LMFDB - Embedded newform 230.6.b.a.139.25

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

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000i q^{2} +26.8618i q^{3} -16.0000 q^{4} +(41.5913 - 37.3519i) q^{5} -107.447 q^{6} -117.217i q^{7} -64.0000i q^{8} -478.554 q^{9} +(149.408 + 166.365i) q^{10} -431.621 q^{11} -429.788i q^{12} -590.216i q^{13} +468.867 q^{14} +(1003.34 + 1117.21i) q^{15} +256.000 q^{16} +455.801i q^{17} -1914.22i q^{18} +1769.15 q^{19} +(-665.460 + 597.631i) q^{20} +3148.65 q^{21} -1726.49i q^{22} +529.000i q^{23} +1719.15 q^{24} +(334.666 - 3107.03i) q^{25} +2360.86 q^{26} -6327.39i q^{27} +1875.47i q^{28} +3359.06 q^{29} +(-4468.86 + 4013.35i) q^{30} +5650.67 q^{31} +1024.00i q^{32} -11594.1i q^{33} -1823.20 q^{34} +(-4378.27 - 4875.19i) q^{35} +7656.86 q^{36} -9203.58i q^{37} +7076.59i q^{38} +15854.2 q^{39} +(-2390.52 - 2661.84i) q^{40} +8201.36 q^{41} +12594.6i q^{42} -3041.74i q^{43} +6905.94 q^{44} +(-19903.7 + 17874.9i) q^{45} -2116.00 q^{46} +27863.1i q^{47} +6876.61i q^{48} +3067.23 q^{49} +(12428.1 + 1338.66i) q^{50} -12243.6 q^{51} +9443.45i q^{52} -34141.0i q^{53} +25309.6 q^{54} +(-17951.7 + 16121.9i) q^{55} -7501.87 q^{56} +47522.4i q^{57} +13436.2i q^{58} -11655.4 q^{59} +(-16053.4 - 17875.4i) q^{60} +21992.0 q^{61} +22602.7i q^{62} +56094.5i q^{63} -4096.00 q^{64} +(-22045.7 - 24547.8i) q^{65} +46376.4 q^{66} -20140.5i q^{67} -7292.81i q^{68} -14209.9 q^{69} +(19500.8 - 17513.1i) q^{70} -31963.9 q^{71} +30627.5i q^{72} -20577.1i q^{73} +36814.3 q^{74} +(83460.2 + 8989.71i) q^{75} -28306.4 q^{76} +50593.3i q^{77} +63416.9i q^{78} +28663.6 q^{79} +(10647.4 - 9562.10i) q^{80} +53676.3 q^{81} +32805.4i q^{82} -54289.6i q^{83} -50378.4 q^{84} +(17025.0 + 18957.3i) q^{85} +12167.0 q^{86} +90230.3i q^{87} +27623.8i q^{88} -28123.0 q^{89} +(-71499.7 - 79614.7i) q^{90} -69183.2 q^{91} -8464.00i q^{92} +151787. i q^{93} -111452. q^{94} +(73581.1 - 66081.1i) q^{95} -27506.4 q^{96} -40366.4i q^{97} +12268.9i q^{98} +206554. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.330532\pi$
$3$			26.8618i			1.72318i	−0.507603	+	0.861591i	$0.669468\pi$
$4$	−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	$-0.850682\pi$
$7$		−	117.217i		−	0.904159i	0.891978	−	0.452079i	$-0.149318\pi$
$8$		−	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	$-0.839071\pi$
$13$		−	590.216i		−	0.968617i	0.874897	−	0.484309i	$-0.160929\pi$
$14$	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	$0.0612572\pi$
$17$			455.801i			0.382519i	−0.981540	+	0.191259i	$0.938743\pi$
$18$		−	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	$-0.813630\pi$
$37$		−	9203.58i		−	1.10523i	0.833437	−	0.552615i	$-0.186370\pi$
$38$			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	$-0.959967\pi$
$43$		−	3041.74i		−	0.250872i	0.992102	−	0.125436i	$-0.0400329\pi$
$44$	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	$0.371754\pi$
$47$			27863.1i			1.83986i	−0.392085	+	0.919929i	$0.628246\pi$
$48$			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	$-0.685612\pi$
$53$		−	34141.0i		−	1.66950i	0.550629	−	0.834750i	$-0.314388\pi$
$54$	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	$-0.911632\pi$
$67$		−	20140.5i		−	0.548131i	0.961711	−	0.274065i	$-0.0883685\pi$
$68$		−	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	$-0.927445\pi$
$73$		−	20577.1i		−	0.451937i	0.974135	−	0.225969i	$-0.0725547\pi$
$74$	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	$-0.857630\pi$
$83$		−	54289.6i		−	0.865011i	0.901631	−	0.432505i	$-0.142370\pi$
$84$	−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	$-0.930111\pi$
$97$		−	40366.4i		−	0.435603i	0.975993	−	0.217801i	$-0.0698885\pi$
$98$			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	$-0.789239\pi$
$103$		−	132389.i		−	1.22959i	0.788687	−	0.614795i	$-0.210761\pi$
$104$	−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	$-0.739256\pi$
$107$		−	173041.i		−	1.46113i	0.682842	−	0.730567i	$-0.260744\pi$
$108$			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	$-0.666069\pi$
$113$		−	235357.i		−	1.73393i	0.498372	−	0.866963i	$-0.333931\pi$
$114$	−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	$0.308256\pi$
$127$			299544.i			1.64798i	−0.566606	+	0.823989i	$0.691744\pi$
$128$		−	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	$0.255281\pi$
$137$			315794.i			1.43748i	−0.695279	+	0.718740i	$0.744719\pi$
$138$		−	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	$-0.866165\pi$
$157$		−	252131.i		−	0.816350i	0.912904	−	0.408175i	$-0.133835\pi$
$158$			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	$0.131107\pi$
$163$			271597.i			0.800674i	−0.916368	+	0.400337i	$0.868893\pi$
$164$	−131222.			−0.380975
$165$	−433062.	−	482214.i	−1.23834	−	1.37889i
$166$	217158.			0.611655
$167$		−	686846.i		−	1.90576i	−0.303348	−	0.952880i	$-0.598105\pi$
$167$		−	686846.i		−	1.90576i	0.303348	−	0.952880i	$-0.401895\pi$
$168$		−	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	$-0.956529\pi$
$173$		−	107188.i		−	0.272290i	0.990689	−	0.136145i	$-0.0434713\pi$
$174$	−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	$-0.890099\pi$
$193$		−	350276.i		−	0.676889i	0.940986	−	0.338444i	$-0.109901\pi$
$194$	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	$0.0355315\pi$
$197$			121355.i			0.222788i	−0.993776	+	0.111394i	$0.964468\pi$
$198$			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	$0.208781\pi$
$223$			905806.i			1.21976i	−0.792495	+	0.609878i	$0.791219\pi$
$224$	120030.			0.159834
$225$	−160156.	+	1.48688e6i	−0.210905	+	1.95803i
$226$	941427.			1.22607
$227$		−	254382.i		−	0.327659i	−0.986489	−	0.163830i	$-0.947615\pi$
$227$		−	254382.i		−	0.327659i	0.986489	−	0.163830i	$-0.0523847\pi$
$228$		−	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	$0.237534\pi$
$233$			1.12515e6i			1.35776i	−0.734251	+	0.678879i	$0.762466\pi$
$234$	−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	$0.0218175\pi$
$257$			145036.i			0.136976i	−0.997652	+	0.0684879i	$0.978183\pi$
$258$			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	$0.294423\pi$
$263$			1.79162e6i			1.59719i	−0.601870	+	0.798594i	$0.705577\pi$
$264$	−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	$-0.997342\pi$
$277$		−	21327.4i		−	0.0167008i	0.999965	−	0.00835041i	$-0.00265805\pi$
$278$			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	$0.245621\pi$
$283$			1.87899e6i			1.39463i	−0.716767	+	0.697313i	$0.754379\pi$
$284$	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	$0.177755\pi$
$293$			1.55725e6i			1.05972i	−0.848086	+	0.529859i	$0.822245\pi$
$294$	−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	$-0.782605\pi$
$307$		−	2.08436e6i		−	1.26219i	0.775704	−	0.631097i	$-0.217395\pi$
$308$		−	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	$-0.877064\pi$
$313$		−	1.30578e6i		−	0.753370i	0.926341	−	0.376685i	$-0.122936\pi$
$314$	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	$0.261662\pi$
$317$			2.62123e6i			1.46507i	−0.680731	+	0.732533i	$0.738338\pi$
$318$			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	$-0.833206\pi$
$337$		−	2.08629e6i		−	1.00069i	0.865825	−	0.500347i	$-0.166794\pi$
$338$			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	$0.0294774\pi$
$347$			414832.i			0.184948i	−0.995715	+	0.0924738i	$0.970523\pi$
$348$		−	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	$0.133746\pi$
$353$			1.91003e6i			0.815839i	−0.913018	+	0.407919i	$0.866254\pi$
$354$	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	$-0.595312\pi$
$367$		−	4.93092e6i		−	1.91101i	0.294976	−	0.955505i	$-0.404688\pi$
$368$			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	$-0.861087\pi$
$373$		−	2.27154e6i		−	0.845373i	0.906276	−	0.422687i	$-0.138913\pi$
$374$	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	$-0.845231\pi$
$383$		−	2.68294e6i		−	0.934575i	0.884105	−	0.467288i	$-0.154769\pi$
$384$	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	$0.168252\pi$
$397$			3.16739e6i			1.00861i	−0.863525	+	0.504307i	$0.831748\pi$
$398$		−	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	$0.132429\pi$
$433$			3.15341e6i			0.808277i	−0.914698	+	0.404138i	$0.867571\pi$
$434$	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	$0.00964311\pi$
$443$			250230.i			0.0605802i	−0.999541	+	0.0302901i	$0.990357\pi$
$444$	−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	$-0.900761\pi$
$457$		−	2.73901e6i		−	0.613484i	0.951793	−	0.306742i	$-0.0992389\pi$
$458$		−	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	$-0.661434\pi$
$463$		−	8.06412e6i		−	1.74825i	0.485698	−	0.874127i	$-0.338566\pi$
$464$	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	$0.197247\pi$
$467$			5.47424e6i			1.16153i	−0.814070	+	0.580766i	$0.802753\pi$
$468$		−	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	$0.226208\pi$
$487$			6.82842e6i			1.30466i	−0.757935	+	0.652330i	$0.773792\pi$
$488$		−	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	$-0.938618\pi$
$503$		−	2.17494e6i		−	0.383290i	0.981464	−	0.191645i	$-0.0613823\pi$
$504$	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	$0.255307\pi$
$523$			8.99272e6i			1.43760i	−0.695219	+	0.718798i	$0.744693\pi$
$524$	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	$0.163134\pi$
$547$			6.86297e6i			0.980717i	−0.871521	+	0.490359i	$0.836866\pi$
$548$		−	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	$0.249917\pi$
$557$			1.03524e7i			1.41384i	−0.707292	+	0.706922i	$0.750083\pi$
$558$		−	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	$0.128076\pi$
$563$			5.89028e6i			0.783186i	−0.920138	+	0.391593i	$0.871924\pi$
$564$	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	$-0.689267\pi$
$577$		−	1.32494e7i		−	1.65674i	0.560178	−	0.828372i	$-0.310733\pi$
$578$			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	$-0.939697\pi$
$587$		−	3.14421e6i		−	0.376631i	0.982109	−	0.188316i	$-0.0603028\pi$
$588$		−	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	$0.0449414\pi$
$593$			2.41001e6i			0.281438i	−0.990050	+	0.140719i	$0.955059\pi$
$594$	−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	$0.139266\pi$
$607$			7.69221e6i			0.847382i	−0.905807	+	0.423691i	$0.860734\pi$
$608$			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	$0.211557\pi$
$613$			1.14763e7i			1.23353i	−0.787147	+	0.616765i	$0.788443\pi$
$614$	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	$0.0364581\pi$
$617$			2.16141e6i			0.228573i	−0.993448	+	0.114286i	$0.963542\pi$
$618$			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	$0.0978235\pi$
$643$			6.34297e6i			0.605013i	−0.953147	+	0.302507i	$0.902177\pi$
$644$	−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	$0.283414\pi$
$647$			1.65532e7i			1.55461i	−0.629123	+	0.777306i	$0.716586\pi$
$648$		−	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	$0.113388\pi$
$653$			7.59986e6i			0.697465i	−0.937222	+	0.348733i	$0.886612\pi$
$654$	−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	$-0.891349\pi$
$673$		−	7.86653e6i		−	0.669493i	0.942308	−	0.334746i	$-0.108651\pi$
$674$	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	$-0.840960\pi$
$677$		−	1.14271e7i		−	0.958215i	0.877756	−	0.479107i	$-0.159040\pi$
$678$			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	$-0.674313\pi$
$683$		−	2.08171e7i		−	1.70753i	0.520656	−	0.853766i	$-0.325687\pi$
$684$	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	$-0.883423\pi$
$727$		−	1.02065e7i		−	0.716208i	0.933682	−	0.358104i	$-0.116577\pi$
$728$			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	$-0.971204\pi$
$733$		−	2.62828e6i		−	0.180681i	0.995911	−	0.0903405i	$-0.0287955\pi$
$734$	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	$0.0877206\pi$
$743$			8.18922e6i			0.544215i	−0.962267	+	0.272107i	$0.912279\pi$
$744$	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	$-0.757202\pi$
$757$		−	2.17873e7i		−	1.38186i	0.722923	−	0.690928i	$-0.242798\pi$
$758$			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	$0.100563\pi$
$773$			1.03233e7i			0.621398i	−0.950508	+	0.310699i	$0.899437\pi$
$774$	−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	$0.0973854\pi$
$787$			1.04668e7i			0.602389i	−0.953563	+	0.301195i	$0.902615\pi$
$788$		−	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	$-0.883329\pi$
$797$		−	1.28535e7i		−	0.716763i	0.933575	−	0.358382i	$-0.116671\pi$
$798$			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	$-0.625507\pi$
$823$		−	3.58804e7i		−	1.84654i	0.384156	−	0.923268i	$-0.374493\pi$
$824$	−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	$-0.670734\pi$
$827$		−	3.38121e7i		−	1.71913i	0.511026	−	0.859565i	$-0.329266\pi$
$828$			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	$0.247326\pi$
$853$			2.97995e7i			1.40228i	−0.713021	+	0.701142i	$0.752674\pi$
$854$	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	$-0.714185\pi$
$857$		−	3.36282e7i		−	1.56406i	0.623244	−	0.782028i	$-0.285815\pi$
$858$		−	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	$0.0772994\pi$
$863$			1.05222e7i			0.480927i	−0.970658	+	0.240463i	$0.922701\pi$
$864$	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	$0.104401\pi$
$877$			1.46747e7i			0.644273i	−0.946693	+	0.322137i	$0.895599\pi$
$878$		−	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	$0.119121\pi$
$883$			1.69389e7i			0.731112i	−0.930789	+	0.365556i	$0.880879\pi$
$884$	−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	$0.263151\pi$
$887$			3.44782e7i			1.47142i	−0.677298	+	0.735709i	$0.736849\pi$
$888$		−	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	$-0.803713\pi$
$907$		−	2.86555e7i		−	1.15662i	0.815818	−	0.578308i	$-0.196287\pi$
$908$			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	$-0.980127\pi$
$937$		−	3.35351e6i		−	0.124782i	0.998052	−	0.0623908i	$-0.0198725\pi$
$938$		−	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	$0.181234\pi$
$947$			2.97558e7i			1.07819i	−0.842244	+	0.539097i	$0.818766\pi$
$948$		−	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	$-0.889327\pi$
$953$		−	1.91059e7i		−	0.681451i	0.940163	−	0.340726i	$-0.110673\pi$
$954$	−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	$-0.967069\pi$
$967$		−	6.00580e6i		−	0.206540i	0.994653	−	0.103270i	$-0.0329306\pi$
$968$		−	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	$-0.849336\pi$
$977$		−	2.72011e7i		−	0.911697i	0.890057	−	0.455849i	$-0.150664\pi$
$978$		−	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	$0.117676\pi$
$983$			2.18935e7i			0.722654i	−0.932439	+	0.361327i	$0.882324\pi$
$984$	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	$-0.960947\pi$
$997$		−	7.68207e6i		−	0.244760i	0.992483	−	0.122380i	$-0.0390526\pi$
$998$		−	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.139.25	yes	26
5.4	even	2	inner	230.6.b.a.139.2	✓	26

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

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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