LMFDB - Embedded newform 50.6.b.c.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,6,Mod(49,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("50.49");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	50.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.01919099065$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.6.b.c.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000i q^{2} -11.0000i q^{3} -16.0000 q^{4} +44.0000 q^{6} +142.000i q^{7} -64.0000i q^{8} +122.000 q^{9} +O(q^{10})$	\(q+4.00000i q^{2} -11.0000i q^{3} -16.0000 q^{4} +44.0000 q^{6} +142.000i q^{7} -64.0000i q^{8} +122.000 q^{9} +777.000 q^{11} +176.000i q^{12} +884.000i q^{13} -568.000 q^{14} +256.000 q^{16} +27.0000i q^{17} +488.000i q^{18} -1145.00 q^{19} +1562.00 q^{21} +3108.00i q^{22} +1854.00i q^{23} -704.000 q^{24} -3536.00 q^{26} -4015.00i q^{27} -2272.00i q^{28} +4920.00 q^{29} +1802.00 q^{31} +1024.00i q^{32} -8547.00i q^{33} -108.000 q^{34} -1952.00 q^{36} -13178.0i q^{37} -4580.00i q^{38} +9724.00 q^{39} -15123.0 q^{41} +6248.00i q^{42} +7844.00i q^{43} -12432.0 q^{44} -7416.00 q^{46} +6732.00i q^{47} -2816.00i q^{48} -3357.00 q^{49} +297.000 q^{51} -14144.0i q^{52} +3414.00i q^{53} +16060.0 q^{54} +9088.00 q^{56} +12595.0i q^{57} +19680.0i q^{58} -33960.0 q^{59} +47402.0 q^{61} +7208.00i q^{62} +17324.0i q^{63} -4096.00 q^{64} +34188.0 q^{66} +13177.0i q^{67} -432.000i q^{68} +20394.0 q^{69} -7548.00 q^{71} -7808.00i q^{72} -59821.0i q^{73} +52712.0 q^{74} +18320.0 q^{76} +110334. i q^{77} +38896.0i q^{78} -75830.0 q^{79} -14519.0 q^{81} -60492.0i q^{82} +46299.0i q^{83} -24992.0 q^{84} -31376.0 q^{86} -54120.0i q^{87} -49728.0i q^{88} +30585.0 q^{89} -125528. q^{91} -29664.0i q^{92} -19822.0i q^{93} -26928.0 q^{94} +11264.0 q^{96} -104018. i q^{97} -13428.0i q^{98} +94794.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{4} + 88 q^{6} + 244 q^{9}+O(q^{10}) $ 2 * q - 32 * q^4 + 88 * q^6 + 244 * q^9	$ 2 q - 32 q^{4} + 88 q^{6} + 244 q^{9} + 1554 q^{11} - 1136 q^{14} + 512 q^{16} - 2290 q^{19} + 3124 q^{21} - 1408 q^{24} - 7072 q^{26} + 9840 q^{29} + 3604 q^{31} - 216 q^{34} - 3904 q^{36} + 19448 q^{39} - 30246 q^{41} - 24864 q^{44} - 14832 q^{46} - 6714 q^{49} + 594 q^{51} + 32120 q^{54} + 18176 q^{56} - 67920 q^{59} + 94804 q^{61} - 8192 q^{64} + 68376 q^{66} + 40788 q^{69} - 15096 q^{71} + 105424 q^{74} + 36640 q^{76} - 151660 q^{79} - 29038 q^{81} - 49984 q^{84} - 62752 q^{86} + 61170 q^{89} - 251056 q^{91} - 53856 q^{94} + 22528 q^{96} + 189588 q^{99}+O(q^{100}) $ 2 * q - 32 * q^4 + 88 * q^6 + 244 * q^9 + 1554 * q^11 - 1136 * q^14 + 512 * q^16 - 2290 * q^19 + 3124 * q^21 - 1408 * q^24 - 7072 * q^26 + 9840 * q^29 + 3604 * q^31 - 216 * q^34 - 3904 * q^36 + 19448 * q^39 - 30246 * q^41 - 24864 * q^44 - 14832 * q^46 - 6714 * q^49 + 594 * q^51 + 32120 * q^54 + 18176 * q^56 - 67920 * q^59 + 94804 * q^61 - 8192 * q^64 + 68376 * q^66 + 40788 * q^69 - 15096 * q^71 + 105424 * q^74 + 36640 * q^76 - 151660 * q^79 - 29038 * q^81 - 49984 * q^84 - 62752 * q^86 + 61170 * q^89 - 251056 * q^91 - 53856 * q^94 + 22528 * q^96 + 189588 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$-1$

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 $

$2$	4.00000i	0.707107i
$2$	4.00000i	0.707107i
$3$	− 11.0000i	− 0.705650i	−0.935689	−	0.352825i	$-0.885221\pi$
$3$	− 11.0000i	− 0.705650i	0.935689	−	0.352825i	$-0.114779\pi$
$4$	−16.0000	−0.500000
$5$	0	0
$5$	0	0
$6$	44.0000	0.498970
$7$	142.000i	1.09533i	0.836699	+	0.547663i	$0.184482\pi$
$7$	142.000i	1.09533i	−0.836699	+	0.547663i	$0.815518\pi$
$8$	− 64.0000i	− 0.353553i
$9$	122.000	0.502058
$10$	0	0
$11$	777.000	1.93615	0.968076	−	0.250658i	$-0.0806470\pi$
$11$	777.000	1.93615	0.968076	+	0.250658i	$0.0806470\pi$
$12$	176.000i	0.352825i
$13$	884.000i	1.45075i	0.688352	+	0.725377i	$0.258335\pi$
$13$	884.000i	1.45075i	−0.688352	+	0.725377i	$0.741665\pi$
$14$	−568.000	−0.774512
$15$	0	0
$16$	256.000	0.250000
$17$	27.0000i	0.0226590i	0.999936	+	0.0113295i	$0.00360637\pi$
$17$	27.0000i	0.0226590i	−0.999936	+	0.0113295i	$0.996394\pi$
$18$	488.000i	0.355008i
$19$	−1145.00	−0.727648	−0.363824	−	0.931468i	$-0.618529\pi$
$19$	−1145.00	−0.727648	−0.363824	+	0.931468i	$0.618529\pi$
$20$	0	0
$21$	1562.00	0.772917
$22$	3108.00i	1.36907i
$23$	1854.00i	0.730786i	0.930853	+	0.365393i	$0.119065\pi$
$23$	1854.00i	0.730786i	−0.930853	+	0.365393i	$0.880935\pi$
$24$	−704.000	−0.249485
$25$	0	0
$26$	−3536.00	−1.02584
$27$	− 4015.00i	− 1.05993i
$28$	− 2272.00i	− 0.547663i
$29$	4920.00	1.08635	0.543175	−	0.839619i	$-0.317222\pi$
$29$	4920.00	1.08635	0.543175	+	0.839619i	$0.317222\pi$
$30$	0	0
$31$	1802.00	0.336783	0.168392	−	0.985720i	$-0.446143\pi$
$31$	1802.00	0.336783	0.168392	+	0.985720i	$0.446143\pi$
$32$	1024.00i	0.176777i
$33$	− 8547.00i	− 1.36625i
$34$	−108.000	−0.0160224
$35$	0	0
$36$	−1952.00	−0.251029
$37$	− 13178.0i	− 1.58251i	−0.611489	−	0.791253i	$-0.709429\pi$
$37$	− 13178.0i	− 1.58251i	0.611489	−	0.791253i	$-0.290571\pi$
$38$	− 4580.00i	− 0.514525i
$39$	9724.00	1.02373
$40$	0	0
$41$	−15123.0	−1.40501	−0.702503	−	0.711681i	$-0.747934\pi$
$41$	−15123.0	−1.40501	−0.702503	+	0.711681i	$0.747934\pi$
$42$	6248.00i	0.546535i
$43$	7844.00i	0.646944i	0.946238	+	0.323472i	$0.104850\pi$
$43$	7844.00i	0.646944i	−0.946238	+	0.323472i	$0.895150\pi$
$44$	−12432.0	−0.968076
$45$	0	0
$46$	−7416.00	−0.516744
$47$	6732.00i	0.444528i	0.974986	+	0.222264i	$0.0713447\pi$
$47$	6732.00i	0.444528i	−0.974986	+	0.222264i	$0.928655\pi$
$48$	− 2816.00i	− 0.176413i
$49$	−3357.00	−0.199738
$50$	0	0
$51$	297.000	0.0159894
$52$	− 14144.0i	− 0.725377i
$53$	3414.00i	0.166945i	0.996510	+	0.0834726i	$0.0266011\pi$
$53$	3414.00i	0.166945i	−0.996510	+	0.0834726i	$0.973399\pi$
$54$	16060.0	0.749482
$55$	0	0
$56$	9088.00	0.387256
$57$	12595.0i	0.513465i
$58$	19680.0i	0.768166i
$59$	−33960.0	−1.27010	−0.635050	−	0.772471i	$-0.719020\pi$
$59$	−33960.0	−1.27010	−0.635050	+	0.772471i	$0.719020\pi$
$60$	0	0
$61$	47402.0	1.63107	0.815534	−	0.578709i	$-0.196443\pi$
$61$	47402.0	1.63107	0.815534	+	0.578709i	$0.196443\pi$
$62$	7208.00i	0.238142i
$63$	17324.0i	0.549917i
$64$	−4096.00	−0.125000
$65$	0	0
$66$	34188.0	0.966082
$67$	13177.0i	0.358616i	0.983793	+	0.179308i	$0.0573858\pi$
$67$	13177.0i	0.358616i	−0.983793	+	0.179308i	$0.942614\pi$
$68$	− 432.000i	− 0.0113295i
$69$	20394.0	0.515679
$70$	0	0
$71$	−7548.00	−0.177699	−0.0888497	−	0.996045i	$-0.528319\pi$
$71$	−7548.00	−0.177699	−0.0888497	+	0.996045i	$0.528319\pi$
$72$	− 7808.00i	− 0.177504i
$73$	− 59821.0i	− 1.31385i	−0.753955	−	0.656926i	$-0.771856\pi$
$73$	− 59821.0i	− 1.31385i	0.753955	−	0.656926i	$-0.228144\pi$
$74$	52712.0	1.11900
$75$	0	0
$76$	18320.0	0.363824
$77$	110334.i	2.12072i
$78$	38896.0i	0.723883i
$79$	−75830.0	−1.36702	−0.683508	−	0.729943i	$-0.739546\pi$
$79$	−75830.0	−1.36702	−0.683508	+	0.729943i	$0.739546\pi$
$80$	0	0
$81$	−14519.0	−0.245881
$82$	− 60492.0i	− 0.993490i
$83$	46299.0i	0.737694i	0.929490	+	0.368847i	$0.120247\pi$
$83$	46299.0i	0.737694i	−0.929490	+	0.368847i	$0.879753\pi$
$84$	−24992.0	−0.386458
$85$	0	0
$86$	−31376.0	−0.457458
$87$	− 54120.0i	− 0.766584i
$88$	− 49728.0i	− 0.684533i
$89$	30585.0	0.409292	0.204646	−	0.978836i	$-0.434396\pi$
$89$	30585.0	0.409292	0.204646	+	0.978836i	$0.434396\pi$
$90$	0	0
$91$	−125528.	−1.58905
$92$	− 29664.0i	− 0.365393i
$93$	− 19822.0i	− 0.237651i
$94$	−26928.0	−0.314329
$95$	0	0
$96$	11264.0	0.124743
$97$	− 104018.i	− 1.12248i	−0.827653	−	0.561241i	$-0.810324\pi$
$97$	− 104018.i	− 1.12248i	0.827653	−	0.561241i	$-0.189676\pi$
$98$	− 13428.0i	− 0.141236i
$99$	94794.0	0.972060
$100$	0	0
$101$	−23898.0	−0.233109	−0.116554	−	0.993184i	$-0.537185\pi$
$101$	−23898.0	−0.233109	−0.116554	+	0.993184i	$0.537185\pi$
$102$	1188.00i	0.0113062i
$103$	− 22636.0i	− 0.210236i	−0.994460	−	0.105118i	$-0.966478\pi$
$103$	− 22636.0i	− 0.210236i	0.994460	−	0.105118i	$-0.0335220\pi$
$104$	56576.0	0.512919
$105$	0	0
$106$	−13656.0	−0.118048
$107$	− 60633.0i	− 0.511976i	−0.966680	−	0.255988i	$-0.917599\pi$
$107$	− 60633.0i	− 0.511976i	0.966680	−	0.255988i	$-0.0824008\pi$
$108$	64240.0i	0.529964i
$109$	7090.00	0.0571584	0.0285792	−	0.999592i	$-0.490902\pi$
$109$	7090.00	0.0571584	0.0285792	+	0.999592i	$0.490902\pi$
$110$	0	0
$111$	−144958.	−1.11670
$112$	36352.0i	0.273831i
$113$	− 128841.i	− 0.949201i	−0.880201	−	0.474600i	$-0.842593\pi$
$113$	− 128841.i	− 0.949201i	0.880201	−	0.474600i	$-0.157407\pi$
$114$	−50380.0	−0.363075
$115$	0	0
$116$	−78720.0	−0.543175
$117$	107848.i	0.728362i
$118$	− 135840.i	− 0.898096i
$119$	−3834.00	−0.0248190
$120$	0	0
$121$	442678.	2.74868
$122$	189608.i	1.15334i
$123$	166353.i	0.991443i
$124$	−28832.0	−0.168392
$125$	0	0
$126$	−69296.0	−0.388850
$127$	− 141338.i	− 0.777588i	−0.921325	−	0.388794i	$-0.872892\pi$
$127$	− 141338.i	− 0.777588i	0.921325	−	0.388794i	$-0.127108\pi$
$128$	− 16384.0i	− 0.0883883i
$129$	86284.0	0.456516
$130$	0	0
$131$	80052.0	0.407562	0.203781	−	0.979016i	$-0.434677\pi$
$131$	80052.0	0.407562	0.203781	+	0.979016i	$0.434677\pi$
$132$	136752.i	0.683123i
$133$	− 162590.i	− 0.797012i
$134$	−52708.0	−0.253580
$135$	0	0
$136$	1728.00	0.00801118
$137$	− 32253.0i	− 0.146814i	−0.997302	−	0.0734072i	$-0.976613\pi$
$137$	− 32253.0i	− 0.146814i	0.997302	−	0.0734072i	$-0.0233873\pi$
$138$	81576.0i	0.364640i
$139$	−394865.	−1.73345	−0.866726	−	0.498785i	$-0.833780\pi$
$139$	−394865.	−1.73345	−0.866726	+	0.498785i	$0.833780\pi$
$140$	0	0
$141$	74052.0	0.313682
$142$	− 30192.0i	− 0.125652i
$143$	686868.i	2.80888i
$144$	31232.0	0.125514
$145$	0	0
$146$	239284.	0.929034
$147$	36927.0i	0.140945i
$148$	210848.i	0.791253i
$149$	491400.	1.81330	0.906650	−	0.421884i	$-0.138631\pi$
$149$	491400.	1.81330	0.906650	+	0.421884i	$0.138631\pi$
$150$	0	0
$151$	200402.	0.715253	0.357626	−	0.933865i	$-0.383586\pi$
$151$	200402.	0.715253	0.357626	+	0.933865i	$0.383586\pi$
$152$	73280.0i	0.257263i
$153$	3294.00i	0.0113761i
$154$	−441336.	−1.49957
$155$	0	0
$156$	−155584.	−0.511863
$157$	22942.0i	0.0742818i	0.999310	+	0.0371409i	$0.0118250\pi$
$157$	22942.0i	0.0742818i	−0.999310	+	0.0371409i	$0.988175\pi$
$158$	− 303320.i	− 0.966626i
$159$	37554.0	0.117805
$160$	0	0
$161$	−263268.	−0.800448
$162$	− 58076.0i	− 0.173864i
$163$	− 336241.i	− 0.991246i	−0.868538	−	0.495623i	$-0.834940\pi$
$163$	− 336241.i	− 0.991246i	0.868538	−	0.495623i	$-0.165060\pi$
$164$	241968.	0.702503
$165$	0	0
$166$	−185196.	−0.521629
$167$	− 59748.0i	− 0.165780i	−0.996559	−	0.0828900i	$-0.973585\pi$
$167$	− 59748.0i	− 0.165780i	0.996559	−	0.0828900i	$-0.0264150\pi$
$168$	− 99968.0i	− 0.273267i
$169$	−410163.	−1.10469
$170$	0	0
$171$	−139690.	−0.365321
$172$	− 125504.i	− 0.323472i
$173$	− 60696.0i	− 0.154186i	−0.997024	−	0.0770930i	$-0.975436\pi$
$173$	− 60696.0i	− 0.154186i	0.997024	−	0.0770930i	$-0.0245638\pi$
$174$	216480.	0.542057
$175$	0	0
$176$	198912.	0.484038
$177$	373560.i	0.896246i
$178$	122340.i	0.289413i
$179$	7995.00	0.0186503	0.00932515	−	0.999957i	$-0.497032\pi$
$179$	7995.00	0.0186503	0.00932515	+	0.999957i	$0.497032\pi$
$180$	0	0
$181$	−454798.	−1.03186	−0.515932	−	0.856630i	$-0.672554\pi$
$181$	−454798.	−1.03186	−0.515932	+	0.856630i	$0.672554\pi$
$182$	− 502112.i	− 1.12363i
$183$	− 521422.i	− 1.15096i
$184$	118656.	0.258372
$185$	0	0
$186$	79288.0	0.168045
$187$	20979.0i	0.0438713i
$188$	− 107712.i	− 0.222264i
$189$	570130.	1.16097
$190$	0	0
$191$	−428298.	−0.849499	−0.424749	−	0.905311i	$-0.639638\pi$
$191$	−428298.	−0.849499	−0.424749	+	0.905311i	$0.639638\pi$
$192$	45056.0i	0.0882063i
$193$	− 835531.i	− 1.61462i	−0.590130	−	0.807308i	$-0.700924\pi$
$193$	− 835531.i	− 1.61462i	0.590130	−	0.807308i	$-0.299076\pi$
$194$	416072.	0.793714
$195$	0	0
$196$	53712.0	0.0998691
$197$	− 678318.i	− 1.24528i	−0.782508	−	0.622641i	$-0.786060\pi$
$197$	− 678318.i	− 1.24528i	0.782508	−	0.622641i	$-0.213940\pi$
$198$	379176.i	0.687350i
$199$	31900.0	0.0571029	0.0285514	−	0.999592i	$-0.490911\pi$
$199$	31900.0	0.0571029	0.0285514	+	0.999592i	$0.490911\pi$
$200$	0	0
$201$	144947.	0.253057
$202$	− 95592.0i	− 0.164833i
$203$	698640.i	1.18991i
$204$	−4752.00	−0.00799468
$205$	0	0
$206$	90544.0	0.148659
$207$	226188.i	0.366897i
$208$	226304.i	0.362689i
$209$	−889665.	−1.40884
$210$	0	0
$211$	−423673.	−0.655126	−0.327563	−	0.944829i	$-0.606227\pi$
$211$	−423673.	−0.655126	−0.327563	+	0.944829i	$0.606227\pi$
$212$	− 54624.0i	− 0.0834726i
$213$	83028.0i	0.125394i
$214$	242532.	0.362022
$215$	0	0
$216$	−256960.	−0.374741
$217$	255884.i	0.368887i
$218$	28360.0i	0.0404171i
$219$	−658031.	−0.927120
$220$	0	0
$221$	−23868.0	−0.0328727
$222$	− 579832.i	− 0.789623i
$223$	398204.i	0.536221i	0.963388	+	0.268110i	$0.0863992\pi$
$223$	398204.i	0.536221i	−0.963388	+	0.268110i	$0.913601\pi$
$224$	−145408.	−0.193628
$225$	0	0
$226$	515364.	0.671186
$227$	1.25761e6i	1.61988i	0.586515	+	0.809938i	$0.300500\pi$
$227$	1.25761e6i	1.61988i	−0.586515	+	0.809938i	$0.699500\pi$
$228$	− 201520.i	− 0.256733i
$229$	−203780.	−0.256787	−0.128393	−	0.991723i	$-0.540982\pi$
$229$	−203780.	−0.256787	−0.128393	+	0.991723i	$0.540982\pi$
$230$	0	0
$231$	1.21367e6	1.49648
$232$	− 314880.i	− 0.384083i
$233$	823974.i	0.994314i	0.867661	+	0.497157i	$0.165623\pi$
$233$	823974.i	0.994314i	−0.867661	+	0.497157i	$0.834377\pi$
$234$	−431392.	−0.515030
$235$	0	0
$236$	543360.	0.635050
$237$	834130.i	0.964635i
$238$	− 15336.0i	− 0.0175497i
$239$	555960.	0.629577	0.314788	−	0.949162i	$-0.398066\pi$
$239$	555960.	0.629577	0.314788	+	0.949162i	$0.398066\pi$
$240$	0	0
$241$	523577.	0.580681	0.290341	−	0.956923i	$-0.406231\pi$
$241$	523577.	0.580681	0.290341	+	0.956923i	$0.406231\pi$
$242$	1.77071e6i	1.94361i
$243$	− 815936.i	− 0.886422i
$244$	−758432.	−0.815534
$245$	0	0
$246$	−665412.	−0.701056
$247$	− 1.01218e6i	− 1.05564i
$248$	− 115328.i	− 0.119071i
$249$	509289.	0.520554
$250$	0	0
$251$	113127.	0.113340	0.0566698	−	0.998393i	$-0.481952\pi$
$251$	113127.	0.113340	0.0566698	+	0.998393i	$0.481952\pi$
$252$	− 277184.i	− 0.274958i
$253$	1.44056e6i	1.41491i
$254$	565352.	0.549838
$255$	0	0
$256$	65536.0	0.0625000
$257$	− 872958.i	− 0.824443i	−0.911084	−	0.412221i	$-0.864753\pi$
$257$	− 872958.i	− 0.824443i	0.911084	−	0.412221i	$-0.135247\pi$
$258$	345136.i	0.322806i
$259$	1.87128e6	1.73336
$260$	0	0
$261$	600240.	0.545411
$262$	320208.i	0.288190i
$263$	− 1.64647e6i	− 1.46779i	−0.679264	−	0.733894i	$-0.737701\pi$
$263$	− 1.64647e6i	− 1.46779i	0.679264	−	0.733894i	$-0.262299\pi$
$264$	−547008.	−0.483041
$265$	0	0
$266$	650360.	0.563572
$267$	− 336435.i	− 0.288817i
$268$	− 210832.i	− 0.179308i
$269$	−1.78872e6	−1.50717	−0.753584	−	0.657352i	$-0.771677\pi$
$269$	−1.78872e6	−1.50717	−0.753584	+	0.657352i	$0.771677\pi$
$270$	0	0
$271$	1.12140e6	0.927552	0.463776	−	0.885953i	$-0.346494\pi$
$271$	1.12140e6	0.927552	0.463776	+	0.885953i	$0.346494\pi$
$272$	6912.00i	0.00566476i
$273$	1.38081e6i	1.12131i
$274$	129012.	0.103813
$275$	0	0
$276$	−326304.	−0.257840
$277$	598312.i	0.468520i	0.972174	+	0.234260i	$0.0752667\pi$
$277$	598312.i	0.468520i	−0.972174	+	0.234260i	$0.924733\pi$
$278$	− 1.57946e6i	− 1.22574i
$279$	219844.	0.169085
$280$	0	0
$281$	−1.53050e6	−1.15629	−0.578145	−	0.815934i	$-0.696223\pi$
$281$	−1.53050e6	−1.15629	−0.578145	+	0.815934i	$0.696223\pi$
$282$	296208.i	0.221806i
$283$	− 1.79700e6i	− 1.33377i	−0.745159	−	0.666887i	$-0.767626\pi$
$283$	− 1.79700e6i	− 1.33377i	0.745159	−	0.666887i	$-0.232374\pi$
$284$	120768.	0.0888497
$285$	0	0
$286$	−2.74747e6	−1.98618
$287$	− 2.14747e6i	− 1.53894i
$288$	124928.i	0.0887521i
$289$	1.41913e6	0.999487
$290$	0	0
$291$	−1.14420e6	−0.792079
$292$	957136.i	0.656926i
$293$	754494.i	0.513437i	0.966486	+	0.256718i	$0.0826412\pi$
$293$	754494.i	0.513437i	−0.966486	+	0.256718i	$0.917359\pi$
$294$	−147708.	−0.0996634
$295$	0	0
$296$	−843392.	−0.559500
$297$	− 3.11965e6i	− 2.05218i
$298$	1.96560e6i	1.28220i
$299$	−1.63894e6	−1.06019
$300$	0	0
$301$	−1.11385e6	−0.708614
$302$	801608.i	0.505760i
$303$	262878.i	0.164493i
$304$	−293120.	−0.181912
$305$	0	0
$306$	−13176.0	−0.00804415
$307$	1.96627e6i	1.19068i	0.803472	+	0.595342i	$0.202983\pi$
$307$	1.96627e6i	1.19068i	−0.803472	+	0.595342i	$0.797017\pi$
$308$	− 1.76534e6i	− 1.06036i
$309$	−248996.	−0.148353
$310$	0	0
$311$	−599298.	−0.351352	−0.175676	−	0.984448i	$-0.556211\pi$
$311$	−599298.	−0.351352	−0.175676	+	0.984448i	$0.556211\pi$
$312$	− 622336.i	− 0.361942i
$313$	− 721366.i	− 0.416193i	−0.978108	−	0.208097i	$-0.933273\pi$
$313$	− 721366.i	− 0.416193i	0.978108	−	0.208097i	$-0.0667268\pi$
$314$	−91768.0	−0.0525251
$315$	0	0
$316$	1.21328e6	0.683508
$317$	− 102348.i	− 0.0572046i	−0.999591	−	0.0286023i	$-0.990894\pi$
$317$	− 102348.i	− 0.0572046i	0.999591	−	0.0286023i	$-0.00910564\pi$
$318$	150216.i	0.0833007i
$319$	3.82284e6	2.10334
$320$	0	0
$321$	−666963.	−0.361276
$322$	− 1.05307e6i	− 0.566003i
$323$	− 30915.0i	− 0.0164878i
$324$	232304.	0.122940
$325$	0	0
$326$	1.34496e6	0.700917
$327$	− 77990.0i	− 0.0403338i
$328$	967872.i	0.496745i
$329$	−955944.	−0.486903
$330$	0	0
$331$	1.31048e6	0.657445	0.328722	−	0.944427i	$-0.393382\pi$
$331$	1.31048e6	0.657445	0.328722	+	0.944427i	$0.393382\pi$
$332$	− 740784.i	− 0.368847i
$333$	− 1.60772e6i	− 0.794509i
$334$	238992.	0.117224
$335$	0	0
$336$	399872.	0.193229
$337$	804397.i	0.385830i	0.981215	+	0.192915i	$0.0617941\pi$
$337$	804397.i	0.385830i	−0.981215	+	0.192915i	$0.938206\pi$
$338$	− 1.64065e6i	− 0.781133i
$339$	−1.41725e6	−0.669804
$340$	0	0
$341$	1.40015e6	0.652063
$342$	− 558760.i	− 0.258321i
$343$	1.90990e6i	0.876547i
$344$	502016.	0.228729
$345$	0	0
$346$	242784.	0.109026
$347$	2.88321e6i	1.28544i	0.766101	+	0.642720i	$0.222194\pi$
$347$	2.88321e6i	1.28544i	−0.766101	+	0.642720i	$0.777806\pi$
$348$	865920.i	0.383292i
$349$	−1.27355e6	−0.559696	−0.279848	−	0.960044i	$-0.590284\pi$
$349$	−1.27355e6	−0.559696	−0.279848	+	0.960044i	$0.590284\pi$
$350$	0	0
$351$	3.54926e6	1.53769
$352$	795648.i	0.342266i
$353$	2.83061e6i	1.20905i	0.796587	+	0.604524i	$0.206637\pi$
$353$	2.83061e6i	1.20905i	−0.796587	+	0.604524i	$0.793363\pi$
$354$	−1.49424e6	−0.633742
$355$	0	0
$356$	−489360.	−0.204646
$357$	42174.0i	0.0175136i
$358$	31980.0i	0.0131878i
$359$	981090.	0.401766	0.200883	−	0.979615i	$-0.435619\pi$
$359$	981090.	0.401766	0.200883	+	0.979615i	$0.435619\pi$
$360$	0	0
$361$	−1.16507e6	−0.470528
$362$	− 1.81919e6i	− 0.729637i
$363$	− 4.86946e6i	− 1.93961i
$364$	2.00845e6	0.794524
$365$	0	0
$366$	2.08569e6	0.813854
$367$	4.19105e6i	1.62427i	0.583470	+	0.812134i	$0.301694\pi$
$367$	4.19105e6i	1.62427i	−0.583470	+	0.812134i	$0.698306\pi$
$368$	474624.i	0.182696i
$369$	−1.84501e6	−0.705394
$370$	0	0
$371$	−484788.	−0.182859
$372$	317152.i	0.118826i
$373$	3.23455e6i	1.20377i	0.798584	+	0.601883i	$0.205583\pi$
$373$	3.23455e6i	1.20377i	−0.798584	+	0.601883i	$0.794417\pi$
$374$	−83916.0	−0.0310217
$375$	0	0
$376$	430848.	0.157165
$377$	4.34928e6i	1.57603i
$378$	2.28052e6i	0.820927i
$379$	−1.39036e6	−0.497196	−0.248598	−	0.968607i	$-0.579970\pi$
$379$	−1.39036e6	−0.497196	−0.248598	+	0.968607i	$0.579970\pi$
$380$	0	0
$381$	−1.55472e6	−0.548705
$382$	− 1.71319e6i	− 0.600686i
$383$	1.14197e6i	0.397795i	0.980020	+	0.198897i	$0.0637361\pi$
$383$	1.14197e6i	0.397795i	−0.980020	+	0.198897i	$0.936264\pi$
$384$	−180224.	−0.0623713
$385$	0	0
$386$	3.34212e6	1.14171
$387$	956968.i	0.324803i
$388$	1.66429e6i	0.561241i
$389$	−3.46299e6	−1.16032	−0.580159	−	0.814503i	$-0.697010\pi$
$389$	−3.46299e6	−1.16032	−0.580159	+	0.814503i	$0.697010\pi$
$390$	0	0
$391$	−50058.0	−0.0165589
$392$	214848.i	0.0706181i
$393$	− 880572.i	− 0.287596i
$394$	2.71327e6	0.880547
$395$	0	0
$396$	−1.51670e6	−0.486030
$397$	− 5.94007e6i	− 1.89154i	−0.324839	−	0.945769i	$-0.605310\pi$
$397$	− 5.94007e6i	− 1.89154i	0.324839	−	0.945769i	$-0.394690\pi$
$398$	127600.i	0.0403778i
$399$	−1.78849e6	−0.562412
$400$	0	0
$401$	−2.27412e6	−0.706241	−0.353121	−	0.935578i	$-0.614879\pi$
$401$	−2.27412e6	−0.706241	−0.353121	+	0.935578i	$0.614879\pi$
$402$	579788.i	0.178939i
$403$	1.59297e6i	0.488590i
$404$	382368.	0.116554
$405$	0	0
$406$	−2.79456e6	−0.841392
$407$	− 1.02393e7i	− 3.06397i
$408$	− 19008.0i	− 0.00565309i
$409$	4.29552e6	1.26972	0.634859	−	0.772628i	$-0.281058\pi$
$409$	4.29552e6	1.26972	0.634859	+	0.772628i	$0.281058\pi$
$410$	0	0
$411$	−354783.	−0.103600
$412$	362176.i	0.105118i
$413$	− 4.82232e6i	− 1.39117i
$414$	−904752.	−0.259435
$415$	0	0
$416$	−905216.	−0.256460
$417$	4.34352e6i	1.22321i
$418$	− 3.55866e6i	− 0.996198i
$419$	−1.79705e6	−0.500062	−0.250031	−	0.968238i	$-0.580441\pi$
$419$	−1.79705e6	−0.500062	−0.250031	+	0.968238i	$0.580441\pi$
$420$	0	0
$421$	−257548.	−0.0708195	−0.0354098	−	0.999373i	$-0.511274\pi$
$421$	−257548.	−0.0708195	−0.0354098	+	0.999373i	$0.511274\pi$
$422$	− 1.69469e6i	− 0.463244i
$423$	821304.i	0.223179i
$424$	218496.	0.0590240
$425$	0	0
$426$	−332112.	−0.0886667
$427$	6.73108e6i	1.78655i
$428$	970128.i	0.255988i
$429$	7.55555e6	1.98209
$430$	0	0
$431$	2.22910e6	0.578012	0.289006	−	0.957327i	$-0.406675\pi$
$431$	2.22910e6	0.578012	0.289006	+	0.957327i	$0.406675\pi$
$432$	− 1.02784e6i	− 0.264982i
$433$	− 4.20585e6i	− 1.07804i	−0.842294	−	0.539019i	$-0.818795\pi$
$433$	− 4.20585e6i	− 1.07804i	0.842294	−	0.539019i	$-0.181205\pi$
$434$	−1.02354e6	−0.260843
$435$	0	0
$436$	−113440.	−0.0285792
$437$	− 2.12283e6i	− 0.531755i
$438$	− 2.63212e6i	− 0.655573i
$439$	−352640.	−0.0873314	−0.0436657	−	0.999046i	$-0.513904\pi$
$439$	−352640.	−0.0873314	−0.0436657	+	0.999046i	$0.513904\pi$
$440$	0	0
$441$	−409554.	−0.100280
$442$	− 95472.0i	− 0.0232445i
$443$	1.28362e6i	0.310761i	0.987855	+	0.155381i	$0.0496604\pi$
$443$	1.28362e6i	0.310761i	−0.987855	+	0.155381i	$0.950340\pi$
$444$	2.31933e6	0.558348
$445$	0	0
$446$	−1.59282e6	−0.379165
$447$	− 5.40540e6i	− 1.27956i
$448$	− 581632.i	− 0.136916i
$449$	2.10398e6	0.492521	0.246260	−	0.969204i	$-0.420798\pi$
$449$	2.10398e6	0.492521	0.246260	+	0.969204i	$0.420798\pi$
$450$	0	0
$451$	−1.17506e7	−2.72031
$452$	2.06146e6i	0.474600i
$453$	− 2.20442e6i	− 0.504719i
$454$	−5.03045e6	−1.14543
$455$	0	0
$456$	806080.	0.181537
$457$	− 825233.i	− 0.184836i	−0.995720	−	0.0924179i	$-0.970540\pi$
$457$	− 825233.i	− 0.184836i	0.995720	−	0.0924179i	$-0.0294596\pi$
$458$	− 815120.i	− 0.181576i
$459$	108405.	0.0240169
$460$	0	0
$461$	4.50145e6	0.986507	0.493254	−	0.869886i	$-0.335807\pi$
$461$	4.50145e6	0.986507	0.493254	+	0.869886i	$0.335807\pi$
$462$	4.85470e6i	1.05817i
$463$	− 1.44212e6i	− 0.312642i	−0.987706	−	0.156321i	$-0.950037\pi$
$463$	− 1.44212e6i	− 0.312642i	0.987706	−	0.156321i	$-0.0499635\pi$
$464$	1.25952e6	0.271588
$465$	0	0
$466$	−3.29590e6	−0.703086
$467$	− 393348.i	− 0.0834612i	−0.999129	−	0.0417306i	$-0.986713\pi$
$467$	− 393348.i	− 0.0834612i	0.999129	−	0.0417306i	$-0.0132871\pi$
$468$	− 1.72557e6i	− 0.364181i
$469$	−1.87113e6	−0.392801
$470$	0	0
$471$	252362.	0.0524169
$472$	2.17344e6i	0.449048i
$473$	6.09479e6i	1.25258i
$474$	−3.33652e6	−0.682100
$475$	0	0
$476$	61344.0	0.0124095
$477$	416508.i	0.0838161i
$478$	2.22384e6i	0.445178i
$479$	9.17697e6	1.82751	0.913757	−	0.406262i	$-0.133168\pi$
$479$	9.17697e6	1.82751	0.913757	+	0.406262i	$0.133168\pi$
$480$	0	0
$481$	1.16494e7	2.29583
$482$	2.09431e6i	0.410604i
$483$	2.89595e6i	0.564837i
$484$	−7.08285e6	−1.37434
$485$	0	0
$486$	3.26374e6	0.626795
$487$	− 6.60598e6i	− 1.26216i	−0.775717	−	0.631080i	$-0.782612\pi$
$487$	− 6.60598e6i	− 1.26216i	0.775717	−	0.631080i	$-0.217388\pi$
$488$	− 3.03373e6i	− 0.576670i
$489$	−3.69865e6	−0.699473
$490$	0	0
$491$	38052.0	0.00712318	0.00356159	−	0.999994i	$-0.498866\pi$
$491$	38052.0	0.00712318	0.00356159	+	0.999994i	$0.498866\pi$
$492$	− 2.66165e6i	− 0.495722i
$493$	132840.i	0.0246157i
$494$	4.04872e6	0.746449
$495$	0	0
$496$	461312.	0.0841958
$497$	− 1.07182e6i	− 0.194639i
$498$	2.03716e6i	0.368087i
$499$	−6.85670e6	−1.23272	−0.616359	−	0.787465i	$-0.711393\pi$
$499$	−6.85670e6	−1.23272	−0.616359	+	0.787465i	$0.711393\pi$
$500$	0	0
$501$	−657228.	−0.116983
$502$	452508.i	0.0801433i
$503$	8.20016e6i	1.44512i	0.691311	+	0.722558i	$0.257034\pi$
$503$	8.20016e6i	1.44512i	−0.691311	+	0.722558i	$0.742966\pi$
$504$	1.10874e6	0.194425
$505$	0	0
$506$	−5.76223e6	−1.00049
$507$	4.51179e6i	0.779524i
$508$	2.26141e6i	0.388794i
$509$	−4.06581e6	−0.695589	−0.347794	−	0.937571i	$-0.613069\pi$
$509$	−4.06581e6	−0.695589	−0.347794	+	0.937571i	$0.613069\pi$
$510$	0	0
$511$	8.49458e6	1.43910
$512$	262144.i	0.0441942i
$513$	4.59718e6i	0.771254i
$514$	3.49183e6	0.582969
$515$	0	0
$516$	−1.38054e6	−0.228258
$517$	5.23076e6i	0.860674i
$518$	7.48510e6i	1.22567i
$519$	−667656.	−0.108801
$520$	0	0
$521$	5.28408e6	0.852854	0.426427	−	0.904522i	$-0.359772\pi$
$521$	5.28408e6	0.852854	0.426427	+	0.904522i	$0.359772\pi$
$522$	2.40096e6i	0.385664i
$523$	2.53383e6i	0.405063i	0.979276	+	0.202532i	$0.0649169\pi$
$523$	2.53383e6i	0.405063i	−0.979276	+	0.202532i	$0.935083\pi$
$524$	−1.28083e6	−0.203781
$525$	0	0
$526$	6.58586e6	1.03788
$527$	48654.0i	0.00763119i
$528$	− 2.18803e6i	− 0.341561i
$529$	2.99903e6	0.465952
$530$	0	0
$531$	−4.14312e6	−0.637663
$532$	2.60144e6i	0.398506i
$533$	− 1.33687e7i	− 2.03832i
$534$	1.34574e6	0.204225
$535$	0	0
$536$	843328.	0.126790
$537$	− 87945.0i	− 0.0131606i
$538$	− 7.15488e6i	− 1.06573i
$539$	−2.60839e6	−0.386723
$540$	0	0
$541$	498752.	0.0732641	0.0366321	−	0.999329i	$-0.488337\pi$
$541$	498752.	0.0732641	0.0366321	+	0.999329i	$0.488337\pi$
$542$	4.48561e6i	0.655878i
$543$	5.00278e6i	0.728135i
$544$	−27648.0	−0.00400559
$545$	0	0
$546$	−5.52323e6	−0.792888
$547$	− 3.00269e6i	− 0.429084i	−0.976715	−	0.214542i	$-0.931174\pi$
$547$	− 3.00269e6i	− 0.429084i	0.976715	−	0.214542i	$-0.0688259\pi$
$548$	516048.i	0.0734072i
$549$	5.78304e6	0.818890
$550$	0	0
$551$	−5.63340e6	−0.790481
$552$	− 1.30522e6i	− 0.182320i
$553$	− 1.07679e7i	− 1.49733i
$554$	−2.39325e6	−0.331294
$555$	0	0
$556$	6.31784e6	0.866726
$557$	1.27373e7i	1.73956i	0.493441	+	0.869779i	$0.335739\pi$
$557$	1.27373e7i	1.73956i	−0.493441	+	0.869779i	$0.664261\pi$
$558$	879376.i	0.119561i
$559$	−6.93410e6	−0.938556
$560$	0	0
$561$	230769.	0.0309578
$562$	− 6.12199e6i	− 0.817621i
$563$	− 5.97082e6i	− 0.793894i	−0.917841	−	0.396947i	$-0.870070\pi$
$563$	− 5.97082e6i	− 0.793894i	0.917841	−	0.396947i	$-0.129930\pi$
$564$	−1.18483e6	−0.156841
$565$	0	0
$566$	7.18800e6	0.943121
$567$	− 2.06170e6i	− 0.269319i
$568$	483072.i	0.0628262i
$569$	9.26906e6	1.20020	0.600102	−	0.799924i	$-0.295127\pi$
$569$	9.26906e6	1.20020	0.600102	+	0.799924i	$0.295127\pi$
$570$	0	0
$571$	−3.89535e6	−0.499984	−0.249992	−	0.968248i	$-0.580428\pi$
$571$	−3.89535e6	−0.499984	−0.249992	+	0.968248i	$0.580428\pi$
$572$	− 1.09899e7i	− 1.40444i
$573$	4.71128e6i	0.599449i
$574$	8.58986e6	1.08819
$575$	0	0
$576$	−499712.	−0.0627572
$577$	− 7.29416e6i	− 0.912086i	−0.889958	−	0.456043i	$-0.849266\pi$
$577$	− 7.29416e6i	− 0.912086i	0.889958	−	0.456043i	$-0.150734\pi$
$578$	5.67651e6i	0.706744i
$579$	−9.19084e6	−1.13935
$580$	0	0
$581$	−6.57446e6	−0.808015
$582$	− 4.57679e6i	− 0.560085i
$583$	2.65268e6i	0.323231i
$584$	−3.82854e6	−0.464517
$585$	0	0
$586$	−3.01798e6	−0.363054
$587$	8.72820e6i	1.04551i	0.852482	+	0.522756i	$0.175096\pi$
$587$	8.72820e6i	1.04551i	−0.852482	+	0.522756i	$0.824904\pi$
$588$	− 590832.i	− 0.0704727i
$589$	−2.06329e6	−0.245060
$590$	0	0
$591$	−7.46150e6	−0.878734
$592$	− 3.37357e6i	− 0.395626i
$593$	− 1.30963e7i	− 1.52937i	−0.644407	−	0.764683i	$-0.722896\pi$
$593$	− 1.30963e7i	− 1.52937i	0.644407	−	0.764683i	$-0.277104\pi$
$594$	1.24786e7	1.45111
$595$	0	0
$596$	−7.86240e6	−0.906650
$597$	− 350900.i	− 0.0402947i
$598$	− 6.55574e6i	− 0.749668i
$599$	1.30168e7	1.48231	0.741155	−	0.671334i	$-0.234279\pi$
$599$	1.30168e7	1.48231	0.741155	+	0.671334i	$0.234279\pi$
$600$	0	0
$601$	−9.93997e6	−1.12253	−0.561266	−	0.827635i	$-0.689686\pi$
$601$	−9.93997e6	−1.12253	−0.561266	+	0.827635i	$0.689686\pi$
$602$	− 4.45539e6i	− 0.501066i
$603$	1.60759e6i	0.180046i
$604$	−3.20643e6	−0.357626
$605$	0	0
$606$	−1.05151e6	−0.116314
$607$	− 1.56438e7i	− 1.72334i	−0.507470	−	0.861670i	$-0.669419\pi$
$607$	− 1.56438e7i	− 1.72334i	0.507470	−	0.861670i	$-0.330581\pi$
$608$	− 1.17248e6i	− 0.128631i
$609$	7.68504e6	0.839659
$610$	0	0
$611$	−5.95109e6	−0.644901
$612$	− 52704.0i	− 0.00568807i
$613$	9.33793e6i	1.00369i	0.864958	+	0.501845i	$0.167345\pi$
$613$	9.33793e6i	1.00369i	−0.864958	+	0.501845i	$0.832655\pi$
$614$	−7.86507e6	−0.841941
$615$	0	0
$616$	7.06138e6	0.749786
$617$	5.06680e6i	0.535823i	0.963444	+	0.267911i	$0.0863334\pi$
$617$	5.06680e6i	0.535823i	−0.963444	+	0.267911i	$0.913667\pi$
$618$	− 995984.i	− 0.104901i
$619$	−1.37670e7	−1.44415	−0.722077	−	0.691813i	$-0.756812\pi$
$619$	−1.37670e7	−1.44415	−0.722077	+	0.691813i	$0.756812\pi$
$620$	0	0
$621$	7.44381e6	0.774580
$622$	− 2.39719e6i	− 0.248443i
$623$	4.34307e6i	0.448308i
$624$	2.48934e6	0.255931
$625$	0	0
$626$	2.88546e6	0.294293
$627$	9.78632e6i	0.994146i
$628$	− 367072.i	− 0.0371409i
$629$	355806.	0.0358580
$630$	0	0
$631$	2.07060e6	0.207025	0.103513	−	0.994628i	$-0.466992\pi$
$631$	2.07060e6	0.207025	0.103513	+	0.994628i	$0.466992\pi$
$632$	4.85312e6i	0.483313i
$633$	4.66040e6i	0.462290i
$634$	409392.	0.0404498
$635$	0	0
$636$	−600864.	−0.0589025
$637$	− 2.96759e6i	− 0.289771i
$638$	1.52914e7i	1.48729i
$639$	−920856.	−0.0892153
$640$	0	0
$641$	−1.79114e7	−1.72181	−0.860903	−	0.508768i	$-0.830101\pi$
$641$	−1.79114e7	−1.72181	−0.860903	+	0.508768i	$0.830101\pi$
$642$	− 2.66785e6i	− 0.255461i
$643$	− 1.71414e7i	− 1.63500i	−0.575929	−	0.817500i	$-0.695359\pi$
$643$	− 1.71414e7i	− 1.63500i	0.575929	−	0.817500i	$-0.304641\pi$
$644$	4.21229e6	0.400224
$645$	0	0
$646$	123660.	0.0116586
$647$	8.48773e6i	0.797133i	0.917139	+	0.398567i	$0.130492\pi$
$647$	8.48773e6i	0.797133i	−0.917139	+	0.398567i	$0.869508\pi$
$648$	929216.i	0.0869319i
$649$	−2.63869e7	−2.45910
$650$	0	0
$651$	2.81472e6	0.260306
$652$	5.37986e6i	0.495623i
$653$	− 2.45479e6i	− 0.225284i	−0.993636	−	0.112642i	$-0.964069\pi$
$653$	− 2.45479e6i	− 0.225284i	0.993636	−	0.112642i	$-0.0359313\pi$
$654$	311960.	0.0285203
$655$	0	0
$656$	−3.87149e6	−0.351252
$657$	− 7.29816e6i	− 0.659630i
$658$	− 3.82378e6i	− 0.344293i
$659$	5.91557e6	0.530619	0.265309	−	0.964163i	$-0.414526\pi$
$659$	5.91557e6	0.530619	0.265309	+	0.964163i	$0.414526\pi$
$660$	0	0
$661$	4.33095e6	0.385549	0.192775	−	0.981243i	$-0.438251\pi$
$661$	4.33095e6	0.385549	0.192775	+	0.981243i	$0.438251\pi$
$662$	5.24191e6i	0.464884i
$663$	262548.i	0.0231966i
$664$	2.96314e6	0.260814
$665$	0	0
$666$	6.43086e6	0.561803
$667$	9.12168e6i	0.793890i
$668$	955968.i	0.0828900i
$669$	4.38024e6	0.378384
$670$	0	0
$671$	3.68314e7	3.15799
$672$	1.59949e6i	0.136634i
$673$	− 9.13985e6i	− 0.777860i	−0.921267	−	0.388930i	$-0.872845\pi$
$673$	− 9.13985e6i	− 0.777860i	0.921267	−	0.388930i	$-0.127155\pi$
$674$	−3.21759e6	−0.272823
$675$	0	0
$676$	6.56261e6	0.552344
$677$	− 4.57229e6i	− 0.383409i	−0.981453	−	0.191704i	$-0.938599\pi$
$677$	− 4.57229e6i	− 0.383409i	0.981453	−	0.191704i	$-0.0614015\pi$
$678$	− 5.66900e6i	− 0.473623i
$679$	1.47706e7	1.22948
$680$	0	0
$681$	1.38337e7	1.14307
$682$	5.60062e6i	0.461078i
$683$	1.53221e7i	1.25681i	0.777888	+	0.628403i	$0.216291\pi$
$683$	1.53221e7i	1.25681i	−0.777888	+	0.628403i	$0.783709\pi$
$684$	2.23504e6	0.182661
$685$	0	0
$686$	−7.63960e6	−0.619813
$687$	2.24158e6i	0.181202i
$688$	2.00806e6i	0.161736i
$689$	−3.01798e6	−0.242196
$690$	0	0
$691$	7.02548e6	0.559733	0.279866	−	0.960039i	$-0.409710\pi$
$691$	7.02548e6	0.559733	0.279866	+	0.960039i	$0.409710\pi$
$692$	971136.i	0.0770930i
$693$	1.34607e7i	1.06472i
$694$	−1.15328e7	−0.908944
$695$	0	0
$696$	−3.46368e6	−0.271028
$697$	− 408321.i	− 0.0318361i
$698$	− 5.09420e6i	− 0.395765i
$699$	9.06371e6	0.701638
$700$	0	0
$701$	7.91125e6	0.608065	0.304033	−	0.952662i	$-0.401667\pi$
$701$	7.91125e6	0.608065	0.304033	+	0.952662i	$0.401667\pi$
$702$	1.41970e7i	1.08731i
$703$	1.50888e7i	1.15151i
$704$	−3.18259e6	−0.242019
$705$	0	0
$706$	−1.13225e7	−0.854927
$707$	− 3.39352e6i	− 0.255330i
$708$	− 5.97696e6i	− 0.448123i
$709$	1.54485e7	1.15418	0.577088	−	0.816682i	$-0.304189\pi$
$709$	1.54485e7	1.15418	0.577088	+	0.816682i	$0.304189\pi$
$710$	0	0
$711$	−9.25126e6	−0.686320
$712$	− 1.95744e6i	− 0.144707i
$713$	3.34091e6i	0.246116i
$714$	−168696.	−0.0123840
$715$	0	0
$716$	−127920.	−0.00932515
$717$	− 6.11556e6i	− 0.444261i
$718$	3.92436e6i	0.284091i
$719$	−2.30544e7	−1.66315	−0.831574	−	0.555414i	$-0.812560\pi$
$719$	−2.30544e7	−1.66315	−0.831574	+	0.555414i	$0.812560\pi$
$720$	0	0
$721$	3.21431e6	0.230277
$722$	− 4.66030e6i	− 0.332714i
$723$	− 5.75935e6i	− 0.409758i
$724$	7.27677e6	0.515932
$725$	0	0
$726$	1.94778e7	1.37151
$727$	− 1.62905e7i	− 1.14314i	−0.820555	−	0.571568i	$-0.806335\pi$
$727$	− 1.62905e7i	− 1.14314i	0.820555	−	0.571568i	$-0.193665\pi$
$728$	8.03379e6i	0.561813i
$729$	−1.25034e7	−0.871384
$730$	0	0
$731$	−211788.	−0.0146591
$732$	8.34275e6i	0.575482i
$733$	1.28279e7i	0.881853i	0.897543	+	0.440927i	$0.145350\pi$
$733$	1.28279e7i	0.881853i	−0.897543	+	0.440927i	$0.854650\pi$
$734$	−1.67642e7	−1.14853
$735$	0	0
$736$	−1.89850e6	−0.129186
$737$	1.02385e7i	0.694335i
$738$	− 7.38002e6i	− 0.498789i
$739$	1.24535e7	0.838840	0.419420	−	0.907792i	$-0.362234\pi$
$739$	1.24535e7	0.838840	0.419420	+	0.907792i	$0.362234\pi$
$740$	0	0
$741$	−1.11340e7	−0.744912
$742$	− 1.93915e6i	− 0.129301i
$743$	− 2.63247e7i	− 1.74941i	−0.484656	−	0.874705i	$-0.661055\pi$
$743$	− 2.63247e7i	− 1.74941i	0.484656	−	0.874705i	$-0.338945\pi$
$744$	−1.26861e6	−0.0840224
$745$	0	0
$746$	−1.29382e7	−0.851192
$747$	5.64848e6i	0.370365i
$748$	− 335664.i	− 0.0219357i
$749$	8.60989e6	0.560780
$750$	0	0
$751$	−1.74994e7	−1.13220	−0.566102	−	0.824335i	$-0.691549\pi$
$751$	−1.74994e7	−1.13220	−0.566102	+	0.824335i	$0.691549\pi$
$752$	1.72339e6i	0.111132i
$753$	− 1.24440e6i	− 0.0799782i
$754$	−1.73971e7	−1.11442
$755$	0	0
$756$	−9.12208e6	−0.580483
$757$	− 3.46381e6i	− 0.219692i	−0.993949	−	0.109846i	$-0.964964\pi$
$757$	− 3.46381e6i	− 0.219692i	0.993949	−	0.109846i	$-0.0350358\pi$
$758$	− 5.56142e6i	− 0.351571i
$759$	1.58461e7	0.998433
$760$	0	0
$761$	−1.26175e7	−0.789792	−0.394896	−	0.918726i	$-0.629219\pi$
$761$	−1.26175e7	−0.789792	−0.394896	+	0.918726i	$0.629219\pi$
$762$	− 6.21887e6i	− 0.387993i
$763$	1.00678e6i	0.0626070i
$764$	6.85277e6	0.424749
$765$	0	0
$766$	−4.56790e6	−0.281284
$767$	− 3.00206e7i	− 1.84260i
$768$	− 720896.i	− 0.0441031i
$769$	−5.70804e6	−0.348074	−0.174037	−	0.984739i	$-0.555681\pi$
$769$	−5.70804e6	−0.348074	−0.174037	+	0.984739i	$0.555681\pi$
$770$	0	0
$771$	−9.60254e6	−0.581768
$772$	1.33685e7i	0.807308i
$773$	1.20827e7i	0.727303i	0.931535	+	0.363652i	$0.118470\pi$
$773$	1.20827e7i	0.727303i	−0.931535	+	0.363652i	$0.881530\pi$
$774$	−3.82787e6	−0.229670
$775$	0	0
$776$	−6.65715e6	−0.396857
$777$	− 2.05840e7i	− 1.22315i
$778$	− 1.38520e7i	− 0.820469i
$779$	1.73158e7	1.02235
$780$	0	0
$781$	−5.86480e6	−0.344053
$782$	− 200232.i	− 0.0117089i
$783$	− 1.97538e7i	− 1.15145i
$784$	−859392.	−0.0499346
$785$	0	0
$786$	3.52229e6	0.203361
$787$	1.37636e7i	0.792126i	0.918223	+	0.396063i	$0.129624\pi$
$787$	1.37636e7i	0.792126i	−0.918223	+	0.396063i	$0.870376\pi$
$788$	1.08531e7i	0.622641i
$789$	−1.81111e7	−1.03575
$790$	0	0
$791$	1.82954e7	1.03968
$792$	− 6.06682e6i	− 0.343675i
$793$	4.19034e7i	2.36628i
$794$	2.37603e7	1.33752
$795$	0	0
$796$	−510400.	−0.0285514
$797$	8.77738e6i	0.489462i	0.969591	+	0.244731i	$0.0786997\pi$
$797$	8.77738e6i	0.489462i	−0.969591	+	0.244731i	$0.921300\pi$
$798$	− 7.15396e6i	− 0.397685i
$799$	−181764.	−0.0100726
$800$	0	0
$801$	3.73137e6	0.205488
$802$	− 9.09649e6i	− 0.499388i
$803$	− 4.64809e7i	− 2.54382i
$804$	−2.31915e6	−0.126529
$805$	0	0
$806$	−6.37187e6	−0.345485
$807$	1.96759e7i	1.06353i
$808$	1.52947e6i	0.0824163i
$809$	1.02046e7	0.548181	0.274091	−	0.961704i	$-0.411623\pi$
$809$	1.02046e7	0.548181	0.274091	+	0.961704i	$0.411623\pi$
$810$	0	0
$811$	−1.17375e6	−0.0626647	−0.0313323	−	0.999509i	$-0.509975\pi$
$811$	−1.17375e6	−0.0626647	−0.0313323	+	0.999509i	$0.509975\pi$
$812$	− 1.11782e7i	− 0.594954i
$813$	− 1.23354e7i	− 0.654527i
$814$	4.09572e7	2.16655
$815$	0	0
$816$	76032.0	0.00399734
$817$	− 8.98138e6i	− 0.470747i
$818$	1.71821e7i	0.897826i
$819$	−1.53144e7	−0.797794
$820$	0	0
$821$	−1.98062e7	−1.02552	−0.512759	−	0.858533i	$-0.671377\pi$
$821$	−1.98062e7	−1.02552	−0.512759	+	0.858533i	$0.671377\pi$
$822$	− 1.41913e6i	− 0.0732560i
$823$	− 3.06722e7i	− 1.57850i	−0.614070	−	0.789251i	$-0.710469\pi$
$823$	− 3.06722e7i	− 1.57850i	0.614070	−	0.789251i	$-0.289531\pi$
$824$	−1.44870e6	−0.0743296
$825$	0	0
$826$	1.92893e7	0.983707
$827$	− 2.55520e7i	− 1.29915i	−0.760296	−	0.649577i	$-0.774946\pi$
$827$	− 2.55520e7i	− 1.29915i	0.760296	−	0.649577i	$-0.225054\pi$
$828$	− 3.61901e6i	− 0.183448i
$829$	9.19402e6	0.464643	0.232321	−	0.972639i	$-0.425368\pi$
$829$	9.19402e6	0.464643	0.232321	+	0.972639i	$0.425368\pi$
$830$	0	0
$831$	6.58143e6	0.330611
$832$	− 3.62086e6i	− 0.181344i
$833$	− 90639.0i	− 0.00452588i
$834$	−1.73741e7	−0.864940
$835$	0	0
$836$	1.42346e7	0.704419
$837$	− 7.23503e6i	− 0.356966i
$838$	− 7.18818e6i	− 0.353597i
$839$	1.56910e7	0.769564	0.384782	−	0.923008i	$-0.374277\pi$
$839$	1.56910e7	0.769564	0.384782	+	0.923008i	$0.374277\pi$
$840$	0	0
$841$	3.69525e6	0.180158
$842$	− 1.03019e6i	− 0.0500770i
$843$	1.68355e7i	0.815937i
$844$	6.77877e6	0.327563
$845$	0	0
$846$	−3.28522e6	−0.157811
$847$	6.28603e7i	3.01070i
$848$	873984.i	0.0417363i
$849$	−1.97670e7	−0.941178
$850$	0	0
$851$	2.44320e7	1.15647
$852$	− 1.32845e6i	− 0.0626968i
$853$	1.60111e6i	0.0753442i	0.999290	+	0.0376721i	$0.0119942\pi$
$853$	1.60111e6i	0.0753442i	−0.999290	+	0.0376721i	$0.988006\pi$
$854$	−2.69243e7	−1.26328
$855$	0	0
$856$	−3.88051e6	−0.181011
$857$	1.64613e7i	0.765616i	0.923828	+	0.382808i	$0.125043\pi$
$857$	1.64613e7i	0.765616i	−0.923828	+	0.382808i	$0.874957\pi$
$858$	3.02222e7i	1.40155i
$859$	−1.96736e7	−0.909705	−0.454853	−	0.890567i	$-0.650308\pi$
$859$	−1.96736e7	−0.909705	−0.454853	+	0.890567i	$0.650308\pi$
$860$	0	0
$861$	−2.36221e7	−1.08595
$862$	8.91641e6i	0.408716i
$863$	3.68068e7i	1.68229i	0.540810	+	0.841145i	$0.318118\pi$
$863$	3.68068e7i	1.68229i	−0.540810	+	0.841145i	$0.681882\pi$
$864$	4.11136e6	0.187370
$865$	0	0
$866$	1.68234e7	0.762288
$867$	− 1.56104e7i	− 0.705288i
$868$	− 4.09414e6i	− 0.184444i
$869$	−5.89199e7	−2.64675
$870$	0	0
$871$	−1.16485e7	−0.520264
$872$	− 453760.i	− 0.0202085i
$873$	− 1.26902e7i	− 0.563550i
$874$	8.49132e6	0.376008
$875$	0	0
$876$	1.05285e7	0.463560
$877$	2.69596e7i	1.18363i	0.806075	+	0.591813i	$0.201588\pi$
$877$	2.69596e7i	1.18363i	−0.806075	+	0.591813i	$0.798412\pi$
$878$	− 1.41056e6i	− 0.0617526i
$879$	8.29943e6	0.362307
$880$	0	0
$881$	3.47335e7	1.50768	0.753839	−	0.657059i	$-0.228200\pi$
$881$	3.47335e7	1.50768	0.753839	+	0.657059i	$0.228200\pi$
$882$	− 1.63822e6i	− 0.0709087i
$883$	2.16187e7i	0.933101i	0.884494	+	0.466551i	$0.154503\pi$
$883$	2.16187e7i	0.933101i	−0.884494	+	0.466551i	$0.845497\pi$
$884$	381888.	0.0164363
$885$	0	0
$886$	−5.13448e6	−0.219741
$887$	− 4.48163e6i	− 0.191261i	−0.995417	−	0.0956306i	$-0.969513\pi$
$887$	− 4.48163e6i	− 0.191261i	0.995417	−	0.0956306i	$-0.0304867\pi$
$888$	9.27731e6i	0.394811i
$889$	2.00700e7	0.851712
$890$	0	0
$891$	−1.12813e7	−0.476062
$892$	− 6.37126e6i	− 0.268110i
$893$	− 7.70814e6i	− 0.323460i
$894$	2.16216e7	0.904782
$895$	0	0
$896$	2.32653e6	0.0968140
$897$	1.80283e7i	0.748124i
$898$	8.41590e6i	0.348265i
$899$	8.86584e6	0.365865
$900$	0	0
$901$	−92178.0	−0.00378282
$902$	− 4.70023e7i	− 1.92355i
$903$	1.22523e7i	0.500034i
$904$	−8.24582e6	−0.335593
$905$	0	0
$906$	8.81769e6	0.356890
$907$	3.36639e7i	1.35877i	0.733782	+	0.679385i	$0.237753\pi$
$907$	3.36639e7i	1.35877i	−0.733782	+	0.679385i	$0.762247\pi$
$908$	− 2.01218e7i	− 0.809938i
$909$	−2.91556e6	−0.117034
$910$	0	0
$911$	−1.03175e6	−0.0411887	−0.0205943	−	0.999788i	$-0.506556\pi$
$911$	−1.03175e6	−0.0411887	−0.0205943	+	0.999788i	$0.506556\pi$
$912$	3.22432e6i	0.128366i
$913$	3.59743e7i	1.42829i
$914$	3.30093e6	0.130699
$915$	0	0
$916$	3.26048e6	0.128393
$917$	1.13674e7i	0.446413i
$918$	433620.i	0.0169825i
$919$	−4.10147e6	−0.160196	−0.0800978	−	0.996787i	$-0.525523\pi$
$919$	−4.10147e6	−0.160196	−0.0800978	+	0.996787i	$0.525523\pi$
$920$	0	0
$921$	2.16289e7	0.840207
$922$	1.80058e7i	0.697566i
$923$	− 6.67243e6i	− 0.257798i
$924$	−1.94188e7	−0.748242
$925$	0	0
$926$	5.76846e6	0.221071
$927$	− 2.76159e6i	− 0.105550i
$928$	5.03808e6i	0.192042i
$929$	−7.71603e6	−0.293329	−0.146664	−	0.989186i	$-0.546854\pi$
$929$	−7.71603e6	−0.293329	−0.146664	+	0.989186i	$0.546854\pi$
$930$	0	0
$931$	3.84376e6	0.145339
$932$	− 1.31836e7i	− 0.497157i
$933$	6.59228e6i	0.247931i
$934$	1.57339e6	0.0590160
$935$	0	0
$936$	6.90227e6	0.257515
$937$	− 4.38458e7i	− 1.63147i	−0.578426	−	0.815735i	$-0.696333\pi$
$937$	− 4.38458e7i	− 1.63147i	0.578426	−	0.815735i	$-0.303667\pi$
$938$	− 7.48454e6i	− 0.277752i
$939$	−7.93503e6	−0.293687
$940$	0	0
$941$	−1.00215e7	−0.368944	−0.184472	−	0.982838i	$-0.559058\pi$
$941$	−1.00215e7	−0.368944	−0.184472	+	0.982838i	$0.559058\pi$
$942$	1.00945e6i	0.0370644i
$943$	− 2.80380e7i	− 1.02676i
$944$	−8.69376e6	−0.317525
$945$	0	0
$946$	−2.43792e7	−0.885708
$947$	− 2.79530e7i	− 1.01287i	−0.862279	−	0.506434i	$-0.830963\pi$
$947$	− 2.79530e7i	− 1.01287i	0.862279	−	0.506434i	$-0.169037\pi$
$948$	− 1.33461e7i	− 0.482317i
$949$	5.28818e7	1.90608
$950$	0	0
$951$	−1.12583e6	−0.0403665
$952$	245376.i	0.00877485i
$953$	− 2.31811e7i	− 0.826803i	−0.910549	−	0.413401i	$-0.864341\pi$
$953$	− 2.31811e7i	− 0.826803i	0.910549	−	0.413401i	$-0.135659\pi$
$954$	−1.66603e6	−0.0592669
$955$	0	0
$956$	−8.89536e6	−0.314788
$957$	− 4.20512e7i	− 1.48422i
$958$	3.67079e7i	1.29225i
$959$	4.57993e6	0.160810
$960$	0	0
$961$	−2.53819e7	−0.886577
$962$	4.65974e7i	1.62339i
$963$	− 7.39723e6i	− 0.257041i
$964$	−8.37723e6	−0.290341
$965$	0	0
$966$	−1.15838e7	−0.399400
$967$	1.58435e6i	0.0544861i	0.999629	+	0.0272430i	$0.00867280\pi$
$967$	1.58435e6i	0.0544861i	−0.999629	+	0.0272430i	$0.991327\pi$
$968$	− 2.83314e7i	− 0.971806i
$969$	−340065.	−0.0116346
$970$	0	0
$971$	3.44552e7	1.17275	0.586376	−	0.810039i	$-0.300554\pi$
$971$	3.44552e7	1.17275	0.586376	+	0.810039i	$0.300554\pi$
$972$	1.30550e7i	0.443211i
$973$	− 5.60708e7i	− 1.89869i
$974$	2.64239e7	0.892483
$975$	0	0
$976$	1.21349e7	0.407767
$977$	2.93599e7i	0.984052i	0.870581	+	0.492026i	$0.163743\pi$
$977$	2.93599e7i	0.984052i	−0.870581	+	0.492026i	$0.836257\pi$
$978$	− 1.47946e7i	− 0.494602i
$979$	2.37645e7	0.792452
$980$	0	0
$981$	864980.	0.0286968
$982$	152208.i	0.00503685i
$983$	8.93957e6i	0.295075i	0.989056	+	0.147538i	$0.0471348\pi$
$983$	8.93957e6i	0.295075i	−0.989056	+	0.147538i	$0.952865\pi$
$984$	1.06466e7	0.350528
$985$	0	0
$986$	−531360.	−0.0174059
$987$	1.05154e7i	0.343583i
$988$	1.61949e7i	0.527819i
$989$	−1.45428e7	−0.472777
$990$	0	0
$991$	−1.78899e7	−0.578660	−0.289330	−	0.957229i	$-0.593433\pi$
$991$	−1.78899e7	−0.578660	−0.289330	+	0.957229i	$0.593433\pi$
$992$	1.84525e6i	0.0595354i
$993$	− 1.44152e7i	− 0.463926i
$994$	4.28726e6	0.137630
$995$	0	0
$996$	−8.14862e6	−0.260277
$997$	− 3.30517e7i	− 1.05307i	−0.850155	−	0.526533i	$-0.823492\pi$
$997$	− 3.30517e7i	− 1.05307i	0.850155	−	0.526533i	$-0.176508\pi$
$998$	− 2.74268e7i	− 0.871663i
$999$	−5.29097e7	−1.67734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.6.b.c.49.2		2
3.2	odd	2		450.6.c.a.199.1		2
4.3	odd	2		400.6.c.g.49.2		2
5.2	odd	4		50.6.a.a.1.1	✓	1
5.3	odd	4		50.6.a.f.1.1	yes	1
5.4	even	2	inner	50.6.b.c.49.1		2
15.2	even	4		450.6.a.n.1.1		1
15.8	even	4		450.6.a.j.1.1		1
15.14	odd	2		450.6.c.a.199.2		2
20.3	even	4		400.6.a.e.1.1		1
20.7	even	4		400.6.a.j.1.1		1
20.19	odd	2		400.6.c.g.49.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.6.a.a.1.1	✓	1	5.2	odd	4
50.6.a.f.1.1	yes	1	5.3	odd	4
50.6.b.c.49.1		2	5.4	even	2	inner
50.6.b.c.49.2		2	1.1	even	1	trivial
400.6.a.e.1.1		1	20.3	even	4
400.6.a.j.1.1		1	20.7	even	4
400.6.c.g.49.1		2	20.19	odd	2
400.6.c.g.49.2		2	4.3	odd	2
450.6.a.j.1.1		1	15.8	even	4
450.6.a.n.1.1		1	15.2	even	4
450.6.c.a.199.1		2	3.2	odd	2
450.6.c.a.199.2		2	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+4.00000i q^{2} -11.0000i q^{3} -16.0000 q^{4} +44.0000 q^{6} +142.000i q^{7} -64.0000i q^{8} +122.000 q^{9} +O(q^{10})\)	\(q+4.00000i q^{2} -11.0000i q^{3} -16.0000 q^{4} +44.0000 q^{6} +142.000i q^{7} -64.0000i q^{8} +122.000 q^{9} +777.000 q^{11} +176.000i q^{12} +884.000i q^{13} -568.000 q^{14} +256.000 q^{16} +27.0000i q^{17} +488.000i q^{18} -1145.00 q^{19} +1562.00 q^{21} +3108.00i q^{22} +1854.00i q^{23} -704.000 q^{24} -3536.00 q^{26} -4015.00i q^{27} -2272.00i q^{28} +4920.00 q^{29} +1802.00 q^{31} +1024.00i q^{32} -8547.00i q^{33} -108.000 q^{34} -1952.00 q^{36} -13178.0i q^{37} -4580.00i q^{38} +9724.00 q^{39} -15123.0 q^{41} +6248.00i q^{42} +7844.00i q^{43} -12432.0 q^{44} -7416.00 q^{46} +6732.00i q^{47} -2816.00i q^{48} -3357.00 q^{49} +297.000 q^{51} -14144.0i q^{52} +3414.00i q^{53} +16060.0 q^{54} +9088.00 q^{56} +12595.0i q^{57} +19680.0i q^{58} -33960.0 q^{59} +47402.0 q^{61} +7208.00i q^{62} +17324.0i q^{63} -4096.00 q^{64} +34188.0 q^{66} +13177.0i q^{67} -432.000i q^{68} +20394.0 q^{69} -7548.00 q^{71} -7808.00i q^{72} -59821.0i q^{73} +52712.0 q^{74} +18320.0 q^{76} +110334. i q^{77} +38896.0i q^{78} -75830.0 q^{79} -14519.0 q^{81} -60492.0i q^{82} +46299.0i q^{83} -24992.0 q^{84} -31376.0 q^{86} -54120.0i q^{87} -49728.0i q^{88} +30585.0 q^{89} -125528. q^{91} -29664.0i q^{92} -19822.0i q^{93} -26928.0 q^{94} +11264.0 q^{96} -104018. i q^{97} -13428.0i q^{98} +94794.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{4} + 88 q^{6} + 244 q^{9}+O(q^{10}) \) 2 * q - 32 * q^4 + 88 * q^6 + 244 * q^9	\( 2 q - 32 q^{4} + 88 q^{6} + 244 q^{9} + 1554 q^{11} - 1136 q^{14} + 512 q^{16} - 2290 q^{19} + 3124 q^{21} - 1408 q^{24} - 7072 q^{26} + 9840 q^{29} + 3604 q^{31} - 216 q^{34} - 3904 q^{36} + 19448 q^{39} - 30246 q^{41} - 24864 q^{44} - 14832 q^{46} - 6714 q^{49} + 594 q^{51} + 32120 q^{54} + 18176 q^{56} - 67920 q^{59} + 94804 q^{61} - 8192 q^{64} + 68376 q^{66} + 40788 q^{69} - 15096 q^{71} + 105424 q^{74} + 36640 q^{76} - 151660 q^{79} - 29038 q^{81} - 49984 q^{84} - 62752 q^{86} + 61170 q^{89} - 251056 q^{91} - 53856 q^{94} + 22528 q^{96} + 189588 q^{99}+O(q^{100}) \) 2 * q - 32 * q^4 + 88 * q^6 + 244 * q^9 + 1554 * q^11 - 1136 * q^14 + 512 * q^16 - 2290 * q^19 + 3124 * q^21 - 1408 * q^24 - 7072 * q^26 + 9840 * q^29 + 3604 * q^31 - 216 * q^34 - 3904 * q^36 + 19448 * q^39 - 30246 * q^41 - 24864 * q^44 - 14832 * q^46 - 6714 * q^49 + 594 * q^51 + 32120 * q^54 + 18176 * q^56 - 67920 * q^59 + 94804 * q^61 - 8192 * q^64 + 68376 * q^66 + 40788 * q^69 - 15096 * q^71 + 105424 * q^74 + 36640 * q^76 - 151660 * q^79 - 29038 * q^81 - 49984 * q^84 - 62752 * q^86 + 61170 * q^89 - 251056 * q^91 - 53856 * q^94 + 22528 * q^96 + 189588 * q^99

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