LMFDB - Embedded newform 115.5.i.a.74.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,5,Mod(14,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 21]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("115.14");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	115.i (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.8875457546$
Analytic rank:	$0$
Dimension:	$460$
Relative dimension:	$46$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			74.15
Character	$\chi$	$=$	115.74
Dual form			115.5.i.a.14.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.944999 + 3.21837i) q^{2} +(6.93728 + 6.01119i) q^{3} +(3.99518 + 2.56754i) q^{4} +(17.7521 - 17.6030i) q^{5} +(-25.9019 + 16.6462i) q^{6} +(19.4786 + 42.6523i) q^{7} +(-52.5982 + 45.5766i) q^{8} +(0.463978 + 3.22704i) q^{9} +O(q^{10})$	\(q+(-0.944999 + 3.21837i) q^{2} +(6.93728 + 6.01119i) q^{3} +(3.99518 + 2.56754i) q^{4} +(17.7521 - 17.6030i) q^{5} +(-25.9019 + 16.6462i) q^{6} +(19.4786 + 42.6523i) q^{7} +(-52.5982 + 45.5766i) q^{8} +(0.463978 + 3.22704i) q^{9} +(39.8771 + 73.7675i) q^{10} +(-9.95524 - 33.9044i) q^{11} +(12.2817 + 41.8275i) q^{12} +(277.513 + 126.736i) q^{13} +(-155.678 + 22.3831i) q^{14} +(228.966 - 15.4056i) q^{15} +(-65.4117 - 143.232i) q^{16} +(-27.8798 + 17.9172i) q^{17} +(-10.8243 - 1.55629i) q^{18} +(12.0707 - 18.7824i) q^{19} +(116.119 - 24.7477i) q^{20} +(-121.262 + 412.981i) q^{21} +118.525 q^{22} +(-381.883 + 366.069i) q^{23} -638.858 q^{24} +(5.27221 - 624.978i) q^{25} +(-670.133 + 773.374i) q^{26} +(385.801 - 600.318i) q^{27} +(-31.6910 + 220.416i) q^{28} +(-877.150 + 563.710i) q^{29} +(-166.791 + 751.455i) q^{30} +(-594.808 - 686.445i) q^{31} +(-579.437 + 83.3105i) q^{32} +(134.744 - 295.047i) q^{33} +(-31.3179 - 106.659i) q^{34} +(1096.59 + 414.285i) q^{35} +(-6.43189 + 14.0839i) q^{36} +(200.047 + 1391.36i) q^{37} +(49.0418 + 56.5972i) q^{38} +(1163.35 + 2547.39i) q^{39} +(-131.444 + 1734.96i) q^{40} +(355.409 - 2471.92i) q^{41} +(-1214.53 - 780.532i) q^{42} +(88.6910 - 102.355i) q^{43} +(47.2782 - 161.015i) q^{44} +(65.0420 + 49.1193i) q^{45} +(-817.266 - 1574.97i) q^{46} +898.358i q^{47} +(407.213 - 1386.84i) q^{48} +(132.521 - 152.938i) q^{49} +(2006.43 + 607.571i) q^{50} +(-301.113 - 43.2936i) q^{51} +(783.314 + 1218.86i) q^{52} +(-949.614 - 2079.36i) q^{53} +(1567.46 + 1808.95i) q^{54} +(-773.544 - 426.632i) q^{55} +(-2968.49 - 1355.66i) q^{56} +(196.642 - 57.7393i) q^{57} +(-985.321 - 3355.70i) q^{58} +(-151.316 + 331.337i) q^{59} +(954.313 + 526.332i) q^{60} +(1187.44 - 1028.92i) q^{61} +(2771.33 - 1265.62i) q^{62} +(-128.603 + 82.6481i) q^{63} +(637.988 - 4437.31i) q^{64} +(7157.36 - 2635.22i) q^{65} +(822.239 + 712.474i) q^{66} +(-2788.60 - 818.806i) q^{67} -157.388 q^{68} +(-4849.74 + 243.953i) q^{69} +(-2369.60 + 3137.74i) q^{70} +(7751.01 + 2275.90i) q^{71} +(-171.482 - 148.590i) q^{72} +(4380.90 - 6816.82i) q^{73} +(-4666.95 - 671.006i) q^{74} +(3793.43 - 4303.95i) q^{75} +(96.4491 - 44.0468i) q^{76} +(1252.19 - 1085.03i) q^{77} +(-9297.80 + 1336.82i) q^{78} +(9657.91 + 4410.62i) q^{79} +(-3682.49 - 1391.22i) q^{80} +(6538.42 - 1919.85i) q^{81} +(7619.70 + 3479.80i) q^{82} +(-828.373 - 5761.46i) q^{83} +(-1544.81 + 1338.58i) q^{84} +(-179.527 + 808.834i) q^{85} +(245.603 + 382.166i) q^{86} +(-9473.60 - 1362.10i) q^{87} +(2068.88 + 1329.59i) q^{88} +(-5380.93 - 4662.61i) q^{89} +(-219.549 + 162.912i) q^{90} +14305.2i q^{91} +(-2465.59 + 482.009i) q^{92} -8337.57i q^{93} +(-2891.25 - 848.947i) q^{94} +(-116.345 - 545.906i) q^{95} +(-4520.51 - 2905.16i) q^{96} +(-975.079 + 6781.82i) q^{97} +(366.977 + 571.028i) q^{98} +(104.792 - 47.8569i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 460 q + 306 q^{4} - 11 q^{5} - 182 q^{6} + 944 q^{9}+O(q^{10}) $ 460 * q + 306 * q^4 - 11 * q^5 - 182 * q^6 + 944 * q^9	$ 460 q + 306 q^{4} - 11 q^{5} - 182 q^{6} + 944 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 1474 q^{15} - 2670 q^{16} - 22 q^{19} + 3157 q^{20} - 22 q^{21} + 3896 q^{24} - 1427 q^{25} - 3166 q^{26} - 2808 q^{29} + 1397 q^{30} + 2684 q^{31} - 12848 q^{34} + 2279 q^{35} + 1114 q^{36} + 12866 q^{39} - 11 q^{40} - 2652 q^{41} + 11110 q^{44} - 5394 q^{46} - 27026 q^{49} - 10931 q^{50} - 22 q^{51} - 51290 q^{54} - 10545 q^{55} + 25322 q^{56} + 41460 q^{59} + 49269 q^{60} - 22506 q^{61} + 68582 q^{64} + 27940 q^{65} - 24332 q^{66} + 7608 q^{69} - 15618 q^{70} + 35838 q^{71} - 59158 q^{74} + 30594 q^{75} - 58520 q^{76} - 17930 q^{79} - 63602 q^{80} + 91888 q^{81} + 92906 q^{84} - 33815 q^{85} + 101486 q^{86} - 22 q^{89} - 37598 q^{90} - 46242 q^{94} + 43336 q^{95} - 210180 q^{96} + 44528 q^{99}+O(q^{100}) $ 460 * q + 306 * q^4 - 11 * q^5 - 182 * q^6 + 944 * q^9 - 11 * q^10 - 22 * q^11 - 22 * q^14 - 1474 * q^15 - 2670 * q^16 - 22 * q^19 + 3157 * q^20 - 22 * q^21 + 3896 * q^24 - 1427 * q^25 - 3166 * q^26 - 2808 * q^29 + 1397 * q^30 + 2684 * q^31 - 12848 * q^34 + 2279 * q^35 + 1114 * q^36 + 12866 * q^39 - 11 * q^40 - 2652 * q^41 + 11110 * q^44 - 5394 * q^46 - 27026 * q^49 - 10931 * q^50 - 22 * q^51 - 51290 * q^54 - 10545 * q^55 + 25322 * q^56 + 41460 * q^59 + 49269 * q^60 - 22506 * q^61 + 68582 * q^64 + 27940 * q^65 - 24332 * q^66 + 7608 * q^69 - 15618 * q^70 + 35838 * q^71 - 59158 * q^74 + 30594 * q^75 - 58520 * q^76 - 17930 * q^79 - 63602 * q^80 + 91888 * q^81 + 92906 * q^84 - 33815 * q^85 + 101486 * q^86 - 22 * q^89 - 37598 * q^90 - 46242 * q^94 + 43336 * q^95 - 210180 * q^96 + 44528 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{1}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.944999	+	3.21837i	−0.236250	+	0.804592i	0.752958	+	0.658069i	$0.228627\pi$
$2$	−0.944999	+	3.21837i	−0.236250	+	0.804592i	−0.989207	+	0.146523i	$0.953192\pi$
$3$	6.93728	+	6.01119i	0.770809	+	0.667910i	0.948713	−	0.316138i	$-0.102386\pi$
$3$	6.93728	+	6.01119i	0.770809	+	0.667910i	−0.177904	+	0.984048i	$0.556932\pi$
$4$	3.99518	+	2.56754i	0.249699	+	0.160471i
$5$	17.7521	−	17.6030i	0.710083	−	0.704118i
$5$	17.7521	−	17.6030i	0.710083	−	0.704118i
$6$	−25.9019	+	16.6462i	−0.719498	+	0.462394i
$7$	19.4786	+	42.6523i	0.397523	+	0.870455i	0.997515	+	0.0704487i	$0.0224431\pi$
$7$	19.4786	+	42.6523i	0.397523	+	0.870455i	−0.599992	+	0.800006i	$0.704830\pi$
$8$	−52.5982	+	45.5766i	−0.821847	+	0.712134i
$9$	0.463978	+	3.22704i	0.00572813	+	0.0398400i
$10$	39.8771	+	73.7675i	0.398771	+	0.737675i
$11$	−9.95524	−	33.9044i	−0.0822747	−	0.280202i	0.908072	−	0.418814i	$-0.137554\pi$
$11$	−9.95524	−	33.9044i	−0.0822747	−	0.280202i	−0.990347	+	0.138612i	$0.955736\pi$
$12$	12.2817	+	41.8275i	0.0852894	+	0.290469i
$13$	277.513	+	126.736i	1.64209	+	0.749917i	0.999862	−	0.0165971i	$-0.00528328\pi$
$13$	277.513	+	126.736i	1.64209	+	0.749917i	0.642227	+	0.766514i	$0.278011\pi$
$14$	−155.678	+	22.3831i	−0.794276	+	0.114200i
$15$	228.966	−	15.4056i	1.01763	−	0.0684692i
$16$	−65.4117	−	143.232i	−0.255514	−	0.559499i
$17$	−27.8798	+	17.9172i	−0.0964697	+	0.0619973i	−0.587986	−	0.808871i	$-0.700079\pi$
$17$	−27.8798	+	17.9172i	−0.0964697	+	0.0619973i	0.491517	+	0.870868i	$0.336443\pi$
$18$	−10.8243	−	1.55629i	−0.0334082	−	0.00480338i
$19$	12.0707	−	18.7824i	0.0334368	−	0.0520287i	−0.824133	−	0.566397i	$-0.808337\pi$
$19$	12.0707	−	18.7824i	0.0334368	−	0.0520287i	0.857570	+	0.514368i	$0.171973\pi$
$20$	116.119	−	24.7477i	0.290298	−	0.0618692i
$21$	−121.262	+	412.981i	−0.274971	+	0.936464i
$22$	118.525			0.244886
$23$	−381.883	+	366.069i	−0.721896	+	0.692002i
$23$	−381.883	+	366.069i	−0.721896	+	0.692002i
$24$	−638.858			−1.10913
$25$	5.27221	−	624.978i	0.00843553	−	0.999964i
$26$	−670.133	+	773.374i	−0.991321	+	1.14405i
$27$	385.801	−	600.318i	0.529220	−	0.823482i
$28$	−31.6910	+	220.416i	−0.0404222	+	0.281142i
$29$	−877.150	+	563.710i	−1.04298	+	0.670285i	−0.945723	−	0.324974i	$-0.894645\pi$
$29$	−877.150	+	563.710i	−1.04298	+	0.670285i	−0.0972611	+	0.995259i	$0.531008\pi$
$30$	−166.791	+	751.455i	−0.185324	+	0.834950i
$31$	−594.808	−	686.445i	−0.618947	−	0.714303i	0.356559	−	0.934273i	$-0.383950\pi$
$31$	−594.808	−	686.445i	−0.618947	−	0.714303i	−0.975507	+	0.219969i	$0.929404\pi$
$32$	−579.437	+	83.3105i	−0.565857	+	0.0813579i
$33$	134.744	−	295.047i	0.123732	−	0.270934i
$34$	−31.3179	−	106.659i	−0.0270916	−	0.0922657i
$35$	1096.59	+	414.285i	0.895177	+	0.338192i
$36$	−6.43189	+	14.0839i	−0.00496288	+	0.0108672i
$37$	200.047	+	1391.36i	0.146127	+	1.01633i	0.922483	+	0.386038i	$0.126157\pi$
$37$	200.047	+	1391.36i	0.146127	+	1.01633i	−0.776356	+	0.630294i	$0.782934\pi$
$38$	49.0418	+	56.5972i	0.0339625	+	0.0391948i
$39$	1163.35	+	2547.39i	0.764860	+	1.67481i
$40$	−131.444	+	1734.96i	−0.0821527	+	1.08435i
$41$	355.409	−	2471.92i	0.211427	−	1.47051i	−0.556970	−	0.830533i	$-0.688036\pi$
$41$	355.409	−	2471.92i	0.211427	−	1.47051i	0.768397	−	0.639974i	$-0.221055\pi$
$42$	−1214.53	−	780.532i	−0.688510	−	0.442479i
$43$	88.6910	−	102.355i	0.0479670	−	0.0553569i	−0.731259	−	0.682100i	$-0.761067\pi$
$43$	88.6910	−	102.355i	0.0479670	−	0.0553569i	0.779226	+	0.626743i	$0.215612\pi$
$44$	47.2782	−	161.015i	0.0244205	−	0.0831688i
$45$	65.0420	+	49.1193i	0.0321195	+	0.0242564i
$46$	−817.266	−	1574.97i	−0.386232	−	0.744317i
$47$			898.358i			0.406681i	0.979108	+	0.203340i	$0.0651798\pi$
$47$			898.358i			0.406681i	−0.979108	+	0.203340i	$0.934820\pi$
$48$	407.213	−	1386.84i	0.176742	−	0.601927i
$49$	132.521	−	152.938i	0.0551941	−	0.0636974i
$50$	2006.43	+	607.571i	0.802571	+	0.243028i
$51$	−301.113	−	43.2936i	−0.115768	−	0.0166450i
$52$	783.314	+	1218.86i	0.289687	+	0.450762i
$53$	−949.614	−	2079.36i	−0.338061	−	0.740251i	0.661895	−	0.749596i	$-0.269752\pi$
$53$	−949.614	−	2079.36i	−0.338061	−	0.740251i	−0.999956	+	0.00934583i	$0.997025\pi$
$54$	1567.46	+	1808.95i	0.537539	+	0.620353i
$55$	−773.544	−	426.632i	−0.255717	−	0.141036i
$56$	−2968.49	−	1355.66i	−0.946584	−	0.432290i
$57$	196.642	−	57.7393i	0.0605239	−	0.0177714i
$58$	−985.321	−	3355.70i	−0.292902	−	0.997532i
$59$	−151.316	+	331.337i	−0.0434693	+	0.0951844i	−0.930121	−	0.367254i	$-0.880298\pi$
$59$	−151.316	+	331.337i	−0.0434693	+	0.0951844i	0.886651	+	0.462438i	$0.153025\pi$
$60$	954.313	+	526.332i	0.265087	+	0.146203i
$61$	1187.44	−	1028.92i	0.319119	−	0.276518i	−0.480540	−	0.876973i	$-0.659559\pi$
$61$	1187.44	−	1028.92i	0.319119	−	0.276518i	0.799659	+	0.600455i	$0.205014\pi$
$62$	2771.33	−	1265.62i	0.720949	−	0.329246i
$63$	−128.603	+	82.6481i	−0.0324019	+	0.0208234i
$64$	637.988	−	4437.31i	0.155759	−	1.08333i
$65$	7157.36	−	2635.22i	1.69405	−	0.623722i
$66$	822.239	+	712.474i	0.188760	+	0.163562i
$67$	−2788.60	−	818.806i	−0.621207	−	0.182403i	−0.0440408	−	0.999030i	$-0.514023\pi$
$67$	−2788.60	−	818.806i	−0.621207	−	0.182403i	−0.577166	+	0.816627i	$0.695841\pi$
$68$	−157.388			−0.0340372
$69$	−4849.74	+	243.953i	−1.01864	+	0.0512398i
$70$	−2369.60	+	3137.74i	−0.483592	+	0.640355i
$71$	7751.01	+	2275.90i	1.53759	+	0.451478i	0.937365	−	0.348350i	$-0.113258\pi$
$71$	7751.01	+	2275.90i	1.53759	+	0.451478i	0.600229	+	0.799828i	$0.295076\pi$
$72$	−171.482	−	148.590i	−0.0330791	−	0.0286632i
$73$	4380.90	−	6816.82i	0.822087	−	1.27919i	−0.135421	−	0.990788i	$-0.543239\pi$
$73$	4380.90	−	6816.82i	0.822087	−	1.27919i	0.957509	−	0.288405i	$-0.0931248\pi$
$74$	−4666.95	−	671.006i	−0.852256	−	0.122536i
$75$	3793.43	−	4303.95i	0.674388	−	0.765147i
$76$	96.4491	−	44.0468i	0.0166982	−	0.00762583i
$77$	1252.19	−	1085.03i	0.211197	−	0.183003i
$78$	−9297.80	+	1336.82i	−1.52824	+	0.219727i
$79$	9657.91	+	4410.62i	1.54749	+	0.706717i	0.992167	−	0.124915i	$-0.0398658\pi$
$79$	9657.91	+	4410.62i	1.54749	+	0.706717i	0.555327	+	0.831632i	$0.312593\pi$
$80$	−3682.49	−	1391.22i	−0.575390	−	0.217378i
$81$	6538.42	−	1919.85i	0.996558	−	0.292616i
$82$	7619.70	+	3479.80i	1.13321	+	0.517519i
$83$	−828.373	−	5761.46i	−0.120246	−	0.836328i	−0.957277	−	0.289173i	$-0.906620\pi$
$83$	−828.373	−	5761.46i	−0.120246	−	0.836328i	0.837031	−	0.547155i	$-0.184289\pi$
$84$	−1544.81	+	1338.58i	−0.218936	+	0.189709i
$85$	−179.527	+	808.834i	−0.0248481	+	0.111949i
$86$	245.603	+	382.166i	0.0332075	+	0.0516719i
$87$	−9473.60	−	1362.10i	−1.25163	−	0.179957i
$88$	2068.88	+	1329.59i	0.267159	+	0.171692i
$89$	−5380.93	−	4662.61i	−0.679325	−	0.588638i	0.245332	−	0.969439i	$-0.421103\pi$
$89$	−5380.93	−	4662.61i	−0.679325	−	0.588638i	−0.924657	+	0.380801i	$0.875648\pi$
$90$	−219.549	+	162.912i	−0.0271048	+	0.0201125i
$91$			14305.2i			1.72747i
$92$	−2465.59	+	482.009i	−0.291303	+	0.0569481i
$93$		−	8337.57i		−	0.963992i
$94$	−2891.25	−	848.947i	−0.327212	−	0.0960782i
$95$	−116.345	−	545.906i	−0.0128914	−	0.0604882i
$96$	−4520.51	−	2905.16i	−0.490507	−	0.315230i
$97$	−975.079	+	6781.82i	−0.103633	+	0.720780i	0.870065	+	0.492937i	$0.164077\pi$
$97$	−975.079	+	6781.82i	−0.103633	+	0.720780i	−0.973698	+	0.227844i	$0.926833\pi$
$98$	366.977	+	571.028i	0.0382109	+	0.0594573i
$99$	104.792	−	47.8569i	0.0106920	−	0.00488286i
$100$	1625.72	−	2483.36i	0.162572	−	0.248336i
$101$	−1237.17	−	8604.74i	−0.121280	−	0.843519i	−0.956109	−	0.293010i	$-0.905343\pi$
$101$	−1237.17	−	8604.74i	−0.121280	−	0.843519i	0.834830	−	0.550508i	$-0.185566\pi$
$102$	423.887	−	928.182i	0.0407427	−	0.0892140i
$103$	−17604.2	+	5169.06i	−1.65937	+	0.487234i	−0.971189	−	0.238310i	$-0.923407\pi$
$103$	−17604.2	+	5169.06i	−1.65937	+	0.487234i	−0.688176	+	0.725544i	$0.741588\pi$
$104$	−20372.9	+	5982.02i	−1.88359	+	0.553071i
$105$	5117.02	+	9465.83i	0.464129	+	0.858579i
$106$	7589.54	−	1091.21i	0.675467	−	0.0971175i
$107$	11798.4	+	13616.1i	1.03052	+	1.18928i	0.981692	+	0.190475i	$0.0610028\pi$
$107$	11798.4	+	13616.1i	1.03052	+	1.18928i	0.0488268	+	0.998807i	$0.484452\pi$
$108$	3082.69	−	1407.82i	0.264291	−	0.120698i
$109$	5606.90	+	8724.51i	0.471921	+	0.734324i	0.992862	−	0.119269i	$-0.0380550\pi$
$109$	5606.90	+	8724.51i	0.471921	+	0.734324i	−0.520941	+	0.853593i	$0.674419\pi$
$110$	2104.06	−	2086.38i	0.173889	−	0.172428i
$111$	−6975.94	+	10854.8i	−0.566183	+	0.880997i
$112$	4835.03	−	5579.92i	0.385445	−	0.444828i
$113$	−10276.7	−	3017.51i	−0.804815	−	0.236315i	−0.146650	−	0.989189i	$-0.546849\pi$
$113$	−10276.7	−	3017.51i	−0.804815	−	0.236315i	−0.658165	+	0.752874i	$0.728667\pi$
$114$			687.430i			0.0528955i
$115$	−335.320	+	13220.7i	−0.0253550	+	0.999679i
$116$	−4951.72			−0.367993
$117$	−280.222	+	954.349i	−0.0204706	+	0.0697165i
$118$	−923.371	−	800.105i	−0.0663150	−	0.0574623i
$119$	−1307.27	−	840.132i	−0.0923148	−	0.0593271i
$120$	−11341.0	+	11245.8i	−0.787573	+	0.780957i
$121$	11266.4	−	7240.47i	0.769510	−	0.494534i
$122$	2189.32	+	4793.95i	0.147092	+	0.322088i
$123$	17324.7	−	15012.0i	1.14514	−	0.992265i
$124$	−613.885	−	4269.67i	−0.0399249	−	0.277684i
$125$	−10907.9	−	11187.5i	−0.698103	−	0.715997i
$126$	−144.463	−	491.994i	−0.00909943	−	0.0309898i
$127$	−2438.42	−	8304.49i	−0.151182	−	0.514879i	0.848720	−	0.528842i	$-0.177374\pi$
$127$	−2438.42	−	8304.49i	−0.151182	−	0.514879i	−0.999903	+	0.0139627i	$0.995555\pi$
$128$	5158.08	+	2355.61i	0.314824	+	0.143775i
$129$	1230.55	−	176.926i	0.0739468	−	0.0106319i
$130$	1717.43	+	25525.3i	0.101623	+	1.51037i
$131$	−3642.59	−	7976.16i	−0.212260	−	0.464784i	0.773315	−	0.634021i	$-0.218597\pi$
$131$	−3642.59	−	7976.16i	−0.212260	−	0.464784i	−0.985575	+	0.169237i	$0.945870\pi$
$132$	1295.87	−	832.806i	0.0743728	−	0.0477965i
$133$	1036.23	+	148.988i	0.0585805	+	0.00842261i
$134$	5270.44	−	8200.96i	0.293520	−	0.456725i
$135$	−3718.60	−	17448.1i	−0.204039	−	0.957373i
$136$	649.818	−	2213.08i	0.0351329	−	0.119652i
$137$	11689.8			0.622828			0.311414	−	0.950274i	$-0.399197\pi$
$137$	11689.8			0.622828			0.311414	+	0.950274i	$0.399197\pi$
$138$	3797.86	−	15838.8i	0.199426	−	0.831694i
$139$	11277.5			0.583694			0.291847	−	0.956465i	$-0.405730\pi$
$139$	11277.5			0.583694			0.291847	+	0.956465i	$0.405730\pi$
$140$	3317.39	+	4470.69i	0.169254	+	0.228096i
$141$	−5400.20	+	6232.16i	−0.271626	+	0.313473i
$142$	−14649.4	+	22794.9i	−0.726512	+	1.13047i
$143$	1534.20	−	10670.6i	0.0750258	−	0.521816i
$144$	431.865	−	277.543i	0.0208268	−	0.0133846i
$145$	−5648.27	+	25447.4i	−0.268645	+	1.21034i
$146$	17799.1	+	20541.2i	0.835011	+	0.963654i
$147$	1838.67	−	264.361i	0.0850883	−	0.0122338i
$148$	−2773.15	+	6072.35i	−0.126605	+	0.277226i
$149$	−4346.73	−	14803.6i	−0.195790	−	0.666799i	−0.997601	−	0.0692219i	$-0.977948\pi$
$149$	−4346.73	−	14803.6i	−0.195790	−	0.666799i	0.801811	−	0.597577i	$-0.203870\pi$
$150$	10266.9	+	16275.9i	0.456308	+	0.723373i
$151$	−5935.90	+	12997.8i	−0.260335	+	0.570054i	−0.993990	−	0.109468i	$-0.965085\pi$
$151$	−5935.90	+	12997.8i	−0.260335	+	0.570054i	0.733655	+	0.679522i	$0.237813\pi$
$152$	221.139	+	1538.06i	0.00957148	+	0.0665711i
$153$	−70.7552	−	81.6559i	−0.00302257	−	0.00348823i
$154$	2308.70	+	5055.35i	0.0973478	+	0.213162i
$155$	−22642.5	−	1715.45i	−0.942458	−	0.0714026i
$156$	−1892.73	+	13164.2i	−0.0777748	+	0.540936i
$157$	5708.87	+	3668.87i	0.231607	+	0.148845i	0.651297	−	0.758823i	$-0.274225\pi$
$157$	5708.87	+	3668.87i	0.231607	+	0.148845i	−0.419691	+	0.907667i	$0.637861\pi$
$158$	−23321.7	+	26914.7i	−0.934214	+	1.07814i
$159$	5911.71	−	20133.4i	0.233840	−	0.796386i
$160$	−8819.70	+	11678.7i	−0.344520	+	0.456201i
$161$	−23052.2	−	9157.65i	−0.889327	−	0.353291i
$162$			22857.3i			0.870953i
$163$	6784.44	−	23105.7i	0.255352	−	0.869647i	−0.727634	−	0.685965i	$-0.759380\pi$
$163$	6784.44	−	23105.7i	0.255352	−	0.869647i	0.982986	−	0.183682i	$-0.0588017\pi$
$164$	7766.69	−	8963.23i	0.288767	−	0.333255i
$165$	−2801.73	−	7609.59i	−0.102910	−	0.279507i
$166$	19325.3	+	2778.56i	0.701311	+	0.100833i
$167$	30.1931	+	46.9814i	0.00108262	+	0.00168458i	0.841794	−	0.539798i	$-0.181499\pi$
$167$	30.1931	+	46.9814i	0.00108262	+	0.00168458i	−0.840712	+	0.541483i	$0.817863\pi$
$168$	−12444.1	−	27248.7i	−0.440904	−	0.965446i
$169$	42248.0	+	48756.8i	1.47922	+	1.70711i
$170$	−2433.47	−	1342.13i	−0.0842032	−	0.0464406i
$171$	66.2120	+	30.2380i	0.00226435	+	0.00103410i
$172$	617.137	−	181.208i	0.0208605	−	0.00612519i
$173$	−15842.6	−	53954.9i	−0.529339	−	1.80276i	−0.593515	−	0.804823i	$-0.702260\pi$
$173$	−15842.6	−	53954.9i	−0.529339	−	1.80276i	0.0641761	−	0.997939i	$-0.479558\pi$
$174$	13336.3	−	29202.4i	0.440490	−	0.964538i
$175$	26759.4	−	11948.8i	0.873777	−	0.390166i
$176$	−4205.00	+	3643.65i	−0.135750	+	0.117628i
$177$	−3041.45	+	1388.99i	−0.0970811	+	0.0443354i
$178$	20091.0	−	12911.7i	0.634104	−	0.407514i
$179$	−36.9767	+	257.178i	−0.00115404	+	0.00802654i	−0.990390	−	0.138300i	$-0.955836\pi$
$179$	−36.9767	+	257.178i	−0.00115404	+	0.00802654i	0.989236	+	0.146327i	$0.0467451\pi$
$180$	133.738	+	363.238i	0.00412773	+	0.0112111i
$181$	−38781.9	−	33604.7i	−1.18378	−	1.02575i	−0.999077	−	0.0429605i	$-0.986321\pi$
$181$	−38781.9	−	33604.7i	−1.18378	−	1.02575i	−0.184707	−	0.982794i	$-0.559134\pi$
$182$	−46039.5	−	13518.4i	−1.38991	−	0.408115i
$183$	14422.6			0.430668
$184$	3402.18	−	36659.5i	0.100490	−	1.08281i
$185$	28043.3	+	21178.1i	0.819380	+	0.618790i
$186$	26833.4	+	7878.99i	0.775621	+	0.227743i
$187$	885.023	+	766.877i	0.0253088	+	0.0219302i
$188$	−2306.57	+	3589.10i	−0.0652607	+	0.101548i
$189$	33119.8	+	4761.91i	0.927181	+	0.133308i
$190$	1866.87	+	141.438i	0.0517139	+	0.00391795i
$191$	−32504.8	+	14844.4i	−0.891006	+	0.406909i	−0.807685	−	0.589614i	$-0.799280\pi$
$191$	−32504.8	+	14844.4i	−0.891006	+	0.406909i	−0.0833206	+	0.996523i	$0.526553\pi$
$192$	31099.4	−	26947.8i	0.843625	−	0.731005i
$193$	−41613.7	+	5983.15i	−1.11718	+	0.160626i	−0.676076	−	0.736832i	$-0.736321\pi$
$193$	−41613.7	+	5983.15i	−1.11718	+	0.160626i	−0.441101	+	0.897457i	$0.645412\pi$
$194$	−20905.0	−	9546.97i	−0.555451	−	0.253666i
$195$	65493.4	+	24743.0i	1.72238	+	0.650702i
$196$	922.119	−	270.759i	0.0240035	−	0.00704807i
$197$	−24077.0	−	10995.6i	−0.620398	−	0.283326i	0.0803150	−	0.996770i	$-0.474407\pi$
$197$	−24077.0	−	10995.6i	−0.620398	−	0.283326i	−0.700713	+	0.713443i	$0.747135\pi$
$198$	54.9929	+	382.484i	0.00140274	+	0.00975625i
$199$	−12125.0	+	10506.4i	−0.306179	+	0.265306i	−0.794374	−	0.607429i	$-0.792201\pi$
$199$	−12125.0	+	10506.4i	−0.306179	+	0.265306i	0.488195	+	0.872735i	$0.337656\pi$
$200$	28207.0	+	33113.0i	0.705176	+	0.827825i
$201$	−14423.3	−	22443.1i	−0.357003	−	0.555507i
$202$	28862.3	+	4149.78i	0.707341	+	0.101700i
$203$	−41129.2	−	26432.1i	−0.998063	−	0.641416i
$204$	−1091.84	−	946.088i	−0.0262361	−	0.0227337i
$205$	−37203.9	−	50138.0i	−0.885279	−	1.19305i
$206$		−	61541.6i		−	1.45022i
$207$	−1358.50	−	1062.50i	−0.0317045	−	0.0247965i
$208$		−	48038.7i		−	1.11036i
$209$	−756.972	−	222.267i	−0.0173295	−	0.00508841i
$210$	−35300.1	+	7523.28i	−0.800456	+	0.170596i
$211$	−18721.0	−	12031.3i	−0.420499	−	0.270238i	0.313234	−	0.949676i	$-0.398587\pi$
$211$	−18721.0	−	12031.3i	−0.420499	−	0.270238i	−0.733733	+	0.679438i	$0.762224\pi$
$212$	1544.98	−	10745.6i	0.0343758	−	0.239089i
$213$	40090.0	+	62381.3i	0.883644	+	1.37498i
$214$	−54971.1	+	25104.5i	−1.20035	+	0.548180i
$215$	−227.299	−	3378.24i	−0.00491723	−	0.0730824i
$216$	7068.02	+	49159.1i	0.151492	+	1.05365i
$217$	17692.4	−	38741.0i	0.375723	−	0.822718i
$218$	−33377.2	+	9800.43i	−0.702323	+	0.206221i
$219$	71368.7	−	20955.7i	1.48806	−	0.436933i
$220$	−1995.05	−	3690.58i	−0.0412200	−	0.0762517i
$221$	−10007.8	+	1438.90i	−0.204905	+	0.0294609i
$222$	−28342.4	−	32708.9i	−0.575083	−	0.663681i
$223$	141.089	−	64.4331i	0.00283715	−	0.00129568i	−0.413996	−	0.910279i	$-0.635867\pi$
$223$	141.089	−	64.4331i	0.00283715	−	0.00129568i	0.416833	+	0.908983i	$0.363140\pi$
$224$	−14840.0	−	23091.5i	−0.295760	−	0.460211i
$225$	2019.27	−	272.963i	0.0398869	−	0.00539185i
$226$	19422.9	−	30222.6i	0.380274	−	0.591719i
$227$	−39005.1	+	45014.3i	−0.756954	+	0.873571i	−0.995223	−	0.0976278i	$-0.968875\pi$
$227$	−39005.1	+	45014.3i	−0.756954	+	0.873571i	0.238269	+	0.971199i	$0.423420\pi$
$228$	933.868	+	274.208i	0.0179645	+	0.00527486i
$229$			41533.2i			0.791998i	0.918251	+	0.395999i	$0.129602\pi$
$229$			41533.2i			0.791998i	−0.918251	+	0.395999i	$0.870398\pi$
$230$	−42232.4	−	13572.8i	−0.798344	−	0.256574i
$231$	15209.1			0.285022
$232$	20444.5	−	69627.6i	0.379840	−	1.29362i
$233$	66367.8	+	57508.0i	1.22249	+	1.05929i	0.996364	+	0.0851957i	$0.0271516\pi$
$233$	66367.8	+	57508.0i	1.22249	+	1.05929i	0.226126	+	0.974098i	$0.427394\pi$
$234$	−2806.64	−	1803.72i	−0.0512572	−	0.0329410i
$235$	15813.8	+	15947.7i	0.286351	+	0.288777i
$236$	−1455.26	+	935.238i	−0.0261286	+	0.0167918i
$237$	40486.6	+	88653.2i	0.720799	+	1.57833i
$238$	3939.22	−	3413.36i	0.0695435	−	0.0602598i
$239$	1683.34	+	11707.9i	0.0294698	+	0.204967i	0.999237	−	0.0390666i	$-0.0124384\pi$
$239$	1683.34	+	11707.9i	0.0294698	+	0.204967i	−0.969767	+	0.244033i	$0.921529\pi$
$240$	−17183.6	−	31787.4i	−0.298326	−	0.551865i
$241$	−6718.93	−	22882.6i	−0.115682	−	0.393977i	0.881213	−	0.472720i	$-0.156728\pi$
$241$	−6718.93	−	22882.6i	−0.115682	−	0.393977i	−0.996895	+	0.0787426i	$0.974909\pi$
$242$	12655.8	+	43101.6i	0.216102	+	0.735975i
$243$	4321.26	+	1973.45i	0.0731809	+	0.0334206i
$244$	7385.84	−	1061.92i	0.124057	−	0.0178367i
$245$	−339.627	−	5047.72i	−0.00565810	−	0.0840937i
$246$	31942.2	+	69943.7i	0.527831	+	1.15579i
$247$	5730.18	−	3682.56i	0.0939235	−	0.0603609i
$248$	62571.7	+	8996.45i	1.01736	+	0.146274i
$249$	28886.6	−	44948.4i	0.465905	−	0.724962i
$250$	46313.3	−	24533.4i	0.741013	−	0.392534i
$251$	16371.9	−	55757.7i	0.259868	−	0.885029i	−0.721422	−	0.692495i	$-0.756511\pi$
$251$	16371.9	−	55757.7i	0.259868	−	0.885029i	0.981290	−	0.192534i	$-0.0616705\pi$
$252$	−725.994			−0.0114323
$253$	16213.1	+	9303.22i	0.253294	+	0.145342i
$254$	29031.2			0.449985
$255$	−6107.48	+	4531.94i	−0.0939252	+	0.0696953i
$256$	34515.6	−	39833.1i	0.526666	−	0.607805i
$257$	−32993.5	+	51338.9i	−0.499531	+	0.777285i	−0.995865	−	0.0908467i	$-0.971043\pi$
$257$	−32993.5	+	51338.9i	−0.499531	+	0.777285i	0.496334	+	0.868131i	$0.334679\pi$
$258$	−593.453	+	4127.56i	−0.00891553	+	0.0620088i
$259$	−55448.0	+	35634.3i	−0.826583	+	0.531212i
$260$	35361.0	+	7848.66i	0.523091	+	0.116104i
$261$	−2226.09	−	2569.05i	−0.0326785	−	0.0377130i
$262$	29112.5	−	4185.74i	0.424108	−	0.0609776i
$263$	−50479.1	+	110534.i	−0.729794	+	1.59803i	0.0698547	+	0.997557i	$0.477746\pi$
$263$	−50479.1	+	110534.i	−0.729794	+	1.59803i	−0.799649	+	0.600468i	$0.794981\pi$
$264$	6359.98	+	21660.1i	0.0912532	+	0.310780i
$265$	−53460.5	−	20197.0i	−0.761275	−	0.287604i
$266$	−1458.73	+	3194.18i	−0.0206164	+	0.0451436i
$267$	−9301.25	−	64691.6i	−0.130472	−	0.907456i
$268$	−9038.61	−	10431.1i	−0.125844	−	0.145232i
$269$	−10738.8	−	23514.7i	−0.148406	−	0.324964i	0.820800	−	0.571216i	$-0.193528\pi$
$269$	−10738.8	−	23514.7i	−0.148406	−	0.324964i	−0.969206	+	0.246252i	$0.920801\pi$
$270$	59668.6	+	4520.62i	0.818499	+	0.0620112i
$271$	−14300.8	+	99464.6i	−0.194726	+	1.35435i	0.624567	+	0.780971i	$0.285275\pi$
$271$	−14300.8	+	99464.6i	−0.194726	+	1.35435i	−0.819293	+	0.573376i	$0.805634\pi$
$272$	4389.98	+	2821.27i	0.0593368	+	0.0381335i
$273$	−85991.3	+	99239.3i	−1.15380	+	1.33155i
$274$	−11046.9	+	37622.3i	−0.147143	+	0.501122i
$275$	−21242.0	+	6043.05i	−0.280886	+	0.0799081i
$276$	−20001.9	−	11477.3i	−0.262575	−	0.150668i
$277$			120227.i			1.56691i	0.621449	+	0.783455i	$0.286544\pi$
$277$			120227.i			1.56691i	−0.621449	+	0.783455i	$0.713456\pi$
$278$	−10657.3	+	36295.3i	−0.137897	+	0.469635i
$279$	1939.21	−	2237.97i	0.0249124	−	0.0287505i
$280$	−76560.5	+	28188.3i	−0.976536	+	0.359545i
$281$	−114885.	−	16517.9i	−1.45496	−	0.209191i	−0.630973	−	0.775805i	$-0.717344\pi$
$281$	−114885.	−	16517.9i	−1.45496	−	0.209191i	−0.823984	+	0.566614i	$0.808253\pi$
$282$	−14954.2	−	23269.2i	−0.188047	−	0.292606i
$283$	17525.6	+	38375.8i	0.218827	+	0.479164i	0.986927	−	0.161165i	$-0.0515252\pi$
$283$	17525.6	+	38375.8i	0.218827	+	0.479164i	−0.768100	+	0.640329i	$0.778798\pi$
$284$	25123.2	+	28993.7i	0.311485	+	0.359473i
$285$	2474.42	−	4486.47i	0.0304638	−	0.0552351i
$286$	32892.2	+	15021.3i	0.402124	+	0.183644i
$287$	112356.	−	32990.7i	1.36406	−	0.400523i
$288$	−537.693	−	1831.21i	−0.00648260	−	0.0220777i
$289$	−34239.6	+	74974.3i	−0.409952	+	0.897670i
$290$	−76561.7	−	42226.0i	−0.910365	−	0.502093i
$291$	−47531.2	+	41186.0i	−0.561297	+	0.486367i
$292$	35005.0	−	15986.2i	0.410548	−	0.187491i
$293$	72464.4	−	46570.0i	0.844091	−	0.542465i	−0.0456353	−	0.998958i	$-0.514531\pi$
$293$	72464.4	−	46570.0i	0.844091	−	0.542465i	0.889727	+	0.456494i	$0.150895\pi$
$294$	−886.731	+	6167.35i	−0.0102588	+	0.0713516i
$295$	3146.33	+	8545.53i	0.0361543	+	0.0981963i
$296$	−73935.5	−	64065.5i	−0.843859	−	0.731208i
$297$	−24194.2	−	7104.06i	−0.274283	−	0.0805366i
$298$	51751.1			0.582757
$299$	−152372.	+	53190.6i	−1.70436	+	0.594967i
$300$	26206.0	−	7455.25i	0.291178	−	0.0828361i
$301$	6093.25	+	1789.14i	0.0672537	+	0.0197475i
$302$	−36222.3	−	31386.8i	−0.397157	−	0.344139i
$303$	43142.1	−	67130.3i	0.469911	−	0.731196i
$304$	−3479.79	−	500.319i	−0.0376536	−	0.00541377i
$305$	2967.45	−	39168.0i	0.0318995	−	0.421048i
$306$	329.662	−	150.552i	0.00352068	−	0.00160784i
$307$	14488.3	−	12554.2i	0.153724	−	0.133203i	−0.574603	−	0.818432i	$-0.694844\pi$
$307$	14488.3	−	12554.2i	0.153724	−	0.133203i	0.728327	+	0.685230i	$0.240298\pi$
$308$	7788.56	−	1119.83i	0.0821024	−	0.0118045i
$309$	−153197.	−	69962.9i	−1.60448	−	0.732742i
$310$	26918.1	−	71251.0i	0.280105	−	0.741425i
$311$	73171.4	−	21485.1i	0.756520	−	0.222134i	0.119344	−	0.992853i	$-0.461921\pi$
$311$	73171.4	−	21485.1i	0.756520	−	0.222134i	0.637176	+	0.770719i	$0.280103\pi$
$312$	−177291.	−	80966.3i	−1.82129	−	0.831754i
$313$	−20802.4	−	144684.i	−0.212337	−	1.47684i	−0.765323	−	0.643646i	$-0.777421\pi$
$313$	−20802.4	−	144684.i	−0.212337	−	1.47684i	0.552986	−	0.833190i	$-0.313488\pi$
$314$	−17202.7	+	14906.2i	−0.174476	+	0.151184i
$315$	−828.119	+	3730.97i	−0.00834587	+	0.0376011i
$316$	27260.6	+	42418.3i	0.272999	+	0.424795i
$317$	−42758.9	−	6147.80i	−0.425508	−	0.0611789i	−0.0737657	−	0.997276i	$-0.523502\pi$
$317$	−42758.9	−	6147.80i	−0.425508	−	0.0611789i	−0.351743	+	0.936097i	$0.614411\pi$
$318$	59210.3	+	38052.1i	0.585521	+	0.376292i
$319$	27844.5	+	24127.4i	0.273626	+	0.237099i
$320$	−66784.1	−	90001.8i	−0.652188	−	0.878924i
$321$			165381.i			1.60500i
$322$	51257.0	−	65536.6i	0.494358	−	0.632081i
$323$			739.921i			0.00709219i
$324$	31051.4	+	9117.52i	0.295795	+	0.0868534i
$325$	80670.3	−	172771.i	0.763742	−	1.63571i
$326$	67951.3	+	43669.6i	0.639385	+	0.410908i
$327$	−13548.0	+	94228.5i	−0.126701	+	0.881225i
$328$	93967.9	+	146217.i	0.873437	+	1.35910i
$329$	−38317.0	+	17498.8i	−0.353997	+	0.161665i
$330$	27138.1	−	1825.94i	0.249202	−	0.0167671i
$331$	−1891.11	−	13153.0i	−0.0172608	−	0.120052i	0.979369	−	0.202079i	$-0.0647697\pi$
$331$	−1891.11	−	13153.0i	−0.0172608	−	0.120052i	−0.996630	+	0.0820270i	$0.973861\pi$
$332$	11483.3	−	25144.9i	0.104182	−	0.228126i
$333$	−4397.15	+	1291.12i	−0.0396536	+	0.0116434i
$334$	−179.736	+	52.7752i	−0.00161117	+	0.000473083i
$335$	−63916.8	+	34552.0i	−0.569541	+	0.307882i
$336$	67083.8	−	9645.20i	0.594209	−	0.0854344i
$337$	−78487.1	−	90579.0i	−0.691097	−	0.797568i	0.296424	−	0.955056i	$-0.404206\pi$
$337$	−78487.1	−	90579.0i	−0.691097	−	0.797568i	−0.987521	+	0.157488i	$0.949660\pi$
$338$	−196842.	+	89894.7i	−1.72300	+	0.786866i
$339$	−53153.4	−	82708.3i	−0.462521	−	0.719697i
$340$	−2793.96	+	2770.49i	−0.0241692	+	0.0239662i
$341$	−17352.1	+	27000.4i	−0.149225	+	0.232199i
$342$	−159.887	+	184.520i	−0.00136698	+	0.00157758i
$343$	117126.	+	34391.3i	0.995555	+	0.292321i
$344$			9425.92i			0.0796538i
$345$	−81798.6	+	89700.4i	−0.687239	+	0.753626i
$346$	188618.			1.57554
$347$	−14782.4	+	50344.1i	−0.122768	+	0.418109i	−0.997826	−	0.0659095i	$-0.979005\pi$
$347$	−14782.4	+	50344.1i	−0.122768	+	0.418109i	0.875058	+	0.484019i	$0.160823\pi$
$348$	−34351.4	−	29765.7i	−0.283652	−	0.245786i
$349$	−132943.	−	85437.5i	−1.09148	−	0.701451i	−0.134298	−	0.990941i	$-0.542878\pi$
$349$	−132943.	−	85437.5i	−1.09148	−	0.701451i	−0.957181	+	0.289490i	$0.906514\pi$
$350$	13168.2	+	97413.4i	0.107495	+	0.795211i
$351$	183147.	−	117701.i	1.48657	−	0.955360i
$352$	8593.03	+	18816.1i	0.0693523	+	0.151860i
$353$	−41266.9	+	35758.0i	−0.331171	+	0.286961i	−0.804535	−	0.593906i	$-0.797585\pi$
$353$	−41266.9	+	35758.0i	−0.331171	+	0.286961i	0.473364	+	0.880867i	$0.343040\pi$
$354$	−1596.10	−	11101.1i	−0.0127366	−	0.0885849i
$355$	177659.	−	96038.7i	1.40971	−	0.762060i
$356$	−9526.33	−	32443.7i	−0.0751668	−	0.255994i
$357$	−4018.71	−	13686.5i	−0.0315319	−	0.107388i
$358$	−792.752	−	362.038i	−0.00618545	−	0.00282480i
$359$	244079.	−	35093.3i	1.89383	−	0.272292i	0.905470	−	0.424411i	$-0.139519\pi$
$359$	244079.	−	35093.3i	1.89383	−	0.272292i	0.988362	+	0.152119i	$0.0486097\pi$
$360$	−5659.78	+	380.809i	−0.0436711	+	0.00293834i
$361$	53930.2	+	118091.i	0.413826	+	0.906153i
$362$	144801.	−	93058.2i	1.10498	−	0.710129i
$363$	121682.	+	17495.2i	0.923449	+	0.132772i
$364$	−36729.3	+	57151.8i	−0.277210	+	0.431348i
$365$	−42226.0	−	198129.i	−0.316953	−	1.48718i
$366$	−13629.4	+	46417.4i	−0.101745	+	0.346512i
$367$	67342.5			0.499985			0.249993	−	0.968248i	$-0.419572\pi$
$367$	67342.5			0.499985			0.249993	+	0.968248i	$0.419572\pi$
$368$	77412.3	+	30752.5i	0.571629	+	0.227083i
$369$	8141.89			0.0597961
$370$	−94659.8	+	70240.4i	−0.691452	+	0.513078i
$371$	70192.4	−	81006.4i	0.509967	−	0.588534i
$372$	21407.1	−	33310.1i	0.154693	−	0.240707i
$373$	−38694.1	+	269123.i	−0.278116	+	1.93434i	0.0714816	+	0.997442i	$0.477227\pi$
$373$	−38694.1	+	269123.i	−0.278116	+	1.93434i	−0.349598	+	0.936900i	$0.613682\pi$
$374$	−3304.44	+	2123.63i	−0.0236241	+	0.0151823i
$375$	−8420.98	−	143180.i	−0.0598825	−	1.01817i
$376$	−40944.1	−	47252.0i	−0.289611	−	0.334229i
$377$	−314863.	+	45270.4i	−2.21533	+	0.318517i
$378$	−46623.8	+	102092.i	−0.326305	+	0.714508i
$379$	−15166.7	−	51652.9i	−0.105587	−	0.359597i	0.889703	−	0.456540i	$-0.150912\pi$
$379$	−15166.7	−	51652.9i	−0.105587	−	0.359597i	−0.995290	+	0.0969434i	$0.969093\pi$
$380$	936.817	−	2479.71i	0.00648765	−	0.0171725i
$381$	33003.8	−	72268.3i	0.227360	−	0.497850i
$382$	−17057.9	−	118640.i	−0.116896	−	0.813028i
$383$	72875.8	+	84103.2i	0.496805	+	0.573343i	0.947671	−	0.319248i	$-0.103430\pi$
$383$	72875.8	+	84103.2i	0.496805	+	0.573343i	−0.450866	+	0.892591i	$0.648885\pi$
$384$	21623.0	+	47347.7i	0.146640	+	0.321097i
$385$	3129.25	−	41303.6i	0.0211115	−	0.278655i
$386$	20068.9	−	139582.i	0.134694	−	0.936820i
$387$	371.454	+	238.719i	0.00248018	+	0.00159391i
$388$	−21308.2	+	24591.0i	−0.141542	+	0.163348i
$389$	−69059.7	+	235196.i	−0.456379	+	1.55428i	0.334552	+	0.942377i	$0.391415\pi$
$389$	−69059.7	+	235196.i	−0.456379	+	1.55428i	−0.790931	+	0.611905i	$0.790403\pi$
$390$	−141523.	+	187400.i	−0.930461	+	1.23208i
$391$	4087.86	−	17048.2i	0.0267388	−	0.111513i
$392$			14084.1i			0.0916552i
$393$	22676.5	−	77229.2i	0.146822	−	0.500030i
$394$	58140.7	−	67097.9i	0.374531	−	0.432232i
$395$	249088.	−	91710.1i	1.59646	−	0.587791i
$396$	541.537	+	77.8613i	0.00345333	+	0.000496514i
$397$	26592.4	+	41378.6i	0.168724	+	0.262540i	0.915311	−	0.402749i	$-0.131945\pi$
$397$	26592.4	+	41378.6i	0.168724	+	0.262540i	−0.746587	+	0.665288i	$0.768309\pi$
$398$	−22355.3	−	48951.3i	−0.141128	−	0.309028i
$399$	6293.03	+	7262.55i	0.0395289	+	0.0456187i
$400$	−89861.5	+	40125.7i	−0.561634	+	0.250786i
$401$	−73437.1	−	33537.6i	−0.456695	−	0.208566i	0.173765	−	0.984787i	$-0.444407\pi$
$401$	−73437.1	−	33537.6i	−0.456695	−	0.208566i	−0.630460	+	0.776221i	$0.717134\pi$
$402$	85860.0	−	25210.8i	0.531299	−	0.156003i
$403$	−78069.8	−	265881.i	−0.480699	−	1.63711i
$404$	17150.3	−	37553.9i	0.105077	−	0.230087i
$405$	82275.4	−	149177.i	0.501603	−	0.909476i
$406$	123935.	−	107391.i	0.751871	−	0.651500i
$407$	45181.7	−	20633.8i	0.272756	−	0.124563i
$408$	17811.2	−	11446.6i	0.106997	−	0.0687630i
$409$	34637.3	−	240908.i	0.207060	−	1.44014i	−0.575622	−	0.817716i	$-0.695240\pi$
$409$	34637.3	−	240908.i	0.207060	−	1.44014i	0.782683	−	0.622421i	$-0.213851\pi$
$410$	196520.	−	72355.5i	1.16907	−	0.430431i
$411$	81095.8	+	70269.9i	0.480081	+	0.415993i
$412$	−83603.7	−	24548.3i	−0.492528	−	0.144619i
$413$	−17079.7			−0.100134
$414$	4703.31	−	3368.11i	0.0274412	−	0.0196510i
$415$	−116124.	−	87696.1i	−0.674258	−	0.509195i
$416$	−171360.	−	50315.8i	−0.990199	−	0.290749i
$417$	78235.5	+	67791.4i	0.449916	+	0.389855i
$418$	1430.67	−	2226.17i	0.00818820	−	0.0127411i
$419$	207947.	+	29898.2i	1.18447	+	0.170301i	0.706265	−	0.707948i	$-0.250379\pi$
$419$	207947.	+	29898.2i	1.18447	+	0.170301i	0.478204	+	0.878249i	$0.341288\pi$
$420$	−3860.52	+	50955.8i	−0.0218850	+	0.288865i
$421$	−140676.	+	64244.5i	−0.793698	+	0.362470i	−0.770645	−	0.637265i	$-0.780066\pi$
$421$	−140676.	+	64244.5i	−0.793698	+	0.362470i	−0.0230529	+	0.999734i	$0.507339\pi$
$422$	56412.4	−	48881.6i	0.316774	−	0.274486i
$423$	−2899.04	+	416.819i	−0.0162022	+	0.00232952i
$424$	144718.	+	66090.6i	0.804992	+	0.367628i
$425$	11050.9	+	17518.7i	0.0611814	+	0.0969893i
$426$	−238651.	+	70074.3i	−1.31506	+	0.386135i
$427$	67015.6	+	30605.0i	0.367553	+	0.167856i
$428$	12176.8	+	84691.6i	0.0664731	+	0.462331i
$429$	74786.2	−	64802.7i	0.406356	−	0.352110i
$430$	11087.2	+	2460.90i	0.0599633	+	0.0133093i
$431$	−170867.	−	265874.i	−0.919823	−	1.43127i	−0.902147	−	0.431428i	$-0.858010\pi$
$431$	−170867.	−	265874.i	−0.919823	−	1.43127i	−0.0176751	−	0.999844i	$-0.505626\pi$
$432$	−111220.	−	15991.1i	−0.595960	−	0.0856861i
$433$	−73462.4	−	47211.4i	−0.391823	−	0.251809i	0.329865	−	0.944028i	$-0.392997\pi$
$433$	−73462.4	−	47211.4i	−0.391823	−	0.251809i	−0.721687	+	0.692219i	$0.756633\pi$
$434$	107963.	+	93550.8i	0.573188	+	0.496670i
$435$	−192153.	+	142583.i	−1.01547	+	0.753512i
$436$			49251.9i			0.259090i
$437$	2266.05	+	11591.4i	0.0118660	+	0.0606976i
$438$			249494.i			1.30051i
$439$	−57492.9	−	16881.5i	−0.298322	−	0.0875953i	0.129146	−	0.991626i	$-0.458776\pi$
$439$	−57492.9	−	16881.5i	−0.298322	−	0.0875953i	−0.427468	+	0.904030i	$0.640594\pi$
$440$	60131.5	−	12815.4i	0.310596	−	0.0661953i
$441$	555.023	+	356.691i	0.00285387	+	0.00183407i
$442$	4826.41	−	33568.4i	0.0247047	−	0.171825i
$443$	88291.4	+	137384.i	0.449895	+	0.700050i	0.989924	−	0.141596i	$-0.0452235\pi$
$443$	88291.4	+	137384.i	0.449895	+	0.700050i	−0.540030	+	0.841646i	$0.681587\pi$
$444$	−55740.2	+	25455.7i	−0.282750	+	0.129128i
$445$	−177598.	+	11949.4i	−0.896848	+	0.0603429i
$446$	74.0408	+	514.965i	0.000372222	+	0.00258886i
$447$	58832.8	−	128826.i	0.294445	−	0.644745i
$448$	201688.	−	59221.0i	1.00490	−	0.295067i
$449$	157398.	−	46216.1i	0.780739	−	0.229246i	0.133008	−	0.991115i	$-0.457536\pi$
$449$	157398.	−	46216.1i	0.780739	−	0.229246i	0.647731	+	0.761869i	$0.275718\pi$
$450$	−1029.72	+	6756.72i	−0.00508502	+	0.0333665i
$451$	−87347.3	+	12558.6i	−0.429434	+	0.0617433i
$452$	−33309.6	−	38441.3i	−0.163039	−	0.188157i
$453$	−119311.	+	54487.6i	−0.581413	+	0.265522i
$454$	−108013.	−	168071.i	−0.524039	−	0.815420i
$455$	251814.	+	253947.i	1.21635	+	1.22665i
$456$	−7711.45	+	11999.3i	−0.0370857	+	0.0577065i
$457$	−40035.9	+	46203.9i	−0.191698	+	0.221231i	−0.843459	−	0.537193i	$-0.819485\pi$
$457$	−40035.9	+	46203.9i	−0.191698	+	0.221231i	0.651762	+	0.758424i	$0.274030\pi$
$458$	−133669.	−	39248.8i	−0.637235	−	0.187109i
$459$			23649.2i			0.112251i
$460$	−35284.5	+	51958.3i	−0.166751	+	0.245549i
$461$	−131444.			−0.618499			−0.309250	−	0.950981i	$-0.600078\pi$
$461$	−131444.			−0.618499			−0.309250	+	0.950981i	$0.600078\pi$
$462$	−14372.5	+	48948.4i	−0.0673364	+	0.229327i
$463$	28154.1	+	24395.7i	0.131335	+	0.113802i	0.718051	−	0.695990i	$-0.245034\pi$
$463$	28154.1	+	24395.7i	0.131335	+	0.113802i	−0.586717	+	0.809792i	$0.699580\pi$
$464$	138117.	+	88762.4i	0.641521	+	0.412281i
$465$	−146766.	−	148009.i	−0.678764	−	0.684514i
$466$	−247799.	+	159251.i	−1.14111	+	0.733349i
$467$	−146294.	−	320340.i	−0.670802	−	1.46885i	−0.872104	−	0.489321i	$-0.837245\pi$
$467$	−146294.	−	320340.i	−0.670802	−	1.46885i	0.201302	−	0.979529i	$-0.435483\pi$
$468$	−3569.87	+	3093.31i	−0.0162990	+	0.0141232i
$469$	−19394.1	−	134889.i	−0.0881708	−	0.613241i
$470$	−66269.6	+	35823.9i	−0.299998	+	0.162173i
$471$	17549.8	+	59769.1i	0.0791097	+	0.269423i
$472$	−7142.23	−	24324.2i	−0.0320590	−	0.109183i
$473$	−4353.23	−	1988.05i	−0.0194576	−	0.00888598i
$474$	−323579.	+	46523.6i	−1.44020	+	0.207070i
$475$	−11674.9	−	7642.94i	−0.0517448	−	0.0338745i
$476$	−3065.70	−	6712.95i	−0.0135306	−	0.0296278i
$477$	6269.59	−	4029.22i	0.0275551	−	0.0177086i
$478$	−39271.1	−	5646.34i	−0.171877	−	0.0247122i
$479$	−122387.	+	190438.i	−0.533414	+	0.830008i	−0.998471	−	0.0552724i	$-0.982397\pi$
$479$	−122387.	+	190438.i	−0.533414	+	0.830008i	0.465057	+	0.885280i	$0.346034\pi$
$480$	−131388.	+	28001.8i	−0.570260	+	0.121536i
$481$	−120820.	+	411474.i	−0.522212	+	1.77849i
$482$	79994.0			0.344321
$483$	−104871.	−	202100.i	−0.449534	−	0.866310i
$484$	63601.4			0.271504
$485$	102070.	+	137556.i	0.433927	+	0.584783i
$486$	−10434.9	+	12042.5i	−0.0441789	+	0.0509852i
$487$	−100415.	+	156249.i	−0.423390	+	0.658808i	−0.985775	−	0.168068i	$-0.946247\pi$
$487$	−100415.	+	156249.i	−0.423390	+	0.658808i	0.562386	+	0.826875i	$0.309884\pi$
$488$	−15562.4	+	108239.i	−0.0653487	+	0.454510i
$489$	185958.	−	119508.i	0.777673	−	0.499780i
$490$	16566.4	+	3677.04i	0.0689978	+	0.0153146i
$491$	16810.9	+	19400.9i	0.0697315	+	0.0804744i	0.789543	−	0.613695i	$-0.210317\pi$
$491$	16810.9	+	19400.9i	0.0697315	+	0.0804744i	−0.719812	+	0.694169i	$0.755772\pi$
$492$	107759.	−	15493.5i	0.445169	−	0.0640056i
$493$	14354.6	−	31432.2i	0.0590605	−	0.129324i
$494$	6436.83	+	21921.8i	0.0263766	+	0.0898303i
$495$	1017.85	−	2694.21i	0.00415407	−	0.0109956i
$496$	−59413.3	+	130097.i	−0.241502	+	0.528815i
$497$	53906.7	+	374930.i	0.218238	+	1.51788i
$498$	117363.	+	135444.i	0.473229	+	0.546136i
$499$	171962.	+	376545.i	0.690609	+	1.51222i	0.850998	+	0.525170i	$0.175998\pi$
$499$	171962.	+	376545.i	0.690609	+	1.51222i	−0.160388	+	0.987054i	$0.551275\pi$
$500$	−14854.5	−	72702.3i	−0.0594181	−	0.290809i
$501$	−72.9559	+	507.419i	−0.000290660	+	0.00202158i
$502$	163977.	+	105382.i	0.650694	+	0.418176i
$503$	219669.	−	253511.i	0.868226	−	1.00199i	−0.131717	−	0.991287i	$-0.542049\pi$
$503$	219669.	−	253511.i	0.868226	−	1.00199i	0.999943	−	0.0106984i	$-0.00340546\pi$
$504$	2997.46	−	10208.4i	0.0118003	−	0.0401881i
$505$	−173431.	−	130974.i	−0.680055	−	0.513573i
$506$	−45262.6	+	43388.2i	−0.176782	+	0.169461i
$507$			592201.i			2.30384i
$508$	11580.2	−	39438.6i	0.0448735	−	0.152825i
$509$	−129701.	+	149683.i	−0.500621	+	0.577747i	−0.948672	−	0.316261i	$-0.897573\pi$
$509$	−129701.	+	149683.i	−0.500621	+	0.577747i	0.448052	+	0.894008i	$0.352118\pi$
$510$	−8813.88	−	23938.8i	−0.0338865	−	0.0920370i
$511$	376087.	+	54073.1i	1.44028	+	0.207081i
$512$	144632.	+	225051.i	0.551726	+	0.858503i
$513$	−6618.51	−	14492.5i	−0.0251493	−	0.0550692i
$514$	−134049.	−	154700.i	−0.507383	−	0.585552i
$515$	−221520.	+	401648.i	−0.835217	+	1.51437i
$516$	5370.53	+	2452.64i	0.0201705	+	0.00921157i
$517$	30458.3	−	8943.37i	0.113953	−	0.0334596i
$518$	−62285.9	−	212126.i	−0.232130	−	0.790561i
$519$	214428.	−	469533.i	0.796063	−	1.74314i
$520$	−256360.	+	464816.i	−0.948076	+	1.71899i
$521$	−95750.2	+	82968.0i	−0.352748	+	0.305658i	−0.813152	−	0.582052i	$-0.802250\pi$
$521$	−95750.2	+	82968.0i	−0.352748	+	0.305658i	0.460404	+	0.887709i	$0.347705\pi$
$522$	10371.8	−	4736.64i	0.0380639	−	0.0173832i
$523$	−319065.	+	205050.i	−1.16647	+	0.749648i	−0.972852	−	0.231429i	$-0.925660\pi$
$523$	−319065.	+	205050.i	−1.16647	+	0.749648i	−0.193623	+	0.981076i	$0.562024\pi$
$524$	5926.35	−	41218.7i	0.0215837	−	0.150118i
$525$	257464.	+	77963.4i	0.934111	+	0.282860i
$526$	−308036.	−	266915.i	−1.11335	−	0.964720i
$527$	28882.3	+	8480.61i	0.103995	+	0.0305356i
$528$	−51073.9			−0.183203
$529$	11828.1	−	279591.i	0.0422673	−	0.999106i
$530$	115522.	−	152970.i	0.411255	−	0.544570i
$531$	−1139.45	−	334.571i	−0.00404114	−	0.00118659i
$532$	3757.39	+	3255.80i	0.0132759	+	0.0115036i
$533$	411912.	−	640947.i	1.44994	−	2.25615i
$534$	216991.	+	31198.6i	0.760956	+	0.109409i
$535$	449130.	+	34027.0i	1.56915	+	0.118882i
$536$	183993.	−	84027.0i	0.640432	−	0.292475i
$537$	−1802.47	+	1561.85i	−0.00625055	+	0.00541613i
$538$	85827.1	−	12340.1i	0.296524	−	0.0426337i
$539$	−6504.54	−	2970.52i	−0.0223892	−	0.0102248i
$540$	29942.4	−	79256.0i	0.102683	−	0.271797i
$541$	65528.3	−	19240.9i	0.223890	−	0.0657400i	−0.167864	−	0.985810i	$-0.553687\pi$
$541$	65528.3	−	19240.9i	0.223890	−	0.0657400i	0.391753	+	0.920070i	$0.371869\pi$
$542$	−306599.	−	140019.i	−1.04369	−	0.476639i
$543$	−67036.8	−	466251.i	−0.227360	−	1.58132i
$544$	14661.9	−	12704.6i	0.0495441	−	0.0429302i
$545$	253111.	+	56180.1i	0.852154	+	0.189143i
$546$	−238127.	−	370533.i	−0.798773	−	1.24291i
$547$	−104512.	−	15026.6i	−0.349294	−	0.0502210i	−0.0345652	−	0.999402i	$-0.511005\pi$
$547$	−104512.	−	15026.6i	−0.349294	−	0.0502210i	−0.314729	+	0.949181i	$0.601914\pi$
$548$	46703.0	+	30014.2i	0.155519	+	0.0999461i
$549$	3871.32	+	3354.52i	0.0128444	+	0.0111298i
$550$	624.886	−	74075.3i	0.00206574	−	0.244877i
$551$			23279.3i			0.0766773i
$552$	243969.	−	233866.i	0.800675	−	0.767518i
$553$			497845.i			1.62796i
$554$	−386936.	−	113615.i	−1.26072	−	0.370182i
$555$	67238.6	+	315492.i	0.218290	+	1.02424i
$556$	45055.8	+	28955.6i	0.145747	+	0.0936662i
$557$	−34816.7	+	242156.i	−0.112222	+	0.780521i	0.853528	+	0.521047i	$0.174458\pi$
$557$	−34816.7	+	242156.i	−0.112222	+	0.780521i	−0.965750	+	0.259474i	$0.916451\pi$
$558$	5370.05	+	8355.97i	0.0172469	+	0.0268366i
$559$	37585.0	−	17164.5i	0.120279	−	0.0549297i
$560$	−12391.3	−	184166.i	−0.0395130	−	0.587263i
$561$	1529.81	+	10640.1i	0.00486085	+	0.0338080i
$562$	161727.	−	354132.i	0.512047	−	1.12123i
$563$	272299.	−	79954.3i	0.859073	−	0.252247i	0.177611	−	0.984101i	$-0.443163\pi$
$563$	272299.	−	79954.3i	0.859073	−	0.252247i	0.681461	+	0.731854i	$0.261345\pi$
$564$	−37576.1	+	11033.3i	−0.118128	+	0.0346856i
$565$	−235549.	+	127333.i	−0.737879	+	0.398881i
$566$	−140069.	+	20138.9i	−0.437230	+	0.0628641i
$567$	209246.	+	241482.i	0.650864	+	0.751137i
$568$	−511417.	+	233556.i	−1.58518	+	0.723927i
$569$	−2122.99	−	3303.44i	−0.00655729	−	0.0102033i	0.837959	−	0.545733i	$-0.183749\pi$
$569$	−2122.99	−	3303.44i	−0.00655729	−	0.0102033i	−0.844517	+	0.535529i	$0.820112\pi$
$570$	12100.8	+	12203.3i	0.0372447	+	0.0375602i
$571$	255058.	−	396878.i	0.782288	−	1.21726i	−0.189610	−	0.981859i	$-0.560722\pi$
$571$	255058.	−	396878.i	0.782288	−	1.21726i	0.971898	−	0.235404i	$-0.0756412\pi$
$572$	33526.7	−	38691.8i	0.102470	−	0.118257i
$573$	−314727.	−	92412.3i	−0.958573	−	0.281463i
$574$			392779.i			1.19213i
$575$	226772.	+	240598.i	0.685888	+	0.727708i
$576$	14615.4			0.0440519
$577$	−10199.0	+	34734.7i	−0.0306342	+	0.104331i	−0.973391	−	0.229151i	$-0.926405\pi$
$577$	−10199.0	+	34734.7i	−0.0306342	+	0.104331i	0.942757	+	0.333481i	$0.108223\pi$
$578$	−208939.	−	181046.i	−0.625408	−	0.541919i
$579$	−324652.	−	208641.i	−0.968414	−	0.622362i
$580$	−87903.2	+	87164.8i	−0.261306	+	0.259111i
$581$	229604.	−	147557.i	0.680185	−	0.437128i
$582$	−87634.9	−	191894.i	−0.258721	−	0.566519i
$583$	−61046.0	+	52896.7i	−0.179606	+	0.155629i
$584$	80259.8	+	558219.i	0.235327	+	1.63674i
$585$	11824.8	+	21874.4i	0.0345528	+	0.0639182i
$586$	81400.9	+	277226.i	0.237047	+	0.807307i
$587$	−145016.	−	493879.i	−0.420862	−	1.43332i	−0.848414	−	0.529333i	$-0.822442\pi$
$587$	−145016.	−	493879.i	−0.420862	−	1.43332i	0.427552	−	0.903991i	$-0.359376\pi$
$588$	8024.58	+	3664.70i	0.0232096	+	0.0105995i
$589$	−20072.8	+	2886.03i	−0.0578599	+	0.00831900i
$590$	−30476.0	+	2050.52i	−0.0875494	+	0.00589061i
$591$	−100932.	−	221011.i	−0.288972	−	0.632760i
$592$	186201.	−	119664.i	0.531299	−	0.341445i
$593$	65777.7	+	9457.41i	0.187055	+	0.0268944i	0.235206	−	0.971946i	$-0.424424\pi$
$593$	65777.7	+	9457.41i	0.187055	+	0.0268944i	−0.0481506	+	0.998840i	$0.515333\pi$
$594$	45727.0	−	71152.5i	0.129598	−	0.201659i
$595$	−37995.6	+	8097.74i	−0.107325	+	0.0228734i
$596$	20643.0	−	70303.4i	0.0581138	−	0.197917i
$597$	−147270.			−0.413206
$598$	−27196.1	−	540653.i	−0.0760508	−	1.51188i
$599$	347132.			0.967477			0.483738	−	0.875213i	$-0.339279\pi$
$599$	347132.			0.967477			0.483738	+	0.875213i	$0.339279\pi$
$600$	−3368.19	+	399272.i	−0.00935608	+	1.10909i
$601$	405842.	−	468367.i	1.12359	−	1.29669i	0.173461	−	0.984841i	$-0.444505\pi$
$601$	405842.	−	468367.i	1.12359	−	1.29669i	0.950131	−	0.311853i	$-0.100949\pi$
$602$	−11516.2	+	17919.6i	−0.0317773	+	0.0494465i
$603$	1348.47	−	9378.82i	0.00370857	−	0.0257937i
$604$	−57087.4	+	36687.8i	−0.156483	+	0.100565i
$605$	72548.1	−	326855.i	0.198205	−	0.892986i
$606$	175281.	+	202285.i	0.477298	+	0.550831i
$607$	−364360.	+	52387.1i	−0.988903	+	0.142183i	−0.617738	−	0.786384i	$-0.711951\pi$
$607$	−364360.	+	52387.1i	−0.988903	+	0.142183i	−0.371165	+	0.928567i	$0.621042\pi$
$608$	−5429.44	+	11888.8i	−0.0146875	+	0.0321611i
$609$	−126436.	−	430602.i	−0.340908	−	1.16103i
$610$	123253.	+	46564.0i	0.331235	+	0.125138i
$611$	−113854.	+	249306.i	−0.304977	+	0.667807i
$612$	−73.0245	−	507.897i	−0.000194969	−	0.00135604i
$613$	−68138.5	−	78636.0i	−0.181331	−	0.209267i	0.657806	−	0.753188i	$-0.271485\pi$
$613$	−68138.5	−	78636.0i	−0.181331	−	0.209267i	−0.839137	+	0.543921i	$0.816939\pi$
$614$	26712.6	+	58492.5i	0.0708566	+	0.155154i
$615$	43295.1	−	571461.i	0.114469	−	1.51090i
$616$	−16411.0	+	114141.i	−0.0432487	+	0.300801i
$617$	357463.	+	229727.i	0.938989	+	0.603451i	0.918108	−	0.396331i	$-0.129717\pi$
$617$	357463.	+	229727.i	0.938989	+	0.603451i	0.0208808	+	0.999782i	$0.493353\pi$
$618$	369938.	−	426931.i	0.968617	−	1.11784i
$619$	−133684.	+	455286.i	−0.348898	+	1.18824i	0.578977	+	0.815344i	$0.303452\pi$
$619$	−133684.	+	455286.i	−0.348898	+	1.18824i	−0.927874	+	0.372893i	$0.878366\pi$
$620$	−86056.5	−	64989.2i	−0.223872	−	0.169067i
$621$	72427.0	+	370481.i	0.187809	+	0.960689i
$622$			255796.i			0.661169i
$623$	94057.5	−	320330.i	0.242336	−	0.825319i
$624$	288769.	−	333258.i	0.741621	−	0.855876i
$625$	−390569.	−	6590.02i	−0.999858	−	0.0168705i
$626$	485305.	+	69776.4i	1.23842	+	0.178057i
$627$	−3915.24	−	6092.23i	−0.00995917	−	0.0154968i
$628$	13388.0	+	29315.6i	0.0339465	+	0.0743325i
$629$	−30506.6	−	35206.5i	−0.0771067	−	0.0889859i
$630$	−11225.1	−	6190.95i	−0.0282818	−	0.0155983i
$631$	76466.8	+	34921.2i	0.192050	+	0.0877063i	0.509119	−	0.860696i	$-0.329971\pi$
$631$	76466.8	+	34921.2i	0.192050	+	0.0877063i	−0.317069	+	0.948403i	$0.602699\pi$
$632$	−709010.	+	208184.i	−1.77508	+	0.521211i
$633$	−57550.8	−	196000.i	−0.143629	−	0.489157i
$634$	60193.0	−	131804.i	0.149750	−	0.327907i
$635$	−189470.	−	104499.i	−0.469888	−	0.259157i
$636$	75311.8	−	65258.0i	0.186187	−	0.161332i
$637$	56159.1	−	25647.0i	0.138402	−	0.0632059i
$638$	−103964.	+	66813.5i	−0.255412	+	0.164143i
$639$	−3748.13	+	26068.8i	−0.00917936	+	0.0638439i
$640$	133032.	−	48980.3i	0.324786	−	0.119581i
$641$	384301.	+	332999.i	0.935310	+	0.810450i	0.982082	−	0.188455i	$-0.0603480\pi$
$641$	384301.	+	332999.i	0.935310	+	0.810450i	−0.0467722	+	0.998906i	$0.514893\pi$
$642$	−532257.	−	156285.i	−1.29137	−	0.379181i
$643$	−571853.			−1.38313			−0.691564	−	0.722315i	$-0.743078\pi$
$643$	−571853.			−1.38313			−0.691564	+	0.722315i	$0.743078\pi$
$644$	−68585.1	−	95774.1i	−0.165370	−	0.230928i
$645$	18730.4	−	24802.1i	0.0450222	−	0.0596169i
$646$	−2381.34	−	699.224i	−0.00570632	−	0.00167553i
$647$	417756.	+	361987.i	0.997962	+	0.864739i	0.990813	−	0.135236i	$-0.0431792\pi$
$647$	417756.	+	361987.i	0.997962	+	0.864739i	0.00714809	+	0.999974i	$0.497725\pi$
$648$	−256409.	+	398979.i	−0.610636	+	0.950168i
$649$	12740.2	+	1831.76i	0.0302473	+	0.00434890i
$650$	479809.	+	422895.i	1.13564	+	1.00094i
$651$	355616.	−	162405.i	0.839112	−	0.383209i
$652$	86429.8	−	74891.9i	0.203315	−	0.176173i
$653$	60413.6	−	8686.17i	0.141680	−	0.0203705i	−0.0711099	−	0.997468i	$-0.522654\pi$
$653$	60413.6	−	8686.17i	0.141680	−	0.0203705i	0.212790	+	0.977098i	$0.431745\pi$
$654$	−290459.	−	132648.i	−0.679093	−	0.310132i
$655$	−205068.	−	77473.1i	−0.477985	−	0.180579i
$656$	−377305.	+	110787.i	−0.876769	+	0.257443i
$657$	24030.8	+	10974.5i	0.0556721	+	0.0254246i
$658$	−20108.1	−	139855.i	−0.0464428	−	0.323017i
$659$	−102536.	+	88847.9i	−0.236105	+	0.204586i	−0.764875	−	0.644179i	$-0.777199\pi$
$659$	−102536.	+	88847.9i	−0.236105	+	0.204586i	0.528770	+	0.848765i	$0.322654\pi$
$660$	8344.56	−	37595.2i	0.0191565	−	0.0863067i
$661$	281341.	+	437774.i	0.643916	+	1.00195i	0.997776	+	0.0666549i	$0.0212327\pi$
$661$	281341.	+	437774.i	0.643916	+	1.00195i	−0.353860	+	0.935298i	$0.615131\pi$
$662$	44118.3	+	6343.25i	0.100671	+	0.0144742i
$663$	−78076.1	−	50176.5i	−0.177620	−	0.114149i
$664$	306159.	+	265288.i	0.694401	+	0.601702i
$665$	21017.9	−	15595.9i	0.0475276	−	0.0352669i
$666$		−	15371.8i		−	0.0346558i
$667$	128612.	−	536368.i	0.289087	−	1.20562i
$668$			265.221i			0.000594367i
$669$	1366.09	+	401.121i	0.00305230	+	0.000896237i
$670$	−50799.9	−	238359.i	−0.113165	−	0.530985i
$671$	−46706.3	−	30016.3i	−0.103736	−	0.0666672i
$672$	35858.1	−	249399.i	0.0794052	−	0.552275i
$673$	−232639.	−	361994.i	−0.513633	−	0.799229i	0.483464	−	0.875364i	$-0.339378\pi$
$673$	−232639.	−	361994.i	−0.513633	−	0.799229i	−0.997097	+	0.0761353i	$0.975742\pi$
$674$	365687.	−	167004.i	0.804988	−	0.367626i
$675$	−373151.	−	244282.i	−0.818988	−	0.536147i
$676$	43603.0	+	303266.i	0.0954165	+	0.663636i
$677$	60068.9	−	131533.i	0.131061	−	0.286983i	−0.832713	−	0.553705i	$-0.813213\pi$
$677$	60068.9	−	131533.i	0.131061	−	0.286983i	0.963773	+	0.266723i	$0.0859407\pi$
$678$	316416.	−	92908.1i	0.688333	−	0.202113i
$679$	−308253.	+	90511.3i	−0.668603	+	0.196320i
$680$	−27421.1	−	50725.4i	−0.0593016	−	0.109700i
$681$	−541178.	+	77809.7i	−1.16693	+	0.167780i
$682$	−70499.5	−	81360.7i	−0.151571	−	0.174923i
$683$	−594418.	+	271462.i	−1.27424	+	0.581925i	−0.933616	−	0.358275i	$-0.883365\pi$
$683$	−594418.	+	271462.i	−1.27424	+	0.581925i	−0.340622	+	0.940200i	$0.610638\pi$
$684$	186.891	+	290.808i	0.000399463	+	0.000621576i
$685$	207519.	−	205776.i	0.442259	−	0.438544i
$686$	−221368.	+	344455.i	−0.470399	+	0.731955i
$687$	−249664.	+	288127.i	−0.528983	+	0.610479i
$688$	−20461.9	−	6008.15i	−0.0432284	−	0.0126930i
$689$		−	697401.i		−	1.46908i
$690$	−211389.	−	348025.i	−0.444002	−	0.730991i
$691$	273632.			0.573074			0.286537	−	0.958069i	$-0.407496\pi$
$691$	273632.			0.573074			0.286537	+	0.958069i	$0.407496\pi$
$692$	75237.6	−	256236.i	0.157117	−	0.535091i
$693$	4082.41	+	3537.43i	0.00850061	+	0.00736582i
$694$	−148057.	−	95150.2i	−0.307404	−	0.197556i
$695$	200200.	−	198518.i	0.414471	−	0.410989i
$696$	560374.	−	360130.i	1.15680	−	0.743432i
$697$	34381.3	+	75284.5i	0.0707712	+	0.154967i
$698$	400601.	−	347122.i	0.822244	−	0.712478i
$699$	114720.	+	797898.i	0.234794	+	1.63303i
$700$	137588.	+	20968.2i	0.280791	+	0.0427923i
$701$	−112264.	−	382335.i	−0.228456	−	0.778051i	−0.991318	−	0.131489i	$-0.958024\pi$
$701$	−112264.	−	382335.i	−0.228456	−	0.778051i	0.762861	−	0.646562i	$-0.223794\pi$
$702$	205733.	+	700662.i	0.417474	+	1.42179i
$703$	28547.7	+	13037.3i	0.0577645	+	0.0263801i
$704$	−156796.	+	22543.8i	−0.316365	+	0.0454864i
$705$	13839.7	+	205693.i	0.0278451	+	0.413849i
$706$	−76085.2	−	166603.i	−0.152648	−	0.334252i
$707$	342913.	−	220377.i	0.686033	−	0.440887i
$708$	−15717.4	−	2259.82i	−0.0313556	−	0.00450825i
$709$	−330005.	+	513498.i	−0.656490	+	1.02152i	0.340210	+	0.940350i	$0.389502\pi$
$709$	−330005.	+	513498.i	−0.656490	+	1.02152i	−0.996700	+	0.0811696i	$0.974134\pi$
$710$	141200.	+	662529.i	0.280104	+	1.31428i
$711$	−9752.19	+	33212.9i	−0.0192914	+	0.0657004i
$712$	495533.			0.977491
$713$	478433.	+	44400.9i	0.941115	+	0.0873400i
$714$	47845.8			0.0938529
$715$	−160599.	−	216432.i	−0.314145	−	0.423360i
$716$	−808.045	+	932.534i	−0.00157619	+	0.00181902i
$717$	−58700.6	+	91339.9i	−0.114184	+	0.177673i
$718$	−117711.	+	818699.i	−0.228333	+	1.58809i
$719$	−275293.	+	176920.i	−0.532522	+	0.342231i	−0.779108	−	0.626890i	$-0.784328\pi$
$719$	−275293.	+	176920.i	−0.532522	+	0.342231i	0.246586	+	0.969121i	$0.420691\pi$
$720$	2780.92	−	12529.0i	0.00536444	−	0.0241687i
$721$	−563378.	−	650173.i	−1.08375	−	1.25072i
$722$	−431024.	+	61971.8i	−0.826850	+	0.118883i
$723$	90940.4	−	199132.i	0.173972	−	0.380946i
$724$	−68659.0	−	233831.i	−0.130985	−	0.446093i
$725$	347682.	+	551171.i	0.661463	+	1.04860i
$726$	−171295.	+	375084.i	−0.324992	+	0.711632i
$727$	88774.5	+	617440.i	0.167965	+	1.16822i	0.883082	+	0.469219i	$0.155464\pi$
$727$	88774.5	+	617440.i	0.167965	+	1.16822i	−0.715117	+	0.699005i	$0.753626\pi$
$728$	−651983.	−	752428.i	−1.23019	−	1.41972i
$729$	−211182.	−	462424.i	−0.397376	−	0.870132i
$730$	677557.	+	51333.2i	1.27145	+	0.0963280i
$731$	−638.768	+	4442.73i	−0.00119539	+	0.00831409i
$732$	57621.0	+	37030.8i	0.107537	+	0.0691100i
$733$	562375.	−	649016.i	1.04669	−	1.20795i	0.0690610	−	0.997612i	$-0.478000\pi$
$733$	562375.	−	649016.i	1.04669	−	1.20795i	0.977630	−	0.210333i	$-0.0674549\pi$
$734$	−63638.6	+	216733.i	−0.118121	+	0.402284i
$735$	27986.7	−	37059.0i	0.0518057	−	0.0685992i
$736$	190780.	−	243929.i	0.352190	−	0.450306i
$737$			102697.i			0.189070i
$738$	−7694.08	+	26203.6i	−0.0141268	+	0.0481115i
$739$	−460582.	+	531540.i	−0.843370	+	0.973301i	−0.999897	−	0.0143728i	$-0.995425\pi$
$739$	−460582.	+	531540.i	−0.843370	+	0.973301i	0.156527	+	0.987674i	$0.449970\pi$
$740$	57662.2	+	156613.i	0.105300	+	0.285998i
$741$	61888.4	+	8898.21i	0.112713	+	0.0162056i
$742$	194377.	+	302456.i	0.353050	+	0.549357i
$743$	157137.	+	344082.i	0.284643	+	0.623282i	0.996904	−	0.0786335i	$-0.0250557\pi$
$743$	157137.	+	344082.i	0.284643	+	0.623282i	−0.712260	+	0.701915i	$0.752328\pi$
$744$	379998.	+	438541.i	0.686492	+	0.792254i
$745$	−337751.	−	186279.i	−0.608532	−	0.335623i
$746$	−829572.	−	378853.i	−1.49065	−	0.680758i
$747$	18208.1	−	5346.39i	0.0326305	−	0.00958119i
$748$	1566.83	+	5336.14i	0.00280040	+	0.00953728i
$749$	−350940.	+	768452.i	−0.625561	+	1.36979i
$750$	468763.	+	108203.i	0.833357	+	0.192361i
$751$	−97019.6	+	84067.9i	−0.172020	+	0.149056i	−0.736616	−	0.676311i	$-0.763577\pi$
$751$	−97019.6	+	84067.9i	−0.172020	+	0.149056i	0.564596	+	0.825367i	$0.309032\pi$
$752$	128673.	−	58763.1i	0.227537	−	0.103913i
$753$	448747.	−	288392.i	0.791428	−	0.508620i
$754$	151848.	−	1.05613e6i	0.267095	−	1.85769i
$755$	123425.	+	335227.i	0.216526	+	0.588092i
$756$	120093.	+	104061.i	0.210123	+	0.182073i
$757$	448746.	+	131764.i	0.783084	+	0.229934i	0.648750	−	0.761002i	$-0.275292\pi$
$757$	448746.	+	131764.i	0.783084	+	0.229934i	0.134334	+	0.990936i	$0.457110\pi$
$758$	180571.			0.314274
$759$	56551.4	+	161999.i	0.0981657	+	0.281209i
$760$	31000.1	+	23411.0i	0.0536705	+	0.0405316i
$761$	71622.0	+	21030.1i	0.123674	+	0.0363139i	0.342984	−	0.939341i	$-0.388562\pi$
$761$	71622.0	+	21030.1i	0.123674	+	0.0363139i	−0.219310	+	0.975655i	$0.570381\pi$
$762$	201398.	+	174512.i	0.346852	+	0.300549i
$763$	−262905.	+	409089.i	−0.451596	+	0.702697i
$764$	−167976.	−	24151.3i	−0.287780	−	0.0413765i
$765$	−2693.44	−	204.060i	−0.00460239	−	0.000348687i
$766$	−339543.	+	155064.i	−0.578678	+	0.264273i
$767$	−83984.6	+	72773.1i	−0.142761	+	0.123703i
$768$	478888.	−	68853.7i	0.811917	−	0.116736i
$769$	−229141.	−	104645.i	−0.387481	−	0.176956i	0.212143	−	0.977239i	$-0.431956\pi$
$769$	−229141.	−	104645.i	−0.387481	−	0.176956i	−0.599624	+	0.800282i	$0.704683\pi$
$770$	129973.	+	49103.0i	0.219216	+	0.0828183i
$771$	−537493.	+	157822.i	−0.904199	+	0.265497i
$772$	−181616.	−	82941.4i	−0.304733	−	0.139167i
$773$	10797.5	+	75098.5i	0.0180703	+	0.125682i	0.996860	−	0.0791869i	$-0.0252324\pi$
$773$	10797.5	+	75098.5i	0.0180703	+	0.125682i	−0.978789	+	0.204869i	$0.934323\pi$
$774$	−1119.31	+	969.887i	−0.00186839	+	0.00161897i
$775$	−432149.	+	368123.i	−0.719499	+	0.612900i
$776$	−257805.	−	401152.i	−0.428122	−	0.666171i
$777$	−598862.	−	86103.4i	−0.991939	−	0.142619i
$778$	−691685.	−	444519.i	−1.14274	−	0.734397i
$779$	−42138.5	−	36513.2i	−0.0694391	−	0.0601693i
$780$	198129.	+	267010.i	0.325656	+	0.438872i
$781$		−	285451.i		−	0.467982i
$782$	51004.4	+	29266.8i	0.0834053	+	0.0478587i
$783$			744049.i			1.21361i
$784$	−30573.9	−	8977.32i	−0.0497415	−	0.0146054i
$785$	165927.	−	35363.0i	0.269264	−	0.0573864i
$786$	227123.	+	145963.i	0.367634	+	0.236264i
$787$	−33938.6	+	236048.i	−0.0547955	+	0.381111i	0.943908	+	0.330208i	$0.107119\pi$
$787$	−33938.6	+	236048.i	−0.0547955	+	0.381111i	−0.998704	+	0.0509028i	$0.983790\pi$
$788$	−67960.2	−	105748.i	−0.109447	−	0.170302i
$789$	−1.01463e6	+	463365.i	−1.62987	+	0.744336i
$790$	59769.3	+	888323.i	0.0957688	+	1.42337i
$791$	−71472.3	−	497101.i	−0.114231	−	0.794495i
$792$	−3330.71	+	7293.25i	−0.00530991	+	0.0116271i
$793$	459932.	−	135048.i	0.731387	−	0.214754i
$794$	−158301.	+	46481.5i	−0.251098	+	0.0737291i
$795$	−249463.	−	461474.i	−0.394704	−	0.730151i
$796$	−75417.2	+	10843.3i	−0.119027	+	0.0171134i
$797$	344561.	+	397644.i	0.542437	+	0.626005i	0.959104	−	0.283054i	$-0.0913475\pi$
$797$	344561.	+	397644.i	0.542437	+	0.626005i	−0.416667	+	0.909059i	$0.636802\pi$
$798$	−29320.5	+	13390.2i	−0.0460432	+	0.0210272i
$799$	−16096.1	−	25046.0i	−0.0252131	−	0.0392324i
$800$	49012.3	+	362575.i	0.0765817	+	0.566523i
$801$	12549.8	−	19527.8i	0.0195601	−	0.0304361i
$802$	177334.	−	204655.i	0.275705	−	0.318180i
$803$	−274733.	−	80669.0i	−0.426069	−	0.125105i
$804$		−	126696.i		−	0.195998i
$805$	−570427.	+	243220.i	−0.880254	+	0.375325i
$806$	929480.			1.43077
$807$	66853.1	−	227681.i	0.102654	−	0.349606i
$808$	457248.	+	396207.i	0.700372	+	0.606876i
$809$	1.05693e6	+	679251.i	1.61492	+	1.03785i	0.959155	+	0.282883i	$0.0912907\pi$
$809$	1.05693e6	+	679251.i	1.61492	+	1.03785i	0.655766	+	0.754964i	$0.272346\pi$
$810$	402356.	+	405764.i	0.613254	+	0.618449i
$811$	540164.	−	347142.i	0.821265	−	0.527795i	−0.0612259	−	0.998124i	$-0.519501\pi$
$811$	540164.	−	347142.i	0.821265	−	0.527795i	0.882491	+	0.470329i	$0.155865\pi$
$812$	−96452.7	−	211202.i	−0.146286	−	0.320321i
$813$	−697109.	+	604049.i	−1.05468	+	0.913883i
$814$	23710.5	+	164910.i	0.0357843	+	0.248885i
$815$	−286290.	−	529600.i	−0.431014	−	0.797319i
$816$	13495.3	+	45960.9i	0.0202676	+	0.0690253i
$817$	−851.905	−	2901.32i	−0.00127628	−	0.00434662i
$818$	742597.	+	339133.i	1.10981	+	0.506831i
$819$	−46163.5	+	6637.31i	−0.0688226	+	0.00989519i
$820$	−19904.6	−	295833.i	−0.0296023	−	0.439965i
$821$	375062.	+	821271.i	0.556438	+	1.21843i	0.953710	+	0.300728i	$0.0972297\pi$
$821$	375062.	+	821271.i	0.556438	+	1.21843i	−0.397272	+	0.917701i	$0.630043\pi$
$822$	−302790.	+	194591.i	−0.448123	+	0.287991i
$823$	9670.65	+	1390.43i	0.0142776	+	0.00205281i	0.149450	−	0.988769i	$-0.452250\pi$
$823$	9670.65	+	1390.43i	0.0142776	+	0.00205281i	−0.135172	+	0.990822i	$0.543159\pi$
$824$	690361.	−	1.07422e6i	1.01677	−	1.58212i
$825$	−183688.	−	85767.3i	−0.269881	−	0.126013i
$826$	16140.3	−	54968.8i	0.0236566	−	0.0805669i
$827$	−954249.			−1.39525			−0.697623	−	0.716465i	$-0.745759\pi$
$827$	−954249.			−1.39525			−0.697623	+	0.716465i	$0.745759\pi$
$828$	−2699.44	−	7732.91i	−0.00393743	−	0.0112793i
$829$	96401.3			0.140273			0.0701365	−	0.997537i	$-0.477657\pi$
$829$	96401.3			0.140273			0.0701365	+	0.997537i	$0.477657\pi$
$830$	391976.	−	290858.i	0.568988	−	0.422206i
$831$	−722709.	+	834051.i	−1.04655	+	1.20779i
$832$	739416.	−	1.15055e6i	1.06818	−	1.66211i
$833$	−954.440	+	6638.27i	−0.00137549	+	0.00956677i
$834$	−292110.	+	187728.i	−0.419967	+	0.269896i
$835$	1363.00	+	302.529i	0.00195489	+	0.000433905i
$836$	−2453.56	−	2831.55i	−0.00351062	−	0.00405147i
$837$	−641563.	+	92242.9i	−0.915775	+	0.131669i
$838$	−292733.	+	640995.i	−0.416853	+	0.912782i
$839$	−153071.	−	521311.i	−0.217455	−	0.740582i	−0.993889	−	0.110384i	$-0.964792\pi$
$839$	−153071.	−	521311.i	−0.217455	−	0.740582i	0.776434	−	0.630198i	$-0.217026\pi$
$840$	−700567.	−	264669.i	−0.992866	−	0.375098i
$841$	157808.	−	345550.i	0.223119	−	0.488562i
$842$	−73824.1	−	513458.i	−0.104130	−	0.724237i
$843$	−697696.	−	805184.i	−0.981773	−	1.13303i
$844$	−43903.0	−	96134.1i	−0.0616324	−	0.134956i
$845$	1.60825e6	+	121845.i	2.25238	+	0.170645i
$846$	1398.11	−	9724.07i	0.00195344	−	0.0135865i
$847$	528276.	+	339503.i	0.736367	+	0.473234i
$848$	−235715.	+	272029.i	−0.327790	+	0.378289i
$849$	−109104.	+	371573.i	−0.151365	+	0.515501i
$850$	−66824.7	+	19010.7i	−0.0924909	+	0.0263124i
$851$	−585728.	−	458105.i	−0.808792	−	0.632566i
$852$			352157.i			0.485129i
$853$	−25495.9	+	86831.0i	−0.0350407	+	0.119338i	−0.975156	−	0.221519i	$-0.928899\pi$
$853$	−25495.9	+	86831.0i	−0.0350407	+	0.119338i	0.940116	+	0.340856i	$0.110717\pi$
$854$	−161828.	+	186759.i	−0.221890	+	0.256075i
$855$	1707.68	−	628.739i	0.00233600	−	0.000860079i
$856$	−1.24115e6	−	178450.i	−1.69386	−	0.243540i
$857$	286712.	+	446133.i	0.390378	+	0.607439i	0.979703	−	0.200457i	$-0.0642426\pi$
$857$	286712.	+	446133.i	0.390378	+	0.607439i	−0.589325	+	0.807896i	$0.700606\pi$
$858$	137886.	+	301928.i	0.187303	+	0.410137i
$859$	68667.5	+	79246.5i	0.0930604	+	0.107397i	0.800370	−	0.599507i	$-0.204637\pi$
$859$	68667.5	+	79246.5i	0.0930604	+	0.107397i	−0.707309	+	0.706904i	$0.750091\pi$
$860$	7765.67	−	14080.2i	0.0104998	−	0.0190376i
$861$	977758.	+	446527.i	1.31894	+	0.602340i
$862$	1.01715e6	−	298663.i	1.36890	−	0.401945i
$863$	−60921.5	−	207480.i	−0.0817992	−	0.278583i	0.908429	−	0.418039i	$-0.137283\pi$
$863$	−60921.5	−	207480.i	−0.0817992	−	0.278583i	−0.990228	+	0.139457i	$0.955464\pi$
$864$	−173535.	+	379988.i	−0.232466	+	0.509029i
$865$	−1.23100e6	−	678934.i	−1.64523	−	0.907393i
$866$	221366.	−	191815.i	0.295172	−	0.255768i
$867$	−688215.	+	314297.i	−0.915558	+	0.418121i
$868$	170153.	−	109351.i	0.225840	−	0.145139i
$869$	53392.8	−	371355.i	0.0707038	−	0.491756i
$870$	−277301.	−	753160.i	−0.366364	−	0.995059i
$871$	−670100.	−	580645.i	−0.883290	−	0.765375i
$872$	−692546.	−	203350.i	−0.910784	−	0.267430i
$873$	−22337.6			−0.0293095
$874$	−39446.7	−	3660.85i	−0.0516402	−	0.00479246i
$875$	264700.	−	683162.i	0.345731	−	0.892293i
$876$	338935.	+	99520.4i	0.441681	+	0.129689i
$877$	−608049.	−	526878.i	−0.790569	−	0.685032i	0.162860	−	0.986649i	$-0.447928\pi$
$877$	−608049.	−	526878.i	−0.790569	−	0.685032i	−0.953429	+	0.301617i	$0.902473\pi$
$878$	108662.	−	169081.i	0.140957	−	0.219333i
$879$	782647.	+	112528.i	1.01295	+	0.145640i
$880$	−10508.4	+	138703.i	−0.0135697	+	0.179110i
$881$	−725456.	+	331305.i	−0.934672	+	0.426851i	−0.823734	−	0.566977i	$-0.808113\pi$
$881$	−725456.	+	331305.i	−0.934672	+	0.426851i	−0.110938	+	0.993827i	$0.535386\pi$
$882$	−1672.46	+	1449.19i	−0.00214990	+	0.00186290i
$883$	−142841.	+	20537.4i	−0.183202	+	0.0263405i	−0.233305	−	0.972404i	$-0.574954\pi$
$883$	−142841.	+	20537.4i	−0.183202	+	0.0263405i	0.0501029	+	0.998744i	$0.484045\pi$
$884$	−43677.2	−	19946.7i	−0.0558921	−	0.0255250i
$885$	−29541.9	+	78195.9i	−0.0377182	+	0.0998384i
$886$	−525588.	+	154327.i	−0.669542	+	0.196595i
$887$	679602.	+	310364.i	0.863789	+	0.394479i	0.797498	−	0.603321i	$-0.206156\pi$
$887$	679602.	+	310364.i	0.863789	+	0.394479i	0.0662904	+	0.997800i	$0.478884\pi$
$888$	−127802.	−	888880.i	−0.162073	−	1.12724i
$889$	306708.	−	265764.i	0.388081	−	0.336274i
$890$	129373.	−	582869.i	0.163329	−	0.735853i
$891$	−130183.	−	202569.i	−0.163983	−	0.255163i
$892$	729.110	+	104.830i	0.000916354	+	0.000131752i
$893$	16873.3	+	10843.8i	0.0211591	+	0.0135981i
$894$	359012.	+	311086.i	0.449194	+	0.389229i
$895$	3870.69	+	5216.35i	0.00483217	+	0.00651209i
$896$			265888.i			0.331194i
$897$	−1.37678e6	−	546936.i	−1.71112	−	0.679754i
$898$			550238.i			0.682336i
$899$	908692.	+	266816.i	1.12434	+	0.330136i
$900$	8768.20	+	4094.04i	0.0108249	+	0.00505437i
$901$	63731.4	+	40957.7i	0.0785062	+	0.0504529i
$902$	42124.7	−	292984.i	0.0517754	−	0.360106i
$903$	31515.7	+	49039.4i	0.0386502	+	0.0601409i
$904$	678062.	−	309661.i	0.829722	−	0.378921i
$905$	−1.28000e6	+	86122.7i	−1.56284	+	0.105153i
$906$	−62612.3	−	435478.i	−0.0762787	−	0.530530i
$907$	371029.	−	812441.i	0.451018	−	0.987591i	−0.538426	−	0.842673i	$-0.680981\pi$
$907$	371029.	−	812441.i	0.451018	−	0.987591i	0.989444	−	0.144918i	$-0.0462919\pi$
$908$	−271408.	+	79692.7i	−0.329194	+	0.0966600i
$909$	27193.8	−	7984.82i	0.0329111	−	0.00966357i
$910$	−1.05526e6	+	570451.i	−1.27431	+	0.688867i
$911$	270653.	−	38914.1i	0.326119	−	0.0468889i	0.0226892	−	0.999743i	$-0.492777\pi$
$911$	270653.	−	38914.1i	0.326119	−	0.0468889i	0.303430	+	0.952854i	$0.401868\pi$
$912$	−21132.8	−	24388.5i	−0.0254078	−	0.0293222i
$913$	−187092.	+	85442.3i	−0.224448	+	0.102502i
$914$	−110867.	−	172513.i	−0.132712	−	0.206504i
$915$	256032.	−	253881.i	0.305810	−	0.303241i
$916$	−106638.	+	165932.i	−0.127093	+	0.197761i
$917$	269249.	−	310730.i	0.320195	−	0.369525i
$918$	−76111.9	−	22348.5i	−0.0903165	−	0.0265193i
$919$		−	813632.i		−	0.963378i	−0.876342	−	0.481689i	$-0.840023\pi$
$919$		−	813632.i		−	0.963378i	0.876342	−	0.481689i	$-0.159977\pi$
$920$	−584919.	−	710670.i	−0.691067	−	0.839639i
$921$	175975.			0.207459
$922$	124215.	−	423036.i	0.146120	−	0.497640i
$923$	1.86257e6	+	1.61392e6i	2.18629	+	1.89444i
$924$	60762.9	+	39049.9i	0.0711696	+	0.0457379i
$925$	870623.	−	117690.i	1.01753	−	0.137548i
$926$	−105120.	+	67556.5i	−0.122592	+	0.0787853i
$927$	−24848.7	−	54411.1i	−0.0289164	−	0.0633182i
$928$	461290.	−	399710.i	0.535647	−	0.464140i
$929$	−108715.	−	756132.i	−0.125968	−	0.876126i	−0.950592	−	0.310444i	$-0.899522\pi$
$929$	−108715.	−	756132.i	−0.125968	−	0.876126i	0.824624	−	0.565682i	$-0.191387\pi$
$930$	615042.	−	332478.i	0.711113	−	0.384412i
$931$	−1272.91	−	4335.12i	−0.00146858	−	0.00500152i
$932$	117497.	+	400157.i	0.135268	+	0.460679i
$933$	636761.	+	290799.i	0.731498	+	0.334064i
$934$	1.16922e6	−	168109.i	1.34030	−	0.192706i
$935$	29210.3	−	1965.36i	0.0334128	−	0.00224812i
$936$	−28756.8	−	62968.6i	−0.0328238	−	0.0718741i
$937$	1.09172e6	−	701607.i	1.24346	−	0.799125i	0.257531	−	0.966270i	$-0.417091\pi$
$937$	1.09172e6	−	701607.i	1.24346	−	0.799125i	0.985932	+	0.167145i	$0.0534547\pi$
$938$	452451.	+	65052.6i	0.514240	+	0.0739365i
$939$	725411.	−	1.12876e6i	0.822722	−	1.28018i
$940$	22232.3	+	104316.i	0.0251610	+	0.118058i
$941$	−105933.	+	360775.i	−0.119633	+	0.407434i	−0.997434	−	0.0715924i	$-0.977192\pi$
$941$	−105933.	+	360775.i	−0.119633	+	0.407434i	0.877801	+	0.479026i	$0.159010\pi$
$942$	−208943.			−0.235465
$943$	769169.	+	1.07409e6i	0.864965	+	1.20786i
$944$	57355.8			0.0643626
$945$	671769.	−	498473.i	0.752240	−	0.558185i
$946$	10512.1	−	12131.6i	0.0117464	−	0.0135561i
$947$	−257551.	+	400758.i	−0.287186	+	0.446871i	−0.954632	−	0.297788i	$-0.903751\pi$
$947$	−257551.	+	400758.i	−0.287186	+	0.446871i	0.667446	+	0.744659i	$0.267388\pi$
$948$	−65870.1	+	458136.i	−0.0732945	+	0.509774i
$949$	2.07969e6	−	1.33654e6i	2.30923	−	1.48405i
$950$	35630.6	−	30351.6i	0.0394799	−	0.0336306i
$951$	−259675.	−	299681.i	−0.287124	−	0.331358i
$952$	107050.	−	15391.5i	0.118118	−	0.0169827i
$953$	−280909.	+	615105.i	−0.309300	+	0.677273i	−0.998899	−	0.0469191i	$-0.985060\pi$
$953$	−280909.	+	615105.i	−0.309300	+	0.677273i	0.689599	+	0.724192i	$0.257787\pi$
$954$	7042.77	+	23985.5i	0.00773832	+	0.0263543i
$955$	−315721.	+	835700.i	−0.346176	+	0.916312i
$956$	−23335.3	+	51097.2i	−0.0255328	+	0.0559090i
$957$	48130.8	+	334757.i	0.0525532	+	0.365516i
$958$	−497244.	−	573850.i	−0.541799	−	0.625270i
$959$	227702.	+	498599.i	0.247588	+	0.542143i
$960$	77718.2	−	1.02582e6i	0.0843297	−	1.11309i
$961$	14020.4	−	97514.0i	0.0151815	−	0.105589i
$962$	−1.21010e6	−	777684.i	−1.30759	−	0.840336i
$963$	−38465.5	+	44391.5i	−0.0414781	+	0.0478682i
$964$	31908.7	−	108671.i	0.0343364	−	0.116939i
$965$	−633409.	+	838738.i	−0.680189	+	0.900683i
$966$	749537.	−	146530.i	0.803228	−	0.157027i
$967$		−	1.33389e6i		−	1.42649i	−0.700916	−	0.713244i	$-0.747225\pi$
$967$		−	1.33389e6i		−	1.42649i	0.700916	−	0.713244i	$-0.252775\pi$
$968$	−262596.	+	894319.i	−0.280244	+	0.954425i
$969$	−4447.80	+	5133.04i	−0.00473694	+	0.00546672i
$970$	−539161.	+	198510.i	−0.573027	+	0.210979i
$971$	433659.	+	62350.8i	0.459949	+	0.0661308i	0.368395	−	0.929669i	$-0.379907\pi$
$971$	433659.	+	62350.8i	0.459949	+	0.0661308i	0.0915544	+	0.995800i	$0.470816\pi$
$972$	12197.3	+	18979.3i	0.0129101	+	0.0200885i
$973$	219671.	+	481013.i	0.232032	+	0.508079i
$974$	−407974.	−	470827.i	−0.430046	−	0.496299i
$975$	1.59819e6	−	713639.i	1.68120	−	0.750705i
$976$	−225047.	−	102775.i	−0.236251	−	0.107892i
$977$	−1.62786e6	+	477983.i	−1.70541	+	0.500753i	−0.981874	−	0.189537i	$-0.939301\pi$
$977$	−1.62786e6	+	477983.i	−1.70541	+	0.500753i	−0.723533	+	0.690289i	$0.757483\pi$
$978$	208891.	+	711416.i	0.218394	+	0.743783i
$979$	−104515.	+	228855.i	−0.109046	+	0.238778i
$980$	11603.4	−	21038.5i	0.0120818	−	0.0219060i
$981$	−25552.9	+	22141.7i	−0.0265523	+	0.0230077i
$982$	−78325.4	+	35770.0i	−0.0812232	+	0.0370934i
$983$	−1.05191e6	+	676024.i	−1.08861	+	0.699609i	−0.956531	−	0.291630i	$-0.905802\pi$
$983$	−1.05191e6	+	676024.i	−1.08861	+	0.699609i	−0.132081	+	0.991239i	$0.542166\pi$
$984$	−227056.	+	1.57921e6i	−0.234499	+	1.63098i
$985$	−620972.	+	228632.i	−0.640029	+	0.235648i
$986$	87595.3	+	75901.8i	0.0901005	+	0.0780725i
$987$	−371005.	−	108937.i	−0.380842	−	0.111825i
$988$	32348.2			0.0331388
$989$	3599.36	+	71554.6i	0.00367987	+	0.0731552i
$990$	7709.08	+	5821.85i	0.00786561	+	0.00594005i
$991$	1.70977e6	+	502035.i	1.74097	+	0.511195i	0.988989	−	0.147988i	$-0.0472798\pi$
$991$	1.70977e6	+	502035.i	1.74097	+	0.511195i	0.751982	+	0.659183i	$0.229098\pi$
$992$	401842.	+	348198.i	0.408350	+	0.353837i
$993$	65945.9	−	102614.i	0.0668789	−	0.104066i
$994$	−1.25760e6	−	180816.i	−1.27283	−	0.183006i
$995$	−30300.8	+	399946.i	−0.0306061	+	0.403976i
$996$	230814.	−	105409.i	0.232672	−	0.106258i
$997$	1.04748e6	−	907648.i	1.05379	−	0.913118i	0.0574332	−	0.998349i	$-0.481708\pi$
$997$	1.04748e6	−	907648.i	1.05379	−	0.913118i	0.996361	+	0.0852314i	$0.0271629\pi$
$998$	−1.37437e6	+	197604.i	−1.37988	+	0.198397i
$999$	912436.	+	416696.i	0.914264	+	0.417530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.5.i.a.74.15	yes	460
5.4	even	2	inner	115.5.i.a.74.32	yes	460
23.14	odd	22	inner	115.5.i.a.14.32	yes	460
115.14	odd	22	inner	115.5.i.a.14.15	✓	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.5.i.a.14.15	✓	460	115.14	odd	22	inner
115.5.i.a.14.32	yes	460	23.14	odd	22	inner
115.5.i.a.74.15	yes	460	1.1	even	1	trivial
115.5.i.a.74.32	yes	460	5.4	even	2	inner

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	115.i (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.944999 + 3.21837i) q^{2} +(6.93728 + 6.01119i) q^{3} +(3.99518 + 2.56754i) q^{4} +(17.7521 - 17.6030i) q^{5} +(-25.9019 + 16.6462i) q^{6} +(19.4786 + 42.6523i) q^{7} +(-52.5982 + 45.5766i) q^{8} +(0.463978 + 3.22704i) q^{9} +O(q^{10})\)	\(q+(-0.944999 + 3.21837i) q^{2} +(6.93728 + 6.01119i) q^{3} +(3.99518 + 2.56754i) q^{4} +(17.7521 - 17.6030i) q^{5} +(-25.9019 + 16.6462i) q^{6} +(19.4786 + 42.6523i) q^{7} +(-52.5982 + 45.5766i) q^{8} +(0.463978 + 3.22704i) q^{9} +(39.8771 + 73.7675i) q^{10} +(-9.95524 - 33.9044i) q^{11} +(12.2817 + 41.8275i) q^{12} +(277.513 + 126.736i) q^{13} +(-155.678 + 22.3831i) q^{14} +(228.966 - 15.4056i) q^{15} +(-65.4117 - 143.232i) q^{16} +(-27.8798 + 17.9172i) q^{17} +(-10.8243 - 1.55629i) q^{18} +(12.0707 - 18.7824i) q^{19} +(116.119 - 24.7477i) q^{20} +(-121.262 + 412.981i) q^{21} +118.525 q^{22} +(-381.883 + 366.069i) q^{23} -638.858 q^{24} +(5.27221 - 624.978i) q^{25} +(-670.133 + 773.374i) q^{26} +(385.801 - 600.318i) q^{27} +(-31.6910 + 220.416i) q^{28} +(-877.150 + 563.710i) q^{29} +(-166.791 + 751.455i) q^{30} +(-594.808 - 686.445i) q^{31} +(-579.437 + 83.3105i) q^{32} +(134.744 - 295.047i) q^{33} +(-31.3179 - 106.659i) q^{34} +(1096.59 + 414.285i) q^{35} +(-6.43189 + 14.0839i) q^{36} +(200.047 + 1391.36i) q^{37} +(49.0418 + 56.5972i) q^{38} +(1163.35 + 2547.39i) q^{39} +(-131.444 + 1734.96i) q^{40} +(355.409 - 2471.92i) q^{41} +(-1214.53 - 780.532i) q^{42} +(88.6910 - 102.355i) q^{43} +(47.2782 - 161.015i) q^{44} +(65.0420 + 49.1193i) q^{45} +(-817.266 - 1574.97i) q^{46} +898.358i q^{47} +(407.213 - 1386.84i) q^{48} +(132.521 - 152.938i) q^{49} +(2006.43 + 607.571i) q^{50} +(-301.113 - 43.2936i) q^{51} +(783.314 + 1218.86i) q^{52} +(-949.614 - 2079.36i) q^{53} +(1567.46 + 1808.95i) q^{54} +(-773.544 - 426.632i) q^{55} +(-2968.49 - 1355.66i) q^{56} +(196.642 - 57.7393i) q^{57} +(-985.321 - 3355.70i) q^{58} +(-151.316 + 331.337i) q^{59} +(954.313 + 526.332i) q^{60} +(1187.44 - 1028.92i) q^{61} +(2771.33 - 1265.62i) q^{62} +(-128.603 + 82.6481i) q^{63} +(637.988 - 4437.31i) q^{64} +(7157.36 - 2635.22i) q^{65} +(822.239 + 712.474i) q^{66} +(-2788.60 - 818.806i) q^{67} -157.388 q^{68} +(-4849.74 + 243.953i) q^{69} +(-2369.60 + 3137.74i) q^{70} +(7751.01 + 2275.90i) q^{71} +(-171.482 - 148.590i) q^{72} +(4380.90 - 6816.82i) q^{73} +(-4666.95 - 671.006i) q^{74} +(3793.43 - 4303.95i) q^{75} +(96.4491 - 44.0468i) q^{76} +(1252.19 - 1085.03i) q^{77} +(-9297.80 + 1336.82i) q^{78} +(9657.91 + 4410.62i) q^{79} +(-3682.49 - 1391.22i) q^{80} +(6538.42 - 1919.85i) q^{81} +(7619.70 + 3479.80i) q^{82} +(-828.373 - 5761.46i) q^{83} +(-1544.81 + 1338.58i) q^{84} +(-179.527 + 808.834i) q^{85} +(245.603 + 382.166i) q^{86} +(-9473.60 - 1362.10i) q^{87} +(2068.88 + 1329.59i) q^{88} +(-5380.93 - 4662.61i) q^{89} +(-219.549 + 162.912i) q^{90} +14305.2i q^{91} +(-2465.59 + 482.009i) q^{92} -8337.57i q^{93} +(-2891.25 - 848.947i) q^{94} +(-116.345 - 545.906i) q^{95} +(-4520.51 - 2905.16i) q^{96} +(-975.079 + 6781.82i) q^{97} +(366.977 + 571.028i) q^{98} +(104.792 - 47.8569i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 460 q + 306 q^{4} - 11 q^{5} - 182 q^{6} + 944 q^{9}+O(q^{10}) \) 460 * q + 306 * q^4 - 11 * q^5 - 182 * q^6 + 944 * q^9	\( 460 q + 306 q^{4} - 11 q^{5} - 182 q^{6} + 944 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 1474 q^{15} - 2670 q^{16} - 22 q^{19} + 3157 q^{20} - 22 q^{21} + 3896 q^{24} - 1427 q^{25} - 3166 q^{26} - 2808 q^{29} + 1397 q^{30} + 2684 q^{31} - 12848 q^{34} + 2279 q^{35} + 1114 q^{36} + 12866 q^{39} - 11 q^{40} - 2652 q^{41} + 11110 q^{44} - 5394 q^{46} - 27026 q^{49} - 10931 q^{50} - 22 q^{51} - 51290 q^{54} - 10545 q^{55} + 25322 q^{56} + 41460 q^{59} + 49269 q^{60} - 22506 q^{61} + 68582 q^{64} + 27940 q^{65} - 24332 q^{66} + 7608 q^{69} - 15618 q^{70} + 35838 q^{71} - 59158 q^{74} + 30594 q^{75} - 58520 q^{76} - 17930 q^{79} - 63602 q^{80} + 91888 q^{81} + 92906 q^{84} - 33815 q^{85} + 101486 q^{86} - 22 q^{89} - 37598 q^{90} - 46242 q^{94} + 43336 q^{95} - 210180 q^{96} + 44528 q^{99}+O(q^{100}) \) 460 * q + 306 * q^4 - 11 * q^5 - 182 * q^6 + 944 * q^9 - 11 * q^10 - 22 * q^11 - 22 * q^14 - 1474 * q^15 - 2670 * q^16 - 22 * q^19 + 3157 * q^20 - 22 * q^21 + 3896 * q^24 - 1427 * q^25 - 3166 * q^26 - 2808 * q^29 + 1397 * q^30 + 2684 * q^31 - 12848 * q^34 + 2279 * q^35 + 1114 * q^36 + 12866 * q^39 - 11 * q^40 - 2652 * q^41 + 11110 * q^44 - 5394 * q^46 - 27026 * q^49 - 10931 * q^50 - 22 * q^51 - 51290 * q^54 - 10545 * q^55 + 25322 * q^56 + 41460 * q^59 + 49269 * q^60 - 22506 * q^61 + 68582 * q^64 + 27940 * q^65 - 24332 * q^66 + 7608 * q^69 - 15618 * q^70 + 35838 * q^71 - 59158 * q^74 + 30594 * q^75 - 58520 * q^76 - 17930 * q^79 - 63602 * q^80 + 91888 * q^81 + 92906 * q^84 - 33815 * q^85 + 101486 * q^86 - 22 * q^89 - 37598 * q^90 - 46242 * q^94 + 43336 * q^95 - 210180 * q^96 + 44528 * q^99

Introduction

L-functions

Modular forms

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Database

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