LMFDB - Embedded newform 325.10.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,10,Mod(1,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("325.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	325.a (trivial)

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:	yes
Analytic conductor:	$167.386646753$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 1602x^{2} + 1544x + 342272 $ x^4 - x^3 - 1602x^2 + 1544x + 342272
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-36.8028$ of defining polynomial
Character	$\chi$	$=$	325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-28.8028 q^{2} +204.594 q^{3} +317.603 q^{4} -5892.88 q^{6} +8862.28 q^{7} +5599.18 q^{8} +22175.6 q^{9} +O(q^{10})$	\(q-28.8028 q^{2} +204.594 q^{3} +317.603 q^{4} -5892.88 q^{6} +8862.28 q^{7} +5599.18 q^{8} +22175.6 q^{9} +36087.9 q^{11} +64979.6 q^{12} +28561.0 q^{13} -255259. q^{14} -323885. q^{16} -327405. q^{17} -638720. q^{18} +265525. q^{19} +1.81317e6 q^{21} -1.03943e6 q^{22} +2.42458e6 q^{23} +1.14556e6 q^{24} -822638. q^{26} +509973. q^{27} +2.81469e6 q^{28} +3.99178e6 q^{29} -6.45220e6 q^{31} +6.46202e6 q^{32} +7.38336e6 q^{33} +9.43018e6 q^{34} +7.04304e6 q^{36} +8.15498e6 q^{37} -7.64787e6 q^{38} +5.84340e6 q^{39} -720241. q^{41} -5.22244e7 q^{42} +4.13245e7 q^{43} +1.14616e7 q^{44} -6.98348e7 q^{46} -3.67369e7 q^{47} -6.62649e7 q^{48} +3.81864e7 q^{49} -6.69850e7 q^{51} +9.07106e6 q^{52} -1.67334e7 q^{53} -1.46887e7 q^{54} +4.96215e7 q^{56} +5.43248e7 q^{57} -1.14975e8 q^{58} -5.89865e7 q^{59} +1.28785e8 q^{61} +1.85842e8 q^{62} +1.96527e8 q^{63} -2.02955e7 q^{64} -2.12662e8 q^{66} +1.91470e8 q^{67} -1.03985e8 q^{68} +4.96054e8 q^{69} +3.40865e8 q^{71} +1.24165e8 q^{72} -3.19890e8 q^{73} -2.34887e8 q^{74} +8.43316e7 q^{76} +3.19821e8 q^{77} -1.68307e8 q^{78} +2.44328e8 q^{79} -3.32145e8 q^{81} +2.07450e7 q^{82} +4.38630e8 q^{83} +5.75868e8 q^{84} -1.19026e9 q^{86} +8.16693e8 q^{87} +2.02063e8 q^{88} -7.90342e8 q^{89} +2.53116e8 q^{91} +7.70054e8 q^{92} -1.32008e9 q^{93} +1.05813e9 q^{94} +1.32209e9 q^{96} +1.65696e8 q^{97} -1.09988e9 q^{98} +8.00272e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 33 q^{2} + 163 q^{3} + 1429 q^{4} - 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9}+O(q^{10}) $ 4 * q + 33 * q^2 + 163 * q^3 + 1429 * q^4 - 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9	\( 4 q + 33 q^{2} + 163 q^{3} + 1429 q^{4} - 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9} - 40140 q^{11} + 155479 q^{12} + 114244 q^{13} - 277653 q^{14} + 726609 q^{16} - 78717 q^{17} - 1691026 q^{18} + 209664 q^{19} + 1138431 q^{21} - 1364090 q^{22} + 4257444 q^{23} + 3561573 q^{24} + 942513 q^{26} + 2077801 q^{27} - 4035181 q^{28} - 1647936 q^{29} - 11366002 q^{31} + 29458959 q^{32} + 14413222 q^{33} + 26257659 q^{34} - 11587714 q^{36} - 4636891 q^{37} - 25172466 q^{38} + 4655443 q^{39} + 13859538 q^{41} - 75564923 q^{42} + 33368081 q^{43} + 66489222 q^{44} + 71369332 q^{46} + 3943005 q^{47} + 620787 q^{48} + 23294923 q^{49} - 19664471 q^{51} + 40813669 q^{52} + 171019326 q^{53} - 64946915 q^{54} - 281552967 q^{56} + 47829030 q^{57} - 79964734 q^{58} - 63389388 q^{59} + 77050190 q^{61} + 95878740 q^{62} + 155695476 q^{63} + 768962465 q^{64} - 42396374 q^{66} + 41174072 q^{67} + 717615423 q^{68} + 546642556 q^{69} + 252460989 q^{71} - 562579254 q^{72} - 594415068 q^{73} - 957058539 q^{74} - 326897170 q^{76} - 561950454 q^{77} - 129352769 q^{78} + 115998984 q^{79} + 437803700 q^{81} + 875148240 q^{82} + 79577862 q^{83} + 108899441 q^{84} - 589924887 q^{86} + 1087526510 q^{87} + 2327564370 q^{88} - 1152240276 q^{89} + 321054201 q^{91} + 4213481460 q^{92} - 1618266556 q^{93} + 1859909503 q^{94} + 3171454029 q^{96} - 1049098084 q^{97} - 420532254 q^{98} + 2132181050 q^{99}+O(q^{100}) \) 4 * q + 33 * q^2 + 163 * q^3 + 1429 * q^4 - 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9 - 40140 * q^11 + 155479 * q^12 + 114244 * q^13 - 277653 * q^14 + 726609 * q^16 - 78717 * q^17 - 1691026 * q^18 + 209664 * q^19 + 1138431 * q^21 - 1364090 * q^22 + 4257444 * q^23 + 3561573 * q^24 + 942513 * q^26 + 2077801 * q^27 - 4035181 * q^28 - 1647936 * q^29 - 11366002 * q^31 + 29458959 * q^32 + 14413222 * q^33 + 26257659 * q^34 - 11587714 * q^36 - 4636891 * q^37 - 25172466 * q^38 + 4655443 * q^39 + 13859538 * q^41 - 75564923 * q^42 + 33368081 * q^43 + 66489222 * q^44 + 71369332 * q^46 + 3943005 * q^47 + 620787 * q^48 + 23294923 * q^49 - 19664471 * q^51 + 40813669 * q^52 + 171019326 * q^53 - 64946915 * q^54 - 281552967 * q^56 + 47829030 * q^57 - 79964734 * q^58 - 63389388 * q^59 + 77050190 * q^61 + 95878740 * q^62 + 155695476 * q^63 + 768962465 * q^64 - 42396374 * q^66 + 41174072 * q^67 + 717615423 * q^68 + 546642556 * q^69 + 252460989 * q^71 - 562579254 * q^72 - 594415068 * q^73 - 957058539 * q^74 - 326897170 * q^76 - 561950454 * q^77 - 129352769 * q^78 + 115998984 * q^79 + 437803700 * q^81 + 875148240 * q^82 + 79577862 * q^83 + 108899441 * q^84 - 589924887 * q^86 + 1087526510 * q^87 + 2327564370 * q^88 - 1152240276 * q^89 + 321054201 * q^91 + 4213481460 * q^92 - 1618266556 * q^93 + 1859909503 * q^94 + 3171454029 * q^96 - 1049098084 * q^97 - 420532254 * q^98 + 2132181050 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−28.8028	−1.27292	−0.636459	−	0.771311i	$-0.719601\pi$
$2$	−28.8028	−1.27292	−0.636459	+	0.771311i	$0.719601\pi$
$3$	204.594	1.45830	0.729150	−	0.684354i	$-0.239916\pi$
$3$	204.594	1.45830	0.729150	+	0.684354i	$0.239916\pi$
$4$	317.603	0.620318
$5$	0	0
$5$	0	0
$6$	−5892.88	−1.85629
$7$	8862.28	1.39510	0.697548	−	0.716538i	$-0.254274\pi$
$7$	8862.28	1.39510	0.697548	+	0.716538i	$0.254274\pi$
$8$	5599.18	0.483303
$9$	22175.6	1.12664
$10$	0	0
$11$	36087.9	0.743181	0.371591	−	0.928397i	$-0.378812\pi$
$11$	36087.9	0.743181	0.371591	+	0.928397i	$0.378812\pi$
$12$	64979.6	0.904610
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−255259.	−1.77584
$15$	0	0
$16$	−323885.	−1.23552
$17$	−327405.	−0.950747	−0.475373	−	0.879784i	$-0.657687\pi$
$17$	−327405.	−0.950747	−0.475373	+	0.879784i	$0.657687\pi$
$18$	−638720.	−1.43412
$19$	265525.	0.467428	0.233714	−	0.972305i	$-0.424912\pi$
$19$	265525.	0.467428	0.233714	+	0.972305i	$0.424912\pi$
$20$	0	0
$21$	1.81317e6	2.03447
$22$	−1.03943e6	−0.946008
$23$	2.42458e6	1.80660	0.903299	−	0.429012i	$-0.141138\pi$
$23$	2.42458e6	1.80660	0.903299	+	0.429012i	$0.141138\pi$
$24$	1.14556e6	0.704801
$25$	0	0
$26$	−822638.	−0.353044
$27$	509973.	0.184676
$28$	2.81469e6	0.865404
$29$	3.99178e6	1.04803	0.524017	−	0.851708i	$-0.324433\pi$
$29$	3.99178e6	1.04803	0.524017	+	0.851708i	$0.324433\pi$
$30$	0	0
$31$	−6.45220e6	−1.25482	−0.627408	−	0.778691i	$-0.715884\pi$
$31$	−6.45220e6	−1.25482	−0.627408	+	0.778691i	$0.715884\pi$
$32$	6.46202e6	1.08942
$33$	7.38336e6	1.08378
$34$	9.43018e6	1.21022
$35$	0	0
$36$	7.04304e6	0.698874
$37$	8.15498e6	0.715344	0.357672	−	0.933847i	$-0.383571\pi$
$37$	8.15498e6	0.715344	0.357672	+	0.933847i	$0.383571\pi$
$38$	−7.64787e6	−0.594997
$39$	5.84340e6	0.404460
$40$	0	0
$41$	−720241.	−0.0398062	−0.0199031	−	0.999802i	$-0.506336\pi$
$41$	−720241.	−0.0398062	−0.0199031	+	0.999802i	$0.506336\pi$
$42$	−5.22244e7	−2.58971
$43$	4.13245e7	1.84332	0.921658	−	0.388004i	$-0.126835\pi$
$43$	4.13245e7	1.84332	0.921658	+	0.388004i	$0.126835\pi$
$44$	1.14616e7	0.461009
$45$	0	0
$46$	−6.98348e7	−2.29965
$47$	−3.67369e7	−1.09815	−0.549076	−	0.835772i	$-0.685020\pi$
$47$	−3.67369e7	−1.09815	−0.549076	+	0.835772i	$0.685020\pi$
$48$	−6.62649e7	−1.80176
$49$	3.81864e7	0.946295
$50$	0	0
$51$	−6.69850e7	−1.38647
$52$	9.07106e6	0.172045
$53$	−1.67334e7	−0.291302	−0.145651	−	0.989336i	$-0.546528\pi$
$53$	−1.67334e7	−0.291302	−0.145651	+	0.989336i	$0.546528\pi$
$54$	−1.46887e7	−0.235077
$55$	0	0
$56$	4.96215e7	0.674255
$57$	5.43248e7	0.681649
$58$	−1.14975e8	−1.33406
$59$	−5.89865e7	−0.633751	−0.316875	−	0.948467i	$-0.602634\pi$
$59$	−5.89865e7	−0.633751	−0.316875	+	0.948467i	$0.602634\pi$
$60$	0	0
$61$	1.28785e8	1.19091	0.595456	−	0.803388i	$-0.296971\pi$
$61$	1.28785e8	1.19091	0.595456	+	0.803388i	$0.296971\pi$
$62$	1.85842e8	1.59728
$63$	1.96527e8	1.57177
$64$	−2.02955e7	−0.151213
$65$	0	0
$66$	−2.12662e8	−1.37956
$67$	1.91470e8	1.16082	0.580410	−	0.814324i	$-0.302892\pi$
$67$	1.91470e8	1.16082	0.580410	+	0.814324i	$0.302892\pi$
$68$	−1.03985e8	−0.589766
$69$	4.96054e8	2.63456
$70$	0	0
$71$	3.40865e8	1.59192	0.795958	−	0.605351i	$-0.206967\pi$
$71$	3.40865e8	1.59192	0.795958	+	0.605351i	$0.206967\pi$
$72$	1.24165e8	0.544508
$73$	−3.19890e8	−1.31840	−0.659200	−	0.751968i	$-0.729105\pi$
$73$	−3.19890e8	−1.31840	−0.659200	+	0.751968i	$0.729105\pi$
$74$	−2.34887e8	−0.910574
$75$	0	0
$76$	8.43316e7	0.289954
$77$	3.19821e8	1.03681
$78$	−1.68307e8	−0.514844
$79$	2.44328e8	0.705751	0.352876	−	0.935670i	$-0.385204\pi$
$79$	2.44328e8	0.705751	0.352876	+	0.935670i	$0.385204\pi$
$80$	0	0
$81$	−3.32145e8	−0.857325
$82$	2.07450e7	0.0506700
$83$	4.38630e8	1.01449	0.507244	−	0.861802i	$-0.330664\pi$
$83$	4.38630e8	1.01449	0.507244	+	0.861802i	$0.330664\pi$
$84$	5.75868e8	1.26202
$85$	0	0
$86$	−1.19026e9	−2.34639
$87$	8.16693e8	1.52835
$88$	2.02063e8	0.359182
$89$	−7.90342e8	−1.33524	−0.667621	−	0.744501i	$-0.732688\pi$
$89$	−7.90342e8	−1.33524	−0.667621	+	0.744501i	$0.732688\pi$
$90$	0	0
$91$	2.53116e8	0.386930
$92$	7.70054e8	1.12067
$93$	−1.32008e9	−1.82990
$94$	1.05813e9	1.39786
$95$	0	0
$96$	1.32209e9	1.58869
$97$	1.65696e8	0.190037	0.0950185	−	0.995476i	$-0.469709\pi$
$97$	1.65696e8	0.190037	0.0950185	+	0.995476i	$0.469709\pi$
$98$	−1.09988e9	−1.20456
$99$	8.00272e8	0.837296
$100$	0	0
$101$	−7.41636e8	−0.709161	−0.354580	−	0.935026i	$-0.615376\pi$
$101$	−7.41636e8	−0.709161	−0.354580	+	0.935026i	$0.615376\pi$
$102$	1.92936e9	1.76487
$103$	−1.42175e9	−1.24467	−0.622336	−	0.782750i	$-0.713816\pi$
$103$	−1.42175e9	−1.24467	−0.622336	+	0.782750i	$0.713816\pi$
$104$	1.59918e8	0.134044
$105$	0	0
$106$	4.81970e8	0.370803
$107$	1.44196e9	1.06347	0.531736	−	0.846910i	$-0.321540\pi$
$107$	1.44196e9	1.06347	0.531736	+	0.846910i	$0.321540\pi$
$108$	1.61969e8	0.114558
$109$	−8.42758e7	−0.0571852	−0.0285926	−	0.999591i	$-0.509103\pi$
$109$	−8.42758e7	−0.0571852	−0.0285926	+	0.999591i	$0.509103\pi$
$110$	0	0
$111$	1.66846e9	1.04319
$112$	−2.87036e9	−1.72367
$113$	−8.60241e8	−0.496326	−0.248163	−	0.968718i	$-0.579827\pi$
$113$	−8.60241e8	−0.496326	−0.248163	+	0.968718i	$0.579827\pi$
$114$	−1.56471e9	−0.867683
$115$	0	0
$116$	1.26780e9	0.650115
$117$	6.33358e8	0.312473
$118$	1.69898e9	0.806712
$119$	−2.90155e9	−1.32638
$120$	0	0
$121$	−1.05561e9	−0.447681
$122$	−3.70936e9	−1.51593
$123$	−1.47357e8	−0.0580494
$124$	−2.04924e9	−0.778386
$125$	0	0
$126$	−5.66052e9	−2.00073
$127$	1.44120e9	0.491596	0.245798	−	0.969321i	$-0.420950\pi$
$127$	1.44120e9	0.491596	0.245798	+	0.969321i	$0.420950\pi$
$128$	−2.72399e9	−0.896934
$129$	8.45474e9	2.68811
$130$	0	0
$131$	−4.54928e9	−1.34965	−0.674827	−	0.737976i	$-0.735782\pi$
$131$	−4.54928e9	−1.34965	−0.674827	+	0.737976i	$0.735782\pi$
$132$	2.34498e9	0.672289
$133$	2.35316e9	0.652107
$134$	−5.51489e9	−1.47763
$135$	0	0
$136$	−1.83320e9	−0.459499
$137$	1.99742e9	0.484426	0.242213	−	0.970223i	$-0.422127\pi$
$137$	1.99742e9	0.484426	0.242213	+	0.970223i	$0.422127\pi$
$138$	−1.42878e10	−3.35358
$139$	3.55325e8	0.0807345	0.0403672	−	0.999185i	$-0.487147\pi$
$139$	3.55325e8	0.0807345	0.0403672	+	0.999185i	$0.487147\pi$
$140$	0	0
$141$	−7.51615e9	−1.60143
$142$	−9.81789e9	−2.02638
$143$	1.03071e9	0.206121
$144$	−7.18235e9	−1.39199
$145$	0	0
$146$	9.21372e9	1.67821
$147$	7.81270e9	1.37998
$148$	2.59005e9	0.443741
$149$	5.92546e9	0.984881	0.492440	−	0.870346i	$-0.336105\pi$
$149$	5.92546e9	0.984881	0.492440	+	0.870346i	$0.336105\pi$
$150$	0	0
$151$	−1.07568e10	−1.68378	−0.841891	−	0.539647i	$-0.818558\pi$
$151$	−1.07568e10	−1.68378	−0.841891	+	0.539647i	$0.818558\pi$
$152$	1.48672e9	0.225909
$153$	−7.26040e9	−1.07115
$154$	−9.21176e9	−1.31977
$155$	0	0
$156$	1.85588e9	0.250894
$157$	−8.87634e9	−1.16597	−0.582983	−	0.812485i	$-0.698114\pi$
$157$	−8.87634e9	−1.16597	−0.582983	+	0.812485i	$0.698114\pi$
$158$	−7.03734e9	−0.898363
$159$	−3.42355e9	−0.424805
$160$	0	0
$161$	2.14873e10	2.52038
$162$	9.56672e9	1.09130
$163$	−2.75052e9	−0.305190	−0.152595	−	0.988289i	$-0.548763\pi$
$163$	−2.75052e9	−0.305190	−0.152595	+	0.988289i	$0.548763\pi$
$164$	−2.28751e8	−0.0246925
$165$	0	0
$166$	−1.26338e10	−1.29136
$167$	9.17849e9	0.913160	0.456580	−	0.889682i	$-0.349074\pi$
$167$	9.17849e9	0.913160	0.456580	+	0.889682i	$0.349074\pi$
$168$	1.01523e10	0.983266
$169$	8.15731e8	0.0769231
$170$	0	0
$171$	5.88818e9	0.526622
$172$	1.31248e10	1.14344
$173$	−9.75049e8	−0.0827598	−0.0413799	−	0.999143i	$-0.513175\pi$
$173$	−9.75049e8	−0.0827598	−0.0413799	+	0.999143i	$0.513175\pi$
$174$	−2.35231e10	−1.94546
$175$	0	0
$176$	−1.16883e10	−0.918218
$177$	−1.20683e10	−0.924198
$178$	2.27641e10	1.69965
$179$	−8.88356e9	−0.646768	−0.323384	−	0.946268i	$-0.604820\pi$
$179$	−8.88356e9	−0.646768	−0.323384	+	0.946268i	$0.604820\pi$
$180$	0	0
$181$	−5.22791e9	−0.362055	−0.181028	−	0.983478i	$-0.557942\pi$
$181$	−5.22791e9	−0.362055	−0.181028	+	0.983478i	$0.557942\pi$
$182$	−7.29045e9	−0.492530
$183$	2.63485e10	1.73671
$184$	1.35757e10	0.873134
$185$	0	0
$186$	3.80220e10	2.32931
$187$	−1.18154e10	−0.706577
$188$	−1.16678e10	−0.681204
$189$	4.51952e9	0.257641
$190$	0	0
$191$	9.23471e9	0.502080	0.251040	−	0.967977i	$-0.419227\pi$
$191$	9.23471e9	0.502080	0.251040	+	0.967977i	$0.419227\pi$
$192$	−4.15232e9	−0.220514
$193$	−1.07065e10	−0.555441	−0.277720	−	0.960662i	$-0.589579\pi$
$193$	−1.07065e10	−0.555441	−0.277720	+	0.960662i	$0.589579\pi$
$194$	−4.77250e9	−0.241901
$195$	0	0
$196$	1.21281e10	0.587004
$197$	2.77001e10	1.31034	0.655169	−	0.755482i	$-0.272597\pi$
$197$	2.77001e10	1.31034	0.655169	+	0.755482i	$0.272597\pi$
$198$	−2.30501e10	−1.06581
$199$	3.32299e10	1.50207	0.751035	−	0.660262i	$-0.229555\pi$
$199$	3.32299e10	1.50207	0.751035	+	0.660262i	$0.229555\pi$
$200$	0	0
$201$	3.91737e10	1.69282
$202$	2.13612e10	0.902703
$203$	3.53763e10	1.46211
$204$	−2.12746e10	−0.860055
$205$	0	0
$206$	4.09503e10	1.58436
$207$	5.37666e10	2.03538
$208$	−9.25048e9	−0.342673
$209$	9.58225e9	0.347383
$210$	0	0
$211$	−1.49261e10	−0.518411	−0.259205	−	0.965822i	$-0.583461\pi$
$211$	−1.49261e10	−0.518411	−0.259205	+	0.965822i	$0.583461\pi$
$212$	−5.31458e9	−0.180700
$213$	6.97389e10	2.32149
$214$	−4.15325e10	−1.35371
$215$	0	0
$216$	2.85543e9	0.0892545
$217$	−5.71812e10	−1.75059
$218$	2.42738e9	0.0727920
$219$	−6.54474e10	−1.92262
$220$	0	0
$221$	−9.35101e9	−0.263690
$222$	−4.80563e10	−1.32789
$223$	−2.23373e10	−0.604865	−0.302433	−	0.953171i	$-0.597799\pi$
$223$	−2.23373e10	−0.604865	−0.302433	+	0.953171i	$0.597799\pi$
$224$	5.72683e10	1.51984
$225$	0	0
$226$	2.47774e10	0.631782
$227$	−5.20726e9	−0.130165	−0.0650824	−	0.997880i	$-0.520731\pi$
$227$	−5.20726e9	−0.130165	−0.0650824	+	0.997880i	$0.520731\pi$
$228$	1.72537e10	0.422840
$229$	1.35573e10	0.325773	0.162887	−	0.986645i	$-0.447920\pi$
$229$	1.35573e10	0.325773	0.162887	+	0.986645i	$0.447920\pi$
$230$	0	0
$231$	6.54335e10	1.51198
$232$	2.23507e10	0.506518
$233$	−2.06224e8	−0.00458393	−0.00229196	−	0.999997i	$-0.500730\pi$
$233$	−2.06224e8	−0.00458393	−0.00229196	+	0.999997i	$0.500730\pi$
$234$	−1.82425e10	−0.397752
$235$	0	0
$236$	−1.87343e10	−0.393127
$237$	4.99880e10	1.02920
$238$	8.35729e10	1.68838
$239$	1.89887e10	0.376448	0.188224	−	0.982126i	$-0.439727\pi$
$239$	1.89887e10	0.376448	0.188224	+	0.982126i	$0.439727\pi$
$240$	0	0
$241$	−6.11533e10	−1.16773	−0.583866	−	0.811850i	$-0.698461\pi$
$241$	−6.11533e10	−1.16773	−0.583866	+	0.811850i	$0.698461\pi$
$242$	3.04045e10	0.569861
$243$	−7.79927e10	−1.43491
$244$	4.09024e10	0.738745
$245$	0	0
$246$	4.24430e9	0.0738920
$247$	7.58366e9	0.129641
$248$	−3.61270e10	−0.606457
$249$	8.97410e10	1.47943
$250$	0	0
$251$	−3.20685e9	−0.0509973	−0.0254986	−	0.999675i	$-0.508117\pi$
$251$	−3.20685e9	−0.0509973	−0.0254986	+	0.999675i	$0.508117\pi$
$252$	6.24174e10	0.974997
$253$	8.74981e10	1.34263
$254$	−4.15107e10	−0.625761
$255$	0	0
$256$	8.88499e10	1.29294
$257$	2.80963e10	0.401744	0.200872	−	0.979617i	$-0.435622\pi$
$257$	2.80963e10	0.401744	0.200872	+	0.979617i	$0.435622\pi$
$258$	−2.43520e11	−3.42174
$259$	7.22717e10	0.997975
$260$	0	0
$261$	8.85201e10	1.18076
$262$	1.31032e11	1.71800
$263$	1.25524e11	1.61780	0.808902	−	0.587944i	$-0.200062\pi$
$263$	1.25524e11	1.61780	0.808902	+	0.587944i	$0.200062\pi$
$264$	4.13408e10	0.523795
$265$	0	0
$266$	−6.77776e10	−0.830078
$267$	−1.61699e11	−1.94718
$268$	6.08116e10	0.720078
$269$	−1.78558e10	−0.207918	−0.103959	−	0.994582i	$-0.533151\pi$
$269$	−1.78558e10	−0.207918	−0.103959	+	0.994582i	$0.533151\pi$
$270$	0	0
$271$	1.25204e11	1.41013	0.705063	−	0.709144i	$-0.250919\pi$
$271$	1.25204e11	1.41013	0.705063	+	0.709144i	$0.250919\pi$
$272$	1.06041e11	1.17467
$273$	5.17859e10	0.564260
$274$	−5.75314e10	−0.616634
$275$	0	0
$276$	1.57548e11	1.63427
$277$	5.55594e10	0.567020	0.283510	−	0.958969i	$-0.408501\pi$
$277$	5.55594e10	0.567020	0.283510	+	0.958969i	$0.408501\pi$
$278$	−1.02344e10	−0.102768
$279$	−1.43081e11	−1.41372
$280$	0	0
$281$	1.01237e11	0.968635	0.484317	−	0.874892i	$-0.339068\pi$
$281$	1.01237e11	0.968635	0.484317	+	0.874892i	$0.339068\pi$
$282$	2.16486e11	2.03849
$283$	1.08041e11	1.00127	0.500635	−	0.865658i	$-0.333100\pi$
$283$	1.08041e11	1.00127	0.500635	+	0.865658i	$0.333100\pi$
$284$	1.08260e11	0.987495
$285$	0	0
$286$	−2.96873e10	−0.262376
$287$	−6.38298e9	−0.0555335
$288$	1.43299e11	1.22738
$289$	−1.13940e10	−0.0960810
$290$	0	0
$291$	3.39003e10	0.277131
$292$	−1.01598e11	−0.817828
$293$	−3.53224e9	−0.0279992	−0.0139996	−	0.999902i	$-0.504456\pi$
$293$	−3.53224e9	−0.0279992	−0.0139996	+	0.999902i	$0.504456\pi$
$294$	−2.25028e11	−1.75660
$295$	0	0
$296$	4.56612e10	0.345728
$297$	1.84039e10	0.137248
$298$	−1.70670e11	−1.25367
$299$	6.92485e10	0.501060
$300$	0	0
$301$	3.66229e11	2.57160
$302$	3.09826e11	2.14332
$303$	−1.51734e11	−1.03417
$304$	−8.59996e10	−0.577518
$305$	0	0
$306$	2.09120e11	1.36348
$307$	1.82031e11	1.16956	0.584781	−	0.811191i	$-0.301180\pi$
$307$	1.82031e11	1.16956	0.584781	+	0.811191i	$0.301180\pi$
$308$	1.01576e11	0.643152
$309$	−2.90881e11	−1.81510
$310$	0	0
$311$	−1.51907e11	−0.920781	−0.460390	−	0.887717i	$-0.652291\pi$
$311$	−1.51907e11	−0.920781	−0.460390	+	0.887717i	$0.652291\pi$
$312$	3.27183e10	0.195477
$313$	−6.10194e10	−0.359351	−0.179675	−	0.983726i	$-0.557505\pi$
$313$	−6.10194e10	−0.359351	−0.179675	+	0.983726i	$0.557505\pi$
$314$	2.55664e11	1.48418
$315$	0	0
$316$	7.75994e10	0.437790
$317$	−6.89227e10	−0.383350	−0.191675	−	0.981458i	$-0.561392\pi$
$317$	−6.89227e10	−0.383350	−0.191675	+	0.981458i	$0.561392\pi$
$318$	9.86080e10	0.540742
$319$	1.44055e11	0.778880
$320$	0	0
$321$	2.95016e11	1.55086
$322$	−6.18896e11	−3.20823
$323$	−8.69341e10	−0.444405
$324$	−1.05490e11	−0.531814
$325$	0	0
$326$	7.92227e10	0.388481
$327$	−1.72423e10	−0.0833931
$328$	−4.03276e9	−0.0192385
$329$	−3.25573e11	−1.53203
$330$	0	0
$331$	4.70422e10	0.215408	0.107704	−	0.994183i	$-0.465650\pi$
$331$	4.70422e10	0.215408	0.107704	+	0.994183i	$0.465650\pi$
$332$	1.39310e11	0.629306
$333$	1.80842e11	0.805934
$334$	−2.64366e11	−1.16238
$335$	0	0
$336$	−5.87258e11	−2.51363
$337$	3.76711e11	1.59101	0.795507	−	0.605944i	$-0.207205\pi$
$337$	3.76711e11	1.59101	0.795507	+	0.605944i	$0.207205\pi$
$338$	−2.34954e10	−0.0979167
$339$	−1.76000e11	−0.723792
$340$	0	0
$341$	−2.32846e11	−0.932556
$342$	−1.69596e11	−0.670346
$343$	−1.92062e10	−0.0749235
$344$	2.31383e11	0.890880
$345$	0	0
$346$	2.80842e10	0.105346
$347$	−1.68331e11	−0.623278	−0.311639	−	0.950201i	$-0.600878\pi$
$347$	−1.68331e11	−0.623278	−0.311639	+	0.950201i	$0.600878\pi$
$348$	2.59384e11	0.948062
$349$	−9.36126e10	−0.337769	−0.168884	−	0.985636i	$-0.554016\pi$
$349$	−9.36126e10	−0.337769	−0.168884	+	0.985636i	$0.554016\pi$
$350$	0	0
$351$	1.45653e10	0.0512199
$352$	2.33201e11	0.809634
$353$	3.49043e11	1.19644	0.598222	−	0.801330i	$-0.295874\pi$
$353$	3.49043e11	1.19644	0.598222	+	0.801330i	$0.295874\pi$
$354$	3.47600e11	1.17643
$355$	0	0
$356$	−2.51015e11	−0.828276
$357$	−5.93640e11	−1.93426
$358$	2.55872e11	0.823282
$359$	5.83173e11	1.85299	0.926493	−	0.376312i	$-0.122808\pi$
$359$	5.83173e11	1.85299	0.926493	+	0.376312i	$0.122808\pi$
$360$	0	0
$361$	−2.52184e11	−0.781512
$362$	1.50579e11	0.460866
$363$	−2.15971e11	−0.652854
$364$	8.03903e10	0.240020
$365$	0	0
$366$	−7.58912e11	−2.21068
$367$	−5.28604e11	−1.52101	−0.760507	−	0.649329i	$-0.775050\pi$
$367$	−5.28604e11	−1.52101	−0.760507	+	0.649329i	$0.775050\pi$
$368$	−7.85286e11	−2.23209
$369$	−1.59718e10	−0.0448472
$370$	0	0
$371$	−1.48296e11	−0.406394
$372$	−4.19261e11	−1.13512
$373$	4.19405e11	1.12187	0.560937	−	0.827858i	$-0.310441\pi$
$373$	4.19405e11	1.12187	0.560937	+	0.827858i	$0.310441\pi$
$374$	3.40316e11	0.899414
$375$	0	0
$376$	−2.05697e11	−0.530740
$377$	1.14009e11	0.290672
$378$	−1.30175e11	−0.327955
$379$	4.24128e11	1.05590	0.527948	−	0.849277i	$-0.322962\pi$
$379$	4.24128e11	1.05590	0.527948	+	0.849277i	$0.322962\pi$
$380$	0	0
$381$	2.94861e11	0.716894
$382$	−2.65986e11	−0.639107
$383$	−6.52696e10	−0.154995	−0.0774973	−	0.996993i	$-0.524693\pi$
$383$	−6.52696e10	−0.154995	−0.0774973	+	0.996993i	$0.524693\pi$
$384$	−5.57311e11	−1.30800
$385$	0	0
$386$	3.08376e11	0.707030
$387$	9.16396e11	2.07675
$388$	5.26254e10	0.117883
$389$	−5.91803e11	−1.31040	−0.655200	−	0.755455i	$-0.727416\pi$
$389$	−5.91803e11	−1.31040	−0.655200	+	0.755455i	$0.727416\pi$
$390$	0	0
$391$	−7.93819e11	−1.71762
$392$	2.13813e11	0.457347
$393$	−9.30755e11	−1.96820
$394$	−7.97842e11	−1.66795
$395$	0	0
$396$	2.54169e11	0.519390
$397$	3.05131e11	0.616495	0.308248	−	0.951306i	$-0.400257\pi$
$397$	3.05131e11	0.616495	0.308248	+	0.951306i	$0.400257\pi$
$398$	−9.57115e11	−1.91201
$399$	4.81441e11	0.950967
$400$	0	0
$401$	2.56722e11	0.495808	0.247904	−	0.968785i	$-0.420258\pi$
$401$	2.56722e11	0.495808	0.247904	+	0.968785i	$0.420258\pi$
$402$	−1.12831e12	−2.15483
$403$	−1.84281e11	−0.348023
$404$	−2.35546e11	−0.439906
$405$	0	0
$406$	−1.01894e12	−1.86114
$407$	2.94296e11	0.531631
$408$	−3.75061e11	−0.670087
$409$	−4.57003e11	−0.807540	−0.403770	−	0.914860i	$-0.632300\pi$
$409$	−4.57003e11	−0.807540	−0.403770	+	0.914860i	$0.632300\pi$
$410$	0	0
$411$	4.08660e11	0.706438
$412$	−4.51551e11	−0.772093
$413$	−5.22755e11	−0.884144
$414$	−1.54863e12	−2.59087
$415$	0	0
$416$	1.84562e11	0.302150
$417$	7.26973e10	0.117735
$418$	−2.75996e11	−0.442190
$419$	−1.65068e11	−0.261637	−0.130818	−	0.991406i	$-0.541760\pi$
$419$	−1.65068e11	−0.261637	−0.130818	+	0.991406i	$0.541760\pi$
$420$	0	0
$421$	−9.10255e10	−0.141219	−0.0706096	−	0.997504i	$-0.522494\pi$
$421$	−9.10255e10	−0.141219	−0.0706096	+	0.997504i	$0.522494\pi$
$422$	4.29913e11	0.659894
$423$	−8.14664e11	−1.23722
$424$	−9.36935e10	−0.140787
$425$	0	0
$426$	−2.00868e12	−2.95507
$427$	1.14133e12	1.66144
$428$	4.57971e11	0.659691
$429$	2.10876e11	0.300587
$430$	0	0
$431$	7.94605e11	1.10918	0.554592	−	0.832122i	$-0.312874\pi$
$431$	7.94605e11	1.10918	0.554592	+	0.832122i	$0.312874\pi$
$432$	−1.65173e11	−0.228171
$433$	8.26325e11	1.12968	0.564840	−	0.825200i	$-0.308938\pi$
$433$	8.26325e11	1.12968	0.564840	+	0.825200i	$0.308938\pi$
$434$	1.64698e12	2.22836
$435$	0	0
$436$	−2.67662e10	−0.0354730
$437$	6.43787e11	0.844453
$438$	1.88507e12	2.44734
$439$	1.21562e12	1.56210	0.781050	−	0.624469i	$-0.214684\pi$
$439$	1.21562e12	1.56210	0.781050	+	0.624469i	$0.214684\pi$
$440$	0	0
$441$	8.46807e11	1.06613
$442$	2.69335e11	0.335655
$443$	8.73136e11	1.07712	0.538561	−	0.842586i	$-0.318968\pi$
$443$	8.73136e11	1.07712	0.538561	+	0.842586i	$0.318968\pi$
$444$	5.29907e11	0.647108
$445$	0	0
$446$	6.43377e11	0.769943
$447$	1.21231e12	1.43625
$448$	−1.79864e11	−0.210957
$449$	1.22107e12	1.41785	0.708927	−	0.705282i	$-0.249179\pi$
$449$	1.22107e12	1.41785	0.708927	+	0.705282i	$0.249179\pi$
$450$	0	0
$451$	−2.59920e10	−0.0295832
$452$	−2.73215e11	−0.307880
$453$	−2.20077e12	−2.45546
$454$	1.49984e11	0.165689
$455$	0	0
$456$	3.04174e11	0.329443
$457$	−6.32643e11	−0.678478	−0.339239	−	0.940700i	$-0.610170\pi$
$457$	−6.32643e11	−0.678478	−0.339239	+	0.940700i	$0.610170\pi$
$458$	−3.90490e11	−0.414682
$459$	−1.66968e11	−0.175580
$460$	0	0
$461$	8.09117e11	0.834367	0.417184	−	0.908822i	$-0.363017\pi$
$461$	8.09117e11	0.834367	0.417184	+	0.908822i	$0.363017\pi$
$462$	−1.88467e12	−1.92463
$463$	−7.69685e11	−0.778393	−0.389196	−	0.921155i	$-0.627247\pi$
$463$	−7.69685e11	−0.778393	−0.389196	+	0.921155i	$0.627247\pi$
$464$	−1.29288e12	−1.29487
$465$	0	0
$466$	5.93984e9	0.00583496
$467$	−1.59708e12	−1.55382	−0.776909	−	0.629613i	$-0.783213\pi$
$467$	−1.59708e12	−1.55382	−0.776909	+	0.629613i	$0.783213\pi$
$468$	2.01156e11	0.193833
$469$	1.69686e12	1.61946
$470$	0	0
$471$	−1.81604e12	−1.70033
$472$	−3.30276e11	−0.306294
$473$	1.49132e12	1.36992
$474$	−1.43980e12	−1.31008
$475$	0	0
$476$	−9.21542e11	−0.822780
$477$	−3.71074e11	−0.328192
$478$	−5.46929e11	−0.479187
$479$	1.61308e12	1.40006	0.700028	−	0.714115i	$-0.253171\pi$
$479$	1.61308e12	1.40006	0.700028	+	0.714115i	$0.253171\pi$
$480$	0	0
$481$	2.32914e11	0.198401
$482$	1.76139e12	1.48643
$483$	4.39617e12	3.67547
$484$	−3.35265e11	−0.277705
$485$	0	0
$486$	2.24641e12	1.82653
$487$	−9.29058e11	−0.748449	−0.374225	−	0.927338i	$-0.622091\pi$
$487$	−9.29058e11	−0.748449	−0.374225	+	0.927338i	$0.622091\pi$
$488$	7.21089e11	0.575572
$489$	−5.62739e11	−0.445058
$490$	0	0
$491$	−2.30662e12	−1.79106	−0.895528	−	0.445005i	$-0.853202\pi$
$491$	−2.30662e12	−1.79106	−0.895528	+	0.445005i	$0.853202\pi$
$492$	−4.68010e10	−0.0360091
$493$	−1.30693e12	−0.996415
$494$	−2.18431e11	−0.165022
$495$	0	0
$496$	2.08977e12	1.55036
$497$	3.02084e12	2.22088
$498$	−2.58480e12	−1.88319
$499$	−1.31410e11	−0.0948800	−0.0474400	−	0.998874i	$-0.515106\pi$
$499$	−1.31410e11	−0.0948800	−0.0474400	+	0.998874i	$0.515106\pi$
$500$	0	0
$501$	1.87786e12	1.33166
$502$	9.23664e10	0.0649153
$503$	1.88419e12	1.31241	0.656203	−	0.754584i	$-0.272162\pi$
$503$	1.88419e12	1.31241	0.656203	+	0.754584i	$0.272162\pi$
$504$	1.10039e12	0.759641
$505$	0	0
$506$	−2.52019e12	−1.70906
$507$	1.66893e11	0.112177
$508$	4.57730e11	0.304946
$509$	−1.00390e11	−0.0662919	−0.0331459	−	0.999451i	$-0.510553\pi$
$509$	−1.00390e11	−0.0662919	−0.0331459	+	0.999451i	$0.510553\pi$
$510$	0	0
$511$	−2.83495e12	−1.83930
$512$	−1.16445e12	−0.748866
$513$	1.35411e11	0.0863226
$514$	−8.09252e11	−0.511387
$515$	0	0
$516$	2.68525e12	1.66748
$517$	−1.32576e12	−0.816126
$518$	−2.08163e12	−1.27034
$519$	−1.99489e11	−0.120689
$520$	0	0
$521$	−1.04516e11	−0.0621462	−0.0310731	−	0.999517i	$-0.509892\pi$
$521$	−1.04516e11	−0.0621462	−0.0310731	+	0.999517i	$0.509892\pi$
$522$	−2.54963e12	−1.50300
$523$	−1.17694e12	−0.687855	−0.343927	−	0.938996i	$-0.611757\pi$
$523$	−1.17694e12	−0.687855	−0.343927	+	0.938996i	$0.611757\pi$
$524$	−1.44487e12	−0.837215
$525$	0	0
$526$	−3.61544e12	−2.05933
$527$	2.11248e12	1.19301
$528$	−2.39136e12	−1.33904
$529$	4.07744e12	2.26379
$530$	0	0
$531$	−1.30806e12	−0.714008
$532$	7.47370e11	0.404514
$533$	−2.05708e10	−0.0110403
$534$	4.65739e12	2.47860
$535$	0	0
$536$	1.07208e12	0.561028
$537$	−1.81752e12	−0.943181
$538$	5.14296e11	0.264663
$539$	1.37807e12	0.703269
$540$	0	0
$541$	−2.98502e12	−1.49817	−0.749083	−	0.662476i	$-0.769506\pi$
$541$	−2.98502e12	−1.49817	−0.749083	+	0.662476i	$0.769506\pi$
$542$	−3.60624e12	−1.79497
$543$	−1.06960e12	−0.527985
$544$	−2.11570e12	−1.03576
$545$	0	0
$546$	−1.49158e12	−0.718257
$547$	−3.78628e12	−1.80830	−0.904148	−	0.427219i	$-0.859493\pi$
$547$	−3.78628e12	−1.80830	−0.904148	+	0.427219i	$0.859493\pi$
$548$	6.34387e11	0.300498
$549$	2.85588e12	1.34173
$550$	0	0
$551$	1.05992e12	0.489880
$552$	2.77750e12	1.27329
$553$	2.16530e12	0.984591
$554$	−1.60027e12	−0.721770
$555$	0	0
$556$	1.12852e11	0.0500811
$557$	−1.00551e12	−0.442627	−0.221313	−	0.975203i	$-0.571034\pi$
$557$	−1.00551e12	−0.442627	−0.221313	+	0.975203i	$0.571034\pi$
$558$	4.12115e12	1.79955
$559$	1.18027e12	0.511244
$560$	0	0
$561$	−2.41735e12	−1.03040
$562$	−2.91591e12	−1.23299
$563$	−2.76515e11	−0.115993	−0.0579964	−	0.998317i	$-0.518471\pi$
$563$	−2.76515e11	−0.115993	−0.0579964	+	0.998317i	$0.518471\pi$
$564$	−2.38715e12	−0.993399
$565$	0	0
$566$	−3.11190e12	−1.27453
$567$	−2.94356e12	−1.19605
$568$	1.90857e12	0.769378
$569$	8.39220e11	0.335638	0.167819	−	0.985818i	$-0.446328\pi$
$569$	8.39220e11	0.335638	0.167819	+	0.985818i	$0.446328\pi$
$570$	0	0
$571$	−1.02285e11	−0.0402672	−0.0201336	−	0.999797i	$-0.506409\pi$
$571$	−1.02285e11	−0.0402672	−0.0201336	+	0.999797i	$0.506409\pi$
$572$	3.27356e11	0.127861
$573$	1.88936e12	0.732184
$574$	1.83848e11	0.0706896
$575$	0	0
$576$	−4.50064e11	−0.170362
$577$	1.44021e12	0.540921	0.270461	−	0.962731i	$-0.412824\pi$
$577$	1.44021e12	0.540921	0.270461	+	0.962731i	$0.412824\pi$
$578$	3.28181e11	0.122303
$579$	−2.19047e12	−0.809999
$580$	0	0
$581$	3.88726e12	1.41531
$582$	−9.76424e11	−0.352765
$583$	−6.03874e11	−0.216490
$584$	−1.79112e12	−0.637187
$585$	0	0
$586$	1.01738e11	0.0356407
$587$	2.13185e11	0.0741116	0.0370558	−	0.999313i	$-0.488202\pi$
$587$	2.13185e11	0.0741116	0.0370558	+	0.999313i	$0.488202\pi$
$588$	2.48134e12	0.856028
$589$	−1.71322e12	−0.586536
$590$	0	0
$591$	5.66727e12	1.91087
$592$	−2.64128e12	−0.883825
$593$	1.76049e12	0.584640	0.292320	−	0.956321i	$-0.405573\pi$
$593$	1.76049e12	0.584640	0.292320	+	0.956321i	$0.405573\pi$
$594$	−5.30084e11	−0.174705
$595$	0	0
$596$	1.88194e12	0.610940
$597$	6.79863e12	2.19047
$598$	−1.99455e12	−0.637808
$599$	−2.06753e12	−0.656191	−0.328096	−	0.944644i	$-0.606407\pi$
$599$	−2.06753e12	−0.656191	−0.328096	+	0.944644i	$0.606407\pi$
$600$	0	0
$601$	−1.24403e12	−0.388951	−0.194476	−	0.980907i	$-0.562301\pi$
$601$	−1.24403e12	−0.388951	−0.194476	+	0.980907i	$0.562301\pi$
$602$	−1.05484e13	−3.27344
$603$	4.24597e12	1.30782
$604$	−3.41639e12	−1.04448
$605$	0	0
$606$	4.37037e12	1.31641
$607$	1.31511e12	0.393200	0.196600	−	0.980484i	$-0.437010\pi$
$607$	1.31511e12	0.393200	0.196600	+	0.980484i	$0.437010\pi$
$608$	1.71583e12	0.509223
$609$	7.23776e12	2.13219
$610$	0	0
$611$	−1.04924e12	−0.304573
$612$	−2.30593e12	−0.664452
$613$	3.08252e12	0.881726	0.440863	−	0.897574i	$-0.354672\pi$
$613$	3.08252e12	0.881726	0.440863	+	0.897574i	$0.354672\pi$
$614$	−5.24301e12	−1.48876
$615$	0	0
$616$	1.79074e12	0.501094
$617$	2.29075e10	0.00636348	0.00318174	−	0.999995i	$-0.498987\pi$
$617$	2.29075e10	0.00636348	0.00318174	+	0.999995i	$0.498987\pi$
$618$	8.37818e12	2.31048
$619$	−4.45350e12	−1.21925	−0.609626	−	0.792689i	$-0.708680\pi$
$619$	−4.45350e12	−1.21925	−0.609626	+	0.792689i	$0.708680\pi$
$620$	0	0
$621$	1.23647e12	0.333635
$622$	4.37535e12	1.17208
$623$	−7.00424e12	−1.86279
$624$	−1.89259e12	−0.499719
$625$	0	0
$626$	1.75753e12	0.457423
$627$	1.96047e12	0.506589
$628$	−2.81915e12	−0.723270
$629$	−2.66998e12	−0.680111
$630$	0	0
$631$	3.83831e12	0.963847	0.481923	−	0.876213i	$-0.339938\pi$
$631$	3.83831e12	0.963847	0.481923	+	0.876213i	$0.339938\pi$
$632$	1.36804e12	0.341092
$633$	−3.05378e12	−0.755998
$634$	1.98517e12	0.487973
$635$	0	0
$636$	−1.08733e12	−0.263515
$637$	1.09064e12	0.262455
$638$	−4.14919e12	−0.991449
$639$	7.55890e12	1.79351
$640$	0	0
$641$	9.09238e11	0.212724	0.106362	−	0.994327i	$-0.466080\pi$
$641$	9.09238e11	0.212724	0.106362	+	0.994327i	$0.466080\pi$
$642$	−8.49729e12	−1.97412
$643$	−8.23839e12	−1.90061	−0.950305	−	0.311321i	$-0.899229\pi$
$643$	−8.23839e12	−1.90061	−0.950305	+	0.311321i	$0.899229\pi$
$644$	6.82444e12	1.56344
$645$	0	0
$646$	2.50395e12	0.565691
$647$	8.73559e12	1.95985	0.979925	−	0.199365i	$-0.0638880\pi$
$647$	8.73559e12	1.95985	0.979925	+	0.199365i	$0.0638880\pi$
$648$	−1.85974e12	−0.414348
$649$	−2.12870e12	−0.470992
$650$	0	0
$651$	−1.16989e13	−2.55289
$652$	−8.73573e11	−0.189315
$653$	6.13232e11	0.131982	0.0659911	−	0.997820i	$-0.478979\pi$
$653$	6.13232e11	0.131982	0.0659911	+	0.997820i	$0.478979\pi$
$654$	4.96627e11	0.106153
$655$	0	0
$656$	2.33275e11	0.0491815
$657$	−7.09375e12	−1.48536
$658$	9.37742e12	1.95015
$659$	−8.83233e12	−1.82428	−0.912139	−	0.409882i	$-0.865570\pi$
$659$	−8.83233e12	−1.82428	−0.912139	+	0.409882i	$0.865570\pi$
$660$	0	0
$661$	−5.61801e12	−1.14466	−0.572329	−	0.820024i	$-0.693960\pi$
$661$	−5.61801e12	−1.14466	−0.572329	+	0.820024i	$0.693960\pi$
$662$	−1.35495e12	−0.274196
$663$	−1.91316e12	−0.384539
$664$	2.45597e12	0.490306
$665$	0	0
$666$	−5.20875e12	−1.02589
$667$	9.67839e12	1.89338
$668$	2.91511e12	0.566450
$669$	−4.57007e12	−0.882075
$670$	0	0
$671$	4.64757e12	0.885064
$672$	1.17167e13	2.21638
$673$	−4.50151e12	−0.845844	−0.422922	−	0.906166i	$-0.638996\pi$
$673$	−4.50151e12	−0.845844	−0.422922	+	0.906166i	$0.638996\pi$
$674$	−1.08503e13	−2.02523
$675$	0	0
$676$	2.59079e11	0.0477168
$677$	−4.33098e12	−0.792387	−0.396193	−	0.918167i	$-0.629669\pi$
$677$	−4.33098e12	−0.792387	−0.396193	+	0.918167i	$0.629669\pi$
$678$	5.06929e12	0.921327
$679$	1.46844e12	0.265120
$680$	0	0
$681$	−1.06537e12	−0.189819
$682$	6.70664e12	1.18707
$683$	−6.25107e12	−1.09916	−0.549580	−	0.835441i	$-0.685212\pi$
$683$	−6.25107e12	−1.09916	−0.549580	+	0.835441i	$0.685212\pi$
$684$	1.87010e12	0.326673
$685$	0	0
$686$	5.53193e11	0.0953715
$687$	2.77375e12	0.475075
$688$	−1.33844e13	−2.27746
$689$	−4.77923e11	−0.0807926
$690$	0	0
$691$	7.34082e12	1.22488	0.612440	−	0.790517i	$-0.290188\pi$
$691$	7.34082e12	1.22488	0.612440	+	0.790517i	$0.290188\pi$
$692$	−3.09679e11	−0.0513374
$693$	7.09223e12	1.16811
$694$	4.84841e12	0.793381
$695$	0	0
$696$	4.57281e12	0.738656
$697$	2.35810e11	0.0378456
$698$	2.69631e12	0.429952
$699$	−4.21922e10	−0.00668474
$700$	0	0
$701$	−1.71509e11	−0.0268259	−0.0134130	−	0.999910i	$-0.504270\pi$
$701$	−1.71509e11	−0.0268259	−0.0134130	+	0.999910i	$0.504270\pi$
$702$	−4.19523e11	−0.0651987
$703$	2.16535e12	0.334372
$704$	−7.32421e11	−0.112379
$705$	0	0
$706$	−1.00534e13	−1.52297
$707$	−6.57259e12	−0.989348
$708$	−3.83292e12	−0.573297
$709$	−1.00896e13	−1.49956	−0.749780	−	0.661687i	$-0.769841\pi$
$709$	−1.00896e13	−1.49956	−0.749780	+	0.661687i	$0.769841\pi$
$710$	0	0
$711$	5.41813e12	0.795126
$712$	−4.42527e12	−0.645327
$713$	−1.56439e13	−2.26695
$714$	1.70985e13	2.46216
$715$	0	0
$716$	−2.82145e12	−0.401202
$717$	3.88497e12	0.548974
$718$	−1.67970e13	−2.35870
$719$	8.18068e12	1.14159	0.570794	−	0.821093i	$-0.306635\pi$
$719$	8.18068e12	1.14159	0.570794	+	0.821093i	$0.306635\pi$
$720$	0	0
$721$	−1.25999e13	−1.73644
$722$	7.26362e12	0.994800
$723$	−1.25116e13	−1.70290
$724$	−1.66040e12	−0.224589
$725$	0	0
$726$	6.22058e12	0.831029
$727$	9.98421e11	0.132559	0.0662795	−	0.997801i	$-0.478887\pi$
$727$	9.98421e11	0.132559	0.0662795	+	0.997801i	$0.478887\pi$
$728$	1.41724e12	0.187005
$729$	−9.41920e12	−1.23521
$730$	0	0
$731$	−1.35298e13	−1.75253
$732$	8.36837e12	1.07731
$733$	2.10457e12	0.269274	0.134637	−	0.990895i	$-0.457013\pi$
$733$	2.10457e12	0.269274	0.134637	+	0.990895i	$0.457013\pi$
$734$	1.52253e13	1.93613
$735$	0	0
$736$	1.56677e13	1.96814
$737$	6.90977e12	0.862700
$738$	4.60033e11	0.0570867
$739$	−1.28931e13	−1.59023	−0.795113	−	0.606461i	$-0.792588\pi$
$739$	−1.28931e13	−1.59023	−0.795113	+	0.606461i	$0.792588\pi$
$740$	0	0
$741$	1.55157e12	0.189056
$742$	4.27135e12	0.517306
$743$	−2.72357e11	−0.0327861	−0.0163930	−	0.999866i	$-0.505218\pi$
$743$	−2.72357e11	−0.0327861	−0.0163930	+	0.999866i	$0.505218\pi$
$744$	−7.39137e12	−0.884396
$745$	0	0
$746$	−1.20801e13	−1.42805
$747$	9.72689e12	1.14296
$748$	−3.75259e12	−0.438303
$749$	1.27790e13	1.48365
$750$	0	0
$751$	−1.40530e13	−1.61209	−0.806045	−	0.591855i	$-0.798396\pi$
$751$	−1.40530e13	−1.61209	−0.806045	+	0.591855i	$0.798396\pi$
$752$	1.18985e13	1.35679
$753$	−6.56102e11	−0.0743693
$754$	−3.28379e12	−0.370002
$755$	0	0
$756$	1.43541e12	0.159819
$757$	−8.53220e12	−0.944342	−0.472171	−	0.881507i	$-0.656530\pi$
$757$	−8.53220e12	−0.944342	−0.472171	+	0.881507i	$0.656530\pi$
$758$	−1.22161e13	−1.34407
$759$	1.79016e13	1.95796
$760$	0	0
$761$	1.13835e13	1.23039	0.615197	−	0.788373i	$-0.289076\pi$
$761$	1.13835e13	1.23039	0.615197	+	0.788373i	$0.289076\pi$
$762$	−8.49283e12	−0.912547
$763$	−7.46876e11	−0.0797789
$764$	2.93297e12	0.311450
$765$	0	0
$766$	1.87995e12	0.197295
$767$	−1.68471e12	−0.175771
$768$	1.81781e13	1.88549
$769$	1.94858e12	0.200933	0.100466	−	0.994940i	$-0.467967\pi$
$769$	1.94858e12	0.200933	0.100466	+	0.994940i	$0.467967\pi$
$770$	0	0
$771$	5.74832e12	0.585864
$772$	−3.40040e12	−0.344550
$773$	1.09355e13	1.10161	0.550807	−	0.834633i	$-0.314320\pi$
$773$	1.09355e13	1.10161	0.550807	+	0.834633i	$0.314320\pi$
$774$	−2.63948e13	−2.64353
$775$	0	0
$776$	9.27760e11	0.0918455
$777$	1.47863e13	1.45535
$778$	1.70456e13	1.66803
$779$	−1.91242e11	−0.0186065
$780$	0	0
$781$	1.23011e13	1.18308
$782$	2.28642e13	2.18638
$783$	2.03570e12	0.193547
$784$	−1.23680e13	−1.16917
$785$	0	0
$786$	2.68084e13	2.50535
$787$	−7.50366e12	−0.697247	−0.348623	−	0.937263i	$-0.613351\pi$
$787$	−7.50366e12	−0.697247	−0.348623	+	0.937263i	$0.613351\pi$
$788$	8.79764e12	0.812827
$789$	2.56814e13	2.35924
$790$	0	0
$791$	−7.62369e12	−0.692423
$792$	4.48087e12	0.404668
$793$	3.67822e12	0.330300
$794$	−8.78865e12	−0.784747
$795$	0	0
$796$	1.05539e13	0.931762
$797$	−1.65844e12	−0.145592	−0.0727962	−	0.997347i	$-0.523192\pi$
$797$	−1.65844e12	−0.145592	−0.0727962	+	0.997347i	$0.523192\pi$
$798$	−1.38669e13	−1.21050
$799$	1.20278e13	1.04406
$800$	0	0
$801$	−1.75263e13	−1.50434
$802$	−7.39433e12	−0.631123
$803$	−1.15441e13	−0.979810
$804$	1.24417e13	1.05009
$805$	0	0
$806$	5.30782e12	0.443005
$807$	−3.65318e12	−0.303207
$808$	−4.15256e12	−0.342740
$809$	−7.07921e12	−0.581054	−0.290527	−	0.956867i	$-0.593831\pi$
$809$	−7.07921e12	−0.581054	−0.290527	+	0.956867i	$0.593831\pi$
$810$	0	0
$811$	−1.84596e13	−1.49840	−0.749201	−	0.662343i	$-0.769562\pi$
$811$	−1.84596e13	−1.49840	−0.749201	+	0.662343i	$0.769562\pi$
$812$	1.12356e13	0.906973
$813$	2.56161e13	2.05639
$814$	−8.47657e12	−0.676722
$815$	0	0
$816$	2.16954e13	1.71302
$817$	1.09727e13	0.861616
$818$	1.31630e13	1.02793
$819$	5.61299e12	0.435930
$820$	0	0
$821$	2.40377e13	1.84650	0.923250	−	0.384200i	$-0.125523\pi$
$821$	2.40377e13	1.84650	0.923250	+	0.384200i	$0.125523\pi$
$822$	−1.17706e13	−0.899237
$823$	1.26494e12	0.0961104	0.0480552	−	0.998845i	$-0.484698\pi$
$823$	1.26494e12	0.0961104	0.0480552	+	0.998845i	$0.484698\pi$
$824$	−7.96062e12	−0.601554
$825$	0	0
$826$	1.50568e13	1.12544
$827$	9.81229e12	0.729450	0.364725	−	0.931115i	$-0.381163\pi$
$827$	9.81229e12	0.729450	0.364725	+	0.931115i	$0.381163\pi$
$828$	1.70764e13	1.26258
$829$	1.26128e13	0.927504	0.463752	−	0.885965i	$-0.346503\pi$
$829$	1.26128e13	0.927504	0.463752	+	0.885965i	$0.346503\pi$
$830$	0	0
$831$	1.13671e13	0.826886
$832$	−5.79658e11	−0.0419389
$833$	−1.25024e13	−0.899687
$834$	−2.09389e12	−0.149867
$835$	0	0
$836$	3.04335e12	0.215488
$837$	−3.29045e12	−0.231734
$838$	4.75441e12	0.333042
$839$	−8.53632e12	−0.594760	−0.297380	−	0.954759i	$-0.596113\pi$
$839$	−8.53632e12	−0.594760	−0.297380	+	0.954759i	$0.596113\pi$
$840$	0	0
$841$	1.42715e12	0.0983759
$842$	2.62179e12	0.179760
$843$	2.07124e13	1.41256
$844$	−4.74056e12	−0.321580
$845$	0	0
$846$	2.34646e13	1.57488
$847$	−9.35511e12	−0.624559
$848$	5.41970e12	0.359910
$849$	2.21046e13	1.46015
$850$	0	0
$851$	1.97724e13	1.29234
$852$	2.21493e13	1.44006
$853$	1.12025e13	0.724507	0.362254	−	0.932080i	$-0.382007\pi$
$853$	1.12025e13	0.724507	0.362254	+	0.932080i	$0.382007\pi$
$854$	−3.28734e13	−2.11487
$855$	0	0
$856$	8.07379e12	0.513979
$857$	2.23241e13	1.41371	0.706856	−	0.707357i	$-0.250113\pi$
$857$	2.23241e13	1.41371	0.706856	+	0.707357i	$0.250113\pi$
$858$	−6.07383e12	−0.382622
$859$	−2.11323e13	−1.32428	−0.662138	−	0.749382i	$-0.730351\pi$
$859$	−2.11323e13	−1.32428	−0.662138	+	0.749382i	$0.730351\pi$
$860$	0	0
$861$	−1.30592e12	−0.0809845
$862$	−2.28869e13	−1.41190
$863$	−1.17061e13	−0.718395	−0.359197	−	0.933262i	$-0.616950\pi$
$863$	−1.17061e13	−0.718395	−0.359197	+	0.933262i	$0.616950\pi$
$864$	3.29546e12	0.201189
$865$	0	0
$866$	−2.38005e13	−1.43799
$867$	−2.33115e12	−0.140115
$868$	−1.81609e13	−1.08592
$869$	8.81730e12	0.524501
$870$	0	0
$871$	5.46859e12	0.321954
$872$	−4.71876e11	−0.0276378
$873$	3.67440e12	0.214103
$874$	−1.85429e13	−1.07492
$875$	0	0
$876$	−2.07863e13	−1.19264
$877$	−1.17836e13	−0.672638	−0.336319	−	0.941748i	$-0.609182\pi$
$877$	−1.17836e13	−0.672638	−0.336319	+	0.941748i	$0.609182\pi$
$878$	−3.50134e13	−1.98842
$879$	−7.22674e11	−0.0408312
$880$	0	0
$881$	−1.93741e13	−1.08350	−0.541751	−	0.840539i	$-0.682238\pi$
$881$	−1.93741e13	−1.08350	−0.541751	+	0.840539i	$0.682238\pi$
$882$	−2.43904e13	−1.35710
$883$	1.50199e13	0.831466	0.415733	−	0.909487i	$-0.363525\pi$
$883$	1.50199e13	0.831466	0.415733	+	0.909487i	$0.363525\pi$
$884$	−2.96991e12	−0.163572
$885$	0	0
$886$	−2.51488e13	−1.37109
$887$	−1.23661e13	−0.670776	−0.335388	−	0.942080i	$-0.608867\pi$
$887$	−1.23661e13	−0.670776	−0.335388	+	0.942080i	$0.608867\pi$
$888$	9.34200e12	0.504175
$889$	1.27723e13	0.685824
$890$	0	0
$891$	−1.19864e13	−0.637148
$892$	−7.09439e12	−0.375209
$893$	−9.75457e12	−0.513306
$894$	−3.49180e13	−1.82823
$895$	0	0
$896$	−2.41408e13	−1.25131
$897$	1.41678e13	0.730696
$898$	−3.51702e13	−1.80481
$899$	−2.57558e13	−1.31509
$900$	0	0
$901$	5.47860e12	0.276954
$902$	7.48644e11	0.0376570
$903$	7.49283e13	3.75017
$904$	−4.81664e12	−0.239876
$905$	0	0
$906$	6.33884e13	3.12560
$907$	−9.76708e12	−0.479217	−0.239608	−	0.970870i	$-0.577019\pi$
$907$	−9.76708e12	−0.479217	−0.239608	+	0.970870i	$0.577019\pi$
$908$	−1.65384e12	−0.0807436
$909$	−1.64462e13	−0.798967
$910$	0	0
$911$	−1.91556e13	−0.921430	−0.460715	−	0.887548i	$-0.652407\pi$
$911$	−1.91556e13	−0.921430	−0.460715	+	0.887548i	$0.652407\pi$
$912$	−1.75950e13	−0.842194
$913$	1.58293e13	0.753949
$914$	1.82219e13	0.863647
$915$	0	0
$916$	4.30586e12	0.202083
$917$	−4.03170e13	−1.88290
$918$	4.80914e12	0.223499
$919$	−2.82464e13	−1.30630	−0.653150	−	0.757229i	$-0.726553\pi$
$919$	−2.82464e13	−1.30630	−0.653150	+	0.757229i	$0.726553\pi$
$920$	0	0
$921$	3.72425e13	1.70557
$922$	−2.33049e13	−1.06208
$923$	9.73546e12	0.441518
$924$	2.07819e13	0.937909
$925$	0	0
$926$	2.21691e13	0.990830
$927$	−3.15281e13	−1.40229
$928$	2.57950e13	1.14175
$929$	1.81017e13	0.797348	0.398674	−	0.917093i	$-0.369471\pi$
$929$	1.81017e13	0.797348	0.398674	+	0.917093i	$0.369471\pi$
$930$	0	0
$931$	1.01395e13	0.442324
$932$	−6.54974e10	−0.00284350
$933$	−3.10792e13	−1.34277
$934$	4.60004e13	1.97788
$935$	0	0
$936$	3.54629e12	0.151019
$937$	−2.51202e13	−1.06462	−0.532310	−	0.846550i	$-0.678676\pi$
$937$	−2.51202e13	−1.06462	−0.532310	+	0.846550i	$0.678676\pi$
$938$	−4.88745e13	−2.06143
$939$	−1.24842e13	−0.524041
$940$	0	0
$941$	8.09156e11	0.0336418	0.0168209	−	0.999859i	$-0.494645\pi$
$941$	8.09156e11	0.0336418	0.0168209	+	0.999859i	$0.494645\pi$
$942$	5.23072e13	2.16438
$943$	−1.74628e12	−0.0719138
$944$	1.91048e13	0.783014
$945$	0	0
$946$	−4.29541e13	−1.74379
$947$	1.25569e13	0.507349	0.253675	−	0.967290i	$-0.418361\pi$
$947$	1.25569e13	0.507349	0.253675	+	0.967290i	$0.418361\pi$
$948$	1.58763e13	0.638430
$949$	−9.13636e12	−0.365658
$950$	0	0
$951$	−1.41012e13	−0.559040
$952$	−1.62463e13	−0.641045
$953$	3.64201e13	1.43029	0.715144	−	0.698977i	$-0.246361\pi$
$953$	3.64201e13	1.43029	0.715144	+	0.698977i	$0.246361\pi$
$954$	1.06880e13	0.417761
$955$	0	0
$956$	6.03087e12	0.233518
$957$	2.94728e13	1.13584
$958$	−4.64612e13	−1.78216
$959$	1.77017e13	0.675821
$960$	0	0
$961$	1.51913e13	0.574564
$962$	−6.70859e12	−0.252548
$963$	3.19763e13	1.19815
$964$	−1.94225e13	−0.724366
$965$	0	0
$966$	−1.26622e14	−4.67857
$967$	−2.96691e13	−1.09115	−0.545575	−	0.838062i	$-0.683689\pi$
$967$	−2.96691e13	−1.09115	−0.545575	+	0.838062i	$0.683689\pi$
$968$	−5.91055e12	−0.216366
$969$	−1.77862e13	−0.648076
$970$	0	0
$971$	−1.05417e13	−0.380563	−0.190281	−	0.981730i	$-0.560940\pi$
$971$	−1.05417e13	−0.380563	−0.190281	+	0.981730i	$0.560940\pi$
$972$	−2.47707e13	−0.890103
$973$	3.14899e12	0.112632
$974$	2.67595e13	0.952714
$975$	0	0
$976$	−4.17114e13	−1.47140
$977$	2.40729e13	0.845285	0.422643	−	0.906296i	$-0.361103\pi$
$977$	2.40729e13	0.845285	0.422643	+	0.906296i	$0.361103\pi$
$978$	1.62085e13	0.566522
$979$	−2.85218e13	−0.992328
$980$	0	0
$981$	−1.86887e12	−0.0644270
$982$	6.64372e13	2.27987
$983$	3.57135e13	1.21995	0.609974	−	0.792421i	$-0.291180\pi$
$983$	3.57135e13	1.21995	0.609974	+	0.792421i	$0.291180\pi$
$984$	−8.25078e11	−0.0280555
$985$	0	0
$986$	3.76432e13	1.26835
$987$	−6.66102e13	−2.23416
$988$	2.40859e12	0.0804187
$989$	1.00195e14	3.33013
$990$	0	0
$991$	2.48780e13	0.819376	0.409688	−	0.912226i	$-0.365638\pi$
$991$	2.48780e13	0.819376	0.409688	+	0.912226i	$0.365638\pi$
$992$	−4.16943e13	−1.36702
$993$	9.62454e12	0.314129
$994$	−8.70089e13	−2.82699
$995$	0	0
$996$	2.85020e13	0.917717
$997$	3.31717e13	1.06326	0.531630	−	0.846977i	$-0.321580\pi$
$997$	3.31717e13	1.06326	0.531630	+	0.846977i	$0.321580\pi$
$998$	3.78497e12	0.120774
$999$	4.15882e12	0.132107

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.10.a.a.1.1		4
5.4	even	2		13.10.a.a.1.4	✓	4
15.14	odd	2		117.10.a.c.1.1		4
20.19	odd	2		208.10.a.g.1.4		4
65.64	even	2		169.10.a.a.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.a.1.4	✓	4	5.4	even	2
117.10.a.c.1.1		4	15.14	odd	2
169.10.a.a.1.1		4	65.64	even	2
208.10.a.g.1.4		4	20.19	odd	2
325.10.a.a.1.1		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q-28.8028 q^{2} +204.594 q^{3} +317.603 q^{4} -5892.88 q^{6} +8862.28 q^{7} +5599.18 q^{8} +22175.6 q^{9} +O(q^{10})\)	\(q-28.8028 q^{2} +204.594 q^{3} +317.603 q^{4} -5892.88 q^{6} +8862.28 q^{7} +5599.18 q^{8} +22175.6 q^{9} +36087.9 q^{11} +64979.6 q^{12} +28561.0 q^{13} -255259. q^{14} -323885. q^{16} -327405. q^{17} -638720. q^{18} +265525. q^{19} +1.81317e6 q^{21} -1.03943e6 q^{22} +2.42458e6 q^{23} +1.14556e6 q^{24} -822638. q^{26} +509973. q^{27} +2.81469e6 q^{28} +3.99178e6 q^{29} -6.45220e6 q^{31} +6.46202e6 q^{32} +7.38336e6 q^{33} +9.43018e6 q^{34} +7.04304e6 q^{36} +8.15498e6 q^{37} -7.64787e6 q^{38} +5.84340e6 q^{39} -720241. q^{41} -5.22244e7 q^{42} +4.13245e7 q^{43} +1.14616e7 q^{44} -6.98348e7 q^{46} -3.67369e7 q^{47} -6.62649e7 q^{48} +3.81864e7 q^{49} -6.69850e7 q^{51} +9.07106e6 q^{52} -1.67334e7 q^{53} -1.46887e7 q^{54} +4.96215e7 q^{56} +5.43248e7 q^{57} -1.14975e8 q^{58} -5.89865e7 q^{59} +1.28785e8 q^{61} +1.85842e8 q^{62} +1.96527e8 q^{63} -2.02955e7 q^{64} -2.12662e8 q^{66} +1.91470e8 q^{67} -1.03985e8 q^{68} +4.96054e8 q^{69} +3.40865e8 q^{71} +1.24165e8 q^{72} -3.19890e8 q^{73} -2.34887e8 q^{74} +8.43316e7 q^{76} +3.19821e8 q^{77} -1.68307e8 q^{78} +2.44328e8 q^{79} -3.32145e8 q^{81} +2.07450e7 q^{82} +4.38630e8 q^{83} +5.75868e8 q^{84} -1.19026e9 q^{86} +8.16693e8 q^{87} +2.02063e8 q^{88} -7.90342e8 q^{89} +2.53116e8 q^{91} +7.70054e8 q^{92} -1.32008e9 q^{93} +1.05813e9 q^{94} +1.32209e9 q^{96} +1.65696e8 q^{97} -1.09988e9 q^{98} +8.00272e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 33 q^{2} + 163 q^{3} + 1429 q^{4} - 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9}+O(q^{10}) \) 4 * q + 33 * q^2 + 163 * q^3 + 1429 * q^4 - 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9	\( 4 q + 33 q^{2} + 163 q^{3} + 1429 q^{4} - 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9} - 40140 q^{11} + 155479 q^{12} + 114244 q^{13} - 277653 q^{14} + 726609 q^{16} - 78717 q^{17} - 1691026 q^{18} + 209664 q^{19} + 1138431 q^{21} - 1364090 q^{22} + 4257444 q^{23} + 3561573 q^{24} + 942513 q^{26} + 2077801 q^{27} - 4035181 q^{28} - 1647936 q^{29} - 11366002 q^{31} + 29458959 q^{32} + 14413222 q^{33} + 26257659 q^{34} - 11587714 q^{36} - 4636891 q^{37} - 25172466 q^{38} + 4655443 q^{39} + 13859538 q^{41} - 75564923 q^{42} + 33368081 q^{43} + 66489222 q^{44} + 71369332 q^{46} + 3943005 q^{47} + 620787 q^{48} + 23294923 q^{49} - 19664471 q^{51} + 40813669 q^{52} + 171019326 q^{53} - 64946915 q^{54} - 281552967 q^{56} + 47829030 q^{57} - 79964734 q^{58} - 63389388 q^{59} + 77050190 q^{61} + 95878740 q^{62} + 155695476 q^{63} + 768962465 q^{64} - 42396374 q^{66} + 41174072 q^{67} + 717615423 q^{68} + 546642556 q^{69} + 252460989 q^{71} - 562579254 q^{72} - 594415068 q^{73} - 957058539 q^{74} - 326897170 q^{76} - 561950454 q^{77} - 129352769 q^{78} + 115998984 q^{79} + 437803700 q^{81} + 875148240 q^{82} + 79577862 q^{83} + 108899441 q^{84} - 589924887 q^{86} + 1087526510 q^{87} + 2327564370 q^{88} - 1152240276 q^{89} + 321054201 q^{91} + 4213481460 q^{92} - 1618266556 q^{93} + 1859909503 q^{94} + 3171454029 q^{96} - 1049098084 q^{97} - 420532254 q^{98} + 2132181050 q^{99}+O(q^{100}) \) 4 * q + 33 * q^2 + 163 * q^3 + 1429 * q^4 - 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9 - 40140 * q^11 + 155479 * q^12 + 114244 * q^13 - 277653 * q^14 + 726609 * q^16 - 78717 * q^17 - 1691026 * q^18 + 209664 * q^19 + 1138431 * q^21 - 1364090 * q^22 + 4257444 * q^23 + 3561573 * q^24 + 942513 * q^26 + 2077801 * q^27 - 4035181 * q^28 - 1647936 * q^29 - 11366002 * q^31 + 29458959 * q^32 + 14413222 * q^33 + 26257659 * q^34 - 11587714 * q^36 - 4636891 * q^37 - 25172466 * q^38 + 4655443 * q^39 + 13859538 * q^41 - 75564923 * q^42 + 33368081 * q^43 + 66489222 * q^44 + 71369332 * q^46 + 3943005 * q^47 + 620787 * q^48 + 23294923 * q^49 - 19664471 * q^51 + 40813669 * q^52 + 171019326 * q^53 - 64946915 * q^54 - 281552967 * q^56 + 47829030 * q^57 - 79964734 * q^58 - 63389388 * q^59 + 77050190 * q^61 + 95878740 * q^62 + 155695476 * q^63 + 768962465 * q^64 - 42396374 * q^66 + 41174072 * q^67 + 717615423 * q^68 + 546642556 * q^69 + 252460989 * q^71 - 562579254 * q^72 - 594415068 * q^73 - 957058539 * q^74 - 326897170 * q^76 - 561950454 * q^77 - 129352769 * q^78 + 115998984 * q^79 + 437803700 * q^81 + 875148240 * q^82 + 79577862 * q^83 + 108899441 * q^84 - 589924887 * q^86 + 1087526510 * q^87 + 2327564370 * q^88 - 1152240276 * q^89 + 321054201 * q^91 + 4213481460 * q^92 - 1618266556 * q^93 + 1859909503 * q^94 + 3171454029 * q^96 - 1049098084 * q^97 - 420532254 * q^98 + 2132181050 * q^99

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