LMFDB - Embedded newform 27.7.f.a.14.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, 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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.4
Character	$\chi$	$=$	27.14
Dual form			27.7.f.a.2.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-9.97059 + 1.75808i) q^{2} +(24.1318 + 12.1101i) q^{3} +(36.1814 - 13.1690i) q^{4} +(60.9980 - 72.6946i) q^{5} +(-261.899 - 78.3191i) q^{6} +(-133.791 - 48.6960i) q^{7} +(223.553 - 129.069i) q^{8} +(435.691 + 584.478i) q^{9} +(-480.383 + 832.047i) q^{10} +(1624.00 + 1935.41i) q^{11} +(1032.60 + 120.370i) q^{12} +(-126.490 + 717.362i) q^{13} +(1419.59 + 250.312i) q^{14} +(2352.33 - 1015.56i) q^{15} +(-3889.75 + 3263.89i) q^{16} +(4210.29 + 2430.81i) q^{17} +(-5371.65 - 5061.61i) q^{18} +(62.0141 + 107.412i) q^{19} +(1249.68 - 3433.47i) q^{20} +(-2638.91 - 2795.35i) q^{21} +(-19594.9 - 16442.1i) q^{22} +(-4137.25 - 11367.0i) q^{23} +(6957.79 - 407.407i) q^{24} +(1149.51 + 6519.18i) q^{25} -7374.90i q^{26} +(3435.93 + 19380.8i) q^{27} -5482.03 q^{28} +(22191.9 - 3913.03i) q^{29} +(-21668.7 + 14261.3i) q^{30} +(14120.1 - 5139.28i) q^{31} +(22425.5 - 26725.7i) q^{32} +(15752.1 + 66371.9i) q^{33} +(-46252.6 - 16834.6i) q^{34} +(-11700.9 + 6755.53i) q^{35} +(23460.9 + 15409.6i) q^{36} +(17270.1 - 29912.7i) q^{37} +(-807.155 - 961.930i) q^{38} +(-11739.8 + 15779.5i) q^{39} +(4253.72 - 24124.0i) q^{40} +(-87091.6 - 15356.6i) q^{41} +(31226.0 + 23231.8i) q^{42} +(-4953.54 + 4156.52i) q^{43} +(84246.1 + 48639.5i) q^{44} +(69064.6 + 3979.63i) q^{45} +(61235.0 + 106062. i) q^{46} +(59675.6 - 163957. i) q^{47} +(-133393. + 31658.3i) q^{48} +(-74595.6 - 62593.1i) q^{49} +(-22922.5 - 62979.1i) q^{50} +(72164.6 + 109647. i) q^{51} +(4870.32 + 27620.9i) q^{52} +277335. i q^{53} +(-68331.3 - 187197. i) q^{54} +239755. q^{55} +(-36194.6 + 6382.08i) q^{56} +(195.749 + 3343.04i) q^{57} +(-214387. + 78030.5i) q^{58} +(66748.6 - 79547.9i) q^{59} +(71736.8 - 67722.2i) q^{60} +(-284660. - 103608. i) q^{61} +(-131750. + 76065.9i) q^{62} +(-29829.8 - 99414.4i) q^{63} +(-14123.1 + 24462.0i) q^{64} +(44432.7 + 52952.8i) q^{65} +(-273745. - 634073. i) q^{66} +(-7050.75 + 39986.8i) q^{67} +(184345. + 32505.1i) q^{68} +(37816.2 - 324409. i) q^{69} +(104788. - 87927.9i) q^{70} +(-8731.10 - 5040.90i) q^{71} +(172838. + 74428.0i) q^{72} +(159295. + 275906. i) q^{73} +(-119604. + 328610. i) q^{74} +(-51208.2 + 171240. i) q^{75} +(3658.26 + 3069.64i) q^{76} +(-123031. - 338024. i) q^{77} +(89310.9 - 177970. i) q^{78} +(11705.7 + 66386.4i) q^{79} +481854. i q^{80} +(-151788. + 509303. i) q^{81} +895353. q^{82} +(-975779. + 172056. i) q^{83} +(-132291. - 66388.0i) q^{84} +(433526. - 157790. i) q^{85} +(42082.2 - 50151.7i) q^{86} +(582919. + 174318. i) q^{87} +(612852. + 223060. i) q^{88} +(-169602. + 97919.9i) q^{89} +(-695611. + 81742.1i) q^{90} +(51856.0 - 89817.2i) q^{91} +(-299383. - 356791. i) q^{92} +(402980. + 46975.1i) q^{93} +(-306750. + 1.73967e6i) q^{94} +(11591.0 + 2043.80i) q^{95} +(864820. - 373365. i) q^{96} +(981600. - 823660. i) q^{97} +(853806. + 492945. i) q^{98} +(-423643. + 1.79244e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18}+ \cdots + 1743822 q^{99}+O(q^{100}) $ 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−9.97059	+	1.75808i	−1.24632	+	0.219760i	−0.757624	−	0.652692i	$-0.773640\pi$
$2$	−9.97059	+	1.75808i	−1.24632	+	0.219760i	−0.488700	+	0.872452i	$0.662529\pi$
$3$	24.1318	+	12.1101i	0.893772	+	0.448522i
$3$	24.1318	+	12.1101i	0.893772	+	0.448522i
$4$	36.1814	−	13.1690i	0.565335	−	0.205765i
$5$	60.9980	−	72.6946i	0.487984	−	0.581556i	−0.464720	−	0.885458i	$-0.653845\pi$
$5$	60.9980	−	72.6946i	0.487984	−	0.581556i	0.952703	+	0.303901i	$0.0982893\pi$
$6$	−261.899	−	78.3191i	−1.21250	−	0.362588i
$7$	−133.791	−	48.6960i	−0.390062	−	0.141971i	0.139542	−	0.990216i	$-0.455437\pi$
$7$	−133.791	−	48.6960i	−0.390062	−	0.141971i	−0.529604	+	0.848245i	$0.677659\pi$
$8$	223.553	−	129.069i	0.436628	−	0.252087i
$9$	435.691	+	584.478i	0.597655	+	0.801753i
$10$	−480.383	+	832.047i	−0.480383	+	0.832047i
$11$	1624.00	+	1935.41i	1.22014	+	1.45410i	0.851356	+	0.524588i	$0.175781\pi$
$11$	1624.00	+	1935.41i	1.22014	+	1.45410i	0.368782	+	0.929516i	$0.379775\pi$
$12$	1032.60	+	120.370i	0.597570	+	0.0696583i
$13$	−126.490	+	717.362i	−0.0575741	+	0.326519i	−0.999968	−	0.00798588i	$-0.997458\pi$
$13$	−126.490	+	717.362i	−0.0575741	+	0.326519i	0.942394	+	0.334505i	$0.108569\pi$
$14$	1419.59	+	250.312i	0.517343	+	0.0912215i
$15$	2352.33	−	1015.56i	0.696987	−	0.300907i
$16$	−3889.75	+	3263.89i	−0.949645	+	0.796847i
$17$	4210.29	+	2430.81i	0.856968	+	0.494771i	0.862996	−	0.505211i	$-0.168585\pi$
$17$	4210.29	+	2430.81i	0.856968	+	0.494771i	−0.00602755	+	0.999982i	$0.501919\pi$
$18$	−5371.65	−	5061.61i	−0.921065	−	0.867903i
$19$	62.0141	+	107.412i	0.00904127	+	0.0156599i	0.870511	−	0.492150i	$-0.163789\pi$
$19$	62.0141	+	107.412i	0.00904127	+	0.0156599i	−0.861469	+	0.507810i	$0.830455\pi$
$20$	1249.68	−	3433.47i	0.156210	−	0.429184i
$21$	−2638.91	−	2795.35i	−0.284949	−	0.301841i
$22$	−19594.9	−	16442.1i	−1.84024	−	1.54415i
$23$	−4137.25	−	11367.0i	−0.340039	−	0.934249i	−0.985382	−	0.170357i	$-0.945508\pi$
$23$	−4137.25	−	11367.0i	−0.340039	−	0.934249i	0.645344	−	0.763892i	$-0.276714\pi$
$24$	6957.79	−	407.407i	0.503312	−	0.0294710i
$25$	1149.51	+	6519.18i	0.0735685	+	0.417227i
$26$		−	7374.90i		−	0.419601i
$27$	3435.93	+	19380.8i	0.174563	+	0.984646i
$28$	−5482.03			−0.249728
$29$	22191.9	−	3913.03i	0.909915	−	0.160443i	0.300950	−	0.953640i	$-0.402696\pi$
$29$	22191.9	−	3913.03i	0.909915	−	0.160443i	0.608965	+	0.793197i	$0.291585\pi$
$30$	−21668.7	+	14261.3i	−0.802544	+	0.528198i
$31$	14120.1	−	5139.28i	0.473971	−	0.172511i	−0.0939796	−	0.995574i	$-0.529959\pi$
$31$	14120.1	−	5139.28i	0.473971	−	0.172511i	0.567950	+	0.823063i	$0.307737\pi$
$32$	22425.5	−	26725.7i	0.684373	−	0.815604i
$33$	15752.1	+	66371.9i	0.438327	+	1.84690i
$34$	−46252.6	−	16834.6i	−1.17679	−	0.428317i
$35$	−11700.9	+	6755.53i	−0.272908	+	0.157563i
$36$	23460.9	+	15409.6i	0.502848	+	0.330282i
$37$	17270.1	−	29912.7i	0.340950	−	0.590542i	−0.643660	−	0.765312i	$-0.722585\pi$
$37$	17270.1	−	29912.7i	0.340950	−	0.590542i	0.984609	+	0.174770i	$0.0559180\pi$
$38$	−807.155	−	961.930i	−0.0147098	−	0.0175304i
$39$	−11739.8	+	15779.5i	−0.197909	+	0.266010i
$40$	4253.72	−	24124.0i	0.0664643	−	0.376938i
$41$	−87091.6	−	15356.6i	−1.26364	−	0.222815i	−0.498623	−	0.866819i	$-0.666161\pi$
$41$	−87091.6	−	15356.6i	−1.26364	−	0.222815i	−0.765022	+	0.644004i	$0.777272\pi$
$42$	31226.0	+	23231.8i	0.421471	+	0.313571i
$43$	−4953.54	+	4156.52i	−0.0623032	+	0.0522786i	−0.673408	−	0.739271i	$-0.735170\pi$
$43$	−4953.54	+	4156.52i	−0.0623032	+	0.0522786i	0.611104	+	0.791550i	$0.290726\pi$
$44$	84246.1	+	48639.5i	0.988990	+	0.570994i
$45$	69064.6	+	3979.63i	0.757911	+	0.0436722i
$46$	61235.0	+	106062.i	0.629109	+	1.08965i
$47$	59675.6	−	163957.i	0.574782	−	1.57920i	−0.222072	−	0.975030i	$-0.571282\pi$
$47$	59675.6	−	163957.i	0.574782	−	1.57920i	0.796855	−	0.604171i	$-0.206496\pi$
$48$	−133393.	+	31658.3i	−1.20617	+	0.286262i
$49$	−74595.6	−	62593.1i	−0.634052	−	0.532033i
$50$	−22922.5	−	62979.1i	−0.183380	−	0.503833i
$51$	72164.6	+	109647.i	0.544018	+	0.826582i
$52$	4870.32	+	27620.9i	0.0346375	+	0.196439i
$53$			277335.i			1.86285i	0.363938	+	0.931423i	$0.381432\pi$
$53$			277335.i			1.86285i	−0.363938	+	0.931423i	$0.618568\pi$
$54$	−68331.3	−	187197.i	−0.433948	−	1.18883i
$55$	239755.			1.44105
$56$	−36194.6	+	6382.08i	−0.206101	+	0.0363411i
$57$	195.749	+	3343.04i	0.00105700	+	0.0180516i
$58$	−214387.	+	78030.5i	−1.09879	+	0.399927i
$59$	66748.6	−	79547.9i	0.325002	−	0.387323i	−0.578660	−	0.815569i	$-0.696424\pi$
$59$	66748.6	−	79547.9i	0.325002	−	0.387323i	0.903662	+	0.428247i	$0.140869\pi$
$60$	71736.8	−	67722.2i	0.332115	−	0.313529i
$61$	−284660.	−	103608.i	−1.25411	−	0.456459i	−0.372323	−	0.928103i	$-0.621439\pi$
$61$	−284660.	−	103608.i	−1.25411	−	0.456459i	−0.881789	+	0.471644i	$0.843661\pi$
$62$	−131750.	+	76065.9i	−0.552809	+	0.319165i
$63$	−29829.8	−	99414.4i	−0.119297	−	0.397583i
$64$	−14123.1	+	24462.0i	−0.0538755	+	0.0933151i
$65$	44432.7	+	52952.8i	0.161794	+	0.192819i
$66$	−273745.	−	634073.i	−0.952171	−	2.20550i
$67$	−7050.75	+	39986.8i	−0.0234429	+	0.132951i	−0.994283	−	0.106777i	$-0.965947\pi$
$67$	−7050.75	+	39986.8i	−0.0234429	+	0.132951i	0.970840	+	0.239728i	$0.0770582\pi$
$68$	184345.	+	32505.1i	0.586280	+	0.103377i
$69$	37816.2	−	324409.i	0.115115	−	0.987520i
$70$	104788.	−	87927.9i	0.305505	−	0.256349i
$71$	−8731.10	−	5040.90i	−0.0243946	−	0.0140842i	0.487753	−	0.872982i	$-0.337817\pi$
$71$	−8731.10	−	5040.90i	−0.0243946	−	0.0140842i	−0.512148	+	0.858897i	$0.671150\pi$
$72$	172838.	+	74428.0i	0.463064	+	0.199406i
$73$	159295.	+	275906.i	0.409480	+	0.709239i	0.994831	−	0.101540i	$-0.0323770\pi$
$73$	159295.	+	275906.i	0.409480	+	0.709239i	−0.585352	+	0.810779i	$0.699044\pi$
$74$	−119604.	+	328610.i	−0.295156	+	0.810934i
$75$	−51208.2	+	171240.i	−0.121382	+	0.405903i
$76$	3658.26	+	3069.64i	0.00833361	+	0.00699273i
$77$	−123031.	−	338024.i	−0.269489	−	0.740415i
$78$	89310.9	−	177970.i	0.188200	−	0.375027i
$79$	11705.7	+	66386.4i	0.0237420	+	0.134647i	0.994375	−	0.105918i	$-0.0337782\pi$
$79$	11705.7	+	66386.4i	0.0237420	+	0.134647i	−0.970633	+	0.240566i	$0.922667\pi$
$80$			481854.i			0.941121i
$81$	−151788.	+	509303.i	−0.285616	+	0.958344i
$82$	895353.			1.62388
$83$	−975779.	+	172056.i	−1.70654	+	0.300910i	−0.939973	−	0.341250i	$-0.889150\pi$
$83$	−975779.	+	172056.i	−1.70654	+	0.300910i	−0.766571	+	0.642160i	$0.778039\pi$
$84$	−132291.	−	66388.0i	−0.223200	−	0.112009i
$85$	433526.	−	157790.i	0.705924	−	0.256935i
$86$	42082.2	−	50151.7i	0.0661612	−	0.0788479i
$87$	582919.	+	174318.i	0.885218	+	0.264718i
$88$	612852.	+	223060.i	0.899307	+	0.327321i
$89$	−169602.	+	97919.9i	−0.240581	+	0.138900i	−0.615444	−	0.788181i	$-0.711023\pi$
$89$	−169602.	+	97919.9i	−0.240581	+	0.138900i	0.374863	+	0.927080i	$0.377690\pi$
$90$	−695611.	+	81742.1i	−0.954199	+	0.112129i
$91$	51856.0	−	89817.2i	0.0688137	−	0.119189i
$92$	−299383.	−	356791.i	−0.384471	−	0.458195i
$93$	402980.	+	46975.1i	0.500997	+	0.0584008i
$94$	−306750.	+	1.73967e6i	−0.369319	+	2.09451i
$95$	11591.0	+	2043.80i	0.0135191	+	0.00238379i
$96$	864820.	−	373365.i	0.977490	−	0.422007i
$97$	981600.	−	823660.i	1.07552	−	0.902470i	0.0799810	−	0.996796i	$-0.474514\pi$
$97$	981600.	−	823660.i	1.07552	−	0.902470i	0.995541	+	0.0943259i	$0.0300696\pi$
$98$	853806.	+	492945.i	0.907153	+	0.523745i
$99$	−423643.	+	1.79244e6i	−0.436610	+	1.84730i
$100$	127442.	+	220735.i	0.127442	+	0.220735i
$101$	144793.	−	397814.i	0.140534	−	0.386115i	−0.849380	−	0.527781i	$-0.823024\pi$
$101$	144793.	−	397814.i	0.140534	−	0.386115i	0.989914	+	0.141667i	$0.0452462\pi$
$102$	−912291.	−	966372.i	−0.859672	−	0.910634i
$103$	−1.47195e6	−	1.23511e6i	−1.34704	−	1.13030i	−0.979756	−	0.200195i	$-0.935842\pi$
$103$	−1.47195e6	−	1.23511e6i	−1.34704	−	1.13030i	−0.367286	−	0.930108i	$-0.619713\pi$
$104$	64311.6	+	176695.i	0.0571728	+	0.157081i
$105$	−364175.	+	21324.0i	−0.314588	+	0.0184204i
$106$	−487578.	−	2.76519e6i	−0.409380	−	2.32171i
$107$		−	1.43594e6i		−	1.17215i	−0.810257	−	0.586075i	$-0.800672\pi$
$107$		−	1.43594e6i		−	1.17215i	0.810257	−	0.586075i	$-0.199328\pi$
$108$	379542.	+	655977.i	0.301292	+	0.520735i
$109$	−1.85981e6			−1.43611			−0.718057	−	0.695984i	$-0.754968\pi$
$109$	−1.85981e6			−1.43611			−0.718057	+	0.695984i	$0.754968\pi$
$110$	−2.39050e6	+	421509.i	−1.79602	+	0.316686i
$111$	779006.	−	512706.i	0.569603	−	0.374886i
$112$	679352.	−	247264.i	0.483550	−	0.175998i
$113$	1.43022e6	−	1.70447e6i	0.991212	−	1.18128i	0.00778556	−	0.999970i	$-0.497522\pi$
$113$	1.43022e6	−	1.70447e6i	0.991212	−	1.18128i	0.983426	−	0.181310i	$-0.0580338\pi$
$114$	−7829.06	−	32987.9i	−0.00528439	−	0.0222659i
$115$	−1.07868e6	−	392609.i	−0.709252	−	0.258147i
$116$	751404.	−	433823.i	0.481393	−	0.277932i
$117$	−474393.	+	238617.i	−0.296197	+	0.148986i
$118$	−525671.	+	910489.i	−0.319940	+	0.554152i
$119$	−444928.	−	530245.i	−0.264028	−	0.314656i
$120$	394795.	−	530644.i	0.228469	−	0.307086i
$121$	−800805.	+	4.54159e6i	−0.452033	+	2.56361i
$122$	3.02037e6	+	532573.i	1.66334	+	0.293292i
$123$	−1.91571e6	−	1.42527e6i	−1.02947	−	0.765918i
$124$	443205.	−	371893.i	0.232455	−	0.195053i
$125$	1.82813e6	+	1.05547e6i	0.936000	+	0.540400i
$126$	472200.	+	938777.i	0.236056	+	0.469300i
$127$	−661639.	−	1.14599e6i	−0.323006	−	0.559462i	0.658101	−	0.752930i	$-0.271360\pi$
$127$	−661639.	−	1.14599e6i	−0.323006	−	0.559462i	−0.981107	+	0.193467i	$0.938027\pi$
$128$	−665862.	+	1.82944e6i	−0.317508	+	0.872346i
$129$	−169874.	+	40316.4i	−0.0791330	+	0.0187808i
$130$	−536115.	−	449854.i	−0.244022	−	0.204758i
$131$	93255.3	+	256217.i	0.0414820	+	0.113971i	0.958704	−	0.284405i	$-0.0917961\pi$
$131$	93255.3	+	256217.i	0.0414820	+	0.113971i	−0.917222	+	0.398376i	$0.869574\pi$
$132$	1.44398e6	+	2.19399e6i	0.627828	+	0.953922i
$133$	−3066.43	−	17390.6i	−0.00130340	−	0.00739195i
$134$		−	411088.i		−	0.170852i
$135$	1.61846e6	+	932416.i	0.657811	+	0.378973i
$136$	1.25496e6			0.498901
$137$	3.97328e6	−	700596.i	1.54521	−	0.272462i	0.664926	−	0.746910i	$-0.268463\pi$
$137$	3.97328e6	−	700596.i	1.54521	−	0.272462i	0.880284	+	0.474447i	$0.157352\pi$
$138$	193289.	+	3.30103e6i	0.0735480	+	1.25607i
$139$	−2.76811e6	+	1.00751e6i	−1.03071	+	0.375149i	−0.801353	−	0.598192i	$-0.795886\pi$
$139$	−2.76811e6	+	1.00751e6i	−1.03071	+	0.375149i	−0.229362	+	0.973341i	$0.573664\pi$
$140$	−334393.	+	398514.i	−0.121863	+	0.145231i
$141$	3.42562e6	−	3.23392e6i	1.22203	−	1.15364i
$142$	95916.5	+	34910.7i	0.0334987	+	0.0121925i
$143$	−1.59381e6	+	920188.i	−0.545041	+	0.314680i
$144$	−3.60240e6	−	851427.i	−1.20644	−	0.285141i
$145$	1.06921e6	−	1.85192e6i	0.350717	−	0.607460i
$146$	−2.07333e6	−	2.47089e6i	−0.666207	−	0.793954i
$147$	−1.04212e6	−	2.41385e6i	−0.328069	−	0.759902i
$148$	230938.	−	1.30972e6i	0.0712378	−	0.404010i
$149$	938820.	+	165539.i	0.283807	+	0.0500429i	0.313740	−	0.949509i	$-0.398418\pi$
$149$	938820.	+	165539.i	0.283807	+	0.0500429i	−0.0299325	+	0.999552i	$0.509529\pi$
$150$	209521.	−	1.79740e6i	0.0620803	−	0.532562i
$151$	−3.13417e6	+	2.62988e6i	−0.910316	+	0.763846i	−0.972179	−	0.234239i	$-0.924740\pi$
$151$	−3.13417e6	+	2.62988e6i	−0.910316	+	0.763846i	0.0618631	+	0.998085i	$0.480296\pi$
$152$	27726.9	+	16008.1i	0.00789534	+	0.00455838i
$153$	413628.	+	3.51990e6i	0.115488	+	0.982780i
$154$	1.82096e6	+	3.15400e6i	0.498584	+	0.863573i
$155$	487697.	−	1.33994e6i	0.130965	−	0.359823i
$156$	−216963.	+	725524.i	−0.0571494	+	0.191108i
$157$	−2.55010e6	−	2.13979e6i	−0.658960	−	0.552933i	0.250815	−	0.968035i	$-0.419301\pi$
$157$	−2.55010e6	−	2.13979e6i	−0.658960	−	0.552933i	−0.909775	+	0.415102i	$0.863746\pi$
$158$	−233426.	−	641332.i	−0.0591803	−	0.162597i
$159$	−3.35856e6	+	6.69260e6i	−0.835528	+	1.66496i
$160$	−574901.	−	3.26043e6i	−0.140357	−	0.796003i
$161$			1.72227e6i			0.412691i
$162$	618019.	−	5.34491e6i	0.145364	−	1.25717i
$163$	2.30993e6			0.533380			0.266690	−	0.963782i	$-0.414070\pi$
$163$	2.30993e6			0.533380			0.266690	+	0.963782i	$0.414070\pi$
$164$	−3.35333e6	+	591282.i	−0.760229	+	0.134049i
$165$	5.78573e6	+	2.90346e6i	1.28797	+	0.646344i
$166$	9.42660e6	−	3.43100e6i	2.06078	−	0.750061i
$167$	1.52636e6	−	1.81904e6i	0.327723	−	0.390565i	−0.576874	−	0.816833i	$-0.695727\pi$
$167$	1.52636e6	−	1.81904e6i	0.327723	−	0.390565i	0.904597	+	0.426268i	$0.140172\pi$
$168$	−950730.	−	284309.i	−0.200507	−	0.0599601i
$169$	4.03711e6	+	1.46939e6i	0.836393	+	0.304422i
$170$	−4.04510e6	+	2.33544e6i	−0.823345	+	0.475359i
$171$	−35760.7	+	83044.1i	−0.00715184	+	0.0166081i
$172$	−124489.	+	215622.i	−0.0244651	+	0.0423747i
$173$	3.26555e6	+	3.89174e6i	0.630694	+	0.751632i	0.982870	−	0.184302i	$-0.0590025\pi$
$173$	3.26555e6	+	3.89174e6i	0.630694	+	0.751632i	−0.352176	+	0.935934i	$0.614558\pi$
$174$	−6.11851e6	−	713230.i	−1.16144	−	0.135389i
$175$	163664.	−	928185.i	0.0305379	−	0.173189i
$176$	−1.26339e7	−	2.22770e6i	−2.31740	−	0.408620i
$177$	2.57410e6	−	1.11130e6i	0.464201	−	0.200407i
$178$	1.51888e6	−	1.27449e6i	0.269317	−	0.225984i
$179$	−2.84156e6	−	1.64058e6i	−0.495447	−	0.286047i	0.231384	−	0.972862i	$-0.425675\pi$
$179$	−2.84156e6	−	1.64058e6i	−0.495447	−	0.286047i	−0.726832	+	0.686816i	$0.759008\pi$
$180$	2.55126e6	−	765521.i	0.437459	−	0.131262i
$181$	324598.	+	562220.i	0.0547407	+	0.0948137i	0.892097	−	0.451843i	$-0.149233\pi$
$181$	324598.	+	562220.i	0.0547407	+	0.0948137i	−0.837357	+	0.546657i	$0.815900\pi$
$182$	−359129.	+	986698.i	−0.0595711	+	0.163670i
$183$	−5.61466e6	−	5.94750e6i	−0.916158	−	0.970468i
$184$	−2.39202e6	−	2.00714e6i	−0.383982	−	0.322199i
$185$	−1.12105e6	−	3.08006e6i	−0.177056	−	0.486457i
$186$	−4.10053e6	+	240103.i	−0.637238	+	0.0373129i
$187$	2.13290e6	+	1.20963e7i	0.326171	+	1.84981i
$188$		−	6.71808e6i		−	1.01105i
$189$	484070.	−	2.76030e6i	0.0717006	−	0.408856i
$190$	−119162.			−0.0173731
$191$	8.13036e6	−	1.43360e6i	1.16684	−	0.205745i	0.443522	−	0.896264i	$-0.353729\pi$
$191$	8.13036e6	−	1.43360e6i	1.16684	−	0.205745i	0.723314	+	0.690519i	$0.242618\pi$
$192$	−637054.	+	419280.i	−0.0900063	+	0.0592380i
$193$	8.86230e6	−	3.22561e6i	1.23275	−	0.448684i	0.358211	−	0.933641i	$-0.383387\pi$
$193$	8.86230e6	−	3.22561e6i	1.23275	−	0.448684i	0.874538	+	0.484957i	$0.161165\pi$
$194$	−8.33907e6	+	9.93811e6i	−1.14212	+	1.36113i
$195$	430978.	+	1.81593e6i	0.0581235	+	0.244904i
$196$	−3.52326e6	−	1.28236e6i	−0.467925	−	0.170311i
$197$	−4.99084e6	+	2.88146e6i	−0.652792	+	0.376889i	−0.789525	−	0.613718i	$-0.789673\pi$
$197$	−4.99084e6	+	2.88146e6i	−0.652792	+	0.376889i	0.136733	+	0.990608i	$0.456340\pi$
$198$	1.07271e6	−	1.86164e7i	0.138194	−	2.39829i
$199$	1.79973e6	−	3.11723e6i	0.228375	−	0.395557i	−0.728952	−	0.684565i	$-0.759992\pi$
$199$	1.79973e6	−	3.11723e6i	0.228375	−	0.395557i	0.957327	+	0.289008i	$0.0933254\pi$
$200$	1.09840e6	+	1.30902e6i	0.137300	+	0.163627i
$201$	−654392.	+	879570.i	−0.0805842	+	0.108313i
$202$	−744276.	+	4.22100e6i	−0.0902984	+	0.512107i
$203$	−3.15963e6	−	557128.i	−0.377701	−	0.0665989i
$204$	4.05495e6	+	3.01685e6i	0.477634	+	0.355355i
$205$	−6.42876e6	+	5.39437e6i	−0.746217	+	0.626151i
$206$	1.68476e7	+	9.72698e6i	1.92725	+	1.11270i
$207$	4.84120e6	−	7.37063e6i	0.545811	−	0.830986i
$208$	−1.84937e6	−	3.20321e6i	−0.205511	−	0.355955i
$209$	−107175.	+	294460.i	−0.0117396	+	0.0322542i
$210$	3.59355e6	−	852863.i	0.388030	−	0.0920919i
$211$	−8.40990e6	−	7.05675e6i	−0.895249	−	0.751203i	0.0740074	−	0.997258i	$-0.476421\pi$
$211$	−8.40990e6	−	7.05675e6i	−0.895249	−	0.751203i	−0.969256	+	0.246055i	$0.920866\pi$
$212$	3.65221e6	+	1.00344e7i	0.383309	+	1.05313i
$213$	−149652.	−	227381.i	−0.0154861	−	0.0235296i
$214$	2.52449e6	+	1.43171e7i	0.257592	+	1.46088i
$215$			613635.i			0.0617440i
$216$	3.26956e6	+	3.88917e6i	0.324436	+	0.385918i
$217$	−2.13940e6			−0.209369
$218$	1.85434e7	−	3.26970e6i	1.78986	−	0.315601i
$219$	502816.	+	8.58719e6i	0.0478715	+	0.817559i
$220$	8.67467e6	−	3.15732e6i	0.814676	−	0.296518i
$221$	−2.27633e6	+	2.71283e6i	−0.210891	+	0.251331i
$222$	−6.86577e6	+	6.48154e6i	−0.627524	+	0.592406i
$223$	1.99653e6	+	726678.i	0.180037	+	0.0655280i	0.430466	−	0.902607i	$-0.358349\pi$
$223$	1.99653e6	+	726678.i	0.180037	+	0.0655280i	−0.250429	+	0.968135i	$0.580572\pi$
$224$	−4.30178e6	+	2.48363e6i	−0.382740	+	0.220975i
$225$	−3.30949e6	+	3.51221e6i	−0.290545	+	0.308342i
$226$	−1.12635e7	+	1.95090e7i	−0.975771	+	1.69009i
$227$	121910.	+	145286.i	0.0104222	+	0.0124207i	0.771230	−	0.636556i	$-0.219642\pi$
$227$	121910.	+	145286.i	0.0104222	+	0.0124207i	−0.760808	+	0.648977i	$0.775197\pi$
$228$	51106.8	+	118378.i	0.00431195	+	0.00998772i
$229$	−156615.	+	888210.i	−0.0130415	+	0.0739621i	−0.990634	−	0.136545i	$-0.956400\pi$
$229$	−156615.	+	888210.i	−0.0130415	+	0.0739621i	0.977592	+	0.210507i	$0.0675114\pi$
$230$	1.14453e7	+	2.01812e6i	0.940688	+	0.165869i
$231$	1.12455e6	−	9.64705e6i	0.0912310	−	0.782633i
$232$	4.45603e6	−	3.73905e6i	0.356848	−	0.299431i
$233$	−6.44223e6	−	3.71942e6i	−0.509294	−	0.294041i	0.223249	−	0.974761i	$-0.428334\pi$
$233$	−6.44223e6	−	3.71942e6i	−0.509294	−	0.294041i	−0.732543	+	0.680720i	$0.761667\pi$
$234$	4.31047e6	−	3.21318e6i	0.336416	−	0.250777i
$235$	−8.27872e6	−	1.43392e7i	−0.637910	−	1.10489i
$236$	1.36750e6	−	3.75717e6i	0.104038	−	0.285841i
$237$	−521466.	+	1.74378e6i	−0.0391724	+	0.130993i
$238$	5.36841e6	+	4.50463e6i	0.398213	+	0.334140i
$239$	−2.60021e6	−	7.14402e6i	−0.190465	−	0.523298i	0.807298	−	0.590143i	$-0.200929\pi$
$239$	−2.60021e6	−	7.14402e6i	−0.190465	−	0.523298i	−0.997763	+	0.0668453i	$0.978707\pi$
$240$	−5.83530e6	+	1.16280e7i	−0.422114	+	0.841147i
$241$	−1.52112e6	−	8.62668e6i	−0.108670	−	0.616301i	−0.989691	−	0.143222i	$-0.954254\pi$
$241$	−1.52112e6	−	8.62668e6i	−0.108670	−	0.616301i	0.881020	−	0.473079i	$-0.156857\pi$
$242$		−	4.66902e7i		−	3.29442i
$243$	−9.83064e6	+	1.04523e7i	−0.685114	+	0.728436i
$244$	−1.16638e7			−0.802916
$245$	−9.10036e6	+	1.60464e6i	−0.618814	+	0.109114i
$246$	2.16065e7	+	1.08428e7i	1.45137	+	0.728344i
$247$	−84897.2	+	30900.1i	−0.00563381	+	0.00205054i
$248$	2.49327e6	−	2.97136e6i	0.163461	−	0.194805i
$249$	−2.56310e7	−	7.66476e6i	−1.66022	−	0.496478i
$250$	−2.00831e7	−	7.30965e6i	−1.28532	−	0.467817i
$251$	−2.29316e7	+	1.32396e7i	−1.45015	+	0.837245i	−0.998489	−	0.0549446i	$-0.982502\pi$
$251$	−2.29316e7	+	1.32396e7i	−1.45015	+	0.837245i	−0.451661	+	0.892189i	$0.649168\pi$
$252$	−2.38847e6	−	3.20413e6i	−0.149251	−	0.200220i
$253$	1.52809e7	−	2.64674e7i	0.943601	−	1.63436i
$254$	8.61169e6	+	1.02630e7i	0.525517	+	0.626287i
$255$	1.23726e7	+	1.44227e6i	0.746176	+	0.0869812i
$256$	3.73664e6	−	2.11915e7i	0.222721	−	1.26311i
$257$	6.58651e6	+	1.16138e6i	0.388022	+	0.0684187i	0.364256	−	0.931299i	$-0.381323\pi$
$257$	6.58651e6	+	1.16138e6i	0.388022	+	0.0684187i	0.0237657	+	0.999718i	$0.492434\pi$
$258$	1.62286e6	−	700631.i	0.0944981	−	0.0407972i
$259$	−3.76722e6	+	3.16108e6i	−0.216831	+	0.181943i
$260$	2.30497e6	+	1.33078e6i	0.131143	+	0.0757155i
$261$	1.19559e7	+	1.12658e7i	0.672451	+	0.633638i
$262$	−1.38026e6	−	2.39068e6i	−0.0767463	−	0.132928i
$263$	6.79907e6	−	1.86803e7i	0.373751	−	1.02687i	−0.600148	−	0.799889i	$-0.704892\pi$
$263$	6.79907e6	−	1.86803e7i	0.373751	−	1.02687i	0.973899	−	0.226983i	$-0.0728861\pi$
$264$	1.20880e7	+	1.28046e7i	0.656964	+	0.695909i
$265$	2.01607e7	+	1.69169e7i	1.08335	+	0.909039i
$266$	61148.1	+	168003.i	0.00324891	+	0.00892632i
$267$	−5.27863e6	+	309086.i	−0.277324	+	0.0162385i
$268$	271478.	+	1.53963e6i	0.0141036	+	0.0799857i
$269$		−	1.98444e7i		−	1.01949i	−0.860327	−	0.509743i	$-0.829740\pi$
$269$		−	1.98444e7i		−	1.01949i	0.860327	−	0.509743i	$-0.170260\pi$
$270$	−1.77763e7	−	6.45134e6i	−0.903129	−	0.327762i
$271$	−1.77711e7			−0.892907			−0.446454	−	0.894807i	$-0.647313\pi$
$271$	−1.77711e7			−0.892907			−0.446454	+	0.894807i	$0.647313\pi$
$272$	−2.43108e7	+	4.28666e6i	−1.20807	+	0.213016i
$273$	2.33908e6	−	1.53947e6i	0.114963	−	0.0756631i
$274$	−3.83842e7	+	1.39707e7i	−1.86595	+	0.679152i
$275$	−1.07505e7	+	1.28119e7i	−0.516929	+	0.616051i
$276$	−2.90389e6	−	1.22356e7i	−0.138119	−	0.581966i
$277$	3.51398e7	+	1.27899e7i	1.65333	+	0.601764i	0.989294	−	0.145933i	$-0.0466184\pi$
$277$	3.51398e7	+	1.27899e7i	1.65333	+	0.601764i	0.664040	+	0.747697i	$0.268841\pi$
$278$	2.58284e7	−	1.49120e7i	1.20216	−	0.694068i
$279$	9.15577e6	+	6.01373e6i	0.421582	+	0.276905i
$280$	−1.74385e6	+	3.02044e6i	−0.0794394	+	0.137593i
$281$	2.08127e6	+	2.48036e6i	0.0938014	+	0.111788i	0.810903	−	0.585180i	$-0.198976\pi$
$281$	2.08127e6	+	2.48036e6i	0.0938014	+	0.111788i	−0.717102	+	0.696968i	$0.754532\pi$
$282$	−2.84700e7	+	3.82666e7i	−1.26952	+	1.70637i
$283$	1.44560e6	−	8.19842e6i	0.0637807	−	0.361718i	−0.936168	−	0.351554i	$-0.885653\pi$
$283$	1.44560e6	−	8.19842e6i	0.0637807	−	0.361718i	0.999948	−	0.0101645i	$-0.00323551\pi$
$284$	−382287.	−	67407.5i	−0.0166892	−	0.00294275i
$285$	254961.	+	189689.i	0.0110138	+	0.00819420i
$286$	1.42735e7	−	1.19769e7i	0.610143	−	0.511971i
$287$	1.09043e7	+	6.29560e6i	0.461266	+	0.266312i
$288$	2.53912e7	+	1.46309e6i	1.06293	+	0.0612481i
$289$	−251115.	−	434944.i	−0.0104035	−	0.0180194i
$290$	−7.40478e6	+	2.03445e7i	−0.303611	+	0.834166i
$291$	3.36624e7	−	7.98915e6i	1.36605	−	0.324207i
$292$	9.39690e6	+	7.88493e6i	0.377430	+	0.316701i
$293$	1.20558e7	+	3.31231e7i	0.479285	+	1.31683i	0.910101	+	0.414386i	$0.136004\pi$
$293$	1.20558e7	+	3.31231e7i	0.479285	+	1.31683i	−0.430816	+	0.902440i	$0.641774\pi$
$294$	1.46343e7	+	2.22353e7i	0.575877	+	0.874987i
$295$	−1.71117e6	−	9.70452e6i	−0.0666541	−	0.378014i
$296$		−	8.91613e6i		−	0.343796i
$297$	−3.19299e7	+	3.81244e7i	−1.21879	+	1.45524i
$298$	−9.65161e6			−0.364713
$299$	8.67759e6	−	1.53009e6i	0.324628	−	0.0572406i
$300$	402272.	+	6.87008e6i	0.0148990	+	0.254447i
$301$	865147.	−	314888.i	0.0317242	−	0.0115467i
$302$	2.66260e7	−	3.17316e7i	0.966685	−	1.15205i
$303$	8.31168e6	−	7.84653e6i	0.298786	−	0.282065i
$304$	−591798.	−	215397.i	−0.0210646	−	0.00766688i
$305$	−2.48954e7	+	1.43733e7i	−0.877443	+	0.506592i
$306$	−1.03124e7	−	3.43683e7i	−0.359911	−	1.19948i
$307$	−9.02470e6	+	1.56312e7i	−0.311902	+	0.540230i	−0.978774	−	0.204942i	$-0.934299\pi$
$307$	−9.02470e6	+	1.56312e7i	−0.311902	+	0.540230i	0.666872	+	0.745172i	$0.267633\pi$
$308$	−8.90284e6	−	1.06100e7i	−0.304703	−	0.363131i
$309$	−2.05635e7	−	4.76310e7i	−0.696982	−	1.61441i
$310$	−2.50691e6	+	1.42174e7i	−0.0841498	+	0.477237i
$311$	9.81559e6	+	1.73075e6i	0.326314	+	0.0575379i	0.334405	−	0.942429i	$-0.391465\pi$
$311$	9.81559e6	+	1.73075e6i	0.326314	+	0.0575379i	−0.00809160	+	0.999967i	$0.502576\pi$
$312$	−587834.	+	5.04279e6i	−0.0193549	+	0.166038i
$313$	−4.19324e6	+	3.51855e6i	−0.136747	+	0.114744i	−0.708595	−	0.705615i	$-0.750671\pi$
$313$	−4.19324e6	+	3.51855e6i	−0.136747	+	0.114744i	0.571849	+	0.820359i	$0.306226\pi$
$314$	2.91880e7	+	1.68517e7i	0.942790	+	0.544320i
$315$	−9.04645e6	−	3.89561e6i	−0.289432	−	0.124636i
$316$	1.29777e6	+	2.24780e6i	0.0411279	+	0.0712355i
$317$	−4.37930e6	+	1.20320e7i	−0.137476	+	0.377712i	−0.989257	−	0.146185i	$-0.953300\pi$
$317$	−4.37930e6	+	1.20320e7i	−0.137476	+	0.377712i	0.851781	+	0.523898i	$0.175523\pi$
$318$	2.17206e7	−	7.26338e7i	0.675446	−	2.25869i
$319$	4.36131e7	+	3.65957e7i	1.34352	+	1.12735i
$320$	916771.	+	2.51881e6i	0.0279776	+	0.0768679i
$321$	1.73893e7	−	3.46517e7i	0.525736	−	1.04764i
$322$	−3.02790e6	−	1.71721e7i	−0.0906930	−	0.514346i
$323$			602978.i			0.0178934i
$324$	1.21509e6	+	2.04262e7i	0.0357250	+	0.600555i
$325$	−4.82202e6			−0.140468
$326$	−2.30314e7	+	4.06106e6i	−0.664764	+	0.117216i
$327$	−4.48806e7	−	2.25225e7i	−1.28356	−	0.644129i
$328$	−2.14517e7	+	7.80777e6i	−0.607911	+	0.221261i
$329$	−1.59681e7	+	1.90301e7i	−0.448401	+	0.534384i
$330$	−6.27916e7	−	1.87774e7i	−1.74727	−	0.522508i
$331$	−1.02584e7	−	3.73374e6i	−0.282874	−	0.102958i	0.196687	−	0.980466i	$-0.436982\pi$
$331$	−1.02584e7	−	3.73374e6i	−0.282874	−	0.102958i	−0.479561	+	0.877509i	$0.659204\pi$
$332$	−3.30393e7	+	1.90752e7i	−0.902851	+	0.521262i
$333$	2.50078e7	−	2.93869e6i	0.677240	−	0.0795833i
$334$	−1.20207e7	+	2.08204e7i	−0.322618	+	0.558791i
$335$	2.47674e6	+	2.95167e6i	0.0658789	+	0.0785114i
$336$	1.93884e7	+	2.26009e6i	0.511122	+	0.0595811i
$337$	4.54260e6	−	2.57624e7i	0.118690	−	0.673125i	−0.866167	−	0.499755i	$-0.833423\pi$
$337$	4.54260e6	−	2.57624e7i	0.118690	−	0.673125i	0.984857	−	0.173370i	$-0.0554656\pi$
$338$	−4.28356e7	−	7.55308e6i	−1.10932	−	0.195602i
$339$	5.51550e7	−	2.38118e7i	1.41575	−	0.611214i
$340$	1.36076e7	−	1.14182e7i	0.346215	−	0.290509i
$341$	3.28777e7	+	1.89819e7i	0.829159	+	0.478715i
$342$	210557.	−	890869.i	0.00526370	−	0.0222708i
$343$	1.53075e7	+	2.65134e7i	0.379334	+	0.657026i
$344$	−570906.	+	1.56855e6i	−0.0140246	+	0.0385321i
$345$	−2.12761e7	−	2.25373e7i	−0.518125	−	0.548839i
$346$	−3.94015e7	−	3.30618e7i	−0.951227	−	0.798175i
$347$	−9.54635e6	−	2.62284e7i	−0.228480	−	0.627745i	0.771483	−	0.636250i	$-0.219515\pi$
$347$	−9.54635e6	−	2.62284e7i	−0.228480	−	0.627745i	−0.999964	+	0.00850455i	$0.997293\pi$
$348$	2.33864e7	−	1.36937e6i	0.554914	−	0.0324925i
$349$	9933.24	+	56334.2i	0.000233676	+	0.00132524i	0.984924	−	0.172986i	$-0.0553414\pi$
$349$	9933.24	+	56334.2i	0.000233676	+	0.00132524i	−0.984691	+	0.174311i	$0.944230\pi$
$350$			9.54229e6i			0.222561i
$351$	−1.43377e7	+	13322.9i	−0.331556	+	0.000308090i
$352$	8.81444e7			2.02100
$353$	−2.73231e7	+	4.81780e6i	−0.621164	+	0.109528i	−0.475368	−	0.879787i	$-0.657685\pi$
$353$	−2.73231e7	+	4.81780e6i	−0.621164	+	0.109528i	−0.145795	+	0.989315i	$0.546574\pi$
$354$	−2.37115e7	+	1.56058e7i	−0.534502	+	0.351785i
$355$	−899025.	+	327218.i	−0.0200949	+	0.00731396i
$356$	−4.84694e6	+	5.77636e6i	−0.107428	+	0.128028i
$357$	−4.31562e6	−	1.81839e7i	−0.0948502	−	0.399653i
$358$	3.12163e7	+	1.13618e7i	0.680350	+	0.247627i
$359$	−3.18617e7	+	1.83954e7i	−0.688630	+	0.397581i	−0.803099	−	0.595846i	$-0.796817\pi$
$359$	−3.18617e7	+	1.83954e7i	−0.688630	+	0.397581i	0.114469	+	0.993427i	$0.463483\pi$
$360$	1.59533e7	−	8.02441e6i	0.341934	−	0.171991i
$361$	2.35152e7	−	4.07296e7i	0.499837	−	0.865742i
$362$	−4.22486e6	−	5.03500e6i	−0.0890609	−	0.106139i
$363$	−7.43240e7	+	9.98990e7i	−1.55385	+	2.08853i
$364$	693424.	−	3.93260e6i	0.0143779	−	0.0815410i
$365$	2.97735e7	+	5.24987e6i	0.612282	+	0.107962i
$366$	6.64376e7	+	4.94290e7i	1.35510	+	1.00818i
$367$	−5.33099e7	+	4.47324e7i	−1.07847	+	0.904948i	−0.995793	−	0.0916281i	$-0.970793\pi$
$367$	−5.33099e7	+	4.47324e7i	−1.07847	+	0.904948i	−0.0826816	+	0.996576i	$0.526348\pi$
$368$	5.31935e7	+	3.07113e7i	1.06737	+	0.616246i
$369$	−2.89694e7	−	5.75939e7i	−0.576582	−	1.14630i
$370$	1.65925e7	+	2.87391e7i	0.327573	+	0.567373i
$371$	1.35051e7	−	3.71050e7i	0.264470	−	0.726625i
$372$	1.51990e7	−	3.60720e6i	0.295248	−	0.0700715i
$373$	1.18708e7	+	9.96079e6i	0.228746	+	0.191941i	0.749956	−	0.661488i	$-0.230075\pi$
$373$	1.18708e7	+	9.96079e6i	0.228746	+	0.191941i	−0.521210	+	0.853429i	$0.674519\pi$
$374$	−4.25326e7	−	1.16857e8i	−0.813030	−	2.23378i
$375$	3.13342e7	+	4.76092e7i	0.594189	+	0.902811i
$376$	−7.82107e6	−	4.43555e7i	−0.147130	−	0.834418i
$377$			1.64146e7i			0.306342i
$378$	26364.7	+	2.83728e7i	0.000488144	+	0.525323i
$379$	8.36659e7			1.53685			0.768424	−	0.639941i	$-0.221041\pi$
$379$	8.36659e7			1.53685			0.768424	+	0.639941i	$0.221041\pi$
$380$	446292.	−	78693.4i	0.00813334	−	0.00143413i
$381$	−2.08848e6	−	3.56674e7i	−0.0377620	−	0.644907i
$382$	−7.85441e7	+	2.85877e7i	−1.40904	+	0.512849i
$383$	3.74148e7	−	4.45892e7i	0.665958	−	0.793658i	−0.322269	−	0.946648i	$-0.604446\pi$
$383$	3.74148e7	−	4.45892e7i	0.665958	−	0.793658i	0.988228	+	0.152990i	$0.0488901\pi$
$384$	−3.82232e7	+	3.60841e7i	−0.675046	+	0.637269i
$385$	−3.20771e7	−	1.16751e7i	−0.562099	−	0.204587i
$386$	−8.26915e7	+	4.77419e7i	−1.43780	+	0.830115i
$387$	−4.58761e6	−	1.08428e6i	−0.0791504	−	0.0187072i
$388$	2.46689e7	−	4.27279e7i	0.422333	−	0.731503i
$389$	−4.28033e7	−	5.10110e7i	−0.727158	−	0.866593i	0.268148	−	0.963378i	$-0.413588\pi$
$389$	−4.28033e7	−	5.10110e7i	−0.727158	−	0.866593i	−0.995305	+	0.0967851i	$0.969144\pi$
$390$	−7.48967e6	−	1.73482e7i	−0.126261	−	0.292456i
$391$	1.02120e7	−	5.79152e7i	0.170837	−	0.968863i
$392$	−2.47549e7	−	4.36496e6i	−0.410963	−	0.0724639i
$393$	−852391.	+	7.31232e6i	−0.0140430	+	0.120470i
$394$	4.46957e7	−	3.75042e7i	0.730764	−	0.613184i
$395$	5.53995e6	+	3.19849e6i	0.0898907	+	0.0518984i
$396$	8.27653e6	+	7.04318e7i	0.133279	+	1.13418i
$397$	1.99741e7	+	3.45961e7i	0.319224	+	0.552911i	0.980326	−	0.197384i	$-0.0632446\pi$
$397$	1.99741e7	+	3.45961e7i	0.319224	+	0.552911i	−0.661103	+	0.750295i	$0.729911\pi$
$398$	−1.24640e7	+	3.42447e7i	−0.197701	+	0.543180i
$399$	136603.	−	456801.i	0.00215051	−	0.00719131i
$400$	−2.57492e7	−	2.16061e7i	−0.402330	−	0.337595i
$401$	3.17423e7	+	8.72114e7i	0.492273	+	1.35251i	0.898595	+	0.438779i	$0.144589\pi$
$401$	3.17423e7	+	8.72114e7i	0.492273	+	1.35251i	−0.406322	+	0.913730i	$0.633189\pi$
$402$	4.97832e6	−	9.92030e6i	0.0766310	−	0.152703i
$403$	1.90068e6	+	1.07793e7i	0.0290397	+	0.164693i
$404$		−	1.63002e7i		−	0.247201i
$405$	2.77648e7	+	4.21006e7i	0.417955	+	0.633758i
$406$	3.24829e7			0.485374
$407$	8.59403e7	−	1.51536e7i	1.27472	−	0.224767i
$408$	3.02846e7	+	1.51977e7i	0.445904	+	0.223768i
$409$	−4.46234e7	+	1.62416e7i	−0.652218	+	0.237388i	−0.646873	−	0.762598i	$-0.723924\pi$
$409$	−4.46234e7	+	1.62416e7i	−0.652218	+	0.237388i	−0.00534478	+	0.999986i	$0.501701\pi$
$410$	5.46147e7	−	6.50873e7i	0.792425	−	0.944375i
$411$	1.04367e8	+	3.12101e7i	1.50327	+	0.449542i
$412$	−6.95224e7	−	2.53041e7i	−0.994106	−	0.361825i
$413$	−1.28040e7	+	7.39242e6i	−0.181760	+	0.104939i
$414$	−3.53114e7	+	8.20008e7i	−0.497639	+	1.15563i
$415$	−4.70130e7	+	8.14289e7i	−0.657770	+	1.13929i
$416$	1.63354e7	+	1.94678e7i	0.226908	+	0.270419i
$417$	−7.90005e7	−	9.20903e6i	−1.08949	−	0.127001i
$418$	550909.	−	3.12436e6i	0.00754311	−	0.0427791i
$419$	6.76442e7	+	1.19275e7i	0.919578	+	0.162146i	0.613349	−	0.789812i	$-0.289822\pi$
$419$	6.76442e7	+	1.19275e7i	0.919578	+	0.162146i	0.306228	+	0.951958i	$0.400933\pi$
$420$	−1.28956e7	+	5.56734e6i	−0.174057	+	0.0751449i
$421$	−1.86100e7	+	1.56156e7i	−0.249402	+	0.209273i	−0.758915	−	0.651190i	$-0.774270\pi$
$421$	−1.86100e7	+	1.56156e7i	−0.249402	+	0.209273i	0.509513	+	0.860463i	$0.329826\pi$
$422$	9.62580e7	+	5.55746e7i	1.28085	+	0.739501i
$423$	1.21830e8	−	3.65556e7i	1.60965	−	0.482985i
$424$	3.57952e7	+	6.19991e7i	0.469599	+	0.813370i
$425$	−1.10071e7	+	3.02418e7i	−0.143386	+	0.393950i
$426$	1.89187e6	+	2.00402e6i	0.0244716	+	0.0259223i
$427$	3.30397e7	+	2.77236e7i	0.424377	+	0.356095i
$428$	−1.89098e7	−	5.19542e7i	−0.241188	−	0.662657i
$429$	−4.96052e7	+	2.90459e6i	−0.628283	+	0.0367886i
$430$	−1.07882e6	−	6.11830e6i	−0.0135689	−	0.0769530i
$431$			2.49856e7i			0.312074i	0.987751	+	0.156037i	$0.0498720\pi$
$431$			2.49856e7i			0.312074i	−0.987751	+	0.156037i	$0.950128\pi$
$432$	−7.66216e7	−	6.41719e7i	−0.950385	−	0.795964i
$433$	−1.32089e8			−1.62705			−0.813526	−	0.581529i	$-0.802455\pi$
$433$	−1.32089e8			−1.62705			−0.813526	+	0.581529i	$0.802455\pi$
$434$	2.13311e7	−	3.76125e6i	0.260942	−	0.0460111i
$435$	4.82288e7	−	3.17420e7i	0.585921	−	0.385626i
$436$	−6.72905e7	+	2.44918e7i	−0.811885	+	0.295502i
$437$	964380.	−	1.14930e6i	0.0115559	−	0.0137718i
$438$	−2.01104e7	−	8.47354e7i	−0.239330	−	1.00842i
$439$	−8.38973e7	−	3.05361e7i	−0.991641	−	0.360928i	−0.205286	−	0.978702i	$-0.565812\pi$
$439$	−8.38973e7	−	3.05361e7i	−0.991641	−	0.360928i	−0.786356	+	0.617774i	$0.788035\pi$
$440$	5.35980e7	−	3.09448e7i	0.629203	−	0.363270i
$441$	4.08370e6	−	7.08707e7i	0.0476144	−	0.826325i
$442$	1.79270e7	−	3.10505e7i	0.207606	−	0.359585i
$443$	−8.53181e7	−	1.01678e8i	−0.981364	−	1.16954i	−0.985521	−	0.169552i	$-0.945768\pi$
$443$	−8.53181e7	−	1.01678e8i	−0.981364	−	1.16954i	0.00415751	−	0.999991i	$-0.498677\pi$
$444$	2.14337e7	−	2.88091e7i	0.244878	−	0.329141i
$445$	−3.22715e6	+	1.83021e7i	−0.0366217	+	0.207692i
$446$	−2.11841e7	−	3.73534e6i	−0.238785	−	0.0421042i
$447$	2.06507e7	+	1.53640e7i	0.231213	+	0.172021i
$448$	3.08075e6	−	2.58506e6i	0.0342628	−	0.0287499i
$449$	−3.23233e7	−	1.86619e7i	−0.357089	−	0.206166i	0.310714	−	0.950504i	$-0.399432\pi$
$449$	−3.23233e7	−	1.86619e7i	−0.357089	−	0.206166i	−0.667803	+	0.744338i	$0.732765\pi$
$450$	2.68228e7	−	4.08371e7i	0.294351	−	0.448144i
$451$	−1.11716e8	−	1.93497e8i	−1.21783	−	2.10934i
$452$	2.93012e7	−	8.05044e7i	0.317300	−	0.871775i
$453$	−1.07482e8	+	2.55088e7i	−1.15622	+	0.274407i
$454$	−1.47094e6	−	1.23426e6i	−0.0157191	−	0.0131899i
$455$	−3.36611e6	−	9.24832e6i	−0.0357350	−	0.0981812i
$456$	475241.	+	722082.i	0.00501210	+	0.00761538i
$457$	−1.03006e7	−	5.84174e7i	−0.107923	−	0.612059i	−0.990013	−	0.140979i	$-0.954975\pi$
$457$	−1.03006e7	−	5.84174e7i	−0.107923	−	0.612059i	0.882090	−	0.471081i	$-0.156136\pi$
$458$		−	9.13132e6i		−	0.0950467i
$459$	−3.26448e7	+	8.99507e7i	−0.337579	+	0.930179i
$460$	−4.41985e7			−0.454082
$461$	−2.12064e7	+	3.73926e6i	−0.216453	+	0.0381666i	−0.280823	−	0.959760i	$-0.590607\pi$
$461$	−2.12064e7	+	3.73926e6i	−0.216453	+	0.0381666i	0.0643697	+	0.997926i	$0.479496\pi$
$462$	5.74790e6	+	9.81638e7i	0.0582885	+	0.995463i
$463$	2.25228e7	−	8.19764e6i	0.226924	−	0.0825935i	−0.226056	−	0.974114i	$-0.572583\pi$
$463$	2.25228e7	−	8.19764e6i	0.226924	−	0.0825935i	0.452980	+	0.891521i	$0.350361\pi$
$464$	−7.35492e7	+	8.76526e7i	−0.736248	+	0.877427i
$465$	2.79958e7	−	2.64291e7i	0.278442	−	0.262859i
$466$	7.07719e7	+	2.57589e7i	0.699363	+	0.254547i
$467$	1.47125e8	−	8.49425e7i	1.44456	−	0.834016i	0.446408	−	0.894829i	$-0.352703\pi$
$467$	1.47125e8	−	8.49425e7i	1.44456	−	0.834016i	0.998149	+	0.0608139i	$0.0193696\pi$
$468$	−1.40219e7	+	1.48808e7i	−0.136794	+	0.145174i
$469$	2.89053e6	−	5.00654e6i	0.0280194	−	0.0485310i
$470$	1.07753e8	+	1.28415e8i	1.03785	+	1.23687i
$471$	−3.56256e7	−	8.25191e7i	−0.340957	−	0.789754i
$472$	4.65474e6	−	2.63984e7i	0.0442659	−	0.251045i
$473$	−1.60892e7	−	2.83695e6i	−0.152037	−	0.0268083i
$474$	2.13360e6	−	1.83033e7i	0.0200345	−	0.171868i
$475$	−628950.	+	527751.i	−0.00586861	+	0.00492435i
$476$	−2.30809e7	−	1.33258e7i	−0.214009	−	0.123558i
$477$	−1.62096e8	+	1.20832e8i	−1.49354	+	1.11334i
$478$	3.84854e7	+	6.66587e7i	0.352381	+	0.610342i
$479$	1.09566e7	−	3.01031e7i	0.0996944	−	0.273908i	−0.879812	−	0.475322i	$-0.842331\pi$
$479$	1.09566e7	−	3.01031e7i	0.0996944	−	0.273908i	0.979506	+	0.201414i	$0.0645537\pi$
$480$	2.56107e7	−	8.56422e7i	0.231578	−	0.774398i
$481$	1.92738e7	+	1.61726e7i	0.173193	+	0.145327i
$482$	3.03329e7	+	8.33388e7i	0.270877	+	0.744229i
$483$	−2.08569e7	+	4.15616e7i	−0.185101	+	0.368851i
$484$	3.08337e7	+	1.74867e8i	0.271951	+	1.54231i
$485$		−	1.21599e8i		−	1.06587i
$486$	7.96413e7	−	1.21498e8i	0.693793	−	1.05843i
$487$	−2.29636e7			−0.198817			−0.0994085	−	0.995047i	$-0.531695\pi$
$487$	−2.29636e7			−0.198817			−0.0994085	+	0.995047i	$0.531695\pi$
$488$	−7.70091e7	+	1.35788e7i	−0.662647	+	0.116843i
$489$	5.57430e7	+	2.79735e7i	0.476720	+	0.239233i
$490$	8.79148e7	−	3.19984e7i	0.747264	−	0.271982i
$491$	−3.71786e7	+	4.43077e7i	−0.314086	+	0.374313i	−0.899873	−	0.436152i	$-0.856341\pi$
$491$	−3.71786e7	+	4.43077e7i	−0.314086	+	0.374313i	0.585787	+	0.810465i	$0.300786\pi$
$492$	−8.80825e7	−	2.63404e7i	−0.739595	−	0.221171i
$493$	1.02946e8	+	3.74693e7i	0.859150	+	0.312705i
$494$	792150.	−	457348.i	0.00657093	−	0.00379373i
$495$	1.04459e8	+	1.40131e8i	0.861252	+	1.15537i
$496$	−3.81494e7	+	6.60768e7i	−0.312639	+	0.541506i
$497$	922672.	+	1.09960e6i	0.00751585	+	0.00895704i
$498$	2.69031e8	+	3.13608e7i	2.17828	+	0.253921i
$499$	−3.38252e7	+	1.91832e8i	−0.272232	+	1.54390i	0.475388	+	0.879776i	$0.342308\pi$
$499$	−3.38252e7	+	1.91832e8i	−0.272232	+	1.54390i	−0.747620	+	0.664127i	$0.768803\pi$
$500$	8.00436e7	+	1.41138e7i	0.640349	+	0.112911i
$501$	5.88627e7	−	2.54125e7i	0.468087	−	0.202085i
$502$	2.05365e8	−	1.72322e8i	1.62336	−	1.36216i
$503$	−1.32381e8	−	7.64301e7i	−1.04021	−	0.600566i	−0.120318	−	0.992735i	$-0.538391\pi$
$503$	−1.32381e8	−	7.64301e7i	−1.04021	−	0.600566i	−0.919893	+	0.392170i	$0.871725\pi$
$504$	−1.94998e7	−	1.83743e7i	−0.152314	−	0.143522i
$505$	−2.00869e7	−	3.47915e7i	−0.155969	−	0.270146i
$506$	−1.05828e8	+	2.90760e8i	−0.816863	+	2.24431i
$507$	7.96284e7	+	8.43488e7i	0.611004	+	0.647225i
$508$	−3.90306e7	−	3.27506e7i	−0.297724	−	0.249820i
$509$	1.62115e7	+	4.45409e7i	0.122934	+	0.337758i	0.985860	−	0.167573i	$-0.0535929\pi$
$509$	1.62115e7	+	4.45409e7i	0.122934	+	0.337758i	−0.862926	+	0.505330i	$0.831371\pi$
$510$	−1.25898e8	+	7.37185e6i	−0.949092	+	0.0555733i
$511$	−7.87667e6	−	4.46708e7i	−0.0590310	−	0.334781i
$512$			9.32630e7i			0.694864i
$513$	−1.86864e6	+	1.57094e6i	−0.0138412	+	0.0116361i
$514$	−6.77132e7			−0.498636
$515$	−1.79572e8	+	3.16634e7i	−1.31467	+	0.231812i
$516$	−5.61536e6	+	3.69577e6i	−0.0408722	+	0.0269002i
$517$	4.14239e8	−	1.50771e8i	2.99764	−	1.09105i
$518$	3.20040e7	−	3.81409e7i	0.230258	−	0.274411i
$519$	3.16745e7	+	1.33461e8i	0.226573	+	0.954667i
$520$	1.67676e7	+	6.10291e6i	0.119251	+	0.0434037i
$521$	−1.50479e8	+	8.68789e7i	−1.06405	+	0.614330i	−0.926550	−	0.376172i	$-0.877240\pi$
$521$	−1.50479e8	+	8.68789e7i	−1.06405	+	0.614330i	−0.137500	+	0.990502i	$0.543907\pi$
$522$	−1.39014e8	−	9.13073e7i	−0.977340	−	0.641939i
$523$	1.79872e7	−	3.11547e7i	0.125736	−	0.217781i	−0.796285	−	0.604922i	$-0.793204\pi$
$523$	1.79872e7	−	3.11547e7i	0.125736	−	0.217781i	0.922020	+	0.387142i	$0.126538\pi$
$524$	6.74822e6	+	8.04222e6i	0.0469024	+	0.0558961i
$525$	1.51899e7	−	2.04168e7i	0.104973	−	0.141095i
$526$	−3.49492e7	+	1.98207e8i	−0.240148	+	1.36195i
$527$	7.19421e7	+	1.26853e7i	0.491531	+	0.0866702i
$528$	−2.77902e8	−	2.06757e8i	−1.88795	−	1.40462i
$529$	1.31007e6	−	1.09928e6i	0.00884971	−	0.00742579i
$530$	−2.30756e8	−	1.33227e8i	−1.54998	−	0.894879i
$531$	7.55758e7	+	4.35481e6i	0.504776	+	0.0290861i
$532$	−339963.	−	588834.i	−0.00225786	−	0.00391073i
$533$	2.20325e7	−	6.05338e7i	0.145506	−	0.399776i
$534$	5.20877e7	−	1.23620e7i	0.342067	−	0.0811833i
$535$	−1.04385e8	−	8.75891e7i	−0.681672	−	0.571991i
$536$	3.58482e6	+	9.84921e6i	0.0232795	+	0.0639598i
$537$	−4.87045e7	−	7.40017e7i	−0.314519	−	0.477880i
$538$	3.48881e7	+	1.97860e8i	0.224043	+	1.27061i
$539$		−	2.46025e8i		−	1.57113i
$540$	7.08372e7	+	1.24227e7i	0.449863	+	0.0788920i
$541$	−1.02622e7			−0.0648111			−0.0324056	−	0.999475i	$-0.510317\pi$
$541$	−1.02622e7			−0.0648111			−0.0324056	+	0.999475i	$0.510317\pi$
$542$	1.77188e8	−	3.12431e7i	1.11285	−	0.196226i
$543$	1.02460e6	+	1.74983e7i	0.00639963	+	0.109294i
$544$	1.59383e8	−	5.80107e7i	0.990023	−	0.360339i
$545$	−1.13445e8	+	1.35198e8i	−0.700800	+	0.835181i
$546$	−2.06154e7	+	1.94617e7i	−0.126653	+	0.119565i
$547$	1.37063e8	+	4.98867e7i	0.837447	+	0.304806i	0.724911	−	0.688842i	$-0.241881\pi$
$547$	1.37063e8	+	4.98867e7i	0.837447	+	0.304806i	0.112535	+	0.993648i	$0.464103\pi$
$548$	1.34533e8	−	7.76725e7i	0.817497	−	0.471982i
$549$	−6.34672e7	−	2.11518e8i	−0.383559	−	1.27829i
$550$	8.46643e7	−	1.46643e8i	0.508876	−	0.881400i
$551$	1.79652e6	+	2.14100e6i	0.0107393	+	0.0127986i
$552$	−3.34171e7	−	7.74036e7i	−0.198679	−	0.460197i
$553$	1.66663e6	−	9.45194e6i	0.00985517	−	0.0558915i
$554$	−3.72851e8	−	6.57436e7i	−2.19283	−	0.386656i
$555$	1.02469e7	−	8.79036e7i	0.0599393	−	0.514195i
$556$	−8.68862e7	+	7.29062e7i	−0.505506	+	0.424170i
$557$	−4.76277e7	−	2.74979e7i	−0.275609	−	0.159123i	0.355825	−	0.934553i	$-0.384200\pi$
$557$	−4.76277e7	−	2.74979e7i	−0.275609	−	0.159123i	−0.631434	+	0.775430i	$0.717533\pi$
$558$	−1.01861e8	−	4.38638e7i	−0.586281	−	0.252466i
$559$	−2.35515e6	−	4.07925e6i	−0.0134829	−	0.0233531i
$560$	2.34644e7	−	6.44678e7i	0.133612	−	0.367095i
$561$	−9.50164e7	+	3.17735e8i	−0.538158	+	1.79960i
$562$	−2.51122e7	−	2.10716e7i	−0.141473	−	0.118710i
$563$	7.37539e7	+	2.02637e8i	0.413295	+	1.13552i	0.955428	+	0.295225i	$0.0953948\pi$
$563$	7.37539e7	+	2.02637e8i	0.413295	+	1.13552i	−0.542133	+	0.840293i	$0.682383\pi$
$564$	8.13566e7	−	1.62120e8i	0.453477	−	0.903645i
$565$	−3.66651e7	−	2.07938e8i	−0.203286	−	1.15289i
$566$			8.42845e7i			0.464835i
$567$	4.51090e7	−	6.07488e7i	0.247465	−	0.333264i
$568$	−2.60249e6			−0.0142018
$569$	1.56179e8	−	2.75386e7i	0.847785	−	0.149487i	0.267153	−	0.963654i	$-0.413917\pi$
$569$	1.56179e8	−	2.75386e7i	0.847785	−	0.149487i	0.580631	+	0.814167i	$0.302806\pi$
$570$	−2.87560e6	−	1.44306e6i	−0.0155276	−	0.00779221i
$571$	−3.79068e7	+	1.37969e7i	−0.203615	+	0.0741096i	−0.441814	−	0.897107i	$-0.645665\pi$
$571$	−3.79068e7	+	1.37969e7i	−0.203615	+	0.0741096i	0.238200	+	0.971216i	$0.423443\pi$
$572$	−4.55485e7	+	5.42826e7i	−0.243381	+	0.290050i
$573$	2.13562e8	+	6.38641e7i	1.13517	+	0.339463i
$574$	−1.19790e8	−	4.36001e7i	−0.633412	−	0.230543i
$575$	6.93478e7	−	4.00379e7i	0.364778	−	0.210605i
$576$	−2.04508e7	+	2.40320e6i	−0.107015	+	0.0125754i
$577$	−3.44340e7	+	5.96414e7i	−0.179250	+	0.310470i	−0.941624	−	0.336667i	$-0.890700\pi$
$577$	−3.44340e7	+	5.96414e7i	−0.179250	+	0.310470i	0.762374	+	0.647137i	$0.224034\pi$
$578$	3.26843e6	+	3.89517e6i	0.0169261	+	0.0201717i
$579$	2.52926e8	+	2.94834e7i	1.30304	+	0.151895i
$580$	1.42975e7	−	8.10854e7i	0.0732786	−	0.415584i
$581$	1.38929e8	+	2.44970e7i	0.708378	+	0.124906i
$582$	−3.21589e8	+	1.38838e8i	−1.63129	+	0.704270i
$583$	−5.36758e8	+	4.50393e8i	−2.70877	+	2.27293i
$584$	7.12216e7	+	4.11198e7i	0.357580	+	0.206449i
$585$	−1.15908e7	+	4.90410e7i	−0.0578959	+	0.244958i
$586$	−1.78437e8	−	3.09062e8i	−0.886731	−	1.53586i
$587$	9.28254e7	−	2.55036e8i	0.458937	−	1.26092i	−0.467341	−	0.884077i	$-0.654788\pi$
$587$	9.28254e7	−	2.55036e8i	0.458937	−	1.26092i	0.926278	−	0.376841i	$-0.122990\pi$
$588$	−6.94932e7	−	7.36128e7i	−0.341830	−	0.362094i
$589$	1.42766e6	+	1.19795e6i	0.00698681	+	0.00586263i
$590$	3.41227e7	+	9.37514e7i	0.166145	+	0.456480i
$591$	−1.55333e8	+	9.09538e6i	−0.752490	+	0.0440614i
$592$	3.04553e7	+	1.72721e8i	0.146791	+	0.832491i
$593$			3.09822e8i			1.48576i	0.669426	+	0.742879i	$0.266540\pi$
$593$			3.09822e8i			1.48576i	−0.669426	+	0.742879i	$0.733460\pi$
$594$	2.51334e8	−	4.36258e8i	1.19920	−	2.08154i
$595$	−6.56857e7			−0.311831
$596$	3.61478e7	−	6.37383e6i	0.170743	−	0.0301066i
$597$	8.11808e7	−	5.34295e7i	0.381532	−	0.251107i
$598$	−8.38306e7	+	3.05118e7i	−0.392012	+	0.142681i
$599$	9.08134e7	−	1.08227e8i	0.422542	−	0.503566i	−0.512213	−	0.858858i	$-0.671174\pi$
$599$	9.08134e7	−	1.08227e8i	0.422542	−	0.503566i	0.934755	+	0.355293i	$0.115619\pi$
$600$	1.06540e7	+	4.48907e7i	0.0493240	+	0.207827i
$601$	1.37922e8	+	5.01997e7i	0.635348	+	0.231248i	0.639557	−	0.768743i	$-0.279118\pi$
$601$	1.37922e8	+	5.01997e7i	0.635348	+	0.231248i	−0.00420951	+	0.999991i	$0.501340\pi$
$602$	−8.07242e6	+	4.66061e6i	−0.0370011	+	0.0213626i
$603$	−2.64434e7	+	1.33009e7i	−0.120605	+	0.0606636i
$604$	−7.87660e7	+	1.36427e8i	−0.357460	+	0.619140i
$605$	2.81301e8	+	3.35242e8i	1.27030	+	1.51388i
$606$	−6.90775e7	+	9.28472e7i	−0.310398	+	0.417206i
$607$	1.72497e6	−	9.78277e6i	0.00771284	−	0.0437417i	−0.980708	−	0.195476i	$-0.937375\pi$
$607$	1.72497e6	−	9.78277e6i	0.00771284	−	0.0437417i	0.988421	+	0.151735i	$0.0484859\pi$
$608$	4.26135e6	+	751391.i	0.0189599	+	0.00334314i
$609$	−6.95008e7	−	5.17080e7i	−0.307708	−	0.228932i
$610$	2.22952e8	−	1.87079e8i	0.982249	−	0.824205i
$611$	1.10069e8	+	6.35481e7i	0.482547	+	0.278599i
$612$	6.13191e7	+	1.21908e8i	0.267511	+	0.531836i
$613$	8.53880e7	+	1.47896e8i	0.370694	+	0.642060i	0.989672	−	0.143347i	$-0.0457866\pi$
$613$	8.53880e7	+	1.47896e8i	0.370694	+	0.642060i	−0.618979	+	0.785408i	$0.712453\pi$
$614$	6.25005e7	−	1.71719e8i	0.270009	−	0.741844i
$615$	−2.20464e8	+	5.23231e7i	−0.947790	+	0.224941i
$616$	−7.11321e7	−	5.96869e7i	−0.304315	−	0.255351i
$617$	−9.12853e7	−	2.50804e8i	−0.388638	−	1.06777i	−0.967615	−	0.252430i	$-0.918770\pi$
$617$	−9.12853e7	−	2.50804e8i	−0.388638	−	1.06777i	0.578977	−	0.815344i	$-0.303452\pi$
$618$	2.88769e8	+	4.38757e8i	1.22345	+	1.85891i
$619$	−2.27041e7	−	1.28761e8i	−0.0957263	−	0.542891i	−0.994522	−	0.104524i	$-0.966668\pi$
$619$	−2.27041e7	−	1.28761e8i	−0.0957263	−	0.542891i	0.898796	−	0.438367i	$-0.144443\pi$
$620$		−	5.49033e7i		−	0.230369i
$621$	2.06086e8	−	1.19239e8i	0.860546	−	0.497903i
$622$	−1.00910e8			−0.419337
$623$	2.74596e7	−	4.84187e6i	0.113561	−	0.0200239i
$624$	−5.83758e6	−	9.96954e7i	−0.0240259	−	0.410319i
$625$	9.10430e7	−	3.31370e7i	0.372912	−	0.135729i
$626$	3.56232e7	−	4.24541e7i	0.145214	−	0.173060i
$627$	−6.15226e6	+	5.80796e6i	−0.0249593	+	0.0235625i
$628$	−1.20445e8	−	4.38385e7i	−0.486307	−	0.177001i
$629$	1.45424e8	−	8.39608e7i	0.584366	−	0.337384i
$630$	9.70472e7	+	2.29371e7i	0.388116	+	0.0917313i
$631$	−1.33783e8	+	2.31719e8i	−0.532492	+	0.922302i	0.466789	+	0.884369i	$0.345411\pi$
$631$	−1.33783e8	+	2.31719e8i	−0.532492	+	0.922302i	−0.999280	+	0.0379335i	$0.987922\pi$
$632$	1.11852e7	+	1.33301e7i	0.0443092	+	0.0528057i
$633$	−1.17488e8	−	2.72137e8i	−0.463216	−	1.07294i
$634$	2.25109e7	−	1.27666e8i	0.0883334	−	0.500963i
$635$	−1.23666e8	−	2.18057e7i	−0.482981	−	0.0851625i
$636$	−3.33827e7	+	2.86376e8i	−0.129763	+	1.11318i
$637$	5.43376e7	−	4.55946e7i	0.210224	−	0.176399i
$638$	−4.99186e8	−	2.88205e8i	−1.92221	−	1.10979i
$639$	−857762.	−	7.29941e6i	−0.00328749	−	0.0279760i
$640$	9.23742e7	+	1.59997e8i	0.352380	+	0.610339i
$641$	7.67803e6	−	2.10952e7i	0.0291525	−	0.0800958i	−0.924263	−	0.381757i	$-0.875319\pi$
$641$	7.67803e6	−	2.10952e7i	0.0291525	−	0.0800958i	0.953415	+	0.301661i	$0.0975412\pi$
$642$	−1.12461e8	+	3.76070e8i	−0.425008	+	1.42123i
$643$	−1.35708e8	−	1.13873e8i	−0.510473	−	0.428337i	0.350823	−	0.936442i	$-0.385902\pi$
$643$	−1.35708e8	−	1.13873e8i	−0.510473	−	0.428337i	−0.861295	+	0.508104i	$0.830346\pi$
$644$	2.26805e7	+	6.23143e7i	0.0849173	+	0.233308i
$645$	−7.43118e6	+	1.48081e7i	−0.0276936	+	0.0551850i
$646$	−1.06009e6	−	6.01204e6i	−0.00393227	−	0.0223010i
$647$			2.72620e8i			1.00657i	0.864120	+	0.503285i	$0.167876\pi$
$647$			2.72620e8i			1.00657i	−0.864120	+	0.503285i	$0.832124\pi$
$648$	3.18023e7	+	1.33448e8i	0.116878	+	0.490440i
$649$	2.62358e8			0.959755
$650$	4.80783e7	−	8.47751e6i	0.175069	−	0.0308694i
$651$	−5.16277e7	−	2.59084e7i	−0.187128	−	0.0939069i
$652$	8.35767e7	−	3.04194e7i	0.301538	−	0.109751i
$653$	−1.80200e8	+	2.14754e8i	−0.647165	+	0.771261i	−0.985484	−	0.169771i	$-0.945697\pi$
$653$	−1.80200e8	+	2.14754e8i	−0.647165	+	0.771261i	0.338319	+	0.941031i	$0.390142\pi$
$654$	4.87082e8	+	1.45659e8i	1.74128	+	0.520718i
$655$	2.43140e7	+	8.84956e6i	0.0865231	+	0.0314918i
$656$	3.88887e8	−	2.24524e8i	1.37756	−	0.795337i
$657$	−9.18579e7	+	2.13314e8i	−0.323907	+	0.752182i
$658$	1.25755e8	−	2.17815e8i	0.441417	−	0.764556i
$659$	−8.48943e7	−	1.01173e8i	−0.296635	−	0.353516i	0.597055	−	0.802200i	$-0.296337\pi$
$659$	−8.48943e7	−	1.01173e8i	−0.296635	−	0.353516i	−0.893690	+	0.448684i	$0.851893\pi$
$660$	2.47571e8	+	2.88592e7i	0.861129	+	0.100381i
$661$	2.92045e7	−	1.65627e8i	0.101122	−	0.573492i	−0.891576	−	0.452870i	$-0.850400\pi$
$661$	2.92045e7	−	1.65627e8i	0.101122	−	0.573492i	0.992699	−	0.120622i	$-0.0384888\pi$
$662$	1.08846e8	+	1.91925e7i	0.375179	+	0.0661542i
$663$	−8.77847e7	+	3.78989e7i	−0.301216	+	0.130043i
$664$	−1.95932e8	+	1.64406e8i	−0.669269	+	0.561583i
$665$	−1.45125e6	−	837877.i	−0.00493487	−	0.00284915i
$666$	−2.44176e8	+	7.32663e7i	−0.826570	+	0.248017i
$667$	−1.36293e8	−	2.36066e8i	−0.459300	−	0.795530i
$668$	3.12709e7	−	8.59162e7i	0.104909	−	0.288234i
$669$	3.93798e7	+	4.17143e7i	0.131521	+	0.139318i
$670$	−2.98838e7	−	2.50755e7i	−0.0993601	−	0.0833730i
$671$	−2.61765e8	−	7.19193e8i	−0.866450	−	2.38055i
$672$	−1.33887e8	+	7.83963e6i	−0.441194	+	0.0258338i
$673$	4.99732e7	+	2.83412e8i	0.163943	+	0.929765i	0.950148	+	0.311800i	$0.100932\pi$
$673$	4.99732e7	+	2.83412e8i	0.163943	+	0.929765i	−0.786205	+	0.617966i	$0.787957\pi$
$674$			2.64852e8i			0.865015i
$675$	−1.22397e8	+	4.46778e7i	−0.397979	+	0.145271i
$676$	1.65419e8			0.535481
$677$	2.13604e8	−	3.76642e7i	0.688405	−	0.121384i	0.181506	−	0.983390i	$-0.441903\pi$
$677$	2.13604e8	−	3.76642e7i	0.688405	−	0.121384i	0.506899	+	0.862005i	$0.330792\pi$
$678$	−5.08064e8	+	3.34385e8i	−1.63016	+	1.07290i
$679$	−1.71438e8	+	6.23985e7i	−0.547645	+	0.199326i
$680$	7.65503e7	−	9.12291e7i	0.243456	−	0.290139i
$681$	1.18247e6	+	4.98237e6i	0.00374412	+	0.0157759i
$682$	−3.61181e8	−	1.31459e8i	−1.13860	−	0.414417i
$683$	9.37113e7	−	5.41042e7i	0.294124	−	0.169812i	−0.345676	−	0.938354i	$-0.612351\pi$
$683$	9.37113e7	−	5.41042e7i	0.294124	−	0.169812i	0.639800	+	0.768541i	$0.279017\pi$
$684$	−200269.	+	3.47558e6i	−0.000625816	+	0.0108607i
$685$	1.91432e8	−	3.31571e8i	0.595585	−	1.03158i
$686$	−1.99237e8	−	2.37442e8i	−0.617161	−	0.735504i
$687$	−1.45357e7	+	1.95375e7i	−0.0448298	+	0.0602558i
$688$	5.70164e6	−	3.23356e7i	0.0175079	−	0.0992923i
$689$	−1.98950e8	−	3.50802e7i	−0.608255	−	0.107252i
$690$	2.51758e8	+	1.87305e8i	0.766364	+	0.570168i
$691$	−6.99958e6	+	5.87335e6i	−0.0212148	+	0.0178013i	−0.653333	−	0.757070i	$-0.726630\pi$
$691$	−6.99958e6	+	5.87335e6i	−0.0212148	+	0.0178013i	0.632119	+	0.774872i	$0.282186\pi$
$692$	1.69403e8	+	9.78046e7i	0.511213	+	0.295149i
$693$	1.43964e8	−	2.19182e8i	0.432568	−	0.658576i
$694$	1.41294e8	+	2.44729e8i	0.422714	+	0.732162i
$695$	−9.56085e7	+	2.62682e8i	−0.284801	+	0.782485i
$696$	1.52812e8	−	3.62672e7i	0.453243	−	0.107569i
$697$	−3.29352e8	−	2.76359e8i	−0.972661	−	0.816160i
$698$	−198081.	−	544222.i	−0.000582473	−	0.00160033i
$699$	−1.10420e8	−	1.67773e8i	−0.323308	−	0.491235i
$700$	−6.30164e6	−	3.57384e7i	−0.0183721	−	0.104193i
$701$			4.78882e8i			1.39019i	0.718918	+	0.695095i	$0.244638\pi$
$701$			4.78882e8i			1.39019i	−0.718918	+	0.695095i	$0.755362\pi$
$702$	1.42931e8	−	2.53396e7i	0.413158	−	0.0732469i
$703$	4.28397e6			0.0123305
$704$	−7.02801e7	+	1.23923e7i	−0.201425	+	0.0355167i
$705$	−2.61319e7	−	4.46286e8i	−0.0745769	−	1.27364i
$706$	2.63957e8	−	9.60726e7i	0.750101	−	0.273014i
$707$	−3.87439e7	+	4.61732e7i	−0.109634	+	0.130657i
$708$	7.84999e7	−	7.41068e7i	0.221192	−	0.208813i
$709$	4.01983e8	+	1.46310e8i	1.12790	+	0.410520i	0.837528	−	0.546395i	$-0.184000\pi$
$709$	4.01983e8	+	1.46310e8i	1.12790	+	0.410520i	0.290368	+	0.956915i	$0.406222\pi$
$710$	8.38853e6	−	4.84312e6i	0.0234375	−	0.0135316i
$711$	−3.37013e7	+	3.57657e7i	−0.0937644	+	0.0995079i
$712$	−2.52768e7	+	4.37806e7i	−0.0700296	+	0.121295i
$713$	−1.16836e8	−	1.39240e8i	−0.322337	−	0.384146i
$714$	7.49981e7	+	1.73717e8i	0.206042	+	0.477252i
$715$	−3.03267e7	+	1.71991e8i	−0.0829673	+	0.470531i
$716$	−1.24416e8	−	2.19380e7i	−0.338952	−	0.0597664i
$717$	2.37670e7	−	2.03887e8i	0.0644788	−	0.553137i
$718$	2.85339e8	−	2.39428e8i	0.770883	−	0.646848i
$719$	−5.10332e8	−	2.94640e8i	−1.37299	−	0.792694i	−0.381683	−	0.924293i	$-0.624655\pi$
$719$	−5.10332e8	−	2.94640e8i	−1.37299	−	0.792694i	−0.991303	+	0.131599i	$0.957989\pi$
$720$	−2.81633e8	+	2.09939e8i	−0.754547	+	0.562466i
$721$	1.36789e8	+	2.36925e8i	0.364960	+	0.632129i
$722$	−1.62855e8	+	4.47440e8i	−0.432702	+	1.18884i
$723$	6.77627e7	−	2.26599e8i	0.179298	−	0.599573i
$724$	1.91483e7	+	1.60673e7i	0.0504561	+	0.0423377i
$725$	5.10195e7	+	1.40175e8i	0.133882	+	0.367838i
$726$	5.65423e8	−	1.12672e9i	1.47762	−	2.94446i
$727$	−7.30630e7	−	4.14361e8i	−0.190149	−	1.07839i	−0.919159	−	0.393886i	$-0.871130\pi$
$727$	−7.30630e7	−	4.14361e8i	−0.190149	−	1.07839i	0.729010	−	0.684503i	$-0.239981\pi$
$728$		−	2.67719e7i		−	0.0693882i
$729$	−3.63809e8	+	1.33182e8i	−0.939055	+	0.343766i
$730$	−3.06089e8			−0.786827
$731$	−3.09595e7	+	5.45900e6i	−0.0792579	+	0.0139753i
$732$	−2.81469e8	−	1.41250e8i	−0.717624	−	0.360126i
$733$	−4.50292e8	+	1.63893e8i	−1.14336	+	0.416148i	−0.843125	−	0.537718i	$-0.819287\pi$
$733$	−4.50292e8	+	1.63893e8i	−1.14336	+	0.416148i	−0.300233	+	0.953866i	$0.597064\pi$
$734$	4.52888e8	−	5.39731e8i	1.14526	−	1.36486i
$735$	−2.39041e8	−	7.14834e7i	−0.602018	−	0.180029i
$736$	−3.96571e8	−	1.44340e8i	−0.994690	−	0.362038i
$737$	−8.88414e7	+	5.12926e7i	−0.221928	+	0.128130i
$738$	3.90097e8	+	5.23314e8i	0.970518	+	1.30195i
$739$	5.55849e7	−	9.62759e7i	0.137728	−	0.238553i	−0.788908	−	0.614511i	$-0.789353\pi$
$739$	5.55849e7	−	9.62759e7i	0.137728	−	0.238553i	0.926636	+	0.375959i	$0.122687\pi$
$740$	−8.11224e7	−	9.66779e7i	−0.200192	−	0.238579i
$741$	−2.42293e6	−	282439.i	−0.00595506	−	0.000694177i
$742$	−6.94202e7	+	3.93702e8i	−0.169932	+	0.963730i
$743$	6.73484e8	+	1.18753e8i	1.64195	+	0.289521i	0.916884	−	0.399154i	$-0.130696\pi$
$743$	6.73484e8	+	1.18753e8i	1.64195	+	0.289521i	0.725070	+	0.688675i	$0.241807\pi$
$744$	9.61505e7	−	4.15106e7i	0.233471	−	0.100795i
$745$	6.92999e7	−	5.81495e7i	0.167596	−	0.140630i
$746$	−1.35871e8	−	7.84451e7i	−0.327273	−	0.188951i
$747$	−5.25701e8	−	4.95358e8i	−1.26118	−	1.18839i
$748$	2.36467e8	+	4.09573e8i	0.565022	+	0.978647i
$749$	−6.99243e7	+	1.92116e8i	−0.166411	+	0.457211i
$750$	−3.96121e8	−	4.19603e8i	−0.938954	−	0.994616i
$751$	5.90120e8	+	4.95170e8i	1.39322	+	1.16905i	0.964015	+	0.265847i	$0.0856517\pi$
$751$	5.90120e8	+	4.95170e8i	1.39322	+	1.16905i	0.429208	+	0.903206i	$0.358793\pi$
$752$	3.03015e8	+	8.32527e8i	0.712543	+	1.95770i
$753$	−7.13714e8	+	4.17909e7i	−1.67163	+	0.0978807i
$754$	−2.88582e7	−	1.63663e8i	−0.0673218	−	0.381801i
$755$			3.88255e8i			0.902145i
$756$	−1.88359e7	−	1.06246e8i	−0.0435933	−	0.245894i
$757$	2.98071e8			0.687119			0.343559	−	0.939131i	$-0.388367\pi$
$757$	2.98071e8			0.687119			0.343559	+	0.939131i	$0.388367\pi$
$758$	−8.34198e8	+	1.47092e8i	−1.91541	+	0.337738i
$759$	6.89279e8	−	4.53652e8i	1.57641	−	1.03752i
$760$	2.85499e6	−	1.03913e6i	0.00650375	−	0.00236717i
$761$	−5.59083e6	+	6.66289e6i	−0.0126859	+	0.0151185i	−0.772350	−	0.635197i	$-0.780919\pi$
$761$	−5.59083e6	+	6.66289e6i	−0.0126859	+	0.0151185i	0.759664	+	0.650316i	$0.225363\pi$
$762$	8.35297e7	+	3.51954e8i	0.188789	+	0.795464i
$763$	2.48826e8	+	9.05653e7i	0.560173	+	0.203886i
$764$	2.75289e8	−	1.58938e8i	0.617318	−	0.356409i
$765$	2.81108e8	+	1.84638e8i	0.627898	+	0.412418i
$766$	−2.94656e8	+	5.10359e8i	−0.655585	+	1.13551i
$767$	4.86216e7	+	5.79450e7i	0.107756	+	0.128419i
$768$	3.46804e8	−	4.66140e8i	0.765597	−	1.02904i
$769$	−1.01404e8	+	5.75090e8i	−0.222985	+	1.26461i	0.643515	+	0.765434i	$0.277476\pi$
$769$	−1.01404e8	+	5.75090e8i	−0.222985	+	1.26461i	−0.866500	+	0.499177i	$0.833636\pi$
$770$	3.40353e8	+	6.00135e7i	0.745517	+	0.131455i
$771$	1.44880e8	+	1.07790e8i	0.316115	+	0.235187i
$772$	2.78173e8	−	2.33415e8i	0.604592	−	0.507313i
$773$	3.58283e8	+	2.06855e8i	0.775688	+	0.447844i	0.834900	−	0.550402i	$-0.185525\pi$
$773$	3.58283e8	+	2.06855e8i	0.775688	+	0.447844i	−0.0592117	+	0.998245i	$0.518859\pi$
$774$	4.76474e7	+	2.74553e6i	0.102758	+	0.00592111i
$775$	4.97350e7	+	8.61435e7i	0.106846	+	0.185062i
$776$	1.13131e8	−	3.10826e8i	0.242102	−	0.665169i
$777$	−1.29191e8	+	3.06611e7i	−0.275403	+	0.0653619i
$778$	5.16456e8	+	4.33358e8i	1.09672	+	0.920254i
$779$	−3.75143e6	−	1.03070e7i	−0.00793569	−	0.0218031i
$780$	3.95073e7	+	6.00275e7i	0.0832519	+	0.126493i
$781$	−4.42311e6	−	2.50847e7i	−0.00928485	−	0.0526570i
$782$			5.95402e8i			1.24506i
$783$	1.52087e8	+	4.16652e8i	0.316817	+	0.867937i
$784$	4.94455e8			1.02607
$785$	−3.11102e8	+	5.48557e7i	−0.643124	+	0.113400i
$786$	−4.35682e6	−	7.44067e7i	−0.00897226	−	0.153230i
$787$	−7.63977e8	+	2.78065e8i	−1.56731	+	0.570456i	−0.972397	−	0.233331i	$-0.925037\pi$
$787$	−7.63977e8	+	2.78065e8i	−1.56731	+	0.570456i	−0.594917	+	0.803787i	$0.702815\pi$
$788$	−1.42630e8	+	1.69979e8i	−0.291495	+	0.347390i
$789$	3.90294e8	−	3.68452e8i	0.794623	−	0.750153i
$790$	−6.08598e7	−	2.21512e7i	−0.123438	−	0.0449278i
$791$	−2.74351e8	+	1.58397e8i	−0.554341	+	0.320049i
$792$	1.36640e8	+	4.55384e8i	0.275045	+	0.916647i
$793$	1.10331e8	−	1.91099e8i	0.221247	−	0.383211i
$794$	−2.59976e8	−	3.09827e8i	−0.519364	−	0.618954i
$795$	2.81651e8	+	6.52384e8i	0.560543	+	1.29838i
$796$	2.40662e7	−	1.36486e8i	0.0477165	−	0.270614i
$797$	8.80204e7	+	1.55204e7i	0.173864	+	0.0306568i	0.259902	−	0.965635i	$-0.416310\pi$
$797$	8.80204e7	+	1.55204e7i	0.173864	+	0.0306568i	−0.0860385	+	0.996292i	$0.527421\pi$
$798$	−558919.	+	4.79473e6i	−0.00109987	+	0.00943530i
$799$	6.49801e8	−	5.45248e8i	1.27391	−	1.06894i
$800$	2.00008e8	+	1.15475e8i	0.390641	+	0.225536i
$801$	−1.31126e8	−	5.64660e7i	−0.255148	−	0.109873i
$802$	−4.69815e8	−	8.13743e8i	−0.910759	−	1.57748i
$803$	−2.75297e8	+	7.56373e8i	−0.531686	+	1.46080i
$804$	−1.20938e7	+	4.04417e7i	−0.0232699	+	0.0778147i
$805$	1.25200e8	+	1.05055e8i	0.240003	+	0.201386i
$806$	−3.79017e7	−	1.04134e8i	−0.0723858	−	0.198878i
$807$	2.40318e8	−	4.78882e8i	0.457262	−	0.911188i
$808$	−1.89765e7	−	1.07621e8i	−0.0359734	−	0.204015i
$809$		−	9.22101e8i		−	1.74154i	−0.491692	−	0.870769i	$-0.663621\pi$
$809$		−	9.22101e8i		−	1.74154i	0.491692	−	0.870769i	$-0.336379\pi$
$810$	−3.50848e8	−	3.70955e8i	−0.660182	−	0.698018i
$811$	−3.15048e7			−0.0590628			−0.0295314	−	0.999564i	$-0.509402\pi$
$811$	−3.15048e7			−0.0590628			−0.0295314	+	0.999564i	$0.509402\pi$
$812$	−1.21657e8	+	2.14514e7i	−0.227231	+	0.0400670i
$813$	−4.28849e8	−	2.15210e8i	−0.798055	−	0.400489i
$814$	−8.30234e8	+	3.02180e8i	−1.53931	+	0.560264i
$815$	1.40901e8	−	1.67920e8i	0.260281	−	0.310191i
$816$	−6.38577e8	−	1.90962e8i	−1.17528	−	0.351460i
$817$	−753648.	−	274305.i	−0.00138198	−	0.000503000i
$818$	4.16367e8	−	2.40390e8i	0.760706	−	0.439194i
$819$	7.50894e7	−	8.82384e6i	0.136687	−	0.0160622i
$820$	−1.61563e8	+	2.79836e8i	−0.293023	+	0.507530i
$821$	2.11678e8	+	2.52269e8i	0.382514	+	0.455862i	0.922606	−	0.385744i	$-0.126055\pi$
$821$	2.11678e8	+	2.52269e8i	0.382514	+	0.455862i	−0.540092	+	0.841606i	$0.681611\pi$
$822$	−1.09547e9	−	1.27698e8i	−1.97235	−	0.229916i
$823$	1.45343e8	−	8.24283e8i	0.260733	−	1.47869i	−0.520184	−	0.854054i	$-0.674137\pi$
$823$	1.45343e8	−	8.24283e8i	0.260733	−	1.47869i	0.780917	−	0.624635i	$-0.214752\pi$
$824$	−4.88473e8	−	8.61310e7i	−0.873091	−	0.153949i
$825$	−4.14583e8	+	1.78986e8i	−0.738329	+	0.318755i
$826$	1.14667e8	−	9.62174e7i	0.203470	−	0.170731i
$827$	1.26625e8	+	7.31069e7i	0.223873	+	0.129253i	0.607742	−	0.794134i	$-0.292075\pi$
$827$	1.26625e8	+	7.31069e7i	0.223873	+	0.129253i	−0.383869	+	0.923388i	$0.625409\pi$
$828$	7.80980e7	−	3.30434e8i	0.137578	−	0.582094i
$829$	7.50532e7	+	1.29996e8i	0.131736	+	0.228174i	0.924346	−	0.381555i	$-0.124611\pi$
$829$	7.50532e7	+	1.29996e8i	0.131736	+	0.228174i	−0.792610	+	0.609729i	$0.791278\pi$
$830$	3.25588e8	−	8.94547e8i	0.569423	−	1.56448i
$831$	6.93102e8	+	7.34190e8i	1.20780	+	1.27940i
$832$	−1.57617e7	−	1.32256e7i	−0.0273673	−	0.0229639i
$833$	−1.61917e8	−	4.44863e8i	−0.280128	−	0.769646i
$834$	8.03872e8	−	4.70700e7i	1.38576	−	0.0811421i
$835$	−3.91298e7	−	2.21916e8i	−0.0672122	−	0.381179i
$836$			1.20653e7i			0.0206500i
$837$	1.48119e8	+	2.56000e8i	0.252600	+	0.436579i
$838$	−6.95422e8			−1.18172
$839$	−5.17802e8	+	9.13025e7i	−0.876754	+	0.154595i	−0.593872	−	0.804559i	$-0.702402\pi$
$839$	−5.17802e8	+	9.13025e7i	−0.876754	+	0.154595i	−0.282882	+	0.959155i	$0.591291\pi$
$840$	−7.86603e7	+	5.17706e7i	−0.132714	+	0.0873465i
$841$	−8.17819e7	+	2.97662e7i	−0.137489	+	0.0500421i
$842$	1.58099e8	−	1.88415e8i	0.264845	−	0.315630i
$843$	2.01874e7	+	8.50600e7i	0.0336975	+	0.141985i
$844$	−3.97212e8	−	1.44573e8i	−0.660686	−	0.240470i
$845$	3.53072e8	−	2.03846e8i	0.585185	−	0.337857i
$846$	−1.15045e9	+	5.78668e8i	−1.90001	+	0.955693i
$847$	3.28298e8	−	5.68629e8i	0.540279	−	0.935790i
$848$	−9.05190e8	−	1.07876e9i	−1.48440	−	1.76904i
$849$	1.34169e8	−	1.80336e8i	0.219244	−	0.294687i
$850$	5.65799e7	−	3.20880e8i	0.0921309	−	0.522500i
$851$	−4.11469e8	−	7.25531e7i	−0.667650	−	0.117725i
$852$	−8.40897e6	−	6.25620e6i	−0.0135964	−	0.0101156i
$853$	2.09968e8	−	1.76184e8i	0.338304	−	0.283871i	−0.457769	−	0.889071i	$-0.651351\pi$
$853$	2.09968e8	−	1.76184e8i	0.338304	−	0.283871i	0.796073	+	0.605200i	$0.206907\pi$
$854$	−3.78165e8	−	2.18334e8i	−0.607167	−	0.350548i
$855$	3.85552e6	+	7.66513e6i	0.00616858	+	0.0122637i
$856$	−1.85334e8	−	3.21008e8i	−0.295484	−	0.511793i
$857$	−2.98044e8	+	8.18871e8i	−0.473520	+	1.30099i	0.441385	+	0.897318i	$0.354487\pi$
$857$	−2.98044e8	+	8.18871e8i	−0.473520	+	1.30099i	−0.914905	+	0.403669i	$0.867735\pi$
$858$	4.89487e8	−	1.16171e8i	0.774959	−	0.183922i
$859$	5.74912e8	+	4.82409e8i	0.907031	+	0.761089i	0.971552	−	0.236827i	$-0.0761074\pi$
$859$	5.74912e8	+	4.82409e8i	0.907031	+	0.761089i	−0.0645207	+	0.997916i	$0.520552\pi$
$860$	8.08093e6	+	2.22022e7i	0.0127047	+	0.0349060i
$861$	1.86900e8	+	2.83976e8i	0.292820	+	0.444911i
$862$	−4.39268e7	−	2.49121e8i	−0.0685816	−	0.388946i
$863$			1.22706e8i			0.190912i	0.995434	+	0.0954560i	$0.0304309\pi$
$863$			1.22706e8i			0.190912i	−0.995434	+	0.0954560i	$0.969569\pi$
$864$	5.95018e8	+	3.42797e8i	0.922547	+	0.531491i
$865$	4.82100e8			0.744885
$866$	1.31700e9	−	2.32223e8i	2.02783	−	0.357562i
$867$	−792650.	−	1.35370e7i	−0.00121625	−	0.0207714i
$868$	−7.74066e7	+	2.81737e7i	−0.118364	+	0.0430809i
$869$	−1.09475e8	+	1.30467e8i	−0.166823	+	0.198812i
$870$	−4.25064e8	+	4.01277e8i	−0.645501	+	0.609377i
$871$	−2.77932e7	−	1.01159e7i	−0.0420614	−	0.0153091i
$872$	−4.15767e8	+	2.40043e8i	−0.627047	+	0.362026i
$873$	9.09086e8	+	2.14863e8i	1.36635	+	0.322937i
$874$	−7.59486e6	+	1.31547e7i	−0.0113759	+	0.0197036i
$875$	−1.93190e8	−	2.30235e8i	−0.288377	−	0.343674i
$876$	1.31277e8	+	3.04075e8i	0.195288	+	0.452344i
$877$	1.58221e8	−	8.97313e8i	0.234565	−	1.33029i	−0.608962	−	0.793200i	$-0.708414\pi$
$877$	1.58221e8	−	8.97313e8i	0.234565	−	1.33029i	0.843527	−	0.537087i	$-0.180475\pi$
$878$	8.90191e8	+	1.56965e8i	1.31522	+	0.231909i
$879$	−1.10195e8	+	9.45319e8i	−0.162254	+	1.39191i
$880$	−9.32586e8	+	7.82533e8i	−1.36849	+	1.14830i
$881$	−3.81660e8	−	2.20352e8i	−0.558148	−	0.322247i	0.194254	−	0.980951i	$-0.437771\pi$
$881$	−3.81660e8	−	2.20352e8i	−0.558148	−	0.322247i	−0.752402	+	0.658705i	$0.771105\pi$
$882$	8.38798e7	+	7.13802e8i	0.122251	+	1.04033i
$883$	3.63100e8	+	6.28908e8i	0.527405	+	0.913492i	0.999490	+	0.0319390i	$0.0101682\pi$
$883$	3.63100e8	+	6.28908e8i	0.527405	+	0.913492i	−0.472085	+	0.881553i	$0.656498\pi$
$884$	−4.66358e7	+	1.28131e8i	−0.0675092	+	0.185480i
$885$	7.62291e7	−	2.54910e8i	0.109974	−	0.367754i
$886$	1.02943e9	+	8.63794e8i	1.48012	+	1.24196i
$887$	−1.48100e8	−	4.06901e8i	−0.212219	−	0.583066i	0.787216	−	0.616677i	$-0.211521\pi$
$887$	−1.48100e8	−	4.06901e8i	−0.212219	−	0.583066i	−0.999435	+	0.0336112i	$0.989299\pi$
$888$	1.07975e8	−	2.15162e8i	0.154200	−	0.307275i
$889$	3.27162e7	+	1.85543e8i	0.0465648	+	0.264082i
$890$		−	1.88156e8i		−	0.266900i
$891$	−1.23222e9	+	5.33338e8i	−1.74202	+	0.753997i
$892$	8.18069e7			0.115264
$893$	2.13117e7	−	3.75782e6i	0.0299270	−	0.00527693i
$894$	−2.32911e8	−	1.16882e8i	−0.325970	−	0.163582i
$895$	−2.92590e8	+	1.06494e8i	−0.408123	+	0.148545i
$896$	1.78173e8	−	2.12338e8i	0.247695	−	0.295192i
$897$	2.27936e8	+	6.81625e7i	0.315817	+	0.0944427i
$898$	3.55092e8	+	1.29243e8i	0.490356	+	0.178475i
$899$	2.93241e8	−	1.69303e8i	0.403595	−	0.233015i
$900$	−7.34898e7	+	1.70659e8i	−0.100809	+	0.234100i
$901$	−6.74148e8	+	1.16766e9i	−0.921682	+	1.59640i
$902$	1.45406e9	+	1.73288e9i	1.98135	+	2.36128i
$903$	2.46909e7	+	2.87820e6i	0.0335331	+	0.00390893i
$904$	9.97367e7	−	5.65635e8i	0.135005	−	0.765651i
$905$	6.06702e7	+	1.06978e7i	0.0818521	+	0.0144327i
$906$	1.02681e9	−	4.43299e8i	1.38072	−	0.596090i
$907$	3.98629e7	−	3.34489e7i	0.0534252	−	0.0448291i	−0.615684	−	0.787993i	$-0.711120\pi$
$907$	3.98629e7	−	3.34489e7i	0.0534252	−	0.0448291i	0.669109	+	0.743164i	$0.266676\pi$
$908$	6.32414e6	+	3.65124e6i	0.00844780	+	0.00487734i
$909$	2.95598e8	−	8.86959e7i	0.393560	−	0.118090i
$910$	4.98214e7	+	8.62932e7i	0.0661138	+	0.114512i
$911$	5.04068e8	−	1.38492e9i	0.666706	−	1.83176i	0.123147	−	0.992388i	$-0.460701\pi$
$911$	5.04068e8	−	1.38492e9i	0.666706	−	1.83176i	0.543559	−	0.839371i	$-0.317077\pi$
$912$	−1.16727e7	−	1.23647e7i	−0.0153882	−	0.0163004i
$913$	−1.91767e9	−	1.60912e9i	−2.51977	−	2.11434i
$914$	2.05405e8	+	5.64346e8i	0.269013	+	0.739107i
$915$	−7.74834e8	+	4.53697e7i	−1.01145	+	0.0592247i
$916$	6.03023e6	+	3.41992e7i	0.00784599	+	0.0444968i
$917$		−	3.88207e7i		−	0.0503449i
$918$	1.67347e8	−	9.54254e8i	0.216316	−	1.23349i
$919$	−9.49416e8			−1.22323			−0.611617	−	0.791154i	$-0.709481\pi$
$919$	−9.49416e8			−1.22323			−0.611617	+	0.791154i	$0.709481\pi$
$920$	−2.91817e8	+	5.14552e7i	−0.374754	+	0.0660793i
$921$	−4.07079e8	+	2.67920e8i	−0.521074	+	0.342947i
$922$	2.04867e8	−	7.45653e7i	0.261384	−	0.0951358i
$923$	4.72055e6	−	5.62573e6i	0.00600327	−	0.00715442i
$924$	−8.63538e7	−	3.63853e8i	−0.109463	−	0.461222i
$925$	2.14859e8	+	7.82022e7i	0.271474	+	0.0988083i
$926$	−2.10154e8	+	1.21332e8i	−0.264670	+	0.152807i
$927$	8.05812e7	−	1.39845e9i	0.101157	−	1.75553i
$928$	3.93087e8	−	6.80846e8i	0.491864	−	0.851933i
$929$	6.96001e8	+	8.29462e8i	0.868086	+	1.03454i	0.999068	+	0.0431598i	$0.0137425\pi$
$929$	6.96001e8	+	8.29462e8i	0.868086	+	1.03454i	−0.130982	+	0.991385i	$0.541813\pi$
$930$	−2.32670e8	+	3.12732e8i	−0.289262	+	0.388798i
$931$	2.09725e6	−	1.18941e7i	0.00259897	−	0.0147395i
$932$	−2.82070e8	−	4.97365e7i	−0.348425	−	0.0614367i
$933$	2.15909e8	+	1.60634e8i	0.265843	+	0.197785i
$934$	−1.31758e9	+	1.10558e9i	−1.61710	+	1.35691i
$935$	1.00944e9	+	5.82798e8i	1.23494	+	0.712990i
$936$	−7.52542e7	+	1.14573e8i	−0.0917705	+	0.139719i
$937$	−2.89510e8	−	5.01446e8i	−0.351921	−	0.609545i	0.634665	−	0.772787i	$-0.281138\pi$
$937$	−2.89510e8	−	5.01446e8i	−0.351921	−	0.609545i	−0.986586	+	0.163243i	$0.947805\pi$
$938$	−2.00183e7	+	5.49999e7i	−0.0242560	+	0.0666429i
$939$	−1.43801e8	+	3.41284e7i	−0.173686	+	0.0412211i
$940$	−4.88368e8	−	4.09789e8i	−0.587981	−	0.493375i
$941$	−3.61373e8	−	9.92864e8i	−0.433697	−	1.19157i	−0.943526	−	0.331298i	$-0.892514\pi$
$941$	−3.61373e8	−	9.92864e8i	−0.433697	−	1.19157i	0.509829	−	0.860276i	$-0.329709\pi$
$942$	5.00284e8	+	7.60131e8i	0.598499	+	0.909360i
$943$	1.85761e8	+	1.05351e9i	0.221524	+	1.25632i
$944$			5.27281e8i			0.626796i
$945$	−1.71131e8	−	2.03562e8i	−0.202784	−	0.241213i
$946$	1.65406e8			0.195379
$947$	1.04919e9	−	1.85001e8i	1.23540	−	0.217834i	0.482454	−	0.875921i	$-0.339745\pi$
$947$	1.04919e9	−	1.85001e8i	1.23540	−	0.217834i	0.752941	+	0.658087i	$0.228634\pi$
$948$	4.09643e6	+	6.99597e7i	0.00480818	+	0.0821151i
$949$	−2.18074e8	+	7.93724e7i	−0.255156	+	0.0928690i
$950$	5.34317e6	−	6.36774e6i	0.00623201	−	0.00742702i
$951$	−2.51390e8	+	2.37321e8i	−0.292285	+	0.275927i
$952$	−1.67903e8	−	6.11118e7i	−0.194602	−	0.0708295i
$953$	−7.83201e7	+	4.52181e7i	−0.0904888	+	0.0522437i	−0.544562	−	0.838721i	$-0.683304\pi$
$953$	−7.83201e7	+	4.52181e7i	−0.0904888	+	0.0522437i	0.454073	+	0.890965i	$0.349971\pi$
$954$	1.40376e9	−	1.48975e9i	1.61677	−	1.71580i
$955$	3.91721e8	−	6.78480e8i	0.449745	−	0.778981i
$956$	−1.88159e8	−	2.24239e8i	−0.215353	−	0.256648i
$957$	6.09286e8	+	1.41128e9i	0.695161	+	1.61019i
$958$	−5.63203e7	+	3.19408e8i	−0.0640573	+	0.363287i
$959$	−5.65706e8	−	9.97493e7i	−0.641409	−	0.113098i
$960$	−8.37965e6	+	7.18856e7i	−0.00947136	+	0.0812509i
$961$	−5.06903e8	+	4.25343e8i	−0.571156	+	0.479257i
$962$	−2.20604e8	−	1.27366e8i	−0.247792	−	0.143063i
$963$	8.39273e8	−	6.25624e8i	0.939776	−	0.700542i
$964$	−1.68641e8	−	2.92094e8i	−0.188248	−	0.326056i
$965$	3.06098e8	−	8.40997e8i	0.340627	−	0.935864i
$966$	1.34887e8	−	4.51062e8i	0.149637	−	0.500386i
$967$	2.19306e8	+	1.84020e8i	0.242534	+	0.203510i	0.755949	−	0.654630i	$-0.227176\pi$
$967$	2.19306e8	+	1.84020e8i	0.242534	+	0.203510i	−0.513416	+	0.858140i	$0.671620\pi$
$968$	4.07154e8	+	1.11865e9i	0.448882	+	1.23329i
$969$	−7.30212e6	+	1.45510e7i	−0.00802561	+	0.0159926i
$970$	2.13781e8	+	1.21241e9i	0.234236	+	1.32842i
$971$			3.39682e8i			0.371035i	0.982641	+	0.185518i	$0.0593962\pi$
$971$			3.39682e8i			0.371035i	−0.982641	+	0.185518i	$0.940604\pi$
$972$	−2.18041e8	+	5.07637e8i	−0.237432	+	0.552782i
$973$	4.19410e8			0.455303
$974$	2.28961e8	−	4.03719e7i	0.247790	−	0.0436921i
$975$	−1.16364e8	−	5.83951e7i	−0.125547	−	0.0630032i
$976$	1.44542e9	−	5.26089e8i	1.55469	−	0.565861i
$977$	−7.15712e8	+	8.52953e8i	−0.767458	+	0.914621i	−0.998295	−	0.0583715i	$-0.981409\pi$
$977$	−7.15712e8	+	8.52953e8i	−0.767458	+	0.914621i	0.230837	+	0.972992i	$0.425854\pi$
$978$	−6.04970e8	−	1.80912e8i	−0.646721	−	0.193397i
$979$	−4.64950e8	−	1.69228e8i	−0.495517	−	0.180353i
$980$	−3.08132e8	+	1.77900e8i	−0.327385	+	0.189016i
$981$	−8.10302e8	−	1.08702e9i	−0.858301	−	1.15141i
$982$	2.92796e8	−	5.07137e8i	0.309194	−	0.535539i
$983$	2.72631e7	+	3.24909e7i	0.0287022	+	0.0342060i	0.780205	−	0.625524i	$-0.215115\pi$
$983$	2.72631e7	+	3.24909e7i	0.0287022	+	0.0342060i	−0.751502	+	0.659730i	$0.770670\pi$
$984$	−6.12221e8	−	7.13662e7i	−0.642574	−	0.0749044i
$985$	−9.49644e7	+	5.38570e8i	−0.0993693	+	0.563551i
$986$	−1.09231e9	−	1.92603e8i	−1.13950	−	0.200925i
$987$	−6.15797e8	+	2.65855e8i	−0.640451	+	0.276499i
$988$	−2.66478e6	+	2.23602e6i	−0.00276306	+	0.00231848i
$989$	6.77412e7	+	3.91104e7i	0.0700268	+	0.0404300i
$990$	−1.28788e9	−	1.21355e9i	−1.32730	−	1.25069i
$991$	4.10358e8	+	7.10761e8i	0.421640	+	0.730302i	0.996100	−	0.0882306i	$-0.0281213\pi$
$991$	4.10358e8	+	7.10761e8i	0.421640	+	0.730302i	−0.574460	+	0.818533i	$0.694788\pi$
$992$	1.79299e8	−	4.92620e8i	0.183672	−	0.504634i
$993$	−2.02337e8	−	2.14332e8i	−0.206646	−	0.218896i
$994$	−1.11328e7	−	9.34150e6i	−0.0113356	−	0.00951169i
$995$	−1.16826e8	−	3.20975e8i	−0.118596	−	0.325839i
$996$	−1.02830e9	+	6.02113e7i	−1.04074	+	0.0609397i
$997$	−3.23842e8	−	1.83660e9i	−0.326775	−	1.85323i	−0.496899	−	0.867808i	$-0.665528\pi$
$997$	−3.23842e8	−	1.83660e9i	−0.326775	−	1.85323i	0.170125	−	0.985423i	$-0.445583\pi$
$998$		−	1.97215e9i		−	1.98403i
$999$	6.39071e8	+	2.31931e8i	0.640993	+	0.232628i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.7.f.a.14.4	yes	102
3.2	odd	2		81.7.f.a.71.14		102
27.2	odd	18	inner	27.7.f.a.2.4	✓	102
27.25	even	9		81.7.f.a.8.14		102

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.7.f.a.2.4	✓	102	27.2	odd	18	inner
27.7.f.a.14.4	yes	102	1.1	even	1	trivial
81.7.f.a.8.14		102	27.25	even	9
81.7.f.a.71.14		102	3.2	odd	2

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.97059 + 1.75808i) q^{2} +(24.1318 + 12.1101i) q^{3} +(36.1814 - 13.1690i) q^{4} +(60.9980 - 72.6946i) q^{5} +(-261.899 - 78.3191i) q^{6} +(-133.791 - 48.6960i) q^{7} +(223.553 - 129.069i) q^{8} +(435.691 + 584.478i) q^{9} +(-480.383 + 832.047i) q^{10} +(1624.00 + 1935.41i) q^{11} +(1032.60 + 120.370i) q^{12} +(-126.490 + 717.362i) q^{13} +(1419.59 + 250.312i) q^{14} +(2352.33 - 1015.56i) q^{15} +(-3889.75 + 3263.89i) q^{16} +(4210.29 + 2430.81i) q^{17} +(-5371.65 - 5061.61i) q^{18} +(62.0141 + 107.412i) q^{19} +(1249.68 - 3433.47i) q^{20} +(-2638.91 - 2795.35i) q^{21} +(-19594.9 - 16442.1i) q^{22} +(-4137.25 - 11367.0i) q^{23} +(6957.79 - 407.407i) q^{24} +(1149.51 + 6519.18i) q^{25} -7374.90i q^{26} +(3435.93 + 19380.8i) q^{27} -5482.03 q^{28} +(22191.9 - 3913.03i) q^{29} +(-21668.7 + 14261.3i) q^{30} +(14120.1 - 5139.28i) q^{31} +(22425.5 - 26725.7i) q^{32} +(15752.1 + 66371.9i) q^{33} +(-46252.6 - 16834.6i) q^{34} +(-11700.9 + 6755.53i) q^{35} +(23460.9 + 15409.6i) q^{36} +(17270.1 - 29912.7i) q^{37} +(-807.155 - 961.930i) q^{38} +(-11739.8 + 15779.5i) q^{39} +(4253.72 - 24124.0i) q^{40} +(-87091.6 - 15356.6i) q^{41} +(31226.0 + 23231.8i) q^{42} +(-4953.54 + 4156.52i) q^{43} +(84246.1 + 48639.5i) q^{44} +(69064.6 + 3979.63i) q^{45} +(61235.0 + 106062. i) q^{46} +(59675.6 - 163957. i) q^{47} +(-133393. + 31658.3i) q^{48} +(-74595.6 - 62593.1i) q^{49} +(-22922.5 - 62979.1i) q^{50} +(72164.6 + 109647. i) q^{51} +(4870.32 + 27620.9i) q^{52} +277335. i q^{53} +(-68331.3 - 187197. i) q^{54} +239755. q^{55} +(-36194.6 + 6382.08i) q^{56} +(195.749 + 3343.04i) q^{57} +(-214387. + 78030.5i) q^{58} +(66748.6 - 79547.9i) q^{59} +(71736.8 - 67722.2i) q^{60} +(-284660. - 103608. i) q^{61} +(-131750. + 76065.9i) q^{62} +(-29829.8 - 99414.4i) q^{63} +(-14123.1 + 24462.0i) q^{64} +(44432.7 + 52952.8i) q^{65} +(-273745. - 634073. i) q^{66} +(-7050.75 + 39986.8i) q^{67} +(184345. + 32505.1i) q^{68} +(37816.2 - 324409. i) q^{69} +(104788. - 87927.9i) q^{70} +(-8731.10 - 5040.90i) q^{71} +(172838. + 74428.0i) q^{72} +(159295. + 275906. i) q^{73} +(-119604. + 328610. i) q^{74} +(-51208.2 + 171240. i) q^{75} +(3658.26 + 3069.64i) q^{76} +(-123031. - 338024. i) q^{77} +(89310.9 - 177970. i) q^{78} +(11705.7 + 66386.4i) q^{79} +481854. i q^{80} +(-151788. + 509303. i) q^{81} +895353. q^{82} +(-975779. + 172056. i) q^{83} +(-132291. - 66388.0i) q^{84} +(433526. - 157790. i) q^{85} +(42082.2 - 50151.7i) q^{86} +(582919. + 174318. i) q^{87} +(612852. + 223060. i) q^{88} +(-169602. + 97919.9i) q^{89} +(-695611. + 81742.1i) q^{90} +(51856.0 - 89817.2i) q^{91} +(-299383. - 356791. i) q^{92} +(402980. + 46975.1i) q^{93} +(-306750. + 1.73967e6i) q^{94} +(11591.0 + 2043.80i) q^{95} +(864820. - 373365. i) q^{96} +(981600. - 823660. i) q^{97} +(853806. + 492945. i) q^{98} +(-423643. + 1.79244e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18}+ \cdots + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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