LMFDB - Embedded newform 4.23.b.a.3.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,23,Mod(3,4)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 23, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 23);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 23 $
Character orbit:	$[\chi]$	$=$	4.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:	$12.2682973937$
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} - 63342 x^{8} - 45742928 x^{7} + 34835133568 x^{6} + 12622768560288 x^{5} + \cdots + 11\!\cdots\!40 $ x^10 - 5x^9 - 63342x^8 - 45742928x^7 + 34835133568x^6 + 12622768560288x^5 + 13335465927292608x^4 - 404504858109047040x^3 - 95573988251584922880x^2 - 1820809561188275535801600*x + 1168838172864011361183920640
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{90}\cdot 3^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.2
Root			$-501.982 - 216.483i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.23.b.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1855.93 + 865.934i) q^{2} -142172. i q^{3} +(2.69462e6 - 3.21422e6i) q^{4} +1.40852e7 q^{5} +(1.23111e8 + 2.63860e8i) q^{6} +7.81741e8i q^{7} +(-2.21772e9 + 8.29872e9i) q^{8} +1.11682e10 q^{9} +O(q^{10})$	\(q+(-1855.93 + 865.934i) q^{2} -142172. i q^{3} +(2.69462e6 - 3.21422e6i) q^{4} +1.40852e7 q^{5} +(1.23111e8 + 2.63860e8i) q^{6} +7.81741e8i q^{7} +(-2.21772e9 + 8.29872e9i) q^{8} +1.11682e10 q^{9} +(-2.61411e10 + 1.21969e10i) q^{10} -4.54625e11i q^{11} +(-4.56971e11 - 3.83099e11i) q^{12} -1.51568e12 q^{13} +(-6.76936e11 - 1.45085e12i) q^{14} -2.00252e12i q^{15} +(-3.07022e12 - 1.73222e13i) q^{16} -3.34233e13 q^{17} +(-2.07274e13 + 9.67096e12i) q^{18} -1.16924e14i q^{19} +(3.79543e13 - 4.52730e13i) q^{20} +1.11141e14 q^{21} +(3.93675e14 + 8.43751e14i) q^{22} +1.02367e15i q^{23} +(1.17984e15 + 3.15297e14i) q^{24} -2.18579e15 q^{25} +(2.81300e15 - 1.31248e15i) q^{26} -6.04931e15i q^{27} +(2.51269e15 + 2.10650e15i) q^{28} -2.04325e16 q^{29} +(1.73405e15 + 3.71653e15i) q^{30} -3.11907e16i q^{31} +(2.06980e16 + 2.94901e16i) q^{32} -6.46349e16 q^{33} +(6.20312e16 - 2.89424e16i) q^{34} +1.10110e16i q^{35} +(3.00942e16 - 3.58972e16i) q^{36} -7.54194e15 q^{37} +(1.01248e17 + 2.17002e17i) q^{38} +2.15487e17i q^{39} +(-3.12370e16 + 1.16889e17i) q^{40} +5.27932e17 q^{41} +(-2.06270e17 + 9.62412e16i) q^{42} -4.97531e17i q^{43} +(-1.46126e18 - 1.22504e18i) q^{44} +1.57307e17 q^{45} +(-8.86433e17 - 1.89986e18i) q^{46} +1.07798e18i q^{47} +(-2.46273e18 + 4.36498e17i) q^{48} +3.29870e18 q^{49} +(4.05667e18 - 1.89275e18i) q^{50} +4.75185e18i q^{51} +(-4.08419e18 + 4.87174e18i) q^{52} +5.00954e18 q^{53} +(5.23830e18 + 1.12271e19i) q^{54} -6.40349e18i q^{55} +(-6.48745e18 - 1.73368e18i) q^{56} -1.66233e19 q^{57} +(3.79212e19 - 1.76932e19i) q^{58} -1.63645e19i q^{59} +(-6.43654e18 - 5.39603e18i) q^{60} -6.52861e19 q^{61} +(2.70091e19 + 5.78876e19i) q^{62} +8.73068e18i q^{63} +(-6.39504e19 - 3.68084e19i) q^{64} -2.13487e19 q^{65} +(1.19958e20 - 5.59695e19i) q^{66} -1.63629e20i q^{67} +(-9.00631e19 + 1.07430e20i) q^{68} +1.45537e20 q^{69} +(-9.53479e18 - 2.04356e19i) q^{70} +3.91076e20i q^{71} +(-2.47680e19 + 9.26821e19i) q^{72} +2.53547e20 q^{73} +(1.39973e19 - 6.53082e18i) q^{74} +3.10758e20i q^{75} +(-3.75819e20 - 3.15066e20i) q^{76} +3.55399e20 q^{77} +(-1.86598e20 - 3.99929e20i) q^{78} -4.85911e20i q^{79} +(-4.32447e19 - 2.43987e20i) q^{80} -5.09570e20 q^{81} +(-9.79803e20 + 4.57154e20i) q^{82} -1.58468e21i q^{83} +(2.99484e20 - 3.57233e20i) q^{84} -4.70774e20 q^{85} +(4.30829e20 + 9.23380e20i) q^{86} +2.90492e21i q^{87} +(3.77281e21 + 1.00823e21i) q^{88} -3.37182e20 q^{89} +(-2.91951e20 + 1.36218e20i) q^{90} -1.18487e21i q^{91} +(3.29031e21 + 2.75841e21i) q^{92} -4.43443e21 q^{93} +(-9.33462e20 - 2.00066e21i) q^{94} -1.64690e21i q^{95} +(4.19266e21 - 2.94267e21i) q^{96} +4.16330e20 q^{97} +(-6.12215e21 + 2.85646e21i) q^{98} -5.07737e21i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 1540 q^{2} + 2264464 q^{4} - 17091100 q^{5} - 791935776 q^{6} + 9804431680 q^{8} - 104309613702 q^{9}+O(q^{10}) $ 10 * q + 1540 * q^2 + 2264464 * q^4 - 17091100 * q^5 - 791935776 * q^6 + 9804431680 * q^8 - 104309613702 * q^9	$ 10 q + 1540 q^{2} + 2264464 q^{4} - 17091100 q^{5} - 791935776 q^{6} + 9804431680 q^{8} - 104309613702 q^{9} + 159414035240 q^{10} + 519021175680 q^{12} - 531230356540 q^{13} - 5894008940736 q^{14} - 27717620084480 q^{16} + 14058178115540 q^{17} + 16283956279140 q^{18} + 233643631625120 q^{20} - 313135665760512 q^{21} + 120589650366240 q^{22} - 20\!\cdots\!36 q^{24}+ \cdots - 23\!\cdots\!20 q^{98}+O(q^{100}) $ 10 * q + 1540 * q^2 + 2264464 * q^4 - 17091100 * q^5 - 791935776 * q^6 + 9804431680 * q^8 - 104309613702 * q^9 + 159414035240 * q^10 + 519021175680 * q^12 - 531230356540 * q^13 - 5894008940736 * q^14 - 27717620084480 * q^16 + 14058178115540 * q^17 + 16283956279140 * q^18 + 233643631625120 * q^20 - 313135665760512 * q^21 + 120589650366240 * q^22 - 2007619616180736 * q^24 + 7710175817606670 * q^25 - 3953973318046744 * q^26 + 1177952265288960 * q^28 - 14464474185570172 * q^29 + 10252783730669760 * q^30 - 73831192092953600 * q^32 + 72906957628179840 * q^33 - 26625976920357496 * q^34 - 36609276067793136 * q^36 + 324587767823538020 * q^37 + 369140808808591200 * q^38 - 1158049295468479360 * q^40 - 1355457345814233100 * q^41 + 2644455724909770240 * q^42 - 1919761520625210240 * q^44 + 9367295763131460 * q^45 + 6132624002565203904 * q^46 - 18374169355003791360 * q^48 + 183553700661552298 * q^49 + 29084394113996178540 * q^50 - 38492433127521128800 * q^52 - 11424344766226018780 * q^53 + 79182840955393027008 * q^54 - 102844865827678657536 * q^56 + 30188516183231506560 * q^57 + 173059696836432320360 * q^58 - 377769459746631548160 * q^60 + 58241718146183220740 * q^61 + 317897221476923285760 * q^62 - 412080172429987966976 * q^64 - 121531695066047433560 * q^65 + 700585278654050000640 * q^66 - 667890522330713878240 * q^68 + 54497497397908094208 * q^69 + 1014396282552321513600 * q^70 - 1244773253376491901120 * q^72 + 83030422224875883380 * q^73 + 801906083011176262184 * q^74 + 286747421140990627200 * q^76 - 704201825495570814720 * q^77 - 964412732782594923840 * q^78 + 1509611955050789726720 * q^80 + 251577744224553978858 * q^81 - 2389572513290905036600 * q^82 + 6185640644326191863808 * q^84 - 1796890366112110859960 * q^85 - 8221838255181360278496 * q^86 + 11178210842814940531200 * q^88 + 3420669206528505615668 * q^89 - 24782809563337507735320 * q^90 + 21476264197983864733440 * q^92 + 15493754050318100597760 * q^93 - 20874543047091388369536 * q^94 + 29250284502468708163584 * q^96 - 20429910746446196146540 * q^97 - 23110416876469762175420 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−1855.93	+	865.934i	−0.906214	+	0.422819i
$2$	−1855.93	+	865.934i	−0.906214	+	0.422819i
$3$		−	142172.i		−	0.802564i	−0.915955	−	0.401282i	$-0.868565\pi$
$3$		−	142172.i		−	0.802564i	0.915955	−	0.401282i	$-0.131435\pi$
$4$	2.69462e6	−	3.21422e6i	0.642448	−	0.766329i
$5$	1.40852e7			0.288465			0.144233	−	0.989544i	$-0.453929\pi$
$5$	1.40852e7			0.288465			0.144233	+	0.989544i	$0.453929\pi$
$6$	1.23111e8	+	2.63860e8i	0.339339	+	0.727295i
$7$			7.81741e8i			0.395352i	0.980267	+	0.197676i	$0.0633395\pi$
$7$			7.81741e8i			0.395352i	−0.980267	+	0.197676i	$0.936661\pi$
$8$	−2.21772e9	+	8.29872e9i	−0.258176	+	0.966098i
$9$	1.11682e10			0.355891
$10$	−2.61411e10	+	1.21969e10i	−0.261411	+	0.121969i
$11$		−	4.54625e11i		−	1.59343i	−0.604353	−	0.796717i	$-0.706568\pi$
$11$		−	4.54625e11i		−	1.59343i	0.604353	−	0.796717i	$-0.293432\pi$
$12$	−4.56971e11	−	3.83099e11i	−0.615028	−	0.515605i
$13$	−1.51568e12			−0.845730			−0.422865	−	0.906193i	$-0.638976\pi$
$13$	−1.51568e12			−0.845730			−0.422865	+	0.906193i	$0.638976\pi$
$14$	−6.76936e11	−	1.45085e12i	−0.167163	−	0.358274i
$15$		−	2.00252e12i		−	0.231512i
$16$	−3.07022e12	−	1.73222e13i	−0.174522	−	0.984653i
$17$	−3.34233e13			−0.975239			−0.487620	−	0.873056i	$-0.662135\pi$
$17$	−3.34233e13			−0.975239			−0.487620	+	0.873056i	$0.662135\pi$
$18$	−2.07274e13	+	9.67096e12i	−0.322514	+	0.150478i
$19$		−	1.16924e14i		−	1.00372i	−0.864948	−	0.501862i	$-0.832649\pi$
$19$		−	1.16924e14i		−	1.00372i	0.864948	−	0.501862i	$-0.167351\pi$
$20$	3.79543e13	−	4.52730e13i	0.185324	−	0.221059i
$21$	1.11141e14			0.317295
$22$	3.93675e14	+	8.43751e14i	0.673734	+	1.44399i
$23$			1.02367e15i			1.07437i	0.843464	+	0.537186i	$0.180513\pi$
$23$			1.02367e15i			1.07437i	−0.843464	+	0.537186i	$0.819487\pi$
$24$	1.17984e15	+	3.15297e14i	0.775355	+	0.207203i
$25$	−2.18579e15			−0.916788
$26$	2.81300e15	−	1.31248e15i	0.766412	−	0.357591i
$27$		−	6.04931e15i		−	1.08819i
$28$	2.51269e15	+	2.10650e15i	0.302970	+	0.253993i
$29$	−2.04325e16			−1.67472			−0.837362	−	0.546649i	$-0.815903\pi$
$29$	−2.04325e16			−1.67472			−0.837362	+	0.546649i	$0.815903\pi$
$30$	1.73405e15	+	3.71653e15i	0.0978876	+	0.209799i
$31$		−	3.11907e16i		−	1.22757i	−0.789473	−	0.613785i	$-0.789646\pi$
$31$		−	3.11907e16i		−	1.22757i	0.789473	−	0.613785i	$-0.210354\pi$
$32$	2.06980e16	+	2.94901e16i	0.574484	+	0.818516i
$33$	−6.46349e16			−1.27883
$34$	6.20312e16	−	2.89424e16i	0.883775	−	0.412350i
$35$			1.10110e16i			0.114045i
$36$	3.00942e16	−	3.58972e16i	0.228642	−	0.272730i
$37$	−7.54194e15			−0.0423901			−0.0211950	−	0.999775i	$-0.506747\pi$
$37$	−7.54194e15			−0.0423901			−0.0211950	+	0.999775i	$0.506747\pi$
$38$	1.01248e17	+	2.17002e17i	0.424393	+	0.909588i
$39$			2.15487e17i			0.678752i
$40$	−3.12370e16	+	1.16889e17i	−0.0744749	+	0.278686i
$41$	5.27932e17			0.959303			0.479651	−	0.877459i	$-0.340763\pi$
$41$	5.27932e17			0.959303			0.479651	+	0.877459i	$0.340763\pi$
$42$	−2.06270e17	+	9.62412e16i	−0.287538	+	0.134159i
$43$		−	4.97531e17i		−	0.535386i	−0.963504	−	0.267693i	$-0.913739\pi$
$43$		−	4.97531e17i		−	0.535386i	0.963504	−	0.267693i	$-0.0862612\pi$
$44$	−1.46126e18	−	1.22504e18i	−1.22110	−	1.02370i
$45$	1.57307e17			0.102662
$46$	−8.86433e17	−	1.89986e18i	−0.454265	−	0.973612i
$47$			1.07798e18i			0.436049i	0.975943	+	0.218025i	$0.0699613\pi$
$47$			1.07798e18i			0.436049i	−0.975943	+	0.218025i	$0.930039\pi$
$48$	−2.46273e18	+	4.36498e17i	−0.790247	+	0.140065i
$49$	3.29870e18			0.843696
$50$	4.05667e18	−	1.89275e18i	0.830806	−	0.387636i
$51$			4.75185e18i			0.782692i
$52$	−4.08419e18	+	4.87174e18i	−0.543337	+	0.648108i
$53$	5.00954e18			0.540460			0.270230	−	0.962796i	$-0.412900\pi$
$53$	5.00954e18			0.540460			0.270230	+	0.962796i	$0.412900\pi$
$54$	5.23830e18	+	1.12271e19i	0.460107	+	0.986132i
$55$		−	6.40349e18i		−	0.459650i
$56$	−6.48745e18	−	1.73368e18i	−0.381949	−	0.102071i
$57$	−1.66233e19			−0.805552
$58$	3.79212e19	−	1.76932e19i	1.51766	−	0.708105i
$59$		−	1.63645e19i		−	0.542665i	−0.962486	−	0.271333i	$-0.912536\pi$
$59$		−	1.63645e19i		−	0.542665i	0.962486	−	0.271333i	$-0.0874643\pi$
$60$	−6.43654e18	−	5.39603e18i	−0.177414	−	0.148734i
$61$	−6.52861e19			−1.50035			−0.750174	−	0.661240i	$-0.770031\pi$
$61$	−6.52861e19			−1.50035			−0.750174	+	0.661240i	$0.770031\pi$
$62$	2.70091e19	+	5.78876e19i	0.519040	+	1.11244i
$63$			8.73068e18i			0.140703i
$64$	−6.39504e19	−	3.68084e19i	−0.866690	−	0.498847i
$65$	−2.13487e19			−0.243964
$66$	1.19958e20	−	5.59695e19i	1.15890	−	0.540715i
$67$		−	1.63629e20i		−	1.33979i	−0.742456	−	0.669895i	$-0.766339\pi$
$67$		−	1.63629e20i		−	1.33979i	0.742456	−	0.669895i	$-0.233661\pi$
$68$	−9.00631e19	+	1.07430e20i	−0.626540	+	0.747354i
$69$	1.45537e20			0.862252
$70$	−9.53479e18	−	2.04356e19i	−0.0482206	−	0.103350i
$71$			3.91076e20i			1.69208i	0.533123	+	0.846038i	$0.321018\pi$
$71$			3.91076e20i			1.69208i	−0.533123	+	0.846038i	$0.678982\pi$
$72$	−2.47680e19	+	9.26821e19i	−0.0918827	+	0.343826i
$73$	2.53547e20			0.808177			0.404088	−	0.914720i	$-0.367589\pi$
$73$	2.53547e20			0.808177			0.404088	+	0.914720i	$0.367589\pi$
$74$	1.39973e19	−	6.53082e18i	0.0384145	−	0.0179233i
$75$			3.10758e20i			0.735781i
$76$	−3.75819e20	−	3.15066e20i	−0.769183	−	0.644840i
$77$	3.55399e20			0.629968
$78$	−1.86598e20	−	3.99929e20i	−0.286990	−	0.615095i
$79$		−	4.85911e20i		−	0.649619i	−0.945779	−	0.324809i	$-0.894700\pi$
$79$		−	4.85911e20i		−	0.649619i	0.945779	−	0.324809i	$-0.105300\pi$
$80$	−4.32447e19	−	2.43987e20i	−0.0503435	−	0.284038i
$81$	−5.09570e20			−0.517450
$82$	−9.79803e20	+	4.57154e20i	−0.869333	+	0.405612i
$83$		−	1.58468e21i		−	1.23051i	−0.788330	−	0.615253i	$-0.789054\pi$
$83$		−	1.58468e21i		−	1.23051i	0.788330	−	0.615253i	$-0.210946\pi$
$84$	2.99484e20	−	3.57233e20i	0.203846	−	0.243153i
$85$	−4.70774e20			−0.281323
$86$	4.30829e20	+	9.23380e20i	0.226371	+	0.485174i
$87$			2.90492e21i			1.34407i
$88$	3.77281e21	+	1.00823e21i	1.53941	+	0.411387i
$89$	−3.37182e20			−0.121499			−0.0607497	−	0.998153i	$-0.519349\pi$
$89$	−3.37182e20			−0.121499			−0.0607497	+	0.998153i	$0.519349\pi$
$90$	−2.91951e20	+	1.36218e20i	−0.0930340	+	0.0434076i
$91$		−	1.18487e21i		−	0.334361i
$92$	3.29031e21	+	2.75841e21i	0.823323	+	0.690228i
$93$	−4.43443e21			−0.985203
$94$	−9.33462e20	−	2.00066e21i	−0.184370	−	0.395154i
$95$		−	1.64690e21i		−	0.289539i
$96$	4.19266e21	−	2.94267e21i	0.656911	−	0.461060i
$97$	4.16330e20			0.0582034			0.0291017	−	0.999576i	$-0.490735\pi$
$97$	4.16330e20			0.0582034			0.0291017	+	0.999576i	$0.490735\pi$
$98$	−6.12215e21	+	2.85646e21i	−0.764570	+	0.356731i
$99$		−	5.07737e21i		−	0.567089i
$100$	−5.88988e21	+	7.02562e21i	−0.588988	+	0.702562i
$101$	5.83595e21			0.523090			0.261545	−	0.965191i	$-0.415768\pi$
$101$	5.83595e21			0.523090			0.261545	+	0.965191i	$0.415768\pi$
$102$	−4.11479e21	−	8.81908e21i	−0.330937	−	0.709286i
$103$			2.51080e21i			0.181386i	0.995879	+	0.0906928i	$0.0289081\pi$
$103$			2.51080e21i			0.181386i	−0.995879	+	0.0906928i	$0.971092\pi$
$104$	3.36136e21	−	1.25782e22i	0.218347	−	0.817058i
$105$	1.56545e21			0.0915287
$106$	−9.29734e21	+	4.33793e21i	−0.489772	+	0.228517i
$107$			1.99926e22i			0.949836i	0.880030	+	0.474918i	$0.157522\pi$
$107$			1.99926e22i			0.949836i	−0.880030	+	0.474918i	$0.842478\pi$
$108$	−1.94438e22	−	1.63006e22i	−0.833912	−	0.699105i
$109$	1.78176e22			0.690489			0.345245	−	0.938513i	$-0.387796\pi$
$109$	1.78176e22			0.690489			0.345245	+	0.938513i	$0.387796\pi$
$110$	5.54500e21	+	1.18844e22i	0.194349	+	0.416541i
$111$			1.07225e21i			0.0340207i
$112$	1.35415e22	−	2.40012e21i	0.389285	−	0.0689976i
$113$	3.75312e22			0.978430			0.489215	−	0.872163i	$-0.337283\pi$
$113$	3.75312e22			0.978430			0.489215	+	0.872163i	$0.337283\pi$
$114$	3.08516e22	−	1.43947e22i	0.730002	−	0.340603i
$115$			1.44187e22i			0.309919i
$116$	−5.50578e22	+	6.56745e22i	−1.07592	+	1.28339i
$117$	−1.69275e22			−0.300988
$118$	1.41706e22	+	3.03714e22i	0.229449	+	0.491771i
$119$		−	2.61284e22i		−	0.385563i
$120$	1.66183e22	+	4.44102e21i	0.223663	+	0.0597709i
$121$	−1.25281e23			−1.53903
$122$	1.21166e23	−	5.65334e22i	1.35964	−	0.634376i
$123$		−	7.50570e22i		−	0.769901i
$124$	−1.00254e23	−	8.40470e22i	−0.940723	−	0.788649i
$125$	−6.43691e22			−0.552927
$126$	−7.56019e21	−	1.62035e22i	−0.0594917	−	0.127507i
$127$		−	1.54008e23i		−	1.11097i	−0.831527	−	0.555484i	$-0.812533\pi$
$127$		−	1.54008e23i		−	1.11097i	0.831527	−	0.555484i	$-0.187467\pi$
$128$	1.50561e23	+	1.29369e22i	0.996329	+	0.0856091i
$129$	−7.07348e22			−0.429681
$130$	3.96217e22	−	1.84866e22i	0.221083	−	0.103153i
$131$			3.53308e23i			1.81205i	0.423228	+	0.906023i	$0.360897\pi$
$131$			3.53308e23i			1.81205i	−0.423228	+	0.906023i	$0.639103\pi$
$132$	−1.74166e23	+	2.07751e23i	−0.821583	+	0.980007i
$133$	9.14042e22			0.396824
$134$	1.41692e23	+	3.03683e23i	0.566489	+	1.21414i
$135$		−	8.52058e22i		−	0.313905i
$136$	7.41234e22	−	2.77370e23i	0.251784	−	0.942176i
$137$	4.71070e23			1.47625			0.738124	−	0.674665i	$-0.235712\pi$
$137$	4.71070e23			1.47625			0.738124	+	0.674665i	$0.235712\pi$
$138$	−2.70107e23	+	1.26026e23i	−0.781385	+	0.364577i
$139$		−	1.52514e23i		−	0.407519i	−0.979021	−	0.203759i	$-0.934684\pi$
$139$		−	1.52514e23i		−	0.407519i	0.979021	−	0.203759i	$-0.0653160\pi$
$140$	3.53917e22	+	2.96704e22i	0.0873964	+	0.0732682i
$141$	1.53259e23			0.349957
$142$	−3.38646e23	−	7.25809e23i	−0.715442	−	1.53338i
$143$			6.89068e23i			1.34761i
$144$	−3.42890e22	−	1.93459e23i	−0.0621108	−	0.350430i
$145$	−2.87796e23			−0.483099
$146$	−4.70564e23	+	2.19555e23i	−0.732381	+	0.341713i
$147$		−	4.68982e23i		−	0.677120i
$148$	−2.03227e22	+	2.42414e22i	−0.0272334	+	0.0324847i
$149$	2.74203e23			0.341211			0.170605	−	0.985339i	$-0.445428\pi$
$149$	2.74203e23			0.341211			0.170605	+	0.985339i	$0.445428\pi$
$150$	−2.69096e23	−	5.76744e23i	−0.311102	−	0.666775i
$151$			7.25305e20i			0.000779425i	1.00000		0.000389712i	$0.000124049\pi$
$151$			7.25305e20i			0.000779425i	−1.00000		0.000389712i	$0.999876\pi$
$152$	9.70319e23	+	2.59304e23i	0.969695	+	0.259138i
$153$	−3.73280e23			−0.347079
$154$	−6.59595e23	+	3.07752e23i	−0.570886	+	0.266362i
$155$		−	4.39327e23i		−	0.354111i
$156$	6.92624e23	+	5.80657e23i	0.520148	+	0.436063i
$157$	−3.09117e23			−0.216385			−0.108192	−	0.994130i	$-0.534506\pi$
$157$	−3.09117e23			−0.216385			−0.108192	+	0.994130i	$0.534506\pi$
$158$	4.20767e23	+	9.01815e23i	0.274671	+	0.588694i
$159$		−	7.12215e23i		−	0.433753i
$160$	2.91536e23	+	4.15375e23i	0.165719	+	0.236113i
$161$	−8.00247e23			−0.424756
$162$	9.45724e23	−	4.41254e23i	0.468920	−	0.218788i
$163$			7.00257e23i			0.324485i	0.986751	+	0.162242i	$0.0518726\pi$
$163$			7.00257e23i			0.324485i	−0.986751	+	0.162242i	$0.948127\pi$
$164$	1.42258e24	−	1.69689e24i	0.616302	−	0.735142i
$165$	−9.10396e23			−0.368899
$166$	1.37223e24	+	2.94106e24i	0.520282	+	1.11510i
$167$			1.71999e24i			0.610444i	0.952281	+	0.305222i	$0.0987307\pi$
$167$			1.71999e24i			0.610444i	−0.952281	+	0.305222i	$0.901269\pi$
$168$	−2.46480e23	+	9.22332e23i	−0.0819182	+	0.306538i
$169$	−9.14541e23			−0.284741
$170$	8.73723e23	−	4.07659e23i	0.254938	−	0.118949i
$171$		−	1.30584e24i		−	0.357216i
$172$	−1.59917e24	−	1.34066e24i	−0.410282	−	0.343957i
$173$	1.85732e24			0.447075			0.223538	−	0.974695i	$-0.428239\pi$
$173$	1.85732e24			0.447075			0.223538	+	0.974695i	$0.428239\pi$
$174$	−2.51547e24	−	5.39132e24i	−0.568300	−	1.21802i
$175$		−	1.70872e24i		−	0.362454i
$176$	−7.87511e24	+	1.39580e24i	−1.56898	+	0.278089i
$177$	−2.32658e24			−0.435523
$178$	6.25785e23	−	2.91977e23i	0.110105	−	0.0513723i
$179$		−	6.45143e24i		−	1.06727i	−0.845716	−	0.533633i	$-0.820826\pi$
$179$		−	6.45143e24i		−	1.06727i	0.845716	−	0.533633i	$-0.179174\pi$
$180$	4.23883e23	−	5.05620e23i	0.0659552	−	0.0786731i
$181$	1.14699e25			1.67918			0.839590	−	0.543221i	$-0.182795\pi$
$181$	1.14699e25			1.67918			0.839590	+	0.543221i	$0.182795\pi$
$182$	1.02602e24	+	2.19904e24i	0.141374	+	0.303003i
$183$			9.28183e24i			1.20413i
$184$	−8.49517e24	−	2.27022e24i	−1.03795	−	0.277378i
$185$	−1.06230e23			−0.0122281
$186$	8.22998e24	−	3.83993e24i	0.892805	−	0.416563i
$187$			1.51951e25i			1.55398i
$188$	3.46487e24	+	2.90475e24i	0.334157	+	0.280139i
$189$	4.72899e24			0.430218
$190$	1.42611e24	+	3.05652e24i	0.122423	+	0.262385i
$191$		−	4.28838e24i		−	0.347477i	−0.984792	−	0.173739i	$-0.944415\pi$
$191$		−	4.28838e24i		−	0.347477i	0.984792	−	0.173739i	$-0.0555848\pi$
$192$	−5.23312e24	+	9.09195e24i	−0.400357	+	0.695574i
$193$	−9.22879e22			−0.00666829			−0.00333414	−	0.999994i	$-0.501061\pi$
$193$	−9.22879e22			−0.00666829			−0.00333414	+	0.999994i	$0.501061\pi$
$194$	−7.72677e23	+	3.60514e23i	−0.0527447	+	0.0246095i
$195$			3.03519e24i			0.195796i
$196$	8.88875e24	−	1.06028e25i	0.542031	−	0.646549i
$197$	−1.49145e25			−0.859963			−0.429982	−	0.902838i	$-0.641480\pi$
$197$	−1.49145e25			−0.859963			−0.429982	+	0.902838i	$0.641480\pi$
$198$	4.39666e24	+	9.42322e24i	0.239776	+	0.513904i
$199$		−	3.75600e25i		−	1.93794i	−0.247171	−	0.968972i	$-0.579501\pi$
$199$		−	3.75600e25i		−	1.93794i	0.247171	−	0.968972i	$-0.420499\pi$
$200$	4.84747e24	−	1.81393e25i	0.236693	−	0.885707i
$201$	−2.32634e25			−1.07527
$202$	−1.08311e25	+	5.05355e24i	−0.474032	+	0.221173i
$203$		−	1.59729e25i		−	0.662106i
$204$	1.52735e25	+	1.28044e25i	0.599800	+	0.502838i
$205$	7.43604e24			0.276725
$206$	−2.17419e24	−	4.65986e24i	−0.0766933	−	0.164374i
$207$			1.14326e25i			0.382360i
$208$	4.65348e24	+	2.62550e25i	0.147598	+	0.832751i
$209$	−5.31566e25			−1.59937
$210$	−2.90536e24	+	1.35558e24i	−0.0829446	+	0.0387001i
$211$			4.58833e25i			1.24322i	0.783327	+	0.621610i	$0.213521\pi$
$211$			4.58833e25i			1.24322i	−0.783327	+	0.621610i	$0.786479\pi$
$212$	1.34988e25	−	1.61018e25i	0.347217	−	0.414170i
$213$	5.56000e25			1.35800
$214$	−1.73123e25	−	3.71049e25i	−0.401609	−	0.860755i
$215$		−	7.00783e24i		−	0.154440i
$216$	5.02015e25	+	1.34157e25i	1.05130	+	0.280945i
$217$	2.43830e25			0.485323
$218$	−3.30681e25	+	1.54288e25i	−0.625731	+	0.291952i
$219$		−	3.60472e25i		−	0.648613i
$220$	−2.05822e25	−	1.72550e25i	−0.352243	−	0.295301i
$221$	5.06591e25			0.824789
$222$	−9.28498e23	−	1.99002e24i	−0.0143846	−	0.0308301i
$223$			8.76759e25i			1.29279i	0.763004	+	0.646393i	$0.223724\pi$
$223$			8.76759e25i			1.29279i	−0.763004	+	0.646393i	$0.776276\pi$
$224$	−2.30536e25	+	1.61805e25i	−0.323602	+	0.227124i
$225$	−2.44115e25			−0.326277
$226$	−6.96552e25	+	3.24995e25i	−0.886667	+	0.413699i
$227$		−	6.56769e24i		−	0.0796394i	−0.999207	−	0.0398197i	$-0.987322\pi$
$227$		−	6.56769e24i		−	0.0796394i	0.999207	−	0.0398197i	$-0.0126784\pi$
$228$	−4.47935e25	+	5.34309e25i	−0.517525	+	0.617318i
$229$	1.68357e26			1.85371			0.926855	−	0.375419i	$-0.122501\pi$
$229$	1.68357e26			1.85371			0.926855	+	0.375419i	$0.122501\pi$
$230$	−1.24856e25	−	2.67600e25i	−0.131040	−	0.280853i
$231$		−	5.05277e25i		−	0.505589i
$232$	4.53135e25	−	1.69563e26i	0.432374	−	1.61795i
$233$	−1.59771e26			−1.45406			−0.727031	−	0.686605i	$-0.759100\pi$
$233$	−1.59771e26			−1.45406			−0.727031	+	0.686605i	$0.759100\pi$
$234$	3.14163e25	−	1.46581e25i	0.272760	−	0.127264i
$235$			1.51836e25i			0.125785i
$236$	−5.25992e25	−	4.40963e25i	−0.415860	−	0.348634i
$237$	−6.90828e25			−0.521361
$238$	2.26254e25	+	4.84923e25i	0.163024	+	0.349403i
$239$		−	3.80579e25i		−	0.261859i	−0.991392	−	0.130930i	$-0.958204\pi$
$239$		−	3.80579e25i		−	0.261859i	0.991392	−	0.130930i	$-0.0417962\pi$
$240$	−3.46881e25	+	6.14817e24i	−0.227959	+	0.0404038i
$241$	−8.73473e25			−0.548355			−0.274178	−	0.961679i	$-0.588406\pi$
$241$	−8.73473e25			−0.548355			−0.274178	+	0.961679i	$0.588406\pi$
$242$	2.32513e26	−	1.08485e26i	1.39469	−	0.650732i
$243$		−	1.17387e26i		−	0.672903i
$244$	−1.75921e26	+	2.09844e26i	−0.963896	+	1.14976i
$245$	4.64629e25			0.243377
$246$	6.49944e25	+	1.39300e26i	0.325529	+	0.697695i
$247$			1.77220e26i			0.848879i
$248$	2.58843e26	+	6.91721e25i	1.18595	+	0.316929i
$249$	−2.25297e26			−0.987559
$250$	1.19464e26	−	5.57394e25i	0.501070	−	0.233788i
$251$		−	1.19823e26i		−	0.480981i	−0.970652	−	0.240490i	$-0.922692\pi$
$251$		−	1.19823e26i		−	0.480981i	0.970652	−	0.240490i	$-0.0773083\pi$
$252$	2.80623e25	+	2.35259e25i	0.107824	+	0.0903940i
$253$	4.65387e26			1.71194
$254$	1.33360e26	+	2.85827e26i	0.469739	+	1.00677i
$255$			6.69308e25i			0.225779i
$256$	−2.90633e26	+	1.06366e26i	−0.939084	+	0.343687i
$257$	−3.60352e26			−1.11548			−0.557741	−	0.830015i	$-0.688332\pi$
$257$	−3.60352e26			−1.11548			−0.557741	+	0.830015i	$0.688332\pi$
$258$	1.31279e26	−	6.12517e25i	0.389383	−	0.181677i
$259$		−	5.89584e24i		−	0.0167590i
$260$	−5.75268e25	+	6.86195e25i	−0.156734	+	0.186957i
$261$	−2.28195e26			−0.596020
$262$	−3.05941e26	−	6.55714e26i	−0.766168	−	1.64210i
$263$		−	1.21151e26i		−	0.290947i	−0.989362	−	0.145474i	$-0.953529\pi$
$263$		−	1.21151e26i		−	0.290947i	0.989362	−	0.145474i	$-0.0464706\pi$
$264$	1.43342e26	−	5.36386e26i	0.330164	−	1.23548i
$265$	7.05605e25			0.155904
$266$	−1.69640e26	+	7.91500e25i	−0.359608	+	0.167785i
$267$			4.79378e25i			0.0975111i
$268$	−5.25939e26	−	4.40918e26i	−1.02672	−	0.860746i
$269$	7.11062e26			1.33239			0.666197	−	0.745776i	$-0.267921\pi$
$269$	7.11062e26			1.33239			0.666197	+	0.745776i	$0.267921\pi$
$270$	7.37826e25	+	1.58136e26i	0.132725	+	0.284465i
$271$		−	1.95819e26i		−	0.338214i	−0.985598	−	0.169107i	$-0.945912\pi$
$271$		−	1.95819e26i		−	0.338214i	0.985598	−	0.169107i	$-0.0540884\pi$
$272$	1.02617e26	+	5.78965e26i	0.170200	+	0.960272i
$273$	−1.68455e26			−0.268346
$274$	−8.74272e26	+	4.07916e26i	−1.33780	+	0.624186i
$275$			9.93716e26i			1.46084i
$276$	3.92168e26	−	4.67789e26i	0.553952	−	0.660770i
$277$	1.09091e27			1.48086			0.740428	−	0.672136i	$-0.234623\pi$
$277$	1.09091e27			1.48086			0.740428	+	0.672136i	$0.234623\pi$
$278$	1.32067e26	+	2.83055e26i	0.172307	+	0.369299i
$279$		−	3.48345e26i		−	0.436881i
$280$	−9.13771e25	−	2.44193e25i	−0.110179	−	0.0294438i
$281$	−3.84634e26			−0.445941			−0.222971	−	0.974825i	$-0.571575\pi$
$281$	−3.84634e26			−0.445941			−0.222971	+	0.974825i	$0.571575\pi$
$282$	−2.84437e26	+	1.32712e26i	−0.317136	+	0.147969i
$283$		−	2.15340e26i		−	0.230927i	−0.993312	−	0.115463i	$-0.963165\pi$
$283$		−	2.15340e26i		−	0.230927i	0.993312	−	0.115463i	$-0.0368353\pi$
$284$	1.25700e27	+	1.05380e27i	1.29669	+	1.08707i
$285$	−2.34143e26			−0.232374
$286$	−5.96687e26	−	1.27886e27i	−0.569797	−	1.22123i
$287$			4.12706e26i			0.379263i
$288$	2.31160e26	+	3.29353e26i	0.204454	+	0.291303i
$289$	−5.74463e25			−0.0489086
$290$	5.34128e26	−	2.49212e26i	0.437792	−	0.204264i
$291$		−	5.91903e25i		−	0.0467119i
$292$	6.83212e26	−	8.14954e26i	0.519211	−	0.619329i
$293$	−5.77037e26			−0.422337			−0.211169	−	0.977450i	$-0.567727\pi$
$293$	−5.77037e26			−0.422337			−0.211169	+	0.977450i	$0.567727\pi$
$294$	4.06108e26	+	8.70397e26i	0.286299	+	0.613616i
$295$		−	2.30498e26i		−	0.156540i
$296$	1.67259e25	−	6.25884e25i	0.0109441	−	0.0409529i
$297$	−2.75017e27			−1.73396
$298$	−5.08900e26	+	2.37441e26i	−0.309210	+	0.144271i
$299$		−	1.55156e27i		−	0.908629i
$300$	9.98844e26	+	8.37375e26i	0.563850	+	0.472701i
$301$	3.88940e26			0.211666
$302$	−6.28066e23	−	1.34611e24i	−0.000329556	−	0.000706326i
$303$		−	8.29708e26i		−	0.419813i
$304$	−2.02538e27	+	3.58982e26i	−0.988319	+	0.175171i
$305$	−9.19568e26			−0.432799
$306$	6.92780e26	−	3.23235e26i	0.314528	−	0.146752i
$307$			1.57842e27i			0.691352i	0.938354	+	0.345676i	$0.112350\pi$
$307$			1.57842e27i			0.691352i	−0.938354	+	0.345676i	$0.887650\pi$
$308$	9.57666e26	−	1.14233e27i	0.404721	−	0.482763i
$309$	3.56965e26			0.145573
$310$	3.80428e26	+	8.15359e26i	0.149725	+	0.320900i
$311$		−	3.44935e27i		−	1.31031i	−0.755496	−	0.655154i	$-0.772604\pi$
$311$		−	3.44935e27i		−	1.31031i	0.755496	−	0.655154i	$-0.227396\pi$
$312$	−1.78827e27	−	4.77890e26i	−0.655741	−	0.175238i
$313$	4.54451e27			1.60879			0.804394	−	0.594096i	$-0.202490\pi$
$313$	4.54451e27			1.60879			0.804394	+	0.594096i	$0.202490\pi$
$314$	5.73698e26	−	2.67675e26i	0.196091	−	0.0914915i
$315$			1.22973e26i			0.0405878i
$316$	−1.56182e27	−	1.30935e27i	−0.497822	−	0.417346i
$317$	−1.36275e27			−0.419531			−0.209766	−	0.977752i	$-0.567270\pi$
$317$	−1.36275e27			−0.419531			−0.209766	+	0.977752i	$0.567270\pi$
$318$	6.16731e26	+	1.32182e27i	0.183399	+	0.393073i
$319$			9.28912e27i			2.66856i
$320$	−9.00756e26	−	5.18455e26i	−0.250010	−	0.143900i
$321$	2.84239e27			0.762304
$322$	1.48520e27	−	6.92961e26i	0.384920	−	0.179595i
$323$			3.90798e27i			0.978870i
$324$	−1.37310e27	+	1.63787e27i	−0.332435	+	0.396537i
$325$	3.31297e27			0.775355
$326$	−6.06377e26	−	1.29963e27i	−0.137198	−	0.294052i
$327$		−	2.53315e27i		−	0.554162i
$328$	−1.17080e27	+	4.38116e27i	−0.247669	+	0.926780i
$329$	−8.42703e26			−0.172393
$330$	1.68963e27	−	7.88343e26i	0.334301	−	0.155977i
$331$		−	7.17243e27i		−	1.37265i	−0.727297	−	0.686323i	$-0.759224\pi$
$331$		−	7.17243e27i		−	1.37265i	0.727297	−	0.686323i	$-0.240776\pi$
$332$	−5.09352e27	−	4.27012e27i	−0.942973	−	0.790536i
$333$	−8.42302e25			−0.0150863
$334$	−1.48940e27	−	3.19218e27i	−0.258108	−	0.553193i
$335$		−	2.30475e27i		−	0.386483i
$336$	−3.41229e26	−	1.92522e27i	−0.0553750	−	0.312426i
$337$	1.19454e27			0.187616			0.0938081	−	0.995590i	$-0.470096\pi$
$337$	1.19454e27			0.187616			0.0938081	+	0.995590i	$0.470096\pi$
$338$	1.69732e27	−	7.91932e26i	0.258036	−	0.120394i
$339$		−	5.33588e27i		−	0.785252i
$340$	−1.26856e27	+	1.51317e27i	−0.180735	+	0.215586i
$341$	−1.41801e28			−1.95605
$342$	1.13077e27	+	2.42354e27i	0.151038	+	0.323715i
$343$			5.63520e27i			0.728910i
$344$	4.12887e27	+	1.10338e27i	0.517235	+	0.138224i
$345$	2.04993e27			0.248730
$346$	−3.44706e27	+	1.60832e27i	−0.405146	+	0.189032i
$347$		−	4.62980e27i		−	0.527155i	−0.964638	−	0.263578i	$-0.915098\pi$
$347$		−	4.62980e27i		−	0.527155i	0.964638	−	0.263578i	$-0.0849025\pi$
$348$	9.33705e27	+	7.82766e27i	1.03000	+	0.863496i
$349$	−7.49349e27			−0.800948			−0.400474	−	0.916308i	$-0.631155\pi$
$349$	−7.49349e27			−0.800948			−0.400474	+	0.916308i	$0.631155\pi$
$350$	1.47964e27	+	3.17126e27i	0.153253	+	0.328461i
$351$			9.16884e27i			0.920314i
$352$	1.34070e28	−	9.40982e27i	1.30425	−	0.915403i
$353$	8.08847e27			0.762684			0.381342	−	0.924434i	$-0.375462\pi$
$353$	8.08847e27			0.762684			0.381342	+	0.924434i	$0.375462\pi$
$354$	4.31796e27	−	2.01466e27i	0.394677	−	0.184148i
$355$			5.50839e27i			0.488105i
$356$	−9.08578e26	+	1.08378e27i	−0.0780571	+	0.0931086i
$357$	−3.71471e27			−0.309439
$358$	5.58651e27	+	1.19734e28i	0.451261	+	0.967172i
$359$		−	1.28986e28i		−	1.01043i	−0.862995	−	0.505213i	$-0.831414\pi$
$359$		−	1.28986e28i		−	1.01043i	0.862995	−	0.505213i	$-0.168586\pi$
$360$	−3.48863e26	+	1.30545e27i	−0.0265050	+	0.0991818i
$361$	−1.01233e26			−0.00746004
$362$	−2.12874e28	+	9.93222e27i	−1.52170	+	0.709989i
$363$			1.78115e28i			1.23517i
$364$	−3.80844e27	−	3.19278e27i	−0.256231	−	0.214810i
$365$	3.57126e27			0.233131
$366$	−8.03745e27	−	1.72264e28i	−0.509128	−	1.09120i
$367$		−	2.96151e28i		−	1.82048i	−0.414077	−	0.910242i	$-0.635895\pi$
$367$		−	2.96151e28i		−	1.82048i	0.414077	−	0.910242i	$-0.364105\pi$
$368$	1.77323e28	−	3.14290e27i	1.05788	−	0.187501i
$369$	5.89608e27			0.341408
$370$	1.97155e26	−	9.19880e25i	0.0110812	−	0.00517026i
$371$			3.91616e27i			0.213672i
$372$	−1.19491e28	+	1.42532e28i	−0.632941	+	0.754990i
$373$	−2.06482e27			−0.106190			−0.0530951	−	0.998589i	$-0.516909\pi$
$373$	−2.06482e27			−0.106190			−0.0530951	+	0.998589i	$0.516909\pi$
$374$	−1.31579e28	−	2.82009e28i	−0.657052	−	1.40824i
$375$			9.15147e27i			0.443759i
$376$	−8.94587e27	−	2.39066e27i	−0.421266	−	0.112578i
$377$	3.09692e28			1.41636
$378$	−8.77666e27	+	4.09499e27i	−0.389870	+	0.181905i
$379$		−	1.46960e27i		−	0.0634114i	−0.999497	−	0.0317057i	$-0.989906\pi$
$379$		−	1.46960e27i		−	0.0634114i	0.999497	−	0.0317057i	$-0.0100939\pi$
$380$	−5.29349e27	−	4.43777e27i	−0.221882	−	0.186014i
$381$	−2.18955e28			−0.891623
$382$	3.71345e27	+	7.95892e27i	0.146920	+	0.314889i
$383$			4.47507e28i			1.72033i	0.510012	+	0.860167i	$0.329641\pi$
$383$			4.47507e28i			1.72033i	−0.510012	+	0.860167i	$0.670359\pi$
$384$	1.83926e27	−	2.14055e28i	0.0687068	−	0.799617i
$385$	5.00587e27			0.181724
$386$	1.71280e26	−	7.99152e25i	0.00604290	−	0.00281948i
$387$		−	5.55655e27i		−	0.190539i
$388$	1.12185e27	−	1.33817e27i	0.0373926	−	0.0446030i
$389$	−3.04549e27			−0.0986761			−0.0493381	−	0.998782i	$-0.515711\pi$
$389$	−3.04549e27			−0.0986761			−0.0493381	+	0.998782i	$0.515711\pi$
$390$	−2.62827e27	−	5.63308e27i	−0.0827865	−	0.177433i
$391$		−	3.42145e28i		−	1.04777i
$392$	−7.31559e27	+	2.73750e28i	−0.217822	+	0.815093i
$393$	5.02304e28			1.45428
$394$	2.76802e28	−	1.29150e28i	0.779311	−	0.363609i
$395$		−	6.84416e27i		−	0.187392i
$396$	−1.63198e28	−	1.36816e28i	−0.434577	−	0.364325i
$397$	−5.26788e28			−1.36440			−0.682198	−	0.731167i	$-0.738976\pi$
$397$	−5.26788e28			−1.36440			−0.682198	+	0.731167i	$0.738976\pi$
$398$	3.25244e28	+	6.97085e28i	0.819400	+	1.75619i
$399$		−	1.29951e28i		−	0.318477i
$400$	6.71086e27	+	3.78627e28i	0.159999	+	0.902718i
$401$	6.59976e27			0.153088			0.0765438	−	0.997066i	$-0.475611\pi$
$401$	6.59976e27			0.153088			0.0765438	+	0.997066i	$0.475611\pi$
$402$	4.31752e28	−	2.01446e28i	0.974422	−	0.454644i
$403$			4.72752e28i			1.03819i
$404$	1.57257e28	−	1.87580e28i	0.336058	−	0.400860i
$405$	−7.17740e27			−0.149266
$406$	1.38315e28	+	2.96445e28i	0.279951	+	0.600010i
$407$			3.42875e27i			0.0675457i
$408$	−3.94342e28	−	1.05383e28i	−0.756157	−	0.202072i
$409$	−8.68767e28			−1.62161			−0.810806	−	0.585315i	$-0.800971\pi$
$409$	−8.68767e28			−1.62161			−0.810806	+	0.585315i	$0.800971\pi$
$410$	−1.38007e28	+	6.43912e27i	−0.250772	+	0.117005i
$411$		−	6.69729e28i		−	1.18478i
$412$	8.07026e27	+	6.76566e27i	0.139001	+	0.116531i
$413$	1.27928e28			0.214544
$414$	−9.89990e27	−	2.12181e28i	−0.161669	−	0.346500i
$415$		−	2.23206e28i		−	0.354958i
$416$	−3.13716e28	−	4.46977e28i	−0.485859	−	0.692243i
$417$	−2.16832e28			−0.327060
$418$	9.86547e28	−	4.60301e28i	1.44937	−	0.676243i
$419$			4.51012e27i			0.0645407i	0.999479	+	0.0322703i	$0.0102737\pi$
$419$			4.51012e27i			0.0645407i	−0.999479	+	0.0322703i	$0.989726\pi$
$420$	4.21830e27	−	5.03170e27i	0.0588024	−	0.0701412i
$421$	−6.04698e28			−0.821175			−0.410587	−	0.911821i	$-0.634676\pi$
$421$	−6.04698e28			−0.821175			−0.410587	+	0.911821i	$0.634676\pi$
$422$	−3.97319e28	−	8.51561e28i	−0.525657	−	1.12662i
$423$			1.20392e28i			0.155186i
$424$	−1.11097e28	+	4.15728e28i	−0.139534	+	0.522137i
$425$	7.30564e28			0.894087
$426$	−1.03190e29	+	4.81459e28i	−1.23064	+	0.574188i
$427$		−	5.10368e28i		−	0.593167i
$428$	6.42607e28	+	5.38726e28i	0.727887	+	0.610220i
$429$	9.79660e28			1.08155
$430$	6.06831e27	+	1.30060e28i	0.0653003	+	0.139956i
$431$			1.00005e29i			1.04899i	0.851412	+	0.524497i	$0.175747\pi$
$431$			1.00005e29i			1.04899i	−0.851412	+	0.524497i	$0.824253\pi$
$432$	−1.04787e29	+	1.85727e28i	−1.07149	+	0.189913i
$433$	5.03076e28			0.501495			0.250748	−	0.968052i	$-0.419324\pi$
$433$	5.03076e28			0.501495			0.250748	+	0.968052i	$0.419324\pi$
$434$	−4.52531e28	+	2.11141e28i	−0.439806	+	0.205204i
$435$			4.09165e28i			0.387718i
$436$	4.80116e28	−	5.72695e28i	0.443603	−	0.529142i
$437$	1.19692e29			1.07837
$438$	3.12145e28	+	6.69009e28i	0.274246	+	0.587782i
$439$			9.30260e28i			0.797067i	0.917154	+	0.398533i	$0.130481\pi$
$439$			9.30260e28i			0.797067i	−0.917154	+	0.398533i	$0.869519\pi$
$440$	5.31408e28	+	1.42011e28i	0.444067	+	0.118671i
$441$	3.68407e28			0.300264
$442$	−9.40196e28	+	4.38675e28i	−0.747435	+	0.348737i
$443$			7.63232e28i			0.591855i	0.955210	+	0.295928i	$0.0956287\pi$
$443$			7.63232e28i			0.591855i	−0.955210	+	0.295928i	$0.904371\pi$
$444$	3.44645e27	+	2.88931e27i	0.0260711	+	0.0218565i
$445$	−4.74928e27			−0.0350484
$446$	−7.59216e28	−	1.62720e29i	−0.546615	−	1.17154i
$447$		−	3.89839e28i		−	0.273844i
$448$	2.87746e28	−	4.99927e28i	0.197220	−	0.342648i
$449$	−8.66448e28			−0.579472			−0.289736	−	0.957107i	$-0.593568\pi$
$449$	−8.66448e28			−0.579472			−0.289736	+	0.957107i	$0.593568\pi$
$450$	4.53059e28	−	2.11387e28i	0.295677	−	0.137956i
$451$		−	2.40011e29i		−	1.52858i
$452$	1.01132e29	−	1.20634e29i	0.628590	−	0.749800i
$453$	1.03118e26			0.000625538
$454$	5.68718e27	+	1.21891e28i	0.0336731	+	0.0721703i
$455$		−	1.66892e28i		−	0.0964516i
$456$	3.68658e28	−	1.37952e29i	0.207974	−	0.778242i
$457$	−3.14849e29			−1.73390			−0.866951	−	0.498394i	$-0.833923\pi$
$457$	−3.14849e29			−1.73390			−0.866951	+	0.498394i	$0.833923\pi$
$458$	−3.12459e29	+	1.45786e29i	−1.67986	+	0.783784i
$459$			2.02188e29i			1.06124i
$460$	4.63447e28	+	3.88528e28i	0.237500	+	0.199107i
$461$	1.77964e28			0.0890477			0.0445239	−	0.999008i	$-0.485823\pi$
$461$	1.77964e28			0.0890477			0.0445239	+	0.999008i	$0.485823\pi$
$462$	4.37537e28	+	9.37757e28i	0.213773	+	0.458172i
$463$		−	2.46093e29i		−	1.17411i	−0.809548	−	0.587054i	$-0.800288\pi$
$463$		−	2.46093e29i		−	1.17411i	0.809548	−	0.587054i	$-0.199712\pi$
$464$	6.27322e28	+	3.53936e29i	0.292276	+	1.64902i
$465$	−6.24599e28			−0.284197
$466$	2.96523e29	−	1.38351e29i	1.31769	−	0.614805i
$467$		−	1.83223e29i		−	0.795232i	−0.917552	−	0.397616i	$-0.869838\pi$
$467$		−	1.83223e29i		−	0.795232i	0.917552	−	0.397616i	$-0.130162\pi$
$468$	−4.56133e28	+	5.44088e28i	−0.193369	+	0.230656i
$469$	1.27915e29			0.529689
$470$	−1.31480e28	−	2.81797e28i	−0.0531843	−	0.113988i
$471$			4.39477e28i			0.173662i
$472$	1.35805e29	+	3.62920e28i	0.524268	+	0.140103i
$473$	−2.26190e29			−0.853102
$474$	1.28213e29	−	5.98211e28i	0.472464	−	0.220441i
$475$			2.55572e29i			0.920201i
$476$	−8.39822e28	−	7.04060e28i	−0.295468	−	0.247704i
$477$	5.59478e28			0.192345
$478$	3.29556e28	+	7.06326e28i	0.110719	+	0.237300i
$479$		−	2.74827e29i		−	0.902337i	−0.892439	−	0.451169i	$-0.851007\pi$
$479$		−	2.74827e29i		−	0.902337i	0.892439	−	0.451169i	$-0.148993\pi$
$480$	5.90546e28	−	4.14481e28i	0.189496	−	0.133000i
$481$	1.14312e28			0.0358505
$482$	1.62110e29	−	7.56369e28i	0.496927	−	0.231855i
$483$			1.13772e29i			0.340894i
$484$	−3.37586e29	+	4.02682e29i	−0.988747	+	1.17940i
$485$	5.86409e27			0.0167896
$486$	1.01650e29	+	2.17862e29i	0.284516	+	0.609794i
$487$			5.48443e29i			1.50077i	0.661003	+	0.750383i	$0.270131\pi$
$487$			5.48443e29i			1.50077i	−0.661003	+	0.750383i	$0.729869\pi$
$488$	1.44786e29	−	5.41791e29i	0.387355	−	1.44948i
$489$	9.95568e28			0.260420
$490$	−8.62318e28	+	4.02338e28i	−0.220552	+	0.102905i
$491$			3.55640e28i			0.0889435i	0.999011	+	0.0444717i	$0.0141605\pi$
$491$			3.55640e28i			0.0889435i	−0.999011	+	0.0444717i	$0.985840\pi$
$492$	−2.41250e29	−	2.02250e29i	−0.589998	−	0.494621i
$493$	6.82921e29			1.63326
$494$	−1.53461e29	−	3.28907e29i	−0.358922	−	0.769266i
$495$		−	7.15158e28i		−	0.163586i
$496$	−5.40291e29	+	9.57622e28i	−1.20873	+	0.214238i
$497$	−3.05720e29			−0.668966
$498$	4.18135e29	−	1.95093e29i	0.894940	−	0.417559i
$499$		−	8.59244e28i		−	0.179891i	−0.995947	−	0.0899457i	$-0.971331\pi$
$499$		−	8.59244e28i		−	0.179891i	0.995947	−	0.0899457i	$-0.0286693\pi$
$500$	−1.73450e29	+	2.06896e29i	−0.355226	+	0.423724i
$501$	2.44535e29			0.489920
$502$	1.03758e29	+	2.22382e29i	0.203368	+	0.435872i
$503$		−	6.17644e29i		−	1.18438i	−0.805799	−	0.592189i	$-0.798264\pi$
$503$		−	6.17644e29i		−	1.18438i	0.805799	−	0.592189i	$-0.201736\pi$
$504$	−7.24534e28	−	1.93622e28i	−0.135932	−	0.0363261i
$505$	8.22007e28			0.150893
$506$	−8.63725e29	+	4.02995e29i	−1.55139	+	0.723842i
$507$			1.30022e29i			0.228523i
$508$	−4.95014e29	−	4.14992e29i	−0.851367	−	0.713739i
$509$	3.18430e28			0.0535942			0.0267971	−	0.999641i	$-0.491469\pi$
$509$	3.18430e28			0.0535942			0.0267971	+	0.999641i	$0.491469\pi$
$510$	−5.79577e28	−	1.24219e29i	−0.0954638	−	0.204604i
$511$			1.98208e29i			0.319515i
$512$	4.47287e29	−	4.49076e29i	0.705694	−	0.708517i
$513$	−7.07309e29			−1.09224
$514$	6.68787e29	−	3.12041e29i	1.01087	−	0.471648i
$515$			3.53652e28i			0.0523234i
$516$	−1.90603e29	+	2.27357e29i	−0.276048	+	0.329277i
$517$	4.90078e29			0.694815
$518$	5.10541e27	+	1.09422e28i	0.00708603	+	0.0151872i
$519$		−	2.64059e29i		−	0.358806i
$520$	4.73455e28	−	1.77167e29i	0.0629857	−	0.235693i
$521$	1.19764e29			0.155995			0.0779976	−	0.996954i	$-0.475147\pi$
$521$	1.19764e29			0.155995			0.0779976	+	0.996954i	$0.475147\pi$
$522$	4.23513e29	−	1.97602e29i	0.540121	−	0.252009i
$523$			2.73824e29i			0.341943i	0.985276	+	0.170971i	$0.0546906\pi$
$523$			2.73824e29i			0.341943i	−0.985276	+	0.170971i	$0.945309\pi$
$524$	1.13561e30	+	9.52031e29i	1.38862	+	1.16414i
$525$	−2.42932e29			−0.290893
$526$	1.04909e29	+	2.24847e29i	0.123018	+	0.263660i
$527$			1.04249e30i			1.19717i
$528$	1.98443e29	+	1.11962e30i	0.223184	+	1.25921i
$529$	−1.40059e29			−0.154276
$530$	−1.30955e29	+	6.11007e28i	−0.141282	+	0.0659192i
$531$		−	1.82763e29i		−	0.193130i
$532$	2.46300e29	−	2.93793e29i	0.254939	−	0.304098i
$533$	−8.00178e29			−0.811311
$534$	−4.15109e28	−	8.89690e28i	−0.0412296	−	0.0883659i
$535$			2.81601e29i			0.273995i
$536$	1.35791e30	+	3.62883e29i	1.29437	+	0.345902i
$537$	−9.17211e29			−0.856549
$538$	−1.31968e30	+	6.15733e29i	−1.20743	+	0.563362i
$539$		−	1.49967e30i		−	1.34437i
$540$	−2.73870e29	−	2.29597e29i	−0.240554	−	0.201667i
$541$	5.29114e29			0.455386			0.227693	−	0.973733i	$-0.426882\pi$
$541$	5.29114e29			0.455386			0.227693	+	0.973733i	$0.426882\pi$
$542$	1.69566e29	+	3.63425e29i	0.143004	+	0.306495i
$543$		−	1.63070e30i		−	1.34765i
$544$	−6.91795e29	−	9.85657e29i	−0.560260	−	0.798248i
$545$	2.50964e29			0.199182
$546$	3.12641e29	−	1.45871e29i	0.243179	−	0.113462i
$547$		−	1.43258e30i		−	1.09209i	−0.837757	−	0.546043i	$-0.816133\pi$
$547$		−	1.43258e30i		−	1.09209i	0.837757	−	0.546043i	$-0.183867\pi$
$548$	1.26936e30	−	1.51412e30i	0.948413	−	1.13129i
$549$	−7.29131e29			−0.533961
$550$	−8.60493e29	−	1.84426e30i	−0.617671	−	1.32383i
$551$			2.38905e30i			1.68096i
$552$	−3.22761e29	+	1.20777e30i	−0.222613	+	0.833020i
$553$	3.79856e29			0.256828
$554$	−2.02465e30	+	9.44658e29i	−1.34197	+	0.626134i
$555$			1.51029e28i			0.00981379i
$556$	−4.90214e29	−	4.10968e29i	−0.312294	−	0.261809i
$557$	−5.49943e29			−0.343487			−0.171744	−	0.985142i	$-0.554940\pi$
$557$	−5.49943e29			−0.343487			−0.171744	+	0.985142i	$0.554940\pi$
$558$	3.01644e29	+	6.46503e29i	0.184722	+	0.395908i
$559$			7.54099e29i			0.452792i
$560$	1.90735e29	−	3.38061e28i	0.112295	−	0.0199034i
$561$	2.16031e30			1.24717
$562$	7.13852e29	−	3.33067e29i	0.404118	−	0.188553i
$563$			2.10715e30i			1.16978i	0.811113	+	0.584889i	$0.198862\pi$
$563$			2.10715e30i			1.16978i	−0.811113	+	0.584889i	$0.801138\pi$
$564$	4.12974e29	−	4.92607e29i	0.224829	−	0.268182i
$565$	5.28635e29			0.282243
$566$	1.86470e29	+	3.99655e29i	0.0976402	+	0.209269i
$567$		−	3.98351e29i		−	0.204575i
$568$	−3.24543e30	−	8.67297e29i	−1.63471	−	0.436854i
$569$	1.70557e30			0.842626			0.421313	−	0.906915i	$-0.361569\pi$
$569$	1.70557e30			0.842626			0.421313	+	0.906915i	$0.361569\pi$
$570$	4.34551e29	−	2.02752e29i	0.210580	−	0.0982521i
$571$			2.51843e30i			1.19710i	0.801084	+	0.598552i	$0.204257\pi$
$571$			2.51843e30i			1.19710i	−0.801084	+	0.598552i	$0.795743\pi$
$572$	2.21482e30	+	1.85678e30i	1.03272	+	0.865772i
$573$	−6.09687e29			−0.278873
$574$	−3.57376e29	−	7.65952e29i	−0.160359	−	0.343693i
$575$		−	2.23754e30i		−	0.984972i
$576$	−7.14214e29	−	4.11086e29i	−0.308447	−	0.177535i
$577$	2.17054e30			0.919676			0.459838	−	0.888003i	$-0.347908\pi$
$577$	2.17054e30			0.919676			0.459838	+	0.888003i	$0.347908\pi$
$578$	1.06616e29	−	4.97447e28i	0.0443217	−	0.0206795i
$579$			1.31207e28i			0.00535173i
$580$	−7.75501e29	+	9.25039e29i	−0.310366	+	0.370213i
$581$	1.23881e30			0.486483
$582$	5.12549e28	+	1.09853e29i	0.0197507	+	0.0423310i
$583$		−	2.27746e30i		−	0.861187i
$584$	−5.62295e29	+	2.10411e30i	−0.208652	+	0.780778i
$585$	−2.38428e29			−0.0868246
$586$	1.07094e30	−	4.99676e29i	0.382728	−	0.178572i
$587$		−	8.45113e29i		−	0.296412i	−0.988957	−	0.148206i	$-0.952650\pi$
$587$		−	8.45113e29i		−	0.296412i	0.988957	−	0.148206i	$-0.0473498\pi$
$588$	−1.50741e30	−	1.26373e30i	−0.518897	−	0.435014i
$589$	−3.64694e30			−1.23214
$590$	1.99596e29	+	4.27788e29i	0.0661881	+	0.141859i
$591$			2.12042e30i			0.690175i
$592$	2.31554e28	+	1.30643e29i	0.00739798	+	0.0417395i
$593$	−3.93283e30			−1.23340			−0.616699	−	0.787199i	$-0.711530\pi$
$593$	−3.93283e30			−1.23340			−0.616699	+	0.787199i	$0.711530\pi$
$594$	5.10411e30	−	2.38146e30i	1.57134	−	0.733151i
$595$		−	3.68024e29i		−	0.111222i
$596$	7.38873e29	−	8.81348e29i	0.219210	−	0.261480i
$597$	−5.33996e30			−1.55532
$598$	1.34355e30	+	2.87959e30i	0.384186	+	0.823412i
$599$		−	5.89888e29i		−	0.165605i	−0.996566	−	0.0828027i	$-0.973613\pi$
$599$		−	5.89888e29i		−	0.165605i	0.996566	−	0.0828027i	$-0.0263871\pi$
$600$	−2.57889e30	−	6.89174e29i	−0.710836	−	0.189961i
$601$	5.28702e30			1.43084			0.715421	−	0.698694i	$-0.246235\pi$
$601$	5.28702e30			1.43084			0.715421	+	0.698694i	$0.246235\pi$
$602$	−7.21844e29	+	3.36796e29i	−0.191815	+	0.0894965i
$603$		−	1.82745e30i		−	0.476820i
$604$	2.33129e27	+	1.95442e27i	0.000597296	+	0.000500740i
$605$	−1.76461e30			−0.443957
$606$	7.18472e29	+	1.53988e30i	0.177505	+	0.380441i
$607$		−	8.14171e29i		−	0.197533i	−0.995111	−	0.0987665i	$-0.968510\pi$
$607$		−	8.14171e29i		−	0.197533i	0.995111	−	0.0987665i	$-0.0314897\pi$
$608$	3.44810e30	−	2.42009e30i	0.821563	−	0.576623i
$609$	−2.27090e30			−0.531382
$610$	1.70665e30	−	7.96285e29i	0.392208	−	0.182996i
$611$		−	1.63388e30i		−	0.368780i
$612$	−1.00585e30	+	1.19980e30i	−0.222980	+	0.265977i
$613$	−2.67900e30			−0.583321			−0.291661	−	0.956522i	$-0.594208\pi$
$613$	−2.67900e30			−0.583321			−0.291661	+	0.956522i	$0.594208\pi$
$614$	−1.36680e30	−	2.92942e30i	−0.292317	−	0.626513i
$615$		−	1.05719e30i		−	0.222090i
$616$	−7.88175e29	+	2.94936e30i	−0.162643	+	0.608610i
$617$	1.90392e30			0.385933			0.192966	−	0.981205i	$-0.438189\pi$
$617$	1.90392e30			0.385933			0.192966	+	0.981205i	$0.438189\pi$
$618$	−6.62501e29	+	3.09108e29i	−0.131921	+	0.0615513i
$619$			2.19366e30i			0.429113i	0.976712	+	0.214557i	$0.0688307\pi$
$619$			2.19366e30i			0.429113i	−0.976712	+	0.214557i	$0.931169\pi$
$620$	−1.41209e30	−	1.18382e30i	−0.271366	−	0.227498i
$621$	6.19251e30			1.16912
$622$	2.98691e30	+	6.40174e30i	0.554023	+	1.18742i
$623$		−	2.63589e29i		−	0.0480351i
$624$	3.73272e30	−	6.61594e29i	0.668336	−	0.118457i
$625$	4.30468e30			0.757288
$626$	−8.43427e30	+	3.93524e30i	−1.45791	+	0.680227i
$627$			7.55736e30i			1.28359i
$628$	−8.32952e29	+	9.93569e29i	−0.139016	+	0.165822i
$629$	2.52076e29			0.0413404
$630$	−1.06487e29	−	2.28230e29i	−0.0171613	−	0.0367812i
$631$			2.86921e30i			0.454400i	0.973848	+	0.227200i	$0.0729572\pi$
$631$			2.86921e30i			0.454400i	−0.973848	+	0.227200i	$0.927043\pi$
$632$	4.03244e30	+	1.07761e30i	0.627595	+	0.167716i
$633$	6.52331e30			0.997763
$634$	2.52916e30	−	1.18005e30i	0.380185	−	0.177386i
$635$		−	2.16923e30i		−	0.320476i
$636$	−2.28922e30	−	1.91915e30i	−0.332398	−	0.278664i
$637$	−4.99979e30			−0.713539
$638$	−8.04376e30	−	1.72399e31i	−1.12832	−	2.41829i
$639$			4.36764e30i			0.602195i
$640$	2.12068e30	+	1.82219e29i	0.287406	+	0.0246953i
$641$	6.07608e30			0.809441			0.404721	−	0.914440i	$-0.367369\pi$
$641$	6.07608e30			0.809441			0.404721	+	0.914440i	$0.367369\pi$
$642$	−5.27526e30	+	2.46132e30i	−0.690811	+	0.322317i
$643$		−	3.30507e29i		−	0.0425461i	−0.999774	−	0.0212730i	$-0.993228\pi$
$643$		−	3.30507e29i		−	0.0425461i	0.999774	−	0.0212730i	$-0.00677193\pi$
$644$	−2.15636e30	+	2.57217e30i	−0.272883	+	0.325503i
$645$	−9.96315e29			−0.123948
$646$	−3.38406e30	−	7.25293e30i	−0.413885	−	0.887066i
$647$		−	8.39132e30i		−	1.00898i	−0.863417	−	0.504491i	$-0.831680\pi$
$647$		−	8.39132e30i		−	1.00898i	0.863417	−	0.504491i	$-0.168320\pi$
$648$	1.13008e30	−	4.22877e30i	0.133593	−	0.499907i
$649$	−7.43974e30			−0.864701
$650$	−6.14863e30	+	2.86881e30i	−0.702638	+	0.327835i
$651$		−	3.46658e30i		−	0.389502i
$652$	2.25078e30	+	1.88693e30i	0.248662	+	0.208464i
$653$	−4.00302e30			−0.434853			−0.217427	−	0.976077i	$-0.569766\pi$
$653$	−4.00302e30			−0.434853			−0.217427	+	0.976077i	$0.569766\pi$
$654$	2.19354e30	+	4.70135e30i	0.234310	+	0.502189i
$655$			4.97642e30i			0.522712i
$656$	−1.62087e30	−	9.14495e30i	−0.167419	−	0.944580i
$657$	2.83167e30			0.287623
$658$	1.56399e30	−	7.29725e29i	0.156225	−	0.0728911i
$659$		−	1.45334e30i		−	0.142767i	−0.997449	−	0.0713837i	$-0.977259\pi$
$659$		−	1.45334e30i		−	0.142767i	0.997449	−	0.0713837i	$-0.0227415\pi$
$660$	−2.45317e30	+	2.92621e30i	−0.236998	+	0.282698i
$661$	−1.71920e30			−0.163347			−0.0816733	−	0.996659i	$-0.526026\pi$
$661$	−1.71920e30			−0.163347			−0.0816733	+	0.996659i	$0.526026\pi$
$662$	6.21085e30	+	1.33115e31i	0.580381	+	1.24391i
$663$		−	7.20230e30i		−	0.661946i
$664$	1.31508e31	+	3.51438e30i	1.18879	+	0.317688i
$665$	1.28745e30			0.114470
$666$	1.56325e29	−	7.29378e28i	0.0136714	−	0.00637876i
$667$		−	2.09162e31i		−	1.79928i
$668$	5.52844e30	+	4.63473e30i	0.467801	+	0.392178i
$669$	1.24650e31			1.03754
$670$	1.99576e30	+	4.27744e30i	0.163412	+	0.350236i
$671$			2.96807e31i			2.39071i
$672$	2.30040e30	+	3.27758e30i	0.182281	+	0.259711i
$673$	−1.96224e31			−1.52963			−0.764814	−	0.644251i	$-0.777169\pi$
$673$	−1.96224e31			−1.52963			−0.764814	+	0.644251i	$0.777169\pi$
$674$	−2.21697e30	+	1.03439e30i	−0.170020	+	0.0793277i
$675$			1.32225e31i			0.997639i
$676$	−2.46434e30	+	2.93954e30i	−0.182931	+	0.218205i
$677$	−1.04450e31			−0.762842			−0.381421	−	0.924401i	$-0.624565\pi$
$677$	−1.04450e31			−0.762842			−0.381421	+	0.924401i	$0.624565\pi$
$678$	4.62052e30	+	9.90300e30i	0.332020	+	0.711607i
$679$			3.25462e29i			0.0230108i
$680$	1.04404e30	−	3.90682e30i	0.0726308	−	0.271785i
$681$	−9.33740e29			−0.0639157
$682$	2.63172e31	−	1.22790e31i	1.77260	−	0.827056i
$683$		−	8.33825e29i		−	0.0552646i	−0.999618	−	0.0276323i	$-0.991203\pi$
$683$		−	8.33825e29i		−	0.0552646i	0.999618	−	0.0276323i	$-0.00879676\pi$
$684$	−4.19724e30	−	3.51873e30i	−0.273745	−	0.229493i
$685$	6.63513e30			0.425846
$686$	−4.87971e30	−	1.04585e31i	−0.308197	−	0.660548i
$687$		−	2.39357e31i		−	1.48772i
$688$	−8.61833e30	+	1.52753e30i	−0.527169	+	0.0934364i
$689$	−7.59288e30			−0.457083
$690$	−3.80451e30	+	1.77510e30i	−0.225403	+	0.105168i
$691$		−	1.37979e31i		−	0.804555i	−0.915518	−	0.402277i	$-0.868219\pi$
$691$		−	1.37979e31i		−	0.804555i	0.915518	−	0.402277i	$-0.131781\pi$
$692$	5.00479e30	−	5.96985e30i	0.287222	−	0.342607i
$693$	3.96919e30			0.224200
$694$	4.00910e30	+	8.59258e30i	0.222891	+	0.477715i
$695$		−	2.14820e30i		−	0.117555i
$696$	−2.41071e31	−	6.44230e30i	−1.29851	−	0.347008i
$697$	−1.76452e31			−0.935549
$698$	1.39074e31	−	6.48887e30i	0.725831	−	0.338656i
$699$			2.27149e31i			1.16698i
$700$	−5.49221e30	−	4.60436e30i	−0.277759	−	0.232858i
$701$	3.45056e31			1.71787			0.858937	−	0.512081i	$-0.171125\pi$
$701$	3.45056e31			1.71787			0.858937	+	0.512081i	$0.171125\pi$
$702$	−7.93961e30	−	1.70167e31i	−0.389127	−	0.834002i
$703$			8.81833e29i			0.0425479i
$704$	−1.67340e31	+	2.90735e31i	−0.794880	+	1.38101i
$705$	2.15868e30			0.100950
$706$	−1.50116e31	+	7.00408e30i	−0.691155	+	0.322477i
$707$			4.56220e30i			0.206805i
$708$	−6.26924e30	+	7.47813e30i	−0.279801	+	0.333754i
$709$	−7.31070e30			−0.321255			−0.160628	−	0.987015i	$-0.551352\pi$
$709$	−7.31070e30			−0.321255			−0.160628	+	0.987015i	$0.551352\pi$
$710$	−4.76990e30	−	1.02232e31i	−0.206380	−	0.442327i
$711$		−	5.42677e30i		−	0.231194i
$712$	7.47775e29	−	2.79818e30i	0.0313683	−	0.117380i
$713$	3.19290e31			1.31887
$714$	6.89424e30	−	3.21670e30i	0.280418	−	0.130837i
$715$			9.70567e30i			0.388740i
$716$	−2.07363e31	−	1.73842e31i	−0.817877	−	0.685663i
$717$	−5.41076e30			−0.210159
$718$	1.11694e31	+	2.39389e31i	0.427228	+	0.915662i
$719$		−	2.02921e31i		−	0.764379i	−0.924084	−	0.382189i	$-0.875170\pi$
$719$		−	2.02921e31i		−	0.764379i	0.924084	−	0.382189i	$-0.124830\pi$
$720$	−4.82968e29	−	2.72491e30i	−0.0179168	−	0.101087i
$721$	−1.96280e30			−0.0717112
$722$	1.87880e29	−	8.76607e28i	0.00676039	−	0.00315425i
$723$			1.24183e31i			0.440090i
$724$	3.09072e31	−	3.68669e31i	1.07879	−	1.28680i
$725$	4.46612e31			1.53537
$726$	−1.54236e31	−	3.30568e31i	−0.522254	−	1.11933i
$727$			3.78326e31i			1.26179i	0.775868	+	0.630896i	$0.217312\pi$
$727$			3.78326e31i			1.26179i	−0.775868	+	0.630896i	$0.782688\pi$
$728$	9.83292e30	+	2.62771e30i	0.323026	+	0.0863242i
$729$	−3.26800e31			−1.05750
$730$	−6.62799e30	+	3.09247e30i	−0.211266	+	0.0985722i
$731$			1.66291e31i			0.522129i
$732$	2.98338e31	+	2.50110e31i	0.922757	+	0.773588i
$733$	2.23524e31			0.681052			0.340526	−	0.940235i	$-0.389395\pi$
$733$	2.23524e31			0.681052			0.340526	+	0.940235i	$0.389395\pi$
$734$	2.56447e31	+	5.49635e31i	0.769736	+	1.64975i
$735$		−	6.60572e30i		−	0.195326i
$736$	−3.01882e31	+	2.11880e31i	−0.879391	+	0.617210i
$737$	−7.43898e31			−2.13487
$738$	−1.09427e31	+	5.10561e30i	−0.309388	+	0.144354i
$739$		−	3.39542e31i		−	0.945812i	−0.881113	−	0.472906i	$-0.843205\pi$
$739$		−	3.39542e31i		−	0.945812i	0.881113	−	0.472906i	$-0.156795\pi$
$740$	−2.86249e29	+	3.41446e29i	−0.00785589	+	0.00937072i
$741$	2.51956e31			0.681279
$742$	−3.39114e30	−	7.26811e30i	−0.0903447	−	0.193633i
$743$			2.09698e31i			0.550450i	0.961380	+	0.275225i	$0.0887523\pi$
$743$			2.09698e31i			0.550450i	−0.961380	+	0.275225i	$0.911248\pi$
$744$	9.83432e30	−	3.68001e31i	0.254356	−	0.951802i
$745$	3.86221e30			0.0984275
$746$	3.83215e30	−	1.78800e30i	0.0962311	−	0.0448993i
$747$		−	1.76981e31i		−	0.437926i
$748$	4.88403e31	+	4.09450e31i	1.19086	+	0.998350i
$749$	−1.56291e31			−0.375520
$750$	−7.92457e30	−	1.69845e31i	−0.187630	−	0.402141i
$751$		−	6.40718e31i		−	1.49495i	−0.664288	−	0.747476i	$-0.731265\pi$
$751$		−	6.40718e31i		−	1.49495i	0.664288	−	0.747476i	$-0.268735\pi$
$752$	1.86730e31	−	3.30964e30i	0.429357	−	0.0761000i
$753$	−1.70354e31			−0.386018
$754$	−5.74765e31	+	2.68173e31i	−1.28353	+	0.598866i
$755$			1.02161e28i			0.000224837i
$756$	1.27428e31	−	1.52000e31i	0.276393	−	0.329689i
$757$	−8.56168e31			−1.83022			−0.915112	−	0.403200i	$-0.867898\pi$
$757$	−8.56168e31			−1.83022			−0.915112	+	0.403200i	$0.867898\pi$
$758$	1.27258e30	+	2.72747e30i	0.0268116	+	0.0574643i
$759$		−	6.61649e31i		−	1.37394i
$760$	1.36672e31	+	3.65236e30i	0.279723	+	0.0747522i
$761$	1.86273e31			0.375768			0.187884	−	0.982191i	$-0.439837\pi$
$761$	1.86273e31			0.375768			0.187884	+	0.982191i	$0.439837\pi$
$762$	4.06365e31	−	1.89601e31i	0.808001	−	0.376995i
$763$			1.39287e31i			0.272987i
$764$	−1.37838e31	−	1.15556e31i	−0.266282	−	0.223236i
$765$	−5.25773e30			−0.100120
$766$	−3.87511e31	−	8.30539e31i	−0.727390	−	1.55899i
$767$			2.48035e31i			0.458948i
$768$	1.51222e31	+	4.13197e31i	0.275831	+	0.753675i
$769$	9.42275e29			0.0169429			0.00847146	−	0.999964i	$-0.497303\pi$
$769$	9.42275e29			0.0169429			0.00847146	+	0.999964i	$0.497303\pi$
$770$	−9.29053e30	+	4.33475e30i	−0.164681	+	0.0768363i
$771$			5.12319e31i			0.895246i
$772$	−2.48681e29	+	2.96634e29i	−0.00428403	+	0.00511011i
$773$	8.43528e30			0.143260			0.0716300	−	0.997431i	$-0.477180\pi$
$773$	8.43528e30			0.143260			0.0716300	+	0.997431i	$0.477180\pi$
$774$	4.81160e30	+	1.03125e31i	0.0805636	+	0.172669i
$775$			6.81763e31i			1.12542i
$776$	−9.23301e29	+	3.45500e30i	−0.0150267	+	0.0562302i
$777$	−8.38222e29			−0.0134502
$778$	5.65221e30	−	2.63720e30i	0.0894217	−	0.0417222i
$779$		−	6.17279e31i		−	0.962874i
$780$	9.75576e30	+	8.17868e30i	0.150045	+	0.125789i
$781$	1.77793e32			2.69621
$782$	2.96275e31	+	6.34996e31i	0.443017	+	0.949504i
$783$			1.23602e32i			1.82242i
$784$	−1.01277e31	−	5.71408e31i	−0.147243	−	0.830749i
$785$	−4.35397e30			−0.0624194
$786$	−9.32240e31	+	4.34962e31i	−1.31789	+	0.614899i
$787$		−	2.42673e31i		−	0.338299i	−0.985590	−	0.169149i	$-0.945898\pi$
$787$		−	2.42673e31i		−	0.338299i	0.985590	−	0.169149i	$-0.0541020\pi$
$788$	−4.01889e31	+	4.79384e31i	−0.552482	+	0.659015i
$789$	−1.72243e31			−0.233504
$790$	5.92659e30	+	1.27023e31i	0.0792331	+	0.169818i
$791$			2.93397e31i			0.386825i
$792$	4.21356e31	+	1.12602e31i	0.547864	+	0.146409i
$793$	9.89530e31			1.26889
$794$	9.77680e31	−	4.56164e31i	1.23644	−	0.576893i
$795$		−	1.00317e31i		−	0.125123i
$796$	−1.20726e32	−	1.01210e32i	−1.48510	−	1.24503i
$797$	−4.17177e31			−0.506149			−0.253075	−	0.967447i	$-0.581442\pi$
$797$	−4.17177e31			−0.506149			−0.253075	+	0.967447i	$0.581442\pi$
$798$	1.12529e31	+	2.41180e31i	0.134658	+	0.288608i
$799$		−	3.60297e31i		−	0.425252i
$800$	−4.52415e31	−	6.44593e31i	−0.526680	−	0.750405i
$801$	−3.76573e30			−0.0432406
$802$	−1.22487e31	+	5.71496e30i	−0.138730	+	0.0647284i
$803$		−	1.15269e32i		−	1.28778i
$804$	−6.26860e31	+	7.47736e31i	−0.690803	+	0.824009i
$805$	−1.12716e31			−0.122527
$806$	−4.09372e31	−	8.77393e31i	−0.438968	−	0.940825i
$807$		−	1.01093e32i		−	1.06933i
$808$	−1.29425e31	+	4.84309e31i	−0.135050	+	0.505356i
$809$	−3.63229e31			−0.373893			−0.186946	−	0.982370i	$-0.559859\pi$
$809$	−3.63229e31			−0.373893			−0.186946	+	0.982370i	$0.559859\pi$
$810$	1.33207e31	−	6.21515e30i	0.135267	−	0.0631127i
$811$			1.59940e32i			1.60224i	0.598501	+	0.801122i	$0.295763\pi$
$811$			1.59940e32i			1.60224i	−0.598501	+	0.801122i	$0.704237\pi$
$812$	−5.13404e31	−	4.30409e31i	−0.507391	−	0.425368i
$813$	−2.78399e31			−0.271439
$814$	−2.96907e30	−	6.36352e30i	−0.0285596	−	0.0612109i
$815$			9.86328e30i			0.0936025i
$816$	8.23125e31	−	1.45892e31i	0.770680	−	0.136597i
$817$	−5.81732e31			−0.537379
$818$	1.61237e32	−	7.52295e31i	1.46953	−	0.685649i
$819$		−	1.32329e31i		−	0.118996i
$820$	2.00373e31	−	2.39010e31i	0.177782	−	0.212063i
$821$	−1.50268e32			−1.31550			−0.657751	−	0.753235i	$-0.728492\pi$
$821$	−1.50268e32			−1.31550			−0.657751	+	0.753235i	$0.728492\pi$
$822$	5.79941e31	+	1.24297e32i	0.500949	+	1.07367i
$823$			9.49253e31i			0.809066i	0.914523	+	0.404533i	$0.132566\pi$
$823$			9.49253e31i			0.809066i	−0.914523	+	0.404533i	$0.867434\pi$
$824$	−2.08364e31	−	5.56825e30i	−0.175236	−	0.0468295i
$825$	1.41278e32			1.17242
$826$	−2.37426e31	+	1.10777e31i	−0.194423	+	0.0907133i
$827$		−	6.30123e31i		−	0.509172i	−0.967050	−	0.254586i	$-0.918061\pi$
$827$		−	6.30123e31i		−	0.509172i	0.967050	−	0.254586i	$-0.0819392\pi$
$828$	3.67470e31	+	3.08066e31i	0.293014	+	0.245646i
$829$	−1.44664e31			−0.113831			−0.0569155	−	0.998379i	$-0.518127\pi$
$829$	−1.44664e31			−0.113831			−0.0569155	+	0.998379i	$0.518127\pi$
$830$	1.93282e31	+	4.14254e31i	0.150083	+	0.321668i
$831$		−	1.55097e32i		−	1.18848i
$832$	9.69286e31	+	5.57899e31i	0.732986	+	0.421890i
$833$	−1.10253e32			−0.822806
$834$	4.02424e31	−	1.87762e31i	0.296386	−	0.138287i
$835$			2.42265e31i			0.176092i
$836$	−1.43237e32	+	1.70857e32i	−1.02751	+	1.22564i
$837$	−1.88682e32			−1.33583
$838$	−3.90546e30	−	8.37044e30i	−0.0272890	−	0.0584877i
$839$			3.26231e31i			0.224980i	0.993653	+	0.112490i	$0.0358826\pi$
$839$			3.26231e31i			0.224980i	−0.993653	+	0.112490i	$0.964117\pi$
$840$	−3.47173e30	+	1.29912e31i	−0.0236305	+	0.0884257i
$841$	2.68634e32			1.80470
$842$	1.12228e32	−	5.23629e31i	0.744160	−	0.347208i
$843$			5.46840e31i			0.357896i
$844$	1.47479e32	+	1.23638e32i	0.952716	+	0.798704i
$845$	−1.28815e31			−0.0821378
$846$	−1.04251e31	−	2.23438e31i	−0.0656157	−	0.140632i
$847$		−	9.79375e31i		−	0.608459i
$848$	−1.53804e31	−	8.67763e31i	−0.0943220	−	0.532166i
$849$	−3.06153e31			−0.185333
$850$	−1.35587e32	+	6.32620e31i	−0.810235	+	0.378037i
$851$		−	7.72047e30i		−	0.0455427i
$852$	1.49821e32	−	1.78711e32i	0.872443	−	1.04067i
$853$	−1.70162e31			−0.0978192			−0.0489096	−	0.998803i	$-0.515575\pi$
$853$	−1.70162e31			−0.0978192			−0.0489096	+	0.998803i	$0.515575\pi$
$854$	4.41945e31	+	9.47205e31i	0.250802	+	0.537536i
$855$		−	1.83930e31i		−	0.103045i
$856$	−1.65913e32	−	4.43380e31i	−0.917634	−	0.245225i
$857$	1.42704e32			0.779194			0.389597	−	0.920985i	$-0.372614\pi$
$857$	1.42704e32			0.779194			0.389597	+	0.920985i	$0.372614\pi$
$858$	−1.81818e32	+	8.48321e31i	−0.980113	+	0.457299i
$859$			1.84617e32i			0.982533i	0.871009	+	0.491267i	$0.163466\pi$
$859$			1.84617e32i			0.982533i	−0.871009	+	0.491267i	$0.836534\pi$
$860$	−2.25247e31	−	1.88834e31i	−0.118352	−	0.0992197i
$861$	5.86751e31			0.304382
$862$	−8.65980e31	−	1.85603e32i	−0.443535	−	0.950613i
$863$		−	4.91230e31i		−	0.248409i	−0.992257	−	0.124204i	$-0.960362\pi$
$863$		−	4.91230e31i		−	0.248409i	0.992257	−	0.124204i	$-0.0396378\pi$
$864$	1.78395e32	−	1.25209e32i	0.890700	−	0.625148i
$865$	2.61608e31			0.128966
$866$	−9.33672e31	+	4.35631e31i	−0.454462	+	0.212042i
$867$			8.16724e30i			0.0392523i
$868$	6.57030e31	−	7.83724e31i	0.311794	−	0.371917i
$869$	−2.20907e32			−1.03512
$870$	−3.54309e31	−	7.59379e31i	−0.163935	−	0.351356i
$871$			2.48010e32i			1.13310i
$872$	−3.95143e31	+	1.47863e32i	−0.178268	+	0.667080i
$873$	4.64967e30			0.0207141
$874$	−2.22139e32	+	1.03645e32i	−0.977236	+	0.455957i
$875$		−	5.03200e31i		−	0.218601i
$876$	−1.15863e32	−	9.71334e31i	−0.497051	−	0.416700i
$877$	4.33620e31			0.183702			0.0918510	−	0.995773i	$-0.470722\pi$
$877$	4.33620e31			0.183702			0.0918510	+	0.995773i	$0.470722\pi$
$878$	−8.05544e31	−	1.72649e32i	−0.337015	−	0.722313i
$879$			8.20383e31i			0.338953i
$880$	−1.10923e32	+	1.96601e31i	−0.452596	+	0.0802189i
$881$	3.95861e32			1.59517			0.797586	−	0.603205i	$-0.206110\pi$
$881$	3.95861e32			1.59517			0.797586	+	0.603205i	$0.206110\pi$
$882$	−6.83737e31	+	3.19016e31i	−0.272104	+	0.126958i
$883$		−	4.40591e32i		−	1.73168i	−0.500320	−	0.865841i	$-0.666784\pi$
$883$		−	4.40591e32i		−	1.73168i	0.500320	−	0.865841i	$-0.333216\pi$
$884$	1.36507e32	−	1.62830e32i	0.529884	−	0.632060i
$885$	−3.27703e31			−0.125633
$886$	−6.60908e31	−	1.41650e32i	−0.250248	−	0.536348i
$887$		−	2.17249e32i		−	0.812454i	−0.913772	−	0.406227i	$-0.866844\pi$
$887$		−	2.17249e32i		−	0.812454i	0.913772	−	0.406227i	$-0.133156\pi$
$888$	−8.89830e30	−	2.37795e30i	−0.0328673	−	0.00878334i
$889$	1.20394e32			0.439224
$890$	8.81432e30	−	4.11257e30i	0.0317613	−	0.0148191i
$891$			2.31663e32i			0.824522i
$892$	2.81810e32	+	2.36253e32i	0.990701	+	0.830548i
$893$	1.26042e32			0.437672
$894$	3.37575e31	+	7.23512e31i	0.115786	+	0.248161i
$895$		−	9.08698e31i		−	0.307869i
$896$	−1.01133e31	+	1.17700e32i	−0.0338458	+	0.393901i
$897$	−2.20589e32			−0.729233
$898$	1.60806e32	−	7.50286e31i	0.525126	−	0.245012i
$899$			6.37303e32i			2.05584i
$900$	−6.57797e31	+	7.84638e31i	−0.209616	+	0.250036i
$901$	−1.67435e32			−0.527078
$902$	2.07834e32	+	4.45443e32i	0.646315	+	1.38523i
$903$		−	5.52963e31i		−	0.169875i
$904$	−8.32336e31	+	3.11461e32i	−0.252607	+	0.945259i
$905$	1.61557e32			0.484385
$906$	−1.91379e29	+	8.92933e28i	−0.000566872	+	0.000264490i
$907$		−	2.29925e32i		−	0.672832i	−0.941713	−	0.336416i	$-0.890785\pi$
$907$		−	2.29925e32i		−	0.672832i	0.941713	−	0.336416i	$-0.109215\pi$
$908$	−2.11100e31	−	1.76974e31i	−0.0610300	−	0.0511642i
$909$	6.51774e31			0.186163
$910$	1.44517e31	+	3.09739e31i	0.0407816	+	0.0874058i
$911$			2.87319e32i			0.801054i	0.916285	+	0.400527i	$0.131173\pi$
$911$			2.87319e32i			0.801054i	−0.916285	+	0.400527i	$0.868827\pi$
$912$	5.10371e31	+	2.87952e32i	0.140586	+	0.793189i
$913$	−7.20437e32			−1.96073
$914$	5.84337e32	−	2.72639e32i	1.57129	−	0.733127i
$915$			1.30737e32i			0.347348i
$916$	4.53659e32	−	5.41137e32i	1.19091	−	1.42055i
$917$	−2.76195e32			−0.716397
$918$	−1.75081e32	−	3.75246e32i	−0.448715	−	0.961715i
$919$		−	3.85526e32i		−	0.976300i	−0.872760	−	0.488150i	$-0.837672\pi$
$919$		−	3.85526e32i		−	0.976300i	0.872760	−	0.488150i	$-0.162328\pi$
$920$	−1.19656e32	−	3.19765e31i	−0.299412	−	0.0800138i
$921$	2.24406e32			0.554854
$922$	−3.30289e31	+	1.54105e31i	−0.0806963	+	0.0376511i
$923$		−	5.92748e32i		−	1.43104i
$924$	−1.62407e32	−	1.36153e32i	−0.387448	−	0.324815i
$925$	1.64851e31			0.0388627
$926$	2.13100e32	+	4.56730e32i	0.496435	+	1.06399i
$927$			2.80412e31i			0.0645536i
$928$	−4.22911e32	−	6.02556e32i	−0.962103	−	1.37079i
$929$	−2.27385e32			−0.511197			−0.255598	−	0.966783i	$-0.582272\pi$
$929$	−2.27385e32			−0.511197			−0.255598	+	0.966783i	$0.582272\pi$
$930$	1.15921e32	−	5.40862e31i	0.257543	−	0.120164i
$931$		−	3.85697e32i		−	0.846838i
$932$	−4.30522e32	+	5.13539e32i	−0.934158	+	1.11429i
$933$	−4.90400e32			−1.05161
$934$	1.58659e32	+	3.40048e32i	0.336239	+	0.720650i
$935$			2.14026e32i			0.448269i
$936$	3.75405e31	−	1.40477e32i	0.0777080	−	0.290784i
$937$	−1.39217e32			−0.284812			−0.142406	−	0.989808i	$-0.545484\pi$
$937$	−1.39217e32			−0.284812			−0.142406	+	0.989808i	$0.545484\pi$
$938$	−2.37401e32	+	1.10766e32i	−0.480012	+	0.223963i
$939$		−	6.46101e32i		−	1.29116i
$940$	4.88035e31	+	4.09141e31i	0.0963927	+	0.0808103i
$941$	9.50409e32			1.85534			0.927672	−	0.373395i	$-0.121806\pi$
$941$	9.50409e32			1.85534			0.927672	+	0.373395i	$0.121806\pi$
$942$	−3.80558e31	−	8.15636e31i	−0.0734278	−	0.157375i
$943$			5.40430e32i			1.03065i
$944$	−2.83470e32	+	5.02427e31i	−0.534337	+	0.0947069i
$945$	6.66089e31			0.124103
$946$	4.19792e32	−	1.95866e32i	0.773093	−	0.360708i
$947$			6.69909e32i			1.21946i	0.792611	+	0.609728i	$0.208721\pi$
$947$			6.69909e32i			1.21946i	−0.792611	+	0.609728i	$0.791279\pi$
$948$	−1.86152e32	+	2.22047e32i	−0.334947	+	0.399534i
$949$	−3.84296e32			−0.683499
$950$	−2.21308e32	−	4.74322e32i	−0.389079	−	0.833899i
$951$			1.93745e32i			0.336701i
$952$	2.16832e32	+	5.79453e31i	0.372492	+	0.0995433i
$953$	5.69209e32			0.966608			0.483304	−	0.875453i	$-0.339437\pi$
$953$	5.69209e32			0.966608			0.483304	+	0.875453i	$0.339437\pi$
$954$	−1.03835e32	+	4.84471e31i	−0.174306	+	0.0813272i
$955$		−	6.04028e31i		−	0.100235i
$956$	−1.22326e32	−	1.02552e32i	−0.200670	−	0.168231i
$957$	1.32065e33			2.14169
$958$	2.37982e32	+	5.10059e32i	0.381526	+	0.817711i
$959$			3.68255e32i			0.583638i
$960$	−7.37096e31	+	1.28062e32i	−0.115489	+	0.200649i
$961$	−3.27267e32			−0.506927
$962$	−2.12155e31	+	9.89866e30i	−0.0324883	+	0.0151583i
$963$			2.23283e32i			0.338038i
$964$	−2.35368e32	+	2.80753e32i	−0.352289	+	0.420221i
$965$	−1.29990e30			−0.00192357
$966$	−9.85194e31	−	2.11153e32i	−0.144136	−	0.308923i
$967$			2.65155e32i			0.383538i	0.981440	+	0.191769i	$0.0614225\pi$
$967$			2.65155e32i			0.383538i	−0.981440	+	0.191769i	$0.938578\pi$
$968$	2.77839e32	−	1.03967e33i	0.397341	−	1.48685i
$969$	5.55605e32			0.785606
$970$	−1.08833e31	+	5.07792e30i	−0.0152150	+	0.00709899i
$971$			5.50462e32i			0.760880i	0.924806	+	0.380440i	$0.124227\pi$
$971$			5.50462e32i			0.760880i	−0.924806	+	0.380440i	$0.875773\pi$
$972$	−3.77309e32	−	3.16314e32i	−0.515665	−	0.432305i
$973$	1.19227e32			0.161113
$974$	−4.74916e32	−	1.01787e33i	−0.634553	−	1.36002i
$975$		−	4.71011e32i		−	0.622272i
$976$	2.00442e32	+	1.13090e33i	0.261843	+	1.47732i
$977$	−1.22238e33			−1.57894			−0.789468	−	0.613791i	$-0.789644\pi$
$977$	−1.22238e33			−1.57894			−0.789468	+	0.613791i	$0.789644\pi$
$978$	−1.84770e32	+	8.62096e31i	−0.235996	+	0.110110i
$979$			1.53291e32i			0.193601i
$980$	1.25200e32	−	1.49342e32i	0.156357	−	0.186507i
$981$	1.98991e32			0.245739
$982$	−3.07961e31	−	6.60042e31i	−0.0376070	−	0.0806018i
$983$		−	1.56408e33i		−	1.88873i	−0.328897	−	0.944366i	$-0.606677\pi$
$983$		−	1.56408e33i		−	1.88873i	0.328897	−	0.944366i	$-0.393323\pi$
$984$	6.22877e32	+	1.66455e32i	0.743800	+	0.198770i
$985$	−2.10074e32			−0.248070
$986$	−1.26745e33	+	5.91364e32i	−1.48008	+	0.690572i
$987$			1.19809e32i			0.138356i
$988$	5.69623e32	+	4.77540e32i	0.650521	+	0.545360i
$989$	5.09308e32			0.575204
$990$	6.19280e31	+	1.32728e32i	0.0691671	+	0.148244i
$991$		−	1.48771e32i		−	0.164327i	−0.996619	−	0.0821635i	$-0.973817\pi$
$991$		−	1.48771e32i		−	0.164327i	0.996619	−	0.0821635i	$-0.0261830\pi$
$992$	9.19817e32	−	6.45584e32i	1.00478	−	0.705220i
$993$	−1.01972e33			−1.10164
$994$	5.67394e32	−	2.64734e32i	0.606226	−	0.282852i
$995$		−	5.29040e32i		−	0.559029i
$996$	−6.07091e32	+	7.24155e32i	−0.634455	+	0.756796i
$997$	−2.27753e31			−0.0235406			−0.0117703	−	0.999931i	$-0.503747\pi$
$997$	−2.27753e31			−0.0235406			−0.0117703	+	0.999931i	$0.503747\pi$
$998$	7.44048e31	+	1.59469e32i	0.0760615	+	0.163020i
$999$			4.56235e31i			0.0461284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.23.b.a.3.2	yes	10
3.2	odd	2		36.23.d.c.19.9		10
4.3	odd	2	inner	4.23.b.a.3.1	✓	10
8.3	odd	2		64.23.c.e.63.3		10
8.5	even	2		64.23.c.e.63.8		10
12.11	even	2		36.23.d.c.19.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.23.b.a.3.1	✓	10	4.3	odd	2	inner
4.23.b.a.3.2	yes	10	1.1	even	1	trivial
36.23.d.c.19.9		10	3.2	odd	2
36.23.d.c.19.10		10	12.11	even	2
64.23.c.e.63.3		10	8.3	odd	2
64.23.c.e.63.8		10	8.5	even	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:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 23 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1855.93 + 865.934i) q^{2} -142172. i q^{3} +(2.69462e6 - 3.21422e6i) q^{4} +1.40852e7 q^{5} +(1.23111e8 + 2.63860e8i) q^{6} +7.81741e8i q^{7} +(-2.21772e9 + 8.29872e9i) q^{8} +1.11682e10 q^{9} +O(q^{10})\)	\(q+(-1855.93 + 865.934i) q^{2} -142172. i q^{3} +(2.69462e6 - 3.21422e6i) q^{4} +1.40852e7 q^{5} +(1.23111e8 + 2.63860e8i) q^{6} +7.81741e8i q^{7} +(-2.21772e9 + 8.29872e9i) q^{8} +1.11682e10 q^{9} +(-2.61411e10 + 1.21969e10i) q^{10} -4.54625e11i q^{11} +(-4.56971e11 - 3.83099e11i) q^{12} -1.51568e12 q^{13} +(-6.76936e11 - 1.45085e12i) q^{14} -2.00252e12i q^{15} +(-3.07022e12 - 1.73222e13i) q^{16} -3.34233e13 q^{17} +(-2.07274e13 + 9.67096e12i) q^{18} -1.16924e14i q^{19} +(3.79543e13 - 4.52730e13i) q^{20} +1.11141e14 q^{21} +(3.93675e14 + 8.43751e14i) q^{22} +1.02367e15i q^{23} +(1.17984e15 + 3.15297e14i) q^{24} -2.18579e15 q^{25} +(2.81300e15 - 1.31248e15i) q^{26} -6.04931e15i q^{27} +(2.51269e15 + 2.10650e15i) q^{28} -2.04325e16 q^{29} +(1.73405e15 + 3.71653e15i) q^{30} -3.11907e16i q^{31} +(2.06980e16 + 2.94901e16i) q^{32} -6.46349e16 q^{33} +(6.20312e16 - 2.89424e16i) q^{34} +1.10110e16i q^{35} +(3.00942e16 - 3.58972e16i) q^{36} -7.54194e15 q^{37} +(1.01248e17 + 2.17002e17i) q^{38} +2.15487e17i q^{39} +(-3.12370e16 + 1.16889e17i) q^{40} +5.27932e17 q^{41} +(-2.06270e17 + 9.62412e16i) q^{42} -4.97531e17i q^{43} +(-1.46126e18 - 1.22504e18i) q^{44} +1.57307e17 q^{45} +(-8.86433e17 - 1.89986e18i) q^{46} +1.07798e18i q^{47} +(-2.46273e18 + 4.36498e17i) q^{48} +3.29870e18 q^{49} +(4.05667e18 - 1.89275e18i) q^{50} +4.75185e18i q^{51} +(-4.08419e18 + 4.87174e18i) q^{52} +5.00954e18 q^{53} +(5.23830e18 + 1.12271e19i) q^{54} -6.40349e18i q^{55} +(-6.48745e18 - 1.73368e18i) q^{56} -1.66233e19 q^{57} +(3.79212e19 - 1.76932e19i) q^{58} -1.63645e19i q^{59} +(-6.43654e18 - 5.39603e18i) q^{60} -6.52861e19 q^{61} +(2.70091e19 + 5.78876e19i) q^{62} +8.73068e18i q^{63} +(-6.39504e19 - 3.68084e19i) q^{64} -2.13487e19 q^{65} +(1.19958e20 - 5.59695e19i) q^{66} -1.63629e20i q^{67} +(-9.00631e19 + 1.07430e20i) q^{68} +1.45537e20 q^{69} +(-9.53479e18 - 2.04356e19i) q^{70} +3.91076e20i q^{71} +(-2.47680e19 + 9.26821e19i) q^{72} +2.53547e20 q^{73} +(1.39973e19 - 6.53082e18i) q^{74} +3.10758e20i q^{75} +(-3.75819e20 - 3.15066e20i) q^{76} +3.55399e20 q^{77} +(-1.86598e20 - 3.99929e20i) q^{78} -4.85911e20i q^{79} +(-4.32447e19 - 2.43987e20i) q^{80} -5.09570e20 q^{81} +(-9.79803e20 + 4.57154e20i) q^{82} -1.58468e21i q^{83} +(2.99484e20 - 3.57233e20i) q^{84} -4.70774e20 q^{85} +(4.30829e20 + 9.23380e20i) q^{86} +2.90492e21i q^{87} +(3.77281e21 + 1.00823e21i) q^{88} -3.37182e20 q^{89} +(-2.91951e20 + 1.36218e20i) q^{90} -1.18487e21i q^{91} +(3.29031e21 + 2.75841e21i) q^{92} -4.43443e21 q^{93} +(-9.33462e20 - 2.00066e21i) q^{94} -1.64690e21i q^{95} +(4.19266e21 - 2.94267e21i) q^{96} +4.16330e20 q^{97} +(-6.12215e21 + 2.85646e21i) q^{98} -5.07737e21i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 1540 q^{2} + 2264464 q^{4} - 17091100 q^{5} - 791935776 q^{6} + 9804431680 q^{8} - 104309613702 q^{9}+O(q^{10}) \) 10 * q + 1540 * q^2 + 2264464 * q^4 - 17091100 * q^5 - 791935776 * q^6 + 9804431680 * q^8 - 104309613702 * q^9	\( 10 q + 1540 q^{2} + 2264464 q^{4} - 17091100 q^{5} - 791935776 q^{6} + 9804431680 q^{8} - 104309613702 q^{9} + 159414035240 q^{10} + 519021175680 q^{12} - 531230356540 q^{13} - 5894008940736 q^{14} - 27717620084480 q^{16} + 14058178115540 q^{17} + 16283956279140 q^{18} + 233643631625120 q^{20} - 313135665760512 q^{21} + 120589650366240 q^{22} - 20\!\cdots\!36 q^{24}+ \cdots - 23\!\cdots\!20 q^{98}+O(q^{100}) \) 10 * q + 1540 * q^2 + 2264464 * q^4 - 17091100 * q^5 - 791935776 * q^6 + 9804431680 * q^8 - 104309613702 * q^9 + 159414035240 * q^10 + 519021175680 * q^12 - 531230356540 * q^13 - 5894008940736 * q^14 - 27717620084480 * q^16 + 14058178115540 * q^17 + 16283956279140 * q^18 + 233643631625120 * q^20 - 313135665760512 * q^21 + 120589650366240 * q^22 - 2007619616180736 * q^24 + 7710175817606670 * q^25 - 3953973318046744 * q^26 + 1177952265288960 * q^28 - 14464474185570172 * q^29 + 10252783730669760 * q^30 - 73831192092953600 * q^32 + 72906957628179840 * q^33 - 26625976920357496 * q^34 - 36609276067793136 * q^36 + 324587767823538020 * q^37 + 369140808808591200 * q^38 - 1158049295468479360 * q^40 - 1355457345814233100 * q^41 + 2644455724909770240 * q^42 - 1919761520625210240 * q^44 + 9367295763131460 * q^45 + 6132624002565203904 * q^46 - 18374169355003791360 * q^48 + 183553700661552298 * q^49 + 29084394113996178540 * q^50 - 38492433127521128800 * q^52 - 11424344766226018780 * q^53 + 79182840955393027008 * q^54 - 102844865827678657536 * q^56 + 30188516183231506560 * q^57 + 173059696836432320360 * q^58 - 377769459746631548160 * q^60 + 58241718146183220740 * q^61 + 317897221476923285760 * q^62 - 412080172429987966976 * q^64 - 121531695066047433560 * q^65 + 700585278654050000640 * q^66 - 667890522330713878240 * q^68 + 54497497397908094208 * q^69 + 1014396282552321513600 * q^70 - 1244773253376491901120 * q^72 + 83030422224875883380 * q^73 + 801906083011176262184 * q^74 + 286747421140990627200 * q^76 - 704201825495570814720 * q^77 - 964412732782594923840 * q^78 + 1509611955050789726720 * q^80 + 251577744224553978858 * q^81 - 2389572513290905036600 * q^82 + 6185640644326191863808 * q^84 - 1796890366112110859960 * q^85 - 8221838255181360278496 * q^86 + 11178210842814940531200 * q^88 + 3420669206528505615668 * q^89 - 24782809563337507735320 * q^90 + 21476264197983864733440 * q^92 + 15493754050318100597760 * q^93 - 20874543047091388369536 * q^94 + 29250284502468708163584 * q^96 - 20429910746446196146540 * q^97 - 23110416876469762175420 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more