LMFDB - Embedded newform 43.10.c.a.36.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,10,Mod(6,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	43.c (of order $3$, degree $2$, 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:	$22.1465409550$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			36.7
Character	$\chi$	$=$	43.36
Dual form			43.10.c.a.6.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-30.5461 q^{2} +(46.1090 + 79.8632i) q^{3} +421.064 q^{4} +(286.168 + 495.658i) q^{5} +(-1408.45 - 2439.51i) q^{6} +(319.069 - 552.644i) q^{7} +2777.74 q^{8} +(5589.41 - 9681.15i) q^{9} +O(q^{10})$	\(q-30.5461 q^{2} +(46.1090 + 79.8632i) q^{3} +421.064 q^{4} +(286.168 + 495.658i) q^{5} +(-1408.45 - 2439.51i) q^{6} +(319.069 - 552.644i) q^{7} +2777.74 q^{8} +(5589.41 - 9681.15i) q^{9} +(-8741.33 - 15140.4i) q^{10} -50651.5 q^{11} +(19414.9 + 33627.5i) q^{12} +(20548.3 - 35590.7i) q^{13} +(-9746.32 + 16881.1i) q^{14} +(-26389.9 + 45708.7i) q^{15} -300434. q^{16} +(-250127. + 433233. i) q^{17} +(-170735. + 295721. i) q^{18} +(-5441.33 - 9424.65i) q^{19} +(120495. + 208704. i) q^{20} +58847.9 q^{21} +1.54721e6 q^{22} +(-992007. - 1.71821e6i) q^{23} +(128079. + 221839. i) q^{24} +(812778. - 1.40777e6i) q^{25} +(-627670. + 1.08716e6i) q^{26} +2.84602e6 q^{27} +(134349. - 232698. i) q^{28} +(2.72855e6 - 4.72599e6i) q^{29} +(806108. - 1.39622e6i) q^{30} +(2.35401e6 + 4.07727e6i) q^{31} +7.75488e6 q^{32} +(-2.33549e6 - 4.04519e6i) q^{33} +(7.64041e6 - 1.32336e7i) q^{34} +365230. q^{35} +(2.35350e6 - 4.07638e6i) q^{36} +(-6.16797e6 - 1.06832e7i) q^{37} +(166211. + 287886. i) q^{38} +3.78985e6 q^{39} +(794901. + 1.37681e6i) q^{40} +2.38216e7 q^{41} -1.79757e6 q^{42} +(-3.06703e6 - 2.22078e7i) q^{43} -2.13275e7 q^{44} +6.39805e6 q^{45} +(3.03020e7 + 5.24845e7i) q^{46} +2.78757e6 q^{47} +(-1.38527e7 - 2.39936e7i) q^{48} +(1.99732e7 + 3.45946e7i) q^{49} +(-2.48272e7 + 4.30020e7i) q^{50} -4.61325e7 q^{51} +(8.65214e6 - 1.49860e7i) q^{52} +(1.50558e7 + 2.60774e7i) q^{53} -8.69348e7 q^{54} +(-1.44949e7 - 2.51058e7i) q^{55} +(886291. - 1.53510e6i) q^{56} +(501789. - 869124. i) q^{57} +(-8.33466e7 + 1.44361e8i) q^{58} +1.06329e7 q^{59} +(-1.11118e7 + 1.92463e7i) q^{60} +(6.27945e7 - 1.08763e8i) q^{61} +(-7.19058e7 - 1.24545e8i) q^{62} +(-3.56682e6 - 6.17791e6i) q^{63} -8.30591e7 q^{64} +2.35211e7 q^{65} +(7.13402e7 + 1.23565e8i) q^{66} +(-1.86972e7 - 3.23845e7i) q^{67} +(-1.05320e8 + 1.82419e8i) q^{68} +(9.14810e7 - 1.58450e8i) q^{69} -1.11564e7 q^{70} +(-6.97508e7 + 1.20812e8i) q^{71} +(1.55259e7 - 2.68917e7i) q^{72} +(1.12564e8 - 1.94967e8i) q^{73} +(1.88408e8 + 3.26331e8i) q^{74} +1.49906e8 q^{75} +(-2.29115e6 - 3.96838e6i) q^{76} +(-1.61613e7 + 2.79923e7i) q^{77} -1.15765e8 q^{78} +(2.61884e8 - 4.53596e8i) q^{79} +(-8.59747e7 - 1.48913e8i) q^{80} +(2.12108e7 + 3.67381e7i) q^{81} -7.27657e8 q^{82} +(1.64704e8 + 2.85275e8i) q^{83} +2.47787e7 q^{84} -2.86314e8 q^{85} +(9.36859e7 + 6.78361e8i) q^{86} +5.03244e8 q^{87} -1.40697e8 q^{88} +(-2.96909e7 - 5.14262e7i) q^{89} -1.95436e8 q^{90} +(-1.31126e7 - 2.27118e7i) q^{91} +(-4.17699e8 - 7.23475e8i) q^{92} +(-2.17082e8 + 3.75998e8i) q^{93} -8.51495e7 q^{94} +(3.11427e6 - 5.39408e6i) q^{95} +(3.57570e8 + 6.19329e8i) q^{96} +7.07290e8 q^{97} +(-6.10103e8 - 1.05673e9i) q^{98} +(-2.83112e8 + 4.90365e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) $ 64 * q - 70 * q^2 + 307 * q^3 + 16038 * q^4 + 681 * q^5 - 1281 * q^6 + 957 * q^7 - 10920 * q^8 - 255339 * q^9	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9} - 6237 q^{10} - 180682 q^{11} + 274344 q^{12} + 115245 q^{13} - 171208 q^{14} + 138833 q^{15} + 4289206 q^{16} + 65180 q^{17} + 603985 q^{18} + 39150 q^{19} - 2709775 q^{20} - 3105162 q^{21} + 598456 q^{22} + 1285907 q^{23} - 292550 q^{24} - 14709917 q^{25} + 5332695 q^{26} - 20118002 q^{27} - 5475298 q^{28} + 1274091 q^{29} + 28424751 q^{30} + 2899781 q^{31} - 16322030 q^{32} + 30668912 q^{33} + 6822099 q^{34} - 14750922 q^{35} - 113819232 q^{36} - 13772217 q^{37} + 2700532 q^{38} + 49876982 q^{39} - 55802359 q^{40} + 5375394 q^{41} - 62768266 q^{42} - 4250879 q^{43} - 125171958 q^{44} + 74719384 q^{45} - 91405220 q^{46} + 46104596 q^{47} + 294588191 q^{48} - 233221733 q^{49} + 380339342 q^{50} + 229598406 q^{51} + 166281612 q^{52} + 125396641 q^{53} - 137752484 q^{54} + 139471854 q^{55} + 41104589 q^{56} - 289586721 q^{57} - 183782516 q^{58} - 637949078 q^{59} - 70735747 q^{60} - 95573327 q^{61} + 181277053 q^{62} + 226632970 q^{63} + 712599660 q^{64} - 498753718 q^{65} - 349240445 q^{66} - 276270786 q^{67} + 1034771928 q^{68} - 199705103 q^{69} + 1780847990 q^{70} + 651945247 q^{71} - 270063054 q^{72} - 182725322 q^{73} - 193737672 q^{74} - 3155252572 q^{75} + 492133584 q^{76} + 216024528 q^{77} + 2562586420 q^{78} - 376932221 q^{79} - 783129021 q^{80} - 2146956496 q^{81} + 2373824428 q^{82} + 1008544071 q^{83} - 9413139208 q^{84} - 1131353054 q^{85} - 1641459050 q^{86} + 5060470018 q^{87} + 369936980 q^{88} + 2244184366 q^{89} + 3302428348 q^{90} + 3951711 q^{91} + 4361095637 q^{92} + 3133616089 q^{93} + 3002217406 q^{94} + 1515822931 q^{95} + 69408612 q^{96} - 6951085934 q^{97} + 1120193981 q^{98} + 1264470179 q^{99}+O(q^{100}) \) 64 * q - 70 * q^2 + 307 * q^3 + 16038 * q^4 + 681 * q^5 - 1281 * q^6 + 957 * q^7 - 10920 * q^8 - 255339 * q^9 - 6237 * q^10 - 180682 * q^11 + 274344 * q^12 + 115245 * q^13 - 171208 * q^14 + 138833 * q^15 + 4289206 * q^16 + 65180 * q^17 + 603985 * q^18 + 39150 * q^19 - 2709775 * q^20 - 3105162 * q^21 + 598456 * q^22 + 1285907 * q^23 - 292550 * q^24 - 14709917 * q^25 + 5332695 * q^26 - 20118002 * q^27 - 5475298 * q^28 + 1274091 * q^29 + 28424751 * q^30 + 2899781 * q^31 - 16322030 * q^32 + 30668912 * q^33 + 6822099 * q^34 - 14750922 * q^35 - 113819232 * q^36 - 13772217 * q^37 + 2700532 * q^38 + 49876982 * q^39 - 55802359 * q^40 + 5375394 * q^41 - 62768266 * q^42 - 4250879 * q^43 - 125171958 * q^44 + 74719384 * q^45 - 91405220 * q^46 + 46104596 * q^47 + 294588191 * q^48 - 233221733 * q^49 + 380339342 * q^50 + 229598406 * q^51 + 166281612 * q^52 + 125396641 * q^53 - 137752484 * q^54 + 139471854 * q^55 + 41104589 * q^56 - 289586721 * q^57 - 183782516 * q^58 - 637949078 * q^59 - 70735747 * q^60 - 95573327 * q^61 + 181277053 * q^62 + 226632970 * q^63 + 712599660 * q^64 - 498753718 * q^65 - 349240445 * q^66 - 276270786 * q^67 + 1034771928 * q^68 - 199705103 * q^69 + 1780847990 * q^70 + 651945247 * q^71 - 270063054 * q^72 - 182725322 * q^73 - 193737672 * q^74 - 3155252572 * q^75 + 492133584 * q^76 + 216024528 * q^77 + 2562586420 * q^78 - 376932221 * q^79 - 783129021 * q^80 - 2146956496 * q^81 + 2373824428 * q^82 + 1008544071 * q^83 - 9413139208 * q^84 - 1131353054 * q^85 - 1641459050 * q^86 + 5060470018 * q^87 + 369936980 * q^88 + 2244184366 * q^89 + 3302428348 * q^90 + 3951711 * q^91 + 4361095637 * q^92 + 3133616089 * q^93 + 3002217406 * q^94 + 1515822931 * q^95 + 69408612 * q^96 - 6951085934 * q^97 + 1120193981 * q^98 + 1264470179 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−30.5461			−1.34996			−0.674980	−	0.737836i	$-0.735848\pi$
$2$	−30.5461			−1.34996			−0.674980	+	0.737836i	$0.735848\pi$
$3$	46.1090	+	79.8632i	0.328655	+	0.569247i	0.982245	−	0.187601i	$-0.0600713\pi$
$3$	46.1090	+	79.8632i	0.328655	+	0.569247i	−0.653590	+	0.756849i	$0.726738\pi$
$4$	421.064			0.822391
$5$	286.168	+	495.658i	0.204765	+	0.354664i	0.950058	−	0.312073i	$-0.101024\pi$
$5$	286.168	+	495.658i	0.204765	+	0.354664i	−0.745293	+	0.666738i	$0.767690\pi$
$6$	−1408.45	−	2439.51i	−0.443671	−	0.768461i
$7$	319.069	−	552.644i	0.0502277	−	0.0869970i	−0.839818	−	0.542867i	$-0.817339\pi$
$7$	319.069	−	552.644i	0.0502277	−	0.0869970i	0.890046	+	0.455870i	$0.150672\pi$
$8$	2777.74			0.239765
$9$	5589.41	−	9681.15i	0.283972	−	0.491853i
$10$	−8741.33	−	15140.4i	−0.276425	−	0.478782i
$11$	−50651.5			−1.04310			−0.521549	−	0.853221i	$-0.674646\pi$
$11$	−50651.5			−1.04310			−0.521549	+	0.853221i	$0.674646\pi$
$12$	19414.9	+	33627.5i	0.270283	+	0.468144i
$13$	20548.3	−	35590.7i	0.199540	−	0.345614i	−0.748839	−	0.662752i	$-0.769388\pi$
$13$	20548.3	−	35590.7i	0.199540	−	0.345614i	0.948379	+	0.317138i	$0.102722\pi$
$14$	−9746.32	+	16881.1i	−0.0678054	+	0.117442i
$15$	−26389.9	+	45708.7i	−0.134594	+	0.233124i
$16$	−300434.			−1.14606
$17$	−250127.	+	433233.i	−0.726341	+	1.25806i	0.232078	+	0.972697i	$0.425447\pi$
$17$	−250127.	+	433233.i	−0.726341	+	1.25806i	−0.958420	+	0.285363i	$0.907886\pi$
$18$	−170735.	+	295721.i	−0.383350	+	0.663982i
$19$	−5441.33	−	9424.65i	−0.00957886	−	0.0165911i	0.861196	−	0.508273i	$-0.169716\pi$
$19$	−5441.33	−	9424.65i	−0.00957886	−	0.0165911i	−0.870775	+	0.491682i	$0.836382\pi$
$20$	120495.	+	208704.i	0.168397	+	0.291672i
$21$	58847.9			0.0660304
$22$	1.54721e6			1.40814
$23$	−992007.	−	1.71821e6i	−0.739162	−	1.28027i	−0.952873	−	0.303369i	$-0.901888\pi$
$23$	−992007.	−	1.71821e6i	−0.739162	−	1.28027i	0.213711	−	0.976897i	$-0.431445\pi$
$24$	128079.	+	221839.i	0.0788002	+	0.136486i
$25$	812778.	−	1.40777e6i	0.416142	−	0.720779i
$26$	−627670.	+	1.08716e6i	−0.269371	+	0.466565i
$27$	2.84602e6			1.03063
$28$	134349.	−	232698.i	0.0413068	−	0.0715455i
$29$	2.72855e6	−	4.72599e6i	0.716376	−	1.24080i	−0.246050	−	0.969257i	$-0.579133\pi$
$29$	2.72855e6	−	4.72599e6i	0.716376	−	1.24080i	0.962426	−	0.271543i	$-0.0875340\pi$
$30$	806108.	−	1.39622e6i	0.181697	−	0.314709i
$31$	2.35401e6	+	4.07727e6i	0.457805	+	0.792942i	0.998845	−	0.0480552i	$-0.0153023\pi$
$31$	2.35401e6	+	4.07727e6i	0.457805	+	0.792942i	−0.541039	+	0.840997i	$0.681969\pi$
$32$	7.75488e6			1.30737
$33$	−2.33549e6	−	4.04519e6i	−0.342820	−	0.593781i
$34$	7.64041e6	−	1.32336e7i	0.980531	−	1.69833i
$35$	365230.			0.0411396
$36$	2.35350e6	−	4.07638e6i	0.233536	−	0.404495i
$37$	−6.16797e6	−	1.06832e7i	−0.541047	−	0.937120i	−0.998844	−	0.0480640i	$-0.984695\pi$
$37$	−6.16797e6	−	1.06832e7i	−0.541047	−	0.937120i	0.457798	−	0.889056i	$-0.348638\pi$
$38$	166211.	+	287886.i	0.0129311	+	0.0223973i
$39$	3.78985e6			0.262320
$40$	794901.	+	1.37681e6i	0.0490957	+	0.0850362i
$41$	2.38216e7			1.31657			0.658285	−	0.752769i	$-0.271282\pi$
$41$	2.38216e7			1.31657			0.658285	+	0.752769i	$0.271282\pi$
$42$	−1.79757e6			−0.0891384
$43$	−3.06703e6	−	2.22078e7i	−0.136808	−	0.990598i
$43$	−3.06703e6	−	2.22078e7i	−0.136808	−	0.990598i
$44$	−2.13275e7			−0.857835
$45$	6.39805e6			0.232590
$46$	3.03020e7	+	5.24845e7i	0.997839	+	1.72831i
$47$	2.78757e6			0.0833271			0.0416635	−	0.999132i	$-0.486734\pi$
$47$	2.78757e6			0.0833271			0.0416635	+	0.999132i	$0.486734\pi$
$48$	−1.38527e7	−	2.39936e7i	−0.376660	−	0.652394i
$49$	1.99732e7	+	3.45946e7i	0.494954	+	0.857286i
$50$	−2.48272e7	+	4.30020e7i	−0.561775	+	0.973023i
$51$	−4.61325e7			−0.954863
$52$	8.65214e6	−	1.49860e7i	0.164100	−	0.284230i
$53$	1.50558e7	+	2.60774e7i	0.262097	+	0.453966i	0.966799	−	0.255538i	$-0.0822525\pi$
$53$	1.50558e7	+	2.60774e7i	0.262097	+	0.453966i	−0.704702	+	0.709504i	$0.748919\pi$
$54$	−8.69348e7			−1.39130
$55$	−1.44949e7	−	2.51058e7i	−0.213591	−	0.369950i
$56$	886291.	−	1.53510e6i	0.0120429	−	0.0208589i
$57$	501789.	−	869124.i	0.00629628	−	0.0109055i
$58$	−8.33466e7	+	1.44361e8i	−0.967079	+	1.67503i
$59$	1.06329e7			0.114240			0.0571199	−	0.998367i	$-0.481808\pi$
$59$	1.06329e7			0.114240			0.0571199	+	0.998367i	$0.481808\pi$
$60$	−1.11118e7	+	1.92463e7i	−0.110689	+	0.191719i
$61$	6.27945e7	−	1.08763e8i	0.580680	−	1.00577i	−0.414718	−	0.909950i	$-0.636120\pi$
$61$	6.27945e7	−	1.08763e8i	0.580680	−	1.00577i	0.995399	−	0.0958182i	$-0.0305467\pi$
$62$	−7.19058e7	−	1.24545e8i	−0.618019	−	1.07044i
$63$	−3.56682e6	−	6.17791e6i	−0.0285265	−	0.0494093i
$64$	−8.30591e7			−0.618839
$65$	2.35211e7			0.163436
$66$	7.13402e7	+	1.23565e8i	0.462793	+	0.801581i
$67$	−1.86972e7	−	3.23845e7i	−0.113355	−	0.196336i	0.803766	−	0.594945i	$-0.202826\pi$
$67$	−1.86972e7	−	3.23845e7i	−0.113355	−	0.196336i	−0.917121	+	0.398609i	$0.869493\pi$
$68$	−1.05320e8	+	1.82419e8i	−0.597336	+	1.03462i
$69$	9.14810e7	−	1.58450e8i	0.485859	−	0.841532i
$70$	−1.11564e7			−0.0555368
$71$	−6.97508e7	+	1.20812e8i	−0.325751	+	0.564218i	−0.981664	−	0.190619i	$-0.938951\pi$
$71$	−6.97508e7	+	1.20812e8i	−0.325751	+	0.564218i	0.655913	+	0.754837i	$0.272284\pi$
$72$	1.55259e7	−	2.68917e7i	0.0680866	−	0.117929i
$73$	1.12564e8	−	1.94967e8i	0.463926	−	0.803543i	−0.535227	−	0.844708i	$-0.679774\pi$
$73$	1.12564e8	−	1.94967e8i	0.463926	−	0.803543i	0.999152	+	0.0411658i	$0.0131072\pi$
$74$	1.88408e8	+	3.26331e8i	0.730391	+	1.26507i
$75$	1.49906e8			0.547069
$76$	−2.29115e6	−	3.96838e6i	−0.00787756	−	0.0136443i
$77$	−1.61613e7	+	2.79923e7i	−0.0523925	+	0.0907464i
$78$	−1.15765e8			−0.354121
$79$	2.61884e8	−	4.53596e8i	0.756461	−	1.31023i	−0.188183	−	0.982134i	$-0.560260\pi$
$79$	2.61884e8	−	4.53596e8i	0.756461	−	1.31023i	0.944645	−	0.328095i	$-0.106407\pi$
$80$	−8.59747e7	−	1.48913e8i	−0.234674	−	0.406468i
$81$	2.12108e7	+	3.67381e7i	0.0547487	+	0.0948275i
$82$	−7.27657e8			−1.77732
$83$	1.64704e8	+	2.85275e8i	0.380936	+	0.659800i	0.991196	−	0.132401i	$-0.0422686\pi$
$83$	1.64704e8	+	2.85275e8i	0.380936	+	0.659800i	−0.610261	+	0.792201i	$0.708935\pi$
$84$	2.47787e7			0.0543028
$85$	−2.86314e8			−0.594918
$86$	9.36859e7	+	6.78361e8i	0.184685	+	1.33727i
$87$	5.03244e8			0.941763
$88$	−1.40697e8			−0.250099
$89$	−2.96909e7	−	5.14262e7i	−0.0501613	−	0.0868819i	0.839855	−	0.542812i	$-0.182640\pi$
$89$	−2.96909e7	−	5.14262e7i	−0.0501613	−	0.0868819i	−0.890016	+	0.455930i	$0.849307\pi$
$90$	−1.95436e8			−0.313987
$91$	−1.31126e7	−	2.27118e7i	−0.0200449	−	0.0347188i
$92$	−4.17699e8	−	7.23475e8i	−0.607880	−	1.05288i
$93$	−2.17082e8	+	3.75998e8i	−0.300920	+	0.521209i
$94$	−8.51495e7			−0.112488
$95$	3.11427e6	−	5.39408e6i	0.00392284	−	0.00679455i
$96$	3.57570e8	+	6.19329e8i	0.429675	+	0.744220i
$97$	7.07290e8			0.811194			0.405597	−	0.914052i	$-0.367064\pi$
$97$	7.07290e8			0.811194			0.405597	+	0.914052i	$0.367064\pi$
$98$	−6.10103e8	−	1.05673e9i	−0.668168	−	1.15730i
$99$	−2.83112e8	+	4.90365e8i	−0.296210	+	0.513051i
$100$	3.42231e8	−	5.92762e8i	0.342231	−	0.592762i
$101$	−4.70407e8	+	8.14769e8i	−0.449808	+	0.779091i	−0.998373	−	0.0570172i	$-0.981841\pi$
$101$	−4.70407e8	+	8.14769e8i	−0.449808	+	0.779091i	0.548565	+	0.836108i	$0.315174\pi$
$102$	1.40917e9			1.28903
$103$	5.67113e8	−	9.82268e8i	0.496480	−	0.859929i	−0.503512	−	0.863988i	$-0.667959\pi$
$103$	5.67113e8	−	9.82268e8i	0.496480	−	0.859929i	0.999992	+	0.00405982i	$0.00129228\pi$
$104$	5.70778e7	−	9.88616e7i	0.0478429	−	0.0828663i
$105$	1.68404e7	+	2.91684e7i	0.0135207	+	0.0234186i
$106$	−4.59896e8	−	7.96563e8i	−0.353821	−	0.612836i
$107$	4.41182e8			0.325380			0.162690	−	0.986677i	$-0.447983\pi$
$107$	4.41182e8			0.325380			0.162690	+	0.986677i	$0.447983\pi$
$108$	1.19836e9			0.847576
$109$	−8.98069e8	−	1.55550e9i	−0.609383	−	1.05548i	−0.991342	−	0.131304i	$-0.958084\pi$
$109$	−8.98069e8	−	1.55550e9i	−0.609383	−	1.05548i	0.381959	−	0.924179i	$-0.375250\pi$
$110$	4.42762e8	+	7.66885e8i	0.288339	+	0.499417i
$111$	5.68799e8	−	9.85188e8i	0.355636	−	0.615979i
$112$	−9.58592e7	+	1.66033e8i	−0.0575642	+	0.0997041i
$113$	1.32706e9			0.765663			0.382831	−	0.923818i	$-0.374949\pi$
$113$	1.32706e9			0.765663			0.382831	+	0.923818i	$0.374949\pi$
$114$	−1.53277e7	+	2.65483e7i	−0.00849972	+	0.0147220i
$115$	5.67762e8	−	9.83393e8i	0.302710	−	0.524309i
$116$	1.14890e9	−	1.98994e9i	0.589141	−	1.02042i
$117$	−2.29706e8	−	3.97862e8i	−0.113328	−	0.196289i
$118$	−3.24794e8			−0.154219
$119$	1.59616e8	+	2.76462e8i	0.0729649	+	0.126379i
$120$	−7.33043e7	+	1.26967e8i	−0.0322711	+	0.0558952i
$121$	2.07629e8			0.0880548
$122$	−1.91813e9	+	3.32229e9i	−0.783895	+	1.35775i
$123$	1.09839e9	+	1.90247e9i	0.432697	+	0.749454i
$124$	9.91189e8	+	1.71679e9i	0.376495	+	0.652108i
$125$	2.04821e9			0.750377
$126$	1.08952e8	+	1.88711e8i	0.0385096	+	0.0667006i
$127$	−5.16610e9			−1.76216			−0.881081	−	0.472965i	$-0.843184\pi$
$127$	−5.16610e9			−1.76216			−0.881081	+	0.472965i	$0.843184\pi$
$128$	−1.43337e9			−0.471968
$129$	1.63217e9	−	1.26892e9i	0.518933	−	0.403442i
$130$	−7.18477e8			−0.220632
$131$	2.82499e9			0.838101			0.419050	−	0.907963i	$-0.362363\pi$
$131$	2.82499e9			0.838101			0.419050	+	0.907963i	$0.362363\pi$
$132$	−9.83392e8	−	1.70328e9i	−0.281932	−	0.488320i
$133$	−6.94464e6			−0.00192450
$134$	5.71127e8	+	9.89220e8i	0.153024	+	0.265046i
$135$	8.14441e8	+	1.41065e9i	0.211036	+	0.365526i
$136$	−6.94788e8	+	1.20341e9i	−0.174152	+	0.301639i
$137$	−4.93211e9			−1.19616			−0.598081	−	0.801436i	$-0.704070\pi$
$137$	−4.93211e9			−1.19616			−0.598081	+	0.801436i	$0.704070\pi$
$138$	−2.79439e9	+	4.84002e9i	−0.655890	+	1.13603i
$139$	−3.99104e9	−	6.91268e9i	−0.906816	−	1.57065i	−0.818461	−	0.574562i	$-0.805172\pi$
$139$	−3.99104e9	−	6.91268e9i	−0.906816	−	1.57065i	−0.0883553	−	0.996089i	$-0.528161\pi$
$140$	1.53785e8			0.0338328
$141$	1.28532e8	+	2.22625e8i	0.0273859	+	0.0474337i
$142$	2.13061e9	−	3.69033e9i	0.439751	−	0.761671i
$143$	−1.04080e9	+	1.80272e9i	−0.208140	+	0.360509i
$144$	−1.67925e9	+	2.90854e9i	−0.325450	+	0.563695i
$145$	3.12330e9			0.586757
$146$	−3.43840e9	+	5.95549e9i	−0.626281	+	1.08475i
$147$	−1.84189e9	+	3.19025e9i	−0.325339	+	0.563503i
$148$	−2.59711e9	−	4.49833e9i	−0.444952	−	0.770679i
$149$	−1.53735e9	−	2.66276e9i	−0.255525	−	0.442582i	0.709513	−	0.704692i	$-0.248915\pi$
$149$	−1.53735e9	−	2.66276e9i	−0.255525	−	0.442582i	−0.965038	+	0.262110i	$0.915582\pi$
$150$	−4.57903e9			−0.738521
$151$	−6.75697e8			−0.105768			−0.0528842	−	0.998601i	$-0.516841\pi$
$151$	−6.75697e8			−0.105768			−0.0528842	+	0.998601i	$0.516841\pi$
$152$	−1.51146e7	−	2.61792e7i	−0.00229668	−	0.00397796i
$153$	2.79613e9	+	4.84304e9i	0.412521	+	0.714507i
$154$	4.93666e8	−	8.55054e8i	0.0707277	−	0.122504i
$155$	−1.34729e9	+	2.33357e9i	−0.187485	+	0.324734i
$156$	1.59577e9			0.215729
$157$	−2.37726e9	+	4.11753e9i	−0.312268	+	0.540864i	−0.978853	−	0.204565i	$-0.934422\pi$
$157$	−2.37726e9	+	4.11753e9i	−0.312268	+	0.540864i	0.666585	+	0.745429i	$0.267755\pi$
$158$	−7.99953e9	+	1.38556e10i	−1.02119	+	1.76876i
$159$	−1.38842e9	+	2.40481e9i	−0.172279	+	0.298396i
$160$	2.21920e9	+	3.84377e9i	0.267705	+	0.463679i
$161$	−1.26608e9			−0.148506
$162$	−6.47906e8	−	1.12221e9i	−0.0739085	−	0.128013i
$163$	4.25689e9	−	7.37315e9i	0.472333	−	0.818104i	−0.527166	−	0.849762i	$-0.676745\pi$
$163$	4.25689e9	−	7.37315e9i	0.472333	−	0.818104i	0.999499	+	0.0316579i	$0.0100787\pi$
$164$	1.00304e10			1.08273
$165$	1.33669e9	−	2.31521e9i	0.140395	−	0.243172i
$166$	−5.03105e9	−	8.71404e9i	−0.514248	−	0.890703i
$167$	−1.20217e9	−	2.08222e9i	−0.119603	−	0.207158i	0.800008	−	0.599990i	$-0.204829\pi$
$167$	−1.20217e9	−	2.08222e9i	−0.119603	−	0.207158i	−0.919610	+	0.392832i	$0.871495\pi$
$168$	1.63464e8			0.0158318
$169$	4.45779e9	+	7.72111e9i	0.420367	+	0.728098i
$170$	8.74577e9			0.803116
$171$	−1.21655e8			−0.0108805
$172$	−1.29142e9	−	9.35090e9i	−0.112509	−	0.814658i
$173$	6.55712e9			0.556552			0.278276	−	0.960501i	$-0.410237\pi$
$173$	6.55712e9			0.556552			0.278276	+	0.960501i	$0.410237\pi$
$174$	−1.53721e10			−1.27134
$175$	−5.18665e8	−	8.98353e8i	−0.0418038	−	0.0724062i
$176$	1.52174e10			1.19546
$177$	4.90273e8	+	8.49177e8i	0.0375455	+	0.0650307i
$178$	9.06942e8	+	1.57087e9i	0.0677157	+	0.117287i
$179$	1.13157e10	−	1.95993e10i	0.823836	−	1.42693i	−0.0789693	−	0.996877i	$-0.525163\pi$
$179$	1.13157e10	−	1.95993e10i	0.823836	−	1.42693i	0.902806	−	0.430049i	$-0.141504\pi$
$180$	2.69399e9			0.191280
$181$	9.59317e9	−	1.66159e10i	0.664368	−	1.15072i	−0.315088	−	0.949062i	$-0.602034\pi$
$181$	9.59317e9	−	1.66159e10i	0.664368	−	1.15072i	0.979456	−	0.201657i	$-0.0646325\pi$
$182$	4.00540e8	+	6.93756e8i	0.0270598	+	0.0468690i
$183$	1.15816e10			0.763374
$184$	−2.75554e9	−	4.77273e9i	−0.177226	−	0.306964i
$185$	3.53016e9	−	6.11441e9i	0.221575	−	0.383780i
$186$	6.63102e9	−	1.14853e10i	0.406230	−	0.703611i
$187$	1.26693e10	−	2.19439e10i	0.757646	−	1.31228i
$188$	1.17375e9			0.0685274
$189$	9.08076e8	−	1.57283e9i	0.0517660	−	0.0896613i
$190$	−9.51288e7	+	1.64768e8i	−0.00529567	+	0.00917237i
$191$	7.26309e9	+	1.25800e10i	0.394886	+	0.683962i	0.993087	−	0.117384i	$-0.0374509\pi$
$191$	7.26309e9	+	1.25800e10i	0.394886	+	0.683962i	−0.598201	+	0.801346i	$0.704118\pi$
$192$	−3.82978e9	−	6.63337e9i	−0.203385	−	0.352272i
$193$	9.03505e9			0.468730			0.234365	−	0.972149i	$-0.424699\pi$
$193$	9.03505e9			0.468730			0.234365	+	0.972149i	$0.424699\pi$
$194$	−2.16049e10			−1.09508
$195$	1.08453e9	+	1.87847e9i	0.0537140	+	0.0930354i
$196$	8.40999e9	+	1.45665e10i	0.407046	+	0.705024i
$197$	−1.74993e10	+	3.03096e10i	−0.827793	+	1.43378i	0.0719724	+	0.997407i	$0.477071\pi$
$197$	−1.74993e10	+	3.03096e10i	−0.827793	+	1.43378i	−0.899766	+	0.436373i	$0.856263\pi$
$198$	8.64797e9	−	1.49787e10i	0.399872	−	0.692599i
$199$	2.87321e8			0.0129876			0.00649380	−	0.999979i	$-0.497933\pi$
$199$	2.87321e8			0.0129876			0.00649380	+	0.999979i	$0.497933\pi$
$200$	2.25769e9	−	3.91043e9i	0.0997765	−	0.172818i
$201$	1.72422e9	−	2.98644e9i	0.0745093	−	0.129054i
$202$	1.43691e10	−	2.48880e10i	0.607223	−	1.05174i
$203$	−1.74119e9	−	3.01584e9i	−0.0719639	−	0.124645i
$204$	−1.94247e10			−0.785271
$205$	6.81699e9	+	1.18074e10i	0.269588	+	0.466940i
$206$	−1.73231e10	+	3.00044e10i	−0.670228	+	1.16087i
$207$	−2.21790e10			−0.839604
$208$	−6.17340e9	+	1.06926e10i	−0.228686	+	0.396096i
$209$	2.75611e8	+	4.77373e8i	0.00999169	+	0.0173061i
$210$	−5.14409e8	−	8.90982e8i	−0.0182525	−	0.0316142i
$211$	−3.61006e10			−1.25385			−0.626923	−	0.779082i	$-0.715686\pi$
$211$	−3.61006e10			−1.25385			−0.626923	+	0.779082i	$0.715686\pi$
$212$	6.33946e9	+	1.09803e10i	0.215546	+	0.373337i
$213$	−1.28646e10			−0.428240
$214$	−1.34764e10			−0.439250
$215$	1.01298e10	−	7.87537e9i	0.323316	−	0.251361i
$216$	7.90550e9			0.247108
$217$	3.00437e9			0.0919781
$218$	2.74325e10	+	4.75145e10i	0.822643	+	1.42486i
$219$	2.07609e10			0.609886
$220$	−6.10327e9	−	1.05712e10i	−0.175655	−	0.304243i
$221$	1.02794e10	+	1.78044e10i	0.289869	+	0.502067i
$222$	−1.73746e10	+	3.00937e10i	−0.480094	+	0.831547i
$223$	−3.81034e10			−1.03179			−0.515895	−	0.856652i	$-0.672541\pi$
$223$	−3.81034e10			−1.03179			−0.515895	+	0.856652i	$0.672541\pi$
$224$	2.47434e9	−	4.28569e9i	0.0656665	−	0.113738i
$225$	−9.08590e9	−	1.57372e10i	−0.236345	−	0.409362i
$226$	−4.05365e10			−1.03361
$227$	8.55103e9	+	1.48108e10i	0.213748	+	0.370223i	0.952885	−	0.303333i	$-0.0980995\pi$
$227$	8.55103e9	+	1.48108e10i	0.213748	+	0.370223i	−0.739136	+	0.673556i	$0.764766\pi$
$228$	2.11285e8	−	3.65957e8i	0.00517800	−	0.00896856i
$229$	5.63691e9	−	9.76342e9i	0.135451	−	0.234608i	−0.790319	−	0.612696i	$-0.790085\pi$
$229$	5.63691e9	−	9.76342e9i	0.135451	−	0.234608i	0.925770	+	0.378088i	$0.123418\pi$
$230$	−1.73429e10	+	3.00388e10i	−0.408646	+	0.707795i
$231$	−2.98073e9			−0.0688762
$232$	7.57921e9	−	1.31276e10i	0.171762	−	0.297501i
$233$	−1.89544e10	+	3.28299e10i	−0.421315	+	0.729740i	−0.996068	−	0.0885872i	$-0.971765\pi$
$233$	−1.89544e10	+	3.28299e10i	−0.421315	+	0.729740i	0.574753	+	0.818327i	$0.305098\pi$
$234$	7.01661e9	+	1.21531e10i	0.152988	+	0.264982i
$235$	7.97716e8	+	1.38168e9i	0.0170625	+	0.0295531i
$236$	4.47713e9			0.0939498
$237$	4.83008e10			0.994460
$238$	−4.87564e9	−	8.44485e9i	−0.0984997	−	0.170607i
$239$	−1.80747e10	−	3.13063e10i	−0.358328	−	0.620642i	0.629354	−	0.777119i	$-0.283320\pi$
$239$	−1.80747e10	−	3.13063e10i	−0.358328	−	0.620642i	−0.987682	+	0.156477i	$0.949986\pi$
$240$	7.92842e9	−	1.37324e10i	0.154254	−	0.267176i
$241$	2.76976e10	−	4.79736e10i	0.528889	−	0.916063i	−0.470543	−	0.882377i	$-0.655942\pi$
$241$	2.76976e10	−	4.79736e10i	0.528889	−	0.916063i	0.999432	−	0.0336861i	$-0.0107246\pi$
$242$	−6.34224e9			−0.118870
$243$	2.60531e10	−	4.51252e10i	0.479326	−	0.830216i
$244$	2.64405e10	−	4.57963e10i	0.477546	−	0.827134i
$245$	−1.14314e10	+	1.97998e10i	−0.202699	+	0.351085i
$246$	−3.35516e10	−	5.81130e10i	−0.584124	−	1.01173i
$247$	−4.47240e8			−0.00764547
$248$	6.53883e9	+	1.13256e10i	0.109766	+	0.190120i
$249$	−1.51886e10	+	2.63075e10i	−0.250393	+	0.433693i
$250$	−6.25648e10			−1.01298
$251$	−1.89210e10	+	3.27722e10i	−0.300894	+	0.521164i	−0.976339	−	0.216247i	$-0.930618\pi$
$251$	−1.89210e10	+	3.27722e10i	−0.300894	+	0.521164i	0.675445	+	0.737411i	$0.263952\pi$
$252$	−1.50186e9	−	2.60130e9i	−0.0234599	−	0.0406338i
$253$	5.02467e10	+	8.70298e10i	0.771019	+	1.33544i
$254$	1.57804e11			2.37885
$255$	−1.32017e10	−	2.28660e10i	−0.195523	−	0.338656i
$256$	8.63100e10			1.25598
$257$	−1.38616e11			−1.98205			−0.991025	−	0.133676i	$-0.957322\pi$
$257$	−1.38616e11			−1.98205			−0.991025	+	0.133676i	$0.957322\pi$
$258$	−4.98563e10	+	3.87606e10i	−0.700538	+	0.544631i
$259$	−7.87204e9			−0.108702
$260$	9.90388e9			0.134408
$261$	−3.05020e10	−	5.28310e10i	−0.406861	−	0.704704i
$262$	−8.62925e10			−1.13140
$263$	1.29052e10	+	2.23525e10i	0.166328	+	0.288088i	0.937126	−	0.348991i	$-0.113476\pi$
$263$	1.29052e10	+	2.23525e10i	0.166328	+	0.288088i	−0.770798	+	0.637079i	$0.780142\pi$
$264$	−6.48739e9	−	1.12365e10i	−0.0821963	−	0.142368i
$265$	−8.61699e9	+	1.49251e10i	−0.107337	+	0.185913i
$266$	2.12132e8			0.00259799
$267$	2.73804e9	−	4.74242e9i	0.0329715	−	0.0571084i
$268$	−7.87272e9	−	1.36359e10i	−0.0932219	−	0.161465i
$269$	−2.04178e10			−0.237752			−0.118876	−	0.992909i	$-0.537929\pi$
$269$	−2.04178e10			−0.237752			−0.118876	+	0.992909i	$0.537929\pi$
$270$	−2.48780e10	−	4.30899e10i	−0.284891	−	0.493445i
$271$	−6.63850e10	+	1.14982e11i	−0.747667	+	1.29500i	0.201271	+	0.979536i	$0.435493\pi$
$271$	−6.63850e10	+	1.14982e11i	−0.747667	+	1.29500i	−0.948938	+	0.315462i	$0.897840\pi$
$272$	7.51467e10	−	1.30158e11i	0.832434	−	1.44182i
$273$	1.20922e9	−	2.09444e9i	0.0131757	−	0.0228210i
$274$	1.50657e11			1.61477
$275$	−4.11684e10	+	7.13058e10i	−0.434077	+	0.751844i
$276$	3.85194e10	−	6.67175e10i	0.399566	−	0.692068i
$277$	−9.07062e9	−	1.57108e10i	−0.0925716	−	0.160339i	0.816021	−	0.578022i	$-0.196175\pi$
$277$	−9.07062e9	−	1.57108e10i	−0.0925716	−	0.160339i	−0.908593	+	0.417684i	$0.862842\pi$
$278$	1.21911e11	+	2.11155e11i	1.22416	+	2.12032i
$279$	5.26302e10			0.520015
$280$	1.01451e9			0.00986386
$281$	−3.71253e10	−	6.43030e10i	−0.355216	−	0.615252i	0.631939	−	0.775018i	$-0.282259\pi$
$281$	−3.71253e10	−	6.43030e10i	−0.355216	−	0.615252i	−0.987155	+	0.159766i	$0.948926\pi$
$282$	−3.92616e9	−	6.80031e9i	−0.0369698	−	0.0640336i
$283$	−8.86902e10	+	1.53616e11i	−0.821933	+	1.42363i	0.0823071	+	0.996607i	$0.473771\pi$
$283$	−8.86902e10	+	1.53616e11i	−0.821933	+	1.42363i	−0.904241	+	0.427023i	$0.859562\pi$
$284$	−2.93695e10	+	5.08695e10i	−0.267895	+	0.464008i
$285$	5.74384e8			0.00515704
$286$	3.17924e10	−	5.50661e10i	0.280981	−	0.486673i
$287$	7.60074e9	−	1.31649e10i	0.0661283	−	0.114538i
$288$	4.33452e10	−	7.50761e10i	0.371257	−	0.643037i
$289$	−6.58333e10	−	1.14027e11i	−0.555143	−	0.961536i
$290$	−9.54047e10			−0.792098
$291$	3.26125e10	+	5.64864e10i	0.266603	+	0.461770i
$292$	4.73968e10	−	8.20937e10i	0.381528	−	0.660826i
$293$	1.26267e11			1.00088			0.500442	−	0.865770i	$-0.333171\pi$
$293$	1.26267e11			1.00088			0.500442	+	0.865770i	$0.333171\pi$
$294$	5.62625e10	−	9.74496e10i	0.439194	−	0.760706i
$295$	3.04280e9	+	5.27028e9i	0.0233924	+	0.0405168i
$296$	−1.71330e10	−	2.96753e10i	−0.129724	−	0.224689i
$297$	−1.44155e11			−1.07504
$298$	4.69599e10	+	8.13370e10i	0.344948	+	0.597468i
$299$	−8.15362e10			−0.589970
$300$	6.31199e10			0.449905
$301$	−1.32516e10	−	5.39084e9i	−0.0930505	−	0.0378536i
$302$	2.06399e10			0.142783
$303$	−8.67600e10			−0.591327
$304$	1.63476e9	+	2.83149e9i	0.0109780	+	0.0190144i
$305$	7.18792e10			0.475613
$306$	−8.54108e10	−	1.47936e11i	−0.556886	−	0.964555i
$307$	5.90676e10	+	1.02308e11i	0.379513	+	0.657336i	0.990991	−	0.133925i	$-0.0427582\pi$
$307$	5.90676e10	+	1.02308e11i	0.379513	+	0.657336i	−0.611478	+	0.791261i	$0.709425\pi$
$308$	−6.80496e9	+	1.17865e10i	−0.0430871	+	0.0746290i
$309$	1.04596e11			0.652683
$310$	4.11544e10	−	7.12814e10i	0.253098	−	0.438378i
$311$	−8.35485e10	−	1.44710e11i	−0.506427	−	0.877157i	−0.999972	−	0.00743718i	$-0.997633\pi$
$311$	−8.35485e10	−	1.44710e11i	−0.506427	−	0.877157i	0.493545	−	0.869720i	$-0.335701\pi$
$312$	1.05272e10			0.0628952
$313$	7.00914e10	+	1.21402e11i	0.412777	+	0.714950i	0.995192	−	0.0979410i	$-0.0312256\pi$
$313$	7.00914e10	+	1.21402e11i	0.412777	+	0.714950i	−0.582415	+	0.812891i	$0.697892\pi$
$314$	7.26159e10	−	1.25774e11i	0.421549	−	0.730144i
$315$	2.04142e9	−	3.53584e9i	0.0116825	−	0.0202347i
$316$	1.10270e11	−	1.90993e11i	0.622107	−	1.07752i
$317$	1.48017e11			0.823273			0.411636	−	0.911348i	$-0.364957\pi$
$317$	1.48017e11			0.823273			0.411636	+	0.911348i	$0.364957\pi$
$318$	4.24107e10	−	7.34576e10i	0.232570	−	0.402823i
$319$	−1.38205e11	+	2.39379e11i	−0.747251	+	1.29428i
$320$	−2.37689e10	−	4.11689e10i	−0.126717	−	0.219480i
$321$	2.03425e10	+	3.52342e10i	0.106938	+	0.185222i
$322$	3.86737e10			0.200477
$323$	5.44409e9			0.0278301
$324$	8.93109e9	+	1.54691e10i	0.0450248	+	0.0779853i
$325$	−3.34024e10	−	5.78546e10i	−0.166074	−	0.287649i
$326$	−1.30031e11	+	2.25221e11i	−0.637630	+	1.10441i
$327$	8.28182e10	−	1.43445e11i	0.400554	−	0.693780i
$328$	6.61702e10			0.315668
$329$	8.89429e8	−	1.54054e9i	0.00418533	−	0.00724920i
$330$	−4.08306e10	+	7.07207e10i	−0.189528	+	0.328272i
$331$	5.58228e10	−	9.66879e10i	0.255614	−	0.442737i	−0.709448	−	0.704758i	$-0.751056\pi$
$331$	5.58228e10	−	9.66879e10i	0.255614	−	0.442737i	0.965062	+	0.262021i	$0.0843889\pi$
$332$	6.93507e10	+	1.20119e11i	0.313278	+	0.542613i
$333$	−1.37901e11			−0.614568
$334$	3.67215e10	+	6.36036e10i	0.161459	+	0.279655i
$335$	1.07011e10	−	1.85348e10i	0.0464223	−	0.0804058i
$336$	−1.76799e10			−0.0756751
$337$	4.82875e10	−	8.36365e10i	0.203939	−	0.353233i	−0.745855	−	0.666108i	$-0.767959\pi$
$337$	4.82875e10	−	8.36365e10i	0.203939	−	0.353233i	0.949794	+	0.312875i	$0.101292\pi$
$338$	−1.36168e11	−	2.35850e11i	−0.567479	−	0.982902i
$339$	6.11895e10	+	1.05983e11i	0.251639	+	0.435852i
$340$	−1.20557e11			−0.489255
$341$	−1.19234e11	−	2.06520e11i	−0.477536	−	0.827117i
$342$	3.71609e9			0.0146882
$343$	5.12425e10			0.199897
$344$	−8.51942e9	−	6.16875e10i	−0.0328018	−	0.237511i
$345$	1.04716e11			0.397948
$346$	−2.00294e11			−0.751323
$347$	8.32633e10	+	1.44216e11i	0.308298	+	0.533988i	0.977990	−	0.208651i	$-0.0669073\pi$
$347$	8.32633e10	+	1.44216e11i	0.308298	+	0.533988i	−0.669692	+	0.742639i	$0.733574\pi$
$348$	2.11898e11			0.774497
$349$	2.14506e11	+	3.71535e11i	0.773971	+	1.34056i	0.935371	+	0.353667i	$0.115066\pi$
$349$	2.14506e11	+	3.71535e11i	0.773971	+	1.34056i	−0.161401	+	0.986889i	$0.551601\pi$
$350$	1.58432e10	+	2.74412e10i	0.0564334	+	0.0977455i
$351$	5.84808e10	−	1.01292e11i	0.205651	−	0.356198i
$352$	−3.92796e11			−1.36372
$353$	4.70638e10	−	8.15169e10i	0.161325	−	0.279422i	−0.774019	−	0.633162i	$-0.781757\pi$
$353$	4.70638e10	−	8.15169e10i	0.161325	−	0.279422i	0.935344	+	0.353739i	$0.115090\pi$
$354$	−1.49759e10	−	2.59391e10i	−0.0506849	−	0.0877889i
$355$	−7.98418e10			−0.266811
$356$	−1.25018e10	−	2.16537e10i	−0.0412522	−	0.0714508i
$357$	−1.47195e10	+	2.54948e10i	−0.0479606	+	0.0830702i
$358$	−3.45649e11	+	5.98682e11i	−1.11215	+	1.92629i
$359$	−2.26740e11	+	3.92725e11i	−0.720449	+	1.24785i	0.240371	+	0.970681i	$0.422731\pi$
$359$	−2.26740e11	+	3.92725e11i	−0.720449	+	1.24785i	−0.960820	+	0.277174i	$0.910602\pi$
$360$	1.77721e10			0.0557671
$361$	1.61285e11	−	2.79353e11i	0.499816	−	0.865708i
$362$	−2.93034e11	+	5.07550e11i	−0.896870	+	1.55342i
$363$	9.57355e9	+	1.65819e10i	0.0289397	+	0.0501250i
$364$	−5.52126e9	−	9.56311e9i	−0.0164847	−	0.0285524i
$365$	1.28850e11			0.379984
$366$	−3.53772e11			−1.03052
$367$	−2.40248e11	−	4.16122e11i	−0.691294	−	1.19736i	−0.971414	−	0.237391i	$-0.923708\pi$
$367$	−2.40248e11	−	4.16122e11i	−0.691294	−	1.19736i	0.280120	−	0.959965i	$-0.409626\pi$
$368$	2.98033e11	+	5.16208e11i	0.847127	+	1.46727i
$369$	1.33149e11	−	2.30621e11i	0.373868	−	0.647559i
$370$	−1.07833e11	+	1.86771e11i	−0.299118	+	0.518087i
$371$	1.92154e10			0.0526582
$372$	−9.14056e10	+	1.58319e11i	−0.247474	+	0.428637i
$373$	1.01291e10	−	1.75440e10i	0.0270944	−	0.0469288i	−0.852160	−	0.523281i	$-0.824708\pi$
$373$	1.01291e10	−	1.75440e10i	0.0270944	−	0.0469288i	0.879255	+	0.476352i	$0.158041\pi$
$374$	−3.86998e11	+	6.70301e11i	−1.02279	+	1.77153i
$375$	9.44410e10	+	1.63577e11i	0.246615	+	0.427150i
$376$	7.74316e9			0.0199790
$377$	−1.12134e11	−	1.94222e11i	−0.285892	−	0.495179i
$378$	−2.77382e10	+	4.80440e10i	−0.0698820	+	0.121039i
$379$	−5.03945e11			−1.25461			−0.627303	−	0.778776i	$-0.715841\pi$
$379$	−5.03945e11			−1.25461			−0.627303	+	0.778776i	$0.715841\pi$
$380$	1.31131e9	−	2.27125e9i	0.00322610	−	0.00558778i
$381$	−2.38204e11	−	4.12581e11i	−0.579144	−	1.00311i
$382$	−2.21859e11	−	3.84271e11i	−0.533080	−	0.923321i
$383$	−1.69219e10			−0.0401842			−0.0200921	−	0.999798i	$-0.506396\pi$
$383$	−1.69219e10			−0.0401842			−0.0200921	+	0.999798i	$0.506396\pi$
$384$	−6.60911e10	−	1.14473e11i	−0.155115	−	0.268666i
$385$	−1.84995e10			−0.0429127
$386$	−2.75985e11			−0.632766
$387$	−2.32140e11	−	9.44361e10i	−0.526078	−	0.214012i
$388$	2.97814e11			0.667118
$389$	−1.90105e10			−0.0420940			−0.0210470	−	0.999778i	$-0.506700\pi$
$389$	−1.90105e10			−0.0420940			−0.0210470	+	0.999778i	$0.506700\pi$
$390$	−3.31283e10	−	5.73799e10i	−0.0725117	−	0.125594i
$391$	9.92512e11			2.14754
$392$	5.54803e10	+	9.60948e10i	0.118673	+	0.205548i
$393$	1.30258e11	+	2.25613e11i	0.275446	+	0.477087i
$394$	5.34534e11	−	9.25841e11i	1.11749	−	1.93554i
$395$	2.99771e11			0.619588
$396$	−1.19208e11	+	2.06475e11i	−0.243601	+	0.421929i
$397$	−2.94136e11	−	5.09458e11i	−0.594280	−	1.02932i	−0.993648	−	0.112532i	$-0.964104\pi$
$397$	−2.94136e11	−	5.09458e11i	−0.594280	−	1.02932i	0.399368	−	0.916791i	$-0.369229\pi$
$398$	−8.77655e9			−0.0175327
$399$	−3.20211e8	−	5.54621e8i	−0.000632496	−	0.00109551i
$400$	−2.44186e11	+	4.22943e11i	−0.476926	+	0.826060i
$401$	4.08227e11	−	7.07069e11i	0.788409	−	1.36556i	−0.138532	−	0.990358i	$-0.544238\pi$
$401$	4.08227e11	−	7.07069e11i	0.788409	−	1.36556i	0.926941	−	0.375207i	$-0.122428\pi$
$402$	−5.26682e10	+	9.12240e10i	−0.100585	+	0.174218i
$403$	1.93484e11			0.365402
$404$	−1.98071e11	+	3.43070e11i	−0.369918	+	0.640717i
$405$	−1.21397e10	+	2.10266e10i	−0.0224213	+	0.0388348i
$406$	5.31867e10	+	9.21220e10i	0.0971484	+	0.168266i
$407$	3.12417e11	+	5.41123e11i	0.564365	+	0.977509i
$408$	−1.28144e11			−0.228943
$409$	7.52116e11			1.32902			0.664508	−	0.747281i	$-0.268641\pi$
$409$	7.52116e11			1.32902			0.664508	+	0.747281i	$0.268641\pi$
$410$	−2.08233e11	−	3.60669e11i	−0.363933	−	0.630350i
$411$	−2.27415e11	−	3.93894e11i	−0.393125	−	0.680912i
$412$	2.38791e11	−	4.13598e11i	0.408300	−	0.707197i
$413$	3.39263e9	−	5.87621e9i	0.00573801	−	0.00993852i
$414$	6.77481e11			1.13343
$415$	−9.42659e10	+	1.63273e11i	−0.156005	+	0.270208i
$416$	1.59349e11	−	2.76001e11i	0.260874	−	0.451847i
$417$	3.68046e11	−	6.37474e11i	0.596060	−	1.03241i
$418$	−8.41885e9	−	1.45819e10i	−0.0134884	−	0.0233626i
$419$	2.91146e11			0.461475			0.230738	−	0.973016i	$-0.425886\pi$
$419$	2.91146e11			0.461475			0.230738	+	0.973016i	$0.425886\pi$
$420$	7.09089e9	+	1.22818e10i	0.0111193	+	0.0192593i
$421$	4.03289e11	−	6.98518e11i	0.625673	−	1.08370i	−0.362737	−	0.931891i	$-0.618158\pi$
$421$	4.03289e11	−	6.98518e11i	0.625673	−	1.08370i	0.988410	−	0.151806i	$-0.0485088\pi$
$422$	1.10273e12			1.69264
$423$	1.55809e10	−	2.69869e10i	0.0236625	−	0.0409847i
$424$	4.18211e10	+	7.24363e10i	0.0628419	+	0.108845i
$425$	4.06596e11	+	7.04244e11i	0.604523	+	1.04706i
$426$	3.92962e11			0.578106
$427$	−4.00716e10	−	6.94060e10i	−0.0583325	−	0.101035i
$428$	1.85766e11			0.267589
$429$	−1.91961e11			−0.273625
$430$	−3.09425e11	+	2.40562e11i	−0.436463	+	0.339327i
$431$	−6.98071e10			−0.0974433			−0.0487216	−	0.998812i	$-0.515515\pi$
$431$	−6.98071e10			−0.0974433			−0.0487216	+	0.998812i	$0.515515\pi$
$432$	−8.55040e11			−1.18116
$433$	1.16104e11	+	2.01097e11i	0.158727	+	0.274923i	0.934410	−	0.356200i	$-0.115928\pi$
$433$	1.16104e11	+	2.01097e11i	0.158727	+	0.274923i	−0.775683	+	0.631123i	$0.782594\pi$
$434$	−9.17717e10			−0.124167
$435$	1.44012e11	+	2.49437e11i	0.192841	+	0.334010i
$436$	−3.78145e11	−	6.54966e11i	−0.501151	−	0.868019i
$437$	−1.07957e10	+	1.86987e10i	−0.0141607	+	0.0245270i
$438$	−6.34166e11			−0.823321
$439$	−8.91778e10	+	1.54460e11i	−0.114595	+	0.198485i	−0.917618	−	0.397464i	$-0.869890\pi$
$439$	−8.91778e10	+	1.54460e11i	−0.114595	+	0.198485i	0.803023	+	0.595948i	$0.203224\pi$
$440$	−4.02630e10	−	6.97375e10i	−0.0512116	−	0.0887012i
$441$	4.46554e11			0.562212
$442$	−3.13995e11	−	5.43855e11i	−0.391311	−	0.677770i
$443$	−2.99329e11	+	5.18453e11i	−0.369260	+	0.639577i	−0.989450	−	0.144875i	$-0.953722\pi$
$443$	−2.99329e11	+	5.18453e11i	−0.369260	+	0.639577i	0.620190	+	0.784452i	$0.287055\pi$
$444$	2.39501e11	−	4.14827e11i	0.292471	−	0.506575i
$445$	1.69932e10	−	2.94331e10i	0.0205426	−	0.0355808i
$446$	1.16391e12			1.39287
$447$	1.41771e11	−	2.45555e11i	0.167959	−	0.290914i
$448$	−2.65016e10	+	4.59021e10i	−0.0310829	+	0.0538371i
$449$	−3.61205e11	−	6.25625e11i	−0.419416	−	0.726449i	0.576465	−	0.817122i	$-0.304432\pi$
$449$	−3.61205e11	−	6.25625e11i	−0.419416	−	0.726449i	−0.995881	+	0.0906725i	$0.971098\pi$
$450$	2.77539e11	+	4.80711e11i	0.319056	+	0.552622i
$451$	−1.20660e12			−1.37331
$452$	5.58777e11			0.629674
$453$	−3.11557e10	−	5.39633e10i	−0.0347613	−	0.0602083i
$454$	−2.61201e11	−	4.52413e11i	−0.288551	−	0.499785i
$455$	7.50485e9	−	1.29988e10i	0.00820901	−	0.0142184i
$456$	1.39384e9	−	2.41420e9i	0.00150963	−	0.00261476i
$457$	−6.16070e11			−0.660704			−0.330352	−	0.943858i	$-0.607167\pi$
$457$	−6.16070e11			−0.660704			−0.330352	+	0.943858i	$0.607167\pi$
$458$	−1.72186e11	+	2.98234e11i	−0.182853	+	0.316711i
$459$	−7.11866e11	+	1.23299e12i	−0.748586	+	1.29659i
$460$	2.39064e11	−	4.14072e11i	0.248946	−	0.431186i
$461$	2.67004e11	+	4.62464e11i	0.275336	+	0.476896i	0.970220	−	0.242226i	$-0.0778776\pi$
$461$	2.67004e11	+	4.62464e11i	0.275336	+	0.476896i	−0.694884	+	0.719122i	$0.744544\pi$
$462$	9.10498e10			0.0929801
$463$	−3.85271e11	−	6.67309e11i	−0.389630	−	0.674858i	0.602770	−	0.797915i	$-0.294064\pi$
$463$	−3.85271e11	−	6.67309e11i	−0.389630	−	0.674858i	−0.992400	+	0.123057i	$0.960730\pi$
$464$	−8.19749e11	+	1.41985e12i	−0.821013	+	1.42204i
$465$	−2.48488e11			−0.246472
$466$	5.78982e11	−	1.00283e12i	0.568759	−	0.985119i
$467$	1.70011e11	+	2.94467e11i	0.165406	+	0.286491i	0.936799	−	0.349867i	$-0.113773\pi$
$467$	1.70011e11	+	2.94467e11i	0.165406	+	0.286491i	−0.771394	+	0.636358i	$0.780440\pi$
$468$	−9.67208e10	−	1.67525e11i	−0.0931995	−	0.161426i
$469$	−2.38628e10			−0.0227742
$470$	−2.43671e10	−	4.22050e10i	−0.0230337	−	0.0398955i
$471$	−4.38452e11			−0.410514
$472$	2.95354e10			0.0273908
$473$	1.55350e11	+	1.12486e12i	0.142704	+	1.03329i
$474$	−1.47540e12			−1.34248
$475$	−1.76904e10			−0.0159447
$476$	6.72084e10	+	1.16408e11i	0.0600057	+	0.103933i
$477$	3.36612e11			0.297713
$478$	5.52112e11	+	9.56286e11i	0.483728	+	0.837842i
$479$	−1.08430e12	−	1.87807e12i	−0.941111	−	1.63005i	−0.763357	−	0.645977i	$-0.776450\pi$
$479$	−1.08430e12	−	1.87807e12i	−0.941111	−	1.63005i	−0.177755	−	0.984075i	$-0.556883\pi$
$480$	−2.04651e11	+	3.54465e11i	−0.175965	+	0.304781i
$481$	−5.06965e11			−0.431842
$482$	−8.46052e11	+	1.46541e12i	−0.713979	+	1.23665i
$483$	−5.83775e10	−	1.01113e11i	−0.0488072	−	0.0845365i
$484$	8.74249e10			0.0724154
$485$	2.02404e11	+	3.50574e11i	0.166105	+	0.287701i
$486$	−7.95820e11	+	1.37840e12i	−0.647070	+	1.12076i
$487$	1.76906e11	−	3.06410e11i	0.142516	−	0.246844i	−0.785928	−	0.618318i	$-0.787814\pi$
$487$	1.76906e11	−	3.06410e11i	0.142516	−	0.246844i	0.928443	+	0.371474i	$0.121148\pi$
$488$	1.74427e11	−	3.02116e11i	0.139227	−	0.241148i
$489$	7.85124e11			0.620938
$490$	3.49184e11	−	6.04805e11i	0.273636	−	0.473951i
$491$	−2.63894e11	+	4.57078e11i	−0.204910	+	0.354914i	−0.950104	−	0.311933i	$-0.899023\pi$
$491$	−2.63894e11	+	4.57078e11i	−0.204910	+	0.354914i	0.745194	+	0.666848i	$0.232357\pi$
$492$	4.62493e11	+	8.01062e11i	0.355846	+	0.616344i
$493$	1.36497e12	+	2.36420e12i	1.04067	+	1.80249i
$494$	1.36614e10			0.0103211
$495$	−3.24071e11			−0.242615
$496$	−7.07225e11	−	1.22495e12i	−0.524674	−	0.908763i
$497$	4.45106e10	+	7.70947e10i	0.0327235	+	0.0566788i
$498$	4.63954e11	−	8.03592e11i	0.338020	−	0.585468i
$499$	−8.46526e11	+	1.46623e12i	−0.611207	+	1.05864i	0.379831	+	0.925056i	$0.375982\pi$
$499$	−8.46526e11	+	1.46623e12i	−0.611207	+	1.05864i	−0.991037	+	0.133585i	$0.957351\pi$
$500$	8.62428e11			0.617103
$501$	1.10862e11	−	1.92018e11i	0.0786161	−	0.136167i
$502$	5.77964e11	−	1.00106e12i	0.406195	−	0.703550i
$503$	−9.62484e11	+	1.66707e12i	−0.670406	+	1.16118i	0.307384	+	0.951586i	$0.400547\pi$
$503$	−9.62484e11	+	1.66707e12i	−0.670406	+	1.16118i	−0.977789	+	0.209591i	$0.932787\pi$
$504$	−9.90769e9	−	1.71606e10i	−0.00683967	−	0.0118467i
$505$	−5.38462e11			−0.368421
$506$	−1.53484e12	−	2.65842e12i	−1.04084	−	1.80280i
$507$	−4.11088e11	+	7.12026e11i	−0.276312	+	0.478586i
$508$	−2.17526e12			−1.44919
$509$	9.23687e11	−	1.59987e12i	0.609951	−	1.05647i	−0.381297	−	0.924452i	$-0.624523\pi$
$509$	9.23687e11	−	1.59987e12i	0.609951	−	1.05647i	0.991248	−	0.132013i	$-0.0421440\pi$
$510$	4.03259e11	+	6.98466e11i	0.263948	+	0.457172i
$511$	−7.18317e10	−	1.24416e11i	−0.0466038	−	0.0807202i
$512$	−1.90255e12			−1.22355
$513$	−1.54861e10	−	2.68227e10i	−0.00987221	−	0.0170992i
$514$	4.23418e12			2.67569
$515$	6.49159e11			0.406648
$516$	6.87247e11	−	5.34298e11i	0.426765	−	0.331787i
$517$	−1.41195e11			−0.0869183
$518$	2.40460e11			0.146744
$519$	3.02343e11	+	5.23673e11i	0.182914	+	0.316816i
$520$	6.53354e10			0.0391863
$521$	−1.58043e12	−	2.73738e12i	−0.939733	−	1.62767i	−0.765969	−	0.642878i	$-0.777740\pi$
$521$	−1.58043e12	−	2.73738e12i	−0.939733	−	1.62767i	−0.173764	−	0.984787i	$-0.555593\pi$
$522$	9.31717e11	+	1.61378e12i	0.549246	+	0.951322i
$523$	3.18933e11	−	5.52408e11i	0.186398	−	0.322851i	−0.757649	−	0.652663i	$-0.773652\pi$
$523$	3.18933e11	−	5.52408e11i	0.186398	−	0.322851i	0.944047	+	0.329812i	$0.106985\pi$
$524$	1.18950e12			0.689246
$525$	4.78302e10	−	8.28444e10i	0.0274780	−	0.0475934i
$526$	−3.94204e11	−	6.82781e11i	−0.224536	−	0.388907i
$527$	−2.35521e12			−1.33009
$528$	7.01661e11	+	1.21531e12i	0.392893	+	0.680511i
$529$	−1.06758e12	+	1.84911e12i	−0.592721	+	1.02662i
$530$	2.63216e11	−	4.55903e11i	0.144901	−	0.250975i
$531$	5.94317e10	−	1.02939e11i	0.0324409	−	0.0561892i
$532$	−2.92414e9			−0.00158269
$533$	4.89493e11	−	8.47827e11i	0.262709	−	0.455025i
$534$	−8.36364e10	+	1.44863e11i	−0.0445102	+	0.0770940i
$535$	1.26252e11	+	2.18675e11i	0.0666266	+	0.115401i
$536$	−5.19360e10	−	8.99557e10i	−0.0271786	−	0.0470747i
$537$	2.08702e12			1.08303
$538$	6.23685e11			0.320956
$539$	−1.01167e12	−	1.75227e12i	−0.516286	−	0.894234i
$540$	3.42932e11	+	5.93975e11i	0.173554	+	0.300605i
$541$	−8.16967e11	+	1.41503e12i	−0.410031	+	0.710195i	−0.994893	−	0.100938i	$-0.967816\pi$
$541$	−8.16967e11	+	1.41503e12i	−0.410031	+	0.710195i	0.584862	+	0.811133i	$0.301149\pi$
$542$	2.02780e12	−	3.51226e12i	1.00932	−	1.74819i
$543$	1.76933e12			0.873392
$544$	−1.93971e12	+	3.35967e12i	−0.949600	+	1.64476i
$545$	5.13998e11	−	8.90271e11i	0.249561	−	0.432253i
$546$	−3.69370e10	+	6.39768e10i	−0.0177867	+	0.0308075i
$547$	1.54490e12	+	2.67584e12i	0.737831	+	1.27796i	0.953470	+	0.301488i	$0.0974833\pi$
$547$	1.54490e12	+	2.67584e12i	0.737831	+	1.27796i	−0.215639	+	0.976473i	$0.569183\pi$
$548$	−2.07673e12			−0.983712
$549$	−7.01968e11	−	1.21584e12i	−0.329793	−	0.571219i
$550$	1.25753e12	−	2.17811e12i	0.585987	−	1.01496i
$551$	−5.93878e10			−0.0274483
$552$	2.54111e11	−	4.40132e11i	0.116492	−	0.201770i
$553$	−1.67118e11	−	2.89457e11i	−0.0759907	−	0.131620i
$554$	2.77072e11	+	4.79903e11i	0.124968	+	0.216451i
$555$	6.51089e11			0.291288
$556$	−1.68048e12	−	2.91068e12i	−0.745757	−	1.29169i
$557$	1.52009e12			0.669144			0.334572	−	0.942370i	$-0.391408\pi$
$557$	1.52009e12			0.669144			0.334572	+	0.942370i	$0.391408\pi$
$558$	−1.60765e12			−0.701999
$559$	−8.53412e11	−	3.47174e11i	−0.369663	−	0.150381i
$560$	−1.09727e11			−0.0471486
$561$	2.33668e12			0.996016
$562$	1.13403e12	+	1.96421e12i	0.479527	+	0.830565i
$563$	1.86712e12			0.783223			0.391611	−	0.920131i	$-0.371918\pi$
$563$	1.86712e12			0.783223			0.391611	+	0.920131i	$0.371918\pi$
$564$	5.41203e10	+	9.37392e10i	0.0225219	+	0.0390090i
$565$	3.79763e11	+	6.57768e11i	0.156781	+	0.271553i
$566$	2.70914e12	−	4.69237e12i	1.10958	−	1.92184i
$567$	2.70708e10			0.0109996
$568$	−1.93749e11	+	3.35584e11i	−0.0781039	+	0.135280i
$569$	−1.43439e12	−	2.48444e12i	−0.573670	−	0.993625i	−0.996185	−	0.0872693i	$-0.972186\pi$
$569$	−1.43439e12	−	2.48444e12i	−0.573670	−	0.993625i	0.422515	−	0.906356i	$-0.361147\pi$
$570$	−1.75452e10			−0.00696180
$571$	−1.42479e12	−	2.46781e12i	−0.560904	−	0.971514i	−0.997418	−	0.0718166i	$-0.977120\pi$
$571$	−1.42479e12	−	2.46781e12i	−0.560904	−	0.971514i	0.436514	−	0.899697i	$-0.356213\pi$
$572$	−4.38244e11	+	7.59061e11i	−0.171172	+	0.296479i
$573$	−6.69788e11	+	1.16011e12i	−0.259562	+	0.449575i
$574$	−2.32173e11	+	4.02135e11i	−0.0892705	+	0.154621i
$575$	−3.22513e12			−1.23039
$576$	−4.64252e11	+	8.04108e11i	−0.175733	+	0.304378i
$577$	−2.65796e11	+	4.60372e11i	−0.0998290	+	0.172909i	−0.911614	−	0.411048i	$-0.865163\pi$
$577$	−2.65796e11	+	4.60372e11i	−0.0998290	+	0.172909i	0.811785	+	0.583957i	$0.198496\pi$
$578$	2.01095e12	+	3.48307e12i	0.749421	+	1.29803i
$579$	4.16597e11	+	7.21568e11i	0.154050	+	0.266823i
$580$	1.31511e12			0.482543
$581$	2.10207e11			0.0765341
$582$	−9.96184e11	−	1.72544e12i	−0.359903	−	0.623371i
$583$	−7.62600e11	−	1.32086e12i	−0.273393	−	0.473531i
$584$	3.12675e11	−	5.41568e11i	0.111233	−	0.192662i
$585$	1.31469e11	−	2.27711e11i	0.0464111	−	0.0803864i
$586$	−3.85695e12			−1.35115
$587$	−1.48985e12	+	2.58049e12i	−0.517930	+	0.897081i	0.481853	+	0.876252i	$0.339964\pi$
$587$	−1.48985e12	+	2.58049e12i	−0.517930	+	0.897081i	−0.999783	+	0.0208286i	$0.993370\pi$
$588$	−7.75553e11	+	1.34330e12i	−0.267555	+	0.463420i
$589$	2.56179e10	−	4.43715e10i	0.00877050	−	0.0151910i
$590$	−9.29457e10	−	1.60987e11i	−0.0315788	−	0.0546960i
$591$	−3.22750e12			−1.08823
$592$	1.85307e12	+	3.20961e12i	0.620074	+	1.07400i
$593$	−2.30600e12	+	3.99411e12i	−0.765797	+	1.32640i	0.174027	+	0.984741i	$0.444322\pi$
$593$	−2.30600e12	+	3.99411e12i	−0.765797	+	1.32640i	−0.939824	+	0.341659i	$0.889011\pi$
$594$	4.40338e12			1.45127
$595$	−9.13539e10	+	1.58230e11i	−0.0298814	+	0.0517561i
$596$	−6.47321e11	−	1.12119e12i	−0.210141	−	0.363976i
$597$	1.32481e10	+	2.29464e10i	0.00426844	+	0.00739316i
$598$	2.49061e12			0.796436
$599$	−1.55506e12	−	2.69345e12i	−0.493546	−	0.854846i	0.506427	−	0.862283i	$-0.330966\pi$
$599$	−1.55506e12	−	2.69345e12i	−0.493546	−	0.854846i	−0.999972	+	0.00743677i	$0.997633\pi$
$600$	4.16399e11			0.131168
$601$	6.12005e12			1.91346			0.956730	−	0.290976i	$-0.0939800\pi$
$601$	6.12005e12			1.91346			0.956730	+	0.290976i	$0.0939800\pi$
$602$	4.04784e11	+	1.64669e11i	0.125614	+	0.0511008i
$603$	−4.18026e11			−0.128758
$604$	−2.84512e11			−0.0869829
$605$	5.94167e10	+	1.02913e11i	0.0180306	+	0.0312299i
$606$	2.65018e12			0.798268
$607$	1.90712e12	+	3.30322e12i	0.570201	+	0.987618i	0.996545	+	0.0830564i	$0.0264681\pi$
$607$	1.90712e12	+	3.30322e12i	0.570201	+	0.987618i	−0.426344	+	0.904561i	$0.640199\pi$
$608$	−4.21968e10	−	7.30871e10i	−0.0125232	−	0.0216907i
$609$	1.60570e11	−	2.78115e11i	0.0473026	−	0.0819306i
$610$	−2.19563e12			−0.642058
$611$	5.72799e10	−	9.92116e10i	0.0166271	−	0.0287990i
$612$	1.17735e12	+	2.03923e12i	0.339253	+	0.587603i
$613$	2.16265e12			0.618606			0.309303	−	0.950964i	$-0.399904\pi$
$613$	2.16265e12			0.618606			0.309303	+	0.950964i	$0.399904\pi$
$614$	−1.80429e12	−	3.12511e12i	−0.512327	−	0.887377i
$615$	−6.28650e11	+	1.08885e12i	−0.177203	+	0.306924i
$616$	−4.48920e10	+	7.77552e10i	−0.0125619	+	0.0217579i
$617$	3.21121e12	−	5.56199e12i	0.892044	−	1.54506i	0.0546222	−	0.998507i	$-0.482605\pi$
$617$	3.21121e12	−	5.56199e12i	0.892044	−	1.54506i	0.837421	−	0.546558i	$-0.184062\pi$
$618$	−3.19500e12			−0.881095
$619$	−6.33581e11	+	1.09739e12i	−0.173458	+	0.300438i	−0.939626	−	0.342202i	$-0.888827\pi$
$619$	−6.33581e11	+	1.09739e12i	−0.173458	+	0.300438i	0.766169	+	0.642640i	$0.222161\pi$
$620$	−5.67294e11	+	9.82582e11i	−0.154186	+	0.267058i
$621$	−2.82327e12	−	4.89005e12i	−0.761799	−	1.31947i
$622$	2.55208e12	+	4.42033e12i	0.683656	+	1.18413i
$623$	−3.78938e10			−0.0100779
$624$	−1.13860e12			−0.300635
$625$	−1.00132e12	−	1.73434e12i	−0.262491	−	0.454648i
$626$	−2.14102e12	−	3.70835e12i	−0.557232	−	0.965154i
$627$	−2.54164e10	+	4.40224e10i	−0.00656764	+	0.0113755i
$628$	−1.00098e12	+	1.73374e12i	−0.256806	+	0.444801i
$629$	6.17111e12			1.57194
$630$	−6.23574e10	+	1.08006e11i	−0.0157709	+	0.0273160i
$631$	−2.26512e12	+	3.92330e12i	−0.568799	+	0.985189i	0.427886	+	0.903833i	$0.359259\pi$
$631$	−2.26512e12	+	3.92330e12i	−0.568799	+	0.985189i	−0.996685	+	0.0813566i	$0.974075\pi$
$632$	7.27445e11	−	1.25997e12i	0.181373	−	0.314148i
$633$	−1.66457e12	−	2.88311e12i	−0.412083	−	0.713748i
$634$	−4.52133e12			−1.11138
$635$	−1.47837e12	−	2.56062e12i	−0.360830	−	0.624976i
$636$	−5.84613e11	+	1.01258e12i	−0.141681	+	0.245398i
$637$	1.64166e12			0.395053
$638$	4.22163e12	−	7.31208e12i	1.00876	−	1.74722i
$639$	7.79731e11	+	1.35053e12i	0.185008	+	0.320444i
$640$	−4.10184e11	−	7.10459e11i	−0.0966426	−	0.167390i
$641$	4.72184e12			1.10472			0.552358	−	0.833607i	$-0.313728\pi$
$641$	4.72184e12			1.10472			0.552358	+	0.833607i	$0.313728\pi$
$642$	−6.21383e11	−	1.07627e12i	−0.144362	−	0.250042i
$643$	1.55455e12			0.358636			0.179318	−	0.983791i	$-0.442611\pi$
$643$	1.55455e12			0.358636			0.179318	+	0.983791i	$0.442611\pi$
$644$	−5.33099e11			−0.122130
$645$	1.09603e12	+	4.45871e11i	0.249346	+	0.101436i
$646$	−1.66296e11			−0.0375695
$647$	4.64966e12			1.04316			0.521581	−	0.853202i	$-0.325343\pi$
$647$	4.64966e12			1.04316			0.521581	+	0.853202i	$0.325343\pi$
$648$	5.89180e10	+	1.02049e11i	0.0131269	+	0.0227364i
$649$	−5.38572e11			−0.119163
$650$	1.02031e12	+	1.76723e12i	0.224193	+	0.388315i
$651$	1.38529e11	+	2.39938e11i	0.0302291	+	0.0523583i
$652$	1.79242e12	−	3.10457e12i	0.388442	−	0.672801i
$653$	−4.88077e12			−1.05046			−0.525230	−	0.850961i	$-0.676021\pi$
$653$	−4.88077e12			−1.05046			−0.525230	+	0.850961i	$0.676021\pi$
$654$	−2.52977e12	+	4.38170e12i	−0.540732	+	0.936575i
$655$	8.08423e11	+	1.40023e12i	0.171614	+	0.297244i
$656$	−7.15682e12			−1.50887
$657$	−1.25834e12	−	2.17951e12i	−0.263483	−	0.456366i
$658$	−2.71686e10	+	4.70573e10i	−0.00565002	+	0.00978613i
$659$	−1.33376e12	+	2.31015e12i	−0.275483	+	0.477150i	−0.970257	−	0.242078i	$-0.922171\pi$
$659$	−1.33376e12	+	2.31015e12i	−0.275483	+	0.477150i	0.694774	+	0.719228i	$0.255504\pi$
$660$	5.62831e11	−	9.74853e11i	0.115460	−	0.199982i
$661$	4.42473e12			0.901530			0.450765	−	0.892643i	$-0.351151\pi$
$661$	4.42473e12			0.901530			0.450765	+	0.892643i	$0.351151\pi$
$662$	−1.70517e12	+	2.95344e12i	−0.345069	+	0.597677i
$663$	−9.47944e11	+	1.64189e12i	−0.190534	+	0.330014i
$664$	4.57504e11	+	7.92420e11i	0.0913352	+	0.158197i
$665$	−1.98734e9	−	3.44217e9i	−0.000394070	−	0.000682550i
$666$	4.21235e12			0.829641
$667$	−1.08270e13			−2.11807
$668$	−5.06190e11	−	8.76746e11i	−0.0983601	−	0.170365i
$669$	−1.75691e12	−	3.04306e12i	−0.339103	−	0.587344i
$670$	−3.26877e11	+	5.66167e11i	−0.0626682	+	0.108545i
$671$	−3.18064e12	+	5.50902e12i	−0.605707	+	1.04912i
$672$	4.56358e11			0.0863265
$673$	−4.89054e12	+	8.47067e12i	−0.918944	+	1.59166i	−0.117922	+	0.993023i	$0.537623\pi$
$673$	−4.89054e12	+	8.47067e12i	−0.918944	+	1.59166i	−0.801022	+	0.598635i	$0.795710\pi$
$674$	−1.47500e12	+	2.55477e12i	−0.275310	+	0.476850i
$675$	2.31318e12	−	4.00655e12i	0.428887	−	0.742853i
$676$	1.87701e12	+	3.25108e12i	0.345706	+	0.598781i
$677$	−8.08656e12			−1.47950			−0.739750	−	0.672882i	$-0.765056\pi$
$677$	−8.08656e12			−1.47950			−0.739750	+	0.672882i	$0.765056\pi$
$678$	−1.86910e12	−	3.23738e12i	−0.339703	−	0.588382i
$679$	2.25674e11	−	3.90880e11i	0.0407444	−	0.0705714i
$680$	−7.95306e11			−0.142641
$681$	−7.88560e11	+	1.36583e12i	−0.140499	+	0.243351i
$682$	3.64214e12	+	6.30837e12i	0.644654	+	1.11657i
$683$	4.33342e12	+	7.50571e12i	0.761970	+	1.31977i	0.941834	+	0.336080i	$0.109101\pi$
$683$	4.33342e12	+	7.50571e12i	0.761970	+	1.31977i	−0.179863	+	0.983692i	$0.557566\pi$
$684$	−5.12247e10			−0.00894801
$685$	−1.41141e12	−	2.44464e12i	−0.244933	−	0.424236i
$686$	−1.56526e12			−0.269853
$687$	1.03965e12			0.178066
$688$	9.21441e11	+	6.67197e12i	0.156790	+	1.13529i
$689$	1.23748e12			0.209196
$690$	−3.19866e12			−0.537214
$691$	4.08953e12	+	7.08327e12i	0.682373	+	1.18191i	0.974255	+	0.225451i	$0.0723855\pi$
$691$	4.08953e12	+	7.08327e12i	0.682373	+	1.18191i	−0.291881	+	0.956455i	$0.594281\pi$
$692$	2.76097e12			0.457703
$693$	1.80665e11	+	3.12920e11i	0.0297559	+	0.0515388i
$694$	−2.54337e12	−	4.40524e12i	−0.416190	−	0.720862i
$695$	2.28422e12	−	3.95638e12i	0.371369	−	0.643230i
$696$	1.39788e12			0.225802
$697$	−5.95843e12	+	1.03203e13i	−0.956279	+	1.65632i
$698$	−6.55231e12	−	1.13489e13i	−1.04483	−	1.80970i
$699$	−3.49587e12			−0.553870
$700$	−2.18391e11	−	3.78264e11i	−0.0343790	−	0.0595462i
$701$	−4.01215e12	+	6.94924e12i	−0.627546	+	1.08694i	0.360497	+	0.932761i	$0.382607\pi$
$701$	−4.01215e12	+	6.94924e12i	−0.627546	+	1.08694i	−0.988043	+	0.154181i	$0.950726\pi$
$702$	−1.78636e12	+	3.09407e12i	−0.277621	+	0.480853i
$703$	−6.71239e10	+	1.16262e11i	−0.0103652	+	0.0179531i
$704$	4.20707e12			0.645510
$705$	−7.35638e10	+	1.27416e11i	−0.0112154	+	0.0194256i
$706$	−1.43761e12	+	2.49002e12i	−0.217782	+	0.377209i
$707$	3.00185e11	+	5.19935e11i	0.0451857	+	0.0782639i
$708$	2.06436e11	+	3.57558e11i	0.0308771	+	0.0534807i
$709$	4.75616e12			0.706885			0.353442	−	0.935456i	$-0.385011\pi$
$709$	4.75616e12			0.706885			0.353442	+	0.935456i	$0.385011\pi$
$710$	2.43886e12			0.360183
$711$	−2.92755e12	−	5.07067e12i	−0.429627	−	0.744136i
$712$	−8.24737e10	−	1.42849e11i	−0.0120269	−	0.0208313i
$713$	4.67039e12	−	8.08936e12i	0.676785	−	1.17223i
$714$	4.49622e11	−	7.78768e11i	0.0647449	−	0.112141i
$715$	−1.19138e12			−0.170480
$716$	4.76461e12	−	8.25255e12i	0.677515	−	1.17349i
$717$	1.66682e12	−	2.88701e12i	0.235533	−	0.407955i
$718$	6.92603e12	−	1.19962e13i	0.972577	−	1.68455i
$719$	−2.75703e12	−	4.77531e12i	−0.384735	−	0.666380i	0.606998	−	0.794704i	$-0.292374\pi$
$719$	−2.75703e12	−	4.77531e12i	−0.384735	−	0.666380i	−0.991732	+	0.128324i	$0.959040\pi$
$720$	−1.92219e12			−0.266563
$721$	−3.61896e11	−	6.26823e11i	−0.0498741	−	0.0863845i
$722$	−4.92662e12	+	8.53315e12i	−0.674732	+	1.16867i
$723$	5.10843e12			0.695289
$724$	4.03934e12	−	6.99634e12i	0.546370	−	0.946340i
$725$	−4.43541e12	−	7.68236e12i	−0.596229	−	1.03270i
$726$	−2.92435e11	−	5.06512e11i	−0.0390674	−	0.0676667i
$727$	8.08269e12			1.07313			0.536564	−	0.843860i	$-0.319722\pi$
$727$	8.08269e12			1.07313			0.536564	+	0.843860i	$0.319722\pi$
$728$	−3.64235e10	−	6.30874e10i	−0.00480608	−	0.00832437i
$729$	5.64011e12			0.739629
$730$	−3.93585e12			−0.512963
$731$	1.03883e13	+	4.22603e12i	1.34560	+	0.547400i
$732$	4.87658e12			0.627792
$733$	1.32851e13			1.69979			0.849896	−	0.526951i	$-0.176665\pi$
$733$	1.32851e13			1.69979			0.849896	+	0.526951i	$0.176665\pi$
$734$	7.33864e12	+	1.27109e13i	0.933219	+	1.61638i
$735$	−2.10836e12			−0.266472
$736$	−7.69290e12	−	1.33245e13i	−0.966362	−	1.67379i
$737$	9.47042e11	+	1.64032e12i	0.118240	+	0.204798i
$738$	−4.06718e12	+	7.04456e12i	−0.504707	+	0.874178i
$739$	−9.80658e12			−1.20953			−0.604766	−	0.796403i	$-0.706733\pi$
$739$	−9.80658e12			−1.20953			−0.604766	+	0.796403i	$0.706733\pi$
$740$	1.48642e12	−	2.57456e12i	0.182221	−	0.315617i
$741$	−2.06218e10	−	3.57180e10i	−0.00251272	−	0.00435216i
$742$	−5.86955e11			−0.0710865
$743$	−7.27626e12	−	1.26029e13i	−0.875908	−	1.51712i	−0.855792	−	0.517320i	$-0.826930\pi$
$743$	−7.27626e12	−	1.26029e13i	−0.875908	−	1.51712i	−0.0201167	−	0.999798i	$-0.506404\pi$
$744$	−6.02998e11	+	1.04442e12i	−0.0721503	+	0.124968i
$745$	8.79880e11	−	1.52400e12i	0.104645	−	0.181251i
$746$	−3.09403e11	+	5.35902e11i	−0.0365763	+	0.0633520i
$747$	3.68238e12			0.432700
$748$	5.33459e12	−	9.23979e12i	0.623081	−	1.07921i
$749$	1.40767e11	−	2.43816e11i	0.0163431	−	0.0283071i
$750$	−2.88480e12	−	4.99663e12i	−0.332921	−	0.576636i
$751$	−2.41446e12	−	4.18196e12i	−0.276974	−	0.479734i	0.693657	−	0.720306i	$-0.255998\pi$
$751$	−2.41446e12	−	4.18196e12i	−0.276974	−	0.479734i	−0.970631	+	0.240572i	$0.922665\pi$
$752$	−8.37482e11			−0.0954982
$753$	−3.48973e12			−0.395561
$754$	3.42526e12	+	5.93272e12i	0.385942	+	0.668472i
$755$	−1.93363e11	−	3.34915e11i	−0.0216577	−	0.0375122i
$756$	3.82358e11	−	6.62264e11i	0.0425718	−	0.0737366i
$757$	7.16007e12	−	1.24016e13i	0.792476	−	1.37261i	−0.131954	−	0.991256i	$-0.542125\pi$
$757$	7.16007e12	−	1.24016e13i	0.792476	−	1.37261i	0.924430	−	0.381353i	$-0.124542\pi$
$758$	1.53936e13			1.69367
$759$	−4.63365e12	+	8.02572e12i	−0.506799	+	0.877801i
$760$	8.65064e9	−	1.49833e10i	0.000940561	−	0.00162910i
$761$	5.40021e12	−	9.35344e12i	0.583686	−	1.01097i	−0.411351	−	0.911477i	$-0.634943\pi$
$761$	5.40021e12	−	9.35344e12i	0.583686	−	1.01097i	0.995038	−	0.0994977i	$-0.0317236\pi$
$762$	7.27620e12	+	1.26027e13i	0.781820	+	1.35415i
$763$	−1.14618e12			−0.122432
$764$	3.05823e12	+	5.29700e12i	0.324750	+	0.562484i
$765$	−1.60033e12	+	2.77185e12i	−0.168940	+	0.292612i
$766$	5.16899e11			0.0542470
$767$	2.18488e11	−	3.78432e11i	0.0227954	−	0.0394829i
$768$	3.97967e12	+	6.89299e12i	0.412783	+	0.714961i
$769$	1.31376e12	+	2.27550e12i	0.135471	+	0.234643i	0.925777	−	0.378069i	$-0.123412\pi$
$769$	1.31376e12	+	2.27550e12i	0.135471	+	0.234643i	−0.790306	+	0.612712i	$0.790078\pi$
$770$	5.65086e11			0.0579304
$771$	−6.39146e12	−	1.10703e13i	−0.651411	−	1.12828i
$772$	3.80433e12			0.385479
$773$	5.71156e12			0.575369			0.287685	−	0.957725i	$-0.407114\pi$
$773$	5.71156e12			0.575369			0.287685	+	0.957725i	$0.407114\pi$
$774$	7.09096e12	+	2.88465e12i	0.710184	+	0.288908i
$775$	7.65315e12			0.762049
$776$	1.96467e12			0.194496
$777$	−3.62972e11	−	6.28686e11i	−0.0357255	−	0.0618784i
$778$	5.80697e11			0.0568252
$779$	−1.29621e11	−	2.24510e11i	−0.0126112	−	0.0218433i
$780$	4.56658e11	+	7.90956e11i	0.0441739	+	0.0765114i
$781$	3.53298e12	−	6.11930e12i	0.339791	−	0.588535i
$782$	−3.03174e13			−2.89909
$783$	7.76551e12	−	1.34503e13i	0.738316	−	1.27880i
$784$	−6.00062e12	−	1.03934e13i	−0.567250	−	0.982505i
$785$	−2.72118e12			−0.255767
$786$	−3.97886e12	−	6.89159e12i	−0.371841	−	0.644048i
$787$	−5.36329e12	+	9.28949e12i	−0.498362	+	0.863188i	−0.999998	−	0.00189034i	$-0.999398\pi$
$787$	−5.36329e12	+	9.28949e12i	−0.498362	+	0.863188i	0.501636	+	0.865079i	$0.332732\pi$
$788$	−7.36831e12	+	1.27623e13i	−0.680769	+	1.17913i
$789$	−1.19009e12	+	2.06130e12i	−0.109329	+	0.189363i
$790$	−9.15685e12			−0.836419
$791$	4.23424e11	−	7.33392e11i	0.0384575	−	0.0666104i
$792$	−7.86412e11	+	1.36211e12i	−0.0710210	+	0.123012i
$793$	−2.58064e12	−	4.46979e12i	−0.231738	−	0.401382i
$794$	8.98471e12	+	1.55620e13i	0.802253	+	1.38954i
$795$	−1.58929e12			−0.141107
$796$	1.20981e11			0.0106809
$797$	3.35750e12	+	5.81536e12i	0.294750	+	0.510521i	0.974927	−	0.222527i	$-0.0714304\pi$
$797$	3.35750e12	+	5.81536e12i	0.294750	+	0.510521i	−0.680177	+	0.733048i	$0.738097\pi$
$798$	9.78118e9	+	1.69415e10i	0.000853844	+	0.00147890i
$799$	−6.97248e11	+	1.20767e12i	−0.0605239	+	0.104830i
$800$	6.30299e12	−	1.09171e13i	0.544054	−	0.942329i
$801$	−6.63819e11			−0.0569775
$802$	−1.24697e13	+	2.15982e13i	−1.06432	+	1.84346i
$803$	−5.70156e12	+	9.87539e12i	−0.483920	+	0.838174i
$804$	7.26007e11	−	1.25748e12i	0.0612757	−	0.106133i
$805$	−3.62311e11	−	6.27541e11i	−0.0304088	−	0.0526697i
$806$	−5.91017e12			−0.493278
$807$	−9.41447e11	−	1.63063e12i	−0.0781385	−	0.135340i
$808$	−1.30667e12	+	2.26322e12i	−0.107849	+	0.186799i
$809$	1.32934e13			1.09110			0.545552	−	0.838077i	$-0.316320\pi$
$809$	1.32934e13			1.09110			0.545552	+	0.838077i	$0.316320\pi$
$810$	3.70821e11	−	6.42280e11i	0.0302678	−	0.0524254i
$811$	1.12032e13	+	1.94045e13i	0.909388	+	1.57511i	0.814917	+	0.579578i	$0.196782\pi$
$811$	1.12032e13	+	1.94045e13i	0.909388	+	1.57511i	0.0944705	+	0.995528i	$0.469884\pi$
$812$	−7.33154e11	−	1.26986e12i	−0.0591825	−	0.102507i
$813$	−1.22438e13			−0.982899
$814$	−9.54313e12	−	1.65292e13i	−0.761870	−	1.31960i
$815$	4.87275e12			0.386870
$816$	1.38598e13			1.09433
$817$	−1.92612e11	+	1.49746e11i	−0.0151246	+	0.0117586i
$818$	−2.29742e13			−1.79412
$819$	−2.93168e11			−0.0227687
$820$	2.87039e12	+	4.97166e12i	0.221707	+	0.384007i
$821$	3.53388e12			0.271461			0.135731	−	0.990746i	$-0.456662\pi$
$821$	3.53388e12			0.271461			0.135731	+	0.990746i	$0.456662\pi$
$822$	6.94663e12	+	1.20319e13i	0.530703	+	0.919204i
$823$	−3.17974e12	−	5.50747e12i	−0.241597	−	0.418459i	0.719572	−	0.694418i	$-0.244338\pi$
$823$	−3.17974e12	−	5.50747e12i	−0.241597	−	0.418459i	−0.961169	+	0.275959i	$0.911005\pi$
$824$	1.57529e12	−	2.72848e12i	0.119039	−	0.206181i
$825$	−7.59295e12			−0.570647
$826$	−1.03632e11	+	1.79495e11i	−0.00774608	+	0.0134166i
$827$	1.19247e12	+	2.06541e12i	0.0886485	+	0.153544i	0.906940	−	0.421260i	$-0.138412\pi$
$827$	1.19247e12	+	2.06541e12i	0.0886485	+	0.153544i	−0.818292	+	0.574803i	$0.805079\pi$
$828$	−9.33876e12			−0.690483
$829$	2.34313e12	+	4.05842e12i	0.172306	+	0.298443i	0.939226	−	0.343300i	$-0.111545\pi$
$829$	2.34313e12	+	4.05842e12i	0.172306	+	0.298443i	−0.766920	+	0.641743i	$0.778211\pi$
$830$	2.87946e12	−	4.98736e12i	0.210600	−	0.364770i
$831$	8.36475e11	−	1.44882e12i	0.0608483	−	0.105392i
$832$	−1.70672e12	+	2.95613e12i	−0.123483	+	0.213879i
$833$	−1.99834e13			−1.43802
$834$	−1.12424e13	+	1.94723e13i	−0.804656	+	1.39371i
$835$	6.88045e11	−	1.19173e12i	0.0489810	−	0.0848376i
$836$	1.16050e11	+	2.01005e11i	0.00821707	+	0.0142324i
$837$	6.69956e12	+	1.16040e13i	0.471826	+	0.817226i
$838$	−8.89339e12			−0.622973
$839$	1.61749e13			1.12697			0.563484	−	0.826127i	$-0.309460\pi$
$839$	1.61749e13			1.12697			0.563484	+	0.826127i	$0.309460\pi$
$840$	4.67783e10	+	8.10223e10i	0.00324181	+	0.00561498i
$841$	−7.63642e12	−	1.32267e13i	−0.526390	−	0.911735i
$842$	−1.23189e13	+	2.13370e13i	−0.844633	+	1.46295i
$843$	3.42363e12	−	5.92990e12i	0.233487	−	0.404411i
$844$	−1.52007e13			−1.03115
$845$	−2.55135e12	+	4.41908e12i	−0.172153	+	0.298178i
$846$	−4.75936e11	+	8.24345e11i	−0.0319434	+	0.0553277i
$847$	6.62478e10	−	1.14745e11i	0.00442279	−	0.00766050i
$848$	−4.52327e12	−	7.83454e12i	−0.300380	−	0.520274i
$849$	−1.63577e13			−1.08053
$850$	−1.24199e13	−	2.15119e13i	−0.816081	−	1.41349i
$851$	−1.22374e13	+	2.11957e13i	−0.799843	+	1.38537i
$852$	−5.41680e12			−0.352180
$853$	8.90813e12	−	1.54293e13i	0.576124	−	0.997876i	−0.419795	−	0.907619i	$-0.637898\pi$
$853$	8.90813e12	−	1.54293e13i	0.576124	−	0.997876i	0.995919	−	0.0902569i	$-0.0287688\pi$
$854$	1.22403e12	+	2.12008e12i	0.0787465	+	0.136393i
$855$	−3.48139e10	−	6.02994e10i	−0.00222795	−	0.00385892i
$856$	1.22549e12			0.0780149
$857$	1.04507e13	+	1.81011e13i	0.661808	+	1.14628i	0.980140	+	0.198305i	$0.0635438\pi$
$857$	1.04507e13	+	1.81011e13i	0.661808	+	1.14628i	−0.318333	+	0.947979i	$0.603123\pi$
$858$	5.86367e12			0.369383
$859$	4.12165e12			0.258286			0.129143	−	0.991626i	$-0.458777\pi$
$859$	4.12165e12			0.258286			0.129143	+	0.991626i	$0.458777\pi$
$860$	4.26529e12	−	3.31603e12i	0.265892	−	0.206717i
$861$	1.40185e12			0.0869336
$862$	2.13233e12			0.131544
$863$	−9.28446e11	−	1.60812e12i	−0.0569781	−	0.0986890i	0.836129	−	0.548532i	$-0.184813\pi$
$863$	−9.28446e11	−	1.60812e12i	−0.0569781	−	0.0986890i	−0.893108	+	0.449843i	$0.851480\pi$
$864$	2.20705e13			1.34741
$865$	1.87644e12	+	3.25009e12i	0.113963	+	0.197389i
$866$	−3.54651e12	−	6.14274e12i	−0.214275	−	0.371135i
$867$	6.07102e12	−	1.05153e13i	0.364901	−	0.632028i
$868$	1.26503e12			0.0756419
$869$	−1.32648e13	+	2.29753e13i	−0.789064	+	1.36670i
$870$	−4.39902e12	−	7.61932e12i	−0.260327	−	0.450899i
$871$	−1.53678e12			−0.0904754
$872$	−2.49460e12	−	4.32078e12i	−0.146109	−	0.253068i
$873$	3.95334e12	−	6.84738e12i	0.230356	−	0.398988i
$874$	3.29766e11	−	5.71171e11i	0.0191163	−	0.0331104i
$875$	6.53521e11	−	1.13193e12i	0.0376897	−	0.0652805i
$876$	8.74169e12			0.501565
$877$	1.32674e13	−	2.29798e13i	0.757335	−	1.31174i	−0.186870	−	0.982385i	$-0.559834\pi$
$877$	1.32674e13	−	2.29798e13i	0.757335	−	1.31174i	0.944205	−	0.329358i	$-0.106832\pi$
$878$	2.72403e12	−	4.71816e12i	0.154699	−	0.267946i
$879$	5.82203e12	+	1.00840e13i	0.328946	+	0.569751i
$880$	4.35475e12	+	7.54265e12i	0.244789	+	0.423986i
$881$	2.03625e13			1.13878			0.569389	−	0.822068i	$-0.307180\pi$
$881$	2.03625e13			1.13878			0.569389	+	0.822068i	$0.307180\pi$
$882$	−1.36405e13			−0.758963
$883$	−1.61122e13	−	2.79071e13i	−0.891932	−	1.54487i	−0.837557	−	0.546350i	$-0.816017\pi$
$883$	−1.61122e13	−	2.79071e13i	−0.891932	−	1.54487i	−0.0543748	−	0.998521i	$-0.517317\pi$
$884$	4.32827e12	+	7.49679e12i	0.238385	+	0.412895i
$885$	−2.80601e11	+	4.86016e11i	−0.0153760	+	0.0266321i
$886$	9.14334e12	−	1.58367e13i	0.498486	−	0.863403i
$887$	−6.68544e12			−0.362638			−0.181319	−	0.983424i	$-0.558037\pi$
$887$	−6.68544e12			−0.362638			−0.181319	+	0.983424i	$0.558037\pi$
$888$	1.57998e12	−	2.73660e12i	0.0852691	−	0.147690i
$889$	−1.64834e12	+	2.85501e12i	−0.0885094	+	0.153303i
$890$	−5.19076e11	+	8.99066e11i	−0.0277317	+	0.0480327i
$891$	−1.07436e12	−	1.86084e12i	−0.0571083	−	0.0989145i
$892$	−1.60440e13			−0.848535
$893$	−1.51681e10	−	2.62719e10i	−0.000798178	−	0.00138248i
$894$	−4.33055e12	+	7.50074e12i	−0.226738	+	0.392722i
$895$	1.29527e13			0.674773
$896$	−4.57343e11	+	7.92141e11i	−0.0237059	+	0.0410598i
$897$	−3.75956e12	−	6.51174e12i	−0.193897	−	0.335839i
$898$	1.10334e13	+	1.91104e13i	0.566194	+	0.980677i
$899$	2.56922e13			1.31184
$900$	−3.82575e12	−	6.62639e12i	−0.194368	−	0.336655i
$901$	−1.50635e13			−0.761488
$902$	3.68569e13			1.85392
$903$	−1.80488e11	−	1.30688e12i	−0.00903347	−	0.0654096i
$904$	3.68623e12			0.183580
$905$	1.09811e13			0.544158
$906$	9.51686e11	+	1.64837e12i	0.0469264	+	0.0812788i
$907$	2.13833e13			1.04916			0.524581	−	0.851360i	$-0.324222\pi$
$907$	2.13833e13			1.04916			0.524581	+	0.851360i	$0.324222\pi$
$908$	3.60053e12	+	6.23631e12i	0.175784	+	0.304468i
$909$	5.25860e12	+	9.10816e12i	0.255466	+	0.442479i
$910$	−2.29244e11	+	3.97062e11i	−0.0110818	+	0.0191943i
$911$	−2.60797e13			−1.25450			−0.627248	−	0.778819i	$-0.715819\pi$
$911$	−2.60797e13			−1.25450			−0.627248	+	0.778819i	$0.715819\pi$
$912$	−1.50754e11	+	2.61114e11i	−0.00721594	+	0.0124984i
$913$	−8.34249e12	−	1.44496e13i	−0.397353	−	0.688236i
$914$	1.88185e13			0.891924
$915$	3.31428e12	+	5.74050e12i	0.156313	+	0.270742i
$916$	2.37350e12	−	4.11102e12i	0.111393	−	0.192939i
$917$	9.01368e11	−	1.56121e12i	0.0420959	−	0.0729123i
$918$	2.17447e13	−	3.76630e13i	1.01056	−	1.75034i
$919$	1.90336e13			0.880239			0.440119	−	0.897939i	$-0.354936\pi$
$919$	1.90336e13			0.880239			0.440119	+	0.897939i	$0.354936\pi$
$920$	1.57710e12	−	2.73161e12i	0.0725793	−	0.125711i
$921$	−5.44710e12	+	9.43466e12i	−0.249458	+	0.432074i
$922$	−8.15592e12	−	1.41265e13i	−0.371692	−	0.643790i
$923$	2.86652e12	+	4.96495e12i	0.130001	+	0.225168i
$924$	−1.25508e12			−0.0566432
$925$	−2.00528e13			−0.900610
$926$	1.17685e13	+	2.03837e13i	0.525984	+	0.911031i
$927$	−6.33965e12	−	1.09806e13i	−0.281972	−	0.488391i
$928$	2.11596e13	−	3.66495e13i	0.936572	−	1.62219i
$929$	−1.31410e13	+	2.27609e13i	−0.578841	+	1.00258i	0.416772	+	0.909011i	$0.363161\pi$
$929$	−1.31410e13	+	2.27609e13i	−0.578841	+	1.00258i	−0.995613	+	0.0935704i	$0.970172\pi$
$930$	7.59035e12			0.332727
$931$	2.17361e11	−	3.76481e11i	0.00948219	−	0.0164236i
$932$	−7.98100e12	+	1.38235e13i	−0.346486	+	0.600131i
$933$	7.70468e12	−	1.33449e13i	0.332880	−	0.576564i
$934$	−5.19317e12	−	8.99483e12i	−0.223291	−	0.386752i
$935$	1.45022e13			0.620559
$936$	−6.38063e11	−	1.10516e12i	−0.0271720	−	0.0470633i
$937$	−1.97655e13	+	3.42348e13i	−0.837682	+	1.45091i	0.0541461	+	0.998533i	$0.482756\pi$
$937$	−1.97655e13	+	3.42348e13i	−0.837682	+	1.45091i	−0.891828	+	0.452375i	$0.850577\pi$
$938$	7.28915e11			0.0307443
$939$	−6.46369e12	+	1.11954e13i	−0.271322	+	0.469944i
$940$	3.35889e11	+	5.81777e11i	0.0140320	+	0.0243042i
$941$	−7.25948e12	−	1.25738e13i	−0.301823	−	0.522773i	0.674726	−	0.738068i	$-0.264262\pi$
$941$	−7.25948e12	−	1.25738e13i	−0.301823	−	0.522773i	−0.976549	+	0.215296i	$0.930928\pi$
$942$	1.33930e13			0.554177
$943$	−2.36312e13	−	4.09305e13i	−0.973158	−	1.68556i
$944$	−3.19448e12			−0.130926
$945$	1.03945e12			0.0423995
$946$	−4.74533e12	−	3.43600e13i	−0.192645	−	1.39490i
$947$	−2.16669e13			−0.875429			−0.437715	−	0.899114i	$-0.644212\pi$
$947$	−2.16669e13			−0.875429			−0.437715	+	0.899114i	$0.644212\pi$
$948$	2.03377e13			0.817834
$949$	−4.62601e12	−	8.01249e12i	−0.185144	−	0.320678i
$950$	5.40371e11			0.0215247
$951$	6.82490e12	+	1.18211e13i	0.270573	+	0.468646i
$952$	4.43371e11	+	7.67941e11i	0.0174945	+	0.0303013i
$953$	−2.05828e13	+	3.56504e13i	−0.808325	+	1.40006i	0.105699	+	0.994398i	$0.466292\pi$
$953$	−2.05828e13	+	3.56504e13i	−0.808325	+	1.40006i	−0.914024	+	0.405661i	$0.867041\pi$
$954$	−1.02822e13			−0.401900
$955$	−4.15693e12	+	7.20002e12i	−0.161718	+	0.280104i
$956$	−7.61061e12	−	1.31820e13i	−0.294686	−	0.510411i
$957$	−2.54901e13			−0.982352
$958$	3.31212e13	+	5.73676e13i	1.27046	+	2.20050i
$959$	−1.57368e12	+	2.72570e12i	−0.0600805	+	0.104062i
$960$	2.19192e12	−	3.79652e12i	0.0832923	−	0.144266i
$961$	2.13708e12	−	3.70153e12i	0.0808286	−	0.139999i
$962$	1.54858e13			0.582970
$963$	2.46595e12	−	4.27115e12i	0.0923986	−	0.160039i
$964$	1.16624e13	−	2.01999e13i	0.434954	−	0.753362i
$965$	2.58555e12	+	4.47830e12i	0.0959797	+	0.166242i
$966$	1.78321e12	+	3.08860e12i	0.0658877	+	0.114121i
$967$	−2.91788e13			−1.07312			−0.536559	−	0.843863i	$-0.680276\pi$
$967$	−2.91788e13			−1.07312			−0.536559	+	0.843863i	$0.680276\pi$
$968$	5.76738e11			0.0211125
$969$	2.51022e11	+	4.34783e11i	0.00914650	+	0.0158422i
$970$	−6.18265e12	−	1.07087e13i	−0.224234	−	0.388385i
$971$	9.17852e12	−	1.58977e13i	0.331349	−	0.573914i	−0.651427	−	0.758711i	$-0.725830\pi$
$971$	9.17852e12	−	1.58977e13i	0.331349	−	0.573914i	0.982777	+	0.184797i	$0.0591628\pi$
$972$	1.09700e13	−	1.90006e13i	0.394193	−	0.682762i
$973$	−5.09367e12			−0.182189
$974$	−5.40379e12	+	9.35963e12i	−0.192390	+	0.333230i
$975$	3.08030e12	−	5.33524e12i	0.109162	−	0.189075i
$976$	−1.88656e13	+	3.26762e13i	−0.665497	+	1.15267i
$977$	1.80710e13	+	3.12999e13i	0.634537	+	1.09905i	0.986613	+	0.163078i	$0.0521423\pi$
$977$	1.80710e13	+	3.12999e13i	0.634537	+	1.09905i	−0.352077	+	0.935971i	$0.614524\pi$
$978$	−2.39825e13			−0.838242
$979$	1.50389e12	+	2.60481e12i	0.0523232	+	0.0906264i
$980$	−4.81335e12	+	8.33696e12i	−0.166698	+	0.288729i
$981$	−2.00787e13			−0.692190
$982$	8.06093e12	−	1.39619e13i	0.276620	−	0.479120i
$983$	2.53403e13	+	4.38907e13i	0.865608	+	1.49928i	0.866442	+	0.499278i	$0.166401\pi$
$983$	2.53403e13	+	4.38907e13i	0.865608	+	1.49928i	−0.000833596		1.00000i	$0.500265\pi$
$984$	3.05105e12	+	5.28457e12i	0.103746	+	0.179693i
$985$	−2.00310e13			−0.678014
$986$	−4.16945e13	−	7.22170e13i	−1.40486	−	2.43329i
$987$	1.64043e11			0.00550212
$988$	−1.88317e11			−0.00628756
$989$	−3.51151e13	+	2.73001e13i	−1.16711	+	0.907363i
$990$	9.89911e12			0.327520
$991$	2.07106e13			0.682122			0.341061	−	0.940041i	$-0.389214\pi$
$991$	2.07106e13			0.682122			0.341061	+	0.940041i	$0.389214\pi$
$992$	1.82551e13	+	3.16187e13i	0.598523	+	1.03667i
$993$	1.02957e13			0.336036
$994$	−1.35963e12	−	2.35494e12i	−0.0441754	−	0.0765141i
$995$	8.22223e10	+	1.42413e11i	0.00265941	+	0.00460624i
$996$	−6.39539e12	+	1.10771e13i	−0.205921	+	0.356665i
$997$	−3.57391e11			−0.0114555			−0.00572776	−	0.999984i	$-0.501823\pi$
$997$	−3.57391e11			−0.0114555			−0.00572776	+	0.999984i	$0.501823\pi$
$998$	2.58581e13	−	4.47875e13i	0.825104	−	1.42912i
$999$	−1.75542e13	−	3.04047e13i	−0.557616	−	0.965820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.36.7	yes	64
43.6	even	3	inner	43.10.c.a.6.7	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.7	✓	64	43.6	even	3	inner
43.10.c.a.36.7	yes	64	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-30.5461 q^{2} +(46.1090 + 79.8632i) q^{3} +421.064 q^{4} +(286.168 + 495.658i) q^{5} +(-1408.45 - 2439.51i) q^{6} +(319.069 - 552.644i) q^{7} +2777.74 q^{8} +(5589.41 - 9681.15i) q^{9} +O(q^{10})\)	\(q-30.5461 q^{2} +(46.1090 + 79.8632i) q^{3} +421.064 q^{4} +(286.168 + 495.658i) q^{5} +(-1408.45 - 2439.51i) q^{6} +(319.069 - 552.644i) q^{7} +2777.74 q^{8} +(5589.41 - 9681.15i) q^{9} +(-8741.33 - 15140.4i) q^{10} -50651.5 q^{11} +(19414.9 + 33627.5i) q^{12} +(20548.3 - 35590.7i) q^{13} +(-9746.32 + 16881.1i) q^{14} +(-26389.9 + 45708.7i) q^{15} -300434. q^{16} +(-250127. + 433233. i) q^{17} +(-170735. + 295721. i) q^{18} +(-5441.33 - 9424.65i) q^{19} +(120495. + 208704. i) q^{20} +58847.9 q^{21} +1.54721e6 q^{22} +(-992007. - 1.71821e6i) q^{23} +(128079. + 221839. i) q^{24} +(812778. - 1.40777e6i) q^{25} +(-627670. + 1.08716e6i) q^{26} +2.84602e6 q^{27} +(134349. - 232698. i) q^{28} +(2.72855e6 - 4.72599e6i) q^{29} +(806108. - 1.39622e6i) q^{30} +(2.35401e6 + 4.07727e6i) q^{31} +7.75488e6 q^{32} +(-2.33549e6 - 4.04519e6i) q^{33} +(7.64041e6 - 1.32336e7i) q^{34} +365230. q^{35} +(2.35350e6 - 4.07638e6i) q^{36} +(-6.16797e6 - 1.06832e7i) q^{37} +(166211. + 287886. i) q^{38} +3.78985e6 q^{39} +(794901. + 1.37681e6i) q^{40} +2.38216e7 q^{41} -1.79757e6 q^{42} +(-3.06703e6 - 2.22078e7i) q^{43} -2.13275e7 q^{44} +6.39805e6 q^{45} +(3.03020e7 + 5.24845e7i) q^{46} +2.78757e6 q^{47} +(-1.38527e7 - 2.39936e7i) q^{48} +(1.99732e7 + 3.45946e7i) q^{49} +(-2.48272e7 + 4.30020e7i) q^{50} -4.61325e7 q^{51} +(8.65214e6 - 1.49860e7i) q^{52} +(1.50558e7 + 2.60774e7i) q^{53} -8.69348e7 q^{54} +(-1.44949e7 - 2.51058e7i) q^{55} +(886291. - 1.53510e6i) q^{56} +(501789. - 869124. i) q^{57} +(-8.33466e7 + 1.44361e8i) q^{58} +1.06329e7 q^{59} +(-1.11118e7 + 1.92463e7i) q^{60} +(6.27945e7 - 1.08763e8i) q^{61} +(-7.19058e7 - 1.24545e8i) q^{62} +(-3.56682e6 - 6.17791e6i) q^{63} -8.30591e7 q^{64} +2.35211e7 q^{65} +(7.13402e7 + 1.23565e8i) q^{66} +(-1.86972e7 - 3.23845e7i) q^{67} +(-1.05320e8 + 1.82419e8i) q^{68} +(9.14810e7 - 1.58450e8i) q^{69} -1.11564e7 q^{70} +(-6.97508e7 + 1.20812e8i) q^{71} +(1.55259e7 - 2.68917e7i) q^{72} +(1.12564e8 - 1.94967e8i) q^{73} +(1.88408e8 + 3.26331e8i) q^{74} +1.49906e8 q^{75} +(-2.29115e6 - 3.96838e6i) q^{76} +(-1.61613e7 + 2.79923e7i) q^{77} -1.15765e8 q^{78} +(2.61884e8 - 4.53596e8i) q^{79} +(-8.59747e7 - 1.48913e8i) q^{80} +(2.12108e7 + 3.67381e7i) q^{81} -7.27657e8 q^{82} +(1.64704e8 + 2.85275e8i) q^{83} +2.47787e7 q^{84} -2.86314e8 q^{85} +(9.36859e7 + 6.78361e8i) q^{86} +5.03244e8 q^{87} -1.40697e8 q^{88} +(-2.96909e7 - 5.14262e7i) q^{89} -1.95436e8 q^{90} +(-1.31126e7 - 2.27118e7i) q^{91} +(-4.17699e8 - 7.23475e8i) q^{92} +(-2.17082e8 + 3.75998e8i) q^{93} -8.51495e7 q^{94} +(3.11427e6 - 5.39408e6i) q^{95} +(3.57570e8 + 6.19329e8i) q^{96} +7.07290e8 q^{97} +(-6.10103e8 - 1.05673e9i) q^{98} +(-2.83112e8 + 4.90365e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) \) 64 * q - 70 * q^2 + 307 * q^3 + 16038 * q^4 + 681 * q^5 - 1281 * q^6 + 957 * q^7 - 10920 * q^8 - 255339 * q^9	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9} - 6237 q^{10} - 180682 q^{11} + 274344 q^{12} + 115245 q^{13} - 171208 q^{14} + 138833 q^{15} + 4289206 q^{16} + 65180 q^{17} + 603985 q^{18} + 39150 q^{19} - 2709775 q^{20} - 3105162 q^{21} + 598456 q^{22} + 1285907 q^{23} - 292550 q^{24} - 14709917 q^{25} + 5332695 q^{26} - 20118002 q^{27} - 5475298 q^{28} + 1274091 q^{29} + 28424751 q^{30} + 2899781 q^{31} - 16322030 q^{32} + 30668912 q^{33} + 6822099 q^{34} - 14750922 q^{35} - 113819232 q^{36} - 13772217 q^{37} + 2700532 q^{38} + 49876982 q^{39} - 55802359 q^{40} + 5375394 q^{41} - 62768266 q^{42} - 4250879 q^{43} - 125171958 q^{44} + 74719384 q^{45} - 91405220 q^{46} + 46104596 q^{47} + 294588191 q^{48} - 233221733 q^{49} + 380339342 q^{50} + 229598406 q^{51} + 166281612 q^{52} + 125396641 q^{53} - 137752484 q^{54} + 139471854 q^{55} + 41104589 q^{56} - 289586721 q^{57} - 183782516 q^{58} - 637949078 q^{59} - 70735747 q^{60} - 95573327 q^{61} + 181277053 q^{62} + 226632970 q^{63} + 712599660 q^{64} - 498753718 q^{65} - 349240445 q^{66} - 276270786 q^{67} + 1034771928 q^{68} - 199705103 q^{69} + 1780847990 q^{70} + 651945247 q^{71} - 270063054 q^{72} - 182725322 q^{73} - 193737672 q^{74} - 3155252572 q^{75} + 492133584 q^{76} + 216024528 q^{77} + 2562586420 q^{78} - 376932221 q^{79} - 783129021 q^{80} - 2146956496 q^{81} + 2373824428 q^{82} + 1008544071 q^{83} - 9413139208 q^{84} - 1131353054 q^{85} - 1641459050 q^{86} + 5060470018 q^{87} + 369936980 q^{88} + 2244184366 q^{89} + 3302428348 q^{90} + 3951711 q^{91} + 4361095637 q^{92} + 3133616089 q^{93} + 3002217406 q^{94} + 1515822931 q^{95} + 69408612 q^{96} - 6951085934 q^{97} + 1120193981 q^{98} + 1264470179 q^{99}+O(q^{100}) \) 64 * q - 70 * q^2 + 307 * q^3 + 16038 * q^4 + 681 * q^5 - 1281 * q^6 + 957 * q^7 - 10920 * q^8 - 255339 * q^9 - 6237 * q^10 - 180682 * q^11 + 274344 * q^12 + 115245 * q^13 - 171208 * q^14 + 138833 * q^15 + 4289206 * q^16 + 65180 * q^17 + 603985 * q^18 + 39150 * q^19 - 2709775 * q^20 - 3105162 * q^21 + 598456 * q^22 + 1285907 * q^23 - 292550 * q^24 - 14709917 * q^25 + 5332695 * q^26 - 20118002 * q^27 - 5475298 * q^28 + 1274091 * q^29 + 28424751 * q^30 + 2899781 * q^31 - 16322030 * q^32 + 30668912 * q^33 + 6822099 * q^34 - 14750922 * q^35 - 113819232 * q^36 - 13772217 * q^37 + 2700532 * q^38 + 49876982 * q^39 - 55802359 * q^40 + 5375394 * q^41 - 62768266 * q^42 - 4250879 * q^43 - 125171958 * q^44 + 74719384 * q^45 - 91405220 * q^46 + 46104596 * q^47 + 294588191 * q^48 - 233221733 * q^49 + 380339342 * q^50 + 229598406 * q^51 + 166281612 * q^52 + 125396641 * q^53 - 137752484 * q^54 + 139471854 * q^55 + 41104589 * q^56 - 289586721 * q^57 - 183782516 * q^58 - 637949078 * q^59 - 70735747 * q^60 - 95573327 * q^61 + 181277053 * q^62 + 226632970 * q^63 + 712599660 * q^64 - 498753718 * q^65 - 349240445 * q^66 - 276270786 * q^67 + 1034771928 * q^68 - 199705103 * q^69 + 1780847990 * q^70 + 651945247 * q^71 - 270063054 * q^72 - 182725322 * q^73 - 193737672 * q^74 - 3155252572 * q^75 + 492133584 * q^76 + 216024528 * q^77 + 2562586420 * q^78 - 376932221 * q^79 - 783129021 * q^80 - 2146956496 * q^81 + 2373824428 * q^82 + 1008544071 * q^83 - 9413139208 * q^84 - 1131353054 * q^85 - 1641459050 * q^86 + 5060470018 * q^87 + 369936980 * q^88 + 2244184366 * q^89 + 3302428348 * q^90 + 3951711 * q^91 + 4361095637 * q^92 + 3133616089 * q^93 + 3002217406 * q^94 + 1515822931 * q^95 + 69408612 * q^96 - 6951085934 * q^97 + 1120193981 * q^98 + 1264470179 * q^99

Introduction

L-functions

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