LMFDB - Embedded newform 230.6.b.a.139.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,6,Mod(139,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 6, names="a")

//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);

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

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			139.6
Character	$\chi$	$=$	230.139
Dual form			230.6.b.a.139.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{2} -5.96211i q^{3} -16.0000 q^{4} +(28.0011 + 48.3833i) q^{5} -23.8485 q^{6} -183.563i q^{7} +64.0000i q^{8} +207.453 q^{9} +O(q^{10})$	\(q-4.00000i q^{2} -5.96211i q^{3} -16.0000 q^{4} +(28.0011 + 48.3833i) q^{5} -23.8485 q^{6} -183.563i q^{7} +64.0000i q^{8} +207.453 q^{9} +(193.533 - 112.004i) q^{10} +76.8201 q^{11} +95.3938i q^{12} +418.482i q^{13} -734.252 q^{14} +(288.467 - 166.946i) q^{15} +256.000 q^{16} +1760.72i q^{17} -829.813i q^{18} +408.198 q^{19} +(-448.017 - 774.132i) q^{20} -1094.42 q^{21} -307.281i q^{22} -529.000i q^{23} +381.575 q^{24} +(-1556.88 + 2709.57i) q^{25} +1673.93 q^{26} -2685.65i q^{27} +2937.01i q^{28} +4719.89 q^{29} +(-667.782 - 1153.87i) q^{30} +5672.23 q^{31} -1024.00i q^{32} -458.011i q^{33} +7042.90 q^{34} +(8881.38 - 5139.96i) q^{35} -3319.25 q^{36} +4287.51i q^{37} -1632.79i q^{38} +2495.04 q^{39} +(-3096.53 + 1792.07i) q^{40} +11419.0 q^{41} +4377.69i q^{42} -20842.3i q^{43} -1229.12 q^{44} +(5808.91 + 10037.3i) q^{45} -2116.00 q^{46} +18859.8i q^{47} -1526.30i q^{48} -16888.4 q^{49} +(10838.3 + 6227.53i) q^{50} +10497.6 q^{51} -6695.71i q^{52} -40078.3i q^{53} -10742.6 q^{54} +(2151.05 + 3716.81i) q^{55} +11748.0 q^{56} -2433.72i q^{57} -18879.6i q^{58} +25490.7 q^{59} +(-4615.47 + 2671.13i) q^{60} -28011.8 q^{61} -22688.9i q^{62} -38080.7i q^{63} -4096.00 q^{64} +(-20247.5 + 11717.9i) q^{65} -1832.04 q^{66} -70855.3i q^{67} -28171.6i q^{68} -3153.96 q^{69} +(-20559.8 - 35525.5i) q^{70} +23049.7 q^{71} +13277.0i q^{72} +26656.4i q^{73} +17150.0 q^{74} +(16154.7 + 9282.31i) q^{75} -6531.17 q^{76} -14101.3i q^{77} -9980.14i q^{78} -208.955 q^{79} +(7168.27 + 12386.1i) q^{80} +34398.9 q^{81} -45675.8i q^{82} +56197.7i q^{83} +17510.8 q^{84} +(-85189.6 + 49302.1i) q^{85} -83369.3 q^{86} -28140.5i q^{87} +4916.49i q^{88} +20170.6 q^{89} +(40149.1 - 23235.6i) q^{90} +76817.8 q^{91} +8464.00i q^{92} -33818.5i q^{93} +75439.2 q^{94} +(11430.0 + 19750.0i) q^{95} -6105.21 q^{96} +7958.79i q^{97} +67553.5i q^{98} +15936.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) $ 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$		−	5.96211i		−	0.382470i	−0.981544	−	0.191235i	$-0.938751\pi$
$3$		−	5.96211i		−	0.382470i	0.981544	−	0.191235i	$-0.0612492\pi$
$4$	−16.0000			−0.500000
$5$	28.0011	+	48.3833i	0.500898	+	0.865506i
$5$	28.0011	+	48.3833i	0.500898	+	0.865506i
$6$	−23.8485			−0.270447
$7$		−	183.563i		−	1.41592i	−0.706250	−	0.707962i	$-0.749615\pi$
$7$		−	183.563i		−	1.41592i	0.706250	−	0.707962i	$-0.250385\pi$
$8$			64.0000i			0.353553i
$9$	207.453			0.853717
$10$	193.533	−	112.004i	0.612005	−	0.354188i
$11$	76.8201			0.191423			0.0957113	−	0.995409i	$-0.469487\pi$
$11$	76.8201			0.191423			0.0957113	+	0.995409i	$0.469487\pi$
$12$			95.3938i			0.191235i
$13$			418.482i			0.686781i	0.939193	+	0.343390i	$0.111575\pi$
$13$			418.482i			0.686781i	−0.939193	+	0.343390i	$0.888425\pi$
$14$	−734.252			−1.00121
$15$	288.467	−	166.946i	0.331030	−	0.191578i
$16$	256.000			0.250000
$17$			1760.72i			1.47764i	0.673902	+	0.738821i	$0.264617\pi$
$17$			1760.72i			1.47764i	−0.673902	+	0.738821i	$0.735383\pi$
$18$		−	829.813i		−	0.603669i
$19$	408.198			0.259410			0.129705	−	0.991553i	$-0.458597\pi$
$19$	408.198			0.259410			0.129705	+	0.991553i	$0.458597\pi$
$20$	−448.017	−	774.132i	−0.250449	−	0.432753i
$21$	−1094.42			−0.541548
$22$		−	307.281i		−	0.135356i
$23$		−	529.000i		−	0.208514i
$23$		−	529.000i		−	0.208514i
$24$	381.575			0.135224
$25$	−1556.88	+	2709.57i	−0.498202	+	0.867061i
$26$	1673.93			0.485627
$27$		−	2685.65i		−	0.708991i
$28$			2937.01i			0.707962i
$29$	4719.89			1.04217			0.521083	−	0.853506i	$-0.325528\pi$
$29$	4719.89			1.04217			0.521083	+	0.853506i	$0.325528\pi$
$30$	−667.782	−	1153.87i	−0.135466	−	0.234074i
$31$	5672.23			1.06011			0.530053	−	0.847964i	$-0.322172\pi$
$31$	5672.23			1.06011			0.530053	+	0.847964i	$0.322172\pi$
$32$		−	1024.00i		−	0.176777i
$33$		−	458.011i		−	0.0732134i
$34$	7042.90			1.04485
$35$	8881.38	−	5139.96i	1.22549	−	0.709234i
$36$	−3319.25			−0.426858
$37$			4287.51i			0.514874i	0.966295	+	0.257437i	$0.0828779\pi$
$37$			4287.51i			0.514874i	−0.966295	+	0.257437i	$0.917122\pi$
$38$		−	1632.79i		−	0.183431i
$39$	2495.04			0.262673
$40$	−3096.53	+	1792.07i	−0.306003	+	0.177094i
$41$	11419.0			1.06088			0.530441	−	0.847722i	$-0.322027\pi$
$41$	11419.0			1.06088			0.530441	+	0.847722i	$0.322027\pi$
$42$			4377.69i			0.382933i
$43$		−	20842.3i		−	1.71900i	−0.511139	−	0.859498i	$-0.670776\pi$
$43$		−	20842.3i		−	1.71900i	0.511139	−	0.859498i	$-0.329224\pi$
$44$	−1229.12			−0.0957113
$45$	5808.91	+	10037.3i	0.427625	+	0.738897i
$46$	−2116.00			−0.147442
$47$			18859.8i			1.24535i	0.782479	+	0.622677i	$0.213955\pi$
$47$			18859.8i			1.24535i	−0.782479	+	0.622677i	$0.786045\pi$
$48$		−	1526.30i		−	0.0956175i
$49$	−16888.4			−1.00484
$50$	10838.3	+	6227.53i	0.613105	+	0.352282i
$51$	10497.6			0.565153
$52$		−	6695.71i		−	0.343390i
$53$		−	40078.3i		−	1.95984i	−0.199401	−	0.979918i	$-0.563900\pi$
$53$		−	40078.3i		−	1.95984i	0.199401	−	0.979918i	$-0.436100\pi$
$54$	−10742.6			−0.501332
$55$	2151.05	+	3716.81i	0.0958833	+	0.165678i
$56$	11748.0			0.500605
$57$		−	2433.72i		−	0.0992166i
$58$		−	18879.6i		−	0.736923i
$59$	25490.7			0.953347			0.476673	−	0.879080i	$-0.341842\pi$
$59$	25490.7			0.953347			0.476673	+	0.879080i	$0.341842\pi$
$60$	−4615.47	+	2671.13i	−0.165515	+	0.0957892i
$61$	−28011.8			−0.963866			−0.481933	−	0.876208i	$-0.660065\pi$
$61$	−28011.8			−0.963866			−0.481933	+	0.876208i	$0.660065\pi$
$62$		−	22688.9i		−	0.749609i
$63$		−	38080.7i		−	1.20880i
$64$	−4096.00			−0.125000
$65$	−20247.5	+	11717.9i	−0.594413	+	0.344007i
$66$	−1832.04			−0.0517697
$67$		−	70855.3i		−	1.92835i	−0.265271	−	0.964174i	$-0.585461\pi$
$67$		−	70855.3i		−	1.92835i	0.265271	−	0.964174i	$-0.414539\pi$
$68$		−	28171.6i		−	0.738821i
$69$	−3153.96			−0.0797505
$70$	−20559.8	−	35525.5i	−0.501504	−	0.866553i
$71$	23049.7			0.542649			0.271325	−	0.962488i	$-0.412538\pi$
$71$	23049.7			0.542649			0.271325	+	0.962488i	$0.412538\pi$
$72$			13277.0i			0.301834i
$73$			26656.4i			0.585457i	0.956196	+	0.292728i	$0.0945632\pi$
$73$			26656.4i			0.585457i	−0.956196	+	0.292728i	$0.905437\pi$
$74$	17150.0			0.364071
$75$	16154.7	+	9282.31i	0.331625	+	0.190547i
$76$	−6531.17			−0.129705
$77$		−	14101.3i		−	0.271040i
$78$		−	9980.14i		−	0.185738i
$79$	−208.955			−0.00376690			−0.00188345	−	0.999998i	$-0.500600\pi$
$79$	−208.955			−0.00376690			−0.00188345	+	0.999998i	$0.500600\pi$
$80$	7168.27	+	12386.1i	0.125225	+	0.216377i
$81$	34398.9			0.582549
$82$		−	45675.8i		−	0.750156i
$83$			56197.7i			0.895412i	0.894181	+	0.447706i	$0.147759\pi$
$83$			56197.7i			0.895412i	−0.894181	+	0.447706i	$0.852241\pi$
$84$	17510.8			0.270774
$85$	−85189.6	+	49302.1i	−1.27891	+	0.740148i
$86$	−83369.3			−1.21551
$87$		−	28140.5i		−	0.398597i
$88$			4916.49i			0.0676781i
$89$	20170.6			0.269925			0.134963	−	0.990851i	$-0.456909\pi$
$89$	20170.6			0.269925			0.134963	+	0.990851i	$0.456909\pi$
$90$	40149.1	−	23235.6i	0.522479	−	0.302377i
$91$	76817.8			0.972430
$92$			8464.00i			0.104257i
$93$		−	33818.5i		−	0.405459i
$94$	75439.2			0.880598
$95$	11430.0	+	19750.0i	0.129938	+	0.224521i
$96$	−6105.21			−0.0676118
$97$			7958.79i			0.0858850i	0.999078	+	0.0429425i	$0.0136732\pi$
$97$			7958.79i			0.0858850i	−0.999078	+	0.0429425i	$0.986327\pi$
$98$			67553.5i			0.710530i
$99$	15936.6			0.163421
$100$	24910.1	−	43353.0i	0.249101	−	0.433530i
$101$	46909.7			0.457571			0.228786	−	0.973477i	$-0.426524\pi$
$101$	46909.7			0.457571			0.228786	+	0.973477i	$0.426524\pi$
$102$		−	41990.6i		−	0.399624i
$103$		−	57744.0i		−	0.536307i	−0.963376	−	0.268154i	$-0.913587\pi$
$103$		−	57744.0i		−	0.536307i	0.963376	−	0.268154i	$-0.0864134\pi$
$104$	−26782.8			−0.242814
$105$	−30645.0	−	52951.8i	−0.271261	−	0.468713i
$106$	−160313.			−1.38581
$107$			14848.5i			0.125379i	0.998033	+	0.0626893i	$0.0199677\pi$
$107$			14848.5i			0.125379i	−0.998033	+	0.0626893i	$0.980032\pi$
$108$			42970.5i			0.354495i
$109$	198406.			1.59952			0.799760	−	0.600320i	$-0.204960\pi$
$109$	198406.			1.59952			0.799760	+	0.600320i	$0.204960\pi$
$110$	14867.2	−	8604.18i	0.117152	−	0.0677997i
$111$	25562.6			0.196924
$112$		−	46992.1i		−	0.353981i
$113$			5570.45i			0.0410388i	0.999789	+	0.0205194i	$0.00653198\pi$
$113$			5570.45i			0.0410388i	−0.999789	+	0.0205194i	$0.993468\pi$
$114$	−9734.90			−0.0701567
$115$	25594.7	−	14812.6i	0.180471	−	0.104444i
$116$	−75518.3			−0.521083
$117$			86815.4i			0.586316i
$118$		−	101963.i		−	0.674118i
$119$	323204.			2.09223
$120$	10684.5	+	18461.9i	0.0677332	+	0.117037i
$121$	−155150.			−0.963357
$122$			112047.i			0.681557i
$123$		−	68081.1i		−	0.405755i
$124$	−90755.7			−0.530053
$125$	−174692.	+	543.677i	−0.999995	+	0.00311219i
$126$	−152323.			−0.854750
$127$		−	357638.i		−	1.96759i	−0.179301	−	0.983794i	$-0.557384\pi$
$127$		−	357638.i		−	1.96759i	0.179301	−	0.983794i	$-0.442616\pi$
$128$			16384.0i			0.0883883i
$129$	−124264.			−0.657464
$130$	46871.7	+	80990.1i	0.243250	+	0.420313i
$131$	126561.			0.644348			0.322174	−	0.946681i	$-0.395586\pi$
$131$	126561.			0.644348			0.322174	+	0.946681i	$0.395586\pi$
$132$			7328.17i			0.0366067i
$133$		−	74930.1i		−	0.367305i
$134$	−283421.			−1.36355
$135$	129941.	−	75201.1i	0.613636	−	0.355132i
$136$	−112686.			−0.522425
$137$			192387.i			0.875740i	0.899038	+	0.437870i	$0.144267\pi$
$137$			192387.i			0.875740i	−0.899038	+	0.437870i	$0.855733\pi$
$138$			12615.8i			0.0563921i
$139$	−247344.			−1.08584			−0.542918	−	0.839786i	$-0.682680\pi$
$139$	−247344.			−1.08584			−0.542918	+	0.839786i	$0.682680\pi$
$140$	−142102.	+	82239.3i	−0.612746	+	0.354617i
$141$	112444.			0.476310
$142$		−	92198.8i		−	0.383711i
$143$			32147.8i			0.131465i
$144$	53108.0			0.213429
$145$	132162.	+	228364.i	0.522019	+	0.902001i
$146$	106626.			0.413981
$147$			100690.i			0.384322i
$148$		−	68600.1i		−	0.257437i
$149$	478387.			1.76528			0.882640	−	0.470049i	$-0.155764\pi$
$149$	478387.			1.76528			0.882640	+	0.470049i	$0.155764\pi$
$150$	37129.2	−	64619.0i	0.134737	−	0.234494i
$151$	−49891.1			−0.178066			−0.0890329	−	0.996029i	$-0.528378\pi$
$151$	−49891.1			−0.178066			−0.0890329	+	0.996029i	$0.528378\pi$
$152$			26124.7i			0.0917154i
$153$			365268.i			1.26149i
$154$	−56405.3			−0.191654
$155$	158828.	+	274441.i	0.531006	+	0.917529i
$156$	−39920.6			−0.131336
$157$			433186.i			1.40257i	0.712880	+	0.701286i	$0.247390\pi$
$157$			433186.i			1.40257i	−0.712880	+	0.701286i	$0.752610\pi$
$158$			835.819i			0.00266360i
$159$	−238951.			−0.749578
$160$	49544.5	−	28673.1i	0.153001	−	0.0885471i
$161$	−97104.8			−0.295241
$162$		−	137596.i		−	0.411925i
$163$			615177.i			1.81356i	0.421609	+	0.906778i	$0.361465\pi$
$163$			615177.i			1.81356i	−0.421609	+	0.906778i	$0.638535\pi$
$164$	−182703.			−0.530441
$165$	22160.0	−	12824.8i	0.0633667	−	0.0366725i
$166$	224791.			0.633152
$167$			310499.i			0.861528i	0.902465	+	0.430764i	$0.141756\pi$
$167$			310499.i			0.861528i	−0.902465	+	0.430764i	$0.858244\pi$
$168$		−	70043.1i		−	0.191466i
$169$	196166.			0.528332
$170$	197209.	+	340758.i	0.523364	+	0.904324i
$171$	84682.0			0.221463
$172$			333477.i			0.859498i
$173$		−	154748.i		−	0.393107i	−0.980493	−	0.196554i	$-0.937025\pi$
$173$		−	154748.i		−	0.393107i	0.980493	−	0.196554i	$-0.0629750\pi$
$174$	−112562.			−0.281851
$175$	497376.	+	285786.i	1.22769	+	0.705416i
$176$	19666.0			0.0478557
$177$		−	151978.i		−	0.364626i
$178$		−	80682.3i		−	0.190866i
$179$	−415724.			−0.969779			−0.484890	−	0.874575i	$-0.661140\pi$
$179$	−415724.			−0.969779			−0.484890	+	0.874575i	$0.661140\pi$
$180$	−92942.5	−	160596.i	−0.213813	−	0.369449i
$181$	−461459.			−1.04698			−0.523488	−	0.852033i	$-0.675369\pi$
$181$	−461459.			−1.04698			−0.523488	+	0.852033i	$0.675369\pi$
$182$		−	307271.i		−	0.687612i
$183$			167010.i			0.368650i
$184$	33856.0			0.0737210
$185$	−207444.	+	120055.i	−0.445626	+	0.257899i
$186$	−135274.			−0.286703
$187$			135259.i			0.282854i
$188$		−	301757.i		−	0.622677i
$189$	−492987.			−1.00388
$190$	78999.9	−	45719.9i	0.158760	−	0.0918801i
$191$	−668198.			−1.32532			−0.662661	−	0.748919i	$-0.730573\pi$
$191$	−668198.			−1.32532			−0.662661	+	0.748919i	$0.730573\pi$
$192$			24420.8i			0.0478087i
$193$		−	189136.i		−	0.365494i	−0.983160	−	0.182747i	$-0.941501\pi$
$193$		−	189136.i		−	0.365494i	0.983160	−	0.182747i	$-0.0584989\pi$
$194$	31835.1			0.0607299
$195$	69863.6	+	120718.i	0.131572	+	0.227345i
$196$	270214.			0.502421
$197$			604807.i			1.11033i	0.831741	+	0.555163i	$0.187344\pi$
$197$			604807.i			1.11033i	−0.831741	+	0.555163i	$0.812656\pi$
$198$		−	63746.3i		−	0.115556i
$199$	98108.2			0.175619			0.0878097	−	0.996137i	$-0.472013\pi$
$199$	98108.2			0.175619			0.0878097	+	0.996137i	$0.472013\pi$
$200$	−173412.	−	99640.4i	−0.306552	−	0.176141i
$201$	−422447.			−0.737535
$202$		−	187639.i		−	0.323552i
$203$		−	866397.i		−	1.47563i
$204$	−167962.			−0.282577
$205$	319743.	+	552486.i	0.531393	+	0.918199i
$206$	−230976.			−0.379226
$207$		−	109743.i		−	0.178012i
$208$			107131.i			0.171695i
$209$	31357.8			0.0496570
$210$	−211807.	+	122580.i	−0.331430	+	0.191810i
$211$	−337970.			−0.522603			−0.261302	−	0.965257i	$-0.584152\pi$
$211$	−337970.			−0.522603			−0.261302	+	0.965257i	$0.584152\pi$
$212$			641253.i			0.979918i
$213$		−	137425.i		−	0.207547i
$214$	59394.0			0.0886560
$215$	1.00842e6	−	583607.i	1.48780	−	0.861042i
$216$	171882.			0.250666
$217$		−	1.04121e6i		−	1.50103i
$218$		−	793626.i		−	1.13103i
$219$	158929.			0.223920
$220$	−34416.7	−	59469.0i	−0.0479416	−	0.0828388i
$221$	−736831.			−1.01482
$222$		−	102250.i		−	0.139246i
$223$			783743.i			1.05539i	0.849435	+	0.527693i	$0.176943\pi$
$223$			783743.i			1.05539i	−0.849435	+	0.527693i	$0.823057\pi$
$224$	−187969.			−0.250302
$225$	−322980.	+	562108.i	−0.425324	+	0.740225i
$226$	22281.8			0.0290188
$227$			1.29877e6i			1.67289i	0.548053	+	0.836444i	$0.315369\pi$
$227$			1.29877e6i			1.67289i	−0.548053	+	0.836444i	$0.684631\pi$
$228$			38939.6i			0.0496083i
$229$	1.37477e6			1.73237			0.866185	−	0.499724i	$-0.166565\pi$
$229$	1.37477e6			1.73237			0.866185	+	0.499724i	$0.166565\pi$
$230$	−59250.2	−	102379.i	−0.0738534	−	0.127612i
$231$	−84073.8			−0.103665
$232$			302073.i			0.368461i
$233$		−	1.27013e6i		−	1.53271i	−0.642418	−	0.766355i	$-0.722068\pi$
$233$		−	1.27013e6i		−	1.53271i	0.642418	−	0.766355i	$-0.277932\pi$
$234$	347261.			0.414588
$235$	−912499.	+	528094.i	−1.07786	+	0.623795i
$236$	−407850.			−0.476673
$237$			1245.81i			0.00144073i
$238$		−	1.29282e6i		−	1.47943i
$239$	−244205.			−0.276541			−0.138271	−	0.990394i	$-0.544154\pi$
$239$	−244205.			−0.276541			−0.138271	+	0.990394i	$0.544154\pi$
$240$	73847.5	−	42738.1i	0.0827575	−	0.0478946i
$241$	667589.			0.740400			0.370200	−	0.928952i	$-0.379289\pi$
$241$	667589.			0.740400			0.370200	+	0.928952i	$0.379289\pi$
$242$			620599.i			0.681197i
$243$		−	857704.i		−	0.931798i
$244$	448189.			0.481933
$245$	−472892.	−	817115.i	−0.503323	−	0.869697i
$246$	−272324.			−0.286912
$247$			170823.i			0.178158i
$248$			363023.i			0.374804i
$249$	335057.			0.342468
$250$	2174.71	+	698768.i	0.00220065	+	0.707103i
$251$	47328.0			0.0474170			0.0237085	−	0.999719i	$-0.492453\pi$
$251$	47328.0			0.0474170			0.0237085	+	0.999719i	$0.492453\pi$
$252$			609292.i			0.604399i
$253$		−	40637.9i		−	0.0399144i
$254$	−1.43055e6			−1.39130
$255$	293945.	+	507910.i	0.283084	+	0.489144i
$256$	65536.0			0.0625000
$257$		−	1.89724e6i		−	1.79180i	−0.444257	−	0.895900i	$-0.646532\pi$
$257$		−	1.89724e6i		−	1.79180i	0.444257	−	0.895900i	$-0.353468\pi$
$258$			497057.i			0.464897i
$259$	787028.			0.729022
$260$	323960.	−	187487.i	0.297206	−	0.172004i
$261$	979157.			0.889715
$262$		−	506242.i		−	0.455623i
$263$		−	1.45620e6i		−	1.29817i	−0.760716	−	0.649084i	$-0.775152\pi$
$263$		−	1.45620e6i		−	1.29817i	0.760716	−	0.649084i	$-0.224848\pi$
$264$	29312.7			0.0258848
$265$	1.93912e6	−	1.12223e6i	1.69625	−	0.981678i
$266$	−299720.			−0.259724
$267$		−	120259.i		−	0.103238i
$268$			1.13368e6i			0.964174i
$269$	−214592.			−0.180814			−0.0904072	−	0.995905i	$-0.528817\pi$
$269$	−214592.			−0.180814			−0.0904072	+	0.995905i	$0.528817\pi$
$270$	−300805.	−	519763.i	−0.251116	−	0.433906i
$271$	−1.72835e6			−1.42958			−0.714790	−	0.699339i	$-0.753478\pi$
$271$	−1.72835e6			−1.42958			−0.714790	+	0.699339i	$0.753478\pi$
$272$			450745.i			0.369410i
$273$		−	457996.i		−	0.371925i
$274$	769550.			0.619242
$275$	−119600.	+	208149.i	−0.0953672	+	0.165975i
$276$	50463.3			0.0398752
$277$			2.25029e6i			1.76213i	0.472992	+	0.881067i	$0.343174\pi$
$277$			2.25029e6i			1.76213i	−0.472992	+	0.881067i	$0.656826\pi$
$278$			989375.i			0.767801i
$279$	1.17672e6			0.905031
$280$	328957.	+	568408.i	0.250752	+	0.433277i
$281$	−1.18081e6			−0.892101			−0.446051	−	0.895008i	$-0.647170\pi$
$281$	−1.18081e6			−0.892101			−0.446051	+	0.895008i	$0.647170\pi$
$282$		−	449777.i		−	0.336802i
$283$			1.19396e6i			0.886184i	0.896476	+	0.443092i	$0.146119\pi$
$283$			1.19396e6i			0.886184i	−0.896476	+	0.443092i	$0.853881\pi$
$284$	−368795.			−0.271325
$285$	117752.	−	68146.9i	0.0858726	−	0.0496974i
$286$	128591.			0.0929601
$287$		−	2.09610e6i		−	1.50213i
$288$		−	212432.i		−	0.150917i
$289$	−1.68029e6			−1.18342
$290$	913455.	−	528648.i	0.637811	−	0.369123i
$291$	47451.2			0.0328484
$292$		−	426503.i		−	0.292728i
$293$		−	70148.4i		−	0.0477363i	−0.999715	−	0.0238682i	$-0.992402\pi$
$293$		−	70148.4i		−	0.0477363i	0.999715	−	0.0238682i	$-0.00759819\pi$
$294$	402762.			0.271756
$295$	713765.	+	1.23332e6i	0.477530	+	0.825128i
$296$	−274400.			−0.182035
$297$		−	206312.i		−	0.135717i
$298$		−	1.91355e6i		−	1.24824i
$299$	221377.			0.143204
$300$	−258476.	−	148517.i	−0.165812	−	0.0952736i
$301$	−3.82588e6			−2.43397
$302$			199564.i			0.125911i
$303$		−	279681.i		−	0.175007i
$304$	104499.			0.0648526
$305$	−784361.	−	1.35530e6i	−0.482799	−	0.834232i
$306$	1.46107e6			0.892006
$307$		−	795406.i		−	0.481663i	−0.970567	−	0.240831i	$-0.922580\pi$
$307$		−	795406.i		−	0.481663i	0.970567	−	0.240831i	$-0.0774200\pi$
$308$			225621.i			0.135520i
$309$	−344276.			−0.205121
$310$	1.09776e6	−	635314.i	0.648791	−	0.375478i
$311$	−196780.			−0.115367			−0.0576833	−	0.998335i	$-0.518371\pi$
$311$	−196780.			−0.115367			−0.0576833	+	0.998335i	$0.518371\pi$
$312$			159682.i			0.0928689i
$313$			1.22721e6i			0.708042i	0.935237	+	0.354021i	$0.115186\pi$
$313$			1.22721e6i			0.708042i	−0.935237	+	0.354021i	$0.884814\pi$
$314$	1.73274e6			0.991768
$315$	1.84247e6	−	1.06630e6i	1.04622	−	0.605485i
$316$	3343.27			0.00188345
$317$		−	1.43948e6i		−	0.804557i	−0.915517	−	0.402279i	$-0.868218\pi$
$317$		−	1.43948e6i		−	0.804557i	0.915517	−	0.402279i	$-0.131782\pi$
$318$			955806.i			0.530032i
$319$	362583.			0.199494
$320$	−114692.	−	198178.i	−0.0626123	−	0.108188i
$321$	88528.5			0.0479535
$322$			388419.i			0.208767i
$323$			718724.i			0.383315i
$324$	−550383.			−0.291275
$325$	−1.13390e6	−	651526.i	−0.595481	−	0.342156i
$326$	2.46071e6			1.28238
$327$		−	1.18292e6i		−	0.611768i
$328$			730813.i			0.375078i
$329$	3.46196e6			1.76333
$330$	−51299.1	−	88640.2i	−0.0259313	−	0.0448070i
$331$	408407.			0.204891			0.102446	−	0.994739i	$-0.467333\pi$
$331$	408407.			0.204891			0.102446	+	0.994739i	$0.467333\pi$
$332$		−	899162.i		−	0.447706i
$333$			889457.i			0.439556i
$334$	1.24200e6			0.609192
$335$	3.42821e6	−	1.98402e6i	1.66900	−	0.965906i
$336$	−280172.			−0.135387
$337$		−	1.23330e6i		−	0.591552i	−0.955257	−	0.295776i	$-0.904422\pi$
$337$		−	1.23330e6i		−	0.591552i	0.955257	−	0.295776i	$-0.0955781\pi$
$338$		−	784664.i		−	0.373587i
$339$	33211.7			0.0156961
$340$	1.36303e6	−	788834.i	0.639454	−	0.370074i
$341$	435742.			0.202929
$342$		−	338728.i		−	0.156598i
$343$			14937.2i			0.00685544i
$344$	1.33391e6			0.607757
$345$	−88314.2	−	152599.i	−0.0399469	−	0.0690245i
$346$	−618994.			−0.277969
$347$			607434.i			0.270817i	0.990790	+	0.135408i	$0.0432346\pi$
$347$			607434.i			0.270817i	−0.990790	+	0.135408i	$0.956765\pi$
$348$			450249.i			0.199299i
$349$	−1.07181e6			−0.471037			−0.235519	−	0.971870i	$-0.575679\pi$
$349$	−1.07181e6			−0.471037			−0.235519	+	0.971870i	$0.575679\pi$
$350$	1.14314e6	−	1.98950e6i	0.498805	−	0.868110i
$351$	1.12390e6			0.486921
$352$		−	78663.8i		−	0.0338391i
$353$			2.01747e6i			0.861728i	0.902417	+	0.430864i	$0.141791\pi$
$353$			2.01747e6i			0.861728i	−0.902417	+	0.430864i	$0.858209\pi$
$354$	−607913.			−0.257830
$355$	645416.	+	1.11522e6i	0.271812	+	0.469667i
$356$	−322729.			−0.134963
$357$		−	1.92698e6i		−	0.800214i
$358$			1.66290e6i			0.685737i
$359$	−333706.			−0.136656			−0.0683279	−	0.997663i	$-0.521766\pi$
$359$	−333706.			−0.136656			−0.0683279	+	0.997663i	$0.521766\pi$
$360$	−642385.	+	371770.i	−0.261240	+	0.151188i
$361$	−2.30947e6			−0.932706
$362$			1.84583e6i			0.740323i
$363$			925020.i			0.368455i
$364$	−1.22908e6			−0.486215
$365$	−1.28973e6	+	746408.i	−0.506717	+	0.293254i
$366$	668039.			0.260675
$367$		−	1.76290e6i		−	0.683224i	−0.939841	−	0.341612i	$-0.889027\pi$
$367$		−	1.76290e6i		−	0.683224i	0.939841	−	0.341612i	$-0.110973\pi$
$368$		−	135424.i		−	0.0521286i
$369$	2.36890e6			0.905692
$370$	480219.	+	829775.i	0.182362	+	0.315105i
$371$	−7.35689e6			−2.77498
$372$			541096.i			0.202729i
$373$		−	2.80456e6i		−	1.04374i	−0.853025	−	0.521871i	$-0.825234\pi$
$373$		−	2.80456e6i		−	1.04374i	0.853025	−	0.521871i	$-0.174766\pi$
$374$	541036.			0.200008
$375$	3241.47	+	1.04153e6i	0.00119032	+	0.382468i
$376$	−1.20703e6			−0.440299
$377$			1.97519e6i			0.715740i
$378$			1.97195e6i			0.709848i
$379$	1.16517e6			0.416669			0.208335	−	0.978058i	$-0.433196\pi$
$379$	1.16517e6			0.416669			0.208335	+	0.978058i	$0.433196\pi$
$380$	−182880.	−	315999.i	−0.0649690	−	0.112261i
$381$	−2.13228e6			−0.752543
$382$			2.67279e6i			0.937144i
$383$		−	1.93822e6i		−	0.675158i	−0.941297	−	0.337579i	$-0.890392\pi$
$383$		−	1.93822e6i		−	0.675158i	0.941297	−	0.337579i	$-0.109608\pi$
$384$	97683.3			0.0338059
$385$	682269.	−	394852.i	0.234587	−	0.135763i
$386$	−756543.			−0.258443
$387$		−	4.32381e6i		−	1.46754i
$388$		−	127341.i		−	0.0429425i
$389$	822755.			0.275674			0.137837	−	0.990455i	$-0.455985\pi$
$389$	822755.			0.275674			0.137837	+	0.990455i	$0.455985\pi$
$390$	482872.	−	279455.i	0.160757	−	0.0930357i
$391$	931423.			0.308110
$392$		−	1.08086e6i		−	0.355265i
$393$		−	754569.i		−	0.246444i
$394$	2.41923e6			0.785120
$395$	−5850.95	−	10109.9i	−0.00188683	−	0.00326028i
$396$	−254985.			−0.0817104
$397$			5.54285e6i			1.76505i	0.470267	+	0.882524i	$0.344157\pi$
$397$			5.54285e6i			1.76505i	−0.470267	+	0.882524i	$0.655843\pi$
$398$		−	392433.i		−	0.124182i
$399$	−446742.			−0.140483
$400$	−398562.	+	693649.i	−0.124551	+	0.216765i
$401$	−3.00841e6			−0.934278			−0.467139	−	0.884184i	$-0.654715\pi$
$401$	−3.00841e6			−0.934278			−0.467139	+	0.884184i	$0.654715\pi$
$402$			1.68979e6i			0.521516i
$403$			2.37372e6i			0.728061i
$404$	−750555.			−0.228786
$405$	963207.	+	1.66433e6i	0.291798	+	0.504200i
$406$	−3.46559e6			−1.04343
$407$			329367.i			0.0985585i
$408$			671849.i			0.199812i
$409$	−1.57926e6			−0.466815			−0.233408	−	0.972379i	$-0.574988\pi$
$409$	−1.57926e6			−0.466815			−0.233408	+	0.972379i	$0.574988\pi$
$410$	2.20995e6	−	1.27897e6i	0.649265	−	0.375752i
$411$	1.14704e6			0.334944
$412$			923903.i			0.268154i
$413$		−	4.67914e6i		−	1.34987i
$414$	−438971.			−0.125874
$415$	−2.71903e6	+	1.57359e6i	−0.774985	+	0.448510i
$416$	428525.			0.121407
$417$			1.47469e6i			0.415299i
$418$		−	125431.i		−	0.0351128i
$419$	−1.62199e6			−0.451349			−0.225674	−	0.974203i	$-0.572459\pi$
$419$	−1.62199e6			−0.451349			−0.225674	+	0.974203i	$0.572459\pi$
$420$	490320.	+	847229.i	0.135630	+	0.234357i
$421$	703553.			0.193460			0.0967301	−	0.995311i	$-0.469162\pi$
$421$	703553.			0.193460			0.0967301	+	0.995311i	$0.469162\pi$
$422$			1.35188e6i			0.369536i
$423$			3.91253e6i			1.06318i
$424$	2.56501e6			0.692907
$425$	−4.77080e6	−	2.74124e6i	−1.28121	−	0.736164i
$426$	−549700.			−0.146758
$427$			5.14194e6i			1.36476i
$428$		−	237576.i		−	0.0626893i
$429$	191669.			0.0502816
$430$	−2.33443e6	−	4.03368e6i	−0.608849	−	1.05204i
$431$	1.46794e6			0.380642			0.190321	−	0.981722i	$-0.439047\pi$
$431$	1.46794e6			0.380642			0.190321	+	0.981722i	$0.439047\pi$
$432$		−	687527.i		−	0.177248i
$433$			1.71999e6i			0.440866i	0.975402	+	0.220433i	$0.0707471\pi$
$433$			1.71999e6i			0.440866i	−0.975402	+	0.220433i	$0.929253\pi$
$434$	−4.16485e6			−1.06139
$435$	1.36153e6	−	787965.i	0.344988	−	0.199657i
$436$	−3.17450e6			−0.799760
$437$		−	215937.i		−	0.0540908i
$438$		−	635715.i		−	0.158335i
$439$	−4.05852e6			−1.00509			−0.502547	−	0.864550i	$-0.667604\pi$
$439$	−4.05852e6			−1.00509			−0.502547	+	0.864550i	$0.667604\pi$
$440$	−237876.	+	137667.i	−0.0585759	+	0.0338999i
$441$	−3.50355e6			−0.857850
$442$			2.94732e6i			0.717583i
$443$			5.49750e6i			1.33093i	0.746428	+	0.665466i	$0.231767\pi$
$443$			5.49750e6i			1.33093i	−0.746428	+	0.665466i	$0.768233\pi$
$444$	−409002.			−0.0984618
$445$	564797.	+	975918.i	0.135205	+	0.233622i
$446$	3.13497e6			0.746271
$447$		−	2.85220e6i		−	0.675167i
$448$			751874.i			0.176991i
$449$	3.26863e6			0.765155			0.382578	−	0.923923i	$-0.375036\pi$
$449$	3.26863e6			0.765155			0.382578	+	0.923923i	$0.375036\pi$
$450$	2.24843e6	+	1.29192e6i	0.523418	+	0.300749i
$451$	877206.			0.203077
$452$		−	89127.3i		−	0.0205194i
$453$			297456.i			0.0681048i
$454$	5.19507e6			1.18291
$455$	2.15098e6	+	3.71669e6i	0.487088	+	0.841644i
$456$	155758.			0.0350784
$457$		−	2.99188e6i		−	0.670121i	−0.942197	−	0.335060i	$-0.891243\pi$
$457$		−	2.99188e6i		−	0.670121i	0.942197	−	0.335060i	$-0.108757\pi$
$458$		−	5.49907e6i		−	1.22497i
$459$	4.72870e6			1.04763
$460$	−409516.	+	237001.i	−0.0902353	+	0.0522222i
$461$	−6.91545e6			−1.51554			−0.757771	−	0.652520i	$-0.773712\pi$
$461$	−6.91545e6			−1.51554			−0.757771	+	0.652520i	$0.773712\pi$
$462$			336295.i			0.0733020i
$463$			1.12663e6i			0.244247i	0.992515	+	0.122123i	$0.0389703\pi$
$463$			1.12663e6i			0.244247i	−0.992515	+	0.122123i	$0.961030\pi$
$464$	1.20829e6			0.260542
$465$	1.63625e6	−	946953.i	0.350927	−	0.203094i
$466$	−5.08054e6			−1.08379
$467$		−	2.00638e6i		−	0.425717i	−0.977083	−	0.212859i	$-0.931723\pi$
$467$		−	2.00638e6i		−	0.425717i	0.977083	−	0.212859i	$-0.0682773\pi$
$468$		−	1.38905e6i		−	0.293158i
$469$	−1.30064e7			−2.73039
$470$	2.11238e6	+	3.65000e6i	0.441090	+	0.762163i
$471$	2.58270e6			0.536441
$472$			1.63140e6i			0.337059i
$473$		−	1.60111e6i		−	0.329055i
$474$	4983.25			0.00101875
$475$	−635516.	+	1.10604e6i	−0.129239	+	0.224924i
$476$	−5.17126e6			−1.04611
$477$		−	8.31437e6i		−	1.67314i
$478$			976820.i			0.195544i
$479$	−1.32757e6			−0.264374			−0.132187	−	0.991225i	$-0.542200\pi$
$479$	−1.32757e6			−0.264374			−0.132187	+	0.991225i	$0.542200\pi$
$480$	−170952.	−	295390.i	−0.0338666	−	0.0585184i
$481$	−1.79424e6			−0.353605
$482$		−	2.67036e6i		−	0.523542i
$483$			578950.i			0.112921i
$484$	2.48239e6			0.481679
$485$	−385072.	+	222854.i	−0.0743340	+	0.0430197i
$486$	−3.43082e6			−0.658881
$487$		−	2.27261e6i		−	0.434212i	−0.976148	−	0.217106i	$-0.930338\pi$
$487$		−	2.27261e6i		−	0.434212i	0.976148	−	0.217106i	$-0.0696618\pi$
$488$		−	1.79276e6i		−	0.340778i
$489$	3.66775e6			0.693630
$490$	−3.26846e6	+	1.89157e6i	−0.614968	+	0.355903i
$491$	−2.07331e6			−0.388115			−0.194058	−	0.980990i	$-0.562165\pi$
$491$	−2.07331e6			−0.388115			−0.194058	+	0.980990i	$0.562165\pi$
$492$			1.08930e6i			0.202878i
$493$			8.31043e6i			1.53995i
$494$	683294.			0.125977
$495$	446241.	+	771064.i	0.0818572	+	0.141442i
$496$	1.45209e6			0.265027
$497$		−	4.23107e6i		−	0.768351i
$498$		−	1.34023e6i		−	0.242162i
$499$	1.95194e6			0.350925			0.175462	−	0.984486i	$-0.443858\pi$
$499$	1.95194e6			0.350925			0.175462	+	0.984486i	$0.443858\pi$
$500$	2.79507e6	−	8698.84i	0.499998	−	0.00155609i
$501$	1.85123e6			0.329509
$502$		−	189312.i		−	0.0335289i
$503$			9.41482e6i			1.65918i	0.558377	+	0.829588i	$0.311424\pi$
$503$			9.41482e6i			1.65918i	−0.558377	+	0.829588i	$0.688576\pi$
$504$	2.43717e6			0.427375
$505$	1.31352e6	+	2.26964e6i	0.229197	+	0.396031i
$506$	−162551.			−0.0282237
$507$		−	1.16956e6i		−	0.202071i
$508$			5.72221e6i			0.983794i
$509$	2.14653e6			0.367234			0.183617	−	0.982998i	$-0.441219\pi$
$509$	2.14653e6			0.367234			0.183617	+	0.982998i	$0.441219\pi$
$510$	2.03164e6	−	1.17578e6i	0.345877	−	0.200171i
$511$	4.89313e6			0.828963
$512$		−	262144.i		−	0.0441942i
$513$		−	1.09628e6i		−	0.183919i
$514$	−7.58896e6			−1.26699
$515$	2.79384e6	−	1.61689e6i	0.464177	−	0.268635i
$516$	1.98823e6			0.328732
$517$			1.44881e6i			0.238389i
$518$		−	3.14811e6i		−	0.515496i
$519$	−922628.			−0.150352
$520$	−749948.	−	1.29584e6i	−0.121625	−	0.210157i
$521$	−1.12025e7			−1.80809			−0.904046	−	0.427436i	$-0.859417\pi$
$521$	−1.12025e7			−1.80809			−0.904046	+	0.427436i	$0.859417\pi$
$522$		−	3.91663e6i		−	0.629123i
$523$		−	2.47603e6i		−	0.395824i	−0.980220	−	0.197912i	$-0.936584\pi$
$523$		−	2.47603e6i		−	0.395824i	0.980220	−	0.197912i	$-0.0634161\pi$
$524$	−2.02497e6			−0.322174
$525$	1.70389e6	−	2.96541e6i	0.269801	−	0.469555i
$526$	−5.82479e6			−0.917944
$527$			9.98723e6i			1.56646i
$528$		−	117251.i		−	0.0183034i
$529$	−279841.			−0.0434783
$530$	−4.48894e6	−	7.75648e6i	−0.694151	−	1.19943i
$531$	5.28812e6			0.813888
$532$			1.19888e6i			0.183653i
$533$			4.77862e6i			0.728593i
$534$	−481037.			−0.0730004
$535$	−718419.	+	415774.i	−0.108516	+	0.0628019i
$536$	4.53474e6			0.681774
$537$			2.47860e6i			0.370911i
$538$			858368.i			0.127855i
$539$	−1.29737e6			−0.192349
$540$	−2.07905e6	+	1.20322e6i	−0.306818	+	0.177566i
$541$	6.48501e6			0.952615			0.476307	−	0.879279i	$-0.341975\pi$
$541$	6.48501e6			0.952615			0.476307	+	0.879279i	$0.341975\pi$
$542$			6.91340e6i			1.01087i
$543$			2.75127e6i			0.400436i
$544$	1.80298e6			0.261213
$545$	5.55559e6	+	9.59955e6i	0.801196	+	1.38439i
$546$	−1.83199e6			−0.262991
$547$			3.28884e6i			0.469974i	0.971998	+	0.234987i	$0.0755048\pi$
$547$			3.28884e6i			0.469974i	−0.971998	+	0.234987i	$0.924495\pi$
$548$		−	3.07820e6i		−	0.437870i
$549$	−5.81114e6			−0.822869
$550$	832597.	+	478399.i	0.117362	+	0.0674348i
$551$	1.92665e6			0.270349
$552$		−	201853.i		−	0.0281961i
$553$			38356.3i			0.00533365i
$554$	9.00115e6			1.24602
$555$	715780.	+	1.23680e6i	0.0986387	+	0.170439i
$556$	3.95750e6			0.542918
$557$		−	6.27610e6i		−	0.857140i	−0.903508	−	0.428570i	$-0.859017\pi$
$557$		−	6.27610e6i		−	0.857140i	0.903508	−	0.428570i	$-0.140983\pi$
$558$		−	4.70689e6i		−	0.639954i
$559$	8.72213e6			1.18057
$560$	2.27363e6	−	1.31583e6i	0.306373	−	0.177308i
$561$	806430.			0.108183
$562$			4.72324e6i			0.630811i
$563$			7.38894e6i			0.982451i	0.871032	+	0.491226i	$0.163451\pi$
$563$			7.38894e6i			0.982451i	−0.871032	+	0.491226i	$0.836549\pi$
$564$	−1.79911e6			−0.238155
$565$	−269517.	+	155979.i	−0.0355193	+	0.0205563i
$566$	4.77584e6			0.626627
$567$		−	6.31437e6i		−	0.824846i
$568$			1.47518e6i			0.191856i
$569$	4.51003e6			0.583982			0.291991	−	0.956421i	$-0.405682\pi$
$569$	4.51003e6			0.583982			0.291991	+	0.956421i	$0.405682\pi$
$570$	−272587.	−	471006.i	−0.0351414	−	0.0607211i
$571$	1.44618e7			1.85623			0.928114	−	0.372297i	$-0.121430\pi$
$571$	1.44618e7			1.85623			0.928114	+	0.372297i	$0.121430\pi$
$572$		−	514365.i		−	0.0657327i
$573$			3.98387e6i			0.506896i
$574$	−8.38439e6			−1.06216
$575$	1.43336e6	+	823590.i	0.180795	+	0.103882i
$576$	−849728.			−0.106715
$577$		−	1.24500e7i		−	1.55679i	−0.627772	−	0.778397i	$-0.716033\pi$
$577$		−	1.24500e7i		−	1.55679i	0.627772	−	0.778397i	$-0.283967\pi$
$578$			6.72117e6i			0.836807i
$579$	−1.12765e6			−0.139790
$580$	−2.11459e6	−	3.65382e6i	−0.261010	−	0.451001i
$581$	1.03158e7			1.26784
$582$		−	189805.i		−	0.0232274i
$583$		−	3.07882e6i		−	0.375157i
$584$	−1.70601e6			−0.206990
$585$	−4.20041e6	+	2.43092e6i	−0.507460	+	0.293685i
$586$	−280594.			−0.0337547
$587$			406131.i			0.0486487i	0.999704	+	0.0243244i	$0.00774345\pi$
$587$			406131.i			0.0486487i	−0.999704	+	0.0243244i	$0.992257\pi$
$588$		−	1.61105e6i		−	0.192161i
$589$	2.31539e6			0.275003
$590$	4.93329e6	−	2.85506e6i	0.583453	−	0.337665i
$591$	3.60593e6			0.424667
$592$			1.09760e6i			0.128718i
$593$		−	9.90800e6i		−	1.15704i	−0.815667	−	0.578521i	$-0.803630\pi$
$593$		−	9.90800e6i		−	1.15704i	0.815667	−	0.578521i	$-0.196370\pi$
$594$	−825249.			−0.0959664
$595$	9.05005e6	+	1.56377e7i	1.04799	+	1.81084i
$596$	−7.65419e6			−0.882640
$597$		−	584932.i		−	0.0671691i
$598$		−	885507.i		−	0.101260i
$599$	1.53764e7			1.75101			0.875503	−	0.483212i	$-0.160530\pi$
$599$	1.53764e7			1.75101			0.875503	+	0.483212i	$0.160530\pi$
$600$	−594068.	+	1.03390e6i	−0.0673686	+	0.117247i
$601$	3.56987e6			0.403149			0.201575	−	0.979473i	$-0.435394\pi$
$601$	3.56987e6			0.403149			0.201575	+	0.979473i	$0.435394\pi$
$602$			1.53035e7i			1.72108i
$603$		−	1.46992e7i		−	1.64626i
$604$	798257.			0.0890329
$605$	−4.34435e6	−	7.50665e6i	−0.482544	−	0.833792i
$606$	−1.11872e6			−0.123749
$607$			1.14019e6i			0.125604i	0.998026	+	0.0628022i	$0.0200037\pi$
$607$			1.14019e6i			0.125604i	−0.998026	+	0.0628022i	$0.979996\pi$
$608$		−	417995.i		−	0.0458577i
$609$	−5.16556e6			−0.564383
$610$	−5.42122e6	+	3.13744e6i	−0.589891	+	0.341390i
$611$	−7.89248e6			−0.855285
$612$		−	5.84429e6i		−	0.630744i
$613$			1.32902e6i			0.142850i	0.997446	+	0.0714249i	$0.0227546\pi$
$613$			1.32902e6i			0.142850i	−0.997446	+	0.0714249i	$0.977245\pi$
$614$	−3.18162e6			−0.340587
$615$	3.29399e6	−	1.90634e6i	0.351184	−	0.203242i
$616$	902486.			0.0958271
$617$		−	1.66400e7i		−	1.75971i	−0.475242	−	0.879855i	$-0.657640\pi$
$617$		−	1.66400e7i		−	1.75971i	0.475242	−	0.879855i	$-0.342360\pi$
$618$			1.37710e6i			0.145043i
$619$	−1.20541e7			−1.26447			−0.632236	−	0.774776i	$-0.717863\pi$
$619$	−1.20541e7			−1.26447			−0.632236	+	0.774776i	$0.717863\pi$
$620$	−2.54126e6	−	4.39106e6i	−0.265503	−	0.458765i
$621$	−1.42071e6			−0.147835
$622$			787120.i			0.0815765i
$623$		−	3.70257e6i		−	0.382193i
$624$	638729.			0.0656682
$625$	−4.91786e6	−	8.43694e6i	−0.503589	−	0.863943i
$626$	4.90885e6			0.500661
$627$		−	186959.i		−	0.0189923i
$628$		−	6.93097e6i		−	0.701286i
$629$	−7.54912e6			−0.760799
$630$	−4.26520e6	−	7.36988e6i	−0.428142	−	0.739791i
$631$	−1.65699e7			−1.65671			−0.828354	−	0.560205i	$-0.810722\pi$
$631$	−1.65699e7			−1.65671			−0.828354	+	0.560205i	$0.810722\pi$
$632$		−	13373.1i		−	0.00133180i
$633$			2.01502e6i			0.199880i
$634$	−5.75791e6			−0.568908
$635$	1.73037e7	−	1.00142e7i	1.70296	−	0.985561i
$636$	3.82322e6			0.374789
$637$		−	7.06748e6i		−	0.690106i
$638$		−	1.45033e6i		−	0.141064i
$639$	4.78173e6			0.463269
$640$	−792711.	+	458769.i	−0.0765007	+	0.0442736i
$641$	2.23365e6			0.214719			0.107359	−	0.994220i	$-0.465760\pi$
$641$	2.23365e6			0.214719			0.107359	+	0.994220i	$0.465760\pi$
$642$		−	354114.i		−	0.0339083i
$643$			1.13710e7i			1.08460i	0.840184	+	0.542302i	$0.182447\pi$
$643$			1.13710e7i			1.08460i	−0.840184	+	0.542302i	$0.817553\pi$
$644$	1.55368e6			0.147620
$645$	−3.47953e6	−	6.01231e6i	−0.329323	−	0.569039i
$646$	2.87490e6			0.271045
$647$			8.86232e6i			0.832313i	0.909293	+	0.416157i	$0.136623\pi$
$647$			8.86232e6i			0.832313i	−0.909293	+	0.416157i	$0.863377\pi$
$648$			2.20153e6i			0.205962i
$649$	1.95820e6			0.182492
$650$	−2.60611e6	+	4.53561e6i	−0.241941	+	0.421068i
$651$	−6.20782e6			−0.574099
$652$		−	9.84283e6i		−	0.906778i
$653$		−	2.35278e6i		−	0.215923i	−0.994155	−	0.107961i	$-0.965568\pi$
$653$		−	2.35278e6i		−	0.215923i	0.994155	−	0.107961i	$-0.0344323\pi$
$654$	−4.73169e6			−0.432585
$655$	3.54383e6	+	6.12342e6i	0.322753	+	0.557687i
$656$	2.92325e6			0.265220
$657$			5.52996e6i			0.499814i
$658$		−	1.38478e7i		−	1.24686i
$659$	−2.11810e6			−0.189991			−0.0949956	−	0.995478i	$-0.530284\pi$
$659$	−2.11810e6			−0.189991			−0.0949956	+	0.995478i	$0.530284\pi$
$660$	−354561.	+	205196.i	−0.0316833	+	0.0183362i
$661$	−8.98664e6			−0.800007			−0.400003	−	0.916514i	$-0.630991\pi$
$661$	−8.98664e6			−0.800007			−0.400003	+	0.916514i	$0.630991\pi$
$662$		−	1.63363e6i		−	0.144880i
$663$			4.39307e6i			0.388136i
$664$	−3.59665e6			−0.316576
$665$	3.62536e6	−	2.09812e6i	0.317905	−	0.183983i
$666$	3.55783e6			0.310813
$667$		−	2.49682e6i		−	0.217307i
$668$		−	4.96799e6i		−	0.430764i
$669$	4.67277e6			0.403654
$670$	−7.93609e6	−	1.37128e7i	−0.682999	−	1.18016i
$671$	−2.15187e6			−0.184506
$672$			1.12069e6i			0.0957331i
$673$			7.91236e6i			0.673393i	0.941613	+	0.336696i	$0.109310\pi$
$673$			7.91236e6i			0.673393i	−0.941613	+	0.336696i	$0.890690\pi$
$674$	−4.93318e6			−0.418290
$675$	7.27695e6	+	4.18124e6i	0.614738	+	0.353221i
$676$	−3.13866e6			−0.264166
$677$		−	1.81282e7i		−	1.52014i	−0.649841	−	0.760070i	$-0.725165\pi$
$677$		−	1.81282e7i		−	1.52014i	0.649841	−	0.760070i	$-0.274835\pi$
$678$		−	132847.i		−	0.0110988i
$679$	1.46094e6			0.121607
$680$	−3.15534e6	−	5.45213e6i	−0.261682	−	0.452162i
$681$	7.74340e6			0.639829
$682$		−	1.74297e6i		−	0.143492i
$683$		−	2.00773e7i		−	1.64685i	−0.567427	−	0.823424i	$-0.692061\pi$
$683$		−	2.00773e7i		−	1.64685i	0.567427	−	0.823424i	$-0.307939\pi$
$684$	−1.35491e6			−0.110731
$685$	−9.30834e6	+	5.38705e6i	−0.757959	+	0.438657i
$686$	59749.0			0.00484753
$687$		−	8.19652e6i		−	0.662579i
$688$		−	5.33563e6i		−	0.429749i
$689$	1.67720e7			1.34598
$690$	−610395.	+	353257.i	−0.0488077	+	0.0282467i
$691$	1.38873e7			1.10643			0.553215	−	0.833039i	$-0.313401\pi$
$691$	1.38873e7			1.10643			0.553215	+	0.833039i	$0.313401\pi$
$692$			2.47597e6i			0.196554i
$693$		−	2.92537e6i		−	0.231391i
$694$	2.42974e6			0.191496
$695$	−6.92589e6	−	1.19673e7i	−0.543893	−	0.939797i
$696$	1.80099e6			0.140925
$697$			2.01056e7i			1.56760i
$698$			4.28725e6i			0.333073i
$699$	−7.57269e6			−0.586215
$700$	−7.95802e6	−	4.57257e6i	−0.613846	−	0.352708i
$701$	6.98907e6			0.537186			0.268593	−	0.963254i	$-0.413441\pi$
$701$	6.98907e6			0.537186			0.268593	+	0.963254i	$0.413441\pi$
$702$		−	4.49559e6i		−	0.344305i
$703$			1.75015e6i			0.133563i
$704$	−314655.			−0.0239278
$705$	3.14856e6	+	5.44042e6i	0.238583	+	0.412249i
$706$	8.06988e6			0.609334
$707$		−	8.61088e6i		−	0.647886i
$708$			2.43165e6i			0.182313i
$709$	−1.58573e7			−1.18472			−0.592358	−	0.805675i	$-0.701803\pi$
$709$	−1.58573e7			−1.18472			−0.592358	+	0.805675i	$0.701803\pi$
$710$	4.46088e6	−	2.58166e6i	0.332104	−	0.192200i
$711$	−43348.3			−0.00321587
$712$			1.29092e6i			0.0954329i
$713$		−	3.00061e6i		−	0.221048i
$714$	−7.70791e6			−0.565837
$715$	−1.55542e6	+	900173.i	−0.113784	+	0.0658508i
$716$	6.65159e6			0.484890
$717$			1.45598e6i			0.105769i
$718$			1.33483e6i			0.0966303i
$719$	−1.45446e7			−1.04925			−0.524624	−	0.851334i	$-0.675794\pi$
$719$	−1.45446e7			−1.04925			−0.524624	+	0.851334i	$0.675794\pi$
$720$	1.48708e6	+	2.56954e6i	0.106906	+	0.184724i
$721$	−1.05997e7			−0.759370
$722$			9.23789e6i			0.659523i
$723$		−	3.98024e6i		−	0.283181i
$724$	7.38334e6			0.523488
$725$	−7.34831e6	+	1.27889e7i	−0.519209	+	0.903622i
$726$	3.70008e6			0.260537
$727$			5.87641e6i			0.412360i	0.978514	+	0.206180i	$0.0661032\pi$
$727$			5.87641e6i			0.412360i	−0.978514	+	0.206180i	$0.933897\pi$
$728$			4.91634e6i			0.343806i
$729$	3.24521e6			0.226164
$730$	2.98563e6	+	5.15890e6i	0.207362	+	0.358303i
$731$	3.66976e7			2.54006
$732$		−	2.67216e6i		−	0.184325i
$733$		−	819760.i		−	0.0563543i	−0.999603	−	0.0281771i	$-0.991030\pi$
$733$		−	819760.i		−	0.0563543i	0.999603	−	0.0281771i	$-0.00897025\pi$
$734$	−7.05161e6			−0.483112
$735$	−4.87173e6	+	2.81944e6i	−0.332633	+	0.192506i
$736$	−541696.			−0.0368605
$737$		−	5.44311e6i		−	0.369130i
$738$		−	9.47559e6i		−	0.640421i
$739$	2.78025e7			1.87272			0.936360	−	0.351042i	$-0.114173\pi$
$739$	2.78025e7			1.87272			0.936360	+	0.351042i	$0.114173\pi$
$740$	3.31910e6	−	1.92088e6i	0.222813	−	0.128950i
$741$	1.01847e6			0.0681400
$742$			2.94276e7i			1.96221i
$743$			1.42989e7i			0.950231i	0.879923	+	0.475115i	$0.157594\pi$
$743$			1.42989e7i			0.950231i	−0.879923	+	0.475115i	$0.842406\pi$
$744$	2.16438e6			0.143351
$745$	1.33953e7	+	2.31459e7i	0.884226	+	1.52786i
$746$	−1.12182e7			−0.738037
$747$			1.16584e7i			0.764428i
$748$		−	2.16415e6i		−	0.141427i
$749$	2.72564e6			0.177527
$750$	4.16613e6	−	12965.9i	0.270446	−	0.000841682i
$751$	9.27882e6			0.600334			0.300167	−	0.953887i	$-0.402958\pi$
$751$	9.27882e6			0.600334			0.300167	+	0.953887i	$0.402958\pi$
$752$			4.82811e6i			0.311338i
$753$		−	282175.i		−	0.0181356i
$754$	7.90075e6			0.506104
$755$	−1.39700e6	−	2.41389e6i	−0.0891928	−	0.154117i
$756$	7.88779e6			0.501939
$757$		−	1.41929e6i		−	0.0900185i	−0.998987	−	0.0450093i	$-0.985668\pi$
$757$		−	1.41929e6i		−	0.0900185i	0.998987	−	0.0450093i	$-0.0143317\pi$
$758$		−	4.66068e6i		−	0.294630i
$759$	−242288.			−0.0152661
$760$	−1.26400e6	+	731519.i	−0.0793802	+	0.0459401i
$761$	−1.84731e7			−1.15632			−0.578159	−	0.815924i	$-0.696229\pi$
$761$	−1.84731e7			−1.15632			−0.578159	+	0.815924i	$0.696229\pi$
$762$			8.52911e6i			0.532128i
$763$		−	3.64201e7i		−	2.26480i
$764$	1.06912e7			0.662661
$765$	−1.76729e7	+	1.02279e7i	−1.09183	+	0.631877i
$766$	−7.75287e6			−0.477409
$767$			1.06674e7i			0.654740i
$768$		−	390733.i		−	0.0239044i
$769$	1.90298e7			1.16043			0.580214	−	0.814464i	$-0.302969\pi$
$769$	1.90298e7			1.16043			0.580214	+	0.814464i	$0.302969\pi$
$770$	−1.57941e6	−	2.72908e6i	−0.0959993	−	0.165878i
$771$	−1.13116e7			−0.685309
$772$			3.02617e6i			0.182747i
$773$		−	6.35197e6i		−	0.382349i	−0.981556	−	0.191174i	$-0.938770\pi$
$773$		−	6.35197e6i		−	0.382349i	0.981556	−	0.191174i	$-0.0612296\pi$
$774$	−1.72952e7			−1.03770
$775$	−8.83099e6	+	1.53693e7i	−0.528147	+	0.919177i
$776$	−509362.			−0.0303649
$777$		−	4.69235e6i		−	0.278829i
$778$		−	3.29102e6i		−	0.194931i
$779$	4.66120e6			0.275203
$780$	−1.11782e6	−	1.93149e6i	−0.0657862	−	0.113673i
$781$	1.77068e6			0.103875
$782$		−	3.72569e6i		−	0.217866i
$783$		−	1.26760e7i		−	0.738886i
$784$	−4.32342e6			−0.251210
$785$	−2.09589e7	+	1.21297e7i	−1.21393	+	0.702546i
$786$	−3.01828e6			−0.174262
$787$		−	794493.i		−	0.0457250i	−0.999739	−	0.0228625i	$-0.992722\pi$
$787$		−	794493.i		−	0.0457250i	0.999739	−	0.0228625i	$-0.00727799\pi$
$788$		−	9.67690e6i		−	0.555163i
$789$	−8.68202e6			−0.496510
$790$	−40439.6	+	23403.8i	−0.00230536	+	0.00133419i
$791$	1.02253e6			0.0581078
$792$			1.01994e6i			0.0577780i
$793$		−	1.17224e7i		−	0.661965i
$794$	2.21714e7			1.24808
$795$	−6.69089e6	−	1.15613e7i	−0.375462	−	0.648765i
$796$	−1.56973e6			−0.0878097
$797$			2.82846e7i			1.57727i	0.614864	+	0.788633i	$0.289211\pi$
$797$			2.82846e7i			1.57727i	−0.614864	+	0.788633i	$0.710789\pi$
$798$			1.78697e6i			0.0993366i
$799$	−3.32069e7			−1.84019
$800$	2.77459e6	+	1.59425e6i	0.153276	+	0.0880705i
$801$	4.18445e6			0.230440
$802$			1.20336e7i			0.660634i
$803$			2.04775e6i			0.112070i
$804$	6.75916e6			0.368767
$805$	−2.71904e6	−	4.69825e6i	−0.147885	−	0.255533i
$806$	9.49490e6			0.514817
$807$			1.27942e6i			0.0691561i
$808$			3.00222e6i			0.161776i
$809$	−2.02342e7			−1.08696			−0.543482	−	0.839421i	$-0.682895\pi$
$809$	−2.02342e7			−1.08696			−0.543482	+	0.839421i	$0.682895\pi$
$810$	6.65733e6	−	3.85283e6i	0.356523	−	0.206332i
$811$	−1.93625e7			−1.03373			−0.516867	−	0.856065i	$-0.672902\pi$
$811$	−1.93625e7			−1.03373			−0.516867	+	0.856065i	$0.672902\pi$
$812$			1.38624e7i			0.737814i
$813$			1.03046e7i			0.546772i
$814$	1.31747e6			0.0696914
$815$	−2.97643e7	+	1.72256e7i	−1.56964	+	0.908406i
$816$	2.68740e6			0.141288
$817$		−	8.50780e6i		−	0.445925i
$818$			6.31704e6i			0.330088i
$819$	1.59361e7			0.830179
$820$	−5.11589e6	−	8.83978e6i	−0.265697	−	0.459100i
$821$	2.57814e7			1.33490			0.667451	−	0.744654i	$-0.267385\pi$
$821$	2.57814e7			1.33490			0.667451	+	0.744654i	$0.267385\pi$
$822$		−	4.58815e6i		−	0.236841i
$823$			2.44993e6i			0.126082i	0.998011	+	0.0630411i	$0.0200799\pi$
$823$			2.44993e6i			0.126082i	−0.998011	+	0.0630411i	$0.979920\pi$
$824$	3.69561e6			0.189613
$825$	1.24101e6	+	713068.i	0.0634805	+	0.0364751i
$826$	−1.87166e7			−0.954500
$827$		−	3.03078e7i		−	1.54096i	−0.637467	−	0.770478i	$-0.720018\pi$
$827$		−	3.03078e7i		−	1.54096i	0.637467	−	0.770478i	$-0.279982\pi$
$828$			1.75588e6i			0.0890061i
$829$	−1.92121e7			−0.970931			−0.485466	−	0.874256i	$-0.661350\pi$
$829$	−1.92121e7			−0.970931			−0.485466	+	0.874256i	$0.661350\pi$
$830$	6.29437e6	+	1.08761e7i	0.317145	+	0.547997i
$831$	1.34165e7			0.673963
$832$		−	1.71410e6i		−	0.0858476i
$833$		−	2.97358e7i		−	1.48480i
$834$	5.89877e6			0.293661
$835$	−1.50230e7	+	8.69431e6i	−0.745658	+	0.431538i
$836$	−501726.			−0.0248285
$837$		−	1.52336e7i		−	0.751606i
$838$			6.48795e6i			0.319152i
$839$	8.70429e6			0.426902			0.213451	−	0.976954i	$-0.431530\pi$
$839$	8.70429e6			0.426902			0.213451	+	0.976954i	$0.431530\pi$
$840$	3.38891e6	−	1.96128e6i	0.165715	−	0.0959051i
$841$	1.76623e6			0.0861105
$842$		−	2.81421e6i		−	0.136797i
$843$			7.04012e6i			0.341202i
$844$	5.40752e6			0.261302
$845$	5.49286e6	+	9.49116e6i	0.264641	+	0.457275i
$846$	1.56501e7			0.751781
$847$			2.84797e7i			1.36404i
$848$		−	1.02600e7i		−	0.489959i
$849$	7.11853e6			0.338939
$850$	−1.09650e7	+	1.90832e7i	−0.520547	+	0.905949i
$851$	2.26809e6			0.107359
$852$			2.19880e6i			0.103774i
$853$			2.55914e7i			1.20426i	0.798397	+	0.602131i	$0.205681\pi$
$853$			2.55914e7i			1.20426i	−0.798397	+	0.602131i	$0.794319\pi$
$854$	2.05677e7			0.965032
$855$	2.37119e6	+	4.09719e6i	0.110930	+	0.191677i
$856$	−950304.			−0.0443280
$857$		−	1.06602e7i		−	0.495810i	−0.968784	−	0.247905i	$-0.920258\pi$
$857$		−	1.06602e7i		−	0.495810i	0.968784	−	0.247905i	$-0.0797421\pi$
$858$		−	766676.i		−	0.0355544i
$859$	−1.66510e7			−0.769940			−0.384970	−	0.922929i	$-0.625788\pi$
$859$	−1.66510e7			−0.769940			−0.384970	+	0.922929i	$0.625788\pi$
$860$	−1.61347e7	+	9.33771e6i	−0.743901	+	0.430521i
$861$	−1.24972e7			−0.574518
$862$		−	5.87178e6i		−	0.269154i
$863$			1.90497e6i			0.0870684i	0.999052	+	0.0435342i	$0.0138617\pi$
$863$			1.90497e6i			0.0870684i	−0.999052	+	0.0435342i	$0.986138\pi$
$864$	−2.75011e6			−0.125333
$865$	7.48723e6	−	4.33312e6i	0.340237	−	0.196907i
$866$	6.87997e6			0.311740
$867$			1.00181e7i			0.452624i
$868$			1.66594e7i			0.750516i
$869$	−16051.9			−0.000721070
$870$	−3.15186e6	−	5.44612e6i	−0.141179	−	0.243944i
$871$	2.96516e7			1.32435
$872$			1.26980e7i			0.565516i
$873$			1.65108e6i			0.0733215i
$874$	−863747.			−0.0382479
$875$	99799.0	+	3.20670e7i	0.00440663	+	1.41592i
$876$	−2.54286e6			−0.111960
$877$			3.40365e7i			1.49433i	0.664640	+	0.747164i	$0.268585\pi$
$877$			3.40365e7i			1.49433i	−0.664640	+	0.747164i	$0.731415\pi$
$878$			1.62341e7i			0.710709i
$879$	−418233.			−0.0182577
$880$	550668.	+	951503.i	0.0239708	+	0.0414194i
$881$	5.53090e6			0.240080			0.120040	−	0.992769i	$-0.461698\pi$
$881$	5.53090e6			0.240080			0.120040	+	0.992769i	$0.461698\pi$
$882$			1.40142e7i			0.606592i
$883$			2.08504e7i			0.899936i	0.893045	+	0.449968i	$0.148565\pi$
$883$			2.08504e7i			0.899936i	−0.893045	+	0.449968i	$0.851435\pi$
$884$	1.17893e7			0.507408
$885$	7.35320e6	−	4.25555e6i	0.315586	−	0.182641i
$886$	2.19900e7			0.941111
$887$			2.04383e7i			0.872242i	0.899888	+	0.436121i	$0.143648\pi$
$887$			2.04383e7i			0.872242i	−0.899888	+	0.436121i	$0.856352\pi$
$888$			1.63601e6i			0.0696230i
$889$	−6.56491e7			−2.78596
$890$	3.90367e6	−	2.25919e6i	0.165196	−	0.0956043i
$891$	2.64253e6			0.111513
$892$		−	1.25399e7i		−	0.527693i
$893$			7.69854e6i			0.323057i
$894$	−1.14088e7			−0.477415
$895$	−1.16407e7	−	2.01141e7i	−0.485761	−	0.839350i
$896$	3.00750e6			0.125151
$897$		−	1.31987e6i		−	0.0547711i
$898$		−	1.30745e7i		−	0.541046i
$899$	2.67723e7			1.10481
$900$	5.16768e6	−	8.99373e6i	0.212662	−	0.370112i
$901$	7.05668e7			2.89593
$902$		−	3.50882e6i		−	0.143597i
$903$			2.28103e7i			0.930920i
$904$	−356509.			−0.0145094
$905$	−1.29213e7	−	2.23269e7i	−0.524428	−	0.906163i
$906$	1.18982e6			0.0481573
$907$		−	3.67382e7i		−	1.48286i	−0.671032	−	0.741429i	$-0.734148\pi$
$907$		−	3.67382e7i		−	1.48286i	0.671032	−	0.741429i	$-0.265852\pi$
$908$		−	2.07803e7i		−	0.836444i
$909$	9.73156e6			0.390636
$910$	1.48668e7	−	8.60391e6i	0.595132	−	0.344423i
$911$	1.39984e7			0.558834			0.279417	−	0.960170i	$-0.409859\pi$
$911$	1.39984e7			0.558834			0.279417	+	0.960170i	$0.409859\pi$
$912$		−	623033.i		−	0.0248041i
$913$			4.31711e6i			0.171402i
$914$	−1.19675e7			−0.473847
$915$	−8.08048e6	+	4.67645e6i	−0.319069	+	0.184656i
$916$	−2.19963e7			−0.866185
$917$		−	2.32318e7i		−	0.912348i
$918$		−	1.89148e7i		−	0.740789i
$919$	−2.07622e7			−0.810932			−0.405466	−	0.914110i	$-0.632891\pi$
$919$	−2.07622e7			−0.810932			−0.405466	+	0.914110i	$0.632891\pi$
$920$	948004.	+	1.63806e6i	0.0369267	+	0.0638060i
$921$	−4.74230e6			−0.184221
$922$			2.76618e7i			1.07165i
$923$			9.64588e6i			0.372681i
$924$	1.34518e6			0.0518323
$925$	−1.16173e7	−	6.67514e6i	−0.446427	−	0.256511i
$926$	4.50652e6			0.172708
$927$		−	1.19792e7i		−	0.457854i
$928$		−	4.83317e6i		−	0.184231i
$929$	−4.38109e7			−1.66549			−0.832746	−	0.553655i	$-0.813233\pi$
$929$	−4.38109e7			−1.66549			−0.832746	+	0.553655i	$0.813233\pi$
$930$	−3.78781e6	−	6.54500e6i	−0.143609	−	0.248143i
$931$	−6.89380e6			−0.260666
$932$			2.03222e7i			0.766355i
$933$			1.17323e6i			0.0441242i
$934$	−8.02552e6			−0.301027
$935$	−6.54428e6	+	3.78740e6i	−0.244812	+	0.141681i
$936$	−5.55618e6			−0.207294
$937$			1.24125e7i			0.461860i	0.972970	+	0.230930i	$0.0741769\pi$
$937$			1.24125e7i			0.461860i	−0.972970	+	0.230930i	$0.925823\pi$
$938$			5.20256e7i			1.93068i
$939$	7.31678e6			0.270805
$940$	1.46000e7	−	8.44951e6i	0.538930	−	0.311898i
$941$	−6.35492e6			−0.233957			−0.116979	−	0.993134i	$-0.537321\pi$
$941$	−6.35492e6			−0.233957			−0.116979	+	0.993134i	$0.537321\pi$
$942$		−	1.03308e7i		−	0.379321i
$943$		−	6.04063e6i		−	0.221209i
$944$	6.52561e6			0.238337
$945$	−1.38041e7	−	2.38523e7i	−0.502840	−	0.868862i
$946$	−6.40444e6			−0.232677
$947$		−	1.41379e7i		−	0.512281i	−0.966640	−	0.256141i	$-0.917549\pi$
$947$		−	1.41379e7i		−	0.512281i	0.966640	−	0.256141i	$-0.0824510\pi$
$948$		−	19933.0i		−	0.000720363i
$949$	−1.11552e7			−0.402080
$950$	4.42416e6	+	2.54206e6i	0.159046	+	0.0913856i
$951$	−8.58234e6			−0.307719
$952$			2.06850e7i			0.739714i
$953$			1.17964e7i			0.420744i	0.977621	+	0.210372i	$0.0674675\pi$
$953$			1.17964e7i			0.420744i	−0.977621	+	0.210372i	$0.932533\pi$
$954$	−3.32575e7			−1.18309
$955$	−1.87102e7	−	3.23296e7i	−0.663851	−	1.14707i
$956$	3.90728e6			0.138271
$957$		−	2.16176e6i		−	0.0763005i
$958$			5.31029e6i			0.186941i
$959$	3.53152e7			1.23998
$960$	−1.18156e6	+	683809.i	−0.0413788	+	0.0239473i
$961$	3.54505e6			0.123827
$962$			7.17697e6i			0.250037i
$963$			3.08037e6i			0.107038i
$964$	−1.06814e7			−0.370200
$965$	9.15100e6	−	5.29600e6i	0.316337	−	0.183075i
$966$	2.31580e6			0.0798469
$967$		−	2.07035e6i		−	0.0711996i	−0.999366	−	0.0355998i	$-0.988666\pi$
$967$		−	2.07035e6i		−	0.0711996i	0.999366	−	0.0355998i	$-0.0113342\pi$
$968$		−	9.92958e6i		−	0.340598i
$969$	4.28512e6			0.146607
$970$	891418.	+	1.54029e6i	0.0304195	+	0.0525621i
$971$	−3.25102e7			−1.10655			−0.553275	−	0.832999i	$-0.686622\pi$
$971$	−3.25102e7			−1.10655			−0.553275	+	0.832999i	$0.686622\pi$
$972$			1.37233e7i			0.465899i
$973$			4.54032e7i			1.53746i
$974$	−9.09043e6			−0.307035
$975$	−3.88448e6	+	6.76046e6i	−0.130864	+	0.227753i
$976$	−7.17103e6			−0.240967
$977$		−	5.20934e7i		−	1.74601i	−0.487712	−	0.873005i	$-0.662168\pi$
$977$		−	5.20934e7i		−	1.74601i	0.487712	−	0.873005i	$-0.337832\pi$
$978$		−	1.46710e7i		−	0.490471i
$979$	1.54951e6			0.0516698
$980$	7.56628e6	+	1.30738e7i	0.251662	+	0.434848i
$981$	4.11600e7			1.36554
$982$			8.29324e6i			0.274439i
$983$		−	1.74266e7i		−	0.575213i	−0.957749	−	0.287606i	$-0.907141\pi$
$983$		−	1.74266e7i		−	0.575213i	0.957749	−	0.287606i	$-0.0928595\pi$
$984$	4.35719e6			0.143456
$985$	−2.92625e7	+	1.69352e7i	−0.960995	+	0.556161i
$986$	3.32417e7			1.08891
$987$		−	2.06406e7i		−	0.674419i
$988$		−	2.73318e6i		−	0.0890790i
$989$	−1.10256e7			−0.358436
$990$	3.08426e6	−	1.78496e6i	0.100014	−	0.0578818i
$991$	−3.21609e7			−1.04026			−0.520132	−	0.854086i	$-0.674117\pi$
$991$	−3.21609e7			−1.04026			−0.520132	+	0.854086i	$0.674117\pi$
$992$		−	5.80836e6i		−	0.187402i
$993$		−	2.43497e6i		−	0.0783646i
$994$	−1.69243e7			−0.543306
$995$	2.74713e6	+	4.74679e6i	0.0879674	+	0.152000i
$996$	−5.36091e6			−0.171234
$997$		−	5.19500e7i		−	1.65519i	−0.561326	−	0.827595i	$-0.689708\pi$
$997$		−	5.19500e7i		−	1.65519i	0.561326	−	0.827595i	$-0.310292\pi$
$998$		−	7.80774e6i		−	0.248141i
$999$	1.15148e7			0.365041

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.b.a.139.6	✓	26
5.4	even	2	inner	230.6.b.a.139.21	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.b.a.139.6	✓	26	1.1	even	1	trivial
230.6.b.a.139.21	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -5.96211i q^{3} -16.0000 q^{4} +(28.0011 + 48.3833i) q^{5} -23.8485 q^{6} -183.563i q^{7} +64.0000i q^{8} +207.453 q^{9} +O(q^{10})\)	\(q-4.00000i q^{2} -5.96211i q^{3} -16.0000 q^{4} +(28.0011 + 48.3833i) q^{5} -23.8485 q^{6} -183.563i q^{7} +64.0000i q^{8} +207.453 q^{9} +(193.533 - 112.004i) q^{10} +76.8201 q^{11} +95.3938i q^{12} +418.482i q^{13} -734.252 q^{14} +(288.467 - 166.946i) q^{15} +256.000 q^{16} +1760.72i q^{17} -829.813i q^{18} +408.198 q^{19} +(-448.017 - 774.132i) q^{20} -1094.42 q^{21} -307.281i q^{22} -529.000i q^{23} +381.575 q^{24} +(-1556.88 + 2709.57i) q^{25} +1673.93 q^{26} -2685.65i q^{27} +2937.01i q^{28} +4719.89 q^{29} +(-667.782 - 1153.87i) q^{30} +5672.23 q^{31} -1024.00i q^{32} -458.011i q^{33} +7042.90 q^{34} +(8881.38 - 5139.96i) q^{35} -3319.25 q^{36} +4287.51i q^{37} -1632.79i q^{38} +2495.04 q^{39} +(-3096.53 + 1792.07i) q^{40} +11419.0 q^{41} +4377.69i q^{42} -20842.3i q^{43} -1229.12 q^{44} +(5808.91 + 10037.3i) q^{45} -2116.00 q^{46} +18859.8i q^{47} -1526.30i q^{48} -16888.4 q^{49} +(10838.3 + 6227.53i) q^{50} +10497.6 q^{51} -6695.71i q^{52} -40078.3i q^{53} -10742.6 q^{54} +(2151.05 + 3716.81i) q^{55} +11748.0 q^{56} -2433.72i q^{57} -18879.6i q^{58} +25490.7 q^{59} +(-4615.47 + 2671.13i) q^{60} -28011.8 q^{61} -22688.9i q^{62} -38080.7i q^{63} -4096.00 q^{64} +(-20247.5 + 11717.9i) q^{65} -1832.04 q^{66} -70855.3i q^{67} -28171.6i q^{68} -3153.96 q^{69} +(-20559.8 - 35525.5i) q^{70} +23049.7 q^{71} +13277.0i q^{72} +26656.4i q^{73} +17150.0 q^{74} +(16154.7 + 9282.31i) q^{75} -6531.17 q^{76} -14101.3i q^{77} -9980.14i q^{78} -208.955 q^{79} +(7168.27 + 12386.1i) q^{80} +34398.9 q^{81} -45675.8i q^{82} +56197.7i q^{83} +17510.8 q^{84} +(-85189.6 + 49302.1i) q^{85} -83369.3 q^{86} -28140.5i q^{87} +4916.49i q^{88} +20170.6 q^{89} +(40149.1 - 23235.6i) q^{90} +76817.8 q^{91} +8464.00i q^{92} -33818.5i q^{93} +75439.2 q^{94} +(11430.0 + 19750.0i) q^{95} -6105.21 q^{96} +7958.79i q^{97} +67553.5i q^{98} +15936.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) \) 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9	\( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26} + 16084 q^{29} - 6200 q^{30} + 418 q^{31} + 3320 q^{34} - 3160 q^{35} + 22400 q^{36} + 71296 q^{39} - 1280 q^{40} - 35826 q^{41} + 21024 q^{44} - 83960 q^{45} - 55016 q^{46} + 53532 q^{49} - 20800 q^{50} - 25430 q^{51} + 98736 q^{54} - 110390 q^{55} - 12928 q^{56} + 126992 q^{59} - 20480 q^{60} - 63662 q^{61} - 106496 q^{64} - 88520 q^{65} - 18664 q^{66} - 9522 q^{69} - 116520 q^{70} - 106514 q^{71} + 183536 q^{74} - 44200 q^{75} - 106080 q^{76} + 324676 q^{79} - 7680 q^{80} - 170702 q^{81} + 160960 q^{84} + 120780 q^{85} - 42768 q^{86} + 465200 q^{89} + 61360 q^{90} - 468838 q^{91} + 107152 q^{94} + 309670 q^{95} - 18432 q^{96} + 523850 q^{99}+O(q^{100}) \) 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

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