LMFDB - Embedded newform 804.2.y.b.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	804.49
Dual form			804.2.y.b.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 - 0.540641i) q^{3} +(-0.355125 - 2.46995i) q^{5} +(1.47905 + 0.141233i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.841254 - 0.540641i) q^{3} +(-0.355125 - 2.46995i) q^{5} +(1.47905 + 0.141233i) q^{7} +(0.415415 + 0.909632i) q^{9} +(-5.48535 - 2.19600i) q^{11} +(-2.97924 - 2.84070i) q^{13} +(-1.03661 + 2.26985i) q^{15} +(-2.20441 + 6.36922i) q^{17} +(3.49676 - 0.333900i) q^{19} +(-1.16790 - 0.918450i) q^{21} +(0.152650 - 3.20453i) q^{23} +(-1.17707 + 0.345620i) q^{25} +(0.142315 - 0.989821i) q^{27} +(-3.60506 + 6.24415i) q^{29} +(1.09094 - 1.04021i) q^{31} +(3.42732 + 4.81300i) q^{33} +(-0.176412 - 3.70335i) q^{35} +(3.11904 + 5.40233i) q^{37} +(0.970499 + 4.00045i) q^{39} +(-4.79453 + 0.924070i) q^{41} +(-8.41053 - 9.70626i) q^{43} +(2.09922 - 1.34909i) q^{45} +(-9.68103 + 4.99092i) q^{47} +(-4.70585 - 0.906977i) q^{49} +(5.29793 - 4.16634i) q^{51} +(5.19018 - 5.98979i) q^{53} +(-3.47603 + 14.3284i) q^{55} +(-3.12218 - 1.60960i) q^{57} +(-11.5248 - 3.38399i) q^{59} +(0.979919 - 0.392300i) q^{61} +(0.485952 + 1.40407i) q^{63} +(-5.95839 + 8.36739i) q^{65} +(-6.24891 + 5.28688i) q^{67} +(-1.86092 + 2.61329i) q^{69} +(0.204053 + 0.589573i) q^{71} +(-6.65132 + 2.66279i) q^{73} +(1.17707 + 0.345620i) q^{75} +(-7.80299 - 4.02272i) q^{77} +(-0.340589 + 1.40392i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(12.0626 - 9.48612i) q^{83} +(16.5145 + 3.18291i) q^{85} +(6.40862 - 3.30387i) q^{87} +(14.0357 - 9.02019i) q^{89} +(-4.00526 - 4.62232i) q^{91} +(-1.48014 + 0.285273i) q^{93} +(-2.06651 - 8.51825i) q^{95} +(2.46726 + 4.27341i) q^{97} +(-0.281142 - 5.90191i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{23}{33}\right)$	$1$

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			0
$2$		0			0
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$4$		0			0
$5$	−0.355125	−	2.46995i	−0.158817	−	1.10460i	−0.900818	−	0.434197i	$-0.857032\pi$
$5$	−0.355125	−	2.46995i	−0.158817	−	1.10460i	0.742001	−	0.670398i	$-0.233877\pi$
$6$		0			0
$7$	1.47905	+	0.141233i	0.559030	+	0.0533809i	0.370747	−	0.928734i	$-0.379102\pi$
$7$	1.47905	+	0.141233i	0.559030	+	0.0533809i	0.188283	+	0.982115i	$0.439708\pi$
$8$		0			0
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$		0			0
$11$	−5.48535	−	2.19600i	−1.65390	−	0.662120i	−0.658033	−	0.752989i	$-0.728611\pi$
$11$	−5.48535	−	2.19600i	−1.65390	−	0.662120i	−0.995863	+	0.0908687i	$0.971036\pi$
$12$		0			0
$13$	−2.97924	−	2.84070i	−0.826293	−	0.787869i	0.153444	−	0.988157i	$-0.450964\pi$
$13$	−2.97924	−	2.84070i	−0.826293	−	0.787869i	−0.979737	+	0.200288i	$0.935812\pi$
$14$		0			0
$15$	−1.03661	+	2.26985i	−0.267650	+	0.586073i
$16$		0			0
$17$	−2.20441	+	6.36922i	−0.534648	+	1.54476i	0.277151	+	0.960826i	$0.410610\pi$
$17$	−2.20441	+	6.36922i	−0.534648	+	1.54476i	−0.811799	+	0.583937i	$0.801512\pi$
$18$		0			0
$19$	3.49676	−	0.333900i	0.802212	−	0.0766020i	0.314108	−	0.949387i	$-0.398295\pi$
$19$	3.49676	−	0.333900i	0.802212	−	0.0766020i	0.488104	+	0.872785i	$0.337689\pi$
$20$		0			0
$21$	−1.16790	−	0.918450i	−0.254857	−	0.200422i
$22$		0			0
$23$	0.152650	−	3.20453i	0.0318298	−	0.668190i	−0.925423	−	0.378937i	$-0.876290\pi$
$23$	0.152650	−	3.20453i	0.0318298	−	0.668190i	0.957252	−	0.289254i	$-0.0934071\pi$
$24$		0			0
$25$	−1.17707	+	0.345620i	−0.235415	+	0.0691240i
$26$		0			0
$27$	0.142315	−	0.989821i	0.0273885	−	0.190491i
$28$		0			0
$29$	−3.60506	+	6.24415i	−0.669443	+	1.15951i	0.308616	+	0.951187i	$0.400134\pi$
$29$	−3.60506	+	6.24415i	−0.669443	+	1.15951i	−0.978060	+	0.208324i	$0.933199\pi$
$30$		0			0
$31$	1.09094	−	1.04021i	0.195939	−	0.186827i	−0.585758	−	0.810486i	$-0.699203\pi$
$31$	1.09094	−	1.04021i	0.195939	−	0.186827i	0.781697	+	0.623659i	$0.214355\pi$
$32$		0			0
$33$	3.42732	+	4.81300i	0.596620	+	0.837836i
$34$		0			0
$35$	−0.176412	−	3.70335i	−0.0298191	−	0.625980i
$36$		0			0
$37$	3.11904	+	5.40233i	0.512767	+	0.888138i	0.999890	+	0.0148049i	$0.00471271\pi$
$37$	3.11904	+	5.40233i	0.512767	+	0.888138i	−0.487124	+	0.873333i	$0.661954\pi$
$38$		0			0
$39$	0.970499	+	4.00045i	0.155404	+	0.640585i
$40$		0			0
$41$	−4.79453	+	0.924070i	−0.748780	+	0.144315i	−0.549345	−	0.835596i	$-0.685123\pi$
$41$	−4.79453	+	0.924070i	−0.748780	+	0.144315i	−0.199435	+	0.979911i	$0.563911\pi$
$42$		0			0
$43$	−8.41053	−	9.70626i	−1.28259	−	1.48019i	−0.794319	−	0.607501i	$-0.792172\pi$
$43$	−8.41053	−	9.70626i	−1.28259	−	1.48019i	−0.488274	−	0.872690i	$-0.662373\pi$
$44$		0			0
$45$	2.09922	−	1.34909i	0.312933	−	0.201110i
$46$		0			0
$47$	−9.68103	+	4.99092i	−1.41212	+	0.728000i	−0.984406	−	0.175913i	$-0.943712\pi$
$47$	−9.68103	+	4.99092i	−1.41212	+	0.728000i	−0.427717	+	0.903913i	$0.640682\pi$
$48$		0			0
$49$	−4.70585	−	0.906977i	−0.672264	−	0.129568i
$50$		0			0
$51$	5.29793	−	4.16634i	0.741858	−	0.583404i
$52$		0			0
$53$	5.19018	−	5.98979i	0.712927	−	0.822761i	−0.277511	−	0.960722i	$-0.589510\pi$
$53$	5.19018	−	5.98979i	0.712927	−	0.822761i	0.990438	+	0.137961i	$0.0440550\pi$
$54$		0			0
$55$	−3.47603	+	14.3284i	−0.468708	+	1.93204i
$56$		0			0
$57$	−3.12218	−	1.60960i	−0.413543	−	0.213196i
$58$		0			0
$59$	−11.5248	−	3.38399i	−1.50040	−	0.440557i	−0.574557	−	0.818464i	$-0.694826\pi$
$59$	−11.5248	−	3.38399i	−1.50040	−	0.440557i	−0.925844	+	0.377907i	$0.876644\pi$
$60$		0			0
$61$	0.979919	−	0.392300i	0.125466	−	0.0502289i	−0.308080	−	0.951360i	$-0.599686\pi$
$61$	0.979919	−	0.392300i	0.125466	−	0.0502289i	0.433546	+	0.901132i	$0.357262\pi$
$62$		0			0
$63$	0.485952	+	1.40407i	0.0612242	+	0.176896i
$64$		0			0
$65$	−5.95839	+	8.36739i	−0.739047	+	1.03785i
$66$		0			0
$67$	−6.24891	+	5.28688i	−0.763426	+	0.645895i
$67$	−6.24891	+	5.28688i	−0.763426	+	0.645895i
$68$		0			0
$69$	−1.86092	+	2.61329i	−0.224028	+	0.314603i
$70$		0			0
$71$	0.204053	+	0.589573i	0.0242167	+	0.0699695i	0.956461	−	0.291859i	$-0.0942738\pi$
$71$	0.204053	+	0.589573i	0.0242167	+	0.0699695i	−0.932245	+	0.361828i	$0.882153\pi$
$72$		0			0
$73$	−6.65132	+	2.66279i	−0.778478	+	0.311656i	−0.726657	−	0.687001i	$-0.758927\pi$
$73$	−6.65132	+	2.66279i	−0.778478	+	0.311656i	−0.0518216	+	0.998656i	$0.516503\pi$
$74$		0			0
$75$	1.17707	+	0.345620i	0.135917	+	0.0399088i
$76$		0			0
$77$	−7.80299	−	4.02272i	−0.889233	−	0.458432i
$78$		0			0
$79$	−0.340589	+	1.40392i	−0.0383192	+	0.157954i	−0.987757	−	0.156002i	$-0.950139\pi$
$79$	−0.340589	+	1.40392i	−0.0383192	+	0.157954i	0.949438	+	0.313956i	$0.101654\pi$
$80$		0			0
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$		0			0
$83$	12.0626	−	9.48612i	1.32404	−	1.04124i	0.328739	−	0.944421i	$-0.393376\pi$
$83$	12.0626	−	9.48612i	1.32404	−	1.04124i	0.995302	−	0.0968166i	$-0.0308660\pi$
$84$		0			0
$85$	16.5145	+	3.18291i	1.79125	+	0.345235i
$86$		0			0
$87$	6.40862	−	3.30387i	0.687076	−	0.354212i
$88$		0			0
$89$	14.0357	−	9.02019i	1.48778	−	0.956138i	0.491417	−	0.870924i	$-0.336479\pi$
$89$	14.0357	−	9.02019i	1.48778	−	0.956138i	0.996363	−	0.0852136i	$-0.0271573\pi$
$90$		0			0
$91$	−4.00526	−	4.62232i	−0.419866	−	0.484551i
$92$		0			0
$93$	−1.48014	+	0.285273i	−0.153483	+	0.0295815i
$94$		0			0
$95$	−2.06651	−	8.51825i	−0.212019	−	0.873954i
$96$		0			0
$97$	2.46726	+	4.27341i	0.250512	+	0.433899i	0.963667	−	0.267107i	$-0.0860677\pi$
$97$	2.46726	+	4.27341i	0.250512	+	0.433899i	−0.713155	+	0.701006i	$0.752734\pi$
$98$		0			0
$99$	−0.281142	−	5.90191i	−0.0282559	−	0.593164i
$100$		0			0
$101$	−5.56064	−	7.80883i	−0.553304	−	0.777007i	0.439308	−	0.898336i	$-0.355224\pi$
$101$	−5.56064	−	7.80883i	−0.553304	−	0.777007i	−0.992612	+	0.121329i	$0.961284\pi$
$102$		0			0
$103$	11.0138	−	10.5017i	1.08523	−	1.03476i	0.0859664	−	0.996298i	$-0.472602\pi$
$103$	11.0138	−	10.5017i	1.08523	−	1.03476i	0.999260	−	0.0384633i	$-0.0122463\pi$
$104$		0			0
$105$	−1.85377	+	3.21083i	−0.180910	+	0.313345i
$106$		0			0
$107$	0.307691	−	2.14004i	0.0297456	−	0.206885i	−0.969529	−	0.244978i	$-0.921219\pi$
$107$	0.307691	−	2.14004i	0.0297456	−	0.206885i	0.999274	+	0.0380928i	$0.0121283\pi$
$108$		0			0
$109$	13.8306	−	4.06102i	1.32473	−	0.388975i	0.458532	−	0.888678i	$-0.348376\pi$
$109$	13.8306	−	4.06102i	1.32473	−	0.388975i	0.866197	+	0.499703i	$0.166557\pi$
$110$		0			0
$111$	0.296820	−	6.23101i	0.0281729	−	0.591421i
$112$		0			0
$113$	−0.263627	−	0.207318i	−0.0247999	−	0.0195029i	0.605682	−	0.795707i	$-0.292900\pi$
$113$	−0.263627	−	0.207318i	−0.0247999	−	0.0195029i	−0.630482	+	0.776204i	$0.717143\pi$
$114$		0			0
$115$	−7.96923	+	0.760970i	−0.743135	+	0.0709608i
$116$		0			0
$117$	1.34637	−	3.89009i	0.124472	−	0.359639i
$118$		0			0
$119$	−4.15998	+	9.10909i	−0.381345	+	0.835029i
$120$		0			0
$121$	17.3056	+	16.5008i	1.57324	+	1.50008i
$122$		0			0
$123$	4.53300	+	1.81474i	0.408727	+	0.163630i
$124$		0			0
$125$	−3.91135	−	8.56467i	−0.349842	−	0.766047i
$126$		0			0
$127$	−8.37607	−	0.799818i	−0.743256	−	0.0709724i	−0.283444	−	0.958989i	$-0.591477\pi$
$127$	−8.37607	−	0.799818i	−0.743256	−	0.0709724i	−0.459812	+	0.888016i	$0.652083\pi$
$128$		0			0
$129$	1.82778	+	12.7125i	0.160927	+	1.11927i
$130$		0			0
$131$	1.98265	+	1.27417i	0.173225	+	0.111325i	0.624380	−	0.781120i	$-0.285352\pi$
$131$	1.98265	+	1.27417i	0.173225	+	0.111325i	−0.451155	+	0.892446i	$0.648988\pi$
$132$		0			0
$133$	5.21906			0.452550
$134$		0			0
$135$	−2.49535			−0.214765
$136$		0			0
$137$	2.51013	+	1.61316i	0.214455	+	0.137822i	0.643458	−	0.765481i	$-0.277499\pi$
$137$	2.51013	+	1.61316i	0.214455	+	0.137822i	−0.429004	+	0.903303i	$0.641135\pi$
$138$		0			0
$139$	−1.32971	−	9.24835i	−0.112785	−	0.784434i	−0.965189	−	0.261552i	$-0.915766\pi$
$139$	−1.32971	−	9.24835i	−0.112785	−	0.784434i	0.852405	−	0.522883i	$-0.175143\pi$
$140$		0			0
$141$	10.8425	+	1.03533i	0.913102	+	0.0871907i
$142$		0			0
$143$	10.1040	+	22.1247i	0.844939	+	1.85016i
$144$		0			0
$145$	16.7030	+	6.68687i	1.38711	+	0.555314i
$146$		0			0
$147$	3.46846	+	3.30717i	0.286074	+	0.272771i
$148$		0			0
$149$	−6.36841	+	13.9449i	−0.521720	+	1.14241i	0.447064	+	0.894502i	$0.352470\pi$
$149$	−6.36841	+	13.9449i	−0.521720	+	1.14241i	−0.968784	+	0.247906i	$0.920258\pi$
$150$		0			0
$151$	4.53268	−	13.0963i	0.368865	−	1.06576i	−0.595993	−	0.802990i	$-0.703241\pi$
$151$	4.53268	−	13.0963i	0.368865	−	1.06576i	0.964857	−	0.262774i	$-0.0846375\pi$
$152$		0			0
$153$	−6.70939	+	0.640669i	−0.542422	+	0.0517950i
$154$		0			0
$155$	−2.95669	−	2.32517i	−0.237487	−	0.186762i
$156$		0			0
$157$	−0.889333	+	18.6694i	−0.0709765	+	1.48998i	0.629888	+	0.776686i	$0.283101\pi$
$157$	−0.889333	+	18.6694i	−0.0709765	+	1.48998i	−0.700864	+	0.713294i	$0.747202\pi$
$158$		0			0
$159$	−7.60459	+	2.23291i	−0.603083	+	0.177081i
$160$		0			0
$161$	0.678362	−	4.71811i	0.0534624	−	0.371839i
$162$		0			0
$163$	−7.00651	+	12.1356i	−0.548793	+	0.950537i	0.449565	+	0.893248i	$0.351579\pi$
$163$	−7.00651	+	12.1356i	−0.548793	+	0.950537i	−0.998358	+	0.0572890i	$0.981754\pi$
$164$		0			0
$165$	10.6707	−	10.1745i	0.830716	−	0.792086i
$166$		0			0
$167$	−11.5995	−	16.2892i	−0.897593	−	1.26049i	−0.964862	−	0.262759i	$-0.915368\pi$
$167$	−11.5995	−	16.2892i	−0.897593	−	1.26049i	0.0672681	−	0.997735i	$-0.478572\pi$
$168$		0			0
$169$	0.187734	+	3.94101i	0.0144410	+	0.303155i
$170$		0			0
$171$	1.75633	+	3.04206i	0.134310	+	0.232632i
$172$		0			0
$173$	−3.46917	−	14.3001i	−0.263756	−	1.08722i	−0.937426	−	0.348185i	$-0.886798\pi$
$173$	−3.46917	−	14.3001i	−0.263756	−	1.08722i	0.673670	−	0.739032i	$-0.264717\pi$
$174$		0			0
$175$	−1.78977	+	0.344950i	−0.135294	+	0.0260758i
$176$		0			0
$177$	7.86575	+	9.07756i	0.591226	+	0.682312i
$178$		0			0
$179$	1.75728	−	1.12934i	0.131345	−	0.0844105i	−0.473318	−	0.880891i	$-0.656944\pi$
$179$	1.75728	−	1.12934i	0.131345	−	0.0844105i	0.604664	+	0.796481i	$0.293308\pi$
$180$		0			0
$181$	−0.862051	+	0.444418i	−0.0640757	+	0.0330333i	−0.489967	−	0.871741i	$-0.662991\pi$
$181$	−0.862051	+	0.444418i	−0.0640757	+	0.0330333i	0.425891	+	0.904775i	$0.359961\pi$
$182$		0			0
$183$	−1.03645	−	0.199760i	−0.0766169	−	0.0147667i
$184$		0			0
$185$	12.2358	−	9.62237i	0.899597	−	0.707451i
$186$		0			0
$187$	26.0788	−	30.0965i	1.90707	−	2.20088i
$188$		0			0
$189$	0.350286	−	1.44390i	0.0254796	−	0.105028i
$190$		0			0
$191$	−0.385144	−	0.198556i	−0.0278680	−	0.0143670i	0.444236	−	0.895910i	$-0.353475\pi$
$191$	−0.385144	−	0.198556i	−0.0278680	−	0.0143670i	−0.472104	+	0.881543i	$0.656505\pi$
$192$		0			0
$193$	−12.1857	−	3.57804i	−0.877146	−	0.257553i	−0.187994	−	0.982170i	$-0.560199\pi$
$193$	−12.1857	−	3.57804i	−0.877146	−	0.257553i	−0.689152	+	0.724617i	$0.742017\pi$
$194$		0			0
$195$	9.53627	−	3.81775i	0.682906	−	0.273394i
$196$		0			0
$197$	2.24805	+	6.49531i	0.160167	+	0.462772i	0.996319	−	0.0857261i	$-0.0273210\pi$
$197$	2.24805	+	6.49531i	0.160167	+	0.462772i	−0.836152	+	0.548498i	$0.815200\pi$
$198$		0			0
$199$	15.4553	−	21.7039i	1.09560	−	1.53855i	0.279939	−	0.960018i	$-0.409686\pi$
$199$	15.4553	−	21.7039i	1.09560	−	1.53855i	0.815659	−	0.578534i	$-0.196375\pi$
$200$		0			0
$201$	8.11522	−	1.06919i	0.572404	−	0.0754149i
$202$		0			0
$203$	−6.21396	+	8.72629i	−0.436135	+	0.612466i
$204$		0			0
$205$	3.98506	+	11.5141i	0.278329	+	0.804179i
$206$		0			0
$207$	2.97835	−	1.19235i	0.207010	−	0.0828743i
$208$		0			0
$209$	−19.9142	−	5.84734i	−1.37750	−	0.404469i
$210$		0			0
$211$	−3.60383	−	1.85791i	−0.248098	−	0.127904i	0.329693	−	0.944088i	$-0.393055\pi$
$211$	−3.60383	−	1.85791i	−0.248098	−	0.127904i	−0.577791	+	0.816185i	$0.696085\pi$
$212$		0			0
$213$	0.147087	−	0.606300i	0.0100782	−	0.0415430i
$214$		0			0
$215$	−20.9872	+	24.2205i	−1.43131	+	1.65183i
$216$		0			0
$217$	1.76047	−	1.38445i	0.119509	−	0.0939827i
$218$		0			0
$219$	7.03506	+	1.35590i	0.475385	+	0.0916230i
$220$		0			0
$221$	24.6605	−	12.7134i	1.65885	−	0.855195i
$222$		0			0
$223$	−15.4018	+	9.89816i	−1.03138	+	0.662830i	−0.942841	−	0.333242i	$-0.891857\pi$
$223$	−15.4018	+	9.89816i	−1.03138	+	0.662830i	−0.0885426	+	0.996072i	$0.528221\pi$
$224$		0			0
$225$	−0.803361	−	0.927128i	−0.0535574	−	0.0618086i
$226$		0			0
$227$	21.4002	−	4.12455i	1.42038	−	0.273756i	0.579498	−	0.814974i	$-0.303249\pi$
$227$	21.4002	−	4.12455i	1.42038	−	0.273756i	0.840883	+	0.541218i	$0.182036\pi$
$228$		0			0
$229$	−0.204044	−	0.841082i	−0.0134836	−	0.0555802i	0.964672	−	0.263453i	$-0.0848613\pi$
$229$	−0.204044	−	0.841082i	−0.0134836	−	0.0555802i	−0.978156	+	0.207872i	$0.933346\pi$
$230$		0			0
$231$	4.38944	+	7.60274i	0.288804	+	0.500224i
$232$		0			0
$233$	−0.695598	−	14.6024i	−0.0455702	−	0.956635i	−0.899682	−	0.436546i	$-0.856202\pi$
$233$	−0.695598	−	14.6024i	−0.0455702	−	0.956635i	0.854112	−	0.520089i	$-0.174101\pi$
$234$		0			0
$235$	15.7653	+	22.1393i	1.02841	+	1.44421i
$236$		0			0
$237$	1.04554	−	0.996921i	0.0679151	−	0.0647570i
$238$		0			0
$239$	3.23505	−	5.60327i	0.209258	−	0.362445i	−0.742223	−	0.670153i	$-0.766229\pi$
$239$	3.23505	−	5.60327i	0.209258	−	0.362445i	0.951481	+	0.307708i	$0.0995619\pi$
$240$		0			0
$241$	2.93940	−	20.4440i	0.189343	−	1.31691i	−0.644369	−	0.764714i	$-0.722880\pi$
$241$	2.93940	−	20.4440i	0.189343	−	1.31691i	0.833713	−	0.552198i	$-0.186211\pi$
$242$		0			0
$243$	0.959493	−	0.281733i	0.0615515	−	0.0180732i
$244$		0			0
$245$	−0.569024	+	11.9453i	−0.0363536	+	0.763157i
$246$		0			0
$247$	−11.3662	−	8.93849i	−0.723215	−	0.568743i
$248$		0			0
$249$	−15.2763	+	1.45871i	−0.968095	+	0.0924419i
$250$		0			0
$251$	2.76248	−	7.98165i	0.174366	−	0.503797i	−0.823626	−	0.567133i	$-0.808053\pi$
$251$	2.76248	−	7.98165i	0.174366	−	0.503797i	0.997992	+	0.0633354i	$0.0201738\pi$
$252$		0			0
$253$	−7.87450	+	17.2427i	−0.495065	+	1.08404i
$254$		0			0
$255$	−12.1721	−	11.6060i	−0.762245	−	0.726799i
$256$		0			0
$257$	24.1495	+	9.66800i	1.50640	+	0.603073i	0.970478	−	0.241191i	$-0.0775380\pi$
$257$	24.1495	+	9.66800i	1.50640	+	0.603073i	0.535927	+	0.844264i	$0.319962\pi$
$258$		0			0
$259$	3.85024	+	8.43085i	0.239242	+	0.523868i
$260$		0			0
$261$	−7.17748	−	0.685366i	−0.444275	−	0.0424231i
$262$		0			0
$263$	0.0507775	+	0.353166i	0.00313108	+	0.0217771i	0.991327	−	0.131418i	$-0.0419529\pi$
$263$	0.0507775	+	0.353166i	0.00313108	+	0.0217771i	−0.988196	+	0.153195i	$0.951044\pi$
$264$		0			0
$265$	−16.6377	−	10.6924i	−1.02204	−	0.656827i
$266$		0			0
$267$	−16.6843			−1.02106
$268$		0			0
$269$	−3.27549			−0.199710			−0.0998551	−	0.995002i	$-0.531838\pi$
$269$	−3.27549			−0.199710			−0.0998551	+	0.995002i	$0.531838\pi$
$270$		0			0
$271$	9.69447	+	6.23026i	0.588897	+	0.378461i	0.800891	−	0.598810i	$-0.204359\pi$
$271$	9.69447	+	6.23026i	0.588897	+	0.378461i	−0.211994	+	0.977271i	$0.567996\pi$
$272$		0			0
$273$	0.870427	+	6.05395i	0.0526806	+	0.366402i
$274$		0			0
$275$	7.21565	+	0.689011i	0.435120	+	0.0415489i
$276$		0			0
$277$	3.43127	+	7.51344i	0.206165	+	0.451439i	0.984264	−	0.176703i	$-0.0565431\pi$
$277$	3.43127	+	7.51344i	0.206165	+	0.451439i	−0.778099	+	0.628142i	$0.783816\pi$
$278$		0			0
$279$	1.39940	+	0.560236i	0.0837800	+	0.0335405i
$280$		0			0
$281$	−1.46621	−	1.39803i	−0.0874666	−	0.0833993i	0.645085	−	0.764111i	$-0.276822\pi$
$281$	−1.46621	−	1.39803i	−0.0874666	−	0.0833993i	−0.732551	+	0.680712i	$0.761671\pi$
$282$		0			0
$283$	7.66627	−	16.7868i	0.455712	−	0.997871i	−0.532732	−	0.846284i	$-0.678835\pi$
$283$	7.66627	−	16.7868i	0.455712	−	0.997871i	0.988444	−	0.151586i	$-0.0484382\pi$
$284$		0			0
$285$	−2.86686	+	8.28325i	−0.169818	+	0.490657i
$286$		0			0
$287$	−7.22188	+	0.689606i	−0.426294	+	0.0407061i
$288$		0			0
$289$	−22.3447	−	17.5720i	−1.31439	−	1.03365i
$290$		0			0
$291$	0.234794	−	4.92892i	0.0137638	−	0.288939i
$292$		0			0
$293$	−3.39791	+	0.997717i	−0.198508	+	0.0582873i	−0.379475	−	0.925202i	$-0.623895\pi$
$293$	−3.39791	+	0.997717i	−0.198508	+	0.0582873i	0.180967	+	0.983489i	$0.442077\pi$
$294$		0			0
$295$	−4.26553	+	29.6674i	−0.248349	+	1.72730i
$296$		0			0
$297$	−2.95430	+	5.11700i	−0.171426	+	0.296918i
$298$		0			0
$299$	−9.55789	+	9.11343i	−0.552747	+	0.527043i
$300$		0			0
$301$	−11.0688	−	15.5439i	−0.637994	−	0.895937i
$302$		0			0
$303$	0.456138	+	9.57551i	0.0262044	+	0.550099i
$304$		0			0
$305$	−1.31696	−	2.28103i	−0.0754087	−	0.130612i
$306$		0			0
$307$	−3.22405	−	13.2897i	−0.184006	−	0.758484i	−0.986762	−	0.162176i	$-0.948149\pi$
$307$	−3.22405	−	13.2897i	−0.184006	−	0.758484i	0.802756	−	0.596308i	$-0.203366\pi$
$308$		0			0
$309$	−14.9431	+	2.88004i	−0.850082	+	0.163840i
$310$		0			0
$311$	17.3083	+	19.9749i	0.981465	+	1.13267i	0.991154	+	0.132718i	$0.0423706\pi$
$311$	17.3083	+	19.9749i	0.981465	+	1.13267i	−0.00968834	+	0.999953i	$0.503084\pi$
$312$		0			0
$313$	7.91102	−	5.08410i	0.447157	−	0.287371i	−0.297619	−	0.954685i	$-0.596193\pi$
$313$	7.91102	−	5.08410i	0.447157	−	0.287371i	0.744776	+	0.667314i	$0.232556\pi$
$314$		0			0
$315$	3.29540	−	1.69890i	0.185675	−	0.0957219i
$316$		0			0
$317$	−25.7843	−	4.96952i	−1.44819	−	0.279116i	−0.596269	−	0.802785i	$-0.703351\pi$
$317$	−25.7843	−	4.96952i	−1.44819	−	0.279116i	−0.851922	+	0.523669i	$0.824563\pi$
$318$		0			0
$319$	33.4872	−	26.3346i	1.87492	−	1.47446i
$320$		0			0
$321$	−1.41584	+	1.63397i	−0.0790244	+	0.0911991i
$322$		0			0
$323$	−5.58161	+	23.0077i	−0.310569	+	1.28018i
$324$		0			0
$325$	4.48859	+	2.31403i	0.248982	+	0.128359i
$326$		0			0
$327$	−13.8306	−	4.06102i	−0.764832	−	0.224575i
$328$		0			0
$329$	−15.0236	+	6.01456i	−0.828280	+	0.331593i
$330$		0			0
$331$	−5.76571	−	16.6589i	−0.316912	−	0.915658i	−0.985148	−	0.171708i	$-0.945071\pi$
$331$	−5.76571	−	16.6589i	−0.316912	−	0.915658i	0.668236	−	0.743950i	$-0.267050\pi$
$332$		0			0
$333$	−3.61844	+	5.08139i	−0.198289	+	0.278458i
$334$		0			0
$335$	15.2775	+	13.5570i	0.834698	+	0.740698i
$336$		0			0
$337$	0.749932	−	1.05313i	0.0408514	−	0.0573678i	−0.793645	−	0.608381i	$-0.791819\pi$
$337$	0.749932	−	1.05313i	0.0408514	−	0.0573678i	0.834496	+	0.551013i	$0.185759\pi$
$338$		0			0
$339$	0.109692	+	0.316935i	0.00595766	+	0.0172135i
$340$		0			0
$341$	−8.26850	+	3.31021i	−0.447765	+	0.179258i
$342$		0			0
$343$	−16.8113	−	4.93624i	−0.907724	−	0.266532i
$344$		0			0
$345$	7.11556	+	3.66832i	0.383089	+	0.197496i
$346$		0			0
$347$	−0.957910	+	3.94856i	−0.0514233	+	0.211970i	−0.991727	−	0.128368i	$-0.959026\pi$
$347$	−0.957910	+	3.94856i	−0.0514233	+	0.211970i	0.940303	+	0.340338i	$0.110541\pi$
$348$		0			0
$349$	1.84876	−	2.13359i	0.0989621	−	0.114208i	−0.704108	−	0.710093i	$-0.748653\pi$
$349$	1.84876	−	2.13359i	0.0989621	−	0.114208i	0.803070	+	0.595885i	$0.203198\pi$
$350$		0			0
$351$	−3.23578	+	2.54464i	−0.172713	+	0.135823i
$352$		0			0
$353$	2.02391	+	0.390077i	0.107722	+	0.0207617i	0.242827	−	0.970070i	$-0.421925\pi$
$353$	2.02391	+	0.390077i	0.107722	+	0.0207617i	−0.135105	+	0.990831i	$0.543137\pi$
$354$		0			0
$355$	1.38375	−	0.713374i	0.0734419	−	0.0378620i
$356$		0			0
$357$	8.42435	−	5.41400i	0.445864	−	0.286539i
$358$		0			0
$359$	−3.53098	−	4.07497i	−0.186358	−	0.215068i	0.654881	−	0.755732i	$-0.272719\pi$
$359$	−3.53098	−	4.07497i	−0.186358	−	0.215068i	−0.841239	+	0.540663i	$0.818173\pi$
$360$		0			0
$361$	−6.54078	+	1.26063i	−0.344252	+	0.0663491i
$362$		0			0
$363$	−5.63736	−	23.2375i	−0.295885	−	1.21965i
$364$		0			0
$365$	8.93900	+	15.4828i	0.467889	+	0.810407i
$366$		0			0
$367$	0.727177	+	15.2653i	0.0379583	+	0.796843i	0.934947	+	0.354789i	$0.115447\pi$
$367$	0.727177	+	15.2653i	0.0379583	+	0.796843i	−0.896988	+	0.442054i	$0.854250\pi$
$368$		0			0
$369$	−2.83228	−	3.97738i	−0.147443	−	0.207054i
$370$		0			0
$371$	8.52252	−	8.12621i	0.442467	−	0.421892i
$372$		0			0
$373$	−16.4002	+	28.4059i	−0.849169	+	1.47080i	0.0327821	+	0.999463i	$0.489563\pi$
$373$	−16.4002	+	28.4059i	−0.849169	+	1.47080i	−0.881951	+	0.471341i	$0.843770\pi$
$374$		0			0
$375$	−1.33997	+	9.31970i	−0.0691958	+	0.481267i
$376$		0			0
$377$	28.4781	−	8.36194i	1.46670	−	0.430662i
$378$		0			0
$379$	−0.958498	+	20.1213i	−0.0492347	+	1.03356i	0.830176	+	0.557501i	$0.188240\pi$
$379$	−0.958498	+	20.1213i	−0.0492347	+	1.03356i	−0.879411	+	0.476063i	$0.842063\pi$
$380$		0			0
$381$	6.61399	+	5.20130i	0.338845	+	0.266471i
$382$		0			0
$383$	−4.20668	+	0.401689i	−0.214951	+	0.0205254i	−0.201976	−	0.979390i	$-0.564736\pi$
$383$	−4.20668	+	0.401689i	−0.214951	+	0.0205254i	−0.0129753	+	0.999916i	$0.504130\pi$
$384$		0			0
$385$	−7.16488	+	20.7016i	−0.365156	+	1.05505i
$386$		0			0
$387$	5.33527	−	11.6826i	0.271207	−	0.593860i
$388$		0			0
$389$	−18.5594	−	17.6963i	−0.940996	−	0.897238i	0.0538584	−	0.998549i	$-0.482848\pi$
$389$	−18.5594	−	17.6963i	−0.940996	−	0.897238i	−0.994855	+	0.101310i	$0.967697\pi$
$390$		0			0
$391$	20.0738	+	8.03636i	1.01518	+	0.406416i
$392$		0			0
$393$	−0.979043	−	2.14381i	−0.0493862	−	0.108141i
$394$		0			0
$395$	3.58858	+	0.342667i	0.180561	+	0.0172415i
$396$		0			0
$397$	4.00435	+	27.8509i	0.200973	+	1.39780i	0.801406	+	0.598121i	$0.204086\pi$
$397$	4.00435	+	27.8509i	0.200973	+	1.39780i	−0.600433	+	0.799675i	$0.705005\pi$
$398$		0			0
$399$	−4.39055	−	2.82164i	−0.219803	−	0.141259i
$400$		0			0
$401$	14.5750			0.727843			0.363922	−	0.931430i	$-0.381438\pi$
$401$	14.5750			0.727843			0.363922	+	0.931430i	$0.381438\pi$
$402$		0			0
$403$	−6.20511			−0.309098
$404$		0			0
$405$	2.09922	+	1.34909i	0.104311	+	0.0670367i
$406$		0			0
$407$	−5.24548	−	36.4831i	−0.260009	−	1.80840i
$408$		0			0
$409$	−15.6492	−	1.49432i	−0.773802	−	0.0738891i	−0.299318	−	0.954153i	$-0.596759\pi$
$409$	−15.6492	−	1.49432i	−0.773802	−	0.0738891i	−0.474484	+	0.880264i	$0.657365\pi$
$410$		0			0
$411$	−1.23951	−	2.71416i	−0.0611407	−	0.133879i
$412$		0			0
$413$	−16.5679	−	6.63278i	−0.815252	−	0.326378i
$414$		0			0
$415$	−27.7140	−	26.4252i	−1.36043	−	1.29716i
$416$		0			0
$417$	−3.88141	+	8.49910i	−0.190073	+	0.416203i
$418$		0			0
$419$	−0.327445	+	0.946089i	−0.0159967	+	0.0462195i	−0.952717	−	0.303860i	$-0.901724\pi$
$419$	−0.327445	+	0.946089i	−0.0159967	+	0.0462195i	0.936720	+	0.350080i	$0.113846\pi$
$420$		0			0
$421$	−17.7600	+	1.69588i	−0.865570	+	0.0826520i	−0.518388	−	0.855146i	$-0.673468\pi$
$421$	−17.7600	+	1.69588i	−0.865570	+	0.0826520i	−0.347183	+	0.937798i	$0.612862\pi$
$422$		0			0
$423$	−8.56154	−	6.73287i	−0.416276	−	0.327363i
$424$		0			0
$425$	0.393421	−	8.25893i	0.0190837	−	0.400617i
$426$		0			0
$427$	1.50476	−	0.441837i	0.0728204	−	0.0213820i
$428$		0			0
$429$	3.46148	−	24.0751i	0.167122	−	1.16236i
$430$		0			0
$431$	−6.12638	+	10.6112i	−0.295097	+	0.511123i	−0.975007	−	0.222172i	$-0.928685\pi$
$431$	−6.12638	+	10.6112i	−0.295097	+	0.511123i	0.679910	+	0.733295i	$0.262019\pi$
$432$		0			0
$433$	−22.9641	+	21.8962i	−1.10359	+	1.05227i	−0.105258	+	0.994445i	$0.533567\pi$
$433$	−22.9641	+	21.8962i	−1.10359	+	1.05227i	−0.998327	+	0.0578216i	$0.981585\pi$
$434$		0			0
$435$	−10.4363	−	14.6557i	−0.500380	−	0.702686i
$436$		0			0
$437$	−0.536211	−	11.2564i	−0.0256504	−	0.538469i
$438$		0			0
$439$	10.8042	+	18.7135i	0.515657	+	0.893145i	0.999835	+	0.0181751i	$0.00578562\pi$
$439$	10.8042	+	18.7135i	0.515657	+	0.893145i	−0.484177	+	0.874970i	$0.660881\pi$
$440$		0			0
$441$	−1.12986	−	4.65736i	−0.0538030	−	0.221779i
$442$		0			0
$443$	−19.9873	+	3.85223i	−0.949625	+	0.183025i	−0.640467	−	0.767986i	$-0.721259\pi$
$443$	−19.9873	+	3.85223i	−0.949625	+	0.183025i	−0.309158	+	0.951011i	$0.600047\pi$
$444$		0			0
$445$	−27.2638	−	31.4641i	−1.29243	−	1.49154i
$446$		0			0
$447$	12.8966	−	8.28815i	0.609989	−	0.392016i
$448$		0			0
$449$	31.3987	−	16.1872i	1.48180	−	0.763919i	0.487761	−	0.872977i	$-0.337814\pi$
$449$	31.3987	−	16.1872i	1.48180	−	0.763919i	0.994035	+	0.109058i	$0.0347834\pi$
$450$		0			0
$451$	28.3289	+	5.45996i	1.33396	+	0.257099i
$452$		0			0
$453$	−10.8935	+	8.56678i	−0.511824	+	0.402502i
$454$		0			0
$455$	−9.99453	+	11.5343i	−0.468551	+	0.540736i
$456$		0			0
$457$	4.61069	−	19.0055i	0.215679	−	0.889041i	−0.756348	−	0.654170i	$-0.773018\pi$
$457$	4.61069	−	19.0055i	0.215679	−	0.889041i	0.972027	−	0.234871i	$-0.0754667\pi$
$458$		0			0
$459$	5.99067	+	3.08841i	0.279621	+	0.144154i
$460$		0			0
$461$	11.0086	+	3.23243i	0.512723	+	0.150549i	0.527852	−	0.849336i	$-0.322998\pi$
$461$	11.0086	+	3.23243i	0.512723	+	0.150549i	−0.0151287	+	0.999886i	$0.504816\pi$
$462$		0			0
$463$	−39.0083	+	15.6166i	−1.81287	+	0.725764i	−0.826126	+	0.563485i	$0.809460\pi$
$463$	−39.0083	+	15.6166i	−1.81287	+	0.725764i	−0.986745	+	0.162279i	$0.948116\pi$
$464$		0			0
$465$	1.23024	+	3.55456i	0.0570512	+	0.164839i
$466$		0			0
$467$	−3.73990	+	5.25196i	−0.173062	+	0.243032i	−0.891992	−	0.452051i	$-0.850693\pi$
$467$	−3.73990	+	5.25196i	−0.173062	+	0.243032i	0.718930	+	0.695082i	$0.244632\pi$
$468$		0			0
$469$	−9.98916	+	6.93703i	−0.461257	+	0.320322i
$470$		0			0
$471$	10.8416	−	15.2249i	0.499554	−	0.701526i
$472$		0			0
$473$	24.8197	+	71.7118i	1.14121	+	3.29731i
$474$		0			0
$475$	−4.00055	+	1.60158i	−0.183558	+	0.0734854i
$476$		0			0
$477$	7.60459	+	2.23291i	0.348190	+	0.102238i
$478$		0			0
$479$	17.2982	+	8.91783i	0.790374	+	0.407466i	0.805631	−	0.592418i	$-0.201826\pi$
$479$	17.2982	+	8.91783i	0.790374	+	0.407466i	−0.0152572	+	0.999884i	$0.504857\pi$
$480$		0			0
$481$	6.05405	−	24.9551i	0.276041	−	1.13786i
$482$		0			0
$483$	−3.12148	+	3.60238i	−0.142032	+	0.163914i
$484$		0			0
$485$	9.67893	−	7.61160i	0.439498	−	0.345625i
$486$		0			0
$487$	−37.1105	−	7.15246i	−1.68164	−	0.324109i	−0.743072	−	0.669211i	$-0.766632\pi$
$487$	−37.1105	−	7.15246i	−1.68164	−	0.324109i	−0.938565	+	0.345102i	$0.887844\pi$
$488$		0			0
$489$	12.4553	−	6.42114i	0.563247	−	0.290374i
$490$		0			0
$491$	10.8557	−	6.97656i	0.489913	−	0.314848i	−0.272258	−	0.962224i	$-0.587770\pi$
$491$	10.8557	−	6.97656i	0.489913	−	0.314848i	0.762170	+	0.647377i	$0.224134\pi$
$492$		0			0
$493$	−31.8234	−	36.7261i	−1.43325	−	1.65406i
$494$		0			0
$495$	−14.4776	+	2.79032i	−0.650718	+	0.125416i
$496$		0			0
$497$	0.218539	+	0.900830i	0.00980281	+	0.0404078i
$498$		0			0
$499$	−13.2811	−	23.0036i	−0.594544	−	1.02978i	−0.993611	−	0.112859i	$-0.963999\pi$
$499$	−13.2811	−	23.0036i	−0.594544	−	1.02978i	0.399067	−	0.916922i	$-0.369334\pi$
$500$		0			0
$501$	0.951501	+	19.9745i	0.0425099	+	0.892393i
$502$		0			0
$503$	0.260265	+	0.365491i	0.0116046	+	0.0162964i	0.820338	−	0.571880i	$-0.193786\pi$
$503$	0.260265	+	0.365491i	0.0116046	+	0.0162964i	−0.808733	+	0.588176i	$0.799846\pi$
$504$		0			0
$505$	−17.3127	+	16.5076i	−0.770404	+	0.734579i
$506$		0			0
$507$	1.97274	−	3.41689i	0.0876125	−	0.151749i
$508$		0			0
$509$	0.909677	−	6.32695i	0.0403207	−	0.280437i	−0.959679	−	0.281098i	$-0.909301\pi$
$509$	0.909677	−	6.32695i	0.0403207	−	0.280437i	1.00000		0.000661179i	$0.000210460\pi$
$510$		0			0
$511$	−10.2137	+	2.99902i	−0.451829	+	0.132669i
$512$		0			0
$513$	0.167139	−	3.50869i	0.00737939	−	0.154912i
$514$		0			0
$515$	−29.8499	−	23.4742i	−1.31534	−	1.03440i
$516$		0			0
$517$	64.0639	−	6.11736i	2.81753	−	0.269041i
$518$		0			0
$519$	−4.81277	+	13.9056i	−0.211257	+	0.610388i
$520$		0			0
$521$	14.3913	−	31.5125i	0.630493	−	1.38059i	−0.277142	−	0.960829i	$-0.589387\pi$
$521$	14.3913	−	31.5125i	0.630493	−	1.38059i	0.907636	−	0.419759i	$-0.137885\pi$
$522$		0			0
$523$	13.2435	+	12.6277i	0.579098	+	0.552169i	0.921994	−	0.387205i	$-0.126559\pi$
$523$	13.2435	+	12.6277i	0.579098	+	0.552169i	−0.342896	+	0.939373i	$0.611408\pi$
$524$		0			0
$525$	1.69214	+	0.677432i	0.0738512	+	0.0295656i
$526$		0			0
$527$	4.22045	+	9.24149i	0.183846	+	0.402566i
$528$		0			0
$529$	12.6502	+	1.20794i	0.550007	+	0.0525193i
$530$		0			0
$531$	−1.70939	−	11.8891i	−0.0741813	−	0.515942i
$532$		0			0
$533$	16.9091	+	10.8668i	0.732413	+	0.470693i
$534$		0			0
$535$	−5.39506			−0.233249
$536$		0			0
$537$	−2.08888			−0.0901420
$538$		0			0
$539$	23.8215	+	15.3091i	1.02606	+	0.659412i
$540$		0			0
$541$	−4.30171	−	29.9191i	−0.184945	−	1.28632i	−0.844863	−	0.534983i	$-0.820318\pi$
$541$	−4.30171	−	29.9191i	−0.184945	−	1.28632i	0.659918	−	0.751338i	$-0.270591\pi$
$542$		0			0
$543$	0.965474	+	0.0921915i	0.0414324	+	0.00395632i
$544$		0			0
$545$	−14.9421	−	32.7187i	−0.640050	−	1.40151i
$546$		0			0
$547$	1.56434	+	0.626266i	0.0668862	+	0.0267772i	0.404864	−	0.914377i	$-0.367319\pi$
$547$	1.56434	+	0.626266i	0.0668862	+	0.0267772i	−0.337978	+	0.941154i	$0.609743\pi$
$548$		0			0
$549$	0.763922	+	0.728398i	0.0326034	+	0.0310873i
$550$		0			0
$551$	−10.5211	+	23.0381i	−0.448215	+	0.981454i
$552$		0			0
$553$	−0.702029	+	2.02838i	−0.0298533	+	0.0862555i
$554$		0			0
$555$	−15.4957	+	1.47966i	−0.657755	+	0.0628080i
$556$		0			0
$557$	18.6575	+	14.6724i	0.790545	+	0.621692i	0.929590	−	0.368594i	$-0.120161\pi$
$557$	18.6575	+	14.6724i	0.790545	+	0.621692i	−0.139045	+	0.990286i	$0.544403\pi$
$558$		0			0
$559$	−2.51561	+	52.8091i	−0.106399	+	2.23359i
$560$		0			0
$561$	−38.2103	+	11.2196i	−1.61324	+	0.473690i
$562$		0			0
$563$	−0.235424	+	1.63741i	−0.00992194	+	0.0690086i	−0.994181	−	0.107724i	$-0.965644\pi$
$563$	−0.235424	+	1.63741i	−0.00992194	+	0.0690086i	0.984259	+	0.176733i	$0.0565528\pi$
$564$		0			0
$565$	−0.418445	+	0.724769i	−0.0176041	+	0.0304912i
$566$		0			0
$567$	−1.07531	+	1.02531i	−0.0451588	+	0.0430589i
$568$		0			0
$569$	18.1493	+	25.4871i	0.760858	+	1.06847i	0.995347	+	0.0963563i	$0.0307188\pi$
$569$	18.1493	+	25.4871i	0.760858	+	1.06847i	−0.234489	+	0.972119i	$0.575342\pi$
$570$		0			0
$571$	−0.225113	−	4.72571i	−0.00942070	−	0.197765i	−0.998671	−	0.0515342i	$-0.983589\pi$
$571$	−0.225113	−	4.72571i	−0.00942070	−	0.197765i	0.989251	−	0.146231i	$-0.0467141\pi$
$572$		0			0
$573$	0.216657	+	0.375260i	0.00905096	+	0.0156767i
$574$		0			0
$575$	0.927868	+	3.82473i	0.0386948	+	0.159502i
$576$		0			0
$577$	−18.7120	+	3.60645i	−0.778993	+	0.150139i	−0.563222	−	0.826306i	$-0.690438\pi$
$577$	−18.7120	+	3.60645i	−0.778993	+	0.150139i	−0.215771	+	0.976444i	$0.569226\pi$
$578$		0			0
$579$	8.31682	+	9.59813i	0.345635	+	0.398885i
$580$		0			0
$581$	19.1810	−	12.3269i	0.795761	−	0.511405i
$582$		0			0
$583$	−41.6236	+	21.4585i	−1.72387	+	0.888718i
$584$		0			0
$585$	−10.0864	−	1.94400i	−0.417023	−	0.0803746i
$586$		0			0
$587$	−31.1811	+	24.5211i	−1.28698	+	1.01209i	−0.288473	+	0.957488i	$0.593148\pi$
$587$	−31.1811	+	24.5211i	−1.28698	+	1.01209i	−0.998508	+	0.0546052i	$0.982610\pi$
$588$		0			0
$589$	3.46744	−	4.00163i	0.142873	−	0.164884i
$590$		0			0
$591$	1.62045	−	6.67959i	0.0666565	−	0.274762i
$592$		0			0
$593$	−40.8279	−	21.0483i	−1.67660	−	0.864348i	−0.990607	−	0.136742i	$-0.956337\pi$
$593$	−40.8279	−	21.0483i	−1.67660	−	0.864348i	−0.685995	−	0.727606i	$-0.740633\pi$
$594$		0			0
$595$	23.9763	+	7.04008i	0.982933	+	0.288615i
$596$		0			0
$597$	−24.7359	+	9.90275i	−1.01237	+	0.405292i
$598$		0			0
$599$	0.854355	+	2.46850i	0.0349080	+	0.100860i	0.961108	−	0.276172i	$-0.0890659\pi$
$599$	0.854355	+	2.46850i	0.0349080	+	0.100860i	−0.926200	+	0.377032i	$0.876945\pi$
$600$		0			0
$601$	17.8996	−	25.1365i	0.730141	−	1.02534i	−0.267941	−	0.963435i	$-0.586343\pi$
$601$	17.8996	−	25.1365i	0.730141	−	1.02534i	0.998082	−	0.0619039i	$-0.0197172\pi$
$602$		0			0
$603$	−7.40501	−	3.48796i	−0.301555	−	0.142041i
$604$		0			0
$605$	34.6106	−	48.6038i	1.40712	−	1.97603i
$606$		0			0
$607$	−12.5606	−	36.2914i	−0.509818	−	1.47302i	−0.847005	−	0.531585i	$-0.821597\pi$
$607$	−12.5606	−	36.2914i	−0.509818	−	1.47302i	0.337187	−	0.941438i	$-0.390524\pi$
$608$		0			0
$609$	9.94531	−	3.98150i	0.403004	−	0.161339i
$610$		0			0
$611$	43.0198	+	12.6318i	1.74040	+	0.511027i
$612$		0			0
$613$	−2.89578	−	1.49288i	−0.116959	−	0.0602968i	0.398754	−	0.917058i	$-0.369443\pi$
$613$	−2.89578	−	1.49288i	−0.116959	−	0.0602968i	−0.515713	+	0.856761i	$0.672473\pi$
$614$		0			0
$615$	2.87254	−	11.8408i	0.115832	−	0.477465i
$616$		0			0
$617$	−22.8331	+	26.3508i	−0.919226	+	1.06084i	0.0787274	+	0.996896i	$0.474914\pi$
$617$	−22.8331	+	26.3508i	−0.919226	+	1.06084i	−0.997953	+	0.0639470i	$0.979631\pi$
$618$		0			0
$619$	27.5173	−	21.6399i	1.10601	−	0.869779i	0.113699	−	0.993515i	$-0.463730\pi$
$619$	27.5173	−	21.6399i	1.10601	−	0.869779i	0.992315	+	0.123736i	$0.0394876\pi$
$620$		0			0
$621$	−3.15019	−	0.607149i	−0.126413	−	0.0243640i
$622$		0			0
$623$	22.0335	−	11.3591i	0.882753	−	0.455091i
$624$		0			0
$625$	−24.9254	+	16.0186i	−0.997016	+	0.640743i
$626$		0			0
$627$	13.5916	+	15.6855i	0.542796	+	0.626420i
$628$		0			0
$629$	−41.2843	+	7.95689i	−1.64611	+	0.317262i
$630$		0			0
$631$	6.34760	+	26.1652i	0.252694	+	1.04162i	0.946820	+	0.321765i	$0.104276\pi$
$631$	6.34760	+	26.1652i	0.252694	+	1.04162i	−0.694126	+	0.719854i	$0.744209\pi$
$632$		0			0
$633$	2.02728	+	3.51135i	0.0805771	+	0.139564i
$634$		0			0
$635$	0.999044	+	20.9725i	0.0396459	+	0.832269i
$636$		0			0
$637$	11.4434	+	16.0700i	0.453404	+	0.636717i
$638$		0			0
$639$	−0.451528	+	0.430531i	−0.0178622	+	0.0170315i
$640$		0			0
$641$	−13.8172	+	23.9322i	−0.545748	+	0.945264i	0.452811	+	0.891606i	$0.350421\pi$
$641$	−13.8172	+	23.9322i	−0.545748	+	0.945264i	−0.998559	+	0.0536573i	$0.982912\pi$
$642$		0			0
$643$	0.825602	−	5.74219i	0.0325586	−	0.226450i	−0.967045	−	0.254606i	$-0.918054\pi$
$643$	0.825602	−	5.74219i	0.0325586	−	0.226450i	0.999604	+	0.0281558i	$0.00896347\pi$
$644$		0			0
$645$	30.7502	−	9.02906i	1.21079	−	0.355519i
$646$		0			0
$647$	−1.14692	+	24.0768i	−0.0450901	+	0.946557i	0.857082	+	0.515180i	$0.172275\pi$
$647$	−1.14692	+	24.0768i	−0.0450901	+	0.946557i	−0.902172	+	0.431377i	$0.858028\pi$
$648$		0			0
$649$	55.7863	+	43.8709i	2.18980	+	1.72208i
$650$		0			0
$651$	−2.22949	+	0.212891i	−0.0873808	+	0.00834385i
$652$		0			0
$653$	5.17802	−	14.9609i	0.202631	−	0.585465i	−0.797202	−	0.603713i	$-0.793687\pi$
$653$	5.17802	−	14.9609i	0.202631	−	0.585465i	0.999834	+	0.0182474i	$0.00580866\pi$
$654$		0			0
$655$	2.44305	−	5.34954i	0.0954580	−	0.209024i
$656$		0			0
$657$	−5.18522	−	4.94409i	−0.202295	−	0.192887i
$658$		0			0
$659$	30.9378	+	12.3856i	1.20516	+	0.482475i	0.885314	−	0.464993i	$-0.153943\pi$
$659$	30.9378	+	12.3856i	1.20516	+	0.482475i	0.319850	+	0.947468i	$0.396367\pi$
$660$		0			0
$661$	−5.95544	−	13.0406i	−0.231640	−	0.507220i	0.757743	−	0.652553i	$-0.226302\pi$
$661$	−5.95544	−	13.0406i	−0.231640	−	0.507220i	−0.989383	+	0.145333i	$0.953575\pi$
$662$		0			0
$663$	−27.6191	−	2.63731i	−1.07264	−	0.102425i
$664$		0			0
$665$	−1.85342	−	12.8908i	−0.0718725	−	0.499884i
$666$		0			0
$667$	19.4592	+	12.5057i	0.753465	+	0.484223i
$668$		0			0
$669$	18.3082			0.707836
$670$		0			0
$671$	−6.23669			−0.240765
$672$		0			0
$673$	9.63727	+	6.19350i	0.371490	+	0.238742i	0.713043	−	0.701121i	$-0.247317\pi$
$673$	9.63727	+	6.19350i	0.371490	+	0.238742i	−0.341553	+	0.939862i	$0.610953\pi$
$674$		0			0
$675$	0.174587	+	1.21428i	0.00671986	+	0.0467377i
$676$		0			0
$677$	3.27965	+	0.313169i	0.126047	+	0.0120361i	0.157889	−	0.987457i	$-0.449531\pi$
$677$	3.27965	+	0.313169i	0.126047	+	0.0120361i	−0.0318417	+	0.999493i	$0.510137\pi$
$678$		0			0
$679$	3.04566	+	6.66907i	0.116882	+	0.255935i
$680$		0			0
$681$	−20.2329	−	8.10003i	−0.775326	−	0.310394i
$682$		0			0
$683$	21.4827	+	20.4837i	0.822013	+	0.783788i	0.979010	−	0.203811i	$-0.0653328\pi$
$683$	21.4827	+	20.4837i	0.822013	+	0.783788i	−0.156997	+	0.987599i	$0.550181\pi$
$684$		0			0
$685$	3.09302	−	6.77277i	0.118178	−	0.258774i
$686$		0			0
$687$	−0.283070	+	0.817878i	−0.0107998	+	0.0312040i
$688$		0			0
$689$	−32.4780	+	3.10128i	−1.23731	+	0.118149i
$690$		0			0
$691$	−1.72884	−	1.35957i	−0.0657681	−	0.0517206i	0.584734	−	0.811225i	$-0.301199\pi$
$691$	−1.72884	−	1.35957i	−0.0657681	−	0.0517206i	−0.650502	+	0.759505i	$0.725441\pi$
$692$		0			0
$693$	0.417716	−	8.76895i	0.0158677	−	0.333105i
$694$		0			0
$695$	−22.3707	+	6.56864i	−0.848570	+	0.249163i
$696$		0			0
$697$	4.68350	−	32.5744i	0.177400	−	1.23384i
$698$		0			0
$699$	−7.30948	+	12.6604i	−0.276470	+	0.478860i
$700$		0			0
$701$	1.28010	−	1.22057i	0.0483488	−	0.0461005i	−0.665520	−	0.746380i	$-0.731790\pi$
$701$	1.28010	−	1.22057i	0.0483488	−	0.0461005i	0.713868	+	0.700280i	$0.246941\pi$
$702$		0			0
$703$	12.7104	+	17.8492i	0.479381	+	0.673196i
$704$		0			0
$705$	−1.29322	−	27.1481i	−0.0487056	−	1.02246i
$706$		0			0
$707$	−7.12163	−	12.3350i	−0.267836	−	0.463906i
$708$		0			0
$709$	5.73098	+	23.6234i	0.215232	+	0.887196i	0.972277	+	0.233834i	$0.0751272\pi$
$709$	5.73098	+	23.6234i	0.215232	+	0.887196i	−0.757045	+	0.653363i	$0.773358\pi$
$710$		0			0
$711$	−1.41854	+	0.273401i	−0.0531994	+	0.0102533i
$712$		0			0
$713$	−3.16685	−	3.65474i	−0.118599	−	0.136871i
$714$		0			0
$715$	51.0587	−	32.8134i	1.90949	−	1.22715i
$716$		0			0
$717$	−5.75085	+	2.96477i	−0.214769	+	0.110721i
$718$		0			0
$719$	28.7183	+	5.53499i	1.07101	+	0.206420i	0.694136	−	0.719844i	$-0.255787\pi$
$719$	28.7183	+	5.53499i	1.07101	+	0.206420i	0.376875	+	0.926264i	$0.376999\pi$
$720$		0			0
$721$	17.7733	−	13.9770i	0.661911	−	0.520532i
$722$		0			0
$723$	−13.5256	+	15.6094i	−0.503024	+	0.580520i
$724$		0			0
$725$	2.08532	−	8.59581i	0.0774469	−	0.319240i
$726$		0			0
$727$	−30.1238	−	15.5299i	−1.11723	−	0.575972i	−0.202194	−	0.979345i	$-0.564807\pi$
$727$	−30.1238	−	15.5299i	−1.11723	−	0.575972i	−0.915036	+	0.403373i	$0.867838\pi$
$728$		0			0
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$		0			0
$731$	80.3616	−	32.1719i	2.97228	−	1.18992i
$732$		0			0
$733$	−13.6465	−	39.4289i	−0.504044	−	1.45634i	−0.854348	−	0.519702i	$-0.826043\pi$
$733$	−13.6465	−	39.4289i	−0.504044	−	1.45634i	0.350304	−	0.936636i	$-0.386078\pi$
$734$		0			0
$735$	6.93681	−	9.74138i	0.255868	−	0.359316i
$736$		0			0
$737$	45.8875	−	15.2778i	1.69029	−	0.562764i
$738$		0			0
$739$	13.7855	−	19.3590i	0.507106	−	0.712131i	−0.479080	−	0.877771i	$-0.659030\pi$
$739$	13.7855	−	19.3590i	0.507106	−	0.712131i	0.986186	+	0.165640i	$0.0529691\pi$
$740$		0			0
$741$	4.72936	+	13.6646i	0.173737	+	0.501981i
$742$		0			0
$743$	−12.7618	+	5.10907i	−0.468187	+	0.187434i	−0.593746	−	0.804652i	$-0.702352\pi$
$743$	−12.7618	+	5.10907i	−0.468187	+	0.187434i	0.125560	+	0.992086i	$0.459927\pi$
$744$		0			0
$745$	36.7047	+	10.7775i	1.34476	+	0.394856i
$746$		0			0
$747$	13.6399	+	7.03184i	0.499056	+	0.257281i
$748$		0			0
$749$	0.757335	−	3.12178i	0.0276724	−	0.114067i
$750$		0			0
$751$	16.0055	−	18.4713i	0.584048	−	0.674027i	−0.384422	−	0.923157i	$-0.625599\pi$
$751$	16.0055	−	18.4713i	0.584048	−	0.674027i	0.968470	+	0.249130i	$0.0801447\pi$
$752$		0			0
$753$	−6.63915	+	5.22109i	−0.241944	+	0.190267i
$754$		0			0
$755$	−33.9570	−	6.54467i	−1.23582	−	0.238185i
$756$		0			0
$757$	−28.1436	+	14.5090i	−1.02290	+	0.527339i	−0.886214	−	0.463276i	$-0.846674\pi$
$757$	−28.1436	+	14.5090i	−1.02290	+	0.527339i	−0.136681	+	0.990615i	$0.543644\pi$
$758$		0			0
$759$	15.9466	−	10.2482i	0.578824	−	0.371988i
$760$		0			0
$761$	−4.12239	−	4.75749i	−0.149437	−	0.172459i	0.676096	−	0.736814i	$-0.263670\pi$
$761$	−4.12239	−	4.75749i	−0.149437	−	0.172459i	−0.825532	+	0.564355i	$0.809125\pi$
$762$		0			0
$763$	21.0297	−	4.05315i	0.761327	−	0.146734i
$764$		0			0
$765$	3.96510	+	16.3443i	0.143358	+	0.590931i
$766$		0			0
$767$	24.7223	+	42.8202i	0.892670	+	1.54615i
$768$		0			0
$769$	−0.368907	−	7.74431i	−0.0133031	−	0.279267i	−0.995711	−	0.0925187i	$-0.970508\pi$
$769$	−0.368907	−	7.74431i	−0.0133031	−	0.279267i	0.982408	−	0.186748i	$-0.0597948\pi$
$770$		0			0
$771$	−15.0889	−	21.1895i	−0.543415	−	0.763119i
$772$		0			0
$773$	−1.34077	+	1.27842i	−0.0482240	+	0.0459815i	−0.713808	−	0.700342i	$-0.753031\pi$
$773$	−1.34077	+	1.27842i	−0.0482240	+	0.0459815i	0.665584	+	0.746323i	$0.268183\pi$
$774$		0			0
$775$	−0.924601	+	1.60146i	−0.0332126	+	0.0575260i
$776$		0			0
$777$	1.31903	−	9.17408i	0.0473201	−	0.329118i
$778$		0			0
$779$	−16.4568	+	4.83215i	−0.589625	+	0.173130i
$780$		0			0
$781$	0.175401	−	3.68212i	0.00627634	−	0.131757i
$782$		0			0
$783$	5.66754	+	4.45700i	0.202541	+	0.159280i
$784$		0			0
$785$	46.4283	−	4.43337i	1.65710	−	0.158234i
$786$		0			0
$787$	4.05711	−	11.7222i	0.144620	−	0.417853i	−0.849306	−	0.527901i	$-0.822979\pi$
$787$	4.05711	−	11.7222i	0.144620	−	0.417853i	0.993926	+	0.110048i	$0.0351005\pi$
$788$		0			0
$789$	0.148219	−	0.324554i	0.00527673	−	0.0115544i
$790$		0			0
$791$	−0.360638	−	0.343868i	−0.0128228	−	0.0122265i
$792$		0			0
$793$	−4.03382	−	1.61490i	−0.143245	−	0.0573468i
$794$		0			0
$795$	8.21575	+	17.9900i	0.291383	+	0.638039i
$796$		0			0
$797$	−31.8158	−	3.03804i	−1.12697	−	0.107613i	−0.485126	−	0.874445i	$-0.661226\pi$
$797$	−31.8158	−	3.03804i	−1.12697	−	0.107613i	−0.641848	+	0.766832i	$0.721832\pi$
$798$		0			0
$799$	−10.4473	−	72.6626i	−0.369599	−	2.57062i
$800$		0			0
$801$	14.0357	+	9.02019i	0.495927	+	0.318713i
$802$		0			0
$803$	42.3323			1.49388
$804$		0			0
$805$	−11.8944			−0.419223
$806$		0			0
$807$	2.75552	+	1.77086i	0.0969989	+	0.0623374i
$808$		0			0
$809$	−4.65221	−	32.3568i	−0.163563	−	1.13761i	−0.891849	−	0.452332i	$-0.850592\pi$
$809$	−4.65221	−	32.3568i	−0.163563	−	1.13761i	0.728287	−	0.685273i	$-0.240317\pi$
$810$		0			0
$811$	−21.4807	−	2.05116i	−0.754290	−	0.0720259i	−0.289175	−	0.957276i	$-0.593381\pi$
$811$	−21.4807	−	2.05116i	−0.754290	−	0.0720259i	−0.465115	+	0.885250i	$0.653987\pi$
$812$		0			0
$813$	−4.78718	−	10.4825i	−0.167894	−	0.367636i
$814$		0			0
$815$	32.4626	+	12.9961i	1.13712	+	0.455232i
$816$		0			0
$817$	−32.6505	−	31.1322i	−1.14230	−	1.08918i
$818$		0			0
$819$	2.54076	−	5.56350i	0.0887815	−	0.194404i
$820$		0			0
$821$	−3.97486	+	11.4846i	−0.138724	+	0.400816i	−0.992868	−	0.119221i	$-0.961960\pi$
$821$	−3.97486	+	11.4846i	−0.138724	+	0.400816i	0.854144	+	0.520036i	$0.174082\pi$
$822$		0			0
$823$	18.6092	−	1.77696i	0.648675	−	0.0619409i	0.234468	−	0.972124i	$-0.424665\pi$
$823$	18.6092	−	1.77696i	0.648675	−	0.0619409i	0.414207	+	0.910183i	$0.364059\pi$
$824$		0			0
$825$	−5.69768	−	4.48071i	−0.198368	−	0.155998i
$826$		0			0
$827$	−0.625643	+	13.1339i	−0.0217557	+	0.456709i	0.961537	+	0.274677i	$0.0885708\pi$
$827$	−0.625643	+	13.1339i	−0.0217557	+	0.456709i	−0.983292	+	0.182033i	$0.941732\pi$
$828$		0			0
$829$	5.77271	−	1.69502i	0.200495	−	0.0588705i	−0.179943	−	0.983677i	$-0.557591\pi$
$829$	5.77271	−	1.69502i	0.200495	−	0.0588705i	0.380438	+	0.924806i	$0.375773\pi$
$830$		0			0
$831$	1.17550	−	8.17579i	0.0407777	−	0.283615i
$832$		0			0
$833$	16.1503	−	27.9732i	0.559576	−	0.969215i
$834$		0			0
$835$	−36.1142	+	34.4348i	−1.24978	+	1.19166i
$836$		0			0
$837$	−0.874365	−	1.22787i	−0.0302225	−	0.0424415i
$838$		0			0
$839$	−0.513991	−	10.7900i	−0.0177449	−	0.372512i	−0.990221	−	0.139509i	$-0.955448\pi$
$839$	−0.513991	−	10.7900i	−0.0177449	−	0.372512i	0.972476	−	0.233003i	$-0.0748553\pi$
$840$		0			0
$841$	−11.4930	−	19.9064i	−0.396309	−	0.686428i
$842$		0			0
$843$	0.477623	+	1.96879i	0.0164502	+	0.0678086i
$844$		0			0
$845$	9.66743	−	1.86324i	0.332570	−	0.0640976i
$846$		0			0
$847$	23.2655	+	26.8498i	0.799410	+	0.922569i
$848$		0			0
$849$	−15.5249	+	9.97724i	−0.532813	+	0.342418i
$850$		0			0
$851$	17.7880	−	9.17037i	0.609766	−	0.314356i
$852$		0			0
$853$	49.7267	+	9.58403i	1.70261	+	0.328151i	0.945619	−	0.325276i	$-0.105457\pi$
$853$	49.7267	+	9.58403i	1.70261	+	0.328151i	0.756989	+	0.653427i	$0.226669\pi$
$854$		0			0
$855$	6.89002	−	5.41837i	0.235634	−	0.185304i
$856$		0			0
$857$	13.0245	−	15.0311i	0.444910	−	0.513453i	−0.488354	−	0.872646i	$-0.662402\pi$
$857$	13.0245	−	15.0311i	0.444910	−	0.513453i	0.933263	+	0.359192i	$0.116948\pi$
$858$		0			0
$859$	−4.49686	+	18.5363i	−0.153431	+	0.632450i	0.842208	+	0.539153i	$0.181256\pi$
$859$	−4.49686	+	18.5363i	−0.153431	+	0.632450i	−0.995638	+	0.0932969i	$0.970259\pi$
$860$		0			0
$861$	6.44826	+	3.32431i	0.219756	+	0.113292i
$862$		0			0
$863$	−31.8357	−	9.34781i	−1.08370	−	0.318203i	−0.309342	−	0.950951i	$-0.600109\pi$
$863$	−31.8357	−	9.34781i	−1.08370	−	0.318203i	−0.774358	+	0.632747i	$0.781927\pi$
$864$		0			0
$865$	−34.0886	+	13.6470i	−1.15905	+	0.464012i
$866$		0			0
$867$	9.29736	+	26.8630i	0.315755	+	0.912314i
$868$		0			0
$869$	4.95127	−	6.95309i	0.167960	−	0.235867i
$870$		0			0
$871$	33.6355	+	2.00040i	1.13969	+	0.0677809i
$872$		0			0
$873$	−2.86230	+	4.01954i	−0.0968741	+	0.136041i
$874$		0			0
$875$	−4.57550	−	13.2200i	−0.154680	−	0.446918i
$876$		0			0
$877$	19.6441	−	7.86433i	0.663335	−	0.265559i	−0.0154670	−	0.999880i	$-0.504924\pi$
$877$	19.6441	−	7.86433i	0.663335	−	0.265559i	0.678802	+	0.734321i	$0.262499\pi$
$878$		0			0
$879$	3.39791	+	0.997717i	0.114609	+	0.0336522i
$880$		0			0
$881$	−6.34951	−	3.27340i	−0.213920	−	0.110284i	0.347936	−	0.937518i	$-0.386883\pi$
$881$	−6.34951	−	3.27340i	−0.213920	−	0.110284i	−0.561857	+	0.827234i	$0.689913\pi$
$882$		0			0
$883$	−0.349405	+	1.44027i	−0.0117584	+	0.0484688i	−0.977389	−	0.211451i	$-0.932181\pi$
$883$	−0.349405	+	1.44027i	−0.0117584	+	0.0484688i	0.965630	+	0.259920i	$0.0836962\pi$
$884$		0			0
$885$	19.6278	−	22.6517i	0.659781	−	0.761428i
$886$		0			0
$887$	−12.3332	+	9.69893i	−0.414108	+	0.325658i	−0.803382	−	0.595464i	$-0.796968\pi$
$887$	−12.3332	+	9.69893i	−0.414108	+	0.325658i	0.389274	+	0.921122i	$0.372726\pi$
$888$		0			0
$889$	−12.2757	−	2.36595i	−0.411714	−	0.0793514i
$890$		0			0
$891$	5.25177	−	2.70748i	0.175941	−	0.0907039i
$892$		0			0
$893$	−32.1858	+	20.6845i	−1.07706	+	0.692182i
$894$		0			0
$895$	−3.41346	−	3.93934i	−0.114099	−	0.131678i
$896$		0			0
$897$	12.9677	−	2.49932i	0.432979	−	0.0834499i
$898$		0			0
$899$	2.56232	+	10.5620i	0.0854582	+	0.352263i
$900$		0			0
$901$	26.7090	+	46.2614i	0.889806	+	1.54119i
$902$		0			0
$903$	0.907969	+	19.0606i	0.0302153	+	0.634298i
$904$		0			0
$905$	1.40383	+	1.97140i	0.0466648	+	0.0655315i
$906$		0			0
$907$	15.1998	−	14.4930i	0.504701	−	0.481232i	−0.394421	−	0.918930i	$-0.629055\pi$
$907$	15.1998	−	14.4930i	0.504701	−	0.481232i	0.899122	+	0.437698i	$0.144206\pi$
$908$		0			0
$909$	4.79318	−	8.30204i	0.158980	−	0.275361i
$910$		0			0
$911$	−3.75571	+	26.1216i	−0.124432	+	0.865446i	0.828007	+	0.560718i	$0.189475\pi$
$911$	−3.75571	+	26.1216i	−0.124432	+	0.865446i	−0.952439	+	0.304728i	$0.901434\pi$
$912$		0			0
$913$	−86.9991	+	25.5452i	−2.87925	+	0.845424i
$914$		0			0
$915$	−0.125327	+	2.63093i	−0.00414317	+	0.0869758i
$916$		0			0
$917$	2.75250	+	2.16459i	0.0908954	+	0.0714810i
$918$		0			0
$919$	−36.6403	+	3.49872i	−1.20865	+	0.115412i	−0.679861	−	0.733341i	$-0.737960\pi$
$919$	−36.6403	+	3.49872i	−1.20865	+	0.115412i	−0.528790	+	0.848753i	$0.677354\pi$
$920$		0			0
$921$	−4.47272	+	12.9231i	−0.147381	+	0.425829i
$922$		0			0
$923$	1.06688	−	2.33614i	0.0351167	−	0.0768949i
$924$		0			0
$925$	−5.53849	−	5.28094i	−0.182105	−	0.173636i
$926$		0			0
$927$	14.1280	+	5.65599i	0.464024	+	0.185767i
$928$		0			0
$929$	1.38905	+	3.04159i	0.0455731	+	0.0997912i	0.931049	−	0.364894i	$-0.118895\pi$
$929$	1.38905	+	3.04159i	0.0455731	+	0.0997912i	−0.885476	+	0.464685i	$0.846167\pi$
$930$		0			0
$931$	−16.7581	−	1.60020i	−0.549223	−	0.0524445i
$932$		0			0
$933$	−3.76146	−	26.1615i	−0.123145	−	0.856490i
$934$		0			0
$935$	−83.5982	−	53.7253i	−2.73395	−	1.75700i
$936$		0			0
$937$	54.0385			1.76536			0.882680	−	0.469975i	$-0.155737\pi$
$937$	54.0385			1.76536			0.882680	+	0.469975i	$0.155737\pi$
$938$		0			0
$939$	−9.40385			−0.306883
$940$		0			0
$941$	−1.27045	−	0.816466i	−0.0414154	−	0.0266160i	0.519769	−	0.854307i	$-0.326018\pi$
$941$	−1.27045	−	0.816466i	−0.0414154	−	0.0266160i	−0.561185	+	0.827691i	$0.689654\pi$
$942$		0			0
$943$	2.22932	+	15.5053i	0.0725966	+	0.504921i
$944$		0			0
$945$	−3.69076	−	0.352425i	−0.120060	−	0.0114644i
$946$		0			0
$947$	1.53124	+	3.35294i	0.0497585	+	0.108956i	0.932878	−	0.360191i	$-0.117289\pi$
$947$	1.53124	+	3.35294i	0.0497585	+	0.108956i	−0.883120	+	0.469147i	$0.844561\pi$
$948$		0			0
$949$	27.3801	+	10.9613i	0.888795	+	0.355820i
$950$		0			0
$951$	19.0044	+	18.1207i	0.616260	+	0.587603i
$952$		0			0
$953$	−2.69371	+	5.89840i	−0.0872578	+	0.191068i	−0.948230	−	0.317584i	$-0.897129\pi$
$953$	−2.69371	+	5.89840i	−0.0872578	+	0.191068i	0.860972	+	0.508652i	$0.169856\pi$
$954$		0			0
$955$	−0.353648	+	1.02180i	−0.0114438	+	0.0330646i
$956$		0			0
$957$	−42.4088	+	4.04955i	−1.37088	+	0.130903i
$958$		0			0
$959$	3.48479	+	2.74047i	0.112530	+	0.0884943i
$960$		0			0
$961$	−1.36692	+	28.6953i	−0.0440943	+	0.925654i
$962$		0			0
$963$	2.07447	−	0.609119i	0.0668488	−	0.0196286i
$964$		0			0
$965$	−4.51014	+	31.3687i	−0.145187	+	1.00979i
$966$		0			0
$967$	−0.292665	+	0.506911i	−0.00941148	+	0.0163012i	−0.870693	−	0.491827i	$-0.836329\pi$
$967$	−0.292665	+	0.506911i	−0.00941148	+	0.0163012i	0.861281	+	0.508128i	$0.169662\pi$
$968$		0			0
$969$	17.1345	−	16.3377i	0.550438	−	0.524842i
$970$		0			0
$971$	16.4686	+	23.1270i	0.528504	+	0.742180i	0.989391	−	0.145279i	$-0.0464080\pi$
$971$	16.4686	+	23.1270i	0.528504	+	0.742180i	−0.460887	+	0.887459i	$0.652469\pi$
$972$		0			0
$973$	−0.660548	−	13.8666i	−0.0211762	−	0.444543i
$974$		0			0
$975$	−2.52499	−	4.37340i	−0.0808643	−	0.140061i
$976$		0			0
$977$	−3.53774	−	14.5827i	−0.113182	−	0.466543i	−0.999990	−	0.00440553i	$-0.998598\pi$
$977$	−3.53774	−	14.5827i	−0.113182	−	0.466543i	0.886808	−	0.462138i	$-0.152917\pi$
$978$		0			0
$979$	−96.7991	+	18.6565i	−3.09371	+	0.596264i
$980$		0			0
$981$	9.43946	+	10.8937i	0.301379	+	0.347810i
$982$		0			0
$983$	26.2217	−	16.8517i	0.836344	−	0.537486i	−0.0509441	−	0.998702i	$-0.516223\pi$
$983$	26.2217	−	16.8517i	0.836344	−	0.537486i	0.887288	+	0.461216i	$0.152587\pi$
$984$		0			0
$985$	15.2448	−	7.85922i	0.485739	−	0.250416i
$986$		0			0
$987$	15.8904	+	3.06263i	0.505797	+	0.0974845i
$988$		0			0
$989$	−32.3879	+	25.4701i	−1.02987	+	0.809902i
$990$		0			0
$991$	−20.8738	+	24.0897i	−0.663078	+	0.765233i	−0.983277	−	0.182117i	$-0.941705\pi$
$991$	−20.8738	+	24.0897i	−0.663078	+	0.765233i	0.320198	+	0.947350i	$0.396250\pi$
$992$		0			0
$993$	−4.15607	+	17.1316i	−0.131889	+	0.543654i
$994$		0			0
$995$	−59.0962	−	30.4662i	−1.87348	−	0.965844i
$996$		0			0
$997$	27.9825	+	8.21640i	0.886215	+	0.260216i	0.692998	−	0.720940i	$-0.256290\pi$
$997$	27.9825	+	8.21640i	0.886215	+	0.260216i	0.193217	+	0.981156i	$0.438108\pi$
$998$		0			0
$999$	5.79123	−	2.31846i	0.183226	−	0.0733528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.49.2	✓	120
67.26	even	33	inner	804.2.y.b.361.2	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.49.2	✓	120	1.1	even	1	trivial
804.2.y.b.361.2	yes	120	67.26	even	33	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 - 0.540641i) q^{3} +(-0.355125 - 2.46995i) q^{5} +(1.47905 + 0.141233i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.841254 - 0.540641i) q^{3} +(-0.355125 - 2.46995i) q^{5} +(1.47905 + 0.141233i) q^{7} +(0.415415 + 0.909632i) q^{9} +(-5.48535 - 2.19600i) q^{11} +(-2.97924 - 2.84070i) q^{13} +(-1.03661 + 2.26985i) q^{15} +(-2.20441 + 6.36922i) q^{17} +(3.49676 - 0.333900i) q^{19} +(-1.16790 - 0.918450i) q^{21} +(0.152650 - 3.20453i) q^{23} +(-1.17707 + 0.345620i) q^{25} +(0.142315 - 0.989821i) q^{27} +(-3.60506 + 6.24415i) q^{29} +(1.09094 - 1.04021i) q^{31} +(3.42732 + 4.81300i) q^{33} +(-0.176412 - 3.70335i) q^{35} +(3.11904 + 5.40233i) q^{37} +(0.970499 + 4.00045i) q^{39} +(-4.79453 + 0.924070i) q^{41} +(-8.41053 - 9.70626i) q^{43} +(2.09922 - 1.34909i) q^{45} +(-9.68103 + 4.99092i) q^{47} +(-4.70585 - 0.906977i) q^{49} +(5.29793 - 4.16634i) q^{51} +(5.19018 - 5.98979i) q^{53} +(-3.47603 + 14.3284i) q^{55} +(-3.12218 - 1.60960i) q^{57} +(-11.5248 - 3.38399i) q^{59} +(0.979919 - 0.392300i) q^{61} +(0.485952 + 1.40407i) q^{63} +(-5.95839 + 8.36739i) q^{65} +(-6.24891 + 5.28688i) q^{67} +(-1.86092 + 2.61329i) q^{69} +(0.204053 + 0.589573i) q^{71} +(-6.65132 + 2.66279i) q^{73} +(1.17707 + 0.345620i) q^{75} +(-7.80299 - 4.02272i) q^{77} +(-0.340589 + 1.40392i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(12.0626 - 9.48612i) q^{83} +(16.5145 + 3.18291i) q^{85} +(6.40862 - 3.30387i) q^{87} +(14.0357 - 9.02019i) q^{89} +(-4.00526 - 4.62232i) q^{91} +(-1.48014 + 0.285273i) q^{93} +(-2.06651 - 8.51825i) q^{95} +(2.46726 + 4.27341i) q^{97} +(-0.281142 - 5.90191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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