LMFDB - Embedded newform 207.4.i.b.127.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,4,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, 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:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.5
Character	$\chi$	$=$	207.127
Dual form			207.4.i.b.163.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.39601 - 1.53982i) q^{2} +(0.0464818 - 0.101781i) q^{4} +(1.22325 - 0.359177i) q^{5} +(-1.84765 - 2.13230i) q^{7} +(3.19731 + 22.2377i) q^{8} +O(q^{10})$	\(q+(2.39601 - 1.53982i) q^{2} +(0.0464818 - 0.101781i) q^{4} +(1.22325 - 0.359177i) q^{5} +(-1.84765 - 2.13230i) q^{7} +(3.19731 + 22.2377i) q^{8} +(2.37784 - 2.74417i) q^{10} +(46.9103 + 30.1474i) q^{11} +(41.6560 - 48.0736i) q^{13} +(-7.71035 - 2.26396i) q^{14} +(42.4891 + 49.0350i) q^{16} +(43.6303 + 95.5370i) q^{17} +(21.0526 - 46.0988i) q^{19} +(0.0203012 - 0.141198i) q^{20} +158.819 q^{22} +(41.4645 - 102.214i) q^{23} +(-103.789 + 66.7014i) q^{25} +(25.7834 - 179.327i) q^{26} +(-0.302910 + 0.0889424i) q^{28} +(25.6108 + 56.0799i) q^{29} +(25.6432 + 178.352i) q^{31} +(4.85820 + 1.42650i) q^{32} +(251.648 + 161.724i) q^{34} +(-3.02601 - 1.94470i) q^{35} +(-6.66337 - 1.95654i) q^{37} +(-20.5417 - 142.870i) q^{38} +(11.8984 + 26.0538i) q^{40} +(182.253 - 53.5143i) q^{41} +(23.4578 - 163.152i) q^{43} +(5.24891 - 3.37327i) q^{44} +(-58.0419 - 308.753i) q^{46} -347.894 q^{47} +(47.6811 - 331.629i) q^{49} +(-145.972 + 319.634i) q^{50} +(-2.95673 - 6.47433i) q^{52} +(-175.609 - 202.664i) q^{53} +(68.2111 + 20.0286i) q^{55} +(41.5101 - 47.9052i) q^{56} +(147.717 + 94.9317i) q^{58} +(-260.298 + 300.400i) q^{59} +(-53.6466 - 373.120i) q^{61} +(336.072 + 387.847i) q^{62} +(-484.199 + 142.174i) q^{64} +(33.6886 - 73.7677i) q^{65} +(-620.815 + 398.974i) q^{67} +11.7518 q^{68} -10.2448 q^{70} +(535.845 - 344.367i) q^{71} +(87.3936 - 191.365i) q^{73} +(-18.9782 + 5.57250i) q^{74} +(-3.71342 - 4.28551i) q^{76} +(-22.3905 - 155.729i) q^{77} +(-99.3022 + 114.601i) q^{79} +(69.5868 + 44.7207i) q^{80} +(354.277 - 408.857i) q^{82} +(-231.505 - 67.9759i) q^{83} +(87.6853 + 101.194i) q^{85} +(-195.020 - 427.035i) q^{86} +(-520.425 + 1139.57i) q^{88} +(-225.970 + 1571.65i) q^{89} -179.473 q^{91} +(-8.47608 - 8.97138i) q^{92} +(-833.556 + 535.694i) q^{94} +(9.19488 - 63.9518i) q^{95} +(534.312 - 156.888i) q^{97} +(-396.405 - 868.006i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8}+O(q^{10}) $ 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8	$ 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8} - 78 q^{10} - 10 q^{11} + 50 q^{13} + 224 q^{14} + 260 q^{16} + 662 q^{17} - 4 q^{19} + 735 q^{20} + 622 q^{22} + 438 q^{23} - 754 q^{25} + 40 q^{26} + 672 q^{28} - 1302 q^{29} + 1528 q^{31} - 1588 q^{32} + 29 q^{34} - 950 q^{35} + 316 q^{37} - 3122 q^{38} - 1939 q^{40} + 1500 q^{41} - 1316 q^{43} + 2901 q^{44} - 1980 q^{46} + 1440 q^{47} - 2310 q^{49} - 195 q^{50} + 6189 q^{52} + 148 q^{53} - 606 q^{55} + 432 q^{56} - 2623 q^{58} - 5264 q^{59} + 1482 q^{61} + 2299 q^{62} - 6780 q^{64} + 1446 q^{65} + 388 q^{67} - 5604 q^{68} + 2984 q^{70} + 3316 q^{71} + 2072 q^{73} + 6556 q^{74} + 9841 q^{76} - 9338 q^{77} + 268 q^{79} - 7980 q^{80} + 7742 q^{82} + 3494 q^{83} - 3842 q^{85} + 4792 q^{86} - 7960 q^{88} + 2754 q^{89} - 5436 q^{91} + 17609 q^{92} - 10961 q^{94} + 2396 q^{95} - 5654 q^{97} - 14411 q^{98}+O(q^{100}) $ 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8 - 78 * q^10 - 10 * q^11 + 50 * q^13 + 224 * q^14 + 260 * q^16 + 662 * q^17 - 4 * q^19 + 735 * q^20 + 622 * q^22 + 438 * q^23 - 754 * q^25 + 40 * q^26 + 672 * q^28 - 1302 * q^29 + 1528 * q^31 - 1588 * q^32 + 29 * q^34 - 950 * q^35 + 316 * q^37 - 3122 * q^38 - 1939 * q^40 + 1500 * q^41 - 1316 * q^43 + 2901 * q^44 - 1980 * q^46 + 1440 * q^47 - 2310 * q^49 - 195 * q^50 + 6189 * q^52 + 148 * q^53 - 606 * q^55 + 432 * q^56 - 2623 * q^58 - 5264 * q^59 + 1482 * q^61 + 2299 * q^62 - 6780 * q^64 + 1446 * q^65 + 388 * q^67 - 5604 * q^68 + 2984 * q^70 + 3316 * q^71 + 2072 * q^73 + 6556 * q^74 + 9841 * q^76 - 9338 * q^77 + 268 * q^79 - 7980 * q^80 + 7742 * q^82 + 3494 * q^83 - 3842 * q^85 + 4792 * q^86 - 7960 * q^88 + 2754 * q^89 - 5436 * q^91 + 17609 * q^92 - 10961 * q^94 + 2396 * q^95 - 5654 * q^97 - 14411 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	2.39601	−	1.53982i	0.847116	−	0.544409i	−0.0435579	−	0.999051i	$-0.513869\pi$
$2$	2.39601	−	1.53982i	0.847116	−	0.544409i	0.890674	+	0.454642i	$0.150233\pi$
$3$		0			0
$3$		0			0
$4$	0.0464818	−	0.101781i	0.00581022	−	0.0127226i
$5$	1.22325	−	0.359177i	0.109410	−	0.0321258i	−0.226569	−	0.973995i	$-0.572751\pi$
$5$	1.22325	−	0.359177i	0.109410	−	0.0321258i	0.335979	+	0.941869i	$0.390933\pi$
$6$		0			0
$7$	−1.84765	−	2.13230i	−0.0997638	−	0.115134i	0.703672	−	0.710525i	$-0.251542\pi$
$7$	−1.84765	−	2.13230i	−0.0997638	−	0.115134i	−0.803436	+	0.595391i	$0.796997\pi$
$8$	3.19731	+	22.2377i	0.141302	+	0.982779i
$9$		0			0
$10$	2.37784	−	2.74417i	0.0751938	−	0.0867782i
$11$	46.9103	+	30.1474i	1.28582	+	0.826345i	0.991594	−	0.129391i	$-0.0413023\pi$
$11$	46.9103	+	30.1474i	1.28582	+	0.826345i	0.294224	+	0.955736i	$0.404939\pi$
$12$		0			0
$13$	41.6560	−	48.0736i	0.888716	−	1.02563i	−0.110779	−	0.993845i	$-0.535335\pi$
$13$	41.6560	−	48.0736i	0.888716	−	1.02563i	0.999495	−	0.0317875i	$-0.0101200\pi$
$14$	−7.71035	−	2.26396i	−0.147191	−	0.0432193i
$15$		0			0
$16$	42.4891	+	49.0350i	0.663892	+	0.766172i
$17$	43.6303	+	95.5370i	0.622464	+	1.36301i	0.913713	+	0.406360i	$0.133202\pi$
$17$	43.6303	+	95.5370i	0.622464	+	1.36301i	−0.291249	+	0.956647i	$0.594071\pi$
$18$		0			0
$19$	21.0526	−	46.0988i	0.254200	−	0.556621i	−0.738910	−	0.673804i	$-0.764659\pi$
$19$	21.0526	−	46.0988i	0.254200	−	0.556621i	0.993110	+	0.117183i	$0.0373865\pi$
$20$	0.0203012	−	0.141198i	0.000226975	−	0.00157864i
$21$		0			0
$22$	158.819			1.53911
$23$	41.4645	−	102.214i	0.375911	−	0.926656i
$23$	41.4645	−	102.214i	0.375911	−	0.926656i
$24$		0			0
$25$	−103.789	+	66.7014i	−0.830315	+	0.533611i
$26$	25.7834	−	179.327i	0.194482	−	1.35265i
$27$		0			0
$28$	−0.302910	+	0.0889424i	−0.00204445	+	0.000600305i
$29$	25.6108	+	56.0799i	0.163993	+	0.359095i	0.973733	−	0.227694i	$-0.0731187\pi$
$29$	25.6108	+	56.0799i	0.163993	+	0.359095i	−0.809739	+	0.586790i	$0.800391\pi$
$30$		0			0
$31$	25.6432	+	178.352i	0.148569	+	1.03332i	0.918564	+	0.395272i	$0.129350\pi$
$31$	25.6432	+	178.352i	0.148569	+	1.03332i	−0.769995	+	0.638050i	$0.779741\pi$
$32$	4.85820	+	1.42650i	0.0268380	+	0.00788036i
$33$		0			0
$34$	251.648	+	161.724i	1.26933	+	0.815750i
$35$	−3.02601	−	1.94470i	−0.0146140	−	0.00939182i
$36$		0			0
$37$	−6.66337	−	1.95654i	−0.0296068	−	0.00869334i	0.266896	−	0.963725i	$-0.414002\pi$
$37$	−6.66337	−	1.95654i	−0.0296068	−	0.00869334i	−0.296502	+	0.955032i	$0.595820\pi$
$38$	−20.5417	−	142.870i	−0.0876920	−	0.609911i
$39$		0			0
$40$	11.8984	+	26.0538i	0.0470325	+	0.102987i
$41$	182.253	−	53.5143i	0.694223	−	0.203842i	0.0844608	−	0.996427i	$-0.473083\pi$
$41$	182.253	−	53.5143i	0.694223	−	0.203842i	0.609762	+	0.792585i	$0.291265\pi$
$42$		0			0
$43$	23.4578	−	163.152i	0.0831924	−	0.578616i	−0.905002	−	0.425408i	$-0.860130\pi$
$43$	23.4578	−	163.152i	0.0831924	−	0.578616i	0.988194	−	0.153208i	$-0.0489604\pi$
$44$	5.24891	−	3.37327i	0.0179842	−	0.0115577i
$45$		0			0
$46$	−58.0419	−	308.753i	−0.186039	−	0.989634i
$47$	−347.894			−1.07969			−0.539846	−	0.841764i	$-0.681518\pi$
$47$	−347.894			−1.07969			−0.539846	+	0.841764i	$0.681518\pi$
$48$		0			0
$49$	47.6811	−	331.629i	0.139012	−	0.966849i
$50$	−145.972	+	319.634i	−0.412871	+	0.904061i
$51$		0			0
$52$	−2.95673	−	6.47433i	−0.00788509	−	0.0172659i
$53$	−175.609	−	202.664i	−0.455127	−	0.525245i	0.481088	−	0.876672i	$-0.340242\pi$
$53$	−175.609	−	202.664i	−0.455127	−	0.525245i	−0.936215	+	0.351427i	$0.885696\pi$
$54$		0			0
$55$	68.2111	+	20.0286i	0.167229	+	0.0491028i
$56$	41.5101	−	47.9052i	0.0990540	−	0.114314i
$57$		0			0
$58$	147.717	+	94.9317i	0.334416	+	0.214916i
$59$	−260.298	+	300.400i	−0.574372	+	0.662861i	−0.966385	−	0.257099i	$-0.917233\pi$
$59$	−260.298	+	300.400i	−0.574372	+	0.662861i	0.392013	+	0.919960i	$0.371779\pi$
$60$		0			0
$61$	−53.6466	−	373.120i	−0.112602	−	0.783166i	−0.965372	−	0.260879i	$-0.915988\pi$
$61$	−53.6466	−	373.120i	−0.112602	−	0.783166i	0.852769	−	0.522288i	$-0.174921\pi$
$62$	336.072	+	387.847i	0.688405	+	0.794462i
$63$		0			0
$64$	−484.199	+	142.174i	−0.945700	+	0.277683i
$65$	33.6886	−	73.7677i	0.0642855	−	0.140766i
$66$		0			0
$67$	−620.815	+	398.974i	−1.13201	+	0.727498i	−0.965979	−	0.258622i	$-0.916731\pi$
$67$	−620.815	+	398.974i	−1.13201	+	0.727498i	−0.166031	+	0.986121i	$0.553095\pi$
$68$	11.7518			0.0209577
$69$		0			0
$70$	−10.2448			−0.0174927
$71$	535.845	−	344.367i	0.895677	−	0.575617i	−0.00982806	−	0.999952i	$-0.503128\pi$
$71$	535.845	−	344.367i	0.895677	−	0.575617i	0.905505	+	0.424335i	$0.139492\pi$
$72$		0			0
$73$	87.3936	−	191.365i	0.140118	−	0.306817i	−0.826543	−	0.562873i	$-0.809696\pi$
$73$	87.3936	−	191.365i	0.140118	−	0.306817i	0.966662	+	0.256056i	$0.0824233\pi$
$74$	−18.9782	+	5.57250i	−0.0298131	+	0.00875393i
$75$		0			0
$76$	−3.71342	−	4.28551i	−0.00560471	−	0.00646818i
$77$	−22.3905	−	155.729i	−0.0331381	−	0.230480i
$78$		0			0
$79$	−99.3022	+	114.601i	−0.141422	+	0.163210i	−0.822042	−	0.569427i	$-0.807165\pi$
$79$	−99.3022	+	114.601i	−0.141422	+	0.163210i	0.680620	+	0.732637i	$0.261711\pi$
$80$	69.5868	+	44.7207i	0.0972506	+	0.0624991i
$81$		0			0
$82$	354.277	−	408.857i	0.477114	−	0.550619i
$83$	−231.505	−	67.9759i	−0.306156	−	0.0898954i	0.125046	−	0.992151i	$-0.460092\pi$
$83$	−231.505	−	67.9759i	−0.306156	−	0.0898954i	−0.431202	+	0.902256i	$0.641910\pi$
$84$		0			0
$85$	87.6853	+	101.194i	0.111892	+	0.129130i
$86$	−195.020	−	427.035i	−0.244530	−	0.535446i
$87$		0			0
$88$	−520.425	+	1139.57i	−0.630425	+	1.38044i
$89$	−225.970	+	1571.65i	−0.269132	+	1.87185i	0.187596	+	0.982246i	$0.439931\pi$
$89$	−225.970	+	1571.65i	−0.269132	+	1.87185i	−0.456727	+	0.889607i	$0.650979\pi$
$90$		0			0
$91$	−179.473			−0.206746
$92$	−8.47608	−	8.97138i	−0.00960536	−	0.0101666i
$93$		0			0
$94$	−833.556	+	535.694i	−0.914625	+	0.587794i
$95$	9.19488	−	63.9518i	0.00993026	−	0.0690665i
$96$		0			0
$97$	534.312	−	156.888i	0.559291	−	0.164223i	0.0101439	−	0.999949i	$-0.496771\pi$
$97$	534.312	−	156.888i	0.559291	−	0.164223i	0.549147	+	0.835726i	$0.314953\pi$
$98$	−396.405	−	868.006i	−0.408602	−	0.894713i
$99$		0			0
$100$	1.96461	+	13.6642i	0.00196461	+	0.0136642i
$101$	−838.230	−	246.126i	−0.825812	−	0.242480i	−0.158595	−	0.987344i	$-0.550696\pi$
$101$	−838.230	−	246.126i	−0.825812	−	0.242480i	−0.667217	+	0.744864i	$0.732515\pi$
$102$		0			0
$103$	870.540	+	559.462i	0.832785	+	0.535198i	0.886162	−	0.463376i	$-0.153362\pi$
$103$	870.540	+	559.462i	0.832785	+	0.535198i	−0.0533768	+	0.998574i	$0.516998\pi$
$104$	1202.24	+	772.630i	1.13355	+	0.728487i
$105$		0			0
$106$	−732.826	−	215.177i	−0.671494	−	0.197168i
$107$	−106.967	−	743.972i	−0.0966438	−	0.672173i	−0.979339	−	0.202226i	$-0.935182\pi$
$107$	−106.967	−	743.972i	−0.0966438	−	0.672173i	0.882695	−	0.469946i	$-0.155727\pi$
$108$		0			0
$109$	−778.196	−	1704.01i	−0.683832	−	1.49738i	−0.858531	−	0.512761i	$-0.828623\pi$
$109$	−778.196	−	1704.01i	−0.683832	−	1.49738i	0.174699	−	0.984622i	$-0.444105\pi$
$110$	194.275	−	57.0442i	0.168394	−	0.0494450i
$111$		0			0
$112$	26.0525	−	181.199i	0.0219797	−	0.152873i
$113$	719.422	−	462.344i	0.598916	−	0.384900i	−0.205770	−	0.978600i	$-0.565970\pi$
$113$	719.422	−	462.344i	0.598916	−	0.384900i	0.804686	+	0.593700i	$0.202334\pi$
$114$		0			0
$115$	14.0083	−	139.926i	0.0113590	−	0.113462i
$116$	6.89829			0.00552147
$117$		0			0
$118$	−161.114	+	1120.57i	−0.125693	+	0.874214i
$119$	123.100	−	269.552i	0.0948285	−	0.207645i
$120$		0			0
$121$	738.794	+	1617.73i	0.555067	+	1.21543i
$122$	−703.076	−	811.392i	−0.521750	−	0.602131i
$123$		0			0
$124$	19.3448	+	5.68014i	0.0140098	+	0.00411364i
$125$	−207.361	+	239.308i	−0.148376	+	0.171235i
$126$		0			0
$127$	−2047.89	−	1316.10i	−1.43087	−	0.919564i	−0.999852	−	0.0172213i	$-0.994518\pi$
$127$	−2047.89	−	1316.10i	−1.43087	−	0.919564i	−0.431018	−	0.902343i	$-0.641846\pi$
$128$	−967.747	+	1116.84i	−0.668262	+	0.771216i
$129$		0			0
$130$	−32.8709	−	228.622i	−0.0221767	−	0.154242i
$131$	182.506	+	210.623i	0.121722	+	0.140475i	0.813340	−	0.581789i	$-0.197647\pi$
$131$	182.506	+	210.623i	0.121722	+	0.140475i	−0.691618	+	0.722264i	$0.743102\pi$
$132$		0			0
$133$	−137.195	+	40.2840i	−0.0894458	+	0.0262636i
$134$	−873.129	+	1911.89i	−0.562887	+	1.23255i
$135$		0			0
$136$	−1985.03	+	1275.70i	−1.25158	+	0.804341i
$137$	−1755.21			−1.09458			−0.547292	−	0.836942i	$-0.684341\pi$
$137$	−1755.21			−1.09458			−0.547292	+	0.836942i	$0.684341\pi$
$138$		0			0
$139$	2225.25			1.35787			0.678933	−	0.734201i	$-0.262443\pi$
$139$	2225.25			1.35787			0.678933	+	0.734201i	$0.262443\pi$
$140$	−0.338587	+	0.217597i	−0.000204399	+	0.000131359i
$141$		0			0
$142$	753.625	−	1650.21i	0.445372	−	0.975229i
$143$	3403.40	−	999.327i	1.99025	−	0.584391i
$144$		0			0
$145$	51.4709	+	59.4006i	0.0294788	+	0.0340204i
$146$	−85.2724	−	593.083i	−0.0483370	−	0.336191i
$147$		0			0
$148$	−0.508864	+	0.587260i	−0.000282624	+	0.000326166i
$149$	−1834.24	−	1178.79i	−1.00850	−	0.648125i	−0.0714966	−	0.997441i	$-0.522778\pi$
$149$	−1834.24	−	1178.79i	−1.00850	−	0.648125i	−0.937005	+	0.349316i	$0.886414\pi$
$150$		0			0
$151$	1898.87	−	2191.41i	1.02336	−	1.18102i	0.0400302	−	0.999198i	$-0.487255\pi$
$151$	1898.87	−	2191.41i	1.02336	−	1.18102i	0.983331	−	0.181823i	$-0.0581999\pi$
$152$	1092.45	+	320.771i	0.582954	+	0.171171i
$153$		0			0
$154$	−293.442	−	338.651i	−0.153547	−	0.177203i
$155$	95.4280	+	208.958i	0.0494514	+	0.108283i
$156$		0			0
$157$	711.709	−	1558.43i	0.361787	−	0.792203i	−0.637968	−	0.770063i	$-0.720225\pi$
$157$	711.709	−	1558.43i	0.361787	−	0.792203i	0.999755	−	0.0221402i	$-0.00704803\pi$
$158$	−61.4640	+	427.492i	−0.0309482	+	0.215249i
$159$		0			0
$160$	6.45514			0.00318952
$161$	−294.563	+	100.441i	−0.144192	+	0.0491668i
$162$		0			0
$163$	−60.4100	+	38.8232i	−0.0290287	+	0.0186556i	−0.555075	−	0.831801i	$-0.687310\pi$
$163$	−60.4100	+	38.8232i	−0.0290287	+	0.0186556i	0.526046	+	0.850456i	$0.323674\pi$
$164$	3.02471	−	21.0373i	0.00144018	−	0.0100167i
$165$		0			0
$166$	−659.357	+	193.605i	−0.308289	+	0.0905219i
$167$	−316.494	−	693.026i	−0.146653	−	0.321125i	0.822023	−	0.569455i	$-0.192846\pi$
$167$	−316.494	−	693.026i	−0.146653	−	0.321125i	−0.968676	+	0.248330i	$0.920118\pi$
$168$		0			0
$169$	−263.183	−	1830.47i	−0.119792	−	0.833170i
$170$	365.915	+	107.442i	0.165085	+	0.0484733i
$171$		0			0
$172$	−15.5154	−	9.97116i	−0.00687814	−	0.00442031i
$173$	−1416.17	−	910.119i	−0.622368	−	0.399972i	0.191109	−	0.981569i	$-0.438792\pi$
$173$	−1416.17	−	910.119i	−0.622368	−	0.399972i	−0.813477	+	0.581597i	$0.802428\pi$
$174$		0			0
$175$	333.994	+	98.0696i	0.144272	+	0.0423621i
$176$	514.897	+	3581.19i	0.220522	+	1.53376i
$177$		0			0
$178$	1878.64	+	4113.64i	0.791067	+	1.73219i
$179$	4114.00	−	1207.98i	1.71785	−	0.504405i	0.733357	−	0.679844i	$-0.237953\pi$
$179$	4114.00	−	1207.98i	1.71785	−	0.504405i	0.984490	+	0.175439i	$0.0561344\pi$
$180$		0			0
$181$	499.436	−	3473.66i	0.205098	−	1.42649i	−0.583765	−	0.811922i	$-0.698421\pi$
$181$	499.436	−	3473.66i	0.205098	−	1.42649i	0.788864	−	0.614568i	$-0.210670\pi$
$182$	−430.019	+	276.357i	−0.175138	+	0.112555i
$183$		0			0
$184$	2405.58	+	595.268i	0.963815	+	0.238498i
$185$	−8.85369			−0.00351857
$186$		0			0
$187$	−833.485	+	5797.01i	−0.325938	+	2.26695i
$188$	−16.1707	+	35.4089i	−0.00627325	+	0.0137365i
$189$		0			0
$190$	−76.4433	−	167.387i	−0.0291883	−	0.0639135i
$191$	−173.116	−	199.787i	−0.0655826	−	0.0756863i	0.722010	−	0.691882i	$-0.243218\pi$
$191$	−173.116	−	199.787i	−0.0655826	−	0.0756863i	−0.787593	+	0.616196i	$0.788673\pi$
$192$		0			0
$193$	4258.16	+	1250.31i	1.58813	+	0.466317i	0.952212	−	0.305439i	$-0.0988031\pi$
$193$	4258.16	+	1250.31i	1.58813	+	0.466317i	0.635919	+	0.771756i	$0.280621\pi$
$194$	1038.64	−	1198.65i	0.384380	−	0.443598i
$195$		0			0
$196$	−31.5372	−	20.2677i	−0.0114932	−	0.00738620i
$197$	−1272.89	+	1468.99i	−0.460354	+	0.531276i	−0.937703	−	0.347437i	$-0.887052\pi$
$197$	−1272.89	+	1468.99i	−0.460354	+	0.531276i	0.477350	+	0.878713i	$0.341598\pi$
$198$		0			0
$199$	−80.2556	−	558.190i	−0.0285888	−	0.198839i	0.970521	−	0.241015i	$-0.0774802\pi$
$199$	−80.2556	−	558.190i	−0.0285888	−	0.198839i	−0.999110	+	0.0421755i	$0.986571\pi$
$200$	−1815.13	−	2094.78i	−0.641747	−	0.740616i
$201$		0			0
$202$	−2387.39	+	701.002i	−0.831567	+	0.244170i
$203$	72.2594	−	158.226i	0.0249833	−	0.0547059i
$204$		0			0
$205$	203.719	−	130.922i	0.0694066	−	0.0446049i
$206$	2947.29			0.996832
$207$		0			0
$208$	4127.22			1.37582
$209$	2377.35	−	1527.83i	0.786816	−	0.505656i
$210$		0			0
$211$	−1609.73	+	3524.81i	−0.525205	+	1.15004i	0.442227	+	0.896903i	$0.354189\pi$
$211$	−1609.73	+	3524.81i	−0.525205	+	1.15004i	−0.967431	+	0.253134i	$0.918539\pi$
$212$	−28.7899	+	8.45347i	−0.00932688	+	0.00273862i
$213$		0			0
$214$	−1401.88	−	1617.85i	−0.447805	−	0.516795i
$215$	−29.9060	−	208.001i	−0.00948639	−	0.0659793i
$216$		0			0
$217$	332.922	−	384.212i	0.104148	−	0.120194i
$218$	−4488.44	−	2884.54i	−1.39447	−	0.896174i
$219$		0			0
$220$	5.20910	−	6.01163i	0.00159635	−	0.00184229i
$221$	6410.27	+	1882.23i	1.95114	+	0.572906i
$222$		0			0
$223$	2886.28	+	3330.95i	0.866726	+	1.00025i	0.999958	+	0.00916980i	$0.00291888\pi$
$223$	2886.28	+	3330.95i	0.866726	+	1.00025i	−0.133232	+	0.991085i	$0.542536\pi$
$224$	−5.93454	−	12.9948i	−0.00177017	−	0.00387613i
$225$		0			0
$226$	1011.81	−	2215.56i	0.297809	−	0.652110i
$227$	−49.7035	+	345.696i	−0.0145328	+	0.101078i	−0.995797	−	0.0915904i	$-0.970805\pi$
$227$	−49.7035	+	345.696i	−0.0145328	+	0.101078i	0.981264	+	0.192668i	$0.0617140\pi$
$228$		0			0
$229$	381.110			0.109976			0.0549878	−	0.998487i	$-0.482488\pi$
$229$	381.110			0.109976			0.0549878	+	0.998487i	$0.482488\pi$
$230$	−181.897	−	356.834i	−0.0521474	−	0.102300i
$231$		0			0
$232$	−1165.20	+	748.831i	−0.329739	+	0.211910i
$233$	199.995	−	1390.99i	0.0562322	−	0.391103i	−0.942196	−	0.335062i	$-0.891243\pi$
$233$	199.995	−	1390.99i	0.0562322	−	0.391103i	0.998428	−	0.0560418i	$-0.0178480\pi$
$234$		0			0
$235$	−425.560	+	124.956i	−0.118130	+	0.0346860i
$236$	18.4759	+	40.4566i	0.00509609	+	0.0111589i
$237$		0			0
$238$	−120.113	−	835.401i	−0.0327132	−	0.227525i
$239$	6276.54	+	1842.96i	1.69873	+	0.498791i	0.980417	−	0.196932i	$-0.0630979\pi$
$239$	6276.54	+	1842.96i	1.69873	+	0.498791i	0.718310	+	0.695723i	$0.244916\pi$
$240$		0			0
$241$	−5453.87	−	3504.99i	−1.45774	−	0.936831i	−0.998831	−	0.0483465i	$-0.984605\pi$
$241$	−5453.87	−	3504.99i	−1.45774	−	0.936831i	−0.458907	−	0.888484i	$-0.651759\pi$
$242$	4261.17	+	2738.49i	1.13189	+	0.727425i
$243$		0			0
$244$	−40.4701	−	11.8831i	−0.0106182	−	0.00311777i
$245$	−60.7880	−	422.790i	−0.0158514	−	0.110249i
$246$		0			0
$247$	−1339.17	−	2932.37i	−0.344977	−	0.755394i
$248$	−3884.16	+	1140.49i	−0.994535	+	0.292022i
$249$		0			0
$250$	−128.348	+	892.683i	−0.0324699	+	0.225833i
$251$	−4691.86	+	3015.28i	−1.17987	+	0.758257i	−0.975363	−	0.220607i	$-0.929196\pi$
$251$	−4691.86	+	3015.28i	−1.17987	+	0.758257i	−0.204509	+	0.978865i	$0.565560\pi$
$252$		0			0
$253$	5026.60	−	3544.84i	1.24909	−	0.880879i
$254$	−6933.30			−1.71273
$255$		0			0
$256$	−24.4544	+	170.084i	−0.00597032	+	0.0415245i
$257$	−796.469	+	1744.02i	−0.193317	+	0.423304i	−0.981324	−	0.192361i	$-0.938385\pi$
$257$	−796.469	+	1744.02i	−0.193317	+	0.423304i	0.788008	+	0.615666i	$0.211113\pi$
$258$		0			0
$259$	8.13965	+	17.8233i	0.00195279	+	0.00427602i
$260$	−5.94224	−	6.85771i	−0.00141739	−	0.00163576i
$261$		0			0
$262$	761.607	+	223.628i	0.179589	+	0.0527320i
$263$	−1149.84	+	1326.98i	−0.269589	+	0.311123i	−0.874361	−	0.485276i	$-0.838719\pi$
$263$	−1149.84	+	1326.98i	−0.269589	+	0.311123i	0.604771	+	0.796399i	$0.293264\pi$
$264$		0			0
$265$	−287.605	−	184.833i	−0.0666696	−	0.0428459i
$266$	−266.689	+	307.776i	−0.0614728	+	0.0709434i
$267$		0			0
$268$	11.7513	+	81.7321i	0.00267845	+	0.0186290i
$269$	3251.77	+	3752.74i	0.737040	+	0.850590i	0.993245	−	0.116033i	$-0.0370177\pi$
$269$	3251.77	+	3752.74i	0.737040	+	0.850590i	−0.256205	+	0.966622i	$0.582472\pi$
$270$		0			0
$271$	−3785.62	+	1111.56i	−0.848561	+	0.249160i	−0.676972	−	0.736009i	$-0.736708\pi$
$271$	−3785.62	+	1111.56i	−0.848561	+	0.249160i	−0.171589	+	0.985169i	$0.554890\pi$
$272$	−2830.85	+	6198.69i	−0.631049	+	1.38180i
$273$		0			0
$274$	−4205.50	+	2702.71i	−0.927240	+	0.595901i
$275$	−6879.67			−1.50858
$276$		0			0
$277$	−5135.37			−1.11391			−0.556957	−	0.830541i	$-0.688031\pi$
$277$	−5135.37			−1.11391			−0.556957	+	0.830541i	$0.688031\pi$
$278$	5331.71	−	3426.48i	1.15027	−	0.739233i
$279$		0			0
$280$	33.5706	−	73.5094i	0.00716510	−	0.0156894i
$281$	78.9165	−	23.1720i	0.0167536	−	0.00491930i	−0.273345	−	0.961916i	$-0.588130\pi$
$281$	78.9165	−	23.1720i	0.0167536	−	0.00491930i	0.290099	+	0.956997i	$0.406312\pi$
$282$		0			0
$283$	−5265.78	−	6077.03i	−1.10607	−	1.27647i	−0.957772	−	0.287530i	$-0.907166\pi$
$283$	−5265.78	−	6077.03i	−1.10607	−	1.27647i	−0.148299	−	0.988943i	$-0.547380\pi$
$284$	−10.1429	−	70.5455i	−0.00211927	−	0.0147398i
$285$		0			0
$286$	6615.77	−	7635.01i	1.36783	−	1.57856i
$287$	−450.849	−	289.743i	−0.0927274	−	0.0595923i
$288$		0			0
$289$	−4006.38	+	4623.61i	−0.815466	+	0.941097i
$290$	214.791	+	63.0683i	0.0434930	+	0.0127707i
$291$		0			0
$292$	−15.4151	−	17.7900i	−0.00308939	−	0.00356534i
$293$	−3574.59	−	7827.25i	−0.712729	−	1.56066i	−0.823822	−	0.566849i	$-0.808162\pi$
$293$	−3574.59	−	7827.25i	−0.712729	−	1.56066i	0.111093	−	0.993810i	$-0.464565\pi$
$294$		0			0
$295$	−210.512	+	460.957i	−0.0415474	+	0.0909761i
$296$	22.2043	−	154.434i	0.00436012	−	0.0303253i
$297$		0			0
$298$	−6209.98			−1.20716
$299$	−3186.55	−	6251.18i	−0.616331	−	1.20908i
$300$		0			0
$301$	−391.232	+	251.430i	−0.0749178	+	0.0481467i
$302$	1175.32	−	8174.54i	0.223948	−	1.55759i
$303$		0			0
$304$	3154.96	−	926.381i	0.595229	−	0.174775i
$305$	−199.639	−	437.149i	−0.0374797	−	0.0820691i
$306$		0			0
$307$	795.115	+	5530.14i	0.147816	+	1.02808i	0.919785	+	0.392424i	$0.128363\pi$
$307$	795.115	+	5530.14i	0.147816	+	1.02808i	−0.771968	+	0.635661i	$0.780728\pi$
$308$	−16.8910	−	4.95964i	−0.00312485	−	0.000917538i
$309$		0			0
$310$	550.404	+	353.723i	0.100841	+	0.0648069i
$311$	1603.24	+	1030.34i	0.292320	+	0.187863i	0.678579	−	0.734528i	$-0.262596\pi$
$311$	1603.24	+	1030.34i	0.292320	+	0.187863i	−0.386258	+	0.922391i	$0.626233\pi$
$312$		0			0
$313$	−8410.04	−	2469.41i	−1.51873	−	0.445941i	−0.587154	−	0.809475i	$-0.699752\pi$
$313$	−8410.04	−	2469.41i	−1.51873	−	0.445941i	−0.931581	+	0.363535i	$0.881570\pi$
$314$	−694.435	−	4829.90i	−0.124807	−	0.868048i
$315$		0			0
$316$	7.04843	+	15.4339i	0.00125476	+	0.00274755i
$317$	−6935.87	+	2036.55i	−1.22889	+	0.360834i	−0.830830	−	0.556527i	$-0.812134\pi$
$317$	−6935.87	+	2036.55i	−1.22889	+	0.360834i	−0.398057	+	0.917360i	$0.630316\pi$
$318$		0			0
$319$	−489.252	+	3402.83i	−0.0858711	+	0.597247i
$320$	−541.228	+	347.826i	−0.0945487	+	0.0607627i
$321$		0			0
$322$	−551.114	+	694.231i	−0.0953801	+	0.120149i
$323$	5322.68			0.916909
$324$		0			0
$325$	−1116.88	+	7768.05i	−0.190625	+	1.32583i
$326$	−84.9622	+	186.041i	−0.0144344	+	0.0316070i
$327$		0			0
$328$	1772.76	+	3881.79i	0.298427	+	0.653464i
$329$	642.787	+	741.815i	0.107714	+	0.124309i
$330$		0			0
$331$	6981.76	+	2050.03i	1.15937	+	0.340422i	0.804188	−	0.594375i	$-0.202600\pi$
$331$	6981.76	+	2050.03i	1.15937	+	0.340422i	0.355183	+	0.934797i	$0.384418\pi$
$332$	−17.6794	+	20.4031i	−0.00292254	+	0.00337279i
$333$		0			0
$334$	−1825.46	−	1173.15i	−0.299056	−	0.192191i
$335$	−616.107	+	711.025i	−0.100482	+	0.115963i
$336$		0			0
$337$	−1553.98	−	10808.2i	−0.251189	−	1.74706i	−0.591096	−	0.806601i	$-0.701305\pi$
$337$	−1553.98	−	10808.2i	−0.251189	−	1.74706i	0.339907	−	0.940459i	$-0.389604\pi$
$338$	−3449.19	−	3980.58i	−0.555063	−	0.640576i
$339$		0			0
$340$	14.3754	−	4.22100i	0.00229299	−	0.000673282i
$341$	−4173.93	+	9139.64i	−0.662848	+	1.45143i
$342$		0			0
$343$	−1609.36	+	1034.27i	−0.253345	+	0.162815i
$344$	3703.14			0.580407
$345$		0			0
$346$	−4794.58			−0.744966
$347$	−4261.84	+	2738.92i	−0.659330	+	0.423726i	−0.827065	−	0.562106i	$-0.809991\pi$
$347$	−4261.84	+	2738.92i	−0.659330	+	0.423726i	0.167735	+	0.985832i	$0.446355\pi$
$348$		0			0
$349$	−4152.28	+	9092.21i	−0.636866	+	1.39454i	0.265728	+	0.964048i	$0.414388\pi$
$349$	−4152.28	+	9092.21i	−0.636866	+	1.39454i	−0.902594	+	0.430494i	$0.858339\pi$
$350$	951.262	−	279.316i	0.145277	−	0.0426573i
$351$		0			0
$352$	184.895	+	213.380i	0.0279969	+	0.0323102i
$353$	−189.245	−	1316.22i	−0.0285339	−	0.198458i	0.970568	−	0.240827i	$-0.0774186\pi$
$353$	−189.245	−	1316.22i	−0.0285339	−	0.198458i	−0.999102	+	0.0423691i	$0.986509\pi$
$354$		0			0
$355$	531.781	−	613.708i	0.0795043	−	0.0917528i
$356$	149.461	+	96.0526i	0.0222511	+	0.0142999i
$357$		0			0
$358$	7997.10	−	9229.14i	1.18061	−	1.36250i
$359$	−4811.66	−	1412.83i	−0.707381	−	0.207706i	−0.0917975	−	0.995778i	$-0.529261\pi$
$359$	−4811.66	−	1412.83i	−0.707381	−	0.207706i	−0.615583	+	0.788072i	$0.711079\pi$
$360$		0			0
$361$	2809.80	+	3242.68i	0.409652	+	0.472763i
$362$	−4152.15	−	9091.94i	−0.602851	−	1.32006i
$363$		0			0
$364$	−8.34224	+	18.2670i	−0.00120124	+	0.00263035i
$365$	38.1698	−	265.476i	0.00547369	−	0.0380703i
$366$		0			0
$367$	−1893.01			−0.269248			−0.134624	−	0.990897i	$-0.542983\pi$
$367$	−1893.01			−0.269248			−0.134624	+	0.990897i	$0.542983\pi$
$368$	6773.85	−	2309.77i	0.959542	−	0.327187i
$369$		0			0
$370$	−21.2135	+	13.6331i	−0.00298064	+	0.00191554i
$371$	−107.676	+	748.903i	−0.0150681	+	0.104801i
$372$		0			0
$373$	8807.18	−	2586.02i	1.22257	−	0.358979i	0.394129	−	0.919055i	$-0.371046\pi$
$373$	8807.18	−	2586.02i	1.22257	−	0.358979i	0.828441	+	0.560076i	$0.189228\pi$
$374$	6929.32	+	15173.1i	0.958039	+	2.09781i
$375$		0			0
$376$	−1112.32	−	7736.38i	−0.152563	−	1.06110i
$377$	3762.81	+	1104.86i	0.514044	+	0.150937i
$378$		0			0
$379$	8889.55	+	5712.97i	1.20482	+	0.774289i	0.979783	−	0.200062i	$-0.0641144\pi$
$379$	8889.55	+	5712.97i	1.20482	+	0.774289i	0.225034	+	0.974351i	$0.427751\pi$
$380$	−6.08168	−	3.90846i	−0.000821009	−	0.000527631i
$381$		0			0
$382$	−722.424	−	212.123i	−0.0967603	−	0.0284114i
$383$	1359.22	+	9453.61i	0.181340	+	1.26125i	0.853600	+	0.520930i	$0.174415\pi$
$383$	1359.22	+	9453.61i	0.181340	+	1.26125i	−0.672260	+	0.740315i	$0.734676\pi$
$384$		0			0
$385$	−83.3234	−	182.453i	−0.0110300	−	0.0241523i
$386$	12127.8	−	3561.05i	1.59920	−	0.469567i
$387$		0			0
$388$	8.86756	−	61.6752i	0.00116026	−	0.00806980i
$389$	−1753.74	+	1127.06i	−0.228582	+	0.146901i	−0.649919	−	0.760003i	$-0.725197\pi$
$389$	−1753.74	+	1127.06i	−0.228582	+	0.146901i	0.421337	+	0.906904i	$0.361561\pi$
$390$		0			0
$391$	11574.3	−	498.232i	1.49703	−	0.0644416i
$392$	7527.14			0.969842
$393$		0			0
$394$	−787.868	+	5479.74i	−0.100742	+	0.700673i
$395$	−80.3089	+	175.852i	−0.0102298	+	0.0224002i
$396$		0			0
$397$	257.681	+	564.242i	0.0325759	+	0.0713312i	0.925220	−	0.379430i	$-0.123880\pi$
$397$	257.681	+	564.242i	0.0325759	+	0.0713312i	−0.892645	+	0.450761i	$0.851153\pi$
$398$	−1051.80	−	1213.85i	−0.132468	−	0.152876i
$399$		0			0
$400$	−7680.62	−	2255.23i	−0.960077	−	0.281904i
$401$	2362.95	−	2726.99i	0.294265	−	0.339600i	−0.589295	−	0.807918i	$-0.700594\pi$
$401$	2362.95	−	2726.99i	0.294265	−	0.339600i	0.883560	+	0.468318i	$0.155140\pi$
$402$		0			0
$403$	9642.23	+	6196.69i	1.19185	+	0.765953i
$404$	−64.0134	+	73.8754i	−0.00788313	+	0.00909762i
$405$		0			0
$406$	−70.5056	−	490.377i	−0.00861856	−	0.0599434i
$407$	−253.596	−	292.666i	−0.0308853	−	0.0356435i
$408$		0			0
$409$	−8141.07	+	2390.43i	−0.984230	+	0.288996i	−0.733969	−	0.679183i	$-0.762334\pi$
$409$	−8141.07	+	2390.43i	−0.984230	+	0.288996i	−0.250261	+	0.968179i	$0.580516\pi$
$410$	286.515	−	627.381i	0.0345122	−	0.0755711i
$411$		0			0
$412$	97.4068	−	62.5995i	0.0116478	−	0.00748558i
$413$	1121.49			0.133619
$414$		0			0
$415$	−307.602			−0.0363846
$416$	270.950	−	174.129i	0.0319337	−	0.0205226i
$417$		0			0
$418$	3343.56	−	7321.38i	0.391241	−	0.856699i
$419$	9820.50	−	2883.56i	1.14502	−	0.336208i	0.346425	−	0.938078i	$-0.387396\pi$
$419$	9820.50	−	2883.56i	1.14502	−	0.336208i	0.798594	+	0.601870i	$0.205577\pi$
$420$		0			0
$421$	−6759.55	−	7800.93i	−0.782518	−	0.903074i	0.214770	−	0.976665i	$-0.431100\pi$
$421$	−6759.55	−	7800.93i	−0.782518	−	0.903074i	−0.997289	+	0.0735904i	$0.976554\pi$
$422$	1570.66	+	10924.2i	0.181181	+	1.26014i
$423$		0			0
$424$	3945.31	−	4553.13i	0.451889	−	0.521508i
$425$	−10900.8	−	7005.52i	−1.24416	−	0.799571i
$426$		0			0
$427$	−696.486	+	803.787i	−0.0789351	+	0.0910960i
$428$	−80.6941	−	23.6939i	−0.00911331	−	0.00267591i
$429$		0			0
$430$	−391.939	−	452.322i	−0.0439557	−	0.0507276i
$431$	4024.87	+	8813.23i	0.449817	+	0.984962i	0.989691	+	0.143216i	$0.0457444\pi$
$431$	4024.87	+	8813.23i	0.449817	+	0.984962i	−0.539875	+	0.841746i	$0.681528\pi$
$432$		0			0
$433$	−2626.78	+	5751.84i	−0.291535	+	0.638374i	−0.997560	−	0.0698137i	$-0.977760\pi$
$433$	−2626.78	+	5751.84i	−0.291535	+	0.638374i	0.706025	+	0.708187i	$0.250487\pi$
$434$	206.065	−	1433.21i	0.0227913	−	0.158517i
$435$		0			0
$436$	−209.608			−0.0230238
$437$	−3839.01	−	4063.34i	−0.420239	−	0.444796i
$438$		0			0
$439$	−469.384	+	301.655i	−0.0510307	+	0.0327954i	−0.565907	−	0.824469i	$-0.691474\pi$
$439$	−469.384	+	301.655i	−0.0510307	+	0.0327954i	0.514877	+	0.857264i	$0.327838\pi$
$440$	−227.299	+	1580.90i	−0.0246274	+	0.171287i
$441$		0			0
$442$	18257.3	−	5360.84i	1.96474	−	0.576899i
$443$	3585.40	+	7850.94i	0.384532	+	0.842008i	0.998607	+	0.0527602i	$0.0168019\pi$
$443$	3585.40	+	7850.94i	0.384532	+	0.842008i	−0.614075	+	0.789248i	$0.710471\pi$
$444$		0			0
$445$	288.086	+	2003.68i	0.0306889	+	0.213446i
$446$	12044.6	+	3536.62i	1.27876	+	0.375479i
$447$		0			0
$448$	1197.79	+	769.771i	0.126317	+	0.0811792i
$449$	−9667.47	−	6212.91i	−1.01612	−	0.653018i	−0.0771473	−	0.997020i	$-0.524581\pi$
$449$	−9667.47	−	6212.91i	−1.01612	−	0.653018i	−0.938969	+	0.344001i	$0.888218\pi$
$450$		0			0
$451$	10162.9	+	2984.09i	1.06109	+	0.311564i
$452$	−13.6178	−	94.7139i	−0.00141710	−	0.00985613i
$453$		0			0
$454$	413.219	+	904.823i	0.0427166	+	0.0935363i
$455$	−219.540	+	64.4628i	−0.0226202	+	0.00664189i
$456$		0			0
$457$	−135.405	+	941.766i	−0.0138600	+	0.0963981i	−0.995577	−	0.0939470i	$-0.970052\pi$
$457$	−135.405	+	941.766i	−0.0138600	+	0.0963981i	0.981717	+	0.190345i	$0.0609607\pi$
$458$	913.141	−	586.840i	0.0931622	−	0.0598717i
$459$		0			0
$460$	−13.5906	−	7.92978i	−0.00137754	−	0.000803756i
$461$	2537.09			0.256321			0.128160	−	0.991753i	$-0.459093\pi$
$461$	2537.09			0.256321			0.128160	+	0.991753i	$0.459093\pi$
$462$		0			0
$463$	682.997	−	4750.35i	0.0685563	−	0.476819i	−0.926403	−	0.376535i	$-0.877116\pi$
$463$	682.997	−	4750.35i	0.0685563	−	0.476819i	0.994959	−	0.100285i	$-0.0319753\pi$
$464$	−1661.70	+	3638.61i	−0.166255	+	0.364048i
$465$		0			0
$466$	−1662.69	−	3640.79i	−0.165285	−	0.361923i
$467$	−863.562	−	996.603i	−0.0855693	−	0.0987523i	0.711350	−	0.702838i	$-0.248084\pi$
$467$	−863.562	−	996.603i	−0.0855693	−	0.0987523i	−0.796920	+	0.604085i	$0.793539\pi$
$468$		0			0
$469$	1997.78	+	586.602i	0.196693	+	0.0577543i
$470$	−827.235	+	954.680i	−0.0811861	+	0.0936938i
$471$		0			0
$472$	−7512.48	−	4827.98i	−0.732606	−	0.470817i
$473$	6019.04	−	6946.34i	0.585107	−	0.675249i
$474$		0			0
$475$	889.816	+	6188.81i	0.0859528	+	0.597815i
$476$	−21.7133	−	25.0585i	−0.00209082	−	0.00241293i
$477$		0			0
$478$	17876.5	−	5249.00i	1.71057	−	0.502267i
$479$	−5649.25	+	12370.1i	−0.538875	+	1.17997i	0.422912	+	0.906171i	$0.361008\pi$
$479$	−5649.25	+	12370.1i	−0.538875	+	1.17997i	−0.961787	+	0.273800i	$0.911719\pi$
$480$		0			0
$481$	−371.628	+	238.831i	−0.0352282	+	0.0226398i
$482$	−18464.6			−1.74489
$483$		0			0
$484$	198.995			0.0186885
$485$	597.244	−	383.826i	0.0559164	−	0.0359353i
$486$		0			0
$487$	1644.02	−	3599.91i	0.152973	−	0.334964i	−0.817594	−	0.575795i	$-0.804693\pi$
$487$	1644.02	−	3599.91i	0.152973	−	0.334964i	0.970567	+	0.240831i	$0.0774199\pi$
$488$	8125.83	−	2385.96i	0.753768	−	0.221326i
$489$		0			0
$490$	−796.669	−	919.405i	−0.0734486	−	0.0847642i
$491$	−1435.91	−	9986.96i	−0.131979	−	0.917933i	−0.942971	−	0.332876i	$-0.891981\pi$
$491$	−1435.91	−	9986.96i	−0.131979	−	0.917933i	0.810992	−	0.585057i	$-0.198928\pi$
$492$		0			0
$493$	−4240.29	+	4893.56i	−0.387370	+	0.447048i
$494$	−7723.98	−	4963.90i	−0.703478	−	0.452098i
$495$		0			0
$496$	−7655.95	+	8835.44i	−0.693069	+	0.799844i
$497$	−1724.35	−	506.315i	−0.155629	−	0.0456968i
$498$		0			0
$499$	1781.94	+	2056.46i	0.159861	+	0.184489i	0.830029	−	0.557720i	$-0.188324\pi$
$499$	1781.94	+	2056.46i	0.159861	+	0.184489i	−0.670169	+	0.742209i	$0.733778\pi$
$500$	14.7184	+	32.2289i	0.00131646	+	0.00288264i
$501$		0			0
$502$	−6598.75	+	14449.2i	−0.586687	+	1.28466i
$503$	−1049.37	+	7298.52i	−0.0930200	+	0.646968i	0.888960	+	0.457984i	$0.151428\pi$
$503$	−1049.37	+	7298.52i	−0.0930200	+	0.646968i	−0.981980	+	0.188984i	$0.939481\pi$
$504$		0			0
$505$	−1113.76			−0.0981423
$506$	6585.35	−	16233.5i	0.578567	−	1.42622i
$507$		0			0
$508$	−229.143	+	147.261i	−0.0200129	+	0.0128615i
$509$	1235.76	−	8594.87i	0.107611	−	0.748450i	−0.862547	−	0.505976i	$-0.831132\pi$
$509$	1235.76	−	8594.87i	0.107611	−	0.748450i	0.970158	−	0.242473i	$-0.0779587\pi$
$510$		0			0
$511$	−569.522	+	167.227i	−0.0493036	+	0.0144769i
$512$	−4707.87	−	10308.8i	−0.406368	−	0.889821i
$513$		0			0
$514$	777.138	+	5405.11i	0.0666889	+	0.463831i
$515$	1265.83	+	371.681i	0.108309	+	0.0318024i
$516$		0			0
$517$	−16319.8	−	10488.1i	−1.38829	−	0.892198i
$518$	46.9474	+	30.1713i	0.00398214	+	0.00255917i
$519$		0			0
$520$	1748.14	+	513.301i	0.147425	+	0.0432879i
$521$	−444.308	−	3090.23i	−0.0373617	−	0.259857i	0.962576	−	0.271012i	$-0.0873582\pi$
$521$	−444.308	−	3090.23i	−0.0373617	−	0.259857i	−0.999938	+	0.0111551i	$0.996449\pi$
$522$		0			0
$523$	−3812.64	−	8348.53i	−0.318767	−	0.698003i	0.680633	−	0.732624i	$-0.261705\pi$
$523$	−3812.64	−	8348.53i	−0.318767	−	0.698003i	−0.999401	+	0.0346213i	$0.988977\pi$
$524$	29.9206	−	8.78548i	0.00249444	−	0.000732434i
$525$		0			0
$526$	−711.703	+	4950.00i	−0.0589957	+	0.410324i
$527$	−15920.4	+	10231.4i	−1.31595	+	0.845708i
$528$		0			0
$529$	−8728.39	−	8476.50i	−0.717382	−	0.696680i
$530$	−973.712			−0.0798026
$531$		0			0
$532$	−2.27691	+	15.8363i	−0.000185558	+	0.00129058i
$533$	5019.31	−	10990.8i	0.407899	−	0.893175i
$534$		0			0
$535$	−398.065	−	871.640i	−0.0321679	−	0.0704379i
$536$	−10857.2	−	12529.9i	−0.874925	−	1.00972i
$537$		0			0
$538$	13569.8	+	3984.45i	1.08743	+	0.319297i
$539$	12234.5	−	14119.4i	0.977695	−	1.12832i
$540$		0			0
$541$	6379.70	+	4099.98i	0.506996	+	0.325826i	0.769009	−	0.639238i	$-0.220750\pi$
$541$	6379.70	+	4099.98i	0.506996	+	0.325826i	−0.262013	+	0.965064i	$0.584386\pi$
$542$	−7358.77	+	8492.48i	−0.583185	+	0.673032i
$543$		0			0
$544$	75.6815	+	526.376i	0.00596474	+	0.0414857i
$545$	−1563.97	−	1804.92i	−0.122923	−	0.141861i
$546$		0			0
$547$	−1959.16	+	575.262i	−0.153140	+	0.0449660i	−0.357404	−	0.933950i	$-0.616338\pi$
$547$	−1959.16	+	575.262i	−0.153140	+	0.0449660i	0.204264	+	0.978916i	$0.434520\pi$
$548$	−81.5855	+	178.647i	−0.00635978	+	0.0139260i
$549$		0			0
$550$	−16483.7	+	10593.5i	−1.27794	+	0.821284i
$551$	3124.39			0.241567
$552$		0			0
$553$	427.840			0.0328998
$554$	−12304.4	+	7907.54i	−0.943615	+	0.606425i
$555$		0			0
$556$	103.434	−	226.488i	0.00788950	−	0.0172756i
$557$	19451.8	−	5711.56i	1.47971	−	0.434482i	0.560469	−	0.828175i	$-0.310621\pi$
$557$	19451.8	−	5711.56i	1.47971	−	0.434482i	0.919242	+	0.393693i	$0.128803\pi$
$558$		0			0
$559$	−6866.17	−	7923.98i	−0.519513	−	0.599550i
$560$	−33.2140	−	231.009i	−0.00250634	−	0.0174320i
$561$		0			0
$562$	153.404	−	177.037i	0.0115141	−	0.0132880i
$563$	11722.8	+	7533.80i	0.877545	+	0.563964i	0.900052	−	0.435783i	$-0.143528\pi$
$563$	11722.8	+	7533.80i	0.877545	+	0.563964i	−0.0225068	+	0.999747i	$0.507165\pi$
$564$		0			0
$565$	713.966	−	823.960i	0.0531624	−	0.0613527i
$566$	−21974.4	−	6452.25i	−1.63189	−	0.479167i
$567$		0			0
$568$	9371.20	+	10814.9i	0.692265	+	0.798917i
$569$	9282.18	+	20325.1i	0.683883	+	1.49749i	0.858476	+	0.512854i	$0.171412\pi$
$569$	9282.18	+	20325.1i	0.683883	+	1.49749i	−0.174593	+	0.984641i	$0.555861\pi$
$570$		0			0
$571$	−5912.40	+	12946.3i	−0.433321	+	0.948840i	0.559456	+	0.828860i	$0.311010\pi$
$571$	−5912.40	+	12946.3i	−0.433321	+	0.948840i	−0.992776	+	0.119980i	$0.961717\pi$
$572$	56.4835	−	392.851i	0.00412883	−	0.0287167i
$573$		0			0
$574$	−1526.39			−0.110993
$575$	2514.24	+	13374.5i	0.182350	+	0.970006i
$576$		0			0
$577$	−1248.30	+	802.237i	−0.0900652	+	0.0578814i	−0.584898	−	0.811107i	$-0.698866\pi$
$577$	−1248.30	+	802.237i	−0.0900652	+	0.0578814i	0.494833	+	0.868988i	$0.335229\pi$
$578$	−2479.79	+	17247.3i	−0.178453	+	1.24117i
$579$		0			0
$580$	8.43831	−	2.47771i	0.000604106	−	0.000177382i
$581$	282.795	+	619.234i	0.0201933	+	0.0442171i
$582$		0			0
$583$	−2128.09	−	14801.2i	−0.151177	−	1.05146i
$584$	4534.96	+	1331.58i	0.321332	+	0.0943515i
$585$		0			0
$586$	−20617.3	−	13249.9i	−1.45340	−	0.934044i
$587$	−12481.3	−	8021.25i	−0.877613	−	0.564007i	0.0224598	−	0.999748i	$-0.492850\pi$
$587$	−12481.3	−	8021.25i	−0.877613	−	0.564007i	−0.900072	+	0.435740i	$0.856487\pi$
$588$		0			0
$589$	8761.69	+	2572.66i	0.612935	+	0.179974i
$590$	205.403	+	1428.61i	0.0143327	+	0.0996861i
$591$		0			0
$592$	−187.181	−	409.870i	−0.0129951	−	0.0284553i
$593$	−7111.95	+	2088.26i	−0.492500	+	0.144611i	−0.518546	−	0.855050i	$-0.673527\pi$
$593$	−7111.95	+	2088.26i	−0.492500	+	0.144611i	0.0260459	+	0.999661i	$0.491708\pi$
$594$		0			0
$595$	53.7649	−	373.943i	0.00370445	−	0.0257650i
$596$	−205.237	+	131.898i	−0.0141055	+	0.00906502i
$597$		0			0
$598$	−17260.7	−	10071.1i	−1.18034	−	0.688695i
$599$	16009.7			1.09205			0.546027	−	0.837768i	$-0.316140\pi$
$599$	16009.7			1.09205			0.546027	+	0.837768i	$0.316140\pi$
$600$		0			0
$601$	2437.23	−	16951.3i	0.165419	−	1.15052i	−0.722787	−	0.691071i	$-0.757139\pi$
$601$	2437.23	−	16951.3i	0.165419	−	1.15052i	0.888206	−	0.459445i	$-0.151952\pi$
$602$	−550.238	+	1204.85i	−0.0372526	+	0.0815717i
$603$		0			0
$604$	−134.781	−	295.129i	−0.00907973	−	0.0198818i
$605$	1484.78	+	1713.53i	0.0997767	+	0.115148i
$606$		0			0
$607$	17264.0	+	5069.18i	1.15441	+	0.338965i	0.802257	−	0.596978i	$-0.203632\pi$
$607$	17264.0	+	5069.18i	1.15441	+	0.338965i	0.352151	+	0.935943i	$0.385450\pi$
$608$	168.038	−	193.926i	0.0112086	−	0.0129354i
$609$		0			0
$610$	−1151.47	−	740.003i	−0.0764288	−	0.0491178i
$611$	−14491.9	+	16724.5i	−0.959539	+	1.10737i
$612$		0			0
$613$	−1865.58	−	12975.4i	−0.122920	−	0.854930i	−0.954220	−	0.299106i	$-0.903312\pi$
$613$	−1865.58	−	12975.4i	−0.122920	−	0.854930i	0.831300	−	0.555825i	$-0.187597\pi$
$614$	10420.5	+	12025.9i	0.684915	+	0.790435i
$615$		0			0
$616$	3391.47	−	995.827i	0.221829	−	0.0651347i
$617$	51.7866	−	113.397i	0.00337901	−	0.00739901i	−0.907935	−	0.419111i	$-0.862342\pi$
$617$	51.7866	−	113.397i	0.00337901	−	0.00739901i	0.911314	+	0.411712i	$0.135069\pi$
$618$		0			0
$619$	−17559.9	+	11285.0i	−1.14021	+	0.732769i	−0.967666	−	0.252233i	$-0.918835\pi$
$619$	−17559.9	+	11285.0i	−1.14021	+	0.732769i	−0.172544	+	0.985002i	$0.555199\pi$
$620$	25.7036			0.00166497
$621$		0			0
$622$	5427.93			0.349904
$623$	3768.76	−	2422.03i	0.242363	−	0.155757i
$624$		0			0
$625$	6238.76	−	13661.0i	0.399281	−	0.874303i
$626$	−23953.0	+	7033.23i	−1.52932	+	0.449048i
$627$		0			0
$628$	−125.536	−	144.877i	−0.00797683	−	0.00920575i
$629$	−103.803	−	721.963i	−0.00658010	−	0.0457656i
$630$		0			0
$631$	−7582.40	+	8750.56i	−0.478369	+	0.552067i	−0.942720	−	0.333584i	$-0.891742\pi$
$631$	−7582.40	+	8750.56i	−0.478369	+	0.552067i	0.464352	+	0.885651i	$0.346287\pi$
$632$	−2865.96	−	1841.84i	−0.180383	−	0.115925i
$633$		0			0
$634$	−13482.5	+	15559.6i	−0.844569	+	0.974685i
$635$	−2977.78	−	874.355i	−0.186094	−	0.0546421i
$636$		0			0
$637$	−13956.4	−	16106.6i	−0.868090	−	1.00183i
$638$	4067.49	+	8906.55i	0.252403	+	0.552686i
$639$		0			0
$640$	−782.649	+	1713.76i	−0.0483389	+	0.105848i
$641$	2182.46	−	15179.4i	0.134481	−	0.935334i	−0.805132	−	0.593095i	$-0.797906\pi$
$641$	2182.46	−	15179.4i	0.134481	−	0.935334i	0.939613	−	0.342239i	$-0.111185\pi$
$642$		0			0
$643$	15094.1			0.925745			0.462872	−	0.886425i	$-0.346819\pi$
$643$	15094.1			0.925745			0.462872	+	0.886425i	$0.346819\pi$
$644$	−3.46885	+	34.6496i	−0.000212255	+	0.00212016i
$645$		0			0
$646$	12753.2	−	8195.96i	0.776728	−	0.499173i
$647$	−1564.14	+	10878.8i	−0.0950428	+	0.661037i	0.885487	+	0.464665i	$0.153825\pi$
$647$	−1564.14	+	10878.8i	−0.0950428	+	0.661037i	−0.980529	+	0.196372i	$0.937084\pi$
$648$		0			0
$649$	−21267.0	+	6244.55i	−1.28629	+	0.377689i
$650$	9285.35	+	20332.1i	0.560310	+	1.22691i
$651$		0			0
$652$	1.14349	+	7.95316i	6.86849e−5	+	0.000477714i
$653$	27798.9	+	8162.49i	1.66593	+	0.489162i	0.972800	−	0.231648i	$-0.0744117\pi$
$653$	27798.9	+	8162.49i	1.66593	+	0.489162i	0.693133	+	0.720810i	$0.256230\pi$
$654$		0			0
$655$	298.901	+	192.092i	0.0178306	+	0.0114590i
$656$	10367.8	+	6663.00i	0.617067	+	0.396565i
$657$		0			0
$658$	2682.38	+	787.619i	0.158921	+	0.0466635i
$659$	−2198.15	−	15288.5i	−0.129936	−	0.903724i	−0.945631	−	0.325242i	$-0.894554\pi$
$659$	−2198.15	−	15288.5i	−0.129936	−	0.903724i	0.815695	−	0.578482i	$-0.196355\pi$
$660$		0			0
$661$	747.235	+	1636.22i	0.0439698	+	0.0962805i	0.930342	−	0.366693i	$-0.119510\pi$
$661$	747.235	+	1636.22i	0.0439698	+	0.0962805i	−0.886372	+	0.462973i	$0.846783\pi$
$662$	19885.0	−	5838.76i	1.16745	−	0.342795i
$663$		0			0
$664$	771.439	−	5365.48i	0.0450868	−	0.313586i
$665$	−153.354	+	98.5544i	−0.00894256	+	0.00574703i
$666$		0			0
$667$	6794.08	−	292.460i	0.394405	−	0.0169777i
$668$	−85.2480			−0.00493764
$669$		0			0
$670$	−381.345	+	2652.32i	−0.0219890	+	0.152937i
$671$	8732.04	−	19120.5i	0.502380	−	1.10006i
$672$		0			0
$673$	5392.55	+	11808.0i	0.308867	+	0.676325i	0.998872	−	0.0474797i	$-0.0151190\pi$
$673$	5392.55	+	11808.0i	0.308867	+	0.676325i	−0.690005	+	0.723805i	$0.742392\pi$
$674$	−20366.0	−	23503.6i	−1.16390	−	1.34321i
$675$		0			0
$676$	−198.541	−	58.2968i	−0.0112961	−	0.00331684i
$677$	20089.3	−	23184.3i	1.14047	−	1.31617i	0.198640	−	0.980073i	$-0.436348\pi$
$677$	20089.3	−	23184.3i	1.14047	−	1.31617i	0.941827	−	0.336097i	$-0.109107\pi$
$678$		0			0
$679$	−1321.76	−	849.441i	−0.0747045	−	0.0480097i
$680$	−1969.97	+	2273.47i	−0.111096	+	0.128211i
$681$		0			0
$682$	4072.63	+	28325.7i	0.228664	+	1.59039i
$683$	−20520.9	−	23682.4i	−1.14965	−	1.32677i	−0.936874	−	0.349667i	$-0.886295\pi$
$683$	−20520.9	−	23682.4i	−1.14965	−	1.32677i	−0.212776	−	0.977101i	$-0.568251\pi$
$684$		0			0
$685$	−2147.06	+	630.433i	−0.119759	+	0.0351644i
$686$	−2263.44	+	4956.25i	−0.125975	+	0.275846i
$687$		0			0
$688$	8996.87	−	5781.94i	0.498550	−	0.320399i
$689$	−17057.9			−0.943187
$690$		0			0
$691$	29803.4			1.64077			0.820386	−	0.571810i	$-0.193758\pi$
$691$	29803.4			1.64077			0.820386	+	0.571810i	$0.193758\pi$
$692$	−158.459	+	101.835i	−0.00870478	+	0.00559422i
$693$		0			0
$694$	−5993.96	+	13124.9i	−0.327849	+	0.717890i
$695$	2722.03	−	799.259i	0.148565	−	0.0436225i
$696$		0			0
$697$	13064.3	+	15077.1i	0.709967	+	0.819346i
$698$	4051.49	+	28178.8i	0.219701	+	1.52805i
$699$		0			0
$700$	25.5062	−	29.4358i	0.00137721	−	0.00158938i
$701$	−15817.5	−	10165.3i	−0.852239	−	0.547700i	0.0400336	−	0.999198i	$-0.487253\pi$
$701$	−15817.5	−	10165.3i	−0.852239	−	0.547700i	−0.892272	+	0.451498i	$0.850890\pi$
$702$		0			0
$703$	−230.476	+	265.983i	−0.0123650	+	0.0142699i
$704$	−27000.1	−	7927.94i	−1.44546	−	0.424425i
$705$		0			0
$706$	−2480.18	−	2862.28i	−0.132214	−	0.152583i
$707$	1023.94	+	2242.12i	0.0544685	+	0.119269i
$708$		0			0
$709$	−5685.14	+	12448.7i	−0.301142	+	0.659409i	−0.998348	−	0.0574620i	$-0.981699\pi$
$709$	−5685.14	+	12448.7i	−0.301142	+	0.659409i	0.697206	+	0.716871i	$0.254426\pi$
$710$	329.151	−	2289.30i	0.0173983	−	0.121008i
$711$		0			0
$712$	−35672.5			−1.87765
$713$	19293.4	+	4774.19i	1.01338	+	0.250764i
$714$		0			0
$715$	3804.25	−	2444.84i	0.198980	−	0.127877i
$716$	68.2768	−	474.875i	0.00356372	−	0.0247862i
$717$		0			0
$718$	−13704.3	+	4023.94i	−0.712310	+	0.209153i
$719$	9470.92	+	20738.4i	0.491246	+	1.07568i	0.979216	+	0.202818i	$0.0650100\pi$
$719$	9470.92	+	20738.4i	0.491246	+	1.07568i	−0.487971	+	0.872860i	$0.662263\pi$
$720$		0			0
$721$	−415.512	−	2889.95i	−0.0214625	−	0.149275i
$722$	11725.4	+	3442.90i	0.604399	+	0.177468i
$723$		0			0
$724$	−330.337	−	212.295i	−0.0169570	−	0.0108976i
$725$	−6398.73	−	4112.22i	−0.327783	−	0.210654i
$726$		0			0
$727$	−23.1835	−	6.80729i	−0.00118271	−	0.000347274i	0.281141	−	0.959666i	$-0.409287\pi$
$727$	−23.1835	−	6.80729i	−0.00118271	−	0.000347274i	−0.282324	+	0.959319i	$0.591105\pi$
$728$	−573.831	−	3991.08i	−0.0292137	−	0.203186i
$729$		0			0
$730$	−317.331	−	694.858i	−0.0160890	−	0.0352299i
$731$	16610.5	−	4877.30i	0.840442	−	0.246776i
$732$		0			0
$733$	−88.5272	+	615.720i	−0.00446088	+	0.0310261i	−0.991930	−	0.126784i	$-0.959534\pi$
$733$	−88.5272	+	615.720i	−0.00446088	+	0.0310261i	0.987469	+	0.157810i	$0.0504435\pi$
$734$	−4535.65	+	2914.89i	−0.228084	+	0.146581i
$735$		0			0
$736$	347.251	−	437.427i	0.0173911	−	0.0219073i
$737$	−41150.7			−2.05672
$738$		0			0
$739$	4570.02	−	31785.2i	0.227484	−	1.58219i	−0.481167	−	0.876629i	$-0.659787\pi$
$739$	4570.02	−	31785.2i	0.227484	−	1.58219i	0.708651	−	0.705559i	$-0.249304\pi$
$740$	−0.411535	+	0.901136i	−2.04437e−5	+	4.47654e-5i
$741$		0			0
$742$	895.184	+	1960.18i	0.0442901	+	0.0969817i
$743$	−16599.9	−	19157.4i	−0.819640	−	0.945916i	0.179644	−	0.983732i	$-0.442505\pi$
$743$	−16599.9	−	19157.4i	−0.819640	−	0.945916i	−0.999285	+	0.0378161i	$0.987960\pi$
$744$		0			0
$745$	−2667.12	−	783.137i	−0.131162	−	0.0385127i
$746$	17120.1	−	19757.6i	0.840228	−	0.969674i
$747$		0			0
$748$	551.283	+	354.288i	0.0269477	+	0.0173183i
$749$	−1388.74	+	1602.69i	−0.0677481	+	0.0781855i
$750$		0			0
$751$	1713.54	+	11918.0i	0.0832598	+	0.579085i	0.988156	+	0.153452i	$0.0490392\pi$
$751$	1713.54	+	11918.0i	0.0832598	+	0.579085i	−0.904896	+	0.425632i	$0.860052\pi$
$752$	−14781.7	−	17059.0i	−0.716799	−	0.827230i
$753$		0			0
$754$	10717.0	−	3146.79i	0.517626	−	0.151989i
$755$	1535.68	−	3362.66i	0.0740251	−	0.162092i
$756$		0			0
$757$	30959.7	−	19896.6i	1.48646	−	0.955288i	0.489953	−	0.871749i	$-0.337014\pi$
$757$	30959.7	−	19896.6i	1.48646	−	0.955288i	0.996505	−	0.0835389i	$-0.0266223\pi$
$758$	30096.4			1.44215
$759$		0			0
$760$	1451.54			0.0692803
$761$	−12213.9	+	7849.41i	−0.581806	+	0.373904i	−0.798191	−	0.602404i	$-0.794210\pi$
$761$	−12213.9	+	7849.41i	−0.581806	+	0.373904i	0.216385	+	0.976308i	$0.430573\pi$
$762$		0			0
$763$	−2195.64	+	4807.77i	−0.104177	+	0.228117i
$764$	−28.3813	+	8.33349i	−0.00134398	+	0.000394627i
$765$		0			0
$766$	17813.6	+	20557.9i	0.840248	+	0.969698i
$767$	3598.34	+	25027.0i	0.169398	+	1.17819i
$768$		0			0
$769$	−8840.63	+	10202.6i	−0.414566	+	0.478434i	−0.924174	−	0.381972i	$-0.875245\pi$
$769$	−8840.63	+	10202.6i	−0.414566	+	0.478434i	0.509608	+	0.860407i	$0.329790\pi$
$770$	−480.588	−	308.855i	−0.0224924	−	0.0144550i
$771$		0			0
$772$	325.184	−	375.283i	0.0151602	−	0.0174958i
$773$	−16310.0	−	4789.05i	−0.758901	−	0.222833i	−0.120685	−	0.992691i	$-0.538509\pi$
$773$	−16310.0	−	4789.05i	−0.758901	−	0.222833i	−0.638216	+	0.769857i	$0.720327\pi$
$774$		0			0
$775$	−14557.8	−	16800.6i	−0.674752	−	0.778705i
$776$	5197.20	+	11380.3i	0.240423	+	0.526454i
$777$		0			0
$778$	−2466.51	+	5400.90i	−0.113661	+	0.248884i
$779$	1369.96	−	9528.27i	0.0630088	−	0.438236i
$780$		0			0
$781$	35518.4			1.62734
$782$	26965.0	−	19016.1i	1.23308	−	0.869585i
$783$		0			0
$784$	18287.4	−	11752.6i	0.833062	−	0.535376i
$785$	310.844	−	2161.97i	0.0141331	−	0.0982980i
$786$		0			0
$787$	28411.8	−	8342.45i	1.28687	−	0.377860i	0.434443	−	0.900699i	$-0.356945\pi$
$787$	28411.8	−	8342.45i	1.28687	−	0.377860i	0.852431	+	0.522839i	$0.175127\pi$
$788$	90.3493	+	197.837i	0.00408447	+	0.00894373i
$789$		0			0
$790$	78.3597	+	545.004i	0.00352900	+	0.0245448i
$791$	−2315.10	−	679.774i	−0.104065	−	0.0305563i
$792$		0			0
$793$	−20171.9	−	12963.7i	−0.903312	−	0.580524i
$794$	1486.24	+	955.146i	0.0664289	+	0.0426912i
$795$		0			0
$796$	−60.5435	−	17.7772i	−0.00269586	−	0.000791576i
$797$	1839.90	+	12796.8i	0.0817726	+	0.568741i	0.988979	+	0.148055i	$0.0473013\pi$
$797$	1839.90	+	12796.8i	0.0817726	+	0.568741i	−0.907207	+	0.420685i	$0.861790\pi$
$798$		0			0
$799$	−15178.7	−	33236.7i	−0.672070	−	1.47163i
$800$	−599.379	+	175.994i	−0.0264891	+	0.00777789i
$801$		0			0
$802$	1462.57	−	10172.4i	0.0643955	−	0.447881i
$803$	9868.83	−	6342.32i	0.433703	−	0.278724i
$804$		0			0
$805$	−324.247	+	228.664i	−0.0141965	+	0.0100116i
$806$	32644.6			1.42662
$807$		0			0
$808$	2793.22	−	19427.3i	0.121615	−	0.845853i
$809$	−14982.7	+	32807.5i	−0.651129	+	1.42577i	0.239433	+	0.970913i	$0.423038\pi$
$809$	−14982.7	+	32807.5i	−0.651129	+	1.42577i	−0.890562	+	0.454861i	$0.849689\pi$
$810$		0			0
$811$	14416.1	+	31567.0i	0.624192	+	1.36679i	0.912431	+	0.409231i	$0.134203\pi$
$811$	14416.1	+	31567.0i	0.624192	+	1.36679i	−0.288239	+	0.957558i	$0.593070\pi$
$812$	−12.7456	−	14.7093i	−0.000550843	−	0.000635707i
$813$		0			0
$814$	−1058.27	−	310.736i	−0.0455680	−	0.0133800i
$815$	−59.9519	+	69.1882i	−0.00257672	+	0.00297369i
$816$		0			0
$817$	−7027.28	−	4516.16i	−0.300922	−	0.193391i
$818$	−15825.2	+	18263.3i	−0.676425	+	0.780636i
$819$		0			0
$820$	−3.85616	−	26.8202i	−0.000164223	−	0.00114220i
$821$	−16223.6	−	18723.1i	−0.689657	−	0.795907i	0.297659	−	0.954672i	$-0.403794\pi$
$821$	−16223.6	−	18723.1i	−0.689657	−	0.795907i	−0.987316	+	0.158766i	$0.949249\pi$
$822$		0			0
$823$	16159.7	−	4744.92i	0.684437	−	0.200969i	0.0790151	−	0.996873i	$-0.474822\pi$
$823$	16159.7	−	4744.92i	0.684437	−	0.200969i	0.605422	+	0.795904i	$0.293004\pi$
$824$	−9657.79	+	21147.6i	−0.408307	+	0.894068i
$825$		0			0
$826$	2687.09	−	1726.89i	0.113191	−	0.0727434i
$827$	−18988.2			−0.798407			−0.399204	−	0.916862i	$-0.630713\pi$
$827$	−18988.2			−0.798407			−0.399204	+	0.916862i	$0.630713\pi$
$828$		0			0
$829$	−32863.8			−1.37685			−0.688425	−	0.725308i	$-0.741698\pi$
$829$	−32863.8			−1.37685			−0.688425	+	0.725308i	$0.741698\pi$
$830$	−737.017	+	473.652i	−0.0308220	+	0.0198081i
$831$		0			0
$832$	−13335.0	+	29199.6i	−0.555658	+	1.21672i
$833$	33763.2	−	9913.77i	1.40435	−	0.412355i
$834$		0			0
$835$	−636.069	−	734.063i	−0.0263618	−	0.0304231i
$836$	−45.0004	−	312.985i	−0.00186169	−	0.0129483i
$837$		0			0
$838$	19089.8	−	22030.8i	0.786930	−	0.908165i
$839$	35204.2	+	22624.3i	1.44861	+	0.930964i	0.999293	+	0.0375907i	$0.0119683\pi$
$839$	35204.2	+	22624.3i	1.44861	+	0.930964i	0.449315	+	0.893373i	$0.351668\pi$
$840$		0			0
$841$	13482.4	−	15559.5i	0.552805	−	0.637971i
$842$	−28208.0	−	8282.60i	−1.15453	−	0.338999i
$843$		0			0
$844$	283.935	+	327.679i	0.0115799	+	0.0133639i
$845$	−979.402	−	2144.59i	−0.0398727	−	0.0873091i
$846$		0			0
$847$	2084.46	−	4564.34i	0.0845609	−	0.185162i
$848$	2476.15	−	17222.0i	0.100273	−	0.697412i
$849$		0			0
$850$	−36905.6			−1.48924
$851$	−476.279	+	599.963i	−0.0191852	+	0.0241674i
$852$		0			0
$853$	16319.4	−	10487.8i	0.655058	−	0.420980i	−0.170453	−	0.985366i	$-0.554523\pi$
$853$	16319.4	−	10487.8i	0.655058	−	0.420980i	0.825511	+	0.564385i	$0.190887\pi$
$854$	−431.096	+	2998.34i	−0.0172738	+	0.120142i
$855$		0			0
$856$	16202.2	−	4757.41i	0.646941	−	0.189959i
$857$	18662.7	+	40865.6i	0.743881	+	1.62887i	0.777064	+	0.629422i	$0.216708\pi$
$857$	18662.7	+	40865.6i	0.743881	+	1.62887i	−0.0331833	+	0.999449i	$0.510565\pi$
$858$		0			0
$859$	6023.71	+	41895.8i	0.239262	+	1.66411i	0.655760	+	0.754969i	$0.272348\pi$
$859$	6023.71	+	41895.8i	0.239262	+	1.66411i	−0.416498	+	0.909137i	$0.636743\pi$
$860$	−22.5606	−	6.62439i	−0.000894546	−	0.000262663i
$861$		0			0
$862$	23214.4	+	14919.0i	0.917269	+	0.589493i
$863$	−11969.4	−	7692.26i	−0.472123	−	0.303415i	0.282858	−	0.959162i	$-0.408718\pi$
$863$	−11969.4	−	7692.26i	−0.472123	−	0.303415i	−0.754981	+	0.655747i	$0.772354\pi$
$864$		0			0
$865$	−2059.22	−	604.642i	−0.0809430	−	0.0237670i
$866$	2563.02	+	17826.2i	0.100572	+	0.699491i
$867$		0			0
$868$	−23.6306	−	51.7439i	−0.000924051	−	0.00202339i
$869$	−8113.22	+	2382.26i	−0.316711	+	0.0929948i
$870$		0			0
$871$	−6680.58	+	46464.5i	−0.259889	+	1.80756i
$872$	35405.3	−	22753.6i	1.37497	−	0.883639i
$873$		0			0
$874$	−15455.1	−	3824.40i	−0.598142	−	0.148012i
$875$	893.409			0.0345174
$876$		0			0
$877$	2441.68	−	16982.3i	0.0940134	−	0.653878i	−0.887262	−	0.461266i	$-0.847395\pi$
$877$	2441.68	−	16982.3i	0.0940134	−	0.653878i	0.981275	−	0.192611i	$-0.0616956\pi$
$878$	−660.153	+	1445.53i	−0.0253748	+	0.0555631i
$879$		0			0
$880$	1916.13	+	4195.73i	0.0734007	+	0.160725i
$881$	3819.73	+	4408.21i	0.146073	+	0.168577i	0.824071	−	0.566487i	$-0.191698\pi$
$881$	3819.73	+	4408.21i	0.146073	+	0.168577i	−0.677998	+	0.735064i	$0.737152\pi$
$882$		0			0
$883$	−13445.9	−	3948.08i	−0.512448	−	0.150468i	0.0152773	−	0.999883i	$-0.495137\pi$
$883$	−13445.9	−	3948.08i	−0.512448	−	0.150468i	−0.527726	+	0.849415i	$0.676955\pi$
$884$	489.535	−	564.954i	0.0186254	−	0.0214949i
$885$		0			0
$886$	20679.7	+	13290.0i	0.784140	+	0.503936i
$887$	16101.1	−	18581.6i	0.609493	−	0.703393i	−0.364183	−	0.931327i	$-0.618652\pi$
$887$	16101.1	−	18581.6i	0.609493	−	0.703393i	0.973676	+	0.227935i	$0.0731972\pi$
$888$		0			0
$889$	977.463	+	6798.40i	0.0368763	+	0.256480i
$890$	3775.56	+	4357.23i	0.142199	+	0.164106i
$891$		0			0
$892$	473.186	−	138.940i	0.0177617	−	0.00521531i
$893$	−7324.08	+	16037.5i	−0.274458	+	0.600979i
$894$		0			0
$895$	4598.55	−	2955.31i	0.171746	−	0.110374i
$896$	4169.50			0.155461
$897$		0			0
$898$	−32730.1			−1.21628
$899$	−9345.23	+	6005.81i	−0.346697	+	0.222809i
$900$		0			0
$901$	11700.0	−	25619.4i	0.432612	−	0.947288i
$902$	28945.3	−	8499.09i	1.06848	−	0.313735i
$903$		0			0
$904$	12581.7	+	14520.1i	0.462900	+	0.534215i
$905$	−636.725	−	4428.52i	−0.0233872	−	0.162662i
$906$		0			0
$907$	−10886.9	+	12564.2i	−0.398560	+	0.459963i	−0.919187	−	0.393822i	$-0.871153\pi$
$907$	−10886.9	+	12564.2i	−0.398560	+	0.459963i	0.520627	+	0.853784i	$0.325698\pi$
$908$	32.8749	+	21.1274i	0.00120153	+	0.000772178i
$909$		0			0
$910$	−426.758	+	492.505i	−0.0155460	+	0.0179411i
$911$	5522.74	+	1621.62i	0.200853	+	0.0589756i	0.380611	−	0.924735i	$-0.375714\pi$
$911$	5522.74	+	1621.62i	0.200853	+	0.0589756i	−0.179759	+	0.983711i	$0.557532\pi$
$912$		0			0
$913$	−8810.66	−	10168.0i	−0.319376	−	0.368579i
$914$	1125.72	+	2464.98i	0.0407390	+	0.0892059i
$915$		0			0
$916$	17.7146	−	38.7897i	0.000638983	−	0.00139918i
$917$	111.905	−	778.316i	0.00402991	−	0.0280286i
$918$		0			0
$919$	12049.1			0.432494			0.216247	−	0.976339i	$-0.430618\pi$
$919$	12049.1			0.432494			0.216247	+	0.976339i	$0.430618\pi$
$920$	3156.43	−	135.872i	0.113113	−	0.00486911i
$921$		0			0
$922$	6078.87	−	3906.65i	0.217133	−	0.139543i
$923$	5766.22	−	40104.9i	0.205631	−	1.43020i
$924$		0			0
$925$	822.091	−	241.388i	0.0292218	−	0.00858030i
$926$	−5678.21	−	12433.6i	−0.201509	−	0.441244i
$927$		0			0
$928$	44.4248	+	308.981i	0.00157146	+	0.0109297i
$929$	−2709.25	−	795.509i	−0.0956811	−	0.0280945i	0.233542	−	0.972347i	$-0.424969\pi$
$929$	−2709.25	−	795.509i	−0.0956811	−	0.0280945i	−0.329223	+	0.944252i	$0.606787\pi$
$930$		0			0
$931$	−14283.9	−	9179.71i	−0.502832	−	0.323150i
$932$	−132.281	−	85.0115i	−0.00464913	−	0.00298782i
$933$		0			0
$934$	−3603.69	−	1058.14i	−0.126249	−	0.0370700i
$935$	1062.60	+	7390.54i	0.0371665	+	0.258499i
$936$		0			0
$937$	6336.55	+	13875.1i	0.220924	+	0.483757i	0.987346	−	0.158581i	$-0.0506919\pi$
$937$	6336.55	+	13875.1i	0.220924	+	0.483757i	−0.766422	+	0.642338i	$0.777965\pi$
$938$	5689.96	−	1670.72i	0.198064	−	0.0581568i
$939$		0			0
$940$	−7.06268	+	49.1220i	−0.000245063	+	0.00170445i
$941$	−35882.3	+	23060.1i	−1.24307	+	0.798872i	−0.985874	−	0.167487i	$-0.946435\pi$
$941$	−35882.3	+	23060.1i	−1.24307	+	0.798872i	−0.257195	+	0.966359i	$0.582798\pi$
$942$		0			0
$943$	2087.12	−	20847.7i	0.0720741	−	0.719932i
$944$	−25790.0			−0.889187
$945$		0			0
$946$	3725.54	−	25911.7i	0.128042	−	0.890552i
$947$	5356.41	−	11728.9i	0.183801	−	0.402469i	−0.795193	−	0.606357i	$-0.792630\pi$
$947$	5356.41	−	11728.9i	0.183801	−	0.402469i	0.978994	+	0.203888i	$0.0653577\pi$
$948$		0			0
$949$	−5559.15	−	12172.8i	−0.190156	−	0.416383i
$950$	11661.7	+	13458.3i	0.398267	+	0.459625i
$951$		0			0
$952$	6387.82	+	1875.63i	0.217469	+	0.0638546i
$953$	14329.1	−	16536.7i	0.487057	−	0.562094i	−0.458020	−	0.888942i	$-0.651441\pi$
$953$	14329.1	−	16536.7i	0.487057	−	0.562094i	0.945077	+	0.326848i	$0.105987\pi$
$954$		0			0
$955$	−283.523	−	182.209i	−0.00960690	−	0.00617398i
$956$	479.323	−	553.168i	0.0162159	−	0.0187142i
$957$		0			0
$958$	5512.14	+	38337.8i	0.185897	+	1.29294i
$959$	3243.02	+	3742.65i	0.109200	+	0.126023i
$960$		0			0
$961$	−2567.69	+	753.942i	−0.0861902	+	0.0253077i
$962$	−522.666	+	1144.48i	−0.0175171	+	0.0383571i
$963$		0			0
$964$	−610.247	+	392.182i	−0.0203887	+	0.0131030i
$965$	5657.86			0.188739
$966$		0			0
$967$	21495.1			0.714826			0.357413	−	0.933946i	$-0.383659\pi$
$967$	21495.1			0.714826			0.357413	+	0.933946i	$0.383659\pi$
$968$	−33612.6	+	21601.5i	−1.11606	+	0.717251i
$969$		0			0
$970$	839.979	−	1839.30i	0.0278042	−	0.0608828i
$971$	−31259.3	+	9178.57i	−1.03312	+	0.303352i	−0.753979	−	0.656898i	$-0.771868\pi$
$971$	−31259.3	+	9178.57i	−1.03312	+	0.303352i	−0.279141	+	0.960250i	$0.590050\pi$
$972$		0			0
$973$	−4111.49	−	4744.91i	−0.135466	−	0.156336i
$974$	−1604.12	−	11156.9i	−0.0527714	−	0.367033i
$975$		0			0
$976$	16016.6	−	18484.1i	0.525284	−	0.606211i
$977$	−39190.6	−	25186.3i	−1.28334	−	0.824750i	−0.292040	−	0.956406i	$-0.594334\pi$
$977$	−39190.6	−	25186.3i	−1.28334	−	0.824750i	−0.991295	+	0.131656i	$0.957971\pi$
$978$		0			0
$979$	−57981.6	+	66914.4i	−1.89285	+	2.18447i
$980$	−45.8575	−	13.4650i	−0.00149476	−	0.000438901i
$981$		0			0
$982$	−18818.6	−	21717.8i	−0.611532	−	0.705746i
$983$	−520.492	−	1139.72i	−0.0168882	−	0.0369800i	0.901000	−	0.433819i	$-0.142834\pi$
$983$	−520.492	−	1139.72i	−0.0168882	−	0.0369800i	−0.917888	+	0.396839i	$0.870107\pi$
$984$		0			0
$985$	−1029.43	+	2254.13i	−0.0332998	+	0.0729164i
$986$	−2624.57	+	18254.3i	−0.0847701	+	0.589589i
$987$		0			0
$988$	−360.706			−0.0116150
$989$	−15703.8	−	9162.74i	−0.504905	−	0.294599i
$990$		0			0
$991$	−48788.7	+	31354.6i	−1.56390	+	1.00506i	−0.582557	+	0.812790i	$0.697948\pi$
$991$	−48788.7	+	31354.6i	−1.56390	+	1.00506i	−0.981343	+	0.192268i	$0.938416\pi$
$992$	−129.839	+	903.051i	−0.00415564	+	0.0289031i
$993$		0			0
$994$	−4911.18	+	1442.05i	−0.156714	+	0.0460153i
$995$	−298.661	−	653.977i	−0.00951578	−	0.0208366i
$996$		0			0
$997$	8671.85	+	60314.1i	0.275467	+	1.91591i	0.386863	+	0.922137i	$0.373558\pi$
$997$	8671.85	+	60314.1i	0.275467	+	1.91591i	−0.111397	+	0.993776i	$0.535532\pi$
$998$	7436.12	+	2183.44i	0.235858	+	0.0692541i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.i.b.127.5		60
3.2	odd	2		69.4.e.b.58.2	yes	60
23.2	even	11	inner	207.4.i.b.163.5		60
69.2	odd	22		69.4.e.b.25.2	✓	60
69.5	even	22		1587.4.a.v.1.8		30
69.41	odd	22		1587.4.a.w.1.8		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.4.e.b.25.2	✓	60	69.2	odd	22
69.4.e.b.58.2	yes	60	3.2	odd	2
207.4.i.b.127.5		60	1.1	even	1	trivial
207.4.i.b.163.5		60	23.2	even	11	inner
1587.4.a.v.1.8		30	69.5	even	22
1587.4.a.w.1.8		30	69.41	odd	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(2.39601 - 1.53982i) q^{2} +(0.0464818 - 0.101781i) q^{4} +(1.22325 - 0.359177i) q^{5} +(-1.84765 - 2.13230i) q^{7} +(3.19731 + 22.2377i) q^{8} +O(q^{10})\)	\(q+(2.39601 - 1.53982i) q^{2} +(0.0464818 - 0.101781i) q^{4} +(1.22325 - 0.359177i) q^{5} +(-1.84765 - 2.13230i) q^{7} +(3.19731 + 22.2377i) q^{8} +(2.37784 - 2.74417i) q^{10} +(46.9103 + 30.1474i) q^{11} +(41.6560 - 48.0736i) q^{13} +(-7.71035 - 2.26396i) q^{14} +(42.4891 + 49.0350i) q^{16} +(43.6303 + 95.5370i) q^{17} +(21.0526 - 46.0988i) q^{19} +(0.0203012 - 0.141198i) q^{20} +158.819 q^{22} +(41.4645 - 102.214i) q^{23} +(-103.789 + 66.7014i) q^{25} +(25.7834 - 179.327i) q^{26} +(-0.302910 + 0.0889424i) q^{28} +(25.6108 + 56.0799i) q^{29} +(25.6432 + 178.352i) q^{31} +(4.85820 + 1.42650i) q^{32} +(251.648 + 161.724i) q^{34} +(-3.02601 - 1.94470i) q^{35} +(-6.66337 - 1.95654i) q^{37} +(-20.5417 - 142.870i) q^{38} +(11.8984 + 26.0538i) q^{40} +(182.253 - 53.5143i) q^{41} +(23.4578 - 163.152i) q^{43} +(5.24891 - 3.37327i) q^{44} +(-58.0419 - 308.753i) q^{46} -347.894 q^{47} +(47.6811 - 331.629i) q^{49} +(-145.972 + 319.634i) q^{50} +(-2.95673 - 6.47433i) q^{52} +(-175.609 - 202.664i) q^{53} +(68.2111 + 20.0286i) q^{55} +(41.5101 - 47.9052i) q^{56} +(147.717 + 94.9317i) q^{58} +(-260.298 + 300.400i) q^{59} +(-53.6466 - 373.120i) q^{61} +(336.072 + 387.847i) q^{62} +(-484.199 + 142.174i) q^{64} +(33.6886 - 73.7677i) q^{65} +(-620.815 + 398.974i) q^{67} +11.7518 q^{68} -10.2448 q^{70} +(535.845 - 344.367i) q^{71} +(87.3936 - 191.365i) q^{73} +(-18.9782 + 5.57250i) q^{74} +(-3.71342 - 4.28551i) q^{76} +(-22.3905 - 155.729i) q^{77} +(-99.3022 + 114.601i) q^{79} +(69.5868 + 44.7207i) q^{80} +(354.277 - 408.857i) q^{82} +(-231.505 - 67.9759i) q^{83} +(87.6853 + 101.194i) q^{85} +(-195.020 - 427.035i) q^{86} +(-520.425 + 1139.57i) q^{88} +(-225.970 + 1571.65i) q^{89} -179.473 q^{91} +(-8.47608 - 8.97138i) q^{92} +(-833.556 + 535.694i) q^{94} +(9.19488 - 63.9518i) q^{95} +(534.312 - 156.888i) q^{97} +(-396.405 - 868.006i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8}+O(q^{10}) \) 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8	\( 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8} - 78 q^{10} - 10 q^{11} + 50 q^{13} + 224 q^{14} + 260 q^{16} + 662 q^{17} - 4 q^{19} + 735 q^{20} + 622 q^{22} + 438 q^{23} - 754 q^{25} + 40 q^{26} + 672 q^{28} - 1302 q^{29} + 1528 q^{31} - 1588 q^{32} + 29 q^{34} - 950 q^{35} + 316 q^{37} - 3122 q^{38} - 1939 q^{40} + 1500 q^{41} - 1316 q^{43} + 2901 q^{44} - 1980 q^{46} + 1440 q^{47} - 2310 q^{49} - 195 q^{50} + 6189 q^{52} + 148 q^{53} - 606 q^{55} + 432 q^{56} - 2623 q^{58} - 5264 q^{59} + 1482 q^{61} + 2299 q^{62} - 6780 q^{64} + 1446 q^{65} + 388 q^{67} - 5604 q^{68} + 2984 q^{70} + 3316 q^{71} + 2072 q^{73} + 6556 q^{74} + 9841 q^{76} - 9338 q^{77} + 268 q^{79} - 7980 q^{80} + 7742 q^{82} + 3494 q^{83} - 3842 q^{85} + 4792 q^{86} - 7960 q^{88} + 2754 q^{89} - 5436 q^{91} + 17609 q^{92} - 10961 q^{94} + 2396 q^{95} - 5654 q^{97} - 14411 q^{98}+O(q^{100}) \) 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8 - 78 * q^10 - 10 * q^11 + 50 * q^13 + 224 * q^14 + 260 * q^16 + 662 * q^17 - 4 * q^19 + 735 * q^20 + 622 * q^22 + 438 * q^23 - 754 * q^25 + 40 * q^26 + 672 * q^28 - 1302 * q^29 + 1528 * q^31 - 1588 * q^32 + 29 * q^34 - 950 * q^35 + 316 * q^37 - 3122 * q^38 - 1939 * q^40 + 1500 * q^41 - 1316 * q^43 + 2901 * q^44 - 1980 * q^46 + 1440 * q^47 - 2310 * q^49 - 195 * q^50 + 6189 * q^52 + 148 * q^53 - 606 * q^55 + 432 * q^56 - 2623 * q^58 - 5264 * q^59 + 1482 * q^61 + 2299 * q^62 - 6780 * q^64 + 1446 * q^65 + 388 * q^67 - 5604 * q^68 + 2984 * q^70 + 3316 * q^71 + 2072 * q^73 + 6556 * q^74 + 9841 * q^76 - 9338 * q^77 + 268 * q^79 - 7980 * q^80 + 7742 * q^82 + 3494 * q^83 - 3842 * q^85 + 4792 * q^86 - 7960 * q^88 + 2754 * q^89 - 5436 * q^91 + 17609 * q^92 - 10961 * q^94 + 2396 * q^95 - 5654 * q^97 - 14411 * q^98

Introduction

L-functions

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