LMFDB - Embedded newform 630.4.g.e.379.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,4,Mod(379,630)]

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, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("630.379");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	630.g (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:	$37.1712033036$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.4
Root			$-1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	630.379
Dual form			630.4.g.e.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -4.00000 q^{4} +(10.7980 + 2.89898i) q^{5} -7.00000i q^{7} -8.00000i q^{8} +O(q^{10})$	\(q+2.00000i q^{2} -4.00000 q^{4} +(10.7980 + 2.89898i) q^{5} -7.00000i q^{7} -8.00000i q^{8} +(-5.79796 + 21.5959i) q^{10} +13.5959 q^{11} -10.8082i q^{13} +14.0000 q^{14} +16.0000 q^{16} -98.7878i q^{17} -7.79796 q^{19} +(-43.1918 - 11.5959i) q^{20} +27.1918i q^{22} -95.3735i q^{23} +(108.192 + 62.6061i) q^{25} +21.6163 q^{26} +28.0000i q^{28} +0.202041 q^{29} -165.596 q^{31} +32.0000i q^{32} +197.576 q^{34} +(20.2929 - 75.5857i) q^{35} +10.9694i q^{37} -15.5959i q^{38} +(23.1918 - 86.3837i) q^{40} -12.3837 q^{41} -358.929i q^{43} -54.3837 q^{44} +190.747 q^{46} -450.565i q^{47} -49.0000 q^{49} +(-125.212 + 216.384i) q^{50} +43.2327i q^{52} -286.504i q^{53} +(146.808 + 39.4143i) q^{55} -56.0000 q^{56} +0.404082i q^{58} +739.069 q^{59} -407.716 q^{61} -331.192i q^{62} -64.0000 q^{64} +(31.3326 - 116.706i) q^{65} +77.8796i q^{67} +395.151i q^{68} +(151.171 + 40.5857i) q^{70} +558.100 q^{71} -28.8286i q^{73} -21.9388 q^{74} +31.1918 q^{76} -95.1714i q^{77} -109.616 q^{79} +(172.767 + 46.3837i) q^{80} -24.7673i q^{82} +1262.75i q^{83} +(286.384 - 1066.71i) q^{85} +717.857 q^{86} -108.767i q^{88} +1390.97 q^{89} -75.6571 q^{91} +381.494i q^{92} +901.131 q^{94} +(-84.2020 - 22.6061i) q^{95} +418.082i q^{97} -98.0000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{4} + 4 q^{5}+O(q^{10}) $ 4 * q - 16 * q^4 + 4 * q^5	$ 4 q - 16 q^{4} + 4 q^{5} + 16 q^{10} - 24 q^{11} + 56 q^{14} + 64 q^{16} + 8 q^{19} - 16 q^{20} + 276 q^{25} + 400 q^{26} + 40 q^{29} - 584 q^{31} + 320 q^{34} - 56 q^{35} - 64 q^{40} + 264 q^{41} + 96 q^{44} - 256 q^{46} - 196 q^{49} - 736 q^{50} + 744 q^{55} - 224 q^{56} + 448 q^{59} - 24 q^{61} - 256 q^{64} - 1168 q^{65} + 56 q^{70} + 312 q^{71} + 1088 q^{74} - 32 q^{76} - 752 q^{79} + 64 q^{80} + 832 q^{85} + 128 q^{86} + 1096 q^{89} - 1400 q^{91} + 2272 q^{94} - 376 q^{95}+O(q^{100}) $ 4 * q - 16 * q^4 + 4 * q^5 + 16 * q^10 - 24 * q^11 + 56 * q^14 + 64 * q^16 + 8 * q^19 - 16 * q^20 + 276 * q^25 + 400 * q^26 + 40 * q^29 - 584 * q^31 + 320 * q^34 - 56 * q^35 - 64 * q^40 + 264 * q^41 + 96 * q^44 - 256 * q^46 - 196 * q^49 - 736 * q^50 + 744 * q^55 - 224 * q^56 + 448 * q^59 - 24 * q^61 - 256 * q^64 - 1168 * q^65 + 56 * q^70 + 312 * q^71 + 1088 * q^74 - 32 * q^76 - 752 * q^79 + 64 * q^80 + 832 * q^85 + 128 * q^86 + 1096 * q^89 - 1400 * q^91 + 2272 * q^94 - 376 * 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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−4.00000			−0.500000
$5$	10.7980	+	2.89898i	0.965799	+	0.259293i
$5$	10.7980	+	2.89898i	0.965799	+	0.259293i
$6$		0			0
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$		−	8.00000i		−	0.353553i
$9$		0			0
$10$	−5.79796	+	21.5959i	−0.183348	+	0.682923i
$11$	13.5959			0.372666			0.186333	−	0.982487i	$-0.440340\pi$
$11$	13.5959			0.372666			0.186333	+	0.982487i	$0.440340\pi$
$12$		0			0
$13$		−	10.8082i		−	0.230588i	−0.993331	−	0.115294i	$-0.963219\pi$
$13$		−	10.8082i		−	0.230588i	0.993331	−	0.115294i	$-0.0367810\pi$
$14$	14.0000			0.267261
$15$		0			0
$16$	16.0000			0.250000
$17$		−	98.7878i		−	1.40939i	−0.709513	−	0.704693i	$-0.751085\pi$
$17$		−	98.7878i		−	1.40939i	0.709513	−	0.704693i	$-0.248915\pi$
$18$		0			0
$19$	−7.79796			−0.0941566			−0.0470783	−	0.998891i	$-0.514991\pi$
$19$	−7.79796			−0.0941566			−0.0470783	+	0.998891i	$0.514991\pi$
$20$	−43.1918	−	11.5959i	−0.482899	−	0.129646i
$21$		0			0
$22$			27.1918i			0.263514i
$23$		−	95.3735i		−	0.864641i	−0.901720	−	0.432320i	$-0.857695\pi$
$23$		−	95.3735i		−	0.864641i	0.901720	−	0.432320i	$-0.142305\pi$
$24$		0			0
$25$	108.192	+	62.6061i	0.865535	+	0.500849i
$26$	21.6163			0.163050
$27$		0			0
$28$			28.0000i			0.188982i
$29$	0.202041			0.00129373			0.000646863	−	1.00000i	$-0.499794\pi$
$29$	0.202041			0.00129373			0.000646863		1.00000i	$0.499794\pi$
$30$		0			0
$31$	−165.596			−0.959416			−0.479708	−	0.877428i	$-0.659257\pi$
$31$	−165.596			−0.959416			−0.479708	+	0.877428i	$0.659257\pi$
$32$			32.0000i			0.176777i
$33$		0			0
$34$	197.576			0.996586
$35$	20.2929	−	75.5857i	0.0980034	−	0.365038i
$36$		0			0
$37$			10.9694i			0.0487393i	0.999703	+	0.0243697i	$0.00775788\pi$
$37$			10.9694i			0.0487393i	−0.999703	+	0.0243697i	$0.992242\pi$
$38$		−	15.5959i		−	0.0665787i
$39$		0			0
$40$	23.1918	−	86.3837i	0.0916738	−	0.341461i
$41$	−12.3837			−0.0471708			−0.0235854	−	0.999722i	$-0.507508\pi$
$41$	−12.3837			−0.0471708			−0.0235854	+	0.999722i	$0.507508\pi$
$42$		0			0
$43$		−	358.929i		−	1.27293i	−0.771305	−	0.636466i	$-0.780395\pi$
$43$		−	358.929i		−	1.27293i	0.771305	−	0.636466i	$-0.219605\pi$
$44$	−54.3837			−0.186333
$45$		0			0
$46$	190.747			0.611393
$47$		−	450.565i		−	1.39833i	−0.714958	−	0.699167i	$-0.753554\pi$
$47$		−	450.565i		−	1.39833i	0.714958	−	0.699167i	$-0.246446\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	−125.212	+	216.384i	−0.354154	+	0.612025i
$51$		0			0
$52$			43.2327i			0.115294i
$53$		−	286.504i		−	0.742535i	−0.928526	−	0.371268i	$-0.878923\pi$
$53$		−	286.504i		−	0.742535i	0.928526	−	0.371268i	$-0.121077\pi$
$54$		0			0
$55$	146.808	+	39.4143i	0.359920	+	0.0966295i
$56$	−56.0000			−0.133631
$57$		0			0
$58$			0.404082i			0.000914803i
$59$	739.069			1.63082			0.815412	−	0.578881i	$-0.196510\pi$
$59$	739.069			1.63082			0.815412	+	0.578881i	$0.196510\pi$
$60$		0			0
$61$	−407.716			−0.855782			−0.427891	−	0.903830i	$-0.640743\pi$
$61$	−407.716			−0.855782			−0.427891	+	0.903830i	$0.640743\pi$
$62$		−	331.192i		−	0.678410i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	31.3326	−	116.706i	0.0597898	−	0.222702i
$66$		0			0
$67$			77.8796i			0.142008i	0.997476	+	0.0710038i	$0.0226202\pi$
$67$			77.8796i			0.142008i	−0.997476	+	0.0710038i	$0.977380\pi$
$68$			395.151i			0.704693i
$69$		0			0
$70$	151.171	+	40.5857i	0.258121	+	0.0692989i
$71$	558.100			0.932877			0.466439	−	0.884554i	$-0.345537\pi$
$71$	558.100			0.932877			0.466439	+	0.884554i	$0.345537\pi$
$72$		0			0
$73$		−	28.8286i		−	0.0462210i	−0.999733	−	0.0231105i	$-0.992643\pi$
$73$		−	28.8286i		−	0.0462210i	0.999733	−	0.0231105i	$-0.00735695\pi$
$74$	−21.9388			−0.0344639
$75$		0			0
$76$	31.1918			0.0470783
$77$		−	95.1714i		−	0.140854i
$78$		0			0
$79$	−109.616			−0.156111			−0.0780557	−	0.996949i	$-0.524871\pi$
$79$	−109.616			−0.156111			−0.0780557	+	0.996949i	$0.524871\pi$
$80$	172.767	+	46.3837i	0.241450	+	0.0648232i
$81$		0			0
$82$		−	24.7673i		−	0.0333548i
$83$			1262.75i			1.66993i	0.550300	+	0.834967i	$0.314513\pi$
$83$			1262.75i			1.66993i	−0.550300	+	0.834967i	$0.685487\pi$
$84$		0			0
$85$	286.384	−	1066.71i	0.365443	−	1.36118i
$86$	717.857			0.900099
$87$		0			0
$88$		−	108.767i		−	0.131757i
$89$	1390.97			1.65665			0.828327	−	0.560245i	$-0.189293\pi$
$89$	1390.97			1.65665			0.828327	+	0.560245i	$0.189293\pi$
$90$		0			0
$91$	−75.6571			−0.0871541
$92$			381.494i			0.432320i
$93$		0			0
$94$	901.131			0.988772
$95$	−84.2020	−	22.6061i	−0.0909363	−	0.0244141i
$96$		0			0
$97$			418.082i			0.437626i	0.975767	+	0.218813i	$0.0702185\pi$
$97$			418.082i			0.437626i	−0.975767	+	0.218813i	$0.929781\pi$
$98$		−	98.0000i		−	0.101015i
$99$		0			0
$100$	−432.767	−	250.424i	−0.432767	−	0.250424i
$101$	1619.37			1.59538			0.797690	−	0.603067i	$-0.206055\pi$
$101$	1619.37			1.59538			0.797690	+	0.603067i	$0.206055\pi$
$102$		0			0
$103$		−	1470.22i		−	1.40646i	−0.710964	−	0.703229i	$-0.751741\pi$
$103$		−	1470.22i		−	1.40646i	0.710964	−	0.703229i	$-0.248259\pi$
$104$	−86.4653			−0.0815252
$105$		0			0
$106$	573.008			0.525052
$107$		−	1201.39i		−	1.08545i	−0.839911	−	0.542725i	$-0.817393\pi$
$107$		−	1201.39i		−	1.08545i	0.839911	−	0.542725i	$-0.182607\pi$
$108$		0			0
$109$	917.718			0.806436			0.403218	−	0.915104i	$-0.367892\pi$
$109$	917.718			0.806436			0.403218	+	0.915104i	$0.367892\pi$
$110$	−78.8286	+	293.616i	−0.0683274	+	0.254502i
$111$		0			0
$112$		−	112.000i		−	0.0944911i
$113$			774.827i			0.645040i	0.946563	+	0.322520i	$0.104530\pi$
$113$			774.827i			0.645040i	−0.946563	+	0.322520i	$0.895470\pi$
$114$		0			0
$115$	276.486	−	1029.84i	0.224195	−	0.835069i
$116$	−0.808164			−0.000646863
$117$		0			0
$118$			1478.14i			1.15317i
$119$	−691.514			−0.532698
$120$		0			0
$121$	−1146.15			−0.861120
$122$		−	815.433i		−	0.605130i
$123$		0			0
$124$	662.384			0.479708
$125$	986.757	+	989.664i	0.706066	+	0.708146i
$126$		0			0
$127$		−	8.15916i		−	0.00570085i	−0.999996	−	0.00285043i	$-0.999093\pi$
$127$		−	8.15916i		−	0.00570085i	0.999996	−	0.00285043i	$-0.000907320\pi$
$128$		−	128.000i		−	0.0883883i
$129$		0			0
$130$	233.412	+	62.6653i	0.157474	+	0.0422778i
$131$	−876.808			−0.584787			−0.292393	−	0.956298i	$-0.594452\pi$
$131$	−876.808			−0.584787			−0.292393	+	0.956298i	$0.594452\pi$
$132$		0			0
$133$			54.5857i			0.0355878i
$134$	−155.759			−0.100415
$135$		0			0
$136$	−790.302			−0.498293
$137$		−	1077.53i		−	0.671970i	−0.941867	−	0.335985i	$-0.890931\pi$
$137$		−	1077.53i		−	0.671970i	0.941867	−	0.335985i	$-0.109069\pi$
$138$		0			0
$139$	1555.72			0.949310			0.474655	−	0.880172i	$-0.342573\pi$
$139$	1555.72			0.949310			0.474655	+	0.880172i	$0.342573\pi$
$140$	−81.1714	+	302.343i	−0.0490017	+	0.182519i
$141$		0			0
$142$			1116.20i			0.659644i
$143$		−	146.947i		−	0.0859323i
$144$		0			0
$145$	2.18163	+	0.585713i	0.00124948	+	0.000335454i
$146$	57.6571			0.0326831
$147$		0			0
$148$		−	43.8775i		−	0.0243697i
$149$	1806.99			0.993519			0.496760	−	0.867888i	$-0.334523\pi$
$149$	1806.99			0.993519			0.496760	+	0.867888i	$0.334523\pi$
$150$		0			0
$151$	949.612			0.511777			0.255889	−	0.966706i	$-0.417632\pi$
$151$	949.612			0.511777			0.255889	+	0.966706i	$0.417632\pi$
$152$			62.3837i			0.0332894i
$153$		0			0
$154$	190.343			0.0995991
$155$	−1788.10	−	480.059i	−0.926603	−	0.248770i
$156$		0			0
$157$			3018.52i			1.53442i	0.641395	+	0.767211i	$0.278356\pi$
$157$			3018.52i			1.53442i	−0.641395	+	0.767211i	$0.721644\pi$
$158$		−	219.233i		−	0.110387i
$159$		0			0
$160$	−92.7673	+	345.535i	−0.0458369	+	0.170731i
$161$	−667.614			−0.326804
$162$		0			0
$163$			741.231i			0.356182i	0.984014	+	0.178091i	$0.0569921\pi$
$163$			741.231i			0.356182i	−0.984014	+	0.178091i	$0.943008\pi$
$164$	49.5347			0.0235854
$165$		0			0
$166$	−2525.49			−1.18082
$167$			52.2591i			0.0242152i	0.999927	+	0.0121076i	$0.00385406\pi$
$167$			52.2591i			0.0242152i	−0.999927	+	0.0121076i	$0.996146\pi$
$168$		0			0
$169$	2080.18			0.946829
$170$	2133.41	+	572.767i	0.962501	+	0.258407i
$171$		0			0
$172$			1435.71i			0.636466i
$173$			155.378i			0.0682840i	0.999417	+	0.0341420i	$0.0108699\pi$
$173$			155.378i			0.0682840i	−0.999417	+	0.0341420i	$0.989130\pi$
$174$		0			0
$175$	438.243	−	757.343i	0.189303	−	0.327141i
$176$	217.535			0.0931664
$177$		0			0
$178$			2781.93i			1.17143i
$179$	−2442.07			−1.01972			−0.509858	−	0.860259i	$-0.670302\pi$
$179$	−2442.07			−1.01972			−0.509858	+	0.860259i	$0.670302\pi$
$180$		0			0
$181$	−1153.49			−0.473693			−0.236846	−	0.971547i	$-0.576114\pi$
$181$	−1153.49			−0.473693			−0.236846	+	0.971547i	$0.576114\pi$
$182$		−	151.314i		−	0.0616273i
$183$		0			0
$184$	−762.988			−0.305697
$185$	−31.8000	+	118.447i	−0.0126378	+	0.0470724i
$186$		0			0
$187$		−	1343.11i		−	0.525230i
$188$			1802.26i			0.699167i
$189$		0			0
$190$	45.2122	−	168.404i	0.0172634	−	0.0643017i
$191$	−4828.85			−1.82934			−0.914668	−	0.404206i	$-0.867548\pi$
$191$	−4828.85			−1.82934			−0.914668	+	0.404206i	$0.867548\pi$
$192$		0			0
$193$			527.437i			0.196714i	0.995151	+	0.0983568i	$0.0313586\pi$
$193$			527.437i			0.196714i	−0.995151	+	0.0983568i	$0.968641\pi$
$194$	−836.163			−0.309449
$195$		0			0
$196$	196.000			0.0714286
$197$		−	2527.48i		−	0.914087i	−0.889444	−	0.457044i	$-0.848908\pi$
$197$		−	2527.48i		−	0.914087i	0.889444	−	0.457044i	$-0.151092\pi$
$198$		0			0
$199$	−5137.31			−1.83002			−0.915010	−	0.403431i	$-0.867817\pi$
$199$	−5137.31			−1.83002			−0.915010	+	0.403431i	$0.867817\pi$
$200$	500.849	−	865.535i	0.177077	−	0.306013i
$201$		0			0
$202$			3238.74i			1.12810i
$203$		−	1.41429i		−	0.000488983i
$204$		0			0
$205$	−133.718	−	35.9000i	−0.0455575	−	0.0122311i
$206$	2940.44			0.994516
$207$		0			0
$208$		−	172.931i		−	0.0576470i
$209$	−106.020			−0.0350889
$210$		0			0
$211$	5766.29			1.88137			0.940683	−	0.339288i	$-0.110186\pi$
$211$	5766.29			1.88137			0.940683	+	0.339288i	$0.110186\pi$
$212$			1146.02i			0.371268i
$213$		0			0
$214$	2402.79			0.767529
$215$	1040.53	−	3875.70i	0.330062	−	1.22940i
$216$		0			0
$217$			1159.17i			0.362625i
$218$			1835.44i			0.570236i
$219$		0			0
$220$	−587.233	−	157.657i	−0.179960	−	0.0483147i
$221$	−1067.71			−0.324987
$222$		0			0
$223$		−	1194.30i		−	0.358637i	−0.983791	−	0.179319i	$-0.942611\pi$
$223$		−	1194.30i		−	0.358637i	0.983791	−	0.179319i	$-0.0573893\pi$
$224$	224.000			0.0668153
$225$		0			0
$226$	−1549.65			−0.456112
$227$		−	3101.45i		−	0.906830i	−0.891300	−	0.453415i	$-0.850206\pi$
$227$		−	3101.45i		−	0.906830i	0.891300	−	0.453415i	$-0.149794\pi$
$228$		0			0
$229$	−2161.00			−0.623594			−0.311797	−	0.950149i	$-0.600931\pi$
$229$	−2161.00			−0.623594			−0.311797	+	0.950149i	$0.600931\pi$
$230$	2059.68	+	552.971i	0.590483	+	0.158530i
$231$		0			0
$232$		−	1.61633i		−	0.000457401i
$233$			3124.28i			0.878449i	0.898377	+	0.439225i	$0.144747\pi$
$233$			3124.28i			0.878449i	−0.898377	+	0.439225i	$0.855253\pi$
$234$		0			0
$235$	1306.18	−	4865.19i	0.362578	−	1.35051i
$236$	−2956.28			−0.815412
$237$		0			0
$238$		−	1383.03i		−	0.376674i
$239$	1632.89			0.441937			0.220969	−	0.975281i	$-0.429078\pi$
$239$	1632.89			0.441937			0.220969	+	0.975281i	$0.429078\pi$
$240$		0			0
$241$	−4947.81			−1.32247			−0.661237	−	0.750177i	$-0.729968\pi$
$241$	−4947.81			−1.32247			−0.661237	+	0.750177i	$0.729968\pi$
$242$		−	2292.30i		−	0.608904i
$243$		0			0
$244$	1630.87			0.427891
$245$	−529.100	−	142.050i	−0.137971	−	0.0370418i
$246$		0			0
$247$			84.2816i			0.0217114i
$248$			1324.77i			0.339205i
$249$		0			0
$250$	−1979.33	+	1973.51i	−0.500735	+	0.499264i
$251$	−6977.04			−1.75453			−0.877265	−	0.480006i	$-0.840635\pi$
$251$	−6977.04			−1.75453			−0.877265	+	0.480006i	$0.840635\pi$
$252$		0			0
$253$		−	1296.69i		−	0.322222i
$254$	16.3183			0.00403111
$255$		0			0
$256$	256.000			0.0625000
$257$		−	3164.36i		−	0.768045i	−0.923324	−	0.384022i	$-0.874539\pi$
$257$		−	3164.36i		−	0.768045i	0.923324	−	0.384022i	$-0.125461\pi$
$258$		0			0
$259$	76.7857			0.0184217
$260$	−125.331	+	466.824i	−0.0298949	+	0.111351i
$261$		0			0
$262$		−	1753.62i		−	0.413507i
$263$		−	496.871i		−	0.116496i	−0.998302	−	0.0582479i	$-0.981449\pi$
$263$		−	496.871i		−	0.116496i	0.998302	−	0.0582479i	$-0.0185514\pi$
$264$		0			0
$265$	830.569	−	3093.66i	0.192534	−	0.717140i
$266$	−109.171			−0.0251644
$267$		0			0
$268$		−	311.518i		−	0.0710038i
$269$	3897.19			0.883330			0.441665	−	0.897180i	$-0.354388\pi$
$269$	3897.19			0.883330			0.441665	+	0.897180i	$0.354388\pi$
$270$		0			0
$271$	−7309.63			−1.63848			−0.819240	−	0.573450i	$-0.805605\pi$
$271$	−7309.63			−1.63848			−0.819240	+	0.573450i	$0.805605\pi$
$272$		−	1580.60i		−	0.352346i
$273$		0			0
$274$	2155.07			0.475154
$275$	1470.97	+	851.188i	0.322555	+	0.186649i
$276$		0			0
$277$		−	8351.24i		−	1.81147i	−0.423844	−	0.905735i	$-0.639320\pi$
$277$		−	8351.24i		−	1.81147i	0.423844	−	0.905735i	$-0.360680\pi$
$278$			3111.43i			0.671264i
$279$		0			0
$280$	−604.686	−	162.343i	−0.129060	−	0.0346494i
$281$	−3816.91			−0.810311			−0.405156	−	0.914248i	$-0.632783\pi$
$281$	−3816.91			−0.810311			−0.405156	+	0.914248i	$0.632783\pi$
$282$		0			0
$283$		−	3683.58i		−	0.773733i	−0.922136	−	0.386866i	$-0.873557\pi$
$283$		−	3683.58i		−	0.773733i	0.922136	−	0.386866i	$-0.126443\pi$
$284$	−2232.40			−0.466439
$285$		0			0
$286$	293.894			0.0607633
$287$			86.6857i			0.0178289i
$288$		0			0
$289$	−4846.02			−0.986367
$290$	−1.17143	+	4.36326i	−0.000237202	+	0.000883516i
$291$		0			0
$292$			115.314i			0.0231105i
$293$			8450.79i			1.68498i	0.538709	+	0.842492i	$0.318912\pi$
$293$			8450.79i			1.68498i	−0.538709	+	0.842492i	$0.681088\pi$
$294$		0			0
$295$	7980.44	+	2142.55i	1.57505	+	0.422861i
$296$	87.7551			0.0172320
$297$		0			0
$298$			3613.98i			0.702524i
$299$	−1030.81			−0.199376
$300$		0			0
$301$	−2512.50			−0.481123
$302$			1899.22i			0.361881i
$303$		0			0
$304$	−124.767			−0.0235391
$305$	−4402.50	−	1181.96i	−0.826514	−	0.221898i
$306$		0			0
$307$		−	3323.79i		−	0.617911i	−0.951076	−	0.308956i	$-0.900021\pi$
$307$		−	3323.79i		−	0.617911i	0.951076	−	0.308956i	$-0.0999795\pi$
$308$			380.686i			0.0704272i
$309$		0			0
$310$	960.118	−	3576.20i	0.175907	−	0.655207i
$311$	−1760.61			−0.321013			−0.160506	−	0.987035i	$-0.551313\pi$
$311$	−1760.61			−0.321013			−0.160506	+	0.987035i	$0.551313\pi$
$312$		0			0
$313$			1717.91i			0.310230i	0.987896	+	0.155115i	$0.0495748\pi$
$313$			1717.91i			0.310230i	−0.987896	+	0.155115i	$0.950425\pi$
$314$	−6037.04			−1.08500
$315$		0			0
$316$	438.465			0.0780557
$317$			9539.06i			1.69012i	0.534674	+	0.845059i	$0.320435\pi$
$317$			9539.06i			1.69012i	−0.534674	+	0.845059i	$0.679565\pi$
$318$		0			0
$319$	2.74693			0.000482128
$320$	−691.069	−	185.535i	−0.120725	−	0.0324116i
$321$		0			0
$322$		−	1335.23i		−	0.231085i
$323$			770.343i			0.132703i
$324$		0			0
$325$	676.657	−	1169.36i	0.115490	−	0.199582i
$326$	−1482.46			−0.251859
$327$		0			0
$328$			99.0694i			0.0166774i
$329$	−3153.96			−0.528521
$330$		0			0
$331$	−452.359			−0.0751175			−0.0375588	−	0.999294i	$-0.511958\pi$
$331$	−452.359			−0.0751175			−0.0375588	+	0.999294i	$0.511958\pi$
$332$		−	5050.99i		−	0.834967i
$333$		0			0
$334$	−104.518			−0.0171227
$335$	−225.771	+	840.941i	−0.0368215	+	0.137151i
$336$		0			0
$337$			5637.61i			0.911277i	0.890165	+	0.455638i	$0.150589\pi$
$337$			5637.61i			0.911277i	−0.890165	+	0.455638i	$0.849411\pi$
$338$			4160.37i			0.669509i
$339$		0			0
$340$	−1145.53	+	4266.82i	−0.182722	+	0.680591i
$341$	−2251.43			−0.357542
$342$		0			0
$343$			343.000i			0.0539949i
$344$	−2871.43			−0.450050
$345$		0			0
$346$	−310.755			−0.0482841
$347$			12313.1i			1.90490i	0.304696	+	0.952450i	$0.401445\pi$
$347$			12313.1i			1.90490i	−0.304696	+	0.952450i	$0.598555\pi$
$348$		0			0
$349$	−7203.55			−1.10486			−0.552432	−	0.833558i	$-0.686300\pi$
$349$	−7203.55			−1.10486			−0.552432	+	0.833558i	$0.686300\pi$
$350$	1514.69	+	876.486i	0.231324	+	0.133858i
$351$		0			0
$352$			435.069i			0.0658786i
$353$		−	7030.58i		−	1.06006i	−0.847980	−	0.530028i	$-0.822181\pi$
$353$		−	7030.58i		−	1.06006i	0.847980	−	0.530028i	$-0.177819\pi$
$354$		0			0
$355$	6026.34	+	1617.92i	0.900972	+	0.241888i
$356$	−5563.87			−0.828327
$357$		0			0
$358$		−	4884.15i		−	0.721048i
$359$	5999.06			0.881946			0.440973	−	0.897520i	$-0.354634\pi$
$359$	5999.06			0.881946			0.440973	+	0.897520i	$0.354634\pi$
$360$		0			0
$361$	−6798.19			−0.991135
$362$		−	2306.98i		−	0.334951i
$363$		0			0
$364$	302.629			0.0435771
$365$	83.5734	−	311.290i	0.0119848	−	0.0446401i
$366$		0			0
$367$		−	9039.02i		−	1.28565i	−0.766014	−	0.642824i	$-0.777763\pi$
$367$		−	9039.02i		−	1.28565i	0.766014	−	0.642824i	$-0.222237\pi$
$368$		−	1525.98i		−	0.216160i
$369$		0			0
$370$	−236.894	−	63.6000i	−0.0332852	−	0.00893624i
$371$	−2005.53			−0.280652
$372$		0			0
$373$			12415.4i			1.72345i	0.507375	+	0.861726i	$0.330616\pi$
$373$			12415.4i			1.72345i	−0.507375	+	0.861726i	$0.669384\pi$
$374$	2686.22			0.371393
$375$		0			0
$376$	−3604.52			−0.494386
$377$		−	2.18369i		−	0.000298318i
$378$		0			0
$379$	−7339.39			−0.994721			−0.497360	−	0.867544i	$-0.665697\pi$
$379$	−7339.39			−0.994721			−0.497360	+	0.867544i	$0.665697\pi$
$380$	336.808	+	90.4245i	0.0454681	+	0.0122070i
$381$		0			0
$382$		−	9657.69i		−	1.29354i
$383$		−	8054.27i		−	1.07455i	−0.843406	−	0.537277i	$-0.819453\pi$
$383$		−	8054.27i		−	1.07455i	0.843406	−	0.537277i	$-0.180547\pi$
$384$		0			0
$385$	275.900	−	1027.66i	0.0365225	−	0.136037i
$386$	−1054.87			−0.139098
$387$		0			0
$388$		−	1672.33i		−	0.218813i
$389$	4405.48			0.574208			0.287104	−	0.957899i	$-0.407307\pi$
$389$	4405.48			0.574208			0.287104	+	0.957899i	$0.407307\pi$
$390$		0			0
$391$	−9421.73			−1.21861
$392$			392.000i			0.0505076i
$393$		0			0
$394$	5054.95			0.646357
$395$	−1183.63	−	317.775i	−0.150772	−	0.0404785i
$396$		0			0
$397$			10950.6i			1.38437i	0.721721	+	0.692184i	$0.243351\pi$
$397$			10950.6i			1.38437i	−0.721721	+	0.692184i	$0.756649\pi$
$398$		−	10274.6i		−	1.29402i
$399$		0			0
$400$	1731.07	+	1001.70i	0.216384	+	0.125212i
$401$	7942.59			0.989112			0.494556	−	0.869146i	$-0.335331\pi$
$401$	7942.59			0.989112			0.494556	+	0.869146i	$0.335331\pi$
$402$		0			0
$403$			1789.79i			0.221230i
$404$	−6477.49			−0.797690
$405$		0			0
$406$	2.82857			0.000345763
$407$			149.139i			0.0181635i
$408$		0			0
$409$	7094.02			0.857645			0.428822	−	0.903389i	$-0.358929\pi$
$409$	7094.02			0.857645			0.428822	+	0.903389i	$0.358929\pi$
$410$	71.8000	−	267.437i	0.00864866	−	0.0322140i
$411$		0			0
$412$			5880.88i			0.703229i
$413$		−	5173.49i		−	0.616394i
$414$		0			0
$415$	−3660.68	+	13635.1i	−0.433001	+	1.61282i
$416$	345.861			0.0407626
$417$		0			0
$418$		−	212.041i		−	0.0248116i
$419$	−2491.00			−0.290438			−0.145219	−	0.989400i	$-0.546389\pi$
$419$	−2491.00			−0.290438			−0.145219	+	0.989400i	$0.546389\pi$
$420$		0			0
$421$	−1567.51			−0.181462			−0.0907311	−	0.995875i	$-0.528920\pi$
$421$	−1567.51			−0.181462			−0.0907311	+	0.995875i	$0.528920\pi$
$422$			11532.6i			1.33033i
$423$		0			0
$424$	−2292.03			−0.262526
$425$	6184.72	−	10688.0i	0.705889	−	1.21987i
$426$		0			0
$427$			2854.01i			0.323455i
$428$			4805.58i			0.542725i
$429$		0			0
$430$	7751.39	+	2081.05i	0.869315	+	0.233389i
$431$	−715.843			−0.0800022			−0.0400011	−	0.999200i	$-0.512736\pi$
$431$	−715.843			−0.0800022			−0.0400011	+	0.999200i	$0.512736\pi$
$432$		0			0
$433$			3583.72i			0.397743i	0.980026	+	0.198871i	$0.0637276\pi$
$433$			3583.72i			0.397743i	−0.980026	+	0.198871i	$0.936272\pi$
$434$	−2318.34			−0.256415
$435$		0			0
$436$	−3670.87			−0.403218
$437$			743.718i			0.0814116i
$438$		0			0
$439$	10290.4			1.11875			0.559376	−	0.828914i	$-0.311041\pi$
$439$	10290.4			1.11875			0.559376	+	0.828914i	$0.311041\pi$
$440$	315.314	−	1174.47i	0.0341637	−	0.127251i
$441$		0			0
$442$		−	2135.43i		−	0.229801i
$443$		−	3716.40i		−	0.398581i	−0.979940	−	0.199291i	$-0.936136\pi$
$443$		−	3716.40i		−	0.398581i	0.979940	−	0.199291i	$-0.0638637\pi$
$444$		0			0
$445$	15019.6	+	4032.39i	1.59999	+	0.429558i
$446$	2388.60			0.253595
$447$		0			0
$448$			448.000i			0.0472456i
$449$	10608.7			1.11504			0.557521	−	0.830163i	$-0.311753\pi$
$449$	10608.7			1.11504			0.557521	+	0.830163i	$0.311753\pi$
$450$		0			0
$451$	−168.367			−0.0175790
$452$		−	3099.31i		−	0.322520i
$453$		0			0
$454$	6202.90			0.641226
$455$	−816.943	−	219.329i	−0.0841733	−	0.0225984i
$456$		0			0
$457$			8241.22i			0.843563i	0.906698	+	0.421781i	$0.138595\pi$
$457$			8241.22i			0.843563i	−0.906698	+	0.421781i	$0.861405\pi$
$458$		−	4322.00i		−	0.440948i
$459$		0			0
$460$	−1105.94	+	4119.36i	−0.112098	+	0.417535i
$461$	15252.5			1.54096			0.770478	−	0.637467i	$-0.220018\pi$
$461$	15252.5			1.54096			0.770478	+	0.637467i	$0.220018\pi$
$462$		0			0
$463$			3541.52i			0.355482i	0.984077	+	0.177741i	$0.0568790\pi$
$463$			3541.52i			0.355482i	−0.984077	+	0.177741i	$0.943121\pi$
$464$	3.23266			0.000323432
$465$		0			0
$466$	−6248.57			−0.621157
$467$			4220.46i			0.418200i	0.977894	+	0.209100i	$0.0670534\pi$
$467$			4220.46i			0.418200i	−0.977894	+	0.209100i	$0.932947\pi$
$468$		0			0
$469$	545.157			0.0536738
$470$	9730.37	+	2612.36i	0.954954	+	0.256381i
$471$		0			0
$472$		−	5912.55i		−	0.576583i
$473$		−	4879.96i		−	0.474378i
$474$		0			0
$475$	−843.675	−	488.200i	−0.0814958	−	0.0471582i
$476$	2766.06			0.266349
$477$		0			0
$478$			3265.78i			0.312497i
$479$	6685.70			0.637740			0.318870	−	0.947798i	$-0.396697\pi$
$479$	6685.70			0.637740			0.318870	+	0.947798i	$0.396697\pi$
$480$		0			0
$481$	118.559			0.0112387
$482$		−	9895.62i		−	0.935131i
$483$		0			0
$484$	4584.60			0.430560
$485$	−1212.01	+	4514.43i	−0.113473	+	0.422659i
$486$		0			0
$487$		−	5921.10i		−	0.550946i	−0.961309	−	0.275473i	$-0.911166\pi$
$487$		−	5921.10i		−	0.550946i	0.961309	−	0.275473i	$-0.0888345\pi$
$488$			3261.73i			0.302565i
$489$		0			0
$490$	284.100	−	1058.20i	0.0261925	−	0.0975604i
$491$	1625.67			0.149420			0.0747100	−	0.997205i	$-0.476197\pi$
$491$	1625.67			0.149420			0.0747100	+	0.997205i	$0.476197\pi$
$492$		0			0
$493$		−	19.9592i		−	0.00182336i
$494$	−168.563			−0.0153523
$495$		0			0
$496$	−2649.53			−0.239854
$497$		−	3906.70i		−	0.352594i
$498$		0			0
$499$	20263.3			1.81786			0.908929	−	0.416952i	$-0.136902\pi$
$499$	20263.3			1.81786			0.908929	+	0.416952i	$0.136902\pi$
$500$	−3947.03	−	3958.66i	−0.353033	−	0.354073i
$501$		0			0
$502$		−	13954.1i		−	1.24064i
$503$			13300.9i			1.17904i	0.807753	+	0.589521i	$0.200684\pi$
$503$			13300.9i			1.17904i	−0.807753	+	0.589521i	$0.799316\pi$
$504$		0			0
$505$	17485.9	+	4694.52i	1.54082	+	0.413670i
$506$	2593.38			0.227845
$507$		0			0
$508$			32.6366i			0.00285043i
$509$	−12280.6			−1.06941			−0.534704	−	0.845039i	$-0.679577\pi$
$509$	−12280.6			−1.06941			−0.534704	+	0.845039i	$0.679577\pi$
$510$		0			0
$511$	−201.800			−0.0174699
$512$			512.000i			0.0441942i
$513$		0			0
$514$	6328.73			0.543090
$515$	4262.14	−	15875.4i	0.364684	−	1.35835i
$516$		0			0
$517$		−	6125.85i		−	0.521111i
$518$			153.571i			0.0130261i
$519$		0			0
$520$	−933.649	−	250.661i	−0.0787369	−	0.0211389i
$521$	−18174.1			−1.52826			−0.764128	−	0.645064i	$-0.776831\pi$
$521$	−18174.1			−1.52826			−0.764128	+	0.645064i	$0.776831\pi$
$522$		0			0
$523$		−	8750.68i		−	0.731626i	−0.930688	−	0.365813i	$-0.880791\pi$
$523$		−	8750.68i		−	0.731626i	0.930688	−	0.365813i	$-0.119209\pi$
$524$	3507.23			0.292393
$525$		0			0
$526$	993.743			0.0823750
$527$			16358.8i			1.35219i
$528$		0			0
$529$	3070.90			0.252396
$530$	6187.32	+	1661.14i	0.507094	+	0.136142i
$531$		0			0
$532$		−	218.343i		−	0.0177939i
$533$			133.845i			0.0108770i
$534$		0			0
$535$	3482.82	−	12972.6i	0.281449	−	1.04833i
$536$	623.037			0.0502073
$537$		0			0
$538$			7794.38i			0.624609i
$539$	−666.200			−0.0532380
$540$		0			0
$541$	−656.045			−0.0521360			−0.0260680	−	0.999660i	$-0.508299\pi$
$541$	−656.045			−0.0521360			−0.0260680	+	0.999660i	$0.508299\pi$
$542$		−	14619.3i		−	1.15858i
$543$		0			0
$544$	3161.21			0.249146
$545$	9909.49	+	2660.45i	0.778855	+	0.209103i
$546$		0			0
$547$			5798.36i			0.453236i	0.973984	+	0.226618i	$0.0727669\pi$
$547$			5798.36i			0.453236i	−0.973984	+	0.226618i	$0.927233\pi$
$548$			4310.13i			0.335985i
$549$		0			0
$550$	−1702.38	+	2941.93i	−0.131981	+	0.228081i
$551$	−1.57551			−0.000121813
$552$		0			0
$553$			767.314i			0.0590046i
$554$	16702.5			1.28090
$555$		0			0
$556$	−6222.87			−0.474655
$557$			10841.0i			0.824680i	0.911030	+	0.412340i	$0.135288\pi$
$557$			10841.0i			0.824680i	−0.911030	+	0.412340i	$0.864712\pi$
$558$		0			0
$559$	−3879.36			−0.293523
$560$	324.686	−	1209.37i	0.0245008	−	0.0912594i
$561$		0			0
$562$		−	7633.81i		−	0.572977i
$563$			844.473i			0.0632155i	0.999500	+	0.0316077i	$0.0100627\pi$
$563$			844.473i			0.0632155i	−0.999500	+	0.0316077i	$0.989937\pi$
$564$		0			0
$565$	−2246.21	+	8366.54i	−0.167254	+	0.622979i
$566$	7367.17			0.547112
$567$		0			0
$568$		−	4464.80i		−	0.329822i
$569$	−12991.7			−0.957187			−0.478593	−	0.878037i	$-0.658853\pi$
$569$	−12991.7			−0.957187			−0.478593	+	0.878037i	$0.658853\pi$
$570$		0			0
$571$	5989.62			0.438980			0.219490	−	0.975615i	$-0.429561\pi$
$571$	5989.62			0.438980			0.219490	+	0.975615i	$0.429561\pi$
$572$			587.788i			0.0429661i
$573$		0			0
$574$	−173.371			−0.0126069
$575$	5970.96	−	10318.6i	0.433055	−	0.748377i
$576$		0			0
$577$			7876.11i			0.568261i	0.958786	+	0.284130i	$0.0917049\pi$
$577$			7876.11i			0.568261i	−0.958786	+	0.284130i	$0.908295\pi$
$578$		−	9692.04i		−	0.697467i
$579$		0			0
$580$	−8.72652	−	2.34285i	−0.000624740	−	0.000167727i
$581$	8839.23			0.631176
$582$		0			0
$583$		−	3895.29i		−	0.276717i
$584$	−230.629			−0.0163416
$585$		0			0
$586$	−16901.6			−1.19146
$587$			18207.9i			1.28028i	0.768260	+	0.640138i	$0.221123\pi$
$587$			18207.9i			1.28028i	−0.768260	+	0.640138i	$0.778877\pi$
$588$		0			0
$589$	1291.31			0.0903353
$590$	−4285.09	+	15960.9i	−0.299008	+	1.11373i
$591$		0			0
$592$			175.510i			0.0121848i
$593$		−	11709.0i		−	0.810848i	−0.914129	−	0.405424i	$-0.867124\pi$
$593$		−	11709.0i		−	0.810848i	0.914129	−	0.405424i	$-0.132876\pi$
$594$		0			0
$595$	−7466.94	−	2004.69i	−0.514479	−	0.138125i
$596$	−7227.96			−0.496760
$597$		0			0
$598$		−	2061.62i		−	0.140980i
$599$	20376.3			1.38990			0.694952	−	0.719056i	$-0.255426\pi$
$599$	20376.3			1.38990			0.694952	+	0.719056i	$0.255426\pi$
$600$		0			0
$601$	−13509.9			−0.916937			−0.458469	−	0.888711i	$-0.651602\pi$
$601$	−13509.9			−0.916937			−0.458469	+	0.888711i	$0.651602\pi$
$602$		−	5025.00i		−	0.340205i
$603$		0			0
$604$	−3798.45			−0.255889
$605$	−12376.1	−	3322.67i	−0.831669	−	0.223282i
$606$		0			0
$607$		−	24253.6i		−	1.62179i	−0.585193	−	0.810894i	$-0.698981\pi$
$607$		−	24253.6i		−	1.62179i	0.585193	−	0.810894i	$-0.301019\pi$
$608$		−	249.535i		−	0.0166447i
$609$		0			0
$610$	2363.92	−	8805.01i	0.156906	−	0.584433i
$611$	−4869.78			−0.322439
$612$		0			0
$613$			696.145i			0.0458679i	0.999737	+	0.0229340i	$0.00730074\pi$
$613$			696.145i			0.0458679i	−0.999737	+	0.0229340i	$0.992699\pi$
$614$	6647.58			0.436929
$615$		0			0
$616$	−761.371			−0.0497996
$617$			19894.8i			1.29811i	0.760740	+	0.649056i	$0.224836\pi$
$617$			19894.8i			1.29811i	−0.760740	+	0.649056i	$0.775164\pi$
$618$		0			0
$619$	−5616.19			−0.364675			−0.182337	−	0.983236i	$-0.558366\pi$
$619$	−5616.19			−0.364675			−0.182337	+	0.983236i	$0.558366\pi$
$620$	7152.39	+	1920.24i	0.463302	+	0.124385i
$621$		0			0
$622$		−	3521.22i		−	0.226990i
$623$		−	9736.77i		−	0.626157i
$624$		0			0
$625$	7785.95	+	13546.9i	0.498301	+	0.867004i
$626$	−3435.82			−0.219366
$627$		0			0
$628$		−	12074.1i		−	0.767211i
$629$	1083.64			0.0686925
$630$		0			0
$631$	−27234.6			−1.71821			−0.859106	−	0.511798i	$-0.828980\pi$
$631$	−27234.6			−1.71821			−0.859106	+	0.511798i	$0.828980\pi$
$632$			876.931i			0.0551937i
$633$		0			0
$634$	−19078.1			−1.19509
$635$	23.6532	−	88.1023i	0.00147819	−	0.00550588i
$636$		0			0
$637$			529.600i			0.0329412i
$638$			5.49387i			0.000340916i
$639$		0			0
$640$	371.069	−	1382.14i	0.0229184	−	0.0853654i
$641$	18064.7			1.11313			0.556563	−	0.830806i	$-0.312120\pi$
$641$	18064.7			1.11313			0.556563	+	0.830806i	$0.312120\pi$
$642$		0			0
$643$		−	2169.88i		−	0.133082i	−0.997784	−	0.0665409i	$-0.978804\pi$
$643$		−	2169.88i		−	0.133082i	0.997784	−	0.0665409i	$-0.0211963\pi$
$644$	2670.46			0.163402
$645$		0			0
$646$	−1540.69			−0.0938351
$647$		−	10954.9i		−	0.665657i	−0.942987	−	0.332829i	$-0.891997\pi$
$647$		−	10954.9i		−	0.665657i	0.942987	−	0.332829i	$-0.108003\pi$
$648$		0			0
$649$	10048.3			0.607752
$650$	2338.71	+	1353.31i	0.141126	+	0.0816636i
$651$		0			0
$652$		−	2964.92i		−	0.178091i
$653$			23846.3i			1.42906i	0.699603	+	0.714532i	$0.253360\pi$
$653$			23846.3i			1.42906i	−0.699603	+	0.714532i	$0.746640\pi$
$654$		0			0
$655$	−9467.74	−	2541.85i	−0.564787	−	0.151631i
$656$	−198.139			−0.0117927
$657$		0			0
$658$		−	6307.91i		−	0.373721i
$659$	29345.7			1.73467			0.867334	−	0.497726i	$-0.165832\pi$
$659$	29345.7			1.73467			0.867334	+	0.497726i	$0.165832\pi$
$660$		0			0
$661$	19909.3			1.17153			0.585764	−	0.810482i	$-0.300794\pi$
$661$	19909.3			1.17153			0.585764	+	0.810482i	$0.300794\pi$
$662$		−	904.718i		−	0.0531161i
$663$		0			0
$664$	10102.0			0.590411
$665$	−158.243	+	589.414i	−0.00922766	+	0.0343707i
$666$		0			0
$667$		−	19.2694i		−	0.00111861i
$668$		−	209.037i		−	0.0121076i
$669$		0			0
$670$	−1681.88	−	451.543i	−0.0969802	−	0.0260367i
$671$	−5543.28			−0.318921
$672$		0			0
$673$		−	14940.2i		−	0.855722i	−0.903845	−	0.427861i	$-0.859267\pi$
$673$		−	14940.2i		−	0.855722i	0.903845	−	0.427861i	$-0.140733\pi$
$674$	−11275.2			−0.644370
$675$		0			0
$676$	−8320.73			−0.473415
$677$			22193.1i			1.25989i	0.776638	+	0.629947i	$0.216924\pi$
$677$			22193.1i			1.25989i	−0.776638	+	0.629947i	$0.783076\pi$
$678$		0			0
$679$	2926.57			0.165407
$680$	−8533.65	−	2291.07i	−0.481251	−	0.129204i
$681$		0			0
$682$		−	4502.86i		−	0.252820i
$683$		−	31363.3i		−	1.75708i	−0.477670	−	0.878539i	$-0.658518\pi$
$683$		−	31363.3i		−	1.75708i	0.477670	−	0.878539i	$-0.341482\pi$
$684$		0			0
$685$	3123.74	−	11635.2i	0.174237	−	0.648987i
$686$	−686.000			−0.0381802
$687$		0			0
$688$		−	5742.86i		−	0.318233i
$689$	−3096.58			−0.171220
$690$		0			0
$691$	3043.95			0.167579			0.0837897	−	0.996483i	$-0.473298\pi$
$691$	3043.95			0.167579			0.0837897	+	0.996483i	$0.473298\pi$
$692$		−	621.510i		−	0.0341420i
$693$		0			0
$694$	−24626.1			−1.34697
$695$	16798.6	+	4509.99i	0.916843	+	0.246149i
$696$		0			0
$697$			1223.36i			0.0664819i
$698$		−	14407.1i		−	0.781256i
$699$		0			0
$700$	−1752.97	+	3029.37i	−0.0946516	+	0.163571i
$701$	−24625.6			−1.32681			−0.663405	−	0.748260i	$-0.730890\pi$
$701$	−24625.6			−1.32681			−0.663405	+	0.748260i	$0.730890\pi$
$702$		0			0
$703$		−	85.5388i		−	0.00458913i
$704$	−870.139			−0.0465832
$705$		0			0
$706$	14061.2			0.749573
$707$		−	11335.6i		−	0.602997i
$708$		0			0
$709$	29005.6			1.53643			0.768215	−	0.640192i	$-0.221145\pi$
$709$	29005.6			1.53643			0.768215	+	0.640192i	$0.221145\pi$
$710$	−3235.84	+	12052.7i	−0.171041	+	0.637083i
$711$		0			0
$712$		−	11127.7i		−	0.585716i
$713$			15793.5i			0.829551i
$714$		0			0
$715$	425.996	−	1586.73i	0.0222816	−	0.0829933i
$716$	9768.29			0.509858
$717$		0			0
$718$			11998.1i			0.623630i
$719$	2287.47			0.118648			0.0593242	−	0.998239i	$-0.481105\pi$
$719$	2287.47			0.118648			0.0593242	+	0.998239i	$0.481105\pi$
$720$		0			0
$721$	−10291.5			−0.531591
$722$		−	13596.4i		−	0.700838i
$723$		0			0
$724$	4613.97			0.236846
$725$	21.8592	+	12.6490i	0.00111977	+	0.000647962i
$726$		0			0
$727$			36915.8i			1.88326i	0.336645	+	0.941632i	$0.390708\pi$
$727$			36915.8i			1.88326i	−0.336645	+	0.941632i	$0.609292\pi$
$728$			605.257i			0.0308136i
$729$		0			0
$730$	622.580	+	167.147i	0.0315653	+	0.00847450i
$731$	−35457.7			−1.79405
$732$		0			0
$733$		−	7943.12i		−	0.400254i	−0.979770	−	0.200127i	$-0.935865\pi$
$733$		−	7943.12i		−	0.400254i	0.979770	−	0.200127i	$-0.0641354\pi$
$734$	18078.0			0.909091
$735$		0			0
$736$	3051.95			0.152848
$737$			1058.84i			0.0529214i
$738$		0			0
$739$	3388.38			0.168665			0.0843327	−	0.996438i	$-0.473124\pi$
$739$	3388.38			0.168665			0.0843327	+	0.996438i	$0.473124\pi$
$740$	127.200	−	473.788i	0.00631888	−	0.0235362i
$741$		0			0
$742$		−	4011.06i		−	0.198451i
$743$		−	26530.0i		−	1.30995i	−0.755652	−	0.654973i	$-0.772680\pi$
$743$		−	26530.0i		−	1.30995i	0.755652	−	0.654973i	$-0.227320\pi$
$744$		0			0
$745$	19511.8	+	5238.43i	0.959540	+	0.257612i
$746$	−24830.9			−1.21866
$747$		0			0
$748$			5372.44i			0.262615i
$749$	−8409.76			−0.410261
$750$		0			0
$751$	11544.9			0.560956			0.280478	−	0.959860i	$-0.409507\pi$
$751$	11544.9			0.560956			0.280478	+	0.959860i	$0.409507\pi$
$752$		−	7209.04i		−	0.349584i
$753$		0			0
$754$	4.36739			0.000210943
$755$	10253.9	+	2752.91i	0.494274	+	0.132700i
$756$		0			0
$757$			38521.4i			1.84952i	0.380555	+	0.924758i	$0.375733\pi$
$757$			38521.4i			1.84952i	−0.380555	+	0.924758i	$0.624267\pi$
$758$		−	14678.8i		−	0.703374i
$759$		0			0
$760$	−180.849	+	673.616i	−0.00863169	+	0.0321508i
$761$	−23725.7			−1.13017			−0.565083	−	0.825034i	$-0.691156\pi$
$761$	−23725.7			−1.13017			−0.565083	+	0.825034i	$0.691156\pi$
$762$		0			0
$763$		−	6424.03i		−	0.304804i
$764$	19315.4			0.914668
$765$		0			0
$766$	16108.5			0.759824
$767$		−	7987.98i		−	0.376049i
$768$		0			0
$769$	39110.5			1.83402			0.917009	−	0.398866i	$-0.130596\pi$
$769$	39110.5			1.83402			0.917009	+	0.398866i	$0.130596\pi$
$770$	2055.31	+	551.800i	0.0961927	+	0.0258253i
$771$		0			0
$772$		−	2109.75i		−	0.0983568i
$773$		−	35966.5i		−	1.67351i	−0.547577	−	0.836755i	$-0.684450\pi$
$773$		−	35966.5i		−	1.67351i	0.547577	−	0.836755i	$-0.315550\pi$
$774$		0			0
$775$	−17916.1	−	10367.3i	−0.830408	−	0.480523i
$776$	3344.65			0.154724
$777$		0			0
$778$			8810.97i			0.406026i
$779$	96.5674			0.00444144
$780$		0			0
$781$	7587.88			0.347651
$782$		−	18843.5i		−	0.861689i
$783$		0			0
$784$	−784.000			−0.0357143
$785$	−8750.63	+	32593.9i	−0.397864	+	1.48194i
$786$		0			0
$787$		−	13194.2i		−	0.597614i	−0.954313	−	0.298807i	$-0.903411\pi$
$787$		−	13194.2i		−	0.597614i	0.954313	−	0.298807i	$-0.0965888\pi$
$788$			10109.9i			0.457044i
$789$		0			0
$790$	635.551	−	2367.27i	0.0286226	−	0.106612i
$791$	5423.79			0.243802
$792$		0			0
$793$			4406.66i			0.197333i
$794$	−21901.2			−0.978896
$795$		0			0
$796$	20549.2			0.915010
$797$			10384.7i			0.461537i	0.973009	+	0.230769i	$0.0741240\pi$
$797$			10384.7i			0.461537i	−0.973009	+	0.230769i	$0.925876\pi$
$798$		0			0
$799$	−44510.3			−1.97079
$800$	−2003.40	+	3462.14i	−0.0885384	+	0.153006i
$801$		0			0
$802$			15885.2i			0.699408i
$803$		−	391.951i		−	0.0172250i
$804$		0			0
$805$	−7208.87	−	1935.40i	−0.315627	−	0.0847378i
$806$	−3579.58			−0.156433
$807$		0			0
$808$		−	12955.0i		−	0.564052i
$809$	1318.94			0.0573196			0.0286598	−	0.999589i	$-0.490876\pi$
$809$	1318.94			0.0573196			0.0286598	+	0.999589i	$0.490876\pi$
$810$		0			0
$811$	−23639.6			−1.02355			−0.511774	−	0.859120i	$-0.671012\pi$
$811$	−23639.6			−1.02355			−0.511774	+	0.859120i	$0.671012\pi$
$812$			5.65715i			0.000244491i
$813$		0			0
$814$	−298.278			−0.0128435
$815$	−2148.81	+	8003.78i	−0.0923554	+	0.344000i
$816$		0			0
$817$			2798.91i			0.119855i
$818$			14188.0i			0.606446i
$819$		0			0
$820$	534.874	+	143.600i	0.0227788	+	0.00611553i
$821$	23351.9			0.992677			0.496338	−	0.868129i	$-0.334678\pi$
$821$	23351.9			0.992677			0.496338	+	0.868129i	$0.334678\pi$
$822$		0			0
$823$			5675.84i			0.240398i	0.992750	+	0.120199i	$0.0383533\pi$
$823$			5675.84i			0.240398i	−0.992750	+	0.120199i	$0.961647\pi$
$824$	−11761.8			−0.497258
$825$		0			0
$826$	10347.0			0.435856
$827$		−	8698.65i		−	0.365758i	−0.983135	−	0.182879i	$-0.941458\pi$
$827$		−	8698.65i		−	0.365758i	0.983135	−	0.182879i	$-0.0585416\pi$
$828$		0			0
$829$	−19561.7			−0.819551			−0.409775	−	0.912186i	$-0.634393\pi$
$829$	−19561.7			−0.819551			−0.409775	+	0.912186i	$0.634393\pi$
$830$	−27270.2	−	7321.35i	−1.14044	−	0.306178i
$831$		0			0
$832$			691.723i			0.0288235i
$833$			4840.60i			0.201341i
$834$		0			0
$835$	−151.498	+	564.292i	−0.00627882	+	0.0233870i
$836$	424.082			0.0175445
$837$		0			0
$838$		−	4982.00i		−	0.205370i
$839$	−32967.7			−1.35658			−0.678290	−	0.734794i	$-0.737279\pi$
$839$	−32967.7			−1.35658			−0.678290	+	0.734794i	$0.737279\pi$
$840$		0			0
$841$	−24389.0			−0.999998
$842$		−	3135.01i		−	0.128313i
$843$		0			0
$844$	−23065.2			−0.940683
$845$	22461.7	+	6030.41i	0.914446	+	0.245506i
$846$		0			0
$847$			8023.06i			0.325473i
$848$		−	4584.07i		−	0.185634i
$849$		0			0
$850$	21376.1	+	12369.4i	0.862580	+	0.499139i
$851$	1046.19			0.0421420
$852$		0			0
$853$			22005.6i			0.883302i	0.897187	+	0.441651i	$0.145607\pi$
$853$			22005.6i			0.883302i	−0.897187	+	0.441651i	$0.854393\pi$
$854$	−5708.03			−0.228717
$855$		0			0
$856$	−9611.15			−0.383764
$857$		−	8008.58i		−	0.319216i	−0.987181	−	0.159608i	$-0.948977\pi$
$857$		−	8008.58i		−	0.319216i	0.987181	−	0.159608i	$-0.0510229\pi$
$858$		0			0
$859$	21100.9			0.838130			0.419065	−	0.907956i	$-0.362358\pi$
$859$	21100.9			0.838130			0.419065	+	0.907956i	$0.362358\pi$
$860$	−4162.11	+	15502.8i	−0.165031	+	0.614698i
$861$		0			0
$862$		−	1431.69i		−	0.0565701i
$863$			30473.1i			1.20199i	0.799253	+	0.600994i	$0.205229\pi$
$863$			30473.1i			1.20199i	−0.799253	+	0.600994i	$0.794771\pi$
$864$		0			0
$865$	−450.436	+	1677.76i	−0.0177055	+	0.0659486i
$866$	−7167.44			−0.281246
$867$		0			0
$868$		−	4636.69i		−	0.181313i
$869$	−1490.33			−0.0581774
$870$		0			0
$871$	841.735			0.0327453
$872$		−	7341.75i		−	0.285118i
$873$		0			0
$874$	−1487.44			−0.0575667
$875$	6927.65	−	6907.30i	0.267654	−	0.266868i
$876$		0			0
$877$			19268.9i			0.741921i	0.928649	+	0.370961i	$0.120972\pi$
$877$			19268.9i			0.741921i	−0.928649	+	0.370961i	$0.879028\pi$
$878$			20580.7i			0.791077i
$879$		0			0
$880$	2348.93	+	630.629i	0.0899800	+	0.0241574i
$881$	25810.9			0.987049			0.493525	−	0.869732i	$-0.335708\pi$
$881$	25810.9			0.987049			0.493525	+	0.869732i	$0.335708\pi$
$882$		0			0
$883$		−	2908.02i		−	0.110830i	−0.998463	−	0.0554149i	$-0.982352\pi$
$883$		−	2908.02i		−	0.110830i	0.998463	−	0.0554149i	$-0.0176482\pi$
$884$	4270.86			0.162494
$885$		0			0
$886$	7432.80			0.281839
$887$		−	50742.2i		−	1.92081i	−0.278615	−	0.960403i	$-0.589875\pi$
$887$		−	50742.2i		−	1.92081i	0.278615	−	0.960403i	$-0.410125\pi$
$888$		0			0
$889$	−57.1141			−0.00215472
$890$	−8064.77	+	30039.2i	−0.303744	+	1.13137i
$891$		0			0
$892$			4777.19i			0.179319i
$893$			3513.49i			0.131662i
$894$		0			0
$895$	−26369.4	−	7079.52i	−0.984840	−	0.264405i
$896$	−896.000			−0.0334077
$897$		0			0
$898$			21217.3i			0.788453i
$899$	−33.4572			−0.00124122
$900$		0			0
$901$	−28303.1			−1.04652
$902$		−	336.735i		−	0.0124302i
$903$		0			0
$904$	6198.61			0.228056
$905$	−12455.4	−	3343.95i	−0.457492	−	0.122825i
$906$		0			0
$907$		−	14210.5i		−	0.520235i	−0.965577	−	0.260117i	$-0.916239\pi$
$907$		−	14210.5i		−	0.520235i	0.965577	−	0.260117i	$-0.0837612\pi$
$908$			12405.8i			0.453415i
$909$		0			0
$910$	438.657	−	1633.89i	0.0159795	−	0.0595195i
$911$	−14523.3			−0.528188			−0.264094	−	0.964497i	$-0.585073\pi$
$911$	−14523.3			−0.528188			−0.264094	+	0.964497i	$0.585073\pi$
$912$		0			0
$913$			17168.2i			0.622327i
$914$	−16482.4			−0.596489
$915$		0			0
$916$	8644.01			0.311797
$917$			6137.66i			0.221029i
$918$		0			0
$919$	−24513.7			−0.879905			−0.439953	−	0.898021i	$-0.645005\pi$
$919$	−24513.7			−0.879905			−0.439953	+	0.898021i	$0.645005\pi$
$920$	−8238.71	−	2211.89i	−0.295242	−	0.0792649i
$921$		0			0
$922$			30505.0i			1.08962i
$923$		−	6032.04i		−	0.215110i
$924$		0			0
$925$	−686.751	+	1186.80i	−0.0244111	+	0.0421856i
$926$	−7083.04			−0.251364
$927$		0			0
$928$			6.46531i			0.000228701i
$929$	−27502.6			−0.971291			−0.485646	−	0.874156i	$-0.661415\pi$
$929$	−27502.6			−0.971291			−0.485646	+	0.874156i	$0.661415\pi$
$930$		0			0
$931$	382.100			0.0134509
$932$		−	12497.1i		−	0.439225i
$933$		0			0
$934$	−8440.91			−0.295712
$935$	3893.65	−	14502.8i	0.136188	−	0.507266i
$936$		0			0
$937$			52359.0i			1.82550i	0.408520	+	0.912749i	$0.366045\pi$
$937$			52359.0i			1.82550i	−0.408520	+	0.912749i	$0.633955\pi$
$938$			1090.31i			0.0379531i
$939$		0			0
$940$	−5224.72	+	19460.7i	−0.181289	+	0.675255i
$941$	873.156			0.0302487			0.0151244	−	0.999886i	$-0.495186\pi$
$941$	873.156			0.0302487			0.0151244	+	0.999886i	$0.495186\pi$
$942$		0			0
$943$			1181.07i			0.0407858i
$944$	11825.1			0.407706
$945$		0			0
$946$	9759.93			0.335436
$947$			25333.0i			0.869283i	0.900604	+	0.434641i	$0.143125\pi$
$947$			25333.0i			0.869283i	−0.900604	+	0.434641i	$0.856875\pi$
$948$		0			0
$949$	−311.584			−0.0106580
$950$	976.400	−	1687.35i	0.0333459	−	0.0576262i
$951$		0			0
$952$			5532.11i			0.188337i
$953$			28335.5i			0.963145i	0.876406	+	0.481573i	$0.159934\pi$
$953$			28335.5i			0.963145i	−0.876406	+	0.481573i	$0.840066\pi$
$954$		0			0
$955$	−52141.7	−	13998.7i	−1.76677	−	0.474333i
$956$	−6531.57			−0.220969
$957$		0			0
$958$			13371.4i			0.450950i
$959$	−7542.73			−0.253981
$960$		0			0
$961$	−2368.99			−0.0795204
$962$			237.118i			0.00794697i
$963$		0			0
$964$	19791.2			0.661237
$965$	−1529.03	+	5695.24i	−0.0510064	+	0.189986i
$966$		0			0
$967$			12644.3i			0.420490i	0.977649	+	0.210245i	$0.0674262\pi$
$967$			12644.3i			0.420490i	−0.977649	+	0.210245i	$0.932574\pi$
$968$			9169.21i			0.304452i
$969$		0			0
$970$	−9028.86	−	2424.02i	−0.298865	−	0.0802377i
$971$	−41862.8			−1.38357			−0.691783	−	0.722106i	$-0.743174\pi$
$971$	−41862.8			−1.38357			−0.691783	+	0.722106i	$0.743174\pi$
$972$		0			0
$973$		−	10890.0i		−	0.358806i
$974$	11842.2			0.389578
$975$		0			0
$976$	−6523.46			−0.213946
$977$			12362.4i			0.404818i	0.979301	+	0.202409i	$0.0648770\pi$
$977$			12362.4i			0.404818i	−0.979301	+	0.202409i	$0.935123\pi$
$978$		0			0
$979$	18911.5			0.617378
$980$	2116.40	+	568.200i	0.0689856	+	0.0185209i
$981$		0			0
$982$			3251.33i			0.105656i
$983$			25887.9i			0.839976i	0.907530	+	0.419988i	$0.137966\pi$
$983$			25887.9i			0.839976i	−0.907530	+	0.419988i	$0.862034\pi$
$984$		0			0
$985$	7327.10	−	27291.6i	0.237016	−	0.882824i
$986$	39.9184			0.00128931
$987$		0			0
$988$		−	337.126i		−	0.0108557i
$989$	−34232.3			−1.10063
$990$		0			0
$991$	9414.31			0.301771			0.150886	−	0.988551i	$-0.451787\pi$
$991$	9414.31			0.301771			0.150886	+	0.988551i	$0.451787\pi$
$992$		−	5299.07i		−	0.169602i
$993$		0			0
$994$	7813.40			0.249322
$995$	−55472.4	−	14892.9i	−1.76743	−	0.474511i
$996$		0			0
$997$		−	12125.8i		−	0.385183i	−0.981279	−	0.192592i	$-0.938311\pi$
$997$		−	12125.8i		−	0.385183i	0.981279	−	0.192592i	$-0.0616892\pi$
$998$			40526.6i			1.28542i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.4.g.e.379.4		4
3.2	odd	2		210.4.g.a.169.1	✓	4
5.4	even	2	inner	630.4.g.e.379.2		4
15.2	even	4		1050.4.a.bg.1.1		2
15.8	even	4		1050.4.a.bc.1.1		2
15.14	odd	2		210.4.g.a.169.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.g.a.169.1	✓	4	3.2	odd	2
210.4.g.a.169.3	yes	4	15.14	odd	2
630.4.g.e.379.2		4	5.4	even	2	inner
630.4.g.e.379.4		4	1.1	even	1	trivial
1050.4.a.bc.1.1		2	15.8	even	4
1050.4.a.bg.1.1		2	15.2	even	4

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	630.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -4.00000 q^{4} +(10.7980 + 2.89898i) q^{5} -7.00000i q^{7} -8.00000i q^{8} +O(q^{10})\)	\(q+2.00000i q^{2} -4.00000 q^{4} +(10.7980 + 2.89898i) q^{5} -7.00000i q^{7} -8.00000i q^{8} +(-5.79796 + 21.5959i) q^{10} +13.5959 q^{11} -10.8082i q^{13} +14.0000 q^{14} +16.0000 q^{16} -98.7878i q^{17} -7.79796 q^{19} +(-43.1918 - 11.5959i) q^{20} +27.1918i q^{22} -95.3735i q^{23} +(108.192 + 62.6061i) q^{25} +21.6163 q^{26} +28.0000i q^{28} +0.202041 q^{29} -165.596 q^{31} +32.0000i q^{32} +197.576 q^{34} +(20.2929 - 75.5857i) q^{35} +10.9694i q^{37} -15.5959i q^{38} +(23.1918 - 86.3837i) q^{40} -12.3837 q^{41} -358.929i q^{43} -54.3837 q^{44} +190.747 q^{46} -450.565i q^{47} -49.0000 q^{49} +(-125.212 + 216.384i) q^{50} +43.2327i q^{52} -286.504i q^{53} +(146.808 + 39.4143i) q^{55} -56.0000 q^{56} +0.404082i q^{58} +739.069 q^{59} -407.716 q^{61} -331.192i q^{62} -64.0000 q^{64} +(31.3326 - 116.706i) q^{65} +77.8796i q^{67} +395.151i q^{68} +(151.171 + 40.5857i) q^{70} +558.100 q^{71} -28.8286i q^{73} -21.9388 q^{74} +31.1918 q^{76} -95.1714i q^{77} -109.616 q^{79} +(172.767 + 46.3837i) q^{80} -24.7673i q^{82} +1262.75i q^{83} +(286.384 - 1066.71i) q^{85} +717.857 q^{86} -108.767i q^{88} +1390.97 q^{89} -75.6571 q^{91} +381.494i q^{92} +901.131 q^{94} +(-84.2020 - 22.6061i) q^{95} +418.082i q^{97} -98.0000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{4} + 4 q^{5}+O(q^{10}) \) 4 * q - 16 * q^4 + 4 * q^5	\( 4 q - 16 q^{4} + 4 q^{5} + 16 q^{10} - 24 q^{11} + 56 q^{14} + 64 q^{16} + 8 q^{19} - 16 q^{20} + 276 q^{25} + 400 q^{26} + 40 q^{29} - 584 q^{31} + 320 q^{34} - 56 q^{35} - 64 q^{40} + 264 q^{41} + 96 q^{44} - 256 q^{46} - 196 q^{49} - 736 q^{50} + 744 q^{55} - 224 q^{56} + 448 q^{59} - 24 q^{61} - 256 q^{64} - 1168 q^{65} + 56 q^{70} + 312 q^{71} + 1088 q^{74} - 32 q^{76} - 752 q^{79} + 64 q^{80} + 832 q^{85} + 128 q^{86} + 1096 q^{89} - 1400 q^{91} + 2272 q^{94} - 376 q^{95}+O(q^{100}) \) 4 * q - 16 * q^4 + 4 * q^5 + 16 * q^10 - 24 * q^11 + 56 * q^14 + 64 * q^16 + 8 * q^19 - 16 * q^20 + 276 * q^25 + 400 * q^26 + 40 * q^29 - 584 * q^31 + 320 * q^34 - 56 * q^35 - 64 * q^40 + 264 * q^41 + 96 * q^44 - 256 * q^46 - 196 * q^49 - 736 * q^50 + 744 * q^55 - 224 * q^56 + 448 * q^59 - 24 * q^61 - 256 * q^64 - 1168 * q^65 + 56 * q^70 + 312 * q^71 + 1088 * q^74 - 32 * q^76 - 752 * q^79 + 64 * q^80 + 832 * q^85 + 128 * q^86 + 1096 * q^89 - 1400 * q^91 + 2272 * q^94 - 376 * q^95

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