LMFDB - Embedded newform 12.7.d.a.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,7,Mod(7,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	12.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:	$2.76064900344$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.50898483.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 8x^{4} - 10x^{3} + 64x^{2} - 40x + 25 $ x^6 + 8x^4 - 10x^3 + 64x^2 - 40x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.5
Root			$0.330560 - 0.572547i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.7.d.a.7.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.46472 - 2.87714i) q^{2} -15.5885i q^{3} +(47.4441 - 42.9542i) q^{4} +18.1171 q^{5} +(-44.8502 - 116.363i) q^{6} +321.465i q^{7} +(230.571 - 457.144i) q^{8} -243.000 q^{9} +O(q^{10})$	\(q+(7.46472 - 2.87714i) q^{2} -15.5885i q^{3} +(47.4441 - 42.9542i) q^{4} +18.1171 q^{5} +(-44.8502 - 116.363i) q^{6} +321.465i q^{7} +(230.571 - 457.144i) q^{8} -243.000 q^{9} +(135.239 - 52.1255i) q^{10} +2014.54i q^{11} +(-669.589 - 739.580i) q^{12} -2844.73 q^{13} +(924.902 + 2399.65i) q^{14} -282.418i q^{15} +(405.881 - 4075.84i) q^{16} +6864.64 q^{17} +(-1813.93 + 699.146i) q^{18} -9839.37i q^{19} +(859.549 - 778.205i) q^{20} +5011.15 q^{21} +(5796.12 + 15038.0i) q^{22} -4624.52i q^{23} +(-7126.17 - 3594.25i) q^{24} -15296.8 q^{25} +(-21235.1 + 8184.71i) q^{26} +3788.00i q^{27} +(13808.3 + 15251.6i) q^{28} -1771.80 q^{29} +(-812.556 - 2108.17i) q^{30} +16203.3i q^{31} +(-8697.00 - 31592.8i) q^{32} +31403.6 q^{33} +(51242.6 - 19750.6i) q^{34} +5824.02i q^{35} +(-11528.9 + 10437.9i) q^{36} -42257.3 q^{37} +(-28309.3 - 73448.2i) q^{38} +44345.0i q^{39} +(4177.28 - 8282.12i) q^{40} -1466.28 q^{41} +(37406.8 - 14417.8i) q^{42} -41213.4i q^{43} +(86532.8 + 95578.0i) q^{44} -4402.45 q^{45} +(-13305.4 - 34520.7i) q^{46} +56084.5i q^{47} +(-63536.1 - 6327.05i) q^{48} +14309.1 q^{49} +(-114186. + 44011.0i) q^{50} -107009. i q^{51} +(-134966. + 122193. i) q^{52} +65132.6 q^{53} +(10898.6 + 28276.3i) q^{54} +36497.6i q^{55} +(146956. + 74120.7i) q^{56} -153381. q^{57} +(-13226.0 + 5097.73i) q^{58} -241024. i q^{59} +(-12131.0 - 13399.0i) q^{60} +304946. q^{61} +(46619.3 + 120953. i) q^{62} -78116.1i q^{63} +(-155818. - 210809. i) q^{64} -51538.3 q^{65} +(234419. - 90352.6i) q^{66} -83722.2i q^{67} +(325686. - 294865. i) q^{68} -72089.1 q^{69} +(16756.5 + 43474.7i) q^{70} +498634. i q^{71} +(-56028.8 + 111086. i) q^{72} +49564.8 q^{73} +(-315439. + 121580. i) q^{74} +238453. i q^{75} +(-422642. - 466820. i) q^{76} -647605. q^{77} +(127587. + 331023. i) q^{78} +896848. i q^{79} +(7353.38 - 73842.4i) q^{80} +59049.0 q^{81} +(-10945.4 + 4218.71i) q^{82} -668710. i q^{83} +(237749. - 215250. i) q^{84} +124367. q^{85} +(-118577. - 307646. i) q^{86} +27619.7i q^{87} +(920935. + 464495. i) q^{88} +219393. q^{89} +(-32863.1 + 12666.5i) q^{90} -914483. i q^{91} +(-198642. - 219406. i) q^{92} +252585. q^{93} +(161363. + 418655. i) q^{94} -178261. i q^{95} +(-492483. + 135573. i) q^{96} +176670. q^{97} +(106813. - 41169.2i) q^{98} -489533. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{2} + 156 q^{4} - 44 q^{5} - 162 q^{6} + 1136 q^{8} - 1458 q^{9}+O(q^{10}) $ 6 * q - 10 * q^2 + 156 * q^4 - 44 * q^5 - 162 * q^6 + 1136 * q^8 - 1458 * q^9	\( 6 q - 10 q^{2} + 156 q^{4} - 44 q^{5} - 162 q^{6} + 1136 q^{8} - 1458 q^{9} + 84 q^{10} - 972 q^{12} - 3348 q^{13} + 4776 q^{14} - 9744 q^{16} + 12220 q^{17} + 2430 q^{18} + 17608 q^{20} - 9720 q^{21} - 13512 q^{22} - 7776 q^{24} + 56418 q^{25} - 59252 q^{26} - 17808 q^{28} - 84860 q^{29} + 57348 q^{30} + 61280 q^{32} + 4536 q^{33} + 109404 q^{34} - 37908 q^{36} + 20796 q^{37} - 128088 q^{38} - 195552 q^{40} - 65252 q^{41} + 210600 q^{42} + 445008 q^{44} + 10692 q^{45} + 81120 q^{46} - 276048 q^{48} - 111546 q^{49} - 743118 q^{50} - 179592 q^{52} + 470308 q^{53} + 39366 q^{54} + 793728 q^{56} - 204120 q^{57} + 529860 q^{58} - 723816 q^{60} + 12924 q^{61} - 513384 q^{62} - 642432 q^{64} + 321512 q^{65} + 771768 q^{66} + 690328 q^{68} + 541728 q^{69} + 938928 q^{70} - 276048 q^{72} - 1283412 q^{73} - 1522916 q^{74} + 67824 q^{76} - 1487328 q^{77} + 396252 q^{78} + 1272352 q^{80} + 354294 q^{81} + 240444 q^{82} - 143856 q^{84} + 814920 q^{85} - 1154568 q^{86} + 489600 q^{88} + 730924 q^{89} - 20412 q^{90} - 1338816 q^{92} - 83592 q^{93} - 390288 q^{94} + 624672 q^{96} + 3249420 q^{97} + 1604918 q^{98}+O(q^{100}) \) 6 * q - 10 * q^2 + 156 * q^4 - 44 * q^5 - 162 * q^6 + 1136 * q^8 - 1458 * q^9 + 84 * q^10 - 972 * q^12 - 3348 * q^13 + 4776 * q^14 - 9744 * q^16 + 12220 * q^17 + 2430 * q^18 + 17608 * q^20 - 9720 * q^21 - 13512 * q^22 - 7776 * q^24 + 56418 * q^25 - 59252 * q^26 - 17808 * q^28 - 84860 * q^29 + 57348 * q^30 + 61280 * q^32 + 4536 * q^33 + 109404 * q^34 - 37908 * q^36 + 20796 * q^37 - 128088 * q^38 - 195552 * q^40 - 65252 * q^41 + 210600 * q^42 + 445008 * q^44 + 10692 * q^45 + 81120 * q^46 - 276048 * q^48 - 111546 * q^49 - 743118 * q^50 - 179592 * q^52 + 470308 * q^53 + 39366 * q^54 + 793728 * q^56 - 204120 * q^57 + 529860 * q^58 - 723816 * q^60 + 12924 * q^61 - 513384 * q^62 - 642432 * q^64 + 321512 * q^65 + 771768 * q^66 + 690328 * q^68 + 541728 * q^69 + 938928 * q^70 - 276048 * q^72 - 1283412 * q^73 - 1522916 * q^74 + 67824 * q^76 - 1487328 * q^77 + 396252 * q^78 + 1272352 * q^80 + 354294 * q^81 + 240444 * q^82 - 143856 * q^84 + 814920 * q^85 - 1154568 * q^86 + 489600 * q^88 + 730924 * q^89 - 20412 * q^90 - 1338816 * q^92 - 83592 * q^93 - 390288 * q^94 + 624672 * q^96 + 3249420 * q^97 + 1604918 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	7.46472	−	2.87714i	0.933090	−	0.359643i
$2$	7.46472	−	2.87714i	0.933090	−	0.359643i
$3$		−	15.5885i		−	0.577350i
$3$		−	15.5885i		−	0.577350i
$4$	47.4441	−	42.9542i	0.741314	−	0.671159i
$5$	18.1171			0.144937			0.0724684	−	0.997371i	$-0.476912\pi$
$5$	18.1171			0.144937			0.0724684	+	0.997371i	$0.476912\pi$
$6$	−44.8502	−	116.363i	−0.207640	−	0.538720i
$7$			321.465i			0.937217i	0.883406	+	0.468608i	$0.155244\pi$
$7$			321.465i			0.937217i	−0.883406	+	0.468608i	$0.844756\pi$
$8$	230.571	−	457.144i	0.450335	−	0.892860i
$9$	−243.000			−0.333333
$10$	135.239	−	52.1255i	0.135239	−	0.0521255i
$11$			2014.54i			1.51355i	0.653674	+	0.756777i	$0.273227\pi$
$11$			2014.54i			1.51355i	−0.653674	+	0.756777i	$0.726773\pi$
$12$	−669.589	−	739.580i	−0.387494	−	0.427998i
$13$	−2844.73			−1.29483			−0.647413	−	0.762139i	$-0.724149\pi$
$13$	−2844.73			−1.29483			−0.647413	+	0.762139i	$0.724149\pi$
$14$	924.902	+	2399.65i	0.337063	+	0.874507i
$15$		−	282.418i		−	0.0836793i
$16$	405.881	−	4075.84i	0.0990920	−	0.995078i
$17$	6864.64			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$17$	6864.64			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$18$	−1813.93	+	699.146i	−0.311030	+	0.119881i
$19$		−	9839.37i		−	1.43452i	−0.696806	−	0.717260i	$-0.745396\pi$
$19$		−	9839.37i		−	1.43452i	0.696806	−	0.717260i	$-0.254604\pi$
$20$	859.549	−	778.205i	0.107444	−	0.0972756i
$21$	5011.15			0.541102
$22$	5796.12	+	15038.0i	0.544339	+	1.41228i
$23$		−	4624.52i		−	0.380087i	−0.981776	−	0.190044i	$-0.939137\pi$
$23$		−	4624.52i		−	0.380087i	0.981776	−	0.190044i	$-0.0608629\pi$
$24$	−7126.17	−	3594.25i	−0.515493	−	0.260001i
$25$	−15296.8			−0.978993
$26$	−21235.1	+	8184.71i	−1.20819	+	0.465675i
$27$			3788.00i			0.192450i
$28$	13808.3	+	15251.6i	0.629021	+	0.694772i
$29$	−1771.80			−0.0726476			−0.0363238	−	0.999340i	$-0.511565\pi$
$29$	−1771.80			−0.0726476			−0.0363238	+	0.999340i	$0.511565\pi$
$30$	−812.556	−	2108.17i	−0.0300947	−	0.0780803i
$31$			16203.3i			0.543900i	0.962311	+	0.271950i	$0.0876685\pi$
$31$			16203.3i			0.543900i	−0.962311	+	0.271950i	$0.912331\pi$
$32$	−8697.00	−	31592.8i	−0.265411	−	0.964135i
$33$	31403.6			0.873850
$34$	51242.6	−	19750.6i	1.30375	−	0.502508i
$35$			5824.02i			0.135837i
$36$	−11528.9	+	10437.9i	−0.247105	+	0.223720i
$37$	−42257.3			−0.834250			−0.417125	−	0.908849i	$-0.636962\pi$
$37$	−42257.3			−0.834250			−0.417125	+	0.908849i	$0.636962\pi$
$38$	−28309.3	−	73448.2i	−0.515915	−	1.33854i
$39$			44345.0i			0.747568i
$40$	4177.28	−	8282.12i	0.0652701	−	0.129408i
$41$	−1466.28			−0.0212749			−0.0106374	−	0.999943i	$-0.503386\pi$
$41$	−1466.28			−0.0212749			−0.0106374	+	0.999943i	$0.503386\pi$
$42$	37406.8	−	14417.8i	0.504897	−	0.194604i
$43$		−	41213.4i		−	0.518362i	−0.965829	−	0.259181i	$-0.916547\pi$
$43$		−	41213.4i		−	0.518362i	0.965829	−	0.259181i	$-0.0834525\pi$
$44$	86532.8	+	95578.0i	1.01583	+	1.12202i
$45$	−4402.45			−0.0483123
$46$	−13305.4	−	34520.7i	−0.136696	−	0.354655i
$47$			56084.5i			0.540193i	0.962833	+	0.270096i	$0.0870556\pi$
$47$			56084.5i			0.540193i	−0.962833	+	0.270096i	$0.912944\pi$
$48$	−63536.1	−	6327.05i	−0.574509	−	0.0572108i
$49$	14309.1			0.121625
$50$	−114186.	+	44011.0i	−0.913489	+	0.352088i
$51$		−	107009.i		−	0.806697i
$52$	−134966.	+	122193.i	−0.959873	+	0.869034i
$53$	65132.6			0.437493			0.218746	−	0.975782i	$-0.429803\pi$
$53$	65132.6			0.437493			0.218746	+	0.975782i	$0.429803\pi$
$54$	10898.6	+	28276.3i	0.0692133	+	0.179573i
$55$			36497.6i			0.219369i
$56$	146956.	+	74120.7i	0.836803	+	0.422061i
$57$	−153381.			−0.828221
$58$	−13226.0	+	5097.73i	−0.0677867	+	0.0261272i
$59$		−	241024.i		−	1.17356i	−0.809747	−	0.586779i	$-0.800396\pi$
$59$		−	241024.i		−	1.17356i	0.809747	−	0.586779i	$-0.199604\pi$
$60$	−12131.0	−	13399.0i	−0.0561621	−	0.0620326i
$61$	304946.			1.34349			0.671743	−	0.740784i	$-0.265546\pi$
$61$	304946.			1.34349			0.671743	+	0.740784i	$0.265546\pi$
$62$	46619.3	+	120953.i	0.195610	+	0.507507i
$63$		−	78116.1i		−	0.312406i
$64$	−155818.	−	210809.i	−0.594397	−	0.804172i
$65$	−51538.3			−0.187668
$66$	234419.	−	90352.6i	0.815381	−	0.314274i
$67$		−	83722.2i		−	0.278366i	−0.990267	−	0.139183i	$-0.955552\pi$
$67$		−	83722.2i		−	0.278366i	0.990267	−	0.139183i	$-0.0444476\pi$
$68$	325686.	−	294865.i	1.03579	−	0.937770i
$69$	−72089.1			−0.219443
$70$	16756.5	+	43474.7i	0.0488529	+	0.126748i
$71$			498634.i			1.39318i	0.717470	+	0.696589i	$0.245300\pi$
$71$			498634.i			1.39318i	−0.717470	+	0.696589i	$0.754700\pi$
$72$	−56028.8	+	111086.i	−0.150112	+	0.297620i
$73$	49564.8			0.127410			0.0637051	−	0.997969i	$-0.479708\pi$
$73$	49564.8			0.127410			0.0637051	+	0.997969i	$0.479708\pi$
$74$	−315439.	+	121580.i	−0.778430	+	0.300032i
$75$			238453.i			0.565222i
$76$	−422642.	−	466820.i	−0.962791	−	1.06343i
$77$	−647605.			−1.41853
$78$	127587.	+	331023.i	0.268858	+	0.697549i
$79$			896848.i			1.81902i	0.415681	+	0.909511i	$0.363543\pi$
$79$			896848.i			1.81902i	−0.415681	+	0.909511i	$0.636457\pi$
$80$	7353.38	−	73842.4i	0.0143621	−	0.144223i
$81$	59049.0			0.111111
$82$	−10945.4	+	4218.71i	−0.0198514	+	0.00765135i
$83$		−	668710.i		−	1.16951i	−0.811210	−	0.584754i	$-0.801191\pi$
$83$		−	668710.i		−	1.16951i	0.811210	−	0.584754i	$-0.198809\pi$
$84$	237749.	−	215250.i	0.401127	−	0.363166i
$85$	124367.			0.202511
$86$	−118577.	−	307646.i	−0.186425	−	0.483678i
$87$			27619.7i			0.0419431i
$88$	920935.	+	464495.i	1.35139	+	0.681606i
$89$	219393.			0.311210			0.155605	−	0.987819i	$-0.450267\pi$
$89$	219393.			0.311210			0.155605	+	0.987819i	$0.450267\pi$
$90$	−32863.1	+	12666.5i	−0.0450797	+	0.0173752i
$91$		−	914483.i		−	1.21353i
$92$	−198642.	−	219406.i	−0.255099	−	0.281764i
$93$	252585.			0.314021
$94$	161363.	+	418655.i	0.194277	+	0.504049i
$95$		−	178261.i		−	0.207915i
$96$	−492483.	+	135573.i	−0.556644	+	0.153235i
$97$	176670.			0.193574			0.0967869	−	0.995305i	$-0.469143\pi$
$97$	176670.			0.193574			0.0967869	+	0.995305i	$0.469143\pi$
$98$	106813.	−	41169.2i	0.113487	−	0.0437416i
$99$		−	489533.i		−	0.504518i
$100$	−725741.	+	657060.i	−0.725741	+	0.657060i
$101$	848459.			0.823506			0.411753	−	0.911295i	$-0.364917\pi$
$101$	848459.			0.823506			0.411753	+	0.911295i	$0.364917\pi$
$102$	−307881.	−	798793.i	−0.290123	−	0.752721i
$103$		−	608025.i		−	0.556429i	−0.960519	−	0.278215i	$-0.910257\pi$
$103$		−	608025.i		−	0.556429i	0.960519	−	0.278215i	$-0.0897427\pi$
$104$	−655914.	+	1.30045e6i	−0.583105	+	1.15610i
$105$	90787.4			0.0784256
$106$	486197.	−	187396.i	0.408220	−	0.157341i
$107$			292806.i			0.239017i	0.992833	+	0.119508i	$0.0381318\pi$
$107$			292806.i			0.239017i	−0.992833	+	0.119508i	$0.961868\pi$
$108$	162710.	+	179718.i	0.129165	+	0.142666i
$109$	−2.18639e6			−1.68829			−0.844147	−	0.536112i	$-0.819892\pi$
$109$	−2.18639e6			−1.68829			−0.844147	+	0.536112i	$0.819892\pi$
$110$	105009.	+	272444.i	0.0788947	+	0.204691i
$111$			658726.i			0.481654i
$112$	1.31024e6	+	130477.i	0.932604	+	0.0928706i
$113$	1.18284e6			0.819765			0.409883	−	0.912138i	$-0.365570\pi$
$113$	1.18284e6			0.819765			0.409883	+	0.912138i	$0.365570\pi$
$114$	−1.14494e6	+	441298.i	−0.772804	+	0.297864i
$115$		−	83782.9i		−	0.0550886i
$116$	−84061.5	+	76106.3i	−0.0538546	+	0.0487581i
$117$	691270.			0.431609
$118$	−693462.	−	1.79918e6i	−0.422062	−	1.09504i
$119$			2.20674e6i			1.30952i
$120$	−129106.	−	65117.4i	−0.0747139	−	0.0376837i
$121$	−2.28681e6			−1.29084
$122$	2.27633e6	−	877373.i	1.25359	−	0.483175i
$123$			22857.1i			0.0122830i
$124$	696000.	+	768751.i	0.365043	+	0.403200i
$125$	−560213.			−0.286829
$126$	−224751.	−	583115.i	−0.112354	−	0.291502i
$127$		−	611850.i		−	0.298699i	−0.988784	−	0.149349i	$-0.952282\pi$
$127$		−	611850.i		−	0.298699i	0.988784	−	0.149349i	$-0.0477179\pi$
$128$	−1.76966e6	−	1.12532e6i	−0.843841	−	0.536594i
$129$	−642453.			−0.299276
$130$	−384719.	+	148283.i	−0.175111	+	0.0674935i
$131$			987022.i			0.439049i	0.975607	+	0.219524i	$0.0704506\pi$
$131$			987022.i			0.439049i	−0.975607	+	0.219524i	$0.929549\pi$
$132$	1.48991e6	−	1.34891e6i	0.647797	−	0.586492i
$133$	3.16302e6			1.34446
$134$	−240881.	−	624963.i	−0.100112	−	0.259740i
$135$			68627.5i			0.0278931i
$136$	1.58279e6	−	3.13813e6i	0.629226	−	1.24754i
$137$	1.21571e6			0.472792			0.236396	−	0.971657i	$-0.424034\pi$
$137$	1.21571e6			0.472792			0.236396	+	0.971657i	$0.424034\pi$
$138$	−538125.	+	207411.i	−0.204760	+	0.0789213i
$139$			2.34793e6i			0.874259i	0.899399	+	0.437130i	$0.144005\pi$
$139$			2.34793e6i			0.874259i	−0.899399	+	0.437130i	$0.855995\pi$
$140$	250166.	+	276315.i	0.0911683	+	0.100698i
$141$	874270.			0.311881
$142$	1.43464e6	+	3.72216e6i	0.501047	+	1.29996i
$143$		−	5.73083e6i		−	1.95979i
$144$	−98629.0	+	990429.i	−0.0330307	+	0.331693i
$145$	−32099.9			−0.0105293
$146$	369987.	−	142605.i	0.118885	−	0.0458222i
$147$		−	223056.i		−	0.0702202i
$148$	−2.00486e6	+	1.81513e6i	−0.618441	+	0.559914i
$149$	−6.55209e6			−1.98071			−0.990355	−	0.138551i	$-0.955755\pi$
$149$	−6.55209e6			−1.98071			−0.990355	+	0.138551i	$0.955755\pi$
$150$	686064.	+	1.77999e6i	0.203278	+	0.527403i
$151$			1.57853e6i			0.458482i	0.973370	+	0.229241i	$0.0736244\pi$
$151$			1.57853e6i			0.458482i	−0.973370	+	0.229241i	$0.926376\pi$
$152$	−4.49801e6	−	2.26868e6i	−1.28083	−	0.646014i
$153$	−1.66811e6			−0.465747
$154$	−4.83419e6	+	1.86325e6i	−1.32361	+	0.510164i
$155$			293557.i			0.0788311i
$156$	1.90480e6	+	2.10391e6i	0.501737	+	0.554183i
$157$	4.83857e6			1.25031			0.625155	−	0.780500i	$-0.285036\pi$
$157$	4.83857e6			1.25031			0.625155	+	0.780500i	$0.285036\pi$
$158$	2.58036e6	+	6.69472e6i	0.654198	+	1.69731i
$159$		−	1.01532e6i		−	0.252587i
$160$	−157564.	−	572369.i	−0.0384679	−	0.139739i
$161$	1.48662e6			0.356224
$162$	440784.	−	169893.i	0.103677	−	0.0399603i
$163$		−	2.74941e6i		−	0.634857i	−0.948282	−	0.317429i	$-0.897181\pi$
$163$		−	2.74941e6i		−	0.634857i	0.948282	−	0.317429i	$-0.102819\pi$
$164$	−69566.5	+	62983.0i	−0.0157713	+	0.0142788i
$165$	568941.			0.126653
$166$	−1.92398e6	−	4.99173e6i	−0.420606	−	1.09126i
$167$		−	2.23120e6i		−	0.479059i	−0.970889	−	0.239530i	$-0.923007\pi$
$167$		−	2.23120e6i		−	0.479059i	0.970889	−	0.239530i	$-0.0769932\pi$
$168$	1.15543e6	−	2.29082e6i	0.243677	−	0.483128i
$169$	3.26570e6			0.676576
$170$	928367.	−	357823.i	0.188961	−	0.0728318i
$171$			2.39097e6i			0.478173i
$172$	−1.77029e6	−	1.95533e6i	−0.347903	−	0.384268i
$173$	2.12407e6			0.410232			0.205116	−	0.978738i	$-0.434243\pi$
$173$	2.12407e6			0.410232			0.205116	+	0.978738i	$0.434243\pi$
$174$	79465.8	+	206173.i	0.0150845	+	0.0391367i
$175$		−	4.91738e6i		−	0.917529i
$176$	8.21094e6	+	817663.i	1.50610	+	0.149981i
$177$	−3.75720e6			−0.677554
$178$	1.63771e6	−	631227.i	0.290387	−	0.111925i
$179$			5.37716e6i			0.937548i	0.883318	+	0.468774i	$0.155304\pi$
$179$			5.37716e6i			0.937548i	−0.883318	+	0.468774i	$0.844696\pi$
$180$	−208870.	+	189104.i	−0.0358145	+	0.0324252i
$181$	−1.20211e6			−0.202725			−0.101362	−	0.994850i	$-0.532320\pi$
$181$	−1.20211e6			−0.202725			−0.101362	+	0.994850i	$0.532320\pi$
$182$	−2.63110e6	−	6.82636e6i	−0.436439	−	1.13234i
$183$		−	4.75363e6i		−	0.775662i
$184$	−2.11407e6	−	1.06628e6i	−0.339365	−	0.171166i
$185$	−765579.			−0.120913
$186$	1.88547e6	−	726723.i	0.293010	−	0.112935i
$187$			1.38291e7i			2.11480i
$188$	2.40906e6	+	2.66088e6i	0.362555	+	0.400452i
$189$	−1.21771e6			−0.180367
$190$	−512882.	−	1.33067e6i	−0.0747751	−	0.194003i
$191$			4.90862e6i			0.704465i	0.935912	+	0.352233i	$0.114577\pi$
$191$			4.90862e6i			0.704465i	−0.935912	+	0.352233i	$0.885423\pi$
$192$	−3.28618e6	+	2.42896e6i	−0.464289	+	0.343175i
$193$	−5.95286e6			−0.828044			−0.414022	−	0.910267i	$-0.635876\pi$
$193$	−5.95286e6			−0.828044			−0.414022	+	0.910267i	$0.635876\pi$
$194$	1.31879e6	−	508304.i	0.180622	−	0.0696175i
$195$			803403.i			0.108350i
$196$	678880.	−	614633.i	0.0901623	−	0.0816297i
$197$	−5.29223e6			−0.692213			−0.346107	−	0.938195i	$-0.612496\pi$
$197$	−5.29223e6			−0.692213			−0.346107	+	0.938195i	$0.612496\pi$
$198$	−1.40846e6	−	3.65423e6i	−0.181446	−	0.470760i
$199$		−	400700.i		−	0.0508464i	−0.999677	−	0.0254232i	$-0.991907\pi$
$199$		−	400700.i		−	0.0508464i	0.999677	−	0.0254232i	$-0.00809333\pi$
$200$	−3.52700e6	+	6.99283e6i	−0.440875	+	0.874104i
$201$	−1.30510e6			−0.160715
$202$	6.33351e6	−	2.44114e6i	0.768406	−	0.296168i
$203$		−	569573.i		−	0.0680865i
$204$	−4.59649e6	−	5.07695e6i	−0.541422	−	0.598015i
$205$	−26564.8			−0.00308351
$206$	−1.74938e6	−	4.53874e6i	−0.200116	−	0.519199i
$207$			1.12376e6i			0.126696i
$208$	−1.15462e6	+	1.15947e7i	−0.128307	+	1.28845i
$209$	1.98218e7			2.17122
$210$	677703.	−	261209.i	0.0731781	−	0.0282052i
$211$		−	5.52565e6i		−	0.588215i	−0.955772	−	0.294107i	$-0.904978\pi$
$211$		−	5.52565e6i		−	0.588215i	0.955772	−	0.294107i	$-0.0950224\pi$
$212$	3.09016e6	−	2.79772e6i	0.324319	−	0.293627i
$213$	7.77293e6			0.804352
$214$	842445.	+	2.18571e6i	0.0859607	+	0.223024i
$215$		−	746666.i		−	0.0751296i
$216$	1.73166e6	+	873403.i	0.171831	+	0.0866670i
$217$	−5.20880e6			−0.509752
$218$	−1.63208e7	+	6.29056e6i	−1.57533	+	0.607183i
$219$		−	772638.i		−	0.0735604i
$220$	1.56772e6	+	1.73159e6i	0.147232	+	0.162622i
$221$	−1.95281e7			−1.80918
$222$	1.89525e6	+	4.91720e6i	0.173224	+	0.449427i
$223$		−	2.20009e7i		−	1.98393i	−0.126515	−	0.991965i	$-0.540379\pi$
$223$		−	2.20009e7i		−	1.98393i	0.126515	−	0.991965i	$-0.459621\pi$
$224$	1.01560e7	−	2.79578e6i	0.903604	−	0.248748i
$225$	3.71712e6			0.326331
$226$	8.82954e6	−	3.40319e6i	0.764915	−	0.294823i
$227$		−	1.01434e7i		−	0.867174i	−0.901112	−	0.433587i	$-0.857248\pi$
$227$		−	1.01434e7i		−	0.867174i	0.901112	−	0.433587i	$-0.142752\pi$
$228$	−7.27700e6	+	6.58834e6i	−0.613971	+	0.555868i
$229$	1.47394e6			0.122736			0.0613680	−	0.998115i	$-0.480454\pi$
$229$	1.47394e6			0.122736			0.0613680	+	0.998115i	$0.480454\pi$
$230$	−241055.	−	625416.i	−0.0198122	−	0.0514026i
$231$			1.00952e7i			0.818987i
$232$	−408527.	+	809969.i	−0.0327157	+	0.0648641i
$233$	1.84195e7			1.45616			0.728081	−	0.685491i	$-0.240412\pi$
$233$	1.84195e7			1.45616			0.728081	+	0.685491i	$0.240412\pi$
$234$	5.16014e6	−	1.98888e6i	0.402730	−	0.155225i
$235$			1.01609e6i			0.0782938i
$236$	−1.03530e7	−	1.14352e7i	−0.787644	−	0.869975i
$237$	1.39805e7			1.05021
$238$	6.34912e6	+	1.64727e7i	0.470959	+	1.22190i
$239$		−	1.58290e7i		−	1.15947i	−0.814806	−	0.579734i	$-0.803157\pi$
$239$		−	1.58290e7i		−	1.15947i	0.814806	−	0.579734i	$-0.196843\pi$
$240$	−1.15109e6	−	114628.i	−0.0832674	−	0.00829194i
$241$	−1.82584e7			−1.30440			−0.652200	−	0.758047i	$-0.726154\pi$
$241$	−1.82584e7			−1.30440			−0.652200	+	0.758047i	$0.726154\pi$
$242$	−1.70704e7	+	6.57948e6i	−1.20447	+	0.464243i
$243$		−	920483.i		−	0.0641500i
$244$	1.44679e7	−	1.30987e7i	0.995944	−	0.901692i
$245$	259239.			0.0176279
$246$	65763.2	+	170622.i	0.00441751	+	0.0114612i
$247$			2.79904e7i			1.85745i
$248$	7.40725e6	+	3.73602e6i	0.485626	+	0.244937i
$249$	−1.04242e7			−0.675216
$250$	−4.18183e6	+	1.61181e6i	−0.267637	+	0.103156i
$251$			2.53628e7i			1.60390i	0.597392	+	0.801949i	$0.296204\pi$
$251$			2.53628e7i			1.60390i	−0.597392	+	0.801949i	$0.703796\pi$
$252$	−3.35541e6	−	3.70614e6i	−0.209674	−	0.231591i
$253$	9.31628e6			0.575282
$254$	−1.76038e6	−	4.56729e6i	−0.107425	−	0.278713i
$255$		−	1.93869e6i		−	0.116920i
$256$	−1.64477e7	−	3.30861e6i	−0.980362	−	0.197209i
$257$	−2.76942e7			−1.63151			−0.815755	−	0.578397i	$-0.803678\pi$
$257$	−2.76942e7			−1.63151			−0.815755	+	0.578397i	$0.803678\pi$
$258$	−4.79573e6	+	1.84843e6i	−0.279252	+	0.107633i
$259$		−	1.35842e7i		−	0.781873i
$260$	−2.44519e6	+	2.21378e6i	−0.139121	+	0.125955i
$261$	430548.			0.0242159
$262$	2.83980e6	+	7.36784e6i	0.157901	+	0.409672i
$263$			2.44482e7i			1.34394i	0.740579	+	0.671969i	$0.234551\pi$
$263$			2.44482e7i			1.34394i	−0.740579	+	0.671969i	$0.765449\pi$
$264$	7.24076e6	−	1.43560e7i	0.393525	−	0.780226i
$265$	1.18001e6			0.0634088
$266$	2.36110e7	−	9.10046e6i	1.25450	−	0.483524i
$267$		−	3.42000e6i		−	0.179677i
$268$	−3.59622e6	−	3.97212e6i	−0.186828	−	0.206356i
$269$	5.72991e6			0.294368			0.147184	−	0.989109i	$-0.452979\pi$
$269$	5.72991e6			0.294368			0.147184	+	0.989109i	$0.452979\pi$
$270$	197451.	+	512285.i	0.0100316	+	0.0260268i
$271$			2.38858e7i			1.20014i	0.799947	+	0.600071i	$0.204861\pi$
$271$			2.38858e7i			1.20014i	−0.799947	+	0.600071i	$0.795139\pi$
$272$	2.78622e6	−	2.79792e7i	0.138455	−	1.39036i
$273$	−1.42554e7			−0.700634
$274$	9.07497e6	−	3.49779e6i	0.441157	−	0.170036i
$275$		−	3.08159e7i		−	1.48176i
$276$	−3.42020e6	+	3.09653e6i	−0.162676	+	0.147281i
$277$	2.39606e6			0.112735			0.0563675	−	0.998410i	$-0.482048\pi$
$277$	2.39606e6			0.112735			0.0563675	+	0.998410i	$0.482048\pi$
$278$	6.75533e6	+	1.75266e7i	0.314421	+	0.815763i
$279$		−	3.93741e6i		−	0.181300i
$280$	2.66242e6	+	1.34285e6i	0.121284	+	0.0611722i
$281$	3.74383e7			1.68732			0.843660	−	0.536878i	$-0.180397\pi$
$281$	3.74383e7			1.68732			0.843660	+	0.536878i	$0.180397\pi$
$282$	6.52618e6	−	2.51540e6i	0.291013	−	0.112166i
$283$		−	1.95433e7i		−	0.862262i	−0.902289	−	0.431131i	$-0.858115\pi$
$283$		−	1.95433e7i		−	0.862262i	0.902289	−	0.431131i	$-0.141885\pi$
$284$	2.14184e7	+	2.36572e7i	0.935044	+	1.03278i
$285$	−2.77881e6			−0.120040
$286$	−1.64884e7	−	4.27790e7i	−0.704825	−	1.82866i
$287$		−	471359.i		−	0.0199391i
$288$	2.11337e6	+	7.67705e6i	0.0884704	+	0.321378i
$289$	2.29857e7			0.952279
$290$	−239617.	+	92356.1i	−0.00982479	+	0.00378679i
$291$		−	2.75401e6i		−	0.111760i
$292$	2.35155e6	−	2.12901e6i	0.0944510	−	0.0855125i
$293$	−2.94374e7			−1.17030			−0.585149	−	0.810926i	$-0.698964\pi$
$293$	−2.94374e7			−1.17030			−0.585149	+	0.810926i	$0.698964\pi$
$294$	−641765.	−	1.66505e6i	−0.0252542	−	0.0655218i
$295$		−	4.36666e6i		−	0.170092i
$296$	−9.74332e6	+	1.93177e7i	−0.375692	+	0.744868i
$297$	−7.63107e6			−0.291283
$298$	−4.89095e7	+	1.88513e7i	−1.84818	+	0.712349i
$299$			1.31555e7i			0.492147i
$300$	1.02426e7	+	1.13132e7i	0.379354	+	0.419007i
$301$	1.32487e7			0.485817
$302$	4.54166e6	+	1.17833e7i	0.164890	+	0.427805i
$303$		−	1.32262e7i		−	0.475452i
$304$	−4.01037e7	−	3.99361e6i	−1.42746	−	0.142149i
$305$	5.52473e6			0.194720
$306$	−1.24520e7	+	4.79939e6i	−0.434583	+	0.167503i
$307$		−	1.00499e7i		−	0.347334i	−0.984804	−	0.173667i	$-0.944438\pi$
$307$		−	1.00499e7i		−	0.347334i	0.984804	−	0.173667i	$-0.0555616\pi$
$308$	−3.07250e7	+	2.78173e7i	−1.05157	+	0.952057i
$309$	−9.47818e6			−0.321255
$310$	844606.	+	2.19132e6i	0.0283510	+	0.0735565i
$311$			1.41913e7i			0.471782i	0.971780	+	0.235891i	$0.0758008\pi$
$311$			1.41913e7i			0.471782i	−0.971780	+	0.235891i	$0.924199\pi$
$312$	2.02721e7	+	1.02247e7i	0.667474	+	0.336656i
$313$	−1.53287e7			−0.499889			−0.249944	−	0.968260i	$-0.580412\pi$
$313$	−1.53287e7			−0.499889			−0.249944	+	0.968260i	$0.580412\pi$
$314$	3.61186e7	−	1.39213e7i	1.16665	−	0.449666i
$315$		−	1.41524e6i		−	0.0452790i
$316$	3.85234e7	+	4.25501e7i	1.22085	+	1.34847i
$317$	−1.32370e7			−0.415539			−0.207769	−	0.978178i	$-0.566620\pi$
$317$	−1.32370e7			−0.415539			−0.207769	+	0.978178i	$0.566620\pi$
$318$	−2.92121e6	−	7.57906e6i	−0.0908410	−	0.235686i
$319$		−	3.56936e6i		−	0.109956i
$320$	−2.82296e6	−	3.81924e6i	−0.0861500	−	0.116554i
$321$	4.56439e6			0.137996
$322$	1.10972e7	−	4.27723e6i	0.332389	−	0.128114i
$323$		−	6.75438e7i		−	2.00437i
$324$	2.80153e6	−	2.53640e6i	0.0823682	−	0.0745732i
$325$	4.35152e7			1.26763
$326$	−7.91044e6	−	2.05235e7i	−0.228322	−	0.592379i
$327$			3.40824e7i			0.974736i
$328$	−338083.	+	670303.i	−0.00958081	+	0.0189955i
$329$	−1.80292e7			−0.506278
$330$	4.24699e6	−	1.63693e6i	0.118179	−	0.0455499i
$331$			3.35208e7i			0.924338i	0.886792	+	0.462169i	$0.152929\pi$
$331$			3.35208e7i			0.924338i	−0.886792	+	0.462169i	$0.847071\pi$
$332$	−2.87239e7	−	3.17263e7i	−0.784926	−	0.866973i
$333$	1.02685e7			0.278083
$334$	−6.41949e6	−	1.66553e7i	−0.172290	−	0.447005i
$335$		−	1.51680e6i		−	0.0403455i
$336$	2.03393e6	−	2.04246e7i	0.0536189	−	0.538439i
$337$	1.45584e7			0.380385			0.190193	−	0.981747i	$-0.439089\pi$
$337$	1.45584e7			0.380385			0.190193	+	0.981747i	$0.439089\pi$
$338$	2.43776e7	−	9.39590e6i	0.631306	−	0.243326i
$339$		−	1.84386e7i		−	0.473292i
$340$	5.90049e6	−	5.34209e6i	0.150124	−	0.135917i
$341$	−3.26422e7			−0.823221
$342$	6.87916e6	+	1.78479e7i	0.171972	+	0.446179i
$343$			4.24199e7i			1.05121i
$344$	−1.88405e7	−	9.50262e6i	−0.462824	−	0.233436i
$345$	−1.30605e6			−0.0318054
$346$	1.58556e7	−	6.11125e6i	0.382784	−	0.147537i
$347$			1.29513e7i			0.309974i	0.987917	+	0.154987i	$0.0495335\pi$
$347$			1.29513e7i			0.309974i	−0.987917	+	0.154987i	$0.950466\pi$
$348$	1.18638e6	+	1.31039e6i	0.0281505	+	0.0310930i
$349$	−3.42411e7			−0.805511			−0.402755	−	0.915308i	$-0.631947\pi$
$349$	−3.42411e7			−0.805511			−0.402755	+	0.915308i	$0.631947\pi$
$350$	−1.41480e7	−	3.67069e7i	−0.329983	−	0.856137i
$351$		−	1.07758e7i		−	0.249189i
$352$	6.36449e7	−	1.75204e7i	1.45927	−	0.401714i
$353$	4.45234e7			1.01219			0.506097	−	0.862476i	$-0.331088\pi$
$353$	4.45234e7			1.01219			0.506097	+	0.862476i	$0.331088\pi$
$354$	−2.80464e7	+	1.08100e7i	−0.632219	+	0.243678i
$355$			9.03380e6i			0.201923i
$356$	1.04089e7	−	9.42386e6i	0.230704	−	0.208871i
$357$	3.43997e7			0.756050
$358$	1.54709e7	+	4.01390e7i	0.337183	+	0.874817i
$359$			5.35591e7i			1.15758i	0.815478	+	0.578789i	$0.196474\pi$
$359$			5.35591e7i			1.15758i	−0.815478	+	0.578789i	$0.803526\pi$
$360$	−1.01508e6	+	2.01256e6i	−0.0217567	+	0.0431361i
$361$	−4.97674e7			−1.05785
$362$	−8.97338e6	+	3.45863e6i	−0.189161	+	0.0729086i
$363$			3.56478e7i			0.745269i
$364$	−3.92809e7	−	4.33868e7i	−0.814473	−	0.899609i
$365$	897969.			0.0184664
$366$	−1.36769e7	−	3.54845e7i	−0.278961	−	0.723762i
$367$		−	7.03367e7i		−	1.42293i	−0.702721	−	0.711466i	$-0.748032\pi$
$367$		−	7.03367e7i		−	1.42293i	0.702721	−	0.711466i	$-0.251968\pi$
$368$	−1.88488e7	−	1.87700e6i	−0.378216	−	0.0376636i
$369$	356307.			0.00709162
$370$	−5.71483e6	+	2.20268e6i	−0.112823	+	0.0434857i
$371$			2.09379e7i			0.410025i
$372$	1.19836e7	−	1.08496e7i	0.232788	−	0.210758i
$373$	−5.92989e7			−1.14267			−0.571335	−	0.820717i	$-0.693574\pi$
$373$	−5.92989e7			−1.14267			−0.571335	+	0.820717i	$0.693574\pi$
$374$	3.97883e7	+	1.03230e8i	0.760572	+	1.97330i
$375$			8.73285e6i			0.165601i
$376$	2.56387e7	+	1.29315e7i	0.482317	+	0.243268i
$377$	5.04031e6			0.0940660
$378$	−9.08986e6	+	3.50353e6i	−0.168299	+	0.0648679i
$379$		−	2.64013e7i		−	0.484962i	−0.970156	−	0.242481i	$-0.922039\pi$
$379$		−	2.64013e7i		−	0.484962i	0.970156	−	0.242481i	$-0.0779612\pi$
$380$	−7.65705e6	−	8.45742e6i	−0.139544	−	0.154130i
$381$	−9.53779e6			−0.172454
$382$	1.41228e7	+	3.66415e7i	0.253356	+	0.657330i
$383$		−	1.35087e7i		−	0.240445i	−0.992747	−	0.120223i	$-0.961639\pi$
$383$		−	1.35087e7i		−	0.240445i	0.992747	−	0.120223i	$-0.0383608\pi$
$384$	−1.75420e7	+	2.75863e7i	−0.309802	+	0.487192i
$385$	−1.17327e7			−0.205597
$386$	−4.44364e7	+	1.71272e7i	−0.772640	+	0.297800i
$387$			1.00148e7i			0.172787i
$388$	8.38193e6	−	7.58870e6i	0.143499	−	0.129919i
$389$	7.99195e7			1.35770			0.678850	−	0.734277i	$-0.262479\pi$
$389$	7.99195e7			1.35770			0.678850	+	0.734277i	$0.262479\pi$
$390$	2.31151e6	+	5.99718e6i	0.0389674	+	0.101100i
$391$		−	3.17457e7i		−	0.531073i
$392$	3.29926e6	−	6.54130e6i	0.0547720	−	0.108594i
$393$	1.53861e7			0.253485
$394$	−3.95050e7	+	1.52265e7i	−0.645897	+	0.248950i
$395$			1.62483e7i			0.263643i
$396$	−2.10275e7	−	2.32254e7i	−0.338611	−	0.374006i
$397$	−1.68170e7			−0.268767			−0.134384	−	0.990929i	$-0.542905\pi$
$397$	−1.68170e7			−0.268767			−0.134384	+	0.990929i	$0.542905\pi$
$398$	−1.15287e6	−	2.99111e6i	−0.0182866	−	0.0474443i
$399$		−	4.93066e7i		−	0.776222i
$400$	−6.20866e6	+	6.23472e7i	−0.0970104	+	0.974175i
$401$	1.59684e7			0.247644			0.123822	−	0.992304i	$-0.460485\pi$
$401$	1.59684e7			0.247644			0.123822	+	0.992304i	$0.460485\pi$
$402$	−9.74220e6	+	3.75496e6i	−0.149961	+	0.0577999i
$403$		−	4.60941e7i		−	0.704256i
$404$	4.02544e7	−	3.64449e7i	0.610477	−	0.552704i
$405$	1.06980e6			0.0161041
$406$	−1.63874e6	−	4.25170e6i	−0.0244868	−	0.0635308i
$407$		−	8.51289e7i		−	1.26268i
$408$	−4.89186e7	−	2.46732e7i	−0.720267	−	0.363284i
$409$	2.48807e7			0.363657			0.181829	−	0.983330i	$-0.441798\pi$
$409$	2.48807e7			0.363657			0.181829	+	0.983330i	$0.441798\pi$
$410$	−198299.	+	76430.8i	−0.00287719	+	0.00110896i
$411$		−	1.89511e7i		−	0.272967i
$412$	−2.61172e7	−	2.88472e7i	−0.373452	−	0.412489i
$413$	7.74809e7			1.09988
$414$	3.23322e6	+	8.38854e6i	0.0455652	+	0.118218i
$415$		−	1.21151e7i		−	0.169505i
$416$	2.47406e7	+	8.98731e7i	0.343662	+	1.24839i
$417$	3.66006e7			0.504754
$418$	1.47964e8	−	5.70302e7i	2.02595	−	0.780865i
$419$			6.79616e7i			0.923893i	0.886908	+	0.461946i	$0.152849\pi$
$419$			6.79616e7i			0.923893i	−0.886908	+	0.461946i	$0.847151\pi$
$420$	4.30733e6	−	3.89970e6i	0.0581380	−	0.0526360i
$421$	5.18899e7			0.695403			0.347701	−	0.937605i	$-0.386962\pi$
$421$	5.18899e7			0.695403			0.347701	+	0.937605i	$0.386962\pi$
$422$	−1.58981e7	−	4.12474e7i	−0.211547	−	0.548857i
$423$		−	1.36285e7i		−	0.180064i
$424$	1.50177e7	−	2.97750e7i	0.197018	−	0.390620i
$425$	−1.05007e8			−1.36789
$426$	5.80228e7	−	2.23639e7i	0.750533	−	0.289280i
$427$			9.80295e7i			1.25914i
$428$	1.25772e7	+	1.38919e7i	0.160418	+	0.177186i
$429$	−8.93348e7			−1.13148
$430$	−2.14827e6	−	5.57366e6i	−0.0270199	−	0.0701027i
$431$		−	8.12246e7i		−	1.01451i	−0.861796	−	0.507255i	$-0.830660\pi$
$431$		−	8.12246e7i		−	1.01451i	0.861796	−	0.507255i	$-0.169340\pi$
$432$	1.54393e7	+	1.53747e6i	0.191503	+	0.0190703i
$433$	−2.94313e7			−0.362532			−0.181266	−	0.983434i	$-0.558019\pi$
$433$	−2.94313e7			−0.362532			−0.181266	+	0.983434i	$0.558019\pi$
$434$	−3.88823e7	+	1.49865e7i	−0.475644	+	0.183329i
$435$			500388.i			0.00607910i
$436$	−1.03731e8	+	9.39145e7i	−1.25155	+	1.13311i
$437$	−4.55024e7			−0.545243
$438$	−2.22299e6	−	5.76753e6i	−0.0264555	−	0.0686384i
$439$			1.11579e8i			1.31883i	0.751779	+	0.659415i	$0.229196\pi$
$439$			1.11579e8i			1.31883i	−0.751779	+	0.659415i	$0.770804\pi$
$440$	1.66847e7	+	8.41530e6i	0.195866	+	0.0987897i
$441$	−3.47710e6			−0.0405417
$442$	−1.45772e8	+	5.61851e7i	−1.68813	+	0.650660i
$443$			1.21911e8i			1.40227i	0.713027	+	0.701137i	$0.247324\pi$
$443$			1.21911e8i			1.40227i	−0.713027	+	0.701137i	$0.752676\pi$
$444$	2.82950e7	+	3.12526e7i	0.323267	+	0.357057i
$445$	3.97477e6			0.0451058
$446$	−6.32998e7	−	1.64231e8i	−0.713507	−	1.85118i
$447$			1.02137e8i			1.14356i
$448$	6.77677e7	−	5.00900e7i	0.753683	−	0.557079i
$449$	−1.37769e8			−1.52199			−0.760997	−	0.648756i	$-0.775290\pi$
$449$	−1.37769e8			−1.52199			−0.760997	+	0.648756i	$0.775290\pi$
$450$	2.77472e7	−	1.06947e7i	0.304496	−	0.117363i
$451$		−	2.95389e6i		−	0.0322006i
$452$	5.61186e7	−	5.08078e7i	0.607703	−	0.550192i
$453$	2.46069e7			0.264705
$454$	−2.91840e7	−	7.57176e7i	−0.311873	−	0.809151i
$455$		−	1.65678e7i		−	0.175886i
$456$	−3.53652e7	+	7.01171e7i	−0.372977	+	0.739485i
$457$	1.10582e8			1.15861			0.579304	−	0.815111i	$-0.303324\pi$
$457$	1.10582e8			1.15861			0.579304	+	0.815111i	$0.303324\pi$
$458$	1.10025e7	−	4.24073e6i	0.114524	−	0.0441412i
$459$			2.60032e7i			0.268899i
$460$	−3.59882e6	−	3.97500e6i	−0.0369732	−	0.0408379i
$461$	−1.72892e7			−0.176471			−0.0882353	−	0.996100i	$-0.528123\pi$
$461$	−1.72892e7			−0.176471			−0.0882353	+	0.996100i	$0.528123\pi$
$462$	2.90452e7	+	7.53575e7i	0.294543	+	0.764189i
$463$		−	7.00921e7i		−	0.706197i	−0.935586	−	0.353099i	$-0.885128\pi$
$463$		−	7.00921e7i		−	0.706197i	0.935586	−	0.353099i	$-0.114872\pi$
$464$	−719140.	+	7.22158e6i	−0.00719879	+	0.0722900i
$465$	4.57610e6			0.0455131
$466$	1.37496e8	−	5.29955e7i	1.35873	−	0.523699i
$467$		−	1.72559e7i		−	0.169428i	−0.996405	−	0.0847142i	$-0.973002\pi$
$467$		−	1.72559e7i		−	0.169428i	0.996405	−	0.0847142i	$-0.0269977\pi$
$468$	3.27967e7	−	2.96929e7i	0.319958	−	0.289678i
$469$	2.69138e7			0.260889
$470$	2.92343e6	+	7.58481e6i	0.0281578	+	0.0730552i
$471$		−	7.54258e7i		−	0.721867i
$472$	−1.10183e8	−	5.55733e7i	−1.04782	−	0.528494i
$473$	8.30260e7			0.784568
$474$	1.04360e8	−	4.02239e7i	0.979943	−	0.377702i
$475$			1.50511e8i			1.40439i
$476$	9.47888e7	+	1.04697e8i	0.878893	+	0.970762i
$477$	−1.58272e7			−0.145831
$478$	−4.55422e7	−	1.18159e8i	−0.416994	−	1.08189i
$479$		−	8.71706e7i		−	0.793165i	−0.917999	−	0.396582i	$-0.870196\pi$
$479$		−	8.71706e7i		−	0.793165i	0.917999	−	0.396582i	$-0.129804\pi$
$480$	−8.92236e6	+	2.45618e6i	−0.0806781	+	0.0222094i
$481$	1.20211e8			1.08021
$482$	−1.36294e8	+	5.25320e7i	−1.21712	+	0.469118i
$483$		−	2.31742e7i		−	0.205666i
$484$	−1.08495e8	+	9.82279e7i	−0.956920	+	0.866361i
$485$	3.20074e6			0.0280560
$486$	−2.64836e6	−	6.87115e6i	−0.0230711	−	0.0598577i
$487$		−	1.54923e8i		−	1.34131i	−0.741769	−	0.670656i	$-0.766013\pi$
$487$		−	1.54923e8i		−	1.34131i	0.741769	−	0.670656i	$-0.233987\pi$
$488$	7.03118e7	−	1.39404e8i	0.605018	−	1.19954i
$489$	−4.28590e7			−0.366535
$490$	1.93514e6	−	745867.i	0.0164484	−	0.00633976i
$491$		−	1.73878e8i		−	1.46893i	−0.678649	−	0.734463i	$-0.737434\pi$
$491$		−	1.73878e8i		−	1.46893i	0.678649	−	0.734463i	$-0.262566\pi$
$492$	981808.	+	1.08443e6i	0.00824387	+	0.00910559i
$493$	−1.21628e7			−0.101506
$494$	8.05324e7	+	2.08941e8i	0.668021	+	1.73317i
$495$		−	8.86892e6i		−	0.0731232i
$496$	6.60421e7	+	6.57661e6i	0.541223	+	0.0538961i
$497$	−1.60294e8			−1.30571
$498$	−7.78134e7	+	2.99918e7i	−0.630037	+	0.242837i
$499$		−	1.63179e7i		−	0.131330i	−0.997842	−	0.0656649i	$-0.979083\pi$
$499$		−	1.63179e7i		−	0.131330i	0.997842	−	0.0656649i	$-0.0209168\pi$
$500$	−2.65788e7	+	2.40635e7i	−0.212630	+	0.192508i
$501$	−3.47810e7			−0.276585
$502$	7.29726e7	+	1.89327e8i	0.576831	+	1.49658i
$503$			1.47262e8i			1.15714i	0.815631	+	0.578572i	$0.196390\pi$
$503$			1.47262e8i			1.15714i	−0.815631	+	0.578572i	$0.803610\pi$
$504$	−3.57103e7	−	1.80113e7i	−0.278934	−	0.140687i
$505$	1.53716e7			0.119356
$506$	6.95434e7	−	2.68043e7i	0.536790	−	0.206896i
$507$		−	5.09073e7i		−	0.390621i
$508$	−2.62815e7	−	2.90286e7i	−0.200474	−	0.221430i
$509$	1.68147e8			1.27507			0.637536	−	0.770421i	$-0.279954\pi$
$509$	1.68147e8			1.27507			0.637536	+	0.770421i	$0.279954\pi$
$510$	−5.57790e6	−	1.44718e7i	−0.0420495	−	0.109097i
$511$			1.59334e7i			0.119411i
$512$	−1.32297e8	+	2.26247e7i	−0.985690	+	0.168567i
$513$	3.72715e7			0.276074
$514$	−2.06730e8	+	7.96803e7i	−1.52235	+	0.586761i
$515$		−	1.10157e7i		−	0.0806471i
$516$	−3.04806e7	+	2.75960e7i	−0.221858	+	0.200862i
$517$	−1.12984e8			−0.817611
$518$	−3.90838e7	−	1.01403e8i	−0.281195	−	0.729558i
$519$		−	3.31109e7i		−	0.236848i
$520$	−1.18833e7	+	2.35604e7i	−0.0845134	+	0.167561i
$521$	1.06640e8			0.754062			0.377031	−	0.926201i	$-0.376945\pi$
$521$	1.06640e8			0.754062			0.377031	+	0.926201i	$0.376945\pi$
$522$	3.21392e6	−	1.23875e6i	0.0225956	−	0.00870907i
$523$		−	1.39482e7i		−	0.0975016i	−0.998811	−	0.0487508i	$-0.984476\pi$
$523$		−	1.39482e7i		−	0.0975016i	0.998811	−	0.0487508i	$-0.0155240\pi$
$524$	4.23967e7	+	4.68283e7i	0.294671	+	0.325473i
$525$	−7.66544e7			−0.529736
$526$	7.03410e7	+	1.82499e8i	0.483338	+	1.25402i
$527$			1.11230e8i			0.759958i
$528$	1.27461e7	−	1.27996e8i	0.0865915	−	0.869550i
$529$	1.26650e8			0.855534
$530$	8.80847e6	−	3.39507e6i	0.0591661	−	0.0228045i
$531$			5.85689e7i			0.391186i
$532$	1.50066e8	−	1.35865e8i	0.996664	−	0.902344i
$533$	4.17119e6			0.0275472
$534$	−9.83985e6	−	2.55294e7i	−0.0646197	−	0.167655i
$535$			5.30479e6i			0.0346423i
$536$	−3.82731e7	−	1.93039e7i	−0.248542	−	0.125358i
$537$	8.38216e7			0.541294
$538$	4.27721e7	−	1.64858e7i	0.274672	−	0.105867i
$539$			2.88262e7i			0.184086i
$540$	2.94783e6	+	3.25597e6i	0.0187207	+	0.0206775i
$541$	−2.59863e8			−1.64117			−0.820585	−	0.571525i	$-0.806352\pi$
$541$	−2.59863e8			−1.64117			−0.820585	+	0.571525i	$0.806352\pi$
$542$	6.87230e7	+	1.78301e8i	0.431623	+	1.11984i
$543$			1.87390e7i			0.117043i
$544$	−5.97018e7	−	2.16873e8i	−0.370843	−	1.34713i
$545$	−3.96110e7			−0.244696
$546$	−1.06412e8	+	4.10148e7i	−0.653754	+	0.251978i
$547$		−	5.56574e7i		−	0.340064i	−0.985439	−	0.170032i	$-0.945613\pi$
$547$		−	5.56574e7i		−	0.340064i	0.985439	−	0.170032i	$-0.0543872\pi$
$548$	5.76785e7	−	5.22200e7i	0.350487	−	0.317318i
$549$	−7.41018e7			−0.447829
$550$	−8.86619e7	−	2.30032e8i	−0.532904	−	1.38261i
$551$			1.74334e7i			0.104214i
$552$	−1.66217e7	+	3.29551e7i	−0.0988230	+	0.195932i
$553$	−2.88306e8			−1.70482
$554$	1.78859e7	−	6.89381e6i	0.105192	−	0.0405443i
$555$			1.19342e7i			0.0698094i
$556$	1.00853e8	+	1.11395e8i	0.586767	+	0.648100i
$557$	2.34214e8			1.35534			0.677670	−	0.735366i	$-0.262990\pi$
$557$	2.34214e8			1.35534			0.677670	+	0.735366i	$0.262990\pi$
$558$	−1.13285e7	−	2.93916e7i	−0.0652033	−	0.169169i
$559$			1.17241e8i			0.671188i
$560$	2.37378e7	+	2.36386e6i	0.135169	+	0.0134604i
$561$	2.15574e8			1.22098
$562$	2.79467e8	−	1.07715e8i	1.57442	−	0.606833i
$563$			2.04860e8i			1.14797i	0.818865	+	0.573986i	$0.194604\pi$
$563$			2.04860e8i			1.14797i	−0.818865	+	0.573986i	$0.805396\pi$
$564$	4.14789e7	−	3.75535e7i	0.231201	−	0.209321i
$565$	2.14296e7			0.118814
$566$	−5.62290e7	−	1.45885e8i	−0.310106	−	0.804568i
$567$			1.89822e7i			0.104135i
$568$	2.27948e8	+	1.14971e8i	1.24391	+	0.627397i
$569$	−2.00875e8			−1.09041			−0.545205	−	0.838303i	$-0.683548\pi$
$569$	−2.00875e8			−1.09041			−0.545205	+	0.838303i	$0.683548\pi$
$570$	−2.07431e7	+	7.99504e6i	−0.112008	+	0.0431714i
$571$		−	3.00477e8i		−	1.61400i	−0.590552	−	0.807000i	$-0.701090\pi$
$571$		−	3.00477e8i		−	1.61400i	0.590552	−	0.807000i	$-0.298910\pi$
$572$	−2.46163e8	−	2.71894e8i	−1.31533	−	1.45282i
$573$	7.65179e7			0.406723
$574$	−1.35617e6	−	3.51857e6i	−0.00717098	−	0.0186050i
$575$			7.07402e7i			0.372103i
$576$	3.78637e7	+	5.12265e7i	0.198132	+	0.268057i
$577$	−4.40346e6			−0.0229227			−0.0114614	−	0.999934i	$-0.503648\pi$
$577$	−4.40346e6			−0.0229227			−0.0114614	+	0.999934i	$0.503648\pi$
$578$	1.71582e8	−	6.61332e7i	0.888562	−	0.342481i
$579$			9.27959e7i			0.478072i
$580$	−1.52295e6	+	1.37882e6i	−0.00780552	+	0.00706683i
$581$	2.14967e8			1.09608
$582$	−7.92368e6	−	2.05579e7i	−0.0401937	−	0.104282i
$583$			1.31212e8i			0.662169i
$584$	1.14282e7	−	2.26582e7i	0.0573773	−	0.113760i
$585$	1.25238e7			0.0625560
$586$	−2.19742e8	+	8.46956e7i	−1.09199	+	0.420889i
$587$		−	3.35558e8i		−	1.65903i	−0.558488	−	0.829513i	$-0.688618\pi$
$587$		−	3.35558e8i		−	1.65903i	0.558488	−	0.829513i	$-0.311382\pi$
$588$	−9.58119e6	−	1.05827e7i	−0.0471289	−	0.0520552i
$589$	1.59431e8			0.780235
$590$	−1.25635e7	−	3.25959e7i	−0.0611723	−	0.158711i
$591$			8.24977e7i			0.399649i
$592$	−1.71514e7	+	1.72234e8i	−0.0826675	+	0.830144i
$593$	−3.72303e8			−1.78538			−0.892692	−	0.450666i	$-0.851186\pi$
$593$	−3.72303e8			−1.78538			−0.892692	+	0.450666i	$0.851186\pi$
$594$	−5.69638e7	+	2.19557e7i	−0.271794	+	0.104758i
$595$			3.99798e7i			0.189797i
$596$	−3.10858e8	+	2.81439e8i	−1.46833	+	1.32937i
$597$	−6.24630e6			−0.0293562
$598$	3.78504e7	+	9.82023e7i	0.176997	+	0.459217i
$599$		−	6.55966e7i		−	0.305211i	−0.988287	−	0.152606i	$-0.951234\pi$
$599$		−	6.55966e7i		−	0.305211i	0.988287	−	0.152606i	$-0.0487665\pi$
$600$	1.09007e8	+	5.49805e7i	0.504664	+	0.254539i
$601$	−7.73351e7			−0.356248			−0.178124	−	0.984008i	$-0.557003\pi$
$601$	−7.73351e7			−0.356248			−0.178124	+	0.984008i	$0.557003\pi$
$602$	9.88976e7	−	3.81183e7i	0.453311	−	0.174721i
$603$			2.03445e7i			0.0927886i
$604$	6.78045e7	+	7.48920e7i	0.307714	+	0.339879i
$605$	−4.14303e7			−0.187091
$606$	−3.80536e7	−	9.87297e7i	−0.170993	−	0.443639i
$607$			3.03128e8i			1.35538i	0.735349	+	0.677689i	$0.237018\pi$
$607$			3.03128e8i			1.35538i	−0.735349	+	0.677689i	$0.762982\pi$
$608$	−3.10853e8	+	8.55730e7i	−1.38307	+	0.380738i
$609$	−8.87876e6			−0.0393098
$610$	4.12406e7	−	1.58954e7i	0.181692	−	0.0700299i
$611$		−	1.59545e8i		−	0.699456i
$612$	−7.91418e7	+	7.16521e7i	−0.345264	+	0.312590i
$613$	−8.22145e7			−0.356917			−0.178458	−	0.983947i	$-0.557111\pi$
$613$	−8.22145e7			−0.356917			−0.178458	+	0.983947i	$0.557111\pi$
$614$	−2.89150e7	−	7.50198e7i	−0.124916	−	0.324094i
$615$			414104.i			0.00178026i
$616$	−1.49319e8	+	2.96049e8i	−0.638812	+	1.26655i
$617$	3.18746e8			1.35703			0.678514	−	0.734588i	$-0.262624\pi$
$617$	3.18746e8			1.35703			0.678514	+	0.734588i	$0.262624\pi$
$618$	−7.07520e7	+	2.72701e7i	−0.299760	+	0.115537i
$619$		−	2.43168e8i		−	1.02526i	−0.858609	−	0.512630i	$-0.828671\pi$
$619$		−	2.43168e8i		−	1.02526i	0.858609	−	0.512630i	$-0.171329\pi$
$620$	1.26095e7	+	1.39275e7i	0.0529082	+	0.0584386i
$621$	1.75177e7			0.0731478
$622$	4.08304e7	+	1.05934e8i	0.169673	+	0.440215i
$623$			7.05274e7i			0.291671i
$624$	1.80743e8	+	1.79988e7i	0.743889	+	0.0740780i
$625$	2.28863e8			0.937421
$626$	−1.14425e8	+	4.41030e7i	−0.466441	+	0.179781i
$627$		−	3.08991e8i		−	1.25356i
$628$	2.29561e8	−	2.07837e8i	0.926872	−	0.839157i
$629$	−2.90081e8			−1.16565
$630$	−4.07184e6	−	1.05643e7i	−0.0162843	−	0.0422494i
$631$		−	2.83810e8i		−	1.12964i	−0.825215	−	0.564819i	$-0.808946\pi$
$631$		−	2.83810e8i		−	1.12964i	0.825215	−	0.564819i	$-0.191054\pi$
$632$	4.09989e8	+	2.06788e8i	1.62413	+	0.819168i
$633$	−8.61364e7			−0.339606
$634$	−9.88105e7	+	3.80848e7i	−0.387735	+	0.149446i
$635$		−	1.10849e7i		−	0.0432924i
$636$	−4.36121e7	−	4.81708e7i	−0.169526	−	0.187246i
$637$	−4.07055e7			−0.157483
$638$	−1.02696e7	−	2.66443e7i	−0.0395449	−	0.102599i
$639$		−	1.21168e8i		−	0.464393i
$640$	−3.20611e7	−	2.03875e7i	−0.122304	−	0.0777721i
$641$	−7.22672e7			−0.274389			−0.137195	−	0.990544i	$-0.543809\pi$
$641$	−7.22672e7			−0.274389			−0.137195	+	0.990544i	$0.543809\pi$
$642$	3.40719e7	−	1.31324e7i	0.128763	−	0.0496294i
$643$			1.96351e8i			0.738585i	0.929313	+	0.369292i	$0.120400\pi$
$643$			1.96351e8i			0.738585i	−0.929313	+	0.369292i	$0.879600\pi$
$644$	7.05314e7	−	6.38566e7i	0.264074	−	0.239083i
$645$	−1.16394e7			−0.0433761
$646$	−1.94333e8	−	5.04195e8i	−0.720857	−	1.87026i
$647$		−	1.91792e8i		−	0.708139i	−0.935219	−	0.354069i	$-0.884798\pi$
$647$		−	1.91792e8i		−	0.708139i	0.935219	−	0.354069i	$-0.115202\pi$
$648$	1.36150e7	−	2.69939e7i	0.0500372	−	0.0992066i
$649$	4.85553e8			1.77624
$650$	3.24829e8	−	1.25200e8i	1.18281	−	0.455893i
$651$			8.11972e7i			0.294305i
$652$	−1.18098e8	−	1.30443e8i	−0.426090	−	0.470628i
$653$	4.55045e8			1.63424			0.817118	−	0.576471i	$-0.195570\pi$
$653$	4.55045e8			1.63424			0.817118	+	0.576471i	$0.195570\pi$
$654$	9.80601e7	+	2.54416e8i	0.350557	+	0.909517i
$655$			1.78820e7i			0.0636343i
$656$	−595136.	+	5.97634e6i	−0.00210817	+	0.0211701i
$657$	−1.20442e7			−0.0424701
$658$	−1.34583e8	+	5.18726e7i	−0.472403	+	0.182079i
$659$			7.59585e6i			0.0265412i	0.999912	+	0.0132706i	$0.00422429\pi$
$659$			7.59585e6i			0.0265412i	−0.999912	+	0.0132706i	$0.995776\pi$
$660$	2.69929e7	−	2.44384e7i	0.0938896	−	0.0850043i
$661$	3.30777e7			0.114533			0.0572665	−	0.998359i	$-0.481762\pi$
$661$	3.30777e7			0.114533			0.0572665	+	0.998359i	$0.481762\pi$
$662$	9.64443e7	+	2.50224e8i	0.332432	+	0.862490i
$663$			3.04413e8i			1.04453i
$664$	−3.05697e8	−	1.54185e8i	−1.04421	−	0.526670i
$665$	5.73047e7			0.194861
$666$	7.66516e7	−	2.95440e7i	0.259477	−	0.100011i
$667$			8.19373e6i			0.0276124i
$668$	−9.58394e7	−	1.05857e8i	−0.321525	−	0.355133i
$669$	−3.42960e8			−1.14542
$670$	−4.36406e6	−	1.13225e7i	−0.0145100	−	0.0376459i
$671$			6.14325e8i			2.03344i
$672$	−4.35819e7	−	1.58316e8i	−0.143615	−	0.521696i
$673$	−3.93583e8			−1.29119			−0.645597	−	0.763679i	$-0.723391\pi$
$673$	−3.93583e8			−1.29119			−0.645597	+	0.763679i	$0.723391\pi$
$674$	1.08674e8	−	4.18866e7i	0.354934	−	0.136803i
$675$		−	5.79441e7i		−	0.188407i
$676$	1.54938e8	−	1.40276e8i	0.501555	−	0.454090i
$677$	−4.60373e8			−1.48369			−0.741847	−	0.670570i	$-0.766050\pi$
$677$	−4.60373e8			−1.48369			−0.741847	+	0.670570i	$0.766050\pi$
$678$	−5.30505e7	−	1.37639e8i	−0.170216	−	0.441624i
$679$			5.67932e7i			0.181421i
$680$	2.86755e7	−	5.68538e7i	0.0911979	−	0.180814i
$681$	−1.58120e8			−0.500663
$682$	−2.43665e8	+	9.39164e7i	−0.768140	+	0.296066i
$683$			1.62181e8i			0.509022i	0.967070	+	0.254511i	$0.0819146\pi$
$683$			1.62181e8i			0.509022i	−0.967070	+	0.254511i	$0.918085\pi$
$684$	1.02702e8	+	1.13437e8i	0.320930	+	0.354476i
$685$	2.20252e7			0.0685249
$686$	1.22048e8	+	3.16653e8i	0.378059	+	0.980869i
$687$		−	2.29764e7i		−	0.0708617i
$688$	−1.67979e8	−	1.67277e7i	−0.515810	−	0.0513655i
$689$	−1.85285e8			−0.566477
$690$	−9.74926e6	+	3.75768e6i	−0.0296773	+	0.0114386i
$691$			1.47670e8i			0.447566i	0.974639	+	0.223783i	$0.0718407\pi$
$691$			1.47670e8i			0.447566i	−0.974639	+	0.223783i	$0.928159\pi$
$692$	1.00774e8	−	9.12375e7i	0.304111	−	0.275331i
$693$	1.57368e8			0.472842
$694$	3.72628e7	+	9.66778e7i	0.111480	+	0.289233i
$695$			4.25376e7i			0.126712i
$696$	1.26262e7	+	6.36830e6i	0.0374493	+	0.0188884i
$697$	−1.00655e7			−0.0297261
$698$	−2.55600e8	+	9.85166e7i	−0.751614	+	0.289696i
$699$		−	2.87131e8i		−	0.840716i
$700$	−2.11222e8	−	2.33301e8i	−0.615807	−	0.680177i
$701$	4.68339e7			0.135959			0.0679793	−	0.997687i	$-0.478345\pi$
$701$	4.68339e7			0.135959			0.0679793	+	0.997687i	$0.478345\pi$
$702$	−3.10036e7	−	8.04386e7i	−0.0896193	−	0.232516i
$703$			4.15785e8i			1.19675i
$704$	4.24683e8	−	3.13901e8i	1.21716	−	0.899652i
$705$	1.58392e7			0.0452030
$706$	3.32355e8	−	1.28100e8i	0.944469	−	0.364029i
$707$			2.72750e8i			0.771804i
$708$	−1.78257e8	+	1.61387e8i	−0.502280	+	0.454747i
$709$	4.58998e8			1.28787			0.643935	−	0.765080i	$-0.277301\pi$
$709$	4.58998e8			1.28787			0.643935	+	0.765080i	$0.277301\pi$
$710$	2.59915e7	+	6.74348e7i	0.0726201	+	0.188412i
$711$		−	2.17934e8i		−	0.606340i
$712$	5.05858e7	−	1.00294e8i	0.140149	−	0.277867i
$713$	7.49326e7			0.206729
$714$	2.56784e8	−	9.89730e7i	0.705462	−	0.271908i
$715$		−	1.03826e8i		−	0.284045i
$716$	2.30971e8	+	2.55114e8i	0.629244	+	0.695017i
$717$	−2.46749e8			−0.669419
$718$	1.54097e8	+	3.99804e8i	0.416315	+	1.08012i
$719$		−	6.83996e8i		−	1.84021i	−0.391675	−	0.920104i	$-0.628104\pi$
$719$		−	6.83996e8i		−	1.84021i	0.391675	−	0.920104i	$-0.371896\pi$
$720$	−1.78687e6	+	1.79437e7i	−0.00478736	+	0.0480745i
$721$	1.95459e8			0.521495
$722$	−3.71500e8	+	1.43188e8i	−0.987068	+	0.380448i
$723$			2.84620e8i			0.753096i
$724$	−5.70328e7	+	5.16354e7i	−0.150283	+	0.136061i
$725$	2.71028e7			0.0711215
$726$	1.02564e8	+	2.66101e8i	0.268031	+	0.695403i
$727$		−	3.68994e8i		−	0.960321i	−0.877181	−	0.480161i	$-0.840578\pi$
$727$		−	3.68994e8i		−	0.960321i	0.877181	−	0.480161i	$-0.159422\pi$
$728$	−4.18051e8	−	2.10854e8i	−1.08351	−	0.546496i
$729$	−1.43489e7			−0.0370370
$730$	6.70309e6	−	2.58359e6i	0.0172308	−	0.00664132i
$731$		−	2.82915e8i		−	0.724275i
$732$	−2.04188e8	−	2.25532e8i	−0.520592	−	0.575009i
$733$	−2.37716e8			−0.603597			−0.301798	−	0.953372i	$-0.597587\pi$
$733$	−2.37716e8			−0.603597			−0.301798	+	0.953372i	$0.597587\pi$
$734$	−2.02369e8	−	5.25044e8i	−0.511747	−	1.32772i
$735$		−	4.04113e6i		−	0.0101775i
$736$	−1.46101e8	+	4.02194e7i	−0.366455	+	0.100879i
$737$	1.68662e8			0.421322
$738$	2.65973e6	−	1.02515e6i	0.00661712	−	0.00255045i
$739$			5.13693e8i			1.27283i	0.771347	+	0.636415i	$0.219583\pi$
$739$			5.13693e8i			1.27283i	−0.771347	+	0.636415i	$0.780417\pi$
$740$	−3.63222e7	+	3.28848e7i	−0.0896348	+	0.0811521i
$741$	4.36327e8			1.07240
$742$	6.02413e7	+	1.56295e8i	0.147463	+	0.382591i
$743$		−	7.49288e8i		−	1.82676i	−0.407105	−	0.913382i	$-0.633462\pi$
$743$		−	7.49288e8i		−	1.82676i	0.407105	−	0.913382i	$-0.366538\pi$
$744$	5.82388e7	−	1.15468e8i	0.141414	−	0.280376i
$745$	−1.18705e8			−0.287078
$746$	−4.42650e8	+	1.70612e8i	−1.06621	+	0.410953i
$747$			1.62497e8i			0.389836i
$748$	5.94017e8	+	6.56108e8i	1.41936	+	1.56773i
$749$	−9.41269e7			−0.224010
$750$	2.51257e7	+	6.51883e7i	0.0595572	+	0.154520i
$751$		−	4.67758e8i		−	1.10434i	−0.833732	−	0.552169i	$-0.813800\pi$
$751$		−	4.67758e8i		−	1.10434i	0.833732	−	0.552169i	$-0.186200\pi$
$752$	2.28591e8	+	2.27636e7i	0.537534	+	0.0535288i
$753$	3.95368e8			0.926011
$754$	3.76245e7	−	1.45017e7i	0.0877721	−	0.0338302i
$755$			2.85984e7i			0.0664509i
$756$	−5.77731e7	+	5.23057e7i	−0.133709	+	0.121055i
$757$	1.30944e8			0.301854			0.150927	−	0.988545i	$-0.451774\pi$
$757$	1.30944e8			0.301854			0.150927	+	0.988545i	$0.451774\pi$
$758$	−7.59604e7	−	1.97078e8i	−0.174413	−	0.452513i
$759$		−	1.45226e8i		−	0.332139i
$760$	−8.14909e7	−	4.11019e7i	−0.185639	−	0.0936312i
$761$	4.54355e7			0.103096			0.0515479	−	0.998671i	$-0.483585\pi$
$761$	4.54355e7			0.103096			0.0515479	+	0.998671i	$0.483585\pi$
$762$	−7.11969e7	+	2.74416e7i	−0.160915	+	0.0620218i
$763$		−	7.02848e8i		−	1.58230i
$764$	2.10846e8	+	2.32885e8i	0.472808	+	0.522230i
$765$	−3.02213e7			−0.0675038
$766$	−3.88664e7	−	1.00838e8i	−0.0864744	−	0.224357i
$767$			6.85650e8i			1.51955i
$768$	−5.15761e7	+	2.56395e8i	−0.113858	+	0.566012i
$769$	3.45661e8			0.760101			0.380051	−	0.924966i	$-0.375907\pi$
$769$	3.45661e8			0.760101			0.380051	+	0.924966i	$0.375907\pi$
$770$	−8.75814e7	+	3.37567e7i	−0.191840	+	0.0739414i
$771$			4.31710e8i			0.941953i
$772$	−2.82428e8	+	2.55700e8i	−0.613841	+	0.555749i
$773$	−2.61756e8			−0.566707			−0.283354	−	0.959016i	$-0.591447\pi$
$773$	−2.61756e8			−0.566707			−0.283354	+	0.959016i	$0.591447\pi$
$774$	2.88142e7	+	7.47580e7i	0.0621417	+	0.161226i
$775$		−	2.47858e8i		−	0.532474i
$776$	4.07350e7	−	8.07635e7i	0.0871730	−	0.172834i
$777$	−2.11757e8			−0.451415
$778$	5.96577e8	−	2.29940e8i	1.26686	−	0.488288i
$779$			1.44273e7i			0.0305192i
$780$	3.45095e7	+	3.81167e7i	0.0727201	+	0.0803214i
$781$	−1.00452e9			−2.10865
$782$	−9.13369e7	−	2.36972e8i	−0.190997	−	0.495539i
$783$		−	6.71158e6i		−	0.0139810i
$784$	5.80777e6	−	5.83214e7i	0.0120521	−	0.121026i
$785$	8.76608e7			0.181216
$786$	1.14853e8	−	4.42682e7i	0.236524	−	0.0911641i
$787$			3.73015e8i			0.765248i	0.923904	+	0.382624i	$0.124980\pi$
$787$			3.73015e8i			0.765248i	−0.923904	+	0.382624i	$0.875020\pi$
$788$	−2.51085e8	+	2.27323e8i	−0.513147	+	0.464585i
$789$	3.81110e8			0.775923
$790$	4.67487e7	+	1.21289e8i	0.0948174	+	0.246003i
$791$			3.80241e8i			0.768297i
$792$	−2.23787e8	−	1.12872e8i	−0.450464	−	0.227202i
$793$	−8.67490e8			−1.73958
$794$	−1.25534e8	+	4.83849e7i	−0.250784	+	0.0966603i
$795$		−	1.83946e7i		−	0.0366091i
$796$	−1.72117e7	−	1.90108e7i	−0.0341260	−	0.0376931i
$797$	1.78465e8			0.352516			0.176258	−	0.984344i	$-0.443601\pi$
$797$	1.78465e8			0.352516			0.176258	+	0.984344i	$0.443601\pi$
$798$	−1.41862e8	−	3.68060e8i	−0.279163	−	0.724285i
$799$			3.85000e8i			0.754779i
$800$	1.33036e8	+	4.83268e8i	0.259836	+	0.943882i
$801$	−5.33126e7			−0.103737
$802$	1.19200e8	−	4.59434e7i	0.231074	−	0.0890635i
$803$			9.98502e7i			0.192842i
$804$	−6.19192e7	+	5.60595e7i	−0.119140	+	0.107865i
$805$	2.69333e7			0.0516299
$806$	−1.32619e8	−	3.44080e8i	−0.253281	−	0.657134i
$807$		−	8.93204e7i		−	0.169953i
$808$	1.95630e8	−	3.87868e8i	0.370854	−	0.735276i
$809$	4.79925e8			0.906417			0.453209	−	0.891404i	$-0.350279\pi$
$809$	4.79925e8			0.906417			0.453209	+	0.891404i	$0.350279\pi$
$810$	7.98573e6	−	3.07796e6i	0.0150266	−	0.00579172i
$811$			5.32497e8i			0.998285i	0.866520	+	0.499142i	$0.166352\pi$
$811$			5.32497e8i			0.998285i	−0.866520	+	0.499142i	$0.833648\pi$
$812$	−2.44655e7	−	2.70229e7i	−0.0456969	−	0.0504735i
$813$	3.72343e8			0.692902
$814$	−2.44928e8	−	6.35464e8i	−0.454115	−	1.17820i
$815$		−	4.98112e7i		−	0.0920141i
$816$	−4.36152e8	−	4.34329e7i	−0.802726	−	0.0799372i
$817$	−4.05514e8			−0.743600
$818$	1.85727e8	−	7.15854e7i	0.339325	−	0.130787i
$819$			2.22219e8i			0.404511i
$820$	−1.26034e6	+	1.14107e6i	−0.00228585	+	0.00206952i
$821$	−3.55317e7			−0.0642075			−0.0321038	−	0.999485i	$-0.510221\pi$
$821$	−3.55317e7			−0.0642075			−0.0321038	+	0.999485i	$0.510221\pi$
$822$	−5.45251e7	−	1.41465e8i	−0.0981705	−	0.254702i
$823$		−	3.74456e8i		−	0.671740i	−0.941908	−	0.335870i	$-0.890970\pi$
$823$		−	3.74456e8i		−	0.671740i	0.941908	−	0.335870i	$-0.109030\pi$
$824$	−2.77955e8	−	1.40193e8i	−0.496813	−	0.250580i
$825$	−4.80373e8			−0.855494
$826$	5.78374e8	−	2.22924e8i	1.02629	−	0.395564i
$827$			8.48563e8i			1.50026i	0.661289	+	0.750131i	$0.270010\pi$
$827$			8.48563e8i			1.50026i	−0.661289	+	0.750131i	$0.729990\pi$
$828$	4.82701e7	+	5.33157e7i	0.0850329	+	0.0939213i
$829$	9.76219e8			1.71350			0.856749	−	0.515733i	$-0.172480\pi$
$829$	9.76219e8			1.71350			0.856749	+	0.515733i	$0.172480\pi$
$830$	−3.48568e7	−	9.04357e7i	−0.0609612	−	0.158163i
$831$		−	3.73509e7i		−	0.0650875i
$832$	4.43260e8	+	5.99695e8i	0.769641	+	1.04126i
$833$	9.82265e7			0.169939
$834$	2.73213e8	−	1.05305e8i	0.470981	−	0.181531i
$835$		−	4.04229e7i		−	0.0694333i
$836$	9.40427e8	−	8.51429e8i	1.60956	−	1.45724i
$837$	−6.13781e7			−0.104674
$838$	1.95535e8	+	5.07314e8i	0.332272	+	0.862075i
$839$		−	7.75818e8i		−	1.31363i	−0.754050	−	0.656817i	$-0.771902\pi$
$839$		−	7.75818e8i		−	1.31363i	0.754050	−	0.656817i	$-0.228098\pi$
$840$	2.09330e7	−	4.15030e7i	0.0353178	−	0.0700231i
$841$	−5.91684e8			−0.994722
$842$	3.87343e8	−	1.49295e8i	0.648873	−	0.250097i
$843$		−	5.83606e8i		−	0.974174i
$844$	−2.37350e8	−	2.62159e8i	−0.394786	−	0.436052i
$845$	5.91650e7			0.0980607
$846$	−3.92112e7	−	1.01733e8i	−0.0647589	−	0.168016i
$847$		−	7.35129e8i		−	1.20980i
$848$	2.64361e7	−	2.65470e8i	0.0433520	−	0.435339i
$849$	−3.04650e8			−0.497827
$850$	−7.83846e8	+	3.02120e8i	−1.27636	+	0.491952i
$851$			1.95420e8i			0.317088i
$852$	3.68780e8	−	3.33880e8i	0.596277	−	0.539848i
$853$	6.53118e8			1.05231			0.526156	−	0.850388i	$-0.323633\pi$
$853$	6.53118e8			1.05231			0.526156	+	0.850388i	$0.323633\pi$
$854$	2.82045e8	+	7.31763e8i	0.452840	+	1.17489i
$855$			4.33174e7i			0.0693049i
$856$	1.33854e8	+	6.75126e7i	0.213408	+	0.107638i
$857$	1.16144e9			1.84524			0.922620	−	0.385711i	$-0.126044\pi$
$857$	1.16144e9			1.84524			0.922620	+	0.385711i	$0.126044\pi$
$858$	−6.66859e8	+	2.57029e8i	−1.05578	+	0.406931i
$859$			5.85890e8i			0.924350i	0.886789	+	0.462175i	$0.152931\pi$
$859$			5.85890e8i			0.924350i	−0.886789	+	0.462175i	$0.847069\pi$
$860$	−3.20724e7	−	3.54249e7i	−0.0504239	−	0.0556946i
$861$	−7.34777e6			−0.0115119
$862$	−2.33695e8	−	6.06319e8i	−0.364861	−	0.946628i
$863$			2.08083e8i			0.323746i	0.986812	+	0.161873i	$0.0517535\pi$
$863$			2.08083e8i			0.323746i	−0.986812	+	0.161873i	$0.948246\pi$
$864$	1.19673e8	−	3.29442e7i	0.185548	−	0.0510784i
$865$	3.84819e7			0.0594577
$866$	−2.19697e8	+	8.46782e7i	−0.338275	+	0.130382i
$867$		−	3.58312e8i		−	0.549799i
$868$	−2.47127e8	+	2.23740e8i	−0.377886	+	0.342124i
$869$	−1.80674e9			−2.75319
$870$	1.43969e6	+	3.73526e6i	0.00218631	+	0.00567234i
$871$			2.38167e8i			0.360436i
$872$	−5.04119e8	+	9.99495e8i	−0.760297	+	1.50741i
$873$	−4.29307e7			−0.0645246
$874$	−3.39663e8	+	1.30917e8i	−0.508760	+	0.196093i
$875$		−	1.80089e8i		−	0.268821i
$876$	−3.31880e7	−	3.66571e7i	−0.0493707	−	0.0545313i
$877$	−3.00844e8			−0.446009			−0.223004	−	0.974817i	$-0.571586\pi$
$877$	−3.00844e8			−0.446009			−0.223004	+	0.974817i	$0.571586\pi$
$878$	3.21029e8	+	8.32906e8i	0.474308	+	1.23059i
$879$			4.58883e8i			0.675672i
$880$	1.48758e8	+	1.48137e7i	0.218290	+	0.0217378i
$881$	−9.89186e7			−0.144661			−0.0723303	−	0.997381i	$-0.523044\pi$
$881$	−9.89186e7			−0.144661			−0.0723303	+	0.997381i	$0.523044\pi$
$882$	−2.59556e7	+	1.00041e7i	−0.0378290	+	0.0145805i
$883$		−	7.02916e8i		−	1.02099i	−0.859881	−	0.510495i	$-0.829462\pi$
$883$		−	7.02916e8i		−	1.02099i	0.859881	−	0.510495i	$-0.170538\pi$
$884$	−9.26491e8	+	8.38812e8i	−1.34117	+	1.21425i
$885$	−6.80695e7			−0.0982025
$886$	3.50756e8	+	9.10034e8i	0.504318	+	1.30845i
$887$		−	4.96480e8i		−	0.711428i	−0.934595	−	0.355714i	$-0.884238\pi$
$887$		−	4.96480e8i		−	0.711428i	0.934595	−	0.355714i	$-0.115762\pi$
$888$	3.01133e8	+	1.51883e8i	0.430050	+	0.216906i
$889$	1.96688e8			0.279945
$890$	2.96706e7	−	1.14360e7i	0.0420877	−	0.0162220i
$891$			1.18957e8i			0.168173i
$892$	−9.45031e8	−	1.04381e9i	−1.33153	−	1.47071i
$893$	5.51836e8			0.774918
$894$	2.93863e8	+	7.62424e8i	0.411275	+	1.06705i
$895$			9.74185e7i			0.135885i
$896$	3.61751e8	−	5.68885e8i	0.502904	−	0.790862i
$897$	2.05074e8			0.284141
$898$	−1.02841e9	+	3.96382e8i	−1.42016	+	0.547374i
$899$		−	2.87091e7i		−	0.0395130i
$900$	1.76355e8	−	1.59666e8i	0.241914	−	0.219020i
$901$	4.47112e8			0.611282
$902$	−8.49876e6	−	2.20499e7i	−0.0115807	−	0.0300461i
$903$		−	2.06526e8i		−	0.280487i
$904$	2.72728e8	−	5.40727e8i	0.369169	−	0.731935i
$905$	−2.17787e7			−0.0293823
$906$	1.83683e8	−	7.07975e7i	0.246993	−	0.0951992i
$907$			7.37237e7i			0.0988064i	0.998779	+	0.0494032i	$0.0157319\pi$
$907$			7.37237e7i			0.0988064i	−0.998779	+	0.0494032i	$0.984268\pi$
$908$	−4.35701e8	−	4.81244e8i	−0.582011	−	0.642848i
$909$	−2.06176e8			−0.274502
$910$	−4.76679e7	−	1.23674e8i	−0.0632560	−	0.164117i
$911$		−	1.81266e8i		−	0.239751i	−0.992789	−	0.119876i	$-0.961750\pi$
$911$		−	1.81266e8i		−	0.239751i	0.992789	−	0.119876i	$-0.0382496\pi$
$912$	−6.22542e7	+	6.25155e8i	−0.0820700	+	0.824144i
$913$	1.34714e9			1.77011
$914$	8.25466e8	−	3.18161e8i	1.08109	−	0.416686i
$915$		−	8.61220e7i		−	0.112422i
$916$	6.99295e7	−	6.33117e7i	0.0909859	−	0.0823754i
$917$	−3.17293e8			−0.411484
$918$	7.48150e7	+	1.94107e8i	0.0967076	+	0.250907i
$919$			6.20059e8i			0.798889i	0.916757	+	0.399445i	$0.130797\pi$
$919$			6.20059e8i			0.798889i	−0.916757	+	0.399445i	$0.869203\pi$
$920$	−3.83009e7	−	1.93179e7i	−0.0491864	−	0.0248083i
$921$	−1.56663e8			−0.200533
$922$	−1.29059e8	+	4.97435e7i	−0.164663	+	0.0634664i
$923$		−	1.41848e9i		−	1.80392i
$924$	4.33629e8	+	4.78955e8i	0.549670	+	0.607126i
$925$	6.46400e8			0.816725
$926$	−2.01665e8	−	5.23218e8i	−0.253979	−	0.658945i
$927$			1.47750e8i			0.185476i
$928$	1.54094e7	+	5.59762e7i	0.0192815	+	0.0700421i
$929$	−9.42146e8			−1.17509			−0.587545	−	0.809191i	$-0.699906\pi$
$929$	−9.42146e8			−1.17509			−0.587545	+	0.809191i	$0.699906\pi$
$930$	3.41593e7	−	1.31661e7i	0.0424679	−	0.0163685i
$931$		−	1.40792e8i		−	0.174473i
$932$	8.73896e8	−	7.91194e8i	1.07947	−	0.977316i
$933$	2.21221e8			0.272383
$934$	−4.96476e7	−	1.28810e8i	−0.0609337	−	0.158092i
$935$			2.50543e8i			0.306512i
$936$	1.59387e8	−	3.16010e8i	0.194368	−	0.385366i
$937$	−4.97228e8			−0.604417			−0.302209	−	0.953242i	$-0.597724\pi$
$937$	−4.97228e8			−0.604417			−0.302209	+	0.953242i	$0.597724\pi$
$938$	2.00904e8	−	7.74348e7i	0.243433	−	0.0938270i
$939$			2.38951e8i			0.288611i
$940$	4.36452e7	+	4.82073e7i	0.0525476	+	0.0580403i
$941$	−1.04531e9			−1.25451			−0.627257	−	0.778812i	$-0.715823\pi$
$941$	−1.04531e9			−1.25451			−0.627257	+	0.778812i	$0.715823\pi$
$942$	−2.17011e8	−	5.63033e8i	−0.259615	−	0.673567i
$943$			6.78086e6i			0.00808630i
$944$	−9.82377e8	−	9.78271e7i	−1.16778	−	0.116290i
$945$	−2.20613e7			−0.0261419
$946$	6.19765e8	−	2.38878e8i	0.732072	−	0.282164i
$947$			8.35622e8i			0.983920i	0.870618	+	0.491960i	$0.163719\pi$
$947$			8.35622e8i			0.983920i	−0.870618	+	0.491960i	$0.836281\pi$
$948$	6.63291e8	−	6.00520e8i	0.778537	−	0.704859i
$949$	−1.40999e8			−0.164974
$950$	4.33041e8	+	1.12352e9i	0.505078	+	1.31042i
$951$			2.06344e8i			0.239912i
$952$	1.00880e9	+	5.08812e8i	1.16921	+	0.589721i
$953$	1.06225e9			1.22730			0.613648	−	0.789580i	$-0.289701\pi$
$953$	1.06225e9			1.22730			0.613648	+	0.789580i	$0.289701\pi$
$954$	−1.18146e8	+	4.55372e7i	−0.136073	+	0.0524471i
$955$			8.89300e7i			0.102103i
$956$	−6.79919e8	−	7.50990e8i	−0.778187	−	0.859529i
$957$	−5.56409e7			−0.0634831
$958$	−2.50802e8	−	6.50704e8i	−0.285256	−	0.740094i
$959$			3.90810e8i			0.443108i
$960$	−5.95361e7	+	4.40056e7i	−0.0672925	+	0.0497387i
$961$	6.24956e8			0.704173
$962$	8.97339e8	−	3.45864e8i	1.00793	−	0.388490i
$963$		−	7.11518e7i		−	0.0796722i
$964$	−8.66251e8	+	7.84273e8i	−0.966970	+	0.875459i
$965$	−1.07848e8			−0.120014
$966$	−6.66754e7	−	1.72989e8i	−0.0739664	−	0.191905i
$967$			1.11583e9i			1.23401i	0.786960	+	0.617004i	$0.211654\pi$
$967$			1.11583e9i			1.23401i	−0.786960	+	0.617004i	$0.788346\pi$
$968$	−5.27273e8	+	1.04540e9i	−0.581312	+	1.15254i
$969$	−1.05290e9			−1.15722
$970$	2.38926e7	−	9.20899e6i	0.0261787	−	0.0100901i
$971$		−	4.61565e8i		−	0.504168i	−0.967705	−	0.252084i	$-0.918884\pi$
$971$		−	4.61565e8i		−	0.504168i	0.967705	−	0.252084i	$-0.0811159\pi$
$972$	−3.95386e7	−	4.36715e7i	−0.0430549	−	0.0475553i
$973$	−7.54777e8			−0.819370
$974$	−4.45737e8	−	1.15646e9i	−0.482393	−	1.25156i
$975$		−	6.78336e8i		−	0.731865i
$976$	1.23772e8	−	1.24291e9i	0.133129	−	1.33687i
$977$	−5.80566e8			−0.622541			−0.311270	−	0.950321i	$-0.600754\pi$
$977$	−5.80566e8			−0.622541			−0.311270	+	0.950321i	$0.600754\pi$
$978$	−3.19930e8	+	1.23312e8i	−0.342010	+	0.131822i
$979$			4.41977e8i			0.471033i
$980$	1.22993e7	−	1.11354e7i	0.0130678	−	0.0118311i
$981$	5.31292e8			0.562764
$982$	−5.00272e8	−	1.29795e9i	−0.528289	−	1.37064i
$983$			1.18156e9i			1.24393i	0.783044	+	0.621966i	$0.213666\pi$
$983$			1.18156e9i			1.24393i	−0.783044	+	0.621966i	$0.786334\pi$
$984$	1.04490e7	+	5.27020e6i	0.0109670	+	0.00553148i
$985$	−9.58798e7			−0.100327
$986$	−9.07917e7	+	3.49941e7i	−0.0947143	+	0.0365060i
$987$			2.81048e8i			0.292300i
$988$	1.20230e9	+	1.32798e9i	1.24665	+	1.37696i
$989$	−1.90592e8			−0.197023
$990$	−2.55172e7	−	6.62040e7i	−0.0262982	−	0.0682305i
$991$			1.27879e9i			1.31395i	0.753911	+	0.656976i	$0.228165\pi$
$991$			1.27879e9i			1.31395i	−0.753911	+	0.656976i	$0.771835\pi$
$992$	5.11908e8	−	1.40920e8i	0.524393	−	0.144357i
$993$	5.22538e8			0.533667
$994$	−1.19655e9	+	4.61188e8i	−1.21834	+	0.469590i
$995$		−	7.25952e6i		−	0.00736951i
$996$	−4.94564e8	+	4.47761e8i	−0.500547	+	0.453177i
$997$	5.57320e8			0.562366			0.281183	−	0.959654i	$-0.409273\pi$
$997$	5.57320e8			0.562366			0.281183	+	0.959654i	$0.409273\pi$
$998$	−4.69490e7	−	1.21809e8i	−0.0472319	−	0.122543i
$999$		−	1.60070e8i		−	0.160551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.7.d.a.7.5	✓	6
3.2	odd	2		36.7.d.e.19.2		6
4.3	odd	2	inner	12.7.d.a.7.6	yes	6
8.3	odd	2		192.7.g.e.127.2		6
8.5	even	2		192.7.g.e.127.5		6
12.11	even	2		36.7.d.e.19.1		6
16.3	odd	4		768.7.b.h.127.3		12
16.5	even	4		768.7.b.h.127.4		12
16.11	odd	4		768.7.b.h.127.10		12
16.13	even	4		768.7.b.h.127.9		12
24.5	odd	2		576.7.g.p.127.4		6
24.11	even	2		576.7.g.p.127.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.7.d.a.7.5	✓	6	1.1	even	1	trivial
12.7.d.a.7.6	yes	6	4.3	odd	2	inner
36.7.d.e.19.1		6	12.11	even	2
36.7.d.e.19.2		6	3.2	odd	2
192.7.g.e.127.2		6	8.3	odd	2
192.7.g.e.127.5		6	8.5	even	2
576.7.g.p.127.3		6	24.11	even	2
576.7.g.p.127.4		6	24.5	odd	2
768.7.b.h.127.3		12	16.3	odd	4
768.7.b.h.127.4		12	16.5	even	4
768.7.b.h.127.9		12	16.13	even	4
768.7.b.h.127.10		12	16.11	odd	4

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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(7.46472 - 2.87714i) q^{2} -15.5885i q^{3} +(47.4441 - 42.9542i) q^{4} +18.1171 q^{5} +(-44.8502 - 116.363i) q^{6} +321.465i q^{7} +(230.571 - 457.144i) q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+(7.46472 - 2.87714i) q^{2} -15.5885i q^{3} +(47.4441 - 42.9542i) q^{4} +18.1171 q^{5} +(-44.8502 - 116.363i) q^{6} +321.465i q^{7} +(230.571 - 457.144i) q^{8} -243.000 q^{9} +(135.239 - 52.1255i) q^{10} +2014.54i q^{11} +(-669.589 - 739.580i) q^{12} -2844.73 q^{13} +(924.902 + 2399.65i) q^{14} -282.418i q^{15} +(405.881 - 4075.84i) q^{16} +6864.64 q^{17} +(-1813.93 + 699.146i) q^{18} -9839.37i q^{19} +(859.549 - 778.205i) q^{20} +5011.15 q^{21} +(5796.12 + 15038.0i) q^{22} -4624.52i q^{23} +(-7126.17 - 3594.25i) q^{24} -15296.8 q^{25} +(-21235.1 + 8184.71i) q^{26} +3788.00i q^{27} +(13808.3 + 15251.6i) q^{28} -1771.80 q^{29} +(-812.556 - 2108.17i) q^{30} +16203.3i q^{31} +(-8697.00 - 31592.8i) q^{32} +31403.6 q^{33} +(51242.6 - 19750.6i) q^{34} +5824.02i q^{35} +(-11528.9 + 10437.9i) q^{36} -42257.3 q^{37} +(-28309.3 - 73448.2i) q^{38} +44345.0i q^{39} +(4177.28 - 8282.12i) q^{40} -1466.28 q^{41} +(37406.8 - 14417.8i) q^{42} -41213.4i q^{43} +(86532.8 + 95578.0i) q^{44} -4402.45 q^{45} +(-13305.4 - 34520.7i) q^{46} +56084.5i q^{47} +(-63536.1 - 6327.05i) q^{48} +14309.1 q^{49} +(-114186. + 44011.0i) q^{50} -107009. i q^{51} +(-134966. + 122193. i) q^{52} +65132.6 q^{53} +(10898.6 + 28276.3i) q^{54} +36497.6i q^{55} +(146956. + 74120.7i) q^{56} -153381. q^{57} +(-13226.0 + 5097.73i) q^{58} -241024. i q^{59} +(-12131.0 - 13399.0i) q^{60} +304946. q^{61} +(46619.3 + 120953. i) q^{62} -78116.1i q^{63} +(-155818. - 210809. i) q^{64} -51538.3 q^{65} +(234419. - 90352.6i) q^{66} -83722.2i q^{67} +(325686. - 294865. i) q^{68} -72089.1 q^{69} +(16756.5 + 43474.7i) q^{70} +498634. i q^{71} +(-56028.8 + 111086. i) q^{72} +49564.8 q^{73} +(-315439. + 121580. i) q^{74} +238453. i q^{75} +(-422642. - 466820. i) q^{76} -647605. q^{77} +(127587. + 331023. i) q^{78} +896848. i q^{79} +(7353.38 - 73842.4i) q^{80} +59049.0 q^{81} +(-10945.4 + 4218.71i) q^{82} -668710. i q^{83} +(237749. - 215250. i) q^{84} +124367. q^{85} +(-118577. - 307646. i) q^{86} +27619.7i q^{87} +(920935. + 464495. i) q^{88} +219393. q^{89} +(-32863.1 + 12666.5i) q^{90} -914483. i q^{91} +(-198642. - 219406. i) q^{92} +252585. q^{93} +(161363. + 418655. i) q^{94} -178261. i q^{95} +(-492483. + 135573. i) q^{96} +176670. q^{97} +(106813. - 41169.2i) q^{98} -489533. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{2} + 156 q^{4} - 44 q^{5} - 162 q^{6} + 1136 q^{8} - 1458 q^{9}+O(q^{10}) \) 6 * q - 10 * q^2 + 156 * q^4 - 44 * q^5 - 162 * q^6 + 1136 * q^8 - 1458 * q^9	\( 6 q - 10 q^{2} + 156 q^{4} - 44 q^{5} - 162 q^{6} + 1136 q^{8} - 1458 q^{9} + 84 q^{10} - 972 q^{12} - 3348 q^{13} + 4776 q^{14} - 9744 q^{16} + 12220 q^{17} + 2430 q^{18} + 17608 q^{20} - 9720 q^{21} - 13512 q^{22} - 7776 q^{24} + 56418 q^{25} - 59252 q^{26} - 17808 q^{28} - 84860 q^{29} + 57348 q^{30} + 61280 q^{32} + 4536 q^{33} + 109404 q^{34} - 37908 q^{36} + 20796 q^{37} - 128088 q^{38} - 195552 q^{40} - 65252 q^{41} + 210600 q^{42} + 445008 q^{44} + 10692 q^{45} + 81120 q^{46} - 276048 q^{48} - 111546 q^{49} - 743118 q^{50} - 179592 q^{52} + 470308 q^{53} + 39366 q^{54} + 793728 q^{56} - 204120 q^{57} + 529860 q^{58} - 723816 q^{60} + 12924 q^{61} - 513384 q^{62} - 642432 q^{64} + 321512 q^{65} + 771768 q^{66} + 690328 q^{68} + 541728 q^{69} + 938928 q^{70} - 276048 q^{72} - 1283412 q^{73} - 1522916 q^{74} + 67824 q^{76} - 1487328 q^{77} + 396252 q^{78} + 1272352 q^{80} + 354294 q^{81} + 240444 q^{82} - 143856 q^{84} + 814920 q^{85} - 1154568 q^{86} + 489600 q^{88} + 730924 q^{89} - 20412 q^{90} - 1338816 q^{92} - 83592 q^{93} - 390288 q^{94} + 624672 q^{96} + 3249420 q^{97} + 1604918 q^{98}+O(q^{100}) \) 6 * q - 10 * q^2 + 156 * q^4 - 44 * q^5 - 162 * q^6 + 1136 * q^8 - 1458 * q^9 + 84 * q^10 - 972 * q^12 - 3348 * q^13 + 4776 * q^14 - 9744 * q^16 + 12220 * q^17 + 2430 * q^18 + 17608 * q^20 - 9720 * q^21 - 13512 * q^22 - 7776 * q^24 + 56418 * q^25 - 59252 * q^26 - 17808 * q^28 - 84860 * q^29 + 57348 * q^30 + 61280 * q^32 + 4536 * q^33 + 109404 * q^34 - 37908 * q^36 + 20796 * q^37 - 128088 * q^38 - 195552 * q^40 - 65252 * q^41 + 210600 * q^42 + 445008 * q^44 + 10692 * q^45 + 81120 * q^46 - 276048 * q^48 - 111546 * q^49 - 743118 * q^50 - 179592 * q^52 + 470308 * q^53 + 39366 * q^54 + 793728 * q^56 - 204120 * q^57 + 529860 * q^58 - 723816 * q^60 + 12924 * q^61 - 513384 * q^62 - 642432 * q^64 + 321512 * q^65 + 771768 * q^66 + 690328 * q^68 + 541728 * q^69 + 938928 * q^70 - 276048 * q^72 - 1283412 * q^73 - 1522916 * q^74 + 67824 * q^76 - 1487328 * q^77 + 396252 * q^78 + 1272352 * q^80 + 354294 * q^81 + 240444 * q^82 - 143856 * q^84 + 814920 * q^85 - 1154568 * q^86 + 489600 * q^88 + 730924 * q^89 - 20412 * q^90 - 1338816 * q^92 - 83592 * q^93 - 390288 * q^94 + 624672 * q^96 + 3249420 * q^97 + 1604918 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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