.0128422i
$753$	−6.79620	−	32.6603i	−0.247667	−	1.19021i
$754$		0			0
$755$		−	4.00545i		−	0.145773i
$756$	1.73736	−	10.1261i	0.0631872	−	0.368282i
$757$	−8.19984			−0.298028			−0.149014	−	0.988835i	$-0.547610\pi$
$757$	−8.19984			−0.298028			−0.149014	+	0.988835i	$0.547610\pi$
$758$	−3.07891			−0.111831
$759$	4.54534	−	6.93406i	0.164985	−	0.251690i
$760$	1.20376	+	1.20376i	0.0436650	+	0.0436650i
$761$	−7.64739	−	7.64739i	−0.277218	−	0.277218i	0.554780	−	0.831997i	$-0.312803\pi$
$761$	−7.64739	−	7.64739i	−0.277218	−	0.277218i	−0.831997	+	0.554780i	$0.812803\pi$
$762$	−11.0329	+	16.8311i	−0.399681	+	0.609727i
$763$	9.24884			0.334831
$764$	9.77702			0.353720
$765$	−3.40454	+	8.64718i	−0.123091	+	0.312639i
$766$		−	5.85620i		−	0.211593i
$767$		0			0
$768$	0.352860	+	1.69573i	0.0127327	+	0.0611893i
$769$	−6.14772	−	6.14772i	−0.221692	−	0.221692i	0.587518	−	0.809211i	$-0.300105\pi$
$769$	−6.14772	−	6.14772i	−0.221692	−	0.221692i	−0.809211	+	0.587518i	$0.800105\pi$
$770$		−	6.69256i		−	0.241183i
$771$	6.43934	+	30.9453i	0.231907	+	1.11447i
$772$	3.79624	+	3.79624i	0.136630	+	0.136630i
$773$	25.8379	−	25.8379i	0.929326	−	0.929326i	−0.0683364	−	0.997662i	$-0.521769\pi$
$773$	25.8379	−	25.8379i	0.929326	−	0.929326i	0.997662	+	0.0683364i	$0.0217691\pi$
$774$	−24.8068	−	9.76687i	−0.891663	−	0.351063i
$775$	29.2716	−	29.2716i	1.05147	−	1.05147i
$776$			5.07499i			0.182182i
$777$	19.4590	−	4.04918i	0.698088	−	0.145264i
$778$	−4.79624	+	4.79624i	−0.171954	+	0.171954i
$779$	−17.8783			−0.640555
$780$		0			0
$781$	48.3966			1.73177
$782$	3.09775	−	3.09775i	0.110775	−	0.110775i
$783$	4.23432	−	2.99411i	0.151322	−	0.107001i
$784$		−	3.09052i		−	0.110376i
$785$	2.38012	−	2.38012i	0.0849502	−	0.0849502i
$786$	6.73222	−	10.2702i	0.240130	−	0.366327i
$787$	−17.0905	+	17.0905i	−0.609211	+	0.609211i	−0.942740	−	0.333529i	$-0.891761\pi$
$787$	−17.0905	+	17.0905i	−0.609211	+	0.609211i	0.333529	+	0.942740i	$0.391761\pi$
$788$	−7.28193	−	7.28193i	−0.259408	−	0.259408i
$789$	6.76960	−	1.40867i	0.241004	−	0.0501500i
$790$		−	0.146563i		−	0.00521449i
$791$	18.5560	+	18.5560i	0.659776	+	0.659776i
$792$	−5.73970	−	13.1944i	−0.203951	−	0.468841i
$793$		0			0
$794$		−	24.4257i		−	0.866835i
$795$	−9.56266	+	14.5881i	−0.339153	+	0.517388i
$796$	18.1544			0.643466
$797$	44.8969			1.59033			0.795164	−	0.606394i	$-0.207385\pi$
$797$	44.8969			1.59033			0.795164	+	0.606394i	$0.207385\pi$
$798$	6.90910	+	4.52898i	0.244579	+	0.160324i
$799$	1.54584	+	1.54584i	0.0546878	+	0.0546878i
$800$	3.18337	+	3.18337i	0.112549	+	0.112549i
$801$	10.0282	+	3.94827i	0.354328	+	0.139505i
$802$	31.3926			1.10851
$803$	11.5697			0.408287
$804$	11.8741	+	7.78358i	0.418767	+	0.274506i
$805$		−	1.39264i		−	0.0490841i
$806$		0			0
$807$	−17.7735	+	3.69845i	−0.625658	+	0.130192i
$808$	−3.59248	−	3.59248i	−0.126383	−	0.126383i
$809$			40.8011i			1.43449i	0.696821	+	0.717245i	$0.254597\pi$
$809$			40.8011i			1.43449i	−0.696821	+	0.717245i	$0.745403\pi$
$810$	4.64663	+	4.33014i	0.163266	+	0.152146i
$811$	23.2794	+	23.2794i	0.817450	+	0.817450i	0.985738	−	0.168288i	$-0.0538237\pi$
$811$	23.2794	+	23.2794i	0.817450	+	0.817450i	−0.168288	+	0.985738i	$0.553824\pi$
$812$	−1.39538	+	1.39538i	−0.0489681	+	0.0489681i
$813$	6.90677	+	4.52745i	0.242231	+	0.158785i
$814$	19.6830	−	19.6830i	0.689889	−	0.689889i
$815$		−	11.3930i		−	0.399078i
$816$	−1.54888	−	7.44338i	−0.0542215	−	0.260570i
$817$	15.1583	−	15.1583i	0.530323	−	0.530323i
$818$	4.28031			0.149658
$819$		0			0
$820$	5.23040			0.182653
$821$	17.7633	−	17.7633i	0.619943	−	0.619943i	−0.325574	−	0.945517i	$-0.605557\pi$
$821$	17.7633	−	17.7633i	0.619943	−	0.619943i	0.945517	+	0.325574i	$0.105557\pi$
$822$	−7.69240	−	36.9671i	−0.268303	−	1.28938i
$823$		−	19.1238i		−	0.666615i	−0.942818	−	0.333308i	$-0.891835\pi$
$823$		−	19.1238i		−	0.666615i	0.942818	−	0.333308i	$-0.108165\pi$
$824$	8.63213	−	8.63213i	0.300715	−	0.300715i
$825$	−31.2782	−	20.5031i	−1.08897	−	0.713828i
$826$	−1.97336	+	1.97336i	−0.0686620	+	0.0686620i
$827$	−12.8615	−	12.8615i	−0.447237	−	0.447237i	0.447198	−	0.894435i	$-0.352422\pi$
$827$	−12.8615	−	12.8615i	−0.447237	−	0.447237i	−0.894435	+	0.447198i	$0.852422\pi$
$828$	−1.19436	−	2.74558i	−0.0415069	−	0.0954156i
$829$		−	39.3926i		−	1.36816i	−0.729406	−	0.684081i	$-0.760203\pi$
$829$		−	39.3926i		−	1.36816i	0.729406	−	0.684081i	$-0.239797\pi$
$830$	−6.47591	−	6.47591i	−0.224782	−	0.224782i
$831$	−46.1886	+	9.61128i	−1.60227	+	0.333412i
$832$		0			0
$833$			13.5658i			0.470028i
$834$	−15.7702	−	10.3375i	−0.546078	−	0.357959i
$835$	7.76568			0.268743
$836$	11.5697			0.400148
$837$	−8.07960	+	47.0914i	−0.279272	+	1.62772i
$838$	−24.1983	−	24.1983i	−0.835916	−	0.835916i
$839$	21.9608	+	21.9608i	0.758169	+	0.758169i	0.975989	−	0.217820i	$-0.0698944\pi$
$839$	21.9608	+	21.9608i	0.758169	+	0.758169i	−0.217820	+	0.975989i	$0.569894\pi$
$840$	−2.02130	−	1.32498i	−0.0697415	−	0.0457162i
$841$	28.0039			0.965652
$842$	4.06366			0.140043
$843$	−3.01684	+	4.60228i	−0.103905	+	0.158511i
$844$		−	11.2943i		−	0.388765i
$845$		0			0
$846$	1.37010	−	0.596009i	0.0471050	−	0.0204912i
$847$	−16.7829	−	16.7829i	−0.576668	−	0.576668i
$848$		−	14.2702i		−	0.490039i
$849$	−5.09383	+	1.05996i	−0.174820	+	0.0363778i
$850$	−13.9734	−	13.9734i	−0.479282	−	0.479282i
$851$	4.09579	−	4.09579i	0.140402	−	0.140402i
$852$	9.58146	−	14.6168i	0.328255	−	0.500764i
$853$	18.8813	−	18.8813i	0.646483	−	0.646483i	−0.305658	−	0.952141i	$-0.598877\pi$
$853$	18.8813	−	18.8813i	0.646483	−	0.646483i	0.952141	+	0.305658i	$0.0988766\pi$
$854$			18.9666i			0.649025i
$855$	−4.68320	+	2.03724i	−0.160162	+	0.0696723i
$856$	−4.79624	+	4.79624i	−0.163932	+	0.163932i
$857$	52.3802			1.78927			0.894637	−	0.446794i	$-0.147434\pi$
$857$	52.3802			1.78927			0.894637	+	0.446794i	$0.147434\pi$
$858$		0			0
$859$	30.9585			1.05629			0.528145	−	0.849154i	$-0.322888\pi$
$859$	30.9585			1.05629			0.528145	+	0.849154i	$0.322888\pi$
$860$	−4.43466	+	4.43466i	−0.151221	+	0.151221i
$861$	24.8495	−	5.17088i	0.846869	−	0.176223i
$862$			9.67516i			0.329537i
$863$	−17.1155	+	17.1155i	−0.582617	+	0.582617i	−0.935622	−	0.353005i	$-0.885160\pi$
$863$	−17.1155	+	17.1155i	−0.582617	+	0.582617i	0.353005	+	0.935622i	$0.385160\pi$
$864$	−5.12132	−	0.878680i	−0.174231	−	0.0298933i
$865$	9.65636	−	9.65636i	0.328326	−	0.328326i
$866$	20.7064	+	20.7064i	0.703633	+	0.703633i
$867$	0.800160	+	3.84530i	0.0271748	+	0.130593i
$868$		−	18.1810i		−	0.617105i
$869$	−0.704335	−	0.704335i	−0.0238929	−	0.0238929i
$870$	−0.248532	−	1.19436i	−0.00842601	−	0.0404926i
$871$		0			0
$872$		−	4.67765i		−	0.158405i
$873$	−14.1665	−	5.57760i	−0.479464	−	0.188773i
$874$	2.40752			0.0814356
$875$	−13.2588			−0.448230
$876$	2.29055	−	3.49431i	0.0773907	−	0.118062i
$877$	36.1117	+	36.1117i	1.21940	+	1.21940i	0.967841	+	0.251564i	$0.0809449\pi$
$877$	36.1117	+	36.1117i	1.21940	+	1.21940i	0.251564	+	0.967841i	$0.419055\pi$
$878$	−12.7279	−	12.7279i	−0.429547	−	0.429547i
$879$	9.38426	−	14.3160i	0.316523	−	0.482866i
$880$	−3.38480			−0.114102
$881$	9.49661			0.319949			0.159975	−	0.987121i	$-0.448859\pi$
$881$	9.49661			0.319949			0.159975	+	0.987121i	$0.448859\pi$
$882$	8.62699	+	3.39659i	0.290486	+	0.114369i
$883$		−	3.64852i		−	0.122783i	−0.998114	−	0.0613913i	$-0.980446\pi$
$883$		−	3.64852i		−	0.122783i	0.998114	−	0.0613913i	$-0.0195538\pi$
$884$		0			0
$885$	−0.351477	−	1.68908i	−0.0118148	−	0.0567778i
$886$	18.8401	+	18.8401i	0.632946	+	0.632946i
$887$			33.6208i			1.12888i	0.825475	+	0.564439i	$0.190907\pi$
$887$			33.6208i			1.12888i	−0.825475	+	0.564439i	$0.809093\pi$
$888$	−2.04789	−	9.84150i	−0.0687228	−	0.330259i
$889$	16.2449	+	16.2449i	0.544837	+	0.544837i
$890$	1.79272	−	1.79272i	0.0600920	−	0.0600920i
$891$	43.1394	−	1.52092i	1.44522	−	0.0509528i
$892$	−6.19436	+	6.19436i	−0.207403	+	0.207403i
$893$			1.20140i			0.0402033i
$894$	6.09187	−	1.26764i	0.203742	−	0.0423963i
$895$	3.53800	−	3.53800i	0.118262	−	0.118262i
$896$	1.97724			0.0660550
$897$		0			0
$898$	−36.7508			−1.22639
$899$	6.48920	−	6.48920i	0.216427	−	0.216427i
$900$	−12.3848	+	5.38753i	−0.412827	+	0.179584i
$901$			62.6387i			2.08680i
$902$	25.1356	−	25.1356i	0.836922	−	0.836922i
$903$	−16.6848	+	25.4532i	−0.555235	+	0.847029i
$904$	9.38480	−	9.38480i	0.312134	−	0.312134i
$905$	−3.09775	−	3.09775i	−0.102973	−	0.102973i
$906$	−9.62442	+	2.00272i	−0.319750	+	0.0665360i
$907$		−	17.8907i		−	0.594050i	−0.954870	−	0.297025i	$-0.904005\pi$
$907$		−	17.8907i		−	0.594050i	0.954870	−	0.297025i	$-0.0959945\pi$
$908$	−13.5658	−	13.5658i	−0.450197	−	0.450197i
$909$	13.9764	−	6.07992i	0.463570	−	0.201658i
$910$		0			0
$911$			22.7554i			0.753921i	0.926229	+	0.376961i	$0.123031\pi$
$911$			22.7554i			0.753921i	−0.926229	+	0.376961i	$0.876969\pi$
$912$	2.29055	−	3.49431i	0.0758479	−	0.115708i
$913$	−62.2422			−2.05991
$914$	−26.7155			−0.883669
$915$	−9.80624	−	6.42808i	−0.324184	−	0.212506i
$916$	3.30760	+	3.30760i	0.109286	+	0.109286i
$917$	−9.91254	−	9.91254i	−0.327341	−	0.327341i
$918$	22.4800	+	3.85696i	0.741950	+	0.127299i
$919$	9.78136			0.322657			0.161329	−	0.986901i	$-0.448422\pi$
$919$	9.78136			0.322657			0.161329	+	0.986901i	$0.448422\pi$
$920$	−0.704335			−0.0232212
$921$	18.1973	+	11.9285i	0.599620	+	0.393057i
$922$		−	35.1289i		−	1.15691i
$923$		0			0
$924$	−16.0811	+	3.34628i	−0.529030	+	0.110085i
$925$	−18.4753	−	18.4753i	−0.607465	−	0.607465i
$926$			19.9325i			0.655024i
$927$	14.6090	+	33.5831i	0.479823	+	1.10301i
$928$	0.705720	+	0.705720i	0.0231664	+	0.0231664i
$929$	−23.5933	+	23.5933i	−0.774072	+	0.774072i	−0.978816	−	0.204744i	$-0.934364\pi$
$929$	−23.5933	+	23.5933i	−0.774072	+	0.774072i	0.204744	+	0.978816i	$0.434364\pi$
$930$	9.40006	+	6.16183i	0.308240	+	0.202054i
$931$	−5.27156	+	5.27156i	−0.172768	+	0.172768i
$932$		−	10.8787i		−	0.356344i
$933$	−4.68320	−	22.5059i	−0.153321	−	0.736809i
$934$	−11.7923	+	11.7923i	−0.385857	+	0.385857i
$935$	14.8576			0.485894
$936$		0			0
$937$	−32.8840			−1.07427			−0.537137	−	0.843495i	$-0.680494\pi$
$937$	−32.8840			−1.07427			−0.537137	+	0.843495i	$0.680494\pi$
$938$	11.4606	−	11.4606i	0.374201	−	0.374201i
$939$	−0.322302	−	1.54888i	−0.0105179	−	0.0505456i
$940$		−	0.351477i		−	0.0114639i
$941$	10.3930	−	10.3930i	0.338801	−	0.338801i	−0.517115	−	0.855916i	$-0.672994\pi$
$941$	10.3930	−	10.3930i	0.338801	−	0.338801i	0.855916	+	0.517115i	$0.172994\pi$
$942$	−6.90910	−	4.52898i	−0.225111	−	0.147562i
$943$	5.23040	−	5.23040i	0.170325	−	0.170325i
$944$	0.998038	+	0.998038i	0.0324834	+	0.0324834i
$945$	5.92008	−	4.18613i	0.192580	−	0.136175i
$946$			42.6230i			1.38579i
$947$	5.88851	+	5.88851i	0.191351	+	0.191351i	0.796280	−	0.604929i	$-0.206798\pi$
$947$	5.88851	+	5.88851i	0.191351	+	0.191351i	−0.604929	+	0.796280i	$0.706798\pi$
$948$	−0.352168	+	0.0732817i	−0.0114379	+	0.00238008i
$949$		0			0
$950$		−	10.8599i		−	0.352340i
$951$	1.11482	+	0.730776i	0.0361506	+	0.0236970i
$952$	−8.67908			−0.281291
$953$	−35.4268			−1.14759			−0.573794	−	0.819000i	$-0.694529\pi$
$953$	−35.4268			−1.14759			−0.573794	+	0.819000i	$0.694529\pi$
$954$	39.8342	+	15.6834i	1.28968	+	0.507769i
$955$	4.87892	+	4.87892i	0.157878	+	0.157878i
$956$	−5.13900	−	5.13900i	−0.166207	−	0.166207i
$957$	−6.93406	−	4.54534i	−0.224146	−	0.146930i
$958$	37.4565			1.21017
$959$	−43.1042			−1.39191
$960$	−0.670116	+	1.02228i	−0.0216279	+	0.0329941i
$961$			53.5510i			1.72745i
$962$		0			0
$963$	−8.11716	−	18.6596i	−0.261572	−	0.601299i
$964$	−5.06388	−	5.06388i	−0.163097	−	0.163097i
$965$			3.78879i			0.121966i
$966$	−3.34628	+	0.696320i	−0.107665	+	0.0224037i
$967$	32.3221	+	32.3221i	1.03941	+	1.03941i	0.999191	+	0.0402185i	$0.0128054\pi$
$967$	32.3221	+	32.3221i	1.03941	+	1.03941i	0.0402185	+	0.999191i	$0.487195\pi$
$968$	−8.48805	+	8.48805i	−0.272816	+	0.272816i
$969$	−10.0544	+	15.3383i	−0.322993	+	0.492736i
$970$	−2.53252	+	2.53252i	−0.0813142	+	0.0813142i
$971$			58.4760i			1.87658i	0.345845	+	0.938292i	$0.387592\pi$
$971$			58.4760i			1.87658i	−0.345845	+	0.938292i	$0.612408\pi$
$972$	8.08130	−	13.3301i	0.259208	−	0.427564i
$973$	−15.2210	+	15.2210i	−0.487963	+	0.487963i
$974$	5.20301			0.166715
$975$		0			0
$976$	9.59248			0.307048
$977$	−34.4720	+	34.4720i	−1.10286	+	1.10286i	−0.108793	+	0.994064i	$0.534699\pi$
$977$	−34.4720	+	34.4720i	−1.10286	+	1.10286i	−0.994064	+	0.108793i	$0.965301\pi$
$978$	−27.3754	+	5.69648i	−0.875369	+	0.182153i
$979$		−	17.2304i		−	0.550686i
$980$	1.54223	−	1.54223i	0.0492647	−	0.0492647i
$981$	13.0574	+	5.14091i	0.416890	+	0.164137i
$982$	28.7868	−	28.7868i	0.918625	−	0.918625i
$983$	26.6891	+	26.6891i	0.851251	+	0.851251i	0.990287	−	0.139037i	$-0.0444005\pi$
$983$	26.6891	+	26.6891i	0.851251	+	0.851251i	−0.139037	+	0.990287i	$0.544401\pi$
$984$	−2.61520	−	12.5678i	−0.0833695	−	0.400646i
$985$		−	7.26764i		−	0.231566i
$986$	−3.09775	−	3.09775i	−0.0986525	−	0.0986525i
$987$	−0.347477	−	1.66986i	−0.0110603	−	0.0531522i
$988$		0			0
$989$			8.86933i			0.282028i
$990$	3.72002	−	9.44846i	0.118230	−	0.300292i
$991$	−13.3049			−0.422644			−0.211322	−	0.977417i	$-0.567777\pi$
$991$	−13.3049			−0.422644			−0.211322	+	0.977417i	$0.567777\pi$
$992$	−9.19516			−0.291947
$993$	−14.2243	+	21.6996i	−0.451394	+	0.688616i
$994$	−14.1078	−	14.1078i	−0.447471	−	0.447471i
$995$	9.05939	+	9.05939i	0.287202	+	0.287202i
$996$	−12.3226	+	18.7985i	−0.390456	+	0.595653i
$997$	15.0838			0.477710			0.238855	−	0.971055i	$-0.423228\pi$
$997$	15.0838			0.477710			0.238855	+	0.971055i	$0.423228\pi$
$998$	−14.8520			−0.470132
$999$	29.7226	+	5.09960i	0.940383	+	0.161344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.g.b.437.2		12
3.2	odd	2	inner	1014.2.g.b.437.5		12
13.5	odd	4	inner	1014.2.g.b.239.5		12
13.8	odd	4		78.2.g.a.5.2	✓	12
13.12	even	2		78.2.g.a.47.5	yes	12
39.5	even	4	inner	1014.2.g.b.239.2		12
39.8	even	4		78.2.g.a.5.5	yes	12
39.38	odd	2		78.2.g.a.47.2	yes	12
52.47	even	4		624.2.bf.f.161.3		12
52.51	odd	2		624.2.bf.f.593.3		12
156.47	odd	4		624.2.bf.f.161.4		12
156.155	even	2		624.2.bf.f.593.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.g.a.5.2	✓	12	13.8	odd	4
78.2.g.a.5.5	yes	12	39.8	even	4
78.2.g.a.47.2	yes	12	39.38	odd	2
78.2.g.a.47.5	yes	12	13.12	even	2
624.2.bf.f.161.3		12	52.47	even	4
624.2.bf.f.161.4		12	156.47	odd	4
624.2.bf.f.593.3		12	52.51	odd	2
624.2.bf.f.593.4		12	156.155	even	2
1014.2.g.b.239.2		12	39.5	even	4	inner
1014.2.g.b.239.5		12	13.5	odd	4	inner
1014.2.g.b.437.2		12	1.1	even	1	trivial
1014.2.g.b.437.5		12	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.352860 + 1.69573i) q^{3} -1.00000i q^{4} +(0.499019 - 0.499019i) q^{5} +(-1.44857 - 0.949550i) q^{6} +(-1.39812 + 1.39812i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.75098 + 1.19671i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.352860 + 1.69573i) q^{3} -1.00000i q^{4} +(0.499019 - 0.499019i) q^{5} +(-1.44857 - 0.949550i) q^{6} +(-1.39812 + 1.39812i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.75098 + 1.19671i) q^{9} +0.705720i q^{10} +(3.39145 + 3.39145i) q^{11} +(1.69573 - 0.352860i) q^{12} -1.97724i q^{14} +(1.02228 + 0.670116i) q^{15} -1.00000 q^{16} +4.38949 q^{17} +(1.09904 - 2.79144i) q^{18} +(1.70572 + 1.70572i) q^{19} +(-0.499019 - 0.499019i) q^{20} +(-2.86417 - 1.87749i) q^{21} -4.79624 q^{22} -0.998038 q^{23} +(-0.949550 + 1.44857i) q^{24} +4.50196i q^{25} +(-3.00000 - 4.24264i) q^{27} +(1.39812 + 1.39812i) q^{28} +0.998038i q^{29} +(-1.19671 + 0.249020i) q^{30} +(-6.50196 - 6.50196i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.55427 + 6.94769i) q^{33} +(-3.10384 + 3.10384i) q^{34} +1.39538i q^{35} +(1.19671 + 2.75098i) q^{36} +(-4.10384 + 4.10384i) q^{37} -2.41225 q^{38} +0.705720 q^{40} +(-5.24068 + 5.24068i) q^{41} +(3.35286 - 0.697689i) q^{42} -8.88676i q^{43} +(3.39145 - 3.39145i) q^{44} +(-0.775612 + 1.96997i) q^{45} +(0.705720 - 0.705720i) q^{46} +(0.352168 + 0.352168i) q^{47} +(-0.352860 - 1.69573i) q^{48} +3.09052i q^{49} +(-3.18337 - 3.18337i) q^{50} +(1.54888 + 7.44338i) q^{51} +14.2702i q^{53} +(5.12132 + 0.878680i) q^{54} +3.38480 q^{55} -1.97724 q^{56} +(-2.29055 + 3.49431i) q^{57} +(-0.705720 - 0.705720i) q^{58} +(-0.998038 - 0.998038i) q^{59} +(0.670116 - 1.02228i) q^{60} -9.59248 q^{61} +9.19516 q^{62} +(2.17306 - 5.51934i) q^{63} +1.00000i q^{64} +(-1.69240 - 8.13311i) q^{66} +(5.79624 + 5.79624i) q^{67} -4.38949i q^{68} +(-0.352168 - 1.69240i) q^{69} +(-0.986681 - 0.986681i) q^{70} +(7.13508 - 7.13508i) q^{71} +(-2.79144 - 1.09904i) q^{72} +(1.70572 - 1.70572i) q^{73} -5.80371i q^{74} +(-7.63409 + 1.58856i) q^{75} +(1.70572 - 1.70572i) q^{76} -9.48332 q^{77} -0.207679 q^{79} +(-0.499019 + 0.499019i) q^{80} +(6.13578 - 6.58424i) q^{81} -7.41144i q^{82} +(-9.17632 + 9.17632i) q^{83} +(-1.87749 + 2.86417i) q^{84} +(2.19044 - 2.19044i) q^{85} +(6.28389 + 6.28389i) q^{86} +(-1.69240 + 0.352168i) q^{87} +4.79624i q^{88} +(-2.54027 - 2.54027i) q^{89} +(-0.844540 - 1.94142i) q^{90} +0.998038i q^{92} +(8.73127 - 13.3198i) q^{93} -0.498040 q^{94} +1.70237 q^{95} +(1.44857 + 0.949550i) q^{96} +(3.58856 + 3.58856i) q^{97} +(-2.18533 - 2.18533i) q^{98} +(-13.3884 - 5.27124i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{7}+O(q^{10}) \) 12 * q + 12 * q^7	\( 12 q + 12 q^{7} - 12 q^{16} + 12 q^{19} - 36 q^{27} - 12 q^{28} - 12 q^{31} - 36 q^{33} - 12 q^{37} + 36 q^{42} - 36 q^{45} + 36 q^{54} + 36 q^{57} + 36 q^{63} + 12 q^{67} + 12 q^{73} + 12 q^{76} + 72 q^{79} + 72 q^{85} - 36 q^{93} - 72 q^{94} + 60 q^{97} - 36 q^{99}+O(q^{100}) \) 12 * q + 12 * q^7 - 12 * q^16 + 12 * q^19 - 36 * q^27 - 12 * q^28 - 12 * q^31 - 36 * q^33 - 12 * q^37 + 36 * q^42 - 36 * q^45 + 36 * q^54 + 36 * q^57 + 36 * q^63 + 12 * q^67 + 12 * q^73 + 12 * q^76 + 72 * q^79 + 72 * q^85 - 36 * q^93 - 72 * q^94 + 60 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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