LMFDB - Embedded newform 351.4.t.a.64.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,4,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, 4, names="a")

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

chi := DirichletCharacter("351.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
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:	$20.7096704120$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			64.10
Character	$\chi$	$=$	351.64
Dual form			351.4.t.a.181.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.81478 + 1.62512i) q^{2} +(1.28200 - 2.22049i) q^{4} +(8.08964 + 4.67056i) q^{5} +(-5.60310 + 3.23495i) q^{7} -17.6683i q^{8} +O(q^{10})$	\(q+(-2.81478 + 1.62512i) q^{2} +(1.28200 - 2.22049i) q^{4} +(8.08964 + 4.67056i) q^{5} +(-5.60310 + 3.23495i) q^{7} -17.6683i q^{8} -30.3608 q^{10} +(28.4864 - 16.4466i) q^{11} +(-28.5009 + 37.2115i) q^{13} +(10.5143 - 18.2114i) q^{14} +(38.9690 + 67.4962i) q^{16} +99.5008 q^{17} -136.315i q^{19} +(20.7419 - 11.9753i) q^{20} +(-53.4553 + 92.5874i) q^{22} +(7.91924 - 13.7165i) q^{23} +(-18.8718 - 32.6869i) q^{25} +(19.7508 - 151.060i) q^{26} +16.5888i q^{28} +(-29.1948 - 50.5668i) q^{29} +(80.0415 + 46.2120i) q^{31} +(-96.9690 - 55.9851i) q^{32} +(-280.073 + 161.700i) q^{34} -60.4361 q^{35} -384.369i q^{37} +(221.528 + 383.697i) q^{38} +(82.5206 - 142.930i) q^{40} +(-33.4192 - 19.2946i) q^{41} +(240.935 + 417.312i) q^{43} -84.3383i q^{44} +51.4787i q^{46} +(232.759 - 134.383i) q^{47} +(-150.570 + 260.795i) q^{49} +(106.240 + 61.3377i) q^{50} +(46.0897 + 110.991i) q^{52} +475.493 q^{53} +307.260 q^{55} +(57.1560 + 98.9970i) q^{56} +(164.354 + 94.8898i) q^{58} +(347.780 + 200.791i) q^{59} +(-119.890 - 207.655i) q^{61} -300.399 q^{62} -259.574 q^{64} +(-404.361 + 167.913i) q^{65} +(671.583 + 387.739i) q^{67} +(127.560 - 220.940i) q^{68} +(170.115 - 98.2157i) q^{70} +769.570i q^{71} +501.277i q^{73} +(624.643 + 1081.91i) q^{74} +(-302.686 - 174.756i) q^{76} +(-106.408 + 184.304i) q^{77} +(418.818 + 725.413i) q^{79} +728.027i q^{80} +125.424 q^{82} +(-19.4098 + 11.2062i) q^{83} +(804.926 + 464.724i) q^{85} +(-1356.36 - 783.095i) q^{86} +(-290.583 - 503.305i) q^{88} +126.567i q^{89} +(39.3159 - 300.699i) q^{91} +(-20.3049 - 35.1692i) q^{92} +(-436.777 + 756.520i) q^{94} +(636.667 - 1102.74i) q^{95} +(72.1507 - 41.6562i) q^{97} -978.776i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 150 q^{4}+O(q^{10}) $ 80 * q + 150 * q^4	$ 80 q + 150 q^{4} - 40 q^{10} - 13 q^{13} - 78 q^{14} - 530 q^{16} - 264 q^{17} - 34 q^{22} + 174 q^{23} + 798 q^{25} + 1032 q^{26} - 642 q^{29} + 2136 q^{35} + 708 q^{38} + 88 q^{40} + 166 q^{43} + 1610 q^{49} + 786 q^{52} - 1296 q^{53} - 508 q^{55} + 888 q^{56} + 838 q^{61} - 3540 q^{62} - 3652 q^{64} + 201 q^{65} - 612 q^{68} - 4458 q^{74} + 2166 q^{77} + 514 q^{79} - 5188 q^{82} + 2338 q^{88} - 1086 q^{91} - 516 q^{92} + 488 q^{94} - 2136 q^{95}+O(q^{100}) $ 80 * q + 150 * q^4 - 40 * q^10 - 13 * q^13 - 78 * q^14 - 530 * q^16 - 264 * q^17 - 34 * q^22 + 174 * q^23 + 798 * q^25 + 1032 * q^26 - 642 * q^29 + 2136 * q^35 + 708 * q^38 + 88 * q^40 + 166 * q^43 + 1610 * q^49 + 786 * q^52 - 1296 * q^53 - 508 * q^55 + 888 * q^56 + 838 * q^61 - 3540 * q^62 - 3652 * q^64 + 201 * q^65 - 612 * q^68 - 4458 * q^74 + 2166 * q^77 + 514 * q^79 - 5188 * q^82 + 2338 * q^88 - 1086 * q^91 - 516 * q^92 + 488 * q^94 - 2136 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.81478	+	1.62512i	−0.995176	+	0.574565i	−0.906817	−	0.421524i	$-0.861495\pi$
$2$	−2.81478	+	1.62512i	−0.995176	+	0.574565i	−0.0883585	+	0.996089i	$0.528162\pi$
$3$		0			0
$3$		0			0
$4$	1.28200	−	2.22049i	0.160250	−	0.277561i
$5$	8.08964	+	4.67056i	0.723560	+	0.417747i	0.816061	−	0.577965i	$-0.196153\pi$
$5$	8.08964	+	4.67056i	0.723560	+	0.417747i	−0.0925018	+	0.995713i	$0.529486\pi$
$6$		0			0
$7$	−5.60310	+	3.23495i	−0.302539	+	0.174671i	−0.643583	−	0.765376i	$-0.722553\pi$
$7$	−5.60310	+	3.23495i	−0.302539	+	0.174671i	0.341044	+	0.940047i	$0.389220\pi$
$8$		−	17.6683i		−	0.780834i
$9$		0			0
$10$	−30.3608			−0.960092
$11$	28.4864	−	16.4466i	0.780816	−	0.450804i	−0.0559037	−	0.998436i	$-0.517804\pi$
$11$	28.4864	−	16.4466i	0.780816	−	0.450804i	0.836719	+	0.547632i	$0.184471\pi$
$12$		0			0
$13$	−28.5009	+	37.2115i	−0.608056	+	0.793894i
$13$	−28.5009	+	37.2115i	−0.608056	+	0.793894i
$14$	10.5143	−	18.2114i	0.200720	−	0.347657i
$15$		0			0
$16$	38.9690	+	67.4962i	0.608890	+	1.05463i
$17$	99.5008			1.41956			0.709779	−	0.704425i	$-0.248795\pi$
$17$	99.5008			1.41956			0.709779	+	0.704425i	$0.248795\pi$
$18$		0			0
$19$		−	136.315i		−	1.64594i	−0.568087	−	0.822968i	$-0.692316\pi$
$19$		−	136.315i		−	1.64594i	0.568087	−	0.822968i	$-0.307684\pi$
$20$	20.7419	−	11.9753i	0.231901	−	0.133888i
$21$		0			0
$22$	−53.4553	+	92.5874i	−0.518033	+	0.897259i
$23$	7.91924	−	13.7165i	0.0717946	−	0.124352i	−0.827893	−	0.560886i	$-0.810461\pi$
$23$	7.91924	−	13.7165i	0.0717946	−	0.124352i	0.899688	+	0.436534i	$0.143794\pi$
$24$		0			0
$25$	−18.8718	−	32.6869i	−0.150974	−	0.261495i
$26$	19.7508	−	151.060i	0.148979	−	1.13943i
$27$		0			0
$28$			16.5888i			0.111964i
$29$	−29.1948	−	50.5668i	−0.186943	−	0.323794i	0.757287	−	0.653082i	$-0.226524\pi$
$29$	−29.1948	−	50.5668i	−0.186943	−	0.323794i	−0.944229	+	0.329288i	$0.893191\pi$
$30$		0			0
$31$	80.0415	+	46.2120i	0.463738	+	0.267739i	0.713615	−	0.700539i	$-0.247057\pi$
$31$	80.0415	+	46.2120i	0.463738	+	0.267739i	−0.249877	+	0.968278i	$0.580390\pi$
$32$	−96.9690	−	55.9851i	−0.535683	−	0.309277i
$33$		0			0
$34$	−280.073	+	161.700i	−1.41271	+	0.815628i
$35$	−60.4361			−0.291873
$36$		0			0
$37$		−	384.369i		−	1.70783i	−0.520410	−	0.853916i	$-0.674221\pi$
$37$		−	384.369i		−	1.70783i	0.520410	−	0.853916i	$-0.325779\pi$
$38$	221.528	+	383.697i	0.945698	+	1.63800i
$39$		0			0
$40$	82.5206	−	142.930i	0.326191	−	0.564980i
$41$	−33.4192	−	19.2946i	−0.127298	−	0.0734953i	0.434999	−	0.900431i	$-0.356749\pi$
$41$	−33.4192	−	19.2946i	−0.127298	−	0.0734953i	−0.562297	+	0.826936i	$0.690082\pi$
$42$		0			0
$43$	240.935	+	417.312i	0.854472	+	1.47999i	0.877134	+	0.480245i	$0.159452\pi$
$43$	240.935	+	417.312i	0.854472	+	1.47999i	−0.0226626	+	0.999743i	$0.507214\pi$
$44$		−	84.3383i		−	0.288966i
$45$		0			0
$46$			51.4787i			0.165003i
$47$	232.759	−	134.383i	0.722369	−	0.417060i	−0.0932547	−	0.995642i	$-0.529727\pi$
$47$	232.759	−	134.383i	0.722369	−	0.417060i	0.815624	+	0.578582i	$0.196394\pi$
$48$		0			0
$49$	−150.570	+	260.795i	−0.438980	+	0.760336i
$50$	106.240	+	61.3377i	0.300492	+	0.173489i
$51$		0			0
$52$	46.0897	+	110.991i	0.122913	+	0.295994i
$53$	475.493			1.23234			0.616170	−	0.787613i	$-0.288684\pi$
$53$	475.493			1.23234			0.616170	+	0.787613i	$0.288684\pi$
$54$		0			0
$55$	307.260			0.753289
$56$	57.1560	+	98.9970i	0.136389	+	0.236233i
$57$		0			0
$58$	164.354	+	94.8898i	0.372081	+	0.214821i
$59$	347.780	+	200.791i	0.767408	+	0.443063i	0.831949	−	0.554852i	$-0.187225\pi$
$59$	347.780	+	200.791i	0.767408	+	0.443063i	−0.0645411	+	0.997915i	$0.520558\pi$
$60$		0			0
$61$	−119.890	−	207.655i	−0.251645	−	0.435861i	0.712334	−	0.701840i	$-0.247638\pi$
$61$	−119.890	−	207.655i	−0.251645	−	0.435861i	−0.963979	+	0.265979i	$0.914305\pi$
$62$	−300.399			−0.615334
$63$		0			0
$64$	−259.574			−0.506981
$65$	−404.361	+	167.913i	−0.771612	+	0.320416i
$66$		0			0
$67$	671.583	+	387.739i	1.22458	+	0.707012i	0.965891	−	0.258948i	$-0.0833758\pi$
$67$	671.583	+	387.739i	1.22458	+	0.707012i	0.258690	+	0.965960i	$0.416709\pi$
$68$	127.560	−	220.940i	0.227484	−	0.394014i
$69$		0			0
$70$	170.115	−	98.2157i	0.290465	−	0.167700i
$71$			769.570i			1.28635i	0.765717	+	0.643177i	$0.222384\pi$
$71$			769.570i			1.28635i	−0.765717	+	0.643177i	$0.777616\pi$
$72$		0			0
$73$			501.277i			0.803699i	0.915706	+	0.401850i	$0.131633\pi$
$73$			501.277i			0.803699i	−0.915706	+	0.401850i	$0.868367\pi$
$74$	624.643	+	1081.91i	0.981261	+	1.69959i
$75$		0			0
$76$	−302.686	−	174.756i	−0.456848	−	0.263761i
$77$	−106.408	+	184.304i	−0.157485	+	0.272772i
$78$		0			0
$79$	418.818	+	725.413i	0.596464	+	1.03311i	0.993338	+	0.115233i	$0.0367615\pi$
$79$	418.818	+	725.413i	0.596464	+	1.03311i	−0.396875	+	0.917873i	$0.629905\pi$
$80$			728.027i			1.01745i
$81$		0			0
$82$	125.424			0.168911
$83$	−19.4098	+	11.2062i	−0.0256687	+	0.0148198i	−0.512779	−	0.858520i	$-0.671384\pi$
$83$	−19.4098	+	11.2062i	−0.0256687	+	0.0148198i	0.487111	+	0.873340i	$0.338051\pi$
$84$		0			0
$85$	804.926	+	464.724i	1.02713	+	0.593016i
$86$	−1356.36	−	783.095i	−1.70070	−	0.981899i
$87$		0			0
$88$	−290.583	−	503.305i	−0.352003	−	0.609687i
$89$			126.567i			0.150742i	0.997156	+	0.0753710i	$0.0240141\pi$
$89$			126.567i			0.150742i	−0.997156	+	0.0753710i	$0.975986\pi$
$90$		0			0
$91$	39.3159	−	300.699i	0.0452904	−	0.346394i
$92$	−20.3049	−	35.1692i	−0.0230102	−	0.0398548i
$93$		0			0
$94$	−436.777	+	756.520i	−0.479256	+	0.830096i
$95$	636.667	−	1102.74i	0.687586	−	1.19093i
$96$		0			0
$97$	72.1507	−	41.6562i	0.0755237	−	0.0436036i	−0.461763	−	0.887004i	$-0.652783\pi$
$97$	72.1507	−	41.6562i	0.0755237	−	0.0436036i	0.537286	+	0.843400i	$0.319449\pi$
$98$		−	978.776i		−	1.00889i
$99$		0			0
$100$	−96.7746			−0.0967746
$101$	−23.5768	−	40.8362i	−0.0232275	−	0.0402313i	0.854178	−	0.519981i	$-0.174061\pi$
$101$	−23.5768	−	40.8362i	−0.0232275	−	0.0402313i	−0.877406	+	0.479749i	$0.840728\pi$
$102$		0			0
$103$	−46.2842	+	80.1666i	−0.0442769	+	0.0766898i	−0.887315	−	0.461165i	$-0.847432\pi$
$103$	−46.2842	+	80.1666i	−0.0442769	+	0.0766898i	0.843038	+	0.537855i	$0.180765\pi$
$104$	657.463	+	503.561i	0.619899	+	0.474791i
$105$		0			0
$106$	−1338.41	+	772.731i	−1.22639	+	0.708059i
$107$	−647.225			−0.584763			−0.292381	−	0.956302i	$-0.594448\pi$
$107$	−647.225			−0.584763			−0.292381	+	0.956302i	$0.594448\pi$
$108$		0			0
$109$			68.6751i			0.0603476i	0.999545	+	0.0301738i	$0.00960607\pi$
$109$			68.6751i			0.0603476i	−0.999545	+	0.0301738i	$0.990394\pi$
$110$	−864.869	+	499.332i	−0.749655	+	0.432813i
$111$		0			0
$112$	−436.694	−	252.125i	−0.368426	−	0.212711i
$113$	849.291	−	1471.02i	0.707032	−	1.22461i	−0.258922	−	0.965898i	$-0.583367\pi$
$113$	849.291	−	1471.02i	0.707032	−	1.22461i	0.965953	−	0.258716i	$-0.0832995\pi$
$114$		0			0
$115$	128.128	−	73.9745i	0.103895	−	0.0599840i
$116$	−149.711			−0.119830
$117$		0			0
$118$	−1305.23			−1.01827
$119$	−557.513	+	321.880i	−0.429472	+	0.247956i
$120$		0			0
$121$	−124.517	+	215.670i	−0.0935514	+	0.162036i
$122$	674.927	+	389.670i	0.500861	+	0.289172i
$123$		0			0
$124$	205.226	−	118.488i	0.148628	−	0.0858104i
$125$		−	1520.21i		−	1.08777i
$126$		0			0
$127$	483.018			0.337487			0.168744	−	0.985660i	$-0.446029\pi$
$127$	483.018			0.337487			0.168744	+	0.985660i	$0.446029\pi$
$128$	1506.40	−	869.719i	1.04022	−	0.600570i
$129$		0			0
$130$	865.310	−	1129.77i	0.583790	−	0.762212i
$131$	−75.0145	+	129.929i	−0.0500309	+	0.0866560i	−0.889956	−	0.456046i	$-0.849265\pi$
$131$	−75.0145	+	129.929i	−0.0500309	+	0.0866560i	0.839925	+	0.542702i	$0.182599\pi$
$132$		0			0
$133$	440.972	+	763.787i	0.287497	+	0.497960i
$134$	−2520.48			−1.62490
$135$		0			0
$136$		−	1758.00i		−	1.10844i
$137$	1536.64	−	887.178i	0.958275	−	0.553261i	0.0626336	−	0.998037i	$-0.480050\pi$
$137$	1536.64	−	887.178i	0.958275	−	0.553261i	0.895642	+	0.444776i	$0.146717\pi$
$138$		0			0
$139$	1462.43	−	2533.00i	0.892384	−	1.54565i	0.0553745	−	0.998466i	$-0.482365\pi$
$139$	1462.43	−	2533.00i	0.892384	−	1.54565i	0.837009	−	0.547189i	$-0.184302\pi$
$140$	−77.4792	+	134.198i	−0.0467727	+	0.0810128i
$141$		0			0
$142$	−1250.64	−	2166.17i	−0.739095	−	1.28015i
$143$	−199.884	+	1528.77i	−0.116889	+	0.893999i
$144$		0			0
$145$		−	545.423i		−	0.312379i
$146$	−814.633	−	1410.99i	−0.461778	−	0.799822i
$147$		0			0
$148$	−853.487	−	492.761i	−0.474028	−	0.273680i
$149$	1934.38	+	1116.82i	1.06356	+	0.614049i	0.926416	−	0.376502i	$-0.122873\pi$
$149$	1934.38	+	1116.82i	1.06356	+	0.614049i	0.137148	+	0.990551i	$0.456207\pi$
$150$		0			0
$151$	−1227.17	+	708.505i	−0.661361	+	0.381837i	−0.792795	−	0.609488i	$-0.791375\pi$
$151$	−1227.17	+	708.505i	−0.661361	+	0.381837i	0.131435	+	0.991325i	$0.458042\pi$
$152$	−2408.45			−1.28520
$153$		0			0
$154$		−	691.702i		−	0.361941i
$155$	431.671	+	747.676i	0.223695	+	0.387450i
$156$		0			0
$157$	−7.80661	+	13.5215i	−0.00396838	+	0.00687344i	−0.868003	−	0.496559i	$-0.834597\pi$
$157$	−7.80661	+	13.5215i	−0.00396838	+	0.00687344i	0.864034	+	0.503433i	$0.167930\pi$
$158$	−2357.76	−	1361.25i	−1.18717	−	0.685415i
$159$		0			0
$160$	−522.963	−	905.799i	−0.258399	−	0.447561i
$161$			102.473i			0.0501617i
$162$		0			0
$163$		−	841.823i		−	0.404519i	−0.979332	−	0.202260i	$-0.935171\pi$
$163$		−	841.823i		−	0.404519i	0.979332	−	0.202260i	$-0.0648285\pi$
$164$	−85.6868	+	49.4713i	−0.0407989	+	0.0235552i
$165$		0			0
$166$	36.4229	−	63.0862i	0.0170299	−	0.0294966i
$167$	−3327.99	−	1921.41i	−1.54208	−	0.890320i	−0.998707	−	0.0508286i	$-0.983814\pi$
$167$	−3327.99	−	1921.41i	−1.54208	−	0.890320i	−0.543373	−	0.839492i	$-0.682853\pi$
$168$		0			0
$169$	−572.397	−	2121.12i	−0.260536	−	0.965464i
$170$	−3020.92			−1.36291
$171$		0			0
$172$	1235.52			0.547717
$173$	1876.45	+	3250.11i	0.824647	+	1.42833i	0.902188	+	0.431342i	$0.141960\pi$
$173$	1876.45	+	3250.11i	0.824647	+	1.42833i	−0.0775409	+	0.996989i	$0.524707\pi$
$174$		0			0
$175$	211.481	+	122.099i	0.0913513	+	0.0527417i
$176$	2220.17	+	1281.82i	0.950861	+	0.548980i
$177$		0			0
$178$	−205.685	−	356.258i	−0.0866111	−	0.150015i
$179$	−2418.17			−1.00973			−0.504867	−	0.863197i	$-0.668459\pi$
$179$	−2418.17			−1.00973			−0.504867	+	0.863197i	$0.668459\pi$
$180$		0			0
$181$	1764.27			0.724516			0.362258	−	0.932078i	$-0.382006\pi$
$181$	1764.27			0.724516			0.362258	+	0.932078i	$0.382006\pi$
$182$	378.005	+	910.296i	0.153954	+	0.370745i
$183$		0			0
$184$	−242.347	−	139.919i	−0.0970981	−	0.0560596i
$185$	1795.22	−	3109.40i	0.713443	−	1.23572i
$186$		0			0
$187$	2834.42	−	1636.45i	1.10841	−	0.639942i
$188$		−	689.118i		−	0.267336i
$189$		0			0
$190$			4138.63i			1.58025i
$191$	88.0254	+	152.465i	0.0333471	+	0.0577589i	0.882217	−	0.470842i	$-0.156050\pi$
$191$	88.0254	+	152.465i	0.0333471	+	0.0577589i	−0.848870	+	0.528601i	$0.822717\pi$
$192$		0			0
$193$	−3675.27	−	2121.92i	−1.37074	−	0.791394i	−0.379715	−	0.925104i	$-0.623978\pi$
$193$	−3675.27	−	2121.92i	−1.37074	−	0.791394i	−0.991021	+	0.133709i	$0.957311\pi$
$194$	−135.392	+	234.507i	−0.0501062	+	0.0867865i
$195$		0			0
$196$	386.062	+	668.679i	0.140693	+	0.243688i
$197$		−	2439.54i		−	0.882285i	−0.897437	−	0.441143i	$-0.854573\pi$
$197$		−	2439.54i		−	0.882285i	0.897437	−	0.441143i	$-0.145427\pi$
$198$		0			0
$199$	−365.385			−0.130158			−0.0650791	−	0.997880i	$-0.520730\pi$
$199$	−365.385			−0.130158			−0.0650791	+	0.997880i	$0.520730\pi$
$200$	−577.520	+	333.432i	−0.204184	+	0.117886i
$201$		0			0
$202$	132.727	+	76.6301i	0.0462310	+	0.0266915i
$203$	327.163	+	188.887i	0.113115	+	0.0653069i
$204$		0			0
$205$	−180.233	−	312.172i	−0.0614049	−	0.106356i
$206$		−	300.869i		−	0.101760i
$207$		0			0
$208$	−3622.29	−	473.608i	−1.20750	−	0.157879i
$209$	−2241.92	−	3883.12i	−0.741995	−	1.28517i
$210$		0			0
$211$	−372.285	+	644.817i	−0.121465	+	0.210384i	−0.920346	−	0.391106i	$-0.872093\pi$
$211$	−372.285	+	644.817i	−0.121465	+	0.210384i	0.798880	+	0.601490i	$0.205426\pi$
$212$	609.582	−	1055.83i	0.197482	−	0.342050i
$213$		0			0
$214$	1821.80	−	1051.82i	0.581942	−	0.335984i
$215$			4501.21i			1.42781i
$216$		0			0
$217$	−597.974			−0.187065
$218$	−111.605	−	193.306i	−0.0346736	−	0.0600564i
$219$		0			0
$220$	393.907	−	682.267i	0.120715	−	0.209084i
$221$	−2835.86	+	3702.58i	−0.863170	+	1.12698i
$222$		0			0
$223$	−3735.03	+	2156.42i	−1.12160	+	0.647555i	−0.941808	−	0.336150i	$-0.890875\pi$
$223$	−3735.03	+	2156.42i	−1.12160	+	0.647555i	−0.179790	+	0.983705i	$0.557542\pi$
$224$	724.437			0.216087
$225$		0			0
$226$			5520.78i			1.62494i
$227$	956.541	−	552.259i	0.279682	−	0.161475i	−0.353597	−	0.935398i	$-0.615042\pi$
$227$	956.541	−	552.259i	0.279682	−	0.161475i	0.633279	+	0.773923i	$0.281708\pi$
$228$		0			0
$229$	−3114.84	−	1798.35i	−0.898840	−	0.518945i	−0.0220160	−	0.999758i	$-0.507008\pi$
$229$	−3114.84	−	1798.35i	−0.898840	−	0.518945i	−0.876824	+	0.480812i	$0.840342\pi$
$230$	−240.434	+	416.444i	−0.0689294	+	0.119389i
$231$		0			0
$232$	−893.427	+	515.821i	−0.252829	+	0.145971i
$233$	3144.44			0.884116			0.442058	−	0.896987i	$-0.354249\pi$
$233$	3144.44			0.884116			0.442058	+	0.896987i	$0.354249\pi$
$234$		0			0
$235$	2510.58			0.696903
$236$	891.708	−	514.828i	0.245954	−	0.142002i
$237$		0			0
$238$	1046.19	−	1812.05i	0.284933	−	0.493519i
$239$	2680.85	+	1547.79i	0.725563	+	0.418904i	0.816797	−	0.576926i	$-0.195748\pi$
$239$	2680.85	+	1547.79i	0.725563	+	0.418904i	−0.0912338	+	0.995830i	$0.529081\pi$
$240$		0			0
$241$	4175.25	−	2410.58i	1.11598	−	0.644312i	0.175609	−	0.984460i	$-0.443811\pi$
$241$	4175.25	−	2410.58i	1.11598	−	0.644312i	0.940372	+	0.340148i	$0.110477\pi$
$242$		−	809.418i		−	0.215005i
$243$		0			0
$244$	−614.795			−0.161304
$245$	−2436.12	+	1406.49i	−0.635256	+	0.366765i
$246$		0			0
$247$	5072.49	+	3885.10i	1.30670	+	1.00082i
$248$	816.484	−	1414.19i	0.209060	−	0.362102i
$249$		0			0
$250$	2470.51	+	4279.05i	0.624995	+	1.08252i
$251$	3992.23			1.00393			0.501967	−	0.864887i	$-0.332610\pi$
$251$	3992.23			1.00393			0.501967	+	0.864887i	$0.332610\pi$
$252$		0			0
$253$		−	520.979i		−	0.129461i
$254$	−1359.59	+	784.959i	−0.335859	+	0.193908i
$255$		0			0
$256$	−1788.49	+	3097.76i	−0.436643	+	0.756288i
$257$	2587.41	−	4481.53i	0.628009	−	1.08774i	−0.359942	−	0.932975i	$-0.617203\pi$
$257$	2587.41	−	4481.53i	0.628009	−	1.08774i	0.987951	−	0.154769i	$-0.0494633\pi$
$258$		0			0
$259$	1243.41	+	2153.66i	0.298309	+	0.516686i
$260$	−145.542	+	1113.14i	−0.0347158	+	0.265516i
$261$		0			0
$262$		−	487.629i		−	0.114984i
$263$	−599.129	−	1037.72i	−0.140471	−	0.243303i	0.787203	−	0.616694i	$-0.211528\pi$
$263$	−599.129	−	1037.72i	−0.140471	−	0.243303i	−0.927674	+	0.373391i	$0.878195\pi$
$264$		0			0
$265$	3846.57	+	2220.82i	0.891671	+	0.514806i
$266$	−2482.48	−	1433.26i	−0.572221	−	0.330372i
$267$		0			0
$268$	1721.94	−	994.163i	0.392479	−	0.226598i
$269$	6299.35			1.42780			0.713900	−	0.700248i	$-0.246927\pi$
$269$	6299.35			1.42780			0.713900	+	0.700248i	$0.246927\pi$
$270$		0			0
$271$			6375.25i			1.42904i	0.699617	+	0.714518i	$0.253354\pi$
$271$			6375.25i			1.42904i	−0.699617	+	0.714518i	$0.746646\pi$
$272$	3877.44	+	6715.92i	0.864354	+	1.49711i
$273$		0			0
$274$	−2883.53	+	4994.42i	−0.635768	+	1.10118i
$275$	−1075.18	−	620.755i	−0.235766	−	0.136120i
$276$		0			0
$277$	0.0249887	+	0.0432816i	5.42030e−6	+	9.38823e-6i	0.866028	−	0.499995i	$-0.166665\pi$
$277$	0.0249887	+	0.0432816i	5.42030e−6	+	9.38823e-6i	−0.866023	+	0.500005i	$0.833332\pi$
$278$			9506.44i			2.05093i
$279$		0			0
$280$			1067.80i			0.227905i
$281$	−4135.13	+	2387.42i	−0.877870	+	0.506838i	−0.869955	−	0.493130i	$-0.835853\pi$
$281$	−4135.13	+	2387.42i	−0.877870	+	0.506838i	−0.00791441	+	0.999969i	$0.502519\pi$
$282$		0			0
$283$	−1231.99	+	2133.88i	−0.258779	+	0.448218i	−0.965915	−	0.258859i	$-0.916653\pi$
$283$	−1231.99	+	2133.88i	−0.258779	+	0.448218i	0.707136	+	0.707077i	$0.249987\pi$
$284$	1708.82	+	986.590i	0.357042	+	0.206138i
$285$		0			0
$286$	−1921.79	−	4627.98i	−0.397336	−	0.956847i
$287$	249.668			0.0513500
$288$		0			0
$289$	4987.40			1.01514
$290$	886.376	+	1535.25i	0.179482	+	0.310872i
$291$		0			0
$292$	1113.08	+	642.638i	0.223076	+	0.128793i
$293$	−1072.10	−	618.974i	−0.213763	−	0.123416i	0.389296	−	0.921113i	$-0.372718\pi$
$293$	−1072.10	−	618.974i	−0.213763	−	0.123416i	−0.603059	+	0.797697i	$0.706052\pi$
$294$		0			0
$295$	1875.61	+	3248.65i	0.370177	+	0.641165i
$296$	−6791.12			−1.33353
$297$		0			0
$298$	−7259.83			−1.41124
$299$	284.707	+	685.620i	0.0550671	+	0.132610i
$300$		0			0
$301$	−2699.97	−	1558.83i	−0.517022	−	0.298503i
$302$	2302.81	−	3988.58i	0.438780	−	0.759989i
$303$		0			0
$304$	9200.74	−	5312.05i	1.73585	−	1.00219i
$305$		−	2239.81i		−	0.420495i
$306$		0			0
$307$		−	4673.94i		−	0.868912i	−0.900693	−	0.434456i	$-0.856941\pi$
$307$		−	4673.94i		−	0.868912i	0.900693	−	0.434456i	$-0.143059\pi$
$308$	272.831	+	472.556i	0.0504739	+	0.0874234i
$309$		0			0
$310$	−2430.12	−	1403.03i	−0.445231	−	0.257054i
$311$	−2442.04	+	4229.73i	−0.445258	+	0.771209i	−0.998070	−	0.0620967i	$-0.980221\pi$
$311$	−2442.04	+	4229.73i	−0.445258	+	0.771209i	0.552812	+	0.833306i	$0.313555\pi$
$312$		0			0
$313$	1417.14	+	2454.57i	0.255916	+	0.443260i	0.965144	−	0.261720i	$-0.0842896\pi$
$313$	1417.14	+	2454.57i	0.255916	+	0.443260i	−0.709228	+	0.704979i	$0.750956\pi$
$314$		−	50.7466i		−	0.00912037i
$315$		0			0
$316$	2147.70			0.382334
$317$	4881.15	−	2818.14i	0.864836	−	0.499313i	−0.000792843	−	1.00000i	$-0.500252\pi$
$317$	4881.15	−	2818.14i	0.864836	−	0.499313i	0.865629	+	0.500686i	$0.166919\pi$
$318$		0			0
$319$	−1663.31	−	960.311i	−0.291935	−	0.168549i
$320$	−2099.86	−	1212.36i	−0.366831	−	0.211790i
$321$		0			0
$322$	−166.531	−	288.440i	−0.0288212	−	0.0499197i
$323$		−	13563.4i		−	2.33650i
$324$		0			0
$325$	1754.19	+	229.358i	0.299400	+	0.0391461i
$326$	1368.06	+	2369.55i	0.232423	+	0.402568i
$327$		0			0
$328$	−340.901	+	590.459i	−0.0573876	+	0.0993982i
$329$	−869.448	+	1505.93i	−0.145697	+	0.252354i
$330$		0			0
$331$	−7545.23	+	4356.24i	−1.25294	+	0.723385i	−0.971692	−	0.236250i	$-0.924082\pi$
$331$	−7545.23	+	4356.24i	−1.25294	+	0.723385i	−0.281248	+	0.959635i	$0.590748\pi$
$332$			57.4656i			0.00949950i
$333$		0			0
$334$	12490.1			2.04619
$335$	3621.91	+	6273.34i	0.590705	+	1.02313i
$336$		0			0
$337$	2635.03	−	4564.00i	0.425932	−	0.737735i	−0.570575	−	0.821245i	$-0.693280\pi$
$337$	2635.03	−	4564.00i	0.425932	−	0.737735i	0.996507	+	0.0835100i	$0.0266130\pi$
$338$	5058.25	+	5040.29i	0.814001	+	0.811112i
$339$		0			0
$340$	2063.83	−	1191.55i	0.329197	−	0.190062i
$341$	3040.12			0.482791
$342$		0			0
$343$		−	4167.53i		−	0.656050i
$344$	7373.18	−	4256.90i	1.15562	−	0.667200i
$345$		0			0
$346$	−10563.6	−	6098.90i	−1.64134	−	0.947627i
$347$	918.399	−	1590.71i	0.142081	−	0.246092i	−0.786199	−	0.617974i	$-0.787954\pi$
$347$	918.399	−	1590.71i	0.142081	−	0.246092i	0.928280	+	0.371881i	$0.121287\pi$
$348$		0			0
$349$	−11253.3	+	6497.08i	−1.72600	+	0.996507i	−0.821246	+	0.570574i	$0.806721\pi$
$349$	−11253.3	+	6497.08i	−1.72600	+	0.996507i	−0.904754	+	0.425933i	$0.859946\pi$
$350$	−793.698			−0.121214
$351$		0			0
$352$	−3683.06			−0.557693
$353$	3831.40	−	2212.06i	0.577691	−	0.333530i	−0.182524	−	0.983201i	$-0.558427\pi$
$353$	3831.40	−	2212.06i	0.577691	−	0.333530i	0.760215	+	0.649671i	$0.225093\pi$
$354$		0			0
$355$	−3594.32	+	6225.55i	−0.537371	+	0.930754i
$356$	281.040	+	162.259i	0.0418402	+	0.0241564i
$357$		0			0
$358$	6806.62	−	3929.80i	1.00486	−	0.580158i
$359$		−	8186.11i		−	1.20347i	−0.798695	−	0.601736i	$-0.794476\pi$
$359$		−	8186.11i		−	1.20347i	0.798695	−	0.601736i	$-0.205524\pi$
$360$		0			0
$361$	−11722.8			−1.70911
$362$	−4966.05	+	2867.15i	−0.721021	+	0.416282i
$363$		0			0
$364$	−617.297	−	472.797i	−0.0888877	−	0.0680805i
$365$	−2341.24	+	4055.15i	−0.335743	+	0.581524i
$366$		0			0
$367$	4429.04	+	7671.32i	0.629957	+	1.09112i	0.987560	+	0.157243i	$0.0502607\pi$
$367$	4429.04	+	7671.32i	0.629957	+	1.09112i	−0.357603	+	0.933874i	$0.616406\pi$
$368$	1234.42			0.174860
$369$		0			0
$370$			11669.7i			1.63968i
$371$	−2664.24	+	1538.20i	−0.372831	+	0.215254i
$372$		0			0
$373$	1129.84	−	1956.93i	0.156838	−	0.271652i	−0.776889	−	0.629638i	$-0.783203\pi$
$373$	1129.84	−	1956.93i	0.156838	−	0.271652i	0.933727	+	0.357986i	$0.116537\pi$
$374$	−5318.85	+	9212.51i	−0.735377	+	1.27371i
$375$		0			0
$376$	−2374.32	−	4112.44i	−0.325655	−	0.564050i
$377$	2713.75	+	354.818i	0.370730	+	0.0484723i
$378$		0			0
$379$		−	14184.3i		−	1.92242i	−0.275817	−	0.961210i	$-0.588948\pi$
$379$		−	14184.3i		−	1.92242i	0.275817	−	0.961210i	$-0.411052\pi$
$380$	−1632.41	−	2827.42i	−0.220371	−	0.381694i
$381$		0			0
$382$	−495.545	−	286.103i	−0.0663725	−	0.0383202i
$383$	708.447	+	409.022i	0.0945169	+	0.0545693i	0.546513	−	0.837450i	$-0.315955\pi$
$383$	708.447	+	409.022i	0.0945169	+	0.0545693i	−0.451997	+	0.892020i	$0.649288\pi$
$384$		0			0
$385$	−1721.61	+	993.970i	−0.227899	+	0.131578i
$386$	13793.5			1.81883
$387$		0			0
$388$		−	213.613i		−	0.0279499i
$389$	−6371.85	−	11036.4i	−0.830502	−	1.43847i	−0.897640	−	0.440729i	$-0.854720\pi$
$389$	−6371.85	−	11036.4i	−0.830502	−	1.43847i	0.0671380	−	0.997744i	$-0.478613\pi$
$390$		0			0
$391$	787.970	−	1364.80i	0.101917	−	0.176525i
$392$	4607.79	+	2660.31i	0.593696	+	0.342770i
$393$		0			0
$394$	3964.54	+	6866.78i	0.506930	+	0.878029i
$395$			7824.44i			0.996685i
$396$		0			0
$397$			1970.75i			0.249141i	0.992211	+	0.124570i	$0.0397553\pi$
$397$			1970.75i			0.249141i	−0.992211	+	0.124570i	$0.960245\pi$
$398$	1028.48	−	593.793i	0.129530	−	0.0747843i
$399$		0			0
$400$	1470.83	−	2547.55i	0.183854	−	0.318444i
$401$	−12106.5	−	6989.68i	−1.50765	−	0.870444i	−0.999960	−	0.00890549i	$-0.997165\pi$
$401$	−12106.5	−	6989.68i	−1.50765	−	0.870444i	−0.507693	−	0.861538i	$-0.669501\pi$
$402$		0			0
$403$	−4000.87	+	1661.38i	−0.494535	+	0.205358i
$404$	−120.902			−0.0148889
$405$		0			0
$406$	−1227.86			−0.150092
$407$	−6321.57	−	10949.3i	−0.769898	−	1.33350i
$408$		0			0
$409$	2278.10	+	1315.26i	0.275415	+	0.159011i	0.631346	−	0.775501i	$-0.282503\pi$
$409$	2278.10	+	1315.26i	0.275415	+	0.159011i	−0.355931	+	0.934512i	$0.615836\pi$
$410$	1014.63	+	585.798i	0.122217	+	0.0705622i
$411$		0			0
$412$	118.673	+	205.547i	0.0141908	+	0.0245791i
$413$	−2598.20			−0.309561
$414$		0			0
$415$	−209.357			−0.0247637
$416$	4847.00	−	2012.74i	0.571259	−	0.237218i
$417$		0			0
$418$	12621.0	+	7286.76i	1.47683	+	0.852649i
$419$	−2188.35	+	3790.34i	−0.255150	+	0.441933i	−0.964936	−	0.262484i	$-0.915458\pi$
$419$	−2188.35	+	3790.34i	−0.255150	+	0.441933i	0.709786	+	0.704417i	$0.248792\pi$
$420$		0			0
$421$	7355.20	−	4246.53i	0.851474	−	0.491599i	−0.00967417	−	0.999953i	$-0.503079\pi$
$421$	7355.20	−	4246.53i	0.851474	−	0.491599i	0.861148	+	0.508355i	$0.169746\pi$
$422$		−	2420.03i		−	0.279159i
$423$		0			0
$424$		−	8401.13i		−	0.962252i
$425$	−1877.76	−	3252.37i	−0.214317	−	0.371208i
$426$		0			0
$427$	1343.51	+	775.676i	0.152265	+	0.0879100i
$428$	−829.743	+	1437.16i	−0.0937083	+	0.162308i
$429$		0			0
$430$	−7314.98	−	12669.9i	−0.820372	−	1.42093i
$431$		−	851.101i		−	0.0951185i	−0.998868	−	0.0475593i	$-0.984856\pi$
$431$		−	851.101i		−	0.0951185i	0.998868	−	0.0475593i	$-0.0151443\pi$
$432$		0			0
$433$	6389.28			0.709121			0.354560	−	0.935033i	$-0.384631\pi$
$433$	6389.28			0.709121			0.354560	+	0.935033i	$0.384631\pi$
$434$	1683.17	−	971.777i	0.186163	−	0.107481i
$435$		0			0
$436$	152.492	+	88.0416i	0.0167501	+	0.00967070i
$437$	−1869.77	−	1079.51i	−0.204675	−	0.118169i
$438$		0			0
$439$	−3417.48	−	5919.24i	−0.371543	−	0.643531i	0.618260	−	0.785973i	$-0.287838\pi$
$439$	−3417.48	−	5919.24i	−0.371543	−	0.643531i	−0.989803	+	0.142442i	$0.954504\pi$
$440$		−	5428.74i		−	0.588193i
$441$		0			0
$442$	1965.22	−	15030.5i	0.211484	−	1.61749i
$443$	−2452.39	−	4247.66i	−0.263017	−	0.455559i	0.704025	−	0.710175i	$-0.251384\pi$
$443$	−2452.39	−	4247.66i	−0.263017	−	0.455559i	−0.967042	+	0.254616i	$0.918051\pi$
$444$		0			0
$445$	−591.137	+	1023.88i	−0.0629721	+	0.109071i
$446$	7008.87	−	12139.7i	0.744125	−	1.28886i
$447$		0			0
$448$	1454.42	−	839.711i	0.153382	−	0.0885549i
$449$			14662.5i			1.54112i	0.637366	+	0.770561i	$0.280024\pi$
$449$			14662.5i			1.54112i	−0.637366	+	0.770561i	$0.719976\pi$
$450$		0			0
$451$	−1269.32			−0.132528
$452$	−2177.58	−	3771.69i	−0.226604	−	0.392489i
$453$		0			0
$454$	−1794.97	+	3108.98i	−0.185555	+	0.321391i
$455$	1722.48	−	2248.92i	0.177475	−	0.231717i
$456$		0			0
$457$	−9706.10	+	5603.82i	−0.993506	+	0.573601i	−0.906320	−	0.422591i	$-0.861121\pi$
$457$	−9706.10	+	5603.82i	−0.993506	+	0.573601i	−0.0871856	+	0.996192i	$0.527787\pi$
$458$	11690.1			1.19267
$459$		0			0
$460$		−	379.341i		−	0.0384498i
$461$	−12830.5	+	7407.70i	−1.29626	+	0.748397i	−0.979756	−	0.200193i	$-0.935843\pi$
$461$	−12830.5	+	7407.70i	−1.29626	+	0.748397i	−0.316506	+	0.948591i	$0.602510\pi$
$462$		0			0
$463$	8387.03	+	4842.25i	0.841853	+	0.486044i	0.857894	−	0.513827i	$-0.171773\pi$
$463$	8387.03	+	4842.25i	0.841853	+	0.486044i	−0.0160404	+	0.999871i	$0.505106\pi$
$464$	2275.38	−	3941.07i	0.227655	−	0.394310i
$465$		0			0
$466$	−8850.91	+	5110.07i	−0.879851	+	0.507982i
$467$	−9860.98			−0.977112			−0.488556	−	0.872532i	$-0.662476\pi$
$467$	−9860.98			−0.977112			−0.488556	+	0.872532i	$0.662476\pi$
$468$		0			0
$469$	−5017.27			−0.493978
$470$	−7066.74	+	4079.98i	−0.693541	+	0.400416i
$471$		0			0
$472$	3547.62	−	6144.66i	0.345959	−	0.599218i
$473$	13726.8	+	7925.14i	1.33437	+	0.770399i
$474$		0			0
$475$	−4455.71	+	2572.51i	−0.430405	+	0.248494i
$476$			1650.60i			0.158940i
$477$		0			0
$478$	−10061.3			−0.962750
$479$	4811.72	−	2778.05i	0.458983	−	0.264994i	−0.252633	−	0.967562i	$-0.581297\pi$
$479$	4811.72	−	2778.05i	0.458983	−	0.264994i	0.711617	+	0.702568i	$0.247963\pi$
$480$		0			0
$481$	14302.9	+	10954.9i	1.35584	+	1.03846i
$482$	−7834.95	+	13570.5i	−0.740398	+	1.28241i
$483$		0			0
$484$	319.262	+	552.977i	0.0299832	+	0.0519325i
$485$	778.231			0.0728612
$486$		0			0
$487$		−	12548.5i		−	1.16761i	−0.811894	−	0.583805i	$-0.801563\pi$
$487$		−	12548.5i		−	1.16761i	0.811894	−	0.583805i	$-0.198437\pi$
$488$	−3668.90	+	2118.24i	−0.340335	+	0.196493i
$489$		0			0
$490$	4571.43	−	7917.94i	0.421461	−	0.729992i
$491$	−6630.65	+	11484.6i	−0.609444	+	1.05559i	0.381888	+	0.924208i	$0.375274\pi$
$491$	−6630.65	+	11484.6i	−0.609444	+	1.05559i	−0.991332	+	0.131379i	$0.958059\pi$
$492$		0			0
$493$	−2904.90	−	5031.44i	−0.265376	−	0.459644i
$494$	−20591.7	−	2692.33i	−1.87543	−	0.245210i
$495$		0			0
$496$			7203.33i			0.652095i
$497$	−2489.52	−	4311.98i	−0.224689	−	0.389173i
$498$		0			0
$499$	7410.77	+	4278.61i	0.664833	+	0.383842i	0.794116	−	0.607766i	$-0.207934\pi$
$499$	7410.77	+	4278.61i	0.664833	+	0.383842i	−0.129283	+	0.991608i	$0.541268\pi$
$500$	−3375.60	−	1948.91i	−0.301923	−	0.174315i
$501$		0			0
$502$	−11237.3	+	6487.84i	−0.999092	+	0.576826i
$503$	14538.3			1.28873			0.644364	−	0.764719i	$-0.277122\pi$
$503$	14538.3			1.28873			0.644364	+	0.764719i	$0.277122\pi$
$504$		0			0
$505$		−	440.467i		−	0.0388130i
$506$	846.651	+	1466.44i	0.0743839	+	0.128837i
$507$		0			0
$508$	619.229	−	1072.54i	0.0540824	−	0.0936734i
$509$	−3743.30	−	2161.20i	−0.325970	−	0.188199i	0.328080	−	0.944650i	$-0.393598\pi$
$509$	−3743.30	−	2161.20i	−0.325970	−	0.188199i	−0.654051	+	0.756451i	$0.726932\pi$
$510$		0			0
$511$	−1621.61	−	2808.71i	−0.140383	−	0.243150i
$512$			2289.49i			0.197621i
$513$		0			0
$514$			16819.4i			1.44333i
$515$	−748.846	+	432.346i	−0.0640740	+	0.0369931i
$516$		0			0
$517$	4420.31	−	7656.19i	0.376025	−	0.651294i
$518$	−6999.88	−	4041.38i	−0.593740	−	0.342796i
$519$		0			0
$520$	2966.73	+	7144.35i	0.250192	+	0.602501i
$521$	3712.85			0.312213			0.156106	−	0.987740i	$-0.450106\pi$
$521$	3712.85			0.312213			0.156106	+	0.987740i	$0.450106\pi$
$522$		0			0
$523$	9455.23			0.790532			0.395266	−	0.918567i	$-0.370652\pi$
$523$	9455.23			0.790532			0.395266	+	0.918567i	$0.370652\pi$
$524$	192.337	+	333.138i	0.0160349	+	0.0277733i
$525$		0			0
$526$	3372.84	+	1947.31i	0.279587	+	0.161419i
$527$	7964.19	+	4598.12i	0.658302	+	0.380071i
$528$		0			0
$529$	5958.07	+	10319.7i	0.489691	+	0.848170i
$530$	−14436.3			−1.18316
$531$		0			0
$532$	2261.31			0.184286
$533$	1670.46	−	693.666i	0.135752	−	0.0563715i
$534$		0			0
$535$	−5235.82	−	3022.90i	−0.423111	−	0.244283i
$536$	6850.67	−	11865.7i	0.552059	−	0.956195i
$537$		0			0
$538$	−17731.3	+	10237.2i	−1.42091	+	0.820364i
$539$			9905.49i			0.791576i
$540$		0			0
$541$			15468.2i			1.22926i	0.788814	+	0.614632i	$0.210695\pi$
$541$			15468.2i			1.22926i	−0.788814	+	0.614632i	$0.789305\pi$
$542$	−10360.5	−	17944.9i	−0.821074	−	1.42214i
$543$		0			0
$544$	−9648.49	−	5570.56i	−0.760433	−	0.439036i
$545$	−320.751	+	555.557i	−0.0252100	+	0.0436651i
$546$		0			0
$547$	−10339.7	−	17908.9i	−0.808218	−	1.39987i	−0.914097	−	0.405495i	$-0.867099\pi$
$547$	−10339.7	−	17908.9i	−0.808218	−	1.39987i	0.105879	−	0.994379i	$-0.466234\pi$
$548$		−	4549.45i		−	0.354640i
$549$		0			0
$550$	4035.19			0.312838
$551$	−6893.01	+	3979.68i	−0.532944	+	0.307696i
$552$		0			0
$553$	−4693.36	−	2709.71i	−0.360907	−	0.208370i
$554$	−0.140675	−	0.0812189i	−1.07883e−5	−	6.22863e-6i
$555$		0			0
$556$	−3749.66	−	6494.61i	−0.286009	−	0.495382i
$557$			8377.79i			0.637304i	0.947872	+	0.318652i	$0.103230\pi$
$557$			8377.79i			0.637304i	−0.947872	+	0.318652i	$0.896770\pi$
$558$		0			0
$559$	−22395.7	−	2928.20i	−1.69452	−	0.221556i
$560$	−2355.13	−	4079.21i	−0.177719	−	0.307818i
$561$		0			0
$562$	7759.67	−	13440.1i	0.582423	−	1.00879i
$563$	−11893.7	+	20600.4i	−0.890334	+	1.54210i	−0.0508578	+	0.998706i	$0.516196\pi$
$563$	−11893.7	+	20600.4i	−0.890334	+	1.54210i	−0.839476	+	0.543397i	$0.817138\pi$
$564$		0			0
$565$	13740.9	−	7933.32i	1.02316	−	0.590721i
$566$		−	8008.53i		−	0.594741i
$567$		0			0
$568$	13597.0			1.00443
$569$	−3737.01	−	6472.69i	−0.275331	−	0.476888i	0.694887	−	0.719119i	$-0.255454\pi$
$569$	−3737.01	−	6472.69i	−0.275331	−	0.476888i	−0.970219	+	0.242231i	$0.922121\pi$
$570$		0			0
$571$	3413.95	−	5913.13i	0.250209	−	0.433374i	−0.713374	−	0.700783i	$-0.752834\pi$
$571$	3413.95	−	5913.13i	0.250209	−	0.433374i	0.963583	+	0.267409i	$0.0861674\pi$
$572$	3138.36	+	2403.72i	0.229408	+	0.175707i
$573$		0			0
$574$	−702.762	+	405.740i	−0.0511023	+	0.0295039i
$575$	−597.801			−0.0433566
$576$		0			0
$577$		−	14789.6i		−	1.06707i	−0.845777	−	0.533536i	$-0.820863\pi$
$577$		−	14789.6i		−	1.06707i	0.845777	−	0.533536i	$-0.179137\pi$
$578$	−14038.4	+	8105.10i	−1.01025	+	0.583266i
$579$		0			0
$580$	−1211.11	−	699.233i	−0.0867043	−	0.0500588i
$581$	72.5033	−	125.579i	0.00517718	−	0.00896714i
$582$		0			0
$583$	13545.1	−	7820.26i	0.962230	−	0.555544i
$584$	8856.69			0.627556
$585$		0			0
$586$	4023.62			0.283642
$587$	12025.7	−	6943.02i	0.845575	−	0.488193i	−0.0135805	−	0.999908i	$-0.504323\pi$
$587$	12025.7	−	6943.02i	0.845575	−	0.488193i	0.859155	+	0.511715i	$0.170990\pi$
$588$		0			0
$589$	6299.38	−	10910.8i	0.440682	−	0.763283i
$590$	−10558.9	−	6096.17i	−0.736783	−	0.425382i
$591$		0			0
$592$	25943.4	−	14978.4i	1.80113	−	1.03988i
$593$			4297.30i			0.297587i	0.988868	+	0.148794i	$0.0475390\pi$
$593$			4297.30i			0.297587i	−0.988868	+	0.148794i	$0.952461\pi$
$594$		0			0
$595$	−6013.44			−0.414331
$596$	4959.76	−	2863.52i	0.340872	−	0.196803i
$597$		0			0
$598$	−1915.60	−	1467.19i	−0.130995	−	0.100331i
$599$	−14570.0	+	25236.1i	−0.993850	+	1.72140i	−0.401023	+	0.916068i	$0.631345\pi$
$599$	−14570.0	+	25236.1i	−0.993850	+	1.72140i	−0.592827	+	0.805330i	$0.701988\pi$
$600$		0			0
$601$	−5202.61	−	9011.18i	−0.353110	−	0.611604i	0.633683	−	0.773593i	$-0.281542\pi$
$601$	−5202.61	−	9011.18i	−0.353110	−	0.611604i	−0.986793	+	0.161989i	$0.948209\pi$
$602$	10133.1			0.686037
$603$		0			0
$604$			3633.22i			0.244757i
$605$	−2014.59	+	1163.13i	−0.135380	+	0.0781617i
$606$		0			0
$607$	−12713.2	+	22019.9i	−0.850104	+	1.47242i	0.0310091	+	0.999519i	$0.490128\pi$
$607$	−12713.2	+	22019.9i	−0.850104	+	1.47242i	−0.881113	+	0.472905i	$0.843205\pi$
$608$	−7631.61	+	13218.3i	−0.509050	+	0.881701i
$609$		0			0
$610$	3639.95	+	6304.57i	0.241602	+	0.418467i
$611$	−1633.22	+	12491.4i	−0.108139	+	0.827081i
$612$		0			0
$613$			977.352i			0.0643962i	0.999482	+	0.0321981i	$0.0102507\pi$
$613$			977.352i			0.0643962i	−0.999482	+	0.0321981i	$0.989749\pi$
$614$	7595.69	+	13156.1i	0.499246	+	0.864720i
$615$		0			0
$616$	3256.33	+	1880.05i	0.212989	+	0.122969i
$617$	23369.0	+	13492.1i	1.52480	+	0.880343i	0.999568	+	0.0293838i	$0.00935450\pi$
$617$	23369.0	+	13492.1i	1.52480	+	0.880343i	0.525231	+	0.850960i	$0.323979\pi$
$618$		0			0
$619$	6587.41	−	3803.25i	0.427739	−	0.246955i	−0.270644	−	0.962680i	$-0.587237\pi$
$619$	6587.41	−	3803.25i	0.427739	−	0.246955i	0.698383	+	0.715724i	$0.253903\pi$
$620$	2213.61			0.143388
$621$		0			0
$622$		−	15874.4i		−	1.02332i
$623$	−409.437	−	709.166i	−0.0263303	−	0.0456054i
$624$		0			0
$625$	4741.24	−	8212.06i	0.303439	−	0.525572i
$626$	−7977.91	−	4606.05i	−0.509363	−	0.294081i
$627$		0			0
$628$	20.0162	+	34.6690i	0.00127187	+	0.00220294i
$629$		−	38245.0i		−	2.42437i
$630$		0			0
$631$			29518.2i			1.86228i	0.364656	+	0.931142i	$0.381187\pi$
$631$			29518.2i			1.86228i	−0.364656	+	0.931142i	$0.618813\pi$
$632$	12816.8	−	7399.77i	0.806684	−	0.465739i
$633$		0			0
$634$	−9159.59	+	15864.9i	−0.573776	+	0.993809i
$635$	3907.44	+	2255.96i	0.244192	+	0.140984i
$636$		0			0
$637$	−5413.20	−	13035.8i	−0.336702	−	0.810830i
$638$	6242.47			0.387369
$639$		0			0
$640$	16248.3			1.00355
$641$	−8343.82	−	14451.9i	−0.514136	−	0.890509i	−0.999866	−	0.0164002i	$-0.994779\pi$
$641$	−8343.82	−	14451.9i	−0.514136	−	0.890509i	0.485730	−	0.874109i	$-0.338554\pi$
$642$		0			0
$643$	−7105.56	−	4102.40i	−0.435794	−	0.251606i	0.266018	−	0.963968i	$-0.414292\pi$
$643$	−7105.56	−	4102.40i	−0.435794	−	0.251606i	−0.701812	+	0.712362i	$0.747625\pi$
$644$	227.541	+	131.371i	0.0139230	+	0.00803842i
$645$		0			0
$646$	22042.2	+	38178.1i	1.34247	+	2.32523i
$647$	11773.5			0.715401			0.357700	−	0.933836i	$-0.383561\pi$
$647$	11773.5			0.715401			0.357700	+	0.933836i	$0.383561\pi$
$648$		0			0
$649$	13209.3			0.798939
$650$	−5310.41	+	2205.17i	−0.320448	+	0.133068i
$651$		0			0
$652$	−1869.26	−	1079.22i	−0.112279	−	0.0648243i
$653$	10049.8	−	17406.8i	0.602265	−	1.04315i	−0.390212	−	0.920725i	$-0.627598\pi$
$653$	10049.8	−	17406.8i	0.602265	−	1.04315i	0.992477	−	0.122429i	$-0.0390684\pi$
$654$		0			0
$655$	−1213.68	+	700.719i	−0.0724007	+	0.0418005i
$656$		−	3007.56i		−	0.179002i
$657$		0			0
$658$		−	5651.81i		−	0.334849i
$659$	3970.48	+	6877.07i	0.234701	+	0.406514i	0.959186	−	0.282777i	$-0.0912556\pi$
$659$	3970.48	+	6877.07i	0.234701	+	0.406514i	−0.724485	+	0.689291i	$0.757922\pi$
$660$		0			0
$661$	−18533.3	−	10700.2i	−1.09056	−	0.629638i	−0.156838	−	0.987624i	$-0.550130\pi$
$661$	−18533.3	−	10700.2i	−1.09056	−	0.629638i	−0.933727	+	0.357986i	$0.883463\pi$
$662$	14158.8	−	24523.7i	0.831264	−	1.43979i
$663$		0			0
$664$	197.995	+	342.937i	0.0115718	+	0.0200430i
$665$			8238.35i			0.480405i
$666$		0			0
$667$	−924.801			−0.0536858
$668$	−8532.96	+	4926.51i	−0.494237	+	0.285348i
$669$		0			0
$670$	−20389.8	−	11772.1i	−1.17571	−	0.678797i
$671$	−6830.46	−	3943.57i	−0.392976	−	0.226885i
$672$		0			0
$673$	−13143.1	−	22764.5i	−0.752791	−	1.30387i	−0.946465	−	0.322806i	$-0.895374\pi$
$673$	−13143.1	−	22764.5i	−0.752791	−	1.30387i	0.193674	−	0.981066i	$-0.437960\pi$
$674$			17128.9i			0.978902i
$675$		0			0
$676$	−5443.75	−	1448.28i	−0.309726	−	0.0824011i
$677$	−1702.82	−	2949.36i	−0.0966684	−	0.167435i	0.813635	−	0.581376i	$-0.197485\pi$
$677$	−1702.82	−	2949.36i	−0.0966684	−	0.167435i	−0.910304	+	0.413941i	$0.864152\pi$
$678$		0			0
$679$	−269.512	+	466.808i	−0.0152326	+	0.0263836i
$680$	8210.86	−	14221.6i	0.463047	−	0.802021i
$681$		0			0
$682$	−8557.29	+	4940.55i	−0.480462	+	0.277395i
$683$		−	30610.8i		−	1.71492i	−0.514549	−	0.857461i	$-0.672041\pi$
$683$		−	30610.8i		−	1.71492i	0.514549	−	0.857461i	$-0.327959\pi$
$684$		0			0
$685$	16574.5			0.924492
$686$	6772.71	+	11730.7i	0.376944	+	0.652886i
$687$		0			0
$688$	−18778.0	+	32524.4i	−1.04056	+	1.80230i
$689$	−13552.0	+	17693.8i	−0.749331	+	0.978347i
$690$		0			0
$691$	−5645.65	+	3259.51i	−0.310811	+	0.179447i	−0.647289	−	0.762244i	$-0.724097\pi$
$691$	−5645.65	+	3259.51i	−0.310811	+	0.179447i	0.336478	+	0.941691i	$0.390764\pi$
$692$	9622.45			0.528599
$693$		0			0
$694$			5970.02i			0.326540i
$695$	23661.0	−	13660.7i	1.29139	−	0.745582i
$696$		0			0
$697$	−3325.23	−	1919.82i	−0.180706	−	0.104331i
$698$	21117.0	−	36575.8i	1.14512	−	1.98340i
$699$		0			0
$700$	542.238	−	313.061i	0.0292781	−	0.0169037i
$701$	−21446.2			−1.15551			−0.577755	−	0.816210i	$-0.696071\pi$
$701$	−21446.2			−1.15551			−0.577755	+	0.816210i	$0.696071\pi$
$702$		0			0
$703$	−52395.2			−2.81098
$704$	−7394.33	+	4269.12i	−0.395859	+	0.228549i
$705$		0			0
$706$	−7189.71	+	12452.9i	−0.383269	+	0.663842i
$707$	264.207	+	152.540i	0.0140545	+	0.00811435i
$708$		0			0
$709$	9187.32	−	5304.30i	0.486653	−	0.280969i	−0.236532	−	0.971624i	$-0.576011\pi$
$709$	9187.32	−	5304.30i	0.486653	−	0.280969i	0.723185	+	0.690654i	$0.242677\pi$
$710$		−	23364.8i		−	1.23502i
$711$		0			0
$712$	2236.21			0.117704
$713$	1267.73	−	731.927i	0.0665877	−	0.0384444i
$714$		0			0
$715$	−8757.18	+	11433.6i	−0.458042	+	0.598032i
$716$	−3100.10	+	5369.52i	−0.161810	+	0.280263i
$717$		0			0
$718$	13303.4	+	23042.1i	0.691473	+	1.19767i
$719$	6348.37			0.329283			0.164641	−	0.986354i	$-0.447353\pi$
$719$	6348.37			0.329283			0.164641	+	0.986354i	$0.447353\pi$
$720$		0			0
$721$		−	598.909i		−	0.0309356i
$722$	32997.0	−	19050.8i	1.70086	−	0.981993i
$723$		0			0
$724$	2261.80	−	3917.55i	0.116104	−	0.201098i
$725$	−1101.92	+	1908.57i	−0.0564470	+	0.0977692i
$726$		0			0
$727$	12477.9	+	21612.4i	0.636562	+	1.10256i	0.986182	+	0.165666i	$0.0529773\pi$
$727$	12477.9	+	21612.4i	0.636562	+	1.10256i	−0.349620	+	0.936891i	$0.613689\pi$
$728$	−5312.83	−	694.643i	−0.270476	−	0.0353643i
$729$		0			0
$730$		−	15219.2i		−	0.771625i
$731$	23973.2	+	41522.9i	1.21297	+	2.10093i
$732$		0			0
$733$	−5325.44	−	3074.64i	−0.268349	−	0.154931i	0.359788	−	0.933034i	$-0.382849\pi$
$733$	−5325.44	−	3074.64i	−0.268349	−	0.154931i	−0.628137	+	0.778103i	$0.716182\pi$
$734$	−24933.6	−	14395.4i	−1.25384	−	0.723902i
$735$		0			0
$736$	−1535.84	+	886.719i	−0.0769183	+	0.0444088i
$737$	25508.0			1.27490
$738$		0			0
$739$			27560.7i			1.37190i	0.727648	+	0.685951i	$0.240614\pi$
$739$			27560.7i			1.37190i	−0.727648	+	0.685951i	$0.759386\pi$
$740$	−4602.94	−	7972.52i	−0.228658	−	0.396048i
$741$		0			0
$742$	4999.50	−	8659.38i	0.247355	−	0.428431i
$743$	6964.89	+	4021.18i	0.343899	+	0.198550i	0.661995	−	0.749508i	$-0.269710\pi$
$743$	6964.89	+	4021.18i	0.343899	+	0.198550i	−0.318096	+	0.948059i	$0.603043\pi$
$744$		0			0
$745$	10432.3	+	18069.3i	0.513034	+	0.888602i
$746$			7344.46i			0.360455i
$747$		0			0
$748$		−	8391.73i		−	0.410203i
$749$	3626.47	−	2093.74i	0.176914	−	0.102141i
$750$		0			0
$751$	−3530.34	+	6114.73i	−0.171536	+	0.297110i	−0.938957	−	0.344034i	$-0.888206\pi$
$751$	−3530.34	+	6114.73i	−0.171536	+	0.297110i	0.767421	+	0.641144i	$0.221540\pi$
$752$	18140.7	+	10473.6i	0.879687	+	0.507887i
$753$		0			0
$754$	−8215.23	+	3411.42i	−0.396792	+	0.164770i
$755$	−13236.5			−0.638045
$756$		0			0
$757$	1001.86			0.0481019			0.0240509	−	0.999711i	$-0.492344\pi$
$757$	1001.86			0.0481019			0.0240509	+	0.999711i	$0.492344\pi$
$758$	23051.1	+	39925.6i	1.10456	+	1.91315i
$759$		0			0
$760$	−19483.5	−	11248.8i	−0.929921	−	0.536890i
$761$	−19643.7	−	11341.3i	−0.935719	−	0.540238i	−0.0471033	−	0.998890i	$-0.514999\pi$
$761$	−19643.7	−	11341.3i	−0.935719	−	0.540238i	−0.888616	+	0.458652i	$0.848332\pi$
$762$		0			0
$763$	−222.161	−	384.794i	−0.0105410	−	0.0182575i
$764$	451.395			0.0213755
$765$		0			0
$766$	−2658.83			−0.125415
$767$	−17383.8	+	7218.71i	−0.818373	+	0.339834i
$768$		0			0
$769$	13432.6	+	7755.34i	0.629900	+	0.363673i	0.780714	−	0.624889i	$-0.214856\pi$
$769$	13432.6	+	7755.34i	0.629900	+	0.363673i	−0.150813	+	0.988562i	$0.548189\pi$
$770$	3230.63	−	5595.62i	0.151200	−	0.261886i
$771$		0			0
$772$	−9423.40	+	5440.60i	−0.439321	+	0.253642i
$773$			19202.7i			0.893499i	0.894659	+	0.446750i	$0.147419\pi$
$773$			19202.7i			0.893499i	−0.894659	+	0.446750i	$0.852581\pi$
$774$		0			0
$775$		−	3488.41i		−	0.161687i
$776$	−735.993	−	1274.78i	−0.0340472	−	0.0589714i
$777$		0			0
$778$	35870.7	+	20710.0i	1.65299	+	0.954355i
$779$	−2630.14	+	4555.53i	−0.120969	+	0.209524i
$780$		0			0
$781$	12656.8	+	21922.3i	0.579894	+	1.00441i
$782$			5122.17i			0.234231i
$783$		0			0
$784$	−23470.2			−1.06916
$785$	−126.305	+	72.9225i	−0.00574272	+	0.00331556i
$786$		0			0
$787$	−17403.0	−	10047.6i	−0.788245	−	0.455093i	0.0510996	−	0.998694i	$-0.483727\pi$
$787$	−17403.0	−	10047.6i	−0.788245	−	0.455093i	−0.839344	+	0.543600i	$0.817061\pi$
$788$	−5416.98	−	3127.50i	−0.244888	−	0.141386i
$789$		0			0
$790$	−12715.6	−	22024.1i	−0.572660	−	0.991877i
$791$			10989.7i			0.493992i
$792$		0			0
$793$	11144.1	+	1457.08i	0.499042	+	0.0652488i
$794$	−3202.69	−	5547.22i	−0.143148	−	0.247939i
$795$		0			0
$796$	−468.424	+	811.334i	−0.0208579	+	0.0361269i
$797$	12012.0	−	20805.3i	0.533859	−	0.924671i	−0.465359	−	0.885122i	$-0.654075\pi$
$797$	12012.0	−	20805.3i	0.533859	−	0.924671i	0.999218	−	0.0395485i	$-0.0125920\pi$
$798$		0			0
$799$	23159.7	−	13371.2i	1.02544	−	0.592041i
$800$			4226.16i			0.186772i
$801$		0			0
$802$	45436.1			2.00051
$803$	8244.32	+	14279.6i	0.362311	+	0.627541i
$804$		0			0
$805$	−478.608	+	828.973i	−0.0209549	+	0.0362950i
$806$	8561.64	−	11178.3i	0.374158	−	0.488510i
$807$		0			0
$808$	−721.505	+	416.561i	−0.0314139	+	0.0181368i
$809$	9049.70			0.393289			0.196644	−	0.980475i	$-0.436996\pi$
$809$	9049.70			0.393289			0.196644	+	0.980475i	$0.436996\pi$
$810$		0			0
$811$			12498.2i			0.541150i	0.962699	+	0.270575i	$0.0872138\pi$
$811$			12498.2i			0.541150i	−0.962699	+	0.270575i	$0.912786\pi$
$812$	838.845	−	484.308i	0.0362533	−	0.0209309i
$813$		0			0
$814$	35587.7	+	20546.6i	1.53237	+	0.884713i
$815$	3931.78	−	6810.05i	0.168987	−	0.292694i
$816$		0			0
$817$	56885.9	−	32843.1i	2.43597	−	1.40641i
$818$	−8549.80			−0.365448
$819$		0			0
$820$	−924.234			−0.0393606
$821$	−20787.0	+	12001.4i	−0.883645	+	0.510173i	−0.871858	−	0.489758i	$-0.837085\pi$
$821$	−20787.0	+	12001.4i	−0.883645	+	0.510173i	−0.0117864	+	0.999931i	$0.503752\pi$
$822$		0			0
$823$	−2440.79	+	4227.58i	−0.103379	+	0.179057i	−0.913075	−	0.407792i	$-0.866299\pi$
$823$	−2440.79	+	4227.58i	−0.103379	+	0.179057i	0.809696	+	0.586850i	$0.199632\pi$
$824$	1416.40	+	817.761i	0.0598820	+	0.0345729i
$825$		0			0
$826$	7313.35	−	4222.37i	0.308068	−	0.177863i
$827$			36016.1i			1.51439i	0.653187	+	0.757197i	$0.273432\pi$
$827$			36016.1i			1.51439i	−0.653187	+	0.757197i	$0.726568\pi$
$828$		0			0
$829$	−4377.50			−0.183398			−0.0916990	−	0.995787i	$-0.529230\pi$
$829$	−4377.50			−0.183398			−0.0916990	+	0.995787i	$0.529230\pi$
$830$	589.296	−	340.230i	0.0246443	−	0.0142284i
$831$		0			0
$832$	7398.10	−	9659.16i	0.308273	−	0.402489i
$833$	−14981.8	+	25949.3i	−0.623157	+	1.07934i
$834$		0			0
$835$	−17948.1	−	31087.1i	−0.743858	−	1.28840i
$836$	−11496.6			−0.475619
$837$		0			0
$838$		−	14225.3i		−	0.586402i
$839$	−20711.7	+	11957.9i	−0.852263	+	0.492054i	−0.861414	−	0.507904i	$-0.830420\pi$
$839$	−20711.7	+	11957.9i	−0.852263	+	0.492054i	0.00915102	+	0.999958i	$0.497087\pi$
$840$		0			0
$841$	10489.8	−	18168.9i	0.430105	−	0.744964i
$842$	−13802.2	+	23906.1i	−0.564911	+	0.978454i
$843$		0			0
$844$	954.540	+	1653.31i	0.0389297	+	0.0674281i
$845$	5276.35	−	19832.6i	0.214807	−	0.807409i
$846$		0			0
$847$		−	1611.23i		−	0.0653629i
$848$	18529.5	+	32094.0i	0.750359	+	1.29966i
$849$		0			0
$850$	10571.0	+	6103.15i	0.426566	+	0.246278i
$851$	−5272.20	−	3043.91i	−0.212372	−	0.122613i
$852$		0			0
$853$	−28289.4	+	16332.9i	−1.13553	+	0.655601i	−0.945321	−	0.326142i	$-0.894251\pi$
$853$	−28289.4	+	16332.9i	−1.13553	+	0.655601i	−0.190214	+	0.981743i	$0.560918\pi$
$854$	−5042.25			−0.202040
$855$		0			0
$856$			11435.3i			0.456603i
$857$	−15973.8	−	27667.4i	−0.636703	−	1.10280i	−0.986152	−	0.165846i	$-0.946964\pi$
$857$	−15973.8	−	27667.4i	−0.636703	−	1.10280i	0.349449	−	0.936955i	$-0.386369\pi$
$858$		0			0
$859$	−6996.89	+	12119.0i	−0.277917	+	0.481366i	−0.970867	−	0.239619i	$-0.922977\pi$
$859$	−6996.89	+	12119.0i	−0.277917	+	0.481366i	0.692950	+	0.720986i	$0.256311\pi$
$860$	9994.89	+	5770.55i	0.396306	+	0.228807i
$861$		0			0
$862$	1383.14	+	2395.66i	0.0546518	+	0.0946597i
$863$			10612.0i			0.418583i	0.977853	+	0.209292i	$0.0671158\pi$
$863$			10612.0i			0.418583i	−0.977853	+	0.209292i	$0.932884\pi$
$864$		0			0
$865$			35056.3i			1.37798i
$866$	−17984.4	+	10383.3i	−0.705700	+	0.407436i
$867$		0			0
$868$	−766.603	+	1327.80i	−0.0299772	+	0.0519220i
$869$	23861.2	+	13776.3i	0.931457	+	0.537777i
$870$		0			0
$871$	−33569.1	+	13939.7i	−1.30591	+	0.542285i
$872$	1213.37			0.0471214
$873$		0			0
$874$	7017.32			0.271584
$875$	4917.80	+	8517.87i	0.190002	+	0.329093i
$876$		0			0
$877$	−2998.55	−	1731.21i	−0.115455	−	0.0666578i	0.441161	−	0.897428i	$-0.354567\pi$
$877$	−2998.55	−	1731.21i	−0.115455	−	0.0666578i	−0.556615	+	0.830770i	$0.687900\pi$
$878$	19238.9	+	11107.6i	0.739501	+	0.426951i
$879$		0			0
$880$	11973.6	+	20738.9i	0.458670	+	0.794440i
$881$	−46965.4			−1.79603			−0.898016	−	0.439963i	$-0.854992\pi$
$881$	−46965.4			−1.79603			−0.898016	+	0.439963i	$0.854992\pi$
$882$		0			0
$883$	−2872.66			−0.109482			−0.0547410	−	0.998501i	$-0.517433\pi$
$883$	−2872.66			−0.109482			−0.0547410	+	0.998501i	$0.517433\pi$
$884$	4585.96	+	11043.7i	0.174482	+	0.420181i
$885$		0			0
$886$	13805.9	+	7970.83i	0.523497	+	0.302241i
$887$	13523.1	−	23422.7i	0.511907	−	0.886648i	−0.487998	−	0.872845i	$-0.662273\pi$
$887$	13523.1	−	23422.7i	0.511907	−	0.886648i	0.999905	−	0.0138036i	$-0.00439395\pi$
$888$		0			0
$889$	−2706.40	+	1562.54i	−0.102103	+	0.0589492i
$890$		−	3842.66i		−	0.144726i
$891$		0			0
$892$			11058.1i			0.415083i
$893$	−18318.5	−	31728.5i	−0.686455	−	1.18897i
$894$		0			0
$895$	−19562.1	−	11294.2i	−0.730603	−	0.421814i
$896$	−5627.00	+	9746.25i	−0.209805	+	0.363392i
$897$		0			0
$898$	−23828.2	−	41271.6i	−0.885475	−	1.53369i
$899$		−	5396.59i		−	0.200207i
$900$		0			0
$901$	47311.9			1.74938
$902$	3572.87	−	2062.80i	0.131889	−	0.0761459i
$903$		0			0
$904$	−25990.3	−	15005.5i	−0.956221	−	0.552074i
$905$	14272.3	+	8240.14i	0.524231	+	0.302665i
$906$		0			0
$907$	5016.16	+	8688.24i	0.183637	+	0.318069i	0.943116	−	0.332463i	$-0.107880\pi$
$907$	5016.16	+	8688.24i	0.183637	+	0.318069i	−0.759479	+	0.650531i	$0.774546\pi$
$908$		−	2831.99i		−	0.103505i
$909$		0			0
$910$	−1193.66	+	9129.46i	−0.0434830	+	0.332570i
$911$	16542.3	+	28652.2i	0.601616	+	1.04203i	0.992576	+	0.121622i	$0.0388096\pi$
$911$	16542.3	+	28652.2i	0.601616	+	1.04203i	−0.390960	+	0.920408i	$0.627857\pi$
$912$		0			0
$913$	−368.610	+	638.450i	−0.0133617	+	0.0231431i
$914$	18213.7	−	31547.1i	0.659142	−	1.14167i
$915$		0			0
$916$	−7986.45	+	4610.98i	−0.288078	+	0.166322i
$917$		−	970.673i		−	0.0349558i
$918$		0			0
$919$	−25742.6			−0.924014			−0.462007	−	0.886876i	$-0.652870\pi$
$919$	−25742.6			−0.924014			−0.462007	+	0.886876i	$0.652870\pi$
$920$	−1307.00	−	2263.79i	−0.0468375	−	0.0811250i
$921$		0			0
$922$	24076.7	−	41702.1i	0.860006	−	1.48957i
$923$	−28636.9	−	21933.4i	−1.02123	−	0.782176i
$924$		0			0
$925$	−12563.8	+	7253.73i	−0.446590	+	0.257839i
$926$	−31476.9			−1.11706
$927$		0			0
$928$			6537.89i			0.231268i
$929$	24645.6	−	14229.2i	0.870395	−	0.502523i	0.00291574	−	0.999996i	$-0.499072\pi$
$929$	24645.6	−	14229.2i	0.870395	−	0.502523i	0.867480	+	0.497473i	$0.165739\pi$
$930$		0			0
$931$	35550.3	+	20525.0i	1.25146	+	0.722533i
$932$	4031.17	−	6982.19i	0.141680	−	0.245396i
$933$		0			0
$934$	27756.5	−	16025.2i	0.972399	−	0.561415i
$935$	30572.6			1.06934
$936$		0			0
$937$	30105.7			1.04964			0.524818	−	0.851214i	$-0.324133\pi$
$937$	30105.7			1.04964			0.524818	+	0.851214i	$0.324133\pi$
$938$	14122.5	−	8153.64i	0.491595	−	0.283823i
$939$		0			0
$940$	3218.57	−	5574.72i	0.111679	−	0.193433i
$941$	−23544.6	−	13593.5i	−0.815655	−	0.470918i	0.0332611	−	0.999447i	$-0.489411\pi$
$941$	−23544.6	−	13593.5i	−0.815655	−	0.470918i	−0.848916	+	0.528528i	$0.822744\pi$
$942$		0			0
$943$	−529.309	+	305.597i	−0.0182785	+	0.0105531i
$944$			31298.4i			1.07911i
$945$		0			0
$946$	−51517.1			−1.77058
$947$	−23808.5	+	13745.9i	−0.816973	+	0.471680i	−0.849372	−	0.527795i	$-0.823019\pi$
$947$	−23808.5	+	13745.9i	−0.816973	+	0.471680i	0.0323984	+	0.999475i	$0.489685\pi$
$948$		0			0
$949$	−18653.3	−	14286.9i	−0.638052	−	0.488694i
$950$	8361.24	−	14482.1i	0.285552	−	0.494591i
$951$		0			0
$952$	5687.06	+	9850.28i	0.193612	+	0.335346i
$953$	−40303.9			−1.36996			−0.684980	−	0.728562i	$-0.740189\pi$
$953$	−40303.9			−1.36996			−0.684980	+	0.728562i	$0.740189\pi$
$954$		0			0
$955$			1644.51i			0.0557227i
$956$	6873.69	−	3968.53i	0.232543	−	0.134259i
$957$		0			0
$958$	−9029.29	+	15639.2i	−0.304513	+	0.527432i
$959$	−5739.95	+	9941.89i	−0.193277	+	0.334766i
$960$		0			0
$961$	−10624.4	−	18402.0i	−0.356632	−	0.617704i
$962$	−58062.6	−	7591.59i	−1.94596	−	0.254431i
$963$		0			0
$964$		−	12361.5i		−	0.413004i
$965$	−19821.1	−	34331.1i	−0.661206	−	1.14524i
$966$		0			0
$967$	−36272.8	−	20942.1i	−1.20626	−	0.696435i	−0.244321	−	0.969694i	$-0.578565\pi$
$967$	−36272.8	−	20942.1i	−1.20626	−	0.696435i	−0.961940	+	0.273259i	$0.911898\pi$
$968$	3810.51	+	2200.00i	0.126523	+	0.0730481i
$969$		0			0
$970$	−2190.55	+	1264.72i	−0.0725097	+	0.0418635i
$971$	34348.3			1.13521			0.567605	−	0.823301i	$-0.307870\pi$
$971$	34348.3			1.13521			0.567605	+	0.823301i	$0.307870\pi$
$972$		0			0
$973$			18923.5i			0.623494i
$974$	20392.7	+	35321.2i	0.670867	+	1.16198i
$975$		0			0
$976$	9343.96	−	16184.2i	0.306448	−	0.530783i
$977$	−17184.0	−	9921.18i	−0.562707	−	0.324879i	0.191524	−	0.981488i	$-0.438657\pi$
$977$	−17184.0	−	9921.18i	−0.562707	−	0.324879i	−0.754231	+	0.656609i	$0.771990\pi$
$978$		0			0
$979$	2081.60	+	3605.43i	0.0679551	+	0.117702i
$980$			7212.50i			0.235097i
$981$		0			0
$982$		−	43102.3i		−	1.40066i
$983$	7289.05	−	4208.33i	0.236505	−	0.136546i	−0.377064	−	0.926187i	$-0.623066\pi$
$983$	7289.05	−	4208.33i	0.236505	−	0.136546i	0.613569	+	0.789641i	$0.289733\pi$
$984$		0			0
$985$	11394.0	−	19735.0i	0.368572	−	0.638386i
$986$	16353.3	+	9441.60i	0.528191	+	0.304951i
$987$		0			0
$988$	15129.8	−	6282.71i	0.487188	−	0.202307i
$989$	7632.09			0.245386
$990$		0			0
$991$	13346.4			0.427814			0.213907	−	0.976854i	$-0.431381\pi$
$991$	13346.4			0.427814			0.213907	+	0.976854i	$0.431381\pi$
$992$	−5174.36	−	8962.26i	−0.165611	−	0.286847i
$993$		0			0
$994$	14014.9	+	8091.53i	0.447210	+	0.258197i
$995$	−2955.84	−	1706.55i	−0.0941772	−	0.0543732i
$996$		0			0
$997$	−7909.96	−	13700.4i	−0.251265	−	0.435203i	0.712610	−	0.701561i	$-0.247513\pi$
$997$	−7909.96	−	13700.4i	−0.251265	−	0.435203i	−0.963874	+	0.266358i	$0.914180\pi$
$998$	−27813.0			−0.882168
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.4.t.a.64.10		80
3.2	odd	2		117.4.t.a.103.31	yes	80
9.2	odd	6		117.4.t.a.25.10	✓	80
9.7	even	3	inner	351.4.t.a.181.31		80
13.12	even	2	inner	351.4.t.a.64.31		80
39.38	odd	2		117.4.t.a.103.10	yes	80
117.25	even	6	inner	351.4.t.a.181.10		80
117.38	odd	6		117.4.t.a.25.31	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.4.t.a.25.10	✓	80	9.2	odd	6
117.4.t.a.25.31	yes	80	117.38	odd	6
117.4.t.a.103.10	yes	80	39.38	odd	2
117.4.t.a.103.31	yes	80	3.2	odd	2
351.4.t.a.64.10		80	1.1	even	1	trivial
351.4.t.a.64.31		80	13.12	even	2	inner
351.4.t.a.181.10		80	117.25	even	6	inner
351.4.t.a.181.31		80	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	351.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.81478 + 1.62512i) q^{2} +(1.28200 - 2.22049i) q^{4} +(8.08964 + 4.67056i) q^{5} +(-5.60310 + 3.23495i) q^{7} -17.6683i q^{8} +O(q^{10})\)	\(q+(-2.81478 + 1.62512i) q^{2} +(1.28200 - 2.22049i) q^{4} +(8.08964 + 4.67056i) q^{5} +(-5.60310 + 3.23495i) q^{7} -17.6683i q^{8} -30.3608 q^{10} +(28.4864 - 16.4466i) q^{11} +(-28.5009 + 37.2115i) q^{13} +(10.5143 - 18.2114i) q^{14} +(38.9690 + 67.4962i) q^{16} +99.5008 q^{17} -136.315i q^{19} +(20.7419 - 11.9753i) q^{20} +(-53.4553 + 92.5874i) q^{22} +(7.91924 - 13.7165i) q^{23} +(-18.8718 - 32.6869i) q^{25} +(19.7508 - 151.060i) q^{26} +16.5888i q^{28} +(-29.1948 - 50.5668i) q^{29} +(80.0415 + 46.2120i) q^{31} +(-96.9690 - 55.9851i) q^{32} +(-280.073 + 161.700i) q^{34} -60.4361 q^{35} -384.369i q^{37} +(221.528 + 383.697i) q^{38} +(82.5206 - 142.930i) q^{40} +(-33.4192 - 19.2946i) q^{41} +(240.935 + 417.312i) q^{43} -84.3383i q^{44} +51.4787i q^{46} +(232.759 - 134.383i) q^{47} +(-150.570 + 260.795i) q^{49} +(106.240 + 61.3377i) q^{50} +(46.0897 + 110.991i) q^{52} +475.493 q^{53} +307.260 q^{55} +(57.1560 + 98.9970i) q^{56} +(164.354 + 94.8898i) q^{58} +(347.780 + 200.791i) q^{59} +(-119.890 - 207.655i) q^{61} -300.399 q^{62} -259.574 q^{64} +(-404.361 + 167.913i) q^{65} +(671.583 + 387.739i) q^{67} +(127.560 - 220.940i) q^{68} +(170.115 - 98.2157i) q^{70} +769.570i q^{71} +501.277i q^{73} +(624.643 + 1081.91i) q^{74} +(-302.686 - 174.756i) q^{76} +(-106.408 + 184.304i) q^{77} +(418.818 + 725.413i) q^{79} +728.027i q^{80} +125.424 q^{82} +(-19.4098 + 11.2062i) q^{83} +(804.926 + 464.724i) q^{85} +(-1356.36 - 783.095i) q^{86} +(-290.583 - 503.305i) q^{88} +126.567i q^{89} +(39.3159 - 300.699i) q^{91} +(-20.3049 - 35.1692i) q^{92} +(-436.777 + 756.520i) q^{94} +(636.667 - 1102.74i) q^{95} +(72.1507 - 41.6562i) q^{97} -978.776i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 150 q^{4}+O(q^{10}) \) 80 * q + 150 * q^4	\( 80 q + 150 q^{4} - 40 q^{10} - 13 q^{13} - 78 q^{14} - 530 q^{16} - 264 q^{17} - 34 q^{22} + 174 q^{23} + 798 q^{25} + 1032 q^{26} - 642 q^{29} + 2136 q^{35} + 708 q^{38} + 88 q^{40} + 166 q^{43} + 1610 q^{49} + 786 q^{52} - 1296 q^{53} - 508 q^{55} + 888 q^{56} + 838 q^{61} - 3540 q^{62} - 3652 q^{64} + 201 q^{65} - 612 q^{68} - 4458 q^{74} + 2166 q^{77} + 514 q^{79} - 5188 q^{82} + 2338 q^{88} - 1086 q^{91} - 516 q^{92} + 488 q^{94} - 2136 q^{95}+O(q^{100}) \) 80 * q + 150 * q^4 - 40 * q^10 - 13 * q^13 - 78 * q^14 - 530 * q^16 - 264 * q^17 - 34 * q^22 + 174 * q^23 + 798 * q^25 + 1032 * q^26 - 642 * q^29 + 2136 * q^35 + 708 * q^38 + 88 * q^40 + 166 * q^43 + 1610 * q^49 + 786 * q^52 - 1296 * q^53 - 508 * q^55 + 888 * q^56 + 838 * q^61 - 3540 * q^62 - 3652 * q^64 + 201 * q^65 - 612 * q^68 - 4458 * q^74 + 2166 * q^77 + 514 * q^79 - 5188 * q^82 + 2338 * q^88 - 1086 * q^91 - 516 * q^92 + 488 * q^94 - 2136 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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