LMFDB - Embedded newform 126.7.c.a.55.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,7,Mod(55,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.55"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	126.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,128,0,0,308] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$28.9868145361$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.211968.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 30x^{2} + 207 $ x^4 + 30*x^2 + 207
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.4
Root			$-3.27984i$ of defining polynomial
Character	$\chi$	$=$	126.55
Dual form			126.7.c.a.55.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+5.65685 q^{2} +32.0000 q^{4} +204.749i q^{5} +(-41.7939 - 340.444i) q^{7} +181.019 q^{8} +1158.23i q^{10} +1177.88 q^{11} +1399.64i q^{13} +(-236.422 - 1925.84i) q^{14} +1024.00 q^{16} +6063.65i q^{17} +3134.94i q^{19} +6551.96i q^{20} +6663.11 q^{22} -8652.59 q^{23} -26297.0 q^{25} +7917.54i q^{26} +(-1337.41 - 10894.2i) q^{28} -32565.6 q^{29} +42298.3i q^{31} +5792.62 q^{32} +34301.2i q^{34} +(69705.5 - 8557.26i) q^{35} +37578.8 q^{37} +17733.9i q^{38} +37063.5i q^{40} +93520.9i q^{41} +92007.0 q^{43} +37692.2 q^{44} -48946.4 q^{46} +24952.4i q^{47} +(-114156. + 28457.0i) q^{49} -148758. q^{50} +44788.4i q^{52} -109.623 q^{53} +241170. i q^{55} +(-7565.51 - 61627.0i) q^{56} -184219. q^{58} -326590. i q^{59} +84599.8i q^{61} +239276. i q^{62} +32768.0 q^{64} -286574. q^{65} -111002. q^{67} +194037. i q^{68} +(394314. - 48407.1i) q^{70} +441825. q^{71} -464201. i q^{73} +212578. q^{74} +100318. i q^{76} +(-49228.3 - 401003. i) q^{77} +595011. q^{79} +209663. i q^{80} +529034. i q^{82} +654116. i q^{83} -1.24152e6 q^{85} +520470. q^{86} +213219. q^{88} -298317. i q^{89} +(476498. - 58496.3i) q^{91} -276883. q^{92} +141152. i q^{94} -641874. q^{95} +169894. i q^{97} +(-645761. + 160977. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 128 q^{4} + 308 q^{7} + 4440 q^{11} - 2688 q^{14} + 4096 q^{16} + 1536 q^{22} - 40584 q^{23} - 40700 q^{25} + 9856 q^{28} + 18264 q^{29} + 84000 q^{35} - 23192 q^{37} - 44696 q^{43} + 142080 q^{44}+ \cdots - 827904 q^{98}+O(q^{100}) $ 4 * q + 128 * q^4 + 308 * q^7 + 4440 * q^11 - 2688 * q^14 + 4096 * q^16 + 1536 * q^22 - 40584 * q^23 - 40700 * q^25 + 9856 * q^28 + 18264 * q^29 + 84000 * q^35 - 23192 * q^37 - 44696 * q^43 + 142080 * q^44 + 33792 * q^46 - 310268 * q^49 - 364800 * q^50 - 248616 * q^53 - 86016 * q^56 - 840192 * q^58 + 131072 * q^64 - 1293600 * q^65 - 434776 * q^67 + 1102080 * q^70 + 451608 * q^71 + 981504 * q^74 + 309624 * q^77 + 2092904 * q^79 - 2117760 * q^85 + 2334720 * q^86 + 49152 * q^88 - 1109472 * q^91 - 1298688 * q^92 + 190560 * q^95 - 827904 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	5.65685			0.707107
$2$	5.65685			0.707107
$3$		0			0
$3$		0			0
$4$	32.0000			0.500000
$5$			204.749i			1.63799i	0.573801	+	0.818995i	$0.305468\pi$
$5$			204.749i			1.63799i	−0.573801	+	0.818995i	$0.694532\pi$
$6$		0			0
$7$	−41.7939	−	340.444i	−0.121848	−	0.992549i
$7$	−41.7939	−	340.444i	−0.121848	−	0.992549i
$8$	181.019			0.353553
$9$		0			0
$10$			1158.23i			1.15823i
$11$	1177.88			0.884960			0.442480	−	0.896778i	$-0.354099\pi$
$11$	1177.88			0.884960			0.442480	+	0.896778i	$0.354099\pi$
$12$		0			0
$13$			1399.64i			0.637067i	0.947912	+	0.318534i	$0.103190\pi$
$13$			1399.64i			0.637067i	−0.947912	+	0.318534i	$0.896810\pi$
$14$	−236.422	−	1925.84i	−0.0861597	−	0.701838i
$15$		0			0
$16$	1024.00			0.250000
$17$			6063.65i			1.23421i	0.786883	+	0.617103i	$0.211694\pi$
$17$			6063.65i			1.23421i	−0.786883	+	0.617103i	$0.788306\pi$
$18$		0			0
$19$			3134.94i			0.457054i	0.973538	+	0.228527i	$0.0733910\pi$
$19$			3134.94i			0.457054i	−0.973538	+	0.228527i	$0.926609\pi$
$20$			6551.96i			0.818995i
$21$		0			0
$22$	6663.11			0.625761
$23$	−8652.59			−0.711152			−0.355576	−	0.934647i	$-0.615715\pi$
$23$	−8652.59			−0.711152			−0.355576	+	0.934647i	$0.615715\pi$
$24$		0			0
$25$	−26297.0			−1.68301
$26$			7917.54i			0.450475i
$27$		0			0
$28$	−1337.41	−	10894.2i	−0.0609241	−	0.496274i
$29$	−32565.6			−1.33526			−0.667629	−	0.744494i	$-0.732691\pi$
$29$	−32565.6			−1.33526			−0.667629	+	0.744494i	$0.732691\pi$
$30$		0			0
$31$			42298.3i			1.41984i	0.704284	+	0.709918i	$0.251268\pi$
$31$			42298.3i			1.41984i	−0.704284	+	0.709918i	$0.748732\pi$
$32$	5792.62			0.176777
$33$		0			0
$34$			34301.2i			0.872715i
$35$	69705.5	−	8557.26i	1.62578	−	0.199586i
$36$		0			0
$37$	37578.8			0.741886			0.370943	−	0.928656i	$-0.379034\pi$
$37$	37578.8			0.741886			0.370943	+	0.928656i	$0.379034\pi$
$38$			17733.9i			0.323186i
$39$		0			0
$40$			37063.5i			0.579117i
$41$			93520.9i			1.35693i	0.734634	+	0.678464i	$0.237354\pi$
$41$			93520.9i			1.35693i	−0.734634	+	0.678464i	$0.762646\pi$
$42$		0			0
$43$	92007.0			1.15722			0.578610	−	0.815605i	$-0.303596\pi$
$43$	92007.0			1.15722			0.578610	+	0.815605i	$0.303596\pi$
$44$	37692.2			0.442480
$45$		0			0
$46$	−48946.4			−0.502861
$47$			24952.4i			0.240336i	0.992754	+	0.120168i	$0.0383433\pi$
$47$			24952.4i			0.240336i	−0.992754	+	0.120168i	$0.961657\pi$
$48$		0			0
$49$	−114156.	+	28457.0i	−0.970306	+	0.241881i
$50$	−148758.			−1.19007
$51$		0			0
$52$			44788.4i			0.318534i
$53$	−109.623			−0.000736330			−0.000368165	−	1.00000i	$-0.500117\pi$
$53$	−109.623			−0.000736330			−0.000368165		1.00000i	$0.500117\pi$
$54$		0			0
$55$			241170.i			1.44956i
$56$	−7565.51	−	61627.0i	−0.0430799	−	0.350919i
$57$		0			0
$58$	−184219.			−0.944170
$59$		−	326590.i		−	1.59018i	−0.606491	−	0.795091i	$-0.707423\pi$
$59$		−	326590.i		−	1.59018i	0.606491	−	0.795091i	$-0.292577\pi$
$60$		0			0
$61$			84599.8i			0.372717i	0.982482	+	0.186359i	$0.0596687\pi$
$61$			84599.8i			0.372717i	−0.982482	+	0.186359i	$0.940331\pi$
$62$			239276.i			1.00398i
$63$		0			0
$64$	32768.0			0.125000
$65$	−286574.			−1.04351
$66$		0			0
$67$	−111002.			−0.369068			−0.184534	−	0.982826i	$-0.559078\pi$
$67$	−111002.			−0.369068			−0.184534	+	0.982826i	$0.559078\pi$
$68$			194037.i			0.617103i
$69$		0			0
$70$	394314.	−	48407.1i	1.14960	−	0.141129i
$71$	441825.			1.23446			0.617228	−	0.786784i	$-0.288256\pi$
$71$	441825.			1.23446			0.617228	+	0.786784i	$0.288256\pi$
$72$		0			0
$73$		−	464201.i		−	1.19327i	−0.802514	−	0.596633i	$-0.796505\pi$
$73$		−	464201.i		−	1.19327i	0.802514	−	0.596633i	$-0.203495\pi$
$74$	212578.			0.524593
$75$		0			0
$76$			100318.i			0.228527i
$77$	−49228.3	−	401003.i	−0.107831	−	0.878366i
$78$		0			0
$79$	595011.			1.20682			0.603412	−	0.797429i	$-0.293807\pi$
$79$	595011.			1.20682			0.603412	+	0.797429i	$0.293807\pi$
$80$			209663.i			0.409497i
$81$		0			0
$82$			529034.i			0.959493i
$83$			654116.i			1.14398i	0.820259	+	0.571992i	$0.193829\pi$
$83$			654116.i			1.14398i	−0.820259	+	0.571992i	$0.806171\pi$
$84$		0			0
$85$	−1.24152e6			−2.02162
$86$	520470.			0.818277
$87$		0			0
$88$	213219.			0.312881
$89$		−	298317.i		−	0.423164i	−0.977360	−	0.211582i	$-0.932139\pi$
$89$		−	298317.i		−	0.423164i	0.977360	−	0.211582i	$-0.0678615\pi$
$90$		0			0
$91$	476498.	−	58496.3i	0.632320	−	0.0776255i
$92$	−276883.			−0.355576
$93$		0			0
$94$			141152.i			0.169943i
$95$	−641874.			−0.748650
$96$		0			0
$97$			169894.i			0.186150i	0.995659	+	0.0930752i	$0.0296697\pi$
$97$			169894.i			0.186150i	−0.995659	+	0.0930752i	$0.970330\pi$
$98$	−645761.	+	160977.i	−0.686110	+	0.171035i
$99$		0			0
$100$	−841505.			−0.841505
$101$		−	1.11818e6i		−	1.08530i	−0.839960	−	0.542648i	$-0.817422\pi$
$101$		−	1.11818e6i		−	1.08530i	0.839960	−	0.542648i	$-0.182578\pi$
$102$		0			0
$103$		−	1.20424e6i		−	1.10205i	−0.834489	−	0.551025i	$-0.814237\pi$
$103$		−	1.20424e6i		−	1.10205i	0.834489	−	0.551025i	$-0.185763\pi$
$104$			253361.i			0.225237i
$105$		0			0
$106$	−620.119			−0.000520664
$107$	122039.			0.0996204			0.0498102	−	0.998759i	$-0.484138\pi$
$107$	122039.			0.0996204			0.0498102	+	0.998759i	$0.484138\pi$
$108$		0			0
$109$	1.10612e6			0.854127			0.427063	−	0.904222i	$-0.359548\pi$
$109$	1.10612e6			0.854127			0.427063	+	0.904222i	$0.359548\pi$
$110$			1.36426e6i			1.02499i
$111$		0			0
$112$	−42797.0	−	348615.i	−0.0304621	−	0.248137i
$113$	−266739.			−0.184864			−0.0924318	−	0.995719i	$-0.529464\pi$
$113$	−266739.			−0.184864			−0.0924318	+	0.995719i	$0.529464\pi$
$114$		0			0
$115$		−	1.77161e6i		−	1.16486i
$116$	−1.04210e6			−0.667629
$117$		0			0
$118$		−	1.84747e6i		−	1.12443i
$119$	2.06434e6	−	253424.i	1.22501	−	0.150386i
$120$		0			0
$121$	−384154.			−0.216845
$122$			478569.i			0.263551i
$123$		0			0
$124$			1.35355e6i			0.709918i
$125$		−	2.18509e6i		−	1.11876i
$126$		0			0
$127$	1.34435e6			0.656297			0.328149	−	0.944626i	$-0.393575\pi$
$127$	1.34435e6			0.656297			0.328149	+	0.944626i	$0.393575\pi$
$128$	185364.			0.0883883
$129$		0			0
$130$	−1.62111e6			−0.737873
$131$		−	3.66483e6i		−	1.63019i	−0.579324	−	0.815097i	$-0.696684\pi$
$131$		−	3.66483e6i		−	1.63019i	0.579324	−	0.815097i	$-0.303316\pi$
$132$		0			0
$133$	1.06727e6	−	131021.i	0.453649	−	0.0556913i
$134$	−627922.			−0.260970
$135$		0			0
$136$			1.09764e6i			0.436358i
$137$	3.33009e6			1.29507			0.647537	−	0.762034i	$-0.275799\pi$
$137$	3.33009e6			1.29507			0.647537	+	0.762034i	$0.275799\pi$
$138$		0			0
$139$		−	1.18963e6i		−	0.442962i	−0.975165	−	0.221481i	$-0.928911\pi$
$139$		−	1.18963e6i		−	0.442962i	0.975165	−	0.221481i	$-0.0710890\pi$
$140$	2.23058e6	−	273832.i	0.812892	−	0.0997931i
$141$		0			0
$142$	2.49934e6			0.872892
$143$			1.64861e6i			0.563779i
$144$		0			0
$145$		−	6.66776e6i		−	2.18714i
$146$		−	2.62592e6i		−	0.843766i
$147$		0			0
$148$	1.20252e6			0.370943
$149$	−1.62144e6			−0.490166			−0.245083	−	0.969502i	$-0.578815\pi$
$149$	−1.62144e6			−0.490166			−0.245083	+	0.969502i	$0.578815\pi$
$150$		0			0
$151$	−4.35030e6			−1.26354			−0.631770	−	0.775156i	$-0.717671\pi$
$151$	−4.35030e6			−1.26354			−0.631770	+	0.775156i	$0.717671\pi$
$152$			567484.i			0.161593i
$153$		0			0
$154$	−278478.	−	2.26842e6i	−0.0762479	−	0.621099i
$155$	−8.66053e6			−2.32568
$156$		0			0
$157$			4.64090e6i			1.19923i	0.800288	+	0.599616i	$0.204680\pi$
$157$			4.64090e6i			1.19923i	−0.800288	+	0.599616i	$0.795320\pi$
$158$	3.36589e6			0.853354
$159$		0			0
$160$			1.18603e6i			0.289558i
$161$	361626.	+	2.94572e6i	0.0866526	+	0.705853i
$162$		0			0
$163$	−5.26597e6			−1.21595			−0.607975	−	0.793956i	$-0.708018\pi$
$163$	−5.26597e6			−1.21595			−0.607975	+	0.793956i	$0.708018\pi$
$164$			2.99267e6i			0.678464i
$165$		0			0
$166$			3.70024e6i			0.808920i
$167$		−	1.99529e6i		−	0.428406i	−0.976789	−	0.214203i	$-0.931285\pi$
$167$		−	1.99529e6i		−	0.428406i	0.976789	−	0.214203i	$-0.0687154\pi$
$168$		0			0
$169$	2.86783e6			0.594145
$170$	−7.02312e6			−1.42950
$171$		0			0
$172$	2.94422e6			0.578610
$173$		−	1.97345e6i		−	0.381142i	−0.981673	−	0.190571i	$-0.938966\pi$
$173$		−	1.97345e6i		−	0.381142i	0.981673	−	0.190571i	$-0.0610340\pi$
$174$		0			0
$175$	1.09906e6	+	8.95267e6i	0.205072	+	1.67047i
$176$	1.20615e6			0.221240
$177$		0			0
$178$		−	1.68754e6i		−	0.299222i
$179$	6.59325e6			1.14958			0.574791	−	0.818300i	$-0.305083\pi$
$179$	6.59325e6			1.14958			0.574791	+	0.818300i	$0.305083\pi$
$180$		0			0
$181$			2.60968e6i			0.440100i	0.975489	+	0.220050i	$0.0706220\pi$
$181$			2.60968e6i			0.440100i	−0.975489	+	0.220050i	$0.929378\pi$
$182$	2.69548e6	−	330905.i	0.447118	−	0.0548895i
$183$		0			0
$184$	−1.56629e6			−0.251430
$185$			7.69420e6i			1.21520i
$186$		0			0
$187$			7.14227e6i			1.09222i
$188$			798475.i			0.120168i
$189$		0			0
$190$	−3.63099e6			−0.529376
$191$	−1.99290e6			−0.286012			−0.143006	−	0.989722i	$-0.545677\pi$
$191$	−1.99290e6			−0.286012			−0.143006	+	0.989722i	$0.545677\pi$
$192$		0			0
$193$	1.24013e7			1.72503			0.862513	−	0.506036i	$-0.168890\pi$
$193$	1.24013e7			1.72503			0.862513	+	0.506036i	$0.168890\pi$
$194$			961068.i			0.131628i
$195$		0			0
$196$	−3.65298e6	+	910624.i	−0.485153	+	0.120940i
$197$	5.13349e6			0.671450			0.335725	−	0.941960i	$-0.391019\pi$
$197$	5.13349e6			0.671450			0.335725	+	0.941960i	$0.391019\pi$
$198$		0			0
$199$			615146.i			0.0780582i	0.999238	+	0.0390291i	$0.0124265\pi$
$199$			615146.i			0.0780582i	−0.999238	+	0.0390291i	$0.987573\pi$
$200$	−4.76027e6			−0.595034
$201$		0			0
$202$		−	6.32539e6i		−	0.767420i
$203$	1.36104e6	+	1.10868e7i	0.162699	+	1.32531i
$204$		0			0
$205$	−1.91483e7			−2.22263
$206$		−	6.81221e6i		−	0.779267i
$207$		0			0
$208$			1.43323e6i			0.159267i
$209$			3.69258e6i			0.404475i
$210$		0			0
$211$	2.56281e6			0.272815			0.136408	−	0.990653i	$-0.456444\pi$
$211$	2.56281e6			0.272815			0.136408	+	0.990653i	$0.456444\pi$
$212$	−3507.92			−0.000368165
$213$		0			0
$214$	690358.			0.0704422
$215$			1.88383e7i			1.89551i
$216$		0			0
$217$	1.44002e7	−	1.76781e6i	1.40926	−	0.173004i
$218$	6.25716e6			0.603959
$219$		0			0
$220$			7.71744e6i			0.724778i
$221$	−8.48691e6			−0.786272
$222$		0			0
$223$			7.82377e6i			0.705507i	0.935716	+	0.352753i	$0.114755\pi$
$223$			7.82377e6i			0.705507i	−0.935716	+	0.352753i	$0.885245\pi$
$224$	−242096.	−	1.97206e6i	−0.0215399	−	0.175459i
$225$		0			0
$226$	−1.50890e6			−0.130718
$227$		−	8.19085e6i		−	0.700247i	−0.936704	−	0.350124i	$-0.886140\pi$
$227$		−	8.19085e6i		−	0.700247i	0.936704	−	0.350124i	$-0.113860\pi$
$228$		0			0
$229$			1.30526e7i			1.08690i	0.839442	+	0.543449i	$0.182882\pi$
$229$			1.30526e7i			1.08690i	−0.839442	+	0.543449i	$0.817118\pi$
$230$		−	1.00217e7i		−	0.823681i
$231$		0			0
$232$	−5.89500e6			−0.472085
$233$	−1.38499e6			−0.109491			−0.0547456	−	0.998500i	$-0.517435\pi$
$233$	−1.38499e6			−0.109491			−0.0547456	+	0.998500i	$0.517435\pi$
$234$		0			0
$235$	−5.10896e6			−0.393667
$236$		−	1.04509e7i		−	0.795091i
$237$		0			0
$238$	1.16776e7	−	1.43358e6i	0.866212	−	0.106339i
$239$	−4.37563e6			−0.320514			−0.160257	−	0.987075i	$-0.551232\pi$
$239$	−4.37563e6			−0.320514			−0.160257	+	0.987075i	$0.551232\pi$
$240$		0			0
$241$		−	8.69878e6i		−	0.621451i	−0.950500	−	0.310726i	$-0.899428\pi$
$241$		−	8.69878e6i		−	0.621451i	0.950500	−	0.310726i	$-0.100572\pi$
$242$	−2.17311e6			−0.153333
$243$		0			0
$244$			2.70719e6i			0.186359i
$245$	−5.82654e6	−	2.33732e7i	−0.396198	−	1.58935i
$246$		0			0
$247$	−4.38777e6			−0.291174
$248$			7.65682e6i			0.501988i
$249$		0			0
$250$		−	1.23607e7i		−	0.791085i
$251$			2.65980e7i			1.68201i	0.541031	+	0.841003i	$0.318034\pi$
$251$			2.65980e7i			1.68201i	−0.541031	+	0.841003i	$0.681966\pi$
$252$		0			0
$253$	−1.01917e7			−0.629342
$254$	7.60478e6			0.464072
$255$		0			0
$256$	1.04858e6			0.0625000
$257$		−	7.54668e6i		−	0.444587i	−0.974980	−	0.222293i	$-0.928646\pi$
$257$		−	7.54668e6i		−	0.444587i	0.974980	−	0.222293i	$-0.0713543\pi$
$258$		0			0
$259$	−1.57056e6	−	1.27935e7i	−0.0903975	−	0.736358i
$260$	−9.17036e6			−0.521755
$261$		0			0
$262$		−	2.07314e7i		−	1.15272i
$263$	1.31684e7			0.723880			0.361940	−	0.932201i	$-0.382115\pi$
$263$	1.31684e7			0.723880			0.361940	+	0.932201i	$0.382115\pi$
$264$		0			0
$265$		−	22445.1i		−	0.00120610i
$266$	6.03739e6	−	741168.i	0.320778	−	0.0393797i
$267$		0			0
$268$	−3.55206e6			−0.184534
$269$		−	1.82863e7i		−	0.939439i	−0.882816	−	0.469719i	$-0.844355\pi$
$269$		−	1.82863e7i		−	0.939439i	0.882816	−	0.469719i	$-0.155645\pi$
$270$		0			0
$271$		−	2.78109e7i		−	1.39736i	−0.715435	−	0.698679i	$-0.753771\pi$
$271$		−	2.78109e7i		−	1.39736i	0.715435	−	0.698679i	$-0.246229\pi$
$272$			6.20918e6i			0.308551i
$273$		0			0
$274$	1.88379e7			0.915756
$275$	−3.09748e7			−1.48940
$276$		0			0
$277$	−5.25419e6			−0.247210			−0.123605	−	0.992331i	$-0.539446\pi$
$277$	−5.25419e6			−0.247210			−0.123605	+	0.992331i	$0.539446\pi$
$278$		−	6.72954e6i		−	0.313221i
$279$		0			0
$280$	1.26180e7	−	1.54903e6i	0.574802	−	0.0705644i
$281$	3.12195e7			1.40704			0.703522	−	0.710674i	$-0.251610\pi$
$281$	3.12195e7			1.40704			0.703522	+	0.710674i	$0.251610\pi$
$282$		0			0
$283$			1.81450e7i			0.800569i	0.916391	+	0.400284i	$0.131089\pi$
$283$			1.81450e7i			0.800569i	−0.916391	+	0.400284i	$0.868911\pi$
$284$	1.41384e7			0.617228
$285$		0			0
$286$			9.32593e6i			0.398652i
$287$	3.18386e7	−	3.90860e6i	1.34682	−	0.165339i
$288$		0			0
$289$	−1.26303e7			−0.523263
$290$		−	3.77186e7i		−	1.54654i
$291$		0			0
$292$		−	1.48544e7i		−	0.596633i
$293$		−	5.83393e6i		−	0.231931i	−0.993253	−	0.115965i	$-0.963004\pi$
$293$		−	5.83393e6i		−	0.231931i	0.993253	−	0.115965i	$-0.0369962\pi$
$294$		0			0
$295$	6.68689e7			2.60470
$296$	6.80248e6			0.262296
$297$		0			0
$298$	−9.17227e6			−0.346599
$299$		−	1.21105e7i		−	0.453052i
$300$		0			0
$301$	−3.84534e6	−	3.13233e7i	−0.141005	−	1.14860i
$302$	−2.46090e7			−0.893457
$303$		0			0
$304$			3.21017e6i			0.114264i
$305$	−1.73217e7			−0.610507
$306$		0			0
$307$		−	2.26871e7i		−	0.784087i	−0.919947	−	0.392043i	$-0.871768\pi$
$307$		−	2.26871e7i		−	0.784087i	0.919947	−	0.392043i	$-0.128232\pi$
$308$	−1.57531e6	−	1.28321e7i	−0.0539154	−	0.439183i
$309$		0			0
$310$	−4.89914e7			−1.64450
$311$			3.96340e7i			1.31761i	0.752314	+	0.658805i	$0.228938\pi$
$311$			3.96340e7i			1.31761i	−0.752314	+	0.658805i	$0.771062\pi$
$312$		0			0
$313$			1.00856e7i			0.328905i	0.986385	+	0.164452i	$0.0525857\pi$
$313$			1.00856e7i			0.328905i	−0.986385	+	0.164452i	$0.947414\pi$
$314$			2.62529e7i			0.847986i
$315$		0			0
$316$	1.90404e7			0.603412
$317$	−2.98372e7			−0.936657			−0.468329	−	0.883554i	$-0.655144\pi$
$317$	−2.98372e7			−0.936657			−0.468329	+	0.883554i	$0.655144\pi$
$318$		0			0
$319$	−3.83584e7			−1.18165
$320$			6.70921e6i			0.204749i
$321$		0			0
$322$	2.04566e6	+	1.66635e7i	0.0612727	+	0.499114i
$323$	−1.90092e7			−0.564099
$324$		0			0
$325$		−	3.68063e7i		−	1.07219i
$326$	−2.97888e7			−0.859807
$327$		0			0
$328$			1.69291e7i			0.479747i
$329$	8.49489e6	−	1.04286e6i	0.238545	−	0.0292845i
$330$		0			0
$331$	1.79016e6			0.0493637			0.0246819	−	0.999695i	$-0.492143\pi$
$331$	1.79016e6			0.0493637			0.0246819	+	0.999695i	$0.492143\pi$
$332$			2.09317e7i			0.571992i
$333$		0			0
$334$		−	1.12870e7i		−	0.302929i
$335$		−	2.27275e7i		−	0.604530i
$336$		0			0
$337$	−1.30113e6			−0.0339964			−0.0169982	−	0.999856i	$-0.505411\pi$
$337$	−1.30113e6			−0.0339964			−0.0169982	+	0.999856i	$0.505411\pi$
$338$	1.62229e7			0.420124
$339$		0			0
$340$	−3.97288e7			−1.01081
$341$			4.98225e7i			1.25650i
$342$		0			0
$343$	1.44590e7	+	3.76743e7i	0.358308	+	0.933603i
$344$	1.66550e7			0.409139
$345$		0			0
$346$		−	1.11635e7i		−	0.269508i
$347$	2.67141e7			0.639370			0.319685	−	0.947524i	$-0.396423\pi$
$347$	2.67141e7			0.639370			0.319685	+	0.947524i	$0.396423\pi$
$348$		0			0
$349$		−	2.39729e7i		−	0.563956i	−0.959421	−	0.281978i	$-0.909010\pi$
$349$		−	2.39729e7i		−	0.563956i	0.959421	−	0.281978i	$-0.0909904\pi$
$350$	6.21720e6	+	5.06440e7i	0.145008	+	1.18120i
$351$		0			0
$352$	6.82302e6			0.156440
$353$		−	7.99792e7i		−	1.81825i	−0.416528	−	0.909123i	$-0.636753\pi$
$353$		−	7.99792e7i		−	1.81825i	0.416528	−	0.909123i	$-0.363247\pi$
$354$		0			0
$355$			9.04632e7i			2.02203i
$356$		−	9.54615e6i		−	0.211582i
$357$		0			0
$358$	3.72970e7			0.812878
$359$	−4.51314e7			−0.975429			−0.487714	−	0.873003i	$-0.662169\pi$
$359$	−4.51314e7			−0.975429			−0.487714	+	0.873003i	$0.662169\pi$
$360$		0			0
$361$	3.72181e7			0.791101
$362$			1.47626e7i			0.311197i
$363$		0			0
$364$	1.52479e7	−	1.87188e6i	0.316160	−	0.0388128i
$365$	9.50445e7			1.95456
$366$		0			0
$367$			6.07183e7i			1.22835i	0.789171	+	0.614174i	$0.210511\pi$
$367$			6.07183e7i			1.22835i	−0.789171	+	0.614174i	$0.789489\pi$
$368$	−8.86025e6			−0.177788
$369$		0			0
$370$			4.35250e7i			0.859277i
$371$	4581.56	+	37320.4i	8.97205e−5	+	0.000730843i
$372$		0			0
$373$	−9.31710e7			−1.79537			−0.897685	−	0.440637i	$-0.854753\pi$
$373$	−9.31710e7			−1.79537			−0.897685	+	0.440637i	$0.854753\pi$
$374$			4.04028e7i			0.772318i
$375$		0			0
$376$			4.51686e6i			0.0849714i
$377$		−	4.55800e7i		−	0.850649i
$378$		0			0
$379$	2.78773e7			0.512075			0.256037	−	0.966667i	$-0.417583\pi$
$379$	2.78773e7			0.512075			0.256037	+	0.966667i	$0.417583\pi$
$380$	−2.05400e7			−0.374325
$381$		0			0
$382$	−1.12735e7			−0.202241
$383$		−	2.63822e6i		−	0.0469586i	−0.999724	−	0.0234793i	$-0.992526\pi$
$383$		−	2.63822e6i		−	0.0469586i	0.999724	−	0.0234793i	$-0.00747438\pi$
$384$		0			0
$385$	8.21049e7	−	1.00794e7i	1.43875	−	0.176626i
$386$	7.01524e7			1.21978
$387$		0			0
$388$			5.43662e6i			0.0930752i
$389$	−3.12589e7			−0.531037			−0.265519	−	0.964106i	$-0.585543\pi$
$389$	−3.12589e7			−0.531037			−0.265519	+	0.964106i	$0.585543\pi$
$390$		0			0
$391$		−	5.24663e7i		−	0.877708i
$392$	−2.06644e7	+	5.15127e6i	−0.343055	+	0.0855177i
$393$		0			0
$394$	2.90394e7			0.474787
$395$			1.21828e8i			1.97677i
$396$		0			0
$397$		−	3.33743e7i		−	0.533385i	−0.963782	−	0.266693i	$-0.914069\pi$
$397$		−	3.33743e7i		−	0.533385i	0.963782	−	0.266693i	$-0.0859309\pi$
$398$			3.47979e6i			0.0551955i
$399$		0			0
$400$	−2.69282e7			−0.420753
$401$	4.06798e6			0.0630878			0.0315439	−	0.999502i	$-0.489958\pi$
$401$	4.06798e6			0.0630878			0.0315439	+	0.999502i	$0.489958\pi$
$402$		0			0
$403$	−5.92023e7			−0.904531
$404$		−	3.57818e7i		−	0.542648i
$405$		0			0
$406$	7.69923e6	+	6.27162e7i	0.115045	+	0.937134i
$407$	4.42634e7			0.656540
$408$		0			0
$409$		−	3.79002e7i		−	0.553952i	−0.960877	−	0.276976i	$-0.910668\pi$
$409$		−	3.79002e7i		−	0.553952i	0.960877	−	0.276976i	$-0.0893322\pi$
$410$	−1.08319e8			−1.57164
$411$		0			0
$412$		−	3.85357e7i		−	0.551025i
$413$	−1.11186e8	+	1.36495e7i	−1.57833	+	0.193761i
$414$		0			0
$415$	−1.33929e8			−1.87384
$416$			8.10756e6i			0.112619i
$417$		0			0
$418$			2.08884e7i			0.286007i
$419$		−	7.34255e7i		−	0.998171i	−0.866553	−	0.499085i	$-0.833669\pi$
$419$		−	7.34255e7i		−	0.998171i	0.866553	−	0.499085i	$-0.166331\pi$
$420$		0			0
$421$	5.94103e6			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$421$	5.94103e6			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$422$	1.44974e7			0.192910
$423$		0			0
$424$	−19843.8			−0.000260332
$425$		−	1.59456e8i		−	2.07718i
$426$		0			0
$427$	2.88015e7	−	3.53576e6i	0.369940	−	0.0454149i
$428$	3.90526e6			0.0498102
$429$		0			0
$430$			1.06566e8i			1.34033i
$431$	−9.58811e7			−1.19757			−0.598785	−	0.800909i	$-0.704350\pi$
$431$	−9.58811e7			−1.19757			−0.598785	+	0.800909i	$0.704350\pi$
$432$		0			0
$433$			1.23332e8i			1.51919i	0.650396	+	0.759595i	$0.274603\pi$
$433$			1.23332e8i			1.51919i	−0.650396	+	0.759595i	$0.725397\pi$
$434$	8.14600e7	−	1.00003e7i	0.996495	−	0.122333i
$435$		0			0
$436$	3.53958e7			0.427063
$437$		−	2.71253e7i		−	0.325035i
$438$		0			0
$439$		−	6.41673e7i		−	0.758438i	−0.925307	−	0.379219i	$-0.876193\pi$
$439$		−	6.41673e7i		−	0.758438i	0.925307	−	0.379219i	$-0.123807\pi$
$440$			4.36564e7i			0.512495i
$441$		0			0
$442$	−4.80092e7			−0.555978
$443$	6.58726e7			0.757693			0.378847	−	0.925459i	$-0.376321\pi$
$443$	6.58726e7			0.757693			0.378847	+	0.925459i	$0.376321\pi$
$444$		0			0
$445$	6.10801e7			0.693138
$446$			4.42579e7i			0.498869i
$447$		0			0
$448$	−1.36950e6	−	1.11557e7i	−0.0152310	−	0.124069i
$449$	1.02206e8			1.12911			0.564555	−	0.825395i	$-0.309048\pi$
$449$	1.02206e8			1.12911			0.564555	+	0.825395i	$0.309048\pi$
$450$		0			0
$451$			1.10157e8i			1.20083i
$452$	−8.53565e6			−0.0924318
$453$		0			0
$454$		−	4.63344e7i		−	0.495150i
$455$	1.19771e7	+	9.75624e7i	0.127150	+	1.03573i
$456$		0			0
$457$	−5.62382e7			−0.589227			−0.294613	−	0.955617i	$-0.595191\pi$
$457$	−5.62382e7			−0.589227			−0.294613	+	0.955617i	$0.595191\pi$
$458$			7.38364e7i			0.768553i
$459$		0			0
$460$		−	5.66914e7i		−	0.582430i
$461$		−	2.46600e7i		−	0.251705i	−0.992049	−	0.125852i	$-0.959833\pi$
$461$		−	2.46600e7i		−	0.251705i	0.992049	−	0.125852i	$-0.0401665\pi$
$462$		0			0
$463$	1.91959e8			1.93404			0.967018	−	0.254707i	$-0.0819791\pi$
$463$	1.91959e8			1.93404			0.967018	+	0.254707i	$0.0819791\pi$
$464$	−3.33472e7			−0.333814
$465$		0			0
$466$	−7.83469e6			−0.0774219
$467$			1.50925e8i			1.48187i	0.671578	+	0.740934i	$0.265617\pi$
$467$			1.50925e8i			1.48187i	−0.671578	+	0.740934i	$0.734383\pi$
$468$		0			0
$469$	4.63921e6	+	3.77900e7i	0.0449703	+	0.366318i
$470$	−2.89007e7			−0.278365
$471$		0			0
$472$		−	5.91191e7i		−	0.562214i
$473$	1.08373e8			1.02409
$474$		0			0
$475$		−	8.24395e7i		−	0.769227i
$476$	6.60587e7	−	8.10956e6i	0.612505	−	0.0751929i
$477$		0			0
$478$	−2.47523e7			−0.226638
$479$		−	4.70415e7i		−	0.428031i	−0.976830	−	0.214015i	$-0.931346\pi$
$479$		−	4.70415e7i		−	0.428031i	0.976830	−	0.214015i	$-0.0686542\pi$
$480$		0			0
$481$			5.25966e7i			0.472631i
$482$		−	4.92077e7i		−	0.439432i
$483$		0			0
$484$	−1.22929e7			−0.108423
$485$	−3.47857e7			−0.304912
$486$		0			0
$487$	−4.36014e7			−0.377497			−0.188748	−	0.982025i	$-0.560443\pi$
$487$	−4.36014e7			−0.377497			−0.188748	+	0.982025i	$0.560443\pi$
$488$			1.53142e7i			0.131775i
$489$		0			0
$490$	−3.29599e7	−	1.32219e8i	−0.280154	−	1.12384i
$491$	−7.78280e7			−0.657494			−0.328747	−	0.944418i	$-0.606626\pi$
$491$	−7.78280e7			−0.657494			−0.328747	+	0.944418i	$0.606626\pi$
$492$		0			0
$493$		−	1.97466e8i		−	1.64798i
$494$	−2.48210e7			−0.205891
$495$		0			0
$496$			4.33135e7i			0.354959i
$497$	−1.84656e7	−	1.50417e8i	−0.150416	−	1.22526i
$498$		0			0
$499$	−6.33741e7			−0.510047			−0.255024	−	0.966935i	$-0.582083\pi$
$499$	−6.33741e7			−0.510047			−0.255024	+	0.966935i	$0.582083\pi$
$500$		−	6.99227e7i		−	0.559382i
$501$		0			0
$502$			1.50461e8i			1.18936i
$503$			1.88800e8i			1.48354i	0.670657	+	0.741768i	$0.266012\pi$
$503$			1.88800e8i			1.48354i	−0.670657	+	0.741768i	$0.733988\pi$
$504$		0			0
$505$	2.28946e8			1.77770
$506$	−5.76531e7			−0.445012
$507$		0			0
$508$	4.30191e7			0.328149
$509$		−	5.84845e7i		−	0.443493i	−0.975104	−	0.221747i	$-0.928824\pi$
$509$		−	5.84845e7i		−	0.443493i	0.975104	−	0.221747i	$-0.0711758\pi$
$510$		0			0
$511$	−1.58034e8	+	1.94008e7i	−1.18437	+	0.145397i
$512$	5.93164e6			0.0441942
$513$		0			0
$514$		−	4.26905e7i		−	0.314370i
$515$	2.46566e8			1.80515
$516$		0			0
$517$			2.93909e7i			0.212687i
$518$	−8.88445e6	−	7.23708e7i	−0.0639207	−	0.520684i
$519$		0			0
$520$	−5.18754e7			−0.368936
$521$		−	1.51011e7i		−	0.106781i	−0.998574	−	0.0533907i	$-0.982997\pi$
$521$		−	1.51011e7i		−	0.106781i	0.998574	−	0.0533907i	$-0.0170029\pi$
$522$		0			0
$523$		−	2.31852e8i		−	1.62071i	−0.585939	−	0.810355i	$-0.699274\pi$
$523$		−	2.31852e8i		−	1.62071i	0.585939	−	0.810355i	$-0.300726\pi$
$524$		−	1.17274e8i		−	0.815097i
$525$		0			0
$526$	7.44918e7			0.511860
$527$	−2.56482e8			−1.75237
$528$		0			0
$529$	−7.31686e7			−0.494262
$530$		−	126969.i		−	0.000852842i
$531$		0			0
$532$	3.41527e7	−	4.19268e6i	0.226824	−	0.0278456i
$533$	−1.30895e8			−0.864455
$534$		0			0
$535$			2.49874e7i			0.163177i
$536$	−2.00935e7			−0.130485
$537$		0			0
$538$		−	1.03443e8i		−	0.664284i
$539$	−1.34462e8	+	3.35190e7i	−0.858682	+	0.214055i
$540$		0			0
$541$	−1.16913e7			−0.0738363			−0.0369181	−	0.999318i	$-0.511754\pi$
$541$	−1.16913e7			−0.0738363			−0.0369181	+	0.999318i	$0.511754\pi$
$542$		−	1.57322e8i		−	0.988082i
$543$		0			0
$544$			3.51244e7i			0.218179i
$545$			2.26476e8i			1.39905i
$546$		0			0
$547$	−1.11900e8			−0.683704			−0.341852	−	0.939754i	$-0.611054\pi$
$547$	−1.11900e8			−0.683704			−0.341852	+	0.939754i	$0.611054\pi$
$548$	1.06563e8			0.647537
$549$		0			0
$550$	−1.75220e8			−1.05316
$551$		−	1.02091e8i		−	0.610285i
$552$		0			0
$553$	−2.48679e7	−	2.02568e8i	−0.147049	−	1.19783i
$554$	−2.97222e7			−0.174804
$555$		0			0
$556$		−	3.80680e7i		−	0.221481i
$557$	1.37837e8			0.797629			0.398815	−	0.917032i	$-0.369422\pi$
$557$	1.37837e8			0.797629			0.398815	+	0.917032i	$0.369422\pi$
$558$		0			0
$559$			1.28776e8i			0.737227i
$560$	7.13784e7	−	8.76263e6i	0.406446	−	0.0498965i
$561$		0			0
$562$	1.76604e8			0.994930
$563$		−	3.73228e7i		−	0.209146i	−0.994517	−	0.104573i	$-0.966652\pi$
$563$		−	3.73228e7i		−	0.209146i	0.994517	−	0.104573i	$-0.0333476\pi$
$564$		0			0
$565$		−	5.46145e7i		−	0.302805i
$566$			1.02644e8i			0.566088i
$567$		0			0
$568$	7.99789e7			0.436446
$569$	−1.41857e8			−0.770042			−0.385021	−	0.922908i	$-0.625806\pi$
$569$	−1.41857e8			−0.770042			−0.385021	+	0.922908i	$0.625806\pi$
$570$		0			0
$571$	2.47829e8			1.33120			0.665600	−	0.746308i	$-0.268176\pi$
$571$	2.47829e8			1.33120			0.665600	+	0.746308i	$0.268176\pi$
$572$			5.27554e7i			0.281890i
$573$		0			0
$574$	1.80107e8	−	2.21104e7i	0.952344	−	0.116913i
$575$	2.27537e8			1.19688
$576$		0			0
$577$		−	1.43601e8i		−	0.747531i	−0.927523	−	0.373766i	$-0.878066\pi$
$577$		−	1.43601e8i		−	0.747531i	0.927523	−	0.373766i	$-0.121934\pi$
$578$	−7.14478e7			−0.370003
$579$		0			0
$580$		−	2.13368e8i		−	1.09357i
$581$	2.22690e8	−	2.73381e7i	1.13546	−	0.139393i
$582$		0			0
$583$	−129123.			−0.000651623
$584$		−	8.40293e7i		−	0.421883i
$585$		0			0
$586$		−	3.30017e7i		−	0.164000i
$587$		−	1.55774e8i		−	0.770160i	−0.922883	−	0.385080i	$-0.874174\pi$
$587$		−	1.55774e8i		−	0.770160i	0.922883	−	0.385080i	$-0.125826\pi$
$588$		0			0
$589$	−1.32603e8			−0.648942
$590$	3.78267e8			1.84180
$591$		0			0
$592$	3.84806e7			0.185472
$593$			6.85593e7i			0.328777i	0.986396	+	0.164389i	$0.0525651\pi$
$593$			6.85593e7i			0.328777i	−0.986396	+	0.164389i	$0.947435\pi$
$594$		0			0
$595$	5.18882e7	+	4.22670e8i	0.246330	+	2.00655i
$596$	−5.18862e7			−0.245083
$597$		0			0
$598$		−	6.85073e7i		−	0.320356i
$599$	−6.44816e7			−0.300024			−0.150012	−	0.988684i	$-0.547931\pi$
$599$	−6.44816e7			−0.300024			−0.150012	+	0.988684i	$0.547931\pi$
$600$		0			0
$601$			2.18773e8i			1.00779i	0.863765	+	0.503895i	$0.168100\pi$
$601$			2.18773e8i			1.00779i	−0.863765	+	0.503895i	$0.831900\pi$
$602$	−2.17525e7	−	1.77191e8i	−0.0997057	−	0.812180i
$603$		0			0
$604$	−1.39210e8			−0.631770
$605$		−	7.86551e7i		−	0.355190i
$606$		0			0
$607$			3.55798e8i			1.59088i	0.606032	+	0.795441i	$0.292760\pi$
$607$			3.55798e8i			1.59088i	−0.606032	+	0.795441i	$0.707240\pi$
$608$			1.81595e7i			0.0807965i
$609$		0			0
$610$	−9.79863e7			−0.431694
$611$	−3.49242e7			−0.153110
$612$		0			0
$613$	1.50352e7			0.0652719			0.0326360	−	0.999467i	$-0.489610\pi$
$613$	1.50352e7			0.0652719			0.0326360	+	0.999467i	$0.489610\pi$
$614$		−	1.28338e8i		−	0.554433i
$615$		0			0
$616$	−8.91128e6	−	7.25893e7i	−0.0381240	−	0.310549i
$617$	−4.45354e7			−0.189605			−0.0948025	−	0.995496i	$-0.530222\pi$
$617$	−4.45354e7			−0.189605			−0.0948025	+	0.995496i	$0.530222\pi$
$618$		0			0
$619$		−	3.58045e7i		−	0.150962i	−0.997147	−	0.0754808i	$-0.975951\pi$
$619$		−	3.58045e7i		−	0.150962i	0.997147	−	0.0754808i	$-0.0240491\pi$
$620$	−2.77137e8			−1.16284
$621$		0			0
$622$			2.24204e8i			0.931691i
$623$	−1.01560e8	+	1.24679e7i	−0.420011	+	0.0515617i
$624$		0			0
$625$	3.65022e7			0.149513
$626$			5.70530e7i			0.232571i
$627$		0			0
$628$			1.48509e8i			0.599616i
$629$			2.27864e8i			0.915640i
$630$		0			0
$631$	−4.30383e8			−1.71304			−0.856520	−	0.516115i	$-0.827378\pi$
$631$	−4.30383e8			−1.71304			−0.856520	+	0.516115i	$0.827378\pi$
$632$	1.07709e8			0.426677
$633$		0			0
$634$	−1.68785e8			−0.662317
$635$			2.75253e8i			1.07501i
$636$		0			0
$637$	−3.98295e7	−	1.59776e8i	−0.154094	−	0.618150i
$638$	−2.16988e8			−0.835553
$639$		0			0
$640$			3.79530e7i			0.144779i
$641$	−1.87109e8			−0.710429			−0.355215	−	0.934785i	$-0.615592\pi$
$641$	−1.87109e8			−0.710429			−0.355215	+	0.934785i	$0.615592\pi$
$642$		0			0
$643$		−	2.52905e8i		−	0.951314i	−0.879631	−	0.475657i	$-0.842210\pi$
$643$		−	2.52905e8i		−	0.951314i	0.879631	−	0.475657i	$-0.157790\pi$
$644$	1.15720e7	+	9.42632e7i	0.0433263	+	0.352927i
$645$		0			0
$646$	−1.07532e8			−0.398878
$647$			1.95969e8i			0.723560i	0.932263	+	0.361780i	$0.117831\pi$
$647$			1.95969e8i			0.723560i	−0.932263	+	0.361780i	$0.882169\pi$
$648$		0			0
$649$		−	3.84684e8i		−	1.40725i
$650$		−	2.08208e8i		−	0.758153i
$651$		0			0
$652$	−1.68511e8			−0.607975
$653$	−1.11109e8			−0.399033			−0.199516	−	0.979894i	$-0.563937\pi$
$653$	−1.11109e8			−0.399033			−0.199516	+	0.979894i	$0.563937\pi$
$654$		0			0
$655$	7.50368e8			2.67024
$656$			9.57654e7i			0.339232i
$657$		0			0
$658$	4.80543e7	−	5.89929e6i	0.168677	−	0.0207072i
$659$	2.24885e8			0.785786			0.392893	−	0.919584i	$-0.371474\pi$
$659$	2.24885e8			0.785786			0.392893	+	0.919584i	$0.371474\pi$
$660$		0			0
$661$			5.19969e8i			1.80042i	0.435458	+	0.900209i	$0.356586\pi$
$661$			5.19969e8i			1.80042i	−0.435458	+	0.900209i	$0.643414\pi$
$662$	1.01267e7			0.0349054
$663$		0			0
$664$			1.18408e8i			0.404460i
$665$	2.68264e7	+	2.18522e8i	0.0912217	+	0.743072i
$666$		0			0
$667$	2.81777e8			0.949571
$668$		−	6.38491e7i		−	0.214203i
$669$		0			0
$670$		−	1.28566e8i		−	0.427467i
$671$			9.96486e7i			0.329840i
$672$		0			0
$673$	−3.68354e8			−1.20842			−0.604212	−	0.796823i	$-0.706512\pi$
$673$	−3.68354e8			−1.20842			−0.604212	+	0.796823i	$0.706512\pi$
$674$	−7.36033e6			−0.0240391
$675$		0			0
$676$	9.17704e7			0.297073
$677$			1.91687e7i			0.0617770i	0.999523	+	0.0308885i	$0.00983367\pi$
$677$			1.91687e7i			0.0617770i	−0.999523	+	0.0308885i	$0.990166\pi$
$678$		0			0
$679$	5.78396e7	−	7.10056e6i	0.184763	−	0.0226821i
$680$	−2.24740e8			−0.714749
$681$		0			0
$682$			2.81838e8i			0.888479i
$683$	3.28267e8			1.03030			0.515152	−	0.857099i	$-0.327736\pi$
$683$	3.28267e8			1.03030			0.515152	+	0.857099i	$0.327736\pi$
$684$		0			0
$685$			6.81833e8i			2.12132i
$686$	8.17926e7	+	2.13118e8i	0.253362	+	0.660157i
$687$		0			0
$688$	9.42152e7			0.289305
$689$		−	153432.i		−	0.000469092i
$690$		0			0
$691$			1.96349e8i			0.595107i	0.954705	+	0.297554i	$0.0961707\pi$
$691$			1.96349e8i			0.595107i	−0.954705	+	0.297554i	$0.903829\pi$
$692$		−	6.31503e7i		−	0.190571i
$693$		0			0
$694$	1.51118e8			0.452103
$695$	2.43574e8			0.725567
$696$		0			0
$697$	−5.67078e8			−1.67473
$698$		−	1.35611e8i		−	0.398777i
$699$		0			0
$700$	3.51698e7	+	2.86486e8i	0.102536	+	0.835235i
$701$	−4.19696e8			−1.21837			−0.609187	−	0.793026i	$-0.708504\pi$
$701$	−4.19696e8			−1.21837			−0.609187	+	0.793026i	$0.708504\pi$
$702$		0			0
$703$			1.17807e8i			0.339082i
$704$	3.85968e7			0.110620
$705$		0			0
$706$		−	4.52430e8i		−	1.28569i
$707$	−3.80678e8	+	4.67332e7i	−1.07721	+	0.132241i
$708$		0			0
$709$	6.46327e8			1.81348			0.906742	−	0.421686i	$-0.138562\pi$
$709$	6.46327e8			1.81348			0.906742	+	0.421686i	$0.138562\pi$
$710$			5.11737e8i			1.42979i
$711$		0			0
$712$		−	5.40012e7i		−	0.149611i
$713$		−	3.65990e8i		−	1.00972i
$714$		0			0
$715$	−3.37550e8			−0.923465
$716$	2.10984e8			0.574791
$717$		0			0
$718$	−2.55302e8			−0.689732
$719$		−	3.24953e8i		−	0.874246i	−0.899402	−	0.437123i	$-0.855998\pi$
$719$		−	3.24953e8i		−	0.874246i	0.899402	−	0.437123i	$-0.144002\pi$
$720$		0			0
$721$	−4.09976e8	+	5.03299e7i	−1.09384	+	0.134283i
$722$	2.10537e8			0.559393
$723$		0			0
$724$			8.35097e7i			0.220050i
$725$	8.56378e8			2.24725
$726$		0			0
$727$		−	5.08659e8i		−	1.32380i	−0.749591	−	0.661902i	$-0.769750\pi$
$727$		−	5.08659e8i		−	1.32380i	0.749591	−	0.661902i	$-0.230250\pi$
$728$	8.62554e7	−	1.05890e7i	0.223559	−	0.0274448i
$729$		0			0
$730$	5.37653e8			1.38208
$731$			5.57899e8i			1.42825i
$732$		0			0
$733$			7.52837e8i			1.91156i	0.294075	+	0.955782i	$0.404989\pi$
$733$			7.52837e8i			1.91156i	−0.294075	+	0.955782i	$0.595011\pi$
$734$			3.43475e8i			0.868573i
$735$		0			0
$736$	−5.01212e7			−0.125715
$737$	−1.30747e8			−0.326611
$738$		0			0
$739$	−1.58548e8			−0.392850			−0.196425	−	0.980519i	$-0.562933\pi$
$739$	−1.58548e8			−0.392850			−0.196425	+	0.980519i	$0.562933\pi$
$740$			2.46214e8i			0.607601i
$741$		0			0
$742$	25917.2	+	211116.i	6.34420e−5	+	0.000516784i
$743$	−5.89089e8			−1.43620			−0.718099	−	0.695941i	$-0.754987\pi$
$743$	−5.89089e8			−1.43620			−0.718099	+	0.695941i	$0.754987\pi$
$744$		0			0
$745$		−	3.31988e8i		−	0.802886i
$746$	−5.27055e8			−1.26952
$747$		0			0
$748$			2.28553e8i			0.546111i
$749$	−5.10050e6	−	4.15475e7i	−0.0121386	−	0.0988781i
$750$		0			0
$751$	−3.67603e8			−0.867879			−0.433939	−	0.900942i	$-0.642877\pi$
$751$	−3.67603e8			−0.867879			−0.433939	+	0.900942i	$0.642877\pi$
$752$			2.55512e7i			0.0600839i
$753$		0			0
$754$		−	2.57839e8i		−	0.601500i
$755$		−	8.90719e8i		−	2.06966i
$756$		0			0
$757$	6.54505e8			1.50878			0.754389	−	0.656427i	$-0.227933\pi$
$757$	6.54505e8			1.50878			0.754389	+	0.656427i	$0.227933\pi$
$758$	1.57698e8			0.362092
$759$		0			0
$760$	−1.16192e8			−0.264688
$761$			6.48428e7i			0.147132i	0.997290	+	0.0735661i	$0.0234380\pi$
$761$			6.48428e7i			0.147132i	−0.997290	+	0.0735661i	$0.976562\pi$
$762$		0			0
$763$	−4.62291e7	−	3.76572e8i	−0.104074	−	0.847763i
$764$	−6.37727e7			−0.143006
$765$		0			0
$766$		−	1.49240e7i		−	0.0332047i
$767$	4.57107e8			1.01305
$768$		0			0
$769$		−	7.56321e8i		−	1.66313i	−0.555425	−	0.831566i	$-0.687444\pi$
$769$		−	7.56321e8i		−	1.66313i	0.555425	−	0.831566i	$-0.312556\pi$
$770$	4.64455e8	−	5.70179e7i	1.01735	−	0.124893i
$771$		0			0
$772$	3.96842e8			0.862513
$773$		−	2.42896e8i		−	0.525875i	−0.964813	−	0.262937i	$-0.915309\pi$
$773$		−	2.42896e8i		−	0.525875i	0.964813	−	0.262937i	$-0.0846913\pi$
$774$		0			0
$775$		−	1.11232e9i		−	2.38960i
$776$			3.07542e7i			0.0658141i
$777$		0			0
$778$	−1.76827e8			−0.375500
$779$	−2.93182e8			−0.620190
$780$		0			0
$781$	5.20418e8			1.09244
$782$		−	2.96794e8i		−	0.620633i
$783$		0			0
$784$	−1.16895e8	+	2.91400e7i	−0.242577	+	0.0604701i
$785$	−9.50219e8			−1.96433
$786$		0			0
$787$			4.68172e8i			0.960465i	0.877141	+	0.480232i	$0.159448\pi$
$787$			4.68172e8i			0.960465i	−0.877141	+	0.480232i	$0.840552\pi$
$788$	1.64272e8			0.335725
$789$		0			0
$790$			6.89162e8i			1.39778i
$791$	1.11481e7	+	9.08098e7i	0.0225253	+	0.183486i
$792$		0			0
$793$	−1.18409e8			−0.237446
$794$		−	1.88794e8i		−	0.377160i
$795$		0			0
$796$			1.96847e7i			0.0390291i
$797$		−	1.00075e8i		−	0.197674i	−0.995104	−	0.0988370i	$-0.968488\pi$
$797$		−	1.00075e8i		−	0.197674i	0.995104	−	0.0988370i	$-0.0315122\pi$
$798$		0			0
$799$	−1.51302e8			−0.296623
$800$	−1.52329e8			−0.297517
$801$		0			0
$802$	2.30119e7			0.0446098
$803$		−	5.46774e8i		−	1.05599i
$804$		0			0
$805$	−6.03133e8	+	7.40424e7i	−1.15618	+	0.141936i
$806$	−3.34899e8			−0.639600
$807$		0			0
$808$		−	2.02412e8i		−	0.383710i
$809$	5.87217e8			1.10906			0.554528	−	0.832165i	$-0.312899\pi$
$809$	5.87217e8			1.10906			0.554528	+	0.832165i	$0.312899\pi$
$810$		0			0
$811$		−	8.86023e8i		−	1.66105i	−0.556983	−	0.830524i	$-0.688041\pi$
$811$		−	8.86023e8i		−	1.66105i	0.556983	−	0.830524i	$-0.311959\pi$
$812$	4.35534e7	+	3.54777e8i	0.0813494	+	0.662654i
$813$		0			0
$814$	2.50391e8			0.464244
$815$		−	1.07820e9i		−	1.99171i
$816$		0			0
$817$			2.88436e8i			0.528912i
$818$		−	2.14396e8i		−	0.391703i
$819$		0			0
$820$	−6.12745e8			−1.11132
$821$	5.51065e8			0.995803			0.497902	−	0.867233i	$-0.334104\pi$
$821$	5.51065e8			0.995803			0.497902	+	0.867233i	$0.334104\pi$
$822$		0			0
$823$	5.33974e8			0.957901			0.478951	−	0.877842i	$-0.341017\pi$
$823$	5.33974e8			0.957901			0.478951	+	0.877842i	$0.341017\pi$
$824$		−	2.17991e8i		−	0.389633i
$825$		0			0
$826$	−6.28961e8	+	7.72131e7i	−1.11605	+	0.137010i
$827$	5.33590e8			0.943390			0.471695	−	0.881762i	$-0.343642\pi$
$827$	5.33590e8			0.943390			0.471695	+	0.881762i	$0.343642\pi$
$828$		0			0
$829$		−	1.11584e9i		−	1.95857i	−0.202476	−	0.979287i	$-0.564899\pi$
$829$		−	1.11584e9i		−	1.95857i	0.202476	−	0.979287i	$-0.435101\pi$
$830$	−7.57619e8			−1.32500
$831$		0			0
$832$			4.58633e7i			0.0796334i
$833$	−1.72553e8	−	6.92199e8i	−0.298530	−	1.19756i
$834$		0			0
$835$	4.08532e8			0.701725
$836$			1.18163e8i			0.202237i
$837$		0			0
$838$		−	4.15357e8i		−	0.705813i
$839$		−	2.23881e8i		−	0.379081i	−0.981873	−	0.189540i	$-0.939300\pi$
$839$		−	2.23881e8i		−	0.379081i	0.981873	−	0.189540i	$-0.0606998\pi$
$840$		0			0
$841$	4.65694e8			0.782912
$842$	3.36075e7			0.0562989
$843$		0			0
$844$	8.20098e7			0.136408
$845$			5.87184e8i			0.973204i
$846$		0			0
$847$	1.60553e7	+	1.30783e8i	0.0264222	+	0.215229i
$848$	−112254.			−0.000184082
$849$		0			0
$850$		−	9.02020e8i		−	1.46879i
$851$	−3.25154e8			−0.527594
$852$		0			0
$853$		−	2.97785e8i		−	0.479795i	−0.970798	−	0.239898i	$-0.922886\pi$
$853$		−	2.97785e8i		−	0.479795i	0.970798	−	0.239898i	$-0.0771139\pi$
$854$	1.62926e8	−	2.00013e7i	0.261587	−	0.0321132i
$855$		0			0
$856$	2.20915e7			0.0352211
$857$			7.86923e8i			1.25023i	0.780533	+	0.625115i	$0.214948\pi$
$857$			7.86923e8i			1.25023i	−0.780533	+	0.625115i	$0.785052\pi$
$858$		0			0
$859$			7.66256e8i			1.20891i	0.796639	+	0.604456i	$0.206609\pi$
$859$			7.66256e8i			1.20891i	−0.796639	+	0.604456i	$0.793391\pi$
$860$			6.02826e8i			0.947757i
$861$		0			0
$862$	−5.42385e8			−0.846811
$863$	1.16650e9			1.81490			0.907452	−	0.420157i	$-0.138025\pi$
$863$	1.16650e9			1.81490			0.907452	+	0.420157i	$0.138025\pi$
$864$		0			0
$865$	4.04061e8			0.624307
$866$			6.97671e8i			1.07423i
$867$		0			0
$868$	4.60807e8	−	5.65700e7i	0.704628	−	0.0865022i
$869$	7.00853e8			1.06799
$870$		0			0
$871$		−	1.55363e8i		−	0.235121i
$872$	2.00229e8			0.301979
$873$		0			0
$874$		−	1.53444e8i		−	0.229835i
$875$	−7.43900e8	+	9.13233e7i	−1.11043	+	0.136319i
$876$		0			0
$877$	7.56442e8			1.12144			0.560721	−	0.828005i	$-0.310524\pi$
$877$	7.56442e8			1.12144			0.560721	+	0.828005i	$0.310524\pi$
$878$		−	3.62985e8i		−	0.536297i
$879$		0			0
$880$			2.46958e8i			0.362389i
$881$			3.69412e8i			0.540235i	0.962827	+	0.270118i	$0.0870626\pi$
$881$			3.69412e8i			0.540235i	−0.962827	+	0.270118i	$0.912937\pi$
$882$		0			0
$883$	−5.87419e8			−0.853230			−0.426615	−	0.904433i	$-0.640294\pi$
$883$	−5.87419e8			−0.853230			−0.426615	+	0.904433i	$0.640294\pi$
$884$	−2.71581e8			−0.393136
$885$		0			0
$886$	3.72632e8			0.535770
$887$		−	2.15522e7i		−	0.0308831i	−0.999881	−	0.0154416i	$-0.995085\pi$
$887$		−	2.15522e7i		−	0.0308831i	0.999881	−	0.0154416i	$-0.00491540\pi$
$888$		0			0
$889$	−5.61856e7	−	4.57675e8i	−0.0799686	−	0.651407i
$890$	3.45521e8			0.490122
$891$		0			0
$892$			2.50361e8i			0.352753i
$893$	−7.82240e7			−0.109846
$894$		0			0
$895$			1.34996e9i			1.88300i
$896$	−7.74708e6	−	6.31060e7i	−0.0107700	−	0.0877297i
$897$		0			0
$898$	5.78163e8			0.798402
$899$		−	1.37747e9i		−	1.89585i
$900$		0			0
$901$		−	664713.i		−	0.000908782i
$902$			6.23140e8i			0.849113i
$903$		0			0
$904$	−4.82849e7			−0.0653591
$905$	−5.34328e8			−0.720879
$906$		0			0
$907$	−1.14115e9			−1.52939			−0.764697	−	0.644390i	$-0.777111\pi$
$907$	−1.14115e9			−1.52939			−0.764697	+	0.644390i	$0.777111\pi$
$908$		−	2.62107e8i		−	0.350124i
$909$		0			0
$910$	6.77524e7	+	5.51896e8i	0.0899085	+	0.732375i
$911$	3.29876e8			0.436310			0.218155	−	0.975914i	$-0.429996\pi$
$911$	3.29876e8			0.436310			0.218155	+	0.975914i	$0.429996\pi$
$912$		0			0
$913$			7.70471e8i			1.01238i
$914$	−3.18131e8			−0.416646
$915$		0			0
$916$			4.17682e8i			0.543449i
$917$	−1.24767e9	+	1.53167e8i	−1.61805	+	0.198636i
$918$		0			0
$919$	−1.10236e8			−0.142029			−0.0710144	−	0.997475i	$-0.522624\pi$
$919$	−1.10236e8			−0.142029			−0.0710144	+	0.997475i	$0.522624\pi$
$920$		−	3.20695e8i		−	0.411840i
$921$		0			0
$922$		−	1.39498e8i		−	0.177982i
$923$			6.18395e8i			0.786432i
$924$		0			0
$925$	−9.88210e8			−1.24860
$926$	1.08588e9			1.36757
$927$		0			0
$928$	−1.88640e8			−0.236042
$929$			4.58674e8i			0.572081i	0.958218	+	0.286040i	$0.0923391\pi$
$929$			4.58674e8i			0.572081i	−0.958218	+	0.286040i	$0.907661\pi$
$930$		0			0
$931$	−8.92109e7	−	3.57870e8i	−0.110553	−	0.443483i
$932$	−4.43197e7			−0.0547456
$933$		0			0
$934$			8.53759e8i			1.04784i
$935$	−1.46237e9			−1.78905
$936$		0			0
$937$			9.98325e8i			1.21354i	0.794878	+	0.606769i	$0.207535\pi$
$937$			9.98325e8i			1.21354i	−0.794878	+	0.606769i	$0.792465\pi$
$938$	2.62433e7	+	2.13772e8i	0.0317988	+	0.259026i
$939$		0			0
$940$	−1.63487e8			−0.196834
$941$			1.08263e9i			1.29930i	0.760231	+	0.649652i	$0.225085\pi$
$941$			1.08263e9i			1.29930i	−0.760231	+	0.649652i	$0.774915\pi$
$942$		0			0
$943$		−	8.09198e8i		−	0.964983i
$944$		−	3.34428e8i		−	0.397545i
$945$		0			0
$946$	6.13053e8			0.724143
$947$	−7.97542e8			−0.939082			−0.469541	−	0.882911i	$-0.655581\pi$
$947$	−7.97542e8			−0.939082			−0.469541	+	0.882911i	$0.655581\pi$
$948$		0			0
$949$	6.49713e8			0.760191
$950$		−	4.66348e8i		−	0.543926i
$951$		0			0
$952$	3.73685e8	−	4.58746e7i	0.433106	−	0.0531694i
$953$	1.15116e9			1.33002			0.665009	−	0.746836i	$-0.268428\pi$
$953$	1.15116e9			1.33002			0.665009	+	0.746836i	$0.268428\pi$
$954$		0			0
$955$		−	4.08043e8i		−	0.468485i
$956$	−1.40020e8			−0.160257
$957$		0			0
$958$		−	2.66107e8i		−	0.302663i
$959$	−1.39178e8	−	1.13371e9i	−0.157803	−	1.28542i
$960$		0			0
$961$	−9.01645e8			−1.01593
$962$			2.97531e8i			0.334201i
$963$		0			0
$964$		−	2.78361e8i		−	0.310726i
$965$			2.53915e9i			2.82557i
$966$		0			0
$967$	−6.50101e8			−0.718954			−0.359477	−	0.933154i	$-0.617045\pi$
$967$	−6.50101e8			−0.718954			−0.359477	+	0.933154i	$0.617045\pi$
$968$	−6.95394e7			−0.0766663
$969$		0			0
$970$	−1.96777e8			−0.215606
$971$		−	4.14091e8i		−	0.452312i	−0.974091	−	0.226156i	$-0.927384\pi$
$971$		−	4.14091e8i		−	0.452312i	0.974091	−	0.226156i	$-0.0726159\pi$
$972$		0			0
$973$	−4.05001e8	+	4.97192e7i	−0.439661	+	0.0539741i
$974$	−2.46647e8			−0.266931
$975$		0			0
$976$			8.66302e7i			0.0931793i
$977$	1.24398e9			1.33392			0.666962	−	0.745091i	$-0.267594\pi$
$977$	1.24398e9			1.33392			0.666962	+	0.745091i	$0.267594\pi$
$978$		0			0
$979$		−	3.51383e8i		−	0.374483i
$980$	−1.86449e8	−	7.47942e8i	−0.198099	−	0.794676i
$981$		0			0
$982$	−4.40262e8			−0.464918
$983$			1.65067e9i			1.73780i	0.494986	+	0.868901i	$0.335173\pi$
$983$			1.65067e9i			1.73780i	−0.494986	+	0.868901i	$0.664827\pi$
$984$		0			0
$985$			1.05107e9i			1.09983i
$986$		−	1.11704e9i		−	1.16530i
$987$		0			0
$988$	−1.40409e8			−0.145587
$989$	−7.96099e8			−0.822959
$990$		0			0
$991$	1.85734e9			1.90841			0.954203	−	0.299159i	$-0.0967060\pi$
$991$	1.85734e9			1.90841			0.954203	+	0.299159i	$0.0967060\pi$
$992$			2.45018e8i			0.250994i
$993$		0			0
$994$	−1.04457e8	−	8.50887e8i	−0.106360	−	0.866388i
$995$	−1.25950e8			−0.127859
$996$		0			0
$997$			1.40620e9i			1.41893i	0.704740	+	0.709466i	$0.251064\pi$
$997$			1.40620e9i			1.41893i	−0.704740	+	0.709466i	$0.748936\pi$
$998$	−3.58498e8			−0.360658
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.7.c.a.55.4		4
3.2	odd	2		14.7.b.a.13.2	yes	4
7.6	odd	2	inner	126.7.c.a.55.3		4
12.11	even	2		112.7.c.c.97.2		4
15.2	even	4		350.7.d.a.349.3		8
15.8	even	4		350.7.d.a.349.6		8
15.14	odd	2		350.7.b.a.251.3		4
21.2	odd	6		98.7.d.b.31.3		8
21.5	even	6		98.7.d.b.31.4		8
21.11	odd	6		98.7.d.b.19.4		8
21.17	even	6		98.7.d.b.19.3		8
21.20	even	2		14.7.b.a.13.1	✓	4
24.5	odd	2		448.7.c.h.321.2		4
24.11	even	2		448.7.c.e.321.3		4
84.83	odd	2		112.7.c.c.97.3		4
105.62	odd	4		350.7.d.a.349.2		8
105.83	odd	4		350.7.d.a.349.7		8
105.104	even	2		350.7.b.a.251.4		4
168.83	odd	2		448.7.c.e.321.2		4
168.125	even	2		448.7.c.h.321.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.7.b.a.13.1	✓	4	21.20	even	2
14.7.b.a.13.2	yes	4	3.2	odd	2
98.7.d.b.19.3		8	21.17	even	6
98.7.d.b.19.4		8	21.11	odd	6
98.7.d.b.31.3		8	21.2	odd	6
98.7.d.b.31.4		8	21.5	even	6
112.7.c.c.97.2		4	12.11	even	2
112.7.c.c.97.3		4	84.83	odd	2
126.7.c.a.55.3		4	7.6	odd	2	inner
126.7.c.a.55.4		4	1.1	even	1	trivial
350.7.b.a.251.3		4	15.14	odd	2
350.7.b.a.251.4		4	105.104	even	2
350.7.d.a.349.2		8	105.62	odd	4
350.7.d.a.349.3		8	15.2	even	4
350.7.d.a.349.6		8	15.8	even	4
350.7.d.a.349.7		8	105.83	odd	4
448.7.c.e.321.2		4	168.83	odd	2
448.7.c.e.321.3		4	24.11	even	2
448.7.c.h.321.2		4	24.5	odd	2
448.7.c.h.321.3		4	168.125	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	126.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.65685 q^{2} +32.0000 q^{4} +204.749i q^{5} +(-41.7939 - 340.444i) q^{7} +181.019 q^{8} +1158.23i q^{10} +1177.88 q^{11} +1399.64i q^{13} +(-236.422 - 1925.84i) q^{14} +1024.00 q^{16} +6063.65i q^{17} +3134.94i q^{19} +6551.96i q^{20} +6663.11 q^{22} -8652.59 q^{23} -26297.0 q^{25} +7917.54i q^{26} +(-1337.41 - 10894.2i) q^{28} -32565.6 q^{29} +42298.3i q^{31} +5792.62 q^{32} +34301.2i q^{34} +(69705.5 - 8557.26i) q^{35} +37578.8 q^{37} +17733.9i q^{38} +37063.5i q^{40} +93520.9i q^{41} +92007.0 q^{43} +37692.2 q^{44} -48946.4 q^{46} +24952.4i q^{47} +(-114156. + 28457.0i) q^{49} -148758. q^{50} +44788.4i q^{52} -109.623 q^{53} +241170. i q^{55} +(-7565.51 - 61627.0i) q^{56} -184219. q^{58} -326590. i q^{59} +84599.8i q^{61} +239276. i q^{62} +32768.0 q^{64} -286574. q^{65} -111002. q^{67} +194037. i q^{68} +(394314. - 48407.1i) q^{70} +441825. q^{71} -464201. i q^{73} +212578. q^{74} +100318. i q^{76} +(-49228.3 - 401003. i) q^{77} +595011. q^{79} +209663. i q^{80} +529034. i q^{82} +654116. i q^{83} -1.24152e6 q^{85} +520470. q^{86} +213219. q^{88} -298317. i q^{89} +(476498. - 58496.3i) q^{91} -276883. q^{92} +141152. i q^{94} -641874. q^{95} +169894. i q^{97} +(-645761. + 160977. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 128 q^{4} + 308 q^{7} + 4440 q^{11} - 2688 q^{14} + 4096 q^{16} + 1536 q^{22} - 40584 q^{23} - 40700 q^{25} + 9856 q^{28} + 18264 q^{29} + 84000 q^{35} - 23192 q^{37} - 44696 q^{43} + 142080 q^{44}+ \cdots - 827904 q^{98}+O(q^{100}) \) 4 * q + 128 * q^4 + 308 * q^7 + 4440 * q^11 - 2688 * q^14 + 4096 * q^16 + 1536 * q^22 - 40584 * q^23 - 40700 * q^25 + 9856 * q^28 + 18264 * q^29 + 84000 * q^35 - 23192 * q^37 - 44696 * q^43 + 142080 * q^44 + 33792 * q^46 - 310268 * q^49 - 364800 * q^50 - 248616 * q^53 - 86016 * q^56 - 840192 * q^58 + 131072 * q^64 - 1293600 * q^65 - 434776 * q^67 + 1102080 * q^70 + 451608 * q^71 + 981504 * q^74 + 309624 * q^77 + 2092904 * q^79 - 2117760 * q^85 + 2334720 * q^86 + 49152 * q^88 - 1109472 * q^91 - 1298688 * q^92 + 190560 * q^95 - 827904 * q^98

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