LMFDB - Embedded newform 10.7.c.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,7,Mod(3,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("10.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	10.c (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:	$2.30054083620$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	10.3
Dual form			10.7.c.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 + 4.00000i) q^{2} +(-23.0000 - 23.0000i) q^{3} -32.0000i q^{4} +(-75.0000 - 100.000i) q^{5} +184.000 q^{6} +(-247.000 + 247.000i) q^{7} +(128.000 + 128.000i) q^{8} +329.000i q^{9} +(700.000 + 100.000i) q^{10} +1402.00 q^{11} +(-736.000 + 736.000i) q^{12} +(-2703.00 - 2703.00i) q^{13} -1976.00i q^{14} +(-575.000 + 4025.00i) q^{15} -1024.00 q^{16} +(2593.00 - 2593.00i) q^{17} +(-1316.00 - 1316.00i) q^{18} -1720.00i q^{19} +(-3200.00 + 2400.00i) q^{20} +11362.0 q^{21} +(-5608.00 + 5608.00i) q^{22} +(2137.00 + 2137.00i) q^{23} -5888.00i q^{24} +(-4375.00 + 15000.0i) q^{25} +21624.0 q^{26} +(-9200.00 + 9200.00i) q^{27} +(7904.00 + 7904.00i) q^{28} -30520.0i q^{29} +(-13800.0 - 18400.0i) q^{30} -37838.0 q^{31} +(4096.00 - 4096.00i) q^{32} +(-32246.0 - 32246.0i) q^{33} +20744.0i q^{34} +(43225.0 + 6175.00i) q^{35} +10528.0 q^{36} +(37113.0 - 37113.0i) q^{37} +(6880.00 + 6880.00i) q^{38} +124338. i q^{39} +(3200.00 - 22400.0i) q^{40} -35438.0 q^{41} +(-45448.0 + 45448.0i) q^{42} +(39177.0 + 39177.0i) q^{43} -44864.0i q^{44} +(32900.0 - 24675.0i) q^{45} -17096.0 q^{46} +(95193.0 - 95193.0i) q^{47} +(23552.0 + 23552.0i) q^{48} -4369.00i q^{49} +(-42500.0 - 77500.0i) q^{50} -119278. q^{51} +(-86496.0 + 86496.0i) q^{52} +(36017.0 + 36017.0i) q^{53} -73600.0i q^{54} +(-105150. - 140200. i) q^{55} -63232.0 q^{56} +(-39560.0 + 39560.0i) q^{57} +(122080. + 122080. i) q^{58} +35960.0i q^{59} +(128800. + 18400.0i) q^{60} +83322.0 q^{61} +(151352. - 151352. i) q^{62} +(-81263.0 - 81263.0i) q^{63} +32768.0i q^{64} +(-67575.0 + 473025. i) q^{65} +257968. q^{66} +(60833.0 - 60833.0i) q^{67} +(-82976.0 - 82976.0i) q^{68} -98302.0i q^{69} +(-197600. + 148200. i) q^{70} -40318.0 q^{71} +(-42112.0 + 42112.0i) q^{72} +(-129023. - 129023. i) q^{73} +296904. i q^{74} +(445625. - 244375. i) q^{75} -55040.0 q^{76} +(-346294. + 346294. i) q^{77} +(-497352. - 497352. i) q^{78} -524640. i q^{79} +(76800.0 + 102400. i) q^{80} +663041. q^{81} +(141752. - 141752. i) q^{82} +(-114423. - 114423. i) q^{83} -363584. i q^{84} +(-453775. - 64825.0i) q^{85} -313416. q^{86} +(-701960. + 701960. i) q^{87} +(179456. + 179456. i) q^{88} -187280. i q^{89} +(-32900.0 + 230300. i) q^{90} +1.33528e6 q^{91} +(68384.0 - 68384.0i) q^{92} +(870274. + 870274. i) q^{93} +761544. i q^{94} +(-172000. + 129000. i) q^{95} -188416. q^{96} +(532833. - 532833. i) q^{97} +(17476.0 + 17476.0i) q^{98} +461258. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} - 46 q^{3} - 150 q^{5} + 368 q^{6} - 494 q^{7} + 256 q^{8} + 1400 q^{10} + 2804 q^{11} - 1472 q^{12} - 5406 q^{13} - 1150 q^{15} - 2048 q^{16} + 5186 q^{17} - 2632 q^{18} - 6400 q^{20} + 22724 q^{21}+ \cdots + 34952 q^{98}+O(q^{100}) $ 2 * q - 8 * q^2 - 46 * q^3 - 150 * q^5 + 368 * q^6 - 494 * q^7 + 256 * q^8 + 1400 * q^10 + 2804 * q^11 - 1472 * q^12 - 5406 * q^13 - 1150 * q^15 - 2048 * q^16 + 5186 * q^17 - 2632 * q^18 - 6400 * q^20 + 22724 * q^21 - 11216 * q^22 + 4274 * q^23 - 8750 * q^25 + 43248 * q^26 - 18400 * q^27 + 15808 * q^28 - 27600 * q^30 - 75676 * q^31 + 8192 * q^32 - 64492 * q^33 + 86450 * q^35 + 21056 * q^36 + 74226 * q^37 + 13760 * q^38 + 6400 * q^40 - 70876 * q^41 - 90896 * q^42 + 78354 * q^43 + 65800 * q^45 - 34192 * q^46 + 190386 * q^47 + 47104 * q^48 - 85000 * q^50 - 238556 * q^51 - 172992 * q^52 + 72034 * q^53 - 210300 * q^55 - 126464 * q^56 - 79120 * q^57 + 244160 * q^58 + 257600 * q^60 + 166644 * q^61 + 302704 * q^62 - 162526 * q^63 - 135150 * q^65 + 515936 * q^66 + 121666 * q^67 - 165952 * q^68 - 395200 * q^70 - 80636 * q^71 - 84224 * q^72 - 258046 * q^73 + 891250 * q^75 - 110080 * q^76 - 692588 * q^77 - 994704 * q^78 + 153600 * q^80 + 1326082 * q^81 + 283504 * q^82 - 228846 * q^83 - 907550 * q^85 - 626832 * q^86 - 1403920 * q^87 + 358912 * q^88 - 65800 * q^90 + 2670564 * q^91 + 136768 * q^92 + 1740548 * q^93 - 344000 * q^95 - 376832 * q^96 + 1065666 * q^97 + 34952 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−4.00000	+	4.00000i	−0.500000	+	0.500000i
$2$	−4.00000	+	4.00000i	−0.500000	+	0.500000i
$3$	−23.0000	−	23.0000i	−0.851852	−	0.851852i	0.138509	−	0.990361i	$-0.455769\pi$
$3$	−23.0000	−	23.0000i	−0.851852	−	0.851852i	−0.990361	+	0.138509i	$0.955769\pi$
$4$		−	32.0000i		−	0.500000i
$5$	−75.0000	−	100.000i	−0.600000	−	0.800000i
$5$	−75.0000	−	100.000i	−0.600000	−	0.800000i
$6$	184.000			0.851852
$7$	−247.000	+	247.000i	−0.720117	+	0.720117i	−0.968629	−	0.248512i	$-0.920058\pi$
$7$	−247.000	+	247.000i	−0.720117	+	0.720117i	0.248512	+	0.968629i	$0.420058\pi$
$8$	128.000	+	128.000i	0.250000	+	0.250000i
$9$			329.000i			0.451303i
$10$	700.000	+	100.000i	0.700000	+	0.100000i
$11$	1402.00			1.05334			0.526672	−	0.850069i	$-0.323440\pi$
$11$	1402.00			1.05334			0.526672	+	0.850069i	$0.323440\pi$
$12$	−736.000	+	736.000i	−0.425926	+	0.425926i
$13$	−2703.00	−	2703.00i	−1.23031	−	1.23031i	−0.963843	−	0.266471i	$-0.914142\pi$
$13$	−2703.00	−	2703.00i	−1.23031	−	1.23031i	−0.266471	−	0.963843i	$-0.585858\pi$
$14$		−	1976.00i		−	0.720117i
$15$	−575.000	+	4025.00i	−0.170370	+	1.19259i
$16$	−1024.00			−0.250000
$17$	2593.00	−	2593.00i	0.527783	−	0.527783i	−0.392127	−	0.919911i	$-0.628261\pi$
$17$	2593.00	−	2593.00i	0.527783	−	0.527783i	0.919911	+	0.392127i	$0.128261\pi$
$18$	−1316.00	−	1316.00i	−0.225652	−	0.225652i
$19$		−	1720.00i		−	0.250765i	−0.992108	−	0.125383i	$-0.959984\pi$
$19$		−	1720.00i		−	0.250765i	0.992108	−	0.125383i	$-0.0400159\pi$
$20$	−3200.00	+	2400.00i	−0.400000	+	0.300000i
$21$	11362.0			1.22687
$22$	−5608.00	+	5608.00i	−0.526672	+	0.526672i
$23$	2137.00	+	2137.00i	0.175639	+	0.175639i	0.789452	−	0.613813i	$-0.210365\pi$
$23$	2137.00	+	2137.00i	0.175639	+	0.175639i	−0.613813	+	0.789452i	$0.710365\pi$
$24$		−	5888.00i		−	0.425926i
$25$	−4375.00	+	15000.0i	−0.280000	+	0.960000i
$26$	21624.0			1.23031
$27$	−9200.00	+	9200.00i	−0.467408	+	0.467408i
$28$	7904.00	+	7904.00i	0.360058	+	0.360058i
$29$		−	30520.0i		−	1.25138i	−0.780070	−	0.625692i	$-0.784817\pi$
$29$		−	30520.0i		−	1.25138i	0.780070	−	0.625692i	$-0.215183\pi$
$30$	−13800.0	−	18400.0i	−0.511111	−	0.681481i
$31$	−37838.0			−1.27012			−0.635058	−	0.772465i	$-0.719024\pi$
$31$	−37838.0			−1.27012			−0.635058	+	0.772465i	$0.719024\pi$
$32$	4096.00	−	4096.00i	0.125000	−	0.125000i
$33$	−32246.0	−	32246.0i	−0.897292	−	0.897292i
$34$			20744.0i			0.527783i
$35$	43225.0	+	6175.00i	1.00816	+	0.144023i
$36$	10528.0			0.225652
$37$	37113.0	−	37113.0i	0.732691	−	0.732691i	−0.238461	−	0.971152i	$-0.576643\pi$
$37$	37113.0	−	37113.0i	0.732691	−	0.732691i	0.971152	+	0.238461i	$0.0766429\pi$
$38$	6880.00	+	6880.00i	0.125383	+	0.125383i
$39$			124338.i			2.09609i
$40$	3200.00	−	22400.0i	0.0500000	−	0.350000i
$41$	−35438.0			−0.514183			−0.257091	−	0.966387i	$-0.582764\pi$
$41$	−35438.0			−0.514183			−0.257091	+	0.966387i	$0.582764\pi$
$42$	−45448.0	+	45448.0i	−0.613433	+	0.613433i
$43$	39177.0	+	39177.0i	0.492749	+	0.492749i	0.909171	−	0.416422i	$-0.136716\pi$
$43$	39177.0	+	39177.0i	0.492749	+	0.492749i	−0.416422	+	0.909171i	$0.636716\pi$
$44$		−	44864.0i		−	0.526672i
$45$	32900.0	−	24675.0i	0.361043	−	0.270782i
$46$	−17096.0			−0.175639
$47$	95193.0	−	95193.0i	0.916878	−	0.916878i	−0.0799233	−	0.996801i	$-0.525468\pi$
$47$	95193.0	−	95193.0i	0.916878	−	0.916878i	0.996801	+	0.0799233i	$0.0254675\pi$
$48$	23552.0	+	23552.0i	0.212963	+	0.212963i
$49$		−	4369.00i		−	0.0371359i
$50$	−42500.0	−	77500.0i	−0.340000	−	0.620000i
$51$	−119278.			−0.899187
$52$	−86496.0	+	86496.0i	−0.615157	+	0.615157i
$53$	36017.0	+	36017.0i	0.241925	+	0.241925i	0.817646	−	0.575721i	$-0.195279\pi$
$53$	36017.0	+	36017.0i	0.241925	+	0.241925i	−0.575721	+	0.817646i	$0.695279\pi$
$54$		−	73600.0i		−	0.467408i
$55$	−105150.	−	140200.i	−0.632006	−	0.842675i
$56$	−63232.0			−0.360058
$57$	−39560.0	+	39560.0i	−0.213615	+	0.213615i
$58$	122080.	+	122080.i	0.625692	+	0.625692i
$59$			35960.0i			0.175091i	0.996161	+	0.0875455i	$0.0279023\pi$
$59$			35960.0i			0.175091i	−0.996161	+	0.0875455i	$0.972098\pi$
$60$	128800.	+	18400.0i	0.596296	+	0.0851852i
$61$	83322.0			0.367088			0.183544	−	0.983011i	$-0.441243\pi$
$61$	83322.0			0.367088			0.183544	+	0.983011i	$0.441243\pi$
$62$	151352.	−	151352.i	0.635058	−	0.635058i
$63$	−81263.0	−	81263.0i	−0.324991	−	0.324991i
$64$			32768.0i			0.125000i
$65$	−67575.0	+	473025.i	−0.246063	+	1.72244i
$66$	257968.			0.897292
$67$	60833.0	−	60833.0i	0.202262	−	0.202262i	−0.598706	−	0.800969i	$-0.704318\pi$
$67$	60833.0	−	60833.0i	0.202262	−	0.202262i	0.800969	+	0.598706i	$0.204318\pi$
$68$	−82976.0	−	82976.0i	−0.263892	−	0.263892i
$69$		−	98302.0i		−	0.299237i
$70$	−197600.	+	148200.i	−0.576093	+	0.432070i
$71$	−40318.0			−0.112648			−0.0563241	−	0.998413i	$-0.517938\pi$
$71$	−40318.0			−0.112648			−0.0563241	+	0.998413i	$0.517938\pi$
$72$	−42112.0	+	42112.0i	−0.112826	+	0.112826i
$73$	−129023.	−	129023.i	−0.331664	−	0.331664i	0.521554	−	0.853218i	$-0.325352\pi$
$73$	−129023.	−	129023.i	−0.331664	−	0.331664i	−0.853218	+	0.521554i	$0.825352\pi$
$74$			296904.i			0.732691i
$75$	445625.	−	244375.i	1.05630	−	0.579259i
$76$	−55040.0			−0.125383
$77$	−346294.	+	346294.i	−0.758530	+	0.758530i
$78$	−497352.	−	497352.i	−1.04805	−	1.04805i
$79$		−	524640.i		−	1.06409i	−0.846715	−	0.532047i	$-0.821423\pi$
$79$		−	524640.i		−	1.06409i	0.846715	−	0.532047i	$-0.178577\pi$
$80$	76800.0	+	102400.i	0.150000	+	0.200000i
$81$	663041.			1.24763
$82$	141752.	−	141752.i	0.257091	−	0.257091i
$83$	−114423.	−	114423.i	−0.200115	−	0.200115i	0.599934	−	0.800049i	$-0.295193\pi$
$83$	−114423.	−	114423.i	−0.200115	−	0.200115i	−0.800049	+	0.599934i	$0.795193\pi$
$84$		−	363584.i		−	0.613433i
$85$	−453775.	−	64825.0i	−0.738897	−	0.105557i
$86$	−313416.			−0.492749
$87$	−701960.	+	701960.i	−1.06599	+	1.06599i
$88$	179456.	+	179456.i	0.263336	+	0.263336i
$89$		−	187280.i		−	0.265657i	−0.991139	−	0.132829i	$-0.957594\pi$
$89$		−	187280.i		−	0.265657i	0.991139	−	0.132829i	$-0.0424060\pi$
$90$	−32900.0	+	230300.i	−0.0451303	+	0.315912i
$91$	1.33528e6			1.77194
$92$	68384.0	−	68384.0i	0.0878195	−	0.0878195i
$93$	870274.	+	870274.i	1.08195	+	1.08195i
$94$			761544.i			0.916878i
$95$	−172000.	+	129000.i	−0.200612	+	0.150459i
$96$	−188416.			−0.212963
$97$	532833.	−	532833.i	0.583816	−	0.583816i	−0.352134	−	0.935950i	$-0.614544\pi$
$97$	532833.	−	532833.i	0.583816	−	0.583816i	0.935950	+	0.352134i	$0.114544\pi$
$98$	17476.0	+	17476.0i	0.0185679	+	0.0185679i
$99$			461258.i			0.475377i
$100$	480000.	+	140000.i	0.480000	+	0.140000i
$101$	−1.70508e6			−1.65493			−0.827466	−	0.561516i	$-0.810218\pi$
$101$	−1.70508e6			−1.65493			−0.827466	+	0.561516i	$0.810218\pi$
$102$	477112.	−	477112.i	0.449593	−	0.449593i
$103$	−665063.	−	665063.i	−0.608627	−	0.608627i	0.333960	−	0.942587i	$-0.391615\pi$
$103$	−665063.	−	665063.i	−0.608627	−	0.608627i	−0.942587	+	0.333960i	$0.891615\pi$
$104$		−	691968.i		−	0.615157i
$105$	−852150.	−	1.13620e6i	−0.736119	−	0.981492i
$106$	−288136.			−0.241925
$107$	309073.	−	309073.i	0.252296	−	0.252296i	−0.569616	−	0.821911i	$-0.692908\pi$
$107$	309073.	−	309073.i	0.252296	−	0.252296i	0.821911	+	0.569616i	$0.192908\pi$
$108$	294400.	+	294400.i	0.233704	+	0.233704i
$109$			362440.i			0.279870i	0.990161	+	0.139935i	$0.0446894\pi$
$109$			362440.i			0.279870i	−0.990161	+	0.139935i	$0.955311\pi$
$110$	981400.	+	140200.i	0.737340	+	0.105334i
$111$	−1.70720e6			−1.24829
$112$	252928.	−	252928.i	0.180029	−	0.180029i
$113$	722657.	+	722657.i	0.500838	+	0.500838i	0.911698	−	0.410861i	$-0.134772\pi$
$113$	722657.	+	722657.i	0.500838	+	0.500838i	−0.410861	+	0.911698i	$0.634772\pi$
$114$		−	316480.i		−	0.213615i
$115$	53425.0	−	373975.i	0.0351278	−	0.245895i
$116$	−976640.			−0.625692
$117$	889287.	−	889287.i	0.555245	−	0.555245i
$118$	−143840.	−	143840.i	−0.0875455	−	0.0875455i
$119$			1.28094e6i			0.760131i
$120$	−588800.	+	441600.i	−0.340741	+	0.255556i
$121$	194043.			0.109532
$122$	−333288.	+	333288.i	−0.183544	+	0.183544i
$123$	815074.	+	815074.i	0.438008	+	0.438008i
$124$			1.21082e6i			0.635058i
$125$	1.82812e6	−	687500.i	0.936000	−	0.352000i
$126$	650104.			0.324991
$127$	−1.94641e6	+	1.94641e6i	−0.950216	+	0.950216i	−0.998818	−	0.0486019i	$-0.984523\pi$
$127$	−1.94641e6	+	1.94641e6i	−0.950216	+	0.950216i	0.0486019	+	0.998818i	$0.484523\pi$
$128$	−131072.	−	131072.i	−0.0625000	−	0.0625000i
$129$		−	1.80214e6i		−	0.839498i
$130$	−1.62180e6	−	2.16240e6i	−0.738188	−	0.984251i
$131$	3.75620e6			1.67084			0.835420	−	0.549612i	$-0.185224\pi$
$131$	3.75620e6			1.67084			0.835420	+	0.549612i	$0.185224\pi$
$132$	−1.03187e6	+	1.03187e6i	−0.448646	+	0.448646i
$133$	424840.	+	424840.i	0.180580	+	0.180580i
$134$			486664.i			0.202262i
$135$	1.61000e6	+	230000.i	0.654372	+	0.0934817i
$136$	663808.			0.263892
$137$	1.04283e6	−	1.04283e6i	0.405558	−	0.405558i	−0.474628	−	0.880186i	$-0.657417\pi$
$137$	1.04283e6	−	1.04283e6i	0.405558	−	0.405558i	0.880186	+	0.474628i	$0.157417\pi$
$138$	393208.	+	393208.i	0.149618	+	0.149618i
$139$			3.24700e6i			1.20903i	0.796593	+	0.604516i	$0.206634\pi$
$139$			3.24700e6i			1.20903i	−0.796593	+	0.604516i	$0.793366\pi$
$140$	197600.	−	1.38320e6i	0.0720117	−	0.504082i
$141$	−4.37888e6			−1.56209
$142$	161272.	−	161272.i	0.0563241	−	0.0563241i
$143$	−3.78961e6	−	3.78961e6i	−1.29594	−	1.29594i
$144$		−	336896.i		−	0.112826i
$145$	−3.05200e6	+	2.28900e6i	−1.00111	+	0.750830i
$146$	1.03218e6			0.331664
$147$	−100487.	+	100487.i	−0.0316343	+	0.0316343i
$148$	−1.18762e6	−	1.18762e6i	−0.366346	−	0.366346i
$149$		−	5.76420e6i		−	1.74253i	−0.490813	−	0.871265i	$-0.663300\pi$
$149$		−	5.76420e6i		−	1.74253i	0.490813	−	0.871265i	$-0.336700\pi$
$150$	−805000.	+	2.76000e6i	−0.238519	+	0.817778i
$151$	1.03280e6			0.299976			0.149988	−	0.988688i	$-0.452077\pi$
$151$	1.03280e6			0.299976			0.149988	+	0.988688i	$0.452077\pi$
$152$	220160.	−	220160.i	0.0626914	−	0.0626914i
$153$	853097.	+	853097.i	0.238190	+	0.238190i
$154$		−	2.77035e6i		−	0.758530i
$155$	2.83785e6	+	3.78380e6i	0.762069	+	1.01609i
$156$	3.97882e6			1.04805
$157$	2.30055e6	−	2.30055e6i	0.594475	−	0.594475i	−0.344362	−	0.938837i	$-0.611905\pi$
$157$	2.30055e6	−	2.30055e6i	0.594475	−	0.594475i	0.938837	+	0.344362i	$0.111905\pi$
$158$	2.09856e6	+	2.09856e6i	0.532047	+	0.532047i
$159$		−	1.65678e6i		−	0.412168i
$160$	−716800.	−	102400.i	−0.175000	−	0.0250000i
$161$	−1.05568e6			−0.252961
$162$	−2.65216e6	+	2.65216e6i	−0.623814	+	0.623814i
$163$	−4.02178e6	−	4.02178e6i	−0.928658	−	0.928658i	0.0689613	−	0.997619i	$-0.478032\pi$
$163$	−4.02178e6	−	4.02178e6i	−0.928658	−	0.928658i	−0.997619	+	0.0689613i	$0.978032\pi$
$164$			1.13402e6i			0.257091i
$165$	−806150.	+	5.64305e6i	−0.179458	+	1.25621i
$166$	915384.			0.200115
$167$	−710167.	+	710167.i	−0.152479	+	0.152479i	−0.779224	−	0.626745i	$-0.784387\pi$
$167$	−710167.	+	710167.i	−0.152479	+	0.152479i	0.626745	+	0.779224i	$0.284387\pi$
$168$	1.45434e6	+	1.45434e6i	0.306716	+	0.306716i
$169$			9.78561e6i			2.02735i
$170$	2.07440e6	−	1.55580e6i	0.422227	−	0.316670i
$171$	565880.			0.113171
$172$	1.25366e6	−	1.25366e6i	0.246375	−	0.246375i
$173$	3.77650e6	+	3.77650e6i	0.729375	+	0.729375i	0.970495	−	0.241120i	$-0.0775148\pi$
$173$	3.77650e6	+	3.77650e6i	0.729375	+	0.729375i	−0.241120	+	0.970495i	$0.577515\pi$
$174$		−	5.61568e6i		−	1.06599i
$175$	−2.62438e6	−	4.78562e6i	−0.489679	−	0.892945i
$176$	−1.43565e6			−0.263336
$177$	827080.	−	827080.i	0.149152	−	0.149152i
$178$	749120.	+	749120.i	0.132829	+	0.132829i
$179$		−	5.46380e6i		−	0.952655i	−0.879268	−	0.476328i	$-0.841968\pi$
$179$		−	5.46380e6i		−	0.952655i	0.879268	−	0.476328i	$-0.158032\pi$
$180$	−789600.	−	1.05280e6i	−0.135391	−	0.180521i
$181$	9.02436e6			1.52188			0.760941	−	0.648821i	$-0.224738\pi$
$181$	9.02436e6			1.52188			0.760941	+	0.648821i	$0.224738\pi$
$182$	−5.34113e6	+	5.34113e6i	−0.885970	+	0.885970i
$183$	−1.91641e6	−	1.91641e6i	−0.312705	−	0.312705i
$184$			547072.i			0.0878195i
$185$	−6.49478e6	−	927825.i	−1.02577	−	0.146538i
$186$	−6.96219e6			−1.08195
$187$	3.63539e6	−	3.63539e6i	0.555937	−	0.555937i
$188$	−3.04618e6	−	3.04618e6i	−0.458439	−	0.458439i
$189$		−	4.54480e6i		−	0.673177i
$190$	172000.	−	1.20400e6i	0.0250765	−	0.175536i
$191$	−4.02120e6			−0.577106			−0.288553	−	0.957464i	$-0.593174\pi$
$191$	−4.02120e6			−0.577106			−0.288553	+	0.957464i	$0.593174\pi$
$192$	753664.	−	753664.i	0.106481	−	0.106481i
$193$	−1.05414e6	−	1.05414e6i	−0.146632	−	0.146632i	0.629980	−	0.776611i	$-0.283063\pi$
$193$	−1.05414e6	−	1.05414e6i	−0.146632	−	0.146632i	−0.776611	+	0.629980i	$0.783063\pi$
$194$			4.26266e6i			0.583816i
$195$	1.24338e7	−	9.32535e6i	1.67687	−	1.25765i
$196$	−139808.			−0.0185679
$197$	−7.29489e6	+	7.29489e6i	−0.954157	+	0.954157i	−0.998994	−	0.0448372i	$-0.985723\pi$
$197$	−7.29489e6	+	7.29489e6i	−0.954157	+	0.954157i	0.0448372	+	0.998994i	$0.485723\pi$
$198$	−1.84503e6	−	1.84503e6i	−0.237689	−	0.237689i
$199$			1.41170e7i			1.79137i	0.444693	+	0.895683i	$0.353313\pi$
$199$			1.41170e7i			1.79137i	−0.444693	+	0.895683i	$0.646687\pi$
$200$	−2.48000e6	+	1.36000e6i	−0.310000	+	0.170000i
$201$	−2.79832e6			−0.344595
$202$	6.82031e6	−	6.82031e6i	0.827466	−	0.827466i
$203$	7.53844e6	+	7.53844e6i	0.901142	+	0.901142i
$204$			3.81690e6i			0.449593i
$205$	2.65785e6	+	3.54380e6i	0.308510	+	0.411346i
$206$	5.32050e6			0.608627
$207$	−703073.	+	703073.i	−0.0792664	+	0.0792664i
$208$	2.76787e6	+	2.76787e6i	0.307579	+	0.307579i
$209$		−	2.41144e6i		−	0.264142i
$210$	7.95340e6	+	1.13620e6i	0.858806	+	0.122687i
$211$	−1.23188e7			−1.31136			−0.655681	−	0.755038i	$-0.727618\pi$
$211$	−1.23188e7			−1.31136			−0.655681	+	0.755038i	$0.727618\pi$
$212$	1.15254e6	−	1.15254e6i	0.120962	−	0.120962i
$213$	927314.	+	927314.i	0.0959595	+	0.0959595i
$214$			2.47258e6i			0.252296i
$215$	979425.	−	6.85598e6i	0.0985498	−	0.689849i
$216$	−2.35520e6			−0.233704
$217$	9.34599e6	−	9.34599e6i	0.914631	−	0.914631i
$218$	−1.44976e6	−	1.44976e6i	−0.139935	−	0.139935i
$219$			5.93506e6i			0.565057i
$220$	−4.48640e6	+	3.36480e6i	−0.421337	+	0.316003i
$221$	−1.40178e7			−1.29868
$222$	6.82879e6	−	6.82879e6i	0.624144	−	0.624144i
$223$	328857.	+	328857.i	0.0296546	+	0.0296546i	0.721779	−	0.692124i	$-0.243325\pi$
$223$	328857.	+	328857.i	0.0296546	+	0.0296546i	−0.692124	+	0.721779i	$0.743325\pi$
$224$			2.02342e6i			0.180029i
$225$	−4.93500e6	−	1.43938e6i	−0.433251	−	0.126365i
$226$	−5.78126e6			−0.500838
$227$	−7.95085e6	+	7.95085e6i	−0.679729	+	0.679729i	−0.959939	−	0.280210i	$-0.909596\pi$
$227$	−7.95085e6	+	7.95085e6i	−0.679729	+	0.679729i	0.280210	+	0.959939i	$0.409596\pi$
$228$	1.26592e6	+	1.26592e6i	0.106807	+	0.106807i
$229$		−	2.28695e7i		−	1.90436i	−0.305532	−	0.952182i	$-0.598834\pi$
$229$		−	2.28695e7i		−	1.90436i	0.305532	−	0.952182i	$-0.401166\pi$
$230$	1.28220e6	+	1.70960e6i	0.105383	+	0.140511i
$231$	1.59295e7			1.29231
$232$	3.90656e6	−	3.90656e6i	0.312846	−	0.312846i
$233$	8.59050e6	+	8.59050e6i	0.679126	+	0.679126i	0.959803	−	0.280676i	$-0.0905587\pi$
$233$	8.59050e6	+	8.59050e6i	0.679126	+	0.679126i	−0.280676	+	0.959803i	$0.590559\pi$
$234$			7.11430e6i			0.555245i
$235$	−1.66588e7	−	2.37982e6i	−1.28363	−	0.183376i
$236$	1.15072e6			0.0875455
$237$	−1.20667e7	+	1.20667e7i	−0.906451	+	0.906451i
$238$	−5.12377e6	−	5.12377e6i	−0.380066	−	0.380066i
$239$		−	9.66576e6i		−	0.708015i	−0.935243	−	0.354007i	$-0.884819\pi$
$239$		−	9.66576e6i		−	0.708015i	0.935243	−	0.354007i	$-0.115181\pi$
$240$	588800.	−	4.12160e6i	0.0425926	−	0.298148i
$241$	1.85926e7			1.32828			0.664141	−	0.747608i	$-0.268798\pi$
$241$	1.85926e7			1.32828			0.664141	+	0.747608i	$0.268798\pi$
$242$	−776172.	+	776172.i	−0.0547661	+	0.0547661i
$243$	−8.54314e6	−	8.54314e6i	−0.595386	−	0.595386i
$244$		−	2.66630e6i		−	0.183544i
$245$	−436900.	+	327675.i	−0.0297087	+	0.0222815i
$246$	−6.52059e6			−0.438008
$247$	−4.64916e6	+	4.64916e6i	−0.308520	+	0.308520i
$248$	−4.84326e6	−	4.84326e6i	−0.317529	−	0.317529i
$249$			5.26346e6i			0.340936i
$250$	−4.56250e6	+	1.00625e7i	−0.292000	+	0.644000i
$251$	1.19350e7			0.754747			0.377373	−	0.926061i	$-0.376827\pi$
$251$	1.19350e7			0.754747			0.377373	+	0.926061i	$0.376827\pi$
$252$	−2.60042e6	+	2.60042e6i	−0.162495	+	0.162495i
$253$	2.99607e6	+	2.99607e6i	0.185008	+	0.185008i
$254$		−	1.55713e7i		−	0.950216i
$255$	8.94585e6	+	1.19278e7i	0.539512	+	0.719349i
$256$	1.04858e6			0.0625000
$257$	1.54304e7	−	1.54304e7i	0.909031	−	0.909031i	−0.0871630	−	0.996194i	$-0.527780\pi$
$257$	1.54304e7	−	1.54304e7i	0.909031	−	0.909031i	0.996194	+	0.0871630i	$0.0277801\pi$
$258$	7.20857e6	+	7.20857e6i	0.419749	+	0.419749i
$259$			1.83338e7i			1.05525i
$260$	1.51368e7	+	2.16240e6i	0.861220	+	0.123031i
$261$	1.00411e7			0.564753
$262$	−1.50248e7	+	1.50248e7i	−0.835420	+	0.835420i
$263$	1.27108e7	+	1.27108e7i	0.698723	+	0.698723i	0.964135	−	0.265412i	$-0.0855081\pi$
$263$	1.27108e7	+	1.27108e7i	0.698723	+	0.698723i	−0.265412	+	0.964135i	$0.585508\pi$
$264$		−	8.25498e6i		−	0.448646i
$265$	900425.	−	6.30298e6i	0.0483849	−	0.338694i
$266$	−3.39872e6			−0.180580
$267$	−4.30744e6	+	4.30744e6i	−0.226300	+	0.226300i
$268$	−1.94666e6	−	1.94666e6i	−0.101131	−	0.101131i
$269$		−	2.54188e6i		−	0.130586i	−0.997866	−	0.0652932i	$-0.979202\pi$
$269$		−	2.54188e6i		−	0.130586i	0.997866	−	0.0652932i	$-0.0207983\pi$
$270$	−7.36000e6	+	5.52000e6i	−0.373927	+	0.280445i
$271$	6.13384e6			0.308194			0.154097	−	0.988056i	$-0.450753\pi$
$271$	6.13384e6			0.308194			0.154097	+	0.988056i	$0.450753\pi$
$272$	−2.65523e6	+	2.65523e6i	−0.131946	+	0.131946i
$273$	−3.07115e7	−	3.07115e7i	−1.50943	−	1.50943i
$274$			8.34266e6i			0.405558i
$275$	−6.13375e6	+	2.10300e7i	−0.294936	+	1.01121i
$276$	−3.14566e6			−0.149618
$277$	−3.00513e6	+	3.00513e6i	−0.141392	+	0.141392i	−0.774260	−	0.632868i	$-0.781878\pi$
$277$	−3.00513e6	+	3.00513e6i	−0.141392	+	0.141392i	0.632868	+	0.774260i	$0.281878\pi$
$278$	−1.29880e7	−	1.29880e7i	−0.604516	−	0.604516i
$279$		−	1.24487e7i		−	0.573207i
$280$	4.74240e6	+	6.32320e6i	0.216035	+	0.288047i
$281$	−6.49352e6			−0.292658			−0.146329	−	0.989236i	$-0.546746\pi$
$281$	−6.49352e6			−0.292658			−0.146329	+	0.989236i	$0.546746\pi$
$282$	1.75155e7	−	1.75155e7i	0.781044	−	0.781044i
$283$	−2.71607e7	−	2.71607e7i	−1.19834	−	1.19834i	−0.974663	−	0.223680i	$-0.928193\pi$
$283$	−2.71607e7	−	2.71607e7i	−1.19834	−	1.19834i	−0.223680	−	0.974663i	$-0.571807\pi$
$284$			1.29018e6i			0.0563241i
$285$	6.92300e6	+	989000.i	0.299061	+	0.0427230i
$286$	3.03168e7			1.29594
$287$	8.75319e6	−	8.75319e6i	0.370272	−	0.370272i
$288$	1.34758e6	+	1.34758e6i	0.0564129	+	0.0564129i
$289$			1.06903e7i			0.442889i
$290$	3.05200e6	−	2.13640e7i	0.125138	−	0.875969i
$291$	−2.45103e7			−0.994649
$292$	−4.12874e6	+	4.12874e6i	−0.165832	+	0.165832i
$293$	−4.78734e6	−	4.78734e6i	−0.190323	−	0.190323i	0.605513	−	0.795836i	$-0.292968\pi$
$293$	−4.78734e6	−	4.78734e6i	−0.190323	−	0.190323i	−0.795836	+	0.605513i	$0.792968\pi$
$294$		−	803896.i		−	0.0316343i
$295$	3.59600e6	−	2.69700e6i	0.140073	−	0.105055i
$296$	9.50093e6			0.366346
$297$	−1.28984e7	+	1.28984e7i	−0.492342	+	0.492342i
$298$	2.30568e7	+	2.30568e7i	0.871265	+	0.871265i
$299$		−	1.15526e7i		−	0.432182i
$300$	−7.82000e6	−	1.42600e7i	−0.289630	−	0.528148i
$301$	−1.93534e7			−0.709674
$302$	−4.13121e6	+	4.13121e6i	−0.149988	+	0.149988i
$303$	3.92168e7	+	3.92168e7i	1.40976	+	1.40976i
$304$			1.76128e6i			0.0626914i
$305$	−6.24915e6	−	8.33220e6i	−0.220253	−	0.293670i
$306$	−6.82478e6			−0.238190
$307$	9.72339e6	−	9.72339e6i	0.336049	−	0.336049i	−0.518829	−	0.854878i	$-0.673632\pi$
$307$	9.72339e6	−	9.72339e6i	0.336049	−	0.336049i	0.854878	+	0.518829i	$0.173632\pi$
$308$	1.10814e7	+	1.10814e7i	0.379265	+	0.379265i
$309$			3.05929e7i			1.03692i
$310$	−2.64866e7	−	3.78380e6i	−0.889081	−	0.127012i
$311$	7.03344e6			0.233823			0.116911	−	0.993142i	$-0.462701\pi$
$311$	7.03344e6			0.233823			0.116911	+	0.993142i	$0.462701\pi$
$312$	−1.59153e7	+	1.59153e7i	−0.524023	+	0.524023i
$313$	2.98895e7	+	2.98895e7i	0.974734	+	0.974734i	0.999689	−	0.0249545i	$-0.00794407\pi$
$313$	2.98895e7	+	2.98895e7i	0.974734	+	0.974734i	−0.0249545	+	0.999689i	$0.507944\pi$
$314$			1.84044e7i			0.594475i
$315$	−2.03158e6	+	1.42210e7i	−0.0649982	+	0.454987i
$316$	−1.67885e7			−0.532047
$317$	2.11266e7	−	2.11266e7i	0.663212	−	0.663212i	−0.292924	−	0.956136i	$-0.594628\pi$
$317$	2.11266e7	−	2.11266e7i	0.663212	−	0.663212i	0.956136	+	0.292924i	$0.0946282\pi$
$318$	6.62713e6	+	6.62713e6i	0.206084	+	0.206084i
$319$		−	4.27890e7i		−	1.31814i
$320$	3.27680e6	−	2.45760e6i	0.100000	−	0.0750000i
$321$	−1.42174e7			−0.429837
$322$	4.22271e6	−	4.22271e6i	0.126481	−	0.126481i
$323$	−4.45996e6	−	4.45996e6i	−0.132350	−	0.132350i
$324$		−	2.12173e7i		−	0.623814i
$325$	5.23706e7	−	2.87194e7i	1.52559	−	0.836614i
$326$	3.21743e7			0.928658
$327$	8.33612e6	−	8.33612e6i	0.238408	−	0.238408i
$328$	−4.53606e6	−	4.53606e6i	−0.128546	−	0.128546i
$329$			4.70253e7i			1.32052i
$330$	−1.93476e7	−	2.57968e7i	−0.538375	−	0.717834i
$331$	−4.23279e7			−1.16719			−0.583596	−	0.812044i	$-0.698355\pi$
$331$	−4.23279e7			−1.16719			−0.583596	+	0.812044i	$0.698355\pi$
$332$	−3.66154e6	+	3.66154e6i	−0.100057	+	0.100057i
$333$	1.22102e7	+	1.22102e7i	0.330666	+	0.330666i
$334$		−	5.68134e6i		−	0.152479i
$335$	−1.06458e7	−	1.52082e6i	−0.283167	−	0.0404524i
$336$	−1.16347e7			−0.306716
$337$	−1.46217e7	+	1.46217e7i	−0.382040	+	0.382040i	−0.871837	−	0.489797i	$-0.837071\pi$
$337$	−1.46217e7	+	1.46217e7i	−0.382040	+	0.382040i	0.489797	+	0.871837i	$0.337071\pi$
$338$	−3.91424e7	−	3.91424e7i	−1.01367	−	1.01367i
$339$		−	3.32422e7i		−	0.853279i
$340$	−2.07440e6	+	1.45208e7i	−0.0527783	+	0.369448i
$341$	−5.30489e7			−1.33787
$342$	−2.26352e6	+	2.26352e6i	−0.0565856	+	0.0565856i
$343$	−2.79802e7	−	2.79802e7i	−0.693374	−	0.693374i
$344$			1.00293e7i			0.246375i
$345$	−9.83020e6	+	7.37265e6i	−0.239389	+	0.179542i
$346$	−3.02120e7			−0.729375
$347$	4.59792e7	−	4.59792e7i	1.10046	−	1.10046i	0.106100	−	0.994355i	$-0.466164\pi$
$347$	4.59792e7	−	4.59792e7i	1.10046	−	1.10046i	0.994355	−	0.106100i	$-0.0338364\pi$
$348$	2.24627e7	+	2.24627e7i	0.532997	+	0.532997i
$349$			5.03359e7i			1.18414i	0.805888	+	0.592068i	$0.201688\pi$
$349$			5.03359e7i			1.18414i	−0.805888	+	0.592068i	$0.798312\pi$
$350$	2.96400e7	+	8.64500e6i	0.691312	+	0.201633i
$351$	4.97352e7			1.15012
$352$	5.74259e6	−	5.74259e6i	0.131668	−	0.131668i
$353$	−1.59140e7	−	1.59140e7i	−0.361789	−	0.361789i	0.502683	−	0.864471i	$-0.332346\pi$
$353$	−1.59140e7	−	1.59140e7i	−0.361789	−	0.361789i	−0.864471	+	0.502683i	$0.832346\pi$
$354$			6.61664e6i			0.149152i
$355$	3.02385e6	+	4.03180e6i	0.0675889	+	0.0901185i
$356$	−5.99296e6			−0.132829
$357$	2.94617e7	−	2.94617e7i	0.647519	−	0.647519i
$358$	2.18552e7	+	2.18552e7i	0.476328	+	0.476328i
$359$			4.47023e7i			0.966155i	0.875578	+	0.483077i	$0.160481\pi$
$359$			4.47023e7i			0.966155i	−0.875578	+	0.483077i	$0.839519\pi$
$360$	7.36960e6	+	1.05280e6i	0.157956	+	0.0225652i
$361$	4.40875e7			0.937117
$362$	−3.60974e7	+	3.60974e7i	−0.760941	+	0.760941i
$363$	−4.46299e6	−	4.46299e6i	−0.0933052	−	0.0933052i
$364$		−	4.27290e7i		−	0.885970i
$365$	−3.22558e6	+	2.25790e7i	−0.0663328	+	0.464330i
$366$	1.53312e7			0.312705
$367$	−2.70624e7	+	2.70624e7i	−0.547480	+	0.547480i	−0.925711	−	0.378231i	$-0.876532\pi$
$367$	−2.70624e7	+	2.70624e7i	−0.547480	+	0.547480i	0.378231	+	0.925711i	$0.376532\pi$
$368$	−2.18829e6	−	2.18829e6i	−0.0439098	−	0.0439098i
$369$		−	1.16591e7i		−	0.232052i
$370$	2.96904e7	−	2.22678e7i	0.586153	−	0.439615i
$371$	−1.77924e7			−0.348428
$372$	2.78488e7	−	2.78488e7i	0.540975	−	0.540975i
$373$	−3.82355e7	−	3.82355e7i	−0.736784	−	0.736784i	0.235170	−	0.971954i	$-0.424435\pi$
$373$	−3.82355e7	−	3.82355e7i	−0.736784	−	0.736784i	−0.971954	+	0.235170i	$0.924435\pi$
$374$			2.90831e7i			0.555937i
$375$	−5.78594e7	−	2.62344e7i	−1.09719	−	0.497481i
$376$	2.43694e7			0.458439
$377$	−8.24956e7	+	8.24956e7i	−1.53960	+	1.53960i
$378$	1.81792e7	+	1.81792e7i	0.336589	+	0.336589i
$379$		−	2.50612e6i		−	0.0460346i	−0.999735	−	0.0230173i	$-0.992673\pi$
$379$		−	2.50612e6i		−	0.0460346i	0.999735	−	0.0230173i	$-0.00732728\pi$
$380$	4.12800e6	+	5.50400e6i	0.0752296	+	0.100306i
$381$	8.95347e7			1.61889
$382$	1.60848e7	−	1.60848e7i	0.288553	−	0.288553i
$383$	4.72095e7	+	4.72095e7i	0.840297	+	0.840297i	0.988897	−	0.148600i	$-0.0474767\pi$
$383$	4.72095e7	+	4.72095e7i	0.840297	+	0.840297i	−0.148600	+	0.988897i	$0.547477\pi$
$384$			6.02931e6i			0.106481i
$385$	6.06014e7	+	8.65735e6i	1.06194	+	0.151706i
$386$	8.43314e6			0.146632
$387$	−1.28892e7	+	1.28892e7i	−0.222379	+	0.222379i
$388$	−1.70507e7	−	1.70507e7i	−0.291908	−	0.291908i
$389$		−	1.00159e8i		−	1.70153i	−0.525547	−	0.850765i	$-0.676139\pi$
$389$		−	1.00159e8i		−	1.70153i	0.525547	−	0.850765i	$-0.323861\pi$
$390$	−1.24338e7	+	8.70366e7i	−0.209609	+	1.46726i
$391$	1.10825e7			0.185399
$392$	559232.	−	559232.i	0.00928397	−	0.00928397i
$393$	−8.63926e7	−	8.63926e7i	−1.42331	−	1.42331i
$394$		−	5.83591e7i		−	0.954157i
$395$	−5.24640e7	+	3.93480e7i	−0.851275	+	0.638457i
$396$	1.47603e7			0.237689
$397$	−7.26282e7	+	7.26282e7i	−1.16074	+	1.16074i	−0.176423	+	0.984314i	$0.556453\pi$
$397$	−7.26282e7	+	7.26282e7i	−1.16074	+	1.16074i	−0.984314	+	0.176423i	$0.943547\pi$
$398$	−5.64682e7	−	5.64682e7i	−0.895683	−	0.895683i
$399$		−	1.95426e7i		−	0.307655i
$400$	4.48000e6	−	1.53600e7i	0.0700000	−	0.240000i
$401$	5.26293e7			0.816196			0.408098	−	0.912938i	$-0.366192\pi$
$401$	5.26293e7			0.816196			0.408098	+	0.912938i	$0.366192\pi$
$402$	1.11933e7	−	1.11933e7i	0.172297	−	0.172297i
$403$	1.02276e8	+	1.02276e8i	1.56264	+	1.56264i
$404$			5.45625e7i			0.827466i
$405$	−4.97281e7	−	6.63041e7i	−0.748577	−	0.998103i
$406$	−6.03075e7			−0.901142
$407$	5.20324e7	−	5.20324e7i	0.771775	−	0.771775i
$408$	−1.52676e7	−	1.52676e7i	−0.224797	−	0.224797i
$409$		−	1.10687e8i		−	1.61781i	−0.587939	−	0.808906i	$-0.700060\pi$
$409$		−	1.10687e8i		−	1.61781i	0.587939	−	0.808906i	$-0.299940\pi$
$410$	−2.48066e7	−	3.54380e6i	−0.359928	−	0.0514183i
$411$	−4.79703e7			−0.690951
$412$	−2.12820e7	+	2.12820e7i	−0.304313	+	0.304313i
$413$	−8.88212e6	−	8.88212e6i	−0.126086	−	0.126086i
$414$		−	5.62458e6i		−	0.0792664i
$415$	−2.86058e6	+	2.00240e7i	−0.0400229	+	0.280161i
$416$	−2.21430e7			−0.307579
$417$	7.46810e7	−	7.46810e7i	1.02992	−	1.02992i
$418$	9.64576e6	+	9.64576e6i	0.132071	+	0.132071i
$419$			9.92484e6i			0.134922i	0.997722	+	0.0674608i	$0.0214898\pi$
$419$			9.92484e6i			0.134922i	−0.997722	+	0.0674608i	$0.978510\pi$
$420$	−3.63584e7	+	2.72688e7i	−0.490746	+	0.368060i
$421$	3.46957e7			0.464975			0.232488	−	0.972599i	$-0.425314\pi$
$421$	3.46957e7			0.464975			0.232488	+	0.972599i	$0.425314\pi$
$422$	4.92754e7	−	4.92754e7i	0.655681	−	0.655681i
$423$	3.13185e7	+	3.13185e7i	0.413790	+	0.413790i
$424$			9.22035e6i			0.120962i
$425$	2.75506e7	+	5.02394e7i	0.358893	+	0.654451i
$426$	−7.41851e6			−0.0959595
$427$	−2.05805e7	+	2.05805e7i	−0.264346	+	0.264346i
$428$	−9.89034e6	−	9.89034e6i	−0.126148	−	0.126148i
$429$			1.74322e8i			2.20790i
$430$	2.35062e7	+	3.13416e7i	0.295649	+	0.394199i
$431$	−2.72975e7			−0.340951			−0.170475	−	0.985362i	$-0.554530\pi$
$431$	−2.72975e7			−0.340951			−0.170475	+	0.985362i	$0.554530\pi$
$432$	9.42080e6	−	9.42080e6i	0.116852	−	0.116852i
$433$	4.50017e7	+	4.50017e7i	0.554326	+	0.554326i	0.927686	−	0.373360i	$-0.121795\pi$
$433$	4.50017e7	+	4.50017e7i	0.554326	+	0.554326i	−0.373360	+	0.927686i	$0.621795\pi$
$434$			7.47679e7i			0.914631i
$435$	1.22843e8	+	1.75490e7i	1.49239	+	0.213199i
$436$	1.15981e7			0.139935
$437$	3.67564e6	−	3.67564e6i	0.0440442	−	0.0440442i
$438$	−2.37402e7	−	2.37402e7i	−0.282529	−	0.282529i
$439$		−	4.79986e7i		−	0.567330i	−0.958924	−	0.283665i	$-0.908450\pi$
$439$		−	4.79986e7i		−	0.567330i	0.958924	−	0.283665i	$-0.0915503\pi$
$440$	4.48640e6	−	3.14048e7i	0.0526672	−	0.368670i
$441$	1.43740e6			0.0167595
$442$	5.60710e7	−	5.60710e7i	0.649339	−	0.649339i
$443$	−3.36631e7	−	3.36631e7i	−0.387206	−	0.387206i	0.486483	−	0.873690i	$-0.338279\pi$
$443$	−3.36631e7	−	3.36631e7i	−0.387206	−	0.387206i	−0.873690	+	0.486483i	$0.838279\pi$
$444$			5.46303e7i			0.624144i
$445$	−1.87280e7	+	1.40460e7i	−0.212526	+	0.159394i
$446$	−2.63086e6			−0.0296546
$447$	−1.32577e8	+	1.32577e8i	−1.48438	+	1.48438i
$448$	−8.09370e6	−	8.09370e6i	−0.0900146	−	0.0900146i
$449$		−	8.64789e7i		−	0.955369i	−0.878532	−	0.477684i	$-0.841476\pi$
$449$		−	8.64789e7i		−	0.955369i	0.878532	−	0.477684i	$-0.158524\pi$
$450$	2.54975e7	−	1.39825e7i	0.279808	−	0.153443i
$451$	−4.96841e7			−0.541611
$452$	2.31250e7	−	2.31250e7i	0.250419	−	0.250419i
$453$	−2.37544e7	−	2.37544e7i	−0.255535	−	0.255535i
$454$		−	6.36068e7i		−	0.679729i
$455$	−1.00146e8	−	1.33528e8i	−1.06316	−	1.41755i
$456$	−1.01274e7			−0.106807
$457$	−3.72501e6	+	3.72501e6i	−0.0390282	+	0.0390282i	−0.726352	−	0.687323i	$-0.758786\pi$
$457$	−3.72501e6	+	3.72501e6i	−0.0390282	+	0.0390282i	0.687323	+	0.726352i	$0.258786\pi$
$458$	9.14779e7	+	9.14779e7i	0.952182	+	0.952182i
$459$			4.77112e7i			0.493381i
$460$	−1.19672e7	−	1.70960e6i	−0.122947	−	0.0175639i
$461$	4.07112e7			0.415538			0.207769	−	0.978178i	$-0.433380\pi$
$461$	4.07112e7			0.415538			0.207769	+	0.978178i	$0.433380\pi$
$462$	−6.37181e7	+	6.37181e7i	−0.646155	+	0.646155i
$463$	−2.69113e7	−	2.69113e7i	−0.271139	−	0.271139i	0.558420	−	0.829559i	$-0.311408\pi$
$463$	−2.69113e7	−	2.69113e7i	−0.271139	−	0.271139i	−0.829559	+	0.558420i	$0.811408\pi$
$464$			3.12525e7i			0.312846i
$465$	2.17568e7	−	1.52298e8i	0.216390	−	1.51473i
$466$	−6.87240e7			−0.679126
$467$	1.38966e8	−	1.38966e8i	1.36446	−	1.36446i	0.496310	−	0.868146i	$-0.334688\pi$
$467$	1.38966e8	−	1.38966e8i	1.36446	−	1.36446i	0.868146	−	0.496310i	$-0.165312\pi$
$468$	−2.84572e7	−	2.84572e7i	−0.277622	−	0.277622i
$469$			3.00515e7i			0.291305i
$470$	7.61544e7	−	5.71158e7i	0.733502	−	0.550127i
$471$	−1.05825e8			−1.01281
$472$	−4.60288e6	+	4.60288e6i	−0.0437727	+	0.0437727i
$473$	5.49262e7	+	5.49262e7i	0.519034	+	0.519034i
$474$		−	9.65338e7i		−	0.906451i
$475$	2.58000e7	+	7.52500e6i	0.240735	+	0.0702143i
$476$	4.09901e7			0.380066
$477$	−1.18496e7	+	1.18496e7i	−0.109181	+	0.109181i
$478$	3.86630e7	+	3.86630e7i	0.354007	+	0.354007i
$479$			3.19942e7i			0.291115i	0.989350	+	0.145558i	$0.0464977\pi$
$479$			3.19942e7i			0.291115i	−0.989350	+	0.145558i	$0.953502\pi$
$480$	1.41312e7	+	1.88416e7i	0.127778	+	0.170370i
$481$	−2.00633e8			−1.80288
$482$	−7.43706e7	+	7.43706e7i	−0.664141	+	0.664141i
$483$	2.42806e7	+	2.42806e7i	0.215485	+	0.215485i
$484$		−	6.20938e6i		−	0.0547661i
$485$	−9.32458e7	−	1.33208e7i	−0.817342	−	0.116763i
$486$	6.83451e7			0.595386
$487$	−7.96441e7	+	7.96441e7i	−0.689551	+	0.689551i	−0.962133	−	0.272581i	$-0.912123\pi$
$487$	−7.96441e7	+	7.96441e7i	−0.689551	+	0.689551i	0.272581	+	0.962133i	$0.412123\pi$
$488$	1.06652e7	+	1.06652e7i	0.0917720	+	0.0917720i
$489$			1.85002e8i			1.58216i
$490$	436900.	−	3.05830e6i	0.00371359	−	0.0259951i
$491$	1.53965e8			1.30070			0.650350	−	0.759634i	$-0.274622\pi$
$491$	1.53965e8			1.30070			0.650350	+	0.759634i	$0.274622\pi$
$492$	2.60824e7	−	2.60824e7i	0.219004	−	0.219004i
$493$	−7.91384e7	−	7.91384e7i	−0.660460	−	0.660460i
$494$		−	3.71933e7i		−	0.308520i
$495$	4.61258e7	−	3.45944e7i	0.380302	−	0.285226i
$496$	3.87461e7			0.317529
$497$	9.95855e6	−	9.95855e6i	0.0811198	−	0.0811198i
$498$	−2.10538e7	−	2.10538e7i	−0.170468	−	0.170468i
$499$			1.02698e8i			0.826537i	0.910609	+	0.413268i	$0.135613\pi$
$499$			1.02698e8i			0.826537i	−0.910609	+	0.413268i	$0.864387\pi$
$500$	−2.20000e7	−	5.85000e7i	−0.176000	−	0.468000i
$501$	3.26677e7			0.259780
$502$	−4.77400e7	+	4.77400e7i	−0.377373	+	0.377373i
$503$	8.43625e7	+	8.43625e7i	0.662896	+	0.662896i	0.956062	−	0.293166i	$-0.0947088\pi$
$503$	8.43625e7	+	8.43625e7i	0.662896	+	0.662896i	−0.293166	+	0.956062i	$0.594709\pi$
$504$		−	2.08033e7i		−	0.162495i
$505$	1.27881e8	+	1.70508e8i	0.992959	+	1.32395i
$506$	−2.39686e7			−0.185008
$507$	2.25069e8	−	2.25069e8i	1.72700	−	1.72700i
$508$	6.22850e7	+	6.22850e7i	0.475108	+	0.475108i
$509$		−	4.03774e7i		−	0.306186i	−0.988212	−	0.153093i	$-0.951077\pi$
$509$		−	4.03774e7i		−	0.306186i	0.988212	−	0.153093i	$-0.0489234\pi$
$510$	−8.34946e7	−	1.19278e7i	−0.629431	−	0.0899187i
$511$	6.37374e7			0.477674
$512$	−4.19430e6	+	4.19430e6i	−0.0312500	+	0.0312500i
$513$	1.58240e7	+	1.58240e7i	0.117210	+	0.117210i
$514$			1.23443e8i			0.909031i
$515$	−1.66266e7	+	1.16386e8i	−0.121725	+	0.852078i
$516$	−5.76685e7			−0.419749
$517$	1.33461e8	−	1.33461e8i	0.965787	−	0.965787i
$518$	−7.33353e7	−	7.33353e7i	−0.527623	−	0.527623i
$519$		−	1.73719e8i		−	1.24264i
$520$	−6.91968e7	+	5.18976e7i	−0.492126	+	0.369094i
$521$	−3.68161e7			−0.260330			−0.130165	−	0.991492i	$-0.541551\pi$
$521$	−3.68161e7			−0.260330			−0.130165	+	0.991492i	$0.541551\pi$
$522$	−4.01643e7	+	4.01643e7i	−0.282377	+	0.282377i
$523$	−1.60054e8	−	1.60054e8i	−1.11882	−	1.11882i	−0.991915	−	0.126907i	$-0.959495\pi$
$523$	−1.60054e8	−	1.60054e8i	−1.11882	−	1.11882i	−0.126907	−	0.991915i	$-0.540505\pi$
$524$		−	1.20198e8i		−	0.835420i
$525$	−4.97088e7	+	1.70430e8i	−0.343522	+	1.17779i
$526$	−1.01686e8			−0.698723
$527$	−9.81139e7	+	9.81139e7i	−0.670346	+	0.670346i
$528$	3.30199e7	+	3.30199e7i	0.224323	+	0.224323i
$529$		−	1.38902e8i		−	0.938302i
$530$	2.16102e7	+	2.88136e7i	0.145155	+	0.193540i
$531$	−1.18308e7			−0.0790191
$532$	1.35949e7	−	1.35949e7i	0.0902902	−	0.0902902i
$533$	9.57889e7	+	9.57889e7i	0.632606	+	0.632606i
$534$		−	3.44595e7i		−	0.226300i
$535$	−5.40878e7	−	7.72682e6i	−0.353214	−	0.0504591i
$536$	1.55732e7			0.101131
$537$	−1.25667e8	+	1.25667e8i	−0.811521	+	0.811521i
$538$	1.01675e7	+	1.01675e7i	0.0652932	+	0.0652932i
$539$		−	6.12534e6i		−	0.0391168i
$540$	7.36000e6	−	5.15200e7i	0.0467408	−	0.327186i
$541$	1.30022e7			0.0821155			0.0410577	−	0.999157i	$-0.486927\pi$
$541$	1.30022e7			0.0821155			0.0410577	+	0.999157i	$0.486927\pi$
$542$	−2.45354e7	+	2.45354e7i	−0.154097	+	0.154097i
$543$	−2.07560e8	−	2.07560e8i	−1.29642	−	1.29642i
$544$		−	2.12419e7i		−	0.131946i
$545$	3.62440e7	−	2.71830e7i	0.223896	−	0.167922i
$546$	2.45692e8			1.50943
$547$	7.28319e7	−	7.28319e7i	0.444999	−	0.444999i	−0.448689	−	0.893688i	$-0.648109\pi$
$547$	7.28319e7	−	7.28319e7i	0.444999	−	0.444999i	0.893688	+	0.448689i	$0.148109\pi$
$548$	−3.33707e7	−	3.33707e7i	−0.202779	−	0.202779i
$549$			2.74129e7i			0.165668i
$550$	−5.95850e7	−	1.08655e8i	−0.358137	−	0.653073i
$551$	−5.24944e7			−0.313804
$552$	1.25827e7	−	1.25827e7i	0.0748092	−	0.0748092i
$553$	1.29586e8	+	1.29586e8i	0.766272	+	0.766272i
$554$		−	2.40410e7i		−	0.141392i
$555$	1.28040e8	+	1.70720e8i	0.748973	+	0.998631i
$556$	1.03904e8			0.604516
$557$	−4.55401e7	+	4.55401e7i	−0.263529	+	0.263529i	−0.826486	−	0.562957i	$-0.809664\pi$
$557$	−4.55401e7	+	4.55401e7i	−0.263529	+	0.263529i	0.562957	+	0.826486i	$0.309664\pi$
$558$	4.97948e7	+	4.97948e7i	0.286603	+	0.286603i
$559$		−	2.11791e8i		−	1.21247i
$560$	−4.42624e7	−	6.32320e6i	−0.252041	−	0.0360058i
$561$	−1.67228e8			−0.947152
$562$	2.59741e7	−	2.59741e7i	0.146329	−	0.146329i
$563$	−1.85012e8	−	1.85012e8i	−1.03675	−	1.03675i	−0.999298	−	0.0374524i	$-0.988076\pi$
$563$	−1.85012e8	−	1.85012e8i	−1.03675	−	1.03675i	−0.0374524	−	0.999298i	$-0.511924\pi$
$564$			1.40124e8i			0.781044i
$565$	1.80664e7	−	1.26465e8i	0.100168	−	0.701173i
$566$	2.17285e8			1.19834
$567$	−1.63771e8	+	1.63771e8i	−0.898438	+	0.898438i
$568$	−5.16070e6	−	5.16070e6i	−0.0281620	−	0.0281620i
$569$			7.17210e7i			0.389323i	0.980871	+	0.194661i	$0.0623608\pi$
$569$			7.17210e7i			0.389323i	−0.980871	+	0.194661i	$0.937639\pi$
$570$	−3.16480e7	+	2.37360e7i	−0.170892	+	0.128169i
$571$	3.09478e8			1.66234			0.831172	−	0.556015i	$-0.187670\pi$
$571$	3.09478e8			1.66234			0.831172	+	0.556015i	$0.187670\pi$
$572$	−1.21267e8	+	1.21267e8i	−0.647972	+	0.647972i
$573$	9.24876e7	+	9.24876e7i	0.491609	+	0.491609i
$574$			7.00255e7i			0.370272i
$575$	−4.14044e7	+	2.27056e7i	−0.217792	+	0.119435i
$576$	−1.07807e7			−0.0564129
$577$	−2.15868e7	+	2.15868e7i	−0.112373	+	0.112373i	−0.761057	−	0.648684i	$-0.775319\pi$
$577$	−2.15868e7	+	2.15868e7i	−0.112373	+	0.112373i	0.648684	+	0.761057i	$0.275319\pi$
$578$	−4.27611e7	−	4.27611e7i	−0.221445	−	0.221445i
$579$			4.84906e7i			0.249817i
$580$	7.32480e7	+	9.76640e7i	0.375415	+	0.500554i
$581$	5.65250e7			0.288212
$582$	9.80413e7	−	9.80413e7i	0.497325	−	0.497325i
$583$	5.04958e7	+	5.04958e7i	0.254830	+	0.254830i
$584$		−	3.30299e7i		−	0.165832i
$585$	−1.55625e8	−	2.22322e7i	−0.777342	−	0.111049i
$586$	3.82987e7			0.190323
$587$	−2.30927e8	+	2.30927e8i	−1.14172	+	1.14172i	−0.153588	+	0.988135i	$0.549083\pi$
$587$	−2.30927e8	+	2.30927e8i	−1.14172	+	1.14172i	−0.988135	+	0.153588i	$0.950917\pi$
$588$	3.21558e6	+	3.21558e6i	0.0158171	+	0.0158171i
$589$			6.50814e7i			0.318501i
$590$	−3.59600e6	+	2.51720e7i	−0.0175091	+	0.122564i
$591$	3.35565e8			1.62560
$592$	−3.80037e7	+	3.80037e7i	−0.183173	+	0.183173i
$593$	−2.66433e7	−	2.66433e7i	−0.127768	−	0.127768i	0.640331	−	0.768099i	$-0.278797\pi$
$593$	−2.66433e7	−	2.66433e7i	−0.127768	−	0.127768i	−0.768099	+	0.640331i	$0.778797\pi$
$594$		−	1.03187e8i		−	0.492342i
$595$	1.28094e8	−	9.60706e7i	0.608105	−	0.456079i
$596$	−1.84454e8			−0.871265
$597$	3.24692e8	−	3.24692e8i	1.52598	−	1.52598i
$598$	4.62105e7	+	4.62105e7i	0.216091	+	0.216091i
$599$			3.14489e8i			1.46327i	0.681695	+	0.731637i	$0.261243\pi$
$599$			3.14489e8i			1.46327i	−0.681695	+	0.731637i	$0.738757\pi$
$600$	8.83200e7	+	2.57600e7i	0.408889	+	0.119259i
$601$	−2.50382e8			−1.15340			−0.576700	−	0.816956i	$-0.695660\pi$
$601$	−2.50382e8			−1.15340			−0.576700	+	0.816956i	$0.695660\pi$
$602$	7.74138e7	−	7.74138e7i	0.354837	−	0.354837i
$603$	2.00141e7	+	2.00141e7i	0.0912816	+	0.0912816i
$604$		−	3.30497e7i		−	0.149988i
$605$	−1.45532e7	−	1.94043e7i	−0.0657193	−	0.0876258i
$606$	−3.13734e8			−1.40976
$607$	9.40326e7	−	9.40326e7i	0.420448	−	0.420448i	−0.464910	−	0.885358i	$-0.653913\pi$
$607$	9.40326e7	−	9.40326e7i	0.420448	−	0.420448i	0.885358	+	0.464910i	$0.153913\pi$
$608$	−7.04512e6	−	7.04512e6i	−0.0313457	−	0.0313457i
$609$		−	3.46768e8i		−	1.53528i
$610$	5.83254e7	+	8.33220e6i	0.256962	+	0.0367088i
$611$	−5.14613e8			−2.25610
$612$	2.72991e7	−	2.72991e7i	0.119095	−	0.119095i
$613$	−1.72963e8	−	1.72963e8i	−0.750880	−	0.750880i	0.223763	−	0.974644i	$-0.428166\pi$
$613$	−1.72963e8	−	1.72963e8i	−0.750880	−	0.750880i	−0.974644	+	0.223763i	$0.928166\pi$
$614$			7.77871e7i			0.336049i
$615$	2.03768e7	−	1.42638e8i	0.0876015	−	0.613211i
$616$	−8.86513e7			−0.379265
$617$	1.31974e8	−	1.31974e8i	0.561868	−	0.561868i	−0.367970	−	0.929838i	$-0.619947\pi$
$617$	1.31974e8	−	1.31974e8i	0.561868	−	0.561868i	0.929838	+	0.367970i	$0.119947\pi$
$618$	−1.22372e8	−	1.22372e8i	−0.518460	−	0.518460i
$619$			4.22584e8i			1.78173i	0.454271	+	0.890863i	$0.349900\pi$
$619$			4.22584e8i			1.78173i	−0.454271	+	0.890863i	$0.650100\pi$
$620$	1.21082e8	−	9.08112e7i	0.508046	−	0.381035i
$621$	−3.93208e7			−0.164190
$622$	−2.81338e7	+	2.81338e7i	−0.116911	+	0.116911i
$623$	4.62582e7	+	4.62582e7i	0.191304	+	0.191304i
$624$		−	1.27322e8i		−	0.524023i
$625$	−2.05859e8	−	1.31250e8i	−0.843200	−	0.537600i
$626$	−2.39116e8			−0.974734
$627$	−5.54631e7	+	5.54631e7i	−0.225010	+	0.225010i
$628$	−7.36177e7	−	7.36177e7i	−0.297237	−	0.297237i
$629$		−	1.92468e8i		−	0.773404i
$630$	−4.87578e7	−	6.50104e7i	−0.194995	−	0.259993i
$631$	2.95144e8			1.17475			0.587376	−	0.809314i	$-0.300161\pi$
$631$	2.95144e8			1.17475			0.587376	+	0.809314i	$0.300161\pi$
$632$	6.71539e7	−	6.71539e7i	0.266024	−	0.266024i
$633$	2.83333e8	+	2.83333e8i	1.11709	+	1.11709i
$634$			1.69013e8i			0.663212i
$635$	3.40621e8	+	4.86602e7i	1.33030	+	0.190043i
$636$	−5.30170e7			−0.206084
$637$	−1.18094e7	+	1.18094e7i	−0.0456888	+	0.0456888i
$638$	1.71156e8	+	1.71156e8i	0.659068	+	0.659068i
$639$		−	1.32646e7i		−	0.0508385i
$640$	−3.27680e6	+	2.29376e7i	−0.0125000	+	0.0875000i
$641$	3.85293e8			1.46291			0.731453	−	0.681891i	$-0.238842\pi$
$641$	3.85293e8			1.46291			0.731453	+	0.681891i	$0.238842\pi$
$642$	5.68694e7	−	5.68694e7i	0.214919	−	0.214919i
$643$	1.75998e8	+	1.75998e8i	0.662024	+	0.662024i	0.955857	−	0.293833i	$-0.0949309\pi$
$643$	1.75998e8	+	1.75998e8i	0.662024	+	0.662024i	−0.293833	+	0.955857i	$0.594931\pi$
$644$			3.37817e7i			0.126481i
$645$	−1.80214e8	+	1.35161e8i	−0.671599	+	0.503699i
$646$	3.56797e7			0.132350
$647$	−1.00835e8	+	1.00835e8i	−0.372304	+	0.372304i	−0.868316	−	0.496012i	$-0.834797\pi$
$647$	−1.00835e8	+	1.00835e8i	−0.372304	+	0.372304i	0.496012	+	0.868316i	$0.334797\pi$
$648$	8.48692e7	+	8.48692e7i	0.311907	+	0.311907i
$649$			5.04159e7i			0.184431i
$650$	−9.46050e7	+	3.24360e8i	−0.344488	+	1.18110i
$651$	−4.29915e8			−1.55826
$652$	−1.28697e8	+	1.28697e8i	−0.464329	+	0.464329i
$653$	1.92563e8	+	1.92563e8i	0.691566	+	0.691566i	0.962576	−	0.271010i	$-0.0873577\pi$
$653$	1.92563e8	+	1.92563e8i	0.691566	+	0.691566i	−0.271010	+	0.962576i	$0.587358\pi$
$654$			6.66890e7i			0.238408i
$655$	−2.81715e8	−	3.75620e8i	−1.00250	−	1.33667i
$656$	3.62885e7			0.128546
$657$	4.24486e7	−	4.24486e7i	0.149681	−	0.149681i
$658$	−1.88101e8	−	1.88101e8i	−0.660259	−	0.660259i
$659$		−	1.31172e8i		−	0.458337i	−0.973387	−	0.229168i	$-0.926399\pi$
$659$		−	1.31172e8i		−	0.458337i	0.973387	−	0.229168i	$-0.0736007\pi$
$660$	1.80578e8	+	2.57968e7i	0.628105	+	0.0897292i
$661$	−1.97154e8			−0.682656			−0.341328	−	0.939944i	$-0.610877\pi$
$661$	−1.97154e8			−0.682656			−0.341328	+	0.939944i	$0.610877\pi$
$662$	1.69312e8	−	1.69312e8i	0.583596	−	0.583596i
$663$	3.22408e8	+	3.22408e8i	1.10628	+	1.10628i
$664$		−	2.92923e7i		−	0.100057i
$665$	1.06210e7	−	7.43470e7i	0.0361161	−	0.252812i
$666$	−9.76814e7			−0.330666
$667$	6.52212e7	−	6.52212e7i	0.219792	−	0.219792i
$668$	2.27253e7	+	2.27253e7i	0.0762397	+	0.0762397i
$669$		−	1.51274e7i		−	0.0505227i
$670$	4.86664e7	−	3.64998e7i	0.161810	−	0.121357i
$671$	1.16817e8			0.386670
$672$	4.65388e7	−	4.65388e7i	0.153358	−	0.153358i
$673$	−1.93253e8	−	1.93253e8i	−0.633987	−	0.633987i	0.315079	−	0.949066i	$-0.397969\pi$
$673$	−1.93253e8	−	1.93253e8i	−0.633987	−	0.633987i	−0.949066	+	0.315079i	$0.897969\pi$
$674$		−	1.16974e8i		−	0.382040i
$675$	−9.77500e7	−	1.78250e8i	−0.317838	−	0.579586i
$676$	3.13139e8			1.01367
$677$	−2.07906e8	+	2.07906e8i	−0.670042	+	0.670042i	−0.957725	−	0.287684i	$-0.907115\pi$
$677$	−2.07906e8	+	2.07906e8i	−0.670042	+	0.670042i	0.287684	+	0.957725i	$0.407115\pi$
$678$	1.32969e8	+	1.32969e8i	0.426639	+	0.426639i
$679$			2.63220e8i			0.840831i
$680$	−4.97856e7	−	6.63808e7i	−0.158335	−	0.211113i
$681$	3.65739e8			1.15806
$682$	2.12196e8	−	2.12196e8i	0.668934	−	0.668934i
$683$	−3.57632e8	−	3.57632e8i	−1.12247	−	1.12247i	−0.991369	−	0.131099i	$-0.958149\pi$
$683$	−3.57632e8	−	3.57632e8i	−1.12247	−	1.12247i	−0.131099	−	0.991369i	$-0.541851\pi$
$684$		−	1.81082e7i		−	0.0565856i
$685$	−1.82496e8	−	2.60708e7i	−0.567781	−	0.0811116i
$686$	2.23841e8			0.693374
$687$	−5.25998e8	+	5.25998e8i	−1.62224	+	1.62224i
$688$	−4.01172e7	−	4.01172e7i	−0.123187	−	0.123187i
$689$		−	1.94708e8i		−	0.595286i
$690$	9.83020e6	−	6.88114e7i	0.0299237	−	0.209466i
$691$	−1.76748e8			−0.535698			−0.267849	−	0.963461i	$-0.586313\pi$
$691$	−1.76748e8			−0.535698			−0.267849	+	0.963461i	$0.586313\pi$
$692$	1.20848e8	−	1.20848e8i	0.364687	−	0.364687i
$693$	−1.13931e8	−	1.13931e8i	−0.342327	−	0.342327i
$694$			3.67833e8i			1.10046i
$695$	3.24700e8	−	2.43525e8i	0.967226	−	0.725419i
$696$	−1.79702e8			−0.532997
$697$	−9.18907e7	+	9.18907e7i	−0.271377	+	0.271377i
$698$	−2.01344e8	−	2.01344e8i	−0.592068	−	0.592068i
$699$		−	3.95163e8i		−	1.15703i
$700$	−1.53140e8	+	8.39800e7i	−0.446472	+	0.244840i
$701$	−3.12897e8			−0.908338			−0.454169	−	0.890916i	$-0.650064\pi$
$701$	−3.12897e8			−0.908338			−0.454169	+	0.890916i	$0.650064\pi$
$702$	−1.98941e8	+	1.98941e8i	−0.575059	+	0.575059i
$703$	−6.38344e7	−	6.38344e7i	−0.183734	−	0.183734i
$704$			4.59407e7i			0.131668i
$705$	3.28416e8	+	4.37888e8i	0.937253	+	1.24967i
$706$	1.27312e8			0.361789
$707$	4.21154e8	−	4.21154e8i	1.19174	−	1.19174i
$708$	−2.64666e7	−	2.64666e7i	−0.0745758	−	0.0745758i
$709$		−	1.07924e8i		−	0.302817i	−0.988471	−	0.151408i	$-0.951619\pi$
$709$		−	1.07924e8i		−	0.302817i	0.988471	−	0.151408i	$-0.0483809\pi$
$710$	−2.82226e7	−	4.03180e6i	−0.0788537	−	0.0112648i
$711$	1.72607e8			0.480229
$712$	2.39718e7	−	2.39718e7i	0.0664143	−	0.0664143i
$713$	−8.08598e7	−	8.08598e7i	−0.223082	−	0.223082i
$714$			2.35693e8i			0.647519i
$715$	−9.47402e7	+	6.63181e8i	−0.259189	+	1.81432i
$716$	−1.74842e8			−0.476328
$717$	−2.22312e8	+	2.22312e8i	−0.603124	+	0.603124i
$718$	−1.78809e8	−	1.78809e8i	−0.483077	−	0.483077i
$719$		−	1.83233e8i		−	0.492967i	−0.969147	−	0.246484i	$-0.920725\pi$
$719$		−	1.83233e8i		−	0.492967i	0.969147	−	0.246484i	$-0.0792752\pi$
$720$	−3.36896e7	+	2.52672e7i	−0.0902606	+	0.0676955i
$721$	3.28541e8			0.876565
$722$	−1.76350e8	+	1.76350e8i	−0.468558	+	0.468558i
$723$	−4.27631e8	−	4.27631e8i	−1.13150	−	1.13150i
$724$		−	2.88780e8i		−	0.760941i
$725$	4.57800e8	+	1.33525e8i	1.20133	+	0.350387i
$726$	3.57039e7			0.0933052
$727$	2.98719e8	−	2.98719e8i	0.777428	−	0.777428i	−0.201965	−	0.979393i	$-0.564733\pi$
$727$	2.98719e8	−	2.98719e8i	0.777428	−	0.777428i	0.979393	+	0.201965i	$0.0647327\pi$
$728$	1.70916e8	+	1.70916e8i	0.442985	+	0.442985i
$729$		−	9.03723e7i		−	0.233267i
$730$	−7.74138e7	−	1.03218e8i	−0.198999	−	0.265331i
$731$	2.03172e8			0.520130
$732$	−6.13250e7	+	6.13250e7i	−0.156352	+	0.156352i
$733$	4.34598e8	+	4.34598e8i	1.10351	+	1.10351i	0.993984	+	0.109524i	$0.0349325\pi$
$733$	4.34598e8	+	4.34598e8i	1.10351	+	1.10351i	0.109524	+	0.993984i	$0.465067\pi$
$734$		−	2.16499e8i		−	0.547480i
$735$	1.75852e7	+	2.51218e6i	0.0442880	+	0.00632685i
$736$	1.75063e7			0.0439098
$737$	8.52879e7	−	8.52879e7i	0.213052	−	0.213052i
$738$	4.66364e7	+	4.66364e7i	0.116026	+	0.116026i
$739$			5.77645e8i			1.43129i	0.698463	+	0.715646i	$0.253867\pi$
$739$			5.77645e8i			1.43129i	−0.698463	+	0.715646i	$0.746133\pi$
$740$	−2.96904e7	+	2.07833e8i	−0.0732691	+	0.512884i
$741$	2.13861e8			0.525627
$742$	7.11696e7	−	7.11696e7i	0.174214	−	0.174214i
$743$	9.71697e7	+	9.71697e7i	0.236900	+	0.236900i	0.815565	−	0.578665i	$-0.196426\pi$
$743$	9.71697e7	+	9.71697e7i	0.236900	+	0.236900i	−0.578665	+	0.815565i	$0.696426\pi$
$744$			2.22790e8i			0.540975i
$745$	−5.76420e8	+	4.32315e8i	−1.39402	+	1.04552i
$746$	3.05884e8			0.736784
$747$	3.76452e7	−	3.76452e7i	0.0903124	−	0.0903124i
$748$	−1.16332e8	−	1.16332e8i	−0.277969	−	0.277969i
$749$			1.52682e8i			0.363365i
$750$	3.36375e8	−	1.26500e8i	0.797333	−	0.299852i
$751$	6.96310e8			1.64393			0.821963	−	0.569540i	$-0.192879\pi$
$751$	6.96310e8			1.64393			0.821963	+	0.569540i	$0.192879\pi$
$752$	−9.74776e7	+	9.74776e7i	−0.229219	+	0.229219i
$753$	−2.74505e8	−	2.74505e8i	−0.642933	−	0.642933i
$754$		−	6.59964e8i		−	1.53960i
$755$	−7.74602e7	−	1.03280e8i	−0.179985	−	0.239981i
$756$	−1.45434e8			−0.336589
$757$	−2.26996e8	+	2.26996e8i	−0.523276	+	0.523276i	−0.918559	−	0.395283i	$-0.870646\pi$
$757$	−2.26996e8	+	2.26996e8i	−0.523276	+	0.523276i	0.395283	+	0.918559i	$0.370646\pi$
$758$	1.00245e7	+	1.00245e7i	0.0230173	+	0.0230173i
$759$		−	1.37819e8i		−	0.315199i
$760$	−3.85280e7	−	5.50400e6i	−0.0877679	−	0.0125383i
$761$	−3.36900e8			−0.764447			−0.382224	−	0.924070i	$-0.624842\pi$
$761$	−3.36900e8			−0.764447			−0.382224	+	0.924070i	$0.624842\pi$
$762$	−3.58139e8	+	3.58139e8i	−0.809444	+	0.809444i

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 4.00000i) q^{2} +(-23.0000 - 23.0000i) q^{3} -32.0000i q^{4} +(-75.0000 - 100.000i) q^{5} +184.000 q^{6} +(-247.000 + 247.000i) q^{7} +(128.000 + 128.000i) q^{8} +329.000i q^{9} +(700.000 + 100.000i) q^{10} +1402.00 q^{11} +(-736.000 + 736.000i) q^{12} +(-2703.00 - 2703.00i) q^{13} -1976.00i q^{14} +(-575.000 + 4025.00i) q^{15} -1024.00 q^{16} +(2593.00 - 2593.00i) q^{17} +(-1316.00 - 1316.00i) q^{18} -1720.00i q^{19} +(-3200.00 + 2400.00i) q^{20} +11362.0 q^{21} +(-5608.00 + 5608.00i) q^{22} +(2137.00 + 2137.00i) q^{23} -5888.00i q^{24} +(-4375.00 + 15000.0i) q^{25} +21624.0 q^{26} +(-9200.00 + 9200.00i) q^{27} +(7904.00 + 7904.00i) q^{28} -30520.0i q^{29} +(-13800.0 - 18400.0i) q^{30} -37838.0 q^{31} +(4096.00 - 4096.00i) q^{32} +(-32246.0 - 32246.0i) q^{33} +20744.0i q^{34} +(43225.0 + 6175.00i) q^{35} +10528.0 q^{36} +(37113.0 - 37113.0i) q^{37} +(6880.00 + 6880.00i) q^{38} +124338. i q^{39} +(3200.00 - 22400.0i) q^{40} -35438.0 q^{41} +(-45448.0 + 45448.0i) q^{42} +(39177.0 + 39177.0i) q^{43} -44864.0i q^{44} +(32900.0 - 24675.0i) q^{45} -17096.0 q^{46} +(95193.0 - 95193.0i) q^{47} +(23552.0 + 23552.0i) q^{48} -4369.00i q^{49} +(-42500.0 - 77500.0i) q^{50} -119278. q^{51} +(-86496.0 + 86496.0i) q^{52} +(36017.0 + 36017.0i) q^{53} -73600.0i q^{54} +(-105150. - 140200. i) q^{55} -63232.0 q^{56} +(-39560.0 + 39560.0i) q^{57} +(122080. + 122080. i) q^{58} +35960.0i q^{59} +(128800. + 18400.0i) q^{60} +83322.0 q^{61} +(151352. - 151352. i) q^{62} +(-81263.0 - 81263.0i) q^{63} +32768.0i q^{64} +(-67575.0 + 473025. i) q^{65} +257968. q^{66} +(60833.0 - 60833.0i) q^{67} +(-82976.0 - 82976.0i) q^{68} -98302.0i q^{69} +(-197600. + 148200. i) q^{70} -40318.0 q^{71} +(-42112.0 + 42112.0i) q^{72} +(-129023. - 129023. i) q^{73} +296904. i q^{74} +(445625. - 244375. i) q^{75} -55040.0 q^{76} +(-346294. + 346294. i) q^{77} +(-497352. - 497352. i) q^{78} -524640. i q^{79} +(76800.0 + 102400. i) q^{80} +663041. q^{81} +(141752. - 141752. i) q^{82} +(-114423. - 114423. i) q^{83} -363584. i q^{84} +(-453775. - 64825.0i) q^{85} -313416. q^{86} +(-701960. + 701960. i) q^{87} +(179456. + 179456. i) q^{88} -187280. i q^{89} +(-32900.0 + 230300. i) q^{90} +1.33528e6 q^{91} +(68384.0 - 68384.0i) q^{92} +(870274. + 870274. i) q^{93} +761544. i q^{94} +(-172000. + 129000. i) q^{95} -188416. q^{96} +(532833. - 532833. i) q^{97} +(17476.0 + 17476.0i) q^{98} +461258. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} - 46 q^{3} - 150 q^{5} + 368 q^{6} - 494 q^{7} + 256 q^{8} + 1400 q^{10} + 2804 q^{11} - 1472 q^{12} - 5406 q^{13} - 1150 q^{15} - 2048 q^{16} + 5186 q^{17} - 2632 q^{18} - 6400 q^{20} + 22724 q^{21}+ \cdots + 34952 q^{98}+O(q^{100}) \) 2 * q - 8 * q^2 - 46 * q^3 - 150 * q^5 + 368 * q^6 - 494 * q^7 + 256 * q^8 + 1400 * q^10 + 2804 * q^11 - 1472 * q^12 - 5406 * q^13 - 1150 * q^15 - 2048 * q^16 + 5186 * q^17 - 2632 * q^18 - 6400 * q^20 + 22724 * q^21 - 11216 * q^22 + 4274 * q^23 - 8750 * q^25 + 43248 * q^26 - 18400 * q^27 + 15808 * q^28 - 27600 * q^30 - 75676 * q^31 + 8192 * q^32 - 64492 * q^33 + 86450 * q^35 + 21056 * q^36 + 74226 * q^37 + 13760 * q^38 + 6400 * q^40 - 70876 * q^41 - 90896 * q^42 + 78354 * q^43 + 65800 * q^45 - 34192 * q^46 + 190386 * q^47 + 47104 * q^48 - 85000 * q^50 - 238556 * q^51 - 172992 * q^52 + 72034 * q^53 - 210300 * q^55 - 126464 * q^56 - 79120 * q^57 + 244160 * q^58 + 257600 * q^60 + 166644 * q^61 + 302704 * q^62 - 162526 * q^63 - 135150 * q^65 + 515936 * q^66 + 121666 * q^67 - 165952 * q^68 - 395200 * q^70 - 80636 * q^71 - 84224 * q^72 - 258046 * q^73 + 891250 * q^75 - 110080 * q^76 - 692588 * q^77 - 994704 * q^78 + 153600 * q^80 + 1326082 * q^81 + 283504 * q^82 - 228846 * q^83 - 907550 * q^85 - 626832 * q^86 - 1403920 * q^87 + 358912 * q^88 - 65800 * q^90 + 2670564 * q^91 + 136768 * q^92 + 1740548 * q^93 - 344000 * q^95 - 376832 * q^96 + 1065666 * q^97 + 34952 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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