LMFDB - Embedded newform 24.10.d.a.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,10,Mod(13,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("24.13");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	24.d (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:	$12.3608600679$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 143 x^{16} - 3116 x^{15} - 6804 x^{14} - 273568 x^{13} + 13308368 x^{12} + \cdots + 35\!\cdots\!00 $ x^18 - 143x^16 - 3116x^15 - 6804x^14 - 273568x^13 + 13308368x^12 + 114642624x^11 + 410038976x^10 + 8938233856x^9 + 893528237824x^8 - 830496445440x^7 - 276067668007936x^6 - 6231752888295424x^5 - 53836398547537920x^4 + 395298533233475584x^3 + 33278997342311628800x^2 + 528496957656524390400x + 3530172528998645760000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{65}\cdot 3^{28} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.5
Root			$-1.14864 + 15.6871i$ of defining polynomial
Character	$\chi$	$=$	24.13
Dual form			24.10.d.a.13.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.5385 - 18.8358i) q^{2} -81.0000i q^{3} +(-197.573 + 472.344i) q^{4} +416.150i q^{5} +(-1525.70 + 1015.62i) q^{6} +10561.7 q^{7} +(11374.2 - 2201.05i) q^{8} -6561.00 q^{9} +O(q^{10})$	\(q+(-12.5385 - 18.8358i) q^{2} -81.0000i q^{3} +(-197.573 + 472.344i) q^{4} +416.150i q^{5} +(-1525.70 + 1015.62i) q^{6} +10561.7 q^{7} +(11374.2 - 2201.05i) q^{8} -6561.00 q^{9} +(7838.50 - 5217.89i) q^{10} +54750.4i q^{11} +(38259.9 + 16003.4i) q^{12} -103511. i q^{13} +(-132428. - 198938. i) q^{14} +33708.1 q^{15} +(-184074. - 186645. i) q^{16} +293266. q^{17} +(82265.0 + 123582. i) q^{18} -759080. i q^{19} +(-196566. - 82219.8i) q^{20} -855501. i q^{21} +(1.03127e6 - 686487. i) q^{22} -875669. q^{23} +(-178285. - 921313. i) q^{24} +1.77994e6 q^{25} +(-1.94971e6 + 1.29787e6i) q^{26} +531441. i q^{27} +(-2.08671e6 + 4.98877e6i) q^{28} -2.12690e6i q^{29} +(-422649. - 634919. i) q^{30} +8.70915e6 q^{31} +(-1.20758e6 + 5.80742e6i) q^{32} +4.43478e6 q^{33} +(-3.67712e6 - 5.52390e6i) q^{34} +4.39526e6i q^{35} +(1.29627e6 - 3.09905e6i) q^{36} +9.75881e6i q^{37} +(-1.42979e7 + 9.51772e6i) q^{38} -8.38439e6 q^{39} +(915966. + 4.73338e6i) q^{40} +1.02465e7 q^{41} +(-1.61140e7 + 1.07267e7i) q^{42} -2.38973e7i q^{43} +(-2.58610e7 - 1.08172e7i) q^{44} -2.73036e6i q^{45} +(1.09796e7 + 1.64939e7i) q^{46} +1.08649e7 q^{47} +(-1.51182e7 + 1.49100e7i) q^{48} +7.11967e7 q^{49} +(-2.23178e7 - 3.35266e7i) q^{50} -2.37546e7i q^{51} +(4.88928e7 + 2.04509e7i) q^{52} +2.54371e7i q^{53} +(1.00101e7 - 6.66347e6i) q^{54} -2.27844e7 q^{55} +(1.20132e8 - 2.32469e7i) q^{56} -6.14855e7 q^{57} +(-4.00618e7 + 2.66681e7i) q^{58} -1.17130e8i q^{59} +(-6.65980e6 + 1.59218e7i) q^{60} -8.80779e6i q^{61} +(-1.09200e8 - 1.64044e8i) q^{62} -6.92955e7 q^{63} +(1.24528e8 - 5.00705e7i) q^{64} +4.30761e7 q^{65} +(-5.56055e7 - 8.35325e7i) q^{66} +1.03646e8i q^{67} +(-5.79414e7 + 1.38523e8i) q^{68} +7.09292e7i q^{69} +(8.27882e7 - 5.51100e7i) q^{70} -4.10162e8 q^{71} +(-7.46263e7 + 1.44411e7i) q^{72} +2.25467e8 q^{73} +(1.83815e8 - 1.22361e8i) q^{74} -1.44175e8i q^{75} +(3.58547e8 + 1.49974e8i) q^{76} +5.78259e8i q^{77} +(1.05128e8 + 1.57926e8i) q^{78} -5.26393e8 q^{79} +(7.76721e7 - 7.66024e7i) q^{80} +4.30467e7 q^{81} +(-1.28476e8 - 1.93001e8i) q^{82} +6.56694e8i q^{83} +(4.04091e8 + 1.69023e8i) q^{84} +1.22043e8i q^{85} +(-4.50124e8 + 2.99636e8i) q^{86} -1.72279e8 q^{87} +(1.20508e8 + 6.22744e8i) q^{88} +3.92379e8 q^{89} +(-5.14284e7 + 3.42346e7i) q^{90} -1.09326e9i q^{91} +(1.73008e8 - 4.13617e8i) q^{92} -7.05441e8i q^{93} +(-1.36230e8 - 2.04650e8i) q^{94} +3.15891e8 q^{95} +(4.70401e8 + 9.78142e7i) q^{96} -4.27535e8 q^{97} +(-8.92698e8 - 1.34104e9i) q^{98} -3.59217e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 34 q^{2} + 512 q^{4} - 3078 q^{6} - 9604 q^{7} + 15844 q^{8} - 118098 q^{9}+O(q^{10}) $ 18 * q + 34 * q^2 + 512 * q^4 - 3078 * q^6 - 9604 * q^7 + 15844 * q^8 - 118098 * q^9	\( 18 q + 34 q^{2} + 512 q^{4} - 3078 q^{6} - 9604 q^{7} + 15844 q^{8} - 118098 q^{9} - 34788 q^{10} - 57996 q^{12} - 209204 q^{14} + 202500 q^{15} - 1928 q^{16} + 203996 q^{17} - 223074 q^{18} + 406744 q^{20} + 4311616 q^{22} - 3465976 q^{23} + 1142748 q^{24} - 5309486 q^{25} - 7786712 q^{26} - 4722944 q^{28} + 1214676 q^{30} + 4737540 q^{31} + 19090184 q^{32} - 26138884 q^{34} - 3359232 q^{36} + 81529688 q^{38} - 18507528 q^{39} + 102781640 q^{40} - 3780956 q^{41} - 37252548 q^{42} - 113955840 q^{44} + 155174504 q^{46} - 112458264 q^{47} + 72347904 q^{48} + 90859338 q^{49} - 240578846 q^{50} - 232023472 q^{52} + 20194758 q^{54} - 76355584 q^{55} + 349245496 q^{56} - 79112376 q^{57} - 368612756 q^{58} - 229298688 q^{60} + 243931700 q^{62} + 63011844 q^{63} + 627902720 q^{64} + 300816016 q^{65} - 43281216 q^{66} - 147591168 q^{68} - 236031704 q^{70} - 408942312 q^{71} - 103952484 q^{72} + 826124308 q^{73} - 478971056 q^{74} + 559419952 q^{76} - 364363272 q^{78} + 382409492 q^{79} - 666994944 q^{80} + 774840978 q^{81} + 547544068 q^{82} + 602616024 q^{84} - 1435000280 q^{86} - 687477132 q^{87} - 2197393664 q^{88} - 458464820 q^{89} + 228244068 q^{90} + 4261704192 q^{92} - 3319581624 q^{94} + 331883504 q^{95} - 569482488 q^{96} + 264098780 q^{97} + 4005878682 q^{98}+O(q^{100}) \) 18 * q + 34 * q^2 + 512 * q^4 - 3078 * q^6 - 9604 * q^7 + 15844 * q^8 - 118098 * q^9 - 34788 * q^10 - 57996 * q^12 - 209204 * q^14 + 202500 * q^15 - 1928 * q^16 + 203996 * q^17 - 223074 * q^18 + 406744 * q^20 + 4311616 * q^22 - 3465976 * q^23 + 1142748 * q^24 - 5309486 * q^25 - 7786712 * q^26 - 4722944 * q^28 + 1214676 * q^30 + 4737540 * q^31 + 19090184 * q^32 - 26138884 * q^34 - 3359232 * q^36 + 81529688 * q^38 - 18507528 * q^39 + 102781640 * q^40 - 3780956 * q^41 - 37252548 * q^42 - 113955840 * q^44 + 155174504 * q^46 - 112458264 * q^47 + 72347904 * q^48 + 90859338 * q^49 - 240578846 * q^50 - 232023472 * q^52 + 20194758 * q^54 - 76355584 * q^55 + 349245496 * q^56 - 79112376 * q^57 - 368612756 * q^58 - 229298688 * q^60 + 243931700 * q^62 + 63011844 * q^63 + 627902720 * q^64 + 300816016 * q^65 - 43281216 * q^66 - 147591168 * q^68 - 236031704 * q^70 - 408942312 * q^71 - 103952484 * q^72 + 826124308 * q^73 - 478971056 * q^74 + 559419952 * q^76 - 364363272 * q^78 + 382409492 * q^79 - 666994944 * q^80 + 774840978 * q^81 + 547544068 * q^82 + 602616024 * q^84 - 1435000280 * q^86 - 687477132 * q^87 - 2197393664 * q^88 - 458464820 * q^89 + 228244068 * q^90 + 4261704192 * q^92 - 3319581624 * q^94 + 331883504 * q^95 - 569482488 * q^96 + 264098780 * q^97 + 4005878682 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−12.5385	−	18.8358i	−0.554128	−	0.832431i
$2$	−12.5385	−	18.8358i	−0.554128	−	0.832431i
$3$		−	81.0000i		−	0.577350i
$3$		−	81.0000i		−	0.577350i
$4$	−197.573	+	472.344i	−0.385884	+	0.922547i
$5$			416.150i			0.297773i	0.988854	+	0.148886i	$0.0475688\pi$
$5$			416.150i			0.297773i	−0.988854	+	0.148886i	$0.952431\pi$
$6$	−1525.70	+	1015.62i	−0.480604	+	0.319926i
$7$	10561.7			1.66262			0.831312	−	0.555806i	$-0.187590\pi$
$7$	10561.7			1.66262			0.831312	+	0.555806i	$0.187590\pi$
$8$	11374.2	−	2201.05i	0.981787	−	0.189987i
$9$	−6561.00			−0.333333
$10$	7838.50	−	5217.89i	0.247875	−	0.165004i
$11$			54750.4i			1.12751i	0.825942	+	0.563755i	$0.190644\pi$
$11$			54750.4i			1.12751i	−0.825942	+	0.563755i	$0.809356\pi$
$12$	38259.9	+	16003.4i	0.532633	+	0.222790i
$13$		−	103511.i		−	1.00517i	−0.864527	−	0.502587i	$-0.832382\pi$
$13$		−	103511.i		−	1.00517i	0.864527	−	0.502587i	$-0.167618\pi$
$14$	−132428.	−	198938.i	−0.921307	−	1.38402i
$15$	33708.1			0.171919
$16$	−184074.	−	186645.i	−0.702187	−	0.711993i
$17$	293266.			0.851613			0.425806	−	0.904814i	$-0.359991\pi$
$17$	293266.			0.851613			0.425806	+	0.904814i	$0.359991\pi$
$18$	82265.0	+	123582.i	0.184709	+	0.277477i
$19$		−	759080.i		−	1.33628i	−0.744037	−	0.668139i	$-0.767091\pi$
$19$		−	759080.i		−	1.33628i	0.744037	−	0.668139i	$-0.232909\pi$
$20$	−196566.	−	82219.8i	−0.274709	−	0.114906i
$21$		−	855501.i		−	0.959917i
$22$	1.03127e6	−	686487.i	0.938574	−	0.624785i
$23$	−875669.			−0.652476			−0.326238	−	0.945288i	$-0.605781\pi$
$23$	−875669.			−0.652476			−0.326238	+	0.945288i	$0.605781\pi$
$24$	−178285.	−	921313.i	−0.109689	−	0.566835i
$25$	1.77994e6			0.911332
$26$	−1.94971e6	+	1.29787e6i	−0.836738	+	0.556995i
$27$			531441.i			0.192450i
$28$	−2.08671e6	+	4.98877e6i	−0.641580	+	1.53385i
$29$		−	2.12690e6i		−	0.558414i	−0.960231	−	0.279207i	$-0.909928\pi$
$29$		−	2.12690e6i		−	0.558414i	0.960231	−	0.279207i	$-0.0900716\pi$
$30$	−422649.	−	634919.i	−0.0952652	−	0.143111i
$31$	8.70915e6			1.69374			0.846872	−	0.531796i	$-0.178483\pi$
$31$	8.70915e6			1.69374			0.846872	+	0.531796i	$0.178483\pi$
$32$	−1.20758e6	+	5.80742e6i	−0.203583	+	0.979058i
$33$	4.43478e6			0.650968
$34$	−3.67712e6	−	5.52390e6i	−0.471902	−	0.708909i
$35$			4.39526e6i			0.495084i
$36$	1.29627e6	−	3.09905e6i	0.128628	−	0.307516i
$37$			9.75881e6i			0.856030i	0.903772	+	0.428015i	$0.140787\pi$
$37$			9.75881e6i			0.856030i	−0.903772	+	0.428015i	$0.859213\pi$
$38$	−1.42979e7	+	9.51772e6i	−1.11236	+	0.740469i
$39$	−8.38439e6			−0.580337
$40$	915966.	+	4.73338e6i	0.0565730	+	0.292349i
$41$	1.02465e7			0.566304			0.283152	−	0.959075i	$-0.408620\pi$
$41$	1.02465e7			0.566304			0.283152	+	0.959075i	$0.408620\pi$
$42$	−1.61140e7	+	1.07267e7i	−0.799065	+	0.531917i
$43$		−	2.38973e7i		−	1.06596i	−0.846128	−	0.532980i	$-0.821072\pi$
$43$		−	2.38973e7i		−	1.06596i	0.846128	−	0.532980i	$-0.178928\pi$
$44$	−2.58610e7	−	1.08172e7i	−1.04018	−	0.435088i
$45$		−	2.73036e6i		−	0.0992575i
$46$	1.09796e7	+	1.64939e7i	0.361555	+	0.543142i
$47$	1.08649e7			0.324778			0.162389	−	0.986727i	$-0.448080\pi$
$47$	1.08649e7			0.324778			0.162389	+	0.986727i	$0.448080\pi$
$48$	−1.51182e7	+	1.49100e7i	−0.411069	+	0.405408i
$49$	7.11967e7			1.76432
$50$	−2.23178e7	−	3.35266e7i	−0.504994	−	0.758621i
$51$		−	2.37546e7i		−	0.491679i
$52$	4.88928e7	+	2.04509e7i	0.927321	+	0.387881i
$53$			2.54371e7i			0.442819i	0.975181	+	0.221409i	$0.0710657\pi$
$53$			2.54371e7i			0.442819i	−0.975181	+	0.221409i	$0.928934\pi$
$54$	1.00101e7	−	6.66347e6i	0.160201	−	0.106642i
$55$	−2.27844e7			−0.335741
$56$	1.20132e8	−	2.32469e7i	1.63234	−	0.315878i
$57$	−6.14855e7			−0.771500
$58$	−4.00618e7	+	2.66681e7i	−0.464842	+	0.309433i
$59$		−	1.17130e8i		−	1.25844i	−0.777226	−	0.629221i	$-0.783374\pi$
$59$		−	1.17130e8i		−	1.25844i	0.777226	−	0.629221i	$-0.216626\pi$
$60$	−6.65980e6	+	1.59218e7i	−0.0663408	+	0.158603i
$61$		−	8.80779e6i		−	0.0814484i	−0.999170	−	0.0407242i	$-0.987033\pi$
$61$		−	8.80779e6i		−	0.0814484i	0.999170	−	0.0407242i	$-0.0129665\pi$
$62$	−1.09200e8	−	1.64044e8i	−0.938552	−	1.40993i
$63$	−6.92955e7			−0.554208
$64$	1.24528e8	−	5.00705e7i	0.927810	−	0.373054i
$65$	4.30761e7			0.299313
$66$	−5.56055e7	−	8.35325e7i	−0.360720	−	0.541886i
$67$			1.03646e8i			0.628372i	0.949361	+	0.314186i	$0.101732\pi$
$67$			1.03646e8i			0.628372i	−0.949361	+	0.314186i	$0.898268\pi$
$68$	−5.79414e7	+	1.38523e8i	−0.328624	+	0.785653i
$69$			7.09292e7i			0.376707i
$70$	8.27882e7	−	5.51100e7i	0.412123	−	0.274340i
$71$	−4.10162e8			−1.91555			−0.957773	−	0.287525i	$-0.907168\pi$
$71$	−4.10162e8			−1.91555			−0.957773	+	0.287525i	$0.907168\pi$
$72$	−7.46263e7	+	1.44411e7i	−0.327262	+	0.0633292i
$73$	2.25467e8			0.929246			0.464623	−	0.885509i	$-0.346190\pi$
$73$	2.25467e8			0.929246			0.464623	+	0.885509i	$0.346190\pi$
$74$	1.83815e8	−	1.22361e8i	0.712587	−	0.474351i
$75$		−	1.44175e8i		−	0.526157i
$76$	3.58547e8	+	1.49974e8i	1.23278	+	0.515648i
$77$			5.78259e8i			1.87462i
$78$	1.05128e8	+	1.57926e8i	0.321581	+	0.483091i
$79$	−5.26393e8			−1.52051			−0.760253	−	0.649627i	$-0.774925\pi$
$79$	−5.26393e8			−1.52051			−0.760253	+	0.649627i	$0.774925\pi$
$80$	7.76721e7	−	7.66024e7i	0.212012	−	0.209092i
$81$	4.30467e7			0.111111
$82$	−1.28476e8	−	1.93001e8i	−0.313805	−	0.471409i
$83$			6.56694e8i			1.51884i	0.650601	+	0.759420i	$0.274517\pi$
$83$			6.56694e8i			1.51884i	−0.650601	+	0.759420i	$0.725483\pi$
$84$	4.04091e8	+	1.69023e8i	0.885568	+	0.370416i
$85$			1.22043e8i			0.253587i
$86$	−4.50124e8	+	2.99636e8i	−0.887338	+	0.590678i
$87$	−1.72279e8			−0.322401
$88$	1.20508e8	+	6.22744e8i	0.214213	+	1.10697i
$89$	3.92379e8			0.662904			0.331452	−	0.943472i	$-0.392462\pi$
$89$	3.92379e8			0.662904			0.331452	+	0.943472i	$0.392462\pi$
$90$	−5.14284e7	+	3.42346e7i	−0.0826251	+	0.0550014i
$91$		−	1.09326e9i		−	1.67123i
$92$	1.73008e8	−	4.13617e8i	0.251780	−	0.601940i
$93$		−	7.05441e8i		−	0.977884i
$94$	−1.36230e8	−	2.04650e8i	−0.179969	−	0.270356i
$95$	3.15891e8			0.397907
$96$	4.70401e8	+	9.78142e7i	0.565259	+	0.117539i
$97$	−4.27535e8			−0.490342			−0.245171	−	0.969480i	$-0.578844\pi$
$97$	−4.27535e8			−0.490342			−0.245171	+	0.969480i	$0.578844\pi$
$98$	−8.92698e8	−	1.34104e9i	−0.977659	−	1.46867i
$99$		−	3.59217e8i		−	0.375836i
$100$	−3.51668e8	+	8.40746e8i	−0.351668	+	0.840746i
$101$			6.57171e8i			0.628394i	0.949358	+	0.314197i	$0.101735\pi$
$101$			6.57171e8i			0.628394i	−0.949358	+	0.314197i	$0.898265\pi$
$102$	−4.47436e8	+	2.97846e8i	−0.409289	+	0.272453i
$103$	−7.28209e7			−0.0637512			−0.0318756	−	0.999492i	$-0.510148\pi$
$103$	−7.28209e7			−0.0637512			−0.0318756	+	0.999492i	$0.510148\pi$
$104$	−2.27833e8	−	1.17736e9i	−0.190970	−	0.986866i
$105$	3.56016e8			0.285837
$106$	4.79127e8	−	3.18943e8i	0.368616	−	0.245378i
$107$		−	7.80852e8i		−	0.575893i	−0.957647	−	0.287946i	$-0.907027\pi$
$107$		−	7.80852e8i		−	0.575893i	0.957647	−	0.287946i	$-0.0929725\pi$
$108$	−2.51023e8	−	1.04998e8i	−0.177544	−	0.0742634i
$109$		−	6.17128e8i		−	0.418751i	−0.977835	−	0.209376i	$-0.932857\pi$
$109$		−	6.17128e8i		−	0.418751i	0.977835	−	0.209376i	$-0.0671432\pi$
$110$	2.85681e8	+	4.29161e8i	0.186044	+	0.279482i
$111$	7.90464e8			0.494229
$112$	−1.94414e9	−	1.97129e9i	−1.16747	−	1.18378i
$113$	3.01950e9			1.74213			0.871067	−	0.491164i	$-0.163428\pi$
$113$	3.01950e9			1.74213			0.871067	+	0.491164i	$0.163428\pi$
$114$	7.70935e8	+	1.15813e9i	0.427510	+	0.642221i
$115$		−	3.64409e8i		−	0.194290i
$116$	1.00463e9	+	4.20218e8i	0.515164	+	0.215483i
$117$			6.79135e8i			0.335058i
$118$	−2.20623e9	+	1.46863e9i	−1.04757	+	0.697338i
$119$	3.09740e9			1.41591
$120$	3.83404e8	−	7.41933e7i	0.168788	−	0.0326625i
$121$	−6.39658e8			−0.271277
$122$	−1.65902e8	+	1.10436e8i	−0.0678002	+	0.0451329i
$123$		−	8.29969e8i		−	0.326956i
$124$	−1.72069e9	+	4.11372e9i	−0.653589	+	1.56256i
$125$			1.55352e9i			0.569142i
$126$	8.68861e8	+	1.30524e9i	0.307102	+	0.461340i
$127$	−1.26724e9			−0.432256			−0.216128	−	0.976365i	$-0.569343\pi$
$127$	−1.26724e9			−0.432256			−0.216128	+	0.976365i	$0.569343\pi$
$128$	−2.50452e9	−	1.71778e9i	−0.824667	−	0.565618i
$129$	−1.93568e9			−0.615432
$130$	−5.40109e8	−	8.11371e8i	−0.165858	−	0.249158i
$131$			4.74712e9i			1.40835i	0.710028	+	0.704173i	$0.248682\pi$
$131$			4.74712e9i			1.40835i	−0.710028	+	0.704173i	$0.751318\pi$
$132$	−8.76191e8	+	2.09474e9i	−0.251198	+	0.600549i
$133$		−	8.01721e9i		−	2.22173i
$134$	1.95226e9	−	1.29957e9i	0.523077	−	0.348199i
$135$	−2.21159e8			−0.0573064
$136$	3.33568e9	−	6.45494e8i	0.836102	−	0.161796i
$137$	−6.92089e9			−1.67849			−0.839247	−	0.543751i	$-0.817004\pi$
$137$	−6.92089e9			−1.67849			−0.839247	+	0.543751i	$0.817004\pi$
$138$	1.33601e9	−	8.89345e8i	0.313583	−	0.208744i
$139$			8.00426e9i			1.81867i	0.416061	+	0.909337i	$0.363410\pi$
$139$			8.00426e9i			1.81867i	−0.416061	+	0.909337i	$0.636590\pi$
$140$	−2.07608e9	−	8.68384e8i	−0.456738	−	0.191045i
$141$		−	8.80060e8i		−	0.187511i
$142$	5.14281e9	+	7.72571e9i	1.06146	+	1.59456i
$143$	5.66727e9			1.13334
$144$	1.20771e9	+	1.22457e9i	0.234062	+	0.237331i
$145$	8.85110e8			0.166280
$146$	−2.82702e9	−	4.24685e9i	−0.514921	−	0.773534i
$147$		−	5.76693e9i		−	1.01863i
$148$	−4.60952e9	−	1.92807e9i	−0.789729	−	0.330328i
$149$			4.29056e9i			0.713142i	0.934268	+	0.356571i	$0.116054\pi$
$149$			4.29056e9i			0.713142i	−0.934268	+	0.356571i	$0.883946\pi$
$150$	−2.71566e9	+	1.80774e9i	−0.437990	+	0.291559i
$151$	−3.45621e9			−0.541008			−0.270504	−	0.962719i	$-0.587190\pi$
$151$	−3.45621e9			−0.541008			−0.270504	+	0.962719i	$0.587190\pi$
$152$	−1.67077e9	−	8.63396e9i	−0.253876	−	1.31194i
$153$	−1.92412e9			−0.283871
$154$	1.08920e10	−	7.25050e9i	1.56050	−	1.03878i
$155$			3.62431e9i			0.504351i
$156$	1.65653e9	−	3.96032e9i	0.223943	−	0.535389i
$157$		−	2.17477e8i		−	0.0285670i	−0.999898	−	0.0142835i	$-0.995453\pi$
$157$		−	2.17477e8i		−	0.0285670i	0.999898	−	0.0142835i	$-0.00454673\pi$
$158$	6.60017e9	+	9.91502e9i	0.842555	+	1.26572i
$159$	2.06040e9			0.255662
$160$	−2.41676e9	−	5.02535e8i	−0.291536	−	0.0606215i
$161$	−9.24858e9			−1.08482
$162$	−5.39741e8	−	8.10818e8i	−0.0615698	−	0.0924924i
$163$		−	4.03995e8i		−	0.0448262i	−0.999749	−	0.0224131i	$-0.992865\pi$
$163$		−	4.03995e8i		−	0.0448262i	0.999749	−	0.0224131i	$-0.00713490\pi$
$164$	−2.02444e9	+	4.83989e9i	−0.218528	+	0.522442i
$165$			1.84553e9i			0.193840i
$166$	1.23693e10	−	8.23395e9i	1.26433	−	0.841631i
$167$	−1.00000e10			−0.994893			−0.497446	−	0.867495i	$-0.665729\pi$
$167$	−1.00000e10			−0.994893			−0.497446	+	0.867495i	$0.665729\pi$
$168$	−1.88300e9	−	9.73066e9i	−0.182372	−	0.942433i
$169$	−1.10019e8			−0.0103747
$170$	2.29877e9	−	1.53023e9i	0.211094	−	0.140520i
$171$			4.98033e9i			0.445426i
$172$	1.12877e10	+	4.72145e9i	0.983398	+	0.411337i
$173$		−	8.68720e9i		−	0.737348i	−0.929559	−	0.368674i	$-0.879812\pi$
$173$		−	8.68720e9i		−	0.737348i	0.929559	−	0.368674i	$-0.120188\pi$
$174$	2.16012e9	+	3.24501e9i	0.178651	+	0.268376i
$175$	1.87993e10			1.51520
$176$	1.02189e10	−	1.00781e10i	0.802778	−	0.791723i
$177$	−9.48751e9			−0.726562
$178$	−4.91984e9	−	7.39076e9i	−0.367334	−	0.551822i
$179$		−	1.63457e10i		−	1.19005i	−0.803707	−	0.595025i	$-0.797142\pi$
$179$		−	1.63457e10i		−	1.19005i	0.803707	−	0.595025i	$-0.202858\pi$
$180$	1.28967e9	+	5.39444e8i	0.0915698	+	0.0383019i
$181$		−	8.18574e9i		−	0.566897i	−0.958987	−	0.283449i	$-0.908521\pi$
$181$		−	8.18574e9i		−	0.566897i	0.958987	−	0.283449i	$-0.0914785\pi$
$182$	−2.05923e10	+	1.37078e10i	−1.39118	+	0.926074i
$183$	−7.13431e8			−0.0470243
$184$	−9.96006e9	+	1.92739e9i	−0.640592	+	0.123962i
$185$	−4.06113e9			−0.254902
$186$	−1.32875e10	+	8.84516e9i	−0.814021	+	0.541873i
$187$			1.60564e10i			0.960201i
$188$	−2.14661e9	+	5.13199e9i	−0.125327	+	0.299623i
$189$			5.61294e9i			0.319972i
$190$	−3.96080e9	−	5.95005e9i	−0.220491	−	0.331230i
$191$	5.80329e9			0.315518			0.157759	−	0.987478i	$-0.449573\pi$
$191$	5.80329e9			0.315518			0.157759	+	0.987478i	$0.449573\pi$
$192$	−4.05571e9	−	1.00868e10i	−0.215383	−	0.535671i
$193$	7.78576e9			0.403918			0.201959	−	0.979394i	$-0.435269\pi$
$193$	7.78576e9			0.403918			0.201959	+	0.979394i	$0.435269\pi$
$194$	5.36064e9	+	8.05295e9i	0.271712	+	0.408176i
$195$		−	3.48916e9i		−	0.172809i
$196$	−1.40665e10	+	3.36293e10i	−0.680823	+	1.62767i
$197$			1.83650e10i			0.868748i	0.900733	+	0.434374i	$0.143030\pi$
$197$			1.83650e10i			0.868748i	−0.900733	+	0.434374i	$0.856970\pi$
$198$	−6.76614e9	+	4.50404e9i	−0.312858	+	0.208262i
$199$	−2.35677e10			−1.06532			−0.532658	−	0.846331i	$-0.678807\pi$
$199$	−2.35677e10			−1.06532			−0.532658	+	0.846331i	$0.678807\pi$
$200$	2.02455e10	−	3.91775e9i	0.894733	−	0.173142i
$201$	8.39535e9			0.362791
$202$	1.23783e10	−	8.23993e9i	0.523095	−	0.348211i
$203$		−	2.24638e10i		−	0.928433i
$204$	1.12203e10	+	4.69325e9i	0.453597	+	0.189731i
$205$			4.26409e9i			0.168630i
$206$	9.13064e8	+	1.37164e9i	0.0353264	+	0.0530685i
$207$	5.74526e9			0.217492
$208$	−1.93198e10	+	1.90537e10i	−0.715676	+	0.705820i
$209$	4.15600e10			1.50667
$210$	−4.46391e9	−	6.70584e9i	−0.158390	−	0.237940i
$211$			3.43201e10i			1.19200i	0.802983	+	0.596001i	$0.203245\pi$
$211$			3.43201e10i			1.19200i	−0.802983	+	0.596001i	$0.796755\pi$
$212$	−1.20151e10	−	5.02567e9i	−0.408521	−	0.170877i
$213$			3.32231e10i			1.10594i
$214$	−1.47080e10	+	9.79070e9i	−0.479391	+	0.319118i
$215$	9.94485e9			0.317413
$216$	1.16973e9	+	6.04473e9i	0.0365631	+	0.188945i
$217$	9.19837e10			2.81606
$218$	−1.16241e10	+	7.73786e9i	−0.348582	+	0.232042i
$219$		−	1.82629e10i		−	0.536500i
$220$	4.50157e9	−	1.07621e10i	0.129557	−	0.309737i
$221$		−	3.03563e10i		−	0.856019i
$222$	−9.91122e9	−	1.48890e10i	−0.273866	−	0.411412i
$223$	−5.62113e10			−1.52213			−0.761065	−	0.648676i	$-0.775323\pi$
$223$	−5.62113e10			−1.52213			−0.761065	+	0.648676i	$0.775323\pi$
$224$	−1.27542e10	+	6.13364e10i	−0.338483	+	1.62780i
$225$	−1.16782e10			−0.303777
$226$	−3.78599e10	−	5.68746e10i	−0.965366	−	1.45021i
$227$		−	6.25184e10i		−	1.56276i	−0.624057	−	0.781379i	$-0.714517\pi$
$227$		−	6.25184e10i		−	1.56276i	0.624057	−	0.781379i	$-0.285483\pi$
$228$	1.21479e10	−	2.90423e10i	0.297710	−	0.711745i
$229$		−	5.27164e10i		−	1.26674i	−0.773851	−	0.633368i	$-0.781672\pi$
$229$		−	5.27164e10i		−	1.26674i	0.773851	−	0.633368i	$-0.218328\pi$
$230$	−6.86393e9	+	4.56914e9i	−0.161733	+	0.107661i
$231$	4.68390e10			1.08231
$232$	−4.68142e9	−	2.41919e10i	−0.106092	−	0.548244i
$233$	−7.37673e10			−1.63969			−0.819846	−	0.572583i	$-0.805941\pi$
$233$	−7.37673e10			−1.63969			−0.819846	+	0.572583i	$0.805941\pi$
$234$	1.27920e10	−	8.51533e9i	0.278913	−	0.185665i
$235$			4.52144e9i			0.0967100i
$236$	5.53256e10	+	2.31416e10i	1.16097	+	0.485613i
$237$			4.26378e10i			0.877865i
$238$	−3.88367e10	−	5.83419e10i	−0.784597	−	1.17865i
$239$	−1.34146e10			−0.265942			−0.132971	−	0.991120i	$-0.542452\pi$
$239$	−1.34146e10			−0.265942			−0.132971	+	0.991120i	$0.542452\pi$
$240$	−6.20479e9	−	6.29144e9i	−0.120719	−	0.122405i
$241$	−2.65736e10			−0.507428			−0.253714	−	0.967279i	$-0.581652\pi$
$241$	−2.65736e10			−0.507428			−0.253714	+	0.967279i	$0.581652\pi$
$242$	8.02035e9	+	1.20485e10i	0.150322	+	0.225820i
$243$		−	3.48678e9i		−	0.0641500i
$244$	4.16031e9	+	1.74018e9i	0.0751400	+	0.0314296i
$245$			2.96285e10i			0.525366i
$246$	−1.56331e10	+	1.04066e10i	−0.272168	+	0.181175i
$247$	−7.85731e10			−1.34319
$248$	9.90598e10	−	1.91693e10i	1.66290	−	0.321790i
$249$	5.31922e10			0.876902
$250$	2.92617e10	−	1.94787e10i	0.473772	−	0.315378i
$251$		−	6.65264e10i		−	1.05794i	−0.848639	−	0.528972i	$-0.822578\pi$
$251$		−	6.65264e10i		−	1.05794i	0.848639	−	0.528972i	$-0.177422\pi$
$252$	1.36909e10	−	3.27314e10i	0.213860	−	0.511283i
$253$		−	4.79432e10i		−	0.735673i
$254$	1.58892e10	+	2.38694e10i	0.239525	+	0.359824i
$255$	9.88546e9			0.146408
$256$	−9.52911e8	+	6.87129e10i	−0.0138667	+	0.999904i
$257$	7.31724e10			1.04628			0.523141	−	0.852246i	$-0.324760\pi$
$257$	7.31724e10			1.04628			0.523141	+	0.852246i	$0.324760\pi$
$258$	2.42705e10	+	3.64600e10i	0.341028	+	0.512305i
$259$			1.03070e11i			1.42326i
$260$	−8.51065e9	+	2.03467e10i	−0.115500	+	0.276131i
$261$			1.39546e10i			0.186138i
$262$	8.94157e10	−	5.95217e10i	1.17235	−	0.780405i
$263$	−7.24021e10			−0.933147			−0.466574	−	0.884482i	$-0.654512\pi$
$263$	−7.24021e10			−0.933147			−0.466574	+	0.884482i	$0.654512\pi$
$264$	5.04422e10	−	9.76118e9i	0.639111	−	0.123676i
$265$	−1.05856e10			−0.131859
$266$	−1.51010e11	+	1.00524e11i	−1.84944	+	1.23112i
$267$		−	3.17827e10i		−	0.382728i
$268$	−4.89567e10	−	2.04777e10i	−0.579703	−	0.242479i
$269$			1.35446e11i			1.57718i	0.614917	+	0.788592i	$0.289190\pi$
$269$			1.35446e11i			1.57718i	−0.614917	+	0.788592i	$0.710810\pi$
$270$	2.77300e9	+	4.16570e9i	0.0317551	+	0.0477036i
$271$	1.79847e10			0.202555			0.101277	−	0.994858i	$-0.467707\pi$
$271$	1.79847e10			0.202555			0.101277	+	0.994858i	$0.467707\pi$
$272$	−5.39827e10	−	5.47366e10i	−0.597991	−	0.606342i
$273$	−8.85537e10			−0.964883
$274$	8.67776e10	+	1.30360e11i	0.930100	+	1.39723i
$275$			9.74527e10i			1.02753i
$276$	−3.35030e10	−	1.40137e10i	−0.347530	−	0.145365i
$277$			1.57486e11i			1.60725i	0.595137	+	0.803624i	$0.297098\pi$
$277$			1.57486e11i			1.60725i	−0.595137	+	0.803624i	$0.702902\pi$
$278$	1.50766e11	−	1.00361e11i	1.51392	−	1.00778i
$279$	−5.71407e10			−0.564582
$280$	9.67419e9	+	4.99927e10i	0.0940597	+	0.486067i
$281$	−1.64916e11			−1.57792			−0.788958	−	0.614448i	$-0.789379\pi$
$281$	−1.64916e11			−1.57792			−0.788958	+	0.614448i	$0.789379\pi$
$282$	−1.65766e10	+	1.10346e10i	−0.156090	+	0.103905i
$283$		−	5.98665e10i		−	0.554811i	−0.960753	−	0.277406i	$-0.910525\pi$
$283$		−	5.98665e10i		−	0.554811i	0.960753	−	0.277406i	$-0.0894746\pi$
$284$	8.10367e10	−	1.93738e11i	0.739179	−	1.76718i
$285$		−	2.55872e10i		−	0.229732i
$286$	−7.10589e10	−	1.06747e11i	−0.628017	−	0.943430i
$287$	1.08221e11			0.941551
$288$	7.92295e9	−	3.81025e10i	0.0678611	−	0.326353i
$289$	−3.25827e10			−0.274756
$290$	−1.10979e10	−	1.66717e10i	−0.0921407	−	0.138417i
$291$			3.46303e10i			0.283099i
$292$	−4.45462e10	+	1.06498e11i	−0.358581	+	0.857273i
$293$		−	1.84626e11i		−	1.46349i	−0.681580	−	0.731743i	$-0.738707\pi$
$293$		−	1.84626e11i		−	1.46349i	0.681580	−	0.731743i	$-0.261293\pi$
$294$	−1.08625e11	+	7.23086e10i	−0.847940	+	0.564452i
$295$	4.87435e10			0.374730
$296$	2.14796e10	+	1.10999e11i	0.162635	+	0.840439i
$297$	−2.90966e10			−0.216989
$298$	8.08161e10	−	5.37972e10i	0.593642	−	0.395172i
$299$			9.06413e10i			0.655852i
$300$	6.81005e10	+	2.84851e10i	0.485405	+	0.203036i
$301$		−	2.52397e11i		−	1.77229i
$302$	4.33356e10	+	6.51003e10i	0.299788	+	0.450352i
$303$	5.32308e10			0.362803
$304$	−1.41678e11	+	1.39727e11i	−0.951419	+	0.938317i
$305$	3.66536e9			0.0242531
$306$	2.41256e10	+	3.62423e10i	0.157301	+	0.236303i
$307$			8.95668e10i			0.575472i	0.957710	+	0.287736i	$0.0929026\pi$
$307$			8.95668e10i			0.575472i	−0.957710	+	0.287736i	$0.907097\pi$
$308$	−2.73137e11	−	1.14248e11i	−1.72943	−	0.723388i
$309$			5.89849e9i			0.0368068i
$310$	6.82667e10	−	4.54434e10i	0.419837	−	0.279475i
$311$	1.93571e11			1.17333			0.586663	−	0.809831i	$-0.300441\pi$
$311$	1.93571e11			1.17333			0.586663	+	0.809831i	$0.300441\pi$
$312$	−9.53660e10	+	1.84545e10i	−0.569768	+	0.110257i
$313$	1.28784e11			0.758423			0.379211	−	0.925310i	$-0.376195\pi$
$313$	1.28784e11			0.758423			0.379211	+	0.925310i	$0.376195\pi$
$314$	−4.09634e9	+	2.72683e9i	−0.0237801	+	0.0158298i
$315$		−	2.88373e10i		−	0.165028i
$316$	1.04001e11	−	2.48639e11i	0.586739	−	1.40274i
$317$		−	8.44213e10i		−	0.469554i	−0.972049	−	0.234777i	$-0.924564\pi$
$317$		−	8.44213e10i		−	0.469554i	0.972049	−	0.234777i	$-0.0754360\pi$
$318$	−2.58344e10	−	3.88093e10i	−0.141669	−	0.212821i
$319$	1.16449e11			0.629617
$320$	2.08368e10	+	5.18225e10i	0.111085	+	0.276276i
$321$	−6.32490e10			−0.332492
$322$	1.15963e11	+	1.74204e11i	0.601131	+	0.903041i
$323$		−	2.22613e11i		−	1.13799i
$324$	−8.50485e9	+	2.03329e10i	−0.0428760	+	0.102505i
$325$		−	1.84244e11i		−	0.916047i
$326$	−7.60956e9	+	5.06549e9i	−0.0373147	+	0.0248394i
$327$	−4.99874e10			−0.241766
$328$	1.16546e11	−	2.25531e10i	0.555990	−	0.107591i
$329$	1.14753e11			0.539984
$330$	3.47620e10	−	2.31402e10i	0.161359	−	0.107412i
$331$			1.47944e11i			0.677440i	0.940887	+	0.338720i	$0.109994\pi$
$331$			1.47944e11i			0.677440i	−0.940887	+	0.338720i	$0.890006\pi$
$332$	−3.10186e11	−	1.29745e11i	−1.40120	−	0.586096i
$333$		−	6.40276e10i		−	0.285343i
$334$	1.25385e11	+	1.88358e11i	0.551298	+	0.828180i
$335$	−4.31324e10			−0.187112
$336$	−1.59675e11	+	1.57476e11i	−0.683453	+	0.674041i
$337$	3.22312e10			0.136126			0.0680631	−	0.997681i	$-0.478318\pi$
$337$	3.22312e10			0.136126			0.0680631	+	0.997681i	$0.478318\pi$
$338$	1.37947e9	+	2.07229e9i	0.00574894	+	0.00863626i
$339$		−	2.44579e11i		−	1.00582i
$340$	−5.76462e10	−	2.41123e10i	−0.233946	−	0.0978551i
$341$			4.76829e11i			1.90971i
$342$	9.38083e10	−	6.24458e10i	0.370786	−	0.246823i
$343$	3.25756e11			1.27078
$344$	−5.25991e10	−	2.71813e11i	−0.202519	−	1.04654i
$345$	−2.95172e10			−0.112173
$346$	−1.63630e11	+	1.08924e11i	−0.613792	+	0.408585i
$347$			4.93727e11i			1.82812i	0.405581	+	0.914059i	$0.367069\pi$
$347$			4.93727e11i			1.82812i	−0.405581	+	0.914059i	$0.632931\pi$
$348$	3.40376e10	−	8.13750e10i	0.124409	−	0.297430i
$349$		−	3.00694e11i		−	1.08495i	−0.840071	−	0.542476i	$-0.817487\pi$
$349$		−	3.00694e11i		−	1.08495i	0.840071	−	0.542476i	$-0.182513\pi$
$350$	−2.35715e11	−	3.54099e11i	−0.839616	−	1.26130i
$351$	5.50100e10			0.193446
$352$	−3.17958e11	−	6.61157e10i	−1.10390	−	0.229542i
$353$	−1.48977e9			−0.00510661			−0.00255330	−	0.999997i	$-0.500813\pi$
$353$	−1.48977e9			−0.00510661			−0.00255330	+	0.999997i	$0.500813\pi$
$354$	1.18959e11	+	1.78705e11i	0.402609	+	0.604813i
$355$		−	1.70689e11i		−	0.570397i
$356$	−7.75233e10	+	1.85338e11i	−0.255804	+	0.611560i
$357$		−	2.50890e11i		−	0.817477i
$358$	−3.07884e11	+	2.04950e11i	−0.990635	+	0.659440i
$359$	1.45640e11			0.462759			0.231380	−	0.972864i	$-0.425676\pi$
$359$	1.45640e11			0.462759			0.231380	+	0.972864i	$0.425676\pi$
$360$	−6.00966e9	−	3.10557e10i	−0.0188577	−	0.0974497i
$361$	−2.53515e11			−0.785637
$362$	−1.54185e11	+	1.02637e11i	−0.471903	+	0.314134i
$363$			5.18123e10i			0.156622i
$364$	5.16393e11	+	2.15997e11i	1.54179	+	0.644900i
$365$			9.38282e10i			0.276704i
$366$	8.94535e9	+	1.34380e10i	0.0260575	+	0.0391445i
$367$	−3.98300e11			−1.14608			−0.573038	−	0.819529i	$-0.694235\pi$
$367$	−3.98300e11			−1.14608			−0.573038	+	0.819529i	$0.694235\pi$
$368$	1.61188e11	+	1.63439e11i	0.458160	+	0.464558i
$369$	−6.72275e10			−0.188768
$370$	5.09204e10	+	7.64945e10i	0.141249	+	0.212189i
$371$			2.68660e11i			0.736241i
$372$	3.33211e11	+	1.39376e11i	0.902144	+	0.377350i
$373$			6.46674e11i			1.72980i	0.501945	+	0.864900i	$0.332618\pi$
$373$			6.46674e11i			1.72980i	−0.501945	+	0.864900i	$0.667382\pi$
$374$	3.02436e11	−	2.01324e11i	0.799302	−	0.532074i
$375$	1.25835e11			0.328594
$376$	1.23580e11	−	2.39143e10i	0.318863	−	0.0617038i
$377$	−2.20158e11			−0.561303
$378$	1.05724e11	−	7.03778e10i	0.266355	−	0.177306i
$379$		−	3.77422e11i		−	0.939616i	−0.882768	−	0.469808i	$-0.844323\pi$
$379$		−	3.77422e11i		−	0.939616i	0.882768	−	0.469808i	$-0.155677\pi$
$380$	−6.24114e10	+	1.49209e11i	−0.153546	+	0.367088i
$381$			1.02646e11i			0.249563i
$382$	−7.27645e10	−	1.09309e11i	−0.174837	−	0.262647i
$383$	−1.17245e11			−0.278419			−0.139210	−	0.990263i	$-0.544456\pi$
$383$	−1.17245e11			−0.278419			−0.139210	+	0.990263i	$0.544456\pi$
$384$	−1.39140e11	+	2.02866e11i	−0.326560	+	0.476122i
$385$	−2.40642e11			−0.558212
$386$	−9.76216e10	−	1.46651e11i	−0.223822	−	0.336234i
$387$			1.56790e11i			0.355320i
$388$	8.44692e10	−	2.01944e11i	0.189215	−	0.452363i
$389$			5.70541e10i			0.126332i	0.998003	+	0.0631661i	$0.0201198\pi$
$389$			5.70541e10i			0.126332i	−0.998003	+	0.0631661i	$0.979880\pi$
$390$	−6.57210e10	+	4.37488e10i	−0.143851	+	0.0957581i
$391$	−2.56804e11			−0.555657
$392$	8.09807e11	−	1.56707e11i	1.73219	−	0.335199i
$393$	3.84517e11			0.813109
$394$	3.45920e11	−	2.30270e11i	0.723173	−	0.481398i
$395$		−	2.19058e11i		−	0.452765i
$396$	1.69674e11	+	7.09715e10i	0.346727	+	0.145029i
$397$			5.50745e11i			1.11274i	0.830935	+	0.556370i	$0.187806\pi$
$397$			5.50745e11i			1.11274i	−0.830935	+	0.556370i	$0.812194\pi$
$398$	2.95503e11	+	4.43916e11i	0.590321	+	0.886802i
$399$	−6.49394e11			−1.28271
$400$	−3.27642e11	−	3.32217e11i	−0.639925	−	0.648861i
$401$	6.57952e11			1.27070			0.635352	−	0.772223i	$-0.280855\pi$
$401$	6.57952e11			1.27070			0.635352	+	0.772223i	$0.280855\pi$
$402$	−1.05265e11	−	1.58133e11i	−0.201033	−	0.301999i
$403$		−	9.01492e11i		−	1.70251i
$404$	−3.10411e11	−	1.29839e11i	−0.579723	−	0.242487i
$405$			1.79139e10i			0.0330858i
$406$	−4.23123e11	+	2.81662e11i	−0.772857	+	0.514471i
$407$	−5.34299e11			−0.965182
$408$	−5.22850e10	−	2.70190e11i	−0.0934128	−	0.482724i
$409$	−4.15936e11			−0.734973			−0.367486	−	0.930029i	$-0.619782\pi$
$409$	−4.15936e11			−0.734973			−0.367486	+	0.930029i	$0.619782\pi$
$410$	8.03175e10	−	5.34653e10i	0.140373	−	0.0934425i
$411$			5.60592e11i			0.969079i
$412$	1.43874e10	−	3.43965e10i	0.0246006	−	0.0588135i
$413$		−	1.23709e12i		−	2.09232i
$414$	−7.20369e10	−	1.08216e11i	−0.120518	−	0.181047i
$415$	−2.73283e11			−0.452269
$416$	6.01131e11	+	1.24998e11i	0.984123	+	0.204637i
$417$	6.48345e11			1.05001
$418$	−5.21099e11	−	7.82814e11i	−0.834886	−	1.25420i
$419$			1.16764e11i			0.185074i	0.995709	+	0.0925369i	$0.0294976\pi$
$419$			1.16764e11i			0.185074i	−0.995709	+	0.0925369i	$0.970502\pi$
$420$	−7.03391e10	+	1.68162e11i	−0.110300	+	0.263698i
$421$			5.40488e11i			0.838527i	0.907865	+	0.419263i	$0.137712\pi$
$421$			5.40488e11i			0.838527i	−0.907865	+	0.419263i	$0.862288\pi$
$422$	6.46445e11	−	4.30322e11i	0.992261	−	0.660522i
$423$	−7.12849e10			−0.108259
$424$	5.59883e10	+	2.89327e11i	0.0841300	+	0.434754i
$425$	5.21998e11			0.776101
$426$	6.25783e11	−	4.16568e11i	0.920620	−	0.612833i
$427$		−	9.30255e10i		−	0.135418i
$428$	3.68831e11	+	1.54275e11i	0.531288	+	0.222228i
$429$		−	4.59049e11i		−	0.654336i
$430$	−1.24693e11	−	1.87319e11i	−0.175888	−	0.264225i
$431$	−6.12492e11			−0.854974			−0.427487	−	0.904022i	$-0.640601\pi$
$431$	−6.12492e11			−0.854974			−0.427487	+	0.904022i	$0.640601\pi$
$432$	9.91906e10	−	9.78245e10i	0.137023	−	0.135136i
$433$	−8.42258e10			−0.115146			−0.0575731	−	0.998341i	$-0.518336\pi$
$433$	−8.42258e10			−0.115146			−0.0575731	+	0.998341i	$0.518336\pi$
$434$	−1.15334e12	−	1.73258e12i	−1.56046	−	2.34418i
$435$		−	7.16939e10i		−	0.0960020i
$436$	2.91497e11	+	1.21928e11i	0.386318	+	0.161589i
$437$			6.64703e11i			0.871889i
$438$	−3.43995e11	+	2.28989e11i	−0.446600	+	0.297290i
$439$	2.78791e11			0.358252			0.179126	−	0.983826i	$-0.442673\pi$
$439$	2.78791e11			0.358252			0.179126	+	0.983826i	$0.442673\pi$
$440$	−2.59155e11	+	5.01495e10i	−0.329626	+	0.0637866i
$441$	−4.67121e11			−0.588107
$442$	−5.71784e11	+	3.80622e11i	−0.712577	+	0.474344i
$443$		−	6.63629e11i		−	0.818669i	−0.912384	−	0.409335i	$-0.865761\pi$
$443$		−	6.63629e11i		−	0.818669i	0.912384	−	0.409335i	$-0.134239\pi$
$444$	−1.56174e11	+	3.73371e11i	−0.190715	+	0.455950i
$445$			1.63288e11i			0.197395i
$446$	7.04805e11	+	1.05878e12i	0.843455	+	1.26707i
$447$	3.47536e11			0.411733
$448$	1.31524e12	−	5.28831e11i	1.54260	−	0.620249i
$449$	−5.42621e10			−0.0630068			−0.0315034	−	0.999504i	$-0.510030\pi$
$449$	−5.42621e10			−0.0630068			−0.0315034	+	0.999504i	$0.510030\pi$
$450$	1.46427e11	+	2.19968e11i	0.168331	+	0.252874i
$451$			5.61002e11i			0.638513i
$452$	−5.96570e11	+	1.42624e12i	−0.672262	+	1.60720i
$453$			2.79953e11i			0.312351i
$454$	−1.17758e12	+	7.83887e11i	−1.30089	+	0.865968i
$455$	4.54958e11			0.497645
$456$	−6.99350e11	+	1.35333e11i	−0.757448	+	0.146575i
$457$	5.47436e11			0.587097			0.293549	−	0.955944i	$-0.405164\pi$
$457$	5.47436e11			0.587097			0.293549	+	0.955944i	$0.405164\pi$
$458$	−9.92954e11	+	6.60984e11i	−1.05447	+	0.701934i
$459$			1.55854e11i			0.163893i
$460$	1.72127e11	+	7.19973e10i	0.179241	+	0.0749732i
$461$		−	5.32000e11i		−	0.548602i	−0.961644	−	0.274301i	$-0.911554\pi$
$461$		−	5.32000e11i		−	0.548602i	0.961644	−	0.274301i	$-0.0884465\pi$
$462$	−5.87290e11	−	8.82249e11i	−0.599741	−	0.900953i
$463$	1.22274e12			1.23658			0.618288	−	0.785951i	$-0.287826\pi$
$463$	1.22274e12			1.23658			0.618288	+	0.785951i	$0.287826\pi$
$464$	−3.96975e11	+	3.91508e11i	−0.397587	+	0.392111i
$465$	2.93569e11			0.291187
$466$	9.24931e11	+	1.38946e12i	0.908600	+	1.36493i
$467$			4.68729e11i			0.456033i	0.973657	+	0.228016i	$0.0732239\pi$
$467$			4.68729e11i			0.456033i	−0.973657	+	0.228016i	$0.926776\pi$
$468$	−3.20786e11	−	1.34179e11i	−0.309107	−	0.129294i
$469$			1.09468e12i			1.04475i
$470$	8.51648e10	−	5.66920e10i	0.0805045	−	0.0535898i
$471$	−1.76156e10			−0.0164932
$472$	−2.57809e11	−	1.33226e12i	−0.239088	−	1.23552i
$473$	1.30839e12			1.20188
$474$	8.03116e11	−	5.34614e11i	0.730762	−	0.486449i
$475$		−	1.35112e12i		−	1.21779i
$476$	−6.11962e11	+	1.46304e12i	−0.546378	+	1.30625i
$477$		−	1.66893e11i		−	0.147606i
$478$	1.68199e11	+	2.52674e11i	0.147366	+	0.221378i
$479$	−1.17454e12			−1.01943			−0.509715	−	0.860343i	$-0.670249\pi$
$479$	−1.17454e12			−1.01943			−0.509715	+	0.860343i	$0.670249\pi$
$480$	−4.07054e10	+	1.95757e11i	−0.0349998	+	0.168319i
$481$	1.01014e12			0.860460
$482$	3.33193e11	+	5.00535e11i	0.281180	+	0.422399i
$483$			7.49135e11i			0.626323i
$484$	1.26379e11	−	3.02139e11i	0.104682	−	0.250266i
$485$		−	1.77919e11i		−	0.146010i
$486$	−6.56763e10	+	4.37190e10i	−0.0534005	+	0.0355473i
$487$	6.70816e11			0.540410			0.270205	−	0.962803i	$-0.412909\pi$
$487$	6.70816e11			0.540410			0.270205	+	0.962803i	$0.412909\pi$
$488$	−1.93864e10	−	1.00182e11i	−0.0154742	−	0.0799650i
$489$	−3.27236e10			−0.0258804
$490$	5.58075e11	−	3.71496e11i	0.437331	−	0.291120i
$491$		−	1.62509e12i		−	1.26186i	−0.775841	−	0.630929i	$-0.782674\pi$
$491$		−	1.62509e12i		−	1.26186i	0.775841	−	0.630929i	$-0.217326\pi$
$492$	3.92031e11	+	1.63979e11i	0.301632	+	0.126167i
$493$		−	6.23749e11i		−	0.475553i
$494$	9.85188e11	+	1.47999e12i	0.744300	+	1.11811i
$495$	1.49488e11			0.111914
$496$	−1.60313e12	−	1.62551e12i	−1.18933	−	1.20593i
$497$	−4.33202e12			−3.18483
$498$	−6.66950e11	−	1.00192e12i	−0.485916	−	0.729961i
$499$			8.66354e11i			0.625523i	0.949832	+	0.312761i	$0.101254\pi$
$499$			8.66354e11i			0.625523i	−0.949832	+	0.312761i	$0.898746\pi$
$500$	−7.33794e11	−	3.06932e11i	−0.525060	−	0.219623i
$501$			8.10001e11i			0.574401i
$502$	−1.25308e12	+	8.34141e11i	−0.880665	+	0.586236i
$503$	−6.42584e10			−0.0447583			−0.0223792	−	0.999750i	$-0.507124\pi$
$503$	−6.42584e10			−0.0447583			−0.0223792	+	0.999750i	$0.507124\pi$
$504$	−7.88184e11	+	1.52523e11i	−0.544114	+	0.105293i
$505$	−2.73481e11			−0.187118
$506$	−9.03048e11	+	6.01136e11i	−0.612397	+	0.407657i
$507$			8.91154e9i			0.00598986i
$508$	2.50372e11	−	5.98572e11i	0.166801	−	0.398777i
$509$		−	2.27663e12i		−	1.50336i	−0.659531	−	0.751678i	$-0.729245\pi$
$509$		−	2.27663e12i		−	1.50336i	0.659531	−	0.751678i	$-0.270755\pi$
$510$	−1.23949e11	−	1.86200e11i	−0.0811290	−	0.121875i
$511$	2.38133e12			1.54499
$512$	1.30621e12	−	8.43607e11i	0.840035	−	0.542532i
$513$	4.03406e11			0.257167
$514$	−9.17472e11	−	1.37826e12i	−0.579774	−	0.870957i
$515$		−	3.03044e10i		−	0.0189834i
$516$	3.82437e11	−	9.14307e11i	0.237485	−	0.567765i
$517$			5.94860e11i			0.366191i
$518$	1.94140e12	−	1.29234e12i	1.18476	−	0.788667i
$519$	−7.03664e11			−0.425708
$520$	4.89957e11	−	9.48126e10i	0.293862	−	0.0568658i
$521$	1.15540e12			0.687011			0.343505	−	0.939151i	$-0.388386\pi$
$521$	1.15540e12			0.687011			0.343505	+	0.939151i	$0.388386\pi$
$522$	2.62846e11	−	1.74970e11i	0.154947	−	0.103144i
$523$			6.71579e11i			0.392500i	0.980554	+	0.196250i	$0.0628764\pi$
$523$			6.71579e11i			0.392500i	−0.980554	+	0.196250i	$0.937124\pi$
$524$	−2.24228e12	−	9.37901e11i	−1.29927	−	0.543459i
$525$		−	1.52274e12i		−	0.874802i
$526$	9.07813e11	+	1.36375e12i	0.517083	+	0.776781i
$527$	2.55410e12			1.44241
$528$	−8.16329e11	−	8.27728e11i	−0.457101	−	0.463484i
$529$	−1.03436e12			−0.574275
$530$	1.32728e11	+	1.99389e11i	0.0730669	+	0.109764i
$531$			7.68489e11i			0.419481i
$532$	3.78688e12	+	1.58398e12i	2.04965	+	0.857329i
$533$		−	1.06063e12i		−	0.569234i
$534$	−5.98651e11	+	3.98507e11i	−0.318595	+	0.212080i
$535$	3.24951e11			0.171485
$536$	2.28131e11	+	1.17890e12i	0.119383	+	0.616927i
$537$	−1.32400e12			−0.687076
$538$	2.55124e12	−	1.69829e12i	1.31290	−	0.873962i
$539$			3.89805e12i			1.98929i
$540$	4.36950e10	−	1.04463e11i	0.0221136	−	0.0528678i
$541$			7.08583e11i			0.355634i	0.984064	+	0.177817i	$0.0569035\pi$
$541$			7.08583e11i			0.355634i	−0.984064	+	0.177817i	$0.943097\pi$
$542$	−2.25501e11	−	3.38756e11i	−0.112241	−	0.168613i
$543$	−6.63045e11			−0.327298
$544$	−3.54143e11	+	1.70312e12i	−0.173374	+	0.833778i
$545$	2.56818e11			0.124693
$546$	1.11033e12	+	1.66798e12i	0.534669	+	0.803199i
$547$		−	5.39817e11i		−	0.257812i	−0.991657	−	0.128906i	$-0.958853\pi$
$547$		−	5.39817e11i		−	0.257812i	0.991657	−	0.128906i	$-0.0411466\pi$
$548$	1.36738e12	−	3.26904e12i	0.647704	−	1.54849i
$549$			5.77879e10i			0.0271495i
$550$	1.83560e12	−	1.22191e12i	0.855352	−	0.569386i
$551$	−1.61449e12			−0.746196
$552$	1.56119e11	+	8.06765e11i	0.0715697	+	0.369846i
$553$	−5.55962e12			−2.52803
$554$	2.96637e12	−	1.97464e12i	1.33792	−	0.890622i
$555$			3.28951e11i			0.147168i
$556$	−3.78077e12	−	1.58142e12i	−1.67781	−	0.701797i
$557$		−	1.59724e12i		−	0.703106i	−0.936168	−	0.351553i	$-0.885654\pi$
$557$		−	1.59724e12i		−	0.703106i	0.936168	−	0.351553i	$-0.114346\pi$
$558$	7.16458e11	+	1.07629e12i	0.312851	+	0.469975i
$559$	−2.47363e12			−1.07147
$560$	8.20352e11	−	8.09054e11i	0.352496	−	0.347641i
$561$	1.30057e12			0.554372
$562$	2.06779e12	+	3.10632e12i	0.874367	+	1.31351i
$563$		−	9.72484e11i		−	0.407939i	−0.978977	−	0.203969i	$-0.934616\pi$
$563$		−	9.72484e11i		−	0.407939i	0.978977	−	0.203969i	$-0.0653843\pi$
$564$	4.15691e11	+	1.73876e11i	0.172988	+	0.0723574i
$565$			1.25656e12i			0.518760i
$566$	−1.12763e12	+	7.50636e11i	−0.461842	+	0.307436i
$567$	4.54648e11			0.184736
$568$	−4.66527e12	+	9.02787e11i	−1.88066	+	0.363930i
$569$	2.51375e11			0.100535			0.0502675	−	0.998736i	$-0.483993\pi$
$569$	2.51375e11			0.100535			0.0502675	+	0.998736i	$0.483993\pi$
$570$	−4.81954e11	+	3.20825e11i	−0.191236	+	0.127301i
$571$		−	5.79852e11i		−	0.228273i	−0.993465	−	0.114136i	$-0.963590\pi$
$571$		−	5.79852e11i		−	0.228273i	0.993465	−	0.114136i	$-0.0364101\pi$
$572$	−1.11970e12	+	2.67690e12i	−0.437339	+	1.04556i
$573$		−	4.70066e11i		−	0.182164i
$574$	−1.35693e12	−	2.03843e12i	−0.521740	−	0.783777i
$575$	−1.55864e12			−0.594622
$576$	−8.17031e11	+	3.28513e11i	−0.309270	+	0.124351i
$577$	6.58678e11			0.247390			0.123695	−	0.992320i	$-0.460526\pi$
$577$	6.58678e11			0.247390			0.123695	+	0.992320i	$0.460526\pi$
$578$	4.08538e11	+	6.13721e11i	0.152250	+	0.228716i
$579$		−	6.30646e11i		−	0.233202i
$580$	−1.74873e11	+	4.18076e11i	−0.0641650	+	0.153402i
$581$			6.93583e12i			2.52526i
$582$	6.52289e11	−	4.34212e11i	0.235660	−	0.156873i
$583$	−1.39269e12			−0.499282
$584$	2.56452e12	−	4.96265e11i	0.912321	−	0.176545i
$585$	−2.82622e11			−0.0997711
$586$	−3.47757e12	+	2.31493e12i	−1.21825	+	0.810959i
$587$			1.53421e12i			0.533353i	0.963786	+	0.266676i	$0.0859255\pi$
$587$			1.53421e12i			0.533353i	−0.963786	+	0.266676i	$0.914075\pi$
$588$	2.72398e12	+	1.13939e12i	0.939735	+	0.393073i
$589$		−	6.61094e12i		−	2.26331i
$590$	−6.11170e11	−	9.18122e11i	−0.207648	−	0.311937i
$591$	1.48757e12			0.501572
$592$	1.82143e12	−	1.79634e12i	0.609487	−	0.601094i
$593$	−2.64973e11			−0.0879946			−0.0439973	−	0.999032i	$-0.514009\pi$
$593$	−2.64973e11			−0.0879946			−0.0439973	+	0.999032i	$0.514009\pi$
$594$	3.64827e11	+	5.48057e11i	0.120240	+	0.180629i
$595$			1.28898e12i			0.421620i
$596$	−2.02662e12	−	8.47698e11i	−0.657907	−	0.275190i
$597$			1.90898e12i			0.615060i
$598$	1.70730e12	−	1.13651e12i	0.545952	−	0.363426i
$599$	4.65955e12			1.47885			0.739423	−	0.673241i	$-0.235098\pi$
$599$	4.65955e12			1.47885			0.739423	+	0.673241i	$0.235098\pi$
$600$	−3.17337e11	−	1.63989e12i	−0.0999633	−	0.516574i
$601$	3.23954e12			1.01286			0.506428	−	0.862282i	$-0.330965\pi$
$601$	3.23954e12			1.01286			0.506428	+	0.862282i	$0.330965\pi$
$602$	−4.75409e12	+	3.16467e12i	−1.47531	+	0.982076i
$603$		−	6.80023e11i		−	0.209457i
$604$	6.82852e11	−	1.63252e12i	0.208766	−	0.499105i
$605$		−	2.66194e11i		−	0.0807790i
$606$	−6.67434e11	−	1.00264e12i	−0.201040	−	0.302009i
$607$	−2.37269e12			−0.709401			−0.354700	−	0.934980i	$-0.615417\pi$
$607$	−2.37269e12			−0.709401			−0.354700	+	0.934980i	$0.615417\pi$
$608$	4.40830e12	+	9.16653e11i	1.30829	+	0.272044i
$609$	−1.81957e12			−0.536031
$610$	−4.59581e10	−	6.90399e10i	−0.0134393	−	0.0201890i
$611$		−	1.12464e12i		−	0.326459i
$612$	3.80153e11	−	9.08847e11i	0.109541	−	0.261884i
$613$			3.48233e12i			0.996088i	0.867152	+	0.498044i	$0.165948\pi$
$613$			3.48233e12i			0.996088i	−0.867152	+	0.498044i	$0.834052\pi$
$614$	1.68706e12	−	1.12303e12i	0.479041	−	0.318885i
$615$	3.45392e11			0.0973585
$616$	1.27278e12	+	6.57725e12i	0.356155	+	1.84048i
$617$	−1.26692e12			−0.351939			−0.175969	−	0.984396i	$-0.556306\pi$
$617$	−1.26692e12			−0.351939			−0.175969	+	0.984396i	$0.556306\pi$
$618$	1.11103e11	−	7.39582e10i	0.0306391	−	0.0203957i
$619$			3.81076e12i			1.04329i	0.853164	+	0.521643i	$0.174681\pi$
$619$			3.81076e12i			1.04329i	−0.853164	+	0.521643i	$0.825319\pi$
$620$	−1.71192e12	−	7.16064e11i	−0.465287	−	0.194621i
$621$		−	4.65366e11i		−	0.125569i
$622$	−2.42709e12	−	3.64606e12i	−0.650173	−	0.976714i
$623$	4.14420e12			1.10216
$624$	1.54335e12	+	1.56490e12i	0.407505	+	0.413196i
$625$	2.82996e12			0.741857
$626$	−1.61475e12	−	2.42574e12i	−0.420263	−	0.631335i
$627$		−	3.36636e12i		−	0.869874i
$628$	1.02724e11	+	4.29675e10i	0.0263544	+	0.0110235i
$629$			2.86193e12i			0.729006i
$630$	−5.43173e11	+	3.61576e11i	−0.137374	+	0.0914466i
$631$	−1.66134e12			−0.417184			−0.208592	−	0.978003i	$-0.566888\pi$
$631$	−1.66134e12			−0.417184			−0.208592	+	0.978003i	$0.566888\pi$
$632$	−5.98731e12	+	1.15862e12i	−1.49281	+	0.288877i
$633$	2.77993e12			0.688203
$634$	−1.59014e12	+	1.05852e12i	−0.390871	+	0.260193i
$635$		−	5.27361e11i		−	0.128714i
$636$	−4.07080e11	+	9.73220e11i	−0.0986557	+	0.235860i
$637$		−	7.36963e12i		−	1.77345i
$638$	−1.46009e12	−	2.19340e12i	−0.348889	−	0.524113i
$639$	2.69107e12			0.638515
$640$	7.14855e11	−	1.04225e12i	0.168425	−	0.245563i
$641$	5.23434e12			1.22462			0.612309	−	0.790618i	$-0.290241\pi$
$641$	5.23434e12			1.22462			0.612309	+	0.790618i	$0.290241\pi$
$642$	7.93047e11	+	1.19134e12i	0.184243	+	0.276777i
$643$		−	7.76746e12i		−	1.79197i	−0.444089	−	0.895983i	$-0.646473\pi$
$643$		−	7.76746e12i		−	1.79197i	0.444089	−	0.895983i	$-0.353527\pi$
$644$	1.82727e12	−	4.36852e12i	0.418616	−	1.00080i
$645$		−	8.05533e11i		−	0.183259i
$646$	−4.19308e12	+	2.79123e12i	−0.947299	+	0.630593i
$647$	−4.78238e12			−1.07294			−0.536470	−	0.843920i	$-0.680242\pi$
$647$	−4.78238e12			−1.07294			−0.536470	+	0.843920i	$0.680242\pi$
$648$	4.89623e11	−	9.47480e10i	0.109087	−	0.0211097i
$649$	6.41290e12			1.41891
$650$	−3.47037e12	+	2.31014e12i	−0.762546	+	0.507607i
$651$		−	7.45068e12i		−	1.62585i
$652$	1.90825e11	+	7.98183e10i	0.0413543	+	0.0172977i
$653$			2.68837e12i			0.578601i	0.957238	+	0.289301i	$0.0934227\pi$
$653$			2.68837e12i			0.578601i	−0.957238	+	0.289301i	$0.906577\pi$
$654$	6.26766e11	+	9.41551e11i	0.133969	+	0.201254i
$655$	−1.97551e12			−0.419367
$656$	−1.88612e12	−	1.91246e12i	−0.397651	−	0.403204i
$657$	−1.47929e12			−0.309749
$658$	−1.43882e12	−	2.16145e12i	−0.299220	−	0.449500i
$659$		−	3.65807e12i		−	0.755557i	−0.925896	−	0.377778i	$-0.876688\pi$
$659$		−	3.65807e12i		−	0.755557i	0.925896	−	0.377778i	$-0.123312\pi$
$660$	−8.71727e11	−	3.64627e11i	−0.178827	−	0.0747999i
$661$		−	3.85004e12i		−	0.784439i	−0.919872	−	0.392219i	$-0.871707\pi$
$661$		−	3.85004e12i		−	0.784439i	0.919872	−	0.392219i	$-0.128293\pi$
$662$	2.78664e12	−	1.85499e12i	0.563922	−	0.375389i
$663$	−2.45886e12			−0.494223
$664$	1.44542e12	+	7.46939e12i	0.288560	+	1.49118i
$665$	3.33636e12			0.661569
$666$	−1.20601e12	+	8.02809e11i	−0.237529	+	0.158117i
$667$			1.86246e12i			0.364352i
$668$	1.97573e12	−	4.72345e12i	0.383913	−	0.917835i
$669$			4.55312e12i			0.878802i
$670$	5.40815e11	+	8.12431e11i	0.103684	+	0.155758i
$671$	4.82230e11			0.0918339
$672$	4.96825e12	+	1.03309e12i	0.939814	+	0.195423i
$673$	3.09913e10			0.00582333			0.00291167	−	0.999996i	$-0.499073\pi$
$673$	3.09913e10			0.00582333			0.00291167	+	0.999996i	$0.499073\pi$
$674$	−4.04130e11	−	6.07099e11i	−0.0754313	−	0.113316i
$675$			9.45935e11i			0.175386i
$676$	2.17367e10	−	5.19668e10i	0.00400345	−	0.00957119i
$677$			9.89140e12i			1.80971i	0.425720	+	0.904855i	$0.360021\pi$
$677$			9.89140e12i			1.80971i	−0.425720	+	0.904855i	$0.639979\pi$
$678$	−4.60684e12	+	3.06665e12i	−0.837278	+	0.557354i
$679$	−4.51551e12			−0.815254
$680$	2.68622e11	+	1.38814e12i	0.0481783	+	0.248968i
$681$	−5.06399e12			−0.902259
$682$	8.98145e12	−	5.97872e12i	1.58971	−	1.05823i
$683$		−	2.51437e12i		−	0.442115i	−0.975261	−	0.221058i	$-0.929049\pi$
$683$		−	2.51437e12i		−	0.442115i	0.975261	−	0.221058i	$-0.0709509\pi$
$684$	−2.35243e12	−	9.83976e11i	−0.410926	−	0.171883i
$685$		−	2.88013e12i		−	0.499809i
$686$	−4.08449e12	−	6.13587e12i	−0.704173	−	1.05783i
$687$	−4.27003e12			−0.731350
$688$	−4.46030e12	+	4.39887e12i	−0.758955	+	0.748503i
$689$	2.63302e12			0.445110
$690$	3.70101e11	+	5.55979e11i	0.0621583	+	0.0933764i
$691$			7.61485e12i			1.27060i	0.772264	+	0.635302i	$0.219124\pi$
$691$			7.61485e12i			1.27060i	−0.772264	+	0.635302i	$0.780876\pi$
$692$	4.10335e12	+	1.71635e12i	0.680239	+	0.284531i
$693$		−	3.79396e12i		−	0.624875i
$694$	9.29973e12	−	6.19059e12i	1.52178	−	1.01301i
$695$	−3.33097e12			−0.541551
$696$	−1.95954e12	+	3.79195e11i	−0.316529	+	0.0612521i
$697$	3.00496e12			0.482272
$698$	−5.66381e12	+	3.77025e12i	−0.903148	+	0.601202i
$699$			5.97515e12i			0.946677i
$700$	−3.71423e12	+	8.87974e12i	−0.584692	+	1.39785i
$701$		−	5.46754e12i		−	0.855187i	−0.903971	−	0.427594i	$-0.859361\pi$
$701$		−	5.46754e12i		−	0.855187i	0.903971	−	0.427594i	$-0.140639\pi$
$702$	−6.89742e11	−	1.03616e12i	−0.107194	−	0.161030i
$703$	7.40772e12			1.14389
$704$	2.74138e12	+	6.81798e12i	0.420622	+	1.04611i
$705$	3.66237e11			0.0558356
$706$	1.86794e10	+	2.80609e10i	0.00282972	+	0.00425090i
$707$			6.94086e12i			1.04478i
$708$	1.87447e12	−	4.48137e12i	0.280369	−	0.670288i
$709$			1.18804e13i			1.76572i	0.469638	+	0.882859i	$0.344384\pi$
$709$			1.18804e13i			1.76572i	−0.469638	+	0.882859i	$0.655616\pi$
$710$	−3.21505e12	+	2.14018e12i	−0.474816	+	0.316073i
$711$	3.45366e12			0.506835
$712$	4.46301e12	−	8.63645e11i	0.650830	−	0.125943i
$713$	−7.62633e12			−1.10513
$714$	−4.72570e12	+	3.14578e12i	−0.680494	+	0.452987i
$715$			2.35843e12i			0.337478i
$716$	7.72080e12	+	3.22946e12i	1.09788	+	0.459221i
$717$			1.08658e12i			0.153542i
$718$	−1.82610e12	−	2.74324e12i	−0.256428	−	0.385216i
$719$	−1.13520e12			−0.158414			−0.0792071	−	0.996858i	$-0.525239\pi$
$719$	−1.13520e12			−0.158414			−0.0792071	+	0.996858i	$0.525239\pi$
$720$	−5.09607e11	+	5.02588e11i	−0.0706706	+	0.0696973i
$721$	−7.69115e11			−0.105994
$722$	3.17870e12	+	4.77516e12i	0.435344	+	0.653989i
$723$			2.15246e12i			0.292963i
$724$	3.86649e12	+	1.61728e12i	0.522989	+	0.218757i
$725$		−	3.78577e12i		−	0.508900i
$726$	9.75925e11	−	6.49648e11i	0.130377	−	0.0867887i
$727$	−8.53103e12			−1.13265			−0.566326	−	0.824181i	$-0.691636\pi$
$727$	−8.53103e12			−1.13265			−0.566326	+	0.824181i	$0.691636\pi$
$728$	−2.40631e12	−	1.24349e13i	−0.317512	−	1.64079i
$729$	−2.82430e11			−0.0370370
$730$	1.76733e12	−	1.17646e12i	0.230337	−	0.153329i
$731$		−	7.00827e12i		−	0.907784i
$732$	1.40954e11	−	3.36985e11i	0.0181459	−	0.0433821i
$733$			2.95638e11i			0.0378262i	0.999821	+	0.0189131i	$0.00602059\pi$
$733$			2.95638e11i			0.0378262i	−0.999821	+	0.0189131i	$0.993979\pi$
$734$	4.99408e12	+	7.50229e12i	0.635073	+	0.954030i
$735$	2.39991e12			0.303320
$736$	1.05744e12	−	5.08538e12i	0.132833	−	0.638812i
$737$	−5.67467e12			−0.708496
$738$	8.42932e11	+	1.26628e12i	0.104602	+	0.157136i
$739$			8.95692e12i			1.10474i	0.833600	+	0.552369i	$0.186276\pi$
$739$			8.95692e12i			1.10474i	−0.833600	+	0.552369i	$0.813724\pi$
$740$	8.02368e11	−	1.91825e12i	0.0983627	−	0.235159i
$741$			6.36442e12i			0.775492i
$742$	5.06042e12	−	3.36859e12i	0.612870	−	0.407972i
$743$	1.50988e12			0.181758			0.0908789	−	0.995862i	$-0.471032\pi$
$743$	1.50988e12			0.181758			0.0908789	+	0.995862i	$0.471032\pi$
$744$	−1.55271e12	−	8.02385e12i	−0.185786	−	0.960073i
$745$	−1.78552e12			−0.212354
$746$	1.21806e13	−	8.10832e12i	1.43994	−	0.958531i
$747$		−	4.30857e12i		−	0.506280i
$748$	−7.58417e12	−	3.17231e12i	−0.885831	−	0.370526i
$749$		−	8.24715e12i		−	0.957494i
$750$	−1.57778e12	−	2.37020e12i	−0.182083	−	0.273532i
$751$	−3.27872e12			−0.376118			−0.188059	−	0.982158i	$-0.560220\pi$
$751$	−3.27872e12			−0.376118			−0.188059	+	0.982158i	$0.560220\pi$
$752$	−1.99995e12	−	2.02788e12i	−0.228055	−	0.231240i
$753$	−5.38864e12			−0.610804
$754$	2.76044e12	+	4.14684e12i	0.311034	+	0.467247i
$755$		−	1.43830e12i		−	0.161097i
$756$	−2.65124e12	−	1.10896e12i	−0.295189	−	0.123472i
$757$		−	1.03608e12i		−	0.114673i	−0.998355	−	0.0573364i	$-0.981739\pi$
$757$		−	1.03608e12i		−	0.114673i	0.998355	−	0.0573364i	$-0.0182608\pi$
$758$	−7.10903e12	+	4.73230e12i	−0.782166	+	0.520668i
$759$	−3.88340e12			−0.424741
$760$	3.59302e12	−	6.95292e11i	0.390659	−	0.0755973i
$761$	−1.14256e13			−1.23495			−0.617475	−	0.786591i	$-0.711844\pi$
$761$	−1.14256e13			−1.23495			−0.617475	+	0.786591i	$0.711844\pi$
$762$	1.93342e12	−	1.28703e12i	0.207744	−	0.138290i
$763$		−	6.51795e12i		−	0.696226i
$764$	−1.14657e12	+	2.74115e12i	−0.121753	+	0.291080i
$765$		−	8.00722e11i		−	0.0845289i
$766$	1.47007e12	+	2.20840e12i	0.154280	+	0.231765i
$767$	−1.21242e13			−1.26495
$768$	5.56574e12	+	7.71858e10i	0.577295	+	0.00800593i
$769$	3.90710e12			0.402889			0.201445	−	0.979500i	$-0.435436\pi$
$769$	3.90710e12			0.402889			0.201445	+	0.979500i	$0.435436\pi$
$770$	3.01729e12	+	4.53269e12i	0.309321	+	0.464673i
$771$		−	5.92697e12i		−	0.604071i
$772$	−1.53825e12	+	3.67756e12i	−0.155865	+	0.372633i
$773$			5.78500e12i			0.582768i	0.956606	+	0.291384i	$0.0941157\pi$
$773$			5.78500e12i			0.582768i	−0.956606	+	0.291384i	$0.905884\pi$
$774$	2.95326e12	−	1.96591e12i	0.295779	−	0.196893i
$775$	1.55018e13			1.54356
$776$	−4.86288e12	+	9.41026e11i	−0.481411	+	0.0931588i
$777$	8.34867e12			0.821718
$778$	1.07466e12	−	7.15372e11i	0.105163	−	0.0700042i
$779$		−	7.77795e12i		−	0.756739i
$780$	1.64809e12	+	6.89363e11i	0.159424	+	0.0666841i
$781$		−	2.24565e13i		−	2.15980i
$782$	3.21994e12	+	4.83711e12i	0.307905	+	0.462546i
$783$	1.13032e12			0.107467
$784$	−1.31055e13	−	1.32885e13i	−1.23888	−	1.25618i
$785$	9.05029e10			0.00850647
$786$	−4.82126e12	−	7.24267e12i	−0.450567	−	0.676858i
$787$			9.01542e11i			0.0837722i	0.999122	+	0.0418861i	$0.0133367\pi$
$787$			9.01542e11i			0.0837722i	−0.999122	+	0.0418861i	$0.986663\pi$
$788$	−8.67462e12	−	3.62843e12i	−0.801461	−	0.335236i
$789$			5.86457e12i			0.538753i
$790$	−4.12613e12	+	2.74666e12i	−0.376896	+	0.250890i
$791$	3.18911e13			2.89652
$792$	−7.90655e11	−	4.08582e12i	−0.0714042	−	0.368991i
$793$	−9.11703e11			−0.0818698
$794$	1.03737e13	−	6.90552e12i	0.926280	−	0.616600i
$795$			8.57437e11i			0.0761290i
$796$	4.65633e12	−	1.11321e13i	0.411088	−	0.982804i
$797$		−	1.98771e12i		−	0.174498i	−0.996187	−	0.0872489i	$-0.972192\pi$
$797$		−	1.98771e12i		−	0.174498i	0.996187	−	0.0872489i	$-0.0278076\pi$
$798$	8.14242e12	+	1.22318e13i	0.710788	+	1.06777i
$799$	3.18632e12			0.276585
$800$	−2.14943e12	+	1.03369e13i	−0.185532	+	0.892246i
$801$	−2.57440e12			−0.220968
$802$	−8.24972e12	−	1.23930e13i	−0.704133	−	1.05777i
$803$			1.23444e13i			1.04773i
$804$	−1.65869e12	+	3.96549e12i	−0.139995	+	0.334692i
$805$		−	3.84880e12i		−	0.323030i
$806$	−1.69803e13	+	1.13033e13i	−1.41722	+	0.943408i
$807$	1.09712e13			0.910588
$808$	1.44647e12	+	7.47481e12i	0.119387	+	0.616949i
$809$	−1.59599e13			−1.30997			−0.654986	−	0.755641i	$-0.727326\pi$
$809$	−1.59599e13			−1.30997			−0.654986	+	0.755641i	$0.727326\pi$
$810$	3.37422e11	−	2.24613e11i	0.0275417	−	0.0183338i
$811$			2.09687e13i			1.70207i	0.525106	+	0.851037i	$0.324026\pi$
$811$			2.09687e13i			1.70207i	−0.525106	+	0.851037i	$0.675974\pi$
$812$	1.06106e13	+	4.43823e12i	0.856523	+	0.358267i
$813$		−	1.45676e12i		−	0.116945i
$814$	6.69930e12	+	1.00639e13i	0.534835	+	0.803448i
$815$	1.68122e11			0.0133480
$816$	−4.43366e12	+	4.37260e12i	−0.350072	+	0.345250i
$817$	−1.81400e13			−1.42442
$818$	5.21520e12	+	7.83447e12i	0.407269	+	0.611814i
$819$			7.17285e12i			0.557076i
$820$	−2.01412e12	−	8.42468e11i	−0.155569	−	0.0650716i
$821$		−	1.06480e13i		−	0.817945i	−0.912547	−	0.408973i	$-0.865887\pi$
$821$		−	1.06480e13i		−	0.817945i	0.912547	−	0.408973i	$-0.134113\pi$
$822$	1.05592e13	−	7.02898e12i	0.806692	−	0.536994i
$823$	−5.17550e12			−0.393236			−0.196618	−	0.980480i	$-0.562996\pi$
$823$	−5.17550e12			−0.393236			−0.196618	+	0.980480i	$0.562996\pi$
$824$	−8.28282e11	+	1.60282e11i	−0.0625901	+	0.0121119i
$825$	7.89367e12			0.593248
$826$	−2.33016e13	+	1.55113e13i	−1.74171	+	1.15941i
$827$		−	1.21139e13i		−	0.900552i	−0.892889	−	0.450276i	$-0.851326\pi$
$827$		−	1.21139e13i		−	0.900552i	0.892889	−	0.450276i	$-0.148674\pi$
$828$	−1.13511e12	+	2.71374e12i	−0.0839267	+	0.200647i
$829$			9.02964e12i			0.664010i	0.943278	+	0.332005i	$0.107725\pi$
$829$			9.02964e12i			0.664010i	−0.943278	+	0.332005i	$0.892275\pi$
$830$	3.42656e12	+	5.14750e12i	0.250615	+	0.376483i
$831$	1.27564e13			0.927945
$832$	−5.18284e12	−	1.28901e13i	−0.374984	−	0.932610i
$833$	2.08796e13			1.50252
$834$	−8.12927e12	−	1.22121e13i	−0.581841	−	0.874063i
$835$		−	4.16150e12i		−	0.296252i
$836$	−8.21111e12	+	1.96306e13i	−0.581398	+	1.38997i
$837$			4.62840e12i			0.325961i
$838$	2.19934e12	−	1.46404e12i	0.154061	−	0.102555i
$839$	3.30696e12			0.230409			0.115205	−	0.993342i	$-0.463248\pi$
$839$	3.30696e12			0.230409			0.115205	+	0.993342i	$0.463248\pi$
$840$	4.04941e12	−	7.83610e11i	0.280631	−	0.0543054i
$841$	9.98343e12			0.688174
$842$	1.01805e13	−	6.77691e12i	0.698016	−	0.464651i
$843$			1.33582e13i			0.911010i
$844$	−1.62109e13	−	6.78071e12i	−1.09968	−	0.459975i
$845$		−	4.57844e10i		−	0.00308931i
$846$	8.93804e11	+	1.34271e12i	0.0599896	+	0.0901185i
$847$	−6.75590e12			−0.451033
$848$	4.74770e12	−	4.68231e12i	0.315284	−	0.310942i
$849$	−4.84919e12			−0.320320
$850$	−6.54506e12	−	9.83223e12i	−0.430060	−	0.646051i
$851$		−	8.54549e12i		−	0.558540i
$852$	−1.56927e13	−	6.56398e12i	−1.02028	−	0.426765i
$853$			1.60549e13i			1.03834i	0.854672	+	0.519168i	$0.173758\pi$
$853$			1.60549e13i			1.03834i	−0.854672	+	0.519168i	$0.826242\pi$
$854$	−1.75221e12	+	1.16640e12i	−0.112726	+	0.0750390i
$855$	−2.07256e12			−0.132636
$856$	−1.71869e12	−	8.88159e12i	−0.109412	−	0.565404i
$857$	1.33261e13			0.843897			0.421949	−	0.906620i	$-0.361346\pi$
$857$	1.33261e13			0.843897			0.421949	+	0.906620i	$0.361346\pi$
$858$	−8.64653e12	+	5.75577e12i	−0.544690	+	0.362586i
$859$		−	5.29072e12i		−	0.331547i	−0.986164	−	0.165774i	$-0.946988\pi$
$859$		−	5.29072e12i		−	0.331547i	0.986164	−	0.165774i	$-0.0530121\pi$
$860$	−1.96483e12	+	4.69739e12i	−0.122485	+	0.292829i
$861$		−	8.76592e12i		−	0.543605i
$862$	7.67972e12	+	1.15368e13i	0.473765	+	0.711707i
$863$	−1.30813e13			−0.802793			−0.401397	−	0.915904i	$-0.631475\pi$
$863$	−1.30813e13			−0.802793			−0.401397	+	0.915904i	$0.631475\pi$
$864$	−3.08630e12	−	6.41759e11i	−0.188420	−	0.0391796i
$865$	3.61518e12			0.219562
$866$	1.05606e12	+	1.58646e12i	0.0638058	+	0.0958513i
$867$			2.63920e12i			0.158630i
$868$	−1.81735e13	+	4.34480e13i	−1.08667	+	2.59795i
$869$		−	2.88202e13i		−	1.71438i
$870$	−1.35041e12	+	8.98933e11i	−0.0799151	+	0.0531974i
$871$	1.07285e13			0.631623
$872$	−1.35833e12	−	7.01936e12i	−0.0795575	−	0.411124i
$873$	2.80506e12			0.163447
$874$	1.25202e13	−	8.33437e12i	0.725788	−	0.483138i
$875$			1.64078e13i			0.946269i
$876$	8.62635e12	+	3.60824e12i	0.494947	+	0.207027i
$877$			1.27920e13i			0.730199i	0.930969	+	0.365099i	$0.118965\pi$
$877$			1.27920e13i			0.730199i	−0.930969	+	0.365099i	$0.881035\pi$
$878$	−3.49562e12	−	5.25125e12i	−0.198518	−	0.298220i
$879$	−1.49547e13			−0.844944
$880$	4.19401e12	+	4.25258e12i	0.235753	+	0.239045i
$881$	7.26763e12			0.406444			0.203222	−	0.979133i	$-0.434859\pi$
$881$	7.26763e12			0.406444			0.203222	+	0.979133i	$0.434859\pi$
$882$	5.85699e12	+	8.79859e12i	0.325886	+	0.489558i
$883$		−	1.11873e13i		−	0.619304i	−0.950850	−	0.309652i	$-0.899787\pi$
$883$		−	1.11873e13i		−	0.619304i	0.950850	−	0.309652i	$-0.100213\pi$
$884$	1.43386e13	+	5.99757e12i	0.789718	+	0.330324i
$885$		−	3.94823e12i		−	0.216350i
$886$	−1.25000e13	+	8.32090e12i	−0.681486	+	0.453648i
$887$	−3.38540e13			−1.83634			−0.918171	−	0.396185i	$-0.870334\pi$
$887$	−3.38540e13			−1.83634			−0.918171	+	0.396185i	$0.870334\pi$
$888$	8.99092e12	−	1.73985e12i	0.485228	−	0.0938974i
$889$	−1.33842e13			−0.718680
$890$	3.07566e12	−	2.04739e12i	0.164317	−	0.109382i
$891$			2.35683e12i			0.125279i
$892$	1.11058e13	−	2.65511e13i	0.587366	−	1.40424i
$893$		−	8.24736e12i		−	0.433994i
$894$	−4.35757e12	−	6.54610e12i	−0.228153	−	0.342739i
$895$	6.80226e12			0.354364
$896$	−2.64520e13	−	1.81428e13i	−1.37111	−	0.940410i
$897$	7.34195e12			0.378656
$898$	6.80364e11	+	1.02207e12i	0.0349139	+	0.0524489i
$899$		−	1.85235e13i		−	0.945811i
$900$	2.30730e12	−	5.51614e12i	0.117223	−	0.280249i
$901$			7.45984e12i			0.377110i
$902$	1.05669e13	−	7.03412e12i	0.531518	−	0.353818i
$903$	−2.04441e13			−1.02323
$904$	3.43445e13	−	6.64606e12i	1.71040	−	0.330984i
$905$	3.40649e12			0.168806
$906$	5.27313e12	−	3.51018e12i	0.260011	−	0.173082i
$907$		−	2.04441e13i		−	1.00308i	−0.865134	−	0.501540i	$-0.832767\pi$
$907$		−	2.04441e13i		−	1.00308i	0.865134	−	0.501540i	$-0.167233\pi$
$908$	2.95302e13	+	1.23519e13i	1.44172	+	0.603043i
$909$		−	4.31170e12i		−	0.209465i
$910$	−5.70449e12	−	8.56948e12i	−0.275759	−	0.414256i
$911$	3.21964e13			1.54873			0.774363	−	0.632742i	$-0.218071\pi$
$911$	3.21964e13			1.54873			0.774363	+	0.632742i	$0.218071\pi$
$912$	1.13179e13	+	1.14759e13i	0.541737	+	0.549302i
$913$	−3.59543e13			−1.71251
$914$	−6.86401e12	−	1.03114e13i	−0.325327	−	0.488718i
$915$		−	2.96894e11i		−	0.0140025i
$916$	2.49003e13	+	1.04153e13i	1.16862	+	0.488813i
$917$			5.01379e13i			2.34155i
$918$	2.93563e12	−	1.95417e12i	0.136430	−	0.0908177i
$919$	1.16757e13			0.539960			0.269980	−	0.962866i	$-0.412983\pi$
$919$	1.16757e13			0.539960			0.269980	+	0.962866i	$0.412983\pi$
$920$	−8.02083e11	−	4.14488e12i	−0.0369126	−	0.190751i
$921$	7.25491e12			0.332249
$922$	−1.00206e13	+	6.67047e12i	−0.456674	+	0.303996i
$923$			4.24562e13i			1.92546i
$924$	−9.25410e12	+	2.21241e13i	−0.417648	+	0.998487i
$925$			1.73701e13i			0.780128i
$926$	−1.53314e13	−	2.30313e13i	−0.685222	−	1.02937i
$927$	4.77778e11			0.0212504
$928$	1.23518e13	+	2.56841e12i	0.546720	+	0.113684i
$929$	−3.09973e12			−0.136538			−0.0682690	−	0.997667i	$-0.521748\pi$
$929$	−3.09973e12			−0.136538			−0.0682690	+	0.997667i	$0.521748\pi$
$930$	−3.68091e12	−	5.52960e12i	−0.161355	−	0.242393i
$931$		−	5.40440e13i		−	2.35762i
$932$	1.45744e13	−	3.48436e13i	0.632731	−	1.51269i
$933$		−	1.56793e13i		−	0.677420i
$934$	8.82887e12	−	5.87715e12i	0.379616	−	0.252700i
$935$	−6.68189e12			−0.285922
$936$	1.49481e12	+	7.72464e12i	0.0636568	+	0.328955i
$937$	1.33365e13			0.565216			0.282608	−	0.959236i	$-0.408801\pi$
$937$	1.33365e13			0.565216			0.282608	+	0.959236i	$0.408801\pi$
$938$	2.06192e13	−	1.37257e13i	0.869680	−	0.578924i
$939$		−	1.04315e13i		−	0.437876i
$940$	−2.13568e12	−	8.93313e11i	−0.0892196	−	0.0373189i
$941$			3.02157e12i			0.125626i	0.998025	+	0.0628130i	$0.0200072\pi$
$941$			3.02157e12i			0.125626i	−0.998025	+	0.0628130i	$0.979993\pi$
$942$	2.20873e11	+	3.31804e11i	0.00913933	+	0.0137294i
$943$	−8.97257e12			−0.369500
$944$	−2.18616e13	+	2.15606e13i	−0.896002	+	0.883662i
$945$	−2.33582e12			−0.0952789
$946$	−1.64052e13	−	2.46445e13i	−0.665995	−	1.00048i
$947$			9.61342e12i			0.388421i	0.980960	+	0.194211i	$0.0622145\pi$
$947$			9.61342e12i			0.388421i	−0.980960	+	0.194211i	$0.937785\pi$
$948$	−2.01397e13	−	8.42407e12i	−0.809872	−	0.338754i
$949$		−	2.33383e13i		−	0.934054i
$950$	−2.54494e13	+	1.69410e13i	−1.01373	+	0.674813i
$951$	−6.83813e12			−0.271097
$952$	3.52306e13	−	6.81753e12i	1.39012	−	0.269005i
$953$	3.02125e12			0.118650			0.0593251	−	0.998239i	$-0.481105\pi$
$953$	3.02125e12			0.118650			0.0593251	+	0.998239i	$0.481105\pi$
$954$	−3.14355e12	+	2.09258e12i	−0.122872	+	0.0817928i
$955$			2.41504e12i			0.0939526i
$956$	2.65035e12	−	6.33630e12i	0.102623	−	0.245344i
$957$		−	9.43235e12i		−	0.363510i
$958$	1.47269e13	+	2.21233e13i	0.564895	+	0.848606i
$959$	−7.30967e13			−2.79070
$960$	4.19762e12	−	1.68778e12i	0.159508	−	0.0641351i
$961$	4.94096e13			1.86877
$962$	−1.26657e13	−	1.90268e13i	−0.476805	−	0.716274i
$963$			5.12317e12i			0.191964i
$964$	5.25022e12	−	1.25519e13i	0.195808	−	0.468126i
$965$			3.24004e12i			0.120276i
$966$	1.41105e13	−	9.39302e12i	0.521371	−	0.347063i
$967$	−2.09650e13			−0.771038			−0.385519	−	0.922700i	$-0.625978\pi$
$967$	−2.09650e13			−0.771038			−0.385519	+	0.922700i	$0.625978\pi$
$968$	−7.27562e12	+	1.40792e12i	−0.266337	+	0.0515393i
$969$	−1.80316e13			−0.657019
$970$	−3.35123e12	+	2.23083e12i	−0.121544	+	0.0809084i
$971$		−	3.32447e12i		−	0.120015i	−0.998198	−	0.0600076i	$-0.980888\pi$
$971$		−	3.32447e12i		−	0.120015i	0.998198	−	0.0600076i	$-0.0191125\pi$
$972$	1.64696e12	+	6.88893e11i	0.0591814	+	0.0247545i
$973$			8.45389e13i			3.02377i
$974$	−8.41102e12	−	1.26353e13i	−0.299456	−	0.449854i
$975$	−1.49237e13			−0.528880
$976$	−1.64393e12	+	1.62129e12i	−0.0579907	+	0.0571920i
$977$	−3.35185e13			−1.17695			−0.588477	−	0.808514i	$-0.700272\pi$
$977$	−3.35185e13			−1.17695			−0.588477	+	0.808514i	$0.700272\pi$
$978$	4.10304e11	+	6.16374e11i	0.0143411	+	0.0215437i
$979$			2.14829e13i			0.747430i
$980$	−1.39948e13	−	5.85377e12i	−0.484675	−	0.202730i
$981$			4.04898e12i			0.139584i
$982$	−3.06098e13	+	2.03762e13i	−1.05041	+	0.699231i
$983$	9.60348e12			0.328048			0.164024	−	0.986456i	$-0.447553\pi$
$983$	9.60348e12			0.328048			0.164024	+	0.986456i	$0.447553\pi$
$984$	−1.82680e12	−	9.44026e12i	−0.0621175	−	0.321001i
$985$	−7.64261e12			−0.258689
$986$	−1.17488e13	+	7.82087e12i	−0.395865	+	0.263517i
$987$		−	9.29496e12i		−	0.311760i
$988$	1.55239e13	−	3.71136e13i	0.518316	−	1.23916i
$989$			2.09261e13i			0.695513i
$990$	−1.87436e12	−	2.81573e12i	−0.0620146	−	0.0931605i
$991$	1.42518e13			0.469394			0.234697	−	0.972069i	$-0.424590\pi$
$991$	1.42518e13			0.469394			0.234697	+	0.972069i	$0.424590\pi$
$992$	−1.05170e13	+	5.05777e13i	−0.344818	+	1.65827i
$993$	1.19835e13			0.391120
$994$	5.43170e13	+	8.15970e13i	1.76481	+	2.65116i
$995$		−	9.80769e12i		−	0.317222i
$996$	−1.05093e13	+	2.51250e13i	−0.338383	+	0.808984i
$997$		−	2.92635e13i		−	0.937988i	−0.883201	−	0.468994i	$-0.844617\pi$
$997$		−	2.92635e13i		−	0.937988i	0.883201	−	0.468994i	$-0.155383\pi$
$998$	1.63185e13	−	1.08628e13i	0.520705	−	0.346620i
$999$	−5.18623e12			−0.164743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.10.d.a.13.5	✓	18
3.2	odd	2		72.10.d.d.37.14		18
4.3	odd	2		96.10.d.a.49.14		18
8.3	odd	2		96.10.d.a.49.5		18
8.5	even	2	inner	24.10.d.a.13.6	yes	18
12.11	even	2		288.10.d.d.145.8		18
24.5	odd	2		72.10.d.d.37.13		18
24.11	even	2		288.10.d.d.145.11		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.10.d.a.13.5	✓	18	1.1	even	1	trivial
24.10.d.a.13.6	yes	18	8.5	even	2	inner
72.10.d.d.37.13		18	24.5	odd	2
72.10.d.d.37.14		18	3.2	odd	2
96.10.d.a.49.5		18	8.3	odd	2
96.10.d.a.49.14		18	4.3	odd	2
288.10.d.d.145.8		18	12.11	even	2
288.10.d.d.145.11		18	24.11	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:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	24.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.5385 - 18.8358i) q^{2} -81.0000i q^{3} +(-197.573 + 472.344i) q^{4} +416.150i q^{5} +(-1525.70 + 1015.62i) q^{6} +10561.7 q^{7} +(11374.2 - 2201.05i) q^{8} -6561.00 q^{9} +O(q^{10})\)	\(q+(-12.5385 - 18.8358i) q^{2} -81.0000i q^{3} +(-197.573 + 472.344i) q^{4} +416.150i q^{5} +(-1525.70 + 1015.62i) q^{6} +10561.7 q^{7} +(11374.2 - 2201.05i) q^{8} -6561.00 q^{9} +(7838.50 - 5217.89i) q^{10} +54750.4i q^{11} +(38259.9 + 16003.4i) q^{12} -103511. i q^{13} +(-132428. - 198938. i) q^{14} +33708.1 q^{15} +(-184074. - 186645. i) q^{16} +293266. q^{17} +(82265.0 + 123582. i) q^{18} -759080. i q^{19} +(-196566. - 82219.8i) q^{20} -855501. i q^{21} +(1.03127e6 - 686487. i) q^{22} -875669. q^{23} +(-178285. - 921313. i) q^{24} +1.77994e6 q^{25} +(-1.94971e6 + 1.29787e6i) q^{26} +531441. i q^{27} +(-2.08671e6 + 4.98877e6i) q^{28} -2.12690e6i q^{29} +(-422649. - 634919. i) q^{30} +8.70915e6 q^{31} +(-1.20758e6 + 5.80742e6i) q^{32} +4.43478e6 q^{33} +(-3.67712e6 - 5.52390e6i) q^{34} +4.39526e6i q^{35} +(1.29627e6 - 3.09905e6i) q^{36} +9.75881e6i q^{37} +(-1.42979e7 + 9.51772e6i) q^{38} -8.38439e6 q^{39} +(915966. + 4.73338e6i) q^{40} +1.02465e7 q^{41} +(-1.61140e7 + 1.07267e7i) q^{42} -2.38973e7i q^{43} +(-2.58610e7 - 1.08172e7i) q^{44} -2.73036e6i q^{45} +(1.09796e7 + 1.64939e7i) q^{46} +1.08649e7 q^{47} +(-1.51182e7 + 1.49100e7i) q^{48} +7.11967e7 q^{49} +(-2.23178e7 - 3.35266e7i) q^{50} -2.37546e7i q^{51} +(4.88928e7 + 2.04509e7i) q^{52} +2.54371e7i q^{53} +(1.00101e7 - 6.66347e6i) q^{54} -2.27844e7 q^{55} +(1.20132e8 - 2.32469e7i) q^{56} -6.14855e7 q^{57} +(-4.00618e7 + 2.66681e7i) q^{58} -1.17130e8i q^{59} +(-6.65980e6 + 1.59218e7i) q^{60} -8.80779e6i q^{61} +(-1.09200e8 - 1.64044e8i) q^{62} -6.92955e7 q^{63} +(1.24528e8 - 5.00705e7i) q^{64} +4.30761e7 q^{65} +(-5.56055e7 - 8.35325e7i) q^{66} +1.03646e8i q^{67} +(-5.79414e7 + 1.38523e8i) q^{68} +7.09292e7i q^{69} +(8.27882e7 - 5.51100e7i) q^{70} -4.10162e8 q^{71} +(-7.46263e7 + 1.44411e7i) q^{72} +2.25467e8 q^{73} +(1.83815e8 - 1.22361e8i) q^{74} -1.44175e8i q^{75} +(3.58547e8 + 1.49974e8i) q^{76} +5.78259e8i q^{77} +(1.05128e8 + 1.57926e8i) q^{78} -5.26393e8 q^{79} +(7.76721e7 - 7.66024e7i) q^{80} +4.30467e7 q^{81} +(-1.28476e8 - 1.93001e8i) q^{82} +6.56694e8i q^{83} +(4.04091e8 + 1.69023e8i) q^{84} +1.22043e8i q^{85} +(-4.50124e8 + 2.99636e8i) q^{86} -1.72279e8 q^{87} +(1.20508e8 + 6.22744e8i) q^{88} +3.92379e8 q^{89} +(-5.14284e7 + 3.42346e7i) q^{90} -1.09326e9i q^{91} +(1.73008e8 - 4.13617e8i) q^{92} -7.05441e8i q^{93} +(-1.36230e8 - 2.04650e8i) q^{94} +3.15891e8 q^{95} +(4.70401e8 + 9.78142e7i) q^{96} -4.27535e8 q^{97} +(-8.92698e8 - 1.34104e9i) q^{98} -3.59217e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 34 q^{2} + 512 q^{4} - 3078 q^{6} - 9604 q^{7} + 15844 q^{8} - 118098 q^{9}+O(q^{10}) \) 18 * q + 34 * q^2 + 512 * q^4 - 3078 * q^6 - 9604 * q^7 + 15844 * q^8 - 118098 * q^9	\( 18 q + 34 q^{2} + 512 q^{4} - 3078 q^{6} - 9604 q^{7} + 15844 q^{8} - 118098 q^{9} - 34788 q^{10} - 57996 q^{12} - 209204 q^{14} + 202500 q^{15} - 1928 q^{16} + 203996 q^{17} - 223074 q^{18} + 406744 q^{20} + 4311616 q^{22} - 3465976 q^{23} + 1142748 q^{24} - 5309486 q^{25} - 7786712 q^{26} - 4722944 q^{28} + 1214676 q^{30} + 4737540 q^{31} + 19090184 q^{32} - 26138884 q^{34} - 3359232 q^{36} + 81529688 q^{38} - 18507528 q^{39} + 102781640 q^{40} - 3780956 q^{41} - 37252548 q^{42} - 113955840 q^{44} + 155174504 q^{46} - 112458264 q^{47} + 72347904 q^{48} + 90859338 q^{49} - 240578846 q^{50} - 232023472 q^{52} + 20194758 q^{54} - 76355584 q^{55} + 349245496 q^{56} - 79112376 q^{57} - 368612756 q^{58} - 229298688 q^{60} + 243931700 q^{62} + 63011844 q^{63} + 627902720 q^{64} + 300816016 q^{65} - 43281216 q^{66} - 147591168 q^{68} - 236031704 q^{70} - 408942312 q^{71} - 103952484 q^{72} + 826124308 q^{73} - 478971056 q^{74} + 559419952 q^{76} - 364363272 q^{78} + 382409492 q^{79} - 666994944 q^{80} + 774840978 q^{81} + 547544068 q^{82} + 602616024 q^{84} - 1435000280 q^{86} - 687477132 q^{87} - 2197393664 q^{88} - 458464820 q^{89} + 228244068 q^{90} + 4261704192 q^{92} - 3319581624 q^{94} + 331883504 q^{95} - 569482488 q^{96} + 264098780 q^{97} + 4005878682 q^{98}+O(q^{100}) \) 18 * q + 34 * q^2 + 512 * q^4 - 3078 * q^6 - 9604 * q^7 + 15844 * q^8 - 118098 * q^9 - 34788 * q^10 - 57996 * q^12 - 209204 * q^14 + 202500 * q^15 - 1928 * q^16 + 203996 * q^17 - 223074 * q^18 + 406744 * q^20 + 4311616 * q^22 - 3465976 * q^23 + 1142748 * q^24 - 5309486 * q^25 - 7786712 * q^26 - 4722944 * q^28 + 1214676 * q^30 + 4737540 * q^31 + 19090184 * q^32 - 26138884 * q^34 - 3359232 * q^36 + 81529688 * q^38 - 18507528 * q^39 + 102781640 * q^40 - 3780956 * q^41 - 37252548 * q^42 - 113955840 * q^44 + 155174504 * q^46 - 112458264 * q^47 + 72347904 * q^48 + 90859338 * q^49 - 240578846 * q^50 - 232023472 * q^52 + 20194758 * q^54 - 76355584 * q^55 + 349245496 * q^56 - 79112376 * q^57 - 368612756 * q^58 - 229298688 * q^60 + 243931700 * q^62 + 63011844 * q^63 + 627902720 * q^64 + 300816016 * q^65 - 43281216 * q^66 - 147591168 * q^68 - 236031704 * q^70 - 408942312 * q^71 - 103952484 * q^72 + 826124308 * q^73 - 478971056 * q^74 + 559419952 * q^76 - 364363272 * q^78 + 382409492 * q^79 - 666994944 * q^80 + 774840978 * q^81 + 547544068 * q^82 + 602616024 * q^84 - 1435000280 * q^86 - 687477132 * q^87 - 2197393664 * q^88 - 458464820 * q^89 + 228244068 * q^90 + 4261704192 * q^92 - 3319581624 * q^94 + 331883504 * q^95 - 569482488 * q^96 + 264098780 * q^97 + 4005878682 * q^98

Introduction

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