LMFDB - Embedded newform 630.4.g.a.379.1

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:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	630.379
Dual form			630.4.g.a.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} -4.00000 q^{4} +(-10.0000 - 5.00000i) q^{5} +7.00000i q^{7} +8.00000i q^{8} +O(q^{10})$	\(q-2.00000i q^{2} -4.00000 q^{4} +(-10.0000 - 5.00000i) q^{5} +7.00000i q^{7} +8.00000i q^{8} +(-10.0000 + 20.0000i) q^{10} +37.0000 q^{11} -51.0000i q^{13} +14.0000 q^{14} +16.0000 q^{16} -41.0000i q^{17} +108.000 q^{19} +(40.0000 + 20.0000i) q^{20} -74.0000i q^{22} -70.0000i q^{23} +(75.0000 + 100.000i) q^{25} -102.000 q^{26} -28.0000i q^{28} -249.000 q^{29} -134.000 q^{31} -32.0000i q^{32} -82.0000 q^{34} +(35.0000 - 70.0000i) q^{35} -334.000i q^{37} -216.000i q^{38} +(40.0000 - 80.0000i) q^{40} -206.000 q^{41} +376.000i q^{43} -148.000 q^{44} -140.000 q^{46} +287.000i q^{47} -49.0000 q^{49} +(200.000 - 150.000i) q^{50} +204.000i q^{52} -6.00000i q^{53} +(-370.000 - 185.000i) q^{55} -56.0000 q^{56} +498.000i q^{58} -2.00000 q^{59} -940.000 q^{61} +268.000i q^{62} -64.0000 q^{64} +(-255.000 + 510.000i) q^{65} +106.000i q^{67} +164.000i q^{68} +(-140.000 - 70.0000i) q^{70} -456.000 q^{71} -650.000i q^{73} -668.000 q^{74} -432.000 q^{76} +259.000i q^{77} +1239.00 q^{79} +(-160.000 - 80.0000i) q^{80} +412.000i q^{82} +428.000i q^{83} +(-205.000 + 410.000i) q^{85} +752.000 q^{86} +296.000i q^{88} -220.000 q^{89} +357.000 q^{91} +280.000i q^{92} +574.000 q^{94} +(-1080.00 - 540.000i) q^{95} -1055.00i q^{97} +98.0000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{4} - 20 q^{5}+O(q^{10}) $ 2 * q - 8 * q^4 - 20 * q^5	$ 2 q - 8 q^{4} - 20 q^{5} - 20 q^{10} + 74 q^{11} + 28 q^{14} + 32 q^{16} + 216 q^{19} + 80 q^{20} + 150 q^{25} - 204 q^{26} - 498 q^{29} - 268 q^{31} - 164 q^{34} + 70 q^{35} + 80 q^{40} - 412 q^{41} - 296 q^{44} - 280 q^{46} - 98 q^{49} + 400 q^{50} - 740 q^{55} - 112 q^{56} - 4 q^{59} - 1880 q^{61} - 128 q^{64} - 510 q^{65} - 280 q^{70} - 912 q^{71} - 1336 q^{74} - 864 q^{76} + 2478 q^{79} - 320 q^{80} - 410 q^{85} + 1504 q^{86} - 440 q^{89} + 714 q^{91} + 1148 q^{94} - 2160 q^{95}+O(q^{100}) $ 2 * q - 8 * q^4 - 20 * q^5 - 20 * q^10 + 74 * q^11 + 28 * q^14 + 32 * q^16 + 216 * q^19 + 80 * q^20 + 150 * q^25 - 204 * q^26 - 498 * q^29 - 268 * q^31 - 164 * q^34 + 70 * q^35 + 80 * q^40 - 412 * q^41 - 296 * q^44 - 280 * q^46 - 98 * q^49 + 400 * q^50 - 740 * q^55 - 112 * q^56 - 4 * q^59 - 1880 * q^61 - 128 * q^64 - 510 * q^65 - 280 * q^70 - 912 * q^71 - 1336 * q^74 - 864 * q^76 + 2478 * q^79 - 320 * q^80 - 410 * q^85 + 1504 * q^86 - 440 * q^89 + 714 * q^91 + 1148 * q^94 - 2160 * 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
$5$	−10.0000	−	5.00000i	−0.894427	−	0.447214i
$5$	−10.0000	−	5.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$			8.00000i			0.353553i
$9$		0			0
$10$	−10.0000	+	20.0000i	−0.316228	+	0.632456i
$11$	37.0000			1.01417			0.507087	−	0.861895i	$-0.330722\pi$
$11$	37.0000			1.01417			0.507087	+	0.861895i	$0.330722\pi$
$12$		0			0
$13$		−	51.0000i		−	1.08807i	−0.839064	−	0.544033i	$-0.816897\pi$
$13$		−	51.0000i		−	1.08807i	0.839064	−	0.544033i	$-0.183103\pi$
$14$	14.0000			0.267261
$15$		0			0
$16$	16.0000			0.250000
$17$		−	41.0000i		−	0.584939i	−0.956275	−	0.292469i	$-0.905523\pi$
$17$		−	41.0000i		−	0.584939i	0.956275	−	0.292469i	$-0.0944770\pi$
$18$		0			0
$19$	108.000			1.30405			0.652024	−	0.758199i	$-0.273920\pi$
$19$	108.000			1.30405			0.652024	+	0.758199i	$0.273920\pi$
$20$	40.0000	+	20.0000i	0.447214	+	0.223607i
$21$		0			0
$22$		−	74.0000i		−	0.717130i
$23$		−	70.0000i		−	0.634609i	−0.948324	−	0.317305i	$-0.897222\pi$
$23$		−	70.0000i		−	0.634609i	0.948324	−	0.317305i	$-0.102778\pi$
$24$		0			0
$25$	75.0000	+	100.000i	0.600000	+	0.800000i
$26$	−102.000			−0.769379
$27$		0			0
$28$		−	28.0000i		−	0.188982i
$29$	−249.000			−1.59442			−0.797209	−	0.603703i	$-0.793691\pi$
$29$	−249.000			−1.59442			−0.797209	+	0.603703i	$0.793691\pi$
$30$		0			0
$31$	−134.000			−0.776358			−0.388179	−	0.921584i	$-0.626896\pi$
$31$	−134.000			−0.776358			−0.388179	+	0.921584i	$0.626896\pi$
$32$		−	32.0000i		−	0.176777i
$33$		0			0
$34$	−82.0000			−0.413614
$35$	35.0000	−	70.0000i	0.169031	−	0.338062i
$36$		0			0
$37$		−	334.000i		−	1.48403i	−0.670381	−	0.742017i	$-0.733869\pi$
$37$		−	334.000i		−	1.48403i	0.670381	−	0.742017i	$-0.266131\pi$
$38$		−	216.000i		−	0.922101i
$39$		0			0
$40$	40.0000	−	80.0000i	0.158114	−	0.316228i
$41$	−206.000			−0.784678			−0.392339	−	0.919821i	$-0.628334\pi$
$41$	−206.000			−0.784678			−0.392339	+	0.919821i	$0.628334\pi$
$42$		0			0
$43$			376.000i			1.33348i	0.745292	+	0.666738i	$0.232310\pi$
$43$			376.000i			1.33348i	−0.745292	+	0.666738i	$0.767690\pi$
$44$	−148.000			−0.507087
$45$		0			0
$46$	−140.000			−0.448736
$47$			287.000i			0.890708i	0.895355	+	0.445354i	$0.146922\pi$
$47$			287.000i			0.890708i	−0.895355	+	0.445354i	$0.853078\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	200.000	−	150.000i	0.565685	−	0.424264i
$51$		0			0
$52$			204.000i			0.544033i
$53$		−	6.00000i		−	0.0155503i	−0.999970	−	0.00777513i	$-0.997525\pi$
$53$		−	6.00000i		−	0.0155503i	0.999970	−	0.00777513i	$-0.00247492\pi$
$54$		0			0
$55$	−370.000	−	185.000i	−0.907105	−	0.453553i
$56$	−56.0000			−0.133631
$57$		0			0
$58$			498.000i			1.12742i
$59$	−2.00000			−0.00441318			−0.00220659	−	0.999998i	$-0.500702\pi$
$59$	−2.00000			−0.00441318			−0.00220659	+	0.999998i	$0.500702\pi$
$60$		0			0
$61$	−940.000			−1.97303			−0.986514	−	0.163679i	$-0.947664\pi$
$61$	−940.000			−1.97303			−0.986514	+	0.163679i	$0.947664\pi$
$62$			268.000i			0.548968i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−255.000	+	510.000i	−0.486598	+	0.973196i
$66$		0			0
$67$			106.000i			0.193283i	0.995319	+	0.0966415i	$0.0308100\pi$
$67$			106.000i			0.193283i	−0.995319	+	0.0966415i	$0.969190\pi$
$68$			164.000i			0.292469i
$69$		0			0
$70$	−140.000	−	70.0000i	−0.239046	−	0.119523i
$71$	−456.000			−0.762215			−0.381107	−	0.924531i	$-0.624457\pi$
$71$	−456.000			−0.762215			−0.381107	+	0.924531i	$0.624457\pi$
$72$		0			0
$73$		−	650.000i		−	1.04215i	−0.853512	−	0.521074i	$-0.825532\pi$
$73$		−	650.000i		−	1.04215i	0.853512	−	0.521074i	$-0.174468\pi$
$74$	−668.000			−1.04937
$75$		0			0
$76$	−432.000			−0.652024
$77$			259.000i			0.383322i
$78$		0			0
$79$	1239.00			1.76454			0.882268	−	0.470747i	$-0.156016\pi$
$79$	1239.00			1.76454			0.882268	+	0.470747i	$0.156016\pi$
$80$	−160.000	−	80.0000i	−0.223607	−	0.111803i
$81$		0			0
$82$			412.000i			0.554851i
$83$			428.000i			0.566013i	0.959118	+	0.283007i	$0.0913319\pi$
$83$			428.000i			0.566013i	−0.959118	+	0.283007i	$0.908668\pi$
$84$		0			0
$85$	−205.000	+	410.000i	−0.261593	+	0.523185i
$86$	752.000			0.942910
$87$		0			0
$88$			296.000i			0.358565i
$89$	−220.000			−0.262022			−0.131011	−	0.991381i	$-0.541822\pi$
$89$	−220.000			−0.262022			−0.131011	+	0.991381i	$0.541822\pi$
$90$		0			0
$91$	357.000			0.411250
$92$			280.000i			0.317305i
$93$		0			0
$94$	574.000			0.629825
$95$	−1080.00	−	540.000i	−1.16638	−	0.583188i
$96$		0			0
$97$		−	1055.00i		−	1.10432i	−0.833738	−	0.552160i	$-0.813804\pi$
$97$		−	1055.00i		−	1.10432i	0.833738	−	0.552160i	$-0.186196\pi$
$98$			98.0000i			0.101015i
$99$		0			0
$100$	−300.000	−	400.000i	−0.300000	−	0.400000i
$101$	−1960.00			−1.93096			−0.965482	−	0.260471i	$-0.916122\pi$
$101$	−1960.00			−1.93096			−0.965482	+	0.260471i	$0.916122\pi$
$102$		0			0
$103$		−	1825.00i		−	1.74585i	−0.487854	−	0.872925i	$-0.662220\pi$
$103$		−	1825.00i		−	1.74585i	0.487854	−	0.872925i	$-0.337780\pi$
$104$	408.000			0.384689
$105$		0			0
$106$	−12.0000			−0.0109957
$107$			144.000i			0.130103i	0.997882	+	0.0650514i	$0.0207211\pi$
$107$			144.000i			0.130103i	−0.997882	+	0.0650514i	$0.979279\pi$
$108$		0			0
$109$	−1681.00			−1.47716			−0.738581	−	0.674165i	$-0.764504\pi$
$109$	−1681.00			−1.47716			−0.738581	+	0.674165i	$0.764504\pi$
$110$	−370.000	+	740.000i	−0.320710	+	0.641420i
$111$		0			0
$112$			112.000i			0.0944911i
$113$			798.000i			0.664332i	0.943221	+	0.332166i	$0.107779\pi$
$113$			798.000i			0.664332i	−0.943221	+	0.332166i	$0.892221\pi$
$114$		0			0
$115$	−350.000	+	700.000i	−0.283806	+	0.567612i
$116$	996.000			0.797209
$117$		0			0
$118$			4.00000i			0.00312059i
$119$	287.000			0.221086
$120$		0			0
$121$	38.0000			0.0285500
$122$			1880.00i			1.39514i
$123$		0			0
$124$	536.000			0.388179
$125$	−250.000	−	1375.00i	−0.178885	−	0.983870i
$126$		0			0
$127$			434.000i			0.303238i	0.988439	+	0.151619i	$0.0484487\pi$
$127$			434.000i			0.303238i	−0.988439	+	0.151619i	$0.951551\pi$
$128$			128.000i			0.0883883i
$129$		0			0
$130$	1020.00	+	510.000i	0.688153	+	0.344077i
$131$	1290.00			0.860365			0.430183	−	0.902742i	$-0.358449\pi$
$131$	1290.00			0.860365			0.430183	+	0.902742i	$0.358449\pi$
$132$		0			0
$133$			756.000i			0.492884i
$134$	212.000			0.136672
$135$		0			0
$136$	328.000			0.206807
$137$		−	192.000i		−	0.119735i	−0.998206	−	0.0598674i	$-0.980932\pi$
$137$		−	192.000i		−	0.119735i	0.998206	−	0.0598674i	$-0.0190678\pi$
$138$		0			0
$139$	−1402.00			−0.855511			−0.427756	−	0.903894i	$-0.640696\pi$
$139$	−1402.00			−0.855511			−0.427756	+	0.903894i	$0.640696\pi$
$140$	−140.000	+	280.000i	−0.0845154	+	0.169031i
$141$		0			0
$142$			912.000i			0.538967i
$143$		−	1887.00i		−	1.10349i
$144$		0			0
$145$	2490.00	+	1245.00i	1.42609	+	0.713046i
$146$	−1300.00			−0.736909
$147$		0			0
$148$			1336.00i			0.742017i
$149$	−302.000			−0.166046			−0.0830228	−	0.996548i	$-0.526457\pi$
$149$	−302.000			−0.166046			−0.0830228	+	0.996548i	$0.526457\pi$
$150$		0			0
$151$	−3167.00			−1.70680			−0.853400	−	0.521257i	$-0.825463\pi$
$151$	−3167.00			−1.70680			−0.853400	+	0.521257i	$0.825463\pi$
$152$			864.000i			0.461050i
$153$		0			0
$154$	518.000			0.271050
$155$	1340.00	+	670.000i	0.694396	+	0.347198i
$156$		0			0
$157$		−	470.000i		−	0.238918i	−0.992839	−	0.119459i	$-0.961884\pi$
$157$		−	470.000i		−	0.238918i	0.992839	−	0.119459i	$-0.0381160\pi$
$158$		−	2478.00i		−	1.24772i
$159$		0			0
$160$	−160.000	+	320.000i	−0.0790569	+	0.158114i
$161$	490.000			0.239860
$162$		0			0
$163$			2390.00i			1.14846i	0.818693	+	0.574231i	$0.194699\pi$
$163$			2390.00i			1.14846i	−0.818693	+	0.574231i	$0.805301\pi$
$164$	824.000			0.392339
$165$		0			0
$166$	856.000			0.400232
$167$			2631.00i			1.21912i	0.792740	+	0.609560i	$0.208654\pi$
$167$			2631.00i			1.21912i	−0.792740	+	0.609560i	$0.791346\pi$
$168$		0			0
$169$	−404.000			−0.183887
$170$	820.000	+	410.000i	0.369948	+	0.184974i
$171$		0			0
$172$		−	1504.00i		−	0.666738i
$173$		−	2243.00i		−	0.985735i	−0.870104	−	0.492867i	$-0.835949\pi$
$173$		−	2243.00i		−	0.985735i	0.870104	−	0.492867i	$-0.164051\pi$
$174$		0			0
$175$	−700.000	+	525.000i	−0.302372	+	0.226779i
$176$	592.000			0.253544
$177$		0			0
$178$			440.000i			0.185277i
$179$	52.0000			0.0217132			0.0108566	−	0.999941i	$-0.496544\pi$
$179$	52.0000			0.0217132			0.0108566	+	0.999941i	$0.496544\pi$
$180$		0			0
$181$	2462.00			1.01104			0.505522	−	0.862814i	$-0.331300\pi$
$181$	2462.00			1.01104			0.505522	+	0.862814i	$0.331300\pi$
$182$		−	714.000i		−	0.290798i
$183$		0			0
$184$	560.000			0.224368
$185$	−1670.00	+	3340.00i	−0.663680	+	1.32736i
$186$		0			0
$187$		−	1517.00i		−	0.593230i
$188$		−	1148.00i		−	0.445354i
$189$		0			0
$190$	−1080.00	+	2160.00i	−0.412376	+	0.824752i
$191$	−3159.00			−1.19674			−0.598370	−	0.801220i	$-0.704185\pi$
$191$	−3159.00			−1.19674			−0.598370	+	0.801220i	$0.704185\pi$
$192$		0			0
$193$		−	2060.00i		−	0.768301i	−0.923271	−	0.384150i	$-0.874494\pi$
$193$		−	2060.00i		−	0.768301i	0.923271	−	0.384150i	$-0.125506\pi$
$194$	−2110.00			−0.780872
$195$		0			0
$196$	196.000			0.0714286
$197$		−	1738.00i		−	0.628565i	−0.949329	−	0.314283i	$-0.898236\pi$
$197$		−	1738.00i		−	0.628565i	0.949329	−	0.314283i	$-0.101764\pi$
$198$		0			0
$199$	894.000			0.318462			0.159231	−	0.987241i	$-0.449099\pi$
$199$	894.000			0.318462			0.159231	+	0.987241i	$0.449099\pi$
$200$	−800.000	+	600.000i	−0.282843	+	0.212132i
$201$		0			0
$202$			3920.00i			1.36540i
$203$		−	1743.00i		−	0.602634i
$204$		0			0
$205$	2060.00	+	1030.00i	0.701837	+	0.350919i
$206$	−3650.00			−1.23450
$207$		0			0
$208$		−	816.000i		−	0.272016i
$209$	3996.00			1.32253
$210$		0			0
$211$	−4083.00			−1.33216			−0.666079	−	0.745881i	$-0.732029\pi$
$211$	−4083.00			−1.33216			−0.666079	+	0.745881i	$0.732029\pi$
$212$			24.0000i			0.00777513i
$213$		0			0
$214$	288.000			0.0919966
$215$	1880.00	−	3760.00i	0.596349	−	1.19270i
$216$		0			0
$217$		−	938.000i		−	0.293436i
$218$			3362.00i			1.04451i
$219$		0			0
$220$	1480.00	+	740.000i	0.453553	+	0.226776i
$221$	−2091.00			−0.636452
$222$		0			0
$223$		−	377.000i		−	0.113210i	−0.998397	−	0.0566049i	$-0.981972\pi$
$223$		−	377.000i		−	0.113210i	0.998397	−	0.0566049i	$-0.0180275\pi$
$224$	224.000			0.0668153
$225$		0			0
$226$	1596.00			0.469754
$227$			2551.00i			0.745885i	0.927855	+	0.372942i	$0.121651\pi$
$227$			2551.00i			0.745885i	−0.927855	+	0.372942i	$0.878349\pi$
$228$		0			0
$229$	−74.0000			−0.0213540			−0.0106770	−	0.999943i	$-0.503399\pi$
$229$	−74.0000			−0.0213540			−0.0106770	+	0.999943i	$0.503399\pi$
$230$	1400.00	+	700.000i	0.401362	+	0.200681i
$231$		0			0
$232$		−	1992.00i		−	0.563712i
$233$			1888.00i			0.530845i	0.964132	+	0.265423i	$0.0855115\pi$
$233$			1888.00i			0.530845i	−0.964132	+	0.265423i	$0.914488\pi$
$234$		0			0
$235$	1435.00	−	2870.00i	0.398337	−	0.796673i
$236$	8.00000			0.00220659
$237$		0			0
$238$		−	574.000i		−	0.156331i
$239$	4997.00			1.35242			0.676211	−	0.736708i	$-0.263621\pi$
$239$	4997.00			1.35242			0.676211	+	0.736708i	$0.263621\pi$
$240$		0			0
$241$	−3830.00			−1.02370			−0.511851	−	0.859074i	$-0.671040\pi$
$241$	−3830.00			−1.02370			−0.511851	+	0.859074i	$0.671040\pi$
$242$		−	76.0000i		−	0.0201879i
$243$		0			0
$244$	3760.00			0.986514
$245$	490.000	+	245.000i	0.127775	+	0.0638877i
$246$		0			0
$247$		−	5508.00i		−	1.41889i
$248$		−	1072.00i		−	0.274484i
$249$		0			0
$250$	−2750.00	+	500.000i	−0.695701	+	0.126491i
$251$	3390.00			0.852490			0.426245	−	0.904608i	$-0.359836\pi$
$251$	3390.00			0.852490			0.426245	+	0.904608i	$0.359836\pi$
$252$		0			0
$253$		−	2590.00i		−	0.643604i
$254$	868.000			0.214422
$255$		0			0
$256$	256.000			0.0625000
$257$		−	7170.00i		−	1.74028i	−0.492803	−	0.870141i	$-0.664028\pi$
$257$		−	7170.00i		−	1.74028i	0.492803	−	0.870141i	$-0.335972\pi$
$258$		0			0
$259$	2338.00			0.560912
$260$	1020.00	−	2040.00i	0.243299	−	0.486598i
$261$		0			0
$262$		−	2580.00i		−	0.608370i
$263$		−	7672.00i		−	1.79877i	−0.437160	−	0.899384i	$-0.644016\pi$
$263$		−	7672.00i		−	1.79877i	0.437160	−	0.899384i	$-0.355984\pi$
$264$		0			0
$265$	−30.0000	+	60.0000i	−0.00695428	+	0.0139086i
$266$	1512.00			0.348521
$267$		0			0
$268$		−	424.000i		−	0.0966415i
$269$	−54.0000			−0.0122395			−0.00611977	−	0.999981i	$-0.501948\pi$
$269$	−54.0000			−0.0122395			−0.00611977	+	0.999981i	$0.501948\pi$
$270$		0			0
$271$	2932.00			0.657219			0.328609	−	0.944466i	$-0.393420\pi$
$271$	2932.00			0.657219			0.328609	+	0.944466i	$0.393420\pi$
$272$		−	656.000i		−	0.146235i
$273$		0			0
$274$	−384.000			−0.0846653
$275$	2775.00	+	3700.00i	0.608505	+	0.811340i
$276$		0			0
$277$			3254.00i			0.705826i	0.935656	+	0.352913i	$0.114809\pi$
$277$			3254.00i			0.705826i	−0.935656	+	0.352913i	$0.885191\pi$
$278$			2804.00i			0.604938i
$279$		0			0
$280$	560.000	+	280.000i	0.119523	+	0.0597614i
$281$	−3327.00			−0.706307			−0.353153	−	0.935565i	$-0.614891\pi$
$281$	−3327.00			−0.706307			−0.353153	+	0.935565i	$0.614891\pi$
$282$		0			0
$283$		−	4627.00i		−	0.971896i	−0.873988	−	0.485948i	$-0.838474\pi$
$283$		−	4627.00i		−	0.971896i	0.873988	−	0.485948i	$-0.161526\pi$
$284$	1824.00			0.381107
$285$		0			0
$286$	−3774.00			−0.780284
$287$		−	1442.00i		−	0.296580i
$288$		0			0
$289$	3232.00			0.657847
$290$	2490.00	−	4980.00i	0.504199	−	1.00840i
$291$		0			0
$292$			2600.00i			0.521074i
$293$		−	4083.00i		−	0.814100i	−0.913406	−	0.407050i	$-0.866557\pi$
$293$		−	4083.00i		−	0.814100i	0.913406	−	0.407050i	$-0.133443\pi$
$294$		0			0
$295$	20.0000	+	10.0000i	0.00394727	+	0.00197364i
$296$	2672.00			0.524685
$297$		0			0
$298$			604.000i			0.117412i
$299$	−3570.00			−0.690496
$300$		0			0
$301$	−2632.00			−0.504007
$302$			6334.00i			1.20689i
$303$		0			0
$304$	1728.00			0.326012
$305$	9400.00	+	4700.00i	1.76473	+	0.882365i
$306$		0			0
$307$		−	4089.00i		−	0.760168i	−0.924952	−	0.380084i	$-0.875895\pi$
$307$		−	4089.00i		−	0.760168i	0.924952	−	0.380084i	$-0.124105\pi$
$308$		−	1036.00i		−	0.191661i
$309$		0			0
$310$	1340.00	−	2680.00i	0.245506	−	0.491012i
$311$	4008.00			0.730781			0.365390	−	0.930854i	$-0.380935\pi$
$311$	4008.00			0.730781			0.365390	+	0.930854i	$0.380935\pi$
$312$		0			0
$313$		−	7355.00i		−	1.32821i	−0.747640	−	0.664104i	$-0.768813\pi$
$313$		−	7355.00i		−	1.32821i	0.747640	−	0.664104i	$-0.231187\pi$
$314$	−940.000			−0.168940
$315$		0			0
$316$	−4956.00			−0.882268
$317$			1684.00i			0.298369i	0.988809	+	0.149184i	$0.0476648\pi$
$317$			1684.00i			0.298369i	−0.988809	+	0.149184i	$0.952335\pi$
$318$		0			0
$319$	−9213.00			−1.61702
$320$	640.000	+	320.000i	0.111803	+	0.0559017i
$321$		0			0
$322$		−	980.000i		−	0.169606i
$323$		−	4428.00i		−	0.762788i
$324$		0			0
$325$	5100.00	−	3825.00i	0.870453	−	0.652839i
$326$	4780.00			0.812085
$327$		0			0
$328$		−	1648.00i		−	0.277426i
$329$	−2009.00			−0.336656
$330$		0			0
$331$	−1460.00			−0.242444			−0.121222	−	0.992625i	$-0.538681\pi$
$331$	−1460.00			−0.242444			−0.121222	+	0.992625i	$0.538681\pi$
$332$		−	1712.00i		−	0.283007i
$333$		0			0
$334$	5262.00			0.862047
$335$	530.000	−	1060.00i	0.0864388	−	0.172878i
$336$		0			0
$337$			7514.00i			1.21458i	0.794480	+	0.607290i	$0.207744\pi$
$337$			7514.00i			1.21458i	−0.794480	+	0.607290i	$0.792256\pi$
$338$			808.000i			0.130028i
$339$		0			0
$340$	820.000	−	1640.00i	0.130796	−	0.261593i
$341$	−4958.00			−0.787363
$342$		0			0
$343$		−	343.000i		−	0.0539949i
$344$	−3008.00			−0.471455
$345$		0			0
$346$	−4486.00			−0.697020
$347$			2862.00i			0.442767i	0.975187	+	0.221384i	$0.0710573\pi$
$347$			2862.00i			0.442767i	−0.975187	+	0.221384i	$0.928943\pi$
$348$		0			0
$349$	6368.00			0.976708			0.488354	−	0.872646i	$-0.337597\pi$
$349$	6368.00			0.976708			0.488354	+	0.872646i	$0.337597\pi$
$350$	1050.00	+	1400.00i	0.160357	+	0.213809i
$351$		0			0
$352$		−	1184.00i		−	0.179282i
$353$		−	3635.00i		−	0.548078i	−0.961719	−	0.274039i	$-0.911640\pi$
$353$		−	3635.00i		−	0.548078i	0.961719	−	0.274039i	$-0.0883597\pi$
$354$		0			0
$355$	4560.00	+	2280.00i	0.681746	+	0.340873i
$356$	880.000			0.131011
$357$		0			0
$358$		−	104.000i		−	0.0153535i
$359$	7116.00			1.04615			0.523075	−	0.852286i	$-0.324785\pi$
$359$	7116.00			1.04615			0.523075	+	0.852286i	$0.324785\pi$
$360$		0			0
$361$	4805.00			0.700539
$362$		−	4924.00i		−	0.714916i
$363$		0			0
$364$	−1428.00			−0.205625
$365$	−3250.00	+	6500.00i	−0.466062	+	0.932125i
$366$		0			0
$367$		−	319.000i		−	0.0453724i	−0.999743	−	0.0226862i	$-0.992778\pi$
$367$		−	319.000i		−	0.0453724i	0.999743	−	0.0226862i	$-0.00722186\pi$
$368$		−	1120.00i		−	0.158652i
$369$		0			0
$370$	6680.00	+	3340.00i	0.938586	+	0.469293i
$371$	42.0000			0.00587744
$372$		0			0
$373$			11652.0i			1.61747i	0.588171	+	0.808737i	$0.299848\pi$
$373$			11652.0i			1.61747i	−0.588171	+	0.808737i	$0.700152\pi$
$374$	−3034.00			−0.419477
$375$		0			0
$376$	−2296.00			−0.314913
$377$			12699.0i			1.73483i
$378$		0			0
$379$	−7748.00			−1.05010			−0.525050	−	0.851071i	$-0.675953\pi$
$379$	−7748.00			−1.05010			−0.525050	+	0.851071i	$0.675953\pi$
$380$	4320.00	+	2160.00i	0.583188	+	0.291594i
$381$		0			0
$382$			6318.00i			0.846223i
$383$			8680.00i			1.15803i	0.815315	+	0.579017i	$0.196564\pi$
$383$			8680.00i			1.15803i	−0.815315	+	0.579017i	$0.803436\pi$
$384$		0			0
$385$	1295.00	−	2590.00i	0.171427	−	0.342854i
$386$	−4120.00			−0.543271
$387$		0			0
$388$			4220.00i			0.552160i
$389$	−1711.00			−0.223011			−0.111505	−	0.993764i	$-0.535567\pi$
$389$	−1711.00			−0.223011			−0.111505	+	0.993764i	$0.535567\pi$
$390$		0			0
$391$	−2870.00			−0.371208
$392$		−	392.000i		−	0.0505076i
$393$		0			0
$394$	−3476.00			−0.444463
$395$	−12390.0	−	6195.00i	−1.57825	−	0.789125i
$396$		0			0
$397$			1589.00i			0.200881i	0.994943	+	0.100440i	$0.0320252\pi$
$397$			1589.00i			0.200881i	−0.994943	+	0.100440i	$0.967975\pi$
$398$		−	1788.00i		−	0.225187i
$399$		0			0
$400$	1200.00	+	1600.00i	0.150000	+	0.200000i
$401$	5147.00			0.640970			0.320485	−	0.947254i	$-0.396154\pi$
$401$	5147.00			0.640970			0.320485	+	0.947254i	$0.396154\pi$
$402$		0			0
$403$			6834.00i			0.844729i
$404$	7840.00			0.965482
$405$		0			0
$406$	−3486.00			−0.426126
$407$		−	12358.0i		−	1.50507i
$408$		0			0
$409$	9100.00			1.10016			0.550081	−	0.835111i	$-0.314597\pi$
$409$	9100.00			1.10016			0.550081	+	0.835111i	$0.314597\pi$
$410$	2060.00	−	4120.00i	0.248137	−	0.496274i
$411$		0			0
$412$			7300.00i			0.872925i
$413$		−	14.0000i		−	0.00166803i
$414$		0			0
$415$	2140.00	−	4280.00i	0.253129	−	0.506258i
$416$	−1632.00			−0.192345
$417$		0			0
$418$		−	7992.00i		−	0.935171i
$419$	2618.00			0.305245			0.152623	−	0.988285i	$-0.451228\pi$
$419$	2618.00			0.305245			0.152623	+	0.988285i	$0.451228\pi$
$420$		0			0
$421$	−3695.00			−0.427751			−0.213876	−	0.976861i	$-0.568609\pi$
$421$	−3695.00			−0.427751			−0.213876	+	0.976861i	$0.568609\pi$
$422$			8166.00i			0.941978i
$423$		0			0
$424$	48.0000			0.00549784
$425$	4100.00	−	3075.00i	0.467951	−	0.350963i
$426$		0			0
$427$		−	6580.00i		−	0.745734i
$428$		−	576.000i		−	0.0650514i
$429$		0			0
$430$	−7520.00	−	3760.00i	−0.843364	−	0.421682i
$431$	−15779.0			−1.76345			−0.881726	−	0.471762i	$-0.843618\pi$
$431$	−15779.0			−1.76345			−0.881726	+	0.471762i	$0.843618\pi$
$432$		0			0
$433$		−	7238.00i		−	0.803317i	−0.915790	−	0.401658i	$-0.868434\pi$
$433$		−	7238.00i		−	0.803317i	0.915790	−	0.401658i	$-0.131566\pi$
$434$	−1876.00			−0.207491
$435$		0			0
$436$	6724.00			0.738581
$437$		−	7560.00i		−	0.827560i
$438$		0			0
$439$	2646.00			0.287669			0.143834	−	0.989602i	$-0.454057\pi$
$439$	2646.00			0.287669			0.143834	+	0.989602i	$0.454057\pi$
$440$	1480.00	−	2960.00i	0.160355	−	0.320710i
$441$		0			0
$442$			4182.00i			0.450039i
$443$			5688.00i			0.610034i	0.952347	+	0.305017i	$0.0986621\pi$
$443$			5688.00i			0.610034i	−0.952347	+	0.305017i	$0.901338\pi$
$444$		0			0
$445$	2200.00	+	1100.00i	0.234360	+	0.117180i
$446$	−754.000			−0.0800514
$447$		0			0
$448$		−	448.000i		−	0.0472456i
$449$	−3285.00			−0.345276			−0.172638	−	0.984985i	$-0.555229\pi$
$449$	−3285.00			−0.345276			−0.172638	+	0.984985i	$0.555229\pi$
$450$		0			0
$451$	−7622.00			−0.795800
$452$		−	3192.00i		−	0.332166i
$453$		0			0
$454$	5102.00			0.527420
$455$	−3570.00	−	1785.00i	−0.367833	−	0.183917i
$456$		0			0
$457$			14834.0i			1.51839i	0.650862	+	0.759196i	$0.274408\pi$
$457$			14834.0i			1.51839i	−0.650862	+	0.759196i	$0.725592\pi$
$458$			148.000i			0.0150995i
$459$		0			0
$460$	1400.00	−	2800.00i	0.141903	−	0.283806i
$461$	9972.00			1.00747			0.503734	−	0.863859i	$-0.331959\pi$
$461$	9972.00			1.00747			0.503734	+	0.863859i	$0.331959\pi$
$462$		0			0
$463$			9096.00i			0.913017i	0.889719	+	0.456509i	$0.150900\pi$
$463$			9096.00i			0.913017i	−0.889719	+	0.456509i	$0.849100\pi$
$464$	−3984.00			−0.398605
$465$		0			0
$466$	3776.00			0.375364
$467$		−	15867.0i		−	1.57224i	−0.618072	−	0.786121i	$-0.712086\pi$
$467$		−	15867.0i		−	1.57224i	0.618072	−	0.786121i	$-0.287914\pi$
$468$		0			0
$469$	−742.000			−0.0730541
$470$	−5740.00	−	2870.00i	−0.563333	−	0.281666i
$471$		0			0
$472$		−	16.0000i		−	0.00156030i
$473$			13912.0i			1.35238i
$474$		0			0
$475$	8100.00	+	10800.0i	0.782428	+	1.04324i
$476$	−1148.00			−0.110543
$477$		0			0
$478$		−	9994.00i		−	0.956307i
$479$	242.000			0.0230841			0.0115420	−	0.999933i	$-0.496326\pi$
$479$	242.000			0.0230841			0.0115420	+	0.999933i	$0.496326\pi$
$480$		0			0
$481$	−17034.0			−1.61473
$482$			7660.00i			0.723866i
$483$		0			0
$484$	−152.000			−0.0142750
$485$	−5275.00	+	10550.0i	−0.493867	+	0.987734i
$486$		0			0
$487$		−	3558.00i		−	0.331064i	−0.986204	−	0.165532i	$-0.947066\pi$
$487$		−	3558.00i		−	0.331064i	0.986204	−	0.165532i	$-0.0529342\pi$
$488$		−	7520.00i		−	0.697571i
$489$		0			0
$490$	490.000	−	980.000i	0.0451754	−	0.0903508i
$491$	−1473.00			−0.135388			−0.0676941	−	0.997706i	$-0.521564\pi$
$491$	−1473.00			−0.135388			−0.0676941	+	0.997706i	$0.521564\pi$
$492$		0			0
$493$			10209.0i			0.932637i
$494$	−11016.0			−1.00331
$495$		0			0
$496$	−2144.00			−0.194090
$497$		−	3192.00i		−	0.288090i
$498$		0			0
$499$	−603.000			−0.0540962			−0.0270481	−	0.999634i	$-0.508611\pi$
$499$	−603.000			−0.0540962			−0.0270481	+	0.999634i	$0.508611\pi$
$500$	1000.00	+	5500.00i	0.0894427	+	0.491935i
$501$		0			0
$502$		−	6780.00i		−	0.602801i
$503$			18387.0i			1.62989i	0.579537	+	0.814946i	$0.303234\pi$
$503$			18387.0i			1.62989i	−0.579537	+	0.814946i	$0.696766\pi$
$504$		0			0
$505$	19600.0	+	9800.00i	1.72711	+	0.863553i
$506$	−5180.00			−0.455097
$507$		0			0
$508$		−	1736.00i		−	0.151619i
$509$	9018.00			0.785296			0.392648	−	0.919689i	$-0.371559\pi$
$509$	9018.00			0.785296			0.392648	+	0.919689i	$0.371559\pi$
$510$		0			0
$511$	4550.00			0.393895
$512$		−	512.000i		−	0.0441942i
$513$		0			0
$514$	−14340.0			−1.23056
$515$	−9125.00	+	18250.0i	−0.780768	+	1.56154i
$516$		0			0
$517$			10619.0i			0.903333i
$518$		−	4676.00i		−	0.396625i
$519$		0			0
$520$	−4080.00	−	2040.00i	−0.344077	−	0.172038i
$521$	−4624.00			−0.388831			−0.194416	−	0.980919i	$-0.562281\pi$
$521$	−4624.00			−0.388831			−0.194416	+	0.980919i	$0.562281\pi$
$522$		0			0
$523$			5876.00i			0.491280i	0.969361	+	0.245640i	$0.0789981\pi$
$523$			5876.00i			0.491280i	−0.969361	+	0.245640i	$0.921002\pi$
$524$	−5160.00			−0.430183
$525$		0			0
$526$	−15344.0			−1.27192
$527$			5494.00i			0.454122i
$528$		0			0
$529$	7267.00			0.597271
$530$	120.000	+	60.0000i	0.00983484	+	0.00491742i
$531$		0			0
$532$		−	3024.00i		−	0.246442i
$533$			10506.0i			0.853781i
$534$		0			0
$535$	720.000	−	1440.00i	0.0581838	−	0.116368i
$536$	−848.000			−0.0683359
$537$		0			0
$538$			108.000i			0.00865467i
$539$	−1813.00			−0.144882
$540$		0			0
$541$	−8537.00			−0.678437			−0.339218	−	0.940708i	$-0.610163\pi$
$541$	−8537.00			−0.678437			−0.339218	+	0.940708i	$0.610163\pi$
$542$		−	5864.00i		−	0.464724i
$543$		0			0
$544$	−1312.00			−0.103404
$545$	16810.0	+	8405.00i	1.32121	+	0.660607i
$546$		0			0
$547$		−	13060.0i		−	1.02085i	−0.859922	−	0.510425i	$-0.829488\pi$
$547$		−	13060.0i		−	1.02085i	0.859922	−	0.510425i	$-0.170512\pi$
$548$			768.000i			0.0598674i
$549$		0			0
$550$	7400.00	−	5550.00i	0.573704	−	0.430278i
$551$	−26892.0			−2.07920
$552$		0			0
$553$			8673.00i			0.666932i
$554$	6508.00			0.499095
$555$		0			0
$556$	5608.00			0.427756
$557$		−	21372.0i		−	1.62578i	−0.582416	−	0.812891i	$-0.697892\pi$
$557$		−	21372.0i		−	1.62578i	0.582416	−	0.812891i	$-0.302108\pi$
$558$		0			0
$559$	19176.0			1.45091
$560$	560.000	−	1120.00i	0.0422577	−	0.0845154i
$561$		0			0
$562$			6654.00i			0.499434i
$563$		−	12704.0i		−	0.950994i	−0.879717	−	0.475497i	$-0.842268\pi$
$563$		−	12704.0i		−	0.950994i	0.879717	−	0.475497i	$-0.157732\pi$
$564$		0			0
$565$	3990.00	−	7980.00i	0.297098	−	0.594197i
$566$	−9254.00			−0.687234
$567$		0			0
$568$		−	3648.00i		−	0.269484i
$569$	8762.00			0.645557			0.322779	−	0.946474i	$-0.395383\pi$
$569$	8762.00			0.645557			0.322779	+	0.946474i	$0.395383\pi$
$570$		0			0
$571$	−24764.0			−1.81496			−0.907479	−	0.420097i	$-0.861996\pi$
$571$	−24764.0			−1.81496			−0.907479	+	0.420097i	$0.861996\pi$
$572$			7548.00i			0.551744i
$573$		0			0
$574$	−2884.00			−0.209714
$575$	7000.00	−	5250.00i	0.507687	−	0.380765i
$576$		0			0
$577$			1811.00i			0.130664i	0.997864	+	0.0653318i	$0.0208106\pi$
$577$			1811.00i			0.130664i	−0.997864	+	0.0653318i	$0.979189\pi$
$578$		−	6464.00i		−	0.465168i
$579$		0			0
$580$	−9960.00	−	4980.00i	−0.713046	−	0.356523i
$581$	−2996.00			−0.213933
$582$		0			0
$583$		−	222.000i		−	0.0157707i
$584$	5200.00			0.368455
$585$		0			0
$586$	−8166.00			−0.575656
$587$		−	10548.0i		−	0.741674i	−0.928698	−	0.370837i	$-0.879071\pi$
$587$		−	10548.0i		−	0.741674i	0.928698	−	0.370837i	$-0.120929\pi$
$588$		0			0
$589$	−14472.0			−1.01241
$590$	20.0000	−	40.0000i	0.00139557	−	0.00279114i
$591$		0			0
$592$		−	5344.00i		−	0.371009i
$593$			17439.0i			1.20765i	0.797119	+	0.603823i	$0.206357\pi$
$593$			17439.0i			1.20765i	−0.797119	+	0.603823i	$0.793643\pi$
$594$		0			0
$595$	−2870.00	−	1435.00i	−0.197745	−	0.0988727i
$596$	1208.00			0.0830228
$597$		0			0
$598$			7140.00i			0.488255i
$599$	2451.00			0.167187			0.0835936	−	0.996500i	$-0.473360\pi$
$599$	2451.00			0.167187			0.0835936	+	0.996500i	$0.473360\pi$
$600$		0			0
$601$	−7792.00			−0.528856			−0.264428	−	0.964405i	$-0.585183\pi$
$601$	−7792.00			−0.528856			−0.264428	+	0.964405i	$0.585183\pi$
$602$			5264.00i			0.356386i
$603$		0			0
$604$	12668.0			0.853400
$605$	−380.000	−	190.000i	−0.0255359	−	0.0127679i
$606$		0			0
$607$		−	1937.00i		−	0.129523i	−0.997901	−	0.0647615i	$-0.979371\pi$
$607$		−	1937.00i		−	0.129523i	0.997901	−	0.0647615i	$-0.0206286\pi$
$608$		−	3456.00i		−	0.230525i
$609$		0			0
$610$	9400.00	−	18800.0i	0.623926	−	1.24785i
$611$	14637.0			0.969148
$612$		0			0
$613$		−	5036.00i		−	0.331814i	−0.986141	−	0.165907i	$-0.946945\pi$
$613$		−	5036.00i		−	0.331814i	0.986141	−	0.165907i	$-0.0530552\pi$
$614$	−8178.00			−0.537520
$615$		0			0
$616$	−2072.00			−0.135525
$617$			27286.0i			1.78038i	0.455592	+	0.890189i	$0.349428\pi$
$617$			27286.0i			1.78038i	−0.455592	+	0.890189i	$0.650572\pi$
$618$		0			0
$619$	−28538.0			−1.85305			−0.926526	−	0.376231i	$-0.877220\pi$
$619$	−28538.0			−1.85305			−0.926526	+	0.376231i	$0.877220\pi$
$620$	−5360.00	−	2680.00i	−0.347198	−	0.173599i
$621$		0			0
$622$		−	8016.00i		−	0.516740i
$623$		−	1540.00i		−	0.0990350i
$624$		0			0
$625$	−4375.00	+	15000.0i	−0.280000	+	0.960000i
$626$	−14710.0			−0.939185
$627$		0			0
$628$			1880.00i			0.119459i
$629$	−13694.0			−0.868069
$630$		0			0
$631$	25007.0			1.57768			0.788838	−	0.614602i	$-0.210683\pi$
$631$	25007.0			1.57768			0.788838	+	0.614602i	$0.210683\pi$
$632$			9912.00i			0.623858i
$633$		0			0
$634$	3368.00			0.210978
$635$	2170.00	−	4340.00i	0.135612	−	0.271225i
$636$		0			0
$637$			2499.00i			0.155438i
$638$			18426.0i			1.14340i
$639$		0			0
$640$	640.000	−	1280.00i	0.0395285	−	0.0790569i
$641$	12130.0			0.747436			0.373718	−	0.927542i	$-0.378083\pi$
$641$	12130.0			0.747436			0.373718	+	0.927542i	$0.378083\pi$
$642$		0			0
$643$		−	14385.0i		−	0.882254i	−0.897445	−	0.441127i	$-0.854579\pi$
$643$		−	14385.0i		−	0.882254i	0.897445	−	0.441127i	$-0.145421\pi$
$644$	−1960.00			−0.119930
$645$		0			0
$646$	−8856.00			−0.539373
$647$			2208.00i			0.134166i	0.997747	+	0.0670830i	$0.0213692\pi$
$647$			2208.00i			0.134166i	−0.997747	+	0.0670830i	$0.978631\pi$
$648$		0			0
$649$	−74.0000			−0.00447574
$650$	−7650.00	−	10200.0i	−0.461627	−	0.615503i
$651$		0			0
$652$		−	9560.00i		−	0.574231i
$653$			22448.0i			1.34527i	0.739977	+	0.672633i	$0.234837\pi$
$653$			22448.0i			1.34527i	−0.739977	+	0.672633i	$0.765163\pi$
$654$		0			0
$655$	−12900.0	−	6450.00i	−0.769534	−	0.384767i
$656$	−3296.00			−0.196169
$657$		0			0
$658$			4018.00i			0.238052i
$659$	8791.00			0.519649			0.259825	−	0.965656i	$-0.416335\pi$
$659$	8791.00			0.519649			0.259825	+	0.965656i	$0.416335\pi$
$660$		0			0
$661$	−13180.0			−0.775556			−0.387778	−	0.921753i	$-0.626757\pi$
$661$	−13180.0			−0.775556			−0.387778	+	0.921753i	$0.626757\pi$
$662$			2920.00i			0.171434i
$663$		0			0
$664$	−3424.00			−0.200116
$665$	3780.00	−	7560.00i	0.220424	−	0.440848i
$666$		0			0
$667$			17430.0i			1.01183i
$668$		−	10524.0i		−	0.609560i
$669$		0			0
$670$	−2120.00	−	1060.00i	−0.122243	−	0.0611215i
$671$	−34780.0			−2.00099
$672$		0			0
$673$			7164.00i			0.410330i	0.978727	+	0.205165i	$0.0657731\pi$
$673$			7164.00i			0.410330i	−0.978727	+	0.205165i	$0.934227\pi$
$674$	15028.0			0.858838
$675$		0			0
$676$	1616.00			0.0919436
$677$		−	12335.0i		−	0.700255i	−0.936702	−	0.350127i	$-0.886138\pi$
$677$		−	12335.0i		−	0.700255i	0.936702	−	0.350127i	$-0.113862\pi$
$678$		0			0
$679$	7385.00			0.417394
$680$	−3280.00	−	1640.00i	−0.184974	−	0.0924870i
$681$		0			0
$682$			9916.00i			0.556750i
$683$		−	15436.0i		−	0.864776i	−0.901688	−	0.432388i	$-0.857671\pi$
$683$		−	15436.0i		−	0.864776i	0.901688	−	0.432388i	$-0.142329\pi$
$684$		0			0
$685$	−960.000	+	1920.00i	−0.0535470	+	0.107094i
$686$	−686.000			−0.0381802
$687$		0			0
$688$			6016.00i			0.333369i
$689$	−306.000			−0.0169197
$690$		0			0
$691$	−19184.0			−1.05614			−0.528071	−	0.849200i	$-0.677084\pi$
$691$	−19184.0			−1.05614			−0.528071	+	0.849200i	$0.677084\pi$
$692$			8972.00i			0.492867i
$693$		0			0
$694$	5724.00			0.313084
$695$	14020.0	+	7010.00i	0.765193	+	0.382596i
$696$		0			0
$697$			8446.00i			0.458989i
$698$		−	12736.0i		−	0.690637i
$699$		0			0
$700$	2800.00	−	2100.00i	0.151186	−	0.113389i
$701$	−32975.0			−1.77667			−0.888337	−	0.459192i	$-0.848139\pi$
$701$	−32975.0			−1.77667			−0.888337	+	0.459192i	$0.848139\pi$
$702$		0			0
$703$		−	36072.0i		−	1.93525i
$704$	−2368.00			−0.126772
$705$		0			0
$706$	−7270.00			−0.387550
$707$		−	13720.0i		−	0.729836i
$708$		0			0
$709$	31497.0			1.66840			0.834199	−	0.551463i	$-0.185930\pi$
$709$	31497.0			1.66840			0.834199	+	0.551463i	$0.185930\pi$
$710$	4560.00	−	9120.00i	0.241033	−	0.482067i
$711$		0			0
$712$		−	1760.00i		−	0.0926387i
$713$			9380.00i			0.492684i
$714$		0			0
$715$	−9435.00	+	18870.0i	−0.493495	+	0.986990i
$716$	−208.000			−0.0108566
$717$		0			0
$718$		−	14232.0i		−	0.739740i
$719$	−18610.0			−0.965279			−0.482640	−	0.875819i	$-0.660322\pi$
$719$	−18610.0			−0.965279			−0.482640	+	0.875819i	$0.660322\pi$
$720$		0			0
$721$	12775.0			0.659869
$722$		−	9610.00i		−	0.495356i
$723$		0			0
$724$	−9848.00			−0.505522
$725$	−18675.0	−	24900.0i	−0.956651	−	1.27553i
$726$		0			0
$727$		−	17508.0i		−	0.893172i	−0.894741	−	0.446586i	$-0.852640\pi$
$727$		−	17508.0i		−	0.893172i	0.894741	−	0.446586i	$-0.147360\pi$
$728$			2856.00i			0.145399i
$729$		0			0
$730$	13000.0	+	6500.00i	0.659112	+	0.329556i
$731$	15416.0			0.780002
$732$		0			0
$733$			4685.00i			0.236077i	0.993009	+	0.118038i	$0.0376606\pi$
$733$			4685.00i			0.236077i	−0.993009	+	0.118038i	$0.962339\pi$
$734$	−638.000			−0.0320831
$735$		0			0
$736$	−2240.00			−0.112184
$737$			3922.00i			0.196023i
$738$		0			0
$739$	25925.0			1.29048			0.645241	−	0.763979i	$-0.276757\pi$
$739$	25925.0			1.29048			0.645241	+	0.763979i	$0.276757\pi$
$740$	6680.00	−	13360.0i	0.331840	−	0.663680i
$741$		0			0
$742$		−	84.0000i		−	0.00415598i
$743$			25578.0i			1.26294i	0.775400	+	0.631471i	$0.217548\pi$
$743$			25578.0i			1.26294i	−0.775400	+	0.631471i	$0.782452\pi$
$744$		0			0
$745$	3020.00	+	1510.00i	0.148516	+	0.0742579i
$746$	23304.0			1.14373
$747$		0			0
$748$			6068.00i			0.296615i
$749$	−1008.00			−0.0491743
$750$		0			0
$751$	−4291.00			−0.208496			−0.104248	−	0.994551i	$-0.533244\pi$
$751$	−4291.00			−0.208496			−0.104248	+	0.994551i	$0.533244\pi$
$752$			4592.00i			0.222677i
$753$		0			0
$754$	25398.0			1.22671
$755$	31670.0	+	15835.0i	1.52661	+	0.763304i
$756$		0			0
$757$		−	31528.0i		−	1.51374i	−0.653563	−	0.756872i	$-0.726726\pi$
$757$		−	31528.0i		−	1.51374i	0.653563	−	0.756872i	$-0.273274\pi$
$758$			15496.0i			0.742533i
$759$		0			0
$760$	4320.00	−	8640.00i	0.206188	−	0.412376i
$761$	23154.0			1.10293			0.551466	−	0.834197i	$-0.314068\pi$
$761$	23154.0			1.10293			0.551466	+	0.834197i	$0.314068\pi$
$762$		0			0
$763$		−	11767.0i		−	0.558315i
$764$	12636.0			0.598370
$765$		0			0
$766$	17360.0			0.818854
$767$			102.000i			0.00480183i
$768$		0			0
$769$	−13992.0			−0.656131			−0.328065	−	0.944655i	$-0.606397\pi$
$769$	−13992.0			−0.656131			−0.328065	+	0.944655i	$0.606397\pi$
$770$	−5180.00	−	2590.00i	−0.242434	−	0.121217i
$771$		0			0
$772$			8240.00i			0.384150i
$773$		−	21681.0i		−	1.00881i	−0.863467	−	0.504406i	$-0.831712\pi$
$773$		−	21681.0i		−	1.00881i	0.863467	−	0.504406i	$-0.168288\pi$
$774$		0			0
$775$	−10050.0	−	13400.0i	−0.465815	−	0.621087i
$776$	8440.00			0.390436
$777$		0			0
$778$			3422.00i			0.157692i
$779$	−22248.0			−1.02326
$780$		0			0
$781$	−16872.0			−0.773019
$782$			5740.00i			0.262483i
$783$		0			0
$784$	−784.000			−0.0357143
$785$	−2350.00	+	4700.00i	−0.106847	+	0.213695i
$786$		0			0
$787$		−	16903.0i		−	0.765600i	−0.923831	−	0.382800i	$-0.874960\pi$
$787$		−	16903.0i		−	0.765600i	0.923831	−	0.382800i	$-0.125040\pi$
$788$			6952.00i			0.314283i
$789$		0			0
$790$	−12390.0	+	24780.0i	−0.557995	+	1.11599i
$791$	−5586.00			−0.251094
$792$		0			0
$793$			47940.0i			2.14678i
$794$	3178.00			0.142044
$795$		0			0
$796$	−3576.00			−0.159231
$797$		−	18905.0i		−	0.840213i	−0.907475	−	0.420106i	$-0.861993\pi$
$797$		−	18905.0i		−	0.840213i	0.907475	−	0.420106i	$-0.138007\pi$
$798$		0			0
$799$	11767.0			0.521009
$800$	3200.00	−	2400.00i	0.141421	−	0.106066i
$801$		0			0
$802$		−	10294.0i		−	0.453234i
$803$		−	24050.0i		−	1.05692i
$804$		0			0
$805$	−4900.00	−	2450.00i	−0.214537	−	0.107269i
$806$	13668.0			0.597314
$807$		0			0
$808$		−	15680.0i		−	0.682699i
$809$	−5571.00			−0.242109			−0.121054	−	0.992646i	$-0.538628\pi$
$809$	−5571.00			−0.242109			−0.121054	+	0.992646i	$0.538628\pi$
$810$		0			0
$811$	10894.0			0.471689			0.235845	−	0.971791i	$-0.424214\pi$
$811$	10894.0			0.471689			0.235845	+	0.971791i	$0.424214\pi$
$812$			6972.00i			0.301317i
$813$		0			0
$814$	−24716.0			−1.06424
$815$	11950.0	−	23900.0i	0.513608	−	1.02722i
$816$		0			0
$817$			40608.0i			1.73892i
$818$		−	18200.0i		−	0.777932i
$819$		0			0
$820$	−8240.00	−	4120.00i	−0.350919	−	0.175459i
$821$	30731.0			1.30636			0.653179	−	0.757204i	$-0.273435\pi$
$821$	30731.0			1.30636			0.653179	+	0.757204i	$0.273435\pi$
$822$		0			0
$823$		−	1038.00i		−	0.0439640i	−0.999758	−	0.0219820i	$-0.993002\pi$
$823$		−	1038.00i		−	0.0439640i	0.999758	−	0.0219820i	$-0.00699766\pi$
$824$	14600.0			0.617251
$825$		0			0
$826$	−28.0000			−0.00117947
$827$		−	7958.00i		−	0.334615i	−0.985905	−	0.167308i	$-0.946493\pi$
$827$		−	7958.00i		−	0.334615i	0.985905	−	0.167308i	$-0.0535073\pi$
$828$		0			0
$829$	30666.0			1.28477			0.642385	−	0.766382i	$-0.277945\pi$
$829$	30666.0			1.28477			0.642385	+	0.766382i	$0.277945\pi$
$830$	−8560.00	−	4280.00i	−0.357978	−	0.178989i
$831$		0			0
$832$			3264.00i			0.136008i
$833$			2009.00i			0.0835627i
$834$		0			0
$835$	13155.0	−	26310.0i	0.545207	−	1.09041i
$836$	−15984.0			−0.661266
$837$		0			0
$838$		−	5236.00i		−	0.215841i
$839$	−5354.00			−0.220311			−0.110155	−	0.993914i	$-0.535135\pi$
$839$	−5354.00			−0.220311			−0.110155	+	0.993914i	$0.535135\pi$
$840$		0			0
$841$	37612.0			1.54217
$842$			7390.00i			0.302466i
$843$		0			0
$844$	16332.0			0.666079
$845$	4040.00	+	2020.00i	0.164474	+	0.0822368i
$846$		0			0
$847$			266.000i			0.0107909i
$848$		−	96.0000i		−	0.00388756i
$849$		0			0
$850$	−6150.00	−	8200.00i	−0.248169	−	0.330891i
$851$	−23380.0			−0.941782
$852$		0			0
$853$			42890.0i			1.72160i	0.508943	+	0.860800i	$0.330037\pi$
$853$			42890.0i			1.72160i	−0.508943	+	0.860800i	$0.669963\pi$
$854$	−13160.0			−0.527314
$855$		0			0
$856$	−1152.00			−0.0459983
$857$		−	22950.0i		−	0.914769i	−0.889269	−	0.457385i	$-0.848786\pi$
$857$		−	22950.0i		−	0.914769i	0.889269	−	0.457385i	$-0.151214\pi$
$858$		0			0
$859$	2824.00			0.112170			0.0560848	−	0.998426i	$-0.482138\pi$
$859$	2824.00			0.112170			0.0560848	+	0.998426i	$0.482138\pi$
$860$	−7520.00	+	15040.0i	−0.298174	+	0.596349i
$861$		0			0
$862$			31558.0i			1.24695i
$863$		−	4866.00i		−	0.191936i	−0.995384	−	0.0959679i	$-0.969405\pi$
$863$		−	4866.00i		−	0.191936i	0.995384	−	0.0959679i	$-0.0305946\pi$
$864$		0			0
$865$	−11215.0	+	22430.0i	−0.440834	+	0.881668i
$866$	−14476.0			−0.568031
$867$		0			0
$868$			3752.00i			0.146718i
$869$	45843.0			1.78955
$870$		0			0
$871$	5406.00			0.210305
$872$		−	13448.0i		−	0.522255i
$873$		0			0
$874$	−15120.0			−0.585173
$875$	9625.00	−	1750.00i	0.371868	−	0.0676123i
$876$		0			0
$877$		−	10676.0i		−	0.411064i	−0.978650	−	0.205532i	$-0.934108\pi$
$877$		−	10676.0i		−	0.411064i	0.978650	−	0.205532i	$-0.0658924\pi$
$878$		−	5292.00i		−	0.203413i
$879$		0			0
$880$	−5920.00	−	2960.00i	−0.226776	−	0.113388i
$881$	29856.0			1.14174			0.570871	−	0.821040i	$-0.306606\pi$
$881$	29856.0			1.14174			0.570871	+	0.821040i	$0.306606\pi$
$882$		0			0
$883$			1944.00i			0.0740893i	0.999314	+	0.0370446i	$0.0117944\pi$
$883$			1944.00i			0.0740893i	−0.999314	+	0.0370446i	$0.988206\pi$
$884$	8364.00			0.318226
$885$		0			0
$886$	11376.0			0.431359
$887$			14628.0i			0.553732i	0.960909	+	0.276866i	$0.0892958\pi$
$887$			14628.0i			0.553732i	−0.960909	+	0.276866i	$0.910704\pi$
$888$		0			0
$889$	−3038.00			−0.114613
$890$	2200.00	−	4400.00i	0.0828586	−	0.165717i
$891$		0			0
$892$			1508.00i			0.0566049i
$893$			30996.0i			1.16152i
$894$		0			0
$895$	−520.000	−	260.000i	−0.0194209	−	0.00971044i
$896$	−896.000			−0.0334077
$897$		0			0
$898$			6570.00i			0.244147i
$899$	33366.0			1.23784
$900$		0			0
$901$	−246.000			−0.00909595
$902$			15244.0i			0.562716i
$903$		0			0
$904$	−6384.00			−0.234877
$905$	−24620.0	−	12310.0i	−0.904306	−	0.452153i
$906$		0			0
$907$		−	12858.0i		−	0.470720i	−0.971908	−	0.235360i	$-0.924373\pi$
$907$		−	12858.0i		−	0.470720i	0.971908	−	0.235360i	$-0.0756269\pi$
$908$		−	10204.0i		−	0.372942i
$909$		0			0
$910$	−3570.00	+	7140.00i	−0.130049	+	0.260097i
$911$	18324.0			0.666412			0.333206	−	0.942854i	$-0.391870\pi$
$911$	18324.0			0.666412			0.333206	+	0.942854i	$0.391870\pi$
$912$		0			0
$913$			15836.0i			0.574036i
$914$	29668.0			1.07367
$915$		0			0
$916$	296.000			0.0106770
$917$			9030.00i			0.325187i
$918$		0			0
$919$	14751.0			0.529478			0.264739	−	0.964320i	$-0.414714\pi$
$919$	14751.0			0.529478			0.264739	+	0.964320i	$0.414714\pi$
$920$	−5600.00	−	2800.00i	−0.200681	−	0.100341i
$921$		0			0
$922$		−	19944.0i		−	0.712387i
$923$			23256.0i			0.829340i
$924$		0			0
$925$	33400.0	−	25050.0i	1.18723	−	0.890420i
$926$	18192.0			0.645601
$927$		0			0
$928$			7968.00i			0.281856i
$929$	−47922.0			−1.69243			−0.846216	−	0.532840i	$-0.821125\pi$
$929$	−47922.0			−1.69243			−0.846216	+	0.532840i	$0.821125\pi$
$930$		0			0
$931$	−5292.00			−0.186292
$932$		−	7552.00i		−	0.265423i
$933$		0			0
$934$	−31734.0			−1.11174
$935$	−7585.00	+	15170.0i	−0.265301	+	0.530601i
$936$		0			0
$937$		−	44987.0i		−	1.56848i	−0.620461	−	0.784238i	$-0.713054\pi$
$937$		−	44987.0i		−	1.56848i	0.620461	−	0.784238i	$-0.286946\pi$
$938$			1484.00i			0.0516571i
$939$		0			0
$940$	−5740.00	+	11480.0i	−0.199168	+	0.398337i
$941$	20356.0			0.705193			0.352597	−	0.935775i	$-0.385299\pi$
$941$	20356.0			0.705193			0.352597	+	0.935775i	$0.385299\pi$
$942$		0			0
$943$			14420.0i			0.497964i
$944$	−32.0000			−0.00110330
$945$		0			0
$946$	27824.0			0.956275
$947$			27786.0i			0.953457i	0.879051	+	0.476728i	$0.158177\pi$
$947$			27786.0i			0.953457i	−0.879051	+	0.476728i	$0.841823\pi$
$948$		0			0
$949$	−33150.0			−1.13392
$950$	21600.0	−	16200.0i	0.737681	−	0.553260i
$951$		0			0
$952$			2296.00i			0.0781657i
$953$		−	48674.0i		−	1.65447i	−0.561859	−	0.827233i	$-0.689914\pi$
$953$		−	48674.0i		−	1.65447i	0.561859	−	0.827233i	$-0.310086\pi$
$954$		0			0
$955$	31590.0	+	15795.0i	1.07040	+	0.535198i
$956$	−19988.0			−0.676211
$957$		0			0
$958$		−	484.000i		−	0.0163229i
$959$	1344.00			0.0452555
$960$		0			0
$961$	−11835.0			−0.397268
$962$			34068.0i			1.14178i
$963$		0			0
$964$	15320.0			0.511851
$965$	−10300.0	+	20600.0i	−0.343595	+	0.687189i
$966$		0			0
$967$		−	11168.0i		−	0.371395i	−0.982607	−	0.185697i	$-0.940546\pi$
$967$		−	11168.0i		−	0.371395i	0.982607	−	0.185697i	$-0.0594544\pi$
$968$			304.000i			0.0100939i
$969$		0			0
$970$	21100.0	+	10550.0i	0.698433	+	0.349217i
$971$	−20094.0			−0.664106			−0.332053	−	0.943261i	$-0.607741\pi$
$971$	−20094.0			−0.664106			−0.332053	+	0.943261i	$0.607741\pi$
$972$		0			0
$973$		−	9814.00i		−	0.323353i
$974$	−7116.00			−0.234098
$975$		0			0
$976$	−15040.0			−0.493257
$977$		−	49104.0i		−	1.60796i	−0.594657	−	0.803980i	$-0.702712\pi$
$977$		−	49104.0i		−	1.60796i	0.594657	−	0.803980i	$-0.297288\pi$
$978$		0			0
$979$	−8140.00			−0.265736
$980$	−1960.00	−	980.000i	−0.0638877	−	0.0319438i
$981$		0			0
$982$			2946.00i			0.0957338i
$983$			27751.0i			0.900427i	0.892921	+	0.450213i	$0.148652\pi$
$983$			27751.0i			0.900427i	−0.892921	+	0.450213i	$0.851348\pi$
$984$		0			0
$985$	−8690.00	+	17380.0i	−0.281103	+	0.562206i
$986$	20418.0			0.659474
$987$		0			0
$988$			22032.0i			0.709445i
$989$	26320.0			0.846236
$990$		0			0
$991$	37600.0			1.20525			0.602625	−	0.798024i	$-0.294121\pi$
$991$	37600.0			1.20525			0.602625	+	0.798024i	$0.294121\pi$
$992$			4288.00i			0.137242i
$993$		0			0
$994$	−6384.00			−0.203710
$995$	−8940.00	−	4470.00i	−0.284841	−	0.142421i
$996$		0			0
$997$		−	10911.0i		−	0.346595i	−0.984870	−	0.173297i	$-0.944558\pi$
$997$		−	10911.0i		−	0.346595i	0.984870	−	0.173297i	$-0.0554422\pi$
$998$			1206.00i			0.0382518i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.4.g.a.379.1		2
3.2	odd	2		70.4.c.a.29.2	yes	2
5.4	even	2	inner	630.4.g.a.379.2		2
12.11	even	2		560.4.g.c.449.1		2
15.2	even	4		350.4.a.i.1.1		1
15.8	even	4		350.4.a.m.1.1		1
15.14	odd	2		70.4.c.a.29.1	✓	2
21.20	even	2		490.4.c.a.99.2		2
60.59	even	2		560.4.g.c.449.2		2
105.62	odd	4		2450.4.a.c.1.1		1
105.83	odd	4		2450.4.a.bn.1.1		1
105.104	even	2		490.4.c.a.99.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.c.a.29.1	✓	2	15.14	odd	2
70.4.c.a.29.2	yes	2	3.2	odd	2
350.4.a.i.1.1		1	15.2	even	4
350.4.a.m.1.1		1	15.8	even	4
490.4.c.a.99.1		2	105.104	even	2
490.4.c.a.99.2		2	21.20	even	2
560.4.g.c.449.1		2	12.11	even	2
560.4.g.c.449.2		2	60.59	even	2
630.4.g.a.379.1		2	1.1	even	1	trivial
630.4.g.a.379.2		2	5.4	even	2	inner
2450.4.a.c.1.1		1	105.62	odd	4
2450.4.a.bn.1.1		1	105.83	odd	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)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -4.00000 q^{4} +(-10.0000 - 5.00000i) q^{5} +7.00000i q^{7} +8.00000i q^{8} +O(q^{10})\)	\(q-2.00000i q^{2} -4.00000 q^{4} +(-10.0000 - 5.00000i) q^{5} +7.00000i q^{7} +8.00000i q^{8} +(-10.0000 + 20.0000i) q^{10} +37.0000 q^{11} -51.0000i q^{13} +14.0000 q^{14} +16.0000 q^{16} -41.0000i q^{17} +108.000 q^{19} +(40.0000 + 20.0000i) q^{20} -74.0000i q^{22} -70.0000i q^{23} +(75.0000 + 100.000i) q^{25} -102.000 q^{26} -28.0000i q^{28} -249.000 q^{29} -134.000 q^{31} -32.0000i q^{32} -82.0000 q^{34} +(35.0000 - 70.0000i) q^{35} -334.000i q^{37} -216.000i q^{38} +(40.0000 - 80.0000i) q^{40} -206.000 q^{41} +376.000i q^{43} -148.000 q^{44} -140.000 q^{46} +287.000i q^{47} -49.0000 q^{49} +(200.000 - 150.000i) q^{50} +204.000i q^{52} -6.00000i q^{53} +(-370.000 - 185.000i) q^{55} -56.0000 q^{56} +498.000i q^{58} -2.00000 q^{59} -940.000 q^{61} +268.000i q^{62} -64.0000 q^{64} +(-255.000 + 510.000i) q^{65} +106.000i q^{67} +164.000i q^{68} +(-140.000 - 70.0000i) q^{70} -456.000 q^{71} -650.000i q^{73} -668.000 q^{74} -432.000 q^{76} +259.000i q^{77} +1239.00 q^{79} +(-160.000 - 80.0000i) q^{80} +412.000i q^{82} +428.000i q^{83} +(-205.000 + 410.000i) q^{85} +752.000 q^{86} +296.000i q^{88} -220.000 q^{89} +357.000 q^{91} +280.000i q^{92} +574.000 q^{94} +(-1080.00 - 540.000i) q^{95} -1055.00i q^{97} +98.0000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{4} - 20 q^{5}+O(q^{10}) \) 2 * q - 8 * q^4 - 20 * q^5	\( 2 q - 8 q^{4} - 20 q^{5} - 20 q^{10} + 74 q^{11} + 28 q^{14} + 32 q^{16} + 216 q^{19} + 80 q^{20} + 150 q^{25} - 204 q^{26} - 498 q^{29} - 268 q^{31} - 164 q^{34} + 70 q^{35} + 80 q^{40} - 412 q^{41} - 296 q^{44} - 280 q^{46} - 98 q^{49} + 400 q^{50} - 740 q^{55} - 112 q^{56} - 4 q^{59} - 1880 q^{61} - 128 q^{64} - 510 q^{65} - 280 q^{70} - 912 q^{71} - 1336 q^{74} - 864 q^{76} + 2478 q^{79} - 320 q^{80} - 410 q^{85} + 1504 q^{86} - 440 q^{89} + 714 q^{91} + 1148 q^{94} - 2160 q^{95}+O(q^{100}) \) 2 * q - 8 * q^4 - 20 * q^5 - 20 * q^10 + 74 * q^11 + 28 * q^14 + 32 * q^16 + 216 * q^19 + 80 * q^20 + 150 * q^25 - 204 * q^26 - 498 * q^29 - 268 * q^31 - 164 * q^34 + 70 * q^35 + 80 * q^40 - 412 * q^41 - 296 * q^44 - 280 * q^46 - 98 * q^49 + 400 * q^50 - 740 * q^55 - 112 * q^56 - 4 * q^59 - 1880 * q^61 - 128 * q^64 - 510 * q^65 - 280 * q^70 - 912 * q^71 - 1336 * q^74 - 864 * q^76 + 2478 * q^79 - 320 * q^80 - 410 * q^85 + 1504 * q^86 - 440 * q^89 + 714 * q^91 + 1148 * q^94 - 2160 * q^95

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