LMFDB - Embedded newform 80.6.q.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(29,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("80.29");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.q (of order $4$, degree $2$, 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:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	80.29
Dual form			80.6.q.a.69.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65319 - 0.203680i) q^{2} +(-12.8690 + 12.8690i) q^{3} +(31.9170 + 2.30288i) q^{4} +(-50.2546 + 24.4842i) q^{5} +(75.3721 - 70.1298i) q^{6} -156.045 q^{7} +(-179.964 - 19.5195i) q^{8} -88.2233i q^{9} +O(q^{10})$	\(q+(-5.65319 - 0.203680i) q^{2} +(-12.8690 + 12.8690i) q^{3} +(31.9170 + 2.30288i) q^{4} +(-50.2546 + 24.4842i) q^{5} +(75.3721 - 70.1298i) q^{6} -156.045 q^{7} +(-179.964 - 19.5195i) q^{8} -88.2233i q^{9} +(289.086 - 128.178i) q^{10} +(-224.357 + 224.357i) q^{11} +(-440.377 + 381.105i) q^{12} +(-555.000 + 555.000i) q^{13} +(882.150 + 31.7832i) q^{14} +(331.640 - 961.815i) q^{15} +(1013.39 + 147.002i) q^{16} +587.077i q^{17} +(-17.9693 + 498.743i) q^{18} +(-1230.66 - 1230.66i) q^{19} +(-1660.36 + 665.732i) q^{20} +(2008.14 - 2008.14i) q^{21} +(1314.03 - 1222.64i) q^{22} +4640.25 q^{23} +(2567.15 - 2064.76i) q^{24} +(1926.05 - 2460.89i) q^{25} +(3250.56 - 3024.48i) q^{26} +(-1991.82 - 1991.82i) q^{27} +(-4980.48 - 359.352i) q^{28} +(1328.63 + 1328.63i) q^{29} +(-2070.73 + 5369.77i) q^{30} +948.066 q^{31} +(-5698.96 - 1037.44i) q^{32} -5774.51i q^{33} +(119.576 - 3318.85i) q^{34} +(7841.97 - 3820.63i) q^{35} +(203.168 - 2815.82i) q^{36} +(1104.09 + 1104.09i) q^{37} +(6706.47 + 7207.79i) q^{38} -14284.6i q^{39} +(9521.93 - 3425.32i) q^{40} +16636.3i q^{41} +(-11761.4 + 10943.4i) q^{42} +(-576.447 - 576.447i) q^{43} +(-7677.48 + 6644.15i) q^{44} +(2160.07 + 4433.62i) q^{45} +(-26232.2 - 945.125i) q^{46} -13916.9i q^{47} +(-14933.2 + 11149.6i) q^{48} +7542.96 q^{49} +(-11389.6 + 13519.5i) q^{50} +(-7555.10 - 7555.10i) q^{51} +(-18992.0 + 16435.8i) q^{52} +(21220.9 + 21220.9i) q^{53} +(10854.5 + 11665.9i) q^{54} +(5781.78 - 16768.2i) q^{55} +(28082.4 + 3045.91i) q^{56} +31674.7 q^{57} +(-7240.37 - 7781.60i) q^{58} +(-27261.2 + 27261.2i) q^{59} +(12799.9 - 29934.5i) q^{60} +(-21412.6 - 21412.6i) q^{61} +(-5359.59 - 193.102i) q^{62} +13766.8i q^{63} +(32006.0 + 7025.60i) q^{64} +(14302.6 - 41480.0i) q^{65} +(-1176.15 + 32644.4i) q^{66} +(-13133.9 + 13133.9i) q^{67} +(-1351.97 + 18737.7i) q^{68} +(-59715.4 + 59715.4i) q^{69} +(-45110.3 + 20001.5i) q^{70} -73610.4i q^{71} +(-1722.07 + 15877.0i) q^{72} -14209.5 q^{73} +(-6016.76 - 6466.52i) q^{74} +(6882.81 + 56455.5i) q^{75} +(-36444.8 - 42112.9i) q^{76} +(35009.8 - 35009.8i) q^{77} +(-2909.49 + 80753.5i) q^{78} -74420.1 q^{79} +(-54526.9 + 17424.6i) q^{80} +72703.9 q^{81} +(3388.47 - 94047.9i) q^{82} +(-21801.7 + 21801.7i) q^{83} +(68718.5 - 59469.4i) q^{84} +(-14374.1 - 29503.3i) q^{85} +(3141.35 + 3376.18i) q^{86} -34196.3 q^{87} +(44755.5 - 35996.9i) q^{88} +41750.6i q^{89} +(-11308.3 - 25504.1i) q^{90} +(86604.8 - 86604.8i) q^{91} +(148103. + 10685.9i) q^{92} +(-12200.7 + 12200.7i) q^{93} +(-2834.60 + 78675.1i) q^{94} +(91977.7 + 31714.5i) q^{95} +(86690.8 - 59989.2i) q^{96} -121694. i q^{97} +(-42641.7 - 1536.35i) q^{98} +(19793.5 + 19793.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−5.65319	−	0.203680i	−0.999352	−	0.0360059i
$2$	−5.65319	−	0.203680i	−0.999352	−	0.0360059i
$3$	−12.8690	+	12.8690i	−0.825548	+	0.825548i	−0.986897	−	0.161349i	$-0.948415\pi$
$3$	−12.8690	+	12.8690i	−0.825548	+	0.825548i	0.161349	+	0.986897i	$0.448415\pi$
$4$	31.9170	+	2.30288i	0.997407	+	0.0719650i
$5$	−50.2546	+	24.4842i	−0.898982	+	0.437986i
$5$	−50.2546	+	24.4842i	−0.898982	+	0.437986i
$6$	75.3721	−	70.1298i	0.854737	−	0.795288i
$7$	−156.045			−1.20366			−0.601830	−	0.798624i	$-0.705562\pi$
$7$	−156.045			−1.20366			−0.601830	+	0.798624i	$0.705562\pi$
$8$	−179.964	−	19.5195i	−0.994169	−	0.107831i
$9$		−	88.2233i		−	0.363059i
$10$	289.086	−	128.178i	0.914169	−	0.405334i
$11$	−224.357	+	224.357i	−0.559060	+	0.559060i	−0.929040	−	0.369980i	$-0.879365\pi$
$11$	−224.357	+	224.357i	−0.559060	+	0.559060i	0.369980	+	0.929040i	$0.379365\pi$
$12$	−440.377	+	381.105i	−0.882818	+	0.763997i
$13$	−555.000	+	555.000i	−0.910824	+	0.910824i	−0.996337	−	0.0855130i	$-0.972747\pi$
$13$	−555.000	+	555.000i	−0.910824	+	0.910824i	0.0855130	+	0.996337i	$0.472747\pi$
$14$	882.150	+	31.7832i	1.20288	+	0.0433388i
$15$	331.640	−	961.815i	0.380574	−	1.10373i
$16$	1013.39	+	147.002i	0.989642	+	0.143557i
$17$			587.077i			0.492689i	0.969182	+	0.246344i	$0.0792294\pi$
$17$			587.077i			0.492689i	−0.969182	+	0.246344i	$0.920771\pi$
$18$	−17.9693	+	498.743i	−0.0130722	+	0.362823i
$19$	−1230.66	−	1230.66i	−0.782083	−	0.782083i	0.198099	−	0.980182i	$-0.436523\pi$
$19$	−1230.66	−	1230.66i	−0.782083	−	0.782083i	−0.980182	+	0.198099i	$0.936523\pi$
$20$	−1660.36	+	665.732i	−0.928170	+	0.372155i
$21$	2008.14	−	2008.14i	0.993679	−	0.993679i
$22$	1314.03	−	1222.64i	0.578827	−	0.538568i
$23$	4640.25			1.82903			0.914517	−	0.404548i	$-0.132571\pi$
$23$	4640.25			1.82903			0.914517	+	0.404548i	$0.132571\pi$
$24$	2567.15	−	2064.76i	0.909754	−	0.731715i
$25$	1926.05	−	2460.89i	0.616336	−	0.787483i
$26$	3250.56	−	3024.48i	0.943028	−	0.877438i
$27$	−1991.82	−	1991.82i	−0.525826	−	0.525826i
$28$	−4980.48	−	359.352i	−1.20054	−	0.0866215i
$29$	1328.63	+	1328.63i	0.293365	+	0.293365i	0.838408	−	0.545043i	$-0.183487\pi$
$29$	1328.63	+	1328.63i	0.293365	+	0.293365i	−0.545043	+	0.838408i	$0.683487\pi$
$30$	−2070.73	+	5369.77i	−0.420068	+	1.08931i
$31$	948.066			0.177188			0.0885940	−	0.996068i	$-0.471763\pi$
$31$	948.066			0.177188			0.0885940	+	0.996068i	$0.471763\pi$
$32$	−5698.96	−	1037.44i	−0.983831	−	0.179097i
$33$		−	5774.51i		−	0.923061i
$34$	119.576	−	3318.85i	0.0177397	−	0.492369i
$35$	7841.97	−	3820.63i	1.08207	−	0.527187i
$36$	203.168	−	2815.82i	0.0261275	−	0.362117i
$37$	1104.09	+	1104.09i	0.132587	+	0.132587i	0.770286	−	0.637699i	$-0.220114\pi$
$37$	1104.09	+	1104.09i	0.132587	+	0.132587i	−0.637699	+	0.770286i	$0.720114\pi$
$38$	6706.47	+	7207.79i	0.753416	+	0.809735i
$39$		−	14284.6i		−	1.50386i
$40$	9521.93	−	3425.32i	0.940968	−	0.338495i
$41$			16636.3i			1.54560i	0.634652	+	0.772798i	$0.281143\pi$
$41$			16636.3i			1.54560i	−0.634652	+	0.772798i	$0.718857\pi$
$42$	−11761.4	+	10943.4i	−1.02881	+	0.957257i
$43$	−576.447	−	576.447i	−0.0475432	−	0.0475432i	0.682935	−	0.730479i	$-0.260703\pi$
$43$	−576.447	−	576.447i	−0.0475432	−	0.0475432i	−0.730479	+	0.682935i	$0.760703\pi$
$44$	−7677.48	+	6644.15i	−0.597843	+	0.517378i
$45$	2160.07	+	4433.62i	0.159015	+	0.326383i
$46$	−26232.2	−	945.125i	−1.82785	−	0.0658559i
$47$		−	13916.9i		−	0.918966i	−0.888187	−	0.459483i	$-0.848035\pi$
$47$		−	13916.9i		−	0.918966i	0.888187	−	0.459483i	$-0.151965\pi$
$48$	−14933.2	+	11149.6i	−0.935510	+	0.698484i
$49$	7542.96			0.448799
$50$	−11389.6	+	13519.5i	−0.644290	+	0.764781i
$51$	−7555.10	−	7555.10i	−0.406738	−	0.406738i
$52$	−18992.0	+	16435.8i	−0.974010	+	0.842915i
$53$	21220.9	+	21220.9i	1.03771	+	1.03771i	0.999261	+	0.0384467i	$0.0122410\pi$
$53$	21220.9	+	21220.9i	1.03771	+	1.03771i	0.0384467	+	0.999261i	$0.487759\pi$
$54$	10854.5	+	11665.9i	0.506552	+	0.544417i
$55$	5781.78	−	16768.2i	0.257724	−	0.747445i
$56$	28082.4	+	3045.91i	1.19664	+	0.129792i
$57$	31674.7			1.29129
$58$	−7240.37	−	7781.60i	−0.282612	−	0.303738i
$59$	−27261.2	+	27261.2i	−1.01956	+	1.01956i	−0.0197592	+	0.999805i	$0.506290\pi$
$59$	−27261.2	+	27261.2i	−1.01956	+	1.01956i	−0.999805	+	0.0197592i	$0.993710\pi$
$60$	12799.9	−	29934.5i	0.459017	−	1.07348i
$61$	−21412.6	−	21412.6i	−0.736793	−	0.736793i	0.235163	−	0.971956i	$-0.424438\pi$
$61$	−21412.6	−	21412.6i	−0.736793	−	0.736793i	−0.971956	+	0.235163i	$0.924438\pi$
$62$	−5359.59	−	193.102i	−0.177073	−	0.00637981i
$63$			13766.8i			0.436999i
$64$	32006.0	+	7025.60i	0.976745	+	0.214404i
$65$	14302.6	−	41480.0i	0.419886	−	1.21774i
$66$	−1176.15	+	32644.4i	−0.0332356	+	0.922463i
$67$	−13133.9	+	13133.9i	−0.357444	+	0.357444i	−0.862870	−	0.505426i	$-0.831335\pi$
$67$	−13133.9	+	13133.9i	−0.357444	+	0.357444i	0.505426	+	0.862870i	$0.331335\pi$
$68$	−1351.97	+	18737.7i	−0.0354564	+	0.491411i
$69$	−59715.4	+	59715.4i	−1.50995	+	1.50995i
$70$	−45110.3	+	20001.5i	−1.10035	+	0.487884i
$71$		−	73610.4i		−	1.73298i	−0.499194	−	0.866490i	$-0.666371\pi$
$71$		−	73610.4i		−	1.73298i	0.499194	−	0.866490i	$-0.333629\pi$
$72$	−1722.07	+	15877.0i	−0.0391489	+	0.360942i
$73$	−14209.5			−0.312084			−0.156042	−	0.987750i	$-0.549874\pi$
$73$	−14209.5			−0.312084			−0.156042	+	0.987750i	$0.549874\pi$
$74$	−6016.76	−	6466.52i	−0.127727	−	0.137275i
$75$	6882.81	+	56455.5i	0.141290	+	1.15892i
$76$	−36444.8	−	42112.9i	−0.723772	−	0.836337i
$77$	35009.8	−	35009.8i	0.672918	−	0.672918i
$78$	−2909.49	+	80753.5i	−0.0541477	+	1.50288i
$79$	−74420.1			−1.34160			−0.670799	−	0.741639i	$-0.734049\pi$
$79$	−74420.1			−1.34160			−0.670799	+	0.741639i	$0.734049\pi$
$80$	−54526.9	+	17424.6i	−0.952546	+	0.304395i
$81$	72703.9			1.23125
$82$	3388.47	−	94047.9i	0.0556505	−	1.54459i
$83$	−21801.7	+	21801.7i	−0.347372	+	0.347372i	−0.859130	−	0.511758i	$-0.828995\pi$
$83$	−21801.7	+	21801.7i	−0.347372	+	0.347372i	0.511758	+	0.859130i	$0.328995\pi$
$84$	68718.5	−	59469.4i	1.06261	−	0.919593i
$85$	−14374.1	−	29503.3i	−0.215791	−	0.442918i
$86$	3141.35	+	3376.18i	0.0458006	+	0.0492242i
$87$	−34196.3			−0.484374
$88$	44755.5	−	35996.9i	0.616084	−	0.495516i
$89$			41750.6i			0.558712i	0.960188	+	0.279356i	$0.0901210\pi$
$89$			41750.6i			0.558712i	−0.960188	+	0.279356i	$0.909879\pi$
$90$	−11308.3	−	25504.1i	−0.147160	−	0.331897i
$91$	86604.8	−	86604.8i	1.09632	−	1.09632i
$92$	148103.	+	10685.9i	1.82429	+	0.131626i
$93$	−12200.7	+	12200.7i	−0.146277	+	0.146277i
$94$	−2834.60	+	78675.1i	−0.0330882	+	0.918370i
$95$	91977.7	+	31714.5i	1.04562	+	0.360536i
$96$	86690.8	−	59989.2i	0.960053	−	0.664347i
$97$		−	121694.i		−	1.31322i	−0.754229	−	0.656611i	$-0.771989\pi$
$97$		−	121694.i		−	1.31322i	0.754229	−	0.656611i	$-0.228011\pi$
$98$	−42641.7	−	1536.35i	−0.448508	−	0.0161594i
$99$	19793.5	+	19793.5i	0.202972	+	0.202972i
$100$	67140.9	−	74108.7i	0.671409	−	0.741087i
$101$	90999.3	−	90999.3i	0.887635	−	0.887635i	−0.106660	−	0.994296i	$-0.534016\pi$
$101$	90999.3	−	90999.3i	0.887635	−	0.887635i	0.994296	+	0.106660i	$0.0340157\pi$
$102$	41171.6	+	44249.2i	0.391829	+	0.421119i
$103$	−37255.2			−0.346014			−0.173007	−	0.984921i	$-0.555348\pi$
$103$	−37255.2			−0.346014			−0.173007	+	0.984921i	$0.555348\pi$
$104$	110713.	−	89046.6i	1.00373	−	0.807298i
$105$	−51750.7	+	150086.i	−0.458082	+	1.32852i
$106$	−115644.	−	124288.i	−0.999671	−	1.07440i
$107$	12971.8	+	12971.8i	0.109532	+	0.109532i	0.759749	−	0.650217i	$-0.225322\pi$
$107$	12971.8	+	12971.8i	0.109532	+	0.109532i	−0.650217	+	0.759749i	$0.725322\pi$
$108$	−58986.2	−	68160.1i	−0.486621	−	0.562303i
$109$	104919.	+	104919.i	0.845838	+	0.845838i	0.989611	−	0.143773i	$-0.0459235\pi$
$109$	104919.	+	104919.i	0.845838	+	0.845838i	−0.143773	+	0.989611i	$0.545923\pi$
$110$	−36100.8	+	93616.0i	−0.284469	+	0.737681i
$111$	−28417.2			−0.218914
$112$	−158135.	−	22938.9i	−1.19119	−	0.172794i
$113$			133216.i			0.981432i	0.871320	+	0.490716i	$0.163265\pi$
$113$			133216.i			0.981432i	−0.871320	+	0.490716i	$0.836735\pi$
$114$	−179063.	−	6451.49i	−1.29046	−	0.0464941i
$115$	−233194.	+	113613.i	−1.64427	+	0.801092i
$116$	39346.2	+	45465.6i	0.271493	+	0.313717i
$117$	48963.9	+	48963.9i	0.330683	+	0.330683i
$118$	159665.	−	148560.i	1.05561	−	0.982193i
$119$		−	91610.2i		−	0.593030i
$120$	−78457.3	+	166618.i	−0.497371	+	1.05626i
$121$			60378.7i			0.374904i
$122$	116688.	+	125411.i	0.709787	+	0.762844i
$123$	−214092.	−	214092.i	−1.27596	−	1.27596i
$124$	30259.5	+	2183.28i	0.176729	+	0.0127513i
$125$	−36540.1	+	170829.i	−0.209168	+	0.977880i
$126$	2804.02	−	77826.1i	0.0157345	−	0.436716i
$127$		−	81760.2i		−	0.449814i	−0.974380	−	0.224907i	$-0.927792\pi$
$127$		−	81760.2i		−	0.449814i	0.974380	−	0.224907i	$-0.0722078\pi$
$128$	−179505.	−	46236.0i	−0.968392	−	0.249434i
$129$	14836.6			0.0784984
$130$	−89303.8	+	231581.i	−0.463459	+	1.20183i
$131$	−169475.	−	169475.i	−0.862836	−	0.862836i	0.128831	−	0.991667i	$-0.458878\pi$
$131$	−169475.	−	169475.i	−0.862836	−	0.862836i	−0.991667	+	0.128831i	$0.958878\pi$
$132$	13298.0	−	184305.i	0.0664281	−	0.920668i
$133$	192037.	+	192037.i	0.941362	+	0.941362i
$134$	76923.7	−	71573.4i	0.370082	−	0.344342i
$135$	148867.	+	51330.2i	0.703012	+	0.242403i
$136$	11459.4	−	105653.i	0.0531270	−	0.489816i
$137$	−236264.			−1.07546			−0.537732	−	0.843116i	$-0.680719\pi$
$137$	−236264.			−1.07546			−0.537732	+	0.843116i	$0.680719\pi$
$138$	349745.	−	325420.i	1.56334	−	1.45461i
$139$	82965.6	−	82965.6i	0.364218	−	0.364218i	−0.501145	−	0.865363i	$-0.667088\pi$
$139$	82965.6	−	82965.6i	0.364218	−	0.364218i	0.865363	+	0.501145i	$0.167088\pi$
$140$	259091.	−	103884.i	1.11720	−	0.447949i
$141$	179097.	+	179097.i	0.758650	+	0.758650i
$142$	−14993.0	+	416134.i	−0.0623974	+	1.73186i
$143$		−	249036.i		−	1.01841i
$144$	12969.0	−	89404.9i	0.0521196	−	0.359298i
$145$	−99300.1	−	34239.3i	−0.392220	−	0.135240i
$146$	80329.0	+	2894.19i	0.311882	+	0.0112369i
$147$	−97070.5	+	97070.5i	−0.370505	+	0.370505i
$148$	32696.8	+	37781.9i	0.122702	+	0.141785i
$149$	−37131.7	+	37131.7i	−0.137018	+	0.137018i	−0.772289	−	0.635271i	$-0.780888\pi$
$149$	−37131.7	+	37131.7i	−0.137018	+	0.137018i	0.635271	+	0.772289i	$0.280888\pi$
$150$	−27410.9	−	320556.i	−0.0994709	−	1.16326i
$151$			87167.0i			0.311107i	0.987827	+	0.155554i	$0.0497161\pi$
$151$			87167.0i			0.311107i	−0.987827	+	0.155554i	$0.950284\pi$
$152$	197452.	+	245495.i	0.693190	+	0.861855i
$153$	51793.8			0.178875
$154$	−205047.	+	190786.i	−0.696711	+	0.648253i
$155$	−47644.7	+	23212.6i	−0.159289	+	0.0776059i
$156$	32895.8	−	455922.i	0.108225	−	1.49996i
$157$	−55100.3	+	55100.3i	−0.178404	+	0.178404i	−0.790660	−	0.612256i	$-0.790262\pi$
$157$	−55100.3	+	55100.3i	−0.178404	+	0.178404i	0.612256	+	0.790660i	$0.290262\pi$
$158$	420711.	+	15157.9i	1.34073	+	0.0483054i
$159$	−546185.			−1.71335
$160$	311800.	−	87398.3i	0.962888	−	0.269900i
$161$	−724086.			−2.20154
$162$	−411009.	−	14808.3i	−1.23045	−	0.0443321i
$163$	−200322.	+	200322.i	−0.590553	+	0.590553i	−0.937781	−	0.347228i	$-0.887123\pi$
$163$	−200322.	+	200322.i	−0.590553	+	0.590553i	0.347228	+	0.937781i	$0.387123\pi$
$164$	−38311.3	+	530980.i	−0.111229	+	1.54159i
$165$	141384.	+	290196.i	0.404288	+	0.829815i
$166$	127690.	−	118809.i	0.359655	−	0.334640i
$167$	691828.			1.91958			0.959791	−	0.280715i	$-0.0905715\pi$
$167$	691828.			1.91958			0.959791	+	0.280715i	$0.0905715\pi$
$168$	−400591.	+	322195.i	−1.09503	+	0.880736i
$169$		−	244757.i		−	0.659201i
$170$	75250.2	+	169715.i	0.199703	+	0.450401i
$171$	−108572.	+	108572.i	−0.283942	+	0.283942i
$172$	−17071.0	−	19726.0i	−0.0439985	−	0.0508414i
$173$	−190951.	+	190951.i	−0.485072	+	0.485072i	−0.906747	−	0.421675i	$-0.861442\pi$
$173$	−190951.	+	190951.i	−0.485072	+	0.485072i	0.421675	+	0.906747i	$0.361442\pi$
$174$	193318.	+	6965.10i	0.484060	+	0.0174403i
$175$	−300550.	+	384008.i	−0.741859	+	0.947863i
$176$	−260343.	+	194381.i	−0.633526	+	0.473012i
$177$		−	701649.i		−	1.68340i
$178$	8503.77	−	236024.i	0.0201169	−	0.558350i
$179$	422789.	+	422789.i	0.986259	+	0.986259i	0.999907	−	0.0136479i	$-0.00434440\pi$
$179$	422789.	+	422789.i	0.986259	+	0.986259i	−0.0136479	+	0.999907i	$0.504344\pi$
$180$	58733.0	+	146483.i	0.135114	+	0.336980i
$181$	474592.	−	474592.i	1.07677	−	1.07677i	0.0799769	−	0.996797i	$-0.474515\pi$
$181$	474592.	−	474592.i	1.07677	−	1.07677i	0.996797	−	0.0799769i	$-0.0254847\pi$
$182$	−507233.	+	471953.i	−1.13509	+	1.05614i
$183$	551119.			1.21652
$184$	−835077.	−	90575.2i	−1.81837	−	0.197226i
$185$	−82518.5	−	28452.9i	−0.177265	−	0.0611220i
$186$	71457.8	−	66487.7i	0.151449	−	0.140916i
$187$	−131715.	−	131715.i	−0.275442	−	0.275442i
$188$	32049.1	−	444188.i	0.0661334	−	0.916583i
$189$	310814.	+	310814.i	0.632915	+	0.632915i
$190$	−513508.	−	198022.i	−1.03196	−	0.397951i
$191$	878066.			1.74158			0.870791	−	0.491654i	$-0.163607\pi$
$191$	878066.			1.74158			0.870791	+	0.491654i	$0.163607\pi$
$192$	−502298.	+	321473.i	−0.983351	+	0.629349i
$193$		−	614493.i		−	1.18747i	−0.804660	−	0.593736i	$-0.797652\pi$
$193$		−	614493.i		−	1.18747i	0.804660	−	0.593736i	$-0.202348\pi$
$194$	−24786.5	+	687956.i	−0.0472837	+	1.31237i
$195$	349747.	+	717867.i	0.658669	+	1.35194i
$196$	240749.	+	17370.5i	0.447635	+	0.0322978i
$197$	−200252.	−	200252.i	−0.367630	−	0.367630i	0.498982	−	0.866612i	$-0.333707\pi$
$197$	−200252.	−	200252.i	−0.367630	−	0.367630i	−0.866612	+	0.498982i	$0.833707\pi$
$198$	−107865.	−	115928.i	−0.195532	−	0.210148i
$199$		−	410791.i		−	0.735339i	−0.929956	−	0.367670i	$-0.880156\pi$
$199$		−	410791.i		−	0.735339i	0.929956	−	0.367670i	$-0.119844\pi$
$200$	−394655.	+	405275.i	−0.697657	+	0.716432i
$201$		−	338042.i		−	0.590174i
$202$	−532971.	+	495901.i	−0.919020	+	0.855100i
$203$	−207326.	−	207326.i	−0.353112	−	0.353112i
$204$	−223738.	−	258535.i	−0.376412	−	0.434954i
$205$	−407325.	−	836049.i	−0.676950	−	1.38946i
$206$	210610.	+	7588.13i	0.345789	+	0.0124585i
$207$		−	409378.i		−	0.664046i
$208$	−644019.	+	480847.i	−1.03214	+	0.770635i
$209$	552213.			0.874462
$210$	323126.	−	837924.i	0.505619	−	1.31116i
$211$	−252493.	−	252493.i	−0.390430	−	0.390430i	0.484411	−	0.874841i	$-0.339034\pi$
$211$	−252493.	−	252493.i	−0.390430	−	0.390430i	−0.874841	+	0.484411i	$0.839034\pi$
$212$	628440.	+	726179.i	0.960338	+	1.10970i
$213$	947294.	+	947294.i	1.43066	+	1.43066i
$214$	−70689.9	−	75974.1i	−0.105517	−	0.113405i
$215$	43083.0	+	14855.3i	0.0635638	+	0.0219172i
$216$	319577.	+	397336.i	0.466059	+	0.579460i
$217$	−147941.			−0.213274
$218$	−571756.	−	614495.i	−0.814834	−	0.875745i
$219$	182862.	−	182862.i	0.257641	−	0.257641i
$220$	223152.	−	521876.i	0.310846	−	0.726960i
$221$	−325827.	−	325827.i	−0.448753	−	0.448753i
$222$	160648.	+	5788.01i	0.218772	+	0.00788219i
$223$		−	717997.i		−	0.966853i	−0.875385	−	0.483426i	$-0.839392\pi$
$223$		−	717997.i		−	0.966853i	0.875385	−	0.483426i	$-0.160608\pi$
$224$	889293.	+	161887.i	1.18420	+	0.215572i
$225$	−217107.	−	169922.i	−0.285903	−	0.223766i
$226$	27133.4	−	753095.i	0.0353373	−	0.980796i
$227$	209176.	−	209176.i	0.269430	−	0.269430i	−0.559440	−	0.828871i	$-0.688984\pi$
$227$	209176.	−	209176.i	0.269430	−	0.269430i	0.828871	+	0.559440i	$0.188984\pi$
$228$	1.01096e6	+	72943.0i	1.28795	+	0.0929280i
$229$	367286.	−	367286.i	0.462824	−	0.462824i	−0.436756	−	0.899580i	$-0.643873\pi$
$229$	367286.	−	367286.i	0.462824	−	0.462824i	0.899580	+	0.436756i	$0.143873\pi$
$230$	1.34143e6	−	594777.i	1.67205	−	0.741369i
$231$			901082.i			1.11105i
$232$	−213171.	−	265039.i	−0.260021	−	0.323289i
$233$	320564.			0.386834			0.193417	−	0.981117i	$-0.438043\pi$
$233$	320564.			0.386834			0.193417	+	0.981117i	$0.438043\pi$
$234$	−266829.	−	286775.i	−0.318562	−	0.342375i
$235$	340745.	+	699391.i	0.402495	+	0.826133i
$236$	−932875.	+	807316.i	−1.09029	+	0.943547i
$237$	957713.	−	957713.i	1.10755	−	1.10755i
$238$	−18659.2	+	517890.i	−0.0213526	+	0.592645i
$239$	391009.			0.442784			0.221392	−	0.975185i	$-0.428940\pi$
$239$	391009.			0.442784			0.221392	+	0.975185i	$0.428940\pi$
$240$	477471.	−	925945.i	0.535080	−	1.03766i
$241$	−1.11756e6			−1.23945			−0.619723	−	0.784821i	$-0.712755\pi$
$241$	−1.11756e6			−1.23945			−0.619723	+	0.784821i	$0.712755\pi$
$242$	12297.9	−	341332.i	0.0134987	−	0.374661i
$243$	−451615.	+	451615.i	−0.490628	+	0.490628i
$244$	−634117.	−	732739.i	−0.681859	−	0.787906i
$245$	−379068.	+	184683.i	−0.403462	+	0.196568i
$246$	1.16670e6	+	1.25391e6i	1.22919	+	1.32108i
$247$	1.36603e6			1.42468
$248$	−170618.	−	18505.8i	−0.176155	−	0.0191063i
$249$		−	561133.i		−	0.573545i
$250$	241362.	−	958283.i	0.244241	−	0.969714i
$251$	10375.7	−	10375.7i	0.0103952	−	0.0103952i	−0.701890	−	0.712285i	$-0.747660\pi$
$251$	10375.7	−	10375.7i	0.0103952	−	0.0103952i	0.712285	+	0.701890i	$0.247660\pi$
$252$	−31703.2	+	439395.i	−0.0314487	+	0.435866i
$253$	−1.04107e6	+	1.04107e6i	−1.02254	+	1.02254i
$254$	−16652.9	+	462206.i	−0.0161959	+	0.449522i
$255$	564659.	+	194698.i	0.543796	+	0.187504i
$256$	1.00536e6	+	297942.i	0.958783	+	0.284140i
$257$		−	1.67916e6i		−	1.58584i	−0.609325	−	0.792921i	$-0.708559\pi$
$257$		−	1.67916e6i		−	1.58584i	0.609325	−	0.792921i	$-0.291441\pi$
$258$	−83874.2	−	3021.92i	−0.0784475	−	0.00282640i
$259$	−172288.	−	172288.i	−0.159590	−	0.159590i
$260$	552019.	−	1.29098e6i	0.506432	−	1.18437i
$261$	117216.	−	117216.i	0.106509	−	0.106509i
$262$	923557.	+	992594.i	0.831209	+	0.893343i
$263$	−893209.			−0.796276			−0.398138	−	0.917326i	$-0.630343\pi$
$263$	−893209.			−0.796276			−0.398138	+	0.917326i	$0.630343\pi$
$264$	−112715.	+	1.03920e6i	−0.0995345	+	0.917679i
$265$	−1.58603e6	−	546872.i	−1.38738	−	0.478378i
$266$	−1.04651e6	−	1.12474e6i	−0.906857	−	0.974646i
$267$	−537290.	−	537290.i	−0.461244	−	0.461244i
$268$	−449442.	+	388950.i	−0.382240	+	0.330794i
$269$	−1.20940e6	−	1.20940e6i	−1.01904	−	1.01904i	−0.999815	−	0.0192222i	$-0.993881\pi$
$269$	−1.20940e6	−	1.20940e6i	−1.01904	−	1.01904i	−0.0192222	−	0.999815i	$-0.506119\pi$
$270$	−831115.	−	320500.i	−0.693828	−	0.267558i
$271$	−925927.			−0.765867			−0.382934	−	0.923776i	$-0.625086\pi$
$271$	−925927.			−0.765867			−0.382934	+	0.923776i	$0.625086\pi$
$272$	−86301.6	+	594940.i	−0.0707288	+	0.487585i
$273$			2.22904e6i			1.81013i
$274$	1.33564e6	+	48122.2i	1.07477	+	0.0387230i
$275$	119994.	+	984241.i	0.0956817	+	0.784819i
$276$	−2.04346e6	+	1.76842e6i	−1.61470	+	1.39738i
$277$	684126.	+	684126.i	0.535719	+	0.535719i	0.922268	−	0.386550i	$-0.126333\pi$
$277$	684126.	+	684126.i	0.535719	+	0.535719i	−0.386550	+	0.922268i	$0.626333\pi$
$278$	−485919.	+	452122.i	−0.377096	+	0.350868i
$279$		−	83641.5i		−	0.0643297i
$280$	−1.48585e6	+	534504.i	−1.13261	+	0.407433i
$281$			1.89554e6i			1.43208i	0.698060	+	0.716039i	$0.254047\pi$
$281$			1.89554e6i			1.43208i	−0.698060	+	0.716039i	$0.745953\pi$
$282$	−975993.	−	1.04895e6i	−0.730843	−	0.785474i
$283$	994859.	+	994859.i	0.738406	+	0.738406i	0.972270	−	0.233863i	$-0.0751368\pi$
$283$	994859.	+	994859.i	0.738406	+	0.738406i	−0.233863	+	0.972270i	$0.575137\pi$
$284$	169516.	−	2.34943e6i	0.124714	−	1.72849i
$285$	−1.59180e6	+	775528.i	−1.16085	+	0.565569i
$286$	−50723.7	+	1.40785e6i	−0.0366687	+	1.01775i
$287$		−	2.59600e6i		−	1.86037i
$288$	−91526.3	+	502781.i	−0.0650226	+	0.357189i
$289$	1.07520e6			0.757258
$290$	554388.	+	213787.i	0.387096	+	0.149275i
$291$	1.56608e6	+	1.56608e6i	1.08413	+	1.08413i
$292$	−453525.	−	32722.8i	−0.311275	−	0.0224592i
$293$	−1.08783e6	−	1.08783e6i	−0.740274	−	0.740274i	0.232357	−	0.972631i	$-0.425356\pi$
$293$	−1.08783e6	−	1.08783e6i	−0.740274	−	0.740274i	−0.972631	+	0.232357i	$0.925356\pi$
$294$	568529.	−	528986.i	0.383605	−	0.356924i
$295$	702532.	−	2.03747e6i	0.470014	−	1.36312i
$296$	−177145.	−	220248.i	−0.117517	−	0.146111i
$297$	893760.			0.587936
$298$	217475.	−	202349.i	0.141863	−	0.131996i
$299$	−2.57534e6	+	2.57534e6i	−1.66593	+	1.66593i
$300$	89668.4	+	1.81774e6i	0.0575223	+	1.16608i
$301$	89951.6	+	89951.6i	0.0572259	+	0.0572259i
$302$	17754.2	−	492771.i	0.0112017	−	0.310905i
$303$			2.34214e6i			1.46557i
$304$	−1.06623e6	−	1.42805e6i	−0.661709	−	0.886255i
$305$	1.60035e6	+	551813.i	0.985069	+	0.339658i
$306$	−292800.	−	10549.4i	−0.178759	−	0.00644054i
$307$	130430.	−	130430.i	0.0789827	−	0.0789827i	−0.666512	−	0.745494i	$-0.732213\pi$
$307$	130430.	−	130430.i	0.0789827	−	0.0789827i	0.745494	+	0.666512i	$0.232213\pi$
$308$	1.19803e6	−	1.03678e6i	0.719600	−	0.622747i
$309$	479437.	−	479437.i	0.285651	−	0.285651i
$310$	274072.	−	121521.i	0.161980	−	0.0718203i
$311$			2.29145e6i			1.34341i	0.740819	+	0.671705i	$0.234438\pi$
$311$			2.29145e6i			1.34341i	−0.740819	+	0.671705i	$0.765562\pi$
$312$	−278828.	+	2.57071e6i	−0.162162	+	1.49509i
$313$	−2.05971e6			−1.18835			−0.594175	−	0.804336i	$-0.702521\pi$
$313$	−2.05971e6			−1.18835			−0.594175	+	0.804336i	$0.702521\pi$
$314$	322715.	−	300269.i	0.184712	−	0.171865i
$315$	−337068.	−	691844.i	−0.191400	−	0.392854i
$316$	−2.37527e6	−	171381.i	−1.33812	−	0.0965481i
$317$	−1.45424e6	+	1.45424e6i	−0.812805	+	0.812805i	−0.985054	−	0.172248i	$-0.944897\pi$
$317$	−1.45424e6	+	1.45424e6i	−0.812805	+	0.812805i	0.172248	+	0.985054i	$0.444897\pi$
$318$	3.08769e6	+	111247.i	1.71224	+	0.0616908i
$319$	−596175.			−0.328017
$320$	−1.78046e6	+	430571.i	−0.971982	+	0.235055i
$321$	−333868.			−0.180848
$322$	4.09339e6	+	147482.i	2.20011	+	0.0792682i
$323$	722489.	−	722489.i	0.385323	−	0.385323i
$324$	2.32049e6	+	167428.i	1.22805	+	0.0886067i
$325$	296834.	+	2.43475e6i	0.155885	+	1.27863i
$326$	1.17326e6	−	1.09165e6i	0.611434	−	0.568907i
$327$	−2.70040e6			−1.39656
$328$	324731.	−	2.99393e6i	0.166663	−	1.53658i
$329$			2.17167e6i			1.10612i
$330$	−740164.	−	1.66933e6i	−0.374148	−	0.843834i
$331$	450474.	−	450474.i	0.225995	−	0.225995i	−0.585022	−	0.811017i	$-0.698914\pi$
$331$	450474.	−	450474.i	0.225995	−	0.225995i	0.811017	+	0.585022i	$0.198914\pi$
$332$	−746052.	+	645639.i	−0.371470	+	0.321473i
$333$	97406.6	−	97406.6i	0.0481369	−	0.0481369i
$334$	−3.91103e6	−	140911.i	−1.91834	−	0.0691162i
$335$	338467.	−	981614.i	0.164780	−	0.477891i
$336$	2.33024e6	−	1.73984e6i	1.12604	−	0.840737i
$337$			290724.i			0.139446i	0.997566	+	0.0697229i	$0.0222115\pi$
$337$			290724.i			0.139446i	−0.997566	+	0.0697229i	$0.977788\pi$
$338$	−49852.0	+	1.38366e6i	−0.0237351	+	0.658774i
$339$	−1.71436e6	−	1.71436e6i	−0.810219	−	0.810219i
$340$	−390836.	−	974760.i	−0.183357	−	0.457299i
$341$	−212705.	+	212705.i	−0.0990587	+	0.0990587i
$342$	635895.	−	591666.i	0.293981	−	0.273534i
$343$	1.44561e6			0.663459
$344$	92487.8	+	114992.i	0.0421394	+	0.0523926i
$345$	1.53889e6	−	4.46306e6i	0.696082	−	2.01876i
$346$	1.11837e6	−	1.04059e6i	0.502223	−	0.467292i
$347$	−1.30870e6	−	1.30870e6i	−0.583468	−	0.583468i	0.352387	−	0.935854i	$-0.385370\pi$
$347$	−1.30870e6	−	1.30870e6i	−0.583468	−	0.583468i	−0.935854	+	0.352387i	$0.885370\pi$
$348$	−1.09144e6	−	78750.0i	−0.483118	−	0.0348580i
$349$	2.32293e6	+	2.32293e6i	1.02087	+	1.02087i	0.999777	+	0.0210976i	$0.00671606\pi$
$349$	2.32293e6	+	2.32293e6i	1.02087	+	1.02087i	0.0210976	+	0.999777i	$0.493284\pi$
$350$	1.77728e6	−	2.10965e6i	0.775507	−	0.920537i
$351$	2.21092e6			0.957869
$352$	1.51136e6	−	1.04585e6i	0.650146	−	0.449895i
$353$		−	4.04213e6i		−	1.72653i	−0.504752	−	0.863265i	$-0.668416\pi$
$353$		−	4.04213e6i		−	1.72653i	0.504752	−	0.863265i	$-0.331584\pi$
$354$	−142912.	+	3.96655e6i	−0.0606122	+	1.68231i
$355$	1.80229e6	+	3.69926e6i	0.759022	+	1.55792i
$356$	−96146.8	+	1.33256e6i	−0.0402077	+	0.557263i
$357$	1.17893e6	+	1.17893e6i	0.489574	+	0.489574i
$358$	−2.30399e6	−	2.47622e6i	−0.950108	−	1.02113i
$359$		−	3.47651e6i		−	1.42366i	−0.702351	−	0.711831i	$-0.747866\pi$
$359$		−	3.47651e6i		−	1.42366i	0.702351	−	0.711831i	$-0.252134\pi$
$360$	−302193.	−	840056.i	−0.122893	−	0.341627i
$361$			552930.i			0.223307i
$362$	−2.77962e6	+	2.58629e6i	−1.11485	+	1.03731i
$363$	−777014.	−	777014.i	−0.309501	−	0.309501i
$364$	2.96361e6	−	2.56473e6i	1.17238	−	1.01458i
$365$	714093.	−	347908.i	0.280558	−	0.136689i
$366$	−3.11558e6	−	112252.i	−1.21573	−	0.0438017i
$367$			2.12117e6i			0.822074i	0.911619	+	0.411037i	$0.134833\pi$
$367$			2.12117e6i			0.822074i	−0.911619	+	0.411037i	$0.865167\pi$
$368$	4.70240e6	+	682127.i	1.81009	+	0.262570i
$369$	1.46771e6			0.561142
$370$	460697.	+	177657.i	0.174949	+	0.0674649i
$371$	−3.31142e6	−	3.31142e6i	−1.24905	−	1.24905i
$372$	−417506.	+	361313.i	−0.156425	+	0.135371i
$373$	−2.71426e6	−	2.71426e6i	−1.01013	−	1.01013i	−0.999948	−	0.0101851i	$-0.996758\pi$
$373$	−2.71426e6	−	2.71426e6i	−1.01013	−	1.01013i	−0.0101851	−	0.999948i	$-0.503242\pi$
$374$	717781.	+	771436.i	0.265346	+	0.285181i
$375$	−1.72816e6	−	2.66863e6i	−0.634609	−	0.979965i
$376$	−271652.	+	2.50455e6i	−0.0990929	+	0.913608i
$377$	−1.47478e6			−0.534408
$378$	−1.69378e6	−	1.82039e6i	−0.609716	−	0.655294i
$379$	505294.	−	505294.i	0.180695	−	0.180695i	−0.610964	−	0.791659i	$-0.709218\pi$
$379$	505294.	−	505294.i	0.180695	−	0.180695i	0.791659	+	0.610964i	$0.209218\pi$
$380$	2.86262e6	+	1.22405e6i	1.01696	+	0.434850i
$381$	1.05217e6	+	1.05217e6i	0.371343	+	0.371343i
$382$	−4.96387e6	−	178844.i	−1.74045	−	0.0627072i
$383$			4.31475e6i			1.50300i	0.659734	+	0.751499i	$0.270669\pi$
$383$			4.31475e6i			1.50300i	−0.659734	+	0.751499i	$0.729331\pi$
$384$	2.90506e6	−	1.71504e6i	1.00537	−	0.593534i
$385$	−902216.	+	2.61659e6i	−0.310212	+	0.899670i
$386$	−125160.	+	3.47384e6i	−0.0427560	+	1.18670i
$387$	−50856.1	+	50856.1i	−0.0172610	+	0.0172610i
$388$	280246.	−	3.88410e6i	0.0945061	−	1.30982i
$389$	−702084.	+	702084.i	−0.235242	+	0.235242i	−0.814877	−	0.579634i	$-0.803195\pi$
$389$	−702084.	+	702084.i	−0.235242	+	0.235242i	0.579634	+	0.814877i	$0.303195\pi$
$390$	−1.83097e6	−	4.12947e6i	−0.609564	−	1.37478i
$391$			2.72418e6i			0.901144i
$392$	−1.35746e6	−	147235.i	−0.446182	−	0.0483943i
$393$	4.36196e6			1.42462
$394$	1.09127e6	+	1.17285e6i	0.354154	+	0.380628i
$395$	3.73995e6	−	1.82211e6i	1.20607	−	0.587602i
$396$	586168.	+	677333.i	0.187838	+	0.217052i
$397$	2.40518e6	−	2.40518e6i	0.765900	−	0.765900i	−0.211482	−	0.977382i	$-0.567829\pi$
$397$	2.40518e6	−	2.40518e6i	0.765900	−	0.765900i	0.977382	+	0.211482i	$0.0678290\pi$
$398$	−83669.8	+	2.32228e6i	−0.0264765	+	0.734862i
$399$	−4.94267e6			−1.55428
$400$	2.31360e6	−	2.21071e6i	0.723001	−	0.690847i
$401$	−4.69367e6			−1.45764			−0.728822	−	0.684703i	$-0.759932\pi$
$401$	−4.69367e6			−1.45764			−0.728822	+	0.684703i	$0.759932\pi$
$402$	−68852.3	+	1.91101e6i	−0.0212497	+	0.589791i
$403$	−526177.	+	526177.i	−0.161387	+	0.161387i
$404$	3.11399e6	−	2.69487e6i	0.949213	−	0.821455i
$405$	−3.65371e6	+	1.78010e6i	−1.10687	+	0.539269i
$406$	1.12982e6	+	1.21428e6i	0.340169	+	0.365597i
$407$	−495422.			−0.148248
$408$	1.21217e6	+	1.50712e6i	0.360508	+	0.448225i
$409$			4.04705e6i			1.19627i	0.801394	+	0.598137i	$0.204092\pi$
$409$			4.04705e6i			1.19627i	−0.801394	+	0.598137i	$0.795908\pi$
$410$	2.13240e6	+	4.80930e6i	0.626482	+	1.41294i
$411$	3.04048e6	−	3.04048e6i	0.887846	−	0.887846i
$412$	−1.18907e6	−	85794.2i	−0.345117	−	0.0249009i
$413$	4.25396e6	−	4.25396e6i	1.22721	−	1.22721i
$414$	−83382.1	+	2.31429e6i	−0.0239096	+	0.663616i
$415$	561839.	−	1.62943e6i	0.160137	−	0.464426i
$416$	3.73870e6	−	2.58714e6i	1.05922	−	0.732972i
$417$			2.13537e6i			0.601359i
$418$	−3.12176e6	−	112475.i	−0.873895	−	0.0314858i
$419$	−4.37567e6	−	4.37567e6i	−1.21761	−	1.21761i	−0.968465	−	0.249150i	$-0.919849\pi$
$419$	−4.37567e6	−	4.37567e6i	−1.21761	−	1.21761i	−0.249150	−	0.968465i	$-0.580151\pi$
$420$	−1.99736e6	+	4.67113e6i	−0.552501	+	1.29211i
$421$	5.08936e6	−	5.08936e6i	1.39945	−	1.39945i	0.597822	−	0.801629i	$-0.296033\pi$
$421$	5.08936e6	−	5.08936e6i	1.39945	−	1.39945i	0.801629	−	0.597822i	$-0.203967\pi$
$422$	1.37596e6	+	1.47882e6i	0.376119	+	0.404235i
$423$	−1.22780e6			−0.333639
$424$	−3.40478e6	−	4.23322e6i	−0.919760	−	1.14355i
$425$	1.44473e6	+	1.13074e6i	0.387984	+	0.303662i
$426$	−5.16229e6	−	5.54817e6i	−1.37822	−	1.48124i
$427$	3.34133e6	+	3.34133e6i	0.886849	+	0.886849i
$428$	384149.	+	443894.i	0.101365	+	0.117130i
$429$	3.20485e6	+	3.20485e6i	0.840747	+	0.840747i
$430$	−240530.	−	92754.9i	−0.0627334	−	0.0241917i
$431$	1.75406e6			0.454831			0.227416	−	0.973798i	$-0.426972\pi$
$431$	1.75406e6			0.454831			0.227416	+	0.973798i	$0.426972\pi$
$432$	−1.72570e6	−	2.31130e6i	−0.444893	−	0.595865i
$433$			2.91386e6i			0.746877i	0.927655	+	0.373438i	$0.121821\pi$
$433$			2.91386e6i			0.746877i	−0.927655	+	0.373438i	$0.878179\pi$
$434$	836336.	+	30132.6i	0.213136	+	0.00767912i
$435$	1.71852e6	−	837268.i	0.435443	−	0.212149i
$436$	3.10708e6	+	3.59031e6i	0.782774	+	0.904515i
$437$	−5.71055e6	−	5.71055e6i	−1.43046	−	1.43046i
$438$	−1.07100e6	+	996510.i	−0.266750	+	0.248197i
$439$			3.92956e6i			0.973157i	0.873637	+	0.486579i	$0.161755\pi$
$439$			3.92956e6i			0.973157i	−0.873637	+	0.486579i	$0.838245\pi$
$440$	−1.36782e6	+	2.90481e6i	−0.336819	+	0.715296i
$441$		−	665464.i		−	0.162940i
$442$	1.77560e6	+	1.90833e6i	0.432304	+	0.464619i
$443$	488185.	+	488185.i	0.118188	+	0.118188i	0.763727	−	0.645539i	$-0.223367\pi$
$443$	488185.	+	488185.i	0.118188	+	0.118188i	−0.645539	+	0.763727i	$0.723367\pi$
$444$	−906992.	−	65441.4i	−0.218346	−	0.0157542i
$445$	−1.02223e6	−	2.09816e6i	−0.244708	−	0.502272i
$446$	−146242.	+	4.05897e6i	−0.0348124	+	0.966226i
$447$		−	955697.i		−	0.226231i
$448$	−4.99436e6	−	1.09631e6i	−1.17567	−	0.258070i
$449$	3.69304e6			0.864506			0.432253	−	0.901752i	$-0.357719\pi$
$449$	3.69304e6			0.864506			0.432253	+	0.901752i	$0.357719\pi$
$450$	1.19274e6	+	1.00482e6i	0.277660	+	0.233915i
$451$	−3.73246e6	−	3.73246e6i	−0.864081	−	0.864081i
$452$	−306781.	+	4.25186e6i	−0.0706288	+	0.978887i
$453$	−1.12175e6	−	1.12175e6i	−0.256834	−	0.256834i
$454$	−1.22511e6	+	1.13990e6i	−0.278957	+	0.259554i
$455$	−2.23184e6	+	6.47274e6i	−0.505400	+	1.46575i
$456$	−5.70030e6	−	618273.i	−1.28376	−	0.139241i
$457$	5.46428e6			1.22389			0.611945	−	0.790900i	$-0.290387\pi$
$457$	5.46428e6			1.22389			0.611945	+	0.790900i	$0.290387\pi$
$458$	−2.15114e6	+	2.00153e6i	−0.479188	+	0.445859i
$459$	1.16935e6	−	1.16935e6i	0.259068	−	0.259068i
$460$	−7.70449e6	+	3.08916e6i	−1.69765	+	0.680685i
$461$	1.40103e6	+	1.40103e6i	0.307041	+	0.307041i	0.843761	−	0.536720i	$-0.180337\pi$
$461$	1.40103e6	+	1.40103e6i	0.307041	+	0.307041i	−0.536720	+	0.843761i	$0.680337\pi$
$462$	183532.	−	5.09399e6i	0.0400044	−	1.11033i
$463$		−	992575.i		−	0.215184i	−0.994195	−	0.107592i	$-0.965686\pi$
$463$		−	992575.i		−	0.215184i	0.994195	−	0.107592i	$-0.0343141\pi$
$464$	1.15111e6	+	1.54174e6i	0.248212	+	0.332441i
$465$	314417.	−	911864.i	0.0674331	−	0.195568i
$466$	−1.81221e6	−	65292.4i	−0.386583	−	0.0139283i
$467$	2.78385e6	−	2.78385e6i	0.590682	−	0.590682i	−0.347133	−	0.937816i	$-0.612845\pi$
$467$	2.78385e6	−	2.78385e6i	0.590682	−	0.590682i	0.937816	+	0.347133i	$0.112845\pi$
$468$	1.45002e6	+	1.67554e6i	0.306028	+	0.353623i
$469$	2.04948e6	−	2.04948e6i	0.430241	−	0.430241i
$470$	−1.78384e6	−	4.02319e6i	−0.372488	−	0.840090i
$471$		−	1.41817e6i		−	0.294562i
$472$	5.43815e6	−	4.37390e6i	1.12356	−	0.903679i
$473$	258660.			0.0531590
$474$	−5.60920e6	+	5.21906e6i	−1.14671	+	1.06696i
$475$	−5.39881e6	+	658199.i	−1.09790	+	0.133851i
$476$	210967.	−	2.92393e6i	0.0426774	−	0.591492i
$477$	1.87218e6	−	1.87218e6i	0.376749	−	0.376749i
$478$	−2.21045e6	−	79640.7i	−0.442497	−	0.0159428i
$479$	−4.52499e6			−0.901113			−0.450556	−	0.892748i	$-0.648774\pi$
$479$	−4.52499e6			−0.901113			−0.450556	+	0.892748i	$0.648774\pi$
$480$	−2.88783e6	+	5.13729e6i	−0.572095	+	1.01773i
$481$	−1.22554e6			−0.241527
$482$	6.31777e6	+	227624.i	1.23864	+	0.0446273i
$483$	9.31828e6	−	9.31828e6i	1.81747	−	1.81747i
$484$	−139045.	+	1.92711e6i	−0.0269800	+	0.373932i
$485$	2.97957e6	+	6.11566e6i	0.575174	+	1.18056i
$486$	2.64505e6	−	2.46108e6i	0.507975	−	0.472644i
$487$	1.74228e6			0.332887			0.166443	−	0.986051i	$-0.446772\pi$
$487$	1.74228e6			0.332887			0.166443	+	0.986051i	$0.446772\pi$
$488$	3.43554e6	+	4.27146e6i	0.653048	+	0.811946i
$489$		−	5.15589e6i		−	0.975060i
$490$	2.18056e6	−	966840.i	0.410278	−	0.181913i
$491$	2.11791e6	−	2.11791e6i	0.396463	−	0.396463i	−0.480520	−	0.876984i	$-0.659552\pi$
$491$	2.11791e6	−	2.11791e6i	0.396463	−	0.396463i	0.876984	+	0.480520i	$0.159552\pi$
$492$	−6.34016e6	−	7.32622e6i	−1.18083	−	1.36448i
$493$	−780007.	+	780007.i	−0.144538	+	0.144538i
$494$	−7.72241e6	−	278232.i	−1.42376	−	0.0512968i
$495$	−1.47934e6	−	510087.i	−0.271366	−	0.0935689i
$496$	960764.	+	139368.i	0.175353	+	0.0254366i
$497$			1.14865e7i			2.08592i
$498$	−114292.	+	3.17219e6i	−0.0206510	+	0.573173i
$499$	−3.11132e6	−	3.11132e6i	−0.559362	−	0.559362i	0.369764	−	0.929126i	$-0.379439\pi$
$499$	−3.11132e6	−	3.11132e6i	−0.559362	−	0.559362i	−0.929126	+	0.369764i	$0.879439\pi$
$500$	−1.55965e6	+	5.36819e6i	−0.278999	+	0.960292i
$501$	−8.90314e6	+	8.90314e6i	−1.58471	+	1.58471i
$502$	−60768.9	+	56542.3i	−0.0107627	+	0.0100142i
$503$	−6.13731e6			−1.08158			−0.540790	−	0.841158i	$-0.681875\pi$
$503$	−6.13731e6			−1.08158			−0.540790	+	0.841158i	$0.681875\pi$
$504$	268720.	−	2.47752e6i	0.0471220	−	0.434451i
$505$	−2.34509e6	+	6.80118e6i	−0.409196	+	1.18674i
$506$	6.09743e6	−	5.67333e6i	1.05869	−	0.985059i
$507$	3.14978e6	+	3.14978e6i	0.544202	+	0.544202i
$508$	188284.	−	2.60954e6i	0.0323709	−	0.448647i
$509$	2.25154e6	+	2.25154e6i	0.385199	+	0.385199i	0.872971	−	0.487772i	$-0.162190\pi$
$509$	2.25154e6	+	2.25154e6i	0.385199	+	0.385199i	−0.487772	+	0.872971i	$0.662190\pi$
$510$	−3.15247e6	−	1.21567e6i	−0.536692	−	0.206963i
$511$	2.21732e6			0.375644
$512$	−5.62278e6	−	1.88909e6i	−0.947930	−	0.318477i
$513$			4.90250e6i			0.822478i
$514$	−342012.	+	9.49262e6i	−0.0570996	+	1.58481i
$515$	1.87224e6	−	912162.i	0.311060	−	0.151549i
$516$	473541.	+	34167.0i	0.0782949	+	0.00564914i
$517$	3.12237e6	+	3.12237e6i	0.513757	+	0.513757i
$518$	938884.	+	1.00907e6i	0.153740	+	0.165232i
$519$		−	4.91470e6i		−	0.800900i
$520$	−3.38362e6	+	7.18572e6i	−0.548748	+	1.16537i
$521$		−	5.74956e6i		−	0.927983i	−0.885840	−	0.463991i	$-0.846417\pi$
$521$		−	5.74956e6i		−	0.927983i	0.885840	−	0.463991i	$-0.153583\pi$
$522$	−686518.	+	638769.i	−0.110275	+	0.102605i
$523$	530642.	+	530642.i	0.0848296	+	0.0848296i	0.748248	−	0.663419i	$-0.230895\pi$
$523$	530642.	+	530642.i	0.0848296	+	0.0848296i	−0.663419	+	0.748248i	$0.730895\pi$
$524$	−5.01887e6	−	5.79943e6i	−0.798505	−	0.922693i
$525$	−1.07403e6	−	8.80959e6i	−0.170066	−	1.39495i
$526$	5.04948e6	+	181929.i	0.795760	+	0.0286706i
$527$			556587.i			0.0872985i
$528$	848867.	−	5.85185e6i	0.132512	−	0.913500i
$529$	1.50956e7			2.34536
$530$	8.85472e6	+	3.41461e6i	1.36926	+	0.528022i
$531$	2.40507e6	+	2.40507e6i	0.370162	+	0.370162i
$532$	5.68702e6	+	6.57150e6i	0.871176	+	1.00667i
$533$	−9.23312e6	−	9.23312e6i	−1.40777	−	1.40777i
$534$	2.92796e6	+	3.14683e6i	0.444337	+	0.477552i
$535$	−969496.	−	334289.i	−0.146441	−	0.0504937i
$536$	2.62000e6	−	2.10727e6i	0.393903	−	0.316816i
$537$	−1.08818e7			−1.62841
$538$	6.59065e6	+	7.08331e6i	0.981685	+	1.05507i
$539$	−1.69232e6	+	1.69232e6i	−0.250905	+	0.250905i
$540$	4.63317e6	+	1.98113e6i	0.683745	+	0.292367i
$541$	−3.82103e6	−	3.82103e6i	−0.561290	−	0.561290i	0.368384	−	0.929674i	$-0.379911\pi$
$541$	−3.82103e6	−	3.82103e6i	−0.561290	−	0.561290i	−0.929674	+	0.368384i	$0.879911\pi$
$542$	5.23444e6	+	188593.i	0.765371	+	0.0275757i
$543$			1.22151e7i			1.77786i
$544$	609056.	−	3.34573e6i	0.0882389	−	0.484723i
$545$	−7.84150e6	−	2.70380e6i	−1.13086	−	0.389927i
$546$	454010.	−	1.26012e7i	0.0651755	−	1.80896i
$547$	−2.22523e6	+	2.22523e6i	−0.317985	+	0.317985i	−0.847993	−	0.530008i	$-0.822189\pi$
$547$	−2.22523e6	+	2.22523e6i	−0.317985	+	0.317985i	0.530008	+	0.847993i	$0.322189\pi$
$548$	−7.54083e6	−	544087.i	−1.07267	−	0.0773957i
$549$	−1.88909e6	+	1.88909e6i	−0.267499	+	0.267499i
$550$	−477880.	−	5.58854e6i	−0.0673615	−	0.787755i
$551$		−	3.27017e6i		−	0.458872i
$552$	1.19122e7	−	9.58101e6i	1.66397	−	1.33833i
$553$	1.16129e7			1.61483
$554$	−3.72815e6	−	4.00683e6i	−0.516082	−	0.554660i
$555$	1.42809e6	−	695771.i	0.196800	−	0.0958813i
$556$	2.83908e6	−	2.45696e6i	0.389484	−	0.337063i
$557$	−4.87327e6	+	4.87327e6i	−0.665552	+	0.665552i	−0.956683	−	0.291131i	$-0.905968\pi$
$557$	−4.87327e6	+	4.87327e6i	−0.665552	+	0.665552i	0.291131	+	0.956683i	$0.405968\pi$
$558$	−17036.1	+	472841.i	−0.00231624	+	0.0642879i
$559$	639857.			0.0866070
$560$	8.50864e6	−	2.71901e6i	1.14654	−	0.366388i
$561$	3.39008e6			0.454782
$562$	386083.	−	1.07158e7i	0.0515632	−	1.43115i
$563$	−780658.	+	780658.i	−0.103798	+	0.103798i	−0.757099	−	0.653301i	$-0.773384\pi$
$563$	−780658.	+	780658.i	−0.103798	+	0.103798i	0.653301	+	0.757099i	$0.273384\pi$
$564$	5.30382e6	+	6.12870e6i	0.702087	+	0.811280i
$565$	−3.26168e6	−	6.69472e6i	−0.429854	−	0.882289i
$566$	−5.42149e6	−	5.82676e6i	−0.711341	−	0.764515i
$567$	−1.13451e7			−1.48200
$568$	−1.43684e6	+	1.32472e7i	−0.186869	+	1.72288i
$569$			2.98448e6i			0.386446i	0.981155	+	0.193223i	$0.0618940\pi$
$569$			2.98448e6i			0.386446i	−0.981155	+	0.193223i	$0.938106\pi$
$570$	9.15669e6	−	4.05999e6i	1.18046	−	0.523405i
$571$	−6.54308e6	+	6.54308e6i	−0.839831	+	0.839831i	−0.988836	−	0.149005i	$-0.952393\pi$
$571$	−6.54308e6	+	6.54308e6i	−0.839831	+	0.839831i	0.149005	+	0.988836i	$0.452393\pi$
$572$	573501.	−	7.94850e6i	0.0732899	−	1.01577i
$573$	−1.12998e7	+	1.12998e7i	−1.43776	+	1.43776i
$574$	−528753.	+	1.46757e7i	−0.0669843	+	1.85917i
$575$	8.93735e6	−	1.14191e7i	1.12730	−	1.44033i
$576$	619821.	−	2.82367e6i	0.0778413	−	0.354616i
$577$		−	4.70035e6i		−	0.587747i	−0.955844	−	0.293874i	$-0.905056\pi$
$577$		−	4.70035e6i		−	0.587747i	0.955844	−	0.293874i	$-0.0949445\pi$
$578$	−6.07829e6	−	218996.i	−0.756767	−	0.0272657i
$579$	7.90792e6	+	7.90792e6i	0.980315	+	0.980315i
$580$	−3.09052e6	−	1.32149e6i	−0.381470	−	0.163115i
$581$	3.40204e6	−	3.40204e6i	0.418118	−	0.418118i
$582$	−8.53435e6	−	9.17230e6i	−1.04439	−	1.12246i
$583$	−9.52214e6			−1.16028
$584$	2.55720e6	+	277362.i	0.310265	+	0.0336523i
$585$	−3.65950e6	−	1.26182e6i	−0.442112	−	0.152443i
$586$	5.92814e6	+	6.37128e6i	0.713140	+	0.766448i
$587$	−3.44337e6	−	3.44337e6i	−0.412466	−	0.412466i	0.470131	−	0.882597i	$-0.344207\pi$
$587$	−3.44337e6	−	3.44337e6i	−0.412466	−	0.412466i	−0.882597	+	0.470131i	$0.844207\pi$
$588$	−3.32174e6	+	2.87466e6i	−0.396207	+	0.342881i
$589$	−1.16674e6	−	1.16674e6i	−0.138576	−	0.138576i
$590$	−4.38653e6	+	1.13751e7i	−0.518790	+	1.34532i
$591$	5.15408e6			0.606992
$592$	956576.	+	1.28118e6i	0.112180	+	0.150248i
$593$			2.46686e6i			0.288077i	0.989572	+	0.144038i	$0.0460089\pi$
$593$			2.46686e6i			0.288077i	−0.989572	+	0.144038i	$0.953991\pi$
$594$	−5.05259e6	−	182041.i	−0.587555	−	0.0211691i
$595$	2.24300e6	+	4.60383e6i	0.259739	+	0.533123i
$596$	−1.27064e6	+	1.09962e6i	−0.146524	+	0.126803i
$597$	5.28647e6	+	5.28647e6i	0.607058	+	0.607058i
$598$	1.50834e7	−	1.40343e7i	1.72483	−	1.60486i
$599$		−	5.16075e6i		−	0.587687i	−0.955854	−	0.293843i	$-0.905066\pi$
$599$		−	5.16075e6i		−	0.587687i	0.955854	−	0.293843i	$-0.0949344\pi$
$600$	−136674.	−	1.02943e7i	−0.0154992	−	1.16740i
$601$		−	2.02863e6i		−	0.229095i	−0.993418	−	0.114548i	$-0.963458\pi$
$601$		−	2.02863e6i		−	0.229095i	0.993418	−	0.114548i	$-0.0365418\pi$
$602$	−490192.	−	526834.i	−0.0551283	−	0.0592493i
$603$	1.15872e6	+	1.15872e6i	0.129773	+	0.129773i
$604$	−200735.	+	2.78211e6i	−0.0223888	+	0.310300i
$605$	−1.47832e6	−	3.03431e6i	−0.164203	−	0.337032i
$606$	477048.	−	1.32406e7i	0.0527692	−	1.46462i
$607$			8.66214e6i			0.954231i	0.878841	+	0.477115i	$0.158318\pi$
$607$			8.66214e6i			0.954231i	−0.878841	+	0.477115i	$0.841682\pi$
$608$	5.73673e6	+	8.29019e6i	0.629369	+	0.909506i
$609$	5.33615e6			0.583022
$610$	−8.93471e6	−	3.44546e6i	−0.972200	−	0.374906i
$611$	7.72390e6	+	7.72390e6i	0.837016	+	0.837016i
$612$	1.65310e6	+	119275.i	0.178411	+	0.0128727i
$613$	−2.59049e6	−	2.59049e6i	−0.278439	−	0.278439i	0.554047	−	0.832486i	$-0.313083\pi$
$613$	−2.59049e6	−	2.59049e6i	−0.278439	−	0.278439i	−0.832486	+	0.554047i	$0.813083\pi$
$614$	−763912.	+	710780.i	−0.0817753	+	0.0760877i
$615$	1.60010e7	+	5.51725e6i	1.70592	+	0.588213i
$616$	−6.98386e6	+	5.61712e6i	−0.741556	+	0.596433i
$617$	1.36722e6			0.144586			0.0722929	−	0.997383i	$-0.476968\pi$
$617$	1.36722e6			0.144586			0.0722929	+	0.997383i	$0.476968\pi$
$618$	−2.80800e6	+	2.61270e6i	−0.295751	+	0.275181i
$619$	−4.91864e6	+	4.91864e6i	−0.515963	+	0.515963i	−0.916347	−	0.400384i	$-0.868877\pi$
$619$	−4.91864e6	+	4.91864e6i	−0.515963	+	0.515963i	0.400384	+	0.916347i	$0.368877\pi$
$620$	−1.57413e6	+	631158.i	−0.164461	+	0.0659415i
$621$	−9.24256e6	−	9.24256e6i	−0.961753	−	0.961753i
$622$	466722.	−	1.29540e7i	0.0483706	−	1.34254i
$623$		−	6.51497e6i		−	0.672500i
$624$	2.09987e6	−	1.44759e7i	0.215889	−	1.48828i
$625$	−2.34629e6	−	9.47958e6i	−0.240260	−	0.970709i
$626$	1.16439e7	+	419521.i	1.18758	+	0.0427876i
$627$	−7.10644e6	+	7.10644e6i	−0.721910	+	0.721910i
$628$	−1.88553e6	+	1.63175e6i	−0.190780	+	0.165103i
$629$	−648187.	+	648187.i	−0.0653241	+	0.0653241i
$630$	1.76459e6	+	3.97978e6i	0.177131	+	0.399491i
$631$			2.16060e6i			0.216023i	0.994150	+	0.108012i	$0.0344484\pi$
$631$			2.16060e6i			0.216023i	−0.994150	+	0.108012i	$0.965552\pi$
$632$	1.33929e7	+	1.45264e6i	1.33378	+	0.144666i
$633$	6.49868e6			0.644638
$634$	8.51726e6	−	7.92487e6i	0.841544	−	0.783013i
$635$	2.00183e6	+	4.10883e6i	0.197012	+	0.404374i
$636$	−1.74326e7	−	1.25780e6i	−1.70891	−	0.123302i
$637$	−4.18634e6	+	4.18634e6i	−0.408777	+	0.408777i
$638$	3.37029e6	+	121429.i	0.327805	+	0.0118106i
$639$	−6.49415e6			−0.629173
$640$	1.01530e7	−	2.07146e6i	0.979815	−	0.199906i
$641$	−554349.			−0.0532891			−0.0266445	−	0.999645i	$-0.508482\pi$
$641$	−554349.			−0.0532891			−0.0266445	+	0.999645i	$0.508482\pi$
$642$	1.88742e6	+	68002.3i	0.180730	+	0.00651158i
$643$	8.08210e6	−	8.08210e6i	0.770898	−	0.770898i	−0.207366	−	0.978263i	$-0.566489\pi$
$643$	8.08210e6	−	8.08210e6i	0.770898	−	0.770898i	0.978263	+	0.207366i	$0.0664890\pi$
$644$	−2.31107e7	−	1.66748e6i	−2.19583	−	0.158434i
$645$	−745609.	+	363263.i	−0.0705686	+	0.0343812i
$646$	−4.23152e6	+	3.93721e6i	−0.398947	+	0.371199i
$647$	−520128.			−0.0488483			−0.0244242	−	0.999702i	$-0.507775\pi$
$647$	−520128.			−0.0488483			−0.0244242	+	0.999702i	$0.507775\pi$
$648$	−1.30841e7	−	1.41914e6i	−1.22407	−	0.132766i
$649$		−	1.22325e7i		−	1.13999i
$650$	−1.18215e6	−	1.38245e7i	−0.109746	−	1.28342i
$651$	1.90385e6	−	1.90385e6i	0.176068	−	0.176068i
$652$	−6.85499e6	+	5.93236e6i	−0.631521	+	0.546523i
$653$	7.53149e6	−	7.53149e6i	0.691191	−	0.691191i	−0.271303	−	0.962494i	$-0.587455\pi$
$653$	7.53149e6	−	7.53149e6i	0.691191	−	0.691191i	0.962494	+	0.271303i	$0.0874546\pi$
$654$	1.52659e7	+	550018.i	1.39565	+	0.0502843i
$655$	1.26664e7	+	4.36745e6i	1.15358	+	0.397763i
$656$	−2.44557e6	+	1.68591e7i	−0.221881	+	1.52959i
$657$			1.25361e6i			0.113305i
$658$	442325.	−	1.22768e7i	0.0398269	−	1.10541i
$659$	682456.	+	682456.i	0.0612155	+	0.0612155i	0.737052	−	0.675836i	$-0.236217\pi$
$659$	682456.	+	682456.i	0.0612155	+	0.0612155i	−0.675836	+	0.737052i	$0.736217\pi$
$660$	3.84428e6	+	9.58778e6i	0.343522	+	0.856758i
$661$	8.43310e6	−	8.43310e6i	0.750730	−	0.750730i	−0.223886	−	0.974615i	$-0.571874\pi$
$661$	8.43310e6	−	8.43310e6i	0.750730	−	0.750730i	0.974615	+	0.223886i	$0.0718743\pi$
$662$	−2.63837e6	+	2.45486e6i	−0.233986	+	0.217712i
$663$	8.38616e6			0.740934
$664$	4.34908e6	−	3.49796e6i	0.382804	−	0.307889i
$665$	−1.43526e7	−	4.94888e6i	−1.25857	−	0.433963i
$666$	−570498.	+	530818.i	−0.0498389	+	0.0463725i
$667$	6.16517e6	+	6.16517e6i	0.536575	+	0.536575i
$668$	2.20811e7	+	1.59320e6i	1.91461	+	0.138143i
$669$	9.23992e6	+	9.23992e6i	0.798183	+	0.798183i
$670$	−2.11335e6	+	5.48031e6i	−0.181880	+	0.471648i
$671$	9.60816e6			0.823823
$672$	−1.35277e7	+	9.36100e6i	−1.15558	+	0.799648i
$673$			3.92414e6i			0.333970i	0.985959	+	0.166985i	$0.0534031\pi$
$673$			3.92414e6i			0.333970i	−0.985959	+	0.166985i	$0.946597\pi$
$674$	59214.6	−	1.64352e6i	0.00502087	−	0.139355i
$675$	−8.73801e6	+	1.06530e6i	−0.738164	+	0.0899937i
$676$	563646.	−	7.81191e6i	0.0474394	−	0.657492i
$677$	3.71085e6	+	3.71085e6i	0.311173	+	0.311173i	0.845364	−	0.534191i	$-0.179384\pi$
$677$	3.71085e6	+	3.71085e6i	0.311173	+	0.311173i	−0.534191	+	0.845364i	$0.679384\pi$
$678$	9.34241e6	+	1.00408e7i	0.780521	+	0.838866i
$679$			1.89896e7i			1.58067i
$680$	2.01093e6	+	5.59010e6i	0.166772	+	0.463604i
$681$			5.38377e6i			0.444855i
$682$	1.24579e6	−	1.15914e6i	0.102561	−	0.0954278i
$683$	−1.21513e7	−	1.21513e7i	−0.996711	−	0.996711i	0.00328325	−	0.999995i	$-0.498955\pi$
$683$	−1.21513e7	−	1.21513e7i	−0.996711	−	0.996711i	−0.999995	+	0.00328325i	$0.998955\pi$
$684$	−3.71534e6	+	3.21528e6i	−0.303640	+	0.262772i
$685$	1.18733e7	−	5.78472e6i	0.966822	−	0.471038i
$686$	−8.17227e6	−	294441.i	−0.663029	−	0.0238884i
$687$			9.45322e6i			0.764166i
$688$	−499429.	−	668907.i	−0.0402256	−	0.0538759i
$689$	−2.35552e7			−1.89034
$690$	−9.60868e6	+	2.49171e7i	−0.768318	+	1.99239i
$691$	1.43382e6	+	1.43382e6i	0.114235	+	0.114235i	0.761914	−	0.647679i	$-0.224260\pi$
$691$	1.43382e6	+	1.43382e6i	0.114235	+	0.114235i	−0.647679	+	0.761914i	$0.724260\pi$
$692$	−6.53432e6	+	5.65484e6i	−0.518722	+	0.448906i
$693$	−3.08867e6	−	3.08867e6i	−0.244309	−	0.244309i
$694$	7.13178e6	+	7.66489e6i	0.562081	+	0.604098i
$695$	−2.13806e6	+	6.20075e6i	−0.167903	+	0.486948i
$696$	6.15410e6	+	667494.i	0.481550	+	0.0522305i
$697$	−9.76676e6			−0.761498
$698$	−1.26588e7	−	1.36051e7i	−0.983456	−	1.05697i
$699$	−4.12534e6	+	4.12534e6i	−0.319350	+	0.319350i
$700$	−1.04770e7	+	1.15643e7i	−0.808149	+	0.892017i
$701$	−1.39647e7	−	1.39647e7i	−1.07334	−	1.07334i	−0.997089	−	0.0762462i	$-0.975707\pi$
$701$	−1.39647e7	−	1.39647e7i	−1.07334	−	1.07334i	−0.0762462	−	0.997089i	$-0.524293\pi$
$702$	−1.24988e7	−	450321.i	−0.957248	−	0.0344889i
$703$		−	2.71752e6i		−	0.207388i
$704$	−8.75702e6	+	5.60453e6i	−0.665924	+	0.426194i
$705$	−1.33855e7	−	4.61542e6i	−1.01429	−	0.349734i
$706$	−823302.	+	2.28509e7i	−0.0621652	+	1.72541i
$707$	−1.42000e7	+	1.42000e7i	−1.06841	+	1.06841i
$708$	1.61581e6	−	2.23946e7i	0.121146	−	1.67903i
$709$	1.13053e6	−	1.13053e6i	0.0844631	−	0.0844631i	−0.663613	−	0.748076i	$-0.730978\pi$
$709$	1.13053e6	−	1.13053e6i	0.0844631	−	0.0844631i	0.748076	+	0.663613i	$0.230978\pi$
$710$	−9.43522e6	−	2.12797e7i	−0.702435	−	1.58424i
$711$			6.56558e6i			0.487079i
$712$	814950.	−	7.51361e6i	0.0602464	−	0.555454i
$713$	4.39926e6			0.324083
$714$	−6.42461e6	−	6.90486e6i	−0.471629	−	0.506885i
$715$	6.09745e6	+	1.25152e7i	0.446050	+	0.915532i
$716$	1.25205e7	+	1.44678e7i	0.912726	+	1.05468i
$717$	−5.03191e6	+	5.03191e6i	−0.365540	+	0.365540i
$718$	−708095.	+	1.96533e7i	−0.0512602	+	1.42274i
$719$	−1.86153e7			−1.34291			−0.671457	−	0.741043i	$-0.734331\pi$
$719$	−1.86153e7			−1.34291			−0.671457	+	0.741043i	$0.734331\pi$
$720$	1.53725e6	+	4.81054e6i	0.110513	+	0.345830i
$721$	5.81347e6			0.416483
$722$	112621.	−	3.12581e6i	0.00804035	−	0.223162i
$723$	1.43819e7	−	1.43819e7i	1.02322	−	1.02322i
$724$	1.62405e7	−	1.40547e7i	1.15147	−	0.996492i
$725$	5.82861e6	−	710598.i	0.411832	−	0.0502087i
$726$	4.23435e6	+	4.55087e6i	0.298157	+	0.320445i
$727$	1.57482e7			1.10508			0.552540	−	0.833486i	$-0.313659\pi$
$727$	1.57482e7			1.10508			0.552540	+	0.833486i	$0.313659\pi$
$728$	−1.72762e7	+	1.38953e7i	−1.20815	+	0.971713i
$729$			6.04338e6i			0.421173i
$730$	−4.10776e6	+	1.82134e6i	−0.285298	+	0.126498i
$731$	338419.	−	338419.i	0.0234240	−	0.0234240i
$732$	1.75901e7	+	1.26916e6i	1.21336	+	0.0875466i
$733$	−1.25861e7	+	1.25861e7i	−0.865229	+	0.865229i	−0.991940	−	0.126711i	$-0.959558\pi$
$733$	−1.25861e7	+	1.25861e7i	−0.865229	+	0.865229i	0.126711	+	0.991940i	$0.459558\pi$
$734$	432041.	−	1.19914e7i	0.0295995	−	0.821541i
$735$	2.50155e6	−	7.25493e6i	0.170801	−	0.495353i
$736$	−2.64446e7	−	4.81397e6i	−1.79946	−	0.327574i
$737$		−	5.89338e6i		−	0.399665i
$738$	−8.29721e6	−	298942.i	−0.560778	−	0.0202044i
$739$	−1.69221e7	−	1.69221e7i	−1.13984	−	1.13984i	−0.988478	−	0.151362i	$-0.951634\pi$
$739$	−1.69221e7	−	1.69221e7i	−1.13984	−	1.13984i	−0.151362	−	0.988478i	$-0.548366\pi$
$740$	−2.56822e6	−	1.09816e6i	−0.172406	−	0.0737204i
$741$	−1.75794e7	+	1.75794e7i	−1.17614	+	1.17614i
$742$	1.80456e7	+	1.93945e7i	1.20326	+	1.29321i
$743$	2.92120e6			0.194128			0.0970641	−	0.995278i	$-0.469055\pi$
$743$	2.92120e6			0.194128			0.0970641	+	0.995278i	$0.469055\pi$
$744$	2.43383e6	−	1.95753e6i	0.161198	−	0.129651i
$745$	956899.	−	2.77518e6i	0.0631649	−	0.183189i
$746$	1.47914e7	+	1.58970e7i	0.973107	+	1.04585i
$747$	1.92342e6	+	1.92342e6i	0.126117	+	0.126117i
$748$	−3.90062e6	−	4.50727e6i	−0.254906	−	0.294550i
$749$	−2.02418e6	−	2.02418e6i	−0.131839	−	0.131839i
$750$	9.22607e6	+	1.54383e7i	0.598913	+	1.00218i
$751$	−2.77456e7			−1.79513			−0.897563	−	0.440887i	$-0.854664\pi$
$751$	−2.77456e7			−1.79513			−0.897563	+	0.440887i	$0.854664\pi$
$752$	2.04582e6	−	1.41033e7i	0.131924	−	0.909447i
$753$			267049.i			0.0171634i
$754$	8.33719e6	+	300383.i	0.534062	+	0.0192418i
$755$	−2.13421e6	−	4.38054e6i	−0.136261	−	0.279680i
$756$	9.20448e6	+	1.06360e7i	0.585727	+	0.676822i
$757$	6.25430e6	+	6.25430e6i	0.396679	+	0.396679i	0.877060	−	0.480381i	$-0.159502\pi$
$757$	6.25430e6	+	6.25430e6i	0.396679	+	0.396679i	−0.480381	+	0.877060i	$0.659502\pi$
$758$	−2.95944e6	+	2.75361e6i	−0.187084	+	0.174072i
$759$		−	2.67952e7i		−	1.68831i
$760$	−1.59336e7	−	7.50282e6i	−1.00065	−	0.471184i
$761$			2.20364e6i			0.137937i	0.997619	+	0.0689683i	$0.0219707\pi$
$761$			2.20364e6i			0.137937i	−0.997619	+	0.0689683i	$0.978029\pi$
$762$	−5.73383e6	−	6.16244e6i	−0.357731	−	0.384472i
$763$	−1.63720e7	−	1.63720e7i	−1.01810	−	1.01810i
$764$	2.80253e7	+	2.02208e6i	1.73707	+	0.125333i
$765$	−2.60288e6	+	1.26813e6i	−0.160805	+	0.0783447i
$766$	878827.	−	2.43921e7i	0.0541167	−	1.50202i
$767$		−	3.02599e7i		−	1.85729i
$768$	−1.67722e7	+	9.10373e6i	−1.02609	+	0.556950i
$769$	1.19488e7			0.728630			0.364315	−	0.931276i	$-0.381303\pi$
$769$	1.19488e7			0.728630			0.364315	+	0.931276i	$0.381303\pi$
$770$	5.63334e6	−	1.46083e7i	0.342404	−	0.887917i
$771$	2.16092e7	+	2.16092e7i	1.30919	+	1.30919i
$772$	1.41510e6	−	1.96128e7i	0.0854565	−	1.18439i
$773$	1.99004e7	+	1.99004e7i	1.19788	+	1.19788i	0.974801	+	0.223077i	$0.0716103\pi$
$773$	1.99004e7	+	1.99004e7i	1.19788	+	1.19788i	0.223077	+	0.974801i	$0.428390\pi$
$774$	297857.	−	277140.i	0.0178713	−	0.0166283i
$775$	1.82602e6	−	2.33308e6i	0.109207	−	0.139533i
$776$	−2.37539e6	+	2.19004e7i	−0.141606	+	1.30557i
$777$	4.43435e6			0.263498
$778$	4.11201e6	−	3.82601e6i	0.243560	−	0.226620i
$779$	2.04735e7	−	2.04735e7i	1.20878	−	1.20878i
$780$	9.50972e6	+	2.37176e7i	0.559669	+	1.39584i
$781$	1.65150e7	+	1.65150e7i	0.968840	+	0.968840i
$782$	554861.	−	1.54003e7i	0.0324465	−	0.900559i
$783$		−	5.29279e6i		−	0.308518i
$784$	7.64398e6	+	1.10883e6i	0.444150	+	0.0644281i
$785$	1.41996e6	−	4.11813e6i	0.0822434	−	0.238521i
$786$	−2.46590e7	−	888444.i	−1.42370	−	0.0512948i
$787$	6.21498e6	−	6.21498e6i	0.357687	−	0.357687i	−0.505273	−	0.862960i	$-0.668608\pi$
$787$	6.21498e6	−	6.21498e6i	0.357687	−	0.357687i	0.862960	+	0.505273i	$0.168608\pi$
$788$	−5.93028e6	−	6.85259e6i	−0.340220	−	0.393133i
$789$	1.14947e7	−	1.14947e7i	0.657364	−	0.657364i
$790$	−2.15138e7	+	9.53900e6i	−1.22645	+	0.543795i
$791$		−	2.07877e7i		−	1.18131i
$792$	−3.17576e6	−	3.94848e6i	−0.179901	−	0.223675i
$793$	2.37680e7			1.34218
$794$	−1.40868e7	+	1.31071e7i	−0.792980	+	0.737826i
$795$	2.74483e7	−	1.33729e7i	1.54027	−	0.750426i
$796$	946002.	−	1.31112e7i	0.0529187	−	0.733433i
$797$	2.10526e7	−	2.10526e7i	1.17398	−	1.17398i	0.192723	−	0.981253i	$-0.438268\pi$
$797$	2.10526e7	−	2.10526e7i	1.17398	−	1.17398i	0.981253	−	0.192723i	$-0.0617320\pi$
$798$	2.79418e7	+	1.00672e6i	1.55327	+	0.0559632i
$799$	8.17032e6			0.452764
$800$	−1.35295e7	+	1.20263e7i	−0.747406	+	0.664367i
$801$	3.68338e6			0.202845
$802$	2.65342e7	+	956006.i	1.45670	+	0.0524837i
$803$	3.18801e6	−	3.18801e6i	0.174474	−	0.174474i
$804$	778470.	−	1.07893e7i	0.0424719	−	0.588644i
$805$	3.63887e7	−	1.77287e7i	1.97914	−	0.964242i
$806$	3.08175e6	−	2.86740e6i	0.167093	−	0.155472i
$807$	3.11276e7			1.68253
$808$	−1.81528e7	+	1.46003e7i	−0.978174	+	0.786745i
$809$			1.68174e7i			0.903417i	0.892166	+	0.451708i	$0.149185\pi$
$809$			1.68174e7i			0.903417i	−0.892166	+	0.451708i	$0.850815\pi$
$810$	2.10176e7	−	9.31903e6i	1.12557	−	0.499066i
$811$	1.71380e6	−	1.71380e6i	0.0914971	−	0.0914971i	−0.659877	−	0.751374i	$-0.729392\pi$
$811$	1.71380e6	−	1.71380e6i	0.0914971	−	0.0914971i	0.751374	+	0.659877i	$0.229392\pi$
$812$	−6.13977e6	−	7.09466e6i	−0.326785	−	0.377608i
$813$	1.19158e7	−	1.19158e7i	0.632260	−	0.632260i
$814$	2.80071e6	+	100908.i	0.148152	+	0.00533781i
$815$	5.16238e6	−	1.49718e7i	0.272242	−	0.789551i
$816$	−6.54567e6	−	8.76691e6i	−0.344135	−	0.460915i
$817$			1.41882e6i			0.0743655i
$818$	824304.	−	2.28787e7i	0.0430729	−	1.19550i
$819$	−7.64056e6	−	7.64056e6i	−0.398030	−	0.398030i
$820$	−1.10753e7	−	2.76222e7i	−0.575202	−	1.43458i
$821$	−1.76443e7	+	1.76443e7i	−0.913578	+	0.913578i	−0.996552	−	0.0829741i	$-0.973558\pi$
$821$	−1.76443e7	+	1.76443e7i	−0.913578	+	0.913578i	0.0829741	+	0.996552i	$0.473558\pi$
$822$	−1.78077e7	+	1.65691e7i	−0.919238	+	0.855303i
$823$	−4.29328e6			−0.220948			−0.110474	−	0.993879i	$-0.535237\pi$
$823$	−4.29328e6			−0.220948			−0.110474	+	0.993879i	$0.535237\pi$
$824$	6.70458e6	+	727201.i	0.343996	+	0.0373110i
$825$	−1.42104e7	−	1.11220e7i	−0.726895	−	0.568916i
$826$	−2.49149e7	+	2.31820e7i	−1.27060	+	1.18223i
$827$	4.77881e6	+	4.77881e6i	0.242972	+	0.242972i	0.818078	−	0.575107i	$-0.195039\pi$
$827$	4.77881e6	+	4.77881e6i	0.242972	+	0.242972i	−0.575107	+	0.818078i	$0.695039\pi$
$828$	942749.	−	1.30661e7i	0.0477881	−	0.662325i
$829$	3.70515e6	+	3.70515e6i	0.187249	+	0.187249i	0.794506	−	0.607257i	$-0.207730\pi$
$829$	3.70515e6	+	3.70515e6i	0.187249	+	0.187249i	−0.607257	+	0.794506i	$0.707730\pi$
$830$	−3.50806e6	+	9.09705e6i	−0.176755	+	0.458359i
$831$	−1.76081e7			−0.884523
$832$	−2.16625e7	+	1.38641e7i	−1.08493	+	0.694358i
$833$			4.42829e6i			0.221118i
$834$	434933.	−	1.20717e7i	0.0216524	−	0.600969i
$835$	−3.47675e7	+	1.69388e7i	−1.72567	+	0.840751i
$836$	1.76250e7	+	1.27168e6i	0.872195	+	0.0629307i
$837$	−1.88838e6	−	1.88838e6i	−0.0931700	−	0.0931700i
$838$	2.38453e7	+	2.56277e7i	1.17298	+	1.26067i
$839$			3.71942e7i			1.82419i	0.409978	+	0.912095i	$0.365536\pi$
$839$			3.71942e7i			1.82419i	−0.409978	+	0.912095i	$0.634464\pi$
$840$	1.22429e7	−	2.59999e7i	0.598666	−	1.27138i
$841$		−	1.69806e7i		−	0.827874i
$842$	−2.98077e7	+	2.77345e7i	−1.44893	+	1.34815i
$843$	−2.43937e7	−	2.43937e7i	−1.18225	−	1.18225i
$844$	−7.47737e6	−	8.64029e6i	−0.361321	−	0.417515i
$845$	5.99267e6	+	1.23002e7i	0.288721	+	0.592610i
$846$	6.94097e6	+	250078.i	0.333422	+	0.0120129i
$847$		−	9.42178e6i		−	0.451257i
$848$	1.83856e7	+	2.46247e7i	0.877989	+	1.17593i
$849$	−2.56057e7			−1.21918
$850$	−7.93701e6	−	6.68654e6i	−0.376799	−	0.317434i
$851$	5.12326e6	+	5.12326e6i	0.242506	+	0.242506i
$852$	2.80533e7	+	3.24163e7i	1.32399	+	1.52991i
$853$	−1.94038e7	−	1.94038e7i	−0.913094	−	0.913094i	0.0834208	−	0.996514i	$-0.473415\pi$
$853$	−1.94038e7	−	1.94038e7i	−0.913094	−	0.913094i	−0.996514	+	0.0834208i	$0.973415\pi$
$854$	−1.82086e7	−	1.95697e7i	−0.854342	−	0.918206i
$855$	2.79796e6	−	8.11458e6i	0.130896	−	0.379621i
$856$	−2.08125e6	−	2.58766e6i	−0.0970823	−	0.120704i
$857$	−3.12788e7			−1.45478			−0.727392	−	0.686222i	$-0.759268\pi$
$857$	−3.12788e7			−1.45478			−0.727392	+	0.686222i	$0.759268\pi$
$858$	−1.74649e7	−	1.87704e7i	−0.809930	−	0.870473i
$859$	−2.71538e7	+	2.71538e7i	−1.25559	+	1.25559i	−0.302410	+	0.953178i	$0.597791\pi$
$859$	−2.71538e7	+	2.71538e7i	−1.25559	+	1.25559i	−0.953178	+	0.302410i	$0.902209\pi$
$860$	1.34087e6	+	573352.i	0.0618217	+	0.0264347i
$861$	3.34080e7	+	3.34080e7i	1.53583	+	1.53583i
$862$	−9.91600e6	−	357266.i	−0.454536	−	0.0163766i
$863$			3.98719e7i			1.82239i	0.411979	+	0.911193i	$0.364838\pi$
$863$			3.98719e7i			1.82239i	−0.411979	+	0.911193i	$0.635162\pi$
$864$	9.28493e6	+	1.34177e7i	0.423150	+	0.611497i
$865$	4.92088e6	−	1.42714e7i	0.223616	−	0.648525i
$866$	593495.	−	1.64726e7i	0.0268919	−	0.746393i
$867$	−1.38367e7	+	1.38367e7i	−0.625153	+	0.625153i
$868$	−4.72183e6	−	340690.i	−0.212721	−	0.0153483i
$869$	1.66967e7	−	1.66967e7i	0.750034	−	0.750034i
$870$	−9.88566e6	+	4.38321e6i	−0.442800	+	0.196333i
$871$		−	1.45787e7i		−	0.651137i
$872$	−1.68336e7	−	2.09296e7i	−0.749699	−	0.932113i
$873$	−1.07362e7			−0.476777
$874$	3.11197e7	+	3.34459e7i	1.37802	+	1.48103i
$875$	5.70189e6	−	2.66569e7i	0.251767	−	1.17704i
$876$	6.25754e6	−	5.41531e6i	0.275514	−	0.238431i
$877$	−1.63696e7	+	1.63696e7i	−0.718685	+	0.718685i	−0.968336	−	0.249651i	$-0.919684\pi$
$877$	−1.63696e7	+	1.63696e7i	−0.718685	+	0.718685i	0.249651	+	0.968336i	$0.419684\pi$
$878$	800373.	−	2.22146e7i	0.0350394	−	0.972526i
$879$	2.79986e7			1.22226
$880$	8.32418e6	−	1.61428e7i	0.362355	−	0.702705i
$881$	2.72762e7			1.18398			0.591990	−	0.805946i	$-0.298343\pi$
$881$	2.72762e7			1.18398			0.591990	+	0.805946i	$0.298343\pi$
$882$	−135542.	+	3.76199e6i	−0.00586680	+	0.162835i
$883$	−9.03967e6	+	9.03967e6i	−0.390167	+	0.390167i	−0.874747	−	0.484580i	$-0.838973\pi$
$883$	−9.03967e6	+	9.03967e6i	−0.390167	+	0.390167i	0.484580	+	0.874747i	$0.338973\pi$
$884$	−9.64910e6	−	1.11498e7i	−0.415295	−	0.479884i
$885$	1.71793e7	+	3.52611e7i	0.737305	+	1.51334i
$886$	−2.66037e6	−	2.85923e6i	−0.113856	−	0.122367i
$887$	7.74189e6			0.330398			0.165199	−	0.986260i	$-0.447173\pi$
$887$	7.74189e6			0.330398			0.165199	+	0.986260i	$0.447173\pi$
$888$	5.11406e6	+	554688.i	0.217638	+	0.0236057i
$889$			1.27582e7i			0.541423i
$890$	5.35150e6	+	1.20695e7i	0.226465	+	0.510757i
$891$	−1.63116e7	+	1.63116e7i	−0.688341	+	0.688341i
$892$	1.65346e6	−	2.29163e7i	0.0695796	−	0.964346i
$893$	−1.71270e7	+	1.71270e7i	−0.718707	+	0.718707i
$894$	−194656.	+	5.40273e6i	−0.00814563	+	0.226084i
$895$	−3.15987e7	−	1.08954e7i	−1.31860	−	0.454661i
$896$	2.80108e7	+	7.21488e6i	1.16561	+	0.300234i
$897$		−	6.62841e7i		−	2.75061i
$898$	−2.08774e7	−	752198.i	−0.863945	−	0.0311273i
$899$	1.25963e6	+	1.25963e6i	0.0519808	+	0.0519808i
$900$	−6.53811e6	−	5.92339e6i	−0.269058	−	0.243761i
$901$	−1.24583e7	+	1.24583e7i	−0.511267	+	0.511267i
$902$	2.03401e7	+	2.18605e7i	0.832409	+	0.894633i
$903$	−2.31518e6			−0.0944854
$904$	2.60031e6	−	2.39741e7i	0.105829	−	0.975710i
$905$	−1.22304e7	+	3.54705e7i	−0.496388	+	1.43961i
$906$	6.11301e6	+	6.56996e6i	0.247420	+	0.265915i
$907$	−5.96341e6	−	5.96341e6i	−0.240700	−	0.240700i	0.576440	−	0.817140i	$-0.304442\pi$
$907$	−5.96341e6	−	5.96341e6i	−0.240700	−	0.240700i	−0.817140	+	0.576440i	$0.804442\pi$
$908$	7.15797e6	−	6.19455e6i	0.288121	−	0.249342i
$909$	−8.02825e6	−	8.02825e6i	−0.322264	−	0.322264i
$910$	1.39354e7	−	3.61370e7i	0.557848	−	1.44660i
$911$	1.46667e6			0.0585511			0.0292756	−	0.999571i	$-0.490680\pi$
$911$	1.46667e6			0.0585511			0.0292756	+	0.999571i	$0.490680\pi$
$912$	3.20989e7	+	4.65625e6i	1.27792	+	0.185374i
$913$		−	9.78274e6i		−	0.388404i
$914$	−3.08906e7	−	1.11296e6i	−1.22310	−	0.0440672i
$915$	−2.76963e7	+	1.34937e7i	−1.09363	+	0.532817i
$916$	1.25685e7	−	1.08769e7i	0.494931	−	0.428317i
$917$	2.64457e7	+	2.64457e7i	1.03856	+	1.03856i
$918$	−6.84875e6	+	6.37240e6i	−0.268228	+	0.249572i
$919$		−	1.85939e7i		−	0.726242i	−0.931742	−	0.363121i	$-0.881711\pi$
$919$		−	1.85939e7i		−	0.726242i	0.931742	−	0.363121i	$-0.118289\pi$
$920$	4.41841e7	−	1.58944e7i	1.72106	−	0.619118i
$921$			3.35702e6i			0.130408i
$922$	−7.63494e6	−	8.20566e6i	−0.295786	−	0.317897i
$923$	4.08538e7	+	4.08538e7i	1.57844	+	1.57844i
$924$	−2.07509e6	+	2.87599e7i	−0.0799569	+	1.10817i
$925$	4.84358e6	−	590508.i	0.186128	−	0.0226919i
$926$	−202168.	+	5.61121e6i	−0.00774790	+	0.215045i
$927$			3.28677e6i			0.125623i
$928$	−6.19343e6	−	8.95018e6i	−0.236081	−	0.341163i
$929$	−3.10394e7			−1.17998			−0.589989	−	0.807412i	$-0.700868\pi$
$929$	−3.10394e7			−1.17998			−0.589989	+	0.807412i	$0.700868\pi$
$930$	−1.96318e6	+	5.09090e6i	−0.0744310	+	0.193013i
$931$	−9.28279e6	−	9.28279e6i	−0.350998	−	0.350998i
$932$	1.02314e7	+	738221.i	0.385831	+	0.0278385i
$933$	−2.94887e7	−	2.94887e7i	−1.10905	−	1.10905i
$934$	−1.63047e7	+	1.51706e7i	−0.611567	+	0.569031i
$935$	9.84421e6	+	3.39435e6i	0.368258	+	0.126978i
$936$	−7.85598e6	−	9.76748e6i	−0.293097	−	0.364412i
$937$	−2.30456e6			−0.0857511			−0.0428756	−	0.999080i	$-0.513652\pi$
$937$	−2.30456e6			−0.0857511			−0.0428756	+	0.999080i	$0.513652\pi$
$938$	−1.20035e7	+	1.11687e7i	−0.445453	+	0.414471i
$939$	2.65064e7	−	2.65064e7i	0.981040	−	0.981040i
$940$	9.26496e6	+	2.31072e7i	0.341998	+	0.852957i
$941$	−1.50994e7	−	1.50994e7i	−0.555884	−	0.555884i	0.372249	−	0.928133i	$-0.378587\pi$
$941$	−1.50994e7	−	1.50994e7i	−0.555884	−	0.555884i	−0.928133	+	0.372249i	$0.878587\pi$
$942$	−288853.	+	8.01720e6i	−0.0106060	+	0.294371i
$943$			7.71964e7i			2.82695i
$944$	−3.16337e7	+	2.36188e7i	−1.15537	+	0.862638i
$945$	−2.32298e7	−	8.00980e6i	−0.846188	−	0.291771i
$946$	−1.46225e6	−	52683.9i	−0.0531245	−	0.00191404i
$947$	−3.42886e7	+	3.42886e7i	−1.24244	+	1.24244i	−0.283450	+	0.958987i	$0.591479\pi$
$947$	−3.42886e7	+	3.42886e7i	−1.24244	+	1.24244i	−0.958987	+	0.283450i	$0.908521\pi$
$948$	3.27729e7	−	2.83619e7i	1.18439	−	1.02498i
$949$	7.88627e6	−	7.88627e6i	0.284254	−	0.284254i
$950$	3.06545e7	−	2.62129e6i	1.10201	−	0.0942337i
$951$		−	3.74292e7i		−	1.34202i
$952$	−1.78818e6	+	1.64865e7i	−0.0639469	+	0.589572i
$953$	5.12032e7			1.82627			0.913134	−	0.407660i	$-0.133655\pi$
$953$	5.12032e7			1.82627			0.913134	+	0.407660i	$0.133655\pi$
$954$	−1.09651e7	+	1.02025e7i	−0.390070	+	0.362939i
$955$	−4.41269e7	+	2.14987e7i	−1.56565	+	0.762789i
$956$	1.24799e7	+	900448.i	0.441636	+	0.0318650i
$957$	7.67219e6	−	7.67219e6i	0.270794	−	0.270794i
$958$	2.55806e7	+	921650.i	0.900528	+	0.0324453i
$959$	3.68677e7			1.29449
$960$	1.73718e7	−	2.84539e7i	0.608368	−	0.996467i
$961$	−2.77303e7			−0.968604
$962$	6.92822e6	+	249618.i	0.241370	+	0.00869639i
$963$	1.14441e6	−	1.14441e6i	0.0397665	−	0.0397665i
$964$	−3.56691e7	−	2.57360e6i	−1.23623	−	0.0891968i
$965$	1.50454e7	+	3.08811e7i	0.520097	+	1.06752i
$966$	−5.45759e7	+	5.07800e7i	−1.88173	+	1.75085i
$967$	−9.31009e6			−0.320175			−0.160088	−	0.987103i	$-0.551178\pi$
$967$	−9.31009e6			−0.320175			−0.160088	+	0.987103i	$0.551178\pi$
$968$	1.17856e6	−	1.08660e7i	0.0404262	−	0.372718i
$969$			1.85955e7i			0.636206i
$970$	−1.55984e7	−	3.51799e7i	−0.532293	−	1.20051i
$971$	−1.54594e7	+	1.54594e7i	−0.526193	+	0.526193i	−0.919435	−	0.393242i	$-0.871354\pi$
$971$	−1.54594e7	+	1.54594e7i	−0.526193	+	0.526193i	0.393242	+	0.919435i	$0.371354\pi$
$972$	−1.54542e7	+	1.33742e7i	−0.524664	+	0.454048i
$973$	−1.29463e7	+	1.29463e7i	−0.438395	+	0.438395i
$974$	−9.84945e6	−	354868.i	−0.332671	−	0.0119859i
$975$	−3.51528e7	−	2.75129e7i	−1.18426	−	0.926882i
$976$	−1.85517e7	−	2.48471e7i	−0.623390	−	0.834933i
$977$			1.91182e7i			0.640781i	0.947286	+	0.320390i	$0.103814\pi$
$977$			1.91182e7i			0.640781i	−0.947286	+	0.320390i	$0.896186\pi$
$978$	−1.05015e6	+	2.91472e7i	−0.0351079	+	0.974428i
$979$	−9.36706e6	−	9.36706e6i	−0.312353	−	0.312353i
$980$	−1.25240e7	+	5.02159e6i	−0.416562	+	0.167023i
$981$	9.25628e6	−	9.25628e6i	0.307089	−	0.307089i
$982$	−1.24043e7	+	1.15415e7i	−0.410481	+	0.381931i
$983$	−1.50993e7			−0.498393			−0.249196	−	0.968453i	$-0.580166\pi$
$983$	−1.50993e7			−0.498393			−0.249196	+	0.968453i	$0.580166\pi$
$984$	3.43499e7	+	4.27079e7i	1.13094	+	1.40611i
$985$	1.49666e7	+	5.16057e6i	0.491509	+	0.169476i
$986$	4.56840e6	−	4.25065e6i	0.149648	−	0.139240i
$987$	−2.79472e7	−	2.79472e7i	−0.913157	−	0.913157i
$988$	4.35996e7	+	3.14580e6i	1.42099	+	0.102527i
$989$	−2.67486e6	−	2.67486e6i	−0.0869581	−	0.0869581i
$990$	8.25911e6	+	3.18493e6i	0.267821	+	0.103279i
$991$	9.68813e6			0.313369			0.156684	−	0.987649i	$-0.449919\pi$
$991$	9.68813e6			0.313369			0.156684	+	0.987649i	$0.449919\pi$
$992$	−5.40299e6	−	983561.i	−0.174323	−	0.0317338i
$993$			1.15943e7i			0.373140i
$994$	2.33957e6	−	6.49354e7i	0.0751053	−	2.08457i
$995$	1.00579e7	+	2.06441e7i	0.322069	+	0.661057i
$996$	1.29222e6	−	1.79097e7i	0.0412752	−	0.572058i
$997$	−2.01669e7	−	2.01669e7i	−0.642543	−	0.642543i	0.308637	−	0.951180i	$-0.400127\pi$
$997$	−2.01669e7	−	2.01669e7i	−0.642543	−	0.642543i	−0.951180	+	0.308637i	$0.900127\pi$
$998$	1.69551e7	+	1.82226e7i	0.538859	+	0.579139i
$999$		−	4.39832e6i		−	0.139435i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.q.a.29.1	✓	116
5.4	even	2	inner	80.6.q.a.29.58	yes	116
16.5	even	4	inner	80.6.q.a.69.58	yes	116
80.69	even	4	inner	80.6.q.a.69.1	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.q.a.29.1	✓	116	1.1	even	1	trivial
80.6.q.a.29.58	yes	116	5.4	even	2	inner
80.6.q.a.69.1	yes	116	80.69	even	4	inner
80.6.q.a.69.58	yes	116	16.5	even	4	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65319 - 0.203680i) q^{2} +(-12.8690 + 12.8690i) q^{3} +(31.9170 + 2.30288i) q^{4} +(-50.2546 + 24.4842i) q^{5} +(75.3721 - 70.1298i) q^{6} -156.045 q^{7} +(-179.964 - 19.5195i) q^{8} -88.2233i q^{9} +O(q^{10})\)	\(q+(-5.65319 - 0.203680i) q^{2} +(-12.8690 + 12.8690i) q^{3} +(31.9170 + 2.30288i) q^{4} +(-50.2546 + 24.4842i) q^{5} +(75.3721 - 70.1298i) q^{6} -156.045 q^{7} +(-179.964 - 19.5195i) q^{8} -88.2233i q^{9} +(289.086 - 128.178i) q^{10} +(-224.357 + 224.357i) q^{11} +(-440.377 + 381.105i) q^{12} +(-555.000 + 555.000i) q^{13} +(882.150 + 31.7832i) q^{14} +(331.640 - 961.815i) q^{15} +(1013.39 + 147.002i) q^{16} +587.077i q^{17} +(-17.9693 + 498.743i) q^{18} +(-1230.66 - 1230.66i) q^{19} +(-1660.36 + 665.732i) q^{20} +(2008.14 - 2008.14i) q^{21} +(1314.03 - 1222.64i) q^{22} +4640.25 q^{23} +(2567.15 - 2064.76i) q^{24} +(1926.05 - 2460.89i) q^{25} +(3250.56 - 3024.48i) q^{26} +(-1991.82 - 1991.82i) q^{27} +(-4980.48 - 359.352i) q^{28} +(1328.63 + 1328.63i) q^{29} +(-2070.73 + 5369.77i) q^{30} +948.066 q^{31} +(-5698.96 - 1037.44i) q^{32} -5774.51i q^{33} +(119.576 - 3318.85i) q^{34} +(7841.97 - 3820.63i) q^{35} +(203.168 - 2815.82i) q^{36} +(1104.09 + 1104.09i) q^{37} +(6706.47 + 7207.79i) q^{38} -14284.6i q^{39} +(9521.93 - 3425.32i) q^{40} +16636.3i q^{41} +(-11761.4 + 10943.4i) q^{42} +(-576.447 - 576.447i) q^{43} +(-7677.48 + 6644.15i) q^{44} +(2160.07 + 4433.62i) q^{45} +(-26232.2 - 945.125i) q^{46} -13916.9i q^{47} +(-14933.2 + 11149.6i) q^{48} +7542.96 q^{49} +(-11389.6 + 13519.5i) q^{50} +(-7555.10 - 7555.10i) q^{51} +(-18992.0 + 16435.8i) q^{52} +(21220.9 + 21220.9i) q^{53} +(10854.5 + 11665.9i) q^{54} +(5781.78 - 16768.2i) q^{55} +(28082.4 + 3045.91i) q^{56} +31674.7 q^{57} +(-7240.37 - 7781.60i) q^{58} +(-27261.2 + 27261.2i) q^{59} +(12799.9 - 29934.5i) q^{60} +(-21412.6 - 21412.6i) q^{61} +(-5359.59 - 193.102i) q^{62} +13766.8i q^{63} +(32006.0 + 7025.60i) q^{64} +(14302.6 - 41480.0i) q^{65} +(-1176.15 + 32644.4i) q^{66} +(-13133.9 + 13133.9i) q^{67} +(-1351.97 + 18737.7i) q^{68} +(-59715.4 + 59715.4i) q^{69} +(-45110.3 + 20001.5i) q^{70} -73610.4i q^{71} +(-1722.07 + 15877.0i) q^{72} -14209.5 q^{73} +(-6016.76 - 6466.52i) q^{74} +(6882.81 + 56455.5i) q^{75} +(-36444.8 - 42112.9i) q^{76} +(35009.8 - 35009.8i) q^{77} +(-2909.49 + 80753.5i) q^{78} -74420.1 q^{79} +(-54526.9 + 17424.6i) q^{80} +72703.9 q^{81} +(3388.47 - 94047.9i) q^{82} +(-21801.7 + 21801.7i) q^{83} +(68718.5 - 59469.4i) q^{84} +(-14374.1 - 29503.3i) q^{85} +(3141.35 + 3376.18i) q^{86} -34196.3 q^{87} +(44755.5 - 35996.9i) q^{88} +41750.6i q^{89} +(-11308.3 - 25504.1i) q^{90} +(86604.8 - 86604.8i) q^{91} +(148103. + 10685.9i) q^{92} +(-12200.7 + 12200.7i) q^{93} +(-2834.60 + 78675.1i) q^{94} +(91977.7 + 31714.5i) q^{95} +(86690.8 - 59989.2i) q^{96} -121694. i q^{97} +(-42641.7 - 1536.35i) q^{98} +(19793.5 + 19793.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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