LMFDB - Embedded newform 351.2.t.c.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(64,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("351.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 $ x^20 - 6x^16 + 9x^14 + 54x^12 + 81x^10 + 486x^8 + 729x^6 - 4374*x^4 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{9} $
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			181.2
Root			$-1.23798 + 1.21137i$ of defining polynomial
Character	$\chi$	$=$	351.181
Dual form			351.2.t.c.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.97712 - 1.14149i) q^{2} +(1.60600 + 2.78168i) q^{4} +(2.78501 - 1.60793i) q^{5} +(-2.09815 - 1.21137i) q^{7} -2.76698i q^{8} -7.34174 q^{10} +(-1.27730 - 0.737448i) q^{11} +(3.56557 - 0.535475i) q^{13} +(2.76553 + 4.79003i) q^{14} +(0.0535232 - 0.0927049i) q^{16} +5.12974 q^{17} +1.13065i q^{19} +(8.94547 + 5.16467i) q^{20} +(1.68358 + 2.91604i) q^{22} +(-4.61735 - 7.99748i) q^{23} +(2.67087 - 4.62608i) q^{25} +(-7.66079 - 3.01136i) q^{26} -7.78182i q^{28} +(0.487293 - 0.844016i) q^{29} +(-3.16380 + 1.82662i) q^{31} +(-5.00419 + 2.88917i) q^{32} +(-10.1421 - 5.85555i) q^{34} -7.79116 q^{35} -4.22691i q^{37} +(1.29063 - 2.23543i) q^{38} +(-4.44910 - 7.70607i) q^{40} +(-3.47188 + 2.00449i) q^{41} +(4.33040 - 7.50047i) q^{43} -4.73737i q^{44} +21.0826i q^{46} +(-1.33337 - 0.769820i) q^{47} +(-0.565185 - 0.978929i) q^{49} +(-10.5613 + 6.09755i) q^{50} +(7.21582 + 9.05828i) q^{52} -0.739889 q^{53} -4.74305 q^{55} +(-3.35182 + 5.80553i) q^{56} +(-1.92687 + 1.11248i) q^{58} +(6.72630 - 3.88343i) q^{59} +(-4.06781 + 7.04566i) q^{61} +8.34028 q^{62} +12.9777 q^{64} +(9.06915 - 7.22448i) q^{65} +(-0.669411 + 0.386485i) q^{67} +(8.23837 + 14.2693i) q^{68} +(15.4041 + 8.89354i) q^{70} -3.01136i q^{71} -9.21010i q^{73} +(-4.82498 + 8.35711i) q^{74} +(-3.14510 + 1.81582i) q^{76} +(1.78664 + 3.09455i) q^{77} +(-1.86858 + 3.23648i) q^{79} -0.344246i q^{80} +9.15243 q^{82} +(12.3640 + 7.13838i) q^{83} +(14.2864 - 8.24826i) q^{85} +(-17.1234 + 9.88621i) q^{86} +(-2.04050 + 3.53425i) q^{88} +8.21257i q^{89} +(-8.12974 - 3.19570i) q^{91} +(14.8309 - 25.6879i) q^{92} +(1.75748 + 3.04405i) q^{94} +(1.81800 + 3.14887i) q^{95} +(13.1880 + 7.61407i) q^{97} +2.58061i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) $ 20 * q + 12 * q^4 - 16 * q^10 - 4 * q^13 + 18 * q^14 + 4 * q^16 + 12 * q^17 - 10 * q^22 - 24 * q^23 - 12 * q^25 + 12 * q^26 - 12 * q^29 + 12 * q^35 - 12 * q^38 - 8 * q^40 + 4 * q^43 - 10 * q^49 - 108 * q^53 + 20 * q^55 - 36 * q^56 - 2 * q^61 + 72 * q^62 + 8 * q^64 + 24 * q^65 - 24 * q^68 + 42 * q^74 + 6 * q^77 - 14 * q^79 - 4 * q^82 + 22 * q^88 - 72 * q^91 + 84 * q^92 + 20 * q^94 - 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.97712	−	1.14149i	−1.39803	−	0.807156i	−0.403848	−	0.914826i	$-0.632328\pi$
$2$	−1.97712	−	1.14149i	−1.39803	−	0.807156i	−0.994187	+	0.107670i	$0.965661\pi$
$3$		0			0
$3$		0			0
$4$	1.60600	+	2.78168i	0.803001	+	1.39084i
$5$	2.78501	−	1.60793i	1.24550	−	0.719088i	0.275289	−	0.961362i	$-0.411227\pi$
$5$	2.78501	−	1.60793i	1.24550	−	0.719088i	0.970208	+	0.242274i	$0.0778933\pi$
$6$		0			0
$7$	−2.09815	−	1.21137i	−0.793025	−	0.457853i	0.0480013	−	0.998847i	$-0.484715\pi$
$7$	−2.09815	−	1.21137i	−0.793025	−	0.457853i	−0.841026	+	0.540994i	$0.818048\pi$
$8$		−	2.76698i		−	0.978274i
$9$		0			0
$10$	−7.34174			−2.32166
$11$	−1.27730	−	0.737448i	−0.385119	−	0.222349i	0.294924	−	0.955521i	$-0.404706\pi$
$11$	−1.27730	−	0.737448i	−0.385119	−	0.222349i	−0.680043	+	0.733172i	$0.738039\pi$
$12$		0			0
$13$	3.56557	−	0.535475i	0.988910	−	0.148514i
$13$	3.56557	−	0.535475i	0.988910	−	0.148514i
$14$	2.76553	+	4.79003i	0.739118	+	1.28019i
$15$		0			0
$16$	0.0535232	−	0.0927049i	0.0133808	−	0.0231762i
$17$	5.12974			1.24414			0.622072	−	0.782960i	$-0.286291\pi$
$17$	5.12974			1.24414			0.622072	+	0.782960i	$0.286291\pi$
$18$		0			0
$19$			1.13065i			0.259389i	0.991554	+	0.129694i	$0.0413996\pi$
$19$			1.13065i			0.259389i	−0.991554	+	0.129694i	$0.958600\pi$
$20$	8.94547	+	5.16467i	2.00027	+	1.15486i
$21$		0			0
$22$	1.68358	+	2.91604i	0.358940	+	0.621703i
$23$	−4.61735	−	7.99748i	−0.962784	−	1.66759i	−0.715455	−	0.698658i	$-0.753781\pi$
$23$	−4.61735	−	7.99748i	−0.962784	−	1.66759i	−0.247328	−	0.968932i	$-0.579553\pi$
$24$		0			0
$25$	2.67087	−	4.62608i	0.534174	−	0.925217i
$26$	−7.66079	−	3.01136i	−1.50240	−	0.590577i
$27$		0			0
$28$		−	7.78182i		−	1.47063i
$29$	0.487293	−	0.844016i	0.0904880	−	0.156730i	−0.817229	−	0.576314i	$-0.804491\pi$
$29$	0.487293	−	0.844016i	0.0904880	−	0.156730i	0.907717	+	0.419584i	$0.137824\pi$
$30$		0			0
$31$	−3.16380	+	1.82662i	−0.568235	+	0.328071i	−0.756444	−	0.654058i	$-0.773065\pi$
$31$	−3.16380	+	1.82662i	−0.568235	+	0.328071i	0.188209	+	0.982129i	$0.439732\pi$
$32$	−5.00419	+	2.88917i	−0.884624	+	0.510738i
$33$		0			0
$34$	−10.1421	−	5.85555i	−1.73936	−	1.00422i
$35$	−7.79116			−1.31695
$36$		0			0
$37$		−	4.22691i		−	0.694900i	−0.937698	−	0.347450i	$-0.887048\pi$
$37$		−	4.22691i		−	0.694900i	0.937698	−	0.347450i	$-0.112952\pi$
$38$	1.29063	−	2.23543i	0.209367	−	0.362634i
$39$		0			0
$40$	−4.44910	−	7.70607i	−0.703465	−	1.21844i
$41$	−3.47188	+	2.00449i	−0.542217	+	0.313049i	−0.745977	−	0.665972i	$-0.768017\pi$
$41$	−3.47188	+	2.00449i	−0.542217	+	0.313049i	0.203760	+	0.979021i	$0.434684\pi$
$42$		0			0
$43$	4.33040	−	7.50047i	0.660379	−	1.14381i	−0.320137	−	0.947371i	$-0.603729\pi$
$43$	4.33040	−	7.50047i	0.660379	−	1.14381i	0.980516	−	0.196439i	$-0.0629377\pi$
$44$		−	4.73737i		−	0.714185i
$45$		0			0
$46$			21.0826i			3.10847i
$47$	−1.33337	−	0.769820i	−0.194492	−	0.112290i	0.399592	−	0.916693i	$-0.369152\pi$
$47$	−1.33337	−	0.769820i	−0.194492	−	0.112290i	−0.594084	+	0.804403i	$0.702485\pi$
$48$		0			0
$49$	−0.565185	−	0.978929i	−0.0807407	−	0.139847i
$50$	−10.5613	+	6.09755i	−1.49359	+	0.862324i
$51$		0			0
$52$	7.21582	+	9.05828i	1.00065	+	1.25616i
$53$	−0.739889			−0.101632			−0.0508158	−	0.998708i	$-0.516182\pi$
$53$	−0.739889			−0.101632			−0.0508158	+	0.998708i	$0.516182\pi$
$54$		0			0
$55$	−4.74305			−0.639553
$56$	−3.35182	+	5.80553i	−0.447906	+	0.775796i
$57$		0			0
$58$	−1.92687	+	1.11248i	−0.253011	+	0.146076i
$59$	6.72630	−	3.88343i	0.875689	−	0.505580i	0.00645471	−	0.999979i	$-0.497945\pi$
$59$	6.72630	−	3.88343i	0.875689	−	0.505580i	0.869235	+	0.494400i	$0.164612\pi$
$60$		0			0
$61$	−4.06781	+	7.04566i	−0.520830	+	0.902104i	0.478877	+	0.877882i	$0.341044\pi$
$61$	−4.06781	+	7.04566i	−0.520830	+	0.902104i	−0.999707	+	0.0242218i	$0.992289\pi$
$62$	8.34028			1.05922
$63$		0			0
$64$	12.9777			1.62222
$65$	9.06915	−	7.22448i	1.12489	−	0.896087i
$66$		0			0
$67$	−0.669411	+	0.386485i	−0.0817816	+	0.0472166i	−0.540333	−	0.841451i	$-0.681702\pi$
$67$	−0.669411	+	0.386485i	−0.0817816	+	0.0472166i	0.458552	+	0.888668i	$0.348368\pi$
$68$	8.23837	+	14.2693i	0.999049	+	1.73040i
$69$		0			0
$70$	15.4041	+	8.89354i	1.84114	+	1.06298i
$71$		−	3.01136i		−	0.357383i	−0.983905	−	0.178692i	$-0.942814\pi$
$71$		−	3.01136i		−	0.357383i	0.983905	−	0.178692i	$-0.0571864\pi$
$72$		0			0
$73$		−	9.21010i		−	1.07796i	−0.842318	−	0.538980i	$-0.818810\pi$
$73$		−	9.21010i		−	1.07796i	0.842318	−	0.538980i	$-0.181190\pi$
$74$	−4.82498	+	8.35711i	−0.560893	+	0.971495i
$75$		0			0
$76$	−3.14510	+	1.81582i	−0.360768	+	0.208289i
$77$	1.78664	+	3.09455i	0.203606	+	0.352656i
$78$		0			0
$79$	−1.86858	+	3.23648i	−0.210232	+	0.364133i	−0.951787	−	0.306759i	$-0.900755\pi$
$79$	−1.86858	+	3.23648i	−0.210232	+	0.364133i	0.741555	+	0.670892i	$0.234089\pi$
$80$		−	0.344246i		−	0.0384879i
$81$		0			0
$82$	9.15243			1.01072
$83$	12.3640	+	7.13838i	1.35713	+	0.783539i	0.989236	−	0.146329i	$-0.0467460\pi$
$83$	12.3640	+	7.13838i	1.35713	+	0.783539i	0.367893	+	0.929868i	$0.380079\pi$
$84$		0			0
$85$	14.2864	−	8.24826i	1.54958	−	0.894649i
$86$	−17.1234	+	9.88621i	−1.84647	+	1.06606i
$87$		0			0
$88$	−2.04050	+	3.53425i	−0.217518	+	0.376752i
$89$			8.21257i			0.870531i	0.900302	+	0.435265i	$0.143345\pi$
$89$			8.21257i			0.870531i	−0.900302	+	0.435265i	$0.856655\pi$
$90$		0			0
$91$	−8.12974	−	3.19570i	−0.852228	−	0.335000i
$92$	14.8309	−	25.6879i	1.54623	−	2.67815i
$93$		0			0
$94$	1.75748	+	3.04405i	0.181271	+	0.313970i
$95$	1.81800	+	3.14887i	0.186523	+	0.323068i
$96$		0			0
$97$	13.1880	+	7.61407i	1.33903	+	0.773092i	0.986664	−	0.162769i	$-0.0520425\pi$
$97$	13.1880	+	7.61407i	1.33903	+	0.773092i	0.352370	+	0.935861i	$0.385376\pi$
$98$			2.58061i			0.260681i
$99$		0			0
$100$	17.1577			1.71577
$101$	−7.45316	+	12.9092i	−0.741617	+	1.28452i	0.210142	+	0.977671i	$0.432607\pi$
$101$	−7.45316	+	12.9092i	−0.741617	+	1.28452i	−0.951759	+	0.306847i	$0.900726\pi$
$102$		0			0
$103$	3.26553	+	5.65606i	0.321762	+	0.557308i	0.980852	−	0.194756i	$-0.0623916\pi$
$103$	3.26553	+	5.65606i	0.321762	+	0.557308i	−0.659090	+	0.752064i	$0.729058\pi$
$104$	−1.48165	−	9.86584i	−0.145287	−	0.967426i
$105$		0			0
$106$	1.46285	+	0.844576i	0.142084	+	0.0820325i
$107$	9.37527			0.906341			0.453171	−	0.891424i	$-0.350293\pi$
$107$	9.37527			0.906341			0.453171	+	0.891424i	$0.350293\pi$
$108$		0			0
$109$			14.5859i			1.39707i	0.715574	+	0.698537i	$0.246165\pi$
$109$			14.5859i			1.39707i	−0.715574	+	0.698537i	$0.753835\pi$
$110$	9.37758	+	5.41415i	0.894117	+	0.516219i
$111$		0			0
$112$	−0.224599	+	0.129672i	−0.0212226	+	0.0122529i
$113$	1.53382	+	2.65665i	0.144290	+	0.249917i	0.929108	−	0.369809i	$-0.120577\pi$
$113$	1.53382	+	2.65665i	0.144290	+	0.249917i	−0.784818	+	0.619726i	$0.787244\pi$
$114$		0			0
$115$	−25.7188	−	14.8487i	−2.39829	−	1.38465i
$116$	3.13037			0.290648
$117$		0			0
$118$	−17.7316			−1.63233
$119$	−10.7630	−	6.21399i	−0.986638	−	0.569636i
$120$		0			0
$121$	−4.41234	−	7.64240i	−0.401122	−	0.694764i
$122$	16.0851	−	9.28674i	1.45628	−	0.840782i
$123$		0			0
$124$	−10.1621	−	5.86711i	−0.912587	−	0.526882i
$125$		−	1.09900i		−	0.0982972i
$126$		0			0
$127$	0.163893			0.0145432			0.00727160	−	0.999974i	$-0.497685\pi$
$127$	0.163893			0.0145432			0.00727160	+	0.999974i	$0.497685\pi$
$128$	−15.6502	−	9.03564i	−1.38329	−	0.798645i
$129$		0			0
$130$	−26.1775	+	3.93132i	−2.29592	+	0.344799i
$131$	3.26584	+	5.65660i	0.285338	+	0.494220i	0.972691	−	0.232104i	$-0.0745609\pi$
$131$	3.26584	+	5.65660i	0.285338	+	0.494220i	−0.687353	+	0.726323i	$0.741228\pi$
$132$		0			0
$133$	1.36963	−	2.37227i	0.118762	−	0.205702i
$134$	1.76467			0.152445
$135$		0			0
$136$		−	14.1939i		−	1.21712i
$137$	−12.0632	−	6.96467i	−1.03063	−	0.595032i	−0.113462	−	0.993542i	$-0.536194\pi$
$137$	−12.0632	−	6.96467i	−1.03063	−	0.595032i	−0.917164	+	0.398511i	$0.869527\pi$
$138$		0			0
$139$	7.09082	+	12.2817i	0.601436	+	1.04172i	0.992604	+	0.121398i	$0.0387377\pi$
$139$	7.09082	+	12.2817i	0.601436	+	1.04172i	−0.391168	+	0.920319i	$0.627929\pi$
$140$	−12.5126	−	21.6725i	−1.05751	−	1.83166i
$141$		0			0
$142$	−3.43744	+	5.95382i	−0.288464	+	0.499634i
$143$	−4.94917	−	1.94546i	−0.413870	−	0.162687i
$144$		0			0
$145$		−	3.13413i		−	0.260275i
$146$	−10.5132	+	18.2095i	−0.870082	+	1.50703i
$147$		0			0
$148$	11.7579	−	6.78843i	0.966493	−	0.558005i
$149$	16.0882	−	9.28851i	1.31799	−	0.760945i	0.334589	−	0.942364i	$-0.391402\pi$
$149$	16.0882	−	9.28851i	1.31799	−	0.760945i	0.983406	+	0.181419i	$0.0580691\pi$
$150$		0			0
$151$	10.2989	+	5.94609i	0.838115	+	0.483886i	0.856623	−	0.515943i	$-0.172558\pi$
$151$	10.2989	+	5.94609i	0.838115	+	0.483886i	−0.0185081	+	0.999829i	$0.505892\pi$
$152$	3.12848			0.253753
$153$		0			0
$154$		−	8.15772i		−	0.657368i
$155$	−5.87415	+	10.1743i	−0.471823	+	0.817222i
$156$		0			0
$157$	−1.99459	−	3.45472i	−0.159185	−	0.275717i	0.775390	−	0.631483i	$-0.217553\pi$
$157$	−1.99459	−	3.45472i	−0.159185	−	0.275717i	−0.934575	+	0.355766i	$0.884220\pi$
$158$	7.38883	−	4.26594i	0.587824	−	0.339380i
$159$		0			0
$160$	−9.29116	+	16.0928i	−0.734531	+	1.27224i
$161$			22.3732i			1.76325i
$162$		0			0
$163$			5.18096i			0.405804i	0.979199	+	0.202902i	$0.0650373\pi$
$163$			5.18096i			0.405804i	−0.979199	+	0.202902i	$0.934963\pi$
$164$	−11.1517	−	6.43843i	−0.870801	−	0.502757i
$165$		0			0
$166$	−16.2968	−	28.2268i	−1.26488	−	2.19083i
$167$	−0.706703	+	0.408015i	−0.0546863	+	0.0315732i	−0.527094	−	0.849807i	$-0.676718\pi$
$167$	−0.706703	+	0.408015i	−0.0546863	+	0.0315732i	0.472408	+	0.881380i	$0.343385\pi$
$168$		0			0
$169$	12.4265	−	3.81854i	0.955887	−	0.293734i
$170$	−37.6612			−2.88848
$171$		0			0
$172$	27.8185			2.12114
$173$	0.261538	−	0.452997i	0.0198844	−	0.0344407i	−0.855912	−	0.517122i	$-0.827004\pi$
$173$	0.261538	−	0.452997i	0.0198844	−	0.0344407i	0.875796	+	0.482681i	$0.160337\pi$
$174$		0			0
$175$	−11.2078	+	6.47081i	−0.847227	+	0.489147i
$176$	−0.136730	+	0.0789411i	−0.0103064	+	0.00595041i
$177$		0			0
$178$	9.37457	−	16.2372i	0.702654	−	1.21703i
$179$	14.1750			1.05949			0.529746	−	0.848156i	$-0.322287\pi$
$179$	14.1750			1.05949			0.529746	+	0.848156i	$0.322287\pi$
$180$		0			0
$181$	−17.9757			−1.33612			−0.668060	−	0.744107i	$-0.732875\pi$
$181$	−17.9757			−1.33612			−0.668060	+	0.744107i	$0.732875\pi$
$182$	12.4256	+	15.5983i	0.921047	+	1.15622i
$183$		0			0
$184$	−22.1289	+	12.7761i	−1.63136	+	0.941867i
$185$	−6.79658	−	11.7720i	−0.499694	−	0.865496i
$186$		0			0
$187$	−6.55220	−	3.78291i	−0.479144	−	0.276634i
$188$		−	4.94532i		−	0.360675i
$189$		0			0
$190$		−	8.30093i		−	0.602213i
$191$	4.64755	−	8.04979i	0.336285	−	0.582462i	−0.647446	−	0.762111i	$-0.724163\pi$
$191$	4.64755	−	8.04979i	0.336285	−	0.582462i	0.983731	+	0.179649i	$0.0574962\pi$
$192$		0			0
$193$	9.93585	−	5.73646i	0.715198	−	0.412920i	−0.0977848	−	0.995208i	$-0.531176\pi$
$193$	9.93585	−	5.73646i	0.715198	−	0.412920i	0.812983	+	0.582288i	$0.197842\pi$
$194$	−17.3828	−	30.1079i	−1.24801	−	2.16162i
$195$		0			0
$196$	1.81538	−	3.14432i	0.129670	−	0.224595i
$197$			11.0296i			0.785828i	0.919575	+	0.392914i	$0.128533\pi$
$197$			11.0296i			0.785828i	−0.919575	+	0.392914i	$0.871467\pi$
$198$		0			0
$199$	−1.38397			−0.0981068			−0.0490534	−	0.998796i	$-0.515620\pi$
$199$	−1.38397			−0.0981068			−0.0490534	+	0.998796i	$0.515620\pi$
$200$	−12.8003	−	7.39024i	−0.905116	−	0.522569i
$201$		0			0
$202$	29.4716	−	17.0154i	2.07361	−	1.19720i
$203$	−2.04482	+	1.18058i	−0.143518	+	0.0828604i
$204$		0			0
$205$	−6.44616	+	11.1651i	−0.450219	+	0.779803i
$206$		−	14.9103i		−	1.03885i
$207$		0			0
$208$	0.141199	−	0.359206i	0.00979042	−	0.0249064i
$209$	0.833794	−	1.44417i	0.0576748	−	0.0998956i
$210$		0			0
$211$	4.59187	+	7.95335i	0.316117	+	0.547531i	0.979674	−	0.200595i	$-0.0642874\pi$
$211$	4.59187	+	7.95335i	0.316117	+	0.547531i	−0.663557	+	0.748126i	$0.730954\pi$
$212$	−1.18826	−	2.05813i	−0.0816102	−	0.141353i
$213$		0			0
$214$	−18.5360	−	10.7018i	−1.26710	−	0.731558i
$215$		−	27.8519i		−	1.89948i
$216$		0			0
$217$	8.85083			0.600833
$218$	16.6496	−	28.8380i	1.12766	−	1.95316i
$219$		0			0
$220$	−7.61735	−	13.1936i	−0.513562	−	0.889515i
$221$	18.2904	−	2.74685i	1.23035	−	0.184773i
$222$		0			0
$223$	5.51495	+	3.18406i	0.369308	+	0.213220i	0.673156	−	0.739500i	$-0.264938\pi$
$223$	5.51495	+	3.18406i	0.369308	+	0.213220i	−0.303848	+	0.952721i	$0.598271\pi$
$224$	13.9994			0.935372
$225$		0			0
$226$		−	7.00336i		−	0.465857i
$227$	−8.83052	−	5.09830i	−0.586102	−	0.338386i	0.177453	−	0.984129i	$-0.443214\pi$
$227$	−8.83052	−	5.09830i	−0.586102	−	0.338386i	−0.763555	+	0.645743i	$0.776548\pi$
$228$		0			0
$229$	−7.02980	+	4.05866i	−0.464542	+	0.268204i	−0.713952	−	0.700194i	$-0.753097\pi$
$229$	−7.02980	+	4.05866i	−0.464542	+	0.268204i	0.249410	+	0.968398i	$0.419763\pi$
$230$	33.8994	+	58.7155i	2.23526	+	3.87158i
$231$		0			0
$232$	−2.33537	−	1.34833i	−0.153325	−	0.0885221i
$233$	−8.37795			−0.548858			−0.274429	−	0.961607i	$-0.588489\pi$
$233$	−8.37795			−0.548858			−0.274429	+	0.961607i	$0.588489\pi$
$234$		0			0
$235$	−4.95126			−0.322985
$236$	21.6049	+	12.4736i	1.40636	+	0.811961i
$237$		0			0
$238$	14.1864	+	24.5716i	0.919570	+	1.59274i
$239$	−3.99453	+	2.30624i	−0.258385	+	0.149178i	−0.623598	−	0.781746i	$-0.714330\pi$
$239$	−3.99453	+	2.30624i	−0.258385	+	0.149178i	0.365213	+	0.930924i	$0.380996\pi$
$240$		0			0
$241$	−6.95910	−	4.01784i	−0.448275	−	0.258812i	0.258826	−	0.965924i	$-0.416664\pi$
$241$	−6.95910	−	4.01784i	−0.448275	−	0.258812i	−0.707101	+	0.707112i	$0.749998\pi$
$242$			20.1466i			1.29507i
$243$		0			0
$244$	−26.1316			−1.67291
$245$	−3.14810	−	1.81756i	−0.201125	−	0.116119i
$246$		0			0
$247$	0.605434	+	4.03140i	0.0385228	+	0.256512i
$248$	5.05422	+	8.75417i	0.320943	+	0.555890i
$249$		0			0
$250$	−1.25449	+	2.17285i	−0.0793411	+	0.137423i
$251$	−17.1127			−1.08015			−0.540073	−	0.841618i	$-0.681604\pi$
$251$	−17.1127			−1.08015			−0.540073	+	0.841618i	$0.681604\pi$
$252$		0			0
$253$			13.6202i			0.856295i
$254$	−0.324037	−	0.187083i	−0.0203319	−	0.0117386i
$255$		0			0
$256$	7.65044	+	13.2509i	0.478152	+	0.828184i
$257$	−4.75712	−	8.23957i	−0.296741	−	0.513971i	0.678647	−	0.734464i	$-0.262566\pi$
$257$	−4.75712	−	8.23957i	−0.296741	−	0.513971i	−0.975388	+	0.220494i	$0.929233\pi$
$258$		0			0
$259$	−5.12034	+	8.86869i	−0.318162	+	0.551073i
$260$	34.6612	+	13.6249i	2.14960	+	0.844981i
$261$		0			0
$262$		−	14.9117i		−	0.921248i
$263$	−13.9945	+	24.2392i	−0.862937	+	1.49465i	0.00614342	+	0.999981i	$0.498044\pi$
$263$	−13.9945	+	24.2392i	−0.862937	+	1.49465i	−0.869081	+	0.494670i	$0.835289\pi$
$264$		0			0
$265$	−2.06060	+	1.18969i	−0.126582	+	0.0730820i
$266$	−5.41584	+	3.12684i	−0.332067	+	0.191719i
$267$		0			0
$268$	−2.15015	−	1.24139i	−0.131341	−	0.0758299i
$269$	11.4199			0.696285			0.348143	−	0.937442i	$-0.386812\pi$
$269$	11.4199			0.696285			0.348143	+	0.937442i	$0.386812\pi$
$270$		0			0
$271$			13.2786i			0.806620i	0.915064	+	0.403310i	$0.132140\pi$
$271$			13.2786i			0.806620i	−0.915064	+	0.403310i	$0.867860\pi$
$272$	0.274560	−	0.475552i	0.0166477	−	0.0288346i
$273$		0			0
$274$	15.9002	+	27.5400i	0.960567	+	1.66375i
$275$	−6.82299	+	3.93925i	−0.411442	+	0.237546i
$276$		0			0
$277$	−0.900995	+	1.56057i	−0.0541356	+	0.0937655i	−0.891823	−	0.452384i	$-0.850574\pi$
$277$	−0.900995	+	1.56057i	−0.0541356	+	0.0937655i	0.837688	+	0.546150i	$0.183907\pi$
$278$		−	32.3764i		−	1.94181i
$279$		0			0
$280$			21.5580i			1.28834i
$281$	9.94035	+	5.73906i	0.592991	+	0.342364i	0.766279	−	0.642507i	$-0.222106\pi$
$281$	9.94035	+	5.73906i	0.592991	+	0.342364i	−0.173288	+	0.984871i	$0.555439\pi$
$282$		0			0
$283$	11.3277	+	19.6201i	0.673360	+	1.16629i	0.976945	+	0.213490i	$0.0684831\pi$
$283$	11.3277	+	19.6201i	0.673360	+	1.16629i	−0.303585	+	0.952804i	$0.598184\pi$
$284$	8.37663	−	4.83625i	0.497062	−	0.286979i
$285$		0			0
$286$	7.56438	+	9.49583i	0.447291	+	0.561500i
$287$	9.71269			0.573322
$288$		0			0
$289$	9.31424			0.547896
$290$	−3.57758	+	6.19655i	−0.210083	+	0.363874i
$291$		0			0
$292$	25.6195	−	14.7914i	1.49927	−	0.865603i
$293$	−14.1753	+	8.18413i	−0.828132	+	0.478122i	−0.853213	−	0.521563i	$-0.825349\pi$
$293$	−14.1753	+	8.18413i	−0.828132	+	0.478122i	0.0250809	+	0.999685i	$0.492016\pi$
$294$		0			0
$295$	12.4886	−	21.6308i	0.727112	−	1.25940i
$296$	−11.6958			−0.679803
$297$		0			0
$298$	−42.4110			−2.45680
$299$	−20.7459	−	26.0431i	−1.19977	−	1.50611i
$300$		0			0
$301$	−18.1716	+	10.4914i	−1.04739	+	0.604714i
$302$	−13.5748	−	23.5123i	−0.781142	−	1.35298i
$303$		0			0
$304$	0.104817	+	0.0605160i	0.00601165	+	0.00347083i
$305$			26.1630i			1.49809i
$306$		0			0
$307$			16.6786i			0.951898i	0.879473	+	0.475949i	$0.157895\pi$
$307$			16.6786i			0.951898i	−0.879473	+	0.475949i	$0.842105\pi$
$308$	−5.73868	+	9.93969i	−0.326992	+	0.566367i
$309$		0			0
$310$	23.2278	−	13.4106i	1.31925	−	0.761670i
$311$	4.05615	+	7.02546i	0.230003	+	0.398377i	0.957809	−	0.287406i	$-0.0927930\pi$
$311$	4.05615	+	7.02546i	0.230003	+	0.398377i	−0.727806	+	0.685784i	$0.759460\pi$
$312$		0			0
$313$	11.0021	−	19.0562i	0.621877	−	1.07712i	−0.367260	−	0.930119i	$-0.619704\pi$
$313$	11.0021	−	19.0562i	0.621877	−	1.07712i	0.989136	−	0.147003i	$-0.0469628\pi$
$314$			9.10720i			0.513949i
$315$		0			0
$316$	−12.0038			−0.675266
$317$	5.82742	+	3.36446i	0.327301	+	0.188967i	0.654642	−	0.755939i	$-0.272819\pi$
$317$	5.82742	+	3.36446i	0.327301	+	0.188967i	−0.327341	+	0.944906i	$0.606153\pi$
$318$		0			0
$319$	−1.24483	+	0.718706i	−0.0696974	+	0.0402398i
$320$	36.1432	−	20.8673i	2.02047	−	1.16652i
$321$		0			0
$322$	25.5388	−	44.2345i	1.42322	−	2.46509i
$323$			5.79994i			0.322717i
$324$		0			0
$325$	7.04602	−	17.9248i	0.390843	−	0.994289i
$326$	5.91402	−	10.2434i	0.327547	−	0.567328i
$327$		0			0
$328$	5.54639	+	9.60662i	0.306248	+	0.530437i
$329$	1.86507	+	3.23039i	0.102824	+	0.178097i
$330$		0			0
$331$	−0.226288	−	0.130648i	−0.0124379	−	0.00718104i	0.493768	−	0.869594i	$-0.335619\pi$
$331$	−0.226288	−	0.130648i	−0.0124379	−	0.00718104i	−0.506206	+	0.862413i	$0.668952\pi$
$332$			45.8570i			2.51673i
$333$		0			0
$334$	1.86298			0.101938
$335$	−1.24288	+	2.15273i	−0.0679058	+	0.117616i
$336$		0			0
$337$	−2.94402	−	5.09920i	−0.160371	−	0.277771i	0.774631	−	0.632414i	$-0.217936\pi$
$337$	−2.94402	−	5.09920i	−0.160371	−	0.277771i	−0.935002	+	0.354643i	$0.884602\pi$
$338$	−28.9276	−	6.63505i	−1.57345	−	0.360899i
$339$		0			0
$340$	45.8880	+	26.4934i	2.48862	+	1.43681i
$341$	5.38815			0.291785
$342$		0			0
$343$			19.6977i			1.06358i
$344$	−20.7536	−	11.9821i	−1.11896	−	0.646032i
$345$		0			0
$346$	−1.03418	+	0.597086i	−0.0555980	+	0.0320995i
$347$	1.59900	+	2.76956i	0.0858391	+	0.148678i	0.905748	−	0.423816i	$-0.139310\pi$
$347$	1.59900	+	2.76956i	0.0858391	+	0.148678i	−0.819909	+	0.572493i	$0.805976\pi$
$348$		0			0
$349$	12.0677	+	6.96727i	0.645967	+	0.372949i	0.786909	−	0.617069i	$-0.211680\pi$
$349$	12.0677	+	6.96727i	0.645967	+	0.372949i	−0.140942	+	0.990018i	$0.545013\pi$
$350$	29.5454			1.57927
$351$		0			0
$352$	8.52245			0.454248
$353$	−13.5867	−	7.84426i	−0.723145	−	0.417508i	0.0927643	−	0.995688i	$-0.470430\pi$
$353$	−13.5867	−	7.84426i	−0.723145	−	0.417508i	−0.815909	+	0.578180i	$0.803763\pi$
$354$		0			0
$355$	−4.84206	−	8.38669i	−0.256990	−	0.445119i
$356$	−22.8447	+	13.1894i	−1.21077	+	0.699036i
$357$		0			0
$358$	−28.0257	−	16.1807i	−1.48121	−	0.855175i
$359$		−	5.86486i		−	0.309535i	−0.987951	−	0.154768i	$-0.950537\pi$
$359$		−	5.86486i		−	0.309535i	0.987951	−	0.154768i	$-0.0494629\pi$
$360$		0			0
$361$	17.7216			0.932718
$362$	35.5400	+	20.5190i	1.86794	+	1.07846i
$363$		0			0
$364$	−4.16697	−	27.7466i	−0.218409	−	1.45432i
$365$	−14.8092	−	25.6503i	−0.775148	−	1.34260i
$366$		0			0
$367$	−1.66786	+	2.88882i	−0.0870617	+	0.150795i	−0.906268	−	0.422704i	$-0.861081\pi$
$367$	−1.66786	+	2.88882i	−0.0870617	+	0.150795i	0.819206	+	0.573499i	$0.194414\pi$
$368$	−0.988541			−0.0515313
$369$		0			0
$370$			31.0329i			1.61332i
$371$	1.55240	+	0.896277i	0.0805964	+	0.0465324i
$372$		0			0
$373$	−13.3206	−	23.0720i	−0.689716	−	1.19462i	−0.971930	−	0.235272i	$-0.924402\pi$
$373$	−13.3206	−	23.0720i	−0.689716	−	1.19462i	0.282214	−	0.959352i	$-0.408931\pi$
$374$	8.63632	+	14.9585i	0.446574	+	0.773488i
$375$		0			0
$376$	−2.13007	+	3.68940i	−0.109850	+	0.190266i
$377$	1.28553	−	3.27033i	0.0662079	−	0.168430i
$378$		0			0
$379$		−	30.4926i		−	1.56630i	−0.621832	−	0.783150i	$-0.713611\pi$
$379$		−	30.4926i		−	1.56630i	0.621832	−	0.783150i	$-0.286389\pi$
$380$	−5.83943	+	10.1142i	−0.299556	+	0.518847i
$381$		0			0
$382$	−18.3775	+	10.6103i	−0.940275	+	0.542868i
$383$	−21.6814	+	12.5178i	−1.10787	+	0.639628i	−0.938276	−	0.345886i	$-0.887578\pi$
$383$	−21.6814	+	12.5178i	−1.10787	+	0.639628i	−0.169592	+	0.985514i	$0.554245\pi$
$384$		0			0
$385$	9.95162	+	5.74557i	0.507182	+	0.292821i
$386$	−26.1925			−1.33316
$387$		0			0
$388$			48.9128i			2.48317i
$389$	−1.05615	+	1.82931i	−0.0535490	+	0.0927495i	−0.891557	−	0.452908i	$-0.850387\pi$
$389$	−1.05615	+	1.82931i	−0.0535490	+	0.0927495i	0.838008	+	0.545657i	$0.183720\pi$
$390$		0			0
$391$	−23.6858	−	41.0250i	−1.19784	−	2.07472i
$392$	−2.70868	+	1.56385i	−0.136809	+	0.0789866i
$393$		0			0
$394$	12.5902	−	21.8069i	0.634286	−	1.09861i
$395$			12.0182i			0.604701i
$396$		0			0
$397$		−	28.7853i		−	1.44469i	−0.691533	−	0.722345i	$-0.743064\pi$
$397$		−	28.7853i		−	1.44469i	0.691533	−	0.722345i	$-0.256936\pi$
$398$	2.73627	+	1.57979i	0.137157	+	0.0791875i
$399$		0			0
$400$	−0.285907	−	0.495206i	−0.0142954	−	0.0247603i
$401$	9.86207	−	5.69387i	0.492488	−	0.284338i	−0.233118	−	0.972448i	$-0.574893\pi$
$401$	9.86207	−	5.69387i	0.492488	−	0.284338i	0.725606	+	0.688110i	$0.241560\pi$
$402$		0			0
$403$	−10.3026	+	8.20707i	−0.513211	+	0.408824i
$404$	−47.8791			−2.38208
$405$		0			0
$406$	5.39048			0.267525
$407$	−3.11713	+	5.39902i	−0.154510	+	0.267620i
$408$		0			0
$409$	−2.90604	+	1.67780i	−0.143695	+	0.0829621i	−0.570124	−	0.821559i	$-0.693105\pi$
$409$	−2.90604	+	1.67780i	−0.143695	+	0.0829621i	0.426429	+	0.904521i	$0.359771\pi$
$410$	25.4897	−	14.7165i	1.25884	−	0.726794i
$411$		0			0
$412$	−10.4889	+	18.1673i	−0.516750	+	0.895037i
$413$	−18.8170			−0.925925
$414$		0			0
$415$	45.9120			2.25373
$416$	−16.2957	+	12.9811i	−0.798962	+	0.636453i
$417$		0			0
$418$	−3.29702	+	1.90354i	−0.161263	+	0.0931050i
$419$	1.03279	+	1.78885i	0.0504552	+	0.0873910i	0.890150	−	0.455668i	$-0.150599\pi$
$419$	1.03279	+	1.78885i	0.0504552	+	0.0873910i	−0.839695	+	0.543059i	$0.817266\pi$
$420$		0			0
$421$	−29.3605	−	16.9513i	−1.43094	−	0.826156i	−0.433752	−	0.901032i	$-0.642811\pi$
$421$	−29.3605	−	16.9513i	−1.43094	−	0.826156i	−0.997193	+	0.0748758i	$0.976144\pi$
$422$		−	20.9663i		−	1.02062i
$423$		0			0
$424$			2.04726i			0.0994236i
$425$	13.7009	−	23.7306i	0.664590	−	1.15110i
$426$		0			0
$427$	17.0697	−	9.85522i	0.826063	−	0.476927i
$428$	15.0567	+	26.0789i	0.727792	+	1.26057i
$429$		0			0
$430$	−31.7927	+	55.0665i	−1.53318	+	2.65554i
$431$		−	30.6212i		−	1.47497i	−0.675364	−	0.737485i	$-0.736013\pi$
$431$		−	30.6212i		−	1.47497i	0.675364	−	0.737485i	$-0.263987\pi$
$432$		0			0
$433$	8.63597			0.415018			0.207509	−	0.978233i	$-0.433464\pi$
$433$	8.63597			0.415018			0.207509	+	0.978233i	$0.433464\pi$
$434$	−17.4991	−	10.1031i	−0.839986	−	0.484966i
$435$		0			0
$436$	−40.5732	+	23.4249i	−1.94310	+	1.12185i
$437$	9.04234	−	5.22060i	0.432554	−	0.249735i
$438$		0			0
$439$	−14.7827	+	25.6043i	−0.705538	+	1.22203i	0.260959	+	0.965350i	$0.415961\pi$
$439$	−14.7827	+	25.6043i	−0.705538	+	1.22203i	−0.966497	+	0.256678i	$0.917372\pi$
$440$			13.1239i			0.625658i
$441$		0			0
$442$	−39.2979	−	15.4475i	−1.86921	−	0.734763i
$443$	15.6331	−	27.0773i	0.742751	−	1.28648i	−0.208487	−	0.978025i	$-0.566854\pi$
$443$	15.6331	−	27.0773i	0.742751	−	1.28648i	0.951238	−	0.308457i	$-0.0998127\pi$
$444$		0			0
$445$	13.2052	+	22.8721i	0.625988	+	1.08424i
$446$	−7.26915	−	12.5905i	−0.344204	−	0.596179i
$447$		0			0
$448$	−27.2292	−	15.7208i	−1.28646	−	0.742738i
$449$			10.8346i			0.511316i	0.966767	+	0.255658i	$0.0822922\pi$
$449$			10.8346i			0.511316i	−0.966767	+	0.255658i	$0.917708\pi$
$450$		0			0
$451$	5.91283			0.278424
$452$	−4.92663	+	8.53318i	−0.231729	+	0.401367i
$453$		0			0
$454$	11.6393	+	20.1599i	0.546261	+	0.946152i
$455$	−27.7799	+	4.17197i	−1.30234	+	0.195585i
$456$		0			0
$457$	13.8936	+	8.02147i	0.649915	+	0.375229i	0.788424	−	0.615133i	$-0.210898\pi$
$457$	13.8936	+	8.02147i	0.649915	+	0.375229i	−0.138509	+	0.990361i	$0.544231\pi$
$458$	18.5317			0.865929
$459$		0			0
$460$		−	95.3883i		−	4.44750i
$461$	22.1953	+	12.8145i	1.03374	+	0.596830i	0.918054	−	0.396456i	$-0.129760\pi$
$461$	22.1953	+	12.8145i	1.03374	+	0.596830i	0.115686	+	0.993286i	$0.463093\pi$
$462$		0			0
$463$	−28.1926	+	16.2770i	−1.31022	+	0.756457i	−0.982133	−	0.188189i	$-0.939738\pi$
$463$	−28.1926	+	16.2770i	−1.31022	+	0.756457i	−0.328090	+	0.944647i	$0.606405\pi$
$464$	−0.0521629	−	0.0903488i	−0.00242160	−	0.00419434i
$465$		0			0
$466$	16.5642	+	9.56335i	0.767322	+	0.443014i
$467$	−16.2179			−0.750474			−0.375237	−	0.926929i	$-0.622439\pi$
$467$	−16.2179			−0.750474			−0.375237	+	0.926929i	$0.622439\pi$
$468$		0			0
$469$	1.87270			0.0864731
$470$	9.78924	+	5.65182i	0.451544	+	0.260699i
$471$		0			0
$472$	−10.7454	−	18.6115i	−0.494596	−	0.856665i
$473$	−11.0624	+	6.38688i	−0.508650	+	0.293669i
$474$		0			0
$475$	5.23048	+	3.01982i	0.239991	+	0.138559i
$476$		−	39.9187i		−	1.82967i
$477$		0			0
$478$	10.5302			0.481641
$479$	−8.86463	−	5.11800i	−0.405035	−	0.233847i	0.283619	−	0.958937i	$-0.408465\pi$
$479$	−8.86463	−	5.11800i	−0.405035	−	0.233847i	−0.688654	+	0.725090i	$0.741798\pi$
$480$		0			0
$481$	−2.26341	−	15.0713i	−0.103202	−	0.687194i
$482$	9.17265	+	15.8875i	0.417803	+	0.723655i
$483$		0			0
$484$	14.1725	−	24.5474i	0.644202	−	1.11579i
$485$	48.9715			2.22368
$486$		0			0
$487$		−	16.0863i		−	0.728940i	−0.931215	−	0.364470i	$-0.881250\pi$
$487$		−	16.0863i		−	0.728940i	0.931215	−	0.364470i	$-0.118750\pi$
$488$	19.4952	+	11.2555i	0.882505	+	0.509515i
$489$		0			0
$490$	4.14944	+	7.18705i	0.187453	+	0.324678i
$491$	2.20943	+	3.82684i	0.0997101	+	0.172703i	0.911565	−	0.411157i	$-0.134875\pi$
$491$	2.20943	+	3.82684i	0.0997101	+	0.172703i	−0.811855	+	0.583860i	$0.801542\pi$
$492$		0			0
$493$	2.49969	−	4.32958i	0.112580	−	0.194995i
$494$	3.40479	−	8.66167i	0.153189	−	0.389707i
$495$		0			0
$496$			0.391066i			0.0175594i
$497$	−3.64786	+	6.31828i	−0.163629	+	0.283414i
$498$		0			0
$499$	−6.39369	+	3.69140i	−0.286221	+	0.165250i	−0.636236	−	0.771494i	$-0.719510\pi$
$499$	−6.39369	+	3.69140i	−0.286221	+	0.165250i	0.350015	+	0.936744i	$0.386176\pi$
$500$	3.05705	−	1.76499i	0.136715	−	0.0789327i
$501$		0			0
$502$	33.8339	+	19.5340i	1.51008	+	0.871847i
$503$	−5.65418			−0.252107			−0.126054	−	0.992023i	$-0.540231\pi$
$503$	−5.65418			−0.252107			−0.126054	+	0.992023i	$0.540231\pi$
$504$		0			0
$505$			47.9366i			2.13315i
$506$	15.5473	−	26.9288i	0.691163	−	1.19713i
$507$		0			0
$508$	0.263213	+	0.455898i	0.0116782	+	0.0202272i
$509$	23.2192	−	13.4056i	1.02917	−	0.594193i	0.112425	−	0.993660i	$-0.464138\pi$
$509$	23.2192	−	13.4056i	1.02917	−	0.594193i	0.916747	+	0.399467i	$0.130805\pi$
$510$		0			0
$511$	−11.1568	+	19.3242i	−0.493548	+	0.854850i
$512$			1.21094i			0.0535165i
$513$		0			0
$514$			21.7208i			0.958065i
$515$	18.1891	+	10.5015i	0.801506	+	0.462750i
$516$		0			0
$517$	1.13540	+	1.96658i	0.0499350	+	0.0864899i
$518$	20.2470	−	11.6896i	0.889604	−	0.513613i
$519$		0			0
$520$	−19.9900	−	25.0941i	−0.876619	−	1.10045i
$521$	20.3407			0.891143			0.445572	−	0.895246i	$-0.353000\pi$
$521$	20.3407			0.891143			0.445572	+	0.895246i	$0.353000\pi$
$522$		0			0
$523$	5.74660			0.251281			0.125641	−	0.992076i	$-0.459901\pi$
$523$	5.74660			0.251281			0.125641	+	0.992076i	$0.459901\pi$
$524$	−10.4899	+	18.1690i	−0.458253	+	0.793717i
$525$		0			0
$526$	55.3376	−	31.9492i	2.41283	−	1.39305i
$527$	−16.2295	+	9.37009i	−0.706967	+	0.408168i
$528$		0			0
$529$	−31.1398	+	53.9357i	−1.35390	+	2.34503i
$530$	5.43208			0.235954
$531$		0			0
$532$	8.79851			0.381464
$533$	−11.3059	+	9.00626i	−0.489712	+	0.390104i
$534$		0			0
$535$	26.1103	−	15.0748i	1.12884	−	0.651739i
$536$	1.06939	+	1.85225i	0.0461908	+	0.0800048i
$537$		0			0
$538$	−22.5786	−	13.0357i	−0.973431	−	0.562011i
$539$			1.66718i			0.0718104i
$540$		0			0
$541$		−	43.0286i		−	1.84994i	−0.380036	−	0.924972i	$-0.624088\pi$
$541$		−	43.0286i		−	1.84994i	0.380036	−	0.924972i	$-0.375912\pi$
$542$	15.1574	−	26.2534i	0.651068	−	1.12768i
$543$		0			0
$544$	−25.6702	+	14.8207i	−1.10060	+	0.635432i
$545$	23.4531	+	40.6219i	1.00462	+	1.74005i
$546$		0			0
$547$	11.1581	−	19.3265i	0.477088	−	0.826340i	−0.522567	−	0.852598i	$-0.675026\pi$
$547$	11.1581	−	19.3265i	0.477088	−	0.826340i	0.999655	+	0.0262576i	$0.00835902\pi$
$548$		−	44.7411i		−	1.91124i
$549$		0			0
$550$	17.9865			0.766946
$551$	0.954285	+	0.550957i	0.0406539	+	0.0234716i
$552$		0			0
$553$	7.84113	−	4.52708i	0.333439	−	0.192511i
$554$	3.56275	−	2.05696i	0.151367	−	0.0873917i
$555$		0			0
$556$	−22.7757	+	39.4487i	−0.965906	+	1.67300i
$557$		−	28.7460i		−	1.21801i	−0.793168	−	0.609003i	$-0.791570\pi$
$557$		−	28.7460i		−	1.21801i	0.793168	−	0.609003i	$-0.208430\pi$
$558$		0			0
$559$	11.4240	−	29.0622i	0.483184	−	1.22920i
$560$	−0.417008	+	0.722279i	−0.0176218	+	0.0305219i
$561$		0			0
$562$	−13.1022	−	22.6936i	−0.552682	−	0.957273i
$563$	−5.91647	−	10.2476i	−0.249350	−	0.431886i	0.713996	−	0.700150i	$-0.246883\pi$
$563$	−5.91647	−	10.2476i	−0.249350	−	0.431886i	−0.963346	+	0.268264i	$0.913550\pi$
$564$		0			0
$565$	8.54342	+	4.93255i	0.359424	+	0.207514i
$566$		−	51.7217i		−	2.17403i
$567$		0			0
$568$	−8.33237			−0.349619
$569$	−4.39661	+	7.61515i	−0.184315	+	0.319244i	−0.943346	−	0.331812i	$-0.892340\pi$
$569$	−4.39661	+	7.61515i	−0.184315	+	0.319244i	0.759030	+	0.651055i	$0.225673\pi$
$570$		0			0
$571$	−15.6380	−	27.0858i	−0.654430	−	1.13351i	−0.982036	−	0.188692i	$-0.939575\pi$
$571$	−15.6380	−	27.0858i	−0.654430	−	1.13351i	0.327606	−	0.944814i	$-0.393758\pi$
$572$	−2.53674	−	16.8914i	−0.106066	−	0.706265i
$573$		0			0
$574$	−19.2032	−	11.0869i	−0.801524	−	0.462760i
$575$	−49.3294			−2.05718
$576$		0			0
$577$			45.2450i			1.88357i	0.336210	+	0.941787i	$0.390855\pi$
$577$			45.2450i			1.88357i	−0.336210	+	0.941787i	$0.609145\pi$
$578$	−18.4154	−	10.6321i	−0.765978	−	0.442238i
$579$		0			0
$580$	8.71813	−	5.03341i	0.362001	−	0.209001i
$581$	−17.2944	−	29.9547i	−0.717492	−	1.24273i
$582$		0			0
$583$	0.945058	+	0.545629i	0.0391403	+	0.0225977i
$584$	−25.4841			−1.05454
$585$		0			0
$586$	37.3684			1.54368
$587$	25.1277	+	14.5075i	1.03713	+	0.598788i	0.919020	−	0.394212i	$-0.128982\pi$
$587$	25.1277	+	14.5075i	1.03713	+	0.598788i	0.118112	+	0.993000i	$0.462316\pi$
$588$		0			0
$589$	−2.06527	−	3.57715i	−0.0850978	−	0.147394i
$590$	−49.3828	+	28.5111i	−2.03306	+	1.17379i
$591$		0			0
$592$	−0.391856	−	0.226238i	−0.0161052	−	0.00929832i
$593$			25.7497i			1.05741i	0.848805	+	0.528707i	$0.177323\pi$
$593$			25.7497i			1.05741i	−0.848805	+	0.528707i	$0.822677\pi$
$594$		0			0
$595$	−39.9666			−1.63847
$596$	51.6753	+	29.8347i	2.11670	+	1.22208i
$597$		0			0
$598$	11.2892	+	75.1715i	0.461651	+	3.07399i
$599$	18.8670	+	32.6786i	0.770885	+	1.33521i	0.937079	+	0.349118i	$0.113519\pi$
$599$	18.8670	+	32.6786i	0.770885	+	1.33521i	−0.166194	+	0.986093i	$0.553148\pi$
$600$		0			0
$601$	−8.46451	+	14.6610i	−0.345274	+	0.598033i	−0.985404	−	0.170235i	$-0.945547\pi$
$601$	−8.46451	+	14.6610i	−0.345274	+	0.598033i	0.640129	+	0.768267i	$0.278881\pi$
$602$	47.9033			1.95239
$603$		0			0
$604$			38.1977i			1.55424i
$605$	−24.5769	−	14.1895i	−0.999192	−	0.576884i
$606$		0			0
$607$	6.13946	+	10.6339i	0.249193	+	0.431615i	0.963302	−	0.268420i	$-0.0865014\pi$
$607$	6.13946	+	10.6339i	0.249193	+	0.431615i	−0.714109	+	0.700034i	$0.753168\pi$
$608$	−3.26664	−	5.65798i	−0.132480	−	0.229461i
$609$		0			0
$610$	29.8648	−	51.7274i	1.20919	−	2.09438i
$611$	−5.16643	−	2.03086i	−0.209011	−	0.0821598i
$612$		0			0
$613$		−	3.84764i		−	0.155405i	−0.996977	−	0.0777023i	$-0.975242\pi$
$613$		−	3.84764i		−	0.155405i	0.996977	−	0.0777023i	$-0.0247584\pi$
$614$	19.0385	−	32.9756i	0.768330	−	1.33079i
$615$		0			0
$616$	8.56254	−	4.94359i	0.344995	−	0.199183i
$617$	29.7198	−	17.1587i	1.19647	−	0.690785i	0.236707	−	0.971581i	$-0.423932\pi$
$617$	29.7198	−	17.1587i	1.19647	−	0.690785i	0.959767	+	0.280796i	$0.0905986\pi$
$618$		0			0
$619$	36.7880	+	21.2396i	1.47864	+	0.853691i	0.999708	−	0.0241630i	$-0.00769205\pi$
$619$	36.7880	+	21.2396i	1.47864	+	0.853691i	0.478928	+	0.877854i	$0.341025\pi$
$620$	−37.7356			−1.51550
$621$		0			0
$622$		−	18.5202i		−	0.742594i
$623$	9.94843	−	17.2312i	0.398575	−	0.690353i
$624$		0			0
$625$	11.5872	+	20.0697i	0.463490	+	0.802788i
$626$	−43.5050	+	25.1176i	−1.73881	+	1.00390i
$627$		0			0
$628$	6.40661	−	11.0966i	0.255652	−	0.442802i
$629$		−	21.6830i		−	0.864557i
$630$		0			0
$631$		−	17.9430i		−	0.714300i	−0.934047	−	0.357150i	$-0.883748\pi$
$631$		−	17.9430i		−	0.714300i	0.934047	−	0.357150i	$-0.116252\pi$
$632$	8.95528	+	5.17033i	0.356222	+	0.205665i
$633$		0			0
$634$	−7.68100	−	13.3039i	−0.305052	−	0.528365i
$635$	0.456446	−	0.263529i	0.0181135	−	0.0104578i
$636$		0			0
$637$	−2.53940	−	3.18780i	−0.100615	−	0.126305i
$638$	3.28158			0.129919
$639$		0			0
$640$	−58.1146			−2.29718
$641$	−8.43114	+	14.6032i	−0.333010	+	0.576790i	−0.983101	−	0.183066i	$-0.941398\pi$
$641$	−8.43114	+	14.6032i	−0.333010	+	0.576790i	0.650090	+	0.759857i	$0.274731\pi$
$642$		0			0
$643$	−43.2179	+	24.9519i	−1.70435	+	0.984006i	−0.763105	+	0.646274i	$0.776326\pi$
$643$	−43.2179	+	24.9519i	−1.70435	+	0.984006i	−0.941242	+	0.337732i	$0.890340\pi$
$644$	−62.2350	+	35.9314i	−2.45240	+	1.41589i
$645$		0			0
$646$	6.62057	−	11.4672i	0.260483	−	0.451170i
$647$	−28.5920			−1.12407			−0.562034	−	0.827114i	$-0.689981\pi$
$647$	−28.5920			−1.12407			−0.562034	+	0.827114i	$0.689981\pi$
$648$		0			0
$649$	−11.4553			−0.449660
$650$	−34.3918	+	27.3965i	−1.34896	+	1.07458i
$651$		0			0
$652$	−14.4118	+	8.32063i	−0.564408	+	0.325861i
$653$	13.2734	+	22.9902i	0.519429	+	0.899677i	0.999745	+	0.0225814i	$0.00718849\pi$
$653$	13.2734	+	22.9902i	0.519429	+	0.899677i	−0.480316	+	0.877095i	$0.659478\pi$
$654$		0			0
$655$	18.1908	+	10.5025i	0.710774	+	0.410366i
$656$			0.429147i			0.0167554i
$657$		0			0
$658$		−	8.51582i		−	0.331981i
$659$	−21.7318	+	37.6406i	−0.846552	+	1.46627i	0.0377144	+	0.999289i	$0.487992\pi$
$659$	−21.7318	+	37.6406i	−0.846552	+	1.46627i	−0.884266	+	0.466983i	$0.845341\pi$
$660$		0			0
$661$	13.6716	−	7.89332i	0.531765	−	0.307015i	−0.209970	−	0.977708i	$-0.567337\pi$
$661$	13.6716	−	7.89332i	0.531765	−	0.307015i	0.741735	+	0.670693i	$0.234003\pi$
$662$	0.298266	+	0.516612i	0.0115924	+	0.0200787i
$663$		0			0
$664$	19.7517	−	34.2110i	0.766516	−	1.32764i
$665$		−	8.80907i		−	0.341601i
$666$		0			0
$667$	−9.00000			−0.348481
$668$	−2.26993	−	1.31055i	−0.0878263	−	0.0507065i
$669$		0			0
$670$	4.91464	−	2.83747i	0.189869	−	0.109621i
$671$	10.3916	−	5.99960i	0.401163	−	0.231612i
$672$		0			0
$673$	8.76355	−	15.1789i	0.337810	−	0.585104i	−0.646210	−	0.763159i	$-0.723647\pi$
$673$	8.76355	−	15.1789i	0.337810	−	0.585104i	0.984021	+	0.178055i	$0.0569805\pi$
$674$			13.4423i			0.517778i
$675$		0			0
$676$	30.5790	+	28.4340i	1.17611	+	1.09362i
$677$	−9.25036	+	16.0221i	−0.355520	+	0.615779i	−0.987207	−	0.159445i	$-0.949030\pi$
$677$	−9.25036	+	16.0221i	−0.355520	+	0.615779i	0.631687	+	0.775224i	$0.282363\pi$
$678$		0			0
$679$	−18.4469	−	31.9509i	−0.707925	−	1.22616i
$680$	−22.8227	−	39.5302i	−0.875212	−	1.51591i
$681$		0			0
$682$	−10.6530	−	6.15052i	−0.407925	−	0.235516i
$683$			4.68607i			0.179307i	0.995973	+	0.0896537i	$0.0285760\pi$
$683$			4.68607i			0.179307i	−0.995973	+	0.0896537i	$0.971424\pi$
$684$		0			0
$685$	−44.7948			−1.71152
$686$	22.4847	−	38.9447i	0.858472	−	1.48692i
$687$		0			0
$688$	−0.463553	−	0.802898i	−0.0176728	−	0.0306102i
$689$	−2.63812	+	0.396192i	−0.100505	+	0.0150937i
$690$		0			0
$691$	−37.3398	−	21.5581i	−1.42047	−	0.820110i	−0.424133	−	0.905600i	$-0.639421\pi$
$691$	−37.3398	−	21.5581i	−1.42047	−	0.820110i	−0.996339	+	0.0854897i	$0.972755\pi$
$692$	1.68012			0.0638686
$693$		0			0
$694$		−	7.30099i		−	0.277142i
$695$	39.4961	+	22.8031i	1.49817	+	0.864970i
$696$		0			0
$697$	−17.8099	+	10.2825i	−0.674596	+	0.389478i
$698$	−15.9061	−	27.5502i	−0.602056	−	1.04279i
$699$		0			0
$700$	−35.9994	−	20.7842i	−1.36065	−	0.785570i
$701$	−35.9226			−1.35678			−0.678389	−	0.734703i	$-0.737322\pi$
$701$	−35.9226			−1.35678			−0.678389	+	0.734703i	$0.737322\pi$
$702$		0			0
$703$	4.77915			0.180249
$704$	−16.5764	−	9.57041i	−0.624748	−	0.360698i
$705$		0			0
$706$	17.9083	+	31.0181i	0.673988	+	1.16738i
$707$	31.2756	−	18.0570i	1.17624	−	0.679104i
$708$		0			0
$709$	−20.9125	−	12.0738i	−0.785384	−	0.453442i	0.0529511	−	0.998597i	$-0.483137\pi$
$709$	−20.9125	−	12.0738i	−0.785384	−	0.453442i	−0.838335	+	0.545156i	$0.816471\pi$
$710$			22.1087i			0.829723i
$711$		0			0
$712$	22.7240			0.851618
$713$	29.2167	+	16.8683i	1.09418	+	0.631722i
$714$		0			0
$715$	−16.9117	+	2.53979i	−0.632461	+	0.0949826i
$716$	22.7651	+	39.4303i	0.850772	+	1.47358i
$717$		0			0
$718$	−6.69468	+	11.5955i	−0.249843	+	0.432741i
$719$	32.3717			1.20726			0.603630	−	0.797265i	$-0.293720\pi$
$719$	32.3717			1.20726			0.603630	+	0.797265i	$0.293720\pi$
$720$		0			0
$721$		−	15.8230i		−	0.589279i
$722$	−35.0378	−	20.2291i	−1.30397	−	0.752848i
$723$		0			0
$724$	−28.8689	−	50.0024i	−1.07291	−	1.85833i
$725$	−2.60299	−	4.50851i	−0.0966727	−	0.167442i
$726$		0			0
$727$	−9.76910	+	16.9206i	−0.362316	+	0.627549i	−0.988342	−	0.152253i	$-0.951347\pi$
$727$	−9.76910	+	16.9206i	−0.362316	+	0.627549i	0.626026	+	0.779802i	$0.284680\pi$
$728$	−8.84243	+	22.4948i	−0.327722	+	0.833713i
$729$		0			0
$730$			67.6182i			2.50266i
$731$	22.2138	−	38.4754i	0.821607	−	1.42307i
$732$		0			0
$733$	35.7224	−	20.6243i	1.31944	−	0.761777i	0.335799	−	0.941934i	$-0.390994\pi$
$733$	35.7224	−	20.6243i	1.31944	−	0.761777i	0.983638	+	0.180157i	$0.0576605\pi$
$734$	6.59513	−	3.80770i	0.243431	−	0.140545i
$735$		0			0
$736$	46.2122	+	26.6806i	1.70340	+	0.983460i
$737$	1.14005			0.0419942
$738$		0			0
$739$			12.6677i			0.465988i	0.972478	+	0.232994i	$0.0748523\pi$
$739$			12.6677i			0.465988i	−0.972478	+	0.232994i	$0.925148\pi$
$740$	21.8306	−	37.8117i	0.802509	−	1.38999i
$741$		0			0
$742$	−2.04618	−	3.54409i	−0.0751177	−	0.130108i
$743$	10.3523	−	5.97690i	0.379789	−	0.219271i	−0.297938	−	0.954585i	$-0.596299\pi$
$743$	10.3523	−	5.97690i	0.379789	−	0.219271i	0.677726	+	0.735314i	$0.262965\pi$
$744$		0			0
$745$	29.8705	−	51.7373i	1.09437	−	1.89551i
$746$			60.8215i			2.22683i
$747$		0			0
$748$		−	24.3015i		−	0.888549i
$749$	−19.6707	−	11.3569i	−0.718751	−	0.414971i
$750$		0			0
$751$	6.59296	+	11.4193i	0.240581	+	0.416698i	0.960880	−	0.276966i	$-0.0893289\pi$
$751$	6.59296	+	11.4193i	0.240581	+	0.416698i	−0.720299	+	0.693663i	$0.755996\pi$
$752$	−0.142732	+	0.0824064i	−0.00520490	+	0.00300505i
$753$		0			0
$754$	−6.27469	+	4.99841i	−0.228511	+	0.182031i
$755$	38.2436			1.39183
$756$		0			0
$757$	−26.1835			−0.951657			−0.475829	−	0.879538i	$-0.657852\pi$
$757$	−26.1835			−0.951657			−0.475829	+	0.879538i	$0.657852\pi$
$758$	−34.8070	+	60.2876i	−1.26425	+	2.18974i
$759$		0			0
$760$	8.71286	−	5.03037i	0.316049	−	0.182471i
$761$	6.00320	−	3.46595i	0.217616	−	0.125640i	−0.387230	−	0.921983i	$-0.626568\pi$
$761$	6.00320	−	3.46595i	0.217616	−	0.125640i	0.604846	+	0.796343i	$0.293235\pi$
$762$		0			0
$763$	17.6688	−	30.6033i	0.639655	−	1.10792i
$764$	29.8559			1.08015
$765$		0			0
$766$	57.1557			2.06512
$767$	21.9036	−	17.4484i	0.790893	−	0.630025i
$768$		0			0
$769$	33.4083	−	19.2883i	1.20473	−	0.695553i	0.243129	−	0.969994i	$-0.421826\pi$
$769$	33.4083	−	19.2883i	1.20473	−	0.695553i	0.961604	+	0.274441i	$0.0884927\pi$
$770$	−13.1170	−	22.7194i	−0.472705	−	0.818749i
$771$		0			0
$772$	31.9140	+	18.4255i	1.14861	+	0.663149i
$773$			34.7210i			1.24883i	0.781093	+	0.624415i	$0.214662\pi$
$773$			34.7210i			1.24883i	−0.781093	+	0.624415i	$0.785338\pi$
$774$		0			0
$775$			19.5147i			0.700988i
$776$	21.0680	−	36.4908i	0.756296	−	1.30994i
$777$		0			0
$778$	4.17627	−	2.41117i	0.149727	−	0.0864447i
$779$	−2.26638	−	3.92548i	−0.0812014	−	0.140645i
$780$		0			0
$781$	−2.22072	+	3.84640i	−0.0794637	+	0.137635i
$782$			108.148i			3.86738i
$783$		0			0
$784$	−0.121002			−0.00432150
$785$	−11.1099	−	6.41430i	−0.396529	−	0.228936i
$786$		0			0
$787$	31.0375	−	17.9195i	1.10637	−	0.638761i	0.168480	−	0.985705i	$-0.446114\pi$
$787$	31.0375	−	17.9195i	1.10637	−	0.638761i	0.937886	+	0.346944i	$0.112781\pi$
$788$	−30.6808	+	17.7136i	−1.09296	+	0.631020i
$789$		0			0
$790$	13.7187	−	23.7614i	0.488088	−	0.845394i
$791$		−	7.43207i		−	0.264254i
$792$		0			0
$793$	−10.7313	+	27.3000i	−0.381079	+	0.969451i
$794$	−32.8581	+	56.9119i	−1.16609	+	2.01973i
$795$		0			0
$796$	−2.22265	−	3.84975i	−0.0787798	−	0.136451i
$797$	−19.4271	−	33.6487i	−0.688144	−	1.19190i	−0.972438	−	0.233163i	$-0.925093\pi$
$797$	−19.4271	−	33.6487i	−0.688144	−	1.19190i	0.284294	−	0.958737i	$-0.408241\pi$
$798$		0			0
$799$	−6.83983	−	3.94898i	−0.241976	−	0.139705i
$800$			30.8664i			1.09129i
$801$		0			0
$802$	−25.9980			−0.918020
$803$	−6.79197	+	11.7640i	−0.239683	+	0.415144i
$804$		0			0
$805$	35.9745	+	62.3097i	1.26793	+	2.19613i
$806$	29.7378	−	4.46601i	1.04747	−	0.157309i
$807$		0			0
$808$	35.7196	+	20.6227i	1.25661	+	0.725505i
$809$	12.2765			0.431619			0.215809	−	0.976435i	$-0.430761\pi$
$809$	12.2765			0.431619			0.215809	+	0.976435i	$0.430761\pi$
$810$		0			0
$811$		−	13.8855i		−	0.487585i	−0.969827	−	0.243792i	$-0.921608\pi$
$811$		−	13.8855i		−	0.487585i	0.969827	−	0.243792i	$-0.0783915\pi$
$812$	−6.56798	−	3.79202i	−0.230491	−	0.133074i
$813$		0			0
$814$	12.3259	−	7.11634i	0.432021	−	0.249428i
$815$	8.33062	+	14.4291i	0.291809	+	0.505428i
$816$		0			0
$817$	8.48039	+	4.89616i	0.296691	+	0.171295i
$818$	7.66079			0.267853
$819$		0			0
$820$	−41.4102			−1.44611
$821$	−7.91360	−	4.56892i	−0.276187	−	0.159456i	0.355509	−	0.934673i	$-0.384307\pi$
$821$	−7.91360	−	4.56892i	−0.276187	−	0.159456i	−0.631696	+	0.775216i	$0.717641\pi$
$822$		0			0
$823$	−1.95741	−	3.39033i	−0.0682310	−	0.118180i	0.829892	−	0.557925i	$-0.188402\pi$
$823$	−1.95741	−	3.39033i	−0.0682310	−	0.118180i	−0.898123	+	0.439745i	$0.855069\pi$
$824$	15.6502	−	9.03564i	0.545200	−	0.314771i
$825$		0			0
$826$	37.2035	+	21.4794i	1.29448	+	0.747366i
$827$		−	18.1786i		−	0.632131i	−0.948737	−	0.316065i	$-0.897638\pi$
$827$		−	18.1786i		−	0.632131i	0.948737	−	0.316065i	$-0.102362\pi$
$828$		0			0
$829$	38.0468			1.32142			0.660711	−	0.750641i	$-0.270255\pi$
$829$	38.0468			1.32142			0.660711	+	0.750641i	$0.270255\pi$
$830$	−90.7735	−	52.4081i	−3.15080	−	1.81911i
$831$		0			0
$832$	46.2730	−	6.94926i	1.60423	−	0.240922i
$833$	−2.89925	−	5.02165i	−0.100453	−	0.173990i
$834$		0			0
$835$	−1.31212	+	2.27266i	−0.0454077	+	0.0786485i
$836$	5.35630			0.185251
$837$		0			0
$838$		−	4.71569i		−	0.162901i
$839$	24.7704	+	14.3012i	0.855171	+	0.493733i	0.862392	−	0.506241i	$-0.168965\pi$
$839$	24.7704	+	14.3012i	0.855171	+	0.493733i	−0.00722153	+	0.999974i	$0.502299\pi$
$840$		0			0
$841$	14.0251	+	24.2922i	0.483624	+	0.837661i
$842$	38.6995	+	67.0295i	1.33367	+	2.30999i
$843$		0			0
$844$	−14.7491	+	25.5462i	−0.507684	+	0.879335i
$845$	28.4681	−	30.6157i	0.979334	−	1.05321i
$846$		0			0
$847$			21.3798i			0.734620i
$848$	−0.0396012	+	0.0685914i	−0.00135991	+	0.00235544i
$849$		0			0
$850$	−54.1765	+	31.2788i	−1.85824	+	1.07286i
$851$	−33.8047	+	19.5171i	−1.15881	+	0.669039i
$852$		0			0
$853$	−26.0272	−	15.0268i	−0.891154	−	0.514508i	−0.0168345	−	0.999858i	$-0.505359\pi$
$853$	−26.0272	−	15.0268i	−0.891154	−	0.514508i	−0.874320	+	0.485350i	$0.838692\pi$
$854$	−44.9986			−1.53982
$855$		0			0
$856$		−	25.9412i		−	0.886650i
$857$	−0.668881	+	1.15854i	−0.0228485	+	0.0395748i	−0.877224	−	0.480082i	$-0.840607\pi$
$857$	−0.668881	+	1.15854i	−0.0228485	+	0.0395748i	0.854375	+	0.519657i	$0.173940\pi$
$858$		0			0
$859$	20.6362	+	35.7429i	0.704097	+	1.21953i	0.967017	+	0.254714i	$0.0819812\pi$
$859$	20.6362	+	35.7429i	0.704097	+	1.21953i	−0.262920	+	0.964818i	$0.584685\pi$
$860$	77.4749	−	44.7301i	2.64187	−	1.52529i
$861$		0			0
$862$	−34.9538	+	60.5417i	−1.19053	+	2.06206i
$863$		−	37.3326i		−	1.27082i	−0.772176	−	0.635408i	$-0.780832\pi$
$863$		−	37.3326i		−	1.27082i	0.772176	−	0.635408i	$-0.219168\pi$
$864$		0			0
$865$		−	1.68214i		−	0.0571944i
$866$	−17.0743	−	9.85788i	−0.580210	−	0.334984i
$867$		0			0
$868$	14.2144	+	24.6201i	0.482469	+	0.835661i
$869$	4.77347	−	2.75597i	0.161929	−	0.0934897i
$870$		0			0
$871$	−2.17988	+	1.73649i	−0.0738623	+	0.0588387i
$872$	40.3588			1.36672
$873$		0			0
$874$	−23.8371			−0.806301
$875$	−1.33129	+	2.30586i	−0.0450057	+	0.0779521i
$876$		0			0
$877$	−34.8042	+	20.0942i	−1.17526	+	0.678534i	−0.954912	−	0.296889i	$-0.904051\pi$
$877$	−34.8042	+	20.0942i	−1.17526	+	0.678534i	−0.220343	+	0.975422i	$0.570718\pi$
$878$	58.4542	−	33.7485i	1.97273	−	1.13896i
$879$		0			0
$880$	−0.253863	+	0.439704i	−0.00855773	+	0.0148224i
$881$	−13.8402			−0.466289			−0.233144	−	0.972442i	$-0.574901\pi$
$881$	−13.8402			−0.466289			−0.233144	+	0.972442i	$0.574901\pi$
$882$		0			0
$883$	−29.1280			−0.980235			−0.490118	−	0.871656i	$-0.663046\pi$
$883$	−29.1280			−0.980235			−0.490118	+	0.871656i	$0.663046\pi$
$884$	37.0153	+	46.4666i	1.24496	+	1.56284i
$885$		0			0
$886$	−61.8170	+	35.6901i	−2.07678	+	1.19903i
$887$	9.07561	+	15.7194i	0.304729	+	0.527806i	0.977201	−	0.212316i	$-0.0681008\pi$
$887$	9.07561	+	15.7194i	0.304729	+	0.527806i	−0.672472	+	0.740123i	$0.734767\pi$
$888$		0			0
$889$	−0.343873	−	0.198535i	−0.0115331	−	0.00665865i
$890$		−	60.2946i		−	2.02108i
$891$		0			0
$892$			20.4544i			0.684864i
$893$	0.870396	−	1.50757i	0.0291267	−	0.0504489i
$894$		0			0
$895$	39.4777	−	22.7924i	1.31959	−	0.761867i
$896$	21.8909	+	37.9162i	0.731324	+	1.26669i
$897$		0			0
$898$	12.3676	−	21.4213i	0.412712	−	0.714838i
$899$			3.56040i			0.118746i
$900$		0			0
$901$	−3.79544			−0.126444
$902$	−11.6904	−	6.74944i	−0.389247	−	0.224732i
$903$		0			0
$904$	7.35090	−	4.24404i	0.244487	−	0.141155i
$905$	−50.0625	+	28.9036i	−1.66413	+	0.960788i
$906$		0			0
$907$	−2.55936	+	4.43293i	−0.0849820	+	0.147193i	−0.905384	−	0.424595i	$-0.860417\pi$
$907$	−2.55936	+	4.43293i	−0.0849820	+	0.147193i	0.820402	+	0.571788i	$0.193750\pi$
$908$		−	32.7515i		−	1.08690i
$909$		0			0
$910$	59.6865	+	23.4620i	1.97859	+	0.777758i
$911$	21.1217	−	36.5839i	0.699794	−	1.21208i	−0.268744	−	0.963212i	$-0.586608\pi$
$911$	21.1217	−	36.5839i	0.699794	−	1.21208i	0.968538	−	0.248867i	$-0.0800582\pi$
$912$		0			0
$913$	−10.5284	−	18.2356i	−0.348438	−	0.603512i
$914$	−18.3129	−	31.7188i	−0.605736	−	1.04916i
$915$		0			0
$916$	−22.5797	−	13.0364i	−0.746056	−	0.430735i
$917$		−	15.8245i		−	0.522571i
$918$		0			0
$919$	37.2207			1.22780			0.613899	−	0.789384i	$-0.289600\pi$
$919$	37.2207			1.22780			0.613899	+	0.789384i	$0.289600\pi$
$920$	−41.0861	+	71.1633i	−1.35457	+	2.34618i
$921$		0			0
$922$	−29.2552	−	50.6715i	−0.963469	−	1.66878i
$923$	−1.61251	−	10.7372i	−0.0530764	−	0.353420i
$924$		0			0
$925$	−19.5541	−	11.2895i	−0.642933	−	0.371198i
$926$	74.3202			2.44231
$927$		0			0
$928$			5.63149i			0.184863i
$929$	−18.3982	−	10.6222i	−0.603624	−	0.348502i	0.166842	−	0.985984i	$-0.446643\pi$
$929$	−18.3982	−	10.6222i	−0.603624	−	0.348502i	−0.770466	+	0.637481i	$0.779976\pi$
$930$		0			0
$931$	1.10683	−	0.639026i	0.0362747	−	0.0209432i
$932$	−13.4550	−	23.3047i	−0.440733	−	0.763372i
$933$		0			0
$934$	32.0647	+	18.5126i	1.04919	+	0.605750i
$935$	−24.3306			−0.795697
$936$		0			0
$937$	−55.6976			−1.81956			−0.909781	−	0.415089i	$-0.863750\pi$
$937$	−55.6976			−1.81956			−0.909781	+	0.415089i	$0.863750\pi$
$938$	−3.70255	−	2.13767i	−0.120892	−	0.0697973i
$939$		0			0
$940$	−7.95173	−	13.7728i	−0.259357	−	0.449219i
$941$	−17.2655	+	9.96821i	−0.562838	+	0.324954i	−0.754284	−	0.656549i	$-0.772016\pi$
$941$	−17.2655	+	9.96821i	−0.562838	+	0.324954i	0.191446	+	0.981503i	$0.438682\pi$
$942$		0			0
$943$	32.0618	+	18.5109i	1.04408	+	0.602797i
$944$		−	0.831414i		−	0.0270602i
$945$		0			0
$946$	29.1622			0.948146
$947$	−28.2364	−	16.3023i	−0.917560	−	0.529754i	−0.0347045	−	0.999398i	$-0.511049\pi$
$947$	−28.2364	−	16.3023i	−0.917560	−	0.529754i	−0.882856	+	0.469644i	$0.844382\pi$
$948$		0			0
$949$	−4.93178	−	32.8392i	−0.160092	−	1.06601i
$950$	−6.89419	−	11.9411i	−0.223677	−	0.387420i
$951$		0			0
$952$	−17.1940	+	29.7808i	−0.557260	+	0.965203i
$953$	15.6146			0.505808			0.252904	−	0.967491i	$-0.418614\pi$
$953$	15.6146			0.505808			0.252904	+	0.967491i	$0.418614\pi$
$954$		0			0
$955$		−	29.8917i		−	0.967273i
$956$	−12.8304	−	7.40766i	−0.414966	−	0.239581i
$957$		0			0
$958$	11.6843	+	20.2378i	0.377502	+	0.653853i
$959$	16.8735	+	29.2258i	0.544875	+	0.943750i
$960$		0			0
$961$	−8.82691	+	15.2887i	−0.284739	+	0.493183i
$962$	−12.7288	+	32.3815i	−0.410392	+	1.04402i
$963$		0			0
$964$		−	25.8106i		−	0.831304i
$965$	18.4477	−	31.9523i	0.593851	−	1.02858i
$966$		0			0
$967$	3.47716	−	2.00754i	0.111818	−	0.0645581i	−0.443048	−	0.896498i	$-0.646103\pi$
$967$	3.47716	−	2.00754i	0.111818	−	0.0645581i	0.554866	+	0.831940i	$0.312770\pi$
$968$	−21.1464	+	12.2089i	−0.679670	+	0.392407i
$969$		0			0
$970$	−96.8226	−	55.9006i	−3.10879	−	1.79486i
$971$	27.3969			0.879209			0.439604	−	0.898192i	$-0.355119\pi$
$971$	27.3969			0.879209			0.439604	+	0.898192i	$0.355119\pi$
$972$		0			0
$973$		−	34.3583i		−	1.10148i
$974$	−18.3624	+	31.8045i	−0.588368	+	1.01908i
$975$		0			0
$976$	0.435445	+	0.754212i	0.0139382	+	0.0241417i
$977$	−33.3866	+	19.2758i	−1.06813	+	0.616687i	−0.927671	−	0.373399i	$-0.878192\pi$
$977$	−33.3866	+	19.2758i	−1.06813	+	0.616687i	−0.140462	+	0.990086i	$0.544859\pi$
$978$		0			0
$979$	6.05634	−	10.4899i	0.193561	−	0.335258i
$980$		−	11.6760i		−	0.372976i
$981$		0			0
$982$		−	10.0882i		−	0.321926i
$983$	40.2933	+	23.2633i	1.28516	+	0.741986i	0.977786	−	0.209604i	$-0.0672176\pi$
$983$	40.2933	+	23.2633i	1.28516	+	0.741986i	0.307370	+	0.951590i	$0.400551\pi$
$984$		0			0
$985$	17.7349	+	30.7177i	0.565079	+	0.978746i
$986$	−9.88435	+	5.70673i	−0.314782	+	0.181739i
$987$		0			0
$988$	−10.2417	+	8.15856i	−0.325833	+	0.259558i
$989$	−79.9798			−2.54321
$990$		0			0
$991$	41.1031			1.30568			0.652841	−	0.757495i	$-0.273577\pi$
$991$	41.1031			1.30568			0.652841	+	0.757495i	$0.273577\pi$
$992$	10.5548	−	18.2815i	0.335116	−	0.580439i
$993$		0			0
$994$	14.4245	−	8.32800i	0.457518	−	0.264148i
$995$	−3.85437	+	2.22532i	−0.122192	+	0.0705474i
$996$		0			0
$997$	27.8886	−	48.3045i	0.883241	−	1.52982i	0.0355252	−	0.999369i	$-0.488690\pi$
$997$	27.8886	−	48.3045i	0.883241	−	1.52982i	0.847716	−	0.530450i	$-0.177977\pi$
$998$	16.8548			0.533529
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.t.c.181.2		20
3.2	odd	2		117.2.t.c.25.9	yes	20
9.2	odd	6		1053.2.b.j.649.2		10
9.4	even	3	inner	351.2.t.c.64.9		20
9.5	odd	6		117.2.t.c.103.2	yes	20
9.7	even	3		1053.2.b.i.649.9		10
13.12	even	2	inner	351.2.t.c.181.9		20
39.38	odd	2		117.2.t.c.25.2	✓	20
117.25	even	6		1053.2.b.i.649.2		10
117.38	odd	6		1053.2.b.j.649.9		10
117.77	odd	6		117.2.t.c.103.9	yes	20
117.103	even	6	inner	351.2.t.c.64.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.t.c.25.2	✓	20	39.38	odd	2
117.2.t.c.25.9	yes	20	3.2	odd	2
117.2.t.c.103.2	yes	20	9.5	odd	6
117.2.t.c.103.9	yes	20	117.77	odd	6
351.2.t.c.64.2		20	117.103	even	6	inner
351.2.t.c.64.9		20	9.4	even	3	inner
351.2.t.c.181.2		20	1.1	even	1	trivial
351.2.t.c.181.9		20	13.12	even	2	inner
1053.2.b.i.649.2		10	117.25	even	6
1053.2.b.i.649.9		10	9.7	even	3
1053.2.b.j.649.2		10	9.2	odd	6
1053.2.b.j.649.9		10	117.38	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.97712 - 1.14149i) q^{2} +(1.60600 + 2.78168i) q^{4} +(2.78501 - 1.60793i) q^{5} +(-2.09815 - 1.21137i) q^{7} -2.76698i q^{8} -7.34174 q^{10} +(-1.27730 - 0.737448i) q^{11} +(3.56557 - 0.535475i) q^{13} +(2.76553 + 4.79003i) q^{14} +(0.0535232 - 0.0927049i) q^{16} +5.12974 q^{17} +1.13065i q^{19} +(8.94547 + 5.16467i) q^{20} +(1.68358 + 2.91604i) q^{22} +(-4.61735 - 7.99748i) q^{23} +(2.67087 - 4.62608i) q^{25} +(-7.66079 - 3.01136i) q^{26} -7.78182i q^{28} +(0.487293 - 0.844016i) q^{29} +(-3.16380 + 1.82662i) q^{31} +(-5.00419 + 2.88917i) q^{32} +(-10.1421 - 5.85555i) q^{34} -7.79116 q^{35} -4.22691i q^{37} +(1.29063 - 2.23543i) q^{38} +(-4.44910 - 7.70607i) q^{40} +(-3.47188 + 2.00449i) q^{41} +(4.33040 - 7.50047i) q^{43} -4.73737i q^{44} +21.0826i q^{46} +(-1.33337 - 0.769820i) q^{47} +(-0.565185 - 0.978929i) q^{49} +(-10.5613 + 6.09755i) q^{50} +(7.21582 + 9.05828i) q^{52} -0.739889 q^{53} -4.74305 q^{55} +(-3.35182 + 5.80553i) q^{56} +(-1.92687 + 1.11248i) q^{58} +(6.72630 - 3.88343i) q^{59} +(-4.06781 + 7.04566i) q^{61} +8.34028 q^{62} +12.9777 q^{64} +(9.06915 - 7.22448i) q^{65} +(-0.669411 + 0.386485i) q^{67} +(8.23837 + 14.2693i) q^{68} +(15.4041 + 8.89354i) q^{70} -3.01136i q^{71} -9.21010i q^{73} +(-4.82498 + 8.35711i) q^{74} +(-3.14510 + 1.81582i) q^{76} +(1.78664 + 3.09455i) q^{77} +(-1.86858 + 3.23648i) q^{79} -0.344246i q^{80} +9.15243 q^{82} +(12.3640 + 7.13838i) q^{83} +(14.2864 - 8.24826i) q^{85} +(-17.1234 + 9.88621i) q^{86} +(-2.04050 + 3.53425i) q^{88} +8.21257i q^{89} +(-8.12974 - 3.19570i) q^{91} +(14.8309 - 25.6879i) q^{92} +(1.75748 + 3.04405i) q^{94} +(1.81800 + 3.14887i) q^{95} +(13.1880 + 7.61407i) q^{97} +2.58061i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) \) 20 * q + 12 * q^4 - 16 * q^10 - 4 * q^13 + 18 * q^14 + 4 * q^16 + 12 * q^17 - 10 * q^22 - 24 * q^23 - 12 * q^25 + 12 * q^26 - 12 * q^29 + 12 * q^35 - 12 * q^38 - 8 * q^40 + 4 * q^43 - 10 * q^49 - 108 * q^53 + 20 * q^55 - 36 * q^56 - 2 * q^61 + 72 * q^62 + 8 * q^64 + 24 * q^65 - 24 * q^68 + 42 * q^74 + 6 * q^77 - 14 * q^79 - 4 * q^82 + 22 * q^88 - 72 * q^91 + 84 * q^92 + 20 * q^94 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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