LMFDB - Embedded newform 69.4.e.b.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,4,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	69.e (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:	$4.07113179040$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	69.13
Dual form			69.4.e.b.16.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56668 + 1.80804i) q^{2} +(-2.52376 - 1.62192i) q^{3} +(0.323978 - 2.25332i) q^{4} +(6.20398 - 13.5848i) q^{5} +(-1.02142 - 7.10410i) q^{6} +(-24.5496 - 7.20842i) q^{7} +(20.6825 - 13.2918i) q^{8} +(3.73874 + 8.18669i) q^{9} +O(q^{10})$	\(q+(1.56668 + 1.80804i) q^{2} +(-2.52376 - 1.62192i) q^{3} +(0.323978 - 2.25332i) q^{4} +(6.20398 - 13.5848i) q^{5} +(-1.02142 - 7.10410i) q^{6} +(-24.5496 - 7.20842i) q^{7} +(20.6825 - 13.2918i) q^{8} +(3.73874 + 8.18669i) q^{9} +(34.2816 - 10.0660i) q^{10} +(-11.9090 + 13.7437i) q^{11} +(-4.47235 + 5.16137i) q^{12} +(86.3921 - 25.3670i) q^{13} +(-25.4282 - 55.6801i) q^{14} +(-37.6909 + 24.2225i) q^{15} +(38.9608 + 11.4399i) q^{16} +(0.0854087 + 0.594031i) q^{17} +(-8.94450 + 19.5857i) q^{18} +(-13.3171 + 92.6227i) q^{19} +(-28.6010 - 18.3807i) q^{20} +(50.2659 + 58.0099i) q^{21} -43.5068 q^{22} +(-110.140 + 6.01038i) q^{23} -73.7560 q^{24} +(-64.2004 - 74.0912i) q^{25} +(181.213 + 116.459i) q^{26} +(3.84250 - 26.7252i) q^{27} +(-24.1964 + 52.9828i) q^{28} +(-10.2601 - 71.3608i) q^{29} +(-102.845 - 30.1980i) q^{30} +(219.303 - 140.937i) q^{31} +(-41.3497 - 90.5432i) q^{32} +(52.3466 - 15.3704i) q^{33} +(-0.940226 + 1.08508i) q^{34} +(-250.230 + 288.781i) q^{35} +(19.6585 - 5.77226i) q^{36} +(53.6514 + 117.480i) q^{37} +(-188.330 + 121.032i) q^{38} +(-259.176 - 76.1010i) q^{39} +(-52.2534 - 363.430i) q^{40} +(-93.5789 + 204.909i) q^{41} +(-26.1340 + 181.766i) q^{42} +(396.280 + 254.674i) q^{43} +(27.1107 + 31.2874i) q^{44} +134.410 q^{45} +(-183.421 - 189.722i) q^{46} +194.164 q^{47} +(-79.7732 - 92.0631i) q^{48} +(262.172 + 168.488i) q^{49} +(33.3788 - 232.154i) q^{50} +(0.747921 - 1.63772i) q^{51} +(-29.1708 - 202.887i) q^{52} +(468.220 + 137.482i) q^{53} +(54.3403 - 34.9224i) q^{54} +(112.823 + 247.047i) q^{55} +(-603.560 + 177.221i) q^{56} +(183.836 - 212.158i) q^{57} +(112.949 - 130.350i) q^{58} +(-133.372 + 39.1616i) q^{59} +(42.3699 + 92.7772i) q^{60} +(-317.541 + 204.071i) q^{61} +(598.398 + 175.705i) q^{62} +(-32.7714 - 227.930i) q^{63} +(233.870 - 512.104i) q^{64} +(191.369 - 1331.00i) q^{65} +(109.801 + 70.5646i) q^{66} +(-202.983 - 234.255i) q^{67} +1.36621 q^{68} +(287.716 + 163.470i) q^{69} -914.160 q^{70} +(-593.068 - 684.437i) q^{71} +(186.142 + 119.626i) q^{72} +(-45.8429 + 318.844i) q^{73} +(-128.355 + 281.058i) q^{74} +(41.8562 + 291.117i) q^{75} +(204.394 + 60.0155i) q^{76} +(391.431 - 251.557i) q^{77} +(-268.452 - 587.828i) q^{78} +(938.227 - 275.488i) q^{79} +(397.122 - 458.303i) q^{80} +(-53.0437 + 61.2157i) q^{81} +(-517.093 + 151.832i) q^{82} +(438.077 + 959.255i) q^{83} +(147.000 - 94.4711i) q^{84} +(8.59968 + 2.52509i) q^{85} +(160.382 + 1115.48i) q^{86} +(-89.8476 + 196.739i) q^{87} +(-63.6285 + 442.546i) q^{88} +(-797.225 - 512.346i) q^{89} +(210.577 + 243.019i) q^{90} -2303.75 q^{91} +(-22.1398 + 250.128i) q^{92} -782.057 q^{93} +(304.192 + 351.056i) q^{94} +(1175.64 + 755.540i) q^{95} +(-42.4973 + 295.575i) q^{96} +(-510.773 + 1118.44i) q^{97} +(106.106 + 737.985i) q^{98} +(-157.040 - 46.1111i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 4 q^{2} + 18 q^{3} - 28 q^{4} - 6 q^{5} + 21 q^{6} - 4 q^{7} - 52 q^{8} - 54 q^{9}+O(q^{10}) $ 60 * q + 4 * q^2 + 18 * q^3 - 28 * q^4 - 6 * q^5 + 21 * q^6 - 4 * q^7 - 52 * q^8 - 54 * q^9	\( 60 q + 4 q^{2} + 18 q^{3} - 28 q^{4} - 6 q^{5} + 21 q^{6} - 4 q^{7} - 52 q^{8} - 54 q^{9} - 78 q^{10} + 10 q^{11} + 84 q^{12} + 50 q^{13} - 224 q^{14} + 150 q^{15} + 260 q^{16} - 662 q^{17} + 36 q^{18} - 4 q^{19} - 735 q^{20} + 12 q^{21} + 622 q^{22} - 438 q^{23} - 108 q^{24} - 754 q^{25} - 40 q^{26} + 162 q^{27} + 672 q^{28} + 1302 q^{29} + 234 q^{30} + 1528 q^{31} + 1588 q^{32} - 492 q^{33} + 29 q^{34} + 950 q^{35} + 243 q^{36} + 316 q^{37} + 3122 q^{38} - 150 q^{39} - 1939 q^{40} - 1500 q^{41} - 2298 q^{42} - 1316 q^{43} - 2901 q^{44} + 936 q^{45} - 1980 q^{46} - 1440 q^{47} - 2265 q^{48} - 2310 q^{49} + 195 q^{50} - 126 q^{51} + 6189 q^{52} - 148 q^{53} + 189 q^{54} - 606 q^{55} - 432 q^{56} + 1398 q^{57} - 2623 q^{58} + 5264 q^{59} + 753 q^{60} + 1482 q^{61} - 2299 q^{62} - 36 q^{63} - 6780 q^{64} - 1446 q^{65} + 1731 q^{66} + 388 q^{67} + 5604 q^{68} - 138 q^{69} + 2984 q^{70} - 3316 q^{71} - 468 q^{72} + 2072 q^{73} - 6556 q^{74} + 1206 q^{75} + 9841 q^{76} + 9338 q^{77} - 3048 q^{78} + 268 q^{79} + 7980 q^{80} - 486 q^{81} + 7742 q^{82} - 3494 q^{83} + 2604 q^{84} - 3842 q^{85} - 4792 q^{86} - 672 q^{87} - 7960 q^{88} - 2754 q^{89} - 702 q^{90} - 5436 q^{91} - 17609 q^{92} + 2280 q^{93} - 10961 q^{94} - 2396 q^{95} + 6852 q^{96} - 5654 q^{97} + 14411 q^{98} + 1476 q^{99}+O(q^{100}) \) 60 * q + 4 * q^2 + 18 * q^3 - 28 * q^4 - 6 * q^5 + 21 * q^6 - 4 * q^7 - 52 * q^8 - 54 * q^9 - 78 * q^10 + 10 * q^11 + 84 * q^12 + 50 * q^13 - 224 * q^14 + 150 * q^15 + 260 * q^16 - 662 * q^17 + 36 * q^18 - 4 * q^19 - 735 * q^20 + 12 * q^21 + 622 * q^22 - 438 * q^23 - 108 * q^24 - 754 * q^25 - 40 * q^26 + 162 * q^27 + 672 * q^28 + 1302 * q^29 + 234 * q^30 + 1528 * q^31 + 1588 * q^32 - 492 * q^33 + 29 * q^34 + 950 * q^35 + 243 * q^36 + 316 * q^37 + 3122 * q^38 - 150 * q^39 - 1939 * q^40 - 1500 * q^41 - 2298 * q^42 - 1316 * q^43 - 2901 * q^44 + 936 * q^45 - 1980 * q^46 - 1440 * q^47 - 2265 * q^48 - 2310 * q^49 + 195 * q^50 - 126 * q^51 + 6189 * q^52 - 148 * q^53 + 189 * q^54 - 606 * q^55 - 432 * q^56 + 1398 * q^57 - 2623 * q^58 + 5264 * q^59 + 753 * q^60 + 1482 * q^61 - 2299 * q^62 - 36 * q^63 - 6780 * q^64 - 1446 * q^65 + 1731 * q^66 + 388 * q^67 + 5604 * q^68 - 138 * q^69 + 2984 * q^70 - 3316 * q^71 - 468 * q^72 + 2072 * q^73 - 6556 * q^74 + 1206 * q^75 + 9841 * q^76 + 9338 * q^77 - 3048 * q^78 + 268 * q^79 + 7980 * q^80 - 486 * q^81 + 7742 * q^82 - 3494 * q^83 + 2604 * q^84 - 3842 * q^85 - 4792 * q^86 - 672 * q^87 - 7960 * q^88 - 2754 * q^89 - 702 * q^90 - 5436 * q^91 - 17609 * q^92 + 2280 * q^93 - 10961 * q^94 - 2396 * q^95 + 6852 * q^96 - 5654 * q^97 + 14411 * q^98 + 1476 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

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 $

$2$	1.56668	+	1.80804i	0.553905	+	0.639240i	0.961788	−	0.273794i	$-0.0882786\pi$
$2$	1.56668	+	1.80804i	0.553905	+	0.639240i	−0.407884	+	0.913034i	$0.633733\pi$
$3$	−2.52376	−	1.62192i	−0.485698	−	0.312139i
$3$	−2.52376	−	1.62192i	−0.485698	−	0.312139i
$4$	0.323978	−	2.25332i	0.0404973	−	0.281665i
$5$	6.20398	−	13.5848i	0.554901	−	1.21506i	−0.399554	−	0.916709i	$-0.630835\pi$
$5$	6.20398	−	13.5848i	0.554901	−	1.21506i	0.954455	−	0.298354i	$-0.0964376\pi$
$6$	−1.02142	−	7.10410i	−0.0694985	−	0.483373i
$7$	−24.5496	−	7.20842i	−1.32555	−	0.389218i	−0.459060	−	0.888405i	$-0.651814\pi$
$7$	−24.5496	−	7.20842i	−1.32555	−	0.389218i	−0.866494	+	0.499187i	$0.833632\pi$
$8$	20.6825	−	13.2918i	0.914046	−	0.587422i
$9$	3.73874	+	8.18669i	0.138472	+	0.303211i
$10$	34.2816	−	10.0660i	1.08408	−	0.318314i
$11$	−11.9090	+	13.7437i	−0.326427	+	0.376716i	−0.895114	−	0.445837i	$-0.852906\pi$
$11$	−11.9090	+	13.7437i	−0.326427	+	0.376716i	0.568687	+	0.822554i	$0.307451\pi$
$12$	−4.47235	+	5.16137i	−0.107588	+	0.124163i
$13$	86.3921	−	25.3670i	1.84314	−	0.541196i	0.843149	−	0.537680i	$-0.180699\pi$
$13$	86.3921	−	25.3670i	1.84314	−	0.541196i	0.999994	−	0.00351590i	$-0.00111915\pi$
$14$	−25.4282	−	55.6801i	−0.485427	−	1.06294i
$15$	−37.6909	+	24.2225i	−0.648783	+	0.416948i
$16$	38.9608	+	11.4399i	0.608763	+	0.178749i
$17$	0.0854087	+	0.594031i	0.00121851	+	0.00847492i	0.990422	−	0.138076i	$-0.0440918\pi$
$17$	0.0854087	+	0.594031i	0.00121851	+	0.00847492i	−0.989203	+	0.146551i	$0.953183\pi$
$18$	−8.94450	+	19.5857i	−0.117124	+	0.256467i
$19$	−13.3171	+	92.6227i	−0.160798	+	1.11837i	0.736336	+	0.676616i	$0.236554\pi$
$19$	−13.3171	+	92.6227i	−0.160798	+	1.11837i	−0.897134	+	0.441758i	$0.854355\pi$
$20$	−28.6010	−	18.3807i	−0.319769	−	0.205503i
$21$	50.2659	+	58.0099i	0.522329	+	0.602800i
$22$	−43.5068			−0.421621
$23$	−110.140	+	6.01038i	−0.998514	+	0.0544891i
$23$	−110.140	+	6.01038i	−0.998514	+	0.0544891i
$24$	−73.7560			−0.627307
$25$	−64.2004	−	74.0912i	−0.513603	−	0.592730i
$26$	181.213	+	116.459i	1.36688	+	0.878440i
$27$	3.84250	−	26.7252i	0.0273885	−	0.190491i
$28$	−24.1964	+	52.9828i	−0.163310	+	0.357600i
$29$	−10.2601	−	71.3608i	−0.0656986	−	0.456944i	−0.995942	−	0.0900001i	$-0.971313\pi$
$29$	−10.2601	−	71.3608i	−0.0656986	−	0.456944i	0.930243	−	0.366944i	$-0.119596\pi$
$30$	−102.845	−	30.1980i	−0.625894	−	0.183779i
$31$	219.303	−	140.937i	1.27058	−	0.816551i	0.280883	−	0.959742i	$-0.409373\pi$
$31$	219.303	−	140.937i	1.27058	−	0.816551i	0.989695	+	0.143191i	$0.0457363\pi$
$32$	−41.3497	−	90.5432i	−0.228427	−	0.500185i
$33$	52.3466	−	15.3704i	0.276133	−	0.0810798i
$34$	−0.940226	+	1.08508i	−0.00474257	+	0.00547322i
$35$	−250.230	+	288.781i	−1.20848	+	1.39466i
$36$	19.6585	−	5.77226i	0.0910116	−	0.0267234i
$37$	53.6514	+	117.480i	0.238385	+	0.521990i	0.990577	−	0.136953i	$-0.0437311\pi$
$37$	53.6514	+	117.480i	0.238385	+	0.521990i	−0.752193	+	0.658943i	$0.771004\pi$
$38$	−188.330	+	121.032i	−0.803976	+	0.516684i
$39$	−259.176	−	76.1010i	−1.06414	−	0.312459i
$40$	−52.2534	−	363.430i	−0.206550	−	1.43658i
$41$	−93.5789	+	204.909i	−0.356453	+	0.780523i	0.643434	+	0.765501i	$0.277509\pi$
$41$	−93.5789	+	204.909i	−0.356453	+	0.780523i	−0.999887	+	0.0150215i	$0.995218\pi$
$42$	−26.1340	+	181.766i	−0.0960133	+	0.667787i
$43$	396.280	+	254.674i	1.40540	+	0.903195i	0.999940	−	0.0109185i	$-0.00347553\pi$
$43$	396.280	+	254.674i	1.40540	+	0.903195i	0.405458	+	0.914113i	$0.367112\pi$
$44$	27.1107	+	31.2874i	0.0928884	+	0.107199i
$45$	134.410			0.445258
$46$	−183.421	−	189.722i	−0.587914	−	0.608109i
$47$	194.164			0.602589			0.301294	−	0.953531i	$-0.402581\pi$
$47$	194.164			0.602589			0.301294	+	0.953531i	$0.402581\pi$
$48$	−79.7732	−	92.0631i	−0.239880	−	0.276837i
$49$	262.172	+	168.488i	0.764350	+	0.491218i
$50$	33.3788	−	232.154i	0.0944094	−	0.656632i
$51$	0.747921	−	1.63772i	0.00205353	−	0.00449659i
$52$	−29.1708	−	202.887i	−0.0777935	−	0.541066i
$53$	468.220	+	137.482i	1.21349	+	0.356313i	0.824996	−	0.565139i	$-0.191177\pi$
$53$	468.220	+	137.482i	1.21349	+	0.356313i	0.388494	+	0.921451i	$0.372995\pi$
$54$	54.3403	−	34.9224i	0.136940	−	0.0880062i
$55$	112.823	+	247.047i	0.276600	+	0.605669i
$56$	−603.560	+	177.221i	−1.44025	+	0.422896i
$57$	183.836	−	212.158i	0.427187	−	0.493000i
$58$	112.949	−	130.350i	0.255706	−	0.295100i
$59$	−133.372	+	39.1616i	−0.294298	+	0.0864138i	−0.425549	−	0.904935i	$-0.639919\pi$
$59$	−133.372	+	39.1616i	−0.294298	+	0.0864138i	0.131251	+	0.991349i	$0.458101\pi$
$60$	42.3699	+	92.7772i	0.0911655	+	0.199625i
$61$	−317.541	+	204.071i	−0.666507	+	0.428338i	−0.829665	−	0.558262i	$-0.811468\pi$
$61$	−317.541	+	204.071i	−0.666507	+	0.428338i	0.163158	+	0.986600i	$0.447832\pi$
$62$	598.398	+	175.705i	1.22575	+	0.359913i
$63$	−32.7714	−	227.930i	−0.0655367	−	0.455818i
$64$	233.870	−	512.104i	0.456777	−	1.00020i
$65$	191.369	−	1331.00i	0.365175	−	2.53985i
$66$	109.801	+	70.5646i	0.204781	+	0.131605i
$67$	−202.983	−	234.255i	−0.370124	−	0.427146i	0.539882	−	0.841741i	$-0.318469\pi$
$67$	−202.983	−	234.255i	−0.370124	−	0.427146i	−0.910006	+	0.414595i	$0.863923\pi$
$68$	1.36621			0.00243643
$69$	287.716	+	163.470i	0.501985	+	0.285210i
$70$	−914.160			−1.56090
$71$	−593.068	−	684.437i	−0.991327	−	1.14405i	−0.989570	−	0.144054i	$-0.953986\pi$
$71$	−593.068	−	684.437i	−0.991327	−	1.14405i	−0.00175727	−	0.999998i	$-0.500559\pi$
$72$	186.142	+	119.626i	0.304682	+	0.195807i
$73$	−45.8429	+	318.844i	−0.0735000	+	0.511204i	0.919500	+	0.393090i	$0.128594\pi$
$73$	−45.8429	+	318.844i	−0.0735000	+	0.511204i	−0.993000	+	0.118114i	$0.962315\pi$
$74$	−128.355	+	281.058i	−0.201634	+	0.441518i
$75$	41.8562	+	291.117i	0.0644419	+	0.448203i
$76$	204.394	+	60.0155i	0.308495	+	0.0905822i
$77$	391.431	−	251.557i	0.579321	−	0.372307i
$78$	−268.452	−	587.828i	−0.389695	−	0.853313i
$79$	938.227	−	275.488i	1.33619	−	0.392340i	0.465880	−	0.884848i	$-0.345738\pi$
$79$	938.227	−	275.488i	1.33619	−	0.392340i	0.870308	+	0.492508i	$0.163920\pi$
$80$	397.122	−	458.303i	0.554995	−	0.640498i
$81$	−53.0437	+	61.2157i	−0.0727623	+	0.0839722i
$82$	−517.093	+	151.832i	−0.696382	+	0.204476i
$83$	438.077	+	959.255i	0.579340	+	1.26858i	0.941673	+	0.336528i	$0.109253\pi$
$83$	438.077	+	959.255i	0.579340	+	1.26858i	−0.362334	+	0.932048i	$0.618020\pi$
$84$	147.000	−	94.4711i	0.190940	−	0.122710i
$85$	8.59968	+	2.52509i	0.0109737	+	0.00322217i
$86$	160.382	+	1115.48i	0.201099	+	1.39867i
$87$	−89.8476	+	196.739i	−0.110720	+	0.242444i
$88$	−63.6285	+	442.546i	−0.0770775	+	0.536086i
$89$	−797.225	−	512.346i	−0.949503	−	0.610208i	−0.0284286	−	0.999596i	$-0.509050\pi$
$89$	−797.225	−	512.346i	−0.949503	−	0.610208i	−0.921074	+	0.389388i	$0.872687\pi$
$90$	210.577	+	243.019i	0.246631	+	0.284627i
$91$	−2303.75			−2.65383
$92$	−22.1398	+	250.128i	−0.0250895	+	0.283453i
$93$	−782.057			−0.871995
$94$	304.192	+	351.056i	0.333777	+	0.385199i
$95$	1175.64	+	755.540i	1.26967	+	0.815966i
$96$	−42.4973	+	295.575i	−0.0451809	+	0.314240i
$97$	−510.773	+	1118.44i	−0.534651	+	1.17072i	0.428938	+	0.903334i	$0.358888\pi$
$97$	−510.773	+	1118.44i	−0.534651	+	1.17072i	−0.963589	+	0.267389i	$0.913839\pi$
$98$	106.106	+	737.985i	0.109371	+	0.760692i
$99$	−157.040	−	46.1111i	−0.159425	−	0.0468115i
$100$	−187.751	+	120.660i	−0.187751	+	0.120660i
$101$	−403.082	−	882.627i	−0.397111	−	0.869551i	−0.997555	−	0.0698846i	$-0.977737\pi$
$101$	−403.082	−	882.627i	−0.397111	−	0.869551i	0.600444	−	0.799667i	$-0.294990\pi$
$102$	4.13282	−	1.21350i	0.00401186	−	0.00117799i
$103$	−253.616	+	292.688i	−0.242616	+	0.279994i	−0.863978	−	0.503530i	$-0.832034\pi$
$103$	−253.616	+	292.688i	−0.242616	+	0.279994i	0.621361	+	0.783524i	$0.286580\pi$
$104$	1449.63	−	1672.96i	1.36681	−	1.57738i
$105$	1099.90	−	322.960i	1.02228	−	0.300169i
$106$	484.977	+	1061.95i	0.444388	+	0.973075i
$107$	−389.393	+	250.248i	−0.351814	+	0.226097i	−0.704596	−	0.709608i	$-0.748872\pi$
$107$	−389.393	+	250.248i	−0.351814	+	0.226097i	0.352783	+	0.935705i	$0.385236\pi$
$108$	−58.9755	−	17.3168i	−0.0525455	−	0.0154288i
$109$	−73.2071	−	509.167i	−0.0643300	−	0.447425i	−0.996374	−	0.0850801i	$-0.972885\pi$
$109$	−73.2071	−	509.167i	−0.0643300	−	0.447425i	0.932044	−	0.362345i	$-0.118024\pi$
$110$	−269.915	+	591.031i	−0.233958	+	0.512297i
$111$	55.1404	−	383.510i	0.0471504	−	0.327939i
$112$	−874.010	−	561.692i	−0.737376	−	0.473883i
$113$	−805.052	−	929.080i	−0.670203	−	0.773456i	0.314205	−	0.949355i	$-0.398262\pi$
$113$	−805.052	−	929.080i	−0.670203	−	0.773456i	−0.984408	+	0.175899i	$0.943717\pi$
$114$	671.603			0.551767
$115$	−601.658	+	1533.52i	−0.487869	+	1.24349i
$116$	−164.123			−0.131366
$117$	530.669	+	612.425i	0.419319	+	0.483920i
$118$	−279.758	−	179.789i	−0.218252	−	0.140262i
$119$	2.18527	−	15.1989i	0.00168339	−	0.0117082i
$120$	−457.581	+	1001.96i	−0.348093	+	0.762218i
$121$	142.356	+	990.106i	0.106954	+	0.743881i
$122$	−866.454	−	254.414i	−0.642992	−	0.188800i
$123$	568.517	−	365.364i	0.416760	−	0.267835i
$124$	−246.527	−	539.820i	−0.178539	−	0.390945i
$125$	386.369	−	113.448i	0.276463	−	0.0811769i
$126$	360.766	−	416.346i	0.255076	−	0.294373i
$127$	−28.1636	+	32.5025i	−0.0196780	+	0.0227097i	−0.765503	−	0.643432i	$-0.777510\pi$
$127$	−28.1636	+	32.5025i	−0.0196780	+	0.0227097i	0.745825	+	0.666142i	$0.232055\pi$
$128$	528.256	−	155.110i	0.364779	−	0.107109i
$129$	−587.055	−	1285.47i	−0.400677	−	0.877360i
$130$	2706.32	−	1739.24i	1.82584	−	1.17340i
$131$	−1281.81	−	376.375i	−0.854906	−	0.251023i	−0.175223	−	0.984529i	$-0.556065\pi$
$131$	−1281.81	−	376.375i	−0.854906	−	0.251023i	−0.679683	+	0.733506i	$0.737883\pi$
$132$	−17.6751	−	122.933i	−0.0116547	−	0.0810604i
$133$	994.593	−	2177.86i	0.648437	−	1.41988i
$134$	105.534	−	734.004i	0.0680353	−	0.473196i
$135$	−339.218	−	218.002i	−0.216261	−	0.138983i
$136$	9.66222	+	11.1508i	0.00609212	+	0.00703068i
$137$	284.337			0.177318			0.0886590	−	0.996062i	$-0.471742\pi$
$137$	284.337			0.177318			0.0886590	+	0.996062i	$0.471742\pi$
$138$	155.197	+	776.309i	0.0957339	+	0.478868i
$139$	1353.39			0.825847			0.412923	−	0.910766i	$-0.364508\pi$
$139$	1353.39			0.825847			0.412923	+	0.910766i	$0.364508\pi$
$140$	569.647	+	657.408i	0.343886	+	0.396865i
$141$	−490.023	−	314.918i	−0.292676	−	0.188092i
$142$	308.345	−	2144.59i	0.182224	−	1.26739i
$143$	−680.205	+	1489.44i	−0.397774	+	0.871003i
$144$	52.0091	+	361.731i	0.0300979	+	0.209335i
$145$	−1033.08	−	303.339i	−0.591672	−	0.173730i
$146$	−648.306	+	416.641i	−0.367494	+	0.236174i
$147$	−388.386	−	850.446i	−0.217915	−	0.477167i
$148$	282.102	−	82.8327i	0.156680	−	0.0460054i
$149$	−711.054	+	820.600i	−0.390952	+	0.451183i	−0.916771	−	0.399414i	$-0.869214\pi$
$149$	−711.054	+	820.600i	−0.390952	+	0.451183i	0.525819	+	0.850597i	$0.323759\pi$
$150$	−460.776	+	531.764i	−0.250815	+	0.289456i
$151$	−242.714	+	71.2672i	−0.130806	+	0.0384082i	−0.346480	−	0.938057i	$-0.612623\pi$
$151$	−242.714	+	71.2672i	−0.130806	+	0.0384082i	0.215674	+	0.976465i	$0.430805\pi$
$152$	955.694	+	2092.68i	0.509980	+	1.11670i
$153$	−4.54382	+	2.92014i	−0.00240096	+	0.00154300i
$154$	1068.07	+	313.615i	0.558882	+	0.164103i
$155$	−554.058	−	3853.56i	−0.287116	−	1.99694i
$156$	−255.448	+	559.352i	−0.131104	+	0.287077i
$157$	14.9262	−	103.814i	0.00758753	−	0.0527725i	−0.985676	−	0.168650i	$-0.946059\pi$
$157$	14.9262	−	103.814i	0.00758753	−	0.0527725i	0.993263	+	0.115878i	$0.0369682\pi$
$158$	1968.00	+	1264.75i	0.990920	+	0.636826i
$159$	−958.690	−	1106.39i	−0.478170	−	0.551838i
$160$	−1486.55			−0.734511
$161$	2747.23	+	646.384i	1.34479	+	0.316411i
$162$	−193.783			−0.0939818
$163$	−943.638	−	1089.02i	−0.453444	−	0.523302i	0.482289	−	0.876012i	$-0.339806\pi$
$163$	−943.638	−	1089.02i	−0.453444	−	0.523302i	−0.935733	+	0.352710i	$0.885260\pi$
$164$	431.408	+	277.249i	0.205411	+	0.132009i
$165$	115.954	−	806.477i	0.0547091	−	0.380510i
$166$	−1048.05	+	2294.91i	−0.490026	+	1.07301i
$167$	172.683	+	1201.04i	0.0800158	+	0.556522i	0.989912	+	0.141686i	$0.0452522\pi$
$167$	172.683	+	1201.04i	0.0800158	+	0.556522i	−0.909896	+	0.414837i	$0.863839\pi$
$168$	1810.68	+	531.664i	0.831530	+	0.244159i
$169$	4971.88	−	3195.23i	2.26303	−	1.45436i
$170$	8.90745	+	19.5046i	0.00401865	+	0.00879962i
$171$	−808.062	+	237.268i	−0.361369	+	0.106107i
$172$	702.248	−	810.437i	0.311313	−	0.359275i
$173$	−632.321	+	729.737i	−0.277887	+	0.320699i	−0.877486	−	0.479602i	$-0.840781\pi$
$173$	−632.321	+	729.737i	−0.277887	+	0.320699i	0.599599	+	0.800300i	$0.295327\pi$
$174$	−496.475	+	145.778i	−0.216308	+	0.0635138i
$175$	1042.01	+	2281.69i	0.450108	+	0.985599i
$176$	−621.211	+	399.228i	−0.266054	+	0.170983i
$177$	400.117	+	117.485i	0.169913	+	0.0498910i
$178$	−322.653	−	2244.10i	−0.135864	−	0.944958i
$179$	−1716.04	+	3757.60i	−0.716551	+	1.56903i	0.102124	+	0.994772i	$0.467436\pi$
$179$	−1716.04	+	3757.60i	−0.716551	+	1.56903i	−0.818675	+	0.574257i	$0.805291\pi$
$180$	43.5459	−	302.868i	0.0180318	−	0.125414i
$181$	788.779	+	506.918i	0.323920	+	0.208171i	0.692487	−	0.721431i	$-0.256515\pi$
$181$	788.779	+	506.918i	0.323920	+	0.208171i	−0.368567	+	0.929601i	$0.620151\pi$
$182$	−3609.24	−	4165.28i	−1.46997	−	1.69643i
$183$	1132.38			0.457422
$184$	−2198.09	+	1588.28i	−0.880680	+	0.636354i
$185$	1928.80			0.766530
$186$	−1225.23	−	1413.99i	−0.483002	−	0.557414i
$187$	−9.18131	−	5.90047i	−0.00359039	−	0.00230741i
$188$	62.9048	−	437.513i	0.0244032	−	0.169728i
$189$	−286.978	+	628.394i	−0.110448	+	0.241846i
$190$	475.806	+	3309.30i	0.181677	+	1.26359i
$191$	−4791.85	−	1407.01i	−1.81532	−	0.533026i	−0.816315	−	0.577607i	$-0.803987\pi$
$191$	−4791.85	−	1407.01i	−1.81532	−	0.533026i	−0.999006	+	0.0445805i	$0.985805\pi$
$192$	−1420.82	+	913.108i	−0.534058	+	0.343218i
$193$	1055.96	+	2312.23i	0.393833	+	0.862374i	0.997859	+	0.0654091i	$0.0208352\pi$
$193$	1055.96	+	2312.23i	0.393833	+	0.862374i	−0.604025	+	0.796965i	$0.706437\pi$
$194$	−2822.40	+	828.732i	−1.04452	+	0.306698i
$195$	−2641.74	+	3048.73i	−0.970150	+	1.11961i
$196$	464.595	−	536.171i	0.169313	−	0.195398i
$197$	2279.68	−	669.375i	0.824470	−	0.242086i	0.157830	−	0.987466i	$-0.449550\pi$
$197$	2279.68	−	669.375i	0.824470	−	0.242086i	0.666640	+	0.745380i	$0.267732\pi$
$198$	−162.660	−	356.176i	−0.0583826	−	0.127840i
$199$	−1791.40	+	1151.26i	−0.638136	+	0.410105i	−0.819314	−	0.573345i	$-0.805645\pi$
$199$	−1791.40	+	1151.26i	−0.638136	+	0.410105i	0.181178	+	0.983450i	$0.442009\pi$
$200$	−2312.63	−	679.050i	−0.817639	−	0.240081i
$201$	132.337	+	920.425i	0.0464395	+	0.322994i
$202$	964.328	−	2111.58i	0.335891	−	0.735498i
$203$	−262.516	+	1825.84i	−0.0907636	+	0.631275i
$204$	−3.44799	−	2.21589i	−0.00118337	−	0.000760506i
$205$	2203.09	+	2542.50i	0.750589	+	0.866225i
$206$	−926.528			−0.313370
$207$	−460.990	−	879.213i	−0.154788	−	0.295215i
$208$	3656.11			1.21878
$209$	−1114.38	−	1286.07i	−0.368821	−	0.425642i
$210$	2307.12	+	1482.70i	0.758126	+	0.487218i
$211$	463.459	−	3223.43i	0.151213	−	1.05171i	−0.762979	−	0.646423i	$-0.776264\pi$
$211$	463.459	−	3223.43i	0.151213	−	1.05171i	0.914191	−	0.405283i	$-0.132827\pi$
$212$	461.484	−	1010.51i	0.149504	−	0.327368i
$213$	386.658	+	2689.27i	0.124382	+	0.865096i
$214$	−1062.51	−	311.982i	−0.339402	−	0.0996573i
$215$	5918.21	−	3803.40i	1.87730	−	1.20646i
$216$	−275.754	−	603.817i	−0.0868643	−	0.190206i
$217$	−6399.73	+	1879.13i	−2.00204	+	0.587851i
$218$	805.904	−	930.062i	0.250379	−	0.288953i
$219$	632.837	−	730.333i	0.195266	−	0.225348i
$220$	593.228	−	174.187i	0.181797	−	0.0533805i
$221$	22.4474	+	49.1530i	0.00683248	+	0.0149610i
$222$	779.791	−	501.141i	0.235748	−	0.151506i
$223$	1829.28	+	537.124i	0.549316	+	0.161294i	0.544601	−	0.838695i	$-0.316681\pi$
$223$	1829.28	+	537.124i	0.549316	+	0.161294i	0.00471458	+	0.999989i	$0.498499\pi$
$224$	362.446	+	2520.87i	0.108111	+	0.751930i
$225$	366.533	−	802.596i	0.108602	−	0.237806i
$226$	418.559	−	2911.14i	0.123195	−	0.856842i
$227$	808.647	+	519.686i	0.236440	+	0.151950i	0.653496	−	0.756930i	$-0.273302\pi$
$227$	808.647	+	519.686i	0.236440	+	0.151950i	−0.417056	+	0.908881i	$0.636938\pi$
$228$	−418.501	−	482.976i	−0.121561	−	0.140289i
$229$	−2604.64			−0.751614			−0.375807	−	0.926698i	$-0.622634\pi$
$229$	−2604.64			−0.751614			−0.375807	+	0.926698i	$0.622634\pi$
$230$	−3715.28	+	1314.72i	−1.06512	+	0.376912i
$231$	−1395.88			−0.397587
$232$	−1160.72	−	1339.54i	−0.328470	−	0.379075i
$233$	2990.76	+	1922.04i	0.840906	+	0.540418i	0.888726	−	0.458438i	$-0.151591\pi$
$233$	2990.76	+	1922.04i	0.840906	+	0.540418i	−0.0478199	+	0.998856i	$0.515227\pi$
$234$	−275.903	+	1918.95i	−0.0770783	+	0.536092i
$235$	1204.59	−	2637.68i	0.334377	−	0.732184i
$236$	45.0340	+	313.218i	0.0124214	+	0.0863930i
$237$	−2814.68	−	826.465i	−0.771448	−	0.226518i
$238$	30.9039	−	19.8607i	0.00841681	−	0.00540916i
$239$	−1178.48	−	2580.50i	−0.318951	−	0.698405i	0.680458	−	0.732787i	$-0.261781\pi$
$239$	−1178.48	−	2580.50i	−0.318951	−	0.698405i	−0.999409	+	0.0343819i	$0.989054\pi$
$240$	−1745.57	+	512.546i	−0.469484	+	0.137853i
$241$	−1650.02	+	1904.22i	−0.441024	+	0.508969i	−0.932127	−	0.362133i	$-0.882049\pi$
$241$	−1650.02	+	1904.22i	−0.441024	+	0.508969i	0.491102	+	0.871102i	$0.336594\pi$
$242$	−1567.13	+	1808.56i	−0.416276	+	0.480409i
$243$	233.157	−	68.4610i	0.0615515	−	0.0180732i
$244$	356.961	+	781.636i	0.0936561	+	0.205078i
$245$	3915.39	−	2516.27i	1.02100	−	0.656157i
$246$	1551.28	+	455.497i	0.402057	+	0.118054i
$247$	1199.07	+	8339.68i	0.308885	+	2.14835i
$248$	2662.41	−	5829.87i	0.681707	−	1.49273i
$249$	450.235	−	3131.46i	0.114588	−	0.796980i
$250$	810.436	+	520.836i	0.205026	+	0.131762i
$251$	1441.32	+	1663.37i	0.362450	+	0.418290i	0.907459	−	0.420140i	$-0.138019\pi$
$251$	1441.32	+	1663.37i	0.362450	+	0.418290i	−0.545009	+	0.838430i	$0.683474\pi$
$252$	−524.217			−0.131042
$253$	1229.05	−	1585.31i	0.305415	−	0.393943i
$254$	−102.889			−0.0254167
$255$	−17.6080	−	20.3207i	−0.00432414	−	0.00499033i
$256$	−2680.81	−	1722.85i	−0.654495	−	0.420619i
$257$	−903.809	+	6286.13i	−0.219370	+	1.52575i	0.521003	+	0.853555i	$0.325558\pi$
$257$	−903.809	+	6286.13i	−0.219370	+	1.52575i	−0.740373	+	0.672196i	$0.765351\pi$
$258$	1404.46	−	3075.34i	0.338907	−	0.742103i
$259$	−470.275	−	3270.83i	−0.112824	−	0.784709i
$260$	−2937.16	−	862.429i	−0.700597	−	0.205714i
$261$	545.849	−	350.796i	0.129453	−	0.0831943i
$262$	−1327.69	−	2907.24i	−0.313073	−	0.685533i
$263$	510.171	−	149.800i	0.119614	−	0.0351219i	−0.221378	−	0.975188i	$-0.571055\pi$
$263$	510.171	−	149.800i	0.119614	−	0.0351219i	0.340992	+	0.940066i	$0.389237\pi$
$264$	878.358	−	1013.68i	0.204770	−	0.236317i
$265$	4772.49	−	5507.75i	1.10631	−	1.27675i
$266$	5495.87	−	1613.73i	1.26682	−	0.371971i
$267$	1181.02	+	2586.08i	0.270702	+	0.592754i
$268$	−593.613	+	381.492i	−0.135301	+	0.0869527i
$269$	1404.56	+	412.417i	0.318356	+	0.0934777i	0.437006	−	0.899458i	$-0.356039\pi$
$269$	1404.56	+	412.417i	0.318356	+	0.0934777i	−0.118651	+	0.992936i	$0.537857\pi$
$270$	−137.288	−	954.861i	−0.0309448	−	0.215226i
$271$	−747.137	+	1636.00i	−0.167474	+	0.366716i	−0.974697	−	0.223530i	$-0.928242\pi$
$271$	−747.137	+	1636.00i	−0.167474	+	0.366716i	0.807223	+	0.590246i	$0.200969\pi$
$272$	−3.46808	+	24.1210i	−0.000773100	+	0.00537703i
$273$	5814.11	+	3736.50i	1.28896	+	0.828364i
$274$	445.465	+	514.094i	0.0982173	+	0.113349i
$275$	1782.85			0.390945
$276$	461.564	−	595.355i	0.100663	−	0.129841i
$277$	−7250.75			−1.57276			−0.786381	−	0.617741i	$-0.788048\pi$
$277$	−7250.75			−1.57276			−0.786381	+	0.617741i	$0.788048\pi$
$278$	2120.32	+	2446.98i	0.457440	+	0.527914i
$279$	1973.72	+	1268.44i	0.423526	+	0.272184i
$280$	−1336.96	+	9298.74i	−0.285352	+	1.98466i
$281$	72.3201	−	158.359i	0.0153532	−	0.0336189i	−0.901800	−	0.432154i	$-0.857754\pi$
$281$	72.3201	−	158.359i	0.0153532	−	0.0336189i	0.917153	+	0.398535i	$0.130481\pi$
$282$	−198.322	−	1379.36i	−0.0418791	−	0.291275i
$283$	−507.071	−	148.889i	−0.106510	−	0.0312741i	0.228043	−	0.973651i	$-0.426767\pi$
$283$	−507.071	−	148.889i	−0.106510	−	0.0312741i	−0.334553	+	0.942377i	$0.608585\pi$
$284$	−1734.40	+	1114.63i	−0.362386	+	0.232891i
$285$	−1741.61	−	3813.60i	−0.361980	−	0.792626i
$286$	−3758.64	+	1103.64i	−0.777109	+	0.228180i
$287$	3774.40	−	4355.88i	0.776291	−	0.895888i
$288$	586.653	−	677.034i	0.120031	−	0.138523i
$289$	4713.64	−	1384.05i	0.959423	−	0.281712i
$290$	−1070.05	−	2343.08i	−0.216674	−	0.474451i
$291$	3103.09	−	1994.23i	0.625107	−	0.401732i
$292$	703.606	+	206.597i	0.141012	+	0.0414048i
$293$	−891.325	−	6199.30i	−0.177719	−	1.23607i	−0.862023	−	0.506869i	$-0.830803\pi$
$293$	−891.325	−	6199.30i	−0.177719	−	1.23607i	0.684304	−	0.729197i	$-0.260106\pi$
$294$	929.168	−	2034.59i	0.184320	−	0.403605i
$295$	−295.435	+	2054.80i	−0.0583082	+	0.405542i
$296$	2671.17	+	1716.66i	0.524523	+	0.337090i
$297$	321.542	+	371.080i	0.0628208	+	0.0724991i
$298$	−2597.68			−0.504964
$299$	−9362.78	+	3313.18i	−1.81092	+	0.640823i
$300$	669.539			0.128853
$301$	−7892.73	−	9108.69i	−1.51139	−	1.74424i
$302$	−509.109	−	327.185i	−0.0970064	−	0.0623422i
$303$	−414.269	+	2881.31i	−0.0785451	+	0.546293i
$304$	−1578.44	+	3456.31i	−0.297796	+	0.652082i
$305$	802.252	+	5579.79i	0.150613	+	1.04753i
$306$	−12.3985	−	3.64051i	−0.00231625	−	0.000680112i
$307$	3888.24	−	2498.82i	0.722846	−	0.464545i	−0.126780	−	0.991931i	$-0.540464\pi$
$307$	3888.24	−	2498.82i	0.722846	−	0.464545i	0.849626	+	0.527386i	$0.176828\pi$
$308$	−440.024	−	963.518i	−0.0814049	−	0.178252i
$309$	1114.78	−	327.330i	0.205236	−	0.0602626i
$310$	6099.38	−	7039.05i	1.11749	−	1.28965i
$311$	−5887.92	+	6795.02i	−1.07355	+	1.23894i	−0.103859	+	0.994592i	$0.533119\pi$
$311$	−5887.92	+	6795.02i	−1.07355	+	1.23894i	−0.969688	+	0.244347i	$0.921426\pi$
$312$	−6371.94	+	1870.97i	−1.15622	+	0.339496i
$313$	513.456	+	1124.31i	0.0927229	+	0.203035i	0.950311	−	0.311302i	$-0.100765\pi$
$313$	513.456	+	1124.31i	0.0927229	+	0.203035i	−0.857588	+	0.514337i	$0.828038\pi$
$314$	211.085	−	135.656i	0.0379371	−	0.0243807i
$315$	−3299.71	−	968.881i	−0.590214	−	0.173302i
$316$	−316.798	−	2203.38i	−0.0563965	−	0.392246i
$317$	1012.88	−	2217.89i	0.179460	−	0.392963i	−0.798428	−	0.602090i	$-0.794335\pi$
$317$	1012.88	−	2217.89i	0.179460	−	0.392963i	0.977888	+	0.209127i	$0.0670622\pi$
$318$	498.438	−	3466.71i	0.0878962	−	0.611331i
$319$	1102.95	+	708.822i	0.193584	+	0.124409i
$320$	−5505.91	−	6354.16i	−0.961844	−	1.11003i
$321$	1388.62			0.241449
$322$	3135.33	+	5979.78i	0.542625	+	1.03491i
$323$	−56.1581			−0.00967406
$324$	120.754	+	139.357i	0.0207053	+	0.0238952i
$325$	−7425.88	−	4772.32i	−1.26743	−	0.814526i
$326$	490.611	−	3412.28i	0.0833511	−	0.579720i
$327$	−641.071	+	1403.75i	−0.108414	+	0.237393i
$328$	788.173	+	5481.87i	0.132682	+	0.922822i
$329$	−4766.64	−	1399.61i	−0.798764	−	0.234538i
$330$	1639.81	−	1053.84i	0.273541	−	0.175794i
$331$	2197.00	+	4810.77i	0.364828	+	0.798863i	0.999656	+	0.0262094i	$0.00834368\pi$
$331$	2197.00	+	4810.77i	0.364828	+	0.798863i	−0.634828	+	0.772653i	$0.718929\pi$
$332$	2303.43	−	676.349i	0.380775	−	0.111806i
$333$	−761.185	+	878.454i	−0.125263	+	0.144562i
$334$	−1900.99	+	2193.86i	−0.311430	+	0.359410i
$335$	−4441.61	+	1304.17i	−0.724391	+	0.212700i
$336$	1294.77	+	2835.15i	0.210225	+	0.460328i
$337$	496.546	−	319.111i	0.0802629	−	0.0515818i	−0.499894	−	0.866087i	$-0.666628\pi$
$337$	496.546	−	319.111i	0.0802629	−	0.0515818i	0.580157	+	0.814505i	$0.302991\pi$
$338$	13566.5	+	3983.47i	2.18319	+	0.641042i
$339$	524.864	+	3650.51i	0.0840905	+	0.584862i
$340$	8.47595	−	18.5597i	0.00135198	−	0.00296042i
$341$	−674.672	+	4692.45i	−0.107142	+	0.745191i
$342$	−1694.97	−	1089.29i	−0.267992	−	0.172228i
$343$	525.367	+	606.306i	0.0827030	+	0.0954444i
$344$	11581.1			1.81516
$345$	4005.70	−	2894.40i	0.625100	−	0.451680i
$346$	−2310.04			−0.358926
$347$	3399.03	+	3922.69i	0.525848	+	0.606861i	0.955085	−	0.296331i	$-0.0957630\pi$
$347$	3399.03	+	3922.69i	0.525848	+	0.606861i	−0.429237	+	0.903192i	$0.641218\pi$
$348$	414.207	+	266.194i	0.0638040	+	0.0410044i
$349$	−1535.45	+	10679.3i	−0.235504	+	1.63797i	0.438137	+	0.898908i	$0.355638\pi$
$349$	−1535.45	+	10679.3i	−0.235504	+	1.63797i	−0.673641	+	0.739058i	$0.735271\pi$
$350$	−2492.90	+	5458.69i	−0.380718	+	0.833655i
$351$	−345.976	−	2406.32i	−0.0526121	−	0.365925i
$352$	1736.83	+	509.979i	0.262992	+	0.0772216i
$353$	−4252.41	+	2732.86i	−0.641169	+	0.412054i	−0.820430	−	0.571747i	$-0.806266\pi$
$353$	−4252.41	+	2732.86i	−0.641169	+	0.412054i	0.179261	+	0.983802i	$0.442629\pi$
$354$	414.437	+	907.491i	0.0622234	+	0.136250i
$355$	−12977.3	+	3810.49i	−1.94018	+	0.569690i
$356$	−1412.76	+	1630.41i	−0.210327	+	0.242730i
$357$	−30.1665	+	34.8140i	−0.00447222	+	0.00516121i
$358$	−9482.39	+	2784.28i	−1.39989	+	0.411044i
$359$	1921.14	+	4206.71i	0.282434	+	0.618445i	0.996677	−	0.0814530i	$-0.0259560\pi$
$359$	1921.14	+	4206.71i	0.282434	+	0.618445i	−0.714243	+	0.699898i	$0.753229\pi$
$360$	2779.93	−	1786.55i	0.406986	−	0.261554i
$361$	−1820.45	−	534.532i	−0.265410	−	0.0779315i
$362$	319.235	+	2220.33i	0.0463497	+	0.322369i
$363$	1246.60	−	2729.68i	0.180247	−	0.394686i
$364$	−746.365	+	5191.08i	−0.107473	+	0.747491i
$365$	4047.03	+	2600.87i	0.580360	+	0.372975i
$366$	1774.08	+	2047.40i	0.253368	+	0.292403i
$367$	2474.30			0.351927			0.175964	−	0.984397i	$-0.443696\pi$
$367$	2474.30			0.351927			0.175964	+	0.984397i	$0.443696\pi$
$368$	−4359.92	−	1025.83i	−0.617599	−	0.145312i
$369$	−2027.39			−0.286021
$370$	3021.81	+	3487.35i	0.424585	+	0.489997i
$371$	−10503.6	−	6750.25i	−1.46986	−	0.944624i
$372$	−253.370	+	1762.22i	−0.0353134	+	0.245610i
$373$	2630.48	−	5759.95i	0.365151	−	0.799568i	−0.634494	−	0.772927i	$-0.718792\pi$
$373$	2630.48	−	5759.95i	0.365151	−	0.799568i	0.999645	−	0.0266409i	$-0.00848106\pi$
$374$	−3.71586	−	25.8443i	−0.000513750	−	0.00357321i
$375$	−1159.11	−	340.345i	−0.159616	−	0.0468675i
$376$	4015.79	−	2580.79i	0.550794	−	0.353974i
$377$	−2696.60	−	5904.74i	−0.368388	−	0.806657i
$378$	−1585.77	+	465.623i	−0.215775	+	0.0633574i
$379$	8559.02	−	9877.63i	1.16002	−	1.33873i	0.229145	−	0.973392i	$-0.426407\pi$
$379$	8559.02	−	9877.63i	1.16002	−	1.33873i	0.930874	−	0.365341i	$-0.119048\pi$
$380$	2083.36	−	2404.32i	0.281247	−	0.324577i
$381$	123.795	−	36.3494i	0.0166462	−	0.00488776i
$382$	−4963.35	−	10868.2i	−0.664783	−	1.45567i
$383$	6727.91	−	4323.76i	0.897598	−	0.576851i	−0.00847901	−	0.999964i	$-0.502699\pi$
$383$	6727.91	−	4323.76i	0.897598	−	0.576851i	0.906077	+	0.423113i	$0.139063\pi$
$384$	−1584.77	−	465.330i	−0.210605	−	0.0618392i
$385$	−988.933	−	6878.18i	−0.130911	−	0.910505i
$386$	−2526.27	+	5531.75i	−0.333118	+	0.729427i
$387$	−603.348	+	4196.38i	−0.0792504	+	0.551199i
$388$	2354.72	+	1513.29i	0.308100	+	0.198004i
$389$	−1734.38	−	2001.58i	−0.226058	−	0.260885i	0.631378	−	0.775475i	$-0.282490\pi$
$389$	−1734.38	−	2001.58i	−0.226058	−	0.260885i	−0.857436	+	0.514590i	$0.827944\pi$
$390$	−9651.01			−1.25307
$391$	−12.9773	−	64.9134i	−0.00167849	−	0.00839593i
$392$	7661.89			0.987204
$393$	2624.54	+	3028.88i	0.336872	+	0.388771i
$394$	4781.79	+	3073.07i	0.611429	+	0.392942i
$395$	2078.28	−	14454.8i	0.264734	−	1.84126i
$396$	−154.780	+	338.922i	−0.0196414	+	0.0430088i
$397$	1866.31	+	12980.5i	0.235938	+	1.64098i	0.671629	+	0.740887i	$0.265595\pi$
$397$	1866.31	+	12980.5i	0.235938	+	1.64098i	−0.435692	+	0.900096i	$0.643496\pi$
$398$	−4888.09	−	1435.27i	−0.615623	−	0.180763i
$399$	−6042.43	+	3883.23i	−0.758145	+	0.487230i
$400$	−1653.70	−	3621.11i	−0.206713	−	0.452638i
$401$	4087.03	−	1200.06i	0.508969	−	0.149447i	−0.0171579	−	0.999853i	$-0.505462\pi$
$401$	4087.03	−	1200.06i	0.508969	−	0.149447i	0.526127	+	0.850406i	$0.323644\pi$
$402$	−1456.84	+	1681.28i	−0.180748	+	0.208594i
$403$	15370.9	−	17738.9i	1.89994	−	2.19265i
$404$	−2119.43	+	622.321i	−0.261004	+	0.0766377i
$405$	502.522	+	1100.37i	0.0616556	+	0.135007i
$406$	−3712.48	+	2385.86i	−0.453811	+	0.291646i
$407$	−2253.54	−	661.700i	−0.274457	−	0.0805879i
$408$	−6.29940	−	43.8133i	−0.000764380	−	0.00531638i
$409$	−2570.29	+	5628.15i	−0.310740	+	0.680426i	−0.998985	−	0.0450529i	$-0.985654\pi$
$409$	−2570.29	+	5628.15i	−0.310740	+	0.680426i	0.688245	+	0.725479i	$0.258382\pi$
$410$	−1145.42	+	7966.58i	−0.137972	+	0.959613i
$411$	−717.599	−	461.173i	−0.0861230	−	0.0553479i
$412$	577.354	+	666.302i	0.0690393	+	0.0796756i
$413$	3556.53			0.423742
$414$	867.432	−	2210.94i	0.102976	−	0.262467i
$415$	15749.1			1.86288
$416$	−5869.10	−	6773.30i	−0.691721	−	0.798289i
$417$	−3415.62	−	2195.09i	−0.401112	−	0.257779i
$418$	579.385	−	4029.71i	0.0677958	−	0.471530i
$419$	2879.50	−	6305.23i	0.335735	−	0.735157i	−0.664188	−	0.747565i	$-0.731223\pi$
$419$	2879.50	−	6305.23i	0.335735	−	0.735157i	0.999923	+	0.0124088i	$0.00394995\pi$
$420$	−371.388	−	2583.06i	−0.0431474	−	0.300097i
$421$	−7342.34	−	2155.91i	−0.849986	−	0.249578i	−0.172404	−	0.985026i	$-0.555154\pi$
$421$	−7342.34	−	2155.91i	−0.849986	−	0.249578i	−0.677581	+	0.735448i	$0.736972\pi$
$422$	6554.19	−	4212.13i	0.756050	−	0.485884i
$423$	725.926	+	1589.56i	0.0834415	+	0.182711i
$424$	11511.3	−	3380.03i	1.31849	−	0.387144i
$425$	38.5292	−	44.4651i	0.00439751	−	0.00507499i
$426$	−4256.54	+	4912.31i	−0.484108	+	0.558691i
$427$	9266.53	−	2720.90i	1.05021	−	0.308369i
$428$	437.733	+	958.502i	0.0494361	+	0.108250i
$429$	4132.43	−	2655.75i	0.465072	−	0.298883i
$430$	16148.7	+	4741.68i	1.81106	+	0.531776i
$431$	−129.588	−	901.308i	−0.0144827	−	0.100730i	0.981298	−	0.192495i	$-0.0616580\pi$
$431$	−129.588	−	901.308i	−0.0144827	−	0.100730i	−0.995781	+	0.0917657i	$0.970749\pi$
$432$	455.441	−	997.278i	0.0507232	−	0.111068i
$433$	1458.62	−	10145.0i	0.161887	−	1.12595i	−0.733186	−	0.680028i	$-0.761968\pi$
$433$	1458.62	−	10145.0i	0.161887	−	1.12595i	0.895073	−	0.445920i	$-0.147123\pi$
$434$	−13423.9	−	8627.00i	−1.48472	−	0.954169i
$435$	2115.25	+	2441.13i	0.233146	+	0.269064i
$436$	−1171.03			−0.128629
$437$	910.055	−	10281.5i	0.0996198	−	1.12547i
$438$	2311.93			0.252210
$439$	−7912.91	−	9131.98i	−0.860279	−	0.992815i	−0.999997	−	0.00262371i	$-0.999165\pi$
$439$	−7912.91	−	9131.98i	−0.860279	−	0.992815i	0.139717	−	0.990191i	$-0.455381\pi$
$440$	5617.16	+	3609.93i	0.608608	+	0.391129i
$441$	−399.165	+	2776.25i	−0.0431017	+	0.299779i
$442$	−53.7029	+	117.593i	−0.00577915	+	0.0126546i
$443$	−1547.83	−	10765.4i	−0.166004	−	1.15458i	−0.887042	−	0.461688i	$-0.847244\pi$
$443$	−1547.83	−	10765.4i	−0.166004	−	1.15458i	0.721038	−	0.692895i	$-0.243665\pi$
$444$	−846.307	−	248.498i	−0.0904593	−	0.0265613i
$445$	−11906.1	+	7651.58i	−1.26832	+	0.815101i
$446$	1894.74	+	4148.91i	0.201163	+	0.440486i
$447$	3125.48	−	917.724i	0.330716	−	0.0971071i
$448$	−9432.87	+	10886.1i	−0.994780	+	1.14804i
$449$	−6869.48	+	7927.80i	−0.722029	+	0.833266i	−0.991549	−	0.129729i	$-0.958589\pi$
$449$	−6869.48	+	7927.80i	−0.722029	+	0.833266i	0.269521	+	0.962995i	$0.413135\pi$
$450$	2025.37	−	594.702i	0.212171	−	0.0622990i
$451$	−1701.78	−	3726.38i	−0.177680	−	0.389065i
$452$	−2354.33	+	1513.04i	−0.244997	+	0.157450i
$453$	728.142	+	213.802i	0.0755211	+	0.0221750i
$454$	327.275	+	2276.25i	0.0338321	+	0.235308i
$455$	−14292.4	+	31296.0i	−1.47261	+	3.22457i
$456$	982.218	−	6831.48i	0.100870	−	0.701564i
$457$	−16034.6	−	10304.8i	−1.64128	−	1.05479i	−0.939585	−	0.342317i	$-0.888788\pi$
$457$	−16034.6	−	10304.8i	−1.64128	−	1.05479i	−0.701700	−	0.712473i	$-0.747575\pi$
$458$	−4080.64	−	4709.31i	−0.416323	−	0.480462i
$459$	16.2038			0.00164777
$460$	3260.60	+	1852.56i	0.330491	+	0.187774i
$461$	12528.0			1.26570			0.632852	−	0.774273i	$-0.281884\pi$
$461$	12528.0			1.26570			0.632852	+	0.774273i	$0.281884\pi$
$462$	−2186.90	−	2523.82i	−0.220225	−	0.254153i
$463$	12348.8	+	7936.09i	1.23952	+	0.796591i	0.985346	−	0.170568i	$-0.0545603\pi$
$463$	12348.8	+	7936.09i	1.23952	+	0.796591i	0.254173	+	0.967159i	$0.418197\pi$
$464$	416.619	−	2897.65i	0.0416833	−	0.289914i
$465$	−4851.86	+	10624.1i	−0.483871	+	1.05953i
$466$	1210.42	+	8418.65i	0.120325	+	0.836881i
$467$	−7411.76	−	2176.29i	−0.734422	−	0.215646i	−0.106928	−	0.994267i	$-0.534101\pi$
$467$	−7411.76	−	2176.29i	−0.734422	−	0.215646i	−0.627495	+	0.778621i	$0.715920\pi$
$468$	1551.91	−	997.355i	0.153285	−	0.0985101i
$469$	3294.54	+	7214.04i	0.324366	+	0.710264i
$470$	6656.24	−	1954.45i	0.653254	−	0.191813i
$471$	−206.049	+	237.793i	−0.0201576	+	0.0232631i
$472$	−2237.94	+	2582.72i	−0.218241	+	0.251863i
$473$	−8219.45	+	2413.45i	−0.799008	+	0.234610i
$474$	−2915.42	−	6383.88i	−0.282510	−	0.618610i
$475$	7717.49	−	4959.73i	0.745480	−	0.479091i
$476$	−33.5400	−	9.84822i	−0.00322963	−	0.000948304i
$477$	625.030	+	4347.18i	0.0599961	+	0.417282i
$478$	2819.37	−	6173.56i	0.269780	−	0.590736i
$479$	302.726	−	2105.50i	0.0288766	−	0.200841i	−0.970276	−	0.242001i	$-0.922196\pi$
$479$	302.726	−	2105.50i	0.0288766	−	0.200841i	0.999153	+	0.0411599i	$0.0131053\pi$
$480$	3751.68	+	2411.06i	0.356750	+	0.229270i
$481$	7615.18	+	8788.38i	0.721876	+	0.833089i
$482$	−6027.96			−0.569639
$483$	−5884.95	−	6087.11i	−0.554399	−	0.573443i
$484$	2277.14			0.213857
$485$	12024.9	+	13877.5i	1.12582	+	1.29927i
$486$	489.062	+	314.301i	0.0456468	+	0.0293354i
$487$	−471.362	+	3278.39i	−0.0438592	+	0.305048i	0.956070	+	0.293139i	$0.0946999\pi$
$487$	−471.362	+	3278.39i	−0.0438592	+	0.305048i	−0.999929	+	0.0119088i	$0.996209\pi$
$488$	−3855.06	+	8441.40i	−0.357603	+	0.783041i
$489$	615.216	+	4278.92i	0.0568937	+	0.395705i
$490$	10683.7	+	3137.01i	0.984979	+	0.289216i
$491$	11948.9	−	7679.12i	1.09827	−	0.705812i	0.139560	−	0.990214i	$-0.455431\pi$
$491$	11948.9	−	7679.12i	1.09827	−	0.705812i	0.958705	+	0.284401i	$0.0917948\pi$
$492$	−639.094	−	1399.42i	−0.0585622	−	0.128233i
$493$	41.5142	−	12.1897i	0.00379251	−	0.00111358i
$494$	−13200.0	+	15233.6i	−1.20222	+	1.38743i
$495$	−1600.68	+	1847.29i	−0.145344	+	0.167736i
$496$	10156.5	−	2982.23i	0.919439	−	0.269972i
$497$	9625.88	+	21077.7i	0.868772	+	1.90235i
$498$	6367.18	−	4091.94i	0.572932	−	0.368201i
$499$	−18276.5	−	5366.45i	−1.63961	−	0.481434i	−0.673421	−	0.739259i	$-0.735176\pi$
$499$	−18276.5	−	5366.45i	−1.63961	−	0.481434i	−0.966192	+	0.257825i	$0.916994\pi$
$500$	−130.460	−	907.368i	−0.0116687	−	0.0811575i
$501$	1512.18	−	3311.22i	0.134849	−	0.295278i
$502$	−749.362	+	5211.93i	−0.0666248	+	0.463386i
$503$	4003.94	+	2573.17i	0.354924	+	0.228096i	0.705937	−	0.708275i	$-0.250526\pi$
$503$	4003.94	+	2573.17i	0.354924	+	0.228096i	−0.351013	+	0.936371i	$0.614163\pi$
$504$	−3707.41	−	4278.58i	−0.327661	−	0.378141i
$505$	−14491.0			−1.27692
$506$	4791.85	−	261.492i	0.420995	−	0.0229738i
$507$	−17730.2			−1.55311
$508$	64.1141	+	73.9916i	0.00559961	+	0.00646230i
$509$	−8529.84	−	5481.80i	−0.742787	−	0.477360i	0.113709	−	0.993514i	$-0.463727\pi$
$509$	−8529.84	−	5481.80i	−0.742787	−	0.477360i	−0.856496	+	0.516154i	$0.827363\pi$
$510$	9.15467	−	63.6722i	0.000794854	−	0.00552833i
$511$	3423.79	−	7497.05i	0.296398	−	0.649021i
$512$	−1711.80	−	11905.8i	−0.147757	−	1.02767i
$513$	2424.19	+	711.805i	0.208636	+	0.0612612i
$514$	−12781.6	+	8214.22i	−1.09683	+	0.704891i
$515$	2402.69	+	5261.16i	0.205583	+	0.450164i
$516$	−3086.77	+	906.358i	−0.263348	+	0.0773259i
$517$	−2312.29	+	2668.53i	−0.196701	+	0.227005i
$518$	5177.04	−	5974.63i	0.439124	−	0.506776i
$519$	2779.40	−	816.106i	0.235072	−	0.0690233i
$520$	−13733.4	−	30072.0i	−1.15817	−	2.53605i
$521$	−11147.3	+	7163.92i	−0.937372	+	0.602412i	−0.917649	−	0.397393i	$-0.869915\pi$
$521$	−11147.3	+	7163.92i	−0.937372	+	0.602412i	−0.0197236	+	0.999805i	$0.506279\pi$
$522$	1489.42	+	437.334i	0.124886	+	0.0366697i
$523$	−1793.08	−	12471.1i	−0.149915	−	1.04268i	−0.916355	−	0.400367i	$-0.868883\pi$
$523$	−1793.08	−	12471.1i	−0.149915	−	1.04268i	0.766439	−	0.642317i	$-0.222027\pi$
$524$	−1263.37	+	2766.40i	−0.105326	+	0.230631i
$525$	1070.94	−	7448.52i	0.0890275	−	0.619200i
$526$	1070.12	+	687.724i	0.0887062	+	0.0570080i
$527$	102.451	+	118.235i	0.00846841	+	0.00977307i
$528$	2215.30			0.182592
$529$	12094.8	−	1323.97i	0.994062	−	0.108816i
$530$	17435.2			1.42894
$531$	−819.248	−	945.463i	−0.0669536	−	0.0772685i
$532$	−4585.18	−	2946.71i	−0.373670	−	0.240143i
$533$	−2886.54	+	20076.3i	−0.234578	+	1.63153i
$534$	−2825.46	+	6186.89i	−0.228969	+	0.501373i
$535$	983.784	+	6842.37i	0.0795004	+	0.552937i
$536$	−7311.86	−	2146.96i	−0.589225	−	0.173012i
$537$	10425.4	−	6700.00i	0.837783	−	0.538410i
$538$	1454.83	+	3185.64i	0.116584	+	0.255284i
$539$	−5437.85	+	1596.70i	−0.434554	+	0.127597i
$540$	−601.128	+	693.739i	−0.0479045	+	0.0552847i
$541$	−6618.65	+	7638.32i	−0.525985	+	0.607019i	−0.955119	−	0.296222i	$-0.904273\pi$
$541$	−6618.65	+	7638.32i	−0.525985	+	0.607019i	0.429134	+	0.903241i	$0.358819\pi$
$542$	−4128.49	+	1212.23i	−0.327184	+	0.0960699i
$543$	−1168.51	−	2558.68i	−0.0923490	−	0.202216i
$544$	50.2538	−	32.2962i	0.00396069	−	0.00254538i
$545$	−7371.11	−	2164.35i	−0.579346	−	0.170111i
$546$	2353.09	+	16366.1i	0.184437	+	1.28279i
$547$	3136.47	−	6867.90i	0.245166	−	0.536838i	−0.746544	−	0.665336i	$-0.768288\pi$
$547$	3136.47	−	6867.90i	0.245166	−	0.536838i	0.991710	+	0.128498i	$0.0410156\pi$
$548$	92.1191	−	640.702i	0.00718090	−	0.0499443i
$549$	−2857.87	−	1836.64i	−0.222169	−	0.142779i
$550$	2793.15	+	3223.47i	0.216546	+	0.249908i
$551$	6746.26			0.521598
$552$	8123.50	−	443.301i	0.626375	−	0.0341814i
$553$	−25019.0			−1.92390
$554$	−11359.6	−	13109.7i	−0.871161	−	1.00537i
$555$	−4867.83	−	3128.36i	−0.372302	−	0.239264i
$556$	438.468	−	3049.61i	0.0334446	−	0.232612i
$557$	9548.81	−	20909.0i	0.726384	−	1.59056i	−0.0783508	−	0.996926i	$-0.524965\pi$
$557$	9548.81	−	20909.0i	0.726384	−	1.59056i	0.804735	−	0.593634i	$-0.202307\pi$
$558$	798.805	+	5555.81i	0.0606024	+	0.421499i
$559$	40695.8	+	11949.4i	3.07916	+	0.904122i
$560$	−13052.8	+	8388.54i	−0.984969	+	0.633001i
$561$	13.6013	+	29.7827i	0.00102362	+	0.00224140i
$562$	399.623	−	117.340i	0.0299948	−	0.00880726i
$563$	8113.07	−	9362.99i	0.607327	−	0.700893i	−0.365922	−	0.930646i	$-0.619246\pi$
$563$	8113.07	−	9362.99i	0.607327	−	0.700893i	0.973249	+	0.229753i	$0.0737917\pi$
$564$	−868.368	+	1002.15i	−0.0648314	+	0.0748194i
$565$	−17615.9	+	5172.50i	−1.31169	+	0.385148i
$566$	−525.219	−	1150.07i	−0.0390046	−	0.0854081i
$567$	1743.47	−	1120.46i	0.129134	−	0.0829893i
$568$	−21363.5	−	6272.90i	−1.57816	−	0.463389i
$569$	−2898.15	−	20157.1i	−0.213527	−	1.48511i	−0.761254	−	0.648454i	$-0.775416\pi$
$569$	−2898.15	−	20157.1i	−0.213527	−	1.48511i	0.547727	−	0.836657i	$-0.315493\pi$
$570$	4166.61	−	9123.61i	0.306176	−	0.670432i
$571$	−1971.17	+	13709.8i	−0.144467	+	1.00479i	0.780612	+	0.625017i	$0.214908\pi$
$571$	−1971.17	+	13709.8i	−0.144467	+	1.00479i	−0.925079	+	0.379775i	$0.876001\pi$
$572$	3135.82	+	2015.27i	0.229222	+	0.147312i
$573$	9811.42	+	11323.0i	0.715319	+	0.825522i
$574$	13788.9			1.00268
$575$	7516.37	+	7774.56i	0.545138	+	0.563863i
$576$	5066.81			0.366523
$577$	5382.36	+	6211.57i	0.388337	+	0.448165i	0.915933	−	0.401330i	$-0.131452\pi$
$577$	5382.36	+	6211.57i	0.388337	+	0.448165i	−0.527596	+	0.849495i	$0.676907\pi$
$578$	9887.19	+	6354.11i	0.711510	+	0.457260i
$579$	1085.27	−	7548.21i	0.0778968	−	0.541784i
$580$	−1018.21	+	2229.58i	−0.0728949	+	0.159618i
$581$	−3839.91	−	26707.2i	−0.274193	−	1.90706i
$582$	8467.21	+	2486.20i	0.603053	+	0.177072i
$583$	−7465.53	+	4797.80i	−0.530344	+	0.340831i
$584$	3289.88	+	7203.83i	0.233110	+	0.510439i
$585$	11611.9	−	3409.57i	0.820675	−	0.240972i
$586$	9812.20	−	11323.9i	0.691703	−	0.798268i
$587$	2288.26	−	2640.79i	0.160897	−	0.185685i	−0.669577	−	0.742743i	$-0.733524\pi$
$587$	2288.26	−	2640.79i	0.160897	−	0.185685i	0.830474	+	0.557058i	$0.188070\pi$
$588$	−2042.16	+	599.631i	−0.143226	+	0.0420550i
$589$	10133.5	+	22189.3i	0.708903	+	1.55228i
$590$	−4178.02	+	2685.05i	−0.291536	+	0.187359i
$591$	−6839.04	−	2008.12i	−0.476008	−	0.139769i
$592$	746.338	+	5190.89i	0.0518147	+	0.360379i
$593$	4071.05	−	8914.36i	0.281919	−	0.617317i	−0.714704	−	0.699427i	$-0.753439\pi$
$593$	4071.05	−	8914.36i	0.281919	−	0.617317i	0.996623	+	0.0821102i	$0.0261659\pi$
$594$	−167.175	+	1162.73i	−0.0115476	+	0.0803152i
$595$	−192.917	−	123.980i	−0.0132921	−	0.00854233i
$596$	1618.71	+	1868.09i	0.111250	+	0.128389i
$597$	6388.33			0.437951
$598$	−20658.9	−	11737.6i	−1.41271	−	0.802655i
$599$	−14512.6			−0.989932			−0.494966	−	0.868912i	$-0.664820\pi$
$599$	−14512.6			−0.989932			−0.494966	+	0.868912i	$0.664820\pi$
$600$	4735.16	+	5464.67i	0.322187	+	0.371824i
$601$	−6600.63	−	4241.97i	−0.447996	−	0.287909i	0.297125	−	0.954838i	$-0.403972\pi$
$601$	−6600.63	−	4241.97i	−0.447996	−	0.287909i	−0.745121	+	0.666929i	$0.767608\pi$
$602$	4103.55	−	28540.8i	0.277821	−	1.93229i
$603$	1158.87	−	2537.57i	0.0782634	−	0.171373i
$604$	81.9538	+	570.001i	0.00552095	+	0.0383990i
$605$	14333.6	+	4208.72i	0.963211	+	0.282824i
$606$	−5858.56	+	3765.07i	−0.392719	+	0.252385i
$607$	−2314.74	−	5068.58i	−0.154782	−	0.338925i	0.816316	−	0.577605i	$-0.196013\pi$
$607$	−2314.74	−	5068.58i	−0.154782	−	0.338925i	−0.971098	+	0.238680i	$0.923285\pi$
$608$	8937.01	−	2624.14i	0.596124	−	0.175038i
$609$	3623.90	−	4182.20i	0.241129	−	0.278278i
$610$	−8831.63	+	10192.2i	−0.586201	+	0.676511i
$611$	16774.2	−	4925.35i	1.11066	−	0.326118i
$612$	5.10790	+	11.1847i	0.000337377	+	0.000738753i
$613$	−17346.3	+	11147.8i	−1.14292	+	0.734509i	−0.968217	−	0.250112i	$-0.919533\pi$
$613$	−17346.3	+	11147.8i	−1.14292	+	0.734509i	−0.174702	+	0.984621i	$0.555896\pi$
$614$	10609.6	+	3115.26i	0.697343	+	0.204759i
$615$	−1436.33	−	9989.92i	−0.0941765	−	0.655012i
$616$	4752.11	−	10405.7i	0.310825	−	0.680611i
$617$	−1812.82	+	12608.4i	−0.118284	+	0.822684i	0.841160	+	0.540786i	$0.181873\pi$
$617$	−1812.82	+	12608.4i	−0.118284	+	0.822684i	−0.959444	+	0.281898i	$0.909036\pi$
$618$	2338.33	+	1502.76i	0.152203	+	0.0978151i
$619$	3851.20	+	4444.52i	0.250069	+	0.288595i	0.866881	−	0.498516i	$-0.166121\pi$
$619$	3851.20	+	4444.52i	0.250069	+	0.288595i	−0.616812	+	0.787111i	$0.711576\pi$
$620$	−8862.80			−0.574095
$621$	−262.586	+	2966.61i	−0.0169681	+	0.191701i
$622$	−21510.2			−1.38662
$623$	15878.4	+	18324.6i	1.02111	+	1.17843i
$624$	−9227.14	−	5929.92i	−0.591957	−	0.380428i
$625$	2599.86	−	18082.4i	0.166391	−	1.15728i
$626$	−1228.39	+	2689.79i	−0.0784284	+	0.171734i
$627$	726.536	+	5053.17i	0.0462760	+	0.321857i
$628$	−229.091	−	67.2671i	−0.0145569	−	0.00427429i
$629$	−65.2045	+	41.9044i	−0.00413335	+	0.00265634i
$630$	−3417.80	−	7483.94i	−0.216140	−	0.473282i
$631$	3599.35	−	1056.87i	0.227081	−	0.0666769i	−0.166213	−	0.986090i	$-0.553154\pi$
$631$	3599.35	−	1056.87i	0.227081	−	0.0666769i	0.393293	+	0.919413i	$0.371336\pi$
$632$	15743.1	−	18168.6i	0.990868	−	1.14352i
$633$	−6397.81	+	7383.47i	−0.401722	+	0.463612i
$634$	5596.90	−	1643.40i	0.350601	−	0.102946i
$635$	266.814	+	584.242i	0.0166743	+	0.0365117i
$636$	−2803.64	+	1801.79i	−0.174798	+	0.112336i
$637$	26923.6	+	7905.49i	1.67465	+	0.491722i
$638$	446.385	+	3104.68i	0.0276999	+	0.192657i
$639$	3385.95	−	7414.19i	0.209618	−	0.459000i
$640$	1170.15	−	8138.56i	0.0722721	−	0.502664i
$641$	−15927.2	−	10235.8i	−0.981416	−	0.630717i	−0.0515707	−	0.998669i	$-0.516423\pi$
$641$	−15927.2	−	10235.8i	−0.981416	−	0.630717i	−0.929845	+	0.367952i	$0.880059\pi$
$642$	2175.52	+	2510.68i	0.133740	+	0.154344i
$643$	−10695.9			−0.655994			−0.327997	−	0.944679i	$-0.606374\pi$
$643$	−10695.9			−0.655994			−0.327997	+	0.944679i	$0.606374\pi$
$644$	2346.55	−	5980.96i	0.143583	−	0.365967i
$645$	−21105.0			−1.28838
$646$	−87.9817	−	101.536i	−0.00535851	−	0.00618405i
$647$	25256.8	+	16231.5i	1.53469	+	0.986287i	0.988936	+	0.148342i	$0.0473937\pi$
$647$	25256.8	+	16231.5i	1.53469	+	0.986287i	0.545756	+	0.837944i	$0.316243\pi$
$648$	−283.407	+	1971.14i	−0.0171810	+	0.119497i
$649$	1050.10	−	2299.40i	0.0635133	−	0.139075i
$650$	−3005.40	−	20903.0i	−0.181356	−	1.26136i
$651$	19199.2	+	5637.39i	1.15588	+	0.339396i
$652$	−2759.62	+	1773.50i	−0.165759	+	0.106527i
$653$	8447.70	+	18497.9i	0.506254	+	1.10854i	0.974386	+	0.224883i	$0.0722001\pi$
$653$	8447.70	+	18497.9i	0.506254	+	1.10854i	−0.468131	+	0.883659i	$0.655073\pi$
$654$	−3542.40	+	1040.14i	−0.211802	+	0.0621908i
$655$	−13065.3	+	15078.2i	−0.779397	+	0.899472i
$656$	−5990.06	+	6912.90i	−0.356513	+	0.411438i
$657$	−2781.67	+	816.773i	−0.165180	+	0.0485013i
$658$	−4937.24	−	10811.0i	−0.292513	−	0.640514i
$659$	−10721.5	+	6890.26i	−0.633761	+	0.407293i	−0.817700	−	0.575644i	$-0.804751\pi$
$659$	−10721.5	+	6890.26i	−0.633761	+	0.407293i	0.183939	+	0.982938i	$0.441115\pi$
$660$	−1779.68	−	522.562i	−0.104961	−	0.0308193i
$661$	2882.80	+	20050.3i	0.169634	+	1.17983i	0.879643	+	0.475635i	$0.157782\pi$
$661$	2882.80	+	20050.3i	0.169634	+	1.17983i	−0.710009	+	0.704192i	$0.751309\pi$
$662$	−5256.08	+	11509.2i	−0.308585	+	0.675707i
$663$	23.0704	−	160.458i	0.00135140	−	0.00939923i
$664$	21810.8	+	14016.9i	1.27473	+	0.819221i
$665$	−23415.3	−	27022.7i	−1.36543	−	1.57578i
$666$	−2780.82			−0.161794
$667$	1558.96	+	7798.03i	0.0904994	+	0.452685i
$668$	2762.27			0.159993
$669$	−3745.48	−	4322.52i	−0.216455	−	0.249803i
$670$	−9316.58	−	5987.40i	−0.537210	−	0.345244i
$671$	976.896	−	6794.46i	0.0562037	−	0.390905i
$672$	3173.92	−	6949.92i	0.182197	−	0.398957i
$673$	−3559.53	−	24757.1i	−0.203878	−	1.41800i	−0.792637	−	0.609693i	$-0.791293\pi$
$673$	−3559.53	−	24757.1i	−0.203878	−	1.41800i	0.588760	−	0.808308i	$-0.299617\pi$
$674$	1354.89	+	397.833i	0.0774312	+	0.0227358i
$675$	−2226.79	+	1431.07i	−0.126977	+	0.0816029i
$676$	−5589.10	−	12238.4i	−0.317996	−	0.696314i
$677$	5616.27	−	1649.09i	0.318835	−	0.0936183i	−0.118399	−	0.992966i	$-0.537776\pi$
$677$	5616.27	−	1649.09i	0.318835	−	0.0936183i	0.437234	+	0.899348i	$0.355958\pi$
$678$	−5777.99	+	6668.15i	−0.327289	+	0.377712i
$679$	20601.4	−	23775.3i	1.16438	−	1.34376i
$680$	211.426	−	62.0802i	0.0119233	−	0.00350098i
$681$	−1197.94	−	2623.12i	−0.0674085	−	0.147604i
$682$	−9541.15	+	6131.72i	−0.535703	+	0.344275i
$683$	−13136.8	−	3857.31i	−0.735967	−	0.216099i	−0.107794	−	0.994173i	$-0.534379\pi$
$683$	−13136.8	−	3857.31i	−0.735967	−	0.216099i	−0.628173	+	0.778074i	$0.716197\pi$
$684$	272.847	+	1897.69i	0.0152523	+	0.106082i
$685$	1764.02	−	3862.67i	0.0983939	−	0.215453i
$686$	−273.146	+	1899.77i	−0.0152023	+	0.105734i
$687$	6573.49	+	4224.53i	0.365057	+	0.234608i
$688$	12526.0	+	14455.7i	0.694110	+	0.801046i
$689$	43938.0			2.42947
$690$	11508.9	+	2707.88i	0.634978	+	0.149402i
$691$	−26534.1			−1.46079			−0.730395	−	0.683025i	$-0.760664\pi$
$691$	−26534.1			−1.46079			−0.730395	+	0.683025i	$0.760664\pi$
$692$	1439.47	+	1661.24i	0.0790759	+	0.0912585i
$693$	3522.88	+	2264.02i	0.193107	+	0.124102i
$694$	−1767.21	+	12291.2i	−0.0966602	+	0.672287i
$695$	8396.38	−	18385.5i	0.458263	−	1.00346i
$696$	756.746	+	5263.29i	0.0412132	+	0.286644i
$697$	−129.715	−	38.0877i	−0.00704921	−	0.00206983i
$698$	−21714.2	+	13954.9i	−1.17750	+	0.756734i
$699$	−4430.55	−	9701.56i	−0.239741	−	0.524960i
$700$	5478.98	−	1608.77i	0.295837	−	0.0868656i
$701$	−20390.0	+	23531.4i	−1.09860	+	1.26786i	−0.137850	+	0.990453i	$0.544019\pi$
$701$	−20390.0	+	23531.4i	−1.09860	+	1.26786i	−0.960754	+	0.277403i	$0.910526\pi$
$702$	3808.69	−	4395.47i	0.204772	−	0.236319i
$703$	−11595.8	+	3404.84i	−0.622111	+	0.182668i
$704$	4253.05	+	9312.87i	0.227688	+	0.498568i
$705$	−7318.20	+	4703.12i	−0.390949	+	0.251248i
$706$	−11603.3	−	3407.03i	−0.618548	−	0.181622i
$707$	3533.17	+	24573.7i	0.187947	+	1.30720i
$708$	394.360	−	863.529i	0.0209336	−	0.0458381i
$709$	1678.15	−	11671.8i	0.0888915	−	0.618254i	−0.895866	−	0.444324i	$-0.853444\pi$
$709$	1678.15	−	11671.8i	0.0888915	−	0.618254i	0.984758	−	0.173931i	$-0.0556468\pi$
$710$	−27220.9	−	17493.8i	−1.43885	−	0.924690i
$711$	5763.12	+	6651.00i	0.303986	+	0.350818i
$712$	−23298.6			−1.22634
$713$	−23307.0	+	16841.0i	−1.22420	+	0.884571i
$714$	−110.207			−0.00577644
$715$	16013.8	+	18480.9i	0.837598	+	0.966640i
$716$	7911.11	+	5084.16i	0.412922	+	0.265369i
$717$	−1211.18	+	8423.97i	−0.0630858	+	0.438771i
$718$	−4596.11	+	10064.1i	−0.238893	+	0.523103i
$719$	−4361.77	−	30336.8i	−0.226240	−	1.57353i	−0.713739	−	0.700411i	$-0.753000\pi$
$719$	−4361.77	−	30336.8i	−0.226240	−	1.57353i	0.487499	−	0.873123i	$-0.337909\pi$
$720$	5236.72	+	1537.64i	0.271057	+	0.0795895i
$721$	8335.99	−	5357.21i	0.430580	−	0.276717i
$722$	−1885.60	−	4128.90i	−0.0971951	−	0.212828i
$723$	7252.74	−	2129.60i	0.373074	−	0.109544i
$724$	1397.80	−	1613.14i	0.0717523	−	0.0828065i
$725$	−4628.50	+	5341.58i	−0.237101	+	0.273629i
$726$	6888.41	−	2022.62i	0.352139	−	0.103397i
$727$	6279.58	+	13750.4i	0.320353	+	0.701476i	0.999470	−	0.0325547i	$-0.0103643\pi$
$727$	6279.58	+	13750.4i	0.320353	+	0.701476i	−0.679117	+	0.734030i	$0.737637\pi$
$728$	−47647.3	+	30621.0i	−2.42572	+	1.55892i
$729$	−699.470	−	205.383i	−0.0355368	−	0.0104345i
$730$	1637.91	+	11391.9i	0.0830437	+	0.577582i
$731$	−117.438	+	257.154i	−0.00594201	+	0.0130112i
$732$	366.868	−	2551.62i	0.0185244	−	0.128840i
$733$	14.7481	+	9.47804i	0.000743157	+	0.000477598i	0.541012	−	0.841015i	$-0.318041\pi$
$733$	14.7481	+	9.47804i	0.000743157	+	0.000477598i	−0.540269	+	0.841492i	$0.681678\pi$
$734$	3876.43	+	4473.64i	0.194934	+	0.224966i
$735$	−13962.7			−0.700710
$736$	5098.46	+	9723.92i	0.255342	+	0.486995i
$737$	5636.84			0.281731
$738$	−3176.28	−	3665.62i	−0.158429	−	0.182836i
$739$	3958.52	+	2543.99i	0.197045	+	0.126633i	0.635443	−	0.772148i	$-0.280818\pi$
$739$	3958.52	+	2543.99i	0.197045	+	0.126633i	−0.438398	+	0.898781i	$0.644454\pi$
$740$	624.889	−	4346.20i	0.0310424	−	0.215905i
$741$	10500.2	−	22992.2i	0.520558	−	1.13986i
$742$	−4251.01	−	29566.4i	−0.210323	−	1.46283i
$743$	−23181.2	−	6806.62i	−1.14460	−	0.336084i	−0.346168	−	0.938172i	$-0.612517\pi$
$743$	−23181.2	−	6806.62i	−1.14460	−	0.336084i	−0.798430	+	0.602088i	$0.794336\pi$
$744$	−16174.9	+	10395.0i	−0.797043	+	0.512228i
$745$	6736.34	+	14750.5i	0.331276	+	0.725393i
$746$	14535.4	−	4267.97i	0.713375	−	0.209466i
$747$	−6215.26	+	7172.80i	−0.304424	+	0.351324i
$748$	−16.2702	+	18.7768i	−0.000795317	+	0.000917844i
$749$	11363.3	−	3336.58i	0.554349	−	0.162772i
$750$	−1200.59	−	2628.93i	−0.0584525	−	0.127993i
$751$	12083.3	−	7765.48i	0.587119	−	0.377319i	−0.213096	−	0.977031i	$-0.568355\pi$
$751$	12083.3	−	7765.48i	0.587119	−	0.377319i	0.800216	+	0.599712i	$0.204718\pi$
$752$	7564.78	+	2221.22i	0.366834	+	0.107712i
$753$	−939.683	−	6535.64i	−0.0454767	−	0.316298i
$754$	6451.32	−	14126.4i	0.311596	−	0.682299i
$755$	−537.639	+	3739.36i	−0.0259162	+	0.180251i
$756$	1323.00	+	850.240i	0.0636468	+	0.0409033i
$757$	−15247.1	−	17596.1i	−0.732057	−	0.844839i	0.260645	−	0.965435i	$-0.416065\pi$
$757$	−15247.1	−	17596.1i	−0.732057	−	0.844839i	−0.992702	+	0.120596i	$0.961519\pi$
$758$	31268.4			1.49831
$759$	−5673.09	+	2007.52i	−0.271304	+	0.0960056i
$760$	34357.7			1.63985
$761$	7041.96	+	8126.85i	0.335441	+	0.387120i	0.898263	−	0.439459i	$-0.144830\pi$
$761$	7041.96	+	8126.85i	0.335441	+	0.387120i	−0.562822	+	0.826578i	$0.690284\pi$
$762$	259.668	+	166.878i	0.0123448	+	0.00793355i
$763$	−1873.08	+	13027.5i	−0.0888729	+	0.618124i
$764$	−4722.91	+	10341.7i	−0.223650	+	0.489726i
$765$	11.4798	+	79.8435i	0.000542551	+	0.00377353i
$766$	18358.0	+	5390.40i	0.865930	+	0.254260i
$767$	−10528.9	+	6766.51i	−0.495667	+	0.318546i
$768$	3971.39	+	8696.14i	0.186595	+	0.408587i
$769$	23472.5	−	6892.16i	1.10070	−	0.323196i	0.319572	−	0.947562i	$-0.396461\pi$
$769$	23472.5	−	6892.16i	1.10070	−	0.323196i	0.781132	+	0.624366i	$0.214643\pi$
$770$	10886.7	−	12563.9i	0.509519	−	0.588017i
$771$	12476.6	−	14398.8i	0.582794	−	0.672580i
$772$	5552.31	−	1630.31i	0.258850	−	0.0760051i
$773$	−14355.7	−	31434.6i	−0.667968	−	1.46265i	−0.874907	−	0.484291i	$-0.839077\pi$
$773$	−14355.7	−	31434.6i	−0.667968	−	1.46265i	0.206939	−	0.978354i	$-0.433650\pi$
$774$	−8532.49	+	5483.50i	−0.396246	+	0.254652i
$775$	−24521.5	−	7200.17i	−1.13657	−	0.333726i
$776$	4302.02	+	29921.2i	0.199012	+	1.38416i
$777$	−4118.18	+	9017.55i	−0.190140	+	0.416349i
$778$	901.730	−	6271.67i	0.0415535	−	0.289011i
$779$	−17733.0	−	11396.3i	−0.815599	−	0.524154i
$780$	6013.91	+	6940.42i	0.276067	+	0.318598i
$781$	16469.5			0.754579
$782$	97.0350	−	125.162i	0.00443729	−	0.00572351i
$783$	−1946.55			−0.0888432
$784$	8286.96	+	9563.66i	0.377504	+	0.435662i
$785$	−1317.70	−	846.832i	−0.0599116	−	0.0385028i
$786$	−1364.54	+	9490.58i	−0.0619230	+	0.430684i
$787$	1469.09	−	3216.86i	0.0665406	−	0.145704i	−0.873440	−	0.486932i	$-0.838116\pi$
$787$	1469.09	−	3216.86i	0.0665406	−	0.145704i	0.939980	+	0.341229i	$0.110843\pi$
$788$	−769.748	−	5353.71i	−0.0347984	−	0.242028i
$789$	−1530.51	−	449.400i	−0.0690593	−	0.0202776i
$790$	29390.9	−	18888.4i	1.32365	−	0.850656i
$791$	13066.5	+	28611.7i	0.587348	+	1.28611i
$792$	−3860.88	+	1133.66i	−0.173220	+	0.0508620i
$793$	−22256.3	+	25685.2i	−0.996653	+	1.15020i
$794$	−20545.3	+	23710.6i	−0.918295	+	1.05977i
$795$	−20977.8	+	6159.63i	−0.935855	+	0.274792i
$796$	2013.79	+	4409.59i	0.0896695	+	0.196349i
$797$	−22486.0	+	14450.9i	−0.999368	+	0.642255i	−0.934621	−	0.355647i	$-0.884261\pi$
$797$	−22486.0	+	14450.9i	−0.999368	+	0.642255i	−0.0647479	+	0.997902i	$0.520624\pi$
$798$	−16487.6	−	4841.20i	−0.731397	−	0.214758i
$799$	16.5833	+	115.339i	0.000734260	+	0.00510689i
$800$	−4053.79	+	8876.56i	−0.179154	+	0.392292i
$801$	1213.80	−	8442.16i	0.0535424	−	0.372396i
$802$	8572.83	+	5509.43i	0.377453	+	0.242574i
$803$	−3836.15	−	4427.16i	−0.168586	−	0.194559i
$804$	2116.89			0.0928567
$805$	25824.8	−	33310.4i	1.13069	−	1.45843i
$806$	56154.0			2.45402
$807$	−2875.87	−	3318.93i	−0.125447	−	0.144773i
$808$	−20068.5	−	12897.2i	−0.873770	−	0.561538i
$809$	5060.26	−	35194.9i	0.219913	−	1.52953i	−0.518442	−	0.855113i	$-0.673488\pi$
$809$	5060.26	−	35194.9i	0.219913	−	1.52953i	0.738355	−	0.674413i	$-0.235603\pi$
$810$	−1202.23	+	2632.51i	−0.0521506	+	0.114194i
$811$	−5286.17	−	36766.1i	−0.228881	−	1.59190i	−0.702834	−	0.711354i	$-0.748082\pi$
$811$	−5286.17	−	36766.1i	−0.228881	−	1.59190i	0.473953	−	0.880550i	$-0.342827\pi$
$812$	4029.15	+	1183.07i	0.174132	+	0.0511299i
$813$	4539.07	−	2917.08i	0.195808	−	0.125838i
$814$	−2334.20	−	5111.18i	−0.100508	−	0.220082i
$815$	−20648.4	+	6062.92i	−0.887462	+	0.260582i
$816$	47.8750	−	55.2507i	0.00205387	−	0.00237030i
$817$	−28865.9	+	33313.0i	−1.23609	+	1.42653i
$818$	−14202.8	+	4170.31i	−0.607076	+	0.178254i
$819$	−8613.11	−	18860.1i	−0.367480	−	0.804669i
$820$	6442.83	−	4140.56i	0.274382	−	0.176335i
$821$	18341.8	+	5385.65i	0.779701	+	0.228941i	0.647280	−	0.762253i	$-0.275907\pi$
$821$	18341.8	+	5385.65i	0.779701	+	0.228941i	0.132422	+	0.991193i	$0.457725\pi$
$822$	−290.426	−	2019.96i	−0.0123233	−	0.0857107i
$823$	−2916.75	+	6386.78i	−0.123538	+	0.270509i	−0.961289	−	0.275542i	$-0.911143\pi$
$823$	−2916.75	+	6386.78i	−0.123538	+	0.270509i	0.837751	+	0.546052i	$0.183870\pi$
$824$	−1355.04	+	9424.54i	−0.0572879	+	0.398446i
$825$	−4499.48	−	2891.64i	−0.189881	−	0.122029i
$826$	5571.95	+	6430.37i	0.234713	+	0.270873i
$827$	−31410.3			−1.32073			−0.660365	−	0.750944i	$-0.729599\pi$
$827$	−31410.3			−1.32073			−0.660365	+	0.750944i	$0.729599\pi$
$828$	−2130.50	+	753.913i	−0.0894202	+	0.0316428i
$829$	14068.0			0.589389			0.294695	−	0.955592i	$-0.404782\pi$
$829$	14068.0			0.589389			0.294695	+	0.955592i	$0.404782\pi$
$830$	24673.8	+	28475.1i	1.03186	+	1.19083i
$831$	18299.2	+	11760.2i	0.763888	+	0.490921i
$832$	7213.98	−	50174.3i	0.300601	−	2.09072i
$833$	−77.6952	+	170.129i	−0.00323167	+	0.00707636i
$834$	−1382.37	−	9614.59i	−0.0573951	−	0.399192i
$835$	17387.2	+	5105.35i	0.720611	+	0.211590i
$836$	−3258.96	+	2094.41i	−0.134825	+	0.0866466i
$837$	−2923.90	−	6402.45i	−0.120747	−	0.264398i
$838$	15911.4	−	4672.01i	0.655907	−	0.192592i
$839$	10082.0	−	11635.3i	0.414863	−	0.478777i	−0.509402	−	0.860528i	$-0.670133\pi$
$839$	10082.0	−	11635.3i	0.414863	−	0.478777i	0.924265	+	0.381751i	$0.124679\pi$
$840$	18456.0	−	21299.3i	0.758086	−	0.874878i
$841$	18414.0	−	5406.83i	0.755012	−	0.221691i
$842$	−7605.12	−	16652.9i	−0.311271	−	0.681588i
$843$	−439.365	+	282.363i	−0.0179508	+	0.0115363i
$844$	−7113.27	−	2088.64i	−0.290105	−	0.0851825i
$845$	−12561.2	−	87365.2i	−0.511384	−	3.55675i
$846$	−1736.70	+	3802.83i	−0.0705778	+	0.154544i
$847$	3642.32	−	25332.9i	0.147759	−	1.02768i
$848$	16669.5	+	10712.8i	0.675037	+	0.433820i
$849$	1038.24	+	1198.19i	0.0419697	+	0.0484356i
$850$	140.758			0.00567994
$851$	−6615.28	−	12616.8i	−0.266473	−	0.508225i
$852$	6185.04			0.248704
$853$	−10122.8	−	11682.3i	−0.406327	−	0.468926i	0.515296	−	0.857012i	$-0.327682\pi$
$853$	−10122.8	−	11682.3i	−0.406327	−	0.468926i	−0.921623	+	0.388086i	$0.873136\pi$
$854$	19437.2	+	12491.5i	0.778837	+	0.500528i
$855$	−1789.95	+	12449.4i	−0.0715966	+	0.497965i
$856$	−4727.37	+	10351.5i	−0.188760	+	0.413326i
$857$	4882.18	+	33956.3i	0.194600	+	1.35347i	0.819640	+	0.572880i	$0.194174\pi$
$857$	4882.18	+	33956.3i	0.194600	+	1.35347i	−0.625040	+	0.780593i	$0.714917\pi$
$858$	11275.9	+	3310.91i	0.448664	+	0.131740i
$859$	−25424.6	+	16339.4i	−1.00987	+	0.649001i	−0.937358	−	0.348366i	$-0.886737\pi$
$859$	−25424.6	+	16339.4i	−1.00987	+	0.649001i	−0.0725076	+	0.997368i	$0.523100\pi$
$860$	−6652.91	−	14567.8i	−0.263793	−	0.577627i
$861$	−16590.6	+	4871.43i	−0.656685	+	0.192820i
$862$	1426.58	−	1646.36i	0.0563684	−	0.0650526i
$863$	12366.4	−	14271.6i	0.487783	−	0.562932i	−0.457489	−	0.889216i	$-0.651251\pi$
$863$	12366.4	−	14271.6i	0.487783	−	0.562932i	0.945272	+	0.326283i	$0.105796\pi$
$864$	−2578.67	+	757.165i	−0.101537	+	0.0298140i
$865$	5990.44	+	13117.2i	0.235470	+	0.515606i
$866$	20627.7	−	13256.6i	0.809421	−	0.520183i
$867$	−14140.9	−	4152.15i	−0.553923	−	0.162646i
$868$	2160.91	+	15029.4i	0.0844999	+	0.587710i
$869$	−7387.10	+	16175.5i	−0.288366	+	0.631434i
$870$	−1099.75	+	7648.92i	−0.0428563	+	0.298072i
$871$	−23478.4	−	15088.7i	−0.913360	−	0.586981i
$872$	−8281.86	−	9557.78i	−0.321628	−	0.371178i
$873$	−11065.9			−0.429010
$874$	20015.2	−	14462.4i	0.774628	−	0.559724i
$875$	−10303.0			−0.398063
$876$	−1440.65	−	1662.60i	−0.0555650	−	0.0641255i
$877$	8287.49	+	5326.05i	0.319098	+	0.205072i	0.690377	−	0.723449i	$-0.257445\pi$
$877$	8287.49	+	5326.05i	0.319098	+	0.205072i	−0.371280	+	0.928521i	$0.621081\pi$
$878$	4114.04	−	28613.8i	0.158135	−	1.09985i
$879$	−7805.30	+	17091.2i	−0.299506	+	0.655828i
$880$	1569.46	+	10915.8i	0.0601210	+	0.418151i
$881$	14063.4	+	4129.40i	0.537808	+	0.157915i	0.539346	−	0.842084i	$-0.318671\pi$
$881$	14063.4	+	4129.40i	0.537808	+	0.157915i	−0.00153795	+	0.999999i	$0.500490\pi$
$882$	−5644.95	+	3627.79i	−0.215505	+	0.138497i
$883$	13440.8	+	29431.4i	0.512254	+	1.12168i	0.972290	+	0.233780i	$0.0751095\pi$
$883$	13440.8	+	29431.4i	0.512254	+	1.12168i	−0.460035	+	0.887901i	$0.652163\pi$
$884$	118.030	−	34.6567i	0.00449070	−	0.00131859i
$885$	4078.33	−	4706.64i	0.154906	−	0.178771i
$886$	17039.4	−	19664.5i	0.646106	−	0.745646i
$887$	19507.8	−	5728.00i	0.738452	−	0.216829i	0.109189	−	0.994021i	$-0.465175\pi$
$887$	19507.8	−	5728.00i	0.738452	−	0.216829i	0.629264	+	0.777192i	$0.283357\pi$
$888$	−3957.11	−	8664.87i	−0.149540	−	0.327448i
$889$	925.696	−	594.909i	0.0349233	−	0.0224439i
$890$	−32487.4	−	9539.17i	−1.22357	−	0.359274i
$891$	−209.634	−	1458.03i	−0.00788214	−	0.0548215i
$892$	1802.96	−	3947.93i	0.0676766	−	0.148191i
$893$	−2585.70	+	17984.0i	−0.0968950	+	0.673919i
$894$	6555.91	+	4213.23i	0.245260	+	0.157619i
$895$	40400.0	+	46624.1i	1.50885	+	1.74131i
$896$	−14086.6			−0.525222
$897$	29003.1	+	6824.04i	1.07958	+	0.254011i
$898$	−25096.1			−0.932592
$899$	−12307.5	−	14203.6i	−0.456593	−	0.526936i
$900$	−1689.76	−	1085.94i	−0.0625836	−	0.0402200i
$901$	−41.6783	+	289.879i	−0.00154107	+	0.0107184i
$902$	4071.31	−	8914.93i	0.150288	−	0.329085i
$903$	5145.76	+	35789.6i	0.189635	+	1.31894i
$904$	−28999.7	−	8515.07i	−1.06694	−	0.313282i
$905$	11780.0	−	7570.52i	0.432684	−	0.278069i
$906$	754.201	+	1651.47i	0.0276564	+	0.0605590i
$907$	9614.15	−	2822.97i	0.351965	−	0.103346i	−0.100971	−	0.994889i	$-0.532195\pi$
$907$	9614.15	−	2822.97i	0.351965	−	0.103346i	0.452936	+	0.891543i	$0.350377\pi$
$908$	1433.00	−	1653.77i	0.0523743	−	0.0604432i
$909$	5718.77	−	6599.82i	0.208669	−	0.240816i
$910$	−78976.2	+	23189.5i	−2.87696	+	0.844752i
$911$	−4300.59	−	9416.98i	−0.156405	−	0.342479i	0.815166	−	0.579227i	$-0.196646\pi$
$911$	−4300.59	−	9416.98i	−0.156405	−	0.342479i	−0.971571	+	0.236748i	$0.923918\pi$
$912$	9589.48	−	6162.79i	0.348179	−	0.223761i
$913$	−18400.7	−	5402.95i	−0.667005	−	0.195850i
$914$	−6489.52	−	45135.6i	−0.234851	−	1.63343i
$915$	7025.29	−	15383.2i	0.253824	−	0.555797i
$916$	−843.848	+	5869.09i	−0.0304383	+	0.211703i
$917$	28755.0	+	18479.7i	1.03552	+	0.665489i
$918$	25.3861	+	29.2971i	0.000912708	+	0.00105332i
$919$	−6733.25			−0.241686			−0.120843	−	0.992672i	$-0.538560\pi$
$919$	−6733.25			−0.241686			−0.120843	+	0.992672i	$0.538560\pi$
$920$	7939.55	+	39714.2i	0.284521	+	1.42320i
$921$	−13865.9			−0.496087
$922$	19627.4	+	22651.3i	0.701079	+	0.809088i
$923$	−68598.5	−	44085.6i	−2.44631	−	1.57215i
$924$	−452.237	+	3145.37i	−0.0161012	+	0.111986i
$925$	5259.81	−	11517.4i	0.186964	−	0.409393i
$926$	4997.80	+	34760.5i	0.177363	+	1.23359i
$927$	−3344.35	−	981.989i	−0.118493	−	0.0347926i
$928$	−6036.98	+	3879.73i	−0.213549	+	0.137240i
$929$	18544.0	+	40605.7i	0.654907	+	1.43405i	0.887193	+	0.461399i	$0.152652\pi$
$929$	18544.0	+	40605.7i	0.654907	+	1.43405i	−0.232286	+	0.972648i	$0.574621\pi$
$930$	−26810.2	+	7872.17i	−0.945312	+	0.277569i
$931$	−19097.2	+	22039.3i	−0.672271	+	0.775843i
$932$	5299.92	−	6116.44i	0.186271	−	0.214968i
$933$	25880.7	−	7599.25i	0.908141	−	0.266654i
$934$	−7677.02	−	16810.3i	−0.268951	−	0.588920i
$935$	−137.117	+	88.1200i	−0.00479596	+	0.00308217i
$936$	19115.8	+	5612.91i	0.667542	+	0.196008i
$937$	4725.21	+	32864.5i	0.164745	+	1.14582i	0.889539	+	0.456859i	$0.151026\pi$
$937$	4725.21	+	32864.5i	0.164745	+	1.14582i	−0.724794	+	0.688966i	$0.758065\pi$
$938$	−7881.82	+	17258.8i	−0.274361	+	0.600767i
$939$	527.707	−	3670.28i	0.0183398	−	0.127556i
$940$	−5553.27	−	3568.87i	−0.192689	−	0.123834i
$941$	−5836.32	−	6735.48i	−0.202188	−	0.233337i	0.645596	−	0.763679i	$-0.276609\pi$
$941$	−5836.32	−	6735.48i	−0.202188	−	0.233337i	−0.847784	+	0.530342i	$0.822064\pi$
$942$	−752.753			−0.0260361
$943$	9075.22	−	23131.2i	0.313393	−	0.798786i
$944$	−5644.31			−0.194604
$945$	6756.22	+	7797.09i	0.232571	+	0.268402i
$946$	−17240.9	−	11080.0i	−0.592546	−	0.380806i
$947$	529.216	−	3680.78i	0.0181597	−	0.126303i	−0.978725	−	0.205177i	$-0.934223\pi$
$947$	529.216	−	3680.78i	0.0181597	−	0.126303i	0.996885	+	0.0788732i	$0.0251322\pi$
$948$	−2774.19	+	6074.62i	−0.0950437	+	0.208117i
$949$	4127.66	+	28708.5i	0.141190	+	0.982000i
$950$	21058.2	+	6183.26i	0.719179	+	0.211170i
$951$	−6153.51	+	3954.62i	−0.209822	+	0.134845i
$952$	−156.824	−	343.397i	−0.00533897	−	0.0116907i
$953$	48515.1	−	14245.3i	1.64906	−	0.484209i	0.680453	−	0.732791i	$-0.261783\pi$
$953$	48515.1	−	14245.3i	1.64906	−	0.484209i	0.968611	+	0.248582i	$0.0799646\pi$
$954$	−6880.67	+	7940.72i	−0.233511	+	0.269487i
$955$	−48842.6	+	56367.4i	−1.65498	+	1.90995i
$956$	−6196.50	+	1819.46i	−0.209633	+	0.0615538i
$957$	−1633.92	−	3577.79i	−0.0551904	−	0.120850i
$958$	4281.12	−	2751.31i	0.144381	−	0.0927878i
$959$	−6980.37	−	2049.62i	−0.235045	−	0.0690153i
$960$	3589.65	+	24966.6i	0.120683	+	0.839367i
$961$	15854.7	−	34717.0i	0.532198	−	1.16535i
$962$	−3959.25	+	27537.2i	−0.132694	+	0.922904i
$963$	−3504.54	−	2252.23i	−0.117271	−	0.0753656i
$964$	3756.25	+	4334.94i	0.125498	+	0.144833i
$965$	37962.4			1.26638
$966$	1785.92	−	20176.8i	0.0594835	−	0.672027i
$967$	−23535.5			−0.782678			−0.391339	−	0.920247i	$-0.627988\pi$
$967$	−23535.5			−0.782678			−0.391339	+	0.920247i	$0.627988\pi$
$968$	16104.6	+	18585.7i	0.534733	+	0.617114i
$969$	141.730	+	91.0841i	0.00469867	+	0.00301965i
$970$	−6251.95	+	43483.3i	−0.206946	+	1.43934i
$971$	−1253.95	+	2745.76i	−0.0414429	+	0.0907474i	−0.929221	−	0.369524i	$-0.879521\pi$
$971$	−1253.95	+	2745.76i	−0.0414429	+	0.0907474i	0.887778	+	0.460272i	$0.152248\pi$
$972$	−78.7268	−	547.557i	−0.00259790	−	0.0180688i
$973$	−33225.1	−	9755.77i	−1.09470	−	0.321434i
$974$	−6665.96	+	4283.95i	−0.219293	+	0.140931i
$975$	11000.8	+	24088.4i	0.361341	+	0.791227i
$976$	−14706.2	+	4318.13i	−0.482310	+	0.141619i
$977$	−26353.1	+	30413.1i	−0.862958	+	0.995907i	0.137027	+	0.990567i	$0.456245\pi$
$977$	−26353.1	+	30413.1i	−0.862958	+	0.995907i	−0.999986	+	0.00533978i	$0.998300\pi$
$978$	−6772.63	+	7816.04i	−0.221437	+	0.255551i
$979$	16535.7	−	4855.31i	0.539818	−	0.158505i
$980$	−4401.45	−	9637.84i	−0.143469	−	0.314153i
$981$	3894.69	−	2502.96i	0.126756	−	0.0814612i
$982$	32604.4	+	9573.50i	1.05952	+	0.311103i
$983$	4970.48	+	34570.5i	0.161275	+	1.12170i	0.896233	+	0.443583i	$0.146293\pi$
$983$	4970.48	+	34570.5i	0.161275	+	1.12170i	−0.734958	+	0.678113i	$0.762798\pi$
$984$	6902.00	−	15113.3i	0.223605	−	0.489628i
$985$	5049.76	−	35121.8i	0.163349	−	1.13612i
$986$	87.0789	+	55.9622i	0.00281253	+	0.00180751i
$987$	9759.80	+	11263.4i	0.314750	+	0.363240i
$988$	19180.4			0.617623
$989$	−45177.1	−	25668.0i	−1.45253	−	0.825274i
$990$	−5847.73			−0.187730
$991$	−3772.73	−	4353.97i	−0.120933	−	0.139564i	0.692054	−	0.721845i	$-0.256706\pi$
$991$	−3772.73	−	4353.97i	−0.120933	−	0.139564i	−0.812988	+	0.582281i	$0.802160\pi$
$992$	−21829.0	−	14028.6i	−0.698661	−	0.449002i
$993$	2257.98	−	15704.6i	0.0721599	−	0.501883i
$994$	−23028.8	+	50426.1i	−0.734839	+	1.60907i
$995$	4525.90	+	31478.3i	0.144202	+	1.00294i
$996$	−6910.30	−	2029.05i	−0.219841	−	0.0645511i
$997$	8457.92	−	5435.57i	0.268671	−	0.172664i	−0.399368	−	0.916791i	$-0.630770\pi$
$997$	8457.92	−	5435.57i	0.268671	−	0.172664i	0.668039	+	0.744126i	$0.267134\pi$
$998$	−18930.6	−	41452.2i	−0.600438	−	1.31477i
$999$	3345.83	−	982.425i	0.105963	−	0.0311137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.4.e.b.13.5	✓	60
3.2	odd	2		207.4.i.b.82.2		60
23.4	even	11		1587.4.a.w.1.9		30
23.16	even	11	inner	69.4.e.b.16.5	yes	60
23.19	odd	22		1587.4.a.v.1.9		30
69.62	odd	22		207.4.i.b.154.2		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.4.e.b.13.5	✓	60	1.1	even	1	trivial
69.4.e.b.16.5	yes	60	23.16	even	11	inner
207.4.i.b.82.2		60	3.2	odd	2
207.4.i.b.154.2		60	69.62	odd	22
1587.4.a.v.1.9		30	23.19	odd	22
1587.4.a.w.1.9		30	23.4	even	11

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.56668 + 1.80804i) q^{2} +(-2.52376 - 1.62192i) q^{3} +(0.323978 - 2.25332i) q^{4} +(6.20398 - 13.5848i) q^{5} +(-1.02142 - 7.10410i) q^{6} +(-24.5496 - 7.20842i) q^{7} +(20.6825 - 13.2918i) q^{8} +(3.73874 + 8.18669i) q^{9} +O(q^{10})\)	\(q+(1.56668 + 1.80804i) q^{2} +(-2.52376 - 1.62192i) q^{3} +(0.323978 - 2.25332i) q^{4} +(6.20398 - 13.5848i) q^{5} +(-1.02142 - 7.10410i) q^{6} +(-24.5496 - 7.20842i) q^{7} +(20.6825 - 13.2918i) q^{8} +(3.73874 + 8.18669i) q^{9} +(34.2816 - 10.0660i) q^{10} +(-11.9090 + 13.7437i) q^{11} +(-4.47235 + 5.16137i) q^{12} +(86.3921 - 25.3670i) q^{13} +(-25.4282 - 55.6801i) q^{14} +(-37.6909 + 24.2225i) q^{15} +(38.9608 + 11.4399i) q^{16} +(0.0854087 + 0.594031i) q^{17} +(-8.94450 + 19.5857i) q^{18} +(-13.3171 + 92.6227i) q^{19} +(-28.6010 - 18.3807i) q^{20} +(50.2659 + 58.0099i) q^{21} -43.5068 q^{22} +(-110.140 + 6.01038i) q^{23} -73.7560 q^{24} +(-64.2004 - 74.0912i) q^{25} +(181.213 + 116.459i) q^{26} +(3.84250 - 26.7252i) q^{27} +(-24.1964 + 52.9828i) q^{28} +(-10.2601 - 71.3608i) q^{29} +(-102.845 - 30.1980i) q^{30} +(219.303 - 140.937i) q^{31} +(-41.3497 - 90.5432i) q^{32} +(52.3466 - 15.3704i) q^{33} +(-0.940226 + 1.08508i) q^{34} +(-250.230 + 288.781i) q^{35} +(19.6585 - 5.77226i) q^{36} +(53.6514 + 117.480i) q^{37} +(-188.330 + 121.032i) q^{38} +(-259.176 - 76.1010i) q^{39} +(-52.2534 - 363.430i) q^{40} +(-93.5789 + 204.909i) q^{41} +(-26.1340 + 181.766i) q^{42} +(396.280 + 254.674i) q^{43} +(27.1107 + 31.2874i) q^{44} +134.410 q^{45} +(-183.421 - 189.722i) q^{46} +194.164 q^{47} +(-79.7732 - 92.0631i) q^{48} +(262.172 + 168.488i) q^{49} +(33.3788 - 232.154i) q^{50} +(0.747921 - 1.63772i) q^{51} +(-29.1708 - 202.887i) q^{52} +(468.220 + 137.482i) q^{53} +(54.3403 - 34.9224i) q^{54} +(112.823 + 247.047i) q^{55} +(-603.560 + 177.221i) q^{56} +(183.836 - 212.158i) q^{57} +(112.949 - 130.350i) q^{58} +(-133.372 + 39.1616i) q^{59} +(42.3699 + 92.7772i) q^{60} +(-317.541 + 204.071i) q^{61} +(598.398 + 175.705i) q^{62} +(-32.7714 - 227.930i) q^{63} +(233.870 - 512.104i) q^{64} +(191.369 - 1331.00i) q^{65} +(109.801 + 70.5646i) q^{66} +(-202.983 - 234.255i) q^{67} +1.36621 q^{68} +(287.716 + 163.470i) q^{69} -914.160 q^{70} +(-593.068 - 684.437i) q^{71} +(186.142 + 119.626i) q^{72} +(-45.8429 + 318.844i) q^{73} +(-128.355 + 281.058i) q^{74} +(41.8562 + 291.117i) q^{75} +(204.394 + 60.0155i) q^{76} +(391.431 - 251.557i) q^{77} +(-268.452 - 587.828i) q^{78} +(938.227 - 275.488i) q^{79} +(397.122 - 458.303i) q^{80} +(-53.0437 + 61.2157i) q^{81} +(-517.093 + 151.832i) q^{82} +(438.077 + 959.255i) q^{83} +(147.000 - 94.4711i) q^{84} +(8.59968 + 2.52509i) q^{85} +(160.382 + 1115.48i) q^{86} +(-89.8476 + 196.739i) q^{87} +(-63.6285 + 442.546i) q^{88} +(-797.225 - 512.346i) q^{89} +(210.577 + 243.019i) q^{90} -2303.75 q^{91} +(-22.1398 + 250.128i) q^{92} -782.057 q^{93} +(304.192 + 351.056i) q^{94} +(1175.64 + 755.540i) q^{95} +(-42.4973 + 295.575i) q^{96} +(-510.773 + 1118.44i) q^{97} +(106.106 + 737.985i) q^{98} +(-157.040 - 46.1111i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 4 q^{2} + 18 q^{3} - 28 q^{4} - 6 q^{5} + 21 q^{6} - 4 q^{7} - 52 q^{8} - 54 q^{9}+O(q^{10}) \) 60 * q + 4 * q^2 + 18 * q^3 - 28 * q^4 - 6 * q^5 + 21 * q^6 - 4 * q^7 - 52 * q^8 - 54 * q^9	\( 60 q + 4 q^{2} + 18 q^{3} - 28 q^{4} - 6 q^{5} + 21 q^{6} - 4 q^{7} - 52 q^{8} - 54 q^{9} - 78 q^{10} + 10 q^{11} + 84 q^{12} + 50 q^{13} - 224 q^{14} + 150 q^{15} + 260 q^{16} - 662 q^{17} + 36 q^{18} - 4 q^{19} - 735 q^{20} + 12 q^{21} + 622 q^{22} - 438 q^{23} - 108 q^{24} - 754 q^{25} - 40 q^{26} + 162 q^{27} + 672 q^{28} + 1302 q^{29} + 234 q^{30} + 1528 q^{31} + 1588 q^{32} - 492 q^{33} + 29 q^{34} + 950 q^{35} + 243 q^{36} + 316 q^{37} + 3122 q^{38} - 150 q^{39} - 1939 q^{40} - 1500 q^{41} - 2298 q^{42} - 1316 q^{43} - 2901 q^{44} + 936 q^{45} - 1980 q^{46} - 1440 q^{47} - 2265 q^{48} - 2310 q^{49} + 195 q^{50} - 126 q^{51} + 6189 q^{52} - 148 q^{53} + 189 q^{54} - 606 q^{55} - 432 q^{56} + 1398 q^{57} - 2623 q^{58} + 5264 q^{59} + 753 q^{60} + 1482 q^{61} - 2299 q^{62} - 36 q^{63} - 6780 q^{64} - 1446 q^{65} + 1731 q^{66} + 388 q^{67} + 5604 q^{68} - 138 q^{69} + 2984 q^{70} - 3316 q^{71} - 468 q^{72} + 2072 q^{73} - 6556 q^{74} + 1206 q^{75} + 9841 q^{76} + 9338 q^{77} - 3048 q^{78} + 268 q^{79} + 7980 q^{80} - 486 q^{81} + 7742 q^{82} - 3494 q^{83} + 2604 q^{84} - 3842 q^{85} - 4792 q^{86} - 672 q^{87} - 7960 q^{88} - 2754 q^{89} - 702 q^{90} - 5436 q^{91} - 17609 q^{92} + 2280 q^{93} - 10961 q^{94} - 2396 q^{95} + 6852 q^{96} - 5654 q^{97} + 14411 q^{98} + 1476 q^{99}+O(q^{100}) \) 60 * q + 4 * q^2 + 18 * q^3 - 28 * q^4 - 6 * q^5 + 21 * q^6 - 4 * q^7 - 52 * q^8 - 54 * q^9 - 78 * q^10 + 10 * q^11 + 84 * q^12 + 50 * q^13 - 224 * q^14 + 150 * q^15 + 260 * q^16 - 662 * q^17 + 36 * q^18 - 4 * q^19 - 735 * q^20 + 12 * q^21 + 622 * q^22 - 438 * q^23 - 108 * q^24 - 754 * q^25 - 40 * q^26 + 162 * q^27 + 672 * q^28 + 1302 * q^29 + 234 * q^30 + 1528 * q^31 + 1588 * q^32 - 492 * q^33 + 29 * q^34 + 950 * q^35 + 243 * q^36 + 316 * q^37 + 3122 * q^38 - 150 * q^39 - 1939 * q^40 - 1500 * q^41 - 2298 * q^42 - 1316 * q^43 - 2901 * q^44 + 936 * q^45 - 1980 * q^46 - 1440 * q^47 - 2265 * q^48 - 2310 * q^49 + 195 * q^50 - 126 * q^51 + 6189 * q^52 - 148 * q^53 + 189 * q^54 - 606 * q^55 - 432 * q^56 + 1398 * q^57 - 2623 * q^58 + 5264 * q^59 + 753 * q^60 + 1482 * q^61 - 2299 * q^62 - 36 * q^63 - 6780 * q^64 - 1446 * q^65 + 1731 * q^66 + 388 * q^67 + 5604 * q^68 - 138 * q^69 + 2984 * q^70 - 3316 * q^71 - 468 * q^72 + 2072 * q^73 - 6556 * q^74 + 1206 * q^75 + 9841 * q^76 + 9338 * q^77 - 3048 * q^78 + 268 * q^79 + 7980 * q^80 - 486 * q^81 + 7742 * q^82 - 3494 * q^83 + 2604 * q^84 - 3842 * q^85 - 4792 * q^86 - 672 * q^87 - 7960 * q^88 - 2754 * q^89 - 702 * q^90 - 5436 * q^91 - 17609 * q^92 + 2280 * q^93 - 10961 * q^94 - 2396 * q^95 + 6852 * q^96 - 5654 * q^97 + 14411 * q^98 + 1476 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more