LMFDB - Embedded newform 819.2.n.e.100.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(100,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("819.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.n (of order $3$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.8
Root			$-1.27528 - 2.20885i$ of defining polynomial
Character	$\chi$	$=$	819.100
Dual form			819.2.n.e.172.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27528 + 2.20885i) q^{2} +(-2.25269 + 3.90177i) q^{4} +(1.39351 - 2.41363i) q^{5} +(2.06947 - 1.64842i) q^{7} -6.39011 q^{8} +O(q^{10})$	\(q+(1.27528 + 2.20885i) q^{2} +(-2.25269 + 3.90177i) q^{4} +(1.39351 - 2.41363i) q^{5} +(2.06947 - 1.64842i) q^{7} -6.39011 q^{8} +7.10846 q^{10} +2.76747 q^{11} +(2.99297 - 2.01050i) q^{13} +(6.28028 + 2.46895i) q^{14} +(-3.64382 - 6.31127i) q^{16} +(-2.94340 + 5.09812i) q^{17} +3.40075 q^{19} +(6.27828 + 10.8743i) q^{20} +(3.52930 + 6.11292i) q^{22} +(-3.67246 - 6.36089i) q^{23} +(-1.38373 - 2.39670i) q^{25} +(8.25778 + 4.04708i) q^{26} +(1.76989 + 11.7880i) q^{28} +(-1.56328 + 2.70768i) q^{29} +(1.93352 + 3.34896i) q^{31} +(2.90367 - 5.02931i) q^{32} -15.0147 q^{34} +(-1.09485 - 7.29202i) q^{35} +(-2.92173 - 5.06059i) q^{37} +(4.33691 + 7.51175i) q^{38} +(-8.90467 + 15.4233i) q^{40} +(-3.24124 + 5.61400i) q^{41} +(2.99197 + 5.18224i) q^{43} +(-6.23423 + 10.7980i) q^{44} +(9.36684 - 16.2238i) q^{46} +(-3.95673 + 6.85325i) q^{47} +(1.56542 - 6.82272i) q^{49} +(3.52930 - 6.11292i) q^{50} +(1.10228 + 16.2069i) q^{52} +(-6.34471 - 10.9894i) q^{53} +(3.85649 - 6.67963i) q^{55} +(-13.2241 + 10.5336i) q^{56} -7.97449 q^{58} +(1.36824 - 2.36987i) q^{59} +9.55263 q^{61} +(-4.93157 + 8.54173i) q^{62} +0.236742 q^{64} +(-0.681870 - 10.0256i) q^{65} -8.68066 q^{67} +(-13.2611 - 22.9689i) q^{68} +(14.7108 - 11.7177i) q^{70} +(1.57062 + 2.72039i) q^{71} +(-4.80291 - 8.31889i) q^{73} +(7.45207 - 12.9074i) q^{74} +(-7.66082 + 13.2689i) q^{76} +(5.72719 - 4.56195i) q^{77} +(-1.88112 + 3.25819i) q^{79} -20.3108 q^{80} -16.5340 q^{82} -4.82088 q^{83} +(8.20331 + 14.2086i) q^{85} +(-7.63120 + 13.2176i) q^{86} -17.6844 q^{88} +(0.877787 + 1.52037i) q^{89} +(2.87972 - 9.09435i) q^{91} +33.0916 q^{92} -20.1838 q^{94} +(4.73897 - 8.20814i) q^{95} +(8.48637 + 14.6988i) q^{97} +(17.0667 - 5.24311i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) $ 16 * q - 6 * q^4 + q^7 - 12 * q^8	$ 16 q - 6 q^{4} + q^{7} - 12 q^{8} + 8 q^{10} - 4 q^{11} + 5 q^{13} + 7 q^{14} - 6 q^{16} + 2 q^{17} + 22 q^{19} + 20 q^{20} + 7 q^{22} - 4 q^{23} + 2 q^{25} + 6 q^{26} - 7 q^{28} - 15 q^{29} + 3 q^{31} - 3 q^{32} - 68 q^{34} + 12 q^{35} + 4 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} + 2 q^{46} - 5 q^{47} + 13 q^{49} + 7 q^{50} + 36 q^{52} - 36 q^{53} - 15 q^{55} - 39 q^{56} - 40 q^{58} + 17 q^{59} + 44 q^{61} + 6 q^{62} - 20 q^{64} + 21 q^{65} - 52 q^{67} - 5 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} - 15 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} - 56 q^{80} + 2 q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} - 48 q^{88} - 20 q^{89} - 7 q^{91} + 94 q^{92} + 40 q^{94} + 7 q^{97} + 3 q^{98}+O(q^{100}) $ 16 * q - 6 * q^4 + q^7 - 12 * q^8 + 8 * q^10 - 4 * q^11 + 5 * q^13 + 7 * q^14 - 6 * q^16 + 2 * q^17 + 22 * q^19 + 20 * q^20 + 7 * q^22 - 4 * q^23 + 2 * q^25 + 6 * q^26 - 7 * q^28 - 15 * q^29 + 3 * q^31 - 3 * q^32 - 68 * q^34 + 12 * q^35 + 4 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 + 2 * q^46 - 5 * q^47 + 13 * q^49 + 7 * q^50 + 36 * q^52 - 36 * q^53 - 15 * q^55 - 39 * q^56 - 40 * q^58 + 17 * q^59 + 44 * q^61 + 6 * q^62 - 20 * q^64 + 21 * q^65 - 52 * q^67 - 5 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 - 15 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 - 56 * q^80 + 2 * q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 - 48 * q^88 - 20 * q^89 - 7 * q^91 + 94 * q^92 + 40 * q^94 + 7 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.27528	+	2.20885i	0.901760	+	1.56189i	0.825208	+	0.564829i	$0.191058\pi$
$2$	1.27528	+	2.20885i	0.901760	+	1.56189i	0.0765522	+	0.997066i	$0.475609\pi$
$3$		0			0
$3$		0			0
$4$	−2.25269	+	3.90177i	−1.12634	+	1.95088i
$5$	1.39351	−	2.41363i	0.623196	−	1.07941i	−0.365691	−	0.930736i	$-0.619167\pi$
$5$	1.39351	−	2.41363i	0.623196	−	1.07941i	0.988887	−	0.148671i	$-0.0474995\pi$
$6$		0			0
$7$	2.06947	−	1.64842i	0.782186	−	0.623044i
$7$	2.06947	−	1.64842i	0.782186	−	0.623044i
$8$	−6.39011			−2.25924
$9$		0			0
$10$	7.10846			2.24789
$11$	2.76747			0.834422			0.417211	−	0.908810i	$-0.363008\pi$
$11$	2.76747			0.834422			0.417211	+	0.908810i	$0.363008\pi$
$12$		0			0
$13$	2.99297	−	2.01050i	0.830101	−	0.557613i
$13$	2.99297	−	2.01050i	0.830101	−	0.557613i
$14$	6.28028	+	2.46895i	1.67847	+	0.659856i
$15$		0			0
$16$	−3.64382	−	6.31127i	−0.910954	−	1.57782i
$17$	−2.94340	+	5.09812i	−0.713880	+	1.23648i	0.249510	+	0.968372i	$0.419730\pi$
$17$	−2.94340	+	5.09812i	−0.713880	+	1.23648i	−0.963390	+	0.268104i	$0.913603\pi$
$18$		0			0
$19$	3.40075			0.780185			0.390093	−	0.920776i	$-0.372443\pi$
$19$	3.40075			0.780185			0.390093	+	0.920776i	$0.372443\pi$
$20$	6.27828	+	10.8743i	1.40386	+	2.43157i
$21$		0			0
$22$	3.52930	+	6.11292i	0.752449	+	1.30328i
$23$	−3.67246	−	6.36089i	−0.765761	−	1.32634i	−0.939843	−	0.341605i	$-0.889029\pi$
$23$	−3.67246	−	6.36089i	−0.765761	−	1.32634i	0.174083	−	0.984731i	$-0.444304\pi$
$24$		0			0
$25$	−1.38373	−	2.39670i	−0.276747	−	0.479339i
$26$	8.25778	+	4.04708i	1.61948	+	0.793697i
$27$		0			0
$28$	1.76989	+	11.7880i	0.334477	+	2.22772i
$29$	−1.56328	+	2.70768i	−0.290294	+	0.502803i	−0.973879	−	0.227067i	$-0.927086\pi$
$29$	−1.56328	+	2.70768i	−0.290294	+	0.502803i	0.683585	+	0.729871i	$0.260420\pi$
$30$		0			0
$31$	1.93352	+	3.34896i	0.347271	+	0.601491i	0.985764	−	0.168137i	$-0.0537751\pi$
$31$	1.93352	+	3.34896i	0.347271	+	0.601491i	−0.638493	+	0.769628i	$0.720442\pi$
$32$	2.90367	−	5.02931i	0.513302	−	0.889065i
$33$		0			0
$34$	−15.0147			−2.57499
$35$	−1.09485	−	7.29202i	−0.185063	−	1.23258i
$36$		0			0
$37$	−2.92173	−	5.06059i	−0.480330	−	0.831956i	0.519415	−	0.854522i	$-0.326150\pi$
$37$	−2.92173	−	5.06059i	−0.480330	−	0.831956i	−0.999745	+	0.0225659i	$0.992816\pi$
$38$	4.33691	+	7.51175i	0.703540	+	1.21857i
$39$		0			0
$40$	−8.90467	+	15.4233i	−1.40795	+	2.43865i
$41$	−3.24124	+	5.61400i	−0.506197	+	0.876759i	0.493777	+	0.869588i	$0.335616\pi$
$41$	−3.24124	+	5.61400i	−0.506197	+	0.876759i	−0.999974	+	0.00717054i	$0.997718\pi$
$42$		0			0
$43$	2.99197	+	5.18224i	0.456271	+	0.790284i	0.998760	−	0.0497783i	$-0.0158515\pi$
$43$	2.99197	+	5.18224i	0.456271	+	0.790284i	−0.542489	+	0.840063i	$0.682518\pi$
$44$	−6.23423	+	10.7980i	−0.939846	+	1.62786i
$45$		0			0
$46$	9.36684	−	16.2238i	1.38106	−	2.39207i
$47$	−3.95673	+	6.85325i	−0.577148	+	0.999650i	0.418656	+	0.908145i	$0.362501\pi$
$47$	−3.95673	+	6.85325i	−0.577148	+	0.999650i	−0.995805	+	0.0915053i	$0.970832\pi$
$48$		0			0
$49$	1.56542	−	6.82272i	0.223631	−	0.974674i
$50$	3.52930	−	6.11292i	0.499118	−	0.864498i
$51$		0			0
$52$	1.10228	+	16.2069i	0.152859	+	2.24749i
$53$	−6.34471	−	10.9894i	−0.871513	−	1.50951i	−0.860431	−	0.509567i	$-0.829806\pi$
$53$	−6.34471	−	10.9894i	−0.871513	−	1.50951i	−0.0110819	−	0.999939i	$-0.503528\pi$
$54$		0			0
$55$	3.85649	−	6.67963i	0.520009	−	0.900682i
$56$	−13.2241	+	10.5336i	−1.76715	+	1.40761i
$57$		0			0
$58$	−7.97449			−1.04710
$59$	1.36824	−	2.36987i	0.178130	−	0.308530i	−0.763110	−	0.646269i	$-0.776329\pi$
$59$	1.36824	−	2.36987i	0.178130	−	0.308530i	0.941240	+	0.337738i	$0.109662\pi$
$60$		0			0
$61$	9.55263			1.22309			0.611544	−	0.791210i	$-0.290549\pi$
$61$	9.55263			1.22309			0.611544	+	0.791210i	$0.290549\pi$
$62$	−4.93157	+	8.54173i	−0.626310	+	1.08480i
$63$		0			0
$64$	0.236742			0.0295928
$65$	−0.681870	−	10.0256i	−0.0845756	−	1.24352i
$66$		0			0
$67$	−8.68066			−1.06051			−0.530255	−	0.847838i	$-0.677904\pi$
$67$	−8.68066			−1.06051			−0.530255	+	0.847838i	$0.677904\pi$
$68$	−13.2611	−	22.9689i	−1.60815	−	2.78539i
$69$		0			0
$70$	14.7108	−	11.7177i	1.75827	−	1.40054i
$71$	1.57062	+	2.72039i	0.186398	+	0.322851i	0.944047	−	0.329812i	$-0.106985\pi$
$71$	1.57062	+	2.72039i	0.186398	+	0.322851i	−0.757649	+	0.652663i	$0.773652\pi$
$72$		0			0
$73$	−4.80291	−	8.31889i	−0.562138	−	0.973652i	−0.997310	−	0.0733045i	$-0.976646\pi$
$73$	−4.80291	−	8.31889i	−0.562138	−	0.973652i	0.435171	−	0.900348i	$-0.356688\pi$
$74$	7.45207	−	12.9074i	0.866285	−	1.50045i
$75$		0			0
$76$	−7.66082	+	13.2689i	−0.878756	+	1.52205i
$77$	5.72719	−	4.56195i	0.652674	−	0.519882i
$78$		0			0
$79$	−1.88112	+	3.25819i	−0.211642	+	0.366575i	−0.952229	−	0.305386i	$-0.901215\pi$
$79$	−1.88112	+	3.25819i	−0.211642	+	0.366575i	0.740586	+	0.671961i	$0.234548\pi$
$80$	−20.3108			−2.27081
$81$		0			0
$82$	−16.5340			−1.82587
$83$	−4.82088			−0.529161			−0.264580	−	0.964364i	$-0.585233\pi$
$83$	−4.82088			−0.529161			−0.264580	+	0.964364i	$0.585233\pi$
$84$		0			0
$85$	8.20331	+	14.2086i	0.889774	+	1.54113i
$86$	−7.63120	+	13.2176i	−0.822894	+	1.42529i
$87$		0			0
$88$	−17.6844			−1.88516
$89$	0.877787	+	1.52037i	0.0930453	+	0.161159i	0.908791	−	0.417251i	$-0.137007\pi$
$89$	0.877787	+	1.52037i	0.0930453	+	0.161159i	−0.815746	+	0.578411i	$0.803673\pi$
$90$		0			0
$91$	2.87972	−	9.09435i	0.301876	−	0.953347i
$92$	33.0916			3.45004
$93$		0			0
$94$	−20.1838			−2.08180
$95$	4.73897	−	8.20814i	0.486208	−	0.842137i
$96$		0			0
$97$	8.48637	+	14.6988i	0.861660	+	1.49244i	0.870325	+	0.492477i	$0.163908\pi$
$97$	8.48637	+	14.6988i	0.861660	+	1.49244i	−0.00866511	+	0.999962i	$0.502758\pi$
$98$	17.0667	−	5.24311i	1.72400	−	0.529634i
$99$		0			0
$100$	12.4685			1.24685
$101$	1.84273			0.183358			0.0916791	−	0.995789i	$-0.470777\pi$
$101$	1.84273			0.183358			0.0916791	+	0.995789i	$0.470777\pi$
$102$		0			0
$103$	−2.38506	+	4.13105i	−0.235007	+	0.407045i	−0.959275	−	0.282474i	$-0.908845\pi$
$103$	−2.38506	+	4.13105i	−0.235007	+	0.407045i	0.724267	+	0.689519i	$0.242178\pi$
$104$	−19.1254	+	12.8473i	−1.87540	+	1.25978i
$105$		0			0
$106$	16.1826	−	28.0291i	1.57179	−	2.72242i
$107$	−6.03771	−	10.4576i	−0.583688	−	1.01098i	−0.995038	−	0.0994995i	$-0.968276\pi$
$107$	−6.03771	−	10.4576i	−0.583688	−	1.01098i	0.411350	−	0.911478i	$-0.365058\pi$
$108$		0			0
$109$	3.40885	+	5.90430i	0.326508	+	0.565529i	0.981816	−	0.189832i	$-0.0607945\pi$
$109$	3.40885	+	5.90430i	0.326508	+	0.565529i	−0.655308	+	0.755362i	$0.727461\pi$
$110$	19.6724			1.87569
$111$		0			0
$112$	−17.9444	−	7.05446i	−1.69559	−	0.666583i
$113$	2.72463	+	4.71920i	0.256312	+	0.443945i	0.965251	−	0.261325i	$-0.0841593\pi$
$113$	2.72463	+	4.71920i	0.256312	+	0.443945i	−0.708939	+	0.705270i	$0.750826\pi$
$114$		0			0
$115$	−20.4704			−1.90888
$116$	−7.04316	−	12.1991i	−0.653941	−	1.13266i
$117$		0			0
$118$	6.97958			0.642522
$119$	2.31257	+	15.4024i	0.211993	+	1.41193i
$120$		0			0
$121$	−3.34113			−0.303739
$122$	12.1823	+	21.1003i	1.10293	+	1.91034i
$123$		0			0
$124$	−17.4225			−1.56458
$125$	6.22211			0.556523
$126$		0			0
$127$	−0.886520	+	1.53550i	−0.0786660	+	0.136253i	−0.902675	−	0.430324i	$-0.858399\pi$
$127$	−0.886520	+	1.53550i	−0.0786660	+	0.136253i	0.824009	+	0.566577i	$0.191733\pi$
$128$	−5.50543	−	9.53569i	−0.486616	−	0.842844i
$129$		0			0
$130$	21.2754	−	14.2916i	1.86598	−	1.25345i
$131$	3.50734	−	6.07490i	0.306438	−	0.530766i	−0.671143	−	0.741328i	$-0.734196\pi$
$131$	3.50734	−	6.07490i	0.306438	−	0.530766i	0.977580	+	0.210562i	$0.0675295\pi$
$132$		0			0
$133$	7.03775	−	5.60586i	0.610250	−	0.486090i
$134$	−11.0703	−	19.1743i	−0.956326	−	1.65641i
$135$		0			0
$136$	18.8087	−	32.5776i	1.61283	−	2.79350i
$137$	−9.82872	+	17.0239i	−0.839725	+	1.45445i	0.0504003	+	0.998729i	$0.483950\pi$
$137$	−9.82872	+	17.0239i	−0.839725	+	1.45445i	−0.890125	+	0.455717i	$0.849383\pi$
$138$		0			0
$139$	−9.17342	−	15.8888i	−0.778079	−	1.34767i	−0.933048	−	0.359753i	$-0.882861\pi$
$139$	−9.17342	−	15.8888i	−0.778079	−	1.34767i	0.154968	−	0.987919i	$-0.450472\pi$
$140$	30.9181	+	12.1548i	2.61306	+	1.02727i
$141$		0			0
$142$	−4.00596	+	6.93852i	−0.336173	+	0.582268i
$143$	8.28295	−	5.56400i	0.692655	−	0.465285i
$144$		0			0
$145$	4.35689	+	7.54635i	0.361820	+	0.626690i
$146$	12.2501	−	21.2178i	1.01383	−	1.75600i
$147$		0			0
$148$	26.3270			2.16407
$149$	8.80290			0.721162			0.360581	−	0.932728i	$-0.382578\pi$
$149$	8.80290			0.721162			0.360581	+	0.932728i	$0.382578\pi$
$150$		0			0
$151$	−4.83567	−	8.37562i	−0.393521	−	0.681598i	0.599390	−	0.800457i	$-0.295410\pi$
$151$	−4.83567	−	8.37562i	−0.393521	−	0.681598i	−0.992911	+	0.118859i	$0.962076\pi$
$152$	−21.7311			−1.76263
$153$		0			0
$154$	17.3805	+	6.83275i	1.40056	+	0.550599i
$155$	10.7775			0.865672
$156$		0			0
$157$	−5.76601	−	9.98702i	−0.460177	−	0.797051i	0.538792	−	0.842439i	$-0.318881\pi$
$157$	−5.76601	−	9.98702i	−0.460177	−	0.797051i	−0.998969	+	0.0453882i	$0.985548\pi$
$158$	−9.59583			−0.763403
$159$		0			0
$160$	−8.09259	−	14.0168i	−0.639775	−	1.10812i
$161$	−18.0855	−	7.10991i	−1.42533	−	0.560339i
$162$		0			0
$163$	−12.1704			−0.953261			−0.476631	−	0.879104i	$-0.658142\pi$
$163$	−12.1704			−0.953261			−0.476631	+	0.879104i	$0.658142\pi$
$164$	−14.6030	−	25.2931i	−1.14030	−	1.97506i
$165$		0			0
$166$	−6.14798	−	10.6486i	−0.477176	−	0.826493i
$167$	−4.54697	+	7.87559i	−0.351855	+	0.609431i	−0.986575	−	0.163311i	$-0.947782\pi$
$167$	−4.54697	+	7.87559i	−0.351855	+	0.609431i	0.634719	+	0.772743i	$0.281116\pi$
$168$		0			0
$169$	4.91577	−	12.0348i	0.378136	−	0.925750i
$170$	−20.9231	+	36.2398i	−1.60473	+	2.77947i
$171$		0			0
$172$	−26.9599			−2.05567
$173$	1.34730			0.102433			0.0512165	−	0.998688i	$-0.483690\pi$
$173$	1.34730			0.102433			0.0512165	+	0.998688i	$0.483690\pi$
$174$		0			0
$175$	−6.81436	−	2.67892i	−0.515117	−	0.202507i
$176$	−10.0841	−	17.4662i	−0.760121	−	1.31657i
$177$		0			0
$178$	−2.23885	+	3.87781i	−0.167809	+	0.290654i
$179$	5.95993			0.445466			0.222733	−	0.974880i	$-0.428502\pi$
$179$	5.95993			0.445466			0.222733	+	0.974880i	$0.428502\pi$
$180$		0			0
$181$	10.4495			0.776707			0.388354	−	0.921510i	$-0.373044\pi$
$181$	10.4495			0.776707			0.388354	+	0.921510i	$0.373044\pi$
$182$	23.7605	−	5.23699i	1.76125	−	0.388192i
$183$		0			0
$184$	23.4674	+	40.6468i	1.73004	+	2.99652i
$185$	−16.2858			−1.19736
$186$		0			0
$187$	−8.14577	+	14.1089i	−0.595677	+	1.03174i
$188$	−17.8265	−	30.8765i	−1.30013	−	2.25190i
$189$		0			0
$190$	24.1741			1.75377
$191$	0.658114			0.0476194			0.0238097	−	0.999717i	$-0.492420\pi$
$191$	0.658114			0.0476194			0.0238097	+	0.999717i	$0.492420\pi$
$192$		0			0
$193$	8.78557			0.632399			0.316200	−	0.948693i	$-0.397593\pi$
$193$	8.78557			0.632399			0.316200	+	0.948693i	$0.397593\pi$
$194$	−21.6450	+	37.4903i	−1.55402	+	2.69165i
$195$		0			0
$196$	23.0943	+	21.4773i	1.64959	+	1.53410i
$197$	9.29781	−	16.1043i	0.662442	−	1.14738i	−0.317530	−	0.948248i	$-0.602854\pi$
$197$	9.29781	−	16.1043i	0.662442	−	1.14738i	0.979972	−	0.199135i	$-0.0638131\pi$
$198$		0			0
$199$	−7.61283	+	13.1858i	−0.539659	+	0.934717i	0.459263	+	0.888300i	$0.348113\pi$
$199$	−7.61283	+	13.1858i	−0.539659	+	0.934717i	−0.998922	+	0.0464164i	$0.985220\pi$
$200$	8.84221	+	15.3151i	0.625238	+	1.08294i
$201$		0			0
$202$	2.35000	+	4.07031i	0.165345	+	0.286386i
$203$	1.22823	+	8.18041i	0.0862051	+	0.574152i
$204$		0			0
$205$	9.03340	+	15.6463i	0.630920	+	1.09279i
$206$	−12.1665			−0.847681
$207$		0			0
$208$	−23.5947	−	11.5636i	−1.63600	−	0.801789i
$209$	9.41145			0.651004
$210$		0			0
$211$	−10.5945	+	18.3503i	−0.729357	+	1.26328i	0.227798	+	0.973708i	$0.426847\pi$
$211$	−10.5945	+	18.3503i	−0.729357	+	1.26328i	−0.957155	+	0.289575i	$0.906486\pi$
$212$	57.1706			3.92649
$213$		0			0
$214$	15.3996	−	26.6728i	1.05269	−	1.82332i
$215$	16.6773			1.13738
$216$		0			0
$217$	9.52186	+	3.74332i	0.646386	+	0.254113i
$218$	−8.69448	+	15.0593i	−0.588865	+	1.01994i
$219$		0			0
$220$	17.3749	+	30.0942i	1.17142	+	2.02895i
$221$	1.44026	+	21.1763i	0.0968825	+	1.42447i
$222$		0			0
$223$	−0.453274	+	0.785093i	−0.0303534	+	0.0525737i	−0.880803	−	0.473483i	$-0.842997\pi$
$223$	−0.453274	+	0.785093i	−0.0303534	+	0.0525737i	0.850450	+	0.526056i	$0.176330\pi$
$224$	−2.28135	−	15.1945i	−0.152429	−	1.01522i
$225$		0			0
$226$	−6.94935	+	12.0366i	−0.462264	+	0.800664i
$227$	0.964045	−	1.66977i	0.0639859	−	0.110827i	−0.832258	−	0.554389i	$-0.812952\pi$
$227$	0.964045	−	1.66977i	0.0639859	−	0.110827i	0.896244	+	0.443562i	$0.146285\pi$
$228$		0			0
$229$	5.05578	−	8.75686i	0.334095	−	0.578670i	−0.649216	−	0.760604i	$-0.724903\pi$
$229$	5.05578	−	8.75686i	0.334095	−	0.578670i	0.983311	+	0.181935i	$0.0582360\pi$
$230$	−26.1055	−	45.2161i	−1.72135	−	2.98146i
$231$		0			0
$232$	9.98953	−	17.3024i	0.655845	−	1.13596i
$233$	−13.1134	+	22.7130i	−0.859085	+	1.48798i	0.0137178	+	0.999906i	$0.495633\pi$
$233$	−13.1134	+	22.7130i	−0.859085	+	1.48798i	−0.872803	+	0.488073i	$0.837700\pi$
$234$		0			0
$235$	11.0275	+	19.1001i	0.719353	+	1.24596i
$236$	6.16444	+	10.6771i	0.401271	+	0.695022i
$237$		0			0
$238$	−31.0724	+	24.7505i	−2.01413	+	1.60434i
$239$	−28.0556			−1.81476			−0.907382	−	0.420306i	$-0.861923\pi$
$239$	−28.0556			−1.81476			−0.907382	+	0.420306i	$0.861923\pi$
$240$		0			0
$241$	2.22625	−	3.85597i	0.143405	−	0.248385i	−0.785372	−	0.619025i	$-0.787528\pi$
$241$	2.22625	−	3.85597i	0.143405	−	0.248385i	0.928777	+	0.370640i	$0.120861\pi$
$242$	−4.26088	−	7.38007i	−0.273900	−	0.474409i
$243$		0			0
$244$	−21.5191	+	37.2721i	−1.37762	+	2.38610i
$245$	−14.2861	−	13.2859i	−0.912704	−	0.848802i
$246$		0			0
$247$	10.1783	−	6.83721i	0.647632	−	0.435041i
$248$	−12.3554	−	21.4002i	−0.784570	−	1.35892i
$249$		0			0
$250$	7.93494	+	13.7437i	0.501850	+	0.869229i
$251$	−1.55413	−	2.69183i	−0.0980956	−	0.169907i	0.812801	−	0.582542i	$-0.197942\pi$
$251$	−1.55413	−	2.69183i	−0.0980956	−	0.169907i	−0.910896	+	0.412635i	$0.864608\pi$
$252$		0			0
$253$	−10.1634	−	17.6035i	−0.638968	−	1.10672i
$254$	−4.52225			−0.283751
$255$		0			0
$256$	14.2787	−	24.7314i	0.892419	−	1.54571i
$257$	−12.9927	−	22.5040i	−0.810461	−	1.40376i	−0.912542	−	0.408984i	$-0.865883\pi$
$257$	−12.9927	−	22.5040i	−0.810461	−	1.40376i	0.102081	−	0.994776i	$-0.467450\pi$
$258$		0			0
$259$	−14.3884	−	5.65650i	−0.894053	−	0.351478i
$260$	40.6535	+	19.9240i	2.52122	+	1.23563i
$261$		0			0
$262$	17.8914			1.10533
$263$	−12.7806			−0.788083			−0.394042	−	0.919093i	$-0.628923\pi$
$263$	−12.7806			−0.788083			−0.394042	+	0.919093i	$0.628923\pi$
$264$		0			0
$265$	−35.3656			−2.17249
$266$	21.3576	+	8.39629i	1.30952	+	0.514810i
$267$		0			0
$268$	19.5548	−	33.8699i	1.19450	−	2.06893i
$269$	0.978744	−	1.69523i	0.0596751	−	0.103360i	−0.834644	−	0.550789i	$-0.814327\pi$
$269$	0.978744	−	1.69523i	0.0596751	−	0.103360i	0.894320	+	0.447429i	$0.147660\pi$
$270$		0			0
$271$	−13.4609	−	23.3150i	−0.817692	−	1.41628i	−0.907379	−	0.420314i	$-0.861920\pi$
$271$	−13.4609	−	23.3150i	−0.817692	−	1.41628i	0.0896863	−	0.995970i	$-0.471414\pi$
$272$	42.9009			2.60125
$273$		0			0
$274$	−50.1376			−3.02892
$275$	−3.82943	−	6.63277i	−0.230924	−	0.399971i
$276$		0			0
$277$	11.5778	−	20.0533i	0.695643	−	1.20489i	−0.274321	−	0.961638i	$-0.588453\pi$
$277$	11.5778	−	20.0533i	0.695643	−	1.20489i	0.969964	−	0.243250i	$-0.0782136\pi$
$278$	23.3974	−	40.5254i	1.40328	−	2.43055i
$279$		0			0
$280$	6.99620	+	46.5968i	0.418103	+	2.78469i
$281$	26.9347			1.60679			0.803396	−	0.595446i	$-0.203024\pi$
$281$	26.9347			1.60679			0.803396	+	0.595446i	$0.203024\pi$
$282$		0			0
$283$	15.2443			0.906181			0.453091	−	0.891464i	$-0.350321\pi$
$283$	15.2443			0.906181			0.453091	+	0.891464i	$0.350321\pi$
$284$	−14.1524			−0.839792
$285$		0			0
$286$	22.8531	+	11.2002i	1.35133	+	0.662279i
$287$	2.54657	+	16.9609i	0.150319	+	1.00117i
$288$		0			0
$289$	−8.82723	−	15.2892i	−0.519249	−	0.899365i
$290$	−11.1125	+	19.2474i	−0.652549	+	1.13025i
$291$		0			0
$292$	43.2778			2.53264
$293$	2.04388	+	3.54010i	0.119405	+	0.206815i	0.919532	−	0.393015i	$-0.128568\pi$
$293$	2.04388	+	3.54010i	0.119405	+	0.206815i	−0.800127	+	0.599830i	$0.795235\pi$
$294$		0			0
$295$	−3.81332	−	6.60486i	−0.222020	−	0.384550i
$296$	18.6702	+	32.3377i	1.08518	+	1.87959i
$297$		0			0
$298$	11.2262	+	19.4443i	0.650315	+	1.12638i
$299$	−23.7801	−	11.6545i	−1.37524	−	0.673995i
$300$		0			0
$301$	14.7343	+	5.79247i	0.849271	+	0.333873i
$302$	12.3337	−	21.3625i	0.709723	−	1.22928i
$303$		0			0
$304$	−12.3917	−	21.4631i	−0.710713	−	1.23099i
$305$	13.3117	−	23.0565i	0.762224	−	1.32021i
$306$		0			0
$307$	1.04296			0.0595250			0.0297625	−	0.999557i	$-0.490525\pi$
$307$	1.04296			0.0595250			0.0297625	+	0.999557i	$0.490525\pi$
$308$	4.89810	+	32.6228i	0.279095	+	1.85886i
$309$		0			0
$310$	13.7444	+	23.8060i	0.780628	+	1.35209i
$311$	3.88724	+	6.73290i	0.220425	+	0.381788i	0.954937	−	0.296808i	$-0.0959221\pi$
$311$	3.88724	+	6.73290i	0.220425	+	0.381788i	−0.734512	+	0.678596i	$0.762589\pi$
$312$		0			0
$313$	−12.1950	+	21.1224i	−0.689304	+	1.19391i	0.282759	+	0.959191i	$0.408750\pi$
$313$	−12.1950	+	21.1224i	−0.689304	+	1.19391i	−0.972063	+	0.234719i	$0.924583\pi$
$314$	14.7066	−	25.4725i	0.829939	−	1.43750i
$315$		0			0
$316$	−8.47514	−	14.6794i	−0.476764	−	0.825779i
$317$	5.38045	−	9.31922i	0.302196	−	0.523419i	−0.674437	−	0.738333i	$-0.735614\pi$
$317$	5.38045	−	9.31922i	0.302196	−	0.523419i	0.976633	+	0.214913i	$0.0689468\pi$
$318$		0			0
$319$	−4.32632	+	7.49341i	−0.242228	+	0.419550i
$320$	0.329903	−	0.571408i	0.0184421	−	0.0319427i
$321$		0			0
$322$	−7.35932	−	49.0153i	−0.410119	−	2.73151i
$323$	−10.0098	+	17.3374i	−0.556958	+	0.964680i
$324$		0			0
$325$	−8.96004	−	4.39125i	−0.497013	−	0.243583i
$326$	−15.5207	−	26.8827i	−0.859613	−	1.48889i
$327$		0			0
$328$	20.7119	−	35.8741i	1.14362	−	1.98081i
$329$	3.10871	+	20.7050i	0.171389	+	1.14150i
$330$		0			0
$331$	−22.9691			−1.26250			−0.631248	−	0.775581i	$-0.717457\pi$
$331$	−22.9691			−1.26250			−0.631248	+	0.775581i	$0.717457\pi$
$332$	10.8599	−	18.8100i	0.596017	−	1.03233i
$333$		0			0
$334$	−23.1947			−1.26916
$335$	−12.0966	+	20.9519i	−0.660906	+	1.14472i
$336$		0			0
$337$	6.99034			0.380788			0.190394	−	0.981708i	$-0.439023\pi$
$337$	6.99034			0.380788			0.190394	+	0.981708i	$0.439023\pi$
$338$	32.8520	−	4.48950i	1.78691	−	0.244196i
$339$		0			0
$340$	−73.9179			−4.00876
$341$	5.35096	+	9.26813i	0.289771	+	0.501898i
$342$		0			0
$343$	−8.00712	−	16.6999i	−0.432344	−	0.901709i
$344$	−19.1190	−	33.1151i	−1.03083	−	1.78545i
$345$		0			0
$346$	1.71818	+	2.97598i	0.0923701	+	0.159990i
$347$	−1.07692	+	1.86528i	−0.0578120	+	0.100133i	−0.893483	−	0.449097i	$-0.851746\pi$
$347$	−1.07692	+	1.86528i	−0.0578120	+	0.100133i	0.835671	+	0.549230i	$0.185079\pi$
$348$		0			0
$349$	−0.756384	+	1.31010i	−0.0404883	+	0.0701278i	−0.885559	−	0.464526i	$-0.846225\pi$
$349$	−0.756384	+	1.31010i	−0.0404883	+	0.0701278i	0.845071	+	0.534654i	$0.179558\pi$
$350$	−2.77289	−	18.4683i	−0.148217	−	0.987171i
$351$		0			0
$352$	8.03582	−	13.9184i	0.428311	−	0.741856i
$353$	32.3938			1.72415			0.862073	−	0.506784i	$-0.169166\pi$
$353$	32.3938			1.72415			0.862073	+	0.506784i	$0.169166\pi$
$354$		0			0
$355$	8.75467			0.464650
$356$	−7.90952			−0.419204
$357$		0			0
$358$	7.60058	+	13.1646i	0.401703	+	0.695771i
$359$	7.93156	−	13.7379i	0.418612	−	0.725057i	−0.577188	−	0.816611i	$-0.695850\pi$
$359$	7.93156	−	13.7379i	0.418612	−	0.725057i	0.995800	+	0.0915543i	$0.0291835\pi$
$360$		0			0
$361$	−7.43492			−0.391311
$362$	13.3261	+	23.0815i	0.700404	+	1.21314i
$363$		0			0
$364$	28.9969	+	31.7227i	1.51985	+	1.66272i
$365$	−26.7716			−1.40129
$366$		0			0
$367$	12.5937			0.657388			0.328694	−	0.944436i	$-0.393391\pi$
$367$	12.5937			0.657388			0.328694	+	0.944436i	$0.393391\pi$
$368$	−26.7635	+	46.3558i	−1.39515	+	2.41646i
$369$		0			0
$370$	−20.7690	−	35.9730i	−1.07973	−	1.87015i
$371$	−31.2453	−	12.2834i	−1.62217	−	0.637723i
$372$		0			0
$373$	−11.7036			−0.605987			−0.302994	−	0.952993i	$-0.597986\pi$
$373$	−11.7036			−0.605987			−0.302994	+	0.952993i	$0.597986\pi$
$374$	−41.5526			−2.14863
$375$		0			0
$376$	25.2839	−	43.7930i	1.30392	−	2.25845i
$377$	0.764942	+	11.2470i	0.0393965	+	0.579249i
$378$		0			0
$379$	−16.4778	+	28.5403i	−0.846406	+	1.46602i	0.0379888	+	0.999278i	$0.487905\pi$
$379$	−16.4778	+	28.5403i	−0.846406	+	1.46602i	−0.884395	+	0.466740i	$0.845428\pi$
$380$	21.3508	+	36.9807i	1.09527	+	1.89707i
$381$		0			0
$382$	0.839280	+	1.45368i	0.0429413	+	0.0743765i
$383$	−12.6361			−0.645672			−0.322836	−	0.946455i	$-0.604636\pi$
$383$	−12.6361			−0.645672			−0.322836	+	0.946455i	$0.604636\pi$
$384$		0			0
$385$	−3.02996	−	20.1804i	−0.154421	−	1.02849i
$386$	11.2041	+	19.4060i	0.570272	+	0.987741i
$387$		0			0
$388$	−76.4685			−3.88210
$389$	0.0593906	+	0.102868i	0.00301122	+	0.00521559i	0.867527	−	0.497390i	$-0.165708\pi$
$389$	0.0593906	+	0.102868i	0.00301122	+	0.00521559i	−0.864516	+	0.502606i	$0.832375\pi$
$390$		0			0
$391$	43.2381			2.18664
$392$	−10.0032	+	43.5979i	−0.505238	+	2.20203i
$393$		0			0
$394$	47.4293			2.38945
$395$	5.24271	+	9.08064i	0.263789	+	0.456897i
$396$		0			0
$397$	6.98302			0.350468			0.175234	−	0.984527i	$-0.443932\pi$
$397$	6.98302			0.350468			0.175234	+	0.984527i	$0.443932\pi$
$398$	−38.8340			−1.94657
$399$		0			0
$400$	−10.0841	+	17.4662i	−0.504207	+	0.873312i
$401$	−9.57584	−	16.5858i	−0.478194	−	0.828257i	0.521493	−	0.853256i	$-0.325375\pi$
$401$	−9.57584	−	16.5858i	−0.478194	−	0.828257i	−0.999687	+	0.0249985i	$0.992042\pi$
$402$		0			0
$403$	12.5201	+	6.13599i	0.623669	+	0.305656i
$404$	−4.15109	+	7.18989i	−0.206524	+	0.357711i
$405$		0			0
$406$	−16.5030	+	13.1453i	−0.819028	+	0.652391i
$407$	−8.08580	−	14.0050i	−0.400798	−	0.694203i
$408$		0			0
$409$	−5.84506	+	10.1239i	−0.289019	+	0.500596i	−0.973576	−	0.228363i	$-0.926663\pi$
$409$	−5.84506	+	10.1239i	−0.289019	+	0.500596i	0.684557	+	0.728960i	$0.259996\pi$
$410$	−23.0403	+	39.9069i	−1.13788	+	1.97086i
$411$		0			0
$412$	−10.7456	−	18.6119i	−0.529398	−	0.916944i
$413$	−1.07500	−	7.15981i	−0.0528972	−	0.352311i
$414$		0			0
$415$	−6.71794	+	11.6358i	−0.329771	+	0.571180i
$416$	−1.42082	−	20.8904i	−0.0696616	−	1.02424i
$417$		0			0
$418$	12.0023	+	20.7885i	0.587049	+	1.01680i
$419$	−7.89905	+	13.6816i	−0.385894	+	0.668388i	−0.991893	−	0.127078i	$-0.959440\pi$
$419$	−7.89905	+	13.6816i	−0.385894	+	0.668388i	0.605999	+	0.795465i	$0.292774\pi$
$420$		0			0
$421$	8.58170			0.418247			0.209123	−	0.977889i	$-0.432939\pi$
$421$	8.58170			0.418247			0.209123	+	0.977889i	$0.432939\pi$
$422$	−54.0440			−2.63082
$423$		0			0
$424$	40.5434	+	70.2232i	1.96896	+	3.41034i
$425$	16.2915			0.790255
$426$		0			0
$427$	19.7689	−	15.7468i	0.956684	−	0.762039i
$428$	54.4043			2.62973
$429$		0			0
$430$	21.2683	+	36.8378i	1.02565	+	1.77648i
$431$	19.4446			0.936615			0.468308	−	0.883565i	$-0.344864\pi$
$431$	19.4446			0.936615			0.468308	+	0.883565i	$0.344864\pi$
$432$		0			0
$433$	2.35409	+	4.07740i	0.113130	+	0.195948i	0.917031	−	0.398816i	$-0.130579\pi$
$433$	2.35409	+	4.07740i	0.113130	+	0.195948i	−0.803900	+	0.594764i	$0.797246\pi$
$434$	3.87463	+	25.8062i	0.185988	+	1.23874i
$435$		0			0
$436$	−30.7163			−1.47104
$437$	−12.4891	−	21.6318i	−0.597435	−	1.03479i
$438$		0			0
$439$	10.3311	+	17.8941i	0.493078	+	0.854037i	0.999968	−	0.00797405i	$-0.00253825\pi$
$439$	10.3311	+	17.8941i	0.493078	+	0.854037i	−0.506890	+	0.862011i	$0.669205\pi$
$440$	−24.6434	+	42.6836i	−1.17483	+	2.03486i
$441$		0			0
$442$	−44.9385	+	30.1870i	−2.13751	+	1.43585i
$443$	−6.14100	+	10.6365i	−0.291768	+	0.505357i	−0.974228	−	0.225566i	$-0.927577\pi$
$443$	−6.14100	+	10.6365i	−0.291768	+	0.505357i	0.682460	+	0.730923i	$0.260910\pi$
$444$		0			0
$445$	4.89282			0.231942
$446$	−2.31221			−0.109486
$447$		0			0
$448$	0.489931	−	0.390251i	0.0231471	−	0.0184376i
$449$	−13.7884	−	23.8822i	−0.650714	−	1.12707i	−0.982950	−	0.183874i	$-0.941136\pi$
$449$	−13.7884	−	23.8822i	−0.650714	−	1.12707i	0.332235	−	0.943196i	$-0.392197\pi$
$450$		0			0
$451$	−8.97003	+	15.5365i	−0.422382	+	0.731587i
$452$	−24.5510			−1.15478
$453$		0			0
$454$	4.91771			0.230800
$455$	−17.9375	−	19.6236i	−0.840922	−	0.919970i
$456$		0			0
$457$	−6.93931	−	12.0192i	−0.324607	−	0.562236i	0.656826	−	0.754042i	$-0.271899\pi$
$457$	−6.93931	−	12.0192i	−0.324607	−	0.562236i	−0.981433	+	0.191806i	$0.938565\pi$
$458$	25.7901			1.20509
$459$		0			0
$460$	46.1134	−	79.8708i	2.15005	−	3.72399i
$461$	12.2050	+	21.1396i	0.568441	+	0.984569i	0.996720	+	0.0809228i	$0.0257867\pi$
$461$	12.2050	+	21.1396i	0.568441	+	0.984569i	−0.428279	+	0.903647i	$0.640880\pi$
$462$		0			0
$463$	−11.6449			−0.541185			−0.270593	−	0.962694i	$-0.587220\pi$
$463$	−11.6449			−0.541185			−0.270593	+	0.962694i	$0.587220\pi$
$464$	22.7852			1.05778
$465$		0			0
$466$	−66.8929			−3.09875
$467$	−2.09483	+	3.62835i	−0.0969370	+	0.167900i	−0.910415	−	0.413695i	$-0.864238\pi$
$467$	−2.09483	+	3.62835i	−0.0969370	+	0.167900i	0.813478	+	0.581595i	$0.197571\pi$
$468$		0			0
$469$	−17.9644	+	14.3094i	−0.829517	+	0.660745i
$470$	−28.1263	+	48.7161i	−1.29737	+	2.24711i
$471$		0			0
$472$	−8.74322	+	15.1437i	−0.402439	+	0.697045i
$473$	8.28017	+	14.3417i	0.380723	+	0.659431i
$474$		0			0
$475$	−4.70573	−	8.15056i	−0.215914	−	0.373973i
$476$	−65.3060	−	25.6736i	−2.99329	−	1.17675i
$477$		0			0
$478$	−35.7788	−	61.9706i	−1.63648	−	2.83447i
$479$	15.0085			0.685754			0.342877	−	0.939380i	$-0.388599\pi$
$479$	15.0085			0.685754			0.342877	+	0.939380i	$0.388599\pi$
$480$		0			0
$481$	−18.9190	−	9.27206i	−0.862632	−	0.422769i
$482$	11.3564			0.517268
$483$		0			0
$484$	7.52652	−	13.0363i	0.342115	−	0.592560i
$485$	47.3033			2.14793
$486$		0			0
$487$	−3.30409	+	5.72285i	−0.149722	+	0.259327i	−0.931125	−	0.364701i	$-0.881171\pi$
$487$	−3.30409	+	5.72285i	−0.149722	+	0.259327i	0.781402	+	0.624027i	$0.214505\pi$
$488$	−61.0423			−2.76326
$489$		0			0
$490$	11.1277	−	48.4990i	0.502699	−	2.19096i
$491$	16.4555	−	28.5018i	0.742628	−	1.28627i	−0.208666	−	0.977987i	$-0.566912\pi$
$491$	16.4555	−	28.5018i	0.742628	−	1.28627i	0.951295	−	0.308283i	$-0.0997544\pi$
$492$		0			0
$493$	−9.20272	−	15.9396i	−0.414470	−	0.717883i
$494$	28.0826	+	13.7631i	1.26350	+	0.619231i
$495$		0			0
$496$	14.0908	−	24.4060i	0.632696	−	1.09586i
$497$	7.73469	+	3.04073i	0.346948	+	0.136395i
$498$		0			0
$499$	−17.9199	+	31.0381i	−0.802204	+	1.38946i	0.115959	+	0.993254i	$0.463006\pi$
$499$	−17.9199	+	31.0381i	−0.802204	+	1.38946i	−0.918163	+	0.396203i	$0.870328\pi$
$500$	−14.0165	+	24.2772i	−0.626835	+	1.08571i
$501$		0			0
$502$	3.96390	−	6.86567i	0.176917	−	0.306430i
$503$	9.67700	+	16.7610i	0.431476	+	0.747338i	0.997001	−	0.0773931i	$-0.0246596\pi$
$503$	9.67700	+	16.7610i	0.431476	+	0.747338i	−0.565525	+	0.824731i	$0.691326\pi$
$504$		0			0
$505$	2.56786	−	4.44766i	0.114268	−	0.197918i
$506$	25.9224	−	44.8989i	1.15239	−	1.99600i
$507$		0			0
$508$	−3.99410	−	6.91799i	−0.177210	−	0.306936i
$509$	5.24874	+	9.09108i	0.232646	+	0.402955i	0.958586	−	0.284803i	$-0.0919282\pi$
$509$	5.24874	+	9.09108i	0.232646	+	0.402955i	−0.725940	+	0.687758i	$0.758595\pi$
$510$		0			0
$511$	−23.6525	−	9.29847i	−1.04633	−	0.411340i
$512$	50.8157			2.24576
$513$		0			0
$514$	33.1386	−	57.3978i	1.46168	−	2.53171i
$515$	6.64721	+	11.5133i	0.292911	+	0.507337i
$516$		0			0
$517$	−10.9501	+	18.9662i	−0.481585	+	0.834130i
$518$	−5.85492	−	38.9955i	−0.257250	−	1.71337i
$519$		0			0
$520$	4.35722	+	64.0645i	0.191077	+	2.80941i
$521$	−10.7923	−	18.6928i	−0.472818	−	0.818945i	0.526698	−	0.850053i	$-0.323430\pi$
$521$	−10.7923	−	18.6928i	−0.472818	−	0.818945i	−0.999516	+	0.0311074i	$0.990097\pi$
$522$		0			0
$523$	−1.73189	−	2.99973i	−0.0757304	−	0.131169i	0.825673	−	0.564149i	$-0.190796\pi$
$523$	−1.73189	−	2.99973i	−0.0757304	−	0.131169i	−0.901404	+	0.432980i	$0.857462\pi$
$524$	15.8019	+	27.3697i	0.690308	+	1.19565i
$525$		0			0
$526$	−16.2988	−	28.2304i	−0.710662	−	1.23090i
$527$	−22.7645			−0.991639
$528$		0			0
$529$	−15.4739	+	26.8016i	−0.672779	+	1.16529i
$530$	−45.1012	−	78.1175i	−1.95907	−	3.39321i
$531$		0			0
$532$	6.01893	+	40.0879i	0.260954	+	1.73803i
$533$	1.58600	+	23.3191i	0.0686973	+	1.01006i
$534$		0			0
$535$	−33.6544			−1.45501
$536$	55.4703			2.39595
$537$		0			0
$538$	4.99270			0.215250
$539$	4.33224	−	18.8816i	0.186603	−	0.813290i
$540$		0			0
$541$	4.46427	−	7.73234i	0.191934	−	0.332439i	−0.753957	−	0.656924i	$-0.771857\pi$
$541$	4.46427	−	7.73234i	0.191934	−	0.332439i	0.945891	+	0.324484i	$0.105191\pi$
$542$	34.3329	−	59.4663i	1.47472	−	2.55430i
$543$		0			0
$544$	17.0934	+	29.6066i	0.732872	+	1.26937i
$545$	19.0010			0.813915
$546$		0			0
$547$	−3.62704			−0.155081			−0.0775405	−	0.996989i	$-0.524707\pi$
$547$	−3.62704			−0.155081			−0.0775405	+	0.996989i	$0.524707\pi$
$548$	−44.2821	−	76.6988i	−1.89164	−	3.27641i
$549$		0			0
$550$	9.76721	−	16.9173i	0.416475	−	0.721357i
$551$	−5.31632	+	9.20813i	−0.226483	+	0.392280i
$552$		0			0
$553$	1.47795	+	9.84361i	0.0628490	+	0.418593i
$554$	59.0598			2.50921
$555$		0			0
$556$	82.6593			3.50554
$557$	20.0447			0.849320			0.424660	−	0.905353i	$-0.360394\pi$
$557$	20.0447			0.849320			0.424660	+	0.905353i	$0.360394\pi$
$558$		0			0
$559$	19.3738	+	9.49495i	0.819424	+	0.401593i
$560$	−42.0325	+	33.4807i	−1.77620	+	1.41482i
$561$		0			0
$562$	34.3494	+	59.4948i	1.44894	+	2.50964i
$563$	−3.77715	+	6.54221i	−0.159188	+	0.275721i	−0.934576	−	0.355763i	$-0.884221\pi$
$563$	−3.77715	+	6.54221i	−0.159188	+	0.275721i	0.775388	+	0.631485i	$0.217554\pi$
$564$		0			0
$565$	15.1872			0.638930
$566$	19.4408	+	33.6725i	0.817158	+	1.41536i
$567$		0			0
$568$	−10.0364	−	17.3836i	−0.421119	−	0.729399i
$569$	14.0828	+	24.3921i	0.590381	+	1.02257i	0.994181	+	0.107723i	$0.0343559\pi$
$569$	14.0828	+	24.3921i	0.590381	+	1.02257i	−0.403800	+	0.914847i	$0.632311\pi$
$570$		0			0
$571$	9.03604	+	15.6509i	0.378146	+	0.654969i	0.990793	−	0.135389i	$-0.0432283\pi$
$571$	9.03604	+	15.6509i	0.378146	+	0.654969i	−0.612646	+	0.790357i	$0.709895\pi$
$572$	3.05053	+	44.8521i	0.127549	+	1.87536i
$573$		0			0
$574$	−34.2166	+	27.2550i	−1.42817	+	1.13760i
$575$	−10.1634	+	17.6035i	−0.423843	+	0.734118i
$576$		0			0
$577$	21.5383	+	37.3054i	0.896651	+	1.55305i	0.831747	+	0.555154i	$0.187341\pi$
$577$	21.5383	+	37.3054i	0.896651	+	1.55305i	0.0649040	+	0.997892i	$0.479326\pi$
$578$	22.5144	−	38.9961i	0.936476	−	1.62202i
$579$		0			0
$580$	−39.2588			−1.63013
$581$	−9.97668	+	7.94684i	−0.413902	+	0.329691i
$582$		0			0
$583$	−17.5588	−	30.4127i	−0.727210	−	1.25956i
$584$	30.6911	+	53.1586i	1.27001	+	2.19972i
$585$		0			0
$586$	−5.21304	+	9.02925i	−0.215349	+	0.372995i
$587$	−2.26101	+	3.91619i	−0.0933220	+	0.161638i	−0.908907	−	0.416999i	$-0.863082\pi$
$587$	−2.26101	+	3.91619i	−0.0933220	+	0.161638i	0.815585	+	0.578637i	$0.196415\pi$
$588$		0			0
$589$	6.57542	+	11.3890i	0.270936	+	0.469274i
$590$	9.72610	−	16.8461i	0.400417	−	0.693543i
$591$		0			0
$592$	−21.2925	+	36.8797i	−0.875117	+	1.51575i
$593$	−1.43449	+	2.48460i	−0.0589073	+	0.102030i	−0.893975	−	0.448117i	$-0.852095\pi$
$593$	−1.43449	+	2.48460i	−0.0589073	+	0.102030i	0.835068	+	0.550147i	$0.185428\pi$
$594$		0			0
$595$	40.3982	+	15.8817i	1.65616	+	0.651085i
$596$	−19.8302	+	34.3469i	−0.812276	+	1.40690i
$597$		0			0
$598$	−4.58337	−	67.3895i	−0.187428	−	2.75576i
$599$	2.94653	+	5.10354i	0.120392	+	0.208525i	0.919922	−	0.392101i	$-0.128252\pi$
$599$	2.94653	+	5.10354i	0.120392	+	0.208525i	−0.799530	+	0.600626i	$0.794918\pi$
$600$		0			0
$601$	−9.46284	+	16.3901i	−0.385997	+	0.668567i	−0.991907	−	0.126967i	$-0.959476\pi$
$601$	−9.46284	+	16.3901i	−0.385997	+	0.668567i	0.605910	+	0.795533i	$0.292809\pi$
$602$	5.99567	+	39.9329i	0.244365	+	1.62754i
$603$		0			0
$604$	43.5730			1.77296
$605$	−4.65590	+	8.06425i	−0.189289	+	0.327858i
$606$		0			0
$607$	43.8783			1.78096			0.890482	−	0.455019i	$-0.150367\pi$
$607$	43.8783			1.78096			0.890482	+	0.455019i	$0.150367\pi$
$608$	9.87466	−	17.1034i	0.400470	−	0.693635i
$609$		0			0
$610$	67.9045			2.74937
$611$	1.93610	+	28.4666i	0.0783263	+	1.15164i
$612$		0			0
$613$	30.5826			1.23522			0.617610	−	0.786484i	$-0.288101\pi$
$613$	30.5826			1.23522			0.617610	+	0.786484i	$0.288101\pi$
$614$	1.33007	+	2.30375i	0.0536773	+	0.0929718i
$615$		0			0
$616$	−36.5974	+	29.1513i	−1.47455	+	1.17454i
$617$	−22.1042	−	38.2856i	−0.889881	−	1.54132i	−0.840015	−	0.542563i	$-0.817454\pi$
$617$	−22.1042	−	38.2856i	−0.889881	−	1.54132i	−0.0498659	−	0.998756i	$-0.515879\pi$
$618$		0			0
$619$	0.184678	+	0.319871i	0.00742283	+	0.0128567i	0.869713	−	0.493558i	$-0.164304\pi$
$619$	0.184678	+	0.319871i	0.00742283	+	0.0128567i	−0.862290	+	0.506415i	$0.830971\pi$
$620$	−24.2784	+	42.0514i	−0.975043	+	1.68882i
$621$		0			0
$622$	−9.91466	+	17.1727i	−0.397542	+	0.688562i
$623$	4.32277	+	1.69940i	0.173188	+	0.0680851i
$624$		0			0
$625$	15.5892	−	27.0013i	0.623569	−	1.08005i
$626$	−62.2084			−2.48635
$627$		0			0
$628$	51.9560			2.07327
$629$	34.3993			1.37159
$630$		0			0
$631$	6.70906	+	11.6204i	0.267083	+	0.462602i	0.968107	−	0.250536i	$-0.0806067\pi$
$631$	6.70906	+	11.6204i	0.267083	+	0.462602i	−0.701024	+	0.713138i	$0.747273\pi$
$632$	12.0206	−	20.8202i	0.478152	−	0.828184i
$633$		0			0
$634$	27.4464			1.09003
$635$	2.47075	+	4.27946i	0.0980486	+	0.169825i
$636$		0			0
$637$	−9.03183	−	23.5675i	−0.357854	−	0.933777i
$638$	−22.0691			−0.873725
$639$		0			0
$640$	−30.6875			−1.21303
$641$	21.5169	−	37.2683i	0.849865	−	1.47201i	−0.0314626	−	0.999505i	$-0.510016\pi$
$641$	21.5169	−	37.2683i	0.849865	−	1.47201i	0.881328	−	0.472505i	$-0.156650\pi$
$642$		0			0
$643$	14.6688	+	25.4071i	0.578482	+	1.00196i	0.995654	+	0.0931324i	$0.0296880\pi$
$643$	14.6688	+	25.4071i	0.578482	+	1.00196i	−0.417172	+	0.908828i	$0.636979\pi$
$644$	68.4821	−	54.5489i	2.69857	−	2.14953i
$645$		0			0
$646$	−51.0611			−2.00897
$647$	18.0070			0.707930			0.353965	−	0.935259i	$-0.384833\pi$
$647$	18.0070			0.707930			0.353965	+	0.935259i	$0.384833\pi$
$648$		0			0
$649$	3.78656	−	6.55852i	0.148636	−	0.257445i
$650$	−1.72695	−	25.3915i	−0.0677366	−	0.995936i
$651$		0			0
$652$	27.4161	−	47.4862i	1.07370	−	1.85970i
$653$	17.3270	+	30.0113i	0.678059	+	1.17443i	0.975565	+	0.219713i	$0.0705120\pi$
$653$	17.3270	+	30.0113i	0.678059	+	1.17443i	−0.297505	+	0.954720i	$0.596155\pi$
$654$		0			0
$655$	−9.77502	−	16.9308i	−0.381942	−	0.661543i
$656$	47.2420			1.84449
$657$		0			0
$658$	−41.7697	+	33.2713i	−1.62835	+	1.29705i
$659$	2.68796	+	4.65569i	0.104708	+	0.181360i	0.913619	−	0.406572i	$-0.133276\pi$
$659$	2.68796	+	4.65569i	0.104708	+	0.181360i	−0.808911	+	0.587931i	$0.799942\pi$
$660$		0			0
$661$	40.4711			1.57414			0.787072	−	0.616861i	$-0.211596\pi$
$661$	40.4711			1.57414			0.787072	+	0.616861i	$0.211596\pi$
$662$	−29.2921	−	50.7353i	−1.13847	−	1.97188i
$663$		0			0
$664$	30.8060			1.19550
$665$	−3.72330	−	24.7983i	−0.144384	−	0.961638i
$666$		0			0
$667$	22.9643			0.889182
$668$	−20.4858	−	35.4825i	−0.792620	−	1.37286i
$669$		0			0
$670$	−61.7061			−2.38392
$671$	26.4366			1.02057
$672$		0			0
$673$	13.1634	−	22.7996i	0.507411	−	0.878861i	−0.492553	−	0.870283i	$-0.663936\pi$
$673$	13.1634	−	22.7996i	0.507411	−	0.878861i	0.999963	−	0.00857837i	$-0.00273061\pi$
$674$	8.91465	+	15.4406i	0.343380	+	0.594751i
$675$		0			0
$676$	35.8831	+	46.2907i	1.38012	+	1.78041i
$677$	1.90262	−	3.29544i	0.0731236	−	0.126654i	−0.827145	−	0.561988i	$-0.810037\pi$
$677$	1.90262	−	3.29544i	0.0731236	−	0.126654i	0.900269	+	0.435335i	$0.143370\pi$
$678$		0			0
$679$	41.7921	+	16.4297i	1.60384	+	0.630513i
$680$	−52.4201	−	90.7942i	−2.01022	−	3.48180i
$681$		0			0
$682$	−13.6480	+	23.6390i	−0.522607	+	0.905182i
$683$	5.19765	−	9.00259i	0.198882	−	0.344474i	−0.749284	−	0.662249i	$-0.769602\pi$
$683$	5.19765	−	9.00259i	0.198882	−	0.344474i	0.948166	+	0.317774i	$0.102935\pi$
$684$		0			0
$685$	27.3928	+	47.4458i	1.04663	+	1.81281i
$686$	26.6762	−	38.9836i	1.01850	−	1.48840i
$687$		0			0
$688$	21.8044	−	37.7663i	0.831284	−	1.43983i
$689$	−41.0837	−	20.1348i	−1.56516	−	0.767075i
$690$		0			0
$691$	4.09958	+	7.10067i	0.155955	+	0.270122i	0.933406	−	0.358821i	$-0.116821\pi$
$691$	4.09958	+	7.10067i	0.155955	+	0.270122i	−0.777451	+	0.628943i	$0.783488\pi$
$692$	−3.03504	+	5.25684i	−0.115375	+	0.199835i
$693$		0			0
$694$	−5.49350			−0.208530
$695$	−51.1329			−1.93958
$696$		0			0
$697$	−19.0806	−	33.0485i	−0.722728	−	1.25180i
$698$	−3.85841			−0.146043
$699$		0			0
$700$	25.8031	−	20.5533i	0.975266	−	0.776841i
$701$	−4.64503			−0.175440			−0.0877201	−	0.996145i	$-0.527958\pi$
$701$	−4.64503			−0.175440			−0.0877201	+	0.996145i	$0.527958\pi$
$702$		0			0
$703$	−9.93608	−	17.2098i	−0.374746	−	0.649080i
$704$	0.655177			0.0246929
$705$		0			0
$706$	41.3112	+	71.5531i	1.55477	+	2.69293i
$707$	3.81347	−	3.03759i	0.143420	−	0.114240i
$708$		0			0
$709$	−44.3975			−1.66738			−0.833691	−	0.552231i	$-0.813777\pi$
$709$	−44.3975			−1.66738			−0.833691	+	0.552231i	$0.813777\pi$
$710$	11.1647	+	19.3378i	0.419003	+	0.725734i
$711$		0			0
$712$	−5.60916	−	9.71534i	−0.210212	−	0.364098i
$713$	14.2016	−	24.5978i	0.531853	−	0.921196i
$714$		0			0
$715$	−1.88705	−	27.7454i	−0.0705718	−	1.03762i
$716$	−13.4258	+	23.2542i	−0.501747	+	0.869052i
$717$		0			0
$718$	40.4599			1.50995
$719$	44.9378			1.67590			0.837949	−	0.545748i	$-0.183754\pi$
$719$	44.9378			1.67590			0.837949	+	0.545748i	$0.183754\pi$
$720$		0			0
$721$	1.87389	+	12.4807i	0.0697874	+	0.464805i
$722$	−9.48161	−	16.4226i	−0.352869	−	0.611187i
$723$		0			0
$724$	−23.5395	+	40.7716i	−0.874839	+	1.51527i
$725$	8.65265			0.321351
$726$		0			0
$727$	−49.7876			−1.84652			−0.923260	−	0.384177i	$-0.874485\pi$
$727$	−49.7876			−1.84652			−0.923260	+	0.384177i	$0.874485\pi$
$728$	−18.4017	+	58.1139i	−0.682012	+	2.15384i
$729$		0			0
$730$	−34.1413	−	59.1345i	−1.26363	−	2.18867i
$731$	−35.2263			−1.30289
$732$		0			0
$733$	9.96819	−	17.2654i	0.368184	−	0.637713i	−0.621098	−	0.783733i	$-0.713313\pi$
$733$	9.96819	−	17.2654i	0.368184	−	0.637713i	0.989282	+	0.146020i	$0.0466465\pi$
$734$	16.0606	+	27.8177i	0.592807	+	1.02677i
$735$		0			0
$736$	−42.6545			−1.57227
$737$	−24.0234			−0.884914
$738$		0			0
$739$	48.0471			1.76744			0.883721	−	0.468014i	$-0.155030\pi$
$739$	48.0471			1.76744			0.883721	+	0.468014i	$0.155030\pi$
$740$	36.6869	−	63.5436i	1.34864	−	2.33591i
$741$		0			0
$742$	−12.7143	−	84.6810i	−0.466757	−	3.10874i
$743$	0.250266	−	0.433473i	0.00918137	−	0.0159026i	−0.861398	−	0.507930i	$-0.830411\pi$
$743$	0.250266	−	0.433473i	0.00918137	−	0.0159026i	0.870580	+	0.492028i	$0.163744\pi$
$744$		0			0
$745$	12.2669	−	21.2469i	0.449425	−	0.778427i
$746$	−14.9253	−	25.8514i	−0.546455	−	0.946488i
$747$		0			0
$748$	−36.6997	−	63.5657i	−1.34187	−	2.32419i
$749$	−29.7334	−	11.6891i	−1.08644	−	0.427109i
$750$		0			0
$751$	−21.9025	−	37.9363i	−0.799235	−	1.38432i	−0.920115	−	0.391648i	$-0.871905\pi$
$751$	−21.9025	−	37.9363i	−0.799235	−	1.38432i	0.120880	−	0.992667i	$-0.461428\pi$
$752$	57.6704			2.10302
$753$		0			0
$754$	−23.8674	+	16.0327i	−0.869200	+	0.583877i
$755$	−26.9542			−0.980963
$756$		0			0
$757$	1.91271	−	3.31291i	0.0695186	−	0.120410i	−0.829171	−	0.558995i	$-0.811187\pi$
$757$	1.91271	−	3.31291i	0.0695186	−	0.120410i	0.898689	+	0.438585i	$0.144520\pi$
$758$	−84.0552			−3.05302
$759$		0			0
$760$	−30.2825	+	52.4509i	−1.09846	+	1.90259i
$761$	5.73144			0.207765			0.103882	−	0.994590i	$-0.466873\pi$
$761$	5.73144			0.207765			0.103882	+	0.994590i	$0.466873\pi$
$762$		0			0
$763$	16.7873	+	6.59956i	0.607740	+	0.238920i
$764$	−1.48252	+	2.56781i	−0.0536358	+	0.0928999i
$765$		0			0
$766$	−16.1145	−	27.9112i	−0.582242	−	1.00847i
$767$	−0.669507	−	9.84380i	−0.0241745	−	0.355439i
$768$		0			0
$769$	8.50053	−	14.7234i	0.306537	−	0.530938i	−0.671065	−	0.741398i	$-0.734163\pi$
$769$	8.50053	−	14.7234i	0.306537	−	0.530938i	0.977602	+	0.210461i	$0.0674964\pi$
$770$	40.7115	−	32.4284i	1.46714	−	1.16864i
$771$		0			0
$772$	−19.7911	+	34.2792i	−0.712298	+	1.23374i
$773$	−6.09320	+	10.5537i	−0.219157	+	0.379591i	−0.954550	−	0.298049i	$-0.903664\pi$
$773$	−6.09320	+	10.5537i	−0.219157	+	0.379591i	0.735393	+	0.677640i	$0.236997\pi$
$774$		0			0
$775$	5.35096	−	9.26813i	0.192212	−	0.332921i
$776$	−54.2288	−	93.9271i	−1.94670	−	3.37179i
$777$		0			0
$778$	−0.151480	+	0.262370i	−0.00543080	+	0.00940643i
$779$	−11.0226	+	19.0918i	−0.394927	+	0.684034i
$780$		0			0
$781$	4.34663	+	7.52858i	0.155535	+	0.269394i
$782$	55.1407	+	95.5066i	1.97183	+	3.41531i
$783$		0			0
$784$	−48.7641	+	14.9809i	−1.74158	+	0.535034i
$785$	−32.1399			−1.14712
$786$		0			0
$787$	2.31021	−	4.00140i	0.0823501	−	0.142635i	−0.821909	−	0.569619i	$-0.807091\pi$
$787$	2.31021	−	4.00140i	0.0823501	−	0.142635i	0.904259	+	0.426984i	$0.140424\pi$
$788$	41.8901	+	72.5558i	1.49227	+	2.58469i
$789$		0			0
$790$	−13.3719	+	23.1608i	−0.475750	+	0.824023i
$791$	13.4178	+	5.27491i	0.477081	+	0.187554i
$792$		0			0
$793$	28.5908	−	19.2056i	1.01529	−	0.682010i
$794$	8.90531	+	15.4245i	0.316038	+	0.547393i
$795$		0			0
$796$	−34.2986	−	59.4069i	−1.21568	−	2.10562i
$797$	9.12087	+	15.7978i	0.323078	+	0.559587i	0.981121	−	0.193393i	$-0.0619491\pi$
$797$	9.12087	+	15.7978i	0.323078	+	0.559587i	−0.658044	+	0.752980i	$0.728616\pi$
$798$		0			0
$799$	−23.2925	−	40.3438i	−0.824029	−	1.42726i
$800$	−16.0716			−0.568218
$801$		0			0
$802$	24.4238	−	42.3032i	0.862433	−	1.49378i
$803$	−13.2919	−	23.0222i	−0.469061	−	0.812437i
$804$		0			0
$805$	−42.3629	+	33.7439i	−1.49310	+	1.18931i
$806$	2.41311	+	35.4801i	0.0849982	+	1.24973i
$807$		0			0
$808$	−11.7752			−0.414251
$809$	34.5921			1.21619			0.608096	−	0.793863i	$-0.291933\pi$
$809$	34.5921			1.21619			0.608096	+	0.793863i	$0.291933\pi$
$810$		0			0
$811$	−11.9774			−0.420582			−0.210291	−	0.977639i	$-0.567441\pi$
$811$	−11.9774			−0.420582			−0.210291	+	0.977639i	$0.567441\pi$
$812$	−34.6849	−	13.6356i	−1.21720	−	0.478516i
$813$		0			0
$814$	20.6233	−	35.7207i	0.722848	−	1.25201i
$815$	−16.9596	+	29.3749i	−0.594069	+	1.02896i
$816$		0			0
$817$	10.1749	+	17.6235i	0.355976	+	0.616568i
$818$	−29.8164			−1.04250
$819$		0			0
$820$	−81.3976			−2.84253
$821$	10.5936	+	18.3486i	0.369719	+	0.640372i	0.989521	−	0.144386i	$-0.0461207\pi$
$821$	10.5936	+	18.3486i	0.369719	+	0.640372i	−0.619803	+	0.784758i	$0.712787\pi$
$822$		0			0
$823$	−9.96806	+	17.2652i	−0.347465	+	0.601827i	−0.985798	−	0.167933i	$-0.946291\pi$
$823$	−9.96806	+	17.2652i	−0.347465	+	0.601827i	0.638334	+	0.769760i	$0.279624\pi$
$824$	15.2408	−	26.3979i	0.530939	−	0.919614i
$825$		0			0
$826$	14.4440	−	11.5053i	0.502572	−	0.400320i
$827$	15.0299			0.522639			0.261320	−	0.965252i	$-0.415842\pi$
$827$	15.0299			0.522639			0.261320	+	0.965252i	$0.415842\pi$
$828$		0			0
$829$	16.0717			0.558195			0.279097	−	0.960263i	$-0.409965\pi$
$829$	16.0717			0.558195			0.279097	+	0.960263i	$0.409965\pi$
$830$	−34.2691			−1.18950
$831$		0			0
$832$	0.708563	−	0.475971i	0.0245650	−	0.0165013i
$833$	30.1754	+	28.0627i	1.04552	+	0.972315i
$834$		0			0
$835$	12.6725	+	21.9494i	0.438550	+	0.759591i
$836$	−21.2011	+	36.7213i	−0.733254	+	1.27003i
$837$		0			0
$838$	−40.2940			−1.39193
$839$	−2.50930	−	4.34624i	−0.0866307	−	0.150049i	0.819454	−	0.573145i	$-0.194277\pi$
$839$	−2.50930	−	4.34624i	−0.0866307	−	0.150049i	−0.906085	+	0.423096i	$0.860943\pi$
$840$		0			0
$841$	9.61231	+	16.6490i	0.331459	+	0.574104i
$842$	10.9441	+	18.9557i	0.377158	+	0.653257i
$843$		0			0
$844$	−47.7323	−	82.6747i	−1.64301	−	2.84578i
$845$	−22.1972	−	28.6354i	−0.763609	−	0.985086i
$846$		0			0
$847$	−6.91437	+	5.50759i	−0.237581	+	0.189243i
$848$	−46.2379	+	80.0864i	−1.58782	+	2.75018i
$849$		0			0
$850$	20.7763	+	35.9856i	0.712621	+	1.23430i
$851$	−21.4599	+	37.1696i	−0.735636	+	1.27416i
$852$		0			0
$853$	−4.22423			−0.144635			−0.0723175	−	0.997382i	$-0.523039\pi$
$853$	−4.22423			−0.144635			−0.0723175	+	0.997382i	$0.523039\pi$
$854$	59.9931	+	23.5850i	2.05292	+	0.807063i
$855$		0			0
$856$	38.5817	+	66.8254i	1.31869	+	2.28404i
$857$	−4.48428	−	7.76700i	−0.153180	−	0.265316i	0.779215	−	0.626757i	$-0.215618\pi$
$857$	−4.48428	−	7.76700i	−0.153180	−	0.265316i	−0.932395	+	0.361441i	$0.882285\pi$
$858$		0			0
$859$	18.3400	−	31.7658i	0.625753	−	1.08384i	−0.362642	−	0.931928i	$-0.618125\pi$
$859$	18.3400	−	31.7658i	0.625753	−	1.08384i	0.988395	−	0.151907i	$-0.0485414\pi$
$860$	−37.5688	+	65.0711i	−1.28109	+	2.21890i
$861$		0			0
$862$	24.7974	+	42.9503i	0.844602	+	1.46289i
$863$	10.4237	−	18.0544i	0.354828	−	0.614580i	−0.632261	−	0.774756i	$-0.717873\pi$
$863$	10.4237	−	18.0544i	0.354828	−	0.614580i	0.987088	+	0.160176i	$0.0512062\pi$
$864$		0			0
$865$	1.87747	−	3.25187i	0.0638359	−	0.110567i
$866$	−6.00426	+	10.3997i	−0.204033	+	0.353395i
$867$		0			0
$868$	−36.0553	+	28.7196i	−1.22380	+	0.974806i
$869$	−5.20593	+	9.01694i	−0.176599	+	0.305879i
$870$		0			0
$871$	−25.9810	+	17.4525i	−0.880331	+	0.591354i
$872$	−21.7829	−	37.7291i	−0.737663	−	1.27767i
$873$		0			0
$874$	31.8543	−	55.1732i	1.07749	−	1.86626i
$875$	12.8765	−	10.2567i	0.435304	−	0.346738i
$876$		0			0
$877$	−27.6200			−0.932662			−0.466331	−	0.884610i	$-0.654425\pi$
$877$	−27.6200			−0.932662			−0.466331	+	0.884610i	$0.654425\pi$
$878$	−26.3502	+	45.6399i	−0.889277	+	1.54027i
$879$		0			0
$880$	−56.2093			−1.89482
$881$	12.7092	−	22.0130i	0.428183	−	0.741635i	−0.568528	−	0.822664i	$-0.692487\pi$
$881$	12.7092	−	22.0130i	0.428183	−	0.741635i	0.996712	+	0.0810283i	$0.0258204\pi$
$882$		0			0
$883$	32.7921			1.10354			0.551771	−	0.833995i	$-0.313952\pi$
$883$	32.7921			1.10354			0.551771	+	0.833995i	$0.313952\pi$
$884$	−85.8692	−	42.0839i	−2.88810	−	1.41543i
$885$		0			0
$886$	−31.3260			−1.05242
$887$	−3.96660	−	6.87036i	−0.133185	−	0.230684i	0.791717	−	0.610888i	$-0.209187\pi$
$887$	−3.96660	−	6.87036i	−0.133185	−	0.230684i	−0.924903	+	0.380204i	$0.875854\pi$
$888$		0			0
$889$	0.696519	+	4.63903i	0.0233605	+	0.155588i
$890$	6.23972	+	10.8075i	0.209156	+	0.362269i
$891$		0			0
$892$	−2.04217	−	3.53713i	−0.0683768	−	0.118432i
$893$	−13.4558	+	23.3062i	−0.450282	+	0.779912i
$894$		0			0
$895$	8.30521	−	14.3850i	0.277613	−	0.480839i
$896$	−27.1122	−	10.6586i	−0.905754	−	0.356078i
$897$		0			0
$898$	35.1682	−	60.9130i	1.17358	−	2.03269i
$899$	−12.0905			−0.403242
$900$		0			0
$901$	74.7001			2.48862
$902$	−45.7572			−1.52355
$903$		0			0
$904$	−17.4107	−	30.1562i	−0.579071	−	1.00298i
$905$	14.5615	−	25.2213i	0.484041	−	0.838384i
$906$		0			0
$907$	−46.2372			−1.53528			−0.767640	−	0.640881i	$-0.778569\pi$
$907$	−46.2372			−1.53528			−0.767640	+	0.640881i	$0.778569\pi$
$908$	4.34338	+	7.52295i	0.144140	+	0.249658i
$909$		0			0
$910$	20.4704	−	64.6469i	0.678586	−	2.14302i
$911$	21.5838			0.715102			0.357551	−	0.933894i	$-0.383612\pi$
$911$	21.5838			0.715102			0.357551	+	0.933894i	$0.383612\pi$
$912$		0			0
$913$	−13.3416			−0.441544
$914$	17.6991	−	30.6558i	0.585436	−	1.01400i
$915$		0			0
$916$	22.7781	+	39.4529i	0.752611	+	1.30356i
$917$	−2.75564	−	18.3534i	−0.0909993	−	0.606082i
$918$		0			0
$919$	−8.80978			−0.290608			−0.145304	−	0.989387i	$-0.546416\pi$
$919$	−8.80978			−0.290608			−0.145304	+	0.989387i	$0.546416\pi$
$920$	130.808			4.31262
$921$		0			0
$922$	−31.1295	+	53.9179i	−1.02520	+	1.77569i
$923$	10.1702	+	4.98432i	0.334755	+	0.164061i
$924$		0			0
$925$	−8.08580	+	14.0050i	−0.265859	+	0.460482i
$926$	−14.8505	−	25.7219i	−0.488019	−	0.845274i
$927$		0			0
$928$	9.07851	+	15.7244i	0.298017	+	0.516180i
$929$	52.4694			1.72147			0.860733	−	0.509057i	$-0.170006\pi$
$929$	52.4694			1.72147			0.860733	+	0.509057i	$0.170006\pi$
$930$		0			0
$931$	5.32359	−	23.2023i	0.174474	−	0.760426i
$932$	−59.0806	−	102.331i	−1.93525	−	3.35195i
$933$		0			0
$934$	−10.6860			−0.349656
$935$	22.7024	+	39.3217i	0.742448	+	1.28596i
$936$		0			0
$937$	−19.3131			−0.630932			−0.315466	−	0.948937i	$-0.602161\pi$
$937$	−19.3131			−0.630932			−0.315466	+	0.948937i	$0.602161\pi$
$938$	−54.5169	−	21.4321i	−1.78004	−	0.699784i
$939$		0			0
$940$	−99.3657			−3.24095
$941$	8.45918	+	14.6517i	0.275761	+	0.477633i	0.970327	−	0.241797i	$-0.0777367\pi$
$941$	8.45918	+	14.6517i	0.275761	+	0.477633i	−0.694566	+	0.719429i	$0.744403\pi$
$942$		0			0
$943$	47.6133			1.55050
$944$	−19.9425			−0.649073
$945$		0			0
$946$	−21.1191	+	36.5793i	−0.686641	+	1.18930i
$947$	−22.3511	−	38.7132i	−0.726313	−	1.25801i	−0.958431	−	0.285323i	$-0.907899\pi$
$947$	−22.3511	−	38.7132i	−0.726313	−	1.25801i	0.232119	−	0.972687i	$-0.425434\pi$
$948$		0			0
$949$	−31.1001	−	15.2419i	−1.00955	−	0.494774i
$950$	12.0023	−	20.7885i	0.389405	−	0.674468i
$951$		0			0
$952$	−14.7775	−	98.4229i	−0.478943	−	3.18990i
$953$	24.8774	+	43.0888i	0.805857	+	1.39578i	0.915711	+	0.401837i	$0.131628\pi$
$953$	24.8774	+	43.0888i	0.805857	+	1.39578i	−0.109855	+	0.993948i	$0.535038\pi$
$954$		0			0
$955$	0.917087	−	1.58844i	0.0296762	−	0.0514008i
$956$	63.2004	−	109.466i	2.04405	−	3.54039i
$957$		0			0
$958$	19.1400	+	33.1515i	0.618386	+	1.07108i
$959$	7.72221	+	51.4322i	0.249363	+	1.66083i
$960$		0			0
$961$	8.02298	−	13.8962i	0.258806	−	0.448265i
$962$	−3.64644	−	53.6137i	−0.117566	−	1.72858i
$963$		0			0
$964$	10.0301	+	17.3726i	0.323047	+	0.559533i
$965$	12.2428	−	21.2051i	0.394109	−	0.682616i
$966$		0			0
$967$	1.92897			0.0620315			0.0310158	−	0.999519i	$-0.490126\pi$
$967$	1.92897			0.0620315			0.0310158	+	0.999519i	$0.490126\pi$
$968$	21.3502			0.686221
$969$		0			0
$970$	60.3251	+	104.486i	1.93692	+	3.35485i
$971$	36.1232			1.15925			0.579624	−	0.814884i	$-0.303199\pi$
$971$	36.1232			1.15925			0.579624	+	0.814884i	$0.303199\pi$
$972$		0			0
$973$	−45.1756	−	17.7598i	−1.44826	−	0.569353i
$974$	−16.8546			−0.540055
$975$		0			0
$976$	−34.8080	−	60.2893i	−1.11418	−	1.92981i
$977$	−32.9682			−1.05475			−0.527373	−	0.849634i	$-0.676823\pi$
$977$	−32.9682			−1.05475			−0.527373	+	0.849634i	$0.676823\pi$
$978$		0			0
$979$	2.42925	+	4.20758i	0.0776391	+	0.134475i
$980$	84.0203	−	25.8121i	2.68393	−	0.824537i
$981$		0			0
$982$	83.9418			2.67869
$983$	−7.52903	−	13.0407i	−0.240139	−	0.415933i	0.720615	−	0.693336i	$-0.243860\pi$
$983$	−7.52903	−	13.0407i	−0.240139	−	0.415933i	−0.960754	+	0.277403i	$0.910526\pi$
$984$		0			0
$985$	−25.9132	−	44.8829i	−0.825662	−	1.43009i
$986$	23.4721	−	40.6549i	0.747504	−	1.29472i
$987$		0			0
$988$	3.74858	+	55.1156i	0.119258	+	1.75346i
$989$	21.9758	−	38.0631i	0.698789	−	1.21034i
$990$		0			0
$991$	36.1351			1.14787			0.573935	−	0.818901i	$-0.305416\pi$
$991$	36.1351			1.14787			0.573935	+	0.818901i	$0.305416\pi$
$992$	22.4573			0.713019
$993$		0			0
$994$	3.14739	+	20.9626i	0.0998292	+	0.664892i
$995$	21.2171	+	36.7491i	0.672627	+	1.16502i
$996$		0			0
$997$	−1.90762	+	3.30409i	−0.0604149	+	0.104642i	−0.894651	−	0.446766i	$-0.852576\pi$
$997$	−1.90762	+	3.30409i	−0.0604149	+	0.104642i	0.834236	+	0.551408i	$0.185909\pi$
$998$	−91.4115			−2.89358
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.e.100.8		16
3.2	odd	2		273.2.j.b.100.1	✓	16
7.4	even	3		819.2.s.e.802.1		16
13.3	even	3		819.2.s.e.289.1		16
21.11	odd	6		273.2.l.b.256.8	yes	16
39.29	odd	6		273.2.l.b.16.8	yes	16
91.81	even	3	inner	819.2.n.e.172.8		16
273.263	odd	6		273.2.j.b.172.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.1	✓	16	3.2	odd	2
273.2.j.b.172.1	yes	16	273.263	odd	6
273.2.l.b.16.8	yes	16	39.29	odd	6
273.2.l.b.256.8	yes	16	21.11	odd	6
819.2.n.e.100.8		16	1.1	even	1	trivial
819.2.n.e.172.8		16	91.81	even	3	inner
819.2.s.e.289.1		16	13.3	even	3
819.2.s.e.802.1		16	7.4	even	3

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.n (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27528 + 2.20885i) q^{2} +(-2.25269 + 3.90177i) q^{4} +(1.39351 - 2.41363i) q^{5} +(2.06947 - 1.64842i) q^{7} -6.39011 q^{8} +O(q^{10})\)	\(q+(1.27528 + 2.20885i) q^{2} +(-2.25269 + 3.90177i) q^{4} +(1.39351 - 2.41363i) q^{5} +(2.06947 - 1.64842i) q^{7} -6.39011 q^{8} +7.10846 q^{10} +2.76747 q^{11} +(2.99297 - 2.01050i) q^{13} +(6.28028 + 2.46895i) q^{14} +(-3.64382 - 6.31127i) q^{16} +(-2.94340 + 5.09812i) q^{17} +3.40075 q^{19} +(6.27828 + 10.8743i) q^{20} +(3.52930 + 6.11292i) q^{22} +(-3.67246 - 6.36089i) q^{23} +(-1.38373 - 2.39670i) q^{25} +(8.25778 + 4.04708i) q^{26} +(1.76989 + 11.7880i) q^{28} +(-1.56328 + 2.70768i) q^{29} +(1.93352 + 3.34896i) q^{31} +(2.90367 - 5.02931i) q^{32} -15.0147 q^{34} +(-1.09485 - 7.29202i) q^{35} +(-2.92173 - 5.06059i) q^{37} +(4.33691 + 7.51175i) q^{38} +(-8.90467 + 15.4233i) q^{40} +(-3.24124 + 5.61400i) q^{41} +(2.99197 + 5.18224i) q^{43} +(-6.23423 + 10.7980i) q^{44} +(9.36684 - 16.2238i) q^{46} +(-3.95673 + 6.85325i) q^{47} +(1.56542 - 6.82272i) q^{49} +(3.52930 - 6.11292i) q^{50} +(1.10228 + 16.2069i) q^{52} +(-6.34471 - 10.9894i) q^{53} +(3.85649 - 6.67963i) q^{55} +(-13.2241 + 10.5336i) q^{56} -7.97449 q^{58} +(1.36824 - 2.36987i) q^{59} +9.55263 q^{61} +(-4.93157 + 8.54173i) q^{62} +0.236742 q^{64} +(-0.681870 - 10.0256i) q^{65} -8.68066 q^{67} +(-13.2611 - 22.9689i) q^{68} +(14.7108 - 11.7177i) q^{70} +(1.57062 + 2.72039i) q^{71} +(-4.80291 - 8.31889i) q^{73} +(7.45207 - 12.9074i) q^{74} +(-7.66082 + 13.2689i) q^{76} +(5.72719 - 4.56195i) q^{77} +(-1.88112 + 3.25819i) q^{79} -20.3108 q^{80} -16.5340 q^{82} -4.82088 q^{83} +(8.20331 + 14.2086i) q^{85} +(-7.63120 + 13.2176i) q^{86} -17.6844 q^{88} +(0.877787 + 1.52037i) q^{89} +(2.87972 - 9.09435i) q^{91} +33.0916 q^{92} -20.1838 q^{94} +(4.73897 - 8.20814i) q^{95} +(8.48637 + 14.6988i) q^{97} +(17.0667 - 5.24311i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) \) 16 * q - 6 * q^4 + q^7 - 12 * q^8	\( 16 q - 6 q^{4} + q^{7} - 12 q^{8} + 8 q^{10} - 4 q^{11} + 5 q^{13} + 7 q^{14} - 6 q^{16} + 2 q^{17} + 22 q^{19} + 20 q^{20} + 7 q^{22} - 4 q^{23} + 2 q^{25} + 6 q^{26} - 7 q^{28} - 15 q^{29} + 3 q^{31} - 3 q^{32} - 68 q^{34} + 12 q^{35} + 4 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} + 2 q^{46} - 5 q^{47} + 13 q^{49} + 7 q^{50} + 36 q^{52} - 36 q^{53} - 15 q^{55} - 39 q^{56} - 40 q^{58} + 17 q^{59} + 44 q^{61} + 6 q^{62} - 20 q^{64} + 21 q^{65} - 52 q^{67} - 5 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} - 15 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} - 56 q^{80} + 2 q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} - 48 q^{88} - 20 q^{89} - 7 q^{91} + 94 q^{92} + 40 q^{94} + 7 q^{97} + 3 q^{98}+O(q^{100}) \) 16 * q - 6 * q^4 + q^7 - 12 * q^8 + 8 * q^10 - 4 * q^11 + 5 * q^13 + 7 * q^14 - 6 * q^16 + 2 * q^17 + 22 * q^19 + 20 * q^20 + 7 * q^22 - 4 * q^23 + 2 * q^25 + 6 * q^26 - 7 * q^28 - 15 * q^29 + 3 * q^31 - 3 * q^32 - 68 * q^34 + 12 * q^35 + 4 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 + 2 * q^46 - 5 * q^47 + 13 * q^49 + 7 * q^50 + 36 * q^52 - 36 * q^53 - 15 * q^55 - 39 * q^56 - 40 * q^58 + 17 * q^59 + 44 * q^61 + 6 * q^62 - 20 * q^64 + 21 * q^65 - 52 * q^67 - 5 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 - 15 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 - 56 * q^80 + 2 * q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 - 48 * q^88 - 20 * q^89 - 7 * q^91 + 94 * q^92 + 40 * q^94 + 7 * q^97 + 3 * q^98

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