LMFDB - Embedded newform 230.5.d.a.91.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(91,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("230.91");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.19
Character	$\chi$	$=$	230.91
Dual form			230.5.d.a.91.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843 q^{2} +11.3074 q^{3} +8.00000 q^{4} -11.1803i q^{5} +31.9821 q^{6} -52.5241i q^{7} +22.6274 q^{8} +46.8567 q^{9} +O(q^{10})$	\(q+2.82843 q^{2} +11.3074 q^{3} +8.00000 q^{4} -11.1803i q^{5} +31.9821 q^{6} -52.5241i q^{7} +22.6274 q^{8} +46.8567 q^{9} -31.6228i q^{10} +103.713i q^{11} +90.4590 q^{12} +233.879 q^{13} -148.561i q^{14} -126.420i q^{15} +64.0000 q^{16} -11.4078i q^{17} +132.531 q^{18} -403.221i q^{19} -89.4427i q^{20} -593.910i q^{21} +293.345i q^{22} +(334.508 - 409.811i) q^{23} +255.857 q^{24} -125.000 q^{25} +661.510 q^{26} -386.071 q^{27} -420.193i q^{28} -616.291 q^{29} -357.571i q^{30} +1178.41 q^{31} +181.019 q^{32} +1172.72i q^{33} -32.2662i q^{34} -587.238 q^{35} +374.854 q^{36} +912.484i q^{37} -1140.48i q^{38} +2644.56 q^{39} -252.982i q^{40} +103.534 q^{41} -1679.83i q^{42} +901.761i q^{43} +829.704i q^{44} -523.874i q^{45} +(946.132 - 1159.12i) q^{46} -2602.73 q^{47} +723.672 q^{48} -357.785 q^{49} -353.553 q^{50} -128.992i q^{51} +1871.03 q^{52} +3039.57i q^{53} -1091.97 q^{54} +1159.55 q^{55} -1188.49i q^{56} -4559.37i q^{57} -1743.13 q^{58} -4646.38 q^{59} -1011.36i q^{60} +3504.00i q^{61} +3333.05 q^{62} -2461.11i q^{63} +512.000 q^{64} -2614.85i q^{65} +3316.96i q^{66} +3514.70i q^{67} -91.2625i q^{68} +(3782.41 - 4633.89i) q^{69} -1660.96 q^{70} +3133.65 q^{71} +1060.25 q^{72} +3152.79 q^{73} +2580.90i q^{74} -1413.42 q^{75} -3225.76i q^{76} +5447.44 q^{77} +7479.94 q^{78} +1850.80i q^{79} -715.542i q^{80} -8160.84 q^{81} +292.837 q^{82} +1205.47i q^{83} -4751.28i q^{84} -127.543 q^{85} +2550.57i q^{86} -6968.63 q^{87} +2346.76i q^{88} -6786.29i q^{89} -1481.74i q^{90} -12284.3i q^{91} +(2676.07 - 3278.49i) q^{92} +13324.7 q^{93} -7361.64 q^{94} -4508.14 q^{95} +2046.85 q^{96} +6344.89i q^{97} -1011.97 q^{98} +4859.65i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9}+O(q^{10}) $ 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9	$ 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9} - 408 q^{13} + 2048 q^{16} + 1024 q^{18} + 1332 q^{23} + 512 q^{24} - 4000 q^{25} + 2208 q^{27} + 3732 q^{29} - 412 q^{31} + 300 q^{35} + 6656 q^{36} - 9208 q^{39} - 6156 q^{41} + 4480 q^{46} + 5184 q^{47} - 13820 q^{49} - 3264 q^{52} - 3328 q^{54} - 6000 q^{55} + 3200 q^{58} - 30468 q^{59} - 10752 q^{62} + 16384 q^{64} - 1168 q^{69} + 4800 q^{70} - 37644 q^{71} + 8192 q^{72} + 19984 q^{73} + 27528 q^{77} + 15744 q^{78} + 69056 q^{81} - 17408 q^{82} + 3300 q^{85} + 28936 q^{87} + 10656 q^{92} + 40648 q^{93} - 23808 q^{94} - 21600 q^{95} + 4096 q^{96} + 43008 q^{98}+O(q^{100}) $ 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9 - 408 * q^13 + 2048 * q^16 + 1024 * q^18 + 1332 * q^23 + 512 * q^24 - 4000 * q^25 + 2208 * q^27 + 3732 * q^29 - 412 * q^31 + 300 * q^35 + 6656 * q^36 - 9208 * q^39 - 6156 * q^41 + 4480 * q^46 + 5184 * q^47 - 13820 * q^49 - 3264 * q^52 - 3328 * q^54 - 6000 * q^55 + 3200 * q^58 - 30468 * q^59 - 10752 * q^62 + 16384 * q^64 - 1168 * q^69 + 4800 * q^70 - 37644 * q^71 + 8192 * q^72 + 19984 * q^73 + 27528 * q^77 + 15744 * q^78 + 69056 * q^81 - 17408 * q^82 + 3300 * q^85 + 28936 * q^87 + 10656 * q^92 + 40648 * q^93 - 23808 * q^94 - 21600 * q^95 + 4096 * q^96 + 43008 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	2.82843			0.707107
$2$	2.82843			0.707107
$3$	11.3074			1.25638			0.628188	−	0.778062i	$-0.283797\pi$
$3$	11.3074			1.25638			0.628188	+	0.778062i	$0.283797\pi$
$4$	8.00000			0.500000
$5$		−	11.1803i		−	0.447214i
$5$		−	11.1803i		−	0.447214i
$6$	31.9821			0.888391
$7$		−	52.5241i		−	1.07192i	−0.844243	−	0.535961i	$-0.819950\pi$
$7$		−	52.5241i		−	1.07192i	0.844243	−	0.535961i	$-0.180050\pi$
$8$	22.6274			0.353553
$9$	46.8567			0.578478
$10$		−	31.6228i		−	0.316228i
$11$			103.713i			0.857132i	0.903510	+	0.428566i	$0.140981\pi$
$11$			103.713i			0.857132i	−0.903510	+	0.428566i	$0.859019\pi$
$12$	90.4590			0.628188
$13$	233.879			1.38390			0.691950	−	0.721945i	$-0.256752\pi$
$13$	233.879			1.38390			0.691950	+	0.721945i	$0.256752\pi$
$14$		−	148.561i		−	0.757963i
$15$		−	126.420i		−	0.561868i
$16$	64.0000			0.250000
$17$		−	11.4078i		−	0.0394734i	−0.999805	−	0.0197367i	$-0.993717\pi$
$17$		−	11.4078i		−	0.0394734i	0.999805	−	0.0197367i	$-0.00628279\pi$
$18$	132.531			0.409046
$19$		−	403.221i		−	1.11695i	−0.829520	−	0.558477i	$-0.811386\pi$
$19$		−	403.221i		−	1.11695i	0.829520	−	0.558477i	$-0.188614\pi$
$20$		−	89.4427i		−	0.223607i
$21$		−	593.910i		−	1.34673i
$22$			293.345i			0.606084i
$23$	334.508	−	409.811i	0.632341	−	0.774691i
$23$	334.508	−	409.811i	0.632341	−	0.774691i
$24$	255.857			0.444196
$25$	−125.000			−0.200000
$26$	661.510			0.978565
$27$	−386.071			−0.529589
$28$		−	420.193i		−	0.535961i
$29$	−616.291			−0.732807			−0.366404	−	0.930456i	$-0.619411\pi$
$29$	−616.291			−0.732807			−0.366404	+	0.930456i	$0.619411\pi$
$30$		−	357.571i		−	0.397301i
$31$	1178.41			1.22623			0.613116	−	0.789993i	$-0.289916\pi$
$31$	1178.41			1.22623			0.613116	+	0.789993i	$0.289916\pi$
$32$	181.019			0.176777
$33$			1172.72i			1.07688i
$34$		−	32.2662i		−	0.0279119i
$35$	−587.238			−0.479378
$36$	374.854			0.289239
$37$			912.484i			0.666534i	0.942833	+	0.333267i	$0.108151\pi$
$37$			912.484i			0.666534i	−0.942833	+	0.333267i	$0.891849\pi$
$38$		−	1140.48i		−	0.789806i
$39$	2644.56			1.73870
$40$		−	252.982i		−	0.158114i
$41$	103.534			0.0615905			0.0307952	−	0.999526i	$-0.490196\pi$
$41$	103.534			0.0615905			0.0307952	+	0.999526i	$0.490196\pi$
$42$		−	1679.83i		−	0.952285i
$43$			901.761i			0.487702i	0.969813	+	0.243851i	$0.0784108\pi$
$43$			901.761i			0.487702i	−0.969813	+	0.243851i	$0.921589\pi$
$44$			829.704i			0.428566i
$45$		−	523.874i		−	0.258703i
$46$	946.132	−	1159.12i	0.447132	−	0.547789i
$47$	−2602.73			−1.17824			−0.589121	−	0.808045i	$-0.700526\pi$
$47$	−2602.73			−1.17824			−0.589121	+	0.808045i	$0.700526\pi$
$48$	723.672			0.314094
$49$	−357.785			−0.149015
$50$	−353.553			−0.141421
$51$		−	128.992i		−	0.0495934i
$52$	1871.03			0.691950
$53$			3039.57i			1.08208i	0.840996	+	0.541041i	$0.181970\pi$
$53$			3039.57i			1.08208i	−0.840996	+	0.541041i	$0.818030\pi$
$54$	−1091.97			−0.374476
$55$	1159.55			0.383321
$56$		−	1188.49i		−	0.378981i
$57$		−	4559.37i		−	1.40331i
$58$	−1743.13			−0.518173
$59$	−4646.38			−1.33478			−0.667391	−	0.744707i	$-0.732589\pi$
$59$	−4646.38			−1.33478			−0.667391	+	0.744707i	$0.732589\pi$
$60$		−	1011.36i		−	0.280934i
$61$			3504.00i			0.941684i	0.882218	+	0.470842i	$0.156050\pi$
$61$			3504.00i			0.941684i	−0.882218	+	0.470842i	$0.843950\pi$
$62$	3333.05			0.867077
$63$		−	2461.11i		−	0.620083i
$64$	512.000			0.125000
$65$		−	2614.85i		−	0.618899i
$66$			3316.96i			0.761469i
$67$			3514.70i			0.782958i	0.920187	+	0.391479i	$0.128036\pi$
$67$			3514.70i			0.782958i	−0.920187	+	0.391479i	$0.871964\pi$
$68$		−	91.2625i		−	0.0197367i
$69$	3782.41	−	4633.89i	0.794457	−	0.973302i
$70$	−1660.96			−0.338971
$71$	3133.65			0.621632			0.310816	−	0.950470i	$-0.399398\pi$
$71$	3133.65			0.621632			0.310816	+	0.950470i	$0.399398\pi$
$72$	1060.25			0.204523
$73$	3152.79			0.591629			0.295815	−	0.955245i	$-0.404409\pi$
$73$	3152.79			0.591629			0.295815	+	0.955245i	$0.404409\pi$
$74$			2580.90i			0.471310i
$75$	−1413.42			−0.251275
$76$		−	3225.76i		−	0.558477i
$77$	5447.44			0.918778
$78$	7479.94			1.22944
$79$			1850.80i			0.296556i	0.988946	+	0.148278i	$0.0473730\pi$
$79$			1850.80i			0.296556i	−0.988946	+	0.148278i	$0.952627\pi$
$80$		−	715.542i		−	0.111803i
$81$	−8160.84			−1.24384
$82$	292.837			0.0435510
$83$			1205.47i			0.174985i	0.996165	+	0.0874923i	$0.0278853\pi$
$83$			1205.47i			0.174985i	−0.996165	+	0.0874923i	$0.972115\pi$
$84$		−	4751.28i		−	0.673367i
$85$	−127.543			−0.0176530
$86$			2550.57i			0.344857i
$87$	−6968.63			−0.920681
$88$			2346.76i			0.303042i
$89$		−	6786.29i		−	0.856747i	−0.903602	−	0.428373i	$-0.859087\pi$
$89$		−	6786.29i		−	0.856747i	0.903602	−	0.428373i	$-0.140913\pi$
$90$		−	1481.74i		−	0.182931i
$91$		−	12284.3i		−	1.48343i
$92$	2676.07	−	3278.49i	0.316170	−	0.387345i
$93$	13324.7			1.54061
$94$	−7361.64			−0.833142
$95$	−4508.14			−0.499517
$96$	2046.85			0.222098
$97$			6344.89i			0.674343i	0.941443	+	0.337171i	$0.109470\pi$
$97$			6344.89i			0.674343i	−0.941443	+	0.337171i	$0.890530\pi$
$98$	−1011.97			−0.105369
$99$			4859.65i			0.495832i
$100$	−1000.00			−0.100000
$101$	−5455.61			−0.534812			−0.267406	−	0.963584i	$-0.586166\pi$
$101$	−5455.61			−0.534812			−0.267406	+	0.963584i	$0.586166\pi$
$102$		−	364.846i		−	0.0350678i
$103$			16317.8i			1.53811i	0.639185	+	0.769053i	$0.279272\pi$
$103$			16317.8i			1.53811i	−0.639185	+	0.769053i	$0.720728\pi$
$104$	5292.08			0.489283
$105$	−6640.12			−0.602278
$106$			8597.20i			0.765148i
$107$			4937.81i			0.431288i	0.976472	+	0.215644i	$0.0691850\pi$
$107$			4937.81i			0.431288i	−0.976472	+	0.215644i	$0.930815\pi$
$108$	−3088.56			−0.264795
$109$		−	6363.94i		−	0.535640i	−0.963469	−	0.267820i	$-0.913697\pi$
$109$		−	6363.94i		−	0.535640i	0.963469	−	0.267820i	$-0.0863033\pi$
$110$	3279.69			0.271049
$111$			10317.8i			0.837416i
$112$		−	3361.54i		−	0.267980i
$113$			1554.77i			0.121762i	0.998145	+	0.0608808i	$0.0193910\pi$
$113$			1554.77i			0.121762i	−0.998145	+	0.0608808i	$0.980609\pi$
$114$		−	12895.8i		−	0.992293i
$115$	−4581.83	−	3739.92i	−0.346452	−	0.282791i
$116$	−4930.33			−0.366404
$117$	10958.8			0.800556
$118$	−13141.9			−0.943834
$119$	−599.185			−0.0423124
$120$		−	2860.56i		−	0.198650i
$121$	3884.61			0.265324
$122$			9910.82i			0.665871i
$123$	1170.69			0.0773807
$124$	9427.28			0.613116
$125$			1397.54i			0.0894427i
$126$		−	6961.07i		−	0.438465i
$127$	−9237.64			−0.572735			−0.286368	−	0.958120i	$-0.592448\pi$
$127$	−9237.64			−0.572735			−0.286368	+	0.958120i	$0.592448\pi$
$128$	1448.15			0.0883883
$129$			10196.5i			0.612737i
$130$		−	7395.91i		−	0.437628i
$131$	−17004.9			−0.990904			−0.495452	−	0.868635i	$-0.664998\pi$
$131$	−17004.9			−0.990904			−0.495452	+	0.868635i	$0.664998\pi$
$132$			9381.78i			0.538440i
$133$	−21178.8			−1.19729
$134$			9941.06i			0.553635i
$135$			4316.40i			0.236840i
$136$		−	258.129i		−	0.0139560i
$137$			15152.5i			0.807317i	0.914910	+	0.403658i	$0.132262\pi$
$137$			15152.5i			0.807317i	−0.914910	+	0.403658i	$0.867738\pi$
$138$	10698.3	−	13106.6i	0.561766	−	0.688228i
$139$	−34318.7			−1.77624			−0.888120	−	0.459612i	$-0.847988\pi$
$139$	−34318.7			−1.77624			−0.888120	+	0.459612i	$0.847988\pi$
$140$	−4697.90			−0.239689
$141$	−29430.1			−1.48031
$142$	8863.30			0.439560
$143$			24256.3i			1.18619i
$144$	2998.83			0.144620
$145$			6890.34i			0.327721i
$146$	8917.44			0.418345
$147$	−4045.60			−0.187218
$148$			7299.88i			0.333267i
$149$			35994.4i			1.62130i	0.585534	+	0.810648i	$0.300885\pi$
$149$			35994.4i			1.62130i	−0.585534	+	0.810648i	$0.699115\pi$
$150$	−3997.76			−0.177678
$151$	11103.3			0.486967			0.243483	−	0.969905i	$-0.421710\pi$
$151$	11103.3			0.486967			0.243483	+	0.969905i	$0.421710\pi$
$152$		−	9123.84i		−	0.394903i
$153$		−	534.533i		−	0.0228345i
$154$	15407.7			0.649674
$155$		−	13175.0i		−	0.548388i
$156$	21156.5			0.869349
$157$		−	45936.4i		−	1.86362i	−0.362944	−	0.931811i	$-0.618228\pi$
$157$		−	45936.4i		−	1.86362i	0.362944	−	0.931811i	$-0.381772\pi$
$158$			5234.86i			0.209697i
$159$			34369.6i			1.35950i
$160$		−	2023.86i		−	0.0790569i
$161$	−21525.0	−	17569.8i	−0.830407	−	0.677819i
$162$	−23082.3			−0.879529
$163$	39913.7			1.50227			0.751133	−	0.660151i	$-0.229508\pi$
$163$	39913.7			1.50227			0.751133	+	0.660151i	$0.229508\pi$
$164$	828.268			0.0307952
$165$	13111.4			0.481595
$166$			3409.58i			0.123733i
$167$	−26936.6			−0.965850			−0.482925	−	0.875662i	$-0.660426\pi$
$167$	−26936.6			−0.965850			−0.482925	+	0.875662i	$0.660426\pi$
$168$		−	13438.7i		−	0.476143i
$169$	26138.4			0.915179
$170$	−360.747			−0.0124826
$171$		−	18893.6i		−	0.646134i
$172$			7214.09i			0.243851i
$173$	−8810.85			−0.294392			−0.147196	−	0.989107i	$-0.547025\pi$
$173$	−8810.85			−0.294392			−0.147196	+	0.989107i	$0.547025\pi$
$174$	−19710.3			−0.651020
$175$			6565.52i			0.214384i
$176$			6637.63i			0.214283i
$177$	−52538.3			−1.67699
$178$		−	19194.5i		−	0.605811i
$179$	45284.7			1.41334			0.706668	−	0.707546i	$-0.250198\pi$
$179$	45284.7			1.41334			0.706668	+	0.707546i	$0.250198\pi$
$180$		−	4190.99i		−	0.129352i
$181$		−	29666.8i		−	0.905552i	−0.891624	−	0.452776i	$-0.850434\pi$
$181$		−	29666.8i		−	0.905552i	0.891624	−	0.452776i	$-0.149566\pi$
$182$		−	34745.2i		−	1.04894i
$183$			39621.1i			1.18311i
$184$	7569.06	−	9272.97i	0.223566	−	0.273894i
$185$	10201.9			0.298083
$186$	37688.0			1.08937
$187$	1183.14			0.0338339
$188$	−20821.9			−0.589121
$189$			20278.0i			0.567678i
$190$	−12751.0			−0.353212
$191$		−	56754.9i		−	1.55574i	−0.628426	−	0.777869i	$-0.716301\pi$
$191$		−	56754.9i		−	1.55574i	0.628426	−	0.777869i	$-0.283699\pi$
$192$	5789.38			0.157047
$193$	−19522.0			−0.524095			−0.262048	−	0.965055i	$-0.584398\pi$
$193$	−19522.0			−0.524095			−0.262048	+	0.965055i	$0.584398\pi$
$194$			17946.1i			0.476833i
$195$		−	29567.1i		−	0.777569i
$196$	−2862.28			−0.0745074
$197$	−19849.0			−0.511453			−0.255727	−	0.966749i	$-0.582315\pi$
$197$	−19849.0			−0.511453			−0.255727	+	0.966749i	$0.582315\pi$
$198$			13745.2i			0.350606i
$199$			66813.6i			1.68717i	0.536997	+	0.843584i	$0.319559\pi$
$199$			66813.6i			1.68717i	−0.536997	+	0.843584i	$0.680441\pi$
$200$	−2828.43			−0.0707107
$201$			39742.0i			0.983688i
$202$	−15430.8			−0.378169
$203$			32370.2i			0.785512i
$204$		−	1031.94i		−	0.0247967i
$205$		−	1157.54i		−	0.0275441i
$206$			46153.6i			1.08761i
$207$	15674.0	−	19202.4i	0.365795	−	0.448142i
$208$	14968.3			0.345975
$209$	41819.2			0.957378
$210$	−18781.1			−0.425875
$211$	−59845.9			−1.34422			−0.672109	−	0.740453i	$-0.734611\pi$
$211$	−59845.9			−1.34422			−0.672109	+	0.740453i	$0.734611\pi$
$212$			24316.6i			0.541041i
$213$	35433.3			0.781003
$214$			13966.2i			0.304967i
$215$	10082.0			0.218107
$216$	−8735.78			−0.187238
$217$		−	61894.9i		−	1.31442i
$218$		−	17999.9i		−	0.378755i
$219$	35649.8			0.743308
$220$	9276.37			0.191661
$221$		−	2668.05i		−	0.0546272i
$222$			29183.2i			0.592143i
$223$	−6670.50			−0.134137			−0.0670685	−	0.997748i	$-0.521365\pi$
$223$	−6670.50			−0.134137			−0.0670685	+	0.997748i	$0.521365\pi$
$224$		−	9507.88i		−	0.189491i
$225$	−5857.09			−0.115696
$226$			4397.56i			0.0860985i
$227$		−	90618.2i		−	1.75859i	−0.476280	−	0.879294i	$-0.658015\pi$
$227$		−	90618.2i		−	1.75859i	0.476280	−	0.879294i	$-0.341985\pi$
$228$		−	36474.9i		−	0.701657i
$229$			48138.3i			0.917952i	0.888449	+	0.458976i	$0.151784\pi$
$229$			48138.3i			0.917952i	−0.888449	+	0.458976i	$0.848216\pi$
$230$	−12959.4	−	10578.1i	−0.244979	−	0.199964i
$231$	61596.2			1.15433
$232$	−13945.1			−0.259087
$233$	68105.2			1.25449			0.627247	−	0.778821i	$-0.284182\pi$
$233$	68105.2			1.25449			0.627247	+	0.778821i	$0.284182\pi$
$234$	30996.2			0.566079
$235$			29099.5i			0.526925i
$236$	−37171.0			−0.667391
$237$			20927.7i			0.372585i
$238$	−1694.75			−0.0299194
$239$	57094.5			0.999535			0.499768	−	0.866159i	$-0.333419\pi$
$239$	57094.5			0.999535			0.499768	+	0.866159i	$0.333419\pi$
$240$		−	8090.90i		−	0.140467i
$241$		−	54612.4i		−	0.940279i	−0.882592	−	0.470140i	$-0.844204\pi$
$241$		−	54612.4i		−	0.940279i	0.882592	−	0.470140i	$-0.155796\pi$
$242$	10987.3			0.187613
$243$	−61006.0			−1.03314
$244$			28032.0i			0.470842i
$245$			4000.15i			0.0666414i
$246$	3311.22			0.0547164
$247$		−	94304.9i		−	1.54575i
$248$	26664.4			0.433539
$249$			13630.7i			0.219846i
$250$			3952.85i			0.0632456i
$251$		−	88084.1i		−	1.39814i	−0.715054	−	0.699069i	$-0.753598\pi$
$251$		−	88084.1i		−	1.39814i	0.715054	−	0.699069i	$-0.246402\pi$
$252$		−	19688.9i		−	0.310042i
$253$	42502.8	+	34692.8i	0.664012	+	0.542000i
$254$	−26128.0			−0.404985
$255$	−1442.18			−0.0221788
$256$	4096.00			0.0625000
$257$	−30629.2			−0.463734			−0.231867	−	0.972747i	$-0.574483\pi$
$257$	−30629.2			−0.463734			−0.231867	+	0.972747i	$0.574483\pi$
$258$			28840.2i			0.433270i
$259$	47927.5			0.714471
$260$		−	20918.8i		−	0.309449i
$261$	−28877.4			−0.423913
$262$	−48097.1			−0.700675
$263$		−	76653.5i		−	1.10821i	−0.832448	−	0.554103i	$-0.813061\pi$
$263$		−	76653.5i		−	1.10821i	0.832448	−	0.554103i	$-0.186939\pi$
$264$			26535.7i			0.380734i
$265$	33983.4			0.483922
$266$	−59902.7			−0.846610
$267$		−	76735.1i		−	1.07640i
$268$			28117.6i			0.391479i
$269$	61162.8			0.845246			0.422623	−	0.906306i	$-0.361109\pi$
$269$	61162.8			0.845246			0.422623	+	0.906306i	$0.361109\pi$
$270$			12208.6i			0.167471i
$271$	108530.			1.47778			0.738891	−	0.673825i	$-0.235350\pi$
$271$	108530.			1.47778			0.738891	+	0.673825i	$0.235350\pi$
$272$		−	730.100i		−	0.00986835i
$273$		−	138903.i		−	1.86375i
$274$			42857.8i			0.570859i
$275$		−	12964.1i		−	0.171426i
$276$	30259.3	−	37071.1i	0.397228	−	0.486651i
$277$	−3124.06			−0.0407155			−0.0203577	−	0.999793i	$-0.506481\pi$
$277$	−3124.06			−0.0407155			−0.0203577	+	0.999793i	$0.506481\pi$
$278$	−97068.0			−1.25599
$279$	55216.4			0.709349
$280$	−13287.7			−0.169486
$281$			135072.i			1.71062i	0.518118	+	0.855309i	$0.326633\pi$
$281$			135072.i			1.71062i	−0.518118	+	0.855309i	$0.673367\pi$
$282$	−83240.9			−1.04674
$283$		−	114921.i		−	1.43491i	−0.696604	−	0.717456i	$-0.745306\pi$
$283$		−	114921.i		−	1.43491i	0.696604	−	0.717456i	$-0.254694\pi$
$284$	25069.2			0.310816
$285$	−50975.3			−0.627581
$286$			68607.2i			0.838760i
$287$		−	5438.01i		−	0.0660201i
$288$	8481.98			0.102261
$289$	83390.9			0.998442
$290$			19488.8i			0.231734i
$291$			71744.1i			0.847228i
$292$	25222.3			0.295815
$293$		−	59299.7i		−	0.690744i	−0.938466	−	0.345372i	$-0.887753\pi$
$293$		−	59299.7i		−	0.690744i	0.938466	−	0.345372i	$-0.112247\pi$
$294$	−11442.7			−0.132383
$295$			51948.1i			0.596933i
$296$			20647.2i			0.235655i
$297$		−	40040.5i		−	0.453928i
$298$			101808.i			1.14643i
$299$	78234.5	−	95846.3i	0.875096	−	1.07209i
$300$	−11307.4			−0.125638
$301$	47364.2			0.522778
$302$	31404.9			0.344337
$303$	−61688.7			−0.671924
$304$		−	25806.1i		−	0.279239i
$305$	39176.0			0.421134
$306$		−	1511.89i		−	0.0161464i
$307$	123291.			1.30815			0.654073	−	0.756432i	$-0.273059\pi$
$307$	123291.			1.30815			0.654073	+	0.756432i	$0.273059\pi$
$308$	43579.5			0.459389
$309$			184511.i			1.93244i
$310$		−	37264.6i		−	0.387769i
$311$	−7245.03			−0.0749065			−0.0374532	−	0.999298i	$-0.511925\pi$
$311$	−7245.03			−0.0749065			−0.0374532	+	0.999298i	$0.511925\pi$
$312$	59839.5			0.614722
$313$			17591.2i			0.179559i	0.995962	+	0.0897796i	$0.0286163\pi$
$313$			17591.2i			0.179559i	−0.995962	+	0.0897796i	$0.971384\pi$
$314$		−	129928.i		−	1.31778i
$315$	−27516.0			−0.277310
$316$			14806.4i			0.148278i
$317$	−135471.			−1.34812			−0.674060	−	0.738677i	$-0.735451\pi$
$317$	−135471.			−1.34812			−0.674060	+	0.738677i	$0.735451\pi$
$318$			97211.8i			0.961313i
$319$		−	63917.4i		−	0.628113i
$320$		−	5724.33i		−	0.0559017i
$321$			55833.7i			0.541859i
$322$	−60881.8	−	49694.8i	−0.587186	−	0.479291i
$323$	−4599.86			−0.0440900
$324$	−65286.7			−0.621921
$325$	−29234.9			−0.276780
$326$	112893.			1.06226
$327$		−	71959.5i		−	0.672965i
$328$	2342.70			0.0217755
$329$			136706.i			1.26298i
$330$	37084.7			0.340539
$331$	149292.			1.36264			0.681320	−	0.731985i	$-0.261406\pi$
$331$	149292.			1.36264			0.681320	+	0.731985i	$0.261406\pi$
$332$			9643.75i			0.0874923i
$333$			42756.1i			0.385575i
$334$	−76188.2			−0.682959
$335$	39295.5			0.350149
$336$		−	38010.2i		−	0.336684i
$337$		−	60284.4i		−	0.530818i	−0.964136	−	0.265409i	$-0.914493\pi$
$337$		−	60284.4i		−	0.530818i	0.964136	−	0.265409i	$-0.0855069\pi$
$338$	73930.7			0.647130
$339$			17580.4i			0.152978i
$340$	−1020.35			−0.00882652
$341$			122216.i			1.05104i
$342$		−	53439.2i		−	0.456886i
$343$		−	107318.i		−	0.912189i
$344$			20404.5i			0.172429i
$345$	−51808.5	−	42288.6i	−0.435274	−	0.355292i
$346$	−24920.9			−0.208166
$347$	−25508.7			−0.211851			−0.105925	−	0.994374i	$-0.533780\pi$
$347$	−25508.7			−0.211851			−0.105925	+	0.994374i	$0.533780\pi$
$348$	−55749.1			−0.460341
$349$	−211061.			−1.73283			−0.866415	−	0.499324i	$-0.833582\pi$
$349$	−211061.			−1.73283			−0.866415	+	0.499324i	$0.833582\pi$
$350$			18570.1i			0.151593i
$351$	−90293.9			−0.732899
$352$			18774.1i			0.151521i
$353$	−138203.			−1.10910			−0.554548	−	0.832151i	$-0.687109\pi$
$353$	−138203.			−1.10910			−0.554548	+	0.832151i	$0.687109\pi$
$354$	−148601.			−1.18581
$355$		−	35035.3i		−	0.278002i
$356$		−	54290.3i		−	0.428373i
$357$	−6775.21			−0.0531602
$358$	128084.			0.999379
$359$		−	36916.0i		−	0.286435i	−0.989691	−	0.143217i	$-0.954255\pi$
$359$		−	36916.0i		−	0.286435i	0.989691	−	0.143217i	$-0.0457448\pi$
$360$		−	11853.9i		−	0.0914655i
$361$	−32265.8			−0.247587
$362$		−	83910.3i		−	0.640322i
$363$	43924.8			0.333347
$364$		−	98274.4i		−	0.741716i
$365$		−	35249.3i		−	0.264585i
$366$			112065.i			0.836583i
$367$			264771.i			1.96579i	0.184160	+	0.982896i	$0.441044\pi$
$367$			264771.i			1.96579i	−0.184160	+	0.982896i	$0.558956\pi$
$368$	21408.5	−	26227.9i	0.158085	−	0.193673i
$369$	4851.25			0.0356287
$370$	28855.3			0.210776
$371$	159651.			1.15991
$372$	106598.			0.770304
$373$			80293.2i			0.577114i	0.957463	+	0.288557i	$0.0931754\pi$
$373$			80293.2i			0.577114i	−0.957463	+	0.288557i	$0.906825\pi$
$374$	3346.42			0.0239242
$375$			15802.5i			0.112374i
$376$	−58893.2			−0.416571
$377$	−144138.			−1.01413
$378$			57354.9i			0.401409i
$379$		−	242851.i		−	1.69068i	−0.534229	−	0.845340i	$-0.679398\pi$
$379$		−	242851.i		−	1.69068i	0.534229	−	0.845340i	$-0.320602\pi$
$380$	−36065.1			−0.249759
$381$	−104454.			−0.719570
$382$		−	160527.i		−	1.10007i
$383$			191078.i			1.30261i	0.758818	+	0.651303i	$0.225777\pi$
$383$			191078.i			1.30261i	−0.758818	+	0.651303i	$0.774223\pi$
$384$	16374.8			0.111049
$385$		−	60904.2i		−	0.410890i
$386$	−55216.6			−0.370591
$387$			42253.6i			0.282125i
$388$			50759.1i			0.337171i
$389$			90095.4i			0.595392i	0.954661	+	0.297696i	$0.0962183\pi$
$389$			90095.4i			0.595392i	−0.954661	+	0.297696i	$0.903782\pi$
$390$		−	83628.3i		−	0.549824i
$391$	−4675.05	−	3816.01i	−0.0305797	−	0.0249606i
$392$	−8095.74			−0.0526847
$393$	−192281.			−1.24495
$394$	−56141.4			−0.361652
$395$	20692.6			0.132624
$396$			38877.2i			0.247916i
$397$	−147200.			−0.933956			−0.466978	−	0.884269i	$-0.654657\pi$
$397$	−147200.			−0.933956			−0.466978	+	0.884269i	$0.654657\pi$
$398$			188977.i			1.19301i
$399$	−239477.			−1.50424
$400$	−8000.00			−0.0500000
$401$			197783.i			1.22999i	0.788533	+	0.614993i	$0.210841\pi$
$401$			197783.i			1.22999i	−0.788533	+	0.614993i	$0.789159\pi$
$402$			112407.i			0.695573i
$403$	275605.			1.69698
$404$	−43644.9			−0.267406
$405$			91241.0i			0.556263i
$406$			91556.6i			0.555441i
$407$	−94636.5			−0.571307
$408$		−	2918.76i		−	0.0175339i
$409$	−69158.8			−0.413429			−0.206714	−	0.978401i	$-0.566277\pi$
$409$	−69158.8			−0.413429			−0.206714	+	0.978401i	$0.566277\pi$
$410$		−	3274.02i		−	0.0194766i
$411$			171335.i			1.01429i
$412$			130542.i			0.769053i
$413$			244047.i			1.43078i
$414$	44332.7	−	54312.7i	0.258656	−	0.316884i
$415$	13477.5			0.0782555
$416$	42336.6			0.244641
$417$	−388055.			−2.23162
$418$	118283.			0.676968
$419$			134964.i			0.768757i	0.923176	+	0.384378i	$0.125584\pi$
$419$			134964.i			0.768757i	−0.923176	+	0.384378i	$0.874416\pi$
$420$	−53120.9			−0.301139
$421$		−	275764.i		−	1.55587i	−0.628344	−	0.777936i	$-0.716267\pi$
$421$		−	275764.i		−	1.55587i	0.628344	−	0.777936i	$-0.283733\pi$
$422$	−169270.			−0.950505
$423$	−121956.			−0.681587
$424$			68777.6i			0.382574i
$425$			1425.98i			0.00789468i
$426$	100221.			0.552253
$427$	184045.			1.00941
$428$			39502.5i			0.215644i
$429$			274275.i			1.49029i
$430$	28516.2			0.154225
$431$		−	7499.97i		−	0.0403743i	−0.999796	−	0.0201871i	$-0.993574\pi$
$431$		−	7499.97i		−	0.0403743i	0.999796	−	0.0201871i	$-0.00642620\pi$
$432$	−24708.5			−0.132397
$433$		−	55687.9i		−	0.297020i	−0.988911	−	0.148510i	$-0.952552\pi$
$433$		−	55687.9i		−	0.297020i	0.988911	−	0.148510i	$-0.0474477\pi$
$434$		−	175065.i		−	0.929439i
$435$			77911.7i			0.411741i
$436$		−	50911.5i		−	0.267820i
$437$	−165244.	−	134881.i	−0.865294	−	0.706296i
$438$	100833.			0.525598
$439$	58154.2			0.301753			0.150877	−	0.988553i	$-0.451790\pi$
$439$	58154.2			0.301753			0.150877	+	0.988553i	$0.451790\pi$
$440$	26237.5			0.135525
$441$	−16764.6			−0.0862018
$442$		−	7546.38i		−	0.0386273i
$443$	−109243.			−0.556656			−0.278328	−	0.960486i	$-0.589780\pi$
$443$	−109243.			−0.556656			−0.278328	+	0.960486i	$0.589780\pi$
$444$			82542.4i			0.418708i
$445$	−75873.0			−0.383149
$446$	−18867.0			−0.0948492
$447$			407002.i			2.03696i
$448$		−	26892.4i		−	0.133990i
$449$	−150447.			−0.746259			−0.373130	−	0.927779i	$-0.621715\pi$
$449$	−150447.			−0.746259			−0.373130	+	0.927779i	$0.621715\pi$
$450$	−16566.4			−0.0818092
$451$			10737.8i			0.0527912i
$452$			12438.2i			0.0608808i
$453$	125549.			0.611813
$454$		−	256307.i		−	1.24351i
$455$	−137343.			−0.663411
$456$		−	103167.i		−	0.496146i
$457$		−	124457.i		−	0.595918i	−0.954579	−	0.297959i	$-0.903694\pi$
$457$		−	124457.i		−	0.595918i	0.954579	−	0.297959i	$-0.0963059\pi$
$458$			136156.i			0.649090i
$459$			4404.22i			0.0209047i
$460$	−36654.6	−	29919.3i	−0.173226	−	0.141396i
$461$	−14768.3			−0.0694910			−0.0347455	−	0.999396i	$-0.511062\pi$
$461$	−14768.3			−0.0694910			−0.0347455	+	0.999396i	$0.511062\pi$
$462$	174220.			0.816235
$463$	54995.1			0.256544			0.128272	−	0.991739i	$-0.459057\pi$
$463$	54995.1			0.256544			0.128272	+	0.991739i	$0.459057\pi$
$464$	−39442.6			−0.183202
$465$		−	148975.i		−	0.688981i
$466$	192631.			0.887061
$467$		−	184306.i		−	0.845096i	−0.906341	−	0.422548i	$-0.861136\pi$
$467$		−	184306.i		−	0.845096i	0.906341	−	0.422548i	$-0.138864\pi$
$468$	87670.5			0.400278
$469$	184606.			0.839269
$470$			82305.7i			0.372593i
$471$		−	519420.i		−	2.34141i
$472$	−105136.			−0.471917
$473$	−93524.3			−0.418025
$474$			59192.6i			0.263457i
$475$			50402.6i			0.223391i
$476$	−4793.48			−0.0211562
$477$			142424.i			0.625961i
$478$	161488.			0.706778
$479$		−	32084.5i		−	0.139837i	−0.997553	−	0.0699187i	$-0.977726\pi$
$479$		−	32084.5i		−	0.139837i	0.997553	−	0.0699187i	$-0.0222740\pi$
$480$		−	22884.5i		−	0.0993252i
$481$			213411.i			0.922416i
$482$		−	154467.i		−	0.664878i
$483$	−243391.	−	198668.i	−1.04330	−	0.851595i
$484$	31076.9			0.132662
$485$	70938.1			0.301575
$486$	−172551.			−0.730541
$487$	420466.			1.77285			0.886426	−	0.462870i	$-0.153180\pi$
$487$	420466.			1.77285			0.886426	+	0.462870i	$0.153180\pi$
$488$			79286.6i			0.332935i
$489$	451319.			1.88741
$490$			11314.1i			0.0471226i
$491$	156193.			0.647887			0.323943	−	0.946077i	$-0.394991\pi$
$491$	156193.			0.647887			0.323943	+	0.946077i	$0.394991\pi$
$492$	9365.54			0.0386904
$493$			7030.53i			0.0289264i
$494$		−	266734.i		−	1.09301i
$495$	54332.6			0.221743
$496$	75418.2			0.306558
$497$		−	164592.i		−	0.666341i
$498$			38553.4i			0.155455i
$499$	365355.			1.46728			0.733642	−	0.679537i	$-0.237819\pi$
$499$	365355.			1.46728			0.733642	+	0.679537i	$0.237819\pi$
$500$			11180.3i			0.0447214i
$501$	−304582.			−1.21347
$502$		−	249140.i		−	0.988633i
$503$		−	355958.i		−	1.40690i	−0.710745	−	0.703449i	$-0.751642\pi$
$503$		−	355958.i		−	1.40690i	0.710745	−	0.703449i	$-0.248358\pi$
$504$		−	55688.6i		−	0.219232i
$505$			60995.6i			0.239175i
$506$	120216.	+	98126.2i	0.469528	+	0.383252i
$507$	295557.			1.14981
$508$	−73901.2			−0.286368
$509$	79705.7			0.307648			0.153824	−	0.988098i	$-0.450841\pi$
$509$	79705.7			0.307648			0.153824	+	0.988098i	$0.450841\pi$
$510$	−4079.10			−0.0156828
$511$		−	165598.i		−	0.634180i
$512$	11585.2			0.0441942
$513$			155672.i			0.591527i
$514$	−86632.4			−0.327910
$515$	182438.			0.687862
$516$			81572.4i			0.306368i
$517$		−	269937.i		−	1.00991i
$518$	135559.			0.505208
$519$	−99627.6			−0.369866
$520$		−	59167.3i		−	0.218814i
$521$			301149.i			1.10945i	0.832035	+	0.554723i	$0.187176\pi$
$521$			301149.i			1.10945i	−0.832035	+	0.554723i	$0.812824\pi$
$522$	−81677.6			−0.299752
$523$		−	256880.i		−	0.939134i	−0.882897	−	0.469567i	$-0.844410\pi$
$523$		−	256880.i		−	0.939134i	0.882897	−	0.469567i	$-0.155590\pi$
$524$	−136039.			−0.495452
$525$			74238.8i			0.269347i
$526$		−	216809.i		−	0.783620i
$527$		−	13443.1i		−	0.0484036i
$528$			75054.2i			0.269220i
$529$	−56049.6	−	274170.i	−0.200291	−	0.979737i
$530$	96119.6			0.342184
$531$	−217714.			−0.772143
$532$	−169430.			−0.598644
$533$	24214.3			0.0852350
$534$		−	217040.i		−	0.761126i
$535$	55206.4			0.192878
$536$			79528.5i			0.276817i
$537$	512051.			1.77568
$538$	172995.			0.597679
$539$		−	37106.9i		−	0.127725i
$540$			34531.2i			0.118420i
$541$	152322.			0.520436			0.260218	−	0.965550i	$-0.416206\pi$
$541$	152322.			0.520436			0.260218	+	0.965550i	$0.416206\pi$
$542$	306969.			1.04495
$543$		−	335453.i		−	1.13771i
$544$		−	2065.03i		−	0.00697798i
$545$	−71151.0			−0.239546
$546$		−	392877.i		−	1.31787i
$547$	422942.			1.41353			0.706766	−	0.707447i	$-0.250153\pi$
$547$	422942.			1.41353			0.706766	+	0.707447i	$0.250153\pi$
$548$			121220.i			0.403658i
$549$			164186.i			0.544744i
$550$		−	36668.1i		−	0.121217i
$551$			248501.i			0.818513i
$552$	85586.2	−	104853.i	0.280883	−	0.344114i
$553$	97211.9			0.317884
$554$	−8836.17			−0.0287902
$555$	115357.			0.374504
$556$	−274550.			−0.888120
$557$		−	256188.i		−	0.825751i	−0.910787	−	0.412875i	$-0.864524\pi$
$557$		−	256188.i		−	0.825751i	0.910787	−	0.412875i	$-0.135476\pi$
$558$	156176.			0.501585
$559$			210903.i			0.674931i
$560$	−37583.2			−0.119844
$561$	13378.2			0.0425081
$562$			382042.i			1.20959i
$563$			94149.3i			0.297030i	0.988910	+	0.148515i	$0.0474493\pi$
$563$			94149.3i			0.297030i	−0.988910	+	0.148515i	$0.952551\pi$
$564$	−235441.			−0.740156
$565$	17382.9			0.0544534
$566$		−	325045.i		−	1.01464i
$567$			428641.i			1.33330i
$568$	70906.4			0.219780
$569$			423934.i			1.30940i	0.755887	+	0.654702i	$0.227206\pi$
$569$			423934.i			1.30940i	−0.755887	+	0.654702i	$0.772794\pi$
$570$	−144180.			−0.443767
$571$			13084.9i			0.0401325i	0.999799	+	0.0200663i	$0.00638772\pi$
$571$			13084.9i			0.0401325i	−0.999799	+	0.0200663i	$0.993612\pi$
$572$			194050.i			0.593093i
$573$		−	641749.i		−	1.95459i
$574$		−	15381.0i		−	0.0466833i
$575$	−41813.5	+	51226.4i	−0.126468	+	0.154938i
$576$	23990.7			0.0723098
$577$	−64042.7			−0.192362			−0.0961808	−	0.995364i	$-0.530663\pi$
$577$	−64042.7			−0.192362			−0.0961808	+	0.995364i	$0.530663\pi$
$578$	235865.			0.706005
$579$	−220743.			−0.658460
$580$			55122.8i			0.163861i
$581$	63316.2			0.187570
$582$			202923.i			0.599080i
$583$	−315243.			−0.927488
$584$	71339.5			0.209172
$585$		−	122523.i		−	0.358020i
$586$		−	167725.i		−	0.488430i
$587$	115705.			0.335796			0.167898	−	0.985804i	$-0.446302\pi$
$587$	115705.			0.335796			0.167898	+	0.985804i	$0.446302\pi$
$588$	−32364.8			−0.0936092
$589$		−	475159.i		−	1.36965i
$590$			146931.i			0.422095i
$591$	−224440.			−0.642577
$592$			58399.0i			0.166633i
$593$	−280918.			−0.798860			−0.399430	−	0.916764i	$-0.630792\pi$
$593$	−280918.			−0.798860			−0.399430	+	0.916764i	$0.630792\pi$
$594$		−	113252.i		−	0.320976i
$595$			6699.10i			0.0189227i
$596$			287955.i			0.810648i
$597$			755486.i			2.11972i
$598$	221281.	−	271094.i	0.618786	−	0.758085i
$599$	−485419.			−1.35289			−0.676445	−	0.736493i	$-0.736481\pi$
$599$	−485419.			−1.35289			−0.676445	+	0.736493i	$0.736481\pi$
$600$	−31982.1			−0.0888391
$601$	356732.			0.987627			0.493814	−	0.869568i	$-0.335602\pi$
$601$	356732.			0.987627			0.493814	+	0.869568i	$0.335602\pi$
$602$	133966.			0.369660
$603$			164687.i			0.452924i
$604$	88826.6			0.243483
$605$		−	43431.3i		−	0.118657i
$606$	−174482.			−0.475122
$607$	−249868.			−0.678161			−0.339081	−	0.940757i	$-0.610116\pi$
$607$	−249868.			−0.678161			−0.339081	+	0.940757i	$0.610116\pi$
$608$		−	72990.7i		−	0.197452i
$609$			366022.i			0.986897i
$610$	110806.			0.297786
$611$	−608725.			−1.63057
$612$		−	4276.26i		−	0.0114173i
$613$			175200.i			0.466244i	0.972447	+	0.233122i	$0.0748942\pi$
$613$			175200.i			0.466244i	−0.972447	+	0.233122i	$0.925106\pi$
$614$	348721.			0.924998
$615$		−	13088.7i		−	0.0346057i
$616$	123261.			0.324837
$617$			565468.i			1.48538i	0.669635	+	0.742691i	$0.266451\pi$
$617$			565468.i			1.48538i	−0.669635	+	0.742691i	$0.733549\pi$
$618$			521877.i			1.36644i
$619$		−	419958.i		−	1.09604i	−0.836467	−	0.548018i	$-0.815383\pi$
$619$		−	419958.i		−	1.09604i	0.836467	−	0.548018i	$-0.184617\pi$
$620$		−	105400.i		−	0.274194i
$621$	−129144.	+	158216.i	−0.334881	+	0.410268i
$622$	−20492.0			−0.0529669
$623$	−356444.			−0.918365
$624$	169252.			0.434674
$625$	15625.0			0.0400000
$626$			49755.5i			0.126968i
$627$	472866.			1.20283
$628$		−	367491.i		−	0.931811i
$629$	10409.5			0.0263103
$630$	−77827.1			−0.196087
$631$		−	353149.i		−	0.886951i	−0.896287	−	0.443475i	$-0.853745\pi$
$631$		−	353149.i		−	0.886951i	0.896287	−	0.443475i	$-0.146255\pi$
$632$			41878.9i			0.104848i
$633$	−676700.			−1.68884
$634$	−383170.			−0.953265
$635$			103280.i			0.256135i
$636$			274956.i			0.679751i
$637$	−83678.3			−0.206222
$638$		−	180786.i		−	0.444143i
$639$	146833.			0.359601
$640$		−	16190.9i		−	0.0395285i
$641$		−	274415.i		−	0.667870i	−0.942596	−	0.333935i	$-0.891623\pi$
$641$		−	274415.i		−	0.667870i	0.942596	−	0.333935i	$-0.108377\pi$
$642$			157922.i			0.383152i
$643$		−	455291.i		−	1.10120i	−0.834768	−	0.550602i	$-0.814398\pi$
$643$		−	455291.i		−	1.10120i	0.834768	−	0.550602i	$-0.185602\pi$
$644$	−172200.	−	140558.i	−0.415204	−	0.338910i
$645$	114001.			0.274024
$646$	−13010.4			−0.0311763
$647$	75821.1			0.181126			0.0905631	−	0.995891i	$-0.471133\pi$
$647$	75821.1			0.181126			0.0905631	+	0.995891i	$0.471133\pi$
$648$	−184659.			−0.439764
$649$		−	481890.i		−	1.14408i
$650$	−82688.8			−0.195713
$651$		−	699869.i		−	1.65141i
$652$	319310.			0.751133
$653$	−516583.			−1.21147			−0.605736	−	0.795666i	$-0.707121\pi$
$653$	−516583.			−1.21147			−0.605736	+	0.795666i	$0.707121\pi$
$654$		−	203532.i		−	0.475858i
$655$			190121.i			0.443146i
$656$	6626.15			0.0153976
$657$	147730.			0.342245
$658$			386664.i			0.893063i
$659$			459022.i			1.05697i	0.848943	+	0.528485i	$0.177240\pi$
$659$			459022.i			1.05697i	−0.848943	+	0.528485i	$0.822760\pi$
$660$	104891.			0.240798
$661$			167895.i			0.384269i	0.981369	+	0.192134i	$0.0615410\pi$
$661$			167895.i			0.384269i	−0.981369	+	0.192134i	$0.938459\pi$
$662$	422262.			0.963533
$663$		−	30168.6i		−	0.0686323i
$664$			27276.6i			0.0618664i
$665$			236786.i			0.535443i
$666$			120932.i			0.272643i
$667$	−206154.	+	252563.i	−0.463384	+	0.567699i
$668$	−215493.			−0.482925
$669$	−75425.8			−0.168526
$670$	111144.			0.247593
$671$	−363411.			−0.807147
$672$		−	107509.i		−	0.238071i
$673$	96305.2			0.212628			0.106314	−	0.994333i	$-0.466095\pi$
$673$	96305.2			0.212628			0.106314	+	0.994333i	$0.466095\pi$
$674$		−	170510.i		−	0.375345i
$675$	48258.8			0.105918
$676$	209108.			0.457590
$677$			71681.4i			0.156397i	0.996938	+	0.0781987i	$0.0249168\pi$
$677$			71681.4i			0.156397i	−0.996938	+	0.0781987i	$0.975083\pi$
$678$			49724.9i			0.108172i
$679$	333260.			0.722842
$680$	−2885.97			−0.00624129
$681$		−	1.02465e6i		−	2.20944i
$682$			345680.i			0.743200i
$683$	−224335.			−0.480902			−0.240451	−	0.970661i	$-0.577295\pi$
$683$	−224335.			−0.480902			−0.240451	+	0.970661i	$0.577295\pi$
$684$		−	151149.i		−	0.323067i
$685$	169410.			0.361043
$686$		−	303541.i		−	0.645015i
$687$			544318.i			1.15329i
$688$			57712.7i			0.121925i
$689$			710892.i			1.49749i
$690$	−146536.	−	119610.i	−0.307785	−	0.251229i
$691$	−355764.			−0.745084			−0.372542	−	0.928015i	$-0.621514\pi$
$691$	−355764.			−0.745084			−0.372542	+	0.928015i	$0.621514\pi$
$692$	−70486.8			−0.147196
$693$	255249.			0.531493
$694$	−72149.6			−0.149801
$695$			383695.i			0.794358i
$696$	−157682.			−0.325510
$697$		−	1181.09i		−	0.00243118i
$698$	−596969.			−1.22530
$699$	770091.			1.57611
$700$			52524.1i			0.107192i
$701$		−	43241.7i		−	0.0879967i	−0.999032	−	0.0439984i	$-0.985990\pi$
$701$		−	43241.7i		−	0.0879967i	0.999032	−	0.0439984i	$-0.0140096\pi$
$702$	−255390.			−0.518238
$703$	367933.			0.744488
$704$			53101.1i			0.107142i
$705$			329038.i			0.662016i
$706$	−390898.			−0.784250
$707$			286551.i			0.573276i
$708$	−420307.			−0.838494
$709$			701529.i			1.39558i	0.716305	+	0.697788i	$0.245832\pi$
$709$			701529.i			1.39558i	−0.716305	+	0.697788i	$0.754168\pi$
$710$		−	99094.7i		−	0.196577i
$711$			86722.6i			0.171551i
$712$		−	153556.i		−	0.302906i
$713$	394188.	−	482926.i	0.775397	−	0.949951i
$714$	−19163.2			−0.0375899
$715$	271194.			0.530478
$716$	362277.			0.706668
$717$	645588.			1.25579
$718$		−	104414.i		−	0.202540i
$719$	−981820.			−1.89921			−0.949607	−	0.313442i	$-0.898518\pi$
$719$	−981820.			−1.89921			−0.949607	+	0.313442i	$0.898518\pi$
$720$		−	33528.0i		−	0.0646758i
$721$	857077.			1.64873
$722$	−91261.6			−0.175071
$723$		−	617522.i		−	1.18134i
$724$		−	237334.i		−	0.452776i
$725$	77036.4			0.146561
$726$	124238.			0.235712
$727$			542585.i			1.02659i	0.858211	+	0.513297i	$0.171576\pi$
$727$			542585.i			1.02659i	−0.858211	+	0.513297i	$0.828424\pi$
$728$		−	277962.i		−	0.524472i
$729$	−28789.4			−0.0541723
$730$		−	99700.0i		−	0.187090i
$731$	10287.1			0.0192513
$732$			316969.i			0.591554i
$733$			777577.i			1.44722i	0.690207	+	0.723612i	$0.257519\pi$
$733$			777577.i			1.44722i	−0.690207	+	0.723612i	$0.742481\pi$
$734$			748884.i			1.39003i
$735$			45231.2i			0.0837267i
$736$	60552.4	−	74183.8i	0.111783	−	0.136947i
$737$	−364520.			−0.671098
$738$	13721.4			0.0251933
$739$	−335800.			−0.614883			−0.307441	−	0.951567i	$-0.599473\pi$
$739$	−335800.			−0.614883			−0.307441	+	0.951567i	$0.599473\pi$
$740$	81615.1			0.149041
$741$		−	1.06634e6i		−	1.94205i
$742$	451560.			0.820178
$743$		−	433853.i		−	0.785895i	−0.919561	−	0.392948i	$-0.871455\pi$
$743$		−	433853.i		−	0.785895i	0.919561	−	0.392948i	$-0.128545\pi$
$744$	301504.			0.544687
$745$	402430.			0.725066
$746$			227104.i			0.408081i
$747$			56484.3i			0.101225i
$748$	9465.11			0.0169170
$749$	259354.			0.462307
$750$			44696.3i			0.0794601i
$751$			699809.i			1.24079i	0.784288	+	0.620397i	$0.213028\pi$
$751$			699809.i			1.24079i	−0.784288	+	0.620397i	$0.786972\pi$
$752$	−166575.			−0.294560
$753$		−	996001.i		−	1.75659i
$754$	−407683.			−0.717100
$755$		−	124139.i		−	0.217778i
$756$			162224.i			0.283839i
$757$		−	960197.i		−	1.67559i	−0.545983	−	0.837796i	$-0.683844\pi$
$757$		−	960197.i		−	1.67559i	0.545983	−	0.837796i	$-0.316156\pi$
$758$		−	686886.i		−	1.19549i
$759$	480595.	+	392285.i	0.834248	+	0.680955i
$760$	−102008.			−0.176606
$761$	371989.			0.642335			0.321167	−	0.947022i	$-0.395925\pi$
$761$	371989.			0.642335			0.321167	+	0.947022i	$0.395925\pi$
$762$	−295439.			−0.508813
$763$	−334260.			−0.574164
$764$		−	454039.i		−	0.777869i
$765$	−5976.26			−0.0102119
$766$			540450.i			0.921081i
$767$	−1.08669e6			−1.84721
$768$	46315.0			0.0785234
$769$		−	589536.i		−	0.996914i	−0.866914	−	0.498457i	$-0.833900\pi$
$769$		−	589536.i		−	0.996914i	0.866914	−	0.498457i	$-0.166100\pi$
$770$		−	172263.i		−	0.290543i
$771$	−346336.			−0.582624
$772$	−156176.			−0.262048
$773$		−	226761.i		−	0.379498i	−0.981833	−	0.189749i	$-0.939233\pi$
$773$		−	226761.i		−	0.379498i	0.981833	−	0.189749i	$-0.0607674\pi$
$774$			119511.i			0.199493i
$775$	−147301.			−0.245247
$776$			143569.i			0.238416i
$777$	541934.			0.897644
$778$			254828.i			0.421006i
$779$		−	41746.9i		−	0.0687937i
$780$		−	236537.i		−	0.388785i
$781$			325000.i			0.532821i
$782$	−13223.0	−	10793.3i	−0.0216231	−	0.0176498i
$783$	237932.			0.388087
$784$	−22898.2			−0.0372537
$785$	−513585.			−0.833437
$786$	−543852.			−0.880310
$787$		−	464196.i		−	0.749466i	−0.927133	−	0.374733i	$-0.877734\pi$
$787$		−	464196.i		−	0.749466i	0.927133	−	0.374733i	$-0.122266\pi$
$788$	−158792.			−0.255727
$789$		−	866750.i		−	1.39232i
$790$	58527.6			0.0937791
$791$	81663.2			0.130519
$792$			109961.i			0.175303i
$793$			819513.i			1.30320i
$794$	−416344.			−0.660406
$795$	384263.			0.607987
$796$			534509.i			0.843584i
$797$		−	144003.i		−	0.226702i	−0.993555	−	0.113351i	$-0.963841\pi$
$797$		−	144003.i		−	0.226702i	0.993555	−	0.113351i	$-0.0361585\pi$
$798$	−677343.			−1.06366
$799$			29691.5i			0.0465092i
$800$	−22627.4			−0.0353553
$801$		−	317983.i		−	0.495609i
$802$			559414.i			0.869731i
$803$			326985.i			0.507104i
$804$			317936.i			0.491844i
$805$	−196436.	+	240657.i	−0.303130	+	0.371369i
$806$	779530.			1.19995
$807$	691591.			1.06195
$808$	−123446.			−0.189084
$809$	1.08175e6			1.65284			0.826420	−	0.563055i	$-0.190374\pi$
$809$	1.08175e6			1.65284			0.826420	+	0.563055i	$0.190374\pi$
$810$			258068.i			0.393337i
$811$	−260113.			−0.395476			−0.197738	−	0.980255i	$-0.563359\pi$
$811$	−260113.			−0.395476			−0.197738	+	0.980255i	$0.563359\pi$
$812$			258961.i			0.392756i
$813$	1.22719e6			1.85665
$814$	−267672.			−0.403975
$815$		−	446249.i		−	0.671834i
$816$		−	8255.51i		−	0.0123983i
$817$	363609.			0.544741
$818$	−195611.			−0.292338
$819$		−	575602.i		−	0.858133i
$820$		−	9260.32i		−	0.0137720i
$821$	−1.20668e6			−1.79022			−0.895109	−	0.445848i	$-0.852902\pi$
$821$	−1.20668e6			−1.79022			−0.895109	+	0.445848i	$0.852902\pi$
$822$			484609.i			0.717213i
$823$	747213.			1.10318			0.551588	−	0.834117i	$-0.314022\pi$
$823$	747213.			1.10318			0.551588	+	0.834117i	$0.314022\pi$
$824$			369229.i			0.543803i
$825$		−	146590.i		−	0.215376i
$826$			690269.i			1.01172i
$827$			1.09810e6i			1.60558i	0.596261	+	0.802790i	$0.296652\pi$
$827$			1.09810e6i			1.60558i	−0.596261	+	0.802790i	$0.703348\pi$
$828$	125392.	−	153619.i	0.182898	−	0.224071i
$829$	−1.09261e6			−1.58985			−0.794927	−	0.606706i	$-0.792491\pi$
$829$	−1.09261e6			−1.58985			−0.794927	+	0.606706i	$0.792491\pi$
$830$	38120.3			0.0553350
$831$	−35324.9			−0.0511539
$832$	119746.			0.172988
$833$			4081.54i			0.00588212i
$834$	−1.09758e6			−1.57800
$835$			301160.i			0.431941i
$836$	334554.			0.478689
$837$	−454949.			−0.649400
$838$			381735.i			0.543593i
$839$		−	113596.i		−	0.161376i	−0.996739	−	0.0806880i	$-0.974288\pi$
$839$		−	113596.i		−	0.161376i	0.996739	−	0.0806880i	$-0.0257117\pi$
$840$	−150249.			−0.212937
$841$	−327466.			−0.462993
$842$		−	779979.i		−	1.10017i
$843$			1.52731e6i			2.14918i
$844$	−478767.			−0.672109
$845$		−	292237.i		−	0.409281i
$846$	−344943.			−0.481955
$847$		−	204036.i		−	0.284407i
$848$			194532.i			0.270521i
$849$		−	1.29945e6i		−	1.80279i
$850$			4033.27i			0.00558238i
$851$	373946.	+	305234.i	0.516357	+	0.421476i
$852$	283467.			0.390502
$853$	−508647.			−0.699066			−0.349533	−	0.936924i	$-0.613660\pi$
$853$	−508647.			−0.699066			−0.349533	+	0.936924i	$0.613660\pi$
$854$	520557.			0.713761
$855$	−211237.			−0.288960
$856$			111730.i			0.152483i
$857$	−801870.			−1.09180			−0.545899	−	0.837851i	$-0.683812\pi$
$857$	−801870.			−1.09180			−0.545899	+	0.837851i	$0.683812\pi$
$858$			775767.i			1.05380i
$859$	−187493.			−0.254097			−0.127048	−	0.991897i	$-0.540550\pi$
$859$	−187493.			−0.254097			−0.127048	+	0.991897i	$0.540550\pi$
$860$	80655.9			0.109053
$861$		−	61489.6i		−	0.0829460i
$862$		−	21213.1i		−	0.0285489i
$863$	−374275.			−0.502538			−0.251269	−	0.967917i	$-0.580848\pi$
$863$	−374275.			−0.502538			−0.251269	+	0.967917i	$0.580848\pi$
$864$	−69886.2			−0.0936191
$865$			98508.3i			0.131656i
$866$		−	157509.i		−	0.210025i
$867$	942932.			1.25442
$868$		−	495160.i		−	0.657212i
$869$	−191952.			−0.254187
$870$			220368.i			0.291145i
$871$			822014.i			1.08354i
$872$		−	144000.i		−	0.189377i
$873$			297301.i			0.390093i
$874$	−467382.	−	381500.i	−0.611855	−	0.499426i
$875$	73404.7			0.0958755
$876$	285198.			0.371654
$877$	−1.05930e6			−1.37728			−0.688638	−	0.725106i	$-0.741791\pi$
$877$	−1.05930e6			−1.37728			−0.688638	+	0.725106i	$0.741791\pi$
$878$	164485.			0.213372
$879$		−	670523.i		−	0.867833i
$880$	74211.0			0.0958303
$881$			1.45596e6i			1.87585i	0.346839	+	0.937925i	$0.387255\pi$
$881$			1.45596e6i			1.87585i	−0.346839	+	0.937925i	$0.612745\pi$
$882$	−47417.5			−0.0609539
$883$	−715968.			−0.918274			−0.459137	−	0.888366i	$-0.651841\pi$
$883$	−715968.			−0.918274			−0.459137	+	0.888366i	$0.651841\pi$
$884$		−	21344.4i		−	0.0273136i
$885$			587396.i			0.749971i
$886$	−308986.			−0.393615
$887$	284603.			0.361736			0.180868	−	0.983507i	$-0.442109\pi$
$887$	284603.			0.361736			0.180868	+	0.983507i	$0.442109\pi$
$888$			233465.i			0.296071i
$889$			485199.i			0.613927i
$890$	−214601.			−0.270927
$891$		−	846385.i		−	1.06614i
$892$	−53364.0			−0.0670685
$893$			1.04948e6i			1.31604i
$894$			1.15118e6i			1.44035i
$895$		−	506298.i		−	0.632063i
$896$		−	76063.1i		−	0.0947453i
$897$	884627.	−	1.08377e6i	1.09945	−	1.34695i
$898$	−425527.			−0.527685
$899$	−726243.			−0.898592
$900$	−46856.7			−0.0578478
$901$	34674.8			0.0427135
$902$			30371.0i			0.0373290i
$903$	535565.			0.656805
$904$			35180.5i			0.0430492i
$905$	−331685.			−0.404975
$906$	355108.			0.432617
$907$		−	1.01423e6i		−	1.23288i	−0.787400	−	0.616442i	$-0.788573\pi$
$907$		−	1.01423e6i		−	1.23288i	0.787400	−	0.616442i	$-0.211427\pi$
$908$		−	724946.i		−	0.879294i
$909$	−255632.			−0.309377
$910$	−388464.			−0.469102
$911$		−	768539.i		−	0.926039i	−0.886348	−	0.463019i	$-0.846766\pi$
$911$		−	768539.i		−	0.926039i	0.886348	−	0.463019i	$-0.153234\pi$
$912$		−	291799.i		−	0.350828i
$913$	−125023.			−0.149985
$914$		−	352017.i		−	0.421378i
$915$	442977.			0.529102
$916$			385106.i			0.458976i
$917$			893168.i			1.06217i
$918$			12457.0i			0.0147818i
$919$		−	901060.i		−	1.06690i	−0.845833	−	0.533449i	$-0.820896\pi$
$919$		−	901060.i		−	1.06690i	0.845833	−	0.533449i	$-0.179104\pi$
$920$	−103675.	−	84624.6i	−0.122489	−	0.0999818i
$921$	1.39410e6			1.64352
$922$	−41771.1			−0.0491376
$923$	732895.			0.860277
$924$	492770.			0.577165
$925$		−	114061.i		−	0.133307i
$926$	155550.			0.181404
$927$			764598.i			0.889761i
$928$	−111561.			−0.129543
$929$	−716561.			−0.830274			−0.415137	−	0.909759i	$-0.636266\pi$
$929$	−716561.			−0.830274			−0.415137	+	0.909759i	$0.636266\pi$
$930$		−	421365.i		−	0.487183i
$931$			144266.i			0.166443i
$932$	544842.			0.627247
$933$	−81922.2			−0.0941106
$934$		−	521296.i		−	0.597573i
$935$		−	13227.9i		−	0.0151310i
$936$	247970.			0.283039
$937$		−	1.32542e6i		−	1.50964i	−0.655931	−	0.754821i	$-0.727724\pi$
$937$		−	1.32542e6i		−	1.50964i	0.655931	−	0.754821i	$-0.272276\pi$
$938$	522146.			0.593453
$939$			198911.i			0.225594i
$940$			232796.i			0.263463i
$941$			736192.i			0.831403i	0.909501	+	0.415702i	$0.136464\pi$
$941$			736192.i			0.831403i	−0.909501	+	0.415702i	$0.863536\pi$
$942$		−	1.46914e6i		−	1.65563i
$943$	34632.8	−	42429.2i	0.0389461	−	0.0477135i
$944$	−297368.			−0.333696
$945$	226715.			0.253873
$946$	−264527.			−0.295588
$947$	562677.			0.627421			0.313711	−	0.949519i	$-0.398428\pi$
$947$	562677.			0.627421			0.313711	+	0.949519i	$0.398428\pi$
$948$			167422.i			0.186293i
$949$	737372.			0.818756
$950$			142560.i			0.157961i
$951$	−1.53182e6			−1.69374
$952$	−13558.0			−0.0149597
$953$		−	1.68404e6i		−	1.85425i	−0.374758	−	0.927123i	$-0.622274\pi$
$953$		−	1.68404e6i		−	1.85425i	0.374758	−	0.927123i	$-0.377726\pi$
$954$			402837.i			0.442621i
$955$	−634539.			−0.695747
$956$	456756.			0.499768
$957$		−	722738.i		−	0.789145i
$958$		−	90748.5i		−	0.0988800i
$959$	795873.			0.865380
$960$		−	64727.2i		−	0.0702335i
$961$	465128.			0.503646
$962$			603618.i			0.652247i
$963$			231370.i			0.249491i
$964$		−	436899.i		−	0.470140i
$965$			218263.i			0.234383i
$966$	−688414.	−	561917.i	−0.737726	−	0.602169i
$967$	−784051.			−0.838478			−0.419239	−	0.907876i	$-0.637703\pi$
$967$	−784051.			−0.838478			−0.419239	+	0.907876i	$0.637703\pi$
$968$	87898.8			0.0938063
$969$	−52012.4			−0.0553936
$970$	200643.			0.213246
$971$		−	1.06124e6i		−	1.12558i	−0.826600	−	0.562790i	$-0.809728\pi$
$971$		−	1.06124e6i		−	1.12558i	0.826600	−	0.562790i	$-0.190272\pi$
$972$	−488048.			−0.516571
$973$			1.80256e6i			1.90399i
$974$	1.18926e6			1.25360
$975$	−330570.			−0.347740
$976$			224256.i			0.235421i
$977$		−	925795.i		−	0.969897i	−0.874543	−	0.484949i	$-0.838838\pi$
$977$		−	925795.i		−	0.969897i	0.874543	−	0.484949i	$-0.161162\pi$
$978$	1.27652e6			1.33460
$979$	703827.			0.734345
$980$			32001.2i			0.0333207i
$981$		−	298194.i		−	0.309856i
$982$	441781.			0.458125
$983$		−	874857.i		−	0.905378i	−0.891668	−	0.452689i	$-0.850465\pi$
$983$		−	874857.i		−	0.905378i	0.891668	−	0.452689i	$-0.149535\pi$
$984$	26489.8			0.0273582
$985$			221918.i			0.228729i
$986$			19885.3i			0.0204541i
$987$			1.54579e6i			1.58678i
$988$		−	754439.i		−	0.772877i
$989$	369552.	+	301646.i	0.377818	+	0.308394i
$990$	153676.			0.156796
$991$	1.43394e6			1.46010			0.730052	−	0.683391i	$-0.239496\pi$
$991$	1.43394e6			1.46010			0.730052	+	0.683391i	$0.239496\pi$
$992$	213315.			0.216769
$993$	1.68810e6			1.71199
$994$		−	465537.i		−	0.471174i
$995$	746998.			0.754525
$996$			109045.i			0.109923i
$997$	−1.12924e6			−1.13604			−0.568021	−	0.823014i	$-0.692291\pi$
$997$	−1.12924e6			−1.13604			−0.568021	+	0.823014i	$0.692291\pi$
$998$	1.03338e6			1.03753
$999$		−	352283.i		−	0.352989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.d.a.91.19	✓	32
23.22	odd	2	inner	230.5.d.a.91.30	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.d.a.91.19	✓	32	1.1	even	1	trivial
230.5.d.a.91.30	yes	32	23.22	odd	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843 q^{2} +11.3074 q^{3} +8.00000 q^{4} -11.1803i q^{5} +31.9821 q^{6} -52.5241i q^{7} +22.6274 q^{8} +46.8567 q^{9} +O(q^{10})\)	\(q+2.82843 q^{2} +11.3074 q^{3} +8.00000 q^{4} -11.1803i q^{5} +31.9821 q^{6} -52.5241i q^{7} +22.6274 q^{8} +46.8567 q^{9} -31.6228i q^{10} +103.713i q^{11} +90.4590 q^{12} +233.879 q^{13} -148.561i q^{14} -126.420i q^{15} +64.0000 q^{16} -11.4078i q^{17} +132.531 q^{18} -403.221i q^{19} -89.4427i q^{20} -593.910i q^{21} +293.345i q^{22} +(334.508 - 409.811i) q^{23} +255.857 q^{24} -125.000 q^{25} +661.510 q^{26} -386.071 q^{27} -420.193i q^{28} -616.291 q^{29} -357.571i q^{30} +1178.41 q^{31} +181.019 q^{32} +1172.72i q^{33} -32.2662i q^{34} -587.238 q^{35} +374.854 q^{36} +912.484i q^{37} -1140.48i q^{38} +2644.56 q^{39} -252.982i q^{40} +103.534 q^{41} -1679.83i q^{42} +901.761i q^{43} +829.704i q^{44} -523.874i q^{45} +(946.132 - 1159.12i) q^{46} -2602.73 q^{47} +723.672 q^{48} -357.785 q^{49} -353.553 q^{50} -128.992i q^{51} +1871.03 q^{52} +3039.57i q^{53} -1091.97 q^{54} +1159.55 q^{55} -1188.49i q^{56} -4559.37i q^{57} -1743.13 q^{58} -4646.38 q^{59} -1011.36i q^{60} +3504.00i q^{61} +3333.05 q^{62} -2461.11i q^{63} +512.000 q^{64} -2614.85i q^{65} +3316.96i q^{66} +3514.70i q^{67} -91.2625i q^{68} +(3782.41 - 4633.89i) q^{69} -1660.96 q^{70} +3133.65 q^{71} +1060.25 q^{72} +3152.79 q^{73} +2580.90i q^{74} -1413.42 q^{75} -3225.76i q^{76} +5447.44 q^{77} +7479.94 q^{78} +1850.80i q^{79} -715.542i q^{80} -8160.84 q^{81} +292.837 q^{82} +1205.47i q^{83} -4751.28i q^{84} -127.543 q^{85} +2550.57i q^{86} -6968.63 q^{87} +2346.76i q^{88} -6786.29i q^{89} -1481.74i q^{90} -12284.3i q^{91} +(2676.07 - 3278.49i) q^{92} +13324.7 q^{93} -7361.64 q^{94} -4508.14 q^{95} +2046.85 q^{96} +6344.89i q^{97} -1011.97 q^{98} +4859.65i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9}+O(q^{10}) \) 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9	\( 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9} - 408 q^{13} + 2048 q^{16} + 1024 q^{18} + 1332 q^{23} + 512 q^{24} - 4000 q^{25} + 2208 q^{27} + 3732 q^{29} - 412 q^{31} + 300 q^{35} + 6656 q^{36} - 9208 q^{39} - 6156 q^{41} + 4480 q^{46} + 5184 q^{47} - 13820 q^{49} - 3264 q^{52} - 3328 q^{54} - 6000 q^{55} + 3200 q^{58} - 30468 q^{59} - 10752 q^{62} + 16384 q^{64} - 1168 q^{69} + 4800 q^{70} - 37644 q^{71} + 8192 q^{72} + 19984 q^{73} + 27528 q^{77} + 15744 q^{78} + 69056 q^{81} - 17408 q^{82} + 3300 q^{85} + 28936 q^{87} + 10656 q^{92} + 40648 q^{93} - 23808 q^{94} - 21600 q^{95} + 4096 q^{96} + 43008 q^{98}+O(q^{100}) \) 32 * q + 256 * q^4 + 64 * q^6 + 832 * q^9 - 408 * q^13 + 2048 * q^16 + 1024 * q^18 + 1332 * q^23 + 512 * q^24 - 4000 * q^25 + 2208 * q^27 + 3732 * q^29 - 412 * q^31 + 300 * q^35 + 6656 * q^36 - 9208 * q^39 - 6156 * q^41 + 4480 * q^46 + 5184 * q^47 - 13820 * q^49 - 3264 * q^52 - 3328 * q^54 - 6000 * q^55 + 3200 * q^58 - 30468 * q^59 - 10752 * q^62 + 16384 * q^64 - 1168 * q^69 + 4800 * q^70 - 37644 * q^71 + 8192 * q^72 + 19984 * q^73 + 27528 * q^77 + 15744 * q^78 + 69056 * q^81 - 17408 * q^82 + 3300 * q^85 + 28936 * q^87 + 10656 * q^92 + 40648 * q^93 - 23808 * q^94 - 21600 * q^95 + 4096 * q^96 + 43008 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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