LMFDB - Embedded newform 115.4.b.a.24.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(24,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("115.24");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.b (of order $2$, degree $1$, 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:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.20
Character	$\chi$	$=$	115.24
Dual form			115.4.b.a.24.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.752118i q^{2} -6.31519i q^{3} +7.43432 q^{4} +(2.89657 + 10.7986i) q^{5} +4.74977 q^{6} +25.4579i q^{7} +11.6084i q^{8} -12.8816 q^{9} +O(q^{10})$	\(q+0.752118i q^{2} -6.31519i q^{3} +7.43432 q^{4} +(2.89657 + 10.7986i) q^{5} +4.74977 q^{6} +25.4579i q^{7} +11.6084i q^{8} -12.8816 q^{9} +(-8.12183 + 2.17857i) q^{10} +29.8906 q^{11} -46.9491i q^{12} -14.6921i q^{13} -19.1473 q^{14} +(68.1952 - 18.2924i) q^{15} +50.7436 q^{16} -44.0791i q^{17} -9.68849i q^{18} -9.77747 q^{19} +(21.5340 + 80.2803i) q^{20} +160.771 q^{21} +22.4812i q^{22} -23.0000i q^{23} +73.3095 q^{24} +(-108.220 + 62.5579i) q^{25} +11.0502 q^{26} -89.1603i q^{27} +189.262i q^{28} -124.275 q^{29} +(13.7581 + 51.2909i) q^{30} +184.024 q^{31} +131.033i q^{32} -188.765i q^{33} +33.1527 q^{34} +(-274.910 + 73.7406i) q^{35} -95.7659 q^{36} +65.7137i q^{37} -7.35382i q^{38} -92.7836 q^{39} +(-125.355 + 33.6247i) q^{40} -130.103 q^{41} +120.919i q^{42} -58.2708i q^{43} +222.216 q^{44} +(-37.3125 - 139.103i) q^{45} +17.2987 q^{46} -163.160i q^{47} -320.456i q^{48} -305.103 q^{49} +(-47.0509 - 81.3941i) q^{50} -278.368 q^{51} -109.226i q^{52} -622.062i q^{53} +67.0591 q^{54} +(86.5802 + 322.776i) q^{55} -295.526 q^{56} +61.7466i q^{57} -93.4692i q^{58} -725.566 q^{59} +(506.985 - 135.992i) q^{60} +606.658 q^{61} +138.408i q^{62} -327.938i q^{63} +307.397 q^{64} +(158.655 - 42.5568i) q^{65} +141.973 q^{66} +944.820i q^{67} -327.698i q^{68} -145.249 q^{69} +(-55.4617 - 206.765i) q^{70} -925.819 q^{71} -149.535i q^{72} +81.1101i q^{73} -49.4245 q^{74} +(395.065 + 683.428i) q^{75} -72.6889 q^{76} +760.950i q^{77} -69.7842i q^{78} -1335.37 q^{79} +(146.983 + 547.960i) q^{80} -910.868 q^{81} -97.8529i q^{82} +78.3594i q^{83} +1195.22 q^{84} +(475.993 - 127.678i) q^{85} +43.8265 q^{86} +784.818i q^{87} +346.983i q^{88} +1408.27 q^{89} +(104.622 - 28.0634i) q^{90} +374.030 q^{91} -170.989i q^{92} -1162.15i q^{93} +122.716 q^{94} +(-28.3212 - 105.583i) q^{95} +827.496 q^{96} -1406.08i q^{97} -229.474i q^{98} -385.038 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9}+O(q^{10}) $ 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9	$ 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9} + 14 q^{10} - 8 q^{11} + 236 q^{14} + 440 q^{16} + 144 q^{19} - 180 q^{20} - 32 q^{21} + 108 q^{24} + 134 q^{25} - 144 q^{26} + 56 q^{29} - 294 q^{30} - 80 q^{31} + 264 q^{34} + 116 q^{35} + 1864 q^{36} - 1200 q^{39} + 650 q^{40} + 268 q^{41} - 1612 q^{44} - 1346 q^{45} + 184 q^{46} - 1474 q^{49} + 120 q^{50} - 1104 q^{51} + 1564 q^{54} + 1160 q^{55} - 2300 q^{56} - 708 q^{59} - 516 q^{60} + 1100 q^{61} + 100 q^{64} + 1164 q^{65} - 1416 q^{66} - 552 q^{69} + 1144 q^{70} + 1360 q^{71} + 1588 q^{74} - 2064 q^{75} + 108 q^{76} + 3968 q^{79} + 2542 q^{80} + 4914 q^{81} - 1948 q^{84} + 124 q^{85} - 6148 q^{86} + 1196 q^{89} + 2760 q^{90} - 544 q^{91} - 2340 q^{94} + 3920 q^{95} + 2960 q^{96} - 3816 q^{99}+O(q^{100}) $ 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9 + 14 * q^10 - 8 * q^11 + 236 * q^14 + 440 * q^16 + 144 * q^19 - 180 * q^20 - 32 * q^21 + 108 * q^24 + 134 * q^25 - 144 * q^26 + 56 * q^29 - 294 * q^30 - 80 * q^31 + 264 * q^34 + 116 * q^35 + 1864 * q^36 - 1200 * q^39 + 650 * q^40 + 268 * q^41 - 1612 * q^44 - 1346 * q^45 + 184 * q^46 - 1474 * q^49 + 120 * q^50 - 1104 * q^51 + 1564 * q^54 + 1160 * q^55 - 2300 * q^56 - 708 * q^59 - 516 * q^60 + 1100 * q^61 + 100 * q^64 + 1164 * q^65 - 1416 * q^66 - 552 * q^69 + 1144 * q^70 + 1360 * q^71 + 1588 * q^74 - 2064 * q^75 + 108 * q^76 + 3968 * q^79 + 2542 * q^80 + 4914 * q^81 - 1948 * q^84 + 124 * q^85 - 6148 * q^86 + 1196 * q^89 + 2760 * q^90 - 544 * q^91 - 2340 * q^94 + 3920 * q^95 + 2960 * q^96 - 3816 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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 $

$2$			0.752118i			0.265914i	0.991122	+	0.132957i	$0.0424472\pi$
$2$			0.752118i			0.265914i	−0.991122	+	0.132957i	$0.957553\pi$
$3$		−	6.31519i		−	1.21536i	−0.794183	−	0.607679i	$-0.792101\pi$
$3$		−	6.31519i		−	1.21536i	0.794183	−	0.607679i	$-0.207899\pi$
$4$	7.43432			0.929290
$5$	2.89657	+	10.7986i	0.259077	+	0.965857i
$5$	2.89657	+	10.7986i	0.259077	+	0.965857i
$6$	4.74977			0.323181
$7$			25.4579i			1.37460i	0.726376	+	0.687298i	$0.241203\pi$
$7$			25.4579i			1.37460i	−0.726376	+	0.687298i	$0.758797\pi$
$8$			11.6084i			0.513025i
$9$	−12.8816			−0.477096
$10$	−8.12183	+	2.17857i	−0.256835	+	0.0688923i
$11$	29.8906			0.819304			0.409652	−	0.912242i	$-0.365650\pi$
$11$	29.8906			0.819304			0.409652	+	0.912242i	$0.365650\pi$
$12$		−	46.9491i		−	1.12942i
$13$		−	14.6921i		−	0.313451i	−0.987642	−	0.156726i	$-0.949906\pi$
$13$		−	14.6921i		−	0.313451i	0.987642	−	0.156726i	$-0.0500938\pi$
$14$	−19.1473			−0.365524
$15$	68.1952	−	18.2924i	1.17386	−	0.314872i
$16$	50.7436			0.792869
$17$		−	44.0791i		−	0.628868i	−0.949279	−	0.314434i	$-0.898185\pi$
$17$		−	44.0791i		−	0.628868i	0.949279	−	0.314434i	$-0.101815\pi$
$18$		−	9.68849i		−	0.126867i
$19$	−9.77747			−0.118058			−0.0590291	−	0.998256i	$-0.518800\pi$
$19$	−9.77747			−0.118058			−0.0590291	+	0.998256i	$0.518800\pi$
$20$	21.5340	+	80.2803i	0.240758	+	0.897561i
$21$	160.771			1.67063
$22$			22.4812i			0.217864i
$23$		−	23.0000i		−	0.208514i
$23$		−	23.0000i		−	0.208514i
$24$	73.3095			0.623510
$25$	−108.220	+	62.5579i	−0.865758	+	0.500463i
$26$	11.0502			0.0833510
$27$		−	89.1603i		−	0.635515i
$28$			189.262i			1.27740i
$29$	−124.275			−0.795766			−0.397883	−	0.917436i	$-0.630255\pi$
$29$	−124.275			−0.795766			−0.397883	+	0.917436i	$0.630255\pi$
$30$	13.7581	+	51.2909i	0.0837288	+	0.312146i
$31$	184.024			1.06618			0.533092	−	0.846057i	$-0.321030\pi$
$31$	184.024			1.06618			0.533092	+	0.846057i	$0.321030\pi$
$32$			131.033i			0.723860i
$33$		−	188.765i		−	0.995748i
$34$	33.1527			0.167225
$35$	−274.910	+	73.7406i	−1.32766	+	0.356127i
$36$	−95.7659			−0.443361
$37$			65.7137i			0.291980i	0.989286	+	0.145990i	$0.0466367\pi$
$37$			65.7137i			0.291980i	−0.989286	+	0.145990i	$0.953363\pi$
$38$		−	7.35382i		−	0.0313933i
$39$	−92.7836			−0.380955
$40$	−125.355	+	33.6247i	−0.495509	+	0.132913i
$41$	−130.103			−0.495578			−0.247789	−	0.968814i	$-0.579704\pi$
$41$	−130.103			−0.495578			−0.247789	+	0.968814i	$0.579704\pi$
$42$			120.919i			0.444243i
$43$		−	58.2708i		−	0.206656i	−0.994647	−	0.103328i	$-0.967051\pi$
$43$		−	58.2708i		−	0.206656i	0.994647	−	0.103328i	$-0.0329491\pi$
$44$	222.216			0.761371
$45$	−37.3125	−	139.103i	−0.123605	−	0.460807i
$46$	17.2987			0.0554469
$47$		−	163.160i		−	0.506369i	−0.967418	−	0.253184i	$-0.918522\pi$
$47$		−	163.160i		−	0.506369i	0.967418	−	0.253184i	$-0.0814780\pi$
$48$		−	320.456i		−	0.963620i
$49$	−305.103			−0.889514
$50$	−47.0509	−	81.3941i	−0.133080	−	0.230217i
$51$	−278.368			−0.764300
$52$		−	109.226i		−	0.291287i
$53$		−	622.062i		−	1.61220i	−0.591777	−	0.806102i	$-0.701573\pi$
$53$		−	622.062i		−	1.61220i	0.591777	−	0.806102i	$-0.298427\pi$
$54$	67.0591			0.168992
$55$	86.5802	+	322.776i	0.212263	+	0.791330i
$56$	−295.526			−0.705202
$57$			61.7466i			0.143483i
$58$		−	93.4692i		−	0.211605i
$59$	−725.566			−1.60103			−0.800514	−	0.599314i	$-0.795440\pi$
$59$	−725.566			−1.60103			−0.800514	+	0.599314i	$0.795440\pi$
$60$	506.985	−	135.992i	1.09086	−	0.292607i
$61$	606.658			1.27335			0.636677	−	0.771130i	$-0.280308\pi$
$61$	606.658			1.27335			0.636677	+	0.771130i	$0.280308\pi$
$62$			138.408i			0.283513i
$63$		−	327.938i		−	0.655815i
$64$	307.397			0.600385
$65$	158.655	−	42.5568i	0.302749	−	0.0812081i
$66$	141.973			0.264783
$67$			944.820i			1.72281i	0.507920	+	0.861404i	$0.330415\pi$
$67$			944.820i			1.72281i	−0.507920	+	0.861404i	$0.669585\pi$
$68$		−	327.698i		−	0.584400i
$69$	−145.249			−0.253420
$70$	−55.4617	−	206.765i	−0.0946991	−	0.353044i
$71$	−925.819			−1.54753			−0.773764	−	0.633474i	$-0.781628\pi$
$71$	−925.819			−1.54753			−0.773764	+	0.633474i	$0.781628\pi$
$72$		−	149.535i		−	0.244762i
$73$			81.1101i			0.130044i	0.997884	+	0.0650220i	$0.0207118\pi$
$73$			81.1101i			0.130044i	−0.997884	+	0.0650220i	$0.979288\pi$
$74$	−49.4245			−0.0776416
$75$	395.065	+	683.428i	0.608242	+	1.05221i
$76$	−72.6889			−0.109710
$77$			760.950i			1.12621i
$78$		−	69.7842i		−	0.101301i
$79$	−1335.37			−1.90179			−0.950894	−	0.309516i	$-0.899833\pi$
$79$	−1335.37			−1.90179			−0.950894	+	0.309516i	$0.899833\pi$
$80$	146.983	+	547.960i	0.205414	+	0.765798i
$81$	−910.868			−1.24948
$82$		−	97.8529i		−	0.131781i
$83$			78.3594i			0.103627i	0.998657	+	0.0518137i	$0.0165002\pi$
$83$			78.3594i			0.103627i	−0.998657	+	0.0518137i	$0.983500\pi$
$84$	1195.22			1.55250
$85$	475.993	−	127.678i	0.607396	−	0.162925i
$86$	43.8265			0.0549527
$87$			784.818i			0.967141i
$88$			346.983i			0.420324i
$89$	1408.27			1.67726			0.838630	−	0.544702i	$-0.183357\pi$
$89$	1408.27			1.67726			0.838630	+	0.544702i	$0.183357\pi$
$90$	104.622	−	28.0634i	0.122535	−	0.0328683i
$91$	374.030			0.430869
$92$		−	170.989i		−	0.193770i
$93$		−	1162.15i		−	1.29580i
$94$	122.716			0.134651
$95$	−28.3212	−	105.583i	−0.0305862	−	0.114027i
$96$	827.496			0.879750
$97$		−	1406.08i		−	1.47181i	−0.677086	−	0.735904i	$-0.736758\pi$
$97$		−	1406.08i		−	1.47181i	0.677086	−	0.735904i	$-0.263242\pi$
$98$		−	229.474i		−	0.236534i
$99$	−385.038			−0.390887
$100$	−804.540	+	465.075i	−0.804540	+	0.465075i
$101$	22.0778			0.0217507			0.0108753	−	0.999941i	$-0.496538\pi$
$101$	22.0778			0.0217507			0.0108753	+	0.999941i	$0.496538\pi$
$102$		−	209.366i		−	0.203238i
$103$		−	401.810i		−	0.384384i	−0.981357	−	0.192192i	$-0.938440\pi$
$103$		−	401.810i		−	0.384384i	0.981357	−	0.192192i	$-0.0615596\pi$
$104$	170.553			0.160808
$105$	465.686	+	1736.11i	0.432822	+	1.61359i
$106$	467.864			0.428708
$107$			65.4400i			0.0591245i	0.999563	+	0.0295622i	$0.00941133\pi$
$107$			65.4400i			0.0591245i	−0.999563	+	0.0295622i	$0.990589\pi$
$108$		−	662.846i		−	0.590578i
$109$	2108.07			1.85244			0.926222	−	0.376980i	$-0.123037\pi$
$109$	2108.07			1.85244			0.926222	+	0.376980i	$0.123037\pi$
$110$	−242.766	+	65.1186i	−0.210426	+	0.0564437i
$111$	414.994			0.354860
$112$			1291.82i			1.08987i
$113$		−	1085.61i		−	0.903765i	−0.892078	−	0.451882i	$-0.850753\pi$
$113$		−	1085.61i		−	0.903765i	0.892078	−	0.451882i	$-0.149247\pi$
$114$	−46.4408			−0.0381542
$115$	248.368	−	66.6212i	0.201395	−	0.0540214i
$116$	−923.897			−0.739497
$117$			189.258i			0.149546i
$118$		−	545.712i		−	0.425736i
$119$	1122.16			0.864439
$120$	212.346	+	791.640i	0.161537	+	0.602221i
$121$	−437.554			−0.328741
$122$			456.279i			0.338603i
$123$			821.625i			0.602305i
$124$	1368.09			0.990794
$125$	−989.004	−	987.419i	−0.707674	−	0.706539i
$126$	246.648			0.174390
$127$		−	1243.72i		−	0.868996i	−0.900673	−	0.434498i	$-0.856926\pi$
$127$		−	1243.72i		−	0.868996i	0.900673	−	0.434498i	$-0.143074\pi$
$128$			1279.46i			0.883511i
$129$	−367.991			−0.251161
$130$	32.0078	+	119.327i	0.0215944	+	0.0805052i
$131$	−959.795			−0.640135			−0.320068	−	0.947395i	$-0.603706\pi$
$131$	−959.795			−0.640135			−0.320068	+	0.947395i	$0.603706\pi$
$132$		−	1403.34i		−	0.925339i
$133$		−	248.914i		−	0.162282i
$134$	−710.617			−0.458119
$135$	962.807	−	258.259i	0.613817	−	0.164648i
$136$	511.689			0.322625
$137$		−	853.640i		−	0.532346i	−0.963925	−	0.266173i	$-0.914241\pi$
$137$		−	853.640i		−	0.532346i	0.963925	−	0.266173i	$-0.0857592\pi$
$138$		−	109.245i		−	0.0673879i
$139$	−1074.03			−0.655380			−0.327690	−	0.944785i	$-0.606270\pi$
$139$	−1074.03			−0.655380			−0.327690	+	0.944785i	$0.606270\pi$
$140$	−2043.76	+	548.211i	−1.23378	+	0.330945i
$141$	−1030.39			−0.615420
$142$		−	696.325i		−	0.411509i
$143$		−	439.156i		−	0.256812i
$144$	−653.659			−0.378275
$145$	−359.970	−	1341.99i	−0.206165	−	0.768596i
$146$	−61.0044			−0.0345805
$147$			1926.79i			1.08108i
$148$			488.536i			0.271334i
$149$	−1702.18			−0.935890			−0.467945	−	0.883758i	$-0.655006\pi$
$149$	−1702.18			−0.935890			−0.467945	+	0.883758i	$0.655006\pi$
$150$	−514.019	+	297.136i	−0.279796	+	0.161740i
$151$	2347.50			1.26514			0.632572	−	0.774502i	$-0.281999\pi$
$151$	2347.50			1.26514			0.632572	+	0.774502i	$0.281999\pi$
$152$		−	113.501i		−	0.0605669i
$153$			567.809i			0.300030i
$154$	−572.325			−0.299476
$155$	533.039	+	1987.20i	0.276224	+	1.02978i
$156$	−689.783			−0.354018
$157$			1365.29i			0.694024i	0.937861	+	0.347012i	$0.112804\pi$
$157$			1365.29i			0.694024i	−0.937861	+	0.347012i	$0.887196\pi$
$158$		−	1004.36i		−	0.505712i
$159$	−3928.44			−1.95941
$160$	−1414.97	+	379.546i	−0.699145	+	0.187536i
$161$	585.531			0.286623
$162$		−	685.080i		−	0.332253i
$163$			1834.48i			0.881518i	0.897625	+	0.440759i	$0.145291\pi$
$163$			1834.48i			0.881518i	−0.897625	+	0.440759i	$0.854709\pi$
$164$	−967.227			−0.460535
$165$	2038.39	−	546.770i	0.961750	−	0.257976i
$166$	−58.9356			−0.0275560
$167$		−	1238.32i		−	0.573796i	−0.957961	−	0.286898i	$-0.907376\pi$
$167$		−	1238.32i		−	0.573796i	0.957961	−	0.286898i	$-0.0926241\pi$
$168$			1866.30i			0.857074i
$169$	1981.14			0.901748
$170$	96.0292	+	358.003i	0.0433241	+	0.161515i
$171$	125.950			0.0563252
$172$		−	433.203i		−	0.192043i
$173$		−	1817.77i		−	0.798860i	−0.916764	−	0.399430i	$-0.869208\pi$
$173$		−	1817.77i		−	0.798860i	0.916764	−	0.399430i	$-0.130792\pi$
$174$	−590.276			−0.257176
$175$	−1592.59	−	2755.04i	−0.687935	−	1.19007i
$176$	1516.76			0.649601
$177$			4582.09i			1.94582i
$178$			1059.18i			0.446007i
$179$	−1569.68			−0.655438			−0.327719	−	0.944775i	$-0.606280\pi$
$179$	−1569.68			−0.655438			−0.327719	+	0.944775i	$0.606280\pi$
$180$	−277.393	−	1034.14i	−0.114865	−	0.428223i
$181$	74.5516			0.0306154			0.0153077	−	0.999883i	$-0.495127\pi$
$181$	74.5516			0.0306154			0.0153077	+	0.999883i	$0.495127\pi$
$182$			281.315i			0.114574i
$183$		−	3831.16i		−	1.54758i
$184$	266.994			0.106973
$185$	−709.616	+	190.344i	−0.282011	+	0.0756454i
$186$	874.072			0.344570
$187$		−	1317.55i		−	0.515234i
$188$		−	1212.98i		−	0.470563i
$189$	2269.83			0.873577
$190$	79.4110	−	21.3009i	0.0303215	−	0.00813330i
$191$	−2792.12			−1.05775			−0.528875	−	0.848700i	$-0.677386\pi$
$191$	−2792.12			−1.05775			−0.528875	+	0.848700i	$0.677386\pi$
$192$		−	1941.27i		−	0.729682i
$193$			4699.46i			1.75272i	0.481660	+	0.876358i	$0.340034\pi$
$193$			4699.46i			1.75272i	−0.481660	+	0.876358i	$0.659966\pi$
$194$	1057.54			0.391374
$195$	−268.754	−	1001.93i	−0.0986969	−	0.367948i
$196$	−2268.24			−0.826617
$197$		−	3539.44i		−	1.28007i	−0.768344	−	0.640037i	$-0.778919\pi$
$197$		−	3539.44i		−	1.28007i	0.768344	−	0.640037i	$-0.221081\pi$
$198$		−	289.594i		−	0.103942i
$199$	286.039			0.101893			0.0509466	−	0.998701i	$-0.483776\pi$
$199$	286.039			0.101893			0.0509466	+	0.998701i	$0.483776\pi$
$200$	−726.199	−	1256.26i	−0.256750	−	0.444156i
$201$	5966.72			2.09383
$202$			16.6051i			0.00578382i
$203$		−	3163.77i		−	1.09386i
$204$	−2069.47			−0.710256
$205$	−376.853	−	1404.93i	−0.128393	−	0.478657i
$206$	302.209			0.102213
$207$			296.277i			0.0994815i
$208$		−	745.532i		−	0.248526i
$209$	−292.254			−0.0967256
$210$	−1305.76	+	350.251i	−0.429075	+	0.115093i
$211$	523.713			0.170872			0.0854358	−	0.996344i	$-0.472772\pi$
$211$	523.713			0.170872			0.0854358	+	0.996344i	$0.472772\pi$
$212$		−	4624.61i		−	1.49820i
$213$			5846.72i			1.88080i
$214$	−49.2186			−0.0157220
$215$	629.243	−	168.786i	0.199600	−	0.0535399i
$216$	1035.01			0.326035
$217$			4684.86i			1.46557i
$218$			1585.52i			0.492591i
$219$	512.225			0.158050
$220$	643.665	+	2399.62i	0.197254	+	0.735375i
$221$	−647.616			−0.197119
$222$			312.125i			0.0943624i
$223$		−	5894.52i		−	1.77007i	−0.465523	−	0.885036i	$-0.654134\pi$
$223$		−	5894.52i		−	1.77007i	0.465523	−	0.885036i	$-0.345866\pi$
$224$	−3335.81			−0.995015
$225$	1394.04	−	805.846i	0.413050	−	0.238769i
$226$	816.506			0.240324
$227$			6239.19i			1.82427i	0.409888	+	0.912136i	$0.365568\pi$
$227$			6239.19i			1.82427i	−0.409888	+	0.912136i	$0.634432\pi$
$228$			459.044i			0.133337i
$229$	3926.05			1.13293			0.566465	−	0.824086i	$-0.308311\pi$
$229$	3926.05			1.13293			0.566465	+	0.824086i	$0.308311\pi$
$230$	50.1070	+	186.802i	0.0143650	+	0.0535538i
$231$	4805.54			1.36875
$232$		−	1442.63i		−	0.408248i
$233$			6356.06i			1.78712i	0.448942	+	0.893561i	$0.351801\pi$
$233$			6356.06i			1.78712i	−0.448942	+	0.893561i	$0.648199\pi$
$234$	−142.345			−0.0397665
$235$	1761.90	−	472.605i	0.489080	−	0.131189i
$236$	−5394.09			−1.48782
$237$			8433.14i			2.31135i
$238$			843.997i			0.229866i
$239$	2869.32			0.776574			0.388287	−	0.921539i	$-0.373067\pi$
$239$	2869.32			0.776574			0.388287	+	0.921539i	$0.373067\pi$
$240$	3460.47	−	928.223i	0.930719	−	0.249652i
$241$	−6359.58			−1.69982			−0.849910	−	0.526927i	$-0.823344\pi$
$241$	−6359.58			−1.69982			−0.849910	+	0.526927i	$0.823344\pi$
$242$		−	329.093i		−	0.0874168i
$243$			3344.97i			0.883045i
$244$	4510.09			1.18332
$245$	−883.754	−	3294.69i	−0.230453	−	0.859143i
$246$	−617.960			−0.160161
$247$			143.652i			0.0370055i
$248$			2136.23i			0.546979i
$249$	494.855			0.125944
$250$	742.656	−	743.848i	0.187879	−	0.188180i
$251$	828.982			0.208466			0.104233	−	0.994553i	$-0.466761\pi$
$251$	828.982			0.208466			0.104233	+	0.994553i	$0.466761\pi$
$252$		−	2438.00i		−	0.609442i
$253$		−	687.483i		−	0.170837i
$254$	935.427			0.231078
$255$	−806.312	−	3005.98i	−0.198013	−	0.738204i
$256$	1496.87			0.365447
$257$		−	4085.76i		−	0.991684i	−0.868413	−	0.495842i	$-0.834860\pi$
$257$		−	4085.76i		−	0.991684i	0.868413	−	0.495842i	$-0.165140\pi$
$258$		−	276.773i		−	0.0667873i
$259$	−1672.93			−0.401355
$260$	1179.49	−	316.381i	0.281341	−	0.0754658i
$261$	1600.86			0.379657
$262$		−	721.880i		−	0.170221i
$263$			4388.26i			1.02887i	0.857531	+	0.514433i	$0.171998\pi$
$263$			4388.26i			1.02887i	−0.857531	+	0.514433i	$0.828002\pi$
$264$	2191.26			0.510844
$265$	6717.40	−	1801.85i	1.55716	−	0.417685i
$266$	187.213			0.0431532
$267$		−	8893.48i		−	2.03847i
$268$			7024.09i			1.60099i
$269$	6359.22			1.44137			0.720685	−	0.693262i	$-0.243827\pi$
$269$	6359.22			1.44137			0.720685	+	0.693262i	$0.243827\pi$
$270$	194.242	+	724.145i	0.0437821	+	0.163222i
$271$	3747.58			0.840033			0.420017	−	0.907516i	$-0.362024\pi$
$271$	3747.58			0.840033			0.420017	+	0.907516i	$0.362024\pi$
$272$		−	2236.73i		−	0.498610i
$273$		−	2362.07i		−	0.523660i
$274$	642.038			0.141558
$275$	−3234.75	+	1869.89i	−0.709319	+	0.410031i
$276$	−1079.83			−0.235500
$277$		−	598.267i		−	0.129770i	−0.997893	−	0.0648852i	$-0.979332\pi$
$277$		−	598.267i		−	0.129770i	0.997893	−	0.0648852i	$-0.0206681\pi$
$278$		−	807.796i		−	0.174275i
$279$	−2370.53			−0.508673
$280$	−856.013	−	3191.27i	−0.182702	−	0.681124i
$281$	−4834.80			−1.02641			−0.513203	−	0.858267i	$-0.671541\pi$
$281$	−4834.80			−1.02641			−0.513203	+	0.858267i	$0.671541\pi$
$282$		−	774.973i		−	0.163649i
$283$			6394.70i			1.34320i	0.740914	+	0.671600i	$0.234393\pi$
$283$			6394.70i			1.34320i	−0.740914	+	0.671600i	$0.765607\pi$
$284$	−6882.83			−1.43810
$285$	−666.777	+	178.853i	−0.138584	+	0.0371732i
$286$	330.297			0.0682898
$287$		−	3312.15i		−	0.681219i
$288$		−	1687.91i		−	0.345351i
$289$	2970.03			0.604525
$290$	1009.34	−	270.740i	0.204380	−	0.0548222i
$291$	−8879.63			−1.78877
$292$			602.998i			0.120849i
$293$		−	749.489i		−	0.149439i	−0.997205	−	0.0747195i	$-0.976194\pi$
$293$		−	749.489i		−	0.149439i	0.997205	−	0.0747195i	$-0.0238061\pi$
$294$	−1449.17			−0.287474
$295$	−2101.66	−	7835.10i	−0.414790	−	1.54636i
$296$	−762.833			−0.149793
$297$		−	2665.05i		−	0.520680i
$298$		−	1280.24i		−	0.248866i
$299$	−337.919			−0.0653591
$300$	2937.04	+	5080.82i	0.565233	+	0.977804i
$301$	1483.45			0.284069
$302$			1765.60i			0.336419i
$303$		−	139.425i		−	0.0264349i
$304$	−496.144			−0.0936047
$305$	1757.23	+	6551.06i	0.329897	+	1.22988i
$306$	−427.060			−0.0797823
$307$			797.542i			0.148268i	0.997248	+	0.0741338i	$0.0236192\pi$
$307$			797.542i			0.148268i	−0.997248	+	0.0741338i	$0.976381\pi$
$308$			5657.15i			1.04658i
$309$	−2537.51			−0.467164
$310$	−1494.61	+	400.909i	−0.273833	+	0.0734519i
$311$	4132.60			0.753500			0.376750	−	0.926315i	$-0.377042\pi$
$311$	4132.60			0.753500			0.376750	+	0.926315i	$0.377042\pi$
$312$		−	1077.07i		−	0.195440i
$313$		−	532.636i		−	0.0961865i	−0.998843	−	0.0480932i	$-0.984686\pi$
$313$		−	532.636i		−	0.0961865i	0.998843	−	0.0480932i	$-0.0153145\pi$
$314$	−1026.86			−0.184551
$315$	3541.28	−	949.897i	0.633423	−	0.169907i
$316$	−9927.59			−1.76731
$317$			2138.53i			0.378901i	0.981890	+	0.189450i	$0.0606706\pi$
$317$			2138.53i			0.378901i	−0.981890	+	0.189450i	$0.939329\pi$
$318$		−	2954.65i		−	0.521033i
$319$	−3714.64			−0.651974
$320$	890.397	+	3319.46i	0.155546	+	0.579885i
$321$	413.266			0.0718575
$322$			440.389i			0.0762171i
$323$			430.982i			0.0742430i
$324$	−6771.68			−1.16112
$325$	919.109	+	1589.98i	0.156871	+	0.271373i
$326$	−1379.75			−0.234408
$327$		−	13312.8i		−	2.25138i
$328$		−	1510.29i		−	0.254244i
$329$	4153.71			0.696053
$330$	411.236	+	1533.11i	0.0685994	+	0.255743i
$331$	−10652.1			−1.76885			−0.884427	−	0.466678i	$-0.845451\pi$
$331$	−10652.1			−1.76885			−0.884427	+	0.466678i	$0.845451\pi$
$332$			582.549i			0.0962998i
$333$		−	846.497i		−	0.139303i
$334$	931.362			0.152580
$335$	−10202.7	+	2736.74i	−1.66399	+	0.446341i
$336$	8158.12			1.32459
$337$			3552.87i			0.574294i	0.957887	+	0.287147i	$0.0927068\pi$
$337$			3552.87i			0.574294i	−0.957887	+	0.287147i	$0.907293\pi$
$338$			1490.05i			0.239788i
$339$	−6855.82			−1.09840
$340$	3538.68	−	949.201i	0.564447	−	0.151405i
$341$	5500.58			0.873529
$342$			94.7290i			0.0149776i
$343$			964.765i			0.151873i
$344$	676.433			0.106020
$345$	−420.725	−	1568.49i	−0.0656553	−	0.244767i
$346$	1367.18			0.212428
$347$			12605.6i			1.95015i	0.221871	+	0.975076i	$0.428784\pi$
$347$			12605.6i			1.95015i	−0.221871	+	0.975076i	$0.571216\pi$
$348$			5834.58i			0.898754i
$349$	−2550.49			−0.391188			−0.195594	−	0.980685i	$-0.562663\pi$
$349$	−2550.49			−0.391188			−0.195594	+	0.980685i	$0.562663\pi$
$350$	2072.12	−	1197.82i	0.316456	−	0.182931i
$351$	−1309.96			−0.199203
$352$			3916.64i			0.593062i
$353$		−	9359.21i		−	1.41116i	−0.708629	−	0.705582i	$-0.750686\pi$
$353$		−	9359.21i		−	1.41116i	0.708629	−	0.705582i	$-0.249314\pi$
$354$	−3446.27			−0.517422
$355$	−2681.70	−	9997.55i	−0.400929	−	1.49469i
$356$	10469.5			1.55866
$357$		−	7086.65i		−	1.05060i
$358$		−	1180.59i		−	0.174290i
$359$	−6568.88			−0.965717			−0.482859	−	0.875698i	$-0.660401\pi$
$359$	−6568.88			−0.965717			−0.482859	+	0.875698i	$0.660401\pi$
$360$	1614.77	−	433.140i	0.236405	−	0.0634124i
$361$	−6763.40			−0.986062
$362$			56.0717i			0.00814105i
$363$			2763.24i			0.399538i
$364$	2780.66			0.400402
$365$	−875.876	+	234.941i	−0.125604	+	0.0336915i
$366$	2881.49			0.411524
$367$			2062.02i			0.293287i	0.989189	+	0.146644i	$0.0468471\pi$
$367$			2062.02i			0.293287i	−0.989189	+	0.146644i	$0.953153\pi$
$368$		−	1167.10i		−	0.165325i
$369$	1675.94			0.236438
$370$	−143.162	−	533.715i	−0.0201152	−	0.0749906i
$371$	15836.4			2.21613
$372$		−	8639.77i		−	1.20417i
$373$		−	3945.27i		−	0.547663i	−0.961778	−	0.273831i	$-0.911709\pi$
$373$		−	3945.27i		−	0.547663i	0.961778	−	0.273831i	$-0.0882910\pi$
$374$	990.953			0.137008
$375$	−6235.74	+	6245.75i	−0.858699	+	0.860077i
$376$	1894.03			0.259780
$377$			1825.86i			0.249434i
$378$			1707.18i			0.232296i
$379$	−2470.90			−0.334885			−0.167443	−	0.985882i	$-0.553551\pi$
$379$	−2470.90			−0.334885			−0.167443	+	0.985882i	$0.553551\pi$
$380$	−210.549	−	784.938i	−0.0284235	−	0.105964i
$381$	−7854.34			−1.05614
$382$		−	2100.00i		−	0.281271i
$383$			9582.90i			1.27849i	0.769001	+	0.639247i	$0.220754\pi$
$383$			9582.90i			1.27849i	−0.769001	+	0.639247i	$0.779246\pi$
$384$	8080.03			1.07378
$385$	−8217.20	+	2204.15i	−1.08776	+	0.291776i
$386$	−3534.55			−0.466072
$387$			750.621i			0.0985948i
$388$		−	10453.2i		−	1.36774i
$389$	7282.26			0.949166			0.474583	−	0.880211i	$-0.342599\pi$
$389$	7282.26			0.949166			0.474583	+	0.880211i	$0.342599\pi$
$390$	753.572	−	202.135i	0.0978426	−	0.0262449i
$391$	−1013.82			−0.131128
$392$		−	3541.77i		−	0.456343i
$393$			6061.29i			0.777994i
$394$	2662.08			0.340390
$395$	−3868.01	−	14420.2i	−0.492710	−	1.83685i
$396$	−2862.50			−0.363247
$397$			8813.21i			1.11416i	0.830458	+	0.557081i	$0.188079\pi$
$397$			8813.21i			1.11416i	−0.830458	+	0.557081i	$0.811921\pi$
$398$			215.135i			0.0270948i
$399$	−1571.94			−0.197231
$400$	−5491.46	+	3174.41i	−0.686433	+	0.396802i
$401$	7998.99			0.996136			0.498068	−	0.867138i	$-0.334043\pi$
$401$	7998.99			0.996136			0.498068	+	0.867138i	$0.334043\pi$
$402$			4487.68i			0.556779i
$403$		−	2703.71i		−	0.334197i
$404$	164.133			0.0202127
$405$	−2638.39	−	9836.10i	−0.323711	−	1.20681i
$406$	2379.53			0.290872
$407$			1964.22i			0.239220i
$408$		−	3231.41i		−	0.392105i
$409$	2359.31			0.285233			0.142616	−	0.989778i	$-0.454449\pi$
$409$	2359.31			0.285233			0.142616	+	0.989778i	$0.454449\pi$
$410$	1056.67	−	283.438i	0.127282	−	0.0341415i
$411$	−5390.89			−0.646991
$412$		−	2987.18i		−	0.357204i
$413$		−	18471.4i		−	2.20077i
$414$	−222.835			−0.0264535
$415$	−846.173	+	226.974i	−0.100089	+	0.0268475i
$416$	1925.15			0.226895
$417$			6782.69i			0.796522i
$418$		−	219.810i		−	0.0257207i
$419$	12005.6			1.39979			0.699897	−	0.714244i	$-0.253229\pi$
$419$	12005.6			1.39979			0.699897	+	0.714244i	$0.253229\pi$
$420$	3462.06	+	12906.8i	0.402217	+	1.49949i
$421$	−8767.51			−1.01497			−0.507485	−	0.861661i	$-0.669425\pi$
$421$	−8767.51			−1.01497			−0.507485	+	0.861661i	$0.669425\pi$
$422$			393.894i			0.0454371i
$423$			2101.76i			0.241587i
$424$	7221.17			0.827101
$425$	2757.49	+	4770.23i	0.314725	+	0.544447i
$426$	−4397.42			−0.500131
$427$			15444.2i			1.75035i
$428$			486.502i			0.0549438i
$429$	−2773.35			−0.312118
$430$	126.947	+	473.265i	0.0142370	+	0.0530765i
$431$	12409.0			1.38683			0.693413	−	0.720540i	$-0.256106\pi$
$431$	12409.0			1.38683			0.693413	+	0.720540i	$0.256106\pi$
$432$		−	4524.32i		−	0.503881i
$433$		−	4722.10i		−	0.524087i	−0.965056	−	0.262044i	$-0.915604\pi$
$433$		−	4722.10i		−	0.524087i	0.965056	−	0.262044i	$-0.0843964\pi$
$434$	−3523.57			−0.389716
$435$	−8474.94	+	2273.28i	−0.934120	+	0.250564i
$436$	15672.0			1.72146
$437$			224.882i			0.0246168i
$438$			385.254i			0.0420278i
$439$	12403.2			1.34845			0.674226	−	0.738525i	$-0.264477\pi$
$439$	12403.2			1.34845			0.674226	+	0.738525i	$0.264477\pi$
$440$	−3746.93	+	1005.06i	−0.405972	+	0.108896i
$441$	3930.22			0.424384
$442$		−	487.084i		−	0.0524168i
$443$		−	1894.04i		−	0.203135i	−0.994829	−	0.101567i	$-0.967614\pi$
$443$		−	1894.04i		−	0.203135i	0.994829	−	0.101567i	$-0.0323858\pi$
$444$	3085.20			0.329768
$445$	4079.15	+	15207.3i	0.434540	+	1.61999i
$446$	4433.37			0.470687
$447$			10749.6i			1.13744i
$448$			7825.67i			0.825286i
$449$	14069.5			1.47880			0.739401	−	0.673265i	$-0.235109\pi$
$449$	14069.5			1.47880			0.739401	+	0.673265i	$0.235109\pi$
$450$	606.091	+	1048.49i	0.0634921	+	0.109836i
$451$	−3888.85			−0.406029
$452$		−	8070.75i		−	0.839859i
$453$		−	14824.9i		−	1.53760i
$454$	−4692.61			−0.485099
$455$	1083.41	+	4039.01i	0.111628	+	0.416157i
$456$	−716.781			−0.0736104
$457$			12073.9i			1.23587i	0.786228	+	0.617936i	$0.212031\pi$
$457$			12073.9i			1.23587i	−0.786228	+	0.617936i	$0.787969\pi$
$458$			2952.86i			0.301262i
$459$	−3930.11			−0.399655
$460$	1846.45	−	495.283i	0.187154	−	0.0502015i
$461$	−3191.86			−0.322472			−0.161236	−	0.986916i	$-0.551548\pi$
$461$	−3191.86			−0.322472			−0.161236	+	0.986916i	$0.551548\pi$
$462$			3614.34i			0.363970i
$463$		−	5072.32i		−	0.509137i	−0.967055	−	0.254569i	$-0.918067\pi$
$463$		−	5072.32i		−	0.509137i	0.967055	−	0.254569i	$-0.0819335\pi$
$464$	−6306.14			−0.630938
$465$	12549.6	−	3366.24i	1.25155	−	0.335711i
$466$	−4780.51			−0.475221
$467$			4040.20i			0.400339i	0.979761	+	0.200169i	$0.0641492\pi$
$467$			4040.20i			0.400339i	−0.979761	+	0.200169i	$0.935851\pi$
$468$			1407.01i			0.138972i
$469$	−24053.1			−2.36817
$470$	355.455	+	1325.16i	0.0348849	+	0.130053i
$471$	8622.05			0.843488
$472$		−	8422.69i		−	0.821368i
$473$		−	1741.75i		−	0.169314i
$474$	−6342.72			−0.614622
$475$	1058.12	−	611.658i	0.102210	−	0.0590838i
$476$	8342.50			0.803314
$477$			8013.16i			0.769176i
$478$			2158.07i			0.206502i
$479$	10825.0			1.03258			0.516292	−	0.856412i	$-0.327312\pi$
$479$	10825.0			1.03258			0.516292	+	0.856412i	$0.327312\pi$
$480$	2396.90	+	8935.80i	0.227923	+	0.849712i
$481$	965.474			0.0915214
$482$		−	4783.16i		−	0.452006i
$483$		−	3697.74i		−	0.348350i
$484$	−3252.92			−0.305496
$485$	15183.7	−	4072.80i	1.42156	−	0.381312i
$486$	−2515.81			−0.234814
$487$		−	1166.89i		−	0.108577i	−0.998525	−	0.0542885i	$-0.982711\pi$
$487$		−	1166.89i		−	0.108577i	0.998525	−	0.0542885i	$-0.0172891\pi$
$488$			7042.35i			0.653263i
$489$	11585.1			1.07136
$490$	2478.00	−	664.688i	0.228458	−	0.0612807i
$491$	−10558.3			−0.970446			−0.485223	−	0.874390i	$-0.661262\pi$
$491$	−10558.3			−0.970446			−0.485223	+	0.874390i	$0.661262\pi$
$492$			6108.22i			0.559715i
$493$			5477.91i			0.500432i
$494$	−108.043			−0.00984028
$495$	−1115.29	−	4157.88i	−0.101270	−	0.377541i
$496$	9338.05			0.845344
$497$		−	23569.4i		−	2.12723i
$498$			372.189i			0.0334904i
$499$	−17354.5			−1.55691			−0.778453	−	0.627703i	$-0.783995\pi$
$499$	−17354.5			−1.55691			−0.778453	+	0.627703i	$0.783995\pi$
$500$	−7352.57	−	7340.78i	−0.657634	−	0.656580i
$501$	−7820.21			−0.697368
$502$			623.493i			0.0554340i
$503$		−	3700.54i		−	0.328030i	−0.986458	−	0.164015i	$-0.947555\pi$
$503$		−	3700.54i		−	0.328030i	0.986458	−	0.164015i	$-0.0524445\pi$
$504$	3806.85			0.336450
$505$	63.9499	+	238.409i	0.00563511	+	0.0210081i
$506$	517.069			0.0454279
$507$		−	12511.3i		−	1.09595i
$508$		−	9246.23i		−	0.807549i
$509$	−6465.51			−0.563023			−0.281512	−	0.959558i	$-0.590836\pi$
$509$	−6465.51			−0.563023			−0.281512	+	0.959558i	$0.590836\pi$
$510$	2260.86	−	606.442i	0.196299	−	0.0526544i
$511$	−2064.89			−0.178758
$512$			11361.5i			0.980688i
$513$			871.763i			0.0750278i
$514$	3072.98			0.263703
$515$	4338.99	−	1163.87i	0.371259	−	0.0995851i
$516$	−2735.76			−0.233402
$517$		−	4876.95i		−	0.414870i
$518$		−	1258.24i		−	0.106726i
$519$	−11479.6			−0.970901
$520$	494.018	+	1841.73i	0.0416618	+	0.155318i
$521$	−11016.6			−0.926384			−0.463192	−	0.886258i	$-0.653296\pi$
$521$	−11016.6			−0.926384			−0.463192	+	0.886258i	$0.653296\pi$
$522$			1204.03i			0.100956i
$523$		−	14924.7i		−	1.24782i	−0.781495	−	0.623911i	$-0.785543\pi$
$523$		−	14924.7i		−	1.24782i	0.781495	−	0.623911i	$-0.214457\pi$
$524$	−7135.42			−0.594871
$525$	−17398.6	+	10057.5i	−1.44636	+	0.836087i
$526$	−3300.49			−0.273590
$527$		−	8111.62i		−	0.670489i
$528$		−	9578.60i		−	0.789498i
$529$	−529.000			−0.0434783
$530$	1355.20	+	5052.28i	0.111068	+	0.414070i
$531$	9346.46			0.763845
$532$		−	1850.50i		−	0.150807i
$533$			1911.49i			0.155339i
$534$	6688.95			0.542058
$535$	−706.660	+	189.552i	−0.0571058	+	0.0153178i
$536$	−10967.9			−0.883844
$537$			9912.82i			0.796592i
$538$			4782.89i			0.383281i
$539$	−9119.71			−0.728783
$540$	7157.82	−	1919.98i	0.570414	−	0.153005i
$541$	−10203.5			−0.810876			−0.405438	−	0.914123i	$-0.632881\pi$
$541$	−10203.5			−0.810876			−0.405438	+	0.914123i	$0.632881\pi$
$542$			2818.62i			0.223377i
$543$		−	470.808i		−	0.0372086i
$544$	5775.80			0.455212
$545$	6106.17	+	22764.2i	0.479926	+	1.78919i
$546$	1776.56			0.139249
$547$			10666.2i			0.833733i	0.908968	+	0.416866i	$0.136872\pi$
$547$			10666.2i			0.833733i	−0.908968	+	0.416866i	$0.863128\pi$
$548$		−	6346.23i		−	0.494703i
$549$	−7814.73			−0.607513
$550$	−1406.38	−	2432.91i	−0.109033	−	0.188618i
$551$	1215.09			0.0939467
$552$		−	1686.12i		−	0.130011i
$553$		−	33995.8i		−	2.61419i
$554$	449.968			0.0345078
$555$	1202.06	+	4481.36i	0.0919363	+	0.342744i
$556$	−7984.66			−0.609038
$557$		−	1967.58i		−	0.149675i	−0.997196	−	0.0748376i	$-0.976156\pi$
$557$		−	1967.58i		−	0.149675i	0.997196	−	0.0748376i	$-0.0238438\pi$
$558$		−	1782.92i		−	0.135263i
$559$	−856.122			−0.0647766
$560$	−13949.9	+	3741.86i	−1.05266	+	0.282362i
$561$	−8320.57			−0.626194
$562$		−	3636.35i		−	0.272936i
$563$			15947.2i			1.19377i	0.802325	+	0.596887i	$0.203596\pi$
$563$			15947.2i			1.19377i	−0.802325	+	0.596887i	$0.796404\pi$
$564$	−7660.22			−0.571903
$565$	11723.1	−	3144.54i	0.872907	−	0.234145i
$566$	−4809.57			−0.357176
$567$		−	23188.8i		−	1.71752i
$568$		−	10747.3i		−	0.793921i
$569$	25178.4			1.85506			0.927532	−	0.373744i	$-0.121926\pi$
$569$	25178.4			1.85506			0.927532	+	0.373744i	$0.121926\pi$
$570$	−134.519	−	501.495i	−0.00988488	−	0.0368515i
$571$	10048.6			0.736464			0.368232	−	0.929734i	$-0.379963\pi$
$571$	10048.6			0.736464			0.368232	+	0.929734i	$0.379963\pi$
$572$		−	3264.83i		−	0.238653i
$573$			17632.7i			1.28555i
$574$	2491.13			0.181146
$575$	1438.83	+	2489.05i	0.104354	+	0.180523i
$576$	−3959.76			−0.286441
$577$			1912.51i			0.137988i	0.997617	+	0.0689938i	$0.0219789\pi$
$577$			1912.51i			0.137988i	−0.997617	+	0.0689938i	$0.978021\pi$
$578$			2233.82i			0.160752i
$579$	29677.9			2.13018
$580$	−2676.13	−	9976.80i	−0.191587	−	0.714248i
$581$	−1994.86			−0.142446
$582$		−	6678.54i		−	0.475660i
$583$		−	18593.8i		−	1.32088i
$584$	−941.561			−0.0667159
$585$	−2043.72	+	548.200i	−0.144440	+	0.0387441i
$586$	563.704			0.0397379
$587$			13861.5i			0.974662i	0.873217	+	0.487331i	$0.162029\pi$
$587$			13861.5i			0.974662i	−0.873217	+	0.487331i	$0.837971\pi$
$588$			14324.3i			1.00464i
$589$	−1799.29			−0.125872
$590$	5892.93	−	1580.69i	0.411200	−	0.110299i
$591$	−22352.2			−1.55575
$592$			3334.55i			0.231502i
$593$		−	5991.56i		−	0.414914i	−0.978244	−	0.207457i	$-0.933481\pi$
$593$		−	5991.56i		−	0.414914i	0.978244	−	0.207457i	$-0.0665187\pi$
$594$	2004.44			0.138456
$595$	3250.42	+	12117.8i	0.223957	+	0.834924i
$596$	−12654.5			−0.869713
$597$		−	1806.39i		−	0.123837i
$598$		−	254.155i		−	0.0173799i
$599$	−15017.3			−1.02435			−0.512177	−	0.858880i	$-0.671161\pi$
$599$	−15017.3			−1.02435			−0.512177	+	0.858880i	$0.671161\pi$
$600$	−7933.53	+	4586.08i	−0.539808	+	0.312044i
$601$	11885.0			0.806655			0.403328	−	0.915056i	$-0.367853\pi$
$601$	11885.0			0.806655			0.403328	+	0.915056i	$0.367853\pi$
$602$			1115.73i			0.0755378i
$603$		−	12170.8i		−	0.821946i
$604$	17452.0			1.17568
$605$	−1267.41	−	4724.97i	−0.0851693	−	0.317517i
$606$	104.864			0.00702941
$607$			24838.3i			1.66088i	0.557108	+	0.830440i	$0.311911\pi$
$607$			24838.3i			1.66088i	−0.557108	+	0.830440i	$0.688089\pi$
$608$		−	1281.17i		−	0.0854577i
$609$	−19979.8			−1.32943
$610$	−4927.17	+	1321.64i	−0.327042	+	0.0877243i
$611$	−2397.17			−0.158722
$612$			4221.27i			0.278815i
$613$			19056.2i			1.25559i	0.778380	+	0.627793i	$0.216042\pi$
$613$			19056.2i			1.25559i	−0.778380	+	0.627793i	$0.783958\pi$
$614$	−599.846			−0.0394264
$615$	−8872.41	+	2379.90i	−0.581740	+	0.156043i
$616$	−8833.44			−0.577775
$617$		−	538.180i		−	0.0351156i	−0.999846	−	0.0175578i	$-0.994411\pi$
$617$		−	538.180i		−	0.0351156i	0.999846	−	0.0175578i	$-0.00558910\pi$
$618$		−	1908.50i		−	0.124225i
$619$	−8769.31			−0.569416			−0.284708	−	0.958614i	$-0.591897\pi$
$619$	−8769.31			−0.569416			−0.284708	+	0.958614i	$0.591897\pi$
$620$	3962.78	+	14773.5i	0.256692	+	0.956965i
$621$	−2050.69			−0.132514
$622$			3108.21i			0.200366i
$623$			35851.5i			2.30555i
$624$	−4708.17			−0.302048
$625$	7798.02	−	13540.0i	0.499073	−	0.866560i
$626$	400.605			0.0255773
$627$			1845.64i			0.117556i
$628$			10150.0i			0.644950i
$629$	2896.60			0.183617
$630$	714.435	+	2663.46i	0.0451806	+	0.168436i
$631$	−11235.2			−0.708821			−0.354411	−	0.935090i	$-0.615318\pi$
$631$	−11235.2			−0.708821			−0.354411	+	0.935090i	$0.615318\pi$
$632$		−	15501.6i		−	0.975665i
$633$		−	3307.35i		−	0.207670i
$634$	−1608.42			−0.100755
$635$	13430.5	−	3602.53i	0.839326	−	0.225137i
$636$	−29205.3			−1.82086
$637$			4482.62i			0.278819i
$638$		−	2793.85i		−	0.173369i
$639$	11926.0			0.738320
$640$	−13816.4	+	3706.05i	−0.853345	+	0.228898i
$641$	12206.6			0.752153			0.376077	−	0.926589i	$-0.377273\pi$
$641$	12206.6			0.752153			0.376077	+	0.926589i	$0.377273\pi$
$642$			310.825i			0.0191079i
$643$		−	26075.8i		−	1.59927i	−0.600489	−	0.799633i	$-0.705027\pi$
$643$		−	26075.8i		−	1.59927i	0.600489	−	0.799633i	$-0.294973\pi$
$644$	4353.02			0.266356
$645$	−1065.91	−	3973.79i	−0.0650702	−	0.242586i
$646$	−324.150			−0.0197423
$647$		−	5223.06i		−	0.317372i	−0.987329	−	0.158686i	$-0.949274\pi$
$647$		−	5223.06i		−	0.317372i	0.987329	−	0.158686i	$-0.0507257\pi$
$648$		−	10573.7i		−	0.641012i
$649$	−21687.6			−1.31173
$650$	−1195.85	+	691.279i	−0.0721618	+	0.0417141i
$651$	29585.8			1.78120
$652$			13638.1i			0.819186i
$653$			17785.4i			1.06584i	0.846164	+	0.532922i	$0.178906\pi$
$653$			17785.4i			1.06584i	−0.846164	+	0.532922i	$0.821094\pi$
$654$	10012.8			0.598674
$655$	−2780.12	−	10364.4i	−0.165844	−	0.618279i
$656$	−6601.90			−0.392928
$657$		−	1044.83i		−	0.0620436i
$658$			3124.08i			0.185090i
$659$	11310.0			0.668554			0.334277	−	0.942475i	$-0.391508\pi$
$659$	11310.0			0.668554			0.334277	+	0.942475i	$0.391508\pi$
$660$	15154.1	−	4064.86i	0.893744	−	0.239734i
$661$	15765.0			0.927666			0.463833	−	0.885923i	$-0.346474\pi$
$661$	15765.0			0.927666			0.463833	+	0.885923i	$0.346474\pi$
$662$		−	8011.62i		−	0.470363i
$663$			4089.82i			0.239571i
$664$	−909.631			−0.0531634
$665$	2687.92	−	720.997i	0.156742	−	0.0420437i
$666$	636.666			0.0370425
$667$			2858.32i			0.165929i
$668$		−	9206.05i		−	0.533223i
$669$	−37225.0			−2.15127
$670$	−2058.35	−	7673.67i	−0.118688	−	0.442477i
$671$	18133.4			1.04326
$672$			21066.3i			1.20930i
$673$		−	22578.2i		−	1.29320i	−0.762827	−	0.646602i	$-0.776189\pi$
$673$		−	22578.2i		−	1.29320i	0.762827	−	0.646602i	$-0.223811\pi$
$674$	−2672.18			−0.152713
$675$	5577.68	+	9648.91i	0.318052	+	0.550202i
$676$	14728.4			0.837986
$677$		−	15197.6i		−	0.862764i	−0.902169	−	0.431382i	$-0.858026\pi$
$677$		−	15197.6i		−	0.862764i	0.902169	−	0.431382i	$-0.141974\pi$
$678$		−	5156.39i		−	0.292079i
$679$	35795.7			2.02314
$680$	1482.15	+	5525.53i	0.0835848	+	0.311609i
$681$	39401.7			2.21714
$682$			4137.09i			0.232284i
$683$		−	7020.00i		−	0.393284i	−0.980475	−	0.196642i	$-0.936996\pi$
$683$		−	7020.00i		−	0.393284i	0.980475	−	0.196642i	$-0.0630036\pi$
$684$	936.349			0.0523424
$685$	9218.12	−	2472.63i	0.514170	−	0.137919i
$686$	−725.618			−0.0403852
$687$		−	24793.8i		−	1.37692i
$688$		−	2956.87i		−	0.163851i
$689$	−9139.42			−0.505347
$690$	1179.69	−	316.435i	0.0650870	−	0.0174587i
$691$	26464.0			1.45693			0.728464	−	0.685084i	$-0.240235\pi$
$691$	26464.0			1.45693			0.728464	+	0.685084i	$0.240235\pi$
$692$		−	13513.9i		−	0.742372i
$693$		−	9802.26i		−	0.537312i
$694$	−9480.89			−0.518573
$695$	−3111.00	−	11598.0i	−0.169794	−	0.633003i
$696$	−9110.50			−0.496168
$697$			5734.82i			0.311653i
$698$		−	1918.27i		−	0.104022i
$699$	40139.7			2.17199
$700$	−11839.8	−	20481.9i	−0.639291	−	1.10592i
$701$	−528.232			−0.0284608			−0.0142304	−	0.999899i	$-0.504530\pi$
$701$	−528.232			−0.0284608			−0.0142304	+	0.999899i	$0.504530\pi$
$702$		−	985.242i		−	0.0529709i
$703$		−	642.514i		−	0.0344706i
$704$	9188.27			0.491897
$705$	−2984.59	−	11126.7i	−0.159441	−	0.594407i
$706$	7039.24			0.375248
$707$			562.053i			0.0298984i
$708$			34064.7i			1.80823i
$709$	−11155.8			−0.590921			−0.295461	−	0.955355i	$-0.595473\pi$
$709$	−11155.8			−0.590921			−0.295461	+	0.955355i	$0.595473\pi$
$710$	7519.34	−	2016.96i	0.397459	−	0.106613i
$711$	17201.8			0.907336
$712$			16347.8i			0.860476i
$713$		−	4232.55i		−	0.222315i
$714$	5330.00			0.279370
$715$	4742.27	−	1272.05i	0.248043	−	0.0665341i
$716$	−11669.5			−0.609092
$717$		−	18120.3i		−	0.943816i
$718$		−	4940.58i		−	0.256798i
$719$	−13883.2			−0.720103			−0.360052	−	0.932932i	$-0.617241\pi$
$719$	−13883.2			−0.720103			−0.360052	+	0.932932i	$0.617241\pi$
$720$	−1893.37	−	7058.61i	−0.0980025	−	0.365359i
$721$	10229.2			0.528372
$722$		−	5086.88i		−	0.262208i
$723$			40162.0i			2.06589i
$724$	554.241			0.0284505
$725$	13449.0	−	7774.36i	0.688941	−	0.398252i
$726$	−2078.28			−0.106243
$727$			30552.9i			1.55866i	0.626615	+	0.779329i	$0.284440\pi$
$727$			30552.9i			1.55866i	−0.626615	+	0.779329i	$0.715560\pi$
$728$			4341.91i			0.221046i
$729$	−3469.30			−0.176259
$730$	−176.704	−	658.762i	−0.00895904	−	0.0333998i
$731$	−2568.52			−0.129959
$732$		−	28482.1i		−	1.43815i
$733$			31880.0i			1.60643i	0.595688	+	0.803216i	$0.296879\pi$
$733$			31880.0i			1.60643i	−0.595688	+	0.803216i	$0.703121\pi$
$734$	−1550.88			−0.0779893
$735$	−20806.6	+	5581.07i	−1.04417	+	0.280083i
$736$	3013.75			0.150935
$737$			28241.2i			1.41150i
$738$			1260.50i			0.0628723i
$739$	−39570.5			−1.96972			−0.984862	−	0.173342i	$-0.944543\pi$
$739$	−39570.5			−1.96972			−0.984862	+	0.173342i	$0.944543\pi$
$740$	−5275.51	+	1415.08i	−0.262070	+	0.0702965i
$741$	907.189			0.0449749
$742$			11910.8i			0.589300i
$743$			25014.3i			1.23511i	0.786528	+	0.617555i	$0.211877\pi$
$743$			25014.3i			1.23511i	−0.786528	+	0.617555i	$0.788123\pi$
$744$	13490.7			0.664776
$745$	−4930.47	−	18381.1i	−0.242468	−	0.903936i
$746$	2967.31			0.145631
$747$		−	1009.40i		−	0.0494402i
$748$		−	9795.08i		−	0.478802i
$749$	−1665.96			−0.0812723
$750$	−4697.54	−	4690.01i	−0.228707	−	0.228340i
$751$	34198.5			1.66168			0.830840	−	0.556511i	$-0.187860\pi$
$751$	34198.5			1.66168			0.830840	+	0.556511i	$0.187860\pi$
$752$		−	8279.33i		−	0.401484i
$753$		−	5235.18i		−	0.253361i
$754$	−1373.26			−0.0663279
$755$	6799.70	+	25349.7i	0.327770	+	1.22195i
$756$	16874.7			0.811806
$757$		−	3276.06i		−	0.157293i	−0.996903	−	0.0786463i	$-0.974940\pi$
$757$		−	3276.06i		−	0.157293i	0.996903	−	0.0786463i	$-0.0250598\pi$
$758$		−	1858.41i		−	0.0890507i
$759$	−4341.58			−0.207628
$760$	1225.65	−	328.764i	0.0584989	−	0.0156915i
$761$	−13305.7			−0.633810			−0.316905	−	0.948457i	$-0.602644\pi$
$761$	−13305.7			−0.633810			−0.316905	+	0.948457i	$0.602644\pi$
$762$		−	5907.40i		−	0.280843i
$763$			53666.9i			2.54636i
$764$	−20757.5			−0.982957
$765$	−6131.55	+	1644.70i	−0.289786	+	0.0777311i
$766$	−7207.48			−0.339970
$767$			10660.1i			0.501844i
$768$		−	9453.01i		−	0.444149i
$769$	10307.7			0.483360			0.241680	−	0.970356i	$-0.422302\pi$
$769$	10307.7			0.483360			0.241680	+	0.970356i	$0.422302\pi$
$770$	−1657.78	−	6180.31i	−0.0775873	−	0.289250i
$771$	−25802.3			−1.20525
$772$			34937.2i			1.62878i
$773$			10286.0i			0.478604i	0.970945	+	0.239302i	$0.0769186\pi$
$773$			10286.0i			0.478604i	−0.970945	+	0.239302i	$0.923081\pi$
$774$	−564.556			−0.0262178
$775$	−19915.0	+	11512.2i	−0.923057	+	0.533586i
$776$	16322.3			0.755074
$777$			10564.9i			0.487790i
$778$			5477.12i			0.252396i
$779$	1272.08			0.0585070
$780$	−1998.01	−	7448.69i	−0.0917180	−	0.341931i
$781$	−27673.2			−1.26790
$782$		−	762.512i		−	0.0348688i
$783$			11080.4i			0.505722i
$784$	−15482.1			−0.705269
$785$	−14743.2	+	3954.65i	−0.670328	+	0.179806i
$786$	−4558.81			−0.206879
$787$		−	12901.1i		−	0.584338i	−0.956367	−	0.292169i	$-0.905623\pi$
$787$		−	12901.1i		−	0.584338i	0.956367	−	0.292169i	$-0.0943769\pi$
$788$		−	26313.3i		−	1.18956i
$789$	27712.7			1.25044
$790$	10845.7	−	2909.20i	0.488445	−	0.131019i
$791$	27637.3			1.24231
$792$		−	4469.69i		−	0.200535i
$793$		−	8913.10i		−	0.399134i
$794$	−6628.58			−0.296271
$795$	−11379.0	−	42421.7i	−0.507638	−	1.89250i
$796$	2126.50			0.0946883
$797$		−	6308.44i		−	0.280372i	−0.990125	−	0.140186i	$-0.955230\pi$
$797$		−	6308.44i		−	0.280372i	0.990125	−	0.140186i	$-0.0447700\pi$
$798$		−	1182.28i		−	0.0524466i
$799$	−7191.95			−0.318439
$800$	−8197.13	−	14180.3i	−0.362265	−	0.626688i
$801$	−18140.7			−0.800214
$802$			6016.19i			0.264887i
$803$			2424.43i			0.106546i
$804$	44358.5			1.94577
$805$	1696.03	+	6322.92i	0.0742575	+	0.276837i
$806$	2033.51			0.0888676
$807$		−	40159.7i		−	1.75178i
$808$			256.288i			0.0111587i
$809$	−30826.3			−1.33967			−0.669836	−	0.742509i	$-0.733636\pi$
$809$	−30826.3			−1.33967			−0.669836	+	0.742509i	$0.733636\pi$
$810$	7397.91	−	1984.38i	0.320909	−	0.0860792i
$811$	−37409.2			−1.61975			−0.809873	−	0.586605i	$-0.800464\pi$
$811$	−37409.2			−1.61975			−0.809873	+	0.586605i	$0.800464\pi$
$812$		−	23520.5i		−	1.01651i
$813$		−	23666.6i		−	1.02094i
$814$	−1477.33			−0.0636121
$815$	−19809.8	+	5313.70i	−0.851420	+	0.228381i
$816$	−14125.4			−0.605990
$817$			569.741i			0.0243974i
$818$			1774.48i			0.0758474i
$819$	−4818.11			−0.205566
$820$	−2801.64	−	10444.7i	−0.119314	−	0.444811i
$821$	−6138.76			−0.260955			−0.130478	−	0.991451i	$-0.541651\pi$
$821$	−6138.76			−0.260955			−0.130478	+	0.991451i	$0.541651\pi$
$822$		−	4054.59i		−	0.172044i
$823$		−	12789.2i		−	0.541682i	−0.962624	−	0.270841i	$-0.912698\pi$
$823$		−	12789.2i		−	0.541682i	0.962624	−	0.270841i	$-0.0873017\pi$
$824$	4664.39			0.197198
$825$	11808.7	+	20428.0i	0.498335	+	0.862077i
$826$	13892.7			0.585215
$827$		−	13392.6i		−	0.563125i	−0.959543	−	0.281563i	$-0.909147\pi$
$827$		−	13392.6i		−	0.563125i	0.959543	−	0.281563i	$-0.0908528\pi$
$828$			2202.62i			0.0924471i
$829$	−12506.0			−0.523945			−0.261973	−	0.965075i	$-0.584373\pi$
$829$	−12506.0			−0.523945			−0.261973	+	0.965075i	$0.584373\pi$
$830$	−170.711	−	636.422i	−0.00713912	−	0.0266151i
$831$	−3778.17			−0.157718
$832$		−	4516.32i		−	0.188191i
$833$			13448.7i			0.559387i
$834$	−5101.38			−0.211806
$835$	13372.1	−	3586.88i	0.554204	−	0.148657i
$836$	−2172.71			−0.0898861
$837$		−	16407.7i		−	0.677576i
$838$			9029.65i			0.372225i
$839$	30719.0			1.26405			0.632024	−	0.774949i	$-0.282224\pi$
$839$	30719.0			1.26405			0.632024	+	0.774949i	$0.282224\pi$
$840$	−20153.5	+	5405.88i	−0.827810	+	0.222048i
$841$	−8944.82			−0.366756
$842$		−	6594.20i		−	0.269895i
$843$			30532.7i			1.24745i
$844$	3893.45			0.158789
$845$	5738.52	+	21393.6i	0.233623	+	0.870960i
$846$	−1580.77			−0.0642413
$847$		−	11139.2i		−	0.451886i
$848$		−	31565.7i		−	1.27827i
$849$	40383.8			1.63247
$850$	−3587.78	+	2073.96i	−0.144776	+	0.0836898i
$851$	1511.41			0.0608820
$852$			43466.4i			1.74781i
$853$		−	28733.4i		−	1.15336i	−0.816972	−	0.576678i	$-0.804349\pi$
$853$		−	28733.4i		−	1.15336i	0.816972	−	0.576678i	$-0.195651\pi$
$854$	−11615.9			−0.465442
$855$	364.822	+	1360.08i	0.0145926	+	0.0544020i
$856$	−759.656			−0.0303324
$857$		−	18108.0i		−	0.721772i	−0.932610	−	0.360886i	$-0.882474\pi$
$857$		−	18108.0i		−	0.721772i	0.932610	−	0.360886i	$-0.117526\pi$
$858$		−	2085.89i		−	0.0829966i
$859$	209.950			0.00833924			0.00416962	−	0.999991i	$-0.498673\pi$
$859$	209.950			0.00833924			0.00416962	+	0.999991i	$0.498673\pi$
$860$	4677.99	−	1254.81i	0.185486	−	0.0497541i
$861$	−20916.8			−0.827925
$862$			9333.07i			0.368777i
$863$			21321.9i			0.841026i	0.907286	+	0.420513i	$0.138150\pi$
$863$			21321.9i			0.841026i	−0.907286	+	0.420513i	$0.861850\pi$
$864$	11682.9			0.460024
$865$	19629.4	−	5265.31i	0.771584	−	0.206967i
$866$	3551.58			0.139362
$867$		−	18756.3i		−	0.734715i
$868$			34828.8i			1.36194i
$869$	−39915.1			−1.55814
$870$	−1709.78	−	6374.16i	−0.0666286	−	0.248396i
$871$	13881.4			0.540016
$872$			24471.4i			0.950350i
$873$			18112.5i			0.702194i
$874$	−169.138			−0.00654596
$875$	25137.6	−	25177.9i	0.971206	−	0.972766i
$876$	3808.05			0.146874
$877$		−	8116.82i		−	0.312526i	−0.987715	−	0.156263i	$-0.950055\pi$
$877$		−	8116.82i		−	0.312526i	0.987715	−	0.156263i	$-0.0499448\pi$
$878$			9328.64i			0.358572i
$879$	−4733.16			−0.181622
$880$	4393.39	+	16378.8i	0.168297	+	0.627421i
$881$	−33635.7			−1.28628			−0.643141	−	0.765748i	$-0.722369\pi$
$881$	−33635.7			−1.28628			−0.643141	+	0.765748i	$0.722369\pi$
$882$			2955.99i			0.112850i
$883$		−	10516.5i		−	0.400804i	−0.979714	−	0.200402i	$-0.935775\pi$
$883$		−	10516.5i		−	0.400804i	0.979714	−	0.200402i	$-0.0642248\pi$
$884$	−4814.58			−0.183181
$885$	−49480.2	+	13272.4i	−1.87939	+	0.504119i
$886$	1424.55			0.0540164
$887$		−	31975.5i		−	1.21041i	−0.796070	−	0.605204i	$-0.793091\pi$
$887$		−	31975.5i		−	1.21041i	0.796070	−	0.605204i	$-0.206909\pi$
$888$			4817.43i			0.182052i
$889$	31662.5			1.19452
$890$	−11437.7	+	3068.00i	−0.430779	+	0.115550i
$891$	−27226.3			−1.02370
$892$		−	43821.7i		−	1.64491i
$893$			1595.29i			0.0597810i
$894$	−8084.94			−0.302462
$895$	−4546.69	−	16950.4i	−0.169809	−	0.633059i
$896$	−32572.3			−1.21447
$897$			2134.02i			0.0794347i
$898$			10582.0i			0.393234i
$899$	−22869.5			−0.848433
$900$	10363.8	−	5990.91i	0.383843	−	0.221886i
$901$	−27419.9			−1.01386
$902$		−	2924.88i		−	0.107969i
$903$		−	9368.27i		−	0.345245i
$904$	12602.2			0.463654
$905$	215.944	+	805.054i	0.00793174	+	0.0295700i
$906$	11150.1			0.408870
$907$		−	47837.5i		−	1.75129i	−0.482958	−	0.875644i	$-0.660438\pi$
$907$		−	47837.5i		−	1.75129i	0.482958	−	0.875644i	$-0.339562\pi$
$908$			46384.1i			1.69528i
$909$	−284.397			−0.0103772
$910$	−3037.81	+	814.850i	−0.110662	+	0.0296835i
$911$	−19733.6			−0.717677			−0.358839	−	0.933400i	$-0.616827\pi$
$911$	−19733.6			−0.717677			−0.358839	+	0.933400i	$0.616827\pi$
$912$			3133.25i			0.113763i
$913$			2342.21i			0.0849023i
$914$	−9081.01			−0.328636
$915$	41371.2	−	11097.2i	1.49474	−	0.400943i
$916$	29187.5			1.05282
$917$		−	24434.3i		−	0.879927i
$918$		−	2955.91i		−	0.106274i
$919$	25597.5			0.918807			0.459404	−	0.888228i	$-0.348063\pi$
$919$	25597.5			0.918807			0.459404	+	0.888228i	$0.348063\pi$
$920$	773.367	+	2883.16i	0.0277143	+	0.103321i
$921$	5036.63			0.180198
$922$		−	2400.66i		−	0.0857499i
$923$			13602.2i			0.485074i
$924$	35725.9			1.27197
$925$	−4110.91	−	7111.52i	−0.146125	−	0.252784i
$926$	3814.98			0.135387
$927$			5175.96i			0.183388i
$928$		−	16284.0i		−	0.576023i
$929$	3535.76			0.124870			0.0624352	−	0.998049i	$-0.480113\pi$
$929$	3535.76			0.124870			0.0624352	+	0.998049i	$0.480113\pi$
$930$	2531.81	+	9438.76i	0.0892704	+	0.332806i
$931$	2983.14			0.105015
$932$			47253.0i			1.66075i
$933$		−	26098.2i		−	0.915772i
$934$	−3038.71			−0.106456
$935$	14227.7	−	3816.38i	0.497642	−	0.133485i
$936$	−2196.99			−0.0767211
$937$			7480.62i			0.260812i	0.991461	+	0.130406i	$0.0416281\pi$
$937$			7480.62i			0.260812i	−0.991461	+	0.130406i	$0.958372\pi$
$938$		−	18090.8i		−	0.629729i
$939$	−3363.70			−0.116901
$940$	13098.5	−	3513.50i	0.454497	−	0.121912i
$941$	−30827.2			−1.06795			−0.533973	−	0.845501i	$-0.679302\pi$
$941$	−30827.2			−1.06795			−0.533973	+	0.845501i	$0.679302\pi$
$942$			6484.80i			0.224295i
$943$			2992.37i			0.103335i
$944$	−36817.9			−1.26941
$945$	6574.74	+	24511.0i	0.226324	+	0.843750i
$946$	1310.00			0.0450230
$947$		−	12784.3i		−	0.438685i	−0.975648	−	0.219342i	$-0.929609\pi$
$947$		−	12784.3i		−	0.438685i	0.975648	−	0.219342i	$-0.0703911\pi$
$948$			62694.6i			2.14792i
$949$	1191.68			0.0407625
$950$	460.039	+	795.828i	0.0157112	+	0.0271790i
$951$	13505.2			0.460500
$952$			13026.5i			0.443479i
$953$			7938.01i			0.269819i	0.990858	+	0.134909i	$0.0430743\pi$
$953$			7938.01i			0.269819i	−0.990858	+	0.134909i	$0.956926\pi$
$954$	−6026.84			−0.204535
$955$	−8087.56	−	30151.0i	−0.274039	−	1.02164i
$956$	21331.5			0.721662
$957$			23458.6i			0.792383i
$958$			8141.70i			0.274579i
$959$	21731.8			0.731760
$960$	20963.0	−	5623.03i	0.704769	−	0.189044i
$961$	4073.87			0.136748
$962$			726.151i			0.0243368i
$963$		−	842.972i		−	0.0282081i
$964$	−47279.2			−1.57963
$965$	−50747.6	+	13612.3i	−1.69287	+	0.454089i
$966$	2781.14			0.0926311
$967$			47112.7i			1.56674i	0.621553	+	0.783372i	$0.286502\pi$
$967$			47112.7i			1.56674i	−0.621553	+	0.783372i	$0.713498\pi$
$968$		−	5079.32i		−	0.168652i
$969$	2721.73			0.0902319
$970$	3063.23	+	11419.9i	0.101396	+	0.378011i
$971$	−8974.52			−0.296608			−0.148304	−	0.988942i	$-0.547381\pi$
$971$	−8974.52			−0.296608			−0.148304	+	0.988942i	$0.547381\pi$
$972$			24867.6i			0.820605i
$973$		−	27342.5i		−	0.900883i
$974$	877.642			0.0288721
$975$	10041.0	−	5804.34i	0.329815	−	0.190654i
$976$	30784.0			1.00960
$977$		−	11925.1i		−	0.390499i	−0.980754	−	0.195249i	$-0.937448\pi$
$977$		−	11925.1i		−	0.390499i	0.980754	−	0.195249i	$-0.0625516\pi$
$978$			8713.35i			0.284890i
$979$	42093.9			1.37419
$980$	−6570.11	−	24493.8i	−0.214158	−	0.798393i
$981$	−27155.3			−0.883794
$982$		−	7941.08i		−	0.258055i
$983$		−	21935.4i		−	0.711730i	−0.934537	−	0.355865i	$-0.884186\pi$
$983$		−	21935.4i		−	0.711730i	0.934537	−	0.355865i	$-0.115814\pi$
$984$	−9537.78			−0.308997
$985$	38221.0	−	10252.2i	1.23637	−	0.331638i
$986$	−4120.04			−0.133072
$987$		−	26231.5i		−	0.845954i
$988$			1067.95i			0.0343888i
$989$	−1340.23			−0.0430908
$990$	3127.22	−	838.831i	0.100393	−	0.0269291i
$991$	14039.4			0.450027			0.225013	−	0.974356i	$-0.427757\pi$
$991$	14039.4			0.450027			0.225013	+	0.974356i	$0.427757\pi$
$992$			24113.2i			0.771768i
$993$			67269.9i			2.14979i
$994$	17727.0			0.565659
$995$	828.531	+	3088.82i	0.0263982	+	0.0984142i
$996$	3678.91			0.117039
$997$		−	3609.91i		−	0.114671i	−0.998355	−	0.0573354i	$-0.981740\pi$
$997$		−	3609.91i		−	0.114671i	0.998355	−	0.0573354i	$-0.0182605\pi$
$998$		−	13052.7i		−	0.414003i
$999$	5859.05			0.185558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.b.a.24.20	yes	34
5.2	odd	4		575.4.a.q.1.8		17
5.3	odd	4		575.4.a.r.1.10		17
5.4	even	2	inner	115.4.b.a.24.15	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.b.a.24.15	✓	34	5.4	even	2	inner
115.4.b.a.24.20	yes	34	1.1	even	1	trivial
575.4.a.q.1.8		17	5.2	odd	4
575.4.a.r.1.10		17	5.3	odd	4

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.752118i q^{2} -6.31519i q^{3} +7.43432 q^{4} +(2.89657 + 10.7986i) q^{5} +4.74977 q^{6} +25.4579i q^{7} +11.6084i q^{8} -12.8816 q^{9} +O(q^{10})\)	\(q+0.752118i q^{2} -6.31519i q^{3} +7.43432 q^{4} +(2.89657 + 10.7986i) q^{5} +4.74977 q^{6} +25.4579i q^{7} +11.6084i q^{8} -12.8816 q^{9} +(-8.12183 + 2.17857i) q^{10} +29.8906 q^{11} -46.9491i q^{12} -14.6921i q^{13} -19.1473 q^{14} +(68.1952 - 18.2924i) q^{15} +50.7436 q^{16} -44.0791i q^{17} -9.68849i q^{18} -9.77747 q^{19} +(21.5340 + 80.2803i) q^{20} +160.771 q^{21} +22.4812i q^{22} -23.0000i q^{23} +73.3095 q^{24} +(-108.220 + 62.5579i) q^{25} +11.0502 q^{26} -89.1603i q^{27} +189.262i q^{28} -124.275 q^{29} +(13.7581 + 51.2909i) q^{30} +184.024 q^{31} +131.033i q^{32} -188.765i q^{33} +33.1527 q^{34} +(-274.910 + 73.7406i) q^{35} -95.7659 q^{36} +65.7137i q^{37} -7.35382i q^{38} -92.7836 q^{39} +(-125.355 + 33.6247i) q^{40} -130.103 q^{41} +120.919i q^{42} -58.2708i q^{43} +222.216 q^{44} +(-37.3125 - 139.103i) q^{45} +17.2987 q^{46} -163.160i q^{47} -320.456i q^{48} -305.103 q^{49} +(-47.0509 - 81.3941i) q^{50} -278.368 q^{51} -109.226i q^{52} -622.062i q^{53} +67.0591 q^{54} +(86.5802 + 322.776i) q^{55} -295.526 q^{56} +61.7466i q^{57} -93.4692i q^{58} -725.566 q^{59} +(506.985 - 135.992i) q^{60} +606.658 q^{61} +138.408i q^{62} -327.938i q^{63} +307.397 q^{64} +(158.655 - 42.5568i) q^{65} +141.973 q^{66} +944.820i q^{67} -327.698i q^{68} -145.249 q^{69} +(-55.4617 - 206.765i) q^{70} -925.819 q^{71} -149.535i q^{72} +81.1101i q^{73} -49.4245 q^{74} +(395.065 + 683.428i) q^{75} -72.6889 q^{76} +760.950i q^{77} -69.7842i q^{78} -1335.37 q^{79} +(146.983 + 547.960i) q^{80} -910.868 q^{81} -97.8529i q^{82} +78.3594i q^{83} +1195.22 q^{84} +(475.993 - 127.678i) q^{85} +43.8265 q^{86} +784.818i q^{87} +346.983i q^{88} +1408.27 q^{89} +(104.622 - 28.0634i) q^{90} +374.030 q^{91} -170.989i q^{92} -1162.15i q^{93} +122.716 q^{94} +(-28.3212 - 105.583i) q^{95} +827.496 q^{96} -1406.08i q^{97} -229.474i q^{98} -385.038 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9}+O(q^{10}) \) 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9	\( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9} + 14 q^{10} - 8 q^{11} + 236 q^{14} + 440 q^{16} + 144 q^{19} - 180 q^{20} - 32 q^{21} + 108 q^{24} + 134 q^{25} - 144 q^{26} + 56 q^{29} - 294 q^{30} - 80 q^{31} + 264 q^{34} + 116 q^{35} + 1864 q^{36} - 1200 q^{39} + 650 q^{40} + 268 q^{41} - 1612 q^{44} - 1346 q^{45} + 184 q^{46} - 1474 q^{49} + 120 q^{50} - 1104 q^{51} + 1564 q^{54} + 1160 q^{55} - 2300 q^{56} - 708 q^{59} - 516 q^{60} + 1100 q^{61} + 100 q^{64} + 1164 q^{65} - 1416 q^{66} - 552 q^{69} + 1144 q^{70} + 1360 q^{71} + 1588 q^{74} - 2064 q^{75} + 108 q^{76} + 3968 q^{79} + 2542 q^{80} + 4914 q^{81} - 1948 q^{84} + 124 q^{85} - 6148 q^{86} + 1196 q^{89} + 2760 q^{90} - 544 q^{91} - 2340 q^{94} + 3920 q^{95} + 2960 q^{96} - 3816 q^{99}+O(q^{100}) \) 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9 + 14 * q^10 - 8 * q^11 + 236 * q^14 + 440 * q^16 + 144 * q^19 - 180 * q^20 - 32 * q^21 + 108 * q^24 + 134 * q^25 - 144 * q^26 + 56 * q^29 - 294 * q^30 - 80 * q^31 + 264 * q^34 + 116 * q^35 + 1864 * q^36 - 1200 * q^39 + 650 * q^40 + 268 * q^41 - 1612 * q^44 - 1346 * q^45 + 184 * q^46 - 1474 * q^49 + 120 * q^50 - 1104 * q^51 + 1564 * q^54 + 1160 * q^55 - 2300 * q^56 - 708 * q^59 - 516 * q^60 + 1100 * q^61 + 100 * q^64 + 1164 * q^65 - 1416 * q^66 - 552 * q^69 + 1144 * q^70 + 1360 * q^71 + 1588 * q^74 - 2064 * q^75 + 108 * q^76 + 3968 * q^79 + 2542 * q^80 + 4914 * q^81 - 1948 * q^84 + 124 * q^85 - 6148 * q^86 + 1196 * q^89 + 2760 * q^90 - 544 * q^91 - 2340 * q^94 + 3920 * q^95 + 2960 * q^96 - 3816 * q^99

Introduction

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