LMFDB - Embedded newform 81.7.f.a.8.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,7,Mod(8,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, 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("81.8");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, 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:	$18.6343807732$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			8.14
Character	$\chi$	$=$	81.8
Dual form			81.7.f.a.71.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(9.97059 + 1.75808i) q^{2} +(36.1814 + 13.1690i) q^{4} +(-60.9980 - 72.6946i) q^{5} +(-133.791 + 48.6960i) q^{7} +(-223.553 - 129.069i) q^{8} +(-480.383 - 832.047i) q^{10} +(-1624.00 + 1935.41i) q^{11} +(-126.490 - 717.362i) q^{13} +(-1419.59 + 250.312i) q^{14} +(-3889.75 - 3263.89i) q^{16} +(-4210.29 + 2430.81i) q^{17} +(62.0141 - 107.412i) q^{19} +(-1249.68 - 3433.47i) q^{20} +(-19594.9 + 16442.1i) q^{22} +(4137.25 - 11367.0i) q^{23} +(1149.51 - 6519.18i) q^{25} -7374.90i q^{26} -5482.03 q^{28} +(-22191.9 - 3913.03i) q^{29} +(14120.1 + 5139.28i) q^{31} +(-22425.5 - 26725.7i) q^{32} +(-46252.6 + 16834.6i) q^{34} +(11700.9 + 6755.53i) q^{35} +(17270.1 + 29912.7i) q^{37} +(807.155 - 961.930i) q^{38} +(4253.72 + 24124.0i) q^{40} +(87091.6 - 15356.6i) q^{41} +(-4953.54 - 4156.52i) q^{43} +(-84246.1 + 48639.5i) q^{44} +(61235.0 - 106062. i) q^{46} +(-59675.6 - 163957. i) q^{47} +(-74595.6 + 62593.1i) q^{49} +(22922.5 - 62979.1i) q^{50} +(4870.32 - 27620.9i) q^{52} +277335. i q^{53} +239755. q^{55} +(36194.6 + 6382.08i) q^{56} +(-214387. - 78030.5i) q^{58} +(-66748.6 - 79547.9i) q^{59} +(-284660. + 103608. i) q^{61} +(131750. + 76065.9i) q^{62} +(-14123.1 - 24462.0i) q^{64} +(-44432.7 + 52952.8i) q^{65} +(-7050.75 - 39986.8i) q^{67} +(-184345. + 32505.1i) q^{68} +(104788. + 87927.9i) q^{70} +(8731.10 - 5040.90i) q^{71} +(159295. - 275906. i) q^{73} +(119604. + 328610. i) q^{74} +(3658.26 - 3069.64i) q^{76} +(123031. - 338024. i) q^{77} +(11705.7 - 66386.4i) q^{79} +481854. i q^{80} +895353. q^{82} +(975779. + 172056. i) q^{83} +(433526. + 157790. i) q^{85} +(-42082.2 - 50151.7i) q^{86} +(612852. - 223060. i) q^{88} +(169602. + 97919.9i) q^{89} +(51856.0 + 89817.2i) q^{91} +(299383. - 356791. i) q^{92} +(-306750. - 1.73967e6i) q^{94} +(-11591.0 + 2043.80i) q^{95} +(981600. + 823660. i) q^{97} +(-853806. + 492945. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q + 6 q^{2} - 6 q^{4} - 210 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} + 12183 q^{14} - 198 q^{16} + 9 q^{17} - 3 q^{19} + 19767 q^{20} - 10806 q^{22} - 14466 q^{23} - 15990 q^{25}+ \cdots - 1179270 q^{98}+O(q^{100}) $ 102 * q + 6 * q^2 - 6 * q^4 - 210 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 492 * q^11 - 6 * q^13 + 12183 * q^14 - 198 * q^16 + 9 * q^17 - 3 * q^19 + 19767 * q^20 - 10806 * q^22 - 14466 * q^23 - 15990 * q^25 - 12 * q^28 + 45690 * q^29 + 18354 * q^31 + 140544 * q^32 - 82278 * q^34 - 268263 * q^35 - 3 * q^37 - 28428 * q^38 - 34593 * q^40 - 234948 * q^41 + 148764 * q^43 + 1222785 * q^44 - 3 * q^46 - 517098 * q^47 - 311262 * q^49 - 1710663 * q^50 - 213057 * q^52 - 12 * q^55 + 3167925 * q^56 + 663789 * q^58 + 230802 * q^59 - 51414 * q^61 - 1777536 * q^62 + 983037 * q^64 - 2264754 * q^65 - 845052 * q^67 + 3979053 * q^68 - 835251 * q^70 + 427689 * q^71 - 257043 * q^73 - 2458185 * q^74 + 2759802 * q^76 - 5459610 * q^77 + 662682 * q^79 - 12 * q^82 + 4926426 * q^83 - 2530881 * q^85 + 6700758 * q^86 - 2860230 * q^88 - 5907321 * q^89 - 451443 * q^91 - 712473 * q^92 + 7395807 * q^94 + 2179119 * q^95 + 272208 * q^97 - 1179270 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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	$-0.226360\pi$
$2$	9.97059	+	1.75808i	1.24632	+	0.219760i	0.488700	+	0.872452i	$0.337471\pi$
$3$		0			0
$3$		0			0
$4$	36.1814	+	13.1690i	0.565335	+	0.205765i
$5$	−60.9980	−	72.6946i	−0.487984	−	0.581556i	0.464720	−	0.885458i	$-0.346155\pi$
$5$	−60.9980	−	72.6946i	−0.487984	−	0.581556i	−0.952703	+	0.303901i	$0.901711\pi$
$6$		0			0
$7$	−133.791	+	48.6960i	−0.390062	+	0.141971i	−0.529604	−	0.848245i	$-0.677659\pi$
$7$	−133.791	+	48.6960i	−0.390062	+	0.141971i	0.139542	+	0.990216i	$0.455437\pi$
$8$	−223.553	−	129.069i	−0.436628	−	0.252087i
$9$		0			0
$10$	−480.383	−	832.047i	−0.480383	−	0.832047i
$11$	−1624.00	+	1935.41i	−1.22014	+	1.45410i	−0.368782	+	0.929516i	$0.620225\pi$
$11$	−1624.00	+	1935.41i	−1.22014	+	1.45410i	−0.851356	+	0.524588i	$0.824219\pi$
$12$		0			0
$13$	−126.490	−	717.362i	−0.0575741	−	0.326519i	0.942394	−	0.334505i	$-0.108569\pi$
$13$	−126.490	−	717.362i	−0.0575741	−	0.326519i	−0.999968	+	0.00798588i	$0.997458\pi$
$14$	−1419.59	+	250.312i	−0.517343	+	0.0912215i
$15$		0			0
$16$	−3889.75	−	3263.89i	−0.949645	−	0.796847i
$17$	−4210.29	+	2430.81i	−0.856968	+	0.494771i	−0.862996	−	0.505211i	$-0.831415\pi$
$17$	−4210.29	+	2430.81i	−0.856968	+	0.494771i	0.00602755	+	0.999982i	$0.498081\pi$
$18$		0			0
$19$	62.0141	−	107.412i	0.00904127	−	0.0156599i	−0.861469	−	0.507810i	$-0.830455\pi$
$19$	62.0141	−	107.412i	0.00904127	−	0.0156599i	0.870511	+	0.492150i	$0.163789\pi$
$20$	−1249.68	−	3433.47i	−0.156210	−	0.429184i
$21$		0			0
$22$	−19594.9	+	16442.1i	−1.84024	+	1.54415i
$23$	4137.25	−	11367.0i	0.340039	−	0.934249i	−0.645344	−	0.763892i	$-0.723286\pi$
$23$	4137.25	−	11367.0i	0.340039	−	0.934249i	0.985382	−	0.170357i	$-0.0544920\pi$
$24$		0			0
$25$	1149.51	−	6519.18i	0.0735685	−	0.417227i
$26$		−	7374.90i		−	0.419601i
$27$		0			0
$28$	−5482.03			−0.249728
$29$	−22191.9	−	3913.03i	−0.909915	−	0.160443i	−0.300950	−	0.953640i	$-0.597304\pi$
$29$	−22191.9	−	3913.03i	−0.909915	−	0.160443i	−0.608965	+	0.793197i	$0.708415\pi$
$30$		0			0
$31$	14120.1	+	5139.28i	0.473971	+	0.172511i	0.567950	−	0.823063i	$-0.307737\pi$
$31$	14120.1	+	5139.28i	0.473971	+	0.172511i	−0.0939796	+	0.995574i	$0.529959\pi$
$32$	−22425.5	−	26725.7i	−0.684373	−	0.815604i
$33$		0			0
$34$	−46252.6	+	16834.6i	−1.17679	+	0.428317i
$35$	11700.9	+	6755.53i	0.272908	+	0.157563i
$36$		0			0
$37$	17270.1	+	29912.7i	0.340950	+	0.590542i	0.984609	−	0.174770i	$-0.0559180\pi$
$37$	17270.1	+	29912.7i	0.340950	+	0.590542i	−0.643660	+	0.765312i	$0.722585\pi$
$38$	807.155	−	961.930i	0.0147098	−	0.0175304i
$39$		0			0
$40$	4253.72	+	24124.0i	0.0664643	+	0.376938i
$41$	87091.6	−	15356.6i	1.26364	−	0.222815i	0.498623	−	0.866819i	$-0.333839\pi$
$41$	87091.6	−	15356.6i	1.26364	−	0.222815i	0.765022	+	0.644004i	$0.222728\pi$
$42$		0			0
$43$	−4953.54	−	4156.52i	−0.0623032	−	0.0522786i	0.611104	−	0.791550i	$-0.290726\pi$
$43$	−4953.54	−	4156.52i	−0.0623032	−	0.0522786i	−0.673408	+	0.739271i	$0.735170\pi$
$44$	−84246.1	+	48639.5i	−0.988990	+	0.570994i
$45$		0			0
$46$	61235.0	−	106062.i	0.629109	−	1.08965i
$47$	−59675.6	−	163957.i	−0.574782	−	1.57920i	−0.796855	−	0.604171i	$-0.793504\pi$
$47$	−59675.6	−	163957.i	−0.574782	−	1.57920i	0.222072	−	0.975030i	$-0.428718\pi$
$48$		0			0
$49$	−74595.6	+	62593.1i	−0.634052	+	0.532033i
$50$	22922.5	−	62979.1i	0.183380	−	0.503833i
$51$		0			0
$52$	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	$0.618568\pi$
$54$		0			0
$55$	239755.			1.44105
$56$	36194.6	+	6382.08i	0.206101	+	0.0363411i
$57$		0			0
$58$	−214387.	−	78030.5i	−1.09879	−	0.399927i
$59$	−66748.6	−	79547.9i	−0.325002	−	0.387323i	0.578660	−	0.815569i	$-0.303576\pi$
$59$	−66748.6	−	79547.9i	−0.325002	−	0.387323i	−0.903662	+	0.428247i	$0.859131\pi$
$60$		0			0
$61$	−284660.	+	103608.i	−1.25411	+	0.456459i	−0.881789	−	0.471644i	$-0.843661\pi$
$61$	−284660.	+	103608.i	−1.25411	+	0.456459i	−0.372323	+	0.928103i	$0.621439\pi$
$62$	131750.	+	76065.9i	0.552809	+	0.319165i
$63$		0			0
$64$	−14123.1	−	24462.0i	−0.0538755	−	0.0933151i
$65$	−44432.7	+	52952.8i	−0.161794	+	0.192819i
$66$		0			0
$67$	−7050.75	−	39986.8i	−0.0234429	−	0.132951i	0.970840	−	0.239728i	$-0.0770582\pi$
$67$	−7050.75	−	39986.8i	−0.0234429	−	0.132951i	−0.994283	+	0.106777i	$0.965947\pi$
$68$	−184345.	+	32505.1i	−0.586280	+	0.103377i
$69$		0			0
$70$	104788.	+	87927.9i	0.305505	+	0.256349i
$71$	8731.10	−	5040.90i	0.0243946	−	0.0140842i	−0.487753	−	0.872982i	$-0.662183\pi$
$71$	8731.10	−	5040.90i	0.0243946	−	0.0140842i	0.512148	+	0.858897i	$0.328850\pi$
$72$		0			0
$73$	159295.	−	275906.i	0.409480	−	0.709239i	−0.585352	−	0.810779i	$-0.699044\pi$
$73$	159295.	−	275906.i	0.409480	−	0.709239i	0.994831	+	0.101540i	$0.0323770\pi$
$74$	119604.	+	328610.i	0.295156	+	0.810934i
$75$		0			0
$76$	3658.26	−	3069.64i	0.00833361	−	0.00699273i
$77$	123031.	−	338024.i	0.269489	−	0.740415i
$78$		0			0
$79$	11705.7	−	66386.4i	0.0237420	−	0.134647i	−0.970633	−	0.240566i	$-0.922667\pi$
$79$	11705.7	−	66386.4i	0.0237420	−	0.134647i	0.994375	+	0.105918i	$0.0337782\pi$
$80$			481854.i			0.941121i
$81$		0			0
$82$	895353.			1.62388
$83$	975779.	+	172056.i	1.70654	+	0.300910i	0.939973	−	0.341250i	$-0.110850\pi$
$83$	975779.	+	172056.i	1.70654	+	0.300910i	0.766571	+	0.642160i	$0.221961\pi$
$84$		0			0
$85$	433526.	+	157790.i	0.705924	+	0.256935i
$86$	−42082.2	−	50151.7i	−0.0661612	−	0.0788479i
$87$		0			0
$88$	612852.	−	223060.i	0.899307	−	0.327321i
$89$	169602.	+	97919.9i	0.240581	+	0.138900i	0.615444	−	0.788181i	$-0.288977\pi$
$89$	169602.	+	97919.9i	0.240581	+	0.138900i	−0.374863	+	0.927080i	$0.622310\pi$
$90$		0			0
$91$	51856.0	+	89817.2i	0.0688137	+	0.119189i
$92$	299383.	−	356791.i	0.384471	−	0.458195i
$93$		0			0
$94$	−306750.	−	1.73967e6i	−0.369319	−	2.09451i
$95$	−11591.0	+	2043.80i	−0.0135191	+	0.00238379i
$96$		0			0
$97$	981600.	+	823660.i	1.07552	+	0.902470i	0.995541	−	0.0943259i	$-0.0300696\pi$
$97$	981600.	+	823660.i	1.07552	+	0.902470i	0.0799810	+	0.996796i	$0.474514\pi$
$98$	−853806.	+	492945.i	−0.907153	+	0.523745i
$99$		0			0
$100$	127442.	−	220735.i	0.127442	−	0.220735i
$101$	−144793.	−	397814.i	−0.140534	−	0.386115i	0.849380	−	0.527781i	$-0.176976\pi$
$101$	−144793.	−	397814.i	−0.140534	−	0.386115i	−0.989914	+	0.141667i	$0.954754\pi$
$102$		0			0
$103$	−1.47195e6	+	1.23511e6i	−1.34704	+	1.13030i	−0.367286	+	0.930108i	$0.619713\pi$
$103$	−1.47195e6	+	1.23511e6i	−1.34704	+	1.13030i	−0.979756	+	0.200195i	$0.935842\pi$
$104$	−64311.6	+	176695.i	−0.0571728	+	0.157081i
$105$		0			0
$106$	−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	$-0.199328\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$	679352.	+	247264.i	0.483550	+	0.175998i
$113$	−1.43022e6	−	1.70447e6i	−0.991212	−	1.18128i	−0.983426	−	0.181310i	$-0.941966\pi$
$113$	−1.43022e6	−	1.70447e6i	−0.991212	−	1.18128i	−0.00778556	−	0.999970i	$-0.502478\pi$
$114$		0			0
$115$	−1.07868e6	+	392609.i	−0.709252	+	0.258147i
$116$	−751404.	−	433823.i	−0.481393	−	0.277932i
$117$		0			0
$118$	−525671.	−	910489.i	−0.319940	−	0.554152i
$119$	444928.	−	530245.i	0.264028	−	0.314656i
$120$		0			0
$121$	−800805.	−	4.54159e6i	−0.452033	−	2.56361i
$122$	−3.02037e6	+	532573.i	−1.66334	+	0.293292i
$123$		0			0
$124$	443205.	+	371893.i	0.232455	+	0.195053i
$125$	−1.82813e6	+	1.05547e6i	−0.936000	+	0.540400i
$126$		0			0
$127$	−661639.	+	1.14599e6i	−0.323006	+	0.559462i	−0.981107	−	0.193467i	$-0.938027\pi$
$127$	−661639.	+	1.14599e6i	−0.323006	+	0.559462i	0.658101	+	0.752930i	$0.271360\pi$
$128$	665862.	+	1.82944e6i	0.317508	+	0.872346i
$129$		0			0
$130$	−536115.	+	449854.i	−0.244022	+	0.204758i
$131$	−93255.3	+	256217.i	−0.0414820	+	0.113971i	−0.958704	−	0.284405i	$-0.908204\pi$
$131$	−93255.3	+	256217.i	−0.0414820	+	0.113971i	0.917222	+	0.398376i	$0.130426\pi$
$132$		0			0
$133$	−3066.43	+	17390.6i	−0.00130340	+	0.00739195i
$134$		−	411088.i		−	0.170852i
$135$		0			0
$136$	1.25496e6			0.498901
$137$	−3.97328e6	−	700596.i	−1.54521	−	0.272462i	−0.664926	−	0.746910i	$-0.731537\pi$
$137$	−3.97328e6	−	700596.i	−1.54521	−	0.272462i	−0.880284	+	0.474447i	$0.842648\pi$
$138$		0			0
$139$	−2.76811e6	−	1.00751e6i	−1.03071	−	0.375149i	−0.229362	−	0.973341i	$-0.573664\pi$
$139$	−2.76811e6	−	1.00751e6i	−1.03071	−	0.375149i	−0.801353	+	0.598192i	$0.795886\pi$
$140$	334393.	+	398514.i	0.121863	+	0.145231i
$141$		0			0
$142$	95916.5	−	34910.7i	0.0334987	−	0.0121925i
$143$	1.59381e6	+	920188.i	0.545041	+	0.314680i
$144$		0			0
$145$	1.06921e6	+	1.85192e6i	0.350717	+	0.607460i
$146$	2.07333e6	−	2.47089e6i	0.666207	−	0.793954i
$147$		0			0
$148$	230938.	+	1.30972e6i	0.0712378	+	0.404010i
$149$	−938820.	+	165539.i	−0.283807	+	0.0500429i	−0.313740	−	0.949509i	$-0.601582\pi$
$149$	−938820.	+	165539.i	−0.283807	+	0.0500429i	0.0299325	+	0.999552i	$0.490471\pi$
$150$		0			0
$151$	−3.13417e6	−	2.62988e6i	−0.910316	−	0.763846i	0.0618631	−	0.998085i	$-0.480296\pi$
$151$	−3.13417e6	−	2.62988e6i	−0.910316	−	0.763846i	−0.972179	+	0.234239i	$0.924740\pi$
$152$	−27726.9	+	16008.1i	−0.00789534	+	0.00455838i
$153$		0			0
$154$	1.82096e6	−	3.15400e6i	0.498584	−	0.863573i
$155$	−487697.	−	1.33994e6i	−0.130965	−	0.359823i
$156$		0			0
$157$	−2.55010e6	+	2.13979e6i	−0.658960	+	0.552933i	−0.909775	−	0.415102i	$-0.863746\pi$
$157$	−2.55010e6	+	2.13979e6i	−0.658960	+	0.552933i	0.250815	+	0.968035i	$0.419301\pi$
$158$	233426.	−	641332.i	0.0591803	−	0.162597i
$159$		0			0
$160$	−574901.	+	3.26043e6i	−0.140357	+	0.796003i
$161$			1.72227e6i			0.412691i
$162$		0			0
$163$	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
$165$		0			0
$166$	9.42660e6	+	3.43100e6i	2.06078	+	0.750061i
$167$	−1.52636e6	−	1.81904e6i	−0.327723	−	0.390565i	0.576874	−	0.816833i	$-0.304273\pi$
$167$	−1.52636e6	−	1.81904e6i	−0.327723	−	0.390565i	−0.904597	+	0.426268i	$0.859828\pi$
$168$		0			0
$169$	4.03711e6	−	1.46939e6i	0.836393	−	0.304422i
$170$	4.04510e6	+	2.33544e6i	0.823345	+	0.475359i
$171$		0			0
$172$	−124489.	−	215622.i	−0.0244651	−	0.0423747i
$173$	−3.26555e6	+	3.89174e6i	−0.630694	+	0.751632i	−0.982870	−	0.184302i	$-0.940997\pi$
$173$	−3.26555e6	+	3.89174e6i	−0.630694	+	0.751632i	0.352176	+	0.935934i	$0.385442\pi$
$174$		0			0
$175$	163664.	+	928185.i	0.0305379	+	0.173189i
$176$	1.26339e7	−	2.22770e6i	2.31740	−	0.408620i
$177$		0			0
$178$	1.51888e6	+	1.27449e6i	0.269317	+	0.225984i
$179$	2.84156e6	−	1.64058e6i	0.495447	−	0.286047i	−0.231384	−	0.972862i	$-0.574325\pi$
$179$	2.84156e6	−	1.64058e6i	0.495447	−	0.286047i	0.726832	+	0.686816i	$0.240992\pi$
$180$		0			0
$181$	324598.	−	562220.i	0.0547407	−	0.0948137i	−0.837357	−	0.546657i	$-0.815900\pi$
$181$	324598.	−	562220.i	0.0547407	−	0.0948137i	0.892097	+	0.451843i	$0.149233\pi$
$182$	359129.	+	986698.i	0.0595711	+	0.163670i
$183$		0			0
$184$	−2.39202e6	+	2.00714e6i	−0.383982	+	0.322199i
$185$	1.12105e6	−	3.08006e6i	0.177056	−	0.486457i
$186$		0			0
$187$	2.13290e6	−	1.20963e7i	0.326171	−	1.84981i
$188$		−	6.71808e6i		−	1.01105i
$189$		0			0
$190$	−119162.			−0.0173731
$191$	−8.13036e6	−	1.43360e6i	−1.16684	−	0.205745i	−0.443522	−	0.896264i	$-0.646271\pi$
$191$	−8.13036e6	−	1.43360e6i	−1.16684	−	0.205745i	−0.723314	+	0.690519i	$0.757382\pi$
$192$		0			0
$193$	8.86230e6	+	3.22561e6i	1.23275	+	0.448684i	0.874538	−	0.484957i	$-0.161165\pi$
$193$	8.86230e6	+	3.22561e6i	1.23275	+	0.448684i	0.358211	+	0.933641i	$0.383387\pi$
$194$	8.33907e6	+	9.93811e6i	1.14212	+	1.36113i
$195$		0			0
$196$	−3.52326e6	+	1.28236e6i	−0.467925	+	0.170311i
$197$	4.99084e6	+	2.88146e6i	0.652792	+	0.376889i	0.789525	−	0.613718i	$-0.210327\pi$
$197$	4.99084e6	+	2.88146e6i	0.652792	+	0.376889i	−0.136733	+	0.990608i	$0.543660\pi$
$198$		0			0
$199$	1.79973e6	+	3.11723e6i	0.228375	+	0.395557i	0.957327	−	0.289008i	$-0.0933254\pi$
$199$	1.79973e6	+	3.11723e6i	0.228375	+	0.395557i	−0.728952	+	0.684565i	$0.759992\pi$
$200$	−1.09840e6	+	1.30902e6i	−0.137300	+	0.163627i
$201$		0			0
$202$	−744276.	−	4.22100e6i	−0.0902984	−	0.512107i
$203$	3.15963e6	−	557128.i	0.377701	−	0.0665989i
$204$		0			0
$205$	−6.42876e6	−	5.39437e6i	−0.746217	−	0.626151i
$206$	−1.68476e7	+	9.72698e6i	−1.92725	+	1.11270i
$207$		0			0
$208$	−1.84937e6	+	3.20321e6i	−0.205511	+	0.355955i
$209$	107175.	+	294460.i	0.0117396	+	0.0322542i
$210$		0			0
$211$	−8.40990e6	+	7.05675e6i	−0.895249	+	0.751203i	−0.969256	−	0.246055i	$-0.920866\pi$
$211$	−8.40990e6	+	7.05675e6i	−0.895249	+	0.751203i	0.0740074	+	0.997258i	$0.476421\pi$
$212$	−3.65221e6	+	1.00344e7i	−0.383309	+	1.05313i
$213$		0			0
$214$	2.52449e6	−	1.43171e7i	0.257592	−	1.46088i
$215$			613635.i			0.0617440i
$216$		0			0
$217$	−2.13940e6			−0.209369
$218$	−1.85434e7	−	3.26970e6i	−1.78986	−	0.315601i
$219$		0			0
$220$	8.67467e6	+	3.15732e6i	0.814676	+	0.296518i
$221$	2.27633e6	+	2.71283e6i	0.210891	+	0.251331i
$222$		0			0
$223$	1.99653e6	−	726678.i	0.180037	−	0.0655280i	−0.250429	−	0.968135i	$-0.580572\pi$
$223$	1.99653e6	−	726678.i	0.180037	−	0.0655280i	0.430466	+	0.902607i	$0.358349\pi$
$224$	4.30178e6	+	2.48363e6i	0.382740	+	0.220975i
$225$		0			0
$226$	−1.12635e7	−	1.95090e7i	−0.975771	−	1.69009i
$227$	−121910.	+	145286.i	−0.0104222	+	0.0124207i	−0.771230	−	0.636556i	$-0.780358\pi$
$227$	−121910.	+	145286.i	−0.0104222	+	0.0124207i	0.760808	+	0.648977i	$0.224803\pi$
$228$		0			0
$229$	−156615.	−	888210.i	−0.0130415	−	0.0739621i	0.977592	−	0.210507i	$-0.0675114\pi$
$229$	−156615.	−	888210.i	−0.0130415	−	0.0739621i	−0.990634	+	0.136545i	$0.956400\pi$
$230$	−1.14453e7	+	2.01812e6i	−0.940688	+	0.165869i
$231$		0			0
$232$	4.45603e6	+	3.73905e6i	0.356848	+	0.299431i
$233$	6.44223e6	−	3.71942e6i	0.509294	−	0.294041i	−0.223249	−	0.974761i	$-0.571666\pi$
$233$	6.44223e6	−	3.71942e6i	0.509294	−	0.294041i	0.732543	+	0.680720i	$0.238333\pi$
$234$		0			0
$235$	−8.27872e6	+	1.43392e7i	−0.637910	+	1.10489i
$236$	−1.36750e6	−	3.75717e6i	−0.104038	−	0.285841i
$237$		0			0
$238$	5.36841e6	−	4.50463e6i	0.398213	−	0.334140i
$239$	2.60021e6	−	7.14402e6i	0.190465	−	0.523298i	−0.807298	−	0.590143i	$-0.799071\pi$
$239$	2.60021e6	−	7.14402e6i	0.190465	−	0.523298i	0.997763	+	0.0668453i	$0.0212934\pi$
$240$		0			0
$241$	−1.52112e6	+	8.62668e6i	−0.108670	+	0.616301i	0.881020	+	0.473079i	$0.156857\pi$
$241$	−1.52112e6	+	8.62668e6i	−0.108670	+	0.616301i	−0.989691	+	0.143222i	$0.954254\pi$
$242$		−	4.66902e7i		−	3.29442i
$243$		0			0
$244$	−1.16638e7			−0.802916
$245$	9.10036e6	+	1.60464e6i	0.618814	+	0.109114i
$246$		0			0
$247$	−84897.2	−	30900.1i	−0.00563381	−	0.00205054i
$248$	−2.49327e6	−	2.97136e6i	−0.163461	−	0.194805i
$249$		0			0
$250$	−2.00831e7	+	7.30965e6i	−1.28532	+	0.467817i
$251$	2.29316e7	+	1.32396e7i	1.45015	+	0.837245i	0.998489	−	0.0549446i	$-0.0174982\pi$
$251$	2.29316e7	+	1.32396e7i	1.45015	+	0.837245i	0.451661	+	0.892189i	$0.350832\pi$
$252$		0			0
$253$	1.52809e7	+	2.64674e7i	0.943601	+	1.63436i
$254$	−8.61169e6	+	1.02630e7i	−0.525517	+	0.626287i
$255$		0			0
$256$	3.73664e6	+	2.11915e7i	0.222721	+	1.26311i
$257$	−6.58651e6	+	1.16138e6i	−0.388022	+	0.0684187i	−0.364256	−	0.931299i	$-0.618677\pi$
$257$	−6.58651e6	+	1.16138e6i	−0.388022	+	0.0684187i	−0.0237657	+	0.999718i	$0.507566\pi$
$258$		0			0
$259$	−3.76722e6	−	3.16108e6i	−0.216831	−	0.181943i
$260$	−2.30497e6	+	1.33078e6i	−0.131143	+	0.0757155i
$261$		0			0
$262$	−1.38026e6	+	2.39068e6i	−0.0767463	+	0.132928i
$263$	−6.79907e6	−	1.86803e7i	−0.373751	−	1.02687i	−0.973899	−	0.226983i	$-0.927114\pi$
$263$	−6.79907e6	−	1.86803e7i	−0.373751	−	1.02687i	0.600148	−	0.799889i	$-0.295108\pi$
$264$		0			0
$265$	2.01607e7	−	1.69169e7i	1.08335	−	0.909039i
$266$	−61148.1	+	168003.i	−0.00324891	+	0.00892632i
$267$		0			0
$268$	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	$-0.170260\pi$
$270$		0			0
$271$	−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
$273$		0			0
$274$	−3.83842e7	−	1.39707e7i	−1.86595	−	0.679152i
$275$	1.07505e7	+	1.28119e7i	0.516929	+	0.616051i
$276$		0			0
$277$	3.51398e7	−	1.27899e7i	1.65333	−	0.601764i	0.664040	−	0.747697i	$-0.268841\pi$
$277$	3.51398e7	−	1.27899e7i	1.65333	−	0.601764i	0.989294	+	0.145933i	$0.0466184\pi$
$278$	−2.58284e7	−	1.49120e7i	−1.20216	−	0.694068i
$279$		0			0
$280$	−1.74385e6	−	3.02044e6i	−0.0794394	−	0.137593i
$281$	−2.08127e6	+	2.48036e6i	−0.0938014	+	0.111788i	−0.810903	−	0.585180i	$-0.801024\pi$
$281$	−2.08127e6	+	2.48036e6i	−0.0938014	+	0.111788i	0.717102	+	0.696968i	$0.245468\pi$
$282$		0			0
$283$	1.44560e6	+	8.19842e6i	0.0637807	+	0.361718i	0.999948	+	0.0101645i	$0.00323551\pi$
$283$	1.44560e6	+	8.19842e6i	0.0637807	+	0.361718i	−0.936168	+	0.351554i	$0.885653\pi$
$284$	382287.	−	67407.5i	0.0166892	−	0.00294275i
$285$		0			0
$286$	1.42735e7	+	1.19769e7i	0.610143	+	0.511971i
$287$	−1.09043e7	+	6.29560e6i	−0.461266	+	0.266312i
$288$		0			0
$289$	−251115.	+	434944.i	−0.0104035	+	0.0180194i
$290$	7.40478e6	+	2.03445e7i	0.303611	+	0.834166i
$291$		0			0
$292$	9.39690e6	−	7.88493e6i	0.377430	−	0.316701i
$293$	−1.20558e7	+	3.31231e7i	−0.479285	+	1.31683i	0.430816	+	0.902440i	$0.358226\pi$
$293$	−1.20558e7	+	3.31231e7i	−0.479285	+	1.31683i	−0.910101	+	0.414386i	$0.863996\pi$
$294$		0			0
$295$	−1.71117e6	+	9.70452e6i	−0.0666541	+	0.378014i
$296$		−	8.91613e6i		−	0.343796i
$297$		0			0
$298$	−9.65161e6			−0.364713
$299$	−8.67759e6	−	1.53009e6i	−0.324628	−	0.0572406i
$300$		0			0
$301$	865147.	+	314888.i	0.0317242	+	0.0115467i
$302$	−2.66260e7	−	3.17316e7i	−0.966685	−	1.15205i
$303$		0			0
$304$	−591798.	+	215397.i	−0.0210646	+	0.00766688i
$305$	2.48954e7	+	1.43733e7i	0.877443	+	0.506592i
$306$		0			0
$307$	−9.02470e6	−	1.56312e7i	−0.311902	−	0.540230i	0.666872	−	0.745172i	$-0.267633\pi$
$307$	−9.02470e6	−	1.56312e7i	−0.311902	−	0.540230i	−0.978774	+	0.204942i	$0.934299\pi$
$308$	8.90284e6	−	1.06100e7i	0.304703	−	0.363131i
$309$		0			0
$310$	−2.50691e6	−	1.42174e7i	−0.0841498	−	0.477237i
$311$	−9.81559e6	+	1.73075e6i	−0.326314	+	0.0575379i	−0.334405	−	0.942429i	$-0.608535\pi$
$311$	−9.81559e6	+	1.73075e6i	−0.326314	+	0.0575379i	0.00809160	+	0.999967i	$0.497424\pi$
$312$		0			0
$313$	−4.19324e6	−	3.51855e6i	−0.136747	−	0.114744i	0.571849	−	0.820359i	$-0.306226\pi$
$313$	−4.19324e6	−	3.51855e6i	−0.136747	−	0.114744i	−0.708595	+	0.705615i	$0.750671\pi$
$314$	−2.91880e7	+	1.68517e7i	−0.942790	+	0.544320i
$315$		0			0
$316$	1.29777e6	−	2.24780e6i	0.0411279	−	0.0712355i
$317$	4.37930e6	+	1.20320e7i	0.137476	+	0.377712i	0.989257	−	0.146185i	$-0.0466996\pi$
$317$	4.37930e6	+	1.20320e7i	0.137476	+	0.377712i	−0.851781	+	0.523898i	$0.824477\pi$
$318$		0			0
$319$	4.36131e7	−	3.65957e7i	1.34352	−	1.12735i
$320$	−916771.	+	2.51881e6i	−0.0279776	+	0.0768679i
$321$		0			0
$322$	−3.02790e6	+	1.71721e7i	−0.0906930	+	0.514346i
$323$			602978.i			0.0178934i
$324$		0			0
$325$	−4.82202e6			−0.140468
$326$	2.30314e7	+	4.06106e6i	0.664764	+	0.117216i
$327$		0			0
$328$	−2.14517e7	−	7.80777e6i	−0.607911	−	0.221261i
$329$	1.59681e7	+	1.90301e7i	0.448401	+	0.534384i
$330$		0			0
$331$	−1.02584e7	+	3.73374e6i	−0.282874	+	0.102958i	−0.479561	−	0.877509i	$-0.659204\pi$
$331$	−1.02584e7	+	3.73374e6i	−0.282874	+	0.102958i	0.196687	+	0.980466i	$0.436982\pi$
$332$	3.30393e7	+	1.90752e7i	0.902851	+	0.521262i
$333$		0			0
$334$	−1.20207e7	−	2.08204e7i	−0.322618	−	0.558791i
$335$	−2.47674e6	+	2.95167e6i	−0.0658789	+	0.0785114i
$336$		0			0
$337$	4.54260e6	+	2.57624e7i	0.118690	+	0.673125i	0.984857	+	0.173370i	$0.0554656\pi$
$337$	4.54260e6	+	2.57624e7i	0.118690	+	0.673125i	−0.866167	+	0.499755i	$0.833423\pi$
$338$	4.28356e7	−	7.55308e6i	1.10932	−	0.195602i
$339$		0			0
$340$	1.36076e7	+	1.14182e7i	0.346215	+	0.290509i
$341$	−3.28777e7	+	1.89819e7i	−0.829159	+	0.478715i
$342$		0			0
$343$	1.53075e7	−	2.65134e7i	0.379334	−	0.657026i
$344$	570906.	+	1.56855e6i	0.0140246	+	0.0385321i
$345$		0			0
$346$	−3.94015e7	+	3.30618e7i	−0.951227	+	0.798175i
$347$	9.54635e6	−	2.62284e7i	0.228480	−	0.627745i	−0.771483	−	0.636250i	$-0.780485\pi$
$347$	9.54635e6	−	2.62284e7i	0.228480	−	0.627745i	0.999964	+	0.00850455i	$0.00270711\pi$
$348$		0			0
$349$	9933.24	−	56334.2i	0.000233676	−	0.00132524i	−0.984691	−	0.174311i	$-0.944230\pi$
$349$	9933.24	−	56334.2i	0.000233676	−	0.00132524i	0.984924	+	0.172986i	$0.0553414\pi$
$350$			9.54229e6i			0.222561i
$351$		0			0
$352$	8.81444e7			2.02100
$353$	2.73231e7	+	4.81780e6i	0.621164	+	0.109528i	0.475368	−	0.879787i	$-0.342315\pi$
$353$	2.73231e7	+	4.81780e6i	0.621164	+	0.109528i	0.145795	+	0.989315i	$0.453426\pi$
$354$		0			0
$355$	−899025.	−	327218.i	−0.0200949	−	0.00731396i
$356$	4.84694e6	+	5.77636e6i	0.107428	+	0.128028i
$357$		0			0
$358$	3.12163e7	−	1.13618e7i	0.680350	−	0.247627i
$359$	3.18617e7	+	1.83954e7i	0.688630	+	0.397581i	0.803099	−	0.595846i	$-0.203183\pi$
$359$	3.18617e7	+	1.83954e7i	0.688630	+	0.397581i	−0.114469	+	0.993427i	$0.536517\pi$
$360$		0			0
$361$	2.35152e7	+	4.07296e7i	0.499837	+	0.865742i
$362$	4.22486e6	−	5.03500e6i	0.0890609	−	0.106139i
$363$		0			0
$364$	693424.	+	3.93260e6i	0.0143779	+	0.0815410i
$365$	−2.97735e7	+	5.24987e6i	−0.612282	+	0.107962i
$366$		0			0
$367$	−5.33099e7	−	4.47324e7i	−1.07847	−	0.904948i	−0.0826816	−	0.996576i	$-0.526348\pi$
$367$	−5.33099e7	−	4.47324e7i	−1.07847	−	0.904948i	−0.995793	+	0.0916281i	$0.970793\pi$
$368$	−5.31935e7	+	3.07113e7i	−1.06737	+	0.616246i
$369$		0			0
$370$	1.65925e7	−	2.87391e7i	0.327573	−	0.567373i
$371$	−1.35051e7	−	3.71050e7i	−0.264470	−	0.726625i
$372$		0			0
$373$	1.18708e7	−	9.96079e6i	0.228746	−	0.191941i	−0.521210	−	0.853429i	$-0.674519\pi$
$373$	1.18708e7	−	9.96079e6i	0.228746	−	0.191941i	0.749956	+	0.661488i	$0.230075\pi$
$374$	4.25326e7	−	1.16857e8i	0.813030	−	2.23378i
$375$		0			0
$376$	−7.82107e6	+	4.43555e7i	−0.147130	+	0.834418i
$377$			1.64146e7i			0.306342i
$378$		0			0
$379$	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
$381$		0			0
$382$	−7.85441e7	−	2.85877e7i	−1.40904	−	0.512849i
$383$	−3.74148e7	−	4.45892e7i	−0.665958	−	0.793658i	0.322269	−	0.946648i	$-0.395554\pi$
$383$	−3.74148e7	−	4.45892e7i	−0.665958	−	0.793658i	−0.988228	+	0.152990i	$0.951110\pi$
$384$		0			0
$385$	−3.20771e7	+	1.16751e7i	−0.562099	+	0.204587i
$386$	8.26915e7	+	4.77419e7i	1.43780	+	0.830115i
$387$		0			0
$388$	2.46689e7	+	4.27279e7i	0.422333	+	0.731503i
$389$	4.28033e7	−	5.10110e7i	0.727158	−	0.866593i	−0.268148	−	0.963378i	$-0.586412\pi$
$389$	4.28033e7	−	5.10110e7i	0.727158	−	0.866593i	0.995305	+	0.0967851i	$0.0308559\pi$
$390$		0			0
$391$	1.02120e7	+	5.79152e7i	0.170837	+	0.968863i
$392$	2.47549e7	−	4.36496e6i	0.410963	−	0.0724639i
$393$		0			0
$394$	4.46957e7	+	3.75042e7i	0.730764	+	0.613184i
$395$	−5.53995e6	+	3.19849e6i	−0.0898907	+	0.0518984i
$396$		0			0
$397$	1.99741e7	−	3.45961e7i	0.319224	−	0.552911i	−0.661103	−	0.750295i	$-0.729911\pi$
$397$	1.99741e7	−	3.45961e7i	0.319224	−	0.552911i	0.980326	+	0.197384i	$0.0632446\pi$
$398$	1.24640e7	+	3.42447e7i	0.197701	+	0.543180i
$399$		0			0
$400$	−2.57492e7	+	2.16061e7i	−0.402330	+	0.337595i
$401$	−3.17423e7	+	8.72114e7i	−0.492273	+	1.35251i	0.406322	+	0.913730i	$0.366811\pi$
$401$	−3.17423e7	+	8.72114e7i	−0.492273	+	1.35251i	−0.898595	+	0.438779i	$0.855411\pi$
$402$		0			0
$403$	1.90068e6	−	1.07793e7i	0.0290397	−	0.164693i
$404$		−	1.63002e7i		−	0.247201i
$405$		0			0
$406$	3.24829e7			0.485374
$407$	−8.59403e7	−	1.51536e7i	−1.27472	−	0.224767i
$408$		0			0
$409$	−4.46234e7	−	1.62416e7i	−0.652218	−	0.237388i	−0.00534478	−	0.999986i	$-0.501701\pi$
$409$	−4.46234e7	−	1.62416e7i	−0.652218	−	0.237388i	−0.646873	+	0.762598i	$0.723924\pi$
$410$	−5.46147e7	−	6.50873e7i	−0.792425	−	0.944375i
$411$		0			0
$412$	−6.95224e7	+	2.53041e7i	−0.994106	+	0.361825i
$413$	1.28040e7	+	7.39242e6i	0.181760	+	0.104939i
$414$		0			0
$415$	−4.70130e7	−	8.14289e7i	−0.657770	−	1.13929i
$416$	−1.63354e7	+	1.94678e7i	−0.226908	+	0.270419i
$417$		0			0
$418$	550909.	+	3.12436e6i	0.00754311	+	0.0427791i
$419$	−6.76442e7	+	1.19275e7i	−0.919578	+	0.162146i	−0.613349	−	0.789812i	$-0.710178\pi$
$419$	−6.76442e7	+	1.19275e7i	−0.919578	+	0.162146i	−0.306228	+	0.951958i	$0.599067\pi$
$420$		0			0
$421$	−1.86100e7	−	1.56156e7i	−0.249402	−	0.209273i	0.509513	−	0.860463i	$-0.329826\pi$
$421$	−1.86100e7	−	1.56156e7i	−0.249402	−	0.209273i	−0.758915	+	0.651190i	$0.774270\pi$
$422$	−9.62580e7	+	5.55746e7i	−1.28085	+	0.739501i
$423$		0			0
$424$	3.57952e7	−	6.19991e7i	0.469599	−	0.813370i
$425$	1.10071e7	+	3.02418e7i	0.143386	+	0.393950i
$426$		0			0
$427$	3.30397e7	−	2.77236e7i	0.424377	−	0.356095i
$428$	1.89098e7	−	5.19542e7i	0.241188	−	0.662657i
$429$		0			0
$430$	−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	$0.950128\pi$
$432$		0			0
$433$	−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
$435$		0			0
$436$	−6.72905e7	−	2.44918e7i	−0.811885	−	0.295502i
$437$	−964380.	−	1.14930e6i	−0.0115559	−	0.0137718i
$438$		0			0
$439$	−8.38973e7	+	3.05361e7i	−0.991641	+	0.360928i	−0.786356	−	0.617774i	$-0.788035\pi$
$439$	−8.38973e7	+	3.05361e7i	−0.991641	+	0.360928i	−0.205286	+	0.978702i	$0.565812\pi$
$440$	−5.35980e7	−	3.09448e7i	−0.629203	−	0.363270i
$441$		0			0
$442$	1.79270e7	+	3.10505e7i	0.207606	+	0.359585i
$443$	8.53181e7	−	1.01678e8i	0.981364	−	1.16954i	−0.00415751	−	0.999991i	$-0.501323\pi$
$443$	8.53181e7	−	1.01678e8i	0.981364	−	1.16954i	0.985521	−	0.169552i	$-0.0542322\pi$
$444$		0			0
$445$	−3.22715e6	−	1.83021e7i	−0.0366217	−	0.207692i
$446$	2.11841e7	−	3.73534e6i	0.238785	−	0.0421042i
$447$		0			0
$448$	3.08075e6	+	2.58506e6i	0.0342628	+	0.0287499i
$449$	3.23233e7	−	1.86619e7i	0.357089	−	0.206166i	−0.310714	−	0.950504i	$-0.600568\pi$
$449$	3.23233e7	−	1.86619e7i	0.357089	−	0.206166i	0.667803	+	0.744338i	$0.267235\pi$
$450$		0			0
$451$	−1.11716e8	+	1.93497e8i	−1.21783	+	2.10934i
$452$	−2.93012e7	−	8.05044e7i	−0.317300	−	0.871775i
$453$		0			0
$454$	−1.47094e6	+	1.23426e6i	−0.0157191	+	0.0131899i
$455$	3.36611e6	−	9.24832e6i	0.0357350	−	0.0981812i
$456$		0			0
$457$	−1.03006e7	+	5.84174e7i	−0.107923	+	0.612059i	0.882090	+	0.471081i	$0.156136\pi$
$457$	−1.03006e7	+	5.84174e7i	−0.107923	+	0.612059i	−0.990013	+	0.140979i	$0.954975\pi$
$458$		−	9.13132e6i		−	0.0950467i
$459$		0			0
$460$	−4.41985e7			−0.454082
$461$	2.12064e7	+	3.73926e6i	0.216453	+	0.0381666i	0.280823	−	0.959760i	$-0.409393\pi$
$461$	2.12064e7	+	3.73926e6i	0.216453	+	0.0381666i	−0.0643697	+	0.997926i	$0.520504\pi$
$462$		0			0
$463$	2.25228e7	+	8.19764e6i	0.226924	+	0.0825935i	0.452980	−	0.891521i	$-0.350361\pi$
$463$	2.25228e7	+	8.19764e6i	0.226924	+	0.0825935i	−0.226056	+	0.974114i	$0.572583\pi$
$464$	7.35492e7	+	8.76526e7i	0.736248	+	0.877427i
$465$		0			0
$466$	7.07719e7	−	2.57589e7i	0.699363	−	0.254547i
$467$	−1.47125e8	−	8.49425e7i	−1.44456	−	0.834016i	−0.446408	−	0.894829i	$-0.647297\pi$
$467$	−1.47125e8	−	8.49425e7i	−1.44456	−	0.834016i	−0.998149	+	0.0608139i	$0.980630\pi$
$468$		0			0
$469$	2.89053e6	+	5.00654e6i	0.0280194	+	0.0485310i
$470$	−1.07753e8	+	1.28415e8i	−1.03785	+	1.23687i
$471$		0			0
$472$	4.65474e6	+	2.63984e7i	0.0442659	+	0.251045i
$473$	1.60892e7	−	2.83695e6i	0.152037	−	0.0268083i
$474$		0			0
$475$	−628950.	−	527751.i	−0.00586861	−	0.00492435i
$476$	2.30809e7	−	1.33258e7i	0.214009	−	0.123558i
$477$		0			0
$478$	3.84854e7	−	6.66587e7i	0.352381	−	0.610342i
$479$	−1.09566e7	−	3.01031e7i	−0.0996944	−	0.273908i	0.879812	−	0.475322i	$-0.157669\pi$
$479$	−1.09566e7	−	3.01031e7i	−0.0996944	−	0.273908i	−0.979506	+	0.201414i	$0.935446\pi$
$480$		0			0
$481$	1.92738e7	−	1.61726e7i	0.173193	−	0.145327i
$482$	−3.03329e7	+	8.33388e7i	−0.270877	+	0.744229i
$483$		0			0
$484$	3.08337e7	−	1.74867e8i	0.271951	−	1.54231i
$485$		−	1.21599e8i		−	1.06587i
$486$		0			0
$487$	−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
$489$		0			0
$490$	8.79148e7	+	3.19984e7i	0.747264	+	0.271982i
$491$	3.71786e7	+	4.43077e7i	0.314086	+	0.374313i	0.899873	−	0.436152i	$-0.143659\pi$
$491$	3.71786e7	+	4.43077e7i	0.314086	+	0.374313i	−0.585787	+	0.810465i	$0.699214\pi$
$492$		0			0
$493$	1.02946e8	−	3.74693e7i	0.859150	−	0.312705i
$494$	−792150.	−	457348.i	−0.00657093	−	0.00379373i
$495$		0			0
$496$	−3.81494e7	−	6.60768e7i	−0.312639	−	0.541506i
$497$	−922672.	+	1.09960e6i	−0.00751585	+	0.00895704i
$498$		0			0
$499$	−3.38252e7	−	1.91832e8i	−0.272232	−	1.54390i	−0.747620	−	0.664127i	$-0.768803\pi$
$499$	−3.38252e7	−	1.91832e8i	−0.272232	−	1.54390i	0.475388	−	0.879776i	$-0.342308\pi$
$500$	−8.00436e7	+	1.41138e7i	−0.640349	+	0.112911i
$501$		0			0
$502$	2.05365e8	+	1.72322e8i	1.62336	+	1.36216i
$503$	1.32381e8	−	7.64301e7i	1.04021	−	0.600566i	0.120318	−	0.992735i	$-0.461609\pi$
$503$	1.32381e8	−	7.64301e7i	1.04021	−	0.600566i	0.919893	+	0.392170i	$0.128275\pi$
$504$		0			0
$505$	−2.00869e7	+	3.47915e7i	−0.155969	+	0.270146i
$506$	1.05828e8	+	2.90760e8i	0.816863	+	2.24431i
$507$		0			0
$508$	−3.90306e7	+	3.27506e7i	−0.297724	+	0.249820i
$509$	−1.62115e7	+	4.45409e7i	−0.122934	+	0.337758i	−0.985860	−	0.167573i	$-0.946407\pi$
$509$	−1.62115e7	+	4.45409e7i	−0.122934	+	0.337758i	0.862926	+	0.505330i	$0.168629\pi$
$510$		0			0
$511$	−7.87667e6	+	4.46708e7i	−0.0590310	+	0.334781i
$512$			9.32630e7i			0.694864i
$513$		0			0
$514$	−6.77132e7			−0.498636
$515$	1.79572e8	+	3.16634e7i	1.31467	+	0.231812i
$516$		0			0
$517$	4.14239e8	+	1.50771e8i	2.99764	+	1.09105i
$518$	−3.20040e7	−	3.81409e7i	−0.230258	−	0.274411i
$519$		0			0
$520$	1.67676e7	−	6.10291e6i	0.119251	−	0.0434037i
$521$	1.50479e8	+	8.68789e7i	1.06405	+	0.614330i	0.926550	−	0.376172i	$-0.122760\pi$
$521$	1.50479e8	+	8.68789e7i	1.06405	+	0.614330i	0.137500	+	0.990502i	$0.456093\pi$
$522$		0			0
$523$	1.79872e7	+	3.11547e7i	0.125736	+	0.217781i	0.922020	−	0.387142i	$-0.126538\pi$
$523$	1.79872e7	+	3.11547e7i	0.125736	+	0.217781i	−0.796285	+	0.604922i	$0.793204\pi$
$524$	−6.74822e6	+	8.04222e6i	−0.0469024	+	0.0558961i
$525$		0			0
$526$	−3.49492e7	−	1.98207e8i	−0.240148	−	1.36195i
$527$	−7.19421e7	+	1.26853e7i	−0.491531	+	0.0866702i
$528$		0			0
$529$	1.31007e6	+	1.09928e6i	0.00884971	+	0.00742579i
$530$	2.30756e8	−	1.33227e8i	1.54998	−	0.894879i
$531$		0			0
$532$	−339963.	+	588834.i	−0.00225786	+	0.00391073i
$533$	−2.20325e7	−	6.05338e7i	−0.145506	−	0.399776i
$534$		0			0
$535$	−1.04385e8	+	8.75891e7i	−0.681672	+	0.571991i
$536$	−3.58482e6	+	9.84921e6i	−0.0232795	+	0.0639598i
$537$		0			0
$538$	3.48881e7	−	1.97860e8i	0.224043	−	1.27061i
$539$		−	2.46025e8i		−	1.57113i
$540$		0			0
$541$	−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
$543$		0			0
$544$	1.59383e8	+	5.80107e7i	0.990023	+	0.360339i
$545$	1.13445e8	+	1.35198e8i	0.700800	+	0.835181i
$546$		0			0
$547$	1.37063e8	−	4.98867e7i	0.837447	−	0.304806i	0.112535	−	0.993648i	$-0.464103\pi$
$547$	1.37063e8	−	4.98867e7i	0.837447	−	0.304806i	0.724911	+	0.688842i	$0.241881\pi$
$548$	−1.34533e8	−	7.76725e7i	−0.817497	−	0.471982i
$549$		0			0
$550$	8.46643e7	+	1.46643e8i	0.508876	+	0.881400i
$551$	−1.79652e6	+	2.14100e6i	−0.0107393	+	0.0127986i
$552$		0			0
$553$	1.66663e6	+	9.45194e6i	0.00985517	+	0.0558915i
$554$	3.72851e8	−	6.57436e7i	2.19283	−	0.386656i
$555$		0			0
$556$	−8.68862e7	−	7.29062e7i	−0.505506	−	0.424170i
$557$	4.76277e7	−	2.74979e7i	0.275609	−	0.159123i	−0.355825	−	0.934553i	$-0.615800\pi$
$557$	4.76277e7	−	2.74979e7i	0.275609	−	0.159123i	0.631434	+	0.775430i	$0.282467\pi$
$558$		0			0
$559$	−2.35515e6	+	4.07925e6i	−0.0134829	+	0.0233531i
$560$	−2.34644e7	−	6.44678e7i	−0.133612	−	0.367095i
$561$		0			0
$562$	−2.51122e7	+	2.10716e7i	−0.141473	+	0.118710i
$563$	−7.37539e7	+	2.02637e8i	−0.413295	+	1.13552i	0.542133	+	0.840293i	$0.317617\pi$
$563$	−7.37539e7	+	2.02637e8i	−0.413295	+	1.13552i	−0.955428	+	0.295225i	$0.904605\pi$
$564$		0			0
$565$	−3.66651e7	+	2.07938e8i	−0.203286	+	1.15289i
$566$			8.42845e7i			0.464835i
$567$		0			0
$568$	−2.60249e6			−0.0142018
$569$	−1.56179e8	−	2.75386e7i	−0.847785	−	0.149487i	−0.267153	−	0.963654i	$-0.586083\pi$
$569$	−1.56179e8	−	2.75386e7i	−0.847785	−	0.149487i	−0.580631	+	0.814167i	$0.697194\pi$
$570$		0			0
$571$	−3.79068e7	−	1.37969e7i	−0.203615	−	0.0741096i	0.238200	−	0.971216i	$-0.423443\pi$
$571$	−3.79068e7	−	1.37969e7i	−0.203615	−	0.0741096i	−0.441814	+	0.897107i	$0.645665\pi$
$572$	4.55485e7	+	5.42826e7i	0.243381	+	0.290050i
$573$		0			0
$574$	−1.19790e8	+	4.36001e7i	−0.633412	+	0.230543i
$575$	−6.93478e7	−	4.00379e7i	−0.364778	−	0.210605i
$576$		0			0
$577$	−3.44340e7	−	5.96414e7i	−0.179250	−	0.310470i	0.762374	−	0.647137i	$-0.224034\pi$
$577$	−3.44340e7	−	5.96414e7i	−0.179250	−	0.310470i	−0.941624	+	0.336667i	$0.890700\pi$
$578$	−3.26843e6	+	3.89517e6i	−0.0169261	+	0.0201717i
$579$		0			0
$580$	1.42975e7	+	8.10854e7i	0.0732786	+	0.415584i
$581$	−1.38929e8	+	2.44970e7i	−0.708378	+	0.124906i
$582$		0			0
$583$	−5.36758e8	−	4.50393e8i	−2.70877	−	2.27293i
$584$	−7.12216e7	+	4.11198e7i	−0.357580	+	0.206449i
$585$		0			0
$586$	−1.78437e8	+	3.09062e8i	−0.886731	+	1.53586i
$587$	−9.28254e7	−	2.55036e8i	−0.458937	−	1.26092i	−0.926278	−	0.376841i	$-0.877010\pi$
$587$	−9.28254e7	−	2.55036e8i	−0.458937	−	1.26092i	0.467341	−	0.884077i	$-0.345212\pi$
$588$		0			0
$589$	1.42766e6	−	1.19795e6i	0.00698681	−	0.00586263i
$590$	−3.41227e7	+	9.37514e7i	−0.166145	+	0.456480i
$591$		0			0
$592$	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	$0.733460\pi$
$594$		0			0
$595$	−6.56857e7			−0.311831
$596$	−3.61478e7	−	6.37383e6i	−0.170743	−	0.0301066i
$597$		0			0
$598$	−8.38306e7	−	3.05118e7i	−0.392012	−	0.142681i
$599$	−9.08134e7	−	1.08227e8i	−0.422542	−	0.503566i	0.512213	−	0.858858i	$-0.328826\pi$
$599$	−9.08134e7	−	1.08227e8i	−0.422542	−	0.503566i	−0.934755	+	0.355293i	$0.884381\pi$
$600$		0			0
$601$	1.37922e8	−	5.01997e7i	0.635348	−	0.231248i	−0.00420951	−	0.999991i	$-0.501340\pi$
$601$	1.37922e8	−	5.01997e7i	0.635348	−	0.231248i	0.639557	+	0.768743i	$0.279118\pi$
$602$	8.07242e6	+	4.66061e6i	0.0370011	+	0.0213626i
$603$		0			0
$604$	−7.87660e7	−	1.36427e8i	−0.357460	−	0.619140i
$605$	−2.81301e8	+	3.35242e8i	−1.27030	+	1.51388i
$606$		0			0
$607$	1.72497e6	+	9.78277e6i	0.00771284	+	0.0437417i	0.988421	−	0.151735i	$-0.0484859\pi$
$607$	1.72497e6	+	9.78277e6i	0.00771284	+	0.0437417i	−0.980708	+	0.195476i	$0.937375\pi$
$608$	−4.26135e6	+	751391.i	−0.0189599	+	0.00334314i
$609$		0			0
$610$	2.22952e8	+	1.87079e8i	0.982249	+	0.824205i
$611$	−1.10069e8	+	6.35481e7i	−0.482547	+	0.278599i
$612$		0			0
$613$	8.53880e7	−	1.47896e8i	0.370694	−	0.642060i	−0.618979	−	0.785408i	$-0.712453\pi$
$613$	8.53880e7	−	1.47896e8i	0.370694	−	0.642060i	0.989672	+	0.143347i	$0.0457866\pi$
$614$	−6.25005e7	−	1.71719e8i	−0.270009	−	0.741844i
$615$		0			0
$616$	−7.11321e7	+	5.96869e7i	−0.304315	+	0.255351i
$617$	9.12853e7	−	2.50804e8i	0.388638	−	1.06777i	−0.578977	−	0.815344i	$-0.696548\pi$
$617$	9.12853e7	−	2.50804e8i	0.388638	−	1.06777i	0.967615	−	0.252430i	$-0.0812299\pi$
$618$		0			0
$619$	−2.27041e7	+	1.28761e8i	−0.0957263	+	0.542891i	0.898796	+	0.438367i	$0.144443\pi$
$619$	−2.27041e7	+	1.28761e8i	−0.0957263	+	0.542891i	−0.994522	+	0.104524i	$0.966668\pi$
$620$		−	5.49033e7i		−	0.230369i
$621$		0			0
$622$	−1.00910e8			−0.419337
$623$	−2.74596e7	−	4.84187e6i	−0.113561	−	0.0200239i
$624$		0			0
$625$	9.10430e7	+	3.31370e7i	0.372912	+	0.135729i
$626$	−3.56232e7	−	4.24541e7i	−0.145214	−	0.173060i
$627$		0			0
$628$	−1.20445e8	+	4.38385e7i	−0.486307	+	0.177001i
$629$	−1.45424e8	−	8.39608e7i	−0.584366	−	0.337384i
$630$		0			0
$631$	−1.33783e8	−	2.31719e8i	−0.532492	−	0.922302i	−0.999280	−	0.0379335i	$-0.987922\pi$
$631$	−1.33783e8	−	2.31719e8i	−0.532492	−	0.922302i	0.466789	−	0.884369i	$-0.345411\pi$
$632$	−1.11852e7	+	1.33301e7i	−0.0443092	+	0.0528057i
$633$		0			0
$634$	2.25109e7	+	1.27666e8i	0.0883334	+	0.500963i
$635$	1.23666e8	−	2.18057e7i	0.482981	−	0.0851625i
$636$		0			0
$637$	5.43376e7	+	4.55946e7i	0.210224	+	0.176399i
$638$	4.99186e8	−	2.88205e8i	1.92221	−	1.10979i
$639$		0			0
$640$	9.23742e7	−	1.59997e8i	0.352380	−	0.610339i
$641$	−7.67803e6	−	2.10952e7i	−0.0291525	−	0.0800958i	0.924263	−	0.381757i	$-0.124681\pi$
$641$	−7.67803e6	−	2.10952e7i	−0.0291525	−	0.0800958i	−0.953415	+	0.301661i	$0.902459\pi$
$642$		0			0
$643$	−1.35708e8	+	1.13873e8i	−0.510473	+	0.428337i	−0.861295	−	0.508104i	$-0.830346\pi$
$643$	−1.35708e8	+	1.13873e8i	−0.510473	+	0.428337i	0.350823	+	0.936442i	$0.385902\pi$
$644$	−2.26805e7	+	6.23143e7i	−0.0849173	+	0.233308i
$645$		0			0
$646$	−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	$0.832124\pi$
$648$		0			0
$649$	2.62358e8			0.959755
$650$	−4.80783e7	−	8.47751e6i	−0.175069	−	0.0308694i
$651$		0			0
$652$	8.35767e7	+	3.04194e7i	0.301538	+	0.109751i
$653$	1.80200e8	+	2.14754e8i	0.647165	+	0.771261i	0.985484	−	0.169771i	$-0.0543027\pi$
$653$	1.80200e8	+	2.14754e8i	0.647165	+	0.771261i	−0.338319	+	0.941031i	$0.609858\pi$
$654$		0			0
$655$	2.43140e7	−	8.84956e6i	0.0865231	−	0.0314918i
$656$	−3.88887e8	−	2.24524e8i	−1.37756	−	0.795337i
$657$		0			0
$658$	1.25755e8	+	2.17815e8i	0.441417	+	0.764556i
$659$	8.48943e7	−	1.01173e8i	0.296635	−	0.353516i	−0.597055	−	0.802200i	$-0.703663\pi$
$659$	8.48943e7	−	1.01173e8i	0.296635	−	0.353516i	0.893690	+	0.448684i	$0.148107\pi$
$660$		0			0
$661$	2.92045e7	+	1.65627e8i	0.101122	+	0.573492i	0.992699	+	0.120622i	$0.0384888\pi$
$661$	2.92045e7	+	1.65627e8i	0.101122	+	0.573492i	−0.891576	+	0.452870i	$0.850400\pi$
$662$	−1.08846e8	+	1.91925e7i	−0.375179	+	0.0661542i
$663$		0			0
$664$	−1.95932e8	−	1.64406e8i	−0.669269	−	0.561583i
$665$	1.45125e6	−	837877.i	0.00493487	−	0.00284915i
$666$		0			0
$667$	−1.36293e8	+	2.36066e8i	−0.459300	+	0.795530i
$668$	−3.12709e7	−	8.59162e7i	−0.104909	−	0.288234i
$669$		0			0
$670$	−2.98838e7	+	2.50755e7i	−0.0993601	+	0.0833730i
$671$	2.61765e8	−	7.19193e8i	0.866450	−	2.38055i
$672$		0			0
$673$	4.99732e7	−	2.83412e8i	0.163943	−	0.929765i	−0.786205	−	0.617966i	$-0.787957\pi$
$673$	4.99732e7	−	2.83412e8i	0.163943	−	0.929765i	0.950148	−	0.311800i	$-0.100932\pi$
$674$			2.64852e8i			0.865015i
$675$		0			0
$676$	1.65419e8			0.535481
$677$	−2.13604e8	−	3.76642e7i	−0.688405	−	0.121384i	−0.181506	−	0.983390i	$-0.558097\pi$
$677$	−2.13604e8	−	3.76642e7i	−0.688405	−	0.121384i	−0.506899	+	0.862005i	$0.669208\pi$
$678$		0			0
$679$	−1.71438e8	−	6.23985e7i	−0.547645	−	0.199326i
$680$	−7.65503e7	−	9.12291e7i	−0.243456	−	0.290139i
$681$		0			0
$682$	−3.61181e8	+	1.31459e8i	−1.13860	+	0.414417i
$683$	−9.37113e7	−	5.41042e7i	−0.294124	−	0.169812i	0.345676	−	0.938354i	$-0.387649\pi$
$683$	−9.37113e7	−	5.41042e7i	−0.294124	−	0.169812i	−0.639800	+	0.768541i	$0.720983\pi$
$684$		0			0
$685$	1.91432e8	+	3.31571e8i	0.595585	+	1.03158i
$686$	1.99237e8	−	2.37442e8i	0.617161	−	0.735504i
$687$		0			0
$688$	5.70164e6	+	3.23356e7i	0.0175079	+	0.0992923i
$689$	1.98950e8	−	3.50802e7i	0.608255	−	0.107252i
$690$		0			0
$691$	−6.99958e6	−	5.87335e6i	−0.0212148	−	0.0178013i	0.632119	−	0.774872i	$-0.282186\pi$
$691$	−6.99958e6	−	5.87335e6i	−0.0212148	−	0.0178013i	−0.653333	+	0.757070i	$0.726630\pi$
$692$	−1.69403e8	+	9.78046e7i	−0.511213	+	0.295149i
$693$		0			0
$694$	1.41294e8	−	2.44729e8i	0.422714	−	0.732162i
$695$	9.56085e7	+	2.62682e8i	0.284801	+	0.782485i
$696$		0			0
$697$	−3.29352e8	+	2.76359e8i	−0.972661	+	0.816160i
$698$	198081.	−	544222.i	0.000582473	−	0.00160033i
$699$		0			0
$700$	−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	$0.755362\pi$
$702$		0			0
$703$	4.28397e6			0.0123305
$704$	7.02801e7	+	1.23923e7i	0.201425	+	0.0355167i
$705$		0			0
$706$	2.63957e8	+	9.60726e7i	0.750101	+	0.273014i
$707$	3.87439e7	+	4.61732e7i	0.109634	+	0.130657i
$708$		0			0
$709$	4.01983e8	−	1.46310e8i	1.12790	−	0.410520i	0.290368	−	0.956915i	$-0.406222\pi$
$709$	4.01983e8	−	1.46310e8i	1.12790	−	0.410520i	0.837528	+	0.546395i	$0.184000\pi$
$710$	−8.38853e6	−	4.84312e6i	−0.0234375	−	0.0135316i
$711$		0			0
$712$	−2.52768e7	−	4.37806e7i	−0.0700296	−	0.121295i
$713$	1.16836e8	−	1.39240e8i	0.322337	−	0.384146i
$714$		0			0
$715$	−3.03267e7	−	1.71991e8i	−0.0829673	−	0.470531i
$716$	1.24416e8	−	2.19380e7i	0.338952	−	0.0597664i
$717$		0			0
$718$	2.85339e8	+	2.39428e8i	0.770883	+	0.646848i
$719$	5.10332e8	−	2.94640e8i	1.37299	−	0.792694i	0.381683	−	0.924293i	$-0.375345\pi$
$719$	5.10332e8	−	2.94640e8i	1.37299	−	0.792694i	0.991303	+	0.131599i	$0.0420112\pi$
$720$		0			0
$721$	1.36789e8	−	2.36925e8i	0.364960	−	0.632129i
$722$	1.62855e8	+	4.47440e8i	0.432702	+	1.18884i
$723$		0			0
$724$	1.91483e7	−	1.60673e7i	0.0504561	−	0.0423377i
$725$	−5.10195e7	+	1.40175e8i	−0.133882	+	0.367838i
$726$		0			0
$727$	−7.30630e7	+	4.14361e8i	−0.190149	+	1.07839i	0.729010	+	0.684503i	$0.239981\pi$
$727$	−7.30630e7	+	4.14361e8i	−0.190149	+	1.07839i	−0.919159	+	0.393886i	$0.871130\pi$
$728$		−	2.67719e7i		−	0.0693882i
$729$		0			0
$730$	−3.06089e8			−0.786827
$731$	3.09595e7	+	5.45900e6i	0.0792579	+	0.0139753i
$732$		0			0
$733$	−4.50292e8	−	1.63893e8i	−1.14336	−	0.416148i	−0.300233	−	0.953866i	$-0.597064\pi$
$733$	−4.50292e8	−	1.63893e8i	−1.14336	−	0.416148i	−0.843125	+	0.537718i	$0.819287\pi$
$734$	−4.52888e8	−	5.39731e8i	−1.14526	−	1.36486i
$735$		0			0
$736$	−3.96571e8	+	1.44340e8i	−0.994690	+	0.362038i
$737$	8.88414e7	+	5.12926e7i	0.221928	+	0.128130i
$738$		0			0
$739$	5.55849e7	+	9.62759e7i	0.137728	+	0.238553i	0.926636	−	0.375959i	$-0.122687\pi$
$739$	5.55849e7	+	9.62759e7i	0.137728	+	0.238553i	−0.788908	+	0.614511i	$0.789353\pi$
$740$	8.11224e7	−	9.66779e7i	0.200192	−	0.238579i
$741$		0			0
$742$	−6.94202e7	−	3.93702e8i	−0.169932	−	0.963730i
$743$	−6.73484e8	+	1.18753e8i	−1.64195	+	0.289521i	−0.916884	−	0.399154i	$-0.869304\pi$
$743$	−6.73484e8	+	1.18753e8i	−1.64195	+	0.289521i	−0.725070	+	0.688675i	$0.758193\pi$
$744$		0			0
$745$	6.92999e7	+	5.81495e7i	0.167596	+	0.140630i
$746$	1.35871e8	−	7.84451e7i	0.327273	−	0.188951i
$747$		0			0
$748$	2.36467e8	−	4.09573e8i	0.565022	−	0.978647i
$749$	6.99243e7	+	1.92116e8i	0.166411	+	0.457211i
$750$		0			0
$751$	5.90120e8	−	4.95170e8i	1.39322	−	1.16905i	0.429208	−	0.903206i	$-0.358793\pi$
$751$	5.90120e8	−	4.95170e8i	1.39322	−	1.16905i	0.964015	−	0.265847i	$-0.0856517\pi$
$752$	−3.03015e8	+	8.32527e8i	−0.712543	+	1.95770i
$753$		0			0
$754$	−2.88582e7	+	1.63663e8i	−0.0673218	+	0.381801i
$755$			3.88255e8i			0.902145i
$756$		0			0
$757$	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
$759$		0			0
$760$	2.85499e6	+	1.03913e6i	0.00650375	+	0.00236717i
$761$	5.59083e6	+	6.66289e6i	0.0126859	+	0.0151185i	0.772350	−	0.635197i	$-0.219081\pi$
$761$	5.59083e6	+	6.66289e6i	0.0126859	+	0.0151185i	−0.759664	+	0.650316i	$0.774637\pi$
$762$		0			0
$763$	2.48826e8	−	9.05653e7i	0.560173	−	0.203886i
$764$	−2.75289e8	−	1.58938e8i	−0.617318	−	0.356409i
$765$		0			0
$766$	−2.94656e8	−	5.10359e8i	−0.655585	−	1.13551i
$767$	−4.86216e7	+	5.79450e7i	−0.107756	+	0.128419i
$768$		0			0
$769$	−1.01404e8	−	5.75090e8i	−0.222985	−	1.26461i	−0.866500	−	0.499177i	$-0.833636\pi$
$769$	−1.01404e8	−	5.75090e8i	−0.222985	−	1.26461i	0.643515	−	0.765434i	$-0.277476\pi$
$770$	−3.40353e8	+	6.00135e7i	−0.745517	+	0.131455i
$771$		0			0
$772$	2.78173e8	+	2.33415e8i	0.604592	+	0.507313i
$773$	−3.58283e8	+	2.06855e8i	−0.775688	+	0.447844i	−0.834900	−	0.550402i	$-0.814475\pi$
$773$	−3.58283e8	+	2.06855e8i	−0.775688	+	0.447844i	0.0592117	+	0.998245i	$0.481141\pi$
$774$		0			0
$775$	4.97350e7	−	8.61435e7i	0.106846	−	0.185062i
$776$	−1.13131e8	−	3.10826e8i	−0.242102	−	0.665169i
$777$		0			0
$778$	5.16456e8	−	4.33358e8i	1.09672	−	0.920254i
$779$	3.75143e6	−	1.03070e7i	0.00793569	−	0.0218031i
$780$		0			0
$781$	−4.42311e6	+	2.50847e7i	−0.00928485	+	0.0526570i
$782$			5.95402e8i			1.24506i
$783$		0			0
$784$	4.94455e8			1.02607
$785$	3.11102e8	+	5.48557e7i	0.643124	+	0.113400i
$786$		0			0
$787$	−7.63977e8	−	2.78065e8i	−1.56731	−	0.570456i	−0.594917	−	0.803787i	$-0.702815\pi$
$787$	−7.63977e8	−	2.78065e8i	−1.56731	−	0.570456i	−0.972397	+	0.233331i	$0.925037\pi$
$788$	1.42630e8	+	1.69979e8i	0.291495	+	0.347390i
$789$		0			0
$790$	−6.08598e7	+	2.21512e7i	−0.123438	+	0.0449278i
$791$	2.74351e8	+	1.58397e8i	0.554341	+	0.320049i
$792$		0			0
$793$	1.10331e8	+	1.91099e8i	0.221247	+	0.383211i
$794$	2.59976e8	−	3.09827e8i	0.519364	−	0.618954i
$795$		0			0
$796$	2.40662e7	+	1.36486e8i	0.0477165	+	0.270614i
$797$	−8.80204e7	+	1.55204e7i	−0.173864	+	0.0306568i	−0.259902	−	0.965635i	$-0.583690\pi$
$797$	−8.80204e7	+	1.55204e7i	−0.173864	+	0.0306568i	0.0860385	+	0.996292i	$0.472579\pi$
$798$		0			0
$799$	6.49801e8	+	5.45248e8i	1.27391	+	1.06894i
$800$	−2.00008e8	+	1.15475e8i	−0.390641	+	0.225536i
$801$		0			0
$802$	−4.69815e8	+	8.13743e8i	−0.910759	+	1.57748i
$803$	2.75297e8	+	7.56373e8i	0.531686	+	1.46080i
$804$		0			0
$805$	1.25200e8	−	1.05055e8i	0.240003	−	0.201386i
$806$	3.79017e7	−	1.04134e8i	0.0723858	−	0.198878i
$807$		0			0
$808$	−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	$-0.336379\pi$
$810$		0			0
$811$	−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
$813$		0			0
$814$	−8.30234e8	−	3.02180e8i	−1.53931	−	0.560264i
$815$	−1.40901e8	−	1.67920e8i	−0.260281	−	0.310191i
$816$		0			0
$817$	−753648.	+	274305.i	−0.00138198	+	0.000503000i
$818$	−4.16367e8	−	2.40390e8i	−0.760706	−	0.439194i
$819$		0			0
$820$	−1.61563e8	−	2.79836e8i	−0.293023	−	0.507530i
$821$	−2.11678e8	+	2.52269e8i	−0.382514	+	0.455862i	−0.922606	−	0.385744i	$-0.873945\pi$
$821$	−2.11678e8	+	2.52269e8i	−0.382514	+	0.455862i	0.540092	+	0.841606i	$0.318389\pi$
$822$		0			0
$823$	1.45343e8	+	8.24283e8i	0.260733	+	1.47869i	0.780917	+	0.624635i	$0.214752\pi$
$823$	1.45343e8	+	8.24283e8i	0.260733	+	1.47869i	−0.520184	+	0.854054i	$0.674137\pi$
$824$	4.88473e8	−	8.61310e7i	0.873091	−	0.153949i
$825$		0			0
$826$	1.14667e8	+	9.62174e7i	0.203470	+	0.170731i
$827$	−1.26625e8	+	7.31069e7i	−0.223873	+	0.129253i	−0.607742	−	0.794134i	$-0.707925\pi$
$827$	−1.26625e8	+	7.31069e7i	−0.223873	+	0.129253i	0.383869	+	0.923388i	$0.374591\pi$
$828$		0			0
$829$	7.50532e7	−	1.29996e8i	0.131736	−	0.228174i	−0.792610	−	0.609729i	$-0.791278\pi$
$829$	7.50532e7	−	1.29996e8i	0.131736	−	0.228174i	0.924346	+	0.381555i	$0.124611\pi$
$830$	−3.25588e8	−	8.94547e8i	−0.569423	−	1.56448i
$831$		0			0
$832$	−1.57617e7	+	1.32256e7i	−0.0273673	+	0.0229639i
$833$	1.61917e8	−	4.44863e8i	0.280128	−	0.769646i
$834$		0			0
$835$	−3.91298e7	+	2.21916e8i	−0.0672122	+	0.381179i
$836$			1.20653e7i			0.0206500i
$837$		0			0
$838$	−6.95422e8			−1.18172
$839$	5.17802e8	+	9.13025e7i	0.876754	+	0.154595i	0.593872	−	0.804559i	$-0.297598\pi$
$839$	5.17802e8	+	9.13025e7i	0.876754	+	0.154595i	0.282882	+	0.959155i	$0.408709\pi$
$840$		0			0
$841$	−8.17819e7	−	2.97662e7i	−0.137489	−	0.0500421i
$842$	−1.58099e8	−	1.88415e8i	−0.264845	−	0.315630i
$843$		0			0
$844$	−3.97212e8	+	1.44573e8i	−0.660686	+	0.240470i
$845$	−3.53072e8	−	2.03846e8i	−0.585185	−	0.337857i
$846$		0			0
$847$	3.28298e8	+	5.68629e8i	0.540279	+	0.935790i
$848$	9.05190e8	−	1.07876e9i	1.48440	−	1.76904i
$849$		0			0
$850$	5.65799e7	+	3.20880e8i	0.0921309	+	0.522500i
$851$	4.11469e8	−	7.25531e7i	0.667650	−	0.117725i
$852$		0			0
$853$	2.09968e8	+	1.76184e8i	0.338304	+	0.283871i	0.796073	−	0.605200i	$-0.206907\pi$
$853$	2.09968e8	+	1.76184e8i	0.338304	+	0.283871i	−0.457769	+	0.889071i	$0.651351\pi$
$854$	3.78165e8	−	2.18334e8i	0.607167	−	0.350548i
$855$		0			0
$856$	−1.85334e8	+	3.21008e8i	−0.295484	+	0.511793i
$857$	2.98044e8	+	8.18871e8i	0.473520	+	1.30099i	0.914905	+	0.403669i	$0.132265\pi$
$857$	2.98044e8	+	8.18871e8i	0.473520	+	1.30099i	−0.441385	+	0.897318i	$0.645513\pi$
$858$		0			0
$859$	5.74912e8	−	4.82409e8i	0.907031	−	0.761089i	−0.0645207	−	0.997916i	$-0.520552\pi$
$859$	5.74912e8	−	4.82409e8i	0.907031	−	0.761089i	0.971552	+	0.236827i	$0.0761074\pi$
$860$	−8.08093e6	+	2.22022e7i	−0.0127047	+	0.0349060i
$861$		0			0
$862$	−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	$0.969569\pi$
$864$		0			0
$865$	4.82100e8			0.744885
$866$	−1.31700e9	−	2.32223e8i	−2.02783	−	0.357562i
$867$		0			0
$868$	−7.74066e7	−	2.81737e7i	−0.118364	−	0.0430809i
$869$	1.09475e8	+	1.30467e8i	0.166823	+	0.198812i
$870$		0			0
$871$	−2.77932e7	+	1.01159e7i	−0.0420614	+	0.0153091i
$872$	4.15767e8	+	2.40043e8i	0.627047	+	0.362026i
$873$		0			0
$874$	−7.59486e6	−	1.31547e7i	−0.0113759	−	0.0197036i
$875$	1.93190e8	−	2.30235e8i	0.288377	−	0.343674i
$876$		0			0
$877$	1.58221e8	+	8.97313e8i	0.234565	+	1.33029i	0.843527	+	0.537087i	$0.180475\pi$
$877$	1.58221e8	+	8.97313e8i	0.234565	+	1.33029i	−0.608962	+	0.793200i	$0.708414\pi$
$878$	−8.90191e8	+	1.56965e8i	−1.31522	+	0.231909i
$879$		0			0
$880$	−9.32586e8	−	7.82533e8i	−1.36849	−	1.14830i
$881$	3.81660e8	−	2.20352e8i	0.558148	−	0.322247i	−0.194254	−	0.980951i	$-0.562229\pi$
$881$	3.81660e8	−	2.20352e8i	0.558148	−	0.322247i	0.752402	+	0.658705i	$0.228895\pi$
$882$		0			0
$883$	3.63100e8	−	6.28908e8i	0.527405	−	0.913492i	−0.472085	−	0.881553i	$-0.656498\pi$
$883$	3.63100e8	−	6.28908e8i	0.527405	−	0.913492i	0.999490	−	0.0319390i	$-0.0101682\pi$
$884$	4.66358e7	+	1.28131e8i	0.0675092	+	0.185480i
$885$		0			0
$886$	1.02943e9	−	8.63794e8i	1.48012	−	1.24196i
$887$	1.48100e8	−	4.06901e8i	0.212219	−	0.583066i	−0.787216	−	0.616677i	$-0.788479\pi$
$887$	1.48100e8	−	4.06901e8i	0.212219	−	0.583066i	0.999435	+	0.0336112i	$0.0107008\pi$
$888$		0			0
$889$	3.27162e7	−	1.85543e8i	0.0465648	−	0.264082i
$890$		−	1.88156e8i		−	0.266900i
$891$		0			0
$892$	8.18069e7			0.115264
$893$	−2.13117e7	−	3.75782e6i	−0.0299270	−	0.00527693i
$894$		0			0
$895$	−2.92590e8	−	1.06494e8i	−0.408123	−	0.148545i
$896$	−1.78173e8	−	2.12338e8i	−0.247695	−	0.295192i
$897$		0			0
$898$	3.55092e8	−	1.29243e8i	0.490356	−	0.178475i
$899$	−2.93241e8	−	1.69303e8i	−0.403595	−	0.233015i
$900$		0			0
$901$	−6.74148e8	−	1.16766e9i	−0.921682	−	1.59640i
$902$	−1.45406e9	+	1.73288e9i	−1.98135	+	2.36128i
$903$		0			0
$904$	9.97367e7	+	5.65635e8i	0.135005	+	0.765651i
$905$	−6.06702e7	+	1.06978e7i	−0.0818521	+	0.0144327i
$906$		0			0
$907$	3.98629e7	+	3.34489e7i	0.0534252	+	0.0448291i	0.669109	−	0.743164i	$-0.266676\pi$
$907$	3.98629e7	+	3.34489e7i	0.0534252	+	0.0448291i	−0.615684	+	0.787993i	$0.711120\pi$
$908$	−6.32414e6	+	3.65124e6i	−0.00844780	+	0.00487734i
$909$		0			0
$910$	4.98214e7	−	8.62932e7i	0.0661138	−	0.114512i
$911$	−5.04068e8	−	1.38492e9i	−0.666706	−	1.83176i	−0.543559	−	0.839371i	$-0.682923\pi$
$911$	−5.04068e8	−	1.38492e9i	−0.666706	−	1.83176i	−0.123147	−	0.992388i	$-0.539299\pi$
$912$		0			0
$913$	−1.91767e9	+	1.60912e9i	−2.51977	+	2.11434i
$914$	−2.05405e8	+	5.64346e8i	−0.269013	+	0.739107i
$915$		0			0
$916$	6.03023e6	−	3.41992e7i	0.00784599	−	0.0444968i
$917$		−	3.88207e7i		−	0.0503449i
$918$		0			0
$919$	−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
$921$		0			0
$922$	2.04867e8	+	7.45653e7i	0.261384	+	0.0951358i
$923$	−4.72055e6	−	5.62573e6i	−0.00600327	−	0.00715442i
$924$		0			0
$925$	2.14859e8	−	7.82022e7i	0.271474	−	0.0988083i
$926$	2.10154e8	+	1.21332e8i	0.264670	+	0.152807i
$927$		0			0
$928$	3.93087e8	+	6.80846e8i	0.491864	+	0.851933i
$929$	−6.96001e8	+	8.29462e8i	−0.868086	+	1.03454i	0.130982	+	0.991385i	$0.458187\pi$
$929$	−6.96001e8	+	8.29462e8i	−0.868086	+	1.03454i	−0.999068	+	0.0431598i	$0.986258\pi$
$930$		0			0
$931$	2.09725e6	+	1.18941e7i	0.00259897	+	0.0147395i
$932$	2.82070e8	−	4.97365e7i	0.348425	−	0.0614367i
$933$		0			0
$934$	−1.31758e9	−	1.10558e9i	−1.61710	−	1.35691i
$935$	−1.00944e9	+	5.82798e8i	−1.23494	+	0.712990i
$936$		0			0
$937$	−2.89510e8	+	5.01446e8i	−0.351921	+	0.609545i	−0.986586	−	0.163243i	$-0.947805\pi$
$937$	−2.89510e8	+	5.01446e8i	−0.351921	+	0.609545i	0.634665	+	0.772787i	$0.281138\pi$
$938$	2.00183e7	+	5.49999e7i	0.0242560	+	0.0666429i
$939$		0			0
$940$	−4.88368e8	+	4.09789e8i	−0.587981	+	0.493375i
$941$	3.61373e8	−	9.92864e8i	0.433697	−	1.19157i	−0.509829	−	0.860276i	$-0.670291\pi$
$941$	3.61373e8	−	9.92864e8i	0.433697	−	1.19157i	0.943526	−	0.331298i	$-0.107486\pi$
$942$		0			0
$943$	1.85761e8	−	1.05351e9i	0.221524	−	1.25632i
$944$			5.27281e8i			0.626796i
$945$		0			0
$946$	1.65406e8			0.195379
$947$	−1.04919e9	−	1.85001e8i	−1.23540	−	0.217834i	−0.482454	−	0.875921i	$-0.660255\pi$
$947$	−1.04919e9	−	1.85001e8i	−1.23540	−	0.217834i	−0.752941	+	0.658087i	$0.771366\pi$
$948$		0			0
$949$	−2.18074e8	−	7.93724e7i	−0.255156	−	0.0928690i
$950$	−5.34317e6	−	6.36774e6i	−0.00623201	−	0.00742702i
$951$		0			0
$952$	−1.67903e8	+	6.11118e7i	−0.194602	+	0.0708295i
$953$	7.83201e7	+	4.52181e7i	0.0904888	+	0.0522437i	0.544562	−	0.838721i	$-0.316696\pi$
$953$	7.83201e7	+	4.52181e7i	0.0904888	+	0.0522437i	−0.454073	+	0.890965i	$0.650029\pi$
$954$		0			0
$955$	3.91721e8	+	6.78480e8i	0.449745	+	0.778981i
$956$	1.88159e8	−	2.24239e8i	0.215353	−	0.256648i
$957$		0			0
$958$	−5.63203e7	−	3.19408e8i	−0.0640573	−	0.363287i
$959$	5.65706e8	−	9.97493e7i	0.641409	−	0.113098i
$960$		0			0
$961$	−5.06903e8	−	4.25343e8i	−0.571156	−	0.479257i
$962$	2.20604e8	−	1.27366e8i	0.247792	−	0.143063i
$963$		0			0
$964$	−1.68641e8	+	2.92094e8i	−0.188248	+	0.326056i
$965$	−3.06098e8	−	8.40997e8i	−0.340627	−	0.935864i
$966$		0			0
$967$	2.19306e8	−	1.84020e8i	0.242534	−	0.203510i	−0.513416	−	0.858140i	$-0.671620\pi$
$967$	2.19306e8	−	1.84020e8i	0.242534	−	0.203510i	0.755949	+	0.654630i	$0.227176\pi$
$968$	−4.07154e8	+	1.11865e9i	−0.448882	+	1.23329i
$969$		0			0
$970$	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	$0.940604\pi$
$972$		0			0
$973$	4.19410e8			0.455303
$974$	−2.28961e8	−	4.03719e7i	−0.247790	−	0.0436921i
$975$		0			0
$976$	1.44542e9	+	5.26089e8i	1.55469	+	0.565861i
$977$	7.15712e8	+	8.52953e8i	0.767458	+	0.914621i	0.998295	−	0.0583715i	$-0.0185908\pi$
$977$	7.15712e8	+	8.52953e8i	0.767458	+	0.914621i	−0.230837	+	0.972992i	$0.574146\pi$
$978$		0			0
$979$	−4.64950e8	+	1.69228e8i	−0.495517	+	0.180353i
$980$	3.08132e8	+	1.77900e8i	0.327385	+	0.189016i
$981$		0			0
$982$	2.92796e8	+	5.07137e8i	0.309194	+	0.535539i
$983$	−2.72631e7	+	3.24909e7i	−0.0287022	+	0.0342060i	−0.780205	−	0.625524i	$-0.784885\pi$
$983$	−2.72631e7	+	3.24909e7i	−0.0287022	+	0.0342060i	0.751502	+	0.659730i	$0.229330\pi$
$984$		0			0
$985$	−9.49644e7	−	5.38570e8i	−0.0993693	−	0.563551i
$986$	1.09231e9	−	1.92603e8i	1.13950	−	0.200925i
$987$		0			0
$988$	−2.66478e6	−	2.23602e6i	−0.00276306	−	0.00231848i
$989$	−6.77412e7	+	3.91104e7i	−0.0700268	+	0.0404300i
$990$		0			0
$991$	4.10358e8	−	7.10761e8i	0.421640	−	0.730302i	−0.574460	−	0.818533i	$-0.694788\pi$
$991$	4.10358e8	−	7.10761e8i	0.421640	−	0.730302i	0.996100	+	0.0882306i	$0.0281213\pi$
$992$	−1.79299e8	−	4.92620e8i	−0.183672	−	0.504634i
$993$		0			0
$994$	−1.11328e7	+	9.34150e6i	−0.0113356	+	0.00951169i
$995$	1.16826e8	−	3.20975e8i	0.118596	−	0.325839i
$996$		0			0
$997$	−3.23842e8	+	1.83660e9i	−0.326775	+	1.85323i	0.170125	+	0.985423i	$0.445583\pi$
$997$	−3.23842e8	+	1.83660e9i	−0.326775	+	1.85323i	−0.496899	+	0.867808i	$0.665528\pi$
$998$		−	1.97215e9i		−	1.98403i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.7.f.a.2.4	✓	102	3.2	odd	2
27.7.f.a.14.4	yes	102	27.13	even	9
81.7.f.a.8.14		102	1.1	even	1	trivial
81.7.f.a.71.14		102	27.14	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(9.97059 + 1.75808i) q^{2} +(36.1814 + 13.1690i) q^{4} +(-60.9980 - 72.6946i) q^{5} +(-133.791 + 48.6960i) q^{7} +(-223.553 - 129.069i) q^{8} +(-480.383 - 832.047i) q^{10} +(-1624.00 + 1935.41i) q^{11} +(-126.490 - 717.362i) q^{13} +(-1419.59 + 250.312i) q^{14} +(-3889.75 - 3263.89i) q^{16} +(-4210.29 + 2430.81i) q^{17} +(62.0141 - 107.412i) q^{19} +(-1249.68 - 3433.47i) q^{20} +(-19594.9 + 16442.1i) q^{22} +(4137.25 - 11367.0i) q^{23} +(1149.51 - 6519.18i) q^{25} -7374.90i q^{26} -5482.03 q^{28} +(-22191.9 - 3913.03i) q^{29} +(14120.1 + 5139.28i) q^{31} +(-22425.5 - 26725.7i) q^{32} +(-46252.6 + 16834.6i) q^{34} +(11700.9 + 6755.53i) q^{35} +(17270.1 + 29912.7i) q^{37} +(807.155 - 961.930i) q^{38} +(4253.72 + 24124.0i) q^{40} +(87091.6 - 15356.6i) q^{41} +(-4953.54 - 4156.52i) q^{43} +(-84246.1 + 48639.5i) q^{44} +(61235.0 - 106062. i) q^{46} +(-59675.6 - 163957. i) q^{47} +(-74595.6 + 62593.1i) q^{49} +(22922.5 - 62979.1i) q^{50} +(4870.32 - 27620.9i) q^{52} +277335. i q^{53} +239755. q^{55} +(36194.6 + 6382.08i) q^{56} +(-214387. - 78030.5i) q^{58} +(-66748.6 - 79547.9i) q^{59} +(-284660. + 103608. i) q^{61} +(131750. + 76065.9i) q^{62} +(-14123.1 - 24462.0i) q^{64} +(-44432.7 + 52952.8i) q^{65} +(-7050.75 - 39986.8i) q^{67} +(-184345. + 32505.1i) q^{68} +(104788. + 87927.9i) q^{70} +(8731.10 - 5040.90i) q^{71} +(159295. - 275906. i) q^{73} +(119604. + 328610. i) q^{74} +(3658.26 - 3069.64i) q^{76} +(123031. - 338024. i) q^{77} +(11705.7 - 66386.4i) q^{79} +481854. i q^{80} +895353. q^{82} +(975779. + 172056. i) q^{83} +(433526. + 157790. i) q^{85} +(-42082.2 - 50151.7i) q^{86} +(612852. - 223060. i) q^{88} +(169602. + 97919.9i) q^{89} +(51856.0 + 89817.2i) q^{91} +(299383. - 356791. i) q^{92} +(-306750. - 1.73967e6i) q^{94} +(-11591.0 + 2043.80i) q^{95} +(981600. + 823660. i) q^{97} +(-853806. + 492945. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q + 6 q^{2} - 6 q^{4} - 210 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} + 12183 q^{14} - 198 q^{16} + 9 q^{17} - 3 q^{19} + 19767 q^{20} - 10806 q^{22} - 14466 q^{23} - 15990 q^{25}+ \cdots - 1179270 q^{98}+O(q^{100}) \) 102 * q + 6 * q^2 - 6 * q^4 - 210 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 492 * q^11 - 6 * q^13 + 12183 * q^14 - 198 * q^16 + 9 * q^17 - 3 * q^19 + 19767 * q^20 - 10806 * q^22 - 14466 * q^23 - 15990 * q^25 - 12 * q^28 + 45690 * q^29 + 18354 * q^31 + 140544 * q^32 - 82278 * q^34 - 268263 * q^35 - 3 * q^37 - 28428 * q^38 - 34593 * q^40 - 234948 * q^41 + 148764 * q^43 + 1222785 * q^44 - 3 * q^46 - 517098 * q^47 - 311262 * q^49 - 1710663 * q^50 - 213057 * q^52 - 12 * q^55 + 3167925 * q^56 + 663789 * q^58 + 230802 * q^59 - 51414 * q^61 - 1777536 * q^62 + 983037 * q^64 - 2264754 * q^65 - 845052 * q^67 + 3979053 * q^68 - 835251 * q^70 + 427689 * q^71 - 257043 * q^73 - 2458185 * q^74 + 2759802 * q^76 - 5459610 * q^77 + 662682 * q^79 - 12 * q^82 + 4926426 * q^83 - 2530881 * q^85 + 6700758 * q^86 - 2860230 * q^88 - 5907321 * q^89 - 451443 * q^91 - 712473 * q^92 + 7395807 * q^94 + 2179119 * q^95 + 272208 * q^97 - 1179270 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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