LMFDB - Embedded newform 196.6.e.g.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,6,Mod(165,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("196.165");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	196.e (of order $3$, degree $2$, not 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:	$31.4352286833$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	196.177
Dual form			196.6.e.g.165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.00000 + 10.3923i) q^{3} +(-27.0000 + 46.7654i) q^{5} +(49.5000 - 85.7365i) q^{9} +O(q^{10})$	\(q+(6.00000 + 10.3923i) q^{3} +(-27.0000 + 46.7654i) q^{5} +(49.5000 - 85.7365i) q^{9} +(-270.000 - 467.654i) q^{11} -418.000 q^{13} -648.000 q^{15} +(-297.000 - 514.419i) q^{17} +(-418.000 + 723.997i) q^{19} +(2052.00 - 3554.17i) q^{23} +(104.500 + 180.999i) q^{25} +4104.00 q^{27} -594.000 q^{29} +(-2128.00 - 3685.80i) q^{31} +(3240.00 - 5611.84i) q^{33} +(149.000 - 258.076i) q^{37} +(-2508.00 - 4343.98i) q^{39} +17226.0 q^{41} -12100.0 q^{43} +(2673.00 + 4629.77i) q^{45} +(648.000 - 1122.37i) q^{47} +(3564.00 - 6173.03i) q^{51} +(-9747.00 - 16882.3i) q^{53} +29160.0 q^{55} -10032.0 q^{57} +(3834.00 + 6640.68i) q^{59} +(17369.0 - 30084.0i) q^{61} +(11286.0 - 19547.9i) q^{65} +(-10906.0 - 18889.7i) q^{67} +49248.0 q^{69} -46872.0 q^{71} +(-33781.0 - 58510.4i) q^{73} +(-1254.00 + 2171.99i) q^{75} +(38456.0 - 66607.7i) q^{79} +(12595.5 + 21816.0i) q^{81} +67716.0 q^{83} +32076.0 q^{85} +(-3564.00 - 6173.03i) q^{87} +(-14877.0 + 25767.7i) q^{89} +(25536.0 - 44229.6i) q^{93} +(-22572.0 - 39095.9i) q^{95} -122398. q^{97} -53460.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 12 q^{3} - 54 q^{5} + 99 q^{9}+O(q^{10}) $ 2 * q + 12 * q^3 - 54 * q^5 + 99 * q^9	$ 2 q + 12 q^{3} - 54 q^{5} + 99 q^{9} - 540 q^{11} - 836 q^{13} - 1296 q^{15} - 594 q^{17} - 836 q^{19} + 4104 q^{23} + 209 q^{25} + 8208 q^{27} - 1188 q^{29} - 4256 q^{31} + 6480 q^{33} + 298 q^{37} - 5016 q^{39} + 34452 q^{41} - 24200 q^{43} + 5346 q^{45} + 1296 q^{47} + 7128 q^{51} - 19494 q^{53} + 58320 q^{55} - 20064 q^{57} + 7668 q^{59} + 34738 q^{61} + 22572 q^{65} - 21812 q^{67} + 98496 q^{69} - 93744 q^{71} - 67562 q^{73} - 2508 q^{75} + 76912 q^{79} + 25191 q^{81} + 135432 q^{83} + 64152 q^{85} - 7128 q^{87} - 29754 q^{89} + 51072 q^{93} - 45144 q^{95} - 244796 q^{97} - 106920 q^{99}+O(q^{100}) $ 2 * q + 12 * q^3 - 54 * q^5 + 99 * q^9 - 540 * q^11 - 836 * q^13 - 1296 * q^15 - 594 * q^17 - 836 * q^19 + 4104 * q^23 + 209 * q^25 + 8208 * q^27 - 1188 * q^29 - 4256 * q^31 + 6480 * q^33 + 298 * q^37 - 5016 * q^39 + 34452 * q^41 - 24200 * q^43 + 5346 * q^45 + 1296 * q^47 + 7128 * q^51 - 19494 * q^53 + 58320 * q^55 - 20064 * q^57 + 7668 * q^59 + 34738 * q^61 + 22572 * q^65 - 21812 * q^67 + 98496 * q^69 - 93744 * q^71 - 67562 * q^73 - 2508 * q^75 + 76912 * q^79 + 25191 * q^81 + 135432 * q^83 + 64152 * q^85 - 7128 * q^87 - 29754 * q^89 + 51072 * q^93 - 45144 * q^95 - 244796 * q^97 - 106920 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	6.00000	+	10.3923i	0.384900	+	0.666667i	0.991755	−	0.128146i	$-0.0409025\pi$
$3$	6.00000	+	10.3923i	0.384900	+	0.666667i	−0.606855	+	0.794812i	$0.707569\pi$
$4$		0			0
$5$	−27.0000	+	46.7654i	−0.482991	+	0.836564i	−0.999809	−	0.0195305i	$-0.993783\pi$
$5$	−27.0000	+	46.7654i	−0.482991	+	0.836564i	0.516819	+	0.856095i	$0.327116\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	49.5000	−	85.7365i	0.203704	−	0.352825i
$10$		0			0
$11$	−270.000	−	467.654i	−0.672794	−	1.16531i	−0.977108	−	0.212742i	$-0.931761\pi$
$11$	−270.000	−	467.654i	−0.672794	−	1.16531i	0.304315	−	0.952572i	$-0.401573\pi$
$12$		0			0
$13$	−418.000			−0.685990			−0.342995	−	0.939337i	$-0.611441\pi$
$13$	−418.000			−0.685990			−0.342995	+	0.939337i	$0.611441\pi$
$14$		0			0
$15$	−648.000			−0.743613
$16$		0			0
$17$	−297.000	−	514.419i	−0.249249	−	0.431713i	0.714068	−	0.700076i	$-0.246851\pi$
$17$	−297.000	−	514.419i	−0.249249	−	0.431713i	−0.963318	+	0.268363i	$0.913517\pi$
$18$		0			0
$19$	−418.000	+	723.997i	−0.265639	+	0.460101i	−0.967731	−	0.251986i	$-0.918916\pi$
$19$	−418.000	+	723.997i	−0.265639	+	0.460101i	0.702092	+	0.712087i	$0.252250\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2052.00	−	3554.17i	0.808831	−	1.40094i	−0.104843	−	0.994489i	$-0.533434\pi$
$23$	2052.00	−	3554.17i	0.808831	−	1.40094i	0.913674	−	0.406448i	$-0.133233\pi$
$24$		0			0
$25$	104.500	+	180.999i	0.0334400	+	0.0579198i
$26$		0			0
$27$	4104.00			1.08342
$28$		0			0
$29$	−594.000			−0.131157			−0.0655785	−	0.997847i	$-0.520889\pi$
$29$	−594.000			−0.131157			−0.0655785	+	0.997847i	$0.520889\pi$
$30$		0			0
$31$	−2128.00	−	3685.80i	−0.397711	−	0.688855i	0.595732	−	0.803183i	$-0.296862\pi$
$31$	−2128.00	−	3685.80i	−0.397711	−	0.688855i	−0.993443	+	0.114328i	$0.963529\pi$
$32$		0			0
$33$	3240.00	−	5611.84i	0.517917	−	0.897059i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	149.000	−	258.076i	0.0178930	−	0.0309915i	−0.856940	−	0.515416i	$-0.827638\pi$
$37$	149.000	−	258.076i	0.0178930	−	0.0309915i	0.874833	+	0.484424i	$0.160971\pi$
$38$		0			0
$39$	−2508.00	−	4343.98i	−0.264038	−	0.457327i
$40$		0			0
$41$	17226.0			1.60039			0.800193	−	0.599742i	$-0.204730\pi$
$41$	17226.0			1.60039			0.800193	+	0.599742i	$0.204730\pi$
$42$		0			0
$43$	−12100.0			−0.997963			−0.498981	−	0.866613i	$-0.666292\pi$
$43$	−12100.0			−0.997963			−0.498981	+	0.866613i	$0.666292\pi$
$44$		0			0
$45$	2673.00	+	4629.77i	0.196774	+	0.340823i
$46$		0			0
$47$	648.000	−	1122.37i	0.0427888	−	0.0741124i	−0.843838	−	0.536598i	$-0.819709\pi$
$47$	648.000	−	1122.37i	0.0427888	−	0.0741124i	0.886627	+	0.462486i	$0.153042\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	3564.00	−	6173.03i	0.191872	−	0.332333i
$52$		0			0
$53$	−9747.00	−	16882.3i	−0.476630	−	0.825547i	0.523011	−	0.852326i	$-0.324808\pi$
$53$	−9747.00	−	16882.3i	−0.476630	−	0.825547i	−0.999641	+	0.0267784i	$0.991475\pi$
$54$		0			0
$55$	29160.0			1.29981
$56$		0			0
$57$	−10032.0			−0.408978
$58$		0			0
$59$	3834.00	+	6640.68i	0.143391	+	0.248361i	0.928772	−	0.370653i	$-0.120866\pi$
$59$	3834.00	+	6640.68i	0.143391	+	0.248361i	−0.785380	+	0.619013i	$0.787533\pi$
$60$		0			0
$61$	17369.0	−	30084.0i	0.597655	−	1.03517i	−0.395512	−	0.918461i	$-0.629433\pi$
$61$	17369.0	−	30084.0i	0.597655	−	1.03517i	0.993166	−	0.116707i	$-0.0372339\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	11286.0	−	19547.9i	0.331327	−	0.573875i
$66$		0			0
$67$	−10906.0	−	18889.7i	−0.296810	−	0.514090i	0.678594	−	0.734513i	$-0.262589\pi$
$67$	−10906.0	−	18889.7i	−0.296810	−	0.514090i	−0.975404	+	0.220423i	$0.929256\pi$
$68$		0			0
$69$	49248.0			1.24528
$70$		0			0
$71$	−46872.0			−1.10349			−0.551744	−	0.834014i	$-0.686037\pi$
$71$	−46872.0			−1.10349			−0.551744	+	0.834014i	$0.686037\pi$
$72$		0			0
$73$	−33781.0	−	58510.4i	−0.741934	−	1.28507i	−0.951614	−	0.307297i	$-0.900575\pi$
$73$	−33781.0	−	58510.4i	−0.741934	−	1.28507i	0.209679	−	0.977770i	$-0.432758\pi$
$74$		0			0
$75$	−1254.00	+	2171.99i	−0.0257421	+	0.0445867i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	38456.0	−	66607.7i	0.693260	−	1.20076i	−0.277503	−	0.960725i	$-0.589507\pi$
$79$	38456.0	−	66607.7i	0.693260	−	1.20076i	0.970764	−	0.240037i	$-0.0771597\pi$
$80$		0			0
$81$	12595.5	+	21816.0i	0.213306	+	0.369457i
$82$		0			0
$83$	67716.0			1.07894			0.539468	−	0.842006i	$-0.318625\pi$
$83$	67716.0			1.07894			0.539468	+	0.842006i	$0.318625\pi$
$84$		0			0
$85$	32076.0			0.481541
$86$		0			0
$87$	−3564.00	−	6173.03i	−0.0504824	−	0.0874380i
$88$		0			0
$89$	−14877.0	+	25767.7i	−0.199086	+	0.344827i	−0.948232	−	0.317578i	$-0.897131\pi$
$89$	−14877.0	+	25767.7i	−0.199086	+	0.344827i	0.749146	+	0.662404i	$0.230464\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	25536.0	−	44229.6i	0.306158	−	0.530281i
$94$		0			0
$95$	−22572.0	−	39095.9i	−0.256603	−	0.444449i
$96$		0			0
$97$	−122398.			−1.32082			−0.660412	−	0.750903i	$-0.729618\pi$
$97$	−122398.			−1.32082			−0.660412	+	0.750903i	$0.729618\pi$
$98$		0			0
$99$	−53460.0			−0.548202
$100$		0			0
$101$	−5643.00	−	9773.96i	−0.0550436	−	0.0953383i	0.837191	−	0.546911i	$-0.184196\pi$
$101$	−5643.00	−	9773.96i	−0.0550436	−	0.0953383i	−0.892234	+	0.451573i	$0.850863\pi$
$102$		0			0
$103$	13628.0	−	23604.4i	0.126572	−	0.219230i	−0.795774	−	0.605594i	$-0.792936\pi$
$103$	13628.0	−	23604.4i	0.126572	−	0.219230i	0.922346	+	0.386364i	$0.126269\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−61182.0	+	105970.i	−0.516612	+	0.894798i	0.483202	+	0.875509i	$0.339474\pi$
$107$	−61182.0	+	105970.i	−0.516612	+	0.894798i	−0.999814	+	0.0192889i	$0.993860\pi$
$108$		0			0
$109$	−49951.0	−	86517.7i	−0.402697	−	0.697491i	0.591354	−	0.806412i	$-0.298594\pi$
$109$	−49951.0	−	86517.7i	−0.402697	−	0.697491i	−0.994050	+	0.108921i	$0.965260\pi$
$110$		0			0
$111$	3576.00			0.0275480
$112$		0			0
$113$	−29646.0			−0.218409			−0.109204	−	0.994019i	$-0.534830\pi$
$113$	−29646.0			−0.218409			−0.109204	+	0.994019i	$0.534830\pi$
$114$		0			0
$115$	110808.	+	191925.i	0.781316	+	1.35328i
$116$		0			0
$117$	−20691.0	+	35837.9i	−0.139739	+	0.242035i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−65274.5	+	113059.i	−0.405303	+	0.702006i
$122$		0			0
$123$	103356.	+	179018.i	0.615989	+	1.06692i
$124$		0			0
$125$	−180036.			−1.03059
$126$		0			0
$127$	336512.			1.85136			0.925681	−	0.378305i	$-0.123493\pi$
$127$	336512.			1.85136			0.925681	+	0.378305i	$0.123493\pi$
$128$		0			0
$129$	−72600.0	−	125747.i	−0.384116	−	0.665308i
$130$		0			0
$131$	−50490.0	+	87451.2i	−0.257056	+	0.445233i	−0.965452	−	0.260582i	$-0.916086\pi$
$131$	−50490.0	+	87451.2i	−0.257056	+	0.445233i	0.708396	+	0.705815i	$0.249419\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−110808.	+	191925.i	−0.523283	+	0.906353i
$136$		0			0
$137$	158571.	+	274653.i	0.721809	+	1.25021i	0.960274	+	0.279059i	$0.0900225\pi$
$137$	158571.	+	274653.i	0.721809	+	1.25021i	−0.238465	+	0.971151i	$0.576644\pi$
$138$		0			0
$139$	−148324.			−0.651140			−0.325570	−	0.945518i	$-0.605556\pi$
$139$	−148324.			−0.651140			−0.325570	+	0.945518i	$0.605556\pi$
$140$		0			0
$141$	15552.0			0.0658777
$142$		0			0
$143$	112860.	+	195479.i	0.461530	+	0.799393i
$144$		0			0
$145$	16038.0	−	27778.6i	0.0633476	−	0.109721i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−98307.0	+	170273.i	−0.362759	+	0.628318i	−0.988414	−	0.151782i	$-0.951499\pi$
$149$	−98307.0	+	170273.i	−0.362759	+	0.628318i	0.625654	+	0.780100i	$0.284832\pi$
$150$		0			0
$151$	−37180.0	−	64397.6i	−0.132699	−	0.229841i	0.792017	−	0.610499i	$-0.209031\pi$
$151$	−37180.0	−	64397.6i	−0.132699	−	0.229841i	−0.924716	+	0.380658i	$0.875698\pi$
$152$		0			0
$153$	−58806.0			−0.203092
$154$		0			0
$155$	229824.			0.768362
$156$		0			0
$157$	−60439.0	−	104683.i	−0.195690	−	0.338945i	0.751437	−	0.659805i	$-0.229361\pi$
$157$	−60439.0	−	104683.i	−0.195690	−	0.338945i	−0.947126	+	0.320861i	$0.896028\pi$
$158$		0			0
$159$	116964.	−	202588.i	0.366910	−	0.635507i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	55670.0	−	96423.3i	0.164116	−	0.284258i	−0.772225	−	0.635350i	$-0.780856\pi$
$163$	55670.0	−	96423.3i	0.164116	−	0.284258i	0.936341	+	0.351091i	$0.114189\pi$
$164$		0			0
$165$	174960.	+	303040.i	0.500298	+	0.866542i
$166$		0			0
$167$	−491832.			−1.36466			−0.682332	−	0.731043i	$-0.739034\pi$
$167$	−491832.			−1.36466			−0.682332	+	0.731043i	$0.739034\pi$
$168$		0			0
$169$	−196569.			−0.529417
$170$		0			0
$171$	41382.0	+	71675.7i	0.108223	+	0.187448i
$172$		0			0
$173$	−353727.	+	612673.i	−0.898572	+	1.55637i	−0.0692518	+	0.997599i	$0.522061\pi$
$173$	−353727.	+	612673.i	−0.898572	+	1.55637i	−0.829320	+	0.558773i	$0.811272\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−46008.0	+	79688.2i	−0.110382	+	0.191188i
$178$		0			0
$179$	−246834.	−	427529.i	−0.575801	−	0.997317i	−0.995954	−	0.0898633i	$-0.971357\pi$
$179$	−246834.	−	427529.i	−0.575801	−	0.997317i	0.420153	−	0.907453i	$-0.361976\pi$
$180$		0			0
$181$	−559450.			−1.26930			−0.634651	−	0.772799i	$-0.718856\pi$
$181$	−559450.			−1.26930			−0.634651	+	0.772799i	$0.718856\pi$
$182$		0			0
$183$	416856.			0.920149
$184$		0			0
$185$	8046.00	+	13936.1i	0.0172843	+	0.0299372i
$186$		0			0
$187$	−160380.	+	277786.i	−0.335387	+	0.580907i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	362016.	−	627030.i	0.718033	−	1.24367i	−0.243745	−	0.969839i	$-0.578376\pi$
$191$	362016.	−	627030.i	0.718033	−	1.24367i	0.961778	−	0.273830i	$-0.0882906\pi$
$192$		0			0
$193$	−3553.00	−	6153.98i	−0.00686597	−	0.0118922i	0.862572	−	0.505934i	$-0.168852\pi$
$193$	−3553.00	−	6153.98i	−0.00686597	−	0.0118922i	−0.869438	+	0.494042i	$0.835519\pi$
$194$		0			0
$195$	270864.			0.510111
$196$		0			0
$197$	−530442.			−0.973806			−0.486903	−	0.873456i	$-0.661873\pi$
$197$	−530442.			−0.973806			−0.486903	+	0.873456i	$0.661873\pi$
$198$		0			0
$199$	−28084.0	−	48642.9i	−0.0502720	−	0.0870737i	0.839794	−	0.542905i	$-0.182675\pi$
$199$	−28084.0	−	48642.9i	−0.0502720	−	0.0870737i	−0.890066	+	0.455831i	$0.849342\pi$
$200$		0			0
$201$	130872.	−	226677.i	0.228484	−	0.395747i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−465102.	+	805580.i	−0.772972	+	1.33883i
$206$		0			0
$207$	−203148.	−	351863.i	−0.329524	−	0.570752i
$208$		0			0
$209$	451440.			0.714882
$210$		0			0
$211$	−339196.			−0.524499			−0.262249	−	0.965000i	$-0.584464\pi$
$211$	−339196.			−0.524499			−0.262249	+	0.965000i	$0.584464\pi$
$212$		0			0
$213$	−281232.	−	487108.i	−0.424733	−	0.735659i
$214$		0			0
$215$	326700.	−	565861.i	0.482007	−	0.834860i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	405372.	−	702125.i	0.571141	−	0.989246i
$220$		0			0
$221$	124146.	+	215027.i	0.170983	+	0.296151i
$222$		0			0
$223$	779360.			1.04948			0.524742	−	0.851261i	$-0.324162\pi$
$223$	779360.			1.04948			0.524742	+	0.851261i	$0.324162\pi$
$224$		0			0
$225$	20691.0			0.0272474
$226$		0			0
$227$	372438.	+	645082.i	0.479722	+	0.830902i	0.999729	−	0.0232592i	$-0.00740430\pi$
$227$	372438.	+	645082.i	0.479722	+	0.830902i	−0.520008	+	0.854162i	$0.674071\pi$
$228$		0			0
$229$	136373.	−	236205.i	0.171846	−	0.297646i	−0.767219	−	0.641385i	$-0.778360\pi$
$229$	136373.	−	236205.i	0.171846	−	0.297646i	0.939065	+	0.343739i	$0.111693\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	76923.0	−	133235.i	0.0928253	−	0.160778i	−0.815874	−	0.578230i	$-0.803744\pi$
$233$	76923.0	−	133235.i	0.0928253	−	0.160778i	0.908699	+	0.417452i	$0.137077\pi$
$234$		0			0
$235$	34992.0	+	60607.9i	0.0413332	+	0.0715912i
$236$		0			0
$237$	922944.			1.06734
$238$		0			0
$239$	1.15474e6			1.30764			0.653820	−	0.756650i	$-0.273166\pi$
$239$	1.15474e6			1.30764			0.653820	+	0.756650i	$0.273166\pi$
$240$		0			0
$241$	−328537.	−	569043.i	−0.364369	−	0.631106i	0.624306	−	0.781180i	$-0.285382\pi$
$241$	−328537.	−	569043.i	−0.364369	−	0.631106i	−0.988675	+	0.150074i	$0.952049\pi$
$242$		0			0
$243$	347490.	−	601870.i	0.377508	−	0.653864i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	174724.	−	302631.i	0.182226	−	0.315625i
$248$		0			0
$249$	406296.	+	703725.i	0.415283	+	0.719291i
$250$		0			0
$251$	1.34190e6			1.34442			0.672211	−	0.740359i	$-0.265345\pi$
$251$	1.34190e6			1.34442			0.672211	+	0.740359i	$0.265345\pi$
$252$		0			0
$253$	−2.21616e6			−2.17671
$254$		0			0
$255$	192456.	+	333344.i	0.185345	+	0.321027i
$256$		0			0
$257$	−66177.0	+	114622.i	−0.0624992	+	0.108252i	−0.895582	−	0.444897i	$-0.853240\pi$
$257$	−66177.0	+	114622.i	−0.0624992	+	0.108252i	0.833083	+	0.553148i	$0.186574\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−29403.0	+	50927.5i	−0.0267172	+	0.0462755i
$262$		0			0
$263$	−471636.	−	816898.i	−0.420453	−	0.728246i	0.575531	−	0.817780i	$-0.304796\pi$
$263$	−471636.	−	816898.i	−0.420453	−	0.728246i	−0.995984	+	0.0895341i	$0.971462\pi$
$264$		0			0
$265$	1.05268e6			0.920831
$266$		0			0
$267$	−357048.			−0.306513
$268$		0			0
$269$	−483759.	−	837895.i	−0.407613	−	0.706007i	0.587008	−	0.809581i	$-0.300306\pi$
$269$	−483759.	−	837895.i	−0.407613	−	0.706007i	−0.994622	+	0.103574i	$0.966972\pi$
$270$		0			0
$271$	259160.	−	448878.i	0.214360	−	0.371283i	−0.738714	−	0.674019i	$-0.764567\pi$
$271$	259160.	−	448878.i	0.214360	−	0.371283i	0.953075	+	0.302736i	$0.0978999\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	56430.0	−	97739.6i	0.0449965	−	0.0779361i
$276$		0			0
$277$	−1.11136e6	−	1.92494e6i	−0.870275	−	1.50736i	−0.861712	−	0.507397i	$-0.830608\pi$
$277$	−1.11136e6	−	1.92494e6i	−0.870275	−	1.50736i	−0.00856270	−	0.999963i	$-0.502726\pi$
$278$		0			0
$279$	−421344.			−0.324061
$280$		0			0
$281$	−196614.			−0.148542			−0.0742709	−	0.997238i	$-0.523663\pi$
$281$	−196614.			−0.148542			−0.0742709	+	0.997238i	$0.523663\pi$
$282$		0			0
$283$	776138.	+	1.34431e6i	0.576067	+	0.997777i	0.995925	+	0.0901872i	$0.0287465\pi$
$283$	776138.	+	1.34431e6i	0.576067	+	0.997777i	−0.419858	+	0.907590i	$0.637920\pi$
$284$		0			0
$285$	270864.	−	469150.i	0.197533	−	0.342137i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	533510.	−	924067.i	0.375749	−	0.650817i
$290$		0			0
$291$	−734388.	−	1.27200e6i	−0.508385	−	0.880549i
$292$		0			0
$293$	−1.07217e6			−0.729616			−0.364808	−	0.931083i	$-0.618865\pi$
$293$	−1.07217e6			−0.729616			−0.364808	+	0.931083i	$0.618865\pi$
$294$		0			0
$295$	−414072.			−0.277026
$296$		0			0
$297$	−1.10808e6	−	1.91925e6i	−0.728920	−	1.26253i
$298$		0			0
$299$	−857736.	+	1.48564e6i	−0.554850	+	0.961029i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	67716.0	−	117288.i	0.0423726	−	0.0733914i
$304$		0			0
$305$	937926.	+	1.62454e6i	0.577323	+	0.999953i
$306$		0			0
$307$	1.58589e6			0.960346			0.480173	−	0.877174i	$-0.340574\pi$
$307$	1.58589e6			0.960346			0.480173	+	0.877174i	$0.340574\pi$
$308$		0			0
$309$	327072.			0.194871
$310$		0			0
$311$	365364.	+	632829.i	0.214203	+	0.371010i	0.953026	−	0.302890i	$-0.0979514\pi$
$311$	365364.	+	632829.i	0.214203	+	0.371010i	−0.738823	+	0.673900i	$0.764618\pi$
$312$		0			0
$313$	−292429.	+	506502.i	−0.168717	+	0.292227i	−0.937969	−	0.346719i	$-0.887296\pi$
$313$	−292429.	+	506502.i	−0.168717	+	0.292227i	0.769252	+	0.638946i	$0.220629\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.24143e6	−	2.15023e6i	0.693865	−	1.20181i	−0.276696	−	0.960957i	$-0.589240\pi$
$317$	1.24143e6	−	2.15023e6i	0.693865	−	1.20181i	0.970562	−	0.240852i	$-0.0774270\pi$
$318$		0			0
$319$	160380.	+	277786.i	0.0882416	+	0.152839i
$320$		0			0
$321$	−1.46837e6			−0.795376
$322$		0			0
$323$	496584.			0.264842
$324$		0			0
$325$	−43681.0	−	75657.7i	−0.0229395	−	0.0397324i
$326$		0			0
$327$	599412.	−	1.03821e6i	0.309996	−	0.536929i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−188974.	+	327313.i	−0.0948052	+	0.164207i	−0.909527	−	0.415644i	$-0.863556\pi$
$331$	−188974.	+	327313.i	−0.0948052	+	0.164207i	0.814722	+	0.579852i	$0.196889\pi$
$332$		0			0
$333$	−14751.0	−	25549.5i	−0.00728972	−	0.0126262i
$334$		0			0
$335$	1.17785e6			0.573426
$336$		0			0
$337$	639122.			0.306555			0.153278	−	0.988183i	$-0.451017\pi$
$337$	639122.			0.306555			0.153278	+	0.988183i	$0.451017\pi$
$338$		0			0
$339$	−177876.	−	308090.i	−0.0840656	−	0.145606i
$340$		0			0
$341$	−1.14912e6	+	1.99033e6i	−0.535155	+	0.926915i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−1.32970e6	+	2.30310e6i	−0.601457	+	1.04175i
$346$		0			0
$347$	1.45233e6	+	2.51551e6i	0.647503	+	1.12151i	0.983717	+	0.179722i	$0.0575199\pi$
$347$	1.45233e6	+	2.51551e6i	0.647503	+	1.12151i	−0.336215	+	0.941785i	$0.609147\pi$
$348$		0			0
$349$	−3.99157e6			−1.75420			−0.877102	−	0.480304i	$-0.840526\pi$
$349$	−3.99157e6			−1.75420			−0.877102	+	0.480304i	$0.840526\pi$
$350$		0			0
$351$	−1.71547e6			−0.743217
$352$		0			0
$353$	−714609.	−	1.23774e6i	−0.305233	−	0.528679i	0.672080	−	0.740478i	$-0.265401\pi$
$353$	−714609.	−	1.23774e6i	−0.305233	−	0.528679i	−0.977313	+	0.211799i	$0.932068\pi$
$354$		0			0
$355$	1.26554e6	−	2.19199e6i	0.532974	−	0.923139i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−580932.	+	1.00620e6i	−0.237897	+	0.412050i	−0.960111	−	0.279620i	$-0.909791\pi$
$359$	−580932.	+	1.00620e6i	−0.237897	+	0.412050i	0.722214	+	0.691670i	$0.243125\pi$
$360$		0			0
$361$	888602.	+	1.53910e6i	0.358872	+	0.621584i
$362$		0			0
$363$	−1.56659e6			−0.624005
$364$		0			0
$365$	3.64835e6			1.43339
$366$		0			0
$367$	544616.	+	943303.i	0.211069	+	0.365583i	0.952049	−	0.305944i	$-0.0989721\pi$
$367$	544616.	+	943303.i	0.211069	+	0.365583i	−0.740980	+	0.671527i	$0.765639\pi$
$368$		0			0
$369$	852687.	−	1.47690e6i	0.326005	−	0.564657i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.75288e6	+	3.03608e6i	−0.652350	+	1.12990i	0.330201	+	0.943911i	$0.392884\pi$
$373$	−1.75288e6	+	3.03608e6i	−0.652350	+	1.12990i	−0.982551	+	0.185993i	$0.940450\pi$
$374$		0			0
$375$	−1.08022e6	−	1.87099e6i	−0.396673	−	0.687057i
$376$		0			0
$377$	248292.			0.0899724
$378$		0			0
$379$	4.04385e6			1.44610			0.723048	−	0.690798i	$-0.242740\pi$
$379$	4.04385e6			1.44610			0.723048	+	0.690798i	$0.242740\pi$
$380$		0			0
$381$	2.01907e6	+	3.49714e6i	0.712589	+	1.23424i
$382$		0			0
$383$	−2.59373e6	+	4.49247e6i	−0.903499	+	1.56491i	−0.0805786	+	0.996748i	$0.525677\pi$
$383$	−2.59373e6	+	4.49247e6i	−0.903499	+	1.56491i	−0.822920	+	0.568157i	$0.807657\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−598950.	+	1.03741e6i	−0.203289	+	0.352106i
$388$		0			0
$389$	475173.	+	823024.i	0.159213	+	0.275765i	0.934585	−	0.355740i	$-0.115771\pi$
$389$	475173.	+	823024.i	0.159213	+	0.275765i	−0.775372	+	0.631504i	$0.782438\pi$
$390$		0			0
$391$	−2.43778e6			−0.806403
$392$		0			0
$393$	−1.21176e6			−0.395763
$394$		0			0
$395$	2.07662e6	+	3.59682e6i	0.669677	+	1.15991i
$396$		0			0
$397$	260369.	−	450972.i	0.0829112	−	0.143606i	−0.821588	−	0.570082i	$-0.806912\pi$
$397$	260369.	−	450972.i	0.0829112	−	0.143606i	0.904499	+	0.426475i	$0.140245\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−382185.	+	661964.i	−0.118690	+	0.205576i	−0.919249	−	0.393677i	$-0.871203\pi$
$401$	−382185.	+	661964.i	−0.118690	+	0.205576i	0.800559	+	0.599254i	$0.204536\pi$
$402$		0			0
$403$	889504.	+	1.54067e6i	0.272826	+	0.472548i
$404$		0			0
$405$	−1.36031e6			−0.412099
$406$		0			0
$407$	−160920.			−0.0481531
$408$		0			0
$409$	−1.32025e6	−	2.28675e6i	−0.390255	−	0.675942i	0.602228	−	0.798324i	$-0.294280\pi$
$409$	−1.32025e6	−	2.28675e6i	−0.390255	−	0.675942i	−0.992483	+	0.122382i	$0.960947\pi$
$410$		0			0
$411$	−1.90285e6	+	3.29584e6i	−0.555649	+	0.962412i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.82833e6	+	3.16676e6i	−0.521116	+	0.902600i
$416$		0			0
$417$	−889944.	−	1.54143e6i	−0.250624	−	0.434093i
$418$		0			0
$419$	−4.98020e6			−1.38584			−0.692918	−	0.721016i	$-0.743675\pi$
$419$	−4.98020e6			−1.38584			−0.692918	+	0.721016i	$0.743675\pi$
$420$		0			0
$421$	−237994.			−0.0654426			−0.0327213	−	0.999465i	$-0.510417\pi$
$421$	−237994.			−0.0654426			−0.0327213	+	0.999465i	$0.510417\pi$
$422$		0			0
$423$	−64152.0	−	111115.i	−0.0174325	−	0.0301939i
$424$		0			0
$425$	62073.0	−	107514.i	0.0166698	−	0.0288729i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.35432e6	+	2.34575e6i	−0.355286	+	0.615373i
$430$		0			0
$431$	1.94119e6	+	3.36224e6i	0.503356	+	0.871838i	0.999992	+	0.00387961i	$0.00123492\pi$
$431$	1.94119e6	+	3.36224e6i	0.503356	+	0.871838i	−0.496636	+	0.867959i	$0.665432\pi$
$432$		0			0
$433$	−66958.0			−0.0171626			−0.00858129	−	0.999963i	$-0.502732\pi$
$433$	−66958.0			−0.0171626			−0.00858129	+	0.999963i	$0.502732\pi$
$434$		0			0
$435$	384912.			0.0975300
$436$		0			0
$437$	1.71547e6	+	2.97128e6i	0.429715	+	0.744287i
$438$		0			0
$439$	3.25068e6	−	5.63034e6i	0.805031	−	1.39435i	−0.111240	−	0.993794i	$-0.535482\pi$
$439$	3.25068e6	−	5.63034e6i	0.805031	−	1.39435i	0.916270	−	0.400560i	$-0.131184\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.30380e6	−	3.99030e6i	0.557745	−	0.966043i	−0.439939	−	0.898028i	$-0.645000\pi$
$443$	2.30380e6	−	3.99030e6i	0.557745	−	0.966043i	0.997684	−	0.0680154i	$-0.0216667\pi$
$444$		0			0
$445$	−803358.	−	1.39146e6i	−0.192313	−	0.333096i
$446$		0			0
$447$	−2.35937e6			−0.558505
$448$		0			0
$449$	3.77671e6			0.884092			0.442046	−	0.896992i	$-0.354253\pi$
$449$	3.77671e6			0.884092			0.442046	+	0.896992i	$0.354253\pi$
$450$		0			0
$451$	−4.65102e6	−	8.05580e6i	−1.07673	−	1.86495i
$452$		0			0
$453$	446160.	−	772772.i	0.102152	−	0.176932i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.59035e6	−	2.75456e6i	0.356206	−	0.616967i	−0.631117	−	0.775687i	$-0.717403\pi$
$457$	1.59035e6	−	2.75456e6i	0.356206	−	0.616967i	0.987324	+	0.158720i	$0.0507368\pi$
$458$		0			0
$459$	−1.21889e6	−	2.11118e6i	−0.270042	−	0.467727i
$460$		0			0
$461$	6.68547e6			1.46514			0.732571	−	0.680691i	$-0.238320\pi$
$461$	6.68547e6			1.46514			0.732571	+	0.680691i	$0.238320\pi$
$462$		0			0
$463$	−4.35122e6			−0.943318			−0.471659	−	0.881781i	$-0.656345\pi$
$463$	−4.35122e6			−0.943318			−0.471659	+	0.881781i	$0.656345\pi$
$464$		0			0
$465$	1.37894e6	+	2.38840e6i	0.295743	+	0.512242i
$466$		0			0
$467$	−3.53997e6	+	6.13141e6i	−0.751117	+	1.30097i	0.196165	+	0.980571i	$0.437151\pi$
$467$	−3.53997e6	+	6.13141e6i	−0.751117	+	1.30097i	−0.947282	+	0.320401i	$0.896182\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	725268.	−	1.25620e6i	0.150642	−	0.260920i
$472$		0			0
$473$	3.26700e6	+	5.65861e6i	0.671423	+	1.16294i
$474$		0			0
$475$	−174724.			−0.0355319
$476$		0			0
$477$	−1.92991e6			−0.388365
$478$		0			0
$479$	−1.61093e6	−	2.79021e6i	−0.320802	−	0.555646i	0.659852	−	0.751396i	$-0.270619\pi$
$479$	−1.61093e6	−	2.79021e6i	−0.320802	−	0.555646i	−0.980654	+	0.195750i	$0.937286\pi$
$480$		0			0
$481$	−62282.0	+	107876.i	−0.0122744	+	0.0212599i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.30475e6	−	5.72399e6i	0.637946	−	1.10495i
$486$		0			0
$487$	−1.14855e6	−	1.98934e6i	−0.219446	−	0.380091i	0.735193	−	0.677858i	$-0.237091\pi$
$487$	−1.14855e6	−	1.98934e6i	−0.219446	−	0.380091i	−0.954639	+	0.297767i	$0.903758\pi$
$488$		0			0
$489$	1.33608e6			0.252674
$490$		0			0
$491$	2.82150e6			0.528173			0.264087	−	0.964499i	$-0.414930\pi$
$491$	2.82150e6			0.528173			0.264087	+	0.964499i	$0.414930\pi$
$492$		0			0
$493$	176418.	+	305565.i	0.0326908	+	0.0566221i
$494$		0			0
$495$	1.44342e6	−	2.50008e6i	0.264777	−	0.458607i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	2.06814e6	−	3.58213e6i	0.371817	−	0.644006i	−0.618028	−	0.786156i	$-0.712068\pi$
$499$	2.06814e6	−	3.58213e6i	0.371817	−	0.644006i	0.989845	+	0.142150i	$0.0454016\pi$
$500$		0			0
$501$	−2.95099e6	−	5.11127e6i	−0.525259	−	0.909776i
$502$		0			0
$503$	8.33263e6			1.46846			0.734230	−	0.678901i	$-0.237543\pi$
$503$	8.33263e6			1.46846			0.734230	+	0.678901i	$0.237543\pi$
$504$		0			0
$505$	609444.			0.106342
$506$		0			0
$507$	−1.17941e6	−	2.04280e6i	−0.203773	−	0.352945i
$508$		0			0
$509$	−2.17050e6	+	3.75942e6i	−0.371335	+	0.643171i	−0.989771	−	0.142664i	$-0.954433\pi$
$509$	−2.17050e6	+	3.75942e6i	−0.371335	+	0.643171i	0.618436	+	0.785835i	$0.287767\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−1.71547e6	+	2.97128e6i	−0.287800	+	0.498484i
$514$		0			0
$515$	735912.	+	1.27464e6i	0.122267	+	0.211772i
$516$		0			0
$517$	−699840.			−0.115152
$518$		0			0
$519$	−8.48945e6			−1.38344
$520$		0			0
$521$	3.37092e6	+	5.83861e6i	0.544070	+	0.942356i	0.998665	+	0.0516581i	$0.0164506\pi$
$521$	3.37092e6	+	5.83861e6i	0.544070	+	0.942356i	−0.454595	+	0.890698i	$0.650216\pi$
$522$		0			0
$523$	3.86098e6	−	6.68741e6i	0.617224	−	1.06906i	−0.372765	−	0.927926i	$-0.621590\pi$
$523$	3.86098e6	−	6.68741e6i	0.617224	−	1.06906i	0.989990	−	0.141138i	$-0.0450763\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.26403e6	+	2.18937e6i	−0.198258	+	0.343394i
$528$		0			0
$529$	−5.20324e6	−	9.01227e6i	−0.808415	−	1.40022i
$530$		0			0
$531$	759132.			0.116837
$532$		0			0
$533$	−7.20047e6			−1.09785
$534$		0			0
$535$	−3.30383e6	−	5.72240e6i	−0.499037	−	0.864358i
$536$		0			0
$537$	2.96201e6	−	5.13035e6i	0.443252	−	0.767735i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	341033.	−	590686.i	0.0500960	−	0.0867689i	−0.839890	−	0.542757i	$-0.817381\pi$
$541$	341033.	−	590686.i	0.0500960	−	0.0867689i	0.889986	+	0.455988i	$0.150714\pi$
$542$		0			0
$543$	−3.35670e6	−	5.81397e6i	−0.488554	−	0.846201i
$544$		0			0
$545$	5.39471e6			0.777995
$546$		0			0
$547$	2.15772e6			0.308337			0.154169	−	0.988045i	$-0.450730\pi$
$547$	2.15772e6			0.308337			0.154169	+	0.988045i	$0.450730\pi$
$548$		0			0
$549$	−1.71953e6	−	2.97832e6i	−0.243489	−	0.421735i
$550$		0			0
$551$	248292.	−	430054.i	0.0348404	−	0.0603454i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−96552.0	+	167233.i	−0.0133054	+	0.0230457i
$556$		0			0
$557$	1.33798e6	+	2.31746e6i	0.182731	+	0.316500i	0.942810	−	0.333331i	$-0.108173\pi$
$557$	1.33798e6	+	2.31746e6i	0.182731	+	0.316500i	−0.760078	+	0.649831i	$0.774839\pi$
$558$		0			0
$559$	5.05780e6			0.684592
$560$		0			0
$561$	−3.84912e6			−0.516362
$562$		0			0
$563$	1.77665e6	+	3.07725e6i	0.236228	+	0.409159i	0.959629	−	0.281269i	$-0.0907554\pi$
$563$	1.77665e6	+	3.07725e6i	0.236228	+	0.409159i	−0.723401	+	0.690428i	$0.757422\pi$
$564$		0			0
$565$	800442.	−	1.38641e6i	0.105489	−	0.182713i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	6.46123e6	−	1.11912e7i	0.836633	−	1.44909i	−0.0560613	−	0.998427i	$-0.517854\pi$
$569$	6.46123e6	−	1.11912e7i	0.836633	−	1.44909i	0.892694	−	0.450663i	$-0.148812\pi$
$570$		0			0
$571$	3.04179e6	+	5.26853e6i	0.390426	+	0.676237i	0.992506	−	0.122199i	$-0.0389945\pi$
$571$	3.04179e6	+	5.26853e6i	0.390426	+	0.676237i	−0.602080	+	0.798436i	$0.705661\pi$
$572$		0			0
$573$	8.68838e6			1.10548
$574$		0			0
$575$	857736.			0.108189
$576$		0			0
$577$	7.91203e6	+	1.37040e7i	0.989347	+	1.71360i	0.620749	+	0.784010i	$0.286829\pi$
$577$	7.91203e6	+	1.37040e7i	0.989347	+	1.71360i	0.368598	+	0.929589i	$0.379838\pi$
$578$		0			0
$579$	42636.0	−	73847.7i	0.00528543	−	0.00915463i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−5.26338e6	+	9.11644e6i	−0.641347	+	1.11085i
$584$		0			0
$585$	−1.11731e6	−	1.93524e6i	−0.134985	−	0.233801i
$586$		0			0
$587$	4.60220e6			0.551278			0.275639	−	0.961261i	$-0.411111\pi$
$587$	4.60220e6			0.551278			0.275639	+	0.961261i	$0.411111\pi$
$588$		0			0
$589$	3.55802e6			0.422590
$590$		0			0
$591$	−3.18265e6	−	5.51251e6i	−0.374818	−	0.649204i
$592$		0			0
$593$	−4.30561e6	+	7.45753e6i	−0.502803	+	0.870880i	0.497192	+	0.867641i	$0.334365\pi$
$593$	−4.30561e6	+	7.45753e6i	−0.502803	+	0.870880i	−0.999995	+	0.00323965i	$0.998969\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	337008.	−	583715.i	0.0386994	−	0.0670294i
$598$		0			0
$599$	3.99114e6	+	6.91286e6i	0.454496	+	0.787210i	0.998659	−	0.0517695i	$-0.0164861\pi$
$599$	3.99114e6	+	6.91286e6i	0.454496	+	0.787210i	−0.544163	+	0.838979i	$0.683153\pi$
$600$		0			0
$601$	1.01740e7			1.14896			0.574481	−	0.818518i	$-0.305204\pi$
$601$	1.01740e7			1.14896			0.574481	+	0.818518i	$0.305204\pi$
$602$		0			0
$603$	−2.15939e6			−0.241845
$604$		0			0
$605$	−3.52482e6	−	6.10517e6i	−0.391515	−	0.678125i
$606$		0			0
$607$	4.97922e6	−	8.62426e6i	0.548516	−	0.950057i	−0.449861	−	0.893099i	$-0.648526\pi$
$607$	4.97922e6	−	8.62426e6i	0.548516	−	0.950057i	0.998377	−	0.0569587i	$-0.0181403\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−270864.	+	469150.i	−0.0293527	+	0.0508404i
$612$		0			0
$613$	−2.09793e6	−	3.63372e6i	−0.225497	−	0.390572i	0.730972	−	0.682408i	$-0.239067\pi$
$613$	−2.09793e6	−	3.63372e6i	−0.225497	−	0.390572i	−0.956468	+	0.291836i	$0.905734\pi$
$614$		0			0
$615$	−1.11624e7			−1.19007
$616$		0			0
$617$	9.12551e6			0.965038			0.482519	−	0.875885i	$-0.339722\pi$
$617$	9.12551e6			0.965038			0.482519	+	0.875885i	$0.339722\pi$
$618$		0			0
$619$	−3.22867e6	−	5.59222e6i	−0.338686	−	0.586621i	0.645500	−	0.763760i	$-0.276649\pi$
$619$	−3.22867e6	−	5.59222e6i	−0.338686	−	0.586621i	−0.984186	+	0.177139i	$0.943316\pi$
$620$		0			0
$621$	8.42141e6	−	1.45863e7i	0.876306	−	1.51781i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	4.53441e6	−	7.85383e6i	0.464324	−	0.804232i
$626$		0			0
$627$	2.70864e6	+	4.69150e6i	0.275158	+	0.476588i
$628$		0			0
$629$	−177012.			−0.0178392
$630$		0			0
$631$	−1.40514e7			−1.40490			−0.702450	−	0.711733i	$-0.747910\pi$
$631$	−1.40514e7			−1.40490			−0.702450	+	0.711733i	$0.747910\pi$
$632$		0			0
$633$	−2.03518e6	−	3.52503e6i	−0.201880	−	0.349666i
$634$		0			0
$635$	−9.08582e6	+	1.57371e7i	−0.894190	+	1.54878i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−2.32016e6	+	4.01864e6i	−0.224785	+	0.389338i
$640$		0			0
$641$	−4.23584e6	−	7.33669e6i	−0.407188	−	0.705270i	0.587386	−	0.809307i	$-0.300157\pi$
$641$	−4.23584e6	−	7.33669e6i	−0.407188	−	0.705270i	−0.994573	+	0.104037i	$0.966824\pi$
$642$		0			0
$643$	488564.			0.0466009			0.0233004	−	0.999729i	$-0.492583\pi$
$643$	488564.			0.0466009			0.0233004	+	0.999729i	$0.492583\pi$
$644$		0			0
$645$	7.84080e6			0.742098
$646$		0			0
$647$	−1.24060e6	−	2.14878e6i	−0.116512	−	0.201804i	0.801871	−	0.597497i	$-0.203838\pi$
$647$	−1.24060e6	−	2.14878e6i	−0.116512	−	0.201804i	−0.918383	+	0.395693i	$0.870505\pi$
$648$		0			0
$649$	2.07036e6	−	3.58597e6i	0.192945	−	0.334191i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.64565e6	−	4.58240e6i	0.242800	−	0.420543i	−0.718711	−	0.695309i	$-0.755267\pi$
$653$	2.64565e6	−	4.58240e6i	0.242800	−	0.420543i	0.961511	+	0.274767i	$0.0886007\pi$
$654$		0			0
$655$	−2.72646e6	−	4.72237e6i	−0.248311	−	0.430087i
$656$		0			0
$657$	−6.68864e6			−0.604539
$658$		0			0
$659$	4.72468e6			0.423798			0.211899	−	0.977292i	$-0.432035\pi$
$659$	4.72468e6			0.423798			0.211899	+	0.977292i	$0.432035\pi$
$660$		0			0
$661$	3.08710e6	+	5.34702e6i	0.274819	+	0.476001i	0.970090	−	0.242747i	$-0.0780486\pi$
$661$	3.08710e6	+	5.34702e6i	0.274819	+	0.476001i	−0.695270	+	0.718748i	$0.744715\pi$
$662$		0			0
$663$	−1.48975e6	+	2.58033e6i	−0.131623	+	0.227977i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.21889e6	+	2.11118e6i	−0.106084	+	0.183743i
$668$		0			0
$669$	4.67616e6	+	8.09935e6i	0.403947	+	0.699656i
$670$		0			0
$671$	−1.87585e7			−1.60839
$672$		0			0
$673$	−9.40925e6			−0.800787			−0.400394	−	0.916343i	$-0.631127\pi$
$673$	−9.40925e6			−0.800787			−0.400394	+	0.916343i	$0.631127\pi$
$674$		0			0
$675$	428868.	+	742821.i	0.0362297	+	0.0627516i
$676$		0			0
$677$	−7.50430e6	+	1.29978e7i	−0.629272	+	1.08993i	0.358426	+	0.933558i	$0.383314\pi$
$677$	−7.50430e6	+	1.29978e7i	−0.629272	+	1.08993i	−0.987698	+	0.156373i	$0.950020\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−4.46926e6	+	7.74098e6i	−0.369290	+	0.639629i
$682$		0			0
$683$	6.48535e6	+	1.12329e7i	0.531963	+	0.921387i	0.999304	+	0.0373096i	$0.0118788\pi$
$683$	6.48535e6	+	1.12329e7i	0.531963	+	0.921387i	−0.467341	+	0.884077i	$0.654788\pi$
$684$		0			0
$685$	−1.71257e7			−1.39451
$686$		0			0
$687$	3.27295e6			0.264574
$688$		0			0
$689$	4.07425e6	+	7.05680e6i	0.326963	+	0.566317i
$690$		0			0
$691$	−1.13278e7	+	1.96203e7i	−0.902506	+	1.56319i	−0.0782761	+	0.996932i	$0.524942\pi$
$691$	−1.13278e7	+	1.96203e7i	−0.902506	+	1.56319i	−0.824230	+	0.566255i	$0.808392\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.00475e6	−	6.93643e6i	0.314495	−	0.544721i
$696$		0			0
$697$	−5.11612e6	−	8.86138e6i	−0.398895	−	0.690907i
$698$		0			0
$699$	1.84615e6			0.142914
$700$		0			0
$701$	1.90169e7			1.46166			0.730828	−	0.682562i	$-0.239134\pi$
$701$	1.90169e7			1.46166			0.730828	+	0.682562i	$0.239134\pi$
$702$		0			0
$703$	124564.	+	215751.i	0.00950614	+	0.0164651i
$704$		0			0
$705$	−419904.	+	727295.i	−0.0318183	+	0.0551109i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−7.56556e6	+	1.31039e7i	−0.565231	+	0.979008i	0.431798	+	0.901971i	$0.357879\pi$
$709$	−7.56556e6	+	1.31039e7i	−0.565231	+	0.979008i	−0.997028	+	0.0770376i	$0.975454\pi$
$710$		0			0
$711$	−3.80714e6	−	6.59417e6i	−0.282439	−	0.489199i
$712$		0			0
$713$	−1.74666e7			−1.28672
$714$		0			0
$715$	−1.21889e7			−0.891659
$716$		0			0
$717$	6.92842e6	+	1.20004e7i	0.503311	+	0.871760i
$718$		0			0
$719$	7.51615e6	−	1.30184e7i	0.542217	−	0.939148i	−0.456559	−	0.889693i	$-0.650918\pi$
$719$	7.51615e6	−	1.30184e7i	0.542217	−	0.939148i	0.998776	−	0.0494547i	$-0.0157484\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	3.94244e6	−	6.82851e6i	0.280492	−	0.485826i
$724$		0			0
$725$	−62073.0	−	107514.i	−0.00438589	−	0.00759658i
$726$		0			0
$727$	−7.41230e6			−0.520136			−0.260068	−	0.965590i	$-0.583745\pi$
$727$	−7.41230e6			−0.520136			−0.260068	+	0.965590i	$0.583745\pi$
$728$		0			0
$729$	1.44612e7			1.00782
$730$		0			0
$731$	3.59370e6	+	6.22447e6i	0.248742	+	0.430833i
$732$		0			0
$733$	1.38964e6	−	2.40693e6i	0.0955306	−	0.165464i	−0.814299	−	0.580445i	$-0.802879\pi$
$733$	1.38964e6	−	2.40693e6i	0.0955306	−	0.165464i	0.909830	+	0.414981i	$0.136212\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.88924e6	+	1.02005e7i	−0.399384	+	0.691753i
$738$		0			0
$739$	6.05231e6	+	1.04829e7i	0.407671	+	0.706107i	0.994628	−	0.103511i	$-0.0330076\pi$
$739$	6.05231e6	+	1.04829e7i	0.407671	+	0.706107i	−0.586957	+	0.809618i	$0.699674\pi$
$740$		0			0
$741$	4.19338e6			0.280555
$742$		0			0
$743$	4.46926e6			0.297005			0.148502	−	0.988912i	$-0.452555\pi$
$743$	4.46926e6			0.297005			0.148502	+	0.988912i	$0.452555\pi$
$744$		0			0
$745$	−5.30858e6	−	9.19473e6i	−0.350419	−	0.606943i
$746$		0			0
$747$	3.35194e6	−	5.80573e6i	0.219783	−	0.380676i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−1.44231e7	+	2.49816e7i	−0.933168	+	1.61629i	−0.155298	+	0.987868i	$0.549634\pi$
$751$	−1.44231e7	+	2.49816e7i	−0.933168	+	1.61629i	−0.777869	+	0.628426i	$0.783700\pi$
$752$		0			0
$753$	8.05140e6	+	1.39454e7i	0.517469	+	0.896282i
$754$		0			0
$755$	4.01544e6			0.256369
$756$		0			0
$757$	9.60868e6			0.609430			0.304715	−	0.952444i	$-0.401439\pi$
$757$	9.60868e6			0.609430			0.304715	+	0.952444i	$0.401439\pi$
$758$		0			0
$759$	−1.32970e7	−	2.30310e7i	−0.837815	−	1.45114i
$760$		0			0
$761$	−2.27294e6	+	3.93685e6i	−0.142274	+	0.246426i	−0.928353	−	0.371700i	$-0.878775\pi$
$761$	−2.27294e6	+	3.93685e6i	−0.142274	+	0.246426i	0.786078	+	0.618127i	$0.212108\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.58776e6	−	2.75008e6i	0.0980916	−	0.169900i
$766$		0			0
$767$	−1.60261e6	−	2.77581e6i	−0.0983649	−	0.170373i
$768$		0			0
$769$	−2.15923e7			−1.31669			−0.658345	−	0.752716i	$-0.728743\pi$
$769$	−2.15923e7			−1.31669			−0.658345	+	0.752716i	$0.728743\pi$
$770$		0			0
$771$	−1.58825e6			−0.0962238
$772$		0			0
$773$	7.42000e6	+	1.28518e7i	0.446638	+	0.773599i	0.998165	−	0.0605578i	$-0.0192879\pi$
$773$	7.42000e6	+	1.28518e7i	0.446638	+	0.773599i	−0.551527	+	0.834157i	$0.685955\pi$
$774$		0			0
$775$	444752.	−	770333.i	0.0265989	−	0.0460706i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−7.20047e6	+	1.24716e7i	−0.425125	+	0.736339i
$780$		0			0
$781$	1.26554e7	+	2.19199e7i	0.742420	+	1.28591i
$782$		0			0
$783$	−2.43778e6			−0.142098
$784$		0			0
$785$	6.52741e6			0.378065
$786$		0			0
$787$	1.24393e7	+	2.15454e7i	0.715909	+	1.23999i	0.962608	+	0.270898i	$0.0873208\pi$
$787$	1.24393e7	+	2.15454e7i	0.715909	+	1.23999i	−0.246699	+	0.969092i	$0.579346\pi$
$788$		0			0
$789$	5.65963e6	−	9.80277e6i	0.323665	−	0.560604i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−7.26024e6	+	1.25751e7i	−0.409985	+	0.710115i
$794$		0			0
$795$	6.31606e6	+	1.09397e7i	0.354428	+	0.613887i
$796$		0			0
$797$	3.16080e7			1.76259			0.881294	−	0.472568i	$-0.156673\pi$
$797$	3.16080e7			1.76259			0.881294	+	0.472568i	$0.156673\pi$
$798$		0			0
$799$	−769824.			−0.0426604
$800$		0			0
$801$	1.47282e6	+	2.55100e6i	0.0811090	+	0.140485i
$802$		0			0
$803$	−1.82417e7	+	3.15956e7i	−0.998338	+	1.72917i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.80511e6	−	1.00547e7i	0.313781	−	0.543484i
$808$		0			0
$809$	1.55004e6	+	2.68475e6i	0.0832669	+	0.144223i	0.904651	−	0.426152i	$-0.140131\pi$
$809$	1.55004e6	+	2.68475e6i	0.0832669	+	0.144223i	−0.821384	+	0.570375i	$0.806798\pi$
$810$		0			0
$811$	1.87180e6			0.0999328			0.0499664	−	0.998751i	$-0.484089\pi$
$811$	1.87180e6			0.0999328			0.0499664	+	0.998751i	$0.484089\pi$
$812$		0			0
$813$	6.21984e6			0.330030
$814$		0			0
$815$	3.00618e6	+	5.20686e6i	0.158533	+	0.274588i
$816$		0			0
$817$	5.05780e6	−	8.76037e6i	0.265098	−	0.459163i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.00092e7	−	1.73364e7i	0.518252	−	0.897640i	−0.481523	−	0.876434i	$-0.659916\pi$
$821$	1.00092e7	−	1.73364e7i	0.518252	−	0.897640i	0.999775	−	0.0212059i	$-0.00675056\pi$
$822$		0			0
$823$	−7.65588e6	−	1.32604e7i	−0.394000	−	0.682427i	0.598973	−	0.800769i	$-0.295576\pi$
$823$	−7.65588e6	−	1.32604e7i	−0.394000	−	0.682427i	−0.992973	+	0.118342i	$0.962242\pi$
$824$		0			0
$825$	1.35432e6			0.0692766
$826$		0			0
$827$	9.59310e6			0.487748			0.243874	−	0.969807i	$-0.421582\pi$
$827$	9.59310e6			0.487748			0.243874	+	0.969807i	$0.421582\pi$
$828$		0			0
$829$	−1.26105e7	−	2.18420e7i	−0.637302	−	1.10384i	−0.986023	−	0.166612i	$-0.946717\pi$
$829$	−1.26105e7	−	2.18420e7i	−0.637302	−	1.10384i	0.348721	−	0.937227i	$-0.386616\pi$
$830$		0			0
$831$	1.33364e7	−	2.30992e7i	0.669938	−	1.16037i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.32795e7	−	2.30007e7i	0.659120	−	1.14163i
$836$		0			0
$837$	−8.73331e6	−	1.51265e7i	−0.430889	−	0.746322i
$838$		0			0
$839$	−1.77623e7			−0.871154			−0.435577	−	0.900151i	$-0.643456\pi$
$839$	−1.77623e7			−0.871154			−0.435577	+	0.900151i	$0.643456\pi$
$840$		0			0
$841$	−2.01583e7			−0.982798
$842$		0			0
$843$	−1.17968e6	−	2.04327e6i	−0.0571738	−	0.0990279i
$844$		0			0
$845$	5.30736e6	−	9.19262e6i	0.255704	−	0.442892i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−9.31366e6	+	1.61317e7i	−0.443456	+	0.768089i
$850$		0			0
$851$	−611496.	−	1.05914e6i	−0.0289447	−	0.0501338i
$852$		0			0
$853$	−486970.			−0.0229155			−0.0114578	−	0.999934i	$-0.503647\pi$
$853$	−486970.			−0.0229155			−0.0114578	+	0.999934i	$0.503647\pi$
$854$		0			0
$855$	−4.46926e6			−0.209084
$856$		0			0
$857$	963171.	+	1.66826e6i	0.0447972	+	0.0775911i	0.887555	−	0.460702i	$-0.152402\pi$
$857$	963171.	+	1.66826e6i	0.0447972	+	0.0775911i	−0.842757	+	0.538294i	$0.819069\pi$
$858$		0			0
$859$	−1.11769e7	+	1.93590e7i	−0.516820	+	0.895158i	0.482989	+	0.875626i	$0.339551\pi$
$859$	−1.11769e7	+	1.93590e7i	−0.516820	+	0.895158i	−0.999809	+	0.0195320i	$0.993782\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.29189e6	+	1.60940e7i	−0.424695	+	0.735593i	−0.996392	−	0.0848718i	$-0.972952\pi$
$863$	−9.29189e6	+	1.60940e7i	−0.424695	+	0.735593i	0.571697	+	0.820465i	$0.306285\pi$
$864$		0			0
$865$	−1.91013e7	−	3.30843e7i	−0.868004	−	1.50343i
$866$		0			0
$867$	1.28043e7			0.578504
$868$		0			0
$869$	−4.15325e7			−1.86569
$870$		0			0
$871$	4.55871e6	+	7.89591e6i	0.203609	+	0.352661i
$872$		0			0
$873$	−6.05870e6	+	1.04940e7i	−0.269057	+	0.466020i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.45524e7	−	2.52055e7i	0.638905	−	1.10662i	−0.346769	−	0.937951i	$-0.612721\pi$
$877$	1.45524e7	−	2.52055e7i	0.638905	−	1.10662i	0.985673	−	0.168665i	$-0.0539456\pi$
$878$		0			0
$879$	−6.43302e6	−	1.11423e7i	−0.280829	−	0.486411i
$880$		0			0
$881$	−3.14696e6			−0.136600			−0.0683001	−	0.997665i	$-0.521758\pi$
$881$	−3.14696e6			−0.136600			−0.0683001	+	0.997665i	$0.521758\pi$
$882$		0			0
$883$	1.59995e7			0.690566			0.345283	−	0.938499i	$-0.387783\pi$
$883$	1.59995e7			0.690566			0.345283	+	0.938499i	$0.387783\pi$
$884$		0			0
$885$	−2.48443e6	−	4.30316e6i	−0.106627	−	0.184684i
$886$		0			0
$887$	1.72937e7	−	2.99536e7i	0.738039	−	1.27832i	−0.215338	−	0.976540i	$-0.569085\pi$
$887$	1.72937e7	−	2.99536e7i	0.738039	−	1.27832i	0.953377	−	0.301781i	$-0.0975813\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	6.80157e6	−	1.17807e7i	0.287022	−	0.497136i
$892$		0			0
$893$	541728.	+	938300.i	0.0227328	+	0.0393743i
$894$		0			0
$895$	2.66581e7			1.11243
$896$		0			0
$897$	−2.05857e7			−0.854248
$898$		0			0
$899$	1.26403e6	+	2.18937e6i	0.0521626	+	0.0903482i
$900$		0			0
$901$	−5.78972e6	+	1.00281e7i	−0.237599	+	0.411534i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.51052e7	−	2.61629e7i	0.613061	−	1.06185i
$906$		0			0
$907$	−8.71982e6	−	1.51032e7i	−0.351957	−	0.609607i	0.634635	−	0.772812i	$-0.281150\pi$
$907$	−8.71982e6	−	1.51032e7i	−0.351957	−	0.609607i	−0.986592	+	0.163205i	$0.947817\pi$
$908$		0			0
$909$	−1.11731e6			−0.0448503
$910$		0			0
$911$	−2.59589e6			−0.103631			−0.0518155	−	0.998657i	$-0.516501\pi$
$911$	−2.59589e6			−0.103631			−0.0518155	+	0.998657i	$0.516501\pi$
$912$		0			0
$913$	−1.82833e7	−	3.16676e7i	−0.725902	−	1.25730i
$914$		0			0
$915$	−1.12551e7	+	1.94944e7i	−0.444424	+	0.769764i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	8.82055e6	−	1.52776e7i	0.344514	−	0.596716i	−0.640751	−	0.767748i	$-0.721377\pi$
$919$	8.82055e6	−	1.52776e7i	0.344514	−	0.596716i	0.985265	+	0.171033i	$0.0547104\pi$
$920$		0			0
$921$	9.51535e6	+	1.64811e7i	0.369637	+	0.640231i
$922$		0			0
$923$	1.95925e7			0.756982
$924$		0			0
$925$	62282.0			0.00239336
$926$		0			0
$927$	−1.34917e6	−	2.33683e6i	−0.0515665	−	0.0893159i
$928$		0			0
$929$	−1.98392e7	+	3.43626e7i	−0.754199	+	1.30631i	0.191573	+	0.981478i	$0.438641\pi$
$929$	−1.98392e7	+	3.43626e7i	−0.754199	+	1.30631i	−0.945772	+	0.324833i	$0.894692\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−4.38437e6	+	7.59395e6i	−0.164893	+	0.285603i
$934$		0			0
$935$	−8.66052e6	−	1.50005e7i	−0.323978	−	0.561146i
$936$		0			0
$937$	3.93413e7			1.46386			0.731930	−	0.681380i	$-0.238620\pi$
$937$	3.93413e7			1.46386			0.731930	+	0.681380i	$0.238620\pi$
$938$		0			0
$939$	−7.01830e6			−0.259757
$940$		0			0
$941$	−2.31253e7	−	4.00542e7i	−0.851361	−	1.47460i	−0.879981	−	0.475009i	$-0.842445\pi$
$941$	−2.31253e7	−	4.00542e7i	−0.851361	−	1.47460i	0.0286202	−	0.999590i	$-0.490889\pi$
$942$		0			0
$943$	3.53478e7	−	6.12241e7i	1.29444	−	2.24204i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.89512e7	−	3.28245e7i	0.686693	−	1.18939i	−0.286208	−	0.958167i	$-0.592395\pi$
$947$	1.89512e7	−	3.28245e7i	0.686693	−	1.18939i	0.972901	−	0.231220i	$-0.0742718\pi$
$948$		0			0
$949$	1.41205e7	+	2.44574e7i	0.508960	+	0.881544i
$950$		0			0
$951$	2.97944e7			1.06828
$952$		0			0
$953$	−2.66462e7			−0.950394			−0.475197	−	0.879879i	$-0.657623\pi$
$953$	−2.66462e7			−0.950394			−0.475197	+	0.879879i	$0.657623\pi$
$954$		0			0
$955$	1.95489e7	+	3.38596e7i	0.693606	+	1.20136i
$956$		0			0
$957$	−1.92456e6	+	3.33344e6i	−0.0679284	+	0.117656i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	5.25781e6	−	9.10679e6i	0.183652	−	0.318095i
$962$		0			0
$963$	6.05702e6	+	1.04911e7i	0.210471	+	0.364547i
$964$		0			0
$965$	383724.			0.0132648
$966$		0			0
$967$	4.09790e7			1.40927			0.704637	−	0.709568i	$-0.251110\pi$
$967$	4.09790e7			1.40927			0.704637	+	0.709568i	$0.251110\pi$
$968$		0			0
$969$	2.97950e6	+	5.16065e6i	0.101938	+	0.176561i
$970$		0			0
$971$	1.36017e7	−	2.35588e7i	0.462961	−	0.801872i	−0.536146	−	0.844125i	$-0.680120\pi$
$971$	1.36017e7	−	2.35588e7i	0.462961	−	0.801872i	0.999107	+	0.0422532i	$0.0134536\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	524172.	−	907893.i	0.0176588	−	0.0305860i
$976$		0			0
$977$	−1.26778e7	−	2.19585e7i	−0.424919	−	0.735982i	0.571494	−	0.820607i	$-0.306364\pi$
$977$	−1.26778e7	−	2.19585e7i	−0.424919	−	0.735982i	−0.996413	+	0.0846247i	$0.973031\pi$
$978$		0			0
$979$	1.60672e7			0.535775
$980$		0			0
$981$	−9.89030e6			−0.328123
$982$		0			0
$983$	−5.95696e6	−	1.03178e7i	−0.196626	−	0.340566i	0.750806	−	0.660522i	$-0.229665\pi$
$983$	−5.95696e6	−	1.03178e7i	−0.196626	−	0.340566i	−0.947432	+	0.319956i	$0.896332\pi$
$984$		0			0
$985$	1.43219e7	−	2.48063e7i	0.470339	−	0.814651i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.48292e7	+	4.30054e7i	−0.807183	+	1.39808i
$990$		0			0
$991$	−1.45965e7	−	2.52819e7i	−0.472134	−	0.817760i	0.527357	−	0.849644i	$-0.323183\pi$
$991$	−1.45965e7	−	2.52819e7i	−0.472134	−	0.817760i	−0.999492	+	0.0318832i	$0.989850\pi$
$992$		0			0
$993$	−4.53538e6			−0.145962
$994$		0			0
$995$	3.03307e6			0.0971237
$996$		0			0
$997$	8.65004e6	+	1.49823e7i	0.275601	+	0.477354i	0.970286	−	0.241959i	$-0.0777900\pi$
$997$	8.65004e6	+	1.49823e7i	0.275601	+	0.477354i	−0.694686	+	0.719313i	$0.744457\pi$
$998$		0			0
$999$	611496.	−	1.05914e6i	0.0193856	−	0.0335769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.6.e.g.177.1		2
7.2	even	3		4.6.a.a.1.1	✓	1
7.3	odd	6		196.6.e.d.165.1		2
7.4	even	3	inner	196.6.e.g.165.1		2
7.5	odd	6		196.6.a.e.1.1		1
7.6	odd	2		196.6.e.d.177.1		2
21.2	odd	6		36.6.a.a.1.1		1
28.19	even	6		784.6.a.d.1.1		1
28.23	odd	6		16.6.a.b.1.1		1
35.2	odd	12		100.6.c.b.49.2		2
35.9	even	6		100.6.a.b.1.1		1
35.23	odd	12		100.6.c.b.49.1		2
56.37	even	6		64.6.a.f.1.1		1
56.51	odd	6		64.6.a.b.1.1		1
63.2	odd	6		324.6.e.d.109.1		2
63.16	even	3		324.6.e.a.109.1		2
63.23	odd	6		324.6.e.d.217.1		2
63.58	even	3		324.6.e.a.217.1		2
77.65	odd	6		484.6.a.a.1.1		1
84.23	even	6		144.6.a.c.1.1		1
91.44	odd	12		676.6.d.a.337.1		2
91.51	even	6		676.6.a.a.1.1		1
91.86	odd	12		676.6.d.a.337.2		2
105.2	even	12		900.6.d.a.649.1		2
105.23	even	12		900.6.d.a.649.2		2
105.44	odd	6		900.6.a.h.1.1		1
112.37	even	12		256.6.b.g.129.2		2
112.51	odd	12		256.6.b.c.129.2		2
112.93	even	12		256.6.b.g.129.1		2
112.107	odd	12		256.6.b.c.129.1		2
140.23	even	12		400.6.c.f.49.2		2
140.79	odd	6		400.6.a.d.1.1		1
140.107	even	12		400.6.c.f.49.1		2
168.107	even	6		576.6.a.bd.1.1		1
168.149	odd	6		576.6.a.bc.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.6.a.a.1.1	✓	1	7.2	even	3
16.6.a.b.1.1		1	28.23	odd	6
36.6.a.a.1.1		1	21.2	odd	6
64.6.a.b.1.1		1	56.51	odd	6
64.6.a.f.1.1		1	56.37	even	6
100.6.a.b.1.1		1	35.9	even	6
100.6.c.b.49.1		2	35.23	odd	12
100.6.c.b.49.2		2	35.2	odd	12
144.6.a.c.1.1		1	84.23	even	6
196.6.a.e.1.1		1	7.5	odd	6
196.6.e.d.165.1		2	7.3	odd	6
196.6.e.d.177.1		2	7.6	odd	2
196.6.e.g.165.1		2	7.4	even	3	inner
196.6.e.g.177.1		2	1.1	even	1	trivial
256.6.b.c.129.1		2	112.107	odd	12
256.6.b.c.129.2		2	112.51	odd	12
256.6.b.g.129.1		2	112.93	even	12
256.6.b.g.129.2		2	112.37	even	12
324.6.e.a.109.1		2	63.16	even	3
324.6.e.a.217.1		2	63.58	even	3
324.6.e.d.109.1		2	63.2	odd	6
324.6.e.d.217.1		2	63.23	odd	6
400.6.a.d.1.1		1	140.79	odd	6
400.6.c.f.49.1		2	140.107	even	12
400.6.c.f.49.2		2	140.23	even	12
484.6.a.a.1.1		1	77.65	odd	6
576.6.a.bc.1.1		1	168.149	odd	6
576.6.a.bd.1.1		1	168.107	even	6
676.6.a.a.1.1		1	91.51	even	6
676.6.d.a.337.1		2	91.44	odd	12
676.6.d.a.337.2		2	91.86	odd	12
784.6.a.d.1.1		1	28.19	even	6
900.6.a.h.1.1		1	105.44	odd	6
900.6.d.a.649.1		2	105.2	even	12
900.6.d.a.649.2		2	105.23	even	12

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	196.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(6.00000 + 10.3923i) q^{3} +(-27.0000 + 46.7654i) q^{5} +(49.5000 - 85.7365i) q^{9} +O(q^{10})\)	\(q+(6.00000 + 10.3923i) q^{3} +(-27.0000 + 46.7654i) q^{5} +(49.5000 - 85.7365i) q^{9} +(-270.000 - 467.654i) q^{11} -418.000 q^{13} -648.000 q^{15} +(-297.000 - 514.419i) q^{17} +(-418.000 + 723.997i) q^{19} +(2052.00 - 3554.17i) q^{23} +(104.500 + 180.999i) q^{25} +4104.00 q^{27} -594.000 q^{29} +(-2128.00 - 3685.80i) q^{31} +(3240.00 - 5611.84i) q^{33} +(149.000 - 258.076i) q^{37} +(-2508.00 - 4343.98i) q^{39} +17226.0 q^{41} -12100.0 q^{43} +(2673.00 + 4629.77i) q^{45} +(648.000 - 1122.37i) q^{47} +(3564.00 - 6173.03i) q^{51} +(-9747.00 - 16882.3i) q^{53} +29160.0 q^{55} -10032.0 q^{57} +(3834.00 + 6640.68i) q^{59} +(17369.0 - 30084.0i) q^{61} +(11286.0 - 19547.9i) q^{65} +(-10906.0 - 18889.7i) q^{67} +49248.0 q^{69} -46872.0 q^{71} +(-33781.0 - 58510.4i) q^{73} +(-1254.00 + 2171.99i) q^{75} +(38456.0 - 66607.7i) q^{79} +(12595.5 + 21816.0i) q^{81} +67716.0 q^{83} +32076.0 q^{85} +(-3564.00 - 6173.03i) q^{87} +(-14877.0 + 25767.7i) q^{89} +(25536.0 - 44229.6i) q^{93} +(-22572.0 - 39095.9i) q^{95} -122398. q^{97} -53460.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 12 q^{3} - 54 q^{5} + 99 q^{9}+O(q^{10}) \) 2 * q + 12 * q^3 - 54 * q^5 + 99 * q^9	\( 2 q + 12 q^{3} - 54 q^{5} + 99 q^{9} - 540 q^{11} - 836 q^{13} - 1296 q^{15} - 594 q^{17} - 836 q^{19} + 4104 q^{23} + 209 q^{25} + 8208 q^{27} - 1188 q^{29} - 4256 q^{31} + 6480 q^{33} + 298 q^{37} - 5016 q^{39} + 34452 q^{41} - 24200 q^{43} + 5346 q^{45} + 1296 q^{47} + 7128 q^{51} - 19494 q^{53} + 58320 q^{55} - 20064 q^{57} + 7668 q^{59} + 34738 q^{61} + 22572 q^{65} - 21812 q^{67} + 98496 q^{69} - 93744 q^{71} - 67562 q^{73} - 2508 q^{75} + 76912 q^{79} + 25191 q^{81} + 135432 q^{83} + 64152 q^{85} - 7128 q^{87} - 29754 q^{89} + 51072 q^{93} - 45144 q^{95} - 244796 q^{97} - 106920 q^{99}+O(q^{100}) \) 2 * q + 12 * q^3 - 54 * q^5 + 99 * q^9 - 540 * q^11 - 836 * q^13 - 1296 * q^15 - 594 * q^17 - 836 * q^19 + 4104 * q^23 + 209 * q^25 + 8208 * q^27 - 1188 * q^29 - 4256 * q^31 + 6480 * q^33 + 298 * q^37 - 5016 * q^39 + 34452 * q^41 - 24200 * q^43 + 5346 * q^45 + 1296 * q^47 + 7128 * q^51 - 19494 * q^53 + 58320 * q^55 - 20064 * q^57 + 7668 * q^59 + 34738 * q^61 + 22572 * q^65 - 21812 * q^67 + 98496 * q^69 - 93744 * q^71 - 67562 * q^73 - 2508 * q^75 + 76912 * q^79 + 25191 * q^81 + 135432 * q^83 + 64152 * q^85 - 7128 * q^87 - 29754 * q^89 + 51072 * q^93 - 45144 * q^95 - 244796 * q^97 - 106920 * q^99

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