LMFDB - Embedded newform 333.3.bb.c.199.6

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			199.6
Character	$\chi$	$=$	333.199
Dual form			333.3.bb.c.82.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.53411 - 0.946963i) q^{2} +(8.12913 - 4.69335i) q^{4} +(1.79898 + 0.482035i) q^{5} +(6.28624 + 10.8881i) q^{7} +(13.9362 - 13.9362i) q^{8} +O(q^{10})$	\(q+(3.53411 - 0.946963i) q^{2} +(8.12913 - 4.69335i) q^{4} +(1.79898 + 0.482035i) q^{5} +(6.28624 + 10.8881i) q^{7} +(13.9362 - 13.9362i) q^{8} +6.81426 q^{10} +2.81763i q^{11} +(-17.5289 - 4.69686i) q^{13} +(32.5269 + 32.5269i) q^{14} +(17.2817 - 29.9328i) q^{16} +(-1.26707 - 4.72877i) q^{17} +(-22.0163 - 5.89926i) q^{19} +(16.8865 - 4.52472i) q^{20} +(2.66819 + 9.95782i) q^{22} +(24.1975 - 24.1975i) q^{23} +(-18.6467 - 10.7657i) q^{25} -66.3970 q^{26} +(102.203 + 59.0071i) q^{28} +(-12.9674 - 12.9674i) q^{29} +(13.4938 + 13.4938i) q^{31} +(12.3262 - 46.0022i) q^{32} +(-8.95594 - 15.5121i) q^{34} +(6.06037 + 22.6176i) q^{35} +(-11.5279 - 35.1583i) q^{37} -83.3946 q^{38} +(31.7887 - 18.3532i) q^{40} +(55.8777 - 32.2610i) q^{41} +(-21.7511 + 21.7511i) q^{43} +(13.2241 + 22.9048i) q^{44} +(62.6026 - 108.431i) q^{46} -53.2430 q^{47} +(-54.5336 + 94.4549i) q^{49} +(-76.0942 - 20.3894i) q^{50} +(-164.539 + 44.0880i) q^{52} +(-0.442496 + 0.766426i) q^{53} +(-1.35819 + 5.06885i) q^{55} +(239.345 + 64.1324i) q^{56} +(-58.1080 - 33.5487i) q^{58} +(16.7826 + 62.6336i) q^{59} +(-3.80616 + 14.2048i) q^{61} +(60.4669 + 34.9106i) q^{62} -35.9958i q^{64} +(-29.2701 - 16.8991i) q^{65} +(63.2306 - 36.5062i) q^{67} +(-32.4939 - 32.4939i) q^{68} +(42.8361 + 74.1943i) q^{70} +(50.4928 + 87.4560i) q^{71} +96.3766i q^{73} +(-74.0345 - 113.337i) q^{74} +(-206.661 + 55.3746i) q^{76} +(-30.6786 + 17.7123i) q^{77} +(41.7399 + 11.1842i) q^{79} +(45.5181 - 45.5181i) q^{80} +(166.928 - 166.928i) q^{82} +(19.3760 - 33.5601i) q^{83} -9.11772i q^{85} +(-56.2734 + 97.4684i) q^{86} +(39.2671 + 39.2671i) q^{88} +(-128.240 + 34.3619i) q^{89} +(-59.0511 - 220.382i) q^{91} +(83.1371 - 310.272i) q^{92} +(-188.167 + 50.4192i) q^{94} +(-36.7632 - 21.2253i) q^{95} +(-50.4222 + 50.4222i) q^{97} +(-103.283 + 385.456i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 36 q^{10} + 4 q^{13} + 6 q^{14} + 26 q^{16} - 46 q^{17} - 156 q^{19} - 68 q^{20} + 32 q^{22} - 10 q^{23} - 90 q^{25} + 164 q^{26} - 48 q^{28} + 28 q^{29} + 120 q^{31} - 90 q^{32} + 46 q^{34} + 186 q^{35} + 56 q^{37} - 4 q^{38} + 216 q^{40} + 30 q^{41} + 250 q^{43} - 284 q^{44} - 18 q^{46} - 232 q^{47} - 164 q^{49} - 226 q^{50} - 488 q^{52} - 122 q^{53} - 250 q^{55} + 632 q^{56} - 360 q^{58} + 258 q^{59} + 108 q^{61} + 186 q^{62} - 162 q^{65} + 60 q^{67} - 214 q^{68} + 246 q^{70} - 174 q^{71} + 8 q^{74} - 498 q^{76} - 666 q^{77} - 104 q^{79} + 24 q^{80} + 1114 q^{82} + 26 q^{83} + 72 q^{86} - 334 q^{88} - 16 q^{89} + 20 q^{91} + 918 q^{92} + 400 q^{94} + 372 q^{95} - 278 q^{97} - 950 q^{98}+O(q^{100}) $ 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8 + 36 * q^10 + 4 * q^13 + 6 * q^14 + 26 * q^16 - 46 * q^17 - 156 * q^19 - 68 * q^20 + 32 * q^22 - 10 * q^23 - 90 * q^25 + 164 * q^26 - 48 * q^28 + 28 * q^29 + 120 * q^31 - 90 * q^32 + 46 * q^34 + 186 * q^35 + 56 * q^37 - 4 * q^38 + 216 * q^40 + 30 * q^41 + 250 * q^43 - 284 * q^44 - 18 * q^46 - 232 * q^47 - 164 * q^49 - 226 * q^50 - 488 * q^52 - 122 * q^53 - 250 * q^55 + 632 * q^56 - 360 * q^58 + 258 * q^59 + 108 * q^61 + 186 * q^62 - 162 * q^65 + 60 * q^67 - 214 * q^68 + 246 * q^70 - 174 * q^71 + 8 * q^74 - 498 * q^76 - 666 * q^77 - 104 * q^79 + 24 * q^80 + 1114 * q^82 + 26 * q^83 + 72 * q^86 - 334 * q^88 - 16 * q^89 + 20 * q^91 + 918 * q^92 + 400 * q^94 + 372 * q^95 - 278 * q^97 - 950 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$38$	$298$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	3.53411	−	0.946963i	1.76706	−	0.473482i	0.778929	−	0.627112i	$-0.215763\pi$
$2$	3.53411	−	0.946963i	1.76706	−	0.473482i	0.988128	+	0.153630i	$0.0490965\pi$
$3$		0			0
$3$		0			0
$4$	8.12913	−	4.69335i	2.03228	−	1.17334i
$5$	1.79898	+	0.482035i	0.359796	+	0.0964069i	0.434188	−	0.900822i	$-0.357035\pi$
$5$	1.79898	+	0.482035i	0.359796	+	0.0964069i	−0.0743928	+	0.997229i	$0.523702\pi$
$6$		0			0
$7$	6.28624	+	10.8881i	0.898034	+	1.55544i	0.830004	+	0.557757i	$0.188338\pi$
$7$	6.28624	+	10.8881i	0.898034	+	1.55544i	0.0680297	+	0.997683i	$0.478329\pi$
$8$	13.9362	−	13.9362i	1.74203	−	1.74203i
$9$		0			0
$10$	6.81426			0.681426
$11$			2.81763i			0.256148i	0.991765	+	0.128074i	$0.0408795\pi$
$11$			2.81763i			0.256148i	−0.991765	+	0.128074i	$0.959121\pi$
$12$		0			0
$13$	−17.5289	−	4.69686i	−1.34838	−	0.361297i	−0.488842	−	0.872372i	$-0.662581\pi$
$13$	−17.5289	−	4.69686i	−1.34838	−	0.361297i	−0.859536	+	0.511075i	$0.829247\pi$
$14$	32.5269	+	32.5269i	2.32335	+	2.32335i
$15$		0			0
$16$	17.2817	−	29.9328i	1.08011	−	1.87080i
$17$	−1.26707	−	4.72877i	−0.0745335	−	0.278163i	0.918594	−	0.395203i	$-0.129326\pi$
$17$	−1.26707	−	4.72877i	−0.0745335	−	0.278163i	−0.993127	+	0.117041i	$0.962659\pi$
$18$		0			0
$19$	−22.0163	−	5.89926i	−1.15875	−	0.310487i	−0.372286	−	0.928118i	$-0.621426\pi$
$19$	−22.0163	−	5.89926i	−1.15875	−	0.310487i	−0.786468	+	0.617631i	$0.788093\pi$
$20$	16.8865	−	4.52472i	0.844324	−	0.226236i
$21$		0			0
$22$	2.66819	+	9.95782i	0.121281	+	0.452628i
$23$	24.1975	−	24.1975i	1.05207	−	1.05207i	0.0534971	−	0.998568i	$-0.482963\pi$
$23$	24.1975	−	24.1975i	1.05207	−	1.05207i	0.998568	−	0.0534971i	$-0.0170368\pi$
$24$		0			0
$25$	−18.6467	−	10.7657i	−0.745867	−	0.430626i
$26$	−66.3970			−2.55373
$27$		0			0
$28$	102.203	+	59.0071i	3.65012	+	2.10740i
$29$	−12.9674	−	12.9674i	−0.447152	−	0.447152i	0.447254	−	0.894407i	$-0.352402\pi$
$29$	−12.9674	−	12.9674i	−0.447152	−	0.447152i	−0.894407	+	0.447254i	$0.852402\pi$
$30$		0			0
$31$	13.4938	+	13.4938i	0.435285	+	0.435285i	0.890422	−	0.455137i	$-0.150410\pi$
$31$	13.4938	+	13.4938i	0.435285	+	0.435285i	−0.455137	+	0.890422i	$0.650410\pi$
$32$	12.3262	−	46.0022i	0.385195	−	1.43757i
$33$		0			0
$34$	−8.95594	−	15.5121i	−0.263410	−	0.456239i
$35$	6.06037	+	22.6176i	0.173153	+	0.646217i
$36$		0			0
$37$	−11.5279	−	35.1583i	−0.311564	−	0.950225i
$37$	−11.5279	−	35.1583i	−0.311564	−	0.950225i
$38$	−83.3946			−2.19459
$39$		0			0
$40$	31.7887	−	18.3532i	0.794718	−	0.458830i
$41$	55.8777	−	32.2610i	1.36287	−	0.786854i	0.372866	−	0.927885i	$-0.378375\pi$
$41$	55.8777	−	32.2610i	1.36287	−	0.786854i	0.990005	+	0.141031i	$0.0450418\pi$
$42$		0			0
$43$	−21.7511	+	21.7511i	−0.505840	+	0.505840i	−0.913247	−	0.407407i	$-0.866433\pi$
$43$	−21.7511	+	21.7511i	−0.505840	+	0.505840i	0.407407	+	0.913247i	$0.366433\pi$
$44$	13.2241	+	22.9048i	0.300548	+	0.520565i
$45$		0			0
$46$	62.6026	−	108.431i	1.36093	−	2.35719i
$47$	−53.2430			−1.13283			−0.566415	−	0.824120i	$-0.691670\pi$
$47$	−53.2430			−1.13283			−0.566415	+	0.824120i	$0.691670\pi$
$48$		0			0
$49$	−54.5336	+	94.4549i	−1.11293	+	1.92765i
$50$	−76.0942	−	20.3894i	−1.52188	−	0.407787i
$51$		0			0
$52$	−164.539	+	44.0880i	−3.16421	+	0.847847i
$53$	−0.442496	+	0.766426i	−0.00834899	+	0.0144609i	−0.870170	−	0.492752i	$-0.835991\pi$
$53$	−0.442496	+	0.766426i	−0.00834899	+	0.0144609i	0.861821	+	0.507213i	$0.169324\pi$
$54$		0			0
$55$	−1.35819	+	5.06885i	−0.0246944	+	0.0921609i
$56$	239.345	+	64.1324i	4.27402	+	1.14522i
$57$		0			0
$58$	−58.1080	−	33.5487i	−1.00186	−	0.578425i
$59$	16.7826	+	62.6336i	0.284451	+	1.06159i	0.949239	+	0.314555i	$0.101855\pi$
$59$	16.7826	+	62.6336i	0.284451	+	1.06159i	−0.664788	+	0.747032i	$0.731478\pi$
$60$		0			0
$61$	−3.80616	+	14.2048i	−0.0623961	+	0.232866i	−0.990081	−	0.140499i	$-0.955129\pi$
$61$	−3.80616	+	14.2048i	−0.0623961	+	0.232866i	0.927685	+	0.373365i	$0.121796\pi$
$62$	60.4669	+	34.9106i	0.975273	+	0.563074i
$63$		0			0
$64$		−	35.9958i		−	0.562434i
$65$	−29.2701	−	16.8991i	−0.450309	−	0.259986i
$66$		0			0
$67$	63.2306	−	36.5062i	0.943740	−	0.544869i	0.0526093	−	0.998615i	$-0.483246\pi$
$67$	63.2306	−	36.5062i	0.943740	−	0.544869i	0.891131	+	0.453747i	$0.149913\pi$
$68$	−32.4939	−	32.4939i	−0.477852	−	0.477852i
$69$		0			0
$70$	42.8361	+	74.1943i	0.611944	+	1.05992i
$71$	50.4928	+	87.4560i	0.711166	+	1.23178i	0.964420	+	0.264375i	$0.0851658\pi$
$71$	50.4928	+	87.4560i	0.711166	+	1.23178i	−0.253254	+	0.967400i	$0.581501\pi$
$72$		0			0
$73$			96.3766i			1.32023i	0.751166	+	0.660114i	$0.229492\pi$
$73$			96.3766i			1.32023i	−0.751166	+	0.660114i	$0.770508\pi$
$74$	−74.0345	−	113.337i	−1.00047	−	1.53158i
$75$		0			0
$76$	−206.661	+	55.3746i	−2.71922	+	0.728613i
$77$	−30.6786	+	17.7123i	−0.398423	+	0.230030i
$78$		0			0
$79$	41.7399	+	11.1842i	0.528353	+	0.141572i	0.513128	−	0.858312i	$-0.328487\pi$
$79$	41.7399	+	11.1842i	0.528353	+	0.141572i	0.0152255	+	0.999884i	$0.495153\pi$
$80$	45.5181	−	45.5181i	0.568976	−	0.568976i
$81$		0			0
$82$	166.928	−	166.928i	2.03571	−	2.03571i
$83$	19.3760	−	33.5601i	0.233445	−	0.404339i	−0.725374	−	0.688354i	$-0.758333\pi$
$83$	19.3760	−	33.5601i	0.233445	−	0.404339i	0.958820	+	0.284015i	$0.0916667\pi$
$84$		0			0
$85$		−	9.11772i		−	0.107267i
$86$	−56.2734	+	97.4684i	−0.654342	+	1.13335i
$87$		0			0
$88$	39.2671	+	39.2671i	0.446217	+	0.446217i
$89$	−128.240	+	34.3619i	−1.44090	+	0.386089i	−0.892850	−	0.450355i	$-0.851297\pi$
$89$	−128.240	+	34.3619i	−1.44090	+	0.386089i	−0.548053	+	0.836444i	$0.684631\pi$
$90$		0			0
$91$	−59.0511	−	220.382i	−0.648914	−	2.42178i
$92$	83.1371	−	310.272i	0.903664	−	3.37252i
$93$		0			0
$94$	−188.167	+	50.4192i	−2.00178	+	0.536374i
$95$	−36.7632	−	21.2253i	−0.386981	−	0.223424i
$96$		0			0
$97$	−50.4222	+	50.4222i	−0.519817	+	0.519817i	−0.917516	−	0.397699i	$-0.869809\pi$
$97$	−50.4222	+	50.4222i	−0.519817	+	0.519817i	0.397699	+	0.917516i	$0.369809\pi$
$98$	−103.283	+	385.456i	−1.05390	+	3.93322i
$99$		0			0
$100$	−202.108			−2.02108
$101$		−	160.223i		−	1.58637i	−0.608984	−	0.793183i	$-0.708422\pi$
$101$		−	160.223i		−	1.58637i	0.608984	−	0.793183i	$-0.291578\pi$
$102$		0			0
$103$	58.6808	+	58.6808i	0.569716	+	0.569716i	0.932049	−	0.362333i	$-0.118020\pi$
$103$	58.6808	+	58.6808i	0.569716	+	0.569716i	−0.362333	+	0.932049i	$0.618020\pi$
$104$	−309.743	+	178.830i	−2.97830	+	1.71952i
$105$		0			0
$106$	−0.838055	+	3.12767i	−0.00790618	+	0.0295063i
$107$	−25.5568	−	44.2656i	−0.238848	−	0.413697i	0.721536	−	0.692377i	$-0.243437\pi$
$107$	−25.5568	−	44.2656i	−0.238848	−	0.413697i	−0.960384	+	0.278680i	$0.910103\pi$
$108$		0			0
$109$	9.66208	+	36.0594i	0.0886429	+	0.330820i	0.995979	−	0.0895860i	$-0.0285544\pi$
$109$	9.66208	+	36.0594i	0.0886429	+	0.330820i	−0.907336	+	0.420406i	$0.861888\pi$
$110$			19.2001i			0.174546i
$111$		0			0
$112$	434.548			3.87989
$113$	137.878	−	36.9444i	1.22016	−	0.326942i	0.409422	−	0.912345i	$-0.365731\pi$
$113$	137.878	−	36.9444i	1.22016	−	0.326942i	0.810742	+	0.585403i	$0.199064\pi$
$114$		0			0
$115$	55.1948	−	31.8667i	0.479955	−	0.277102i
$116$	−166.274	−	44.5531i	−1.43340	−	0.384079i
$117$		0			0
$118$	118.623	+	205.462i	1.00528	+	1.74120i
$119$	43.5221	−	43.5221i	0.365732	−	0.365732i
$120$		0			0
$121$	113.061			0.934388
$122$			53.8057i			0.441030i
$123$		0			0
$124$	173.024	+	46.3618i	1.39536	+	0.373885i
$125$	−61.2791	−	61.2791i	−0.490233	−	0.490233i
$126$		0			0
$127$	18.1642	−	31.4614i	0.143025	−	0.247727i	−0.785609	−	0.618723i	$-0.787650\pi$
$127$	18.1642	−	31.4614i	0.143025	−	0.247727i	0.928635	+	0.370996i	$0.120984\pi$
$128$	15.2183	+	56.7955i	0.118893	+	0.443715i
$129$		0			0
$130$	−119.447	−	32.0056i	−0.918820	−	0.246197i
$131$	28.0498	−	7.51592i	0.214121	−	0.0573734i	−0.150164	−	0.988661i	$-0.547980\pi$
$131$	28.0498	−	7.51592i	0.214121	−	0.0573734i	0.364285	+	0.931288i	$0.381314\pi$
$132$		0			0
$133$	−74.1683	−	276.800i	−0.557656	−	2.08120i
$134$	188.894	−	188.894i	1.40966	−	1.40966i
$135$		0			0
$136$	−83.5593	−	48.2430i	−0.614407	−	0.354728i
$137$	133.327			0.973191			0.486595	−	0.873627i	$-0.338239\pi$
$137$	133.327			0.973191			0.486595	+	0.873627i	$0.338239\pi$
$138$		0			0
$139$	52.5034	+	30.3128i	0.377722	+	0.218078i	0.676827	−	0.736142i	$-0.263355\pi$
$139$	52.5034	+	30.3128i	0.377722	+	0.218078i	−0.299105	+	0.954220i	$0.596688\pi$
$140$	155.418	+	155.418i	1.11013	+	1.11013i
$141$		0			0
$142$	261.265	+	261.265i	1.83989	+	1.83989i
$143$	13.2340	−	49.3900i	0.0925454	−	0.345384i
$144$		0			0
$145$	−17.0774	−	29.5788i	−0.117775	−	0.203992i
$146$	91.2651	+	340.606i	0.625103	+	2.33292i
$147$		0			0
$148$	−258.722	−	231.702i	−1.74812	−	1.56555i
$149$	−154.637			−1.03783			−0.518916	−	0.854826i	$-0.673664\pi$
$149$	−154.637			−1.03783			−0.518916	+	0.854826i	$0.673664\pi$
$150$		0			0
$151$	43.4176	−	25.0672i	0.287534	−	0.166008i	−0.349295	−	0.937013i	$-0.613579\pi$
$151$	43.4176	−	25.0672i	0.287534	−	0.166008i	0.636829	+	0.771005i	$0.280246\pi$
$152$	−389.038	+	224.611i	−2.55946	+	1.47770i
$153$		0			0
$154$	−91.6487	+	91.6487i	−0.595121	+	0.595121i
$155$	17.7706	+	30.7796i	0.114649	+	0.198578i
$156$		0			0
$157$	−112.886	+	195.525i	−0.719020	+	1.24538i	0.242368	+	0.970184i	$0.422076\pi$
$157$	−112.886	+	195.525i	−0.719020	+	1.24538i	−0.961388	+	0.275195i	$0.911258\pi$
$158$	158.105			1.00066
$159$		0			0
$160$	44.3493	−	76.8152i	0.277183	−	0.480095i
$161$	415.576	+	111.353i	2.58121	+	0.691634i
$162$		0			0
$163$	−42.0005	+	11.2540i	−0.257672	+	0.0690429i	−0.385342	−	0.922774i	$-0.625917\pi$
$163$	−42.0005	+	11.2540i	−0.257672	+	0.0690429i	0.127671	+	0.991817i	$0.459250\pi$
$164$	302.825	−	524.508i	1.84649	−	3.19822i
$165$		0			0
$166$	36.6966	−	136.954i	0.221064	−	0.825022i
$167$	−117.598	−	31.5103i	−0.704179	−	0.188684i	−0.111078	−	0.993812i	$-0.535430\pi$
$167$	−117.598	−	31.5103i	−0.704179	−	0.188684i	−0.593102	+	0.805127i	$0.702097\pi$
$168$		0			0
$169$	138.844	+	80.1617i	0.821563	+	0.474330i
$170$	−8.63414	−	32.2231i	−0.0507891	−	0.189547i
$171$		0			0
$172$	−74.7319	+	278.903i	−0.434488	+	1.62153i
$173$	176.878	+	102.120i	1.02241	+	0.590291i	0.914802	−	0.403902i	$-0.132346\pi$
$173$	176.878	+	102.120i	1.02241	+	0.590291i	0.107612	+	0.994193i	$0.465680\pi$
$174$		0			0
$175$		−	270.702i		−	1.54687i
$176$	84.3395	+	48.6934i	0.479202	+	0.276667i
$177$		0			0
$178$	−420.677	+	242.878i	−2.36335	+	1.36448i
$179$	−150.148	−	150.148i	−0.838818	−	0.838818i	0.149885	−	0.988703i	$-0.452110\pi$
$179$	−150.148	−	150.148i	−0.838818	−	0.838818i	−0.988703	+	0.149885i	$0.952110\pi$
$180$		0			0
$181$	63.0251	+	109.163i	0.348205	+	0.603108i	0.985931	−	0.167155i	$-0.0534581\pi$
$181$	63.0251	+	109.163i	0.348205	+	0.603108i	−0.637726	+	0.770263i	$0.720125\pi$
$182$	−417.387	−	722.936i	−2.29334	−	3.97217i
$183$		0			0
$184$		−	674.444i		−	3.66545i
$185$	−3.79086	−	68.8059i	−0.0204911	−	0.371924i
$186$		0			0
$187$	13.3239	−	3.57013i	0.0712508	−	0.0190916i
$188$	−432.819	+	249.888i	−2.30223	+	1.32919i
$189$		0			0
$190$	−150.025	−	40.1991i	−0.789605	−	0.211574i
$191$	3.27924	−	3.27924i	0.0171688	−	0.0171688i	−0.698470	−	0.715639i	$-0.746136\pi$
$191$	3.27924	−	3.27924i	0.0171688	−	0.0171688i	0.715639	+	0.698470i	$0.246136\pi$
$192$		0			0
$193$	155.302	−	155.302i	0.804675	−	0.804675i	−0.179147	−	0.983822i	$-0.557334\pi$
$193$	155.302	−	155.302i	0.804675	−	0.804675i	0.983822	+	0.179147i	$0.0573338\pi$
$194$	−130.450	+	225.946i	−0.672422	+	1.16467i
$195$		0			0
$196$			1023.78i			5.22337i
$197$	−121.496	+	210.436i	−0.616729	+	1.06821i	0.373350	+	0.927691i	$0.378209\pi$
$197$	−121.496	+	210.436i	−0.616729	+	1.06821i	−0.990079	+	0.140515i	$0.955124\pi$
$198$		0			0
$199$	−140.319	−	140.319i	−0.705122	−	0.705122i	0.260383	−	0.965505i	$-0.416151\pi$
$199$	−140.319	−	140.319i	−0.705122	−	0.705122i	−0.965505	+	0.260383i	$0.916151\pi$
$200$	−409.897	+	109.832i	−2.04948	+	0.549158i
$201$		0			0
$202$	−151.725	−	566.246i	−0.751115	−	2.80320i
$203$	59.6741	−	222.707i	0.293961	−	1.09708i
$204$		0			0
$205$	116.074	−	31.1019i	0.566213	−	0.151716i
$206$	262.953	+	151.816i	1.27647	+	0.736971i
$207$		0			0
$208$	−443.520	+	443.520i	−2.13231	+	2.13231i
$209$	16.6219	−	62.0338i	0.0795306	−	0.296812i
$210$		0			0
$211$	169.207			0.801930			0.400965	−	0.916093i	$-0.368675\pi$
$211$	169.207			0.801930			0.400965	+	0.916093i	$0.368675\pi$
$212$			8.30717i			0.0391847i
$213$		0			0
$214$	−132.238	−	132.238i	−0.617937	−	0.617937i
$215$	−49.6145	+	28.6450i	−0.230765	+	0.133232i
$216$		0			0
$217$	−62.0966	+	231.748i	−0.286159	+	1.06796i
$218$	68.2938	+	118.288i	0.313274	+	0.542607i
$219$		0			0
$220$	12.7490	+	47.5798i	0.0579499	+	0.216272i
$221$			88.8414i			0.401997i
$222$		0			0
$223$	−250.297			−1.12241			−0.561205	−	0.827677i	$-0.689662\pi$
$223$	−250.297			−1.12241			−0.561205	+	0.827677i	$0.689662\pi$
$224$	578.361	−	154.971i	2.58197	−	0.691837i
$225$		0			0
$226$	452.293	−	261.132i	2.00130	−	1.15545i
$227$	7.76954	+	2.08184i	0.0342271	+	0.00917111i	0.275892	−	0.961189i	$-0.411027\pi$
$227$	7.76954	+	2.08184i	0.0342271	+	0.00917111i	−0.241665	+	0.970360i	$0.577693\pi$
$228$		0			0
$229$	−50.6920	−	87.8012i	−0.221363	−	0.383411i	0.733859	−	0.679301i	$-0.237717\pi$
$229$	−50.6920	−	87.8012i	−0.221363	−	0.383411i	−0.955222	+	0.295890i	$0.904384\pi$
$230$	164.888	−	164.888i	0.716905	−	0.716905i
$231$		0			0
$232$	−361.434			−1.55790
$233$			301.599i			1.29442i	0.762313	+	0.647209i	$0.224064\pi$
$233$			301.599i			1.29442i	−0.762313	+	0.647209i	$0.775936\pi$
$234$		0			0
$235$	−95.7830	−	25.6650i	−0.407587	−	0.109213i
$236$	430.390	+	430.390i	1.82369	+	1.82369i
$237$		0			0
$238$	112.598	−	195.026i	0.473102	−	0.819437i
$239$	−71.9348	−	268.464i	−0.300982	−	1.12328i	−0.936349	−	0.351071i	$-0.885818\pi$
$239$	−71.9348	−	268.464i	−0.300982	−	1.12328i	0.635367	−	0.772211i	$-0.280849\pi$
$240$		0			0
$241$	3.67517	+	0.984759i	0.0152497	+	0.00408614i	0.266436	−	0.963853i	$-0.414154\pi$
$241$	3.67517	+	0.984759i	0.0152497	+	0.00408614i	−0.251186	+	0.967939i	$0.580821\pi$
$242$	399.570	−	107.065i	1.65112	−	0.442416i
$243$		0			0
$244$	35.7273	+	133.336i	0.146424	+	0.546460i
$245$	−143.635	+	143.635i	−0.586266	+	0.586266i
$246$		0			0
$247$	358.214	+	206.815i	1.45026	+	0.837308i
$248$	376.106			1.51656
$249$		0			0
$250$	−274.596	−	158.538i	−1.09839	−	0.634153i
$251$	−134.695	−	134.695i	−0.536634	−	0.536634i	0.385904	−	0.922539i	$-0.373889\pi$
$251$	−134.695	−	134.695i	−0.536634	−	0.536634i	−0.922539	+	0.385904i	$0.873889\pi$
$252$		0			0
$253$	68.1795	+	68.1795i	0.269484	+	0.269484i
$254$	34.4017	−	128.389i	0.135440	−	0.505468i
$255$		0			0
$256$	179.558	+	311.004i	0.701399	+	1.21486i
$257$	−28.6163	−	106.797i	−0.111347	−	0.415554i	0.887640	−	0.460537i	$-0.152343\pi$
$257$	−28.6163	−	106.797i	−0.111347	−	0.415554i	−0.998988	+	0.0449833i	$0.985677\pi$
$258$		0			0
$259$	310.340	−	346.530i	1.19822	−	1.33795i
$260$	−317.254			−1.22021
$261$		0			0
$262$	92.0139	−	53.1242i	0.351198	−	0.202764i
$263$	115.964	−	66.9519i	0.440928	−	0.254570i	−0.263063	−	0.964779i	$-0.584733\pi$
$263$	115.964	−	66.9519i	0.440928	−	0.254570i	0.703991	+	0.710209i	$0.251399\pi$
$264$		0			0
$265$	−1.16549	+	1.16549i	−0.00439806	+	0.00439806i
$266$	−524.238	−	908.007i	−1.97082	−	3.41356i
$267$		0			0
$268$	342.673	−	593.527i	1.27863	−	2.21465i
$269$	89.9289			0.334308			0.167154	−	0.985931i	$-0.446542\pi$
$269$	89.9289			0.334308			0.167154	+	0.985931i	$0.446542\pi$
$270$		0			0
$271$	42.2955	−	73.2580i	0.156072	−	0.270325i	−0.777377	−	0.629035i	$-0.783450\pi$
$271$	42.2955	−	73.2580i	0.156072	−	0.270325i	0.933449	+	0.358711i	$0.116783\pi$
$272$	−163.442	−	43.7943i	−0.600891	−	0.161008i
$273$		0			0
$274$	471.193	−	126.256i	1.71968	−	0.460788i
$275$	30.3336	−	52.5394i	0.110304	−	0.191052i
$276$		0			0
$277$	11.7035	−	43.6780i	0.0422509	−	0.157682i	−0.941577	−	0.336797i	$-0.890657\pi$
$277$	11.7035	−	43.6780i	0.0422509	−	0.157682i	0.983828	+	0.179114i	$0.0573232\pi$
$278$	214.258	+	57.4103i	0.770713	+	0.206512i
$279$		0			0
$280$	399.663	+	230.745i	1.42737	+	0.824091i
$281$	−88.8483	−	331.586i	−0.316186	−	1.18002i	−0.922880	−	0.385087i	$-0.874171\pi$
$281$	−88.8483	−	331.586i	−0.316186	−	1.18002i	0.606694	−	0.794935i	$-0.292495\pi$
$282$		0			0
$283$	106.494	−	397.440i	0.376303	−	1.40438i	−0.475129	−	0.879916i	$-0.657599\pi$
$283$	106.494	−	397.440i	0.376303	−	1.40438i	0.851432	−	0.524465i	$-0.175735\pi$
$284$	820.924	+	473.961i	2.89058	+	1.66888i
$285$		0			0
$286$		−	187.082i		−	0.654132i
$287$	702.521	+	405.601i	2.44781	+	1.41324i
$288$		0			0
$289$	229.526	−	132.517i	0.794206	−	0.458535i
$290$	−88.3634	−	88.3634i	−0.304701	−	0.304701i
$291$		0			0
$292$	452.329	+	783.457i	1.54907	+	2.68307i
$293$	25.3936	+	43.9830i	0.0866675	+	0.150113i	0.906101	−	0.423062i	$-0.139045\pi$
$293$	25.3936	+	43.9830i	0.0866675	+	0.150113i	−0.819433	+	0.573175i	$0.805712\pi$
$294$		0			0
$295$			120.766i			0.409377i
$296$	−650.630	−	329.319i	−2.19807	−	1.11257i
$297$		0			0
$298$	−546.504	+	146.435i	−1.83391	+	0.491394i
$299$	−537.808	+	310.504i	−1.79869	+	1.03847i
$300$		0			0
$301$	−373.560	−	100.095i	−1.24106	−	0.332542i
$302$	129.705	−	129.705i	0.429487	−	0.429487i
$303$		0			0
$304$	−557.061	+	557.061i	−1.83244	+	1.83244i
$305$	−13.6944	+	23.7194i	−0.0448997	+	0.0777686i
$306$		0			0
$307$			606.614i			1.97594i	0.154636	+	0.987971i	$0.450579\pi$
$307$			606.614i			1.97594i	−0.154636	+	0.987971i	$0.549421\pi$
$308$	−166.260	+	287.971i	−0.539805	+	0.934970i
$309$		0			0
$310$	91.9506	+	91.9506i	0.296615	+	0.296615i
$311$	57.8195	−	15.4927i	0.185915	−	0.0498157i	−0.164660	−	0.986350i	$-0.552653\pi$
$311$	57.8195	−	15.4927i	0.185915	−	0.0498157i	0.350575	+	0.936535i	$0.385986\pi$
$312$		0			0
$313$	56.6509	+	211.424i	0.180993	+	0.675476i	0.995453	+	0.0952555i	$0.0303668\pi$
$313$	56.6509	+	211.424i	0.180993	+	0.675476i	−0.814460	+	0.580220i	$0.802967\pi$
$314$	−213.798	+	797.905i	−0.680886	+	2.54110i
$315$		0			0
$316$	391.800	−	104.983i	1.23987	−	0.332223i
$317$	299.487	+	172.909i	0.944755	+	0.545455i	0.891448	−	0.453124i	$-0.149690\pi$
$317$	299.487	+	172.909i	0.944755	+	0.545455i	0.0533074	+	0.998578i	$0.483024\pi$
$318$		0			0
$319$	36.5373	−	36.5373i	0.114537	−	0.114537i
$320$	17.3512	−	64.7556i	0.0542225	−	0.202361i
$321$		0			0
$322$	1574.14			4.88863
$323$			111.585i			0.345464i
$324$		0			0
$325$	276.291	+	276.291i	0.850127	+	0.850127i
$326$	−137.777	+	79.5458i	−0.422630	+	0.244005i
$327$		0			0
$328$	329.128	−	1228.32i	1.00344	−	3.74488i
$329$	−334.698	−	579.714i	−1.01732	−	1.76205i
$330$		0			0
$331$	−66.2716	−	247.329i	−0.200216	−	0.747217i	−0.990855	−	0.134934i	$-0.956918\pi$
$331$	−66.2716	−	247.329i	−0.200216	−	0.747217i	0.790638	−	0.612284i	$-0.209749\pi$
$332$		−	363.753i		−	1.09564i
$333$		0			0
$334$	−445.444			−1.33366
$335$	131.348	−	35.1945i	0.392083	−	0.105058i
$336$		0			0
$337$	−405.767	+	234.269i	−1.20406	+	0.695162i	−0.961454	−	0.274964i	$-0.911334\pi$
$337$	−405.767	+	234.269i	−1.20406	+	0.695162i	−0.242601	+	0.970126i	$0.578001\pi$
$338$	566.601	+	151.820i	1.67634	+	0.449173i
$339$		0			0
$340$	−42.7927	−	74.1191i	−0.125861	−	0.217997i
$341$	−38.0206	+	38.0206i	−0.111497	+	0.111497i
$342$		0			0
$343$	−755.192			−2.20173
$344$			606.257i			1.76237i
$345$		0			0
$346$	721.810	+	193.408i	2.08616	+	0.558984i
$347$	−179.419	−	179.419i	−0.517059	−	0.517059i	0.399621	−	0.916680i	$-0.369142\pi$
$347$	−179.419	−	179.419i	−0.517059	−	0.517059i	−0.916680	+	0.399621i	$0.869142\pi$
$348$		0			0
$349$	−147.409	+	255.319i	−0.422375	+	0.731574i	−0.996171	−	0.0874235i	$-0.972137\pi$
$349$	−147.409	+	255.319i	−0.422375	+	0.731574i	0.573797	+	0.818998i	$0.305470\pi$
$350$	−256.345	−	956.692i	−0.732414	−	2.73341i
$351$		0			0
$352$	129.617	+	34.7308i	0.368230	+	0.0986670i
$353$	440.047	−	117.910i	1.24659	−	0.334023i	0.425572	−	0.904924i	$-0.360073\pi$
$353$	440.047	−	117.910i	1.24659	−	0.334023i	0.821019	+	0.570901i	$0.193406\pi$
$354$		0			0
$355$	48.6785	+	181.671i	0.137123	+	0.511749i
$356$	−881.209	+	881.209i	−2.47531	+	2.47531i
$357$		0			0
$358$	−672.827	−	388.457i	−1.87940	−	1.08507i
$359$	−196.536			−0.547455			−0.273727	−	0.961807i	$-0.588257\pi$
$359$	−196.536			−0.547455			−0.273727	+	0.961807i	$0.588257\pi$
$360$		0			0
$361$	137.282	+	79.2599i	0.380283	+	0.219557i
$362$	326.111	+	326.111i	0.900858	+	0.900858i
$363$		0			0
$364$	−1514.36	−	1514.36i	−4.16034	−	4.16034i
$365$	−46.4569	+	173.379i	−0.127279	+	0.475012i
$366$		0			0
$367$	−35.7272	−	61.8812i	−0.0973492	−	0.168614i	0.813237	−	0.581932i	$-0.197703\pi$
$367$	−35.7272	−	61.8812i	−0.0973492	−	0.168614i	−0.910587	+	0.413318i	$0.864370\pi$
$368$	−306.125	−	1142.47i	−0.831861	−	3.10455i
$369$		0			0
$370$	−78.5540	−	239.578i	−0.212308	−	0.647508i
$371$	−11.1265			−0.0299907
$372$		0			0
$373$	−173.248	+	100.025i	−0.464471	+	0.268162i	−0.713922	−	0.700225i	$-0.753083\pi$
$373$	−173.248	+	100.025i	−0.464471	+	0.268162i	0.249452	+	0.968387i	$0.419750\pi$
$374$	43.7074	−	25.2345i	0.116865	−	0.0674719i
$375$		0			0
$376$	−742.007	+	742.007i	−1.97342	+	1.97342i
$377$	166.399	+	288.211i	0.441376	+	0.764485i
$378$		0			0
$379$	−226.227	+	391.837i	−0.596906	+	1.03387i	0.396369	+	0.918091i	$0.370270\pi$
$379$	−226.227	+	391.837i	−0.596906	+	1.03387i	−0.993275	+	0.115780i	$0.963063\pi$
$380$	−398.471			−1.04861
$381$		0			0
$382$	8.48390	−	14.6945i	0.0222092	−	0.0384674i
$383$	−313.127	−	83.9021i	−0.817564	−	0.219066i	−0.174283	−	0.984696i	$-0.555761\pi$
$383$	−313.127	−	83.9021i	−0.817564	−	0.219066i	−0.643281	+	0.765630i	$0.722427\pi$
$384$		0			0
$385$	−63.7280	+	17.0759i	−0.165527	+	0.0443529i
$386$	401.791	−	695.922i	1.04091	−	1.80291i
$387$		0			0
$388$	−173.239	+	646.538i	−0.446493	+	1.66633i
$389$	−106.674	−	28.5832i	−0.274226	−	0.0734787i	0.119085	−	0.992884i	$-0.462004\pi$
$389$	−106.674	−	28.5832i	−0.274226	−	0.0734787i	−0.393311	+	0.919405i	$0.628671\pi$
$390$		0			0
$391$	−145.084	−	83.7644i	−0.371059	−	0.214231i
$392$	556.353	+	2076.34i	1.41927	+	5.29678i
$393$		0			0
$394$	−230.104	+	858.758i	−0.584019	+	2.17959i
$395$	69.6980	+	40.2402i	0.176451	+	0.101874i
$396$		0			0
$397$		−	613.127i		−	1.54440i	−0.635380	−	0.772200i	$-0.719156\pi$
$397$		−	613.127i		−	1.54440i	0.635380	−	0.772200i	$-0.280844\pi$
$398$	−628.782	−	363.027i	−1.57985	−	0.912129i
$399$		0			0
$400$	−644.493	+	372.098i	−1.61123	+	0.930246i
$401$	213.710	+	213.710i	0.532942	+	0.532942i	0.921447	−	0.388504i	$-0.127008\pi$
$401$	213.710	+	213.710i	0.532942	+	0.532942i	−0.388504	+	0.921447i	$0.627008\pi$
$402$		0			0
$403$	−173.154	−	299.911i	−0.429662	−	0.744196i
$404$	−751.983	−	1302.47i	−1.86134	−	3.22394i
$405$		0			0
$406$		−	843.580i		−	2.07778i
$407$	99.0631	−	32.4813i	0.243398	−	0.0798065i
$408$		0			0
$409$	−494.080	+	132.388i	−1.20802	+	0.323688i	−0.805985	−	0.591937i	$-0.798364\pi$
$409$	−494.080	+	132.388i	−1.20802	+	0.323688i	−0.402035	+	0.915624i	$0.631697\pi$
$410$	380.765	−	219.835i	0.928696	−	0.536183i
$411$		0			0
$412$	752.433	+	201.614i	1.82629	+	0.489354i
$413$	−576.460	+	576.460i	−1.39579	+	1.39579i
$414$		0			0
$415$	51.0341	−	51.0341i	0.122974	−	0.122974i
$416$	−432.132	+	748.474i	−1.03878	+	1.79922i
$417$		0			0
$418$		−	234.975i		−	0.562141i
$419$	136.576	−	236.557i	0.325958	−	0.564575i	−0.655748	−	0.754980i	$-0.727647\pi$
$419$	136.576	−	236.557i	0.325958	−	0.564575i	0.981706	+	0.190405i	$0.0609800\pi$
$420$		0			0
$421$	−507.072	−	507.072i	−1.20445	−	1.20445i	−0.972800	−	0.231648i	$-0.925588\pi$
$421$	−507.072	−	507.072i	−1.20445	−	1.20445i	−0.231648	−	0.972800i	$-0.574412\pi$
$422$	597.998	−	160.233i	1.41706	−	0.379699i
$423$		0			0
$424$	4.51436	+	16.8478i	0.0106471	+	0.0397354i
$425$	−27.2817	+	101.817i	−0.0641922	+	0.239568i
$426$		0			0
$427$	−178.589	+	47.8529i	−0.418242	+	0.112068i
$428$	−415.508	−	239.894i	−0.970814	−	0.560500i
$429$		0			0
$430$	−148.218	+	148.218i	−0.344692	+	0.344692i
$431$	−26.6095	+	99.3080i	−0.0617390	+	0.230413i	−0.989900	−	0.141765i	$-0.954722\pi$
$431$	−26.6095	+	99.3080i	−0.0617390	+	0.230413i	0.928161	+	0.372178i	$0.121389\pi$
$432$		0			0
$433$	139.549			0.322285			0.161142	−	0.986931i	$-0.448482\pi$
$433$	139.549			0.322285			0.161142	+	0.986931i	$0.448482\pi$
$434$			877.825i			2.02264i
$435$		0			0
$436$	247.784	+	247.784i	0.568311	+	0.568311i
$437$	−675.487	+	389.993i	−1.54574	+	0.892432i
$438$		0			0
$439$	−93.1227	+	347.539i	−0.212125	+	0.791660i	0.775034	+	0.631919i	$0.217733\pi$
$439$	−93.1227	+	347.539i	−0.212125	+	0.791660i	−0.987159	+	0.159741i	$0.948934\pi$
$440$	51.7125	+	89.5687i	0.117528	+	0.203565i
$441$		0			0
$442$	84.1295	+	313.976i	0.190338	+	0.710352i
$443$		−	586.402i		−	1.32371i	−0.749634	−	0.661853i	$-0.769770\pi$
$443$		−	586.402i		−	1.32371i	0.749634	−	0.661853i	$-0.230230\pi$
$444$		0			0
$445$	−247.265			−0.555652
$446$	−884.579	+	237.022i	−1.98336	+	0.531440i
$447$		0			0
$448$	391.925	−	226.278i	0.874833	−	0.505085i
$449$	577.353	+	154.701i	1.28586	+	0.344546i	0.836088	−	0.548595i	$-0.184837\pi$
$449$	577.353	+	154.701i	1.28586	+	0.344546i	0.449776	+	0.893141i	$0.351504\pi$
$450$		0			0
$451$	90.8995	+	157.443i	0.201551	+	0.349097i
$452$	947.438	−	947.438i	2.09610	−	2.09610i
$453$		0			0
$454$	29.4299			0.0648235
$455$		−	424.927i		−	0.933905i
$456$		0			0
$457$	−76.6647	−	20.5422i	−0.167756	−	0.0449502i	0.173963	−	0.984752i	$-0.444343\pi$
$457$	−76.6647	−	20.5422i	−0.167756	−	0.0449502i	−0.341720	+	0.939802i	$0.611009\pi$
$458$	−262.296	−	262.296i	−0.572699	−	0.572699i
$459$		0			0
$460$	299.124	−	518.097i	0.650269	−	1.12630i
$461$	130.384	+	486.600i	0.282829	+	1.05553i	0.950412	+	0.310995i	$0.100662\pi$
$461$	130.384	+	486.600i	0.282829	+	1.05553i	−0.667583	+	0.744535i	$0.732671\pi$
$462$		0			0
$463$	493.688	+	132.283i	1.06628	+	0.285709i	0.748964	−	0.662611i	$-0.230552\pi$
$463$	493.688	+	132.283i	1.06628	+	0.285709i	0.317316	+	0.948320i	$0.397218\pi$
$464$	−612.251	+	164.052i	−1.31951	+	0.353560i
$465$		0			0
$466$	285.603	+	1065.89i	0.612883	+	2.28731i
$467$	128.649	−	128.649i	0.275480	−	0.275480i	−0.555822	−	0.831302i	$-0.687596\pi$
$467$	128.649	−	128.649i	0.275480	−	0.275480i	0.831302	+	0.555822i	$0.187596\pi$
$468$		0			0
$469$	794.965	+	458.973i	1.69502	+	0.978621i
$470$	−362.812			−0.771940
$471$		0			0
$472$	1106.76	+	638.990i	2.34484	+	1.35379i
$473$	−61.2865	−	61.2865i	−0.129570	−	0.129570i
$474$		0			0
$475$	347.022	+	347.022i	0.730572	+	0.730572i
$476$	149.532	−	558.061i	0.314143	−	1.17240i
$477$		0			0
$478$	−508.451	−	880.664i	−1.06371	−	1.84239i
$479$	47.2453	+	176.322i	0.0986331	+	0.368104i	0.997545	−	0.0700252i	$-0.0223080\pi$
$479$	47.2453	+	176.322i	0.0986331	+	0.368104i	−0.898912	+	0.438129i	$0.855641\pi$
$480$		0			0
$481$	36.9375	+	670.432i	0.0767930	+	1.39383i
$482$	13.9210			0.0288818
$483$		0			0
$484$	919.087	−	530.635i	1.89894	−	1.09635i
$485$	−115.014	+	66.4032i	−0.237142	+	0.136914i
$486$		0			0
$487$	616.564	−	616.564i	1.26605	−	1.26605i	0.317933	−	0.948113i	$-0.397011\pi$
$487$	616.564	−	616.564i	1.26605	−	1.26605i	0.948113	−	0.317933i	$-0.102989\pi$
$488$	144.918	+	251.005i	0.296963	+	0.514354i
$489$		0			0
$490$	−371.606	+	643.641i	−0.758380	+	1.31355i
$491$	227.776			0.463902			0.231951	−	0.972728i	$-0.425489\pi$
$491$	227.776			0.463902			0.231951	+	0.972728i	$0.425489\pi$
$492$		0			0
$493$	−44.8893	+	77.7505i	−0.0910533	+	0.157709i
$494$	1461.82	+	391.693i	2.95914	+	0.792900i
$495$		0			0
$496$	637.105	−	170.712i	1.28449	−	0.344177i
$497$	−634.819	+	1099.54i	−1.27730	+	2.21235i
$498$		0			0
$499$	−139.389	+	520.206i	−0.279336	+	1.04250i	0.673543	+	0.739148i	$0.264772\pi$
$499$	−139.389	+	520.206i	−0.279336	+	1.04250i	−0.952879	+	0.303349i	$0.901895\pi$
$500$	−785.750	−	210.541i	−1.57150	−	0.421082i
$501$		0			0
$502$	−603.580	−	348.477i	−1.20235	−	0.694177i
$503$	−31.4313	−	117.303i	−0.0624876	−	0.233207i	0.927618	−	0.373530i	$-0.121853\pi$
$503$	−31.4313	−	117.303i	−0.0624876	−	0.233207i	−0.990106	+	0.140323i	$0.955186\pi$
$504$		0			0
$505$	77.2330	−	288.237i	0.152937	−	0.570767i
$506$	305.518	+	176.391i	0.603790	+	0.348598i
$507$		0			0
$508$		−	341.004i		−	0.671269i
$509$	253.714	+	146.482i	0.498455	+	0.287783i	0.728075	−	0.685497i	$-0.240415\pi$
$509$	253.714	+	146.482i	0.498455	+	0.287783i	−0.229620	+	0.973280i	$0.573748\pi$
$510$		0			0
$511$	−1049.36	+	605.846i	−2.05353	+	1.18561i
$512$	762.779	+	762.779i	1.48980	+	1.48980i
$513$		0			0
$514$	−202.266	−	350.335i	−0.393514	−	0.681587i
$515$	77.2792	+	133.852i	0.150057	+	0.259906i
$516$		0			0
$517$		−	150.019i		−	0.290172i
$518$	768.625	−	1518.56i	1.48383	−	2.93158i
$519$		0			0
$520$	−643.424	+	172.405i	−1.23735	+	0.331548i
$521$	−585.238	+	337.888i	−1.12330	+	0.648537i	−0.942241	−	0.334936i	$-0.891285\pi$
$521$	−585.238	+	337.888i	−1.12330	+	0.648537i	−0.181057	+	0.983473i	$0.557952\pi$
$522$		0			0
$523$	−147.725	−	39.5829i	−0.282457	−	0.0756842i	0.114809	−	0.993388i	$-0.463374\pi$
$523$	−147.725	−	39.5829i	−0.282457	−	0.0756842i	−0.397266	+	0.917703i	$0.630041\pi$
$524$	192.745	−	192.745i	0.367835	−	0.367835i
$525$		0			0
$526$	346.429	−	346.429i	0.658611	−	0.658611i
$527$	46.7116	−	80.9068i	0.0886368	−	0.153523i
$528$		0			0
$529$		−	642.038i		−	1.21368i
$530$	−3.01529	+	5.22263i	−0.00568922	+	0.00985402i
$531$		0			0
$532$	−1902.04	−	1902.04i	−3.57527	−	3.57527i
$533$	−1131.00	+	303.051i	−2.12195	+	0.568576i
$534$		0			0
$535$	−24.6385	−	91.9521i	−0.0460533	−	0.171873i
$536$	372.437	−	1389.95i	0.694845	−	2.59320i
$537$		0			0
$538$	317.819	−	85.1593i	0.590742	−	0.158289i
$539$	−266.139	−	153.655i	−0.493764	−	0.285075i
$540$		0			0
$541$	−180.657	+	180.657i	−0.333932	+	0.333932i	−0.854077	−	0.520146i	$-0.825878\pi$
$541$	−180.657	+	180.657i	−0.333932	+	0.333932i	0.520146	+	0.854077i	$0.325878\pi$
$542$	80.1046	−	298.954i	0.147794	−	0.551576i
$543$		0			0
$544$	−233.152			−0.428588
$545$			69.5275i			0.127573i
$546$		0			0
$547$	−49.0918	−	49.0918i	−0.0897474	−	0.0897474i	0.660808	−	0.750555i	$-0.270214\pi$
$547$	−49.0918	−	49.0918i	−0.0897474	−	0.0897474i	−0.750555	+	0.660808i	$0.770214\pi$
$548$	1083.83	−	625.751i	1.97780	−	1.14188i
$549$		0			0
$550$	57.4496	−	214.405i	0.104454	−	0.389827i
$551$	208.997	+	361.993i	0.379304	+	0.656975i
$552$		0			0
$553$	140.613	+	524.774i	0.254273	+	0.948958i
$554$		−	165.446i		−	0.298639i
$555$		0			0
$556$	569.075			1.02352
$557$	−355.249	+	95.1887i	−0.637790	+	0.170895i	−0.563202	−	0.826319i	$-0.690431\pi$
$557$	−355.249	+	95.1887i	−0.637790	+	0.170895i	−0.0745878	+	0.997214i	$0.523764\pi$
$558$		0			0
$559$	483.435	−	279.111i	0.864822	−	0.499305i
$560$	781.742	+	209.467i	1.39597	+	0.374049i
$561$		0			0
$562$	−628.000	−	1087.73i	−1.11744	−	1.93546i
$563$	−63.3011	+	63.3011i	−0.112435	+	0.112435i	−0.761086	−	0.648651i	$-0.775334\pi$
$563$	−63.3011	+	63.3011i	−0.112435	+	0.112435i	0.648651	+	0.761086i	$0.275334\pi$
$564$		0			0
$565$	265.849			0.470529
$566$		−	1505.44i		−	2.65980i
$567$		0			0
$568$	1922.49	+	515.129i	3.38466	+	0.906916i
$569$	−795.505	−	795.505i	−1.39808	−	1.39808i	−0.805556	−	0.592519i	$-0.798133\pi$
$569$	−795.505	−	795.505i	−1.39808	−	1.39808i	−0.592519	−	0.805556i	$-0.701867\pi$
$570$		0			0
$571$	265.970	−	460.673i	0.465796	−	0.806782i	−0.533441	−	0.845837i	$-0.679101\pi$
$571$	265.970	−	460.673i	0.465796	−	0.806782i	0.999237	+	0.0390549i	$0.0124347\pi$
$572$	−124.224	−	463.609i	−0.217174	−	0.810505i
$573$		0			0
$574$	2866.88	+	768.178i	4.99456	+	1.33829i
$575$	−711.705	+	190.701i	−1.23775	+	0.331653i
$576$		0			0
$577$	288.654	+	1077.27i	0.500266	+	1.86702i	0.498271	+	0.867021i	$0.333968\pi$
$577$	288.654	+	1077.27i	0.500266	+	1.86702i	0.00199500	+	0.999998i	$0.499365\pi$
$578$	685.681	−	685.681i	1.18630	−	1.18630i
$579$		0			0
$580$	−277.648	−	160.300i	−0.478703	−	0.276379i
$581$	487.207			0.838567
$582$		0			0
$583$	−2.15950	−	1.24679i	−0.00370412	−	0.00213858i
$584$	1343.13	+	1343.13i	2.29987	+	2.29987i
$585$		0			0
$586$	131.394	+	131.394i	0.224222	+	0.224222i
$587$	83.8832	−	313.057i	0.142902	−	0.533316i	−0.856938	−	0.515419i	$-0.827636\pi$
$587$	83.8832	−	313.057i	0.142902	−	0.533316i	0.999840	−	0.0178970i	$-0.00569708\pi$
$588$		0			0
$589$	−217.481	−	376.688i	−0.369238	−	0.639539i
$590$	114.361	+	426.802i	0.193833	+	0.723393i
$591$		0			0
$592$	−1251.61	−	262.535i	−2.11420	−	0.443471i
$593$	151.892			0.256142			0.128071	−	0.991765i	$-0.459121\pi$
$593$	151.892			0.256142			0.128071	+	0.991765i	$0.459121\pi$
$594$		0			0
$595$	99.2745	−	57.3161i	0.166848	−	0.0963296i
$596$	−1257.06	+	725.765i	−2.10917	+	1.21773i
$597$		0			0
$598$	−1606.64	+	1606.64i	−2.68669	+	2.68669i
$599$	225.050	+	389.799i	0.375710	+	0.650749i	0.990433	−	0.137994i	$-0.0440654\pi$
$599$	225.050	+	389.799i	0.375710	+	0.650749i	−0.614723	+	0.788743i	$0.710732\pi$
$600$		0			0
$601$	152.390	−	263.947i	0.253560	−	0.439180i	−0.710943	−	0.703250i	$-0.751732\pi$
$601$	152.390	−	263.947i	0.253560	−	0.439180i	0.964504	+	0.264070i	$0.0850650\pi$
$602$	−1414.99			−2.35049
$603$		0			0
$604$	235.298	−	407.548i	0.389566	−	0.674749i
$605$	203.394	+	54.4993i	0.336189	+	0.0900815i
$606$		0			0
$607$	82.1764	−	22.0191i	0.135381	−	0.0362753i	−0.190492	−	0.981689i	$-0.561008\pi$
$607$	82.1764	−	22.0191i	0.135381	−	0.0362753i	0.325873	+	0.945413i	$0.394342\pi$
$608$	−542.757	+	940.084i	−0.892693	+	1.54619i
$609$		0			0
$610$	−25.9362	+	96.7952i	−0.0425184	+	0.158681i
$611$	933.293	+	250.075i	1.52748	+	0.409288i
$612$		0			0
$613$	−366.864	−	211.809i	−0.598472	−	0.345528i	0.169968	−	0.985450i	$-0.445634\pi$
$613$	−366.864	−	211.809i	−0.598472	−	0.345528i	−0.768440	+	0.639921i	$0.778967\pi$
$614$	574.442	+	2143.85i	0.935573	+	3.49160i
$615$		0			0
$616$	−180.701	+	674.386i	−0.293346	+	1.09478i
$617$	−141.088	−	81.4571i	−0.228668	−	0.132021i	0.381290	−	0.924456i	$-0.375480\pi$
$617$	−141.088	−	81.4571i	−0.228668	−	0.132021i	−0.609957	+	0.792434i	$0.708813\pi$
$618$		0			0
$619$		−	6.57995i		−	0.0106300i	−0.999986	−	0.00531499i	$-0.998308\pi$
$619$		−	6.57995i		−	0.0106300i	0.999986	−	0.00531499i	$-0.00169182\pi$
$620$	288.919	+	166.808i	0.465999	+	0.269044i
$621$		0			0
$622$	189.670	−	109.506i	0.304935	−	0.176054i
$623$	−1180.28	−	1180.28i	−1.89452	−	1.89452i
$624$		0			0
$625$	188.440	+	326.388i	0.301505	+	0.522221i
$626$	400.421	+	693.550i	0.639651	+	1.10791i
$627$		0			0
$628$			2119.26i			3.37462i
$629$	−151.649	+	99.0607i	−0.241095	+	0.157489i
$630$		0			0
$631$	639.615	−	171.384i	1.01365	−	0.271607i	0.286498	−	0.958081i	$-0.407509\pi$
$631$	639.615	−	171.384i	1.01365	−	0.271607i	0.727155	+	0.686474i	$0.240842\pi$
$632$	737.562	−	425.832i	1.16703	−	0.673784i
$633$		0			0
$634$	1222.16	+	327.477i	1.92770	+	0.516525i
$635$	47.8425	−	47.8425i	0.0753425	−	0.0753425i
$636$		0			0
$637$	1399.56	−	1399.56i	2.19710	−	2.19710i
$638$	94.5277	−	163.727i	0.148162	−	0.256625i
$639$		0			0
$640$			109.510i			0.171109i
$641$	23.8591	−	41.3252i	0.0372217	−	0.0644699i	−0.846814	−	0.531888i	$-0.821483\pi$
$641$	23.8591	−	41.3252i	0.0372217	−	0.0644699i	0.884036	+	0.467419i	$0.154816\pi$
$642$		0			0
$643$	−156.851	−	156.851i	−0.243936	−	0.243936i	0.574540	−	0.818476i	$-0.305181\pi$
$643$	−156.851	−	156.851i	−0.243936	−	0.243936i	−0.818476	+	0.574540i	$0.805181\pi$
$644$	3900.89	−	1045.24i	6.05728	−	1.62304i
$645$		0			0
$646$	105.667	+	394.354i	0.163571	+	0.610454i
$647$	141.760	−	529.056i	0.219104	−	0.817706i	−0.765578	−	0.643343i	$-0.777547\pi$
$647$	141.760	−	529.056i	0.219104	−	0.817706i	0.984682	−	0.174363i	$-0.0557865\pi$
$648$		0			0
$649$	−176.478	+	47.2872i	−0.271923	+	0.0728616i
$650$	1238.08	+	714.807i	1.90474	+	1.09970i
$651$		0			0
$652$	−288.608	+	288.608i	−0.442650	+	0.442650i
$653$	71.5920	−	267.185i	0.109636	−	0.409166i	−0.889194	−	0.457530i	$-0.848734\pi$
$653$	71.5920	−	267.185i	0.109636	−	0.409166i	0.998830	+	0.0483644i	$0.0154009\pi$
$654$		0			0
$655$	54.0839			0.0825708
$656$		−	2230.10i		−	3.39955i
$657$		0			0
$658$	−1731.83	−	1731.83i	−2.63196	−	2.63196i
$659$	690.229	−	398.504i	1.04739	−	0.604710i	0.125471	−	0.992097i	$-0.459956\pi$
$659$	690.229	−	398.504i	1.04739	−	0.604710i	0.921917	+	0.387388i	$0.126622\pi$
$660$		0			0
$661$	20.0923	−	74.9855i	0.0303968	−	0.113443i	−0.949061	−	0.315094i	$-0.897964\pi$
$661$	20.0923	−	74.9855i	0.0303968	−	0.113443i	0.979457	+	0.201651i	$0.0646307\pi$
$662$	−468.423	−	811.332i	−0.707587	−	1.22558i
$663$		0			0
$664$	−197.674	−	737.729i	−0.297702	−	1.11104i
$665$		−	533.708i		−	0.802569i
$666$		0			0
$667$	−627.558			−0.940867
$668$	−1103.86	+	295.778i	−1.65248	+	0.442781i
$669$		0			0
$670$	430.870	−	248.763i	0.643089	−	0.371288i
$671$	−40.0238	−	10.7244i	−0.0596480	−	0.0159826i
$672$		0			0
$673$	−219.713	−	380.554i	−0.326468	−	0.565459i	0.655341	−	0.755333i	$-0.272525\pi$
$673$	−219.713	−	380.554i	−0.326468	−	0.565459i	−0.981808	+	0.189875i	$0.939192\pi$
$674$	−1212.18	+	1212.18i	−1.79849	+	1.79849i
$675$		0			0
$676$	1504.91			2.22620
$677$			926.895i			1.36912i	0.728956	+	0.684561i	$0.240006\pi$
$677$			926.895i			1.36912i	−0.728956	+	0.684561i	$0.759994\pi$
$678$		0			0
$679$	−865.967	−	232.035i	−1.27536	−	0.341731i
$680$	−127.067	−	127.067i	−0.186863	−	0.186863i
$681$		0			0
$682$	−98.3651	+	170.373i	−0.144230	+	0.249814i
$683$	242.665	+	905.637i	0.355292	+	1.32597i	0.880116	+	0.474758i	$0.157465\pi$
$683$	242.665	+	905.637i	0.355292	+	1.32597i	−0.524824	+	0.851211i	$0.675869\pi$
$684$		0			0
$685$	239.853	+	64.2683i	0.350150	+	0.0938223i
$686$	−2668.94	+	715.139i	−3.89058	+	1.04248i
$687$		0			0
$688$	275.175	+	1026.97i	0.399964	+	1.49269i
$689$	11.3563	−	11.3563i	0.0164823	−	0.0164823i
$690$		0			0
$691$	−813.533	−	469.693i	−1.17733	−	0.679730i	−0.221932	−	0.975062i	$-0.571236\pi$
$691$	−813.533	−	469.693i	−1.17733	−	0.679730i	−0.955395	+	0.295332i	$0.904570\pi$
$692$	1917.15			2.77044
$693$		0			0
$694$	−803.992	−	464.185i	−1.15849	−	0.668855i
$695$	79.8406	+	79.8406i	0.114879	+	0.114879i
$696$		0			0
$697$	−223.356	−	223.356i	−0.320453	−	0.320453i
$698$	−279.181	+	1041.92i	−0.399973	+	1.49272i
$699$		0			0
$700$	−1270.50	−	2200.57i	−1.81500	−	3.14367i
$701$	−219.486	−	819.131i	−0.313104	−	1.16852i	−0.925742	−	0.378155i	$-0.876559\pi$
$701$	−219.486	−	819.131i	−0.313104	−	1.16852i	0.612639	−	0.790363i	$-0.290108\pi$
$702$		0			0
$703$	46.3935	+	842.063i	0.0659935	+	1.19781i
$704$	101.423			0.144066
$705$		0			0
$706$	1443.52	−	833.416i	2.04464	−	1.18048i
$707$	1744.52	−	1007.20i	2.46750	−	1.42461i
$708$		0			0
$709$	−268.055	+	268.055i	−0.378074	+	0.378074i	−0.870407	−	0.492333i	$-0.836144\pi$
$709$	−268.055	+	268.055i	−0.378074	+	0.378074i	0.492333	+	0.870407i	$0.336144\pi$
$710$	344.071	+	595.948i	0.484607	+	0.839364i
$711$		0			0
$712$	−1308.31	+	2266.06i	−1.83752	+	3.18267i
$713$	653.034			0.915897
$714$		0			0
$715$	47.6153	−	82.4722i	0.0665949	−	0.115346i
$716$	−1925.28	−	515.876i	−2.68893	−	0.720497i
$717$		0			0
$718$	−694.582	+	186.113i	−0.967384	+	0.259210i
$719$	34.8926	−	60.4358i	0.0485294	−	0.0840553i	−0.840740	−	0.541439i	$-0.817880\pi$
$719$	34.8926	−	60.4358i	0.0485294	−	0.0840553i	0.889270	+	0.457383i	$0.151213\pi$
$720$		0			0
$721$	−270.040	+	1007.80i	−0.374535	+	1.39778i
$722$	560.227	+	150.112i	0.775938	+	0.207912i
$723$		0			0
$724$	1024.68	+	591.598i	1.41530	+	0.817124i
$725$	102.196	+	381.402i	0.140960	+	0.526072i
$726$		0			0
$727$	119.307	−	445.261i	0.164109	−	0.612464i	−0.834043	−	0.551699i	$-0.813980\pi$
$727$	119.307	−	445.261i	0.164109	−	0.612464i	0.998152	−	0.0607643i	$-0.0193538\pi$
$728$	−3894.24	−	2248.34i	−5.34923	−	3.08838i
$729$		0			0
$730$			656.735i			0.899637i
$731$	130.416	+	75.2957i	0.178408	+	0.103004i
$732$		0			0
$733$	−134.539	+	77.6759i	−0.183545	+	0.105970i	−0.588957	−	0.808164i	$-0.700461\pi$
$733$	−134.539	+	77.6759i	−0.183545	+	0.105970i	0.405412	+	0.914134i	$0.367128\pi$
$734$	−184.863	−	184.863i	−0.251857	−	0.251857i
$735$		0			0
$736$	−814.874	−	1411.40i	−1.10717	−	1.91767i
$737$	102.861	+	178.160i	0.139567	+	0.241737i
$738$		0			0
$739$			415.316i			0.561997i	0.959708	+	0.280999i	$0.0906657\pi$
$739$			415.316i			0.561997i	−0.959708	+	0.280999i	$0.909334\pi$
$740$	−353.747	−	541.540i	−0.478036	−	0.731811i
$741$		0			0
$742$	−39.3225	+	10.5364i	−0.0529953	+	0.0142000i
$743$	896.762	−	517.746i	1.20695	−	0.696831i	0.244856	−	0.969559i	$-0.421259\pi$
$743$	896.762	−	517.746i	1.20695	−	0.696831i	0.962091	+	0.272728i	$0.0879260\pi$
$744$		0			0
$745$	−278.188	−	74.5403i	−0.373407	−	0.100054i
$746$	−517.557	+	517.557i	−0.693776	+	0.693776i
$747$		0			0
$748$	91.5558	−	91.5558i	0.122401	−	0.122401i
$749$	321.312	−	556.528i	0.428988	−	0.743028i
$750$		0			0
$751$			768.600i			1.02344i	0.859154	+	0.511718i	$0.170991\pi$
$751$			768.600i			1.02344i	−0.859154	+	0.511718i	$0.829009\pi$
$752$	−920.131	+	1593.71i	−1.22358	+	2.11930i
$753$		0			0
$754$	860.997	+	860.997i	1.14191	+	1.14191i
$755$	90.1905	−	24.1665i	0.119458	−	0.0320086i
$756$		0			0
$757$	−275.375	−	1027.71i	−0.363771	−	1.35761i	−0.869079	−	0.494674i	$-0.835288\pi$
$757$	−275.375	−	1027.71i	−0.363771	−	1.35761i	0.505307	−	0.862939i	$-0.331379\pi$
$758$	−428.458	+	1599.03i	−0.565248	+	2.10953i
$759$		0			0
$760$	−808.141	+	216.541i	−1.06334	+	0.284922i
$761$	−779.030	−	449.773i	−1.02369	−	0.591029i	−0.108521	−	0.994094i	$-0.534611\pi$
$761$	−779.030	−	449.773i	−1.02369	−	0.591029i	−0.915171	+	0.403065i	$0.867945\pi$
$762$		0			0
$763$	−331.879	+	331.879i	−0.434966	+	0.434966i
$764$	11.2667	−	42.0480i	0.0147470	−	0.0550367i
$765$		0			0
$766$	−1186.08			−1.54841
$767$		−	1176.73i		−	1.53419i
$768$		0			0
$769$	141.603	+	141.603i	0.184139	+	0.184139i	0.793157	−	0.609017i	$-0.208436\pi$
$769$	141.603	+	141.603i	0.184139	+	0.184139i	−0.609017	+	0.793157i	$0.708436\pi$
$770$	−209.052	+	120.696i	−0.271496	+	0.156748i
$771$		0			0
$772$	533.583	−	1991.36i	0.691170	−	2.57948i
$773$	336.923	+	583.569i	0.435865	+	0.754940i	0.997366	−	0.0725361i	$-0.0231093\pi$
$773$	336.923	+	583.569i	0.435865	+	0.754940i	−0.561501	+	0.827476i	$0.689776\pi$
$774$		0			0
$775$	−106.345	−	396.885i	−0.137219	−	0.512110i
$776$			1405.39i			1.81107i
$777$		0			0
$778$	−404.066			−0.519365
$779$	−1420.54	+	380.632i	−1.82354	+	0.488616i
$780$		0			0
$781$	−246.419	+	142.270i	−0.315517	+	0.182164i
$782$	−592.066	−	158.644i	−0.757118	−	0.202869i
$783$		0			0
$784$	1884.87	+	3264.69i	2.40417	+	4.16414i
$785$	−297.329	+	297.329i	−0.378763	+	0.378763i
$786$		0			0
$787$	638.668			0.811523			0.405761	−	0.913979i	$-0.367006\pi$
$787$	638.668			0.811523			0.405761	+	0.913979i	$0.367006\pi$
$788$			2280.89i			2.89453i
$789$		0			0
$790$	284.427	+	76.2119i	0.360034	+	0.0964708i
$791$	1268.99	+	1268.99i	1.60429	+	1.60429i
$792$		0			0
$793$	133.436	−	231.118i	0.168267	−	0.291447i
$794$	−580.608	−	2166.86i	−0.731245	−	2.72904i
$795$		0			0
$796$	−1799.24	−	482.105i	−2.26035	−	0.605660i
$797$	1171.72	−	313.962i	1.47017	−	0.393930i	0.567178	−	0.823595i	$-0.308035\pi$
$797$	1171.72	−	313.962i	1.47017	−	0.393930i	0.902988	+	0.429665i	$0.141368\pi$
$798$		0			0
$799$	67.4626	+	251.774i	0.0844338	+	0.315111i
$800$	−725.088	+	725.088i	−0.906359	+	0.906359i
$801$		0			0
$802$	957.651	+	552.900i	1.19408	+	0.689401i
$803$	−271.553			−0.338173
$804$		0			0
$805$	693.935	+	400.644i	0.862031	+	0.497694i
$806$	−895.950	−	895.950i	−1.11160	−	1.11160i
$807$		0			0
$808$	−2232.90	−	2232.90i	−2.76349	−	2.76349i
$809$	−189.670	+	707.856i	−0.234449	+	0.874977i	0.743947	+	0.668239i	$0.232952\pi$
$809$	−189.670	+	707.856i	−0.234449	+	0.874977i	−0.978396	+	0.206738i	$0.933715\pi$
$810$		0			0
$811$	−107.767	−	186.658i	−0.132882	−	0.230158i	0.791904	−	0.610645i	$-0.209090\pi$
$811$	−107.767	−	186.658i	−0.132882	−	0.230158i	−0.924786	+	0.380487i	$0.875756\pi$
$812$	−560.143	−	2090.48i	−0.689831	−	2.57448i
$813$		0			0
$814$	319.342	−	208.602i	0.392312	−	0.256267i
$815$	−80.9827			−0.0993653
$816$		0			0
$817$	607.195	−	350.564i	0.743201	−	0.429087i
$818$	−1620.77	+	935.751i	−1.98138	+	1.14395i
$819$		0			0
$820$	797.606	−	797.606i	0.972690	−	0.972690i
$821$	201.722	+	349.393i	0.245703	+	0.425570i	0.962329	−	0.271888i	$-0.0876479\pi$
$821$	201.722	+	349.393i	0.245703	+	0.425570i	−0.716626	+	0.697458i	$0.754315\pi$
$822$		0			0
$823$	616.064	−	1067.05i	0.748559	−	1.29654i	−0.199954	−	0.979805i	$-0.564079\pi$
$823$	616.064	−	1067.05i	0.748559	−	1.29654i	0.948513	−	0.316738i	$-0.102587\pi$
$824$	1635.58			1.98492
$825$		0			0
$826$	−1491.39	+	2583.16i	−1.80556	+	3.12732i
$827$	186.617	+	50.0040i	0.225656	+	0.0604643i	0.369875	−	0.929081i	$-0.379400\pi$
$827$	186.617	+	50.0040i	0.225656	+	0.0604643i	−0.144219	+	0.989546i	$0.546067\pi$
$828$		0			0
$829$	1138.29	−	305.005i	1.37309	−	0.367919i	0.504485	−	0.863421i	$-0.331683\pi$
$829$	1138.29	−	305.005i	1.37309	−	0.367919i	0.868607	+	0.495502i	$0.165016\pi$
$830$	132.033	−	228.688i	0.159076	−	0.275527i
$831$		0			0
$832$	−169.067	+	630.967i	−0.203206	+	0.758374i
$833$	515.753	+	138.196i	0.619151	+	0.165901i
$834$		0			0
$835$	−196.367	−	113.373i	−0.235170	−	0.135776i
$836$	−156.025	−	582.293i	−0.186633	−	0.696523i
$837$		0			0
$838$	258.665	−	965.352i	0.308670	−	1.15197i
$839$	−533.588	−	308.067i	−0.635980	−	0.367184i	0.147084	−	0.989124i	$-0.453011\pi$
$839$	−533.588	−	308.067i	−0.635980	−	0.367184i	−0.783065	+	0.621941i	$0.786345\pi$
$840$		0			0
$841$		−	504.692i		−	0.600110i
$842$	−2272.23	−	1311.87i	−2.69861	−	1.55804i
$843$		0			0
$844$	1375.51	−	794.149i	1.62975	−	0.940935i
$845$	211.137	+	211.137i	0.249866	+	0.249866i
$846$		0			0
$847$	710.728	+	1231.02i	0.839112	+	1.45339i
$848$	15.2942	+	26.4903i	0.0180356	+	0.0312386i
$849$		0			0
$850$			385.666i			0.453725i
$851$	−1129.69	−	571.798i	−1.32748	−	0.671913i
$852$		0			0
$853$	115.719	−	31.0068i	0.135661	−	0.0363503i	−0.190349	−	0.981716i	$-0.560962\pi$
$853$	115.719	−	31.0068i	0.135661	−	0.0363503i	0.326011	+	0.945366i	$0.394295\pi$
$854$	−585.841	+	338.235i	−0.685996	+	0.396060i
$855$		0			0
$856$	−973.060	−	260.731i	−1.13675	−	0.304592i
$857$	467.730	−	467.730i	0.545776	−	0.545776i	−0.379440	−	0.925216i	$-0.623883\pi$
$857$	467.730	−	467.730i	0.545776	−	0.545776i	0.925216	+	0.379440i	$0.123883\pi$
$858$		0			0
$859$	−694.804	+	694.804i	−0.808853	+	0.808853i	−0.984460	−	0.175608i	$-0.943811\pi$
$859$	−694.804	+	694.804i	−0.808853	+	0.808853i	0.175608	+	0.984460i	$0.443811\pi$
$860$	−268.882	+	465.717i	−0.312653	+	0.541532i
$861$		0			0
$862$			376.164i			0.436385i
$863$	−565.724	+	979.863i	−0.655532	+	1.13541i	0.326228	+	0.945291i	$0.394222\pi$
$863$	−565.724	+	979.863i	−0.655532	+	1.13541i	−0.981760	+	0.190124i	$0.939111\pi$
$864$		0			0
$865$	268.973	+	268.973i	0.310952	+	0.310952i
$866$	493.184	−	132.148i	0.569496	−	0.152596i
$867$		0			0
$868$	582.882	+	2175.35i	0.671523	+	2.50616i
$869$	−31.5128	+	117.607i	−0.0362633	+	0.135337i
$870$		0			0
$871$	−1279.83	+	342.929i	−1.46938	+	0.393719i
$872$	637.184	+	367.879i	0.730716	+	0.421879i
$873$		0			0
$874$	−2017.94	+	2017.94i	−2.30886	+	2.30886i
$875$	281.997	−	1052.43i	0.322282	−	1.20277i
$876$		0			0
$877$	−257.605			−0.293734			−0.146867	−	0.989156i	$-0.546919\pi$
$877$	−257.605			−0.293734			−0.146867	+	0.989156i	$0.546919\pi$
$878$			1316.43i			1.49935i
$879$		0			0
$880$	128.253	+	128.253i	0.145742	+	0.145742i
$881$	1264.34	−	729.968i	1.43512	−	0.828567i	0.437615	−	0.899162i	$-0.355823\pi$
$881$	1264.34	−	729.968i	1.43512	−	0.828567i	0.997505	+	0.0705951i	$0.0224898\pi$
$882$		0			0
$883$	382.536	−	1427.64i	0.433223	−	1.61681i	−0.312059	−	0.950063i	$-0.601019\pi$
$883$	382.536	−	1427.64i	0.433223	−	1.61681i	0.745282	−	0.666749i	$-0.232315\pi$
$884$	416.964	+	722.203i	0.471679	+	0.816972i
$885$		0			0
$886$	−555.301	−	2072.41i	−0.626750	−	2.33906i
$887$		−	1119.69i		−	1.26234i	−0.775645	−	0.631169i	$-0.782575\pi$
$887$		−	1119.69i		−	1.26234i	0.775645	−	0.631169i	$-0.217425\pi$
$888$		0			0
$889$	456.739			0.513767
$890$	−873.863	+	234.151i	−0.981869	+	0.263091i
$891$		0			0
$892$	−2034.70	+	1174.73i	−2.28105	+	1.31697i
$893$	1172.22	+	314.094i	1.31267	+	0.351729i
$894$		0			0
$895$	−197.737	−	342.490i	−0.220935	−	0.382671i
$896$	−522.728	+	522.728i	−0.583402	+	0.583402i
$897$		0			0
$898$	2186.93			2.43533
$899$		−	349.960i		−	0.389278i
$900$		0			0
$901$	4.18492	+	1.12135i	0.00464475	+	0.00124456i
$902$	470.342	+	470.342i	0.521443	+	0.521443i
$903$		0			0
$904$	1406.64	−	2436.37i	1.55602	−	2.69510i
$905$	60.7605	+	226.761i	0.0671387	+	0.250565i
$906$		0			0
$907$	30.7442	+	8.23789i	0.0338966	+	0.00908256i	0.275727	−	0.961236i	$-0.411081\pi$
$907$	30.7442	+	8.23789i	0.0338966	+	0.00908256i	−0.241831	+	0.970318i	$0.577748\pi$
$908$	72.9304	−	19.5416i	0.0803199	−	0.0215216i
$909$		0			0
$910$	−402.390	−	1501.74i	−0.442187	−	1.65026i
$911$	−12.1318	+	12.1318i	−0.0133170	+	0.0133170i	−0.713734	−	0.700417i	$-0.752997\pi$
$911$	−12.1318	+	12.1318i	−0.0133170	+	0.0133170i	0.700417	+	0.713734i	$0.252997\pi$
$912$		0			0
$913$	94.5600	+	54.5942i	0.103571	+	0.0597965i
$914$	−290.395			−0.317718
$915$		0			0
$916$	−824.164	−	475.831i	−0.899742	−	0.519466i
$917$	258.162	+	258.162i	0.281528	+	0.281528i
$918$		0			0
$919$	380.156	+	380.156i	0.413662	+	0.413662i	0.883012	−	0.469350i	$-0.155512\pi$
$919$	380.156	+	380.156i	0.413662	+	0.413662i	−0.469350	+	0.883012i	$0.655512\pi$
$920$	325.105	−	1213.31i	0.353375	−	1.31881i
$921$		0			0
$922$	921.584	+	1596.23i	0.999549	+	1.73127i
$923$	−474.315	−	1770.17i	−0.513884	−	1.91784i
$924$		0			0
$925$	−163.546	+	779.691i	−0.176807	+	0.842909i
$926$	1870.02			2.01946
$927$		0			0
$928$	−756.369	+	436.690i	−0.815053	+	0.470571i
$929$	981.441	−	566.635i	1.05645	−	0.609941i	0.132001	−	0.991250i	$-0.457860\pi$
$929$	981.441	−	566.635i	1.05645	−	0.609941i	0.924448	+	0.381309i	$0.124526\pi$
$930$		0			0
$931$	1757.84	−	1757.84i	1.88812	−	1.88812i
$932$	1415.51	+	2451.74i	1.51879	+	2.63062i
$933$		0			0
$934$	332.835	−	576.487i	0.356354	−	0.617224i
$935$	25.6903			0.0274763
$936$		0			0
$937$	−622.705	+	1078.56i	−0.664573	+	1.15107i	0.314828	+	0.949149i	$0.398053\pi$
$937$	−622.705	+	1078.56i	−0.664573	+	1.15107i	−0.979401	+	0.201925i	$0.935280\pi$
$938$	3244.13	+	869.262i	3.45856	+	0.926718i
$939$		0			0
$940$	−899.087	+	240.910i	−0.956476	+	0.256287i
$941$	226.685	−	392.631i	0.240898	−	0.417248i	−0.720072	−	0.693899i	$-0.755891\pi$
$941$	226.685	−	392.631i	0.240898	−	0.417248i	0.960970	+	0.276651i	$0.0892246\pi$
$942$		0			0
$943$	571.465	−	2132.74i	0.606007	−	2.26165i
$944$	2164.83	+	580.065i	2.29326	+	0.614476i
$945$		0			0
$946$	−274.630	−	158.557i	−0.290306	−	0.167608i
$947$	−228.573	−	853.048i	−0.241366	−	0.900790i	−0.975175	−	0.221434i	$-0.928926\pi$
$947$	−228.573	−	853.048i	−0.241366	−	0.900790i	0.733809	−	0.679355i	$-0.237740\pi$
$948$		0			0
$949$	452.667	−	1689.38i	0.476994	−	1.78017i
$950$	1555.03	+	897.798i	1.63688	+	0.945051i
$951$		0			0
$952$		−	1213.07i		−	1.27423i
$953$	−541.459	−	312.611i	−0.568162	−	0.328029i	0.188253	−	0.982121i	$-0.439718\pi$
$953$	−541.459	−	312.611i	−0.568162	−	0.328029i	−0.756415	+	0.654092i	$0.773051\pi$
$954$		0			0
$955$	7.47999	−	4.31858i	0.00783245	−	0.00452207i
$956$	−1844.76	−	1844.76i	−1.92967	−	1.92967i
$957$		0			0
$958$	333.940	+	578.402i	0.348581	+	0.603760i
$959$	838.126	+	1451.68i	0.873958	+	1.51374i
$960$		0			0
$961$		−	596.833i		−	0.621054i
$962$	765.416	+	2334.41i	0.795651	+	2.42662i
$963$		0			0
$964$	34.4977	−	9.24364i	0.0357860	−	0.00958884i
$965$	354.246	−	204.524i	0.367095	−	0.211942i
$966$		0			0
$967$	368.331	+	98.6941i	0.380901	+	0.102062i	0.444189	−	0.895933i	$-0.353492\pi$
$967$	368.331	+	98.6941i	0.380901	+	0.102062i	−0.0632878	+	0.997995i	$0.520159\pi$
$968$	1575.64	−	1575.64i	1.62773	−	1.62773i
$969$		0			0
$970$	−343.590	+	343.590i	−0.354217	+	0.354217i
$971$	158.128	−	273.885i	0.162850	−	0.282065i	−0.773039	−	0.634358i	$-0.781265\pi$
$971$	158.128	−	273.885i	0.162850	−	0.282065i	0.935890	+	0.352293i	$0.114598\pi$
$972$		0			0
$973$			762.215i			0.783366i
$974$	1595.15	−	2762.87i	1.63773	−	2.83663i
$975$		0			0
$976$	359.412	+	359.412i	0.368250	+	0.368250i
$977$	−1695.48	+	454.303i	−1.73539	+	0.464998i	−0.981415	−	0.191899i	$-0.938535\pi$
$977$	−1695.48	+	454.303i	−1.73539	+	0.464998i	−0.753980	+	0.656897i	$0.771869\pi$
$978$		0			0
$979$	−96.8190	−	361.333i	−0.0988958	−	0.369084i
$980$	−493.498	+	1841.76i	−0.503569	+	1.87935i
$981$		0			0
$982$	804.985	−	215.695i	0.819741	−	0.219649i
$983$	949.401	+	548.137i	0.965820	+	0.557616i	0.897959	−	0.440078i	$-0.145049\pi$
$983$	949.401	+	548.137i	0.965820	+	0.557616i	0.0678605	+	0.997695i	$0.478383\pi$
$984$		0			0
$985$	−320.005	+	320.005i	−0.324879	+	0.324879i
$986$	−85.0170	+	317.288i	−0.0862241	+	0.321793i
$987$		0			0
$988$	3882.63			3.92978
$989$			1052.64i			1.06435i
$990$		0			0
$991$	628.249	+	628.249i	0.633955	+	0.633955i	0.949058	−	0.315103i	$-0.102039\pi$
$991$	628.249	+	628.249i	0.633955	+	0.633955i	−0.315103	+	0.949058i	$0.602039\pi$
$992$	787.075	−	454.418i	0.793422	−	0.458082i
$993$		0			0
$994$	−1202.30	+	4487.05i	−1.20956	+	4.51413i
$995$	−184.793	−	320.070i	−0.185721	−	0.321679i
$996$		0			0
$997$	−40.5198	−	151.222i	−0.0406417	−	0.151677i	0.942623	−	0.333859i	$-0.108351\pi$
$997$	−40.5198	−	151.222i	−0.0406417	−	0.151677i	−0.983265	+	0.182182i	$0.941684\pi$
$998$			1970.46i			1.97441i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.3.bb.c.199.6		24
3.2	odd	2		111.3.l.a.88.1	yes	24
37.8	odd	12	inner	333.3.bb.c.82.6		24
111.8	even	12		111.3.l.a.82.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.3.l.a.82.1	✓	24	111.8	even	12
111.3.l.a.88.1	yes	24	3.2	odd	2
333.3.bb.c.82.6		24	37.8	odd	12	inner
333.3.bb.c.199.6		24	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(3.53411 - 0.946963i) q^{2} +(8.12913 - 4.69335i) q^{4} +(1.79898 + 0.482035i) q^{5} +(6.28624 + 10.8881i) q^{7} +(13.9362 - 13.9362i) q^{8} +O(q^{10})\)	\(q+(3.53411 - 0.946963i) q^{2} +(8.12913 - 4.69335i) q^{4} +(1.79898 + 0.482035i) q^{5} +(6.28624 + 10.8881i) q^{7} +(13.9362 - 13.9362i) q^{8} +6.81426 q^{10} +2.81763i q^{11} +(-17.5289 - 4.69686i) q^{13} +(32.5269 + 32.5269i) q^{14} +(17.2817 - 29.9328i) q^{16} +(-1.26707 - 4.72877i) q^{17} +(-22.0163 - 5.89926i) q^{19} +(16.8865 - 4.52472i) q^{20} +(2.66819 + 9.95782i) q^{22} +(24.1975 - 24.1975i) q^{23} +(-18.6467 - 10.7657i) q^{25} -66.3970 q^{26} +(102.203 + 59.0071i) q^{28} +(-12.9674 - 12.9674i) q^{29} +(13.4938 + 13.4938i) q^{31} +(12.3262 - 46.0022i) q^{32} +(-8.95594 - 15.5121i) q^{34} +(6.06037 + 22.6176i) q^{35} +(-11.5279 - 35.1583i) q^{37} -83.3946 q^{38} +(31.7887 - 18.3532i) q^{40} +(55.8777 - 32.2610i) q^{41} +(-21.7511 + 21.7511i) q^{43} +(13.2241 + 22.9048i) q^{44} +(62.6026 - 108.431i) q^{46} -53.2430 q^{47} +(-54.5336 + 94.4549i) q^{49} +(-76.0942 - 20.3894i) q^{50} +(-164.539 + 44.0880i) q^{52} +(-0.442496 + 0.766426i) q^{53} +(-1.35819 + 5.06885i) q^{55} +(239.345 + 64.1324i) q^{56} +(-58.1080 - 33.5487i) q^{58} +(16.7826 + 62.6336i) q^{59} +(-3.80616 + 14.2048i) q^{61} +(60.4669 + 34.9106i) q^{62} -35.9958i q^{64} +(-29.2701 - 16.8991i) q^{65} +(63.2306 - 36.5062i) q^{67} +(-32.4939 - 32.4939i) q^{68} +(42.8361 + 74.1943i) q^{70} +(50.4928 + 87.4560i) q^{71} +96.3766i q^{73} +(-74.0345 - 113.337i) q^{74} +(-206.661 + 55.3746i) q^{76} +(-30.6786 + 17.7123i) q^{77} +(41.7399 + 11.1842i) q^{79} +(45.5181 - 45.5181i) q^{80} +(166.928 - 166.928i) q^{82} +(19.3760 - 33.5601i) q^{83} -9.11772i q^{85} +(-56.2734 + 97.4684i) q^{86} +(39.2671 + 39.2671i) q^{88} +(-128.240 + 34.3619i) q^{89} +(-59.0511 - 220.382i) q^{91} +(83.1371 - 310.272i) q^{92} +(-188.167 + 50.4192i) q^{94} +(-36.7632 - 21.2253i) q^{95} +(-50.4222 + 50.4222i) q^{97} +(-103.283 + 385.456i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8}+O(q^{10}) \) 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8	\( 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8} + 36 q^{10} + 4 q^{13} + 6 q^{14} + 26 q^{16} - 46 q^{17} - 156 q^{19} - 68 q^{20} + 32 q^{22} - 10 q^{23} - 90 q^{25} + 164 q^{26} - 48 q^{28} + 28 q^{29} + 120 q^{31} - 90 q^{32} + 46 q^{34} + 186 q^{35} + 56 q^{37} - 4 q^{38} + 216 q^{40} + 30 q^{41} + 250 q^{43} - 284 q^{44} - 18 q^{46} - 232 q^{47} - 164 q^{49} - 226 q^{50} - 488 q^{52} - 122 q^{53} - 250 q^{55} + 632 q^{56} - 360 q^{58} + 258 q^{59} + 108 q^{61} + 186 q^{62} - 162 q^{65} + 60 q^{67} - 214 q^{68} + 246 q^{70} - 174 q^{71} + 8 q^{74} - 498 q^{76} - 666 q^{77} - 104 q^{79} + 24 q^{80} + 1114 q^{82} + 26 q^{83} + 72 q^{86} - 334 q^{88} - 16 q^{89} + 20 q^{91} + 918 q^{92} + 400 q^{94} + 372 q^{95} - 278 q^{97} - 950 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8 + 36 * q^10 + 4 * q^13 + 6 * q^14 + 26 * q^16 - 46 * q^17 - 156 * q^19 - 68 * q^20 + 32 * q^22 - 10 * q^23 - 90 * q^25 + 164 * q^26 - 48 * q^28 + 28 * q^29 + 120 * q^31 - 90 * q^32 + 46 * q^34 + 186 * q^35 + 56 * q^37 - 4 * q^38 + 216 * q^40 + 30 * q^41 + 250 * q^43 - 284 * q^44 - 18 * q^46 - 232 * q^47 - 164 * q^49 - 226 * q^50 - 488 * q^52 - 122 * q^53 - 250 * q^55 + 632 * q^56 - 360 * q^58 + 258 * q^59 + 108 * q^61 + 186 * q^62 - 162 * q^65 + 60 * q^67 - 214 * q^68 + 246 * q^70 - 174 * q^71 + 8 * q^74 - 498 * q^76 - 666 * q^77 - 104 * q^79 + 24 * q^80 + 1114 * q^82 + 26 * q^83 + 72 * q^86 - 334 * q^88 - 16 * q^89 + 20 * q^91 + 918 * q^92 + 400 * q^94 + 372 * q^95 - 278 * q^97 - 950 * q^98

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