LMFDB - Embedded newform 333.3.bb.b.82.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,3,Mod(82,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("333.82");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	333.bb (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:	$9.07359280320$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 111)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			82.4
Character	$\chi$	$=$	333.82
Dual form			333.3.bb.b.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.839390 + 0.224914i) q^{2} +(-2.81011 - 1.62242i) q^{4} +(2.87694 - 0.770875i) q^{5} +(-5.46857 + 9.47184i) q^{7} +(-4.45178 - 4.45178i) q^{8} +O(q^{10})$	\(q+(0.839390 + 0.224914i) q^{2} +(-2.81011 - 1.62242i) q^{4} +(2.87694 - 0.770875i) q^{5} +(-5.46857 + 9.47184i) q^{7} +(-4.45178 - 4.45178i) q^{8} +2.58826 q^{10} -6.33599i q^{11} +(-10.7008 + 2.86727i) q^{13} +(-6.72061 + 6.72061i) q^{14} +(3.75416 + 6.50240i) q^{16} +(-3.46151 + 12.9185i) q^{17} +(-17.0020 + 4.55567i) q^{19} +(-9.33522 - 2.50136i) q^{20} +(1.42505 - 5.31837i) q^{22} +(-9.85072 - 9.85072i) q^{23} +(-13.9681 + 8.06448i) q^{25} -9.62702 q^{26} +(30.7346 - 17.7446i) q^{28} +(-23.8103 + 23.8103i) q^{29} +(-8.78892 + 8.78892i) q^{31} +(8.20659 + 30.6274i) q^{32} +(-5.81111 + 10.0651i) q^{34} +(-8.43116 + 31.4655i) q^{35} +(34.3742 - 13.6901i) q^{37} -15.2959 q^{38} +(-16.2393 - 9.37575i) q^{40} +(28.7377 + 16.5917i) q^{41} +(2.92862 + 2.92862i) q^{43} +(-10.2796 + 17.8048i) q^{44} +(-6.05303 - 10.4842i) q^{46} -49.3667 q^{47} +(-35.3105 - 61.1596i) q^{49} +(-13.5385 + 3.62762i) q^{50} +(34.7223 + 9.30382i) q^{52} +(-38.6025 - 66.8615i) q^{53} +(-4.88425 - 18.2283i) q^{55} +(66.5114 - 17.8217i) q^{56} +(-25.3414 + 14.6309i) q^{58} +(12.5719 - 46.9189i) q^{59} +(20.4520 + 76.3280i) q^{61} +(-9.35408 + 5.40058i) q^{62} -2.47921i q^{64} +(-28.5753 + 16.4979i) q^{65} +(-54.5535 - 31.4965i) q^{67} +(30.6865 - 30.6865i) q^{68} +(-14.1541 + 24.5156i) q^{70} +(65.9394 - 114.210i) q^{71} +45.6809i q^{73} +(31.9324 - 3.76008i) q^{74} +(55.1687 + 14.7824i) q^{76} +(60.0135 + 34.6488i) q^{77} +(102.419 - 27.4431i) q^{79} +(15.8131 + 15.8131i) q^{80} +(20.3904 + 20.3904i) q^{82} +(-19.4307 - 33.6549i) q^{83} +39.8343i q^{85} +(1.79956 + 3.11694i) q^{86} +(-28.2064 + 28.2064i) q^{88} +(142.743 + 38.2480i) q^{89} +(31.3597 - 117.036i) q^{91} +(11.6996 + 43.6636i) q^{92} +(-41.4379 - 11.1032i) q^{94} +(-45.4019 + 26.2128i) q^{95} +(-33.5594 - 33.5594i) q^{97} +(-15.8836 - 59.2786i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8}+O(q^{10}) $ 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8	$ 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8} - 60 q^{10} + 28 q^{13} - 42 q^{14} + 26 q^{16} - 10 q^{17} + 60 q^{19} + 4 q^{20} - 64 q^{22} - 34 q^{23} - 162 q^{25} + 44 q^{26} - 48 q^{28} - 32 q^{29} + 90 q^{32} + 46 q^{34} + 30 q^{35} + 80 q^{37} + 284 q^{38} - 144 q^{40} + 30 q^{41} + 130 q^{43} + 16 q^{44} + 78 q^{46} + 56 q^{47} - 20 q^{49} - 70 q^{50} + 16 q^{52} + 190 q^{53} + 350 q^{55} - 376 q^{56} + 336 q^{58} + 258 q^{59} - 84 q^{61} + 474 q^{62} + 54 q^{65} - 372 q^{67} + 434 q^{68} + 102 q^{70} - 66 q^{71} + 416 q^{74} + 702 q^{76} - 198 q^{77} + 88 q^{79} - 900 q^{80} - 470 q^{82} - 166 q^{83} - 432 q^{86} + 530 q^{88} - 304 q^{89} + 524 q^{91} - 330 q^{92} - 344 q^{94} - 1080 q^{95} - 110 q^{97} - 926 q^{98}+O(q^{100}) $ 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8 - 60 * q^10 + 28 * q^13 - 42 * q^14 + 26 * q^16 - 10 * q^17 + 60 * q^19 + 4 * q^20 - 64 * q^22 - 34 * q^23 - 162 * q^25 + 44 * q^26 - 48 * q^28 - 32 * q^29 + 90 * q^32 + 46 * q^34 + 30 * q^35 + 80 * q^37 + 284 * q^38 - 144 * q^40 + 30 * q^41 + 130 * q^43 + 16 * q^44 + 78 * q^46 + 56 * q^47 - 20 * q^49 - 70 * q^50 + 16 * q^52 + 190 * q^53 + 350 * q^55 - 376 * q^56 + 336 * q^58 + 258 * q^59 - 84 * q^61 + 474 * q^62 + 54 * q^65 - 372 * q^67 + 434 * q^68 + 102 * q^70 - 66 * q^71 + 416 * q^74 + 702 * q^76 - 198 * q^77 + 88 * q^79 - 900 * q^80 - 470 * q^82 - 166 * q^83 - 432 * q^86 + 530 * q^88 - 304 * q^89 + 524 * q^91 - 330 * q^92 - 344 * q^94 - 1080 * q^95 - 110 * q^97 - 926 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	0.839390	+	0.224914i	0.419695	+	0.112457i	0.462485	−	0.886627i	$-0.346958\pi$
$2$	0.839390	+	0.224914i	0.419695	+	0.112457i	−0.0427899	+	0.999084i	$0.513625\pi$
$3$		0			0
$3$		0			0
$4$	−2.81011	−	1.62242i	−0.702528	−	0.405605i
$5$	2.87694	−	0.770875i	0.575389	−	0.154175i	0.0406218	−	0.999175i	$-0.487066\pi$
$5$	2.87694	−	0.770875i	0.575389	−	0.154175i	0.534767	+	0.845000i	$0.320399\pi$
$6$		0			0
$7$	−5.46857	+	9.47184i	−0.781224	+	1.35312i	0.150005	+	0.988685i	$0.452071\pi$
$7$	−5.46857	+	9.47184i	−0.781224	+	1.35312i	−0.931229	+	0.364435i	$0.881262\pi$
$8$	−4.45178	−	4.45178i	−0.556472	−	0.556472i
$9$		0			0
$10$	2.58826			0.258826
$11$		−	6.33599i		−	0.575999i	−0.957631	−	0.287999i	$-0.907010\pi$
$11$		−	6.33599i		−	0.575999i	0.957631	−	0.287999i	$-0.0929901\pi$
$12$		0			0
$13$	−10.7008	+	2.86727i	−0.823138	+	0.220559i	−0.645718	−	0.763576i	$-0.723442\pi$
$13$	−10.7008	+	2.86727i	−0.823138	+	0.220559i	−0.177420	+	0.984135i	$0.556775\pi$
$14$	−6.72061	+	6.72061i	−0.480044	+	0.480044i
$15$		0			0
$16$	3.75416	+	6.50240i	0.234635	+	0.406400i
$17$	−3.46151	+	12.9185i	−0.203618	+	0.759914i	0.786248	+	0.617911i	$0.212021\pi$
$17$	−3.46151	+	12.9185i	−0.203618	+	0.759914i	−0.989866	+	0.142003i	$0.954646\pi$
$18$		0			0
$19$	−17.0020	+	4.55567i	−0.894841	+	0.239772i	−0.676799	−	0.736167i	$-0.736634\pi$
$19$	−17.0020	+	4.55567i	−0.894841	+	0.239772i	−0.218042	+	0.975939i	$0.569967\pi$
$20$	−9.33522	−	2.50136i	−0.466761	−	0.125068i
$21$		0			0
$22$	1.42505	−	5.31837i	0.0647751	−	0.241744i
$23$	−9.85072	−	9.85072i	−0.428292	−	0.428292i	0.459754	−	0.888046i	$-0.347938\pi$
$23$	−9.85072	−	9.85072i	−0.428292	−	0.428292i	−0.888046	+	0.459754i	$0.847938\pi$
$24$		0			0
$25$	−13.9681	+	8.06448i	−0.558723	+	0.322579i
$26$	−9.62702			−0.370270
$27$		0			0
$28$	30.7346	−	17.7446i	1.09766	−	0.633737i
$29$	−23.8103	+	23.8103i	−0.821046	+	0.821046i	−0.986258	−	0.165212i	$-0.947169\pi$
$29$	−23.8103	+	23.8103i	−0.821046	+	0.821046i	0.165212	+	0.986258i	$0.447169\pi$
$30$		0			0
$31$	−8.78892	+	8.78892i	−0.283514	+	0.283514i	−0.834509	−	0.550995i	$-0.814248\pi$
$31$	−8.78892	+	8.78892i	−0.283514	+	0.283514i	0.550995	+	0.834509i	$0.314248\pi$
$32$	8.20659	+	30.6274i	0.256456	+	0.957106i
$33$		0			0
$34$	−5.81111	+	10.0651i	−0.170915	+	0.296034i
$35$	−8.43116	+	31.4655i	−0.240890	+	0.899015i
$36$		0			0
$37$	34.3742	−	13.6901i	0.929031	−	0.370002i
$37$	34.3742	−	13.6901i	0.929031	−	0.370002i
$38$	−15.2959			−0.402524
$39$		0			0
$40$	−16.2393	−	9.37575i	−0.405982	−	0.234394i
$41$	28.7377	+	16.5917i	0.700920	+	0.404676i	0.807690	−	0.589608i	$-0.200718\pi$
$41$	28.7377	+	16.5917i	0.700920	+	0.404676i	−0.106770	+	0.994284i	$0.534051\pi$
$42$		0			0
$43$	2.92862	+	2.92862i	0.0681074	+	0.0681074i	0.740340	−	0.672233i	$-0.234665\pi$
$43$	2.92862	+	2.92862i	0.0681074	+	0.0681074i	−0.672233	+	0.740340i	$0.734665\pi$
$44$	−10.2796	+	17.8048i	−0.233628	+	0.404655i
$45$		0			0
$46$	−6.05303	−	10.4842i	−0.131588	−	0.227917i
$47$	−49.3667			−1.05035			−0.525177	−	0.850993i	$-0.676001\pi$
$47$	−49.3667			−1.05035			−0.525177	+	0.850993i	$0.676001\pi$
$48$		0			0
$49$	−35.3105	−	61.1596i	−0.720622	−	1.24815i
$50$	−13.5385	+	3.62762i	−0.270770	+	0.0725525i
$51$		0			0
$52$	34.7223	+	9.30382i	0.667737	+	0.178920i
$53$	−38.6025	−	66.8615i	−0.728349	−	1.26154i	−0.957581	−	0.288165i	$-0.906955\pi$
$53$	−38.6025	−	66.8615i	−0.728349	−	1.26154i	0.229232	−	0.973372i	$-0.426379\pi$
$54$		0			0
$55$	−4.88425	−	18.2283i	−0.0888046	−	0.331423i
$56$	66.5114	−	17.8217i	1.18770	−	0.318244i
$57$		0			0
$58$	−25.3414	+	14.6309i	−0.436921	+	0.252256i
$59$	12.5719	−	46.9189i	0.213083	−	0.795235i	−0.773750	−	0.633491i	$-0.781621\pi$
$59$	12.5719	−	46.9189i	0.213083	−	0.795235i	0.986833	−	0.161744i	$-0.0517120\pi$
$60$		0			0
$61$	20.4520	+	76.3280i	0.335279	+	1.25128i	0.903566	+	0.428448i	$0.140940\pi$
$61$	20.4520	+	76.3280i	0.335279	+	1.25128i	−0.568287	+	0.822830i	$0.692394\pi$
$62$	−9.35408	+	5.40058i	−0.150872	+	0.0871062i
$63$		0			0
$64$		−	2.47921i		−	0.0387377i
$65$	−28.5753	+	16.4979i	−0.439619	+	0.253814i
$66$		0			0
$67$	−54.5535	−	31.4965i	−0.814231	−	0.470096i	0.0341922	−	0.999415i	$-0.489114\pi$
$67$	−54.5535	−	31.4965i	−0.814231	−	0.470096i	−0.848423	+	0.529319i	$0.822448\pi$
$68$	30.6865	−	30.6865i	0.451272	−	0.451272i
$69$		0			0
$70$	−14.1541	+	24.5156i	−0.202201	+	0.350222i
$71$	65.9394	−	114.210i	0.928724	−	1.60860i	0.143265	−	0.989684i	$-0.454240\pi$
$71$	65.9394	−	114.210i	0.928724	−	1.60860i	0.785459	−	0.618913i	$-0.212427\pi$
$72$		0			0
$73$			45.6809i			0.625766i	0.949792	+	0.312883i	$0.101295\pi$
$73$			45.6809i			0.625766i	−0.949792	+	0.312883i	$0.898705\pi$
$74$	31.9324	−	3.76008i	0.431519	−	0.0508118i
$75$		0			0
$76$	55.1687	+	14.7824i	0.725904	+	0.194505i
$77$	60.0135	+	34.6488i	0.779396	+	0.449984i
$78$		0			0
$79$	102.419	−	27.4431i	1.29644	−	0.347381i	0.456339	−	0.889806i	$-0.349161\pi$
$79$	102.419	−	27.4431i	1.29644	−	0.347381i	0.840104	+	0.542425i	$0.182494\pi$
$80$	15.8131	+	15.8131i	0.197663	+	0.197663i
$81$		0			0
$82$	20.3904	+	20.3904i	0.248664	+	0.248664i
$83$	−19.4307	−	33.6549i	−0.234104	−	0.405481i	0.724908	−	0.688846i	$-0.241882\pi$
$83$	−19.4307	−	33.6549i	−0.234104	−	0.405481i	−0.959012	+	0.283365i	$0.908549\pi$
$84$		0			0
$85$			39.8343i			0.468638i
$86$	1.79956	+	3.11694i	0.0209252	+	0.0362435i
$87$		0			0
$88$	−28.2064	+	28.2064i	−0.320528	+	0.320528i
$89$	142.743	+	38.2480i	1.60386	+	0.429752i	0.946205	−	0.323569i	$-0.104883\pi$
$89$	142.743	+	38.2480i	1.60386	+	0.429752i	0.657653	+	0.753321i	$0.271549\pi$
$90$		0			0
$91$	31.3597	−	117.036i	0.344612	−	1.28611i
$92$	11.6996	+	43.6636i	0.127170	+	0.474605i
$93$		0			0
$94$	−41.4379	−	11.1032i	−0.440828	−	0.118120i
$95$	−45.4019	+	26.2128i	−0.477915	+	0.275924i
$96$		0			0
$97$	−33.5594	−	33.5594i	−0.345973	−	0.345973i	0.512634	−	0.858607i	$-0.328670\pi$
$97$	−33.5594	−	33.5594i	−0.345973	−	0.345973i	−0.858607	+	0.512634i	$0.828670\pi$
$98$	−15.8836	−	59.2786i	−0.162078	−	0.604883i
$99$		0			0
$100$	52.3358			0.523358
$101$			57.4444i			0.568757i	0.958712	+	0.284378i	$0.0917872\pi$
$101$			57.4444i			0.568757i	−0.958712	+	0.284378i	$0.908213\pi$
$102$		0			0
$103$	−16.8592	+	16.8592i	−0.163682	+	0.163682i	−0.784195	−	0.620514i	$-0.786924\pi$
$103$	−16.8592	+	16.8592i	−0.163682	+	0.163682i	0.620514	+	0.784195i	$0.286924\pi$
$104$	60.4020	+	34.8731i	0.580788	+	0.335318i
$105$		0			0
$106$	−17.3645	−	64.8051i	−0.163816	−	0.611369i
$107$	−34.7098	+	60.1192i	−0.324391	+	0.561862i	−0.981389	−	0.192031i	$-0.938493\pi$
$107$	−34.7098	+	60.1192i	−0.324391	+	0.561862i	0.656998	+	0.753892i	$0.271826\pi$
$108$		0			0
$109$	−43.6493	+	162.901i	−0.400452	+	1.49451i	0.411840	+	0.911256i	$0.364886\pi$
$109$	−43.6493	+	162.901i	−0.400452	+	1.49451i	−0.812292	+	0.583251i	$0.801780\pi$
$110$		−	16.3992i		−	0.149083i
$111$		0			0
$112$	−82.1196			−0.733211
$113$	−127.959	−	34.2866i	−1.13238	−	0.303421i	−0.356498	−	0.934296i	$-0.616029\pi$
$113$	−127.959	−	34.2866i	−1.13238	−	0.303421i	−0.775885	+	0.630875i	$0.782696\pi$
$114$		0			0
$115$	−35.9336	−	20.7463i	−0.312466	−	0.180403i
$116$	105.540	−	28.2794i	0.909828	−	0.243788i
$117$		0			0
$118$	21.1054	−	36.5557i	0.178859	−	0.309794i
$119$	−103.433	−	103.433i	−0.869183	−	0.869183i
$120$		0			0
$121$	80.8552			0.668225
$122$			68.6689i			0.562860i
$123$		0			0
$124$	38.9572	−	10.4385i	0.314171	−	0.0841818i
$125$	−86.6204	+	86.6204i	−0.692963	+	0.692963i
$126$		0			0
$127$	35.3092	+	61.1573i	0.278025	+	0.481553i	0.970894	−	0.239510i	$-0.0769869\pi$
$127$	35.3092	+	61.1573i	0.278025	+	0.481553i	−0.692869	+	0.721064i	$0.743654\pi$
$128$	33.3840	−	124.591i	0.260812	−	0.973364i
$129$		0			0
$130$	−27.6964	+	7.42123i	−0.213049	+	0.0570864i
$131$	−153.258	−	41.0653i	−1.16991	−	0.313475i	−0.378990	−	0.925401i	$-0.623729\pi$
$131$	−153.258	−	41.0653i	−1.16991	−	0.313475i	−0.790916	+	0.611925i	$0.790395\pi$
$132$		0			0
$133$	49.8260	−	185.953i	0.374631	−	1.39814i
$134$	−38.7076	−	38.7076i	−0.288863	−	0.288863i
$135$		0			0
$136$	72.9203	−	42.1006i	0.536179	−	0.309563i
$137$	267.889			1.95540			0.977698	−	0.210015i	$-0.0673513\pi$
$137$	267.889			1.95540			0.977698	+	0.210015i	$0.0673513\pi$
$138$		0			0
$139$	33.6275	−	19.4148i	0.241924	−	0.139675i	−0.374137	−	0.927374i	$-0.622061\pi$
$139$	33.6275	−	19.4148i	0.241924	−	0.139675i	0.616061	+	0.787699i	$0.288728\pi$
$140$	74.7428	−	74.7428i	0.533877	−	0.533877i
$141$		0			0
$142$	81.0364	−	81.0364i	0.570679	−	0.570679i
$143$	18.1670	+	67.8001i	0.127042	+	0.474126i
$144$		0			0
$145$	−50.1462	+	86.8557i	−0.345836	+	0.599005i
$146$	−10.2743	+	38.3441i	−0.0703717	+	0.262631i
$147$		0			0
$148$	−118.806	−	17.2987i	−0.802745	−	0.116883i
$149$	154.757			1.03864			0.519320	−	0.854580i	$-0.326185\pi$
$149$	154.757			1.03864			0.519320	+	0.854580i	$0.326185\pi$
$150$		0			0
$151$	110.927	+	64.0435i	0.734614	+	0.424129i	0.820108	−	0.572209i	$-0.193914\pi$
$151$	110.927	+	64.0435i	0.734614	+	0.424129i	−0.0854940	+	0.996339i	$0.527247\pi$
$152$	95.9699	+	55.4083i	0.631381	+	0.364528i
$153$		0			0
$154$	42.5817	+	42.5817i	0.276505	+	0.276505i
$155$	−18.5101	+	32.0604i	−0.119420	+	0.206841i
$156$		0			0
$157$	−145.302	−	251.670i	−0.925489	−	1.60299i	−0.790773	−	0.612110i	$-0.790321\pi$
$157$	−145.302	−	251.670i	−0.925489	−	1.60299i	−0.134716	−	0.990884i	$-0.543012\pi$
$158$	92.1418			0.583176
$159$		0			0
$160$	47.2198	+	81.7870i	0.295123	+	0.511169i
$161$	147.174	−	39.4351i	0.914123	−	0.244939i
$162$		0			0
$163$	128.748	+	34.4978i	0.789863	+	0.211643i	0.631128	−	0.775678i	$-0.282592\pi$
$163$	128.748	+	34.4978i	0.789863	+	0.211643i	0.158734	+	0.987321i	$0.449259\pi$
$164$	−53.8375	−	93.2492i	−0.328277	−	0.568593i
$165$		0			0
$166$	−8.74045	−	32.6198i	−0.0526533	−	0.196505i
$167$	−254.319	+	68.1447i	−1.52287	+	0.408052i	−0.920686	−	0.390305i	$-0.872370\pi$
$167$	−254.319	+	68.1447i	−1.52287	+	0.408052i	−0.602185	+	0.798357i	$0.705703\pi$
$168$		0			0
$169$	−40.0726	+	23.1360i	−0.237116	+	0.136899i
$170$	−8.95928	+	33.4365i	−0.0527016	+	0.196685i
$171$		0			0
$172$	−3.47830	−	12.9812i	−0.0202227	−	0.0754720i
$173$	−243.861	+	140.793i	−1.40960	+	0.813834i	−0.995350	−	0.0963286i	$-0.969290\pi$
$173$	−243.861	+	140.793i	−1.40960	+	0.813834i	−0.414252	+	0.910162i	$0.635957\pi$
$174$		0			0
$175$		−	176.405i		−	1.00803i
$176$	41.1992	−	23.7863i	0.234086	−	0.135150i
$177$		0			0
$178$	111.215	+	64.2099i	0.624802	+	0.360730i
$179$	−107.356	+	107.356i	−0.599752	+	0.599752i	−0.940247	−	0.340494i	$-0.889406\pi$
$179$	−107.356	+	107.356i	−0.599752	+	0.599752i	0.340494	+	0.940247i	$0.389406\pi$
$180$		0			0
$181$	−148.979	+	258.039i	−0.823087	+	1.42563i	0.0802859	+	0.996772i	$0.474417\pi$
$181$	−148.979	+	258.039i	−0.823087	+	1.42563i	−0.903373	+	0.428856i	$0.858917\pi$
$182$	52.6460	−	91.1856i	0.289264	−	0.501020i
$183$		0			0
$184$			87.7065i			0.476666i
$185$	88.3392	−	65.8837i	0.477509	−	0.356128i
$186$		0			0
$187$	81.8517	+	21.9321i	0.437709	+	0.117284i
$188$	138.726	+	80.0934i	0.737904	+	0.426029i
$189$		0			0
$190$	−44.0055	+	11.7912i	−0.231608	+	0.0620592i
$191$	−163.944	−	163.944i	−0.858344	−	0.858344i	0.132799	−	0.991143i	$-0.457603\pi$
$191$	−163.944	−	163.944i	−0.858344	−	0.858344i	−0.991143	+	0.132799i	$0.957603\pi$
$192$		0			0
$193$	−120.743	−	120.743i	−0.625613	−	0.625613i	0.321348	−	0.946961i	$-0.395864\pi$
$193$	−120.743	−	120.743i	−0.625613	−	0.625613i	−0.946961	+	0.321348i	$0.895864\pi$
$194$	−20.6215	−	35.7174i	−0.106296	−	0.184110i
$195$		0			0
$196$			229.154i			1.16915i
$197$	−3.09455	−	5.35991i	−0.0157084	−	0.0272077i	0.858064	−	0.513542i	$-0.171667\pi$
$197$	−3.09455	−	5.35991i	−0.0157084	−	0.0272077i	−0.873773	+	0.486334i	$0.838334\pi$
$198$		0			0
$199$	−61.0856	+	61.0856i	−0.306963	+	0.306963i	−0.843730	−	0.536767i	$-0.819645\pi$
$199$	−61.0856	+	61.0856i	−0.306963	+	0.306963i	0.536767	+	0.843730i	$0.319645\pi$
$200$	98.0841	+	26.2816i	0.490420	+	0.131408i
$201$		0			0
$202$	−12.9201	+	48.2183i	−0.0639607	+	0.238704i
$203$	−95.3192	−	355.736i	−0.469552	−	1.75239i
$204$		0			0
$205$	95.4669	+	25.5803i	0.465692	+	0.124782i
$206$	−17.9433	+	10.3596i	−0.0871035	+	0.0502892i
$207$		0			0
$208$	−58.8166	−	58.8166i	−0.282772	−	0.282772i
$209$	28.8647	+	107.724i	0.138108	+	0.515428i
$210$		0			0
$211$	−237.879			−1.12739			−0.563695	−	0.825983i	$-0.690621\pi$
$211$	−237.879			−1.12739			−0.563695	+	0.825983i	$0.690621\pi$
$212$			250.518i			1.18169i
$213$		0			0
$214$	−42.6567	+	42.6567i	−0.199330	+	0.199330i
$215$	10.6831	+	6.16787i	0.0496886	+	0.0286878i
$216$		0			0
$217$	−35.1844	−	131.310i	−0.162140	−	0.605116i
$218$	−73.2775	+	126.920i	−0.336135	+	0.582204i
$219$		0			0
$220$	−15.8486	+	59.1478i	−0.0720391	+	0.268854i
$221$		−	148.164i		−	0.670423i
$222$		0			0
$223$	−143.250			−0.642375			−0.321188	−	0.947016i	$-0.604082\pi$
$223$	−143.250			−0.642375			−0.321188	+	0.947016i	$0.604082\pi$
$224$	−334.976	−	89.7566i	−1.49543	−	0.400699i
$225$		0			0
$226$	−99.6962	−	57.5596i	−0.441134	−	0.254689i
$227$	−179.275	+	48.0367i	−0.789759	+	0.211615i	−0.631083	−	0.775715i	$-0.717389\pi$
$227$	−179.275	+	48.0367i	−0.789759	+	0.211615i	−0.158676	+	0.987331i	$0.550723\pi$
$228$		0			0
$229$	−130.418	+	225.891i	−0.569511	+	0.986422i	0.427103	+	0.904203i	$0.359534\pi$
$229$	−130.418	+	225.891i	−0.569511	+	0.986422i	−0.996614	+	0.0822190i	$0.973799\pi$
$230$	−25.4962	−	25.4962i	−0.110853	−	0.110853i
$231$		0			0
$232$	211.997			0.913778
$233$		−	34.5543i		−	0.148302i	−0.997247	−	0.0741509i	$-0.976375\pi$
$233$		−	34.5543i		−	0.148302i	0.997247	−	0.0741509i	$-0.0236246\pi$
$234$		0			0
$235$	−142.025	+	38.0555i	−0.604362	+	0.161938i
$236$	−111.451	+	111.451i	−0.472248	+	0.472248i
$237$		0			0
$238$	−63.5570	−	110.084i	−0.267046	−	0.462537i
$239$	−85.7750	+	320.117i	−0.358891	+	1.33940i	0.516625	+	0.856211i	$0.327188\pi$
$239$	−85.7750	+	320.117i	−0.358891	+	1.33940i	−0.875517	+	0.483188i	$0.839479\pi$
$240$		0			0
$241$	315.290	−	84.4816i	1.30826	−	0.350546i	0.463690	−	0.885997i	$-0.346525\pi$
$241$	315.290	−	84.4816i	1.30826	−	0.350546i	0.844566	+	0.535451i	$0.179858\pi$
$242$	67.8691	+	18.1855i	0.280451	+	0.0751466i
$243$		0			0
$244$	66.3635	−	247.672i	0.271982	−	1.01505i
$245$	−148.733	−	148.733i	−0.607072	−	0.607072i
$246$		0			0
$247$	168.872	−	97.4985i	0.683693	−	0.394731i
$248$	78.2527			0.315535
$249$		0			0
$250$	−92.1904	+	53.2262i	−0.368762	+	0.212905i
$251$	−51.8100	+	51.8100i	−0.206414	+	0.206414i	−0.802741	−	0.596327i	$-0.796626\pi$
$251$	−51.8100	+	51.8100i	−0.206414	+	0.206414i	0.596327	+	0.802741i	$0.296626\pi$
$252$		0			0
$253$	−62.4141	+	62.4141i	−0.246696	+	0.246696i
$254$	15.8830	+	59.2763i	0.0625317	+	0.233371i
$255$		0			0
$256$	51.0859	−	88.4833i	0.199554	−	0.345638i
$257$	−43.0602	+	160.703i	−0.167549	+	0.625302i	0.830152	+	0.557537i	$0.188254\pi$
$257$	−43.0602	+	160.703i	−0.167549	+	0.625302i	−0.997701	+	0.0677653i	$0.978413\pi$
$258$		0			0
$259$	−58.3074	+	400.451i	−0.225125	+	1.54614i
$260$	107.066			0.411793
$261$		0			0
$262$	−119.407	−	68.9396i	−0.455751	−	0.263128i
$263$	256.466	+	148.071i	0.975157	+	0.563007i	0.900804	−	0.434225i	$-0.142978\pi$
$263$	256.466	+	148.071i	0.975157	+	0.563007i	0.0743524	+	0.997232i	$0.476311\pi$
$264$		0			0
$265$	−162.599	−	162.599i	−0.613581	−	0.613581i
$266$	83.6468	−	144.881i	0.314462	−	0.544664i
$267$		0			0
$268$	102.201	+	177.017i	0.381347	+	0.660512i
$269$	213.881			0.795096			0.397548	−	0.917581i	$-0.369861\pi$
$269$	213.881			0.795096			0.397548	+	0.917581i	$0.369861\pi$
$270$		0			0
$271$	−135.625	−	234.910i	−0.500462	−	0.866825i	−1.00000		0.000533065i	$-0.999830\pi$
$271$	−135.625	−	234.910i	−0.500462	−	0.866825i	0.499538	−	0.866292i	$-0.333503\pi$
$272$	−96.9966	+	25.9902i	−0.356605	+	0.0955520i
$273$		0			0
$274$	224.864	+	60.2520i	0.820670	+	0.219898i
$275$	51.0964	+	88.5016i	0.185805	+	0.321824i
$276$		0			0
$277$	56.1726	+	209.639i	0.202789	+	0.756820i	0.990112	+	0.140279i	$0.0447999\pi$
$277$	56.1726	+	209.639i	0.202789	+	0.756820i	−0.787323	+	0.616541i	$0.788533\pi$
$278$	32.5932	−	8.73332i	0.117242	−	0.0314148i
$279$		0			0
$280$	177.611	−	102.544i	0.634326	−	0.366228i
$281$	89.7404	−	334.916i	0.319361	−	1.19187i	−0.600499	−	0.799625i	$-0.705032\pi$
$281$	89.7404	−	334.916i	0.319361	−	1.19187i	0.919860	−	0.392246i	$-0.128302\pi$
$282$		0			0
$283$	15.8003	+	58.9675i	0.0558315	+	0.208366i	0.988207	−	0.153126i	$-0.0489341\pi$
$283$	15.8003	+	58.9675i	0.0558315	+	0.208366i	−0.932375	+	0.361492i	$0.882267\pi$
$284$	−370.594	+	213.963i	−1.30491	+	0.753390i
$285$		0			0
$286$			60.9967i			0.213275i
$287$	−314.308	+	181.466i	−1.09515	+	0.632286i
$288$		0			0
$289$	95.3749	+	55.0647i	0.330017	+	0.190535i
$290$	−61.6272	+	61.6272i	−0.212508	+	0.212508i
$291$		0			0
$292$	74.1135	−	128.368i	0.253814	−	0.439618i
$293$	12.6117	−	21.8442i	0.0430435	−	0.0745535i	−0.843701	−	0.536813i	$-0.819628\pi$
$293$	12.6117	−	21.8442i	0.0430435	−	0.0745535i	0.886745	+	0.462260i	$0.152961\pi$
$294$		0			0
$295$		−	144.674i		−	0.490421i
$296$	−213.971	−	92.0810i	−0.722876	−	0.311085i
$297$		0			0
$298$	129.902	+	34.8071i	0.435912	+	0.116802i
$299$	133.655	+	77.1658i	0.447007	+	0.258080i
$300$		0			0
$301$	−43.7547	+	11.7240i	−0.145365	+	0.0389503i
$302$	78.7064	+	78.7064i	0.260617	+	0.260617i
$303$		0			0
$304$	−93.4510	−	93.4510i	−0.307405	−	0.307405i
$305$	117.679	+	203.825i	0.385832	+	0.668280i
$306$		0			0
$307$		−	40.0715i		−	0.130526i	−0.997868	−	0.0652630i	$-0.979211\pi$
$307$		−	40.0715i		−	0.130526i	0.997868	−	0.0652630i	$-0.0207886\pi$
$308$	−112.430	−	194.734i	−0.365032	−	0.632253i
$309$		0			0
$310$	−22.7480	+	22.7480i	−0.0733806	+	0.0733806i
$311$	326.416	+	87.4629i	1.04957	+	0.281231i	0.742074	−	0.670318i	$-0.233842\pi$
$311$	326.416	+	87.4629i	1.04957	+	0.281231i	0.307496	+	0.951549i	$0.400509\pi$
$312$		0			0
$313$	63.3144	−	236.292i	0.202282	−	0.754928i	−0.787978	−	0.615703i	$-0.788872\pi$
$313$	63.3144	−	236.292i	0.202282	−	0.754928i	0.990261	−	0.139225i	$-0.0444612\pi$
$314$	−65.3608	−	243.930i	−0.208155	−	0.776846i
$315$		0			0
$316$	−332.333	−	89.0483i	−1.05169	−	0.281799i
$317$	−378.958	+	218.792i	−1.19545	+	0.690195i	−0.959538	−	0.281579i	$-0.909142\pi$
$317$	−378.958	+	218.792i	−1.19545	+	0.690195i	−0.235914	+	0.971774i	$0.575808\pi$
$318$		0			0
$319$	150.862	+	150.862i	0.472921	+	0.472921i
$320$	−1.91116	−	7.13256i	−0.00597239	−	0.0222892i
$321$		0			0
$322$	132.406			0.411198
$323$		−	235.410i		−	0.728824i
$324$		0			0
$325$	126.346	−	126.346i	0.388758	−	0.388758i
$326$	100.310	+	57.9142i	0.307701	+	0.177651i
$327$		0			0
$328$	−54.0712	−	201.797i	−0.164851	−	0.615234i
$329$	269.965	−	467.593i	0.820562	−	1.42126i
$330$		0			0
$331$	−61.8158	+	230.700i	−0.186755	+	0.696978i	0.807494	+	0.589876i	$0.200824\pi$
$331$	−61.8158	+	230.700i	−0.186755	+	0.696978i	−0.994248	+	0.107101i	$0.965843\pi$
$332$			126.099i			0.379815i
$333$		0			0
$334$	−228.800			−0.685029
$335$	−181.227	−	48.5596i	−0.540976	−	0.144954i
$336$		0			0
$337$	−448.969	−	259.212i	−1.33225	−	0.769176i	−0.346607	−	0.938010i	$-0.612666\pi$
$337$	−448.969	−	259.212i	−1.33225	−	0.769176i	−0.985644	+	0.168835i	$0.946000\pi$
$338$	−38.8402	+	10.4072i	−0.114912	+	0.0307905i
$339$		0			0
$340$	64.6279	−	111.939i	0.190082	−	0.329232i
$341$	55.6865	+	55.6865i	0.163304	+	0.163304i
$342$		0			0
$343$	236.472			0.689422
$344$		−	26.0751i		−	0.0757997i
$345$		0			0
$346$	−236.361	+	63.3327i	−0.683124	+	0.183042i
$347$	90.0238	−	90.0238i	0.259435	−	0.259435i	−0.565389	−	0.824824i	$-0.691274\pi$
$347$	90.0238	−	90.0238i	0.259435	−	0.259435i	0.824824	+	0.565389i	$0.191274\pi$
$348$		0			0
$349$	255.418	+	442.396i	0.731855	+	1.26761i	0.956089	+	0.293076i	$0.0946787\pi$
$349$	255.418	+	442.396i	0.731855	+	1.26761i	−0.224234	+	0.974535i	$0.571988\pi$
$350$	39.6758	−	148.072i	0.113360	−	0.423063i
$351$		0			0
$352$	194.055	−	51.9968i	0.551292	−	0.147718i
$353$	552.475	+	148.035i	1.56509	+	0.419363i	0.934269	−	0.356569i	$-0.116053\pi$
$353$	552.475	+	148.035i	1.56509	+	0.419363i	0.630817	+	0.775932i	$0.282720\pi$
$354$		0			0
$355$	101.662	−	379.408i	0.286372	−	1.06875i
$356$	−339.071	−	339.071i	−0.952445	−	0.952445i
$357$		0			0
$358$	−114.259	+	65.9675i	−0.319159	+	0.184267i
$359$	−195.484			−0.544522			−0.272261	−	0.962223i	$-0.587771\pi$
$359$	−195.484			−0.544522			−0.272261	+	0.962223i	$0.587771\pi$
$360$		0			0
$361$	−44.3219	+	25.5893i	−0.122775	+	0.0708844i
$362$	−183.088	+	183.088i	−0.505767	+	0.505767i
$363$		0			0
$364$	−278.006	+	278.006i	−0.763752	+	0.763752i
$365$	35.2142	+	131.421i	0.0964774	+	0.360058i
$366$		0			0
$367$	−299.706	+	519.106i	−0.816638	+	1.41446i	0.0915072	+	0.995804i	$0.470832\pi$
$367$	−299.706	+	519.106i	−0.816638	+	1.41446i	−0.908146	+	0.418655i	$0.862502\pi$
$368$	27.0721	−	101.035i	0.0735656	−	0.274551i
$369$		0			0
$370$	88.9692	−	35.4334i	0.240457	−	0.0957660i
$371$	844.402			2.27602
$372$		0			0
$373$	43.8575	+	25.3211i	0.117580	+	0.0678851i	0.557637	−	0.830085i	$-0.311708\pi$
$373$	43.8575	+	25.3211i	0.117580	+	0.0678851i	−0.440056	+	0.897970i	$0.645042\pi$
$374$	63.7726	+	36.8191i	0.170515	+	0.0984469i
$375$		0			0
$376$	219.769	+	219.769i	0.584493	+	0.584493i
$377$	186.519	−	323.060i	0.494744	−	0.856922i
$378$		0			0
$379$	266.507	+	461.605i	0.703186	+	1.21795i	0.967342	+	0.253474i	$0.0815732\pi$
$379$	266.507	+	461.605i	0.703186	+	1.21795i	−0.264156	+	0.964480i	$0.585093\pi$
$380$	170.113			0.447665
$381$		0			0
$382$	−100.739	−	174.486i	−0.263716	−	0.456769i
$383$	368.803	−	98.8204i	0.962931	−	0.258017i	0.257091	−	0.966387i	$-0.417236\pi$
$383$	368.803	−	98.8204i	0.962931	−	0.258017i	0.705841	+	0.708371i	$0.250569\pi$
$384$		0			0
$385$	199.365	+	53.4197i	0.517832	+	0.138753i
$386$	−74.1938	−	128.507i	−0.192212	−	0.332921i
$387$		0			0
$388$	39.8583	+	148.753i	0.102728	+	0.383385i
$389$	301.734	−	80.8494i	0.775666	−	0.207839i	0.150793	−	0.988565i	$-0.451817\pi$
$389$	301.734	−	80.8494i	0.775666	−	0.207839i	0.624873	+	0.780726i	$0.285151\pi$
$390$		0			0
$391$	161.355	−	93.1585i	0.412673	−	0.238257i
$392$	−115.074	+	429.464i	−0.293557	+	1.09557i
$393$		0			0
$394$	−1.39201	−	5.19506i	−0.00353303	−	0.0131854i
$395$	273.498	−	157.904i	0.692401	−	0.399758i
$396$		0			0
$397$			271.335i			0.683463i	0.939798	+	0.341731i	$0.111013\pi$
$397$			271.335i			0.683463i	−0.939798	+	0.341731i	$0.888987\pi$
$398$	−65.0136	+	37.5356i	−0.163351	+	0.0943106i
$399$		0			0
$400$	−104.877	−	60.5507i	−0.262192	−	0.151377i
$401$	−95.5383	+	95.5383i	−0.238250	+	0.238250i	−0.816125	−	0.577875i	$-0.803882\pi$
$401$	−95.5383	+	95.5383i	−0.238250	+	0.238250i	0.577875	+	0.816125i	$0.303882\pi$
$402$		0			0
$403$	68.8482	−	119.249i	0.170839	−	0.295902i
$404$	93.1990	−	161.425i	0.230691	−	0.399568i
$405$		0			0
$406$		−	320.040i		−	0.788275i
$407$	−86.7401	−	217.794i	−0.213121	−	0.535121i
$408$		0			0
$409$	−155.983	−	41.7954i	−0.381375	−	0.102189i	0.0630378	−	0.998011i	$-0.479921\pi$
$409$	−155.983	−	41.7954i	−0.381375	−	0.102189i	−0.444413	+	0.895822i	$0.646588\pi$
$410$	74.3806	+	42.9437i	0.181416	+	0.104741i
$411$		0			0
$412$	74.7290	−	20.0236i	0.181381	−	0.0486009i
$413$	375.658	+	375.658i	0.909584	+	0.909584i
$414$		0			0
$415$	−81.8446	−	81.8446i	−0.197216	−	0.197216i
$416$	−175.634	−	304.207i	−0.422197	−	0.731266i
$417$		0			0
$418$			96.9148i			0.231854i
$419$	−71.4483	−	123.752i	−0.170521	−	0.295351i	0.768081	−	0.640353i	$-0.221212\pi$
$419$	−71.4483	−	123.752i	−0.170521	−	0.295351i	−0.938602	+	0.345001i	$0.887878\pi$
$420$		0			0
$421$	450.075	−	450.075i	1.06906	−	1.06906i	0.0716309	−	0.997431i	$-0.477180\pi$
$421$	450.075	−	450.075i	1.06906	−	1.06906i	0.997431	−	0.0716309i	$-0.0228204\pi$
$422$	−199.674	−	53.5024i	−0.473160	−	0.126783i
$423$		0			0
$424$	−125.803	+	469.502i	−0.296705	+	1.10732i
$425$	−55.8305	−	208.362i	−0.131366	−	0.490264i
$426$		0			0
$427$	−834.810	−	223.687i	−1.95506	−	0.523856i
$428$	195.077	−	112.628i	0.455788	−	0.263149i
$429$		0			0
$430$	7.58001	+	7.58001i	0.0176279	+	0.0176279i
$431$	22.3868	+	83.5486i	0.0519415	+	0.193848i	0.987021	−	0.160589i	$-0.0513392\pi$
$431$	22.3868	+	83.5486i	0.0519415	+	0.193848i	−0.935080	+	0.354437i	$0.884673\pi$
$432$		0			0
$433$	526.542			1.21603			0.608016	−	0.793925i	$-0.291966\pi$
$433$	526.542			1.21603			0.608016	+	0.793925i	$0.291966\pi$
$434$		−	118.134i		−	0.272198i
$435$		0			0
$436$	386.954	−	386.954i	0.887508	−	0.887508i
$437$	212.358	+	122.605i	0.485946	+	0.280561i
$438$		0			0
$439$	−163.175	−	608.976i	−0.371696	−	1.38719i	−0.858113	−	0.513462i	$-0.828363\pi$
$439$	−163.175	−	608.976i	−0.371696	−	1.38719i	0.486416	−	0.873727i	$-0.338304\pi$
$440$	−59.4047	+	102.892i	−0.135011	+	0.233845i
$441$		0			0
$442$	33.3240	−	124.367i	0.0753937	−	0.281373i
$443$		−	296.442i		−	0.669170i	−0.942366	−	0.334585i	$-0.891404\pi$
$443$		−	296.442i		−	0.669170i	0.942366	−	0.334585i	$-0.108596\pi$
$444$		0			0
$445$	440.149			0.989098
$446$	−120.242	−	32.2188i	−0.269602	−	0.0722396i
$447$		0			0
$448$	23.4827	+	13.5578i	0.0524168	+	0.0302628i
$449$	31.6269	−	8.47440i	0.0704385	−	0.0188739i	−0.223428	−	0.974721i	$-0.571725\pi$
$449$	31.6269	−	8.47440i	0.0704385	−	0.0188739i	0.293866	+	0.955847i	$0.405058\pi$
$450$		0			0
$451$	105.125	−	182.082i	0.233093	−	0.403729i
$452$	303.953	+	303.953i	0.672462	+	0.672462i
$453$		0			0
$454$	−161.286			−0.355256
$455$		−	360.880i		−	0.793144i
$456$		0			0
$457$	494.945	−	132.620i	1.08303	−	0.290197i	0.327194	−	0.944957i	$-0.393897\pi$
$457$	494.945	−	132.620i	1.08303	−	0.290197i	0.755837	+	0.654760i	$0.227230\pi$
$458$	−160.277	+	160.277i	−0.349951	+	0.349951i
$459$		0			0
$460$	67.3184	+	116.599i	0.146344	+	0.253476i
$461$	−93.7354	+	349.825i	−0.203330	+	0.758840i	0.786621	+	0.617436i	$0.211828\pi$
$461$	−93.7354	+	349.825i	−0.203330	+	0.758840i	−0.989952	+	0.141404i	$0.954838\pi$
$462$		0			0
$463$	248.595	−	66.6109i	0.536922	−	0.143868i	0.0198394	−	0.999803i	$-0.493685\pi$
$463$	248.595	−	66.6109i	0.536922	−	0.143868i	0.517083	+	0.855935i	$0.327018\pi$
$464$	−244.212	−	65.4365i	−0.526319	−	0.141027i
$465$		0			0
$466$	7.77175	−	29.0045i	0.0166776	−	0.0622415i
$467$	−593.852	−	593.852i	−1.27163	−	1.27163i	−0.945232	−	0.326400i	$-0.894164\pi$
$467$	−593.852	−	593.852i	−1.27163	−	1.27163i	−0.326400	−	0.945232i	$-0.605836\pi$
$468$		0			0
$469$	596.659	−	344.481i	1.27219	−	0.734501i
$470$	−127.774			−0.271859
$471$		0			0
$472$	−264.840	+	152.905i	−0.561101	+	0.323952i
$473$	18.5557	−	18.5557i	0.0392298	−	0.0392298i
$474$		0			0
$475$	200.746	−	200.746i	0.422623	−	0.422623i
$476$	122.846	+	458.469i	0.258081	+	0.963170i
$477$		0			0
$478$	−143.997	+	249.411i	−0.301250	+	0.521780i
$479$	84.8442	−	316.643i	0.177128	−	0.661050i	−0.819052	−	0.573720i	$-0.805500\pi$
$479$	84.8442	−	316.643i	0.177128	−	0.661050i	0.996179	−	0.0873302i	$-0.0278335\pi$
$480$		0			0
$481$	−328.577	+	245.054i	−0.683113	+	0.509468i
$482$	283.652			0.588490
$483$		0			0
$484$	−227.212	−	131.181i	−0.469447	−	0.271035i
$485$	−122.419	−	70.6785i	−0.252410	−	0.145729i
$486$		0			0
$487$	−76.0200	−	76.0200i	−0.156099	−	0.156099i	0.624737	−	0.780835i	$-0.285206\pi$
$487$	−76.0200	−	76.0200i	−0.156099	−	0.156099i	−0.780835	+	0.624737i	$0.785206\pi$
$488$	248.747	−	430.843i	0.509728	−	0.882876i
$489$		0			0
$490$	−91.3927	−	158.297i	−0.186516	−	0.323055i
$491$	−817.859			−1.66570			−0.832851	−	0.553498i	$-0.813293\pi$
$491$	−817.859			−1.66570			−0.832851	+	0.553498i	$0.813293\pi$
$492$		0			0
$493$	−225.175	−	390.014i	−0.456744	−	0.791103i
$494$	163.678	−	43.8575i	0.331333	−	0.0887804i
$495$		0			0
$496$	−90.1442	−	24.1541i	−0.181742	−	0.0486977i
$497$	721.189	+	1249.14i	1.45108	+	2.51335i
$498$		0			0
$499$	25.0774	+	93.5901i	0.0502553	+	0.187555i	0.986490	−	0.163819i	$-0.0523812\pi$
$499$	25.0774	+	93.5901i	0.0502553	+	0.187555i	−0.936235	+	0.351374i	$0.885715\pi$
$500$	383.948	−	102.878i	0.767895	−	0.205757i
$501$		0			0
$502$	−55.1416	+	31.8360i	−0.109844	+	0.0634183i
$503$	−10.4723	+	39.0833i	−0.0208198	+	0.0777004i	−0.975554	−	0.219759i	$-0.929473\pi$
$503$	−10.4723	+	39.0833i	−0.0208198	+	0.0777004i	0.954734	+	0.297460i	$0.0961394\pi$
$504$		0			0
$505$	44.2825	+	165.264i	0.0876880	+	0.327256i
$506$	−66.4275	+	38.3519i	−0.131280	+	0.0757944i
$507$		0			0
$508$		−	229.145i		−	0.451073i
$509$	−730.902	+	421.986i	−1.43596	+	0.829050i	−0.997566	−	0.0697344i	$-0.977785\pi$
$509$	−730.902	+	421.986i	−1.43596	+	0.829050i	−0.438391	+	0.898784i	$0.644451\pi$
$510$		0			0
$511$	−432.682	−	249.809i	−0.846736	−	0.488863i
$512$	−302.044	+	302.044i	−0.589931	+	0.589931i
$513$		0			0
$514$	−72.2885	+	125.207i	−0.140639	+	0.243594i
$515$	−35.5066	+	61.4993i	−0.0689449	+	0.119416i
$516$		0			0
$517$			312.787i			0.605003i
$518$	−139.010	+	323.021i	−0.268358	+	0.623592i
$519$		0			0
$520$	200.656	+	53.7656i	0.385877	+	0.103395i
$521$	240.655	+	138.942i	0.461910	+	0.266684i	0.712847	−	0.701320i	$-0.247405\pi$
$521$	240.655	+	138.942i	0.461910	+	0.266684i	−0.250937	+	0.968003i	$0.580739\pi$
$522$		0			0
$523$	337.271	−	90.3715i	0.644878	−	0.172795i	0.0784660	−	0.996917i	$-0.474998\pi$
$523$	337.271	−	90.3715i	0.644878	−	0.172795i	0.566412	+	0.824122i	$0.308331\pi$
$524$	364.046	+	364.046i	0.694745	+	0.694745i
$525$		0			0
$526$	181.972	+	181.972i	0.345954	+	0.345954i
$527$	−83.1170	−	143.963i	−0.157717	−	0.273174i
$528$		0			0
$529$		−	334.927i		−	0.633132i
$530$	−99.9132	−	173.055i	−0.188515	−	0.326518i
$531$		0			0
$532$	−441.710	+	441.710i	−0.830283	+	0.830283i
$533$	−355.089	−	95.1458i	−0.666208	−	0.178510i
$534$		0			0
$535$	−53.5139	+	199.716i	−0.100026	+	0.373302i
$536$	102.645	+	383.075i	0.191501	+	0.714693i
$537$		0			0
$538$	179.530	+	48.1048i	0.333698	+	0.0894141i
$539$	−387.506	+	223.727i	−0.718936	+	0.415078i
$540$		0			0
$541$	487.843	+	487.843i	0.901743	+	0.901743i	0.995587	−	0.0938443i	$-0.0299156\pi$
$541$	487.843	+	487.843i	0.901743	+	0.901743i	−0.0938443	+	0.995587i	$0.529916\pi$
$542$	−61.0079	−	227.685i	−0.112561	−	0.420082i
$543$		0			0
$544$	−424.068			−0.779537
$545$			502.306i			0.921662i
$546$		0			0
$547$	−194.421	+	194.421i	−0.355431	+	0.355431i	−0.862126	−	0.506694i	$-0.830867\pi$
$547$	−194.421	+	194.421i	−0.355431	+	0.355431i	0.506694	+	0.862126i	$0.330867\pi$
$548$	−752.799	−	434.629i	−1.37372	−	0.793118i
$549$		0			0
$550$	22.9846	+	85.7796i	0.0417902	+	0.155963i
$551$	296.351	−	513.295i	0.537842	−	0.931569i
$552$		0			0
$553$	−300.149	+	1120.17i	−0.542764	+	2.02562i
$554$			188.603i			0.340439i
$555$		0			0
$556$	−125.996			−0.226611
$557$	−732.168	−	196.184i	−1.31449	−	0.352215i	−0.467576	−	0.883953i	$-0.654873\pi$
$557$	−732.168	−	196.184i	−1.31449	−	0.352215i	−0.846909	+	0.531738i	$0.821539\pi$
$558$		0			0
$559$	−39.7356	−	22.9414i	−0.0710834	−	0.0410400i
$560$	−236.254	+	63.3039i	−0.421881	+	0.113043i
$561$		0			0
$562$	150.654	−	260.941i	0.268068	−	0.464308i
$563$	183.672	+	183.672i	0.326237	+	0.326237i	0.851154	−	0.524917i	$-0.175903\pi$
$563$	183.672	+	183.672i	0.326237	+	0.326237i	−0.524917	+	0.851154i	$0.675903\pi$
$564$		0			0
$565$	−394.562			−0.698340
$566$			53.0505i			0.0937287i
$567$		0			0
$568$	−801.988	+	214.892i	−1.41195	+	0.378331i
$569$	−328.416	+	328.416i	−0.577180	+	0.577180i	−0.934125	−	0.356945i	$-0.883818\pi$
$569$	−328.416	+	328.416i	−0.577180	+	0.577180i	0.356945	+	0.934125i	$0.383818\pi$
$570$		0			0
$571$	109.245	+	189.217i	0.191321	+	0.331378i	0.945688	−	0.325075i	$-0.105389\pi$
$571$	109.245	+	189.217i	0.191321	+	0.331378i	−0.754367	+	0.656453i	$0.772056\pi$
$572$	58.9489	−	220.000i	0.103058	−	0.384616i
$573$		0			0
$574$	−304.641	+	81.6284i	−0.530734	+	0.142210i
$575$	217.037	+	58.1548i	0.377455	+	0.101139i
$576$		0			0
$577$	−158.993	+	593.369i	−0.275551	+	1.02837i	0.679921	+	0.733286i	$0.262014\pi$
$577$	−158.993	+	593.369i	−0.275551	+	1.02837i	−0.955471	+	0.295084i	$0.904652\pi$
$578$	67.6719	+	67.6719i	0.117079	+	0.117079i
$579$		0			0
$580$	281.833	−	162.716i	0.485919	−	0.280545i
$581$	425.032			0.731552
$582$		0			0
$583$	−423.634	+	244.585i	−0.726644	+	0.419528i
$584$	203.361	−	203.361i	0.348221	−	0.348221i
$585$		0			0
$586$	15.4992	−	15.4992i	0.0264492	−	0.0264492i
$587$	20.3196	+	75.8340i	0.0346161	+	0.129189i	0.981072	−	0.193645i	$-0.0620310\pi$
$587$	20.3196	+	75.8340i	0.0346161	+	0.129189i	−0.946456	+	0.322834i	$0.895364\pi$
$588$		0			0
$589$	109.390	−	189.468i	0.185721	−	0.321678i
$590$	32.5393	−	121.438i	0.0551513	−	0.205827i
$591$		0			0
$592$	218.065	+	172.120i	0.368352	+	0.290743i
$593$	−66.4442			−0.112048			−0.0560238	−	0.998429i	$-0.517842\pi$
$593$	−66.4442			−0.112048			−0.0560238	+	0.998429i	$0.517842\pi$
$594$		0			0
$595$	−377.304	−	217.836i	−0.634124	−	0.366112i
$596$	−434.886	−	251.081i	−0.729674	−	0.421278i
$597$		0			0
$598$	94.8331	+	94.8331i	0.158584	+	0.158584i
$599$	359.773	−	623.145i	0.600622	−	1.04031i	−0.392104	−	0.919921i	$-0.628253\pi$
$599$	359.773	−	623.145i	0.600622	−	1.04031i	0.992727	−	0.120388i	$-0.0384138\pi$
$600$		0			0
$601$	−202.538	−	350.806i	−0.337001	−	0.583703i	0.646866	−	0.762604i	$-0.276079\pi$
$601$	−202.538	−	350.806i	−0.337001	−	0.583703i	−0.983867	+	0.178901i	$0.942746\pi$
$602$	−39.3642			−0.0653890
$603$		0			0
$604$	−207.811	−	359.939i	−0.344058	−	0.595926i
$605$	232.616	−	62.3293i	0.384489	−	0.103024i
$606$		0			0
$607$	−419.994	−	112.537i	−0.691918	−	0.185399i	−0.104311	−	0.994545i	$-0.533264\pi$
$607$	−419.994	−	112.537i	−0.691918	−	0.185399i	−0.587608	+	0.809146i	$0.699930\pi$
$608$	−279.056	−	483.340i	−0.458974	−	0.794967i
$609$		0			0
$610$	52.9351	+	197.556i	0.0867789	+	0.323863i
$611$	528.262	−	141.547i	0.864586	−	0.231665i
$612$		0			0
$613$	418.273	−	241.490i	0.682338	−	0.393948i	−0.118398	−	0.992966i	$-0.537776\pi$
$613$	418.273	−	241.490i	0.682338	−	0.393948i	0.800735	+	0.599018i	$0.204442\pi$
$614$	9.01263	−	33.6356i	0.0146786	−	0.0547811i
$615$		0			0
$616$	−112.918	−	421.416i	−0.183308	−	0.684116i
$617$	−776.808	+	448.490i	−1.25901	+	0.726888i	−0.972882	−	0.231304i	$-0.925701\pi$
$617$	−776.808	+	448.490i	−1.25901	+	0.726888i	−0.286126	+	0.958192i	$0.592368\pi$
$618$		0			0
$619$		−	534.291i		−	0.863151i	−0.902077	−	0.431576i	$-0.857958\pi$
$619$		−	534.291i		−	0.863151i	0.902077	−	0.431576i	$-0.142042\pi$
$620$	104.031	−	60.0622i	0.167792	−	0.0968745i
$621$		0			0
$622$	254.319	+	146.831i	0.408873	+	0.236063i
$623$	−1142.88	+	1142.88i	−1.83448	+	1.83448i
$624$		0			0
$625$	19.1834	−	33.2266i	0.0306934	−	0.0531626i
$626$	106.291	−	184.101i	0.169794	−	0.294091i
$627$		0			0
$628$			942.962i			1.50153i
$629$	57.8690	+	491.452i	0.0920016	+	0.781322i
$630$		0			0
$631$	−360.942	−	96.7142i	−0.572016	−	0.153271i	−0.0387950	−	0.999247i	$-0.512352\pi$
$631$	−360.942	−	96.7142i	−0.572016	−	0.153271i	−0.533221	+	0.845976i	$0.679019\pi$
$632$	−578.117	−	333.776i	−0.914742	−	0.528127i
$633$		0			0
$634$	−367.303	+	98.4186i	−0.579342	+	0.155234i
$635$	148.727	+	148.727i	0.234216	+	0.234216i
$636$		0			0
$637$	553.211	+	553.211i	0.868463	+	0.868463i
$638$	92.7010	+	160.563i	0.145299	+	0.251666i
$639$		0			0
$640$		−	384.175i		−	0.600273i
$641$	−285.023	−	493.675i	−0.444654	−	0.770163i	0.553374	−	0.832933i	$-0.313340\pi$
$641$	−285.023	−	493.675i	−0.444654	−	0.770163i	−0.998028	+	0.0627695i	$0.980007\pi$
$642$		0			0
$643$	308.385	−	308.385i	0.479603	−	0.479603i	−0.425402	−	0.905005i	$-0.639867\pi$
$643$	308.385	−	308.385i	0.479603	−	0.479603i	0.905005	+	0.425402i	$0.139867\pi$
$644$	−477.555	−	127.961i	−0.741545	−	0.198696i
$645$		0			0
$646$	52.9470	−	197.601i	0.0819613	−	0.305884i
$647$	79.2766	+	295.864i	0.122530	+	0.457286i	0.999740	−	0.0228203i	$-0.00726457\pi$
$647$	79.2766	+	295.864i	0.122530	+	0.457286i	−0.877210	+	0.480107i	$0.840598\pi$
$648$		0			0
$649$	−297.278	−	79.6553i	−0.458055	−	0.122735i
$650$	134.471	−	77.6369i	0.206879	−	0.119441i
$651$		0			0
$652$	−305.825	−	305.825i	−0.469057	−	0.469057i
$653$	−92.8822	−	346.641i	−0.142239	−	0.530844i	−0.999863	−	0.0165661i	$-0.994727\pi$
$653$	−92.8822	−	346.641i	−0.142239	−	0.530844i	0.857624	−	0.514278i	$-0.171940\pi$
$654$		0			0
$655$	−472.570			−0.721481
$656$			249.152i			0.379805i
$657$		0			0
$658$	331.774	−	331.774i	0.504216	−	0.504216i
$659$	−68.9449	−	39.8054i	−0.104620	−	0.0604027i	0.446777	−	0.894645i	$-0.352572\pi$
$659$	−68.9449	−	39.8054i	−0.104620	−	0.0604027i	−0.551397	+	0.834243i	$0.685905\pi$
$660$		0			0
$661$	305.478	+	1140.06i	0.462145	+	1.72475i	0.666185	+	0.745786i	$0.267926\pi$
$661$	305.478	+	1140.06i	0.462145	+	1.72475i	−0.204041	+	0.978962i	$0.565407\pi$
$662$	−103.775	+	179.744i	−0.156760	+	0.271516i
$663$		0			0
$664$	−63.3231	+	236.325i	−0.0953662	+	0.355911i
$665$		−	573.386i		−	0.862234i
$666$		0			0
$667$	469.098			0.703295
$668$	825.225	+	221.118i	1.23537	+	0.331016i
$669$		0			0
$670$	−141.198	−	81.5209i	−0.210744	−	0.121673i
$671$	483.613	−	129.584i	0.720735	−	0.193120i
$672$		0			0
$673$	461.235	−	798.883i	0.685342	−	1.18705i	−0.287987	−	0.957634i	$-0.592986\pi$
$673$	461.235	−	798.883i	0.685342	−	1.18705i	0.973329	−	0.229413i	$-0.0736807\pi$
$674$	−318.559	−	318.559i	−0.472640	−	0.472640i
$675$		0			0
$676$	150.145			0.222108
$677$		−	353.536i		−	0.522210i	−0.965310	−	0.261105i	$-0.915913\pi$
$677$		−	353.536i		−	0.522210i	0.965310	−	0.261105i	$-0.0840869\pi$
$678$		0			0
$679$	501.392	−	134.347i	0.738426	−	0.197861i
$680$	177.333	−	177.333i	0.260784	−	0.260784i
$681$		0			0
$682$	34.2180	+	59.2674i	0.0501731	+	0.0869023i
$683$	−206.173	+	769.447i	−0.301864	+	1.12657i	0.633748	+	0.773539i	$0.281516\pi$
$683$	−206.173	+	769.447i	−0.301864	+	1.12657i	−0.935612	+	0.353031i	$0.885151\pi$
$684$		0			0
$685$	770.702	−	206.509i	1.12511	−	0.301473i
$686$	198.492	+	53.1858i	0.289347	+	0.0775303i
$687$		0			0
$688$	−8.04854	+	30.0376i	−0.0116985	+	0.0436592i
$689$	604.787	+	604.787i	0.877775	+	0.877775i
$690$		0			0
$691$	−698.421	+	403.233i	−1.01074	+	0.583550i	−0.911408	−	0.411504i	$-0.865004\pi$
$691$	−698.421	+	403.233i	−1.01074	+	0.583550i	−0.0993310	+	0.995054i	$0.531670\pi$
$692$	913.703			1.32038
$693$		0			0
$694$	95.8127	−	55.3175i	0.138059	−	0.0797082i
$695$	81.7779	−	81.7779i	0.117666	−	0.117666i
$696$		0			0
$697$	−313.817	+	313.817i	−0.450239	+	0.450239i
$698$	114.894	+	428.790i	0.164604	+	0.614312i
$699$		0			0
$700$	−286.202	+	495.717i	−0.408860	+	0.708167i
$701$	301.630	−	1125.70i	0.430285	−	1.60585i	−0.321820	−	0.946801i	$-0.604294\pi$
$701$	301.630	−	1125.70i	0.430285	−	1.60585i	0.752104	−	0.659044i	$-0.229039\pi$
$702$		0			0
$703$	−522.061	+	389.355i	−0.742619	+	0.553848i
$704$	−15.7083			−0.0223129
$705$		0			0
$706$	430.447	+	248.519i	0.609698	+	0.352009i
$707$	−544.105	−	314.139i	−0.769596	−	0.444327i
$708$		0			0
$709$	−227.622	−	227.622i	−0.321047	−	0.321047i	0.528122	−	0.849169i	$-0.322896\pi$
$709$	−227.622	−	227.622i	−0.321047	−	0.321047i	−0.849169	+	0.528122i	$0.822896\pi$
$710$	170.668	−	295.606i	0.240378	−	0.416347i
$711$		0			0
$712$	−465.190	−	805.733i	−0.653357	−	1.13165i
$713$	173.154			0.242853
$714$		0			0
$715$	104.531	+	181.053i	0.146197	+	0.253220i
$716$	475.857	−	127.506i	0.664605	−	0.178080i
$717$		0			0
$718$	−164.087	−	43.9669i	−0.228533	−	0.0612353i
$719$	556.155	+	963.288i	0.773511	+	1.33976i	0.935627	+	0.352989i	$0.114835\pi$
$719$	556.155	+	963.288i	0.773511	+	1.33976i	−0.162116	+	0.986772i	$0.551832\pi$
$720$		0			0
$721$	−67.4920	−	251.883i	−0.0936088	−	0.349353i
$722$	−42.9587	+	11.5108i	−0.0594996	+	0.0159429i
$723$		0			0
$724$	837.294	−	483.412i	1.15648	−	0.667696i
$725$	140.567	−	524.602i	0.193885	−	0.723589i
$726$		0			0
$727$	311.339	+	1161.93i	0.428252	+	1.59826i	0.756717	+	0.653742i	$0.226802\pi$
$727$	311.339	+	1161.93i	0.428252	+	1.59826i	−0.328465	+	0.944516i	$0.606531\pi$
$728$	−660.625	+	381.412i	−0.907452	+	0.523918i
$729$		0			0
$730$			118.234i			0.161964i
$731$	−47.9709	+	27.6960i	−0.0656236	+	0.0378878i
$732$		0			0
$733$	278.666	+	160.888i	0.380171	+	0.219492i	0.677893	−	0.735161i	$-0.262893\pi$
$733$	278.666	+	160.888i	0.380171	+	0.219492i	−0.297722	+	0.954653i	$0.596227\pi$
$734$	−368.325	+	368.325i	−0.501805	+	0.501805i
$735$		0			0
$736$	220.861	−	382.543i	0.300083	−	0.519759i
$737$	−199.561	+	345.650i	−0.270775	+	0.468996i
$738$		0			0
$739$		−	937.608i		−	1.26875i	−0.773024	−	0.634376i	$-0.781257\pi$
$739$		−	937.608i		−	1.26875i	0.773024	−	0.634376i	$-0.218743\pi$
$740$	−355.134	+	41.8174i	−0.479911	+	0.0565100i
$741$		0			0
$742$	708.782	+	189.918i	0.955232	+	0.255954i
$743$	−898.656	−	518.839i	−1.20950	−	0.698303i	−0.246847	−	0.969054i	$-0.579395\pi$
$743$	−898.656	−	518.839i	−1.20950	−	0.698303i	−0.962649	+	0.270751i	$0.912728\pi$
$744$		0			0
$745$	445.228	−	119.299i	0.597622	−	0.160132i
$746$	31.1185	+	31.1185i	0.0417138	+	0.0417138i
$747$		0			0
$748$	−194.429	−	194.429i	−0.259932	−	0.259932i
$749$	−379.626	−	657.532i	−0.506844	−	0.877880i
$750$		0			0
$751$		−	950.310i		−	1.26539i	−0.774400	−	0.632696i	$-0.781948\pi$
$751$		−	950.310i		−	1.26539i	0.774400	−	0.632696i	$-0.218052\pi$
$752$	−185.331	−	321.002i	−0.246450	−	0.426864i
$753$		0			0
$754$	229.222	−	229.222i	0.304009	−	0.304009i
$755$	368.499	+	98.7391i	0.488078	+	0.130780i
$756$		0			0
$757$	−241.508	+	901.318i	−0.319032	+	1.19065i	0.601144	+	0.799141i	$0.294712\pi$
$757$	−241.508	+	901.318i	−0.319032	+	1.19065i	−0.920176	+	0.391504i	$0.871955\pi$
$758$	119.882	+	447.407i	0.158156	+	0.590247i
$759$		0			0
$760$	318.813	+	85.4256i	0.419491	+	0.112402i
$761$	426.364	−	246.161i	0.560267	−	0.323471i	−0.192985	−	0.981202i	$-0.561817\pi$
$761$	426.364	−	246.161i	0.560267	−	0.323471i	0.753253	+	0.657731i	$0.228484\pi$
$762$		0			0
$763$	−1304.28	−	1304.28i	−1.70940	−	1.70940i
$764$	194.715	+	726.685i	0.254862	+	0.951159i
$765$		0			0
$766$	331.795			0.433153
$767$			538.116i			0.701586i
$768$		0			0
$769$	−224.087	+	224.087i	−0.291400	+	0.291400i	−0.837633	−	0.546233i	$-0.816061\pi$
$769$	−224.087	+	224.087i	−0.291400	+	0.291400i	0.546233	+	0.837633i	$0.316061\pi$
$770$	155.330	+	89.6800i	0.201728	+	0.116468i
$771$		0			0
$772$	143.406	+	535.198i	0.185759	+	0.693262i
$773$	−427.358	+	740.206i	−0.552857	+	0.957576i	0.445210	+	0.895426i	$0.353129\pi$
$773$	−427.358	+	740.206i	−0.552857	+	0.957576i	−0.998067	+	0.0621497i	$0.980204\pi$
$774$		0			0
$775$	51.8863	−	193.642i	0.0669501	−	0.249861i
$776$			298.798i			0.385049i
$777$		0			0
$778$	271.457			0.348916
$779$	−564.184	−	151.173i	−0.724242	−	0.194060i
$780$		0			0
$781$	−723.636	−	417.791i	−0.926551	−	0.534944i
$782$	156.393	−	41.9053i	0.199991	−	0.0535873i
$783$		0			0
$784$	265.123	−	459.206i	0.338167	−	0.585722i
$785$	−612.031	−	612.031i	−0.779657	−	0.779657i
$786$		0			0
$787$	464.239			0.589884			0.294942	−	0.955515i	$-0.404700\pi$
$787$	464.239			0.589884			0.294942	+	0.955515i	$0.404700\pi$
$788$			20.0826i			0.0254855i
$789$		0			0
$790$	265.087	−	71.0298i	0.335553	−	0.0899111i
$791$	1024.51	−	1024.51i	1.29521	−	1.29521i
$792$		0			0
$793$	−437.706	−	758.128i	−0.551962	−	0.956026i
$794$	−61.0269	+	227.756i	−0.0768601	+	0.286846i
$795$		0			0
$796$	270.764	−	72.5510i	0.340156	−	0.0911444i
$797$	379.419	+	101.665i	0.476059	+	0.127560i	0.488867	−	0.872358i	$-0.337410\pi$
$797$	379.419	+	101.665i	0.476059	+	0.127560i	−0.0128080	+	0.999918i	$0.504077\pi$
$798$		0			0
$799$	170.883	−	637.745i	0.213871	−	0.798179i
$800$	−361.624	−	361.624i	−0.452030	−	0.452030i
$801$		0			0
$802$	−101.682	+	58.7060i	−0.126785	+	0.0731995i
$803$	289.434			0.360440
$804$		0			0
$805$	393.011	−	226.905i	0.488213	−	0.281870i
$806$	84.6111	−	84.6111i	0.104977	−	0.104977i
$807$		0			0
$808$	255.730	−	255.730i	0.316498	−	0.316498i
$809$	167.614	+	625.543i	0.207186	+	0.773230i	0.988772	+	0.149432i	$0.0477445\pi$
$809$	167.614	+	625.543i	0.207186	+	0.773230i	−0.781586	+	0.623798i	$0.785589\pi$
$810$		0			0
$811$	−309.082	+	535.347i	−0.381113	+	0.660107i	−0.991222	−	0.132211i	$-0.957792\pi$
$811$	−309.082	+	535.347i	−0.381113	+	0.660107i	0.610109	+	0.792318i	$0.291126\pi$
$812$	−309.295	+	1154.31i	−0.380905	+	1.42156i
$813$		0			0
$814$	−23.8238	−	202.323i	−0.0292676	−	0.248554i
$815$	396.993			0.487108
$816$		0			0
$817$	−63.1341	−	36.4505i	−0.0772755	−	0.0446150i
$818$	−121.530	−	70.1653i	−0.148569	−	0.0857766i
$819$		0			0
$820$	−226.771	−	226.771i	−0.276550	−	0.276550i
$821$	−13.4409	+	23.2804i	−0.0163714	+	0.0283561i	−0.874095	−	0.485755i	$-0.838545\pi$
$821$	−13.4409	+	23.2804i	−0.0163714	+	0.0283561i	0.857724	+	0.514111i	$0.171878\pi$
$822$		0			0
$823$	573.831	+	993.904i	0.697243	+	1.20766i	0.969419	+	0.245412i	$0.0789233\pi$
$823$	573.831	+	993.904i	0.697243	+	1.20766i	−0.272176	+	0.962247i	$0.587743\pi$
$824$	150.107			0.182169
$825$		0			0
$826$	230.833	+	399.814i	0.279459	+	0.484037i
$827$	−734.444	+	196.794i	−0.888082	+	0.237961i	−0.673891	−	0.738831i	$-0.735378\pi$
$827$	−734.444	+	196.794i	−0.888082	+	0.237961i	−0.214191	+	0.976792i	$0.568712\pi$
$828$		0			0
$829$	108.023	+	28.9447i	0.130306	+	0.0349153i	0.323382	−	0.946268i	$-0.395180\pi$
$829$	108.023	+	28.9447i	0.130306	+	0.0349153i	−0.193077	+	0.981184i	$0.561847\pi$
$830$	−50.2915	−	87.1075i	−0.0605922	−	0.104949i
$831$		0			0
$832$	7.10857	+	26.5295i	0.00854396	+	0.0318865i
$833$	912.320	−	244.455i	1.09522	−	0.293464i
$834$		0			0
$835$	−679.131	+	392.097i	−0.813331	+	0.469577i
$836$	93.6611	−	349.548i	0.112035	−	0.418120i
$837$		0			0
$838$	−32.1394	−	119.946i	−0.0383526	−	0.143134i
$839$	957.349	−	552.726i	1.14106	−	0.658791i	0.194367	−	0.980929i	$-0.437735\pi$
$839$	957.349	−	552.726i	1.14106	−	0.658791i	0.946693	+	0.322138i	$0.104402\pi$
$840$		0			0
$841$		−	292.863i		−	0.348231i
$842$	479.017	−	276.560i	0.568903	−	0.328457i
$843$		0			0
$844$	668.468	+	385.940i	0.792023	+	0.457275i
$845$	−97.4518	+	97.4518i	−0.115328	+	0.115328i
$846$		0			0
$847$	−442.163	+	765.848i	−0.522034	+	0.904189i
$848$	289.840	−	502.018i	0.341793	−	0.592002i
$849$		0			0
$850$		−	187.454i		−	0.220534i
$851$	−473.467	−	203.753i	−0.556366	−	0.239428i
$852$		0			0
$853$	−1131.05	−	303.064i	−1.32597	−	0.355291i	−0.474756	−	0.880117i	$-0.657464\pi$
$853$	−1131.05	−	303.064i	−1.32597	−	0.355291i	−0.851210	+	0.524826i	$0.824130\pi$
$854$	−650.421	−	375.521i	−0.761617	−	0.439720i
$855$		0			0
$856$	422.158	−	113.117i	0.493175	−	0.132146i
$857$	632.243	+	632.243i	0.737740	+	0.737740i	0.972140	−	0.234400i	$-0.0753127\pi$
$857$	632.243	+	632.243i	0.737740	+	0.737740i	−0.234400	+	0.972140i	$0.575313\pi$
$858$		0			0
$859$	489.799	+	489.799i	0.570197	+	0.570197i	0.932183	−	0.361986i	$-0.117901\pi$
$859$	489.799	+	489.799i	0.570197	+	0.570197i	−0.361986	+	0.932183i	$0.617901\pi$
$860$	−20.0137	−	34.6648i	−0.0232718	−	0.0403079i
$861$		0			0
$862$			75.1650i			0.0871983i
$863$	−397.143	−	687.872i	−0.460189	−	0.797071i	0.538781	−	0.842446i	$-0.318885\pi$
$863$	−397.143	−	687.872i	−0.460189	−	0.797071i	−0.998970	+	0.0453753i	$0.985552\pi$
$864$		0			0
$865$	−593.040	+	593.040i	−0.685596	+	0.685596i
$866$	441.974	+	118.427i	0.510363	+	0.136751i
$867$		0			0
$868$	−114.168	+	426.080i	−0.131530	+	0.490875i
$869$	−173.879	−	648.925i	−0.200091	−	0.746750i
$870$		0			0
$871$	674.074	+	180.618i	0.773908	+	0.207368i
$872$	919.518	−	530.884i	1.05449	−	0.608812i
$873$		0			0
$874$	150.676	+	150.676i	0.172398	+	0.172398i
$875$	−346.765	−	1294.14i	−0.396303	−	1.47902i
$876$		0			0
$877$	588.625			0.671180			0.335590	−	0.942008i	$-0.391064\pi$
$877$	588.625			0.671180			0.335590	+	0.942008i	$0.391064\pi$
$878$		−	547.868i		−	0.623996i
$879$		0			0
$880$	100.191	−	100.191i	0.113854	−	0.113854i
$881$	524.575	+	302.864i	0.595432	+	0.343773i	0.767242	−	0.641357i	$-0.221628\pi$
$881$	524.575	+	302.864i	0.595432	+	0.343773i	−0.171811	+	0.985130i	$0.554962\pi$
$882$		0			0
$883$	−97.3896	−	363.463i	−0.110294	−	0.411623i	0.888598	−	0.458687i	$-0.151680\pi$
$883$	−97.3896	−	363.463i	−0.110294	−	0.411623i	−0.998892	+	0.0470643i	$0.985013\pi$
$884$	−240.383	+	416.356i	−0.271927	+	0.470991i
$885$		0			0
$886$	66.6740	−	248.831i	0.0752528	−	0.280847i
$887$		−	249.481i		−	0.281264i	−0.990062	−	0.140632i	$-0.955087\pi$
$887$		−	249.481i		−	0.281264i	0.990062	−	0.140632i	$-0.0449135\pi$
$888$		0			0
$889$	−772.362			−0.868799
$890$	369.456	+	98.9956i	0.415120	+	0.111231i
$891$		0			0
$892$	402.548	+	232.411i	0.451287	+	0.260551i
$893$	839.331	−	224.898i	0.939900	−	0.251846i
$894$		0			0
$895$	−226.098	+	391.614i	−0.252624	+	0.437557i
$896$	997.540	+	997.540i	1.11333	+	1.11333i
$897$		0			0
$898$	28.4533			0.0316852
$899$		−	418.534i		−	0.465555i
$900$		0			0
$901$	997.375	−	267.246i	1.10696	−	0.296610i
$902$	129.194	−	129.194i	0.143230	−	0.143230i
$903$		0			0
$904$	417.010	+	722.283i	0.461294	+	0.798986i
$905$	−229.688	+	857.207i	−0.253799	+	0.947190i
$906$		0			0
$907$	−838.124	+	224.575i	−0.924061	+	0.247601i	−0.689321	−	0.724457i	$-0.742091\pi$
$907$	−838.124	+	224.575i	−0.924061	+	0.247601i	−0.234741	+	0.972058i	$0.575424\pi$
$908$	581.720	+	155.871i	0.640660	+	0.171664i
$909$		0			0
$910$	81.1670	−	302.919i	0.0891945	−	0.332878i
$911$	−364.488	−	364.488i	−0.400096	−	0.400096i	0.478171	−	0.878267i	$-0.341300\pi$
$911$	−364.488	−	364.488i	−0.400096	−	0.400096i	−0.878267	+	0.478171i	$0.841300\pi$
$912$		0			0
$913$	−213.237	+	123.112i	−0.233556	+	0.134844i
$914$	445.280			0.487177
$915$		0			0
$916$	732.978	−	423.185i	0.800195	−	0.461993i
$917$	1227.06	−	1227.06i	1.33813	−	1.33813i
$918$		0			0
$919$	−866.598	+	866.598i	−0.942980	+	0.942980i	−0.998460	−	0.0554801i	$-0.982331\pi$
$919$	−866.598	+	866.598i	−0.942980	+	0.942980i	0.0554801	+	0.998460i	$0.482331\pi$
$920$	67.6107	+	252.327i	0.0734899	+	0.274268i
$921$		0			0
$922$	−157.361	+	272.557i	−0.170674	+	0.295615i
$923$	−378.132	+	1411.21i	−0.409677	+	1.52894i
$924$		0			0
$925$	−369.738	+	468.433i	−0.399716	+	0.506414i
$926$	223.650			0.241523
$927$		0			0
$928$	−924.649	−	533.847i	−0.996389	−	0.575266i
$929$	424.498	+	245.084i	0.456941	+	0.263815i	0.710757	−	0.703438i	$-0.248353\pi$
$929$	424.498	+	245.084i	0.456941	+	0.263815i	−0.253816	+	0.967252i	$0.581686\pi$
$930$		0			0
$931$	878.971	+	878.971i	0.944115	+	0.944115i
$932$	−56.0616	+	97.1015i	−0.0601519	+	0.104186i
$933$		0			0
$934$	−364.908	−	632.039i	−0.390694	−	0.676701i
$935$	252.389			0.269935
$936$		0			0
$937$	−139.606	−	241.805i	−0.148993	−	0.258063i	0.781863	−	0.623451i	$-0.214270\pi$
$937$	−139.606	−	241.805i	−0.148993	−	0.258063i	−0.930855	+	0.365388i	$0.880936\pi$
$938$	578.308	−	154.957i	0.616533	−	0.165200i
$939$		0			0
$940$	460.848	+	123.484i	0.490264	+	0.131366i
$941$	−690.183	−	1195.43i	−0.733457	−	1.27038i	−0.955397	−	0.295324i	$-0.904572\pi$
$941$	−690.183	−	1195.43i	−0.733457	−	1.27038i	0.221940	−	0.975060i	$-0.428761\pi$
$942$		0			0
$943$	−119.647	−	446.528i	−0.126879	−	0.473518i
$944$	352.282	−	94.3938i	0.373181	−	0.0999934i
$945$		0			0
$946$	19.7489	−	11.4020i	0.0208762	−	0.0120529i
$947$	473.814	−	1768.30i	0.500331	−	1.86726i	0.00248403	−	0.999997i	$-0.499209\pi$
$947$	473.814	−	1768.30i	0.500331	−	1.86726i	0.497847	−	0.867265i	$-0.334124\pi$
$948$		0			0
$949$	−130.979	−	488.822i	−0.138018	−	0.515091i
$950$	213.655	−	123.354i	0.224900	−	0.129846i
$951$		0			0
$952$			920.920i			0.967353i
$953$	−1511.32	+	872.559i	−1.58585	+	0.915591i	−0.591870	+	0.806033i	$0.701610\pi$
$953$	−1511.32	+	872.559i	−1.58585	+	0.915591i	−0.993980	+	0.109558i	$0.965056\pi$
$954$		0			0
$955$	−598.037	−	345.277i	−0.626216	−	0.361546i
$956$	760.400	−	760.400i	0.795398	−	0.795398i
$957$		0			0
$958$	142.435	−	246.704i	0.148679	−	0.257520i
$959$	−1464.97	+	2537.40i	−1.52760	+	2.64589i
$960$		0			0
$961$			806.510i			0.839240i
$962$	−330.921	+	131.795i	−0.343992	+	0.137001i
$963$		0			0
$964$	−1023.06	−	274.129i	−1.06127	−	0.284366i
$965$	−440.449	−	254.294i	−0.456424	−	0.263517i
$966$		0			0
$967$	1277.86	−	342.402i	1.32147	−	0.354087i	0.471941	−	0.881630i	$-0.343554\pi$
$967$	1277.86	−	342.402i	1.32147	−	0.354087i	0.849528	+	0.527544i	$0.176887\pi$
$968$	−359.950	−	359.950i	−0.371849	−	0.371849i
$969$		0			0
$970$	−86.8604	−	86.8604i	−0.0895468	−	0.0895468i
$971$	−733.438	−	1270.35i	−0.755343	−	1.30829i	−0.945204	−	0.326481i	$-0.894137\pi$
$971$	−733.438	−	1270.35i	−0.755343	−	1.30829i	0.189861	−	0.981811i	$-0.439196\pi$
$972$		0			0
$973$			424.685i			0.436470i
$974$	−46.7125	−	80.9084i	−0.0479594	−	0.0830681i
$975$		0			0
$976$	−419.535	+	419.535i	−0.429852	+	0.429852i
$977$	255.189	+	68.3777i	0.261197	+	0.0699875i	0.387041	−	0.922063i	$-0.373497\pi$
$977$	255.189	+	68.3777i	0.261197	+	0.0699875i	−0.125844	+	0.992050i	$0.540164\pi$
$978$		0			0
$979$	242.339	−	904.420i	0.247537	−	0.923820i
$980$	176.649	+	659.262i	0.180254	+	0.672717i
$981$		0			0
$982$	−686.503	−	183.948i	−0.699087	−	0.187320i
$983$	−1114.29	+	643.337i	−1.13356	+	0.654463i	−0.944829	−	0.327565i	$-0.893772\pi$
$983$	−1114.29	+	643.337i	−1.13356	+	0.654463i	−0.188735	+	0.982028i	$0.560439\pi$
$984$		0			0
$985$	−13.0347	−	13.0347i	−0.0132332	−	0.0132332i
$986$	−101.290	−	378.019i	−0.102728	−	0.383386i
$987$		0			0
$988$	−632.733			−0.640419
$989$		−	57.6980i		−	0.0583397i
$990$		0			0
$991$	490.932	−	490.932i	0.495390	−	0.495390i	−0.414609	−	0.910000i	$-0.636082\pi$
$991$	490.932	−	490.932i	0.495390	−	0.495390i	0.910000	+	0.414609i	$0.136082\pi$
$992$	−341.309	−	197.055i	−0.344061	−	0.198644i
$993$		0			0
$994$	324.411	+	1210.72i	0.326369	+	1.21803i
$995$	−128.650	+	222.829i	−0.129297	+	0.223949i
$996$		0			0
$997$	394.255	−	1471.38i	0.395441	−	1.47581i	−0.425586	−	0.904918i	$-0.639932\pi$
$997$	394.255	−	1471.38i	0.395441	−	1.47581i	0.821027	−	0.570889i	$-0.193401\pi$
$998$			84.1989i			0.0843676i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.3.bb.b.82.4		24
3.2	odd	2		111.3.l.b.82.3	✓	24
37.14	odd	12	inner	333.3.bb.b.199.4		24
111.14	even	12		111.3.l.b.88.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.3.l.b.82.3	✓	24	3.2	odd	2
111.3.l.b.88.3	yes	24	111.14	even	12
333.3.bb.b.82.4		24	1.1	even	1	trivial
333.3.bb.b.199.4		24	37.14	odd	12	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:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	333.bb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.839390 + 0.224914i) q^{2} +(-2.81011 - 1.62242i) q^{4} +(2.87694 - 0.770875i) q^{5} +(-5.46857 + 9.47184i) q^{7} +(-4.45178 - 4.45178i) q^{8} +O(q^{10})\)	\(q+(0.839390 + 0.224914i) q^{2} +(-2.81011 - 1.62242i) q^{4} +(2.87694 - 0.770875i) q^{5} +(-5.46857 + 9.47184i) q^{7} +(-4.45178 - 4.45178i) q^{8} +2.58826 q^{10} -6.33599i q^{11} +(-10.7008 + 2.86727i) q^{13} +(-6.72061 + 6.72061i) q^{14} +(3.75416 + 6.50240i) q^{16} +(-3.46151 + 12.9185i) q^{17} +(-17.0020 + 4.55567i) q^{19} +(-9.33522 - 2.50136i) q^{20} +(1.42505 - 5.31837i) q^{22} +(-9.85072 - 9.85072i) q^{23} +(-13.9681 + 8.06448i) q^{25} -9.62702 q^{26} +(30.7346 - 17.7446i) q^{28} +(-23.8103 + 23.8103i) q^{29} +(-8.78892 + 8.78892i) q^{31} +(8.20659 + 30.6274i) q^{32} +(-5.81111 + 10.0651i) q^{34} +(-8.43116 + 31.4655i) q^{35} +(34.3742 - 13.6901i) q^{37} -15.2959 q^{38} +(-16.2393 - 9.37575i) q^{40} +(28.7377 + 16.5917i) q^{41} +(2.92862 + 2.92862i) q^{43} +(-10.2796 + 17.8048i) q^{44} +(-6.05303 - 10.4842i) q^{46} -49.3667 q^{47} +(-35.3105 - 61.1596i) q^{49} +(-13.5385 + 3.62762i) q^{50} +(34.7223 + 9.30382i) q^{52} +(-38.6025 - 66.8615i) q^{53} +(-4.88425 - 18.2283i) q^{55} +(66.5114 - 17.8217i) q^{56} +(-25.3414 + 14.6309i) q^{58} +(12.5719 - 46.9189i) q^{59} +(20.4520 + 76.3280i) q^{61} +(-9.35408 + 5.40058i) q^{62} -2.47921i q^{64} +(-28.5753 + 16.4979i) q^{65} +(-54.5535 - 31.4965i) q^{67} +(30.6865 - 30.6865i) q^{68} +(-14.1541 + 24.5156i) q^{70} +(65.9394 - 114.210i) q^{71} +45.6809i q^{73} +(31.9324 - 3.76008i) q^{74} +(55.1687 + 14.7824i) q^{76} +(60.0135 + 34.6488i) q^{77} +(102.419 - 27.4431i) q^{79} +(15.8131 + 15.8131i) q^{80} +(20.3904 + 20.3904i) q^{82} +(-19.4307 - 33.6549i) q^{83} +39.8343i q^{85} +(1.79956 + 3.11694i) q^{86} +(-28.2064 + 28.2064i) q^{88} +(142.743 + 38.2480i) q^{89} +(31.3597 - 117.036i) q^{91} +(11.6996 + 43.6636i) q^{92} +(-41.4379 - 11.1032i) q^{94} +(-45.4019 + 26.2128i) q^{95} +(-33.5594 - 33.5594i) q^{97} +(-15.8836 - 59.2786i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8}+O(q^{10}) \) 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8	\( 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8} - 60 q^{10} + 28 q^{13} - 42 q^{14} + 26 q^{16} - 10 q^{17} + 60 q^{19} + 4 q^{20} - 64 q^{22} - 34 q^{23} - 162 q^{25} + 44 q^{26} - 48 q^{28} - 32 q^{29} + 90 q^{32} + 46 q^{34} + 30 q^{35} + 80 q^{37} + 284 q^{38} - 144 q^{40} + 30 q^{41} + 130 q^{43} + 16 q^{44} + 78 q^{46} + 56 q^{47} - 20 q^{49} - 70 q^{50} + 16 q^{52} + 190 q^{53} + 350 q^{55} - 376 q^{56} + 336 q^{58} + 258 q^{59} - 84 q^{61} + 474 q^{62} + 54 q^{65} - 372 q^{67} + 434 q^{68} + 102 q^{70} - 66 q^{71} + 416 q^{74} + 702 q^{76} - 198 q^{77} + 88 q^{79} - 900 q^{80} - 470 q^{82} - 166 q^{83} - 432 q^{86} + 530 q^{88} - 304 q^{89} + 524 q^{91} - 330 q^{92} - 344 q^{94} - 1080 q^{95} - 110 q^{97} - 926 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8 - 60 * q^10 + 28 * q^13 - 42 * q^14 + 26 * q^16 - 10 * q^17 + 60 * q^19 + 4 * q^20 - 64 * q^22 - 34 * q^23 - 162 * q^25 + 44 * q^26 - 48 * q^28 - 32 * q^29 + 90 * q^32 + 46 * q^34 + 30 * q^35 + 80 * q^37 + 284 * q^38 - 144 * q^40 + 30 * q^41 + 130 * q^43 + 16 * q^44 + 78 * q^46 + 56 * q^47 - 20 * q^49 - 70 * q^50 + 16 * q^52 + 190 * q^53 + 350 * q^55 - 376 * q^56 + 336 * q^58 + 258 * q^59 - 84 * q^61 + 474 * q^62 + 54 * q^65 - 372 * q^67 + 434 * q^68 + 102 * q^70 - 66 * q^71 + 416 * q^74 + 702 * q^76 - 198 * q^77 + 88 * q^79 - 900 * q^80 - 470 * q^82 - 166 * q^83 - 432 * q^86 + 530 * q^88 - 304 * q^89 + 524 * q^91 - 330 * q^92 - 344 * q^94 - 1080 * q^95 - 110 * q^97 - 926 * q^98

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