LMFDB - Embedded newform 115.4.b.a.24.5

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			24.5
Character	$\chi$	$=$	115.24
Dual form			115.4.b.a.24.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.93784i q^{2} -9.92307i q^{3} -16.3822 q^{4} +(10.8531 - 2.68512i) q^{5} -48.9985 q^{6} +14.6304i q^{7} +41.3902i q^{8} -71.4673 q^{9} +O(q^{10})$	\(q-4.93784i q^{2} -9.92307i q^{3} -16.3822 q^{4} +(10.8531 - 2.68512i) q^{5} -48.9985 q^{6} +14.6304i q^{7} +41.3902i q^{8} -71.4673 q^{9} +(-13.2587 - 53.5909i) q^{10} +49.6504 q^{11} +162.562i q^{12} -59.3405i q^{13} +72.2427 q^{14} +(-26.6446 - 107.696i) q^{15} +73.3201 q^{16} +4.26973i q^{17} +352.894i q^{18} +2.76389 q^{19} +(-177.798 + 43.9883i) q^{20} +145.179 q^{21} -245.165i q^{22} -23.0000i q^{23} +410.718 q^{24} +(110.580 - 58.2838i) q^{25} -293.014 q^{26} +441.252i q^{27} -239.679i q^{28} +180.876 q^{29} +(-531.786 + 131.567i) q^{30} -131.384 q^{31} -30.9212i q^{32} -492.684i q^{33} +21.0832 q^{34} +(39.2845 + 158.786i) q^{35} +1170.79 q^{36} +225.061i q^{37} -13.6477i q^{38} -588.840 q^{39} +(111.138 + 449.213i) q^{40} -241.227 q^{41} -716.869i q^{42} -202.199i q^{43} -813.385 q^{44} +(-775.643 + 191.898i) q^{45} -113.570 q^{46} -194.140i q^{47} -727.560i q^{48} +128.951 q^{49} +(-287.796 - 546.027i) q^{50} +42.3688 q^{51} +972.131i q^{52} +295.209i q^{53} +2178.83 q^{54} +(538.861 - 133.317i) q^{55} -605.556 q^{56} -27.4263i q^{57} -893.137i q^{58} +380.629 q^{59} +(436.499 + 1764.31i) q^{60} +97.7301 q^{61} +648.755i q^{62} -1045.60i q^{63} +433.877 q^{64} +(-159.336 - 644.029i) q^{65} -2432.79 q^{66} -584.711i q^{67} -69.9477i q^{68} -228.231 q^{69} +(784.058 - 193.980i) q^{70} -799.270 q^{71} -2958.04i q^{72} +227.677i q^{73} +1111.32 q^{74} +(-578.355 - 1097.30i) q^{75} -45.2788 q^{76} +726.406i q^{77} +2907.59i q^{78} -59.6191 q^{79} +(795.751 - 196.873i) q^{80} +2448.96 q^{81} +1191.14i q^{82} -132.222i q^{83} -2378.35 q^{84} +(11.4647 + 46.3398i) q^{85} -998.425 q^{86} -1794.85i q^{87} +2055.04i q^{88} +1150.24 q^{89} +(947.563 + 3830.00i) q^{90} +868.177 q^{91} +376.792i q^{92} +1303.74i q^{93} -958.632 q^{94} +(29.9968 - 7.42138i) q^{95} -306.833 q^{96} +1564.05i q^{97} -636.737i q^{98} -3548.38 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	4.93784i		−	1.74579i	−0.487909	−	0.872895i	$-0.662240\pi$
$2$		−	4.93784i		−	1.74579i	0.487909	−	0.872895i	$-0.337760\pi$
$3$		−	9.92307i		−	1.90970i	−0.297096	−	0.954848i	$-0.596018\pi$
$3$		−	9.92307i		−	1.90970i	0.297096	−	0.954848i	$-0.403982\pi$
$4$	−16.3822			−2.04778
$5$	10.8531	−	2.68512i	0.970732	−	0.240164i
$5$	10.8531	−	2.68512i	0.970732	−	0.240164i
$6$	−48.9985			−3.33393
$7$			14.6304i			0.789969i	0.918688	+	0.394984i	$0.129250\pi$
$7$			14.6304i			0.789969i	−0.918688	+	0.394984i	$0.870750\pi$
$8$			41.3902i			1.82921i
$9$	−71.4673			−2.64694
$10$	−13.2587	−	53.5909i	−0.419277	−	1.69469i
$11$	49.6504			1.36092			0.680461	−	0.732784i	$-0.261779\pi$
$11$	49.6504			1.36092			0.680461	+	0.732784i	$0.261779\pi$
$12$			162.562i			3.91064i
$13$		−	59.3405i		−	1.26601i	−0.774149	−	0.633003i	$-0.781822\pi$
$13$		−	59.3405i		−	1.26601i	0.774149	−	0.633003i	$-0.218178\pi$
$14$	72.2427			1.37912
$15$	−26.6446	−	107.696i	−0.458641	−	1.85380i
$16$	73.3201			1.14563
$17$			4.26973i			0.0609153i	0.999536	+	0.0304577i	$0.00969647\pi$
$17$			4.26973i			0.0609153i	−0.999536	+	0.0304577i	$0.990304\pi$
$18$			352.894i			4.62099i
$19$	2.76389			0.0333726			0.0166863	−	0.999861i	$-0.494688\pi$
$19$	2.76389			0.0333726			0.0166863	+	0.999861i	$0.494688\pi$
$20$	−177.798	+	43.9883i	−1.98785	+	0.491804i
$21$	145.179			1.50860
$22$		−	245.165i		−	2.37588i
$23$		−	23.0000i		−	0.208514i
$23$		−	23.0000i		−	0.208514i
$24$	410.718			3.49322
$25$	110.580	−	58.2838i	0.884642	−	0.466271i
$26$	−293.014			−2.21018
$27$			441.252i			3.14515i
$28$		−	239.679i		−	1.61768i
$29$	180.876			1.15820			0.579101	−	0.815256i	$-0.303404\pi$
$29$	180.876			1.15820			0.579101	+	0.815256i	$0.303404\pi$
$30$	−531.786	+	131.567i	−3.23635	+	0.800691i
$31$	−131.384			−0.761204			−0.380602	−	0.924739i	$-0.624283\pi$
$31$	−131.384			−0.761204			−0.380602	+	0.924739i	$0.624283\pi$
$32$		−	30.9212i		−	0.170817i
$33$		−	492.684i		−	2.59895i
$34$	21.0832			0.106345
$35$	39.2845	+	158.786i	0.189722	+	0.766848i
$36$	1170.79			5.42035
$37$			225.061i			0.999996i	0.866027	+	0.499998i	$0.166666\pi$
$37$			225.061i			0.999996i	−0.866027	+	0.499998i	$0.833334\pi$
$38$		−	13.6477i		−	0.0582616i
$39$	−588.840			−2.41769
$40$	111.138	+	449.213i	0.439310	+	1.77567i
$41$	−241.227			−0.918861			−0.459430	−	0.888214i	$-0.651946\pi$
$41$	−241.227			−0.918861			−0.459430	+	0.888214i	$0.651946\pi$
$42$		−	716.869i		−	2.63370i
$43$		−	202.199i		−	0.717094i	−0.933512	−	0.358547i	$-0.883272\pi$
$43$		−	202.199i		−	0.717094i	0.933512	−	0.358547i	$-0.116728\pi$
$44$	−813.385			−2.78687
$45$	−775.643	+	191.898i	−2.56947	+	0.635700i
$46$	−113.570			−0.364022
$47$		−	194.140i		−	0.602515i	−0.953543	−	0.301258i	$-0.902594\pi$
$47$		−	194.140i		−	0.602515i	0.953543	−	0.301258i	$-0.0974064\pi$
$48$		−	727.560i		−	2.18780i
$49$	128.951			0.375949
$50$	−287.796	−	546.027i	−0.814011	−	1.54440i
$51$	42.3688			0.116330
$52$			972.131i			2.59250i
$53$			295.209i			0.765095i	0.923936	+	0.382547i	$0.124953\pi$
$53$			295.209i			0.765095i	−0.923936	+	0.382547i	$0.875047\pi$
$54$	2178.83			5.49076
$55$	538.861	−	133.317i	1.32109	−	0.326845i
$56$	−605.556			−1.44502
$57$		−	27.4263i		−	0.0637316i
$58$		−	893.137i		−	2.02198i
$59$	380.629			0.839893			0.419946	−	0.907549i	$-0.362049\pi$
$59$	380.629			0.839893			0.419946	+	0.907549i	$0.362049\pi$
$60$	436.499	+	1764.31i	0.939196	+	3.79618i
$61$	97.7301			0.205132			0.102566	−	0.994726i	$-0.467295\pi$
$61$	97.7301			0.205132			0.102566	+	0.994726i	$0.467295\pi$
$62$			648.755i			1.32890i
$63$		−	1045.60i		−	2.09100i
$64$	433.877			0.847415
$65$	−159.336	−	644.029i	−0.304050	−	1.22895i
$66$	−2432.79			−4.53721
$67$		−	584.711i		−	1.06618i	−0.846059	−	0.533089i	$-0.821031\pi$
$67$		−	584.711i		−	1.06618i	0.846059	−	0.533089i	$-0.178969\pi$
$68$		−	69.9477i		−	0.124741i
$69$	−228.231			−0.398199
$70$	784.058	−	193.980i	1.33876	−	0.331216i
$71$	−799.270			−1.33600			−0.667999	−	0.744162i	$-0.732849\pi$
$71$	−799.270			−1.33600			−0.667999	+	0.744162i	$0.732849\pi$
$72$		−	2958.04i		−	4.84179i
$73$			227.677i			0.365035i	0.983203	+	0.182518i	$0.0584247\pi$
$73$			227.677i			0.365035i	−0.983203	+	0.182518i	$0.941575\pi$
$74$	1111.32			1.74578
$75$	−578.355	−	1097.30i	−0.890435	−	1.68940i
$76$	−45.2788			−0.0683399
$77$			726.406i			1.07509i
$78$			2907.59i			4.22077i
$79$	−59.6191			−0.0849073			−0.0424536	−	0.999098i	$-0.513517\pi$
$79$	−59.6191			−0.0849073			−0.0424536	+	0.999098i	$0.513517\pi$
$80$	795.751	−	196.873i	1.11210	−	0.275139i
$81$	2448.96			3.35934
$82$			1191.14i			1.60414i
$83$		−	132.222i		−	0.174858i	−0.996171	−	0.0874289i	$-0.972135\pi$
$83$		−	132.222i		−	0.174858i	0.996171	−	0.0874289i	$-0.0278651\pi$
$84$	−2378.35			−3.08928
$85$	11.4647	+	46.3398i	0.0146297	+	0.0591325i
$86$	−998.425			−1.25190
$87$		−	1794.85i		−	2.21181i
$88$			2055.04i			2.48941i
$89$	1150.24			1.36994			0.684971	−	0.728570i	$-0.259815\pi$
$89$	1150.24			1.36994			0.684971	+	0.728570i	$0.259815\pi$
$90$	947.563	+	3830.00i	1.10980	+	4.48575i
$91$	868.177			1.00011
$92$			376.792i			0.426992i
$93$			1303.74i			1.45367i
$94$	−958.632			−1.05186
$95$	29.9968	−	7.42138i	0.0323959	−	0.00801492i
$96$	−306.833			−0.326209
$97$			1564.05i			1.63717i	0.574384	+	0.818586i	$0.305241\pi$
$97$			1564.05i			1.63717i	−0.574384	+	0.818586i	$0.694759\pi$
$98$		−	636.737i		−	0.656328i
$99$	−3548.38			−3.60228
$100$	−1811.55	+	954.820i	−1.81155	+	0.954820i
$101$	204.854			0.201819			0.100910	−	0.994896i	$-0.467825\pi$
$101$	204.854			0.201819			0.100910	+	0.994896i	$0.467825\pi$
$102$		−	209.210i		−	0.203087i
$103$			696.894i			0.666670i	0.942809	+	0.333335i	$0.108174\pi$
$103$			696.894i			0.666670i	−0.942809	+	0.333335i	$0.891826\pi$
$104$	2456.11			2.31579
$105$	1575.64	−	389.822i	1.46445	−	0.362312i
$106$	1457.69			1.33569
$107$		−	789.395i		−	0.713212i	−0.934255	−	0.356606i	$-0.883934\pi$
$107$		−	789.395i		−	0.713212i	0.934255	−	0.356606i	$-0.116066\pi$
$108$		−	7228.70i		−	6.44057i
$109$	−943.068			−0.828711			−0.414356	−	0.910115i	$-0.635993\pi$
$109$	−943.068			−0.828711			−0.414356	+	0.910115i	$0.635993\pi$
$110$	−658.299	−	2660.81i	−0.570603	−	2.30635i
$111$	2233.30			1.90969
$112$			1072.70i			0.905009i
$113$		−	821.592i		−	0.683973i	−0.939705	−	0.341986i	$-0.888900\pi$
$113$		−	821.592i		−	0.683973i	0.939705	−	0.341986i	$-0.111100\pi$
$114$	−135.427			−0.111262
$115$	−61.7578	−	249.622i	−0.0500778	−	0.202412i
$116$	−2963.16			−2.37174
$117$			4240.90i			3.35104i
$118$		−	1879.48i		−	1.46628i
$119$	−62.4679			−0.0481212
$120$	4457.57	−	1102.83i	3.39099	−	0.838948i
$121$	1134.16			0.852110
$122$		−	482.576i		−	0.358117i
$123$			2393.71i			1.75474i
$124$	2152.37			1.55878
$125$	1043.64	−	929.483i	0.746769	−	0.665084i
$126$	−5162.99			−3.65044
$127$		−	995.920i		−	0.695855i	−0.937521	−	0.347928i	$-0.886885\pi$
$127$		−	995.920i		−	0.695855i	0.937521	−	0.347928i	$-0.113115\pi$
$128$		−	2389.78i		−	1.65023i
$129$	−2006.43			−1.36943
$130$	−3180.11	+	786.777i	−2.14549	+	0.530807i
$131$	346.440			0.231058			0.115529	−	0.993304i	$-0.463144\pi$
$131$	346.440			0.231058			0.115529	+	0.993304i	$0.463144\pi$
$132$			8071.27i			5.32208i
$133$			40.4369i			0.0263634i
$134$	−2887.21			−1.86132
$135$	1184.81	+	4788.96i	0.755352	+	3.05310i
$136$	−176.725			−0.111427
$137$		−	1664.02i		−	1.03771i	−0.854861	−	0.518857i	$-0.826358\pi$
$137$		−	1664.02i		−	1.03771i	0.854861	−	0.518857i	$-0.173642\pi$
$138$			1126.97i			0.695172i
$139$	−1606.86			−0.980520			−0.490260	−	0.871576i	$-0.663098\pi$
$139$	−1606.86			−0.980520			−0.490260	+	0.871576i	$0.663098\pi$
$140$	−643.568	−	2601.27i	−0.388510	−	1.57034i
$141$	−1926.46			−1.15062
$142$			3946.67i			2.33237i
$143$		−	2946.28i		−	1.72294i
$144$	−5239.99			−3.03240
$145$	1963.07	−	485.674i	1.12430	−	0.278159i
$146$	1124.23			0.637275
$147$		−	1279.58i		−	0.717948i
$148$		−	3687.01i		−	2.04777i
$149$	3443.48			1.89330			0.946648	−	0.322270i	$-0.104446\pi$
$149$	3443.48			1.89330			0.946648	+	0.322270i	$0.104446\pi$
$150$	−5418.27	+	2855.82i	−2.94933	+	1.55451i
$151$	1088.66			0.586716			0.293358	−	0.956003i	$-0.405227\pi$
$151$	1088.66			0.586716			0.293358	+	0.956003i	$0.405227\pi$
$152$			114.398i			0.0610454i
$153$		−	305.146i		−	0.161239i
$154$	3586.88			1.87687
$155$	−1425.93	+	352.783i	−0.738925	+	0.182814i
$156$	9646.52			4.95089
$157$		−	518.382i		−	0.263512i	−0.991282	−	0.131756i	$-0.957938\pi$
$157$		−	518.382i		−	0.263512i	0.991282	−	0.131756i	$-0.0420616\pi$
$158$			294.390i			0.148230i
$159$	2929.38			1.46110
$160$	−83.0272	−	335.592i	−0.0410242	−	0.165818i
$161$	336.500			0.164720
$162$		−	12092.5i		−	5.86469i
$163$		−	436.814i		−	0.209901i	−0.994477	−	0.104951i	$-0.966532\pi$
$163$		−	436.814i		−	0.209901i	0.994477	−	0.104951i	$-0.0334685\pi$
$164$	3951.84			1.88163
$165$	−1322.92	−	5347.16i	−0.624175	−	2.52288i
$166$	−652.889			−0.305265
$167$			213.639i			0.0989932i	0.998774	+	0.0494966i	$0.0157617\pi$
$167$			213.639i			0.0989932i	−0.998774	+	0.0494966i	$0.984238\pi$
$168$			6008.98i			2.75954i
$169$	−1324.29			−0.602773
$170$	228.819	−	56.6110i	0.103233	−	0.0255404i
$171$	−197.528			−0.0883353
$172$			3312.47i			1.46845i
$173$			1690.95i			0.743125i	0.928408	+	0.371563i	$0.121178\pi$
$173$			1690.95i			0.743125i	−0.928408	+	0.371563i	$0.878822\pi$
$174$	−8862.66			−3.86136
$175$	852.718	+	1617.84i	0.368339	+	0.698840i
$176$	3640.37			1.55911
$177$		−	3777.01i		−	1.60394i
$178$		−	5679.68i		−	2.39163i
$179$	−4615.46			−1.92724			−0.963620	−	0.267275i	$-0.913877\pi$
$179$	−4615.46			−1.92724			−0.963620	+	0.267275i	$0.913877\pi$
$180$	12706.8	−	3143.72i	5.26170	−	1.30177i
$181$	4768.61			1.95827			0.979137	−	0.203199i	$-0.0651339\pi$
$181$	4768.61			1.95827			0.979137	+	0.203199i	$0.0651339\pi$
$182$		−	4286.92i		−	1.74597i
$183$		−	969.783i		−	0.391740i
$184$	951.974			0.381416
$185$	604.316	+	2442.62i	0.240163	+	0.970728i
$186$	6437.64			2.53780
$187$			211.993i			0.0829010i
$188$			3180.45i			1.23382i
$189$	−6455.70			−2.48457
$190$	−36.6456	−	148.120i	−0.0139924	−	0.0565564i
$191$	−1445.48			−0.547600			−0.273800	−	0.961787i	$-0.588281\pi$
$191$	−1445.48			−0.547600			−0.273800	+	0.961787i	$0.588281\pi$
$192$		−	4305.39i		−	1.61831i
$193$		−	534.816i		−	0.199466i	−0.995014	−	0.0997329i	$-0.968201\pi$
$193$		−	534.816i		−	0.199466i	0.995014	−	0.0997329i	$-0.0317988\pi$
$194$	7723.05			2.85816
$195$	−6390.74	+	1581.11i	−2.34693	+	0.580643i
$196$	−2112.50			−0.769861
$197$			4817.07i			1.74214i	0.491158	+	0.871071i	$0.336574\pi$
$197$			4817.07i			1.74214i	−0.491158	+	0.871071i	$0.663426\pi$
$198$			17521.3i			6.28881i
$199$	2352.78			0.838110			0.419055	−	0.907961i	$-0.362361\pi$
$199$	2352.78			0.838110			0.419055	+	0.907961i	$0.362361\pi$
$200$	2412.38	+	4576.94i	0.852905	+	1.61819i
$201$	−5802.13			−2.03607
$202$		−	1011.54i		−	0.352334i
$203$			2646.30i			0.914944i
$204$	−694.096			−0.238218
$205$	−2618.06	+	647.723i	−0.891968	+	0.220678i
$206$	3441.15			1.16386
$207$			1643.75i			0.551924i
$208$		−	4350.85i		−	1.45037i
$209$	137.228			0.0454176
$210$	−1924.88	−	7780.27i	−0.632521	−	2.55662i
$211$	2031.12			0.662691			0.331345	−	0.943510i	$-0.392497\pi$
$211$	2031.12			0.662691			0.331345	+	0.943510i	$0.392497\pi$
$212$		−	4836.18i		−	1.56675i
$213$			7931.21i			2.55135i
$214$	−3897.91			−1.24512
$215$	−542.928	−	2194.49i	−0.172220	−	0.696106i
$216$	−18263.5			−5.75312
$217$		−	1922.21i		−	0.601328i
$218$			4656.72i			1.44676i
$219$	2259.26			0.697106
$220$	−8827.76	+	2184.04i	−2.70531	+	0.669307i
$221$	253.368			0.0771192
$222$		−	11027.7i		−	3.33391i
$223$			488.279i			0.146626i	0.997309	+	0.0733129i	$0.0233572\pi$
$223$			488.279i			0.146626i	−0.997309	+	0.0733129i	$0.976643\pi$
$224$	452.391			0.134940
$225$	−7902.87	+	4165.39i	−2.34159	+	1.23419i
$226$	−4056.89			−1.19407
$227$			4515.69i			1.32034i	0.751117	+	0.660169i	$0.229515\pi$
$227$			4515.69i			1.32034i	−0.751117	+	0.660169i	$0.770485\pi$
$228$			449.304i			0.130508i
$229$	4238.50			1.22309			0.611545	−	0.791209i	$-0.290548\pi$
$229$	4238.50			1.22309			0.611545	+	0.791209i	$0.290548\pi$
$230$	−1232.59	+	304.950i	−0.353368	+	0.0874252i
$231$	7208.18			2.05309
$232$			7486.50i			2.11859i
$233$		−	4691.76i		−	1.31917i	−0.751629	−	0.659586i	$-0.770732\pi$
$233$		−	4691.76i		−	1.31917i	0.751629	−	0.659586i	$-0.229268\pi$
$234$	20940.9			5.85021
$235$	−521.289	−	2107.02i	−0.144703	−	0.584881i
$236$	−6235.56			−1.71992
$237$			591.604i			0.162147i
$238$			308.456i			0.0840095i
$239$	−3901.43			−1.05591			−0.527955	−	0.849272i	$-0.677041\pi$
$239$	−3901.43			−1.05591			−0.527955	+	0.849272i	$0.677041\pi$
$240$	−1953.59	−	7896.30i	−0.525431	−	2.12377i
$241$	−2733.36			−0.730586			−0.365293	−	0.930893i	$-0.619031\pi$
$241$	−2733.36			−0.730586			−0.365293	+	0.930893i	$0.619031\pi$
$242$		−	5600.29i		−	1.48760i
$243$		−	12387.4i		−	3.27016i
$244$	−1601.04			−0.420066
$245$	1399.51	−	346.248i	0.364946	−	0.0902896i
$246$	11819.8			3.06341
$247$		−	164.011i		−	0.0422500i
$248$		−	5438.02i		−	1.39240i
$249$	−1312.04			−0.333925
$250$	−4589.64	−	5153.33i	−1.16110	−	1.30370i
$251$	−2537.49			−0.638107			−0.319054	−	0.947737i	$-0.603365\pi$
$251$	−2537.49			−0.638107			−0.319054	+	0.947737i	$0.603365\pi$
$252$			17129.2i			4.28191i
$253$		−	1141.96i		−	0.283772i
$254$	−4917.69			−1.21482
$255$	459.833	−	113.765i	0.112925	−	0.0279383i
$256$	−8329.35			−2.03353
$257$			5048.93i			1.22546i	0.790292	+	0.612730i	$0.209929\pi$
$257$			5048.93i			1.22546i	−0.790292	+	0.612730i	$0.790071\pi$
$258$			9907.44i			2.39074i
$259$	−3292.74			−0.789965
$260$	2610.29	+	10550.6i	0.622628	+	2.51663i
$261$	−12926.7			−3.06569
$262$		−	1710.66i		−	0.403378i
$263$			7962.29i			1.86683i	0.358801	+	0.933414i	$0.383186\pi$
$263$			7962.29i			1.86683i	−0.358801	+	0.933414i	$0.616814\pi$
$264$	20392.3			4.75401
$265$	792.671	+	3203.93i	0.183749	+	0.742702i
$266$	199.671			0.0460249
$267$		−	11413.9i		−	2.61617i
$268$			9578.89i			2.18330i
$269$	−4166.33			−0.944332			−0.472166	−	0.881510i	$-0.656528\pi$
$269$	−4166.33			−0.944332			−0.472166	+	0.881510i	$0.656528\pi$
$270$	23647.1	−	5850.42i	5.33006	−	1.31869i
$271$	2277.86			0.510591			0.255296	−	0.966863i	$-0.417827\pi$
$271$	2277.86			0.510591			0.255296	+	0.966863i	$0.417827\pi$
$272$			313.057i			0.0697862i
$273$		−	8614.98i		−	1.90990i
$274$	−8216.66			−1.81163
$275$	5490.35	−	2893.81i	1.20393	−	0.634558i
$276$	3738.93			0.815424
$277$			6491.79i			1.40814i	0.710133	+	0.704068i	$0.248635\pi$
$277$			6491.79i			1.40814i	−0.710133	+	0.704068i	$0.751365\pi$
$278$			7934.42i			1.71178i
$279$	9389.68			2.01486
$280$	−6572.17	+	1625.99i	−1.40272	+	0.347041i
$281$	539.476			0.114528			0.0572641	−	0.998359i	$-0.481762\pi$
$281$	539.476			0.114528			0.0572641	+	0.998359i	$0.481762\pi$
$282$			9512.57i			2.00874i
$283$		−	1795.65i		−	0.377174i	−0.982056	−	0.188587i	$-0.939609\pi$
$283$		−	1795.65i		−	0.377174i	0.982056	−	0.188587i	$-0.0603908\pi$
$284$	13093.8			2.73583
$285$	−73.6429	−	297.661i	−0.0153061	−	0.0618663i
$286$	−14548.2			−3.00789
$287$		−	3529.25i		−	0.725872i
$288$			2209.86i			0.452142i
$289$	4894.77			0.996289
$290$	−2398.18	−	9693.32i	−0.485607	−	1.96280i
$291$	15520.2			3.12650
$292$		−	3729.86i		−	0.747513i
$293$			7265.56i			1.44866i	0.689451	+	0.724332i	$0.257852\pi$
$293$			7265.56i			1.44866i	−0.689451	+	0.724332i	$0.742148\pi$
$294$	−6318.38			−1.25339
$295$	4131.01	−	1022.03i	0.815311	−	0.201712i
$296$	−9315.33			−1.82920
$297$			21908.3i			4.28030i
$298$		−	17003.4i		−	3.30530i
$299$	−1364.83			−0.263981
$300$	9474.75	+	17976.2i	1.82342	+	3.45951i
$301$	2958.26			0.566482
$302$		−	5375.64i		−	1.02428i
$303$		−	2032.78i		−	0.385414i
$304$	202.649			0.0382326
$305$	1060.68	−	262.417i	0.199128	−	0.0492654i
$306$	−1506.76			−0.281489
$307$			2110.08i			0.392276i	0.980576	+	0.196138i	$0.0628400\pi$
$307$			2110.08i			0.392276i	−0.980576	+	0.196138i	$0.937160\pi$
$308$		−	11900.2i		−	2.20154i
$309$	6915.32			1.27314
$310$	1741.98	+	7041.01i	0.319155	+	1.29001i
$311$	−1081.72			−0.197231			−0.0986157	−	0.995126i	$-0.531441\pi$
$311$	−1081.72			−0.197231			−0.0986157	+	0.995126i	$0.531441\pi$
$312$		−	24372.2i		−	4.42245i
$313$			6308.02i			1.13914i	0.821943	+	0.569569i	$0.192890\pi$
$313$			6308.02i			1.13914i	−0.821943	+	0.569569i	$0.807110\pi$
$314$	−2559.69			−0.460037
$315$	−2807.55	−	11348.0i	−0.502183	−	2.02980i
$316$	976.695			0.173871
$317$		−	5347.44i		−	0.947452i	−0.880672	−	0.473726i	$-0.842909\pi$
$317$		−	5347.44i		−	0.947452i	0.880672	−	0.473726i	$-0.157091\pi$
$318$		−	14464.8i		−	2.55077i
$319$	8980.57			1.57622
$320$	4708.91	−	1165.01i	0.822613	−	0.203519i
$321$	−7833.22			−1.36202
$322$		−	1661.58i		−	0.287566i
$323$			11.8011i			0.00203291i
$324$	−40119.4			−6.87918
$325$	−3458.59	−	6561.89i	−0.590302	−	1.11996i
$326$	−2156.92			−0.366444
$327$			9358.13i			1.58259i
$328$		−	9984.42i		−	1.68079i
$329$	2840.35			0.475968
$330$	−26403.4	+	6532.34i	−4.40442	+	1.08968i
$331$	9504.40			1.57827			0.789137	−	0.614217i	$-0.210528\pi$
$331$	9504.40			1.57827			0.789137	+	0.614217i	$0.210528\pi$
$332$			2166.09i			0.358071i
$333$		−	16084.5i		−	2.64692i
$334$	1054.91			0.172821
$335$	−1570.02	−	6345.94i	−0.256058	−	1.03497i
$336$	10644.5			1.72829
$337$			3543.43i			0.572768i	0.958115	+	0.286384i	$0.0924534\pi$
$337$			3543.43i			0.572768i	−0.958115	+	0.286384i	$0.907547\pi$
$338$			6539.14i			1.05232i
$339$	−8152.72			−1.30618
$340$	−187.818	−	759.151i	−0.0299584	−	0.121090i
$341$	−6523.28			−1.03594
$342$			975.360i			0.154215i
$343$			6904.84i			1.08696i
$344$	8369.05			1.31171
$345$	−2477.01	+	612.827i	−0.386545	+	0.0956333i
$346$	8349.65			1.29734
$347$			3310.17i			0.512101i	0.966663	+	0.256051i	$0.0824214\pi$
$347$			3310.17i			0.512101i	−0.966663	+	0.256051i	$0.917579\pi$
$348$			29403.6i			4.52931i
$349$	8528.48			1.30808			0.654039	−	0.756461i	$-0.273073\pi$
$349$	8528.48			1.30808			0.654039	+	0.756461i	$0.273073\pi$
$350$	7988.62	−	4210.58i	1.22003	−	0.643043i
$351$	26184.1			3.98178
$352$		−	1535.25i		−	0.232469i
$353$			9031.49i			1.36175i	0.732400	+	0.680875i	$0.238400\pi$
$353$			9031.49i			1.36175i	−0.732400	+	0.680875i	$0.761600\pi$
$354$	−18650.3			−2.80014
$355$	−8674.57	+	2146.14i	−1.29690	+	0.320859i
$356$	−18843.5			−2.80534
$357$			619.873i			0.0918969i
$358$			22790.4i			3.36456i
$359$	4778.50			0.702506			0.351253	−	0.936281i	$-0.385756\pi$
$359$	4778.50			0.702506			0.351253	+	0.936281i	$0.385756\pi$
$360$	−7942.71	−	32104.0i	−1.16283	−	4.70008i
$361$	−6851.36			−0.998886
$362$		−	23546.6i		−	3.41874i
$363$		−	11254.3i		−	1.62727i
$364$	−14222.7			−2.04800
$365$	611.340	+	2471.01i	0.0876685	+	0.354352i
$366$	−4788.63			−0.683895
$367$		−	7468.84i		−	1.06232i	−0.847273	−	0.531158i	$-0.821757\pi$
$367$		−	7468.84i		−	1.06232i	0.847273	−	0.531158i	$-0.178243\pi$
$368$		−	1686.36i		−	0.238880i
$369$	17239.8			2.43217
$370$	12061.2	−	2984.02i	1.69469	−	0.419275i
$371$	−4319.03			−0.604401
$372$		−	21358.1i		−	2.97679i
$373$		−	3340.14i		−	0.463662i	−0.972756	−	0.231831i	$-0.925528\pi$
$373$		−	3340.14i		−	0.463662i	0.972756	−	0.231831i	$-0.0744717\pi$
$374$	1046.79			0.144728
$375$	−9223.32	−	10356.1i	−1.27011	−	1.42610i
$376$	8035.49			1.10212
$377$		−	10733.3i		−	1.46629i
$378$			31877.2i			4.33753i
$379$	−4597.32			−0.623084			−0.311542	−	0.950232i	$-0.600845\pi$
$379$	−4597.32			−0.623084			−0.311542	+	0.950232i	$0.600845\pi$
$380$	−491.416	+	121.579i	−0.0663397	+	0.0164128i
$381$	−9882.58			−1.32887
$382$			7137.57i			0.955994i
$383$		−	1088.35i		−	0.145201i	−0.997361	−	0.0726004i	$-0.976870\pi$
$383$		−	1088.35i		−	0.145201i	0.997361	−	0.0726004i	$-0.0231298\pi$
$384$	−23714.0			−3.15143
$385$	1950.49	+	7883.77i	0.258198	+	1.04362i
$386$	−2640.84			−0.348225
$387$			14450.6i			1.89810i
$388$		−	25622.7i		−	3.35257i
$389$	3633.05			0.473530			0.236765	−	0.971567i	$-0.423913\pi$
$389$	3633.05			0.473530			0.236765	+	0.971567i	$0.423913\pi$
$390$	7807.24	+	31556.5i	1.01368	+	4.09724i
$391$	98.2037			0.0127017
$392$			5337.29i			0.687688i
$393$		−	3437.75i		−	0.441250i
$394$	23785.9			3.04141
$395$	−647.053	+	160.084i	−0.0824222	+	0.0203917i
$396$	58130.4			7.37667
$397$		−	10607.3i		−	1.34097i	−0.741925	−	0.670483i	$-0.766087\pi$
$397$		−	10607.3i		−	1.34097i	0.741925	−	0.670483i	$-0.233913\pi$
$398$		−	11617.6i		−	1.46316i
$399$	401.258			0.0503460
$400$	8107.75	−	4273.38i	1.01347	−	0.534172i
$401$	−9738.13			−1.21272			−0.606358	−	0.795192i	$-0.707370\pi$
$401$	−9738.13			−1.21272			−0.606358	+	0.795192i	$0.707370\pi$
$402$			28650.0i			3.55456i
$403$			7796.41i			0.963689i
$404$	−3355.97			−0.413282
$405$	26578.8	−	6575.74i	3.26102	−	0.806793i
$406$	13067.0			1.59730
$407$			11174.4i			1.36092i
$408$			1753.65i			0.212791i
$409$	−6399.47			−0.773676			−0.386838	−	0.922148i	$-0.626433\pi$
$409$	−6399.47			−0.773676			−0.386838	+	0.922148i	$0.626433\pi$
$410$	3198.35	+	12927.6i	0.385257	+	1.55719i
$411$	−16512.2			−1.98172
$412$		−	11416.7i		−	1.36519i
$413$			5568.77i			0.663489i
$414$	8116.56			0.963544
$415$	−355.031	−	1435.02i	−0.0419946	−	0.169740i
$416$	−1834.88			−0.216256
$417$			15945.0i			1.87249i
$418$		−	677.611i		−	0.0792895i
$419$	−661.239			−0.0770970			−0.0385485	−	0.999257i	$-0.512273\pi$
$419$	−661.239			−0.0770970			−0.0385485	+	0.999257i	$0.512273\pi$
$420$	−25812.6	+	6386.17i	−2.99887	+	0.741936i
$421$	3020.66			0.349687			0.174843	−	0.984596i	$-0.444058\pi$
$421$	3020.66			0.349687			0.174843	+	0.984596i	$0.444058\pi$
$422$		−	10029.3i		−	1.15692i
$423$			13874.7i			1.59482i
$424$	−12218.7			−1.39952
$425$	248.856	+	472.147i	0.0284030	+	0.0538883i
$426$	39163.0			4.45412
$427$			1429.83i			0.162048i
$428$			12932.1i			1.46050i
$429$	−29236.1			−3.29028
$430$	−10836.0	+	2680.89i	−1.21525	+	0.300661i
$431$	−1407.03			−0.157249			−0.0786246	−	0.996904i	$-0.525053\pi$
$431$	−1407.03			−0.157249			−0.0786246	+	0.996904i	$0.525053\pi$
$432$			32352.6i			3.60316i
$433$		−	10211.3i		−	1.13331i	−0.823955	−	0.566656i	$-0.808237\pi$
$433$		−	10211.3i		−	1.13331i	0.823955	−	0.566656i	$-0.191763\pi$
$434$	−9491.56			−1.04979
$435$	−4819.38	−	19479.7i	−0.531199	−	2.14708i
$436$	15449.6			1.69702
$437$		−	63.5695i		−	0.00695868i
$438$		−	11155.8i		−	1.21700i
$439$	−7741.56			−0.841650			−0.420825	−	0.907142i	$-0.638259\pi$
$439$	−7741.56			−0.841650			−0.420825	+	0.907142i	$0.638259\pi$
$440$	5518.02	+	22303.6i	0.597867	+	2.41655i
$441$	−9215.74			−0.995113
$442$		−	1251.09i		−	0.134634i
$443$		−	6933.73i		−	0.743637i	−0.928305	−	0.371819i	$-0.878734\pi$
$443$		−	6933.73i		−	0.743637i	0.928305	−	0.371819i	$-0.121266\pi$
$444$	−36586.4			−3.91062
$445$	12483.6	−	3088.52i	1.32985	−	0.329011i
$446$	2411.04			0.255978
$447$		−	34169.9i		−	3.61562i
$448$			6347.80i			0.669432i
$449$	14142.2			1.48644			0.743218	−	0.669050i	$-0.233299\pi$
$449$	14142.2			1.48644			0.743218	+	0.669050i	$0.233299\pi$
$450$	20568.0	+	39023.1i	2.15463	+	4.08793i
$451$	−11977.0			−1.25050
$452$			13459.5i			1.40063i
$453$		−	10802.9i		−	1.12045i
$454$	22297.7			2.30503
$455$	9422.42	−	2331.16i	0.970835	−	0.240190i
$456$	1135.18			0.116578
$457$		−	4127.06i		−	0.422441i	−0.977438	−	0.211221i	$-0.932256\pi$
$457$		−	4127.06i		−	0.422441i	0.977438	−	0.211221i	$-0.0677438\pi$
$458$		−	20929.0i		−	2.13526i
$459$	−1884.02			−0.191588
$460$	1011.73	+	4089.36i	0.102548	+	0.414495i
$461$	−4196.72			−0.423993			−0.211997	−	0.977270i	$-0.567997\pi$
$461$	−4196.72			−0.423993			−0.211997	+	0.977270i	$0.567997\pi$
$462$		−	35592.8i		−	3.58426i
$463$			4195.23i			0.421099i	0.977583	+	0.210549i	$0.0675253\pi$
$463$			4195.23i			0.421099i	−0.977583	+	0.210549i	$0.932475\pi$
$464$	13261.9			1.32687
$465$	3500.69	+	14149.6i	0.349119	+	1.41112i
$466$	−23167.1			−2.30300
$467$			17075.5i			1.69199i	0.533191	+	0.845995i	$0.320993\pi$
$467$			17075.5i			1.69199i	−0.533191	+	0.845995i	$0.679007\pi$
$468$		−	69475.5i		−	6.86220i
$469$	8554.58			0.842247
$470$	−10404.1	+	2574.04i	−1.02108	+	0.252621i
$471$	−5143.94			−0.503228
$472$			15754.3i			1.53634i
$473$		−	10039.2i		−	0.975909i
$474$	2921.25			0.283075
$475$	305.632	−	161.090i	0.0295228	−	0.0155607i
$476$	1023.36			0.0985417
$477$		−	21097.8i		−	2.02516i
$478$			19264.6i			1.84340i
$479$	−19810.1			−1.88966			−0.944828	−	0.327567i	$-0.893771\pi$
$479$	−19810.1			−1.88966			−0.944828	+	0.327567i	$0.893771\pi$
$480$	−3330.10	+	823.885i	−0.316661	+	0.0783438i
$481$	13355.2			1.26600
$482$			13496.9i			1.27545i
$483$		−	3339.11i		−	0.314565i
$484$	−18580.1			−1.74493
$485$	4199.67	+	16974.9i	0.393190	+	1.58926i
$486$	−61166.8			−5.70901
$487$		−	2377.27i		−	0.221200i	−0.993865	−	0.110600i	$-0.964723\pi$
$487$		−	2377.27i		−	0.221200i	0.993865	−	0.110600i	$-0.0352773\pi$
$488$			4045.07i			0.375229i
$489$	−4334.54			−0.400848
$490$	−1709.71	−	6910.58i	−0.157627	−	0.637119i
$491$	−1387.20			−0.127502			−0.0637512	−	0.997966i	$-0.520306\pi$
$491$	−1387.20			−0.127502			−0.0637512	+	0.997966i	$0.520306\pi$
$492$		−	39214.3i		−	3.59333i
$493$			772.292i			0.0705523i
$494$	−809.858			−0.0737596
$495$	−38510.9	+	9527.82i	−3.49684	+	0.865138i
$496$	−9633.11			−0.872055
$497$		−	11693.7i		−	1.05540i
$498$			6478.66i			0.582963i
$499$	20050.9			1.79880			0.899400	−	0.437127i	$-0.144004\pi$
$499$	20050.9			1.79880			0.899400	+	0.437127i	$0.144004\pi$
$500$	−17097.2	+	15227.0i	−1.52922	+	1.36195i
$501$	2119.95			0.189047
$502$			12529.7i			1.11400i
$503$			1805.66i			0.160060i	0.996792	+	0.0800300i	$0.0255016\pi$
$503$			1805.66i			0.160060i	−0.996792	+	0.0800300i	$0.974498\pi$
$504$	43277.5			3.82486
$505$	2223.31	−	550.058i	0.195913	−	0.0484699i
$506$	−5638.81			−0.495406
$507$			13141.0i			1.15111i
$508$			16315.4i			1.42496i
$509$	−7747.36			−0.674648			−0.337324	−	0.941389i	$-0.609522\pi$
$509$	−7747.36			−0.674648			−0.337324	+	0.941389i	$0.609522\pi$
$510$	−561.754	−	2270.58i	−0.0487743	−	0.197143i
$511$	−3331.01			−0.288367
$512$			22010.7i			1.89989i
$513$			1219.57i			0.104962i
$514$	24930.8			2.13940
$515$	1871.24	+	7563.47i	0.160110	+	0.647158i
$516$	32869.9			2.80429
$517$		−	9639.12i		−	0.819977i
$518$			16259.0i			1.37911i
$519$	16779.4			1.41914
$520$	26656.5	−	6594.96i	2.24801	−	0.556170i
$521$	−9274.56			−0.779896			−0.389948	−	0.920837i	$-0.627507\pi$
$521$	−9274.56			−0.779896			−0.389948	+	0.920837i	$0.627507\pi$
$522$			63830.1i			5.35205i
$523$		−	2478.63i		−	0.207233i	−0.994617	−	0.103616i	$-0.966959\pi$
$523$		−	2478.63i		−	0.207233i	0.994617	−	0.103616i	$-0.0330414\pi$
$524$	−5675.46			−0.473156
$525$	16053.9	−	8461.58i	1.33457	−	0.703416i
$526$	39316.5			3.25909
$527$		−	560.975i		−	0.0463690i
$528$		−	36123.6i		−	2.97742i
$529$	−529.000			−0.0434783
$530$	15820.5	−	3914.08i	1.29660	−	0.320786i
$531$	−27202.5			−2.22314
$532$		−	662.448i		−	0.0539864i
$533$			14314.5i			1.16328i
$534$	−56359.9			−4.56728
$535$	−2119.62	−	8567.40i	−0.171288	−	0.692338i
$536$	24201.3			1.95026
$537$			45799.6i			3.68044i
$538$			20572.6i			1.64861i
$539$	6402.44			0.511637
$540$	−19409.9	−	78453.9i	−1.54680	−	6.25207i
$541$	2379.90			0.189131			0.0945655	−	0.995519i	$-0.469854\pi$
$541$	2379.90			0.189131			0.0945655	+	0.995519i	$0.469854\pi$
$542$		−	11247.7i		−	0.891385i
$543$		−	47319.2i		−	3.73971i
$544$	132.025			0.0104054
$545$	−10235.2	+	2532.25i	−0.804457	+	0.199027i
$546$	−42539.4			−3.33428
$547$		−	11098.5i		−	0.867529i	−0.901026	−	0.433765i	$-0.857185\pi$
$547$		−	11098.5i		−	0.867529i	0.901026	−	0.433765i	$-0.142815\pi$
$548$			27260.4i			2.12501i
$549$	−6984.51			−0.542972
$550$	−14289.2	−	27110.5i	−1.10781	−	2.10181i
$551$	499.922			0.0386523
$552$		−	9446.51i		−	0.728388i
$553$		−	872.253i		−	0.0670741i
$554$	32055.4			2.45831
$555$	24238.2	−	5996.67i	1.85379	−	0.458639i
$556$	26324.0			2.00789
$557$		−	18917.3i		−	1.43905i	−0.694465	−	0.719526i	$-0.744359\pi$
$557$		−	18917.3i		−	1.43905i	0.694465	−	0.719526i	$-0.255641\pi$
$558$		−	46364.7i		−	3.51752i
$559$	−11998.6			−0.907846
$560$	2880.34	+	11642.2i	0.217351	+	0.878522i
$561$	2103.62			0.158316
$562$		−	2663.85i		−	0.199942i
$563$		−	6813.52i		−	0.510045i	−0.966935	−	0.255023i	$-0.917917\pi$
$563$		−	6813.52i		−	0.510045i	0.966935	−	0.255023i	$-0.0820829\pi$
$564$	31559.8			2.35622
$565$	−2206.07	−	8916.84i	−0.164266	−	0.663954i
$566$	−8866.63			−0.658467
$567$			35829.3i			2.65377i
$568$		−	33081.9i		−	2.44382i
$569$	−721.625			−0.0531671			−0.0265836	−	0.999647i	$-0.508463\pi$
$569$	−721.625			−0.0531671			−0.0265836	+	0.999647i	$0.508463\pi$
$570$	−1469.80	+	363.637i	−0.108006	+	0.0267212i
$571$	2414.48			0.176958			0.0884788	−	0.996078i	$-0.471799\pi$
$571$	2414.48			0.176958			0.0884788	+	0.996078i	$0.471799\pi$
$572$			48266.6i			3.52820i
$573$			14343.6i			1.04575i
$574$	−17426.9			−1.26722
$575$	−1340.53	−	2543.35i	−0.0972242	−	0.184461i
$576$	−31008.0			−2.24305
$577$		−	4827.40i		−	0.348297i	−0.984719	−	0.174148i	$-0.944283\pi$
$577$		−	4827.40i		−	0.348297i	0.984719	−	0.174148i	$-0.0557172\pi$
$578$		−	24169.6i		−	1.73931i
$579$	−5307.02			−0.380919
$580$	−32159.5	+	7956.44i	−2.30233	+	0.569609i
$581$	1934.46			0.138132
$582$		−	76636.3i		−	5.45821i
$583$			14657.2i			1.04123i
$584$	−9423.60			−0.667725
$585$	11387.3	+	46027.0i	0.804801	+	3.25296i
$586$	35876.2			2.52906
$587$		−	11517.0i		−	0.809811i	−0.914359	−	0.404905i	$-0.867304\pi$
$587$		−	11517.0i		−	0.809811i	0.914359	−	0.404905i	$-0.132696\pi$
$588$			20962.5i			1.47020i
$589$	−363.132			−0.0254034
$590$	−5046.64	−	20398.3i	−0.352147	−	1.42336i
$591$	47800.1			3.32696
$592$			16501.5i			1.14562i
$593$			15371.6i			1.06448i	0.846594	+	0.532239i	$0.178649\pi$
$593$			15371.6i			1.06448i	−0.846594	+	0.532239i	$0.821351\pi$
$594$	108180.			7.47250
$595$	−677.972	+	167.734i	−0.0467128	+	0.0115570i
$596$	−56412.0			−3.87706
$597$		−	23346.8i		−	1.60054i
$598$			6739.32i			0.460855i
$599$	−11791.9			−0.804347			−0.402174	−	0.915563i	$-0.631745\pi$
$599$	−11791.9			−0.804347			−0.402174	+	0.915563i	$0.631745\pi$
$600$	45417.3	−	23938.2i	3.09025	−	1.62879i
$601$	−14311.6			−0.971349			−0.485675	−	0.874140i	$-0.661426\pi$
$601$	−14311.6			−0.971349			−0.485675	+	0.874140i	$0.661426\pi$
$602$		−	14607.4i		−	0.988958i
$603$			41787.7i			2.82210i
$604$	−17834.7			−1.20147
$605$	12309.2	−	3045.35i	0.827171	−	0.204647i
$606$	−10037.6			−0.672851
$607$			5793.61i			0.387406i	0.981060	+	0.193703i	$0.0620498\pi$
$607$			5793.61i			0.387406i	−0.981060	+	0.193703i	$0.937950\pi$
$608$		−	85.4629i		−	0.00570062i
$609$	26259.4			1.74726
$610$	−1295.77	−	5237.45i	−0.0860071	−	0.347636i
$611$	−11520.4			−0.762788
$612$			4998.97i			0.330182i
$613$			10587.0i			0.697561i	0.937204	+	0.348780i	$0.113404\pi$
$613$			10587.0i			0.697561i	−0.937204	+	0.348780i	$0.886596\pi$
$614$	10419.2			0.684831
$615$	6427.40	+	25979.2i	0.421427	+	1.70339i
$616$	−30066.1			−1.96655
$617$			8577.61i			0.559678i	0.960047	+	0.279839i	$0.0902812\pi$
$617$			8577.61i			0.559678i	−0.960047	+	0.279839i	$0.909719\pi$
$618$		−	34146.7i		−	2.22263i
$619$	4955.89			0.321800			0.160900	−	0.986971i	$-0.448560\pi$
$619$	4955.89			0.321800			0.160900	+	0.986971i	$0.448560\pi$
$620$	23359.9	−	5779.38i	1.51316	−	0.374363i
$621$	10148.8			0.655808
$622$			5341.38i			0.344325i
$623$			16828.5i			1.08221i
$624$	−43173.8			−2.76977
$625$	8830.99	−	12890.1i	0.565183	−	0.824965i
$626$	31148.0			1.98870
$627$		−	1361.72i		−	0.0867337i
$628$			8492.27i			0.539615i
$629$	−960.950			−0.0609151
$630$	−56034.5	+	13863.2i	−3.54360	+	0.876706i
$631$	−15094.8			−0.952319			−0.476160	−	0.879359i	$-0.657972\pi$
$631$	−15094.8			−0.952319			−0.476160	+	0.879359i	$0.657972\pi$
$632$		−	2467.65i		−	0.155313i
$633$		−	20154.9i		−	1.26554i
$634$	−26404.8			−1.65405
$635$	−2674.17	−	10808.8i	−0.167120	−	0.675489i
$636$	−47989.8			−2.99201
$637$		−	7651.99i		−	0.475954i
$638$		−	44344.6i		−	2.75175i
$639$	57121.7			3.53630
$640$	−6416.85	−	25936.6i	−0.396326	−	1.60193i
$641$	−23638.5			−1.45657			−0.728287	−	0.685272i	$-0.759683\pi$
$641$	−23638.5			−1.45657			−0.728287	+	0.685272i	$0.759683\pi$
$642$			38679.2i			2.37780i
$643$			11988.0i			0.735240i	0.929976	+	0.367620i	$0.119827\pi$
$643$			11988.0i			0.735240i	−0.929976	+	0.367620i	$0.880173\pi$
$644$	−5512.63			−0.337310
$645$	−21776.1	+	5387.51i	−1.32935	+	0.328889i
$646$	58.2717			0.00354902
$647$			7122.84i			0.432810i	0.976304	+	0.216405i	$0.0694331\pi$
$647$			7122.84i			0.432810i	−0.976304	+	0.216405i	$0.930567\pi$
$648$			101363.i			6.14491i
$649$	18898.4			1.14303
$650$	−32401.5	+	17078.0i	−1.95522	+	1.03054i
$651$	−19074.2			−1.14835
$652$			7156.00i			0.429832i
$653$			4361.92i			0.261402i	0.991422	+	0.130701i	$0.0417227\pi$
$653$			4361.92i			0.261402i	−0.991422	+	0.130701i	$0.958277\pi$
$654$	46208.9			2.76286
$655$	3759.95	−	930.232i	0.224295	−	0.0554919i
$656$	−17686.8			−1.05267
$657$		−	16271.5i		−	0.966225i
$658$		−	14025.2i		−	0.830941i
$659$	−4012.62			−0.237192			−0.118596	−	0.992943i	$-0.537839\pi$
$659$	−4012.62			−0.237192			−0.118596	+	0.992943i	$0.537839\pi$
$660$	21672.3	+	87598.4i	1.27817	+	5.16631i
$661$	5108.11			0.300579			0.150289	−	0.988642i	$-0.451979\pi$
$661$	5108.11			0.300579			0.150289	+	0.988642i	$0.451979\pi$
$662$		−	46931.2i		−	2.75534i
$663$		−	2514.18i		−	0.147274i
$664$	5472.68			0.319851
$665$	108.578	+	438.867i	0.00633154	+	0.0255918i
$666$	−79422.7			−4.62097
$667$		−	4160.15i		−	0.241502i
$668$		−	3499.88i		−	0.202716i
$669$	4845.22			0.280011
$670$	−31335.2	+	7752.51i	−1.80684	+	0.447023i
$671$	4852.34			0.279169
$672$		−	4489.10i		−	0.257695i
$673$		−	25911.3i		−	1.48411i	−0.670339	−	0.742055i	$-0.733851\pi$
$673$		−	25911.3i		−	1.48411i	0.670339	−	0.742055i	$-0.266149\pi$
$674$	17496.9			0.999933
$675$	25717.9	+	48793.7i	1.46649	+	2.78233i
$676$	21694.9			1.23435
$677$			20728.6i			1.17676i	0.808585	+	0.588379i	$0.200234\pi$
$677$			20728.6i			1.17676i	−0.808585	+	0.588379i	$0.799766\pi$
$678$			40256.8i			2.28031i
$679$	−22882.8			−1.29331
$680$	−1918.01	+	474.527i	−0.108165	+	0.0267607i
$681$	44809.5			2.52144
$682$			32210.9i			1.80853i
$683$		−	13174.7i		−	0.738091i	−0.929411	−	0.369046i	$-0.879685\pi$
$683$		−	13174.7i		−	0.738091i	0.929411	−	0.369046i	$-0.120315\pi$
$684$	3235.95			0.180891
$685$	−4468.09	−	18059.8i	−0.249222	−	1.00734i
$686$	34095.0			1.89760
$687$		−	42058.9i		−	2.33573i
$688$		−	14825.2i		−	0.821522i
$689$	17517.8			0.968615
$690$	3026.04	+	12231.1i	0.166956	+	0.674826i
$691$	−4753.07			−0.261672			−0.130836	−	0.991404i	$-0.541766\pi$
$691$	−4753.07			−0.261672			−0.130836	+	0.991404i	$0.541766\pi$
$692$		−	27701.6i		−	1.52176i
$693$		−	51914.3i		−	2.84569i
$694$	16345.1			0.894021
$695$	−17439.5	+	4314.62i	−0.951822	+	0.235486i
$696$	74289.1			4.04586
$697$		−	1029.97i		−	0.0559727i
$698$		−	42112.3i		−	2.28363i
$699$	−46556.6			−2.51922
$700$	−13969.4	−	26503.8i	−0.754279	−	1.43107i
$701$	23366.3			1.25896			0.629481	−	0.777016i	$-0.283267\pi$
$701$	23366.3			1.25896			0.629481	+	0.777016i	$0.283267\pi$
$702$		−	129293.i		−	6.95134i
$703$			622.045i			0.0333725i
$704$	21542.1			1.15327
$705$	−20908.1	+	5172.79i	−1.11694	+	0.276338i
$706$	44596.0			2.37733
$707$			2997.11i			0.159431i
$708$			61875.9i			3.28452i
$709$	−16971.9			−0.899001			−0.449500	−	0.893280i	$-0.648398\pi$
$709$	−16971.9			−0.899001			−0.449500	+	0.893280i	$0.648398\pi$
$710$	10597.3	+	42833.6i	0.560153	+	2.26411i
$711$	4260.82			0.224744
$712$			47608.5i			2.50590i
$713$			3021.84i			0.158722i
$714$	3060.83			0.160433
$715$	−7911.11	−	31976.3i	−0.413788	−	1.67251i
$716$	75611.7			3.94657
$717$			38714.2i			2.01647i
$718$		−	23595.5i		−	1.22643i
$719$	−24287.2			−1.25975			−0.629874	−	0.776697i	$-0.716893\pi$
$719$	−24287.2			−1.25975			−0.629874	+	0.776697i	$0.716893\pi$
$720$	−56870.2	+	14070.0i	−2.94365	+	0.728275i
$721$	−10195.9			−0.526648
$722$			33830.9i			1.74385i
$723$			27123.3i			1.39520i
$724$	−78120.5			−4.01012
$725$	20001.3	−	10542.2i	1.02459	−	0.540036i
$726$	−55572.1			−2.84087
$727$			1290.09i			0.0658142i	0.999458	+	0.0329071i	$0.0104765\pi$
$727$			1290.09i			0.0658142i	−0.999458	+	0.0329071i	$0.989523\pi$
$728$			35934.0i			1.82940i
$729$	−56798.8			−2.88568
$730$	12201.4	−	3018.70i	0.618623	−	0.153051i
$731$	863.334			0.0436820
$732$			15887.2i			0.802197i
$733$			37629.8i			1.89616i	0.318025	+	0.948082i	$0.396980\pi$
$733$			37629.8i			1.89616i	−0.318025	+	0.948082i	$0.603020\pi$
$734$	−36879.9			−1.85458
$735$	−3435.84	−	13887.5i	−0.172426	−	0.696935i
$736$	−711.188			−0.0356179
$737$		−	29031.1i		−	1.45098i
$738$		−	85127.5i		−	4.24605i
$739$	−28327.7			−1.41008			−0.705041	−	0.709167i	$-0.749071\pi$
$739$	−28327.7			−1.41008			−0.705041	+	0.709167i	$0.749071\pi$
$740$	−9900.06	−	40015.5i	−0.491802	−	1.98784i
$741$	−1627.49			−0.0806846
$742$			21326.7i			1.05516i
$743$		−	24051.6i		−	1.18758i	−0.804622	−	0.593788i	$-0.797632\pi$
$743$		−	24051.6i		−	1.18758i	0.804622	−	0.593788i	$-0.202368\pi$
$744$	−53961.9			−2.65906
$745$	37372.5	−	9246.17i	1.83788	−	0.454702i
$746$	−16493.1			−0.809457
$747$			9449.52i			0.462838i
$748$		−	3472.93i		−	0.169763i
$749$	11549.2			0.563416
$750$	−51136.9	+	45543.3i	−2.48967	+	2.21734i
$751$	7103.36			0.345147			0.172573	−	0.984997i	$-0.444792\pi$
$751$	7103.36			0.345147			0.172573	+	0.984997i	$0.444792\pi$
$752$		−	14234.4i		−	0.690257i
$753$			25179.7i			1.21859i
$754$	−52999.2			−2.55984
$755$	11815.4	−	2923.19i	0.569544	−	0.140908i
$756$	105759.			5.08785
$757$			27385.7i			1.31486i	0.753516	+	0.657430i	$0.228356\pi$
$757$			27385.7i			1.31486i	−0.753516	+	0.657430i	$0.771644\pi$
$758$			22700.8i			1.08777i
$759$	−11331.7			−0.541918
$760$	307.172	+	1241.57i	0.0146609	+	0.0592588i
$761$	33273.9			1.58499			0.792495	−	0.609878i	$-0.208782\pi$
$761$	33273.9			1.58499			0.792495	+	0.609878i	$0.208782\pi$
$762$			48798.6i			2.31993i
$763$		−	13797.5i		−	0.654656i
$764$	23680.3			1.12136
$765$	−819.353	−	3311.78i	−0.0387239	−	0.156520i
$766$	−5374.08			−0.253490
$767$		−	22586.7i		−	1.06331i
$768$			82652.7i			3.88343i
$769$	−17498.2			−0.820550			−0.410275	−	0.911962i	$-0.634567\pi$
$769$	−17498.2			−0.820550			−0.410275	+	0.911962i	$0.634567\pi$
$770$	38928.8	−	9631.19i	1.82194	−	0.450759i
$771$	50100.9			2.34026
$772$			8761.49i			0.408462i
$773$			13441.0i			0.625404i	0.949851	+	0.312702i	$0.101234\pi$
$773$			13441.0i			0.625404i	−0.949851	+	0.312702i	$0.898766\pi$
$774$	71354.7			3.31369
$775$	−14528.5	+	7657.59i	−0.673393	+	0.354927i
$776$	−64736.5			−2.99472
$777$			32674.1i			1.50859i
$778$		−	17939.4i		−	0.826684i
$779$	−666.725			−0.0306648
$780$	104695.	−	25902.1i	4.80599	−	1.18903i
$781$	−39684.1			−1.81819
$782$		−	484.914i		−	0.0221745i
$783$			79812.0i			3.64272i
$784$	9454.66			0.430697
$785$	−1391.92	−	5626.06i	−0.0632863	−	0.255800i
$786$	−16975.0			−0.770330
$787$			29810.5i			1.35023i	0.737713	+	0.675114i	$0.235906\pi$
$787$			29810.5i			1.35023i	−0.737713	+	0.675114i	$0.764094\pi$
$788$		−	78914.4i		−	3.56752i
$789$	79010.3			3.56507
$790$	790.471	+	3195.04i	0.0355996	+	0.143892i
$791$	12020.3			0.540317
$792$		−	146868.i		−	6.58930i
$793$		−	5799.35i		−	0.259699i
$794$	−52377.0			−2.34105
$795$	31792.9	−	7865.73i	1.41833	−	0.350904i
$796$	−38543.8			−1.71627
$797$		−	18131.8i		−	0.805847i	−0.915234	−	0.402924i	$-0.867994\pi$
$797$		−	18131.8i		−	0.805847i	0.915234	−	0.402924i	$-0.132006\pi$
$798$		−	1981.35i		−	0.0878935i
$799$	828.924			0.0367024
$800$	−1802.21	−	3419.28i	−0.0796471	−	0.151112i
$801$	−82204.3			−3.62615
$802$			48085.3i			2.11715i
$803$			11304.2i			0.496785i
$804$	95052.0			4.16943
$805$	3652.07	−	903.543i	0.159899	−	0.0395599i
$806$	38497.4			1.68240
$807$			41342.7i			1.80339i
$808$			8478.96i			0.369169i
$809$	−43101.5			−1.87314			−0.936568	−	0.350486i	$-0.886016\pi$
$809$	−43101.5			−1.87314			−0.936568	+	0.350486i	$0.886016\pi$
$810$	−32469.9	−	131242.i	−1.40849	−	5.69305i
$811$	−35896.4			−1.55425			−0.777123	−	0.629349i	$-0.783322\pi$
$811$	−35896.4			−1.55425			−0.777123	+	0.629349i	$0.783322\pi$
$812$		−	43352.3i		−	1.87360i
$813$		−	22603.4i		−	0.975074i
$814$	55177.2			2.37587
$815$	−1172.90	−	4740.80i	−0.0504109	−	0.203758i
$816$	3106.48			0.133270
$817$		−	558.856i		−	0.0239313i
$818$			31599.6i			1.35068i
$819$	−62046.2			−2.64722
$820$	42889.7	−	10611.2i	1.82655	−	0.451900i
$821$	9724.88			0.413399			0.206699	−	0.978404i	$-0.433728\pi$
$821$	9724.88			0.413399			0.206699	+	0.978404i	$0.433728\pi$
$822$			81534.5i			3.45966i
$823$			13867.5i			0.587351i	0.955905	+	0.293675i	$0.0948785\pi$
$823$			13867.5i			0.587351i	−0.955905	+	0.293675i	$0.905122\pi$
$824$	−28844.6			−1.21948
$825$	−28715.5	−	54481.1i	−1.21181	−	2.29914i
$826$	27497.7			1.15831
$827$			17119.4i			0.719829i	0.932985	+	0.359915i	$0.117194\pi$
$827$			17119.4i			0.719829i	−0.932985	+	0.359915i	$0.882806\pi$
$828$		−	26928.3i		−	1.13022i
$829$	−40928.7			−1.71473			−0.857366	−	0.514707i	$-0.827901\pi$
$829$	−40928.7			−1.71473			−0.857366	+	0.514707i	$0.827901\pi$
$830$	−7085.88	+	1753.09i	−0.296331	+	0.0733138i
$831$	64418.4			2.68911
$832$		−	25746.5i		−	1.07283i
$833$			550.583i			0.0229011i
$834$	78733.8			3.26898
$835$	573.646	+	2318.65i	0.0237747	+	0.0960959i
$836$	−2248.11			−0.0930053
$837$		−	57973.6i		−	2.39410i
$838$			3265.09i			0.134595i
$839$	40257.8			1.65656			0.828280	−	0.560314i	$-0.189320\pi$
$839$	40257.8			1.65656			0.828280	+	0.560314i	$0.189320\pi$
$840$	16134.8	+	65216.1i	0.662743	+	2.67877i
$841$	8327.20			0.341433
$842$		−	14915.5i		−	0.610479i
$843$		−	5353.26i		−	0.218714i
$844$	−33274.2			−1.35705
$845$	−14372.7	+	3555.88i	−0.585131	+	0.144765i
$846$	68510.8			2.78422
$847$			16593.2i			0.673140i
$848$			21644.7i			0.876513i
$849$	−17818.4			−0.720288
$850$	2331.39	−	1228.81i	0.0940776	−	0.0495857i
$851$	5176.41			0.208513
$852$		−	129931.i		−	5.22461i
$853$		−	18689.7i		−	0.750202i	−0.926984	−	0.375101i	$-0.877608\pi$
$853$		−	18689.7i		−	0.750202i	0.926984	−	0.375101i	$-0.122392\pi$
$854$	7060.29			0.282902
$855$	−2143.79	+	530.386i	−0.0857499	+	0.0212150i
$856$	32673.2			1.30461
$857$			37949.6i			1.51264i	0.654202	+	0.756320i	$0.273005\pi$
$857$			37949.6i			1.51264i	−0.654202	+	0.756320i	$0.726995\pi$
$858$			144363.i			5.74414i
$859$	5723.08			0.227321			0.113661	−	0.993520i	$-0.463742\pi$
$859$	5723.08			0.227321			0.113661	+	0.993520i	$0.463742\pi$
$860$	8894.39	+	35950.6i	0.352670	+	1.42547i
$861$	−35021.0			−1.38619
$862$			6947.70i			0.274524i
$863$			24223.2i			0.955465i	0.878505	+	0.477733i	$0.158541\pi$
$863$			24223.2i			0.955465i	−0.878505	+	0.477733i	$0.841459\pi$
$864$	13644.0			0.537245
$865$	4540.41	+	18352.1i	0.178472	+	0.721376i
$866$	−50421.8			−1.97852
$867$		−	48571.1i		−	1.90261i
$868$			31490.1i			1.23139i
$869$	−2960.11			−0.115552
$870$	−96187.5	+	23797.3i	−3.74835	+	0.927362i
$871$	−34697.1			−1.34979
$872$		−	39033.8i		−	1.51588i
$873$		−	111779.i		−	4.33349i
$874$	−313.896			−0.0121484
$875$	13598.7	+	15268.9i	0.525395	+	0.589924i
$876$	−37011.7			−1.42752
$877$		−	3593.55i		−	0.138364i	−0.997604	−	0.0691822i	$-0.977961\pi$
$877$		−	3593.55i		−	0.138364i	0.997604	−	0.0691822i	$-0.0220390\pi$
$878$			38226.6i			1.46934i
$879$	72096.6			2.76651
$880$	39509.3	−	9774.83i	1.51348	−	0.374442i
$881$	−13697.2			−0.523805			−0.261902	−	0.965094i	$-0.584350\pi$
$881$	−13697.2			−0.523805			−0.261902	+	0.965094i	$0.584350\pi$
$882$			45505.8i			1.73726i
$883$		−	46387.3i		−	1.76790i	−0.467581	−	0.883950i	$-0.654874\pi$
$883$		−	46387.3i		−	1.76790i	0.467581	−	0.883950i	$-0.345126\pi$
$884$	−4150.73			−0.157923
$885$	−10141.7	−	40992.3i	−0.385209	−	1.55700i
$886$	−34237.6			−1.29823
$887$			14377.1i			0.544233i	0.962264	+	0.272117i	$0.0877237\pi$
$887$			14377.1i			0.544233i	−0.962264	+	0.272117i	$0.912276\pi$
$888$			92436.6i			3.49321i
$889$	14570.7			0.549704
$890$	−15250.6	−	61642.2i	−0.574385	−	2.32163i
$891$	121592.			4.57180
$892$		−	7999.10i		−	0.300258i
$893$		−	536.582i		−	0.0201075i
$894$	−168726.			−6.31211
$895$	−50092.2	+	12393.1i	−1.87083	+	0.462855i
$896$	34963.6			1.30363
$897$			13543.3i			0.504123i
$898$		−	69831.7i		−	2.59500i
$899$	−23764.3			−0.881628
$900$	129467.	−	68238.4i	4.79507	−	2.52735i
$901$	−1260.46			−0.0466060
$902$			59140.5i			2.18311i
$903$		−	29355.0i		−	1.08181i
$904$	34005.9			1.25113
$905$	51754.2	−	12804.3i	1.90096	−	0.470308i
$906$	−53342.8			−1.95607
$907$		−	41654.0i		−	1.52492i	−0.647038	−	0.762458i	$-0.723993\pi$
$907$		−	41654.0i		−	1.52492i	0.647038	−	0.762458i	$-0.276007\pi$
$908$		−	73977.1i		−	2.70376i
$909$	−14640.4			−0.534203
$910$	−11510.9	−	46526.4i	−0.419321	−	1.69487i
$911$	−29936.3			−1.08873			−0.544365	−	0.838849i	$-0.683229\pi$
$911$	−29936.3			−1.08873			−0.544365	+	0.838849i	$0.683229\pi$
$912$		−	2010.90i		−	0.0730126i
$913$		−	6564.85i		−	0.237968i
$914$	−20378.7			−0.737493
$915$	−2603.98	−	10525.2i	−0.0940820	−	0.380274i
$916$	−69436.1			−2.50462
$917$			5068.56i			0.182529i
$918$			9303.01i			0.334472i
$919$	47172.2			1.69322			0.846608	−	0.532216i	$-0.178641\pi$
$919$	47172.2			1.69322			0.846608	+	0.532216i	$0.178641\pi$
$920$	10331.9	−	2556.17i	0.370252	−	0.0916025i
$921$	20938.5			0.749127
$922$			20722.7i			0.740203i
$923$			47429.1i			1.69138i
$924$	−118086.			−4.20427
$925$	13117.4	+	24887.3i	0.466269	+	0.884638i
$926$	20715.4			0.735150
$927$		−	49805.1i		−	1.76463i
$928$		−	5592.91i		−	0.197841i
$929$	−43685.0			−1.54280			−0.771399	−	0.636352i	$-0.780443\pi$
$929$	−43685.0			−1.54280			−0.771399	+	0.636352i	$0.780443\pi$
$930$	69868.4	−	17285.8i	2.46352	−	0.609489i
$931$	356.405			0.0125464
$932$			76861.5i			2.70138i
$933$			10734.0i			0.376652i
$934$	84316.0			2.95386
$935$	569.228	+	2300.79i	0.0199099	+	0.0804747i
$936$	−175532.			−6.12974
$937$			50300.2i			1.75372i	0.480747	+	0.876859i	$0.340366\pi$
$937$			50300.2i			1.75372i	−0.480747	+	0.876859i	$0.659634\pi$
$938$		−	42241.1i		−	1.47039i
$939$	62594.9			2.17541
$940$	8539.89	+	34517.8i	0.296320	+	1.19771i
$941$	−13061.4			−0.452488			−0.226244	−	0.974071i	$-0.572645\pi$
$941$	−13061.4			−0.452488			−0.226244	+	0.974071i	$0.572645\pi$
$942$			25400.0i			0.878530i
$943$			5548.22i			0.191596i
$944$	27907.8			0.962203
$945$	−70064.5	+	17334.3i	−2.41185	+	0.596705i
$946$	−49572.2			−1.70373
$947$		−	421.764i		−	0.0144725i	−0.999974	−	0.00723627i	$-0.997697\pi$
$947$		−	421.764i		−	0.0144725i	0.999974	−	0.00723627i	$-0.00230340\pi$
$948$		−	9691.81i		−	0.332042i
$949$	13510.5			0.462137
$950$	−795.438	−	1509.16i	−0.0271657	−	0.0515407i
$951$	−53063.0			−1.80934
$952$		−	2585.56i		−	0.0880236i
$953$		−	2229.19i		−	0.0757717i	−0.999282	−	0.0378858i	$-0.987938\pi$
$953$		−	2229.19i		−	0.0757717i	0.999282	−	0.0378858i	$-0.0120623\pi$
$954$	−104177.			−3.53550
$955$	−15688.0	+	3881.30i	−0.531573	+	0.131514i
$956$	63914.2			2.16227
$957$		−	89114.8i		−	3.01011i
$958$			97818.9i			3.29894i
$959$	24345.3			0.819762
$960$	−11560.5	−	46726.9i	−0.388659	−	1.57094i
$961$	−12529.2			−0.420568
$962$		−	65946.0i		−	2.21017i
$963$			56415.9i			1.88783i
$964$	44778.6			1.49608
$965$	−1436.05	−	5804.42i	−0.0479046	−	0.193628i
$966$	−16488.0			−0.549164
$967$		−	23408.1i		−	0.778442i	−0.921144	−	0.389221i	$-0.872744\pi$
$967$		−	23408.1i		−	0.778442i	0.921144	−	0.389221i	$-0.127256\pi$
$968$			46943.0i			1.55868i
$969$	117.103			0.00388223
$970$	83819.1	−	20737.3i	2.77450	−	0.686428i
$971$	4542.42			0.150127			0.0750635	−	0.997179i	$-0.476084\pi$
$971$	4542.42			0.150127			0.0750635	+	0.997179i	$0.476084\pi$
$972$			202933.i			6.69657i
$973$		−	23509.1i		−	0.774580i
$974$	−11738.6			−0.386169
$975$	−65114.0	+	34319.8i	−2.13879	+	1.12730i
$976$	7165.58			0.235005
$977$			45666.7i			1.49540i	0.664037	+	0.747700i	$0.268842\pi$
$977$			45666.7i			1.49540i	−0.664037	+	0.747700i	$0.731158\pi$
$978$			21403.2i			0.699796i
$979$	57109.7			1.86438
$980$	−22927.2	+	5672.32i	−0.747329	+	0.184893i
$981$	67398.5			2.19355
$982$			6849.79i			0.222592i
$983$		−	52524.3i		−	1.70424i	−0.523349	−	0.852118i	$-0.675318\pi$
$983$		−	52524.3i		−	1.70424i	0.523349	−	0.852118i	$-0.324682\pi$
$984$	−99076.1			−3.20979
$985$	12934.4	+	52280.2i	0.418400	+	1.69115i
$986$	3813.45			0.123169
$987$		−	28185.0i		−	0.908955i
$988$			2686.86i			0.0865187i
$989$	−4650.57			−0.149524
$990$	47046.8	+	190161.i	1.51035	+	6.10475i
$991$	−48204.6			−1.54518			−0.772588	−	0.634907i	$-0.781038\pi$
$991$	−48204.6			−1.54518			−0.772588	+	0.634907i	$0.781038\pi$
$992$			4062.56i			0.130027i
$993$		−	94312.8i		−	3.01402i
$994$	−57741.4			−1.84250
$995$	25535.0	−	6317.49i	0.813581	−	0.201284i
$996$	21494.2			0.683806
$997$		−	29363.0i		−	0.932735i	−0.884591	−	0.466367i	$-0.845563\pi$
$997$		−	29363.0i		−	0.932735i	0.884591	−	0.466367i	$-0.154437\pi$
$998$		−	99008.0i		−	3.14032i
$999$	−99308.7			−3.14513

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.b.a.24.5	✓	34
5.2	odd	4		575.4.a.q.1.16		17
5.3	odd	4		575.4.a.r.1.2		17
5.4	even	2	inner	115.4.b.a.24.30	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.b.a.24.5	✓	34	1.1	even	1	trivial
115.4.b.a.24.30	yes	34	5.4	even	2	inner
575.4.a.q.1.16		17	5.2	odd	4
575.4.a.r.1.2		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)

\(f(q)\)	\(=\)	\(q-4.93784i q^{2} -9.92307i q^{3} -16.3822 q^{4} +(10.8531 - 2.68512i) q^{5} -48.9985 q^{6} +14.6304i q^{7} +41.3902i q^{8} -71.4673 q^{9} +O(q^{10})\)	\(q-4.93784i q^{2} -9.92307i q^{3} -16.3822 q^{4} +(10.8531 - 2.68512i) q^{5} -48.9985 q^{6} +14.6304i q^{7} +41.3902i q^{8} -71.4673 q^{9} +(-13.2587 - 53.5909i) q^{10} +49.6504 q^{11} +162.562i q^{12} -59.3405i q^{13} +72.2427 q^{14} +(-26.6446 - 107.696i) q^{15} +73.3201 q^{16} +4.26973i q^{17} +352.894i q^{18} +2.76389 q^{19} +(-177.798 + 43.9883i) q^{20} +145.179 q^{21} -245.165i q^{22} -23.0000i q^{23} +410.718 q^{24} +(110.580 - 58.2838i) q^{25} -293.014 q^{26} +441.252i q^{27} -239.679i q^{28} +180.876 q^{29} +(-531.786 + 131.567i) q^{30} -131.384 q^{31} -30.9212i q^{32} -492.684i q^{33} +21.0832 q^{34} +(39.2845 + 158.786i) q^{35} +1170.79 q^{36} +225.061i q^{37} -13.6477i q^{38} -588.840 q^{39} +(111.138 + 449.213i) q^{40} -241.227 q^{41} -716.869i q^{42} -202.199i q^{43} -813.385 q^{44} +(-775.643 + 191.898i) q^{45} -113.570 q^{46} -194.140i q^{47} -727.560i q^{48} +128.951 q^{49} +(-287.796 - 546.027i) q^{50} +42.3688 q^{51} +972.131i q^{52} +295.209i q^{53} +2178.83 q^{54} +(538.861 - 133.317i) q^{55} -605.556 q^{56} -27.4263i q^{57} -893.137i q^{58} +380.629 q^{59} +(436.499 + 1764.31i) q^{60} +97.7301 q^{61} +648.755i q^{62} -1045.60i q^{63} +433.877 q^{64} +(-159.336 - 644.029i) q^{65} -2432.79 q^{66} -584.711i q^{67} -69.9477i q^{68} -228.231 q^{69} +(784.058 - 193.980i) q^{70} -799.270 q^{71} -2958.04i q^{72} +227.677i q^{73} +1111.32 q^{74} +(-578.355 - 1097.30i) q^{75} -45.2788 q^{76} +726.406i q^{77} +2907.59i q^{78} -59.6191 q^{79} +(795.751 - 196.873i) q^{80} +2448.96 q^{81} +1191.14i q^{82} -132.222i q^{83} -2378.35 q^{84} +(11.4647 + 46.3398i) q^{85} -998.425 q^{86} -1794.85i q^{87} +2055.04i q^{88} +1150.24 q^{89} +(947.563 + 3830.00i) q^{90} +868.177 q^{91} +376.792i q^{92} +1303.74i q^{93} -958.632 q^{94} +(29.9968 - 7.42138i) q^{95} -306.833 q^{96} +1564.05i q^{97} -636.737i q^{98} -3548.38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9}+O(q^{10}) \) 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

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