LMFDB - Embedded newform 784.2.j.a.195.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(195,784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("784.195"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			195.18
Character	$\chi$	$=$	784.195
Dual form			784.2.j.a.587.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.714421 - 1.22049i) q^{2} +(1.43319 + 1.43319i) q^{3} +(-0.979204 - 1.74389i) q^{4} +(-1.82200 - 1.82200i) q^{5} +(2.77309 - 0.725295i) q^{6} +(-2.82797 - 0.0507629i) q^{8} +1.10805i q^{9} +(-3.52541 + 0.922061i) q^{10} +(-3.69842 - 3.69842i) q^{11} +(1.09594 - 3.90271i) q^{12} +(0.848888 - 0.848888i) q^{13} -5.22253i q^{15} +(-2.08232 + 3.41525i) q^{16} -2.58596i q^{17} +(1.35237 + 0.791616i) q^{18} +(3.45869 + 3.45869i) q^{19} +(-1.39326 + 4.96148i) q^{20} +(-7.15612 + 1.87166i) q^{22} -6.31934 q^{23} +(-3.98026 - 4.12577i) q^{24} +1.63936i q^{25} +(-0.429597 - 1.64252i) q^{26} +(2.71152 - 2.71152i) q^{27} +(-3.92758 - 3.92758i) q^{29} +(-6.37406 - 3.73109i) q^{30} -1.17078 q^{31} +(2.68064 + 4.98138i) q^{32} -10.6010i q^{33} +(-3.15615 - 1.84747i) q^{34} +(1.93232 - 1.08501i) q^{36} +(4.42235 - 4.42235i) q^{37} +(6.69227 - 1.75034i) q^{38} +2.43323 q^{39} +(5.06007 + 5.24505i) q^{40} +4.77063 q^{41} +(4.80121 + 4.80121i) q^{43} +(-2.82813 + 10.0711i) q^{44} +(2.01887 - 2.01887i) q^{45} +(-4.51467 + 7.71270i) q^{46} -6.78527 q^{47} +(-7.87905 + 1.91034i) q^{48} +(2.00083 + 1.17120i) q^{50} +(3.70617 - 3.70617i) q^{51} +(-2.31160 - 0.649134i) q^{52} +(5.38707 - 5.38707i) q^{53} +(-1.37222 - 5.24655i) q^{54} +13.4770i q^{55} +9.91391i q^{57} +(-7.59953 + 1.98763i) q^{58} +(0.592462 - 0.592462i) q^{59} +(-9.10753 + 5.11392i) q^{60} +(3.20342 - 3.20342i) q^{61} +(-0.836430 + 1.42893i) q^{62} +(7.99485 + 0.287112i) q^{64} -3.09335 q^{65} +(-12.9385 - 7.57361i) q^{66} +(-0.275920 + 0.275920i) q^{67} +(-4.50964 + 2.53218i) q^{68} +(-9.05679 - 9.05679i) q^{69} +3.83330 q^{71} +(0.0562480 - 3.13354i) q^{72} +9.69181 q^{73} +(-2.23802 - 8.55686i) q^{74} +(-2.34951 + 2.34951i) q^{75} +(2.64482 - 9.41835i) q^{76} +(1.73835 - 2.96974i) q^{78} -1.10178i q^{79} +(10.0166 - 2.42860i) q^{80} +11.0964 q^{81} +(3.40824 - 5.82251i) q^{82} +(9.73434 + 9.73434i) q^{83} +(-4.71162 + 4.71162i) q^{85} +(9.28993 - 2.42975i) q^{86} -11.2579i q^{87} +(10.2713 + 10.6468i) q^{88} -15.8223 q^{89} +(-1.02169 - 3.90634i) q^{90} +(6.18792 + 11.0202i) q^{92} +(-1.67795 - 1.67795i) q^{93} +(-4.84754 + 8.28137i) q^{94} -12.6035i q^{95} +(-3.29740 + 10.9811i) q^{96} -1.12228i q^{97} +(4.09804 - 4.09804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{2} + 8 q^{4} + 4 q^{8} - 4 q^{11} - 16 q^{16} + 60 q^{18} - 28 q^{22} + 24 q^{23} - 24 q^{29} + 36 q^{30} + 24 q^{32} + 16 q^{36} - 12 q^{37} + 8 q^{39} - 52 q^{44} - 32 q^{46} + 68 q^{51} - 12 q^{53}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q + 4 * q^2 + 8 * q^4 + 4 * q^8 - 4 * q^11 - 16 * q^16 + 60 * q^18 - 28 * q^22 + 24 * q^23 - 24 * q^29 + 36 * q^30 + 24 * q^32 + 16 * q^36 - 12 * q^37 + 8 * q^39 - 52 * q^44 - 32 * q^46 + 68 * q^51 - 12 * q^53 - 36 * q^58 - 156 * q^60 - 16 * q^64 + 8 * q^65 - 12 * q^67 - 80 * q^71 + 8 * q^72 - 124 * q^74 + 4 * q^78 + 16 * q^81 - 28 * q^85 - 60 * q^88 - 20 * q^92 - 20 * q^93 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.714421	−	1.22049i	0.505172	−	0.863019i
$2$	0.714421	−	1.22049i	0.505172	−	0.863019i
$3$	1.43319	+	1.43319i	0.827451	+	0.827451i	0.987164	−	0.159712i	$-0.0510567\pi$
$3$	1.43319	+	1.43319i	0.827451	+	0.827451i	−0.159712	+	0.987164i	$0.551057\pi$
$4$	−0.979204	−	1.74389i	−0.489602	−	0.871946i
$5$	−1.82200	−	1.82200i	−0.814823	−	0.814823i	0.170530	−	0.985353i	$-0.445452\pi$
$5$	−1.82200	−	1.82200i	−0.814823	−	0.814823i	−0.985353	+	0.170530i	$0.945452\pi$
$6$	2.77309	−	0.725295i	1.13211	−	0.296100i
$7$		0			0
$7$		0			0
$8$	−2.82797	−	0.0507629i	−0.999839	−	0.0179474i
$9$			1.10805i			0.369351i
$10$	−3.52541	+	0.922061i	−1.11483	+	0.291581i
$11$	−3.69842	−	3.69842i	−1.11511	−	1.11511i	−0.992448	−	0.122666i	$-0.960856\pi$
$11$	−3.69842	−	3.69842i	−1.11511	−	1.11511i	−0.122666	−	0.992448i	$-0.539144\pi$
$12$	1.09594	−	3.90271i	0.316371	−	1.12661i
$13$	0.848888	−	0.848888i	0.235439	−	0.235439i	−0.579519	−	0.814958i	$-0.696760\pi$
$13$	0.848888	−	0.848888i	0.235439	−	0.235439i	0.814958	+	0.579519i	$0.196760\pi$
$14$		0			0
$15$		−	5.22253i		−	1.34845i
$16$	−2.08232	+	3.41525i	−0.520580	+	0.853813i
$17$		−	2.58596i		−	0.627188i	−0.949557	−	0.313594i	$-0.898467\pi$
$17$		−	2.58596i		−	0.627188i	0.949557	−	0.313594i	$-0.101533\pi$
$18$	1.35237	+	0.791616i	0.318757	+	0.186586i
$19$	3.45869	+	3.45869i	0.793479	+	0.793479i	0.982058	−	0.188579i	$-0.0603883\pi$
$19$	3.45869	+	3.45869i	0.793479	+	0.793479i	−0.188579	+	0.982058i	$0.560388\pi$
$20$	−1.39326	+	4.96148i	−0.311543	+	1.10942i
$21$		0			0
$22$	−7.15612	+	1.87166i	−1.52569	+	0.399039i
$23$	−6.31934			−1.31767			−0.658836	−	0.752286i	$-0.728951\pi$
$23$	−6.31934			−1.31767			−0.658836	+	0.752286i	$0.728951\pi$
$24$	−3.98026	−	4.12577i	−0.812467	−	0.842168i
$25$			1.63936i			0.327872i
$26$	−0.429597	−	1.64252i	−0.0842510	−	0.322126i
$27$	2.71152	−	2.71152i	0.521831	−	0.521831i
$28$		0			0
$29$	−3.92758	−	3.92758i	−0.729333	−	0.729333i	0.241154	−	0.970487i	$-0.422474\pi$
$29$	−3.92758	−	3.92758i	−0.729333	−	0.729333i	−0.970487	+	0.241154i	$0.922474\pi$
$30$	−6.37406	−	3.73109i	−1.16374	−	0.681201i
$31$	−1.17078			−0.210278			−0.105139	−	0.994458i	$-0.533529\pi$
$31$	−1.17078			−0.210278			−0.105139	+	0.994458i	$0.533529\pi$
$32$	2.68064	+	4.98138i	0.473874	+	0.880593i
$33$		−	10.6010i		−	1.84541i
$34$	−3.15615	−	1.84747i	−0.541275	−	0.316838i
$35$		0			0
$36$	1.93232	−	1.08501i	0.322054	−	0.180835i
$37$	4.42235	−	4.42235i	0.727029	−	0.727029i	−0.242997	−	0.970027i	$-0.578131\pi$
$37$	4.42235	−	4.42235i	0.727029	−	0.727029i	0.970027	+	0.242997i	$0.0781307\pi$
$38$	6.69227	−	1.75034i	1.08563	−	0.283943i
$39$	2.43323			0.389629
$40$	5.06007	+	5.24505i	0.800068	+	0.829315i
$41$	4.77063			0.745047			0.372523	−	0.928023i	$-0.378493\pi$
$41$	4.77063			0.745047			0.372523	+	0.928023i	$0.378493\pi$
$42$		0			0
$43$	4.80121	+	4.80121i	0.732177	+	0.732177i	0.971051	−	0.238873i	$-0.0767781\pi$
$43$	4.80121	+	4.80121i	0.732177	+	0.732177i	−0.238873	+	0.971051i	$0.576778\pi$
$44$	−2.82813	+	10.0711i	−0.426357	+	1.51828i
$45$	2.01887	−	2.01887i	0.300955	−	0.300955i
$46$	−4.51467	+	7.71270i	−0.665652	+	1.13718i
$47$	−6.78527			−0.989733			−0.494867	−	0.868969i	$-0.664783\pi$
$47$	−6.78527			−0.989733			−0.494867	+	0.868969i	$0.664783\pi$
$48$	−7.87905	+	1.91034i	−1.13724	+	0.275734i
$49$		0			0
$50$	2.00083	+	1.17120i	0.282960	+	0.165632i
$51$	3.70617	−	3.70617i	0.518967	−	0.518967i
$52$	−2.31160	−	0.649134i	−0.320562	−	0.0900187i
$53$	5.38707	−	5.38707i	0.739971	−	0.739971i	−0.232602	−	0.972572i	$-0.574724\pi$
$53$	5.38707	−	5.38707i	0.739971	−	0.739971i	0.972572	+	0.232602i	$0.0747238\pi$
$54$	−1.37222	−	5.24655i	−0.186735	−	0.713965i
$55$			13.4770i			1.81724i
$56$		0			0
$57$			9.91391i			1.31313i
$58$	−7.59953	+	1.98763i	−0.997867	+	0.260989i
$59$	0.592462	−	0.592462i	0.0771320	−	0.0771320i	−0.667488	−	0.744620i	$-0.732631\pi$
$59$	0.592462	−	0.592462i	0.0771320	−	0.0771320i	0.744620	+	0.667488i	$0.232631\pi$
$60$	−9.10753	+	5.11392i	−1.17578	+	0.660205i
$61$	3.20342	−	3.20342i	0.410156	−	0.410156i	−0.471637	−	0.881793i	$-0.656337\pi$
$61$	3.20342	−	3.20342i	0.410156	−	0.410156i	0.881793	+	0.471637i	$0.156337\pi$
$62$	−0.836430	+	1.42893i	−0.106227	+	0.181474i
$63$		0			0
$64$	7.99485	+	0.287112i	0.999356	+	0.0358890i
$65$	−3.09335			−0.383682
$66$	−12.9385	−	7.57361i	−1.59262	−	0.932247i
$67$	−0.275920	+	0.275920i	−0.0337089	+	0.0337089i	−0.723760	−	0.690051i	$-0.757588\pi$
$67$	−0.275920	+	0.275920i	−0.0337089	+	0.0337089i	0.690051	+	0.723760i	$0.257588\pi$
$68$	−4.50964	+	2.53218i	−0.546874	+	0.307072i
$69$	−9.05679	−	9.05679i	−1.09031	−	1.09031i
$70$		0			0
$71$	3.83330			0.454929			0.227465	−	0.973786i	$-0.426956\pi$
$71$	3.83330			0.454929			0.227465	+	0.973786i	$0.426956\pi$
$72$	0.0562480	−	3.13354i	0.00662889	−	0.369291i
$73$	9.69181			1.13434			0.567170	−	0.823601i	$-0.308038\pi$
$73$	9.69181			1.13434			0.567170	+	0.823601i	$0.308038\pi$
$74$	−2.23802	−	8.55686i	−0.260165	−	0.994715i
$75$	−2.34951	+	2.34951i	−0.271298	+	0.271298i
$76$	2.64482	−	9.41835i	0.303382	−	1.08036i
$77$		0			0
$78$	1.73835	−	2.96974i	0.196830	−	0.336257i
$79$		−	1.10178i		−	0.123960i	−0.998077	−	0.0619798i	$-0.980259\pi$
$79$		−	1.10178i		−	0.123960i	0.998077	−	0.0619798i	$-0.0197414\pi$
$80$	10.0166	−	2.42860i	1.11989	−	0.271526i
$81$	11.0964			1.23293
$82$	3.40824	−	5.82251i	0.376377	−	0.642989i
$83$	9.73434	+	9.73434i	1.06848	+	1.06848i	0.997476	+	0.0710068i	$0.0226212\pi$
$83$	9.73434	+	9.73434i	1.06848	+	1.06848i	0.0710068	+	0.997476i	$0.477379\pi$
$84$		0			0
$85$	−4.71162	+	4.71162i	−0.511047	+	0.511047i
$86$	9.28993	−	2.42975i	1.00176	−	0.262007i
$87$		−	11.2579i		−	1.20698i
$88$	10.2713	+	10.6468i	1.09492	+	1.13495i
$89$	−15.8223			−1.67716			−0.838582	−	0.544775i	$-0.816615\pi$
$89$	−15.8223			−1.67716			−0.838582	+	0.544775i	$0.816615\pi$
$90$	−1.02169	−	3.90634i	−0.107696	−	0.411764i
$91$		0			0
$92$	6.18792	+	11.0202i	0.645135	+	1.14894i
$93$	−1.67795	−	1.67795i	−0.173995	−	0.173995i
$94$	−4.84754	+	8.28137i	−0.499986	+	0.854158i
$95$		−	12.6035i		−	1.29309i
$96$	−3.29740	+	10.9811i	−0.336540	+	1.12075i
$97$		−	1.12228i		−	0.113950i	−0.998376	−	0.0569750i	$-0.981854\pi$
$97$		−	1.12228i		−	0.113950i	0.998376	−	0.0569750i	$-0.0181455\pi$
$98$		0			0
$99$	4.09804	−	4.09804i	0.411868	−	0.411868i
$100$	2.85887	−	1.60527i	0.285887	−	0.160527i
$101$	10.2613	+	10.2613i	1.02104	+	1.02104i	0.999774	+	0.0212662i	$0.00676975\pi$
$101$	10.2613	+	10.2613i	1.02104	+	1.02104i	0.0212662	+	0.999774i	$0.493230\pi$
$102$	−1.87558	−	7.17112i	−0.185711	−	0.710046i
$103$		−	0.856691i		−	0.0844122i	−0.999109	−	0.0422061i	$-0.986561\pi$
$103$		−	0.856691i		−	0.0844122i	0.999109	−	0.0422061i	$-0.0134386\pi$
$104$	−2.44372	+	2.35754i	−0.239627	+	0.231176i
$105$		0			0
$106$	−2.72624	−	10.4235i	−0.264796	−	1.01242i
$107$	3.73045	+	3.73045i	0.360636	+	0.360636i	0.864047	−	0.503411i	$-0.167922\pi$
$107$	3.73045	+	3.73045i	0.360636	+	0.360636i	−0.503411	+	0.864047i	$0.667922\pi$
$108$	−7.38372	−	2.07346i	−0.710498	−	0.199519i
$109$	−9.79400	−	9.79400i	−0.938095	−	0.938095i	0.0600977	−	0.998192i	$-0.480859\pi$
$109$	−9.79400	−	9.79400i	−0.938095	−	0.938095i	−0.998192	+	0.0600977i	$0.980859\pi$
$110$	16.4486	+	9.62827i	1.56831	+	0.918020i
$111$	12.6761			1.20316
$112$		0			0
$113$	−8.67774			−0.816333			−0.408167	−	0.912907i	$-0.633832\pi$
$113$	−8.67774			−0.816333			−0.408167	+	0.912907i	$0.633832\pi$
$114$	12.0999	+	7.08271i	1.13326	+	0.663357i
$115$	11.5138	+	11.5138i	1.07367	+	1.07367i
$116$	−3.00337	+	10.6952i	−0.278856	+	0.993022i
$117$	0.940612	+	0.940612i	0.0869596	+	0.0869596i
$118$	−0.299828	−	1.14636i	−0.0276014	−	0.105531i
$119$		0			0
$120$	−0.265111	+	14.7692i	−0.0242012	+	1.34823i
$121$			16.3566i			1.48696i
$122$	−1.62116	−	6.19834i	−0.146773	−	0.561171i
$123$	6.83720	+	6.83720i	0.616490	+	0.616490i
$124$	1.14643	+	2.04171i	0.102953	+	0.183351i
$125$	−6.12308	+	6.12308i	−0.547665	+	0.547665i
$126$		0			0
$127$		−	14.0559i		−	1.24726i	−0.781721	−	0.623628i	$-0.785658\pi$
$127$		−	14.0559i		−	1.24726i	0.781721	−	0.623628i	$-0.214342\pi$
$128$	6.06211	−	9.55253i	0.535820	−	0.844332i
$129$			13.7621i			1.21168i
$130$	−2.20995	+	3.77540i	−0.193826	+	0.331125i
$131$	10.6822	+	10.6822i	0.933304	+	0.933304i	0.997911	−	0.0646069i	$-0.0205794\pi$
$131$	10.6822	+	10.6822i	0.933304	+	0.933304i	−0.0646069	+	0.997911i	$0.520579\pi$
$132$	−18.4871	+	10.3806i	−1.60909	+	0.903514i
$133$		0			0
$134$	0.139635	+	0.533881i	0.0120626	+	0.0461203i
$135$	−9.88076			−0.850400
$136$	−0.131271	+	7.31303i	−0.0112564	+	0.627087i
$137$		−	5.04671i		−	0.431170i	−0.976485	−	0.215585i	$-0.930834\pi$
$137$		−	5.04671i		−	0.431170i	0.976485	−	0.215585i	$-0.0691658\pi$
$138$	−17.5241	+	4.58338i	−1.49175	+	0.390163i
$139$	−3.77959	+	3.77959i	−0.320581	+	0.320581i	−0.848990	−	0.528409i	$-0.822789\pi$
$139$	−3.77959	+	3.77959i	−0.320581	+	0.320581i	0.528409	+	0.848990i	$0.322789\pi$
$140$		0			0
$141$	−9.72456	−	9.72456i	−0.818956	−	0.818956i
$142$	2.73859	−	4.67851i	0.229818	−	0.392612i
$143$	−6.27908			−0.525083
$144$	−3.78428	−	2.30732i	−0.315357	−	0.192277i
$145$			14.3121i			1.18855i
$146$	6.92404	−	11.8288i	0.573037	−	0.978957i
$147$		0			0
$148$	−12.0425	−	3.38172i	−0.989885	−	0.277975i
$149$	0.192817	−	0.192817i	0.0157962	−	0.0157962i	−0.699165	−	0.714961i	$-0.746445\pi$
$149$	0.192817	−	0.192817i	0.0157962	−	0.0157962i	0.714961	+	0.699165i	$0.246445\pi$
$150$	1.18902	+	4.54610i	0.0970831	+	0.371188i
$151$	9.16056			0.745476			0.372738	−	0.927937i	$-0.378419\pi$
$151$	9.16056			0.745476			0.372738	+	0.927937i	$0.378419\pi$
$152$	−9.60551	−	9.95666i	−0.779110	−	0.807592i
$153$	2.86538			0.231652
$154$		0			0
$155$	2.13316	+	2.13316i	0.171340	+	0.171340i
$156$	−2.38263	−	4.24329i	−0.190763	−	0.339735i
$157$	−10.5358	+	10.5358i	−0.840849	+	0.840849i	−0.988969	−	0.148120i	$-0.952678\pi$
$157$	−10.5358	+	10.5358i	−0.840849	+	0.840849i	0.148120	+	0.988969i	$0.452678\pi$
$158$	−1.34471	−	0.787134i	−0.106979	−	0.0626210i
$159$	15.4414			1.22458
$160$	4.19196	−	13.9602i	0.331404	−	1.10365i
$161$		0			0
$162$	7.92749	−	13.5430i	0.622842	−	1.06404i
$163$	13.6590	−	13.6590i	1.06985	−	1.06985i	0.0724835	−	0.997370i	$-0.476908\pi$
$163$	13.6590	−	13.6590i	1.06985	−	1.06985i	0.997370	−	0.0724835i	$-0.0230924\pi$
$164$	−4.67142	−	8.31946i	−0.364776	−	0.649640i
$165$	−19.3151	+	19.3151i	−1.50368	+	1.50368i
$166$	18.8351	−	4.92627i	1.46189	−	0.382353i
$167$		−	3.48341i		−	0.269554i	−0.990876	−	0.134777i	$-0.956968\pi$
$167$		−	3.48341i		−	0.269554i	0.990876	−	0.134777i	$-0.0430318\pi$
$168$		0			0
$169$			11.5588i			0.889137i
$170$	2.38441	+	9.11658i	0.182876	+	0.699210i
$171$	−3.83241	+	3.83241i	−0.293072	+	0.293072i
$172$	3.67143	−	13.0742i	0.279944	−	0.996895i
$173$	0.0517881	−	0.0517881i	0.00393737	−	0.00393737i	−0.705135	−	0.709073i	$-0.749114\pi$
$173$	0.0517881	−	0.0517881i	0.00393737	−	0.00393737i	0.709073	+	0.705135i	$0.249114\pi$
$174$	−13.7402	−	8.04290i	−1.04164	−	0.609730i
$175$		0			0
$176$	20.3323	−	4.92974i	1.53260	−	0.371593i
$177$	1.69822			0.127646
$178$	−11.3038	+	19.3110i	−0.847257	+	1.44742i
$179$	2.20071	−	2.20071i	0.164489	−	0.164489i	−0.620063	−	0.784552i	$-0.712893\pi$
$179$	2.20071	−	2.20071i	0.164489	−	0.164489i	0.784552	+	0.620063i	$0.212893\pi$
$180$	−5.49758	−	1.54381i	−0.409765	−	0.115069i
$181$	3.34414	+	3.34414i	0.248568	+	0.248568i	0.820383	−	0.571815i	$-0.193760\pi$
$181$	3.34414	+	3.34414i	0.248568	+	0.248568i	−0.571815	+	0.820383i	$0.693760\pi$
$182$		0			0
$183$	9.18219			0.678767
$184$	17.8709	+	0.320788i	1.31746	+	0.0236488i
$185$	−16.1150			−1.18480
$186$	−3.24668	+	0.849160i	−0.238058	+	0.0622635i
$187$	−9.56396	+	9.56396i	−0.699386	+	0.699386i
$188$	6.64416	+	11.8328i	0.484575	+	0.862994i
$189$		0			0
$190$	−15.3824	−	9.00419i	−1.11596	−	0.653233i
$191$		−	0.313041i		−	0.0226508i	−0.999936	−	0.0113254i	$-0.996395\pi$
$191$		−	0.313041i		−	0.0226508i	0.999936	−	0.0113254i	$-0.00360507\pi$
$192$	11.0466	+	11.8696i	0.797222	+	0.856615i
$193$	−10.3561			−0.745450			−0.372725	−	0.927942i	$-0.621576\pi$
$193$	−10.3561			−0.745450			−0.372725	+	0.927942i	$0.621576\pi$
$194$	−1.36973	−	0.801779i	−0.0983410	−	0.0575644i
$195$	−4.43334	−	4.43334i	−0.317478	−	0.317478i
$196$		0			0
$197$	0.112804	−	0.112804i	0.00803695	−	0.00803695i	−0.703077	−	0.711114i	$-0.748191\pi$
$197$	0.112804	−	0.112804i	0.00803695	−	0.00803695i	0.711114	+	0.703077i	$0.248191\pi$
$198$	−2.07390	−	7.92935i	−0.147386	−	0.563514i
$199$		−	21.3316i		−	1.51216i	−0.654482	−	0.756078i	$-0.727113\pi$
$199$		−	21.3316i		−	1.51216i	0.654482	−	0.756078i	$-0.272887\pi$
$200$	0.0832188	−	4.63607i	0.00588446	−	0.327820i
$201$	−0.790889			−0.0557850
$202$	19.8548	−	5.19296i	1.39698	−	0.365375i
$203$		0			0
$204$	−10.0923	−	2.83406i	−0.706599	−	0.198424i
$205$	−8.69208	−	8.69208i	−0.607081	−	0.607081i
$206$	−1.04558	−	0.612038i	−0.0728493	−	0.0426427i
$207$		−	7.00216i		−	0.486684i
$208$	1.13151	+	4.66682i	0.0784561	+	0.323586i
$209$		−	25.5834i		−	1.76964i
$210$		0			0
$211$	7.71946	−	7.71946i	0.531430	−	0.531430i	−0.389568	−	0.920998i	$-0.627376\pi$
$211$	7.71946	−	7.71946i	0.531430	−	0.531430i	0.920998	+	0.389568i	$0.127376\pi$
$212$	−14.6695	−	4.11943i	−1.00751	−	0.282923i
$213$	5.49384	+	5.49384i	0.376432	+	0.376432i
$214$	7.21811	−	1.88787i	0.493420	−	0.129052i
$215$		−	17.4956i		−	1.19319i
$216$	−7.80573	+	7.53044i	−0.531113	+	0.512382i
$217$		0			0
$218$	−18.9505	+	4.95646i	−1.28349	+	0.335694i
$219$	13.8902	+	13.8902i	0.938611	+	0.938611i
$220$	23.5025	−	13.1967i	1.58454	−	0.889725i
$221$	−2.19519	−	2.19519i	−0.147665	−	0.147665i
$222$	9.05608	−	15.4711i	0.607804	−	1.03835i
$223$	−9.74121			−0.652319			−0.326160	−	0.945315i	$-0.605755\pi$
$223$	−9.74121			−0.652319			−0.326160	+	0.945315i	$0.605755\pi$
$224$		0			0
$225$	−1.81650			−0.121100
$226$	−6.19957	+	10.5911i	−0.412389	+	0.704511i
$227$	0.737245	+	0.737245i	0.0489327	+	0.0489327i	0.731150	−	0.682217i	$-0.238984\pi$
$227$	0.737245	+	0.737245i	0.0489327	+	0.0489327i	−0.682217	+	0.731150i	$0.738984\pi$
$228$	17.2888	−	9.70774i	1.14498	−	0.642911i
$229$	3.80206	+	3.80206i	0.251247	+	0.251247i	0.821482	−	0.570234i	$-0.193148\pi$
$229$	3.80206	+	3.80206i	0.251247	+	0.251247i	−0.570234	+	0.821482i	$0.693148\pi$
$230$	22.2783	−	5.82681i	1.46899	−	0.384209i
$231$		0			0
$232$	10.9077	+	11.3065i	0.716126	+	0.742305i
$233$		−	12.7849i		−	0.837565i	−0.908087	−	0.418782i	$-0.862457\pi$
$233$		−	12.7849i		−	0.837565i	0.908087	−	0.418782i	$-0.137543\pi$
$234$	1.82000	−	0.476016i	0.118977	−	0.0311182i
$235$	12.3628	+	12.3628i	0.806457	+	0.806457i
$236$	−1.61333	−	0.453049i	−0.105019	−	0.0294910i
$237$	1.57905	−	1.57905i	0.102571	−	0.102571i
$238$		0			0
$239$			26.2285i			1.69658i	0.529530	+	0.848291i	$0.322368\pi$
$239$			26.2285i			1.69658i	−0.529530	+	0.848291i	$0.677632\pi$
$240$	17.8363	+	10.8750i	1.15133	+	0.701977i
$241$		−	22.0466i		−	1.42014i	−0.704129	−	0.710072i	$-0.748662\pi$
$241$		−	22.0466i		−	1.42014i	0.704129	−	0.710072i	$-0.251338\pi$
$242$	19.9630	+	11.6855i	1.28327	+	0.751171i
$243$	7.76864	+	7.76864i	0.498359	+	0.498359i
$244$	−8.72321	−	2.44962i	−0.558446	−	0.156821i
$245$		0			0
$246$	13.2294	−	3.46011i	0.843475	−	0.220609i
$247$	5.87208			0.373632
$248$	3.31093	+	0.0594322i	0.210244	+	0.00377395i
$249$			27.9023i			1.76823i
$250$	3.09871	+	11.8476i	0.195980	+	0.749310i
$251$	15.4991	−	15.4991i	0.978295	−	0.978295i	−0.0214744	−	0.999769i	$-0.506836\pi$
$251$	15.4991	−	15.4991i	0.978295	−	0.978295i	0.999769	+	0.0214744i	$0.00683604\pi$
$252$		0			0
$253$	23.3715	+	23.3715i	1.46936	+	1.46936i
$254$	−17.1551	−	10.0418i	−1.07641	−	0.630079i
$255$	−13.5053			−0.845733
$256$	−7.32789	−	14.2233i	−0.457993	−	0.888956i
$257$		−	1.89372i		−	0.118127i	−0.998254	−	0.0590633i	$-0.981189\pi$
$257$		−	1.89372i		−	0.118127i	0.998254	−	0.0590633i	$-0.0188114\pi$
$258$	16.7965	+	9.83191i	1.04570	+	0.612108i
$259$		0			0
$260$	3.02902	+	5.39446i	0.187852	+	0.334550i
$261$	4.35196	−	4.35196i	0.269380	−	0.269380i
$262$	20.6690	−	5.40593i	1.27694	−	0.333979i
$263$	−9.35219			−0.576680			−0.288340	−	0.957528i	$-0.593103\pi$
$263$	−9.35219			−0.576680			−0.288340	+	0.957528i	$0.593103\pi$
$264$	−0.538140	+	29.9795i	−0.0331202	+	1.84511i
$265$	−19.6305			−1.20589
$266$		0			0
$267$	−22.6764	−	22.6764i	−1.38777	−	1.38777i
$268$	0.751355	+	0.210992i	0.0458963	+	0.0128884i
$269$	18.8600	−	18.8600i	1.14992	−	1.14992i	0.163348	−	0.986568i	$-0.447771\pi$
$269$	18.8600	−	18.8600i	1.14992	−	1.14992i	0.986568	−	0.163348i	$-0.0522294\pi$
$270$	−7.05903	+	12.0594i	−0.429599	+	0.733911i
$271$	8.60151			0.522504			0.261252	−	0.965271i	$-0.415865\pi$
$271$	8.60151			0.522504			0.261252	+	0.965271i	$0.415865\pi$
$272$	8.83171	+	5.38480i	0.535501	+	0.326501i
$273$		0			0
$274$	−6.15948	−	3.60548i	−0.372108	−	0.217815i
$275$	6.06304	−	6.06304i	0.365615	−	0.365615i
$276$	−6.92562	+	24.6625i	−0.416874	+	1.48451i
$277$	18.1220	−	18.1220i	1.08884	−	1.08884i	0.0931953	−	0.995648i	$-0.470292\pi$
$277$	18.1220	−	18.1220i	1.08884	−	1.08884i	0.995648	−	0.0931953i	$-0.0297081\pi$
$278$	1.91274	+	7.31318i	0.114719	+	0.438615i
$279$		−	1.29729i		−	0.0776664i
$280$		0			0
$281$		−	23.2859i		−	1.38912i	−0.719434	−	0.694561i	$-0.755599\pi$
$281$		−	23.2859i		−	1.38912i	0.719434	−	0.694561i	$-0.244401\pi$
$282$	−18.8162	+	4.92132i	−1.12049	+	0.293060i
$283$	−7.17907	+	7.17907i	−0.426752	+	0.426752i	−0.887520	−	0.460769i	$-0.847574\pi$
$283$	−7.17907	+	7.17907i	−0.426752	+	0.426752i	0.460769	+	0.887520i	$0.347574\pi$
$284$	−3.75358	−	6.68486i	−0.222734	−	0.396674i
$285$	18.0631	−	18.0631i	1.06997	−	1.06997i
$286$	−4.48591	+	7.66357i	−0.265257	+	0.453156i
$287$		0			0
$288$	−5.51964	+	2.97028i	−0.325248	+	0.175026i
$289$	10.3128			0.606635
$290$	17.4678	+	10.2249i	1.02574	+	0.600425i
$291$	1.60843	−	1.60843i	0.0942880	−	0.0942880i
$292$	−9.49026	−	16.9015i	−0.555375	−	0.989084i
$293$	0.0961358	+	0.0961358i	0.00561631	+	0.00561631i	0.709909	−	0.704293i	$-0.248736\pi$
$293$	0.0961358	+	0.0961358i	0.00561631	+	0.00561631i	−0.704293	+	0.709909i	$0.748736\pi$
$294$		0			0
$295$	−2.15893			−0.125698
$296$	−12.7308	+	12.2818i	−0.739961	+	0.713864i
$297$	−20.0566			−1.16380
$298$	−0.0975790	−	0.373084i	−0.00565260	−	0.0216122i
$299$	−5.36441	+	5.36441i	−0.310232	+	0.310232i
$300$	6.39795	+	1.79664i	0.369386	+	0.103729i
$301$		0			0
$302$	6.54450	−	11.1804i	0.376594	−	0.643360i
$303$			29.4128i			1.68972i
$304$	−19.0144	+	4.61020i	−1.09055	+	0.264413i
$305$	−11.6732			−0.668408
$306$	2.04709	−	3.49718i	0.117024	−	0.199920i
$307$	−16.2451	−	16.2451i	−0.927157	−	0.927157i	0.0703642	−	0.997521i	$-0.477584\pi$
$307$	−16.2451	−	16.2451i	−0.927157	−	0.927157i	−0.997521	+	0.0703642i	$0.977584\pi$
$308$		0			0
$309$	1.22780	−	1.22780i	0.0698470	−	0.0698470i
$310$	4.12748	−	1.07953i	0.234425	−	0.0613132i
$311$			14.2183i			0.806245i	0.915146	+	0.403122i	$0.132075\pi$
$311$			14.2183i			0.806245i	−0.915146	+	0.403122i	$0.867925\pi$
$312$	−6.88111	−	0.123518i	−0.389566	−	0.00699283i
$313$	−26.8805			−1.51938			−0.759689	−	0.650287i	$-0.774649\pi$
$313$	−26.8805			−1.51938			−0.759689	+	0.650287i	$0.774649\pi$
$314$	5.33187	+	20.3859i	0.300895	+	1.15044i
$315$		0			0
$316$	−1.92138	+	1.07886i	−0.108086	+	0.0606909i
$317$	−11.3452	−	11.3452i	−0.637210	−	0.637210i	0.312656	−	0.949866i	$-0.398781\pi$
$317$	−11.3452	−	11.3452i	−0.637210	−	0.637210i	−0.949866	+	0.312656i	$0.898781\pi$
$318$	11.0316	−	18.8461i	0.618623	−	1.05683i
$319$			29.0516i			1.62658i
$320$	−14.0435	−	15.0897i	−0.785055	−	0.843541i
$321$			10.6929i			0.596818i
$322$		0			0
$323$	8.94405	−	8.94405i	0.497660	−	0.497660i
$324$	−10.8656	−	19.3509i	−0.603645	−	1.07505i
$325$	1.39163	+	1.39163i	0.0771940	+	0.0771940i
$326$	−6.91241	−	26.4289i	−0.382843	−	1.46376i
$327$		−	28.0733i		−	1.55246i
$328$	−13.4912	−	0.242171i	−0.744927	−	0.0133717i
$329$		0			0
$330$	9.77481	+	37.3730i	0.538086	+	2.05732i
$331$	−13.4302	−	13.4302i	−0.738190	−	0.738190i	0.234038	−	0.972227i	$-0.424806\pi$
$331$	−13.4302	−	13.4302i	−0.738190	−	0.738190i	−0.972227	+	0.234038i	$0.924806\pi$
$332$	7.44374	−	26.5075i	0.408528	−	1.45479i
$333$	4.90019	+	4.90019i	0.268529	+	0.268529i
$334$	−4.25147	−	2.48862i	−0.232630	−	0.136171i
$335$	1.00545			0.0549336
$336$		0			0
$337$	15.6500			0.852513			0.426256	−	0.904602i	$-0.359832\pi$
$337$	15.6500			0.852513			0.426256	+	0.904602i	$0.359832\pi$
$338$	14.1074	+	8.25784i	0.767342	+	0.449167i
$339$	−12.4368	−	12.4368i	−0.675476	−	0.675476i
$340$	12.8302	+	3.60292i	0.695815	+	0.195396i
$341$	4.33003	+	4.33003i	0.234484	+	0.234484i
$342$	1.93947	+	7.41539i	0.104875	+	0.400978i
$343$		0			0
$344$	−13.3340	−	13.8214i	−0.718919	−	0.745200i
$345$			33.0029i			1.77682i
$346$	−0.0262084	−	0.100205i	−0.00140897	−	0.00538708i
$347$	−13.8619	−	13.8619i	−0.744146	−	0.744146i	0.229227	−	0.973373i	$-0.426380\pi$
$347$	−13.8619	−	13.8619i	−0.744146	−	0.744146i	−0.973373	+	0.229227i	$0.926380\pi$
$348$	−19.6326	+	11.0238i	−1.05242	+	0.590937i
$349$	−7.34147	+	7.34147i	−0.392980	+	0.392980i	−0.875748	−	0.482768i	$-0.839631\pi$
$349$	−7.34147	+	7.34147i	−0.392980	+	0.392980i	0.482768	+	0.875748i	$0.339631\pi$
$350$		0			0
$351$		−	4.60354i		−	0.245719i
$352$	8.50912	−	28.3373i	0.453538	−	1.51038i
$353$			12.0704i			0.642441i	0.947004	+	0.321221i	$0.104093\pi$
$353$			12.0704i			0.642441i	−0.947004	+	0.321221i	$0.895907\pi$
$354$	1.21324	−	2.07266i	0.0644832	−	0.110161i
$355$	−6.98427	−	6.98427i	−0.370687	−	0.370687i
$356$	15.4933	+	27.5925i	0.821143	+	1.46240i
$357$		0			0
$358$	−1.11371	−	4.25818i	−0.0588616	−	0.225052i
$359$	−1.73675			−0.0916620			−0.0458310	−	0.998949i	$-0.514594\pi$
$359$	−1.73675			−0.0916620			−0.0458310	+	0.998949i	$0.514594\pi$
$360$	−5.81179	+	5.60682i	−0.306308	+	0.295506i
$361$			4.92512i			0.259217i
$362$	6.47062	−	1.69237i	0.340088	−	0.0889491i
$363$	−23.4420	+	23.4420i	−1.23039	+	1.23039i
$364$		0			0
$365$	−17.6585	−	17.6585i	−0.924287	−	0.924287i
$366$	6.55996	−	11.2068i	0.342894	−	0.585789i
$367$	10.4351			0.544706			0.272353	−	0.962197i	$-0.412198\pi$
$367$	10.4351			0.544706			0.272353	+	0.962197i	$0.412198\pi$
$368$	13.1589	−	21.5821i	0.685954	−	1.12505i
$369$			5.28610i			0.275184i
$370$	−11.5129	+	19.6683i	−0.598528	+	1.02250i
$371$		0			0
$372$	−1.28311	+	4.56921i	−0.0665260	+	0.236903i
$373$	−7.76406	+	7.76406i	−0.402008	+	0.402008i	−0.878940	−	0.476932i	$-0.841749\pi$
$373$	−7.76406	+	7.76406i	−0.402008	+	0.402008i	0.476932	+	0.878940i	$0.341749\pi$
$374$	4.84004	+	18.5054i	0.250273	+	0.956894i
$375$	−17.5510			−0.906332
$376$	19.1885	+	0.344440i	0.989574	+	0.0177631i
$377$	−6.66815			−0.343427
$378$		0			0
$379$	19.3486	+	19.3486i	0.993870	+	0.993870i	0.999981	−	0.00611151i	$-0.00194537\pi$
$379$	19.3486	+	19.3486i	0.993870	+	0.993870i	−0.00611151	+	0.999981i	$0.501945\pi$
$380$	−21.9791	+	12.3414i	−1.12750	+	0.633099i
$381$	20.1447	−	20.1447i	1.03204	−	1.03204i
$382$	−0.382064	−	0.223643i	−0.0195481	−	0.0114426i
$383$	−17.8263			−0.910879			−0.455440	−	0.890267i	$-0.650518\pi$
$383$	−17.8263			−0.910879			−0.455440	+	0.890267i	$0.650518\pi$
$384$	22.3787	−	5.00243i	1.14201	−	0.255279i
$385$		0			0
$386$	−7.39863	+	12.6396i	−0.376581	+	0.643337i
$387$	−5.31999	+	5.31999i	−0.270430	+	0.270430i
$388$	−1.95713	+	1.09894i	−0.0993582	+	0.0557901i
$389$	−4.41294	+	4.41294i	−0.223745	+	0.223745i	−0.810073	−	0.586329i	$-0.800573\pi$
$389$	−4.41294	+	4.41294i	−0.223745	+	0.223745i	0.586329	+	0.810073i	$0.300573\pi$
$390$	−8.57814	+	2.24359i	−0.434371	+	0.113608i
$391$			16.3416i			0.826429i
$392$		0			0
$393$			30.6190i			1.54453i
$394$	−0.0570868	−	0.218266i	−0.00287599	−	0.0109961i
$395$	−2.00744	+	2.00744i	−0.101005	+	0.101005i
$396$	−11.1594	−	3.13372i	−0.560779	−	0.157475i
$397$	−4.99372	+	4.99372i	−0.250628	+	0.250628i	−0.821228	−	0.570600i	$-0.806711\pi$
$397$	−4.99372	+	4.99372i	−0.250628	+	0.250628i	0.570600	+	0.821228i	$0.306711\pi$
$398$	−26.0350	−	15.2397i	−1.30502	−	0.763899i
$399$		0			0
$400$	−5.59883	−	3.41367i	−0.279942	−	0.170684i
$401$	−20.9900			−1.04819			−0.524096	−	0.851659i	$-0.675597\pi$
$401$	−20.9900			−1.04819			−0.524096	+	0.851659i	$0.675597\pi$
$402$	−0.565028	+	0.965274i	−0.0281810	+	0.0481435i
$403$	−0.993860	+	0.993860i	−0.0495077	+	0.0495077i
$404$	7.84671	−	27.9426i	0.390389	−	1.39020i
$405$	−20.2176	−	20.2176i	−1.00462	−	1.00462i
$406$		0			0
$407$	−32.7114			−1.62144
$408$	−10.6691	+	10.2928i	−0.528198	+	0.509570i
$409$	−36.1916			−1.78956			−0.894780	−	0.446508i	$-0.852667\pi$
$409$	−36.1916			−1.78956			−0.894780	+	0.446508i	$0.852667\pi$
$410$	−16.8184	+	4.39881i	−0.830603	+	0.217242i
$411$	7.23289	−	7.23289i	0.356772	−	0.356772i
$412$	−1.49398	+	0.838875i	−0.0736029	+	0.0413284i
$413$		0			0
$414$	−8.54608	−	5.00249i	−0.420017	−	0.245859i
$415$		−	35.4719i		−	1.74125i
$416$	6.50419	+	1.95308i	0.318894	+	0.0957575i
$417$	−10.8337			−0.530530
$418$	−31.2243	−	18.2773i	−1.52723	−	0.893972i
$419$	5.15413	+	5.15413i	0.251796	+	0.251796i	0.821707	−	0.569911i	$-0.193022\pi$
$419$	5.15413	+	5.15413i	0.251796	+	0.251796i	−0.569911	+	0.821707i	$0.693022\pi$
$420$		0			0
$421$	−7.75876	+	7.75876i	−0.378139	+	0.378139i	−0.870430	−	0.492292i	$-0.836159\pi$
$421$	−7.75876	+	7.75876i	−0.378139	+	0.378139i	0.492292	+	0.870430i	$0.336159\pi$
$422$	−3.90660	−	14.9365i	−0.190170	−	0.727097i
$423$		−	7.51843i		−	0.365559i
$424$	−15.5079	+	14.9610i	−0.753132	+	0.726571i
$425$	4.23933			0.205638
$426$	10.6301	−	2.78027i	0.515030	−	0.134705i
$427$		0			0
$428$	2.85263	−	10.1584i	0.137887	−	0.491024i
$429$	−8.99910	−	8.99910i	−0.434480	−	0.434480i
$430$	−21.3532	−	12.4992i	−1.02974	−	0.602766i
$431$			24.7968i			1.19442i	0.802085	+	0.597209i	$0.203724\pi$
$431$			24.7968i			1.19442i	−0.802085	+	0.597209i	$0.796276\pi$
$432$	3.61427	+	14.9067i	0.173892	+	0.717201i
$433$			4.84981i			0.233067i	0.993187	+	0.116534i	$0.0371782\pi$
$433$			4.84981i			0.233067i	−0.993187	+	0.116534i	$0.962822\pi$
$434$		0			0
$435$	−20.5119	+	20.5119i	−0.983471	+	0.983471i
$436$	−7.48935	+	26.6700i	−0.358675	+	1.27726i
$437$	−21.8566	−	21.8566i	−1.04555	−	1.04555i
$438$	26.8763	−	7.02942i	1.28420	−	0.335879i
$439$			37.2342i			1.77709i	0.458788	+	0.888546i	$0.348284\pi$
$439$			37.2342i			1.77709i	−0.458788	+	0.888546i	$0.651716\pi$
$440$	0.684133	−	38.1126i	0.0326148	−	1.81695i
$441$		0			0
$442$	−4.24751	+	1.11092i	−0.202033	+	0.0528412i
$443$	17.7945	+	17.7945i	0.845441	+	0.845441i	0.989560	−	0.144119i	$-0.0460350\pi$
$443$	17.7945	+	17.7945i	0.845441	+	0.845441i	−0.144119	+	0.989560i	$0.546035\pi$
$444$	−12.4125	−	22.1058i	−0.589071	−	1.04909i
$445$	28.8283	+	28.8283i	1.36659	+	1.36659i
$446$	−6.95933	+	11.8891i	−0.329534	+	0.562964i
$447$	0.552685			0.0261411
$448$		0			0
$449$	0.885883			0.0418074			0.0209037	−	0.999781i	$-0.493346\pi$
$449$	0.885883			0.0418074			0.0209037	+	0.999781i	$0.493346\pi$
$450$	−1.29775	+	2.21702i	−0.0611763	+	0.104511i
$451$	−17.6438	−	17.6438i	−0.830812	−	0.830812i
$452$	8.49728	+	15.1330i	0.399678	+	0.711799i
$453$	13.1288	+	13.1288i	0.616845	+	0.616845i
$454$	1.42651	−	0.373098i	0.0669492	−	0.0175104i
$455$		0			0
$456$	0.503259	−	28.0363i	0.0235673	−	1.31292i
$457$			34.6766i			1.62210i	0.584975	+	0.811052i	$0.301104\pi$
$457$			34.6766i			1.62210i	−0.584975	+	0.811052i	$0.698896\pi$
$458$	7.35667	−	1.92411i	0.343754	−	0.0899080i
$459$	−7.01188	−	7.01188i	−0.327286	−	0.327286i
$460$	8.80449	−	31.3533i	0.410511	−	1.46185i
$461$	4.11212	−	4.11212i	0.191520	−	0.191520i	−0.604832	−	0.796353i	$-0.706760\pi$
$461$	4.11212	−	4.11212i	0.191520	−	0.191520i	0.796353	+	0.604832i	$0.206760\pi$
$462$		0			0
$463$			11.6892i			0.543245i	0.962404	+	0.271623i	$0.0875603\pi$
$463$			11.6892i			0.543245i	−0.962404	+	0.271623i	$0.912440\pi$
$464$	21.5921	−	5.23520i	1.00239	−	0.243038i
$465$			6.11444i			0.283550i
$466$	−15.6038	−	9.13379i	−0.722834	−	0.423115i
$467$	17.8096	+	17.8096i	0.824132	+	0.824132i	0.986698	−	0.162566i	$-0.0519770\pi$
$467$	17.8096	+	17.8096i	0.824132	+	0.824132i	−0.162566	+	0.986698i	$0.551977\pi$
$468$	0.719275	−	2.56138i	0.0332485	−	0.118400i
$469$		0			0
$470$	23.9209	−	6.25643i	1.10339	−	0.288588i
$471$	−30.1996			−1.39152
$472$	−1.70554	+	1.64539i	−0.0785039	+	0.0757353i
$473$		−	35.5137i		−	1.63292i
$474$	−0.799113	−	3.05533i	−0.0367045	−	0.140336i
$475$	−5.67005	+	5.67005i	−0.260160	+	0.260160i
$476$		0			0
$477$	5.96915	+	5.96915i	0.273309	+	0.273309i
$478$	32.0117	+	18.7382i	1.46418	+	0.857066i
$479$	24.3079			1.11066			0.555328	−	0.831632i	$-0.312593\pi$
$479$	24.3079			1.11066			0.555328	+	0.831632i	$0.312593\pi$
$480$	26.0154	−	13.9997i	1.18744	−	0.638996i
$481$		−	7.50815i		−	0.342342i
$482$	−26.9077	−	15.7505i	−1.22561	−	0.717417i
$483$		0			0
$484$	28.5241	−	16.0164i	1.29655	−	0.728018i
$485$	−2.04479	+	2.04479i	−0.0928490	+	0.0928490i
$486$	15.0317	−	3.93148i	0.681850	−	0.178336i
$487$	−31.0001			−1.40475			−0.702373	−	0.711809i	$-0.747876\pi$
$487$	−31.0001			−1.40475			−0.702373	+	0.711809i	$0.747876\pi$
$488$	−9.22179	+	8.89656i	−0.417451	+	0.402728i
$489$	39.1517			1.77050
$490$		0			0
$491$	8.29080	+	8.29080i	0.374159	+	0.374159i	0.868989	−	0.494831i	$-0.164770\pi$
$491$	8.29080	+	8.29080i	0.374159	+	0.374159i	−0.494831	+	0.868989i	$0.664770\pi$
$492$	5.22833	−	18.6184i	0.235711	−	0.839380i
$493$	−10.1566	+	10.1566i	−0.457429	+	0.457429i
$494$	4.19514	−	7.16683i	0.188748	−	0.322451i
$495$	−14.9332			−0.671199
$496$	2.43794	−	3.99851i	0.109467	−	0.179538i
$497$		0			0
$498$	34.0545	+	19.9340i	1.52602	+	0.893263i
$499$	−16.8125	+	16.8125i	−0.752630	+	0.752630i	−0.974969	−	0.222339i	$-0.928631\pi$
$499$	−16.8125	+	16.8125i	−0.752630	+	0.752630i	0.222339	+	0.974969i	$0.428631\pi$
$500$	16.6737	+	4.68225i	0.745672	+	0.209396i
$501$	4.99238	−	4.99238i	0.223043	−	0.223043i
$502$	−7.84365	−	29.9894i	−0.350079	−	1.33849i
$503$		−	3.42708i		−	0.152806i	−0.997077	−	0.0764029i	$-0.975656\pi$
$503$		−	3.42708i		−	0.152806i	0.997077	−	0.0764029i	$-0.0243435\pi$
$504$		0			0
$505$		−	37.3923i		−	1.66393i
$506$	45.2219	−	11.8277i	2.01036	−	0.525803i
$507$	−16.5659	+	16.5659i	−0.735717	+	0.735717i
$508$	−24.5119	+	13.7636i	−1.08754	+	0.610659i
$509$	26.0099	−	26.0099i	1.15287	−	1.15287i	0.166896	−	0.985975i	$-0.446626\pi$
$509$	26.0099	−	26.0099i	1.15287	−	1.15287i	0.985975	−	0.166896i	$-0.0533744\pi$
$510$	−9.64846	+	16.4831i	−0.427241	+	0.729883i
$511$		0			0
$512$	−22.5946	−	1.21779i	−0.998551	−	0.0538191i
$513$	18.7566			0.828124
$514$	−2.31127	−	1.35291i	−0.101946	−	0.0596743i
$515$	−1.56089	+	1.56089i	−0.0687810	+	0.0687810i
$516$	23.9996	−	13.4759i	1.05652	−	0.593242i
$517$	25.0947	+	25.0947i	1.10367	+	1.10367i
$518$		0			0
$519$	0.148444			0.00651597
$520$	8.74789	+	0.157027i	0.383620	+	0.00688610i
$521$	13.6486			0.597957			0.298979	−	0.954260i	$-0.403354\pi$
$521$	13.6486			0.597957			0.298979	+	0.954260i	$0.403354\pi$
$522$	−2.20240	−	8.42068i	−0.0963965	−	0.368563i
$523$	13.4813	−	13.4813i	0.589498	−	0.589498i	−0.347998	−	0.937495i	$-0.613138\pi$
$523$	13.4813	−	13.4813i	0.589498	−	0.589498i	0.937495	+	0.347998i	$0.113138\pi$
$524$	8.16851	−	29.0885i	0.356843	−	1.27074i
$525$		0			0
$526$	−6.68140	+	11.4143i	−0.291323	+	0.497686i
$527$			3.02759i			0.131884i
$528$	36.2052	+	22.0748i	1.57563	+	0.960681i
$529$	16.9340			0.736262
$530$	−14.0244	+	23.9588i	−0.609182	+	1.04071i
$531$	0.656479	+	0.656479i	0.0284888	+	0.0284888i
$532$		0			0
$533$	4.04973	−	4.04973i	0.175413	−	0.175413i
$534$	−43.8768	+	11.4759i	−1.89874	+	0.496609i
$535$		−	13.5938i		−	0.587710i
$536$	0.794299	−	0.766286i	0.0343085	−	0.0330985i
$537$	6.30805			0.272213
$538$	−9.54452	−	36.4925i	−0.411493	−	1.57331i
$539$		0			0
$540$	9.67528	+	17.2310i	0.416358	+	0.741503i
$541$	−0.333702	−	0.333702i	−0.0143470	−	0.0143470i	0.699897	−	0.714244i	$-0.253229\pi$
$541$	−0.333702	−	0.333702i	−0.0143470	−	0.0143470i	−0.714244	+	0.699897i	$0.753229\pi$
$542$	6.14510	−	10.4981i	0.263955	−	0.450931i
$543$			9.58556i			0.411356i
$544$	12.8817	−	6.93202i	0.552297	−	0.297208i
$545$			35.6893i			1.52876i
$546$		0			0
$547$	9.02908	−	9.02908i	0.386056	−	0.386056i	−0.487222	−	0.873278i	$-0.661990\pi$
$547$	9.02908	−	9.02908i	0.386056	−	0.386056i	0.873278	+	0.487222i	$0.161990\pi$
$548$	−8.80092	+	4.94176i	−0.375957	+	0.211102i
$549$	3.54955	+	3.54955i	0.151491	+	0.151491i
$550$	−3.06833	−	11.7315i	−0.130834	−	0.500231i
$551$		−	27.1686i		−	1.15742i
$552$	25.1526	+	26.0721i	1.07057	+	1.10970i
$553$		0			0
$554$	−9.17100	−	35.0644i	−0.389638	−	1.48975i
$555$	−23.0959	−	23.0959i	−0.980364	−	0.980364i
$556$	10.2922	+	2.89021i	0.436486	+	0.122572i
$557$	4.91696	+	4.91696i	0.208338	+	0.208338i	0.803561	−	0.595223i	$-0.202936\pi$
$557$	4.91696	+	4.91696i	0.208338	+	0.208338i	−0.595223	+	0.803561i	$0.702936\pi$
$558$	−1.58333	−	0.926809i	−0.0670276	−	0.0392349i
$559$	8.15137			0.344766
$560$		0			0
$561$	−27.4139			−1.15742
$562$	−28.4203	−	16.6360i	−1.19884	−	0.701746i
$563$	21.7464	+	21.7464i	0.916500	+	0.916500i	0.996773	−	0.0802729i	$-0.0255792\pi$
$563$	21.7464	+	21.7464i	0.916500	+	0.916500i	−0.0802729	+	0.996773i	$0.525579\pi$
$564$	−7.43626	+	26.4809i	−0.313123	+	1.11505i
$565$	15.8108	+	15.8108i	0.665167	+	0.665167i
$566$	3.63312	+	13.8909i	0.152711	+	0.583878i
$567$		0			0
$568$	−10.8405	−	0.194590i	−0.454856	−	0.00816480i
$569$		−	39.1128i		−	1.63969i	−0.572584	−	0.819846i	$-0.694059\pi$
$569$		−	39.1128i		−	1.63969i	0.572584	−	0.819846i	$-0.305941\pi$
$570$	−9.14123	−	34.9506i	−0.382884	−	1.46392i
$571$	3.87913	+	3.87913i	0.162337	+	0.162337i	0.783601	−	0.621264i	$-0.213381\pi$
$571$	3.87913	+	3.87913i	0.162337	+	0.162337i	−0.621264	+	0.783601i	$0.713381\pi$
$572$	6.14850	+	10.9500i	0.257082	+	0.457844i
$573$	0.448646	−	0.448646i	0.0187425	−	0.0187425i
$574$		0			0
$575$		−	10.3597i		−	0.432028i
$576$	−0.318136	+	8.85871i	−0.0132556	+	0.369113i
$577$			34.7362i			1.44609i	0.690802	+	0.723044i	$0.257258\pi$
$577$			34.7362i			1.44609i	−0.690802	+	0.723044i	$0.742742\pi$
$578$	7.36769	−	12.5867i	0.306455	−	0.523537i
$579$	−14.8423	−	14.8423i	−0.616823	−	0.616823i
$580$	24.9587	−	14.0145i	1.03636	−	0.581919i
$581$		0			0
$582$	−0.813982	−	3.11218i	−0.0337406	−	0.129004i
$583$	−39.8472			−1.65030
$584$	−27.4082	−	0.491985i	−1.13416	−	0.0203585i
$585$		−	3.42759i		−	0.141713i
$586$	0.186015	−	0.0486515i	0.00768419	−	0.00200978i
$587$	25.6897	−	25.6897i	1.06033	−	1.06033i	0.0622695	−	0.998059i	$-0.480166\pi$
$587$	25.6897	−	25.6897i	1.06033	−	1.06033i	0.998059	−	0.0622695i	$-0.0198338\pi$
$588$		0			0
$589$	−4.04937	−	4.04937i	−0.166851	−	0.166851i
$590$	−1.54239	+	2.63496i	−0.0634991	+	0.108480i
$591$	0.323338			0.0133004
$592$	5.89469	+	24.3122i	0.242270	+	0.999224i
$593$		−	24.4029i		−	1.00211i	−0.865416	−	0.501054i	$-0.832946\pi$
$593$		−	24.4029i		−	1.00211i	0.865416	−	0.501054i	$-0.167054\pi$
$594$	−14.3289	+	24.4790i	−0.587921	+	1.00438i
$595$		0			0
$596$	−0.525059	−	0.147445i	−0.0215072	−	0.00603957i
$597$	30.5722	−	30.5722i	1.25124	−	1.25124i
$598$	2.71477	+	10.3797i	0.111015	+	0.424456i
$599$	26.7558			1.09321			0.546606	−	0.837390i	$-0.315920\pi$
$599$	26.7558			1.09321			0.546606	+	0.837390i	$0.315920\pi$
$600$	6.76362	−	6.52509i	0.276124	−	0.266386i
$601$	16.1853			0.660212			0.330106	−	0.943944i	$-0.392915\pi$
$601$	16.1853			0.660212			0.330106	+	0.943944i	$0.392915\pi$
$602$		0			0
$603$	−0.305733	−	0.305733i	−0.0124504	−	0.0124504i
$604$	−8.97006	−	15.9750i	−0.364987	−	0.650015i
$605$	29.8016	−	29.8016i	1.21161	−	1.21161i
$606$	35.8981	+	21.0131i	1.45826	+	0.853600i
$607$	−5.03295			−0.204281			−0.102141	−	0.994770i	$-0.532569\pi$
$607$	−5.03295			−0.204281			−0.102141	+	0.994770i	$0.532569\pi$
$608$	−7.95758	+	26.5006i	−0.322723	+	1.07474i
$609$		0			0
$610$	−8.33962	+	14.2471i	−0.337661	+	0.576849i
$611$	−5.75993	+	5.75993i	−0.233022	+	0.233022i
$612$	−2.80579	−	4.99692i	−0.113417	−	0.201988i
$613$	−0.321378	+	0.321378i	−0.0129803	+	0.0129803i	−0.713567	−	0.700587i	$-0.752922\pi$
$613$	−0.321378	+	0.321378i	−0.0129803	+	0.0129803i	0.700587	+	0.713567i	$0.252922\pi$
$614$	−31.4329	+	8.22118i	−1.26853	+	0.331780i
$615$		−	24.9147i		−	1.00466i
$616$		0			0
$617$			4.35363i			0.175271i	0.996153	+	0.0876353i	$0.0279310\pi$
$617$			4.35363i			0.175271i	−0.996153	+	0.0876353i	$0.972069\pi$
$618$	−0.621353	−	2.37568i	−0.0249945	−	0.0955640i
$619$	3.47374	−	3.47374i	0.139621	−	0.139621i	−0.633842	−	0.773463i	$-0.718523\pi$
$619$	3.47374	−	3.47374i	0.139621	−	0.139621i	0.773463	+	0.633842i	$0.218523\pi$
$620$	1.63120	−	5.80880i	0.0655106	−	0.233287i
$621$	−17.1350	+	17.1350i	−0.687603	+	0.687603i
$622$	17.3533	+	10.1578i	0.695804	+	0.407292i
$623$		0			0
$624$	−5.06676	+	8.31009i	−0.202833	+	0.332670i
$625$	30.5093			1.22037
$626$	−19.2040	+	32.8075i	−0.767547	+	1.31125i
$627$	36.6658	−	36.6658i	1.46429	−	1.46429i
$628$	28.6900	+	8.05661i	1.14486	+	0.321494i
$629$	−11.4360	−	11.4360i	−0.455984	−	0.455984i
$630$		0			0
$631$	−22.0158			−0.876434			−0.438217	−	0.898869i	$-0.644390\pi$
$631$	−22.0158			−0.876434			−0.438217	+	0.898869i	$0.644390\pi$
$632$	−0.0559295	+	3.11580i	−0.00222475	+	0.123940i
$633$	22.1269			0.879464
$634$	−21.9520	+	5.74148i	−0.871825	+	0.228023i
$635$	−25.6098	+	25.6098i	−1.01629	+	1.01629i
$636$	−15.1202	−	26.9281i	−0.599556	−	1.06777i
$637$		0			0
$638$	35.4573	+	20.7551i	1.40377	+	0.821703i
$639$			4.24750i			0.168028i
$640$	−28.4499	+	6.35955i	−1.12458	+	0.251383i
$641$	−23.9674			−0.946655			−0.473328	−	0.880886i	$-0.656947\pi$
$641$	−23.9674			−0.946655			−0.473328	+	0.880886i	$0.656947\pi$
$642$	13.0506	+	7.63922i	0.515065	+	0.301496i
$643$	−30.4232	−	30.4232i	−1.19977	−	1.19977i	−0.974235	−	0.225537i	$-0.927586\pi$
$643$	−30.4232	−	30.4232i	−1.19977	−	1.19977i	−0.225537	−	0.974235i	$-0.572414\pi$
$644$		0			0
$645$	25.0745	−	25.0745i	0.987306	−	0.987306i
$646$	−4.52632	−	17.3060i	−0.178086	−	0.680894i
$647$			6.29719i			0.247568i	0.992309	+	0.123784i	$0.0395030\pi$
$647$			6.29719i			0.247568i	−0.992309	+	0.123784i	$0.960497\pi$
$648$	−31.3802	−	0.563285i	−1.23273	−	0.0221279i
$649$	−4.38234			−0.172022
$650$	2.69269	−	0.704266i	0.105616	−	0.0276236i
$651$		0			0
$652$	−37.1947	−	10.4449i	−1.45666	−	0.409052i
$653$	22.5298	+	22.5298i	0.881660	+	0.881660i	0.993703	−	0.112043i	$-0.0357396\pi$
$653$	22.5298	+	22.5298i	0.881660	+	0.881660i	−0.112043	+	0.993703i	$0.535740\pi$
$654$	−34.2632	−	20.0561i	−1.33980	−	0.784257i
$655$		−	38.9257i		−	1.52095i
$656$	−9.93397	+	16.2929i	−0.387856	+	0.636130i
$657$			10.7390i			0.418970i
$658$		0			0
$659$	−3.27251	+	3.27251i	−0.127479	+	0.127479i	−0.767968	−	0.640489i	$-0.778732\pi$
$659$	−3.27251	+	3.27251i	−0.127479	+	0.127479i	0.640489	+	0.767968i	$0.278732\pi$
$660$	52.5969	+	14.7700i	2.04733	+	0.574922i
$661$	−10.4890	−	10.4890i	−0.407976	−	0.407976i	0.473056	−	0.881032i	$-0.343151\pi$
$661$	−10.4890	−	10.4890i	−0.407976	−	0.407976i	−0.881032	+	0.473056i	$0.843151\pi$
$662$	−25.9862	+	6.79663i	−1.00998	+	0.264158i
$663$		−	6.29224i		−	0.244370i
$664$	−27.0343	−	28.0226i	−1.04913	−	1.08749i
$665$		0			0
$666$	9.48145	−	2.47985i	0.367399	−	0.0960921i
$667$	24.8197	+	24.8197i	0.961022	+	0.961022i
$668$	−6.07469	+	3.41097i	−0.235037	+	0.131974i
$669$	−13.9610	−	13.9610i	−0.539762	−	0.539762i
$670$	0.718315	−	1.22714i	0.0277509	−	0.0474087i
$671$	−23.6951			−0.914740
$672$		0			0
$673$	1.09724			0.0422955			0.0211478	−	0.999776i	$-0.493268\pi$
$673$	1.09724			0.0422955			0.0211478	+	0.999776i	$0.493268\pi$
$674$	11.1807	−	19.1008i	0.430666	−	0.735734i
$675$	4.44515	+	4.44515i	0.171094	+	0.171094i
$676$	20.1573	−	11.3184i	0.775279	−	0.435323i
$677$	−11.7557	−	11.7557i	−0.451807	−	0.451807i	0.444147	−	0.895954i	$-0.353507\pi$
$677$	−11.7557	−	11.7557i	−0.451807	−	0.451807i	−0.895954	+	0.444147i	$0.853507\pi$
$678$	−24.0642	+	6.29392i	−0.924180	+	0.241717i
$679$		0			0
$680$	13.5635	−	13.0852i	0.520137	−	0.501793i
$681$			2.11322i			0.0809788i
$682$	8.37823	−	2.19130i	0.320819	−	0.0839093i
$683$	13.7567	+	13.7567i	0.526384	+	0.526384i	0.919492	−	0.393108i	$-0.128600\pi$
$683$	13.7567	+	13.7567i	0.526384	+	0.526384i	−0.393108	+	0.919492i	$0.628600\pi$
$684$	10.4360	+	2.93060i	0.399032	+	0.112054i
$685$	−9.19511	+	9.19511i	−0.351327	+	0.351327i
$686$		0			0
$687$			10.8981i			0.415790i
$688$	−26.3950	+	6.39969i	−1.00630	+	0.243986i
$689$		−	9.14603i		−	0.348436i
$690$	40.2798	+	23.5780i	1.53343	+	0.897600i
$691$	0.913410	+	0.913410i	0.0347478	+	0.0347478i	0.724267	−	0.689519i	$-0.242178\pi$
$691$	0.913410	+	0.913410i	0.0347478	+	0.0347478i	−0.689519	+	0.724267i	$0.742178\pi$
$692$	−0.141024	−	0.0396017i	−0.00536092	−	0.00150543i
$693$		0			0
$694$	−26.8216	+	7.01511i	−1.01813	+	0.266290i
$695$	13.7728			0.522433
$696$	−0.571485	+	31.8371i	−0.0216621	+	1.20678i
$697$		−	12.3367i		−	0.467284i
$698$	3.71531	+	14.2051i	0.140626	+	0.537672i
$699$	18.3231	−	18.3231i	0.693044	−	0.693044i
$700$		0			0
$701$	4.42004	+	4.42004i	0.166942	+	0.166942i	0.785634	−	0.618692i	$-0.212337\pi$
$701$	4.42004	+	4.42004i	0.166942	+	0.166942i	−0.618692	+	0.785634i	$0.712337\pi$
$702$	−5.61859	−	3.28887i	−0.212060	−	0.124130i
$703$	30.5911			1.15376
$704$	−28.5064	−	30.6301i	−1.07438	−	1.15442i
$705$			35.4363i			1.33461i
$706$	14.7318	+	8.62334i	0.554439	+	0.324544i
$707$		0			0
$708$	−1.66290	−	2.96151i	−0.0624957	−	0.111300i
$709$	16.2358	−	16.2358i	0.609750	−	0.609750i	−0.333131	−	0.942881i	$-0.608105\pi$
$709$	16.2358	−	16.2358i	0.609750	−	0.609750i	0.942881	+	0.333131i	$0.108105\pi$
$710$	−13.5140	+	3.53454i	−0.507170	+	0.132649i
$711$	1.22083			0.0457846
$712$	44.7451	+	0.803188i	1.67689	+	0.0301008i
$713$	7.39855			0.277078
$714$		0			0
$715$	11.4405	+	11.4405i	0.427849	+	0.427849i
$716$	−5.99274	−	1.68286i	−0.223959	−	0.0628913i
$717$	−37.5904	+	37.5904i	−1.40384	+	1.40384i
$718$	−1.24077	+	2.11969i	−0.0463051	+	0.0791060i
$719$	−7.07123			−0.263712			−0.131856	−	0.991269i	$-0.542094\pi$
$719$	−7.07123			−0.263712			−0.131856	+	0.991269i	$0.542094\pi$
$720$	2.69102	+	11.0989i	0.100288	+	0.413631i
$721$		0			0
$722$	6.01107	+	3.51861i	0.223709	+	0.130949i
$723$	31.5968	−	31.5968i	1.17510	−	1.17510i
$724$	2.55722	−	9.10641i	0.0950385	−	0.338437i
$725$	6.43872	−	6.43872i	0.239128	−	0.239128i
$726$	11.8633	+	45.3583i	0.440289	+	1.68340i
$727$			21.2964i			0.789838i	0.918716	+	0.394919i	$0.129227\pi$
$727$			21.2964i			0.789838i	−0.918716	+	0.394919i	$0.870773\pi$
$728$		0			0
$729$		−	11.0213i		−	0.408196i
$730$	−34.1676	+	8.93644i	−1.26460	+	0.330753i
$731$	12.4157	−	12.4157i	0.459213	−	0.459213i
$732$	−8.99124	−	16.0128i	−0.332326	−	0.591848i
$733$	−19.6915	+	19.6915i	−0.727324	+	0.727324i	−0.970086	−	0.242762i	$-0.921947\pi$
$733$	−19.6915	+	19.6915i	−0.727324	+	0.727324i	0.242762	+	0.970086i	$0.421947\pi$
$734$	7.45504	−	12.7359i	0.275171	−	0.470092i
$735$		0			0
$736$	−16.9398	−	31.4790i	−0.624411	−	1.16033i
$737$	2.04093			0.0751786
$738$	6.45165	+	3.77651i	0.237489	+	0.139015i
$739$	−19.6401	+	19.6401i	−0.722472	+	0.722472i	−0.969108	−	0.246636i	$-0.920675\pi$
$739$	−19.6401	+	19.6401i	−0.722472	+	0.722472i	0.246636	+	0.969108i	$0.420675\pi$
$740$	15.7799	+	28.1029i	0.580081	+	1.03308i
$741$	8.41580	+	8.41580i	0.309162	+	0.309162i
$742$		0			0
$743$	−4.98267			−0.182796			−0.0913982	−	0.995814i	$-0.529134\pi$
$743$	−4.98267			−0.182796			−0.0913982	+	0.995814i	$0.529134\pi$
$744$	4.66001	+	4.83036i	0.170844	+	0.177090i
$745$	−0.702624			−0.0257422
$746$	3.92917	+	15.0228i	0.143857	+	0.550024i
$747$	−10.7862	+	10.7862i	−0.394645	+	0.394645i
$748$	26.0436	+	7.31345i	0.952248	+	0.267406i
$749$		0			0
$750$	−12.5388	+	21.4209i	−0.457854	+	0.782181i
$751$			16.3335i			0.596018i	0.954563	+	0.298009i	$0.0963226\pi$
$751$			16.3335i			0.596018i	−0.954563	+	0.298009i	$0.903677\pi$
$752$	14.1291	−	23.1734i	0.515235	−	0.845047i
$753$	44.4263			1.61898
$754$	−4.76387	+	8.13842i	−0.173490	+	0.296384i
$755$	−16.6905	−	16.6905i	−0.607431	−	0.607431i
$756$		0			0
$757$	38.1458	−	38.1458i	1.38643	−	1.38643i	0.553747	−	0.832685i	$-0.313198\pi$
$757$	38.1458	−	38.1458i	1.38643	−	1.38643i	0.832685	−	0.553747i	$-0.186802\pi$
$758$	37.4378	−	9.79176i	1.35980	−	0.355653i
$759$			66.9916i			2.43164i
$760$	−0.639789	+	35.6423i	−0.0232076	+	1.29288i
$761$	33.0136			1.19674			0.598371	−	0.801219i	$-0.295815\pi$
$761$	33.0136			1.19674			0.598371	+	0.801219i	$0.295815\pi$
$762$	−10.1946	−	38.9782i	−0.369313	−	1.41203i
$763$		0			0
$764$	−0.545909	+	0.306531i	−0.0197503	+	0.0110899i
$765$	−5.22072	−	5.22072i	−0.188756	−	0.188756i
$766$	−12.7355	+	21.7568i	−0.460151	+	0.786105i
$767$		−	1.00587i		−	0.0363198i
$768$	9.88240	−	30.8869i	0.356600	−	1.11453i
$769$		−	18.6850i		−	0.673800i	−0.941540	−	0.336900i	$-0.890622\pi$
$769$		−	18.6850i		−	0.673800i	0.941540	−	0.336900i	$-0.109378\pi$
$770$		0			0
$771$	2.71405	−	2.71405i	0.0977441	−	0.0977441i
$772$	10.1408	+	18.0600i	0.364974	+	0.649992i
$773$	24.6966	+	24.6966i	0.888275	+	0.888275i	0.994357	−	0.106083i	$-0.0338308\pi$
$773$	24.6966	+	24.6966i	0.888275	+	0.888275i	−0.106083	+	0.994357i	$0.533831\pi$
$774$	2.69229	+	10.2937i	0.0967725	+	0.370000i
$775$		−	1.91933i		−	0.0689444i
$776$	−0.0569701	+	3.17377i	−0.00204511	+	0.113932i
$777$		0			0
$778$	2.23326	+	8.53865i	0.0800662	+	0.306126i
$779$	16.5001	+	16.5001i	0.591179	+	0.591179i
$780$	−3.39013	+	12.0724i	−0.121386	+	0.432262i
$781$	−14.1771	−	14.1771i	−0.507298	−	0.507298i
$782$	19.9448	+	11.6748i	0.713223	+	0.417489i
$783$	−21.2994			−0.761178
$784$		0			0
$785$	38.3925			1.37029
$786$	37.3703	+	21.8749i	1.33296	+	0.780252i
$787$	17.2340	+	17.2340i	0.614325	+	0.614325i	0.944070	−	0.329745i	$-0.106963\pi$
$787$	17.2340	+	17.2340i	0.614325	+	0.614325i	−0.329745	+	0.944070i	$0.606963\pi$
$788$	−0.307176	−	0.0862598i	−0.0109427	−	0.00307288i
$789$	−13.4034	−	13.4034i	−0.477175	−	0.477175i
$790$	1.01591	+	3.88422i	0.0361443	+	0.138194i
$791$		0			0
$792$	−11.7972	+	11.3811i	−0.419194	+	0.404410i
$793$		−	5.43868i		−	0.193133i
$794$	2.52718	+	9.66242i	0.0896862	+	0.342907i
$795$	−28.1341	−	28.1341i	−0.997815	−	0.997815i
$796$	−37.2000	+	20.8880i	−1.31852	+	0.740354i
$797$	25.8769	−	25.8769i	0.916608	−	0.916608i	−0.0801732	−	0.996781i	$-0.525547\pi$
$797$	25.8769	−	25.8769i	0.916608	−	0.916608i	0.996781	+	0.0801732i	$0.0255473\pi$
$798$		0			0
$799$			17.5465i			0.620749i
$800$	−8.16629	+	4.39453i	−0.288722	+	0.155370i
$801$		−	17.5320i		−	0.619462i
$802$	−14.9957	+	25.6182i	−0.529518	+	0.904610i
$803$	−35.8443	−	35.8443i	−1.26492	−	1.26492i
$804$	0.774442	+	1.37922i	0.0273124	+	0.0486415i
$805$		0			0
$806$	0.502964	+	1.92303i	0.0177162	+	0.0677360i
$807$	54.0599			1.90300
$808$	−28.4978	−	29.5396i	−1.00255	−	1.03920i
$809$			23.0197i			0.809331i	0.914465	+	0.404665i	$0.132612\pi$
$809$			23.0197i			0.809331i	−0.914465	+	0.404665i	$0.867388\pi$
$810$	−39.1193	+	10.2315i	−1.37451	+	0.359500i
$811$	−8.31612	+	8.31612i	−0.292019	+	0.292019i	−0.837877	−	0.545859i	$-0.816204\pi$
$811$	−8.31612	+	8.31612i	−0.292019	+	0.292019i	0.545859	+	0.837877i	$0.316204\pi$
$812$		0			0
$813$	12.3276	+	12.3276i	0.432347	+	0.432347i
$814$	−23.3697	+	39.9240i	−0.819107	+	1.39933i
$815$	−49.7733			−1.74348
$816$	4.94007	+	20.3749i	0.172937	+	0.713265i
$817$			33.2118i			1.16193i
$818$	−25.8561	+	44.1716i	−0.904036	+	1.54442i
$819$		0			0
$820$	−6.64673	+	23.6694i	−0.232114	+	0.826570i
$821$	−1.59482	+	1.59482i	−0.0556596	+	0.0556596i	−0.734389	−	0.678729i	$-0.762531\pi$
$821$	−1.59482	+	1.59482i	−0.0556596	+	0.0556596i	0.678729	+	0.734389i	$0.262531\pi$
$822$	−3.66035	−	13.9950i	−0.127670	−	0.488132i
$823$	8.74544			0.304847			0.152423	−	0.988315i	$-0.451292\pi$
$823$	8.74544			0.304847			0.152423	+	0.988315i	$0.451292\pi$
$824$	−0.0434881	+	2.42270i	−0.00151498	+	0.0843986i
$825$	17.3789			0.605057
$826$		0			0
$827$	−2.25129	−	2.25129i	−0.0782850	−	0.0782850i	0.666880	−	0.745165i	$-0.267629\pi$
$827$	−2.25129	−	2.25129i	−0.0782850	−	0.0782850i	−0.745165	+	0.666880i	$0.767629\pi$
$828$	−12.2110	+	6.85654i	−0.424362	+	0.238281i
$829$	4.58643	−	4.58643i	0.159293	−	0.159293i	−0.622960	−	0.782254i	$-0.714070\pi$
$829$	4.58643	−	4.58643i	0.159293	−	0.159293i	0.782254	+	0.622960i	$0.214070\pi$
$830$	−43.2932	−	25.3419i	−1.50273	−	0.879630i
$831$	51.9443			1.80193
$832$	7.03045	−	6.54300i	0.243737	−	0.226838i
$833$		0			0
$834$	−7.73984	+	13.2225i	−0.268009	+	0.457857i
$835$	−6.34677	+	6.34677i	−0.219639	+	0.219639i
$836$	−44.6146	+	25.0513i	−1.54303	+	0.866418i
$837$	−3.17459	+	3.17459i	−0.109730	+	0.109730i
$838$	9.97280	−	2.60836i	0.344505	−	0.0901042i
$839$		−	15.8804i		−	0.548253i	−0.961694	−	0.274126i	$-0.911611\pi$
$839$		−	15.8804i		−	0.548253i	0.961694	−	0.274126i	$-0.0883886\pi$
$840$		0			0
$841$			1.85175i			0.0638536i
$842$	3.92648	+	15.0125i	0.135316	+	0.517366i
$843$	33.3731	−	33.3731i	1.14943	−	1.14943i
$844$	−21.0208	−	5.90298i	−0.723567	−	0.203189i
$845$	21.0601	−	21.0601i	0.724489	−	0.724489i
$846$	−9.17619	−	5.37133i	−0.315484	−	0.184670i
$847$		0			0
$848$	7.18060	+	29.6158i	0.246583	+	1.01701i
$849$	−20.5779			−0.706232
$850$	3.02867	−	5.17407i	0.103882	−	0.177469i
$851$	−27.9463	+	27.9463i	−0.957987	+	0.957987i
$852$	4.20107	−	14.9602i	0.143926	−	0.512530i
$853$	31.2018	+	31.2018i	1.06833	+	1.06833i	0.997488	+	0.0708400i	$0.0225680\pi$
$853$	31.2018	+	31.2018i	1.06833	+	1.06833i	0.0708400	+	0.997488i	$0.477432\pi$
$854$		0			0
$855$	13.9653			0.477603
$856$	−10.3602	−	10.7390i	−0.354106	−	0.367051i
$857$	−0.513545			−0.0175424			−0.00877118	−	0.999962i	$-0.502792\pi$
$857$	−0.513545			−0.0175424			−0.00877118	+	0.999962i	$0.502792\pi$
$858$	−17.4125	+	4.55418i	−0.594452	+	0.155477i
$859$	14.9840	−	14.9840i	0.511248	−	0.511248i	−0.403661	−	0.914909i	$-0.632262\pi$
$859$	14.9840	−	14.9840i	0.511248	−	0.511248i	0.914909	+	0.403661i	$0.132262\pi$
$860$	−30.5104	+	17.1318i	−1.04040	+	0.584188i
$861$		0			0
$862$	30.2643	+	17.7154i	1.03081	+	0.603387i
$863$		−	47.8726i		−	1.62960i	−0.579741	−	0.814801i	$-0.696846\pi$
$863$		−	47.8726i		−	1.62960i	0.579741	−	0.814801i	$-0.303154\pi$
$864$	20.7757	+	6.23852i	0.706803	+	0.212239i
$865$	−0.188716			−0.00641652
$866$	5.91916	+	3.46481i	0.201141	+	0.117739i
$867$	14.7802	+	14.7802i	0.501961	+	0.501961i
$868$		0			0
$869$	−4.07483	+	4.07483i	−0.138229	+	0.138229i
$870$	10.3805	+	39.6888i	0.351931	+	1.34558i
$871$			0.468449i			0.0158728i
$872$	27.2000	+	28.1943i	0.921107	+	0.954780i
$873$	1.24354			0.0420875
$874$	−42.2907	+	11.0610i	−1.43051	+	0.374144i
$875$		0			0
$876$	10.6217	−	37.8243i	0.358873	−	1.27796i
$877$	16.0031	+	16.0031i	0.540387	+	0.540387i	0.923642	−	0.383255i	$-0.125197\pi$
$877$	16.0031	+	16.0031i	0.540387	+	0.540387i	−0.383255	+	0.923642i	$0.625197\pi$
$878$	45.4441	+	26.6009i	1.53366	+	0.897737i
$879$			0.275561i			0.00929445i
$880$	−46.0274	−	28.0635i	−1.55158	−	0.946019i
$881$			17.7026i			0.596417i	0.954501	+	0.298209i	$0.0963891\pi$
$881$			17.7026i			0.596417i	−0.954501	+	0.298209i	$0.903611\pi$
$882$		0			0
$883$	−13.2141	+	13.2141i	−0.444691	+	0.444691i	−0.893585	−	0.448894i	$-0.851818\pi$
$883$	−13.2141	+	13.2141i	−0.444691	+	0.444691i	0.448894	+	0.893585i	$0.351818\pi$
$884$	−1.67864	+	5.97772i	−0.0564587	+	0.201052i
$885$	−3.09415	−	3.09415i	−0.104009	−	0.104009i
$886$	34.4308	−	9.00527i	1.15672	−	0.302538i
$887$			51.2242i			1.71994i	0.510344	+	0.859970i	$0.329518\pi$
$887$			51.2242i			1.71994i	−0.510344	+	0.859970i	$0.670482\pi$
$888$	−35.8477	−	0.643476i	−1.20297	−	0.0215937i
$889$		0			0
$890$	55.7803	−	14.5892i	1.86976	−	0.489030i
$891$	−41.0390	−	41.0390i	−1.37486	−	1.37486i
$892$	9.53863	+	16.9876i	0.319377	+	0.568787i
$893$	−23.4682	−	23.4682i	−0.785332	−	0.785332i
$894$	0.394850	−	0.674548i	0.0132058	−	0.0225603i
$895$	−8.01938			−0.268058
$896$		0			0
$897$	−15.3764			−0.513403
$898$	0.632894	−	1.08121i	0.0211199	−	0.0360806i
$899$	4.59833	+	4.59833i	0.153363	+	0.153363i
$900$	1.77872	+	3.16778i	0.0592908	+	0.105593i
$901$	−13.9308	−	13.9308i	−0.464101	−	0.464101i
$902$	−34.1391	+	8.92899i	−1.13671	+	0.297303i
$903$		0			0
$904$	24.5404	+	0.440508i	0.816202	+	0.0146511i
$905$		−	12.1860i		−	0.405078i
$906$	25.4031	−	6.64411i	0.843962	−	0.220736i
$907$	−6.00802	−	6.00802i	−0.199493	−	0.199493i	0.600290	−	0.799783i	$-0.295052\pi$
$907$	−6.00802	−	6.00802i	−0.199493	−	0.199493i	−0.799783	+	0.600290i	$0.795052\pi$
$908$	0.563763	−	2.00759i	0.0187091	−	0.0666242i
$909$	−11.3701	+	11.3701i	−0.377122	+	0.377122i
$910$		0			0
$911$		−	19.6850i		−	0.652192i	−0.945337	−	0.326096i	$-0.894267\pi$
$911$		−	19.6850i		−	0.652192i	0.945337	−	0.326096i	$-0.105733\pi$
$912$	−33.8585	−	20.6439i	−1.12117	−	0.683589i
$913$		−	72.0033i		−	2.38296i
$914$	42.3225	+	24.7737i	1.39991	+	0.819442i
$915$	−16.7299	−	16.7299i	−0.553075	−	0.553075i
$916$	2.90739	−	10.3534i	0.0960630	−	0.342086i
$917$		0			0
$918$	−13.5674	+	3.54851i	−0.447790	+	0.117118i
$919$	35.4627			1.16981			0.584903	−	0.811104i	$-0.301133\pi$
$919$	35.4627			1.16981			0.584903	+	0.811104i	$0.301133\pi$
$920$	−31.9763	−	33.1453i	−1.05423	−	1.09277i
$921$		−	46.5646i		−	1.53435i
$922$	−2.08102	−	7.95659i	−0.0685349	−	0.262036i
$923$	3.25404	−	3.25404i	0.107108	−	0.107108i
$924$		0			0
$925$	7.24983	+	7.24983i	0.238373	+	0.238373i
$926$	14.2666	+	8.35105i	0.468831	+	0.274432i
$927$	0.949258			0.0311777
$928$	9.03637	−	30.0932i	0.296633	−	0.987857i
$929$			43.9670i			1.44251i	0.692670	+	0.721255i	$0.256434\pi$
$929$			43.9670i			1.44251i	−0.692670	+	0.721255i	$0.743566\pi$
$930$	7.46262	+	4.36828i	0.244709	+	0.143242i
$931$		0			0
$932$	−22.2954	+	12.5190i	−0.730311	+	0.410073i
$933$	−20.3775	+	20.3775i	−0.667128	+	0.667128i
$934$	34.4601	−	9.01294i	1.12757	−	0.294912i
$935$	34.8511			1.13975
$936$	−2.61228	−	2.70777i	−0.0853849	−	0.0885063i
$937$	−32.7634			−1.07033			−0.535167	−	0.844746i	$-0.679751\pi$
$937$	−32.7634			−1.07033			−0.535167	+	0.844746i	$0.679751\pi$
$938$		0			0
$939$	−38.5248	−	38.5248i	−1.25721	−	1.25721i
$940$	9.45365	−	33.6650i	0.308344	−	1.09803i
$941$	−21.6724	+	21.6724i	−0.706500	+	0.706500i	−0.965798	−	0.259297i	$-0.916509\pi$
$941$	−21.6724	+	21.6724i	−0.706500	+	0.706500i	0.259297	+	0.965798i	$0.416509\pi$
$942$	−21.5752	+	36.8584i	−0.702959	+	1.20091i
$943$	−30.1472			−0.981728
$944$	0.789712	+	3.25710i	0.0257029	+	0.106010i
$945$		0			0
$946$	−43.3442	−	25.3718i	−1.40924	−	0.824907i
$947$	−8.13565	+	8.13565i	−0.264373	+	0.264373i	−0.826828	−	0.562455i	$-0.809857\pi$
$947$	−8.13565	+	8.13565i	−0.264373	+	0.264373i	0.562455	+	0.826828i	$0.309857\pi$
$948$	−4.29992	−	1.20748i	−0.139655	−	0.0392173i
$949$	8.22726	−	8.22726i	0.267068	−	0.267068i
$950$	2.86945	+	10.9711i	0.0930972	+	0.355948i
$951$		−	32.5196i		−	1.05452i
$952$		0			0
$953$			31.6828i			1.02631i	0.858297	+	0.513153i	$0.171523\pi$
$953$			31.6828i			1.02631i	−0.858297	+	0.513153i	$0.828477\pi$
$954$	11.5498	−	3.02082i	0.373939	−	0.0978025i
$955$	−0.570360	+	0.570360i	−0.0184564	+	0.0184564i
$956$	45.7397	−	25.6831i	1.47933	−	0.830650i
$957$	−41.6364	+	41.6364i	−1.34592	+	1.34592i
$958$	17.3661	−	29.6676i	0.561072	−	0.958516i
$959$		0			0
$960$	1.49945	−	41.7533i	0.0483946	−	1.34758i
$961$	−29.6293			−0.955783
$962$	−9.16364	−	5.36399i	−0.295448	−	0.172942i
$963$	−4.13354	+	4.13354i	−0.133201	+	0.133201i
$964$	−38.4468	+	21.5881i	−1.23829	+	0.695305i
$965$	18.8688	+	18.8688i	0.607409	+	0.607409i
$966$		0			0
$967$	15.2574			0.490645			0.245322	−	0.969442i	$-0.421106\pi$
$967$	15.2574			0.490645			0.245322	+	0.969442i	$0.421106\pi$
$968$	0.830307	−	46.2559i	0.0266871	−	1.48672i
$969$	25.6370			0.823579
$970$	1.03481	+	3.95649i	0.0332257	+	0.127035i
$971$	21.4270	−	21.4270i	0.687625	−	0.687625i	−0.274081	−	0.961707i	$-0.588374\pi$
$971$	21.4270	−	21.4270i	0.687625	−	0.687625i	0.961707	+	0.274081i	$0.0883737\pi$
$972$	5.94059	−	21.1548i	0.190544	−	0.678539i
$973$		0			0
$974$	−22.1471	+	37.8353i	−0.709639	+	1.21232i
$975$			3.98894i			0.127748i
$976$	4.26994	+	17.6110i	0.136677	+	0.563715i
$977$	50.3441			1.61065			0.805325	−	0.592834i	$-0.201991\pi$
$977$	50.3441			1.61065			0.805325	+	0.592834i	$0.201991\pi$
$978$	27.9708	−	47.7844i	0.894409	−	1.52798i
$979$	58.5176	+	58.5176i	1.87023	+	1.87023i
$980$		0			0
$981$	10.8523	−	10.8523i	0.346486	−	0.346486i
$982$	16.0420	−	4.19573i	0.511920	−	0.133891i
$983$			9.98285i			0.318404i	0.987246	+	0.159202i	$0.0508920\pi$
$983$			9.98285i			0.318404i	−0.987246	+	0.159202i	$0.949108\pi$
$984$	−18.9883	−	19.6825i	−0.605326	−	0.627455i
$985$	−0.411057			−0.0130974
$986$	5.13995	+	19.6521i	0.163689	+	0.625850i
$987$		0			0
$988$	−5.74997	−	10.2403i	−0.182931	−	0.325787i
$989$	−30.3405	−	30.3405i	−0.964770	−	0.964770i
$990$	−10.6686	+	18.2259i	−0.339071	+	0.579258i
$991$		−	47.2120i		−	1.49974i	−0.661587	−	0.749869i	$-0.730117\pi$
$991$		−	47.2120i		−	1.49974i	0.661587	−	0.749869i	$-0.269883\pi$
$992$	−3.13843	−	5.83210i	−0.0996454	−	0.185169i
$993$		−	38.4959i		−	1.22163i
$994$		0			0
$995$	−38.8661	+	38.8661i	−1.23214	+	1.23214i
$996$	48.6585	−	27.3220i	1.54181	−	0.865731i
$997$	24.5944	+	24.5944i	0.778911	+	0.778911i	0.979646	−	0.200734i	$-0.0643328\pi$
$997$	24.5944	+	24.5944i	0.778911	+	0.778911i	−0.200734	+	0.979646i	$0.564333\pi$
$998$	8.50831	+	32.5307i	0.269326	+	1.02974i
$999$		−	23.9825i		−	0.758774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.j.a.195.18		56
7.2	even	3		784.2.w.f.227.1		56
7.3	odd	6		784.2.w.f.19.10		56
7.4	even	3		112.2.v.a.19.10	yes	56
7.5	odd	6		112.2.v.a.3.1	✓	56
7.6	odd	2	inner	784.2.j.a.195.17		56
16.11	odd	4	inner	784.2.j.a.587.17		56
28.11	odd	6		448.2.z.a.47.3		56
28.19	even	6		448.2.z.a.367.3		56
56.5	odd	6		896.2.z.b.479.3		56
56.11	odd	6		896.2.z.a.607.12		56
56.19	even	6		896.2.z.a.479.12		56
56.53	even	6		896.2.z.b.607.3		56
112.5	odd	12		448.2.z.a.143.3		56
112.11	odd	12		112.2.v.a.75.1	yes	56
112.19	even	12		896.2.z.b.31.3		56
112.27	even	4	inner	784.2.j.a.587.18		56
112.53	even	12		448.2.z.a.271.3		56
112.59	even	12		784.2.w.f.411.1		56
112.61	odd	12		896.2.z.a.31.12		56
112.67	odd	12		896.2.z.b.159.3		56
112.75	even	12		112.2.v.a.59.10	yes	56
112.107	odd	12		784.2.w.f.619.10		56
112.109	even	12		896.2.z.a.159.12		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.1	✓	56	7.5	odd	6
112.2.v.a.19.10	yes	56	7.4	even	3
112.2.v.a.59.10	yes	56	112.75	even	12
112.2.v.a.75.1	yes	56	112.11	odd	12
448.2.z.a.47.3		56	28.11	odd	6
448.2.z.a.143.3		56	112.5	odd	12
448.2.z.a.271.3		56	112.53	even	12
448.2.z.a.367.3		56	28.19	even	6
784.2.j.a.195.17		56	7.6	odd	2	inner
784.2.j.a.195.18		56	1.1	even	1	trivial
784.2.j.a.587.17		56	16.11	odd	4	inner
784.2.j.a.587.18		56	112.27	even	4	inner
784.2.w.f.19.10		56	7.3	odd	6
784.2.w.f.227.1		56	7.2	even	3
784.2.w.f.411.1		56	112.59	even	12
784.2.w.f.619.10		56	112.107	odd	12
896.2.z.a.31.12		56	112.61	odd	12
896.2.z.a.159.12		56	112.109	even	12
896.2.z.a.479.12		56	56.19	even	6
896.2.z.a.607.12		56	56.11	odd	6
896.2.z.b.31.3		56	112.19	even	12
896.2.z.b.159.3		56	112.67	odd	12
896.2.z.b.479.3		56	56.5	odd	6
896.2.z.b.607.3		56	56.53	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.714421 - 1.22049i) q^{2} +(1.43319 + 1.43319i) q^{3} +(-0.979204 - 1.74389i) q^{4} +(-1.82200 - 1.82200i) q^{5} +(2.77309 - 0.725295i) q^{6} +(-2.82797 - 0.0507629i) q^{8} +1.10805i q^{9} +(-3.52541 + 0.922061i) q^{10} +(-3.69842 - 3.69842i) q^{11} +(1.09594 - 3.90271i) q^{12} +(0.848888 - 0.848888i) q^{13} -5.22253i q^{15} +(-2.08232 + 3.41525i) q^{16} -2.58596i q^{17} +(1.35237 + 0.791616i) q^{18} +(3.45869 + 3.45869i) q^{19} +(-1.39326 + 4.96148i) q^{20} +(-7.15612 + 1.87166i) q^{22} -6.31934 q^{23} +(-3.98026 - 4.12577i) q^{24} +1.63936i q^{25} +(-0.429597 - 1.64252i) q^{26} +(2.71152 - 2.71152i) q^{27} +(-3.92758 - 3.92758i) q^{29} +(-6.37406 - 3.73109i) q^{30} -1.17078 q^{31} +(2.68064 + 4.98138i) q^{32} -10.6010i q^{33} +(-3.15615 - 1.84747i) q^{34} +(1.93232 - 1.08501i) q^{36} +(4.42235 - 4.42235i) q^{37} +(6.69227 - 1.75034i) q^{38} +2.43323 q^{39} +(5.06007 + 5.24505i) q^{40} +4.77063 q^{41} +(4.80121 + 4.80121i) q^{43} +(-2.82813 + 10.0711i) q^{44} +(2.01887 - 2.01887i) q^{45} +(-4.51467 + 7.71270i) q^{46} -6.78527 q^{47} +(-7.87905 + 1.91034i) q^{48} +(2.00083 + 1.17120i) q^{50} +(3.70617 - 3.70617i) q^{51} +(-2.31160 - 0.649134i) q^{52} +(5.38707 - 5.38707i) q^{53} +(-1.37222 - 5.24655i) q^{54} +13.4770i q^{55} +9.91391i q^{57} +(-7.59953 + 1.98763i) q^{58} +(0.592462 - 0.592462i) q^{59} +(-9.10753 + 5.11392i) q^{60} +(3.20342 - 3.20342i) q^{61} +(-0.836430 + 1.42893i) q^{62} +(7.99485 + 0.287112i) q^{64} -3.09335 q^{65} +(-12.9385 - 7.57361i) q^{66} +(-0.275920 + 0.275920i) q^{67} +(-4.50964 + 2.53218i) q^{68} +(-9.05679 - 9.05679i) q^{69} +3.83330 q^{71} +(0.0562480 - 3.13354i) q^{72} +9.69181 q^{73} +(-2.23802 - 8.55686i) q^{74} +(-2.34951 + 2.34951i) q^{75} +(2.64482 - 9.41835i) q^{76} +(1.73835 - 2.96974i) q^{78} -1.10178i q^{79} +(10.0166 - 2.42860i) q^{80} +11.0964 q^{81} +(3.40824 - 5.82251i) q^{82} +(9.73434 + 9.73434i) q^{83} +(-4.71162 + 4.71162i) q^{85} +(9.28993 - 2.42975i) q^{86} -11.2579i q^{87} +(10.2713 + 10.6468i) q^{88} -15.8223 q^{89} +(-1.02169 - 3.90634i) q^{90} +(6.18792 + 11.0202i) q^{92} +(-1.67795 - 1.67795i) q^{93} +(-4.84754 + 8.28137i) q^{94} -12.6035i q^{95} +(-3.29740 + 10.9811i) q^{96} -1.12228i q^{97} +(4.09804 - 4.09804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{2} + 8 q^{4} + 4 q^{8} - 4 q^{11} - 16 q^{16} + 60 q^{18} - 28 q^{22} + 24 q^{23} - 24 q^{29} + 36 q^{30} + 24 q^{32} + 16 q^{36} - 12 q^{37} + 8 q^{39} - 52 q^{44} - 32 q^{46} + 68 q^{51} - 12 q^{53}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q + 4 * q^2 + 8 * q^4 + 4 * q^8 - 4 * q^11 - 16 * q^16 + 60 * q^18 - 28 * q^22 + 24 * q^23 - 24 * q^29 + 36 * q^30 + 24 * q^32 + 16 * q^36 - 12 * q^37 + 8 * q^39 - 52 * q^44 - 32 * q^46 + 68 * q^51 - 12 * q^53 - 36 * q^58 - 156 * q^60 - 16 * q^64 + 8 * q^65 - 12 * q^67 - 80 * q^71 + 8 * q^72 - 124 * q^74 + 4 * q^78 + 16 * q^81 - 28 * q^85 - 60 * q^88 - 20 * q^92 - 20 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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