LMFDB - Embedded newform 351.2.t.c.181.9

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			181.9
Root			$1.23798 - 1.21137i$ of defining polynomial
Character	$\chi$	$=$	351.181
Dual form			351.2.t.c.64.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.97712 + 1.14149i) q^{2} +(1.60600 + 2.78168i) q^{4} +(-2.78501 + 1.60793i) q^{5} +(2.09815 + 1.21137i) q^{7} +2.76698i q^{8} -7.34174 q^{10} +(1.27730 + 0.737448i) q^{11} +(-2.24652 + 2.82013i) q^{13} +(2.76553 + 4.79003i) q^{14} +(0.0535232 - 0.0927049i) q^{16} +5.12974 q^{17} -1.13065i q^{19} +(-8.94547 - 5.16467i) q^{20} +(1.68358 + 2.91604i) q^{22} +(-4.61735 - 7.99748i) q^{23} +(2.67087 - 4.62608i) q^{25} +(-7.66079 + 3.01136i) q^{26} +7.78182i q^{28} +(0.487293 - 0.844016i) q^{29} +(3.16380 - 1.82662i) q^{31} +(5.00419 - 2.88917i) q^{32} +(10.1421 + 5.85555i) q^{34} -7.79116 q^{35} +4.22691i q^{37} +(1.29063 - 2.23543i) q^{38} +(-4.44910 - 7.70607i) q^{40} +(3.47188 - 2.00449i) q^{41} +(4.33040 - 7.50047i) q^{43} +4.73737i q^{44} -21.0826i q^{46} +(1.33337 + 0.769820i) q^{47} +(-0.565185 - 0.978929i) q^{49} +(10.5613 - 6.09755i) q^{50} +(-11.4526 - 1.71995i) q^{52} -0.739889 q^{53} -4.74305 q^{55} +(-3.35182 + 5.80553i) q^{56} +(1.92687 - 1.11248i) q^{58} +(-6.72630 + 3.88343i) q^{59} +(-4.06781 + 7.04566i) q^{61} +8.34028 q^{62} +12.9777 q^{64} +(1.72201 - 11.4664i) q^{65} +(0.669411 - 0.386485i) q^{67} +(8.23837 + 14.2693i) q^{68} +(-15.4041 - 8.89354i) q^{70} +3.01136i q^{71} +9.21010i q^{73} +(-4.82498 + 8.35711i) q^{74} +(3.14510 - 1.81582i) q^{76} +(1.78664 + 3.09455i) q^{77} +(-1.86858 + 3.23648i) q^{79} +0.344246i q^{80} +9.15243 q^{82} +(-12.3640 - 7.13838i) q^{83} +(-14.2864 + 8.24826i) q^{85} +(17.1234 - 9.88621i) q^{86} +(-2.04050 + 3.53425i) q^{88} -8.21257i q^{89} +(-8.12974 + 3.19570i) q^{91} +(14.8309 - 25.6879i) q^{92} +(1.75748 + 3.04405i) q^{94} +(1.81800 + 3.14887i) q^{95} +(-13.1880 - 7.61407i) q^{97} -2.58061i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.994187	−	0.107670i	$-0.0343391\pi$
$2$	1.97712	+	1.14149i	1.39803	+	0.807156i	0.403848	+	0.914826i	$0.367672\pi$
$3$		0			0
$3$		0			0
$4$	1.60600	+	2.78168i	0.803001	+	1.39084i
$5$	−2.78501	+	1.60793i	−1.24550	+	0.719088i	−0.970208	−	0.242274i	$-0.922107\pi$
$5$	−2.78501	+	1.60793i	−1.24550	+	0.719088i	−0.275289	+	0.961362i	$0.588773\pi$
$6$		0			0
$7$	2.09815	+	1.21137i	0.793025	+	0.457853i	0.841026	−	0.540994i	$-0.181952\pi$
$7$	2.09815	+	1.21137i	0.793025	+	0.457853i	−0.0480013	+	0.998847i	$0.515285\pi$
$8$			2.76698i			0.978274i
$9$		0			0
$10$	−7.34174			−2.32166
$11$	1.27730	+	0.737448i	0.385119	+	0.222349i	0.680043	−	0.733172i	$-0.261961\pi$
$11$	1.27730	+	0.737448i	0.385119	+	0.222349i	−0.294924	+	0.955521i	$0.595294\pi$
$12$		0			0
$13$	−2.24652	+	2.82013i	−0.623072	+	0.782164i
$13$	−2.24652	+	2.82013i	−0.623072	+	0.782164i
$14$	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	$-0.958600\pi$
$19$		−	1.13065i		−	0.259389i	0.991554	−	0.129694i	$-0.0413996\pi$
$20$	−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	−0.188209	−	0.982129i	$-0.560268\pi$
$31$	3.16380	−	1.82662i	0.568235	−	0.328071i	0.756444	+	0.654058i	$0.226935\pi$
$32$	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	$0.112952\pi$
$37$			4.22691i			0.694900i	−0.937698	+	0.347450i	$0.887048\pi$
$38$	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	−0.203760	−	0.979021i	$-0.565316\pi$
$41$	3.47188	−	2.00449i	0.542217	−	0.313049i	0.745977	+	0.665972i	$0.231983\pi$
$42$		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	0.594084	−	0.804403i	$-0.297515\pi$
$47$	1.33337	+	0.769820i	0.194492	+	0.112290i	−0.399592	+	0.916693i	$0.630848\pi$
$48$		0			0
$49$	−0.565185	−	0.978929i	−0.0807407	−	0.139847i
$50$	10.5613	−	6.09755i	1.49359	−	0.862324i
$51$		0			0
$52$	−11.4526	−	1.71995i	−1.58819	−	0.238514i
$53$	−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	−0.869235	−	0.494400i	$-0.835388\pi$
$59$	−6.72630	+	3.88343i	−0.875689	+	0.505580i	−0.00645471	+	0.999979i	$0.502055\pi$
$60$		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
$65$	1.72201	−	11.4664i	0.213589	−	1.42223i
$66$		0			0
$67$	0.669411	−	0.386485i	0.0817816	−	0.0472166i	−0.458552	−	0.888668i	$-0.651632\pi$
$67$	0.669411	−	0.386485i	0.0817816	−	0.0472166i	0.540333	+	0.841451i	$0.318298\pi$
$68$	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	$0.0571864\pi$
$71$			3.01136i			0.357383i	−0.983905	+	0.178692i	$0.942814\pi$
$72$		0			0
$73$			9.21010i			1.07796i	0.842318	+	0.538980i	$0.181190\pi$
$73$			9.21010i			1.07796i	−0.842318	+	0.538980i	$0.818810\pi$
$74$	−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	−0.367893	−	0.929868i	$-0.619921\pi$
$83$	−12.3640	−	7.13838i	−1.35713	−	0.783539i	−0.989236	+	0.146329i	$0.953254\pi$
$84$		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	$-0.856655\pi$
$89$		−	8.21257i		−	0.870531i	0.900302	−	0.435265i	$-0.143345\pi$
$90$		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	−0.352370	−	0.935861i	$-0.614624\pi$
$97$	−13.1880	−	7.61407i	−1.33903	−	0.773092i	−0.986664	+	0.162769i	$0.947957\pi$
$98$		−	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	$0.729058\pi$
$104$	−7.80325	−	6.21607i	−0.765171	−	0.609535i
$105$		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	$-0.753835\pi$
$109$		−	14.5859i		−	1.39707i	0.715574	−	0.698537i	$-0.246165\pi$
$110$	−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
$130$	16.4934	−	20.7047i	1.44656	−	1.81592i
$131$	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	0.917164	−	0.398511i	$-0.130473\pi$
$137$	12.0632	+	6.96467i	1.03063	+	0.595032i	0.113462	+	0.993542i	$0.463806\pi$
$138$		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	−0.983406	−	0.181419i	$-0.941931\pi$
$149$	−16.0882	+	9.28851i	−1.31799	+	0.760945i	−0.334589	+	0.942364i	$0.608598\pi$
$150$		0			0
$151$	−10.2989	−	5.94609i	−0.838115	−	0.483886i	0.0185081	−	0.999829i	$-0.494108\pi$
$151$	−10.2989	−	5.94609i	−0.838115	−	0.483886i	−0.856623	+	0.515943i	$0.827442\pi$
$152$	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	$-0.934963\pi$
$163$		−	5.18096i		−	0.405804i	0.979199	−	0.202902i	$-0.0650373\pi$
$164$	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	−0.472408	−	0.881380i	$-0.656615\pi$
$167$	0.706703	−	0.408015i	0.0546863	−	0.0315732i	0.527094	+	0.849807i	$0.323282\pi$
$168$		0			0
$169$	−2.90631	−	12.6710i	−0.223562	−	0.974690i
$170$	−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	$0.732875\pi$
$182$	−19.7213	−	2.96174i	−1.46184	−	0.219539i
$183$		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	−0.812983	−	0.582288i	$-0.802158\pi$
$193$	−9.93585	+	5.73646i	−0.715198	+	0.412920i	0.0977848	+	0.995208i	$0.468824\pi$
$194$	−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	$-0.871467\pi$
$197$		−	11.0296i		−	0.785828i	0.919575	−	0.392914i	$-0.128533\pi$
$198$		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
$221$	−11.5241	+	14.4666i	−0.775192	+	0.973126i
$222$		0			0
$223$	−5.51495	−	3.18406i	−0.369308	−	0.213220i	0.303848	−	0.952721i	$-0.401729\pi$
$223$	−5.51495	−	3.18406i	−0.369308	−	0.213220i	−0.673156	+	0.739500i	$0.735062\pi$
$224$	13.9994			0.935372
$225$		0			0
$226$			7.00336i			0.465857i
$227$	8.83052	+	5.09830i	0.586102	+	0.338386i	0.763555	−	0.645743i	$-0.223452\pi$
$227$	8.83052	+	5.09830i	0.586102	+	0.338386i	−0.177453	+	0.984129i	$0.556786\pi$
$228$		0			0
$229$	7.02980	−	4.05866i	0.464542	−	0.268204i	−0.249410	−	0.968398i	$-0.580237\pi$
$229$	7.02980	−	4.05866i	0.464542	−	0.268204i	0.713952	+	0.700194i	$0.246903\pi$
$230$	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	−0.365213	−	0.930924i	$-0.619004\pi$
$239$	3.99453	−	2.30624i	0.258385	−	0.149178i	0.623598	+	0.781746i	$0.285670\pi$
$240$		0			0
$241$	6.95910	+	4.01784i	0.448275	+	0.258812i	0.707101	−	0.707112i	$-0.250002\pi$
$241$	6.95910	+	4.01784i	0.448275	+	0.258812i	−0.258826	+	0.965924i	$0.583336\pi$
$242$		−	20.1466i		−	1.29507i
$243$		0			0
$244$	−26.1316			−1.67291
$245$	3.14810	+	1.81756i	0.201125	+	0.116119i
$246$		0			0
$247$	3.18858	+	2.54002i	0.202885	+	0.161618i
$248$	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	$-0.867860\pi$
$271$		−	13.2786i		−	0.806620i	0.915064	−	0.403310i	$-0.132140\pi$
$272$	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	0.173288	−	0.984871i	$-0.444561\pi$
$281$	−9.94035	−	5.73906i	−0.592991	−	0.342364i	−0.766279	+	0.642507i	$0.777894\pi$
$282$		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
$286$	−12.0058	−	1.80303i	−0.709919	−	0.106615i
$287$	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	−0.0250809	−	0.999685i	$-0.507984\pi$
$293$	14.1753	−	8.18413i	0.828132	−	0.478122i	0.853213	+	0.521563i	$0.174651\pi$
$294$		0			0
$295$	12.4886	−	21.6308i	0.727112	−	1.25940i
$296$	−11.6958			−0.679803
$297$		0			0
$298$	−42.4110			−2.45680
$299$	32.9269	+	4.94495i	1.90421	+	0.285974i
$300$		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	$-0.842105\pi$
$307$		−	16.6786i		−	0.951898i	0.879473	−	0.475949i	$-0.157895\pi$
$308$	−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	0.327341	−	0.944906i	$-0.393847\pi$
$317$	−5.82742	−	3.36446i	−0.327301	−	0.188967i	−0.654642	+	0.755939i	$0.727181\pi$
$318$		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	0.506206	−	0.862413i	$-0.331048\pi$
$331$	0.226288	+	0.130648i	0.0124379	+	0.00718104i	−0.493768	+	0.869594i	$0.664381\pi$
$332$		−	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	$0.884602\pi$
$338$	8.71766	−	28.3695i	0.474178	−	1.54310i
$339$		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	0.140942	−	0.990018i	$-0.454987\pi$
$349$	−12.0677	−	6.96727i	−0.645967	−	0.372949i	−0.786909	+	0.617069i	$0.788320\pi$
$350$	29.5454			1.57927
$351$		0			0
$352$	8.52245			0.454248
$353$	13.5867	+	7.84426i	0.723145	+	0.417508i	0.815909	−	0.578180i	$-0.196237\pi$
$353$	13.5867	+	7.84426i	0.723145	+	0.417508i	−0.0927643	+	0.995688i	$0.529570\pi$
$354$		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	$0.0494629\pi$
$359$			5.86486i			0.309535i	−0.987951	+	0.154768i	$0.950537\pi$
$360$		0			0
$361$	17.7216			0.932718
$362$	−35.5400	−	20.5190i	−1.86794	−	1.07846i
$363$		0			0
$364$	−21.9458	−	17.4820i	−1.15027	−	0.916306i
$365$	−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	$0.286389\pi$
$379$			30.4926i			1.56630i	−0.621832	+	0.783150i	$0.713611\pi$
$380$	−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	0.169592	−	0.985514i	$-0.445755\pi$
$383$	21.6814	−	12.5178i	1.10787	−	0.639628i	0.938276	+	0.345886i	$0.112422\pi$
$384$		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	$0.256936\pi$
$397$			28.7853i			1.44469i	−0.691533	+	0.722345i	$0.743064\pi$
$398$	−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	−0.725606	−	0.688110i	$-0.758440\pi$
$401$	−9.86207	+	5.69387i	−0.492488	+	0.284338i	0.233118	+	0.972448i	$0.425107\pi$
$402$		0			0
$403$	−1.95622	+	13.0259i	−0.0974462	+	0.648865i
$404$	−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	−0.426429	−	0.904521i	$-0.640229\pi$
$409$	2.90604	−	1.67780i	0.143695	−	0.0829621i	0.570124	+	0.821559i	$0.306895\pi$
$410$	−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
$416$	−3.09416	+	20.6031i	−0.151703	+	1.01015i
$417$		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	0.997193	−	0.0748758i	$-0.0238560\pi$
$421$	29.3605	+	16.9513i	1.43094	+	0.826156i	0.433752	+	0.901032i	$0.357189\pi$
$422$			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	$0.263987\pi$
$431$			30.6212i			1.47497i	−0.675364	+	0.737485i	$0.736013\pi$
$432$		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	$-0.917708\pi$
$449$		−	10.8346i		−	0.511316i	0.966767	−	0.255658i	$-0.0822922\pi$
$450$		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
$455$	17.5030	−	21.9721i	0.820553	−	1.03007i
$456$		0			0
$457$	−13.8936	−	8.02147i	−0.649915	−	0.375229i	0.138509	−	0.990361i	$-0.455769\pi$
$457$	−13.8936	−	8.02147i	−0.649915	−	0.375229i	−0.788424	+	0.615133i	$0.789102\pi$
$458$	18.5317			0.865929
$459$		0			0
$460$			95.3883i			4.44750i
$461$	−22.1953	−	12.8145i	−1.03374	−	0.596830i	−0.115686	−	0.993286i	$-0.536907\pi$
$461$	−22.1953	−	12.8145i	−1.03374	−	0.596830i	−0.918054	+	0.396456i	$0.870240\pi$
$462$		0			0
$463$	28.1926	−	16.2770i	1.31022	−	0.756457i	0.328090	−	0.944647i	$-0.393595\pi$
$463$	28.1926	−	16.2770i	1.31022	−	0.756457i	0.982133	+	0.188189i	$0.0602619\pi$
$464$	−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	0.688654	−	0.725090i	$-0.258202\pi$
$479$	8.86463	+	5.11800i	0.405035	+	0.233847i	−0.283619	+	0.958937i	$0.591535\pi$
$480$		0			0
$481$	−11.9205	−	9.49584i	−0.543526	−	0.432973i
$482$	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	$0.118750\pi$
$487$			16.0863i			0.728940i	−0.931215	+	0.364470i	$0.881250\pi$
$488$	−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	−0.350015	−	0.936744i	$-0.613824\pi$
$499$	6.39369	−	3.69140i	0.286221	−	0.165250i	0.636236	+	0.771494i	$0.280490\pi$
$500$	−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	−0.916747	−	0.399467i	$-0.869195\pi$
$509$	−23.2192	+	13.4056i	−1.02917	+	0.594193i	−0.112425	+	0.993660i	$0.535862\pi$
$510$		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
$520$	31.7272	+	4.76477i	1.39133	+	0.208949i
$521$	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
$533$	−2.14671	+	14.2943i	−0.0929843	+	0.619155i
$534$		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	$0.375912\pi$
$541$			43.0286i			1.84994i	−0.380036	+	0.924972i	$0.624088\pi$
$542$	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	$0.208430\pi$
$557$			28.7460i			1.21801i	−0.793168	+	0.609003i	$0.791570\pi$
$558$		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	$-0.393758\pi$
$572$	−13.3600	−	10.6426i	−0.558610	−	0.444989i
$573$		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	$-0.609145\pi$
$577$		−	45.2450i		−	1.88357i	0.336210	−	0.941787i	$-0.390855\pi$
$578$	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	−0.118112	−	0.993000i	$-0.537684\pi$
$587$	−25.1277	−	14.5075i	−1.03713	−	0.598788i	−0.919020	+	0.394212i	$0.871018\pi$
$588$		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	$-0.822677\pi$
$593$		−	25.7497i		−	1.05741i	0.848805	−	0.528707i	$-0.177323\pi$
$594$		0			0
$595$	−39.9666			−1.63847
$596$	−51.6753	−	29.8347i	−2.11670	−	1.22208i
$597$		0			0
$598$	59.4559	+	47.3625i	2.43133	+	1.93680i
$599$	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	$0.0247584\pi$
$613$			3.84764i			0.155405i	−0.996977	+	0.0777023i	$0.975242\pi$
$614$	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	−0.959767	−	0.280796i	$-0.909401\pi$
$617$	−29.7198	+	17.1587i	−1.19647	+	0.690785i	−0.236707	+	0.971581i	$0.576068\pi$
$618$		0			0
$619$	−36.7880	−	21.2396i	−1.47864	−	0.853691i	−0.478928	−	0.877854i	$-0.658975\pi$
$619$	−36.7880	−	21.2396i	−1.47864	−	0.853691i	−0.999708	+	0.0241630i	$0.992308\pi$
$620$	−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	$0.116252\pi$
$631$			17.9430i			0.714300i	−0.934047	+	0.357150i	$0.883748\pi$
$632$	−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
$637$	4.03041	+	0.605285i	0.159691	+	0.0239823i
$638$	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	$-0.223674\pi$
$643$	43.2179	−	24.9519i	1.70435	−	0.984006i	0.941242	−	0.337732i	$-0.109660\pi$
$644$	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
$650$	−6.53017	+	43.4824i	−0.256134	+	1.70552i
$651$		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	−0.741735	−	0.670693i	$-0.765997\pi$
$661$	−13.6716	+	7.89332i	−0.531765	+	0.307015i	0.209970	+	0.977708i	$0.432663\pi$
$662$	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	$-0.971424\pi$
$683$		−	4.68607i		−	0.179307i	0.995973	−	0.0896537i	$-0.0285760\pi$
$684$		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
$689$	1.66217	−	2.08659i	0.0633238	−	0.0794926i
$690$		0			0
$691$	37.3398	+	21.5581i	1.42047	+	0.820110i	0.996339	−	0.0854897i	$-0.0272455\pi$
$691$	37.3398	+	21.5581i	1.42047	+	0.820110i	0.424133	+	0.905600i	$0.360579\pi$
$692$	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	0.838335	−	0.545156i	$-0.183529\pi$
$709$	20.9125	+	12.0738i	0.785384	+	0.453442i	−0.0529511	+	0.998597i	$0.516863\pi$
$710$		−	22.1087i		−	0.829723i
$711$		0			0
$712$	22.7240			0.851618
$713$	−29.2167	−	16.8683i	−1.09418	−	0.631722i
$714$		0			0
$715$	10.6554	−	13.3760i	0.398488	−	0.500236i
$716$	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	−0.983638	−	0.180157i	$-0.942340\pi$
$733$	−35.7224	+	20.6243i	−1.31944	+	0.761777i	−0.335799	+	0.941934i	$0.609006\pi$
$734$	−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	$-0.925148\pi$
$739$		−	12.6677i		−	0.465988i	0.972478	−	0.232994i	$-0.0748523\pi$
$740$	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	−0.677726	−	0.735314i	$-0.737035\pi$
$743$	−10.3523	+	5.97690i	−0.379789	+	0.219271i	0.297938	+	0.954585i	$0.403701\pi$
$744$		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
$754$	−1.19141	+	7.93324i	−0.0433886	+	0.288912i
$755$	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	−0.604846	−	0.796343i	$-0.706765\pi$
$761$	−6.00320	+	3.46595i	−0.217616	+	0.125640i	0.387230	+	0.921983i	$0.373432\pi$
$762$		0			0
$763$	17.6688	−	30.6033i	0.639655	−	1.10792i
$764$	29.8559			1.08015
$765$		0			0
$766$	57.1557			2.06512
$767$	4.15896	−	27.6933i	0.150171	−	0.999946i
$768$		0			0
$769$	−33.4083	+	19.2883i	−1.20473	+	0.695553i	−0.961604	−	0.274441i	$-0.911507\pi$
$769$	−33.4083	+	19.2883i	−1.20473	+	0.695553i	−0.243129	+	0.969994i	$0.578174\pi$
$770$	−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	$-0.785338\pi$
$773$		−	34.7210i		−	1.24883i	0.781093	−	0.624415i	$-0.214662\pi$
$774$		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	−0.937886	−	0.346944i	$-0.887219\pi$
$787$	−31.0375	+	17.9195i	−1.10637	+	0.638761i	−0.168480	+	0.985705i	$0.553886\pi$
$788$	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
$806$	−18.7366	+	23.5207i	−0.659968	+	0.828482i
$807$		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	$0.0783915\pi$
$811$			13.8855i			0.487585i	−0.969827	+	0.243792i	$0.921608\pi$
$812$	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	0.631696	−	0.775216i	$-0.282359\pi$
$821$	7.91360	+	4.56892i	0.276187	+	0.159456i	−0.355509	+	0.934673i	$0.615693\pi$
$822$		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	$0.102362\pi$
$827$			18.1786i			0.632131i	−0.948737	+	0.316065i	$0.897638\pi$
$828$		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
$832$	−29.1548	+	36.5990i	−1.01076	+	1.26884i
$833$	−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	0.00722153	−	0.999974i	$-0.497701\pi$
$839$	−24.7704	−	14.3012i	−0.855171	−	0.493733i	−0.862392	+	0.506241i	$0.831035\pi$
$840$		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	0.874320	−	0.485350i	$-0.161308\pi$
$853$	26.0272	+	15.0268i	0.891154	+	0.514508i	0.0168345	+	0.999858i	$0.494641\pi$
$854$	−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	$0.219168\pi$
$863$			37.3326i			1.27082i	−0.772176	+	0.635408i	$0.780832\pi$
$864$		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
$871$	−0.413906	+	2.75607i	−0.0140247	+	0.0933860i
$872$	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	0.220343	−	0.975422i	$-0.429282\pi$
$877$	34.8042	−	20.0942i	1.17526	−	0.678534i	0.954912	+	0.296889i	$0.0959490\pi$
$878$	−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	$0.663046\pi$
$884$	−58.7489	−	8.82288i	−1.97594	−	0.296746i
$885$		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
$923$	−8.49245	−	6.76508i	−0.279532	−	0.222675i
$924$		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	0.770466	−	0.637481i	$-0.220024\pi$
$929$	18.3982	+	10.6222i	0.603624	+	0.348502i	−0.166842	+	0.985984i	$0.553357\pi$
$930$		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	−0.191446	−	0.981503i	$-0.561318\pi$
$941$	17.2655	−	9.96821i	0.562838	−	0.324954i	0.754284	+	0.656549i	$0.227984\pi$
$942$		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	0.882856	−	0.469644i	$-0.155618\pi$
$947$	28.2364	+	16.3023i	0.917560	+	0.529754i	0.0347045	+	0.999398i	$0.488951\pi$
$948$		0			0
$949$	−25.9737	−	20.6907i	−0.843143	−	0.671647i
$950$	−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	−0.554866	−	0.831940i	$-0.687230\pi$
$967$	−3.47716	+	2.00754i	−0.111818	+	0.0645581i	0.443048	+	0.896498i	$0.353897\pi$
$968$	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	0.140462	−	0.990086i	$-0.455141\pi$
$977$	33.3866	−	19.2758i	1.06813	−	0.616687i	0.927671	+	0.373399i	$0.121808\pi$
$978$		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	−0.307370	−	0.951590i	$-0.599449\pi$
$983$	−40.2933	−	23.2633i	−1.28516	−	0.741986i	−0.977786	+	0.209604i	$0.932782\pi$
$984$		0			0
$985$	17.7349	+	30.7177i	0.565079	+	0.978746i
$986$	9.88435	−	5.70673i	0.314782	−	0.181739i
$987$		0			0
$988$	−1.94466	+	12.9489i	−0.0618677	+	0.411959i
$989$	−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.181.9		20
3.2	odd	2		117.2.t.c.25.2	✓	20
9.2	odd	6		1053.2.b.j.649.9		10
9.4	even	3	inner	351.2.t.c.64.2		20
9.5	odd	6		117.2.t.c.103.9	yes	20
9.7	even	3		1053.2.b.i.649.2		10
13.12	even	2	inner	351.2.t.c.181.2		20
39.38	odd	2		117.2.t.c.25.9	yes	20
117.25	even	6		1053.2.b.i.649.9		10
117.38	odd	6		1053.2.b.j.649.2		10
117.77	odd	6		117.2.t.c.103.2	yes	20
117.103	even	6	inner	351.2.t.c.64.9		20

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

\(f(q)\)	\(=\)	\(q+(1.97712 + 1.14149i) q^{2} +(1.60600 + 2.78168i) q^{4} +(-2.78501 + 1.60793i) q^{5} +(2.09815 + 1.21137i) q^{7} +2.76698i q^{8} -7.34174 q^{10} +(1.27730 + 0.737448i) q^{11} +(-2.24652 + 2.82013i) q^{13} +(2.76553 + 4.79003i) q^{14} +(0.0535232 - 0.0927049i) q^{16} +5.12974 q^{17} -1.13065i q^{19} +(-8.94547 - 5.16467i) q^{20} +(1.68358 + 2.91604i) q^{22} +(-4.61735 - 7.99748i) q^{23} +(2.67087 - 4.62608i) q^{25} +(-7.66079 + 3.01136i) q^{26} +7.78182i q^{28} +(0.487293 - 0.844016i) q^{29} +(3.16380 - 1.82662i) q^{31} +(5.00419 - 2.88917i) q^{32} +(10.1421 + 5.85555i) q^{34} -7.79116 q^{35} +4.22691i q^{37} +(1.29063 - 2.23543i) q^{38} +(-4.44910 - 7.70607i) q^{40} +(3.47188 - 2.00449i) q^{41} +(4.33040 - 7.50047i) q^{43} +4.73737i q^{44} -21.0826i q^{46} +(1.33337 + 0.769820i) q^{47} +(-0.565185 - 0.978929i) q^{49} +(10.5613 - 6.09755i) q^{50} +(-11.4526 - 1.71995i) q^{52} -0.739889 q^{53} -4.74305 q^{55} +(-3.35182 + 5.80553i) q^{56} +(1.92687 - 1.11248i) q^{58} +(-6.72630 + 3.88343i) q^{59} +(-4.06781 + 7.04566i) q^{61} +8.34028 q^{62} +12.9777 q^{64} +(1.72201 - 11.4664i) q^{65} +(0.669411 - 0.386485i) q^{67} +(8.23837 + 14.2693i) q^{68} +(-15.4041 - 8.89354i) q^{70} +3.01136i q^{71} +9.21010i q^{73} +(-4.82498 + 8.35711i) q^{74} +(3.14510 - 1.81582i) q^{76} +(1.78664 + 3.09455i) q^{77} +(-1.86858 + 3.23648i) q^{79} +0.344246i q^{80} +9.15243 q^{82} +(-12.3640 - 7.13838i) q^{83} +(-14.2864 + 8.24826i) q^{85} +(17.1234 - 9.88621i) q^{86} +(-2.04050 + 3.53425i) q^{88} -8.21257i q^{89} +(-8.12974 + 3.19570i) q^{91} +(14.8309 - 25.6879i) q^{92} +(1.75748 + 3.04405i) q^{94} +(1.81800 + 3.14887i) q^{95} +(-13.1880 - 7.61407i) q^{97} -2.58061i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more