LMFDB - Embedded newform 819.2.dx.a.503.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(503,819)]

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([3, 3, 4]))

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

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

chi := DirichletCharacter("819.503");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dx (of order $6$, 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:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			503.15
Character	$\chi$	$=$	819.503
Dual form			819.2.dx.a.692.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.569266 - 0.328666i) q^{2} +(-0.783957 - 1.35785i) q^{4} -1.53259 q^{5} +(-2.25245 + 1.38797i) q^{7} +2.34530i q^{8} +O(q^{10})$	\(q+(-0.569266 - 0.328666i) q^{2} +(-0.783957 - 1.35785i) q^{4} -1.53259 q^{5} +(-2.25245 + 1.38797i) q^{7} +2.34530i q^{8} +(0.872452 + 0.503710i) q^{10} +(4.04129 + 2.33324i) q^{11} +(-3.00017 - 1.99974i) q^{13} +(1.73842 - 0.0498218i) q^{14} +(-0.797093 + 1.38061i) q^{16} +(-0.402797 - 0.697666i) q^{17} +(5.24196 - 3.02645i) q^{19} +(1.20149 + 2.08103i) q^{20} +(-1.53371 - 2.65647i) q^{22} +(5.00969 + 2.89235i) q^{23} -2.65117 q^{25} +(1.05065 + 2.12444i) q^{26} +(3.65049 + 1.97039i) q^{28} +(2.95047 + 1.70345i) q^{29} +3.33911i q^{31} +(4.96970 - 2.86926i) q^{32} +0.529543i q^{34} +(3.45208 - 2.12719i) q^{35} +(5.16725 - 8.94995i) q^{37} -3.97876 q^{38} -3.59439i q^{40} +(4.26925 - 7.39455i) q^{41} +(0.374423 + 0.648520i) q^{43} -7.31665i q^{44} +(-1.90123 - 3.29303i) q^{46} -3.40994 q^{47} +(3.14707 - 6.25268i) q^{49} +(1.50922 + 0.871349i) q^{50} +(-0.363350 + 5.64151i) q^{52} +3.36989i q^{53} +(-6.19364 - 3.57590i) q^{55} +(-3.25522 - 5.28268i) q^{56} +(-1.11973 - 1.93944i) q^{58} +(6.01065 + 10.4108i) q^{59} +(5.38423 - 3.10858i) q^{61} +(1.09745 - 1.90084i) q^{62} -0.583740 q^{64} +(4.59803 + 3.06478i) q^{65} +(-0.0773636 + 0.133998i) q^{67} +(-0.631552 + 1.09388i) q^{68} +(-2.66429 + 0.0763564i) q^{70} +(7.08338 - 4.08959i) q^{71} +6.84401i q^{73} +(-5.88309 + 3.39660i) q^{74} +(-8.21894 - 4.74521i) q^{76} +(-12.3413 + 0.353691i) q^{77} +1.07810 q^{79} +(1.22162 - 2.11590i) q^{80} +(-4.86068 + 2.80631i) q^{82} +6.36278 q^{83} +(0.617323 + 1.06924i) q^{85} -0.492241i q^{86} +(-5.47216 + 9.47806i) q^{88} +(-0.637871 + 1.10483i) q^{89} +(9.53333 + 0.340163i) q^{91} -9.06991i q^{92} +(1.94117 + 1.12073i) q^{94} +(-8.03377 + 4.63830i) q^{95} +(9.76704 - 5.63900i) q^{97} +(-3.84656 + 2.52510i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 32 q^{4} - 2 q^{7}+O(q^{10}) $ 72 * q + 32 * q^4 - 2 * q^7	$ 72 q + 32 q^{4} - 2 q^{7} - 24 q^{16} + 24 q^{22} + 56 q^{25} - 8 q^{28} + 16 q^{37} - 4 q^{43} + 32 q^{46} + 26 q^{49} - 40 q^{58} - 64 q^{64} + 60 q^{67} - 40 q^{70} - 72 q^{79} - 80 q^{85} - 24 q^{88} + 2 q^{91}+O(q^{100}) $ 72 * q + 32 * q^4 - 2 * q^7 - 24 * q^16 + 24 * q^22 + 56 * q^25 - 8 * q^28 + 16 * q^37 - 4 * q^43 + 32 * q^46 + 26 * q^49 - 40 * q^58 - 64 * q^64 + 60 * q^67 - 40 * q^70 - 72 * q^79 - 80 * q^85 - 24 * q^88 + 2 * q^91

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.569266	−	0.328666i	−0.402532	−	0.232402i	0.285044	−	0.958514i	$-0.407992\pi$
$2$	−0.569266	−	0.328666i	−0.402532	−	0.232402i	−0.687576	+	0.726113i	$0.741325\pi$
$3$		0			0
$3$		0			0
$4$	−0.783957	−	1.35785i	−0.391979	−	0.678927i
$5$	−1.53259			−0.685395			−0.342698	−	0.939446i	$-0.611341\pi$
$5$	−1.53259			−0.685395			−0.342698	+	0.939446i	$0.611341\pi$
$6$		0			0
$7$	−2.25245	+	1.38797i	−0.851346	+	0.524604i
$7$	−2.25245	+	1.38797i	−0.851346	+	0.524604i
$8$			2.34530i			0.829190i
$9$		0			0
$10$	0.872452	+	0.503710i	0.275893	+	0.159287i
$11$	4.04129	+	2.33324i	1.21850	+	0.703499i	0.964596	−	0.263732i	$-0.0849534\pi$
$11$	4.04129	+	2.33324i	1.21850	+	0.703499i	0.253900	+	0.967231i	$0.418287\pi$
$12$		0			0
$13$	−3.00017	−	1.99974i	−0.832098	−	0.554628i
$13$	−3.00017	−	1.99974i	−0.832098	−	0.554628i
$14$	1.73842	−	0.0498218i	0.464613	−	0.0133154i
$15$		0			0
$16$	−0.797093	+	1.38061i	−0.199273	+	0.345151i
$17$	−0.402797	−	0.697666i	−0.0976927	−	0.169209i	0.813037	−	0.582213i	$-0.197813\pi$
$17$	−0.402797	−	0.697666i	−0.0976927	−	0.169209i	−0.910729	+	0.413004i	$0.864480\pi$
$18$		0			0
$19$	5.24196	−	3.02645i	1.20259	−	0.694314i	0.241458	−	0.970411i	$-0.422374\pi$
$19$	5.24196	−	3.02645i	1.20259	−	0.694314i	0.961130	+	0.276097i	$0.0890411\pi$
$20$	1.20149	+	2.08103i	0.268660	+	0.465333i
$21$		0			0
$22$	−1.53371	−	2.65647i	−0.326989	−	0.566361i
$23$	5.00969	+	2.89235i	1.04459	+	0.603096i	0.921131	−	0.389253i	$-0.127267\pi$
$23$	5.00969	+	2.89235i	1.04459	+	0.603096i	0.123462	+	0.992349i	$0.460600\pi$
$24$		0			0
$25$	−2.65117			−0.530234
$26$	1.05065	+	2.12444i	0.206049	+	0.416637i
$27$		0			0
$28$	3.65049	+	1.97039i	0.689878	+	0.372368i
$29$	2.95047	+	1.70345i	0.547888	+	0.316323i	0.748270	−	0.663394i	$-0.230885\pi$
$29$	2.95047	+	1.70345i	0.547888	+	0.316323i	−0.200382	+	0.979718i	$0.564218\pi$
$30$		0			0
$31$			3.33911i			0.599721i	0.953983	+	0.299861i	$0.0969402\pi$
$31$			3.33911i			0.599721i	−0.953983	+	0.299861i	$0.903060\pi$
$32$	4.96970	−	2.86926i	0.878528	−	0.507218i
$33$		0			0
$34$			0.529543i			0.0908159i
$35$	3.45208	−	2.12719i	0.583508	−	0.359561i
$36$		0			0
$37$	5.16725	−	8.94995i	0.849491	−	1.47136i	−0.0321718	−	0.999482i	$-0.510242\pi$
$37$	5.16725	−	8.94995i	0.849491	−	1.47136i	0.881663	−	0.471880i	$-0.156424\pi$
$38$	−3.97876			−0.645440
$39$		0			0
$40$		−	3.59439i		−	0.568323i
$41$	4.26925	−	7.39455i	0.666744	−	1.15484i	−0.312065	−	0.950061i	$-0.601021\pi$
$41$	4.26925	−	7.39455i	0.666744	−	1.15484i	0.978809	−	0.204774i	$-0.0656461\pi$
$42$		0			0
$43$	0.374423	+	0.648520i	0.0570990	+	0.0988984i	0.893162	−	0.449735i	$-0.148482\pi$
$43$	0.374423	+	0.648520i	0.0570990	+	0.0988984i	−0.836063	+	0.548633i	$0.815148\pi$
$44$		−	7.31665i		−	1.10303i
$45$		0			0
$46$	−1.90123	−	3.29303i	−0.280321	−	0.485531i
$47$	−3.40994			−0.497392			−0.248696	−	0.968582i	$-0.580002\pi$
$47$	−3.40994			−0.497392			−0.248696	+	0.968582i	$0.580002\pi$
$48$		0			0
$49$	3.14707	−	6.25268i	0.449581	−	0.893240i
$50$	1.50922	+	0.871349i	0.213436	+	0.123227i
$51$		0			0
$52$	−0.363350	+	5.64151i	−0.0503875	+	0.782336i
$53$			3.36989i			0.462890i	0.972848	+	0.231445i	$0.0743454\pi$
$53$			3.36989i			0.462890i	−0.972848	+	0.231445i	$0.925655\pi$
$54$		0			0
$55$	−6.19364	−	3.57590i	−0.835151	−	0.482175i
$56$	−3.25522	−	5.28268i	−0.434997	−	0.705928i
$57$		0			0
$58$	−1.11973	−	1.93944i	−0.147028	−	0.254661i
$59$	6.01065	+	10.4108i	0.782520	+	1.35536i	0.930469	+	0.366370i	$0.119399\pi$
$59$	6.01065	+	10.4108i	0.782520	+	1.35536i	−0.147949	+	0.988995i	$0.547267\pi$
$60$		0			0
$61$	5.38423	−	3.10858i	0.689379	−	0.398013i	−0.114000	−	0.993481i	$-0.536366\pi$
$61$	5.38423	−	3.10858i	0.689379	−	0.398013i	0.803380	+	0.595467i	$0.203033\pi$
$62$	1.09745	−	1.90084i	0.139376	−	0.241407i
$63$		0			0
$64$	−0.583740			−0.0729675
$65$	4.59803	+	3.06478i	0.570316	+	0.380140i
$66$		0			0
$67$	−0.0773636	+	0.133998i	−0.00945147	+	0.0163704i	−0.870712	−	0.491792i	$-0.836342\pi$
$67$	−0.0773636	+	0.133998i	−0.00945147	+	0.0163704i	0.861261	+	0.508163i	$0.169675\pi$
$68$	−0.631552	+	1.09388i	−0.0765869	+	0.132652i
$69$		0			0
$70$	−2.66429	+	0.0763564i	−0.318444	+	0.00912634i
$71$	7.08338	−	4.08959i	0.840642	−	0.485345i	−0.0168402	−	0.999858i	$-0.505361\pi$
$71$	7.08338	−	4.08959i	0.840642	−	0.485345i	0.857483	+	0.514513i	$0.172027\pi$
$72$		0			0
$73$			6.84401i			0.801031i	0.916290	+	0.400515i	$0.131169\pi$
$73$			6.84401i			0.801031i	−0.916290	+	0.400515i	$0.868831\pi$
$74$	−5.88309	+	3.39660i	−0.683895	+	0.394847i
$75$		0			0
$76$	−8.21894	−	4.74521i	−0.942777	−	0.544313i
$77$	−12.3413	+	0.353691i	−1.40642	+	0.0403069i
$78$		0			0
$79$	1.07810			0.121296			0.0606478	−	0.998159i	$-0.480683\pi$
$79$	1.07810			0.121296			0.0606478	+	0.998159i	$0.480683\pi$
$80$	1.22162	−	2.11590i	0.136581	−	0.236565i
$81$		0			0
$82$	−4.86068	+	2.80631i	−0.536772	+	0.309905i
$83$	6.36278			0.698406			0.349203	−	0.937047i	$-0.386452\pi$
$83$	6.36278			0.698406			0.349203	+	0.937047i	$0.386452\pi$
$84$		0			0
$85$	0.617323	+	1.06924i	0.0669581	+	0.115975i
$86$		−	0.492241i		−	0.0530797i
$87$		0			0
$88$	−5.47216	+	9.47806i	−0.583334	+	1.01036i
$89$	−0.637871	+	1.10483i	−0.0676142	+	0.117111i	−0.897851	−	0.440300i	$-0.854872\pi$
$89$	−0.637871	+	1.10483i	−0.0676142	+	0.117111i	0.830236	+	0.557411i	$0.188205\pi$
$90$		0			0
$91$	9.53333	+	0.340163i	0.999364	+	0.0356587i
$92$		−	9.06991i		−	0.945603i
$93$		0			0
$94$	1.94117	+	1.12073i	0.200216	+	0.115595i
$95$	−8.03377	+	4.63830i	−0.824248	+	0.475880i
$96$		0			0
$97$	9.76704	−	5.63900i	0.991693	−	0.572554i	0.0859130	−	0.996303i	$-0.472619\pi$
$97$	9.76704	−	5.63900i	0.991693	−	0.572554i	0.905780	+	0.423749i	$0.139286\pi$
$98$	−3.84656	+	2.52510i	−0.388561	+	0.255074i
$99$		0			0
$100$	2.07840	+	3.59990i	0.207840	+	0.359990i
$101$	−7.59723	+	13.1588i	−0.755953	+	1.30935i	0.188946	+	0.981987i	$0.439493\pi$
$101$	−7.59723	+	13.1588i	−0.755953	+	1.30935i	−0.944899	+	0.327362i	$0.893841\pi$
$102$		0			0
$103$			11.9591i			1.17836i	0.808000	+	0.589182i	$0.200550\pi$
$103$			11.9591i			1.17836i	−0.808000	+	0.589182i	$0.799450\pi$
$104$	4.69000	−	7.03632i	0.459893	−	0.689968i
$105$		0			0
$106$	1.10757	−	1.91837i	0.107577	−	0.186328i
$107$	−1.67813	−	0.968872i	−0.162231	−	0.0936643i	0.416686	−	0.909050i	$-0.363191\pi$
$107$	−1.67813	−	0.968872i	−0.162231	−	0.0936643i	−0.578918	+	0.815386i	$0.696525\pi$
$108$		0			0
$109$	18.7291			1.79393			0.896963	−	0.442105i	$-0.145768\pi$
$109$	18.7291			1.79393			0.896963	+	0.442105i	$0.145768\pi$
$110$	2.35055	+	4.07128i	0.224117	+	0.388181i
$111$		0			0
$112$	−0.120830	−	4.21609i	−0.0114173	−	0.398383i
$113$	−12.5827	+	7.26462i	−1.18368	+	0.683398i	−0.956863	−	0.290539i	$-0.906165\pi$
$113$	−12.5827	+	7.26462i	−1.18368	+	0.683398i	−0.226818	+	0.973937i	$0.572832\pi$
$114$		0			0
$115$	−7.67780	−	4.43278i	−0.715959	−	0.413359i
$116$		−	5.34174i		−	0.495968i
$117$		0			0
$118$		−	7.90199i		−	0.727437i
$119$	1.87562	+	1.01239i	0.171938	+	0.0928052i
$120$		0			0
$121$	5.38803	+	9.33234i	0.489821	+	0.848395i
$122$	−4.08674			−0.369996
$123$		0			0
$124$	4.53402	−	2.61772i	0.407167	−	0.235078i
$125$	11.7261			1.04881
$126$		0			0
$127$	2.14235	−	3.71066i	0.190103	−	0.329268i	−0.755181	−	0.655516i	$-0.772451\pi$
$127$	2.14235	−	3.71066i	0.190103	−	0.329268i	0.945284	+	0.326248i	$0.105785\pi$
$128$	−9.60710	−	5.54666i	−0.849156	−	0.490260i
$129$		0			0
$130$	−1.61022	−	3.25589i	−0.141225	−	0.285561i
$131$	15.2887			1.33578			0.667890	−	0.744260i	$-0.267198\pi$
$131$	15.2887			1.33578			0.667890	+	0.744260i	$0.267198\pi$
$132$		0			0
$133$	−7.60663	+	14.0926i	−0.659578	+	1.22198i
$134$	0.0880810	−	0.0508536i	0.00760904	−	0.00439308i
$135$		0			0
$136$	1.63624	−	0.944683i	0.140306	−	0.0810059i
$137$	4.32107	−	2.49477i	0.369174	−	0.213143i	−0.303924	−	0.952696i	$-0.598297\pi$
$137$	4.32107	−	2.49477i	0.369174	−	0.213143i	0.673098	+	0.739554i	$0.264963\pi$
$138$		0			0
$139$	7.17932	−	4.14498i	0.608942	−	0.351573i	−0.163609	−	0.986525i	$-0.552314\pi$
$139$	7.17932	−	4.14498i	0.608942	−	0.351573i	0.772551	+	0.634952i	$0.218980\pi$
$140$	−5.59470	−	3.01980i	−0.472839	−	0.255219i
$141$		0			0
$142$	−5.37644			−0.451181
$143$	−7.45869	−	15.0817i	−0.623727	−	1.26119i
$144$		0			0
$145$	−4.52186	−	2.61070i	−0.375520	−	0.216807i
$146$	2.24939	−	3.89606i	0.186161	−	0.322440i
$147$		0			0
$148$	−16.2036			−1.33193
$149$	−19.4729	+	11.2427i	−1.59528	+	0.921036i	−0.602902	+	0.797815i	$0.705989\pi$
$149$	−19.4729	+	11.2427i	−1.59528	+	0.921036i	−0.992379	+	0.123221i	$0.960678\pi$
$150$		0			0
$151$	−9.04739			−0.736266			−0.368133	−	0.929773i	$-0.620003\pi$
$151$	−9.04739			−0.736266			−0.368133	+	0.929773i	$0.620003\pi$
$152$	7.09794	+	12.2940i	0.575719	+	0.997174i
$153$		0			0
$154$	7.14172	+	3.85482i	0.575496	+	0.310630i
$155$		−	5.11748i		−	0.411046i
$156$		0			0
$157$			17.9034i			1.42885i	0.699714	+	0.714423i	$0.253311\pi$
$157$			17.9034i			1.42885i	−0.699714	+	0.714423i	$0.746689\pi$
$158$	−0.613725	−	0.354334i	−0.0488254	−	0.0281893i
$159$		0			0
$160$	−7.61652	+	4.39740i	−0.602138	+	0.347645i
$161$	−15.2986	+	0.438445i	−1.20570	+	0.0345543i
$162$		0			0
$163$	−2.90044	−	5.02370i	−0.227180	−	0.393487i	0.729791	−	0.683670i	$-0.239617\pi$
$163$	−2.90044	−	5.02370i	−0.227180	−	0.393487i	−0.956971	+	0.290183i	$0.906284\pi$
$164$	−13.3876			−1.04540
$165$		0			0
$166$	−3.62212	−	2.09123i	−0.281131	−	0.162311i
$167$	6.81599	−	11.8056i	0.527437	−	0.913547i	−0.472052	−	0.881571i	$-0.656486\pi$
$167$	6.81599	−	11.8056i	0.527437	−	0.913547i	0.999489	−	0.0319766i	$-0.0101802\pi$
$168$		0			0
$169$	5.00207	+	11.9991i	0.384774	+	0.923011i
$170$		−	0.811573i		−	0.0622448i
$171$		0			0
$172$	0.587064	−	1.01682i	0.0447632	−	0.0775321i
$173$	−11.1351	−	19.2866i	−0.846588	−	1.46633i	−0.884235	−	0.467042i	$-0.845320\pi$
$173$	−11.1351	−	19.2866i	−0.846588	−	1.46633i	0.0376475	−	0.999291i	$-0.488014\pi$
$174$		0			0
$175$	5.97162	−	3.67975i	0.451412	−	0.278163i
$176$	−6.44257	+	3.71962i	−0.485627	+	0.280377i
$177$		0			0
$178$	0.726237	−	0.419293i	0.0544338	−	0.0314273i
$179$	−2.38132	−	1.37486i	−0.177988	−	0.102762i	0.408359	−	0.912821i	$-0.366101\pi$
$179$	−2.38132	−	1.37486i	−0.177988	−	0.102762i	−0.586347	+	0.810060i	$0.699435\pi$
$180$		0			0
$181$			13.1570i			0.977950i	0.872298	+	0.488975i	$0.162629\pi$
$181$			13.1570i			0.977950i	−0.872298	+	0.488975i	$0.837371\pi$
$182$	−5.31520	−	3.32692i	−0.393989	−	0.246608i
$183$		0			0
$184$	−6.78344	+	11.7493i	−0.500081	+	0.866167i
$185$	−7.91928	+	13.7166i	−0.582237	+	1.00846i
$186$		0			0
$187$		−	3.75930i		−	0.274907i
$188$	2.67325	+	4.63021i	0.194967	+	0.337693i
$189$		0			0
$190$	6.09781			0.442381
$191$	7.95723	−	4.59411i	0.575765	−	0.332418i	−0.183683	−	0.982985i	$-0.558802\pi$
$191$	7.95723	−	4.59411i	0.575765	−	0.332418i	0.759449	+	0.650567i	$0.225469\pi$
$192$		0			0
$193$	−4.02664	+	6.97435i	−0.289844	+	0.502025i	−0.973772	−	0.227525i	$-0.926937\pi$
$193$	−4.02664	+	6.97435i	−0.289844	+	0.502025i	0.683928	+	0.729549i	$0.260270\pi$
$194$	−7.41340			−0.532251
$195$		0			0
$196$	−10.9574	+	0.628576i	−0.782671	+	0.0448983i
$197$	−1.75097	−	1.01092i	−0.124751	−	0.0720251i	0.436326	−	0.899789i	$-0.356279\pi$
$197$	−1.75097	−	1.01092i	−0.124751	−	0.0720251i	−0.561077	+	0.827764i	$0.689613\pi$
$198$		0			0
$199$	−7.29795	+	4.21348i	−0.517338	+	0.298685i	−0.735845	−	0.677150i	$-0.763215\pi$
$199$	−7.29795	+	4.21348i	−0.517338	+	0.298685i	0.218507	+	0.975835i	$0.429881\pi$
$200$		−	6.21780i		−	0.439665i
$201$		0			0
$202$	8.64970	−	4.99390i	0.608591	−	0.351370i
$203$	−9.01013	+	0.258223i	−0.632387	+	0.0181237i
$204$		0			0
$205$	−6.54301	+	11.3328i	−0.456983	+	0.791518i
$206$	3.93055	−	6.80791i	0.273854	−	0.474329i
$207$		0			0
$208$	5.15227	−	2.54807i	0.357246	−	0.176677i
$209$	28.2457			1.95380
$210$		0			0
$211$	2.89400	−	5.01255i	0.199231	−	0.345078i	−0.749048	−	0.662515i	$-0.769489\pi$
$211$	2.89400	−	5.01255i	0.199231	−	0.345078i	0.948279	+	0.317437i	$0.102822\pi$
$212$	4.57582	−	2.64185i	0.314269	−	0.181443i
$213$		0			0
$214$	0.636870	+	1.10309i	0.0435356	+	0.0754058i
$215$	−0.573837	−	0.993915i	−0.0391354	−	0.0677845i
$216$		0			0
$217$	−4.63459	−	7.52117i	−0.314616	−	0.510570i
$218$	−10.6619	−	6.15563i	−0.722113	−	0.416912i
$219$		0			0
$220$			11.2134i			0.756009i
$221$	−0.186689	+	2.89861i	−0.0125581	+	0.194981i
$222$		0			0
$223$	−20.2269	−	11.6780i	−1.35449	−	0.782017i	−0.365619	−	0.930765i	$-0.619143\pi$
$223$	−20.2269	−	11.6780i	−1.35449	−	0.782017i	−0.988875	+	0.148747i	$0.952476\pi$
$224$	−7.21156	+	13.3607i	−0.481842	+	0.892698i
$225$		0			0
$226$	9.55054			0.635292
$227$	12.2467	+	21.2119i	0.812840	+	1.40788i	0.910868	+	0.412697i	$0.135413\pi$
$227$	12.2467	+	21.2119i	0.812840	+	1.40788i	−0.0980281	+	0.995184i	$0.531254\pi$
$228$		0			0
$229$		−	23.0063i		−	1.52030i	−0.649746	−	0.760151i	$-0.725125\pi$
$229$		−	23.0063i		−	1.52030i	0.649746	−	0.760151i	$-0.274875\pi$
$230$	2.91381	+	5.04687i	0.192131	+	0.332781i
$231$		0			0
$232$	−3.99512	+	6.91975i	−0.262292	+	0.454304i
$233$			11.5350i			0.755686i	0.925870	+	0.377843i	$0.123334\pi$
$233$			11.5350i			0.755686i	−0.925870	+	0.377843i	$0.876666\pi$
$234$		0			0
$235$	5.22605			0.340910
$236$	9.42419	−	16.3232i	0.613462	−	1.06255i
$237$		0			0
$238$	−0.734991	−	1.19277i	−0.0476424	−	0.0773158i
$239$			9.13839i			0.591114i	0.955325	+	0.295557i	$0.0955051\pi$
$239$			9.13839i			0.591114i	−0.955325	+	0.295557i	$0.904495\pi$
$240$		0			0
$241$	9.29790	−	5.36814i	0.598930	−	0.345793i	−0.169690	−	0.985497i	$-0.554277\pi$
$241$	9.29790	−	5.36814i	0.598930	−	0.345793i	0.768621	+	0.639705i	$0.220943\pi$
$242$		−	7.08345i		−	0.455341i
$243$		0			0
$244$	−8.44201	−	4.87399i	−0.540444	−	0.312026i
$245$	−4.82316	+	9.58279i	−0.308140	+	0.612222i
$246$		0			0
$247$	−21.7789	−	1.40270i	−1.38576	−	0.0892518i
$248$	−7.83122			−0.497283
$249$		0			0
$250$	−6.67527	−	3.85397i	−0.422181	−	0.243747i
$251$	4.29806	+	7.44445i	0.271291	+	0.469890i	0.969193	−	0.246304i	$-0.0792161\pi$
$251$	4.29806	+	7.44445i	0.271291	+	0.469890i	−0.697902	+	0.716194i	$0.745883\pi$
$252$		0			0
$253$	13.4971	+	23.3776i	0.848555	+	1.46974i
$254$	−2.43913	+	1.40824i	−0.153045	+	0.0883605i
$255$		0			0
$256$	4.22974	+	7.32612i	0.264359	+	0.457883i
$257$	9.05891	−	15.6905i	0.565079	−	0.978746i	−0.431963	−	0.901891i	$-0.642179\pi$
$257$	9.05891	−	15.6905i	0.565079	−	0.978746i	0.997042	−	0.0768547i	$-0.0244878\pi$
$258$		0			0
$259$	0.783294	+	27.3313i	0.0486715	+	1.69829i
$260$	0.556866	−	8.64612i	0.0345354	−	0.536209i
$261$		0			0
$262$	−8.70334	−	5.02487i	−0.537694	−	0.310438i
$263$	−10.9794	−	6.33893i	−0.677016	−	0.390875i	0.121714	−	0.992565i	$-0.461161\pi$
$263$	−10.9794	−	6.33893i	−0.677016	−	0.390875i	−0.798730	+	0.601690i	$0.794494\pi$
$264$		0			0
$265$		−	5.16466i		−	0.317263i
$266$	8.96196	−	5.52241i	0.549493	−	0.338601i
$267$		0			0
$268$	0.242599			0.0148191
$269$	−1.13650	−	1.96847i	−0.0692934	−	0.120020i	0.829297	−	0.558808i	$-0.188741\pi$
$269$	−1.13650	−	1.96847i	−0.0692934	−	0.120020i	−0.898590	+	0.438788i	$0.855408\pi$
$270$		0			0
$271$	5.18941	+	2.99611i	0.315234	+	0.182000i	0.649266	−	0.760561i	$-0.275076\pi$
$271$	5.18941	+	2.99611i	0.315234	+	0.182000i	−0.334032	+	0.942562i	$0.608409\pi$
$272$	1.28427			0.0778702
$273$		0			0
$274$	−3.27979			−0.198139
$275$	−10.7141	−	6.18582i	−0.646087	−	0.373019i
$276$		0			0
$277$	−10.9568	−	18.9778i	−0.658332	−	1.14026i	−0.981047	−	0.193769i	$-0.937929\pi$
$277$	−10.9568	−	18.9778i	−0.658332	−	1.14026i	0.322715	−	0.946496i	$-0.395404\pi$
$278$	−5.44926			−0.326825
$279$		0			0
$280$	4.98891	+	8.09619i	0.298145	+	0.483840i
$281$			24.6150i			1.46841i	0.678929	+	0.734204i	$0.262445\pi$
$281$			24.6150i			1.46841i	−0.678929	+	0.734204i	$0.737555\pi$
$282$		0			0
$283$	6.12695	+	3.53740i	0.364210	+	0.210276i	0.670926	−	0.741525i	$-0.265897\pi$
$283$	6.12695	+	3.53740i	0.364210	+	0.210276i	−0.306716	+	0.951801i	$0.599230\pi$
$284$	−11.1061	−	6.41213i	−0.659028	−	0.380490i
$285$		0			0
$286$	−0.710848	+	11.0369i	−0.0420333	+	0.652626i
$287$	0.647167	+	22.5815i	0.0382010	+	1.33294i
$288$		0			0
$289$	8.17551	−	14.1604i	0.480912	−	0.832964i
$290$	1.71609	+	2.97236i	0.100773	+	0.174543i
$291$		0			0
$292$	9.29316	−	5.36541i	0.543841	−	0.313987i
$293$	7.46327	+	12.9268i	0.436009	+	0.755190i	0.997377	−	0.0723764i	$-0.0230583\pi$
$293$	7.46327	+	12.9268i	0.436009	+	0.755190i	−0.561369	+	0.827566i	$0.689725\pi$
$294$		0			0
$295$	−9.21186	−	15.9554i	−0.536335	−	0.928960i
$296$	20.9903	+	12.1188i	1.22004	+	0.704390i
$297$		0			0
$298$	14.7803			0.856202
$299$	−9.24599	−	18.6956i	−0.534710	−	1.08120i
$300$		0			0
$301$	−1.74350	−	0.941070i	−0.100494	−	0.0542424i
$302$	5.15037	+	2.97357i	0.296371	+	0.171110i
$303$		0			0
$304$			9.64943i			0.553433i
$305$	−8.25181	+	4.76418i	−0.472497	+	0.272796i
$306$		0			0
$307$		−	31.8918i		−	1.82016i	−0.414431	−	0.910081i	$-0.636019\pi$
$307$		−	31.8918i		−	1.82016i	0.414431	−	0.910081i	$-0.363981\pi$
$308$	10.1553	+	16.4804i	0.578652	+	0.939057i
$309$		0			0
$310$	−1.68194	+	2.91321i	−0.0955279	+	0.165459i
$311$	−34.8602			−1.97674			−0.988369	−	0.152075i	$-0.951404\pi$
$311$	−34.8602			−1.97674			−0.988369	+	0.152075i	$0.951404\pi$
$312$		0			0
$313$		−	5.99084i		−	0.338622i	−0.985563	−	0.169311i	$-0.945846\pi$
$313$		−	5.99084i		−	0.338622i	0.985563	−	0.169311i	$-0.0541543\pi$
$314$	5.88424	−	10.1918i	0.332067	−	0.575156i
$315$		0			0
$316$	−0.845184	−	1.46390i	−0.0475453	−	0.0823509i
$317$			10.0010i			0.561713i	0.959750	+	0.280857i	$0.0906185\pi$
$317$			10.0010i			0.561713i	−0.959750	+	0.280857i	$0.909381\pi$
$318$		0			0
$319$	7.94914	+	13.7683i	0.445066	+	0.770877i
$320$	0.894634			0.0500115
$321$		0			0
$322$	8.85307	+	4.77853i	0.493362	+	0.266297i
$323$	−4.22289	−	2.43809i	−0.234968	−	0.135659i
$324$		0			0
$325$	7.95396	+	5.30165i	0.441206	+	0.294083i
$326$			3.81310i			0.211188i
$327$		0			0
$328$	17.3425	+	10.0127i	0.957578	+	0.552858i
$329$	7.68073	−	4.73291i	0.423452	−	0.260934i
$330$		0			0
$331$	−11.7954	−	20.4302i	−0.648334	−	1.12295i	−0.983521	−	0.180795i	$-0.942133\pi$
$331$	−11.7954	−	20.4302i	−0.648334	−	1.12295i	0.335187	−	0.942152i	$-0.391200\pi$
$332$	−4.98815	−	8.63973i	−0.273760	−	0.474167i
$333$		0			0
$334$	−7.76022	+	4.48037i	−0.424620	+	0.245155i
$335$	0.118567	−	0.205364i	0.00647799	−	0.0112202i
$336$		0			0
$337$	7.60616			0.414334			0.207167	−	0.978306i	$-0.433576\pi$
$337$	7.60616			0.414334			0.207167	+	0.978306i	$0.433576\pi$
$338$	1.09620	−	8.47471i	0.0596254	−	0.460964i
$339$		0			0
$340$	0.967910	−	1.67647i	0.0524923	−	0.0909193i
$341$	−7.79094	+	13.4943i	−0.421903	+	0.730758i
$342$		0			0
$343$	1.58993	+	18.4519i	0.0858483	+	0.996308i
$344$	−1.52098	+	0.878137i	−0.0820056	+	0.0473460i
$345$		0			0
$346$			14.6389i			0.786995i
$347$	27.4947	−	15.8741i	1.47599	−	0.852164i	0.476358	−	0.879251i	$-0.341957\pi$
$347$	27.4947	−	15.8741i	1.47599	−	0.852164i	0.999633	+	0.0270873i	$0.00862323\pi$
$348$		0			0
$349$	−22.0169	−	12.7114i	−1.17854	−	0.680428i	−0.222860	−	0.974850i	$-0.571539\pi$
$349$	−22.0169	−	12.7114i	−1.17854	−	0.680428i	−0.955675	+	0.294423i	$0.904873\pi$
$350$	−4.60885	+	0.132086i	−0.246354	+	0.00706030i
$351$		0			0
$352$	26.7787			1.42731
$353$	13.0905	−	22.6734i	0.696737	−	1.20678i	−0.272855	−	0.962055i	$-0.587968\pi$
$353$	13.0905	−	22.6734i	0.696737	−	1.20678i	0.969592	−	0.244728i	$-0.0786988\pi$
$354$		0			0
$355$	−10.8559	+	6.26766i	−0.576172	+	0.332653i
$356$	2.00026			0.106013
$357$		0			0
$358$	0.903737	+	1.56532i	0.0477640	+	0.0827297i
$359$		−	29.1909i		−	1.54064i	−0.637660	−	0.770318i	$-0.720098\pi$
$359$		−	29.1909i		−	1.54064i	0.637660	−	0.770318i	$-0.279902\pi$
$360$		0			0
$361$	8.81875	−	15.2745i	0.464145	−	0.803922i
$362$	4.32425	−	7.48982i	0.227277	−	0.393656i
$363$		0			0
$364$	−7.01183	−	13.2115i	−0.367520	−	0.692473i
$365$		−	10.4891i		−	0.549022i
$366$		0			0
$367$	12.7918	+	7.38535i	0.667727	+	0.385512i	0.795215	−	0.606328i	$-0.207358\pi$
$367$	12.7918	+	7.38535i	0.667727	+	0.385512i	−0.127488	+	0.991840i	$0.540691\pi$
$368$	−7.98638	+	4.61094i	−0.416319	+	0.240362i
$369$		0			0
$370$	9.01636	−	5.20560i	0.468738	−	0.270626i
$371$	−4.67732	−	7.59052i	−0.242834	−	0.394080i
$372$		0			0
$373$	8.82812	+	15.2908i	0.457103	+	0.791726i	0.998806	−	0.0488441i	$-0.0155538\pi$
$373$	8.82812	+	15.2908i	0.457103	+	0.791726i	−0.541703	+	0.840570i	$0.682220\pi$
$374$	−1.23555	+	2.14004i	−0.0638889	+	0.110659i
$375$		0			0
$376$		−	7.99736i		−	0.412432i
$377$	−5.44545	−	11.0108i	−0.280455	−	0.567087i
$378$		0			0
$379$	16.9787	−	29.4080i	0.872139	−	1.51059i	0.0123591	−	0.999924i	$-0.496066\pi$
$379$	16.9787	−	29.4080i	0.872139	−	1.51059i	0.859780	−	0.510665i	$-0.170601\pi$
$380$	12.5963	+	7.27246i	0.646175	+	0.373069i
$381$		0			0
$382$	−6.03971			−0.309019
$383$	4.76747	+	8.25749i	0.243606	+	0.421938i	0.961739	−	0.273968i	$-0.0883363\pi$
$383$	4.76747	+	8.25749i	0.243606	+	0.421938i	−0.718133	+	0.695906i	$0.755003\pi$
$384$		0			0
$385$	18.9141	−	0.542064i	0.963953	−	0.0276261i
$386$	4.58446	−	2.64684i	0.233343	−	0.134721i
$387$		0			0
$388$	−15.3139	−	8.84148i	−0.777445	−	0.448858i
$389$			16.8123i			0.852419i	0.904624	+	0.426210i	$0.140151\pi$
$389$			16.8123i			0.852419i	−0.904624	+	0.426210i	$0.859849\pi$
$390$		0			0
$391$		−	4.66012i		−	0.235672i
$392$	14.6644	+	7.38083i	0.740666	+	0.372788i
$393$		0			0
$394$	0.664510	+	1.15097i	0.0334775	+	0.0579848i
$395$	−1.65228			−0.0831354
$396$		0			0
$397$	−21.6865	+	12.5207i	−1.08841	+	0.628396i	−0.933154	−	0.359478i	$-0.882955\pi$
$397$	−21.6865	+	12.5207i	−1.08841	+	0.628396i	−0.155260	+	0.987874i	$0.549621\pi$
$398$	5.53930			0.277660
$399$		0			0
$400$	2.11323	−	3.66022i	0.105661	−	0.183011i
$401$	22.2709	+	12.8581i	1.11215	+	0.642103i	0.939387	−	0.342860i	$-0.111396\pi$
$401$	22.2709	+	12.8581i	1.11215	+	0.642103i	0.172768	+	0.984963i	$0.444729\pi$
$402$		0			0
$403$	6.67735	−	10.0179i	0.332622	−	0.499027i
$404$	23.8236			1.18527
$405$		0			0
$406$	5.21403	+	2.81433i	0.258768	+	0.139673i
$407$	41.7648	−	24.1129i	2.07020	−	1.19523i
$408$		0			0
$409$	13.6967	−	7.90778i	0.677257	−	0.391015i	−0.121564	−	0.992584i	$-0.538791\pi$
$409$	13.6967	−	7.90778i	0.677257	−	0.391015i	0.798821	+	0.601569i	$0.205458\pi$
$410$	7.44942	−	4.30093i	0.367901	−	0.212408i
$411$		0			0
$412$	16.2387	−	9.37542i	0.800023	−	0.461894i
$413$	−27.9885	−	15.1071i	−1.37723	−	0.743371i
$414$		0			0
$415$	−9.75154			−0.478684
$416$	−20.6477	−	1.32985i	−1.01234	−	0.0652012i
$417$		0			0
$418$	−16.0793	−	9.28341i	−0.786466	−	0.454066i
$419$	−6.98331	+	12.0954i	−0.341157	+	0.590901i	−0.984648	−	0.174553i	$-0.944152\pi$
$419$	−6.98331	+	12.0954i	−0.341157	+	0.590901i	0.643491	+	0.765454i	$0.277485\pi$
$420$		0			0
$421$	−25.4862			−1.24212			−0.621060	−	0.783763i	$-0.713298\pi$
$421$	−25.4862			−1.24212			−0.621060	+	0.783763i	$0.713298\pi$
$422$	−3.29491	+	1.90232i	−0.160394	+	0.0926033i
$423$		0			0
$424$	−7.90342			−0.383824
$425$	1.06788	+	1.84963i	0.0518000	+	0.0897202i
$426$		0			0
$427$	−7.81307	+	14.4751i	−0.378101	+	0.700499i
$428$			3.03822i			0.146858i
$429$		0			0
$430$			0.754403i			0.0363806i
$431$	28.6504	+	16.5413i	1.38004	+	0.796767i	0.992164	−	0.124943i	$-0.0398749\pi$
$431$	28.6504	+	16.5413i	1.38004	+	0.796767i	0.387878	+	0.921711i	$0.373208\pi$
$432$		0			0
$433$	13.8289	−	7.98414i	0.664576	−	0.383693i	−0.129442	−	0.991587i	$-0.541319\pi$
$433$	13.8289	−	7.98414i	0.664576	−	0.383693i	0.794018	+	0.607894i	$0.207985\pi$
$434$	0.166360	+	5.80478i	0.00798555	+	0.278638i
$435$		0			0
$436$	−14.6828	−	25.4314i	−0.703181	−	1.21795i
$437$	35.0141			1.67495
$438$		0			0
$439$	15.2260	+	8.79076i	0.726700	+	0.419560i	0.817214	−	0.576335i	$-0.195518\pi$
$439$	15.2260	+	8.79076i	0.726700	+	0.419560i	−0.0905139	+	0.995895i	$0.528851\pi$
$440$	8.38658	−	14.5260i	0.399814	−	0.692499i
$441$		0			0
$442$	1.05895	−	1.58872i	0.0503691	−	0.0755678i
$443$		−	8.95157i		−	0.425302i	−0.977128	−	0.212651i	$-0.931790\pi$
$443$		−	8.95157i		−	0.425302i	0.977128	−	0.212651i	$-0.0682098\pi$
$444$		0			0
$445$	0.977595	−	1.69324i	0.0463424	−	0.0802675i
$446$	7.67633	+	13.2958i	0.363485	+	0.629574i
$447$		0			0
$448$	1.31485	−	0.810215i	0.0621206	−	0.0382790i
$449$	24.4891	−	14.1388i	1.15571	−	0.667251i	0.205440	−	0.978670i	$-0.434137\pi$
$449$	24.4891	−	14.1388i	1.15571	−	0.667251i	0.950273	+	0.311418i	$0.100804\pi$
$450$		0			0
$451$	34.5066	−	19.9224i	1.62485	−	0.938108i
$452$	19.7286	+	11.3903i	0.927955	+	0.535755i
$453$		0			0
$454$		−	16.1003i		−	0.755623i
$455$	−14.6107	−	0.521330i	−0.684959	−	0.0244403i
$456$		0			0
$457$	1.11023	−	1.92297i	0.0519342	−	0.0899526i	−0.838890	−	0.544302i	$-0.816795\pi$
$457$	1.11023	−	1.92297i	0.0519342	−	0.0899526i	0.890824	+	0.454349i	$0.150128\pi$
$458$	−7.56140	+	13.0967i	−0.353321	+	0.611970i
$459$		0			0
$460$			13.9005i			0.648112i
$461$	11.2445	+	19.4761i	0.523710	+	0.907092i	0.999619	+	0.0275978i	$0.00878578\pi$
$461$	11.2445	+	19.4761i	0.523710	+	0.907092i	−0.475909	+	0.879494i	$0.657881\pi$
$462$		0			0
$463$	−8.92299			−0.414687			−0.207343	−	0.978268i	$-0.566482\pi$
$463$	−8.92299			−0.414687			−0.207343	+	0.978268i	$0.566482\pi$
$464$	−4.70360	+	2.71562i	−0.218359	+	0.126070i
$465$		0			0
$466$	3.79118	−	6.56651i	0.175623	−	0.304188i
$467$	−15.0697			−0.697345			−0.348672	−	0.937245i	$-0.613367\pi$
$467$	−15.0697			−0.697345			−0.348672	+	0.937245i	$0.613367\pi$
$468$		0			0
$469$	−0.0117274	−	0.409202i	−0.000541521	−	0.0188952i
$470$	−2.97501	−	1.71762i	−0.137227	−	0.0792281i
$471$		0			0
$472$	−24.4164	+	14.0968i	−1.12386	+	0.648858i
$473$			3.49448i			0.160676i
$474$		0			0
$475$	−13.8973	+	8.02362i	−0.637652	+	0.368149i
$476$	−0.0957357	−	3.34049i	−0.00438804	−	0.153111i
$477$		0			0
$478$	3.00348	−	5.20218i	0.137376	−	0.237942i
$479$	−15.2122	+	26.3482i	−0.695062	+	1.20388i	0.275098	+	0.961416i	$0.411290\pi$
$479$	−15.2122	+	26.3482i	−0.695062	+	1.20388i	−0.970160	+	0.242466i	$0.922044\pi$
$480$		0			0
$481$	−33.4002	+	16.5182i	−1.52292	+	0.753165i
$482$	−7.05731			−0.321451
$483$		0			0
$484$	8.44797	−	14.6323i	0.383999	−	0.665105i
$485$	−14.9689	+	8.64228i	−0.679701	+	0.392426i
$486$		0			0
$487$	−7.43249	−	12.8735i	−0.336798	−	0.583352i	0.647030	−	0.762464i	$-0.276011\pi$
$487$	−7.43249	−	12.8735i	−0.336798	−	0.583352i	−0.983829	+	0.179112i	$0.942677\pi$
$488$	7.29058	+	12.6276i	0.330029	+	0.571627i
$489$		0			0
$490$	5.89520	−	3.86995i	0.266318	−	0.174826i
$491$	1.88709	+	1.08951i	0.0851632	+	0.0491690i	0.541977	−	0.840393i	$-0.317676\pi$
$491$	1.88709	+	1.08951i	0.0851632	+	0.0491690i	−0.456814	+	0.889562i	$0.651009\pi$
$492$		0			0
$493$		−	2.74459i		−	0.123610i
$494$	11.9370	+	7.95649i	0.537069	+	0.357979i
$495$		0			0
$496$	−4.60999	−	2.66158i	−0.206995	−	0.119508i
$497$	−10.2787	+	19.0431i	−0.461064	+	0.854201i
$498$		0			0
$499$	20.8960			0.935435			0.467717	−	0.883878i	$-0.345077\pi$
$499$	20.8960			0.935435			0.467717	+	0.883878i	$0.345077\pi$
$500$	−9.19276	−	15.9223i	−0.411113	−	0.712068i
$501$		0			0
$502$		−	5.65050i		−	0.252194i
$503$	7.19291	+	12.4585i	0.320716	+	0.555497i	0.980636	−	0.195839i	$-0.0627431\pi$
$503$	7.19291	+	12.4585i	0.320716	+	0.555497i	−0.659920	+	0.751336i	$0.729410\pi$
$504$		0			0
$505$	11.6434	−	20.1670i	0.518126	−	0.897421i
$506$		−	17.7441i		−	0.788823i
$507$		0			0
$508$	−6.71804			−0.298065
$509$	15.5822	−	26.9892i	0.690671	−	1.19628i	−0.280947	−	0.959723i	$-0.590649\pi$
$509$	15.5822	−	26.9892i	0.690671	−	1.19628i	0.971618	−	0.236554i	$-0.0760180\pi$
$510$		0			0
$511$	−9.49929	−	15.4158i	−0.420224	−	0.681954i
$512$			16.6260i			0.734771i
$513$		0			0
$514$	−10.3139	+	5.95471i	−0.454925	+	0.262651i
$515$		−	18.3284i		−	0.807645i
$516$		0			0
$517$	−13.7806	−	7.95622i	−0.606069	−	0.349914i
$518$	8.53697	−	15.8162i	0.375093	−	0.694925i
$519$		0			0
$520$	−7.18785	+	10.7838i	−0.315208	+	0.472900i
$521$	10.7379			0.470436			0.235218	−	0.971943i	$-0.424420\pi$
$521$	10.7379			0.470436			0.235218	+	0.971943i	$0.424420\pi$
$522$		0			0
$523$	17.8605	+	10.3117i	0.780984	+	0.450901i	0.836779	−	0.547541i	$-0.184436\pi$
$523$	17.8605	+	10.3117i	0.780984	+	0.450901i	−0.0557951	+	0.998442i	$0.517769\pi$
$524$	−11.9857	−	20.7598i	−0.523597	−	0.906897i
$525$		0			0
$526$	4.16678	+	7.21708i	0.181680	+	0.314680i
$527$	2.32958	−	1.34498i	0.101478	−	0.0585884i
$528$		0			0
$529$	5.23135	+	9.06096i	0.227450	+	0.393955i
$530$	−1.69745	+	2.94007i	−0.0737325	+	0.127708i
$531$		0			0
$532$	25.0990	−	0.719317i	1.08818	−	0.0311863i
$533$	−27.5957	+	13.6475i	−1.19530	+	0.591141i
$534$		0			0
$535$	2.57189	+	1.48488i	0.111193	+	0.0641971i
$536$	−0.314266	−	0.181441i	−0.0135742	−	0.00783707i
$537$		0			0
$538$			1.49411i			0.0644157i
$539$	27.3072	−	17.9260i	1.17621	−	0.772129i
$540$		0			0
$541$	7.75429			0.333383			0.166692	−	0.986009i	$-0.446692\pi$
$541$	7.75429			0.333383			0.166692	+	0.986009i	$0.446692\pi$
$542$	−1.96944	−	3.41116i	−0.0845945	−	0.146522i
$543$		0			0
$544$	−4.00357	−	2.31146i	−0.171652	−	0.0991031i
$545$	−28.7041			−1.22955
$546$		0			0
$547$	−40.0177			−1.71104			−0.855518	−	0.517774i	$-0.826761\pi$
$547$	−40.0177			−1.71104			−0.855518	+	0.517774i	$0.826761\pi$
$548$	−6.77507	−	3.91159i	−0.289417	−	0.167095i
$549$		0			0
$550$	4.06613	+	7.04275i	0.173381	+	0.300304i
$551$	20.6216			0.878512
$552$		0			0
$553$	−2.42836	+	1.49637i	−0.103265	+	0.0636322i
$554$			14.4046i			0.611991i
$555$		0			0
$556$	−11.2566	−	6.49898i	−0.477384	−	0.275618i
$557$	−15.4946	−	8.94580i	−0.656527	−	0.379046i	0.134426	−	0.990924i	$-0.457081\pi$
$557$	−15.4946	−	8.94580i	−0.656527	−	0.379046i	−0.790952	+	0.611878i	$0.790414\pi$
$558$		0			0
$559$	0.173538	−	2.69442i	0.00733989	−	0.113962i
$560$	0.185182	+	6.46153i	0.00782539	+	0.273050i
$561$		0			0
$562$	8.09012	−	14.0125i	0.341261	−	0.591081i
$563$	0.714912	+	1.23826i	0.0301299	+	0.0521866i	0.880697	−	0.473680i	$-0.157075\pi$
$563$	0.714912	+	1.23826i	0.0301299	+	0.0521866i	−0.850567	+	0.525866i	$0.823741\pi$
$564$		0			0
$565$	19.2841	−	11.1337i	0.811289	−	0.468398i
$566$	−2.32524	−	4.02744i	−0.0977373	−	0.169286i
$567$		0			0
$568$	9.59133	+	16.6127i	0.402443	+	0.697052i
$569$	3.54861	+	2.04879i	0.148766	+	0.0858899i	0.572535	−	0.819880i	$-0.305960\pi$
$569$	3.54861	+	2.04879i	0.148766	+	0.0858899i	−0.423770	+	0.905770i	$0.639293\pi$
$570$		0			0
$571$	−33.4543			−1.40002			−0.700010	−	0.714133i	$-0.746821\pi$
$571$	−33.4543			−1.40002			−0.700010	+	0.714133i	$0.746821\pi$
$572$	−14.6314	+	21.9512i	−0.611770	+	0.917826i
$573$		0			0
$574$	7.05335	−	13.0676i	0.294401	−	0.545430i
$575$	−13.2815	−	7.66810i	−0.553878	−	0.319782i
$576$		0			0
$577$			11.7590i			0.489533i	0.969582	+	0.244767i	$0.0787114\pi$
$577$			11.7590i			0.489533i	−0.969582	+	0.244767i	$0.921289\pi$
$578$	−9.30808	+	5.37402i	−0.387165	+	0.223530i
$579$		0			0
$580$			8.18670i			0.339934i
$581$	−14.3319	+	8.83137i	−0.594586	+	0.366387i
$582$		0			0
$583$	−7.86277	+	13.6187i	−0.325643	+	0.564030i
$584$	−16.0513			−0.664207
$585$		0			0
$586$		−	9.81169i		−	0.405317i
$587$	20.4836	−	35.4786i	0.845448	−	1.46436i	−0.0397838	−	0.999208i	$-0.512667\pi$
$587$	20.4836	−	35.4786i	0.845448	−	1.46436i	0.885232	−	0.465150i	$-0.154000\pi$
$588$		0			0
$589$	10.1056	+	17.5035i	0.416395	+	0.721217i
$590$			12.1105i			0.498582i
$591$		0			0
$592$	8.23756	+	14.2679i	0.338562	+	0.586406i
$593$	14.1873			0.582602			0.291301	−	0.956631i	$-0.405912\pi$
$593$	14.1873			0.582602			0.291301	+	0.956631i	$0.405912\pi$
$594$		0			0
$595$	−2.87456	−	1.55157i	−0.117845	−	0.0636083i
$596$	30.5318	+	17.6276i	1.25063	+	0.722053i
$597$		0			0
$598$	−0.881186	+	13.6816i	−0.0360344	+	0.559484i
$599$		−	0.467682i		−	0.0191090i	−0.999954	−	0.00955449i	$-0.996959\pi$
$599$		−	0.467682i		−	0.0191090i	0.999954	−	0.00955449i	$-0.00304134\pi$
$600$		0			0
$601$	8.69308	+	5.01895i	0.354598	+	0.204727i	0.666709	−	0.745318i	$-0.267703\pi$
$601$	8.69308	+	5.01895i	0.354598	+	0.204727i	−0.312110	+	0.950046i	$0.601036\pi$
$602$	0.683217	+	1.10875i	0.0278458	+	0.0451892i
$603$		0			0
$604$	7.09277	+	12.2850i	0.288601	+	0.499871i
$605$	−8.25764	−	14.3027i	−0.335721	−	0.581486i
$606$		0			0
$607$	−6.04714	+	3.49132i	−0.245446	+	0.141708i	−0.617677	−	0.786432i	$-0.711926\pi$
$607$	−6.04714	+	3.49132i	−0.245446	+	0.141708i	0.372231	+	0.928140i	$0.378593\pi$
$608$	17.3673	−	30.0811i	0.704338	−	1.21995i
$609$		0			0
$610$	6.26330			0.253594
$611$	10.2304	+	6.81901i	0.413879	+	0.275868i
$612$		0			0
$613$	−19.2053	+	33.2646i	−0.775695	+	1.34354i	0.158708	+	0.987326i	$0.449267\pi$
$613$	−19.2053	+	33.2646i	−0.775695	+	1.34354i	−0.934403	+	0.356217i	$0.884066\pi$
$614$	−10.4818	+	18.1549i	−0.423009	+	0.732673i
$615$		0			0
$616$	−0.829514	−	28.9441i	−0.0334221	−	1.16619i
$617$	−18.8756	+	10.8978i	−0.759903	+	0.438730i	−0.829261	−	0.558862i	$-0.811238\pi$
$617$	−18.8756	+	10.8978i	−0.759903	+	0.438730i	0.0693582	+	0.997592i	$0.477905\pi$
$618$		0			0
$619$		−	25.9815i		−	1.04428i	−0.852859	−	0.522142i	$-0.825133\pi$
$619$		−	25.9815i		−	1.04428i	0.852859	−	0.522142i	$-0.174867\pi$
$620$	−6.94879	+	4.01189i	−0.279070	+	0.161121i
$621$		0			0
$622$	19.8447	+	11.4573i	0.795700	+	0.459398i
$623$	−0.0966936	−	3.37391i	−0.00387395	−	0.135173i
$624$		0			0
$625$	−4.71547			−0.188619
$626$	−1.96899	+	3.41038i	−0.0786965	+	0.136306i
$627$		0			0
$628$	24.3102	−	14.0355i	0.970082	−	0.560077i
$629$	−8.32543			−0.331956
$630$		0			0
$631$	1.51986	+	2.63247i	0.0605046	+	0.104797i	0.894691	−	0.446685i	$-0.147396\pi$
$631$	1.51986	+	2.63247i	0.0605046	+	0.104797i	−0.834186	+	0.551482i	$0.814062\pi$
$632$			2.52847i			0.100577i
$633$		0			0
$634$	3.28699	−	5.69324i	0.130543	−	0.226108i
$635$	−3.28334	+	5.68692i	−0.130296	+	0.225678i
$636$		0			0
$637$	−21.9455	+	12.4658i	−0.869512	+	0.493913i
$638$		−	10.4504i		−	0.413737i
$639$		0			0
$640$	14.7237	+	8.50076i	0.582007	+	0.336022i
$641$	−19.5650	+	11.2959i	−0.772772	+	0.446160i	−0.833863	−	0.551972i	$-0.813875\pi$
$641$	−19.5650	+	11.2959i	−0.772772	+	0.446160i	0.0610905	+	0.998132i	$0.480542\pi$
$642$		0			0
$643$	−2.07238	+	1.19649i	−0.0817266	+	0.0471849i	−0.540306	−	0.841468i	$-0.681692\pi$
$643$	−2.07238	+	1.19649i	−0.0817266	+	0.0471849i	0.458580	+	0.888653i	$0.348358\pi$
$644$	12.5888	+	20.4295i	0.496067	+	0.805036i
$645$		0			0
$646$	1.60263	+	2.77584i	0.0630548	+	0.109214i
$647$	2.94743	−	5.10510i	0.115875	−	0.200702i	−0.802254	−	0.596983i	$-0.796366\pi$
$647$	2.94743	−	5.10510i	0.115875	−	0.200702i	0.918129	+	0.396281i	$0.129699\pi$
$648$		0			0
$649$			56.0972i			2.20201i
$650$	−2.78545	−	5.63225i	−0.109254	−	0.220915i
$651$		0			0
$652$	−4.54764	+	7.87674i	−0.178099	+	0.308477i
$653$	−5.32824	−	3.07626i	−0.208510	−	0.120383i	0.392109	−	0.919919i	$-0.371746\pi$
$653$	−5.32824	−	3.07626i	−0.208510	−	0.120383i	−0.600619	+	0.799536i	$0.705079\pi$
$654$		0			0
$655$	−23.4313			−0.915536
$656$	6.80597	+	11.7883i	0.265729	+	0.460255i
$657$		0			0
$658$	−5.92793	+	0.169890i	−0.231095	+	0.00662299i
$659$	−12.9972	+	7.50393i	−0.506298	+	0.292312i	−0.731311	−	0.682044i	$-0.761091\pi$
$659$	−12.9972	+	7.50393i	−0.506298	+	0.292312i	0.225012	+	0.974356i	$0.427758\pi$
$660$		0			0
$661$	4.33558	+	2.50315i	0.168634	+	0.0973611i	0.581942	−	0.813230i	$-0.302293\pi$
$661$	4.33558	+	2.50315i	0.168634	+	0.0973611i	−0.413307	+	0.910592i	$0.635626\pi$
$662$			15.5070i			0.602696i
$663$		0			0
$664$			14.9227i			0.579112i
$665$	11.6578	−	21.5982i	0.452072	−	0.837542i
$666$		0			0
$667$	9.85396	+	17.0676i	0.381547	+	0.660859i
$668$	−21.3738			−0.826976
$669$		0			0
$670$	−0.134992	+	0.0779377i	−0.00521520	+	0.00301100i
$671$	29.0123			1.12001
$672$		0			0
$673$	−19.5458	+	33.8543i	−0.753435	+	1.30499i	0.192714	+	0.981255i	$0.438271\pi$
$673$	−19.5458	+	33.8543i	−0.753435	+	1.30499i	−0.946149	+	0.323732i	$0.895062\pi$
$674$	−4.32993	−	2.49988i	−0.166783	−	0.0962920i
$675$		0			0
$676$	12.3717	−	16.1989i	0.475833	−	0.623034i
$677$	−43.0300			−1.65378			−0.826888	−	0.562367i	$-0.809891\pi$
$677$	−43.0300			−1.65378			−0.826888	+	0.562367i	$0.809891\pi$
$678$		0			0
$679$	−14.1730	+	26.2580i	−0.543910	+	1.00769i
$680$	−2.50768	+	1.44781i	−0.0961652	+	0.0555210i
$681$		0			0
$682$	8.87024	−	5.12123i	0.339659	−	0.196102i
$683$	−19.7569	+	11.4067i	−0.755979	+	0.436464i	−0.827850	−	0.560949i	$-0.810436\pi$
$683$	−19.7569	+	11.4067i	−0.755979	+	0.436464i	0.0718714	+	0.997414i	$0.477103\pi$
$684$		0			0
$685$	−6.62243	+	3.82346i	−0.253030	+	0.146087i
$686$	5.15941	−	11.0266i	0.196987	−	0.420997i
$687$		0			0
$688$	−1.19380			−0.0455132
$689$	6.73891	−	10.1103i	0.256732	−	0.385170i
$690$		0			0
$691$	1.45897	+	0.842338i	0.0555019	+	0.0320440i	0.527494	−	0.849559i	$-0.323132\pi$
$691$	1.45897	+	0.842338i	0.0555019	+	0.0320440i	−0.471992	+	0.881603i	$0.656465\pi$
$692$	−17.4589	+	30.2397i	−0.663689	+	1.14954i
$693$		0			0
$694$	−20.8690			−0.792178
$695$	−11.0030	+	6.35256i	−0.417366	+	0.240966i
$696$		0			0
$697$	−6.87857			−0.260544
$698$	8.35564	+	14.4724i	0.316265	+	0.547788i
$699$		0			0
$700$	−9.67806	−	5.22383i	−0.365796	−	0.197442i
$701$		−	13.1431i		−	0.496409i	−0.968708	−	0.248205i	$-0.920160\pi$
$701$		−	13.1431i		−	0.496409i	0.968708	−	0.248205i	$-0.0798405\pi$
$702$		0			0
$703$		−	62.5536i		−	2.35926i
$704$	−2.35906	−	1.36201i	−0.0889105	−	0.0513325i
$705$		0			0
$706$	−14.9040	+	8.60480i	−0.560918	+	0.323846i
$707$	−1.15165	−	40.1843i	−0.0433122	−	1.51129i
$708$		0			0
$709$	−2.77050	−	4.79865i	−0.104048	−	0.180217i	0.809301	−	0.587395i	$-0.199846\pi$
$709$	−2.77050	−	4.79865i	−0.104048	−	0.180217i	−0.913349	+	0.407177i	$0.866513\pi$
$710$	8.23987			0.309237
$711$		0			0
$712$	−2.59115	−	1.49600i	−0.0971075	−	0.0560650i
$713$	−9.65786	+	16.7279i	−0.361690	+	0.626465i
$714$		0			0
$715$	11.4311	+	23.1140i	0.427500	+	0.864415i
$716$			4.31132i			0.161121i
$717$		0			0
$718$	−9.59405	+	16.6174i	−0.358047	+	0.620155i
$719$	−6.93490	−	12.0116i	−0.258628	−	0.447957i	0.707247	−	0.706967i	$-0.249937\pi$
$719$	−6.93490	−	12.0116i	−0.258628	−	0.447957i	−0.965875	+	0.259010i	$0.916604\pi$
$720$		0			0
$721$	−16.5989	−	26.9373i	−0.618175	−	1.00320i
$722$	−10.0404	+	5.79684i	−0.373666	+	0.215736i
$723$		0			0
$724$	17.8652	−	10.3145i	0.663956	−	0.383335i
$725$	−7.82219	−	4.51614i	−0.290509	−	0.167725i
$726$		0			0
$727$			9.43866i			0.350061i	0.984563	+	0.175030i	$0.0560023\pi$
$727$			9.43866i			0.350061i	−0.984563	+	0.175030i	$0.943998\pi$
$728$	−0.797785	+	22.3585i	−0.0295679	+	0.828663i
$729$		0			0
$730$	−3.44740	+	5.97107i	−0.127594	+	0.220999i
$731$	0.301634	−	0.522445i	0.0111563	−	0.0193233i
$732$		0			0
$733$		−	23.8875i		−	0.882305i	−0.897432	−	0.441152i	$-0.854570\pi$
$733$		−	23.8875i		−	0.882305i	0.897432	−	0.441152i	$-0.145430\pi$
$734$	−4.85463	−	8.40847i	−0.179188	−	0.310362i
$735$		0			0
$736$	33.1956			1.22361
$737$	−0.625298	+	0.361016i	−0.0230332	+	0.0132982i
$738$		0			0
$739$	−6.29471	+	10.9028i	−0.231555	+	0.401064i	−0.958266	−	0.285879i	$-0.907715\pi$
$739$	−6.29471	+	10.9028i	−0.231555	+	0.401064i	0.726711	+	0.686943i	$0.241048\pi$
$740$	24.8335			0.912898
$741$		0			0
$742$	0.167894	+	5.85830i	0.00616359	+	0.215065i
$743$	−25.4744	−	14.7076i	−0.934564	−	0.539571i	−0.0463116	−	0.998927i	$-0.514747\pi$
$743$	−25.4744	−	14.7076i	−0.934564	−	0.539571i	−0.888252	+	0.459356i	$0.848080\pi$
$744$		0			0
$745$	29.8440	−	17.2304i	1.09340	−	0.631274i
$746$		−	11.6060i		−	0.424926i
$747$		0			0
$748$	−5.10457	+	2.94713i	−0.186642	+	0.107758i
$749$	5.12468	−	0.146869i	0.187252	−	0.00536649i
$750$		0			0
$751$	16.8814	−	29.2394i	0.616011	−	1.06696i	−0.374195	−	0.927350i	$-0.622081\pi$
$751$	16.8814	−	29.2394i	0.616011	−	1.06696i	0.990206	−	0.139612i	$-0.0445857\pi$
$752$	2.71804	−	4.70779i	0.0991168	−	0.171675i
$753$		0			0
$754$	−0.518976	+	8.05783i	−0.0189000	+	0.293449i
$755$	13.8659			0.504633
$756$		0			0
$757$	3.61215	−	6.25644i	0.131286	−	0.227394i	−0.792887	−	0.609369i	$-0.791423\pi$
$757$	3.61215	−	6.25644i	0.131286	−	0.227394i	0.924173	+	0.381975i	$0.124756\pi$
$758$	−19.3308	+	11.1607i	−0.702128	+	0.405374i
$759$		0			0
$760$	−10.8782	−	18.8416i	−0.394595	−	0.683458i
$761$	−1.67309	−	2.89788i	−0.0606496	−	0.105048i	0.834106	−	0.551604i	$-0.185984\pi$
$761$	−1.67309	−	2.89788i	−0.0606496	−	0.105048i	−0.894756	+	0.446555i	$0.852651\pi$
$762$		0			0
$763$	−42.1865	+	25.9955i	−1.52725	+	0.941101i
$764$	−12.4763	−	7.20318i	−0.451375	−	0.260602i
$765$		0			0
$766$		−	6.26762i		−	0.226458i
$767$	2.78583	−	43.2538i	0.100590	−	1.56180i
$768$		0			0
$769$	9.93480	+	5.73586i	0.358258	+	0.206840i	0.668316	−	0.743877i	$-0.267015\pi$
$769$	9.93480	+	5.73586i	0.358258	+	0.206840i	−0.310058	+	0.950718i	$0.600349\pi$
$770$	−10.9453	−	5.90785i	−0.394442	−	0.212904i
$771$		0			0
$772$	12.6269			0.454451
$773$	17.5010	+	30.3126i	0.629467	+	1.09027i	0.987659	+	0.156621i	$0.0500601\pi$
$773$	17.5010	+	30.3126i	0.629467	+	1.09027i	−0.358192	+	0.933648i	$0.616607\pi$
$774$		0			0
$775$		−	8.85253i		−	0.317992i
$776$	13.2252	+	22.9067i	0.474756	+	0.822302i
$777$		0			0
$778$	5.52564	−	9.57069i	0.198104	−	0.343126i
$779$		−	51.6826i		−	1.85172i
$780$		0			0
$781$	38.1680			1.36576
$782$	−1.53162	+	2.65285i	−0.0547707	+	0.0948657i
$783$		0			0
$784$	6.12398	+	9.32882i	0.218713	+	0.333172i
$785$		−	27.4386i		−	0.979324i
$786$		0			0
$787$	13.0230	−	7.51885i	0.464221	−	0.268018i	−0.249596	−	0.968350i	$-0.580298\pi$
$787$	13.0230	−	7.51885i	0.464221	−	0.268018i	0.713817	+	0.700332i	$0.246965\pi$
$788$			3.17007i			0.112929i
$789$		0			0
$790$	0.940589	+	0.543049i	0.0334647	+	0.0193208i
$791$	18.2588	−	33.8276i	0.649209	−	1.20277i
$792$		0			0
$793$	−22.3700	−	1.44077i	−0.794381	−	0.0511633i
$794$	16.4605			0.584162
$795$		0			0
$796$	11.4426	+	6.60637i	0.405571	+	0.234157i
$797$	3.33858	+	5.78260i	0.118259	+	0.204830i	0.919078	−	0.394076i	$-0.128935\pi$
$797$	3.33858	+	5.78260i	0.118259	+	0.204830i	−0.800819	+	0.598906i	$0.795602\pi$
$798$		0			0
$799$	1.37352	+	2.37900i	0.0485915	+	0.0841630i
$800$	−13.1755	+	7.60689i	−0.465825	+	0.268944i
$801$		0			0
$802$	−8.45204	−	14.6394i	−0.298452	−	0.516934i
$803$	−15.9687	+	27.6586i	−0.563524	+	0.976052i
$804$		0			0
$805$	23.4465	−	0.671957i	0.826379	−	0.0236834i
$806$	−7.09373	+	3.50823i	−0.249866	+	0.123572i
$807$		0			0
$808$	−30.8614	−	17.8178i	−1.08570	−	0.626829i
$809$	−23.8895	−	13.7926i	−0.839911	−	0.484923i	0.0173231	−	0.999850i	$-0.494486\pi$
$809$	−23.8895	−	13.7926i	−0.839911	−	0.484923i	−0.857234	+	0.514927i	$0.827819\pi$
$810$		0			0
$811$			16.5527i			0.581245i	0.956838	+	0.290622i	$0.0938623\pi$
$811$			16.5527i			0.581245i	−0.956838	+	0.290622i	$0.906138\pi$
$812$	7.41419	+	12.0320i	0.260187	+	0.422241i
$813$		0			0
$814$	−31.7004			−1.11110
$815$	4.44518	+	7.69928i	0.155708	+	0.269694i
$816$		0			0
$817$	3.92542	+	2.26634i	0.137333	+	0.0792893i
$818$	−10.3961			−0.363490
$819$		0			0
$820$	20.5177			0.716511
$821$	−29.8114	−	17.2116i	−1.04043	−	0.600690i	−0.120471	−	0.992717i	$-0.538441\pi$
$821$	−29.8114	−	17.2116i	−1.04043	−	0.600690i	−0.919954	+	0.392027i	$0.871774\pi$
$822$		0			0
$823$	9.29945	+	16.1071i	0.324158	+	0.561459i	0.981342	−	0.192272i	$-0.0615856\pi$
$823$	9.29945	+	16.1071i	0.324158	+	0.561459i	−0.657183	+	0.753731i	$0.728252\pi$
$824$	−28.0477			−0.977088
$825$		0			0
$826$	10.9677	+	17.7988i	0.381616	+	0.619301i
$827$			47.4905i			1.65141i	0.564104	+	0.825704i	$0.309222\pi$
$827$			47.4905i			1.65141i	−0.564104	+	0.825704i	$0.690778\pi$
$828$		0			0
$829$	−41.2885	−	23.8379i	−1.43401	−	0.827925i	−0.436585	−	0.899663i	$-0.643812\pi$
$829$	−41.2885	−	23.8379i	−1.43401	−	0.827925i	−0.997424	+	0.0717376i	$0.977146\pi$
$830$	5.55122	+	3.20500i	0.192686	+	0.111247i
$831$		0			0
$832$	1.75132	+	1.16733i	0.0607161	+	0.0404698i
$833$	−5.62991	+	0.322963i	−0.195065	+	0.0111900i
$834$		0			0
$835$	−10.4461	+	18.0932i	−0.361503	+	0.626141i
$836$	−22.1434	−	38.3536i	−0.765847	−	1.32649i
$837$		0			0
$838$	7.95072	−	4.59035i	0.274653	−	0.158571i
$839$	−24.5733	−	42.5621i	−0.848363	−	1.46941i	−0.882668	−	0.469997i	$-0.844255\pi$
$839$	−24.5733	−	42.5621i	−0.848363	−	1.46941i	0.0343051	−	0.999411i	$-0.489078\pi$
$840$		0			0
$841$	−8.69649	−	15.0628i	−0.299879	−	0.519406i
$842$	14.5084	+	8.37644i	0.499993	+	0.288671i
$843$		0			0
$844$	−9.07508			−0.312377
$845$	−7.66612	−	18.3898i	−0.263723	−	0.632627i
$846$		0			0
$847$	−25.0893	−	13.5422i	−0.862079	−	0.465316i
$848$	−4.65249	−	2.68612i	−0.159767	−	0.0922417i
$849$		0			0
$850$		−	1.40391i		−	0.0481537i
$851$	51.7727	−	29.8910i	1.77475	−	1.02465i
$852$		0			0
$853$			50.0821i			1.71478i	0.514668	+	0.857390i	$0.327915\pi$
$853$			50.0821i			1.71478i	−0.514668	+	0.857390i	$0.672085\pi$
$854$	9.20519	−	5.67229i	0.314995	−	0.194102i
$855$		0			0
$856$	2.27230	−	3.93574i	0.0776656	−	0.134521i
$857$	1.83000			0.0625115			0.0312557	−	0.999511i	$-0.490049\pi$
$857$	1.83000			0.0625115			0.0312557	+	0.999511i	$0.490049\pi$
$858$		0			0
$859$			34.2418i			1.16831i	0.811641	+	0.584157i	$0.198575\pi$
$859$			34.2418i			1.16831i	−0.811641	+	0.584157i	$0.801425\pi$
$860$	−0.899728	+	1.55837i	−0.0306805	+	0.0531401i
$861$		0			0
$862$	−10.8731	−	18.8328i	−0.370341	−	0.641449i
$863$		−	5.86941i		−	0.199797i	−0.994998	−	0.0998985i	$-0.968148\pi$
$863$		−	5.86941i		−	0.199797i	0.994998	−	0.0998985i	$-0.0318518\pi$
$864$		0			0
$865$	17.0656	+	29.5584i	0.580247	+	1.00502i
$866$	−10.4965			−0.356684
$867$		0			0
$868$	−6.57933	+	12.1894i	−0.223317	+	0.413734i
$869$	4.35691	+	2.51547i	0.147798	+	0.0853313i
$870$		0			0
$871$	0.500065	−	0.247309i	0.0169441	−	0.00837975i
$872$			43.9255i			1.48751i
$873$		0			0
$874$	−19.9324	−	11.5080i	−0.674222	−	0.389262i
$875$	−26.4125	+	16.2755i	−0.892904	+	0.550213i
$876$		0			0
$877$	24.8787	+	43.0912i	0.840095	+	1.45509i	0.889814	+	0.456324i	$0.150834\pi$
$877$	24.8787	+	43.0912i	0.840095	+	1.45509i	−0.0497184	+	0.998763i	$0.515832\pi$
$878$	−5.77845	−	10.0086i	−0.195013	−	0.337773i
$879$		0			0
$880$	9.87382	−	5.70065i	0.332846	−	0.192169i
$881$	−26.1741	+	45.3348i	−0.881827	+	1.52737i	−0.0325192	+	0.999471i	$0.510353\pi$
$881$	−26.1741	+	45.3348i	−0.881827	+	1.52737i	−0.849308	+	0.527898i	$0.822980\pi$
$882$		0			0
$883$	−43.2991			−1.45713			−0.728566	−	0.684976i	$-0.759813\pi$
$883$	−43.2991			−1.45713			−0.728566	+	0.684976i	$0.759813\pi$
$884$	4.08224	−	2.01889i	0.137301	−	0.0679026i
$885$		0			0
$886$	−2.94208	+	5.09583i	−0.0988410	+	0.171198i
$887$	−6.35657	+	11.0099i	−0.213433	+	0.369677i	−0.952787	−	0.303641i	$-0.901798\pi$
$887$	−6.35657	+	11.0099i	−0.213433	+	0.369677i	0.739354	+	0.673317i	$0.235131\pi$
$888$		0			0
$889$	0.324755	+	11.3316i	0.0108919	+	0.380050i
$890$	−1.11302	+	0.642604i	−0.0373086	+	0.0215401i
$891$		0			0
$892$			36.6202i			1.22614i
$893$	−17.8748	+	10.3200i	−0.598157	+	0.345346i
$894$		0			0
$895$	3.64959	+	2.10709i	0.121992	+	0.0704323i
$896$	29.3381	−	0.840808i	0.980118	−	0.0280894i
$897$		0			0
$898$	−18.5878			−0.620282
$899$	−5.68801	+	9.85193i	−0.189706	+	0.328580i
$900$		0			0
$901$	2.35106	−	1.35738i	0.0783251	−	0.0452210i
$902$	−26.1912			−0.872072
$903$		0			0
$904$	−17.0378	−	29.5103i	−0.566667	−	0.981497i
$905$		−	20.1642i		−	0.670282i
$906$		0			0
$907$	−11.2211	+	19.4356i	−0.372592	+	0.645348i	−0.989963	−	0.141324i	$-0.954864\pi$
$907$	−11.2211	+	19.4356i	−0.372592	+	0.645348i	0.617372	+	0.786672i	$0.288198\pi$
$908$	19.2017	−	33.2584i	0.637232	−	1.10372i
$909$		0			0
$910$	8.14602	+	5.09881i	0.270038	+	0.169024i
$911$		−	50.1307i		−	1.66090i	−0.557090	−	0.830452i	$-0.688082\pi$
$911$		−	50.1307i		−	1.66090i	0.557090	−	0.830452i	$-0.311918\pi$
$912$		0			0
$913$	25.7139	+	14.8459i	0.851005	+	0.491328i
$914$	−1.26403	+	0.729787i	−0.0418103	+	0.0241392i
$915$		0			0
$916$	−31.2393	+	18.0360i	−1.03217	+	0.595926i
$917$	−34.4370	+	21.2203i	−1.13721	+	0.700755i
$918$		0			0
$919$	0.152218	+	0.263649i	0.00502120	+	0.00869698i	0.868525	−	0.495645i	$-0.165068\pi$
$919$	0.152218	+	0.263649i	0.00502120	+	0.00869698i	−0.863504	+	0.504342i	$0.831735\pi$
$920$	10.3962	−	18.0068i	0.342753	−	0.593666i
$921$		0			0
$922$		−	14.7828i		−	0.486845i
$923$	−29.4295	−	1.89545i	−0.968683	−	0.0623895i
$924$		0			0
$925$	−13.6993	+	23.7278i	−0.450429	+	0.780166i
$926$	5.07956	+	2.93268i	0.166925	+	0.0963740i
$927$		0			0
$928$	19.5506			0.641780
$929$	8.93061	+	15.4683i	0.293004	+	0.507497i	0.974519	−	0.224307i	$-0.0720118\pi$
$929$	8.93061	+	15.4683i	0.293004	+	0.507497i	−0.681515	+	0.731804i	$0.738678\pi$
$930$		0			0
$931$	−2.42660	−	42.3007i	−0.0795287	−	1.38635i
$932$	15.6629	−	9.04298i	0.513055	−	0.296213i
$933$		0			0
$934$	8.57870	+	4.95291i	0.280704	+	0.162064i
$935$			5.76146i			0.188420i
$936$		0			0
$937$		−	36.5107i		−	1.19275i	−0.802705	−	0.596377i	$-0.796606\pi$
$937$		−	36.5107i		−	1.19275i	0.802705	−	0.596377i	$-0.203394\pi$
$938$	−0.127815	+	0.236799i	−0.00417330	+	0.00773177i
$939$		0			0
$940$	−4.09700	−	7.09621i	−0.133629	−	0.231453i
$941$	27.2178			0.887274			0.443637	−	0.896207i	$-0.353688\pi$
$941$	27.2178			0.887274			0.443637	+	0.896207i	$0.353688\pi$
$942$		0			0
$943$	42.7752	−	24.6963i	1.39295	−	0.804222i
$944$	−19.1642			−0.623741
$945$		0			0
$946$	1.14852	−	1.98929i	0.0373415	−	0.0646774i
$947$	9.04632	+	5.22289i	0.293966	+	0.169721i	0.639729	−	0.768601i	$-0.279047\pi$
$947$	9.04632	+	5.22289i	0.293966	+	0.169721i	−0.345763	+	0.938322i	$0.612380\pi$
$948$		0			0
$949$	13.6862	−	20.5332i	0.444274	−	0.666536i
$950$	10.5484			0.342234
$951$		0			0
$952$	−2.37435	+	4.39890i	−0.0769532	+	0.142569i
$953$	6.21930	−	3.59072i	0.201463	−	0.116315i	−0.395875	−	0.918305i	$-0.629559\pi$
$953$	6.21930	−	3.59072i	0.201463	−	0.116315i	0.597338	+	0.801990i	$0.296225\pi$
$954$		0			0
$955$	−12.1952	+	7.04089i	−0.394627	+	0.227838i
$956$	12.4086	−	7.16411i	0.401323	−	0.231704i
$957$		0			0
$958$	17.3195	−	9.99944i	0.559569	−	0.323067i
$959$	−6.27032	+	11.6169i	−0.202479	+	0.375128i
$960$		0			0
$961$	19.8504			0.640334
$962$	24.4426	+	1.57426i	0.788061	+	0.0507562i
$963$		0			0
$964$	−14.5783	−	8.41679i	−0.469536	−	0.271087i
$965$	6.17119	−	10.6888i	0.198658	−	0.344085i
$966$		0			0
$967$	47.5074			1.52773			0.763867	−	0.645374i	$-0.223298\pi$
$967$	47.5074			1.52773			0.763867	+	0.645374i	$0.223298\pi$
$968$	−21.8872	+	12.6366i	−0.703481	+	0.406155i
$969$		0			0
$970$	11.3617			0.364802
$971$	−0.815991	−	1.41334i	−0.0261864	−	0.0453562i	0.852635	−	0.522507i	$-0.175003\pi$
$971$	−0.815991	−	1.41334i	−0.0261864	−	0.0453562i	−0.878822	+	0.477150i	$0.841670\pi$
$972$		0			0
$973$	−10.4179	+	19.3011i	−0.333984	+	0.618764i
$974$			9.77123i			0.313090i
$975$		0			0
$976$			9.91132i			0.317254i
$977$	−14.2055	−	8.20154i	−0.454474	−	0.262391i	0.255244	−	0.966877i	$-0.417844\pi$
$977$	−14.2055	−	8.20154i	−0.454474	−	0.262391i	−0.709718	+	0.704486i	$0.751178\pi$
$978$		0			0
$979$	−5.15565	+	2.97661i	−0.164775	+	0.0951330i
$980$	16.7932	−	0.963350i	0.536439	−	0.0307731i
$981$		0			0
$982$	−0.716171	−	1.24045i	−0.0228539	−	0.0395842i
$983$	41.9338			1.33748			0.668740	−	0.743496i	$-0.266834\pi$
$983$	41.9338			1.33748			0.668740	+	0.743496i	$0.266834\pi$
$984$		0			0
$985$	2.68351	+	1.54933i	0.0855038	+	0.0493656i
$986$	−0.902053	+	1.56240i	−0.0287272	+	0.0497570i
$987$		0			0
$988$	15.1691	+	30.6722i	0.482592	+	0.975813i
$989$			4.33185i			0.137745i
$990$		0			0
$991$	16.4537	−	28.4986i	0.522669	−	0.905289i	−0.476983	−	0.878912i	$-0.658270\pi$
$991$	16.4537	−	28.4986i	0.522669	−	0.905289i	0.999652	−	0.0263763i	$-0.00839682\pi$
$992$	9.58076	+	16.5944i	0.304189	+	0.526872i
$993$		0			0
$994$	12.1102	−	7.46235i	0.384111	−	0.236691i
$995$	11.1848	−	6.45753i	0.354581	−	0.204717i
$996$		0			0
$997$	−3.44557	+	1.98930i	−0.109122	+	0.0630018i	−0.553568	−	0.832804i	$-0.686734\pi$
$997$	−3.44557	+	1.98930i	−0.109122	+	0.0630018i	0.444446	+	0.895806i	$0.353401\pi$
$998$	−11.8954	−	6.86781i	−0.376542	−	0.217397i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dx.a.503.15	✓	72
3.2	odd	2	inner	819.2.dx.a.503.22	yes	72
7.6	odd	2	inner	819.2.dx.a.503.16	yes	72
13.3	even	3	inner	819.2.dx.a.692.21	yes	72
21.20	even	2	inner	819.2.dx.a.503.21	yes	72
39.29	odd	6	inner	819.2.dx.a.692.16	yes	72
91.55	odd	6	inner	819.2.dx.a.692.22	yes	72
273.146	even	6	inner	819.2.dx.a.692.15	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.dx.a.503.15	✓	72	1.1	even	1	trivial
819.2.dx.a.503.16	yes	72	7.6	odd	2	inner
819.2.dx.a.503.21	yes	72	21.20	even	2	inner
819.2.dx.a.503.22	yes	72	3.2	odd	2	inner
819.2.dx.a.692.15	yes	72	273.146	even	6	inner
819.2.dx.a.692.16	yes	72	39.29	odd	6	inner
819.2.dx.a.692.21	yes	72	13.3	even	3	inner
819.2.dx.a.692.22	yes	72	91.55	odd	6	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.569266 - 0.328666i) q^{2} +(-0.783957 - 1.35785i) q^{4} -1.53259 q^{5} +(-2.25245 + 1.38797i) q^{7} +2.34530i q^{8} +O(q^{10})\)	\(q+(-0.569266 - 0.328666i) q^{2} +(-0.783957 - 1.35785i) q^{4} -1.53259 q^{5} +(-2.25245 + 1.38797i) q^{7} +2.34530i q^{8} +(0.872452 + 0.503710i) q^{10} +(4.04129 + 2.33324i) q^{11} +(-3.00017 - 1.99974i) q^{13} +(1.73842 - 0.0498218i) q^{14} +(-0.797093 + 1.38061i) q^{16} +(-0.402797 - 0.697666i) q^{17} +(5.24196 - 3.02645i) q^{19} +(1.20149 + 2.08103i) q^{20} +(-1.53371 - 2.65647i) q^{22} +(5.00969 + 2.89235i) q^{23} -2.65117 q^{25} +(1.05065 + 2.12444i) q^{26} +(3.65049 + 1.97039i) q^{28} +(2.95047 + 1.70345i) q^{29} +3.33911i q^{31} +(4.96970 - 2.86926i) q^{32} +0.529543i q^{34} +(3.45208 - 2.12719i) q^{35} +(5.16725 - 8.94995i) q^{37} -3.97876 q^{38} -3.59439i q^{40} +(4.26925 - 7.39455i) q^{41} +(0.374423 + 0.648520i) q^{43} -7.31665i q^{44} +(-1.90123 - 3.29303i) q^{46} -3.40994 q^{47} +(3.14707 - 6.25268i) q^{49} +(1.50922 + 0.871349i) q^{50} +(-0.363350 + 5.64151i) q^{52} +3.36989i q^{53} +(-6.19364 - 3.57590i) q^{55} +(-3.25522 - 5.28268i) q^{56} +(-1.11973 - 1.93944i) q^{58} +(6.01065 + 10.4108i) q^{59} +(5.38423 - 3.10858i) q^{61} +(1.09745 - 1.90084i) q^{62} -0.583740 q^{64} +(4.59803 + 3.06478i) q^{65} +(-0.0773636 + 0.133998i) q^{67} +(-0.631552 + 1.09388i) q^{68} +(-2.66429 + 0.0763564i) q^{70} +(7.08338 - 4.08959i) q^{71} +6.84401i q^{73} +(-5.88309 + 3.39660i) q^{74} +(-8.21894 - 4.74521i) q^{76} +(-12.3413 + 0.353691i) q^{77} +1.07810 q^{79} +(1.22162 - 2.11590i) q^{80} +(-4.86068 + 2.80631i) q^{82} +6.36278 q^{83} +(0.617323 + 1.06924i) q^{85} -0.492241i q^{86} +(-5.47216 + 9.47806i) q^{88} +(-0.637871 + 1.10483i) q^{89} +(9.53333 + 0.340163i) q^{91} -9.06991i q^{92} +(1.94117 + 1.12073i) q^{94} +(-8.03377 + 4.63830i) q^{95} +(9.76704 - 5.63900i) q^{97} +(-3.84656 + 2.52510i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 32 q^{4} - 2 q^{7}+O(q^{10}) \) 72 * q + 32 * q^4 - 2 * q^7	\( 72 q + 32 q^{4} - 2 q^{7} - 24 q^{16} + 24 q^{22} + 56 q^{25} - 8 q^{28} + 16 q^{37} - 4 q^{43} + 32 q^{46} + 26 q^{49} - 40 q^{58} - 64 q^{64} + 60 q^{67} - 40 q^{70} - 72 q^{79} - 80 q^{85} - 24 q^{88} + 2 q^{91}+O(q^{100}) \) 72 * q + 32 * q^4 - 2 * q^7 - 24 * q^16 + 24 * q^22 + 56 * q^25 - 8 * q^28 + 16 * q^37 - 4 * q^43 + 32 * q^46 + 26 * q^49 - 40 * q^58 - 64 * q^64 + 60 * q^67 - 40 * q^70 - 72 * q^79 - 80 * q^85 - 24 * q^88 + 2 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more