LMFDB - Embedded newform 333.3.bb.b.208.5

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			208.5
Character	$\chi$	$=$	333.208
Dual form			333.3.bb.b.325.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.682073 + 2.54553i) q^{2} +(-2.55040 + 1.47247i) q^{4} +(-2.05541 + 7.67090i) q^{5} +(4.48853 + 7.77437i) q^{7} +(1.96605 + 1.96605i) q^{8} +O(q^{10})$	\(q+(0.682073 + 2.54553i) q^{2} +(-2.55040 + 1.47247i) q^{4} +(-2.05541 + 7.67090i) q^{5} +(4.48853 + 7.77437i) q^{7} +(1.96605 + 1.96605i) q^{8} -20.9284 q^{10} -5.76392i q^{11} +(2.66434 - 9.94345i) q^{13} +(-16.7284 + 16.7284i) q^{14} +(-9.55354 + 16.5472i) q^{16} +(20.8215 - 5.57911i) q^{17} +(-2.53465 + 9.45945i) q^{19} +(-6.05308 - 22.5904i) q^{20} +(14.6722 - 3.93141i) q^{22} +(-25.8908 - 25.8908i) q^{23} +(-32.9673 - 19.0337i) q^{25} +27.1286 q^{26} +(-22.8951 - 13.2185i) q^{28} +(-31.4656 + 31.4656i) q^{29} +(2.82708 - 2.82708i) q^{31} +(-37.8950 - 10.1539i) q^{32} +(28.4036 + 49.1964i) q^{34} +(-68.8622 + 18.4516i) q^{35} +(29.1654 - 22.7680i) q^{37} -25.8081 q^{38} +(-19.1224 + 11.0403i) q^{40} +(-31.0148 + 17.9064i) q^{41} +(27.8194 + 27.8194i) q^{43} +(8.48722 + 14.7003i) q^{44} +(48.2465 - 83.5653i) q^{46} +29.5585 q^{47} +(-15.7939 + 27.3558i) q^{49} +(25.9647 - 96.9017i) q^{50} +(7.84634 + 29.2830i) q^{52} +(40.6436 - 70.3968i) q^{53} +(44.2144 + 11.8472i) q^{55} +(-6.46010 + 24.1094i) q^{56} +(-101.559 - 58.6348i) q^{58} +(85.7984 - 22.9896i) q^{59} +(33.7241 + 9.03634i) q^{61} +(9.12470 + 5.26815i) q^{62} -26.9602i q^{64} +(70.7989 + 40.8758i) q^{65} +(15.9499 - 9.20869i) q^{67} +(-44.8881 + 44.8881i) q^{68} +(-93.9380 - 162.705i) q^{70} +(32.1250 + 55.6421i) q^{71} +106.296i q^{73} +(77.8494 + 58.7120i) q^{74} +(-7.46442 - 27.8576i) q^{76} +(44.8108 - 25.8715i) q^{77} +(16.8272 - 62.8001i) q^{79} +(-107.296 - 107.296i) q^{80} +(-66.7357 - 66.7357i) q^{82} +(-5.05258 + 8.75133i) q^{83} +171.187i q^{85} +(-51.8403 + 89.7901i) q^{86} +(11.3321 - 11.3321i) q^{88} +(-8.52539 - 31.8172i) q^{89} +(89.2631 - 23.9180i) q^{91} +(104.156 + 27.9084i) q^{92} +(20.1611 + 75.2421i) q^{94} +(-67.3527 - 38.8861i) q^{95} +(-98.6688 - 98.6688i) q^{97} +(-80.4075 - 21.5451i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.682073	+	2.54553i	0.341036	+	1.27277i	0.897175	+	0.441675i	$0.145616\pi$
$2$	0.682073	+	2.54553i	0.341036	+	1.27277i	−0.556138	+	0.831090i	$0.687718\pi$
$3$		0			0
$3$		0			0
$4$	−2.55040	+	1.47247i	−0.637600	+	0.368118i
$5$	−2.05541	+	7.67090i	−0.411082	+	1.53418i	0.381473	+	0.924380i	$0.375417\pi$
$5$	−2.05541	+	7.67090i	−0.411082	+	1.53418i	−0.792555	+	0.609800i	$0.791250\pi$
$6$		0			0
$7$	4.48853	+	7.77437i	0.641219	+	1.11062i	0.985161	+	0.171633i	$0.0549043\pi$
$7$	4.48853	+	7.77437i	0.641219	+	1.11062i	−0.343942	+	0.938991i	$0.611762\pi$
$8$	1.96605	+	1.96605i	0.245756	+	0.245756i
$9$		0			0
$10$	−20.9284			−2.09284
$11$		−	5.76392i		−	0.523993i	−0.965069	−	0.261996i	$-0.915619\pi$
$11$		−	5.76392i		−	0.523993i	0.965069	−	0.261996i	$-0.0843808\pi$
$12$		0			0
$13$	2.66434	−	9.94345i	0.204949	−	0.764881i	−0.784516	−	0.620109i	$-0.787088\pi$
$13$	2.66434	−	9.94345i	0.204949	−	0.764881i	0.989465	−	0.144772i	$-0.0462449\pi$
$14$	−16.7284	+	16.7284i	−1.19488	+	1.19488i
$15$		0			0
$16$	−9.55354	+	16.5472i	−0.597096	+	1.03420i
$17$	20.8215	−	5.57911i	1.22479	−	0.328183i	0.412244	−	0.911073i	$-0.364745\pi$
$17$	20.8215	−	5.57911i	1.22479	−	0.328183i	0.812551	+	0.582891i	$0.198078\pi$
$18$		0			0
$19$	−2.53465	+	9.45945i	−0.133403	+	0.497866i	−0.999999	−	0.00114351i	$-0.999636\pi$
$19$	−2.53465	+	9.45945i	−0.133403	+	0.497866i	0.866597	+	0.499009i	$0.166303\pi$
$20$	−6.05308	−	22.5904i	−0.302654	−	1.12952i
$21$		0			0
$22$	14.6722	−	3.93141i	0.666920	−	0.178701i
$23$	−25.8908	−	25.8908i	−1.12569	−	1.12569i	−0.990870	−	0.134818i	$-0.956955\pi$
$23$	−25.8908	−	25.8908i	−1.12569	−	1.12569i	−0.134818	−	0.990870i	$-0.543045\pi$
$24$		0			0
$25$	−32.9673	−	19.0337i	−1.31869	−	0.761348i
$26$	27.1286			1.04341
$27$		0			0
$28$	−22.8951	−	13.2185i	−0.817682	−	0.472089i
$29$	−31.4656	+	31.4656i	−1.08502	+	1.08502i	−0.0889888	+	0.996033i	$0.528364\pi$
$29$	−31.4656	+	31.4656i	−1.08502	+	1.08502i	−0.996033	+	0.0889888i	$0.971636\pi$
$30$		0			0
$31$	2.82708	−	2.82708i	0.0911962	−	0.0911962i	−0.660037	−	0.751233i	$-0.729459\pi$
$31$	2.82708	−	2.82708i	0.0911962	−	0.0911962i	0.751233	+	0.660037i	$0.229459\pi$
$32$	−37.8950	−	10.1539i	−1.18422	−	0.317310i
$33$		0			0
$34$	28.4036	+	49.1964i	0.835399	+	1.44695i
$35$	−68.8622	+	18.4516i	−1.96749	+	0.527188i
$36$		0			0
$37$	29.1654	−	22.7680i	0.788254	−	0.615350i
$37$	29.1654	−	22.7680i	0.788254	−	0.615350i
$38$	−25.8081			−0.679161
$39$		0			0
$40$	−19.1224	+	11.0403i	−0.478059	+	0.276008i
$41$	−31.0148	+	17.9064i	−0.756459	+	0.436742i	−0.828023	−	0.560694i	$-0.810534\pi$
$41$	−31.0148	+	17.9064i	−0.756459	+	0.436742i	0.0715639	+	0.997436i	$0.477201\pi$
$42$		0			0
$43$	27.8194	+	27.8194i	0.646964	+	0.646964i	0.952258	−	0.305294i	$-0.0987549\pi$
$43$	27.8194	+	27.8194i	0.646964	+	0.646964i	−0.305294	+	0.952258i	$0.598755\pi$
$44$	8.48722	+	14.7003i	0.192891	+	0.334098i
$45$		0			0
$46$	48.2465	−	83.5653i	1.04884	−	1.81664i
$47$	29.5585			0.628905			0.314452	−	0.949273i	$-0.398179\pi$
$47$	29.5585			0.628905			0.314452	+	0.949273i	$0.398179\pi$
$48$		0			0
$49$	−15.7939	+	27.3558i	−0.322324	+	0.558281i
$50$	25.9647	−	96.9017i	0.519295	−	1.93803i
$51$		0			0
$52$	7.84634	+	29.2830i	0.150891	+	0.563134i
$53$	40.6436	−	70.3968i	0.766861	−	1.32824i	−0.172396	−	0.985028i	$-0.555151\pi$
$53$	40.6436	−	70.3968i	0.766861	−	1.32824i	0.939257	−	0.343214i	$-0.111516\pi$
$54$		0			0
$55$	44.2144	+	11.8472i	0.803899	+	0.215404i
$56$	−6.46010	+	24.1094i	−0.115359	+	0.430525i
$57$		0			0
$58$	−101.559	−	58.6348i	−1.75101	−	1.01095i
$59$	85.7984	−	22.9896i	1.45421	−	0.389655i	0.556725	−	0.830697i	$-0.312058\pi$
$59$	85.7984	−	22.9896i	1.45421	−	0.389655i	0.897486	+	0.441043i	$0.145391\pi$
$60$		0			0
$61$	33.7241	+	9.03634i	0.552854	+	0.148137i	0.524421	−	0.851459i	$-0.324282\pi$
$61$	33.7241	+	9.03634i	0.552854	+	0.148137i	0.0284327	+	0.999596i	$0.490948\pi$
$62$	9.12470	+	5.26815i	0.147173	+	0.0849701i
$63$		0			0
$64$		−	26.9602i		−	0.421253i
$65$	70.7989	+	40.8758i	1.08921	+	0.628858i
$66$		0			0
$67$	15.9499	−	9.20869i	0.238058	−	0.137443i	−0.376226	−	0.926528i	$-0.622778\pi$
$67$	15.9499	−	9.20869i	0.238058	−	0.137443i	0.614284	+	0.789085i	$0.289445\pi$
$68$	−44.8881	+	44.8881i	−0.660119	+	0.660119i
$69$		0			0
$70$	−93.9380	−	162.705i	−1.34197	−	2.32436i
$71$	32.1250	+	55.6421i	0.452465	+	0.783692i	0.998538	−	0.0540452i	$-0.0172115\pi$
$71$	32.1250	+	55.6421i	0.452465	+	0.783692i	−0.546074	+	0.837737i	$0.683878\pi$
$72$		0			0
$73$			106.296i			1.45611i	0.685517	+	0.728057i	$0.259576\pi$
$73$			106.296i			1.45611i	−0.685517	+	0.728057i	$0.740424\pi$
$74$	77.8494	+	58.7120i	1.05202	+	0.793405i
$75$		0			0
$76$	−7.46442	−	27.8576i	−0.0982160	−	0.366547i
$77$	44.8108	−	25.8715i	0.581959	−	0.335994i
$78$		0			0
$79$	16.8272	−	62.8001i	0.213003	−	0.794937i	−0.773857	−	0.633360i	$-0.781675\pi$
$79$	16.8272	−	62.8001i	0.213003	−	0.794937i	0.986860	−	0.161577i	$-0.0516581\pi$
$80$	−107.296	−	107.296i	−1.34119	−	1.34119i
$81$		0			0
$82$	−66.7357	−	66.7357i	−0.813850	−	0.813850i
$83$	−5.05258	+	8.75133i	−0.0608745	+	0.105438i	−0.894857	−	0.446354i	$-0.852722\pi$
$83$	−5.05258	+	8.75133i	−0.0608745	+	0.105438i	0.833982	+	0.551792i	$0.186056\pi$
$84$		0			0
$85$			171.187i			2.01397i
$86$	−51.8403	+	89.7901i	−0.602795	+	1.04407i
$87$		0			0
$88$	11.3321	−	11.3321i	0.128774	−	0.128774i
$89$	−8.52539	−	31.8172i	−0.0957909	−	0.357497i	0.901347	−	0.433097i	$-0.142579\pi$
$89$	−8.52539	−	31.8172i	−0.0957909	−	0.357497i	−0.997138	+	0.0756005i	$0.975913\pi$
$90$		0			0
$91$	89.2631	−	23.9180i	0.980913	−	0.262835i
$92$	104.156	+	27.9084i	1.13213	+	0.303352i
$93$		0			0
$94$	20.1611	+	75.2421i	0.214479	+	0.800448i
$95$	−67.3527	−	38.8861i	−0.708976	−	0.409328i
$96$		0			0
$97$	−98.6688	−	98.6688i	−1.01720	−	1.01720i	−0.999849	−	0.0173542i	$-0.994476\pi$
$97$	−98.6688	−	98.6688i	−1.01720	−	1.01720i	−0.0173542	−	0.999849i	$-0.505524\pi$
$98$	−80.4075	−	21.5451i	−0.820485	−	0.219848i
$99$		0			0
$100$	112.106			1.12106
$101$		−	104.921i		−	1.03882i	−0.854526	−	0.519409i	$-0.826152\pi$
$101$		−	104.921i		−	1.03882i	0.854526	−	0.519409i	$-0.173848\pi$
$102$		0			0
$103$	−116.329	+	116.329i	−1.12941	+	1.12941i	−0.139137	+	0.990273i	$0.544433\pi$
$103$	−116.329	+	116.329i	−1.12941	+	1.12941i	−0.990273	+	0.139137i	$0.955567\pi$
$104$	24.7875	−	14.3111i	0.238341	−	0.137606i
$105$		0			0
$106$	206.919	+	55.4438i	1.95207	+	0.523055i
$107$	75.0462	+	129.984i	0.701366	+	1.21480i	0.967987	+	0.251001i	$0.0807596\pi$
$107$	75.0462	+	129.984i	0.701366	+	1.21480i	−0.266621	+	0.963802i	$0.585907\pi$
$108$		0			0
$109$	−79.3477	+	21.2611i	−0.727960	+	0.195056i	−0.603721	−	0.797196i	$-0.706316\pi$
$109$	−79.3477	+	21.2611i	−0.727960	+	0.195056i	−0.124239	+	0.992252i	$0.539649\pi$
$110$			120.630i			1.09664i
$111$		0			0
$112$	−171.525			−1.53148
$113$	26.4674	+	98.7777i	0.234225	+	0.874139i	0.978497	+	0.206262i	$0.0661299\pi$
$113$	26.4674	+	98.7777i	0.234225	+	0.874139i	−0.744272	+	0.667877i	$0.767203\pi$
$114$		0			0
$115$	251.822	−	145.390i	2.18976	−	1.26426i
$116$	33.9176	−	126.582i	0.292393	−	1.09123i
$117$		0			0
$118$	117.042	+	202.722i	0.991878	+	1.71798i
$119$	136.832	+	136.832i	1.14985	+	1.14985i
$120$		0			0
$121$	87.7772			0.725432
$122$			92.0092i			0.754173i
$123$		0			0
$124$	−3.04739	+	11.3730i	−0.0245757	+	0.0917177i
$125$	73.3798	−	73.3798i	0.587039	−	0.587039i
$126$		0			0
$127$	−49.1011	+	85.0456i	−0.386623	+	0.669650i	−0.991993	−	0.126294i	$-0.959692\pi$
$127$	−49.1011	+	85.0456i	−0.386623	+	0.669650i	0.605370	+	0.795944i	$0.293025\pi$
$128$	−82.9519	+	22.2269i	−0.648061	+	0.173648i
$129$		0			0
$130$	−55.7605	+	208.101i	−0.428927	+	1.60078i
$131$	−45.5833	−	170.119i	−0.347964	−	1.29862i	−0.889111	−	0.457692i	$-0.848676\pi$
$131$	−45.5833	−	170.119i	−0.347964	−	1.29862i	0.541147	−	0.840928i	$-0.317990\pi$
$132$		0			0
$133$	−84.9181	+	22.7537i	−0.638482	+	0.171081i
$134$	34.3200	+	34.3200i	0.256119	+	0.256119i
$135$		0			0
$136$	51.9048	+	29.9673i	0.381653	+	0.220348i
$137$	199.399			1.45547			0.727735	−	0.685858i	$-0.240573\pi$
$137$	199.399			1.45547			0.727735	+	0.685858i	$0.240573\pi$
$138$		0			0
$139$	153.680	+	88.7272i	1.10561	+	0.638325i	0.937689	−	0.347475i	$-0.112961\pi$
$139$	153.680	+	88.7272i	1.10561	+	0.638325i	0.167923	+	0.985800i	$0.446294\pi$
$140$	148.457	−	148.457i	1.06040	−	1.06040i
$141$		0			0
$142$	−119.727	+	119.727i	−0.843149	+	0.843149i
$143$	−57.3133	−	15.3570i	−0.400792	−	0.107392i
$144$		0			0
$145$	−176.695	−	306.044i	−1.21858	−	2.11065i
$146$	−270.581	+	72.5018i	−1.85329	+	0.496588i
$147$		0			0
$148$	−40.8582	+	101.013i	−0.276069	+	0.682518i
$149$	−288.906			−1.93896			−0.969482	−	0.245163i	$-0.921158\pi$
$149$	−288.906			−1.93896			−0.969482	+	0.245163i	$0.921158\pi$
$150$		0			0
$151$	−45.5498	+	26.2982i	−0.301654	+	0.174160i	−0.643186	−	0.765710i	$-0.722388\pi$
$151$	−45.5498	+	26.2982i	−0.301654	+	0.174160i	0.341531	+	0.939870i	$0.389054\pi$
$152$	−23.5810	+	13.6145i	−0.155138	+	0.0895689i
$153$		0			0
$154$	96.4211	+	96.4211i	0.626111	+	0.626111i
$155$	15.8754	+	27.4971i	0.102422	+	0.177401i
$156$		0			0
$157$	−14.0838	+	24.3938i	−0.0897056	+	0.155375i	−0.907387	−	0.420297i	$-0.861926\pi$
$157$	−14.0838	+	24.3938i	−0.0897056	+	0.155375i	0.817681	+	0.575672i	$0.195259\pi$
$158$	171.337			1.08441
$159$		0			0
$160$	155.779	−	269.818i	0.973622	−	1.68636i
$161$	85.0730	−	317.497i	0.528404	−	1.97203i
$162$		0			0
$163$	−14.6382	−	54.6304i	−0.0898047	−	0.335156i	0.906376	−	0.422472i	$-0.138838\pi$
$163$	−14.6382	−	54.6304i	−0.0898047	−	0.335156i	−0.996181	+	0.0873165i	$0.972171\pi$
$164$	52.7335	−	91.3370i	0.321545	−	0.556933i
$165$		0			0
$166$	−25.7230	−	6.89246i	−0.154958	−	0.0415208i
$167$	1.59113	−	5.93817i	0.00952771	−	0.0355579i	−0.960998	−	0.276554i	$-0.910807\pi$
$167$	1.59113	−	5.93817i	0.00952771	−	0.0355579i	0.970526	+	0.240996i	$0.0774742\pi$
$168$		0			0
$169$	54.5847	+	31.5145i	0.322987	+	0.186476i
$170$	−435.762	+	116.762i	−2.56330	+	0.686835i
$171$		0			0
$172$	−111.914	−	29.9873i	−0.650663	−	0.174345i
$173$	140.255	+	80.9763i	0.810723	+	0.468071i	0.847207	−	0.531263i	$-0.178282\pi$
$173$	140.255	+	80.9763i	0.810723	+	0.468071i	−0.0364839	+	0.999334i	$0.511616\pi$
$174$		0			0
$175$		−	341.734i		−	1.95276i
$176$	95.3768	+	55.0658i	0.541914	+	0.312874i
$177$		0			0
$178$	75.1767	−	43.4033i	0.422341	−	0.243839i
$179$	−22.7693	+	22.7693i	−0.127203	+	0.127203i	−0.767842	−	0.640639i	$-0.778669\pi$
$179$	−22.7693	+	22.7693i	−0.127203	+	0.127203i	0.640639	+	0.767842i	$0.278669\pi$
$180$		0			0
$181$	−27.8544	−	48.2453i	−0.153892	−	0.266549i	0.778763	−	0.627318i	$-0.215847\pi$
$181$	−27.8544	−	48.2453i	−0.153892	−	0.266549i	−0.932655	+	0.360770i	$0.882514\pi$
$182$	121.768	+	210.908i	0.669054	+	1.15884i
$183$		0			0
$184$		−	101.805i		−	0.553289i
$185$	114.704	+	270.522i	0.620021	+	1.46228i
$186$		0			0
$187$	−32.1575	−	120.014i	−0.171965	−	0.641784i
$188$	−75.3860	+	43.5241i	−0.400990	+	0.231511i
$189$		0			0
$190$	53.0463	−	197.972i	0.279191	−	1.04196i
$191$	177.534	+	177.534i	0.929500	+	0.929500i	0.997673	−	0.0681735i	$-0.0217172\pi$
$191$	177.534	+	177.534i	0.929500	+	0.929500i	−0.0681735	+	0.997673i	$0.521717\pi$
$192$		0			0
$193$	−26.2738	−	26.2738i	−0.136134	−	0.136134i	0.635756	−	0.771890i	$-0.280688\pi$
$193$	−26.2738	−	26.2738i	−0.136134	−	0.136134i	−0.771890	+	0.635756i	$0.780688\pi$
$194$	183.865	−	318.464i	0.947758	−	1.64156i
$195$		0			0
$196$		−	93.0242i		−	0.474613i
$197$	107.747	−	186.624i	0.546941	−	0.947329i	−0.451541	−	0.892250i	$-0.649126\pi$
$197$	107.747	−	186.624i	0.546941	−	0.947329i	0.998482	−	0.0550787i	$-0.0175410\pi$
$198$		0			0
$199$	−75.9458	+	75.9458i	−0.381637	+	0.381637i	−0.871692	−	0.490055i	$-0.836977\pi$
$199$	−75.9458	+	75.9458i	−0.381637	+	0.381637i	0.490055	+	0.871692i	$0.336977\pi$
$200$	−27.3942	−	102.236i	−0.136971	−	0.511182i
$201$		0			0
$202$	267.079	−	71.5635i	1.32217	−	0.354275i
$203$	−385.860	−	103.391i	−1.90079	−	0.509314i
$204$		0			0
$205$	−73.6101	−	274.717i	−0.359074	−	1.34008i
$206$	−375.464	−	216.775i	−1.82264	−	1.05230i
$207$		0			0
$208$	139.083	+	139.083i	0.668666	+	0.668666i
$209$	54.5235	+	14.6095i	0.260878	+	0.0699021i
$210$		0			0
$211$	19.6949			0.0933406			0.0466703	−	0.998910i	$-0.485139\pi$
$211$	19.6949			0.0933406			0.0466703	+	0.998910i	$0.485139\pi$
$212$			239.387i			1.12918i
$213$		0			0
$214$	−279.691	+	279.691i	−1.30697	+	1.30697i
$215$	−270.580	+	156.220i	−1.25851	+	0.726603i
$216$		0			0
$217$	34.6682	+	9.28933i	0.159761	+	0.0428080i
$218$	−108.242	−	187.480i	−0.496522	−	0.860001i
$219$		0			0
$220$	−130.209	+	34.8895i	−0.591860	+	0.158588i
$221$		−	221.902i		−	1.00408i
$222$		0			0
$223$	−116.480			−0.522332			−0.261166	−	0.965294i	$-0.584107\pi$
$223$	−116.480			−0.522332			−0.261166	+	0.965294i	$0.584107\pi$
$224$	−91.1525	−	340.186i	−0.406931	−	1.51869i
$225$		0			0
$226$	−233.389	+	134.747i	−1.03269	+	0.596226i
$227$	38.8775	−	145.093i	0.171266	−	0.639175i	−0.825891	−	0.563830i	$-0.809327\pi$
$227$	38.8775	−	145.093i	0.171266	−	0.639175i	0.997157	−	0.0753454i	$-0.0240059\pi$
$228$		0			0
$229$	−147.636	−	255.714i	−0.644700	−	1.11665i	−0.984371	−	0.176109i	$-0.943649\pi$
$229$	−147.636	−	255.714i	−0.644700	−	1.11665i	0.339671	−	0.940544i	$-0.389684\pi$
$230$	541.855	+	541.855i	2.35589	+	2.35589i
$231$		0			0
$232$	−123.726			−0.533300
$233$		−	149.091i		−	0.639876i	−0.947439	−	0.319938i	$-0.896338\pi$
$233$		−	149.091i		−	0.639876i	0.947439	−	0.319938i	$-0.103662\pi$
$234$		0			0
$235$	−60.7549	+	226.740i	−0.258532	+	0.964853i
$236$	−184.969	+	184.969i	−0.783766	+	0.783766i
$237$		0			0
$238$	−254.981	+	441.640i	−1.07135	+	1.85563i
$239$	−187.279	+	50.1812i	−0.783594	+	0.209963i	−0.628368	−	0.777916i	$-0.716277\pi$
$239$	−187.279	+	50.1812i	−0.783594	+	0.209963i	−0.155225	+	0.987879i	$0.549610\pi$
$240$		0			0
$241$	88.0454	−	328.590i	0.365334	−	1.36344i	−0.501634	−	0.865080i	$-0.667268\pi$
$241$	88.0454	−	328.590i	0.365334	−	1.36344i	0.866968	−	0.498364i	$-0.166066\pi$
$242$	59.8705	+	223.440i	0.247399	+	0.923304i
$243$		0			0
$244$	−99.3157	+	26.6116i	−0.407032	+	0.109064i
$245$	−177.380	−	177.380i	−0.724002	−	0.724002i
$246$		0			0
$247$	87.3064	+	50.4064i	0.353467	+	0.204074i
$248$	11.1163			0.0448240
$249$		0			0
$250$	236.841	+	136.740i	0.947364	+	0.546961i
$251$	−17.4034	+	17.4034i	−0.0693362	+	0.0693362i	−0.740925	−	0.671588i	$-0.765612\pi$
$251$	−17.4034	+	17.4034i	−0.0693362	+	0.0693362i	0.671588	+	0.740925i	$0.265612\pi$
$252$		0			0
$253$	−149.233	+	149.233i	−0.589853	+	0.589853i
$254$	−249.977	−	66.9810i	−0.984160	−	0.263705i
$255$		0			0
$256$	−167.079	−	289.389i	−0.652652	−	1.13043i
$257$	376.401	−	100.856i	1.46459	−	0.392437i	0.563520	−	0.826103i	$-0.309447\pi$
$257$	376.401	−	100.856i	1.46459	−	0.392437i	0.901074	+	0.433666i	$0.142780\pi$
$258$		0			0
$259$	307.916	+	124.548i	1.18887	+	0.480879i
$260$	−240.754			−0.925977
$261$		0			0
$262$	401.952	−	232.067i	1.53417	−	0.885753i
$263$	−67.3191	+	38.8667i	−0.255966	+	0.147782i	−0.622493	−	0.782625i	$-0.713880\pi$
$263$	−67.3191	+	38.8667i	−0.255966	+	0.147782i	0.366527	+	0.930407i	$0.380547\pi$
$264$		0			0
$265$	456.467	+	456.467i	1.72252	+	1.72252i
$266$	−115.841	−	200.642i	−0.435491	−	0.754293i
$267$		0			0
$268$	−27.1191	+	46.9717i	−0.101191	+	0.175267i
$269$	431.858			1.60542			0.802711	−	0.596368i	$-0.203390\pi$
$269$	431.858			1.60542			0.802711	+	0.596368i	$0.203390\pi$
$270$		0			0
$271$	−35.9902	+	62.3369i	−0.132805	+	0.230026i	−0.924757	−	0.380558i	$-0.875732\pi$
$271$	−35.9902	+	62.3369i	−0.132805	+	0.230026i	0.791952	+	0.610584i	$0.209065\pi$
$272$	−106.600	+	397.838i	−0.391913	+	1.46264i
$273$		0			0
$274$	136.005	+	507.577i	0.496368	+	1.85247i
$275$	−109.709	+	190.021i	−0.398941	+	0.690986i
$276$		0			0
$277$	120.179	+	32.2019i	0.433860	+	0.116252i	0.469137	−	0.883125i	$-0.344565\pi$
$277$	120.179	+	32.2019i	0.433860	+	0.116252i	−0.0352777	+	0.999378i	$0.511232\pi$
$278$	−121.037	+	451.716i	−0.435384	+	1.62488i
$279$		0			0
$280$	−171.663	−	99.1095i	−0.613081	−	0.353963i
$281$	−20.6123	+	5.52304i	−0.0733533	+	0.0196550i	−0.295309	−	0.955402i	$-0.595423\pi$
$281$	−20.6123	+	5.52304i	−0.0733533	+	0.0196550i	0.221956	+	0.975057i	$0.428756\pi$
$282$		0			0
$283$	−465.216	−	124.654i	−1.64387	−	0.440474i	−0.685984	−	0.727617i	$-0.740628\pi$
$283$	−465.216	−	124.654i	−1.64387	−	0.440474i	−0.957888	+	0.287142i	$0.907295\pi$
$284$	−163.863	−	94.6064i	−0.576983	−	0.333121i
$285$		0			0
$286$		−	156.367i		−	0.546739i
$287$	−278.422	−	160.747i	−0.970112	−	0.560094i
$288$		0			0
$289$	152.128	−	87.8309i	0.526393	−	0.303913i
$290$	658.527	−	658.527i	2.27078	−	2.27078i
$291$		0			0
$292$	−156.519	−	271.098i	−0.536022	−	0.928418i
$293$	−159.101	−	275.572i	−0.543008	−	0.940517i	−0.998729	−	0.0503948i	$-0.983952\pi$
$293$	−159.101	−	275.572i	−0.543008	−	0.940517i	0.455721	−	0.890122i	$-0.349381\pi$
$294$		0			0
$295$			705.404i			2.39120i
$296$	102.103	+	12.5776i	0.344944	+	0.0424920i
$297$		0			0
$298$	−197.055	−	735.418i	−0.661257	−	2.46785i
$299$	−326.426	+	188.462i	−1.09173	+	0.630309i
$300$		0			0
$301$	−91.4101	+	341.147i	−0.303688	+	1.13338i
$302$	−98.0111	−	98.0111i	−0.324540	−	0.324540i
$303$		0			0
$304$	−132.313	−	132.313i	−0.435239	−	0.435239i
$305$	−138.634	+	240.121i	−0.454537	+	0.787281i
$306$		0			0
$307$		−	385.712i		−	1.25639i	−0.778056	−	0.628195i	$-0.783794\pi$
$307$		−	385.712i		−	1.25639i	0.778056	−	0.628195i	$-0.216206\pi$
$308$	−76.1903	+	131.966i	−0.247371	+	0.428460i
$309$		0			0
$310$	−59.1664	+	59.1664i	−0.190860	+	0.190860i
$311$	−23.7371	−	88.5881i	−0.0763251	−	0.284849i	0.917205	−	0.398415i	$-0.130439\pi$
$311$	−23.7371	−	88.5881i	−0.0763251	−	0.284849i	−0.993531	+	0.113566i	$0.963773\pi$
$312$		0			0
$313$	62.6223	−	16.7796i	0.200071	−	0.0536089i	−0.157392	−	0.987536i	$-0.550309\pi$
$313$	62.6223	−	16.7796i	0.200071	−	0.0536089i	0.357463	+	0.933927i	$0.383642\pi$
$314$	−71.7014	−	19.2123i	−0.228348	−	0.0611858i
$315$		0			0
$316$	49.5553	+	184.943i	0.156821	+	0.585262i
$317$	−130.544	−	75.3693i	−0.411809	−	0.237758i	0.279758	−	0.960071i	$-0.409746\pi$
$317$	−130.544	−	75.3693i	−0.411809	−	0.237758i	−0.691567	+	0.722312i	$0.743079\pi$
$318$		0			0
$319$	181.365	+	181.365i	0.568543	+	0.568543i
$320$	206.809	+	55.4143i	0.646278	+	0.173170i
$321$		0			0
$322$	866.224			2.69014
$323$			211.101i			0.653564i
$324$		0			0
$325$	−277.097	+	277.097i	−0.852606	+	0.852606i
$326$	129.079	−	74.5238i	0.395948	−	0.228600i
$327$		0			0
$328$	−96.1814	−	25.7717i	−0.293236	−	0.0785723i
$329$	132.674	+	229.799i	0.403266	+	0.698477i
$330$		0			0
$331$	385.026	−	103.167i	1.16322	−	0.311684i	0.374969	−	0.927037i	$-0.377653\pi$
$331$	385.026	−	103.167i	1.16322	−	0.311684i	0.788251	+	0.615353i	$0.210987\pi$
$332$		−	29.7592i		−	0.0896361i
$333$		0			0
$334$	16.2010			0.0485061
$335$	37.8553	+	141.278i	0.113001	+	0.421725i
$336$		0			0
$337$	9.02944	−	5.21315i	0.0267936	−	0.0154693i	−0.486543	−	0.873656i	$-0.661742\pi$
$337$	9.02944	−	5.21315i	0.0267936	−	0.0154693i	0.513337	+	0.858187i	$0.328409\pi$
$338$	−42.9904	+	160.442i	−0.127190	+	0.474681i
$339$		0			0
$340$	−252.068	−	436.595i	−0.741378	−	1.28410i
$341$	−16.2951	−	16.2951i	−0.0477862	−	0.0477862i
$342$		0			0
$343$	156.311			0.455718
$344$			109.389i			0.317990i
$345$		0			0
$346$	−110.463	+	412.255i	−0.319259	+	1.19149i
$347$	−387.414	+	387.414i	−1.11647	+	1.11647i	−0.124210	+	0.992256i	$0.539640\pi$
$347$	−387.414	+	387.414i	−1.11647	+	1.11647i	−0.992256	+	0.124210i	$0.960360\pi$
$348$		0			0
$349$	125.562	−	217.481i	0.359778	−	0.623154i	−0.628146	−	0.778096i	$-0.716186\pi$
$349$	125.562	−	217.481i	0.359778	−	0.623154i	0.987924	+	0.154942i	$0.0495191\pi$
$350$	869.893	−	233.087i	2.48541	−	0.665963i
$351$		0			0
$352$	−58.5264	+	218.424i	−0.166268	+	0.620521i
$353$	−82.4646	−	307.762i	−0.233611	−	0.871847i	−0.978770	−	0.204961i	$-0.934293\pi$
$353$	−82.4646	−	307.762i	−0.233611	−	0.871847i	0.745160	−	0.666886i	$-0.232373\pi$
$354$		0			0
$355$	−492.855	+	132.060i	−1.38832	+	0.372000i
$356$	68.5931	+	68.5931i	0.192677	+	0.192677i
$357$		0			0
$358$	−73.4901	−	42.4296i	−0.205280	−	0.118518i
$359$	391.139			1.08952			0.544762	−	0.838591i	$-0.316620\pi$
$359$	391.139			1.08952			0.544762	+	0.838591i	$0.316620\pi$
$360$		0			0
$361$	229.578	+	132.547i	0.635951	+	0.367167i
$362$	103.811	−	103.811i	0.286771	−	0.286771i
$363$		0			0
$364$	−192.438	+	192.438i	−0.528675	+	0.528675i
$365$	−815.388	−	218.483i	−2.23394	−	0.598583i
$366$		0			0
$367$	−239.453	−	414.745i	−0.652461	−	1.13010i	−0.982524	−	0.186136i	$-0.940403\pi$
$367$	−239.453	−	414.745i	−0.652461	−	1.13010i	0.330063	−	0.943959i	$-0.392930\pi$
$368$	675.770	−	181.072i	1.83633	−	0.492044i
$369$		0			0
$370$	−610.386	+	476.498i	−1.64969	+	1.28783i
$371$	729.721			1.96690
$372$		0			0
$373$	178.871	−	103.271i	0.479546	−	0.276866i	−0.240681	−	0.970604i	$-0.577371\pi$
$373$	178.871	−	103.271i	0.479546	−	0.276866i	0.720227	+	0.693738i	$0.244038\pi$
$374$	283.564	−	163.716i	0.758193	−	0.437743i
$375$		0			0
$376$	58.1134	+	58.1134i	0.154557	+	0.154557i
$377$	229.042	+	396.712i	0.607538	+	1.05229i
$378$		0			0
$379$	123.878	−	214.563i	0.326854	−	0.566129i	−0.655031	−	0.755602i	$-0.727345\pi$
$379$	123.878	−	214.563i	0.326854	−	0.566129i	0.981886	+	0.189473i	$0.0606780\pi$
$380$	229.035			0.602724
$381$		0			0
$382$	−330.828	+	573.011i	−0.866042	+	1.50003i
$383$	25.3402	−	94.5709i	0.0661624	−	0.246922i	−0.924922	−	0.380157i	$-0.875870\pi$
$383$	25.3402	−	94.5709i	0.0661624	−	0.246922i	0.991084	+	0.133235i	$0.0425366\pi$
$384$		0			0
$385$	106.353	+	396.916i	0.276242	+	1.03095i
$386$	48.9601	−	84.8015i	0.126840	−	0.219693i
$387$		0			0
$388$	396.932	+	106.358i	1.02302	+	0.274117i
$389$	48.5167	−	181.067i	0.124722	−	0.465467i	−0.875108	−	0.483928i	$-0.839210\pi$
$389$	48.5167	−	181.067i	0.124722	−	0.465467i	0.999830	+	0.0184603i	$0.00587644\pi$
$390$		0			0
$391$	−683.534	−	394.639i	−1.74817	−	1.00931i
$392$	−84.8341	+	22.7312i	−0.216414	+	0.0579879i
$393$		0			0
$394$	548.548	+	146.983i	1.39225	+	0.373053i
$395$	447.146	+	258.160i	1.13202	+	0.653569i
$396$		0			0
$397$		−	171.518i		−	0.432035i	−0.976389	−	0.216018i	$-0.930693\pi$
$397$		−	171.518i		−	0.432035i	0.976389	−	0.216018i	$-0.0693069\pi$
$398$	−245.123	−	141.522i	−0.615887	−	0.355582i
$399$		0			0
$400$	629.909	−	363.678i	1.57477	−	0.909196i
$401$	−325.273	+	325.273i	−0.811154	+	0.811154i	−0.984807	−	0.173653i	$-0.944443\pi$
$401$	−325.273	+	325.273i	−0.811154	+	0.811154i	0.173653	+	0.984807i	$0.444443\pi$
$402$		0			0
$403$	−20.5787	−	35.6433i	−0.0510637	−	0.0884449i
$404$	154.493	+	267.589i	0.382408	+	0.662350i
$405$		0			0
$406$		−	1052.74i		−	2.59295i
$407$	−131.233	−	168.107i	−0.322439	−	0.413039i
$408$		0			0
$409$	−22.6772	−	84.6325i	−0.0554455	−	0.206925i	0.932646	−	0.360793i	$-0.117494\pi$
$409$	−22.6772	−	84.6325i	−0.0554455	−	0.206925i	−0.988092	+	0.153867i	$0.950827\pi$
$410$	649.092	−	374.753i	1.58315	−	0.914033i
$411$		0			0
$412$	125.394	−	467.978i	0.304355	−	1.13587i
$413$	563.839	+	563.839i	1.36523	+	1.36523i
$414$		0			0
$415$	−56.7455	−	56.7455i	−0.136736	−	0.136736i
$416$	−201.930	+	349.753i	−0.485409	+	0.840753i
$417$		0			0
$418$			148.756i			0.355876i
$419$	−39.2536	+	67.9893i	−0.0936840	+	0.162266i	−0.909059	−	0.416668i	$-0.863198\pi$
$419$	−39.2536	+	67.9893i	−0.0936840	+	0.162266i	0.815375	+	0.578934i	$0.196531\pi$
$420$		0			0
$421$	257.327	−	257.327i	0.611229	−	0.611229i	−0.332037	−	0.943266i	$-0.607736\pi$
$421$	257.327	−	257.327i	0.611229	−	0.611229i	0.943266	+	0.332037i	$0.107736\pi$
$422$	13.4333	+	50.1339i	0.0318325	+	0.118801i
$423$		0			0
$424$	218.311	−	58.4961i	0.514883	−	0.137963i
$425$	−792.621	−	212.382i	−1.86499	−	0.499723i
$426$		0			0
$427$	81.1199	+	302.743i	0.189976	+	0.709001i
$428$	−382.796	−	221.007i	−0.894382	−	0.516372i
$429$		0			0
$430$	−582.218	−	582.218i	−1.35399	−	1.35399i
$431$	−598.540	−	160.378i	−1.38872	−	0.372107i	−0.514441	−	0.857526i	$-0.672001\pi$
$431$	−598.540	−	160.378i	−1.38872	−	0.372107i	−0.874282	+	0.485419i	$0.838667\pi$
$432$		0			0
$433$	320.497			0.740177			0.370088	−	0.928997i	$-0.379327\pi$
$433$	320.497			0.740177			0.370088	+	0.928997i	$0.379327\pi$
$434$			94.5850i			0.217938i
$435$		0			0
$436$	171.062	−	171.062i	0.392343	−	0.392343i
$437$	310.537	−	179.289i	0.710612	−	0.410272i
$438$		0			0
$439$	−652.917	−	174.948i	−1.48728	−	0.398516i	−0.578463	−	0.815708i	$-0.696347\pi$
$439$	−652.917	−	174.948i	−1.48728	−	0.398516i	−0.908818	+	0.417192i	$0.863014\pi$
$440$	63.6354	+	110.220i	0.144626	+	0.250500i
$441$		0			0
$442$	564.859	−	151.354i	1.27796	−	0.342429i
$443$		−	559.485i		−	1.26295i	−0.775398	−	0.631473i	$-0.782451\pi$
$443$		−	559.485i		−	1.26295i	0.775398	−	0.631473i	$-0.217549\pi$
$444$		0			0
$445$	261.590			0.587842
$446$	−79.4479	−	296.504i	−0.178134	−	0.664806i
$447$		0			0
$448$	209.598	−	121.012i	0.467854	−	0.270115i
$449$	−52.6010	+	196.309i	−0.117151	+	0.437215i	−0.999439	−	0.0334961i	$-0.989336\pi$
$449$	−52.6010	+	196.309i	−0.117151	+	0.437215i	0.882287	+	0.470711i	$0.156003\pi$
$450$		0			0
$451$	103.211	+	178.767i	0.228850	+	0.396379i
$452$	−212.950	−	212.950i	−0.471128	−	0.471128i
$453$		0			0
$454$	395.855			0.871928
$455$			733.889i			1.61294i
$456$		0			0
$457$	197.163	−	735.823i	0.431429	−	1.61012i	−0.318041	−	0.948077i	$-0.603025\pi$
$457$	197.163	−	735.823i	0.431429	−	1.61012i	0.749470	−	0.662039i	$-0.230308\pi$
$458$	550.228	−	550.228i	1.20137	−	1.20137i
$459$		0			0
$460$	−428.165	+	741.603i	−0.930793	+	1.61218i
$461$	534.264	−	143.156i	1.15892	−	0.310533i	0.372388	−	0.928077i	$-0.378539\pi$
$461$	534.264	−	143.156i	1.15892	−	0.310533i	0.786536	+	0.617545i	$0.211872\pi$
$462$		0			0
$463$	−217.788	+	812.796i	−0.470385	+	1.75550i	0.168005	+	0.985786i	$0.446267\pi$
$463$	−217.788	+	812.796i	−0.470385	+	1.75550i	−0.638390	+	0.769713i	$0.720399\pi$
$464$	−220.060	−	821.276i	−0.474268	−	1.76999i
$465$		0			0
$466$	379.516	−	101.691i	0.814411	−	0.218221i
$467$	557.781	+	557.781i	1.19439	+	1.19439i	0.975821	+	0.218570i	$0.0701392\pi$
$467$	557.781	+	557.781i	1.19439	+	1.19439i	0.218570	+	0.975821i	$0.429861\pi$
$468$		0			0
$469$	143.183	+	82.6670i	0.305295	+	0.176262i
$470$	−618.614			−1.31620
$471$		0			0
$472$	213.882	+	123.485i	0.453140	+	0.261621i
$473$	160.349	−	160.349i	0.339004	−	0.339004i
$474$		0			0
$475$	263.609	−	263.609i	0.554967	−	0.554967i
$476$	−550.458	−	147.495i	−1.15642	−	0.309863i
$477$		0			0
$478$	−255.476	−	442.497i	−0.534468	−	0.925725i
$479$	−704.700	+	188.824i	−1.47119	+	0.394204i	−0.903339	−	0.428928i	$-0.858891\pi$
$479$	−704.700	+	188.824i	−1.47119	+	0.394204i	−0.567850	+	0.823132i	$0.692225\pi$
$480$		0			0
$481$	−148.686	−	350.666i	−0.309118	−	0.729036i
$482$	896.489			1.85994
$483$		0			0
$484$	−223.867	+	129.250i	−0.462535	+	0.267045i
$485$	959.683	−	554.073i	1.97873	−	1.14242i
$486$		0			0
$487$	42.2305	+	42.2305i	0.0867157	+	0.0867157i	0.749134	−	0.662418i	$-0.230470\pi$
$487$	42.2305	+	42.2305i	0.0867157	+	0.0867157i	−0.662418	+	0.749134i	$0.730470\pi$
$488$	48.5372	+	84.0690i	0.0994616	+	0.172272i
$489$		0			0
$490$	330.541	−	572.514i	0.674573	−	1.16840i
$491$	410.667			0.836390			0.418195	−	0.908357i	$-0.362663\pi$
$491$	410.667			0.836390			0.418195	+	0.908357i	$0.362663\pi$
$492$		0			0
$493$	−479.612	+	830.712i	−0.972843	+	1.68501i
$494$	−68.7617	+	256.622i	−0.139194	+	0.519478i
$495$		0			0
$496$	19.7717	+	73.7890i	0.0398623	+	0.148768i
$497$	−288.388	+	499.503i	−0.580258	+	1.00504i
$498$		0			0
$499$	334.968	+	89.7545i	0.671279	+	0.179869i	0.578331	−	0.815802i	$-0.303704\pi$
$499$	334.968	+	89.7545i	0.671279	+	0.179869i	0.0929483	+	0.995671i	$0.470371\pi$
$500$	−79.0980	+	295.198i	−0.158196	+	0.590395i
$501$		0			0
$502$	−56.1713	−	32.4305i	−0.111895	−	0.0646026i
$503$	−418.030	+	112.011i	−0.831074	+	0.222686i	−0.649182	−	0.760633i	$-0.724889\pi$
$503$	−418.030	+	112.011i	−0.831074	+	0.222686i	−0.181892	+	0.983319i	$0.558222\pi$
$504$		0			0
$505$	804.835	+	215.655i	1.59373	+	0.427040i
$506$	−481.664	−	278.089i	−0.951905	−	0.549583i
$507$		0			0
$508$		−	289.200i		−	0.569292i
$509$	−606.326	−	350.062i	−1.19121	−	0.687746i	−0.232629	−	0.972565i	$-0.574733\pi$
$509$	−606.326	−	350.062i	−1.19121	−	0.687746i	−0.958581	+	0.284820i	$0.908066\pi$
$510$		0			0
$511$	−826.387	+	477.115i	−1.61720	+	0.933688i
$512$	379.789	−	379.789i	0.741775	−	0.741775i
$513$		0			0
$514$	513.465	+	889.348i	0.998959	+	1.73025i
$515$	−653.245	−	1131.45i	−1.26844	−	2.19700i
$516$		0			0
$517$		−	170.373i		−	0.329541i
$518$	−107.019	+	868.761i	−0.206600	+	1.67714i
$519$		0			0
$520$	58.8303	+	219.558i	0.113135	+	0.422226i
$521$	−324.325	+	187.249i	−0.622505	+	0.359403i	−0.777844	−	0.628458i	$-0.783686\pi$
$521$	−324.325	+	187.249i	−0.622505	+	0.359403i	0.155339	+	0.987861i	$0.450353\pi$
$522$		0			0
$523$	−147.219	+	549.428i	−0.281489	+	1.05053i	0.669877	+	0.742472i	$0.266347\pi$
$523$	−147.219	+	549.428i	−0.281489	+	1.05053i	−0.951367	+	0.308061i	$0.900320\pi$
$524$	366.752	+	366.752i	0.699908	+	0.699908i
$525$		0			0
$526$	−144.853	−	144.853i	−0.275386	−	0.275386i
$527$	43.0915	−	74.6367i	0.0817676	−	0.141626i
$528$		0			0
$529$			811.671i			1.53435i
$530$	−850.608	+	1473.30i	−1.60492	+	2.77980i
$531$		0			0
$532$	183.071	−	183.071i	0.344118	−	0.344118i
$533$	95.4176	+	356.103i	0.179020	+	0.668111i
$534$		0			0
$535$	−1151.34	+	308.502i	−2.15204	+	0.576638i
$536$	49.4630	+	13.2536i	0.0922817	+	0.0247268i
$537$		0			0
$538$	294.559	+	1099.31i	0.547507	+	2.04333i
$539$	157.676	+	91.0346i	0.292535	+	0.168895i
$540$		0			0
$541$	−416.481	−	416.481i	−0.769836	−	0.769836i	0.208241	−	0.978077i	$-0.433226\pi$
$541$	−416.481	−	416.481i	−0.769836	−	0.769836i	−0.978077	+	0.208241i	$0.933226\pi$
$542$	−183.229	−	49.0959i	−0.338060	−	0.0905829i
$543$		0			0
$544$	−845.680			−1.55456
$545$		−	652.368i		−	1.19701i
$546$		0			0
$547$	−448.488	+	448.488i	−0.819905	+	0.819905i	−0.986094	−	0.166189i	$-0.946854\pi$
$547$	−448.488	+	448.488i	−0.819905	+	0.819905i	0.166189	+	0.986094i	$0.446854\pi$
$548$	−508.548	+	293.610i	−0.928008	+	0.535785i
$549$		0			0
$550$	−558.534	−	149.659i	−1.01552	−	0.272107i
$551$	−217.893	−	377.402i	−0.395450	−	0.684940i
$552$		0			0
$553$	563.760	−	151.059i	1.01946	−	0.273163i
$554$			327.884i			0.591848i
$555$		0			0
$556$	−522.594			−0.939917
$557$	97.0341	+	362.136i	0.174208	+	0.650155i	0.996685	+	0.0813558i	$0.0259250\pi$
$557$	97.0341	+	362.136i	0.174208	+	0.650155i	−0.822477	+	0.568799i	$0.807408\pi$
$558$		0			0
$559$	350.742	−	202.501i	0.627445	−	0.362256i
$560$	352.555	−	1315.75i	0.629563	−	2.34956i
$561$		0			0
$562$	−28.1181	−	48.7020i	−0.0500323	−	0.0866584i
$563$	186.307	+	186.307i	0.330919	+	0.330919i	0.852935	−	0.522016i	$-0.174820\pi$
$563$	186.307	+	186.307i	0.330919	+	0.330919i	−0.522016	+	0.852935i	$0.674820\pi$
$564$		0			0
$565$	−812.115			−1.43737
$566$		−	1269.24i		−	2.24248i
$567$		0			0
$568$	−46.2357	+	172.554i	−0.0814010	+	0.303793i
$569$	−222.465	+	222.465i	−0.390976	+	0.390976i	−0.875035	−	0.484059i	$-0.839162\pi$
$569$	−222.465	+	222.465i	−0.390976	+	0.390976i	0.484059	+	0.875035i	$0.339162\pi$
$570$		0			0
$571$	22.3338	−	38.6833i	0.0391135	−	0.0677466i	−0.845806	−	0.533491i	$-0.820880\pi$
$571$	22.3338	−	38.6833i	0.0391135	−	0.0677466i	0.884919	+	0.465744i	$0.154213\pi$
$572$	168.785	−	45.2257i	0.295078	−	0.0790659i
$573$		0			0
$574$	219.282	−	818.373i	0.382025	−	1.42574i
$575$	360.754	+	1346.35i	0.627397	+	2.34148i
$576$		0			0
$577$	−260.009	+	69.6693i	−0.450623	+	0.120744i	−0.476991	−	0.878908i	$-0.658272\pi$
$577$	−260.009	+	69.6693i	−0.450623	+	0.120744i	0.0263680	+	0.999652i	$0.491606\pi$
$578$	327.338	+	327.338i	0.566329	+	0.566329i
$579$		0			0
$580$	901.285	+	520.357i	1.55394	+	0.897167i
$581$	−90.7148			−0.156136
$582$		0			0
$583$	−405.762	−	234.267i	−0.695989	−	0.401829i
$584$	−208.983	+	208.983i	−0.357848	+	0.357848i
$585$		0			0
$586$	592.957	−	592.957i	1.01187	−	1.01187i
$587$	−384.783	−	103.102i	−0.655508	−	0.175643i	−0.0842903	−	0.996441i	$-0.526862\pi$
$587$	−384.783	−	103.102i	−0.655508	−	0.175643i	−0.571218	+	0.820798i	$0.693529\pi$
$588$		0			0
$589$	19.5770	+	33.9083i	0.0332377	+	0.0575693i
$590$	−1795.63	+	481.137i	−3.04344	+	0.815486i
$591$		0			0
$592$	98.1136	+	700.120i	0.165732	+	1.18264i
$593$	−569.784			−0.960850			−0.480425	−	0.877036i	$-0.659518\pi$
$593$	−569.784			−0.960850			−0.480425	+	0.877036i	$0.659518\pi$
$594$		0			0
$595$	−1330.87	+	768.379i	−2.23676	+	1.29139i
$596$	736.825	−	425.406i	1.23628	−	0.713768i
$597$		0			0
$598$	−702.383	−	702.383i	−1.17455	−	1.17455i
$599$	123.216	+	213.417i	0.205703	+	0.356289i	0.950357	−	0.311163i	$-0.100718\pi$
$599$	123.216	+	213.417i	0.205703	+	0.356289i	−0.744653	+	0.667452i	$0.767385\pi$
$600$		0			0
$601$	451.524	−	782.062i	0.751287	−	1.30127i	−0.195911	−	0.980622i	$-0.562767\pi$
$601$	451.524	−	782.062i	0.751287	−	1.30127i	0.947199	−	0.320647i	$-0.103900\pi$
$602$	−930.748			−1.54609
$603$		0			0
$604$	77.4468	−	134.142i	0.128223	−	0.222089i
$605$	−180.418	+	673.330i	−0.298212	+	1.11294i
$606$		0			0
$607$	115.591	+	431.393i	0.190431	+	0.710696i	0.993403	+	0.114680i	$0.0365841\pi$
$607$	115.591	+	431.393i	0.190431	+	0.710696i	−0.802972	+	0.596017i	$0.796749\pi$
$608$	192.101	−	332.729i	0.315956	−	0.547251i
$609$		0			0
$610$	−705.793	−	189.117i	−1.15704	−	0.310027i
$611$	78.7540	−	293.914i	0.128894	−	0.481037i
$612$		0			0
$613$	455.629	+	263.057i	0.743277	+	0.429131i	0.823260	−	0.567665i	$-0.192153\pi$
$613$	455.629	+	263.057i	0.743277	+	0.429131i	−0.0799825	+	0.996796i	$0.525486\pi$
$614$	981.841	−	263.083i	1.59909	−	0.428475i
$615$		0			0
$616$	138.965	+	37.2355i	0.225592	+	0.0604472i
$617$	556.088	+	321.058i	0.901277	+	0.520353i	0.877614	−	0.479367i	$-0.159134\pi$
$617$	556.088	+	321.058i	0.901277	+	0.520353i	0.0236628	+	0.999720i	$0.492467\pi$
$618$		0			0
$619$		−	1127.98i		−	1.82227i	−0.412113	−	0.911133i	$-0.635209\pi$
$619$		−	1127.98i		−	1.82227i	0.412113	−	0.911133i	$-0.364791\pi$
$620$	−80.9775	−	46.7524i	−0.130609	−	0.0754070i
$621$		0			0
$622$	209.313	−	120.847i	0.336516	−	0.194288i
$623$	209.092	−	209.092i	0.335621	−	0.335621i
$624$		0			0
$625$	−63.7790	−	110.468i	−0.102046	−	0.176750i
$626$	85.4260	+	147.962i	0.136463	+	0.236361i
$627$		0			0
$628$		−	82.9520i		−	0.132089i
$629$	480.243	−	636.780i	0.763502	−	1.01237i
$630$		0			0
$631$	16.0763	+	59.9976i	0.0254775	+	0.0950834i	0.977494	−	0.210964i	$-0.0676602\pi$
$631$	16.0763	+	59.9976i	0.0254775	+	0.0950834i	−0.952016	+	0.306047i	$0.900994\pi$
$632$	156.551	−	90.3847i	0.247707	−	0.143014i
$633$		0			0
$634$	102.815	−	383.710i	0.162168	−	0.605221i
$635$	−551.453	−	551.453i	−0.868430	−	0.868430i
$636$		0			0
$637$	229.931	+	229.931i	0.360959	+	0.360959i
$638$	−337.967	+	585.375i	−0.529728	+	0.917516i
$639$		0			0
$640$		−	682.001i		−	1.06563i
$641$	−230.371	+	399.014i	−0.359393	+	0.622487i	−0.987860	−	0.155350i	$-0.950350\pi$
$641$	−230.371	+	399.014i	−0.359393	+	0.622487i	0.628466	+	0.777837i	$0.283683\pi$
$642$		0			0
$643$	389.902	−	389.902i	0.606380	−	0.606380i	−0.335618	−	0.941998i	$-0.608945\pi$
$643$	389.902	−	389.902i	0.606380	−	0.606380i	0.941998	+	0.335618i	$0.108945\pi$
$644$	250.536	+	935.011i	0.389030	+	1.45188i
$645$		0			0
$646$	−537.364	+	143.986i	−0.831833	+	0.222889i
$647$	174.048	+	46.6360i	0.269008	+	0.0720804i	0.390801	−	0.920475i	$-0.372198\pi$
$647$	174.048	+	46.6360i	0.269008	+	0.0720804i	−0.121794	+	0.992555i	$0.538865\pi$
$648$		0			0
$649$	−132.510	−	494.535i	−0.204176	−	0.761996i
$650$	−894.359	−	516.358i	−1.37594	−	0.794398i
$651$		0			0
$652$	117.775	+	117.775i	0.180636	+	0.180636i
$653$	61.2257	+	16.4054i	0.0937606	+	0.0251231i	0.305394	−	0.952226i	$-0.401212\pi$
$653$	61.2257	+	16.4054i	0.0937606	+	0.0251231i	−0.211634	+	0.977349i	$0.567878\pi$
$654$		0			0
$655$	1398.66			2.13536
$656$		−	684.278i		−	1.04311i
$657$		0			0
$658$	−494.466	+	494.466i	−0.751468	+	0.751468i
$659$	696.601	−	402.183i	1.05706	−	0.610292i	0.132440	−	0.991191i	$-0.457719\pi$
$659$	696.601	−	402.183i	1.05706	−	0.610292i	0.924617	+	0.380899i	$0.124385\pi$
$660$		0			0
$661$	−1122.16	−	300.682i	−1.69767	−	0.454889i	−0.725319	−	0.688413i	$-0.758308\pi$
$661$	−1122.16	−	300.682i	−1.69767	−	0.454889i	−0.972351	+	0.233524i	$0.924974\pi$
$662$	525.231	+	909.727i	0.793401	+	1.37421i
$663$		0			0
$664$	−27.1391	+	7.27191i	−0.0408722	+	0.0109517i
$665$		−	698.167i		−	1.04987i
$666$		0			0
$667$	1629.34			2.44279
$668$	4.68579	+	17.4876i	0.00701465	+	0.0261790i
$669$		0			0
$670$	−333.807	+	192.724i	−0.498219	+	0.287647i
$671$	52.0848	−	194.383i	0.0776226	−	0.289691i
$672$		0			0
$673$	−319.649	−	553.649i	−0.474962	−	0.822658i	0.524627	−	0.851332i	$-0.324205\pi$
$673$	−319.649	−	553.649i	−0.474962	−	0.822658i	−0.999589	+	0.0286740i	$0.990872\pi$
$674$	19.4290	+	19.4290i	0.0288264	+	0.0288264i
$675$		0			0
$676$	−185.617			−0.274582
$677$		−	56.1891i		−	0.0829971i	−0.999139	−	0.0414986i	$-0.986787\pi$
$677$		−	56.1891i		−	0.0829971i	0.999139	−	0.0414986i	$-0.0132132\pi$
$678$		0			0
$679$	324.209	−	1209.97i	0.477480	−	1.78198i
$680$	−336.562	+	336.562i	−0.494943	+	0.494943i
$681$		0			0
$682$	30.3652	−	52.5940i	0.0445237	−	0.0771174i
$683$	−442.037	+	118.444i	−0.647200	+	0.173417i	−0.567462	−	0.823399i	$-0.692075\pi$
$683$	−442.037	+	118.444i	−0.647200	+	0.173417i	−0.0797372	+	0.996816i	$0.525408\pi$
$684$		0			0
$685$	−409.848	+	1529.57i	−0.598318	+	2.23295i
$686$	106.616	+	397.895i	0.155416	+	0.580022i
$687$		0			0
$688$	−726.108	+	194.560i	−1.05539	+	0.282791i
$689$	−591.699	−	591.699i	−0.858779	−	0.858779i
$690$		0			0
$691$	1021.99	+	590.048i	1.47901	+	0.853905i	0.999718	−	0.0237522i	$-0.00756126\pi$
$691$	1021.99	+	590.048i	1.47901	+	0.853905i	0.479289	+	0.877657i	$0.340895\pi$
$692$	−476.942			−0.689222
$693$		0			0
$694$	−1250.42	−	721.929i	−1.80175	−	1.04024i
$695$	−996.493	+	996.493i	−1.43380	+	1.43380i
$696$		0			0
$697$	−545.874	+	545.874i	−0.783176	+	0.783176i
$698$	639.246	+	171.286i	0.915826	+	0.245395i
$699$		0			0
$700$	503.194	+	871.557i	0.718848	+	1.24508i
$701$	448.902	−	120.283i	0.640374	−	0.171588i	0.0760010	−	0.997108i	$-0.475785\pi$
$701$	448.902	−	120.283i	0.640374	−	0.171588i	0.564373	+	0.825520i	$0.309118\pi$
$702$		0			0
$703$	141.448	+	333.597i	0.201207	+	0.474534i
$704$	−155.396			−0.220733
$705$		0			0
$706$	727.170	−	419.832i	1.02999	−	0.594663i
$707$	815.691	−	470.940i	1.15374	−	0.666110i
$708$		0			0
$709$	94.9446	+	94.9446i	0.133913	+	0.133913i	0.770886	−	0.636973i	$-0.219814\pi$
$709$	94.9446	+	94.9446i	0.133913	+	0.133913i	−0.636973	+	0.770886i	$0.719814\pi$
$710$	−672.326	−	1164.50i	−0.946938	−	1.64015i
$711$		0			0
$712$	45.7928	−	79.3154i	0.0643157	−	0.111398i
$713$	−146.391			−0.205317
$714$		0			0
$715$	235.605	−	408.079i	0.329517	−	0.570740i
$716$	24.5436	−	91.5979i	0.0342787	−	0.127930i
$717$		0			0
$718$	266.785	+	995.657i	0.371567	+	1.38671i
$719$	194.964	−	337.688i	0.271160	−	0.469663i	−0.697999	−	0.716099i	$-0.745926\pi$
$719$	194.964	−	337.688i	0.271160	−	0.469663i	0.969159	+	0.246436i	$0.0792594\pi$
$720$		0			0
$721$	−1426.53	−	382.239i	−1.97855	−	0.530150i
$722$	−180.814	+	674.806i	−0.250434	+	0.934634i
$723$		0			0
$724$	142.080	+	82.0299i	0.196243	+	0.113301i
$725$	1636.25	−	438.431i	2.25689	−	0.604732i
$726$		0			0
$727$	−200.797	−	53.8035i	−0.276200	−	0.0740076i	0.118060	−	0.993006i	$-0.462332\pi$
$727$	−200.797	−	53.8035i	−0.276200	−	0.0740076i	−0.394260	+	0.918999i	$0.628999\pi$
$728$	222.519	+	128.471i	0.305658	+	0.176472i
$729$		0			0
$730$		−	2224.62i		−	3.04742i
$731$	734.450	+	424.035i	1.00472	+	0.580075i
$732$		0			0
$733$	164.746	−	95.1159i	0.224755	−	0.129762i	−0.383395	−	0.923584i	$-0.625245\pi$
$733$	164.746	−	95.1159i	0.224755	−	0.129762i	0.608150	+	0.793822i	$0.291912\pi$
$734$	892.421	−	892.421i	1.21583	−	1.21583i
$735$		0			0
$736$	718.239	+	1244.03i	0.975868	+	1.69025i
$737$	−53.0781	−	91.9341i	−0.0720192	−	0.124741i
$738$		0			0
$739$			468.089i			0.633409i	0.948524	+	0.316704i	$0.102576\pi$
$739$			468.089i			0.633409i	−0.948524	+	0.316704i	$0.897424\pi$
$740$	−690.878	−	521.041i	−0.933618	−	0.704110i
$741$		0			0
$742$	497.723	+	1857.53i	0.670785	+	2.50341i
$743$	−302.696	+	174.761i	−0.407396	+	0.235210i	−0.689670	−	0.724123i	$-0.742245\pi$
$743$	−302.696	+	174.761i	−0.407396	+	0.235210i	0.282274	+	0.959334i	$0.408911\pi$
$744$		0			0
$745$	593.820	−	2216.17i	0.797073	−	2.97472i
$746$	384.882	+	384.882i	0.515928	+	0.515928i
$747$		0			0
$748$	258.731	+	258.731i	0.345897	+	0.345897i
$749$	−673.695	+	1166.87i	−0.899459	+	1.55791i
$750$		0			0
$751$			593.954i			0.790885i	0.918491	+	0.395442i	$0.129409\pi$
$751$			593.954i			0.790885i	−0.918491	+	0.395442i	$0.870591\pi$
$752$	−282.388	+	489.111i	−0.375517	+	0.650414i
$753$		0			0
$754$	−853.619	+	853.619i	−1.13212	+	1.13212i
$755$	−108.107	−	403.462i	−0.143188	−	0.534386i
$756$		0			0
$757$	1185.29	−	317.598i	1.56577	−	0.419548i	0.631288	−	0.775549i	$-0.282527\pi$
$757$	1185.29	−	317.598i	1.56577	−	0.419548i	0.934486	+	0.356001i	$0.115860\pi$
$758$	630.670	+	168.987i	0.832018	+	0.222939i
$759$		0			0
$760$	−55.9667	−	208.870i	−0.0736404	−	0.274830i
$761$	12.3721	+	7.14302i	0.0162576	+	0.00938636i	0.508107	−	0.861294i	$-0.330346\pi$
$761$	12.3721	+	7.14302i	0.0162576	+	0.00938636i	−0.491849	+	0.870680i	$0.663679\pi$
$762$		0			0
$763$	−521.446	−	521.446i	−0.683416	−	0.683416i
$764$	−714.199	−	191.369i	−0.934815	−	0.250483i
$765$		0			0
$766$	258.017			0.336837
$767$		−	914.385i		−	1.19216i
$768$		0			0
$769$	988.203	−	988.203i	1.28505	−	1.28505i	0.347292	−	0.937757i	$-0.387101\pi$
$769$	988.203	−	988.203i	1.28505	−	1.28505i	0.937757	−	0.347292i	$-0.112899\pi$
$770$	−937.821	+	541.451i	−1.21795	+	0.703183i
$771$		0			0
$772$	105.696	+	28.3212i	0.136912	+	0.0366855i
$773$	−456.280	−	790.300i	−0.590272	−	1.02238i	−0.994196	−	0.107588i	$-0.965687\pi$
$773$	−456.280	−	790.300i	−0.590272	−	1.02238i	0.403924	−	0.914793i	$-0.367646\pi$
$774$		0			0
$775$	−147.011	+	39.3915i	−0.189692	+	0.0508278i
$776$		−	387.975i		−	0.499967i
$777$		0			0
$778$	494.003			0.634965
$779$	−90.7731	−	338.770i	−0.116525	−	0.434878i
$780$		0			0
$781$	320.717	−	185.166i	0.410649	−	0.237088i
$782$	538.345	−	2009.13i	0.688420	−	2.56922i
$783$		0			0
$784$	−301.775	−	522.689i	−0.384916	−	0.666695i
$785$	−158.175	−	158.175i	−0.201496	−	0.201496i
$786$		0			0
$787$	−119.620			−0.151995			−0.0759976	−	0.997108i	$-0.524214\pi$
$787$	−119.620			−0.151995			−0.0759976	+	0.997108i	$0.524214\pi$
$788$			634.620i			0.805356i
$789$		0			0
$790$	−352.168	+	1314.31i	−0.445782	+	1.66368i
$791$	−649.134	+	649.134i	−0.820650	+	0.820650i
$792$		0			0
$793$	179.705	−	311.258i	0.226614	−	0.392507i
$794$	436.604	−	116.988i	0.549879	−	0.147340i
$795$		0			0
$796$	81.8639	−	305.520i	0.102844	−	0.383819i
$797$	−93.8133	−	350.116i	−0.117708	−	0.439292i	0.881767	−	0.471685i	$-0.156354\pi$
$797$	−93.8133	−	350.116i	−0.117708	−	0.439292i	−0.999475	+	0.0323926i	$0.989687\pi$
$798$		0			0
$799$	615.453	−	164.910i	0.770279	−	0.206396i
$800$	1056.03	+	1056.03i	1.32004	+	1.32004i
$801$		0			0
$802$	−1049.85	−	606.132i	−1.30904	−	0.755775i
$803$	612.684			0.762993
$804$		0			0
$805$	2260.63	+	1305.17i	2.80823	+	1.62133i
$806$	76.6949	−	76.6949i	0.0951550	−	0.0951550i
$807$		0			0
$808$	206.279	−	206.279i	0.255295	−	0.255295i
$809$	1117.68	+	299.480i	1.38155	+	0.370186i	0.871685	−	0.490067i	$-0.163028\pi$
$809$	1117.68	+	299.480i	1.38155	+	0.370186i	0.509868	+	0.860253i	$0.329694\pi$
$810$		0			0
$811$	376.535	+	652.177i	0.464284	+	0.804164i	0.999169	−	0.0407609i	$-0.0129782\pi$
$811$	376.535	+	652.177i	0.464284	+	0.804164i	−0.534884	+	0.844925i	$0.679645\pi$
$812$	1136.34	−	304.481i	1.39943	−	0.374976i
$813$		0			0
$814$	338.411	−	448.718i	0.415739	−	0.551251i
$815$	449.151			0.551106
$816$		0			0
$817$	−333.669	+	192.644i	−0.408408	+	0.235794i
$818$	199.967	−	115.451i	0.244458	−	0.141138i
$819$		0			0
$820$	592.248	+	592.248i	0.722254	+	0.722254i
$821$	−493.496	−	854.759i	−0.601091	−	1.04112i	−0.992656	−	0.120970i	$-0.961400\pi$
$821$	−493.496	−	854.759i	−0.601091	−	1.04112i	0.391565	−	0.920150i	$-0.371934\pi$
$822$		0			0
$823$	−71.1678	+	123.266i	−0.0864736	+	0.149777i	−0.906018	−	0.423239i	$-0.860893\pi$
$823$	−71.1678	+	123.266i	−0.0864736	+	0.149777i	0.819545	+	0.573015i	$0.194226\pi$
$824$	−457.417			−0.555118
$825$		0			0
$826$	−1050.69	+	1819.85i	−1.27202	+	2.20321i
$827$	−209.939	+	783.504i	−0.253856	+	0.947405i	0.714867	+	0.699261i	$0.246487\pi$
$827$	−209.939	+	783.504i	−0.253856	+	0.947405i	−0.968723	+	0.248144i	$0.920179\pi$
$828$		0			0
$829$	−210.761	−	786.572i	−0.254236	−	0.948820i	−0.968514	−	0.248958i	$-0.919912\pi$
$829$	−210.761	−	786.572i	−0.254236	−	0.948820i	0.714279	−	0.699861i	$-0.246755\pi$
$830$	105.743	−	183.152i	0.127401	−	0.220665i
$831$		0			0
$832$	−268.077	−	71.8311i	−0.322208	−	0.0863355i
$833$	−176.231	+	657.704i	−0.211562	+	0.789561i
$834$		0			0
$835$	42.2807	+	24.4108i	0.0506355	+	0.0292344i
$836$	−160.569	+	43.0243i	−0.192068	+	0.0514645i
$837$		0			0
$838$	−199.843	−	53.5476i	−0.238476	−	0.0638993i
$839$	531.184	+	306.679i	0.633116	+	0.365530i	0.781958	−	0.623331i	$-0.214221\pi$
$839$	531.184	+	306.679i	0.633116	+	0.365530i	−0.148842	+	0.988861i	$0.547555\pi$
$840$		0			0
$841$		−	1139.17i		−	1.35454i
$842$	830.551	+	479.519i	0.986403	+	0.569500i
$843$		0			0
$844$	−50.2298	+	29.0002i	−0.0595140	+	0.0343604i
$845$	−353.939	+	353.939i	−0.418862	+	0.418862i
$846$		0			0
$847$	393.991	+	682.412i	0.465161	+	0.805682i
$848$	776.581	+	1345.08i	0.915779	+	1.58618i
$849$		0			0
$850$		−	2162.50i		−	2.54412i
$851$	−1344.60	−	165.635i	−1.58002	−	0.194636i
$852$		0			0
$853$	−203.897	−	760.953i	−0.239035	−	0.892090i	−0.976288	−	0.216474i	$-0.930544\pi$
$853$	−203.897	−	760.953i	−0.239035	−	0.892090i	0.737254	−	0.675616i	$-0.236122\pi$
$854$	−715.313	+	412.986i	−0.837603	+	0.483590i
$855$		0			0
$856$	−108.010	+	403.098i	−0.126180	+	0.470909i
$857$	−823.091	−	823.091i	−0.960433	−	0.960433i	0.0388134	−	0.999246i	$-0.487642\pi$
$857$	−823.091	−	823.091i	−0.960433	−	0.960433i	−0.999246	+	0.0388134i	$0.987642\pi$
$858$		0			0
$859$	−686.679	−	686.679i	−0.799394	−	0.799394i	0.183606	−	0.983000i	$-0.441223\pi$
$859$	−686.679	−	686.679i	−0.799394	−	0.799394i	−0.983000	+	0.183606i	$0.941223\pi$
$860$	460.059	−	796.845i	0.534952	−	0.926564i
$861$		0			0
$862$		−	1632.99i		−	1.89442i
$863$	−1.99255	+	3.45121i	−0.00230887	+	0.00399908i	−0.867178	−	0.497999i	$-0.834068\pi$
$863$	−1.99255	+	3.45121i	−0.00230887	+	0.00399908i	0.864869	+	0.501998i	$0.167402\pi$
$864$		0			0
$865$	−909.443	+	909.443i	−1.05138	+	1.05138i
$866$	218.602	+	815.834i	0.252427	+	0.942071i
$867$		0			0
$868$	−102.096	+	27.3566i	−0.117622	+	0.0315168i
$869$	−361.974	−	96.9908i	−0.416541	−	0.111612i
$870$		0			0
$871$	−49.0702	−	183.132i	−0.0563377	−	0.210255i
$872$	−197.801	−	114.201i	−0.226837	−	0.130964i
$873$		0			0
$874$	668.194	+	668.194i	0.764524	+	0.764524i
$875$	899.850	+	241.114i	1.02840	+	0.275559i
$876$		0			0
$877$	−554.373			−0.632124			−0.316062	−	0.948738i	$-0.602361\pi$
$877$	−554.373			−0.632124			−0.316062	+	0.948738i	$0.602361\pi$
$878$		−	1781.35i		−	2.02887i
$879$		0			0
$880$	−618.443	+	618.443i	−0.702776	+	0.702776i
$881$	−563.395	+	325.276i	−0.639495	+	0.369212i	−0.784420	−	0.620230i	$-0.787039\pi$
$881$	−563.395	+	325.276i	−0.639495	+	0.369212i	0.144925	+	0.989443i	$0.453706\pi$
$882$		0			0
$883$	−728.740	−	195.265i	−0.825301	−	0.221139i	−0.178638	−	0.983915i	$-0.557169\pi$
$883$	−728.740	−	195.265i	−0.825301	−	0.221139i	−0.646663	+	0.762776i	$0.723836\pi$
$884$	326.745	+	565.940i	0.369622	+	0.640203i
$885$		0			0
$886$	1424.19	−	381.609i	1.60743	−	0.430710i
$887$			949.283i			1.07022i	0.844783	+	0.535109i	$0.179729\pi$
$887$			949.283i			1.07022i	−0.844783	+	0.535109i	$0.820271\pi$
$888$		0			0
$889$	−881.567			−0.991639
$890$	178.423	+	665.884i	0.200476	+	0.748185i
$891$		0			0
$892$	297.071	−	171.514i	0.333039	−	0.192280i
$893$	−74.9206	+	279.607i	−0.0838976	+	0.313110i
$894$		0			0
$895$	−127.861	−	221.461i	−0.142861	−	0.247442i
$896$	−545.132	−	545.132i	−0.608406	−	0.608406i
$897$		0			0
$898$	−535.589			−0.596425
$899$			177.912i			0.197900i
$900$		0			0
$901$	453.510	−	1692.52i	0.503341	−	1.87849i
$902$	−384.659	+	384.659i	−0.426451	+	0.426451i
$903$		0			0
$904$	−142.165	+	246.237i	−0.157262	+	0.272387i
$905$	427.337	−	114.505i	0.472196	−	0.126524i
$906$		0			0
$907$	−43.2883	+	161.554i	−0.0477269	+	0.178119i	−0.985675	−	0.168657i	$-0.946057\pi$
$907$	−43.2883	+	161.554i	−0.0477269	+	0.178119i	0.937948	+	0.346776i	$0.112724\pi$
$908$	114.492	+	427.291i	0.126093	+	0.470584i
$909$		0			0
$910$	−1868.14	+	500.566i	−2.05290	+	0.550072i
$911$	848.443	+	848.443i	0.931331	+	0.931331i	0.997789	−	0.0664580i	$-0.0211698\pi$
$911$	848.443	+	848.443i	0.931331	+	0.931331i	−0.0664580	+	0.997789i	$0.521170\pi$
$912$		0			0
$913$	50.4420	+	29.1227i	0.0552486	+	0.0318978i
$914$	2007.54			2.19643
$915$		0			0
$916$	753.063	+	434.781i	0.822121	+	0.474652i
$917$	1117.97	−	1117.97i	1.21916	−	1.21916i
$918$		0			0
$919$	−205.760	+	205.760i	−0.223896	+	0.223896i	−0.810137	−	0.586241i	$-0.800607\pi$
$919$	−205.760	+	205.760i	−0.223896	+	0.223896i	0.586241	+	0.810137i	$0.300607\pi$
$920$	780.937	+	209.251i	0.848844	+	0.227447i
$921$		0			0
$922$	728.814	+	1262.34i	0.790470	+	1.36913i
$923$	638.867	−	171.184i	0.692163	−	0.185465i
$924$		0			0
$925$	−1394.86	+	195.474i	−1.50796	+	0.211323i
$926$	−2217.54			−2.39476
$927$		0			0
$928$	1511.89	−	872.889i	1.62919	−	0.940613i
$929$	514.166	−	296.854i	0.553462	−	0.319541i	−0.197055	−	0.980392i	$-0.563138\pi$
$929$	514.166	−	296.854i	0.553462	−	0.319541i	0.750517	+	0.660851i	$0.229804\pi$
$930$		0			0
$931$	−218.739	−	218.739i	−0.234950	−	0.234950i
$932$	219.533	+	380.242i	0.235550	+	0.407985i
$933$		0			0
$934$	−1039.40	+	1800.29i	−1.11285	+	1.92751i
$935$	986.708			1.05530
$936$		0			0
$937$	−722.546	+	1251.49i	−0.771127	+	1.33563i	0.165818	+	0.986156i	$0.446973\pi$
$937$	−722.546	+	1251.49i	−0.771127	+	1.33563i	−0.936946	+	0.349475i	$0.886360\pi$
$938$	−112.770	+	420.863i	−0.120224	+	0.448681i
$939$		0			0
$940$	−178.920	−	667.739i	−0.190340	−	0.710360i
$941$	162.435	−	281.346i	0.172620	−	0.298987i	−0.766715	−	0.641988i	$-0.778110\pi$
$941$	162.435	−	281.346i	0.172620	−	0.298987i	0.939335	+	0.343001i	$0.111443\pi$
$942$		0			0
$943$	1266.61	+	339.388i	1.34317	+	0.359902i
$944$	−439.264	+	1639.36i	−0.465322	+	1.73661i
$945$		0			0
$946$	517.543	+	298.804i	0.547086	+	0.315860i
$947$	−183.919	+	49.2811i	−0.194213	+	0.0520391i	−0.354614	−	0.935013i	$-0.615388\pi$
$947$	−183.919	+	49.2811i	−0.194213	+	0.0520391i	0.160401	+	0.987052i	$0.448721\pi$
$948$		0			0
$949$	1056.95	+	283.210i	1.11375	+	0.298430i
$950$	850.826	+	491.224i	0.895606	+	0.517078i
$951$		0			0
$952$			538.036i			0.565164i
$953$	−1072.60	−	619.267i	−1.12550	−	0.649808i	−0.182701	−	0.983169i	$-0.558484\pi$
$953$	−1072.60	−	619.267i	−1.12550	−	0.649808i	−0.942799	+	0.333361i	$0.891817\pi$
$954$		0			0
$955$	−1726.76	+	996.943i	−1.80812	+	1.04392i
$956$	403.745	−	403.745i	0.422328	−	0.422328i
$957$		0			0
$958$	−961.313	−	1665.04i	−1.00346	−	1.73804i
$959$	895.011	+	1550.20i	0.933275	+	1.61648i
$960$		0			0
$961$			945.015i			0.983366i
$962$	791.217	−	617.664i	0.822471	−	0.642062i
$963$		0			0
$964$	259.289	+	967.680i	0.268972	+	1.00382i
$965$	255.547	−	147.540i	0.264816	−	0.152891i
$966$		0			0
$967$	−376.545	+	1405.29i	−0.389395	+	1.45324i	0.441725	+	0.897150i	$0.354367\pi$
$967$	−376.545	+	1405.29i	−0.389395	+	1.45324i	−0.831121	+	0.556092i	$0.812300\pi$
$968$	172.574	+	172.574i	0.178279	+	0.178279i
$969$		0			0
$970$	2064.98	+	2064.98i	2.12885	+	2.12885i
$971$	410.709	−	711.368i	0.422975	−	0.732614i	−0.573254	−	0.819378i	$-0.694319\pi$
$971$	410.709	−	711.368i	0.422975	−	0.732614i	0.996229	+	0.0867637i	$0.0276525\pi$
$972$		0			0
$973$			1593.02i			1.63723i
$974$	−78.6948	+	136.303i	−0.0807955	+	0.139942i
$975$		0			0
$976$	−471.711	+	471.711i	−0.483310	+	0.483310i
$977$	−15.3995	−	57.4717i	−0.0157620	−	0.0588247i	0.957597	−	0.288111i	$-0.0930273\pi$
$977$	−15.3995	−	57.4717i	−0.0157620	−	0.0588247i	−0.973359	+	0.229287i	$0.926361\pi$
$978$		0			0
$979$	−183.392	+	49.1397i	−0.187326	+	0.0501937i
$980$	713.579	+	191.203i	0.728142	+	0.195105i
$981$		0			0
$982$	280.105	+	1045.37i	0.285239	+	1.06453i
$983$	−450.826	−	260.285i	−0.458623	−	0.264786i	0.252842	−	0.967508i	$-0.418635\pi$
$983$	−450.826	−	260.285i	−0.458623	−	0.264786i	−0.711465	+	0.702722i	$0.751968\pi$
$984$		0			0
$985$	1210.11	+	1210.11i	1.22854	+	1.22854i
$986$	−2441.73	−	654.260i	−2.47640	−	0.663550i
$987$		0			0
$988$	−296.888			−0.300494
$989$		−	1440.54i		−	1.45656i
$990$		0			0
$991$	608.226	−	608.226i	0.613750	−	0.613750i	−0.330171	−	0.943921i	$-0.607107\pi$
$991$	608.226	−	608.226i	0.613750	−	0.613750i	0.943921	+	0.330171i	$0.107107\pi$
$992$	−135.838	+	78.4262i	−0.136934	+	0.0790587i
$993$		0			0
$994$	−1468.20	−	393.403i	−1.47706	−	0.395778i
$995$	−426.473	−	738.672i	−0.428616	−	0.742384i
$996$		0			0
$997$	−1326.39	+	355.406i	−1.33038	+	0.356476i	−0.852859	−	0.522142i	$-0.825133\pi$
$997$	−1326.39	+	355.406i	−1.33038	+	0.356476i	−0.477526	+	0.878618i	$0.658466\pi$
$998$			913.891i			0.915723i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.3.bb.b.208.5		24
3.2	odd	2		111.3.l.b.97.2	✓	24
37.29	odd	12	inner	333.3.bb.b.325.5		24
111.29	even	12		111.3.l.b.103.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.3.l.b.97.2	✓	24	3.2	odd	2
111.3.l.b.103.2	yes	24	111.29	even	12
333.3.bb.b.208.5		24	1.1	even	1	trivial
333.3.bb.b.325.5		24	37.29	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)

\(f(q)\)	\(=\)	\(q+(0.682073 + 2.54553i) q^{2} +(-2.55040 + 1.47247i) q^{4} +(-2.05541 + 7.67090i) q^{5} +(4.48853 + 7.77437i) q^{7} +(1.96605 + 1.96605i) q^{8} +O(q^{10})\)	\(q+(0.682073 + 2.54553i) q^{2} +(-2.55040 + 1.47247i) q^{4} +(-2.05541 + 7.67090i) q^{5} +(4.48853 + 7.77437i) q^{7} +(1.96605 + 1.96605i) q^{8} -20.9284 q^{10} -5.76392i q^{11} +(2.66434 - 9.94345i) q^{13} +(-16.7284 + 16.7284i) q^{14} +(-9.55354 + 16.5472i) q^{16} +(20.8215 - 5.57911i) q^{17} +(-2.53465 + 9.45945i) q^{19} +(-6.05308 - 22.5904i) q^{20} +(14.6722 - 3.93141i) q^{22} +(-25.8908 - 25.8908i) q^{23} +(-32.9673 - 19.0337i) q^{25} +27.1286 q^{26} +(-22.8951 - 13.2185i) q^{28} +(-31.4656 + 31.4656i) q^{29} +(2.82708 - 2.82708i) q^{31} +(-37.8950 - 10.1539i) q^{32} +(28.4036 + 49.1964i) q^{34} +(-68.8622 + 18.4516i) q^{35} +(29.1654 - 22.7680i) q^{37} -25.8081 q^{38} +(-19.1224 + 11.0403i) q^{40} +(-31.0148 + 17.9064i) q^{41} +(27.8194 + 27.8194i) q^{43} +(8.48722 + 14.7003i) q^{44} +(48.2465 - 83.5653i) q^{46} +29.5585 q^{47} +(-15.7939 + 27.3558i) q^{49} +(25.9647 - 96.9017i) q^{50} +(7.84634 + 29.2830i) q^{52} +(40.6436 - 70.3968i) q^{53} +(44.2144 + 11.8472i) q^{55} +(-6.46010 + 24.1094i) q^{56} +(-101.559 - 58.6348i) q^{58} +(85.7984 - 22.9896i) q^{59} +(33.7241 + 9.03634i) q^{61} +(9.12470 + 5.26815i) q^{62} -26.9602i q^{64} +(70.7989 + 40.8758i) q^{65} +(15.9499 - 9.20869i) q^{67} +(-44.8881 + 44.8881i) q^{68} +(-93.9380 - 162.705i) q^{70} +(32.1250 + 55.6421i) q^{71} +106.296i q^{73} +(77.8494 + 58.7120i) q^{74} +(-7.46442 - 27.8576i) q^{76} +(44.8108 - 25.8715i) q^{77} +(16.8272 - 62.8001i) q^{79} +(-107.296 - 107.296i) q^{80} +(-66.7357 - 66.7357i) q^{82} +(-5.05258 + 8.75133i) q^{83} +171.187i q^{85} +(-51.8403 + 89.7901i) q^{86} +(11.3321 - 11.3321i) q^{88} +(-8.52539 - 31.8172i) q^{89} +(89.2631 - 23.9180i) q^{91} +(104.156 + 27.9084i) q^{92} +(20.1611 + 75.2421i) q^{94} +(-67.3527 - 38.8861i) q^{95} +(-98.6688 - 98.6688i) q^{97} +(-80.4075 - 21.5451i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8}+O(q^{10}) \) 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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