LMFDB - Embedded newform 230.5.c.a.229.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(229,230)]

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([1, 1]))

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

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

chi := DirichletCharacter("230.229");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.c (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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.1
Character	$\chi$	$=$	230.229
Dual form			230.5.c.a.229.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} -9.09812i q^{3} -8.00000 q^{4} +(-21.5641 + 12.6486i) q^{5} -25.7334 q^{6} +94.0651 q^{7} +22.6274i q^{8} -1.77586 q^{9} +O(q^{10})$	\(q-2.82843i q^{2} -9.09812i q^{3} -8.00000 q^{4} +(-21.5641 + 12.6486i) q^{5} -25.7334 q^{6} +94.0651 q^{7} +22.6274i q^{8} -1.77586 q^{9} +(35.7757 + 60.9926i) q^{10} -189.571i q^{11} +72.7850i q^{12} -27.4274i q^{13} -266.056i q^{14} +(115.079 + 196.193i) q^{15} +64.0000 q^{16} +179.847 q^{17} +5.02288i q^{18} -320.508i q^{19} +(172.513 - 101.189i) q^{20} -855.816i q^{21} -536.187 q^{22} +(-117.888 + 515.697i) q^{23} +205.867 q^{24} +(305.024 - 545.514i) q^{25} -77.5763 q^{26} -720.791i q^{27} -752.520 q^{28} -801.113 q^{29} +(554.918 - 325.492i) q^{30} -714.903 q^{31} -181.019i q^{32} -1724.74 q^{33} -508.685i q^{34} +(-2028.43 + 1189.79i) q^{35} +14.2069 q^{36} +1763.54 q^{37} -906.533 q^{38} -249.537 q^{39} +(-286.206 - 487.941i) q^{40} +990.461 q^{41} -2420.61 q^{42} -1570.28 q^{43} +1516.57i q^{44} +(38.2948 - 22.4622i) q^{45} +(1458.61 + 333.436i) q^{46} +992.778i q^{47} -582.280i q^{48} +6447.24 q^{49} +(-1542.95 - 862.738i) q^{50} -1636.27i q^{51} +219.419i q^{52} -1104.67 q^{53} -2038.70 q^{54} +(2397.81 + 4087.93i) q^{55} +2128.45i q^{56} -2916.02 q^{57} +2265.89i q^{58} -4652.38 q^{59} +(-920.631 - 1569.55i) q^{60} -3794.84i q^{61} +2022.05i q^{62} -167.046 q^{63} -512.000 q^{64} +(346.919 + 591.447i) q^{65} +4878.30i q^{66} -4644.30 q^{67} -1438.78 q^{68} +(4691.88 + 1072.56i) q^{69} +(3365.25 + 5737.27i) q^{70} -3892.76 q^{71} -40.1831i q^{72} -4789.25i q^{73} -4988.03i q^{74} +(-4963.15 - 2775.15i) q^{75} +2564.06i q^{76} -17832.0i q^{77} +705.799i q^{78} -7382.38i q^{79} +(-1380.10 + 809.513i) q^{80} -6701.69 q^{81} -2801.45i q^{82} -940.014 q^{83} +6846.52i q^{84} +(-3878.25 + 2274.83i) q^{85} +4441.42i q^{86} +7288.63i q^{87} +4289.50 q^{88} -10344.7i q^{89} +(-63.5326 - 108.314i) q^{90} -2579.96i q^{91} +(943.100 - 4125.58i) q^{92} +6504.28i q^{93} +2808.00 q^{94} +(4053.99 + 6911.48i) q^{95} -1646.94 q^{96} +3384.03 q^{97} -18235.5i q^{98} +336.651i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9}+O(q^{10}) $ 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9	$ 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9} + 3072 q^{16} + 512 q^{24} + 1488 q^{25} - 384 q^{26} - 2940 q^{29} + 4732 q^{31} + 2556 q^{35} + 12864 q^{36} + 2736 q^{39} + 828 q^{41} - 64 q^{46} + 32572 q^{49} - 3264 q^{50} + 10112 q^{54} + 12824 q^{55} + 7092 q^{59} - 24576 q^{64} + 14000 q^{69} - 6592 q^{70} - 12708 q^{71} + 24728 q^{75} - 13040 q^{81} - 15700 q^{85} - 9728 q^{94} - 46608 q^{95} - 4096 q^{96}+O(q^{100}) $ 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9 + 3072 * q^16 + 512 * q^24 + 1488 * q^25 - 384 * q^26 - 2940 * q^29 + 4732 * q^31 + 2556 * q^35 + 12864 * q^36 + 2736 * q^39 + 828 * q^41 - 64 * q^46 + 32572 * q^49 - 3264 * q^50 + 10112 * q^54 + 12824 * q^55 + 7092 * q^59 - 24576 * q^64 + 14000 * q^69 - 6592 * q^70 - 12708 * q^71 + 24728 * q^75 - 13040 * q^81 - 15700 * q^85 - 9728 * q^94 - 46608 * q^95 - 4096 * q^96

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 $

$2$		−	2.82843i		−	0.707107i
$2$		−	2.82843i		−	0.707107i
$3$		−	9.09812i		−	1.01090i	−0.862855	−	0.505451i	$-0.831326\pi$
$3$		−	9.09812i		−	1.01090i	0.862855	−	0.505451i	$-0.168674\pi$
$4$	−8.00000			−0.500000
$5$	−21.5641	+	12.6486i	−0.862565	+	0.505946i
$5$	−21.5641	+	12.6486i	−0.862565	+	0.505946i
$6$	−25.7334			−0.714816
$7$	94.0651			1.91970			0.959848	−	0.280522i	$-0.0905076\pi$
$7$	94.0651			1.91970			0.959848	+	0.280522i	$0.0905076\pi$
$8$			22.6274i			0.353553i
$9$	−1.77586			−0.0219242
$10$	35.7757	+	60.9926i	0.357757	+	0.609926i
$11$		−	189.571i		−	1.56670i	−0.621580	−	0.783350i	$-0.713509\pi$
$11$		−	189.571i		−	1.56670i	0.621580	−	0.783350i	$-0.286491\pi$
$12$			72.7850i			0.505451i
$13$		−	27.4274i		−	0.162292i	−0.996702	−	0.0811460i	$-0.974142\pi$
$13$		−	27.4274i		−	0.162292i	0.996702	−	0.0811460i	$-0.0258580\pi$
$14$		−	266.056i		−	1.35743i
$15$	115.079	+	196.193i	0.511462	+	0.871970i
$16$	64.0000			0.250000
$17$	179.847			0.622309			0.311155	−	0.950359i	$-0.399284\pi$
$17$	179.847			0.622309			0.311155	+	0.950359i	$0.399284\pi$
$18$			5.02288i			0.0155027i
$19$		−	320.508i		−	0.887833i	−0.896068	−	0.443917i	$-0.853589\pi$
$19$		−	320.508i		−	0.887833i	0.896068	−	0.443917i	$-0.146411\pi$
$20$	172.513	−	101.189i	0.431283	−	0.252973i
$21$		−	855.816i		−	1.94062i
$22$	−536.187			−1.10782
$23$	−117.888	+	515.697i	−0.222850	+	0.974853i
$23$	−117.888	+	515.697i	−0.222850	+	0.974853i
$24$	205.867			0.357408
$25$	305.024	−	545.514i	0.488038	−	0.872822i
$26$	−77.5763			−0.114758
$27$		−	720.791i		−	0.988739i
$28$	−752.520			−0.959848
$29$	−801.113			−0.952572			−0.476286	−	0.879290i	$-0.658017\pi$
$29$	−801.113			−0.952572			−0.476286	+	0.879290i	$0.658017\pi$
$30$	554.918	−	325.492i	0.616576	−	0.361658i
$31$	−714.903			−0.743916			−0.371958	−	0.928250i	$-0.621313\pi$
$31$	−714.903			−0.743916			−0.371958	+	0.928250i	$0.621313\pi$
$32$		−	181.019i		−	0.176777i
$33$	−1724.74			−1.58378
$34$		−	508.685i		−	0.440039i
$35$	−2028.43	+	1189.79i	−1.65586	+	0.971261i
$36$	14.2069			0.0109621
$37$	1763.54			1.28819			0.644097	−	0.764944i	$-0.277233\pi$
$37$	1763.54			1.28819			0.644097	+	0.764944i	$0.277233\pi$
$38$	−906.533			−0.627793
$39$	−249.537			−0.164061
$40$	−286.206	−	487.941i	−0.178879	−	0.304963i
$41$	990.461			0.589210			0.294605	−	0.955619i	$-0.404812\pi$
$41$	990.461			0.589210			0.294605	+	0.955619i	$0.404812\pi$
$42$	−2420.61			−1.37223
$43$	−1570.28			−0.849258			−0.424629	−	0.905367i	$-0.639596\pi$
$43$	−1570.28			−0.849258			−0.424629	+	0.905367i	$0.639596\pi$
$44$			1516.57i			0.783350i
$45$	38.2948	−	22.4622i	0.0189110	−	0.0110924i
$46$	1458.61	+	333.436i	0.689325	+	0.157579i
$47$			992.778i			0.449424i	0.974425	+	0.224712i	$0.0721441\pi$
$47$			992.778i			0.449424i	−0.974425	+	0.224712i	$0.927856\pi$
$48$		−	582.280i		−	0.252726i
$49$	6447.24			2.68523
$50$	−1542.95	−	862.738i	−0.617179	−	0.345095i
$51$		−	1636.27i		−	0.629094i
$52$			219.419i			0.0811460i
$53$	−1104.67			−0.393260			−0.196630	−	0.980478i	$-0.563000\pi$
$53$	−1104.67			−0.393260			−0.196630	+	0.980478i	$0.563000\pi$
$54$	−2038.70			−0.699144
$55$	2397.81	+	4087.93i	0.792665	+	1.35138i
$56$			2128.45i			0.678715i
$57$	−2916.02			−0.897513
$58$			2265.89i			0.673570i
$59$	−4652.38			−1.33651			−0.668253	−	0.743934i	$-0.732958\pi$
$59$	−4652.38			−1.33651			−0.668253	+	0.743934i	$0.732958\pi$
$60$	−920.631	−	1569.55i	−0.255731	−	0.435985i
$61$		−	3794.84i		−	1.01984i	−0.860221	−	0.509922i	$-0.829674\pi$
$61$		−	3794.84i		−	1.01984i	0.860221	−	0.509922i	$-0.170326\pi$
$62$			2022.05i			0.526028i
$63$	−167.046			−0.0420877
$64$	−512.000			−0.125000
$65$	346.919	+	591.447i	0.0821109	+	0.139988i
$66$			4878.30i			1.11990i
$67$	−4644.30			−1.03460			−0.517298	−	0.855805i	$-0.673062\pi$
$67$	−4644.30			−1.03460			−0.517298	+	0.855805i	$0.673062\pi$
$68$	−1438.78			−0.311155
$69$	4691.88	+	1072.56i	0.985481	+	0.225279i
$70$	3365.25	+	5737.27i	0.686785	+	1.17087i
$71$	−3892.76			−0.772220			−0.386110	−	0.922453i	$-0.626181\pi$
$71$	−3892.76			−0.772220			−0.386110	+	0.922453i	$0.626181\pi$
$72$		−	40.1831i		−	0.00775136i
$73$		−	4789.25i		−	0.898714i	−0.893352	−	0.449357i	$-0.851653\pi$
$73$		−	4789.25i		−	0.898714i	0.893352	−	0.449357i	$-0.148347\pi$
$74$		−	4988.03i		−	0.910890i
$75$	−4963.15	−	2775.15i	−0.882338	−	0.493359i
$76$			2564.06i			0.443917i
$77$		−	17832.0i		−	3.00759i
$78$			705.799i			0.116009i
$79$		−	7382.38i		−	1.18288i	−0.806347	−	0.591442i	$-0.798559\pi$
$79$		−	7382.38i		−	1.18288i	0.806347	−	0.591442i	$-0.201441\pi$
$80$	−1380.10	+	809.513i	−0.215641	+	0.126486i
$81$	−6701.69			−1.02144
$82$		−	2801.45i		−	0.416634i
$83$	−940.014			−0.136451			−0.0682257	−	0.997670i	$-0.521734\pi$
$83$	−940.014			−0.136451			−0.0682257	+	0.997670i	$0.521734\pi$
$84$			6846.52i			0.970312i
$85$	−3878.25	+	2274.83i	−0.536783	+	0.314855i
$86$			4441.42i			0.600516i
$87$			7288.63i			0.962958i
$88$	4289.50			0.553912
$89$		−	10344.7i		−	1.30599i	−0.757364	−	0.652993i	$-0.773513\pi$
$89$		−	10344.7i		−	1.30599i	0.757364	−	0.652993i	$-0.226487\pi$
$90$	−63.5326	−	108.314i	−0.00784353	−	0.0133721i
$91$		−	2579.96i		−	0.311551i
$92$	943.100	−	4125.58i	0.111425	−	0.487426i
$93$			6504.28i			0.752027i
$94$	2808.00			0.317791
$95$	4053.99	+	6911.48i	0.449195	+	0.765814i
$96$	−1646.94			−0.178704
$97$	3384.03			0.359659			0.179829	−	0.983698i	$-0.442445\pi$
$97$	3384.03			0.359659			0.179829	+	0.983698i	$0.442445\pi$
$98$		−	18235.5i		−	1.89874i
$99$			336.651i			0.0343486i
$100$	−2440.19	+	4364.11i	−0.244019	+	0.436411i
$101$	−2234.30			−0.219027			−0.109514	−	0.993985i	$-0.534929\pi$
$101$	−2234.30			−0.219027			−0.109514	+	0.993985i	$0.534929\pi$
$102$	−4628.08			−0.444837
$103$	16070.8			1.51482			0.757412	−	0.652938i	$-0.226464\pi$
$103$	16070.8			1.51482			0.757412	+	0.652938i	$0.226464\pi$
$104$	620.610			0.0573789
$105$	10824.9	+	18454.9i	0.981850	+	1.67392i
$106$			3124.47i			0.278077i
$107$	−2230.86			−0.194852			−0.0974260	−	0.995243i	$-0.531061\pi$
$107$	−2230.86			−0.194852			−0.0974260	+	0.995243i	$0.531061\pi$
$108$			5766.33i			0.494370i
$109$			6239.15i			0.525137i	0.964913	+	0.262568i	$0.0845695\pi$
$109$			6239.15i			0.525137i	−0.964913	+	0.262568i	$0.915430\pi$
$110$	11562.4	−	6782.04i	0.955571	−	0.560499i
$111$		−	16044.9i		−	1.30224i
$112$	6020.16			0.479924
$113$	24507.1			1.91927			0.959635	−	0.281250i	$-0.0907489\pi$
$113$	24507.1			1.91927			0.959635	+	0.281250i	$0.0907489\pi$
$114$			8247.75i			0.634638i
$115$	−3980.72	−	12611.7i	−0.301000	−	0.953624i
$116$	6408.90			0.476286
$117$			48.7071i			0.00355812i
$118$			13158.9i			0.945052i
$119$	16917.4			1.19464
$120$	−4439.34	+	2603.94i	−0.308288	+	0.180829i
$121$	−21296.1			−1.45455
$122$	−10733.4			−0.721139
$123$		−	9011.34i		−	0.595634i
$124$	5719.23			0.371958
$125$	322.430	+	15621.7i	0.0206355	+	0.999787i
$126$			472.478i			0.0297605i
$127$			17165.5i			1.06427i	0.846661	+	0.532133i	$0.178609\pi$
$127$			17165.5i			1.06427i	−0.846661	+	0.532133i	$0.821391\pi$
$128$			1448.15i			0.0883883i
$129$			14286.6i			0.858517i
$130$	1672.87	−	981.234i	0.0989861	−	0.0580612i
$131$	−26268.1			−1.53068			−0.765342	−	0.643624i	$-0.777430\pi$
$131$	−26268.1			−1.53068			−0.765342	+	0.643624i	$0.777430\pi$
$132$	13797.9			0.791891
$133$		−	30148.6i		−	1.70437i
$134$			13136.1i			0.731570i
$135$	9117.02	+	15543.2i	0.500248	+	0.852852i
$136$			4069.48i			0.220020i
$137$	7284.79			0.388129			0.194064	−	0.980989i	$-0.437833\pi$
$137$	7284.79			0.388129			0.194064	+	0.980989i	$0.437833\pi$
$138$	3033.64	−	13270.6i	0.159297	−	0.696840i
$139$	−1463.89			−0.0757667			−0.0378834	−	0.999282i	$-0.512062\pi$
$139$	−1463.89			−0.0757667			−0.0378834	+	0.999282i	$0.512062\pi$
$140$	16227.5	−	9518.36i	0.827931	−	0.485631i
$141$	9032.42			0.454324
$142$			11010.4i			0.546042i
$143$	−5199.43			−0.254263
$144$	−113.655			−0.00548104
$145$	17275.3	−	10133.0i	0.821656	−	0.481950i
$146$	−13546.0			−0.635487
$147$		−	58657.7i		−	2.71451i
$148$	−14108.3			−0.644097
$149$		−	12331.3i		−	0.555439i	−0.960662	−	0.277719i	$-0.910421\pi$
$149$		−	12331.3i		−	0.555439i	0.960662	−	0.277719i	$-0.0895785\pi$
$150$	−7849.30	+	14037.9i	−0.348858	+	0.623907i
$151$	838.095			0.0367570			0.0183785	−	0.999831i	$-0.494150\pi$
$151$	838.095			0.0367570			0.0183785	+	0.999831i	$0.494150\pi$
$152$	7252.27			0.313897
$153$	−319.383			−0.0136436
$154$	−50436.5			−2.12669
$155$	15416.3	−	9042.55i	0.641676	−	0.376381i
$156$	1996.30			0.0820307
$157$	41094.1			1.66717			0.833586	−	0.552390i	$-0.186284\pi$
$157$	41094.1			1.66717			0.833586	+	0.552390i	$0.186284\pi$
$158$	−20880.5			−0.836426
$159$			10050.4i			0.397548i
$160$	2289.65	+	3903.53i	0.0894394	+	0.152481i
$161$	−11089.1	+	48509.1i	−0.427804	+	1.87142i
$162$			18955.2i			0.722270i
$163$		−	27517.7i		−	1.03571i	−0.855469	−	0.517853i	$-0.826731\pi$
$163$		−	27517.7i		−	1.03571i	0.855469	−	0.517853i	$-0.173269\pi$
$164$	−7923.69			−0.294605
$165$	37192.5	−	21815.6i	1.36612	−	0.801307i
$166$			2658.76i			0.0964857i
$167$			24224.8i			0.868613i	0.900765	+	0.434307i	$0.143007\pi$
$167$			24224.8i			0.868613i	−0.900765	+	0.434307i	$0.856993\pi$
$168$	19364.9			0.686114
$169$	27808.7			0.973661
$170$	6434.18	+	10969.4i	0.222636	+	0.379563i
$171$			569.176i			0.0194650i
$172$	12562.2			0.424629
$173$			44448.6i			1.48514i	0.669771	+	0.742568i	$0.266392\pi$
$173$			44448.6i			1.48514i	−0.669771	+	0.742568i	$0.733608\pi$
$174$	20615.3			0.680914
$175$	28692.1	−	51313.8i	0.936885	−	1.67555i
$176$		−	12132.5i		−	0.391675i
$177$			42327.9i			1.35108i
$178$	−29259.3			−0.923471
$179$	56141.5			1.75218			0.876089	−	0.482150i	$-0.160144\pi$
$179$	56141.5			1.75218			0.876089	+	0.482150i	$0.160144\pi$
$180$	−306.359	+	179.697i	−0.00945551	+	0.00554622i
$181$			41955.1i			1.28064i	0.768107	+	0.640321i	$0.221199\pi$
$181$			41955.1i			1.28064i	−0.768107	+	0.640321i	$0.778801\pi$
$182$	−7297.22			−0.220300
$183$	−34525.9			−1.03096
$184$	−11668.9	−	2667.49i	−0.344663	−	0.0787893i
$185$	−38029.1	+	22306.3i	−1.11115	+	0.651756i
$186$	18396.9			0.531763
$187$		−	34093.8i		−	0.974973i
$188$		−	7942.22i		−	0.224712i
$189$		−	67801.3i		−	1.89808i
$190$	19548.6	−	11466.4i	0.541513	−	0.317629i
$191$			8678.66i			0.237895i	0.992901	+	0.118948i	$0.0379521\pi$
$191$			8678.66i			0.237895i	−0.992901	+	0.118948i	$0.962048\pi$
$192$			4658.24i			0.126363i
$193$		−	60484.1i		−	1.62378i	−0.583813	−	0.811888i	$-0.698440\pi$
$193$		−	60484.1i		−	1.62378i	0.583813	−	0.811888i	$-0.301560\pi$
$194$		−	9571.48i		−	0.254317i
$195$	5381.06	−	3156.31i	0.141514	−	0.0830062i
$196$	−51577.9			−1.34261
$197$			63134.5i			1.62680i	0.581705	+	0.813400i	$0.302386\pi$
$197$			63134.5i			1.62680i	−0.581705	+	0.813400i	$0.697614\pi$
$198$	952.192			0.0242881
$199$			2109.28i			0.0532633i	0.999645	+	0.0266317i	$0.00847812\pi$
$199$			2109.28i			0.0532633i	−0.999645	+	0.0266317i	$0.991522\pi$
$200$	12343.6	+	6901.90i	0.308589	+	0.172548i
$201$			42254.4i			1.04588i
$202$			6319.54i			0.154876i
$203$	−75356.7			−1.82865
$204$			13090.2i			0.314547i
$205$	−21358.4	+	12528.0i	−0.508232	+	0.298108i
$206$		−	45455.0i		−	1.07114i
$207$	209.351	−	915.804i	0.00488579	−	0.0213728i
$208$		−	1755.35i		−	0.0405730i
$209$	−60758.9			−1.39097
$210$	52198.4	−	30617.4i	1.18364	−	0.694273i
$211$	5662.44			0.127186			0.0635930	−	0.997976i	$-0.479744\pi$
$211$	5662.44			0.127186			0.0635930	+	0.997976i	$0.479744\pi$
$212$	8837.34			0.196630
$213$			35416.8i			0.780639i
$214$			6309.82i			0.137781i
$215$	33861.7	−	19861.9i	0.732541	−	0.429678i
$216$	16309.6			0.349572
$217$	−67247.4			−1.42809
$218$	17647.0			0.371328
$219$	−43573.1			−0.908512
$220$	−19182.5	−	32703.4i	−0.396333	−	0.675691i
$221$		−	4932.74i		−	0.100996i
$222$	−45381.8			−0.920821
$223$			70937.9i			1.42649i	0.700915	+	0.713245i	$0.252775\pi$
$223$			70937.9i			1.42649i	−0.700915	+	0.713245i	$0.747225\pi$
$224$		−	17027.6i		−	0.339357i
$225$	−541.679	+	968.755i	−0.0106998	+	0.0191359i
$226$		−	69316.7i		−	1.35713i
$227$	82861.6			1.60806			0.804028	−	0.594591i	$-0.202686\pi$
$227$	82861.6			1.60806			0.804028	+	0.594591i	$0.202686\pi$
$228$	23328.2			0.448757
$229$			40934.5i			0.780583i	0.920691	+	0.390291i	$0.127626\pi$
$229$			40934.5i			0.780583i	−0.920691	+	0.390291i	$0.872374\pi$
$230$	−35671.2	+	11259.2i	−0.674314	+	0.212839i
$231$	−162238.			−3.04038
$232$		−	18127.1i		−	0.336785i
$233$		−	21322.8i		−	0.392764i	−0.980527	−	0.196382i	$-0.937081\pi$
$233$		−	21322.8i		−	0.392764i	0.980527	−	0.196382i	$-0.0629193\pi$
$234$	137.764			0.00251597
$235$	−12557.3	−	21408.4i	−0.227384	−	0.387658i
$236$	37219.0			0.668253
$237$	−67165.8			−1.19578
$238$		−	47849.5i		−	0.844741i
$239$	6241.60			0.109270			0.0546349	−	0.998506i	$-0.482601\pi$
$239$	6241.60			0.109270			0.0546349	+	0.998506i	$0.482601\pi$
$240$	7365.05	+	12556.4i	0.127865	+	0.217992i
$241$		−	6759.58i		−	0.116382i	−0.998305	−	0.0581909i	$-0.981467\pi$
$241$		−	6759.58i		−	0.116382i	0.998305	−	0.0581909i	$-0.0185332\pi$
$242$			60234.4i			1.02852i
$243$			2588.74i			0.0438405i
$244$			30358.7i			0.509922i
$245$	−139029.	+	81548.7i	−2.31619	+	1.35858i
$246$	−25487.9			−0.421177
$247$	−8790.68			−0.144088
$248$		−	16176.4i		−	0.263014i
$249$			8552.36i			0.137939i
$250$	44184.8	−	911.969i	0.706956	−	0.0145915i
$251$		−	35038.1i		−	0.556151i	−0.960559	−	0.278076i	$-0.910303\pi$
$251$		−	35038.1i		−	0.556151i	0.960559	−	0.278076i	$-0.0896966\pi$
$252$	1336.37			0.0210439
$253$	97761.1	+	22348.0i	1.52730	+	0.349139i
$254$	48551.5			0.752550
$255$	20696.6	+	35284.8i	0.318287	+	0.542635i
$256$	4096.00			0.0625000
$257$		−	45117.0i		−	0.683084i	−0.939867	−	0.341542i	$-0.889051\pi$
$257$		−	45117.0i		−	0.683084i	0.939867	−	0.341542i	$-0.110949\pi$
$258$	40408.6			0.607063
$259$	165887.			2.47294
$260$	−2775.35	−	4731.58i	−0.0410555	−	0.0699938i
$261$	1422.66			0.0208843
$262$			74297.3i			1.08236i
$263$	−100629.			−1.45482			−0.727412	−	0.686201i	$-0.759277\pi$
$263$	−100629.			−1.45482			−0.727412	+	0.686201i	$0.759277\pi$
$264$		−	39026.4i		−	0.559952i
$265$	23821.2	−	13972.5i	0.339213	−	0.198968i
$266$	−85273.1			−1.20517
$267$	−94117.5			−1.32022
$268$	37154.4			0.517298
$269$	95645.3			1.32178			0.660890	−	0.750483i	$-0.270179\pi$
$269$	95645.3			1.32178			0.660890	+	0.750483i	$0.270179\pi$
$270$	43962.9	−	25786.8i	0.603058	−	0.353729i
$271$	5890.57			0.0802082			0.0401041	−	0.999196i	$-0.487231\pi$
$271$	5890.57			0.0802082			0.0401041	+	0.999196i	$0.487231\pi$
$272$	11510.2			0.155577
$273$	−23472.8			−0.314948
$274$		−	20604.5i		−	0.274448i
$275$	−103414.	−	57823.6i	−1.36745	−	0.764610i
$276$	−37535.0	−	8580.44i	−0.492741	−	0.112640i
$277$		−	73925.2i		−	0.963458i	−0.876320	−	0.481729i	$-0.840009\pi$
$277$		−	73925.2i		−	0.963458i	0.876320	−	0.481729i	$-0.159991\pi$
$278$			4140.50i			0.0535752i
$279$	1269.57			0.0163097
$280$	−26922.0	−	45898.2i	−0.343393	−	0.585436i
$281$		−	10603.5i		−	0.134288i	−0.997743	−	0.0671439i	$-0.978611\pi$
$281$		−	10603.5i		−	0.134288i	0.997743	−	0.0671439i	$-0.0213887\pi$
$282$		−	25547.5i		−	0.321256i
$283$	60720.2			0.758159			0.379080	−	0.925364i	$-0.376241\pi$
$283$	60720.2			0.758159			0.379080	+	0.925364i	$0.376241\pi$
$284$	31142.1			0.386110
$285$	62881.5	−	36883.7i	0.774164	−	0.454093i
$286$			14706.2i			0.179791i
$287$	93167.8			1.13110
$288$			321.464i			0.00387568i
$289$	−51175.9			−0.612731
$290$	−28660.4	−	48862.0i	−0.340790	−	0.580998i
$291$		−	30788.3i		−	0.363580i
$292$			38314.0i			0.449357i
$293$	−35903.3			−0.418215			−0.209108	−	0.977893i	$-0.567056\pi$
$293$	−35903.3			−0.418215			−0.209108	+	0.977893i	$0.567056\pi$
$294$	−165909.			−1.91945
$295$	100324.	−	58846.2i	1.15282	−	0.676199i
$296$			39904.3i			0.455445i
$297$	−136641.			−1.54906
$298$	−34878.2			−0.392754
$299$	14144.2	+	3233.34i	0.158211	+	0.0361667i
$300$	39705.2	+	22201.2i	0.441169	+	0.246680i
$301$	−147708.			−1.63032
$302$		−	2370.49i		−	0.0259911i
$303$			20327.9i			0.221415i
$304$		−	20512.5i		−	0.221958i
$305$	47999.6	+	81832.5i	0.515986	+	0.879683i
$306$			903.353i			0.00964749i
$307$			187113.i			1.98530i	0.121022	+	0.992650i	$0.461383\pi$
$307$			187113.i			1.98530i	−0.121022	+	0.992650i	$0.538617\pi$
$308$			142656.i			1.50379i
$309$		−	146214.i		−	1.53134i
$310$	−25576.2	−	43603.8i	−0.266142	−	0.453734i
$311$	−147317.			−1.52311			−0.761555	−	0.648100i	$-0.775564\pi$
$311$	−147317.			−1.52311			−0.761555	+	0.648100i	$0.775564\pi$
$312$		−	5646.39i		−	0.0580045i
$313$	−14391.8			−0.146901			−0.0734506	−	0.997299i	$-0.523401\pi$
$313$	−14391.8			−0.146901			−0.0734506	+	0.997299i	$0.523401\pi$
$314$		−	116232.i		−	1.17887i
$315$	3602.21	−	2112.91i	0.0363034	−	0.0212941i
$316$			59059.1i			0.591442i
$317$		−	105340.i		−	1.04827i	−0.851635	−	0.524136i	$-0.824388\pi$
$317$		−	105340.i		−	1.04827i	0.851635	−	0.524136i	$-0.175612\pi$
$318$	28426.8			0.281109
$319$			151868.i			1.49240i
$320$	11040.8	−	6476.10i	0.107821	−	0.0632432i
$321$			20296.6i			0.196976i
$322$	137204.	+	31364.7i	1.32329	+	0.302503i
$323$		−	57642.5i		−	0.552507i
$324$	53613.5			0.510722
$325$	−14962.0	−	8366.00i	−0.141652	−	0.0792047i
$326$	−77831.8			−0.732355
$327$	56764.5			0.530862
$328$			22411.6i			0.208317i
$329$			93385.7i			0.862757i
$330$	−61703.8	−	105196.i	−0.566610	−	0.965990i
$331$	−32415.9			−0.295871			−0.147936	−	0.988997i	$-0.547263\pi$
$331$	−32415.9			−0.295871			−0.147936	+	0.988997i	$0.547263\pi$
$332$	7520.11			0.0682257
$333$	−3131.79			−0.0282426
$334$	68517.9			0.614202
$335$	100150.	−	58744.1i	0.892406	−	0.523449i
$336$		−	54772.2i		−	0.485156i
$337$	−137438.			−1.21017			−0.605084	−	0.796162i	$-0.706860\pi$
$337$	−137438.			−1.21017			−0.605084	+	0.796162i	$0.706860\pi$
$338$		−	78655.0i		−	0.688483i
$339$		−	222969.i		−	1.94019i
$340$	31026.0	−	18198.6i	0.268391	−	0.157427i
$341$			135525.i			1.16549i
$342$	1609.87			0.0137638
$343$	380609.			3.23513
$344$		−	35531.3i		−	0.300258i
$345$	−114743.	+	36217.1i	−0.964021	+	0.304282i
$346$	125720.			1.05015
$347$		−	170004.i		−	1.41189i	−0.708267	−	0.705945i	$-0.750523\pi$
$347$		−	170004.i		−	1.41189i	0.708267	−	0.705945i	$-0.249477\pi$
$348$		−	58309.0i		−	0.481479i
$349$	148522.			1.21938			0.609691	−	0.792639i	$-0.291294\pi$
$349$	148522.			1.21938			0.609691	+	0.792639i	$0.291294\pi$
$350$	−145137.	−	81153.5i	−1.18479	−	0.662478i
$351$	−19769.4			−0.160465
$352$	−34316.0			−0.276956
$353$			155184.i			1.24537i	0.782473	+	0.622685i	$0.213958\pi$
$353$			155184.i			1.24537i	−0.782473	+	0.622685i	$0.786042\pi$
$354$	119721.			0.955356
$355$	83944.0	−	49238.1i	0.666090	−	0.390701i
$356$			82757.7i			0.652993i
$357$		−	153916.i		−	1.20767i
$358$		−	158792.i		−	1.23898i
$359$			109782.i			0.851809i	0.904768	+	0.425905i	$0.140044\pi$
$359$			109782.i			0.851809i	−0.904768	+	0.425905i	$0.859956\pi$
$360$	508.261	+	866.513i	0.00392177	+	0.00668606i
$361$	27595.7			0.211752
$362$	118667.			0.905551
$363$			193754.i			1.47041i
$364$			20639.6i			0.155776i
$365$	60577.4	+	103276.i	0.454700	+	0.775199i
$366$			97654.1i			0.729001i
$367$	110990.			0.824045			0.412022	−	0.911174i	$-0.364823\pi$
$367$	110990.			0.824045			0.412022	+	0.911174i	$0.364823\pi$
$368$	−7544.80	+	33004.6i	−0.0557124	+	0.243713i
$369$	−1758.92			−0.0129179
$370$	63091.8	+	107563.i	0.460861	+	0.785702i
$371$	−103911.			−0.754939
$372$		−	52034.2i		−	0.376013i
$373$	5058.08			0.0363553			0.0181777	−	0.999835i	$-0.494214\pi$
$373$	5058.08			0.0363553			0.0181777	+	0.999835i	$0.494214\pi$
$374$	−96431.9			−0.689410
$375$	142128.	−	2933.51i	1.01069	−	0.0208605i
$376$	−22464.0			−0.158895
$377$			21972.4i			0.154595i
$378$	−191771.			−1.34214
$379$			248798.i			1.73208i	0.499975	+	0.866040i	$0.333343\pi$
$379$			248798.i			1.73208i	−0.499975	+	0.866040i	$0.666657\pi$
$380$	−32431.9	−	55291.8i	−0.224598	−	0.382907i
$381$	156174.			1.07587
$382$	24547.0			0.168217
$383$	−15884.8			−0.108289			−0.0541444	−	0.998533i	$-0.517243\pi$
$383$	−15884.8			−0.108289			−0.0541444	+	0.998533i	$0.517243\pi$
$384$	13175.5			0.0893520
$385$	225550.	+	384531.i	1.52168	+	2.59424i
$386$	−171075.			−1.14818
$387$	2788.59			0.0186193
$388$	−27072.2			−0.179829
$389$		−	81186.2i		−	0.536516i	−0.963347	−	0.268258i	$-0.913552\pi$
$389$		−	81186.2i		−	0.536516i	0.963347	−	0.268258i	$-0.0864480\pi$
$390$	−8927.39	−	15219.9i	−0.0586942	−	0.100065i
$391$	−21201.8	+	92746.8i	−0.138682	+	0.606660i
$392$			145884.i			0.949372i
$393$			238990.i			1.54737i
$394$	178571.			1.15032
$395$	93377.1	+	159195.i	0.598475	+	1.02032i
$396$		−	2693.21i		−	0.0171743i
$397$		−	74961.5i		−	0.475617i	−0.971312	−	0.237808i	$-0.923571\pi$
$397$		−	74961.5i		−	0.475617i	0.971312	−	0.237808i	$-0.0764291\pi$
$398$	5965.95			0.0376629
$399$	−274296.			−1.72295
$400$	19521.5	−	34912.9i	0.122010	−	0.218206i
$401$		−	46813.7i		−	0.291128i	−0.989349	−	0.145564i	$-0.953500\pi$
$401$		−	46813.7i		−	0.291128i	0.989349	−	0.145564i	$-0.0464997\pi$
$402$	119514.			0.739546
$403$			19607.9i			0.120732i
$404$	17874.4			0.109514
$405$	144516.	−	84767.3i	0.881062	−	0.516795i
$406$			213141.i			1.29305i
$407$		−	334315.i		−	2.01821i
$408$	37024.7			0.222418
$409$	−52071.2			−0.311280			−0.155640	−	0.987814i	$-0.549744\pi$
$409$	−52071.2			−0.311280			−0.155640	+	0.987814i	$0.549744\pi$
$410$	35434.5	+	60410.8i	0.210794	+	0.359374i
$411$		−	66277.9i		−	0.392360i
$412$	−128566.			−0.757412
$413$	−437626.			−2.56568
$414$	−2590.29	−	592.135i	−0.0151129	−	0.00345478i
$415$	20270.6	−	11889.9i	0.117698	−	0.0690370i
$416$	−4964.88			−0.0286895
$417$			13318.6i			0.0765928i
$418$			171852.i			0.983564i
$419$			201096.i			1.14545i	0.819749	+	0.572723i	$0.194113\pi$
$419$			201096.i			1.14545i	−0.819749	+	0.572723i	$0.805887\pi$
$420$	−86599.2	−	147639.i	−0.490925	−	0.836958i
$421$			144213.i			0.813656i	0.913505	+	0.406828i	$0.133365\pi$
$421$			144213.i			0.813656i	−0.913505	+	0.406828i	$0.866635\pi$
$422$		−	16015.8i		−	0.0899340i
$423$		−	1763.03i		−	0.00985325i
$424$		−	24995.8i		−	0.139038i
$425$	54857.8	−	98109.3i	0.303711	−	0.543166i
$426$	100174.			0.551995
$427$		−	356962.i		−	1.95779i
$428$	17846.9			0.0974260
$429$			47305.0i			0.257035i
$430$	−56177.9	−	95775.3i	−0.303829	−	0.517985i
$431$		−	49881.8i		−	0.268527i	−0.990946	−	0.134263i	$-0.957133\pi$
$431$		−	49881.8i		−	0.268527i	0.990946	−	0.134263i	$-0.0428669\pi$
$432$		−	46130.6i		−	0.247185i
$433$	56166.5			0.299572			0.149786	−	0.988718i	$-0.452141\pi$
$433$	56166.5			0.299572			0.149786	+	0.988718i	$0.452141\pi$
$434$			190204.i			1.00981i
$435$	−92191.2	−	157173.i	−0.487204	−	0.830614i
$436$		−	49913.2i		−	0.262568i
$437$	165285.	+	37783.9i	0.865507	+	0.197853i
$438$			123243.i			0.642415i
$439$	−58568.8			−0.303905			−0.151952	−	0.988388i	$-0.548556\pi$
$439$	−58568.8			−0.303905			−0.151952	+	0.988388i	$0.548556\pi$
$440$	−92499.3	+	54256.3i	−0.477786	+	0.280249i
$441$	−11449.4			−0.0588714
$442$	−13951.9			−0.0714149
$443$		−	226193.i		−	1.15258i	−0.817244	−	0.576292i	$-0.804499\pi$
$443$		−	226193.i		−	1.15258i	0.817244	−	0.576292i	$-0.195501\pi$
$444$			128359.i			0.651119i
$445$	130847.	+	223075.i	0.660758	+	1.12650i
$446$	200643.			1.00868
$447$	−112192.			−0.561494
$448$	−48161.3			−0.239962
$449$	306198.			1.51883			0.759417	−	0.650605i	$-0.225484\pi$
$449$	306198.			1.51883			0.759417	+	0.650605i	$0.225484\pi$
$450$	2740.05	+	1532.10i	0.0135311	+	0.00756592i
$451$		−	187763.i		−	0.923115i
$452$	−196057.			−0.959635
$453$		−	7625.09i		−	0.0371577i
$454$		−	234368.i		−	1.13707i
$455$	32632.9	+	55634.5i	0.157628	+	0.268733i
$456$		−	65982.0i		−	0.317319i
$457$	266435.			1.27573			0.637865	−	0.770149i	$-0.279818\pi$
$457$	266435.			1.27573			0.637865	+	0.770149i	$0.279818\pi$
$458$	115780.			0.551955
$459$		−	129632.i		−	0.615302i
$460$	31845.8	+	100893.i	0.150500	+	0.476812i
$461$	309401.			1.45586			0.727930	−	0.685652i	$-0.240483\pi$
$461$	309401.			1.45586			0.727930	+	0.685652i	$0.240483\pi$
$462$			458877.i			2.14987i
$463$		−	109245.i		−	0.509611i	−0.966992	−	0.254806i	$-0.917989\pi$
$463$		−	109245.i		−	0.509611i	0.966992	−	0.254806i	$-0.0820115\pi$
$464$	−51271.2			−0.238143
$465$	−82270.3	−	140259.i	−0.380485	−	0.648672i
$466$	−60309.9			−0.277726
$467$	94155.4			0.431729			0.215865	−	0.976423i	$-0.430743\pi$
$467$	94155.4			0.431729			0.215865	+	0.976423i	$0.430743\pi$
$468$		−	389.657i		−	0.00177906i
$469$	−436866.			−1.98611
$470$	−60552.1	+	35517.4i	−0.274115	+	0.160785i
$471$		−	373879.i		−	1.68535i
$472$		−	105271.i		−	0.472526i
$473$			297679.i			1.33053i
$474$			189974.i			0.845545i
$475$	−174841.	−	97762.6i	−0.774921	−	0.433297i
$476$	−135339.			−0.597322
$477$	1961.73			0.00862190
$478$		−	17653.9i		−	0.0772654i
$479$		−	67640.9i		−	0.294808i	−0.989076	−	0.147404i	$-0.952908\pi$
$479$		−	67640.9i		−	0.294808i	0.989076	−	0.147404i	$-0.0470917\pi$
$480$	35514.8	−	20831.5i	0.154144	−	0.0904145i
$481$		−	48369.1i		−	0.209064i
$482$	−19119.0			−0.0822944
$483$	441342.	+	100890.i	1.89182	+	0.432468i
$484$	170369.			0.727276
$485$	−72973.7	+	42803.4i	−0.310229	+	0.181968i
$486$	7322.05			0.0309999
$487$		−	40554.3i		−	0.170993i	−0.996338	−	0.0854967i	$-0.972752\pi$
$487$		−	40554.3i		−	0.170993i	0.996338	−	0.0854967i	$-0.0272477\pi$
$488$	85867.4			0.360569
$489$	−250359.			−1.04700
$490$	230655.	+	393234.i	0.960661	+	1.63779i
$491$	−24244.0			−0.100564			−0.0502818	−	0.998735i	$-0.516012\pi$
$491$	−24244.0			−0.100564			−0.0502818	+	0.998735i	$0.516012\pi$
$492$			72090.7i			0.297817i
$493$	−144078.			−0.592795
$494$			24863.8i			0.101886i
$495$	−4258.17	−	7259.58i	−0.0173785	−	0.0296279i
$496$	−45753.8			−0.185979
$497$	−366173.			−1.48243
$498$	24189.7			0.0975377
$499$	42263.6			0.169733			0.0848663	−	0.996392i	$-0.472954\pi$
$499$	42263.6			0.169733			0.0848663	+	0.996392i	$0.472954\pi$
$500$	−2579.44	−	124973.i	−0.0103178	−	0.499894i
$501$	220400.			0.878083
$502$	−99102.6			−0.393258
$503$	184547.			0.729410			0.364705	−	0.931123i	$-0.381170\pi$
$503$	184547.			0.729410			0.364705	+	0.931123i	$0.381170\pi$
$504$		−	3779.82i		−	0.0148803i
$505$	48180.7	−	28260.8i	0.188925	−	0.110816i
$506$	63209.8	−	276510.i	0.246878	−	1.07997i
$507$		−	253007.i		−	0.984277i
$508$		−	137324.i		−	0.532133i
$509$	−357587.			−1.38021			−0.690106	−	0.723708i	$-0.742436\pi$
$509$	−357587.			−1.38021			−0.690106	+	0.723708i	$0.742436\pi$
$510$	99800.6	−	58538.9i	0.383701	−	0.225063i
$511$		−	450501.i		−	1.72526i
$512$		−	11585.2i		−	0.0441942i
$513$	−231019.			−0.877836
$514$	−127610.			−0.483013
$515$	−346552.	+	203273.i	−1.30663	+	0.766418i
$516$		−	114293.i		−	0.429259i
$517$	188202.			0.704113
$518$		−	469200.i		−	1.74863i
$519$	404399.			1.50133
$520$	−13382.9	+	7849.87i	−0.0494931	+	0.0290306i
$521$			133248.i			0.490892i	0.969410	+	0.245446i	$0.0789344\pi$
$521$			133248.i			0.490892i	−0.969410	+	0.245446i	$0.921066\pi$
$522$		−	4023.90i		−	0.0147675i
$523$	253254.			0.925876			0.462938	−	0.886391i	$-0.346795\pi$
$523$	253254.			0.925876			0.462938	+	0.886391i	$0.346795\pi$
$524$	210144.			0.765342
$525$	−466859.	−	261044.i	−1.69382	−	0.947099i
$526$			284621.i			1.02872i
$527$	−128574.			−0.462946
$528$	−110383.			−0.395946
$529$	−252046.	−	121589.i	−0.900676	−	0.434491i
$530$	−39520.3	−	67376.5i	−0.140692	−	0.239859i
$531$	8261.96			0.0293018
$532$			241189.i			0.852185i
$533$		−	27165.7i		−	0.0956240i
$534$			266204.i			0.933540i
$535$	48106.6	−	28217.3i	0.168073	−	0.0985845i
$536$		−	105088.i		−	0.365785i
$537$		−	510783.i		−	1.77128i
$538$		−	270526.i		−	0.934640i
$539$		−	1.22221e6i		−	4.20695i
$540$	−72936.2	−	124346.i	−0.250124	−	0.426426i
$541$	316655.			1.08191			0.540956	−	0.841051i	$-0.318062\pi$
$541$	316655.			1.08191			0.540956	+	0.841051i	$0.318062\pi$
$542$		−	16661.1i		−	0.0567158i
$543$	381713.			1.29461
$544$		−	32555.9i		−	0.110010i
$545$	−78916.7	−	134542.i	−0.265691	−	0.452965i
$546$			66391.0i			0.222702i
$547$			510089.i			1.70479i	0.522898	+	0.852395i	$0.324851\pi$
$547$			510089.i			1.70479i	−0.522898	+	0.852395i	$0.675149\pi$
$548$	−58278.3			−0.194064
$549$			6739.10i			0.0223592i
$550$	−163550.	+	292498.i	−0.540661	+	0.966934i
$551$			256763.i			0.845725i
$552$	−24269.2	+	106165.i	−0.0796483	+	0.348420i
$553$		−	694424.i		−	2.27078i
$554$	−209092.			−0.681268
$555$	202946.	+	345994.i	0.658861	+	1.12327i
$556$	11711.1			0.0378834
$557$	58011.0			0.186982			0.0934910	−	0.995620i	$-0.470197\pi$
$557$	58011.0			0.186982			0.0934910	+	0.995620i	$0.470197\pi$
$558$		−	3590.88i		−	0.0115327i
$559$			43068.6i			0.137828i
$560$	−129820.	+	76146.9i	−0.413966	+	0.242815i
$561$	−310190.			−0.985603
$562$	−29991.2			−0.0949559
$563$	−485426.			−1.53146			−0.765731	−	0.643161i	$-0.777623\pi$
$563$	−485426.			−1.53146			−0.765731	+	0.643161i	$0.777623\pi$
$564$	−72259.3			−0.227162
$565$	−528475.	+	309982.i	−1.65550	+	0.971046i
$566$		−	171743.i		−	0.536100i
$567$	−630395.			−1.96086
$568$		−	88083.1i		−	0.273021i
$569$		−	38135.1i		−	0.117788i	−0.998264	−	0.0588939i	$-0.981243\pi$
$569$		−	38135.1i		−	0.117788i	0.998264	−	0.0588939i	$-0.0187574\pi$
$570$	−104323.	−	177856.i	−0.321092	−	0.547416i
$571$			554496.i			1.70069i	0.526222	+	0.850347i	$0.323608\pi$
$571$			554496.i			1.70069i	−0.526222	+	0.850347i	$0.676392\pi$
$572$	41595.4			0.127132
$573$	78959.5			0.240489
$574$		−	263518.i		−	0.799810i
$575$	245361.	+	221609.i	0.742114	+	0.670274i
$576$	909.239			0.00274052
$577$			284845.i			0.855572i	0.903880	+	0.427786i	$0.140706\pi$
$577$			284845.i			0.855572i	−0.903880	+	0.427786i	$0.859294\pi$
$578$			144747.i			0.433266i
$579$	−550291.			−1.64148
$580$	−138202.	+	81063.9i	−0.410828	+	0.240975i
$581$	−88422.5			−0.261945
$582$	−87082.5			−0.257090
$583$			209413.i			0.616121i
$584$	108368.			0.317743
$585$	−616.078	−	1050.33i	−0.00180021	−	0.00306911i
$586$			101550.i			0.295723i
$587$			174758.i			0.507180i	0.967312	+	0.253590i	$0.0816113\pi$
$587$			174758.i			0.507180i	−0.967312	+	0.253590i	$0.918389\pi$
$588$			469262.i			1.35725i
$589$			229132.i			0.660473i
$590$	−166442.	−	283760.i	−0.478145	−	0.815169i
$591$	574405.			1.64454
$592$	112866.			0.322048
$593$			514660.i			1.46356i	0.681540	+	0.731781i	$0.261311\pi$
$593$			514660.i			1.46356i	−0.681540	+	0.731781i	$0.738689\pi$
$594$			386479.i			1.09535i
$595$	−364808.	+	213982.i	−1.03046	+	0.604425i
$596$			98650.3i			0.277719i
$597$	19190.5			0.0538440
$598$	9145.27	−	40005.9i	0.0255737	−	0.111872i
$599$	−123294.			−0.343627			−0.171813	−	0.985130i	$-0.554963\pi$
$599$	−123294.			−0.343627			−0.171813	+	0.985130i	$0.554963\pi$
$600$	62794.4	−	112303.i	0.174429	−	0.311954i
$601$	493334.			1.36582			0.682908	−	0.730504i	$-0.260715\pi$
$601$	493334.			1.36582			0.682908	+	0.730504i	$0.260715\pi$
$602$			417782.i			1.15281i
$603$	8247.61			0.0226826
$604$	−6704.76			−0.0183785
$605$	459232.	−	269367.i	1.25465	−	0.735924i
$606$	57496.0			0.156564
$607$			20201.2i			0.0548277i	0.999624	+	0.0274139i	$0.00872719\pi$
$607$			20201.2i			0.0548277i	−0.999624	+	0.0274139i	$0.991273\pi$
$608$	−58018.1			−0.156948
$609$			685605.i			1.84858i
$610$	231457.	−	135763.i	0.622029	−	0.364857i
$611$	27229.3			0.0729380
$612$	2555.07			0.00682181
$613$	−211955.			−0.564057			−0.282029	−	0.959406i	$-0.591007\pi$
$613$	−211955.			−0.564057			−0.282029	+	0.959406i	$0.591007\pi$
$614$	529234.			1.40382
$615$	113981.	+	194322.i	0.301358	+	0.513773i
$616$	403492.			1.06334
$617$	−399887.			−1.05043			−0.525215	−	0.850969i	$-0.676015\pi$
$617$	−399887.			−1.05043			−0.525215	+	0.850969i	$0.676015\pi$
$618$	−413555.			−1.08282
$619$		−	632918.i		−	1.65183i	−0.563793	−	0.825916i	$-0.690659\pi$
$619$		−	632918.i		−	1.65183i	0.563793	−	0.825916i	$-0.309341\pi$
$620$	−123330.	+	72340.4i	−0.320838	+	0.188190i
$621$	371710.	+	84972.3i	0.963875	+	0.220340i
$622$			416675.i			1.07700i
$623$		−	973076.i		−	2.50709i
$624$	−15970.4			−0.0410154
$625$	−204546.	−	332790.i	−0.523637	−	0.851941i
$626$			40706.0i			0.103875i
$627$			552792.i			1.40613i
$628$	−328753.			−0.833586
$629$	317168.			0.801655
$630$	−5976.20	−	10188.6i	−0.0150572	−	0.0256704i
$631$		−	239328.i		−	0.601083i	−0.953769	−	0.300542i	$-0.902833\pi$
$631$		−	239328.i		−	0.601083i	0.953769	−	0.300542i	$-0.0971674\pi$
$632$	167044.			0.418213
$633$		−	51517.6i		−	0.128573i
$634$	−297946.			−0.741240
$635$	−217121.	−	370160.i	−0.538461	−	0.917999i
$636$		−	80403.2i		−	0.198774i
$637$		−	176831.i		−	0.435791i
$638$	429547.			1.05528
$639$	6912.99			0.0169303
$640$	−18317.2	−	31228.2i	−0.0447197	−	0.0762407i
$641$			446527.i			1.08676i	0.839488	+	0.543378i	$0.182855\pi$
$641$			446527.i			1.08676i	−0.839488	+	0.543378i	$0.817145\pi$
$642$	57407.6			0.139283
$643$	−732186.			−1.77092			−0.885462	−	0.464713i	$-0.846158\pi$
$643$	−732186.			−1.77092			−0.885462	+	0.464713i	$0.846158\pi$
$644$	88712.8	−	388073.i	0.213902	−	0.935710i
$645$	−180706.	−	308078.i	−0.434363	−	0.740527i
$646$	−163038.			−0.390682
$647$			46258.1i			0.110504i	0.998472	+	0.0552521i	$0.0175963\pi$
$647$			46258.1i			0.110504i	−0.998472	+	0.0552521i	$0.982404\pi$
$648$		−	151642.i		−	0.361135i
$649$			881955.i			2.09390i
$650$	−23662.6	+	42318.9i	−0.0560062	+	0.100163i
$651$			611825.i			1.44366i
$652$			220142.i			0.517853i
$653$		−	118651.i		−	0.278255i	−0.990274	−	0.139128i	$-0.955570\pi$
$653$		−	118651.i		−	0.278255i	0.990274	−	0.139128i	$-0.0444298\pi$
$654$		−	160554.i		−	0.375376i
$655$	566448.	−	332255.i	1.32031	−	0.774442i
$656$	63389.5			0.147302
$657$			8505.02i			0.0197035i
$658$	264135.			0.610061
$659$			596519.i			1.37358i	0.726857	+	0.686789i	$0.240980\pi$
$659$			596519.i			1.37358i	−0.726857	+	0.686789i	$0.759020\pi$
$660$	−297540.	+	174525.i	−0.683058	+	0.400654i
$661$		−	420135.i		−	0.961581i	−0.876836	−	0.480790i	$-0.840350\pi$
$661$		−	420135.i		−	0.961581i	0.876836	−	0.480790i	$-0.159650\pi$
$662$			91686.1i			0.209212i
$663$	−44878.7			−0.102097
$664$		−	21270.1i		−	0.0482429i
$665$	381339.	+	650128.i	0.862318	+	1.47013i
$666$			8858.04i			0.0199705i
$667$	94441.2	−	413132.i	0.212280	−	0.928617i
$668$		−	193798.i		−	0.434307i
$669$	645402.			1.44204
$670$	−166153.	−	283268.i	−0.370134	−	0.631027i
$671$	−719391.			−1.59779
$672$	−154919.			−0.343057
$673$			278120.i			0.614048i	0.951702	+	0.307024i	$0.0993332\pi$
$673$			278120.i			0.614048i	−0.951702	+	0.307024i	$0.900667\pi$
$674$			388732.i			0.855718i
$675$	−393202.	−	219859.i	−0.862994	−	0.482543i
$676$	−222470.			−0.486831
$677$	420406.			0.917259			0.458629	−	0.888628i	$-0.348341\pi$
$677$	420406.			0.917259			0.458629	+	0.888628i	$0.348341\pi$
$678$	−630652.			−1.37192
$679$	318319.			0.690435
$680$	−51473.4	−	87754.9i	−0.111318	−	0.189781i
$681$		−	753885.i		−	1.62559i
$682$	383322.			0.824129
$683$			389411.i			0.834771i	0.908730	+	0.417385i	$0.137053\pi$
$683$			389411.i			0.834771i	−0.908730	+	0.417385i	$0.862947\pi$
$684$		−	4553.41i		−	0.00973250i
$685$	−157090.	+	92142.6i	−0.334786	+	0.196372i
$686$		−	1.07653e6i		−	2.28758i
$687$	372428.			0.789093
$688$	−100498.			−0.212315
$689$			30298.1i			0.0638230i
$690$	102437.	+	324541.i	0.215160	+	0.681666i
$691$	−505037.			−1.05771			−0.528856	−	0.848712i	$-0.677379\pi$
$691$	−505037.			−1.05771			−0.528856	+	0.848712i	$0.677379\pi$
$692$		−	355589.i		−	0.742568i
$693$			31667.1i			0.0659388i
$694$	−480844.			−0.998356
$695$	31567.5	−	18516.2i	0.0653538	−	0.0383338i
$696$	−164923.			−0.340457
$697$	178132.			0.366671
$698$		−	420083.i		−	0.862233i
$699$	−193997.			−0.397046
$700$	−229537.	+	410510.i	−0.468442	+	0.837776i
$701$		−	815421.i		−	1.65938i	−0.558225	−	0.829690i	$-0.688517\pi$
$701$		−	815421.i		−	1.65938i	0.558225	−	0.829690i	$-0.311483\pi$
$702$			55916.3i			0.113466i
$703$		−	565227.i		−	1.14370i
$704$			97060.3i			0.195838i
$705$	−194776.	+	114248.i	−0.391884	+	0.229863i
$706$	438927.			0.880609
$707$	−210169.			−0.420465
$708$		−	338623.i		−	0.675539i
$709$			503229.i			1.00109i	0.865711	+	0.500545i	$0.166867\pi$
$709$			503229.i			1.00109i	−0.865711	+	0.500545i	$0.833133\pi$
$710$	−139266.	−	237430.i	−0.276267	−	0.470997i
$711$			13110.1i			0.0259337i
$712$	234074.			0.461736
$713$	84278.2	−	368674.i	0.165782	−	0.725209i
$714$	−435341.			−0.853951
$715$	112121.	−	65765.7i	0.219319	−	0.128643i
$716$	−449132.			−0.876089
$717$		−	56786.8i		−	0.110461i
$718$	310511.			0.602320
$719$	−71431.6			−0.138176			−0.0690880	−	0.997611i	$-0.522009\pi$
$719$	−71431.6			−0.138176			−0.0690880	+	0.997611i	$0.522009\pi$
$720$	2450.87	−	1437.58i	0.00472776	−	0.00277311i
$721$	1.51170e6			2.90800
$722$		−	78052.5i		−	0.149731i
$723$	−61499.5			−0.117651
$724$		−	335641.i		−	0.640321i
$725$	−244359.	+	437018.i	−0.464892	+	0.831426i
$726$	548020.			1.03974
$727$	592367.			1.12078			0.560392	−	0.828227i	$-0.310650\pi$
$727$	592367.			1.12078			0.560392	+	0.828227i	$0.310650\pi$
$728$	58377.7			0.110150
$729$	−519284.			−0.977125
$730$	292108.	−	171339.i	0.548149	−	0.321522i
$731$	−282411.			−0.528501
$732$	276207.			0.515482
$733$	971809.			1.80873			0.904364	−	0.426763i	$-0.140346\pi$
$733$	971809.			1.80873			0.904364	+	0.426763i	$0.140346\pi$
$734$		−	313927.i		−	0.582688i
$735$	741941.	+	1.26490e6i	1.37339	+	2.34144i
$736$	93351.2	+	21339.9i	0.172331	+	0.0393946i
$737$			880424.i			1.62090i
$738$			4974.97i			0.00913435i
$739$	403037.			0.737999			0.369000	−	0.929430i	$-0.379700\pi$
$739$	403037.			0.737999			0.369000	+	0.929430i	$0.379700\pi$
$740$	304233.	−	178451.i	0.555576	−	0.325878i
$741$			79978.7i			0.145659i
$742$			293904.i			0.533823i
$743$	−702726.			−1.27294			−0.636471	−	0.771301i	$-0.719606\pi$
$743$	−702726.			−1.27294			−0.636471	+	0.771301i	$0.719606\pi$
$744$	−147175.			−0.265882
$745$	155974.	+	265914.i	0.281022	+	0.479102i
$746$		−	14306.4i		−	0.0257071i
$747$	1669.33			0.00299158
$748$			272751.i			0.487486i
$749$	−209846.			−0.374056
$750$	−8297.21	−	401998.i	−0.0147506	−	0.714664i
$751$		−	18624.7i		−	0.0330225i	−0.999864	−	0.0165112i	$-0.994744\pi$
$751$		−	18624.7i		−	0.0330225i	0.999864	−	0.0165112i	$-0.00525593\pi$
$752$			63537.8i			0.112356i
$753$	−318781.			−0.562215
$754$	62147.4			0.109315
$755$	−18072.8	+	10600.8i	−0.0317053	+	0.0185970i
$756$			542410.i			0.949039i
$757$	77260.1			0.134823			0.0674114	−	0.997725i	$-0.478526\pi$
$757$	77260.1			0.134823			0.0674114	+	0.997725i	$0.478526\pi$
$758$	703706.			1.22477
$759$	203325.	−	889443.i	0.352945	−	1.54395i
$760$	−156389.	+	91731.3i	−0.270756	+	0.158815i
$761$	612224.			1.05716			0.528580	−	0.848883i	$-0.322725\pi$
$761$	612224.			1.05716			0.528580	+	0.848883i	$0.322725\pi$
$762$		−	441728.i		−	0.760755i
$763$			586886.i			1.00810i
$764$		−	69429.3i		−	0.118948i
$765$	6887.23	−	4039.76i	0.0117685	−	0.00690293i
$766$			44929.0i			0.0765718i
$767$			127602.i			0.216904i
$768$		−	37265.9i		−	0.0631814i
$769$		−	1.09082e6i		−	1.84459i	−0.386481	−	0.922297i	$-0.626309\pi$
$769$		−	1.09082e6i		−	1.84459i	0.386481	−	0.922297i	$-0.373691\pi$
$770$	1.08762e6	−	637953.i	1.83441	−	1.07599i
$771$	−410480.			−0.690531
$772$			483872.i			0.811888i
$773$	1.11125e6			1.85974			0.929870	−	0.367889i	$-0.119919\pi$
$773$	1.11125e6			1.85974			0.929870	+	0.367889i	$0.119919\pi$
$774$		−	7887.32i		−	0.0131658i
$775$	−218063.	+	389990.i	−0.363059	+	0.649306i
$776$			76571.9i			0.127159i
$777$		−	1.50926e6i		−	2.49990i
$778$	−229629.			−0.379374
$779$		−	317451.i		−	0.523120i
$780$	−43048.5	+	25250.5i	−0.0707569	+	0.0415031i
$781$			737954.i			1.20984i
$782$	262328.	+	59967.7i	0.428973	+	0.0980626i
$783$			577435.i			0.941846i
$784$	412623.			0.671307
$785$	−886159.	+	519785.i	−1.43805	+	0.843498i
$786$	675966.			1.09416
$787$	1.14853e6			1.85436			0.927179	−	0.374618i	$-0.122226\pi$
$787$	1.14853e6			1.85436			0.927179	+	0.374618i	$0.122226\pi$
$788$		−	505076.i		−	0.813400i
$789$			915533.i			1.47069i
$790$	450271.	−	264110.i	0.721472	−	0.423186i
$791$	2.30527e6			3.68441
$792$	−7617.54			−0.0121441
$793$	−104082.			−0.165513
$794$	−212023.			−0.336312
$795$	−127124.	−	216728.i	−0.201137	−	0.342911i
$796$		−	16874.2i		−	0.0266317i
$797$	−624889.			−0.983754			−0.491877	−	0.870665i	$-0.663689\pi$
$797$	−624889.			−0.983754			−0.491877	+	0.870665i	$0.663689\pi$
$798$			775825.i			1.21831i
$799$			178549.i			0.279681i
$800$	−98748.6	−	55215.2i	−0.154295	−	0.0862738i
$801$			18370.7i			0.0286326i
$802$	−132409.			−0.205859
$803$	−907901.			−1.40802
$804$		−	338035.i		−	0.522938i
$805$	−374447.	−	1.18632e6i	−0.577828	−	1.83067i
$806$	55459.5			0.0853702
$807$		−	870193.i		−	1.33619i
$808$		−	50556.4i		−	0.0774378i
$809$	851607.			1.30120			0.650598	−	0.759423i	$-0.274519\pi$
$809$	851607.			1.30120			0.650598	+	0.759423i	$0.274519\pi$
$810$	−239758.	−	408753.i	−0.365429	−	0.623005i
$811$	726728.			1.10492			0.552459	−	0.833540i	$-0.313689\pi$
$811$	726728.			1.10492			0.552459	+	0.833540i	$0.313689\pi$
$812$	602854.			0.914324
$813$		−	53593.2i		−	0.0810827i
$814$	−945586.			−1.42709
$815$	348061.	+	593395.i	0.524011	+	0.893365i
$816$		−	104722.i		−	0.157274i
$817$			503287.i			0.754000i
$818$			147280.i			0.220108i
$819$			4581.63i			0.00683050i
$820$	170868.	−	100224.i	0.254116	−	0.149054i
$821$	−1.23396e6			−1.83069			−0.915347	−	0.402667i	$-0.868083\pi$
$821$	−1.23396e6			−1.83069			−0.915347	+	0.402667i	$0.868083\pi$
$822$	−187462.			−0.277441
$823$		−	1.12220e6i		−	1.65680i	−0.560139	−	0.828399i	$-0.689252\pi$
$823$		−	1.12220e6i		−	1.65680i	0.560139	−	0.828399i	$-0.310748\pi$
$824$			363640.i			0.535571i
$825$	−526087.	+	940869.i	−0.772946	+	1.38236i
$826$			1.23779e6i			1.81421i
$827$	−594839.			−0.869737			−0.434869	−	0.900494i	$-0.643205\pi$
$827$	−594839.			−0.869737			−0.434869	+	0.900494i	$0.643205\pi$
$828$	−1674.81	+	7326.44i	−0.00244290	+	0.0106864i
$829$	87439.9			0.127233			0.0636166	−	0.997974i	$-0.479737\pi$
$829$	87439.9			0.127233			0.0636166	+	0.997974i	$0.479737\pi$
$830$	−33629.7	−	57333.9i	−0.0488165	−	0.0832253i
$831$	−672580.			−0.973962
$832$			14042.8i			0.0202865i
$833$	1.15952e6			1.67104
$834$	37670.8			0.0541593
$835$	−306410.	−	522386.i	−0.439471	−	0.749236i
$836$	486071.			0.695485
$837$			515296.i			0.735539i
$838$	568785.			0.809953
$839$			950132.i			1.34977i	0.737923	+	0.674885i	$0.235807\pi$
$839$			950132.i			1.34977i	−0.737923	+	0.674885i	$0.764193\pi$
$840$	−417587.	+	244940.i	−0.591819	+	0.347137i
$841$	−65498.9			−0.0926066
$842$	407897.			0.575342
$843$	−96472.0			−0.135752
$844$	−45299.5			−0.0635930
$845$	−599671.	+	351743.i	−0.839847	+	0.492620i
$846$	−4986.61			−0.00696730
$847$	−2.00322e6			−2.79230
$848$	−70698.7			−0.0983150
$849$		−	552440.i		−	0.766425i
$850$	−277495.	−	155161.i	−0.384076	−	0.214756i
$851$	−207899.	+	909451.i	−0.287074	+	1.25580i
$852$		−	283335.i		−	0.390320i
$853$			911683.i			1.25299i	0.779427	+	0.626493i	$0.215510\pi$
$853$			911683.i			1.25299i	−0.779427	+	0.626493i	$0.784490\pi$
$854$	−1.00964e6			−1.38437
$855$	−7199.30	−	12273.8i	−0.00984823	−	0.0167898i
$856$		−	50478.6i		−	0.0688906i
$857$		−	920235.i		−	1.25296i	−0.779438	−	0.626480i	$-0.784495\pi$
$857$		−	920235.i		−	1.25296i	0.779438	−	0.626480i	$-0.215505\pi$
$858$	133799.			0.181751
$859$	−173480.			−0.235106			−0.117553	−	0.993067i	$-0.537505\pi$
$859$	−173480.			−0.235106			−0.117553	+	0.993067i	$0.537505\pi$
$860$	−270894.	+	158895.i	−0.366270	+	0.214839i
$861$		−	847652.i		−	1.14343i
$862$	−141087.			−0.189877
$863$			280432.i			0.376535i	0.982118	+	0.188268i	$0.0602872\pi$
$863$			280432.i			0.376535i	−0.982118	+	0.188268i	$0.939713\pi$
$864$	−130477.			−0.174786
$865$	−562214.	−	958496.i	−0.751397	−	1.28103i
$866$		−	158863.i		−	0.211830i
$867$			465605.i			0.619411i
$868$	537979.			0.714046
$869$	−1.39948e6			−1.85323
$870$	−444552.	+	260756.i	−0.587333	+	0.344505i
$871$			127381.i			0.167907i
$872$	−141176.			−0.185664
$873$	−6009.55			−0.00788522
$874$	106869.	−	467497.i	0.139904	−	0.612006i
$875$	30329.4	+	1.46945e6i	0.0396139	+	1.91929i
$876$	348585.			0.454256
$877$		−	293085.i		−	0.381061i	−0.981681	−	0.190531i	$-0.938979\pi$
$877$		−	293085.i		−	0.381061i	0.981681	−	0.190531i	$-0.0610209\pi$
$878$			165658.i			0.214893i
$879$			326653.i			0.422775i
$880$	153460.	+	261628.i	0.198166	+	0.337846i
$881$			256411.i			0.330357i	0.986264	+	0.165179i	$0.0528201\pi$
$881$			256411.i			0.330357i	−0.986264	+	0.165179i	$0.947180\pi$
$882$			32383.7i			0.0416284i
$883$		−	1.24275e6i		−	1.59390i	−0.604043	−	0.796952i	$-0.706444\pi$
$883$		−	1.24275e6i		−	1.59390i	0.604043	−	0.796952i	$-0.293556\pi$
$884$			39461.9i			0.0504979i
$885$	−535390.	−	912764.i	−0.683571	−	1.16539i
$886$	−639772.			−0.815000
$887$		−	346063.i		−	0.439854i	−0.975516	−	0.219927i	$-0.929418\pi$
$887$		−	346063.i		−	0.439854i	0.975516	−	0.219927i	$-0.0705819\pi$
$888$	363054.			0.460411
$889$			1.61468e6i			2.04307i
$890$	630951.	−	370090.i	0.796554	−	0.467226i
$891$			1.27044e6i			1.60030i
$892$		−	567503.i		−	0.713245i
$893$	318193.			0.399014
$894$			317326.i			0.397036i
$895$	−1.21064e6	+	710114.i	−1.51137	+	0.886506i
$896$			136221.i			0.169679i
$897$	29417.4	−	128686.i	0.0365611	−	0.159936i
$898$		−	866060.i		−	1.07398i
$899$	572718.			0.708634
$900$	4333.43	−	7750.04i	0.00534992	−	0.00956795i
$901$	−198672.			−0.244729
$902$	−531073.			−0.652741
$903$			1.34387e6i			1.64809i
$904$			554533.i			0.678564i
$905$	−530675.	−	904726.i	−0.647935	−	1.10464i
$906$	−21567.0			−0.0262745
$907$	1.13082e6			1.37461			0.687303	−	0.726371i	$-0.258795\pi$
$907$	1.13082e6			1.37461			0.687303	+	0.726371i	$0.258795\pi$
$908$	−662893.			−0.804028
$909$	3967.79			0.00480199
$910$	157358.	−	92299.9i	0.190023	−	0.111460i
$911$		−	1.35988e6i		−	1.63857i	−0.573386	−	0.819286i	$-0.694370\pi$
$911$		−	1.35988e6i		−	1.63857i	0.573386	−	0.819286i	$-0.305630\pi$
$912$	−186625.			−0.224378
$913$			178199.i			0.213779i
$914$		−	753591.i		−	0.902077i
$915$	744522.	−	436706.i	0.889273	−	0.521611i
$916$		−	327476.i		−	0.390291i
$917$	−2.47091e6			−2.93845
$918$	−366656.			−0.435084
$919$			424475.i			0.502599i	0.967909	+	0.251299i	$0.0808579\pi$
$919$			424475.i			0.502599i	−0.967909	+	0.251299i	$0.919142\pi$
$920$	285370.	−	90073.5i	0.337157	−	0.106420i
$921$	1.70237e6			2.00694
$922$		−	875118.i		−	1.02945i
$923$			106768.i			0.125325i
$924$	1.29790e6			1.52019
$925$	537921.	−	962034.i	0.628688	−	1.12436i
$926$	−308991.			−0.360349
$927$	−28539.4			−0.0332112
$928$			145017.i			0.168393i
$929$	1.52431e6			1.76621			0.883106	−	0.469174i	$-0.155448\pi$
$929$	1.52431e6			1.76621			0.883106	+	0.469174i	$0.155448\pi$
$930$	−396713.	+	232695.i	−0.458681	+	0.269043i
$931$		−	2.06639e6i		−	2.38404i
$932$			170582.i			0.196382i
$933$			1.34031e6i			1.53972i
$934$		−	266312.i		−	0.305279i
$935$	431240.	+	735204.i	0.493283	+	0.840978i
$936$	−1102.12			−0.00125798
$937$	301890.			0.343850			0.171925	−	0.985110i	$-0.445001\pi$
$937$	301890.			0.343850			0.171925	+	0.985110i	$0.445001\pi$
$938$			1.23564e6i			1.40439i
$939$			130938.i			0.148503i
$940$	100458.	+	171267.i	0.113692	+	0.193829i
$941$		−	986711.i		−	1.11432i	−0.830405	−	0.557161i	$-0.811891\pi$
$941$		−	986711.i		−	1.11432i	0.830405	−	0.557161i	$-0.188109\pi$
$942$	−1.05749e6			−1.19172
$943$	−116763.	+	510778.i	−0.131305	+	0.574393i
$944$	−297752.			−0.334126
$945$	857593.	+	1.46208e6i	0.960324	+	1.63722i
$946$	841963.			0.940829
$947$		−	945465.i		−	1.05425i	−0.849786	−	0.527127i	$-0.823269\pi$
$947$		−	945465.i		−	1.05425i	0.849786	−	0.527127i	$-0.176731\pi$
$948$	537327.			0.597890
$949$	−131356.			−0.145854
$950$	−276514.	+	494526.i	−0.306387	+	0.547952i
$951$	−958394.			−1.05970
$952$			382796.i			0.422371i
$953$	−410045.			−0.451488			−0.225744	−	0.974187i	$-0.572481\pi$
$953$	−410045.			−0.451488			−0.225744	+	0.974187i	$0.572481\pi$
$954$		−	5548.62i		−	0.00609660i
$955$	−109773.	−	187148.i	−0.120362	−	0.205200i
$956$	−49932.8			−0.0546349
$957$	1.38171e6			1.50867
$958$	−191317.			−0.208460
$959$	685244.			0.745089
$960$	−58920.4	−	100451.i	−0.0639327	−	0.108996i
$961$	−412434.			−0.446589
$962$	−136809.			−0.147830
$963$	3961.69			0.00427197
$964$			54076.6i			0.0581909i
$965$	765041.	+	1.30429e6i	0.821543	+	1.40061i
$966$	285360.	−	1.24830e6i	0.305801	−	1.33772i
$967$			805249.i			0.861147i	0.902555	+	0.430574i	$0.141689\pi$
$967$			805249.i			0.861147i	−0.902555	+	0.430574i	$0.858311\pi$
$968$		−	481876.i		−	0.514262i
$969$	−524439.			−0.558531
$970$	121066.	+	206401.i	0.128671	+	0.219365i
$971$			891617.i			0.945671i	0.881151	+	0.472835i	$0.156770\pi$
$971$			891617.i			0.945671i	−0.881151	+	0.472835i	$0.843230\pi$
$972$		−	20709.9i		−	0.0219202i
$973$	−137701.			−0.145449
$974$	−114705.			−0.120911
$975$	−76114.9	+	136126.i	−0.0800683	+	0.143196i
$976$		−	242870.i		−	0.254961i
$977$	−383886.			−0.402173			−0.201087	−	0.979573i	$-0.564447\pi$
$977$	−383886.			−0.402173			−0.201087	+	0.979573i	$0.564447\pi$
$978$			708123.i			0.740340i
$979$	−1.96106e6			−2.04609
$980$	1.11223e6	−	652390.i	1.15809	−	0.679290i
$981$		−	11079.8i		−	0.0115132i
$982$			68572.3i			0.0711092i
$983$	552369.			0.571640			0.285820	−	0.958283i	$-0.407734\pi$
$983$	552369.			0.571640			0.285820	+	0.958283i	$0.407734\pi$
$984$	203903.			0.210588
$985$	−798565.	−	1.36144e6i	−0.823072	−	1.40322i
$986$			407514.i			0.419169i
$987$	849635.			0.872164
$988$	70325.5			0.0720441
$989$	185116.	−	809788.i	0.189257	−	0.827902i
$990$	−20533.2	+	12043.9i	−0.0209501	+	0.0122885i
$991$	−1.60047e6			−1.62967			−0.814837	−	0.579690i	$-0.803174\pi$
$991$	−1.60047e6			−1.62967			−0.814837	+	0.579690i	$0.803174\pi$
$992$			129411.i			0.131507i
$993$			294924.i			0.299097i
$994$			1.03569e6i			1.04823i
$995$	−26679.5	−	45484.8i	−0.0269483	−	0.0459431i
$996$		−	68418.9i		−	0.0689696i
$997$			463648.i			0.466443i	0.972424	+	0.233221i	$0.0749266\pi$
$997$			463648.i			0.466443i	−0.972424	+	0.233221i	$0.925073\pi$
$998$		−	119540.i		−	0.120019i
$999$		−	1.27114e6i		−	1.27369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.c.a.229.1	✓	48
5.4	even	2	inner	230.5.c.a.229.48	yes	48
23.22	odd	2	inner	230.5.c.a.229.47	yes	48
115.114	odd	2	inner	230.5.c.a.229.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.c.a.229.1	✓	48	1.1	even	1	trivial
230.5.c.a.229.2	yes	48	115.114	odd	2	inner
230.5.c.a.229.47	yes	48	23.22	odd	2	inner
230.5.c.a.229.48	yes	48	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} -9.09812i q^{3} -8.00000 q^{4} +(-21.5641 + 12.6486i) q^{5} -25.7334 q^{6} +94.0651 q^{7} +22.6274i q^{8} -1.77586 q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} -9.09812i q^{3} -8.00000 q^{4} +(-21.5641 + 12.6486i) q^{5} -25.7334 q^{6} +94.0651 q^{7} +22.6274i q^{8} -1.77586 q^{9} +(35.7757 + 60.9926i) q^{10} -189.571i q^{11} +72.7850i q^{12} -27.4274i q^{13} -266.056i q^{14} +(115.079 + 196.193i) q^{15} +64.0000 q^{16} +179.847 q^{17} +5.02288i q^{18} -320.508i q^{19} +(172.513 - 101.189i) q^{20} -855.816i q^{21} -536.187 q^{22} +(-117.888 + 515.697i) q^{23} +205.867 q^{24} +(305.024 - 545.514i) q^{25} -77.5763 q^{26} -720.791i q^{27} -752.520 q^{28} -801.113 q^{29} +(554.918 - 325.492i) q^{30} -714.903 q^{31} -181.019i q^{32} -1724.74 q^{33} -508.685i q^{34} +(-2028.43 + 1189.79i) q^{35} +14.2069 q^{36} +1763.54 q^{37} -906.533 q^{38} -249.537 q^{39} +(-286.206 - 487.941i) q^{40} +990.461 q^{41} -2420.61 q^{42} -1570.28 q^{43} +1516.57i q^{44} +(38.2948 - 22.4622i) q^{45} +(1458.61 + 333.436i) q^{46} +992.778i q^{47} -582.280i q^{48} +6447.24 q^{49} +(-1542.95 - 862.738i) q^{50} -1636.27i q^{51} +219.419i q^{52} -1104.67 q^{53} -2038.70 q^{54} +(2397.81 + 4087.93i) q^{55} +2128.45i q^{56} -2916.02 q^{57} +2265.89i q^{58} -4652.38 q^{59} +(-920.631 - 1569.55i) q^{60} -3794.84i q^{61} +2022.05i q^{62} -167.046 q^{63} -512.000 q^{64} +(346.919 + 591.447i) q^{65} +4878.30i q^{66} -4644.30 q^{67} -1438.78 q^{68} +(4691.88 + 1072.56i) q^{69} +(3365.25 + 5737.27i) q^{70} -3892.76 q^{71} -40.1831i q^{72} -4789.25i q^{73} -4988.03i q^{74} +(-4963.15 - 2775.15i) q^{75} +2564.06i q^{76} -17832.0i q^{77} +705.799i q^{78} -7382.38i q^{79} +(-1380.10 + 809.513i) q^{80} -6701.69 q^{81} -2801.45i q^{82} -940.014 q^{83} +6846.52i q^{84} +(-3878.25 + 2274.83i) q^{85} +4441.42i q^{86} +7288.63i q^{87} +4289.50 q^{88} -10344.7i q^{89} +(-63.5326 - 108.314i) q^{90} -2579.96i q^{91} +(943.100 - 4125.58i) q^{92} +6504.28i q^{93} +2808.00 q^{94} +(4053.99 + 6911.48i) q^{95} -1646.94 q^{96} +3384.03 q^{97} -18235.5i q^{98} +336.651i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9}+O(q^{10}) \) 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9	\( 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9} + 3072 q^{16} + 512 q^{24} + 1488 q^{25} - 384 q^{26} - 2940 q^{29} + 4732 q^{31} + 2556 q^{35} + 12864 q^{36} + 2736 q^{39} + 828 q^{41} - 64 q^{46} + 32572 q^{49} - 3264 q^{50} + 10112 q^{54} + 12824 q^{55} + 7092 q^{59} - 24576 q^{64} + 14000 q^{69} - 6592 q^{70} - 12708 q^{71} + 24728 q^{75} - 13040 q^{81} - 15700 q^{85} - 9728 q^{94} - 46608 q^{95} - 4096 q^{96}+O(q^{100}) \) 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9 + 3072 * q^16 + 512 * q^24 + 1488 * q^25 - 384 * q^26 - 2940 * q^29 + 4732 * q^31 + 2556 * q^35 + 12864 * q^36 + 2736 * q^39 + 828 * q^41 - 64 * q^46 + 32572 * q^49 - 3264 * q^50 + 10112 * q^54 + 12824 * q^55 + 7092 * q^59 - 24576 * q^64 + 14000 * q^69 - 6592 * q^70 - 12708 * q^71 + 24728 * q^75 - 13040 * q^81 - 15700 * q^85 - 9728 * q^94 - 46608 * q^95 - 4096 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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