LMFDB - Embedded newform 144.7.q.c.65.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,7,Mod(65,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("144.65");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	144.q (of order $6$, 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:	$33.1277880413$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600 $ x^12 + 370x^10 + 51793x^8 + 3491832x^6 + 117603792x^4 + 1832032512*x^2 + 10453017600
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{13} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.5
Root			$-4.28281i$ of defining polynomial
Character	$\chi$	$=$	144.65
Dual form			144.7.q.c.113.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(22.5447 - 14.8572i) q^{3} +(156.951 - 90.6160i) q^{5} +(-104.306 + 180.663i) q^{7} +(287.526 - 669.903i) q^{9} +O(q^{10})$	\(q+(22.5447 - 14.8572i) q^{3} +(156.951 - 90.6160i) q^{5} +(-104.306 + 180.663i) q^{7} +(287.526 - 669.903i) q^{9} +(-2301.99 - 1329.05i) q^{11} +(-438.599 - 759.676i) q^{13} +(2192.12 - 4374.77i) q^{15} -4428.53i q^{17} +4194.21 q^{19} +(332.607 + 5622.69i) q^{21} +(-10399.9 + 6004.40i) q^{23} +(8610.01 - 14913.0i) q^{25} +(-3470.70 - 19374.6i) q^{27} +(2288.79 + 1321.43i) q^{29} +(2902.50 + 5027.28i) q^{31} +(-71643.7 + 4238.04i) q^{33} +37807.1i q^{35} +41579.5 q^{37} +(-21174.8 - 10610.3i) q^{39} +(-64721.2 + 37366.8i) q^{41} +(73052.9 - 126531. i) q^{43} +(-15576.2 - 131197. i) q^{45} +(22319.7 + 12886.3i) q^{47} +(37065.1 + 64198.6i) q^{49} +(-65795.6 - 99839.7i) q^{51} -197505. i q^{53} -481734. q^{55} +(94557.3 - 62314.3i) q^{57} +(31321.5 - 18083.5i) q^{59} +(-11967.3 + 20728.0i) q^{61} +(91036.1 + 121820. i) q^{63} +(-137678. - 79488.2i) q^{65} +(176540. + 305776. i) q^{67} +(-145255. + 289881. i) q^{69} -496781. i q^{71} -382139. q^{73} +(-27455.3 - 464129. i) q^{75} +(480222. - 277257. i) q^{77} +(193328. - 334855. i) q^{79} +(-366098. - 385229. i) q^{81} +(-359691. - 207667. i) q^{83} +(-401295. - 695064. i) q^{85} +(71232.8 - 4213.73i) q^{87} -405654. i q^{89} +182994. q^{91} +(140128. + 70215.4i) q^{93} +(658288. - 380063. i) q^{95} +(-178244. + 308727. i) q^{97} +(-1.55222e6 + 1.15997e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 42 q^{3} + 432 q^{5} - 240 q^{7} + 2190 q^{9}+O(q^{10}) $ 12 * q + 42 * q^3 + 432 * q^5 - 240 * q^7 + 2190 * q^9	$ 12 q + 42 q^{3} + 432 q^{5} - 240 q^{7} + 2190 q^{9} - 378 q^{11} + 1680 q^{13} + 10872 q^{15} + 2820 q^{19} + 24876 q^{21} + 76248 q^{23} + 8094 q^{25} - 127008 q^{27} + 97092 q^{29} - 21480 q^{31} - 246258 q^{33} - 25536 q^{37} - 42204 q^{39} - 410562 q^{41} - 71430 q^{43} + 13716 q^{45} - 347652 q^{47} - 135954 q^{49} - 336402 q^{51} - 580392 q^{55} - 522282 q^{57} - 369738 q^{59} + 135744 q^{61} + 103800 q^{63} - 753840 q^{65} + 289938 q^{67} + 2059272 q^{69} - 977700 q^{73} + 2115342 q^{75} - 159192 q^{77} + 764796 q^{79} - 1428282 q^{81} - 396900 q^{83} + 1619568 q^{85} - 3072636 q^{87} - 355584 q^{91} - 2526576 q^{93} + 2089260 q^{95} - 38874 q^{97} - 4398804 q^{99}+O(q^{100}) $ 12 * q + 42 * q^3 + 432 * q^5 - 240 * q^7 + 2190 * q^9 - 378 * q^11 + 1680 * q^13 + 10872 * q^15 + 2820 * q^19 + 24876 * q^21 + 76248 * q^23 + 8094 * q^25 - 127008 * q^27 + 97092 * q^29 - 21480 * q^31 - 246258 * q^33 - 25536 * q^37 - 42204 * q^39 - 410562 * q^41 - 71430 * q^43 + 13716 * q^45 - 347652 * q^47 - 135954 * q^49 - 336402 * q^51 - 580392 * q^55 - 522282 * q^57 - 369738 * q^59 + 135744 * q^61 + 103800 * q^63 - 753840 * q^65 + 289938 * q^67 + 2059272 * q^69 - 977700 * q^73 + 2115342 * q^75 - 159192 * q^77 + 764796 * q^79 - 1428282 * q^81 - 396900 * q^83 + 1619568 * q^85 - 3072636 * q^87 - 355584 * q^91 - 2526576 * q^93 + 2089260 * q^95 - 38874 * q^97 - 4398804 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	22.5447	−	14.8572i	0.834989	−	0.550267i
$3$	22.5447	−	14.8572i	0.834989	−	0.550267i
$4$		0			0
$5$	156.951	−	90.6160i	1.25561	−	0.724928i	0.283394	−	0.959004i	$-0.408540\pi$
$5$	156.951	−	90.6160i	1.25561	−	0.724928i	0.972218	+	0.234076i	$0.0752064\pi$
$6$		0			0
$7$	−104.306	+	180.663i	−0.304099	+	0.526715i	−0.977060	−	0.212963i	$-0.931689\pi$
$7$	−104.306	+	180.663i	−0.304099	+	0.526715i	0.672961	+	0.739678i	$0.265022\pi$
$8$		0			0
$9$	287.526	−	669.903i	0.394412	−	0.918934i
$10$		0			0
$11$	−2301.99	−	1329.05i	−1.72952	−	0.998538i	−0.891782	−	0.452465i	$-0.850545\pi$
$11$	−2301.99	−	1329.05i	−1.72952	−	0.998538i	−0.837737	−	0.546074i	$-0.816122\pi$
$12$		0			0
$13$	−438.599	−	759.676i	−0.199636	−	0.345779i	0.748775	−	0.662825i	$-0.230642\pi$
$13$	−438.599	−	759.676i	−0.199636	−	0.345779i	−0.948410	+	0.317046i	$0.897309\pi$
$14$		0			0
$15$	2192.12	−	4374.77i	0.649517	−	1.29623i
$16$		0			0
$17$		−	4428.53i		−	0.901389i	−0.892678	−	0.450695i	$-0.851176\pi$
$17$		−	4428.53i		−	0.901389i	0.892678	−	0.450695i	$-0.148824\pi$
$18$		0			0
$19$	4194.21			0.611491			0.305745	−	0.952113i	$-0.401094\pi$
$19$	4194.21			0.611491			0.305745	+	0.952113i	$0.401094\pi$
$20$		0			0
$21$	332.607	+	5622.69i	0.0359148	+	0.607136i
$22$		0			0
$23$	−10399.9	+	6004.40i	−0.854766	+	0.493499i	−0.862256	−	0.506473i	$-0.830949\pi$
$23$	−10399.9	+	6004.40i	−0.854766	+	0.493499i	0.00749035	+	0.999972i	$0.497616\pi$
$24$		0			0
$25$	8610.01	−	14913.0i	0.551041	−	0.954431i
$26$		0			0
$27$	−3470.70	−	19374.6i	−0.176330	−	0.984331i
$28$		0			0
$29$	2288.79	+	1321.43i	0.0938450	+	0.0541815i	0.546188	−	0.837663i	$-0.316078\pi$
$29$	2288.79	+	1321.43i	0.0938450	+	0.0541815i	−0.452343	+	0.891844i	$0.649412\pi$
$30$		0			0
$31$	2902.50	+	5027.28i	0.0974289	+	0.168752i	0.910620	−	0.413245i	$-0.135605\pi$
$31$	2902.50	+	5027.28i	0.0974289	+	0.168752i	−0.813191	+	0.581997i	$0.802271\pi$
$32$		0			0
$33$	−71643.7	+	4238.04i	−1.99359	+	0.117930i
$34$		0			0
$35$			37807.1i			0.881799i
$36$		0			0
$37$	41579.5			0.820869			0.410435	−	0.911890i	$-0.365377\pi$
$37$	41579.5			0.820869			0.410435	+	0.911890i	$0.365377\pi$
$38$		0			0
$39$	−21174.8	−	10610.3i	−0.356964	−	0.178868i
$40$		0			0
$41$	−64721.2	+	37366.8i	−0.939063	+	0.542168i	−0.889666	−	0.456611i	$-0.849063\pi$
$41$	−64721.2	+	37366.8i	−0.939063	+	0.542168i	−0.0493965	+	0.998779i	$0.515730\pi$
$42$		0			0
$43$	73052.9	−	126531.i	0.918824	−	1.59145i	0.117620	−	0.993059i	$-0.462474\pi$
$43$	73052.9	−	126531.i	0.918824	−	1.59145i	0.801204	−	0.598391i	$-0.204193\pi$
$44$		0			0
$45$	−15576.2	−	131197.i	−0.170933	−	1.43974i
$46$		0			0
$47$	22319.7	+	12886.3i	0.214978	+	0.124118i	0.603623	−	0.797270i	$-0.293723\pi$
$47$	22319.7	+	12886.3i	0.214978	+	0.124118i	−0.388645	+	0.921388i	$0.627057\pi$
$48$		0			0
$49$	37065.1	+	64198.6i	0.315048	+	0.545679i
$50$		0			0
$51$	−65795.6	−	99839.7i	−0.496005	−	0.752650i
$52$		0			0
$53$		−	197505.i		−	1.32663i	−0.748340	−	0.663316i	$-0.769149\pi$
$53$		−	197505.i		−	1.32663i	0.748340	−	0.663316i	$-0.230851\pi$
$54$		0			0
$55$	−481734.			−2.89547
$56$		0			0
$57$	94557.3	−	62314.3i	0.510588	−	0.336483i
$58$		0			0
$59$	31321.5	−	18083.5i	0.152506	−	0.0880493i	−0.421805	−	0.906687i	$-0.638603\pi$
$59$	31321.5	−	18083.5i	0.152506	−	0.0880493i	0.574311	+	0.818637i	$0.305270\pi$
$60$		0			0
$61$	−11967.3	+	20728.0i	−0.0527239	+	0.0913204i	−0.891183	−	0.453644i	$-0.850124\pi$
$61$	−11967.3	+	20728.0i	−0.0527239	+	0.0913204i	0.838459	+	0.544965i	$0.183457\pi$
$62$		0			0
$63$	91036.1	+	121820.i	0.364076	+	0.487189i
$64$		0			0
$65$	−137678.	−	79488.2i	−0.501330	−	0.289443i
$66$		0			0
$67$	176540.	+	305776.i	0.586973	+	1.01667i	0.994626	+	0.103530i	$0.0330138\pi$
$67$	176540.	+	305776.i	0.586973	+	1.01667i	−0.407653	+	0.913137i	$0.633653\pi$
$68$		0			0
$69$	−145255.	+	289881.i	−0.442163	+	0.882416i
$70$		0			0
$71$		−	496781.i		−	1.38800i	−0.719974	−	0.694001i	$-0.755846\pi$
$71$		−	496781.i		−	1.38800i	0.719974	−	0.694001i	$-0.244154\pi$
$72$		0			0
$73$	−382139.			−0.982319			−0.491160	−	0.871070i	$-0.663427\pi$
$73$	−382139.			−0.982319			−0.491160	+	0.871070i	$0.663427\pi$
$74$		0			0
$75$	−27455.3	−	464129.i	−0.0650792	−	1.10016i
$76$		0			0
$77$	480222.	−	277257.i	1.05189	−	0.607309i
$78$		0			0
$79$	193328.	−	334855.i	0.392116	−	0.679165i	−0.600613	−	0.799540i	$-0.705077\pi$
$79$	193328.	−	334855.i	0.392116	−	0.679165i	0.992728	+	0.120376i	$0.0384099\pi$
$80$		0			0
$81$	−366098.	−	385229.i	−0.688879	−	0.724877i
$82$		0			0
$83$	−359691.	−	207667.i	−0.629064	−	0.363190i	0.151326	−	0.988484i	$-0.451646\pi$
$83$	−359691.	−	207667.i	−0.629064	−	0.363190i	−0.780389	+	0.625294i	$0.784979\pi$
$84$		0			0
$85$	−401295.	−	695064.i	−0.653442	−	1.13180i
$86$		0			0
$87$	71232.8	−	4213.73i	0.108174	−	0.00639896i
$88$		0			0
$89$		−	405654.i		−	0.575421i	−0.957717	−	0.287710i	$-0.907106\pi$
$89$		−	405654.i		−	0.575421i	0.957717	−	0.287710i	$-0.0928941\pi$
$90$		0			0
$91$	182994.			0.242836
$92$		0			0
$93$	140128.	+	70215.4i	0.174211	+	0.0872939i
$94$		0			0
$95$	658288.	−	380063.i	0.767795	−	0.443287i
$96$		0			0
$97$	−178244.	+	308727.i	−0.195298	+	0.338267i	−0.946998	−	0.321239i	$-0.895901\pi$
$97$	−178244.	+	308727.i	−0.195298	+	0.338267i	0.751700	+	0.659505i	$0.229234\pi$
$98$		0			0
$99$	−1.55222e6	+	1.15997e6i	−1.59973	+	1.19548i
$100$		0			0
$101$	1.41963e6	+	819621.i	1.37787	+	0.795516i	0.991903	−	0.126995i	$-0.0405332\pi$
$101$	1.41963e6	+	819621.i	1.37787	+	0.795516i	0.385971	+	0.922511i	$0.373867\pi$
$102$		0			0
$103$	462737.	+	801484.i	0.423470	+	0.733472i	0.996276	−	0.0862192i	$-0.0274785\pi$
$103$	462737.	+	801484.i	0.423470	+	0.733472i	−0.572806	+	0.819691i	$0.694145\pi$
$104$		0			0
$105$	561709.	+	852350.i	0.485225	+	0.736292i
$106$		0			0
$107$			266819.i			0.217804i	0.994053	+	0.108902i	$0.0347334\pi$
$107$			266819.i			0.217804i	−0.994053	+	0.108902i	$0.965267\pi$
$108$		0			0
$109$	169960.			0.131240			0.0656200	−	0.997845i	$-0.479097\pi$
$109$	169960.			0.131240			0.0656200	+	0.997845i	$0.479097\pi$
$110$		0			0
$111$	937397.	−	617756.i	0.685417	−	0.451698i
$112$		0			0
$113$	−1.65439e6	+	955161.i	−1.14657	+	0.661974i	−0.948050	−	0.318122i	$-0.896948\pi$
$113$	−1.65439e6	+	955161.i	−1.14657	+	0.661974i	−0.198523	+	0.980096i	$0.563615\pi$
$114$		0			0
$115$	−1.08819e6	+	1.88480e6i	−0.715503	+	1.23929i
$116$		0			0
$117$	−635018.	+	75392.0i	−0.396486	+	0.0470726i
$118$		0			0
$119$	800071.	+	461921.i	0.474775	+	0.274111i
$120$		0			0
$121$	2.64699e6	+	4.58473e6i	1.49416	+	2.58796i
$122$		0			0
$123$	−903952.	+	1.80400e6i	−0.485769	+	0.969440i
$124$		0			0
$125$		−	289070.i		−	0.148004i
$126$		0			0
$127$	1.75663e6			0.857571			0.428786	−	0.903406i	$-0.358942\pi$
$127$	1.75663e6			0.857571			0.428786	+	0.903406i	$0.358942\pi$
$128$		0			0
$129$	−232949.	−	3.93797e6i	−0.108515	−	1.83444i
$130$		0			0
$131$	2.07548e6	−	1.19828e6i	0.923221	−	0.533022i	0.0385598	−	0.999256i	$-0.487723\pi$
$131$	2.07548e6	−	1.19828e6i	0.923221	−	0.533022i	0.884661	+	0.466234i	$0.154390\pi$
$132$		0			0
$133$	−437481.	+	757740.i	−0.185954	+	0.322081i
$134$		0			0
$135$	−2.30038e6	−	2.72637e6i	−0.934971	−	1.10811i
$136$		0			0
$137$	1.15495e6	+	666808.i	0.449159	+	0.259322i	0.707475	−	0.706739i	$-0.249834\pi$
$137$	1.15495e6	+	666808.i	0.449159	+	0.259322i	−0.258316	+	0.966060i	$0.583168\pi$
$138$		0			0
$139$	1.08878e6	+	1.88583e6i	0.405412	+	0.702194i	0.994369	−	0.105970i	$-0.0337948\pi$
$139$	1.08878e6	+	1.88583e6i	0.405412	+	0.702194i	−0.588957	+	0.808164i	$0.700461\pi$
$140$		0			0
$141$	694644.	−	41091.3i	0.247802	−	0.0146586i
$142$		0			0
$143$			2.33169e6i			0.797375i
$144$		0			0
$145$	478971.			0.157111
$146$		0			0
$147$	1.78943e6	+	896653.i	0.563330	+	0.282275i
$148$		0			0
$149$	3.35022e6	−	1.93425e6i	1.01278	−	0.584727i	0.100774	−	0.994909i	$-0.467868\pi$
$149$	3.35022e6	−	1.93425e6i	1.01278	−	0.584727i	0.912004	+	0.410182i	$0.134535\pi$
$150$		0			0
$151$	480879.	−	832907.i	0.139671	−	0.241917i	−0.787701	−	0.616057i	$-0.788729\pi$
$151$	480879.	−	832907.i	0.139671	−	0.241917i	0.927372	+	0.374141i	$0.122062\pi$
$152$		0			0
$153$	−2.96668e6	−	1.27332e6i	−0.828317	−	0.355519i
$154$		0			0
$155$	911105.	+	526027.i	0.244666	+	0.141258i
$156$		0			0
$157$	796173.	+	1.37901e6i	0.205735	+	0.356344i	0.950367	−	0.311132i	$-0.100708\pi$
$157$	796173.	+	1.37901e6i	0.205735	+	0.356344i	−0.744632	+	0.667476i	$0.767375\pi$
$158$		0			0
$159$	−2.93437e6	−	4.45269e6i	−0.730002	−	1.10772i
$160$		0			0
$161$		−	2.50518e6i		−	0.600290i
$162$		0			0
$163$	−702280.			−0.162161			−0.0810807	−	0.996708i	$-0.525837\pi$
$163$	−702280.			−0.162161			−0.0810807	+	0.996708i	$0.525837\pi$
$164$		0			0
$165$	−1.08606e7	+	7.15723e6i	−2.41769	+	1.59328i
$166$		0			0
$167$	3.27789e6	−	1.89249e6i	0.703794	−	0.406335i	−0.104965	−	0.994476i	$-0.533473\pi$
$167$	3.27789e6	−	1.89249e6i	0.703794	−	0.406335i	0.808759	+	0.588140i	$0.200140\pi$
$168$		0			0
$169$	2.02867e6	−	3.51375e6i	0.420291	−	0.727966i
$170$		0			0
$171$	1.20595e6	−	2.80972e6i	0.241179	−	0.561919i
$172$		0			0
$173$	3.78706e6	+	2.18646e6i	0.731416	+	0.422283i	0.818940	−	0.573879i	$-0.194562\pi$
$173$	3.78706e6	+	2.18646e6i	0.731416	+	0.422283i	−0.0875242	+	0.996162i	$0.527896\pi$
$174$		0			0
$175$	1.79615e6	+	3.11102e6i	0.335142	+	0.580483i
$176$		0			0
$177$	437463.	−	873037.i	0.0788900	−	0.157439i
$178$		0			0
$179$		−	49288.2i		−	0.00859377i	−0.999991	−	0.00429688i	$-0.998632\pi$
$179$		−	49288.2i		−	0.00859377i	0.999991	−	0.00429688i	$-0.00136775\pi$
$180$		0			0
$181$	−4.52205e6			−0.762605			−0.381303	−	0.924450i	$-0.624524\pi$
$181$	−4.52205e6			−0.762605			−0.381303	+	0.924450i	$0.624524\pi$
$182$		0			0
$183$	38160.9	+	645107.i	0.00622681	+	0.105264i
$184$		0			0
$185$	6.52596e6	−	3.76777e6i	1.03069	−	0.595071i
$186$		0			0
$187$	−5.88575e6	+	1.01944e7i	−0.900072	+	1.55897i
$188$		0			0
$189$	3.86229e6	+	1.39386e6i	0.572083	+	0.206458i
$190$		0			0
$191$	−1.07831e6	−	622561.i	−0.154754	−	0.0893473i	0.420623	−	0.907235i	$-0.361811\pi$
$191$	−1.07831e6	−	622561.i	−0.154754	−	0.0893473i	−0.575377	+	0.817888i	$0.695145\pi$
$192$		0			0
$193$	5.47671e6	+	9.48595e6i	0.761812	+	1.31950i	0.941915	+	0.335850i	$0.109024\pi$
$193$	5.47671e6	+	9.48595e6i	0.761812	+	1.31950i	−0.180103	+	0.983648i	$0.557643\pi$
$194$		0			0
$195$	−4.28487e6	+	253469.i	−0.577875	+	0.0341839i
$196$		0			0
$197$		−	1.07910e7i		−	1.41144i	−0.708492	−	0.705719i	$-0.750624\pi$
$197$		−	1.07910e7i		−	1.41144i	0.708492	−	0.705719i	$-0.249376\pi$
$198$		0			0
$199$	−5.05948e6			−0.642017			−0.321008	−	0.947076i	$-0.604022\pi$
$199$	−5.05948e6			−0.642017			−0.321008	+	0.947076i	$0.604022\pi$
$200$		0			0
$201$	8.52301e6	+	4.27073e6i	1.04955	+	0.525913i
$202$		0			0
$203$	−477468.	+	275666.i	−0.0570763	+	0.0329530i
$204$		0			0
$205$	−6.77205e6	+	1.17295e7i	−0.786066	+	1.36151i
$206$		0			0
$207$	1.03211e6	+	8.69337e6i	0.116363	+	0.980115i
$208$		0			0
$209$	−9.65504e6	−	5.57434e6i	−1.05758	−	0.610597i
$210$		0			0
$211$	−1.72915e6	−	2.99498e6i	−0.184071	−	0.318821i	0.759192	−	0.650867i	$-0.225594\pi$
$211$	−1.72915e6	−	2.99498e6i	−0.184071	−	0.318821i	−0.943263	+	0.332046i	$0.892261\pi$
$212$		0			0
$213$	−7.38079e6	−	1.11998e7i	−0.763772	−	1.15897i
$214$		0			0
$215$		−	2.64791e7i		−	2.66432i
$216$		0			0
$217$	−1.21099e6			−0.118512
$218$		0			0
$219$	−8.61520e6	+	5.67752e6i	−0.820225	+	0.540538i
$220$		0			0
$221$	−3.36425e6	+	1.94235e6i	−0.311681	+	0.179949i
$222$		0			0
$223$	3.78005e6	−	6.54724e6i	0.340865	−	0.590396i	−0.643728	−	0.765254i	$-0.722613\pi$
$223$	3.78005e6	−	6.54724e6i	0.340865	−	0.590396i	0.984594	+	0.174858i	$0.0559467\pi$
$224$		0			0
$225$	−7.51464e6	−	1.00557e7i	−0.659722	−	0.882809i
$226$		0			0
$227$	4.44652e6	+	2.56720e6i	0.380139	+	0.219473i	0.677879	−	0.735174i	$-0.262899\pi$
$227$	4.44652e6	+	2.56720e6i	0.380139	+	0.219473i	−0.297740	+	0.954647i	$0.596233\pi$
$228$		0			0
$229$	−9.32792e6	−	1.61564e7i	−0.776744	−	1.34536i	−0.933809	−	0.357772i	$-0.883536\pi$
$229$	−9.32792e6	−	1.61564e7i	−0.776744	−	1.34536i	0.157064	−	0.987588i	$-0.449797\pi$
$230$		0			0
$231$	6.70721e6	−	1.33854e7i	0.544134	−	1.08592i
$232$		0			0
$233$		−	421669.i		−	0.0333352i	−0.999861	−	0.0166676i	$-0.994694\pi$
$233$		−	421669.i		−	0.0333352i	0.999861	−	0.0166676i	$-0.00530571\pi$
$234$		0			0
$235$	4.67081e6			0.359905
$236$		0			0
$237$	−616479.	−	1.04215e7i	−0.0463098	−	0.782863i
$238$		0			0
$239$	1.93062e7	−	1.11465e7i	1.41418	−	0.816475i	0.418398	−	0.908264i	$-0.362592\pi$
$239$	1.93062e7	−	1.11465e7i	1.41418	−	0.816475i	0.995779	+	0.0917886i	$0.0292584\pi$
$240$		0			0
$241$	−4.91596e6	+	8.51470e6i	−0.351202	+	0.608300i	−0.986460	−	0.164000i	$-0.947560\pi$
$241$	−4.91596e6	+	8.51470e6i	−0.351202	+	0.608300i	0.635258	+	0.772300i	$0.280894\pi$
$242$		0			0
$243$	−1.39770e7	−	3.24567e6i	−0.974082	−	0.226196i
$244$		0			0
$245$	1.16348e7	+	6.71737e6i	0.791155	+	0.456774i
$246$		0			0
$247$	−1.83958e6	−	3.18624e6i	−0.122075	−	0.211441i
$248$		0			0
$249$	−1.11945e7	+	662203.i	−0.725113	+	0.0428936i
$250$		0			0
$251$			1.55511e7i			0.983422i	0.870759	+	0.491711i	$0.163628\pi$
$251$			1.55511e7i			0.983422i	−0.870759	+	0.491711i	$0.836372\pi$
$252$		0			0
$253$	3.19207e7			1.97111
$254$		0			0
$255$	−1.93738e7	−	9.70787e6i	−1.16841	−	0.585468i
$256$		0			0
$257$	−1.84675e6	+	1.06622e6i	−0.108795	+	0.0628128i	−0.553410	−	0.832909i	$-0.686674\pi$
$257$	−1.84675e6	+	1.06622e6i	−0.108795	+	0.0628128i	0.444615	+	0.895722i	$0.353340\pi$
$258$		0			0
$259$	−4.33699e6	+	7.51188e6i	−0.249625	+	0.432364i
$260$		0			0
$261$	1.54332e6	−	1.15332e6i	0.0868028	−	0.0648676i
$262$		0			0
$263$	911256.	+	526114.i	0.0500925	+	0.0289209i	0.524837	−	0.851203i	$-0.324126\pi$
$263$	911256.	+	526114.i	0.0500925	+	0.0289209i	−0.474745	+	0.880124i	$0.657460\pi$
$264$		0			0
$265$	−1.78971e7	−	3.09987e7i	−0.961712	−	1.66573i
$266$		0			0
$267$	−6.02689e6	−	9.14534e6i	−0.316635	−	0.480470i
$268$		0			0
$269$			9.68762e6i			0.497692i	0.968543	+	0.248846i	$0.0800512\pi$
$269$			9.68762e6i			0.497692i	−0.968543	+	0.248846i	$0.919949\pi$
$270$		0			0
$271$	2.05637e7			1.03322			0.516610	−	0.856221i	$-0.327194\pi$
$271$	2.05637e7			1.03322			0.516610	+	0.856221i	$0.327194\pi$
$272$		0			0
$273$	4.12554e6	−	2.71878e6i	0.202765	−	0.133625i
$274$		0			0
$275$	−3.96403e7	+	2.28864e7i	−1.90607	+	1.10047i
$276$		0			0
$277$	−1.00696e7	+	1.74411e7i	−0.473776	+	0.820604i	−0.999549	−	0.0300208i	$-0.990443\pi$
$277$	−1.00696e7	+	1.74411e7i	−0.473776	+	0.820604i	0.525773	+	0.850625i	$0.323776\pi$
$278$		0			0
$279$	4.20234e6	−	498920.i	0.193499	−	0.0229730i
$280$		0			0
$281$	1.75923e7	+	1.01569e7i	0.792873	+	0.457766i	0.840973	−	0.541077i	$-0.181983\pi$
$281$	1.75923e7	+	1.01569e7i	0.792873	+	0.457766i	−0.0480998	+	0.998843i	$0.515317\pi$
$282$		0			0
$283$	1.13075e7	+	1.95852e7i	0.498894	+	0.864110i	0.999999	−	0.00127619i	$-0.000406222\pi$
$283$	1.13075e7	+	1.95852e7i	0.498894	+	0.864110i	−0.501105	+	0.865387i	$0.667073\pi$
$284$		0			0
$285$	9.19423e6	−	1.83487e7i	0.397174	−	0.792632i
$286$		0			0
$287$		−	1.55903e7i		−	0.659491i
$288$		0			0
$289$	4.52573e6			0.187497
$290$		0			0
$291$	568377.	+	9.60836e6i	0.0230652	+	0.389915i
$292$		0			0
$293$	−3.34647e6	+	1.93209e6i	−0.133041	+	0.0768111i	−0.565043	−	0.825061i	$-0.691141\pi$
$293$	−3.34647e6	+	1.93209e6i	−0.133041	+	0.0768111i	0.432002	+	0.901872i	$0.357807\pi$
$294$		0			0
$295$	3.27730e6	−	5.67646e6i	0.127659	−	0.221111i
$296$		0			0
$297$	−1.77604e7	+	4.92129e7i	−0.677926	+	1.87849i
$298$		0			0
$299$	9.12281e6	+	5.26705e6i	0.341283	+	0.197040i
$300$		0			0
$301$	1.52397e7	+	2.63959e7i	0.558827	+	0.967916i
$302$		0			0
$303$	4.41823e7	−	2.61358e6i	1.58826	−	0.0939523i
$304$		0			0
$305$			4.33772e6i			0.152884i
$306$		0			0
$307$	3.02526e6			0.104556			0.0522779	−	0.998633i	$-0.483352\pi$
$307$	3.02526e6			0.104556			0.0522779	+	0.998633i	$0.483352\pi$
$308$		0			0
$309$	2.23401e7	+	1.11942e7i	0.757198	+	0.379419i
$310$		0			0
$311$	−3.30190e7	+	1.90635e7i	−1.09770	+	0.633755i	−0.935615	−	0.353022i	$-0.885154\pi$
$311$	−3.30190e7	+	1.90635e7i	−1.09770	+	0.633755i	−0.162081	+	0.986777i	$0.551821\pi$
$312$		0			0
$313$	1.13148e7	−	1.95979e7i	0.368990	−	0.639110i	−0.620417	−	0.784272i	$-0.713037\pi$
$313$	1.13148e7	−	1.95979e7i	0.368990	−	0.639110i	0.989408	+	0.145161i	$0.0463702\pi$
$314$		0			0
$315$	2.53271e7	+	1.08705e7i	0.810315	+	0.347792i
$316$		0			0
$317$	−2.07004e7	−	1.19514e7i	−0.649831	−	0.375180i	0.138560	−	0.990354i	$-0.455753\pi$
$317$	−2.07004e7	−	1.19514e7i	−0.649831	−	0.375180i	−0.788392	+	0.615174i	$0.789086\pi$
$318$		0			0
$319$	−3.51251e6	−	6.08385e6i	−0.108205	−	0.187416i
$320$		0			0
$321$	3.96418e6	+	6.01535e6i	0.119850	+	0.181864i
$322$		0			0
$323$		−	1.85742e7i		−	0.551191i
$324$		0			0
$325$	−1.51054e7			−0.440029
$326$		0			0
$327$	3.83169e6	−	2.52513e6i	0.109584	−	0.0722171i
$328$		0			0
$329$	−4.65615e6	+	2.68823e6i	−0.130749	+	0.0754881i
$330$		0			0
$331$	−1.41912e7	+	2.45799e7i	−0.391324	+	0.677792i	−0.992624	−	0.121230i	$-0.961316\pi$
$331$	−1.41912e7	+	2.45799e7i	−0.391324	+	0.677792i	0.601301	+	0.799023i	$0.294649\pi$
$332$		0			0
$333$	1.19552e7	−	2.78542e7i	0.323761	−	0.754325i
$334$		0			0
$335$	5.54164e7	+	3.19946e7i	1.47402	+	0.851026i
$336$		0			0
$337$	1.56151e7	+	2.70461e7i	0.407994	+	0.706666i	0.994665	−	0.103159i	$-0.0328951\pi$
$337$	1.56151e7	+	2.70461e7i	0.407994	+	0.706666i	−0.586671	+	0.809825i	$0.699562\pi$
$338$		0			0
$339$	−2.31066e7	+	4.61134e7i	−0.593113	+	1.18366i
$340$		0			0
$341$		−	1.54303e7i		−	0.389146i
$342$		0			0
$343$	−4.00074e7			−0.991420
$344$		0			0
$345$	3.46998e6	+	5.86597e7i	0.0845026	+	1.42851i
$346$		0			0
$347$	1.73955e7	−	1.00433e7i	0.416340	−	0.240374i	−0.277170	−	0.960821i	$-0.589397\pi$
$347$	1.73955e7	−	1.00433e7i	0.416340	−	0.240374i	0.693510	+	0.720447i	$0.256063\pi$
$348$		0			0
$349$	1.84002e7	−	3.18701e7i	0.432859	−	0.749733i	−0.564260	−	0.825597i	$-0.690838\pi$
$349$	1.84002e7	−	3.18701e7i	0.432859	−	0.749733i	0.997118	+	0.0758644i	$0.0241716\pi$
$350$		0			0
$351$	−1.31962e7	+	1.11343e7i	−0.305159	+	0.257479i
$352$		0			0
$353$	−2.05019e7	−	1.18368e7i	−0.466089	−	0.269097i	0.248512	−	0.968629i	$-0.420058\pi$
$353$	−2.05019e7	−	1.18368e7i	−0.466089	−	0.269097i	−0.714601	+	0.699532i	$0.753392\pi$
$354$		0			0
$355$	−4.50163e7	−	7.79705e7i	−1.00620	−	1.74279i
$356$		0			0
$357$	2.49002e7	−	1.47296e6i	0.547266	−	0.0323732i
$358$		0			0
$359$			3.67159e7i			0.793544i	0.917917	+	0.396772i	$0.129870\pi$
$359$			3.67159e7i			0.793544i	−0.917917	+	0.396772i	$0.870130\pi$
$360$		0			0
$361$	−2.94545e7			−0.626079
$362$		0			0
$363$	1.27792e8	+	6.40343e7i	2.67167	+	1.33873i
$364$		0			0
$365$	−5.99773e7	+	3.46279e7i	−1.23341	+	0.712111i
$366$		0			0
$367$	4.15020e7	−	7.18836e7i	0.839597	−	1.45422i	−0.0506351	−	0.998717i	$-0.516125\pi$
$367$	4.15020e7	−	7.18836e7i	0.839597	−	1.45422i	0.890232	−	0.455507i	$-0.150542\pi$
$368$		0			0
$369$	6.42308e6	+	5.41008e7i	0.127839	+	1.07677i
$370$		0			0
$371$	3.56819e7	+	2.06009e7i	0.698756	+	0.403427i
$372$		0			0
$373$	3.06825e7	+	5.31436e7i	0.591241	+	1.02406i	0.994066	+	0.108782i	$0.0346950\pi$
$373$	3.06825e7	+	5.31436e7i	0.591241	+	1.02406i	−0.402825	+	0.915277i	$0.631972\pi$
$374$		0			0
$375$	−4.29478e6	−	6.51700e6i	−0.0814418	−	0.123582i
$376$		0			0
$377$		−	2.31832e6i		−	0.0432662i
$378$		0			0
$379$	−8.94442e6			−0.164299			−0.0821495	−	0.996620i	$-0.526178\pi$
$379$	−8.94442e6			−0.164299			−0.0821495	+	0.996620i	$0.526178\pi$
$380$		0			0
$381$	3.96028e7	−	2.60987e7i	0.716062	−	0.471894i
$382$		0			0
$383$	−7.60170e7	+	4.38884e7i	−1.35305	+	0.781184i	−0.988676	−	0.150068i	$-0.952051\pi$
$383$	−7.60170e7	+	4.38884e7i	−1.35305	+	0.781184i	−0.364375	+	0.931252i	$0.618717\pi$
$384$		0			0
$385$	5.02477e7	−	8.70317e7i	0.880510	−	1.52509i
$386$		0			0
$387$	−6.37591e7	−	8.53195e7i	−1.10004	−	1.47203i
$388$		0			0
$389$	8.09387e7	+	4.67300e7i	1.37501	+	0.793865i	0.991554	−	0.129693i	$-0.0413991\pi$
$389$	8.09387e7	+	4.67300e7i	1.37501	+	0.793865i	0.383460	+	0.923558i	$0.374732\pi$
$390$		0			0
$391$	2.65907e7	+	4.60564e7i	0.444835	+	0.770477i
$392$		0			0
$393$	2.89880e7	−	5.78508e7i	0.477574	−	0.953086i
$394$		0			0
$395$		−	7.00746e7i		−	1.13702i
$396$		0			0
$397$	−1.21583e8			−1.94313			−0.971566	−	0.236767i	$-0.923912\pi$
$397$	−1.21583e8			−1.94313			−0.971566	+	0.236767i	$0.923912\pi$
$398$		0			0
$399$	1.39502e6	+	2.35828e7i	0.0219616	+	0.371258i
$400$		0			0
$401$	1.85999e7	−	1.07387e7i	0.288455	−	0.166540i	−0.348790	−	0.937201i	$-0.613407\pi$
$401$	1.85999e7	−	1.07387e7i	0.288455	−	0.166540i	0.637245	+	0.770661i	$0.280074\pi$
$402$		0			0
$403$	2.54607e6	−	4.40993e6i	0.0389005	−	0.0673777i
$404$		0			0
$405$	−9.23676e7	−	2.72879e7i	−1.39045	−	0.410776i
$406$		0			0
$407$	−9.57156e7	−	5.52614e7i	−1.41971	−	0.819670i
$408$		0			0
$409$	−5.80930e7	−	1.00620e8i	−0.849090	−	1.47067i	−0.882022	−	0.471209i	$-0.843818\pi$
$409$	−5.80930e7	−	1.00620e8i	−0.849090	−	1.47067i	0.0329322	−	0.999458i	$-0.489515\pi$
$410$		0			0
$411$	3.59448e7	−	2.12629e6i	0.517739	−	0.0306265i
$412$		0			0
$413$			7.54485e6i			0.107103i
$414$		0			0
$415$	−7.52720e7			−1.05315
$416$		0			0
$417$	5.25644e7	+	2.63391e7i	0.724909	+	0.363239i
$418$		0			0
$419$	−2.73269e7	+	1.57772e7i	−0.371492	+	0.214481i	−0.674110	−	0.738631i	$-0.735473\pi$
$419$	−2.73269e7	+	1.57772e7i	−0.371492	+	0.214481i	0.302618	+	0.953112i	$0.402139\pi$
$420$		0			0
$421$	7.50313e6	−	1.29958e7i	0.100553	−	0.174163i	−0.811359	−	0.584548i	$-0.801272\pi$
$421$	7.50313e6	−	1.29958e7i	0.100553	−	0.174163i	0.911913	+	0.410384i	$0.134605\pi$
$422$		0			0
$423$	1.50500e7	−	1.12469e7i	0.198846	−	0.148597i
$424$		0			0
$425$	−6.60425e7	−	3.81297e7i	−0.860314	−	0.496702i
$426$		0			0
$427$	−2.49652e6	−	4.32411e6i	−0.0320665	−	0.0555409i
$428$		0			0
$429$	3.46424e7	+	5.25672e7i	0.438769	+	0.665799i
$430$		0			0
$431$			6.49322e7i			0.811014i	0.914092	+	0.405507i	$0.132905\pi$
$431$			6.49322e7i			0.811014i	−0.914092	+	0.405507i	$0.867095\pi$
$432$		0			0
$433$	8.31669e7			1.02444			0.512220	−	0.858854i	$-0.328823\pi$
$433$	8.31669e7			1.02444			0.512220	+	0.858854i	$0.328823\pi$
$434$		0			0
$435$	1.07983e7	−	7.11618e6i	0.131186	−	0.0864528i
$436$		0			0
$437$	−4.36195e7	+	2.51838e7i	−0.522681	+	0.301770i
$438$		0			0
$439$	1.63576e7	−	2.83321e7i	0.193341	−	0.334877i	−0.753014	−	0.658004i	$-0.771401\pi$
$439$	1.63576e7	−	2.83321e7i	0.193341	−	0.334877i	0.946356	+	0.323127i	$0.104734\pi$
$440$		0			0
$441$	5.36640e7	−	6.37122e6i	0.625701	−	0.0742859i
$442$		0			0
$443$	−9.29959e7	−	5.36912e7i	−1.06968	−	0.617578i	−0.141584	−	0.989926i	$-0.545219\pi$
$443$	−9.29959e7	−	5.36912e7i	−1.06968	−	0.617578i	−0.928093	+	0.372348i	$0.878553\pi$
$444$		0			0
$445$	−3.67587e7	−	6.36680e7i	−0.417139	−	0.722505i
$446$		0			0
$447$	4.67921e7	−	9.33819e7i	0.523901	−	1.04554i
$448$		0			0
$449$		−	3.79594e7i		−	0.419354i	−0.977771	−	0.209677i	$-0.932759\pi$
$449$		−	3.79594e7i		−	0.419354i	0.977771	−	0.209677i	$-0.0672413\pi$
$450$		0			0
$451$	1.98650e8			2.16550
$452$		0			0
$453$	−1.53341e6	−	2.59222e7i	−0.0164954	−	0.278854i
$454$		0			0
$455$	2.87212e7	−	1.65822e7i	0.304907	−	0.176038i
$456$		0			0
$457$	−1.27236e7	+	2.20379e7i	−0.133309	+	0.230898i	−0.924950	−	0.380088i	$-0.875894\pi$
$457$	−1.27236e7	+	2.20379e7i	−0.133309	+	0.230898i	0.791641	+	0.610986i	$0.209227\pi$
$458$		0			0
$459$	−8.58009e7	+	1.53701e7i	−0.887266	+	0.158942i
$460$		0			0
$461$	5.64160e7	+	3.25718e7i	0.575837	+	0.332460i	0.759477	−	0.650534i	$-0.225455\pi$
$461$	5.64160e7	+	3.25718e7i	0.575837	+	0.332460i	−0.183640	+	0.982994i	$0.558788\pi$
$462$		0			0
$463$	1.44914e7	+	2.50999e7i	0.146005	+	0.252888i	0.929747	−	0.368198i	$-0.120025\pi$
$463$	1.44914e7	+	2.50999e7i	0.146005	+	0.252888i	−0.783742	+	0.621086i	$0.786692\pi$
$464$		0			0
$465$	2.83559e7	−	1.67737e6i	0.282023	−	0.0166829i
$466$		0			0
$467$			6.09985e7i			0.598919i	0.954109	+	0.299460i	$0.0968064\pi$
$467$			6.09985e7i			0.598919i	−0.954109	+	0.299460i	$0.903194\pi$
$468$		0			0
$469$	−7.36566e7			−0.713991
$470$		0			0
$471$	3.84378e7	+	1.92605e7i	0.367871	+	0.184334i
$472$		0			0
$473$	−3.36334e8	+	1.94183e8i	−3.17825	+	1.83496i
$474$		0			0
$475$	3.61122e7	−	6.25482e7i	0.336956	−	0.583626i
$476$		0			0
$477$	−1.32309e8	−	5.67878e7i	−1.21909	−	0.523239i
$478$		0			0
$479$	8.59855e7	+	4.96437e7i	0.782381	+	0.451708i	0.837274	−	0.546784i	$-0.184148\pi$
$479$	8.59855e7	+	4.96437e7i	0.782381	+	0.451708i	−0.0548922	+	0.998492i	$0.517482\pi$
$480$		0			0
$481$	−1.82367e7	−	3.15870e7i	−0.163875	−	0.283839i
$482$		0			0
$483$	−3.72200e7	−	5.64785e7i	−0.330320	−	0.501235i
$484$		0			0
$485$			6.46069e7i			0.566309i
$486$		0			0
$487$	−1.05049e8			−0.909504			−0.454752	−	0.890618i	$-0.650272\pi$
$487$	−1.05049e8			−0.909504			−0.454752	+	0.890618i	$0.650272\pi$
$488$		0			0
$489$	−1.58327e7	+	1.04339e7i	−0.135403	+	0.0892321i
$490$		0			0
$491$	−1.64341e8	+	9.48823e7i	−1.38836	+	0.801569i	−0.993130	−	0.117014i	$-0.962668\pi$
$491$	−1.64341e8	+	9.48823e7i	−1.38836	+	0.801569i	−0.395228	+	0.918583i	$0.629334\pi$
$492$		0			0
$493$	5.85199e6	−	1.01360e7i	0.0488386	−	0.0845909i
$494$		0			0
$495$	−1.38511e8	+	3.22715e8i	−1.14201	+	2.66075i
$496$		0			0
$497$	8.97500e7	+	5.18172e7i	0.731081	+	0.422090i
$498$		0			0
$499$	−1.01002e8	−	1.74941e8i	−0.812887	−	1.40796i	−0.910835	−	0.412771i	$-0.864561\pi$
$499$	−1.01002e8	−	1.74941e8i	−0.812887	−	1.40796i	0.0979477	−	0.995192i	$-0.468772\pi$
$500$		0			0
$501$	4.57819e7	−	9.13660e7i	0.364066	−	0.726560i
$502$		0			0
$503$		−	1.88347e8i		−	1.47998i	−0.672619	−	0.739989i	$-0.734831\pi$
$503$		−	1.88347e8i		−	1.47998i	0.672619	−	0.739989i	$-0.265169\pi$
$504$		0			0
$505$	2.97083e8			2.30677
$506$		0			0
$507$	−6.46894e6	−	1.09357e8i	−0.0496374	−	0.839116i
$508$		0			0
$509$	1.43572e8	−	8.28912e7i	1.08872	−	0.628572i	0.155484	−	0.987838i	$-0.450306\pi$
$509$	1.43572e8	−	8.28912e7i	1.08872	−	0.628572i	0.933235	+	0.359266i	$0.116973\pi$
$510$		0			0
$511$	3.98593e7	−	6.90384e7i	0.298722	−	0.517402i
$512$		0			0
$513$	−1.45569e7	−	8.12612e7i	−0.107824	−	0.601909i
$514$		0			0
$515$	1.45255e8	+	8.38628e7i	1.06343	+	0.613971i
$516$		0			0
$517$	−3.42531e7	−	5.93281e7i	−0.247873	−	0.429328i
$518$		0			0
$519$	1.17863e8	−	6.97211e6i	0.843092	−	0.0498726i
$520$		0			0
$521$		−	2.76446e8i		−	1.95478i	−0.211451	−	0.977389i	$-0.567819\pi$
$521$		−	2.76446e8i		−	1.95478i	0.211451	−	0.977389i	$-0.432181\pi$
$522$		0			0
$523$	−8.78008e7			−0.613753			−0.306876	−	0.951749i	$-0.599284\pi$
$523$	−8.78008e7			−0.613753			−0.306876	+	0.951749i	$0.599284\pi$
$524$		0			0
$525$	8.67148e7	+	4.34513e7i	0.599260	+	0.300279i
$526$		0			0
$527$	2.22635e7	−	1.28538e7i	0.152111	−	0.0878214i
$528$		0			0
$529$	−1.91221e6	+	3.31204e6i	−0.0129172	+	0.0223732i
$530$		0			0
$531$	−3.10842e6	−	2.61818e7i	−0.0207614	−	0.174870i
$532$		0			0
$533$	5.67733e7	+	3.27781e7i	0.374941	+	0.216472i
$534$		0			0
$535$	2.41780e7	+	4.18776e7i	0.157892	+	0.273477i
$536$		0			0
$537$	−732285.	−	1.11119e6i	−0.00472887	−	0.00717570i
$538$		0			0
$539$		−	1.97046e8i		−	1.25835i
$540$		0			0
$541$	−1.60020e8			−1.01061			−0.505305	−	0.862941i	$-0.668620\pi$
$541$	−1.60020e8			−1.01061			−0.505305	+	0.862941i	$0.668620\pi$
$542$		0			0
$543$	−1.01948e8	+	6.71851e7i	−0.636767	+	0.419637i
$544$		0			0
$545$	2.66754e7	−	1.54011e7i	0.164787	−	0.0951395i
$546$		0			0
$547$	−1.10308e7	+	1.91059e7i	−0.0673977	+	0.116736i	−0.897755	−	0.440495i	$-0.854803\pi$
$547$	−1.10308e7	+	1.91059e7i	−0.0673977	+	0.116736i	0.830357	+	0.557231i	$0.188136\pi$
$548$		0			0
$549$	1.04448e7	+	1.39768e7i	0.0631225	+	0.0844676i
$550$		0			0
$551$	9.59966e6	+	5.54237e6i	0.0573854	+	0.0331315i
$552$		0			0
$553$	4.03306e7	+	6.98546e7i	0.238484	+	0.413066i
$554$		0			0
$555$	9.11473e7	−	1.81901e8i	0.533169	−	1.06403i
$556$		0			0
$557$		−	1.71224e8i		−	0.990830i	−0.868657	−	0.495415i	$-0.835016\pi$
$557$		−	1.71224e8i		−	0.990830i	0.868657	−	0.495415i	$-0.164984\pi$
$558$		0			0
$559$	−1.28164e8			−0.733720
$560$		0			0
$561$	1.87683e7	+	3.17276e8i	0.106301	+	1.79700i
$562$		0			0
$563$	1.92436e8	−	1.11103e8i	1.07835	−	0.622586i	0.147900	−	0.989002i	$-0.452749\pi$
$563$	1.92436e8	−	1.11103e8i	1.07835	−	0.622586i	0.930451	+	0.366416i	$0.119415\pi$
$564$		0			0
$565$	−1.73106e8	+	2.99828e8i	−0.959767	+	1.66237i
$566$		0			0
$567$	1.07783e8	−	2.59588e7i	0.591290	−	0.142408i
$568$		0			0
$569$	−2.25736e8	−	1.30329e8i	−1.22536	−	0.707461i	−0.259303	−	0.965796i	$-0.583493\pi$
$569$	−2.25736e8	−	1.30329e8i	−1.22536	−	0.707461i	−0.966056	+	0.258335i	$0.916826\pi$
$570$		0			0
$571$	6.09463e7	+	1.05562e8i	0.327370	+	0.567022i	0.981989	−	0.188937i	$-0.0605042\pi$
$571$	6.09463e7	+	1.05562e8i	0.327370	+	0.567022i	−0.654619	+	0.755959i	$0.727171\pi$
$572$		0			0
$573$	−3.35596e7	+	1.98520e6i	−0.178383	+	0.0105521i
$574$		0			0
$575$			2.06792e8i			1.08775i
$576$		0			0
$577$	1.22005e8			0.635111			0.317555	−	0.948240i	$-0.397138\pi$
$577$	1.22005e8			0.635111			0.317555	+	0.948240i	$0.397138\pi$
$578$		0			0
$579$	2.64406e8	+	1.32489e8i	1.36218	+	0.682565i
$580$		0			0
$581$	7.50357e7	−	4.33219e7i	0.382595	−	0.220891i
$582$		0			0
$583$	−2.62495e8	+	4.54654e8i	−1.32469	+	2.29444i
$584$		0			0
$585$	−9.28353e7	+	6.93757e7i	−0.463709	+	0.346529i
$586$		0			0
$587$	1.15748e8	+	6.68273e7i	0.572269	+	0.330400i	0.758055	−	0.652191i	$-0.226150\pi$
$587$	1.15748e8	+	6.68273e7i	0.572269	+	0.330400i	−0.185786	+	0.982590i	$0.559483\pi$
$588$		0			0
$589$	1.21737e7	+	2.10855e7i	0.0595768	+	0.103190i
$590$		0			0
$591$	−1.60324e8	−	2.43279e8i	−0.776668	−	1.17853i
$592$		0			0
$593$		−	1.98748e7i		−	0.0953100i	−0.998864	−	0.0476550i	$-0.984825\pi$
$593$		−	1.98748e7i		−	0.0953100i	0.998864	−	0.0476550i	$-0.0151748\pi$
$594$		0			0
$595$	1.67430e8			0.794844
$596$		0			0
$597$	−1.14064e8	+	7.51697e7i	−0.536077	+	0.353281i
$598$		0			0
$599$	−3.37964e8	+	1.95123e8i	−1.57250	+	0.907881i	−0.576634	+	0.817002i	$0.695634\pi$
$599$	−3.37964e8	+	1.95123e8i	−1.57250	+	0.907881i	−0.995862	+	0.0908789i	$0.971032\pi$
$600$		0			0
$601$	−7.89071e7	+	1.36671e8i	−0.363490	+	0.629583i	−0.988533	−	0.151007i	$-0.951748\pi$
$601$	−7.89071e7	+	1.36671e8i	−0.363490	+	0.629583i	0.625043	+	0.780591i	$0.285082\pi$
$602$		0			0
$603$	2.55600e8	−	3.03459e7i	1.16576	−	0.138404i
$604$		0			0
$605$	8.30899e8	+	4.79720e8i	3.75217	+	2.16631i
$606$		0			0
$607$	1.74295e8	+	3.01887e8i	0.779325	+	1.34983i	0.932332	+	0.361605i	$0.117771\pi$
$607$	1.74295e8	+	3.01887e8i	0.779325	+	1.34983i	−0.153007	+	0.988225i	$0.548896\pi$
$608$		0			0
$609$	−6.66873e6	+	1.33087e7i	−0.0295251	+	0.0589227i
$610$		0			0
$611$		−	2.26076e7i		−	0.0991132i
$612$		0			0
$613$	1.41726e7			0.0615273			0.0307636	−	0.999527i	$-0.490206\pi$
$613$	1.41726e7			0.0615273			0.0307636	+	0.999527i	$0.490206\pi$
$614$		0			0
$615$	2.15945e7	+	3.65053e8i	0.0928362	+	1.56939i
$616$		0			0
$617$	−1.81599e8	+	1.04846e8i	−0.773140	+	0.446373i	−0.833994	−	0.551774i	$-0.813951\pi$
$617$	−1.81599e8	+	1.04846e8i	−0.773140	+	0.446373i	0.0608535	+	0.998147i	$0.480618\pi$
$618$		0			0
$619$	−8.36020e7	+	1.44803e8i	−0.352488	+	0.610528i	−0.986685	−	0.162644i	$-0.947998\pi$
$619$	−8.36020e7	+	1.44803e8i	−0.352488	+	0.610528i	0.634196	+	0.773172i	$0.281331\pi$
$620$		0			0
$621$	1.52428e8	+	1.80655e8i	0.636487	+	0.754354i
$622$		0			0
$623$	7.32867e7	+	4.23121e7i	0.303083	+	0.174985i
$624$		0			0
$625$	1.08337e8	+	1.87645e8i	0.443749	+	0.768595i
$626$		0			0
$627$	−3.00489e8	+	1.77753e7i	−1.21906	+	0.0721129i
$628$		0			0
$629$		−	1.84136e8i		−	0.739923i
$630$		0			0
$631$	3.36933e8			1.34108			0.670541	−	0.741872i	$-0.266062\pi$
$631$	3.36933e8			1.34108			0.670541	+	0.741872i	$0.266062\pi$
$632$		0			0
$633$	−8.34804e7	−	4.18305e7i	−0.329134	−	0.164923i
$634$		0			0
$635$	2.75706e8	−	1.59179e8i	1.07678	−	0.621677i
$636$		0			0
$637$	3.25134e7	−	5.63149e7i	0.125789	−	0.217874i
$638$		0			0
$639$	−3.32795e8	−	1.42838e8i	−1.27548	−	0.547444i
$640$		0			0
$641$	−8.63536e7	−	4.98563e7i	−0.327873	−	0.189298i	0.327023	−	0.945016i	$-0.393954\pi$
$641$	−8.63536e7	−	4.98563e7i	−0.327873	−	0.189298i	−0.654897	+	0.755719i	$0.727288\pi$
$642$		0			0
$643$	−1.34692e8	−	2.33294e8i	−0.506652	−	0.877547i	−0.999970	−	0.00769844i	$-0.997549\pi$
$643$	−1.34692e8	−	2.33294e8i	−0.506652	−	0.877547i	0.493318	−	0.869849i	$-0.335784\pi$
$644$		0			0
$645$	−3.93405e8	−	5.96962e8i	−1.46609	−	2.22468i
$646$		0			0
$647$		−	7.78039e7i		−	0.287269i	−0.989631	−	0.143634i	$-0.954121\pi$
$647$		−	7.78039e7i		−	0.287269i	0.989631	−	0.143634i	$-0.0458790\pi$
$648$		0			0
$649$	−9.61357e7			−0.351682
$650$		0			0
$651$	−2.73015e7	+	1.79920e7i	−0.0989562	+	0.0652133i
$652$		0			0
$653$	1.95063e8	−	1.12620e8i	0.700543	−	0.404459i	−0.107007	−	0.994258i	$-0.534127\pi$
$653$	1.95063e8	−	1.12620e8i	0.700543	−	0.404459i	0.807550	+	0.589800i	$0.200793\pi$
$654$		0			0
$655$	2.17167e8	−	3.76144e8i	0.772805	−	1.33854i
$656$		0			0
$657$	−1.09875e8	+	2.55996e8i	−0.387438	+	0.902686i
$658$		0			0
$659$	1.98537e8	+	1.14625e8i	0.693722	+	0.400521i	0.805005	−	0.593268i	$-0.202163\pi$
$659$	1.98537e8	+	1.14625e8i	0.693722	+	0.400521i	−0.111283	+	0.993789i	$0.535496\pi$
$660$		0			0
$661$	1.05495e8	+	1.82722e8i	0.365280	+	0.632684i	0.988821	−	0.149107i	$-0.0476398\pi$
$661$	1.05495e8	+	1.82722e8i	0.365280	+	0.632684i	−0.623541	+	0.781791i	$0.714306\pi$
$662$		0			0
$663$	−4.69880e7	+	9.37730e7i	−0.161230	+	0.321764i
$664$		0			0
$665$			1.58571e8i			0.539212i
$666$		0			0
$667$	−3.17376e7			−0.106954
$668$		0			0
$669$	−1.20537e7	−	2.03766e8i	−0.0402570	−	0.680541i
$670$		0			0
$671$	5.50973e7	−	3.18104e7i	0.182374	−	0.105294i
$672$		0			0
$673$	2.87715e8	−	4.98336e8i	0.943880	−	1.63485i	0.185901	−	0.982568i	$-0.440479\pi$
$673$	2.87715e8	−	4.98336e8i	0.943880	−	1.63485i	0.757978	−	0.652280i	$-0.226187\pi$
$674$		0			0
$675$	−3.18816e8	−	1.15057e8i	−1.03664	−	0.374112i
$676$		0			0
$677$	−3.05834e8	−	1.76573e8i	−0.985644	−	0.569062i	−0.0816747	−	0.996659i	$-0.526027\pi$
$677$	−3.05834e8	−	1.76573e8i	−0.985644	−	0.569062i	−0.903969	+	0.427597i	$0.859360\pi$
$678$		0			0
$679$	−3.71837e7	−	6.44041e7i	−0.118780	−	0.205733i
$680$		0			0
$681$	1.38387e8	−	8.18619e6i	0.438181	−	0.0259203i
$682$		0			0
$683$		−	4.65139e8i		−	1.45989i	−0.683506	−	0.729945i	$-0.739546\pi$
$683$		−	4.65139e8i		−	1.45989i	0.683506	−	0.729945i	$-0.260454\pi$
$684$		0			0
$685$	2.41694e8			0.751959
$686$		0			0
$687$	−4.50334e8	−	2.25655e8i	−1.38888	−	0.695944i
$688$		0			0
$689$	−1.50040e8	+	8.66255e7i	−0.458721	+	0.264843i
$690$		0			0
$691$	−5.96318e7	+	1.03285e8i	−0.180736	+	0.313043i	−0.942131	−	0.335244i	$-0.891181\pi$
$691$	−5.96318e7	+	1.03285e8i	−0.180736	+	0.313043i	0.761396	+	0.648288i	$0.224515\pi$
$692$		0			0
$693$	−4.76584e7	−	4.01421e8i	−0.143199	−	1.20615i
$694$		0			0
$695$	3.41772e8	+	1.97322e8i	1.01808	+	0.587789i
$696$		0			0
$697$	1.65480e8	+	2.86619e8i	0.488705	+	0.846461i
$698$		0			0
$699$	−6.26482e6	−	9.50639e6i	−0.0183433	−	0.0278345i
$700$		0			0
$701$			3.55114e8i			1.03089i	0.856921	+	0.515447i	$0.172374\pi$
$701$			3.55114e8i			1.03089i	−0.856921	+	0.515447i	$0.827626\pi$
$702$		0			0
$703$	1.74393e8			0.501954
$704$		0			0
$705$	1.05302e8	−	6.93952e7i	0.300517	−	0.198044i
$706$		0			0
$707$	−2.96151e8	+	1.70983e8i	−0.838020	+	0.483831i
$708$		0			0
$709$	−3.01326e8	+	5.21912e8i	−0.845470	+	1.46440i	0.0397425	+	0.999210i	$0.487346\pi$
$709$	−3.01326e8	+	5.21912e8i	−0.845470	+	1.46440i	−0.885212	+	0.465187i	$0.845987\pi$
$710$		0			0
$711$	−1.68733e8	−	2.25791e8i	−0.469452	−	0.628199i
$712$		0			0
$713$	−6.03717e7	−	3.48556e7i	−0.166558	−	0.0961621i
$714$		0			0
$715$	2.11288e8	+	3.65962e8i	0.578039	+	1.00119i
$716$		0			0
$717$	2.69648e8	−	5.38130e8i	0.731542	−	1.45992i
$718$		0			0
$719$		−	3.36046e8i		−	0.904092i	−0.891995	−	0.452046i	$-0.850694\pi$
$719$		−	3.36046e8i		−	0.904092i	0.891995	−	0.452046i	$-0.149306\pi$
$720$		0			0
$721$	−1.93065e8			−0.515107
$722$		0			0
$723$	1.56758e7	+	2.64999e8i	0.0414778	+	0.701179i
$724$		0			0
$725$	3.94130e7	−	2.27551e7i	0.103425	−	0.0597124i
$726$		0			0
$727$	−2.56241e8	+	4.43823e8i	−0.666877	+	1.15507i	0.311895	+	0.950116i	$0.399036\pi$
$727$	−2.56241e8	+	4.43823e8i	−0.666877	+	1.15507i	−0.978773	+	0.204949i	$0.934297\pi$
$728$		0			0
$729$	−3.63329e8	+	1.34487e8i	−0.937816	+	0.347134i
$730$		0			0
$731$	−5.60348e8	−	3.23517e8i	−1.43452	−	0.828218i
$732$		0			0
$733$	1.79393e7	+	3.10717e7i	0.0455505	+	0.0788957i	0.887902	−	0.460033i	$-0.152162\pi$
$733$	1.79393e7	+	3.10717e7i	0.0455505	+	0.0788957i	−0.842351	+	0.538929i	$0.818829\pi$
$734$		0			0
$735$	3.62105e8	−	2.14201e7i	0.911953	−	0.0539461i
$736$		0			0
$737$		−	9.38524e8i		−	2.34446i
$738$		0			0
$739$	3.58948e7			0.0889403			0.0444701	−	0.999011i	$-0.485840\pi$
$739$	3.58948e7			0.0889403			0.0444701	+	0.999011i	$0.485840\pi$
$740$		0			0
$741$	−8.88115e7	−	4.45019e7i	−0.218280	−	0.109376i
$742$		0			0
$743$	3.77466e8	−	2.17930e8i	0.920261	−	0.531313i	0.0365427	−	0.999332i	$-0.488366\pi$
$743$	3.77466e8	−	2.17930e8i	0.920261	−	0.531313i	0.883718	+	0.468019i	$0.155032\pi$
$744$		0			0
$745$	3.50548e8	−	6.07166e8i	0.847771	−	1.46838i
$746$		0			0
$747$	−2.42537e8	+	1.81248e8i	−0.581858	+	0.434822i
$748$		0			0
$749$	−4.82043e7	−	2.78308e7i	−0.114720	−	0.0662338i
$750$		0			0
$751$	−2.14559e8	−	3.71627e8i	−0.506556	−	0.877380i	−0.999971	−	0.00758650i	$-0.997585\pi$
$751$	−2.14559e8	−	3.71627e8i	−0.506556	−	0.877380i	0.493416	−	0.869794i	$-0.335748\pi$
$752$		0			0
$753$	2.31046e8	+	3.50595e8i	0.541145	+	0.821146i
$754$		0			0
$755$		−	1.74301e8i		−	0.405005i
$756$		0			0
$757$	−8.26773e8			−1.90589			−0.952947	−	0.303136i	$-0.901966\pi$
$757$	−8.26773e8			−1.90589			−0.952947	+	0.303136i	$0.901966\pi$
$758$		0			0
$759$	7.19643e8	−	4.74253e8i	1.64586	−	1.08464i
$760$		0			0
$761$	3.22643e8	−	1.86278e8i	0.732097	−	0.422677i	−0.0870916	−	0.996200i	$-0.527757\pi$
$761$	3.22643e8	−	1.86278e8i	0.732097	−	0.422677i	0.819189	+	0.573524i	$0.194424\pi$
$762$		0			0
$763$	−1.77278e7	+	3.07054e7i	−0.0399099	+	0.0691260i
$764$		0			0
$765$	−5.81008e8	+	6.89798e7i	−1.29777	+	0.154077i
$766$		0			0
$767$	−2.74752e7	−	1.58628e7i	−0.0608912	−	0.0351555i
$768$		0			0
$769$	−2.05010e8	−	3.55087e8i	−0.450812	−	0.780829i	0.547625	−	0.836724i	$-0.315532\pi$
$769$	−2.05010e8	−	3.55087e8i	−0.450812	−	0.780829i	−0.998437	+	0.0558948i	$0.982199\pi$
$770$		0			0
$771$	−2.57933e7	+	5.14752e7i	−0.0562787	+	0.112314i
$772$		0			0
$773$			6.77485e8i			1.46677i	0.679815	+	0.733384i	$0.262060\pi$
$773$			6.77485e8i			1.46677i	−0.679815	+	0.733384i	$0.737940\pi$
$774$		0			0
$775$	9.99624e7			0.214749
$776$		0			0
$777$	1.38296e7	+	2.33789e8i	0.0294814	+	0.498380i
$778$		0			0
$779$	−2.71454e8	+	1.56724e8i	−0.574228	+	0.331531i
$780$		0			0
$781$	−6.60249e8	+	1.14359e9i	−1.38597	+	2.40058i
$782$		0			0
$783$	1.76585e7	−	4.89306e7i	0.0367848	−	0.101928i
$784$		0			0
$785$	2.49921e8	+	1.44292e8i	0.516647	+	0.298286i
$786$		0			0
$787$	2.70650e8	+	4.68779e8i	0.555244	+	0.961710i	0.997885	+	0.0650114i	$0.0207084\pi$
$787$	2.70650e8	+	4.68779e8i	0.555244	+	0.961710i	−0.442641	+	0.896699i	$0.645958\pi$
$788$		0			0
$789$	2.83606e7	−	1.67765e6i	0.0577410	−	0.00341563i
$790$		0			0
$791$		−	3.98516e8i		−	0.805222i
$792$		0			0
$793$	2.09954e7			0.0421022
$794$		0			0
$795$	−8.64039e8	−	4.32955e8i	−1.71962	−	0.861671i
$796$		0			0
$797$	5.31873e8	−	3.07077e8i	1.05059	−	0.606557i	0.127774	−	0.991803i	$-0.459217\pi$
$797$	5.31873e8	−	3.07077e8i	1.05059	−	0.606557i	0.922814	+	0.385246i	$0.125883\pi$
$798$		0			0
$799$	5.70672e7	−	9.88432e7i	0.111878	−	0.193779i
$800$		0			0
$801$	−2.71749e8	−	1.16636e8i	−0.528774	−	0.226953i
$802$		0			0
$803$	8.79680e8	+	5.07883e8i	1.69894	+	0.980883i
$804$		0			0
$805$	−2.27009e8	−	3.93192e8i	−0.435167	−	0.753731i
$806$		0			0
$807$	1.43931e8	+	2.18404e8i	0.273863	+	0.415567i
$808$		0			0
$809$		−	1.54965e8i		−	0.292677i	−0.989235	−	0.146338i	$-0.953251\pi$
$809$		−	1.54965e8i		−	0.292677i	0.989235	−	0.146338i	$-0.0467489\pi$
$810$		0			0
$811$	−8.47410e8			−1.58866			−0.794330	−	0.607487i	$-0.792178\pi$
$811$	−8.47410e8			−1.58866			−0.794330	+	0.607487i	$0.792178\pi$
$812$		0			0
$813$	4.63602e8	−	3.05519e8i	0.862727	−	0.568548i
$814$		0			0
$815$	−1.10224e8	+	6.36378e7i	−0.203612	+	0.117555i
$816$		0			0
$817$	3.06400e8	−	5.30700e8i	0.561852	−	0.973157i
$818$		0			0
$819$	5.26156e7	−	1.22588e8i	0.0957773	−	0.223150i
$820$		0			0
$821$	−2.24729e8	−	1.29747e8i	−0.406096	−	0.234460i	0.283015	−	0.959116i	$-0.408665\pi$
$821$	−2.24729e8	−	1.29747e8i	−0.406096	−	0.234460i	−0.689111	+	0.724656i	$0.741999\pi$
$822$		0			0
$823$	−1.94060e8	−	3.36121e8i	−0.348126	−	0.602971i	0.637791	−	0.770210i	$-0.279848\pi$
$823$	−1.94060e8	−	3.36121e8i	−0.348126	−	0.602971i	−0.985916	+	0.167238i	$0.946515\pi$
$824$		0			0
$825$	−5.53652e8	+	1.10491e9i	−0.985995	+	1.96773i
$826$		0			0
$827$			7.11216e8i			1.25743i	0.777635	+	0.628716i	$0.216419\pi$
$827$			7.11216e8i			1.25743i	−0.777635	+	0.628716i	$0.783581\pi$
$828$		0			0
$829$	9.26204e8			1.62571			0.812855	−	0.582466i	$-0.197912\pi$
$829$	9.26204e8			1.62571			0.812855	+	0.582466i	$0.197912\pi$
$830$		0			0
$831$	3.21096e7	+	5.42810e8i	0.0559541	+	0.945898i
$832$		0			0
$833$	2.84305e8	−	1.64144e8i	0.491869	−	0.283981i
$834$		0			0
$835$	3.42980e8	−	5.94059e8i	0.589128	−	1.02040i
$836$		0			0
$837$	8.73278e7	−	7.36830e7i	0.148928	−	0.125658i
$838$		0			0
$839$	−5.79914e8	−	3.34814e8i	−0.981924	−	0.566914i	−0.0790734	−	0.996869i	$-0.525196\pi$
$839$	−5.79914e8	−	3.34814e8i	−0.981924	−	0.566914i	−0.902850	+	0.429955i	$0.858529\pi$
$840$		0			0
$841$	−2.93919e8	−	5.09083e8i	−0.494129	−	0.855856i
$842$		0			0
$843$	5.47517e8	−	3.23880e7i	0.913934	−	0.0540632i
$844$		0			0
$845$		−	7.35318e8i		−	1.21872i
$846$		0			0
$847$	−1.10439e9			−1.81749
$848$		0			0
$849$	5.45907e8	+	2.73544e8i	0.892063	+	0.446997i
$850$		0			0
$851$	−4.32424e8	+	2.49660e8i	−0.701651	+	0.405098i
$852$		0			0
$853$	1.01924e8	−	1.76538e8i	0.164221	−	0.284440i	−0.772157	−	0.635432i	$-0.780822\pi$
$853$	1.01924e8	−	1.76538e8i	0.164221	−	0.284440i	0.936379	+	0.350992i	$0.114156\pi$
$854$		0			0
$855$	−6.53301e7	−	5.50267e8i	−0.104524	−	0.880390i
$856$		0			0
$857$	−3.04635e8	−	1.75881e8i	−0.483992	−	0.279433i	0.238087	−	0.971244i	$-0.423480\pi$
$857$	−3.04635e8	−	1.75881e8i	−0.483992	−	0.279433i	−0.722079	+	0.691811i	$0.756813\pi$
$858$		0			0
$859$	1.89638e8	+	3.28462e8i	0.299189	+	0.518210i	0.975951	−	0.217992i	$-0.0699507\pi$
$859$	1.89638e8	+	3.28462e8i	0.299189	+	0.518210i	−0.676762	+	0.736202i	$0.736617\pi$
$860$		0			0
$861$	−2.31629e8	−	3.51479e8i	−0.362896	−	0.550667i
$862$		0			0
$863$		−	5.09276e7i		−	0.0792358i	−0.999215	−	0.0396179i	$-0.987386\pi$
$863$		−	5.09276e7i		−	0.0792358i	0.999215	−	0.0396179i	$-0.0126141\pi$
$864$		0			0
$865$	7.92514e8			1.22450
$866$		0			0
$867$	1.02031e8	−	6.72397e7i	0.156558	−	0.103174i
$868$		0			0
$869$	−8.90080e8	+	5.13888e8i	−1.35634	+	0.783086i
$870$		0			0
$871$	1.54860e8	−	2.68226e8i	0.234361	−	0.405926i
$872$		0			0
$873$	1.55567e8	+	2.08173e8i	0.233817	+	0.312883i
$874$		0			0
$875$	5.22243e7	+	3.01517e7i	0.0779559	+	0.0450078i
$876$		0			0
$877$	4.47593e8	+	7.75254e8i	0.663567	+	1.14933i	0.979672	+	0.200608i	$0.0642916\pi$
$877$	4.47593e8	+	7.75254e8i	0.663567	+	1.14933i	−0.316105	+	0.948724i	$0.602375\pi$
$878$		0			0
$879$	−4.67398e7	+	9.32776e7i	−0.0688208	+	0.137344i
$880$		0			0
$881$			5.82577e8i			0.851973i	0.904730	+	0.425986i	$0.140073\pi$
$881$			5.82577e8i			0.851973i	−0.904730	+	0.425986i	$0.859927\pi$
$882$		0			0
$883$	2.10539e7			0.0305810			0.0152905	−	0.999883i	$-0.495133\pi$
$883$	2.10539e7			0.0305810			0.0152905	+	0.999883i	$0.495133\pi$
$884$		0			0
$885$	−1.04505e7	−	1.76666e8i	−0.0150768	−	0.254872i
$886$		0			0
$887$	9.71754e8	−	5.61043e8i	1.39247	−	0.803942i	0.398881	−	0.917003i	$-0.369399\pi$
$887$	9.71754e8	−	5.61043e8i	1.39247	−	0.803942i	0.993588	+	0.113060i	$0.0360653\pi$
$888$		0			0
$889$	−1.83227e8	+	3.17359e8i	−0.260787	+	0.451695i
$890$		0			0
$891$	3.30764e8	+	1.37336e9i	0.467612	+	1.94156i
$892$		0			0
$893$	9.36135e7	+	5.40478e7i	0.131457	+	0.0758968i
$894$		0			0
$895$	−4.46630e6	−	7.73585e6i	−0.00622986	−	0.0107904i
$896$		0			0
$897$	2.83925e8	−	1.67954e7i	0.393392	−	0.0232709i
$898$		0			0
$899$			1.53418e7i			0.0211154i
$900$		0			0
$901$	−8.74656e8			−1.19581
$902$		0			0
$903$	7.35745e8	+	3.68669e8i	0.999227	+	0.500695i
$904$		0			0
$905$	−7.09743e8	+	4.09770e8i	−0.957536	+	0.552834i
$906$		0			0
$907$	3.15685e8	−	5.46783e8i	0.423089	−	0.732812i	−0.573150	−	0.819450i	$-0.694279\pi$
$907$	3.15685e8	−	5.46783e8i	0.423089	−	0.732812i	0.996240	+	0.0866378i	$0.0276123\pi$
$908$		0			0
$909$	9.57246e8	−	7.15348e8i	1.27448	−	0.952414i
$910$		0			0
$911$	−1.13526e8	−	6.55445e7i	−0.150156	−	0.0866924i	0.423040	−	0.906111i	$-0.360963\pi$
$911$	−1.13526e8	−	6.55445e7i	−0.150156	−	0.0866924i	−0.573195	+	0.819419i	$0.694296\pi$
$912$		0			0
$913$	5.52003e8	+	9.56097e8i	0.725319	+	1.25629i
$914$		0			0
$915$	6.44465e7	+	9.77926e7i	0.0841271	+	0.127656i
$916$		0			0
$917$			4.99951e8i			0.648365i
$918$		0			0
$919$	7.88351e8			1.01572			0.507859	−	0.861440i	$-0.330437\pi$
$919$	7.88351e8			1.01572			0.507859	+	0.861440i	$0.330437\pi$
$920$		0			0
$921$	6.82036e7	−	4.49470e7i	0.0873029	−	0.0575336i
$922$		0			0
$923$	−3.77393e8	+	2.17888e8i	−0.479942	+	0.277094i
$924$		0			0
$925$	3.58000e8	−	6.20074e8i	0.452333	−	0.783463i
$926$		0			0
$927$	6.69966e8	−	7.95412e7i	0.841033	−	0.0998511i
$928$		0			0
$929$	−8.26532e8	−	4.77199e8i	−1.03089	−	0.595185i	−0.113651	−	0.993521i	$-0.536255\pi$
$929$	−8.26532e8	−	4.77199e8i	−1.03089	−	0.595185i	−0.917240	+	0.398336i	$0.869588\pi$
$930$		0			0
$931$	1.55459e8	+	2.69262e8i	0.192649	+	0.333677i
$932$		0			0
$933$	−4.61172e8	+	9.20351e8i	−0.567829	+	1.13320i
$934$		0			0
$935$			2.13337e9i			2.60995i
$936$		0			0
$937$	−4.59379e8			−0.558409			−0.279205	−	0.960232i	$-0.590071\pi$
$937$	−4.59379e8			−0.558409			−0.279205	+	0.960232i	$0.590071\pi$
$938$		0			0
$939$	−3.60803e7	−	6.09935e8i	−0.0435787	−	0.736693i
$940$		0			0
$941$	−1.27228e8	+	7.34552e7i	−0.152691	+	0.0881563i	−0.574399	−	0.818575i	$-0.694764\pi$
$941$	−1.27228e8	+	7.34552e7i	−0.152691	+	0.0881563i	0.421708	+	0.906732i	$0.361431\pi$
$942$		0			0
$943$	4.48730e8	−	7.77224e8i	0.535119	−	0.926853i
$944$		0			0
$945$	7.32498e8	−	1.31217e8i	0.867982	−	0.155488i
$946$		0			0
$947$	−3.87438e8	−	2.23687e8i	−0.456197	−	0.263385i	0.254247	−	0.967139i	$-0.418172\pi$
$947$	−3.87438e8	−	2.23687e8i	−0.456197	−	0.263385i	−0.710444	+	0.703754i	$0.751506\pi$
$948$		0			0
$949$	1.67606e8	+	2.90302e8i	0.196106	+	0.339665i
$950$		0			0
$951$	−6.44248e8	+	3.81101e7i	−0.749051	+	0.0443097i
$952$		0			0
$953$		−	1.69556e8i		−	0.195900i	−0.995191	−	0.0979500i	$-0.968771\pi$
$953$		−	1.69556e8i		−	0.195900i	0.995191	−	0.0979500i	$-0.0312285\pi$
$954$		0			0
$955$	−2.25656e8			−0.259081
$956$		0			0
$957$	−1.69577e8	−	8.49723e7i	−0.193478	−	0.0969486i
$958$		0			0
$959$	−2.40935e8	+	1.39104e8i	−0.273177	+	0.157719i
$960$		0			0
$961$	4.26903e8	−	7.39417e8i	0.481015	−	0.833143i
$962$		0			0
$963$	1.78743e8	+	7.67174e7i	0.200147	+	0.0859043i
$964$		0			0
$965$	1.71916e9	+	9.92556e8i	1.91308	+	1.10452i
$966$		0			0
$967$	−1.92132e8	−	3.32782e8i	−0.212481	−	0.368027i	0.740010	−	0.672596i	$-0.234821\pi$
$967$	−1.92132e8	−	3.32782e8i	−0.212481	−	0.368027i	−0.952490	+	0.304569i	$0.901488\pi$
$968$		0			0
$969$	−2.75961e8	−	4.18749e8i	−0.303302	−	0.460238i
$970$		0			0
$971$			3.23298e8i			0.353139i	0.984288	+	0.176569i	$0.0565000\pi$
$971$			3.23298e8i			0.353139i	−0.984288	+	0.176569i	$0.943500\pi$
$972$		0			0
$973$	−4.54265e8			−0.493141
$974$		0			0
$975$	−3.40546e8	+	2.24424e8i	−0.367420	+	0.242134i
$976$		0			0
$977$	−1.07518e9	+	6.20753e8i	−1.15291	+	0.665634i	−0.949595	−	0.313479i	$-0.898505\pi$
$977$	−1.07518e9	+	6.20753e8i	−1.15291	+	0.665634i	−0.203317	+	0.979113i	$0.565172\pi$
$978$		0			0
$979$	−5.39136e8	+	9.33811e8i	−0.574580	+	0.995202i
$980$		0			0
$981$	4.88678e7	−	1.13856e8i	0.0517626	−	0.120601i
$982$		0			0
$983$	−5.98285e8	−	3.45420e8i	−0.629866	−	0.363653i	0.150834	−	0.988559i	$-0.451804\pi$
$983$	−5.98285e8	−	3.45420e8i	−0.629866	−	0.363653i	−0.780700	+	0.624906i	$0.785137\pi$
$984$		0			0
$985$	−9.77835e8	−	1.69366e9i	−1.02319	−	1.77222i
$986$		0			0
$987$	−6.50318e7	+	1.29783e8i	−0.0676355	+	0.134979i
$988$		0			0
$989$			1.75456e9i			1.81376i
$990$		0			0
$991$	1.68628e9			1.73264			0.866321	−	0.499487i	$-0.166478\pi$
$991$	1.68628e9			1.73264			0.866321	+	0.499487i	$0.166478\pi$
$992$		0			0
$993$	4.52525e7	+	7.64989e8i	0.0462163	+	0.781281i
$994$		0			0
$995$	−7.94092e8	+	4.58469e8i	−0.806124	+	0.465416i
$996$		0			0
$997$	7.84012e8	−	1.35795e9i	0.791110	−	1.37024i	−0.134170	−	0.990958i	$-0.542837\pi$
$997$	7.84012e8	−	1.35795e9i	0.791110	−	1.37024i	0.925280	−	0.379285i	$-0.123830\pi$
$998$		0			0
$999$	−1.44310e8	−	8.05586e8i	−0.144744	−	0.808007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.7.q.c.65.5		12
3.2	odd	2		432.7.q.b.305.2		12
4.3	odd	2		18.7.d.a.11.1	yes	12
9.4	even	3		432.7.q.b.17.2		12
9.5	odd	6	inner	144.7.q.c.113.5		12
12.11	even	2		54.7.d.a.35.4		12
36.7	odd	6		162.7.b.c.161.12		12
36.11	even	6		162.7.b.c.161.1		12
36.23	even	6		18.7.d.a.5.1	✓	12
36.31	odd	6		54.7.d.a.17.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.7.d.a.5.1	✓	12	36.23	even	6
18.7.d.a.11.1	yes	12	4.3	odd	2
54.7.d.a.17.4		12	36.31	odd	6
54.7.d.a.35.4		12	12.11	even	2
144.7.q.c.65.5		12	1.1	even	1	trivial
144.7.q.c.113.5		12	9.5	odd	6	inner
162.7.b.c.161.1		12	36.11	even	6
162.7.b.c.161.12		12	36.7	odd	6
432.7.q.b.17.2		12	9.4	even	3
432.7.q.b.305.2		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	144.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(22.5447 - 14.8572i) q^{3} +(156.951 - 90.6160i) q^{5} +(-104.306 + 180.663i) q^{7} +(287.526 - 669.903i) q^{9} +O(q^{10})\)	\(q+(22.5447 - 14.8572i) q^{3} +(156.951 - 90.6160i) q^{5} +(-104.306 + 180.663i) q^{7} +(287.526 - 669.903i) q^{9} +(-2301.99 - 1329.05i) q^{11} +(-438.599 - 759.676i) q^{13} +(2192.12 - 4374.77i) q^{15} -4428.53i q^{17} +4194.21 q^{19} +(332.607 + 5622.69i) q^{21} +(-10399.9 + 6004.40i) q^{23} +(8610.01 - 14913.0i) q^{25} +(-3470.70 - 19374.6i) q^{27} +(2288.79 + 1321.43i) q^{29} +(2902.50 + 5027.28i) q^{31} +(-71643.7 + 4238.04i) q^{33} +37807.1i q^{35} +41579.5 q^{37} +(-21174.8 - 10610.3i) q^{39} +(-64721.2 + 37366.8i) q^{41} +(73052.9 - 126531. i) q^{43} +(-15576.2 - 131197. i) q^{45} +(22319.7 + 12886.3i) q^{47} +(37065.1 + 64198.6i) q^{49} +(-65795.6 - 99839.7i) q^{51} -197505. i q^{53} -481734. q^{55} +(94557.3 - 62314.3i) q^{57} +(31321.5 - 18083.5i) q^{59} +(-11967.3 + 20728.0i) q^{61} +(91036.1 + 121820. i) q^{63} +(-137678. - 79488.2i) q^{65} +(176540. + 305776. i) q^{67} +(-145255. + 289881. i) q^{69} -496781. i q^{71} -382139. q^{73} +(-27455.3 - 464129. i) q^{75} +(480222. - 277257. i) q^{77} +(193328. - 334855. i) q^{79} +(-366098. - 385229. i) q^{81} +(-359691. - 207667. i) q^{83} +(-401295. - 695064. i) q^{85} +(71232.8 - 4213.73i) q^{87} -405654. i q^{89} +182994. q^{91} +(140128. + 70215.4i) q^{93} +(658288. - 380063. i) q^{95} +(-178244. + 308727. i) q^{97} +(-1.55222e6 + 1.15997e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 42 q^{3} + 432 q^{5} - 240 q^{7} + 2190 q^{9}+O(q^{10}) \) 12 * q + 42 * q^3 + 432 * q^5 - 240 * q^7 + 2190 * q^9	\( 12 q + 42 q^{3} + 432 q^{5} - 240 q^{7} + 2190 q^{9} - 378 q^{11} + 1680 q^{13} + 10872 q^{15} + 2820 q^{19} + 24876 q^{21} + 76248 q^{23} + 8094 q^{25} - 127008 q^{27} + 97092 q^{29} - 21480 q^{31} - 246258 q^{33} - 25536 q^{37} - 42204 q^{39} - 410562 q^{41} - 71430 q^{43} + 13716 q^{45} - 347652 q^{47} - 135954 q^{49} - 336402 q^{51} - 580392 q^{55} - 522282 q^{57} - 369738 q^{59} + 135744 q^{61} + 103800 q^{63} - 753840 q^{65} + 289938 q^{67} + 2059272 q^{69} - 977700 q^{73} + 2115342 q^{75} - 159192 q^{77} + 764796 q^{79} - 1428282 q^{81} - 396900 q^{83} + 1619568 q^{85} - 3072636 q^{87} - 355584 q^{91} - 2526576 q^{93} + 2089260 q^{95} - 38874 q^{97} - 4398804 q^{99}+O(q^{100}) \) 12 * q + 42 * q^3 + 432 * q^5 - 240 * q^7 + 2190 * q^9 - 378 * q^11 + 1680 * q^13 + 10872 * q^15 + 2820 * q^19 + 24876 * q^21 + 76248 * q^23 + 8094 * q^25 - 127008 * q^27 + 97092 * q^29 - 21480 * q^31 - 246258 * q^33 - 25536 * q^37 - 42204 * q^39 - 410562 * q^41 - 71430 * q^43 + 13716 * q^45 - 347652 * q^47 - 135954 * q^49 - 336402 * q^51 - 580392 * q^55 - 522282 * q^57 - 369738 * q^59 + 135744 * q^61 + 103800 * q^63 - 753840 * q^65 + 289938 * q^67 + 2059272 * q^69 - 977700 * q^73 + 2115342 * q^75 - 159192 * q^77 + 764796 * q^79 - 1428282 * q^81 - 396900 * q^83 + 1619568 * q^85 - 3072636 * q^87 - 355584 * q^91 - 2526576 * q^93 + 2089260 * q^95 - 38874 * q^97 - 4398804 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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