LMFDB - Embedded newform 630.3.h.e.559.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,3,Mod(559,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, 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("630.559");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	630.h (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:	$17.1662566547$
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} + 96 x^{14} - 532 x^{13} + 3236 x^{12} - 12864 x^{11} + 49526 x^{10} - 141436 x^{9} + \cdots + 33750 $ x^16 - 8x^15 + 96x^14 - 532x^13 + 3236x^12 - 12864x^11 + 49526x^10 - 141436x^9 + 362298x^8 - 722060x^7 + 1208164x^6 - 1570812x^5 + 1591101x^4 - 1183860x^3 + 619650x^2 - 202500*x + 33750
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			559.15
Root			$0.500000 - 2.68650i$ of defining polynomial
Character	$\chi$	$=$	630.559
Dual form			630.3.h.e.559.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -2.00000 q^{4} +(4.59769 - 1.96501i) q^{5} +(-6.81963 + 1.57881i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+1.41421i q^{2} -2.00000 q^{4} +(4.59769 - 1.96501i) q^{5} +(-6.81963 + 1.57881i) q^{7} -2.82843i q^{8} +(2.77894 + 6.50212i) q^{10} +8.15965 q^{11} -14.6064 q^{13} +(-2.23278 - 9.64441i) q^{14} +4.00000 q^{16} +5.81421 q^{17} +33.7736i q^{19} +(-9.19538 + 3.93001i) q^{20} +11.5395i q^{22} +37.2576i q^{23} +(17.2775 - 18.0690i) q^{25} -20.6566i q^{26} +(13.6393 - 3.15763i) q^{28} +9.25305 q^{29} -19.2558i q^{31} +5.65685i q^{32} +8.22253i q^{34} +(-28.2522 + 20.6595i) q^{35} +63.4350i q^{37} -47.7631 q^{38} +(-5.55788 - 13.0042i) q^{40} -8.25880i q^{41} +42.0893i q^{43} -16.3193 q^{44} -52.6901 q^{46} +23.3380 q^{47} +(44.0147 - 21.5339i) q^{49} +(25.5534 + 24.4341i) q^{50} +29.2128 q^{52} +71.3497i q^{53} +(37.5155 - 16.0337i) q^{55} +(4.46556 + 19.2888i) q^{56} +13.0858i q^{58} +42.9350i q^{59} -34.2864i q^{61} +27.2318 q^{62} -8.00000 q^{64} +(-67.1557 + 28.7017i) q^{65} +4.99889i q^{67} -11.6284 q^{68} +(-29.2170 - 39.9546i) q^{70} +38.8120 q^{71} -124.629 q^{73} -89.7107 q^{74} -67.5472i q^{76} +(-55.6458 + 12.8826i) q^{77} -56.1842 q^{79} +(18.3908 - 7.86002i) q^{80} +11.6797 q^{82} -90.3980 q^{83} +(26.7319 - 11.4249i) q^{85} -59.5233 q^{86} -23.0790i q^{88} -16.2289i q^{89} +(99.6102 - 23.0608i) q^{91} -74.5151i q^{92} +33.0048i q^{94} +(66.3653 + 155.280i) q^{95} -82.7605 q^{97} +(30.4535 + 62.2462i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{4}+O(q^{10}) $ 16 * q - 32 * q^4	$ 16 q - 32 q^{4} - 96 q^{11} - 16 q^{14} + 64 q^{16} + 24 q^{25} - 64 q^{29} + 8 q^{35} + 192 q^{44} - 176 q^{46} + 224 q^{49} + 96 q^{50} + 32 q^{56} - 128 q^{64} - 368 q^{65} - 56 q^{70} + 384 q^{71} - 224 q^{74} - 608 q^{79} - 440 q^{85} - 416 q^{86} + 224 q^{91} + 560 q^{95}+O(q^{100}) $ 16 * q - 32 * q^4 - 96 * q^11 - 16 * q^14 + 64 * q^16 + 24 * q^25 - 64 * q^29 + 8 * q^35 + 192 * q^44 - 176 * q^46 + 224 * q^49 + 96 * q^50 + 32 * q^56 - 128 * q^64 - 368 * q^65 - 56 * q^70 + 384 * q^71 - 224 * q^74 - 608 * q^79 - 440 * q^85 - 416 * q^86 + 224 * q^91 + 560 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$		0			0
$3$		0			0
$4$	−2.00000			−0.500000
$5$	4.59769	−	1.96501i	0.919538	−	0.393001i
$5$	4.59769	−	1.96501i	0.919538	−	0.393001i
$6$		0			0
$7$	−6.81963	+	1.57881i	−0.974233	+	0.225545i
$7$	−6.81963	+	1.57881i	−0.974233	+	0.225545i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	2.77894	+	6.50212i	0.277894	+	0.650212i
$11$	8.15965			0.741786			0.370893	−	0.928676i	$-0.379052\pi$
$11$	8.15965			0.741786			0.370893	+	0.928676i	$0.379052\pi$
$12$		0			0
$13$	−14.6064			−1.12357			−0.561785	−	0.827284i	$-0.689885\pi$
$13$	−14.6064			−1.12357			−0.561785	+	0.827284i	$0.689885\pi$
$14$	−2.23278	−	9.64441i	−0.159484	−	0.688887i
$15$		0			0
$16$	4.00000			0.250000
$17$	5.81421			0.342012			0.171006	−	0.985270i	$-0.445298\pi$
$17$	5.81421			0.342012			0.171006	+	0.985270i	$0.445298\pi$
$18$		0			0
$19$			33.7736i			1.77756i	0.458337	+	0.888778i	$0.348445\pi$
$19$			33.7736i			1.77756i	−0.458337	+	0.888778i	$0.651555\pi$
$20$	−9.19538	+	3.93001i	−0.459769	+	0.196501i
$21$		0			0
$22$			11.5395i			0.524522i
$23$			37.2576i			1.61989i	0.586503	+	0.809947i	$0.300504\pi$
$23$			37.2576i			1.61989i	−0.586503	+	0.809947i	$0.699496\pi$
$24$		0			0
$25$	17.2775	−	18.0690i	0.691100	−	0.722759i
$26$		−	20.6566i		−	0.794483i
$27$		0			0
$28$	13.6393	−	3.15763i	0.487116	−	0.112772i
$29$	9.25305			0.319071			0.159535	−	0.987192i	$-0.449000\pi$
$29$	9.25305			0.319071			0.159535	+	0.987192i	$0.449000\pi$
$30$		0			0
$31$		−	19.2558i		−	0.621154i	−0.950548	−	0.310577i	$-0.899478\pi$
$31$		−	19.2558i		−	0.621154i	0.950548	−	0.310577i	$-0.100522\pi$
$32$			5.65685i			0.176777i
$33$		0			0
$34$			8.22253i			0.241839i
$35$	−28.2522	+	20.6595i	−0.807205	+	0.590272i
$36$		0			0
$37$			63.4350i			1.71446i	0.514933	+	0.857230i	$0.327817\pi$
$37$			63.4350i			1.71446i	−0.514933	+	0.857230i	$0.672183\pi$
$38$	−47.7631			−1.25692
$39$		0			0
$40$	−5.55788	−	13.0042i	−0.138947	−	0.325106i
$41$		−	8.25880i		−	0.201434i	−0.994915	−	0.100717i	$-0.967886\pi$
$41$		−	8.25880i		−	0.201434i	0.994915	−	0.100717i	$-0.0321137\pi$
$42$		0			0
$43$			42.0893i			0.978822i	0.872053	+	0.489411i	$0.162788\pi$
$43$			42.0893i			0.978822i	−0.872053	+	0.489411i	$0.837212\pi$
$44$	−16.3193			−0.370893
$45$		0			0
$46$	−52.6901			−1.14544
$47$	23.3380			0.496552			0.248276	−	0.968689i	$-0.420136\pi$
$47$	23.3380			0.496552			0.248276	+	0.968689i	$0.420136\pi$
$48$		0			0
$49$	44.0147	−	21.5339i	0.898259	−	0.439466i
$50$	25.5534	+	24.4341i	0.511068	+	0.488682i
$51$		0			0
$52$	29.2128			0.561785
$53$			71.3497i			1.34622i	0.739542	+	0.673110i	$0.235042\pi$
$53$			71.3497i			1.34622i	−0.739542	+	0.673110i	$0.764958\pi$
$54$		0			0
$55$	37.5155	−	16.0337i	0.682100	−	0.291523i
$56$	4.46556	+	19.2888i	0.0797422	+	0.344443i
$57$		0			0
$58$			13.0858i			0.225617i
$59$			42.9350i			0.727712i	0.931455	+	0.363856i	$0.118540\pi$
$59$			42.9350i			0.727712i	−0.931455	+	0.363856i	$0.881460\pi$
$60$		0			0
$61$		−	34.2864i		−	0.562072i	−0.959697	−	0.281036i	$-0.909322\pi$
$61$		−	34.2864i		−	0.562072i	0.959697	−	0.281036i	$-0.0906781\pi$
$62$	27.2318			0.439222
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−67.1557	+	28.7017i	−1.03316	+	0.441564i
$66$		0			0
$67$			4.99889i			0.0746102i	0.999304	+	0.0373051i	$0.0118773\pi$
$67$			4.99889i			0.0746102i	−0.999304	+	0.0373051i	$0.988123\pi$
$68$	−11.6284			−0.171006
$69$		0			0
$70$	−29.2170	−	39.9546i	−0.417385	−	0.570780i
$71$	38.8120			0.546648			0.273324	−	0.961922i	$-0.411877\pi$
$71$	38.8120			0.546648			0.273324	+	0.961922i	$0.411877\pi$
$72$		0			0
$73$	−124.629			−1.70725			−0.853626	−	0.520886i	$-0.825602\pi$
$73$	−124.629			−1.70725			−0.853626	+	0.520886i	$0.825602\pi$
$74$	−89.7107			−1.21231
$75$		0			0
$76$		−	67.5472i		−	0.888778i
$77$	−55.6458	+	12.8826i	−0.722672	+	0.167306i
$78$		0			0
$79$	−56.1842			−0.711192			−0.355596	−	0.934640i	$-0.615722\pi$
$79$	−56.1842			−0.711192			−0.355596	+	0.934640i	$0.615722\pi$
$80$	18.3908	−	7.86002i	0.229884	−	0.0982503i
$81$		0			0
$82$	11.6797			0.142435
$83$	−90.3980			−1.08913			−0.544566	−	0.838718i	$-0.683306\pi$
$83$	−90.3980			−1.08913			−0.544566	+	0.838718i	$0.683306\pi$
$84$		0			0
$85$	26.7319	−	11.4249i	0.314493	−	0.134411i
$86$	−59.5233			−0.692131
$87$		0			0
$88$		−	23.0790i		−	0.262261i
$89$		−	16.2289i		−	0.182347i	−0.995835	−	0.0911736i	$-0.970938\pi$
$89$		−	16.2289i		−	0.182347i	0.995835	−	0.0911736i	$-0.0290618\pi$
$90$		0			0
$91$	99.6102	−	23.0608i	1.09462	−	0.253415i
$92$		−	74.5151i		−	0.809947i
$93$		0			0
$94$			33.0048i			0.351115i
$95$	66.3653	+	155.280i	0.698582	+	1.63453i
$96$		0			0
$97$	−82.7605			−0.853201			−0.426601	−	0.904440i	$-0.640289\pi$
$97$	−82.7605			−0.853201			−0.426601	+	0.904440i	$0.640289\pi$
$98$	30.4535	+	62.2462i	0.310750	+	0.635165i
$99$		0			0
$100$	−34.5550	+	36.1379i	−0.345550	+	0.361379i
$101$			87.2055i			0.863420i	0.902012	+	0.431710i	$0.142090\pi$
$101$			87.2055i			0.863420i	−0.902012	+	0.431710i	$0.857910\pi$
$102$		0			0
$103$	187.567			1.82104			0.910521	−	0.413462i	$-0.135681\pi$
$103$	187.567			1.82104			0.910521	+	0.413462i	$0.135681\pi$
$104$			41.3131i			0.397242i
$105$		0			0
$106$	−100.904			−0.951922
$107$		−	157.858i		−	1.47531i	−0.675180	−	0.737653i	$-0.735934\pi$
$107$		−	157.858i		−	1.47531i	0.675180	−	0.737653i	$-0.264066\pi$
$108$		0			0
$109$	−112.073			−1.02819			−0.514097	−	0.857732i	$-0.671873\pi$
$109$	−112.073			−1.02819			−0.514097	+	0.857732i	$0.671873\pi$
$110$	22.6751	+	53.0550i	0.206138	+	0.482318i
$111$		0			0
$112$	−27.2785	+	6.31526i	−0.243558	+	0.0563862i
$113$		−	141.987i		−	1.25653i	−0.778001	−	0.628263i	$-0.783766\pi$
$113$		−	141.987i		−	1.25653i	0.778001	−	0.628263i	$-0.216234\pi$
$114$		0			0
$115$	73.2113	+	171.299i	0.636620	+	1.48955i
$116$	−18.5061			−0.159535
$117$		0			0
$118$	−60.7192			−0.514570
$119$	−39.6507	+	9.17955i	−0.333199	+	0.0771391i
$120$		0			0
$121$	−54.4202			−0.449754
$122$	48.4883			0.397445
$123$		0			0
$124$			38.5116i			0.310577i
$125$	43.9310	−	117.026i	0.351448	−	0.936207i
$126$		0			0
$127$			202.414i			1.59381i	0.604104	+	0.796905i	$0.293531\pi$
$127$			202.414i			1.59381i	−0.604104	+	0.796905i	$0.706469\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		0			0
$130$	−40.5903	−	94.9725i	−0.312233	−	0.730558i
$131$		−	141.260i		−	1.07832i	−0.842203	−	0.539160i	$-0.818742\pi$
$131$		−	141.260i		−	1.07832i	0.842203	−	0.539160i	$-0.181258\pi$
$132$		0			0
$133$	−53.3222	−	230.323i	−0.400919	−	1.73175i
$134$	−7.06949			−0.0527574
$135$		0			0
$136$		−	16.4451i		−	0.120920i
$137$			50.6430i			0.369657i	0.982771	+	0.184829i	$0.0591730\pi$
$137$			50.6430i			0.369657i	−0.982771	+	0.184829i	$0.940827\pi$
$138$		0			0
$139$			74.0256i			0.532559i	0.963896	+	0.266279i	$0.0857943\pi$
$139$			74.0256i			0.532559i	−0.963896	+	0.266279i	$0.914206\pi$
$140$	56.5043	−	41.3190i	0.403602	−	0.295136i
$141$		0			0
$142$			54.8885i			0.386538i
$143$	−119.183			−0.833448
$144$		0			0
$145$	42.5426	−	18.1823i	0.293397	−	0.125395i
$146$		−	176.253i		−	1.20721i
$147$		0			0
$148$		−	126.870i		−	0.857230i
$149$	226.979			1.52335			0.761676	−	0.647958i	$-0.224377\pi$
$149$	226.979			1.52335			0.761676	+	0.647958i	$0.224377\pi$
$150$		0			0
$151$	294.426			1.94984			0.974920	−	0.222558i	$-0.0714406\pi$
$151$	294.426			1.94984			0.974920	+	0.222558i	$0.0714406\pi$
$152$	95.5261			0.628461
$153$		0			0
$154$	−18.2187	−	78.6950i	−0.118303	−	0.511006i
$155$	−37.8377	−	88.5321i	−0.244114	−	0.571175i
$156$		0			0
$157$	65.8596			0.419488			0.209744	−	0.977756i	$-0.432737\pi$
$157$	65.8596			0.419488			0.209744	+	0.977756i	$0.432737\pi$
$158$		−	79.4564i		−	0.502889i
$159$		0			0
$160$	11.1158	+	26.0085i	0.0694734	+	0.162553i
$161$	−58.8227	−	254.083i	−0.365359	−	1.57815i
$162$		0			0
$163$			28.2075i			0.173052i	0.996250	+	0.0865260i	$0.0275766\pi$
$163$			28.2075i			0.173052i	−0.996250	+	0.0865260i	$0.972423\pi$
$164$			16.5176i			0.100717i
$165$		0			0
$166$		−	127.842i		−	0.770133i
$167$	128.461			0.769227			0.384614	−	0.923078i	$-0.374335\pi$
$167$	128.461			0.769227			0.384614	+	0.923078i	$0.374335\pi$
$168$		0			0
$169$	44.3469			0.262408
$170$	16.1573	+	37.8046i	0.0950431	+	0.222380i
$171$		0			0
$172$		−	84.1786i		−	0.489411i
$173$	112.446			0.649976			0.324988	−	0.945718i	$-0.394640\pi$
$173$	112.446			0.649976			0.324988	+	0.945718i	$0.394640\pi$
$174$		0			0
$175$	−89.2986	+	150.502i	−0.510278	+	0.860010i
$176$	32.6386			0.185446
$177$		0			0
$178$	22.9511			0.128939
$179$	68.9019			0.384927			0.192464	−	0.981304i	$-0.438352\pi$
$179$	68.9019			0.384927			0.192464	+	0.981304i	$0.438352\pi$
$180$		0			0
$181$		−	166.537i		−	0.920094i	−0.887895	−	0.460047i	$-0.847833\pi$
$181$		−	166.537i		−	0.920094i	0.887895	−	0.460047i	$-0.152167\pi$
$182$	32.6129	+	140.870i	0.179192	+	0.774012i
$183$		0			0
$184$	105.380			0.572719
$185$	124.650	+	291.655i	0.673785	+	1.57651i
$186$		0			0
$187$	47.4419			0.253700
$188$	−46.6759			−0.248276
$189$		0			0
$190$	−219.600	+	93.8547i	−1.15579	+	0.493972i
$191$	148.289			0.776382			0.388191	−	0.921579i	$-0.373100\pi$
$191$	148.289			0.776382			0.388191	+	0.921579i	$0.373100\pi$
$192$		0			0
$193$		−	35.1886i		−	0.182324i	−0.995836	−	0.0911622i	$-0.970942\pi$
$193$		−	35.1886i		−	0.182324i	0.995836	−	0.0911622i	$-0.0290582\pi$
$194$		−	117.041i		−	0.603304i
$195$		0			0
$196$	−88.0294	+	43.0677i	−0.449130	+	0.219733i
$197$		−	193.634i		−	0.982915i	−0.870902	−	0.491457i	$-0.836464\pi$
$197$		−	193.634i		−	0.982915i	0.870902	−	0.491457i	$-0.163536\pi$
$198$		0			0
$199$			181.838i			0.913759i	0.889529	+	0.456880i	$0.151033\pi$
$199$			181.838i			0.913759i	−0.889529	+	0.456880i	$0.848967\pi$
$200$	−51.1068	−	48.8682i	−0.255534	−	0.244341i
$201$		0			0
$202$	−123.327			−0.610530
$203$	−63.1023	+	14.6088i	−0.310849	+	0.0719647i
$204$		0			0
$205$	−16.2286	−	37.9714i	−0.0791638	−	0.185226i
$206$			265.260i			1.28767i
$207$		0			0
$208$	−58.4256			−0.280892
$209$			275.580i			1.31857i
$210$		0			0
$211$	175.914			0.833717			0.416859	−	0.908971i	$-0.363131\pi$
$211$	175.914			0.833717			0.416859	+	0.908971i	$0.363131\pi$
$212$		−	142.699i		−	0.673110i
$213$		0			0
$214$	223.244			1.04320
$215$	82.7058	+	193.514i	0.384678	+	0.900064i
$216$		0			0
$217$	30.4013	+	131.317i	0.140098	+	0.605149i
$218$		−	158.495i		−	0.727042i
$219$		0			0
$220$	−75.0310	+	32.0675i	−0.341050	+	0.145761i
$221$	−84.9246			−0.384274
$222$		0			0
$223$	−20.5675			−0.0922308			−0.0461154	−	0.998936i	$-0.514684\pi$
$223$	−20.5675			−0.0922308			−0.0461154	+	0.998936i	$0.514684\pi$
$224$	−8.93112	−	38.5776i	−0.0398711	−	0.172222i
$225$		0			0
$226$	200.801			0.888498
$227$	−414.087			−1.82417			−0.912085	−	0.410001i	$-0.865528\pi$
$227$	−414.087			−1.82417			−0.912085	+	0.410001i	$0.865528\pi$
$228$		0			0
$229$			195.520i			0.853799i	0.904299	+	0.426899i	$0.140394\pi$
$229$			195.520i			0.853799i	−0.904299	+	0.426899i	$0.859606\pi$
$230$	−242.253	+	103.536i	−1.05327	+	0.450158i
$231$		0			0
$232$		−	26.1716i		−	0.112808i
$233$			81.3006i			0.348930i	0.984663	+	0.174465i	$0.0558195\pi$
$233$			81.3006i			0.348930i	−0.984663	+	0.174465i	$0.944180\pi$
$234$		0			0
$235$	107.301	−	45.8592i	0.456599	−	0.195146i
$236$		−	85.8700i		−	0.363856i
$237$		0			0
$238$	−12.9818	−	56.0746i	−0.0545456	−	0.235608i
$239$	249.265			1.04295			0.521475	−	0.853267i	$-0.325382\pi$
$239$	249.265			1.04295			0.521475	+	0.853267i	$0.325382\pi$
$240$		0			0
$241$		−	262.343i		−	1.08856i	−0.838904	−	0.544280i	$-0.816803\pi$
$241$		−	262.343i		−	1.08856i	0.838904	−	0.544280i	$-0.183197\pi$
$242$		−	76.9618i		−	0.318024i
$243$		0			0
$244$			68.5728i			0.281036i
$245$	160.052	−	185.495i	0.653272	−	0.757123i
$246$		0			0
$247$		−	493.310i		−	1.99721i
$248$	−54.4636			−0.219611
$249$		0			0
$250$	165.500	+	62.1278i	0.661999	+	0.248511i
$251$			141.917i			0.565406i	0.959208	+	0.282703i	$0.0912310\pi$
$251$			141.917i			0.565406i	−0.959208	+	0.282703i	$0.908769\pi$
$252$		0			0
$253$			304.008i			1.20161i
$254$	−286.257			−1.12699
$255$		0			0
$256$	16.0000			0.0625000
$257$	170.843			0.664757			0.332379	−	0.943146i	$-0.392149\pi$
$257$	170.843			0.664757			0.332379	+	0.943146i	$0.392149\pi$
$258$		0			0
$259$	−100.152	−	432.604i	−0.386688	−	1.67028i
$260$	134.311	−	57.4033i	0.516582	−	0.220782i
$261$		0			0
$262$	199.772			0.762488
$263$		−	383.417i		−	1.45786i	−0.684588	−	0.728930i	$-0.740018\pi$
$263$		−	383.417i		−	1.45786i	0.684588	−	0.728930i	$-0.259982\pi$
$264$		0			0
$265$	140.203	+	328.044i	0.529066	+	1.23790i
$266$	325.726	−	75.4090i	1.22454	−	0.283492i
$267$		0			0
$268$		−	9.99777i		−	0.0373051i
$269$			154.512i			0.574393i	0.957872	+	0.287196i	$0.0927232\pi$
$269$			154.512i			0.574393i	−0.957872	+	0.287196i	$0.907277\pi$
$270$		0			0
$271$		−	320.328i		−	1.18202i	−0.806664	−	0.591010i	$-0.798729\pi$
$271$		−	320.328i		−	1.18202i	0.806664	−	0.591010i	$-0.201271\pi$
$272$	23.2568			0.0855030
$273$		0			0
$274$	−71.6200			−0.261387
$275$	140.978	−	147.436i	0.512648	−	0.536132i
$276$		0			0
$277$		−	222.854i		−	0.804526i	−0.915524	−	0.402263i	$-0.868224\pi$
$277$		−	222.854i		−	0.804526i	0.915524	−	0.402263i	$-0.131776\pi$
$278$	−104.688			−0.376576
$279$		0			0
$280$	58.4339	+	79.9092i	0.208693	+	0.285390i
$281$	−218.973			−0.779263			−0.389631	−	0.920971i	$-0.627398\pi$
$281$	−218.973			−0.779263			−0.389631	+	0.920971i	$0.627398\pi$
$282$		0			0
$283$	−36.3957			−0.128607			−0.0643034	−	0.997930i	$-0.520483\pi$
$283$	−36.3957			−0.128607			−0.0643034	+	0.997930i	$0.520483\pi$
$284$	−77.6240			−0.273324
$285$		0			0
$286$		−	168.550i		−	0.589337i
$287$	13.0391	+	56.3219i	0.0454324	+	0.196244i
$288$		0			0
$289$	−255.195			−0.883028
$290$	25.7136	+	60.1644i	0.0886677	+	0.207463i
$291$		0			0
$292$	249.259			0.853626
$293$	−168.440			−0.574882			−0.287441	−	0.957798i	$-0.592805\pi$
$293$	−168.440			−0.574882			−0.287441	+	0.957798i	$0.592805\pi$
$294$		0			0
$295$	84.3675	+	197.402i	0.285991	+	0.669158i
$296$	179.421			0.606153
$297$		0			0
$298$			320.997i			1.07717i
$299$		−	544.199i		−	1.82006i
$300$		0			0
$301$	−66.4512	−	287.034i	−0.220768	−	0.953600i
$302$			416.381i			1.37874i
$303$		0			0
$304$			135.094i			0.444389i
$305$	−67.3730	−	157.638i	−0.220895	−	0.516847i
$306$		0			0
$307$	−223.400			−0.727688			−0.363844	−	0.931460i	$-0.618536\pi$
$307$	−223.400			−0.727688			−0.363844	+	0.931460i	$0.618536\pi$
$308$	111.292	−	25.7651i	0.361336	−	0.0836530i
$309$		0			0
$310$	125.203	−	53.5106i	0.403882	−	0.172615i
$311$		−	46.0396i		−	0.148037i	−0.997257	−	0.0740186i	$-0.976418\pi$
$311$		−	46.0396i		−	0.148037i	0.997257	−	0.0740186i	$-0.0235824\pi$
$312$		0			0
$313$	80.0375			0.255711			0.127855	−	0.991793i	$-0.459191\pi$
$313$	80.0375			0.255711			0.127855	+	0.991793i	$0.459191\pi$
$314$			93.1395i			0.296623i
$315$		0			0
$316$	112.368			0.355596
$317$			185.237i			0.584343i	0.956366	+	0.292171i	$0.0943777\pi$
$317$			185.237i			0.584343i	−0.956366	+	0.292171i	$0.905622\pi$
$318$		0			0
$319$	75.5016			0.236682
$320$	−36.7815	+	15.7200i	−0.114942	+	0.0491251i
$321$		0			0
$322$	359.327	−	83.1879i	1.11592	−	0.258348i
$323$			196.367i			0.607946i
$324$		0			0
$325$	−252.362	+	263.923i	−0.776499	+	0.812070i
$326$	−39.8914			−0.122366
$327$		0			0
$328$	−23.3594			−0.0712177
$329$	−159.156	+	36.8463i	−0.483757	+	0.111995i
$330$		0			0
$331$	61.4686			0.185706			0.0928529	−	0.995680i	$-0.470401\pi$
$331$	61.4686			0.185706			0.0928529	+	0.995680i	$0.470401\pi$
$332$	180.796			0.544566
$333$		0			0
$334$			181.671i			0.543926i
$335$	9.82284	+	22.9833i	0.0293219	+	0.0686069i
$336$		0			0
$337$		−	656.501i		−	1.94807i	−0.226387	−	0.974037i	$-0.572691\pi$
$337$		−	656.501i		−	1.94807i	0.226387	−	0.974037i	$-0.427309\pi$
$338$			62.7160i			0.185550i
$339$		0			0
$340$	−53.4638	+	22.8499i	−0.157247	+	0.0672056i
$341$		−	157.120i		−	0.460764i
$342$		0			0
$343$	−266.166	+	216.344i	−0.775994	+	0.630740i
$344$	119.047			0.346066
$345$		0			0
$346$			159.022i			0.459603i
$347$			321.323i			0.926002i	0.886358	+	0.463001i	$0.153227\pi$
$347$			321.323i			0.926002i	−0.886358	+	0.463001i	$0.846773\pi$
$348$		0			0
$349$		−	185.135i		−	0.530474i	−0.964183	−	0.265237i	$-0.914550\pi$
$349$		−	185.135i		−	0.530474i	0.964183	−	0.265237i	$-0.0854501\pi$
$350$	−212.842	−	126.287i	−0.608119	−	0.360821i
$351$		0			0
$352$			46.1579i			0.131130i
$353$	597.338			1.69218			0.846088	−	0.533043i	$-0.178952\pi$
$353$	597.338			1.69218			0.846088	+	0.533043i	$0.178952\pi$
$354$		0			0
$355$	178.446	−	76.2658i	0.502664	−	0.214833i
$356$			32.4578i			0.0911736i
$357$		0			0
$358$			97.4421i			0.272185i
$359$	−239.446			−0.666982			−0.333491	−	0.942753i	$-0.608227\pi$
$359$	−239.446			−0.666982			−0.333491	+	0.942753i	$0.608227\pi$
$360$		0			0
$361$	−779.655			−2.15971
$362$	235.519			0.650604
$363$		0			0
$364$	−199.220	+	46.1216i	−0.547309	+	0.126708i
$365$	−573.007	+	244.898i	−1.56988	+	0.670952i
$366$		0			0
$367$	−398.743			−1.08649			−0.543246	−	0.839573i	$-0.682805\pi$
$367$	−398.743			−1.08649			−0.543246	+	0.839573i	$0.682805\pi$
$368$			149.030i			0.404973i
$369$		0			0
$370$	−412.462	+	176.282i	−1.11476	+	0.476438i
$371$	−112.648	−	486.578i	−0.303633	−	1.31153i
$372$		0			0
$373$		−	34.7064i		−	0.0930466i	−0.998917	−	0.0465233i	$-0.985186\pi$
$373$		−	34.7064i		−	0.0930466i	0.998917	−	0.0465233i	$-0.0148142\pi$
$374$			67.0929i			0.179393i
$375$		0			0
$376$		−	66.0097i		−	0.175558i
$377$	−135.154			−0.358498
$378$		0			0
$379$	−109.217			−0.288172			−0.144086	−	0.989565i	$-0.546024\pi$
$379$	−109.217			−0.288172			−0.144086	+	0.989565i	$0.546024\pi$
$380$	−132.731	−	310.561i	−0.349291	−	0.817265i
$381$		0			0
$382$			209.712i			0.548985i
$383$	336.420			0.878381			0.439191	−	0.898394i	$-0.355265\pi$
$383$	336.420			0.878381			0.439191	+	0.898394i	$0.355265\pi$
$384$		0			0
$385$	−230.528	+	168.574i	−0.598773	+	0.437855i
$386$	49.7642			0.128923
$387$		0			0
$388$	165.521			0.426601
$389$	311.173			0.799930			0.399965	−	0.916530i	$-0.369022\pi$
$389$	311.173			0.799930			0.399965	+	0.916530i	$0.369022\pi$
$390$		0			0
$391$			216.623i			0.554023i
$392$	−60.9069	−	124.492i	−0.155375	−	0.317583i
$393$		0			0
$394$	273.840			0.695026
$395$	−258.317	+	110.402i	−0.653968	+	0.279499i
$396$		0			0
$397$	41.2679			0.103949			0.0519747	−	0.998648i	$-0.483448\pi$
$397$	41.2679			0.103949			0.0519747	+	0.998648i	$0.483448\pi$
$398$	−257.158			−0.646125
$399$		0			0
$400$	69.1100	−	72.2759i	0.172775	−	0.180690i
$401$	495.642			1.23601			0.618007	−	0.786173i	$-0.287940\pi$
$401$	495.642			1.23601			0.618007	+	0.786173i	$0.287940\pi$
$402$		0			0
$403$			281.258i			0.697910i
$404$		−	174.411i		−	0.431710i
$405$		0			0
$406$	−20.6600	−	89.2402i	−0.0508867	−	0.219803i
$407$			517.608i			1.27176i
$408$		0			0
$409$			359.920i			0.880001i	0.897998	+	0.440000i	$0.145022\pi$
$409$			359.920i			0.880001i	−0.897998	+	0.440000i	$0.854978\pi$
$410$	53.6997	−	22.9507i	0.130975	−	0.0559773i
$411$		0			0
$412$	−375.135			−0.910521
$413$	−67.7863	−	292.801i	−0.164132	−	0.708960i
$414$		0			0
$415$	−415.622	+	177.633i	−1.00150	+	0.428030i
$416$		−	82.6263i		−	0.198621i
$417$		0			0
$418$	−389.730			−0.932367
$419$			482.910i			1.15253i	0.817263	+	0.576265i	$0.195490\pi$
$419$			482.910i			1.15253i	−0.817263	+	0.576265i	$0.804510\pi$
$420$		0			0
$421$	−523.520			−1.24351			−0.621757	−	0.783210i	$-0.713581\pi$
$421$	−523.520			−1.24351			−0.621757	+	0.783210i	$0.713581\pi$
$422$			248.780i			0.589527i
$423$		0			0
$424$	201.807			0.475961
$425$	100.455	−	105.057i	0.236365	−	0.247192i
$426$		0			0
$427$	54.1319	+	233.821i	0.126773	+	0.547589i
$428$			315.715i			0.737653i
$429$		0			0
$430$	−273.670	+	116.964i	−0.636441	+	0.272008i
$431$	−517.027			−1.19960			−0.599799	−	0.800150i	$-0.704753\pi$
$431$	−517.027			−1.19960			−0.599799	+	0.800150i	$0.704753\pi$
$432$		0			0
$433$	567.712			1.31111			0.655557	−	0.755146i	$-0.272434\pi$
$433$	567.712			1.31111			0.655557	+	0.755146i	$0.272434\pi$
$434$	−185.711	+	42.9939i	−0.427905	+	0.0990644i
$435$		0			0
$436$	224.146			0.514097
$437$	−1258.32			−2.87945
$438$		0			0
$439$			622.875i			1.41885i	0.704781	+	0.709425i	$0.251045\pi$
$439$			622.875i			1.41885i	−0.704781	+	0.709425i	$0.748955\pi$
$440$	−45.3503	−	106.110i	−0.103069	−	0.241159i
$441$		0			0
$442$		−	120.102i		−	0.271723i
$443$			476.699i			1.07607i	0.842923	+	0.538035i	$0.180833\pi$
$443$			476.699i			1.07607i	−0.842923	+	0.538035i	$0.819167\pi$
$444$		0			0
$445$	−31.8899	−	74.6154i	−0.0716626	−	0.167675i
$446$		−	29.0868i		−	0.0652170i
$447$		0			0
$448$	54.5570	−	12.6305i	0.121779	−	0.0281931i
$449$	−861.931			−1.91967			−0.959834	−	0.280570i	$-0.909477\pi$
$449$	−861.931			−1.91967			−0.959834	+	0.280570i	$0.909477\pi$
$450$		0			0
$451$		−	67.3889i		−	0.149421i
$452$			283.975i			0.628263i
$453$		0			0
$454$		−	585.607i		−	1.28988i
$455$	412.662	−	301.761i	0.906950	−	0.663211i
$456$		0			0
$457$			27.5401i			0.0602629i	0.999546	+	0.0301314i	$0.00959258\pi$
$457$			27.5401i			0.0602629i	−0.999546	+	0.0301314i	$0.990407\pi$
$458$	−276.507			−0.603727
$459$		0			0
$460$	−146.423	−	342.597i	−0.318310	−	0.744777i
$461$		−	378.183i		−	0.820353i	−0.912006	−	0.410176i	$-0.865467\pi$
$461$		−	378.183i		−	0.820353i	0.912006	−	0.410176i	$-0.134533\pi$
$462$		0			0
$463$		−	724.994i		−	1.56586i	−0.622108	−	0.782931i	$-0.713724\pi$
$463$		−	724.994i		−	1.56586i	0.622108	−	0.782931i	$-0.286276\pi$
$464$	37.0122			0.0797676
$465$		0			0
$466$	−114.976			−0.246731
$467$	−371.451			−0.795398			−0.397699	−	0.917516i	$-0.630191\pi$
$467$	−371.451			−0.795398			−0.397699	+	0.917516i	$0.630191\pi$
$468$		0			0
$469$	−7.89231	−	34.0905i	−0.0168280	−	0.0726877i
$470$	64.8547	+	151.746i	0.137989	+	0.322864i
$471$		0			0
$472$	121.438			0.257285
$473$			343.434i			0.726076i
$474$		0			0
$475$	610.254	+	583.523i	1.28475	+	1.22847i
$476$	79.3015	−	18.3591i	0.166600	−	0.0385695i
$477$		0			0
$478$			352.514i			0.737477i
$479$			860.650i			1.79677i	0.439214	+	0.898383i	$0.355257\pi$
$479$			860.650i			1.79677i	−0.439214	+	0.898383i	$0.644743\pi$
$480$		0			0
$481$		−	926.558i		−	1.92632i
$482$	371.009			0.769728
$483$		0			0
$484$	108.840			0.224877
$485$	−380.507	+	162.625i	−0.784551	+	0.335309i
$486$		0			0
$487$			887.173i			1.82171i	0.412726	+	0.910855i	$0.364577\pi$
$487$			887.173i			1.82171i	−0.412726	+	0.910855i	$0.635423\pi$
$488$	−96.9766			−0.198723
$489$		0			0
$490$	262.330	+	226.347i	0.535367	+	0.461933i
$491$	50.1823			0.102204			0.0511021	−	0.998693i	$-0.483727\pi$
$491$	50.1823			0.102204			0.0511021	+	0.998693i	$0.483727\pi$
$492$		0			0
$493$	53.7991			0.109126
$494$	697.646			1.41224
$495$		0			0
$496$		−	77.0231i		−	0.155289i
$497$	−264.683	+	61.2769i	−0.532562	+	0.123294i
$498$		0			0
$499$	160.443			0.321529			0.160765	−	0.986993i	$-0.448604\pi$
$499$	160.443			0.321529			0.160765	+	0.986993i	$0.448604\pi$
$500$	−87.8620	+	234.052i	−0.175724	+	0.468104i
$501$		0			0
$502$	−200.701			−0.399802
$503$	742.042			1.47523			0.737616	−	0.675220i	$-0.235951\pi$
$503$	742.042			1.47523			0.737616	+	0.675220i	$0.235951\pi$
$504$		0			0
$505$	171.359	+	400.944i	0.339325	+	0.793948i
$506$	−429.933			−0.849670
$507$		0			0
$508$		−	404.828i		−	0.796905i
$509$		−	978.447i		−	1.92229i	−0.276038	−	0.961147i	$-0.589021\pi$
$509$		−	978.447i		−	1.92229i	0.276038	−	0.961147i	$-0.410979\pi$
$510$		0			0
$511$	849.927	−	196.767i	1.66326	−	0.385062i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$			241.608i			0.470054i
$515$	862.377	−	368.571i	1.67452	−	0.715672i
$516$		0			0
$517$	190.429			0.368335
$518$	611.794	−	141.637i	1.18107	−	0.273430i
$519$		0			0
$520$	81.1805	+	189.945i	0.156116	+	0.365279i
$521$			575.650i			1.10489i	0.833548	+	0.552447i	$0.186306\pi$
$521$			575.650i			1.10489i	−0.833548	+	0.552447i	$0.813694\pi$
$522$		0			0
$523$	339.090			0.648355			0.324178	−	0.945996i	$-0.394912\pi$
$523$	339.090			0.648355			0.324178	+	0.945996i	$0.394912\pi$
$524$			282.520i			0.539160i
$525$		0			0
$526$	542.234			1.03086
$527$		−	111.957i		−	0.212442i
$528$		0			0
$529$	−859.125			−1.62406
$530$	−463.924	+	198.276i	−0.875328	+	0.374106i
$531$		0			0
$532$	106.644	+	460.647i	0.200459	+	0.865877i
$533$			120.631i			0.226325i
$534$		0			0
$535$	−310.191	−	725.781i	−0.579797	−	1.35660i
$536$	14.1390			0.0263787
$537$		0			0
$538$	−218.512			−0.406157
$539$	359.144	−	175.709i	0.666316	−	0.325990i
$540$		0			0
$541$	35.8638			0.0662916			0.0331458	−	0.999451i	$-0.489447\pi$
$541$	35.8638			0.0662916			0.0331458	+	0.999451i	$0.489447\pi$
$542$	453.012			0.835815
$543$		0			0
$544$			32.8901i			0.0604598i
$545$	−515.277	+	220.224i	−0.945463	+	0.404081i
$546$		0			0
$547$		−	700.845i		−	1.28125i	−0.767853	−	0.640626i	$-0.778675\pi$
$547$		−	700.845i		−	1.28125i	0.767853	−	0.640626i	$-0.221325\pi$
$548$		−	101.286i		−	0.184829i
$549$		0			0
$550$	208.507	+	199.373i	0.379103	+	0.362497i
$551$			312.508i			0.567166i
$552$		0			0
$553$	383.155	−	88.7044i	0.692867	−	0.160406i
$554$	315.163			0.568886
$555$		0			0
$556$		−	148.051i		−	0.266279i
$557$		−	639.349i		−	1.14784i	−0.818910	−	0.573922i	$-0.805421\pi$
$557$		−	639.349i		−	1.14784i	0.818910	−	0.573922i	$-0.194579\pi$
$558$		0			0
$559$		−	614.773i		−	1.09977i
$560$	−113.009	+	82.6380i	−0.201801	+	0.147568i
$561$		0			0
$562$		−	309.674i		−	0.551022i
$563$	−227.519			−0.404120			−0.202060	−	0.979373i	$-0.564764\pi$
$563$	−227.519			−0.404120			−0.202060	+	0.979373i	$0.564764\pi$
$564$		0			0
$565$	−279.006	−	652.814i	−0.493816	−	1.15542i
$566$		−	51.4713i		−	0.0909387i
$567$		0			0
$568$		−	109.777i		−	0.193269i
$569$	−613.901			−1.07891			−0.539456	−	0.842014i	$-0.681370\pi$
$569$	−613.901			−1.07891			−0.539456	+	0.842014i	$0.681370\pi$
$570$		0			0
$571$	366.674			0.642161			0.321081	−	0.947052i	$-0.395954\pi$
$571$	366.674			0.642161			0.321081	+	0.947052i	$0.395954\pi$
$572$	238.366			0.416724
$573$		0			0
$574$	−79.6513	+	18.4401i	−0.138765	+	0.0321256i
$575$	673.206	+	643.718i	1.17079	+	1.11951i
$576$		0			0
$577$	62.1951			0.107790			0.0538952	−	0.998547i	$-0.482836\pi$
$577$	62.1951			0.107790			0.0538952	+	0.998547i	$0.482836\pi$
$578$		−	360.900i		−	0.624395i
$579$		0			0
$580$	−85.0853	+	36.3646i	−0.146699	+	0.0626975i
$581$	616.481	−	142.722i	1.06107	−	0.245648i
$582$		0			0
$583$			582.188i			0.998607i
$584$			352.505i			0.603605i
$585$		0			0
$586$		−	238.211i		−	0.406503i
$587$	−176.872			−0.301315			−0.150658	−	0.988586i	$-0.548139\pi$
$587$	−176.872			−0.301315			−0.150658	+	0.988586i	$0.548139\pi$
$588$		0			0
$589$	650.337			1.10414
$590$	−279.168	+	119.314i	−0.473166	+	0.202226i
$591$		0			0
$592$			253.740i			0.428615i
$593$	154.878			0.261176			0.130588	−	0.991437i	$-0.458313\pi$
$593$	154.878			0.261176			0.130588	+	0.991437i	$0.458313\pi$
$594$		0			0
$595$	−164.264	+	120.119i	−0.276074	+	0.201880i
$596$	−453.959			−0.761676
$597$		0			0
$598$	769.613			1.28698
$599$	−900.825			−1.50388			−0.751940	−	0.659231i	$-0.770882\pi$
$599$	−900.825			−1.50388			−0.751940	+	0.659231i	$0.770882\pi$
$600$		0			0
$601$			682.387i			1.13542i	0.823229	+	0.567710i	$0.192170\pi$
$601$			682.387i			1.13542i	−0.823229	+	0.567710i	$0.807830\pi$
$602$	405.927	−	93.9762i	0.674297	−	0.156107i
$603$		0			0
$604$	−588.851			−0.974920
$605$	−250.207	+	106.936i	−0.413566	+	0.176754i
$606$		0			0
$607$	−367.814			−0.605954			−0.302977	−	0.952998i	$-0.597981\pi$
$607$	−367.814			−0.605954			−0.302977	+	0.952998i	$0.597981\pi$
$608$	−191.052			−0.314231
$609$		0			0
$610$	222.934	−	95.2798i	0.365466	−	0.156196i
$611$	−340.883			−0.557911
$612$		0			0
$613$			117.271i			0.191306i	0.995415	+	0.0956532i	$0.0304940\pi$
$613$			117.271i			0.191306i	−0.995415	+	0.0956532i	$0.969506\pi$
$614$		−	315.936i		−	0.514553i
$615$		0			0
$616$	36.4374	+	157.390i	0.0591516	+	0.255503i
$617$		−	1070.18i		−	1.73449i	−0.497881	−	0.867245i	$-0.665888\pi$
$617$		−	1070.18i		−	1.73449i	0.497881	−	0.867245i	$-0.334112\pi$
$618$		0			0
$619$			532.192i			0.859761i	0.902886	+	0.429880i	$0.141444\pi$
$619$			532.192i			0.859761i	−0.902886	+	0.429880i	$0.858556\pi$
$620$	75.6754	+	177.064i	0.122057	+	0.285587i
$621$		0			0
$622$	65.1098			0.104678
$623$	25.6224	+	110.675i	0.0411275	+	0.177649i
$624$		0			0
$625$	−27.9756	−	624.374i	−0.0447610	−	0.998998i
$626$			113.190i			0.180815i
$627$		0			0
$628$	−131.719			−0.209744
$629$			368.825i			0.586366i
$630$		0			0
$631$	472.933			0.749498			0.374749	−	0.927126i	$-0.377729\pi$
$631$	472.933			0.749498			0.374749	+	0.927126i	$0.377729\pi$
$632$			158.913i			0.251444i
$633$		0			0
$634$	−261.964			−0.413193
$635$	397.745	+	930.636i	0.626369	+	1.46557i
$636$		0			0
$637$	−642.896	+	314.532i	−1.00926	+	0.493771i
$638$			106.775i			0.167359i
$639$		0			0
$640$	−22.2315	−	52.0169i	−0.0347367	−	0.0812764i
$641$	486.990			0.759734			0.379867	−	0.925041i	$-0.375970\pi$
$641$	486.990			0.759734			0.379867	+	0.925041i	$0.375970\pi$
$642$		0			0
$643$	111.425			0.173289			0.0866447	−	0.996239i	$-0.472386\pi$
$643$	111.425			0.173289			0.0866447	+	0.996239i	$0.472386\pi$
$644$	117.645	+	508.165i	0.182679	+	0.789077i
$645$		0			0
$646$	−277.704			−0.429883
$647$	737.696			1.14018			0.570090	−	0.821583i	$-0.306908\pi$
$647$	737.696			1.14018			0.570090	+	0.821583i	$0.306908\pi$
$648$		0			0
$649$			350.334i			0.539806i
$650$	−373.243	−	356.894i	−0.574220	−	0.549068i
$651$		0			0
$652$		−	56.4149i		−	0.0865260i
$653$		−	193.734i		−	0.296682i	−0.988936	−	0.148341i	$-0.952607\pi$
$653$		−	193.734i		−	0.296682i	0.988936	−	0.148341i	$-0.0473934\pi$
$654$		0			0
$655$	−277.577	−	649.469i	−0.423781	−	0.991556i
$656$		−	33.0352i		−	0.0503585i
$657$		0			0
$658$	−52.1085	−	225.081i	−0.0791923	−	0.342068i
$659$	823.339			1.24938			0.624688	−	0.780874i	$-0.285226\pi$
$659$	823.339			1.24938			0.624688	+	0.780874i	$0.285226\pi$
$660$		0			0
$661$			657.833i			0.995208i	0.867404	+	0.497604i	$0.165787\pi$
$661$			657.833i			0.995208i	−0.867404	+	0.497604i	$0.834213\pi$
$662$			86.9298i			0.131314i
$663$		0			0
$664$			255.684i			0.385066i
$665$	−697.746	−	954.177i	−1.04924	−	1.43485i
$666$		0			0
$667$			344.746i			0.516860i
$668$	−256.922			−0.384614
$669$		0			0
$670$	−32.5033	+	13.8916i	−0.0485124	+	0.0207337i
$671$		−	279.765i		−	0.416937i
$672$		0			0
$673$		−	727.300i		−	1.08068i	−0.841446	−	0.540342i	$-0.818295\pi$
$673$		−	727.300i		−	1.08068i	0.841446	−	0.540342i	$-0.181705\pi$
$674$	928.433			1.37750
$675$		0			0
$676$	−88.6938			−0.131204
$677$	−385.964			−0.570110			−0.285055	−	0.958511i	$-0.592012\pi$
$677$	−385.964			−0.570110			−0.285055	+	0.958511i	$0.592012\pi$
$678$		0			0
$679$	564.396	−	130.663i	0.831217	−	0.192435i
$680$	−32.3146	−	75.6093i	−0.0475215	−	0.111190i
$681$		0			0
$682$	222.202			0.325809
$683$		−	236.488i		−	0.346249i	−0.984900	−	0.173124i	$-0.944614\pi$
$683$		−	236.488i		−	0.346249i	0.984900	−	0.173124i	$-0.0553863\pi$
$684$		0			0
$685$	99.5138	+	232.841i	0.145276	+	0.339914i
$686$	−305.957	−	376.415i	−0.446001	−	0.548711i
$687$		0			0
$688$			168.357i			0.244705i
$689$		−	1042.16i		−	1.51257i
$690$		0			0
$691$			337.426i			0.488316i	0.969735	+	0.244158i	$0.0785116\pi$
$691$			337.426i			0.488316i	−0.969735	+	0.244158i	$0.921488\pi$
$692$	−224.892			−0.324988
$693$		0			0
$694$	−454.419			−0.654782
$695$	145.461	+	340.347i	0.209296	+	0.489708i
$696$		0			0
$697$		−	48.0184i		−	0.0688929i
$698$	261.821			0.375101
$699$		0			0
$700$	178.597	−	301.003i	0.255139	−	0.430005i
$701$	−89.2192			−0.127274			−0.0636371	−	0.997973i	$-0.520270\pi$
$701$	−89.2192			−0.127274			−0.0636371	+	0.997973i	$0.520270\pi$
$702$		0			0
$703$	−2142.43			−3.04755
$704$	−65.2772			−0.0927232
$705$		0			0
$706$			844.764i			1.19655i
$707$	−137.681	−	594.709i	−0.194740	−	0.841172i
$708$		0			0
$709$	569.646			0.803450			0.401725	−	0.915760i	$-0.368411\pi$
$709$	569.646			0.803450			0.401725	+	0.915760i	$0.368411\pi$
$710$	107.856	+	252.360i	0.151910	+	0.355437i
$711$		0			0
$712$	−45.9023			−0.0644695
$713$	717.423			1.00620
$714$		0			0
$715$	−547.967	+	234.195i	−0.766387	+	0.327546i
$716$	−137.804			−0.192464
$717$		0			0
$718$		−	338.628i		−	0.471627i
$719$		−	1261.33i		−	1.75428i	−0.480233	−	0.877141i	$-0.659448\pi$
$719$		−	1261.33i		−	1.75428i	0.480233	−	0.877141i	$-0.340552\pi$
$720$		0			0
$721$	−1279.14	+	296.134i	−1.77412	+	0.410727i
$722$		−	1102.60i		−	1.52714i
$723$		0			0
$724$			333.074i			0.460047i
$725$	159.870	−	167.193i	0.220510	−	0.230611i
$726$		0			0
$727$	307.746			0.423310			0.211655	−	0.977344i	$-0.432115\pi$
$727$	307.746			0.423310			0.211655	+	0.977344i	$0.432115\pi$
$728$	−65.2258	−	281.740i	−0.0895958	−	0.387006i
$729$		0			0
$730$	−346.337	−	810.355i	−0.474435	−	1.11008i
$731$			244.716i			0.334769i
$732$		0			0
$733$	633.490			0.864243			0.432121	−	0.901815i	$-0.357765\pi$
$733$	633.490			0.864243			0.432121	+	0.901815i	$0.357765\pi$
$734$		−	563.908i		−	0.768266i
$735$		0			0
$736$	−210.761			−0.286359
$737$			40.7891i			0.0553448i
$738$		0			0
$739$	749.557			1.01428			0.507142	−	0.861862i	$-0.330702\pi$
$739$	749.557			1.01428			0.507142	+	0.861862i	$0.330702\pi$
$740$	−249.300	−	583.309i	−0.336893	−	0.788256i
$741$		0			0
$742$	688.126	−	159.308i	0.927393	−	0.214701i
$743$			145.699i			0.196095i	0.995182	+	0.0980476i	$0.0312597\pi$
$743$			145.699i			0.196095i	−0.995182	+	0.0980476i	$0.968740\pi$
$744$		0			0
$745$	1043.58	−	446.016i	1.40078	−	0.598679i
$746$	49.0822			0.0657939
$747$		0			0
$748$	−94.8837			−0.126850
$749$	249.228	+	1076.53i	0.332748	+	1.43729i
$750$		0			0
$751$	156.811			0.208803			0.104402	−	0.994535i	$-0.466707\pi$
$751$	156.811			0.208803			0.104402	+	0.994535i	$0.466707\pi$
$752$	93.3518			0.124138
$753$		0			0
$754$		−	191.136i		−	0.253496i
$755$	1353.68	−	578.548i	1.79295	−	0.766289i
$756$		0			0
$757$			296.377i			0.391515i	0.980652	+	0.195758i	$0.0627166\pi$
$757$			296.377i			0.391515i	−0.980652	+	0.195758i	$0.937283\pi$
$758$		−	154.457i		−	0.203769i
$759$		0			0
$760$	439.199	−	187.709i	0.577894	−	0.246986i
$761$			312.747i			0.410968i	0.978660	+	0.205484i	$0.0658769\pi$
$761$			312.747i			0.410968i	−0.978660	+	0.205484i	$0.934123\pi$
$762$		0			0
$763$	764.297	−	176.942i	1.00170	−	0.231904i
$764$	−296.578			−0.388191
$765$		0			0
$766$			475.770i			0.621109i
$767$		−	627.125i		−	0.817634i
$768$		0			0
$769$		−	91.1460i		−	0.118525i	−0.998242	−	0.0592627i	$-0.981125\pi$
$769$		−	91.1460i		−	0.118525i	0.998242	−	0.0592627i	$-0.0188750\pi$
$770$	−238.400	−	326.015i	−0.309610	−	0.423396i
$771$		0			0
$772$			70.3772i			0.0911622i
$773$	417.539			0.540154			0.270077	−	0.962839i	$-0.412951\pi$
$773$	417.539			0.540154			0.270077	+	0.962839i	$0.412951\pi$
$774$		0			0
$775$	−347.932	−	332.692i	−0.448945	−	0.429280i
$776$			234.082i			0.301652i
$777$		0			0
$778$			440.065i			0.565636i
$779$	278.929			0.358061
$780$		0			0
$781$	316.692			0.405496
$782$	−306.351			−0.391754
$783$		0			0
$784$	176.059	−	86.1354i	0.224565	−	0.109867i
$785$	302.802	−	129.414i	0.385735	−	0.164859i
$786$		0			0
$787$	−318.111			−0.404207			−0.202104	−	0.979364i	$-0.564778\pi$
$787$	−318.111			−0.404207			−0.202104	+	0.979364i	$0.564778\pi$
$788$			387.268i			0.491457i
$789$		0			0
$790$	−156.132	−	365.316i	−0.197636	−	0.462425i
$791$	224.172	+	968.302i	0.283403	+	1.22415i
$792$		0			0
$793$			500.801i			0.631527i
$794$			58.3616i			0.0735033i
$795$		0			0
$796$		−	363.676i		−	0.456880i
$797$	1188.06			1.49067			0.745335	−	0.666690i	$-0.232289\pi$
$797$	1188.06			1.49067			0.745335	+	0.666690i	$0.232289\pi$
$798$		0			0
$799$	135.692			0.169827
$800$	102.214	+	97.7363i	0.127767	+	0.122170i
$801$		0			0
$802$			700.943i			0.873994i
$803$	−1016.93			−1.26642
$804$		0			0
$805$	−769.723	−	1052.61i	−0.956177	−	1.30759i
$806$	−397.758			−0.493497
$807$		0			0
$808$	246.654			0.305265
$809$	223.374			0.276111			0.138055	−	0.990425i	$-0.455915\pi$
$809$	223.374			0.276111			0.138055	+	0.990425i	$0.455915\pi$
$810$		0			0
$811$			366.185i			0.451523i	0.974183	+	0.225761i	$0.0724870\pi$
$811$			366.185i			0.451523i	−0.974183	+	0.225761i	$0.927513\pi$
$812$	126.205	−	29.2177i	0.155424	−	0.0359824i
$813$		0			0
$814$	−732.008			−0.899272
$815$	55.4278	+	129.689i	0.0680096	+	0.159128i
$816$		0			0
$817$	−1421.51			−1.73991
$818$	−509.004			−0.622255
$819$		0			0
$820$	32.4572	+	75.9428i	0.0395819	+	0.0926132i
$821$	1547.39			1.88476			0.942381	−	0.334543i	$-0.108582\pi$
$821$	1547.39			1.88476			0.942381	+	0.334543i	$0.108582\pi$
$822$		0			0
$823$		−	1284.25i		−	1.56045i	−0.625499	−	0.780225i	$-0.715105\pi$
$823$		−	1284.25i		−	1.56045i	0.625499	−	0.780225i	$-0.284895\pi$
$824$		−	530.521i		−	0.643836i
$825$		0			0
$826$	414.083	−	95.8644i	0.501311	−	0.116059i
$827$		−	807.319i		−	0.976202i	−0.872787	−	0.488101i	$-0.837690\pi$
$827$		−	807.319i		−	0.976202i	0.872787	−	0.488101i	$-0.162310\pi$
$828$		0			0
$829$		−	623.615i		−	0.752250i	−0.926569	−	0.376125i	$-0.877256\pi$
$829$		−	623.615i		−	0.752250i	0.926569	−	0.376125i	$-0.122744\pi$
$830$	−251.210	−	587.778i	−0.302663	−	0.708166i
$831$		0			0
$832$	116.851			0.140446
$833$	255.911	−	125.202i	0.307216	−	0.150303i
$834$		0			0
$835$	590.623	−	252.426i	0.707333	−	0.302307i
$836$		−	551.161i		−	0.659283i
$837$		0			0
$838$	−682.938			−0.814962
$839$			1146.31i			1.36628i	0.730286	+	0.683142i	$0.239387\pi$
$839$			1146.31i			1.36628i	−0.730286	+	0.683142i	$0.760613\pi$
$840$		0			0
$841$	−755.381			−0.898194
$842$		−	740.368i		−	0.879297i
$843$		0			0
$844$	−351.829			−0.416859
$845$	203.893	−	87.1419i	0.241294	−	0.103127i
$846$		0			0
$847$	371.126	−	85.9194i	0.438165	−	0.101440i
$848$			285.399i			0.336555i
$849$		0			0
$850$	148.573	+	142.065i	0.174791	+	0.167135i
$851$	−2363.43			−2.77724
$852$		0			0
$853$	948.920			1.11245			0.556225	−	0.831032i	$-0.312249\pi$
$853$	948.920			1.11245			0.556225	+	0.831032i	$0.312249\pi$
$854$	−330.672	+	76.5540i	−0.387204	+	0.0896417i
$855$		0			0
$856$	−446.489			−0.521599
$857$	−868.842			−1.01382			−0.506909	−	0.862000i	$-0.669212\pi$
$857$	−868.842			−1.01382			−0.506909	+	0.862000i	$0.669212\pi$
$858$		0			0
$859$		−	119.981i		−	0.139675i	−0.997558	−	0.0698377i	$-0.977752\pi$
$859$		−	119.981i		−	0.139675i	0.997558	−	0.0698377i	$-0.0222482\pi$
$860$	−165.412	−	387.027i	−0.192339	−	0.450032i
$861$		0			0
$862$		−	731.187i		−	0.848245i
$863$		−	788.430i		−	0.913592i	−0.889571	−	0.456796i	$-0.848997\pi$
$863$		−	788.430i		−	0.913592i	0.889571	−	0.456796i	$-0.151003\pi$
$864$		0			0
$865$	516.991	−	220.957i	0.597678	−	0.255441i
$866$			802.866i			0.927097i
$867$		0			0
$868$	−60.8026	−	262.635i	−0.0700491	−	0.302574i
$869$	−458.443			−0.527552
$870$		0			0
$871$		−	73.0157i		−	0.0838298i
$872$			316.990i			0.363521i
$873$		0			0
$874$		−	1779.53i		−	2.03608i
$875$	−114.831	+	867.432i	−0.131235	+	0.991351i
$876$		0			0
$877$			234.663i			0.267574i	0.991010	+	0.133787i	$0.0427139\pi$
$877$			234.663i			0.267574i	−0.991010	+	0.133787i	$0.957286\pi$
$878$	−880.879			−1.00328
$879$		0			0
$880$	150.062	−	64.1350i	0.170525	−	0.0728807i
$881$			750.816i			0.852232i	0.904669	+	0.426116i	$0.140118\pi$
$881$			750.816i			0.852232i	−0.904669	+	0.426116i	$0.859882\pi$
$882$		0			0
$883$			1293.79i			1.46522i	0.680649	+	0.732610i	$0.261698\pi$
$883$			1293.79i			1.46522i	−0.680649	+	0.732610i	$0.738302\pi$
$884$	169.849			0.192137
$885$		0			0
$886$	−674.154			−0.760896
$887$	728.248			0.821024			0.410512	−	0.911855i	$-0.365350\pi$
$887$	728.248			0.821024			0.410512	+	0.911855i	$0.365350\pi$
$888$		0			0
$889$	−319.574	−	1380.39i	−0.359476	−	1.55274i
$890$	105.522	−	45.0991i	0.118564	−	0.0506731i
$891$		0			0
$892$	41.1349			0.0461154
$893$			788.206i			0.882650i
$894$		0			0
$895$	316.790	−	135.393i	0.353955	−	0.151277i
$896$	17.8622	+	77.1553i	0.0199355	+	0.0861108i
$897$		0			0
$898$		−	1218.95i		−	1.35741i
$899$		−	178.175i		−	0.198192i
$900$		0			0
$901$			414.842i			0.460424i
$902$	95.3022			0.105657
$903$		0			0
$904$	−401.601			−0.444249
$905$	−327.246	−	765.685i	−0.361598	−	0.846061i
$906$		0			0
$907$			913.713i			1.00740i	0.863878	+	0.503700i	$0.168028\pi$
$907$			913.713i			1.00740i	−0.863878	+	0.503700i	$0.831972\pi$
$908$	828.173			0.912085
$909$		0			0
$910$	426.755	+	583.593i	0.468961	+	0.641311i
$911$	1331.32			1.46138			0.730690	−	0.682709i	$-0.239198\pi$
$911$	1331.32			1.46138			0.730690	+	0.682709i	$0.239198\pi$
$912$		0			0
$913$	−737.615			−0.807903
$914$	−38.9476			−0.0426123
$915$		0			0
$916$		−	391.040i		−	0.426899i
$917$	223.023	+	963.341i	0.243210	+	1.05053i
$918$		0			0
$919$	−111.140			−0.120936			−0.0604678	−	0.998170i	$-0.519259\pi$
$919$	−111.140			−0.120936			−0.0604678	+	0.998170i	$0.519259\pi$
$920$	484.506	−	207.073i	0.526637	−	0.225079i
$921$		0			0
$922$	534.831			0.580077
$923$	−566.904			−0.614197
$924$		0			0
$925$	1146.21	+	1096.00i	1.23914	+	1.18486i
$926$	1025.30			1.10723
$927$		0			0
$928$			52.3431i			0.0564042i
$929$			571.383i			0.615051i	0.951540	+	0.307526i	$0.0995010\pi$
$929$			571.383i			0.615051i	−0.951540	+	0.307526i	$0.900499\pi$
$930$		0			0
$931$	727.275	+	1486.53i	0.781176	+	1.59671i
$932$		−	162.601i		−	0.174465i
$933$		0			0
$934$		−	525.311i		−	0.562431i
$935$	218.123	−	93.2235i	0.233287	−	0.0997043i
$936$		0			0
$937$	1657.10			1.76852			0.884259	−	0.466997i	$-0.154664\pi$
$937$	1657.10			1.76852			0.884259	+	0.466997i	$0.154664\pi$
$938$	48.2113	−	11.1614i	0.0513980	−	0.0118992i
$939$		0			0
$940$	−214.601	+	91.7184i	−0.228299	+	0.0975728i
$941$			519.083i			0.551629i	0.961211	+	0.275815i	$0.0889476\pi$
$941$			519.083i			0.551629i	−0.961211	+	0.275815i	$0.911052\pi$
$942$		0			0
$943$	307.703			0.326302
$944$			171.740i			0.181928i
$945$		0			0
$946$	−485.689			−0.513413
$947$		−	558.258i		−	0.589502i	−0.955574	−	0.294751i	$-0.904763\pi$
$947$		−	558.258i		−	0.589502i	0.955574	−	0.294751i	$-0.0952366\pi$
$948$		0			0
$949$	1820.39			1.91822
$950$	−825.226	+	863.029i	−0.868659	+	0.908452i
$951$		0			0
$952$	25.9637	+	112.149i	0.0272728	+	0.117804i
$953$		−	291.413i		−	0.305784i	−0.988243	−	0.152892i	$-0.951141\pi$
$953$		−	291.413i		−	0.305784i	0.988243	−	0.152892i	$-0.0488587\pi$
$954$		0			0
$955$	681.786	−	291.389i	0.713912	−	0.305119i
$956$	−498.530			−0.521475
$957$		0			0
$958$	−1217.14			−1.27050
$959$	−79.9559	−	345.367i	−0.0833742	−	0.360132i
$960$		0			0
$961$	590.215			0.614167
$962$	1310.35			1.36211
$963$		0			0
$964$			524.686i			0.544280i
$965$	−69.1458	−	161.786i	−0.0716537	−	0.167654i
$966$		0			0
$967$		−	323.558i		−	0.334600i	−0.985906	−	0.167300i	$-0.946495\pi$
$967$		−	323.558i		−	0.334600i	0.985906	−	0.167300i	$-0.0535048\pi$
$968$			153.924i			0.159012i
$969$		0			0
$970$	−229.986	−	538.118i	−0.237099	−	0.554761i
$971$		−	219.659i		−	0.226219i	−0.993583	−	0.113110i	$-0.963919\pi$
$971$		−	219.659i		−	0.226219i	0.993583	−	0.113110i	$-0.0360812\pi$
$972$		0			0
$973$	−116.873	−	504.827i	−0.120116	−	0.518836i
$974$	−1254.65			−1.28814
$975$		0			0
$976$		−	137.146i		−	0.140518i
$977$			1302.29i			1.33295i	0.745527	+	0.666475i	$0.232198\pi$
$977$			1302.29i			1.33295i	−0.745527	+	0.666475i	$0.767802\pi$
$978$		0			0
$979$		−	132.422i		−	0.135263i
$980$	−320.104	+	370.990i	−0.326636	+	0.378561i
$981$		0			0
$982$			70.9685i			0.0722693i
$983$	−649.905			−0.661144			−0.330572	−	0.943781i	$-0.607242\pi$
$983$	−649.905			−0.661144			−0.330572	+	0.943781i	$0.607242\pi$
$984$		0			0
$985$	−380.492	−	890.270i	−0.386287	−	0.903827i
$986$			76.0834i			0.0771637i
$987$		0			0
$988$			986.621i			0.998604i
$989$	−1568.15			−1.58559
$990$		0			0
$991$	−575.568			−0.580795			−0.290397	−	0.956906i	$-0.593788\pi$
$991$	−575.568			−0.580795			−0.290397	+	0.956906i	$0.593788\pi$
$992$	108.927			0.109806
$993$		0			0
$994$	−86.6587	−	374.319i	−0.0871818	−	0.376578i
$995$	357.313	+	836.035i	0.359108	+	0.840236i
$996$		0			0
$997$	−705.512			−0.707635			−0.353817	−	0.935315i	$-0.615117\pi$
$997$	−705.512			−0.707635			−0.353817	+	0.935315i	$0.615117\pi$
$998$			226.901i			0.227355i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.h.e.559.15		16
3.2	odd	2		210.3.h.a.139.5	yes	16
5.4	even	2	inner	630.3.h.e.559.2		16
7.6	odd	2	inner	630.3.h.e.559.10		16
12.11	even	2		1680.3.bd.a.769.2		16
15.2	even	4		1050.3.f.e.601.10		16
15.8	even	4		1050.3.f.e.601.7		16
15.14	odd	2		210.3.h.a.139.12	yes	16
21.20	even	2		210.3.h.a.139.4	✓	16
35.34	odd	2	inner	630.3.h.e.559.7		16
60.59	even	2		1680.3.bd.a.769.16		16
84.83	odd	2		1680.3.bd.a.769.15		16
105.62	odd	4		1050.3.f.e.601.14		16
105.83	odd	4		1050.3.f.e.601.3		16
105.104	even	2		210.3.h.a.139.13	yes	16
420.419	odd	2		1680.3.bd.a.769.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.h.a.139.4	✓	16	21.20	even	2
210.3.h.a.139.5	yes	16	3.2	odd	2
210.3.h.a.139.12	yes	16	15.14	odd	2
210.3.h.a.139.13	yes	16	105.104	even	2
630.3.h.e.559.2		16	5.4	even	2	inner
630.3.h.e.559.7		16	35.34	odd	2	inner
630.3.h.e.559.10		16	7.6	odd	2	inner
630.3.h.e.559.15		16	1.1	even	1	trivial
1050.3.f.e.601.3		16	105.83	odd	4
1050.3.f.e.601.7		16	15.8	even	4
1050.3.f.e.601.10		16	15.2	even	4
1050.3.f.e.601.14		16	105.62	odd	4
1680.3.bd.a.769.1		16	420.419	odd	2
1680.3.bd.a.769.2		16	12.11	even	2
1680.3.bd.a.769.15		16	84.83	odd	2
1680.3.bd.a.769.16		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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	630.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -2.00000 q^{4} +(4.59769 - 1.96501i) q^{5} +(-6.81963 + 1.57881i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+1.41421i q^{2} -2.00000 q^{4} +(4.59769 - 1.96501i) q^{5} +(-6.81963 + 1.57881i) q^{7} -2.82843i q^{8} +(2.77894 + 6.50212i) q^{10} +8.15965 q^{11} -14.6064 q^{13} +(-2.23278 - 9.64441i) q^{14} +4.00000 q^{16} +5.81421 q^{17} +33.7736i q^{19} +(-9.19538 + 3.93001i) q^{20} +11.5395i q^{22} +37.2576i q^{23} +(17.2775 - 18.0690i) q^{25} -20.6566i q^{26} +(13.6393 - 3.15763i) q^{28} +9.25305 q^{29} -19.2558i q^{31} +5.65685i q^{32} +8.22253i q^{34} +(-28.2522 + 20.6595i) q^{35} +63.4350i q^{37} -47.7631 q^{38} +(-5.55788 - 13.0042i) q^{40} -8.25880i q^{41} +42.0893i q^{43} -16.3193 q^{44} -52.6901 q^{46} +23.3380 q^{47} +(44.0147 - 21.5339i) q^{49} +(25.5534 + 24.4341i) q^{50} +29.2128 q^{52} +71.3497i q^{53} +(37.5155 - 16.0337i) q^{55} +(4.46556 + 19.2888i) q^{56} +13.0858i q^{58} +42.9350i q^{59} -34.2864i q^{61} +27.2318 q^{62} -8.00000 q^{64} +(-67.1557 + 28.7017i) q^{65} +4.99889i q^{67} -11.6284 q^{68} +(-29.2170 - 39.9546i) q^{70} +38.8120 q^{71} -124.629 q^{73} -89.7107 q^{74} -67.5472i q^{76} +(-55.6458 + 12.8826i) q^{77} -56.1842 q^{79} +(18.3908 - 7.86002i) q^{80} +11.6797 q^{82} -90.3980 q^{83} +(26.7319 - 11.4249i) q^{85} -59.5233 q^{86} -23.0790i q^{88} -16.2289i q^{89} +(99.6102 - 23.0608i) q^{91} -74.5151i q^{92} +33.0048i q^{94} +(66.3653 + 155.280i) q^{95} -82.7605 q^{97} +(30.4535 + 62.2462i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4}+O(q^{10}) \) 16 * q - 32 * q^4	\( 16 q - 32 q^{4} - 96 q^{11} - 16 q^{14} + 64 q^{16} + 24 q^{25} - 64 q^{29} + 8 q^{35} + 192 q^{44} - 176 q^{46} + 224 q^{49} + 96 q^{50} + 32 q^{56} - 128 q^{64} - 368 q^{65} - 56 q^{70} + 384 q^{71} - 224 q^{74} - 608 q^{79} - 440 q^{85} - 416 q^{86} + 224 q^{91} + 560 q^{95}+O(q^{100}) \) 16 * q - 32 * q^4 - 96 * q^11 - 16 * q^14 + 64 * q^16 + 24 * q^25 - 64 * q^29 + 8 * q^35 + 192 * q^44 - 176 * q^46 + 224 * q^49 + 96 * q^50 + 32 * q^56 - 128 * q^64 - 368 * q^65 - 56 * q^70 + 384 * q^71 - 224 * q^74 - 608 * q^79 - 440 * q^85 - 416 * q^86 + 224 * q^91 + 560 * q^95

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