LMFDB - Embedded newform 115.4.b.a.24.10

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			24.10
Character	$\chi$	$=$	115.24
Dual form			115.4.b.a.24.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.00148i q^{2} +1.85196i q^{3} -1.00888 q^{4} +(-6.22111 + 9.28966i) q^{5} +5.55862 q^{6} +4.63746i q^{7} -20.9837i q^{8} +23.5702 q^{9} +O(q^{10})$	\(q-3.00148i q^{2} +1.85196i q^{3} -1.00888 q^{4} +(-6.22111 + 9.28966i) q^{5} +5.55862 q^{6} +4.63746i q^{7} -20.9837i q^{8} +23.5702 q^{9} +(27.8827 + 18.6725i) q^{10} +70.0921 q^{11} -1.86840i q^{12} -4.48318i q^{13} +13.9193 q^{14} +(-17.2041 - 11.5212i) q^{15} -71.0532 q^{16} +62.4472i q^{17} -70.7456i q^{18} +107.068 q^{19} +(6.27636 - 9.37215i) q^{20} -8.58839 q^{21} -210.380i q^{22} -23.0000i q^{23} +38.8610 q^{24} +(-47.5955 - 115.584i) q^{25} -13.4562 q^{26} +93.6540i q^{27} -4.67864i q^{28} -1.08351 q^{29} +(-34.5808 + 51.6377i) q^{30} -129.836 q^{31} +45.3951i q^{32} +129.808i q^{33} +187.434 q^{34} +(-43.0804 - 28.8502i) q^{35} -23.7796 q^{36} +13.3561i q^{37} -321.364i q^{38} +8.30266 q^{39} +(194.931 + 130.542i) q^{40} -298.172 q^{41} +25.7779i q^{42} -120.590i q^{43} -70.7145 q^{44} +(-146.633 + 218.960i) q^{45} -69.0340 q^{46} +542.588i q^{47} -131.588i q^{48} +321.494 q^{49} +(-346.923 + 142.857i) q^{50} -115.650 q^{51} +4.52299i q^{52} +78.0212i q^{53} +281.101 q^{54} +(-436.051 + 651.131i) q^{55} +97.3112 q^{56} +198.286i q^{57} +3.25213i q^{58} -12.3641 q^{59} +(17.3568 + 11.6236i) q^{60} -81.5896 q^{61} +389.700i q^{62} +109.306i q^{63} -432.173 q^{64} +(41.6472 + 27.8904i) q^{65} +389.615 q^{66} -1007.70i q^{67} -63.0017i q^{68} +42.5951 q^{69} +(-86.5932 + 129.305i) q^{70} +201.271 q^{71} -494.591i q^{72} -520.072i q^{73} +40.0881 q^{74} +(214.057 - 88.1449i) q^{75} -108.019 q^{76} +325.049i q^{77} -24.9203i q^{78} -1103.03 q^{79} +(442.030 - 660.060i) q^{80} +462.953 q^{81} +894.957i q^{82} -227.736i q^{83} +8.66466 q^{84} +(-580.113 - 388.491i) q^{85} -361.949 q^{86} -2.00662i q^{87} -1470.79i q^{88} -727.623 q^{89} +(657.203 + 440.116i) q^{90} +20.7906 q^{91} +23.2042i q^{92} -240.451i q^{93} +1628.57 q^{94} +(-666.085 + 994.629i) q^{95} -84.0699 q^{96} -1013.99i q^{97} -964.958i q^{98} +1652.09 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	3.00148i		−	1.06118i	−0.847628	−	0.530592i	$-0.821970\pi$
$2$		−	3.00148i		−	1.06118i	0.847628	−	0.530592i	$-0.178030\pi$
$3$			1.85196i			0.356410i	0.983993	+	0.178205i	$0.0570290\pi$
$3$			1.85196i			0.356410i	−0.983993	+	0.178205i	$0.942971\pi$
$4$	−1.00888			−0.126110
$5$	−6.22111	+	9.28966i	−0.556433	+	0.830892i
$5$	−6.22111	+	9.28966i	−0.556433	+	0.830892i
$6$	5.55862			0.378216
$7$			4.63746i			0.250399i	0.992132	+	0.125200i	$0.0399572\pi$
$7$			4.63746i			0.250399i	−0.992132	+	0.125200i	$0.960043\pi$
$8$		−	20.9837i		−	0.927357i
$9$	23.5702			0.872972
$10$	27.8827	+	18.6725i	0.881729	+	0.590478i
$11$	70.0921			1.92123			0.960616	−	0.277879i	$-0.0896314\pi$
$11$	70.0921			1.92123			0.960616	+	0.277879i	$0.0896314\pi$
$12$		−	1.86840i		−	0.0449468i
$13$		−	4.48318i		−	0.0956469i	−0.998856	−	0.0478235i	$-0.984772\pi$
$13$		−	4.48318i		−	0.0956469i	0.998856	−	0.0478235i	$-0.0152285\pi$
$14$	13.9193			0.265720
$15$	−17.2041	−	11.5212i	−0.296138	−	0.198318i
$16$	−71.0532			−1.11021
$17$			62.4472i			0.890921i	0.895302	+	0.445461i	$0.146960\pi$
$17$			62.4472i			0.890921i	−0.895302	+	0.445461i	$0.853040\pi$
$18$		−	70.7456i		−	0.926383i
$19$	107.068			1.29280			0.646400	−	0.762999i	$-0.276274\pi$
$19$	107.068			1.29280			0.646400	+	0.762999i	$0.276274\pi$
$20$	6.27636	−	9.37215i	0.0701718	−	0.104784i
$21$	−8.58839			−0.0892448
$22$		−	210.380i		−	2.03878i
$23$		−	23.0000i		−	0.208514i
$23$		−	23.0000i		−	0.208514i
$24$	38.8610			0.330519
$25$	−47.5955	−	115.584i	−0.380764	−	0.924672i
$26$	−13.4562			−0.101499
$27$			93.6540i			0.667545i
$28$		−	4.67864i		−	0.0315779i
$29$	−1.08351			−0.00693803			−0.00346901	−	0.999994i	$-0.501104\pi$
$29$	−1.08351			−0.00693803			−0.00346901	+	0.999994i	$0.501104\pi$
$30$	−34.5808	+	51.6377i	−0.210452	+	0.314257i
$31$	−129.836			−0.752233			−0.376116	−	0.926572i	$-0.622741\pi$
$31$	−129.836			−0.752233			−0.376116	+	0.926572i	$0.622741\pi$
$32$			45.3951i			0.250775i
$33$			129.808i			0.684746i
$34$	187.434			0.945431
$35$	−43.0804	−	28.8502i	−0.208055	−	0.139331i
$36$	−23.7796			−0.110091
$37$			13.3561i			0.0593440i	0.999560	+	0.0296720i	$0.00944628\pi$
$37$			13.3561i			0.0593440i	−0.999560	+	0.0296720i	$0.990554\pi$
$38$		−	321.364i		−	1.37190i
$39$	8.30266			0.0340895
$40$	194.931	+	130.542i	0.770534	+	0.516013i
$41$	−298.172			−1.13577			−0.567886	−	0.823107i	$-0.692239\pi$
$41$	−298.172			−1.13577			−0.567886	+	0.823107i	$0.692239\pi$
$42$			25.7779i			0.0947051i
$43$		−	120.590i		−	0.427670i	−0.976870	−	0.213835i	$-0.931404\pi$
$43$		−	120.590i		−	0.427670i	0.976870	−	0.213835i	$-0.0685955\pi$
$44$	−70.7145			−0.242287
$45$	−146.633	+	218.960i	−0.485751	+	0.725346i
$46$	−69.0340			−0.221272
$47$			542.588i			1.68393i	0.539534	+	0.841964i	$0.318600\pi$
$47$			542.588i			1.68393i	−0.539534	+	0.841964i	$0.681400\pi$
$48$		−	131.588i		−	0.395688i
$49$	321.494			0.937300
$50$	−346.923	+	142.857i	−0.981247	+	0.404061i
$51$	−115.650			−0.317533
$52$			4.52299i			0.0120620i
$53$			78.0212i			0.202208i	0.994876	+	0.101104i	$0.0322375\pi$
$53$			78.0212i			0.202208i	−0.994876	+	0.101104i	$0.967762\pi$
$54$	281.101			0.708388
$55$	−436.051	+	651.131i	−1.06904	+	1.59634i
$56$	97.3112			0.232210
$57$			198.286i			0.460766i
$58$			3.25213i			0.00736252i
$59$	−12.3641			−0.0272826			−0.0136413	−	0.999907i	$-0.504342\pi$
$59$	−12.3641			−0.0272826			−0.0136413	+	0.999907i	$0.504342\pi$
$60$	17.3568	+	11.6236i	0.0373460	+	0.0250099i
$61$	−81.5896			−0.171254			−0.0856269	−	0.996327i	$-0.527289\pi$
$61$	−81.5896			−0.171254			−0.0856269	+	0.996327i	$0.527289\pi$
$62$			389.700i			0.798257i
$63$			109.306i			0.218592i
$64$	−432.173			−0.844088
$65$	41.6472	+	27.8904i	0.0794723	+	0.0532211i
$66$	389.615			0.726641
$67$		−	1007.70i		−	1.83747i	−0.394879	−	0.918733i	$-0.629213\pi$
$67$		−	1007.70i		−	1.83747i	0.394879	−	0.918733i	$-0.370787\pi$
$68$		−	63.0017i		−	0.112354i
$69$	42.5951			0.0743166
$70$	−86.5932	+	129.305i	−0.147855	+	0.220784i
$71$	201.271			0.336430			0.168215	−	0.985750i	$-0.446200\pi$
$71$	201.271			0.336430			0.168215	+	0.985750i	$0.446200\pi$
$72$		−	494.591i		−	0.809557i
$73$		−	520.072i		−	0.833833i	−0.908945	−	0.416917i	$-0.863111\pi$
$73$		−	520.072i		−	0.833833i	0.908945	−	0.416917i	$-0.136889\pi$
$74$	40.0881			0.0629749
$75$	214.057	−	88.1449i	0.329562	−	0.135708i
$76$	−108.019			−0.163035
$77$			325.049i			0.481076i
$78$		−	24.9203i		−	0.0361752i
$79$	−1103.03			−1.57089			−0.785447	−	0.618929i	$-0.787567\pi$
$79$	−1103.03			−1.57089			−0.785447	+	0.618929i	$0.787567\pi$
$80$	442.030	−	660.060i	0.617756	−	0.922462i
$81$	462.953			0.635052
$82$			894.957i			1.20526i
$83$		−	227.736i		−	0.301172i	−0.988597	−	0.150586i	$-0.951884\pi$
$83$		−	227.736i		−	0.301172i	0.988597	−	0.150586i	$-0.0481161\pi$
$84$	8.66466			0.0112547
$85$	−580.113	−	388.491i	−0.740260	−	0.495738i
$86$	−361.949			−0.453837
$87$		−	2.00662i		−	0.00247278i
$88$		−	1470.79i		−	1.78167i
$89$	−727.623			−0.866605			−0.433303	−	0.901248i	$-0.642652\pi$
$89$	−727.623			−0.866605			−0.433303	+	0.901248i	$0.642652\pi$
$90$	657.203	+	440.116i	0.769725	+	0.515471i
$91$	20.7906			0.0239499
$92$			23.2042i			0.0262958i
$93$		−	240.451i		−	0.268103i
$94$	1628.57			1.78696
$95$	−666.085	+	994.629i	−0.719357	+	1.07418i
$96$	−84.0699			−0.0893786
$97$		−	1013.99i		−	1.06140i	−0.847561	−	0.530698i	$-0.821930\pi$
$97$		−	1013.99i		−	1.06140i	0.847561	−	0.530698i	$-0.178070\pi$
$98$		−	964.958i		−	0.994647i
$99$	1652.09			1.67718
$100$	48.0182	+	116.610i	0.0480182	+	0.116610i
$101$	20.1077			0.0198098			0.00990489	−	0.999951i	$-0.496847\pi$
$101$	20.1077			0.0198098			0.00990489	+	0.999951i	$0.496847\pi$
$102$			347.120i			0.336961i
$103$		−	1819.95i		−	1.74102i	−0.492150	−	0.870510i	$-0.663789\pi$
$103$		−	1819.95i		−	1.74102i	0.492150	−	0.870510i	$-0.336211\pi$
$104$	−94.0737			−0.0886989
$105$	53.4294	−	79.7832i	0.0496588	−	0.0741528i
$106$	234.179			0.214580
$107$			1961.72i			1.77240i	0.463303	+	0.886200i	$0.346664\pi$
$107$			1961.72i			1.77240i	−0.463303	+	0.886200i	$0.653336\pi$
$108$		−	94.4857i		−	0.0841842i
$109$	−1566.33			−1.37639			−0.688197	−	0.725524i	$-0.741597\pi$
$109$	−1566.33			−1.37639			−0.688197	+	0.725524i	$0.741597\pi$
$110$	1954.36	+	1308.80i	1.69401	+	1.13444i
$111$	−24.7350			−0.0211508
$112$		−	329.507i		−	0.277995i
$113$			445.303i			0.370713i	0.982671	+	0.185357i	$0.0593440\pi$
$113$			445.303i			0.370713i	−0.982671	+	0.185357i	$0.940656\pi$
$114$	595.153			0.488957
$115$	213.662	+	143.086i	0.173253	+	0.116024i
$116$	1.09313			0.000874955
$117$		−	105.670i		−	0.0834971i
$118$			37.1106i			0.0289518i
$119$	−289.596			−0.223086
$120$	−241.758	+	361.005i	−0.183912	+	0.274626i
$121$	3581.90			2.69113
$122$			244.890i			0.181732i
$123$		−	552.202i		−	0.404800i
$124$	130.989			0.0948641
$125$	1369.83	+	276.915i	0.980173	+	0.198144i
$126$	328.080			0.231966
$127$			675.895i			0.472252i	0.971722	+	0.236126i	$0.0758778\pi$
$127$			675.895i			0.472252i	−0.971722	+	0.236126i	$0.924122\pi$
$128$			1660.32i			1.14651i
$129$	223.328			0.152426
$130$	83.7124	−	125.003i	0.0564774	−	0.0843347i
$131$	−1426.38			−0.951323			−0.475661	−	0.879628i	$-0.657791\pi$
$131$	−1426.38			−0.951323			−0.475661	+	0.879628i	$0.657791\pi$
$132$		−	130.960i		−	0.0863533i
$133$			496.526i			0.323716i
$134$	−3024.59			−1.94989
$135$	−870.014	−	582.632i	−0.554658	−	0.371444i
$136$	1310.37			0.826202
$137$		−	1180.24i		−	0.736017i	−0.929822	−	0.368009i	$-0.880040\pi$
$137$		−	1180.24i		−	0.736017i	0.929822	−	0.368009i	$-0.119960\pi$
$138$		−	127.848i		−	0.0788635i
$139$	−1947.20			−1.18820			−0.594099	−	0.804392i	$-0.702491\pi$
$139$	−1947.20			−1.18820			−0.594099	+	0.804392i	$0.702491\pi$
$140$	43.4630	+	29.1064i	0.0262378	+	0.0175710i
$141$	−1004.85			−0.600168
$142$		−	604.112i		−	0.357014i
$143$		−	314.235i		−	0.183760i
$144$	−1674.74			−0.969179
$145$	6.74064	−	10.0654i	0.00386055	−	0.00576475i
$146$	−1560.99			−0.884850
$147$			595.394i			0.334063i
$148$		−	13.4747i		−	0.00748388i
$149$	372.849			0.205000			0.102500	−	0.994733i	$-0.467316\pi$
$149$	372.849			0.205000			0.102500	+	0.994733i	$0.467316\pi$
$150$	−264.565	−	642.487i	−0.144011	−	0.349726i
$151$	−1656.34			−0.892653			−0.446327	−	0.894870i	$-0.647268\pi$
$151$	−1656.34			−0.892653			−0.446327	+	0.894870i	$0.647268\pi$
$152$		−	2246.69i		−	1.19889i
$153$			1471.89i			0.777749i
$154$	975.629			0.510509
$155$	807.724	−	1206.13i	0.418567	−	0.625025i
$156$	−8.37639			−0.00429903
$157$			2509.44i			1.27564i	0.770187	+	0.637819i	$0.220163\pi$
$157$			2509.44i			1.27564i	−0.770187	+	0.637819i	$0.779837\pi$
$158$			3310.72i			1.66701i
$159$	−144.492			−0.0720690
$160$	−421.705	−	282.408i	−0.208367	−	0.139539i
$161$	106.662			0.0522119
$162$		−	1389.54i		−	0.673907i
$163$		−	2371.01i		−	1.13934i	−0.821874	−	0.569669i	$-0.807071\pi$
$163$		−	2371.01i		−	1.13934i	0.821874	−	0.569669i	$-0.192929\pi$
$164$	300.820			0.143232
$165$	−1205.87	−	807.548i	−0.568950	−	0.381015i
$166$	−683.546			−0.319599
$167$			595.496i			0.275933i	0.990437	+	0.137967i	$0.0440566\pi$
$167$			595.496i			0.275933i	−0.990437	+	0.137967i	$0.955943\pi$
$168$			180.216i			0.0827618i
$169$	2176.90			0.990852
$170$	−1166.05	+	1741.20i	−0.526069	+	0.785551i
$171$	2523.63			1.12858
$172$			121.661i			0.0539335i
$173$		−	2099.76i		−	0.922787i	−0.887196	−	0.461393i	$-0.847350\pi$
$173$		−	2099.76i		−	0.922787i	0.887196	−	0.461393i	$-0.152650\pi$
$174$	−6.02282			−0.00262407
$175$	536.017	−	220.722i	0.231537	−	0.0953431i
$176$	−4980.27			−2.13296
$177$		−	22.8978i		−	0.00972377i
$178$			2183.95i			0.919627i
$179$	−3881.56			−1.62079			−0.810395	−	0.585884i	$-0.800747\pi$
$179$	−3881.56			−1.62079			−0.810395	+	0.585884i	$0.800747\pi$
$180$	147.935	−	220.904i	0.0612580	−	0.0914734i
$181$	1335.26			0.548336			0.274168	−	0.961682i	$-0.411598\pi$
$181$	1335.26			0.548336			0.274168	+	0.961682i	$0.411598\pi$
$182$		−	62.4025i		−	0.0254153i
$183$		−	151.101i		−	0.0610365i
$184$	−482.625			−0.193367
$185$	−124.074	−	83.0898i	−0.0493085	−	0.0330210i
$186$	−721.708			−0.284507
$187$			4377.05i			1.71167i
$188$		−	547.406i		−	0.212360i
$189$	−434.317			−0.167153
$190$	2985.36	+	1999.24i	1.13990	+	0.763369i
$191$	2863.68			1.08486			0.542431	−	0.840100i	$-0.317504\pi$
$191$	2863.68			1.08486			0.542431	+	0.840100i	$0.317504\pi$
$192$		−	800.367i		−	0.300841i
$193$			1817.70i			0.677930i	0.940799	+	0.338965i	$0.110077\pi$
$193$			1817.70i			0.677930i	−0.940799	+	0.338965i	$0.889923\pi$
$194$	−3043.48			−1.12634
$195$	−51.6518	+	77.1289i	−0.0189685	+	0.0283247i
$196$	−324.349			−0.118203
$197$		−	2199.03i		−	0.795302i	−0.917537	−	0.397651i	$-0.869826\pi$
$197$		−	2199.03i		−	0.795302i	0.917537	−	0.397651i	$-0.130174\pi$
$198$		−	4958.71i		−	1.77980i
$199$	−1875.06			−0.667935			−0.333968	−	0.942585i	$-0.608388\pi$
$199$	−1875.06			−0.667935			−0.333968	+	0.942585i	$0.608388\pi$
$200$	−2425.38	+	998.730i	−0.857502	+	0.353104i
$201$	1866.22			0.654891
$202$		−	60.3528i		−	0.0210218i
$203$		−	5.02474i		−	0.00173728i
$204$	116.677			0.0400441
$205$	1854.96	−	2769.92i	0.631981	−	0.943704i
$206$	−5462.55			−1.84754
$207$		−	542.116i		−	0.182027i
$208$			318.544i			0.106188i
$209$	7504.65			2.48377
$210$	−239.468	−	160.367i	−0.0786897	−	0.0526971i
$211$	−2011.27			−0.656216			−0.328108	−	0.944640i	$-0.606411\pi$
$211$	−2011.27			−0.656216			−0.328108	+	0.944640i	$0.606411\pi$
$212$		−	78.7141i		−	0.0255005i
$213$			372.746i			0.119907i
$214$	5888.07			1.88084
$215$	1120.24	+	750.205i	0.355348	+	0.237970i
$216$	1965.21			0.619053
$217$		−	602.109i		−	0.188359i
$218$			4701.30i			1.46061i
$219$	963.152			0.297186
$220$	439.923	−	656.913i	0.134816	−	0.201314i
$221$	279.962			0.0852139
$222$			74.2415i			0.0224449i
$223$			5097.82i			1.53083i	0.643537	+	0.765415i	$0.277466\pi$
$223$			5097.82i			1.53083i	−0.643537	+	0.765415i	$0.722534\pi$
$224$	−210.518			−0.0627939
$225$	−1121.84	−	2724.34i	−0.332396	−	0.807213i
$226$	1336.57			0.393394
$227$			4526.58i			1.32352i	0.749715	+	0.661761i	$0.230191\pi$
$227$			4526.58i			1.32352i	−0.749715	+	0.661761i	$0.769809\pi$
$228$		−	200.047i		−	0.0581072i
$229$	3909.67			1.12820			0.564100	−	0.825706i	$-0.309223\pi$
$229$	3909.67			1.12820			0.564100	+	0.825706i	$0.309223\pi$
$230$	429.468	−	641.303i	0.123123	−	0.183853i
$231$	−601.978			−0.171460
$232$			22.7361i			0.00643403i
$233$		−	479.688i		−	0.134873i	−0.997724	−	0.0674365i	$-0.978518\pi$
$233$		−	479.688i		−	0.134873i	0.997724	−	0.0674365i	$-0.0214820\pi$
$234$	−317.165			−0.0886057
$235$	−5040.46	−	3375.50i	−1.39916	−	0.936993i
$236$	12.4739			0.00344060
$237$		−	2042.77i		−	0.559882i
$238$			869.218i			0.236735i
$239$	5592.88			1.51370			0.756848	−	0.653591i	$-0.226738\pi$
$239$	5592.88			1.51370			0.756848	+	0.653591i	$0.226738\pi$
$240$	1222.40	+	818.621i	0.328774	+	0.220174i
$241$	5802.50			1.55092			0.775460	−	0.631397i	$-0.217518\pi$
$241$	5802.50			1.55092			0.775460	+	0.631397i	$0.217518\pi$
$242$		−	10751.0i		−	2.85579i
$243$			3386.03i			0.893884i
$244$	82.3141			0.0215968
$245$	−2000.05	+	2986.57i	−0.521545	+	0.778795i
$246$	−1657.42			−0.429567
$247$		−	480.007i		−	0.123652i
$248$			2724.44i			0.697589i
$249$	421.758			0.107341
$250$	831.155	−	4111.53i	0.210268	−	1.04014i
$251$	−1009.96			−0.253977			−0.126988	−	0.991904i	$-0.540531\pi$
$251$	−1009.96			−0.253977			−0.126988	+	0.991904i	$0.540531\pi$
$252$		−	110.277i		−	0.0275666i
$253$		−	1612.12i		−	0.400605i
$254$	2028.68			0.501146
$255$	719.469	−	1074.34i	0.176686	−	0.263836i
$256$	1526.03			0.372566
$257$		−	3339.27i		−	0.810499i	−0.914206	−	0.405249i	$-0.867185\pi$
$257$		−	3339.27i		−	0.810499i	0.914206	−	0.405249i	$-0.132815\pi$
$258$		−	670.314i		−	0.161752i
$259$	−61.9384			−0.0148597
$260$	−42.0170	−	28.1380i	−0.0100223	−	0.00671172i
$261$	−25.5386			−0.00605671
$262$			4281.25i			1.00953i
$263$		−	56.7202i		−	0.0132985i	−0.999978	−	0.00664927i	$-0.997883\pi$
$263$		−	56.7202i		−	0.0132985i	0.999978	−	0.00664927i	$-0.00211654\pi$
$264$	2723.85			0.635004
$265$	−724.791	−	485.379i	−0.168013	−	0.112515i
$266$	1490.31			0.343522
$267$		−	1347.53i		−	0.308867i
$268$			1016.65i			0.231723i
$269$	−4624.65			−1.04821			−0.524107	−	0.851652i	$-0.675601\pi$
$269$	−4624.65			−1.04821			−0.524107	+	0.851652i	$0.675601\pi$
$270$	−1748.76	+	2611.33i	−0.394171	+	0.588594i
$271$	−2283.18			−0.511784			−0.255892	−	0.966705i	$-0.582369\pi$
$271$	−2283.18			−0.511784			−0.255892	+	0.966705i	$0.582369\pi$
$272$		−	4437.07i		−	0.989106i
$273$			38.5033i			0.00853599i
$274$	−3542.46			−0.781049
$275$	−3336.07	−	8101.52i	−0.731536	−	1.77651i
$276$	−42.9733			−0.00937206
$277$		−	7838.09i		−	1.70016i	−0.526651	−	0.850082i	$-0.676552\pi$
$277$		−	7838.09i		−	1.70016i	0.526651	−	0.850082i	$-0.323448\pi$
$278$			5844.49i			1.26090i
$279$	−3060.26			−0.656678
$280$	−605.384	+	903.987i	−0.129209	+	0.192941i
$281$	1213.38			0.257595			0.128798	−	0.991671i	$-0.458888\pi$
$281$	1213.38			0.257595			0.128798	+	0.991671i	$0.458888\pi$
$282$			3016.04i			0.636888i
$283$			4124.97i			0.866445i	0.901287	+	0.433222i	$0.142624\pi$
$283$			4124.97i			0.866445i	−0.901287	+	0.433222i	$0.857376\pi$
$284$	−203.059			−0.0424272
$285$	−1842.01	−	1233.56i	−0.382847	−	0.256386i
$286$	−943.171			−0.195003
$287$		−	1382.76i		−	0.284397i
$288$			1069.97i			0.218919i
$289$	1013.35			0.206260
$290$	−30.2112	−	20.2319i	−0.00611746	−	0.00409675i
$291$	1877.87			0.378292
$292$			524.690i			0.105155i
$293$		−	3180.35i		−	0.634123i	−0.948405	−	0.317061i	$-0.897304\pi$
$293$		−	3180.35i		−	0.634123i	0.948405	−	0.317061i	$-0.102696\pi$
$294$	1787.06			0.354502
$295$	76.9186	−	114.858i	0.0151809	−	0.0226689i
$296$	280.261			0.0550331
$297$			6564.40i			1.28251i
$298$		−	1119.10i		−	0.217543i
$299$	−103.113			−0.0199438
$300$	−215.958	+	88.9277i	−0.0415611	+	0.0171141i
$301$	559.232			0.107088
$302$			4971.46i			0.947269i
$303$			37.2386i			0.00706040i
$304$	−7607.56			−1.43527
$305$	507.578	−	757.940i	0.0952913	−	0.142293i
$306$	4417.86			0.825335
$307$			676.187i			0.125707i	0.998023	+	0.0628535i	$0.0200201\pi$
$307$			676.187i			0.125707i	−0.998023	+	0.0628535i	$0.979980\pi$
$308$		−	327.936i		−	0.0606684i
$309$	3370.48			0.620517
$310$	−3620.18	−	2424.37i	−0.663266	−	0.444177i
$311$	−2569.81			−0.468554			−0.234277	−	0.972170i	$-0.575272\pi$
$311$	−2569.81			−0.468554			−0.234277	+	0.972170i	$0.575272\pi$
$312$		−	174.221i		−	0.0316131i
$313$		−	8661.99i		−	1.56423i	−0.623133	−	0.782116i	$-0.714141\pi$
$313$		−	8661.99i		−	1.56423i	0.623133	−	0.782116i	$-0.285859\pi$
$314$	7532.03			1.35368
$315$	−1015.42	−	680.006i	−0.181626	−	0.121632i
$316$	1112.82			0.198105
$317$			8629.98i			1.52905i	0.644596	+	0.764524i	$0.277026\pi$
$317$			8629.98i			1.52905i	−0.644596	+	0.764524i	$0.722974\pi$
$318$			433.690i			0.0764784i
$319$	−75.9455			−0.0133296
$320$	2688.60	−	4014.74i	0.469679	−	0.701346i
$321$	−3633.03			−0.631701
$322$		−	320.143i		−	0.0554064i
$323$			6686.12i			1.15178i
$324$	−467.064			−0.0800865
$325$	−518.184	+	213.379i	−0.0884421	+	0.0364189i
$326$	−7116.55			−1.20905
$327$		−	2900.77i		−	0.490560i
$328$			6256.75i			1.05327i
$329$	−2516.23			−0.421655
$330$	−2423.84	+	3619.39i	−0.404327	+	0.603760i
$331$	−17.0421			−0.00282997			−0.00141498	−	0.999999i	$-0.500450\pi$
$331$	−17.0421			−0.00282997			−0.00141498	+	0.999999i	$0.500450\pi$
$332$			229.759i			0.0379809i
$333$			314.807i			0.0518057i
$334$	1787.37			0.292816
$335$	9361.20	+	6269.02i	1.52674	+	1.02243i
$336$	610.233			0.0990801
$337$			7071.96i			1.14313i	0.820557	+	0.571564i	$0.193663\pi$
$337$			7071.96i			1.14313i	−0.820557	+	0.571564i	$0.806337\pi$
$338$		−	6533.92i		−	1.05148i
$339$	−824.683			−0.132126
$340$	585.264	+	391.941i	0.0933541	+	0.0625175i
$341$	−9100.47			−1.44521
$342$		−	7574.62i		−	1.19763i
$343$			3081.57i			0.485099i
$344$	−2530.43			−0.396603
$345$	−264.989	+	395.694i	−0.0413522	+	0.0617491i
$346$	−6302.40			−0.979246
$347$			3476.24i			0.537793i	0.963169	+	0.268896i	$0.0866589\pi$
$347$			3476.24i			0.537793i	−0.963169	+	0.268896i	$0.913341\pi$
$348$			2.02444i			0.000311842i
$349$	−10465.9			−1.60523			−0.802615	−	0.596497i	$-0.796559\pi$
$349$	−10465.9			−1.60523			−0.802615	+	0.596497i	$0.796559\pi$
$350$	−662.494	−	1608.84i	−0.101177	−	0.245704i
$351$	419.868			0.0638487
$352$			3181.84i			0.481797i
$353$			272.482i			0.0410843i	0.999789	+	0.0205422i	$0.00653923\pi$
$353$			272.482i			0.0410843i	−0.999789	+	0.0205422i	$0.993461\pi$
$354$	−68.7274			−0.0103187
$355$	−1252.13	+	1869.74i	−0.187201	+	0.279537i
$356$	734.084			0.109288
$357$		−	536.321i		−	0.0795101i
$358$			11650.4i			1.71995i
$359$	−1299.34			−0.191022			−0.0955108	−	0.995428i	$-0.530448\pi$
$359$	−1299.34			−0.191022			−0.0955108	+	0.995428i	$0.530448\pi$
$360$	4594.58	+	3076.91i	0.672655	+	0.450465i
$361$	4604.66			0.671330
$362$		−	4007.74i		−	0.581884i
$363$			6633.53i			0.959146i
$364$	−20.9752			−0.00302033
$365$	4831.29	+	3235.43i	0.692826	+	0.463973i
$366$	−453.525			−0.0647709
$367$			964.042i			0.137119i	0.997647	+	0.0685594i	$0.0218403\pi$
$367$			964.042i			0.137119i	−0.997647	+	0.0685594i	$0.978160\pi$
$368$			1634.22i			0.231494i
$369$	−7027.99			−0.991497
$370$	−249.392	+	372.404i	−0.0350413	+	0.0523254i
$371$	−361.821			−0.0506329
$372$			242.586i			0.0338105i
$373$		−	10855.9i		−	1.50697i	−0.657467	−	0.753483i	$-0.728372\pi$
$373$		−	10855.9i		−	1.50697i	0.657467	−	0.753483i	$-0.271628\pi$
$374$	13137.6			1.81639
$375$	−512.836	+	2536.87i	−0.0706206	+	0.349343i
$376$	11385.5			1.56160
$377$			4.85757i			0.000663601i
$378$			1303.59i			0.177380i
$379$	−9239.76			−1.25228			−0.626141	−	0.779710i	$-0.715366\pi$
$379$	−9239.76			−1.25228			−0.626141	+	0.779710i	$0.715366\pi$
$380$	672.000	−	1003.46i	0.0907181	−	0.135464i
$381$	−1251.73			−0.168315
$382$		−	8595.28i		−	1.15124i
$383$		−	9306.05i		−	1.24156i	−0.783985	−	0.620779i	$-0.786816\pi$
$383$		−	9306.05i		−	1.24156i	0.783985	−	0.620779i	$-0.213184\pi$
$384$	−3074.84			−0.408626
$385$	−3019.60	−	2022.17i	−0.399722	−	0.267686i
$386$	5455.78			0.719408
$387$		−	2842.34i		−	0.373344i
$388$			1023.00i			0.133853i
$389$	5841.85			0.761423			0.380712	−	0.924694i	$-0.375679\pi$
$389$	5841.85			0.761423			0.380712	+	0.924694i	$0.375679\pi$
$390$	231.501	+	155.032i	0.0300577	+	0.0201291i
$391$	1436.28			0.185770
$392$		−	6746.13i		−	0.869212i
$393$		−	2641.60i		−	0.339061i
$394$	−6600.34			−0.843961
$395$	6862.07	−	10246.8i	0.874097	−	1.30524i
$396$	−1666.76			−0.211509
$397$			11883.2i			1.50227i	0.660147	+	0.751137i	$0.270494\pi$
$397$			11883.2i			1.50227i	−0.660147	+	0.751137i	$0.729506\pi$
$398$			5627.94i			0.708802i
$399$	−919.546			−0.115376
$400$	3381.81	+	8212.62i	0.422727	+	1.02658i
$401$	−6104.05			−0.760154			−0.380077	−	0.924955i	$-0.624103\pi$
$401$	−6104.05			−0.760154			−0.380077	+	0.924955i	$0.624103\pi$
$402$		−	5601.42i		−	0.694959i
$403$			582.078i			0.0719488i
$404$	−20.2862			−0.00249821
$405$	−2880.08	+	4300.68i	−0.353364	+	0.527660i
$406$	−15.0817			−0.00184357
$407$			936.157i			0.114014i
$408$			2426.76i			0.294467i
$409$	6612.24			0.799399			0.399699	−	0.916646i	$-0.369114\pi$
$409$	6612.24			0.799399			0.399699	+	0.916646i	$0.369114\pi$
$410$	−8313.85	−	5567.63i	−1.00144	−	0.670648i
$411$	2185.75			0.262324
$412$			1836.11i			0.219560i
$413$		−	57.3381i		−	0.00683154i
$414$	−1627.15			−0.193164
$415$	2115.59	+	1416.77i	0.250242	+	0.167582i
$416$	203.514			0.0239858
$417$		−	3606.14i		−	0.423485i
$418$		−	22525.1i		−	2.63573i
$419$	2677.47			0.312179			0.156090	−	0.987743i	$-0.450111\pi$
$419$	2677.47			0.312179			0.156090	+	0.987743i	$0.450111\pi$
$420$	−53.9038	+	80.4917i	−0.00626247	+	0.00935141i
$421$	6839.72			0.791799			0.395900	−	0.918294i	$-0.370433\pi$
$421$	6839.72			0.791799			0.395900	+	0.918294i	$0.370433\pi$
$422$			6036.79i			0.696366i
$423$			12788.9i			1.47002i
$424$	1637.17			0.187519
$425$	7217.89	−	2972.20i	0.823810	−	0.339231i
$426$	1118.79			0.127243
$427$		−	378.369i		−	0.0428818i
$428$		−	1979.14i		−	0.223517i
$429$	581.951			0.0654938
$430$	2251.72	−	3362.38i	0.252530	−	0.377089i
$431$	−5917.58			−0.661345			−0.330673	−	0.943746i	$-0.607276\pi$
$431$	−5917.58			−0.661345			−0.330673	+	0.943746i	$0.607276\pi$
$432$		−	6654.42i		−	0.741113i
$433$		−	12628.2i		−	1.40155i	−0.713382	−	0.700775i	$-0.752838\pi$
$433$		−	12628.2i		−	1.40155i	0.713382	−	0.700775i	$-0.247162\pi$
$434$	−1807.22			−0.199883
$435$	18.6408	+	12.4834i	0.00205461	+	0.00137594i
$436$	1580.24			0.173577
$437$		−	2462.57i		−	0.269567i
$438$		−	2890.88i		−	0.315369i
$439$	−11504.1			−1.25071			−0.625355	−	0.780340i	$-0.715046\pi$
$439$	−11504.1			−1.25071			−0.625355	+	0.780340i	$0.715046\pi$
$440$	13663.1	+	9149.96i	1.48038	+	0.991380i
$441$	7577.69			0.818237
$442$		−	840.300i		−	0.0904275i
$443$		−	7586.49i		−	0.813645i	−0.913507	−	0.406823i	$-0.866637\pi$
$443$		−	7586.49i		−	0.813645i	0.913507	−	0.406823i	$-0.133363\pi$
$444$	24.9546			0.00266733
$445$	4526.62	−	6759.37i	0.482208	−	0.720056i
$446$	15301.0			1.62449
$447$			690.502i			0.0730640i
$448$		−	2004.19i		−	0.211359i
$449$	−13825.1			−1.45311			−0.726556	−	0.687108i	$-0.758880\pi$
$449$	−13825.1			−1.45311			−0.726556	+	0.687108i	$0.758880\pi$
$450$	−8177.06	+	3367.17i	−0.856601	+	0.352734i
$451$	−20899.5			−2.18208
$452$		−	449.257i		−	0.0467506i
$453$		−	3067.46i		−	0.318150i
$454$	13586.4			1.40450
$455$	−129.341	+	193.137i	−0.0133265	+	0.0198998i
$456$	4160.78			0.427295
$457$			7103.77i			0.727135i	0.931568	+	0.363567i	$0.118441\pi$
$457$			7103.77i			0.727135i	−0.931568	+	0.363567i	$0.881559\pi$
$458$		−	11734.8i		−	1.19723i
$459$	−5848.43			−0.594730
$460$	−215.559	−	144.356i	−0.0218489	−	0.0146318i
$461$	9424.49			0.952152			0.476076	−	0.879404i	$-0.342059\pi$
$461$	9424.49			0.952152			0.476076	+	0.879404i	$0.342059\pi$
$462$			1806.83i			0.181950i
$463$			2384.81i			0.239377i	0.992812	+	0.119688i	$0.0381896\pi$
$463$			2384.81i			0.239377i	−0.992812	+	0.119688i	$0.961810\pi$
$464$	76.9869			0.00770264
$465$	2233.71	+	1495.87i	0.222765	+	0.149181i
$466$	−1439.77			−0.143125
$467$			12732.2i			1.26162i	0.775936	+	0.630811i	$0.217278\pi$
$467$			12732.2i			1.26162i	−0.775936	+	0.630811i	$0.782722\pi$
$468$			106.608i			0.0105298i
$469$	4673.18			0.460101
$470$	−10131.5	+	15128.8i	−0.994322	+	1.48477i
$471$	−4647.38			−0.454649
$472$			259.445i			0.0253007i
$473$		−	8452.41i		−	0.821654i
$474$	−6131.32			−0.594137
$475$	−5095.98	−	12375.4i	−0.492252	−	1.19542i
$476$	292.168			0.0281334
$477$			1838.98i			0.176522i
$478$		−	16786.9i		−	1.60631i
$479$	7516.86			0.717023			0.358512	−	0.933525i	$-0.383284\pi$
$479$	7516.86			0.717023			0.358512	+	0.933525i	$0.383284\pi$
$480$	523.008	−	780.980i	0.0497332	−	0.0742640i
$481$	59.8778			0.00567608
$482$		−	17416.1i		−	1.64581i
$483$			197.533i			0.0186088i
$484$	−3613.71			−0.339379
$485$	9419.65	+	6308.17i	0.881906	+	0.590596i
$486$	10163.1			0.948575
$487$		−	2100.90i		−	0.195484i	−0.995212	−	0.0977421i	$-0.968838\pi$
$487$		−	2100.90i		−	0.195484i	0.995212	−	0.0977421i	$-0.0311620\pi$
$488$			1712.05i			0.158813i
$489$	4391.02			0.406071
$490$	8964.13	+	6003.11i	0.826445	+	0.553455i
$491$	−8863.36			−0.814660			−0.407330	−	0.913281i	$-0.633540\pi$
$491$	−8863.36			−0.814660			−0.407330	+	0.913281i	$0.633540\pi$
$492$			557.106i			0.0510493i
$493$		−	67.6621i		−	0.00618124i
$494$	−1440.73			−0.131218
$495$	−10277.8	+	15347.3i	−0.933240	+	1.39356i
$496$	9225.26			0.835134
$497$			933.388i			0.0842418i
$498$		−	1265.90i		−	0.113908i
$499$	7113.92			0.638202			0.319101	−	0.947721i	$-0.396619\pi$
$499$	7113.92			0.638202			0.319101	+	0.947721i	$0.396619\pi$
$500$	−1382.00	−	279.374i	−0.123610	−	0.0249880i
$501$	−1102.83			−0.0983452
$502$			3031.37i			0.269516i
$503$			8350.84i			0.740250i	0.928982	+	0.370125i	$0.120685\pi$
$503$			8350.84i			0.740250i	−0.928982	+	0.370125i	$0.879315\pi$
$504$	2293.65			0.202713
$505$	−125.092	+	186.793i	−0.0110228	+	0.0164598i
$506$	−4838.74			−0.425115
$507$			4031.53i			0.353149i
$508$		−	681.897i		−	0.0595557i
$509$	7279.13			0.633874			0.316937	−	0.948447i	$-0.397346\pi$
$509$	7279.13			0.633874			0.316937	+	0.948447i	$0.397346\pi$
$510$	−3224.62	−	2159.47i	−0.279978	−	0.187496i
$511$	2411.82			0.208791
$512$			8702.21i			0.751146i
$513$			10027.4i			0.863002i
$514$	−10022.8			−0.860088
$515$	16906.7	+	11322.1i	1.44660	+	0.968762i
$516$	−225.311			−0.0192224
$517$			38031.1i			3.23522i
$518$			185.907i			0.0157689i
$519$	3888.68			0.328890
$520$	585.243	−	873.913i	0.0493550	−	0.0736992i
$521$	19200.3			1.61455			0.807275	−	0.590175i	$-0.200941\pi$
$521$	19200.3			1.61455			0.807275	+	0.590175i	$0.200941\pi$
$522$			76.6536i			0.00642727i
$523$			3390.81i			0.283499i	0.989903	+	0.141749i	$0.0452727\pi$
$523$			3390.81i			0.283499i	−0.989903	+	0.141749i	$0.954727\pi$
$524$	1439.05			0.119971
$525$	408.769	+	992.681i	0.0339812	+	0.0825222i
$526$	−170.245			−0.0141122
$527$		−	8107.88i		−	0.670180i
$528$		−	9223.25i		−	0.760209i
$529$	−529.000			−0.0434783
$530$	−1456.85	+	2175.44i	−0.119399	+	0.178293i
$531$	−291.425			−0.0238169
$532$		−	500.935i		−	0.0408239i
$533$			1336.76i			0.108633i
$534$	−4044.58			−0.327764
$535$	−18223.7	−	12204.1i	−1.47267	−	0.986222i
$536$	−21145.3			−1.70399
$537$		−	7188.49i		−	0.577665i
$538$			13880.8i			1.11235i
$539$	22534.2			1.80077
$540$	877.740	+	587.806i	0.0699480	+	0.0468429i
$541$	−22372.5			−1.77795			−0.888973	−	0.457959i	$-0.848581\pi$
$541$	−22372.5			−1.77795			−0.888973	+	0.457959i	$0.848581\pi$
$542$			6852.93i			0.543097i
$543$			2472.84i			0.195432i
$544$	−2834.79			−0.223421
$545$	9744.30	−	14550.6i	0.765871	−	1.14364i
$546$	115.567			0.00905825
$547$		−	1961.29i		−	0.153306i	−0.997058	−	0.0766531i	$-0.975577\pi$
$547$		−	1961.29i		−	0.153306i	0.997058	−	0.0766531i	$-0.0244234\pi$
$548$			1190.72i			0.0928192i
$549$	−1923.09			−0.149500
$550$	−24316.6	+	10013.1i	−1.88520	+	0.776294i
$551$	−116.010			−0.00896948
$552$		−	893.802i		−	0.0689180i
$553$		−	5115.26i		−	0.393351i
$554$	−23525.9			−1.80419
$555$	153.879	−	229.779i	0.0117690	−	0.0175740i
$556$	1964.49			0.149844
$557$		−	10380.6i		−	0.789662i	−0.918754	−	0.394831i	$-0.870803\pi$
$557$		−	10380.6i		−	0.789662i	0.918754	−	0.394831i	$-0.129197\pi$
$558$			9185.32i			0.696856i
$559$	−540.627			−0.0409054
$560$	3061.00	+	2049.90i	0.230984	+	0.154686i
$561$	−8106.12			−0.610054
$562$		−	3641.94i		−	0.273356i
$563$		−	22307.8i		−	1.66992i	−0.550314	−	0.834958i	$-0.685492\pi$
$563$		−	22307.8i		−	1.66992i	0.550314	−	0.834958i	$-0.314508\pi$
$564$	1013.77			0.0756872
$565$	−4136.71	−	2770.28i	−0.308023	−	0.206277i
$566$	12381.0			0.919457
$567$			2146.93i			0.159017i
$568$		−	4223.42i		−	0.311991i
$569$	12046.6			0.887557			0.443778	−	0.896137i	$-0.353638\pi$
$569$	12046.6			0.887557			0.443778	+	0.896137i	$0.353638\pi$
$570$	−3702.51	+	5528.76i	−0.272072	+	0.406271i
$571$	−16459.1			−1.20629			−0.603147	−	0.797630i	$-0.706087\pi$
$571$	−16459.1			−1.20629			−0.603147	+	0.797630i	$0.706087\pi$
$572$			317.026i			0.0231740i
$573$			5303.42i			0.386656i
$574$	−4150.33			−0.301797
$575$	−2658.43	+	1094.70i	−0.192807	+	0.0793948i
$576$	−10186.4			−0.736865
$577$			23457.0i			1.69242i	0.532849	+	0.846210i	$0.321121\pi$
$577$			23457.0i			1.69242i	−0.532849	+	0.846210i	$0.678879\pi$
$578$		−	3041.56i		−	0.218879i
$579$	−3366.30			−0.241621
$580$	−6.80050	+	10.1548i	−0.000486854	+	0.000726993i
$581$	1056.12			0.0754134
$582$		−	5636.40i		−	0.401437i
$583$			5468.67i			0.388489i
$584$	−10913.0			−0.773262
$585$	981.635	+	657.383i	0.0693771	+	0.0464606i
$586$	−9545.75			−0.672920
$587$		−	25643.6i		−	1.80311i	−0.432666	−	0.901554i	$-0.642427\pi$
$587$		−	25643.6i		−	1.80311i	0.432666	−	0.901554i	$-0.357573\pi$
$588$		−	600.681i		−	0.0421287i
$589$	−13901.3			−0.972486
$590$	−344.745	−	230.869i	−0.0240558	−	0.0161097i
$591$	4072.51			0.283453
$592$		−	948.994i		−	0.0658841i
$593$			2370.35i			0.164146i	0.996626	+	0.0820730i	$0.0261541\pi$
$593$			2370.35i			0.164146i	−0.996626	+	0.0820730i	$0.973846\pi$
$594$	19702.9			1.36098
$595$	1801.61	−	2690.25i	0.124133	−	0.185361i
$596$	−376.160			−0.0258526
$597$		−	3472.53i		−	0.238059i
$598$			309.492i			0.0211640i
$599$	7893.70			0.538444			0.269222	−	0.963078i	$-0.413233\pi$
$599$	7893.70			0.538444			0.269222	+	0.963078i	$0.413233\pi$
$600$	−1849.61	−	4491.71i	−0.125850	−	0.305622i
$601$	−2543.59			−0.172638			−0.0863188	−	0.996268i	$-0.527510\pi$
$601$	−2543.59			−0.172638			−0.0863188	+	0.996268i	$0.527510\pi$
$602$		−	1678.52i		−	0.113640i
$603$		−	23751.8i		−	1.60406i
$604$	1671.04			0.112572
$605$	−22283.4	+	33274.6i	−1.49744	+	2.23604i
$606$	111.771			0.00749238
$607$		−	17729.4i		−	1.18552i	−0.805378	−	0.592762i	$-0.798037\pi$
$607$		−	17729.4i		−	1.18552i	0.805378	−	0.592762i	$-0.201963\pi$
$608$			4860.38i			0.324202i
$609$	9.30561			0.000619183
$610$	−2274.94	−	1523.49i	−0.150999	−	0.101122i
$611$	2432.52			0.161063
$612$		−	1484.97i		−	0.0980820i
$613$		−	11100.6i		−	0.731400i	−0.930733	−	0.365700i	$-0.880830\pi$
$613$		−	11100.6i		−	0.731400i	0.930733	−	0.365700i	$-0.119170\pi$
$614$	2029.56			0.133398
$615$	5129.77	+	3435.31i	0.336345	+	0.225244i
$616$	6820.74			0.446129
$617$			8011.81i			0.522761i	0.965236	+	0.261380i	$0.0841777\pi$
$617$			8011.81i			0.522761i	−0.965236	+	0.261380i	$0.915822\pi$
$618$		−	10116.4i		−	0.658482i
$619$	11470.8			0.744830			0.372415	−	0.928066i	$-0.378530\pi$
$619$	11470.8			0.744830			0.372415	+	0.928066i	$0.378530\pi$
$620$	−814.896	+	1216.84i	−0.0527855	+	0.0788218i
$621$	2154.04			0.139193
$622$			7713.22i			0.497222i
$623$		−	3374.32i		−	0.216997i
$624$	−589.931			−0.0378464
$625$	−11094.3	+	11002.6i	−0.710037	+	0.704164i
$626$	−25998.8			−1.65994
$627$			13898.3i			0.885239i
$628$		−	2531.72i		−	0.160871i
$629$	−834.051			−0.0528709
$630$	−2041.02	+	3047.75i	−0.129074	+	0.192739i
$631$	23465.8			1.48044			0.740222	−	0.672363i	$-0.234721\pi$
$631$	23465.8			1.48044			0.740222	+	0.672363i	$0.234721\pi$
$632$			23145.7i			1.45678i
$633$		−	3724.79i		−	0.233882i
$634$	25902.7			1.62260
$635$	−6278.83	−	4204.82i	−0.392390	−	0.262777i
$636$	145.775			0.00908862
$637$		−	1441.31i		−	0.0896499i
$638$			227.949i			0.0141451i
$639$	4744.01			0.293694
$640$	−15423.8	−	10329.0i	−0.952624	−	0.637955i
$641$	7241.32			0.446201			0.223101	−	0.974795i	$-0.428382\pi$
$641$	7241.32			0.446201			0.223101	+	0.974795i	$0.428382\pi$
$642$			10904.5i			0.670350i
$643$		−	4642.90i		−	0.284756i	−0.989812	−	0.142378i	$-0.954525\pi$
$643$		−	4642.90i		−	0.284756i	0.989812	−	0.142378i	$-0.0454748\pi$
$644$	−107.609			−0.00658444
$645$	−1389.35	+	2074.64i	−0.0848148	+	0.126649i
$646$	20068.3			1.22225
$647$		−	4962.37i		−	0.301531i	−0.988570	−	0.150766i	$-0.951826\pi$
$647$		−	4962.37i		−	0.301531i	0.988570	−	0.150766i	$-0.0481739\pi$
$648$		−	9714.47i		−	0.588921i
$649$	−866.626			−0.0524161
$650$	640.453	+	1555.32i	0.0386472	+	0.0938532i
$651$	1115.08			0.0671329
$652$			2392.07i			0.143682i
$653$		−	22290.2i		−	1.33581i	−0.744248	−	0.667903i	$-0.767192\pi$
$653$		−	22290.2i		−	1.33581i	0.744248	−	0.667903i	$-0.232808\pi$
$654$	−8706.61			−0.520574
$655$	8873.66	−	13250.6i	0.529348	−	0.790447i
$656$	21186.1			1.26094
$657$		−	12258.2i		−	0.727913i
$658$			7552.42i			0.447453i
$659$	15206.5			0.898881			0.449441	−	0.893310i	$-0.351623\pi$
$659$	15206.5			0.898881			0.449441	+	0.893310i	$0.351623\pi$
$660$	1216.58	+	814.719i	0.0717503	+	0.0480498i
$661$	−12506.9			−0.735948			−0.367974	−	0.929836i	$-0.619948\pi$
$661$	−12506.9			−0.735948			−0.367974	+	0.929836i	$0.619948\pi$
$662$			51.1516i			0.00300312i
$663$			518.478i			0.0303711i
$664$	−4778.75			−0.279295
$665$	−4612.56	−	3088.94i	−0.268973	−	0.180126i
$666$	944.886			0.0549753
$667$			24.9207i			0.00144668i
$668$		−	600.784i		−	0.0347979i
$669$	−9440.95			−0.545603
$670$	18816.3	−	28097.4i	1.08498	−	1.62015i
$671$	−5718.78			−0.329018
$672$		−	389.871i		−	0.0223804i
$673$			22563.7i			1.29237i	0.763181	+	0.646185i	$0.223637\pi$
$673$			22563.7i			1.29237i	−0.763181	+	0.646185i	$0.776363\pi$
$674$	21226.4			1.21307
$675$	10824.9	−	4457.51i	0.617261	−	0.254177i
$676$	−2196.23			−0.124956
$677$		−	28705.7i		−	1.62961i	−0.579732	−	0.814807i	$-0.696843\pi$
$677$		−	28705.7i		−	1.62961i	0.579732	−	0.814807i	$-0.303157\pi$
$678$			2475.27i			0.140210i
$679$	4702.36			0.265773
$680$	−8151.98	+	12172.9i	−0.459726	+	0.686485i
$681$	−8383.04			−0.471716
$682$			27314.9i			1.53364i
$683$			25920.9i			1.45218i	0.687601	+	0.726088i	$0.258664\pi$
$683$			25920.9i			1.45218i	−0.687601	+	0.726088i	$0.741336\pi$
$684$	−2546.04			−0.142325
$685$	10964.0	+	7342.38i	0.611551	+	0.409545i
$686$	9249.26			0.514779
$687$			7240.54i			0.402102i
$688$			8568.31i			0.474802i
$689$	349.783			0.0193406
$690$	1187.67	+	795.358i	0.0655271	+	0.0438823i
$691$	24160.6			1.33012			0.665059	−	0.746790i	$-0.268406\pi$
$691$	24160.6			1.33012			0.665059	+	0.746790i	$0.268406\pi$
$692$			2118.41i			0.116373i
$693$			7661.49i			0.419966i
$694$	10433.9			0.570697
$695$	12113.8	−	18088.8i	0.661153	−	0.987265i
$696$	−42.1063			−0.00229315
$697$		−	18620.0i		−	1.01188i
$698$			31413.1i			1.70344i
$699$	888.363			0.0480700
$700$	−540.776	+	222.682i	−0.0291992	+	0.0120237i
$701$	−26012.4			−1.40153			−0.700767	−	0.713390i	$-0.747159\pi$
$701$	−26012.4			−1.40153			−0.700767	+	0.713390i	$0.747159\pi$
$702$		−	1260.22i		−	0.0677551i
$703$			1430.02i			0.0767199i
$704$	−30291.9			−1.62169
$705$	6251.29	−	9334.72i	0.333953	−	0.498675i
$706$	817.849			0.0435980
$707$			93.2486i			0.00496036i
$708$			23.1012i			0.00122626i
$709$	26847.7			1.42213			0.711063	−	0.703128i	$-0.248214\pi$
$709$	26847.7			1.42213			0.711063	+	0.703128i	$0.248214\pi$
$710$	5611.99	+	3758.25i	0.296640	+	0.198654i
$711$	−25998.7			−1.37135
$712$			15268.2i			0.803653i
$713$			2986.23i			0.156851i
$714$	−1609.76			−0.0843748
$715$	2919.14	+	1954.89i	0.152685	+	0.102250i
$716$	3916.03			0.204398
$717$			10357.8i			0.539496i
$718$			3899.95i			0.202709i
$719$	−2305.77			−0.119598			−0.0597988	−	0.998210i	$-0.519046\pi$
$719$	−2305.77			−0.119598			−0.0597988	+	0.998210i	$0.519046\pi$
$720$	10418.8	−	15557.8i	0.539283	−	0.805284i
$721$	8439.96			0.435951
$722$		−	13820.8i		−	0.712405i
$723$			10746.0i			0.552763i
$724$	−1347.11			−0.0691506
$725$	51.5702	+	125.236i	0.00264175	+	0.00641540i
$726$	19910.4			1.01783
$727$		−	9913.78i		−	0.505752i	−0.967499	−	0.252876i	$-0.918624\pi$
$727$		−	9913.78i		−	0.505752i	0.967499	−	0.252876i	$-0.0813765\pi$
$728$		−	436.263i		−	0.0222102i
$729$	6228.95			0.316463
$730$	9711.07	−	14501.0i	0.492360	−	0.735215i
$731$	7530.51			0.381020
$732$			152.442i			0.00769731i
$733$		−	10235.4i		−	0.515763i	−0.966177	−	0.257882i	$-0.916976\pi$
$733$		−	10235.4i		−	0.515763i	0.966177	−	0.257882i	$-0.0830244\pi$
$734$	2893.55			0.145508
$735$	−5531.00	−	3704.01i	−0.277570	−	0.185884i
$736$	1044.09			0.0522902
$737$		−	70631.8i		−	3.53020i
$738$			21094.4i			1.05216i
$739$	8771.34			0.436616			0.218308	−	0.975880i	$-0.429946\pi$
$739$	8771.34			0.436616			0.218308	+	0.975880i	$0.429946\pi$
$740$	125.175	+	83.8277i	0.00621830	+	0.00416428i
$741$	888.953			0.0440709
$742$			1086.00i			0.0537307i
$743$			4644.04i			0.229305i	0.993406	+	0.114652i	$0.0365754\pi$
$743$			4644.04i			0.229305i	−0.993406	+	0.114652i	$0.963425\pi$
$744$	−5045.55			−0.248627
$745$	−2319.54	+	3463.64i	−0.114069	+	0.170333i
$746$	−32583.8			−1.59917
$747$		−	5367.80i		−	0.262915i
$748$		−	4415.92i		−	0.215858i
$749$	−9097.41			−0.443808
$750$	7614.38	+	1539.27i	0.370717	+	0.0749414i
$751$	30170.2			1.46595			0.732973	−	0.680257i	$-0.238132\pi$
$751$	30170.2			1.46595			0.732973	+	0.680257i	$0.238132\pi$
$752$		−	38552.6i		−	1.86951i
$753$		−	1870.40i		−	0.0905197i
$754$	14.5799			0.000704202
$755$	10304.2	−	15386.8i	0.496702	−	0.741699i
$756$	438.174			0.0210797
$757$			31955.0i			1.53425i	0.641500	+	0.767123i	$0.278312\pi$
$757$			31955.0i			1.53425i	−0.641500	+	0.767123i	$0.721688\pi$
$758$			27733.0i			1.32890i
$759$	2985.58			0.142779
$760$	20871.0	+	13976.9i	0.996146	+	0.667101i
$761$	248.185			0.0118222			0.00591111	−	0.999983i	$-0.498118\pi$
$761$	248.185			0.0118222			0.00591111	+	0.999983i	$0.498118\pi$
$762$			3757.04i			0.178613i
$763$		−	7263.78i		−	0.344648i
$764$	−2889.11			−0.136812
$765$	−13673.4	−	9156.82i	−0.646226	−	0.432766i
$766$	−27931.9			−1.31752
$767$			55.4305i			0.00260949i
$768$			2826.15i			0.132786i
$769$	8682.30			0.407142			0.203571	−	0.979060i	$-0.434745\pi$
$769$	8682.30			0.407142			0.203571	+	0.979060i	$0.434745\pi$
$770$	−6069.50	+	9063.26i	−0.284064	+	0.424178i
$771$	6184.20			0.288870
$772$		−	1833.84i		−	0.0854938i
$773$			32085.1i			1.49291i	0.665435	+	0.746456i	$0.268246\pi$
$773$			32085.1i			1.49291i	−0.665435	+	0.746456i	$0.731754\pi$
$774$	−8531.22			−0.396187
$775$	6179.61	+	15007.0i	0.286423	+	0.695569i
$776$	−21277.3			−0.984294
$777$		−	114.707i		−	0.00529615i
$778$		−	17534.2i		−	0.808009i
$779$	−31924.8			−1.46833
$780$	52.1105	−	77.8138i	0.00239212	−	0.00357203i
$781$	14107.5			0.646360
$782$		−	4310.98i		−	0.197136i
$783$		−	101.475i		−	0.00463145i
$784$	−22843.2			−1.04060
$785$	−23311.8	−	15611.5i	−1.05992	−	0.709807i
$786$	−7928.69			−0.359806
$787$			21570.4i			0.977003i	0.872563	+	0.488502i	$0.162456\pi$
$787$			21570.4i			0.977003i	−0.872563	+	0.488502i	$0.837544\pi$
$788$			2218.56i			0.100295i
$789$	105.043			0.00473973
$790$	−30755.5	−	20596.4i	−1.38510	−	0.927577i
$791$	−2065.08			−0.0928263
$792$		−	34666.9i		−	1.55535i
$793$			365.781i			0.0163799i
$794$	35667.3			1.59419
$795$	898.902	−	1342.28i	0.0401016	−	0.0598816i
$796$	1891.71			0.0842333
$797$			21181.9i			0.941406i	0.882292	+	0.470703i	$0.156000\pi$
$797$			21181.9i			0.941406i	−0.882292	+	0.470703i	$0.844000\pi$
$798$			2760.00i			0.122435i
$799$	−33883.1			−1.50025
$800$	5246.95	−	2160.60i	0.231885	−	0.0954861i
$801$	−17150.3			−0.756522
$802$			18321.2i			0.806663i
$803$		−	36452.9i		−	1.60199i
$804$	−1882.79			−0.0825883
$805$	−663.554	+	990.850i	−0.0290524	+	0.0433825i
$806$	1747.09			0.0763508
$807$		−	8564.65i		−	0.373594i
$808$		−	421.933i		−	0.0183708i
$809$	14567.6			0.633090			0.316545	−	0.948577i	$-0.397477\pi$
$809$	14567.6			0.633090			0.316545	+	0.948577i	$0.397477\pi$
$810$	12908.4	+	8644.51i	0.559944	+	0.374984i
$811$	−20407.4			−0.883603			−0.441802	−	0.897113i	$-0.645660\pi$
$811$	−20407.4			−0.883603			−0.441802	+	0.897113i	$0.645660\pi$
$812$			5.06936i			0.000219088i
$813$		−	4228.36i		−	0.182405i
$814$	2809.86			0.120989
$815$	22025.9	+	14750.3i	0.946668	+	0.633966i
$816$	8217.27			0.352527
$817$		−	12911.4i		−	0.552892i
$818$		−	19846.5i		−	0.848309i
$819$	490.039			0.0209076
$820$	−1871.43	+	2794.51i	−0.0796992	+	0.119011i
$821$	12247.9			0.520651			0.260326	−	0.965521i	$-0.416170\pi$
$821$	12247.9			0.520651			0.260326	+	0.965521i	$0.416170\pi$
$822$		−	6560.48i		−	0.278374i
$823$		−	2765.32i		−	0.117124i	−0.998284	−	0.0585621i	$-0.981348\pi$
$823$		−	2765.32i		−	0.117124i	0.998284	−	0.0585621i	$-0.0186516\pi$
$824$	−38189.3			−1.61455
$825$	15003.7	−	6178.26i	0.633165	−	0.260727i
$826$	−172.099			−0.00724951
$827$			31989.4i			1.34508i	0.740061	+	0.672540i	$0.234797\pi$
$827$			31989.4i			1.34508i	−0.740061	+	0.672540i	$0.765203\pi$
$828$			546.930i			0.0229555i
$829$	−39864.4			−1.67014			−0.835071	−	0.550142i	$-0.814574\pi$
$829$	−39864.4			−1.67014			−0.835071	+	0.550142i	$0.814574\pi$
$830$	4252.42	−	6349.91i	0.177836	−	0.265553i
$831$	14515.8			0.605955
$832$			1937.51i			0.0807344i
$833$			20076.4i			0.835060i
$834$	−10823.8			−0.449396
$835$	−5531.95	−	3704.64i	−0.229271	−	0.153538i
$836$	−7571.29			−0.313228
$837$		−	12159.7i		−	0.502150i
$838$		−	8036.38i		−	0.331279i
$839$	−17789.5			−0.732018			−0.366009	−	0.930611i	$-0.619276\pi$
$839$	−17789.5			−0.732018			−0.366009	+	0.930611i	$0.619276\pi$
$840$	−1674.15	−	1121.15i	−0.0687662	−	0.0460514i
$841$	−24387.8			−0.999952
$842$		−	20529.3i		−	0.840244i
$843$			2247.13i			0.0918094i
$844$	2029.13			0.0827554
$845$	−13542.7	+	20222.7i	−0.551343	+	0.823291i
$846$	38385.7			1.55996
$847$			16610.9i			0.673858i
$848$		−	5543.66i		−	0.224493i
$849$	−7639.27			−0.308809
$850$	−8921.01	−	21664.4i	−0.359986	−	0.874213i
$851$	307.190			0.0123741
$852$		−	376.056i		−	0.0151214i
$853$			12460.7i			0.500173i	0.968223	+	0.250087i	$0.0804591\pi$
$853$			12460.7i			0.500173i	−0.968223	+	0.250087i	$0.919541\pi$
$854$	−1135.67			−0.0455055
$855$	−15699.8	+	23443.7i	−0.627978	+	0.937727i
$856$	41164.2			1.64365
$857$			15396.2i			0.613681i	0.951761	+	0.306840i	$0.0992718\pi$
$857$			15396.2i			0.613681i	−0.951761	+	0.306840i	$0.900728\pi$
$858$		−	1746.71i		−	0.0695010i
$859$	29631.3			1.17696			0.588479	−	0.808513i	$-0.299727\pi$
$859$	29631.3			1.17696			0.588479	+	0.808513i	$0.299727\pi$
$860$	−1130.19	−	756.867i	−0.0448129	−	0.0300104i
$861$	2560.82			0.101362
$862$			17761.5i			0.701809i
$863$			36680.3i			1.44683i	0.690415	+	0.723414i	$0.257428\pi$
$863$			36680.3i			1.44683i	−0.690415	+	0.723414i	$0.742572\pi$
$864$	−4251.43			−0.167404
$865$	19506.1	+	13062.9i	0.766736	+	0.513469i
$866$	−37903.2			−1.48730
$867$			1876.69i			0.0735129i
$868$			607.456i			0.0237539i
$869$	−77313.7			−3.01805
$870$	37.4686	−	55.9499i	0.00146012	−	0.00218032i
$871$	−4517.70			−0.175748
$872$			32867.3i			1.27641i
$873$		−	23900.1i		−	0.926569i
$874$	−7391.37			−0.286060
$875$	−1284.18	+	6352.55i	−0.0496152	+	0.245435i
$876$	−971.705			−0.0374782
$877$			38864.4i			1.49641i	0.663465	+	0.748207i	$0.269085\pi$
$877$			38864.4i			1.49641i	−0.663465	+	0.748207i	$0.730915\pi$
$878$			34529.4i			1.32723i
$879$	5889.88			0.226007
$880$	30982.8	−	46265.0i	1.18685	−	1.77226i
$881$	25765.2			0.985302			0.492651	−	0.870227i	$-0.336028\pi$
$881$	25765.2			0.985302			0.492651	+	0.870227i	$0.336028\pi$
$882$		−	22744.3i		−	0.868299i
$883$			36307.1i			1.38373i	0.722028	+	0.691863i	$0.243210\pi$
$883$			36307.1i			1.38373i	−0.722028	+	0.691863i	$0.756790\pi$
$884$	−282.448			−0.0107463
$885$	212.713	+	142.450i	0.00807940	+	0.00541063i
$886$	−22770.7			−0.863427
$887$		−	29180.6i		−	1.10461i	−0.833643	−	0.552304i	$-0.813749\pi$
$887$		−	29180.6i		−	1.10461i	0.833643	−	0.552304i	$-0.186251\pi$
$888$			519.031i			0.0196143i
$889$	−3134.44			−0.118252
$890$	−20288.1	−	13586.6i	−0.764111	−	0.511711i
$891$	32449.4			1.22008
$892$		−	5143.09i		−	0.193053i
$893$			58094.1i			2.17698i
$894$	2072.53			0.0775343
$895$	24147.6	−	36058.3i	0.901861	−	1.34670i
$896$	−7699.67			−0.287085
$897$		−	190.961i		−	0.00710815i
$898$			41495.8i			1.54202i
$899$	140.679			0.00521901
$900$	1131.80	+	2748.54i	0.0419185	+	0.101798i
$901$	−4872.20			−0.180152
$902$			62729.4i			2.31559i
$903$			1035.68i			0.0381673i
$904$	9344.10			0.343784
$905$	−8306.77	+	12404.1i	−0.305112	+	0.455608i
$906$	−9206.93			−0.337616
$907$		−	10796.4i		−	0.395245i	−0.980278	−	0.197622i	$-0.936678\pi$
$907$		−	10796.4i		−	0.395245i	0.980278	−	0.197622i	$-0.0633220\pi$
$908$		−	4566.77i		−	0.166909i
$909$	473.943			0.0172934
$910$	579.698	+	388.213i	0.0211174	+	0.0141419i
$911$	27051.1			0.983801			0.491901	−	0.870651i	$-0.336302\pi$
$911$	27051.1			0.983801			0.491901	+	0.870651i	$0.336302\pi$
$912$		−	14088.9i		−	0.511546i
$913$		−	15962.5i		−	0.578622i
$914$	21321.8			0.771623
$915$	1403.67	+	940.014i	0.0507148	+	0.0339627i
$916$	−3944.38			−0.142277
$917$		−	6614.78i		−	0.238211i
$918$			17553.9i			0.631118i
$919$	31635.3			1.13553			0.567766	−	0.823190i	$-0.307808\pi$
$919$	31635.3			1.13553			0.567766	+	0.823190i	$0.307808\pi$
$920$	3002.47	−	4483.42i	0.107596	−	0.160667i
$921$	−1252.27			−0.0448032
$922$		−	28287.4i		−	1.01041i
$923$		−	902.335i		−	0.0321785i
$924$	607.324			0.0216228
$925$	1543.75	−	635.691i	0.0548738	−	0.0225961i
$926$	7157.96			0.254023
$927$		−	42896.7i		−	1.51986i
$928$		−	49.1861i		−	0.00173988i
$929$	14350.2			0.506799			0.253399	−	0.967362i	$-0.418451\pi$
$929$	14350.2			0.506799			0.253399	+	0.967362i	$0.418451\pi$
$930$	4489.83	−	6704.42i	0.158309	−	0.236394i
$931$	34421.9			1.21174
$932$			483.948i			0.0170088i
$933$		−	4759.18i		−	0.166997i
$934$	38215.5			1.33881
$935$	−40661.3	−	27230.1i	−1.42221	−	0.952428i
$936$	−2217.34			−0.0774317
$937$		−	12715.3i		−	0.443318i	−0.975124	−	0.221659i	$-0.928853\pi$
$937$		−	12715.3i		−	0.443318i	0.975124	−	0.221659i	$-0.0711472\pi$
$938$		−	14026.4i		−	0.488251i
$939$	16041.6			0.557507
$940$	5085.22	+	3405.48i	0.176448	+	0.118164i
$941$	39022.8			1.35187			0.675934	−	0.736962i	$-0.263741\pi$
$941$	39022.8			1.35187			0.675934	+	0.736962i	$0.263741\pi$
$942$			13949.0i			0.482466i
$943$			6857.96i			0.236825i
$944$	878.510			0.0302893
$945$	2701.94	−	4034.66i	0.0930095	−	0.138886i
$946$	−25369.7			−0.871925
$947$		−	1892.80i		−	0.0649500i	−0.999473	−	0.0324750i	$-0.989661\pi$
$947$		−	1892.80i		−	0.0649500i	0.999473	−	0.0324750i	$-0.0103389\pi$
$948$			2060.91i			0.0706067i
$949$	−2331.58			−0.0797536
$950$	−37144.5	+	15295.5i	−1.26856	+	0.522369i
$951$	−15982.4			−0.544967
$952$			6076.80i			0.206881i
$953$			2287.30i			0.0777471i	0.999244	+	0.0388736i	$0.0123770\pi$
$953$			2287.30i			0.0777471i	−0.999244	+	0.0388736i	$0.987623\pi$
$954$	5519.66			0.187322
$955$	−17815.3	+	26602.6i	−0.603654	+	0.901404i
$956$	−5642.55			−0.190892
$957$		−	140.648i		−	0.00475079i
$958$		−	22561.7i		−	0.760893i
$959$	5473.30			0.184298
$960$	7435.14	+	4979.17i	0.249967	+	0.167398i
$961$	−12933.6			−0.434146
$962$		−	179.722i		−	0.00602336i
$963$			46238.3i			1.54726i
$964$	−5854.02			−0.195586
$965$	−16885.8	−	11308.1i	−0.563287	−	0.377223i
$966$	592.891			0.0197474
$967$		−	40118.9i		−	1.33417i	−0.744984	−	0.667083i	$-0.767543\pi$
$967$		−	40118.9i		−	1.33417i	0.744984	−	0.667083i	$-0.232457\pi$
$968$		−	75161.5i		−	2.49564i
$969$	−12382.4			−0.410506
$970$	18933.8	−	28272.9i	0.626731	−	0.935864i
$971$	−7522.78			−0.248628			−0.124314	−	0.992243i	$-0.539673\pi$
$971$	−7522.78			−0.248628			−0.124314	+	0.992243i	$0.539673\pi$
$972$		−	3416.10i		−	0.112728i
$973$		−	9030.08i		−	0.297524i
$974$	−6305.80			−0.207444
$975$	−395.170	−	959.655i	−0.0129801	−	0.0315216i
$976$	5797.20			0.190127
$977$			7848.52i			0.257008i	0.991709	+	0.128504i	$0.0410175\pi$
$977$			7848.52i			0.257008i	−0.991709	+	0.128504i	$0.958983\pi$
$978$		−	13179.6i		−	0.430916i
$979$	−51000.6			−1.66495
$980$	2017.81	−	3013.09i	0.0657720	−	0.0982139i
$981$	−36918.7			−1.20155
$982$			26603.2i			0.864503i
$983$			23763.8i			0.771055i	0.922696	+	0.385528i	$0.125981\pi$
$983$			23763.8i			0.771055i	−0.922696	+	0.385528i	$0.874019\pi$
$984$	−11587.3			−0.375394
$985$	20428.2	+	13680.4i	0.660810	+	0.442532i
$986$	−203.087			−0.00655942
$987$		−	4659.96i		−	0.150282i
$988$			484.270i			0.0155938i
$989$	−2773.57			−0.0891754
$990$	46064.7	+	30848.7i	1.47882	+	0.990339i
$991$	6057.69			0.194176			0.0970882	−	0.995276i	$-0.469047\pi$
$991$	6057.69			0.194176			0.0970882	+	0.995276i	$0.469047\pi$
$992$		−	5893.91i		−	0.188641i
$993$		−	31.5613i		−	0.00100863i
$994$	2801.55			0.0893960
$995$	11664.9	−	17418.6i	0.371661	−	0.554982i
$996$	−425.504			−0.0135367
$997$		−	22096.0i		−	0.701893i	−0.936395	−	0.350947i	$-0.885860\pi$
$997$		−	22096.0i		−	0.701893i	0.936395	−	0.350947i	$-0.114140\pi$
$998$		−	21352.3i		−	0.677249i
$999$	−1250.85			−0.0396148

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.b.a.24.10	✓	34
5.2	odd	4		575.4.a.q.1.13		17
5.3	odd	4		575.4.a.r.1.5		17
5.4	even	2	inner	115.4.b.a.24.25	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.b.a.24.10	✓	34	1.1	even	1	trivial
115.4.b.a.24.25	yes	34	5.4	even	2	inner
575.4.a.q.1.13		17	5.2	odd	4
575.4.a.r.1.5		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)

\(f(q)\)	\(=\)	\(q-3.00148i q^{2} +1.85196i q^{3} -1.00888 q^{4} +(-6.22111 + 9.28966i) q^{5} +5.55862 q^{6} +4.63746i q^{7} -20.9837i q^{8} +23.5702 q^{9} +O(q^{10})\)	\(q-3.00148i q^{2} +1.85196i q^{3} -1.00888 q^{4} +(-6.22111 + 9.28966i) q^{5} +5.55862 q^{6} +4.63746i q^{7} -20.9837i q^{8} +23.5702 q^{9} +(27.8827 + 18.6725i) q^{10} +70.0921 q^{11} -1.86840i q^{12} -4.48318i q^{13} +13.9193 q^{14} +(-17.2041 - 11.5212i) q^{15} -71.0532 q^{16} +62.4472i q^{17} -70.7456i q^{18} +107.068 q^{19} +(6.27636 - 9.37215i) q^{20} -8.58839 q^{21} -210.380i q^{22} -23.0000i q^{23} +38.8610 q^{24} +(-47.5955 - 115.584i) q^{25} -13.4562 q^{26} +93.6540i q^{27} -4.67864i q^{28} -1.08351 q^{29} +(-34.5808 + 51.6377i) q^{30} -129.836 q^{31} +45.3951i q^{32} +129.808i q^{33} +187.434 q^{34} +(-43.0804 - 28.8502i) q^{35} -23.7796 q^{36} +13.3561i q^{37} -321.364i q^{38} +8.30266 q^{39} +(194.931 + 130.542i) q^{40} -298.172 q^{41} +25.7779i q^{42} -120.590i q^{43} -70.7145 q^{44} +(-146.633 + 218.960i) q^{45} -69.0340 q^{46} +542.588i q^{47} -131.588i q^{48} +321.494 q^{49} +(-346.923 + 142.857i) q^{50} -115.650 q^{51} +4.52299i q^{52} +78.0212i q^{53} +281.101 q^{54} +(-436.051 + 651.131i) q^{55} +97.3112 q^{56} +198.286i q^{57} +3.25213i q^{58} -12.3641 q^{59} +(17.3568 + 11.6236i) q^{60} -81.5896 q^{61} +389.700i q^{62} +109.306i q^{63} -432.173 q^{64} +(41.6472 + 27.8904i) q^{65} +389.615 q^{66} -1007.70i q^{67} -63.0017i q^{68} +42.5951 q^{69} +(-86.5932 + 129.305i) q^{70} +201.271 q^{71} -494.591i q^{72} -520.072i q^{73} +40.0881 q^{74} +(214.057 - 88.1449i) q^{75} -108.019 q^{76} +325.049i q^{77} -24.9203i q^{78} -1103.03 q^{79} +(442.030 - 660.060i) q^{80} +462.953 q^{81} +894.957i q^{82} -227.736i q^{83} +8.66466 q^{84} +(-580.113 - 388.491i) q^{85} -361.949 q^{86} -2.00662i q^{87} -1470.79i q^{88} -727.623 q^{89} +(657.203 + 440.116i) q^{90} +20.7906 q^{91} +23.2042i q^{92} -240.451i q^{93} +1628.57 q^{94} +(-666.085 + 994.629i) q^{95} -84.0699 q^{96} -1013.99i q^{97} -964.958i q^{98} +1652.09 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9}+O(q^{10}) \) 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

L-functions

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