LMFDB - Embedded newform 115.4.b.a.24.7

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			24.7
Character	$\chi$	$=$	115.24
Dual form			115.4.b.a.24.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.60232i q^{2} +8.84330i q^{3} -4.97671 q^{4} +(-8.81390 + 6.87860i) q^{5} +31.8564 q^{6} -13.0981i q^{7} -10.8909i q^{8} -51.2040 q^{9} +O(q^{10})$	\(q-3.60232i q^{2} +8.84330i q^{3} -4.97671 q^{4} +(-8.81390 + 6.87860i) q^{5} +31.8564 q^{6} -13.0981i q^{7} -10.8909i q^{8} -51.2040 q^{9} +(24.7789 + 31.7505i) q^{10} -43.2873 q^{11} -44.0106i q^{12} +82.1312i q^{13} -47.1836 q^{14} +(-60.8296 - 77.9440i) q^{15} -79.0460 q^{16} -15.5900i q^{17} +184.453i q^{18} -104.117 q^{19} +(43.8642 - 34.2328i) q^{20} +115.831 q^{21} +155.935i q^{22} +23.0000i q^{23} +96.3112 q^{24} +(30.3697 - 121.255i) q^{25} +295.863 q^{26} -214.044i q^{27} +65.1855i q^{28} -53.8327 q^{29} +(-280.779 + 219.128i) q^{30} +270.783 q^{31} +197.622i q^{32} -382.802i q^{33} -56.1602 q^{34} +(90.0967 + 115.446i) q^{35} +254.828 q^{36} +294.327i q^{37} +375.062i q^{38} -726.311 q^{39} +(74.9139 + 95.9910i) q^{40} -167.636 q^{41} -417.259i q^{42} -51.4584i q^{43} +215.428 q^{44} +(451.307 - 352.212i) q^{45} +82.8534 q^{46} +278.791i q^{47} -699.028i q^{48} +171.439 q^{49} +(-436.798 - 109.401i) q^{50} +137.867 q^{51} -408.743i q^{52} -314.913i q^{53} -771.053 q^{54} +(381.530 - 297.756i) q^{55} -142.650 q^{56} -920.735i q^{57} +193.923i q^{58} +418.863 q^{59} +(302.731 + 387.905i) q^{60} -27.1566 q^{61} -975.445i q^{62} +670.676i q^{63} +79.5303 q^{64} +(-564.948 - 723.896i) q^{65} -1378.98 q^{66} +823.536i q^{67} +77.5870i q^{68} -203.396 q^{69} +(415.872 - 324.557i) q^{70} +93.0926 q^{71} +557.656i q^{72} +908.940i q^{73} +1060.26 q^{74} +(1072.29 + 268.568i) q^{75} +518.159 q^{76} +566.982i q^{77} +2616.40i q^{78} -84.2670 q^{79} +(696.704 - 543.726i) q^{80} +510.343 q^{81} +603.877i q^{82} -1255.31i q^{83} -576.455 q^{84} +(107.238 + 137.409i) q^{85} -185.370 q^{86} -476.059i q^{87} +471.435i q^{88} -839.289 q^{89} +(-1268.78 - 1625.75i) q^{90} +1075.76 q^{91} -114.464i q^{92} +2394.61i q^{93} +1004.29 q^{94} +(917.674 - 716.177i) q^{95} -1747.63 q^{96} -169.933i q^{97} -617.579i q^{98} +2216.48 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	3.60232i		−	1.27361i	−0.771024	−	0.636806i	$-0.780255\pi$
$2$		−	3.60232i		−	1.27361i	0.771024	−	0.636806i	$-0.219745\pi$
$3$			8.84330i			1.70189i	0.525251	+	0.850947i	$0.323971\pi$
$3$			8.84330i			1.70189i	−0.525251	+	0.850947i	$0.676029\pi$
$4$	−4.97671			−0.622089
$5$	−8.81390	+	6.87860i	−0.788339	+	0.615241i
$5$	−8.81390	+	6.87860i	−0.788339	+	0.615241i
$6$	31.8564			2.16755
$7$		−	13.0981i		−	0.707232i	−0.935391	−	0.353616i	$-0.884952\pi$
$7$		−	13.0981i		−	0.707232i	0.935391	−	0.353616i	$-0.115048\pi$
$8$		−	10.8909i		−	0.481313i
$9$	−51.2040			−1.89645
$10$	24.7789	+	31.7505i	0.783578	+	1.00404i
$11$	−43.2873			−1.18651			−0.593254	−	0.805015i	$-0.702157\pi$
$11$	−43.2873			−1.18651			−0.593254	+	0.805015i	$0.702157\pi$
$12$		−	44.0106i		−	1.05873i
$13$			82.1312i			1.75224i	0.482095	+	0.876119i	$0.339876\pi$
$13$			82.1312i			1.75224i	−0.482095	+	0.876119i	$0.660124\pi$
$14$	−47.1836			−0.900739
$15$	−60.8296	−	77.9440i	−1.04708	−	1.34167i
$16$	−79.0460			−1.23509
$17$		−	15.5900i		−	0.222420i	−0.993797	−	0.111210i	$-0.964527\pi$
$17$		−	15.5900i		−	0.222420i	0.993797	−	0.111210i	$-0.0354726\pi$
$18$			184.453i			2.41534i
$19$	−104.117			−1.25716			−0.628579	−	0.777746i	$-0.716363\pi$
$19$	−104.117			−1.25716			−0.628579	+	0.777746i	$0.716363\pi$
$20$	43.8642	−	34.2328i	0.490417	−	0.382734i
$21$	115.831			1.20363
$22$			155.935i			1.51115i
$23$			23.0000i			0.208514i
$23$			23.0000i			0.208514i
$24$	96.3112			0.819143
$25$	30.3697	−	121.255i	0.242957	−	0.970037i
$26$	295.863			2.23167
$27$		−	214.044i		−	1.52566i
$28$			65.1855i			0.439961i
$29$	−53.8327			−0.344706			−0.172353	−	0.985035i	$-0.555137\pi$
$29$	−53.8327			−0.344706			−0.172353	+	0.985035i	$0.555137\pi$
$30$	−280.779	+	219.128i	−1.70877	+	1.33357i
$31$	270.783			1.56884			0.784419	−	0.620231i	$-0.212961\pi$
$31$	270.783			1.56884			0.784419	+	0.620231i	$0.212961\pi$
$32$			197.622i			1.09172i
$33$		−	382.802i		−	2.01931i
$34$	−56.1602			−0.283276
$35$	90.0967	+	115.446i	0.435118	+	0.557539i
$36$	254.828			1.17976
$37$			294.327i			1.30776i	0.756598	+	0.653880i	$0.226860\pi$
$37$			294.327i			1.30776i	−0.756598	+	0.653880i	$0.773140\pi$
$38$			375.062i			1.60113i
$39$	−726.311			−2.98212
$40$	74.9139	+	95.9910i	0.296123	+	0.379438i
$41$	−167.636			−0.638544			−0.319272	−	0.947663i	$-0.603438\pi$
$41$	−167.636			−0.638544			−0.319272	+	0.947663i	$0.603438\pi$
$42$		−	417.259i		−	1.53296i
$43$		−	51.4584i		−	0.182496i	−0.995828	−	0.0912480i	$-0.970914\pi$
$43$		−	51.4584i		−	0.182496i	0.995828	−	0.0912480i	$-0.0290856\pi$
$44$	215.428			0.738114
$45$	451.307	−	352.212i	1.49504	−	1.16677i
$46$	82.8534			0.265567
$47$			278.791i			0.865231i	0.901579	+	0.432615i	$0.142409\pi$
$47$			278.791i			0.865231i	−0.901579	+	0.432615i	$0.857591\pi$
$48$		−	699.028i		−	2.10200i
$49$	171.439			0.499823
$50$	−436.798	−	109.401i	−1.23545	−	0.309434i
$51$	137.867			0.378535
$52$		−	408.743i		−	1.09005i
$53$		−	314.913i		−	0.816163i	−0.912945	−	0.408082i	$-0.866198\pi$
$53$		−	314.913i		−	0.816163i	0.912945	−	0.408082i	$-0.133802\pi$
$54$	−771.053			−1.94309
$55$	381.530	−	297.756i	0.935372	−	0.729989i
$56$	−142.650			−0.340400
$57$		−	920.735i		−	2.13955i
$58$			193.923i			0.439022i
$59$	418.863			0.924260			0.462130	−	0.886812i	$-0.347085\pi$
$59$	418.863			0.924260			0.462130	+	0.886812i	$0.347085\pi$
$60$	302.731	+	387.905i	0.651374	+	0.834638i
$61$	−27.1566			−0.0570007			−0.0285003	−	0.999594i	$-0.509073\pi$
$61$	−27.1566			−0.0570007			−0.0285003	+	0.999594i	$0.509073\pi$
$62$		−	975.445i		−	1.99809i
$63$			670.676i			1.34123i
$64$	79.5303			0.155333
$65$	−564.948	−	723.896i	−1.07805	−	1.38136i
$66$	−1378.98			−2.57182
$67$			823.536i			1.50166i	0.660498	+	0.750828i	$0.270345\pi$
$67$			823.536i			1.50166i	−0.660498	+	0.750828i	$0.729655\pi$
$68$			77.5870i			0.138365i
$69$	−203.396			−0.354870
$70$	415.872	−	324.557i	0.710088	−	0.554172i
$71$	93.0926			0.155607			0.0778033	−	0.996969i	$-0.475209\pi$
$71$	93.0926			0.155607			0.0778033	+	0.996969i	$0.475209\pi$
$72$			557.656i			0.912783i
$73$			908.940i			1.45731i	0.684883	+	0.728653i	$0.259853\pi$
$73$			908.940i			1.45731i	−0.684883	+	0.728653i	$0.740147\pi$
$74$	1060.26			1.66558
$75$	1072.29	+	268.568i	1.65090	+	0.413488i
$76$	518.159			0.782064
$77$			566.982i			0.839137i
$78$			2616.40i			3.79807i
$79$	−84.2670			−0.120010			−0.0600049	−	0.998198i	$-0.519112\pi$
$79$	−84.2670			−0.120010			−0.0600049	+	0.998198i	$0.519112\pi$
$80$	696.704	−	543.726i	0.973673	−	0.759880i
$81$	510.343			0.700059
$82$			603.877i			0.813257i
$83$		−	1255.31i		−	1.66010i	−0.557691	−	0.830049i	$-0.688313\pi$
$83$		−	1255.31i		−	1.66010i	0.557691	−	0.830049i	$-0.311687\pi$
$84$	−576.455			−0.748767
$85$	107.238	+	137.409i	0.136842	+	0.175342i
$86$	−185.370			−0.232429
$87$		−	476.059i		−	0.586654i
$88$			471.435i			0.571082i
$89$	−839.289			−0.999601			−0.499801	−	0.866141i	$-0.666593\pi$
$89$	−839.289			−0.999601			−0.499801	+	0.866141i	$0.666593\pi$
$90$	−1268.78	−	1625.75i	−1.48601	−	1.90410i
$91$	1075.76			1.23924
$92$		−	114.464i		−	0.129714i
$93$			2394.61i			2.67000i
$94$	1004.29			1.10197
$95$	917.674	−	716.177i	0.991067	−	0.773455i
$96$	−1747.63			−1.85799
$97$		−	169.933i		−	0.177877i	−0.996037	−	0.0889386i	$-0.971653\pi$
$97$		−	169.933i		−	0.177877i	0.996037	−	0.0889386i	$-0.0283475\pi$
$98$		−	617.579i		−	0.636581i
$99$	2216.48			2.25015
$100$	−151.141	+	603.449i	−0.151141	+	0.603449i
$101$	−1474.10			−1.45226			−0.726131	−	0.687556i	$-0.758684\pi$
$101$	−1474.10			−1.45226			−0.726131	+	0.687556i	$0.758684\pi$
$102$		−	496.642i		−	0.482107i
$103$			341.854i			0.327028i	0.986541	+	0.163514i	$0.0522829\pi$
$103$			341.854i			0.327028i	−0.986541	+	0.163514i	$0.947717\pi$
$104$	894.479			0.843374
$105$	−1020.92	+	796.753i	−0.948872	+	0.740525i
$106$	−1134.42			−1.03948
$107$			1687.45i			1.52460i	0.647225	+	0.762299i	$0.275930\pi$
$107$			1687.45i			1.52460i	−0.647225	+	0.762299i	$0.724070\pi$
$108$			1065.23i			0.949093i
$109$	188.936			0.166026			0.0830128	−	0.996548i	$-0.473546\pi$
$109$	188.936			0.166026			0.0830128	+	0.996548i	$0.473546\pi$
$110$	−1072.61	−	1374.39i	−0.929723	−	1.19130i
$111$	−2602.83			−2.22567
$112$			1035.35i			0.873498i
$113$		−	916.975i		−	0.763378i	−0.924291	−	0.381689i	$-0.875343\pi$
$113$		−	916.975i		−	0.763378i	0.924291	−	0.381689i	$-0.124657\pi$
$114$	−3316.78			−2.72496
$115$	−158.208	−	202.720i	−0.128287	−	0.164380i
$116$	267.910			0.214438
$117$		−	4205.45i		−	3.32302i
$118$		−	1508.88i		−	1.17715i
$119$	−204.200			−0.157302
$120$	−848.877	+	662.486i	−0.645763	+	0.503970i
$121$	542.786			0.407803
$122$			97.8267i			0.0725968i
$123$		−	1482.45i		−	1.08673i
$124$	−1347.61			−0.975956
$125$	566.387	+	1277.63i	0.405273	+	0.914196i
$126$	2415.99			1.70820
$127$		−	2105.43i		−	1.47107i	−0.677484	−	0.735537i	$-0.736930\pi$
$127$		−	2105.43i		−	1.47107i	0.677484	−	0.735537i	$-0.263070\pi$
$128$			1294.48i			0.893886i
$129$	455.062			0.310589
$130$	−2607.70	+	2035.12i	−1.75931	+	1.37302i
$131$	−317.535			−0.211780			−0.105890	−	0.994378i	$-0.533769\pi$
$131$	−317.535			−0.211780			−0.105890	+	0.994378i	$0.533769\pi$
$132$			1905.10i			1.25619i
$133$			1363.73i			0.889102i
$134$	2966.64			1.91253
$135$	1472.32	+	1886.56i	0.938645	+	1.20273i
$136$	−169.789			−0.107053
$137$		−	1162.55i		−	0.724990i	−0.931986	−	0.362495i	$-0.881925\pi$
$137$		−	1162.55i		−	0.724990i	0.931986	−	0.362495i	$-0.118075\pi$
$138$			732.697i			0.451966i
$139$	1873.81			1.14341			0.571707	−	0.820458i	$-0.306281\pi$
$139$	1873.81			1.14341			0.571707	+	0.820458i	$0.306281\pi$
$140$	−448.385	−	574.539i	−0.270682	−	0.346838i
$141$	−2465.43			−1.47253
$142$		−	335.349i		−	0.198182i
$143$		−	3555.23i		−	2.07905i
$144$	4047.48			2.34229
$145$	474.476	−	370.294i	0.271746	−	0.212077i
$146$	3274.29			1.85604
$147$			1516.09i			0.850646i
$148$		−	1464.78i		−	0.813543i
$149$	−1697.35			−0.933237			−0.466619	−	0.884459i	$-0.654528\pi$
$149$	−1697.35			−0.933237			−0.466619	+	0.884459i	$0.654528\pi$
$150$	967.469	−	3862.74i	0.526623	−	2.10261i
$151$	−708.765			−0.381977			−0.190988	−	0.981592i	$-0.561169\pi$
$151$	−708.765			−0.381977			−0.190988	+	0.981592i	$0.561169\pi$
$152$			1133.92i			0.605086i
$153$			798.271i			0.421807i
$154$	2042.45			1.06874
$155$	−2386.65	+	1862.61i	−1.23678	+	0.965213i
$156$	3614.64			1.85515
$157$		−	85.5997i		−	0.0435134i	−0.999763	−	0.0217567i	$-0.993074\pi$
$157$		−	85.5997i		−	0.0435134i	0.999763	−	0.0217567i	$-0.00692591\pi$
$158$			303.557i			0.152846i
$159$	2784.87			1.38902
$160$	−1359.36	−	1741.82i	−0.671670	−	0.860645i
$161$	301.257			0.147468
$162$		−	1838.42i		−	0.891604i
$163$			2458.34i			1.18130i	0.806928	+	0.590650i	$0.201129\pi$
$163$			2458.34i			1.18130i	−0.806928	+	0.590650i	$0.798871\pi$
$164$	834.274			0.397231
$165$	2633.14	+	3373.98i	1.24236	+	1.59190i
$166$	−4522.02			−2.11432
$167$		−	881.994i		−	0.408687i	−0.978899	−	0.204344i	$-0.934494\pi$
$167$		−	881.994i		−	0.408687i	0.978899	−	0.204344i	$-0.0655060\pi$
$168$		−	1261.50i		−	0.579324i
$169$	−4548.53			−2.07034
$170$	494.991	−	386.304i	0.223318	−	0.174283i
$171$	5331.19			2.38413
$172$			256.093i			0.113529i
$173$		−	322.337i		−	0.141658i	−0.997488	−	0.0708290i	$-0.977436\pi$
$173$		−	322.337i		−	0.141658i	0.997488	−	0.0708290i	$-0.0225645\pi$
$174$	−1714.92			−0.747170
$175$	−1588.21	−	397.786i	−0.686041	−	0.171827i
$176$	3421.69			1.46545
$177$			3704.13i			1.57299i
$178$			3023.39i			1.27310i
$179$	−3365.29			−1.40521			−0.702607	−	0.711578i	$-0.747981\pi$
$179$	−3365.29			−1.40521			−0.702607	+	0.711578i	$0.747981\pi$
$180$	−2246.02	+	1752.86i	−0.930049	+	0.725835i
$181$	74.7539			0.0306984			0.0153492	−	0.999882i	$-0.495114\pi$
$181$	74.7539			0.0306984			0.0153492	+	0.999882i	$0.495114\pi$
$182$		−	3875.25i		−	1.57831i
$183$		−	240.154i		−	0.0970092i
$184$	250.490			0.100361
$185$	−2024.56	−	2594.17i	−0.804587	−	1.03096i
$186$	8626.16			3.40054
$187$			674.849i			0.263903i
$188$		−	1387.46i		−	0.538250i
$189$	−2803.57			−1.07899
$190$	−2579.90	−	3305.76i	−0.985082	−	1.26224i
$191$	729.657			0.276420			0.138210	−	0.990403i	$-0.455865\pi$
$191$	729.657			0.276420			0.138210	+	0.990403i	$0.455865\pi$
$192$			703.310i			0.264360i
$193$			1175.76i			0.438514i	0.975667	+	0.219257i	$0.0703633\pi$
$193$			1175.76i			0.438514i	−0.975667	+	0.219257i	$0.929637\pi$
$194$	−612.153			−0.226547
$195$	6401.63	−	4996.00i	2.35092	−	1.83472i
$196$	−853.204			−0.310934
$197$		−	1511.81i		−	0.546761i	−0.961906	−	0.273380i	$-0.911858\pi$
$197$		−	1511.81i		−	0.546761i	0.961906	−	0.273380i	$-0.0881418\pi$
$198$		−	7984.48i		−	2.86582i
$199$	−4344.46			−1.54759			−0.773795	−	0.633436i	$-0.781644\pi$
$199$	−4344.46			−1.54759			−0.773795	+	0.633436i	$0.781644\pi$
$200$	−1320.57	−	330.752i	−0.466891	−	0.116938i
$201$	−7282.78			−2.55566
$202$			5310.18i			1.84962i
$203$			705.107i			0.243787i
$204$	−686.125			−0.235482
$205$	1477.52	−	1153.10i	0.503389	−	0.392858i
$206$	1231.47			0.416507
$207$		−	1177.69i		−	0.395436i
$208$		−	6492.14i		−	2.16418i
$209$	4506.93			1.49163
$210$	2870.16	+	3677.68i	0.943142	+	1.20850i
$211$	−320.612			−0.104606			−0.0523029	−	0.998631i	$-0.516656\pi$
$211$	−320.612			−0.104606			−0.0523029	+	0.998631i	$0.516656\pi$
$212$			1567.23i			0.507726i
$213$			823.246i			0.264826i
$214$	6078.74			1.94175
$215$	353.962	+	453.549i	0.112279	+	0.143869i
$216$	−2331.12			−0.734317
$217$		−	3546.74i		−	1.10953i
$218$		−	680.608i		−	0.211452i
$219$	−8038.03			−2.48018
$220$	−1898.76	+	1481.84i	−0.581884	+	0.454118i
$221$	1280.43			0.389732
$222$			9376.21i			2.83464i
$223$			4432.43i			1.33102i	0.746389	+	0.665510i	$0.231786\pi$
$223$			4432.43i			1.33102i	−0.746389	+	0.665510i	$0.768214\pi$
$224$	2588.48			0.772099
$225$	−1555.05	+	6208.72i	−0.460756	+	1.83962i
$226$	−3303.24			−0.972248
$227$			3118.22i			0.911735i	0.890048	+	0.455867i	$0.150671\pi$
$227$			3118.22i			0.911735i	−0.890048	+	0.455867i	$0.849329\pi$
$228$			4582.23i			1.33099i
$229$	4766.21			1.37537			0.687686	−	0.726008i	$-0.258627\pi$
$229$	4766.21			1.37537			0.687686	+	0.726008i	$0.258627\pi$
$230$	−730.261	+	569.915i	−0.209357	+	0.163387i
$231$	−5013.99			−1.42812
$232$			586.285i			0.165911i
$233$			2860.82i			0.804370i	0.915558	+	0.402185i	$0.131749\pi$
$233$			2860.82i			0.804370i	−0.915558	+	0.402185i	$0.868251\pi$
$234$	−15149.4			−4.23224
$235$	−1917.69	−	2457.24i	−0.532325	−	0.682095i
$236$	−2084.56			−0.574972
$237$		−	745.199i		−	0.204244i
$238$			735.593i			0.200342i
$239$	4982.61			1.34853			0.674264	−	0.738491i	$-0.264461\pi$
$239$	4982.61			1.34853			0.674264	+	0.738491i	$0.264461\pi$
$240$	4808.34	+	6161.16i	1.29324	+	1.65709i
$241$	−5722.17			−1.52945			−0.764725	−	0.644357i	$-0.777125\pi$
$241$	−5722.17			−1.52945			−0.764725	+	0.644357i	$0.777125\pi$
$242$		−	1955.29i		−	0.519384i
$243$		−	1266.05i		−	0.334228i
$244$	135.150			0.0354595
$245$	−1511.05	+	1179.26i	−0.394030	+	0.307512i
$246$	−5340.27			−1.38408
$247$		−	8551.22i		−	2.20284i
$248$		−	2949.05i		−	0.755102i
$249$	11101.1			2.82531
$250$	4602.42	−	2040.31i	1.16433	−	0.516161i
$251$	6357.71			1.59878			0.799392	−	0.600810i	$-0.205155\pi$
$251$	6357.71			1.59878			0.799392	+	0.600810i	$0.205155\pi$
$252$		−	3337.76i		−	0.834362i
$253$		−	995.607i		−	0.247404i
$254$	−7584.42			−1.87358
$255$	−1215.15	+	948.334i	−0.298414	+	0.232890i
$256$	5299.39			1.29380
$257$			3189.94i			0.774253i	0.922027	+	0.387126i	$0.126532\pi$
$257$			3189.94i			0.774253i	−0.922027	+	0.387126i	$0.873468\pi$
$258$		−	1639.28i		−	0.395570i
$259$	3855.13			0.924889
$260$	2811.58	+	3602.62i	0.670641	+	0.859327i
$261$	2756.45			0.653717
$262$			1143.86i			0.269725i
$263$		−	1950.80i		−	0.457383i	−0.973499	−	0.228691i	$-0.926555\pi$
$263$		−	1950.80i		−	0.457383i	0.973499	−	0.228691i	$-0.0734447\pi$
$264$	−4169.05			−0.971921
$265$	2166.16	+	2775.61i	0.502137	+	0.643413i
$266$	4912.60			1.13237
$267$		−	7422.09i		−	1.70122i
$268$		−	4098.50i		−	0.934163i
$269$	−232.997			−0.0528106			−0.0264053	−	0.999651i	$-0.508406\pi$
$269$	−232.997			−0.0528106			−0.0264053	+	0.999651i	$0.508406\pi$
$270$	6795.99	−	5303.77i	1.53182	−	1.19547i
$271$	−175.073			−0.0392433			−0.0196216	−	0.999807i	$-0.506246\pi$
$271$	−175.073			−0.0392433			−0.0196216	+	0.999807i	$0.506246\pi$
$272$			1232.33i			0.274709i
$273$			9513.31i			2.10905i
$274$	−4187.89			−0.923356
$275$	−1314.62	+	5248.78i	−0.288271	+	1.15096i
$276$	1012.24			0.220760
$277$			4866.78i			1.05565i	0.849352	+	0.527827i	$0.176993\pi$
$277$			4866.78i			1.05565i	−0.849352	+	0.527827i	$0.823007\pi$
$278$		−	6750.07i		−	1.45627i
$279$	−13865.2			−2.97522
$280$	1257.30	−	981.231i	0.268350	−	0.209428i
$281$	−4635.93			−0.984186			−0.492093	−	0.870543i	$-0.663768\pi$
$281$	−4635.93			−0.984186			−0.492093	+	0.870543i	$0.663768\pi$
$282$			8881.28i			1.87543i
$283$		−	5393.07i		−	1.13281i	−0.824128	−	0.566404i	$-0.808334\pi$
$283$		−	5393.07i		−	1.13281i	0.824128	−	0.566404i	$-0.191666\pi$
$284$	−463.295			−0.0968011
$285$	6333.37	+	8115.27i	1.31634	+	1.68669i
$286$	−12807.1			−2.64790
$287$			2195.71i			0.451599i
$288$		−	10119.1i		−	2.07039i
$289$	4669.95			0.950529
$290$	−1333.92	−	1709.22i	−0.270104	−	0.346099i
$291$	1502.77			0.302728
$292$		−	4523.53i		−	0.906574i
$293$			1401.19i			0.279380i	0.990195	+	0.139690i	$0.0446105\pi$
$293$			1401.19i			0.279380i	−0.990195	+	0.139690i	$0.955389\pi$
$294$	5461.44			1.08339
$295$	−3691.82	+	2881.19i	−0.728630	+	0.568642i
$296$	3205.48			0.629441
$297$			9265.36i			1.81020i
$298$			6114.40i			1.18858i
$299$	−1889.02			−0.365367
$300$	−5336.48	−	1336.59i	−1.02701	−	0.257226i
$301$	−674.008			−0.129067
$302$			2553.20i			0.486491i
$303$		−	13035.9i		−	2.47160i
$304$	8230.01			1.55271
$305$	239.355	−	186.799i	0.0449359	−	0.0350692i
$306$	2875.63			0.537218
$307$		−	442.884i		−	0.0823346i	−0.999152	−	0.0411673i	$-0.986892\pi$
$307$		−	442.884i		−	0.0823346i	0.999152	−	0.0411673i	$-0.0131077\pi$
$308$		−	2821.70i		−	0.522018i
$309$	−3023.12			−0.556567
$310$	6709.70	+	8597.48i	1.22931	+	1.57517i
$311$	4835.61			0.881680			0.440840	−	0.897586i	$-0.354681\pi$
$311$	4835.61			0.881680			0.440840	+	0.897586i	$0.354681\pi$
$312$			7910.15i			1.43533i
$313$			742.601i			0.134103i	0.997750	+	0.0670516i	$0.0213592\pi$
$313$			742.601i			0.134103i	−0.997750	+	0.0670516i	$0.978641\pi$
$314$	−308.357			−0.0554192
$315$	−4613.32	−	5911.27i	−0.825177	−	1.05734i
$316$	419.372			0.0746568
$317$		−	7004.97i		−	1.24113i	−0.784155	−	0.620565i	$-0.786903\pi$
$317$		−	7004.97i		−	1.24113i	0.784155	−	0.620565i	$-0.213097\pi$
$318$		−	10032.0i		−	1.76908i
$319$	2330.27			0.408997
$320$	−700.972	+	547.057i	−0.122455	+	0.0955669i
$321$	−14922.6			−2.59471
$322$		−	1085.22i		−	0.187817i
$323$			1623.18i			0.279617i
$324$	−2539.83			−0.435499
$325$	9958.78	+	2494.30i	1.69974	+	0.425719i
$326$	8855.72			1.50452
$327$			1670.82i			0.282558i
$328$			1825.70i			0.307339i
$329$	3651.64			0.611919
$330$	12154.2	−	9485.43i	2.02747	−	1.58229i
$331$	4377.62			0.726937			0.363468	−	0.931607i	$-0.381593\pi$
$331$	4377.62			0.726937			0.363468	+	0.931607i	$0.381593\pi$
$332$			6247.31i			1.03273i
$333$		−	15070.7i		−	2.48009i
$334$	−3177.23			−0.520509
$335$	−5664.77	−	7258.56i	−0.923880	−	1.18381i
$336$	−9155.95			−1.48660
$337$		−	3600.42i		−	0.581981i	−0.956726	−	0.290991i	$-0.906015\pi$
$337$		−	3600.42i		−	0.581981i	0.956726	−	0.290991i	$-0.0939848\pi$
$338$			16385.3i			2.63681i
$339$	8109.09			1.29919
$340$	−533.690	−	683.844i	−0.0851276	−	0.109078i
$341$	−11721.4			−1.86144
$342$		−	19204.7i		−	3.03646i
$343$		−	6738.19i		−	1.06072i
$344$	−560.426			−0.0878376
$345$	1792.71	−	1399.08i	0.279758	−	0.218330i
$346$	−1161.16			−0.180417
$347$			4851.18i			0.750504i	0.926923	+	0.375252i	$0.122444\pi$
$347$			4851.18i			0.750504i	−0.926923	+	0.375252i	$0.877556\pi$
$348$			2369.21i			0.364951i
$349$	−6997.54			−1.07327			−0.536633	−	0.843816i	$-0.680304\pi$
$349$	−6997.54			−1.07327			−0.536633	+	0.843816i	$0.680304\pi$
$350$	−1432.95	+	5721.23i	−0.218841	+	0.873750i
$351$	17579.6			2.67331
$352$		−	8554.52i		−	1.29533i
$353$			11261.2i			1.69794i	0.528437	+	0.848972i	$0.322778\pi$
$353$			11261.2i			1.69794i	−0.528437	+	0.848972i	$0.677222\pi$
$354$	13343.5			2.00338
$355$	−820.509	+	640.347i	−0.122671	+	0.0957355i
$356$	4176.90			0.621841
$357$		−	1805.80i		−	0.267712i
$358$			12122.8i			1.78970i
$359$	4202.08			0.617764			0.308882	−	0.951100i	$-0.400045\pi$
$359$	4202.08			0.617764			0.308882	+	0.951100i	$0.400045\pi$
$360$	−3835.89	−	4915.12i	−0.561581	−	0.719583i
$361$	3981.28			0.580447
$362$		−	269.287i		−	0.0390979i
$363$			4800.03i			0.694039i
$364$	−5353.76			−0.770916
$365$	−6252.24	−	8011.31i	−0.896595	−	1.14885i
$366$	−865.111			−0.123552
$367$		−	8530.24i		−	1.21328i	−0.794976	−	0.606641i	$-0.792516\pi$
$367$		−	8530.24i		−	1.21328i	0.794976	−	0.606641i	$-0.207484\pi$
$368$		−	1818.06i		−	0.257535i
$369$	8583.62			1.21096
$370$	−9345.04	+	7293.11i	−1.31304	+	1.02473i
$371$	−4124.77			−0.577217
$372$		−	11917.3i		−	1.66098i
$373$		−	916.636i		−	0.127243i	−0.997974	−	0.0636215i	$-0.979735\pi$
$373$		−	916.636i		−	0.127243i	0.997974	−	0.0636215i	$-0.0202650\pi$
$374$	2431.02			0.336110
$375$	−11298.4	+	5008.73i	−1.55586	+	0.689733i
$376$	3036.27			0.416446
$377$		−	4421.34i		−	0.604007i
$378$			10099.3i			1.37422i
$379$	7066.55			0.957742			0.478871	−	0.877885i	$-0.341046\pi$
$379$	7066.55			0.957742			0.478871	+	0.877885i	$0.341046\pi$
$380$	−4567.00	+	3564.21i	−0.616532	+	0.481158i
$381$	18618.9			2.50361
$382$		−	2628.46i		−	0.352051i
$383$		−	7203.32i		−	0.961025i	−0.876988	−	0.480512i	$-0.840451\pi$
$383$		−	7203.32i		−	0.961025i	0.876988	−	0.480512i	$-0.159549\pi$
$384$	−11447.5			−1.52130
$385$	−3900.04	−	4997.32i	−0.516271	−	0.661525i
$386$	4235.47			0.558496
$387$			2634.88i			0.346094i
$388$			845.708i			0.110655i
$389$	−4235.11			−0.552002			−0.276001	−	0.961157i	$-0.589009\pi$
$389$	−4235.11			−0.552002			−0.276001	+	0.961157i	$0.589009\pi$
$390$	−17997.2	−	23060.7i	−2.33673	−	2.99417i
$391$	358.570			0.0463777
$392$		−	1867.12i		−	0.240571i
$393$		−	2808.06i		−	0.360427i
$394$	−5446.02			−0.696361
$395$	742.721	−	579.639i	0.0946085	−	0.0738350i
$396$	−11030.8			−1.39979
$397$			6614.52i			0.836205i	0.908400	+	0.418103i	$0.137305\pi$
$397$			6614.52i			0.836205i	−0.908400	+	0.418103i	$0.862695\pi$
$398$			15650.1i			1.97103i
$399$	−12059.9			−1.51316
$400$	−2400.60	+	9584.70i	−0.300075	+	1.19809i
$401$	6621.91			0.824644			0.412322	−	0.911038i	$-0.364718\pi$
$401$	6621.91			0.824644			0.412322	+	0.911038i	$0.364718\pi$
$402$			26234.9i			3.25492i
$403$			22239.7i			2.74898i
$404$	7336.17			0.903436
$405$	−4498.12	+	3510.45i	−0.551884	+	0.430705i
$406$	2540.02			0.310491
$407$		−	12740.6i		−	1.55167i
$408$		−	1501.49i		−	0.182194i
$409$	−7243.23			−0.875683			−0.437842	−	0.899052i	$-0.644257\pi$
$409$	−7243.23			−0.875683			−0.437842	+	0.899052i	$0.644257\pi$
$410$	−4153.83	−	5322.51i	−0.500349	−	0.641123i
$411$	10280.8			1.23386
$412$		−	1701.31i		−	0.203441i
$413$		−	5486.32i		−	0.653666i
$414$	−4242.43			−0.503632
$415$	8634.77	+	11064.2i	1.02136	+	1.30872i
$416$	−16230.9			−1.91295
$417$			16570.7i			1.94597i
$418$		−	16235.4i		−	1.89976i
$419$	7720.71			0.900194			0.450097	−	0.892980i	$-0.351389\pi$
$419$	7720.71			0.900194			0.450097	+	0.892980i	$0.351389\pi$
$420$	5080.82	−	3965.21i	0.590283	−	0.460672i
$421$	−6297.29			−0.729005			−0.364502	−	0.931202i	$-0.618761\pi$
$421$	−6297.29			−0.729005			−0.364502	+	0.931202i	$0.618761\pi$
$422$			1154.95i			0.133227i
$423$		−	14275.2i		−	1.64086i
$424$	−3429.68			−0.392830
$425$	−1890.36	−	473.464i	−0.215755	−	0.0540385i
$426$	2965.60			0.337286
$427$			355.700i			0.0403127i
$428$		−	8397.95i		−	0.948435i
$429$	31440.0			3.53832
$430$	1633.83	−	1275.08i	0.183233	−	0.143000i
$431$	−10285.2			−1.14946			−0.574732	−	0.818342i	$-0.694894\pi$
$431$	−10285.2			−1.14946			−0.574732	+	0.818342i	$0.694894\pi$
$432$			16919.3i			1.88433i
$433$			3632.65i			0.403173i	0.979471	+	0.201587i	$0.0646097\pi$
$433$			3632.65i			0.403173i	−0.979471	+	0.201587i	$0.935390\pi$
$434$	−12776.5			−1.41311
$435$	3274.62	+	4195.94i	0.360933	+	0.462482i
$436$	−940.280			−0.103283
$437$		−	2394.68i		−	0.262136i
$438$			28955.6i			3.15879i
$439$	16637.1			1.80876			0.904378	−	0.426731i	$-0.140335\pi$
$439$	16637.1			1.80876			0.904378	+	0.426731i	$0.140335\pi$
$440$	−3242.82	−	4155.18i	−0.351353	−	0.450206i
$441$	−8778.38			−0.947887
$442$		−	4612.50i		−	0.496368i
$443$			8786.15i			0.942308i	0.882051	+	0.471154i	$0.156162\pi$
$443$			8786.15i			0.942308i	−0.882051	+	0.471154i	$0.843838\pi$
$444$	12953.5			1.38456
$445$	7397.41	−	5773.14i	0.788025	−	0.614995i
$446$	15967.0			1.69520
$447$		−	15010.2i		−	1.58827i
$448$		−	1041.70i		−	0.109856i
$449$	−12923.9			−1.35838			−0.679192	−	0.733961i	$-0.737670\pi$
$449$	−12923.9			−1.35838			−0.679192	+	0.733961i	$0.737670\pi$
$450$	22365.8	+	5601.79i	2.34297	+	0.586824i
$451$	7256.49			0.757638
$452$			4563.52i			0.474889i
$453$		−	6267.83i		−	0.650084i
$454$	11232.8			1.16120
$455$	−9481.67	+	7399.75i	−0.976940	+	0.762430i
$456$	−10027.6			−1.02979
$457$		−	8399.20i		−	0.859733i	−0.902892	−	0.429867i	$-0.858561\pi$
$457$		−	8399.20i		−	0.859733i	0.902892	−	0.429867i	$-0.141439\pi$
$458$		−	17169.4i		−	1.75169i
$459$	−3336.94			−0.339336
$460$	787.354	+	1008.88i	0.0798056	+	0.102259i
$461$	251.161			0.0253747			0.0126873	−	0.999920i	$-0.495961\pi$
$461$	251.161			0.0253747			0.0126873	+	0.999920i	$0.495961\pi$
$462$			18062.0i			1.81887i
$463$			5288.99i			0.530886i	0.964127	+	0.265443i	$0.0855182\pi$
$463$			5288.99i			0.530886i	−0.964127	+	0.265443i	$0.914482\pi$
$464$	4255.26			0.425745
$465$	−16471.6	−	21105.9i	−1.64269	−	2.10486i
$466$	10305.6			1.02446
$467$			12066.3i			1.19564i	0.801631	+	0.597820i	$0.203966\pi$
$467$			12066.3i			1.19564i	−0.801631	+	0.597820i	$0.796034\pi$
$468$			20929.3i			2.06721i
$469$	10786.8			1.06202
$470$	−8851.75	+	6908.14i	−0.868725	+	0.677976i
$471$	756.984			0.0740552
$472$		−	4561.78i		−	0.444858i
$473$			2227.49i			0.216533i
$474$	−2684.44			−0.260128
$475$	−3161.99	+	12624.6i	−0.305436	+	1.21949i
$476$	1016.24			0.0978560
$477$			16124.8i			1.54781i
$478$		−	17948.9i		−	1.71750i
$479$	−6475.83			−0.617721			−0.308860	−	0.951107i	$-0.599948\pi$
$479$	−6475.83			−0.617721			−0.308860	+	0.951107i	$0.599948\pi$
$480$	15403.5	−	12021.3i	1.46473	−	1.14311i
$481$	−24173.4			−2.29151
$482$			20613.1i			1.94793i
$483$			2664.10i			0.250975i
$484$	−2701.29			−0.253690
$485$	1168.90	+	1497.77i	0.109437	+	0.140228i
$486$	−4560.73			−0.425677
$487$			8310.84i			0.773306i	0.922225	+	0.386653i	$0.126369\pi$
$487$			8310.84i			0.773306i	−0.922225	+	0.386653i	$0.873631\pi$
$488$			295.758i			0.0274352i
$489$	−21739.8			−2.01045
$490$	4248.08	+	5443.28i	0.391651	+	0.501842i
$491$	11736.8			1.07876			0.539382	−	0.842061i	$-0.318658\pi$
$491$	11736.8			1.07876			0.539382	+	0.842061i	$0.318658\pi$
$492$			7377.74i			0.676045i
$493$			839.253i			0.0766695i
$494$	−30804.2			−2.80556
$495$	−19535.8	+	15246.3i	−1.77388	+	1.38438i
$496$	−21404.3			−1.93766
$497$		−	1219.34i		−	0.110050i
$498$		−	39989.6i		−	3.59835i
$499$	12310.5			1.10440			0.552198	−	0.833713i	$-0.313789\pi$
$499$	12310.5			1.10440			0.552198	+	0.833713i	$0.313789\pi$
$500$	−2818.74	−	6358.38i	−0.252116	−	0.568711i
$501$	7799.74			0.695543
$502$		−	22902.5i		−	2.03623i
$503$			12639.9i			1.12045i	0.828340	+	0.560225i	$0.189285\pi$
$503$			12639.9i			1.12045i	−0.828340	+	0.560225i	$0.810715\pi$
$504$	7304.24			0.645549
$505$	12992.6	−	10139.8i	1.14488	−	0.893491i
$506$	−3586.49			−0.315097
$507$		−	40224.0i		−	3.52349i
$508$			10478.1i			0.915139i
$509$	−7574.15			−0.659564			−0.329782	−	0.944057i	$-0.606975\pi$
$509$	−7574.15			−0.659564			−0.329782	+	0.944057i	$0.606975\pi$
$510$	3416.20	+	4377.35i	0.296612	+	0.380064i
$511$	11905.4			1.03065
$512$		−	8734.22i		−	0.753910i
$513$			22285.5i			1.91799i
$514$	11491.2			0.986098
$515$	−2351.48	−	3013.07i	−0.201201	−	0.257809i
$516$	−2264.71			−0.193214
$517$		−	12068.1i		−	1.02660i
$518$		−	13887.4i		−	1.17795i
$519$	2850.53			0.241087
$520$	−7883.85	+	6152.76i	−0.664865	+	0.518878i
$521$	7578.91			0.637309			0.318655	−	0.947871i	$-0.396769\pi$
$521$	7578.91			0.637309			0.318655	+	0.947871i	$0.396769\pi$
$522$		−	9929.62i		−	0.832582i
$523$		−	6487.64i		−	0.542418i	−0.962520	−	0.271209i	$-0.912577\pi$
$523$		−	6487.64i		−	0.542418i	0.962520	−	0.271209i	$-0.0874235\pi$
$524$	1580.28			0.131746
$525$	3517.74	−	14045.0i	0.292432	−	1.16757i
$526$	−7027.42			−0.582528
$527$		−	4221.50i		−	0.348940i
$528$			30259.0i			2.49404i
$529$	−529.000			−0.0434783
$530$	9998.65	−	7803.21i	0.819459	−	0.639528i
$531$	−21447.5			−1.75281
$532$		−	6786.90i		−	0.553101i
$533$		−	13768.1i		−	1.11888i
$534$	−26736.7			−2.16669
$535$	−11607.3	−	14873.0i	−0.937995	−	1.20190i
$536$	8969.01			0.722766
$537$		−	29760.2i		−	2.39153i
$538$			839.328i			0.0672602i
$539$	−7421.14			−0.593044
$540$	−7327.31	−	9388.85i	−0.583921	−	0.748207i
$541$	−17183.2			−1.36555			−0.682775	−	0.730629i	$-0.739227\pi$
$541$	−17183.2			−1.36555			−0.682775	+	0.730629i	$0.739227\pi$
$542$			630.669i			0.0499807i
$543$			661.071i			0.0522454i
$544$	3080.93			0.242820
$545$	−1665.26	+	1299.62i	−0.130885	+	0.102146i
$546$	34270.0			2.68612
$547$		−	17078.8i		−	1.33498i	−0.744618	−	0.667491i	$-0.767368\pi$
$547$		−	17078.8i		−	1.33498i	0.744618	−	0.667491i	$-0.232632\pi$
$548$			5785.69i			0.451008i
$549$	1390.53			0.108099
$550$	18907.8	+	4735.68i	1.46587	+	0.367146i
$551$	5604.88			0.433350
$552$			2215.16i			0.170803i
$553$			1103.74i			0.0848748i
$554$	17531.7			1.34449
$555$	22941.0	−	17903.8i	1.75458	−	1.36932i
$556$	−9325.42			−0.711305
$557$			9711.39i			0.738752i	0.929280	+	0.369376i	$0.120428\pi$
$557$			9711.39i			0.738752i	−0.929280	+	0.369376i	$0.879572\pi$
$558$			49946.7i			3.78927i
$559$	4226.34			0.319776
$560$	−7121.79	−	9125.51i	−0.537412	−	0.688613i
$561$	−5967.89			−0.449135
$562$			16700.1i			1.25347i
$563$			20304.8i			1.51998i	0.649937	+	0.759988i	$0.274795\pi$
$563$			20304.8i			1.51998i	−0.649937	+	0.759988i	$0.725205\pi$
$564$	12269.7			0.916045
$565$	6307.50	+	8082.12i	0.469661	+	0.601801i
$566$	−19427.6			−1.44276
$567$		−	6684.54i		−	0.495104i
$568$		−	1013.86i		−	0.0748954i
$569$	−6542.46			−0.482028			−0.241014	−	0.970522i	$-0.577480\pi$
$569$	−6542.46			−0.482028			−0.241014	+	0.970522i	$0.577480\pi$
$570$	29233.8	−	22814.8i	2.14819	−	1.67651i
$571$	22612.2			1.65725			0.828625	−	0.559804i	$-0.189124\pi$
$571$	22612.2			1.65725			0.828625	+	0.559804i	$0.189124\pi$
$572$			17693.4i			1.29335i
$573$			6452.58i			0.470437i
$574$	7909.66			0.575162
$575$	2788.86	+	698.503i	0.202267	+	0.0506601i
$576$	−4072.27			−0.294580
$577$			14807.4i			1.06836i	0.845372	+	0.534179i	$0.179379\pi$
$577$			14807.4i			1.06836i	−0.845372	+	0.534179i	$0.820621\pi$
$578$		−	16822.7i		−	1.21061i
$579$	−10397.6			−0.746304
$580$	−2361.33	+	1842.84i	−0.169050	+	0.131931i
$581$	−16442.2			−1.17407
$582$		−	5413.46i		−	0.385558i
$583$			13631.7i			0.968385i
$584$	9899.14			0.701420
$585$	28927.6	+	37066.4i	2.04446	+	2.61967i
$586$	5047.52			0.355821
$587$			1725.45i			0.121323i	0.998158	+	0.0606617i	$0.0193211\pi$
$587$			1725.45i			0.121323i	−0.998158	+	0.0606617i	$0.980679\pi$
$588$		−	7545.14i		−	0.529177i
$589$	−28193.0			−1.97228
$590$	10379.0	+	13299.1i	0.724230	+	0.927993i
$591$	13369.4			0.930529
$592$		−	23265.4i		−	1.61521i
$593$			23111.9i			1.60049i	0.599672	+	0.800246i	$0.295298\pi$
$593$			23111.9i			1.60049i	−0.599672	+	0.800246i	$0.704702\pi$
$594$	33376.8			2.30550
$595$	1799.80	−	1404.61i	0.124008	−	0.0967788i
$596$	8447.22			0.580556
$597$		−	38419.3i		−	2.63383i
$598$			6804.84i			0.465336i
$599$	−16471.7			−1.12357			−0.561784	−	0.827284i	$-0.689885\pi$
$599$	−16471.7			−1.12357			−0.561784	+	0.827284i	$0.689885\pi$
$600$	2924.94	−	11678.2i	0.199017	−	0.794599i
$601$	23643.3			1.60471			0.802353	−	0.596850i	$-0.203581\pi$
$601$	23643.3			1.60471			0.802353	+	0.596850i	$0.203581\pi$
$602$			2427.99i			0.164381i
$603$		−	42168.3i		−	2.84781i
$604$	3527.32			0.237623
$605$	−4784.07	+	3733.61i	−0.321487	+	0.250897i
$606$	−46959.6			−3.14786
$607$		−	9471.70i		−	0.633352i	−0.948534	−	0.316676i	$-0.897433\pi$
$607$		−	9471.70i		−	0.633352i	0.948534	−	0.316676i	$-0.102567\pi$
$608$		−	20575.8i		−	1.37246i
$609$	−6235.48			−0.414900
$610$	−672.911	−	862.234i	−0.0446645	−	0.0572309i
$611$	−22897.4			−1.51609
$612$		−	3972.77i		−	0.262401i
$613$		−	3320.37i		−	0.218774i	−0.993999	−	0.109387i	$-0.965111\pi$
$613$		−	3320.37i		−	0.218774i	0.993999	−	0.109387i	$-0.0348887\pi$
$614$	−1595.41			−0.104862
$615$	10197.2	+	13066.2i	0.668603	+	0.856715i
$616$	6174.92			0.403887
$617$			18952.4i			1.23662i	0.785934	+	0.618310i	$0.212182\pi$
$617$			18952.4i			1.23662i	−0.785934	+	0.618310i	$0.787818\pi$
$618$			10890.2i			0.708851i
$619$	−2453.33			−0.159302			−0.0796509	−	0.996823i	$-0.525381\pi$
$619$	−2453.33			−0.159302			−0.0796509	+	0.996823i	$0.525381\pi$
$620$	11877.7	−	9269.65i	0.769385	−	0.600448i
$621$	4923.00			0.318121
$622$		−	17419.4i		−	1.12292i
$623$			10993.1i			0.706950i
$624$	57412.0			3.68320
$625$	−13780.4	−	7364.93i	−0.881943	−	0.471355i
$626$	2675.09			0.170795
$627$			39856.1i			2.53860i
$628$			426.005i			0.0270692i
$629$	4588.57			0.290871
$630$	−21294.3	+	16618.6i	−1.34664	+	1.05096i
$631$	28278.9			1.78410			0.892049	−	0.451939i	$-0.149268\pi$
$631$	28278.9			1.78410			0.892049	+	0.451939i	$0.149268\pi$
$632$			917.740i			0.0577623i
$633$		−	2835.27i		−	0.178028i
$634$	−25234.1			−1.58072
$635$	14482.4	+	18557.0i	0.905065	+	1.15971i
$636$	−13859.5			−0.864096
$637$			14080.5i			0.875809i
$638$		−	8394.38i		−	0.520904i
$639$	−4766.72			−0.295099
$640$	−8904.24	−	11409.5i	−0.549955	−	0.704685i
$641$	28141.7			1.73405			0.867027	−	0.498261i	$-0.166028\pi$
$641$	28141.7			1.73405			0.867027	+	0.498261i	$0.166028\pi$
$642$			53756.1i			3.30465i
$643$			27200.7i			1.66826i	0.551567	+	0.834131i	$0.314030\pi$
$643$			27200.7i			1.66826i	−0.551567	+	0.834131i	$0.685970\pi$
$644$	−1499.27			−0.0917382
$645$	−4010.87	+	3130.19i	−0.244849	+	0.191087i
$646$	5847.22			0.356123
$647$			18295.9i			1.11172i	0.831275	+	0.555862i	$0.187612\pi$
$647$			18295.9i			1.11172i	−0.831275	+	0.555862i	$0.812388\pi$
$648$		−	5558.08i		−	0.336947i
$649$	−18131.4			−1.09664
$650$	8985.26	−	35874.7i	0.542201	−	2.16480i
$651$	31364.9			1.88831
$652$		−	12234.4i		−	0.734873i
$653$			21460.6i			1.28609i	0.765827	+	0.643047i	$0.222330\pi$
$653$			21460.6i			1.28609i	−0.765827	+	0.643047i	$0.777670\pi$
$654$	6018.83			0.359870
$655$	2798.72	−	2184.19i	0.166954	−	0.130295i
$656$	13250.9			0.788662
$657$		−	46541.4i		−	2.76370i
$658$		−	13154.4i		−	0.779347i
$659$	−12995.2			−0.768167			−0.384083	−	0.923298i	$-0.625482\pi$
$659$	−12995.2			−0.768167			−0.384083	+	0.923298i	$0.625482\pi$
$660$	−13104.4	−	16791.3i	−0.772861	−	0.990305i
$661$	−28097.3			−1.65334			−0.826669	−	0.562688i	$-0.809767\pi$
$661$	−28097.3			−1.65334			−0.826669	+	0.562688i	$0.809767\pi$
$662$		−	15769.6i		−	0.925835i
$663$			11323.2i			0.663283i
$664$	−13671.4			−0.799026
$665$	−9380.57	−	12019.8i	−0.547012	−	0.700914i
$666$	−54289.6			−3.15868
$667$		−	1238.15i		−	0.0718762i
$668$			4389.43i			0.254240i
$669$	−39197.3			−2.26526
$670$	−26147.7	+	20406.3i	−1.50772	+	1.17666i
$671$	1175.53			0.0676318
$672$			22890.7i			1.31403i
$673$		−	22271.4i		−	1.27563i	−0.770189	−	0.637815i	$-0.779838\pi$
$673$		−	22271.4i		−	1.27563i	0.770189	−	0.637815i	$-0.220162\pi$
$674$	−12969.9			−0.741218
$675$	−25953.8	−	6500.43i	−1.47994	−	0.370669i
$676$	22636.7			1.28793
$677$		−	14528.4i		−	0.824773i	−0.911009	−	0.412386i	$-0.864695\pi$
$677$		−	14528.4i		−	0.824773i	0.911009	−	0.412386i	$-0.135305\pi$
$678$		−	29211.5i		−	1.65466i
$679$	−2225.80			−0.125800
$680$	1496.50	−	1167.91i	0.0843944	−	0.0658636i
$681$	−27575.4			−1.55168
$682$			42224.4i			2.37075i
$683$		−	18232.0i		−	1.02142i	−0.859754	−	0.510708i	$-0.829383\pi$
$683$		−	18232.0i		−	1.02142i	0.859754	−	0.510708i	$-0.170617\pi$
$684$	−26531.8			−1.48314
$685$	7996.74	+	10246.6i	0.446043	+	0.571538i
$686$	−24273.1			−1.35095
$687$			42149.1i			2.34074i
$688$			4067.58i			0.225400i
$689$	25864.2			1.43011
$690$	−5039.93	−	6457.92i	−0.278068	−	0.356303i
$691$	−20341.1			−1.11984			−0.559921	−	0.828546i	$-0.689168\pi$
$691$	−20341.1			−1.11984			−0.559921	+	0.828546i	$0.689168\pi$
$692$			1604.18i			0.0881239i
$693$		−	29031.7i		−	1.59138i
$694$	17475.5			0.955851
$695$	−16515.6	+	12889.2i	−0.901398	+	0.703475i
$696$	−5184.69			−0.282364
$697$			2613.44i			0.142025i
$698$			25207.4i			1.36692i
$699$	−25299.1			−1.36895
$700$	7904.05	+	1979.66i	0.426778	+	0.106892i
$701$	21375.9			1.15172			0.575862	−	0.817547i	$-0.304667\pi$
$701$	21375.9			1.15172			0.575862	+	0.817547i	$0.304667\pi$
$702$		−	63327.5i		−	3.40476i
$703$		−	30644.4i		−	1.64406i
$704$	−3442.65			−0.184303
$705$	21730.1	−	16958.7i	1.16085	−	0.905961i
$706$	40566.5			2.16252
$707$			19308.0i			1.02709i
$708$		−	18434.4i		−	0.978541i
$709$	−31136.2			−1.64929			−0.824643	−	0.565653i	$-0.808624\pi$
$709$	−31136.2			−1.64929			−0.824643	+	0.565653i	$0.808624\pi$
$710$	2306.74	+	2955.74i	0.121930	+	0.156235i
$711$	4314.81			0.227592
$712$			9140.58i			0.481121i
$713$			6228.00i			0.327125i
$714$	−6505.07			−0.340961
$715$	24455.0	+	31335.5i	1.27911	+	1.63899i
$716$	16748.0			0.874168
$717$			44062.7i			2.29505i
$718$		−	15137.2i		−	0.786792i
$719$	1642.41			0.0851901			0.0425951	−	0.999092i	$-0.486437\pi$
$719$	1642.41			0.0851901			0.0425951	+	0.999092i	$0.486437\pi$
$720$	−35674.0	+	27841.0i	−1.84652	+	1.44107i
$721$	4477.65			0.231285
$722$		−	14341.9i		−	0.739264i
$723$		−	50602.9i		−	2.60296i
$724$	−372.028			−0.0190971
$725$	−1634.88	+	6527.47i	−0.0837490	+	0.334378i
$726$	17291.2			0.883936
$727$			6574.16i			0.335381i	0.985840	+	0.167690i	$0.0536309\pi$
$727$			6574.16i			0.335381i	−0.985840	+	0.167690i	$0.946369\pi$
$728$		−	11716.0i		−	0.596461i
$729$	24975.4			1.26888
$730$	−28859.3	+	22522.6i	−1.46319	+	1.14191i
$731$	−802.237			−0.0405907
$732$			1195.18i			0.0603483i
$733$			6567.05i			0.330913i	0.986217	+	0.165457i	$0.0529098\pi$
$733$			6567.05i			0.330913i	−0.986217	+	0.165457i	$0.947090\pi$
$734$	−30728.6			−1.54525
$735$	−10428.6	−	13362.7i	−0.523352	−	0.670598i
$736$	−4545.31			−0.227639
$737$		−	35648.6i		−	1.78173i
$738$		−	30920.9i		−	1.54230i
$739$	−11935.9			−0.594139			−0.297070	−	0.954856i	$-0.596009\pi$
$739$	−11935.9			−0.594139			−0.297070	+	0.954856i	$0.596009\pi$
$740$	10075.6	+	12910.4i	0.500525	+	0.641347i
$741$	75621.1			3.74900
$742$			14858.7i			0.735150i
$743$			21036.6i			1.03870i	0.854561	+	0.519352i	$0.173827\pi$
$743$			21036.6i			1.03870i	−0.854561	+	0.519352i	$0.826173\pi$
$744$	26079.4			1.28510
$745$	14960.3	−	11675.4i	0.735707	−	0.574166i
$746$	−3302.02			−0.162058
$747$			64276.9i			3.14828i
$748$		−	3358.53i		−	0.164171i
$749$	22102.4			1.07824
$750$	18043.1	+	40700.6i	0.878452	+	1.98157i
$751$	−20636.1			−1.00269			−0.501346	−	0.865247i	$-0.667161\pi$
$751$	−20636.1			−1.00269			−0.501346	+	0.865247i	$0.667161\pi$
$752$		−	22037.3i		−	1.06864i
$753$			56223.1i			2.72096i
$754$	−15927.1			−0.769271
$755$	6246.99	−	4875.31i	0.301127	−	0.235008i
$756$	13952.5			0.671229
$757$		−	3508.43i		−	0.168449i	−0.996447	−	0.0842247i	$-0.973159\pi$
$757$		−	3508.43i		−	0.168449i	0.996447	−	0.0842247i	$-0.0268413\pi$
$758$		−	25456.0i		−	1.21979i
$759$	8804.45			0.421056
$760$	−7799.79	−	9994.26i	−0.372274	−	0.477013i
$761$	8738.51			0.416256			0.208128	−	0.978102i	$-0.433263\pi$
$761$	8738.51			0.416256			0.208128	+	0.978102i	$0.433263\pi$
$762$		−	67071.4i		−	3.18863i
$763$		−	2474.71i		−	0.117419i
$764$	−3631.29			−0.171958
$765$	−5490.99	−	7035.89i	−0.259513	−	0.332527i
$766$	−25948.7			−1.22397
$767$			34401.7i			1.61952i
$768$			46864.1i			2.20190i
$769$	25104.1			1.17721			0.588606	−	0.808420i	$-0.299677\pi$
$769$	25104.1			1.17721			0.588606	+	0.808420i	$0.299677\pi$
$770$	−18001.9	+	14049.2i	−0.842526	+	0.657530i
$771$	−28209.6			−1.31770
$772$		−	5851.42i		−	0.272794i
$773$		−	15385.9i		−	0.715900i	−0.933741	−	0.357950i	$-0.883476\pi$
$773$		−	15385.9i		−	0.715900i	0.933741	−	0.357950i	$-0.116524\pi$
$774$	9491.67			0.440789
$775$	8223.58	−	32833.6i	0.381161	−	1.52183i
$776$	−1850.72			−0.0856145
$777$			34092.1i			1.57406i
$778$			15256.2i			0.703037i
$779$	17453.7			0.802751
$780$	−31859.1	+	24863.7i	−1.46248	+	1.14136i
$781$	−4029.72			−0.184629
$782$		−	1291.69i		−	0.0590672i
$783$			11522.5i			0.525903i
$784$	−13551.6			−0.617329
$785$	588.806	+	754.467i	0.0267712	+	0.0343033i
$786$	−10115.5			−0.459044
$787$		−	15157.9i		−	0.686559i	−0.939233	−	0.343279i	$-0.888462\pi$
$787$		−	15157.9i		−	0.686559i	0.939233	−	0.343279i	$-0.111538\pi$
$788$			7523.83i			0.340134i
$789$	17251.5			0.778417
$790$	−2088.05	−	2675.52i	−0.0940371	−	0.120495i
$791$	−12010.6			−0.539885
$792$		−	24139.4i		−	1.08303i
$793$		−	2230.40i		−	0.0998788i
$794$	23827.6			1.06500
$795$	−24545.6	+	19156.0i	−1.09502	+	0.854584i
$796$	21621.1			0.962738
$797$			31219.2i			1.38750i	0.720214	+	0.693752i	$0.244043\pi$
$797$			31219.2i			1.38750i	−0.720214	+	0.693752i	$0.755957\pi$
$798$			43443.6i			1.92718i
$799$	4346.36			0.192444
$800$	23962.6	+	6001.73i	1.05901	+	0.265241i
$801$	42975.0			1.89569
$802$		−	23854.2i		−	1.05028i
$803$		−	39345.5i		−	1.72911i
$804$	36244.3			1.58985
$805$	−2655.25	+	2072.22i	−0.116255	+	0.0907284i
$806$	80114.5			3.50113
$807$		−	2060.46i		−	0.0898781i
$808$			16054.2i			0.698992i
$809$	29431.9			1.27907			0.639536	−	0.768761i	$-0.279127\pi$
$809$	29431.9			1.27907			0.639536	+	0.768761i	$0.279127\pi$
$810$	12645.8	+	16203.7i	0.548551	+	0.702887i
$811$	18515.7			0.801693			0.400846	−	0.916145i	$-0.368716\pi$
$811$	18515.7			0.801693			0.400846	+	0.916145i	$0.368716\pi$
$812$		−	3509.11i		−	0.151657i
$813$		−	1548.22i		−	0.0667879i
$814$	−45895.8			−1.97622
$815$	−16909.9	−	21667.5i	−0.726784	−	0.931265i
$816$	−10897.9			−0.467526
$817$			5357.68i			0.229426i
$818$			26092.4i			1.11528i
$819$	−55083.4			−2.35015
$820$	−7353.21	+	5738.64i	−0.313153	+	0.244393i
$821$	−9013.10			−0.383142			−0.191571	−	0.981479i	$-0.561358\pi$
$821$	−9013.10			−0.383142			−0.191571	+	0.981479i	$0.561358\pi$
$822$		−	37034.8i		−	1.57146i
$823$		−	18087.0i		−	0.766065i	−0.923735	−	0.383033i	$-0.874880\pi$
$823$		−	18087.0i		−	0.766065i	0.923735	−	0.383033i	$-0.125120\pi$
$824$	3723.09			0.157403
$825$	−46416.6	−	11625.6i	−1.95881	−	0.490607i
$826$	−19763.5			−0.832517
$827$			8626.10i			0.362707i	0.983418	+	0.181354i	$0.0580478\pi$
$827$			8626.10i			0.362707i	−0.983418	+	0.181354i	$0.941952\pi$
$828$			5861.03i			0.245996i
$829$	18045.8			0.756040			0.378020	−	0.925797i	$-0.376605\pi$
$829$	18045.8			0.756040			0.378020	+	0.925797i	$0.376605\pi$
$830$	39856.7	−	31105.2i	1.66680	−	1.30082i
$831$	−43038.4			−1.79661
$832$			6531.91i			0.272180i
$833$		−	2672.74i		−	0.111170i
$834$	59692.9			2.47841
$835$	6066.89	+	7773.81i	0.251441	+	0.322184i
$836$	−22429.7			−0.927926
$837$		−	57959.3i		−	2.39351i
$838$		−	27812.5i		−	1.14650i
$839$	35148.2			1.44631			0.723153	−	0.690688i	$-0.242692\pi$
$839$	35148.2			1.44631			0.723153	+	0.690688i	$0.242692\pi$
$840$	8677.32	+	11118.7i	0.356424	+	0.456704i
$841$	−21491.0			−0.881178
$842$			22684.9i			0.928470i
$843$		−	40996.9i		−	1.67498i
$844$	1595.59			0.0650741
$845$	40090.3	−	31287.5i	1.63213	−	1.27376i
$846$	−51423.9			−2.08982
$847$		−	7109.48i		−	0.288412i
$848$			24892.6i			1.00804i
$849$	47692.6			1.92792
$850$	−1705.57	+	6809.69i	−0.0688241	+	0.274789i
$851$	−6769.53			−0.272687
$852$		−	4097.06i		−	0.164745i
$853$		−	42491.4i		−	1.70560i	−0.522235	−	0.852802i	$-0.674902\pi$
$853$		−	42491.4i		−	1.70560i	0.522235	−	0.852802i	$-0.325098\pi$
$854$	1281.35			0.0513428
$855$	−46988.6	+	36671.2i	−1.87950	+	1.46682i
$856$	18377.8			0.733808
$857$		−	36447.7i		−	1.45278i	−0.687284	−	0.726388i	$-0.741197\pi$
$857$		−	36447.7i		−	1.45278i	0.687284	−	0.726388i	$-0.258803\pi$
$858$		−	113257.i		−	4.50644i
$859$	11724.8			0.465712			0.232856	−	0.972511i	$-0.425193\pi$
$859$	11724.8			0.465712			0.232856	+	0.972511i	$0.425193\pi$
$860$	−1761.56	−	2257.18i	−0.0698475	−	0.0894991i
$861$	−19417.3			−0.768573
$862$			37050.5i			1.46397i
$863$			4830.08i			0.190519i	0.995452	+	0.0952594i	$0.0303680\pi$
$863$			4830.08i			0.190519i	−0.995452	+	0.0952594i	$0.969632\pi$
$864$	42299.8			1.66559
$865$	2217.23	+	2841.05i	0.0871538	+	0.111675i
$866$	13086.0			0.513486
$867$			41297.8i			1.61770i
$868$			17651.1i			0.690228i
$869$	3647.69			0.142393
$870$	15115.1	−	11796.2i	0.589023	−	0.459689i
$871$	−67638.0			−2.63126
$872$		−	2057.68i		−	0.0799102i
$873$			8701.26i			0.337334i
$874$	−8626.42			−0.333859
$875$	16734.5	−	7418.60i	0.646548	−	0.286622i
$876$	40003.0			1.54289
$877$		−	6737.03i		−	0.259399i	−0.991553	−	0.129700i	$-0.958599\pi$
$877$		−	6737.03i		−	0.259399i	0.991553	−	0.129700i	$-0.0414013\pi$
$878$		−	59932.1i		−	2.30366i
$879$	−12391.1			−0.475475
$880$	−30158.4	+	23536.4i	−1.15527	+	0.901605i
$881$	−35249.2			−1.34799			−0.673993	−	0.738737i	$-0.735422\pi$
$881$	−35249.2			−1.34799			−0.673993	+	0.738737i	$0.735422\pi$
$882$			31622.5i			1.20724i
$883$			1535.95i			0.0585376i	0.999572	+	0.0292688i	$0.00931787\pi$
$883$			1535.95i			0.0585376i	−0.999572	+	0.0292688i	$0.990682\pi$
$884$	−6372.31			−0.242448
$885$	−25479.3	−	32647.9i	−0.967769	−	1.24005i
$886$	31650.5			1.20013
$887$			8233.79i			0.311684i	0.987782	+	0.155842i	$0.0498091\pi$
$887$			8233.79i			0.311684i	−0.987782	+	0.155842i	$0.950191\pi$
$888$			28347.0i			1.07124i
$889$	−27577.1			−1.04039
$890$	−20796.7	−	26647.8i	−0.783266	−	1.00364i
$891$	−22091.4			−0.830627
$892$		−	22058.9i		−	0.828013i
$893$		−	29026.8i		−	1.08773i
$894$	−54071.5			−2.02284
$895$	29661.3	−	23148.5i	1.10779	−	0.864545i
$896$	16955.3			0.632184
$897$		−	16705.1i		−	0.621816i
$898$			46555.8i			1.73005i
$899$	−14577.0			−0.540788
$900$	7739.03	−	30899.0i	0.286631	−	1.14441i
$901$	−4909.50			−0.181531
$902$		−	26140.2i		−	0.964937i
$903$		−	5960.46i		−	0.219658i
$904$	−9986.64			−0.367423
$905$	−658.873	+	514.202i	−0.0242008	+	0.0188869i
$906$	−22578.7			−0.827956
$907$		−	43170.8i		−	1.58044i	−0.612822	−	0.790221i	$-0.709966\pi$
$907$		−	43170.8i		−	1.58044i	0.612822	−	0.790221i	$-0.290034\pi$
$908$		−	15518.5i		−	0.567180i
$909$	75479.9			2.75414
$910$	26656.3	+	34156.0i	0.971040	+	1.24424i
$911$	5824.68			0.211833			0.105917	−	0.994375i	$-0.466222\pi$
$911$	5824.68			0.211833			0.105917	+	0.994375i	$0.466222\pi$
$912$			72780.5i			2.64255i
$913$			54338.9i			1.96972i
$914$	−30256.6			−1.09497
$915$	1651.92	+	2116.69i	0.0596840	+	0.0764761i
$916$	−23720.1			−0.855603
$917$			4159.11i			0.149777i
$918$			12020.7i			0.432182i
$919$	−13010.1			−0.466990			−0.233495	−	0.972358i	$-0.575016\pi$
$919$	−13010.1			−0.466990			−0.233495	+	0.972358i	$0.575016\pi$
$920$	−2207.79	+	1723.02i	−0.0791182	+	0.0617459i
$921$	3916.56			0.140125
$922$		−	904.762i		−	0.0323175i
$923$			7645.81i			0.272660i
$924$	24953.2			0.888419
$925$	35688.5	+	8938.63i	1.26858	+	0.317730i
$926$	19052.6			0.676143
$927$		−	17504.3i		−	0.620191i
$928$		−	10638.5i		−	0.376322i
$929$	377.165			0.0133201			0.00666006	−	0.999978i	$-0.497880\pi$
$929$	377.165			0.0133201			0.00666006	+	0.999978i	$0.497880\pi$
$930$	−76030.1	+	59335.9i	−2.68078	+	2.09215i
$931$	−17849.7			−0.628357
$932$		−	14237.4i		−	0.500390i
$933$			42762.8i			1.50053i
$934$	43466.8			1.52278
$935$	−4642.02	−	5948.05i	−0.162364	−	0.208045i
$936$	−45800.9			−1.59941
$937$		−	2171.31i		−	0.0757029i	−0.999283	−	0.0378514i	$-0.987949\pi$
$937$		−	2171.31i		−	0.0757029i	0.999283	−	0.0378514i	$-0.0120514\pi$
$938$		−	38857.4i		−	1.35260i
$939$	−6567.05			−0.228229
$940$	9543.79	+	12228.9i	0.331153	+	0.424324i
$941$	−33788.7			−1.17054			−0.585271	−	0.810837i	$-0.699012\pi$
$941$	−33788.7			−1.17054			−0.585271	+	0.810837i	$0.699012\pi$
$942$		−	2726.90i		−	0.0943176i
$943$		−	3855.62i		−	0.133146i
$944$	−33109.5			−1.14155
$945$	24710.4	−	19284.6i	0.850612	−	0.663840i
$946$	8024.14			0.275779
$947$		−	2577.92i		−	0.0884596i	−0.999021	−	0.0442298i	$-0.985917\pi$
$947$		−	2577.92i		−	0.0884596i	0.999021	−	0.0442298i	$-0.0140834\pi$
$948$			3708.64i			0.127058i
$949$	−74652.3			−2.55355
$950$	45478.0	+	11390.5i	1.55316	+	0.389007i
$951$	61947.1			2.11227
$952$			2223.91i			0.0757116i
$953$			21604.7i			0.734360i	0.930150	+	0.367180i	$0.119677\pi$
$953$			21604.7i			0.734360i	−0.930150	+	0.367180i	$0.880323\pi$
$954$	58086.8			1.97131
$955$	−6431.13	+	5019.02i	−0.217912	+	0.170065i
$956$	−24797.0			−0.838904
$957$			20607.3i			0.696070i
$958$			23328.0i			0.786737i
$959$	−15227.3			−0.512736
$960$	−4837.79	−	6198.91i	−0.162645	−	0.208405i
$961$	43532.2			1.46125
$962$			87080.5i			2.91849i
$963$		−	86404.3i		−	2.89132i
$964$	28477.6			0.951453
$965$	−8087.59	−	10363.0i	−0.269792	−	0.345698i
$966$	9596.96			0.319645
$967$		−	15016.0i		−	0.499360i	−0.968328	−	0.249680i	$-0.919675\pi$
$967$		−	15016.0i		−	0.499360i	0.968328	−	0.249680i	$-0.0803254\pi$
$968$		−	5911.41i		−	0.196281i
$969$	−14354.3			−0.475878
$970$	5395.46	−	4210.76i	0.178596	−	0.139381i
$971$	−32612.7			−1.07785			−0.538924	−	0.842354i	$-0.681169\pi$
$971$	−32612.7			−1.07785			−0.538924	+	0.842354i	$0.681169\pi$
$972$			6300.78i			0.207919i
$973$		−	24543.4i		−	0.808659i
$974$	29938.3			0.984893
$975$	−22057.8	+	88068.5i	−0.724529	+	2.89277i
$976$	2146.62			0.0704012
$977$			13511.9i			0.442459i	0.975222	+	0.221230i	$0.0710070\pi$
$977$			13511.9i			0.442459i	−0.975222	+	0.221230i	$0.928993\pi$
$978$			78313.8i			2.56053i
$979$	36330.5			1.18604
$980$	7520.05	−	5868.85i	0.245122	−	0.191299i
$981$	−9674.29			−0.314859
$982$		−	42279.6i		−	1.37393i
$983$			17566.0i			0.569958i	0.958534	+	0.284979i	$0.0919866\pi$
$983$			17566.0i			0.569958i	−0.958534	+	0.284979i	$0.908013\pi$
$984$	−16145.2			−0.523059
$985$	10399.1	+	13324.9i	0.336390	+	0.431033i
$986$	3023.26			0.0976472
$987$			32292.5i			1.04142i
$988$			42557.0i			1.37036i
$989$	1183.54			0.0380530
$990$	54922.0	+	70374.4i	1.76317	+	2.25924i
$991$	10376.0			0.332599			0.166300	−	0.986075i	$-0.446818\pi$
$991$	10376.0			0.332599			0.166300	+	0.986075i	$0.446818\pi$
$992$			53512.7i			1.71273i
$993$			38712.7i			1.23717i
$994$	−4392.45			−0.140161
$995$	38291.6	−	29883.8i	1.22003	−	0.952140i
$996$	−55246.8			−1.75759
$997$		−	49298.7i		−	1.56600i	−0.622020	−	0.783002i	$-0.713688\pi$
$997$		−	49298.7i		−	1.56600i	0.622020	−	0.783002i	$-0.286312\pi$
$998$		−	44346.3i		−	1.40657i
$999$	62998.9			1.99519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.b.a.24.7	✓	34
5.2	odd	4		575.4.a.r.1.14		17
5.3	odd	4		575.4.a.q.1.4		17
5.4	even	2	inner	115.4.b.a.24.28	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.b.a.24.7	✓	34	1.1	even	1	trivial
115.4.b.a.24.28	yes	34	5.4	even	2	inner
575.4.a.q.1.4		17	5.3	odd	4
575.4.a.r.1.14		17	5.2	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)

\(f(q)\)	\(=\)	\(q-3.60232i q^{2} +8.84330i q^{3} -4.97671 q^{4} +(-8.81390 + 6.87860i) q^{5} +31.8564 q^{6} -13.0981i q^{7} -10.8909i q^{8} -51.2040 q^{9} +O(q^{10})\)	\(q-3.60232i q^{2} +8.84330i q^{3} -4.97671 q^{4} +(-8.81390 + 6.87860i) q^{5} +31.8564 q^{6} -13.0981i q^{7} -10.8909i q^{8} -51.2040 q^{9} +(24.7789 + 31.7505i) q^{10} -43.2873 q^{11} -44.0106i q^{12} +82.1312i q^{13} -47.1836 q^{14} +(-60.8296 - 77.9440i) q^{15} -79.0460 q^{16} -15.5900i q^{17} +184.453i q^{18} -104.117 q^{19} +(43.8642 - 34.2328i) q^{20} +115.831 q^{21} +155.935i q^{22} +23.0000i q^{23} +96.3112 q^{24} +(30.3697 - 121.255i) q^{25} +295.863 q^{26} -214.044i q^{27} +65.1855i q^{28} -53.8327 q^{29} +(-280.779 + 219.128i) q^{30} +270.783 q^{31} +197.622i q^{32} -382.802i q^{33} -56.1602 q^{34} +(90.0967 + 115.446i) q^{35} +254.828 q^{36} +294.327i q^{37} +375.062i q^{38} -726.311 q^{39} +(74.9139 + 95.9910i) q^{40} -167.636 q^{41} -417.259i q^{42} -51.4584i q^{43} +215.428 q^{44} +(451.307 - 352.212i) q^{45} +82.8534 q^{46} +278.791i q^{47} -699.028i q^{48} +171.439 q^{49} +(-436.798 - 109.401i) q^{50} +137.867 q^{51} -408.743i q^{52} -314.913i q^{53} -771.053 q^{54} +(381.530 - 297.756i) q^{55} -142.650 q^{56} -920.735i q^{57} +193.923i q^{58} +418.863 q^{59} +(302.731 + 387.905i) q^{60} -27.1566 q^{61} -975.445i q^{62} +670.676i q^{63} +79.5303 q^{64} +(-564.948 - 723.896i) q^{65} -1378.98 q^{66} +823.536i q^{67} +77.5870i q^{68} -203.396 q^{69} +(415.872 - 324.557i) q^{70} +93.0926 q^{71} +557.656i q^{72} +908.940i q^{73} +1060.26 q^{74} +(1072.29 + 268.568i) q^{75} +518.159 q^{76} +566.982i q^{77} +2616.40i q^{78} -84.2670 q^{79} +(696.704 - 543.726i) q^{80} +510.343 q^{81} +603.877i q^{82} -1255.31i q^{83} -576.455 q^{84} +(107.238 + 137.409i) q^{85} -185.370 q^{86} -476.059i q^{87} +471.435i q^{88} -839.289 q^{89} +(-1268.78 - 1625.75i) q^{90} +1075.76 q^{91} -114.464i q^{92} +2394.61i q^{93} +1004.29 q^{94} +(917.674 - 716.177i) q^{95} -1747.63 q^{96} -169.933i q^{97} -617.579i q^{98} +2216.48 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9}+O(q^{10}) \) 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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