LMFDB - Embedded newform 230.6.b.a.139.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,6,Mod(139,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.139"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [26] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.2
Character	$\chi$	$=$	230.139
Dual form			230.6.b.a.139.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000i q^{2} -26.8618i q^{3} -16.0000 q^{4} +(41.5913 + 37.3519i) q^{5} -107.447 q^{6} +117.217i q^{7} +64.0000i q^{8} -478.554 q^{9} +(149.408 - 166.365i) q^{10} -431.621 q^{11} +429.788i q^{12} +590.216i q^{13} +468.867 q^{14} +(1003.34 - 1117.21i) q^{15} +256.000 q^{16} -455.801i q^{17} +1914.22i q^{18} +1769.15 q^{19} +(-665.460 - 597.631i) q^{20} +3148.65 q^{21} +1726.49i q^{22} -529.000i q^{23} +1719.15 q^{24} +(334.666 + 3107.03i) q^{25} +2360.86 q^{26} +6327.39i q^{27} -1875.47i q^{28} +3359.06 q^{29} +(-4468.86 - 4013.35i) q^{30} +5650.67 q^{31} -1024.00i q^{32} +11594.1i q^{33} -1823.20 q^{34} +(-4378.27 + 4875.19i) q^{35} +7656.86 q^{36} +9203.58i q^{37} -7076.59i q^{38} +15854.2 q^{39} +(-2390.52 + 2661.84i) q^{40} +8201.36 q^{41} -12594.6i q^{42} +3041.74i q^{43} +6905.94 q^{44} +(-19903.7 - 17874.9i) q^{45} -2116.00 q^{46} -27863.1i q^{47} -6876.61i q^{48} +3067.23 q^{49} +(12428.1 - 1338.66i) q^{50} -12243.6 q^{51} -9443.45i q^{52} +34141.0i q^{53} +25309.6 q^{54} +(-17951.7 - 16121.9i) q^{55} -7501.87 q^{56} -47522.4i q^{57} -13436.2i q^{58} -11655.4 q^{59} +(-16053.4 + 17875.4i) q^{60} +21992.0 q^{61} -22602.7i q^{62} -56094.5i q^{63} -4096.00 q^{64} +(-22045.7 + 24547.8i) q^{65} +46376.4 q^{66} +20140.5i q^{67} +7292.81i q^{68} -14209.9 q^{69} +(19500.8 + 17513.1i) q^{70} -31963.9 q^{71} -30627.5i q^{72} +20577.1i q^{73} +36814.3 q^{74} +(83460.2 - 8989.71i) q^{75} -28306.4 q^{76} -50593.3i q^{77} -63416.9i q^{78} +28663.6 q^{79} +(10647.4 + 9562.10i) q^{80} +53676.3 q^{81} -32805.4i q^{82} +54289.6i q^{83} -50378.4 q^{84} +(17025.0 - 18957.3i) q^{85} +12167.0 q^{86} -90230.3i q^{87} -27623.8i q^{88} -28123.0 q^{89} +(-71499.7 + 79614.7i) q^{90} -69183.2 q^{91} +8464.00i q^{92} -151787. i q^{93} -111452. q^{94} +(73581.1 + 66081.1i) q^{95} -27506.4 q^{96} +40366.4i q^{97} -12268.9i q^{98} +206554. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26}+ \cdots + 523850 q^{99}+O(q^{100}) $ 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9 + 80 * q^10 - 1314 * q^11 + 808 * q^14 + 1280 * q^15 + 6656 * q^16 + 6630 * q^19 + 480 * q^20 - 10060 * q^21 + 1152 * q^24 - 10470 * q^25 - 376 * q^26 + 16084 * q^29 - 6200 * q^30 + 418 * q^31 + 3320 * q^34 - 3160 * q^35 + 22400 * q^36 + 71296 * q^39 - 1280 * q^40 - 35826 * q^41 + 21024 * q^44 - 83960 * q^45 - 55016 * q^46 + 53532 * q^49 - 20800 * q^50 - 25430 * q^51 + 98736 * q^54 - 110390 * q^55 - 12928 * q^56 + 126992 * q^59 - 20480 * q^60 - 63662 * q^61 - 106496 * q^64 - 88520 * q^65 - 18664 * q^66 - 9522 * q^69 - 116520 * q^70 - 106514 * q^71 + 183536 * q^74 - 44200 * q^75 - 106080 * q^76 + 324676 * q^79 - 7680 * q^80 - 170702 * q^81 + 160960 * q^84 + 120780 * q^85 - 42768 * q^86 + 465200 * q^89 + 61360 * q^90 - 468838 * q^91 + 107152 * q^94 + 309670 * q^95 - 18432 * q^96 + 523850 * q^99

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 $

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$		−	26.8618i		−	1.72318i	−0.507603	−	0.861591i	$-0.669468\pi$
$3$		−	26.8618i		−	1.72318i	0.507603	−	0.861591i	$-0.330532\pi$
$4$	−16.0000			−0.500000
$5$	41.5913	+	37.3519i	0.744007	+	0.668172i
$5$	41.5913	+	37.3519i	0.744007	+	0.668172i
$6$	−107.447			−1.21847
$7$			117.217i			0.904159i	0.891978	+	0.452079i	$0.149318\pi$
$7$			117.217i			0.904159i	−0.891978	+	0.452079i	$0.850682\pi$
$8$			64.0000i			0.353553i
$9$	−478.554			−1.96936
$10$	149.408	−	166.365i	0.472469	−	0.526092i
$11$	−431.621			−1.07553			−0.537763	−	0.843096i	$-0.680731\pi$
$11$	−431.621			−1.07553			−0.537763	+	0.843096i	$0.680731\pi$
$12$			429.788i			0.861591i
$13$			590.216i			0.968617i	0.874897	+	0.484309i	$0.160929\pi$
$13$			590.216i			0.968617i	−0.874897	+	0.484309i	$0.839071\pi$
$14$	468.867			0.639337
$15$	1003.34	−	1117.21i	1.15138	−	1.28206i
$16$	256.000			0.250000
$17$		−	455.801i		−	0.382519i	−0.981540	−	0.191259i	$-0.938743\pi$
$17$		−	455.801i		−	0.382519i	0.981540	−	0.191259i	$-0.0612572\pi$
$18$			1914.22i			1.39255i
$19$	1769.15			1.12429			0.562147	−	0.827037i	$-0.309975\pi$
$19$	1769.15			1.12429			0.562147	+	0.827037i	$0.309975\pi$
$20$	−665.460	−	597.631i	−0.372004	−	0.334086i
$21$	3148.65			1.55803
$22$			1726.49i			0.760512i
$23$		−	529.000i		−	0.208514i
$23$		−	529.000i		−	0.208514i
$24$	1719.15			0.609237
$25$	334.666	+	3107.03i	0.107093	+	0.994249i
$26$	2360.86			0.684916
$27$			6327.39i			1.67038i
$28$		−	1875.47i		−	0.452079i
$29$	3359.06			0.741691			0.370845	−	0.928695i	$-0.379068\pi$
$29$	3359.06			0.741691			0.370845	+	0.928695i	$0.379068\pi$
$30$	−4468.86	−	4013.35i	−0.906553	−	0.814150i
$31$	5650.67			1.05608			0.528038	−	0.849221i	$-0.322928\pi$
$31$	5650.67			1.05608			0.528038	+	0.849221i	$0.322928\pi$
$32$		−	1024.00i		−	0.176777i
$33$			11594.1i			1.85333i
$34$	−1823.20			−0.270482
$35$	−4378.27	+	4875.19i	−0.604133	+	0.672700i
$36$	7656.86			0.984679
$37$			9203.58i			1.10523i	0.833437	+	0.552615i	$0.186370\pi$
$37$			9203.58i			1.10523i	−0.833437	+	0.552615i	$0.813630\pi$
$38$		−	7076.59i		−	0.794996i
$39$	15854.2			1.66910
$40$	−2390.52	+	2661.84i	−0.236234	+	0.263046i
$41$	8201.36			0.761949			0.380975	−	0.924585i	$-0.375589\pi$
$41$	8201.36			0.761949			0.380975	+	0.924585i	$0.375589\pi$
$42$		−	12594.6i		−	1.10169i
$43$			3041.74i			0.250872i	0.992102	+	0.125436i	$0.0400329\pi$
$43$			3041.74i			0.250872i	−0.992102	+	0.125436i	$0.959967\pi$
$44$	6905.94			0.537763
$45$	−19903.7	−	17874.9i	−1.46522	−	1.31587i
$46$	−2116.00			−0.147442
$47$		−	27863.1i		−	1.83986i	−0.392085	−	0.919929i	$-0.628246\pi$
$47$		−	27863.1i		−	1.83986i	0.392085	−	0.919929i	$-0.371754\pi$
$48$		−	6876.61i		−	0.430796i
$49$	3067.23			0.182497
$50$	12428.1	−	1338.66i	0.703040	−	0.0757262i
$51$	−12243.6			−0.659150
$52$		−	9443.45i		−	0.484309i
$53$			34141.0i			1.66950i	0.550629	+	0.834750i	$0.314388\pi$
$53$			34141.0i			1.66950i	−0.550629	+	0.834750i	$0.685612\pi$
$54$	25309.6			1.18114
$55$	−17951.7	−	16121.9i	−0.800200	−	0.718637i
$56$	−7501.87			−0.319668
$57$		−	47522.4i		−	1.93736i
$58$		−	13436.2i		−	0.524455i
$59$	−11655.4			−0.435909			−0.217954	−	0.975959i	$-0.569938\pi$
$59$	−11655.4			−0.435909			−0.217954	+	0.975959i	$0.569938\pi$
$60$	−16053.4	+	17875.4i	−0.575691	+	0.641030i
$61$	21992.0			0.756728			0.378364	−	0.925657i	$-0.376487\pi$
$61$	21992.0			0.756728			0.378364	+	0.925657i	$0.376487\pi$
$62$		−	22602.7i		−	0.746759i
$63$		−	56094.5i		−	1.78061i
$64$	−4096.00			−0.125000
$65$	−22045.7	+	24547.8i	−0.647203	+	0.720658i
$66$	46376.4			1.31050
$67$			20140.5i			0.548131i	0.961711	+	0.274065i	$0.0883685\pi$
$67$			20140.5i			0.548131i	−0.961711	+	0.274065i	$0.911632\pi$
$68$			7292.81i			0.191259i
$69$	−14209.9			−0.359308
$70$	19500.8	+	17513.1i	0.475671	+	0.427187i
$71$	−31963.9			−0.752512			−0.376256	−	0.926516i	$-0.622789\pi$
$71$	−31963.9			−0.752512			−0.376256	+	0.926516i	$0.622789\pi$
$72$		−	30627.5i		−	0.696273i
$73$			20577.1i			0.451937i	0.974135	+	0.225969i	$0.0725547\pi$
$73$			20577.1i			0.451937i	−0.974135	+	0.225969i	$0.927445\pi$
$74$	36814.3			0.781515
$75$	83460.2	−	8989.71i	1.71327	−	0.184541i
$76$	−28306.4			−0.562147
$77$		−	50593.3i		−	0.972447i
$78$		−	63416.9i		−	1.18024i
$79$	28663.6			0.516730			0.258365	−	0.966047i	$-0.416816\pi$
$79$	28663.6			0.516730			0.258365	+	0.966047i	$0.416816\pi$
$80$	10647.4	+	9562.10i	0.186002	+	0.167043i
$81$	53676.3			0.909013
$82$		−	32805.4i		−	0.538780i
$83$			54289.6i			0.865011i	0.901631	+	0.432505i	$0.142370\pi$
$83$			54289.6i			0.865011i	−0.901631	+	0.432505i	$0.857630\pi$
$84$	−50378.4			−0.779015
$85$	17025.0	−	18957.3i	0.255588	−	0.284597i
$86$	12167.0			0.177393
$87$		−	90230.3i		−	1.27807i
$88$		−	27623.8i		−	0.380256i
$89$	−28123.0			−0.376346			−0.188173	−	0.982136i	$-0.560257\pi$
$89$	−28123.0			−0.376346			−0.188173	+	0.982136i	$0.560257\pi$
$90$	−71499.7	+	79614.7i	−0.930460	+	1.03606i
$91$	−69183.2			−0.875784
$92$			8464.00i			0.104257i
$93$		−	151787.i		−	1.81981i
$94$	−111452.			−1.30098
$95$	73581.1	+	66081.1i	0.836483	+	0.751222i
$96$	−27506.4			−0.304619
$97$			40366.4i			0.435603i	0.975993	+	0.217801i	$0.0698885\pi$
$97$			40366.4i			0.435603i	−0.975993	+	0.217801i	$0.930111\pi$
$98$		−	12268.9i		−	0.129045i
$99$	206554.			2.11810
$100$	−5354.65	−	49712.5i	−0.0535465	−	0.497125i
$101$	−6286.80			−0.0613234			−0.0306617	−	0.999530i	$-0.509761\pi$
$101$	−6286.80			−0.0613234			−0.0306617	+	0.999530i	$0.509761\pi$
$102$			48974.4i			0.466089i
$103$			132389.i			1.22959i	0.788687	+	0.614795i	$0.210761\pi$
$103$			132389.i			1.22959i	−0.788687	+	0.614795i	$0.789239\pi$
$104$	−37773.8			−0.342458
$105$	130956.	+	117608.i	1.15919	+	1.04103i
$106$	136564.			1.18052
$107$			173041.i			1.46113i	0.682842	+	0.730567i	$0.260744\pi$
$107$			173041.i			1.46113i	−0.682842	+	0.730567i	$0.739256\pi$
$108$		−	101238.i		−	0.835190i
$109$	130523.			1.05226			0.526129	−	0.850405i	$-0.323643\pi$
$109$	130523.			1.05226			0.526129	+	0.850405i	$0.323643\pi$
$110$	−64487.6	+	71806.7i	−0.508153	+	0.565827i
$111$	247224.			1.90451
$112$			30007.5i			0.226040i
$113$			235357.i			1.73393i	0.498372	+	0.866963i	$0.333931\pi$
$113$			235357.i			1.73393i	−0.498372	+	0.866963i	$0.666069\pi$
$114$	−190090.			−1.36992
$115$	19759.2	−	22001.8i	0.139323	−	0.155136i
$116$	−53745.0			−0.370845
$117$		−	282450.i		−	1.90755i
$118$			46621.5i			0.308234i
$119$	53427.5			0.345858
$120$	71501.7	+	64213.7i	0.453277	+	0.407075i
$121$	25246.0			0.156758
$122$		−	87967.9i		−	0.535087i
$123$		−	220303.i		−	1.31298i
$124$	−90410.7			−0.528038
$125$	−102134.	+	141726.i	−0.584651	+	0.811285i
$126$	−224378.			−1.25908
$127$		−	299544.i		−	1.64798i	−0.566606	−	0.823989i	$-0.691744\pi$
$127$		−	299544.i		−	1.64798i	0.566606	−	0.823989i	$-0.308256\pi$
$128$			16384.0i			0.0883883i
$129$	81706.6			0.432297
$130$	98191.2	+	88182.8i	0.509582	+	0.457641i
$131$	−141597.			−0.720903			−0.360452	−	0.932778i	$-0.617377\pi$
$131$	−141597.			−0.720903			−0.360452	+	0.932778i	$0.617377\pi$
$132$		−	185506.i		−	0.926665i
$133$			207374.i			1.01654i
$134$	80562.2			0.387587
$135$	−236340.	+	263164.i	−1.11610	+	1.24278i
$136$	29171.3			0.135241
$137$		−	315794.i		−	1.43748i	−0.695279	−	0.718740i	$-0.744719\pi$
$137$		−	315794.i		−	1.43748i	0.695279	−	0.718740i	$-0.255281\pi$
$138$			56839.5i			0.254069i
$139$	299255.			1.31373			0.656864	−	0.754009i	$-0.271883\pi$
$139$	299255.			1.31373			0.656864	+	0.754009i	$0.271883\pi$
$140$	70052.4	−	78003.1i	0.302067	−	0.336350i
$141$	−748451.			−3.17041
$142$			127855.i			0.532106i
$143$		−	254750.i		−	1.04177i
$144$	−122510.			−0.492340
$145$	139708.	+	125467.i	0.551823	+	0.495577i
$146$	82308.6			0.319568
$147$		−	82391.3i		−	0.314476i
$148$		−	147257.i		−	0.552615i
$149$	−358442.			−1.32267			−0.661337	−	0.750089i	$-0.730011\pi$
$149$	−358442.			−1.32267			−0.661337	+	0.750089i	$0.730011\pi$
$150$	−35958.8	−	333841.i	−0.130490	−	1.21147i
$151$	201705.			0.719903			0.359951	−	0.932971i	$-0.382793\pi$
$151$	201705.			0.719903			0.359951	+	0.932971i	$0.382793\pi$
$152$			113225.i			0.397498i
$153$			218125.i			0.753316i
$154$	−202373.			−0.687624
$155$	235018.	+	211063.i	0.785729	+	0.705641i
$156$	−253668.			−0.834552
$157$			252131.i			0.816350i	0.912904	+	0.408175i	$0.133835\pi$
$157$			252131.i			0.816350i	−0.912904	+	0.408175i	$0.866165\pi$
$158$		−	114655.i		−	0.365383i
$159$	917087.			2.87685
$160$	38248.4	−	42589.4i	0.118117	−	0.131523i
$161$	62007.7			0.188530
$162$		−	214705.i		−	0.642769i
$163$		−	271597.i		−	0.800674i	−0.916368	−	0.400337i	$-0.868893\pi$
$163$		−	271597.i		−	0.800674i	0.916368	−	0.400337i	$-0.131107\pi$
$164$	−131222.			−0.380975
$165$	−433062.	+	482214.i	−1.23834	+	1.37889i
$166$	217158.			0.611655
$167$			686846.i			1.90576i	0.303348	+	0.952880i	$0.401895\pi$
$167$			686846.i			1.90576i	−0.303348	+	0.952880i	$0.598105\pi$
$168$			201513.i			0.550847i
$169$	22938.6			0.0617803
$170$	−75829.3	−	68100.2i	−0.201240	−	0.180728i
$171$	−846633.			−2.21414
$172$		−	48667.9i		−	0.125436i
$173$			107188.i			0.272290i	0.990689	+	0.136145i	$0.0434713\pi$
$173$			107188.i			0.272290i	−0.990689	+	0.136145i	$0.956529\pi$
$174$	−360921.			−0.903731
$175$	−364196.	+	39228.4i	−0.898959	+	0.0968291i
$176$	−110495.			−0.268882
$177$			313084.i			0.751151i
$178$			112492.i			0.266117i
$179$	675507.			1.57579			0.787893	−	0.615812i	$-0.211172\pi$
$179$	675507.			1.57579			0.787893	+	0.615812i	$0.211172\pi$
$180$	318459.	+	285999.i	0.732608	+	0.657935i
$181$	−777303.			−1.76357			−0.881787	−	0.471647i	$-0.843660\pi$
$181$	−777303.			−1.76357			−0.881787	+	0.471647i	$0.843660\pi$
$182$			276733.i			0.619273i
$183$		−	590743.i		−	1.30398i
$184$	33856.0			0.0737210
$185$	−343772.	+	382789.i	−0.738483	+	0.822299i
$186$	−607147.			−1.28680
$187$			196733.i			0.411409i
$188$			445809.i			0.919929i
$189$	−741677.			−1.51029
$190$	264324.	−	294324.i	0.531194	−	0.591483i
$191$	−449907.			−0.892358			−0.446179	−	0.894944i	$-0.647215\pi$
$191$	−449907.			−0.892358			−0.446179	+	0.894944i	$0.647215\pi$
$192$			110026.i			0.215398i
$193$			350276.i			0.676889i	0.940986	+	0.338444i	$0.109901\pi$
$193$			350276.i			0.676889i	−0.940986	+	0.338444i	$0.890099\pi$
$194$	161466.			0.308018
$195$	659397.	+	592186.i	1.24183	+	1.11525i
$196$	−49075.7			−0.0912487
$197$		−	121355.i		−	0.222788i	−0.993776	−	0.111394i	$-0.964468\pi$
$197$		−	121355.i		−	0.222788i	0.993776	−	0.111394i	$-0.0355315\pi$
$198$		−	826217.i		−	1.49772i
$199$	−209357.			−0.374762			−0.187381	−	0.982287i	$-0.560000\pi$
$199$	−209357.			−0.374762			−0.187381	+	0.982287i	$0.560000\pi$
$200$	−198850.	+	21418.6i	−0.351520	+	0.0378631i
$201$	541010.			0.944529
$202$			25147.2i			0.0433622i
$203$			393738.i			0.670606i
$204$	195898.			0.329575
$205$	341105.	+	306337.i	0.566896	+	0.509113i
$206$	529557.			0.869451
$207$			253155.i			0.410640i
$208$			151095.i			0.242154i
$209$	−763602.			−1.20921
$210$	470432.	−	523825.i	0.736121	−	0.819668i
$211$	1.10895e6			1.71477			0.857386	−	0.514674i	$-0.172087\pi$
$211$	1.10895e6			1.71477			0.857386	+	0.514674i	$0.172087\pi$
$212$		−	546256.i		−	0.834750i
$213$			858605.i			1.29671i
$214$	692164.			1.03318
$215$	−113615.	+	126510.i	−0.167625	+	0.186650i
$216$	−404953.			−0.590569
$217$			662353.i			0.954861i
$218$		−	522094.i		−	0.744059i
$219$	552738.			0.778770
$220$	287227.	+	257950.i	0.400100	+	0.359318i
$221$	269021.			0.370514
$222$		−	988897.i		−	1.34669i
$223$		−	905806.i		−	1.21976i	−0.792495	−	0.609878i	$-0.791219\pi$
$223$		−	905806.i		−	1.21976i	0.792495	−	0.609878i	$-0.208781\pi$
$224$	120030.			0.159834
$225$	−160156.	−	1.48688e6i	−0.210905	−	1.95803i
$226$	941427.			1.22607
$227$			254382.i			0.327659i	0.986489	+	0.163830i	$0.0523847\pi$
$227$			254382.i			0.327659i	−0.986489	+	0.163830i	$0.947615\pi$
$228$			760358.i			0.968682i
$229$	−852673.			−1.07447			−0.537234	−	0.843433i	$-0.680531\pi$
$229$	−852673.			−1.07447			−0.537234	+	0.843433i	$0.680531\pi$
$230$	−88007.1	−	79036.7i	−0.109698	−	0.0985165i
$231$	−1.35902e6			−1.67570
$232$			214980.i			0.262227i
$233$		−	1.12515e6i		−	1.35776i	−0.734251	−	0.678879i	$-0.762466\pi$
$233$		−	1.12515e6i		−	1.35776i	0.734251	−	0.678879i	$-0.237534\pi$
$234$	−1.12980e6			−1.34884
$235$	1.04074e6	−	1.15886e6i	1.22934	−	1.36887i
$236$	186486.			0.217954
$237$		−	769956.i		−	0.890420i
$238$		−	213710.i		−	0.244558i
$239$	1.19650e6			1.35494			0.677468	−	0.735552i	$-0.263077\pi$
$239$	1.19650e6			1.35494			0.677468	+	0.735552i	$0.263077\pi$
$240$	256855.	−	286007.i	0.287845	−	0.320515i
$241$	−234746.			−0.260349			−0.130174	−	0.991491i	$-0.541554\pi$
$241$	−234746.			−0.260349			−0.130174	+	0.991491i	$0.541554\pi$
$242$		−	100984.i		−	0.110845i
$243$			95716.8i			0.103985i
$244$	−351872.			−0.378364
$245$	127570.	+	114567.i	0.135779	+	0.121940i
$246$	−881211.			−0.928415
$247$			1.04418e6i			1.08901i
$248$			361643.i			0.373380i
$249$	1.45831e6			1.49057
$250$	566903.	+	408537.i	0.573665	+	0.413411i
$251$	431980.			0.432792			0.216396	−	0.976306i	$-0.430570\pi$
$251$	431980.			0.432792			0.216396	+	0.976306i	$0.430570\pi$
$252$			897513.i			0.890306i
$253$			228328.i			0.224263i
$254$	−1.19818e6			−1.16530
$255$	−509227.	−	457323.i	−0.490412	−	0.440425i
$256$	65536.0			0.0625000
$257$		−	145036.i		−	0.136976i	−0.997652	−	0.0684879i	$-0.978183\pi$
$257$		−	145036.i		−	0.136976i	0.997652	−	0.0684879i	$-0.0218175\pi$
$258$		−	326826.i		−	0.305680i
$259$	−1.07881e6			−0.999303
$260$	352731.	−	392765.i	0.323601	−	0.360329i
$261$	−1.60749e6			−1.46065
$262$			566389.i			0.509756i
$263$		−	1.79162e6i		−	1.59719i	−0.601870	−	0.798594i	$-0.705577\pi$
$263$		−	1.79162e6i		−	1.59719i	0.601870	−	0.798594i	$-0.294423\pi$
$264$	−742023.			−0.655251
$265$	−1.27523e6	+	1.41997e6i	−1.11551	+	1.24212i
$266$	829495.			0.718803
$267$			755434.i			0.648513i
$268$		−	322249.i		−	0.274065i
$269$	831782.			0.700856			0.350428	−	0.936590i	$-0.386036\pi$
$269$	831782.			0.700856			0.350428	+	0.936590i	$0.386036\pi$
$270$	1.05266e6	+	945362.i	0.878775	+	0.789203i
$271$	254514.			0.210518			0.105259	−	0.994445i	$-0.466433\pi$
$271$	254514.			0.210518			0.105259	+	0.994445i	$0.466433\pi$
$272$		−	116685.i		−	0.0956297i
$273$			1.85838e6i			1.50914i
$274$	−1.26317e6			−1.01645
$275$	−144449.	−	1.34106e6i	−0.115181	−	1.06934i
$276$	227358.			0.179654
$277$			21327.4i			0.0167008i	0.999965	+	0.00835041i	$0.00265805\pi$
$277$			21327.4i			0.0167008i	−0.999965	+	0.00835041i	$0.997342\pi$
$278$		−	1.19702e6i		−	0.928945i
$279$	−2.70415e6			−2.07979
$280$	−312012.	−	280209.i	−0.237835	−	0.213593i
$281$	113691.			0.0858938			0.0429469	−	0.999077i	$-0.486325\pi$
$281$	113691.			0.0858938			0.0429469	+	0.999077i	$0.486325\pi$
$282$			2.99380e6i			2.24182i
$283$		−	1.87899e6i		−	1.39463i	−0.716767	−	0.697313i	$-0.754379\pi$
$283$		−	1.87899e6i		−	1.39463i	0.716767	−	0.697313i	$-0.245621\pi$
$284$	511422.			0.376256
$285$	1.77505e6	−	1.97652e6i	1.29449	−	1.44141i
$286$	−1.01900e6			−0.736645
$287$			961336.i			0.688923i
$288$			490039.i			0.348137i
$289$	1.21210e6			0.853679
$290$	501870.	−	558830.i	0.350426	−	0.390198i
$291$	1.08431e6			0.750623
$292$		−	329234.i		−	0.225969i
$293$		−	1.55725e6i		−	1.05972i	−0.848086	−	0.529859i	$-0.822245\pi$
$293$		−	1.55725e6i		−	1.05972i	0.848086	−	0.529859i	$-0.177755\pi$
$294$	−329565.			−0.222368
$295$	−484761.	−	435350.i	−0.324319	−	0.291262i
$296$	−589029.			−0.390758
$297$		−	2.73104e6i		−	1.79654i
$298$			1.43377e6i			0.935272i
$299$	312224.			0.201971
$300$	−1.33536e6	+	143835.i	−0.856636	+	0.0922704i
$301$	−356543.			−0.226828
$302$		−	806819.i		−	0.509048i
$303$			168874.i			0.105671i
$304$	452902.			0.281074
$305$	914674.	+	821443.i	0.563011	+	0.505624i
$306$	872501.			0.532675
$307$			2.08436e6i			1.26219i	0.775704	+	0.631097i	$0.217395\pi$
$307$			2.08436e6i			1.26219i	−0.775704	+	0.631097i	$0.782605\pi$
$308$			809492.i			0.486223i
$309$	3.55621e6			2.11881
$310$	844253.	−	940073.i	0.498963	−	0.555594i
$311$	−494021.			−0.289630			−0.144815	−	0.989459i	$-0.546259\pi$
$311$	−494021.			−0.289630			−0.144815	+	0.989459i	$0.546259\pi$
$312$			1.01467e6i			0.590118i
$313$			1.30578e6i			0.753370i	0.926341	+	0.376685i	$0.122936\pi$
$313$			1.30578e6i			0.753370i	−0.926341	+	0.376685i	$0.877064\pi$
$314$	1.00852e6			0.577247
$315$	2.09524e6	−	2.33304e6i	1.18975	−	1.32479i
$316$	−458618.			−0.258365
$317$		−	2.62123e6i		−	1.46507i	−0.680731	−	0.732533i	$-0.738338\pi$
$317$		−	2.62123e6i		−	1.46507i	0.680731	−	0.732533i	$-0.261662\pi$
$318$		−	3.66835e6i		−	2.03424i
$319$	−1.44984e6			−0.797708
$320$	−170358.	−	152994.i	−0.0930009	−	0.0835215i
$321$	4.64819e6			2.51780
$322$		−	248031.i		−	0.133311i
$323$		−	806379.i		−	0.430064i
$324$	−858821.			−0.454507
$325$	−1.83382e6	+	197525.i	−0.963047	+	0.103732i
$326$	−1.08639e6			−0.566162
$327$		−	3.50609e6i		−	1.81323i
$328$			524887.i			0.269390i
$329$	3.26602e6			1.66352
$330$	1.92885e6	+	1.73225e6i	0.975022	+	0.875640i
$331$	−3.65353e6			−1.83291			−0.916457	−	0.400133i	$-0.868964\pi$
$331$	−3.65353e6			−1.83291			−0.916457	+	0.400133i	$0.868964\pi$
$332$		−	868634.i		−	0.432505i
$333$		−	4.40441e6i		−	2.17659i
$334$	2.74738e6			1.34758
$335$	−752288.	+	837671.i	−0.366246	+	0.407813i
$336$	806054.			0.389508
$337$			2.08629e6i			1.00069i	0.865825	+	0.500347i	$0.166794\pi$
$337$			2.08629e6i			1.00069i	−0.865825	+	0.500347i	$0.833206\pi$
$338$		−	91754.4i		−	0.0436853i
$339$	6.32210e6			2.98787
$340$	−272401.	+	303317.i	−0.127794	+	0.142298i
$341$	−2.43895e6			−1.13584
$342$			3.38653e6i			1.56563i
$343$			2.32959e6i			1.06917i
$344$	−194672.			−0.0886965
$345$	−591006.	−	530766.i	−0.267328	−	0.240080i
$346$	428753.			0.192538
$347$		−	414832.i		−	0.184948i	−0.995715	−	0.0924738i	$-0.970523\pi$
$347$		−	414832.i		−	0.184948i	0.995715	−	0.0924738i	$-0.0294774\pi$
$348$			1.44368e6i			0.639034i
$349$	658547.			0.289417			0.144708	−	0.989474i	$-0.453776\pi$
$349$	658547.			0.289417			0.144708	+	0.989474i	$0.453776\pi$
$350$	156914.	+	1.45678e6i	0.0684685	+	0.635660i
$351$	−3.73453e6			−1.61796
$352$			441980.i			0.190128i
$353$		−	1.91003e6i		−	0.815839i	−0.913018	−	0.407919i	$-0.866254\pi$
$353$		−	1.91003e6i		−	0.815839i	0.913018	−	0.407919i	$-0.133746\pi$
$354$	1.25233e6			0.531144
$355$	−1.32942e6	−	1.19391e6i	−0.559874	−	0.502807i
$356$	449969.			0.188173
$357$		−	1.43516e6i		−	0.595976i
$358$		−	2.70203e6i		−	1.11425i
$359$	3.45324e6			1.41413			0.707067	−	0.707147i	$-0.250018\pi$
$359$	3.45324e6			1.41413			0.707067	+	0.707147i	$0.250018\pi$
$360$	1.14399e6	−	1.27383e6i	0.465230	−	0.518032i
$361$	653783.			0.264038
$362$			3.10921e6i			1.24704i
$363$		−	678153.i		−	0.270123i
$364$	1.10693e6			0.437892
$365$	−768596.	+	855829.i	−0.301972	+	0.336244i
$366$	−2.36297e6			−0.922053
$367$			4.93092e6i			1.91101i	0.294976	+	0.955505i	$0.404688\pi$
$367$			4.93092e6i			1.91101i	−0.294976	+	0.955505i	$0.595312\pi$
$368$		−	135424.i		−	0.0521286i
$369$	−3.92479e6			−1.50055
$370$	1.53115e6	+	1.37509e6i	0.581453	+	0.522186i
$371$	−4.00190e6			−1.50949
$372$			2.42859e6i			0.909906i
$373$			2.27154e6i			0.845373i	0.906276	+	0.422687i	$0.138913\pi$
$373$			2.27154e6i			0.845373i	−0.906276	+	0.422687i	$0.861087\pi$
$374$	786933.			0.290910
$375$	3.80700e6	+	2.74351e6i	1.39799	+	1.00746i
$376$	1.78324e6			0.650488
$377$			1.98257e6i			0.718415i
$378$			2.96671e6i			1.06794i
$379$	4.82813e6			1.72656			0.863278	−	0.504728i	$-0.168407\pi$
$379$	4.82813e6			1.72656			0.863278	+	0.504728i	$0.168407\pi$
$380$	−1.17730e6	−	1.05730e6i	−0.418241	−	0.375611i
$381$	−8.04628e6			−2.83977
$382$			1.79963e6i			0.630992i
$383$			2.68294e6i			0.934575i	0.884105	+	0.467288i	$0.154769\pi$
$383$			2.68294e6i			0.934575i	−0.884105	+	0.467288i	$0.845231\pi$
$384$	440103.			0.152309
$385$	1.88976e6	−	2.10424e6i	0.649761	−	0.723507i
$386$	1.40110e6			0.478633
$387$		−	1.45564e6i		−	0.494056i
$388$		−	645862.i		−	0.217801i
$389$	−3.86485e6			−1.29497			−0.647483	−	0.762080i	$-0.724178\pi$
$389$	−3.86485e6			−1.29497			−0.647483	+	0.762080i	$0.724178\pi$
$390$	2.36874e6	−	2.63759e6i	0.788600	−	0.878103i
$391$	−241119.			−0.0797607
$392$			196303.i			0.0645225i
$393$			3.80355e6i			1.24225i
$394$	−485419.			−0.157535
$395$	1.19216e6	+	1.07064e6i	0.384451	+	0.345264i
$396$	−3.30487e6			−1.05905
$397$		−	3.16739e6i		−	1.00861i	−0.863525	−	0.504307i	$-0.831748\pi$
$397$		−	3.16739e6i		−	1.00861i	0.863525	−	0.504307i	$-0.168252\pi$
$398$			837430.i			0.264997i
$399$	5.57042e6			1.75168
$400$	85674.4	+	795399.i	0.0267733	+	0.248562i
$401$	−4.63478e6			−1.43936			−0.719678	−	0.694308i	$-0.755711\pi$
$401$	−4.63478e6			−1.43936			−0.719678	+	0.694308i	$0.755711\pi$
$402$		−	2.16404e6i		−	0.667883i
$403$			3.33511e6i			1.02293i
$404$	100589.			0.0306617
$405$	2.23247e6	+	2.00491e6i	0.676312	+	0.607377i
$406$	1.57495e6			0.474190
$407$		−	3.97246e6i		−	1.18870i
$408$		−	783591.i		−	0.233045i
$409$	−3.61968e6			−1.06995			−0.534974	−	0.844869i	$-0.679678\pi$
$409$	−3.61968e6			−1.06995			−0.534974	+	0.844869i	$0.679678\pi$
$410$	1.22535e6	−	1.36442e6i	0.359997	−	0.400856i
$411$	−8.48277e6			−2.47704
$412$		−	2.11823e6i		−	0.614795i
$413$		−	1.36620e6i		−	0.394131i
$414$	1.01262e6			0.290366
$415$	−2.02782e6	+	2.25797e6i	−0.577976	+	0.643574i
$416$	604381.			0.171229
$417$		−	8.03853e6i		−	2.26379i
$418$			3.05441e6i			0.855040i
$419$	1.71063e6			0.476015			0.238007	−	0.971263i	$-0.423506\pi$
$419$	1.71063e6			0.476015			0.238007	+	0.971263i	$0.423506\pi$
$420$	−2.09530e6	−	1.88173e6i	−0.579593	−	0.520516i
$421$	5.12281e6			1.40865			0.704324	−	0.709878i	$-0.251250\pi$
$421$	5.12281e6			1.40865			0.704324	+	0.709878i	$0.251250\pi$
$422$		−	4.43581e6i		−	1.21253i
$423$			1.33340e7i			3.62334i
$424$	−2.18502e6			−0.590258
$425$	1.41619e6	−	152541.i	0.380319	−	0.0409651i
$426$	3.43442e6			0.916916
$427$			2.57783e6i			0.684202i
$428$		−	2.76866e6i		−	0.730567i
$429$	−6.84302e6			−1.79517
$430$	506040.	+	454460.i	0.131982	+	0.118529i
$431$	−5.24857e6			−1.36097			−0.680484	−	0.732763i	$-0.738230\pi$
$431$	−5.24857e6			−1.36097			−0.680484	+	0.732763i	$0.738230\pi$
$432$			1.61981e6i			0.417595i
$433$		−	3.15341e6i		−	0.808277i	−0.914698	−	0.404138i	$-0.867571\pi$
$433$		−	3.15341e6i		−	0.808277i	0.914698	−	0.404138i	$-0.132429\pi$
$434$	2.64941e6			0.675189
$435$	3.37028e6	−	3.75279e6i	0.853969	−	0.950892i
$436$	−2.08837e6			−0.526129
$437$		−	935879.i		−	0.234432i
$438$		−	2.21095e6i		−	0.550674i
$439$	−7.46039e6			−1.84757			−0.923783	−	0.382916i	$-0.874920\pi$
$439$	−7.46039e6			−1.84757			−0.923783	+	0.382916i	$0.874920\pi$
$440$	1.03180e6	−	1.14891e6i	0.254076	−	0.282913i
$441$	−1.46784e6			−0.359403
$442$		−	1.07608e6i		−	0.261993i
$443$		−	250230.i		−	0.0605802i	−0.999541	−	0.0302901i	$-0.990357\pi$
$443$		−	250230.i		−	0.0605802i	0.999541	−	0.0302901i	$-0.00964311\pi$
$444$	−3.95559e6			−0.952256
$445$	−1.16967e6	−	1.05045e6i	−0.280004	−	0.251464i
$446$	−3.62322e6			−0.862497
$447$			9.62837e6i			2.27921i
$448$		−	480120.i		−	0.113020i
$449$	−3.52812e6			−0.825901			−0.412950	−	0.910754i	$-0.635502\pi$
$449$	−3.52812e6			−0.825901			−0.412950	+	0.910754i	$0.635502\pi$
$450$	−5.94752e6	+	640623.i	−1.38454	+	0.149132i
$451$	−3.53988e6			−0.819497
$452$		−	3.76571e6i		−	0.866963i
$453$		−	5.41815e6i		−	1.24052i
$454$	1.01753e6			0.231690
$455$	−2.87741e6	−	2.58412e6i	−0.651589	−	0.585174i
$456$	3.04143e6			0.684962
$457$			2.73901e6i			0.613484i	0.951793	+	0.306742i	$0.0992389\pi$
$457$			2.73901e6i			0.613484i	−0.951793	+	0.306742i	$0.900761\pi$
$458$			3.41069e6i			0.759764i
$459$	2.88403e6			0.638952
$460$	−316147.	+	352028.i	−0.0696617	+	0.0775681i
$461$	−5.14651e6			−1.12787			−0.563937	−	0.825818i	$-0.690714\pi$
$461$	−5.14651e6			−1.12787			−0.563937	+	0.825818i	$0.690714\pi$
$462$			5.43610e6i			1.18490i
$463$			8.06412e6i			1.74825i	0.485698	+	0.874127i	$0.338566\pi$
$463$			8.06412e6i			1.74825i	−0.485698	+	0.874127i	$0.661434\pi$
$464$	859920.			0.185423
$465$	5.66953e6	−	6.31301e6i	1.21595	−	1.35395i
$466$	−4.50062e6			−0.960079
$467$		−	5.47424e6i		−	1.16153i	−0.814070	−	0.580766i	$-0.802753\pi$
$467$		−	5.47424e6i		−	1.16153i	0.814070	−	0.580766i	$-0.197247\pi$
$468$			4.51920e6i			0.953777i
$469$	−2.36081e6			−0.495597
$470$	−4.63544e6	−	4.16296e6i	−0.967936	−	0.869276i
$471$	6.77267e6			1.40672
$472$		−	745943.i		−	0.154117i
$473$		−	1.31288e6i		−	0.269819i
$474$	−3.07982e6			−0.629622
$475$	592073.	+	5.49679e6i	0.120404	+	1.11783i
$476$	−854840.			−0.172929
$477$		−	1.63383e7i		−	3.28784i
$478$		−	4.78601e6i		−	0.958084i
$479$	−5.99647e6			−1.19415			−0.597073	−	0.802187i	$-0.703670\pi$
$479$	−5.99647e6			−1.19415			−0.597073	+	0.802187i	$0.703670\pi$
$480$	−1.14403e6	−	1.02742e6i	−0.226638	−	0.203537i
$481$	−5.43210e6			−1.07054
$482$			938983.i			0.184094i
$483$		−	1.66563e6i		−	0.324872i
$484$	−403936.			−0.0783790
$485$	−1.50776e6	+	1.67889e6i	−0.291057	+	0.324092i
$486$	382867.			0.0735288
$487$		−	6.82842e6i		−	1.30466i	−0.757935	−	0.652330i	$-0.773792\pi$
$487$		−	6.82842e6i		−	1.30466i	0.757935	−	0.652330i	$-0.226208\pi$
$488$			1.40749e6i			0.267544i
$489$	−7.29557e6			−1.37971
$490$	458268.	−	510280.i	0.0862243	−	0.0960105i
$491$	9.40676e6			1.76091			0.880454	−	0.474132i	$-0.157238\pi$
$491$	9.40676e6			1.76091			0.880454	+	0.474132i	$0.157238\pi$
$492$			3.52485e6i			0.656489i
$493$		−	1.53106e6i		−	0.283711i
$494$	4.17671e6			0.770047
$495$	8.59085e6	+	7.71520e6i	1.57588	+	1.41525i
$496$	1.44657e6			0.264019
$497$		−	3.74670e6i		−	0.680390i
$498$		−	5.83326e6i		−	1.05399i
$499$	−4.77154e6			−0.857842			−0.428921	−	0.903342i	$-0.641106\pi$
$499$	−4.77154e6			−0.857842			−0.428921	+	0.903342i	$0.641106\pi$
$500$	1.63415e6	−	2.26761e6i	0.292326	−	0.405642i
$501$	1.84499e7			3.28397
$502$		−	1.72792e6i		−	0.306030i
$503$			2.17494e6i			0.383290i	0.981464	+	0.191645i	$0.0613823\pi$
$503$			2.17494e6i			0.383290i	−0.981464	+	0.191645i	$0.938618\pi$
$504$	3.59005e6			0.629541
$505$	−261476.	−	234824.i	−0.0456250	−	0.0409745i
$506$	913311.			0.158578
$507$		−	616171.i		−	0.106459i
$508$			4.79270e6i			0.823989i
$509$	7.75150e6			1.32615			0.663073	−	0.748555i	$-0.269252\pi$
$509$	7.75150e6			1.32615			0.663073	+	0.748555i	$0.269252\pi$
$510$	−1.82929e6	+	2.03691e6i	−0.311428	+	0.346774i
$511$	−2.41199e6			−0.408623
$512$		−	262144.i		−	0.0441942i
$513$			1.11941e7i			1.87800i
$514$	−580145.			−0.0968565
$515$	−4.94500e6	+	5.50624e6i	−0.821577	+	0.914823i
$516$	−1.30730e6			−0.216149
$517$			1.20263e7i			1.97882i
$518$			4.31526e6i			0.706614i
$519$	2.87926e6			0.469205
$520$	−1.57106e6	−	1.41092e6i	−0.254791	−	0.228821i
$521$	1.65026e6			0.266354			0.133177	−	0.991092i	$-0.457482\pi$
$521$	1.65026e6			0.266354			0.133177	+	0.991092i	$0.457482\pi$
$522$			6.42997e6i			1.03284i
$523$		−	8.99272e6i		−	1.43760i	−0.695219	−	0.718798i	$-0.744693\pi$
$523$		−	8.99272e6i		−	1.43760i	0.695219	−	0.718798i	$-0.255307\pi$
$524$	2.26556e6			0.360452
$525$	1.05374e6	+	9.78294e6i	0.166854	+	1.54907i
$526$	−7.16647e6			−1.12938
$527$		−	2.57558e6i		−	0.403969i
$528$			2.96809e6i			0.463332i
$529$	−279841.			−0.0434783
$530$	5.67987e6	+	5.10093e6i	0.878312	+	0.788787i
$531$	5.57772e6			0.858461
$532$		−	3.31798e6i		−	0.508270i
$533$			4.84057e6i			0.738037i
$534$	3.02174e6			0.458568
$535$	−6.46342e6	+	7.19700e6i	−0.976288	+	1.08709i
$536$	−1.28899e6			−0.193794
$537$		−	1.81453e7i		−	2.71537i
$538$		−	3.32713e6i		−	0.495580i
$539$	−1.32388e6			−0.196281
$540$	3.78145e6	−	4.21063e6i	0.558051	−	0.621388i
$541$	−3.67890e6			−0.540411			−0.270206	−	0.962803i	$-0.587092\pi$
$541$	−3.67890e6			−0.540411			−0.270206	+	0.962803i	$0.587092\pi$
$542$		−	1.01806e6i		−	0.148858i
$543$			2.08797e7i			3.03896i
$544$	−466740.			−0.0676204
$545$	5.42863e6	+	4.87530e6i	0.782887	+	0.703089i
$546$	7.43352e6			1.06712
$547$		−	6.86297e6i		−	0.980717i	−0.871521	−	0.490359i	$-0.836866\pi$
$547$		−	6.86297e6i		−	0.980717i	0.871521	−	0.490359i	$-0.163134\pi$
$548$			5.05270e6i			0.718740i
$549$	−1.05244e7			−1.49027
$550$	−5.36424e6	+	577796.i	−0.756139	+	0.0814456i
$551$	5.94267e6			0.833879
$552$		−	909432.i		−	0.127035i
$553$			3.35986e6i			0.467206i
$554$	85309.5			0.0118093
$555$	1.02824e7	+	9.23431e6i	1.41697	+	1.27254i
$556$	−4.78809e6			−0.656864
$557$		−	1.03524e7i		−	1.41384i	−0.707292	−	0.706922i	$-0.750083\pi$
$557$		−	1.03524e7i		−	1.41384i	0.707292	−	0.706922i	$-0.249917\pi$
$558$			1.08166e7i			1.47064i
$559$	−1.79528e6			−0.242999
$560$	−1.12084e6	+	1.24805e6i	−0.151033	+	0.168175i
$561$	5.28460e6			0.708933
$562$		−	454766.i		−	0.0607361i
$563$		−	5.89028e6i		−	0.783186i	−0.920138	−	0.391593i	$-0.871924\pi$
$563$		−	5.89028e6i		−	0.783186i	0.920138	−	0.391593i	$-0.128076\pi$
$564$	1.19752e7			1.58521
$565$	−8.79103e6	+	9.78879e6i	−1.15856	+	1.29005i
$566$	−7.51595e6			−0.986150
$567$			6.29176e6i			0.821892i
$568$		−	2.04569e6i		−	0.266053i
$569$	−1.64596e6			−0.213128			−0.106564	−	0.994306i	$-0.533985\pi$
$569$	−1.64596e6			−0.213128			−0.106564	+	0.994306i	$0.533985\pi$
$570$	−7.90607e6	−	7.10022e6i	−1.01923	−	0.915344i
$571$	−3.27781e6			−0.420721			−0.210360	−	0.977624i	$-0.567464\pi$
$571$	−3.27781e6			−0.420721			−0.210360	+	0.977624i	$0.567464\pi$
$572$			4.07599e6i			0.520887i
$573$			1.20853e7i			1.53770i
$574$	3.84535e6			0.487142
$575$	1.64362e6	−	177038.i	0.207315	−	0.0223304i
$576$	1.96016e6			0.246170
$577$			1.32494e7i			1.65674i	0.560178	+	0.828372i	$0.310733\pi$
$577$			1.32494e7i			1.65674i	−0.560178	+	0.828372i	$0.689267\pi$
$578$		−	4.84841e6i		−	0.603642i
$579$	9.40903e6			1.16640
$580$	−2.23532e6	−	2.00748e6i	−0.275912	−	0.247788i
$581$	−6.36365e6			−0.782107
$582$		−	4.33725e6i		−	0.530771i
$583$		−	1.47360e7i		−	1.79559i
$584$	−1.31694e6			−0.159784
$585$	1.05501e7	−	1.17475e7i	1.27457	−	1.41923i
$586$	−6.22901e6			−0.749334
$587$			3.14421e6i			0.376631i	0.982109	+	0.188316i	$0.0603028\pi$
$587$			3.14421e6i			0.376631i	−0.982109	+	0.188316i	$0.939697\pi$
$588$			1.31826e6i			0.157238i
$589$	9.99686e6			1.18734
$590$	−1.74140e6	+	1.93904e6i	−0.205953	+	0.229328i
$591$	−3.25980e6			−0.383904
$592$			2.35612e6i			0.276307i
$593$		−	2.41001e6i		−	0.281438i	−0.990050	−	0.140719i	$-0.955059\pi$
$593$		−	2.41001e6i		−	0.281438i	0.990050	−	0.140719i	$-0.0449414\pi$
$594$	−1.09242e7			−1.27035
$595$	2.22212e6	+	1.99562e6i	0.257321	+	0.231092i
$596$	5.73507e6			0.661337
$597$			5.62371e6i			0.645784i
$598$		−	1.24890e6i		−	0.142815i
$599$	−5.53205e6			−0.629968			−0.314984	−	0.949097i	$-0.601999\pi$
$599$	−5.53205e6			−0.629968			−0.314984	+	0.949097i	$0.601999\pi$
$600$	575341.	+	5.34146e6i	0.0652450	+	0.605733i
$601$	1.33069e7			1.50276			0.751381	−	0.659869i	$-0.229388\pi$
$601$	1.33069e7			1.50276			0.751381	+	0.659869i	$0.229388\pi$
$602$			1.42617e6i			0.160391i
$603$		−	9.63834e6i		−	1.07947i
$604$	−3.22728e6			−0.359951
$605$	1.05001e6	+	942988.i	0.116629	+	0.104741i
$606$	675497.			0.0747209
$607$		−	7.69221e6i		−	0.847382i	−0.905807	−	0.423691i	$-0.860734\pi$
$607$		−	7.69221e6i		−	0.847382i	0.905807	−	0.423691i	$-0.139266\pi$
$608$		−	1.81161e6i		−	0.198749i
$609$	1.05765e7			1.15558
$610$	3.28577e6	−	3.65870e6i	0.357530	−	0.398109i
$611$	1.64452e7			1.78212
$612$		−	3.49000e6i		−	0.376658i
$613$		−	1.14763e7i		−	1.23353i	−0.787147	−	0.616765i	$-0.788443\pi$
$613$		−	1.14763e7i		−	1.23353i	0.787147	−	0.616765i	$-0.211557\pi$
$614$	8.33743e6			0.892506
$615$	8.22874e6	−	9.16267e6i	0.877295	−	0.976865i
$616$	3.23797e6			0.343812
$617$		−	2.16141e6i		−	0.228573i	−0.993448	−	0.114286i	$-0.963542\pi$
$617$		−	2.16141e6i		−	0.228573i	0.993448	−	0.114286i	$-0.0364581\pi$
$618$		−	1.42248e7i		−	1.49822i
$619$	9.03776e6			0.948056			0.474028	−	0.880510i	$-0.342800\pi$
$619$	9.03776e6			0.948056			0.474028	+	0.880510i	$0.342800\pi$
$620$	−3.76029e6	−	3.37701e6i	−0.392864	−	0.352820i
$621$	3.34719e6			0.348298
$622$			1.97608e6i			0.204800i
$623$		−	3.29649e6i		−	0.340276i
$624$	4.05868e6			0.417276
$625$	−9.54162e6	+	2.07963e6i	−0.977062	+	0.212954i
$626$	5.22311e6			0.532713
$627$			2.05117e7i			2.08369i
$628$		−	4.03409e6i		−	0.408175i
$629$	4.19500e6			0.422771
$630$	−9.33217e6	−	8.38096e6i	−0.936766	−	0.841284i
$631$	−1.08548e7			−1.08530			−0.542648	−	0.839960i	$-0.682578\pi$
$631$	−1.08548e7			−1.08530			−0.542648	+	0.839960i	$0.682578\pi$
$632$			1.83447e6i			0.182692i
$633$		−	2.97884e7i		−	2.95487i
$634$	−1.04849e7			−1.03596
$635$	1.11885e7	−	1.24584e7i	1.10113	−	1.22611i
$636$	−1.46734e7			−1.43843
$637$			1.81033e6i			0.176770i
$638$			5.79937e6i			0.564065i
$639$	1.52964e7			1.48196
$640$	−611974.	+	681431.i	−0.0590586	+	0.0657616i
$641$	−1.45321e6			−0.139695			−0.0698477	−	0.997558i	$-0.522251\pi$
$641$	−1.45321e6			−0.139695			−0.0698477	+	0.997558i	$0.522251\pi$
$642$		−	1.85927e7i		−	1.78035i
$643$		−	6.34297e6i		−	0.605013i	−0.953147	−	0.302507i	$-0.902177\pi$
$643$		−	6.34297e6i		−	0.605013i	0.953147	−	0.302507i	$-0.0978235\pi$
$644$	−992123.			−0.0942650
$645$	3.39828e6	+	3.05190e6i	0.321632	+	0.288849i
$646$	−3.22551e6			−0.304101
$647$		−	1.65532e7i		−	1.55461i	−0.629123	−	0.777306i	$-0.716586\pi$
$647$		−	1.65532e7i		−	1.55461i	0.629123	−	0.777306i	$-0.283414\pi$
$648$			3.43528e6i			0.321385i
$649$	5.03070e6			0.468832
$650$	790100.	+	7.33527e6i	0.0733497	+	0.680977i
$651$	1.77920e7			1.64540
$652$			4.34555e6i			0.400337i
$653$		−	7.59986e6i		−	0.697465i	−0.937222	−	0.348733i	$-0.886612\pi$
$653$		−	7.59986e6i		−	0.697465i	0.937222	−	0.348733i	$-0.113388\pi$
$654$	−1.40244e7			−1.28215
$655$	−5.88921e6	−	5.28894e6i	−0.536357	−	0.481687i
$656$	2.09955e6			0.190487
$657$		−	9.84728e6i		−	0.890026i
$658$		−	1.30641e7i		−	1.17629i
$659$	−3.69368e6			−0.331318			−0.165659	−	0.986183i	$-0.552975\pi$
$659$	−3.69368e6			−0.331318			−0.165659	+	0.986183i	$0.552975\pi$
$660$	6.92900e6	−	7.71542e6i	0.619171	−	0.689445i
$661$	−4.26313e6			−0.379512			−0.189756	−	0.981831i	$-0.560770\pi$
$661$	−4.26313e6			−0.379512			−0.189756	+	0.981831i	$0.560770\pi$
$662$			1.46141e7i			1.29607i
$663$		−	7.22637e6i		−	0.638464i
$664$	−3.47453e6			−0.305827
$665$	−7.74581e6	+	8.62493e6i	−0.679223	+	0.756313i
$666$	−1.76176e7			−1.53908
$667$		−	1.77694e6i		−	0.154653i
$668$		−	1.09895e7i		−	0.952880i
$669$	−2.43315e7			−2.10186
$670$	3.35068e6	+	3.00915e6i	0.288367	+	0.258975i
$671$	−9.49221e6			−0.813881
$672$		−	3.22422e6i		−	0.275423i
$673$			7.86653e6i			0.669493i	0.942308	+	0.334746i	$0.108651\pi$
$673$			7.86653e6i			0.669493i	−0.942308	+	0.334746i	$0.891349\pi$
$674$	8.34518e6			0.707597
$675$	−1.96594e7	+	2.11756e6i	−1.66077	+	0.178886i
$676$	−367017.			−0.0308901
$677$			1.14271e7i			0.958215i	0.877756	+	0.479107i	$0.159040\pi$
$677$			1.14271e7i			0.958215i	−0.877756	+	0.479107i	$0.840960\pi$
$678$		−	2.52884e7i		−	2.11274i
$679$	−4.73162e6			−0.393854
$680$	1.21327e6	+	1.08960e6i	0.100620	+	0.0903641i
$681$	6.83316e6			0.564616
$682$			9.75579e6i			0.803159i
$683$			2.08171e7i			1.70753i	0.520656	+	0.853766i	$0.325687\pi$
$683$			2.08171e7i			1.70753i	−0.520656	+	0.853766i	$0.674313\pi$
$684$	1.35461e7			1.10707
$685$	1.17955e7	−	1.31343e7i	0.960484	−	1.06950i
$686$	9.31837e6			0.756014
$687$			2.29043e7i			1.85150i
$688$			778686.i			0.0627179i
$689$	−2.01505e7			−1.61711
$690$	−2.12306e6	+	2.36403e6i	−0.169762	+	0.189029i
$691$	923178.			0.0735513			0.0367756	−	0.999324i	$-0.488291\pi$
$691$	923178.			0.0735513			0.0367756	+	0.999324i	$0.488291\pi$
$692$		−	1.71501e6i		−	0.136145i
$693$			2.42116e7i			1.91510i
$694$	−1.65933e6			−0.130778
$695$	1.24464e7	+	1.11778e7i	0.977422	+	0.877795i
$696$	5.77474e6			0.451866
$697$		−	3.73818e6i		−	0.291460i
$698$		−	2.63419e6i		−	0.204648i
$699$	−3.02236e7			−2.33966
$700$	5.82713e6	−	627655.i	0.449479	−	0.0484145i
$701$	1.56158e7			1.20024			0.600121	−	0.799909i	$-0.295119\pi$
$701$	1.56158e7			1.20024			0.600121	+	0.799909i	$0.295119\pi$
$702$			1.49381e7i			1.14407i
$703$			1.62825e7i			1.24260i
$704$	1.76792e6			0.134441
$705$	−3.11290e7	−	2.79561e7i	−2.35881	−	2.11838i
$706$	−7.64014e6			−0.576885
$707$		−	736918.i		−	0.0554460i
$708$		−	5.00934e6i		−	0.375575i
$709$	1.23664e7			0.923908			0.461954	−	0.886904i	$-0.347149\pi$
$709$	1.23664e7			0.923908			0.461954	+	0.886904i	$0.347149\pi$
$710$	−4.77565e6	+	5.31767e6i	−0.355538	+	0.395891i
$711$	−1.37171e7			−1.01763
$712$		−	1.79988e6i		−	0.133058i
$713$		−	2.98920e6i		−	0.220207i
$714$	−5.74062e6			−0.421419
$715$	9.51539e6	−	1.05954e7i	0.696084	−	0.775087i
$716$	−1.08081e7			−0.787893
$717$		−	3.21401e7i		−	2.33480i
$718$		−	1.38130e7i		−	0.999943i
$719$	7.41015e6			0.534571			0.267285	−	0.963617i	$-0.413873\pi$
$719$	7.41015e6			0.534571			0.267285	+	0.963617i	$0.413873\pi$
$720$	−5.09534e6	−	4.57598e6i	−0.366304	−	0.328967i
$721$	−1.55183e7			−1.11174
$722$		−	2.61513e6i		−	0.186703i
$723$			6.30568e6i			0.448628i
$724$	1.24368e7			0.881787
$725$	1.12416e6	+	1.04367e7i	0.0794299	+	0.737425i
$726$	−2.71261e6			−0.191005
$727$			1.02065e7i			0.716208i	0.933682	+	0.358104i	$0.116577\pi$
$727$			1.02065e7i			0.716208i	−0.933682	+	0.358104i	$0.883423\pi$
$728$		−	4.42772e6i		−	0.309636i
$729$	1.56145e7			1.08820
$730$	3.42332e6	+	3.07439e6i	0.237761	+	0.213526i
$731$	1.38643e6			0.0959631
$732$			9.45189e6i			0.651990i
$733$			2.62828e6i			0.180681i	0.995911	+	0.0903405i	$0.0287955\pi$
$733$			2.62828e6i			0.180681i	−0.995911	+	0.0903405i	$0.971204\pi$
$734$	1.97237e7			1.35129
$735$	3.07747e6	−	3.42676e6i	0.210124	−	0.233973i
$736$	−541696.			−0.0368605
$737$		−	8.69309e6i		−	0.589529i
$738$			1.56992e7i			1.06105i
$739$	2.78382e6			0.187513			0.0937564	−	0.995595i	$-0.470113\pi$
$739$	2.78382e6			0.187513			0.0937564	+	0.995595i	$0.470113\pi$
$740$	5.50035e6	−	6.12462e6i	0.369242	−	0.411149i
$741$	2.80485e7			1.87656
$742$			1.60076e7i			1.06737i
$743$		−	8.18922e6i		−	0.544215i	−0.962267	−	0.272107i	$-0.912279\pi$
$743$		−	8.18922e6i		−	0.544215i	0.962267	−	0.272107i	$-0.0877206\pi$
$744$	9.71436e6			0.643401
$745$	−1.49080e7	−	1.33885e7i	−0.984079	−	0.883773i
$746$	9.08616e6			0.597769
$747$		−	2.59805e7i		−	1.70352i
$748$		−	3.14773e6i		−	0.205705i
$749$	−2.02833e7			−1.32110
$750$	1.09740e7	−	1.52280e7i	0.712382	−	0.988530i
$751$	1.35672e7			0.877792			0.438896	−	0.898538i	$-0.355370\pi$
$751$	1.35672e7			0.877792			0.438896	+	0.898538i	$0.355370\pi$
$752$		−	7.13295e6i		−	0.459965i
$753$		−	1.16037e7i		−	0.745779i
$754$	7.93028e6			0.507996
$755$	8.38916e6	+	7.53407e6i	0.535613	+	0.481019i
$756$	1.18668e7			0.755145
$757$			2.17873e7i			1.38186i	0.722923	+	0.690928i	$0.242798\pi$
$757$			2.17873e7i			1.38186i	−0.722923	+	0.690928i	$0.757202\pi$
$758$		−	1.93125e7i		−	1.22086i
$759$	6.13328e6			0.386446
$760$	−4.22919e6	+	4.70919e6i	−0.265597	+	0.295741i
$761$	−3.22261e6			−0.201719			−0.100859	−	0.994901i	$-0.532159\pi$
$761$	−3.22261e6			−0.201719			−0.100859	+	0.994901i	$0.532159\pi$
$762$			3.21851e7i			2.00802i
$763$			1.52995e7i			0.951408i
$764$	7.19851e6			0.446179
$765$	−8.14740e6	+	9.07211e6i	−0.503345	+	0.560473i
$766$	1.07318e7			0.660844
$767$		−	6.87918e6i		−	0.422229i
$768$		−	1.76041e6i		−	0.107699i
$769$	−4.02074e6			−0.245183			−0.122591	−	0.992457i	$-0.539120\pi$
$769$	−4.02074e6			−0.245183			−0.122591	+	0.992457i	$0.539120\pi$
$770$	−8.41695e6	−	7.55902e6i	−0.511597	−	0.459451i
$771$	−3.89593e6			−0.236034
$772$		−	5.60442e6i		−	0.338444i
$773$		−	1.03233e7i		−	0.621398i	−0.950508	−	0.310699i	$-0.899437\pi$
$773$		−	1.03233e7i		−	0.621398i	0.950508	−	0.310699i	$-0.100563\pi$
$774$	−5.82255e6			−0.349350
$775$	1.89108e6	+	1.75568e7i	0.113098	+	1.05000i
$776$	−2.58345e6			−0.154009
$777$			2.89788e7i			1.72198i
$778$			1.54594e7i			0.915679i
$779$	1.45094e7			0.856655
$780$	−1.05504e7	−	9.47498e6i	−0.620913	−	0.557624i
$781$	1.37963e7			0.809346
$782$			964474.i			0.0563993i
$783$			2.12541e7i			1.23891i
$784$	785212.			0.0456243
$785$	−9.41757e6	+	1.04864e7i	−0.545462	+	0.607370i
$786$	1.52142e7			0.878402
$787$		−	1.04668e7i		−	0.602389i	−0.953563	−	0.301195i	$-0.902615\pi$
$787$		−	1.04668e7i		−	0.602389i	0.953563	−	0.301195i	$-0.0973854\pi$
$788$			1.94168e6i			0.111394i
$789$	−4.81260e7			−2.75225
$790$	4.28257e6	−	4.76863e6i	0.244139	−	0.271848i
$791$	−2.75878e7			−1.56774
$792$			1.32195e7i			0.748861i
$793$			1.29800e7i			0.732980i
$794$	−1.26695e7			−0.713197
$795$	3.81428e7	+	3.42550e7i	2.14040	+	1.92223i
$796$	3.34972e6			0.187381
$797$			1.28535e7i			0.716763i	0.933575	+	0.358382i	$0.116671\pi$
$797$			1.28535e7i			0.716763i	−0.933575	+	0.358382i	$0.883329\pi$
$798$		−	2.22817e7i		−	1.23863i
$799$	−1.27000e7			−0.703780
$800$	3.18160e6	−	342698.i	0.175760	−	0.0189316i
$801$	1.34584e7			0.741160
$802$			1.85391e7i			1.01778i
$803$		−	8.88154e6i		−	0.486070i
$804$	−8.65617e6			−0.472265
$805$	2.57898e6	+	2.31611e6i	0.140268	+	0.125970i
$806$	1.33404e7			0.723324
$807$		−	2.23431e7i		−	1.20770i
$808$		−	402355.i		−	0.0216811i
$809$	8.26723e6			0.444108			0.222054	−	0.975034i	$-0.428724\pi$
$809$	8.26723e6			0.444108			0.222054	+	0.975034i	$0.428724\pi$
$810$	8.01966e6	−	8.92986e6i	0.429480	−	0.478225i
$811$	2.45999e6			0.131335			0.0656676	−	0.997842i	$-0.479082\pi$
$811$	2.45999e6			0.131335			0.0656676	+	0.997842i	$0.479082\pi$
$812$		−	6.29981e6i		−	0.335303i
$813$		−	6.83670e6i		−	0.362760i
$814$	−1.58898e7			−0.840541
$815$	1.01447e7	−	1.12961e7i	0.534988	−	0.595707i
$816$	−3.13436e6			−0.164787
$817$			5.38129e6i			0.282053i
$818$			1.44787e7i			0.756567i
$819$	3.31079e7			1.72473
$820$	−5.45768e6	−	4.90138e6i	−0.283448	−	0.254556i
$821$	1.35274e7			0.700417			0.350208	−	0.936672i	$-0.386111\pi$
$821$	1.35274e7			0.700417			0.350208	+	0.936672i	$0.386111\pi$
$822$			3.39311e7i			1.75153i
$823$			3.58804e7i			1.84654i	0.384156	+	0.923268i	$0.374493\pi$
$823$			3.58804e7i			1.84654i	−0.384156	+	0.923268i	$0.625507\pi$
$824$	−8.47292e6			−0.434725
$825$	−3.60232e7	+	3.88015e6i	−1.84267	+	0.198479i
$826$	−5.46482e6			−0.278693
$827$			3.38121e7i			1.71913i	0.511026	+	0.859565i	$0.329266\pi$
$827$			3.38121e7i			1.71913i	−0.511026	+	0.859565i	$0.670734\pi$
$828$		−	4.05048e6i		−	0.205320i
$829$	−1.17504e7			−0.593834			−0.296917	−	0.954903i	$-0.595959\pi$
$829$	−1.17504e7			−0.593834			−0.296917	+	0.954903i	$0.595959\pi$
$830$	9.03189e6	+	8.11129e6i	0.455076	+	0.408691i
$831$	572891.			0.0287786
$832$		−	2.41752e6i		−	0.121077i
$833$		−	1.39805e6i		−	0.0698087i
$834$	−3.21541e7			−1.60074
$835$	−2.56550e7	+	2.85668e7i	−1.27337	+	1.41790i
$836$	1.22176e7			0.604604
$837$			3.57540e7i			1.76405i
$838$		−	6.84251e6i		−	0.336593i
$839$	2.99880e7			1.47076			0.735382	−	0.677653i	$-0.237003\pi$
$839$	2.99880e7			1.47076			0.735382	+	0.677653i	$0.237003\pi$
$840$	−7.52692e6	+	8.38120e6i	−0.368060	+	0.409834i
$841$	−9.22786e6			−0.449895
$842$		−	2.04912e7i		−	0.996065i
$843$		−	3.05395e6i		−	0.148011i
$844$	−1.77432e7			−0.857386
$845$	954045.	+	856801.i	0.0459650	+	0.0412798i
$846$	5.33359e7			2.56209
$847$			2.95926e6i			0.141734i
$848$			8.74010e6i			0.417375i
$849$	−5.04729e7			−2.40320
$850$	−610164.	−	5.66474e6i	−0.0289667	−	0.268926i
$851$	4.86869e6			0.230456
$852$		−	1.37377e7i		−	0.648357i
$853$		−	2.97995e7i		−	1.40228i	−0.713021	−	0.701142i	$-0.752674\pi$
$853$		−	2.97995e7i		−	1.40228i	0.713021	−	0.701142i	$-0.247326\pi$
$854$	1.03113e7			0.483804
$855$	−3.52125e7	−	3.16234e7i	−1.64733	−	1.47942i
$856$	−1.10746e7			−0.516589
$857$			3.36282e7i			1.56406i	0.623244	+	0.782028i	$0.285815\pi$
$857$			3.36282e7i			1.56406i	−0.623244	+	0.782028i	$0.714185\pi$
$858$			2.73721e7i			1.26937i
$859$	−548701.			−0.0253719			−0.0126859	−	0.999920i	$-0.504038\pi$
$859$	−548701.			−0.0253719			−0.0126859	+	0.999920i	$0.504038\pi$
$860$	1.81784e6	−	2.02416e6i	0.0838126	−	0.0933251i
$861$	2.58232e7			1.18714
$862$			2.09943e7i			0.962350i
$863$		−	1.05222e7i		−	0.480927i	−0.970658	−	0.240463i	$-0.922701\pi$
$863$		−	1.05222e7i		−	0.480927i	0.970658	−	0.240463i	$-0.0772994\pi$
$864$	6.47925e6			0.295284
$865$	−4.00369e6	+	4.45809e6i	−0.181936	+	0.202586i
$866$	−1.26136e7			−0.571538
$867$		−	3.25592e7i		−	1.47105i
$868$		−	1.05976e7i		−	0.477430i
$869$	−1.23718e7			−0.555757
$870$	−1.50112e7	−	1.34811e7i	−0.672382	−	0.603848i
$871$	−1.18873e7			−0.530929
$872$			8.35350e6i			0.372029i
$873$		−	1.93175e7i		−	0.857858i
$874$	−3.74352e6			−0.165768
$875$	−1.66126e7	−	1.19719e7i	−0.733530	−	0.528617i
$876$	−8.84381e6			−0.389385
$877$		−	1.46747e7i		−	0.644273i	−0.946693	−	0.322137i	$-0.895599\pi$
$877$		−	1.46747e7i		−	0.644273i	0.946693	−	0.322137i	$-0.104401\pi$
$878$			2.98416e7i			1.30643i
$879$	−4.18306e7			−1.82609
$880$	−4.59563e6	−	4.12720e6i	−0.200050	−	0.179659i
$881$	−1.62640e7			−0.705972			−0.352986	−	0.935629i	$-0.614834\pi$
$881$	−1.62640e7			−0.705972			−0.352986	+	0.935629i	$0.614834\pi$
$882$			5.87135e6i			0.254136i
$883$		−	1.69389e7i		−	0.731112i	−0.930789	−	0.365556i	$-0.880879\pi$
$883$		−	1.69389e7i		−	0.731112i	0.930789	−	0.365556i	$-0.119121\pi$
$884$	−4.30433e6			−0.185257
$885$	−1.16943e7	+	1.30215e7i	−0.501898	+	0.558861i
$886$	−1.00092e6			−0.0428367
$887$		−	3.44782e7i		−	1.47142i	−0.677298	−	0.735709i	$-0.736849\pi$
$887$		−	3.44782e7i		−	1.47142i	0.677298	−	0.735709i	$-0.263151\pi$
$888$			1.58224e7i			0.673347i
$889$	3.51116e7			1.49003
$890$	−4.20180e6	+	4.67869e6i	−0.177812	+	0.197993i
$891$	−2.31678e7			−0.977668
$892$			1.44929e7i			0.609878i
$893$		−	4.92939e7i		−	2.06854i
$894$	3.85135e7			1.61164
$895$	2.80952e7	+	2.52315e7i	1.17240	+	1.05290i
$896$	−1.92048e6			−0.0799171
$897$		−	8.38689e6i		−	0.348032i
$898$			1.41125e7i			0.584000i
$899$	1.89809e7			0.783282
$900$	2.56249e6	+	2.37901e7i	0.105452	+	0.979016i
$901$	1.55615e7			0.638615
$902$			1.41595e7i			0.579472i
$903$			9.57738e6i			0.390865i
$904$	−1.50628e7			−0.613036
$905$	−3.23290e7	−	2.90338e7i	−1.31211	−	1.17837i
$906$	−2.16726e7			−0.877183
$907$			2.86555e7i			1.15662i	0.815818	+	0.578308i	$0.196287\pi$
$907$			2.86555e7i			1.15662i	−0.815818	+	0.578308i	$0.803713\pi$
$908$		−	4.07012e6i		−	0.163830i
$909$	3.00857e6			0.120768
$910$	−1.03365e7	+	1.15097e7i	−0.413780	+	0.460743i
$911$	2.02300e7			0.807606			0.403803	−	0.914846i	$-0.367688\pi$
$911$	2.02300e7			0.807606			0.403803	+	0.914846i	$0.367688\pi$
$912$		−	1.21657e7i		−	0.484341i
$913$		−	2.34326e7i		−	0.930342i
$914$	1.09560e7			0.433799
$915$	2.20654e7	−	2.45698e7i	0.871283	−	0.970171i
$916$	1.36428e7			0.537234
$917$		−	1.65976e7i		−	0.651811i
$918$		−	1.15361e7i		−	0.451807i
$919$	−6.54020e6			−0.255448			−0.127724	−	0.991810i	$-0.540767\pi$
$919$	−6.54020e6			−0.255448			−0.127724	+	0.991810i	$0.540767\pi$
$920$	1.40811e6	+	1.26459e6i	0.0548489	+	0.0492583i
$921$	5.59895e7			2.17499
$922$			2.05860e7i			0.797527i
$923$		−	1.88656e7i		−	0.728896i
$924$	2.17444e7			0.837852
$925$	−2.85958e7	+	3.08012e6i	−1.09887	+	0.118362i
$926$	3.22565e7			1.23620
$927$		−	6.33555e7i		−	2.42150i
$928$		−	3.43968e6i		−	0.131114i
$929$	4.70275e7			1.78777			0.893886	−	0.448294i	$-0.147968\pi$
$929$	4.70275e7			1.78777			0.893886	+	0.448294i	$0.147968\pi$
$930$	−2.52520e7	−	2.26781e7i	−0.957390	−	0.859805i
$931$	5.42639e6			0.205181
$932$			1.80025e7i			0.678879i
$933$			1.32703e7i			0.499086i
$934$	−2.18970e7			−0.821328
$935$	−7.34837e6	+	8.18239e6i	−0.274892	+	0.306091i
$936$	1.80768e7			0.674422
$937$			3.35351e6i			0.124782i	0.998052	+	0.0623908i	$0.0198725\pi$
$937$			3.35351e6i			0.124782i	−0.998052	+	0.0623908i	$0.980127\pi$
$938$			9.44324e6i			0.350440i
$939$	3.50755e7			1.29819
$940$	−1.66518e7	+	1.85418e7i	−0.614671	+	0.684434i
$941$	−3.75069e7			−1.38082			−0.690409	−	0.723419i	$-0.742569\pi$
$941$	−3.75069e7			−1.38082			−0.690409	+	0.723419i	$0.742569\pi$
$942$		−	2.70907e7i		−	0.994701i
$943$		−	4.33852e6i		−	0.158877i
$944$	−2.98377e6			−0.108977
$945$	−3.08473e7	−	2.77031e7i	−1.12367	−	1.00913i
$946$	−5.25153e6			−0.190791
$947$		−	2.97558e7i		−	1.07819i	−0.842244	−	0.539097i	$-0.818766\pi$
$947$		−	2.97558e7i		−	1.07819i	0.842244	−	0.539097i	$-0.181234\pi$
$948$			1.23193e7i			0.445210i
$949$	−1.21450e7			−0.437754
$950$	2.19872e7	−	2.36829e6i	0.790424	−	0.0851385i
$951$	−7.04109e7			−2.52458
$952$			3.41936e6i			0.122279i
$953$			1.91059e7i			0.681451i	0.940163	+	0.340726i	$0.110673\pi$
$953$			1.91059e7i			0.681451i	−0.940163	+	0.340726i	$0.889327\pi$
$954$	−6.53532e7			−2.32486
$955$	−1.87122e7	−	1.68049e7i	−0.663920	−	0.596248i
$956$	−1.91440e7			−0.677468
$957$			3.89453e7i			1.37460i
$958$			2.39859e7i			0.844388i
$959$	3.70163e7			1.29971
$960$	−4.10968e6	+	4.57611e6i	−0.143923	+	0.160257i
$961$	3.30088e6			0.115298
$962$			2.17284e7i			0.756989i
$963$		−	8.28095e7i		−	2.87749i
$964$	3.75593e6			0.130174
$965$	−1.30835e7	+	1.45684e7i	−0.452278	+	0.503610i
$966$	−6.66254e6			−0.229719
$967$			6.00580e6i			0.206540i	0.994653	+	0.103270i	$0.0329306\pi$
$967$			6.00580e6i			0.206540i	−0.994653	+	0.103270i	$0.967069\pi$
$968$			1.61575e6i			0.0554223i
$969$	−2.16607e7			−0.741078
$970$	6.71556e6	+	6.03105e6i	0.229167	+	0.205809i
$971$	2.22673e7			0.757914			0.378957	−	0.925414i	$-0.376283\pi$
$971$	2.22673e7			0.757914			0.378957	+	0.925414i	$0.376283\pi$
$972$		−	1.53147e6i		−	0.0519927i
$973$			3.50778e7i			1.18782i
$974$	−2.73137e7			−0.922534
$975$	5.30587e6	+	4.92595e7i	0.178749	+	1.65951i
$976$	5.62995e6			0.189182
$977$			2.72011e7i			0.911697i	0.890057	+	0.455849i	$0.150664\pi$
$977$			2.72011e7i			0.911697i	−0.890057	+	0.455849i	$0.849336\pi$
$978$			2.91823e7i			0.975600i
$979$	1.21385e7			0.404770
$980$	−2.04112e6	−	1.83307e6i	−0.0678896	−	0.0609698i
$981$	−6.24625e7			−2.07227
$982$		−	3.76271e7i		−	1.24515i
$983$		−	2.18935e7i		−	0.722654i	−0.932439	−	0.361327i	$-0.882324\pi$
$983$		−	2.18935e7i		−	0.722654i	0.932439	−	0.361327i	$-0.117676\pi$
$984$	1.40994e7			0.464208
$985$	4.53284e6	−	5.04730e6i	0.148860	−	0.165756i
$986$	−6.12425e6			−0.200614
$987$		−	8.77310e7i		−	2.86655i
$988$		−	1.67069e7i		−	0.544506i
$989$	1.60908e6			0.0523103
$990$	3.08608e7	−	3.43634e7i	1.00073	−	1.11432i
$991$	2.78010e6			0.0899242			0.0449621	−	0.998989i	$-0.485683\pi$
$991$	2.78010e6			0.0899242			0.0449621	+	0.998989i	$0.485683\pi$
$992$		−	5.78628e6i		−	0.186690i
$993$			9.81401e7i			3.15845i
$994$	−1.49868e7			−0.481108
$995$	−8.70744e6	−	7.81991e6i	−0.278826	−	0.250406i
$996$	−2.33330e7			−0.745286
$997$			7.68207e6i			0.244760i	0.992483	+	0.122380i	$0.0390526\pi$
$997$			7.68207e6i			0.244760i	−0.992483	+	0.122380i	$0.960947\pi$
$998$			1.90862e7i			0.606586i
$999$	−5.82347e7			−1.84615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.b.a.139.2	✓	26
5.4	even	2	inner	230.6.b.a.139.25	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.b.a.139.2	✓	26	1.1	even	1	trivial
230.6.b.a.139.25	yes	26	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -26.8618i q^{3} -16.0000 q^{4} +(41.5913 + 37.3519i) q^{5} -107.447 q^{6} +117.217i q^{7} +64.0000i q^{8} -478.554 q^{9} +(149.408 - 166.365i) q^{10} -431.621 q^{11} +429.788i q^{12} +590.216i q^{13} +468.867 q^{14} +(1003.34 - 1117.21i) q^{15} +256.000 q^{16} -455.801i q^{17} +1914.22i q^{18} +1769.15 q^{19} +(-665.460 - 597.631i) q^{20} +3148.65 q^{21} +1726.49i q^{22} -529.000i q^{23} +1719.15 q^{24} +(334.666 + 3107.03i) q^{25} +2360.86 q^{26} +6327.39i q^{27} -1875.47i q^{28} +3359.06 q^{29} +(-4468.86 - 4013.35i) q^{30} +5650.67 q^{31} -1024.00i q^{32} +11594.1i q^{33} -1823.20 q^{34} +(-4378.27 + 4875.19i) q^{35} +7656.86 q^{36} +9203.58i q^{37} -7076.59i q^{38} +15854.2 q^{39} +(-2390.52 + 2661.84i) q^{40} +8201.36 q^{41} -12594.6i q^{42} +3041.74i q^{43} +6905.94 q^{44} +(-19903.7 - 17874.9i) q^{45} -2116.00 q^{46} -27863.1i q^{47} -6876.61i q^{48} +3067.23 q^{49} +(12428.1 - 1338.66i) q^{50} -12243.6 q^{51} -9443.45i q^{52} +34141.0i q^{53} +25309.6 q^{54} +(-17951.7 - 16121.9i) q^{55} -7501.87 q^{56} -47522.4i q^{57} -13436.2i q^{58} -11655.4 q^{59} +(-16053.4 + 17875.4i) q^{60} +21992.0 q^{61} -22602.7i q^{62} -56094.5i q^{63} -4096.00 q^{64} +(-22045.7 + 24547.8i) q^{65} +46376.4 q^{66} +20140.5i q^{67} +7292.81i q^{68} -14209.9 q^{69} +(19500.8 + 17513.1i) q^{70} -31963.9 q^{71} -30627.5i q^{72} +20577.1i q^{73} +36814.3 q^{74} +(83460.2 - 8989.71i) q^{75} -28306.4 q^{76} -50593.3i q^{77} -63416.9i q^{78} +28663.6 q^{79} +(10647.4 + 9562.10i) q^{80} +53676.3 q^{81} -32805.4i q^{82} +54289.6i q^{83} -50378.4 q^{84} +(17025.0 - 18957.3i) q^{85} +12167.0 q^{86} -90230.3i q^{87} -27623.8i q^{88} -28123.0 q^{89} +(-71499.7 + 79614.7i) q^{90} -69183.2 q^{91} +8464.00i q^{92} -151787. i q^{93} -111452. q^{94} +(73581.1 + 66081.1i) q^{95} -27506.4 q^{96} +40366.4i q^{97} -12268.9i q^{98} +206554. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26}+ \cdots + 523850 q^{99}+O(q^{100}) \) 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9 + 80 * q^10 - 1314 * q^11 + 808 * q^14 + 1280 * q^15 + 6656 * q^16 + 6630 * q^19 + 480 * q^20 - 10060 * q^21 + 1152 * q^24 - 10470 * q^25 - 376 * q^26 + 16084 * q^29 - 6200 * q^30 + 418 * q^31 + 3320 * q^34 - 3160 * q^35 + 22400 * q^36 + 71296 * q^39 - 1280 * q^40 - 35826 * q^41 + 21024 * q^44 - 83960 * q^45 - 55016 * q^46 + 53532 * q^49 - 20800 * q^50 - 25430 * q^51 + 98736 * q^54 - 110390 * q^55 - 12928 * q^56 + 126992 * q^59 - 20480 * q^60 - 63662 * q^61 - 106496 * q^64 - 88520 * q^65 - 18664 * q^66 - 9522 * q^69 - 116520 * q^70 - 106514 * q^71 + 183536 * q^74 - 44200 * q^75 - 106080 * q^76 + 324676 * q^79 - 7680 * q^80 - 170702 * q^81 + 160960 * q^84 + 120780 * q^85 - 42768 * q^86 + 465200 * q^89 + 61360 * q^90 - 468838 * q^91 + 107152 * q^94 + 309670 * q^95 - 18432 * q^96 + 523850 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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