LMFDB - Embedded newform 315.3.e.e.244.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(244,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("315.244");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 72 x^{14} - 292 x^{13} + 1148 x^{12} - 2304 x^{11} + 4996 x^{10} - 4490 x^{9} + \cdots + 1849 $ x^16 - 8x^15 + 72x^14 - 292x^13 + 1148x^12 - 2304x^11 + 4996x^10 - 4490x^9 + 9786x^8 - 5744x^7 + 8608x^6 + 4740x^5 + 22841x^4 + 22790x^3 + 18930x^2 + 8170*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			244.13
Root			$-0.366025 + 0.842173i$ of defining polynomial
Character	$\chi$	$=$	315.244
Dual form			315.3.e.e.244.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.30086i q^{2} -1.29396 q^{4} +(-3.65761 - 3.40909i) q^{5} +(6.39480 + 2.84720i) q^{7} +6.22623i q^{8} +O(q^{10})$	\(q+2.30086i q^{2} -1.29396 q^{4} +(-3.65761 - 3.40909i) q^{5} +(6.39480 + 2.84720i) q^{7} +6.22623i q^{8} +(7.84383 - 8.41565i) q^{10} +13.9015 q^{11} -3.78588 q^{13} +(-6.55102 + 14.7135i) q^{14} -19.5015 q^{16} +14.8567 q^{17} +6.94906i q^{19} +(4.73278 + 4.41121i) q^{20} +31.9853i q^{22} +40.2857i q^{23} +(1.75623 + 24.9382i) q^{25} -8.71077i q^{26} +(-8.27458 - 3.68415i) q^{28} -9.88885 q^{29} +34.7764i q^{31} -19.9653i q^{32} +34.1833i q^{34} +(-13.6833 - 32.2144i) q^{35} -30.4393i q^{37} -15.9888 q^{38} +(21.2258 - 22.7731i) q^{40} -44.6778i q^{41} +26.0309i q^{43} -17.9879 q^{44} -92.6918 q^{46} +23.7033 q^{47} +(32.7869 + 36.4146i) q^{49} +(-57.3794 + 4.04085i) q^{50} +4.89875 q^{52} -59.5338i q^{53} +(-50.8462 - 47.3914i) q^{55} +(-17.7273 + 39.8155i) q^{56} -22.7529i q^{58} +81.0347i q^{59} -78.8493i q^{61} -80.0155 q^{62} -32.0687 q^{64} +(13.8473 + 12.9064i) q^{65} -29.9557i q^{67} -19.2240 q^{68} +(74.1208 - 31.4834i) q^{70} +117.475 q^{71} -22.2333 q^{73} +70.0365 q^{74} -8.99177i q^{76} +(88.8971 + 39.5803i) q^{77} +142.799 q^{79} +(71.3289 + 66.4823i) q^{80} +102.797 q^{82} -160.872 q^{83} +(-54.3402 - 50.6480i) q^{85} -59.8935 q^{86} +86.5538i q^{88} -66.3844i q^{89} +(-24.2099 - 10.7792i) q^{91} -52.1279i q^{92} +54.5380i q^{94} +(23.6899 - 25.4169i) q^{95} -45.1538 q^{97} +(-83.7849 + 75.4379i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{4}+O(q^{10}) $ 16 * q - 32 * q^4	$ 16 q - 32 q^{4} + 56 q^{11} + 84 q^{14} + 112 q^{16} + 16 q^{25} + 32 q^{29} + 4 q^{35} - 568 q^{44} - 96 q^{46} - 152 q^{49} + 96 q^{50} - 444 q^{56} - 992 q^{64} + 296 q^{65} + 504 q^{70} + 56 q^{71} + 48 q^{74} + 464 q^{79} + 608 q^{85} + 456 q^{86} - 88 q^{91} + 24 q^{95}+O(q^{100}) $ 16 * q - 32 * q^4 + 56 * q^11 + 84 * q^14 + 112 * q^16 + 16 * q^25 + 32 * q^29 + 4 * q^35 - 568 * q^44 - 96 * q^46 - 152 * q^49 + 96 * q^50 - 444 * q^56 - 992 * q^64 + 296 * q^65 + 504 * q^70 + 56 * q^71 + 48 * q^74 + 464 * q^79 + 608 * q^85 + 456 * q^86 - 88 * q^91 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$			2.30086i			1.15043i	0.818002	+	0.575215i	$0.195082\pi$
$2$			2.30086i			1.15043i	−0.818002	+	0.575215i	$0.804918\pi$
$3$		0			0
$3$		0			0
$4$	−1.29396			−0.323489
$5$	−3.65761	−	3.40909i	−0.731522	−	0.681818i
$5$	−3.65761	−	3.40909i	−0.731522	−	0.681818i
$6$		0			0
$7$	6.39480	+	2.84720i	0.913542	+	0.406744i
$7$	6.39480	+	2.84720i	0.913542	+	0.406744i
$8$			6.22623i			0.778279i
$9$		0			0
$10$	7.84383	−	8.41565i	0.784383	−	0.841565i
$11$	13.9015			1.26377			0.631885	−	0.775062i	$-0.282281\pi$
$11$	13.9015			1.26377			0.631885	+	0.775062i	$0.282281\pi$
$12$		0			0
$13$	−3.78588			−0.291221			−0.145611	−	0.989342i	$-0.546515\pi$
$13$	−3.78588			−0.291221			−0.145611	+	0.989342i	$0.546515\pi$
$14$	−6.55102	+	14.7135i	−0.467930	+	1.05097i
$15$		0			0
$16$	−19.5015			−1.21884
$17$	14.8567			0.873926			0.436963	−	0.899479i	$-0.356054\pi$
$17$	14.8567			0.873926			0.436963	+	0.899479i	$0.356054\pi$
$18$		0			0
$19$			6.94906i			0.365740i	0.983137	+	0.182870i	$0.0585387\pi$
$19$			6.94906i			0.365740i	−0.983137	+	0.182870i	$0.941461\pi$
$20$	4.73278	+	4.41121i	0.236639	+	0.220560i
$21$		0			0
$22$			31.9853i			1.45388i
$23$			40.2857i			1.75155i	0.482716	+	0.875777i	$0.339650\pi$
$23$			40.2857i			1.75155i	−0.482716	+	0.875777i	$0.660350\pi$
$24$		0			0
$25$	1.75623	+	24.9382i	0.0702494	+	0.997529i
$26$		−	8.71077i		−	0.335030i
$27$		0			0
$28$	−8.27458	−	3.68415i	−0.295521	−	0.131577i
$29$	−9.88885			−0.340995			−0.170497	−	0.985358i	$-0.554537\pi$
$29$	−9.88885			−0.340995			−0.170497	+	0.985358i	$0.554537\pi$
$30$		0			0
$31$			34.7764i			1.12182i	0.827877	+	0.560909i	$0.189548\pi$
$31$			34.7764i			1.12182i	−0.827877	+	0.560909i	$0.810452\pi$
$32$		−	19.9653i		−	0.623916i
$33$		0			0
$34$			34.1833i			1.00539i
$35$	−13.6833	−	32.2144i	−0.390952	−	0.920411i
$36$		0			0
$37$		−	30.4393i		−	0.822683i	−0.911481	−	0.411342i	$-0.865060\pi$
$37$		−	30.4393i		−	0.822683i	0.911481	−	0.411342i	$-0.134940\pi$
$38$	−15.9888			−0.420758
$39$		0			0
$40$	21.2258	−	22.7731i	0.530644	−	0.569328i
$41$		−	44.6778i		−	1.08970i	−0.838532	−	0.544852i	$-0.816586\pi$
$41$		−	44.6778i		−	1.08970i	0.838532	−	0.544852i	$-0.183414\pi$
$42$		0			0
$43$			26.0309i			0.605370i	0.953091	+	0.302685i	$0.0978831\pi$
$43$			26.0309i			0.605370i	−0.953091	+	0.302685i	$0.902117\pi$
$44$	−17.9879			−0.408816
$45$		0			0
$46$	−92.6918			−2.01504
$47$	23.7033			0.504326			0.252163	−	0.967685i	$-0.418858\pi$
$47$	23.7033			0.504326			0.252163	+	0.967685i	$0.418858\pi$
$48$		0			0
$49$	32.7869	+	36.4146i	0.669119	+	0.743155i
$50$	−57.3794	+	4.04085i	−1.14759	+	0.0808170i
$51$		0			0
$52$	4.89875			0.0942068
$53$		−	59.5338i		−	1.12328i	−0.827382	−	0.561640i	$-0.810171\pi$
$53$		−	59.5338i		−	1.12328i	0.827382	−	0.561640i	$-0.189829\pi$
$54$		0			0
$55$	−50.8462	−	47.3914i	−0.924476	−	0.861661i
$56$	−17.7273	+	39.8155i	−0.316560	+	0.710991i
$57$		0			0
$58$		−	22.7529i		−	0.392291i
$59$			81.0347i			1.37347i	0.726908	+	0.686735i	$0.240957\pi$
$59$			81.0347i			1.37347i	−0.726908	+	0.686735i	$0.759043\pi$
$60$		0			0
$61$		−	78.8493i		−	1.29261i	−0.763079	−	0.646306i	$-0.776313\pi$
$61$		−	78.8493i		−	1.29261i	0.763079	−	0.646306i	$-0.223687\pi$
$62$	−80.0155			−1.29057
$63$		0			0
$64$	−32.0687			−0.501073
$65$	13.8473	+	12.9064i	0.213035	+	0.198560i
$66$		0			0
$67$		−	29.9557i		−	0.447101i	−0.974692	−	0.223550i	$-0.928235\pi$
$67$		−	29.9557i		−	0.447101i	0.974692	−	0.223550i	$-0.0717647\pi$
$68$	−19.2240			−0.282705
$69$		0			0
$70$	74.1208	−	31.4834i	1.05887	−	0.449762i
$71$	117.475			1.65457			0.827286	−	0.561780i	$-0.189883\pi$
$71$	117.475			1.65457			0.827286	+	0.561780i	$0.189883\pi$
$72$		0			0
$73$	−22.2333			−0.304566			−0.152283	−	0.988337i	$-0.548662\pi$
$73$	−22.2333			−0.304566			−0.152283	+	0.988337i	$0.548662\pi$
$74$	70.0365			0.946439
$75$		0			0
$76$		−	8.99177i		−	0.118313i
$77$	88.8971	+	39.5803i	1.15451	+	0.514030i
$78$		0			0
$79$	142.799			1.80758			0.903791	−	0.427974i	$-0.140772\pi$
$79$	142.799			1.80758			0.903791	+	0.427974i	$0.140772\pi$
$80$	71.3289	+	66.4823i	0.891611	+	0.831029i
$81$		0			0
$82$	102.797			1.25363
$83$	−160.872			−1.93822			−0.969108	−	0.246636i	$-0.920675\pi$
$83$	−160.872			−1.93822			−0.969108	+	0.246636i	$0.920675\pi$
$84$		0			0
$85$	−54.3402	−	50.6480i	−0.639296	−	0.595858i
$86$	−59.8935			−0.696436
$87$		0			0
$88$			86.5538i			0.983566i
$89$		−	66.3844i		−	0.745892i	−0.927853	−	0.372946i	$-0.878348\pi$
$89$		−	66.3844i		−	0.745892i	0.927853	−	0.372946i	$-0.121652\pi$
$90$		0			0
$91$	−24.2099	−	10.7792i	−0.266043	−	0.118452i
$92$		−	52.1279i		−	0.566608i
$93$		0			0
$94$			54.5380i			0.580192i
$95$	23.6899	−	25.4169i	0.249368	−	0.267547i
$96$		0			0
$97$	−45.1538			−0.465503			−0.232751	−	0.972536i	$-0.574773\pi$
$97$	−45.1538			−0.465503			−0.232751	+	0.972536i	$0.574773\pi$
$98$	−83.7849	+	75.4379i	−0.854948	+	0.769775i
$99$		0			0
$100$	−2.27249	−	32.2690i	−0.0227249	−	0.322690i
$101$		−	130.221i		−	1.28932i	−0.764471	−	0.644658i	$-0.777000\pi$
$101$		−	130.221i		−	1.28932i	0.764471	−	0.644658i	$-0.223000\pi$
$102$		0			0
$103$	−4.07795			−0.0395917			−0.0197959	−	0.999804i	$-0.506302\pi$
$103$	−4.07795			−0.0395917			−0.0197959	+	0.999804i	$0.506302\pi$
$104$		−	23.5717i		−	0.226651i
$105$		0			0
$106$	136.979			1.29225
$107$			31.3454i			0.292948i	0.989215	+	0.146474i	$0.0467924\pi$
$107$			31.3454i			0.292948i	−0.989215	+	0.146474i	$0.953208\pi$
$108$		0			0
$109$	62.4441			0.572881			0.286441	−	0.958098i	$-0.407528\pi$
$109$	62.4441			0.572881			0.286441	+	0.958098i	$0.407528\pi$
$110$	109.041	−	116.990i	0.991281	−	1.06354i
$111$		0			0
$112$	−124.708	−	55.5248i	−1.11347	−	0.495757i
$113$			61.9010i			0.547796i	0.961759	+	0.273898i	$0.0883131\pi$
$113$			61.9010i			0.547796i	−0.961759	+	0.273898i	$0.911687\pi$
$114$		0			0
$115$	137.338	−	147.350i	1.19424	−	1.28130i
$116$	12.7957			0.110308
$117$		0			0
$118$	−186.450			−1.58008
$119$	95.0059	+	42.3002i	0.798369	+	0.355464i
$120$		0			0
$121$	72.2510			0.597116
$122$	181.421			1.48706
$123$		0			0
$124$		−	44.9990i		−	0.362896i
$125$	78.5930	−	97.2015i	0.628744	−	0.777612i
$126$		0			0
$127$		−	185.310i		−	1.45913i	−0.683910	−	0.729566i	$-0.739722\pi$
$127$		−	185.310i		−	1.45913i	0.683910	−	0.729566i	$-0.260278\pi$
$128$		−	153.647i		−	1.20036i
$129$		0			0
$130$	−29.6958	+	31.8606i	−0.228429	+	0.245082i
$131$			92.8188i			0.708541i	0.935143	+	0.354270i	$0.115271\pi$
$131$			92.8188i			0.708541i	−0.935143	+	0.354270i	$0.884729\pi$
$132$		0			0
$133$	−19.7854	+	44.4378i	−0.148762	+	0.334119i
$134$	68.9240			0.514358
$135$		0			0
$136$			92.5015i			0.680158i
$137$		−	88.9332i		−	0.649147i	−0.945860	−	0.324574i	$-0.894779\pi$
$137$		−	88.9332i		−	0.649147i	0.945860	−	0.324574i	$-0.105221\pi$
$138$		0			0
$139$		−	38.1205i		−	0.274248i	−0.990554	−	0.137124i	$-0.956214\pi$
$139$		−	38.1205i		−	0.274248i	0.990554	−	0.137124i	$-0.0437859\pi$
$140$	17.7056	+	41.6840i	0.126468	+	0.297743i
$141$		0			0
$142$			270.293i			1.90347i
$143$	−52.6293			−0.368037
$144$		0			0
$145$	36.1696	+	33.7120i	0.249445	+	0.232496i
$146$		−	51.1557i		−	0.350381i
$147$		0			0
$148$			39.3871i			0.266129i
$149$	−132.122			−0.886724			−0.443362	−	0.896343i	$-0.646214\pi$
$149$	−132.122			−0.886724			−0.443362	+	0.896343i	$0.646214\pi$
$150$		0			0
$151$	149.537			0.990310			0.495155	−	0.868805i	$-0.335111\pi$
$151$	149.537			0.990310			0.495155	+	0.868805i	$0.335111\pi$
$152$	−43.2664			−0.284647
$153$		0			0
$154$	−91.0688	+	204.540i	−0.591356	+	1.32818i
$155$	118.556	−	127.198i	0.764875	−	0.820635i
$156$		0			0
$157$	−29.5598			−0.188279			−0.0941396	−	0.995559i	$-0.530010\pi$
$157$	−29.5598			−0.188279			−0.0941396	+	0.995559i	$0.530010\pi$
$158$			328.560i			2.07950i
$159$		0			0
$160$	−68.0635	+	73.0253i	−0.425397	+	0.456408i
$161$	−114.702	+	257.619i	−0.712433	+	1.60012i
$162$		0			0
$163$		−	240.158i		−	1.47337i	−0.676239	−	0.736683i	$-0.736391\pi$
$163$		−	240.158i		−	1.47337i	0.676239	−	0.736683i	$-0.263609\pi$
$164$			57.8111i			0.352507i
$165$		0			0
$166$		−	370.144i		−	2.22978i
$167$	−207.335			−1.24153			−0.620764	−	0.783997i	$-0.713178\pi$
$167$	−207.335			−1.24153			−0.620764	+	0.783997i	$0.713178\pi$
$168$		0			0
$169$	−154.667			−0.915190
$170$	116.534	−	125.029i	0.685493	−	0.735466i
$171$		0			0
$172$		−	33.6828i		−	0.195831i
$173$	−68.3717			−0.395212			−0.197606	−	0.980282i	$-0.563317\pi$
$173$	−68.3717			−0.395212			−0.197606	+	0.980282i	$0.563317\pi$
$174$		0			0
$175$	−59.7735	+	164.475i	−0.341563	+	0.939859i
$176$	−271.100			−1.54034
$177$		0			0
$178$	152.741			0.858097
$179$	−142.187			−0.794342			−0.397171	−	0.917745i	$-0.630008\pi$
$179$	−142.187			−0.794342			−0.397171	+	0.917745i	$0.630008\pi$
$180$		0			0
$181$			266.458i			1.47214i	0.676903	+	0.736072i	$0.263322\pi$
$181$			266.458i			1.47214i	−0.676903	+	0.736072i	$0.736678\pi$
$182$	24.8013	−	55.7036i	0.136271	−	0.306064i
$183$		0			0
$184$	−250.828			−1.36320
$185$	−103.770	+	111.335i	−0.560920	+	0.601811i
$186$		0			0
$187$	206.531			1.10444
$188$	−30.6710			−0.163144
$189$		0			0
$190$	58.4808	+	54.5072i	0.307794	+	0.286880i
$191$	32.5201			0.170262			0.0851312	−	0.996370i	$-0.472869\pi$
$191$	32.5201			0.170262			0.0851312	+	0.996370i	$0.472869\pi$
$192$		0			0
$193$		−	106.194i		−	0.550228i	−0.961412	−	0.275114i	$-0.911284\pi$
$193$		−	106.194i		−	0.550228i	0.961412	−	0.275114i	$-0.0887156\pi$
$194$		−	103.892i		−	0.535528i
$195$		0			0
$196$	−42.4247	−	47.1188i	−0.216453	−	0.240402i
$197$		−	75.6061i		−	0.383787i	−0.981416	−	0.191894i	$-0.938537\pi$
$197$		−	75.6061i		−	0.383787i	0.981416	−	0.191894i	$-0.0614629\pi$
$198$		0			0
$199$		−	319.273i		−	1.60439i	−0.597065	−	0.802193i	$-0.703667\pi$
$199$		−	319.273i		−	1.60439i	0.597065	−	0.802193i	$-0.296333\pi$
$200$	−155.271	+	10.9347i	−0.776356	+	0.0546736i
$201$		0			0
$202$	299.620			1.48327
$203$	−63.2372	−	28.1556i	−0.311513	−	0.138697i
$204$		0			0
$205$	−152.311	+	163.414i	−0.742979	+	0.797142i
$206$		−	9.38279i		−	0.0455475i
$207$		0			0
$208$	73.8303			0.354953
$209$			96.6021i			0.462211i
$210$		0			0
$211$	−57.1113			−0.270670			−0.135335	−	0.990800i	$-0.543211\pi$
$211$	−57.1113			−0.270670			−0.135335	+	0.990800i	$0.543211\pi$
$212$			77.0341i			0.363368i
$213$		0			0
$214$	−72.1214			−0.337016
$215$	88.7417	−	95.2110i	0.412752	−	0.442842i
$216$		0			0
$217$	−99.0154	+	222.388i	−0.456292	+	1.02483i
$218$			143.675i			0.659060i
$219$		0			0
$220$	65.7927	+	61.3223i	0.299058	+	0.278738i
$221$	−56.2458			−0.254506
$222$		0			0
$223$	−418.459			−1.87650			−0.938250	−	0.345958i	$-0.887554\pi$
$223$	−418.459			−1.87650			−0.938250	+	0.345958i	$0.887554\pi$
$224$	56.8453	−	127.674i	0.253774	−	0.569973i
$225$		0			0
$226$	−142.425			−0.630201
$227$	195.112			0.859525			0.429762	−	0.902942i	$-0.358597\pi$
$227$	195.112			0.859525			0.429762	+	0.902942i	$0.358597\pi$
$228$		0			0
$229$		−	133.938i		−	0.584883i	−0.956283	−	0.292441i	$-0.905532\pi$
$229$		−	133.938i		−	0.584883i	0.956283	−	0.292441i	$-0.0944676\pi$
$230$	339.031	+	315.995i	1.47405	+	1.37389i
$231$		0			0
$232$		−	61.5703i		−	0.265389i
$233$			72.7709i			0.312321i	0.987732	+	0.156161i	$0.0499117\pi$
$233$			72.7709i			0.312321i	−0.987732	+	0.156161i	$0.950088\pi$
$234$		0			0
$235$	−86.6975	−	80.8067i	−0.368926	−	0.343858i
$236$		−	104.855i		−	0.444302i
$237$		0			0
$238$	−97.3268	+	218.595i	−0.408936	+	0.918467i
$239$	−257.788			−1.07861			−0.539305	−	0.842111i	$-0.681313\pi$
$239$	−257.788			−1.07861			−0.539305	+	0.842111i	$0.681313\pi$
$240$		0			0
$241$			241.558i			1.00231i	0.865357	+	0.501157i	$0.167092\pi$
$241$			241.558i			1.00231i	−0.865357	+	0.501157i	$0.832908\pi$
$242$			166.239i			0.686940i
$243$		0			0
$244$			102.027i			0.418145i
$245$	4.21900	−	244.964i	0.0172204	−	0.999852i
$246$		0			0
$247$		−	26.3083i		−	0.106511i
$248$	−216.526			−0.873087
$249$		0			0
$250$	223.647	+	180.832i	0.894588	+	0.723326i
$251$			202.953i			0.808577i	0.914631	+	0.404289i	$0.132481\pi$
$251$			202.953i			0.808577i	−0.914631	+	0.404289i	$0.867519\pi$
$252$		0			0
$253$			560.031i			2.21356i
$254$	426.372			1.67863
$255$		0			0
$256$	225.245			0.879862
$257$	385.602			1.50040			0.750198	−	0.661214i	$-0.229958\pi$
$257$	385.602			1.50040			0.750198	+	0.661214i	$0.229958\pi$
$258$		0			0
$259$	86.6668	−	194.653i	0.334621	−	0.751556i
$260$	−17.9177	−	16.7003i	−0.0689144	−	0.0642319i
$261$		0			0
$262$	−213.563			−0.815126
$263$		−	117.392i		−	0.446358i	−0.974777	−	0.223179i	$-0.928357\pi$
$263$		−	117.392i		−	0.446358i	0.974777	−	0.223179i	$-0.0716434\pi$
$264$		0			0
$265$	−202.956	+	217.752i	−0.765872	+	0.821704i
$266$	−102.245	−	45.5234i	−0.384380	−	0.171141i
$267$		0			0
$268$			38.7614i			0.144632i
$269$		−	372.769i		−	1.38576i	−0.721054	−	0.692879i	$-0.756342\pi$
$269$		−	372.769i		−	1.38576i	0.721054	−	0.692879i	$-0.243658\pi$
$270$		0			0
$271$			98.6583i			0.364053i	0.983294	+	0.182026i	$0.0582656\pi$
$271$			98.6583i			0.364053i	−0.983294	+	0.182026i	$0.941734\pi$
$272$	−289.729			−1.06518
$273$		0			0
$274$	204.623			0.746798
$275$	24.4143	+	346.678i	0.0887791	+	1.26065i
$276$		0			0
$277$		−	70.1485i		−	0.253244i	−0.991951	−	0.126622i	$-0.959587\pi$
$277$		−	70.1485i		−	0.253244i	0.991951	−	0.126622i	$-0.0404135\pi$
$278$	87.7099			0.315503
$279$		0			0
$280$	200.574	−	85.1954i	0.716336	−	0.304269i
$281$	184.983			0.658303			0.329151	−	0.944277i	$-0.393237\pi$
$281$	184.983			0.658303			0.329151	+	0.944277i	$0.393237\pi$
$282$		0			0
$283$	43.9638			0.155349			0.0776746	−	0.996979i	$-0.475250\pi$
$283$	43.9638			0.155349			0.0776746	+	0.996979i	$0.475250\pi$
$284$	−152.007			−0.535236
$285$		0			0
$286$		−	121.093i		−	0.423401i
$287$	127.207	−	285.706i	0.443230	−	0.995490i
$288$		0			0
$289$	−68.2771			−0.236253
$290$	−77.5665	+	83.2211i	−0.267471	+	0.286969i
$291$		0			0
$292$	28.7689			0.0985236
$293$	192.547			0.657157			0.328579	−	0.944477i	$-0.393430\pi$
$293$	192.547			0.657157			0.328579	+	0.944477i	$0.393430\pi$
$294$		0			0
$295$	276.255	−	296.393i	0.936456	−	1.00472i
$296$	189.522			0.640277
$297$		0			0
$298$		−	303.994i		−	1.02011i
$299$		−	152.517i		−	0.510090i
$300$		0			0
$301$	−74.1154	+	166.462i	−0.246230	+	0.553032i
$302$			344.063i			1.13928i
$303$		0			0
$304$		−	135.517i		−	0.445780i
$305$	−268.804	+	288.400i	−0.881325	+	0.945574i
$306$		0			0
$307$	364.110			1.18603			0.593013	−	0.805193i	$-0.297938\pi$
$307$	364.110			1.18603			0.593013	+	0.805193i	$0.297938\pi$
$308$	−115.029	−	51.2152i	−0.373470	−	0.166283i
$309$		0			0
$310$	292.666	+	272.780i	0.944083	+	0.879935i
$311$		−	400.969i		−	1.28929i	−0.764482	−	0.644645i	$-0.777005\pi$
$311$		−	400.969i		−	1.28929i	0.764482	−	0.644645i	$-0.222995\pi$
$312$		0			0
$313$	353.929			1.13076			0.565381	−	0.824830i	$-0.308729\pi$
$313$	353.929			1.13076			0.565381	+	0.824830i	$0.308729\pi$
$314$		−	68.0130i		−	0.216602i
$315$		0			0
$316$	−184.776			−0.584733
$317$		−	115.117i		−	0.363144i	−0.983378	−	0.181572i	$-0.941881\pi$
$317$		−	115.117i		−	0.363144i	0.983378	−	0.181572i	$-0.0581186\pi$
$318$		0			0
$319$	−137.470			−0.430939
$320$	117.295	+	109.325i	0.366546	+	0.341640i
$321$		0			0
$322$	−592.745	−	263.913i	−1.84082	−	0.819604i
$323$			103.240i			0.319630i
$324$		0			0
$325$	−6.64889	−	94.4131i	−0.0204581	−	0.290502i
$326$	552.571			1.69500
$327$		0			0
$328$	278.174			0.848093
$329$	151.578	+	67.4882i	0.460723	+	0.205131i
$330$		0			0
$331$	−217.808			−0.658031			−0.329016	−	0.944324i	$-0.606717\pi$
$331$	−217.808			−0.658031			−0.329016	+	0.944324i	$0.606717\pi$
$332$	208.161			0.626991
$333$		0			0
$334$		−	477.049i		−	1.42829i
$335$	−102.122	+	109.566i	−0.304841	+	0.327064i
$336$		0			0
$337$			257.680i			0.764629i	0.924032	+	0.382315i	$0.124873\pi$
$337$			257.680i			0.764629i	−0.924032	+	0.382315i	$0.875127\pi$
$338$		−	355.867i		−	1.05286i
$339$		0			0
$340$	70.3138	+	65.5362i	0.206805	+	0.192753i
$341$			483.443i			1.41772i
$342$		0			0
$343$	105.985	+	326.215i	0.308996	+	0.951063i
$344$	−162.075			−0.471147
$345$		0			0
$346$		−	157.314i		−	0.454664i
$347$			87.2838i			0.251538i	0.992060	+	0.125769i	$0.0401399\pi$
$347$			87.2838i			0.251538i	−0.992060	+	0.125769i	$0.959860\pi$
$348$		0			0
$349$		−	31.2851i		−	0.0896421i	−0.998995	−	0.0448211i	$-0.985728\pi$
$349$		−	31.2851i		−	0.0896421i	0.998995	−	0.0448211i	$-0.0142718\pi$
$350$	−378.435	−	137.530i	−1.08124	−	0.392944i
$351$		0			0
$352$		−	277.547i		−	0.788486i
$353$	−174.245			−0.493611			−0.246806	−	0.969065i	$-0.579381\pi$
$353$	−174.245			−0.493611			−0.246806	+	0.969065i	$0.579381\pi$
$354$		0			0
$355$	−429.677	−	400.482i	−1.21036	−	1.12812i
$356$			85.8984i			0.241288i
$357$		0			0
$358$		−	327.153i		−	0.913835i
$359$	−251.691			−0.701089			−0.350545	−	0.936546i	$-0.614004\pi$
$359$	−251.691			−0.701089			−0.350545	+	0.936546i	$0.614004\pi$
$360$		0			0
$361$	312.711			0.866234
$362$	−613.083			−1.69360
$363$		0			0
$364$	31.3265	+	13.9478i	0.0860619	+	0.0383180i
$365$	81.3207	+	75.7953i	0.222797	+	0.207658i
$366$		0			0
$367$	−356.321			−0.970903			−0.485451	−	0.874264i	$-0.661345\pi$
$367$	−356.321			−0.970903			−0.485451	+	0.874264i	$0.661345\pi$
$368$		−	785.632i		−	2.13487i
$369$		0			0
$370$	−256.166	−	238.761i	−0.692341	−	0.645299i
$371$	169.505	−	380.707i	0.456887	−	1.02616i
$372$		0			0
$373$		−	611.275i		−	1.63881i	−0.573217	−	0.819404i	$-0.694305\pi$
$373$		−	611.275i		−	1.63881i	0.573217	−	0.819404i	$-0.305695\pi$
$374$			475.198i			1.27058i
$375$		0			0
$376$			147.582i			0.392506i
$377$	37.4380			0.0993050
$378$		0			0
$379$	157.934			0.416713			0.208356	−	0.978053i	$-0.433189\pi$
$379$	157.934			0.416713			0.208356	+	0.978053i	$0.433189\pi$
$380$	−30.6537	+	32.8884i	−0.0806677	+	0.0865484i
$381$		0			0
$382$			74.8243i			0.195875i
$383$	330.386			0.862626			0.431313	−	0.902202i	$-0.358050\pi$
$383$	330.386			0.862626			0.431313	+	0.902202i	$0.358050\pi$
$384$		0			0
$385$	−190.218	−	447.828i	−0.494073	−	1.16319i
$386$	244.337			0.632999
$387$		0			0
$388$	58.4269			0.150585
$389$	43.6493			0.112209			0.0561046	−	0.998425i	$-0.482132\pi$
$389$	43.6493			0.112209			0.0561046	+	0.998425i	$0.482132\pi$
$390$		0			0
$391$			598.515i			1.53073i
$392$	−226.726	+	204.138i	−0.578382	+	0.520761i
$393$		0			0
$394$	173.959			0.441520
$395$	−522.303	−	486.814i	−1.32229	−	1.23244i
$396$		0			0
$397$	436.537			1.09959			0.549795	−	0.835299i	$-0.314706\pi$
$397$	436.537			1.09959			0.549795	+	0.835299i	$0.314706\pi$
$398$	734.602			1.84573
$399$		0			0
$400$	−34.2492	−	486.333i	−0.0856230	−	1.21583i
$401$	−662.494			−1.65210			−0.826052	−	0.563593i	$-0.809419\pi$
$401$	−662.494			−1.65210			−0.826052	+	0.563593i	$0.809419\pi$
$402$		0			0
$403$		−	131.659i		−	0.326697i
$404$			168.500i			0.417079i
$405$		0			0
$406$	64.7820	−	145.500i	0.159562	−	0.358374i
$407$		−	423.151i		−	1.03968i
$408$		0			0
$409$			6.80523i			0.0166387i	0.999965	+	0.00831936i	$0.00264816\pi$
$409$			6.80523i			0.0166387i	−0.999965	+	0.00831936i	$0.997352\pi$
$410$	−375.993	−	350.446i	−0.917056	−	0.854745i
$411$		0			0
$412$	5.27668			0.0128075
$413$	−230.722	+	518.201i	−0.558650	+	1.25472i
$414$		0			0
$415$	588.407	+	548.427i	1.41785	+	1.32151i
$416$			75.5862i			0.181697i
$417$		0			0
$418$	−222.268			−0.531742
$419$			560.059i			1.33666i	0.743867	+	0.668328i	$0.232990\pi$
$419$			560.059i			1.33666i	−0.743867	+	0.668328i	$0.767010\pi$
$420$		0			0
$421$	−374.770			−0.890191			−0.445095	−	0.895483i	$-0.646830\pi$
$421$	−374.770			−0.890191			−0.445095	+	0.895483i	$0.646830\pi$
$422$		−	131.405i		−	0.311387i
$423$		0			0
$424$	370.671			0.874225
$425$	26.0919	+	370.501i	0.0613928	+	0.871767i
$426$		0			0
$427$	224.500	−	504.225i	0.525761	−	1.18086i
$428$		−	40.5596i		−	0.0947653i
$429$		0			0
$430$	219.067	+	204.182i	0.509458	+	0.474842i
$431$	710.190			1.64777			0.823887	−	0.566755i	$-0.191801\pi$
$431$	710.190			1.64777			0.823887	+	0.566755i	$0.191801\pi$
$432$		0			0
$433$	−131.951			−0.304736			−0.152368	−	0.988324i	$-0.548690\pi$
$433$	−131.951			−0.304736			−0.152368	+	0.988324i	$0.548690\pi$
$434$	−511.683	−	227.821i	−1.17899	−	0.524932i
$435$		0			0
$436$	−80.7998			−0.185321
$437$	−279.948			−0.640613
$438$		0			0
$439$			792.806i			1.80594i	0.429707	+	0.902968i	$0.358617\pi$
$439$			792.806i			1.80594i	−0.429707	+	0.902968i	$0.641383\pi$
$440$	295.069	−	316.580i	0.670612	−	0.719500i
$441$		0			0
$442$		−	129.414i		−	0.292791i
$443$		−	302.328i		−	0.682457i	−0.939980	−	0.341228i	$-0.889157\pi$
$443$		−	302.328i		−	0.682457i	0.939980	−	0.341228i	$-0.110843\pi$
$444$		0			0
$445$	−226.310	+	242.808i	−0.508562	+	0.545637i
$446$		−	962.816i		−	2.15878i
$447$		0			0
$448$	−205.073	−	91.3060i	−0.457751	−	0.203808i
$449$	72.8787			0.162313			0.0811567	−	0.996701i	$-0.474139\pi$
$449$	72.8787			0.162313			0.0811567	+	0.996701i	$0.474139\pi$
$450$		0			0
$451$		−	621.088i		−	1.37713i
$452$		−	80.0971i		−	0.177206i
$453$		0			0
$454$			448.926i			0.988823i
$455$	51.8033	+	121.960i	0.113853	+	0.268043i
$456$		0			0
$457$			501.515i			1.09741i	0.836017	+	0.548703i	$0.184878\pi$
$457$			501.515i			1.09741i	−0.836017	+	0.548703i	$0.815122\pi$
$458$	308.173			0.672867
$459$		0			0
$460$	−177.709	+	190.664i	−0.386323	+	0.414486i
$461$			225.746i			0.489688i	0.969562	+	0.244844i	$0.0787368\pi$
$461$			225.746i			0.489688i	−0.969562	+	0.244844i	$0.921263\pi$
$462$		0			0
$463$			200.854i			0.433810i	0.976193	+	0.216905i	$0.0695963\pi$
$463$			200.854i			0.433810i	−0.976193	+	0.216905i	$0.930404\pi$
$464$	192.847			0.415619
$465$		0			0
$466$	−167.436			−0.359304
$467$	−146.079			−0.312804			−0.156402	−	0.987694i	$-0.549990\pi$
$467$	−146.079			−0.312804			−0.156402	+	0.987694i	$0.549990\pi$
$468$		0			0
$469$	85.2901	−	191.561i	0.181855	−	0.408445i
$470$	185.925	−	199.479i	0.395585	−	0.424423i
$471$		0			0
$472$	−504.541			−1.06894
$473$			361.868i			0.765049i
$474$		0			0
$475$	−173.297	+	12.2042i	−0.364836	+	0.0256930i
$476$	−122.933	−	54.7346i	−0.258263	−	0.114989i
$477$		0			0
$478$		−	593.133i		−	1.24086i
$479$		−	609.973i		−	1.27343i	−0.771099	−	0.636715i	$-0.780293\pi$
$479$		−	609.973i		−	1.27343i	0.771099	−	0.636715i	$-0.219707\pi$
$480$		0			0
$481$			115.239i			0.239583i
$482$	−555.790			−1.15309
$483$		0			0
$484$	−93.4896			−0.193160
$485$	165.155	+	153.933i	0.340526	+	0.317388i
$486$		0			0
$487$			806.827i			1.65673i	0.560189	+	0.828365i	$0.310728\pi$
$487$			806.827i			1.65673i	−0.560189	+	0.828365i	$0.689272\pi$
$488$	490.934			1.00601
$489$		0			0
$490$	563.627	+	9.70732i	1.15026	+	0.0198109i
$491$	369.272			0.752081			0.376040	−	0.926603i	$-0.377285\pi$
$491$	369.272			0.752081			0.376040	+	0.926603i	$0.377285\pi$
$492$		0			0
$493$	−146.916			−0.298004
$494$	60.5316			0.122534
$495$		0			0
$496$		−	678.191i		−	1.36732i
$497$	751.227	+	334.474i	1.51152	+	0.672987i
$498$		0			0
$499$	417.437			0.836547			0.418274	−	0.908321i	$-0.362635\pi$
$499$	417.437			0.836547			0.418274	+	0.908321i	$0.362635\pi$
$500$	−101.696	+	125.774i	−0.203392	+	0.251549i
$501$		0			0
$502$	−466.966			−0.930212
$503$	577.214			1.14754			0.573771	−	0.819016i	$-0.305480\pi$
$503$	577.214			1.14754			0.573771	+	0.819016i	$0.305480\pi$
$504$		0			0
$505$	−443.934	+	476.297i	−0.879078	+	0.943163i
$506$	−1288.55			−2.54655
$507$		0			0
$508$			239.783i			0.472013i
$509$			241.834i			0.475116i	0.971373	+	0.237558i	$0.0763469\pi$
$509$			241.834i			0.475116i	−0.971373	+	0.237558i	$0.923653\pi$
$510$		0			0
$511$	−142.177	−	63.3027i	−0.278234	−	0.123880i
$512$		−	96.3300i		−	0.188145i
$513$		0			0
$514$			887.215i			1.72610i
$515$	14.9155	+	13.9021i	0.0289622	+	0.0269943i
$516$		0			0
$517$	329.511			0.637352
$518$	447.869	+	199.408i	0.864612	+	0.384958i
$519$		0			0
$520$	−80.3581	+	86.2162i	−0.154535	+	0.165800i
$521$			811.283i			1.55716i	0.627543	+	0.778582i	$0.284061\pi$
$521$			811.283i			1.55716i	−0.627543	+	0.778582i	$0.715939\pi$
$522$		0			0
$523$	−50.9274			−0.0973755			−0.0486878	−	0.998814i	$-0.515504\pi$
$523$	−50.9274			−0.0973755			−0.0486878	+	0.998814i	$0.515504\pi$
$524$		−	120.103i		−	0.229205i
$525$		0			0
$526$	270.103			0.513503
$527$			516.664i			0.980386i
$528$		0			0
$529$	−1093.94			−2.06794
$530$	−501.016	−	466.974i	−0.945313	−	0.881082i
$531$		0			0
$532$	25.6014	−	57.5005i	0.0481229	−	0.108084i
$533$			169.145i			0.317345i
$534$		0			0
$535$	106.859	−	114.649i	0.199737	−	0.214298i
$536$	186.511			0.347969
$537$		0			0
$538$	857.688			1.59422
$539$	455.786	+	506.217i	0.845613	+	0.939177i
$540$		0			0
$541$	222.529			0.411329			0.205665	−	0.978623i	$-0.434064\pi$
$541$	222.529			0.411329			0.205665	+	0.978623i	$0.434064\pi$
$542$	−226.999			−0.418817
$543$		0			0
$544$		−	296.619i		−	0.545256i
$545$	−228.396	−	212.877i	−0.419075	−	0.390601i
$546$		0			0
$547$		−	489.442i		−	0.894775i	−0.894340	−	0.447387i	$-0.852355\pi$
$547$		−	489.442i		−	0.894775i	0.894340	−	0.447387i	$-0.147645\pi$
$548$			115.076i			0.209992i
$549$		0			0
$550$	−797.658	+	56.1738i	−1.45029	+	0.102134i
$551$		−	68.7182i		−	0.124715i
$552$		0			0
$553$	913.171	+	406.578i	1.65130	+	0.735222i
$554$	161.402			0.291339
$555$		0			0
$556$			49.3262i			0.0887162i
$557$			489.578i			0.878955i	0.898254	+	0.439478i	$0.144836\pi$
$557$			489.578i			0.878955i	−0.898254	+	0.439478i	$0.855164\pi$
$558$		0			0
$559$		−	98.5499i		−	0.176297i
$560$	266.845	+	628.229i	0.476509	+	1.12184i
$561$		0			0
$562$			425.620i			0.757331i
$563$	301.482			0.535492			0.267746	−	0.963490i	$-0.413721\pi$
$563$	301.482			0.535492			0.267746	+	0.963490i	$0.413721\pi$
$564$		0			0
$565$	211.026	−	226.410i	0.373497	−	0.400725i
$566$			101.155i			0.178718i
$567$		0			0
$568$			731.424i			1.28772i
$569$	847.144			1.48883			0.744415	−	0.667718i	$-0.232729\pi$
$569$	847.144			1.48883			0.744415	+	0.667718i	$0.232729\pi$
$570$		0			0
$571$	−220.035			−0.385350			−0.192675	−	0.981263i	$-0.561716\pi$
$571$	−220.035			−0.385350			−0.192675	+	0.981263i	$0.561716\pi$
$572$	68.0999			0.119056
$573$		0			0
$574$	657.369	+	292.685i	1.14524	+	0.509905i
$575$	−1004.66	+	70.7512i	−1.74723	+	0.123046i
$576$		0			0
$577$	772.580			1.33896			0.669480	−	0.742830i	$-0.266517\pi$
$577$	772.580			1.33896			0.669480	+	0.742830i	$0.266517\pi$
$578$		−	157.096i		−	0.271792i
$579$		0			0
$580$	−46.8018	−	43.6218i	−0.0806928	−	0.0752099i
$581$	−1028.74	−	458.035i	−1.77064	−	0.788357i
$582$		0			0
$583$		−	827.608i		−	1.41957i
$584$		−	138.430i		−	0.237037i
$585$		0			0
$586$			443.024i			0.756013i
$587$	−258.261			−0.439967			−0.219984	−	0.975504i	$-0.570600\pi$
$587$	−258.261			−0.439967			−0.219984	+	0.975504i	$0.570600\pi$
$588$		0			0
$589$	−241.663			−0.410294
$590$	681.960	+	635.623i	1.15586	+	1.07733i
$591$		0			0
$592$			593.612i			1.00272i
$593$	−502.713			−0.847745			−0.423873	−	0.905722i	$-0.639330\pi$
$593$	−502.713			−0.847745			−0.423873	+	0.905722i	$0.639330\pi$
$594$		0			0
$595$	−203.289	−	478.601i	−0.341663	−	0.804372i
$596$	170.960			0.286845
$597$		0			0
$598$	350.920			0.586823
$599$	122.194			0.203997			0.101998	−	0.994785i	$-0.467476\pi$
$599$	122.194			0.203997			0.101998	+	0.994785i	$0.467476\pi$
$600$		0			0
$601$		−	703.680i		−	1.17085i	−0.810727	−	0.585424i	$-0.800928\pi$
$601$		−	703.680i		−	1.17085i	0.810727	−	0.585424i	$-0.199072\pi$
$602$	−383.007	−	170.529i	−0.636224	−	0.283271i
$603$		0			0
$604$	−193.494			−0.320354
$605$	−264.266	−	246.310i	−0.436804	−	0.407124i
$606$		0			0
$607$	−1031.87			−1.69995			−0.849976	−	0.526821i	$-0.823384\pi$
$607$	−1031.87			−1.69995			−0.849976	+	0.526821i	$0.823384\pi$
$608$	138.740			0.228191
$609$		0			0
$610$	−663.568	−	618.481i	−1.08782	−	1.01390i
$611$	−89.7379			−0.146870
$612$		0			0
$613$			78.3530i			0.127819i	0.997956	+	0.0639094i	$0.0203569\pi$
$613$			78.3530i			0.127819i	−0.997956	+	0.0639094i	$0.979643\pi$
$614$			837.766i			1.36444i
$615$		0			0
$616$	−246.436	+	553.494i	−0.400059	+	0.898529i
$617$		−	450.989i		−	0.730938i	−0.930823	−	0.365469i	$-0.880909\pi$
$617$		−	450.989i		−	0.730938i	0.930823	−	0.365469i	$-0.119091\pi$
$618$		0			0
$619$			574.725i			0.928473i	0.885711	+	0.464237i	$0.153671\pi$
$619$			574.725i			0.928473i	−0.885711	+	0.464237i	$0.846329\pi$
$620$	−153.406	+	164.589i	−0.247429	+	0.265466i
$621$		0			0
$622$	922.574			1.48324
$623$	189.010	−	424.515i	0.303387	−	0.681404i
$624$		0			0
$625$	−618.831	+	87.5948i	−0.990130	+	0.140152i
$626$			814.340i			1.30086i
$627$		0			0
$628$	38.2491			0.0609062
$629$		−	452.229i		−	0.718964i
$630$		0			0
$631$	1094.51			1.73456			0.867279	−	0.497823i	$-0.165867\pi$
$631$	1094.51			1.73456			0.867279	+	0.497823i	$0.165867\pi$
$632$			889.099i			1.40680i
$633$		0			0
$634$	264.867			0.417772
$635$	−631.737	+	677.791i	−0.994862	+	1.06739i
$636$		0			0
$637$	−124.127	−	137.861i	−0.194862	−	0.216423i
$638$		−	316.298i		−	0.495765i
$639$		0			0
$640$	−523.795	+	561.980i	−0.818430	+	0.878093i
$641$	−145.856			−0.227544			−0.113772	−	0.993507i	$-0.536293\pi$
$641$	−145.856			−0.227544			−0.113772	+	0.993507i	$0.536293\pi$
$642$		0			0
$643$	42.9913			0.0668605			0.0334302	−	0.999441i	$-0.489357\pi$
$643$	42.9913			0.0668605			0.0334302	+	0.999441i	$0.489357\pi$
$644$	148.419	−	333.348i	0.230464	−	0.517620i
$645$		0			0
$646$	−237.542			−0.367711
$647$	832.962			1.28742			0.643711	−	0.765269i	$-0.277394\pi$
$647$	832.962			1.28742			0.643711	+	0.765269i	$0.277394\pi$
$648$		0			0
$649$			1126.50i			1.73575i
$650$	217.231	−	15.2982i	0.334202	−	0.0235356i
$651$		0			0
$652$			310.754i			0.476617i
$653$		−	1209.46i		−	1.85217i	−0.377319	−	0.926083i	$-0.623154\pi$
$653$		−	1209.46i		−	1.85217i	0.377319	−	0.926083i	$-0.376846\pi$
$654$		0			0
$655$	316.428	−	339.495i	0.483096	−	0.518313i
$656$			871.285i			1.32818i
$657$		0			0
$658$	−155.281	+	348.760i	−0.235989	+	0.530030i
$659$	−370.831			−0.562718			−0.281359	−	0.959603i	$-0.590785\pi$
$659$	−370.831			−0.562718			−0.281359	+	0.959603i	$0.590785\pi$
$660$		0			0
$661$		−	1199.95i		−	1.81536i	−0.419663	−	0.907680i	$-0.637852\pi$
$661$		−	1199.95i		−	1.81536i	0.419663	−	0.907680i	$-0.362148\pi$
$662$		−	501.146i		−	0.757019i
$663$		0			0
$664$		−	1001.63i		−	1.50847i
$665$	223.860	−	95.0861i	0.336631	−	0.142987i
$666$		0			0
$667$		−	398.380i		−	0.597271i
$668$	268.282			0.401620
$669$		0			0
$670$	−252.097	−	234.968i	−0.376264	−	0.350698i
$671$		−	1096.12i		−	1.63356i
$672$		0			0
$673$			826.484i			1.22806i	0.789283	+	0.614030i	$0.210452\pi$
$673$			826.484i			1.22806i	−0.789283	+	0.614030i	$0.789548\pi$
$674$	−592.886			−0.879653
$675$		0			0
$676$	200.132			0.296054
$677$	122.010			0.180221			0.0901106	−	0.995932i	$-0.471278\pi$
$677$	122.010			0.180221			0.0901106	+	0.995932i	$0.471278\pi$
$678$		0			0
$679$	−288.749	−	128.562i	−0.425256	−	0.189340i
$680$	315.346	−	338.335i	0.463744	−	0.497551i
$681$		0			0
$682$	−1112.33			−1.63099
$683$		−	185.065i		−	0.270960i	−0.990780	−	0.135480i	$-0.956742\pi$
$683$		−	185.065i		−	0.270960i	0.990780	−	0.135480i	$-0.0432576\pi$
$684$		0			0
$685$	−303.181	+	325.283i	−0.442600	+	0.474866i
$686$	−750.574	+	243.858i	−1.09413	+	0.355478i
$687$		0			0
$688$		−	507.642i		−	0.737852i
$689$			225.388i			0.327123i
$690$		0			0
$691$			1052.60i			1.52329i	0.647993	+	0.761647i	$0.275609\pi$
$691$			1052.60i			1.52329i	−0.647993	+	0.761647i	$0.724391\pi$
$692$	88.4699			0.127847
$693$		0			0
$694$	−200.828			−0.289377
$695$	−129.956	+	139.430i	−0.186987	+	0.200619i
$696$		0			0
$697$		−	663.767i		−	0.952320i
$698$	71.9826			0.103127
$699$		0			0
$700$	77.3442	−	212.824i	0.110492	−	0.304034i
$701$	−658.867			−0.939896			−0.469948	−	0.882694i	$-0.655727\pi$
$701$	−658.867			−0.939896			−0.469948	+	0.882694i	$0.655727\pi$
$702$		0			0
$703$	211.524			0.300888
$704$	−445.802			−0.633241
$705$		0			0
$706$		−	400.913i		−	0.567865i
$707$	370.765	−	832.736i	0.524421	−	1.17784i
$708$		0			0
$709$	−277.453			−0.391331			−0.195665	−	0.980671i	$-0.562687\pi$
$709$	−277.453			−0.391331			−0.195665	+	0.980671i	$0.562687\pi$
$710$	921.452	−	988.626i	1.29782	−	1.39243i
$711$		0			0
$712$	413.325			0.580512
$713$	−1400.99			−1.96492
$714$		0			0
$715$	192.497	+	179.418i	0.269227	+	0.250934i
$716$	183.984			0.256961
$717$		0			0
$718$		−	579.106i		−	0.806554i
$719$		−	159.264i		−	0.221507i	−0.993848	−	0.110753i	$-0.964674\pi$
$719$		−	159.264i		−	0.221507i	0.993848	−	0.110753i	$-0.0353264\pi$
$720$		0			0
$721$	−26.0777	−	11.6108i	−0.0361687	−	0.0161037i
$722$			719.503i			0.996542i
$723$		0			0
$724$		−	344.785i		−	0.476222i
$725$	−17.3671	−	246.610i	−0.0239547	−	0.340152i
$726$		0			0
$727$	−1259.85			−1.73295			−0.866473	−	0.499224i	$-0.833618\pi$
$727$	−1259.85			−1.73295			−0.866473	+	0.499224i	$0.833618\pi$
$728$	67.1136	−	150.736i	0.0921889	−	0.207056i
$729$		0			0
$730$	−174.394	+	187.108i	−0.238896	+	0.256312i
$731$			386.735i			0.529049i
$732$		0			0
$733$	−1204.99			−1.64391			−0.821955	−	0.569552i	$-0.807117\pi$
$733$	−1204.99			−1.64391			−0.821955	+	0.569552i	$0.807117\pi$
$734$		−	819.845i		−	1.11696i
$735$		0			0
$736$	804.317			1.09282
$737$		−	416.429i		−	0.565033i
$738$		0			0
$739$	400.880			0.542463			0.271232	−	0.962514i	$-0.412569\pi$
$739$	400.880			0.542463			0.271232	+	0.962514i	$0.412569\pi$
$740$	134.274	−	144.063i	0.181451	−	0.194679i
$741$		0			0
$742$	875.953	+	390.007i	1.18053	+	0.525616i
$743$			22.1088i			0.0297561i	0.999889	+	0.0148780i	$0.00473600\pi$
$743$			22.1088i			0.0297561i	−0.999889	+	0.0148780i	$0.995264\pi$
$744$		0			0
$745$	483.250	+	450.415i	0.648658	+	0.604584i
$746$	1406.46			1.88533
$747$		0			0
$748$	−267.241			−0.357275
$749$	−89.2468	+	200.448i	−0.119155	+	0.267620i
$750$		0			0
$751$	−616.731			−0.821213			−0.410606	−	0.911813i	$-0.634683\pi$
$751$	−616.731			−0.821213			−0.410606	+	0.911813i	$0.634683\pi$
$752$	−462.250			−0.614695
$753$		0			0
$754$			86.1395i			0.114243i
$755$	−546.947	−	509.784i	−0.724434	−	0.675211i
$756$		0			0
$757$		−	1153.11i		−	1.52326i	−0.648011	−	0.761631i	$-0.724399\pi$
$757$		−	1153.11i		−	1.52326i	0.648011	−	0.761631i	$-0.275601\pi$
$758$			363.384i			0.479399i
$759$		0			0
$760$	158.252	+	147.499i	0.208226	+	0.194078i
$761$		−	974.653i		−	1.28075i	−0.768061	−	0.640377i	$-0.778778\pi$
$761$		−	974.653i		−	1.28075i	0.768061	−	0.640377i	$-0.221222\pi$
$762$		0			0
$763$	399.317	+	177.791i	0.523351	+	0.233016i
$764$	−42.0796			−0.0550780
$765$		0			0
$766$			760.172i			0.992391i
$767$		−	306.787i		−	0.399984i
$768$		0			0
$769$			436.595i			0.567744i	0.958862	+	0.283872i	$0.0916191\pi$
$769$			436.595i			0.567744i	−0.958862	+	0.283872i	$0.908381\pi$
$770$	1030.39	−	437.665i	1.33817	−	0.568396i
$771$		0			0
$772$			137.410i			0.177993i
$773$	852.655			1.10305			0.551524	−	0.834159i	$-0.314047\pi$
$773$	852.655			1.10305			0.551524	+	0.834159i	$0.314047\pi$
$774$		0			0
$775$	−867.261	+	61.0755i	−1.11905	+	0.0788070i
$776$		−	281.138i		−	0.362291i
$777$		0			0
$778$			100.431i			0.129089i
$779$	310.469			0.398548
$780$		0			0
$781$	1633.07			2.09100
$782$	−1377.10			−1.76100
$783$		0			0
$784$	−639.393	−	710.139i	−0.815552	−	0.905790i
$785$	108.118	+	100.772i	0.137730	+	0.128372i
$786$		0			0
$787$	853.855			1.08495			0.542474	−	0.840072i	$-0.317488\pi$
$787$	853.855			1.08495			0.542474	+	0.840072i	$0.317488\pi$
$788$			97.8309i			0.124151i
$789$		0			0
$790$	1120.09	−	1201.75i	1.41784	−	1.52120i
$791$	−176.245	+	395.844i	−0.222812	+	0.500435i
$792$		0			0
$793$			298.514i			0.376436i
$794$			1004.41i			1.26500i
$795$		0			0
$796$			413.125i			0.519001i
$797$	364.023			0.456741			0.228371	−	0.973574i	$-0.426660\pi$
$797$	364.023			0.456741			0.228371	+	0.973574i	$0.426660\pi$
$798$		0			0
$799$	352.154			0.440744
$800$	497.899	−	35.0638i	0.622374	−	0.0438297i
$801$		0			0
$802$		−	1524.31i		−	1.90063i
$803$	−309.076			−0.384901
$804$		0			0
$805$	1297.78	−	551.242i	1.61215	−	0.684773i
$806$	302.929			0.375842
$807$		0			0
$808$	810.785			1.00345
$809$	−1240.40			−1.53325			−0.766623	−	0.642097i	$-0.778064\pi$
$809$	−1240.40			−1.53325			−0.766623	+	0.642097i	$0.778064\pi$
$810$		0			0
$811$		−	468.274i		−	0.577403i	−0.957419	−	0.288701i	$-0.906777\pi$
$811$		−	468.274i		−	0.577403i	0.957419	−	0.288701i	$-0.0932235\pi$
$812$	81.8261	+	36.4321i	0.100771	+	0.0448671i
$813$		0			0
$814$	973.611			1.19608
$815$	−818.722	+	878.406i	−1.00457	+	1.07780i
$816$		0			0
$817$	−180.890			−0.221408
$818$	−15.6579			−0.0191417
$819$		0			0
$820$	197.083	−	211.451i	0.240345	−	0.257867i
$821$	542.526			0.660811			0.330406	−	0.943839i	$-0.392814\pi$
$821$	542.526			0.660811			0.330406	+	0.943839i	$0.392814\pi$
$822$		0			0
$823$		−	719.260i		−	0.873948i	−0.899474	−	0.436974i	$-0.856050\pi$
$823$		−	719.260i		−	0.873948i	0.899474	−	0.436974i	$-0.143950\pi$
$824$		−	25.3902i		−	0.0308134i
$825$		0			0
$826$	−1192.31	−	530.860i	−1.44347	−	0.642688i
$827$			668.223i			0.808008i	0.914757	+	0.404004i	$0.132382\pi$
$827$			668.223i			0.808008i	−0.914757	+	0.404004i	$0.867618\pi$
$828$		0			0
$829$		−	122.101i		−	0.147287i	−0.997285	−	0.0736437i	$-0.976537\pi$
$829$		−	122.101i		−	0.147287i	0.997285	−	0.0736437i	$-0.0234628\pi$
$830$	−1261.85	+	1353.84i	−1.52030	+	1.63113i
$831$		0			0
$832$	121.408			0.145923
$833$	487.106	+	541.002i	0.584761	+	0.649463i
$834$		0			0
$835$	758.351	+	706.824i	0.908205	+	0.846496i
$836$		−	124.999i		−	0.149520i
$837$		0			0
$838$	−1288.62			−1.53773
$839$		−	215.223i		−	0.256524i	−0.991740	−	0.128262i	$-0.959060\pi$
$839$		−	215.223i		−	0.256524i	0.991740	−	0.128262i	$-0.0409398\pi$
$840$		0			0
$841$	−743.211			−0.883723
$842$		−	862.294i		−	1.02410i
$843$		0			0
$844$	73.8995			0.0875587
$845$	565.712	+	527.274i	0.669482	+	0.623993i
$846$		0			0
$847$	462.031	+	205.713i	0.545491	+	0.242873i
$848$			1161.00i			1.36910i
$849$		0			0
$850$	−852.471	+	60.0339i	−1.00291	+	0.0706281i
$851$	1226.27			1.44097
$852$		0			0
$853$	−732.200			−0.858382			−0.429191	−	0.903214i	$-0.641201\pi$
$853$	−732.200			−0.858382			−0.429191	+	0.903214i	$0.641201\pi$
$854$	1160.15	+	516.543i	1.35849	+	0.604851i
$855$		0			0
$856$	−195.164			−0.227995
$857$	−239.155			−0.279061			−0.139530	−	0.990218i	$-0.544559\pi$
$857$	−239.155			−0.279061			−0.139530	+	0.990218i	$0.544559\pi$
$858$		0			0
$859$		−	1157.68i		−	1.34770i	−0.738867	−	0.673851i	$-0.764639\pi$
$859$		−	1157.68i		−	1.34770i	0.738867	−	0.673851i	$-0.235361\pi$
$860$	−114.828	+	123.199i	−0.133521	+	0.143254i
$861$		0			0
$862$			1634.05i			1.89565i
$863$			25.5880i			0.0296500i	0.999890	+	0.0148250i	$0.00471912\pi$
$863$			25.5880i			0.0296500i	−0.999890	+	0.0148250i	$0.995281\pi$
$864$		0			0
$865$	250.077	+	233.085i	0.289106	+	0.269462i
$866$		−	303.600i		−	0.350578i
$867$		0			0
$868$	128.121	−	287.760i	0.147605	−	0.331520i
$869$	1985.12			2.28437
$870$		0			0
$871$			113.409i			0.130205i
$872$			388.791i			0.445861i
$873$		0			0
$874$		−	644.121i		−	0.736980i
$875$	779.339	−	397.814i	0.890673	−	0.454644i
$876$		0			0
$877$			289.049i			0.329589i	0.986328	+	0.164794i	$0.0526960\pi$
$877$			289.049i			0.329589i	−0.986328	+	0.164794i	$0.947304\pi$
$878$	−1824.14			−2.07760
$879$		0			0
$880$	991.577	+	924.203i	1.12679	+	1.05023i
$881$			700.483i			0.795100i	0.917580	+	0.397550i	$0.130140\pi$
$881$			700.483i			0.795100i	−0.917580	+	0.397550i	$0.869860\pi$
$882$		0			0
$883$		−	1412.32i		−	1.59946i	−0.600362	−	0.799729i	$-0.704977\pi$
$883$		−	1412.32i		−	1.59946i	0.600362	−	0.799729i	$-0.295023\pi$
$884$	72.7796			0.0823298
$885$		0			0
$886$	695.615			0.785119
$887$	505.344			0.569722			0.284861	−	0.958569i	$-0.408052\pi$
$887$	505.344			0.569722			0.284861	+	0.958569i	$0.408052\pi$
$888$		0			0
$889$	527.615	−	1185.02i	0.593493	−	1.33298i
$890$	−558.668	−	520.708i	−0.627717	−	0.585065i
$891$		0			0
$892$	541.468			0.607027
$893$			164.716i			0.184452i
$894$		0			0
$895$	520.066	+	484.729i	0.581079	+	0.541597i
$896$	437.463	−	982.539i	0.488240	−	1.09658i
$897$		0			0
$898$			167.684i			0.186730i
$899$		−	343.898i		−	0.382534i
$900$		0			0
$901$		−	884.479i		−	0.981664i
$902$	1429.04			1.58430
$903$		0			0
$904$	−385.410			−0.426338
$905$	908.379	−	974.600i	1.00373	−	1.07691i
$906$		0			0
$907$			696.108i			0.767484i	0.923440	+	0.383742i	$0.125365\pi$
$907$			696.108i			0.767484i	−0.923440	+	0.383742i	$0.874635\pi$
$908$	−252.466			−0.278047
$909$		0			0
$910$	−280.612	+	119.192i	−0.308365	+	0.130980i
$911$	214.709			0.235685			0.117843	−	0.993032i	$-0.462402\pi$
$911$	214.709			0.235685			0.117843	+	0.993032i	$0.462402\pi$
$912$		0			0
$913$	−2236.36			−2.44946
$914$	−1153.92			−1.26249
$915$		0			0
$916$			173.310i			0.189203i
$917$	−264.274	+	593.558i	−0.288194	+	0.647282i
$918$		0			0
$919$	−564.974			−0.614771			−0.307385	−	0.951585i	$-0.599454\pi$
$919$	−564.974			−0.614771			−0.307385	+	0.951585i	$0.599454\pi$
$920$	917.432	+	855.096i	0.997209	+	0.929452i
$921$		0			0
$922$	−519.411			−0.563352
$923$	−444.745			−0.481847
$924$		0			0
$925$	759.102	−	53.4585i	0.820651	−	0.0577930i
$926$	−462.137			−0.499068
$927$		0			0
$928$			197.434i			0.212752i
$929$		−	1302.09i		−	1.40160i	−0.713356	−	0.700802i	$-0.752826\pi$
$929$		−	1302.09i		−	1.40160i	0.713356	−	0.700802i	$-0.247174\pi$
$930$		0			0
$931$	−253.047	+	227.838i	−0.271801	+	0.244724i
$932$		−	94.1622i		−	0.101032i
$933$		0			0
$934$		−	336.108i		−	0.359859i
$935$	−755.409	−	704.081i	−0.807924	−	0.753028i
$936$		0			0
$937$	−226.044			−0.241242			−0.120621	−	0.992699i	$-0.538489\pi$
$937$	−226.044			−0.241242			−0.120621	+	0.992699i	$0.538489\pi$
$938$	440.755	+	196.241i	0.469888	+	0.209212i
$939$		0			0
$940$	112.183	+	104.560i	0.119343	+	0.111234i
$941$		−	415.187i		−	0.441219i	−0.975362	−	0.220610i	$-0.929195\pi$
$941$		−	415.187i		−	0.441219i	0.975362	−	0.220610i	$-0.0708047\pi$
$942$		0			0
$943$	1799.88			1.90867
$944$		−	1580.30i		−	1.67405i
$945$		0			0
$946$	−832.608			−0.880135
$947$		−	483.972i		−	0.511058i	−0.966801	−	0.255529i	$-0.917750\pi$
$947$		−	483.972i		−	0.511058i	0.966801	−	0.255529i	$-0.0822496\pi$
$948$		0			0
$949$	84.1725			0.0886960
$950$	−28.0801	−	398.733i	−0.0295580	−	0.419718i
$951$		0			0
$952$	−263.371	+	591.528i	−0.276650	+	0.621353i
$953$			1028.28i			1.07899i	0.841989	+	0.539495i	$0.181385\pi$
$953$			1028.28i			1.07899i	−0.841989	+	0.539495i	$0.818615\pi$
$954$		0			0
$955$	−118.946	−	110.864i	−0.124551	−	0.116088i
$956$	333.566			0.348918
$957$		0			0
$958$	1403.46			1.46499
$959$	253.211	−	568.709i	0.264036	−	0.593023i
$960$		0			0
$961$	−248.395			−0.258476
$962$	−265.150			−0.275623
$963$		0			0
$964$		−	312.565i		−	0.324237i
$965$	−362.025	+	388.416i	−0.375155	+	0.402504i
$966$		0			0
$967$		−	1470.69i		−	1.52088i	−0.649407	−	0.760441i	$-0.724983\pi$
$967$		−	1470.69i		−	1.52088i	0.649407	−	0.760441i	$-0.275017\pi$
$968$			449.851i			0.464723i
$969$		0			0
$970$	−354.179	+	379.998i	−0.365133	+	0.391751i
$971$			1218.45i			1.25484i	0.778680	+	0.627422i	$0.215890\pi$
$971$			1218.45i			1.25484i	−0.778680	+	0.627422i	$0.784110\pi$
$972$		0			0
$973$	108.537	−	243.773i	0.111549	−	0.250537i
$974$	−1856.40			−1.90595
$975$		0			0
$976$			1537.68i			1.57549i
$977$		−	183.273i		−	0.187587i	−0.995592	−	0.0937936i	$-0.970101\pi$
$977$		−	183.273i		−	0.187587i	0.995592	−	0.0937936i	$-0.0298994\pi$
$978$		0			0
$979$		−	922.841i		−	0.942637i
$980$	−5.45919	+	316.972i	−0.00557061	+	0.323441i
$981$		0			0
$982$			849.642i			0.865216i
$983$	973.748			0.990588			0.495294	−	0.868725i	$-0.335060\pi$
$983$	973.748			0.990588			0.495294	+	0.868725i	$0.335060\pi$
$984$		0			0
$985$	−257.748	+	276.538i	−0.261673	+	0.280749i
$986$		−	338.033i		−	0.342833i
$987$		0			0
$988$			34.0417i			0.0344552i
$989$	−1048.68			−1.06034
$990$		0			0
$991$	−1177.71			−1.18841			−0.594205	−	0.804313i	$-0.702533\pi$
$991$	−1177.71			−1.18841			−0.594205	+	0.804313i	$0.702533\pi$
$992$	694.320			0.699920
$993$		0			0
$994$	−769.579	+	1728.47i	−0.774224	+	1.73890i
$995$	−1088.43	+	1167.78i	−1.09390	+	1.17364i
$996$		0			0
$997$	703.562			0.705679			0.352839	−	0.935684i	$-0.385216\pi$
$997$	703.562			0.705679			0.352839	+	0.935684i	$0.385216\pi$
$998$			960.464i			0.962389i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.e.e.244.13		16
3.2	odd	2		105.3.e.a.34.4	yes	16
5.4	even	2	inner	315.3.e.e.244.4		16
7.6	odd	2	inner	315.3.e.e.244.14		16
12.11	even	2		1680.3.bd.c.769.6		16
15.2	even	4		525.3.h.e.76.13		16
15.8	even	4		525.3.h.e.76.4		16
15.14	odd	2		105.3.e.a.34.13	yes	16
21.20	even	2		105.3.e.a.34.3	✓	16
35.34	odd	2	inner	315.3.e.e.244.3		16
60.59	even	2		1680.3.bd.c.769.12		16
84.83	odd	2		1680.3.bd.c.769.11		16
105.62	odd	4		525.3.h.e.76.14		16
105.83	odd	4		525.3.h.e.76.3		16
105.104	even	2		105.3.e.a.34.14	yes	16
420.419	odd	2		1680.3.bd.c.769.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.e.a.34.3	✓	16	21.20	even	2
105.3.e.a.34.4	yes	16	3.2	odd	2
105.3.e.a.34.13	yes	16	15.14	odd	2
105.3.e.a.34.14	yes	16	105.104	even	2
315.3.e.e.244.3		16	35.34	odd	2	inner
315.3.e.e.244.4		16	5.4	even	2	inner
315.3.e.e.244.13		16	1.1	even	1	trivial
315.3.e.e.244.14		16	7.6	odd	2	inner
525.3.h.e.76.3		16	105.83	odd	4
525.3.h.e.76.4		16	15.8	even	4
525.3.h.e.76.13		16	15.2	even	4
525.3.h.e.76.14		16	105.62	odd	4
1680.3.bd.c.769.5		16	420.419	odd	2
1680.3.bd.c.769.6		16	12.11	even	2
1680.3.bd.c.769.11		16	84.83	odd	2
1680.3.bd.c.769.12		16	60.59	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.30086i q^{2} -1.29396 q^{4} +(-3.65761 - 3.40909i) q^{5} +(6.39480 + 2.84720i) q^{7} +6.22623i q^{8} +O(q^{10})\)	\(q+2.30086i q^{2} -1.29396 q^{4} +(-3.65761 - 3.40909i) q^{5} +(6.39480 + 2.84720i) q^{7} +6.22623i q^{8} +(7.84383 - 8.41565i) q^{10} +13.9015 q^{11} -3.78588 q^{13} +(-6.55102 + 14.7135i) q^{14} -19.5015 q^{16} +14.8567 q^{17} +6.94906i q^{19} +(4.73278 + 4.41121i) q^{20} +31.9853i q^{22} +40.2857i q^{23} +(1.75623 + 24.9382i) q^{25} -8.71077i q^{26} +(-8.27458 - 3.68415i) q^{28} -9.88885 q^{29} +34.7764i q^{31} -19.9653i q^{32} +34.1833i q^{34} +(-13.6833 - 32.2144i) q^{35} -30.4393i q^{37} -15.9888 q^{38} +(21.2258 - 22.7731i) q^{40} -44.6778i q^{41} +26.0309i q^{43} -17.9879 q^{44} -92.6918 q^{46} +23.7033 q^{47} +(32.7869 + 36.4146i) q^{49} +(-57.3794 + 4.04085i) q^{50} +4.89875 q^{52} -59.5338i q^{53} +(-50.8462 - 47.3914i) q^{55} +(-17.7273 + 39.8155i) q^{56} -22.7529i q^{58} +81.0347i q^{59} -78.8493i q^{61} -80.0155 q^{62} -32.0687 q^{64} +(13.8473 + 12.9064i) q^{65} -29.9557i q^{67} -19.2240 q^{68} +(74.1208 - 31.4834i) q^{70} +117.475 q^{71} -22.2333 q^{73} +70.0365 q^{74} -8.99177i q^{76} +(88.8971 + 39.5803i) q^{77} +142.799 q^{79} +(71.3289 + 66.4823i) q^{80} +102.797 q^{82} -160.872 q^{83} +(-54.3402 - 50.6480i) q^{85} -59.8935 q^{86} +86.5538i q^{88} -66.3844i q^{89} +(-24.2099 - 10.7792i) q^{91} -52.1279i q^{92} +54.5380i q^{94} +(23.6899 - 25.4169i) q^{95} -45.1538 q^{97} +(-83.7849 + 75.4379i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4}+O(q^{10}) \) 16 * q - 32 * q^4	\( 16 q - 32 q^{4} + 56 q^{11} + 84 q^{14} + 112 q^{16} + 16 q^{25} + 32 q^{29} + 4 q^{35} - 568 q^{44} - 96 q^{46} - 152 q^{49} + 96 q^{50} - 444 q^{56} - 992 q^{64} + 296 q^{65} + 504 q^{70} + 56 q^{71} + 48 q^{74} + 464 q^{79} + 608 q^{85} + 456 q^{86} - 88 q^{91} + 24 q^{95}+O(q^{100}) \) 16 * q - 32 * q^4 + 56 * q^11 + 84 * q^14 + 112 * q^16 + 16 * q^25 + 32 * q^29 + 4 * q^35 - 568 * q^44 - 96 * q^46 - 152 * q^49 + 96 * q^50 - 444 * q^56 - 992 * q^64 + 296 * q^65 + 504 * q^70 + 56 * q^71 + 48 * q^74 + 464 * q^79 + 608 * q^85 + 456 * q^86 - 88 * q^91 + 24 * q^95

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