LMFDB - Embedded newform 624.2.cn.d.305.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(305,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))

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

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

chi := DirichletCharacter("624.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.cn (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.2
Root			$0.500000 + 1.33108i$ of defining polynomial
Character	$\chi$	$=$	624.305
Dual form			624.2.cn.d.401.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933998 - 1.45865i) q^{3} +(-2.76293 - 2.76293i) q^{5} +(0.657464 - 2.45369i) q^{7} +(-1.25529 + 2.72474i) q^{9} +O(q^{10})$	\(q+(-0.933998 - 1.45865i) q^{3} +(-2.76293 - 2.76293i) q^{5} +(0.657464 - 2.45369i) q^{7} +(-1.25529 + 2.72474i) q^{9} +(0.150860 + 0.563016i) q^{11} +(-1.20856 - 3.39697i) q^{13} +(-1.44957 + 6.61072i) q^{15} +(0.547000 + 0.947432i) q^{17} +(-1.32717 - 0.355613i) q^{19} +(-4.19313 + 1.33273i) q^{21} +(0.876460 - 1.51807i) q^{23} +10.2676i q^{25} +(5.14688 - 0.713876i) q^{27} +(5.12973 + 2.96165i) q^{29} +(-6.49983 + 6.49983i) q^{31} +(0.680339 - 0.745907i) q^{33} +(-8.59591 + 4.96285i) q^{35} +(-2.98942 + 0.801012i) q^{37} +(-3.82618 + 4.93562i) q^{39} +(-5.11781 + 1.37131i) q^{41} +(-3.26299 + 1.88389i) q^{43} +(10.9966 - 4.05999i) q^{45} +(5.51114 - 5.51114i) q^{47} +(0.473846 + 0.273575i) q^{49} +(0.871071 - 1.68278i) q^{51} -3.04435i q^{53} +(1.13876 - 1.97239i) q^{55} +(0.720857 + 2.26801i) q^{57} +(-8.19009 - 2.19453i) q^{59} +(-4.67266 - 8.09329i) q^{61} +(5.86037 + 4.87153i) q^{63} +(-6.04642 + 12.7248i) q^{65} +(-1.70856 - 6.37644i) q^{67} +(-3.03294 + 0.139433i) q^{69} +(-0.220122 + 0.821505i) q^{71} +(-5.18078 - 5.18078i) q^{73} +(14.9768 - 9.58993i) q^{75} +1.48065 q^{77} +13.1089 q^{79} +(-5.84847 - 6.84072i) q^{81} +(5.15394 + 5.15394i) q^{83} +(1.10637 - 4.12902i) q^{85} +(-0.471158 - 10.2486i) q^{87} +(-2.50797 - 9.35988i) q^{89} +(-9.12969 + 0.732051i) q^{91} +(15.5518 + 3.41012i) q^{93} +(2.68434 + 4.64941i) q^{95} +(-0.592450 - 0.158747i) q^{97} +(-1.72345 - 0.295697i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} - 24 q^{13} + 16 q^{19} - 24 q^{21} - 16 q^{31} - 24 q^{33} + 16 q^{37} - 48 q^{39} + 24 q^{45} + 24 q^{49} + 24 q^{55} - 24 q^{57} - 24 q^{61} + 24 q^{63} - 32 q^{67} - 48 q^{69} + 56 q^{73} + 96 q^{79} + 24 q^{81} - 24 q^{85} - 48 q^{87} + 16 q^{91} - 24 q^{93} + 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 - 24 * q^13 + 16 * q^19 - 24 * q^21 - 16 * q^31 - 24 * q^33 + 16 * q^37 - 48 * q^39 + 24 * q^45 + 24 * q^49 + 24 * q^55 - 24 * q^57 - 24 * q^61 + 24 * q^63 - 32 * q^67 - 48 * q^69 + 56 * q^73 + 96 * q^79 + 24 * q^81 - 24 * q^85 - 48 * q^87 + 16 * q^91 - 24 * q^93 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$-1$	$1$

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			0
$2$		0			0
$3$	−0.933998	−	1.45865i	−0.539244	−	0.842150i
$3$	−0.933998	−	1.45865i	−0.539244	−	0.842150i
$4$		0			0
$5$	−2.76293	−	2.76293i	−1.23562	−	1.23562i	−0.961773	−	0.273849i	$-0.911703\pi$
$5$	−2.76293	−	2.76293i	−1.23562	−	1.23562i	−0.273849	−	0.961773i	$-0.588297\pi$
$6$		0			0
$7$	0.657464	−	2.45369i	0.248498	−	0.927407i	−0.723095	−	0.690749i	$-0.757281\pi$
$7$	0.657464	−	2.45369i	0.248498	−	0.927407i	0.971593	−	0.236659i	$-0.0760523\pi$
$8$		0			0
$9$	−1.25529	+	2.72474i	−0.418432	+	0.908248i
$10$		0			0
$11$	0.150860	+	0.563016i	0.0454859	+	0.169756i	0.984932	−	0.172940i	$-0.0553267\pi$
$11$	0.150860	+	0.563016i	0.0454859	+	0.169756i	−0.939446	+	0.342696i	$0.888660\pi$
$12$		0			0
$13$	−1.20856	−	3.39697i	−0.335195	−	0.942149i
$13$	−1.20856	−	3.39697i	−0.335195	−	0.942149i
$14$		0			0
$15$	−1.44957	+	6.61072i	−0.374277	+	1.70688i
$16$		0			0
$17$	0.547000	+	0.947432i	0.132667	+	0.229786i	0.924704	−	0.380687i	$-0.124313\pi$
$17$	0.547000	+	0.947432i	0.132667	+	0.229786i	−0.792037	+	0.610473i	$0.790979\pi$
$18$		0			0
$19$	−1.32717	−	0.355613i	−0.304473	−	0.0815832i	0.103348	−	0.994645i	$-0.467044\pi$
$19$	−1.32717	−	0.355613i	−0.304473	−	0.0815832i	−0.407821	+	0.913062i	$0.633711\pi$
$20$		0			0
$21$	−4.19313	+	1.33273i	−0.915017	+	0.290826i
$22$		0			0
$23$	0.876460	−	1.51807i	0.182755	−	0.316540i	−0.760063	−	0.649849i	$-0.774832\pi$
$23$	0.876460	−	1.51807i	0.182755	−	0.316540i	0.942818	+	0.333309i	$0.108165\pi$
$24$		0			0
$25$			10.2676i			2.05352i
$26$		0			0
$27$	5.14688	−	0.713876i	0.990518	−	0.137386i
$28$		0			0
$29$	5.12973	+	2.96165i	0.952566	+	0.549965i	0.893877	−	0.448312i	$-0.147975\pi$
$29$	5.12973	+	2.96165i	0.952566	+	0.549965i	0.0586892	+	0.998276i	$0.481308\pi$
$30$		0			0
$31$	−6.49983	+	6.49983i	−1.16740	+	1.16740i	−0.184588	+	0.982816i	$0.559095\pi$
$31$	−6.49983	+	6.49983i	−1.16740	+	1.16740i	−0.982816	+	0.184588i	$0.940905\pi$
$32$		0			0
$33$	0.680339	−	0.745907i	0.118432	−	0.129846i
$34$		0			0
$35$	−8.59591	+	4.96285i	−1.45297	+	0.838875i
$36$		0			0
$37$	−2.98942	+	0.801012i	−0.491457	+	0.131686i	−0.496032	−	0.868304i	$-0.665210\pi$
$37$	−2.98942	+	0.801012i	−0.491457	+	0.131686i	0.00457534	+	0.999990i	$0.498544\pi$
$38$		0			0
$39$	−3.82618	+	4.93562i	−0.612679	+	0.790332i
$40$		0			0
$41$	−5.11781	+	1.37131i	−0.799268	+	0.214163i	−0.635262	−	0.772296i	$-0.719108\pi$
$41$	−5.11781	+	1.37131i	−0.799268	+	0.214163i	−0.164005	+	0.986459i	$0.552441\pi$
$42$		0			0
$43$	−3.26299	+	1.88389i	−0.497602	+	0.287290i	−0.727723	−	0.685872i	$-0.759421\pi$
$43$	−3.26299	+	1.88389i	−0.497602	+	0.287290i	0.230121	+	0.973162i	$0.426088\pi$
$44$		0			0
$45$	10.9966	−	4.05999i	1.63927	−	0.605228i
$46$		0			0
$47$	5.51114	−	5.51114i	0.803883	−	0.803883i	−0.179817	−	0.983700i	$-0.557551\pi$
$47$	5.51114	−	5.51114i	0.803883	−	0.803883i	0.983700	+	0.179817i	$0.0575506\pi$
$48$		0			0
$49$	0.473846	+	0.273575i	0.0676922	+	0.0390821i
$50$		0			0
$51$	0.871071	−	1.68278i	0.121974	−	0.235636i
$52$		0			0
$53$		−	3.04435i		−	0.418173i	−0.977897	−	0.209087i	$-0.932951\pi$
$53$		−	3.04435i		−	0.418173i	0.977897	−	0.209087i	$-0.0670490\pi$
$54$		0			0
$55$	1.13876	−	1.97239i	0.153551	−	0.265957i
$56$		0			0
$57$	0.720857	+	2.26801i	0.0954799	+	0.300405i
$58$		0			0
$59$	−8.19009	−	2.19453i	−1.06626	−	0.285703i	−0.317304	−	0.948324i	$-0.602777\pi$
$59$	−8.19009	−	2.19453i	−1.06626	−	0.285703i	−0.748955	+	0.662621i	$0.769444\pi$
$60$		0			0
$61$	−4.67266	−	8.09329i	−0.598273	−	1.03624i	−0.993076	−	0.117474i	$-0.962520\pi$
$61$	−4.67266	−	8.09329i	−0.598273	−	1.03624i	0.394803	−	0.918766i	$-0.370813\pi$
$62$		0			0
$63$	5.86037	+	4.87153i	0.738337	+	0.613755i
$64$		0			0
$65$	−6.04642	+	12.7248i	−0.749966	+	1.57831i
$66$		0			0
$67$	−1.70856	−	6.37644i	−0.208734	−	0.779006i	−0.988279	−	0.152659i	$-0.951216\pi$
$67$	−1.70856	−	6.37644i	−0.208734	−	0.779006i	0.779545	−	0.626346i	$-0.215450\pi$
$68$		0			0
$69$	−3.03294	+	0.139433i	−0.365124	+	0.0167858i
$70$		0			0
$71$	−0.220122	+	0.821505i	−0.0261236	+	0.0974947i	−0.977757	−	0.209742i	$-0.932738\pi$
$71$	−0.220122	+	0.821505i	−0.0261236	+	0.0974947i	0.951633	+	0.307237i	$0.0994043\pi$
$72$		0			0
$73$	−5.18078	−	5.18078i	−0.606365	−	0.606365i	0.335629	−	0.941994i	$-0.391051\pi$
$73$	−5.18078	−	5.18078i	−0.606365	−	0.606365i	−0.941994	+	0.335629i	$0.891051\pi$
$74$		0			0
$75$	14.9768	−	9.58993i	1.72937	−	1.10735i
$76$		0			0
$77$	1.48065			0.168736
$78$		0			0
$79$	13.1089			1.47486			0.737431	−	0.675422i	$-0.236039\pi$
$79$	13.1089			1.47486			0.737431	+	0.675422i	$0.236039\pi$
$80$		0			0
$81$	−5.84847	−	6.84072i	−0.649830	−	0.760080i
$82$		0			0
$83$	5.15394	+	5.15394i	0.565719	+	0.565719i	0.930926	−	0.365208i	$-0.119002\pi$
$83$	5.15394	+	5.15394i	0.565719	+	0.565719i	−0.365208	+	0.930926i	$0.619002\pi$
$84$		0			0
$85$	1.10637	−	4.12902i	0.120002	−	0.447855i
$86$		0			0
$87$	−0.471158	−	10.2486i	−0.0505135	−	1.09877i
$88$		0			0
$89$	−2.50797	−	9.35988i	−0.265844	−	0.992145i	−0.961731	−	0.273994i	$-0.911655\pi$
$89$	−2.50797	−	9.35988i	−0.265844	−	0.992145i	0.695887	−	0.718151i	$-0.255011\pi$
$90$		0			0
$91$	−9.12969	+	0.732051i	−0.957051	+	0.0767398i
$92$		0			0
$93$	15.5518	+	3.41012i	1.61264	+	0.353613i
$94$		0			0
$95$	2.68434	+	4.64941i	0.275407	+	0.477019i
$96$		0			0
$97$	−0.592450	−	0.158747i	−0.0601542	−	0.0161183i	0.228616	−	0.973517i	$-0.426580\pi$
$97$	−0.592450	−	0.158747i	−0.0601542	−	0.0161183i	−0.288771	+	0.957398i	$0.593247\pi$
$98$		0			0
$99$	−1.72345	−	0.295697i	−0.173213	−	0.0297187i
$100$		0			0
$101$	2.91789	−	5.05394i	0.290341	−	0.502886i	−0.683549	−	0.729904i	$-0.739565\pi$
$101$	2.91789	−	5.05394i	0.290341	−	0.502886i	0.973890	+	0.227019i	$0.0728979\pi$
$102$		0			0
$103$		−	2.07313i		−	0.204272i	−0.994770	−	0.102136i	$-0.967432\pi$
$103$		−	2.07313i		−	0.204272i	0.994770	−	0.102136i	$-0.0325677\pi$
$104$		0			0
$105$	15.2676	+	7.90310i	1.48997	+	0.771263i
$106$		0			0
$107$	−2.99520	−	1.72928i	−0.289557	−	0.167176i	0.348185	−	0.937426i	$-0.386798\pi$
$107$	−2.99520	−	1.72928i	−0.289557	−	0.167176i	−0.637742	+	0.770250i	$0.720131\pi$
$108$		0			0
$109$	−10.9901	+	10.9901i	−1.05266	+	1.05266i	−0.0541251	+	0.998534i	$0.517237\pi$
$109$	−10.9901	+	10.9901i	−1.05266	+	1.05266i	−0.998534	+	0.0541251i	$0.982763\pi$
$110$		0			0
$111$	3.96050	+	3.61236i	0.375914	+	0.342870i
$112$		0			0
$113$	−9.43719	+	5.44856i	−0.887776	+	0.512558i	−0.873214	−	0.487336i	$-0.837969\pi$
$113$	−9.43719	+	5.44856i	−0.887776	+	0.512558i	−0.0145614	+	0.999894i	$0.504635\pi$
$114$		0			0
$115$	−6.61594	+	1.77274i	−0.616940	+	0.165308i
$116$		0			0
$117$	10.7730	+	0.971173i	0.995961	+	0.0897850i
$118$		0			0
$119$	2.68434	−	0.719266i	0.246073	−	0.0659350i
$120$		0			0
$121$	9.23205	−	5.33013i	0.839277	−	0.484557i
$122$		0			0
$123$	6.78029	+	6.18427i	0.611358	+	0.557617i
$124$		0			0
$125$	14.5541	−	14.5541i	1.30175	−	1.30175i
$126$		0			0
$127$	−8.06551	−	4.65662i	−0.715698	−	0.413209i	0.0974690	−	0.995239i	$-0.468925\pi$
$127$	−8.06551	−	4.65662i	−0.715698	−	0.413209i	−0.813167	+	0.582030i	$0.802259\pi$
$128$		0			0
$129$	5.79555	+	3.00000i	0.510270	+	0.264135i
$130$		0			0
$131$			0.917828i			0.0801910i	0.999196	+	0.0400955i	$0.0127662\pi$
$131$			0.917828i			0.0801910i	−0.999196	+	0.0400955i	$0.987234\pi$
$132$		0			0
$133$	−1.74513	+	3.02265i	−0.151322	+	0.262097i
$134$		0			0
$135$	−16.1929	−	12.2481i	−1.39366	−	1.05415i
$136$		0			0
$137$	8.32493	+	2.23066i	0.711247	+	0.190578i	0.596263	−	0.802789i	$-0.296652\pi$
$137$	8.32493	+	2.23066i	0.711247	+	0.190578i	0.114984	+	0.993367i	$0.463318\pi$
$138$		0			0
$139$	1.65662	+	2.86936i	0.140513	+	0.243376i	0.927690	−	0.373352i	$-0.121791\pi$
$139$	1.65662	+	2.86936i	0.140513	+	0.243376i	−0.787177	+	0.616727i	$0.788458\pi$
$140$		0			0
$141$	−13.1862	−	2.89141i	−1.11048	−	0.243500i
$142$		0			0
$143$	1.73022	−	1.19291i	0.144689	−	0.0997557i
$144$		0			0
$145$	−5.99026	−	22.3559i	−0.497464	−	1.85656i
$146$		0			0
$147$	−0.0435221	−	0.946692i	−0.00358964	−	0.0780818i
$148$		0			0
$149$	2.03304	−	7.58742i	0.166553	−	0.621585i	−0.831284	−	0.555848i	$-0.812394\pi$
$149$	2.03304	−	7.58742i	0.166553	−	0.621585i	0.997837	−	0.0657369i	$-0.0209398\pi$
$150$		0			0
$151$	−10.2600	−	10.2600i	−0.834946	−	0.834946i	0.153243	−	0.988189i	$-0.451028\pi$
$151$	−10.2600	−	10.2600i	−0.834946	−	0.834946i	−0.988189	+	0.153243i	$0.951028\pi$
$152$		0			0
$153$	−3.26816	+	0.301129i	−0.264215	+	0.0243449i
$154$		0			0
$155$	35.9172			2.88494
$156$		0			0
$157$	−6.71547			−0.535953			−0.267976	−	0.963425i	$-0.586355\pi$
$157$	−6.71547			−0.535953			−0.267976	+	0.963425i	$0.586355\pi$
$158$		0			0
$159$	−4.44062	+	2.84341i	−0.352164	+	0.225497i
$160$		0			0
$161$	−3.14864	−	3.14864i	−0.248148	−	0.248148i
$162$		0			0
$163$	0.407550	−	1.52100i	0.0319217	−	0.119134i	−0.948127	−	0.317893i	$-0.897025\pi$
$163$	0.407550	−	1.52100i	0.0319217	−	0.119134i	0.980048	+	0.198760i	$0.0636913\pi$
$164$		0			0
$165$	−3.94062	+	0.181161i	−0.306777	+	0.0141034i
$166$		0			0
$167$	−6.32673	−	23.6117i	−0.489577	−	1.82713i	−0.558499	−	0.829505i	$-0.688623\pi$
$167$	−6.32673	−	23.6117i	−0.489577	−	1.82713i	0.0689223	−	0.997622i	$-0.478044\pi$
$168$		0			0
$169$	−10.0788	+	8.21088i	−0.775289	+	0.631606i
$170$		0			0
$171$	2.63494	−	3.16979i	0.201499	−	0.242400i
$172$		0			0
$173$	10.3837	+	17.9850i	0.789456	+	1.36738i	0.926301	+	0.376785i	$0.122971\pi$
$173$	10.3837	+	17.9850i	0.789456	+	1.36738i	−0.136845	+	0.990593i	$0.543696\pi$
$174$		0			0
$175$	25.1935	+	6.75058i	1.90445	+	0.510296i
$176$		0			0
$177$	4.44849	+	13.9961i	0.334369	+	1.05201i
$178$		0			0
$179$	−7.00018	+	12.1247i	−0.523218	+	0.906241i	0.476416	+	0.879220i	$0.341935\pi$
$179$	−7.00018	+	12.1247i	−0.523218	+	0.906241i	−0.999635	+	0.0270211i	$0.991398\pi$
$180$		0			0
$181$		−	25.5405i		−	1.89841i	−0.314653	−	0.949207i	$-0.601888\pi$
$181$		−	25.5405i		−	1.89841i	0.314653	−	0.949207i	$-0.398112\pi$
$182$		0			0
$183$	−7.44098	+	14.3749i	−0.550053	+	1.06262i
$184$		0			0
$185$	10.4727	+	6.04642i	0.769968	+	0.444541i
$186$		0			0
$187$	−0.450899	+	0.450899i	−0.0329730	+	0.0329730i
$188$		0			0
$189$	1.63226	−	13.0982i	0.118729	−	0.952753i
$190$		0			0
$191$	−20.4783	+	11.8231i	−1.48176	+	0.855493i	−0.999786	−	0.0206939i	$-0.993412\pi$
$191$	−20.4783	+	11.8231i	−1.48176	+	0.855493i	−0.481972	+	0.876187i	$0.660079\pi$
$192$		0			0
$193$	10.2375	−	2.74313i	0.736912	−	0.197455i	0.129207	−	0.991618i	$-0.458757\pi$
$193$	10.2375	−	2.74313i	0.736912	−	0.197455i	0.607705	+	0.794163i	$0.292090\pi$
$194$		0			0
$195$	24.2083	−	3.06533i	1.73359	−	0.219513i
$196$		0			0
$197$	3.34959	−	0.897520i	0.238649	−	0.0639457i	−0.137512	−	0.990500i	$-0.543911\pi$
$197$	3.34959	−	0.897520i	0.238649	−	0.0639457i	0.376161	+	0.926554i	$0.377244\pi$
$198$		0			0
$199$	2.67432	−	1.54402i	0.189577	−	0.109453i	−0.402207	−	0.915549i	$-0.631757\pi$
$199$	2.67432	−	1.54402i	0.189577	−	0.109453i	0.591785	+	0.806096i	$0.298424\pi$
$200$		0			0
$201$	−7.70517	+	8.44777i	−0.543481	+	0.595860i
$202$		0			0
$203$	10.6396	−	10.6396i	0.746752	−	0.746752i
$204$		0			0
$205$	17.9290	+	10.3513i	1.25222	+	0.722968i
$206$		0			0
$207$	3.03615	+	4.29376i	0.211027	+	0.298437i
$208$		0			0
$209$		−	0.800864i		−	0.0553969i
$210$		0			0
$211$	−2.47900	+	4.29376i	−0.170662	+	0.295595i	−0.938651	−	0.344867i	$-0.887924\pi$
$211$	−2.47900	+	4.29376i	−0.170662	+	0.295595i	0.767990	+	0.640462i	$0.221257\pi$
$212$		0			0
$213$	1.40388	−	0.446205i	0.0961921	−	0.0305734i
$214$		0			0
$215$	14.2205	+	3.81037i	0.969829	+	0.259865i
$216$		0			0
$217$	11.6752	+	20.2220i	0.792561	+	1.37276i
$218$		0			0
$219$	−2.71809	+	12.3958i	−0.183671	+	0.837628i
$220$		0			0
$221$	2.55731	−	3.00317i	0.172023	−	0.202015i
$222$		0			0
$223$	−4.93415	−	18.4145i	−0.330415	−	1.23313i	−0.908755	−	0.417330i	$-0.862966\pi$
$223$	−4.93415	−	18.4145i	−0.330415	−	1.23313i	0.578340	−	0.815796i	$-0.303701\pi$
$224$		0			0
$225$	−27.9766	−	12.8889i	−1.86511	−	0.859258i
$226$		0			0
$227$	1.38733	−	5.17758i	0.0920803	−	0.343648i	−0.904480	−	0.426515i	$-0.859741\pi$
$227$	1.38733	−	5.17758i	0.0920803	−	0.343648i	0.996561	+	0.0828671i	$0.0264077\pi$
$228$		0			0
$229$	2.78436	+	2.78436i	0.183996	+	0.183996i	0.793094	−	0.609099i	$-0.208469\pi$
$229$	2.78436	+	2.78436i	0.183996	+	0.183996i	−0.609099	+	0.793094i	$0.708469\pi$
$230$		0			0
$231$	−1.38293	−	2.15975i	−0.0909899	−	0.142101i
$232$		0			0
$233$	−3.83663			−0.251346			−0.125673	−	0.992072i	$-0.540109\pi$
$233$	−3.83663			−0.251346			−0.125673	+	0.992072i	$0.540109\pi$
$234$		0			0
$235$	−30.4538			−1.98659
$236$		0			0
$237$	−12.2437	−	19.1212i	−0.795311	−	1.24205i
$238$		0			0
$239$	0.751524	+	0.751524i	0.0486121	+	0.0486121i	0.730995	−	0.682383i	$-0.239056\pi$
$239$	0.751524	+	0.751524i	0.0486121	+	0.0486121i	−0.682383	+	0.730995i	$0.739056\pi$
$240$		0			0
$241$	−7.23751	+	27.0107i	−0.466209	+	1.73991i	0.186642	+	0.982428i	$0.440240\pi$
$241$	−7.23751	+	27.0107i	−0.466209	+	1.73991i	−0.652851	+	0.757487i	$0.726427\pi$
$242$		0			0
$243$	−4.51572	+	14.9201i	−0.289684	+	0.957122i
$244$		0			0
$245$	−0.553335	−	2.06507i	−0.0353513	−	0.131933i
$246$		0			0
$247$	0.395956	+	4.93812i	0.0251941	+	0.314205i
$248$		0			0
$249$	2.70400	−	12.3315i	0.171359	−	0.781480i
$250$		0			0
$251$	−7.56320	−	13.0998i	−0.477385	−	0.826855i	0.522279	−	0.852775i	$-0.325082\pi$
$251$	−7.56320	−	13.0998i	−0.477385	−	0.826855i	−0.999664	+	0.0259196i	$0.991749\pi$
$252$		0			0
$253$	0.986923	+	0.264445i	0.0620473	+	0.0166255i
$254$		0			0
$255$	−7.05612	+	2.24270i	−0.441871	+	0.140443i
$256$		0			0
$257$	0.178601	−	0.309345i	0.0111408	−	0.0192964i	−0.860401	−	0.509617i	$-0.829787\pi$
$257$	0.178601	−	0.309345i	0.0111408	−	0.0192964i	0.871542	+	0.490321i	$0.163120\pi$
$258$		0			0
$259$			7.86174i			0.488505i
$260$		0			0
$261$	−14.5091	+	10.2595i	−0.898088	+	0.635044i
$262$		0			0
$263$	1.86002	+	1.07389i	0.114694	+	0.0662186i	0.556250	−	0.831015i	$-0.312240\pi$
$263$	1.86002	+	1.07389i	0.114694	+	0.0662186i	−0.441556	+	0.897234i	$0.645573\pi$
$264$		0			0
$265$	−8.41133	+	8.41133i	−0.516704	+	0.516704i
$266$		0			0
$267$	−11.3103	+	12.4004i	−0.692180	+	0.758889i
$268$		0			0
$269$	−21.2380	+	12.2618i	−1.29490	+	0.747612i	−0.979519	−	0.201352i	$-0.935467\pi$
$269$	−21.2380	+	12.2618i	−1.29490	+	0.747612i	−0.315384	+	0.948964i	$0.602133\pi$
$270$		0			0
$271$	21.1790	−	5.67488i	1.28653	−	0.344725i	0.450189	−	0.892934i	$-0.351357\pi$
$271$	21.1790	−	5.67488i	1.28653	−	0.344725i	0.836341	+	0.548209i	$0.184690\pi$
$272$		0			0
$273$	9.59491	+	12.6332i	0.580710	+	0.764599i
$274$		0			0
$275$	−5.78083	+	1.54897i	−0.348597	+	0.0934063i
$276$		0			0
$277$	−16.1517	+	9.32517i	−0.970460	+	0.560295i	−0.899376	−	0.437175i	$-0.855979\pi$
$277$	−16.1517	+	9.32517i	−0.970460	+	0.560295i	−0.0710833	+	0.997470i	$0.522646\pi$
$278$		0			0
$279$	−9.55117	−	25.8696i	−0.571814	−	1.54877i
$280$		0			0
$281$	11.2782	−	11.2782i	0.672801	−	0.672801i	−0.285560	−	0.958361i	$-0.592180\pi$
$281$	11.2782	−	11.2782i	0.672801	−	0.672801i	0.958361	+	0.285560i	$0.0921797\pi$
$282$		0			0
$283$	−4.08342	−	2.35756i	−0.242734	−	0.140143i	0.373699	−	0.927550i	$-0.378089\pi$
$283$	−4.08342	−	2.35756i	−0.242734	−	0.140143i	−0.616433	+	0.787408i	$0.711423\pi$
$284$		0			0
$285$	4.27467	−	8.25803i	0.253210	−	0.489164i
$286$		0			0
$287$			13.4591i			0.794466i
$288$		0			0
$289$	7.90158	−	13.6859i	0.464799	−	0.805055i
$290$		0			0
$291$	0.321793	+	1.01244i	0.0188638	+	0.0593505i
$292$		0			0
$293$	−20.6276	−	5.52716i	−1.20508	−	0.322900i	−0.400250	−	0.916406i	$-0.631077\pi$
$293$	−20.6276	−	5.52716i	−1.20508	−	0.322900i	−0.804830	+	0.593506i	$0.797743\pi$
$294$		0			0
$295$	16.5653	+	28.6920i	0.964471	+	1.67051i
$296$		0			0
$297$	1.17838	+	2.79008i	0.0683766	+	0.161897i
$298$		0			0
$299$	−6.21610	−	1.14262i	−0.359486	−	0.0660795i
$300$		0			0
$301$	2.47718	+	9.24496i	0.142782	+	0.532870i
$302$		0			0
$303$	−10.0972	+	0.464197i	−0.580070	+	0.0266674i
$304$		0			0
$305$	−9.45097	+	35.2715i	−0.541161	+	2.01964i
$306$		0			0
$307$	16.2259	+	16.2259i	0.926063	+	0.926063i	0.997449	−	0.0713857i	$-0.0227421\pi$
$307$	16.2259	+	16.2259i	0.926063	+	0.926063i	−0.0713857	+	0.997449i	$0.522742\pi$
$308$		0			0
$309$	−3.02397	+	1.93630i	−0.172027	+	0.110152i
$310$		0			0
$311$	−32.8464			−1.86255			−0.931275	−	0.364317i	$-0.881303\pi$
$311$	−32.8464			−1.86255			−0.931275	+	0.364317i	$0.881303\pi$
$312$		0			0
$313$	11.0629			0.625311			0.312655	−	0.949867i	$-0.398782\pi$
$313$	11.0629			0.625311			0.312655	+	0.949867i	$0.398782\pi$
$314$		0			0
$315$	−2.73210	−	29.6515i	−0.153936	−	1.67067i
$316$		0			0
$317$	−17.5500	−	17.5500i	−0.985704	−	0.985704i	0.0141948	−	0.999899i	$-0.495481\pi$
$317$	−17.5500	−	17.5500i	−0.985704	−	0.985704i	−0.999899	+	0.0141948i	$0.995481\pi$
$318$		0			0
$319$	−0.893587	+	3.33491i	−0.0500313	+	0.186719i
$320$		0			0
$321$	0.275105	+	5.98408i	0.0153549	+	0.333999i
$322$		0			0
$323$	−0.389041	−	1.45192i	−0.0216468	−	0.0807870i
$324$		0			0
$325$	34.8787	−	12.4090i	1.93472	−	0.688329i
$326$		0			0
$327$	26.2954	+	5.76592i	1.45414	+	0.318856i
$328$		0			0
$329$	−9.89925	−	17.1460i	−0.545763	−	0.945290i
$330$		0			0
$331$	−4.46639	−	1.19677i	−0.245495	−	0.0657803i	0.133973	−	0.990985i	$-0.457226\pi$
$331$	−4.46639	−	1.19677i	−0.245495	−	0.0657803i	−0.379468	+	0.925205i	$0.623893\pi$
$332$		0			0
$333$	1.57005	−	9.15090i	0.0860380	−	0.501466i
$334$		0			0
$335$	−12.8970	+	22.3383i	−0.704640	+	1.22047i
$336$		0			0
$337$		−	7.78436i		−	0.424041i	−0.977265	−	0.212021i	$-0.931996\pi$
$337$		−	7.78436i		−	0.424041i	0.977265	−	0.212021i	$-0.0680044\pi$
$338$		0			0
$339$	16.7618	+	8.67656i	0.910378	+	0.471246i
$340$		0			0
$341$	−4.64007	−	2.67895i	−0.251274	−	0.145073i
$342$		0			0
$343$	13.5564	−	13.5564i	0.731976	−	0.731976i
$344$		0			0
$345$	8.76507	+	7.99458i	0.471895	+	0.430414i
$346$		0			0
$347$	−9.39077	+	5.42177i	−0.504123	+	0.291056i	−0.730415	−	0.683004i	$-0.760673\pi$
$347$	−9.39077	+	5.42177i	−0.504123	+	0.291056i	0.226292	+	0.974060i	$0.427340\pi$
$348$		0			0
$349$	14.8487	−	3.97869i	0.794830	−	0.212974i	0.161517	−	0.986870i	$-0.448361\pi$
$349$	14.8487	−	3.97869i	0.794830	−	0.212974i	0.633313	+	0.773896i	$0.281695\pi$
$350$		0			0
$351$	−8.64533	−	16.6210i	−0.461454	−	0.887164i
$352$		0			0
$353$	−1.80378	+	0.483321i	−0.0960054	+	0.0257246i	−0.306502	−	0.951870i	$-0.599159\pi$
$353$	−1.80378	+	0.483321i	−0.0960054	+	0.0257246i	0.210497	+	0.977595i	$0.432492\pi$
$354$		0			0
$355$	2.87795	−	1.66158i	0.152745	−	0.0881876i
$356$		0			0
$357$	−3.55632	−	3.24370i	−0.188220	−	0.171675i
$358$		0			0
$359$	12.1336	−	12.1336i	0.640387	−	0.640387i	−0.310264	−	0.950650i	$-0.600417\pi$
$359$	12.1336	−	12.1336i	0.640387	−	0.640387i	0.950650	+	0.310264i	$0.100417\pi$
$360$		0			0
$361$	−14.8196	−	8.55608i	−0.779978	−	0.450320i
$362$		0			0
$363$	−16.3975	−	8.48796i	−0.860645	−	0.445503i
$364$		0			0
$365$			28.6283i			1.49847i
$366$		0			0
$367$	−4.53141	+	7.84863i	−0.236538	+	0.409695i	−0.959718	−	0.280964i	$-0.909346\pi$
$367$	−4.53141	+	7.84863i	−0.236538	+	0.409695i	0.723181	+	0.690659i	$0.242679\pi$
$368$		0			0
$369$	2.68788	−	15.6661i	0.139926	−	0.815546i
$370$		0			0
$371$	−7.46988	−	2.00155i	−0.387817	−	0.103915i
$372$		0			0
$373$	3.78793	+	6.56090i	0.196132	+	0.339710i	0.947271	−	0.320434i	$-0.103829\pi$
$373$	3.78793	+	6.56090i	0.196132	+	0.339710i	−0.751139	+	0.660144i	$0.770495\pi$
$374$		0			0
$375$	−34.8227	−	7.63575i	−1.79823	−	0.394308i
$376$		0			0
$377$	3.86103	−	21.0048i	0.198853	−	1.08180i
$378$		0			0
$379$	−3.12578	−	11.6656i	−0.160561	−	0.599221i	−0.998565	−	0.0535568i	$-0.982944\pi$
$379$	−3.12578	−	11.6656i	−0.160561	−	0.599221i	0.838004	−	0.545664i	$-0.183722\pi$
$380$		0			0
$381$	0.740806	+	16.1140i	0.0379526	+	0.825545i
$382$		0			0
$383$	−9.53291	+	35.5773i	−0.487109	+	1.81792i	0.0832617	+	0.996528i	$0.473466\pi$
$383$	−9.53291	+	35.5773i	−0.487109	+	1.81792i	−0.570371	+	0.821387i	$0.693200\pi$
$384$		0			0
$385$	−4.09094	−	4.09094i	−0.208494	−	0.208494i
$386$		0			0
$387$	−1.03710	−	11.2557i	−0.0527188	−	0.572157i
$388$		0			0
$389$	14.1012			0.714961			0.357481	−	0.933921i	$-0.383636\pi$
$389$	14.1012			0.714961			0.357481	+	0.933921i	$0.383636\pi$
$390$		0			0
$391$	1.91770			0.0969820
$392$		0			0
$393$	1.33879	−	0.857250i	0.0675328	−	0.0432425i
$394$		0			0
$395$	−36.2189	−	36.2189i	−1.82237	−	1.82237i
$396$		0			0
$397$	−2.03222	+	7.58436i	−0.101994	+	0.380648i	−0.997987	−	0.0634210i	$-0.979799\pi$
$397$	−2.03222	+	7.58436i	−0.101994	+	0.380648i	0.895992	+	0.444069i	$0.146466\pi$
$398$		0			0
$399$	6.03892	−	0.277626i	0.302324	−	0.0138987i
$400$		0			0
$401$	−5.65677	−	21.1113i	−0.282485	−	1.05425i	−0.950657	−	0.310243i	$-0.899590\pi$
$401$	−5.65677	−	21.1113i	−0.282485	−	1.05425i	0.668172	−	0.744007i	$-0.267077\pi$
$402$		0			0
$403$	29.9351	+	14.2243i	1.49118	+	0.708561i
$404$		0			0
$405$	−2.74151	+	35.0594i	−0.136227	+	1.74211i
$406$		0			0
$407$	−0.901965	−	1.56225i	−0.0447088	−	0.0774378i
$408$		0			0
$409$	2.16512	+	0.580141i	0.107058	+	0.0286861i	0.311950	−	0.950098i	$-0.399018\pi$
$409$	2.16512	+	0.580141i	0.107058	+	0.0286861i	−0.204892	+	0.978785i	$0.565684\pi$
$410$		0			0
$411$	−4.52173	−	14.2266i	−0.223041	−	0.701744i
$412$		0			0
$413$	−10.7694	+	18.6531i	−0.529926	+	0.917860i
$414$		0			0
$415$		−	28.4800i		−	1.39803i
$416$		0			0
$417$	2.63809	−	5.09640i	0.129188	−	0.249572i
$418$		0			0
$419$	28.9126	+	16.6927i	1.41247	+	0.815491i	0.995621	−	0.0934844i	$-0.0298005\pi$
$419$	28.9126	+	16.6927i	1.41247	+	0.815491i	0.416851	+	0.908975i	$0.363134\pi$
$420$		0			0
$421$	2.25285	−	2.25285i	0.109797	−	0.109797i	−0.650074	−	0.759871i	$-0.725262\pi$
$421$	2.25285	−	2.25285i	0.109797	−	0.109797i	0.759871	+	0.650074i	$0.225262\pi$
$422$		0			0
$423$	8.09835	+	21.9346i	0.393755	+	1.06650i
$424$		0			0
$425$	−9.72786	+	5.61638i	−0.471870	+	0.272435i
$426$		0			0
$427$	−22.9305	+	6.14422i	−1.10969	+	0.297339i
$428$		0			0
$429$	−3.35605	−	1.40961i	−0.162032	−	0.0680567i
$430$		0			0
$431$	20.9452	−	5.61224i	1.00889	−	0.270332i	0.283727	−	0.958905i	$-0.408429\pi$
$431$	20.9452	−	5.61224i	1.00889	−	0.270332i	0.725167	+	0.688573i	$0.241762\pi$
$432$		0			0
$433$	26.0258	−	15.0260i	1.25072	−	0.722103i	0.279466	−	0.960155i	$-0.409842\pi$
$433$	26.0258	−	15.0260i	1.25072	−	0.722103i	0.971252	+	0.238053i	$0.0765091\pi$
$434$		0			0
$435$	−27.0145	+	29.6181i	−1.29525	+	1.42008i
$436$		0			0
$437$	−1.70306	+	1.70306i	−0.0814682	+	0.0814682i
$438$		0			0
$439$	18.0531	+	10.4229i	0.861626	+	0.497460i	0.864557	−	0.502535i	$-0.167599\pi$
$439$	18.0531	+	10.4229i	0.861626	+	0.497460i	−0.00293019	+	0.999996i	$0.500933\pi$
$440$		0			0
$441$	−1.34024	+	0.947691i	−0.0638209	+	0.0451282i
$442$		0			0
$443$			13.0363i			0.619374i	0.950839	+	0.309687i	$0.100224\pi$
$443$			13.0363i			0.619374i	−0.950839	+	0.309687i	$0.899776\pi$
$444$		0			0
$445$	−18.9314	+	32.7901i	−0.897433	+	1.55440i
$446$		0			0
$447$	−12.9662	+	4.12114i	−0.613281	+	0.194923i
$448$		0			0
$449$	18.3916	+	4.92801i	0.867953	+	0.232567i	0.665202	−	0.746663i	$-0.268345\pi$
$449$	18.3916	+	4.92801i	0.867953	+	0.232567i	0.202750	+	0.979230i	$0.435012\pi$
$450$		0			0
$451$	−1.54414	−	2.67453i	−0.0727109	−	0.125939i
$452$		0			0
$453$	−5.38288	+	24.5485i	−0.252910	+	1.15339i
$454$		0			0
$455$	27.2473	+	23.2021i	1.27737	+	1.08773i
$456$		0			0
$457$	−5.50257	−	20.5359i	−0.257399	−	0.960627i	−0.966740	−	0.255761i	$-0.917674\pi$
$457$	−5.50257	−	20.5359i	−0.257399	−	0.960627i	0.709341	−	0.704866i	$-0.248993\pi$
$458$		0			0
$459$	3.49169	+	4.48583i	0.162978	+	0.209381i
$460$		0			0
$461$	−0.395195	+	1.47489i	−0.0184061	+	0.0686924i	−0.974518	−	0.224309i	$-0.927987\pi$
$461$	−0.395195	+	1.47489i	−0.0184061	+	0.0686924i	0.956112	+	0.293002i	$0.0946541\pi$
$462$		0			0
$463$	21.3272	+	21.3272i	0.991159	+	0.991159i	0.999961	−	0.00880240i	$-0.00280193\pi$
$463$	21.3272	+	21.3272i	0.991159	+	0.991159i	−0.00880240	+	0.999961i	$0.502802\pi$
$464$		0			0
$465$	−33.5466	−	52.3905i	−1.55569	−	2.42955i
$466$		0			0
$467$	11.2935			0.522601			0.261300	−	0.965258i	$-0.415849\pi$
$467$	11.2935			0.522601			0.261300	+	0.965258i	$0.415849\pi$
$468$		0			0
$469$	−16.7691			−0.774326
$470$		0			0
$471$	6.27224	+	9.79549i	0.289009	+	0.451352i
$472$		0			0
$473$	−1.55291	−	1.55291i	−0.0714031	−	0.0714031i
$474$		0			0
$475$	3.65130	−	13.6268i	0.167533	−	0.625241i
$476$		0			0
$477$	8.29507	+	3.82155i	0.379805	+	0.174977i
$478$		0			0
$479$	−7.52517	−	28.0843i	−0.343834	−	1.28320i	−0.893969	−	0.448129i	$-0.852090\pi$
$479$	−7.52517	−	28.0843i	−0.343834	−	1.28320i	0.550135	−	0.835076i	$-0.314576\pi$
$480$		0			0
$481$	6.33390	+	9.18688i	0.288801	+	0.418885i
$482$		0			0
$483$	−1.65193	+	7.53358i	−0.0751653	+	0.342790i
$484$		0			0
$485$	1.19829	+	2.07551i	0.0544118	+	0.0942440i
$486$		0			0
$487$	−2.44743	−	0.655786i	−0.110903	−	0.0297165i	0.202940	−	0.979191i	$-0.434950\pi$
$487$	−2.44743	−	0.655786i	−0.110903	−	0.0297165i	−0.313844	+	0.949475i	$0.601617\pi$
$488$		0			0
$489$	−2.59924	+	0.826137i	−0.117542	+	0.0373592i
$490$		0			0
$491$	18.4575	−	31.9694i	0.832978	−	1.44276i	−0.0626890	−	0.998033i	$-0.519968\pi$
$491$	18.4575	−	31.9694i	0.832978	−	1.44276i	0.895667	−	0.444726i	$-0.146699\pi$
$492$		0			0
$493$			6.48009i			0.291849i
$494$		0			0
$495$	3.94478	+	5.57877i	0.177305	+	0.250747i
$496$		0			0
$497$	1.87100	+	1.08022i	0.0839256	+	0.0484545i
$498$		0			0
$499$	−22.3461	+	22.3461i	−1.00035	+	1.00035i	−0.000347536		1.00000i	$0.500111\pi$
$499$	−22.3461	+	22.3461i	−1.00035	+	1.00035i	−1.00000		0.000347536i	$0.999889\pi$
$500$		0			0
$501$	−28.5319	+	31.2817i	−1.27471	+	1.39756i
$502$		0			0
$503$	20.2177	−	11.6727i	0.901464	−	0.520460i	0.0237889	−	0.999717i	$-0.492427\pi$
$503$	20.2177	−	11.6727i	0.901464	−	0.520460i	0.877675	+	0.479257i	$0.159094\pi$
$504$		0			0
$505$	−22.0256	+	5.90175i	−0.980128	+	0.262625i
$506$		0			0
$507$	21.3903	+	7.03239i	0.949977	+	0.312319i
$508$		0			0
$509$	18.0113	−	4.82612i	0.798338	−	0.213914i	0.163484	−	0.986546i	$-0.447727\pi$
$509$	18.0113	−	4.82612i	0.798338	−	0.213914i	0.634854	+	0.772632i	$0.281060\pi$
$510$		0			0
$511$	−16.1182	+	9.30585i	−0.713028	+	0.411667i
$512$		0			0
$513$	−7.08463	−	0.882866i	−0.312794	−	0.0389795i
$514$		0			0
$515$	−5.72793	+	5.72793i	−0.252403	+	0.252403i
$516$		0			0
$517$	3.93427	+	2.27145i	0.173029	+	0.0998984i
$518$		0			0
$519$	16.5355	−	31.9441i	0.725827	−	1.40219i
$520$		0			0
$521$			20.1922i			0.884637i	0.896858	+	0.442318i	$0.145844\pi$
$521$			20.1922i			0.884637i	−0.896858	+	0.442318i	$0.854156\pi$
$522$		0			0
$523$	14.1118	−	24.4424i	0.617066	−	1.06879i	−0.372952	−	0.927850i	$-0.621655\pi$
$523$	14.1118	−	24.4424i	0.617066	−	1.06879i	0.990018	−	0.140939i	$-0.0450121\pi$
$524$		0			0
$525$	−13.6840	−	43.0534i	−0.597218	−	1.87901i
$526$		0			0
$527$	−9.71355	−	2.60274i	−0.423129	−	0.113377i
$528$		0			0
$529$	9.96363	+	17.2575i	0.433201	+	0.750327i
$530$		0			0
$531$	16.2605	−	19.5611i	0.705646	−	0.848880i
$532$		0			0
$533$	10.8435	+	15.7277i	0.469684	+	0.681243i
$534$		0			0
$535$	3.49765	+	13.0534i	0.151217	+	0.564349i
$536$		0			0
$537$	24.2238	−	1.11363i	1.04533	−	0.0480569i
$538$		0			0
$539$	−0.0825429	+	0.308054i	−0.00355537	+	0.0132688i
$540$		0			0
$541$	−13.2334	−	13.2334i	−0.568947	−	0.568947i	0.362887	−	0.931833i	$-0.381791\pi$
$541$	−13.2334	−	13.2334i	−0.568947	−	0.568947i	−0.931833	+	0.362887i	$0.881791\pi$
$542$		0			0
$543$	−37.2546	+	23.8548i	−1.59875	+	1.02371i
$544$		0			0
$545$	60.7298			2.60138
$546$		0			0
$547$	14.7212			0.629433			0.314717	−	0.949186i	$-0.398091\pi$
$547$	14.7212			0.629433			0.314717	+	0.949186i	$0.398091\pi$
$548$		0			0
$549$	27.9177	−	2.57235i	1.19150	−	0.109785i
$550$		0			0
$551$	−5.75480	−	5.75480i	−0.245163	−	0.245163i
$552$		0			0
$553$	8.61860	−	32.1651i	0.366500	−	1.36780i
$554$		0			0
$555$	−0.961903	−	20.9233i	−0.0408305	−	0.888145i
$556$		0			0
$557$	3.19111	+	11.9094i	0.135212	+	0.504616i	0.999997	+	0.00247467i	$0.000787714\pi$
$557$	3.19111	+	11.9094i	0.135212	+	0.504616i	−0.864785	+	0.502142i	$0.832546\pi$
$558$		0			0
$559$	10.3430	+	8.80748i	0.437464	+	0.372517i
$560$		0			0
$561$	1.07884	+	0.236563i	0.0455487	+	0.00998771i
$562$		0			0
$563$	9.86628	+	17.0889i	0.415814	+	0.720211i	0.995514	−	0.0946194i	$-0.0301634\pi$
$563$	9.86628	+	17.0889i	0.415814	+	0.720211i	−0.579700	+	0.814830i	$0.696830\pi$
$564$		0			0
$565$	41.1283	+	11.0203i	1.73028	+	0.463628i
$566$		0			0
$567$	−20.6302	+	9.85280i	−0.866385	+	0.413779i
$568$		0			0
$569$	17.4503	−	30.2248i	0.731555	−	1.26709i	−0.224663	−	0.974436i	$-0.572128\pi$
$569$	17.4503	−	30.2248i	0.731555	−	1.26709i	0.956218	−	0.292654i	$-0.0945384\pi$
$570$		0			0
$571$			2.37582i			0.0994248i	0.998764	+	0.0497124i	$0.0158305\pi$
$571$			2.37582i			0.0994248i	−0.998764	+	0.0497124i	$0.984170\pi$
$572$		0			0
$573$	36.3725	+	18.8278i	1.51948	+	0.786542i
$574$		0			0
$575$	15.5870	+	8.99915i	0.650022	+	0.375291i
$576$		0			0
$577$	3.78848	−	3.78848i	0.157716	−	0.157716i	−0.623838	−	0.781554i	$-0.714427\pi$
$577$	3.78848	−	3.78848i	0.157716	−	0.157716i	0.781554	+	0.623838i	$0.214427\pi$
$578$		0			0
$579$	−13.5631	−	12.3708i	−0.563662	−	0.514114i
$580$		0			0
$581$	16.0347	−	9.25764i	0.665232	−	0.384072i
$582$		0			0
$583$	1.71402	−	0.459269i	0.0709873	−	0.0190210i
$584$		0			0
$585$	−27.0817	−	32.4483i	−1.11969	−	1.34157i
$586$		0			0
$587$	9.81579	−	2.63013i	0.405141	−	0.108557i	−0.0504929	−	0.998724i	$-0.516079\pi$
$587$	9.81579	−	2.63013i	0.405141	−	0.108557i	0.455634	+	0.890167i	$0.349413\pi$
$588$		0			0
$589$	10.9378	−	6.31493i	0.450683	−	0.260202i
$590$		0			0
$591$	−4.43768	−	4.04759i	−0.182542	−	0.166495i
$592$		0			0
$593$	9.76893	−	9.76893i	0.401162	−	0.401162i	−0.477481	−	0.878642i	$-0.658450\pi$
$593$	9.76893	−	9.76893i	0.401162	−	0.401162i	0.878642	+	0.477481i	$0.158450\pi$
$594$		0			0
$595$	−9.40393	−	5.42936i	−0.385523	−	0.222582i
$596$		0			0
$597$	−4.74998	−	2.45877i	−0.194404	−	0.100631i
$598$		0			0
$599$		−	35.2538i		−	1.44043i	−0.693750	−	0.720216i	$-0.744043\pi$
$599$		−	35.2538i		−	1.44043i	0.693750	−	0.720216i	$-0.255957\pi$
$600$		0			0
$601$	−4.57192	+	7.91880i	−0.186493	+	0.323015i	−0.944078	−	0.329721i	$-0.893045\pi$
$601$	−4.57192	+	7.91880i	−0.186493	+	0.323015i	0.757586	+	0.652736i	$0.226379\pi$
$602$		0			0
$603$	19.5189	+	3.34892i	0.794872	+	0.136378i
$604$		0			0
$605$	−40.2343	−	10.7808i	−1.63576	−	0.438300i
$606$		0			0
$607$	−9.96393	−	17.2580i	−0.404423	−	0.700482i	0.589831	−	0.807527i	$-0.299194\pi$
$607$	−9.96393	−	17.2580i	−0.404423	−	0.700482i	−0.994254	+	0.107045i	$0.965861\pi$
$608$		0			0
$609$	−25.4567	−	5.58203i	−1.03156	−	0.226195i
$610$		0			0
$611$	−25.3817	−	12.0606i	−1.02683	−	0.487920i
$612$		0			0
$613$	−3.88890	−	14.5136i	−0.157071	−	0.586198i	−0.998919	−	0.0464829i	$-0.985199\pi$
$613$	−3.88890	−	14.5136i	−0.157071	−	0.586198i	0.841848	−	0.539715i	$-0.181468\pi$
$614$		0			0
$615$	−1.64676	−	35.8202i	−0.0664036	−	1.44441i
$616$		0			0
$617$	2.63629	−	9.83876i	0.106133	−	0.396094i	−0.892338	−	0.451367i	$-0.850936\pi$
$617$	2.63629	−	9.83876i	0.106133	−	0.396094i	0.998471	+	0.0552736i	$0.0176031\pi$
$618$		0			0
$619$	−18.1131	−	18.1131i	−0.728027	−	0.728027i	0.242199	−	0.970226i	$-0.422131\pi$
$619$	−18.1131	−	18.1131i	−0.728027	−	0.728027i	−0.970226	+	0.242199i	$0.922131\pi$
$620$		0			0
$621$	3.42732	−	8.43903i	0.137534	−	0.338647i
$622$		0			0
$623$	−24.6151			−0.986185
$624$		0			0
$625$	−29.0857			−1.16343
$626$		0			0
$627$	−1.16818	+	0.748005i	−0.0466525	+	0.0298725i
$628$		0			0
$629$	−2.39412	−	2.39412i	−0.0954596	−	0.0954596i
$630$		0			0
$631$	5.19785	−	19.3987i	0.206923	−	0.772248i	−0.781931	−	0.623364i	$-0.785765\pi$
$631$	5.19785	−	19.3987i	0.206923	−	0.772248i	0.988855	−	0.148884i	$-0.0475680\pi$
$632$		0			0
$633$	8.57846	−	0.394376i	0.340963	−	0.0156750i
$634$		0			0
$635$	9.41853	+	35.1504i	0.373763	+	1.39490i
$636$		0			0
$637$	0.356653	−	1.94027i	0.0141311	−	0.0768763i
$638$		0			0
$639$	−1.96207	−	1.63101i	−0.0776184	−	0.0645216i
$640$		0			0
$641$	−22.3417	−	38.6969i	−0.882443	−	1.52844i	−0.848617	−	0.529008i	$-0.822564\pi$
$641$	−22.3417	−	38.6969i	−0.882443	−	1.52844i	−0.0338257	−	0.999428i	$-0.510769\pi$
$642$		0			0
$643$	−8.68244	−	2.32645i	−0.342402	−	0.0917463i	0.0835204	−	0.996506i	$-0.473384\pi$
$643$	−8.68244	−	2.32645i	−0.342402	−	0.0917463i	−0.425922	+	0.904760i	$0.640050\pi$
$644$		0			0
$645$	−7.72393	−	24.3015i	−0.304130	−	0.956872i
$646$		0			0
$647$	18.9869	−	32.8862i	0.746451	−	1.29289i	−0.203063	−	0.979166i	$-0.565090\pi$
$647$	18.9869	−	32.8862i	0.746451	−	1.29289i	0.949514	−	0.313725i	$-0.101577\pi$
$648$		0			0
$649$		−	4.94222i		−	0.193999i
$650$		0			0
$651$	18.5921	−	35.9172i	0.728682	−	1.40771i
$652$		0			0
$653$	16.0116	+	9.24428i	0.626581	+	0.361757i	0.779427	−	0.626493i	$-0.215510\pi$
$653$	16.0116	+	9.24428i	0.626581	+	0.361757i	−0.152846	+	0.988250i	$0.548844\pi$
$654$		0			0
$655$	2.53590	−	2.53590i	0.0990857	−	0.0990857i
$656$		0			0
$657$	20.6197	−	7.61290i	0.804452	−	0.297008i
$658$		0			0
$659$	−0.644195	+	0.371926i	−0.0250943	+	0.0144882i	−0.512495	−	0.858690i	$-0.671279\pi$
$659$	−0.644195	+	0.371926i	−0.0250943	+	0.0144882i	0.487400	+	0.873179i	$0.337945\pi$
$660$		0			0
$661$	27.0849	−	7.25737i	1.05348	−	0.282279i	0.309790	−	0.950805i	$-0.399741\pi$
$661$	27.0849	−	7.25737i	1.05348	−	0.282279i	0.743689	+	0.668526i	$0.233075\pi$
$662$		0			0
$663$	−6.76909	−	0.925255i	−0.262890	−	0.0359339i
$664$		0			0
$665$	13.1731	−	3.52971i	0.510829	−	0.136876i
$666$		0			0
$667$	8.99201	−	5.19154i	0.348172	−	0.201017i
$668$		0			0
$669$	−22.2517	+	24.3963i	−0.860302	+	0.943214i
$670$		0			0
$671$	3.85174	−	3.85174i	0.148695	−	0.148695i
$672$		0			0
$673$	23.9347	+	13.8187i	0.922615	+	0.532672i	0.884468	−	0.466600i	$-0.154521\pi$
$673$	23.9347	+	13.8187i	0.922615	+	0.532672i	0.0381465	+	0.999272i	$0.487855\pi$
$674$		0			0
$675$	7.32980	+	52.8461i	0.282124	+	2.03405i
$676$		0			0
$677$		−	34.0927i		−	1.31029i	−0.755504	−	0.655145i	$-0.772608\pi$
$677$		−	34.0927i		−	1.31029i	0.755504	−	0.655145i	$-0.227392\pi$
$678$		0			0
$679$	−0.779030	+	1.34932i	−0.0298964	+	0.0517821i
$680$		0			0
$681$	−8.84802	+	2.81223i	−0.339057	+	0.107765i
$682$		0			0
$683$	22.5100	+	6.03154i	0.861322	+	0.230790i	0.662331	−	0.749211i	$-0.269567\pi$
$683$	22.5100	+	6.03154i	0.861322	+	0.230790i	0.198990	+	0.980001i	$0.436234\pi$
$684$		0			0
$685$	−16.8381	−	29.1644i	−0.643350	−	1.11431i
$686$		0			0
$687$	1.46081	−	6.66198i	0.0557333	−	0.254170i
$688$		0			0
$689$	−10.3415	+	3.67928i	−0.393981	+	0.140169i
$690$		0			0
$691$	−2.64500	−	9.87128i	−0.100621	−	0.375521i	0.897191	−	0.441643i	$-0.145604\pi$
$691$	−2.64500	−	9.87128i	−0.100621	−	0.375521i	−0.997812	+	0.0661216i	$0.978937\pi$
$692$		0			0
$693$	−1.85865	+	4.03440i	−0.0706045	+	0.153254i
$694$		0			0
$695$	3.35070	−	12.5050i	0.127099	−	0.474341i
$696$		0			0
$697$	−4.09867	−	4.09867i	−0.155248	−	0.155248i
$698$		0			0
$699$	3.58340	+	5.59628i	0.135537	+	0.211671i
$700$		0			0
$701$	−31.9420			−1.20643			−0.603217	−	0.797577i	$-0.706115\pi$
$701$	−31.9420			−1.20643			−0.603217	+	0.797577i	$0.706115\pi$
$702$		0			0
$703$	4.25230			0.160379
$704$		0			0
$705$	28.4438	+	44.4214i	1.07126	+	1.67301i
$706$		0			0
$707$	−10.4824	−	10.4824i	−0.394231	−	0.394231i
$708$		0			0
$709$	1.92196	−	7.17283i	0.0721805	−	0.269381i	−0.920399	−	0.390981i	$-0.872136\pi$
$709$	1.92196	−	7.17283i	0.0721805	−	0.269381i	0.992579	+	0.121600i	$0.0388024\pi$
$710$		0			0
$711$	−16.4555	+	35.7183i	−0.617129	+	1.33954i
$712$		0			0
$713$	4.17038	+	15.5641i	0.156182	+	0.582879i
$714$		0			0
$715$	−8.07641	−	1.48458i	−0.302041	−	0.0555200i
$716$		0			0
$717$	0.394286	−	1.79813i	0.0147249	−	0.0671524i
$718$		0			0
$719$	14.4593	+	25.0442i	0.539240	+	0.933992i	0.998945	+	0.0459198i	$0.0146219\pi$
$719$	14.4593	+	25.0442i	0.539240	+	0.933992i	−0.459705	+	0.888072i	$0.652045\pi$
$720$		0			0
$721$	−5.08682	−	1.36301i	−0.189443	−	0.0507612i
$722$		0			0
$723$	46.1589	−	14.6710i	1.71667	−	0.545621i
$724$		0			0
$725$	−30.4091	+	52.6700i	−1.12936	+	1.95612i
$726$		0			0
$727$			13.5518i			0.502608i	0.967908	+	0.251304i	$0.0808594\pi$
$727$			13.5518i			0.502608i	−0.967908	+	0.251304i	$0.919141\pi$
$728$		0			0
$729$	25.9808	−	7.34847i	0.962250	−	0.272166i
$730$		0			0
$731$	−3.56971	−	2.06098i	−0.132031	−	0.0762279i
$732$		0			0
$733$	−13.9665	+	13.9665i	−0.515864	+	0.515864i	−0.916317	−	0.400453i	$-0.868853\pi$
$733$	−13.9665	+	13.9665i	−0.515864	+	0.515864i	0.400453	+	0.916317i	$0.368853\pi$
$734$		0			0
$735$	−2.49540	+	2.73589i	−0.0920441	+	0.100915i
$736$		0			0
$737$	3.33228	−	1.92390i	0.122746	−	0.0708676i
$738$		0			0
$739$	1.90239	−	0.509744i	0.0699806	−	0.0187512i	−0.223659	−	0.974667i	$-0.571800\pi$
$739$	1.90239	−	0.509744i	0.0699806	−	0.0187512i	0.293639	+	0.955916i	$0.405133\pi$
$740$		0			0
$741$	6.83314	−	5.18975i	0.251022	−	0.190650i
$742$		0			0
$743$	5.78030	−	1.54883i	0.212059	−	0.0568210i	−0.151226	−	0.988499i	$-0.548322\pi$
$743$	5.78030	−	1.54883i	0.212059	−	0.0568210i	0.363284	+	0.931678i	$0.381655\pi$
$744$		0			0
$745$	−26.5807	+	15.3464i	−0.973841	+	0.562247i
$746$		0			0
$747$	−20.5129	+	7.57346i	−0.750527	+	0.277098i
$748$		0			0
$749$	−6.21235	+	6.21235i	−0.226994	+	0.226994i
$750$		0			0
$751$	15.1590	+	8.75204i	0.553159	+	0.319366i	0.750395	−	0.660990i	$-0.229863\pi$
$751$	15.1590	+	8.75204i	0.553159	+	0.319366i	−0.197236	+	0.980356i	$0.563197\pi$
$752$		0			0
$753$	−12.0440	+	23.2673i	−0.438909	+	0.847906i
$754$		0			0
$755$			56.6953i			2.06335i
$756$		0			0
$757$	−4.00168	+	6.93111i	−0.145443	+	0.251915i	−0.929538	−	0.368726i	$-0.879794\pi$
$757$	−4.00168	+	6.93111i	−0.145443	+	0.251915i	0.784095	+	0.620641i	$0.213128\pi$
$758$		0			0
$759$	−0.536052	−	1.68656i	−0.0194575	−	0.0612183i
$760$		0			0
$761$	18.9310	+	5.07254i	0.686247	+	0.183879i	0.585062	−	0.810988i	$-0.301070\pi$
$761$	18.9310	+	5.07254i	0.686247	+	0.183879i	0.101185	+	0.994868i	$0.467737\pi$
$762$		0			0
$763$	19.7407	+	34.1918i	0.714660	+	1.23783i
$764$		0			0
$765$	9.86170	+	8.19770i	0.356551	+	0.296389i
$766$		0			0
$767$	2.44349	+	30.4737i	0.0882293	+	1.10034i
$768$		0			0
$769$	11.1131	+	41.4747i	0.400749	+	1.49561i	0.811764	+	0.583986i	$0.198508\pi$
$769$	11.1131	+	41.4747i	0.400749	+	1.49561i	−0.411015	+	0.911629i	$0.634826\pi$
$770$		0			0
$771$	−0.618038	+	0.0284129i	−0.0222581	+	0.00102327i
$772$		0			0
$773$	−2.39809	+	8.94981i	−0.0862535	+	0.321902i	−0.995549	−	0.0942495i	$-0.969955\pi$
$773$	−2.39809	+	8.94981i	−0.0862535	+	0.321902i	0.909295	+	0.416152i	$0.136622\pi$
$774$		0			0
$775$	−66.7377	−	66.7377i	−2.39729	−	2.39729i
$776$		0			0
$777$	11.4675	−	7.34285i	0.411394	−	0.263423i
$778$		0			0
$779$	7.27984			0.260827
$780$		0			0
$781$	−0.495728			−0.0177385
$782$		0			0
$783$	28.5163	+	11.5813i	1.01909	+	0.413881i
$784$		0			0
$785$	18.5544	+	18.5544i	0.662235	+	0.662235i
$786$		0			0
$787$	11.0255	−	41.1479i	0.393018	−	1.46676i	−0.432112	−	0.901820i	$-0.642231\pi$
$787$	11.0255	−	41.1479i	0.393018	−	1.46676i	0.825130	−	0.564943i	$-0.191102\pi$
$788$		0			0
$789$	−0.170841	−	3.71612i	−0.00608209	−	0.132297i
$790$		0			0
$791$	7.16447	+	26.7382i	0.254739	+	0.950699i
$792$		0			0
$793$	−21.8454	+	25.6541i	−0.775754	+	0.911004i
$794$		0			0
$795$	20.1253	+	4.41298i	0.713771	+	0.156512i
$796$		0			0
$797$	−10.5161	−	18.2144i	−0.372499	−	0.645187i	0.617450	−	0.786610i	$-0.288166\pi$
$797$	−10.5161	−	18.2144i	−0.372499	−	0.645187i	−0.989949	+	0.141423i	$0.954832\pi$
$798$		0			0
$799$	8.23603	+	2.20684i	0.291370	+	0.0780723i
$800$		0			0
$801$	28.6515	+	4.91582i	1.01235	+	0.173692i
$802$		0			0
$803$	2.13529	−	3.69844i	0.0753529	−	0.130515i
$804$		0			0
$805$			17.3990i			0.613233i
$806$		0			0
$807$	37.7218	+	19.5262i	1.32787	+	0.687356i
$808$		0			0
$809$	−23.4871	−	13.5603i	−0.825762	−	0.476754i	0.0266373	−	0.999645i	$-0.491520\pi$
$809$	−23.4871	−	13.5603i	−0.825762	−	0.476754i	−0.852399	+	0.522891i	$0.824853\pi$
$810$		0			0
$811$	−39.1597	+	39.1597i	−1.37508	+	1.37508i	−0.522359	+	0.852726i	$0.674948\pi$
$811$	−39.1597	+	39.1597i	−1.37508	+	1.37508i	−0.852726	+	0.522359i	$0.825052\pi$
$812$		0			0
$813$	−28.0588	−	25.5923i	−0.984063	−	0.897560i
$814$		0			0
$815$	−5.32844	+	3.07638i	−0.186647	+	0.107761i
$816$		0			0
$817$	5.00047	−	1.33987i	0.174944	−	0.0468762i
$818$		0			0
$819$	9.46580	−	25.7950i	0.330762	−	0.901350i
$820$		0			0
$821$	−8.30053	+	2.22412i	−0.289690	+	0.0776223i	−0.400738	−	0.916193i	$-0.631246\pi$
$821$	−8.30053	+	2.22412i	−0.289690	+	0.0776223i	0.111047	+	0.993815i	$0.464579\pi$
$822$		0			0
$823$	7.37175	−	4.25608i	0.256963	−	0.148358i	−0.365985	−	0.930621i	$-0.619268\pi$
$823$	7.37175	−	4.25608i	0.256963	−	0.148358i	0.622948	+	0.782263i	$0.285935\pi$
$824$		0			0
$825$	7.65868	+	6.98545i	0.266641	+	0.243202i
$826$		0			0
$827$	−18.9976	+	18.9976i	−0.660613	+	0.660613i	−0.955524	−	0.294912i	$-0.904710\pi$
$827$	−18.9976	+	18.9976i	−0.660613	+	0.660613i	0.294912	+	0.955524i	$0.404710\pi$
$828$		0			0
$829$	14.3179	+	8.26645i	0.497282	+	0.287106i	0.727590	−	0.686012i	$-0.240640\pi$
$829$	14.3179	+	8.26645i	0.497282	+	0.287106i	−0.230309	+	0.973118i	$0.573974\pi$
$830$		0			0
$831$	28.6877	+	14.8499i	0.995167	+	0.515136i
$832$		0			0
$833$			0.598582i			0.0207396i
$834$		0			0
$835$	−47.7572	+	82.7179i	−1.65271	+	2.86257i
$836$		0			0
$837$	−28.8138	+	38.0939i	−0.995950	+	1.31672i
$838$		0			0
$839$	−40.0647	−	10.7353i	−1.38319	−	0.370623i	−0.510908	−	0.859635i	$-0.670691\pi$
$839$	−40.0647	−	10.7353i	−1.38319	−	0.370623i	−0.872277	+	0.489012i	$0.837357\pi$
$840$		0			0
$841$	3.04274	+	5.27017i	0.104922	+	0.181730i
$842$		0			0
$843$	−26.9847	−	5.91708i	−0.929402	−	0.203795i
$844$		0			0
$845$	50.5331	+	5.16081i	1.73839	+	0.177537i
$846$		0			0
$847$	−7.00873	−	26.1570i	−0.240823	−	0.898763i
$848$		0			0
$849$	0.375057	+	8.15822i	0.0128719	+	0.279990i
$850$		0			0
$851$	−1.40411	+	5.24021i	−0.0481323	+	0.179632i
$852$		0			0
$853$	−13.7858	−	13.7858i	−0.472018	−	0.472018i	0.430549	−	0.902567i	$-0.358320\pi$
$853$	−13.7858	−	13.7858i	−0.472018	−	0.472018i	−0.902567	+	0.430549i	$0.858320\pi$
$854$		0			0
$855$	−16.0381	+	1.47775i	−0.548491	+	0.0505381i
$856$		0			0
$857$	−41.5499			−1.41932			−0.709659	−	0.704545i	$-0.751151\pi$
$857$	−41.5499			−1.41932			−0.709659	+	0.704545i	$0.751151\pi$
$858$		0			0
$859$	−44.2270			−1.50900			−0.754502	−	0.656298i	$-0.772122\pi$
$859$	−44.2270			−1.50900			−0.754502	+	0.656298i	$0.772122\pi$
$860$		0			0
$861$	19.6321	−	12.5708i	0.669059	−	0.428411i
$862$		0			0
$863$	−14.7459	−	14.7459i	−0.501956	−	0.501956i	0.410089	−	0.912045i	$-0.365498\pi$
$863$	−14.7459	−	14.7459i	−0.501956	−	0.501956i	−0.912045	+	0.410089i	$0.865498\pi$
$864$		0			0
$865$	21.0021	−	78.3809i	0.714093	−	2.66503i
$866$		0			0
$867$	−27.3430	+	1.25703i	−0.928617	+	0.0426911i
$868$		0			0
$869$	1.97760	+	7.38050i	0.0670855	+	0.250366i
$870$		0			0
$871$	−19.5956	+	13.5102i	−0.663973	+	0.457777i
$872$		0			0
$873$	1.17624	−	1.41500i	0.0398098	−	0.0478906i
$874$		0			0
$875$	−26.1424	−	45.2799i	−0.883773	−	1.53074i
$876$		0			0
$877$	−43.6140	−	11.6863i	−1.47274	−	0.394620i	−0.568870	−	0.822427i	$-0.692619\pi$
$877$	−43.6140	−	11.6863i	−1.47274	−	0.394620i	−0.903870	+	0.427808i	$0.859286\pi$
$878$		0			0
$879$	11.2040	+	35.2508i	0.377902	+	1.18898i
$880$		0			0
$881$	15.5665	−	26.9620i	0.524448	−	0.908371i	−0.475146	−	0.879907i	$-0.657605\pi$
$881$	15.5665	−	26.9620i	0.524448	−	0.908371i	0.999595	−	0.0284646i	$-0.00906178\pi$
$882$		0			0
$883$		−	45.7983i		−	1.54123i	−0.637298	−	0.770617i	$-0.719948\pi$
$883$		−	45.7983i		−	1.54123i	0.637298	−	0.770617i	$-0.280052\pi$
$884$		0			0
$885$	26.3795	−	50.9612i	0.886737	−	1.71304i
$886$		0			0
$887$	−25.6110	−	14.7865i	−0.859933	−	0.496482i	0.00405708	−	0.999992i	$-0.498709\pi$
$887$	−25.6110	−	14.7865i	−0.859933	−	0.496482i	−0.863990	+	0.503509i	$0.832042\pi$
$888$		0			0
$889$	−16.7287	+	16.7287i	−0.561062	+	0.561062i
$890$		0			0
$891$	2.96914	−	4.32477i	0.0994698	−	0.144885i
$892$		0			0
$893$	−9.27404	+	5.35437i	−0.310344	+	0.179177i
$894$		0			0
$895$	52.8407	−	14.1586i	1.76627	−	0.473271i
$896$		0			0
$897$	4.13915	+	10.1343i	0.138202	+	0.338374i
$898$		0			0
$899$	−52.5926	+	14.0921i	−1.75406	+	0.469999i
$900$		0			0
$901$	2.88431	−	1.66526i	0.0960903	−	0.0554778i
$902$		0			0
$903$	11.1714	−	12.2481i	0.371762	−	0.407591i
$904$		0			0
$905$	−70.5668	+	70.5668i	−2.34572	+	2.34572i
$906$		0			0
$907$	50.3199	+	29.0522i	1.67085	+	0.964663i	0.967166	+	0.254145i	$0.0817942\pi$
$907$	50.3199	+	29.0522i	1.67085	+	0.964663i	0.703679	+	0.710518i	$0.251539\pi$
$908$		0			0
$909$	10.1079	+	14.2947i	0.335257	+	0.474125i
$910$		0			0
$911$		−	52.8673i		−	1.75157i	−0.482701	−	0.875785i	$-0.660344\pi$
$911$		−	52.8673i		−	1.75157i	0.482701	−	0.875785i	$-0.339656\pi$
$912$		0			0
$913$	−2.12423	+	3.67928i	−0.0703018	+	0.121766i
$914$		0			0
$915$	60.2758	−	19.1579i	1.99266	−	0.633340i
$916$		0			0
$917$	2.25207	+	0.603439i	0.0743697	+	0.0199273i
$918$		0			0
$919$	−3.07508	−	5.32620i	−0.101438	−	0.175695i	0.810840	−	0.585269i	$-0.199011\pi$
$919$	−3.07508	−	5.32620i	−0.101438	−	0.175695i	−0.912277	+	0.409573i	$0.865678\pi$
$920$		0			0
$921$	8.51290	−	38.8229i	0.280510	−	1.27926i
$922$		0			0
$923$	3.05665	−	0.245094i	0.100611	−	0.00806735i
$924$		0			0
$925$	−8.22447	−	30.6942i	−0.270419	−	1.00922i
$926$		0			0
$927$	5.64876	+	2.60239i	0.185530	+	0.0854738i
$928$		0			0
$929$	−9.26432	+	34.5749i	−0.303952	+	1.13437i	0.629891	+	0.776684i	$0.283100\pi$
$929$	−9.26432	+	34.5749i	−0.303952	+	1.13437i	−0.933843	+	0.357682i	$0.883567\pi$
$930$		0			0
$931$	−0.531585	−	0.531585i	−0.0174220	−	0.0174220i
$932$		0			0
$933$	30.6785	+	47.9113i	1.00437	+	1.56855i
$934$		0			0
$935$	2.49161			0.0814844
$936$		0			0
$937$	−13.8585			−0.452737			−0.226369	−	0.974042i	$-0.572685\pi$
$937$	−13.8585			−0.452737			−0.226369	+	0.974042i	$0.572685\pi$
$938$		0			0
$939$	−10.3327	−	16.1368i	−0.337195	−	0.526605i
$940$		0			0
$941$	−10.8257	−	10.8257i	−0.352908	−	0.352908i	0.508283	−	0.861190i	$-0.330281\pi$
$941$	−10.8257	−	10.8257i	−0.352908	−	0.352908i	−0.861190	+	0.508283i	$0.830281\pi$
$942$		0			0
$943$	−2.40380	+	8.97112i	−0.0782786	+	0.292140i
$944$		0			0
$945$	−40.6993	+	31.6796i	−1.32395	+	1.03054i
$946$		0			0
$947$	5.50870	+	20.5588i	0.179009	+	0.668070i	0.995834	+	0.0911846i	$0.0290653\pi$
$947$	5.50870	+	20.5588i	0.179009	+	0.668070i	−0.816825	+	0.576885i	$0.804268\pi$
$948$		0			0
$949$	−11.3376	+	23.8602i	−0.368036	+	0.774536i
$950$		0			0
$951$	−9.20755	+	41.9908i	−0.298575	+	1.36165i
$952$		0			0
$953$	10.3217	+	17.8776i	0.334351	+	0.579114i	0.983360	−	0.181667i	$-0.0581494\pi$
$953$	10.3217	+	17.8776i	0.334351	+	0.579114i	−0.649009	+	0.760781i	$0.724816\pi$
$954$		0			0
$955$	89.2468	+	23.9136i	2.88796	+	0.773826i
$956$		0			0
$957$	5.69907	−	1.81138i	0.184225	−	0.0585535i
$958$		0			0
$959$	10.9467	−	18.9602i	0.353487	−	0.612257i
$960$		0			0
$961$		−	53.4956i		−	1.72566i
$962$		0			0
$963$	8.47170	−	5.99040i	0.272997	−	0.193038i
$964$		0			0
$965$	−35.8646	−	20.7065i	−1.15452	−	0.666565i
$966$		0			0
$967$	3.56933	−	3.56933i	0.114782	−	0.114782i	−0.647383	−	0.762165i	$-0.724137\pi$
$967$	3.56933	−	3.56933i	0.114782	−	0.114782i	0.762165	+	0.647383i	$0.224137\pi$
$968$		0			0
$969$	−1.75447	+	1.92356i	−0.0563618	+	0.0617938i
$970$		0			0
$971$	32.0913	−	18.5279i	1.02986	−	0.594590i	0.112916	−	0.993605i	$-0.463981\pi$
$971$	32.0913	−	18.5279i	1.02986	−	0.594590i	0.916945	+	0.399014i	$0.130648\pi$
$972$		0			0
$973$	8.12969	−	2.17834i	0.260626	−	0.0698345i
$974$		0			0
$975$	−50.6770	−	39.2857i	−1.62296	−	1.25815i
$976$		0			0
$977$	47.1501	−	12.6338i	1.50847	−	0.404192i	0.592540	−	0.805541i	$-0.298125\pi$
$977$	47.1501	−	12.6338i	1.50847	−	0.404192i	0.915925	+	0.401349i	$0.131458\pi$
$978$		0			0
$979$	4.89141	−	2.82406i	0.156330	−	0.0902573i
$980$		0			0
$981$	−16.1494	−	43.7410i	−0.515610	−	1.39654i
$982$		0			0
$983$	−33.9032	+	33.9032i	−1.08134	+	1.08134i	−0.0849587	+	0.996384i	$0.527076\pi$
$983$	−33.9032	+	33.9032i	−1.08134	+	1.08134i	−0.996384	+	0.0849587i	$0.972924\pi$
$984$		0			0
$985$	−11.7345	−	6.77491i	−0.373892	−	0.215867i
$986$		0			0
$987$	−15.7641	+	30.4538i	−0.501776	+	0.969357i
$988$		0			0
$989$			6.60462i			0.210015i
$990$		0			0
$991$	−24.3508	+	42.1768i	−0.773529	+	1.33979i	0.162089	+	0.986776i	$0.448177\pi$
$991$	−24.3508	+	42.1768i	−0.773529	+	1.33979i	−0.935618	+	0.353015i	$0.885156\pi$
$992$		0			0
$993$	2.42595	+	7.63267i	0.0769850	+	0.242215i
$994$		0			0
$995$	−11.6550	−	3.12294i	−0.369488	−	0.0990039i
$996$		0			0
$997$	2.76696	+	4.79252i	0.0876306	+	0.151781i	0.906509	−	0.422186i	$-0.138737\pi$
$997$	2.76696	+	4.79252i	0.0876306	+	0.151781i	−0.818879	+	0.573967i	$0.805404\pi$
$998$		0			0
$999$	−14.8143	+	6.25678i	−0.468705	+	0.197956i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cn.d.305.2		16
3.2	odd	2	inner	624.2.cn.d.305.4		16
4.3	odd	2		78.2.k.a.71.4	yes	16
12.11	even	2		78.2.k.a.71.1	yes	16
13.11	odd	12	inner	624.2.cn.d.401.4		16
39.11	even	12	inner	624.2.cn.d.401.2		16
52.7	even	12		1014.2.g.c.437.7		16
52.11	even	12		78.2.k.a.11.1	✓	16
52.19	even	12		1014.2.g.d.437.3		16
52.35	odd	6		1014.2.g.c.239.3		16
52.43	odd	6		1014.2.g.d.239.7		16
156.11	odd	12		78.2.k.a.11.4	yes	16
156.35	even	6		1014.2.g.c.239.7		16
156.59	odd	12		1014.2.g.c.437.3		16
156.71	odd	12		1014.2.g.d.437.7		16
156.95	even	6		1014.2.g.d.239.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.11.1	✓	16	52.11	even	12
78.2.k.a.11.4	yes	16	156.11	odd	12
78.2.k.a.71.1	yes	16	12.11	even	2
78.2.k.a.71.4	yes	16	4.3	odd	2
624.2.cn.d.305.2		16	1.1	even	1	trivial
624.2.cn.d.305.4		16	3.2	odd	2	inner
624.2.cn.d.401.2		16	39.11	even	12	inner
624.2.cn.d.401.4		16	13.11	odd	12	inner
1014.2.g.c.239.3		16	52.35	odd	6
1014.2.g.c.239.7		16	156.35	even	6
1014.2.g.c.437.3		16	156.59	odd	12
1014.2.g.c.437.7		16	52.7	even	12
1014.2.g.d.239.3		16	156.95	even	6
1014.2.g.d.239.7		16	52.43	odd	6
1014.2.g.d.437.3		16	52.19	even	12
1014.2.g.d.437.7		16	156.71	odd	12

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.933998 - 1.45865i) q^{3} +(-2.76293 - 2.76293i) q^{5} +(0.657464 - 2.45369i) q^{7} +(-1.25529 + 2.72474i) q^{9} +O(q^{10})\)	\(q+(-0.933998 - 1.45865i) q^{3} +(-2.76293 - 2.76293i) q^{5} +(0.657464 - 2.45369i) q^{7} +(-1.25529 + 2.72474i) q^{9} +(0.150860 + 0.563016i) q^{11} +(-1.20856 - 3.39697i) q^{13} +(-1.44957 + 6.61072i) q^{15} +(0.547000 + 0.947432i) q^{17} +(-1.32717 - 0.355613i) q^{19} +(-4.19313 + 1.33273i) q^{21} +(0.876460 - 1.51807i) q^{23} +10.2676i q^{25} +(5.14688 - 0.713876i) q^{27} +(5.12973 + 2.96165i) q^{29} +(-6.49983 + 6.49983i) q^{31} +(0.680339 - 0.745907i) q^{33} +(-8.59591 + 4.96285i) q^{35} +(-2.98942 + 0.801012i) q^{37} +(-3.82618 + 4.93562i) q^{39} +(-5.11781 + 1.37131i) q^{41} +(-3.26299 + 1.88389i) q^{43} +(10.9966 - 4.05999i) q^{45} +(5.51114 - 5.51114i) q^{47} +(0.473846 + 0.273575i) q^{49} +(0.871071 - 1.68278i) q^{51} -3.04435i q^{53} +(1.13876 - 1.97239i) q^{55} +(0.720857 + 2.26801i) q^{57} +(-8.19009 - 2.19453i) q^{59} +(-4.67266 - 8.09329i) q^{61} +(5.86037 + 4.87153i) q^{63} +(-6.04642 + 12.7248i) q^{65} +(-1.70856 - 6.37644i) q^{67} +(-3.03294 + 0.139433i) q^{69} +(-0.220122 + 0.821505i) q^{71} +(-5.18078 - 5.18078i) q^{73} +(14.9768 - 9.58993i) q^{75} +1.48065 q^{77} +13.1089 q^{79} +(-5.84847 - 6.84072i) q^{81} +(5.15394 + 5.15394i) q^{83} +(1.10637 - 4.12902i) q^{85} +(-0.471158 - 10.2486i) q^{87} +(-2.50797 - 9.35988i) q^{89} +(-9.12969 + 0.732051i) q^{91} +(15.5518 + 3.41012i) q^{93} +(2.68434 + 4.64941i) q^{95} +(-0.592450 - 0.158747i) q^{97} +(-1.72345 - 0.295697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} - 24 q^{13} + 16 q^{19} - 24 q^{21} - 16 q^{31} - 24 q^{33} + 16 q^{37} - 48 q^{39} + 24 q^{45} + 24 q^{49} + 24 q^{55} - 24 q^{57} - 24 q^{61} + 24 q^{63} - 32 q^{67} - 48 q^{69} + 56 q^{73} + 96 q^{79} + 24 q^{81} - 24 q^{85} - 48 q^{87} + 16 q^{91} - 24 q^{93} + 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 - 24 * q^13 + 16 * q^19 - 24 * q^21 - 16 * q^31 - 24 * q^33 + 16 * q^37 - 48 * q^39 + 24 * q^45 + 24 * q^49 + 24 * q^55 - 24 * q^57 - 24 * q^61 + 24 * q^63 - 32 * q^67 - 48 * q^69 + 56 * q^73 + 96 * q^79 + 24 * q^81 - 24 * q^85 - 48 * q^87 + 16 * q^91 - 24 * q^93 + 16 * q^97

Introduction

L-functions

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