LMFDB - Embedded newform 294.8.e.a.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,8,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("294.67");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	294.e (of order $3$, degree $2$, not 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:	$91.8411974923$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.8.e.a.67.1

$q$-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 + 6.92820i) q^{2} +(-13.5000 - 23.3827i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(-235.000 + 407.032i) q^{5} +216.000 q^{6} +512.000 q^{8} +(-364.500 + 631.333i) q^{9} +(-1880.00 - 3256.26i) q^{10} +(3634.00 + 6294.27i) q^{11} +(-864.000 + 1496.49i) q^{12} +11382.0 q^{13} +12690.0 q^{15} +(-2048.00 + 3547.24i) q^{16} +(-10421.0 - 18049.7i) q^{17} +(-2916.00 - 5050.66i) q^{18} +(6842.00 - 11850.7i) q^{19} +30080.0 q^{20} -58144.0 q^{22} +(23368.0 - 40474.6i) q^{23} +(-6912.00 - 11971.9i) q^{24} +(-71387.5 - 123647. i) q^{25} +(-45528.0 + 78856.8i) q^{26} +19683.0 q^{27} +2774.00 q^{29} +(-50760.0 + 87918.9i) q^{30} +(5616.00 + 9727.20i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(98118.0 - 169945. i) q^{33} +166736. q^{34} +46656.0 q^{36} +(119849. - 207585. i) q^{37} +(54736.0 + 94805.5i) q^{38} +(-153657. - 266142. i) q^{39} +(-120320. + 208400. i) q^{40} +52962.0 q^{41} -874732. q^{43} +(232576. - 402833. i) q^{44} +(-171315. - 296726. i) q^{45} +(186944. + 323797. i) q^{46} +(225648. - 390834. i) q^{47} +110592. q^{48} +1.14220e6 q^{50} +(-281367. + 487342. i) q^{51} +(-364224. - 630854. i) q^{52} +(971769. + 1.68315e6i) q^{53} +(-78732.0 + 136368. i) q^{54} -3.41596e6 q^{55} -369468. q^{57} +(-11096.0 + 19218.8i) q^{58} +(-781954. - 1.35438e6i) q^{59} +(-406080. - 703351. i) q^{60} +(1.59185e6 - 2.75716e6i) q^{61} -89856.0 q^{62} +262144. q^{64} +(-2.67477e6 + 4.63284e6i) q^{65} +(784944. + 1.35956e6i) q^{66} +(-1.06434e6 - 1.84349e6i) q^{67} +(-666944. + 1.15518e6i) q^{68} -1.26187e6 q^{69} +5.69454e6 q^{71} +(-186624. + 323242. i) q^{72} +(1.12694e6 + 1.95192e6i) q^{73} +(958792. + 1.66068e6i) q^{74} +(-1.92746e6 + 3.33846e6i) q^{75} -875776. q^{76} +2.45851e6 q^{78} +(-66456.0 + 115105. i) q^{79} +(-962560. - 1.66720e6i) q^{80} +(-265720. - 460241. i) q^{81} +(-211848. + 366931. i) q^{82} +6.95052e6 q^{83} +9.79574e6 q^{85} +(3.49893e6 - 6.06032e6i) q^{86} +(-37449.0 - 64863.6i) q^{87} +(1.86061e6 + 3.22267e6i) q^{88} +(5.31326e6 - 9.20283e6i) q^{89} +2.74104e6 q^{90} -2.99110e6 q^{92} +(151632. - 262634. i) q^{93} +(1.80518e6 + 3.12667e6i) q^{94} +(3.21574e6 + 5.56983e6i) q^{95} +(-442368. + 766204. i) q^{96} +2.40709e6 q^{97} -5.29837e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} - 27 q^{3} - 64 q^{4} - 470 q^{5} + 432 q^{6} + 1024 q^{8} - 729 q^{9} - 3760 q^{10} + 7268 q^{11} - 1728 q^{12} + 22764 q^{13} + 25380 q^{15} - 4096 q^{16} - 20842 q^{17} - 5832 q^{18} + 13684 q^{19}+ \cdots - 10596744 q^{99}+O(q^{100}) $ 2 * q - 8 * q^2 - 27 * q^3 - 64 * q^4 - 470 * q^5 + 432 * q^6 + 1024 * q^8 - 729 * q^9 - 3760 * q^10 + 7268 * q^11 - 1728 * q^12 + 22764 * q^13 + 25380 * q^15 - 4096 * q^16 - 20842 * q^17 - 5832 * q^18 + 13684 * q^19 + 60160 * q^20 - 116288 * q^22 + 46736 * q^23 - 13824 * q^24 - 142775 * q^25 - 91056 * q^26 + 39366 * q^27 + 5548 * q^29 - 101520 * q^30 + 11232 * q^31 - 32768 * q^32 + 196236 * q^33 + 333472 * q^34 + 93312 * q^36 + 239698 * q^37 + 109472 * q^38 - 307314 * q^39 - 240640 * q^40 + 105924 * q^41 - 1749464 * q^43 + 465152 * q^44 - 342630 * q^45 + 373888 * q^46 + 451296 * q^47 + 221184 * q^48 + 2284400 * q^50 - 562734 * q^51 - 728448 * q^52 + 1943538 * q^53 - 157464 * q^54 - 6831920 * q^55 - 738936 * q^57 - 22192 * q^58 - 1563908 * q^59 - 812160 * q^60 + 3183690 * q^61 - 179712 * q^62 + 524288 * q^64 - 5349540 * q^65 + 1569888 * q^66 - 2128684 * q^67 - 1333888 * q^68 - 2523744 * q^69 + 11389088 * q^71 - 373248 * q^72 + 2253878 * q^73 + 1917584 * q^74 - 3854925 * q^75 - 1751552 * q^76 + 4917024 * q^78 - 132912 * q^79 - 1925120 * q^80 - 531441 * q^81 - 423696 * q^82 + 13901048 * q^83 + 19591480 * q^85 + 6997856 * q^86 - 74898 * q^87 + 3721216 * q^88 + 10626510 * q^89 + 5482080 * q^90 - 5982208 * q^92 + 303264 * q^93 + 3610368 * q^94 + 6431480 * q^95 - 884736 * q^96 + 4814180 * q^97 - 10596744 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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	+	6.92820i	−0.353553	+	0.612372i
$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$3$	−13.5000	−	23.3827i	−0.288675	−	0.500000i
$3$	−13.5000	−	23.3827i	−0.288675	−	0.500000i
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	−235.000	+	407.032i	−0.840762	+	1.45624i	0.0484902	+	0.998824i	$0.484559\pi$
$5$	−235.000	+	407.032i	−0.840762	+	1.45624i	−0.889252	+	0.457418i	$0.848774\pi$
$6$	216.000			0.408248
$7$		0			0
$7$		0			0
$8$	512.000			0.353553
$9$	−364.500	+	631.333i	−0.166667	+	0.288675i
$10$	−1880.00	−	3256.26i	−0.594508	−	1.02972i
$11$	3634.00	+	6294.27i	0.823210	+	1.42584i	0.903280	+	0.429052i	$0.141152\pi$
$11$	3634.00	+	6294.27i	0.823210	+	1.42584i	−0.0800700	+	0.996789i	$0.525514\pi$
$12$	−864.000	+	1496.49i	−0.144338	+	0.250000i
$13$	11382.0			1.43687			0.718434	−	0.695595i	$-0.244859\pi$
$13$	11382.0			1.43687			0.718434	+	0.695595i	$0.244859\pi$
$14$		0			0
$15$	12690.0			0.970828
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−10421.0	−	18049.7i	−0.514444	−	0.891043i	−0.999860	−	0.0167597i	$-0.994665\pi$
$17$	−10421.0	−	18049.7i	−0.514444	−	0.891043i	0.485415	−	0.874284i	$-0.338668\pi$
$18$	−2916.00	−	5050.66i	−0.117851	−	0.204124i
$19$	6842.00	−	11850.7i	0.228847	−	0.396375i	−0.728620	−	0.684919i	$-0.759838\pi$
$19$	6842.00	−	11850.7i	0.228847	−	0.396375i	0.957467	+	0.288544i	$0.0931711\pi$
$20$	30080.0			0.840762
$21$		0			0
$22$	−58144.0			−1.16419
$23$	23368.0	−	40474.6i	0.400474	−	0.693641i	−0.593309	−	0.804975i	$-0.702179\pi$
$23$	23368.0	−	40474.6i	0.400474	−	0.693641i	0.993783	+	0.111334i	$0.0355122\pi$
$24$	−6912.00	−	11971.9i	−0.102062	−	0.176777i
$25$	−71387.5	−	123647.i	−0.913760	−	1.58268i
$26$	−45528.0	+	78856.8i	−0.508010	+	0.879898i
$27$	19683.0			0.192450
$28$		0			0
$29$	2774.00			0.0211210			0.0105605	−	0.999944i	$-0.496638\pi$
$29$	2774.00			0.0211210			0.0105605	+	0.999944i	$0.496638\pi$
$30$	−50760.0	+	87918.9i	−0.343239	+	0.594508i
$31$	5616.00	+	9727.20i	0.0338580	+	0.0586438i	0.882458	−	0.470391i	$-0.155887\pi$
$31$	5616.00	+	9727.20i	0.0338580	+	0.0586438i	−0.848600	+	0.529035i	$0.822554\pi$
$32$	−16384.0	−	28377.9i	−0.0883883	−	0.153093i
$33$	98118.0	−	169945.i	0.475280	−	0.823210i
$34$	166736.			0.727534
$35$		0			0
$36$	46656.0			0.166667
$37$	119849.	−	207585.i	0.388981	−	0.673735i	−0.603332	−	0.797490i	$-0.706161\pi$
$37$	119849.	−	207585.i	0.388981	−	0.673735i	0.992313	+	0.123755i	$0.0394938\pi$
$38$	54736.0	+	94805.5i	0.161819	+	0.280279i
$39$	−153657.	−	266142.i	−0.414788	−	0.718434i
$40$	−120320.	+	208400.i	−0.297254	+	0.514859i
$41$	52962.0			0.120011			0.0600055	−	0.998198i	$-0.480888\pi$
$41$	52962.0			0.120011			0.0600055	+	0.998198i	$0.480888\pi$
$42$		0			0
$43$	−874732.			−1.67778			−0.838891	−	0.544300i	$-0.816795\pi$
$43$	−874732.			−1.67778			−0.838891	+	0.544300i	$0.816795\pi$
$44$	232576.	−	402833.i	0.411605	−	0.712921i
$45$	−171315.	−	296726.i	−0.280254	−	0.485414i
$46$	186944.	+	323797.i	0.283178	+	0.490478i
$47$	225648.	−	390834.i	0.317022	−	0.549098i	−0.662843	−	0.748758i	$-0.730651\pi$
$47$	225648.	−	390834.i	0.317022	−	0.549098i	0.979865	+	0.199660i	$0.0639839\pi$
$48$	110592.			0.144338
$49$		0			0
$50$	1.14220e6			1.29225
$51$	−281367.	+	487342.i	−0.297014	+	0.514444i
$52$	−364224.	−	630854.i	−0.359217	−	0.622182i
$53$	971769.	+	1.68315e6i	0.896597	+	1.55295i	0.831815	+	0.555053i	$0.187302\pi$
$53$	971769.	+	1.68315e6i	0.896597	+	1.55295i	0.0647824	+	0.997899i	$0.479365\pi$
$54$	−78732.0	+	136368.i	−0.0680414	+	0.117851i
$55$	−3.41596e6			−2.76849
$56$		0			0
$57$	−369468.			−0.264250
$58$	−11096.0	+	19218.8i	−0.00746738	+	0.0129339i
$59$	−781954.	−	1.35438e6i	−0.495677	−	0.858539i	0.504310	−	0.863523i	$-0.331747\pi$
$59$	−781954.	−	1.35438e6i	−0.495677	−	0.858539i	−0.999988	+	0.00498408i	$0.998414\pi$
$60$	−406080.	−	703351.i	−0.242707	−	0.420381i
$61$	1.59185e6	−	2.75716e6i	0.897938	−	1.55527i	0.0678122	−	0.997698i	$-0.478398\pi$
$61$	1.59185e6	−	2.75716e6i	0.897938	−	1.55527i	0.830126	−	0.557576i	$-0.188269\pi$
$62$	−89856.0			−0.0478824
$63$		0			0
$64$	262144.			0.125000
$65$	−2.67477e6	+	4.63284e6i	−1.20806	+	2.09243i
$66$	784944.	+	1.35956e6i	0.336074	+	0.582097i
$67$	−1.06434e6	−	1.84349e6i	−0.432334	−	0.748824i	0.564740	−	0.825269i	$-0.308977\pi$
$67$	−1.06434e6	−	1.84349e6i	−0.432334	−	0.748824i	−0.997074	+	0.0764445i	$0.975643\pi$
$68$	−666944.	+	1.15518e6i	−0.257222	+	0.445522i
$69$	−1.26187e6			−0.462427
$70$		0			0
$71$	5.69454e6			1.88823			0.944115	−	0.329617i	$-0.106920\pi$
$71$	5.69454e6			1.88823			0.944115	+	0.329617i	$0.106920\pi$
$72$	−186624.	+	323242.i	−0.0589256	+	0.102062i
$73$	1.12694e6	+	1.95192e6i	0.339055	+	0.587261i	0.984255	−	0.176753i	$-0.0565593\pi$
$73$	1.12694e6	+	1.95192e6i	0.339055	+	0.587261i	−0.645200	+	0.764014i	$0.723226\pi$
$74$	958792.	+	1.66068e6i	0.275051	+	0.476402i
$75$	−1.92746e6	+	3.33846e6i	−0.527560	+	0.913760i
$76$	−875776.			−0.228847
$77$		0			0
$78$	2.45851e6			0.586599
$79$	−66456.0	+	115105.i	−0.0151649	+	0.0262664i	−0.873508	−	0.486809i	$-0.838161\pi$
$79$	−66456.0	+	115105.i	−0.0151649	+	0.0262664i	0.858343	+	0.513076i	$0.171494\pi$
$80$	−962560.	−	1.66720e6i	−0.210190	−	0.364060i
$81$	−265720.	−	460241.i	−0.0555556	−	0.0962250i
$82$	−211848.	+	366931.i	−0.0424303	+	0.0734914i
$83$	6.95052e6			1.33427			0.667136	−	0.744936i	$-0.267520\pi$
$83$	6.95052e6			1.33427			0.667136	+	0.744936i	$0.267520\pi$
$84$		0			0
$85$	9.79574e6			1.73010
$86$	3.49893e6	−	6.06032e6i	0.593185	−	1.02743i
$87$	−37449.0	−	64863.6i	−0.00609709	−	0.0105605i
$88$	1.86061e6	+	3.22267e6i	0.291049	+	0.504111i
$89$	5.31326e6	−	9.20283e6i	0.798906	−	1.38375i	−0.121423	−	0.992601i	$-0.538746\pi$
$89$	5.31326e6	−	9.20283e6i	0.798906	−	1.38375i	0.920329	−	0.391145i	$-0.127921\pi$
$90$	2.74104e6			0.396339
$91$		0			0
$92$	−2.99110e6			−0.400474
$93$	151632.	−	262634.i	0.0195479	−	0.0338580i
$94$	1.80518e6	+	3.12667e6i	0.224168	+	0.388271i
$95$	3.21574e6	+	5.56983e6i	0.384812	+	0.666513i
$96$	−442368.	+	766204.i	−0.0510310	+	0.0883883i
$97$	2.40709e6			0.267788			0.133894	−	0.990996i	$-0.457252\pi$
$97$	2.40709e6			0.267788			0.133894	+	0.990996i	$0.457252\pi$
$98$		0			0
$99$	−5.29837e6			−0.548807
$100$	−4.56880e6	+	7.91339e6i	−0.456880	+	0.791339i
$101$	−3.88788e6	−	6.73400e6i	−0.375481	−	0.650351i	0.614918	−	0.788591i	$-0.289189\pi$
$101$	−3.88788e6	−	6.73400e6i	−0.375481	−	0.650351i	−0.990399	+	0.138239i	$0.955856\pi$
$102$	−2.25094e6	−	3.89874e6i	−0.210021	−	0.363767i
$103$	6.61701e6	−	1.14610e7i	0.596666	−	1.03346i	−0.396643	−	0.917973i	$-0.629825\pi$
$103$	6.61701e6	−	1.14610e7i	0.596666	−	1.03346i	0.993309	−	0.115484i	$-0.0368418\pi$
$104$	5.82758e6			0.508010
$105$		0			0
$106$	−1.55483e7			−1.26798
$107$	3.60472e6	−	6.24356e6i	0.284465	−	0.492708i	−0.688014	−	0.725697i	$-0.741517\pi$
$107$	3.60472e6	−	6.24356e6i	0.284465	−	0.492708i	0.972479	+	0.232989i	$0.0748508\pi$
$108$	−629856.	−	1.09094e6i	−0.0481125	−	0.0833333i
$109$	−1.94519e6	−	3.36916e6i	−0.143869	−	0.249189i	0.785081	−	0.619393i	$-0.212621\pi$
$109$	−1.94519e6	−	3.36916e6i	−0.143869	−	0.249189i	−0.928951	+	0.370204i	$0.879288\pi$
$110$	1.36638e7	−	2.36665e7i	0.978810	−	1.69535i
$111$	−6.47185e6			−0.449157
$112$		0			0
$113$	1.46647e7			0.956091			0.478046	−	0.878335i	$-0.341345\pi$
$113$	1.46647e7			0.956091			0.478046	+	0.878335i	$0.341345\pi$
$114$	1.47787e6	−	2.55975e6i	0.0934264	−	0.161819i
$115$	1.09830e7	+	1.90230e7i	0.673406	+	1.16637i
$116$	−88768.0	−	153751.i	−0.00528024	−	0.00914564i
$117$	−4.14874e6	+	7.18583e6i	−0.239478	+	0.414788i
$118$	1.25113e7			0.700994
$119$		0			0
$120$	6.49728e6			0.343239
$121$	−1.66683e7	+	2.88704e7i	−0.855349	+	1.48151i
$122$	1.27348e7	+	2.20573e7i	0.634938	+	1.09974i
$123$	−714987.	−	1.23839e6i	−0.0346442	−	0.0600055i
$124$	359424.	−	622541.i	0.0169290	−	0.0293219i
$125$	3.03855e7			1.39149
$126$		0			0
$127$	3.87331e6			0.167791			0.0838957	−	0.996475i	$-0.473264\pi$
$127$	3.87331e6			0.167791			0.0838957	+	0.996475i	$0.473264\pi$
$128$	−1.04858e6	+	1.81619e6i	−0.0441942	+	0.0765466i
$129$	1.18089e7	+	2.04536e7i	0.484334	+	0.838891i
$130$	−2.13982e7	−	3.70627e7i	−0.854230	−	1.47957i
$131$	−1.13738e7	+	1.97000e7i	−0.442035	+	0.765627i	−0.997840	−	0.0656854i	$-0.979077\pi$
$131$	−1.13738e7	+	1.97000e7i	−0.442035	+	0.765627i	0.555805	+	0.831312i	$0.312410\pi$
$132$	−1.25591e7			−0.475280
$133$		0			0
$134$	1.70295e7			0.611413
$135$	−4.62550e6	+	8.01161e6i	−0.161805	+	0.280254i
$136$	−5.33555e6	−	9.24145e6i	−0.181883	−	0.315031i
$137$	2.11191e7	+	3.65794e7i	0.701703	+	1.21539i	0.967868	+	0.251458i	$0.0809100\pi$
$137$	2.11191e7	+	3.65794e7i	0.701703	+	1.21539i	−0.266165	+	0.963927i	$0.585757\pi$
$138$	5.04749e6	−	8.74251e6i	0.163493	−	0.283178i
$139$	−2.02320e6			−0.0638978			−0.0319489	−	0.999490i	$-0.510171\pi$
$139$	−2.02320e6			−0.0638978			−0.0319489	+	0.999490i	$0.510171\pi$
$140$		0			0
$141$	−1.21850e7			−0.366065
$142$	−2.27782e7	+	3.94530e7i	−0.667590	+	1.15630i
$143$	4.13622e7	+	7.16414e7i	1.18284	+	2.04875i
$144$	−1.49299e6	−	2.58594e6i	−0.0416667	−	0.0721688i
$145$	−651890.	+	1.12911e6i	−0.0177577	+	0.0307572i
$146$	−1.80310e7			−0.479496
$147$		0			0
$148$	−1.53407e7			−0.388981
$149$	−3.16509e7	+	5.48209e7i	−0.783851	+	1.35767i	0.145832	+	0.989309i	$0.453414\pi$
$149$	−3.16509e7	+	5.48209e7i	−0.783851	+	1.35767i	−0.929683	+	0.368360i	$0.879919\pi$
$150$	−1.54197e7	−	2.67077e7i	−0.373041	−	0.646126i
$151$	2.69813e7	+	4.67330e7i	0.637739	+	1.10460i	0.985928	+	0.167173i	$0.0534637\pi$
$151$	2.69813e7	+	4.67330e7i	0.637739	+	1.10460i	−0.348188	+	0.937425i	$0.613203\pi$
$152$	3.50310e6	−	6.06755e6i	0.0809097	−	0.140140i
$153$	1.51938e7			0.342963
$154$		0			0
$155$	−5.27904e6			−0.113866
$156$	−9.83405e6	+	1.70331e7i	−0.207394	+	0.359217i
$157$	−2.91683e7	−	5.05211e7i	−0.601538	−	1.04189i	−0.992588	−	0.121525i	$-0.961222\pi$
$157$	−2.91683e7	−	5.05211e7i	−0.601538	−	1.04189i	0.391050	−	0.920369i	$-0.372112\pi$
$158$	−531648.	−	920841.i	−0.0107232	−	0.0185731i
$159$	2.62378e7	−	4.54451e7i	0.517651	−	0.896597i
$160$	1.54010e7			0.297254
$161$		0			0
$162$	4.25153e6			0.0785674
$163$	−3.02922e7	+	5.24677e7i	−0.547867	+	0.948933i	0.450554	+	0.892749i	$0.351227\pi$
$163$	−3.02922e7	+	5.24677e7i	−0.547867	+	0.948933i	−0.998420	+	0.0561836i	$0.982107\pi$
$164$	−1.69478e6	−	2.93545e6i	−0.0300027	−	0.0519663i
$165$	4.61155e7	+	7.98743e7i	0.799195	+	1.38425i
$166$	−2.78021e7	+	4.81546e7i	−0.471736	+	0.817071i
$167$	5.94193e7			0.987234			0.493617	−	0.869680i	$-0.335675\pi$
$167$	5.94193e7			0.987234			0.493617	+	0.869680i	$0.335675\pi$
$168$		0			0
$169$	6.68014e7			1.06459
$170$	−3.91830e7	+	6.78669e7i	−0.611682	+	1.05947i
$171$	4.98782e6	+	8.63915e6i	0.0762824	+	0.132125i
$172$	2.79914e7	+	4.84826e7i	0.419445	+	0.726501i
$173$	−2.79283e7	+	4.83732e7i	−0.410094	+	0.710303i	−0.994900	−	0.100870i	$-0.967837\pi$
$173$	−2.79283e7	+	4.83732e7i	−0.410094	+	0.710303i	0.584806	+	0.811173i	$0.301171\pi$
$174$	599184.			0.00862259
$175$		0			0
$176$	−2.97697e7			−0.411605
$177$	−2.11128e7	+	3.65684e7i	−0.286180	+	0.495677i
$178$	4.25060e7	+	7.36226e7i	0.564912	+	0.978456i
$179$	−4.01126e7	−	6.94771e7i	−0.522752	−	0.905432i	−0.999650	−	0.0264736i	$-0.991572\pi$
$179$	−4.01126e7	−	6.94771e7i	−0.522752	−	0.905432i	0.476898	−	0.878959i	$-0.341761\pi$
$180$	−1.09642e7	+	1.89905e7i	−0.140127	+	0.242707i
$181$	−7.18632e7			−0.900807			−0.450403	−	0.892825i	$-0.648720\pi$
$181$	−7.18632e7			−0.900807			−0.450403	+	0.892825i	$0.648720\pi$
$182$		0			0
$183$	−8.59596e7			−1.03685
$184$	1.19644e7	−	2.07230e7i	0.141589	−	0.245239i
$185$	5.63290e7	+	9.75647e7i	0.654081	+	1.13290i
$186$	1.21306e6	+	2.10107e6i	0.0138225	+	0.0239412i
$187$	7.57398e7	−	1.31185e8i	0.846991	−	1.46703i
$188$	−2.88829e7			−0.317022
$189$		0			0
$190$	−5.14518e7			−0.544206
$191$	8.37176e6	−	1.45003e7i	0.0869361	−	0.150578i	−0.819278	−	0.573396i	$-0.805626\pi$
$191$	8.37176e6	−	1.45003e7i	0.0869361	−	0.150578i	0.906215	+	0.422818i	$0.138959\pi$
$192$	−3.53894e6	−	6.12963e6i	−0.0360844	−	0.0625000i
$193$	6.73511e7	+	1.16656e8i	0.674364	+	1.16803i	0.976654	+	0.214816i	$0.0689153\pi$
$193$	6.73511e7	+	1.16656e8i	0.674364	+	1.16803i	−0.302291	+	0.953216i	$0.597751\pi$
$194$	−9.62836e6	+	1.66768e7i	−0.0946774	+	0.163986i
$195$	1.44438e8			1.39495
$196$		0			0
$197$	−5.89413e7			−0.549273			−0.274636	−	0.961548i	$-0.588557\pi$
$197$	−5.89413e7			−0.549273			−0.274636	+	0.961548i	$0.588557\pi$
$198$	2.11935e7	−	3.67082e7i	0.194032	−	0.336074i
$199$	−6.56866e7	−	1.13773e8i	−0.590869	−	1.02341i	−0.994116	−	0.108324i	$-0.965452\pi$
$199$	−6.56866e7	−	1.13773e8i	−0.590869	−	1.02341i	0.403247	−	0.915091i	$-0.367882\pi$
$200$	−3.65504e7	−	6.33071e7i	−0.323063	−	0.559561i
$201$	−2.87372e7	+	4.97743e7i	−0.249608	+	0.432334i
$202$	6.22060e7			0.531010
$203$		0			0
$204$	3.60150e7			0.297014
$205$	−1.24461e7	+	2.15572e7i	−0.100901	+	0.174765i
$206$	5.29361e7	+	9.16880e7i	0.421907	+	0.730764i
$207$	1.70353e7	+	2.95060e7i	0.133491	+	0.231214i
$208$	−2.33103e7	+	4.03747e7i	−0.179608	+	0.311091i
$209$	9.94553e7			0.753557
$210$		0			0
$211$	−2.96600e7			−0.217362			−0.108681	−	0.994077i	$-0.534663\pi$
$211$	−2.96600e7			−0.217362			−0.108681	+	0.994077i	$0.534663\pi$
$212$	6.21932e7	−	1.07722e8i	0.448299	−	0.776476i
$213$	−7.68763e7	−	1.33154e8i	−0.545085	−	0.944115i
$214$	2.88378e7	+	4.99485e7i	0.201147	+	0.348397i
$215$	2.05562e8	−	3.56044e8i	1.41061	−	2.44326i
$216$	1.00777e7			0.0680414
$217$		0			0
$218$	3.11230e7			0.203462
$219$	3.04274e7	−	5.27017e7i	0.195754	−	0.339055i
$220$	1.09311e8	+	1.89332e8i	0.692123	+	1.19879i
$221$	−1.18612e8	−	2.05442e8i	−0.739188	−	1.28031i
$222$	2.58874e7	−	4.48383e7i	0.158801	−	0.275051i
$223$	3.16037e8			1.90841			0.954203	−	0.299161i	$-0.0967068\pi$
$223$	3.16037e8			1.90841			0.954203	+	0.299161i	$0.0967068\pi$
$224$		0			0
$225$	1.04083e8			0.609173
$226$	−5.86589e7	+	1.01600e8i	−0.338029	+	0.585484i
$227$	−2.38028e7	−	4.12277e7i	−0.135063	−	0.233937i	0.790558	−	0.612387i	$-0.209790\pi$
$227$	−2.38028e7	−	4.12277e7i	−0.135063	−	0.233937i	−0.925622	+	0.378450i	$0.876457\pi$
$228$	1.18230e7	+	2.04780e7i	0.0660625	+	0.114424i
$229$	5.21444e7	−	9.03168e7i	0.286935	−	0.496986i	−0.686142	−	0.727468i	$-0.740697\pi$
$229$	5.21444e7	−	9.03168e7i	0.286935	−	0.496986i	0.973077	+	0.230482i	$0.0740303\pi$
$230$	−1.75727e8			−0.952340
$231$		0			0
$232$	1.42029e6			0.00746738
$233$	−1.17529e8	+	2.03567e8i	−0.608697	+	1.05429i	0.382759	+	0.923848i	$0.374974\pi$
$233$	−1.17529e8	+	2.03567e8i	−0.608697	+	1.05429i	−0.991456	+	0.130445i	$0.958359\pi$
$234$	−3.31899e7	−	5.74866e7i	−0.169337	−	0.293299i
$235$	1.06055e8	+	1.83692e8i	0.533079	+	0.923320i
$236$	−5.00451e7	+	8.66806e7i	−0.247839	+	0.429269i
$237$	3.58862e6			0.0175109
$238$		0			0
$239$	3.74362e7			0.177378			0.0886888	−	0.996059i	$-0.471732\pi$
$239$	3.74362e7			0.177378			0.0886888	+	0.996059i	$0.471732\pi$
$240$	−2.59891e7	+	4.50145e7i	−0.121353	+	0.210190i
$241$	−4.93834e6	−	8.55345e6i	−0.0227259	−	0.0393624i	0.854439	−	0.519552i	$-0.173901\pi$
$241$	−4.93834e6	−	8.55345e6i	−0.0227259	−	0.0393624i	−0.877165	+	0.480190i	$0.840568\pi$
$242$	−1.33347e8	−	2.30963e8i	−0.604823	−	1.04758i
$243$	−7.17445e6	+	1.24265e7i	−0.0320750	+	0.0555556i
$244$	−2.03756e8			−0.897938
$245$		0			0
$246$	1.14398e7			0.0489943
$247$	7.78756e7	−	1.34885e8i	0.328823	−	0.569538i
$248$	2.87539e6	+	4.98033e6i	0.0119706	+	0.0207337i
$249$	−9.38321e7	−	1.62522e8i	−0.385171	−	0.667136i
$250$	−1.21542e8	+	2.10517e8i	−0.491967	+	0.852113i
$251$	1.32438e8			0.528634			0.264317	−	0.964436i	$-0.414853\pi$
$251$	1.32438e8			0.528634			0.264317	+	0.964436i	$0.414853\pi$
$252$		0			0
$253$	3.39677e8			1.31870
$254$	−1.54932e7	+	2.68351e7i	−0.0593232	+	0.102751i
$255$	−1.32242e8	−	2.29051e8i	−0.499437	−	0.865050i
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	−1.66334e8	+	2.88098e8i	−0.611243	+	1.05870i	0.379788	+	0.925074i	$0.375997\pi$
$257$	−1.66334e8	+	2.88098e8i	−0.611243	+	1.05870i	−0.991031	+	0.133631i	$0.957336\pi$
$258$	−1.88942e8			−0.684951
$259$		0			0
$260$	3.42371e8			1.20806
$261$	−1.01112e6	+	1.75132e6i	−0.00352016	+	0.00609709i
$262$	−9.09905e7	−	1.57600e8i	−0.312566	−	0.541380i
$263$	4.75614e7	+	8.23788e7i	0.161217	+	0.279235i	0.935305	−	0.353842i	$-0.115125\pi$
$263$	4.75614e7	+	8.23788e7i	0.161217	+	0.279235i	−0.774089	+	0.633077i	$0.781792\pi$
$264$	5.02364e7	−	8.70120e7i	0.168037	−	0.291049i
$265$	−9.13463e8			−3.01530
$266$		0			0
$267$	−2.86916e8			−0.922497
$268$	−6.81179e7	+	1.17984e8i	−0.216167	+	0.374412i
$269$	1.34427e8	+	2.32835e8i	0.421071	+	0.729316i	0.996044	−	0.0888560i	$-0.0283211\pi$
$269$	1.34427e8	+	2.32835e8i	0.421071	+	0.729316i	−0.574974	+	0.818172i	$0.694988\pi$
$270$	−3.70040e7	−	6.40929e7i	−0.114413	−	0.198169i
$271$	−2.26442e8	+	3.92209e8i	−0.691137	+	1.19708i	0.280329	+	0.959904i	$0.409557\pi$
$271$	−2.26442e8	+	3.92209e8i	−0.691137	+	1.19708i	−0.971466	+	0.237180i	$0.923777\pi$
$272$	8.53688e7			0.257222
$273$		0			0
$274$	−3.37906e8			−0.992358
$275$	5.18844e8	−	8.98665e8i	1.50443	−	2.60575i
$276$	4.03799e7	+	6.99400e7i	0.115607	+	0.200237i
$277$	8.23547e6	+	1.42643e7i	0.0232814	+	0.0403246i	0.877431	−	0.479702i	$-0.159255\pi$
$277$	8.23547e6	+	1.42643e7i	0.0232814	+	0.0403246i	−0.854150	+	0.520027i	$0.825922\pi$
$278$	8.09278e6	−	1.40171e7i	0.0225913	−	0.0391293i
$279$	−8.18813e6			−0.0225720
$280$		0			0
$281$	5.08113e8			1.36612			0.683059	−	0.730363i	$-0.260649\pi$
$281$	5.08113e8			1.36612			0.683059	+	0.730363i	$0.260649\pi$
$282$	4.87400e7	−	8.44201e7i	0.129424	−	0.224168i
$283$	1.28748e8	+	2.22998e8i	0.337666	+	0.584855i	0.983993	−	0.178205i	$-0.0570291\pi$
$283$	1.28748e8	+	2.22998e8i	0.337666	+	0.584855i	−0.646327	+	0.763061i	$0.723696\pi$
$284$	−1.82225e8	−	3.15624e8i	−0.472057	−	0.817627i
$285$	8.68250e7	−	1.50385e8i	0.222171	−	0.384812i
$286$	−6.61795e8			−1.67279
$287$		0			0
$288$	2.38879e7			0.0589256
$289$	−1.20251e7	+	2.08282e7i	−0.0293054	+	0.0507585i
$290$	−5.21512e6	−	9.03285e6i	−0.0125566	−	0.0217486i
$291$	−3.24957e7	−	5.62842e7i	−0.0773038	−	0.133894i
$292$	7.21241e7	−	1.24923e8i	0.169528	−	0.293630i
$293$	7.33847e7			0.170439			0.0852195	−	0.996362i	$-0.472841\pi$
$293$	7.33847e7			0.170439			0.0852195	+	0.996362i	$0.472841\pi$
$294$		0			0
$295$	7.35037e8			1.66699
$296$	6.13627e7	−	1.06283e8i	0.137526	−	0.238201i
$297$	7.15280e7	+	1.23890e8i	0.158427	+	0.274403i
$298$	−2.53207e8	−	4.38567e8i	−0.554266	−	0.960017i
$299$	2.65975e8	−	4.60681e8i	0.575428	−	0.996670i
$300$	2.46715e8			0.527560
$301$		0			0
$302$	−4.31701e8			−0.901900
$303$	−1.04973e8	+	1.81818e8i	−0.216784	+	0.375481i
$304$	2.80248e7	+	4.85404e7i	0.0572118	+	0.0990937i
$305$	7.48167e8	+	1.29586e9i	1.50990	+	2.61523i
$306$	−6.07753e7	+	1.05266e8i	−0.121256	+	0.210021i
$307$	−9.31624e7			−0.183762			−0.0918811	−	0.995770i	$-0.529288\pi$
$307$	−9.31624e7			−0.183762			−0.0918811	+	0.995770i	$0.529288\pi$
$308$		0			0
$309$	−3.57319e8			−0.688971
$310$	2.11162e7	−	3.65743e7i	0.0402577	−	0.0697284i
$311$	−3.05467e8	−	5.29085e8i	−0.575842	−	0.997387i	−0.995950	−	0.0899130i	$-0.971341\pi$
$311$	−3.05467e8	−	5.29085e8i	−0.575842	−	0.997387i	0.420108	−	0.907474i	$-0.361992\pi$
$312$	−7.86724e7	−	1.36265e8i	−0.146650	−	0.254005i
$313$	1.06115e8	−	1.83797e8i	0.195602	−	0.338793i	−0.751496	−	0.659738i	$-0.770667\pi$
$313$	1.06115e8	−	1.83797e8i	0.195602	−	0.338793i	0.947098	+	0.320945i	$0.104001\pi$
$314$	4.66694e8			0.850703
$315$		0			0
$316$	8.50637e6			0.0151649
$317$	5.51972e8	−	9.56044e8i	0.973218	−	1.68566i	0.287522	−	0.957774i	$-0.407168\pi$
$317$	5.51972e8	−	9.56044e8i	0.973218	−	1.68566i	0.685695	−	0.727889i	$-0.259498\pi$
$318$	2.09902e8	+	3.63561e8i	0.366034	+	0.633990i
$319$	1.00807e7	+	1.74603e7i	0.0173870	+	0.0301151i
$320$	−6.16038e7	+	1.06701e8i	−0.105095	+	0.182030i
$321$	−1.94655e8			−0.328472
$322$		0			0
$323$	−2.85202e8			−0.470916
$324$	−1.70061e7	+	2.94555e7i	−0.0277778	+	0.0481125i
$325$	−8.12533e8	−	1.40735e9i	−1.31295	−	2.27410i
$326$	−2.42338e8	−	4.19742e8i	−0.387400	−	0.670997i
$327$	−5.25200e7	+	9.09674e7i	−0.0830631	+	0.143869i
$328$	2.71165e7			0.0424303
$329$		0			0
$330$	−7.37847e8			−1.13023
$331$	3.35294e8	−	5.80746e8i	0.508192	−	0.880214i	−0.491763	−	0.870729i	$-0.663647\pi$
$331$	3.35294e8	−	5.80746e8i	0.508192	−	0.880214i	0.999955	−	0.00948492i	$-0.00301919\pi$
$332$	−2.22417e8	−	3.85237e8i	−0.333568	−	0.577757i
$333$	8.73699e7	+	1.51329e8i	0.129660	+	0.224578i
$334$	−2.37677e8	+	4.11669e8i	−0.349040	+	0.604555i
$335$	1.00048e9			1.45396
$336$		0			0
$337$	−6.84122e8			−0.973709			−0.486854	−	0.873483i	$-0.661856\pi$
$337$	−6.84122e8			−0.973709			−0.486854	+	0.873483i	$0.661856\pi$
$338$	−2.67206e8	+	4.62814e8i	−0.376389	+	0.651925i
$339$	−1.97974e8	−	3.42901e8i	−0.276000	−	0.478046i
$340$	−3.13464e8	−	5.42935e8i	−0.432525	−	0.749155i
$341$	−4.08171e7	+	7.06973e7i	−0.0557445	+	0.0965522i
$342$	−7.98051e7			−0.107880
$343$		0			0
$344$	−4.47863e8			−0.593185
$345$	2.96540e8	−	5.13622e8i	0.388791	−	0.673406i
$346$	−2.23426e8	−	3.86986e8i	−0.289980	−	0.502260i
$347$	−2.18776e8	−	3.78932e8i	−0.281091	−	0.486865i	0.690562	−	0.723273i	$-0.257363\pi$
$347$	−2.18776e8	−	3.78932e8i	−0.281091	−	0.486865i	−0.971654	+	0.236408i	$0.924030\pi$
$348$	−2.39674e6	+	4.15127e6i	−0.00304855	+	0.00528024i
$349$	9.39833e6			0.0118348			0.00591741	−	0.999982i	$-0.498116\pi$
$349$	9.39833e6			0.0118348			0.00591741	+	0.999982i	$0.498116\pi$
$350$		0			0
$351$	2.24032e8			0.276525
$352$	1.19079e8	−	2.06251e8i	0.145524	−	0.252055i
$353$	−7.07359e8	−	1.22518e9i	−0.855911	−	1.48248i	−0.875797	−	0.482679i	$-0.839664\pi$
$353$	−7.07359e8	−	1.22518e9i	−0.855911	−	1.48248i	0.0198865	−	0.999802i	$-0.493670\pi$
$354$	−1.68902e8	−	2.92547e8i	−0.202359	−	0.350497i
$355$	−1.33822e9	+	2.31786e9i	−1.58755	+	2.74972i
$356$	−6.80097e8			−0.798906
$357$		0			0
$358$	6.41802e8			0.739282
$359$	1.53792e8	−	2.66375e8i	0.175429	−	0.303852i	−0.764881	−	0.644172i	$-0.777202\pi$
$359$	1.53792e8	−	2.66375e8i	0.175429	−	0.303852i	0.940310	+	0.340320i	$0.110535\pi$
$360$	−8.77133e7	−	1.51924e8i	−0.0990847	−	0.171620i
$361$	3.53310e8	+	6.11951e8i	0.395258	+	0.684607i
$362$	2.87453e8	−	4.97883e8i	0.318483	−	0.551629i
$363$	9.00090e8			0.987672
$364$		0			0
$365$	−1.05932e9			−1.14026
$366$	3.43839e8	−	5.95546e8i	0.366582	−	0.634938i
$367$	6.15636e8	+	1.06631e9i	0.650119	+	1.12604i	0.983094	+	0.183103i	$0.0586143\pi$
$367$	6.15636e8	+	1.06631e9i	0.650119	+	1.12604i	−0.332975	+	0.942936i	$0.608052\pi$
$368$	9.57153e7	+	1.65784e8i	0.100118	+	0.173410i
$369$	−1.93046e7	+	3.34366e7i	−0.0200018	+	0.0346442i
$370$	−9.01264e8			−0.925010
$371$		0			0
$372$	−1.94089e7			−0.0195479
$373$	−9.17958e8	+	1.58995e9i	−0.915887	+	1.58636i	−0.110291	+	0.993899i	$0.535178\pi$
$373$	−9.17958e8	+	1.58995e9i	−0.915887	+	1.58636i	−0.805597	+	0.592464i	$0.798155\pi$
$374$	6.05919e8	+	1.04948e9i	0.598913	+	1.03735i
$375$	−4.10204e8	−	7.10495e8i	−0.401690	−	0.695747i
$376$	1.15532e8	−	2.00107e8i	0.112084	−	0.194135i
$377$	3.15737e7			0.0303480
$378$		0			0
$379$	−6.48934e8			−0.612298			−0.306149	−	0.951984i	$-0.599041\pi$
$379$	−6.48934e8			−0.612298			−0.306149	+	0.951984i	$0.599041\pi$
$380$	2.05807e8	−	3.56469e8i	0.192406	−	0.333257i
$381$	−5.22897e7	−	9.05684e7i	−0.0484372	−	0.0838957i
$382$	6.69741e7	+	1.16003e8i	0.0614731	+	0.106475i
$383$	3.40160e8	−	5.89175e8i	0.309377	−	0.535857i	−0.668849	−	0.743398i	$-0.733213\pi$
$383$	3.40160e8	−	5.89175e8i	0.309377	−	0.535857i	0.978226	+	0.207541i	$0.0665462\pi$
$384$	5.66231e7			0.0510310
$385$		0			0
$386$	−1.07762e9			−0.953694
$387$	3.18840e8	−	5.52247e8i	0.279630	−	0.484334i
$388$	−7.70269e7	−	1.33414e8i	−0.0669470	−	0.115956i
$389$	−1.36853e8	−	2.37036e8i	−0.117877	−	0.204169i	0.801049	−	0.598599i	$-0.204276\pi$
$389$	−1.36853e8	−	2.37036e8i	−0.117877	−	0.204169i	−0.918926	+	0.394430i	$0.870942\pi$
$390$	−5.77750e8	+	1.00069e9i	−0.493190	+	0.854230i
$391$	−9.74072e8			−0.824086
$392$		0			0
$393$	6.14186e8			0.510418
$394$	2.35765e8	−	4.08357e8i	0.194197	−	0.336359i
$395$	−3.12343e7	−	5.40994e7i	−0.0255001	−	0.0441675i
$396$	1.69548e8	+	2.93666e8i	0.137202	+	0.237640i
$397$	6.05171e8	−	1.04819e9i	0.485413	−	0.840759i	−0.514447	−	0.857522i	$-0.672003\pi$
$397$	6.05171e8	−	1.04819e9i	0.485413	−	0.840759i	0.999859	+	0.0167629i	$0.00533605\pi$
$398$	1.05099e9			0.835615
$399$		0			0
$400$	5.84806e8			0.456880
$401$	2.98551e8	−	5.17106e8i	0.231214	−	0.400474i	−0.726952	−	0.686688i	$-0.759064\pi$
$401$	2.98551e8	−	5.17106e8i	0.231214	−	0.400474i	0.958166	+	0.286215i	$0.0923970\pi$
$402$	−2.29898e8	−	3.98195e8i	−0.176500	−	0.305706i
$403$	6.39213e7	+	1.10715e8i	0.0486495	+	0.0842633i
$404$	−2.48824e8	+	4.30976e8i	−0.187740	+	0.325176i
$405$	2.49777e8			0.186836
$406$		0			0
$407$	1.74213e9			1.28085
$408$	−1.44060e8	+	2.49519e8i	−0.105010	+	0.181883i
$409$	5.98836e8	+	1.03721e9i	0.432789	+	0.749612i	0.997112	−	0.0759416i	$-0.0241962\pi$
$409$	5.98836e8	+	1.03721e9i	0.432789	+	0.749612i	−0.564323	+	0.825554i	$0.690863\pi$
$410$	−9.95686e7	−	1.72458e8i	−0.0713475	−	0.123577i
$411$	5.70216e8	−	9.87643e8i	0.405128	−	0.701703i
$412$	−8.46978e8			−0.596666
$413$		0			0
$414$	−2.72564e8			−0.188785
$415$	−1.63337e9	+	2.82909e9i	−1.12180	+	1.94302i
$416$	−1.86483e8	−	3.22997e8i	−0.127002	−	0.219975i
$417$	2.73131e7	+	4.73078e7i	0.0184457	+	0.0319489i
$418$	−3.97821e8	+	6.89047e8i	−0.266423	+	0.461457i
$419$	−1.68680e9			−1.12025			−0.560125	−	0.828408i	$-0.689247\pi$
$419$	−1.68680e9			−1.12025			−0.560125	+	0.828408i	$0.689247\pi$
$420$		0			0
$421$	−9.60356e8			−0.627256			−0.313628	−	0.949546i	$-0.601544\pi$
$421$	−9.60356e8			−0.627256			−0.313628	+	0.949546i	$0.601544\pi$
$422$	1.18640e8	−	2.05491e8i	0.0768489	−	0.133106i
$423$	1.64497e8	+	2.84918e8i	0.105674	+	0.183033i
$424$	4.97546e8	+	8.61774e8i	0.316995	+	0.549052i
$425$	−1.48786e9	+	2.57705e9i	−0.940157	+	1.62840i
$426$	1.23002e9			0.770866
$427$		0			0
$428$	−4.61404e8			−0.284465
$429$	1.11678e9	−	1.93432e9i	0.682915	−	1.18284i
$430$	1.64450e9	+	2.84835e9i	0.997455	+	1.72764i
$431$	5.15829e7	+	8.93442e7i	0.0310338	+	0.0537522i	0.881125	−	0.472883i	$-0.156787\pi$
$431$	5.15829e7	+	8.93442e7i	0.0310338	+	0.0537522i	−0.850091	+	0.526635i	$0.823453\pi$
$432$	−4.03108e7	+	6.98203e7i	−0.0240563	+	0.0416667i
$433$	−2.33278e9			−1.38091			−0.690455	−	0.723375i	$-0.742590\pi$
$433$	−2.33278e9			−1.38091			−0.690455	+	0.723375i	$0.742590\pi$
$434$		0			0
$435$	3.52021e7			0.0205048
$436$	−1.24492e8	+	2.15626e8i	−0.0719347	+	0.124595i
$437$	−3.19768e8	−	5.53854e8i	−0.183295	−	0.317475i
$438$	2.43419e8	+	4.21614e8i	0.138419	+	0.239748i
$439$	7.80794e8	−	1.35237e9i	0.440464	−	0.762906i	−0.557260	−	0.830338i	$-0.688147\pi$
$439$	7.80794e8	−	1.35237e9i	0.440464	−	0.762906i	0.997724	+	0.0674320i	$0.0214806\pi$
$440$	−1.74897e9			−0.978810
$441$		0			0
$442$	1.89779e9			1.04537
$443$	−8.12404e8	+	1.40712e9i	−0.443975	+	0.768988i	−0.997980	−	0.0635255i	$-0.979766\pi$
$443$	−8.12404e8	+	1.40712e9i	−0.443975	+	0.768988i	0.554005	+	0.832513i	$0.313099\pi$
$444$	2.07099e8	+	3.58706e8i	0.112289	+	0.194490i
$445$	2.49723e9	+	4.32533e9i	1.34338	+	2.32680i
$446$	−1.26415e9	+	2.18957e9i	−0.674723	+	1.16865i
$447$	1.70915e9			0.905113
$448$		0			0
$449$	−8.18478e8			−0.426722			−0.213361	−	0.976973i	$-0.568441\pi$
$449$	−8.18478e8			−0.426722			−0.213361	+	0.976973i	$0.568441\pi$
$450$	−4.16332e8	+	7.21108e8i	−0.215375	+	0.373041i
$451$	1.92464e8	+	3.33357e8i	0.0987942	+	0.171117i
$452$	−4.69271e8	−	8.12801e8i	−0.239023	−	0.414000i
$453$	7.28495e8	−	1.26179e9i	0.368199	−	0.637739i
$454$	3.80845e8			0.191008
$455$		0			0
$456$	−1.89168e8			−0.0934264
$457$	7.66628e8	−	1.32784e9i	0.375732	−	0.650786i	−0.614705	−	0.788757i	$-0.710725\pi$
$457$	7.66628e8	−	1.32784e9i	0.375732	−	0.650786i	0.990436	+	0.137971i	$0.0440581\pi$
$458$	4.17155e8	+	7.22534e8i	0.202894	+	0.351422i
$459$	−2.05117e8	−	3.55272e8i	−0.0990048	−	0.171481i
$460$	7.02909e8	−	1.21747e9i	0.336703	−	0.583187i
$461$	3.43507e9			1.63299			0.816494	−	0.577354i	$-0.195915\pi$
$461$	3.43507e9			1.63299			0.816494	+	0.577354i	$0.195915\pi$
$462$		0			0
$463$	1.73200e9			0.810990			0.405495	−	0.914097i	$-0.367099\pi$
$463$	1.73200e9			0.810990			0.405495	+	0.914097i	$0.367099\pi$
$464$	−5.68115e6	+	9.84004e6i	−0.00264012	+	0.00457282i
$465$	7.12670e7	+	1.23438e8i	0.0328703	+	0.0569330i
$466$	−9.40236e8	−	1.62854e9i	−0.430414	−	0.745498i
$467$	2.40744e8	−	4.16980e8i	0.109382	−	0.189455i	−0.806138	−	0.591728i	$-0.798446\pi$
$467$	2.40744e8	−	4.16980e8i	0.109382	−	0.189455i	0.915520	+	0.402272i	$0.131779\pi$
$468$	5.31039e8			0.239478
$469$		0			0
$470$	−1.69687e9			−0.753888
$471$	−7.87545e8	+	1.36407e9i	−0.347298	+	0.601538i
$472$	−4.00360e8	−	6.93445e8i	−0.175248	−	0.303539i
$473$	−3.17878e9	−	5.50580e9i	−1.38117	−	2.39225i
$474$	−1.43545e7	+	2.48627e7i	−0.00619104	+	0.0107232i
$475$	−1.95373e9			−0.836445
$476$		0			0
$477$	−1.41684e9			−0.597732
$478$	−1.49745e8	+	2.59365e8i	−0.0627125	+	0.108621i
$479$	8.29697e8	+	1.43708e9i	0.344941	+	0.597456i	0.985343	−	0.170584i	$-0.0545655\pi$
$479$	8.29697e8	+	1.43708e9i	0.344941	+	0.597456i	−0.640402	+	0.768040i	$0.721232\pi$
$480$	−2.07913e8	−	3.60116e8i	−0.0858099	−	0.148627i
$481$	1.36412e9	−	2.36273e9i	0.558914	−	0.968068i
$482$	7.90134e7			0.0321393
$483$		0			0
$484$	2.13355e9			0.855349
$485$	−5.65666e8	+	9.79763e8i	−0.225146	+	0.389964i
$486$	−5.73956e7	−	9.94121e7i	−0.0226805	−	0.0392837i
$487$	−8.60083e8	−	1.48971e9i	−0.337434	−	0.584453i	0.646515	−	0.762901i	$-0.276226\pi$
$487$	−8.60083e8	−	1.48971e9i	−0.337434	−	0.584453i	−0.983949	+	0.178448i	$0.942892\pi$
$488$	8.15025e8	−	1.41166e9i	0.317469	−	0.549872i
$489$	1.63578e9			0.632622
$490$		0			0
$491$	−6.67098e8			−0.254334			−0.127167	−	0.991881i	$-0.540588\pi$
$491$	−6.67098e8			−0.254334			−0.127167	+	0.991881i	$0.540588\pi$
$492$	−4.57592e7	+	7.92572e7i	−0.0173221	+	0.0300027i
$493$	−2.89079e7	−	5.00699e7i	−0.0108655	−	0.0188197i
$494$	6.23005e8	+	1.07908e9i	0.232513	+	0.402724i
$495$	1.24512e9	−	2.15661e9i	0.461415	−	0.799195i
$496$	−4.60063e7			−0.0169290
$497$		0			0
$498$	1.50131e9			0.544714
$499$	2.72989e8	−	4.72830e8i	0.0983541	−	0.170354i	−0.812649	−	0.582753i	$-0.801976\pi$
$499$	2.72989e8	−	4.72830e8i	0.0983541	−	0.170354i	0.911004	+	0.412399i	$0.135309\pi$
$500$	−9.72336e8	−	1.68414e9i	−0.347874	−	0.602535i
$501$	−8.02161e8	−	1.38938e9i	−0.284990	−	0.493617i
$502$	−5.29753e8	+	9.17559e8i	−0.186900	+	0.323721i
$503$	4.13284e9			1.44797			0.723987	−	0.689813i	$-0.242307\pi$
$503$	4.13284e9			1.44797			0.723987	+	0.689813i	$0.242307\pi$
$504$		0			0
$505$	3.65460e9			1.26276
$506$	−1.35871e9	+	2.35335e9i	−0.466229	+	0.807533i
$507$	−9.01819e8	−	1.56200e9i	−0.307320	−	0.532295i
$508$	−1.23946e8	−	2.14681e8i	−0.0419478	−	0.0726558i
$509$	9.56065e8	−	1.65595e9i	0.321348	−	0.556590i	−0.659419	−	0.751776i	$-0.729198\pi$
$509$	9.56065e8	−	1.65595e9i	0.321348	−	0.556590i	0.980766	+	0.195185i	$0.0625309\pi$
$510$	2.11588e9			0.706310
$511$		0			0
$512$	1.34218e8			0.0441942
$513$	1.34671e8	−	2.33257e8i	0.0440417	−	0.0762824i
$514$	−1.33067e9	−	2.30479e9i	−0.432214	−	0.748617i
$515$	3.11000e9	+	5.38667e9i	1.00331	+	1.73778i
$516$	7.55768e8	−	1.30903e9i	0.242167	−	0.419445i
$517$	3.28002e9			1.04390
$518$		0			0
$519$	1.50813e9			0.473536
$520$	−1.36948e9	+	2.37201e9i	−0.427115	+	0.739785i
$521$	−3.10587e7	−	5.37952e7i	−0.00962169	−	0.0166652i	0.861174	−	0.508309i	$-0.169729\pi$
$521$	−3.10587e7	−	5.37952e7i	−0.00962169	−	0.0166652i	−0.870796	+	0.491644i	$0.836396\pi$
$522$	−8.08898e6	−	1.40105e7i	−0.00248913	−	0.00431130i
$523$	−3.41037e8	+	5.90694e8i	−0.104243	+	0.180554i	−0.913429	−	0.406999i	$-0.866575\pi$
$523$	−3.41037e8	+	5.90694e8i	−0.104243	+	0.180554i	0.809186	+	0.587553i	$0.199909\pi$
$524$	1.45585e9			0.442035
$525$		0			0
$526$	−7.60983e8			−0.227995
$527$	1.17049e8	−	2.02734e8i	0.0348361	−	0.0603379i
$528$	4.01891e8	+	6.96096e8i	0.118820	+	0.205802i
$529$	6.10286e8	+	1.05705e9i	0.179241	+	0.310455i
$530$	3.65385e9	−	6.32866e9i	1.06607	−	1.84649i
$531$	1.14009e9			0.330452
$532$		0			0
$533$	6.02813e8			0.172440
$534$	1.14766e9	−	1.98781e9i	0.326152	−	0.564912i
$535$	1.69422e9	+	2.93447e9i	0.478334	+	0.828499i
$536$	−5.44943e8	−	9.43869e8i	−0.152853	−	0.264749i
$537$	−1.08304e9	+	1.87588e9i	−0.301811	+	0.522752i
$538$	−2.15084e9			−0.595484
$539$		0			0
$540$	5.92065e8			0.161805
$541$	−1.10271e8	+	1.90994e8i	−0.0299412	+	0.0518597i	−0.880608	−	0.473846i	$-0.842865\pi$
$541$	−1.10271e8	+	1.90994e8i	−0.0299412	+	0.0518597i	0.850667	+	0.525706i	$0.176199\pi$
$542$	−1.81153e9	−	3.13767e9i	−0.488708	−	0.846466i
$543$	9.70153e8	+	1.68036e9i	0.260041	+	0.450403i
$544$	−3.41475e8	+	5.91453e8i	−0.0909417	+	0.157516i
$545$	1.82848e9			0.483840
$546$		0			0
$547$	5.39461e9			1.40930			0.704652	−	0.709553i	$-0.251103\pi$
$547$	5.39461e9			1.40930			0.704652	+	0.709553i	$0.251103\pi$
$548$	1.35162e9	−	2.34108e9i	0.350852	−	0.607693i
$549$	1.16046e9	+	2.00997e9i	0.299313	+	0.518425i
$550$	4.15075e9	+	7.18932e9i	1.06379	+	1.84255i
$551$	1.89797e7	−	3.28738e7i	0.00483347	−	0.00837181i
$552$	−6.46078e8			−0.163493
$553$		0			0
$554$	−1.31768e8			−0.0329249
$555$	1.52088e9	−	2.63425e9i	0.377634	−	0.654081i
$556$	6.47423e7	+	1.12137e8i	0.0159745	+	0.0276686i
$557$	6.11934e8	+	1.05990e9i	0.150041	+	0.259879i	0.931242	−	0.364400i	$-0.118726\pi$
$557$	6.11934e8	+	1.05990e9i	0.150041	+	0.259879i	−0.781201	+	0.624280i	$0.785393\pi$
$558$	3.27525e7	−	5.67290e7i	0.00798040	−	0.0138225i
$559$	−9.95620e9			−2.41075
$560$		0			0
$561$	−4.08995e9			−0.978021
$562$	−2.03245e9	+	3.52031e9i	−0.482996	+	0.836574i
$563$	1.83547e9	+	3.17913e9i	0.433479	+	0.750807i	0.997170	−	0.0751784i	$-0.0239526\pi$
$563$	1.83547e9	+	3.17913e9i	0.433479	+	0.750807i	−0.563691	+	0.825985i	$0.690619\pi$
$564$	3.89920e8	+	6.75361e8i	0.0915163	+	0.158511i
$565$	−3.44621e9	+	5.96901e9i	−0.803845	+	1.39230i
$566$	−2.05997e9			−0.477532
$567$		0			0
$568$	2.91561e9			0.667590
$569$	−2.50185e9	+	4.33333e9i	−0.569335	+	0.986118i	0.427296	+	0.904112i	$0.359466\pi$
$569$	−2.50185e9	+	4.33333e9i	−0.569335	+	0.986118i	−0.996632	+	0.0820062i	$0.973867\pi$
$570$	6.94600e8	+	1.20308e9i	0.157099	+	0.272103i
$571$	−7.55829e8	−	1.30913e9i	−0.169902	−	0.294278i	0.768484	−	0.639870i	$-0.221012\pi$
$571$	−7.55829e8	−	1.30913e9i	−0.169902	−	0.294278i	−0.938385	+	0.345591i	$0.887678\pi$
$572$	2.64718e9	−	4.58505e9i	0.591422	−	1.02437i
$573$	−4.52075e8			−0.100385
$574$		0			0
$575$	−6.67273e9			−1.46375
$576$	−9.55515e7	+	1.65500e8i	−0.0208333	+	0.0360844i
$577$	2.19560e9	+	3.80289e9i	0.475814	+	0.824135i	0.999616	−	0.0277054i	$-0.00882004\pi$
$577$	2.19560e9	+	3.80289e9i	0.475814	+	0.824135i	−0.523802	+	0.851840i	$0.675487\pi$
$578$	−9.62012e7	−	1.66625e8i	−0.0207221	−	0.0358917i
$579$	1.81848e9	−	3.14970e9i	0.389344	−	0.674364i
$580$	8.34419e7			0.0177577
$581$		0			0
$582$	5.19931e8			0.109324
$583$	−7.06282e9	+	1.22332e10i	−1.47618	+	2.55681i
$584$	5.76993e8	+	9.99381e8i	0.119874	+	0.207628i
$585$	−1.94991e9	−	3.37734e9i	−0.402688	−	0.697476i
$586$	−2.93539e8	+	5.08424e8i	−0.0602593	+	0.104372i
$587$	−6.47628e9			−1.32158			−0.660789	−	0.750572i	$-0.729778\pi$
$587$	−6.47628e9			−1.32158			−0.660789	+	0.750572i	$0.729778\pi$
$588$		0			0
$589$	1.53699e8			0.0309932
$590$	−2.94015e9	+	5.09248e9i	−0.589369	+	1.02082i
$591$	7.95708e8	+	1.37821e9i	0.158561	+	0.274636i
$592$	4.90902e8	+	8.50266e8i	0.0972452	+	0.168434i
$593$	−2.64092e8	+	4.57420e8i	−0.0520072	+	0.0900791i	−0.890857	−	0.454284i	$-0.849895\pi$
$593$	−2.64092e8	+	4.57420e8i	−0.0520072	+	0.0900791i	0.838850	+	0.544363i	$0.183229\pi$
$594$	−1.14445e9			−0.224049
$595$		0			0
$596$	4.05131e9			0.783851
$597$	−1.77354e9	+	3.07186e9i	−0.341138	+	0.590869i
$598$	2.12780e9	+	3.68545e9i	0.406889	+	0.704752i
$599$	4.51711e9	+	7.82387e9i	0.858751	+	1.48740i	0.873121	+	0.487503i	$0.162092\pi$
$599$	4.51711e9	+	7.82387e9i	0.858751	+	1.48740i	−0.0143708	+	0.999897i	$0.504575\pi$
$600$	−9.86861e8	+	1.70929e9i	−0.186520	+	0.323063i
$601$	5.03992e9			0.947028			0.473514	−	0.880786i	$-0.342985\pi$
$601$	5.03992e9			0.947028			0.473514	+	0.880786i	$0.342985\pi$
$602$		0			0
$603$	1.55181e9			0.288223
$604$	1.72680e9	−	2.99091e9i	0.318870	−	0.552299i
$605$	−7.83411e9	−	1.35691e10i	−1.43829	−	2.49119i
$606$	−8.39781e8	−	1.45454e9i	−0.153289	−	0.265505i
$607$	−2.98281e9	+	5.16638e9i	−0.541334	+	0.937617i	0.457494	+	0.889213i	$0.348747\pi$
$607$	−2.98281e9	+	5.16638e9i	−0.541334	+	0.937617i	−0.998828	+	0.0484046i	$0.984586\pi$
$608$	−4.48397e8			−0.0809097
$609$		0			0
$610$	−1.19707e10			−2.13533
$611$	2.56833e9	−	4.44847e9i	0.455518	−	0.788981i
$612$	−4.86202e8	−	8.42127e8i	−0.0857407	−	0.148507i
$613$	−2.71175e9	−	4.69689e9i	−0.475487	−	0.823567i	0.524119	−	0.851645i	$-0.324395\pi$
$613$	−2.71175e9	−	4.69689e9i	−0.475487	−	0.823567i	−0.999606	+	0.0280780i	$0.991061\pi$
$614$	3.72649e8	−	6.45448e8i	0.0649697	−	0.112531i
$615$	6.72088e8			0.116510
$616$		0			0
$617$	2.18073e9			0.373770			0.186885	−	0.982382i	$-0.440161\pi$
$617$	2.18073e9			0.373770			0.186885	+	0.982382i	$0.440161\pi$
$618$	1.42927e9	−	2.47558e9i	0.243588	−	0.421907i
$619$	2.67868e9	+	4.63960e9i	0.453945	+	0.786255i	0.998627	−	0.0523875i	$-0.0166831\pi$
$619$	2.67868e9	+	4.63960e9i	0.453945	+	0.786255i	−0.544682	+	0.838642i	$0.683350\pi$
$620$	1.68929e8	+	2.92594e8i	0.0284665	+	0.0493054i
$621$	4.59952e8	−	7.96661e8i	0.0770712	−	0.133491i
$622$	4.88747e9			0.814363
$623$		0			0
$624$	1.25876e9			0.207394
$625$	−1.56344e9	+	2.70796e9i	−0.256155	+	0.443673i
$626$	8.48924e8	+	1.47038e9i	0.138312	+	0.239563i
$627$	−1.34265e9	−	2.32553e9i	−0.217533	−	0.376778i
$628$	−1.86677e9	+	3.23335e9i	−0.300769	+	0.520947i
$629$	−4.99579e9			−0.800436
$630$		0			0
$631$	1.14559e10			1.81521			0.907607	−	0.419822i	$-0.137907\pi$
$631$	1.14559e10			1.81521			0.907607	+	0.419822i	$0.137907\pi$
$632$	−3.40255e7	+	5.89338e7i	−0.00536160	+	0.00928656i
$633$	4.00410e8	+	6.93531e8i	0.0627469	+	0.108681i
$634$	4.41578e9	+	7.64836e9i	0.688169	+	1.19194i
$635$	−9.10228e8	+	1.57656e9i	−0.141072	+	0.244345i
$636$	−3.35843e9			−0.517651
$637$		0			0
$638$	−1.61291e8			−0.0245889
$639$	−2.07566e9	+	3.59515e9i	−0.314705	+	0.545085i
$640$	−4.92831e8	−	8.53608e8i	−0.0743135	−	0.128715i
$641$	−5.06437e9	−	8.77175e9i	−0.759491	−	1.31548i	−0.943110	−	0.332480i	$-0.892115\pi$
$641$	−5.06437e9	−	8.77175e9i	−0.759491	−	1.31548i	0.183619	−	0.982997i	$-0.441219\pi$
$642$	7.78620e8	−	1.34861e9i	0.116132	−	0.201147i
$643$	−4.99152e9			−0.740448			−0.370224	−	0.928943i	$-0.620719\pi$
$643$	−4.99152e9			−0.740448			−0.370224	+	0.928943i	$0.620719\pi$
$644$		0			0
$645$	−1.11003e10			−1.62884
$646$	1.14081e9	−	1.97594e9i	0.166494	−	0.288376i
$647$	2.77118e9	+	4.79983e9i	0.402254	+	0.696724i	0.993998	−	0.109402i	$-0.0348936\pi$
$647$	2.77118e9	+	4.79983e9i	0.402254	+	0.696724i	−0.591744	+	0.806126i	$0.701560\pi$
$648$	−1.36049e8	−	2.35644e8i	−0.0196419	−	0.0340207i
$649$	5.68324e9	−	9.84366e9i	0.816093	−	1.41351i
$650$	1.30005e10			1.85680
$651$		0			0
$652$	3.87741e9			0.547867
$653$	3.71295e9	−	6.43101e9i	0.521822	−	0.903822i	−0.477856	−	0.878438i	$-0.658586\pi$
$653$	3.71295e9	−	6.43101e9i	0.521822	−	0.903822i	0.999678	−	0.0253840i	$-0.00808085\pi$
$654$	−4.20160e8	−	7.27739e8i	−0.0587345	−	0.101731i
$655$	−5.34569e9	−	9.25901e9i	−0.743292	−	1.28742i
$656$	−1.08466e8	+	1.87869e8i	−0.0150014	+	0.0259831i
$657$	−1.64308e9			−0.226037
$658$		0			0
$659$	8.68127e8			0.118164			0.0590819	−	0.998253i	$-0.481183\pi$
$659$	8.68127e8			0.118164			0.0590819	+	0.998253i	$0.481183\pi$
$660$	2.95139e9	−	5.11196e9i	0.399597	−	0.692123i
$661$	−1.68460e9	−	2.91781e9i	−0.226878	−	0.392964i	0.730003	−	0.683443i	$-0.239518\pi$
$661$	−1.68460e9	−	2.91781e9i	−0.226878	−	0.392964i	−0.956881	+	0.290480i	$0.906185\pi$
$662$	2.68235e9	+	4.64597e9i	0.359346	+	0.622405i
$663$	−3.20252e9	+	5.54693e9i	−0.426771	+	0.739188i
$664$	3.55867e9			0.471736
$665$		0			0
$666$	−1.39792e9			−0.183367
$667$	6.48228e7	−	1.12276e8i	0.00845839	−	0.0146504i
$668$	−1.90142e9	−	3.29335e9i	−0.246808	−	0.427485i
$669$	−4.26650e9	−	7.38979e9i	−0.550909	−	0.954203i
$670$	−4.00193e9	+	6.93154e9i	−0.514052	+	0.890365i
$671$	2.31391e10			2.95677
$672$		0			0
$673$	−3.43406e9			−0.434265			−0.217133	−	0.976142i	$-0.569670\pi$
$673$	−3.43406e9			−0.434265			−0.217133	+	0.976142i	$0.569670\pi$
$674$	2.73649e9	−	4.73974e9i	0.344258	−	0.596272i
$675$	−1.40512e9	−	2.43374e9i	−0.175853	−	0.304587i
$676$	−2.13765e9	−	3.70251e9i	−0.266147	−	0.460981i
$677$	−6.44496e9	+	1.11630e10i	−0.798289	+	1.38268i	0.122441	+	0.992476i	$0.460928\pi$
$677$	−6.44496e9	+	1.11630e10i	−0.798289	+	1.38268i	−0.920730	+	0.390201i	$0.872406\pi$
$678$	3.16758e9			0.390323
$679$		0			0
$680$	5.01542e9			0.611682
$681$	−6.42676e8	+	1.11315e9i	−0.0779789	+	0.135063i
$682$	−3.26537e8	−	5.65578e8i	−0.0394173	−	0.0682727i
$683$	3.26006e9	+	5.64659e9i	0.391519	+	0.678131i	0.992650	−	0.121019i	$-0.0386163\pi$
$683$	3.26006e9	+	5.64659e9i	0.391519	+	0.678131i	−0.601131	+	0.799151i	$0.705283\pi$
$684$	3.19220e8	−	5.52906e8i	0.0381412	−	0.0660625i
$685$	−1.98520e10			−2.35986
$686$		0			0
$687$	−2.81580e9			−0.331324
$688$	1.79145e9	−	3.10288e9i	0.209723	−	0.363250i
$689$	1.10607e10	+	1.91577e10i	1.28829	+	2.23139i
$690$	2.37232e9	+	4.10898e9i	0.274917	+	0.476170i
$691$	7.56322e9	−	1.30999e10i	0.872035	−	1.51041i	0.0121462	−	0.999926i	$-0.496134\pi$
$691$	7.56322e9	−	1.30999e10i	0.872035	−	1.51041i	0.859888	−	0.510482i	$-0.170533\pi$
$692$	3.57482e9			0.410094
$693$		0			0
$694$	3.50042e9			0.397523
$695$	4.75451e8	−	8.23505e8i	0.0537228	−	0.0930507i
$696$	−1.91739e7	−	3.32101e7i	−0.00215565	−	0.00373369i
$697$	−5.51917e8	−	9.55948e8i	−0.0617389	−	0.106935i
$698$	−3.75933e7	+	6.51135e7i	−0.00418424	+	0.00724732i
$699$	6.34659e9			0.702862
$700$		0			0
$701$	−8.52704e9			−0.934943			−0.467472	−	0.884008i	$-0.654835\pi$
$701$	−8.52704e9			−0.934943			−0.467472	+	0.884008i	$0.654835\pi$
$702$	−8.96128e8	+	1.55214e9i	−0.0977665	+	0.169337i
$703$	−1.64001e9	−	2.84059e9i	−0.178034	−	0.308365i
$704$	9.52631e8	+	1.65001e9i	0.102901	+	0.178230i
$705$	2.86347e9	−	4.95968e9i	0.307773	−	0.533079i
$706$	1.13177e10			1.21044
$707$		0			0
$708$	2.70243e9			0.286180
$709$	4.92290e9	−	8.52671e9i	0.518751	−	0.898503i	−0.481012	−	0.876714i	$-0.659731\pi$
$709$	4.92290e9	−	8.52671e9i	0.518751	−	0.898503i	0.999763	−	0.0217886i	$-0.00693609\pi$
$710$	−1.07057e10	−	1.85429e10i	−1.12257	−	1.94434i
$711$	−4.84464e7	−	8.39117e7i	−0.00505496	−	0.00875546i
$712$	2.72039e9	−	4.71185e9i	0.282456	−	0.489228i
$713$	5.24939e8			0.0542370
$714$		0			0
$715$	−3.88805e10			−3.97796
$716$	−2.56721e9	+	4.44653e9i	−0.261376	+	0.452716i
$717$	−5.05388e8	−	8.75359e8i	−0.0512045	−	0.0886888i
$718$	1.23033e9	+	2.13100e9i	0.124047	+	0.214856i
$719$	−2.01398e9	+	3.48831e9i	−0.202071	+	0.349997i	−0.949195	−	0.314687i	$-0.898100\pi$
$719$	−2.01398e9	+	3.48831e9i	−0.202071	+	0.349997i	0.747125	+	0.664684i	$0.231434\pi$
$720$	1.40341e9			0.140127
$721$		0			0
$722$	−5.65296e9			−0.558979
$723$	−1.33335e8	+	2.30943e8i	−0.0131208	+	0.0227259i
$724$	2.29962e9	+	3.98306e9i	0.225202	+	0.390061i
$725$	−1.98029e8	−	3.42996e8i	−0.0192995	−	0.0334277i
$726$	−3.60036e9	+	6.23600e9i	−0.349195	+	0.604823i
$727$	−5.95463e9			−0.574757			−0.287379	−	0.957817i	$-0.592784\pi$
$727$	−5.95463e9			−0.574757			−0.287379	+	0.957817i	$0.592784\pi$
$728$		0			0
$729$	3.87420e8			0.0370370
$730$	4.23729e9	−	7.33920e9i	0.403142	−	0.698263i
$731$	9.11558e9	+	1.57887e10i	0.863125	+	1.49498i
$732$	2.75071e9	+	4.76437e9i	0.259212	+	0.448969i
$733$	−8.27724e9	+	1.43366e10i	−0.776286	+	1.34457i	0.157783	+	0.987474i	$0.449565\pi$
$733$	−8.27724e9	+	1.43366e10i	−0.776286	+	1.34457i	−0.934069	+	0.357092i	$0.883768\pi$
$734$	−9.85018e9			−0.919407
$735$		0			0
$736$	−1.53145e9			−0.141589
$737$	7.73564e9	−	1.33985e10i	0.711803	−	1.23288i
$738$	−1.54437e8	−	2.67493e8i	−0.0141434	−	0.0244971i
$739$	−5.72231e9	−	9.91134e9i	−0.521574	−	0.903393i	−0.999685	−	0.0250936i	$-0.992012\pi$
$739$	−5.72231e9	−	9.91134e9i	−0.521574	−	0.903393i	0.478111	−	0.878299i	$-0.341322\pi$
$740$	3.60506e9	−	6.24414e9i	0.327040	−	0.566450i
$741$	−4.20528e9			−0.379692
$742$		0			0
$743$	−4.25895e8			−0.0380927			−0.0190464	−	0.999819i	$-0.506063\pi$
$743$	−4.25895e8			−0.0380927			−0.0190464	+	0.999819i	$0.506063\pi$
$744$	7.76356e7	−	1.34469e8i	0.00691123	−	0.0119706i
$745$	−1.48759e10	−	2.57658e10i	−1.31806	−	2.28295i
$746$	−7.34367e9	−	1.27196e10i	−0.647630	−	1.12173i
$747$	−2.53347e9	+	4.38809e9i	−0.222379	+	0.385171i
$748$	−9.69470e9			−0.846991
$749$		0			0
$750$	6.56327e9			0.568075
$751$	1.47518e8	−	2.55508e8i	0.0127088	−	0.0220123i	−0.859601	−	0.510966i	$-0.829288\pi$
$751$	1.47518e8	−	2.55508e8i	0.0127088	−	0.0220123i	0.872310	+	0.488953i	$0.162621\pi$
$752$	9.24254e8	+	1.60086e9i	0.0792554	+	0.137274i
$753$	−1.78792e9	−	3.09676e9i	−0.152604	−	0.264317i
$754$	−1.26295e8	+	2.18749e8i	−0.0107296	+	0.0185843i
$755$	−2.53624e10			−2.14475
$756$		0			0
$757$	1.87377e10			1.56994			0.784968	−	0.619537i	$-0.212680\pi$
$757$	1.87377e10			1.56994			0.784968	+	0.619537i	$0.212680\pi$
$758$	2.59573e9	−	4.49594e9i	0.216480	−	0.374955i
$759$	−4.58564e9	−	7.94257e9i	−0.380675	−	0.659348i
$760$	1.64646e9	+	2.85175e9i	0.136051	+	0.235648i
$761$	−2.03748e9	+	3.52902e9i	−0.167590	+	0.290274i	−0.937572	−	0.347792i	$-0.886932\pi$
$761$	−2.03748e9	+	3.52902e9i	−0.167590	+	0.290274i	0.769982	+	0.638065i	$0.220265\pi$
$762$	8.36635e8			0.0685005
$763$		0			0
$764$	−1.07159e9			−0.0869361
$765$	−3.57055e9	+	6.18437e9i	−0.288350	+	0.499437i
$766$	2.72128e9	+	4.71340e9i	0.218763	+	0.378908i
$767$	−8.90020e9	−	1.54156e10i	−0.712223	−	1.23361i
$768$	−2.26492e8	+	3.92296e8i	−0.0180422	+	0.0312500i
$769$	1.19604e10			0.948425			0.474213	−	0.880410i	$-0.342733\pi$
$769$	1.19604e10			0.948425			0.474213	+	0.880410i	$0.342733\pi$
$770$		0			0
$771$	8.98201e9			0.705803
$772$	4.31047e9	−	7.46595e9i	0.337182	−	0.584016i
$773$	−2.33651e8	−	4.04696e8i	−0.0181945	−	0.0315138i	0.856785	−	0.515674i	$-0.172458\pi$
$773$	−2.33651e8	−	4.04696e8i	−0.0181945	−	0.0315138i	−0.874979	+	0.484160i	$0.839125\pi$
$774$	2.55072e9	+	4.41797e9i	0.197728	+	0.342476i
$775$	8.01824e8	−	1.38880e9i	0.0618762	−	0.107173i
$776$	1.23243e9			0.0946774
$777$		0			0
$778$	2.18964e9			0.166703
$779$	3.62366e8	−	6.27636e8i	0.0274642	−	0.0475693i
$780$	−4.62200e9	−	8.00554e9i	−0.348738	−	0.604032i
$781$	2.06940e10	+	3.58430e10i	1.55441	+	2.69232i
$782$	3.89629e9	−	6.74857e9i	0.291358	−	0.504647i
$783$	5.46006e7			0.00406473
$784$		0			0
$785$	2.74182e10			2.02300
$786$	−2.45674e9	+	4.25521e9i	−0.180460	+	0.312566i
$787$	4.03993e9	+	6.99737e9i	0.295436	+	0.511709i	0.975086	−	0.221827i	$-0.0712019\pi$
$787$	4.03993e9	+	6.99737e9i	0.295436	+	0.511709i	−0.679651	+	0.733536i	$0.737869\pi$
$788$	1.88612e9	+	3.26686e9i	0.137318	+	0.237842i
$789$	1.28416e9	−	2.22423e9i	0.0930784	−	0.161217i
$790$	4.99749e8			0.0360626
$791$		0			0
$792$	−2.71277e9			−0.194032
$793$	1.81184e10	−	3.13820e10i	1.29022	−	2.23472i
$794$	4.84137e9	+	8.38549e9i	0.343239	+	0.594507i
$795$	1.23317e10	+	2.13592e10i	0.870442	+	1.50765i
$796$	−4.20394e9	+	7.28144e9i	−0.295434	+	0.511707i
$797$	−1.48799e10			−1.04111			−0.520555	−	0.853828i	$-0.674275\pi$
$797$	−1.48799e10			−1.04111			−0.520555	+	0.853828i	$0.674275\pi$
$798$		0			0
$799$	−9.40591e9			−0.652360
$800$	−2.33923e9	+	4.05166e9i	−0.161531	+	0.279781i
$801$	3.87336e9	+	6.70886e9i	0.266302	+	0.461249i
$802$	2.38841e9	+	4.13685e9i	0.163493	+	0.283178i
$803$	−8.19059e9	+	1.41865e10i	−0.558227	+	0.966878i
$804$	3.67837e9			0.249608
$805$		0			0
$806$	−1.02274e9			−0.0688007
$807$	3.62954e9	−	6.28655e9i	0.243105	−	0.421071i
$808$	−1.99059e9	−	3.44781e9i	−0.132752	−	0.229934i
$809$	−3.57566e9	−	6.19323e9i	−0.237431	−	0.411242i	0.722546	−	0.691323i	$-0.242972\pi$
$809$	−3.57566e9	−	6.19323e9i	−0.237431	−	0.411242i	−0.959976	+	0.280081i	$0.909639\pi$
$810$	−9.99109e8	+	1.73051e9i	−0.0660565	+	0.114413i
$811$	2.13058e9			0.140257			0.0701286	−	0.997538i	$-0.477659\pi$
$811$	2.13058e9			0.140257			0.0701286	+	0.997538i	$0.477659\pi$
$812$		0			0
$813$	1.22279e10			0.798056
$814$	−6.96850e9	+	1.20698e10i	−0.452850	+	0.784358i
$815$	−1.42374e10	−	2.46598e10i	−0.921250	−	1.59565i
$816$	−1.15248e9	−	1.99615e9i	−0.0742536	−	0.128611i
$817$	−5.98492e9	+	1.03662e10i	−0.383955	+	0.665030i
$818$	−9.58137e9			−0.612056
$819$		0			0
$820$	1.59310e9			0.100901
$821$	−1.02026e9	+	1.76714e9i	−0.0643442	+	0.111447i	−0.896403	−	0.443240i	$-0.853829\pi$
$821$	−1.02026e9	+	1.76714e9i	−0.0643442	+	0.111447i	0.832059	+	0.554688i	$0.187162\pi$
$822$	4.56173e9	+	7.90114e9i	0.286469	+	0.496179i
$823$	−1.49569e10	−	2.59062e10i	−0.935283	−	1.61996i	−0.774128	−	0.633029i	$-0.781812\pi$
$823$	−1.49569e10	−	2.59062e10i	−0.935283	−	1.61996i	−0.161155	−	0.986929i	$-0.551522\pi$
$824$	3.38791e9	−	5.86803e9i	0.210953	−	0.365382i
$825$	−2.80176e10			−1.73717
$826$		0			0
$827$	1.05103e10			0.646170			0.323085	−	0.946370i	$-0.395280\pi$
$827$	1.05103e10			0.646170			0.323085	+	0.946370i	$0.395280\pi$
$828$	1.09026e9	−	1.88838e9i	0.0667456	−	0.115607i
$829$	−9.55730e9	−	1.65537e10i	−0.582632	−	1.00915i	−0.995166	−	0.0982059i	$-0.968690\pi$
$829$	−9.55730e9	−	1.65537e10i	−0.582632	−	1.00915i	0.412534	−	0.910942i	$-0.364644\pi$
$830$	−1.30670e10	−	2.26327e10i	−0.793235	−	1.37392i
$831$	2.22358e8	−	3.85135e8i	0.0134415	−	0.0232814i
$832$	2.98372e9			0.179608
$833$		0			0
$834$	−4.37010e8			−0.0260862
$835$	−1.39635e10	+	2.41856e10i	−0.830028	+	1.43765i
$836$	−3.18257e9	−	5.51237e9i	−0.188389	−	0.326300i
$837$	1.10540e8	+	1.91460e8i	0.00651597	+	0.0112860i
$838$	6.74720e9	−	1.16865e10i	0.396068	−	0.686010i
$839$	2.31635e9			0.135406			0.0677028	−	0.997706i	$-0.478433\pi$
$839$	2.31635e9			0.135406			0.0677028	+	0.997706i	$0.478433\pi$
$840$		0			0
$841$	−1.72422e10			−0.999554
$842$	3.84142e9	−	6.65354e9i	0.221768	−	0.384114i
$843$	−6.85953e9	−	1.18811e10i	−0.394365	−	0.683059i
$844$	9.49121e8	+	1.64393e9i	0.0543404	+	0.0941203i
$845$	−1.56983e10	+	2.71903e10i	−0.895066	+	1.55030i
$846$	−2.63196e9			−0.149445
$847$		0			0
$848$	−7.96073e9			−0.448299
$849$	3.47619e9	−	6.02095e9i	0.194952	−	0.337666i
$850$	−1.19029e10	−	2.06164e10i	−0.664791	−	1.15145i
$851$	−5.60126e9	−	9.70167e9i	−0.311553	−	0.539626i
$852$	−4.92009e9	+	8.52184e9i	−0.272542	+	0.472057i
$853$	−8.57597e8			−0.0473110			−0.0236555	−	0.999720i	$-0.507530\pi$
$853$	−8.57597e8			−0.0473110			−0.0236555	+	0.999720i	$0.507530\pi$
$854$		0			0
$855$	−4.68855e9			−0.256541
$856$	1.84562e9	−	3.19670e9i	0.100573	−	0.174198i
$857$	1.36933e10	+	2.37174e10i	0.743146	+	1.28717i	0.951056	+	0.309018i	$0.100000\pi$
$857$	1.36933e10	+	2.37174e10i	0.743146	+	1.28717i	−0.207911	+	0.978148i	$0.566666\pi$
$858$	8.93423e9	+	1.54745e10i	0.482894	+	0.836397i
$859$	5.09578e9	−	8.82615e9i	0.274306	−	0.475111i	−0.695654	−	0.718377i	$-0.744885\pi$
$859$	5.09578e9	−	8.82615e9i	0.274306	−	0.475111i	0.969960	+	0.243266i	$0.0782187\pi$
$860$	−2.63119e10			−1.41061
$861$		0			0
$862$	−8.25327e8			−0.0438885
$863$	−1.85337e9	+	3.21014e9i	−0.0981578	+	0.170014i	−0.910922	−	0.412578i	$-0.864628\pi$
$863$	−1.85337e9	+	3.21014e9i	−0.0981578	+	0.170014i	0.812764	+	0.582593i	$0.197962\pi$
$864$	−3.22486e8	−	5.58563e8i	−0.0170103	−	0.0294628i
$865$	−1.31263e10	−	2.27354e10i	−0.689582	−	1.19439i
$866$	9.33110e9	−	1.61619e10i	0.488225	−	0.845631i
$867$	6.49358e8			0.0338390
$868$		0			0
$869$	−9.66004e8			−0.0499356
$870$	−1.40808e8	+	2.43887e8i	−0.00724954	+	0.0125566i
$871$	−1.21143e10	−	2.09827e10i	−0.621207	−	1.07596i
$872$	−9.95936e8	−	1.72501e9i	−0.0508655	−	0.0881017i
$873$	−8.77384e8	+	1.51967e9i	−0.0446313	+	0.0773038i
$874$	5.11628e9			0.259218
$875$		0			0
$876$	−3.89470e9			−0.195754
$877$	−1.09341e9	+	1.89383e9i	−0.0547372	+	0.0948076i	−0.892096	−	0.451847i	$-0.850765\pi$
$877$	−1.09341e9	+	1.89383e9i	−0.0547372	+	0.0948076i	0.837358	+	0.546654i	$0.184099\pi$
$878$	6.24635e9	+	1.08190e10i	0.311455	+	0.539456i
$879$	−9.90694e8	−	1.71593e9i	−0.0492015	−	0.0852195i
$880$	6.99589e9	−	1.21172e10i	0.346062	−	0.599396i
$881$	−9.10532e9			−0.448621			−0.224310	−	0.974518i	$-0.572013\pi$
$881$	−9.10532e9			−0.448621			−0.224310	+	0.974518i	$0.572013\pi$
$882$		0			0
$883$	1.99391e10			0.974639			0.487319	−	0.873224i	$-0.337975\pi$
$883$	1.99391e10			0.974639			0.487319	+	0.873224i	$0.337975\pi$
$884$	−7.59116e9	+	1.31483e10i	−0.369594	+	0.640156i
$885$	−9.92300e9	−	1.71871e10i	−0.481217	−	0.833493i
$886$	−6.49923e9	−	1.12570e10i	−0.313938	−	0.543757i
$887$	3.62213e9	−	6.27371e9i	0.174273	−	0.301850i	−0.765636	−	0.643274i	$-0.777576\pi$
$887$	3.62213e9	−	6.27371e9i	0.174273	−	0.301850i	0.939910	+	0.341424i	$0.110909\pi$
$888$	−3.31359e9			−0.158801
$889$		0			0
$890$	−3.99557e10			−1.89982
$891$	1.93126e9	−	3.34503e9i	0.0914678	−	0.158427i
$892$	−1.01132e10	−	1.75165e10i	−0.477101	−	0.826364i
$893$	−3.08777e9	−	5.34817e9i	−0.145099	−	0.251319i
$894$	−6.83658e9	+	1.18413e10i	−0.320006	+	0.554266i
$895$	3.77059e10			1.75804
$896$		0			0
$897$	−1.43626e10			−0.664447
$898$	3.27391e9	−	5.67058e9i	0.150869	−	0.261313i
$899$	1.55788e7	+	2.69832e7i	0.000715113	+	0.00123861i
$900$	−3.33066e9	−	5.76886e9i	−0.152293	−	0.263780i
$901$	2.02536e10	−	3.50803e10i	0.922498	−	1.59781i
$902$	−3.07942e9			−0.139716
$903$		0			0
$904$	7.50834e9			0.338029
$905$	1.68879e10	−	2.92506e10i	0.757364	−	1.31179i
$906$	5.82796e9	+	1.00943e10i	0.260356	+	0.450950i
$907$	−4.37667e9	−	7.58061e9i	−0.194768	−	0.337349i	0.752056	−	0.659099i	$-0.229062\pi$
$907$	−4.37667e9	−	7.58061e9i	−0.194768	−	0.337349i	−0.946825	+	0.321750i	$0.895729\pi$
$908$	−1.52338e9	+	2.63857e9i	−0.0675317	+	0.116968i
$909$	5.66852e9			0.250320
$910$		0			0
$911$	1.99869e10			0.875853			0.437926	−	0.899011i	$-0.355713\pi$
$911$	1.99869e10			0.875853			0.437926	+	0.899011i	$0.355713\pi$
$912$	7.56670e8	−	1.31059e9i	0.0330312	−	0.0572118i
$913$	2.52582e10	+	4.37485e10i	1.09839	+	1.90246i
$914$	6.13302e9	+	1.06227e10i	0.265682	+	0.460176i
$915$	2.02005e10	−	3.49883e10i	0.871743	−	1.50990i
$916$	−6.67449e9			−0.286935
$917$		0			0
$918$	3.28186e9			0.140014
$919$	4.96537e9	−	8.60028e9i	0.211032	−	0.365518i	−0.741006	−	0.671498i	$-0.765651\pi$
$919$	4.96537e9	−	8.60028e9i	0.211032	−	0.365518i	0.952038	+	0.305981i	$0.0989843\pi$
$920$	5.62328e9	+	9.73980e9i	0.238085	+	0.412375i
$921$	1.25769e9	+	2.17839e9i	0.0530476	+	0.0918811i
$922$	−1.37403e10	+	2.37989e10i	−0.577348	+	0.999996i
$923$	6.48153e10			2.71314
$924$		0			0
$925$	−3.42229e10			−1.42174
$926$	−6.92802e9	+	1.19997e10i	−0.286728	+	0.496628i
$927$	4.82380e9	+	8.35507e9i	0.198889	+	0.344486i
$928$	−4.54492e7	−	7.87204e7i	−0.00186685	−	0.00323347i
$929$	−9.79538e9	+	1.69661e10i	−0.400836	+	0.694267i	−0.993827	−	0.110941i	$-0.964613\pi$
$929$	−9.79538e9	+	1.69661e10i	−0.400836	+	0.694267i	0.592991	+	0.805209i	$0.297947\pi$
$930$	−1.14027e9			−0.0464856
$931$		0			0
$932$	1.50438e10			0.608697
$933$	−8.24761e9	+	1.42853e10i	−0.332462	+	0.575842i
$934$	1.92595e9	+	3.33584e9i	0.0773448	+	0.133965i
$935$	3.55977e10	+	6.16571e10i	1.42423	+	2.46685i
$936$	−2.12415e9	+	3.67914e9i	−0.0846683	+	0.146650i
$937$	4.20286e10			1.66900			0.834500	−	0.551009i	$-0.185757\pi$
$937$	4.20286e10			1.66900			0.834500	+	0.551009i	$0.185757\pi$
$938$		0			0
$939$	−5.73024e9			−0.225862
$940$	6.78749e9	−	1.17563e10i	0.266540	−	0.461660i
$941$	4.97715e9	+	8.62068e9i	0.194723	+	0.337270i	0.946810	−	0.321794i	$-0.104286\pi$
$941$	4.97715e9	+	8.62068e9i	0.194723	+	0.337270i	−0.752087	+	0.659064i	$0.770953\pi$
$942$	−6.30036e9	−	1.09125e10i	−0.245577	−	0.425352i
$943$	1.23762e9	−	2.14361e9i	0.0480612	−	0.0832445i
$944$	6.40577e9			0.247839
$945$		0			0
$946$	5.08604e10			1.95326
$947$	1.21725e10	−	2.10834e10i	0.465751	−	0.806705i	−0.533484	−	0.845810i	$-0.679117\pi$
$947$	1.21725e10	−	2.10834e10i	0.465751	−	0.806705i	0.999235	+	0.0391052i	$0.0124507\pi$
$948$	−1.14836e8	−	1.98902e8i	−0.00437773	−	0.00758245i
$949$	1.28268e10	+	2.22167e10i	0.487178	+	0.843816i
$950$	7.81493e9	−	1.35359e10i	0.295728	−	0.512216i
$951$	−2.98065e10			−1.12378
$952$		0			0
$953$	1.71198e10			0.640727			0.320364	−	0.947295i	$-0.396195\pi$
$953$	1.71198e10			0.640727			0.320364	+	0.947295i	$0.396195\pi$
$954$	5.66736e9	−	9.81615e9i	0.211330	−	0.366034i
$955$	3.93473e9	+	6.81515e9i	0.146185	+	0.253200i
$956$	−1.19796e9	−	2.07492e9i	−0.0443444	−	0.0768068i
$957$	2.72179e8	−	4.71428e8i	0.0100384	−	0.0173870i
$958$	−1.32751e10			−0.487821
$959$		0			0
$960$	3.32661e9			0.121353
$961$	1.36932e10	−	2.37174e10i	0.497707	−	0.862054i
$962$	1.09130e10	+	1.89018e10i	0.395212	+	0.684527i
$963$	2.62784e9	+	4.55156e9i	0.0948216	+	0.164236i
$964$	−3.16054e8	+	5.47421e8i	−0.0113629	+	0.0196812i
$965$	−6.33100e10			−2.26792
$966$		0			0
$967$	−5.29443e10			−1.88290			−0.941448	−	0.337157i	$-0.890535\pi$
$967$	−5.29443e10			−1.88290			−0.941448	+	0.337157i	$0.890535\pi$
$968$	−8.53418e9	+	1.47816e10i	−0.302411	+	0.523792i
$969$	3.85023e9	+	6.66879e9i	0.135942	+	0.235458i
$970$	−4.52533e9	−	7.83810e9i	−0.159202	−	0.275746i
$971$	1.22361e10	−	2.11936e10i	0.428920	−	0.742912i	−0.567857	−	0.823127i	$-0.692227\pi$
$971$	1.22361e10	−	2.11936e10i	0.428920	−	0.742912i	0.996778	+	0.0802153i	$0.0255608\pi$
$972$	9.18330e8			0.0320750
$973$		0			0
$974$	1.37613e10			0.477204
$975$	−2.19384e10	+	3.79984e10i	−0.758033	+	1.31295i
$976$	6.52020e9	+	1.12933e10i	0.224485	+	0.388819i
$977$	1.60839e10	+	2.78582e10i	0.551774	+	0.955700i	0.998147	+	0.0608529i	$0.0193821\pi$
$977$	1.60839e10	+	2.78582e10i	0.551774	+	0.955700i	−0.446373	+	0.894847i	$0.647285\pi$
$978$	−6.54313e9	+	1.13330e10i	−0.223666	+	0.387400i
$979$	7.72335e10			2.63067
$980$		0			0
$981$	2.83608e9			0.0959130
$982$	2.66839e9	−	4.62179e9i	0.0899206	−	0.155747i
$983$	−9.27819e9	−	1.60703e10i	−0.311549	−	0.539618i	0.667149	−	0.744924i	$-0.267514\pi$
$983$	−9.27819e9	−	1.60703e10i	−0.311549	−	0.539618i	−0.978698	+	0.205306i	$0.934181\pi$
$984$	−3.66073e8	−	6.34058e8i	−0.0122486	−	0.0212151i
$985$	1.38512e10	−	2.39910e10i	0.461807	−	0.799874i
$986$	4.62526e8			0.0153662
$987$		0			0
$988$	−9.96808e9			−0.328823
$989$	−2.04407e10	+	3.54044e10i	−0.671908	+	1.16378i
$990$	9.96094e9	+	1.72529e10i	0.326270	+	0.565116i
$991$	−8.00744e9	−	1.38693e10i	−0.261358	−	0.452685i	0.705245	−	0.708964i	$-0.250837\pi$
$991$	−8.00744e9	−	1.38693e10i	−0.261358	−	0.452685i	−0.966603	+	0.256278i	$0.917504\pi$
$992$	1.84025e8	−	3.18741e8i	0.00598530	−	0.0103668i
$993$	−1.81059e10			−0.586809
$994$		0			0
$995$	6.17454e10			1.98712
$996$	−6.00525e9	+	1.04014e10i	−0.192586	+	0.333568i
$997$	−1.60482e10	−	2.77964e10i	−0.512855	−	0.888290i	−0.999889	−	0.0149074i	$-0.995255\pi$
$997$	−1.60482e10	−	2.77964e10i	−0.512855	−	0.888290i	0.487034	−	0.873383i	$-0.338079\pi$
$998$	2.18391e9	+	3.78264e9i	0.0695469	+	0.120459i
$999$	2.35899e9	−	4.08589e9i	0.0748594	−	0.129660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.8.e.a.79.1		2
7.2	even	3		42.8.a.f.1.1	✓	1
7.3	odd	6		294.8.e.f.67.1		2
7.4	even	3	inner	294.8.e.a.67.1		2
7.5	odd	6		294.8.a.k.1.1		1
7.6	odd	2		294.8.e.f.79.1		2
21.2	odd	6		126.8.a.a.1.1		1
28.23	odd	6		336.8.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.8.a.f.1.1	✓	1	7.2	even	3
126.8.a.a.1.1		1	21.2	odd	6
294.8.a.k.1.1		1	7.5	odd	6
294.8.e.a.67.1		2	7.4	even	3	inner
294.8.e.a.79.1		2	1.1	even	1	trivial
294.8.e.f.67.1		2	7.3	odd	6
294.8.e.f.79.1		2	7.6	odd	2
336.8.a.f.1.1		1	28.23	odd	6

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 6.92820i) q^{2} +(-13.5000 - 23.3827i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(-235.000 + 407.032i) q^{5} +216.000 q^{6} +512.000 q^{8} +(-364.500 + 631.333i) q^{9} +(-1880.00 - 3256.26i) q^{10} +(3634.00 + 6294.27i) q^{11} +(-864.000 + 1496.49i) q^{12} +11382.0 q^{13} +12690.0 q^{15} +(-2048.00 + 3547.24i) q^{16} +(-10421.0 - 18049.7i) q^{17} +(-2916.00 - 5050.66i) q^{18} +(6842.00 - 11850.7i) q^{19} +30080.0 q^{20} -58144.0 q^{22} +(23368.0 - 40474.6i) q^{23} +(-6912.00 - 11971.9i) q^{24} +(-71387.5 - 123647. i) q^{25} +(-45528.0 + 78856.8i) q^{26} +19683.0 q^{27} +2774.00 q^{29} +(-50760.0 + 87918.9i) q^{30} +(5616.00 + 9727.20i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(98118.0 - 169945. i) q^{33} +166736. q^{34} +46656.0 q^{36} +(119849. - 207585. i) q^{37} +(54736.0 + 94805.5i) q^{38} +(-153657. - 266142. i) q^{39} +(-120320. + 208400. i) q^{40} +52962.0 q^{41} -874732. q^{43} +(232576. - 402833. i) q^{44} +(-171315. - 296726. i) q^{45} +(186944. + 323797. i) q^{46} +(225648. - 390834. i) q^{47} +110592. q^{48} +1.14220e6 q^{50} +(-281367. + 487342. i) q^{51} +(-364224. - 630854. i) q^{52} +(971769. + 1.68315e6i) q^{53} +(-78732.0 + 136368. i) q^{54} -3.41596e6 q^{55} -369468. q^{57} +(-11096.0 + 19218.8i) q^{58} +(-781954. - 1.35438e6i) q^{59} +(-406080. - 703351. i) q^{60} +(1.59185e6 - 2.75716e6i) q^{61} -89856.0 q^{62} +262144. q^{64} +(-2.67477e6 + 4.63284e6i) q^{65} +(784944. + 1.35956e6i) q^{66} +(-1.06434e6 - 1.84349e6i) q^{67} +(-666944. + 1.15518e6i) q^{68} -1.26187e6 q^{69} +5.69454e6 q^{71} +(-186624. + 323242. i) q^{72} +(1.12694e6 + 1.95192e6i) q^{73} +(958792. + 1.66068e6i) q^{74} +(-1.92746e6 + 3.33846e6i) q^{75} -875776. q^{76} +2.45851e6 q^{78} +(-66456.0 + 115105. i) q^{79} +(-962560. - 1.66720e6i) q^{80} +(-265720. - 460241. i) q^{81} +(-211848. + 366931. i) q^{82} +6.95052e6 q^{83} +9.79574e6 q^{85} +(3.49893e6 - 6.06032e6i) q^{86} +(-37449.0 - 64863.6i) q^{87} +(1.86061e6 + 3.22267e6i) q^{88} +(5.31326e6 - 9.20283e6i) q^{89} +2.74104e6 q^{90} -2.99110e6 q^{92} +(151632. - 262634. i) q^{93} +(1.80518e6 + 3.12667e6i) q^{94} +(3.21574e6 + 5.56983e6i) q^{95} +(-442368. + 766204. i) q^{96} +2.40709e6 q^{97} -5.29837e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} - 27 q^{3} - 64 q^{4} - 470 q^{5} + 432 q^{6} + 1024 q^{8} - 729 q^{9} - 3760 q^{10} + 7268 q^{11} - 1728 q^{12} + 22764 q^{13} + 25380 q^{15} - 4096 q^{16} - 20842 q^{17} - 5832 q^{18} + 13684 q^{19}+ \cdots - 10596744 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 - 27 * q^3 - 64 * q^4 - 470 * q^5 + 432 * q^6 + 1024 * q^8 - 729 * q^9 - 3760 * q^10 + 7268 * q^11 - 1728 * q^12 + 22764 * q^13 + 25380 * q^15 - 4096 * q^16 - 20842 * q^17 - 5832 * q^18 + 13684 * q^19 + 60160 * q^20 - 116288 * q^22 + 46736 * q^23 - 13824 * q^24 - 142775 * q^25 - 91056 * q^26 + 39366 * q^27 + 5548 * q^29 - 101520 * q^30 + 11232 * q^31 - 32768 * q^32 + 196236 * q^33 + 333472 * q^34 + 93312 * q^36 + 239698 * q^37 + 109472 * q^38 - 307314 * q^39 - 240640 * q^40 + 105924 * q^41 - 1749464 * q^43 + 465152 * q^44 - 342630 * q^45 + 373888 * q^46 + 451296 * q^47 + 221184 * q^48 + 2284400 * q^50 - 562734 * q^51 - 728448 * q^52 + 1943538 * q^53 - 157464 * q^54 - 6831920 * q^55 - 738936 * q^57 - 22192 * q^58 - 1563908 * q^59 - 812160 * q^60 + 3183690 * q^61 - 179712 * q^62 + 524288 * q^64 - 5349540 * q^65 + 1569888 * q^66 - 2128684 * q^67 - 1333888 * q^68 - 2523744 * q^69 + 11389088 * q^71 - 373248 * q^72 + 2253878 * q^73 + 1917584 * q^74 - 3854925 * q^75 - 1751552 * q^76 + 4917024 * q^78 - 132912 * q^79 - 1925120 * q^80 - 531441 * q^81 - 423696 * q^82 + 13901048 * q^83 + 19591480 * q^85 + 6997856 * q^86 - 74898 * q^87 + 3721216 * q^88 + 10626510 * q^89 + 5482080 * q^90 - 5982208 * q^92 + 303264 * q^93 + 3610368 * q^94 + 6431480 * q^95 - 884736 * q^96 + 4814180 * q^97 - 10596744 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more