LMFDB - Embedded newform 43.11.b.b.42.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,11,Mod(42,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	43.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$27.3203618650$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.32
Character	$\chi$	$=$	43.42
Dual form			43.11.b.b.42.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+57.1045i q^{2} -18.6474i q^{3} -2236.92 q^{4} -2202.14i q^{5} +1064.85 q^{6} -1818.95i q^{7} -69263.1i q^{8} +58701.3 q^{9} +O(q^{10})$	\(q+57.1045i q^{2} -18.6474i q^{3} -2236.92 q^{4} -2202.14i q^{5} +1064.85 q^{6} -1818.95i q^{7} -69263.1i q^{8} +58701.3 q^{9} +125752. q^{10} +84875.6 q^{11} +41712.7i q^{12} -196611. q^{13} +103870. q^{14} -41064.1 q^{15} +1.66462e6 q^{16} +562240. q^{17} +3.35210e6i q^{18} +2.47979e6i q^{19} +4.92600e6i q^{20} -33918.6 q^{21} +4.84678e6i q^{22} +4.25931e6 q^{23} -1.29157e6 q^{24} +4.91622e6 q^{25} -1.12273e7i q^{26} -2.19573e6i q^{27} +4.06884e6i q^{28} -7153.04i q^{29} -2.34494e6i q^{30} +9.25813e6 q^{31} +2.41321e7i q^{32} -1.58271e6i q^{33} +3.21064e7i q^{34} -4.00557e6 q^{35} -1.31310e8 q^{36} +2.64139e7i q^{37} -1.41607e8 q^{38} +3.66627e6i q^{39} -1.52527e8 q^{40} -1.16242e8 q^{41} -1.93690e6i q^{42} +(8.45157e7 + 1.20285e8i) q^{43} -1.89860e8 q^{44} -1.29268e8i q^{45} +2.43225e8i q^{46} +3.14889e7 q^{47} -3.10409e7i q^{48} +2.79167e8 q^{49} +2.80738e8i q^{50} -1.04843e7i q^{51} +4.39802e8 q^{52} +2.99781e8 q^{53} +1.25386e8 q^{54} -1.86908e8i q^{55} -1.25986e8 q^{56} +4.62416e7 q^{57} +408471. q^{58} +6.98652e6 q^{59} +9.18569e7 q^{60} +1.07131e9i q^{61} +5.28681e8i q^{62} -1.06775e8i q^{63} +3.26525e8 q^{64} +4.32964e8i q^{65} +9.03797e7 q^{66} +1.30677e9 q^{67} -1.25768e9 q^{68} -7.94249e7i q^{69} -2.28736e8i q^{70} +1.39477e9i q^{71} -4.06583e9i q^{72} -7.73274e8i q^{73} -1.50835e9 q^{74} -9.16747e7i q^{75} -5.54709e9i q^{76} -1.54384e8i q^{77} -2.09361e8 q^{78} -2.98734e8 q^{79} -3.66573e9i q^{80} +3.42531e9 q^{81} -6.63792e9i q^{82} +3.52379e9 q^{83} +7.58731e7 q^{84} -1.23813e9i q^{85} +(-6.86883e9 + 4.82622e9i) q^{86} -133385. q^{87} -5.87875e9i q^{88} +8.07639e9i q^{89} +7.38179e9 q^{90} +3.57625e8i q^{91} -9.52772e9 q^{92} -1.72640e8i q^{93} +1.79815e9i q^{94} +5.46083e9 q^{95} +4.50000e8 q^{96} -7.54869e9 q^{97} +1.59417e10i q^{98} +4.98231e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) $ 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9	$ 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9} - 254122 q^{10} - 218200 q^{11} - 191008 q^{13} - 1380228 q^{14} - 512732 q^{15} + 2224308 q^{16} - 1070678 q^{17} + 17857352 q^{21} + 8915254 q^{23} - 39666730 q^{24} - 82938284 q^{25} - 55042410 q^{31} - 179227232 q^{35} + 394381042 q^{36} + 709061882 q^{38} + 433255366 q^{40} + 80370626 q^{41} + 1585062 q^{43} + 324477888 q^{44} - 544910502 q^{47} - 2479345922 q^{49} - 987059452 q^{52} - 915886820 q^{53} - 297150836 q^{54} + 2172449592 q^{56} - 2398069428 q^{57} + 930519014 q^{58} + 3394816764 q^{59} - 5474941192 q^{60} + 2925325476 q^{64} + 455136192 q^{66} + 3405920388 q^{67} + 664008226 q^{68} + 16264108918 q^{74} - 17800086268 q^{78} - 13853150858 q^{79} + 20444701546 q^{81} + 113867236 q^{83} - 30401949428 q^{84} + 19291204884 q^{86} - 5221634730 q^{87} - 6984391876 q^{90} + 41423783058 q^{92} + 4107406010 q^{95} + 33148445474 q^{96} + 15795117154 q^{97} + 1345877600 q^{99}+O(q^{100}) $ 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9 - 254122 * q^10 - 218200 * q^11 - 191008 * q^13 - 1380228 * q^14 - 512732 * q^15 + 2224308 * q^16 - 1070678 * q^17 + 17857352 * q^21 + 8915254 * q^23 - 39666730 * q^24 - 82938284 * q^25 - 55042410 * q^31 - 179227232 * q^35 + 394381042 * q^36 + 709061882 * q^38 + 433255366 * q^40 + 80370626 * q^41 + 1585062 * q^43 + 324477888 * q^44 - 544910502 * q^47 - 2479345922 * q^49 - 987059452 * q^52 - 915886820 * q^53 - 297150836 * q^54 + 2172449592 * q^56 - 2398069428 * q^57 + 930519014 * q^58 + 3394816764 * q^59 - 5474941192 * q^60 + 2925325476 * q^64 + 455136192 * q^66 + 3405920388 * q^67 + 664008226 * q^68 + 16264108918 * q^74 - 17800086268 * q^78 - 13853150858 * q^79 + 20444701546 * q^81 + 113867236 * q^83 - 30401949428 * q^84 + 19291204884 * q^86 - 5221634730 * q^87 - 6984391876 * q^90 + 41423783058 * q^92 + 4107406010 * q^95 + 33148445474 * q^96 + 15795117154 * q^97 + 1345877600 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$			57.1045i			1.78451i	0.451528	+	0.892257i	$0.350879\pi$
$2$			57.1045i			1.78451i	−0.451528	+	0.892257i	$0.649121\pi$
$3$		−	18.6474i		−	0.0767382i	−0.999264	−	0.0383691i	$-0.987784\pi$
$3$		−	18.6474i		−	0.0767382i	0.999264	−	0.0383691i	$-0.0122163\pi$
$4$	−2236.92			−2.18449
$5$		−	2202.14i		−	0.704683i	−0.935871	−	0.352342i	$-0.885385\pi$
$5$		−	2202.14i		−	0.704683i	0.935871	−	0.352342i	$-0.114615\pi$
$6$	1064.85			0.136940
$7$		−	1818.95i		−	0.108226i	−0.998535	−	0.0541128i	$-0.982767\pi$
$7$		−	1818.95i		−	0.108226i	0.998535	−	0.0541128i	$-0.0172331\pi$
$8$		−	69263.1i		−	2.11374i
$9$	58701.3			0.994111
$10$	125752.			1.25752
$11$	84875.6			0.527011			0.263505	−	0.964658i	$-0.415121\pi$
$11$	84875.6			0.527011			0.263505	+	0.964658i	$0.415121\pi$
$12$			41712.7i			0.167634i
$13$	−196611.			−0.529530			−0.264765	−	0.964313i	$-0.585294\pi$
$13$	−196611.			−0.529530			−0.264765	+	0.964313i	$0.585294\pi$
$14$	103870.			0.193130
$15$	−41064.1			−0.0540761
$16$	1.66462e6			1.58751
$17$	562240.			0.395983			0.197992	−	0.980204i	$-0.436558\pi$
$17$	562240.			0.395983			0.197992	+	0.980204i	$0.436558\pi$
$18$			3.35210e6i			1.77401i
$19$			2.47979e6i			1.00149i	0.865595	+	0.500745i	$0.166941\pi$
$19$			2.47979e6i			1.00149i	−0.865595	+	0.500745i	$0.833059\pi$
$20$			4.92600e6i			1.53937i
$21$	−33918.6			−0.00830503
$22$			4.84678e6i			0.940458i
$23$	4.25931e6			0.661759			0.330879	−	0.943673i	$-0.392655\pi$
$23$	4.25931e6			0.661759			0.330879	+	0.943673i	$0.392655\pi$
$24$	−1.29157e6			−0.162205
$25$	4.91622e6			0.503421
$26$		−	1.12273e7i		−	0.944953i
$27$		−	2.19573e6i		−	0.153024i
$28$			4.06884e6i			0.236418i
$29$		−	7153.04i		−	0.000348739i	−1.00000		0.000174370i	$-0.999944\pi$
$29$		−	7153.04i		−	0.000348739i	1.00000		0.000174370i	$-5.55036e-5\pi$
$30$		−	2.34494e6i		−	0.0964996i
$31$	9.25813e6			0.323381			0.161691	−	0.986841i	$-0.448305\pi$
$31$	9.25813e6			0.323381			0.161691	+	0.986841i	$0.448305\pi$
$32$			2.41321e7i			0.719192i
$33$		−	1.58271e6i		−	0.0404419i
$34$			3.21064e7i			0.706638i
$35$	−4.00557e6			−0.0762648
$36$	−1.31310e8			−2.17163
$37$			2.64139e7i			0.380911i	0.981696	+	0.190455i	$0.0609964\pi$
$37$			2.64139e7i			0.380911i	−0.981696	+	0.190455i	$0.939004\pi$
$38$	−1.41607e8			−1.78717
$39$			3.66627e6i			0.0406352i
$40$	−1.52527e8			−1.48952
$41$	−1.16242e8			−1.00333			−0.501664	−	0.865063i	$-0.667279\pi$
$41$	−1.16242e8			−1.00333			−0.501664	+	0.865063i	$0.667279\pi$
$42$		−	1.93690e6i		−	0.0148204i
$43$	8.45157e7	+	1.20285e8i	0.574904	+	0.818221i
$43$	8.45157e7	+	1.20285e8i	0.574904	+	0.818221i
$44$	−1.89860e8			−1.15125
$45$		−	1.29268e8i		−	0.700534i
$46$			2.43225e8i			1.18092i
$47$	3.14889e7			0.137299			0.0686496	−	0.997641i	$-0.478131\pi$
$47$	3.14889e7			0.137299			0.0686496	+	0.997641i	$0.478131\pi$
$48$		−	3.10409e7i		−	0.121823i
$49$	2.79167e8			0.988287
$50$			2.80738e8i			0.898362i
$51$		−	1.04843e7i		−	0.0303870i
$52$	4.39802e8			1.15675
$53$	2.99781e8			0.716844			0.358422	−	0.933560i	$-0.383315\pi$
$53$	2.99781e8			0.716844			0.358422	+	0.933560i	$0.383315\pi$
$54$	1.25386e8			0.273074
$55$		−	1.86908e8i		−	0.371376i
$56$	−1.25986e8			−0.228761
$57$	4.62416e7			0.0768526
$58$	408471.			0.000622330
$59$	6.98652e6			0.00977239			0.00488620	−	0.999988i	$-0.498445\pi$
$59$	6.98652e6			0.00977239			0.00488620	+	0.999988i	$0.498445\pi$
$60$	9.18569e7			0.118129
$61$			1.07131e9i			1.26843i	0.773158	+	0.634214i	$0.218676\pi$
$61$			1.07131e9i			1.26843i	−0.773158	+	0.634214i	$0.781324\pi$
$62$			5.28681e8i			0.577079i
$63$		−	1.06775e8i		−	0.107588i
$64$	3.26525e8			0.304100
$65$			4.32964e8i			0.373151i
$66$	9.03797e7			0.0721691
$67$	1.30677e9			0.967888			0.483944	−	0.875099i	$-0.339204\pi$
$67$	1.30677e9			0.967888			0.483944	+	0.875099i	$0.339204\pi$
$68$	−1.25768e9			−0.865022
$69$		−	7.94249e7i		−	0.0507822i
$70$		−	2.28736e8i		−	0.136096i
$71$			1.39477e9i			0.773055i	0.922278	+	0.386528i	$0.126326\pi$
$71$			1.39477e9i			0.773055i	−0.922278	+	0.386528i	$0.873674\pi$
$72$		−	4.06583e9i		−	2.10129i
$73$		−	7.73274e8i		−	0.373009i	−0.982454	−	0.186504i	$-0.940284\pi$
$73$		−	7.73274e8i		−	0.373009i	0.982454	−	0.186504i	$-0.0597158\pi$
$74$	−1.50835e9			−0.679741
$75$		−	9.16747e7i		−	0.0386316i
$76$		−	5.54709e9i		−	2.18775i
$77$		−	1.54384e8i		−	0.0570361i
$78$	−2.09361e8			−0.0725140
$79$	−2.98734e8			−0.0970844			−0.0485422	−	0.998821i	$-0.515458\pi$
$79$	−2.98734e8			−0.0970844			−0.0485422	+	0.998821i	$0.515458\pi$
$80$		−	3.66573e9i		−	1.11869i
$81$	3.42531e9			0.982368
$82$		−	6.63792e9i		−	1.79045i
$83$	3.52379e9			0.894582			0.447291	−	0.894389i	$-0.352389\pi$
$83$	3.52379e9			0.894582			0.447291	+	0.894389i	$0.352389\pi$
$84$	7.58731e7			0.0181423
$85$		−	1.23813e9i		−	0.279043i
$86$	−6.86883e9	+	4.82622e9i	−1.46013	+	1.02592i
$87$	−133385.			−2.67616e−5
$88$		−	5.87875e9i		−	1.11396i
$89$			8.07639e9i			1.44633i	0.690676	+	0.723164i	$0.257313\pi$
$89$			8.07639e9i			1.44633i	−0.690676	+	0.723164i	$0.742687\pi$
$90$	7.38179e9			1.25011
$91$			3.57625e8i			0.0573087i
$92$	−9.52772e9			−1.44561
$93$		−	1.72640e8i		−	0.0248157i
$94$			1.79815e9i			0.245012i
$95$	5.46083e9			0.705734
$96$	4.50000e8			0.0551895
$97$	−7.54869e9			−0.879049			−0.439524	−	0.898231i	$-0.644853\pi$
$97$	−7.54869e9			−0.879049			−0.439524	+	0.898231i	$0.644853\pi$
$98$			1.59417e10i			1.76361i
$99$	4.98231e9			0.523907
$100$	−1.09972e10			−1.09972
$101$	3.95675e9			0.376471			0.188236	−	0.982124i	$-0.439723\pi$
$101$	3.95675e9			0.376471			0.188236	+	0.982124i	$0.439723\pi$
$102$	5.98700e8			0.0542261
$103$	1.14870e10			0.990876			0.495438	−	0.868643i	$-0.335008\pi$
$103$	1.14870e10			0.990876			0.495438	+	0.868643i	$0.335008\pi$
$104$			1.36179e10i			1.11929i
$105$			7.46934e7i			0.00585242i
$106$			1.71188e10i			1.27922i
$107$	7.45115e9			0.531257			0.265628	−	0.964076i	$-0.414421\pi$
$107$	7.45115e9			0.531257			0.265628	+	0.964076i	$0.414421\pi$
$108$			4.91168e9i			0.334281i
$109$	1.68687e10			1.09635			0.548175	−	0.836363i	$-0.315323\pi$
$109$	1.68687e10			1.09635			0.548175	+	0.836363i	$0.315323\pi$
$110$	1.06733e10			0.662725
$111$	4.92549e8			0.0292304
$112$		−	3.02786e9i		−	0.171809i
$113$		−	1.10472e10i		−	0.599596i	−0.954003	−	0.299798i	$-0.903081\pi$
$113$		−	1.10472e10i		−	0.599596i	0.954003	−	0.299798i	$-0.0969192\pi$
$114$			2.64060e9i			0.137144i
$115$		−	9.37957e9i		−	0.466331i
$116$			1.60008e7i			0.000761818i
$117$	−1.15413e10			−0.526412
$118$			3.98961e8i			0.0174390i
$119$		−	1.02268e9i		−	0.0428555i
$120$			2.84422e9i			0.114303i
$121$	−1.87336e10			−0.722260
$122$	−6.11765e10			−2.26353
$123$			2.16760e9i			0.0769935i
$124$	−2.07097e10			−0.706424
$125$		−	3.23314e10i		−	1.05944i
$126$	6.09730e9			0.191993
$127$	−4.21274e10			−1.27510			−0.637552	−	0.770407i	$-0.720053\pi$
$127$	−4.21274e10			−1.27510			−0.637552	+	0.770407i	$0.720053\pi$
$128$			4.33573e10i			1.26186i
$129$	2.24301e9	−	1.57600e9i	0.0627888	−	0.0441170i
$130$	−2.47241e10			−0.665893
$131$		−	2.65584e9i		−	0.0688407i	−0.999407	−	0.0344203i	$-0.989042\pi$
$131$		−	2.65584e9i		−	0.0688407i	0.999407	−	0.0344203i	$-0.0109585\pi$
$132$			3.54039e9i			0.0883449i
$133$	4.51061e9			0.108387
$134$			7.46224e10i			1.72721i
$135$	−4.83530e9			−0.107834
$136$		−	3.89424e10i		−	0.837006i
$137$		−	1.39044e10i		−	0.288104i	−0.989570	−	0.144052i	$-0.953987\pi$
$137$		−	1.39044e10i		−	0.288104i	0.989570	−	0.144052i	$-0.0460133\pi$
$138$	4.53552e9			0.0906215
$139$	2.23725e10			0.431162			0.215581	−	0.976486i	$-0.430835\pi$
$139$	2.23725e10			0.431162			0.215581	+	0.976486i	$0.430835\pi$
$140$	8.96013e9			0.166600
$141$		−	5.87185e8i		−	0.0105361i
$142$	−7.96475e10			−1.37953
$143$	−1.66875e10			−0.279068
$144$	9.77156e10			1.57816
$145$	−1.57520e7			−0.000245751
$146$	4.41574e10			0.665639
$147$		−	5.20573e9i		−	0.0758394i
$148$		−	5.90856e10i		−	0.832096i
$149$		−	9.63861e10i		−	1.31245i	−0.754565	−	0.656225i	$-0.772152\pi$
$149$		−	9.63861e10i		−	1.31245i	0.754565	−	0.656225i	$-0.227848\pi$
$150$	5.23503e9			0.0689387
$151$		−	8.29933e10i		−	1.05720i	−0.848870	−	0.528601i	$-0.822717\pi$
$151$		−	8.29933e10i		−	1.05720i	0.848870	−	0.528601i	$-0.177283\pi$
$152$	1.71758e11			2.11689
$153$	3.30042e10			0.393651
$154$	8.81603e9			0.101782
$155$		−	2.03877e10i		−	0.227882i
$156$		−	8.20116e9i		−	0.0887671i
$157$		−	1.42899e11i		−	1.49807i	−0.662532	−	0.749034i	$-0.730518\pi$
$157$		−	1.42899e11i		−	1.49807i	0.662532	−	0.749034i	$-0.269482\pi$
$158$		−	1.70591e10i		−	0.173249i
$159$		−	5.59013e9i		−	0.0550093i
$160$	5.31421e10			0.506803
$161$		−	7.74746e9i		−	0.0716192i
$162$			1.95600e11i			1.75305i
$163$			1.25418e11i			1.08999i	0.838440	+	0.544993i	$0.183468\pi$
$163$			1.25418e11i			1.08999i	−0.838440	+	0.544993i	$0.816532\pi$
$164$	2.60023e11			2.19176
$165$	−3.48534e9			−0.0284987
$166$			2.01224e11i			1.59639i
$167$	5.76436e10			0.443781			0.221891	−	0.975072i	$-0.428777\pi$
$167$	5.76436e10			0.443781			0.221891	+	0.975072i	$0.428777\pi$
$168$			2.34931e9i			0.0175547i
$169$	−9.92027e10			−0.719598
$170$	7.07026e10			0.497956
$171$			1.45567e11i			0.995593i
$172$	−1.89055e11	−	2.69069e11i	−1.25587	−	1.78740i
$173$	1.26919e11			0.819021			0.409511	−	0.912305i	$-0.365699\pi$
$173$	1.26919e11			0.819021			0.409511	+	0.912305i	$0.365699\pi$
$174$		−	7.61690e6i		−	4.77565e-5i
$175$		−	8.94235e9i		−	0.0544831i
$176$	1.41286e11			0.836635
$177$		−	1.30280e8i		−	0.000749915i
$178$	−4.61198e11			−2.58099
$179$		−	2.41061e11i		−	1.31179i	−0.754854	−	0.655893i	$-0.772292\pi$
$179$		−	2.41061e11i		−	1.31179i	0.754854	−	0.655893i	$-0.227708\pi$
$180$			2.89162e11i			1.53031i
$181$	−2.48789e11			−1.28067			−0.640336	−	0.768095i	$-0.721205\pi$
$181$	−2.48789e11			−1.28067			−0.640336	+	0.768095i	$0.721205\pi$
$182$	−2.04220e10			−0.102268
$183$	1.99771e10			0.0973368
$184$		−	2.95013e11i		−	1.39879i
$185$	5.81669e10			0.268421
$186$	9.85851e9			0.0442840
$187$	4.77204e10			0.208688
$188$	−7.04380e10			−0.299929
$189$	−3.99392e9			−0.0165612
$190$			3.11838e11i			1.25939i
$191$		−	1.27186e11i		−	0.500347i	−0.968201	−	0.250174i	$-0.919512\pi$
$191$		−	1.27186e11i		−	0.500347i	0.968201	−	0.250174i	$-0.0804877\pi$
$192$		−	6.08884e9i		−	0.0233361i
$193$	−1.33168e11			−0.497293			−0.248647	−	0.968594i	$-0.579986\pi$
$193$	−1.33168e11			−0.497293			−0.248647	+	0.968594i	$0.579986\pi$
$194$		−	4.31064e11i		−	1.56867i
$195$	8.07363e9			0.0286349
$196$	−6.24473e11			−2.15890
$197$	3.13724e11			1.05734			0.528672	−	0.848826i	$-0.322690\pi$
$197$	3.13724e11			1.05734			0.528672	+	0.848826i	$0.322690\pi$
$198$			2.84512e11i			0.934920i
$199$		−	4.99495e11i		−	1.60054i	−0.599642	−	0.800268i	$-0.704690\pi$
$199$		−	4.99495e11i		−	1.60054i	0.599642	−	0.800268i	$-0.295310\pi$
$200$		−	3.40513e11i		−	1.06410i
$201$		−	2.43678e10i		−	0.0742739i
$202$			2.25948e11i			0.671818i
$203$	−1.30110e7			−3.77425e−5
$204$			2.34525e10i			0.0663802i
$205$			2.55980e11i			0.707028i
$206$			6.55957e11i			1.76823i
$207$	2.50027e11			0.657862
$208$	−3.27283e11			−0.840634
$209$			2.10474e11i			0.527796i
$210$	−4.26532e9			−0.0104437
$211$		−	4.50429e11i		−	1.07700i	−0.842627	−	0.538498i	$-0.818992\pi$
$211$		−	4.50429e11i		−	1.07700i	0.842627	−	0.538498i	$-0.181008\pi$
$212$	−6.70586e11			−1.56594
$213$	2.60088e10			0.0593228
$214$			4.25494e11i			0.948035i
$215$	2.64885e11	−	1.86115e11i	0.576587	−	0.405125i
$216$	−1.52083e11			−0.323454
$217$		−	1.68401e10i		−	0.0349981i
$218$			9.63279e11i			1.95645i
$219$	−1.44195e10			−0.0286240
$220$			4.18097e11i			0.811267i
$221$	−1.10542e11			−0.209685
$222$			2.81267e10i			0.0521620i
$223$			7.34909e11i			1.33263i	0.745671	+	0.666315i	$0.232129\pi$
$223$			7.34909e11i			1.33263i	−0.745671	+	0.666315i	$0.767871\pi$
$224$	4.38950e10			0.0778350
$225$	2.88589e11			0.500457
$226$	6.30842e11			1.06999
$227$			8.22389e11i			1.36442i	0.731156	+	0.682210i	$0.238981\pi$
$227$			8.22389e11i			1.36442i	−0.731156	+	0.682210i	$0.761019\pi$
$228$	−1.03439e11			−0.167884
$229$	8.77283e11			1.39304			0.696518	−	0.717539i	$-0.254732\pi$
$229$	8.77283e11			1.39304			0.696518	+	0.717539i	$0.254732\pi$
$230$	5.35615e11			0.832173
$231$	−2.87886e9			−0.00437684
$232$	−4.95442e8			−0.000737144
$233$			6.34864e11i			0.924488i	0.886753	+	0.462244i	$0.152956\pi$
$233$			6.34864e11i			0.924488i	−0.886753	+	0.462244i	$0.847044\pi$
$234$		−	6.59060e11i		−	0.939389i
$235$		−	6.93428e10i		−	0.0967524i
$236$	−1.56283e10			−0.0213477
$237$			5.57061e9i			0.00745008i
$238$	5.83998e10			0.0764763
$239$	−7.00573e9			−0.00898388			−0.00449194	−	0.999990i	$-0.501430\pi$
$239$	−7.00573e9			−0.00898388			−0.00449194	+	0.999990i	$0.501430\pi$
$240$	−6.83562e10			−0.0858464
$241$			1.92126e11i			0.236321i	0.992995	+	0.118160i	$0.0376997\pi$
$241$			1.92126e11i			0.236321i	−0.992995	+	0.118160i	$0.962300\pi$
$242$		−	1.06977e12i		−	1.28888i
$243$		−	1.93529e11i		−	0.228410i
$244$		−	2.39643e12i		−	2.77087i
$245$		−	6.14763e11i		−	0.696430i
$246$	−1.23780e11			−0.137396
$247$		−	4.87553e11i		−	0.530319i
$248$		−	6.41247e11i		−	0.683544i
$249$		−	6.57095e10i		−	0.0686486i
$250$	1.84627e12			1.89058
$251$	−7.65495e11			−0.768375			−0.384188	−	0.923255i	$-0.625518\pi$
$251$	−7.65495e11			−0.768375			−0.384188	+	0.923255i	$0.625518\pi$
$252$			2.38846e11i			0.235026i
$253$	3.61511e11			0.348754
$254$		−	2.40566e12i		−	2.27544i
$255$	−2.30878e10			−0.0214132
$256$	−2.14153e12			−1.94771
$257$			2.15015e12i			1.91780i	0.283745	+	0.958900i	$0.408423\pi$
$257$			2.15015e12i			1.91780i	−0.283745	+	0.958900i	$0.591577\pi$
$258$	8.99964e10	+	1.28086e11i	0.0787275	+	0.112048i
$259$	4.80454e10			0.0412243
$260$		−	9.68504e11i		−	0.815145i
$261$		−	4.19893e8i		−	0.000346686i
$262$	1.51660e11			0.122847
$263$			9.92900e11i			0.789090i	0.918877	+	0.394545i	$0.129098\pi$
$263$			9.92900e11i			0.789090i	−0.918877	+	0.394545i	$0.870902\pi$
$264$	−1.09623e11			−0.0854836
$265$		−	6.60158e11i		−	0.505148i
$266$			2.57576e11i			0.193418i
$267$	1.50603e11			0.110989
$268$	−2.92314e12			−2.11434
$269$	3.87961e11			0.275440			0.137720	−	0.990471i	$-0.456023\pi$
$269$	3.87961e11			0.275440			0.137720	+	0.990471i	$0.456023\pi$
$270$		−	2.76117e11i		−	0.192431i
$271$	1.29080e11			0.0883107			0.0441554	−	0.999025i	$-0.485940\pi$
$271$	1.29080e11			0.0883107			0.0441554	+	0.999025i	$0.485940\pi$
$272$	9.35918e11			0.628627
$273$	6.66876e9			0.00439776
$274$	7.94004e11			0.514126
$275$	4.17268e11			0.265308
$276$			1.77667e11i			0.110933i
$277$		−	1.08344e12i		−	0.664364i	−0.943215	−	0.332182i	$-0.892215\pi$
$277$		−	1.08344e12i		−	0.664364i	0.943215	−	0.332182i	$-0.107785\pi$
$278$			1.27757e12i			0.769415i
$279$	5.43464e11			0.321477
$280$			2.77438e11i			0.161204i
$281$	−5.74014e11			−0.327635			−0.163818	−	0.986491i	$-0.552381\pi$
$281$	−5.74014e11			−0.327635			−0.163818	+	0.986491i	$0.552381\pi$
$282$	3.35309e10			0.0188018
$283$	−2.28530e12			−1.25896			−0.629478	−	0.777018i	$-0.716731\pi$
$283$	−2.28530e12			−1.25896			−0.629478	+	0.777018i	$0.716731\pi$
$284$		−	3.11998e12i		−	1.68873i
$285$		−	1.01830e11i		−	0.0541567i
$286$		−	9.52928e11i		−	0.498001i
$287$			2.11438e11i			0.108586i
$288$			1.41658e12i			0.714957i
$289$	−1.69988e12			−0.843197
$290$		−	8.99508e8i		−	0.000438546i
$291$			1.40763e11i			0.0674566i
$292$			1.72975e12i			0.814834i
$293$	−1.26450e12			−0.585572			−0.292786	−	0.956178i	$-0.594582\pi$
$293$	−1.26450e12			−0.585572			−0.292786	+	0.956178i	$0.594582\pi$
$294$	2.97270e11			0.135336
$295$		−	1.53853e10i		−	0.00688644i
$296$	1.82950e12			0.805146
$297$		−	1.86364e11i		−	0.0806456i
$298$	5.50407e12			2.34209
$299$	−8.37425e11			−0.350421
$300$			2.05069e11i			0.0843904i
$301$	2.18793e11	−	1.53730e11i	0.0885525	−	0.0622193i
$302$	4.73929e12			1.88659
$303$		−	7.37830e10i		−	0.0288897i
$304$			4.12792e12i			1.58988i
$305$	2.35917e12			0.893840
$306$			1.88469e12i			0.702477i
$307$	2.50470e11			0.0918469			0.0459235	−	0.998945i	$-0.485377\pi$
$307$	2.50470e11			0.0918469			0.0459235	+	0.998945i	$0.485377\pi$
$308$			3.45345e11i			0.124595i
$309$		−	2.14202e11i		−	0.0760380i
$310$	1.16423e12			0.406658
$311$	−4.53328e12			−1.55815			−0.779077	−	0.626928i	$-0.784312\pi$
$311$	−4.53328e12			−1.55815			−0.779077	+	0.626928i	$0.784312\pi$
$312$	2.53937e11			0.0858922
$313$			3.19354e12i			1.06304i	0.847045	+	0.531522i	$0.178380\pi$
$313$			3.19354e12i			1.06304i	−0.847045	+	0.531522i	$0.821620\pi$
$314$	8.16018e12			2.67332
$315$	−2.35132e11			−0.0758157
$316$	6.68244e11			0.212080
$317$	−4.16251e12			−1.30035			−0.650173	−	0.759786i	$-0.725304\pi$
$317$	−4.16251e12			−1.30035			−0.650173	+	0.759786i	$0.725304\pi$
$318$	3.19221e11			0.0981649
$319$		−	6.07119e8i		−	0.000183789i
$320$		−	7.19053e11i		−	0.214295i
$321$		−	1.38944e11i		−	0.0407677i
$322$	4.42414e11			0.127806
$323$			1.39424e12i			0.396574i
$324$	−7.66213e12			−2.14597
$325$	−9.66582e11			−0.266577
$326$	−7.16192e12			−1.94510
$327$		−	3.14557e11i		−	0.0841320i
$328$			8.05126e12i			2.12077i
$329$		−	5.72766e10i		−	0.0148593i
$330$		−	1.99028e11i		−	0.0508563i
$331$			2.33766e12i			0.588358i	0.955750	+	0.294179i	$0.0950461\pi$
$331$			2.33766e12i			0.588358i	−0.955750	+	0.294179i	$0.904954\pi$
$332$	−7.88244e12			−1.95421
$333$			1.55053e12i			0.378668i
$334$			3.29171e12i			0.791934i
$335$		−	2.87768e12i		−	0.682055i
$336$	−5.64617e10			−0.0131843
$337$	−6.43508e12			−1.48049			−0.740244	−	0.672339i	$-0.765290\pi$
$337$	−6.43508e12			−1.48049			−0.740244	+	0.672339i	$0.765290\pi$
$338$		−	5.66492e12i		−	1.28413i
$339$	−2.06001e11			−0.0460119
$340$			2.76959e12i			0.609567i
$341$	7.85790e11			0.170426
$342$	−8.31251e12			−1.77665
$343$		−	1.02160e12i		−	0.215184i
$344$	8.33134e12	−	5.85381e12i	1.72951	−	1.21520i
$345$	−1.74904e11			−0.0357854
$346$			7.24762e12i			1.46155i
$347$		−	6.74519e12i		−	1.34075i	−0.742024	−	0.670373i	$-0.766134\pi$
$347$		−	6.74519e12i		−	1.34075i	0.742024	−	0.670373i	$-0.233866\pi$
$348$	2.98372e8			5.84605e−5
$349$		−	3.87004e12i		−	0.747462i	−0.927537	−	0.373731i	$-0.878078\pi$
$349$		−	3.87004e12i		−	0.747462i	0.927537	−	0.373731i	$-0.121922\pi$
$350$	5.10648e11			0.0972258
$351$			4.31705e11i			0.0810310i
$352$			2.04823e12i			0.379022i
$353$	2.15226e12			0.392665			0.196332	−	0.980537i	$-0.437097\pi$
$353$	2.15226e12			0.392665			0.196332	+	0.980537i	$0.437097\pi$
$354$	7.43958e9			0.00133823
$355$	3.07147e12			0.544759
$356$		−	1.80662e13i		−	3.15949i
$357$	−1.90704e10			−0.00328865
$358$	1.37657e13			2.34090
$359$	6.07414e12			1.01862			0.509310	−	0.860583i	$-0.329901\pi$
$359$	6.07414e12			1.01862			0.509310	+	0.860583i	$0.329901\pi$
$360$	−8.95351e12			−1.48075
$361$	−1.82909e10			−0.00298331
$362$		−	1.42070e13i		−	2.28538i
$363$			3.49332e11i			0.0554249i
$364$		−	7.99977e11i		−	0.125190i
$365$	−1.70285e12			−0.262853
$366$			1.14078e12i			0.173699i
$367$	−2.68441e12			−0.403198			−0.201599	−	0.979468i	$-0.564614\pi$
$367$	−2.68441e12			−0.403198			−0.201599	+	0.979468i	$0.564614\pi$
$368$	7.09015e12			1.05055
$369$	−6.82354e12			−0.997419
$370$			3.32159e12i			0.479002i
$371$		−	5.45286e11i		−	0.0775809i
$372$			3.86181e11i			0.0542097i
$373$			8.55286e12i			1.18459i	0.805722	+	0.592294i	$0.201778\pi$
$373$			8.55286e12i			1.18459i	−0.805722	+	0.592294i	$0.798222\pi$
$374$			2.72505e12i			0.372406i
$375$	−6.02896e11			−0.0812992
$376$		−	2.18102e12i		−	0.290215i
$377$			1.40636e9i			0.000184668i
$378$		−	2.28071e11i		−	0.0295536i
$379$	1.36576e13			1.74654			0.873269	−	0.487238i	$-0.161996\pi$
$379$	1.36576e13			1.74654			0.873269	+	0.487238i	$0.161996\pi$
$380$	−1.22154e13			−1.54167
$381$			7.85565e11i			0.0978492i
$382$	7.26287e12			0.892877
$383$			5.32035e12i			0.645574i	0.946472	+	0.322787i	$0.104620\pi$
$383$			5.32035e12i			0.645574i	−0.946472	+	0.322787i	$0.895380\pi$
$384$	8.08500e11			0.0968331
$385$	−3.39975e11			−0.0401924
$386$		−	7.60447e12i		−	0.887427i
$387$	4.96118e12	+	7.06091e12i	0.571518	+	0.813403i
$388$	1.68858e13			1.92027
$389$			7.76096e12i			0.871299i	0.900116	+	0.435650i	$0.143481\pi$
$389$			7.76096e12i			0.871299i	−0.900116	+	0.435650i	$0.856519\pi$
$390$			4.61040e11i			0.0510994i
$391$	2.39475e12			0.262045
$392$		−	1.93359e13i		−	2.08898i
$393$	−4.95244e10			−0.00528271
$394$			1.79150e13i			1.88685i
$395$			6.57853e11i			0.0684138i
$396$	−1.11450e13			−1.14447
$397$	−8.18970e12			−0.830454			−0.415227	−	0.909718i	$-0.636298\pi$
$397$	−8.18970e12			−0.830454			−0.415227	+	0.909718i	$0.636298\pi$
$398$	2.85234e13			2.85618
$399$		−	8.41110e10i		−	0.00831741i
$400$	8.18366e12			0.799186
$401$	1.19369e13			1.15125			0.575626	−	0.817713i	$-0.304758\pi$
$401$	1.19369e13			1.15125			0.575626	+	0.817713i	$0.304758\pi$
$402$	1.39151e12			0.132543
$403$	−1.82025e12			−0.171240
$404$	−8.85093e12			−0.822398
$405$		−	7.54299e12i		−	0.692259i
$406$		−	7.42986e8i		−	6.73520e-5i
$407$			2.24189e12i			0.200744i
$408$	−7.26174e11			−0.0642303
$409$			2.10211e13i			1.83670i	0.395766	+	0.918351i	$0.370479\pi$
$409$			2.10211e13i			1.83670i	−0.395766	+	0.918351i	$0.629521\pi$
$410$	−1.46176e13			−1.26170
$411$	−2.59281e11			−0.0221086
$412$	−2.56954e13			−2.16456
$413$		−	1.27081e10i		−	0.00105762i
$414$			1.42776e13i			1.17396i
$415$		−	7.75987e12i		−	0.630397i
$416$		−	4.74463e12i		−	0.380834i
$417$		−	4.17189e11i		−	0.0330866i
$418$	−1.20190e13			−0.941860
$419$		−	1.65091e13i		−	1.27836i	−0.769056	−	0.639181i	$-0.779273\pi$
$419$		−	1.65091e13i		−	1.27836i	0.769056	−	0.639181i	$-0.220727\pi$
$420$		−	1.67083e11i		−	0.0127846i
$421$		−	2.29197e13i		−	1.73300i	−0.499176	−	0.866501i	$-0.666364\pi$
$421$		−	2.29197e13i		−	1.73300i	0.499176	−	0.866501i	$-0.333636\pi$
$422$	2.57215e13			1.92192
$423$	1.84844e12			0.136491
$424$		−	2.07637e13i		−	1.51522i
$425$	2.76410e12			0.199346
$426$			1.48522e12i			0.105862i
$427$	1.94866e12			0.137276
$428$	−1.66676e13			−1.16053
$429$			3.11177e11i			0.0214152i
$430$	1.06280e13	+	1.51261e13i	0.722951	+	1.02893i
$431$	2.74183e13			1.84355			0.921773	−	0.387731i	$-0.126741\pi$
$431$	2.74183e13			1.84355			0.921773	+	0.387731i	$0.126741\pi$
$432$		−	3.65507e12i		−	0.242928i
$433$		−	1.02469e13i		−	0.673216i	−0.941645	−	0.336608i	$-0.890720\pi$
$433$		−	1.02469e13i		−	0.673216i	0.941645	−	0.336608i	$-0.109280\pi$
$434$	9.61642e11			0.0624547
$435$			2.93733e8i			1.88585e-5i
$436$	−3.77340e13			−2.39497
$437$			1.05622e13i			0.662745i
$438$		−	8.23419e11i		−	0.0510799i
$439$	−2.04098e13			−1.25175			−0.625873	−	0.779925i	$-0.715257\pi$
$439$	−2.04098e13			−1.25175			−0.625873	+	0.779925i	$0.715257\pi$
$440$	−1.29458e13			−0.784992
$441$	1.63874e13			0.982467
$442$		−	6.31246e12i		−	0.374186i
$443$	1.64922e13			0.966630			0.483315	−	0.875447i	$-0.339433\pi$
$443$	1.64922e13			0.966630			0.483315	+	0.875447i	$0.339433\pi$
$444$	−1.10179e12			−0.0638535
$445$	1.77853e13			1.01920
$446$	−4.19666e13			−2.37810
$447$	−1.79735e12			−0.100715
$448$		−	5.93932e11i		−	0.0329114i
$449$			4.44530e11i			0.0243596i	0.999926	+	0.0121798i	$0.00387704\pi$
$449$			4.44530e11i			0.0243596i	−0.999926	+	0.0121798i	$0.996123\pi$
$450$			1.64797e13i			0.893072i
$451$	−9.86609e12			−0.528764
$452$			2.47116e13i			1.30981i
$453$	−1.54761e12			−0.0811278
$454$	−4.69621e13			−2.43483
$455$	7.87538e11			0.0403845
$456$		−	3.20283e12i		−	0.162446i
$457$			3.80983e12i			0.191128i	0.995423	+	0.0955641i	$0.0304655\pi$
$457$			3.80983e12i			0.191128i	−0.995423	+	0.0955641i	$0.969534\pi$
$458$			5.00968e13i			2.48589i
$459$		−	1.23453e12i		−	0.0605951i
$460$			2.09813e13i			1.01869i
$461$	−3.28817e13			−1.57924			−0.789622	−	0.613594i	$-0.789723\pi$
$461$	−3.28817e13			−1.57924			−0.789622	+	0.613594i	$0.789723\pi$
$462$		−	1.64396e11i		−	0.00781054i
$463$		−	3.09113e13i		−	1.45282i	−0.687262	−	0.726410i	$-0.741188\pi$
$463$		−	3.09113e13i		−	1.45282i	0.687262	−	0.726410i	$-0.258812\pi$
$464$		−	1.19071e10i		−	0.000553627i
$465$	−3.80177e11			−0.0174872
$466$	−3.62536e13			−1.64976
$467$			2.24409e11i			0.0101031i	0.999987	+	0.00505156i	$0.00160797\pi$
$467$			2.24409e11i			0.0101031i	−0.999987	+	0.00505156i	$0.998392\pi$
$468$	2.58169e13			1.14994
$469$		−	2.37695e12i		−	0.104750i
$470$	3.95978e12			0.172656
$471$	−2.66470e12			−0.114959
$472$		−	4.83908e11i		−	0.0206563i
$473$	7.17332e12	+	1.02093e13i	0.302980	+	0.431211i
$474$	−3.18107e11			−0.0132948
$475$			1.21912e13i			0.504172i
$476$			2.28766e12i			0.0936175i
$477$	1.75975e13			0.712623
$478$		−	4.00058e11i		−	0.0160319i
$479$	−1.96576e13			−0.779566			−0.389783	−	0.920907i	$-0.627450\pi$
$479$	−1.96576e13			−0.779566			−0.389783	+	0.920907i	$0.627450\pi$
$480$		−	9.90962e11i		−	0.0388911i
$481$		−	5.19325e12i		−	0.201704i
$482$	−1.09713e13			−0.421718
$483$	−1.44470e11			−0.00549593
$484$	4.19054e13			1.57777
$485$			1.66232e13i			0.619451i
$486$	1.10514e13			0.407600
$487$	3.32804e13			1.21491			0.607454	−	0.794355i	$-0.292191\pi$
$487$	3.32804e13			1.21491			0.607454	+	0.794355i	$0.292191\pi$
$488$	7.42022e13			2.68113
$489$	2.33871e12			0.0836436
$490$	3.51057e13			1.24279
$491$		−	2.31126e13i		−	0.809918i	−0.914335	−	0.404959i	$-0.867286\pi$
$491$		−	2.31126e13i		−	0.809918i	0.914335	−	0.404959i	$-0.132714\pi$
$492$		−	4.84875e12i		−	0.168192i
$493$		−	4.02172e9i		−	0.000138095i
$494$	2.78415e13			0.946362
$495$		−	1.09717e13i		−	0.369189i
$496$	1.54113e13			0.513371
$497$	2.53701e12			0.0836643
$498$	3.75231e12			0.122504
$499$		−	8.58315e11i		−	0.0277424i	−0.999904	−	0.0138712i	$-0.995585\pi$
$499$		−	8.58315e11i		−	0.0277424i	0.999904	−	0.0138712i	$-0.00441548\pi$
$500$			7.23228e13i			2.31433i
$501$		−	1.07490e12i		−	0.0340550i
$502$		−	4.37131e13i		−	1.37118i
$503$			3.88625e12i			0.120696i	0.998177	+	0.0603478i	$0.0192210\pi$
$503$			3.88625e12i			0.120696i	−0.998177	+	0.0603478i	$0.980779\pi$
$504$	−7.39553e12			−0.227414
$505$		−	8.71330e12i		−	0.265293i
$506$			2.06439e13i			0.622357i
$507$			1.84987e12i			0.0552206i
$508$	9.42355e13			2.78545
$509$	−5.83701e13			−1.70845			−0.854223	−	0.519906i	$-0.825967\pi$
$509$	−5.83701e13			−1.70845			−0.854223	+	0.519906i	$0.825967\pi$
$510$		−	1.31842e12i		−	0.0382122i
$511$	−1.40654e12			−0.0403691
$512$		−	7.78932e13i		−	2.21386i
$513$	5.44496e12			0.153253
$514$	−1.22783e14			−3.42234
$515$		−	2.52959e13i		−	0.698254i
$516$	−5.01743e12	+	3.52537e12i	−0.137162	+	0.0963733i
$517$	2.67264e12			0.0723581
$518$			2.74361e12i			0.0735653i
$519$		−	2.36670e12i		−	0.0628502i
$520$	2.99884e13			0.788744
$521$			1.80423e13i			0.470006i	0.971995	+	0.235003i	$0.0755100\pi$
$521$			1.80423e13i			0.470006i	−0.971995	+	0.235003i	$0.924490\pi$
$522$	2.39777e10			0.000618665
$523$		−	6.85020e13i		−	1.75063i	−0.483552	−	0.875316i	$-0.660653\pi$
$523$		−	6.85020e13i		−	1.75063i	0.483552	−	0.875316i	$-0.339347\pi$
$524$			5.94089e12i			0.150382i
$525$	−1.66751e11			−0.00418093
$526$	−5.66990e13			−1.40814
$527$	5.20529e12			0.128054
$528$		−	2.63461e12i		−	0.0642018i
$529$	−2.32848e13			−0.562075
$530$	3.76980e13			0.901444
$531$	4.10118e11			0.00971484
$532$	−1.00899e13			−0.236770
$533$	2.28544e13			0.531292
$534$			8.60013e12i			0.198061i
$535$		−	1.64084e13i		−	0.374368i
$536$		−	9.05109e13i		−	2.04586i
$537$	−4.49516e12			−0.100664
$538$			2.21543e13i			0.491526i
$539$	2.36944e13			0.520838
$540$	1.08162e13			0.235562
$541$	−6.10736e13			−1.31785			−0.658926	−	0.752207i	$-0.728989\pi$
$541$	−6.10736e13			−1.31785			−0.658926	+	0.752207i	$0.728989\pi$
$542$			7.37106e12i			0.157592i
$543$			4.63926e12i			0.0982765i
$544$			1.35680e13i			0.284788i
$545$		−	3.71472e13i		−	0.772580i
$546$			3.80816e11i			0.00784787i
$547$	−7.67144e13			−1.56653			−0.783267	−	0.621685i	$-0.786448\pi$
$547$	−7.67144e13			−1.56653			−0.783267	+	0.621685i	$0.786448\pi$
$548$			3.11030e13i			0.629362i
$549$			6.28872e13i			1.26096i
$550$			2.38278e13i			0.473447i
$551$	1.77380e10			0.000349259
$552$	−5.50121e12			−0.107340
$553$			5.43382e11i			0.0105070i
$554$	6.18693e13			1.18557
$555$		−	1.08466e12i		−	0.0205982i
$556$	−5.00455e13			−0.941870
$557$	−2.21154e13			−0.412496			−0.206248	−	0.978500i	$-0.566125\pi$
$557$	−2.21154e13			−0.412496			−0.206248	+	0.978500i	$0.566125\pi$
$558$			3.10342e13i			0.573680i
$559$	−1.66167e13	−	2.36494e13i	−0.304429	−	0.433273i
$560$	−6.66777e12			−0.121071
$561$		−	8.89861e11i		−	0.0160143i
$562$		−	3.27787e13i		−	0.584670i
$563$	2.34950e13			0.415369			0.207685	−	0.978196i	$-0.433407\pi$
$563$	2.34950e13			0.415369			0.207685	+	0.978196i	$0.433407\pi$
$564$			1.31348e12i			0.0230160i
$565$	−2.43273e13			−0.422525
$566$		−	1.30501e14i		−	2.24662i
$567$		−	6.23045e12i		−	0.106317i
$568$	9.66059e13			1.63404
$569$	1.92419e11			0.00322616			0.00161308	−	0.999999i	$-0.499487\pi$
$569$	1.92419e11			0.00322616			0.00161308	+	0.999999i	$0.499487\pi$
$570$	5.81496e12			0.0966434
$571$		−	6.65935e13i		−	1.09711i	−0.836114	−	0.548556i	$-0.815178\pi$
$571$		−	6.65935e13i		−	1.09711i	0.836114	−	0.548556i	$-0.184822\pi$
$572$	3.73285e13			0.609621
$573$	−2.37168e12			−0.0383957
$574$	−1.20740e13			−0.193773
$575$	2.09397e13			0.333143
$576$	1.91675e13			0.302310
$577$			6.72009e13i			1.05074i	0.850873	+	0.525371i	$0.176074\pi$
$577$			6.72009e13i			1.05074i	−0.850873	+	0.525371i	$0.823926\pi$
$578$		−	9.70707e13i		−	1.50470i
$579$			2.48323e12i			0.0381614i
$580$	3.52359e10			0.000536840
$581$		−	6.40960e12i		−	0.0968166i
$582$	−8.03821e12			−0.120377
$583$	2.54441e13			0.377785
$584$	−5.35593e13			−0.788444
$585$			2.54155e13i			0.370954i
$586$		−	7.22085e13i		−	1.04496i
$587$			9.27329e12i			0.133059i	0.997784	+	0.0665293i	$0.0211926\pi$
$587$			9.27329e12i			0.133059i	−0.997784	+	0.0665293i	$0.978807\pi$
$588$			1.16448e13i			0.165670i
$589$			2.29582e13i			0.323863i
$590$	8.78567e11			0.0122890
$591$		−	5.85012e12i		−	0.0811386i
$592$			4.39691e13i			0.604699i
$593$			1.26589e14i			1.72632i	0.504927	+	0.863162i	$0.331519\pi$
$593$			1.26589e14i			1.72632i	−0.504927	+	0.863162i	$0.668481\pi$
$594$	1.06422e13			0.143913
$595$	−2.25209e12			−0.0301996
$596$			2.15608e14i			2.86704i
$597$	−9.31427e12			−0.122822
$598$		−	4.78207e13i		−	0.625331i
$599$	9.12594e13			1.18343			0.591716	−	0.806146i	$-0.298451\pi$
$599$	9.12594e13			1.18343			0.591716	+	0.806146i	$0.298451\pi$
$600$	−6.34967e12			−0.0816572
$601$			8.65963e13i			1.10440i	0.833711	+	0.552201i	$0.186212\pi$
$601$			8.65963e13i			1.10440i	−0.833711	+	0.552201i	$0.813788\pi$
$602$	8.77864e12	+	1.24940e13i	0.111031	+	0.158023i
$603$	7.67090e13			0.962188
$604$			1.85649e14i			2.30945i
$605$			4.12538e13i			0.508964i
$606$	4.21334e12			0.0515541
$607$			2.96451e13i			0.359758i	0.983689	+	0.179879i	$0.0575706\pi$
$607$			2.96451e13i			0.359758i	−0.983689	+	0.179879i	$0.942429\pi$
$608$	−5.98425e13			−0.720264
$609$			2.42621e8i			2.89629e-6i
$610$			1.34719e14i			1.59507i
$611$	−6.19105e12			−0.0727040
$612$	−7.38277e13			−0.859928
$613$	−2.80351e13			−0.323891			−0.161946	−	0.986800i	$-0.551777\pi$
$613$	−2.80351e13			−0.323891			−0.161946	+	0.986800i	$0.551777\pi$
$614$			1.43030e13i			0.163902i
$615$	4.77336e12			0.0542561
$616$	−1.06931e13			−0.120559
$617$	1.75598e13			0.196378			0.0981891	−	0.995168i	$-0.468695\pi$
$617$	1.75598e13			0.196378			0.0981891	+	0.995168i	$0.468695\pi$
$618$	1.22319e13			0.135691
$619$	−4.13205e13			−0.454686			−0.227343	−	0.973815i	$-0.573004\pi$
$619$	−4.13205e13			−0.454686			−0.227343	+	0.973815i	$0.573004\pi$
$620$			4.56056e13i			0.497805i
$621$		−	9.35230e12i		−	0.101265i
$622$		−	2.58870e14i		−	2.78055i
$623$	1.46905e13			0.156530
$624$			6.10297e12i			0.0645087i
$625$	−2.31882e13			−0.243146
$626$	−1.82366e14			−1.89702
$627$	3.92478e12			0.0405021
$628$			3.19654e14i			3.27252i
$629$			1.48509e13i			0.150834i
$630$		−	1.34271e13i		−	0.135294i
$631$		−	1.03967e14i		−	1.03932i	−0.854373	−	0.519660i	$-0.826059\pi$
$631$		−	1.03967e14i		−	1.03932i	0.854373	−	0.519660i	$-0.173941\pi$
$632$			2.06912e13i			0.205211i
$633$	−8.39932e12			−0.0826467
$634$		−	2.37698e14i		−	2.32049i
$635$			9.27702e13i			0.898545i
$636$			1.25047e13i			0.120167i
$637$	−5.48872e13			−0.523328
$638$	3.46692e10			0.000327975
$639$			8.18747e13i			0.768503i
$640$	9.54787e13			0.889215
$641$		−	8.81924e13i		−	0.814969i	−0.913212	−	0.407484i	$-0.866406\pi$
$641$		−	8.81924e13i		−	0.814969i	0.913212	−	0.407484i	$-0.133594\pi$
$642$	7.93434e12			0.0727505
$643$	1.86707e14			1.69866			0.849329	−	0.527865i	$-0.177007\pi$
$643$	1.86707e14			1.69866			0.849329	+	0.527865i	$0.177007\pi$
$644$			1.73304e13i			0.156452i
$645$	−3.47056e12	−	4.93941e12i	−0.0310886	−	0.0442462i
$646$	−7.96171e13			−0.707691
$647$		−	4.89851e13i		−	0.432058i	−0.976387	−	0.216029i	$-0.930689\pi$
$647$		−	4.89851e13i		−	0.432058i	0.976387	−	0.216029i	$-0.0693106\pi$
$648$		−	2.37247e14i		−	2.07647i
$649$	5.92985e11			0.00515016
$650$		−	5.51961e13i		−	0.475710i
$651$	−3.14023e11			−0.00268569
$652$		−	2.80549e14i		−	2.38107i
$653$			1.63337e14i			1.37569i	0.725859	+	0.687844i	$0.241442\pi$
$653$			1.63337e14i			1.37569i	−0.725859	+	0.687844i	$0.758558\pi$
$654$	1.79626e13			0.150135
$655$	−5.84852e12			−0.0485109
$656$	−1.93499e14			−1.59279
$657$		−	4.53921e13i		−	0.370812i
$658$	3.27075e12			0.0265166
$659$	1.48601e14			1.19562			0.597811	−	0.801637i	$-0.296037\pi$
$659$	1.48601e14			1.19562			0.597811	+	0.801637i	$0.296037\pi$
$660$	7.79642e12			0.0622552
$661$	−2.25306e13			−0.178552			−0.0892761	−	0.996007i	$-0.528455\pi$
$661$	−2.25306e13			−0.178552			−0.0892761	+	0.996007i	$0.528455\pi$
$662$	−1.33491e14			−1.04993
$663$			2.06132e12i			0.0160908i
$664$		−	2.44069e14i		−	1.89091i
$665$		−	9.93297e12i		−	0.0763785i
$666$	−8.85420e13			−0.675738
$667$		−	3.04670e10i		−	0.000230781i
$668$	−1.28944e14			−0.969436
$669$	1.37041e13			0.102264
$670$	1.64329e14			1.21714
$671$			9.09281e13i			0.668475i
$672$		−	8.18527e11i		−	0.00597292i
$673$			1.63307e14i			1.18285i	0.806361	+	0.591424i	$0.201434\pi$
$673$			1.63307e14i			1.18285i	−0.806361	+	0.591424i	$0.798566\pi$
$674$		−	3.67472e14i		−	2.64195i
$675$		−	1.07947e13i		−	0.0770358i
$676$	2.21908e14			1.57196
$677$			2.03834e13i			0.143329i	0.997429	+	0.0716643i	$0.0228310\pi$
$677$			2.03834e13i			0.143329i	−0.997429	+	0.0716643i	$0.977169\pi$
$678$		−	1.17635e13i		−	0.0821088i
$679$			1.37307e13i			0.0951356i
$680$	−8.57565e13			−0.589824
$681$	1.53354e13			0.104703
$682$			4.48721e13i			0.304127i
$683$	−2.61360e14			−1.75847			−0.879235	−	0.476389i	$-0.841946\pi$
$683$	−2.61360e14			−1.75847			−0.879235	+	0.476389i	$0.841946\pi$
$684$		−	3.25621e14i		−	2.17486i
$685$	−3.06194e13			−0.203022
$686$	5.83377e13			0.383998
$687$		−	1.63590e13i		−	0.106899i
$688$	1.40687e14	+	2.00230e14i	0.912665	+	1.29893i
$689$	−5.89401e13			−0.379590
$690$		−	9.98782e12i		−	0.0638595i
$691$			1.06175e14i			0.673957i	0.941512	+	0.336979i	$0.109405\pi$
$691$			1.06175e14i			0.673957i	−0.941512	+	0.336979i	$0.890595\pi$
$692$	−2.83907e14			−1.78914
$693$		−	9.06256e12i		−	0.0567002i
$694$	3.85180e14			2.39258
$695$		−	4.92673e13i		−	0.303833i
$696$			9.23868e9i			5.65671e-5i
$697$	−6.53557e13			−0.397301
$698$	2.20997e14			1.33386
$699$	1.18385e13			0.0709435
$700$			2.00033e13i			0.119018i
$701$	−1.75520e14			−1.03690			−0.518449	−	0.855109i	$-0.673490\pi$
$701$	−1.75520e14			−1.03690			−0.518449	+	0.855109i	$0.673490\pi$
$702$	−2.46523e13			−0.144601
$703$	−6.55008e13			−0.381478
$704$	2.77140e13			0.160264
$705$	−1.29306e12			−0.00742460
$706$			1.22904e14i			0.700716i
$707$		−	7.19712e12i		−	0.0407438i
$708$			2.91426e11i			0.00163818i
$709$	−1.11019e14			−0.619678			−0.309839	−	0.950789i	$-0.600275\pi$
$709$	−1.11019e14			−0.619678			−0.309839	+	0.950789i	$0.600275\pi$
$710$			1.75395e14i			0.972130i
$711$	−1.75361e13			−0.0965127
$712$	5.59395e14			3.05716
$713$	3.94332e13			0.214001
$714$		−	1.08900e12i		−	0.00586865i
$715$			3.67481e13i			0.196655i
$716$			5.39235e14i			2.86558i
$717$			1.30638e11i			0.000689406i
$718$			3.46860e14i			1.81774i
$719$	2.29173e14			1.19267			0.596333	−	0.802737i	$-0.296624\pi$
$719$	2.29173e14			1.19267			0.596333	+	0.802737i	$0.296624\pi$
$720$		−	2.15183e14i		−	1.11210i
$721$		−	2.08942e13i		−	0.107238i
$722$		−	1.04449e12i		−	0.00532377i
$723$	3.58265e12			0.0181348
$724$	5.56521e14			2.79762
$725$		−	3.51659e10i		−	0.000175563i
$726$	−1.99484e13			−0.0989065
$727$		−	2.63433e14i		−	1.29717i	−0.761142	−	0.648586i	$-0.775361\pi$
$727$		−	2.63433e14i		−	1.29717i	0.761142	−	0.648586i	$-0.224639\pi$
$728$	2.47702e13			0.121136
$729$	1.98652e14			0.964841
$730$		−	9.72405e13i		−	0.469065i
$731$	4.75181e13	+	6.76292e13i	0.227652	+	0.324002i
$732$	−4.46872e13			−0.212631
$733$			6.84831e13i			0.323641i	0.986820	+	0.161820i	$0.0517365\pi$
$733$			6.84831e13i			0.323641i	−0.986820	+	0.161820i	$0.948263\pi$
$734$		−	1.53292e14i		−	0.719512i
$735$	−1.14637e13			−0.0534427
$736$			1.02786e14i			0.475932i
$737$	1.10913e14			0.510087
$738$		−	3.89654e14i		−	1.77991i
$739$		−	3.18534e14i		−	1.44522i	−0.691256	−	0.722610i	$-0.742942\pi$
$739$		−	3.18534e14i		−	1.44522i	0.691256	−	0.722610i	$-0.257058\pi$
$740$	−1.30115e14			−0.586364
$741$	−9.09159e12			−0.0406957
$742$	3.11382e13			0.138444
$743$		−	1.06741e14i		−	0.471396i	−0.971826	−	0.235698i	$-0.924262\pi$
$743$		−	1.06741e14i		−	0.471396i	0.971826	−	0.235698i	$-0.0757376\pi$
$744$	−1.19576e13			−0.0524539
$745$	−2.12255e14			−0.924862
$746$	−4.88406e14			−2.11391
$747$	2.06851e14			0.889314
$748$	−1.06747e14			−0.455876
$749$		−	1.35532e13i		−	0.0574956i
$750$		−	3.44281e13i		−	0.145080i
$751$		−	3.69630e14i		−	1.54728i	−0.633628	−	0.773638i	$-0.718435\pi$
$751$		−	3.69630e14i		−	1.54728i	0.633628	−	0.773638i	$-0.281565\pi$
$752$	5.24171e13			0.217964
$753$			1.42745e13i			0.0589637i
$754$	−8.03097e10			−0.000329542
$755$	−1.82762e14			−0.744993
$756$	8.93408e12			0.0361777
$757$			7.07825e13i			0.284739i	0.989814	+	0.142369i	$0.0454721\pi$
$757$			7.07825e13i			0.284739i	−0.989814	+	0.142369i	$0.954528\pi$
$758$			7.79909e14i			3.11672i
$759$		−	6.74124e12i		−	0.0267628i
$760$		−	3.78234e14i		−	1.49174i
$761$			2.27363e14i			0.890833i	0.895323	+	0.445417i	$0.146944\pi$
$761$			2.27363e14i			0.890833i	−0.895323	+	0.445417i	$0.853056\pi$
$762$	−4.48593e13			−0.174613
$763$		−	3.06833e13i		−	0.118653i
$764$			2.84504e14i			1.09300i
$765$		−	7.26797e13i		−	0.277400i
$766$	−3.03816e14			−1.15204
$767$	−1.37362e12			−0.00517477
$768$			3.99340e13i			0.149464i
$769$	−2.60420e14			−0.968374			−0.484187	−	0.874965i	$-0.660885\pi$
$769$	−2.60420e14			−0.968374			−0.484187	+	0.874965i	$0.660885\pi$
$770$		−	1.94141e13i		−	0.0717238i
$771$	4.00947e13			0.147168
$772$	2.97885e14			1.08633
$773$		−	1.78304e14i		−	0.646045i	−0.946391	−	0.323023i	$-0.895301\pi$
$773$		−	1.78304e14i		−	0.646045i	0.946391	−	0.323023i	$-0.104699\pi$
$774$	−4.03209e14	+	2.83305e14i	−1.45153	+	1.01988i
$775$	4.55151e13			0.162797
$776$			5.22845e14i			1.85808i
$777$		−	8.95921e11i		−	0.00316348i
$778$	−4.43185e14			−1.55485
$779$		−	2.88255e14i		−	1.00482i
$780$	−1.80601e13			−0.0625527
$781$			1.18382e14i			0.407408i
$782$			1.36751e14i			0.467624i
$783$	−1.57062e10			−5.33656e−5
$784$	4.64708e14			1.56892
$785$	−3.14683e14			−1.05566
$786$		−	2.82806e12i		−	0.00942707i
$787$	−3.33113e14			−1.10336			−0.551680	−	0.834056i	$-0.686013\pi$
$787$	−3.33113e14			−1.10336			−0.551680	+	0.834056i	$0.686013\pi$
$788$	−7.01775e14			−2.30976
$789$	1.85150e13			0.0605534
$790$	−3.75664e13			−0.122085
$791$	−2.00942e13			−0.0648916
$792$		−	3.45090e14i		−	1.10740i
$793$		−	2.10631e14i		−	0.671670i
$794$		−	4.67669e14i		−	1.48196i
$795$	−1.23102e13			−0.0387641
$796$			1.11733e15i			3.49636i
$797$	3.13392e14			0.974532			0.487266	−	0.873254i	$-0.337994\pi$
$797$	3.13392e14			0.974532			0.487266	+	0.873254i	$0.337994\pi$
$798$	4.80311e12			0.0148425
$799$	1.77043e13			0.0543682
$800$			1.18639e14i			0.362057i
$801$			4.74094e14i			1.43781i
$802$			6.81651e14i			2.05442i
$803$		−	6.56321e13i		−	0.196580i
$804$			5.45088e13i			0.162251i
$805$	−1.70609e13			−0.0504689
$806$		−	1.03944e14i		−	0.305580i
$807$		−	7.23445e12i		−	0.0211367i
$808$		−	2.74057e14i		−	0.795763i
$809$	−5.35034e14			−1.54397			−0.771984	−	0.635642i	$-0.780736\pi$
$809$	−5.35034e14			−1.54397			−0.771984	+	0.635642i	$0.780736\pi$
$810$	4.30738e14			1.23535
$811$		−	4.81889e14i		−	1.37354i	−0.726873	−	0.686772i	$-0.759027\pi$
$811$		−	4.81889e14i		−	1.37354i	0.726873	−	0.686772i	$-0.240973\pi$
$812$	2.91046e10			8.24481e−5
$813$		−	2.40701e12i		−	0.00677680i
$814$	−1.28022e14			−0.358231
$815$	2.76187e14			0.768096
$816$		−	1.74524e13i		−	0.0482397i
$817$	−2.98283e14	+	2.09581e14i	−0.819441	+	0.575760i
$818$	−1.20040e15			−3.27762
$819$			2.09930e13i			0.0569712i
$820$		−	5.72606e14i		−	1.54450i
$821$	3.85049e14			1.03229			0.516143	−	0.856503i	$-0.327367\pi$
$821$	3.85049e14			1.03229			0.516143	+	0.856503i	$0.327367\pi$
$822$		−	1.48061e13i		−	0.0394531i
$823$	8.97443e13			0.237688			0.118844	−	0.992913i	$-0.462081\pi$
$823$	8.97443e13			0.237688			0.118844	+	0.992913i	$0.462081\pi$
$824$		−	7.95622e14i		−	2.09445i
$825$		−	7.78094e12i		−	0.0203593i
$826$	7.25690e11			0.00188734
$827$	6.58096e14			1.70123			0.850613	−	0.525793i	$-0.176231\pi$
$827$	6.58096e14			1.70123			0.850613	+	0.525793i	$0.176231\pi$
$828$	−5.59290e14			−1.43709
$829$		−	4.31626e14i		−	1.10239i	−0.834377	−	0.551194i	$-0.814172\pi$
$829$		−	4.31626e14i		−	1.10239i	0.834377	−	0.551194i	$-0.185828\pi$
$830$	4.43123e14			1.12495
$831$	−2.02033e13			−0.0509821
$832$	−6.41984e13			−0.161030
$833$	1.56959e14			0.391345
$834$	2.38233e13			0.0590435
$835$		−	1.26939e14i		−	0.312725i
$836$		−	4.70813e14i		−	1.15297i
$837$		−	2.03284e13i		−	0.0494853i
$838$	9.42745e14			2.28126
$839$			3.83588e14i			0.922688i	0.887221	+	0.461344i	$0.152633\pi$
$839$			3.83588e14i			0.922688i	−0.887221	+	0.461344i	$0.847367\pi$
$840$	5.17349e12			0.0123705
$841$	4.20707e14			1.00000
$842$	1.30882e15			3.09257
$843$			1.07038e13i			0.0251421i
$844$			1.00757e15i			2.35269i
$845$			2.18458e14i			0.507089i
$846$			1.05554e14i			0.243569i
$847$			3.40753e13i			0.0781670i
$848$	4.99023e14			1.13800
$849$			4.26148e13i			0.0966100i
$850$			1.57842e14i			0.355736i
$851$			1.12505e14i			0.252071i
$852$	−5.81795e13			−0.129590
$853$	−1.46909e14			−0.325314			−0.162657	−	0.986683i	$-0.552006\pi$
$853$	−1.46909e14			−0.325314			−0.162657	+	0.986683i	$0.552006\pi$
$854$			1.11277e14i			0.244972i
$855$	3.20558e14			0.701578
$856$		−	5.16089e14i		−	1.12294i
$857$	4.19235e14			0.906888			0.453444	−	0.891285i	$-0.350195\pi$
$857$	4.19235e14			0.906888			0.453444	+	0.891285i	$0.350195\pi$
$858$	−1.77696e13			−0.0382157
$859$		−	3.29596e14i		−	0.704719i	−0.935865	−	0.352360i	$-0.885379\pi$
$859$		−	3.29596e14i		−	0.704719i	0.935865	−	0.352360i	$-0.114621\pi$
$860$	−5.92526e14	+	4.16324e14i	−1.25955	+	0.884992i
$861$	3.94276e12			0.00833267
$862$			1.56571e15i			3.28983i
$863$		−	6.83525e14i		−	1.42791i	−0.700192	−	0.713954i	$-0.746902\pi$
$863$		−	6.83525e14i		−	1.42791i	0.700192	−	0.713954i	$-0.253098\pi$
$864$	5.29876e13			0.110054
$865$		−	2.79492e14i		−	0.577151i
$866$	5.85145e14			1.20136
$867$			3.16983e13i			0.0647054i
$868$			3.76698e13i			0.0764531i
$869$	−2.53553e13			−0.0511645
$870$	−1.67735e10			−3.36532e−5
$871$	−2.56925e14			−0.512525
$872$		−	1.16838e15i		−	2.31740i
$873$	−4.43118e14			−0.873872
$874$	−6.03148e14			−1.18268
$875$	−5.88092e13			−0.114658
$876$	3.22553e13			0.0625289
$877$	3.46402e14			0.667701			0.333851	−	0.942626i	$-0.391652\pi$
$877$	3.46402e14			0.667701			0.333851	+	0.942626i	$0.391652\pi$
$878$		−	1.16549e15i		−	2.23376i
$879$			2.35796e13i			0.0449357i
$880$		−	3.11131e14i		−	0.589563i
$881$	2.94182e14			0.554289			0.277144	−	0.960828i	$-0.410612\pi$
$881$	2.94182e14			0.554289			0.277144	+	0.960828i	$0.410612\pi$
$882$			9.35796e14i			1.75323i
$883$	−1.25729e14			−0.234224			−0.117112	−	0.993119i	$-0.537364\pi$
$883$	−1.25729e14			−0.234224			−0.117112	+	0.993119i	$0.537364\pi$
$884$	2.47274e14			0.458055
$885$	−2.86895e11			−0.000528453
$886$			9.41779e14i			1.72496i
$887$			4.57414e14i			0.833090i	0.909115	+	0.416545i	$0.136759\pi$
$887$			4.57414e14i			0.833090i	−0.909115	+	0.416545i	$0.863241\pi$
$888$		−	3.41155e13i		−	0.0617855i
$889$			7.66275e13i			0.137999i
$890$			1.01562e15i			1.81878i
$891$	2.90725e14			0.517719
$892$		−	1.64393e15i		−	2.91112i
$893$			7.80858e13i			0.137504i
$894$		−	1.02637e14i		−	0.179727i
$895$	−5.30850e14			−0.924393
$896$	7.88647e13			0.136566
$897$			1.56158e13i			0.0268907i
$898$	−2.53847e13			−0.0434700
$899$		−	6.62238e10i		−	0.000112776i
$900$	−6.45549e14			−1.09324
$901$	1.68549e14			0.283858
$902$		−	5.63398e14i		−	0.943588i
$903$	−2.86665e12	−	4.07991e12i	−0.00477459	−	0.00679535i
$904$	−7.65160e14			−1.26739
$905$			5.47867e14i			0.902469i
$906$		−	8.83753e13i		−	0.144774i
$907$	−2.39048e14			−0.389447			−0.194724	−	0.980858i	$-0.562381\pi$
$907$	−2.39048e14			−0.389447			−0.194724	+	0.980858i	$0.562381\pi$
$908$		−	1.83962e15i		−	2.98056i
$909$	2.32266e14			0.374254
$910$			4.49719e13i			0.0720667i
$911$			5.26630e14i			0.839294i	0.907687	+	0.419647i	$0.137846\pi$
$911$			5.26630e14i			0.839294i	−0.907687	+	0.419647i	$0.862154\pi$
$912$	7.69748e13			0.122004
$913$	2.99084e14			0.471454
$914$	−2.17558e14			−0.341071
$915$		−	4.39923e13i		−	0.0685916i
$916$	−1.96241e15			−3.04307
$917$	−4.83083e12			−0.00745032
$918$	7.04971e13			0.108133
$919$	7.60464e14			1.16012			0.580058	−	0.814575i	$-0.303030\pi$
$919$	7.60464e14			1.16012			0.580058	+	0.814575i	$0.303030\pi$
$920$	−6.49658e14			−0.985702
$921$		−	4.67062e12i		−	0.00704816i
$922$		−	1.87769e15i		−	2.81818i
$923$		−	2.74226e14i		−	0.409356i
$924$	6.43978e12			0.00956117
$925$			1.29856e14i			0.191759i
$926$	1.76517e15			2.59258
$927$	6.74300e14			0.985041
$928$	1.72618e11			0.000250811
$929$			3.27786e14i			0.473709i	0.971545	+	0.236855i	$0.0761165\pi$
$929$			3.27786e14i			0.473709i	−0.971545	+	0.236855i	$0.923883\pi$
$930$		−	2.17098e13i		−	0.0312062i
$931$			6.92275e14i			0.989760i
$932$		−	1.42014e15i		−	2.01954i
$933$			8.45338e13i			0.119570i
$934$	−1.28147e13			−0.0180292
$935$		−	1.05087e14i		−	0.147059i
$936$			7.99386e14i			1.11270i
$937$		−	9.81273e14i		−	1.35860i	−0.733860	−	0.679300i	$-0.762283\pi$
$937$		−	9.81273e14i		−	1.35860i	0.733860	−	0.679300i	$-0.237717\pi$
$938$	1.35734e14			0.186928
$939$	5.95512e13			0.0815760
$940$			1.55114e14i			0.211355i
$941$	−3.45253e14			−0.467939			−0.233969	−	0.972244i	$-0.575172\pi$
$941$	−3.45253e14			−0.467939			−0.233969	+	0.972244i	$0.575172\pi$
$942$		−	1.52166e14i		−	0.205146i
$943$	−4.95109e14			−0.663961
$944$	1.16299e13			0.0155138
$945$			8.79516e12i			0.0116704i
$946$	−5.82997e14	+	4.09629e14i	−0.769503	+	0.540673i
$947$	−7.34535e13			−0.0964412			−0.0482206	−	0.998837i	$-0.515355\pi$
$947$	−7.34535e13			−0.0964412			−0.0482206	+	0.998837i	$0.515355\pi$
$948$		−	1.24610e13i		−	0.0162746i
$949$			1.52034e14i			0.197519i
$950$	−6.96172e14			−0.899701
$951$			7.76199e13i			0.0997862i
$952$	−7.08342e13			−0.0905855
$953$		−	2.74344e14i		−	0.349005i	−0.984657	−	0.174502i	$-0.944168\pi$
$953$		−	2.74344e14i		−	0.349005i	0.984657	−	0.174502i	$-0.0558316\pi$
$954$			1.00490e15i			1.27169i
$955$	−2.80080e14			−0.352586
$956$	1.56712e13			0.0196252
$957$	−1.13212e10			−1.41037e−5
$958$		−	1.12254e15i		−	1.39115i
$959$	−2.52914e13			−0.0311803
$960$	−1.34085e13			−0.0164446
$961$	−7.33915e14			−0.895424
$962$	2.96558e14			0.359943
$963$	4.37392e14			0.528128
$964$		−	4.29771e14i		−	0.516241i
$965$			2.93254e14i			0.350434i
$966$		−	8.24986e12i		−	0.00980756i
$967$	−8.62206e14			−1.01971			−0.509857	−	0.860259i	$-0.670302\pi$
$967$	−8.62206e14			−1.01971			−0.509857	+	0.860259i	$0.670302\pi$
$968$			1.29754e15i			1.52667i
$969$	2.59988e13			0.0304323
$970$	−9.49261e14			−1.10542
$971$	8.55599e14			0.991230			0.495615	−	0.868542i	$-0.334943\pi$
$971$	8.55599e14			0.991230			0.495615	+	0.868542i	$0.334943\pi$
$972$			4.32908e14i			0.498959i
$973$		−	4.06944e13i		−	0.0466628i
$974$			1.90046e15i			2.16802i
$975$			1.80242e13i			0.0204566i
$976$			1.78333e15i			2.01364i
$977$	2.37846e14			0.267192			0.133596	−	0.991036i	$-0.457348\pi$
$977$	2.37846e14			0.267192			0.133596	+	0.991036i	$0.457348\pi$
$978$			1.33551e14i			0.149263i
$979$			6.85488e14i			0.762231i
$980$			1.37517e15i			1.52134i
$981$	9.90215e14			1.08989
$982$	1.31983e15			1.44531
$983$			3.50277e14i			0.381631i	0.981626	+	0.190816i	$0.0611133\pi$
$983$			3.50277e14i			0.381631i	−0.981626	+	0.190816i	$0.938887\pi$
$984$	1.50135e14			0.162744
$985$		−	6.90862e14i		−	0.745093i
$986$	2.29658e11			0.000246432
$987$	−1.06806e12			−0.00114027
$988$			1.09062e15i			1.15848i
$989$	3.59978e14	+	5.12333e14i	0.380448	+	0.541465i
$990$	6.26534e14			0.658823
$991$			2.02632e14i			0.212002i	0.994366	+	0.106001i	$0.0338047\pi$
$991$			2.02632e14i			0.212002i	−0.994366	+	0.106001i	$0.966195\pi$
$992$			2.23418e14i			0.232573i
$993$	4.35912e13			0.0451495
$994$			1.44875e14i			0.149300i
$995$	−1.09996e15			−1.12787
$996$			1.46987e14i			0.149962i
$997$			2.81153e14i			0.285408i	0.989765	+	0.142704i	$0.0455797\pi$
$997$			2.81153e14i			0.285408i	−0.989765	+	0.142704i	$0.954420\pi$
$998$	4.90136e13			0.0495067
$999$	5.79978e13			0.0582886

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.b.b.42.32	yes	34
43.42	odd	2	inner	43.11.b.b.42.3	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.b.b.42.3	✓	34	43.42	odd	2	inner
43.11.b.b.42.32	yes	34	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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+57.1045i q^{2} -18.6474i q^{3} -2236.92 q^{4} -2202.14i q^{5} +1064.85 q^{6} -1818.95i q^{7} -69263.1i q^{8} +58701.3 q^{9} +O(q^{10})\)	\(q+57.1045i q^{2} -18.6474i q^{3} -2236.92 q^{4} -2202.14i q^{5} +1064.85 q^{6} -1818.95i q^{7} -69263.1i q^{8} +58701.3 q^{9} +125752. q^{10} +84875.6 q^{11} +41712.7i q^{12} -196611. q^{13} +103870. q^{14} -41064.1 q^{15} +1.66462e6 q^{16} +562240. q^{17} +3.35210e6i q^{18} +2.47979e6i q^{19} +4.92600e6i q^{20} -33918.6 q^{21} +4.84678e6i q^{22} +4.25931e6 q^{23} -1.29157e6 q^{24} +4.91622e6 q^{25} -1.12273e7i q^{26} -2.19573e6i q^{27} +4.06884e6i q^{28} -7153.04i q^{29} -2.34494e6i q^{30} +9.25813e6 q^{31} +2.41321e7i q^{32} -1.58271e6i q^{33} +3.21064e7i q^{34} -4.00557e6 q^{35} -1.31310e8 q^{36} +2.64139e7i q^{37} -1.41607e8 q^{38} +3.66627e6i q^{39} -1.52527e8 q^{40} -1.16242e8 q^{41} -1.93690e6i q^{42} +(8.45157e7 + 1.20285e8i) q^{43} -1.89860e8 q^{44} -1.29268e8i q^{45} +2.43225e8i q^{46} +3.14889e7 q^{47} -3.10409e7i q^{48} +2.79167e8 q^{49} +2.80738e8i q^{50} -1.04843e7i q^{51} +4.39802e8 q^{52} +2.99781e8 q^{53} +1.25386e8 q^{54} -1.86908e8i q^{55} -1.25986e8 q^{56} +4.62416e7 q^{57} +408471. q^{58} +6.98652e6 q^{59} +9.18569e7 q^{60} +1.07131e9i q^{61} +5.28681e8i q^{62} -1.06775e8i q^{63} +3.26525e8 q^{64} +4.32964e8i q^{65} +9.03797e7 q^{66} +1.30677e9 q^{67} -1.25768e9 q^{68} -7.94249e7i q^{69} -2.28736e8i q^{70} +1.39477e9i q^{71} -4.06583e9i q^{72} -7.73274e8i q^{73} -1.50835e9 q^{74} -9.16747e7i q^{75} -5.54709e9i q^{76} -1.54384e8i q^{77} -2.09361e8 q^{78} -2.98734e8 q^{79} -3.66573e9i q^{80} +3.42531e9 q^{81} -6.63792e9i q^{82} +3.52379e9 q^{83} +7.58731e7 q^{84} -1.23813e9i q^{85} +(-6.86883e9 + 4.82622e9i) q^{86} -133385. q^{87} -5.87875e9i q^{88} +8.07639e9i q^{89} +7.38179e9 q^{90} +3.57625e8i q^{91} -9.52772e9 q^{92} -1.72640e8i q^{93} +1.79815e9i q^{94} +5.46083e9 q^{95} +4.50000e8 q^{96} -7.54869e9 q^{97} +1.59417e10i q^{98} +4.98231e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) \) 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9} - 254122 q^{10} - 218200 q^{11} - 191008 q^{13} - 1380228 q^{14} - 512732 q^{15} + 2224308 q^{16} - 1070678 q^{17} + 17857352 q^{21} + 8915254 q^{23} - 39666730 q^{24} - 82938284 q^{25} - 55042410 q^{31} - 179227232 q^{35} + 394381042 q^{36} + 709061882 q^{38} + 433255366 q^{40} + 80370626 q^{41} + 1585062 q^{43} + 324477888 q^{44} - 544910502 q^{47} - 2479345922 q^{49} - 987059452 q^{52} - 915886820 q^{53} - 297150836 q^{54} + 2172449592 q^{56} - 2398069428 q^{57} + 930519014 q^{58} + 3394816764 q^{59} - 5474941192 q^{60} + 2925325476 q^{64} + 455136192 q^{66} + 3405920388 q^{67} + 664008226 q^{68} + 16264108918 q^{74} - 17800086268 q^{78} - 13853150858 q^{79} + 20444701546 q^{81} + 113867236 q^{83} - 30401949428 q^{84} + 19291204884 q^{86} - 5221634730 q^{87} - 6984391876 q^{90} + 41423783058 q^{92} + 4107406010 q^{95} + 33148445474 q^{96} + 15795117154 q^{97} + 1345877600 q^{99}+O(q^{100}) \) 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9 - 254122 * q^10 - 218200 * q^11 - 191008 * q^13 - 1380228 * q^14 - 512732 * q^15 + 2224308 * q^16 - 1070678 * q^17 + 17857352 * q^21 + 8915254 * q^23 - 39666730 * q^24 - 82938284 * q^25 - 55042410 * q^31 - 179227232 * q^35 + 394381042 * q^36 + 709061882 * q^38 + 433255366 * q^40 + 80370626 * q^41 + 1585062 * q^43 + 324477888 * q^44 - 544910502 * q^47 - 2479345922 * q^49 - 987059452 * q^52 - 915886820 * q^53 - 297150836 * q^54 + 2172449592 * q^56 - 2398069428 * q^57 + 930519014 * q^58 + 3394816764 * q^59 - 5474941192 * q^60 + 2925325476 * q^64 + 455136192 * q^66 + 3405920388 * q^67 + 664008226 * q^68 + 16264108918 * q^74 - 17800086268 * q^78 - 13853150858 * q^79 + 20444701546 * q^81 + 113867236 * q^83 - 30401949428 * q^84 + 19291204884 * q^86 - 5221634730 * q^87 - 6984391876 * q^90 + 41423783058 * q^92 + 4107406010 * q^95 + 33148445474 * q^96 + 15795117154 * q^97 + 1345877600 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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