LMFDB - Embedded newform 225.3.o.b.193.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,3,Mod(7,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("225.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.o (of order $12$, degree $4$, 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:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.6
Character	$\chi$	$=$	225.193
Dual form			225.3.o.b.7.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.725667 + 0.194442i) q^{2} +(-2.68329 + 1.34163i) q^{3} +(-2.97532 - 1.71780i) q^{4} +(-2.20804 + 0.451834i) q^{6} +(1.79727 + 0.481578i) q^{7} +(-3.94998 - 3.94998i) q^{8} +(5.40005 - 7.19996i) q^{9} +(5.82294 + 10.0856i) q^{11} +(10.2883 + 0.617573i) q^{12} +(19.8070 - 5.30726i) q^{13} +(1.21058 + 0.698930i) q^{14} +(4.77288 + 8.26686i) q^{16} +(10.0254 - 10.0254i) q^{17} +(5.31861 - 4.17477i) q^{18} +10.8032i q^{19} +(-5.46870 + 1.11907i) q^{21} +(2.26444 + 8.45102i) q^{22} +(1.34569 - 0.360576i) q^{23} +(15.8983 + 5.29951i) q^{24} +15.4052 q^{26} +(-4.83020 + 26.5644i) q^{27} +(-4.52021 - 4.52021i) q^{28} +(20.7968 - 12.0070i) q^{29} +(21.6233 - 37.4526i) q^{31} +(7.63926 + 28.5101i) q^{32} +(-29.1558 - 19.2504i) q^{33} +(9.22442 - 5.32572i) q^{34} +(-28.4350 + 12.1460i) q^{36} +(32.5443 - 32.5443i) q^{37} +(-2.10058 + 7.83949i) q^{38} +(-46.0274 + 40.8145i) q^{39} +(-20.5409 + 35.5778i) q^{41} +(-4.18605 - 0.251275i) q^{42} +(-2.14721 + 8.01349i) q^{43} -40.0106i q^{44} +1.04663 q^{46} +(-17.2577 - 4.62418i) q^{47} +(-23.8981 - 15.7789i) q^{48} +(-39.4370 - 22.7689i) q^{49} +(-13.4506 + 40.3513i) q^{51} +(-68.0488 - 18.2336i) q^{52} +(51.3281 + 51.3281i) q^{53} +(-8.67035 + 18.3377i) q^{54} +(-5.19697 - 9.00141i) q^{56} +(-14.4938 - 28.9880i) q^{57} +(17.4262 - 4.66933i) q^{58} +(24.3449 + 14.0555i) q^{59} +(-41.1002 - 71.1876i) q^{61} +(22.9736 - 22.9736i) q^{62} +(13.1727 - 10.3398i) q^{63} -16.0088i q^{64} +(-17.4143 - 19.6385i) q^{66} +(-8.65757 - 32.3105i) q^{67} +(-47.0502 + 12.6071i) q^{68} +(-3.12710 + 2.77294i) q^{69} +99.6917 q^{71} +(-49.7697 + 7.10958i) q^{72} +(22.3583 + 22.3583i) q^{73} +(29.9443 - 17.2883i) q^{74} +(18.5577 - 32.1428i) q^{76} +(5.60840 + 20.9308i) q^{77} +(-41.3366 + 20.6681i) q^{78} +(-52.9926 + 30.5953i) q^{79} +(-22.6788 - 77.7603i) q^{81} +(-21.8237 + 21.8237i) q^{82} +(-13.3760 + 49.9199i) q^{83} +(18.1935 + 6.06456i) q^{84} +(-3.11631 + 5.39761i) q^{86} +(-39.6947 + 60.1198i) q^{87} +(16.8375 - 62.8384i) q^{88} +113.914i q^{89} +38.1544 q^{91} +(-4.62324 - 1.23879i) q^{92} +(-7.77386 + 129.506i) q^{93} +(-11.6242 - 6.71123i) q^{94} +(-58.7483 - 66.2517i) q^{96} +(29.5689 + 7.92297i) q^{97} +(-24.1909 - 24.1909i) q^{98} +(104.060 + 12.5380i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + 6 q^{3} - 24 q^{6} + 2 q^{7} + 24 q^{8} + 8 q^{11} + 30 q^{12} + 2 q^{13} + 28 q^{16} - 28 q^{17} - 48 q^{18} + 12 q^{21} - 14 q^{22} - 82 q^{23} - 112 q^{26} + 198 q^{27} + 88 q^{28} - 4 q^{31}+ \cdots + 1876 q^{98}+O(q^{100}) $ 40 * q + 2 * q^2 + 6 * q^3 - 24 * q^6 + 2 * q^7 + 24 * q^8 + 8 * q^11 + 30 * q^12 + 2 * q^13 + 28 * q^16 - 28 * q^17 - 48 * q^18 + 12 * q^21 - 14 * q^22 - 82 * q^23 - 112 * q^26 + 198 * q^27 + 88 * q^28 - 4 * q^31 + 14 * q^32 - 96 * q^33 + 264 * q^36 + 92 * q^37 - 330 * q^38 - 28 * q^41 - 498 * q^42 + 2 * q^43 - 136 * q^46 - 64 * q^47 + 510 * q^48 - 396 * q^51 + 74 * q^52 + 608 * q^53 - 192 * q^56 + 114 * q^57 - 30 * q^58 + 92 * q^61 + 100 * q^62 - 24 * q^63 + 588 * q^66 + 80 * q^67 - 626 * q^68 + 248 * q^71 + 162 * q^72 + 8 * q^73 - 96 * q^76 - 338 * q^77 - 1062 * q^78 + 204 * q^81 - 104 * q^82 - 370 * q^83 - 328 * q^86 - 534 * q^87 + 210 * q^88 + 152 * q^91 - 388 * q^92 + 1062 * q^93 - 876 * q^96 - 292 * q^97 + 1876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.725667	+	0.194442i	0.362833	+	0.0972209i	0.435630	−	0.900126i	$-0.356526\pi$
$2$	0.725667	+	0.194442i	0.362833	+	0.0972209i	−0.0727965	+	0.997347i	$0.523192\pi$
$3$	−2.68329	+	1.34163i	−0.894429	+	0.447210i
$3$	−2.68329	+	1.34163i	−0.894429	+	0.447210i
$4$	−2.97532	−	1.71780i	−0.743829	−	0.429450i
$5$		0			0
$5$		0			0
$6$	−2.20804	+	0.451834i	−0.368007	+	0.0753056i
$7$	1.79727	+	0.481578i	0.256753	+	0.0687969i	0.384900	−	0.922958i	$-0.374236\pi$
$7$	1.79727	+	0.481578i	0.256753	+	0.0687969i	−0.128146	+	0.991755i	$0.540903\pi$
$8$	−3.94998	−	3.94998i	−0.493747	−	0.493747i
$9$	5.40005	−	7.19996i	0.600006	−	0.799996i
$10$		0			0
$11$	5.82294	+	10.0856i	0.529358	+	0.916875i	0.999414	+	0.0342381i	$0.0109005\pi$
$11$	5.82294	+	10.0856i	0.529358	+	0.916875i	−0.470056	+	0.882637i	$0.655766\pi$
$12$	10.2883	+	0.617573i	0.857357	+	0.0514644i
$13$	19.8070	−	5.30726i	1.52361	−	0.408251i	0.602684	−	0.797980i	$-0.294098\pi$
$13$	19.8070	−	5.30726i	1.52361	−	0.408251i	0.920930	+	0.389729i	$0.127431\pi$
$14$	1.21058	+	0.698930i	0.0864702	+	0.0499236i
$15$		0			0
$16$	4.77288	+	8.26686i	0.298305	+	0.516679i
$17$	10.0254	−	10.0254i	0.589728	−	0.589728i	−0.347830	−	0.937558i	$-0.613081\pi$
$17$	10.0254	−	10.0254i	0.589728	−	0.589728i	0.937558	+	0.347830i	$0.113081\pi$
$18$	5.31861	−	4.17477i	0.295478	−	0.231932i
$19$			10.8032i			0.568587i	0.958737	+	0.284294i	$0.0917590\pi$
$19$			10.8032i			0.568587i	−0.958737	+	0.284294i	$0.908241\pi$
$20$		0			0
$21$	−5.46870	+	1.11907i	−0.260414	+	0.0532889i
$22$	2.26444	+	8.45102i	0.102929	+	0.384137i
$23$	1.34569	−	0.360576i	0.0585081	−	0.0156772i	−0.229446	−	0.973321i	$-0.573692\pi$
$23$	1.34569	−	0.360576i	0.0585081	−	0.0156772i	0.287954	+	0.957644i	$0.407025\pi$
$24$	15.8983	+	5.29951i	0.662430	+	0.220813i
$25$		0			0
$26$	15.4052			0.592508
$27$	−4.83020	+	26.5644i	−0.178896	+	0.983868i
$28$	−4.52021	−	4.52021i	−0.161436	−	0.161436i
$29$	20.7968	−	12.0070i	0.717130	−	0.414035i	−0.0965656	−	0.995327i	$-0.530786\pi$
$29$	20.7968	−	12.0070i	0.717130	−	0.414035i	0.813695	+	0.581292i	$0.197452\pi$
$30$		0			0
$31$	21.6233	−	37.4526i	0.697524	−	1.20815i	−0.271798	−	0.962354i	$-0.587618\pi$
$31$	21.6233	−	37.4526i	0.697524	−	1.20815i	0.969322	−	0.245793i	$-0.0790484\pi$
$32$	7.63926	+	28.5101i	0.238727	+	0.890941i
$33$	−29.1558	−	19.2504i	−0.883509	−	0.583345i
$34$	9.22442	−	5.32572i	0.271307	−	0.156639i
$35$		0			0
$36$	−28.4350	+	12.1460i	−0.789860	+	0.337388i
$37$	32.5443	−	32.5443i	0.879576	−	0.879576i	−0.113915	−	0.993491i	$-0.536339\pi$
$37$	32.5443	−	32.5443i	0.879576	−	0.879576i	0.993491	+	0.113915i	$0.0363391\pi$
$38$	−2.10058	+	7.83949i	−0.0552785	+	0.206302i
$39$	−46.0274	+	40.8145i	−1.18019	+	1.04653i
$40$		0			0
$41$	−20.5409	+	35.5778i	−0.500997	+	0.867752i	0.499002	+	0.866601i	$0.333700\pi$
$41$	−20.5409	+	35.5778i	−0.500997	+	0.867752i	−0.999999	+	0.00115173i	$0.999633\pi$
$42$	−4.18605	−	0.251275i	−0.0996678	−	0.00598274i
$43$	−2.14721	+	8.01349i	−0.0499351	+	0.186360i	−0.986388	−	0.164432i	$-0.947421\pi$
$43$	−2.14721	+	8.01349i	−0.0499351	+	0.186360i	0.936453	+	0.350792i	$0.114088\pi$
$44$		−	40.0106i		−	0.909331i
$45$		0			0
$46$	1.04663			0.0227528
$47$	−17.2577	−	4.62418i	−0.367185	−	0.0983868i	0.0705087	−	0.997511i	$-0.477538\pi$
$47$	−17.2577	−	4.62418i	−0.367185	−	0.0983868i	−0.437693	+	0.899124i	$0.644204\pi$
$48$	−23.8981	−	15.7789i	−0.497876	−	0.328728i
$49$	−39.4370	−	22.7689i	−0.804836	−	0.464672i
$50$		0			0
$51$	−13.4506	+	40.3513i	−0.263737	+	0.791202i
$52$	−68.0488	−	18.2336i	−1.30863	−	0.350647i
$53$	51.3281	+	51.3281i	0.968455	+	0.968455i	0.999517	−	0.0310621i	$-0.00988897\pi$
$53$	51.3281	+	51.3281i	0.968455	+	0.968455i	−0.0310621	+	0.999517i	$0.509889\pi$
$54$	−8.67035	+	18.3377i	−0.160562	+	0.339588i
$55$		0			0
$56$	−5.19697	−	9.00141i	−0.0928030	−	0.160739i
$57$	−14.4938	−	28.9880i	−0.254278	−	0.508561i
$58$	17.4262	−	4.66933i	0.300451	−	0.0805057i
$59$	24.3449	+	14.0555i	0.412625	+	0.238229i	0.691917	−	0.721977i	$-0.256766\pi$
$59$	24.3449	+	14.0555i	0.412625	+	0.238229i	−0.279292	+	0.960206i	$0.590100\pi$
$60$		0			0
$61$	−41.1002	−	71.1876i	−0.673774	−	1.16701i	−0.976826	−	0.214036i	$-0.931339\pi$
$61$	−41.1002	−	71.1876i	−0.673774	−	1.16701i	0.303052	−	0.952974i	$-0.401994\pi$
$62$	22.9736	−	22.9736i	0.370542	−	0.370542i
$63$	13.1727	−	10.3398i	0.209091	−	0.164123i
$64$		−	16.0088i		−	0.250137i
$65$		0			0
$66$	−17.4143	−	19.6385i	−0.263853	−	0.297552i
$67$	−8.65757	−	32.3105i	−0.129217	−	0.482246i	0.870737	−	0.491748i	$-0.163642\pi$
$67$	−8.65757	−	32.3105i	−0.129217	−	0.482246i	−0.999955	+	0.00950210i	$0.996975\pi$
$68$	−47.0502	+	12.6071i	−0.691915	+	0.185398i
$69$	−3.12710	+	2.77294i	−0.0453203	+	0.0401876i
$70$		0			0
$71$	99.6917			1.40411			0.702054	−	0.712123i	$-0.252266\pi$
$71$	99.6917			1.40411			0.702054	+	0.712123i	$0.252266\pi$
$72$	−49.7697	+	7.10958i	−0.691246	+	0.0987442i
$73$	22.3583	+	22.3583i	0.306278	+	0.306278i	0.843464	−	0.537186i	$-0.180513\pi$
$73$	22.3583	+	22.3583i	0.306278	+	0.306278i	−0.537186	+	0.843464i	$0.680513\pi$
$74$	29.9443	−	17.2883i	0.404653	−	0.233626i
$75$		0			0
$76$	18.5577	−	32.1428i	0.244180	−	0.422932i
$77$	5.60840	+	20.9308i	0.0728363	+	0.271829i
$78$	−41.3366	+	20.6681i	−0.529956	+	0.264976i
$79$	−52.9926	+	30.5953i	−0.670793	+	0.387282i	−0.796377	−	0.604801i	$-0.793253\pi$
$79$	−52.9926	+	30.5953i	−0.670793	+	0.387282i	0.125584	+	0.992083i	$0.459919\pi$
$80$		0			0
$81$	−22.6788	−	77.7603i	−0.279986	−	0.960004i
$82$	−21.8237	+	21.8237i	−0.266142	+	0.266142i
$83$	−13.3760	+	49.9199i	−0.161157	+	0.601444i	0.837343	+	0.546678i	$0.184108\pi$
$83$	−13.3760	+	49.9199i	−0.161157	+	0.601444i	−0.998499	+	0.0547660i	$0.982559\pi$
$84$	18.1935	+	6.06456i	0.216589	+	0.0721971i
$85$		0			0
$86$	−3.11631	+	5.39761i	−0.0362362	+	0.0627630i
$87$	−39.6947	+	60.1198i	−0.456261	+	0.691033i
$88$	16.8375	−	62.8384i	0.191335	−	0.714073i
$89$			113.914i			1.27993i	0.768402	+	0.639967i	$0.221052\pi$
$89$			113.914i			1.27993i	−0.768402	+	0.639967i	$0.778948\pi$
$90$		0			0
$91$	38.1544			0.419279
$92$	−4.62324	−	1.23879i	−0.0502526	−	0.0134651i
$93$	−7.77386	+	129.506i	−0.0835899	+	1.39254i
$94$	−11.6242	−	6.71123i	−0.123662	−	0.0713960i
$95$		0			0
$96$	−58.7483	−	66.2517i	−0.611962	−	0.690122i
$97$	29.5689	+	7.92297i	0.304834	+	0.0816801i	0.407994	−	0.912985i	$-0.366229\pi$
$97$	29.5689	+	7.92297i	0.304834	+	0.0816801i	−0.103160	+	0.994665i	$0.532895\pi$
$98$	−24.1909	−	24.1909i	−0.246845	−	0.246845i
$99$	104.060	+	12.5380i	1.05111	+	0.126646i
$100$		0			0
$101$	29.8920	+	51.7745i	0.295961	+	0.512619i	0.975208	−	0.221291i	$-0.0710270\pi$
$101$	29.8920	+	51.7745i	0.295961	+	0.512619i	−0.679247	+	0.733909i	$0.737694\pi$
$102$	−17.6066	+	26.6662i	−0.172614	+	0.261433i
$103$	48.8939	−	13.1011i	0.474698	−	0.127195i	−0.0135348	−	0.999908i	$-0.504308\pi$
$103$	48.8939	−	13.1011i	0.474698	−	0.127195i	0.488233	+	0.872713i	$0.337642\pi$
$104$	−99.2006	−	57.2735i	−0.953852	−	0.550707i
$105$		0			0
$106$	27.2668	+	47.2274i	0.257234	+	0.445542i
$107$	14.8359	−	14.8359i	0.138653	−	0.138653i	−0.634374	−	0.773027i	$-0.718742\pi$
$107$	14.8359	−	14.8359i	0.138653	−	0.138653i	0.773027	+	0.634374i	$0.218742\pi$
$108$	60.0038	−	70.7403i	0.555591	−	0.655003i
$109$		−	115.290i		−	1.05770i	−0.848714	−	0.528852i	$-0.822623\pi$
$109$		−	115.290i		−	1.05770i	0.848714	−	0.528852i	$-0.177377\pi$
$110$		0			0
$111$	−43.6633	+	130.988i	−0.393363	+	1.18007i
$112$	4.59703	+	17.1563i	0.0410449	+	0.153182i
$113$	−101.212	+	27.1198i	−0.895686	+	0.239998i	−0.677163	−	0.735833i	$-0.736791\pi$
$113$	−101.212	+	27.1198i	−0.895686	+	0.239998i	−0.218523	+	0.975832i	$0.570124\pi$
$114$	−4.88123	−	23.8538i	−0.0428178	−	0.209244i
$115$		0			0
$116$	−82.5026			−0.711229
$117$	68.7466	−	171.269i	0.587578	−	1.46384i
$118$	14.9333	+	14.9333i	0.126553	+	0.126553i
$119$	22.8463	−	13.1903i	0.191986	−	0.110843i
$120$		0			0
$121$	−7.31319	+	12.6668i	−0.0604396	+	0.104684i
$122$	−15.9832	−	59.6501i	−0.131010	−	0.488935i
$123$	7.38473	−	123.024i	0.0600385	−	1.00019i
$124$	−128.672	+	74.2889i	−1.03768	+	0.599104i
$125$		0			0
$126$	11.5695	−	4.94189i	0.0918213	−	0.0392213i
$127$	−56.0831	+	56.0831i	−0.441599	+	0.441599i	−0.892549	−	0.450950i	$-0.851085\pi$
$127$	−56.0831	+	56.0831i	−0.441599	+	0.441599i	0.450950	+	0.892549i	$0.351085\pi$
$128$	33.6698	−	125.657i	0.263045	−	0.981699i
$129$	−4.98957	−	24.3832i	−0.0386788	−	0.189017i
$130$		0			0
$131$	−2.31731	+	4.01371i	−0.0176894	+	0.0306390i	−0.874735	−	0.484602i	$-0.838964\pi$
$131$	−2.31731	+	4.01371i	−0.0176894	+	0.0306390i	0.857045	+	0.515241i	$0.172298\pi$
$132$	53.6794	+	107.360i	0.406662	+	0.813332i
$133$	−5.20256	+	19.4162i	−0.0391170	+	0.145987i
$134$		−	25.1300i		−	0.187538i
$135$		0			0
$136$	−79.1999			−0.582352
$137$	−2.29751	−	0.615617i	−0.0167702	−	0.00449355i	0.250424	−	0.968136i	$-0.419430\pi$
$137$	−2.29751	−	0.615617i	−0.0167702	−	0.00449355i	−0.267194	+	0.963643i	$0.586097\pi$
$138$	−2.80841	+	1.40419i	−0.0203508	+	0.0101753i
$139$	221.925	+	128.128i	1.59658	+	0.921786i	0.992140	+	0.125136i	$0.0399367\pi$
$139$	221.925	+	128.128i	1.59658	+	0.921786i	0.604441	+	0.796650i	$0.293397\pi$
$140$		0			0
$141$	52.5112	−	10.7454i	0.372420	−	0.0762087i
$142$	72.3429	+	19.3842i	0.509457	+	0.136509i
$143$	168.862	+	168.862i	1.18085	+	1.18085i
$144$	85.2949	+	10.2770i	0.592325	+	0.0713680i
$145$		0			0
$146$	11.8773	+	20.5721i	0.0813513	+	0.140905i
$147$	136.368	+	8.18575i	0.927675	+	0.0556854i
$148$	−152.734	+	40.9250i	−1.03199	+	0.276520i
$149$	−81.5954	−	47.1091i	−0.547620	−	0.316168i	0.200542	−	0.979685i	$-0.435730\pi$
$149$	−81.5954	−	47.1091i	−0.547620	−	0.316168i	−0.748161	+	0.663517i	$0.769063\pi$
$150$		0			0
$151$	14.0475	+	24.3310i	0.0930299	+	0.161133i	0.908785	−	0.417265i	$-0.137011\pi$
$151$	14.0475	+	24.3310i	0.0930299	+	0.161133i	−0.815755	+	0.578398i	$0.803678\pi$
$152$	42.6722	−	42.6722i	0.280738	−	0.280738i
$153$	−18.0447	−	126.320i	−0.117939	−	0.825619i
$154$			16.2793i			0.105710i
$155$		0			0
$156$	207.057	−	42.3704i	1.32729	−	0.271605i
$157$	−9.98621	−	37.2690i	−0.0636064	−	0.237382i	0.926803	−	0.375549i	$-0.122546\pi$
$157$	−9.98621	−	37.2690i	−0.0636064	−	0.237382i	−0.990409	+	0.138166i	$0.955879\pi$
$158$	−44.4040	+	11.8980i	−0.281038	+	0.0753039i
$159$	−206.591	−	68.8647i	−1.29932	−	0.433111i
$160$		0			0
$161$	2.59221			0.0161007
$162$	−1.33742	−	60.8378i	−0.00825566	−	0.375542i
$163$	−140.797	−	140.797i	−0.863787	−	0.863787i	0.127989	−	0.991776i	$-0.459148\pi$
$163$	−140.797	−	140.797i	−0.863787	−	0.863787i	−0.991776	+	0.127989i	$0.959148\pi$
$164$	122.231	−	70.5703i	0.745313	−	0.430306i
$165$		0			0
$166$	−19.4130	+	33.6243i	−0.116946	+	0.202556i
$167$	73.2232	+	273.273i	0.438462	+	1.63636i	0.732642	+	0.680614i	$0.238287\pi$
$167$	73.2232	+	273.273i	0.438462	+	1.63636i	−0.294180	+	0.955750i	$0.595047\pi$
$168$	26.0215	+	17.1810i	0.154890	+	0.102268i
$169$	217.791	−	125.742i	1.28870	−	0.744033i
$170$		0			0
$171$	77.7823	+	58.3376i	0.454867	+	0.341156i
$172$	20.1542	−	20.1542i	0.117176	−	0.117176i
$173$	80.2289	−	299.418i	0.463751	−	1.73074i	−0.197248	−	0.980354i	$-0.563200\pi$
$173$	80.2289	−	299.418i	0.463751	−	1.73074i	0.660998	−	0.750387i	$-0.270133\pi$
$174$	−40.4949	+	35.9087i	−0.232729	+	0.206372i
$175$		0			0
$176$	−55.5843	+	96.2748i	−0.315820	+	0.547016i
$177$	−84.1816	−	5.05315i	−0.475602	−	0.0285489i
$178$	−22.1497	+	82.6637i	−0.124436	+	0.464403i
$179$			151.884i			0.848512i	0.905542	+	0.424256i	$0.139464\pi$
$179$			151.884i			0.848512i	−0.905542	+	0.424256i	$0.860536\pi$
$180$		0			0
$181$	48.0978			0.265734			0.132867	−	0.991134i	$-0.457582\pi$
$181$	48.0978			0.265734			0.132867	+	0.991134i	$0.457582\pi$
$182$	27.6874	+	7.41881i	0.152128	+	0.0407627i
$183$	205.791	+	135.876i	1.12454	+	0.742489i
$184$	−6.73969	−	3.89116i	−0.0366288	−	0.0211476i
$185$		0			0
$186$	−30.8227	+	92.4669i	−0.165713	+	0.497134i
$187$	159.489	+	42.7350i	0.852883	+	0.228529i
$188$	43.4036	+	43.4036i	0.230870	+	0.230870i
$189$	−21.4741	+	45.4174i	−0.113619	+	0.240304i
$190$		0			0
$191$	−181.698	−	314.711i	−0.951300	−	1.64770i	−0.742617	−	0.669717i	$-0.766416\pi$
$191$	−181.698	−	314.711i	−0.951300	−	1.64770i	−0.208683	−	0.977983i	$-0.566918\pi$
$192$	21.4779	+	42.9562i	0.111864	+	0.223730i
$193$	−11.5607	+	3.09769i	−0.0599001	+	0.0160502i	−0.288645	−	0.957436i	$-0.593205\pi$
$193$	−11.5607	+	3.09769i	−0.0599001	+	0.0160502i	0.228745	+	0.973486i	$0.426538\pi$
$194$	19.9166	+	11.4989i	0.102663	+	0.0592725i
$195$		0			0
$196$	78.2250	+	135.490i	0.399107	+	0.691274i
$197$	−45.3414	+	45.3414i	−0.230159	+	0.230159i	−0.812759	−	0.582600i	$-0.802036\pi$
$197$	−45.3414	+	45.3414i	−0.230159	+	0.230159i	0.582600	+	0.812759i	$0.302036\pi$
$198$	73.0751	+	29.3321i	0.369066	+	0.148142i
$199$			17.0082i			0.0854685i	0.999086	+	0.0427343i	$0.0136069\pi$
$199$			17.0082i			0.0854685i	−0.999086	+	0.0427343i	$0.986393\pi$
$200$		0			0
$201$	66.5795	+	75.0831i	0.331241	+	0.373548i
$202$	11.6245	+	43.3833i	0.0575471	+	0.214769i
$203$	43.1598	−	11.5646i	0.212610	−	0.0569686i
$204$	109.335	−	96.9524i	0.535957	−	0.475257i
$205$		0			0
$206$	38.0281			0.184602
$207$	4.67065	−	11.6360i	0.0225635	−	0.0562126i
$208$	138.411	+	138.411i	0.665436	+	0.665436i
$209$	−108.957	+	62.9061i	−0.521323	+	0.300986i
$210$		0			0
$211$	−148.887	+	257.879i	−0.705624	+	1.22218i	0.260842	+	0.965382i	$0.416000\pi$
$211$	−148.887	+	257.879i	−0.705624	+	1.22218i	−0.966466	+	0.256795i	$0.917333\pi$
$212$	−64.5460	−	240.889i	−0.304462	−	1.13627i
$213$	−267.501	+	133.749i	−1.25588	+	0.627932i
$214$	13.6506	−	7.88119i	0.0637879	−	0.0368280i
$215$		0			0
$216$	124.008	−	85.8497i	0.574111	−	0.397452i
$217$	56.8993	−	56.8993i	0.262209	−	0.262209i
$218$	22.4172	−	83.6620i	0.102831	−	0.383771i
$219$	−89.9903	−	29.9971i	−0.410915	−	0.136973i
$220$		0			0
$221$	145.365	−	251.779i	0.657760	−	1.13927i
$222$	−57.1545	+	86.5638i	−0.257453	+	0.389927i
$223$	8.27356	−	30.8773i	0.0371012	−	0.138463i	−0.944891	−	0.327385i	$-0.893833\pi$
$223$	8.27356	−	30.8773i	0.0371012	−	0.138463i	0.981992	+	0.188922i	$0.0604992\pi$
$224$			54.9194i			0.245176i
$225$		0			0
$226$	−78.7197			−0.348317
$227$	−377.838	−	101.241i	−1.66449	−	0.445997i	−0.700870	−	0.713289i	$-0.747205\pi$
$227$	−377.838	−	101.241i	−1.66449	−	0.445997i	−0.963616	+	0.267292i	$0.913871\pi$
$228$	−6.67174	+	111.146i	−0.0292620	+	0.487482i
$229$	−217.228	−	125.417i	−0.948594	−	0.547671i	−0.0559502	−	0.998434i	$-0.517819\pi$
$229$	−217.228	−	125.417i	−0.948594	−	0.547671i	−0.892644	+	0.450762i	$0.851152\pi$
$230$		0			0
$231$	−43.1304	−	48.6390i	−0.186712	−	0.210558i
$232$	−129.574	−	34.7193i	−0.558509	−	0.149652i
$233$	−239.086	−	239.086i	−1.02612	−	1.02612i	−0.999650	−	0.0264709i	$-0.991573\pi$
$233$	−239.086	−	239.086i	−1.02612	−	1.02612i	−0.0264709	−	0.999650i	$-0.508427\pi$
$234$	83.1890	−	110.917i	0.355508	−	0.474004i
$235$		0			0
$236$	−48.2891	−	83.6392i	−0.204615	−	0.354404i
$237$	101.147	−	153.193i	0.426780	−	0.646382i
$238$	19.1436	−	5.12950i	0.0804352	−	0.0215525i
$239$	33.8483	+	19.5423i	0.141625	+	0.0817672i	0.569138	−	0.822242i	$-0.307277\pi$
$239$	33.8483	+	19.5423i	0.141625	+	0.0817672i	−0.427513	+	0.904009i	$0.640610\pi$
$240$		0			0
$241$	−41.8525	−	72.4907i	−0.173662	−	0.300791i	0.766036	−	0.642798i	$-0.222227\pi$
$241$	−41.8525	−	72.4907i	−0.173662	−	0.300791i	−0.939697	+	0.342007i	$0.888893\pi$
$242$	−7.76989	+	7.76989i	−0.0321070	+	0.0321070i
$243$	165.179	+	178.227i	0.679751	+	0.733443i
$244$			282.408i			1.15741i
$245$		0			0
$246$	29.2798	−	87.8384i	0.119024	−	0.357067i
$247$	57.3352	+	213.978i	0.232126	+	0.866307i
$248$	−233.348	+	62.5254i	−0.940920	+	0.252119i
$249$	−31.0824	−	151.895i	−0.124829	−	0.610020i
$250$		0			0
$251$	−116.674			−0.464837			−0.232418	−	0.972616i	$-0.574664\pi$
$251$	−116.674			−0.464837			−0.232418	+	0.972616i	$0.574664\pi$
$252$	−56.9546	+	8.13594i	−0.226011	+	0.0322855i
$253$	11.4725	+	11.4725i	0.0453458	+	0.0453458i
$254$	−51.6025	+	29.7927i	−0.203159	+	0.117294i
$255$		0			0
$256$	16.8485	−	29.1825i	0.0658146	−	0.113994i
$257$	1.23843	+	4.62189i	0.00481880	+	0.0179840i	0.968293	−	0.249816i	$-0.0803701\pi$
$257$	1.23843	+	4.62189i	0.00481880	+	0.0179840i	−0.963475	+	0.267800i	$0.913703\pi$
$258$	1.12036	−	18.6643i	0.00434247	−	0.0723422i
$259$	74.1637	−	42.8184i	0.286346	−	0.165322i
$260$		0			0
$261$	25.8536	−	214.574i	0.0990559	−	0.822124i
$262$	−2.46203	+	2.46203i	−0.00939706	+	0.00939706i
$263$	25.3145	−	94.4750i	0.0962529	−	0.359221i	−0.900954	−	0.433916i	$-0.857132\pi$
$263$	25.3145	−	94.4750i	0.0962529	−	0.359221i	0.997206	+	0.0746949i	$0.0237983\pi$
$264$	39.1261	+	191.203i	0.148205	+	0.724255i
$265$		0			0
$266$	−7.55065	+	13.0781i	−0.0283859	+	0.0491658i
$267$	−152.831	−	305.664i	−0.572400	−	1.14481i
$268$	−29.7440	+	111.006i	−0.110985	+	0.414201i
$269$			212.871i			0.791340i	0.918393	+	0.395670i	$0.129488\pi$
$269$			212.871i			0.791340i	−0.918393	+	0.395670i	$0.870512\pi$
$270$		0			0
$271$	−180.243			−0.665102			−0.332551	−	0.943085i	$-0.607909\pi$
$271$	−180.243			−0.665102			−0.332551	+	0.943085i	$0.607909\pi$
$272$	130.728	+	35.0285i	0.480618	+	0.128781i
$273$	−102.379	+	51.1891i	−0.375016	+	0.187506i
$274$	−1.54753	−	0.893465i	−0.00564791	−	0.00326082i
$275$		0			0
$276$	14.0675	−	2.87864i	0.0509691	−	0.0104299i
$277$	−316.123	−	84.7048i	−1.14124	−	0.305794i	−0.361789	−	0.932260i	$-0.617834\pi$
$277$	−316.123	−	84.7048i	−1.14124	−	0.305794i	−0.779448	+	0.626467i	$0.784501\pi$
$278$	136.130	+	136.130i	0.489676	+	0.489676i
$279$	−152.890	−	357.932i	−0.547994	−	1.28291i
$280$		0			0
$281$	−15.6356	−	27.0816i	−0.0556426	−	0.0963758i	0.836862	−	0.547413i	$-0.184387\pi$
$281$	−15.6356	−	27.0816i	−0.0556426	−	0.0963758i	−0.892505	+	0.451037i	$0.851054\pi$
$282$	40.1950	+	2.41278i	0.142535	+	0.00855596i
$283$	−195.826	+	52.4715i	−0.691966	+	0.185412i	−0.587629	−	0.809130i	$-0.699939\pi$
$283$	−195.826	+	52.4715i	−0.691966	+	0.185412i	−0.104337	+	0.994542i	$0.533272\pi$
$284$	−296.614	−	171.250i	−1.04442	−	0.602995i
$285$		0			0
$286$	89.7036	+	155.371i	0.313649	+	0.543256i
$287$	−54.0511	+	54.0511i	−0.188331	+	0.188331i
$288$	246.524	+	98.9537i	0.855986	+	0.343589i
$289$			87.9840i			0.304443i
$290$		0			0
$291$	−89.9715	+	18.4110i	−0.309181	+	0.0632679i
$292$	−28.1159	−	104.930i	−0.0962875	−	0.359350i
$293$	37.6696	−	10.0935i	0.128565	−	0.0344490i	−0.193963	−	0.981009i	$-0.562134\pi$
$293$	37.6696	−	10.0935i	0.128565	−	0.0344490i	0.322528	+	0.946560i	$0.395467\pi$
$294$	97.3662	+	32.4558i	0.331178	+	0.110394i
$295$		0			0
$296$	−257.098			−0.868576
$297$	−296.045	+	105.967i	−0.996784	+	0.356793i
$298$	−50.0510	−	50.0510i	−0.167957	−	0.167957i
$299$	24.7403	−	14.2838i	0.0827435	−	0.0477720i
$300$		0			0
$301$	−7.71824	+	13.3684i	−0.0256420	+	0.0444132i
$302$	5.46285	+	20.3876i	0.0180889	+	0.0675087i
$303$	−149.671	−	98.8217i	−0.493964	−	0.326144i
$304$	−89.3082	+	51.5621i	−0.293777	+	0.169612i
$305$		0			0
$306$	11.4674	−	95.1747i	0.0374751	−	0.311028i
$307$	28.4359	−	28.4359i	0.0926251	−	0.0926251i	−0.659276	−	0.751901i	$-0.729137\pi$
$307$	28.4359	−	28.4359i	0.0926251	−	0.0926251i	0.751901	+	0.659276i	$0.229137\pi$
$308$	19.2682	−	71.9100i	0.0625591	−	0.233474i
$309$	−113.619	+	100.751i	−0.367701	+	0.326057i
$310$		0			0
$311$	−215.953	+	374.041i	−0.694381	+	1.20270i	0.276007	+	0.961156i	$0.410989\pi$
$311$	−215.953	+	374.041i	−0.694381	+	1.20270i	−0.970389	+	0.241548i	$0.922345\pi$
$312$	343.024	+	20.5906i	1.09943	+	0.0659956i
$313$	−53.6933	+	200.386i	−0.171544	+	0.640211i	0.825571	+	0.564299i	$0.190853\pi$
$313$	−53.6933	+	200.386i	−0.171544	+	0.640211i	−0.997115	+	0.0759119i	$0.975813\pi$
$314$		−	28.9866i		−	0.0923141i
$315$		0			0
$316$	210.226			0.665274
$317$	−342.998	−	91.9060i	−1.08201	−	0.289924i	−0.326593	−	0.945165i	$-0.605900\pi$
$317$	−342.998	−	91.9060i	−1.08201	−	0.289924i	−0.755420	+	0.655241i	$0.772567\pi$
$318$	−136.526	−	90.1428i	−0.429328	−	0.283468i
$319$	242.196	+	139.832i	0.759237	+	0.438345i
$320$		0			0
$321$	−19.9046	+	59.7132i	−0.0620082	+	0.186022i
$322$	1.88108	+	0.504034i	0.00584187	+	0.00156532i
$323$	108.306	+	108.306i	0.335311	+	0.335311i
$324$	−66.1000	+	270.319i	−0.204012	+	0.834319i
$325$		0			0
$326$	−74.7950	−	129.549i	−0.229432	−	0.397389i
$327$	154.676	+	309.356i	0.473016	+	0.946042i
$328$	221.668	−	59.3957i	0.675816	−	0.181084i
$329$	−28.7899	−	16.6218i	−0.0875072	−	0.0505223i
$330$		0			0
$331$	−187.451	−	324.675i	−0.566318	−	0.980891i	−0.996926	−	0.0783519i	$-0.975034\pi$
$331$	−187.451	−	324.675i	−0.566318	−	0.980891i	0.430608	−	0.902539i	$-0.358299\pi$
$332$	125.550	−	125.550i	0.378163	−	0.378163i
$333$	−58.5767	−	410.059i	−0.175906	−	1.23141i
$334$			212.543i			0.636355i
$335$		0			0
$336$	−35.3526	−	39.8678i	−0.105216	−	0.118654i
$337$	38.4732	+	143.584i	0.114164	+	0.426065i	0.999223	−	0.0394135i	$-0.0125490\pi$
$337$	38.4732	+	143.584i	0.114164	+	0.426065i	−0.885059	+	0.465478i	$0.845882\pi$
$338$	182.493	−	48.8988i	0.539920	−	0.144671i
$339$	235.197	−	208.560i	0.693797	−	0.615221i
$340$		0			0
$341$	503.643			1.47696
$342$	45.1007	+	57.4578i	0.131873	+	0.168005i
$343$	−124.383	−	124.383i	−0.362633	−	0.362633i
$344$	40.1345	−	23.1717i	0.116670	−	0.0673595i
$345$		0			0
$346$	116.439	−	201.678i	0.336528	−	0.582884i
$347$	62.5014	+	233.258i	0.180119	+	0.672214i	0.995623	+	0.0934622i	$0.0297934\pi$
$347$	62.5014	+	233.258i	0.180119	+	0.672214i	−0.815504	+	0.578752i	$0.803540\pi$
$348$	221.378	−	110.688i	0.636144	−	0.318069i
$349$	331.191	−	191.213i	0.948971	−	0.547889i	0.0562101	−	0.998419i	$-0.482098\pi$
$349$	331.191	−	191.213i	0.948971	−	0.547889i	0.892761	+	0.450530i	$0.148765\pi$
$350$		0			0
$351$	45.3127	+	551.796i	0.129096	+	1.57207i
$352$	−243.059	+	243.059i	−0.690509	+	0.690509i
$353$	−134.782	+	503.013i	−0.381819	+	1.42497i	0.461302	+	0.887243i	$0.347382\pi$
$353$	−134.782	+	503.013i	−0.381819	+	1.42497i	−0.843121	+	0.537724i	$0.819284\pi$
$354$	−60.1052	−	20.0353i	−0.169789	−	0.0565969i
$355$		0			0
$356$	195.682	−	338.931i	0.549668	−	0.952052i
$357$	−43.6067	+	66.0448i	−0.122148	+	0.184999i
$358$	−29.5325	+	110.217i	−0.0824931	+	0.307868i
$359$		−	326.956i		−	0.910741i	−0.890302	−	0.455370i	$-0.849507\pi$
$359$		−	326.956i		−	0.910741i	0.890302	−	0.455370i	$-0.150493\pi$
$360$		0			0
$361$	244.292			0.676709
$362$	34.9030	+	9.35222i	0.0964170	+	0.0258349i
$363$	2.62919	−	43.8003i	0.00724296	−	0.120662i
$364$	−113.521	−	65.5417i	−0.311872	−	0.180060i
$365$		0			0
$366$	122.916	+	138.615i	0.335836	+	0.378729i
$367$	505.039	+	135.325i	1.37613	+	0.368733i	0.869713	−	0.493557i	$-0.164304\pi$
$367$	505.039	+	135.325i	1.37613	+	0.368733i	0.506415	+	0.862290i	$0.330970\pi$
$368$	9.40362	+	9.40362i	0.0255533	+	0.0255533i
$369$	145.237	+	340.016i	0.393597	+	0.921452i
$370$		0			0
$371$	67.5322	+	116.969i	0.182028	+	0.315281i
$372$	245.596	−	371.969i	0.660204	−	0.999916i
$373$	23.4631	−	6.28693i	0.0629039	−	0.0168550i	−0.227230	−	0.973841i	$-0.572967\pi$
$373$	23.4631	−	6.28693i	0.0629039	−	0.0168550i	0.290134	+	0.956986i	$0.406300\pi$
$374$	107.426	+	62.0227i	0.287237	+	0.165836i
$375$		0			0
$376$	49.9020	+	86.4328i	0.132718	+	0.229874i
$377$	348.197	−	348.197i	0.923598	−	0.923598i
$378$	−24.4141	+	28.7825i	−0.0645874	+	0.0761441i
$379$		−	364.939i		−	0.962900i	−0.876474	−	0.481450i	$-0.840110\pi$
$379$		−	364.939i		−	0.962900i	0.876474	−	0.481450i	$-0.159890\pi$
$380$		0			0
$381$	75.2442	−	225.730i	0.197491	−	0.592466i
$382$	−70.6595	−	263.705i	−0.184972	−	0.690327i
$383$	−3.24720	+	0.870084i	−0.00847832	+	0.00227176i	−0.263056	−	0.964781i	$-0.584730\pi$
$383$	−3.24720	+	0.870084i	−0.00847832	+	0.00227176i	0.254577	+	0.967052i	$0.418064\pi$
$384$	78.2401	+	382.347i	0.203750	+	0.995696i
$385$		0			0
$386$	−8.99155			−0.0232942
$387$	46.1018	+	58.7331i	0.119126	+	0.151765i
$388$	−74.3668	−	74.3668i	−0.191667	−	0.191667i
$389$	131.808	−	76.0995i	0.338838	−	0.195628i	−0.320920	−	0.947106i	$-0.603992\pi$
$389$	131.808	−	76.0995i	0.338838	−	0.195628i	0.659758	+	0.751478i	$0.270659\pi$
$390$		0			0
$391$	9.87610	−	17.1059i	0.0252586	−	0.0437491i
$392$	65.8383	+	245.712i	0.167955	+	0.626816i
$393$	0.833107	−	13.8789i	0.00211986	−	0.0353153i
$394$	−41.7190	+	24.0865i	−0.105886	+	0.0611332i
$395$		0			0
$396$	−288.074	−	216.059i	−0.727461	−	0.545604i
$397$	275.868	−	275.868i	0.694882	−	0.694882i	−0.268420	−	0.963302i	$-0.586502\pi$
$397$	275.868	−	275.868i	0.694882	−	0.694882i	0.963302	+	0.268420i	$0.0865016\pi$
$398$	−3.30711	+	12.3423i	−0.00830933	+	0.0310108i
$399$	−12.0894	−	59.0792i	−0.0302994	−	0.148068i
$400$		0			0
$401$	−337.489	+	584.548i	−0.841618	+	1.45773i	0.0469080	+	0.998899i	$0.485063\pi$
$401$	−337.489	+	584.548i	−0.841618	+	1.45773i	−0.888526	+	0.458826i	$0.848270\pi$
$402$	33.7152	+	67.4311i	0.0838688	+	0.167739i
$403$	229.521	−	856.582i	0.569530	−	2.12551i
$404$		−	205.394i		−	0.508401i
$405$		0			0
$406$	33.5683			0.0826805
$407$	517.733	+	138.726i	1.27207	+	0.340850i
$408$	212.516	−	106.257i	0.520873	−	0.260434i
$409$	−375.213	−	216.629i	−0.917390	−	0.529655i	−0.0345887	−	0.999402i	$-0.511012\pi$
$409$	−375.213	−	216.629i	−0.917390	−	0.529655i	−0.882802	+	0.469746i	$0.844345\pi$
$410$		0			0
$411$	6.99082	−	1.43054i	0.0170093	−	0.00348063i
$412$	−167.980	−	45.0101i	−0.407718	−	0.109248i
$413$	36.9856	+	36.9856i	0.0895534	+	0.0895534i
$414$	5.65186	−	7.53570i	0.0136518	−	0.0182022i
$415$		0			0
$416$	302.621	+	524.155i	0.727455	+	1.25999i
$417$	−767.388	−	46.0639i	−1.84026	−	0.110465i
$418$	−91.2977	+	24.4631i	−0.218416	+	0.0585243i
$419$	432.869	+	249.917i	1.03310	+	0.596461i	0.917871	−	0.396878i	$-0.129907\pi$
$419$	432.869	+	249.917i	1.03310	+	0.596461i	0.115229	+	0.993339i	$0.463240\pi$
$420$		0			0
$421$	15.0425	+	26.0544i	0.0357304	+	0.0618869i	0.883338	−	0.468737i	$-0.155291\pi$
$421$	15.0425	+	26.0544i	0.0357304	+	0.0618869i	−0.847607	+	0.530624i	$0.821958\pi$
$422$	−158.185	+	158.185i	−0.374845	+	0.374845i
$423$	−126.486	+	99.2837i	−0.299022	+	0.234713i
$424$		−	405.490i		−	0.956344i
$425$		0			0
$426$	−220.123	+	45.0441i	−0.516721	+	0.105737i
$427$	−39.5859	−	147.737i	−0.0927071	−	0.345987i
$428$	−69.6265	+	18.6564i	−0.162679	+	0.0435896i
$429$	−679.655	−	226.554i	−1.58428	−	0.528099i
$430$		0			0
$431$	515.749			1.19663			0.598316	−	0.801260i	$-0.295837\pi$
$431$	515.749			1.19663			0.598316	+	0.801260i	$0.295837\pi$
$432$	−242.659	+	86.8581i	−0.561710	+	0.201060i
$433$	305.797	+	305.797i	0.706229	+	0.706229i	0.965740	−	0.259511i	$-0.0835613\pi$
$433$	305.797	+	305.797i	0.706229	+	0.706229i	−0.259511	+	0.965740i	$0.583561\pi$
$434$	52.3535	−	30.2263i	0.120630	−	0.0696458i
$435$		0			0
$436$	−198.045	+	343.024i	−0.454231	+	0.786752i
$437$	3.89535	+	14.5377i	0.00891385	+	0.0332669i
$438$	−59.4703	−	39.2658i	−0.135777	−	0.0896480i
$439$	−437.591	+	252.643i	−0.996790	+	0.575497i	−0.907297	−	0.420491i	$-0.861858\pi$
$439$	−437.591	+	252.643i	−0.996790	+	0.575497i	−0.0894929	+	0.995987i	$0.528525\pi$
$440$		0			0
$441$	−376.897	+	160.991i	−0.854642	+	0.365059i
$442$	154.443	−	154.443i	0.349418	−	0.349418i
$443$	52.3076	−	195.215i	0.118076	−	0.440665i	−0.881423	−	0.472328i	$-0.843414\pi$
$443$	52.3076	−	195.215i	0.118076	−	0.440665i	0.999499	+	0.0316632i	$0.0100804\pi$
$444$	354.923	−	314.726i	0.799377	−	0.708843i
$445$		0			0
$446$	12.0077	−	20.7979i	0.0269231	−	0.0466321i
$447$	282.147	+	16.9364i	0.631201	+	0.0378890i
$448$	7.70948	−	28.7722i	0.0172087	−	0.0642236i
$449$			145.089i			0.323138i	0.986861	+	0.161569i	$0.0516554\pi$
$449$			145.089i			0.323138i	−0.986861	+	0.161569i	$0.948345\pi$
$450$		0			0
$451$	−478.433			−1.06083
$452$	347.726	+	93.1728i	0.769305	+	0.206135i
$453$	−70.3367	−	46.4405i	−0.155269	−	0.102518i
$454$	−254.499	−	146.935i	−0.560570	−	0.323645i
$455$		0			0
$456$	−57.2514	+	171.752i	−0.125551	+	0.376649i
$457$	286.527	+	76.7746i	0.626973	+	0.167997i	0.558296	−	0.829642i	$-0.311455\pi$
$457$	286.527	+	76.7746i	0.626973	+	0.167997i	0.0686775	+	0.997639i	$0.478122\pi$
$458$	−133.249	−	133.249i	−0.290936	−	0.290936i
$459$	217.894	+	314.743i	0.474714	+	0.685714i
$460$		0			0
$461$	143.044	+	247.759i	0.310291	+	0.537439i	0.978425	−	0.206601i	$-0.0662403\pi$
$461$	143.044	+	247.759i	0.310291	+	0.537439i	−0.668135	+	0.744040i	$0.732907\pi$
$462$	−21.8408	−	43.6821i	−0.0472745	−	0.0945499i
$463$	241.707	−	64.7653i	0.522046	−	0.139882i	0.0118333	−	0.999930i	$-0.496233\pi$
$463$	241.707	−	64.7653i	0.522046	−	0.139882i	0.510213	+	0.860048i	$0.329567\pi$
$464$	198.521	+	114.616i	0.427846	+	0.247017i
$465$		0			0
$466$	−127.008	−	219.985i	−0.272550	−	0.472071i
$467$	71.3291	−	71.3291i	0.152739	−	0.152739i	−0.626601	−	0.779340i	$-0.715554\pi$
$467$	71.3291	−	71.3291i	0.152739	−	0.152739i	0.779340	+	0.626601i	$0.215554\pi$
$468$	−498.749	+	391.486i	−1.06570	+	0.836509i
$469$		−	62.2401i		−	0.132708i
$470$		0			0
$471$	76.7972	+	86.6057i	0.163051	+	0.183876i
$472$	−40.6427	−	151.681i	−0.0861074	−	0.321357i
$473$	−93.3241	+	25.0061i	−0.197302	+	0.0528670i
$474$	103.186	−	91.4995i	0.217692	−	0.193037i
$475$		0			0
$476$	−90.6334			−0.190406
$477$	646.735	−	92.3858i	1.35584	−	0.193681i
$478$	20.7628	+	20.7628i	0.0434367	+	0.0434367i
$479$	−169.803	+	98.0357i	−0.354494	+	0.204667i	−0.666663	−	0.745359i	$-0.732278\pi$
$479$	−169.803	+	98.0357i	−0.354494	+	0.204667i	0.312169	+	0.950027i	$0.398945\pi$
$480$		0			0
$481$	471.883	−	817.325i	0.981046	−	1.69922i
$482$	−16.2758	−	60.7419i	−0.0337671	−	0.126021i
$483$	−6.95565	+	3.47779i	−0.0144009	+	0.00720040i
$484$	43.5181	−	25.1252i	0.0899135	−	0.0519116i
$485$		0			0
$486$	85.2105	+	161.451i	0.175330	+	0.332204i
$487$	−660.124	+	660.124i	−1.35549	+	1.35549i	−0.476100	+	0.879391i	$0.657950\pi$
$487$	−660.124	+	660.124i	−1.35549	+	1.35549i	−0.879391	+	0.476100i	$0.842050\pi$
$488$	−118.845	+	443.534i	−0.243534	+	0.908882i
$489$	566.697	+	188.901i	1.15889	+	0.386301i
$490$		0			0
$491$	393.999	−	682.426i	0.802442	−	1.38987i	−0.115562	−	0.993300i	$-0.536867\pi$
$491$	393.999	−	682.426i	0.802442	−	1.38987i	0.918004	−	0.396570i	$-0.129800\pi$
$492$	−233.302	+	353.349i	−0.474192	+	0.718190i
$493$	88.1204	−	328.870i	0.178743	−	0.667079i
$494$			166.425i			0.336892i
$495$		0			0
$496$	412.820			0.832299
$497$	179.173	+	48.0093i	0.360510	+	0.0965983i
$498$	6.97925	−	116.269i	0.0140146	−	0.233472i
$499$	144.756	+	83.5751i	0.290093	+	0.167485i	0.637984	−	0.770050i	$-0.279769\pi$
$499$	144.756	+	83.5751i	0.290093	+	0.167485i	−0.347891	+	0.937535i	$0.613102\pi$
$500$		0			0
$501$	−563.110	−	635.031i	−1.12397	−	1.26753i
$502$	−84.6664	−	22.6863i	−0.168658	−	0.0451918i
$503$	−249.990	−	249.990i	−0.496998	−	0.496998i	0.413504	−	0.910502i	$-0.364305\pi$
$503$	−249.990	−	249.990i	−0.496998	−	0.496998i	−0.910502	+	0.413504i	$0.864305\pi$
$504$	−92.8737	−	11.1901i	−0.184273	−	0.0222027i
$505$		0			0
$506$	6.09446	+	10.5559i	0.0120444	+	0.0208615i
$507$	−415.696	+	629.596i	−0.819914	+	1.24181i
$508$	263.204	−	70.5254i	0.518119	−	0.138830i
$509$	95.6645	+	55.2319i	0.187946	+	0.108511i	0.591021	−	0.806656i	$-0.298725\pi$
$509$	95.6645	+	55.2319i	0.187946	+	0.108511i	−0.403075	+	0.915167i	$0.632059\pi$
$510$		0			0
$511$	29.4167	+	50.9513i	0.0575670	+	0.0997089i
$512$	−350.050	+	350.050i	−0.683691	+	0.683691i
$513$	−286.980	−	52.1814i	−0.559415	−	0.101718i
$514$			3.59475i			0.00699368i
$515$		0			0
$516$	−27.0400	+	81.1190i	−0.0524031	+	0.157207i
$517$	−53.8526	−	200.981i	−0.104164	−	0.388744i
$518$	62.1438	−	16.6514i	0.119969	−	0.0321455i
$519$	186.432	+	911.062i	0.359213	+	1.75542i
$520$		0			0
$521$	−415.088			−0.796715			−0.398357	−	0.917230i	$-0.630420\pi$
$521$	−415.088			−0.796715			−0.398357	+	0.917230i	$0.630420\pi$
$522$	60.4833	−	150.682i	0.115868	−	0.288664i
$523$	384.585	+	384.585i	0.735344	+	0.735344i	0.971673	−	0.236329i	$-0.0759444\pi$
$523$	384.585	+	384.585i	0.735344	+	0.735344i	−0.236329	+	0.971673i	$0.575944\pi$
$524$	13.7895	−	7.96136i	0.0263158	−	0.0151934i
$525$		0			0
$526$	36.7398	−	63.6352i	0.0698475	−	0.120979i
$527$	−158.695	−	592.257i	−0.301129	−	1.12383i
$528$	19.9833	−	332.907i	0.0378472	−	0.630505i
$529$	−456.447	+	263.530i	−0.862848	+	0.498166i
$530$		0			0
$531$	232.663	−	99.3815i	0.438160	−	0.187159i
$532$	48.8325	−	48.8325i	0.0917904	−	0.0917904i
$533$	−218.032	+	813.705i	−0.409065	+	1.52665i
$534$	−51.4702	−	251.527i	−0.0963862	−	0.471024i
$535$		0			0
$536$	−93.4285	+	161.823i	−0.174307	+	0.301908i
$537$	−203.772	−	407.547i	−0.379463	−	0.758933i
$538$	−41.3909	+	154.473i	−0.0769348	+	0.287125i
$539$		−	530.329i		−	0.983912i
$540$		0			0
$541$	251.489			0.464859			0.232430	−	0.972613i	$-0.425332\pi$
$541$	251.489			0.464859			0.232430	+	0.972613i	$0.425332\pi$
$542$	−130.796	−	35.0467i	−0.241321	−	0.0646618i
$543$	−129.060	+	64.5295i	−0.237680	+	0.118839i
$544$	362.411	+	209.238i	0.666196	+	0.384628i
$545$		0			0
$546$	−84.2465	+	17.2394i	−0.154298	+	0.0315741i
$547$	−539.479	−	144.553i	−0.986251	−	0.264265i	−0.270576	−	0.962699i	$-0.587214\pi$
$547$	−539.479	−	144.553i	−0.986251	−	0.264265i	−0.715675	+	0.698433i	$0.753881\pi$
$548$	5.77833	+	5.77833i	0.0105444	+	0.0105444i
$549$	−734.491	−	88.4973i	−1.33787	−	0.161197i
$550$		0			0
$551$	129.714	+	224.671i	0.235415	+	0.407751i
$552$	23.3050	+	1.39893i	0.0422193	+	0.00253429i
$553$	−109.976	+	29.4681i	−0.198872	+	0.0532876i
$554$	−212.930	−	122.935i	−0.384349	−	0.221904i
$555$		0			0
$556$	−440.197	−	762.444i	−0.791722	−	1.37130i
$557$	−302.419	+	302.419i	−0.542943	+	0.542943i	−0.924391	−	0.381447i	$-0.875426\pi$
$557$	−302.419	+	302.419i	−0.542943	+	0.542943i	0.381447	+	0.924391i	$0.375426\pi$
$558$	−41.3504	−	289.468i	−0.0741046	−	0.518760i
$559$			170.119i			0.304327i
$560$		0			0
$561$	−485.290	+	99.3053i	−0.865044	+	0.177015i
$562$	−6.08041	−	22.6924i	−0.0108192	−	0.0403780i
$563$	874.123	−	234.221i	1.55262	−	0.416022i	0.622300	−	0.782779i	$-0.286198\pi$
$563$	874.123	−	234.221i	1.55262	−	0.416022i	0.930317	+	0.366756i	$0.119532\pi$
$564$	−174.696	−	58.2327i	−0.309745	−	0.103250i
$565$		0			0
$566$	−152.307			−0.269094
$567$	−3.31241	−	150.678i	−0.00584199	−	0.265747i
$568$	−393.780	−	393.780i	−0.693274	−	0.693274i
$569$	194.081	−	112.053i	0.341092	−	0.196929i	−0.319663	−	0.947531i	$-0.603570\pi$
$569$	194.081	−	112.053i	0.341092	−	0.196929i	0.660755	+	0.750602i	$0.270236\pi$
$570$		0			0
$571$	−28.3061	+	49.0275i	−0.0495728	+	0.0858626i	−0.889747	−	0.456454i	$-0.849119\pi$
$571$	−28.3061	+	49.0275i	−0.0495728	+	0.0858626i	0.840174	+	0.542317i	$0.182453\pi$
$572$	−212.347	−	792.488i	−0.371235	−	1.38547i
$573$	909.774	+	600.687i	1.58774	+	1.04832i
$574$	−49.7329	+	28.7133i	−0.0866426	+	0.0500232i
$575$		0			0
$576$	−115.263	−	86.4483i	−0.200109	−	0.150084i
$577$	450.543	−	450.543i	0.780838	−	0.780838i	−0.199135	−	0.979972i	$-0.563813\pi$
$577$	450.543	−	450.543i	0.780838	−	0.780838i	0.979972	+	0.199135i	$0.0638131\pi$
$578$	−17.1078	+	63.8471i	−0.0295982	+	0.110462i
$579$	26.8648	−	23.8222i	0.0463986	−	0.0411437i
$580$		0			0
$581$	−48.0806	+	83.2781i	−0.0827550	+	0.143336i
$582$	−68.8692	−	4.13400i	−0.118332	−	0.00710309i
$583$	−218.796	+	816.557i	−0.375293	+	1.40061i
$584$		−	176.630i		−	0.302448i
$585$		0			0
$586$	29.2982			0.0499969
$587$	−335.371	−	89.8623i	−0.571330	−	0.153087i	−0.0384234	−	0.999262i	$-0.512234\pi$
$587$	−335.371	−	89.8623i	−0.571330	−	0.153087i	−0.532906	+	0.846174i	$0.678900\pi$
$588$	−391.677	−	258.609i	−0.666118	−	0.439810i
$589$	404.606	+	233.599i	0.686937	+	0.396603i
$590$		0			0
$591$	60.8326	−	182.495i	0.102932	−	0.308791i
$592$	424.369	+	113.709i	0.716840	+	0.192077i
$593$	235.628	+	235.628i	0.397350	+	0.397350i	0.877297	−	0.479948i	$-0.159344\pi$
$593$	235.628	+	235.628i	0.397350	+	0.397350i	−0.479948	+	0.877297i	$0.659344\pi$
$594$	−235.434	+	19.3335i	−0.396354	+	0.0325480i
$595$		0			0
$596$	161.848	+	280.329i	0.271557	+	0.470351i
$597$	−22.8188	−	45.6380i	−0.0382224	−	0.0764455i
$598$	20.7306	−	5.55474i	0.0346665	−	0.00928887i
$599$	−513.829	−	296.659i	−0.857811	−	0.495258i	0.00546746	−	0.999985i	$-0.498260\pi$
$599$	−513.829	−	296.659i	−0.857811	−	0.495258i	−0.863279	+	0.504727i	$0.831593\pi$
$600$		0			0
$601$	269.249	+	466.354i	0.448002	+	0.775963i	0.998256	−	0.0590349i	$-0.0188023\pi$
$601$	269.249	+	466.354i	0.448002	+	0.775963i	−0.550254	+	0.834998i	$0.685469\pi$
$602$	−8.20024	+	8.20024i	−0.0136217	+	0.0136217i
$603$	−279.386	−	112.144i	−0.463326	−	0.185977i
$604$		−	96.5233i		−	0.159807i
$605$		0			0
$606$	−89.3962	−	100.814i	−0.147519	−	0.166360i
$607$	−105.915	−	395.280i	−0.174489	−	0.651203i	−0.996638	−	0.0819303i	$-0.973892\pi$
$607$	−105.915	−	395.280i	−0.174489	−	0.651203i	0.822149	−	0.569273i	$-0.192775\pi$
$608$	−307.999	+	82.5281i	−0.506577	+	0.135737i
$609$	−100.295	+	88.9357i	−0.164687	+	0.146036i
$610$		0			0
$611$	−366.364			−0.599614
$612$	−163.303	+	406.839i	−0.266836	+	0.664769i
$613$	10.5026	+	10.5026i	0.0171331	+	0.0171331i	0.715621	−	0.698488i	$-0.246144\pi$
$613$	10.5026	+	10.5026i	0.0171331	+	0.0171331i	−0.698488	+	0.715621i	$0.746144\pi$
$614$	26.1641	−	15.1059i	0.0426126	−	0.0246024i
$615$		0			0
$616$	60.5232	−	104.829i	0.0982520	−	0.170177i
$617$	113.048	+	421.900i	0.183222	+	0.683793i	0.995004	+	0.0998331i	$0.0318309\pi$
$617$	113.048	+	421.900i	0.183222	+	0.683793i	−0.811782	+	0.583960i	$0.801502\pi$
$618$	−102.040	+	51.0196i	−0.165114	+	0.0825560i
$619$	−8.91186	+	5.14527i	−0.0143972	+	0.00831222i	−0.507181	−	0.861839i	$-0.669313\pi$
$619$	−8.91186	+	5.14527i	−0.0143972	+	0.00831222i	0.492784	+	0.870152i	$0.335979\pi$
$620$		0			0
$621$	3.07855	+	37.4890i	0.00495740	+	0.0603688i
$622$	−229.439	+	229.439i	−0.368873	+	0.368873i
$623$	−54.8585	+	204.735i	−0.0880554	+	0.328627i
$624$	−557.091	−	185.699i	−0.892775	−	0.297595i
$625$		0			0
$626$	−77.9268	+	134.973i	−0.124484	+	0.215612i
$627$	207.965	−	314.975i	0.331682	−	0.502352i
$628$	−34.3086	+	128.042i	−0.0546316	+	0.203888i
$629$		−	652.537i		−	1.03742i
$630$		0			0
$631$	154.559			0.244943			0.122472	−	0.992472i	$-0.460918\pi$
$631$	154.559			0.244943			0.122472	+	0.992472i	$0.460918\pi$
$632$	330.170	+	88.4689i	0.522421	+	0.139982i
$633$	53.5268	−	891.715i	0.0845606	−	1.40871i
$634$	−231.032	−	133.386i	−0.364403	−	0.210388i
$635$		0			0
$636$	496.379	+	559.777i	0.780471	+	0.880153i
$637$	−901.968	−	241.682i	−1.41596	−	0.379406i
$638$	148.565	+	148.565i	0.232860	+	0.232860i
$639$	538.341	−	717.776i	0.842474	−	1.12328i
$640$		0			0
$641$	−302.816	−	524.493i	−0.472412	−	0.818242i	0.527089	−	0.849810i	$-0.323283\pi$
$641$	−302.816	−	524.493i	−0.472412	−	0.818242i	−0.999502	+	0.0315680i	$0.989950\pi$
$642$	−26.0549	+	39.4616i	−0.0405839	+	0.0614666i
$643$	−450.687	+	120.761i	−0.700912	+	0.187809i	−0.591639	−	0.806203i	$-0.701519\pi$
$643$	−450.687	+	120.761i	−0.700912	+	0.187809i	−0.109273	+	0.994012i	$0.534852\pi$
$644$	−7.71265	−	4.45290i	−0.0119762	−	0.00691444i
$645$		0			0
$646$	57.5346	+	99.6529i	0.0890629	+	0.154261i
$647$	117.084	−	117.084i	0.180965	−	0.180965i	−0.610811	−	0.791776i	$-0.709157\pi$
$647$	117.084	−	117.084i	0.180965	−	0.180965i	0.791776	+	0.610811i	$0.209157\pi$
$648$	−217.571	+	396.732i	−0.335757	+	0.612241i
$649$			327.378i			0.504434i
$650$		0			0
$651$	−76.3392	+	229.015i	−0.117265	+	0.351789i
$652$	177.055	+	660.778i	0.271557	+	1.01346i
$653$	−322.638	+	86.4506i	−0.494086	+	0.132390i	−0.497254	−	0.867605i	$-0.665658\pi$
$653$	−322.638	+	86.4506i	−0.494086	+	0.132390i	0.00316798	+	0.999995i	$0.498992\pi$
$654$	52.0918	+	254.565i	0.0796511	+	0.389242i
$655$		0			0
$656$	−392.156			−0.597799
$657$	281.715	−	40.2428i	0.428790	−	0.0612524i
$658$	−17.6599	−	17.6599i	−0.0268387	−	0.0268387i
$659$	−1062.27	+	613.303i	−1.61195	+	0.930657i	−0.623027	+	0.782200i	$0.714097\pi$
$659$	−1062.27	+	613.303i	−1.61195	+	0.930657i	−0.988919	+	0.148457i	$0.952569\pi$
$660$		0			0
$661$	79.8777	−	138.352i	0.120844	−	0.209307i	−0.799257	−	0.600989i	$-0.794773\pi$
$661$	79.8777	−	138.352i	0.120844	−	0.209307i	0.920101	+	0.391682i	$0.128107\pi$
$662$	−72.8967	−	272.054i	−0.110116	−	0.410958i
$663$	−52.2607	+	870.622i	−0.0788246	+	1.31316i
$664$	250.017	−	144.347i	0.376532	−	0.217391i
$665$		0			0
$666$	37.2254	−	308.956i	0.0558940	−	0.463897i
$667$	23.6565	−	23.6565i	0.0354670	−	0.0354670i
$668$	251.566	−	938.856i	0.376595	−	1.40547i
$669$	19.2257	+	93.9528i	0.0287379	+	0.140438i
$670$		0			0
$671$	478.648	−	829.042i	0.713335	−	1.23553i
$672$	−73.6815	−	147.364i	−0.109645	−	0.219292i
$673$	−12.3181	+	45.9717i	−0.0183032	+	0.0683086i	−0.974473	−	0.224503i	$-0.927924\pi$
$673$	−12.3181	+	45.9717i	−0.0183032	+	0.0683086i	0.956170	+	0.292811i	$0.0945908\pi$
$674$			111.675i			0.165690i
$675$		0			0
$676$	−863.996			−1.27810
$677$	141.633	+	37.9504i	0.209206	+	0.0560567i	0.361900	−	0.932217i	$-0.382128\pi$
$677$	141.633	+	37.9504i	0.209206	+	0.0560567i	−0.152694	+	0.988274i	$0.548795\pi$
$678$	211.228	−	105.613i	0.311545	−	0.155771i
$679$	49.3279	+	28.4795i	0.0726479	+	0.0419433i
$680$		0			0
$681$	1149.68	−	235.260i	1.68822	−	0.345462i
$682$	365.477	+	97.9293i	0.535890	+	0.143591i
$683$	−882.608	−	882.608i	−1.29225	−	1.29225i	−0.933391	−	0.358860i	$-0.883165\pi$
$683$	−882.608	−	882.608i	−1.29225	−	1.29225i	−0.358860	−	0.933391i	$-0.616835\pi$
$684$	−131.215	−	307.187i	−0.191834	−	0.449104i
$685$		0			0
$686$	−66.0754	−	114.446i	−0.0963198	−	0.166831i
$687$	751.148	+	45.0890i	1.09337	+	0.0656318i
$688$	−76.4948	+	20.4967i	−0.111184	+	0.0297917i
$689$	1289.07	+	744.243i	1.87092	+	1.08018i
$690$		0			0
$691$	253.832	+	439.650i	0.367340	+	0.636252i	0.989149	−	0.146917i	$-0.0469351\pi$
$691$	253.832	+	439.650i	0.367340	+	0.636252i	−0.621808	+	0.783169i	$0.713602\pi$
$692$	−753.047	+	753.047i	−1.08822	+	1.08822i
$693$	180.987	+	72.6473i	0.261164	+	0.104830i
$694$			181.421i			0.261413i
$695$		0			0
$696$	394.265	−	80.6788i	0.566473	−	0.115918i
$697$	150.751	+	562.611i	0.216286	+	0.807189i
$698$	277.514	−	74.3597i	0.397585	−	0.106532i
$699$	962.302	+	320.771i	1.37668	+	0.458900i
$700$		0			0
$701$	194.042			0.276807			0.138403	−	0.990376i	$-0.455803\pi$
$701$	194.042			0.276807			0.138403	+	0.990376i	$0.455803\pi$
$702$	−74.4103	+	409.231i	−0.105998	+	0.582950i
$703$	351.581	+	351.581i	0.500115	+	0.500115i
$704$	161.459	−	93.2182i	0.229345	−	0.132412i
$705$		0			0
$706$	−195.614	+	338.813i	−0.277073	+	0.479905i
$707$	28.7907	+	107.448i	0.0407223	+	0.151978i
$708$	241.787	+	159.642i	0.341506	+	0.225483i
$709$	414.499	−	239.311i	0.584625	−	0.337534i	−0.178344	−	0.983968i	$-0.557074\pi$
$709$	414.499	−	239.311i	0.584625	−	0.337534i	0.762969	+	0.646435i	$0.223741\pi$
$710$		0			0
$711$	−65.8781	+	546.761i	−0.0926555	+	0.769003i
$712$	449.958	−	449.958i	0.631963	−	0.631963i
$713$	15.5936	−	58.1962i	0.0218705	−	0.0816216i
$714$	−44.4858	+	39.4475i	−0.0623050	+	0.0552486i
$715$		0			0
$716$	260.906	−	451.902i	0.364393	−	0.631148i
$717$	−117.043	−	7.02575i	−0.163240	−	0.00979881i
$718$	63.5739	−	237.261i	0.0885430	−	0.330447i
$719$			443.536i			0.616879i	0.951244	+	0.308439i	$0.0998067\pi$
$719$			443.536i			0.616879i	−0.951244	+	0.308439i	$0.900193\pi$
$720$		0			0
$721$	94.1849			0.130631
$722$	177.274	+	47.5005i	0.245532	+	0.0657902i
$723$	209.558	+	138.363i	0.289845	+	0.191373i
$724$	−143.106	−	82.6224i	−0.197660	−	0.114119i
$725$		0			0
$726$	10.4245	−	31.2732i	0.0143588	−	0.0430760i
$727$	280.010	+	75.0285i	0.385158	+	0.103203i	0.446202	−	0.894932i	$-0.352776\pi$
$727$	280.010	+	75.0285i	0.385158	+	0.103203i	−0.0610438	+	0.998135i	$0.519443\pi$
$728$	−150.709	−	150.709i	−0.207018	−	0.207018i
$729$	−682.338	−	256.623i	−0.935992	−	0.352021i
$730$		0			0
$731$	58.8116	+	101.865i	0.0804536	+	0.139350i
$732$	−378.887	−	757.781i	−0.517605	−	1.03522i
$733$	987.435	−	264.583i	1.34712	−	0.360958i	0.488046	−	0.872818i	$-0.337710\pi$
$733$	987.435	−	264.583i	1.34712	−	0.360958i	0.859069	+	0.511859i	$0.171043\pi$
$734$	340.177	+	196.401i	0.463457	+	0.267577i
$735$		0			0
$736$	20.5601	+	35.6111i	0.0279349	+	0.0483847i
$737$	275.459	−	275.459i	0.373757	−	0.373757i
$738$	39.2805	+	274.978i	0.0532256	+	0.372599i
$739$		−	153.917i		−	0.208277i	−0.994563	−	0.104138i	$-0.966791\pi$
$739$		−	153.917i		−	0.208277i	0.994563	−	0.104138i	$-0.0332085\pi$
$740$		0			0
$741$	−440.926	−	497.241i	−0.595042	−	0.671041i
$742$	26.2622	+	98.0117i	0.0353938	+	0.132091i
$743$	1261.02	−	337.889i	1.69720	−	0.454763i	0.724966	−	0.688784i	$-0.241855\pi$
$743$	1261.02	−	337.889i	1.69720	−	0.454763i	0.972231	+	0.234021i	$0.0751886\pi$
$744$	542.254	−	480.841i	0.728836	−	0.646291i
$745$		0			0
$746$	18.2489			0.0244623
$747$	287.190	+	365.877i	0.384458	+	0.489795i
$748$	−401.121	−	401.121i	−0.536258	−	0.536258i
$749$	33.8088	−	19.5195i	0.0451385	−	0.0260607i
$750$		0			0
$751$	−728.908	+	1262.51i	−0.970583	+	1.68110i	−0.276783	+	0.960933i	$0.589268\pi$
$751$	−728.908	+	1262.51i	−0.970583	+	1.68110i	−0.693801	+	0.720167i	$0.744065\pi$
$752$	−44.1413	−	164.737i	−0.0586985	−	0.219066i
$753$	313.070	−	156.533i	0.415763	−	0.207880i
$754$	320.379	−	184.971i	0.424905	−	0.245319i
$755$		0			0
$756$	141.910	−	98.2432i	0.187712	−	0.129951i
$757$	575.216	−	575.216i	0.759863	−	0.759863i	−0.216434	−	0.976297i	$-0.569443\pi$
$757$	575.216	−	575.216i	0.759863	−	0.759863i	0.976297	+	0.216434i	$0.0694426\pi$
$758$	70.9594	−	264.824i	0.0936140	−	0.349372i
$759$	−46.1758	−	15.3921i	−0.0608376	−	0.0202795i
$760$		0			0
$761$	−506.722	+	877.668i	−0.665863	+	1.15331i	0.313187	+	0.949691i	$0.398603\pi$
$761$	−506.722	+	877.668i	−0.665863	+	1.15331i	−0.979051	+	0.203618i	$0.934730\pi$
$762$	98.4935	−	149.174i	0.129257	−	0.195766i
$763$	55.5211	−	207.207i	0.0727668	−	0.271569i
$764$			1248.49i			1.63414i
$765$		0			0
$766$	−2.52556			−0.00329708
$767$	556.794	+	149.193i	0.725938	+	0.194515i
$768$	−6.05728	+	100.910i	−0.00788709	+	0.131393i
$769$	−486.081	−	280.639i	−0.632095	−	0.364940i	0.149468	−	0.988767i	$-0.452244\pi$
$769$	−486.081	−	280.639i	−0.632095	−	0.364940i	−0.781563	+	0.623827i	$0.785577\pi$
$770$		0			0
$771$	−9.52393	−	10.7403i	−0.0123527	−	0.0139304i
$772$	39.7180	+	10.6424i	0.0514482	+	0.0137855i
$773$	−445.834	−	445.834i	−0.576758	−	0.576758i	0.357251	−	0.934008i	$-0.383714\pi$
$773$	−445.834	−	445.834i	−0.576758	−	0.576758i	−0.934008	+	0.357251i	$0.883714\pi$
$774$	22.0343	+	51.5847i	0.0284681	+	0.0666469i
$775$		0			0
$776$	−85.5009	−	148.092i	−0.110182	−	0.190840i
$777$	−141.556	+	214.394i	−0.182183	+	0.275926i
$778$	110.446	−	29.5938i	0.141961	−	0.0380383i
$779$	−384.353	−	221.906i	−0.493393	−	0.284860i
$780$		0			0
$781$	580.499	+	1005.45i	0.743276	+	1.28739i
$782$	10.4929	−	10.4929i	0.0134180	−	0.0134180i
$783$	218.507	+	610.451i	0.279064	+	0.779630i
$784$		−	434.693i		−	0.554456i
$785$		0			0
$786$	3.30320	−	9.90946i	0.00420254	−	0.0126075i
$787$	362.598	+	1353.23i	0.460734	+	1.71948i	0.670659	+	0.741766i	$0.266011\pi$
$787$	362.598	+	1353.23i	0.460734	+	1.71948i	−0.209925	+	0.977717i	$0.567322\pi$
$788$	212.793	−	57.0176i	0.270041	−	0.0723573i
$789$	58.8245	+	287.466i	0.0745558	+	0.364343i
$790$		0			0
$791$	−194.967			−0.246482
$792$	−361.511	−	460.560i	−0.456453	−	0.581515i
$793$	−1191.88	−	1191.88i	−1.50300	−	1.50300i
$794$	253.828	−	146.548i	0.319683	−	0.184569i
$795$		0			0
$796$	29.2167	−	50.6049i	0.0367045	−	0.0635740i
$797$	122.829	+	458.403i	0.154114	+	0.575160i	0.999180	+	0.0404981i	$0.0128945\pi$
$797$	122.829	+	458.403i	0.154114	+	0.575160i	−0.845066	+	0.534662i	$0.820439\pi$
$798$	2.71456	−	45.2225i	0.00340171	−	0.0566698i
$799$	−219.374	+	126.655i	−0.274560	+	0.158517i
$800$		0			0
$801$	820.177	+	615.142i	1.02394	+	0.767968i
$802$	−358.565	+	358.565i	−0.447088	+	0.447088i
$803$	−95.3064	+	355.688i	−0.118688	+	0.442949i
$804$	−69.1175	−	337.766i	−0.0859670	−	0.420107i
$805$		0			0
$806$	333.111	−	576.965i	0.413289	−	0.715837i
$807$	−285.594	−	571.193i	−0.353895	−	0.707798i
$808$	86.4352	−	322.581i	0.106974	−	0.399234i
$809$		−	806.321i		−	0.996689i	−0.866979	−	0.498344i	$-0.833941\pi$
$809$		−	806.321i		−	0.996689i	0.866979	−	0.498344i	$-0.166059\pi$
$810$		0			0
$811$	−928.637			−1.14505			−0.572526	−	0.819887i	$-0.694036\pi$
$811$	−928.637			−1.14505			−0.572526	+	0.819887i	$0.694036\pi$
$812$	−148.280	−	39.7315i	−0.182611	−	0.0489304i
$813$	483.642	−	241.819i	0.594886	−	0.297440i
$814$	348.727	+	201.338i	0.428412	+	0.247344i
$815$		0			0
$816$	−397.776	+	81.3974i	−0.487471	+	0.0997517i
$817$	−86.5709	−	23.1966i	−0.105962	−	0.0283924i
$818$	−230.158	−	230.158i	−0.281366	−	0.281366i
$819$	206.036	−	274.710i	0.251570	−	0.335422i
$820$		0			0
$821$	−259.589	−	449.622i	−0.316187	−	0.547652i	0.663502	−	0.748174i	$-0.269069\pi$
$821$	−259.589	−	449.622i	−0.316187	−	0.547652i	−0.979689	+	0.200523i	$0.935736\pi$
$822$	5.35116	+	0.321213i	0.00650993	+	0.000390770i
$823$	−1245.48	+	333.724i	−1.51334	+	0.405497i	−0.917542	−	0.397639i	$-0.869830\pi$
$823$	−1245.48	+	333.724i	−1.51334	+	0.405497i	−0.595795	+	0.803136i	$0.703163\pi$
$824$	−244.879	−	141.381i	−0.297183	−	0.171579i
$825$		0			0
$826$	19.6477	+	34.0307i	0.0237865	+	0.0411994i
$827$	380.149	−	380.149i	0.459672	−	0.459672i	−0.438876	−	0.898548i	$-0.644623\pi$
$827$	380.149	−	380.149i	0.459672	−	0.459672i	0.898548	+	0.438876i	$0.144623\pi$
$828$	−33.8850	+	26.5976i	−0.0409239	+	0.0321227i
$829$			511.167i			0.616606i	0.951288	+	0.308303i	$0.0997611\pi$
$829$			511.167i			0.616606i	−0.951288	+	0.308303i	$0.900239\pi$
$830$		0			0
$831$	961.890	−	196.833i	1.15751	−	0.236862i
$832$	−84.9628	−	317.086i	−0.102119	−	0.381113i
$833$	−623.637	+	167.103i	−0.748664	+	0.200604i
$834$	−547.911	−	182.639i	−0.656968	−	0.218992i
$835$		0			0
$836$	432.240			0.517034
$837$	890.462	+	755.313i	1.06387	+	0.902405i
$838$	265.524	+	265.524i	0.316855	+	0.316855i
$839$	−889.044	+	513.290i	−1.05965	+	0.611788i	−0.925335	−	0.379151i	$-0.876216\pi$
$839$	−889.044	+	513.290i	−1.05965	+	0.611788i	−0.134313	+	0.990939i	$0.542883\pi$
$840$		0			0
$841$	−132.163	+	228.913i	−0.157150	+	0.272192i
$842$	5.84978	+	21.8317i	0.00694749	+	0.0259284i
$843$	78.2882	+	51.6905i	0.0928686	+	0.0613173i
$844$	885.970	−	511.515i	1.04973	−	0.606061i
$845$		0			0
$846$	−111.092	+	47.4527i	−0.131314	+	0.0560906i
$847$	−19.2439	+	19.2439i	−0.0227200	+	0.0227200i
$848$	−179.340	+	669.305i	−0.211486	+	0.789275i
$849$	455.061	−	403.523i	0.535996	−	0.475292i
$850$		0			0
$851$	32.0597	−	55.5291i	0.0376730	−	0.0652516i
$852$	1025.66	+	61.5669i	1.20382	+	0.0722616i
$853$	−360.478	+	1345.32i	−0.422600	+	1.57717i	0.346508	+	0.938047i	$0.387367\pi$
$853$	−360.478	+	1345.32i	−0.422600	+	1.57717i	−0.769108	+	0.639119i	$0.779299\pi$
$854$		−	114.905i		−	0.134549i
$855$		0			0
$856$	−117.203			−0.136919
$857$	−319.058	−	85.4914i	−0.372297	−	0.0997566i	0.0678191	−	0.997698i	$-0.478396\pi$
$857$	−319.058	−	85.4914i	−0.372297	−	0.0997566i	−0.440116	+	0.897941i	$0.645063\pi$
$858$	−449.151	−	296.556i	−0.523486	−	0.345637i
$859$	264.795	+	152.879i	0.308259	+	0.177974i	0.646147	−	0.763213i	$-0.276379\pi$
$859$	264.795	+	152.879i	0.308259	+	0.177974i	−0.337888	+	0.941186i	$0.609713\pi$
$860$		0			0
$861$	72.5180	−	217.551i	0.0842253	−	0.252673i
$862$	374.262	+	100.283i	0.434178	+	0.116338i
$863$	−386.017	−	386.017i	−0.447297	−	0.447297i	0.447158	−	0.894455i	$-0.352436\pi$
$863$	−386.017	−	386.017i	−0.447297	−	0.447297i	−0.894455	+	0.447158i	$0.852436\pi$
$864$	−794.254	+	65.2230i	−0.919275	+	0.0754895i
$865$		0			0
$866$	162.447	+	281.367i	0.187583	+	0.324904i
$867$	−118.042	−	236.086i	−0.136150	−	0.272303i
$868$	−267.035	+	71.5518i	−0.307644	+	0.0824329i
$869$	−617.145	−	356.309i	−0.710179	−	0.410022i
$870$		0			0
$871$	−342.961	−	594.025i	−0.393755	−	0.682004i
$872$	−455.392	+	455.392i	−0.522238	+	0.522238i
$873$	216.719	−	170.111i	0.248246	−	0.194857i
$874$			11.3069i			0.0129370i
$875$		0			0
$876$	216.221	+	243.836i	0.246827	+	0.278352i
$877$	−108.142	−	403.592i	−0.123309	−	0.460196i	0.876465	−	0.481466i	$-0.159896\pi$
$877$	−108.142	−	403.592i	−0.123309	−	0.460196i	−0.999774	+	0.0212701i	$0.993229\pi$
$878$	−366.669	+	98.2488i	−0.417619	+	0.111901i
$879$	−87.5366	+	77.6226i	−0.0995865	+	0.0883078i
$880$		0			0
$881$	−1495.93			−1.69799			−0.848993	−	0.528403i	$-0.822791\pi$
$881$	−1495.93			−1.69799			−0.848993	+	0.528403i	$0.822791\pi$
$882$	−304.805	+	43.5413i	−0.345584	+	0.0493665i
$883$	158.383	+	158.383i	0.179369	+	0.179369i	0.791081	−	0.611712i	$-0.209519\pi$
$883$	158.383	+	158.383i	0.179369	+	0.179369i	−0.611712	+	0.791081i	$0.709519\pi$
$884$	−865.014	+	499.416i	−0.978522	+	0.564950i
$885$		0			0
$886$	75.9157	−	131.490i	0.0856837	−	0.148408i
$887$	−355.206	−	1325.65i	−0.400458	−	1.49453i	−0.812281	−	0.583266i	$-0.801775\pi$
$887$	−355.206	−	1325.65i	−0.400458	−	1.49453i	0.411823	−	0.911264i	$-0.364892\pi$
$888$	689.869	−	344.931i	0.776879	−	0.388436i
$889$	−127.805	+	73.7883i	−0.143763	+	0.0830014i
$890$		0			0
$891$	652.204	−	681.524i	0.731991	−	0.764898i
$892$	−77.6576	+	77.6576i	−0.0870601	+	0.0870601i
$893$	49.9557	−	186.437i	0.0559415	−	0.208776i
$894$	201.451	+	67.1513i	0.225337	+	0.0751133i
$895$		0			0
$896$	121.028	−	209.626i	0.135076	−	0.233958i
$897$	−47.2217	+	71.5199i	−0.0526440	+	0.0797324i
$898$	−28.2113	+	105.286i	−0.0314157	+	0.117245i
$899$		−	1038.52i		−	1.15520i
$900$		0			0
$901$	1029.17			1.14225
$902$	−347.183	−	93.0274i	−0.384903	−	0.103135i
$903$	2.77482	−	46.2262i	0.00307288	−	0.0511918i
$904$	506.909	+	292.664i	0.560741	+	0.323744i
$905$		0			0
$906$	−42.0111	−	47.3767i	−0.0463698	−	0.0522922i
$907$	−535.743	−	143.552i	−0.590676	−	0.158271i	−0.0489140	−	0.998803i	$-0.515576\pi$
$907$	−535.743	−	143.552i	−0.590676	−	0.158271i	−0.541762	+	0.840532i	$0.682243\pi$
$908$	950.276	+	950.276i	1.04656	+	1.04656i
$909$	534.193	+	64.3637i	0.587671	+	0.0708072i
$910$		0			0
$911$	−484.409	−	839.021i	−0.531733	−	0.920989i	−0.999314	−	0.0370382i	$-0.988208\pi$
$911$	−484.409	−	839.021i	−0.531733	−	0.920989i	0.467581	−	0.883950i	$-0.345126\pi$
$912$	170.462	−	258.175i	0.186910	−	0.283086i
$913$	−581.361	+	155.775i	−0.636759	+	0.170619i
$914$	192.995	+	111.426i	0.211154	+	0.121910i
$915$		0			0
$916$	430.882	+	746.309i	0.470395	+	0.814748i
$917$	−6.09776	+	6.09776i	−0.00664968	+	0.00664968i
$918$	96.9190	+	270.766i	0.105576	+	0.294952i
$919$			600.903i			0.653866i	0.945048	+	0.326933i	$0.106015\pi$
$919$			600.903i			0.653866i	−0.945048	+	0.326933i	$0.893985\pi$
$920$		0			0
$921$	−38.1512	+	114.452i	−0.0414237	+	0.124270i
$922$	55.6275	+	207.604i	0.0603335	+	0.225168i
$923$	1974.59	−	529.090i	2.13932	−	0.573229i
$924$	44.7745	+	218.806i	0.0484572	+	0.236803i
$925$		0			0
$926$	187.992			0.203015
$927$	169.702	−	422.780i	0.183066	−	0.456074i
$928$	501.193	+	501.193i	0.540079	+	0.540079i
$929$	435.996	−	251.722i	0.469318	−	0.270961i	−0.246636	−	0.969108i	$-0.579325\pi$
$929$	435.996	−	251.722i	0.469318	−	0.270961i	0.715954	+	0.698147i	$0.245992\pi$
$930$		0			0
$931$	245.976	−	426.044i	0.264207	−	0.457619i
$932$	300.655	+	1122.06i	0.322591	+	1.20393i
$933$	77.6380	−	1293.39i	0.0832133	−	1.38627i
$934$	65.6305	−	37.8918i	0.0702682	−	0.0405694i
$935$		0			0
$936$	−948.056	+	404.960i	−1.01288	+	0.432650i
$937$	−1181.10	+	1181.10i	−1.26051	+	1.26051i	−0.309660	+	0.950847i	$0.600215\pi$
$937$	−1181.10	+	1181.10i	−1.26051	+	1.26051i	−0.950847	+	0.309660i	$0.899785\pi$
$938$	12.1021	−	45.1656i	0.0129020	−	0.0481509i
$939$	−124.770	−	609.730i	−0.132875	−	0.649339i
$940$		0			0
$941$	−576.616	+	998.729i	−0.612770	+	1.06135i	0.378002	+	0.925805i	$0.376611\pi$
$941$	−576.616	+	998.729i	−0.612770	+	1.06135i	−0.990771	+	0.135543i	$0.956722\pi$
$942$	38.8894	+	77.7795i	0.0412838	+	0.0825684i
$943$	−14.8131	+	55.2832i	−0.0157085	+	0.0586248i
$944$			268.341i			0.284259i
$945$		0			0
$946$	−72.5844			−0.0767277
$947$	−1323.45	−	354.616i	−1.39751	−	0.374463i	−0.520063	−	0.854128i	$-0.674091\pi$
$947$	−1323.45	−	354.616i	−1.39751	−	0.374463i	−0.877451	+	0.479665i	$0.840758\pi$
$948$	−564.098	+	282.046i	−0.595040	+	0.297517i
$949$	561.512	+	324.189i	0.591688	+	0.341611i
$950$		0			0
$951$	1043.67	−	213.566i	1.09744	−	0.224570i
$952$	−142.344	−	38.1409i	−0.149521	−	0.0400640i
$953$	−77.4456	−	77.4456i	−0.0812650	−	0.0812650i	0.665306	−	0.746571i	$-0.268301\pi$
$953$	−77.4456	−	77.4456i	−0.0812650	−	0.0812650i	−0.746571	+	0.665306i	$0.768301\pi$
$954$	487.278	+	58.7110i	0.510773	+	0.0615420i
$955$		0			0
$956$	−67.1397	−	116.289i	−0.0702298	−	0.121642i
$957$	−837.486	−	50.2716i	−0.875116	−	0.0525304i
$958$	−142.282	+	38.1245i	−0.148520	+	0.0397959i
$959$	−3.83279	−	2.21286i	−0.00399666	−	0.00230747i
$960$		0			0
$961$	−454.630	−	787.443i	−0.473080	−	0.819399i
$962$	501.352	−	501.352i	0.521156	−	0.521156i
$963$	−26.7032	−	186.932i	−0.0277292	−	0.194114i
$964$			287.577i			0.298316i
$965$		0			0
$966$	−5.72371	+	1.17125i	−0.00592517	+	0.00121247i
$967$	−417.733	−	1559.00i	−0.431989	−	1.61220i	−0.748172	−	0.663505i	$-0.769068\pi$
$967$	−417.733	−	1559.00i	−0.431989	−	1.61220i	0.316183	−	0.948698i	$-0.397599\pi$
$968$	78.9205	−	21.1467i	0.0815295	−	0.0218458i
$969$	−435.921	−	145.309i	−0.449867	−	0.149958i
$970$		0			0
$971$	158.612			0.163349			0.0816745	−	0.996659i	$-0.473973\pi$
$971$	158.612			0.163349			0.0816745	+	0.996659i	$0.473973\pi$
$972$	−185.304	−	814.026i	−0.190642	−	0.837475i
$973$	337.156	+	337.156i	0.346511	+	0.346511i
$974$	−607.386	+	350.674i	−0.623599	+	0.360035i
$975$		0			0
$976$	392.332	−	679.539i	0.401980	−	0.696249i
$977$	−2.86555	−	10.6944i	−0.00293301	−	0.0109461i	0.964444	−	0.264288i	$-0.0851369\pi$
$977$	−2.86555	−	10.6944i	−0.00293301	−	0.0109461i	−0.967377	+	0.253342i	$0.918470\pi$
$978$	374.503	+	247.269i	0.382927	+	0.252831i
$979$	−1148.89	+	663.315i	−1.17354	+	0.677543i
$980$		0			0
$981$	−830.082	−	622.571i	−0.846159	−	0.634629i
$982$	418.604	−	418.604i	0.426277	−	0.426277i
$983$	−295.182	+	1101.63i	−0.300287	+	1.12069i	0.636640	+	0.771161i	$0.280324\pi$
$983$	−295.182	+	1101.63i	−0.300287	+	1.12069i	−0.936927	+	0.349525i	$0.886343\pi$
$984$	−515.111	+	456.772i	−0.523486	+	0.464199i
$985$		0			0
$986$	127.892	−	221.516i	0.129708	−	0.224661i
$987$	99.5518	+	5.97578i	0.100863	+	0.00605449i
$988$	196.981	−	735.142i	0.199373	−	0.744071i
$989$			11.5579i			0.0116864i
$990$		0			0
$991$	−95.8581			−0.0967287			−0.0483643	−	0.998830i	$-0.515401\pi$
$991$	−95.8581			−0.0967287			−0.0483643	+	0.998830i	$0.515401\pi$
$992$	1232.96	+	330.371i	1.24291	+	0.333036i
$993$	938.579	+	619.706i	0.945195	+	0.624074i
$994$	120.685	+	69.6776i	0.121414	+	0.0700982i
$995$		0			0
$996$	−168.445	+	505.329i	−0.169122	+	0.507359i
$997$	850.093	+	227.782i	0.852651	+	0.228467i	0.658571	−	0.752518i	$-0.271161\pi$
$997$	850.093	+	227.782i	0.852651	+	0.228467i	0.194080	+	0.980986i	$0.437828\pi$
$998$	88.7943	+	88.7943i	0.0889723	+	0.0889723i
$999$	707.325	+	1021.72i	0.708033	+	1.02274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.3.o.b.193.6		40
5.2	odd	4	inner	225.3.o.b.157.5		40
5.3	odd	4		45.3.k.a.22.6	yes	40
5.4	even	2		45.3.k.a.13.5	yes	40
9.7	even	3	inner	225.3.o.b.43.5		40
15.8	even	4		135.3.l.a.37.5		40
15.14	odd	2		135.3.l.a.118.6		40
45.4	even	6		405.3.g.h.163.6		20
45.7	odd	12	inner	225.3.o.b.7.6		40
45.13	odd	12		405.3.g.h.82.6		20
45.14	odd	6		405.3.g.g.163.5		20
45.23	even	12		405.3.g.g.82.5		20
45.29	odd	6		135.3.l.a.73.5		40
45.34	even	6		45.3.k.a.43.6	yes	40
45.38	even	12		135.3.l.a.127.6		40
45.43	odd	12		45.3.k.a.7.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.5	✓	40	45.43	odd	12
45.3.k.a.13.5	yes	40	5.4	even	2
45.3.k.a.22.6	yes	40	5.3	odd	4
45.3.k.a.43.6	yes	40	45.34	even	6
135.3.l.a.37.5		40	15.8	even	4
135.3.l.a.73.5		40	45.29	odd	6
135.3.l.a.118.6		40	15.14	odd	2
135.3.l.a.127.6		40	45.38	even	12
225.3.o.b.7.6		40	45.7	odd	12	inner
225.3.o.b.43.5		40	9.7	even	3	inner
225.3.o.b.157.5		40	5.2	odd	4	inner
225.3.o.b.193.6		40	1.1	even	1	trivial
405.3.g.g.82.5		20	45.23	even	12
405.3.g.g.163.5		20	45.14	odd	6
405.3.g.h.82.6		20	45.13	odd	12
405.3.g.h.163.6		20	45.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.725667 + 0.194442i) q^{2} +(-2.68329 + 1.34163i) q^{3} +(-2.97532 - 1.71780i) q^{4} +(-2.20804 + 0.451834i) q^{6} +(1.79727 + 0.481578i) q^{7} +(-3.94998 - 3.94998i) q^{8} +(5.40005 - 7.19996i) q^{9} +(5.82294 + 10.0856i) q^{11} +(10.2883 + 0.617573i) q^{12} +(19.8070 - 5.30726i) q^{13} +(1.21058 + 0.698930i) q^{14} +(4.77288 + 8.26686i) q^{16} +(10.0254 - 10.0254i) q^{17} +(5.31861 - 4.17477i) q^{18} +10.8032i q^{19} +(-5.46870 + 1.11907i) q^{21} +(2.26444 + 8.45102i) q^{22} +(1.34569 - 0.360576i) q^{23} +(15.8983 + 5.29951i) q^{24} +15.4052 q^{26} +(-4.83020 + 26.5644i) q^{27} +(-4.52021 - 4.52021i) q^{28} +(20.7968 - 12.0070i) q^{29} +(21.6233 - 37.4526i) q^{31} +(7.63926 + 28.5101i) q^{32} +(-29.1558 - 19.2504i) q^{33} +(9.22442 - 5.32572i) q^{34} +(-28.4350 + 12.1460i) q^{36} +(32.5443 - 32.5443i) q^{37} +(-2.10058 + 7.83949i) q^{38} +(-46.0274 + 40.8145i) q^{39} +(-20.5409 + 35.5778i) q^{41} +(-4.18605 - 0.251275i) q^{42} +(-2.14721 + 8.01349i) q^{43} -40.0106i q^{44} +1.04663 q^{46} +(-17.2577 - 4.62418i) q^{47} +(-23.8981 - 15.7789i) q^{48} +(-39.4370 - 22.7689i) q^{49} +(-13.4506 + 40.3513i) q^{51} +(-68.0488 - 18.2336i) q^{52} +(51.3281 + 51.3281i) q^{53} +(-8.67035 + 18.3377i) q^{54} +(-5.19697 - 9.00141i) q^{56} +(-14.4938 - 28.9880i) q^{57} +(17.4262 - 4.66933i) q^{58} +(24.3449 + 14.0555i) q^{59} +(-41.1002 - 71.1876i) q^{61} +(22.9736 - 22.9736i) q^{62} +(13.1727 - 10.3398i) q^{63} -16.0088i q^{64} +(-17.4143 - 19.6385i) q^{66} +(-8.65757 - 32.3105i) q^{67} +(-47.0502 + 12.6071i) q^{68} +(-3.12710 + 2.77294i) q^{69} +99.6917 q^{71} +(-49.7697 + 7.10958i) q^{72} +(22.3583 + 22.3583i) q^{73} +(29.9443 - 17.2883i) q^{74} +(18.5577 - 32.1428i) q^{76} +(5.60840 + 20.9308i) q^{77} +(-41.3366 + 20.6681i) q^{78} +(-52.9926 + 30.5953i) q^{79} +(-22.6788 - 77.7603i) q^{81} +(-21.8237 + 21.8237i) q^{82} +(-13.3760 + 49.9199i) q^{83} +(18.1935 + 6.06456i) q^{84} +(-3.11631 + 5.39761i) q^{86} +(-39.6947 + 60.1198i) q^{87} +(16.8375 - 62.8384i) q^{88} +113.914i q^{89} +38.1544 q^{91} +(-4.62324 - 1.23879i) q^{92} +(-7.77386 + 129.506i) q^{93} +(-11.6242 - 6.71123i) q^{94} +(-58.7483 - 66.2517i) q^{96} +(29.5689 + 7.92297i) q^{97} +(-24.1909 - 24.1909i) q^{98} +(104.060 + 12.5380i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 6 q^{3} - 24 q^{6} + 2 q^{7} + 24 q^{8} + 8 q^{11} + 30 q^{12} + 2 q^{13} + 28 q^{16} - 28 q^{17} - 48 q^{18} + 12 q^{21} - 14 q^{22} - 82 q^{23} - 112 q^{26} + 198 q^{27} + 88 q^{28} - 4 q^{31}+ \cdots + 1876 q^{98}+O(q^{100}) \) 40 * q + 2 * q^2 + 6 * q^3 - 24 * q^6 + 2 * q^7 + 24 * q^8 + 8 * q^11 + 30 * q^12 + 2 * q^13 + 28 * q^16 - 28 * q^17 - 48 * q^18 + 12 * q^21 - 14 * q^22 - 82 * q^23 - 112 * q^26 + 198 * q^27 + 88 * q^28 - 4 * q^31 + 14 * q^32 - 96 * q^33 + 264 * q^36 + 92 * q^37 - 330 * q^38 - 28 * q^41 - 498 * q^42 + 2 * q^43 - 136 * q^46 - 64 * q^47 + 510 * q^48 - 396 * q^51 + 74 * q^52 + 608 * q^53 - 192 * q^56 + 114 * q^57 - 30 * q^58 + 92 * q^61 + 100 * q^62 - 24 * q^63 + 588 * q^66 + 80 * q^67 - 626 * q^68 + 248 * q^71 + 162 * q^72 + 8 * q^73 - 96 * q^76 - 338 * q^77 - 1062 * q^78 + 204 * q^81 - 104 * q^82 - 370 * q^83 - 328 * q^86 - 534 * q^87 + 210 * q^88 + 152 * q^91 - 388 * q^92 + 1062 * q^93 - 876 * q^96 - 292 * q^97 + 1876 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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