LMFDB - Embedded newform 8.14.b.b.5.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,14,Mod(5,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	8.b (of order $2$, degree $1$, 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:	$8.57847431615$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5 x^{9} + 752 x^{8} + 708 x^{7} - 743866 x^{6} + 96647426 x^{5} + 2540283092 x^{4} + \cdots + 31\!\cdots\!68 $ x^10 - 5x^9 + 752x^8 + 708x^7 - 743866x^6 + 96647426x^5 + 2540283092x^4 - 180067834748x^3 + 15101451375489x^2 - 802096030557765*x + 31616997813655668
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{48}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.9
Root			$37.4606 - 15.6556i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.14.b.b.5.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(84.9212 - 31.3112i) q^{2} -1415.71i q^{3} +(6231.21 - 5317.98i) q^{4} -2384.10i q^{5} +(-44327.5 - 120223. i) q^{6} -317448. q^{7} +(362649. - 646716. i) q^{8} -409898. q^{9} +O(q^{10})$	\(q+(84.9212 - 31.3112i) q^{2} -1415.71i q^{3} +(6231.21 - 5317.98i) q^{4} -2384.10i q^{5} +(-44327.5 - 120223. i) q^{6} -317448. q^{7} +(362649. - 646716. i) q^{8} -409898. q^{9} +(-74649.0 - 202460. i) q^{10} +1.40906e6i q^{11} +(-7.52869e6 - 8.82156e6i) q^{12} -2.51242e7i q^{13} +(-2.69581e7 + 9.93969e6i) q^{14} -3.37518e6 q^{15} +(1.05471e7 - 6.62749e7i) q^{16} +1.11400e8 q^{17} +(-3.48090e7 + 1.28344e7i) q^{18} +3.64846e8i q^{19} +(-1.26786e7 - 1.48558e7i) q^{20} +4.49413e8i q^{21} +(4.41194e7 + 1.19659e8i) q^{22} +7.49063e8 q^{23} +(-9.15559e8 - 5.13405e8i) q^{24} +1.21502e9 q^{25} +(-7.86670e8 - 2.13358e9i) q^{26} -1.67680e9i q^{27} +(-1.97809e9 + 1.68818e9i) q^{28} +2.83628e9i q^{29} +(-2.86624e8 + 1.05681e8i) q^{30} -2.93414e9 q^{31} +(-1.17947e9 - 5.95838e9i) q^{32} +1.99481e9 q^{33} +(9.46024e9 - 3.48808e9i) q^{34} +7.56826e8i q^{35} +(-2.55416e9 + 2.17983e9i) q^{36} -8.46017e9i q^{37} +(1.14238e10 + 3.09832e10i) q^{38} -3.55684e10 q^{39} +(-1.54183e9 - 8.64591e8i) q^{40} +3.90644e10 q^{41} +(1.40717e10 + 3.81647e10i) q^{42} -2.17473e10i q^{43} +(7.49334e9 + 8.78014e9i) q^{44} +9.77236e8i q^{45} +(6.36113e10 - 2.34541e10i) q^{46} -1.15068e11 q^{47} +(-9.38257e10 - 1.49316e10i) q^{48} +3.88420e9 q^{49} +(1.03181e11 - 3.80438e10i) q^{50} -1.57710e11i q^{51} +(-1.33610e11 - 1.56554e11i) q^{52} +1.71179e11i q^{53} +(-5.25026e10 - 1.42396e11i) q^{54} +3.35933e9 q^{55} +(-1.15122e11 + 2.05299e11i) q^{56} +5.16515e11 q^{57} +(8.88074e10 + 2.40860e11i) q^{58} +2.45442e11i q^{59} +(-2.10314e10 + 1.79491e10i) q^{60} +2.71473e11i q^{61} +(-2.49170e11 + 9.18715e10i) q^{62} +1.30121e11 q^{63} +(-2.86727e11 - 4.69062e11i) q^{64} -5.98985e10 q^{65} +(1.69402e11 - 6.24600e10i) q^{66} +6.82198e11i q^{67} +(6.94158e11 - 5.92424e11i) q^{68} -1.06045e12i q^{69} +(2.36972e10 + 6.42706e10i) q^{70} -2.90719e11 q^{71} +(-1.48649e11 + 2.65088e11i) q^{72} -1.48745e12 q^{73} +(-2.64899e11 - 7.18448e11i) q^{74} -1.72011e12i q^{75} +(1.94024e12 + 2.27344e12i) q^{76} -4.47303e11i q^{77} +(-3.02051e12 + 1.11369e12i) q^{78} +1.58653e12 q^{79} +(-1.58006e11 - 2.51454e10i) q^{80} -3.02736e12 q^{81} +(3.31740e12 - 1.22316e12i) q^{82} -7.79952e11i q^{83} +(2.38997e12 + 2.80039e12i) q^{84} -2.65589e11i q^{85} +(-6.80935e11 - 1.84681e12i) q^{86} +4.01533e12 q^{87} +(9.11260e11 + 5.10994e11i) q^{88} -4.10498e12 q^{89} +(3.05985e10 + 8.29881e10i) q^{90} +7.97562e12i q^{91} +(4.66757e12 - 3.98350e12i) q^{92} +4.15387e12i q^{93} +(-9.77175e12 + 3.60294e12i) q^{94} +8.69829e11 q^{95} +(-8.43531e12 + 1.66979e12i) q^{96} +1.11567e13 q^{97} +(3.29851e11 - 1.21619e11i) q^{98} -5.77570e11i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 110 q^{2} - 4716 q^{4} - 267668 q^{6} + 586960 q^{7} - 270712 q^{8} + 2014054 q^{9}+O(q^{10}) $ 10 * q + 110 * q^2 - 4716 * q^4 - 267668 * q^6 + 586960 * q^7 - 270712 * q^8 + 2014054 * q^9	\( 10 q + 110 q^{2} - 4716 q^{4} - 267668 q^{6} + 586960 q^{7} - 270712 q^{8} + 2014054 q^{9} - 4542088 q^{10} + 27987880 q^{12} + 1408688 q^{14} - 145914416 q^{15} + 56624912 q^{16} + 217326004 q^{17} - 147615262 q^{18} + 21655184 q^{20} - 177987876 q^{22} - 78679952 q^{23} + 320199056 q^{24} - 3076402574 q^{25} + 3734872040 q^{26} - 1653812448 q^{28} + 6338232752 q^{30} + 648233792 q^{31} - 11298380000 q^{32} + 15484079688 q^{33} - 6096822724 q^{34} + 4004708940 q^{36} - 18764968628 q^{38} - 63497510288 q^{39} + 7466802592 q^{40} + 59324640356 q^{41} + 53897620960 q^{42} + 13325704392 q^{44} - 55046867440 q^{46} - 10176534816 q^{47} - 301841943264 q^{48} + 182708552058 q^{49} + 326454435302 q^{50} - 53296499536 q^{52} + 35449773752 q^{54} - 123010753008 q^{55} - 462152447680 q^{56} - 511372324504 q^{57} + 766482705096 q^{58} + 1813082440992 q^{60} - 1665308528960 q^{62} - 898991123792 q^{63} - 2180548996032 q^{64} + 1577231990240 q^{65} + 2269525079448 q^{66} + 2338280915304 q^{68} - 6070110714688 q^{70} + 726361179984 q^{71} - 3600753685960 q^{72} - 633240365532 q^{73} + 7528513982264 q^{74} + 10338420845032 q^{76} - 8252024440816 q^{78} + 5445103565344 q^{79} - 15406871881920 q^{80} - 9674575380574 q^{81} + 12273334206796 q^{82} + 20362643366464 q^{84} - 26794541719396 q^{86} + 7632221772720 q^{87} - 27677491769136 q^{88} + 5506344808004 q^{89} + 31454099524040 q^{90} + 33971694298464 q^{92} - 45356008560096 q^{94} - 14214732035504 q^{95} - 35398666935232 q^{96} + 1361133320788 q^{97} + 54325451514942 q^{98}+O(q^{100}) \) 10 * q + 110 * q^2 - 4716 * q^4 - 267668 * q^6 + 586960 * q^7 - 270712 * q^8 + 2014054 * q^9 - 4542088 * q^10 + 27987880 * q^12 + 1408688 * q^14 - 145914416 * q^15 + 56624912 * q^16 + 217326004 * q^17 - 147615262 * q^18 + 21655184 * q^20 - 177987876 * q^22 - 78679952 * q^23 + 320199056 * q^24 - 3076402574 * q^25 + 3734872040 * q^26 - 1653812448 * q^28 + 6338232752 * q^30 + 648233792 * q^31 - 11298380000 * q^32 + 15484079688 * q^33 - 6096822724 * q^34 + 4004708940 * q^36 - 18764968628 * q^38 - 63497510288 * q^39 + 7466802592 * q^40 + 59324640356 * q^41 + 53897620960 * q^42 + 13325704392 * q^44 - 55046867440 * q^46 - 10176534816 * q^47 - 301841943264 * q^48 + 182708552058 * q^49 + 326454435302 * q^50 - 53296499536 * q^52 + 35449773752 * q^54 - 123010753008 * q^55 - 462152447680 * q^56 - 511372324504 * q^57 + 766482705096 * q^58 + 1813082440992 * q^60 - 1665308528960 * q^62 - 898991123792 * q^63 - 2180548996032 * q^64 + 1577231990240 * q^65 + 2269525079448 * q^66 + 2338280915304 * q^68 - 6070110714688 * q^70 + 726361179984 * q^71 - 3600753685960 * q^72 - 633240365532 * q^73 + 7528513982264 * q^74 + 10338420845032 * q^76 - 8252024440816 * q^78 + 5445103565344 * q^79 - 15406871881920 * q^80 - 9674575380574 * q^81 + 12273334206796 * q^82 + 20362643366464 * q^84 - 26794541719396 * q^86 + 7632221772720 * q^87 - 27677491769136 * q^88 + 5506344808004 * q^89 + 31454099524040 * q^90 + 33971694298464 * q^92 - 45356008560096 * q^94 - 14214732035504 * q^95 - 35398666935232 * q^96 + 1361133320788 * q^97 + 54325451514942 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	84.9212	−	31.3112i	0.938255	−	0.345944i
$2$	84.9212	−	31.3112i	0.938255	−	0.345944i
$3$		−	1415.71i		−	1.12120i	−0.828085	−	0.560602i	$-0.810570\pi$
$3$		−	1415.71i		−	1.12120i	0.828085	−	0.560602i	$-0.189430\pi$
$4$	6231.21	−	5317.98i	0.760646	−	0.649167i
$5$		−	2384.10i		−	0.0682368i	−0.999418	−	0.0341184i	$-0.989138\pi$
$5$		−	2384.10i		−	0.0682368i	0.999418	−	0.0341184i	$-0.0108623\pi$
$6$	−44327.5	−	120223.i	−0.387873	−	1.05198i
$7$	−317448.			−1.01985			−0.509924	−	0.860220i	$-0.670326\pi$
$7$	−317448.			−1.01985			−0.509924	+	0.860220i	$0.670326\pi$
$8$	362649.	−	646716.i	0.489105	−	0.872225i
$9$	−409898.			−0.257098
$10$	−74649.0	−	202460.i	−0.0236061	−	0.0640236i
$11$			1.40906e6i			0.239815i	0.992785	+	0.119908i	$0.0382598\pi$
$11$			1.40906e6i			0.239815i	−0.992785	+	0.119908i	$0.961740\pi$
$12$	−7.52869e6	−	8.82156e6i	−0.727849	−	0.852839i
$13$		−	2.51242e7i		−	1.44364i	−0.692079	−	0.721822i	$-0.743305\pi$
$13$		−	2.51242e7i		−	1.44364i	0.692079	−	0.721822i	$-0.256695\pi$
$14$	−2.69581e7	+	9.93969e6i	−0.956877	+	0.352810i
$15$	−3.37518e6			−0.0765074
$16$	1.05471e7	−	6.62749e7i	0.157164	−	0.987572i
$17$	1.11400e8			1.11936			0.559678	−	0.828710i	$-0.310925\pi$
$17$	1.11400e8			1.11936			0.559678	+	0.828710i	$0.310925\pi$
$18$	−3.48090e7	+	1.28344e7i	−0.241224	+	0.0889416i
$19$			3.64846e8i			1.77915i	0.456792	+	0.889573i	$0.348998\pi$
$19$			3.64846e8i			1.77915i	−0.456792	+	0.889573i	$0.651002\pi$
$20$	−1.26786e7	−	1.48558e7i	−0.0442971	−	0.0519041i
$21$			4.49413e8i			1.14346i
$22$	4.41194e7	+	1.19659e8i	0.0829625	+	0.225008i
$23$	7.49063e8			1.05509			0.527543	−	0.849528i	$-0.323113\pi$
$23$	7.49063e8			1.05509			0.527543	+	0.849528i	$0.323113\pi$
$24$	−9.15559e8	−	5.13405e8i	−0.977942	−	0.548386i
$25$	1.21502e9			0.995344
$26$	−7.86670e8	−	2.13358e9i	−0.499420	−	1.35451i
$27$		−	1.67680e9i		−	0.832944i
$28$	−1.97809e9	+	1.68818e9i	−0.775743	+	0.662051i
$29$			2.83628e9i			0.885446i	0.896659	+	0.442723i	$0.145987\pi$
$29$			2.83628e9i			0.885446i	−0.896659	+	0.442723i	$0.854013\pi$
$30$	−2.86624e8	+	1.05681e8i	−0.0717835	+	0.0264672i
$31$	−2.93414e9			−0.593786			−0.296893	−	0.954911i	$-0.595950\pi$
$31$	−2.93414e9			−0.593786			−0.296893	+	0.954911i	$0.595950\pi$
$32$	−1.17947e9	−	5.95838e9i	−0.194184	−	0.980965i
$33$	1.99481e9			0.268882
$34$	9.46024e9	−	3.48808e9i	1.05024	−	0.387234i
$35$			7.56826e8i			0.0695912i
$36$	−2.55416e9	+	2.17983e9i	−0.195561	+	0.166900i
$37$		−	8.46017e9i		−	0.542086i	−0.962567	−	0.271043i	$-0.912631\pi$
$37$		−	8.46017e9i		−	0.542086i	0.962567	−	0.271043i	$-0.0873685\pi$
$38$	1.14238e10	+	3.09832e10i	0.615485	+	1.66929i
$39$	−3.55684e10			−1.61862
$40$	−1.54183e9	−	8.64591e8i	−0.0595179	−	0.0333750i
$41$	3.90644e10			1.28436			0.642180	−	0.766554i	$-0.278030\pi$
$41$	3.90644e10			1.28436			0.642180	+	0.766554i	$0.278030\pi$
$42$	1.40717e10	+	3.81647e10i	0.395572	+	1.07285i
$43$		−	2.17473e10i		−	0.524639i	−0.964981	−	0.262319i	$-0.915513\pi$
$43$		−	2.17473e10i		−	0.524639i	0.964981	−	0.262319i	$-0.0844874\pi$
$44$	7.49334e9	+	8.78014e9i	0.155680	+	0.182414i
$45$			9.77236e8i			0.0175436i
$46$	6.36113e10	−	2.34541e10i	0.989940	−	0.365000i
$47$	−1.15068e11			−1.55711			−0.778557	−	0.627574i	$-0.784048\pi$
$47$	−1.15068e11			−1.55711			−0.778557	+	0.627574i	$0.784048\pi$
$48$	−9.38257e10	−	1.49316e10i	−1.10727	−	0.176213i
$49$	3.88420e9			0.0400892
$50$	1.03181e11	−	3.80438e10i	0.933887	−	0.344333i
$51$		−	1.57710e11i		−	1.25503i
$52$	−1.33610e11	−	1.56554e11i	−0.937166	−	1.09810i
$53$			1.71179e11i			1.06086i	0.847729	+	0.530430i	$0.177970\pi$
$53$			1.71179e11i			1.06086i	−0.847729	+	0.530430i	$0.822030\pi$
$54$	−5.25026e10	−	1.42396e11i	−0.288152	−	0.781514i
$55$	3.35933e9			0.0163642
$56$	−1.15122e11	+	2.05299e11i	−0.498812	+	0.889537i
$57$	5.16515e11			1.99479
$58$	8.88074e10	+	2.40860e11i	0.306314	+	0.830774i
$59$			2.45442e11i			0.757549i	0.925489	+	0.378774i	$0.123654\pi$
$59$			2.45442e11i			0.757549i	−0.925489	+	0.378774i	$0.876346\pi$
$60$	−2.10314e10	+	1.79491e10i	−0.0581950	+	0.0496661i
$61$			2.71473e11i			0.674657i	0.941387	+	0.337328i	$0.109523\pi$
$61$			2.71473e11i			0.674657i	−0.941387	+	0.337328i	$0.890477\pi$
$62$	−2.49170e11	+	9.18715e10i	−0.557122	+	0.205416i
$63$	1.30121e11			0.262201
$64$	−2.86727e11	−	4.69062e11i	−0.521553	−	0.853219i
$65$	−5.98985e10			−0.0985097
$66$	1.69402e11	−	6.24600e10i	0.252280	−	0.0930179i
$67$			6.82198e11i			0.921350i	0.887569	+	0.460675i	$0.152393\pi$
$67$			6.82198e11i			0.921350i	−0.887569	+	0.460675i	$0.847607\pi$
$68$	6.94158e11	−	5.92424e11i	0.851433	−	0.726649i
$69$		−	1.06045e12i		−	1.18297i
$70$	2.36972e10	+	6.42706e10i	0.0240746	+	0.0652943i
$71$	−2.90719e11			−0.269336			−0.134668	−	0.990891i	$-0.542997\pi$
$71$	−2.90719e11			−0.269336			−0.134668	+	0.990891i	$0.542997\pi$
$72$	−1.48649e11	+	2.65088e11i	−0.125748	+	0.224248i
$73$	−1.48745e12			−1.15039			−0.575194	−	0.818017i	$-0.695073\pi$
$73$	−1.48745e12			−1.15039			−0.575194	+	0.818017i	$0.695073\pi$
$74$	−2.64899e11	−	7.18448e11i	−0.187531	−	0.508615i
$75$		−	1.72011e12i		−	1.11598i
$76$	1.94024e12	+	2.27344e12i	1.15496	+	1.35330i
$77$		−	4.47303e11i		−	0.244575i
$78$	−3.02051e12	+	1.11369e12i	−1.51868	+	0.559951i
$79$	1.58653e12			0.734296			0.367148	−	0.930162i	$-0.380334\pi$
$79$	1.58653e12			0.734296			0.367148	+	0.930162i	$0.380334\pi$
$80$	−1.58006e11	−	2.51454e10i	−0.0673888	−	0.0107244i
$81$	−3.02736e12			−1.19100
$82$	3.31740e12	−	1.22316e12i	1.20506	−	0.444316i
$83$		−	7.79952e11i		−	0.261855i	−0.991392	−	0.130927i	$-0.958205\pi$
$83$		−	7.79952e11i		−	0.261855i	0.991392	−	0.130927i	$-0.0417955\pi$
$84$	2.38997e12	+	2.80039e12i	0.742295	+	0.869766i
$85$		−	2.65589e11i		−	0.0763812i
$86$	−6.80935e11	−	1.84681e12i	−0.181495	−	0.492245i
$87$	4.01533e12			0.992765
$88$	9.11260e11	+	5.10994e11i	0.209173	+	0.117295i
$89$	−4.10498e12			−0.875540			−0.437770	−	0.899087i	$-0.644232\pi$
$89$	−4.10498e12			−0.875540			−0.437770	+	0.899087i	$0.644232\pi$
$90$	3.05985e10	+	8.29881e10i	0.00606909	+	0.0164604i
$91$			7.97562e12i			1.47230i
$92$	4.66757e12	−	3.98350e12i	0.802546	−	0.684927i
$93$			4.15387e12i			0.665755i
$94$	−9.77175e12	+	3.60294e12i	−1.46097	+	0.538673i
$95$	8.69829e11			0.121403
$96$	−8.43531e12	+	1.66979e12i	−1.09986	+	0.217720i
$97$	1.11567e13			1.35994			0.679971	−	0.733239i	$-0.261992\pi$
$97$	1.11567e13			1.35994			0.679971	+	0.733239i	$0.261992\pi$
$98$	3.29851e11	−	1.21619e11i	0.0376139	−	0.0138686i
$99$		−	5.77570e11i		−	0.0616561i
$100$	7.57104e12	−	6.46144e12i	0.757104	−	0.646144i
$101$		−	1.76850e13i		−	1.65774i	−0.559444	−	0.828868i	$-0.688985\pi$
$101$		−	1.76850e13i		−	1.65774i	0.559444	−	0.828868i	$-0.311015\pi$
$102$	−4.93809e12	−	1.33929e13i	−0.434168	−	1.17753i
$103$	1.25010e11			0.0103158			0.00515790	−	0.999987i	$-0.498358\pi$
$103$	1.25010e11			0.0103158			0.00515790	+	0.999987i	$0.498358\pi$
$104$	−1.62482e13	−	9.11127e12i	−1.25918	−	0.706094i
$105$	1.07144e12			0.0780259
$106$	5.35984e12	+	1.45368e13i	0.366998	+	0.995358i
$107$		−	5.03372e12i		−	0.324261i	−0.986769	−	0.162130i	$-0.948164\pi$
$107$		−	5.03372e12i		−	0.324261i	0.986769	−	0.162130i	$-0.0518365\pi$
$108$	−8.91716e12	−	1.04485e13i	−0.540720	−	0.633576i
$109$			3.05175e13i			1.74291i	0.490472	+	0.871457i	$0.336825\pi$
$109$			3.05175e13i			1.74291i	−0.490472	+	0.871457i	$0.663175\pi$
$110$	2.85278e11	−	1.05185e11i	0.0153538	−	0.00566110i
$111$	−1.19771e13			−0.607789
$112$	−3.34816e12	+	2.10388e13i	−0.160284	+	1.00717i
$113$	5.08544e12			0.229783			0.114892	−	0.993378i	$-0.463348\pi$
$113$	5.08544e12			0.229783			0.114892	+	0.993378i	$0.463348\pi$
$114$	4.38631e13	−	1.61727e13i	1.87162	−	0.690084i
$115$		−	1.78584e12i		−	0.0719957i
$116$	1.50833e13	+	1.76735e13i	0.574802	+	0.673511i
$117$			1.02984e13i			0.371159i
$118$	7.68509e12	+	2.08432e13i	0.262069	+	0.710774i
$119$	−3.53638e13			−1.14157
$120$	−1.22401e12	+	2.18278e12i	−0.0374201	+	0.0667317i
$121$	3.25373e13			0.942489
$122$	8.50016e12	+	2.30538e13i	0.233393	+	0.633000i
$123$		−	5.53037e13i		−	1.44003i
$124$	−1.82832e13	+	1.56037e13i	−0.451661	+	0.385466i
$125$		−	5.80700e12i		−	0.136156i
$126$	1.10501e13	−	4.07426e12i	0.246012	−	0.0907069i
$127$	−2.64256e13			−0.558858			−0.279429	−	0.960166i	$-0.590145\pi$
$127$	−2.64256e13			−0.558858			−0.279429	+	0.960166i	$0.590145\pi$
$128$	−3.90361e13	−	3.08555e13i	−0.784515	−	0.620109i
$129$	−3.07878e13			−0.588227
$130$	−5.08665e12	+	1.87550e12i	−0.0924272	+	0.0340788i
$131$			7.50964e12i			0.129824i	0.997891	+	0.0649121i	$0.0206767\pi$
$131$			7.50964e12i			0.129824i	−0.997891	+	0.0649121i	$0.979323\pi$
$132$	1.24301e13	−	1.06084e13i	0.204524	−	0.174549i
$133$		−	1.15820e14i		−	1.81446i
$134$	2.13605e13	+	5.79331e13i	0.318735	+	0.864461i
$135$	−3.99764e12			−0.0568375
$136$	4.03992e13	−	7.20443e13i	0.547482	−	0.976330i
$137$	2.25954e13			0.291969			0.145985	−	0.989287i	$-0.453365\pi$
$137$	2.25954e13			0.291969			0.145985	+	0.989287i	$0.453365\pi$
$138$	−3.32041e13	−	9.00549e13i	−0.409240	−	1.10992i
$139$			1.14864e14i			1.35079i	0.737458	+	0.675393i	$0.236026\pi$
$139$			1.14864e14i			1.35079i	−0.737458	+	0.675393i	$0.763974\pi$
$140$	4.02478e12	+	4.71595e12i	0.0451763	+	0.0529342i
$141$			1.62903e14i			1.74584i
$142$	−2.46882e13	+	9.10278e12i	−0.252706	+	0.0931750i
$143$	3.54014e13			0.346208
$144$	−4.32325e12	+	2.71659e13i	−0.0404067	+	0.253903i
$145$	6.76196e12			0.0604200
$146$	−1.26316e14	+	4.65740e13i	−1.07936	+	0.397969i
$147$		−	5.49888e12i		−	0.0449482i
$148$	−4.49910e13	−	5.27171e13i	−0.351904	−	0.412335i
$149$		−	6.70523e13i		−	0.501999i	−0.967987	−	0.251000i	$-0.919241\pi$
$149$		−	6.70523e13i		−	0.501999i	0.967987	−	0.251000i	$-0.0807593\pi$
$150$	−5.38588e13	−	1.46074e14i	−0.386067	−	1.04708i
$151$	2.60422e14			1.78784			0.893918	−	0.448231i	$-0.147946\pi$
$151$	2.60422e14			1.78784			0.893918	+	0.448231i	$0.147946\pi$
$152$	2.35952e14	+	1.32311e14i	1.55182	+	0.870189i
$153$	−4.56627e13			−0.287785
$154$	−1.40056e13	−	3.79855e13i	−0.0846091	−	0.229474i
$155$			6.99527e12i			0.0405180i
$156$	−2.21634e14	+	1.89152e14i	−1.23120	+	1.05075i
$157$			8.89796e13i			0.474179i	0.971488	+	0.237090i	$0.0761935\pi$
$157$			8.89796e13i			0.474179i	−0.971488	+	0.237090i	$0.923806\pi$
$158$	1.34730e14	−	4.96761e13i	0.688958	−	0.254025i
$159$	2.42340e14			1.18944
$160$	−1.42054e13	+	2.81198e12i	−0.0669379	+	0.0132505i
$161$	−2.37789e14			−1.07603
$162$	−2.57087e14	+	9.47904e13i	−1.11746	+	0.412019i
$163$			1.43591e13i			0.0599664i	0.999550	+	0.0299832i	$0.00954538\pi$
$163$			1.43591e13i			0.0599664i	−0.999550	+	0.0299832i	$0.990455\pi$
$164$	2.43419e14	−	2.07744e14i	0.976943	−	0.833764i
$165$		−	4.75582e12i		−	0.0183476i
$166$	−2.44213e13	−	6.62345e13i	−0.0905870	−	0.245687i
$167$	−3.16007e14			−1.12730			−0.563650	−	0.826014i	$-0.690603\pi$
$167$	−3.16007e14			−1.12730			−0.563650	+	0.826014i	$0.690603\pi$
$168$	2.90642e14	+	1.62979e14i	0.997352	+	0.559270i
$169$	−3.28350e14			−1.08411
$170$	−8.31592e12	−	2.25541e13i	−0.0264236	−	0.0716651i
$171$		−	1.49550e14i		−	0.457416i
$172$	−1.15652e14	−	1.35512e14i	−0.340578	−	0.399064i
$173$		−	5.70549e14i		−	1.61805i	−0.587771	−	0.809027i	$-0.699994\pi$
$173$		−	5.70549e14i		−	1.61805i	0.587771	−	0.809027i	$-0.300006\pi$
$174$	3.40987e14	−	1.25725e14i	0.931467	−	0.343441i
$175$	−3.85705e14			−1.01510
$176$	9.33851e13	+	1.48615e13i	0.236835	+	0.0376904i
$177$	3.47473e14			0.849367
$178$	−3.48600e14	+	1.28532e14i	−0.821480	+	0.302888i
$179$			3.77361e13i			0.0857456i	0.999081	+	0.0428728i	$0.0136510\pi$
$179$			3.77361e13i			0.0857456i	−0.999081	+	0.0428728i	$0.986349\pi$
$180$	5.19692e12	+	6.08937e12i	0.0113887	+	0.0133445i
$181$		−	1.46717e14i		−	0.310148i	−0.987903	−	0.155074i	$-0.950438\pi$
$181$		−	1.46717e14i		−	0.310148i	0.987903	−	0.155074i	$-0.0495616\pi$
$182$	2.49727e14	+	6.77299e14i	0.509332	+	1.38139i
$183$	3.84326e14			0.756428
$184$	2.71647e14	−	4.84431e14i	0.516047	−	0.920272i
$185$	−2.01699e13			−0.0369902
$186$	1.30063e14	+	3.52752e14i	0.230314	+	0.624648i
$187$			1.56969e14i			0.268438i
$188$	−7.17016e14	+	6.11931e14i	−1.18441	+	1.01083i
$189$			5.32296e14i			0.849476i
$190$	7.38669e13	−	2.72354e13i	0.113907	−	0.0419987i
$191$	−5.17437e14			−0.771153			−0.385576	−	0.922676i	$-0.625997\pi$
$191$	−5.17437e14			−0.771153			−0.385576	+	0.922676i	$0.625997\pi$
$192$	−6.64054e14	+	4.05921e14i	−0.956633	+	0.584767i
$193$	8.13631e14			1.13320			0.566598	−	0.823995i	$-0.308259\pi$
$193$	8.13631e14			1.13320			0.566598	+	0.823995i	$0.308259\pi$
$194$	9.47443e14	−	3.49331e14i	1.27597	−	0.470464i
$195$			8.47986e13i			0.110449i
$196$	2.42033e13	−	2.06561e13i	0.0304937	−	0.0260246i
$197$			1.27500e15i			1.55410i	0.629439	+	0.777050i	$0.283285\pi$
$197$			1.27500e15i			1.55410i	−0.629439	+	0.777050i	$0.716715\pi$
$198$	−1.80844e13	−	4.90479e13i	−0.0213295	−	0.0578491i
$199$	−1.93695e14			−0.221092			−0.110546	−	0.993871i	$-0.535260\pi$
$199$	−1.93695e14			−0.221092			−0.110546	+	0.993871i	$0.535260\pi$
$200$	4.40626e14	−	7.85772e14i	0.486827	−	0.868164i
$201$	9.65792e14			1.03302
$202$	−5.53739e14	−	1.50183e15i	−0.573484	−	1.55538i
$203$		−	9.00371e14i		−	0.903020i
$204$	−8.38697e14	−	9.82723e14i	−0.814721	−	0.954630i
$205$		−	9.31334e13i		−	0.0876406i
$206$	1.06160e13	−	3.91422e12i	0.00967886	−	0.00356869i
$207$	−3.07040e14			−0.271261
$208$	−1.66510e15	−	2.64988e14i	−1.42570	−	0.226890i
$209$	−5.14090e14			−0.426666
$210$	9.09882e13	−	3.35482e13i	0.0732082	−	0.0269926i
$211$		−	7.41305e14i		−	0.578310i	−0.957282	−	0.289155i	$-0.906626\pi$
$211$		−	7.41305e14i		−	0.578310i	0.957282	−	0.289155i	$-0.0933743\pi$
$212$	9.10328e14	+	1.06666e15i	0.688676	+	0.806939i
$213$			4.11572e14i			0.301980i
$214$	−1.57612e14	−	4.27469e14i	−0.112176	−	0.304239i
$215$	−5.18477e13			−0.0357997
$216$	−1.08441e15	−	6.08089e14i	−0.726515	−	0.407397i
$217$	9.31436e14			0.605571
$218$	9.55540e14	+	2.59158e15i	0.602950	+	1.63530i
$219$			2.10579e15i			1.28982i
$220$	2.09327e13	−	1.78648e13i	0.0124474	−	0.0106231i
$221$		−	2.79884e15i		−	1.61595i
$222$	−1.01711e15	+	3.75018e14i	−0.570261	+	0.210261i
$223$	7.76195e14			0.422658			0.211329	−	0.977415i	$-0.432221\pi$
$223$	7.76195e14			0.422658			0.211329	+	0.977415i	$0.432221\pi$
$224$	3.74422e14	+	1.89148e15i	0.198038	+	1.00043i
$225$	−4.98034e14			−0.255901
$226$	4.31862e14	−	1.59231e14i	0.215595	−	0.0794921i
$227$		−	2.58078e14i		−	0.125194i	−0.998039	−	0.0625968i	$-0.980062\pi$
$227$		−	2.58078e14i		−	0.125194i	0.998039	−	0.0625968i	$-0.0199382\pi$
$228$	3.21851e15	−	2.74681e15i	1.51733	−	1.29495i
$229$			1.51272e15i			0.693151i	0.938022	+	0.346575i	$0.112656\pi$
$229$			1.51272e15i			0.693151i	−0.938022	+	0.346575i	$0.887344\pi$
$230$	−5.59169e13	−	1.51656e14i	−0.0249064	−	0.0675503i
$231$	−6.33249e14			−0.274218
$232$	1.83427e15	+	1.02857e15i	0.772308	+	0.433076i
$233$	−2.03207e15			−0.832002			−0.416001	−	0.909364i	$-0.636569\pi$
$233$	−2.03207e15			−0.832002			−0.416001	+	0.909364i	$0.636569\pi$
$234$	3.22454e14	+	8.74548e14i	0.128400	+	0.348242i
$235$			2.74334e14i			0.106252i
$236$	1.30525e15	+	1.52940e15i	0.491776	+	0.576227i
$237$		−	2.24605e15i		−	0.823296i
$238$	−3.00313e15	+	1.10728e15i	−1.07109	+	0.394920i
$239$	−2.38480e15			−0.827687			−0.413844	−	0.910348i	$-0.635814\pi$
$239$	−2.38480e15			−0.827687			−0.413844	+	0.910348i	$0.635814\pi$
$240$	−3.55984e13	+	2.23689e14i	−0.0120242	+	0.0755566i
$241$	−3.98380e15			−1.30975			−0.654873	−	0.755739i	$-0.727278\pi$
$241$	−3.98380e15			−1.30975			−0.654873	+	0.755739i	$0.727278\pi$
$242$	2.76310e15	−	1.01878e15i	0.884295	−	0.326048i
$243$			1.61249e15i			0.502409i
$244$	1.44369e15	+	1.69161e15i	0.437965	+	0.513175i
$245$		−	9.26031e12i		−	0.00273556i
$246$	−1.73163e15	−	4.69646e15i	−0.498169	−	1.35111i
$247$	9.16647e15			2.56846
$248$	−1.06406e15	+	1.89755e15i	−0.290423	+	0.517915i
$249$	−1.10418e15			−0.293593
$250$	−1.81824e14	−	4.93137e14i	−0.0471023	−	0.127749i
$251$		−	6.79110e15i		−	1.71420i	−0.515151	−	0.857099i	$-0.672264\pi$
$251$		−	6.79110e15i		−	1.71420i	0.515151	−	0.857099i	$-0.327736\pi$
$252$	8.10813e14	−	6.91982e14i	0.199442	−	0.170212i
$253$			1.05547e15i			0.253025i
$254$	−2.24410e15	+	8.27420e14i	−0.524351	+	0.193333i
$255$	−3.75995e14			−0.0856390
$256$	−4.28112e15	−	1.39802e15i	−0.950599	−	0.310423i
$257$	−7.36721e14			−0.159492			−0.0797458	−	0.996815i	$-0.525411\pi$
$257$	−7.36721e14			−0.159492			−0.0797458	+	0.996815i	$0.525411\pi$
$258$	−2.61453e15	+	9.64003e14i	−0.551907	+	0.203493i
$259$			2.68567e15i			0.552845i
$260$	−3.73240e14	+	3.18539e14i	−0.0749310	+	0.0639492i
$261$		−	1.16258e15i		−	0.227647i
$262$	2.35136e14	+	6.37728e14i	0.0449119	+	0.121808i
$263$	4.33694e14			0.0808110			0.0404055	−	0.999183i	$-0.487135\pi$
$263$	4.33694e14			0.0808110			0.0404055	+	0.999183i	$0.487135\pi$
$264$	7.23417e14	−	1.29008e15i	0.131511	−	0.234525i
$265$	4.08108e14			0.0723898
$266$	−3.62646e15	−	9.83555e15i	−0.627700	−	1.70243i
$267$			5.81144e15i			0.981660i
$268$	3.62791e15	+	4.25092e15i	0.598110	+	0.700821i
$269$			3.36599e15i			0.541655i	0.962628	+	0.270827i	$0.0872973\pi$
$269$			3.36599e15i			0.541655i	−0.962628	+	0.270827i	$0.912703\pi$
$270$	−3.39485e14	+	1.25171e14i	−0.0533280	+	0.0196626i
$271$	−8.64352e14			−0.132553			−0.0662766	−	0.997801i	$-0.521112\pi$
$271$	−8.64352e14			−0.132553			−0.0662766	+	0.997801i	$0.521112\pi$
$272$	1.17495e15	−	7.38303e15i	0.175923	−	1.10544i
$273$	1.12911e16			1.65075
$274$	1.91883e15	−	7.07491e14i	0.273942	−	0.101005i
$275$			1.71203e15i			0.238698i
$276$	−5.63946e15	−	6.60791e15i	−0.767943	−	0.899818i
$277$			4.29153e15i			0.570813i	0.958407	+	0.285407i	$0.0921286\pi$
$277$			4.29153e15i			0.570813i	−0.958407	+	0.285407i	$0.907871\pi$
$278$	3.59653e15	+	9.75436e15i	0.467296	+	1.26738i
$279$	1.20270e15			0.152661
$280$	4.89452e14	+	2.74463e14i	0.0606991	+	0.0340374i
$281$	−1.75304e14			−0.0212422			−0.0106211	−	0.999944i	$-0.503381\pi$
$281$	−1.75304e14			−0.0212422			−0.0106211	+	0.999944i	$0.503381\pi$
$282$	5.10070e15	+	1.38339e16i	0.603963	+	1.63805i
$283$			1.04579e16i			1.21013i	0.796177	+	0.605064i	$0.206853\pi$
$283$			1.04579e16i			1.21013i	−0.796177	+	0.605064i	$0.793147\pi$
$284$	−1.81153e15	+	1.54604e15i	−0.204869	+	0.174844i
$285$		−	1.23142e15i		−	0.136118i
$286$	3.00633e15	−	1.10846e15i	0.324831	−	0.119768i
$287$	−1.24009e16			−1.30985
$288$	4.83464e14	+	2.44233e15i	0.0499244	+	0.252205i
$289$	2.50543e15			0.252956
$290$	5.74234e14	−	2.11725e14i	0.0566894	−	0.0209019i
$291$		−	1.57946e16i		−	1.52477i
$292$	−9.26862e15	+	7.91023e15i	−0.875038	+	0.746794i
$293$		−	1.28392e16i		−	1.18549i	−0.805390	−	0.592745i	$-0.798044\pi$
$293$		−	1.28392e16i		−	1.18549i	0.805390	−	0.592745i	$-0.201956\pi$
$294$	−1.72177e14	−	4.66972e14i	−0.0155495	−	0.0421729i
$295$	5.85157e14			0.0516927
$296$	−5.47133e15	−	3.06808e15i	−0.472821	−	0.265137i
$297$	2.36270e15			0.199753
$298$	−2.09949e15	−	5.69416e15i	−0.173664	−	0.471004i
$299$		−	1.88196e16i		−	1.52317i
$300$	−9.14750e15	−	1.07184e16i	−0.724460	−	0.848868i
$301$			6.90364e15i			0.535052i
$302$	2.21153e16	−	8.15414e15i	1.67745	−	0.618490i
$303$	−2.50367e16			−1.85866
$304$	2.41802e16	+	3.84808e15i	1.75704	+	0.279619i
$305$	6.47218e14			0.0460364
$306$	−3.87773e15	+	1.42976e15i	−0.270015	+	0.0995572i
$307$		−	8.53937e15i		−	0.582139i	−0.956702	−	0.291069i	$-0.905989\pi$
$307$		−	8.53937e15i		−	0.582139i	0.956702	−	0.291069i	$-0.0940110\pi$
$308$	−2.37874e15	−	2.78724e15i	−0.158770	−	0.186035i
$309$		−	1.76977e14i		−	0.0115661i
$310$	2.19031e14	+	5.94046e14i	0.0140170	+	0.0380163i
$311$	3.52686e15			0.221027			0.110513	−	0.993875i	$-0.464750\pi$
$311$	3.52686e15			0.221027			0.110513	+	0.993875i	$0.464750\pi$
$312$	−1.28989e16	+	2.30027e16i	−0.791675	+	1.41180i
$313$	−1.00518e16			−0.604234			−0.302117	−	0.953271i	$-0.597693\pi$
$313$	−1.00518e16			−0.604234			−0.302117	+	0.953271i	$0.597693\pi$
$314$	2.78606e15	+	7.55625e15i	0.164039	+	0.444901i
$315$		−	3.10222e14i		−	0.0178918i
$316$	9.88599e15	−	8.43711e15i	0.558540	−	0.476681i
$317$			3.13051e16i			1.73273i	0.499414	+	0.866363i	$0.333549\pi$
$317$			3.13051e16i			1.73273i	−0.499414	+	0.866363i	$0.666451\pi$
$318$	2.05798e16	−	7.58795e15i	1.11600	−	0.411480i
$319$	−3.99648e15			−0.212343
$320$	−1.11829e15	+	6.83584e14i	−0.0582209	+	0.0355891i
$321$	−7.12626e15			−0.363562
$322$	−2.01933e16	+	7.44546e15i	−1.00959	+	0.372245i
$323$			4.06440e16i			1.99150i
$324$	−1.88641e16	+	1.60994e16i	−0.905928	+	0.773157i
$325$		−	3.05264e16i		−	1.43692i
$326$	4.49602e14	+	1.21939e15i	0.0207450	+	0.0562638i
$327$	4.32037e16			1.95416
$328$	1.41667e16	−	2.52636e16i	0.628186	−	1.12025i
$329$	3.65282e16			1.58802
$330$	−1.48911e14	−	4.03870e14i	−0.00634724	−	0.0172148i
$331$		−	4.89913e15i		−	0.204756i	−0.994746	−	0.102378i	$-0.967355\pi$
$331$		−	4.89913e15i		−	0.204756i	0.994746	−	0.102378i	$-0.0326452\pi$
$332$	−4.14777e15	−	4.86005e15i	−0.169987	−	0.199179i
$333$			3.46781e15i			0.139369i
$334$	−2.68357e16	+	9.89457e15i	−1.05770	+	0.389982i
$335$	1.62643e15			0.0628700
$336$	2.97848e16	+	4.74001e15i	1.12925	+	0.179711i
$337$	−2.53208e16			−0.941636			−0.470818	−	0.882230i	$-0.656041\pi$
$337$	−2.53208e16			−0.941636			−0.470818	+	0.882230i	$0.656041\pi$
$338$	−2.78838e16	+	1.02810e16i	−1.01717	+	0.375041i
$339$		−	7.19948e15i		−	0.257634i
$340$	−1.41239e15	−	1.65494e15i	−0.0495842	−	0.0580991i
$341$		−	4.13437e15i		−	0.142399i
$342$	−4.68259e15	−	1.26999e16i	−0.158240	−	0.429173i
$343$	2.95242e16			0.978963
$344$	−1.40643e16	−	7.88664e15i	−0.457603	−	0.256603i
$345$	−2.52822e15			−0.0807218
$346$	−1.78646e16	−	4.84517e16i	−0.559756	−	1.51815i
$347$			5.14894e16i			1.58335i	0.610943	+	0.791674i	$0.290790\pi$
$347$			5.14894e16i			1.58335i	−0.610943	+	0.791674i	$0.709210\pi$
$348$	2.50204e16	−	2.13534e16i	0.755143	−	0.644470i
$349$		−	3.91636e16i		−	1.16016i	−0.814560	−	0.580079i	$-0.803022\pi$
$349$		−	3.91636e16i		−	1.16016i	0.814560	−	0.580079i	$-0.196978\pi$
$350$	−3.27546e16	+	1.20769e16i	−0.952422	+	0.351167i
$351$	−4.21282e16			−1.20248
$352$	8.39571e15	−	1.66195e15i	0.235250	−	0.0465683i
$353$	1.84699e15			0.0508077			0.0254038	−	0.999677i	$-0.491913\pi$
$353$	1.84699e15			0.0508077			0.0254038	+	0.999677i	$0.491913\pi$
$354$	2.95079e16	−	1.08798e16i	0.796923	−	0.293833i
$355$			6.93102e14i			0.0183786i
$356$	−2.55790e16	+	2.18302e16i	−0.665976	+	0.568372i
$357$			5.00647e16i			1.27994i
$358$	1.18156e15	+	3.20459e15i	0.0296631	+	0.0804512i
$359$	6.56490e16			1.61850			0.809252	−	0.587461i	$-0.199872\pi$
$359$	6.56490e16			1.61850			0.809252	+	0.587461i	$0.199872\pi$
$360$	6.31994e14	+	3.54394e14i	0.0153019	+	0.00858065i
$361$	−9.10600e16			−2.16536
$362$	−4.59389e15	−	1.24594e16i	−0.107294	−	0.290998i
$363$		−	4.60632e16i		−	1.05672i
$364$	4.24142e16	+	4.96978e16i	0.955767	+	1.11990i
$365$			3.54623e15i			0.0784988i
$366$	3.26374e16	−	1.20337e16i	0.709723	−	0.261682i
$367$	6.75272e15			0.144261			0.0721305	−	0.997395i	$-0.477020\pi$
$367$	6.75272e15			0.144261			0.0721305	+	0.997395i	$0.477020\pi$
$368$	7.90047e15	−	4.96441e16i	0.165822	−	1.04197i
$369$	−1.60124e16			−0.330207
$370$	−1.71285e15	+	6.31544e14i	−0.0347063	+	0.0127965i
$371$		−	5.43406e16i		−	1.08192i
$372$	2.20902e16	+	2.58837e16i	0.432186	+	0.506404i
$373$		−	6.35460e16i		−	1.22175i	−0.791729	−	0.610873i	$-0.790819\pi$
$373$		−	6.35460e16i		−	1.22175i	0.791729	−	0.610873i	$-0.209181\pi$
$374$	4.91491e15	+	1.33300e16i	0.0928645	+	0.251864i
$375$	−8.22099e15			−0.152659
$376$	−4.17295e16	+	7.44166e16i	−0.761592	+	1.35815i
$377$	7.12592e16			1.27827
$378$	1.66668e16	+	4.52032e16i	0.293871	+	0.797025i
$379$			1.76761e16i			0.306360i	0.988198	+	0.153180i	$0.0489515\pi$
$379$			1.76761e16i			0.306360i	−0.988198	+	0.153180i	$0.951048\pi$
$380$	5.42009e15	−	4.62573e15i	0.0923449	−	0.0788110i
$381$			3.74109e16i			0.626594i
$382$	−4.39413e16	+	1.62016e16i	−0.723538	+	0.266775i
$383$	−1.13626e17			−1.83944			−0.919718	−	0.392580i	$-0.871583\pi$
$383$	−1.13626e17			−1.83944			−0.919718	+	0.392580i	$0.871583\pi$
$384$	−4.36823e16	+	5.52636e16i	−0.695269	+	0.879602i
$385$	−1.06641e15			−0.0166890
$386$	6.90945e16	−	2.54758e16i	1.06323	−	0.392022i
$387$			8.91417e15i			0.134884i
$388$	6.95199e16	−	5.93312e16i	1.03444	−	0.882830i
$389$			5.13314e16i			0.751122i	0.926798	+	0.375561i	$0.122550\pi$
$389$			5.13314e16i			0.751122i	−0.926798	+	0.375561i	$0.877450\pi$
$390$	2.65515e15	+	7.20120e15i	0.0382093	+	0.103630i
$391$	8.34458e16			1.18102
$392$	1.40860e15	−	2.51197e15i	0.0196078	−	0.0349668i
$393$	1.06314e16			0.145560
$394$	3.99218e16	+	1.08274e17i	0.537631	+	1.45814i
$395$		−	3.78243e15i		−	0.0501061i
$396$	−3.07150e15	−	3.59896e15i	−0.0400251	−	0.0468984i
$397$		−	6.00314e16i		−	0.769556i	−0.923009	−	0.384778i	$-0.874278\pi$
$397$		−	6.00314e16i		−	0.769556i	0.923009	−	0.384778i	$-0.125722\pi$
$398$	−1.64488e16	+	6.06484e15i	−0.207441	+	0.0764855i
$399$	−1.63967e17			−2.03438
$400$	1.28150e16	−	8.05252e16i	0.156433	−	0.982974i
$401$	1.01141e17			1.21475			0.607376	−	0.794415i	$-0.292222\pi$
$401$	1.01141e17			1.21475			0.607376	+	0.794415i	$0.292222\pi$
$402$	8.20162e16	−	3.02401e16i	0.969237	−	0.357367i
$403$			7.37178e16i			0.857215i
$404$	−9.40483e16	−	1.10199e17i	−1.07615	−	1.26095i
$405$			7.21752e15i			0.0812700i
$406$	−2.81917e16	−	7.64605e16i	−0.312394	−	0.847263i
$407$	1.19209e16			0.130000
$408$	−1.01993e17	−	5.71934e16i	−1.09466	−	0.613839i
$409$	−7.36411e16			−0.777891			−0.388945	−	0.921261i	$-0.627161\pi$
$409$	−7.36411e16			−0.777891			−0.388945	+	0.921261i	$0.627161\pi$
$410$	−2.91612e15	−	7.90899e15i	−0.0303187	−	0.0822292i
$411$		−	3.19885e16i		−	0.327357i
$412$	7.78964e14	−	6.64801e14i	0.00784667	−	0.00669668i
$413$		−	7.79151e16i		−	0.772585i
$414$	−2.60742e16	+	9.61379e15i	−0.254512	+	0.0938410i
$415$	−1.85948e15			−0.0178681
$416$	−1.49700e17	+	2.96333e16i	−1.41616	+	0.280333i
$417$	1.62613e17			1.51451
$418$	−4.36571e16	+	1.60968e16i	−0.400322	+	0.147602i
$419$		−	2.79559e16i		−	0.252396i	−0.992005	−	0.126198i	$-0.959723\pi$
$419$		−	2.79559e16i		−	0.252396i	0.992005	−	0.126198i	$-0.0402775\pi$
$420$	6.67639e15	−	5.69791e15i	0.0593501	−	0.0506518i
$421$			1.82667e17i			1.59892i	0.600718	+	0.799461i	$0.294882\pi$
$421$			1.82667e17i			1.59892i	−0.600718	+	0.799461i	$0.705118\pi$
$422$	−2.32112e16	−	6.29525e16i	−0.200063	−	0.542602i
$423$	4.71663e16			0.400331
$424$	1.10704e17	+	6.20781e16i	0.925309	+	0.518872i
$425$	1.35353e17			1.11414
$426$	1.28868e16	+	3.49512e16i	0.104468	+	0.283335i
$427$		−	8.61786e16i		−	0.688047i
$428$	−2.67692e16	−	3.13661e16i	−0.210499	−	0.246647i
$429$		−	5.01180e16i		−	0.388169i
$430$	−4.40296e15	+	1.62341e15i	−0.0335892	+	0.0123847i
$431$	−3.02335e16			−0.227189			−0.113594	−	0.993527i	$-0.536236\pi$
$431$	−3.02335e16			−0.227189			−0.113594	+	0.993527i	$0.536236\pi$
$432$	−1.11129e17	−	1.76854e16i	−0.822593	−	0.130909i
$433$	−8.25641e16			−0.602033			−0.301016	−	0.953619i	$-0.597326\pi$
$433$	−8.25641e16			−0.602033			−0.301016	+	0.953619i	$0.597326\pi$
$434$	7.90987e16	−	2.91644e16i	0.568180	−	0.209493i
$435$		−	9.57294e15i		−	0.0677431i
$436$	1.62291e17	+	1.90161e17i	1.13144	+	1.32574i
$437$			2.73293e17i			1.87715i
$438$	6.59350e16	+	1.78826e17i	0.446205	+	1.21018i
$439$	1.89165e17			1.26131			0.630653	−	0.776065i	$-0.282787\pi$
$439$	1.89165e17			1.26131			0.630653	+	0.776065i	$0.282787\pi$
$440$	1.21826e15	−	2.17253e15i	0.00800382	−	0.0142733i
$441$	−1.59213e15			−0.0103069
$442$	−8.76352e16	−	2.37681e17i	−0.559028	−	1.51617i
$443$			1.83331e17i			1.15242i	0.817301	+	0.576210i	$0.195469\pi$
$443$			1.83331e17i			1.15242i	−0.817301	+	0.576210i	$0.804531\pi$
$444$	−7.46319e16	+	6.36940e16i	−0.462312	+	0.394556i
$445$			9.78667e15i			0.0597441i
$446$	6.59154e16	−	2.43036e16i	0.396561	−	0.146216i
$447$	−9.49263e16			−0.562844
$448$	9.10208e16	+	1.48903e17i	0.531904	+	0.870153i
$449$	−3.31235e17			−1.90781			−0.953904	−	0.300111i	$-0.902976\pi$
$449$	−3.31235e17			−1.90781			−0.953904	+	0.300111i	$0.902976\pi$
$450$	−4.22936e16	+	1.55941e16i	−0.240101	+	0.0885275i
$451$			5.50441e16i			0.308009i
$452$	3.16884e16	−	2.70442e16i	0.174784	−	0.149168i
$453$		−	3.68681e17i		−	2.00453i
$454$	−8.08073e15	−	2.19163e16i	−0.0433100	−	0.117464i
$455$	1.90147e16			0.100465
$456$	1.87314e17	−	3.34038e17i	0.975660	−	1.73990i
$457$	−1.50721e17			−0.773961			−0.386980	−	0.922088i	$-0.626482\pi$
$457$	−1.50721e17			−0.773961			−0.386980	+	0.922088i	$0.626482\pi$
$458$	4.73651e16	+	1.28462e17i	0.239791	+	0.650352i
$459$		−	1.86795e17i		−	0.932361i
$460$	−9.49705e15	−	1.11279e16i	−0.0467372	−	0.0547632i
$461$		−	1.21235e17i		−	0.588261i	−0.955765	−	0.294131i	$-0.904970\pi$
$461$		−	1.21235e17i		−	0.588261i	0.955765	−	0.294131i	$-0.0950301\pi$
$462$	−5.37762e16	+	1.98278e16i	−0.257287	+	0.0948641i
$463$	−8.74764e15			−0.0412681			−0.0206340	−	0.999787i	$-0.506568\pi$
$463$	−8.74764e15			−0.0412681			−0.0206340	+	0.999787i	$0.506568\pi$
$464$	1.87974e17	+	2.99146e16i	0.874442	+	0.139161i
$465$	9.90324e15			0.0454290
$466$	−1.72565e17	+	6.36265e16i	−0.780630	+	0.287826i
$467$		−	2.95016e17i		−	1.31609i	−0.752978	−	0.658045i	$-0.771383\pi$
$467$		−	2.95016e17i		−	1.31609i	0.752978	−	0.658045i	$-0.228617\pi$
$468$	5.47664e16	+	6.41712e16i	0.240944	+	0.282320i
$469$		−	2.16562e17i		−	0.939636i
$470$	8.58975e15	+	2.32968e16i	0.0367574	+	0.0996919i
$471$	1.25969e17			0.531652
$472$	1.58731e17	+	8.90094e16i	0.660753	+	0.370521i
$473$	3.06432e16			0.125816
$474$	−7.03268e16	−	1.90738e17i	−0.284814	−	0.772462i
$475$			4.43295e17i			1.77086i
$476$	−2.20359e17	+	1.88064e17i	−0.868332	+	0.741071i
$477$		−	7.01661e16i		−	0.272746i
$478$	−2.02520e17	+	7.46712e16i	−0.776582	+	0.286333i
$479$	−2.73322e17			−1.03394			−0.516969	−	0.856004i	$-0.672940\pi$
$479$	−2.73322e17			−1.03394			−0.516969	+	0.856004i	$0.672940\pi$
$480$	3.98093e15	+	2.01106e16i	0.0148565	+	0.0750511i
$481$	−2.12555e17			−0.782579
$482$	−3.38309e17	+	1.24738e17i	−1.22888	+	0.453098i
$483$			3.36639e17i			1.20645i
$484$	2.02747e17	−	1.73032e17i	0.716900	−	0.611833i
$485$		−	2.65987e16i		−	0.0927982i
$486$	5.04892e16	+	1.36935e17i	0.173805	+	0.471387i
$487$	5.51673e17			1.87389			0.936943	−	0.349482i	$-0.113642\pi$
$487$	5.51673e17			1.87389			0.936943	+	0.349482i	$0.113642\pi$
$488$	1.75566e17	+	9.84496e16i	0.588453	+	0.329978i
$489$	2.03283e16			0.0672346
$490$	−2.89952e14	−	7.86397e14i	−0.000946349	−	0.00256665i
$491$		−	4.05694e17i		−	1.30668i	−0.757065	−	0.653340i	$-0.773367\pi$
$491$		−	4.05694e17i		−	1.30668i	0.757065	−	0.653340i	$-0.226633\pi$
$492$	−2.94104e17	−	3.44609e17i	−0.934819	−	1.09535i
$493$			3.15962e17i			0.991128i
$494$	7.78428e17	−	2.87014e17i	2.40987	−	0.888541i
$495$	−1.37698e15			−0.00420721
$496$	−3.09467e16	+	1.94460e17i	−0.0933220	+	0.586406i
$497$	9.22882e16			0.274682
$498$	−9.37685e16	+	3.45733e16i	−0.275465	+	0.101567i
$499$		−	4.14431e16i		−	0.120171i	−0.998193	−	0.0600853i	$-0.980863\pi$
$499$		−	4.14431e16i		−	0.120171i	0.998193	−	0.0600853i	$-0.0191373\pi$
$500$	−3.08815e16	−	3.61846e16i	−0.0883879	−	0.103566i
$501$			4.47373e17i			1.26393i
$502$	−2.12638e17	−	5.76709e17i	−0.593016	−	1.60836i
$503$	−2.67191e16			−0.0735579			−0.0367789	−	0.999323i	$-0.511710\pi$
$503$	−2.67191e16			−0.0735579			−0.0367789	+	0.999323i	$0.511710\pi$
$504$	4.71884e16	−	8.41515e16i	0.128244	−	0.228698i
$505$	−4.21627e16			−0.113119
$506$	3.30482e16	+	8.96321e16i	0.0875325	+	0.237402i
$507$			4.64846e17i			1.21551i
$508$	−1.64664e17	+	1.40531e17i	−0.425093	+	0.362792i
$509$			2.27992e17i			0.581104i	0.956859	+	0.290552i	$0.0938389\pi$
$509$			2.27992e17i			0.581104i	−0.956859	+	0.290552i	$0.906161\pi$
$510$	−3.19300e16	+	1.17729e16i	−0.0803512	+	0.0296263i
$511$	4.72188e17			1.17322
$512$	−4.07331e17	+	1.53257e16i	−0.999293	+	0.0375980i
$513$	6.11773e17			1.48193
$514$	−6.25632e16	+	2.30676e16i	−0.149644	+	0.0551751i
$515$		−	2.98036e14i		−	0.000703918i
$516$	−1.91845e17	+	1.63729e17i	−0.447433	+	0.381858i
$517$		−	1.62138e17i		−	0.373419i
$518$	8.40915e16	+	2.28070e17i	0.191253	+	0.518710i
$519$	−8.07729e17			−1.81417
$520$	−2.17221e16	+	3.87373e16i	−0.0481816	+	0.0859226i
$521$	2.69956e17			0.591355			0.295678	−	0.955288i	$-0.404455\pi$
$521$	2.69956e17			0.591355			0.295678	+	0.955288i	$0.404455\pi$
$522$	−3.64020e16	−	9.87281e16i	−0.0787529	−	0.213591i
$523$		−	8.10541e17i		−	1.73187i	−0.500161	−	0.865933i	$-0.666726\pi$
$523$		−	8.10541e17i		−	1.73187i	0.500161	−	0.865933i	$-0.333274\pi$
$524$	3.99361e16	+	4.67942e16i	0.0842776	+	0.0987503i
$525$			5.46045e17i			1.13813i
$526$	3.68298e16	−	1.35795e16i	0.0758214	−	0.0279561i
$527$	−3.26864e17			−0.664657
$528$	2.10395e16	−	1.32206e17i	0.0422586	−	0.265540i
$529$	5.70597e16			0.113205
$530$	3.46570e16	−	1.27784e16i	0.0679201	−	0.0250428i
$531$		−	1.00606e17i		−	0.194765i
$532$	−6.15927e17	−	7.21698e17i	−1.17789	−	1.38016i
$533$		−	9.81462e17i		−	1.85416i
$534$	1.81964e17	+	4.93515e17i	0.339599	+	0.921047i
$535$	−1.20009e16			−0.0221265
$536$	4.41188e17	+	2.47399e17i	0.803624	+	0.450637i
$537$	5.34231e16			0.0961383
$538$	1.05393e17	+	2.85844e17i	0.187382	+	0.508210i
$539$			5.47307e15i			0.00961399i
$540$	−2.49102e16	+	2.12594e16i	−0.0432332	+	0.0368970i
$541$		−	3.09047e17i		−	0.529959i	−0.964254	−	0.264980i	$-0.914635\pi$
$541$		−	3.09047e17i		−	0.529959i	0.964254	−	0.264980i	$-0.0853653\pi$
$542$	−7.34018e16	+	2.70639e16i	−0.124369	+	0.0458559i
$543$	−2.07708e17			−0.347739
$544$	−1.31394e17	−	6.63765e17i	−0.217361	−	1.09805i
$545$	7.27565e16			0.118931
$546$	9.58856e17	−	3.53539e17i	1.54882	−	0.571065i
$547$			4.33397e17i			0.691780i	0.938275	+	0.345890i	$0.112423\pi$
$547$			4.33397e17i			0.691780i	−0.938275	+	0.345890i	$0.887577\pi$
$548$	1.40797e17	−	1.20162e17i	0.222085	−	0.189537i
$549$		−	1.11276e17i		−	0.173453i
$550$	5.36059e16	+	1.45388e17i	0.0825762	+	0.223960i
$551$	−1.03481e18			−1.57534
$552$	−6.85812e17	−	3.84573e17i	−1.03181	−	0.578594i
$553$	−5.03640e17			−0.748871
$554$	1.34373e17	+	3.64442e17i	0.197469	+	0.535568i
$555$			2.85546e16i			0.0414736i
$556$	6.10843e17	+	7.15740e17i	0.876886	+	1.02747i
$557$			3.35954e17i			0.476674i	0.971183	+	0.238337i	$0.0766022\pi$
$557$			3.35954e17i			0.476674i	−0.971183	+	0.238337i	$0.923398\pi$
$558$	1.02134e17	−	3.76580e16i	0.143235	−	0.0528122i
$559$	−5.46383e17			−0.757392
$560$	5.01586e16	+	7.98235e15i	0.0687263	+	0.0109373i
$561$	2.22222e17			0.300974
$562$	−1.48870e16	+	5.48898e15i	−0.0199306	+	0.00734861i
$563$		−	4.77847e17i		−	0.632389i	−0.948694	−	0.316195i	$-0.897595\pi$
$563$		−	4.77847e17i		−	0.632389i	0.948694	−	0.316195i	$-0.102405\pi$
$564$	8.66314e17	+	1.01508e18i	1.13334	+	1.32797i
$565$		−	1.21242e16i		−	0.0156797i
$566$	3.27449e17	+	8.88095e17i	0.418636	+	1.13541i
$567$	9.61029e17			1.21464
$568$	−1.05429e17	+	1.88013e17i	−0.131733	+	0.234921i
$569$	−3.86358e16			−0.0477265			−0.0238633	−	0.999715i	$-0.507597\pi$
$569$	−3.86358e16			−0.0477265			−0.0238633	+	0.999715i	$0.507597\pi$
$570$	−3.85573e16	−	1.04574e17i	−0.0470891	−	0.127713i
$571$			8.78096e17i			1.06025i	0.847920	+	0.530124i	$0.177855\pi$
$571$			8.78096e17i			1.06025i	−0.847920	+	0.530124i	$0.822145\pi$
$572$	2.20594e17	−	1.88264e17i	0.263341	−	0.224747i
$573$			7.32538e17i			0.864619i
$574$	−1.05310e18	+	3.88288e17i	−1.22897	+	0.453135i
$575$	9.10126e17			1.05017
$576$	1.17529e17	+	1.92268e17i	0.134090	+	0.219361i
$577$	3.37219e17			0.380425			0.190213	−	0.981743i	$-0.439082\pi$
$577$	3.37219e17			0.380425			0.190213	+	0.981743i	$0.439082\pi$
$578$	2.12764e17	−	7.84480e16i	0.237338	−	0.0875087i
$579$		−	1.15186e18i		−	1.27054i
$580$	4.21352e16	−	3.59599e16i	0.0459582	−	0.0392227i
$581$			2.47594e17i			0.267052i
$582$	−4.94550e17	−	1.34130e18i	−0.527486	−	1.43063i
$583$	−2.41202e17			−0.254410
$584$	−5.39423e17	+	9.61958e17i	−0.562660	+	1.00340i
$585$	2.45523e16			0.0253267
$586$	−4.02011e17	−	1.09032e18i	−0.410113	−	1.11229i
$587$			5.59350e16i			0.0564334i	0.999602	+	0.0282167i	$0.00898284\pi$
$587$			5.59350e16i			0.0564334i	−0.999602	+	0.0282167i	$0.991017\pi$
$588$	−2.92429e16	−	3.42647e16i	−0.0291789	−	0.0341896i
$589$		−	1.07051e18i		−	1.05643i
$590$	4.96922e16	−	1.83220e16i	0.0485010	−	0.0178828i
$591$	1.80502e18			1.74246
$592$	−5.60697e17	−	8.92305e16i	−0.535349	−	0.0851966i
$593$	−1.85096e18			−1.74800			−0.874000	−	0.485927i	$-0.838482\pi$
$593$	−1.85096e18			−1.74800			−0.874000	+	0.485927i	$0.838482\pi$
$594$	2.00644e17	−	7.39792e16i	0.187419	−	0.0691031i
$595$			8.43106e16i			0.0778972i
$596$	−3.56583e17	−	4.17817e17i	−0.325881	−	0.381844i
$597$			2.74215e17i			0.247890i
$598$	−5.89265e17	−	1.59818e18i	−0.526930	−	1.42912i
$599$	−5.05656e17			−0.447281			−0.223641	−	0.974672i	$-0.571794\pi$
$599$	−5.05656e17			−0.447281			−0.223641	+	0.974672i	$0.571794\pi$
$600$	−1.11242e18	−	6.23796e17i	−0.973389	−	0.545833i
$601$	1.45684e16			0.0126103			0.00630517	−	0.999980i	$-0.497993\pi$
$601$	1.45684e16			0.0126103			0.00630517	+	0.999980i	$0.497993\pi$
$602$	2.16161e17	+	5.86265e17i	0.185098	+	0.502015i
$603$		−	2.79632e17i		−	0.236878i
$604$	1.62274e18	−	1.38492e18i	1.35991	−	1.16060i
$605$		−	7.75720e16i		−	0.0643124i
$606$	−2.12615e18	+	7.83931e17i	−1.74390	+	0.642992i
$607$	1.20617e18			0.978772			0.489386	−	0.872067i	$-0.337221\pi$
$607$	1.20617e18			0.978772			0.489386	+	0.872067i	$0.337221\pi$
$608$	2.17390e18	−	4.30327e17i	1.74528	−	0.345482i
$609$	−1.27466e18			−1.01247
$610$	5.49625e16	−	2.02652e16i	0.0431939	−	0.0159260i
$611$			2.89100e18i			2.24792i
$612$	−2.84534e17	+	2.42833e17i	−0.218902	+	0.186820i
$613$			1.01082e18i			0.769450i	0.923031	+	0.384725i	$0.125704\pi$
$613$			1.01082e18i			0.769450i	−0.923031	+	0.384725i	$0.874296\pi$
$614$	−2.67378e17	−	7.25173e17i	−0.201387	−	0.546195i
$615$	−1.31849e17			−0.0982630
$616$	−2.89278e17	−	1.62214e17i	−0.213324	−	0.119623i
$617$	1.35500e18			0.988751			0.494376	−	0.869248i	$-0.335397\pi$
$617$	1.35500e18			0.988751			0.494376	+	0.869248i	$0.335397\pi$
$618$	−5.54138e15	−	1.50291e16i	−0.00400123	−	0.0108520i
$619$		−	3.64418e17i		−	0.260382i	−0.991489	−	0.130191i	$-0.958441\pi$
$619$		−	3.64418e17i		−	0.260382i	0.991489	−	0.130191i	$-0.0415590\pi$
$620$	3.72007e16	+	4.35890e16i	0.0263030	+	0.0308199i
$621$		−	1.25603e18i		−	0.878827i
$622$	2.99505e17	−	1.10430e17i	0.207380	−	0.0764629i
$623$	1.30312e18			0.892918
$624$	−3.75145e17	+	2.35729e18i	−0.254390	+	1.59850i
$625$	1.46933e18			0.986053
$626$	−8.53610e17	+	3.14734e17i	−0.566926	+	0.209031i
$627$			7.27800e17i			0.478380i
$628$	4.73191e17	+	5.54451e17i	0.307822	+	0.360683i
$629$		−	9.42465e17i		−	0.606787i
$630$	−9.71343e15	−	2.63444e16i	−0.00618955	−	0.0167871i
$631$	−2.16455e18			−1.36514			−0.682571	−	0.730819i	$-0.739138\pi$
$631$	−2.16455e18			−1.36514			−0.682571	+	0.730819i	$0.739138\pi$
$632$	5.75353e17	−	1.02603e18i	0.359148	−	0.640472i
$633$	−1.04947e18			−0.648404
$634$	9.80202e17	+	2.65847e18i	0.599426	+	1.62574i
$635$			6.30013e16i			0.0381347i
$636$	1.51007e18	−	1.28876e18i	0.904744	−	0.772146i
$637$		−	9.75874e16i		−	0.0578745i
$638$	−3.39386e17	+	1.25135e17i	−0.199232	+	0.0734588i
$639$	1.19165e17			0.0692458
$640$	−7.35626e16	+	9.30658e16i	−0.0423143	+	0.0535328i
$641$	−6.48038e17			−0.368997			−0.184499	−	0.982833i	$-0.559066\pi$
$641$	−6.48038e17			−0.368997			−0.184499	+	0.982833i	$0.559066\pi$
$642$	−6.05170e17	+	2.23132e17i	−0.341114	+	0.125772i
$643$		−	1.13754e18i		−	0.634738i	−0.948302	−	0.317369i	$-0.897201\pi$
$643$		−	1.13754e18i		−	0.634738i	0.948302	−	0.317369i	$-0.102799\pi$
$644$	−1.48171e18	+	1.26455e18i	−0.818475	+	0.698521i
$645$			7.34010e16i			0.0401387i
$646$	1.27261e18	+	3.45153e18i	0.688946	+	1.86853i
$647$	4.00139e17			0.214453			0.107227	−	0.994235i	$-0.465803\pi$
$647$	4.00139e17			0.214453			0.107227	+	0.994235i	$0.465803\pi$
$648$	−1.09787e18	+	1.95784e18i	−0.582523	+	1.03882i
$649$	−3.45842e17			−0.181672
$650$	−9.55819e17	−	2.59234e18i	−0.497094	−	1.34820i
$651$		−	1.31864e18i		−	0.678968i
$652$	7.63614e16	+	8.94747e16i	0.0389282	+	0.0456132i
$653$		−	5.15814e17i		−	0.260350i	−0.991491	−	0.130175i	$-0.958446\pi$
$653$		−	5.15814e17i		−	0.260350i	0.991491	−	0.130175i	$-0.0415539\pi$
$654$	3.66891e18	−	1.35276e18i	1.83350	−	0.676030i
$655$	1.79037e16			0.00885880
$656$	4.12018e17	−	2.58899e18i	0.201856	−	1.26840i
$657$	6.09703e17			0.295763
$658$	3.10202e18	−	1.14374e18i	1.48997	−	0.549365i
$659$		−	2.76356e18i		−	1.31436i	−0.753734	−	0.657180i	$-0.771749\pi$
$659$		−	2.76356e18i		−	1.31436i	0.753734	−	0.657180i	$-0.228251\pi$
$660$	−2.52913e16	−	2.96345e16i	−0.0119107	−	0.0139560i
$661$			2.27112e18i			1.05909i	0.848283	+	0.529543i	$0.177636\pi$
$661$			2.27112e18i			1.05909i	−0.848283	+	0.529543i	$0.822364\pi$
$662$	−1.53398e17	−	4.16040e17i	−0.0708341	−	0.192114i
$663$	−3.96233e18			−1.81181
$664$	−5.04408e17	−	2.82849e17i	−0.228396	−	0.128074i
$665$	−2.76125e17			−0.123813
$666$	1.08581e17	+	2.94490e17i	0.0482140	+	0.130764i
$667$			2.12455e18i			0.934221i
$668$	−1.96911e18	+	1.68052e18i	−0.857476	+	0.731806i
$669$		−	1.09886e18i		−	0.473886i
$670$	1.38118e17	−	5.09254e16i	0.0589881	−	0.0217495i
$671$	−3.82521e17			−0.161793
$672$	2.67777e18	−	5.30071e17i	1.12169	−	0.222041i
$673$	3.76617e17			0.156243			0.0781217	−	0.996944i	$-0.475108\pi$
$673$	3.76617e17			0.156243			0.0781217	+	0.996944i	$0.475108\pi$
$674$	−2.15027e18	+	7.92826e17i	−0.883495	+	0.325753i
$675$		−	2.03734e18i		−	0.829066i
$676$	−2.04602e18	+	1.74616e18i	−0.824623	+	0.703768i
$677$			2.97834e18i			1.18891i	0.804130	+	0.594453i	$0.202631\pi$
$677$			2.97834e18i			1.18891i	−0.804130	+	0.594453i	$0.797369\pi$
$678$	−2.25425e17	−	6.11389e17i	−0.0891269	−	0.241727i
$679$	−3.54168e18			−1.38693
$680$	−1.71760e17	−	9.63156e16i	−0.0666216	−	0.0373584i
$681$	−3.65362e17			−0.140368
$682$	−1.29452e17	−	3.51096e17i	−0.0492619	−	0.133606i
$683$		−	1.79679e18i		−	0.677270i	−0.940918	−	0.338635i	$-0.890035\pi$
$683$		−	1.79679e18i		−	0.677270i	0.940918	−	0.338635i	$-0.109965\pi$
$684$	−7.95302e17	−	9.31877e17i	−0.296939	−	0.347932i
$685$		−	5.38697e16i		−	0.0199231i
$686$	2.50723e18	−	9.24439e17i	0.918517	−	0.338666i
$687$	2.14156e18			0.777163
$688$	−1.44130e18	−	2.29372e17i	−0.518119	−	0.0824546i
$689$	4.30074e18			1.53151
$690$	−2.14700e17	+	7.91618e16i	−0.0757377	+	0.0279252i
$691$		−	8.70716e17i		−	0.304277i	−0.988359	−	0.152139i	$-0.951384\pi$
$691$		−	8.70716e17i		−	0.304277i	0.988359	−	0.152139i	$-0.0486160\pi$
$692$	−3.03417e18	−	3.55521e18i	−1.05039	−	1.23077i
$693$			1.83348e17i			0.0628798i
$694$	1.61220e18	+	4.37254e18i	0.547750	+	1.48559i
$695$	2.73846e17			0.0921734
$696$	1.45616e18	−	2.59678e18i	0.485566	−	0.865915i
$697$	4.35179e18			1.43765
$698$	−1.22626e18	−	3.32582e18i	−0.401349	−	1.08852i
$699$			2.87681e18i			0.932844i
$700$	−2.40341e18	+	2.05117e18i	−0.772131	+	0.658969i
$701$		−	3.25269e18i		−	1.03532i	−0.855586	−	0.517661i	$-0.826803\pi$
$701$		−	3.25269e18i		−	1.03532i	0.855586	−	0.517661i	$-0.173197\pi$
$702$	−3.57757e18	+	1.31909e18i	−1.12823	+	0.415989i
$703$	3.08666e18			0.964450
$704$	6.60936e17	−	4.04015e17i	0.204615	−	0.125076i
$705$	3.88376e17			0.119131
$706$	1.56849e17	−	5.78316e16i	0.0476706	−	0.0175766i
$707$			5.61406e18i			1.69064i
$708$	2.16518e18	−	1.84786e18i	0.646068	−	0.551381i
$709$		−	6.65027e17i		−	0.196625i	−0.995156	−	0.0983125i	$-0.968656\pi$
$709$		−	6.65027e17i		−	0.196625i	0.995156	−	0.0983125i	$-0.0313445\pi$
$710$	2.17019e16	+	5.88590e16i	0.00635797	+	0.0172438i
$711$	−6.50314e17			−0.188786
$712$	−1.48867e18	+	2.65476e18i	−0.428231	+	0.763668i
$713$	−2.19786e18			−0.626494
$714$	1.56759e18	+	4.25155e18i	0.442785	+	1.20091i
$715$		−	8.44004e16i		−	0.0236241i
$716$	2.00679e17	+	2.35141e17i	0.0556632	+	0.0652220i
$717$			3.37618e18i			0.928006i
$718$	5.57499e18	−	2.05555e18i	1.51857	−	0.559911i
$719$	3.90552e18			1.05424			0.527122	−	0.849790i	$-0.323271\pi$
$719$	3.90552e18			1.05424			0.527122	+	0.849790i	$0.323271\pi$
$720$	6.47662e16	+	1.03070e16i	0.0173256	+	0.00275723i
$721$	−3.96842e16			−0.0105205
$722$	−7.73292e18	+	2.85120e18i	−2.03166	+	0.749094i
$723$			5.63989e18i			1.46849i
$724$	−7.80237e17	−	9.14224e17i	−0.201338	−	0.235913i
$725$			3.44613e18i			0.881323i
$726$	−1.44230e18	−	3.91174e18i	−0.365566	−	0.991475i
$727$	−5.10127e18			−1.28146			−0.640730	−	0.767766i	$-0.721368\pi$
$727$	−5.10127e18			−1.28146			−0.640730	+	0.767766i	$0.721368\pi$
$728$	5.15796e18	+	2.89235e18i	1.28417	+	0.720108i
$729$	−2.54377e18			−0.627696
$730$	1.11037e17	+	3.01150e17i	0.0271562	+	0.0736519i
$731$		−	2.42265e18i		−	0.587257i
$732$	2.39482e18	−	2.04384e18i	0.575374	−	0.491048i
$733$			3.11289e18i			0.741289i	0.928775	+	0.370645i	$0.120863\pi$
$733$			3.11289e18i			0.741289i	−0.928775	+	0.370645i	$0.879137\pi$
$734$	5.73449e17	−	2.11436e17i	0.135354	−	0.0499062i
$735$	−1.31099e16			−0.00306712
$736$	−8.83501e17	−	4.46321e18i	−0.204881	−	1.03500i
$737$	−9.61257e17			−0.220953
$738$	−1.35979e18	+	5.01369e17i	−0.309818	+	0.114233i
$739$		−	7.69864e18i		−	1.73870i	−0.494195	−	0.869351i	$-0.664537\pi$
$739$		−	7.69864e18i		−	1.73870i	0.494195	−	0.869351i	$-0.335463\pi$
$740$	−1.25683e17	+	1.07263e17i	−0.0281365	+	0.0240128i
$741$		−	1.29770e19i		−	2.87976i
$742$	−1.70147e18	−	4.61466e18i	−0.374282	−	1.01511i
$743$	6.25892e18			1.36481			0.682405	−	0.730974i	$-0.260934\pi$
$743$	6.25892e18			1.36481			0.682405	+	0.730974i	$0.260934\pi$
$744$	2.68638e18	+	1.50640e18i	0.580688	+	0.325624i
$745$	−1.59859e17			−0.0342548
$746$	−1.98970e18	−	5.39640e18i	−0.422655	−	1.14631i
$747$			3.19701e17i			0.0673225i
$748$	8.34759e17	+	9.78109e17i	0.174261	+	0.204186i
$749$			1.59794e18i			0.330696i
$750$	−6.98136e17	+	2.57410e17i	−0.143233	+	0.0528113i
$751$	−2.41477e18			−0.491153			−0.245577	−	0.969377i	$-0.578977\pi$
$751$	−2.41477e18			−0.491153			−0.245577	+	0.969377i	$0.578977\pi$
$752$	−1.21364e18	+	7.62615e18i	−0.244723	+	1.53776i
$753$	−9.61420e18			−1.92197
$754$	6.05141e18	−	2.23121e18i	1.19934	−	0.442209i
$755$		−	6.20871e17i		−	0.121996i
$756$	2.83074e18	+	3.31685e18i	0.551452	+	0.646151i
$757$		−	3.19891e18i		−	0.617844i	−0.951087	−	0.308922i	$-0.900032\pi$
$757$		−	3.19891e18i		−	0.617844i	0.951087	−	0.308922i	$-0.0999682\pi$
$758$	5.53462e17	+	1.50108e18i	0.105983	+	0.287444i
$759$	1.49424e18			0.283693
$760$	3.15443e17	−	5.62532e17i	0.0593789	−	0.105891i
$761$	−5.76395e18			−1.07577			−0.537886	−	0.843018i	$-0.680777\pi$
$761$	−5.76395e18			−1.07577			−0.537886	+	0.843018i	$0.680777\pi$
$762$	1.17138e18	+	3.17698e18i	0.216766	+	0.587905i
$763$		−	9.68770e18i		−	1.77751i
$764$	−3.22426e18	+	2.75172e18i	−0.586574	+	0.500607i
$765$			1.08864e17i			0.0196375i
$766$	−9.64923e18	+	3.55776e18i	−1.72586	+	0.636341i
$767$	6.16653e18			1.09363
$768$	−1.97918e18	+	6.06080e18i	−0.348047	+	1.06582i
$769$	−2.49093e18			−0.434351			−0.217176	−	0.976133i	$-0.569684\pi$
$769$	−2.49093e18			−0.434351			−0.217176	+	0.976133i	$0.569684\pi$
$770$	−9.05610e16	+	3.33907e16i	−0.0156585	+	0.00577346i
$771$			1.04298e18i			0.178823i
$772$	5.06991e18	−	4.32687e18i	0.861961	−	0.735633i
$773$			3.96232e18i			0.668009i	0.942571	+	0.334005i	$0.108400\pi$
$773$			3.96232e18i			0.668009i	−0.942571	+	0.334005i	$0.891600\pi$
$774$	2.79114e17	+	7.57002e17i	0.0466622	+	0.126555i
$775$	−3.56503e18			−0.591021
$776$	4.04598e18	−	7.21523e18i	0.665155	−	1.18618i
$777$	3.80211e18			0.619852
$778$	1.60725e18	+	4.35912e18i	0.259846	+	0.704744i
$779$			1.42525e19i			2.28506i
$780$	4.50957e17	+	5.28398e17i	0.0717001	+	0.0840129i
$781$		−	4.09640e17i		−	0.0645908i
$782$	7.08632e18	−	2.61279e18i	1.10809	−	0.408565i
$783$	4.75586e18			0.737527
$784$	4.09672e16	−	2.57425e17i	0.00630060	−	0.0395910i
$785$	2.12136e17			0.0323565
$786$	9.02834e17	−	3.32884e17i	0.136572	−	0.0503554i
$787$			4.01666e18i			0.602600i	0.953529	+	0.301300i	$0.0974205\pi$
$787$			4.01666e18i			0.602600i	−0.953529	+	0.301300i	$0.902579\pi$
$788$	6.78040e18	+	7.94478e18i	1.00887	+	1.18212i
$789$		−	6.13982e17i		−	0.0906057i
$790$	−1.18433e17	−	3.21209e17i	−0.0173339	−	0.0470123i
$791$	−1.61436e18			−0.234344
$792$	−3.73524e17	−	2.09455e17i	−0.0537780	−	0.0301563i
$793$	6.82054e18			0.973965
$794$	−1.87966e18	−	5.09794e18i	−0.266223	−	0.722040i
$795$		−	5.77761e17i		−	0.0811637i
$796$	−1.20696e18	+	1.03007e18i	−0.168173	+	0.143526i
$797$			1.33185e18i			0.184068i	0.995756	+	0.0920338i	$0.0293368\pi$
$797$			1.33185e18i			0.184068i	−0.995756	+	0.0920338i	$0.970663\pi$
$798$	−1.39242e19	+	5.13400e18i	−1.90877	+	0.703780i
$799$	−1.28186e19			−1.74296
$800$	−1.43308e18	−	7.23955e18i	−0.193280	−	0.976397i
$801$	1.68262e18			0.225100
$802$	8.58899e18	−	3.16684e18i	1.13975	−	0.420236i
$803$		−	2.09591e18i		−	0.275880i
$804$	6.01805e18	−	5.13606e18i	0.785763	−	0.670603i
$805$			5.66911e17i			0.0734246i
$806$	2.30820e18	+	6.26021e18i	0.296548	+	0.804287i
$807$	4.76525e18			0.607306
$808$	−1.14372e19	−	6.41344e18i	−1.44592	−	0.810807i
$809$	2.65212e18			0.332604			0.166302	−	0.986075i	$-0.446817\pi$
$809$	2.65212e18			0.332604			0.166302	+	0.986075i	$0.446817\pi$
$810$	2.25989e17	+	6.12920e17i	0.0281148	+	0.0762520i
$811$			5.40937e18i			0.667592i	0.942645	+	0.333796i	$0.108330\pi$
$811$			5.40937e18i			0.667592i	−0.942645	+	0.333796i	$0.891670\pi$
$812$	−4.78815e18	−	5.61040e18i	−0.586210	−	0.686878i
$813$			1.22367e18i			0.148619i
$814$	1.01233e18	−	3.73258e17i	0.121974	−	0.0449728i
$815$	3.42335e16			0.00409192
$816$	−1.04522e19	−	1.66339e18i	−1.23943	−	0.197245i
$817$	7.93443e18			0.933409
$818$	−6.25369e18	+	2.30579e18i	−0.729860	+	0.269106i
$819$		−	3.26919e18i		−	0.378525i
$820$	−4.95281e17	−	5.80334e17i	−0.0568934	−	0.0666634i
$821$		−	9.60867e18i		−	1.09505i	−0.836790	−	0.547523i	$-0.815571\pi$
$821$		−	9.60867e18i		−	1.09505i	0.836790	−	0.547523i	$-0.184429\pi$
$822$	−1.00160e18	−	2.71650e18i	−0.113247	−	0.307145i
$823$	4.48399e18			0.502997			0.251498	−	0.967858i	$-0.419077\pi$
$823$	4.48399e18			0.502997			0.251498	+	0.967858i	$0.419077\pi$
$824$	4.53348e16	−	8.08460e16i	0.00504551	−	0.00899770i
$825$	2.42373e18			0.267630
$826$	−2.43962e18	−	6.61664e18i	−0.267271	−	0.724882i
$827$		−	9.62703e18i		−	1.04642i	−0.852203	−	0.523211i	$-0.824734\pi$
$827$		−	9.62703e18i		−	1.04642i	0.852203	−	0.523211i	$-0.175266\pi$
$828$	−1.91323e18	+	1.63283e18i	−0.206333	+	0.176094i
$829$			1.12704e19i			1.20597i	0.797753	+	0.602984i	$0.206022\pi$
$829$			1.12704e19i			1.20597i	−0.797753	+	0.602984i	$0.793978\pi$
$830$	−1.57909e17	+	5.82227e16i	−0.0167649	+	0.00618137i
$831$	6.07555e18			0.639998
$832$	−1.17848e19	+	7.20378e18i	−1.23174	+	0.752937i
$833$	4.32701e17			0.0448741
$834$	1.38093e19	−	5.09162e18i	1.42099	−	0.523934i
$835$			7.53391e17i			0.0769234i
$836$	−3.20340e18	+	2.73392e18i	−0.324542	+	0.276978i
$837$			4.91995e18i			0.494590i
$838$	−8.75334e17	−	2.37405e18i	−0.0873148	−	0.236812i
$839$	−1.51849e19			−1.50300			−0.751501	−	0.659732i	$-0.770670\pi$
$839$	−1.51849e19			−1.50300			−0.751501	+	0.659732i	$0.770670\pi$
$840$	3.88558e17	−	6.92919e17i	0.0381628	−	0.0680561i
$841$	2.21615e18			0.215986
$842$	5.71954e18	+	1.55123e19i	0.553137	+	1.50020i
$843$			2.48178e17i			0.0238169i
$844$	−3.94224e18	−	4.61923e18i	−0.375420	−	0.439889i
$845$			7.82817e17i			0.0739762i
$846$	4.00542e18	−	1.47684e18i	0.375613	−	0.138492i
$847$	−1.03289e19			−0.961195
$848$	1.13449e19	+	1.80545e18i	1.04768	+	0.166730i
$849$	1.48053e19			1.35680
$850$	1.14944e19	−	4.23808e18i	1.04535	−	0.385431i
$851$		−	6.33721e18i		−	0.571947i
$852$	2.18873e18	+	2.56459e18i	0.196036	+	0.229700i
$853$			1.75981e17i			0.0156422i	0.999969	+	0.00782111i	$0.00248956\pi$
$853$			1.75981e17i			0.0156422i	−0.999969	+	0.00782111i	$0.997510\pi$
$854$	−2.69836e18	−	7.31839e18i	−0.238026	−	0.645564i
$855$	−3.56541e17			−0.0312126
$856$	−3.25538e18	−	1.82547e18i	−0.282828	−	0.158597i
$857$	−1.54615e19			−1.33314			−0.666571	−	0.745442i	$-0.732239\pi$
$857$	−1.54615e19			−1.33314			−0.666571	+	0.745442i	$0.732239\pi$
$858$	−1.56926e18	−	4.25608e18i	−0.134285	−	0.364202i
$859$		−	7.20321e18i		−	0.611745i	−0.952072	−	0.305873i	$-0.901052\pi$
$859$		−	7.20321e18i		−	0.611745i	0.952072	−	0.305873i	$-0.0989482\pi$
$860$	−3.23074e17	+	2.75725e17i	−0.0272309	+	0.0232400i
$861$			1.75561e19i			1.46861i
$862$	−2.56747e18	+	9.46650e17i	−0.213161	+	0.0785945i
$863$	−1.11261e19			−0.916797			−0.458398	−	0.888747i	$-0.651577\pi$
$863$	−1.11261e19			−0.916797			−0.458398	+	0.888747i	$0.651577\pi$
$864$	−9.99100e18	+	1.97774e18i	−0.817089	+	0.161744i
$865$	−1.36024e18			−0.110411
$866$	−7.01144e18	+	2.58519e18i	−0.564860	+	0.208269i
$867$		−	3.54695e18i		−	0.283616i
$868$	5.80398e18	−	4.95336e18i	0.460625	−	0.393117i
$869$			2.23551e18i			0.176095i
$870$	−2.99741e17	−	8.12945e17i	−0.0234353	−	0.0635603i
$871$	1.71397e19			1.33010
$872$	1.97361e19	+	1.10671e19i	1.52021	+	0.852468i
$873$	−4.57312e18			−0.349639
$874$	8.55715e18	+	2.32084e19i	0.649389	+	1.76125i
$875$			1.84342e18i			0.138858i
$876$	1.11986e19	+	1.31216e19i	0.837308	+	0.981096i
$877$		−	2.17444e19i		−	1.61380i	−0.590688	−	0.806900i	$-0.701144\pi$
$877$		−	2.17444e19i		−	1.61380i	0.590688	−	0.806900i	$-0.298856\pi$
$878$	1.60641e19	−	5.92298e18i	1.18343	−	0.436341i
$879$	−1.81765e19			−1.32918
$880$	3.54313e16	−	2.22639e17i	0.00257187	−	0.0161608i
$881$	2.54349e18			0.183268			0.0916338	−	0.995793i	$-0.470791\pi$
$881$	2.54349e18			0.183268			0.0916338	+	0.995793i	$0.470791\pi$
$882$	−1.35205e17	+	4.98515e16i	−0.00967047	+	0.00356560i
$883$			2.29535e19i			1.62969i	0.579681	+	0.814844i	$0.303177\pi$
$883$			2.29535e19i			1.62969i	−0.579681	+	0.814844i	$0.696823\pi$
$884$	−1.48842e19	−	1.74402e19i	−1.04902	−	1.22917i
$885$		−	8.28410e17i		−	0.0579581i
$886$	5.74031e18	+	1.55687e19i	0.398673	+	1.08126i
$887$	1.69166e19			1.16630			0.583149	−	0.812365i	$-0.301820\pi$
$887$	1.69166e19			1.16630			0.583149	+	0.812365i	$0.301820\pi$
$888$	−4.34349e18	+	7.74579e18i	−0.297272	+	0.530129i
$889$	8.38877e18			0.569950
$890$	3.06433e17	+	8.31096e17i	0.0206681	+	0.0560552i
$891$		−	4.26572e18i		−	0.285619i
$892$	4.83664e18	−	4.12779e18i	0.321493	−	0.274376i
$893$		−	4.19823e19i		−	2.77033i
$894$	−8.06126e18	+	2.97226e18i	−0.528091	+	0.194712i
$895$	8.99664e16			0.00585101
$896$	1.23919e19	+	9.79503e18i	0.800086	+	0.632417i
$897$	−2.66430e19			−1.70778
$898$	−2.81288e19	+	1.03714e19i	−1.79001	+	0.659994i
$899$		−	8.32203e18i		−	0.525765i
$900$	−3.10335e18	+	2.64853e18i	−0.194650	+	0.166123i
$901$			1.90694e19i			1.18748i
$902$	1.72350e18	+	4.67441e18i	0.106554	+	0.288991i
$903$	9.77351e18			0.599902
$904$	1.84423e18	−	3.28883e18i	0.112388	−	0.200423i
$905$	−3.49787e17			−0.0211635
$906$	−1.15439e19	−	3.13088e19i	−0.693454	−	1.88076i
$907$			6.80309e18i			0.405750i	0.979205	+	0.202875i	$0.0650285\pi$
$907$			6.80309e18i			0.405750i	−0.979205	+	0.202875i	$0.934971\pi$
$908$	−1.37245e18	−	1.60814e18i	−0.0812716	−	0.0952280i
$909$			7.24904e18i			0.426202i
$910$	1.61475e18	−	5.95372e17i	0.0942617	−	0.0347552i
$911$	−1.18952e19			−0.689447			−0.344724	−	0.938704i	$-0.612027\pi$
$911$	−1.18952e19			−0.689447			−0.344724	+	0.938704i	$0.612027\pi$
$912$	5.44775e18	−	3.42320e19i	0.313510	−	1.97000i
$913$	1.09900e18			0.0627967
$914$	−1.27994e19	+	4.71927e18i	−0.726173	+	0.267747i
$915$		−	9.16270e17i		−	0.0516162i
$916$	8.04460e18	+	9.42607e18i	0.449971	+	0.527242i
$917$		−	2.38392e18i		−	0.132401i
$918$	−5.84880e18	−	1.58629e19i	−0.322544	−	0.874792i
$919$	2.12090e19			1.16137			0.580683	−	0.814130i	$-0.302786\pi$
$919$	2.12090e19			1.16137			0.580683	+	0.814130i	$0.302786\pi$
$920$	−1.15493e18	−	6.47633e17i	−0.0627964	−	0.0352134i
$921$	−1.20892e19			−0.652696
$922$	−3.79600e18	−	1.02954e19i	−0.203505	−	0.551939i
$923$			7.30408e18i			0.388825i
$924$	−3.94591e18	+	3.36760e18i	−0.208583	+	0.178013i
$925$		−	1.02793e19i		−	0.539562i
$926$	−7.42860e17	+	2.73900e17i	−0.0387200	+	0.0142764i
$927$	−5.12414e16			−0.00265218
$928$	1.68996e19	−	3.34532e18i	0.868591	−	0.171939i
$929$	4.89201e18			0.249681			0.124841	−	0.992177i	$-0.460158\pi$
$929$	4.89201e18			0.249681			0.124841	+	0.992177i	$0.460158\pi$
$930$	8.40995e17	−	3.10083e17i	0.0426240	−	0.0157159i
$931$			1.41714e18i			0.0713246i
$932$	−1.26622e19	+	1.08065e19i	−0.632859	+	0.540108i
$933$		−	4.99299e18i		−	0.247816i
$934$	−9.23732e18	−	2.50531e19i	−0.455293	−	1.23483i
$935$	3.74230e17			0.0183174
$936$	6.66011e18	+	3.73469e18i	0.323734	+	0.181536i
$937$	−3.82987e18			−0.184874			−0.0924372	−	0.995719i	$-0.529466\pi$
$937$	−3.82987e18			−0.184874			−0.0924372	+	0.995719i	$0.529466\pi$
$938$	−6.78084e18	−	1.83907e19i	−0.325061	−	0.881619i
$939$			1.42304e19i			0.677470i
$940$	1.45890e18	+	1.70943e18i	0.0689756	+	0.0808205i
$941$			2.73101e19i			1.28231i	0.767413	+	0.641153i	$0.221543\pi$
$941$			2.73101e19i			1.28231i	−0.767413	+	0.641153i	$0.778457\pi$
$942$	1.06974e19	−	3.94424e18i	0.498825	−	0.183922i
$943$	2.92617e19			1.35511
$944$	1.62666e19	+	2.58871e18i	0.748135	+	0.119060i
$945$	1.26904e18			0.0579655
$946$	2.60226e18	−	9.59477e17i	0.118048	−	0.0435253i
$947$		−	8.00635e18i		−	0.360711i	−0.983601	−	0.180356i	$-0.942275\pi$
$947$		−	8.00635e18i		−	0.360711i	0.983601	−	0.180356i	$-0.0577248\pi$
$948$	−1.19445e19	−	1.39956e19i	−0.534457	−	0.626237i
$949$			3.73710e19i			1.66075i
$950$	1.38801e19	+	3.76452e19i	0.612619	+	1.66152i
$951$	4.43188e19			1.94274
$952$	−1.28246e19	+	2.28703e19i	−0.558348	+	0.995708i
$953$	−9.72737e18			−0.420622			−0.210311	−	0.977635i	$-0.567448\pi$
$953$	−9.72737e18			−0.420622			−0.210311	+	0.977635i	$0.567448\pi$
$954$	−2.19699e18	−	5.95859e18i	−0.0943546	−	0.255905i
$955$			1.23362e18i			0.0526210i
$956$	−1.48602e19	+	1.26823e19i	−0.629577	+	0.537307i
$957$			5.65784e18i			0.238080i
$958$	−2.32109e19	+	8.55806e18i	−0.970097	+	0.357684i
$959$	−7.17288e18			−0.297764
$960$	9.67754e17	+	1.58317e18i	0.0399027	+	0.0652776i
$961$	−1.58084e19			−0.647419
$962$	−1.80504e19	+	6.65536e18i	−0.734259	+	0.270728i
$963$			2.06331e18i			0.0833669i
$964$	−2.48239e19	+	2.11858e19i	−0.996253	+	0.850244i
$965$		−	1.93977e18i		−	0.0773256i
$966$	1.05406e19	+	2.85877e19i	0.417362	+	1.13195i
$967$	−1.20531e19			−0.474054			−0.237027	−	0.971503i	$-0.576173\pi$
$967$	−1.20531e19			−0.474054			−0.237027	+	0.971503i	$0.576173\pi$
$968$	1.17996e19	−	2.10424e19i	0.460976	−	0.822062i
$969$	5.75399e19			2.23287
$970$	−8.32839e17	−	2.25879e18i	−0.0321029	−	0.0870684i
$971$			7.69872e18i			0.294777i	0.989079	+	0.147388i	$0.0470867\pi$
$971$			7.69872e18i			0.294777i	−0.989079	+	0.147388i	$0.952913\pi$
$972$	8.57520e18	+	1.00478e19i	0.326147	+	0.382155i
$973$		−	3.64633e19i		−	1.37760i
$974$	4.68487e19	−	1.72736e19i	1.75818	−	0.648259i
$975$	−4.32163e19			−1.61108
$976$	1.79918e19	+	2.86326e18i	0.666273	+	0.106032i
$977$	−1.13281e19			−0.416716			−0.208358	−	0.978053i	$-0.566812\pi$
$977$	−1.13281e19			−0.416716			−0.208358	+	0.978053i	$0.566812\pi$
$978$	1.72630e18	−	6.36503e17i	0.0630832	−	0.0232594i
$979$		−	5.78416e18i		−	0.209968i
$980$	−4.92461e16	−	5.77030e16i	−0.00177583	−	0.00208079i
$981$		−	1.25090e19i		−	0.448101i
$982$	−1.27028e19	−	3.44520e19i	−0.452038	−	1.22600i
$983$	−2.86975e17			−0.0101449			−0.00507243	−	0.999987i	$-0.501615\pi$
$983$	−2.86975e17			−0.0101449			−0.00507243	+	0.999987i	$0.501615\pi$
$984$	−3.57658e19	−	2.00559e19i	−1.25603	−	0.704325i
$985$	3.03972e18			0.106047
$986$	9.89316e18	+	2.68319e19i	0.342875	+	0.929931i
$987$		−	5.17132e19i		−	1.78049i
$988$	5.71182e19	−	4.87471e19i	1.95369	−	1.66736i
$989$		−	1.62901e19i		−	0.553539i
$990$	−1.16935e17	+	4.31150e16i	−0.00394744	+	0.00145546i
$991$	−3.67463e19			−1.23235			−0.616176	−	0.787609i	$-0.711319\pi$
$991$	−3.67463e19			−1.23235			−0.616176	+	0.787609i	$0.711319\pi$
$992$	3.46074e18	+	1.74827e19i	0.115304	+	0.582483i
$993$	−6.93573e18			−0.229573
$994$	7.83722e18	−	2.88966e18i	0.257721	−	0.0950243i
$995$			4.61788e17i			0.0150866i
$996$	−6.88040e18	+	5.87202e18i	−0.223320	+	0.190591i
$997$		−	1.28091e19i		−	0.413047i	−0.978442	−	0.206523i	$-0.933785\pi$
$997$		−	1.28091e19i		−	0.413047i	0.978442	−	0.206523i	$-0.0662149\pi$
$998$	−1.29763e18	−	3.51939e18i	−0.0415723	−	0.112751i
$999$	−1.41860e19			−0.451527

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.14.b.b.5.9	✓	10
3.2	odd	2		72.14.d.c.37.2		10
4.3	odd	2		32.14.b.b.17.9		10
8.3	odd	2		32.14.b.b.17.2		10
8.5	even	2	inner	8.14.b.b.5.10	yes	10
24.5	odd	2		72.14.d.c.37.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.14.b.b.5.9	✓	10	1.1	even	1	trivial
8.14.b.b.5.10	yes	10	8.5	even	2	inner
32.14.b.b.17.2		10	8.3	odd	2
32.14.b.b.17.9		10	4.3	odd	2
72.14.d.c.37.1		10	24.5	odd	2
72.14.d.c.37.2		10	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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(84.9212 - 31.3112i) q^{2} -1415.71i q^{3} +(6231.21 - 5317.98i) q^{4} -2384.10i q^{5} +(-44327.5 - 120223. i) q^{6} -317448. q^{7} +(362649. - 646716. i) q^{8} -409898. q^{9} +O(q^{10})\)	\(q+(84.9212 - 31.3112i) q^{2} -1415.71i q^{3} +(6231.21 - 5317.98i) q^{4} -2384.10i q^{5} +(-44327.5 - 120223. i) q^{6} -317448. q^{7} +(362649. - 646716. i) q^{8} -409898. q^{9} +(-74649.0 - 202460. i) q^{10} +1.40906e6i q^{11} +(-7.52869e6 - 8.82156e6i) q^{12} -2.51242e7i q^{13} +(-2.69581e7 + 9.93969e6i) q^{14} -3.37518e6 q^{15} +(1.05471e7 - 6.62749e7i) q^{16} +1.11400e8 q^{17} +(-3.48090e7 + 1.28344e7i) q^{18} +3.64846e8i q^{19} +(-1.26786e7 - 1.48558e7i) q^{20} +4.49413e8i q^{21} +(4.41194e7 + 1.19659e8i) q^{22} +7.49063e8 q^{23} +(-9.15559e8 - 5.13405e8i) q^{24} +1.21502e9 q^{25} +(-7.86670e8 - 2.13358e9i) q^{26} -1.67680e9i q^{27} +(-1.97809e9 + 1.68818e9i) q^{28} +2.83628e9i q^{29} +(-2.86624e8 + 1.05681e8i) q^{30} -2.93414e9 q^{31} +(-1.17947e9 - 5.95838e9i) q^{32} +1.99481e9 q^{33} +(9.46024e9 - 3.48808e9i) q^{34} +7.56826e8i q^{35} +(-2.55416e9 + 2.17983e9i) q^{36} -8.46017e9i q^{37} +(1.14238e10 + 3.09832e10i) q^{38} -3.55684e10 q^{39} +(-1.54183e9 - 8.64591e8i) q^{40} +3.90644e10 q^{41} +(1.40717e10 + 3.81647e10i) q^{42} -2.17473e10i q^{43} +(7.49334e9 + 8.78014e9i) q^{44} +9.77236e8i q^{45} +(6.36113e10 - 2.34541e10i) q^{46} -1.15068e11 q^{47} +(-9.38257e10 - 1.49316e10i) q^{48} +3.88420e9 q^{49} +(1.03181e11 - 3.80438e10i) q^{50} -1.57710e11i q^{51} +(-1.33610e11 - 1.56554e11i) q^{52} +1.71179e11i q^{53} +(-5.25026e10 - 1.42396e11i) q^{54} +3.35933e9 q^{55} +(-1.15122e11 + 2.05299e11i) q^{56} +5.16515e11 q^{57} +(8.88074e10 + 2.40860e11i) q^{58} +2.45442e11i q^{59} +(-2.10314e10 + 1.79491e10i) q^{60} +2.71473e11i q^{61} +(-2.49170e11 + 9.18715e10i) q^{62} +1.30121e11 q^{63} +(-2.86727e11 - 4.69062e11i) q^{64} -5.98985e10 q^{65} +(1.69402e11 - 6.24600e10i) q^{66} +6.82198e11i q^{67} +(6.94158e11 - 5.92424e11i) q^{68} -1.06045e12i q^{69} +(2.36972e10 + 6.42706e10i) q^{70} -2.90719e11 q^{71} +(-1.48649e11 + 2.65088e11i) q^{72} -1.48745e12 q^{73} +(-2.64899e11 - 7.18448e11i) q^{74} -1.72011e12i q^{75} +(1.94024e12 + 2.27344e12i) q^{76} -4.47303e11i q^{77} +(-3.02051e12 + 1.11369e12i) q^{78} +1.58653e12 q^{79} +(-1.58006e11 - 2.51454e10i) q^{80} -3.02736e12 q^{81} +(3.31740e12 - 1.22316e12i) q^{82} -7.79952e11i q^{83} +(2.38997e12 + 2.80039e12i) q^{84} -2.65589e11i q^{85} +(-6.80935e11 - 1.84681e12i) q^{86} +4.01533e12 q^{87} +(9.11260e11 + 5.10994e11i) q^{88} -4.10498e12 q^{89} +(3.05985e10 + 8.29881e10i) q^{90} +7.97562e12i q^{91} +(4.66757e12 - 3.98350e12i) q^{92} +4.15387e12i q^{93} +(-9.77175e12 + 3.60294e12i) q^{94} +8.69829e11 q^{95} +(-8.43531e12 + 1.66979e12i) q^{96} +1.11567e13 q^{97} +(3.29851e11 - 1.21619e11i) q^{98} -5.77570e11i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 110 q^{2} - 4716 q^{4} - 267668 q^{6} + 586960 q^{7} - 270712 q^{8} + 2014054 q^{9}+O(q^{10}) \) 10 * q + 110 * q^2 - 4716 * q^4 - 267668 * q^6 + 586960 * q^7 - 270712 * q^8 + 2014054 * q^9	\( 10 q + 110 q^{2} - 4716 q^{4} - 267668 q^{6} + 586960 q^{7} - 270712 q^{8} + 2014054 q^{9} - 4542088 q^{10} + 27987880 q^{12} + 1408688 q^{14} - 145914416 q^{15} + 56624912 q^{16} + 217326004 q^{17} - 147615262 q^{18} + 21655184 q^{20} - 177987876 q^{22} - 78679952 q^{23} + 320199056 q^{24} - 3076402574 q^{25} + 3734872040 q^{26} - 1653812448 q^{28} + 6338232752 q^{30} + 648233792 q^{31} - 11298380000 q^{32} + 15484079688 q^{33} - 6096822724 q^{34} + 4004708940 q^{36} - 18764968628 q^{38} - 63497510288 q^{39} + 7466802592 q^{40} + 59324640356 q^{41} + 53897620960 q^{42} + 13325704392 q^{44} - 55046867440 q^{46} - 10176534816 q^{47} - 301841943264 q^{48} + 182708552058 q^{49} + 326454435302 q^{50} - 53296499536 q^{52} + 35449773752 q^{54} - 123010753008 q^{55} - 462152447680 q^{56} - 511372324504 q^{57} + 766482705096 q^{58} + 1813082440992 q^{60} - 1665308528960 q^{62} - 898991123792 q^{63} - 2180548996032 q^{64} + 1577231990240 q^{65} + 2269525079448 q^{66} + 2338280915304 q^{68} - 6070110714688 q^{70} + 726361179984 q^{71} - 3600753685960 q^{72} - 633240365532 q^{73} + 7528513982264 q^{74} + 10338420845032 q^{76} - 8252024440816 q^{78} + 5445103565344 q^{79} - 15406871881920 q^{80} - 9674575380574 q^{81} + 12273334206796 q^{82} + 20362643366464 q^{84} - 26794541719396 q^{86} + 7632221772720 q^{87} - 27677491769136 q^{88} + 5506344808004 q^{89} + 31454099524040 q^{90} + 33971694298464 q^{92} - 45356008560096 q^{94} - 14214732035504 q^{95} - 35398666935232 q^{96} + 1361133320788 q^{97} + 54325451514942 q^{98}+O(q^{100}) \) 10 * q + 110 * q^2 - 4716 * q^4 - 267668 * q^6 + 586960 * q^7 - 270712 * q^8 + 2014054 * q^9 - 4542088 * q^10 + 27987880 * q^12 + 1408688 * q^14 - 145914416 * q^15 + 56624912 * q^16 + 217326004 * q^17 - 147615262 * q^18 + 21655184 * q^20 - 177987876 * q^22 - 78679952 * q^23 + 320199056 * q^24 - 3076402574 * q^25 + 3734872040 * q^26 - 1653812448 * q^28 + 6338232752 * q^30 + 648233792 * q^31 - 11298380000 * q^32 + 15484079688 * q^33 - 6096822724 * q^34 + 4004708940 * q^36 - 18764968628 * q^38 - 63497510288 * q^39 + 7466802592 * q^40 + 59324640356 * q^41 + 53897620960 * q^42 + 13325704392 * q^44 - 55046867440 * q^46 - 10176534816 * q^47 - 301841943264 * q^48 + 182708552058 * q^49 + 326454435302 * q^50 - 53296499536 * q^52 + 35449773752 * q^54 - 123010753008 * q^55 - 462152447680 * q^56 - 511372324504 * q^57 + 766482705096 * q^58 + 1813082440992 * q^60 - 1665308528960 * q^62 - 898991123792 * q^63 - 2180548996032 * q^64 + 1577231990240 * q^65 + 2269525079448 * q^66 + 2338280915304 * q^68 - 6070110714688 * q^70 + 726361179984 * q^71 - 3600753685960 * q^72 - 633240365532 * q^73 + 7528513982264 * q^74 + 10338420845032 * q^76 - 8252024440816 * q^78 + 5445103565344 * q^79 - 15406871881920 * q^80 - 9674575380574 * q^81 + 12273334206796 * q^82 + 20362643366464 * q^84 - 26794541719396 * q^86 + 7632221772720 * q^87 - 27677491769136 * q^88 + 5506344808004 * q^89 + 31454099524040 * q^90 + 33971694298464 * q^92 - 45356008560096 * q^94 - 14214732035504 * q^95 - 35398666935232 * q^96 + 1361133320788 * q^97 + 54325451514942 * q^98

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