LMFDB - Embedded newform 143.4.q.a.3.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(3,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 10]))

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

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

chi := DirichletCharacter("143.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.q (of order $15$, degree $8$, 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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			3.15
Character	$\chi$	$=$	143.3
Dual form			143.4.q.a.48.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47923 - 0.658595i) q^{2} +(-5.15589 + 5.72620i) q^{3} +(-3.59867 - 3.99673i) q^{4} +(6.90200 + 5.01460i) q^{5} +(11.3980 - 5.07471i) q^{6} +(17.3187 + 19.2343i) q^{7} +(6.69396 + 20.6019i) q^{8} +(-3.38386 - 32.1953i) q^{9} +O(q^{10})$	\(q+(-1.47923 - 0.658595i) q^{2} +(-5.15589 + 5.72620i) q^{3} +(-3.59867 - 3.99673i) q^{4} +(6.90200 + 5.01460i) q^{5} +(11.3980 - 5.07471i) q^{6} +(17.3187 + 19.2343i) q^{7} +(6.69396 + 20.6019i) q^{8} +(-3.38386 - 32.1953i) q^{9} +(-6.90705 - 11.9634i) q^{10} +(-28.3028 - 23.0207i) q^{11} +41.4405 q^{12} +(31.9509 + 34.2949i) q^{13} +(-12.9507 - 39.8580i) q^{14} +(-64.3006 + 13.6675i) q^{15} +(-0.830940 + 7.90587i) q^{16} +(-31.4348 + 13.9957i) q^{17} +(-16.1981 + 49.8527i) q^{18} +(-128.301 - 27.2712i) q^{19} +(-4.79605 - 45.6314i) q^{20} -199.433 q^{21} +(26.7049 + 52.6930i) q^{22} +(27.0416 + 46.8374i) q^{23} +(-152.484 - 67.8902i) q^{24} +(-16.1357 - 49.6605i) q^{25} +(-24.6763 - 71.7727i) q^{26} +(33.4915 + 24.3330i) q^{27} +(14.5502 - 138.436i) q^{28} +(-179.899 + 38.2387i) q^{29} +(104.117 + 22.1307i) q^{30} +(20.6818 - 15.0262i) q^{31} +(93.0844 - 161.227i) q^{32} +(277.747 - 43.3748i) q^{33} +55.7168 q^{34} +(23.0811 + 219.602i) q^{35} +(-116.498 + 129.385i) q^{36} +(-157.887 + 33.5599i) q^{37} +(171.826 + 124.839i) q^{38} +(-361.115 + 6.13680i) q^{39} +(-57.1085 + 175.762i) q^{40} +(250.380 - 278.075i) q^{41} +(295.007 + 131.346i) q^{42} +(-244.310 + 423.158i) q^{43} +(9.84469 + 195.963i) q^{44} +(138.091 - 239.180i) q^{45} +(-9.15380 - 87.0926i) q^{46} +(48.3312 + 148.748i) q^{47} +(-40.9863 - 45.5199i) q^{48} +(-34.1701 + 325.106i) q^{49} +(-8.83781 + 84.0862i) q^{50} +(81.9325 - 252.162i) q^{51} +(22.0864 - 251.115i) q^{52} +(207.794 - 150.971i) q^{53} +(-33.5160 - 58.0514i) q^{54} +(-79.9060 - 300.816i) q^{55} +(-280.333 + 485.552i) q^{56} +(817.666 - 594.069i) q^{57} +(291.295 + 61.9168i) q^{58} +(-190.941 - 212.061i) q^{59} +(286.022 + 207.807i) q^{60} +(312.213 - 139.006i) q^{61} +(-40.4894 + 8.60628i) q^{62} +(560.651 - 622.666i) q^{63} +(-192.427 + 139.806i) q^{64} +(48.5505 + 396.924i) q^{65} +(-439.418 - 118.762i) q^{66} +(-193.336 - 334.868i) q^{67} +(169.061 + 75.2707i) q^{68} +(-407.623 - 86.6430i) q^{69} +(110.486 - 340.042i) q^{70} +(-854.063 + 380.253i) q^{71} +(640.632 - 285.228i) q^{72} +(-277.448 + 853.898i) q^{73} +(255.653 + 54.3407i) q^{74} +(367.560 + 163.648i) q^{75} +(352.717 + 610.924i) q^{76} +(-47.3778 - 943.074i) q^{77} +(538.213 + 228.751i) q^{78} +(168.375 - 122.331i) q^{79} +(-45.3799 + 50.3995i) q^{80} +(542.946 - 115.407i) q^{81} +(-553.509 + 246.438i) q^{82} +(-682.804 - 496.086i) q^{83} +(717.695 + 797.081i) q^{84} +(-287.146 - 61.0348i) q^{85} +(640.081 - 465.046i) q^{86} +(708.577 - 1227.29i) q^{87} +(284.813 - 737.190i) q^{88} +(-459.839 - 796.465i) q^{89} +(-361.791 + 262.856i) q^{90} +(-106.291 + 1208.50i) q^{91} +(89.8826 - 276.630i) q^{92} +(-20.5901 + 195.902i) q^{93} +(26.4719 - 251.863i) q^{94} +(-748.778 - 831.603i) q^{95} +(443.284 + 1364.29i) q^{96} +(118.904 + 1131.30i) q^{97} +(264.659 - 458.402i) q^{98} +(-645.386 + 989.113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 3 q^{2} - 3 q^{3} + 149 q^{4} - 12 q^{5} - 35 q^{6} - 3 q^{7} - 44 q^{8} + 369 q^{9}+O(q^{10}) $ 320 * q - 3 * q^2 - 3 * q^3 + 149 * q^4 - 12 * q^5 - 35 * q^6 - 3 * q^7 - 44 * q^8 + 369 * q^9	\( 320 q - 3 q^{2} - 3 q^{3} + 149 q^{4} - 12 q^{5} - 35 q^{6} - 3 q^{7} - 44 q^{8} + 369 q^{9} - 80 q^{10} + 30 q^{11} - 220 q^{12} - 114 q^{13} + 4 q^{14} - 33 q^{15} + 637 q^{16} + 143 q^{17} + 72 q^{18} + 17 q^{19} - 377 q^{20} - 524 q^{21} + 283 q^{22} + 196 q^{23} - 1137 q^{24} - 1324 q^{25} + 632 q^{26} + 192 q^{27} - 279 q^{28} + 943 q^{29} + 1617 q^{30} + 260 q^{31} - 52 q^{32} - 1244 q^{33} - 3508 q^{34} + 1253 q^{35} + 282 q^{36} + 333 q^{37} - 694 q^{38} - 1106 q^{39} - 296 q^{40} - 1751 q^{41} - 895 q^{42} - 2200 q^{43} - 252 q^{44} - 282 q^{45} + 485 q^{46} + 2116 q^{47} - 825 q^{48} + 1607 q^{49} + 348 q^{50} + 1768 q^{51} - 2431 q^{52} + 428 q^{53} + 8326 q^{54} - 1379 q^{55} + 7630 q^{56} - 888 q^{57} - 331 q^{58} - 1097 q^{59} - 1820 q^{60} + 885 q^{61} - 437 q^{62} + 540 q^{63} + 1148 q^{64} + 2324 q^{65} - 1686 q^{66} - 5184 q^{67} + 3834 q^{68} - 4905 q^{69} + 4078 q^{70} + 843 q^{71} + 1155 q^{72} - 972 q^{73} + 5631 q^{74} - 3431 q^{75} - 3090 q^{76} + 602 q^{77} + 1252 q^{78} + 1140 q^{79} + 8631 q^{80} - 3809 q^{81} + 4015 q^{82} - 5292 q^{83} - 5060 q^{84} + 391 q^{85} + 3388 q^{86} - 7600 q^{87} - 7229 q^{88} + 6276 q^{89} + 7374 q^{90} - 4602 q^{91} + 8158 q^{92} - 2599 q^{93} + 11081 q^{94} + 2305 q^{95} - 30114 q^{96} + 1377 q^{97} + 5102 q^{98} - 5812 q^{99}+O(q^{100}) \) 320 * q - 3 * q^2 - 3 * q^3 + 149 * q^4 - 12 * q^5 - 35 * q^6 - 3 * q^7 - 44 * q^8 + 369 * q^9 - 80 * q^10 + 30 * q^11 - 220 * q^12 - 114 * q^13 + 4 * q^14 - 33 * q^15 + 637 * q^16 + 143 * q^17 + 72 * q^18 + 17 * q^19 - 377 * q^20 - 524 * q^21 + 283 * q^22 + 196 * q^23 - 1137 * q^24 - 1324 * q^25 + 632 * q^26 + 192 * q^27 - 279 * q^28 + 943 * q^29 + 1617 * q^30 + 260 * q^31 - 52 * q^32 - 1244 * q^33 - 3508 * q^34 + 1253 * q^35 + 282 * q^36 + 333 * q^37 - 694 * q^38 - 1106 * q^39 - 296 * q^40 - 1751 * q^41 - 895 * q^42 - 2200 * q^43 - 252 * q^44 - 282 * q^45 + 485 * q^46 + 2116 * q^47 - 825 * q^48 + 1607 * q^49 + 348 * q^50 + 1768 * q^51 - 2431 * q^52 + 428 * q^53 + 8326 * q^54 - 1379 * q^55 + 7630 * q^56 - 888 * q^57 - 331 * q^58 - 1097 * q^59 - 1820 * q^60 + 885 * q^61 - 437 * q^62 + 540 * q^63 + 1148 * q^64 + 2324 * q^65 - 1686 * q^66 - 5184 * q^67 + 3834 * q^68 - 4905 * q^69 + 4078 * q^70 + 843 * q^71 + 1155 * q^72 - 972 * q^73 + 5631 * q^74 - 3431 * q^75 - 3090 * q^76 + 602 * q^77 + 1252 * q^78 + 1140 * q^79 + 8631 * q^80 - 3809 * q^81 + 4015 * q^82 - 5292 * q^83 - 5060 * q^84 + 391 * q^85 + 3388 * q^86 - 7600 * q^87 - 7229 * q^88 + 6276 * q^89 + 7374 * q^90 - 4602 * q^91 + 8158 * q^92 - 2599 * q^93 + 11081 * q^94 + 2305 * q^95 - 30114 * q^96 + 1377 * q^97 + 5102 * q^98 - 5812 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.47923	−	0.658595i	−0.522986	−	0.232849i	0.128225	−	0.991745i	$-0.459072\pi$
$2$	−1.47923	−	0.658595i	−0.522986	−	0.232849i	−0.651211	+	0.758897i	$0.725739\pi$
$3$	−5.15589	+	5.72620i	−0.992252	+	1.10201i	0.00253122	+	0.999997i	$0.499194\pi$
$3$	−5.15589	+	5.72620i	−0.992252	+	1.10201i	−0.994783	+	0.102011i	$0.967472\pi$
$4$	−3.59867	−	3.99673i	−0.449834	−	0.499592i
$5$	6.90200	+	5.01460i	0.617334	+	0.448519i	0.851989	−	0.523559i	$-0.175396\pi$
$5$	6.90200	+	5.01460i	0.617334	+	0.448519i	−0.234655	+	0.972079i	$0.575396\pi$
$6$	11.3980	−	5.07471i	0.775535	−	0.345290i
$7$	17.3187	+	19.2343i	0.935121	+	1.03856i	0.999175	+	0.0406108i	$0.0129304\pi$
$7$	17.3187	+	19.2343i	0.935121	+	1.03856i	−0.0640539	+	0.997946i	$0.520403\pi$
$8$	6.69396	+	20.6019i	0.295834	+	0.910483i
$9$	−3.38386	−	32.1953i	−0.125328	−	1.19242i
$10$	−6.90705	−	11.9634i	−0.218420	−	0.378315i
$11$	−28.3028	−	23.0207i	−0.775782	−	0.631001i
$11$	−28.3028	−	23.0207i	−0.775782	−	0.631001i
$12$	41.4405			0.996903
$13$	31.9509	+	34.2949i	0.681661	+	0.731668i
$13$	31.9509	+	34.2949i	0.681661	+	0.731668i
$14$	−12.9507	−	39.8580i	−0.247229	−	0.760893i
$15$	−64.3006	+	13.6675i	−1.10682	+	0.235262i
$16$	−0.830940	+	7.90587i	−0.0129834	+	0.123529i
$17$	−31.4348	+	13.9957i	−0.448474	+	0.199674i	−0.618531	−	0.785761i	$-0.712272\pi$
$17$	−31.4348	+	13.9957i	−0.448474	+	0.199674i	0.170056	+	0.985434i	$0.445605\pi$
$18$	−16.1981	+	49.8527i	−0.212108	+	0.652800i
$19$	−128.301	−	27.2712i	−1.54917	−	0.329286i	−0.647621	−	0.761963i	$-0.724236\pi$
$19$	−128.301	−	27.2712i	−1.54917	−	0.329286i	−0.901549	+	0.432677i	$0.857569\pi$
$20$	−4.79605	−	45.6314i	−0.0536215	−	0.510174i
$21$	−199.433			−2.07237
$22$	26.7049	+	52.6930i	0.258796	+	0.510645i
$23$	27.0416	+	46.8374i	0.245155	+	0.424620i	0.962175	−	0.272432i	$-0.0878280\pi$
$23$	27.0416	+	46.8374i	0.245155	+	0.424620i	−0.717021	+	0.697052i	$0.754495\pi$
$24$	−152.484	−	67.8902i	−1.29690	−	0.577418i
$25$	−16.1357	−	49.6605i	−0.129086	−	0.397284i
$26$	−24.6763	−	71.7727i	−0.186132	−	0.541376i
$27$	33.4915	+	24.3330i	0.238720	+	0.173440i
$28$	14.5502	−	138.436i	0.0982049	−	0.934357i
$29$	−179.899	+	38.2387i	−1.15194	+	0.244853i	−0.744017	−	0.668161i	$-0.767082\pi$
$29$	−179.899	+	38.2387i	−1.15194	+	0.244853i	−0.407928	+	0.913014i	$0.633748\pi$
$30$	104.117	+	22.1307i	0.633633	+	0.134683i
$31$	20.6818	−	15.0262i	0.119825	−	0.0870578i	−0.526259	−	0.850324i	$-0.676406\pi$
$31$	20.6818	−	15.0262i	0.119825	−	0.0870578i	0.646084	+	0.763267i	$0.276406\pi$
$32$	93.0844	−	161.227i	0.514223	−	0.890661i
$33$	277.747	−	43.3748i	1.46514	−	0.228806i
$34$	55.7168			0.281040
$35$	23.0811	+	219.602i	0.111469	+	1.06056i
$36$	−116.498	+	129.385i	−0.539345	+	0.599003i
$37$	−157.887	+	33.5599i	−0.701525	+	0.149114i	−0.544847	−	0.838536i	$-0.683412\pi$
$37$	−157.887	+	33.5599i	−0.701525	+	0.149114i	−0.156679	+	0.987650i	$0.550079\pi$
$38$	171.826	+	124.839i	0.733521	+	0.532934i
$39$	−361.115	+	6.13680i	−1.48268	+	0.0251968i
$40$	−57.1085	+	175.762i	−0.225741	+	0.694759i
$41$	250.380	−	278.075i	0.953727	−	1.05922i	−0.0444584	−	0.999011i	$-0.514156\pi$
$41$	250.380	−	278.075i	0.953727	−	1.05922i	0.998186	−	0.0602102i	$-0.0191771\pi$
$42$	295.007	+	131.346i	1.08382	+	0.482549i
$43$	−244.310	+	423.158i	−0.866441	+	1.50072i	−0.000832456		1.00000i	$0.500265\pi$
$43$	−244.310	+	423.158i	−0.866441	+	1.50072i	−0.865609	+	0.500721i	$0.833068\pi$
$44$	9.84469	+	195.963i	0.0337305	+	0.671420i
$45$	138.091	−	239.180i	0.457453	−	0.792331i
$46$	−9.15380	−	87.0926i	−0.0293403	−	0.279154i
$47$	48.3312	+	148.748i	0.149997	+	0.461642i	0.997620	−	0.0689569i	$-0.0219671\pi$
$47$	48.3312	+	148.748i	0.149997	+	0.461642i	−0.847623	+	0.530599i	$0.821967\pi$
$48$	−40.9863	−	45.5199i	−0.123247	−	0.136880i
$49$	−34.1701	+	325.106i	−0.0996211	+	0.947832i
$50$	−8.83781	+	84.0862i	−0.0249971	+	0.237832i
$51$	81.9325	−	252.162i	0.224958	−	0.692349i
$52$	22.0864	−	251.115i	0.0589006	−	0.669682i
$53$	207.794	−	150.971i	0.538542	−	0.391274i	−0.285001	−	0.958527i	$-0.591994\pi$
$53$	207.794	−	150.971i	0.538542	−	0.391274i	0.823543	+	0.567253i	$0.191994\pi$
$54$	−33.5160	−	58.0514i	−0.0844620	−	0.146292i
$55$	−79.9060	−	300.816i	−0.195900	−	0.737491i
$56$	−280.333	+	485.552i	−0.668949	+	1.15865i
$57$	817.666	−	594.069i	1.90004	−	1.38046i
$58$	291.295	+	61.9168i	0.659465	+	0.140174i
$59$	−190.941	−	212.061i	−0.421328	−	0.467933i	0.494690	−	0.869070i	$-0.335282\pi$
$59$	−190.941	−	212.061i	−0.421328	−	0.467933i	−0.916018	+	0.401137i	$0.868615\pi$
$60$	286.022	+	207.807i	0.615422	+	0.447130i
$61$	312.213	−	139.006i	0.655324	−	0.291769i	−0.0520123	−	0.998646i	$-0.516564\pi$
$61$	312.213	−	139.006i	0.655324	−	0.291769i	0.707336	+	0.706878i	$0.249897\pi$
$62$	−40.4894	+	8.60628i	−0.0829380	+	0.0176290i
$63$	560.651	−	622.666i	1.12120	−	1.24521i
$64$	−192.427	+	139.806i	−0.375833	+	0.273059i
$65$	48.5505	+	396.924i	0.0926453	+	0.757422i
$66$	−439.418	−	118.762i	−0.819525	−	0.221493i
$67$	−193.336	−	334.868i	−0.352533	−	0.610606i	0.634159	−	0.773202i	$-0.281346\pi$
$67$	−193.336	−	334.868i	−0.352533	−	0.610606i	−0.986693	+	0.162597i	$0.948013\pi$
$68$	169.061	+	75.2707i	0.301495	+	0.134234i
$69$	−407.623	−	86.6430i	−0.711190	−	0.151168i
$70$	110.486	−	340.042i	0.188652	−	0.580612i
$71$	−854.063	+	380.253i	−1.42759	+	0.635602i	−0.967638	−	0.252343i	$-0.918799\pi$
$71$	−854.063	+	380.253i	−1.42759	+	0.635602i	−0.459949	+	0.887946i	$0.652132\pi$
$72$	640.632	−	285.228i	1.04860	−	0.466867i
$73$	−277.448	+	853.898i	−0.444834	+	1.36906i	0.437833	+	0.899057i	$0.355746\pi$
$73$	−277.448	+	853.898i	−0.444834	+	1.36906i	−0.882666	+	0.470001i	$0.844254\pi$
$74$	255.653	+	54.3407i	0.401609	+	0.0853646i
$75$	367.560	+	163.648i	0.565896	+	0.251953i
$76$	352.717	+	610.924i	0.532361	+	0.922077i
$77$	−47.3778	−	943.074i	−0.0701194	−	1.39576i
$78$	538.213	+	228.751i	0.781290	+	0.332063i
$79$	168.375	−	122.331i	0.239793	−	0.174220i	−0.461398	−	0.887193i	$-0.652652\pi$
$79$	168.375	−	122.331i	0.239793	−	0.174220i	0.701191	+	0.712973i	$0.252652\pi$
$80$	−45.3799	+	50.3995i	−0.0634204	+	0.0704354i
$81$	542.946	−	115.407i	0.744781	−	0.158308i
$82$	−553.509	+	246.438i	−0.745424	+	0.331884i
$83$	−682.804	−	496.086i	−0.902982	−	0.656055i	0.0362481	−	0.999343i	$-0.488459\pi$
$83$	−682.804	−	496.086i	−0.902982	−	0.656055i	−0.939230	+	0.343288i	$0.888459\pi$
$84$	717.695	+	797.081i	0.932225	+	1.03534i
$85$	−287.146	−	61.0348i	−0.366416	−	0.0778841i
$86$	640.081	−	465.046i	0.802577	−	0.583107i
$87$	708.577	−	1227.29i	0.873189	−	1.51241i
$88$	284.813	−	737.190i	0.345013	−	0.893008i
$89$	−459.839	−	796.465i	−0.547672	−	0.948596i	−0.998433	−	0.0559518i	$-0.982181\pi$
$89$	−459.839	−	796.465i	−0.547672	−	0.948596i	0.450761	−	0.892645i	$-0.351153\pi$
$90$	−361.791	+	262.856i	−0.423735	+	0.307861i
$91$	−106.291	+	1208.50i	−0.122443	+	1.39214i
$92$	89.8826	−	276.630i	0.101858	−	0.313486i
$93$	−20.5901	+	195.902i	−0.0229580	+	0.218431i
$94$	26.4719	−	251.863i	0.0290465	−	0.276359i
$95$	−748.778	−	831.603i	−0.808664	−	0.898112i
$96$	443.284	+	1364.29i	0.471276	+	1.45044i
$97$	118.904	+	1131.30i	0.124462	+	1.18418i	0.861295	+	0.508106i	$0.169654\pi$
$97$	118.904	+	1131.30i	0.124462	+	1.18418i	−0.736832	+	0.676076i	$0.763679\pi$
$98$	264.659	−	458.402i	0.272802	−	0.472506i
$99$	−645.386	+	989.113i	−0.655189	+	1.00414i
$100$	−140.413	+	243.202i	−0.140413	+	0.243202i
$101$	−672.846	−	299.570i	−0.662878	−	0.295132i	0.0475847	−	0.998867i	$-0.484848\pi$
$101$	−672.846	−	299.570i	−0.662878	−	0.295132i	−0.710463	+	0.703735i	$0.751514\pi$
$102$	−287.270	+	319.045i	−0.278862	+	0.309708i
$103$	−451.397	+	1389.26i	−0.431820	+	1.32900i	0.464491	+	0.885578i	$0.346237\pi$
$103$	−451.397	+	1389.26i	−0.431820	+	1.32900i	−0.896311	+	0.443427i	$0.853763\pi$
$104$	−492.661	+	887.818i	−0.464513	+	0.837094i
$105$	−1376.49	−	1000.08i	−1.27935	−	0.929500i
$106$	−406.804	+	86.4689i	−0.372758	+	0.0792321i
$107$	−512.538	+	569.231i	−0.463074	+	0.514295i	−0.928774	−	0.370647i	$-0.879136\pi$
$107$	−512.538	+	569.231i	−0.463074	+	0.514295i	0.465700	+	0.884943i	$0.345803\pi$
$108$	−23.2725	−	221.423i	−0.0207352	−	0.197282i
$109$	1559.67			1.37054			0.685270	−	0.728289i	$-0.259684\pi$
$109$	1559.67			1.37054			0.685270	+	0.728289i	$0.259684\pi$
$110$	−79.9168	+	497.601i	−0.0692706	+	0.431313i
$111$	621.877	−	1077.12i	0.531765	−	0.921045i
$112$	−166.455	+	120.937i	−0.140433	+	0.102031i
$113$	845.054	+	179.622i	0.703504	+	0.149534i	0.545755	−	0.837945i	$-0.316243\pi$
$113$	845.054	+	179.622i	0.703504	+	0.149534i	0.157749	+	0.987479i	$0.449576\pi$
$114$	−1600.77	+	340.253i	−1.31513	+	0.279541i
$115$	−48.2296	+	458.874i	−0.0391081	+	0.372089i
$116$	800.227	+	581.399i	0.640511	+	0.465358i
$117$	996.014	−	1144.72i	0.787022	−	0.904523i
$118$	142.783	+	439.440i	0.111392	+	0.342828i
$119$	−813.608	−	362.242i	−0.626751	−	0.279047i
$120$	−712.002	−	1233.22i	−0.541638	−	0.938145i
$121$	271.092	+	1303.10i	0.203675	+	0.979038i
$122$	−553.383			−0.410663
$123$	301.382	+	2867.45i	0.220932	+	2.10203i
$124$	−134.483	−	28.5853i	−0.0973946	−	0.0207019i
$125$	467.200	−	1437.89i	0.334301	−	1.02887i
$126$	−1239.42	+	551.823i	−0.876317	+	0.390161i
$127$	−91.7385	+	872.833i	−0.0640982	+	0.609854i	0.914573	+	0.404421i	$0.132527\pi$
$127$	−91.7385	+	872.833i	−0.0640982	+	0.609854i	−0.978671	+	0.205433i	$0.934140\pi$
$128$	−1080.09	+	229.579i	−0.745836	+	0.158532i
$129$	−1163.45	−	3580.73i	−0.794077	−	2.44392i
$130$	189.595	−	619.117i	0.127912	−	0.417693i
$131$	26.9243			0.0179571			0.00897857	−	0.999960i	$-0.497142\pi$
$131$	26.9243			0.0179571			0.00897857	+	0.999960i	$0.497142\pi$
$132$	−1172.88	−	953.990i	−0.773379	−	0.629047i
$133$	−1697.46	−	2940.08i	−1.10668	−	1.91682i
$134$	65.4459	+	622.676i	0.0421915	+	0.401425i
$135$	109.138	+	335.893i	0.0695786	+	0.214141i
$136$	−498.761	−	553.930i	−0.314474	−	0.349258i
$137$	−958.981	+	426.966i	−0.598039	+	0.266264i	−0.683351	−	0.730090i	$-0.739478\pi$
$137$	−958.981	+	426.966i	−0.598039	+	0.266264i	0.0853119	+	0.996354i	$0.472811\pi$
$138$	545.906	+	396.624i	0.336743	+	0.244658i
$139$	1259.59	+	1398.92i	0.768611	+	0.853629i	0.992659	−	0.120949i	$-0.0385937\pi$
$139$	1259.59	+	1398.92i	0.768611	+	0.853629i	−0.224047	+	0.974578i	$0.571927\pi$
$140$	794.628	−	882.524i	0.479703	−	0.532764i
$141$	−1100.95	−	490.176i	−0.657567	−	0.292768i
$142$	1513.79			0.894607
$143$	−114.807	−	1706.17i	−0.0671373	−	0.997744i
$144$	257.343			0.148925
$145$	−1433.41	−	638.197i	−0.820956	−	0.365513i
$146$	972.782	−	1080.38i	0.551425	−	0.612419i
$147$	−1685.45	−	1871.88i	−0.945669	−	1.05027i
$148$	702.313	+	510.260i	0.390066	+	0.283400i
$149$	2338.14	−	1041.01i	1.28556	−	0.572366i	0.353756	−	0.935338i	$-0.384904\pi$
$149$	2338.14	−	1041.01i	1.28556	−	0.572366i	0.931800	+	0.362972i	$0.118238\pi$
$150$	−435.927	−	484.146i	−0.237289	−	0.263536i
$151$	319.400	+	983.011i	0.172135	+	0.529777i	0.999491	−	0.0319009i	$-0.0101561\pi$
$151$	319.400	+	983.011i	0.172135	+	0.529777i	−0.827356	+	0.561678i	$0.810156\pi$
$152$	−297.003	−	2825.79i	−0.158487	−	1.50791i
$153$	556.966	+	964.693i	0.294301	+	0.509744i
$154$	−551.021	+	1426.22i	−0.288328	+	0.746289i
$155$	218.097			0.113019
$156$	1324.06	+	1421.20i	0.679550	+	0.729402i
$157$	−612.452	−	1884.93i	−0.311331	−	0.958178i	−0.977238	−	0.212144i	$-0.931955\pi$
$157$	−612.452	−	1884.93i	−0.311331	−	0.958178i	0.665907	−	0.746034i	$-0.268045\pi$
$158$	−329.632	+	70.0654i	−0.165975	+	0.0352791i
$159$	−206.873	+	1968.26i	−0.103183	+	0.981719i
$160$	1450.96	−	646.007i	0.716926	−	0.319196i
$161$	−432.562	+	1331.29i	−0.211743	+	0.651678i
$162$	−879.147	−	186.868i	−0.426372	−	0.0906282i
$163$	299.796	+	2852.37i	0.144060	+	1.37064i	0.792730	+	0.609573i	$0.208659\pi$
$163$	299.796	+	2852.37i	0.144060	+	1.37064i	−0.648669	+	0.761070i	$0.724674\pi$
$164$	−2012.43			−0.958197
$165$	2134.52	+	1093.42i	1.00710	+	0.515894i
$166$	683.304	+	1183.52i	0.319486	+	0.553366i
$167$	2004.41	+	892.420i	0.928777	+	0.413518i	0.814653	−	0.579948i	$-0.196927\pi$
$167$	2004.41	+	892.420i	0.928777	+	0.413518i	0.114124	+	0.993467i	$0.463594\pi$
$168$	−1335.00	−	4108.70i	−0.613079	−	1.88686i
$169$	−155.275	+	2191.51i	−0.0706760	+	0.997499i
$170$	384.557	+	279.397i	0.173495	+	0.126052i
$171$	−443.851	+	4222.96i	−0.198492	+	1.88852i
$172$	2570.44	−	546.364i	1.13950	−	0.242209i
$173$	−1254.33	−	266.616i	−0.551243	−	0.117170i	−0.0761347	−	0.997098i	$-0.524258\pi$
$173$	−1254.33	−	266.616i	−0.551243	−	0.117170i	−0.475109	+	0.879927i	$0.657591\pi$
$174$	−1856.44	+	1348.78i	−0.808828	+	0.587648i
$175$	675.739	−	1170.41i	0.291892	−	0.505572i
$176$	205.517	−	204.629i	0.0880194	−	0.0876392i
$177$	2198.77			0.933729
$178$	155.659	+	1481.00i	0.0655459	+	0.623628i
$179$	371.486	−	412.577i	0.155118	−	0.172276i	−0.660577	−	0.750759i	$-0.729688\pi$
$179$	371.486	−	412.577i	0.155118	−	0.172276i	0.815695	+	0.578482i	$0.196355\pi$
$180$	−1452.88	+	308.820i	−0.601620	+	0.127878i
$181$	256.018	+	186.008i	0.105136	+	0.0763860i	0.639111	−	0.769114i	$-0.279302\pi$
$181$	256.018	+	186.008i	0.105136	+	0.0763860i	−0.533975	+	0.845500i	$0.679302\pi$
$182$	953.139	−	1717.64i	0.388194	−	0.699561i
$183$	−813.759	+	2504.49i	−0.328715	+	1.01168i
$184$	−783.923	+	870.635i	−0.314085	+	0.348826i
$185$	−1258.02	−	560.109i	−0.499956	−	0.222595i
$186$	159.478	−	276.223i	0.0628681	−	0.108891i
$187$	1211.88	+	327.536i	0.473913	+	0.128085i
$188$	420.579	−	728.464i	0.163159	−	0.282599i
$189$	111.999	+	1065.60i	0.0431045	+	0.410112i
$190$	559.925	+	1723.27i	0.213796	+	0.657996i
$191$	1816.77	+	2017.73i	0.688256	+	0.764386i	0.981461	−	0.191664i	$-0.0613883\pi$
$191$	1816.77	+	2017.73i	0.688256	+	0.764386i	−0.293204	+	0.956050i	$0.594722\pi$
$192$	191.573	−	1822.70i	0.0720084	−	0.685114i
$193$	−286.132	+	2722.36i	−0.106716	+	1.01534i	0.801830	+	0.597552i	$0.203860\pi$
$193$	−286.132	+	2722.36i	−0.106716	+	1.01534i	−0.908546	+	0.417784i	$0.862807\pi$
$194$	569.179	−	1751.75i	0.210643	−	0.648292i
$195$	−2523.19	−	1768.49i	−0.926612	−	0.649457i
$196$	1422.33	−	1033.38i	0.518342	−	0.376597i
$197$	424.920	+	735.983i	0.153677	+	0.266176i	0.932576	−	0.360973i	$-0.117555\pi$
$197$	424.920	+	735.983i	0.153677	+	0.266176i	−0.778900	+	0.627148i	$0.784222\pi$
$198$	1606.10	−	1038.08i	0.576467	−	0.372590i
$199$	1626.70	−	2817.53i	0.579466	−	1.00366i	−0.416074	−	0.909331i	$-0.636594\pi$
$199$	1626.70	−	2817.53i	0.579466	−	1.00366i	0.995541	−	0.0943343i	$-0.0300723\pi$
$200$	915.089	−	664.851i	0.323533	−	0.235060i
$201$	2914.34	+	619.462i	1.02269	+	0.217380i
$202$	797.998	+	886.266i	0.277955	+	0.308700i
$203$	−3851.11	−	2797.99i	−1.33150	−	0.967393i
$204$	−1302.67	+	579.988i	−0.447086	+	0.199055i
$205$	3122.56	−	663.721i	1.06385	−	0.226128i
$206$	1582.68	−	1757.74i	0.535293	−	0.594503i
$207$	1416.44	−	1029.10i	0.475599	−	0.345543i
$208$	−297.680	+	224.103i	−0.0992327	+	0.0747055i
$209$	3003.46	+	3725.43i	0.994038	+	1.23298i
$210$	1377.49	+	2385.89i	0.452648	+	0.784009i
$211$	856.876	+	381.506i	0.279572	+	0.124474i	0.541733	−	0.840551i	$-0.317768\pi$
$211$	856.876	+	381.506i	0.279572	+	0.124474i	−0.262161	+	0.965024i	$0.584435\pi$
$212$	−1351.18	−	287.201i	−0.437732	−	0.0930428i
$213$	2226.05	−	6851.08i	0.716087	−	2.20389i
$214$	1133.05	−	504.468i	0.361934	−	0.161143i
$215$	−3808.20	+	1695.52i	−1.20799	+	0.537830i
$216$	−277.115	+	852.872i	−0.0872930	+	0.268660i
$217$	647.202	+	137.567i	0.202465	+	0.0430353i
$218$	−2307.10	−	1027.19i	−0.716774	−	0.319128i
$219$	−3459.10	−	5991.33i	−1.06732	−	1.84866i
$220$	−914.726	+	1401.90i	−0.280322	+	0.429619i
$221$	−1484.35	−	630.878i	−0.451803	−	0.192025i
$222$	−1629.29	+	1183.75i	−0.492570	+	0.357873i
$223$	−498.387	+	553.514i	−0.149661	+	0.166216i	−0.813314	−	0.581825i	$-0.802339\pi$
$223$	−498.387	+	553.514i	−0.149661	+	0.166216i	0.663653	+	0.748041i	$0.269005\pi$
$224$	4713.19	−	1001.82i	1.40586	−	0.298825i
$225$	−1544.23	+	687.537i	−0.457550	+	0.203715i
$226$	−1131.73	−	822.250i	−0.333104	−	0.242014i
$227$	4092.72	+	4545.43i	1.19667	+	1.32903i	0.931022	+	0.364962i	$0.118918\pi$
$227$	4092.72	+	4545.43i	1.19667	+	1.32903i	0.265644	+	0.964071i	$0.414415\pi$
$228$	−5316.85	−	1130.13i	−1.54437	−	0.328266i
$229$	−3893.43	+	2828.74i	−1.12352	+	0.816282i	−0.984738	−	0.174041i	$-0.944317\pi$
$229$	−3893.43	+	2828.74i	−1.12352	+	0.816282i	−0.138778	+	0.990324i	$0.544317\pi$
$230$	373.555	−	647.016i	0.107093	−	0.185491i
$231$	5644.50	+	4591.09i	1.60771	+	1.30767i
$232$	−1992.03	−	3450.29i	−0.563719	−	0.976390i
$233$	3358.81	−	2440.32i	0.944390	−	0.686140i	−0.00508331	−	0.999987i	$-0.501618\pi$
$233$	3358.81	−	2440.32i	0.944390	−	0.686140i	0.949473	+	0.313848i	$0.101618\pi$
$234$	−2227.24	+	1037.33i	−0.622218	+	0.289796i
$235$	−412.330	+	1269.02i	−0.114457	+	0.352263i
$236$	−160.418	+	1526.28i	−0.0442472	+	0.420984i
$237$	−167.628	+	1594.88i	−0.0459435	+	0.437124i
$238$	964.942	+	1071.68i	0.262806	+	0.291876i
$239$	−57.4577	−	176.837i	−0.0155508	−	0.0478603i	0.942980	−	0.332849i	$-0.108010\pi$
$239$	−57.4577	−	176.837i	−0.0155508	−	0.0478603i	−0.958531	+	0.284989i	$0.908010\pi$
$240$	−54.6236	−	519.709i	−0.0146914	−	0.139779i
$241$	2473.76	−	4284.68i	0.661199	−	1.14523i	−0.319102	−	0.947720i	$-0.603381\pi$
$241$	2473.76	−	4284.68i	0.661199	−	1.14523i	0.980301	−	0.197510i	$-0.0632853\pi$
$242$	457.208	−	2106.12i	0.121448	−	0.559449i
$243$	−2697.40	+	4672.03i	−0.712091	+	1.23338i
$244$	−1679.12	−	747.593i	−0.440552	−	0.196147i
$245$	−1866.12	+	2072.54i	−0.486620	+	0.540447i
$246$	1442.68	−	4440.11i	0.373910	−	1.15078i
$247$	−3164.07	−	5271.40i	−0.815081	−	1.35794i
$248$	448.012	+	325.500i	0.114713	+	0.0833438i
$249$	6361.16	−	1352.11i	1.61896	−	0.344121i
$250$	−1638.09	+	1819.28i	−0.414407	+	0.460245i
$251$	−694.566	−	6608.36i	−0.174664	−	1.66182i	−0.633835	−	0.773468i	$-0.718520\pi$
$251$	−694.566	−	6608.36i	−0.174664	−	1.66182i	0.459172	−	0.888348i	$-0.348146\pi$
$252$	−4506.23			−1.12645
$253$	312.879	−	1948.14i	0.0777493	−	0.484105i
$254$	710.546	−	1230.70i	0.175526	−	0.304020i
$255$	1829.99	−	1329.57i	0.449406	−	0.326512i
$256$	3610.13	+	767.357i	0.881379	+	0.187343i
$257$	−6989.14	+	1485.59i	−1.69638	+	0.360578i	−0.951745	−	0.306889i	$-0.900712\pi$
$257$	−6989.14	+	1485.59i	−1.69638	+	0.360578i	−0.744639	+	0.667467i	$0.767379\pi$
$258$	−637.242	+	6062.96i	−0.153771	+	1.46304i
$259$	−3379.90	−	2455.64i	−0.810874	−	0.589135i
$260$	1411.68	−	1622.44i	0.336726	−	0.386999i
$261$	1839.86	+	5662.50i	0.436338	+	1.34291i
$262$	−39.8272	−	17.7322i	−0.00939134	−	0.00418130i
$263$	−1143.45	−	1980.52i	−0.268093	−	0.464351i	0.700276	−	0.713872i	$-0.253060\pi$
$263$	−1143.45	−	1980.52i	−0.268093	−	0.464351i	−0.968369	+	0.249521i	$0.919727\pi$
$264$	2752.83	+	5431.77i	0.641762	+	1.26630i
$265$	2191.26			0.507954
$266$	574.604	+	5466.99i	0.132448	+	1.26016i
$267$	6931.60	+	1473.36i	1.58879	+	0.337708i
$268$	−642.623	+	1977.79i	−0.146472	+	0.450794i
$269$	−4172.05	+	1857.52i	−0.945631	+	0.421022i	−0.820838	−	0.571161i	$-0.806493\pi$
$269$	−4172.05	+	1857.52i	−0.945631	+	0.421022i	−0.124793	+	0.992183i	$0.539827\pi$
$270$	59.7770	−	568.740i	0.0134737	−	0.128194i
$271$	−5026.41	+	1068.40i	−1.12669	+	0.239485i	−0.733312	−	0.679892i	$-0.762027\pi$
$271$	−5026.41	+	1068.40i	−1.12669	+	0.239485i	−0.393377	+	0.919377i	$0.628693\pi$
$272$	−84.5276	−	260.149i	−0.0188428	−	0.0579922i
$273$	−6372.07	−	6839.53i	−1.41266	−	1.51629i
$274$	1699.75			0.374765
$275$	−686.538	+	1776.99i	−0.150545	+	0.389659i
$276$	1120.61	+	1940.96i	0.244395	+	0.423305i
$277$	−540.643	−	5143.87i	−0.117271	−	1.11576i	−0.881948	−	0.471346i	$-0.843768\pi$
$277$	−540.643	−	5143.87i	−0.117271	−	1.11576i	0.764677	−	0.644413i	$-0.222898\pi$
$278$	−941.902	−	2898.88i	−0.203207	−	0.625407i
$279$	−553.758	−	615.010i	−0.118827	−	0.131970i
$280$	−4369.71	+	1945.52i	−0.932643	+	0.415239i
$281$	4439.62	+	3225.57i	0.942511	+	0.684774i	0.949024	−	0.315204i	$-0.102073\pi$
$281$	4439.62	+	3225.57i	0.942511	+	0.684774i	−0.00651267	+	0.999979i	$0.502073\pi$
$282$	1305.73	+	1450.16i	0.275728	+	0.306227i
$283$	−1561.05	+	1733.73i	−0.327898	+	0.364167i	−0.884442	−	0.466651i	$-0.845460\pi$
$283$	−1561.05	+	1733.73i	−0.327898	+	0.364167i	0.556544	+	0.830818i	$0.312127\pi$
$284$	4593.27	+	2045.05i	0.959719	+	0.427294i
$285$	8622.54			1.79212
$286$	−953.852	+	2599.43i	−0.197211	+	0.537439i
$287$	9684.86			1.99191
$288$	−5505.72	−	2451.31i	−1.12649	−	0.501544i
$289$	−2495.17	+	2771.17i	−0.507871	+	0.564048i
$290$	1700.03	+	1888.08i	0.344239	+	0.382317i
$291$	−7091.08	−	5151.97i	−1.42848	−	1.03785i
$292$	4411.25	−	1964.01i	0.884071	−	0.393614i
$293$	4076.44	+	4527.35i	0.812793	+	0.902698i	0.996776	−	0.0802312i	$-0.0255659\pi$
$293$	4076.44	+	4527.35i	0.812793	+	0.902698i	−0.183983	+	0.982929i	$0.558899\pi$
$294$	1260.35	+	3878.96i	0.250018	+	0.769475i
$295$	−254.472	−	2421.14i	−0.0502235	−	0.477844i
$296$	−1748.29	−	3028.12i	−0.343301	−	0.594614i
$297$	−387.738	−	1459.69i	−0.0757537	−	0.285184i
$298$	−4144.24			−0.805603
$299$	−742.277	+	2423.88i	−0.143569	+	0.468819i
$300$	−668.671	−	2057.96i	−0.128686	−	0.396054i
$301$	−12370.3	+	2629.39i	−2.36881	+	0.503506i
$302$	174.941	−	1664.45i	0.0333335	−	0.317147i
$303$	5184.52	−	2308.30i	0.982980	−	0.437651i
$304$	322.213	−	991.669i	0.0607900	−	0.187092i
$305$	2851.95	+	606.201i	0.535417	+	0.113806i
$306$	−188.538	−	1793.82i	−0.0352222	−	0.335116i
$307$	−2803.08			−0.521109			−0.260554	−	0.965459i	$-0.583905\pi$
$307$	−2803.08			−0.521109			−0.260554	+	0.965459i	$0.583905\pi$
$308$	−3598.72	+	3583.17i	−0.665766	+	0.662890i
$309$	−5627.81	−	9747.65i	−1.03610	−	1.79458i
$310$	−322.615	−	143.637i	−0.0591074	−	0.0263163i
$311$	736.306	+	2266.12i	0.134251	+	0.413182i	0.995473	−	0.0950471i	$-0.0303002\pi$
$311$	736.306	+	2266.12i	0.134251	+	0.413182i	−0.861222	+	0.508230i	$0.830300\pi$
$312$	−2543.72	−	7398.57i	−0.461569	−	1.34250i
$313$	2051.70	+	1490.65i	0.370508	+	0.269190i	0.757421	−	0.652926i	$-0.226459\pi$
$313$	2051.70	+	1490.65i	0.370508	+	0.269190i	−0.386914	+	0.922116i	$0.626459\pi$
$314$	−335.451	+	3191.60i	−0.0602885	+	0.573607i
$315$	6992.03	−	1486.20i	1.25065	−	0.265835i
$316$	−1094.85	−	232.718i	−0.194906	−	0.0414285i
$317$	−3577.20	+	2598.99i	−0.633803	+	0.460485i	−0.857716	−	0.514125i	$-0.828117\pi$
$317$	−3577.20	+	2598.99i	−0.633803	+	0.460485i	0.223913	+	0.974609i	$0.428117\pi$
$318$	1602.30	−	2775.27i	0.282555	−	0.489400i
$319$	5971.92	+	3059.14i	1.04816	+	0.536925i
$320$	−2029.20			−0.354487
$321$	−616.939	−	5869.79i	−0.107272	−	1.02062i
$322$	1516.64	−	1684.40i	0.262481	−	0.291515i
$323$	4414.79	−	938.393i	0.760513	−	0.161652i
$324$	−2415.13	−	1754.70i	−0.414118	−	0.300874i
$325$	1187.55	−	2140.07i	0.202688	−	0.365261i
$326$	1435.09	−	4416.75i	0.243811	−	0.750372i
$327$	−8041.47	+	8930.96i	−1.35992	+	1.51035i
$328$	7404.91	+	3296.88i	1.24655	+	0.554999i
$329$	−2024.04	+	3505.75i	−0.339177	+	0.587471i
$330$	−2437.32	−	3023.20i	−0.406576	−	0.504308i
$331$	−5826.34	+	10091.5i	−0.967506	+	1.67577i	−0.264781	+	0.964309i	$0.585300\pi$
$331$	−5826.34	+	10091.5i	−0.967506	+	1.67577i	−0.702725	+	0.711461i	$0.748034\pi$
$332$	474.466	+	4514.24i	0.0784328	+	0.746238i
$333$	1614.74	+	4969.64i	0.265727	+	0.817822i
$334$	−2377.23	−	2640.19i	−0.389451	−	0.432529i
$335$	344.822	−	3280.76i	0.0562377	−	0.535066i
$336$	165.717	−	1576.69i	0.0269066	−	0.255999i
$337$	−718.164	+	2210.28i	−0.116086	+	0.357275i	−0.992172	−	0.124880i	$-0.960146\pi$
$337$	−718.164	+	2210.28i	−0.116086	+	0.357275i	0.876086	+	0.482154i	$0.160146\pi$
$338$	1673.00	−	3139.48i	0.269229	−	0.505222i
$339$	−5385.56	+	3912.84i	−0.862842	+	0.626891i
$340$	789.405	+	1367.29i	0.125916	+	0.218093i
$341$	−931.268	−	50.8272i	−0.147891	−	0.00807169i
$342$	3437.78	−	5954.40i	0.543549	−	0.941454i
$343$	337.183	−	244.978i	0.0530792	−	0.0385643i
$344$	−10353.3	−	2200.65i	−1.62270	−	0.344916i
$345$	−2378.94	−	2642.08i	−0.371240	−	0.412303i
$346$	1679.85	+	1220.48i	0.261010	+	0.189635i
$347$	−3220.69	+	1433.94i	−0.498258	+	0.221839i	−0.640449	−	0.768001i	$-0.721252\pi$
$347$	−3220.69	+	1433.94i	−0.498258	+	0.221839i	0.142191	+	0.989839i	$0.454585\pi$
$348$	−7455.10	+	1584.63i	−1.14838	+	0.244095i
$349$	−554.593	+	615.938i	−0.0850622	+	0.0944711i	−0.784173	−	0.620542i	$-0.786913\pi$
$349$	−554.593	+	615.938i	−0.0850622	+	0.0944711i	0.699111	+	0.715013i	$0.253579\pi$
$350$	−1770.40	+	1286.27i	−0.270377	+	0.196440i
$351$	235.588	+	1926.05i	0.0358255	+	0.292891i
$352$	−6346.10	+	2420.29i	−0.960933	+	0.366483i
$353$	−1425.29	−	2468.67i	−0.214902	−	0.372221i	0.738340	−	0.674428i	$-0.235610\pi$
$353$	−1425.29	−	2468.67i	−0.214902	−	0.372221i	−0.953242	+	0.302207i	$0.902277\pi$
$354$	−3252.49	−	1448.10i	−0.488328	−	0.217417i
$355$	−7801.56	−	1658.27i	−1.16638	−	0.247921i
$356$	−1528.45	+	4704.07i	−0.227549	+	0.700324i
$357$	6269.14	−	2791.20i	0.929407	−	0.413799i
$358$	−821.233	+	365.637i	−0.121239	+	0.0539790i
$359$	1657.66	−	5101.76i	0.243700	−	0.750030i	−0.752148	−	0.658994i	$-0.770982\pi$
$359$	1657.66	−	5101.76i	0.243700	−	0.750030i	0.995848	−	0.0910360i	$-0.0290178\pi$
$360$	5851.94	+	1243.87i	0.856734	+	0.182105i
$361$	9451.38	+	4208.02i	1.37795	+	0.613504i
$362$	−256.205	−	443.761i	−0.0371985	−	0.0644297i
$363$	−8859.53	−	5166.32i	−1.28101	−	0.747001i
$364$	5212.55	−	3924.17i	0.750582	−	0.565062i
$365$	−6196.90	+	4502.31i	−0.888659	+	0.645649i
$366$	2853.18	−	3168.78i	0.407481	−	0.452554i
$367$	9508.25	−	2021.04i	1.35239	−	0.287459i	0.525964	−	0.850507i	$-0.323704\pi$
$367$	9508.25	−	2021.04i	1.35239	−	0.287459i	0.826425	+	0.563047i	$0.190371\pi$
$368$	−392.760	+	174.868i	−0.0556359	+	0.0247707i
$369$	−9799.96	−	7120.09i	−1.38256	−	1.00449i
$370$	1492.02	+	1657.06i	0.209639	+	0.232828i
$371$	6502.56	+	1382.16i	0.909962	+	0.193418i
$372$	857.065	−	622.694i	0.119454	−	0.0867881i
$373$	1707.65	−	2957.74i	0.237048	−	0.410579i	−0.722818	−	0.691038i	$-0.757154\pi$
$373$	1707.65	−	2957.74i	0.237048	−	0.410579i	0.959866	+	0.280460i	$0.0904869\pi$
$374$	−1576.94	−	1282.64i	−0.218026	−	0.177336i
$375$	5824.84	+	10088.9i	0.802115	+	1.38930i
$376$	−2740.97	+	1991.43i	−0.375943	+	0.273139i
$377$	−7059.33	−	4947.85i	−0.964387	−	0.675934i
$378$	536.128	−	1650.03i	0.0729509	−	0.224520i
$379$	−1173.55	+	11165.6i	−0.159053	+	1.51329i	0.565889	+	0.824481i	$0.308533\pi$
$379$	−1173.55	+	11165.6i	−0.159053	+	1.51329i	−0.724943	+	0.688809i	$0.758134\pi$
$380$	−629.084	+	5985.34i	−0.0849246	+	0.808003i
$381$	−4525.02	−	5025.55i	−0.608462	−	0.675765i
$382$	−1358.55	−	4181.20i	−0.181962	−	0.560023i
$383$	−328.963	−	3129.87i	−0.0438883	−	0.417569i	−0.994304	−	0.106586i	$-0.966008\pi$
$383$	−328.963	−	3129.87i	−0.0438883	−	0.417569i	0.950415	−	0.310984i	$-0.100658\pi$
$384$	4254.19	−	7368.47i	0.565353	−	0.979220i
$385$	4402.13	−	6746.68i	0.582737	−	0.893098i
$386$	2216.19	−	3838.55i	0.292231	−	0.506158i
$387$	14450.4	+	6433.73i	1.89807	+	0.845077i
$388$	4093.59	−	4546.39i	0.535620	−	0.594866i
$389$	788.227	−	2425.91i	0.102737	−	0.316192i	−0.886456	−	0.462814i	$-0.846840\pi$
$389$	788.227	−	2425.91i	0.102737	−	0.316192i	0.989193	+	0.146622i	$0.0468399\pi$
$390$	2567.65	+	4277.76i	0.333380	+	0.555417i
$391$	−1505.57	−	1093.86i	−0.194731	−	0.141480i
$392$	−6926.54	+	1472.28i	−0.892457	+	0.189698i
$393$	−138.819	+	154.174i	−0.0178180	+	0.0197889i
$394$	−143.839	−	1368.54i	−0.0183921	−	0.174990i
$395$	1775.57			0.226173
$396$	6275.75	−	980.062i	0.796385	−	0.124369i
$397$	−5331.26	+	9234.01i	−0.673975	+	1.16736i	0.302792	+	0.953057i	$0.402081\pi$
$397$	−5331.26	+	9234.01i	−0.673975	+	1.16736i	−0.976767	+	0.214303i	$0.931252\pi$
$398$	−4261.87	+	3096.43i	−0.536755	+	0.389975i
$399$	25587.4	+	5438.77i	3.21046	+	0.682404i
$400$	406.018	−	86.3017i	0.0507522	−	0.0107877i
$401$	−848.970	+	8077.41i	−0.105725	+	1.00590i	0.805109	+	0.593128i	$0.202107\pi$
$401$	−848.970	+	8077.41i	−0.105725	+	1.00590i	−0.910833	+	0.412775i	$0.864560\pi$
$402$	−3903.00	−	2835.69i	−0.484238	−	0.351820i
$403$	1176.13	+	229.178i	0.145377	+	0.0283280i
$404$	1224.05	+	3767.24i	0.150740	+	0.463929i
$405$	4326.13	+	1926.12i	0.530783	+	0.236320i
$406$	3853.93	+	6675.19i	0.471101	+	0.815971i
$407$	5241.21	+	2684.83i	0.638322	+	0.326983i
$408$	5743.47			0.696922
$409$	−417.386	−	3971.16i	−0.0504606	−	0.480101i	−0.990347	−	0.138613i	$-0.955736\pi$
$409$	−417.386	−	3971.16i	−0.0504606	−	0.480101i	0.939886	−	0.341488i	$-0.110931\pi$
$410$	−5056.10	−	1074.71i	−0.609032	−	0.129454i
$411$	2499.51	−	7692.71i	0.299980	−	0.923244i
$412$	7176.92	−	3195.37i	0.858207	−	0.382098i
$413$	772.016	−	7345.24i	0.0919817	−	0.875147i
$414$	−2772.99	+	589.418i	−0.329191	+	0.0699717i
$415$	−2225.04	−	6847.98i	−0.263188	−	0.810010i
$416$	8503.38	−	1959.03i	1.00219	−	0.230888i
$417$	−14504.8			−1.70336
$418$	−1989.26	−	7488.83i	−0.232770	−	0.876293i
$419$	−2724.13	−	4718.33i	−0.317619	−	0.550132i	0.662372	−	0.749175i	$-0.269550\pi$
$419$	−2724.13	−	4718.33i	−0.317619	−	0.550132i	−0.979991	+	0.199043i	$0.936217\pi$
$420$	956.491	+	9100.40i	0.111124	+	1.05727i
$421$	3644.12	+	11215.5i	0.421861	+	1.29836i	0.905968	+	0.423347i	$0.139145\pi$
$421$	3644.12	+	11215.5i	0.421861	+	1.29836i	−0.484106	+	0.875009i	$0.660855\pi$
$422$	−1016.26	−	1128.67i	−0.117229	−	0.130196i
$423$	4625.44	−	2059.38i	0.531671	−	0.236715i
$424$	4501.26	+	3270.36i	0.515567	+	0.374582i
$425$	1202.26	+	1335.24i	0.137219	+	0.152397i
$426$	−7804.93	+	8668.25i	−0.887676	+	0.985864i
$427$	8080.80	+	3597.81i	0.915826	+	0.407752i
$428$	4119.52			0.465244
$429$	10361.8	+	8139.44i	1.16614	+	0.916028i
$430$	6749.85			0.756993
$431$	5741.64	+	2556.34i	0.641682	+	0.285695i	0.701668	−	0.712504i	$-0.252439\pi$
$431$	5741.64	+	2556.34i	0.641682	+	0.285695i	−0.0599859	+	0.998199i	$0.519106\pi$
$432$	−220.203	+	244.560i	−0.0245243	+	0.0272370i
$433$	4159.63	+	4619.74i	0.461661	+	0.512727i	0.928356	−	0.371692i	$-0.121222\pi$
$433$	4159.63	+	4619.74i	0.461661	+	0.512727i	−0.466695	+	0.884418i	$0.654555\pi$
$434$	−866.759	−	629.737i	−0.0958658	−	0.0696506i
$435$	11045.0	−	4917.54i	1.21739	−	0.542018i
$436$	−5612.73	−	6233.57i	−0.616516	−	0.684710i
$437$	−2192.14	−	6746.73i	−0.239964	−	0.738535i
$438$	1170.93	+	11140.7i	0.127738	+	1.21535i
$439$	4181.01	+	7241.72i	0.454553	+	0.787308i	0.998662	−	0.0517057i	$-0.0164658\pi$
$439$	4181.01	+	7241.72i	0.454553	+	0.787308i	−0.544110	+	0.839014i	$0.683132\pi$
$440$	5662.49	−	3659.86i	0.613520	−	0.396539i
$441$	10582.5			1.14270
$442$	1780.20	+	1910.80i	0.191574	+	0.205628i
$443$	−489.557	−	1506.70i	−0.0525046	−	0.161593i	0.921366	−	0.388696i	$-0.127074\pi$
$443$	−489.557	−	1506.70i	−0.0525046	−	0.161593i	−0.973871	+	0.227104i	$0.927074\pi$
$444$	−6542.91	+	1390.74i	−0.699353	+	0.148652i
$445$	820.140	−	7803.11i	0.0873671	−	0.831242i
$446$	1101.77	−	490.539i	0.116974	−	0.0520801i
$447$	−6094.18	+	18756.0i	−0.644843	+	1.98462i
$448$	−6021.65	−	1279.94i	−0.635037	−	0.134981i
$449$	−1220.38	−	11611.2i	−0.128271	−	1.22041i	−0.849451	−	0.527667i	$-0.823067\pi$
$449$	−1220.38	−	11611.2i	−0.128271	−	1.22041i	0.721181	−	0.692747i	$-0.243600\pi$
$450$	2737.08			0.286727
$451$	−13487.9	+	2106.36i	−1.40825	+	0.219922i
$452$	−2323.17	−	4023.86i	−0.241754	−	0.418731i
$453$	−7275.71	−	3239.35i	−0.754619	−	0.335978i
$454$	−3060.47	−	9419.17i	−0.316377	−	0.973708i
$455$	−6793.75	+	7808.04i	−0.699991	+	0.804498i
$456$	17712.4	+	12868.8i	1.81899	+	1.32157i
$457$	1418.68	−	13497.9i	0.145215	−	1.38163i	−0.642830	−	0.766009i	$-0.722240\pi$
$457$	1418.68	−	13497.9i	0.145215	−	1.38163i	0.788045	−	0.615618i	$-0.211094\pi$
$458$	7622.27	−	1620.16i	0.777654	−	0.165295i
$459$	−1393.36	−	296.167i	−0.141691	−	0.0301174i
$460$	2007.56	−	1458.58i	0.203485	−	0.147840i
$461$	−4560.71	+	7899.38i	−0.460766	+	0.798071i	−0.998999	−	0.0447254i	$-0.985759\pi$
$461$	−4560.71	+	7899.38i	−0.460766	+	0.798071i	0.538233	+	0.842796i	$0.319092\pi$
$462$	−5325.84	−	10508.7i	−0.536321	−	1.05825i
$463$	−5765.15			−0.578681			−0.289340	−	0.957226i	$-0.593436\pi$
$463$	−5765.15			−0.578681			−0.289340	+	0.957226i	$0.593436\pi$
$464$	−152.825	−	1454.03i	−0.0152903	−	0.145478i
$465$	−1124.48	+	1248.86i	−0.112143	+	0.124548i
$466$	−6575.63	+	1397.69i	−0.653670	+	0.138942i
$467$	−5001.43	−	3633.75i	−0.495586	−	0.360064i	0.311742	−	0.950167i	$-0.399087\pi$
$467$	−5001.43	−	3633.75i	−0.495586	−	0.360064i	−0.807329	+	0.590102i	$0.799087\pi$
$468$	−8159.46	+	138.662i	−0.805921	+	0.0136959i
$469$	3092.64	−	9518.16i	0.304488	−	0.937116i
$470$	1445.70	−	1605.62i	0.141884	−	0.157578i
$471$	13951.2	+	6211.49i	1.36484	+	0.607665i
$472$	3090.71	−	5353.27i	0.301402	−	0.522043i
$473$	16656.1	−	6352.33i	1.61913	−	0.617506i
$474$	1298.34	−	2248.79i	0.125811	−	0.217912i
$475$	715.920	+	6811.53i	0.0691551	+	0.657967i
$476$	1480.13	+	4555.36i	0.142524	+	0.438644i
$477$	−5563.70	−	6179.12i	−0.534056	−	0.593129i
$478$	−31.4707	+	299.423i	−0.00301137	+	0.0286513i
$479$	981.459	−	9337.95i	0.0936200	−	0.890735i	−0.842415	−	0.538829i	$-0.818867\pi$
$479$	981.459	−	9337.95i	0.0936200	−	0.890735i	0.936035	−	0.351906i	$-0.114466\pi$
$480$	−3781.81	+	11639.2i	−0.359615	+	1.10678i
$481$	−6195.56	−	4342.44i	−0.587304	−	0.411639i
$482$	−6481.12	+	4708.81i	−0.612463	+	0.444980i
$483$	−5392.98	−	9340.91i	−0.508052	−	0.879972i
$484$	4232.57	−	5772.92i	0.397499	−	0.542160i
$485$	−4852.31	+	8404.46i	−0.454293	+	0.786859i
$486$	7067.04	−	5134.51i	0.659604	−	0.479230i
$487$	−3108.34	−	660.699i	−0.289225	−	0.0614766i	0.0610145	−	0.998137i	$-0.480566\pi$
$487$	−3108.34	−	660.699i	−0.289225	−	0.0614766i	−0.350239	+	0.936660i	$0.613900\pi$
$488$	4953.73	+	5501.67i	0.459518	+	0.510346i
$489$	−17879.0	−	12989.8i	−1.65340	−	1.20127i
$490$	4125.38	−	1836.74i	0.380338	−	0.169337i
$491$	−7250.91	+	1541.23i	−0.666454	+	0.141659i	−0.528702	−	0.848808i	$-0.677321\pi$
$491$	−7250.91	+	1541.23i	−0.666454	+	0.141659i	−0.137752	+	0.990467i	$0.543988\pi$
$492$	10375.9	−	11523.6i	0.950773	−	1.05594i
$493$	5119.91	−	3719.84i	0.467727	−	0.339823i
$494$	1208.67	+	9881.45i	0.110082	+	0.899974i
$495$	−9414.46	+	3590.51i	−0.854845	+	0.326023i
$496$	101.610	+	175.994i	0.00919844	+	0.0159322i
$497$	−22105.2	−	9841.86i	−1.99508	−	0.888265i
$498$	−10300.1	−	2189.35i	−0.926824	−	0.197002i
$499$	1700.75	−	5234.37i	0.152577	−	0.469584i	−0.845330	−	0.534244i	$-0.820596\pi$
$499$	1700.75	−	5234.37i	0.152577	−	0.469584i	0.997907	+	0.0646601i	$0.0205963\pi$
$500$	−7428.18	+	3307.24i	−0.664397	+	0.295809i
$501$	−15444.7	+	6876.42i	−1.37728	+	0.613205i
$502$	−3324.81	+	10232.7i	−0.295604	+	0.909777i
$503$	−8708.58	−	1851.07i	−0.771961	−	0.164085i	−0.194940	−	0.980815i	$-0.562451\pi$
$503$	−8708.58	−	1851.07i	−0.771961	−	0.164085i	−0.577020	+	0.816730i	$0.695785\pi$
$504$	16581.1	+	7382.37i	1.46544	+	0.652454i
$505$	−3141.76	−	5441.69i	−0.276844	−	0.479509i
$506$	−1745.86	+	2675.69i	−0.153385	+	0.235077i
$507$	−11748.4	−	12188.3i	−1.02912	−	1.06766i
$508$	3818.62	−	2774.39i	0.333511	−	0.242310i
$509$	4778.06	−	5306.57i	0.416078	−	0.462101i	−0.498275	−	0.867019i	$-0.666033\pi$
$509$	4778.06	−	5306.57i	0.416078	−	0.462101i	0.914353	+	0.404918i	$0.132700\pi$
$510$	−3582.62	+	761.510i	−0.311061	+	0.0661181i
$511$	−21229.2	+	9451.85i	−1.83782	+	0.818249i
$512$	2311.80	+	1679.62i	0.199547	+	0.144979i
$513$	−3633.40	−	4035.30i	−0.312706	−	0.347296i
$514$	11316.9	+	2405.49i	0.971146	+	0.206423i
$515$	−10082.1	+	7325.08i	−0.862661	+	0.626760i
$516$	−10124.3	+	17535.9i	−0.863758	+	1.49607i
$517$	2056.39	−	5322.61i	0.174932	−	0.452781i
$518$	3382.37	+	5858.43i	0.286897	+	0.496920i
$519$	7993.90	−	5807.91i	0.676095	−	0.491212i
$520$	−7852.40	+	3657.23i	−0.662212	+	0.308423i
$521$	−5103.70	+	15707.6i	−0.429170	+	1.32085i	0.469775	+	0.882786i	$0.344335\pi$
$521$	−5103.70	+	15707.6i	−0.429170	+	1.32085i	−0.898945	+	0.438062i	$0.855665\pi$
$522$	1007.72	−	9587.85i	0.0844959	−	0.803925i
$523$	−544.398	+	5179.60i	−0.0455160	+	0.433055i	0.947907	+	0.318549i	$0.103195\pi$
$523$	−544.398	+	5179.60i	−0.0455160	+	0.433055i	−0.993422	+	0.114507i	$0.963471\pi$
$524$	−96.8918	−	107.609i	−0.00807774	−	0.00897124i
$525$	3217.99	+	9903.95i	0.267513	+	0.823322i
$526$	387.069	+	3682.72i	0.0320856	+	0.305274i
$527$	−439.828	+	761.804i	−0.0363552	+	0.0629690i
$528$	112.124	+	2231.88i	0.00924162	+	0.183958i
$529$	4621.01	−	8003.82i	0.379798	−	0.657830i
$530$	−3241.37	−	1443.15i	−0.265653	−	0.118276i
$531$	−6181.25	+	6864.97i	−0.505166	+	0.561044i
$532$	−5642.13	+	17364.7i	−0.459807	+	1.41514i
$533$	17536.4	−	298.015i	1.42512	−	0.0242185i
$534$	−9283.07	−	6744.55i	−0.752280	−	0.546564i
$535$	−6392.00	+	1358.66i	−0.516542	+	0.109794i
$536$	5604.72	−	6224.67i	0.451655	−	0.501614i
$537$	447.156	+	4254.40i	0.0359333	+	0.341883i
$538$	7394.78			0.592586
$539$	8451.29	−	8414.79i	0.675367	−	0.672450i
$540$	949.721	−	1644.96i	0.0756842	−	0.131089i
$541$	11972.6	−	8698.63i	0.951468	−	0.691282i	0.000314344	−	1.00000i	$-0.499900\pi$
$541$	11972.6	−	8698.63i	0.951468	−	0.691282i	0.951154	+	0.308718i	$0.0998999\pi$
$542$	8138.85	+	1729.97i	0.645007	+	0.137100i
$543$	−2385.12	+	506.973i	−0.188500	+	0.0400668i
$544$	−669.610	+	6370.92i	−0.0527745	+	0.502116i
$545$	10764.8	+	7821.10i	0.846081	+	0.614714i
$546$	4921.27	+	14313.8i	0.385734	+	1.12193i
$547$	−7007.93	−	21568.2i	−0.547783	−	1.68590i	−0.714279	−	0.699861i	$-0.753245\pi$
$547$	−7007.93	−	21568.2i	−0.547783	−	1.68590i	0.166495	−	0.986042i	$-0.446755\pi$
$548$	5157.53	+	2296.28i	0.402042	+	0.179000i
$549$	−5531.82	−	9581.39i	−0.430040	−	0.744852i
$550$	2185.86	−	2176.42i	0.169464	−	0.168732i
$551$	24124.0			1.86518
$552$	−943.605	−	8977.80i	−0.0727581	−	0.692247i
$553$	5269.00	+	1119.96i	0.405173	+	0.0861221i
$554$	−2587.99	+	7965.03i	−0.198472	+	0.610833i
$555$	9693.53	−	4315.84i	0.741383	−	0.330085i
$556$	1058.24	−	10068.5i	0.0807183	−	0.767984i
$557$	−18754.8	+	3986.45i	−1.42669	+	0.303252i	−0.855600	−	0.517638i	$-0.826812\pi$
$557$	−18754.8	+	3986.45i	−1.42669	+	0.303252i	−0.571087	+	0.820889i	$0.693478\pi$
$558$	414.092	+	1274.44i	0.0314156	+	0.0966872i
$559$	−22318.1	+	5141.70i	−1.68865	+	0.389036i
$560$	−1755.32			−0.132457
$561$	−8123.88	+	5250.74i	−0.611391	+	0.395163i
$562$	−4442.87	−	7695.27i	−0.333472	−	0.577590i
$563$	309.744	+	2947.02i	0.0231868	+	0.220608i	0.999979	+	0.00642029i	$0.00204366\pi$
$563$	309.744	+	2947.02i	0.0231868	+	0.220608i	−0.976793	+	0.214187i	$0.931290\pi$
$564$	2002.87	+	6164.20i	0.149532	+	0.460212i
$565$	4931.83	+	5477.35i	0.367228	+	0.407848i
$566$	3450.98	−	1536.47i	0.256282	−	0.114104i
$567$	11622.9	+	8444.51i	0.860873	+	0.625461i
$568$	−13551.0	−	15049.9i	−1.00103	−	1.11176i
$569$	2850.93	−	3166.28i	0.210048	−	0.233282i	−0.628910	−	0.777478i	$-0.716499\pi$
$569$	2850.93	−	3166.28i	0.210048	−	0.233282i	0.838958	+	0.544196i	$0.183165\pi$
$570$	−12754.7	−	5678.77i	−0.937257	−	0.417294i
$571$	−570.637			−0.0418221			−0.0209110	−	0.999781i	$-0.506657\pi$
$571$	−570.637			−0.0418221			−0.0209110	+	0.999781i	$0.506657\pi$
$572$	−6405.97	+	6598.81i	−0.468264	+	0.482361i
$573$	−20921.0			−1.52528
$574$	−14326.1	−	6378.40i	−1.04174	−	0.463814i
$575$	1889.63	−	2098.65i	0.137049	−	0.152208i
$576$	5152.23	+	5722.14i	0.372702	+	0.413928i
$577$	3734.14	+	2713.01i	0.269418	+	0.195744i	0.714289	−	0.699851i	$-0.246750\pi$
$577$	3734.14	+	2713.01i	0.269418	+	0.195744i	−0.444871	+	0.895595i	$0.646750\pi$
$578$	5516.00	−	2455.88i	0.396947	−	0.176732i
$579$	−14113.5	−	15674.7i	−1.01302	−	1.12507i
$580$	2607.69	+	8025.64i	0.186687	+	0.574563i
$581$	−2283.38	−	21724.9i	−0.163047	−	1.55129i
$582$	7096.26	+	12291.1i	0.505412	+	0.875399i
$583$	−9356.62	−	510.670i	−0.664685	−	0.0362775i
$584$	−19449.1			−1.37810
$585$	12614.8	−	2906.23i	0.891551	−	0.205398i
$586$	−3048.30	−	9381.71i	−0.214888	−	0.661356i
$587$	4638.02	−	985.841i	0.326118	−	0.0693186i	−0.0419433	−	0.999120i	$-0.513355\pi$
$587$	4638.02	−	985.841i	0.326118	−	0.0693186i	0.368062	+	0.929801i	$0.380022\pi$
$588$	−1416.02	+	13472.6i	−0.0993126	+	0.944896i
$589$	−3063.28	+	1363.86i	−0.214296	+	0.0954106i
$590$	−1218.13	+	3749.01i	−0.0849992	+	0.261601i
$591$	−6405.22	−	1361.47i	−0.445813	−	0.0947605i
$592$	−134.126	−	1276.12i	−0.00931170	−	0.0885949i
$593$	25179.0			1.74364			0.871821	−	0.489825i	$-0.162939\pi$
$593$	25179.0			1.74364			0.871821	+	0.489825i	$0.162939\pi$
$594$	−387.791	+	2414.58i	−0.0267866	+	0.166787i
$595$	−3799.03	−	6580.11i	−0.261756	−	0.453375i
$596$	−12574.8	−	5598.67i	−0.864237	−	0.384783i
$597$	7746.64	+	23841.7i	0.531070	+	1.63446i
$598$	2694.36	−	3096.62i	0.184248	−	0.211756i
$599$	10238.1	+	7438.41i	0.698359	+	0.507388i	0.879397	−	0.476088i	$-0.157946\pi$
$599$	10238.1	+	7438.41i	0.698359	+	0.507388i	−0.181038	+	0.983476i	$0.557946\pi$
$600$	−911.032	+	8667.89i	−0.0619878	+	0.589775i
$601$	27623.4	−	5871.53i	1.87484	−	0.398510i	0.878052	−	0.478566i	$-0.158843\pi$
$601$	27623.4	−	5871.53i	1.87484	−	0.398510i	0.996790	+	0.0800558i	$0.0255098\pi$
$602$	20030.2	+	4257.55i	1.35610	+	0.288247i
$603$	−10126.9	+	7357.64i	−0.683914	+	0.496893i
$604$	2779.42	−	4814.09i	0.187240	−	0.324309i
$605$	−4663.45	+	10353.4i	−0.313382	+	0.695746i
$606$	−9189.33			−0.615992
$607$	−146.331	−	1392.25i	−0.00978483	−	0.0930964i	0.988540	−	0.150962i	$-0.0482371\pi$
$607$	−146.331	−	1392.25i	−0.00978483	−	0.0930964i	−0.998324	+	0.0578657i	$0.981570\pi$
$608$	−16339.6	+	18147.0i	−1.08990	+	1.21046i
$609$	35877.8	−	7626.06i	2.38726	−	0.507428i
$610$	−3819.45	−	2774.99i	−0.253516	−	0.184190i
$611$	−3557.07	+	6410.16i	−0.235522	+	0.424431i
$612$	1851.28	−	5697.66i	0.122277	−	0.376330i
$613$	14239.8	−	15814.9i	0.938238	−	1.04202i	−0.0607992	−	0.998150i	$-0.519365\pi$
$613$	14239.8	−	15814.9i	0.938238	−	1.04202i	0.999037	−	0.0438689i	$-0.0139684\pi$
$614$	4146.40	+	1846.10i	0.272533	+	0.121339i
$615$	−12299.0	+	21302.5i	−0.806412	+	1.39675i
$616$	19112.0	−	7288.97i	1.25007	−	0.476755i
$617$	−11455.1	+	19840.7i	−0.747428	+	1.29458i	0.201624	+	0.979463i	$0.435378\pi$
$617$	−11455.1	+	19840.7i	−0.747428	+	1.29458i	−0.949052	+	0.315120i	$0.897955\pi$
$618$	1905.06	+	18125.4i	0.124001	+	1.17979i
$619$	−6050.69	−	18622.1i	−0.392888	−	1.20919i	−0.930594	−	0.366053i	$-0.880709\pi$
$619$	−6050.69	−	18622.1i	−0.392888	−	1.20919i	0.537706	−	0.843132i	$-0.319291\pi$
$620$	−784.859	−	871.674i	−0.0508398	−	0.0564633i
$621$	−234.031	+	2226.65i	−0.0151229	+	0.143885i
$622$	403.289	−	3837.03i	0.0259974	−	0.247349i
$623$	7355.67	−	22638.4i	0.473032	−	1.45584i
$624$	251.548	−	2860.03i	0.0161378	−	0.183482i
$625$	5154.61	−	3745.04i	0.329895	−	0.239683i
$626$	−2053.20	−	3556.25i	−0.131090	−	0.227055i
$627$	−36818.1	−	2009.47i	−2.34509	−	0.127992i
$628$	−5329.56	+	9231.07i	−0.338651	+	0.586560i
$629$	4493.45	−	3264.68i	0.284842	−	0.206950i
$630$	−11321.6	−	2406.48i	−0.715975	−	0.152185i
$631$	3342.77	+	3712.52i	0.210893	+	0.234221i	0.839306	−	0.543660i	$-0.182962\pi$
$631$	3342.77	+	3712.52i	0.210893	+	0.234221i	−0.628413	+	0.777880i	$0.716295\pi$
$632$	3647.35	+	2649.96i	0.229563	+	0.166787i
$633$	−6602.54	+	2939.64i	−0.414577	+	0.184582i
$634$	7003.17	−	1488.57i	0.438693	−	0.0932471i
$635$	−5010.09	+	5564.26i	−0.313101	+	0.347734i
$636$	8611.09	−	6256.32i	0.536874	−	0.390062i
$637$	−12241.2	+	9215.60i	−0.761406	+	0.573211i
$638$	−6819.09	−	8458.25i	−0.423151	−	0.524867i
$639$	15132.4	+	26210.1i	0.936820	+	1.62262i
$640$	−8606.00	−	3831.64i	−0.531534	−	0.236654i
$641$	−10800.0	−	2295.61i	−0.665483	−	0.141453i	−0.137229	−	0.990539i	$-0.543820\pi$
$641$	−10800.0	−	2295.61i	−0.665483	−	0.141453i	−0.528254	+	0.849087i	$0.677153\pi$
$642$	−2953.22	+	9089.07i	−0.181549	+	0.558749i
$643$	12198.1	−	5430.95i	0.748129	−	0.333089i	0.00298818	−	0.999996i	$-0.499049\pi$
$643$	12198.1	−	5430.95i	0.748129	−	0.333089i	0.745141	+	0.666907i	$0.232382\pi$
$644$	6877.45	−	3062.04i	0.420822	−	0.187362i
$645$	9925.78	−	30548.4i	0.605934	−	1.86487i
$646$	−7148.51	−	1519.46i	−0.435378	−	0.0925425i
$647$	−18819.7	−	8379.07i	−1.14355	−	0.509142i	−0.254557	−	0.967058i	$-0.581930\pi$
$647$	−18819.7	−	8379.07i	−1.14355	−	0.509142i	−0.888996	+	0.457915i	$0.848596\pi$
$648$	6012.05	+	10413.2i	0.364469	+	0.631278i
$649$	522.346	+	10397.5i	0.0315930	+	0.628872i
$650$	−3166.10	+	2383.54i	−0.191053	+	0.143831i
$651$	−4124.64	+	2996.73i	−0.248322	+	0.180416i
$652$	10321.3	−	11463.0i	0.619959	−	0.688534i
$653$	9705.19	−	2062.90i	0.581613	−	0.123626i	0.0922961	−	0.995732i	$-0.470579\pi$
$653$	9705.19	−	2062.90i	0.581613	−	0.123626i	0.489317	+	0.872106i	$0.337246\pi$
$654$	17777.1	−	7914.86i	1.06290	−	0.473234i
$655$	185.832	+	135.015i	0.0110856	+	0.00805413i
$656$	1990.38	+	2210.54i	0.118462	+	0.131566i
$657$	28430.3	+	6043.05i	1.68824	+	0.358846i
$658$	5302.89	−	3852.77i	0.314176	−	0.228263i
$659$	12175.3	−	21088.2i	0.719698	−	1.24655i	−0.241421	−	0.970421i	$-0.577613\pi$
$659$	12175.3	−	21088.2i	0.719698	−	1.24655i	0.961119	−	0.276134i	$-0.0890533\pi$
$660$	−3311.34	−	12466.0i	−0.195294	−	0.735207i
$661$	7711.23	+	13356.2i	0.453755	+	0.785927i	0.998616	−	0.0525996i	$-0.0167507\pi$
$661$	7711.23	+	13356.2i	0.453755	+	0.785927i	−0.544860	+	0.838527i	$0.683417\pi$
$662$	15264.7	−	11090.5i	0.896193	−	0.651122i
$663$	11265.7	−	5246.96i	0.659915	−	0.307353i
$664$	5649.65	−	17387.8i	0.330194	−	1.01623i
$665$	3027.48	−	28804.5i	0.176542	−	1.67969i
$666$	884.420	−	8414.70i	0.0514573	−	0.489584i
$667$	−6655.75	−	7391.95i	−0.386374	−	0.429112i
$668$	−3646.45	−	11222.6i	−0.211206	−	0.650024i
$669$	−599.906	−	5707.72i	−0.0346692	−	0.329855i
$670$	−2670.76	+	4625.89i	−0.154001	+	0.266737i
$671$	−12036.5	−	3253.11i	−0.692495	−	0.187161i
$672$	−18564.1	+	32154.0i	−1.06566	+	1.84578i
$673$	−8353.13	−	3719.05i	−0.478439	−	0.213015i	0.153325	−	0.988176i	$-0.451002\pi$
$673$	−8353.13	−	3719.05i	−0.478439	−	0.213015i	−0.631764	+	0.775161i	$0.717669\pi$
$674$	2518.01	−	2796.53i	0.143902	−	0.159819i
$675$	667.981	−	2055.84i	0.0380898	−	0.117228i
$676$	9317.65	−	7265.92i	0.530135	−	0.413400i
$677$	25269.8	+	18359.6i	1.43456	+	1.04227i	0.989145	+	0.146943i	$0.0469432\pi$
$677$	25269.8	+	18359.6i	1.43456	+	1.04227i	0.445413	+	0.895325i	$0.353057\pi$
$678$	10543.4	−	2241.08i	0.597225	−	0.126944i
$679$	−19700.5	+	21879.6i	−1.11345	+	1.23661i
$680$	−664.712	−	6324.31i	−0.0374861	−	0.356656i
$681$	−47129.6			−2.65200
$682$	1344.08	+	688.513i	0.0754657	+	0.0386577i
$683$	1940.67	−	3361.35i	0.108723	−	0.188314i	−0.806530	−	0.591193i	$-0.798657\pi$
$683$	1940.67	−	3361.35i	0.108723	−	0.188314i	0.915253	+	0.402879i	$0.131991\pi$
$684$	18475.3	−	13423.1i	1.03278	−	0.750358i
$685$	−8759.95	−	1861.99i	−0.488614	−	0.103858i
$686$	−660.111	+	140.311i	−0.0367393	+	0.00780918i
$687$	3876.17	−	36879.3i	0.215262	−	2.04808i
$688$	−3142.42	−	2283.10i	−0.174133	−	0.126515i
$689$	11816.8	+	2302.60i	0.653386	+	0.127318i
$690$	1778.93	+	5474.99i	0.0981490	+	0.302072i
$691$	20343.1	+	9057.32i	1.11995	+	0.498635i	0.881341	−	0.472480i	$-0.156641\pi$
$691$	20343.1	+	9057.32i	1.11995	+	0.498635i	0.238611	+	0.971115i	$0.423308\pi$
$692$	3448.34	+	5972.70i	0.189431	+	0.328104i
$693$	−30202.2	+	4716.57i	−1.65554	+	0.258539i
$694$	5708.52			0.312237
$695$	1678.69	+	15971.7i	0.0916205	+	0.871711i
$696$	30027.7	+	6382.59i	1.63534	+	0.347603i
$697$	−3978.80	+	12245.5i	−0.216224	+	0.665468i
$698$	1226.02	−	545.861i	0.0664838	−	0.0296005i
$699$	−3343.91	+	31815.2i	−0.180942	+	1.72155i
$700$	−7109.60	+	1511.19i	−0.383882	+	0.0815967i
$701$	4463.15	+	13736.2i	0.240472	+	0.740096i	0.996348	+	0.0853818i	$0.0272110\pi$
$701$	4463.15	+	13736.2i	0.240472	+	0.740096i	−0.755877	+	0.654714i	$0.772789\pi$
$702$	919.997	−	3004.22i	0.0494630	−	0.161520i
$703$	21172.2			1.13588
$704$	8664.64	+	472.903i	0.463865	+	0.0253170i
$705$	−5140.74	−	8904.03i	−0.274626	−	0.475667i
$706$	482.472	+	4590.42i	0.0257197	+	0.244706i
$707$	−5890.77	−	18129.9i	−0.313359	−	0.964421i
$708$	−7912.68	−	8787.92i	−0.420023	−	0.466483i
$709$	−16807.7	+	7483.27i	−0.890305	+	0.396390i	−0.800334	−	0.599555i	$-0.795344\pi$
$709$	−16807.7	+	7483.27i	−0.890305	+	0.396390i	−0.0899717	+	0.995944i	$0.528678\pi$
$710$	10448.2	+	7591.04i	0.552271	+	0.401249i
$711$	−4508.25	−	5006.92i	−0.237795	−	0.264098i
$712$	13330.5	−	14805.1i	0.701661	−	0.779274i
$713$	1263.06	+	562.350i	0.0663421	+	0.0295374i
$714$	−11111.8			−0.582419
$715$	7763.37	−	12351.7i	0.406061	−	0.646053i
$716$	−2985.82			−0.155845
$717$	1308.85	+	582.737i	0.0681727	+	0.0303525i
$718$	−5812.06	+	6454.95i	−0.302095	+	0.335510i
$719$	1019.95	+	1132.76i	0.0529034	+	0.0587552i	0.769016	−	0.639230i	$-0.220747\pi$
$719$	1019.95	+	1132.76i	0.0529034	+	0.0587552i	−0.716112	+	0.697985i	$0.754080\pi$
$720$	1776.18	+	1290.47i	0.0919367	+	0.0667959i
$721$	−34539.0	+	15377.8i	−1.78405	+	0.794311i
$722$	−11209.4	−	12449.3i	−0.577797	−	0.641708i
$723$	11780.5	+	36256.6i	0.605976	+	1.86500i
$724$	−177.901	−	1692.62i	−0.00913211	−	0.0868863i
$725$	4801.75	+	8316.87i	0.245976	+	0.426042i
$726$	9702.76	+	13477.0i	0.496010	+	0.688952i
$727$	−1230.91			−0.0627948			−0.0313974	−	0.999507i	$-0.509996\pi$
$727$	−1230.91			−0.0627948			−0.0313974	+	0.999507i	$0.509996\pi$
$728$	−25608.8	+	5899.84i	−1.30375	+	0.300361i
$729$	−8214.23	−	25280.8i	−0.417326	−	1.28440i
$730$	12131.8	−	2578.70i	0.615095	−	0.130742i
$731$	1757.47	−	16721.2i	0.0889224	−	0.846040i
$732$	12938.2	−	5760.48i	0.653294	−	0.290865i
$733$	−7216.07	+	22208.8i	−0.363617	+	1.11910i	0.587225	+	0.809424i	$0.300220\pi$
$733$	−7216.07	+	22208.8i	−0.363617	+	1.11910i	−0.950842	+	0.309676i	$0.899780\pi$
$734$	−15395.9	−	3272.51i	−0.774215	−	0.164565i
$735$	−2246.24	−	21371.5i	−0.112726	−	1.07252i
$736$	10068.6			0.504257
$737$	−2236.96	+	13928.4i	−0.111804	+	0.696146i
$738$	9807.13	+	16986.4i	0.489167	+	0.847262i
$739$	16022.8	+	7133.81i	0.797575	+	0.355103i	0.764725	−	0.644357i	$-0.222875\pi$
$739$	16022.8	+	7133.81i	0.797575	+	0.355103i	0.0328504	+	0.999460i	$0.489542\pi$
$740$	2288.62	+	7043.64i	0.113691	+	0.349904i
$741$	46498.7	+	9060.67i	2.30523	+	0.449193i
$742$	−8708.48	−	6327.08i	−0.430861	−	0.313039i
$743$	−331.114	+	3150.34i	−0.0163491	+	0.155552i	−0.999651	−	0.0264325i	$-0.991585\pi$
$743$	−331.114	+	3150.34i	−0.0163491	+	0.155552i	0.983301	+	0.181984i	$0.0582520\pi$
$744$	−4173.78	+	887.164i	−0.205670	+	0.0437164i
$745$	21358.1	+	4539.80i	1.05033	+	0.223255i
$746$	−4473.96	+	3250.52i	−0.219575	+	0.159531i
$747$	−13661.1	+	23661.7i	−0.669122	+	1.15895i
$748$	−3052.10	−	6022.27i	−0.149192	−	0.294380i
$749$	−19825.3			−0.967155
$750$	−1971.76	−	18760.0i	−0.0959979	−	0.913359i
$751$	2719.53	−	3020.34i	0.132140	−	0.146756i	−0.673443	−	0.739239i	$-0.735185\pi$
$751$	2719.53	−	3020.34i	0.132140	−	0.146756i	0.805583	+	0.592483i	$0.201852\pi$
$752$	−1216.14	+	258.500i	−0.0589737	+	0.0125353i
$753$	41421.9	+	30094.7i	2.00464	+	1.45646i
$754$	7183.74	+	11968.2i	0.346971	+	0.578060i
$755$	−2724.91	+	8386.40i	−0.131350	+	0.404255i
$756$	3855.88	−	4282.39i	0.185499	−	0.206017i
$757$	−30973.6	−	13790.3i	−1.48713	−	0.662112i	−0.507266	−	0.861790i	$-0.669344\pi$
$757$	−30973.6	−	13790.3i	−1.48713	−	0.662112i	−0.979862	+	0.199678i	$0.936010\pi$
$758$	9089.54	−	15743.5i	0.435550	−	0.754395i
$759$	9542.28	+	11836.0i	0.456341	+	0.566035i
$760$	12120.3	−	20993.0i	0.578486	−	1.00197i
$761$	1385.38	+	13181.0i	0.0659921	+	0.627873i	0.976669	+	0.214752i	$0.0688945\pi$
$761$	1385.38	+	13181.0i	0.0659921	+	0.627873i	−0.910676	+	0.413120i	$0.864439\pi$
$762$	3383.74	+	10414.1i	0.160866	+	0.495095i
$763$	27011.4	+	29999.2i	1.28162	+	1.42338i
$764$	1526.36	−	14522.3i	0.0722796	−	0.687694i
$765$	−993.369	+	9451.27i	−0.0469481	+	0.446682i
$766$	−1574.71	+	4846.45i	−0.0742774	+	0.228602i
$767$	1171.87	−	13323.8i	0.0551680	−	0.627244i
$768$	−23007.5	+	16715.9i	−1.08100	+	0.785395i
$769$	−7630.82	−	13217.0i	−0.357834	−	0.619787i	0.629765	−	0.776786i	$-0.283151\pi$
$769$	−7630.82	−	13217.0i	−0.357834	−	0.619787i	−0.987599	+	0.156999i	$0.949818\pi$
$770$	−10955.1	+	7080.66i	−0.512720	+	0.331388i
$771$	27528.5	−	47680.8i	1.28588	−	2.22721i
$772$	11910.3	−	8653.31i	0.555258	−	0.403419i
$773$	−4369.34	−	928.733i	−0.203305	−	0.0432137i	0.105134	−	0.994458i	$-0.466473\pi$
$773$	−4369.34	−	928.733i	−0.203305	−	0.0432137i	−0.308438	+	0.951244i	$0.599806\pi$
$774$	−17138.2	−	19033.9i	−0.795892	−	0.883927i
$775$	−1079.93	−	784.612i	−0.0500543	−	0.0363666i
$776$	−22510.9	+	10022.5i	−1.04136	+	0.463642i
$777$	31487.9	−	6692.95i	1.45382	−	0.309020i
$778$	−2763.66	+	3069.36i	−0.127355	+	0.141442i
$779$	−39707.4	+	28849.1i	−1.82627	+	1.32686i
$780$	2011.96	+	16448.7i	0.0923584	+	0.755076i
$781$	32926.0	+	8898.94i	1.50856	+	0.407720i
$782$	1506.67	+	2609.63i	0.0688982	+	0.119335i
$783$	−6955.54	−	3096.81i	−0.317460	−	0.141342i
$784$	−2541.86	−	540.288i	−0.115792	−	0.0246122i
$785$	5225.04	−	16081.0i	0.237566	−	0.731154i
$786$	306.883	−	136.633i	0.0139264	−	0.00620043i
$787$	−20177.0	+	8983.38i	−0.913891	+	0.406891i	−0.809145	−	0.587608i	$-0.800070\pi$
$787$	−20177.0	+	8983.38i	−0.913891	+	0.406891i	−0.104746	+	0.994499i	$0.533403\pi$
$788$	1412.38	−	4346.85i	0.0638501	−	0.196510i
$789$	17236.4	+	3663.71i	0.777734	+	0.165312i
$790$	−2626.47	−	1169.38i	−0.118285	−	0.0526641i
$791$	11180.3	+	19364.9i	0.502562	+	0.870462i
$792$	−24697.8	−	6675.08i	−1.10808	−	0.299481i
$793$	14742.7	+	6265.92i	0.660187	+	0.280592i
$794$	13967.6	−	10148.1i	0.624298	−	0.453579i
$795$	−11297.9	+	12547.6i	−0.504018	+	0.559769i
$796$	−17114.9	+	3637.88i	−0.762086	+	0.161986i
$797$	10566.8	−	4704.64i	0.469630	−	0.209093i	−0.158256	−	0.987398i	$-0.550587\pi$
$797$	10566.8	−	4704.64i	0.469630	−	0.209093i	0.627886	+	0.778305i	$0.283920\pi$
$798$	−34267.7	−	24896.9i	−1.52013	−	1.10444i
$799$	−3601.12	−	3999.45i	−0.159447	−	0.177084i
$800$	−9508.59	−	2021.11i	−0.420224	−	0.0893214i
$801$	−24086.3	+	17499.8i	−1.06248	+	0.771939i
$802$	6575.57	−	11389.2i	0.289515	−	0.501455i
$803$	27509.9	−	17780.6i	1.20897	−	0.781399i
$804$	−8011.93	−	13877.1i	−0.351442	−	0.608715i
$805$	−9661.42	+	7019.43i	−0.423006	+	0.307332i
$806$	−1588.82	−	1113.60i	−0.0694342	−	0.0486660i
$807$	10874.1	−	33467.2i	0.474335	−	1.45985i
$808$	1667.71	−	15867.2i	0.0726112	−	0.690850i
$809$	−3324.82	+	31633.5i	−0.144492	+	1.37475i	0.646494	+	0.762919i	$0.276235\pi$
$809$	−3324.82	+	31633.5i	−0.144492	+	1.37475i	−0.790986	+	0.611834i	$0.790432\pi$
$810$	−5130.80	−	5698.33i	−0.222565	−	0.247184i
$811$	−3455.40	−	10634.6i	−0.149612	−	0.460459i	0.847963	−	0.530055i	$-0.177829\pi$
$811$	−3455.40	−	10634.6i	−0.149612	−	0.460459i	−0.997575	+	0.0695964i	$0.977829\pi$
$812$	2676.05	+	25460.9i	0.115654	+	1.10037i
$813$	19797.8	−	34290.8i	0.854045	−	1.47925i
$814$	−5984.72	−	7423.31i	−0.257696	−	0.319640i
$815$	−12234.3	+	21190.4i	−0.525827	+	0.910758i
$816$	1925.48	+	857.280i	0.0826046	+	0.0367779i
$817$	42885.2	−	47628.9i	1.83643	−	2.03956i
$818$	−1997.98	+	6149.14i	−0.0854006	+	0.262836i
$819$	39267.6	−	667.314i	1.67536	−	0.0284711i
$820$	−13889.8	−	10091.5i	−0.591528	−	0.429770i
$821$	10032.8	−	2132.53i	0.426487	−	0.0906526i	0.0103326	−	0.999947i	$-0.496711\pi$
$821$	10032.8	−	2132.53i	0.426487	−	0.0906526i	0.416154	+	0.909294i	$0.363378\pi$
$822$	−8763.73	+	9733.11i	−0.371862	+	0.412994i
$823$	598.762	+	5696.84i	0.0253603	+	0.241287i	0.999857	+	0.0168870i	$0.00537555\pi$
$823$	598.762	+	5696.84i	0.0253603	+	0.241287i	−0.974497	+	0.224400i	$0.927958\pi$
$824$	−31642.9			−1.33778
$825$	−6635.66	−	13093.2i	−0.280029	−	0.552541i
$826$	−5979.53	+	10356.8i	−0.251882	+	0.436272i
$827$	−12196.1	+	8861.00i	−0.512818	+	0.372584i	−0.813892	−	0.581017i	$-0.802655\pi$
$827$	−12196.1	+	8861.00i	−0.512818	+	0.372584i	0.301073	+	0.953601i	$0.402655\pi$
$828$	−9210.33	−	1957.72i	−0.386571	−	0.0821683i
$829$	−36142.8	+	7682.39i	−1.51422	+	0.321858i	−0.888752	−	0.458389i	$-0.848427\pi$
$829$	−36142.8	+	7682.39i	−1.51422	+	0.321858i	−0.625472	+	0.780247i	$0.715093\pi$
$830$	−1218.70	+	11595.1i	−0.0509658	+	0.484907i
$831$	32242.3	+	23425.4i	1.34594	+	0.977881i
$832$	−10942.8	−	2132.31i	−0.455979	−	0.0888515i
$833$	−3475.96	−	10697.9i	−0.144580	−	0.444970i
$834$	21455.9	+	9552.78i	0.890835	+	0.396625i
$835$	9359.30	+	16210.8i	0.387895	+	0.671853i
$836$	4081.05	−	25410.7i	0.168835	−	1.05125i
$837$	1058.30			0.0437039
$838$	922.141	+	8773.58i	0.0380129	+	0.361669i
$839$	−4161.83	−	884.624i	−0.171254	−	0.0364012i	0.121486	−	0.992593i	$-0.461234\pi$
$839$	−4161.83	−	884.624i	−0.171254	−	0.0364012i	−0.292741	+	0.956192i	$0.594567\pi$
$840$	11389.3	−	35052.7i	0.467820	−	1.43980i
$841$	8620.96	−	3838.30i	0.353477	−	0.157378i
$842$	1995.95	−	18990.2i	0.0816925	−	0.777252i
$843$	−41360.5	+	8791.44i	−1.68984	+	0.359186i
$844$	−1558.84	−	4797.62i	−0.0635753	−	0.195665i
$845$	−12061.2	+	14347.1i	−0.491028	+	0.584091i
$846$	−8198.38			−0.333175
$847$	−20369.3	+	27782.3i	−0.826326	+	1.12705i
$848$	1020.89	+	1768.24i	0.0413416	+	0.0716057i
$849$	−1879.03	−	17877.8i	−0.0759579	−	0.722691i
$850$	−899.029	−	2766.93i	−0.0362782	−	0.111653i
$851$	−5841.36	−	6487.49i	−0.235299	−	0.261326i
$852$	−35392.8	+	15757.9i	−1.42316	+	0.633634i
$853$	−22926.9	−	16657.3i	−0.920282	−	0.668624i	0.0233122	−	0.999728i	$-0.492579\pi$
$853$	−22926.9	−	16657.3i	−0.920282	−	0.668624i	−0.943594	+	0.331104i	$0.892579\pi$
$854$	−9583.86	−	10644.0i	−0.384020	−	0.426497i
$855$	−24239.9	+	26921.1i	−0.969576	+	1.07682i
$856$	−15158.1	−	6748.84i	−0.605250	−	0.269475i
$857$	3237.20			0.129032			0.0645162	−	0.997917i	$-0.479450\pi$
$857$	3237.20			0.129032			0.0645162	+	0.997917i	$0.479450\pi$
$858$	−9966.90	−	18864.3i	−0.396579	−	0.750603i
$859$	−23024.5			−0.914534			−0.457267	−	0.889329i	$-0.651172\pi$
$859$	−23024.5			−0.914534			−0.457267	+	0.889329i	$0.651172\pi$
$860$	20481.0	+	9118.73i	0.812089	+	0.361565i
$861$	−49934.1	+	55457.4i	−1.97648	+	2.19510i
$862$	−6809.60	−	7562.83i	−0.269067	−	0.298830i
$863$	−4516.45	−	3281.39i	−0.178148	−	0.129432i	0.495138	−	0.868814i	$-0.335118\pi$
$863$	−4516.45	−	3281.39i	−0.178148	−	0.129432i	−0.673286	+	0.739382i	$0.735118\pi$
$864$	7040.66	−	3134.71i	0.277232	−	0.123432i
$865$	−7320.43	−	8130.16i	−0.287748	−	0.319576i
$866$	−3110.51	−	9573.17i	−0.122055	−	0.375646i
$867$	−3003.42	−	28575.7i	−0.117649	−	1.11935i
$868$	−1779.25	−	3081.75i	−0.0695757	−	0.120509i
$869$	−7581.63	−	413.794i	−0.295960	−	0.0161530i
$870$	−19576.7			−0.762888
$871$	5306.97	−	17329.8i	0.206452	−	0.674164i
$872$	10440.3	+	32132.1i	0.405452	+	1.24785i
$873$	36020.0	−	7656.28i	1.39644	−	0.296822i
$874$	−1200.68	+	11423.7i	−0.0464686	+	0.442119i
$875$	35748.3	−	15916.2i	1.38116	−	0.614931i
$876$	−11497.6	+	35385.9i	−0.443456	+	1.36482i
$877$	−27464.9	−	5837.84i	−1.05749	−	0.224777i	−0.353830	−	0.935310i	$-0.615121\pi$
$877$	−27464.9	−	5837.84i	−1.05749	−	0.224777i	−0.703664	+	0.710532i	$0.748454\pi$
$878$	−1415.31	−	13465.7i	−0.0544013	−	0.517593i
$879$	−46942.2			−1.80128
$880$	2444.61	−	381.766i	0.0936452	−	0.0146242i
$881$	11718.6	+	20297.3i	0.448139	+	0.776200i	0.998265	−	0.0588820i	$-0.0187536\pi$
$881$	11718.6	+	20297.3i	0.448139	+	0.776200i	−0.550126	+	0.835082i	$0.685420\pi$
$882$	−15653.9	−	6969.59i	−0.597614	−	0.266075i
$883$	2875.91	+	8851.16i	0.109606	+	0.337333i	0.990784	−	0.135452i	$-0.0432487\pi$
$883$	2875.91	+	8851.16i	0.109606	+	0.337333i	−0.881178	+	0.472785i	$0.843249\pi$
$884$	2820.25	+	8202.89i	0.107302	+	0.312096i
$885$	15175.9	+	11026.0i	0.576423	+	0.418795i
$886$	−268.139	+	2551.18i	−0.0101674	+	0.0967364i
$887$	30936.6	−	6575.79i	1.17108	−	0.248921i	0.418998	−	0.907987i	$-0.362381\pi$
$887$	30936.6	−	6575.79i	1.17108	−	0.248921i	0.752085	+	0.659066i	$0.229048\pi$
$888$	26353.6	+	5601.63i	0.995910	+	0.211687i
$889$	−18377.2	+	13351.8i	−0.693308	+	0.503717i
$890$	−6352.26	+	11002.4i	−0.239245	+	0.414385i
$891$	−18023.6	−	9232.68i	−0.677681	−	0.347145i
$892$	4005.78			0.150363
$893$	−2144.40	−	20402.6i	−0.0803578	−	0.764553i
$894$	21367.3	−	23730.8i	0.799361	−	0.887780i
$895$	4632.90	−	984.754i	0.173029	−	0.0367784i
$896$	−23121.5	−	16798.7i	−0.862092	−	0.626346i
$897$	−10052.5	−	16747.7i	−0.374186	−	0.623400i
$898$	−5841.84	+	17979.3i	−0.217088	+	0.668127i
$899$	−3146.06	+	3494.05i	−0.116715	+	0.129625i
$900$	8305.09	+	3697.67i	0.307596	+	0.136951i
$901$	−4419.03	+	7653.98i	−0.163395	+	0.283009i
$902$	21339.0	+	5767.30i	0.787706	+	0.212894i
$903$	48723.5	−	84391.7i	1.79559	−	3.11005i
$904$	1956.21	+	18612.1i	0.0719718	+	0.684766i
$905$	834.282	+	2567.65i	0.0306436	+	0.0943113i
$906$	8629.01	+	9583.49i	0.316424	+	0.351424i
$907$	778.545	−	7407.36i	0.0285018	−	0.271177i	−0.970985	−	0.239141i	$-0.923134\pi$
$907$	778.545	−	7407.36i	0.0285018	−	0.271177i	0.999487	−	0.0320360i	$-0.0101991\pi$
$908$	3438.49	−	32715.0i	0.125672	−	1.19569i
$909$	−7367.93	+	22676.1i	−0.268843	+	0.827415i
$910$	15191.8	−	7075.55i	0.553412	−	0.257750i
$911$	43272.6	−	31439.4i	1.57375	−	1.14340i	0.650297	−	0.759680i	$-0.274645\pi$
$911$	43272.6	−	31439.4i	1.57375	−	1.14340i	0.923452	−	0.383715i	$-0.125355\pi$
$912$	4017.20	+	6957.99i	0.145858	+	0.252634i
$913$	7904.97	+	29759.3i	0.286546	+	1.07874i
$914$	−10988.2	+	19032.1i	−0.397655	+	0.688759i
$915$	−18175.6	+	13205.3i	−0.656685	+	0.477109i
$916$	25316.9	+	5381.28i	0.913204	+	0.194108i
$917$	466.293	+	517.871i	0.0167921	+	0.0186495i
$918$	1866.04	+	1355.76i	0.0670898	+	0.0487436i
$919$	23377.0	−	10408.1i	0.839102	−	0.373592i	0.0582455	−	0.998302i	$-0.481449\pi$
$919$	23377.0	−	10408.1i	0.839102	−	0.373592i	0.780857	+	0.624710i	$0.214783\pi$
$920$	−9776.52	+	2078.06i	−0.350350	+	0.0744693i
$921$	14452.4	−	16051.0i	0.517071	−	0.574266i
$922$	11948.8	−	8681.32i	0.426804	−	0.310091i
$923$	−40328.9	−	17140.5i	−1.43818	−	0.611254i
$924$	−1963.36	−	39081.4i	−0.0699023	−	1.39143i
$925$	4214.22	+	7299.23i	0.149797	+	0.259457i
$926$	8527.98	+	3796.90i	0.302642	+	0.134745i
$927$	46254.9	+	9831.79i	1.63885	+	0.348348i
$928$	−10580.7	+	32564.0i	−0.374275	+	1.15190i
$929$	28253.2	−	12579.1i	0.997800	−	0.444249i	0.158173	−	0.987411i	$-0.449440\pi$
$929$	28253.2	−	12579.1i	0.997800	−	0.444249i	0.839628	+	0.543162i	$0.182773\pi$
$930$	2485.86	−	1106.78i	0.0876502	−	0.0390244i
$931$	13250.1	−	40779.6i	0.466438	−	1.43555i
$932$	−21840.6	−	4642.35i	−0.767609	−	0.163160i
$933$	−16772.6	−	7467.62i	−0.588541	−	0.262035i
$934$	5005.09	+	8669.07i	0.175344	+	0.303705i
$935$	6721.96	+	8337.76i	0.235114	+	0.291630i
$936$	30250.6	+	12857.1i	1.05638	+	0.448982i
$937$	20223.1	−	14693.0i	0.705081	−	0.512271i	−0.176502	−	0.984300i	$-0.556478\pi$
$937$	20223.1	−	14693.0i	0.705081	−	0.512271i	0.881583	+	0.472029i	$0.156478\pi$
$938$	−10843.3	+	12042.7i	−0.377449	+	0.419200i
$939$	−19114.1	+	4062.82i	−0.664286	+	0.141198i
$940$	6555.79	−	2918.83i	0.227475	−	0.101278i
$941$	8761.74	+	6365.78i	0.303533	+	0.220530i	0.729117	−	0.684389i	$-0.239931\pi$
$941$	8761.74	+	6365.78i	0.303533	+	0.220530i	−0.425584	+	0.904919i	$0.639931\pi$
$942$	−16546.2	−	18376.4i	−0.572298	−	0.635601i
$943$	19795.0	+	4207.55i	0.683577	+	0.145299i
$944$	1835.19	−	1333.34i	0.0632736	−	0.0459710i
$945$	−4570.55	+	7916.42i	−0.157333	+	0.272509i
$946$	−28821.7	−	1573.05i	−0.990566	−	0.0540636i
$947$	22048.4	+	38188.9i	0.756575	+	1.31043i	0.944587	+	0.328260i	$0.106462\pi$
$947$	22048.4	+	38188.9i	0.756575	+	1.31043i	−0.188012	+	0.982167i	$0.560205\pi$
$948$	6977.53	−	5069.47i	0.239050	−	0.173680i
$949$	−38149.0	+	17767.8i	−1.30492	+	0.607763i
$950$	3427.03	−	10547.3i	0.117039	−	0.360210i
$951$	3561.34	−	33883.8i	0.121435	−	1.15537i
$952$	2016.60	−	19186.7i	0.0686539	−	0.653198i
$953$	35765.0	+	39721.1i	1.21568	+	1.35015i	0.918547	+	0.395311i	$0.129363\pi$
$953$	35765.0	+	39721.1i	1.21568	+	1.35015i	0.297132	+	0.954837i	$0.403970\pi$
$954$	4160.45	+	12804.6i	0.141195	+	0.434552i
$955$	2421.26	+	23036.7i	0.0820420	+	0.780577i
$956$	−499.998	+	866.021i	−0.0169154	+	0.0292983i
$957$	−48307.8	+	18423.8i	−1.63174	+	0.622315i
$958$	−7601.73	+	13166.6i	−0.256368	+	0.444043i
$959$	−24820.7	−	11050.9i	−0.835769	−	0.372108i
$960$	10462.3	−	11619.6i	0.351740	−	0.390647i
$961$	−9003.97	+	27711.4i	−0.302238	+	0.930193i
$962$	6304.75	+	10503.8i	0.211303	+	0.352034i
$963$	20060.9	+	14575.1i	0.671291	+	0.487721i
$964$	−26027.0	+	5532.20i	−0.869577	+	0.184834i
$965$	−15626.4	+	17354.9i	−0.521277	+	0.578937i
$966$	1825.57	+	17369.1i	0.0608041	+	0.578512i
$967$	−1532.24			−0.0509551			−0.0254776	−	0.999675i	$-0.508111\pi$
$967$	−1532.24			−0.0509551			−0.0254776	+	0.999675i	$0.508111\pi$
$968$	−25031.6	+	14307.9i	−0.831144	+	0.475076i
$969$	−17388.8	+	30118.2i	−0.576479	+	0.998491i
$970$	12712.8	−	9236.40i	0.420808	−	0.305735i
$971$	−512.498	−	108.935i	−0.0169380	−	0.00360029i	0.199435	−	0.979911i	$-0.436089\pi$
$971$	−512.498	−	108.935i	−0.0169380	−	0.00360029i	−0.216373	+	0.976311i	$0.569423\pi$
$972$	28379.9	−	6032.34i	0.936508	−	0.199061i
$973$	−5092.80	+	48454.8i	−0.167798	+	1.59649i
$974$	4162.82	+	3024.46i	0.136946	+	0.0994970i
$975$	6131.59	+	17834.1i	0.201403	+	0.585794i
$976$	839.534	+	2583.82i	0.0275336	+	0.0847398i
$977$	21954.4	+	9774.73i	0.718919	+	0.320083i	0.733386	−	0.679812i	$-0.237939\pi$
$977$	21954.4	+	9774.73i	0.718919	+	0.320083i	−0.0144676	+	0.999895i	$0.504605\pi$
$978$	17892.0	+	30989.9i	0.584994	+	1.01324i
$979$	−5320.49	+	33128.0i	−0.173691	+	1.08149i
$980$	14998.9			0.488901
$981$	−5277.69	−	50213.8i	−0.171767	−	1.63426i
$982$	11740.8	+	2495.58i	0.381531	+	0.0810970i
$983$	−10468.5	+	32218.8i	−0.339668	+	1.04539i	0.624709	+	0.780858i	$0.285218\pi$
$983$	−10468.5	+	32218.8i	−0.339668	+	1.04539i	−0.964377	+	0.264533i	$0.914782\pi$
$984$	−57057.5	+	25403.7i	−1.84850	+	0.823007i
$985$	−757.860	+	7210.55i	−0.0245151	+	0.233246i
$986$	−10023.4	+	2130.54i	−0.323742	+	0.0688135i
$987$	−9638.85	−	29665.3i	−0.310849	−	0.956695i
$988$	−9681.92	+	31616.0i	−0.311764	+	1.01806i
$989$	−26426.1			−0.849648
$990$	16290.8	+	889.128i	0.522986	+	0.0285438i
$991$	−26708.4	−	46260.4i	−0.856126	−	1.48285i	−0.875596	−	0.483044i	$-0.839531\pi$
$991$	−26708.4	−	46260.4i	−0.856126	−	1.48285i	0.0194697	−	0.999810i	$-0.493802\pi$
$992$	−497.477	−	4733.17i	−0.0159223	−	0.151490i
$993$	−27746.0	−	85393.6i	−0.886701	−	2.72899i
$994$	26216.8	+	29116.7i	0.836566	+	0.929101i
$995$	25356.3	−	11289.3i	0.807887	−	0.359695i
$996$	−28295.7	−	20558.1i	−0.900186	−	0.654023i
$997$	−37949.8	−	42147.5i	−1.20550	−	1.33884i	−0.925456	−	0.378854i	$-0.876318\pi$
$997$	−37949.8	−	42147.5i	−1.20550	−	1.33884i	−0.280042	−	0.959988i	$-0.590349\pi$
$998$	−5963.12	+	6622.72i	−0.189138	+	0.210059i
$999$	−6104.48	−	2717.89i	−0.193330	−	0.0860763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.q.a.3.15	✓	320
11.4	even	5	inner	143.4.q.a.81.26	yes	320
13.9	even	3	inner	143.4.q.a.113.26	yes	320
143.48	even	15	inner	143.4.q.a.48.15	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.q.a.3.15	✓	320	1.1	even	1	trivial
143.4.q.a.48.15	yes	320	143.48	even	15	inner
143.4.q.a.81.26	yes	320	11.4	even	5	inner
143.4.q.a.113.26	yes	320	13.9	even	3	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.47923 - 0.658595i) q^{2} +(-5.15589 + 5.72620i) q^{3} +(-3.59867 - 3.99673i) q^{4} +(6.90200 + 5.01460i) q^{5} +(11.3980 - 5.07471i) q^{6} +(17.3187 + 19.2343i) q^{7} +(6.69396 + 20.6019i) q^{8} +(-3.38386 - 32.1953i) q^{9} +O(q^{10})\)	\(q+(-1.47923 - 0.658595i) q^{2} +(-5.15589 + 5.72620i) q^{3} +(-3.59867 - 3.99673i) q^{4} +(6.90200 + 5.01460i) q^{5} +(11.3980 - 5.07471i) q^{6} +(17.3187 + 19.2343i) q^{7} +(6.69396 + 20.6019i) q^{8} +(-3.38386 - 32.1953i) q^{9} +(-6.90705 - 11.9634i) q^{10} +(-28.3028 - 23.0207i) q^{11} +41.4405 q^{12} +(31.9509 + 34.2949i) q^{13} +(-12.9507 - 39.8580i) q^{14} +(-64.3006 + 13.6675i) q^{15} +(-0.830940 + 7.90587i) q^{16} +(-31.4348 + 13.9957i) q^{17} +(-16.1981 + 49.8527i) q^{18} +(-128.301 - 27.2712i) q^{19} +(-4.79605 - 45.6314i) q^{20} -199.433 q^{21} +(26.7049 + 52.6930i) q^{22} +(27.0416 + 46.8374i) q^{23} +(-152.484 - 67.8902i) q^{24} +(-16.1357 - 49.6605i) q^{25} +(-24.6763 - 71.7727i) q^{26} +(33.4915 + 24.3330i) q^{27} +(14.5502 - 138.436i) q^{28} +(-179.899 + 38.2387i) q^{29} +(104.117 + 22.1307i) q^{30} +(20.6818 - 15.0262i) q^{31} +(93.0844 - 161.227i) q^{32} +(277.747 - 43.3748i) q^{33} +55.7168 q^{34} +(23.0811 + 219.602i) q^{35} +(-116.498 + 129.385i) q^{36} +(-157.887 + 33.5599i) q^{37} +(171.826 + 124.839i) q^{38} +(-361.115 + 6.13680i) q^{39} +(-57.1085 + 175.762i) q^{40} +(250.380 - 278.075i) q^{41} +(295.007 + 131.346i) q^{42} +(-244.310 + 423.158i) q^{43} +(9.84469 + 195.963i) q^{44} +(138.091 - 239.180i) q^{45} +(-9.15380 - 87.0926i) q^{46} +(48.3312 + 148.748i) q^{47} +(-40.9863 - 45.5199i) q^{48} +(-34.1701 + 325.106i) q^{49} +(-8.83781 + 84.0862i) q^{50} +(81.9325 - 252.162i) q^{51} +(22.0864 - 251.115i) q^{52} +(207.794 - 150.971i) q^{53} +(-33.5160 - 58.0514i) q^{54} +(-79.9060 - 300.816i) q^{55} +(-280.333 + 485.552i) q^{56} +(817.666 - 594.069i) q^{57} +(291.295 + 61.9168i) q^{58} +(-190.941 - 212.061i) q^{59} +(286.022 + 207.807i) q^{60} +(312.213 - 139.006i) q^{61} +(-40.4894 + 8.60628i) q^{62} +(560.651 - 622.666i) q^{63} +(-192.427 + 139.806i) q^{64} +(48.5505 + 396.924i) q^{65} +(-439.418 - 118.762i) q^{66} +(-193.336 - 334.868i) q^{67} +(169.061 + 75.2707i) q^{68} +(-407.623 - 86.6430i) q^{69} +(110.486 - 340.042i) q^{70} +(-854.063 + 380.253i) q^{71} +(640.632 - 285.228i) q^{72} +(-277.448 + 853.898i) q^{73} +(255.653 + 54.3407i) q^{74} +(367.560 + 163.648i) q^{75} +(352.717 + 610.924i) q^{76} +(-47.3778 - 943.074i) q^{77} +(538.213 + 228.751i) q^{78} +(168.375 - 122.331i) q^{79} +(-45.3799 + 50.3995i) q^{80} +(542.946 - 115.407i) q^{81} +(-553.509 + 246.438i) q^{82} +(-682.804 - 496.086i) q^{83} +(717.695 + 797.081i) q^{84} +(-287.146 - 61.0348i) q^{85} +(640.081 - 465.046i) q^{86} +(708.577 - 1227.29i) q^{87} +(284.813 - 737.190i) q^{88} +(-459.839 - 796.465i) q^{89} +(-361.791 + 262.856i) q^{90} +(-106.291 + 1208.50i) q^{91} +(89.8826 - 276.630i) q^{92} +(-20.5901 + 195.902i) q^{93} +(26.4719 - 251.863i) q^{94} +(-748.778 - 831.603i) q^{95} +(443.284 + 1364.29i) q^{96} +(118.904 + 1131.30i) q^{97} +(264.659 - 458.402i) q^{98} +(-645.386 + 989.113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 3 q^{2} - 3 q^{3} + 149 q^{4} - 12 q^{5} - 35 q^{6} - 3 q^{7} - 44 q^{8} + 369 q^{9}+O(q^{10}) \) 320 * q - 3 * q^2 - 3 * q^3 + 149 * q^4 - 12 * q^5 - 35 * q^6 - 3 * q^7 - 44 * q^8 + 369 * q^9	\( 320 q - 3 q^{2} - 3 q^{3} + 149 q^{4} - 12 q^{5} - 35 q^{6} - 3 q^{7} - 44 q^{8} + 369 q^{9} - 80 q^{10} + 30 q^{11} - 220 q^{12} - 114 q^{13} + 4 q^{14} - 33 q^{15} + 637 q^{16} + 143 q^{17} + 72 q^{18} + 17 q^{19} - 377 q^{20} - 524 q^{21} + 283 q^{22} + 196 q^{23} - 1137 q^{24} - 1324 q^{25} + 632 q^{26} + 192 q^{27} - 279 q^{28} + 943 q^{29} + 1617 q^{30} + 260 q^{31} - 52 q^{32} - 1244 q^{33} - 3508 q^{34} + 1253 q^{35} + 282 q^{36} + 333 q^{37} - 694 q^{38} - 1106 q^{39} - 296 q^{40} - 1751 q^{41} - 895 q^{42} - 2200 q^{43} - 252 q^{44} - 282 q^{45} + 485 q^{46} + 2116 q^{47} - 825 q^{48} + 1607 q^{49} + 348 q^{50} + 1768 q^{51} - 2431 q^{52} + 428 q^{53} + 8326 q^{54} - 1379 q^{55} + 7630 q^{56} - 888 q^{57} - 331 q^{58} - 1097 q^{59} - 1820 q^{60} + 885 q^{61} - 437 q^{62} + 540 q^{63} + 1148 q^{64} + 2324 q^{65} - 1686 q^{66} - 5184 q^{67} + 3834 q^{68} - 4905 q^{69} + 4078 q^{70} + 843 q^{71} + 1155 q^{72} - 972 q^{73} + 5631 q^{74} - 3431 q^{75} - 3090 q^{76} + 602 q^{77} + 1252 q^{78} + 1140 q^{79} + 8631 q^{80} - 3809 q^{81} + 4015 q^{82} - 5292 q^{83} - 5060 q^{84} + 391 q^{85} + 3388 q^{86} - 7600 q^{87} - 7229 q^{88} + 6276 q^{89} + 7374 q^{90} - 4602 q^{91} + 8158 q^{92} - 2599 q^{93} + 11081 q^{94} + 2305 q^{95} - 30114 q^{96} + 1377 q^{97} + 5102 q^{98} - 5812 q^{99}+O(q^{100}) \) 320 * q - 3 * q^2 - 3 * q^3 + 149 * q^4 - 12 * q^5 - 35 * q^6 - 3 * q^7 - 44 * q^8 + 369 * q^9 - 80 * q^10 + 30 * q^11 - 220 * q^12 - 114 * q^13 + 4 * q^14 - 33 * q^15 + 637 * q^16 + 143 * q^17 + 72 * q^18 + 17 * q^19 - 377 * q^20 - 524 * q^21 + 283 * q^22 + 196 * q^23 - 1137 * q^24 - 1324 * q^25 + 632 * q^26 + 192 * q^27 - 279 * q^28 + 943 * q^29 + 1617 * q^30 + 260 * q^31 - 52 * q^32 - 1244 * q^33 - 3508 * q^34 + 1253 * q^35 + 282 * q^36 + 333 * q^37 - 694 * q^38 - 1106 * q^39 - 296 * q^40 - 1751 * q^41 - 895 * q^42 - 2200 * q^43 - 252 * q^44 - 282 * q^45 + 485 * q^46 + 2116 * q^47 - 825 * q^48 + 1607 * q^49 + 348 * q^50 + 1768 * q^51 - 2431 * q^52 + 428 * q^53 + 8326 * q^54 - 1379 * q^55 + 7630 * q^56 - 888 * q^57 - 331 * q^58 - 1097 * q^59 - 1820 * q^60 + 885 * q^61 - 437 * q^62 + 540 * q^63 + 1148 * q^64 + 2324 * q^65 - 1686 * q^66 - 5184 * q^67 + 3834 * q^68 - 4905 * q^69 + 4078 * q^70 + 843 * q^71 + 1155 * q^72 - 972 * q^73 + 5631 * q^74 - 3431 * q^75 - 3090 * q^76 + 602 * q^77 + 1252 * q^78 + 1140 * q^79 + 8631 * q^80 - 3809 * q^81 + 4015 * q^82 - 5292 * q^83 - 5060 * q^84 + 391 * q^85 + 3388 * q^86 - 7600 * q^87 - 7229 * q^88 + 6276 * q^89 + 7374 * q^90 - 4602 * q^91 + 8158 * q^92 - 2599 * q^93 + 11081 * q^94 + 2305 * q^95 - 30114 * q^96 + 1377 * q^97 + 5102 * q^98 - 5812 * q^99

Introduction

L-functions

Modular forms

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