LMFDB - Embedded newform 325.6.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,6,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, 6, names="a")

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

chi := DirichletCharacter("325.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
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:	$52.1247414392$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.168897.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 100x + 256 $ x^3 - x^2 - 100*x + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-10.6486$ 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)

$f(q)$	$=$	$q+8.64858 q^{2} -10.2870 q^{3} +42.7979 q^{4} -88.9676 q^{6} -2.86088 q^{7} +93.3863 q^{8} -137.178 q^{9} +O(q^{10})$	\(q+8.64858 q^{2} -10.2870 q^{3} +42.7979 q^{4} -88.9676 q^{6} -2.86088 q^{7} +93.3863 q^{8} -137.178 q^{9} +571.711 q^{11} -440.260 q^{12} -169.000 q^{13} -24.7426 q^{14} -561.873 q^{16} +855.571 q^{17} -1186.40 q^{18} -2355.90 q^{19} +29.4298 q^{21} +4944.49 q^{22} -2509.66 q^{23} -960.662 q^{24} -1461.61 q^{26} +3910.88 q^{27} -122.440 q^{28} -5497.50 q^{29} -144.924 q^{31} -7847.77 q^{32} -5881.17 q^{33} +7399.47 q^{34} -5870.95 q^{36} +515.975 q^{37} -20375.2 q^{38} +1738.50 q^{39} -13928.9 q^{41} +254.526 q^{42} -7753.58 q^{43} +24468.0 q^{44} -21705.0 q^{46} -8344.77 q^{47} +5779.97 q^{48} -16798.8 q^{49} -8801.22 q^{51} -7232.84 q^{52} +5976.21 q^{53} +33823.6 q^{54} -267.168 q^{56} +24235.1 q^{57} -47545.6 q^{58} +2110.84 q^{59} -17394.2 q^{61} -1253.38 q^{62} +392.452 q^{63} -49892.1 q^{64} -50863.8 q^{66} +3121.05 q^{67} +36616.6 q^{68} +25816.8 q^{69} +43323.3 q^{71} -12810.6 q^{72} -6808.31 q^{73} +4462.45 q^{74} -100828. q^{76} -1635.60 q^{77} +15035.5 q^{78} -1280.80 q^{79} -6896.72 q^{81} -120465. q^{82} -7148.44 q^{83} +1259.53 q^{84} -67057.5 q^{86} +56552.6 q^{87} +53390.0 q^{88} +107123. q^{89} +483.489 q^{91} -107408. q^{92} +1490.82 q^{93} -72170.4 q^{94} +80729.7 q^{96} -42456.2 q^{97} -145286. q^{98} -78426.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 7 q^{2} - 8 q^{3} + 121 q^{4} - 199 q^{6} + 60 q^{7} - 327 q^{8} - 191 q^{9}+O(q^{10}) $ 3 * q - 7 * q^2 - 8 * q^3 + 121 * q^4 - 199 * q^6 + 60 * q^7 - 327 * q^8 - 191 * q^9	\( 3 q - 7 q^{2} - 8 q^{3} + 121 q^{4} - 199 q^{6} + 60 q^{7} - 327 q^{8} - 191 q^{9} + 556 q^{11} + 1091 q^{12} - 507 q^{13} - 793 q^{14} + 2785 q^{16} - 908 q^{17} - 976 q^{18} + 148 q^{19} + 1390 q^{21} + 3410 q^{22} - 3624 q^{23} - 13377 q^{24} + 1183 q^{26} + 4276 q^{27} + 6661 q^{28} - 8758 q^{29} - 2608 q^{31} - 34871 q^{32} + 1828 q^{33} + 15989 q^{34} - 4678 q^{36} + 20632 q^{37} - 33786 q^{38} + 1352 q^{39} - 10998 q^{41} - 13603 q^{42} - 2032 q^{43} + 49790 q^{44} - 3408 q^{46} - 34260 q^{47} + 76223 q^{48} - 44571 q^{49} + 13468 q^{51} - 20449 q^{52} + 12570 q^{53} + 55595 q^{54} - 49287 q^{56} - 1716 q^{57} + 19126 q^{58} + 63948 q^{59} - 12754 q^{61} + 40340 q^{62} + 1648 q^{63} + 117393 q^{64} - 112354 q^{66} - 56132 q^{67} + 49175 q^{68} - 20112 q^{69} + 77580 q^{71} - 28794 q^{72} + 43026 q^{73} - 131519 q^{74} - 99638 q^{76} + 21052 q^{77} + 33631 q^{78} - 61872 q^{79} - 108221 q^{81} - 142260 q^{82} - 98092 q^{83} + 104723 q^{84} - 69897 q^{86} - 139072 q^{87} - 158010 q^{88} + 33694 q^{89} - 10140 q^{91} - 300864 q^{92} - 105392 q^{93} + 72843 q^{94} - 243641 q^{96} - 76334 q^{97} + 54636 q^{98} - 60332 q^{99}+O(q^{100}) \) 3 * q - 7 * q^2 - 8 * q^3 + 121 * q^4 - 199 * q^6 + 60 * q^7 - 327 * q^8 - 191 * q^9 + 556 * q^11 + 1091 * q^12 - 507 * q^13 - 793 * q^14 + 2785 * q^16 - 908 * q^17 - 976 * q^18 + 148 * q^19 + 1390 * q^21 + 3410 * q^22 - 3624 * q^23 - 13377 * q^24 + 1183 * q^26 + 4276 * q^27 + 6661 * q^28 - 8758 * q^29 - 2608 * q^31 - 34871 * q^32 + 1828 * q^33 + 15989 * q^34 - 4678 * q^36 + 20632 * q^37 - 33786 * q^38 + 1352 * q^39 - 10998 * q^41 - 13603 * q^42 - 2032 * q^43 + 49790 * q^44 - 3408 * q^46 - 34260 * q^47 + 76223 * q^48 - 44571 * q^49 + 13468 * q^51 - 20449 * q^52 + 12570 * q^53 + 55595 * q^54 - 49287 * q^56 - 1716 * q^57 + 19126 * q^58 + 63948 * q^59 - 12754 * q^61 + 40340 * q^62 + 1648 * q^63 + 117393 * q^64 - 112354 * q^66 - 56132 * q^67 + 49175 * q^68 - 20112 * q^69 + 77580 * q^71 - 28794 * q^72 + 43026 * q^73 - 131519 * q^74 - 99638 * q^76 + 21052 * q^77 + 33631 * q^78 - 61872 * q^79 - 108221 * q^81 - 142260 * q^82 - 98092 * q^83 + 104723 * q^84 - 69897 * q^86 - 139072 * q^87 - 158010 * q^88 + 33694 * q^89 - 10140 * q^91 - 300864 * q^92 - 105392 * q^93 + 72843 * q^94 - 243641 * q^96 - 76334 * q^97 + 54636 * q^98 - 60332 * 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 $

$2$	8.64858	1.52887	0.764433	−	0.644703i	$-0.223019\pi$
$2$	8.64858	1.52887	0.764433	+	0.644703i	$0.223019\pi$
$3$	−10.2870	−0.659909	−0.329954	−	0.943997i	$-0.607033\pi$
$3$	−10.2870	−0.659909	−0.329954	+	0.943997i	$0.607033\pi$
$4$	42.7979	1.33743
$5$	0	0
$5$	0	0
$6$	−88.9676	−1.00891
$7$	−2.86088	−0.0220676	−0.0110338	−	0.999939i	$-0.503512\pi$
$7$	−2.86088	−0.0220676	−0.0110338	+	0.999939i	$0.503512\pi$
$8$	93.3863	0.515892
$9$	−137.178	−0.564520
$10$	0	0
$11$	571.711	1.42461	0.712304	−	0.701871i	$-0.247652\pi$
$11$	571.711	1.42461	0.712304	+	0.701871i	$0.247652\pi$
$12$	−440.260	−0.882585
$13$	−169.000	−0.277350
$13$	−169.000	−0.277350
$14$	−24.7426	−0.0337384
$15$	0	0
$16$	−561.873	−0.548704
$17$	855.571	0.718015	0.359008	−	0.933335i	$-0.383115\pi$
$17$	855.571	0.718015	0.359008	+	0.933335i	$0.383115\pi$
$18$	−1186.40	−0.863076
$19$	−2355.90	−1.49718	−0.748589	−	0.663034i	$-0.769268\pi$
$19$	−2355.90	−1.49718	−0.748589	+	0.663034i	$0.769268\pi$
$20$	0	0
$21$	29.4298	0.0145626
$22$	4944.49	2.17804
$23$	−2509.66	−0.989227	−0.494613	−	0.869113i	$-0.664690\pi$
$23$	−2509.66	−0.989227	−0.494613	+	0.869113i	$0.664690\pi$
$24$	−960.662	−0.340441
$25$	0	0
$26$	−1461.61	−0.424031
$27$	3910.88	1.03244
$28$	−122.440	−0.0295140
$29$	−5497.50	−1.21387	−0.606933	−	0.794753i	$-0.707600\pi$
$29$	−5497.50	−1.21387	−0.606933	+	0.794753i	$0.707600\pi$
$30$	0	0
$31$	−144.924	−0.0270854	−0.0135427	−	0.999908i	$-0.504311\pi$
$31$	−144.924	−0.0270854	−0.0135427	+	0.999908i	$0.504311\pi$
$32$	−7847.77	−1.35479
$33$	−5881.17	−0.940111
$34$	7399.47	1.09775
$35$	0	0
$36$	−5870.95	−0.755009
$37$	515.975	0.0619618	0.0309809	−	0.999520i	$-0.490137\pi$
$37$	515.975	0.0619618	0.0309809	+	0.999520i	$0.490137\pi$
$38$	−20375.2	−2.28899
$39$	1738.50	0.183026
$40$	0	0
$41$	−13928.9	−1.29407	−0.647033	−	0.762462i	$-0.723991\pi$
$41$	−13928.9	−1.29407	−0.647033	+	0.762462i	$0.723991\pi$
$42$	254.526	0.0222643
$43$	−7753.58	−0.639486	−0.319743	−	0.947504i	$-0.603597\pi$
$43$	−7753.58	−0.639486	−0.319743	+	0.947504i	$0.603597\pi$
$44$	24468.0	1.90532
$45$	0	0
$46$	−21705.0	−1.51240
$47$	−8344.77	−0.551023	−0.275512	−	0.961298i	$-0.588847\pi$
$47$	−8344.77	−0.551023	−0.275512	+	0.961298i	$0.588847\pi$
$48$	5779.97	0.362095
$49$	−16798.8	−0.999513
$50$	0	0
$51$	−8801.22	−0.473825
$52$	−7232.84	−0.370937
$53$	5976.21	0.292238	0.146119	−	0.989267i	$-0.453322\pi$
$53$	5976.21	0.292238	0.146119	+	0.989267i	$0.453322\pi$
$54$	33823.6	1.57846
$55$	0	0
$56$	−267.168	−0.0113845
$57$	24235.1	0.988001
$58$	−47545.6	−1.85584
$59$	2110.84	0.0789451	0.0394726	−	0.999221i	$-0.487432\pi$
$59$	2110.84	0.0789451	0.0394726	+	0.999221i	$0.487432\pi$
$60$	0	0
$61$	−17394.2	−0.598522	−0.299261	−	0.954171i	$-0.596740\pi$
$61$	−17394.2	−0.598522	−0.299261	+	0.954171i	$0.596740\pi$
$62$	−1253.38	−0.0414099
$63$	392.452	0.0124576
$64$	−49892.1	−1.52259
$65$	0	0
$66$	−50863.8	−1.43730
$67$	3121.05	0.0849402	0.0424701	−	0.999098i	$-0.486477\pi$
$67$	3121.05	0.0849402	0.0424701	+	0.999098i	$0.486477\pi$
$68$	36616.6	0.960298
$69$	25816.8	0.652800
$70$	0	0
$71$	43323.3	1.01994	0.509971	−	0.860191i	$-0.329656\pi$
$71$	43323.3	1.01994	0.509971	+	0.860191i	$0.329656\pi$
$72$	−12810.6	−0.291231
$73$	−6808.31	−0.149531	−0.0747657	−	0.997201i	$-0.523821\pi$
$73$	−6808.31	−0.149531	−0.0747657	+	0.997201i	$0.523821\pi$
$74$	4462.45	0.0947314
$75$	0	0
$76$	−100828.	−2.00238
$77$	−1635.60	−0.0314377
$78$	15035.5	0.279822
$79$	−1280.80	−0.0230895	−0.0115447	−	0.999933i	$-0.503675\pi$
$79$	−1280.80	−0.0230895	−0.0115447	+	0.999933i	$0.503675\pi$
$80$	0	0
$81$	−6896.72	−0.116797
$82$	−120465.	−1.97846
$83$	−7148.44	−0.113898	−0.0569490	−	0.998377i	$-0.518137\pi$
$83$	−7148.44	−0.113898	−0.0569490	+	0.998377i	$0.518137\pi$
$84$	1259.53	0.0194765
$85$	0	0
$86$	−67057.5	−0.977690
$87$	56552.6	0.801041
$88$	53390.0	0.734943
$89$	107123.	1.43353	0.716765	−	0.697315i	$-0.245622\pi$
$89$	107123.	1.43353	0.716765	+	0.697315i	$0.245622\pi$
$90$	0	0
$91$	483.489	0.00612045
$92$	−107408.	−1.32303
$93$	1490.82	0.0178739
$94$	−72170.4	−0.842441
$95$	0	0
$96$	80729.7	0.894036
$97$	−42456.2	−0.458155	−0.229077	−	0.973408i	$-0.573571\pi$
$97$	−42456.2	−0.458155	−0.229077	+	0.973408i	$0.573571\pi$
$98$	−145286.	−1.52812
$99$	−78426.5	−0.804220
$100$	0	0
$101$	−87947.3	−0.857866	−0.428933	−	0.903336i	$-0.641110\pi$
$101$	−87947.3	−0.857866	−0.428933	+	0.903336i	$0.641110\pi$
$102$	−76118.1	−0.724415
$103$	−96885.8	−0.899844	−0.449922	−	0.893068i	$-0.648548\pi$
$103$	−96885.8	−0.899844	−0.449922	+	0.893068i	$0.648548\pi$
$104$	−15782.3	−0.143083
$105$	0	0
$106$	51685.7	0.446792
$107$	−106509.	−0.899346	−0.449673	−	0.893193i	$-0.648460\pi$
$107$	−106509.	−0.899346	−0.449673	+	0.893193i	$0.648460\pi$
$108$	167377.	1.38082
$109$	−142520.	−1.14897	−0.574485	−	0.818515i	$-0.694798\pi$
$109$	−142520.	−1.14897	−0.574485	+	0.818515i	$0.694798\pi$
$110$	0	0
$111$	−5307.81	−0.0408892
$112$	1607.45	0.0121086
$113$	209540.	1.54373	0.771864	−	0.635787i	$-0.219324\pi$
$113$	209540.	1.54373	0.771864	+	0.635787i	$0.219324\pi$
$114$	209599.	1.51052
$115$	0	0
$116$	−235282.	−1.62346
$117$	23183.2	0.156570
$118$	18255.8	0.120697
$119$	−2447.69	−0.0158449
$120$	0	0
$121$	165803.	1.02951
$122$	−150435.	−0.915061
$123$	143286.	0.853966
$124$	−6202.42	−0.0362249
$125$	0	0
$126$	3394.15	0.0190460
$127$	54468.2	0.299663	0.149832	−	0.988712i	$-0.452127\pi$
$127$	54468.2	0.299663	0.149832	+	0.988712i	$0.452127\pi$
$128$	−180367.	−0.973043
$129$	79760.8	0.422003
$130$	0	0
$131$	258252.	1.31482	0.657408	−	0.753535i	$-0.271653\pi$
$131$	258252.	1.31482	0.657408	+	0.753535i	$0.271653\pi$
$132$	−251702.	−1.25734
$133$	6739.97	0.0330391
$134$	26992.6	0.129862
$135$	0	0
$136$	79898.6	0.370418
$137$	−293754.	−1.33716	−0.668580	−	0.743641i	$-0.733097\pi$
$137$	−293754.	−1.33716	−0.668580	+	0.743641i	$0.733097\pi$
$138$	223279.	0.998044
$139$	180400.	0.791955	0.395977	−	0.918260i	$-0.370406\pi$
$139$	180400.	0.791955	0.395977	+	0.918260i	$0.370406\pi$
$140$	0	0
$141$	85842.4	0.363625
$142$	374685.	1.55936
$143$	−96619.2	−0.395115
$144$	77076.9	0.309755
$145$	0	0
$146$	−58882.2	−0.228614
$147$	172809.	0.659588
$148$	22082.6	0.0828698
$149$	516009.	1.90411	0.952054	−	0.305930i	$-0.0989675\pi$
$149$	516009.	1.90411	0.952054	+	0.305930i	$0.0989675\pi$
$150$	0	0
$151$	−333770.	−1.19126	−0.595628	−	0.803260i	$-0.703097\pi$
$151$	−333770.	−1.19126	−0.595628	+	0.803260i	$0.703097\pi$
$152$	−220009.	−0.772381
$153$	−117366.	−0.405334
$154$	−14145.6	−0.0480640
$155$	0	0
$156$	74404.0	0.244785
$157$	265860.	0.860804	0.430402	−	0.902637i	$-0.358372\pi$
$157$	265860.	0.860804	0.430402	+	0.902637i	$0.358372\pi$
$158$	−11077.1	−0.0353007
$159$	−61477.0	−0.192850
$160$	0	0
$161$	7179.86	0.0218299
$162$	−59646.8	−0.178566
$163$	231417.	0.682223	0.341112	−	0.940023i	$-0.389197\pi$
$163$	231417.	0.682223	0.341112	+	0.940023i	$0.389197\pi$
$164$	−596127.	−1.73073
$165$	0	0
$166$	−61823.8	−0.174135
$167$	656226.	1.82080	0.910400	−	0.413730i	$-0.135774\pi$
$167$	656226.	1.82080	0.910400	+	0.413730i	$0.135774\pi$
$168$	2748.34	0.00751273
$169$	28561.0	0.0769231
$170$	0	0
$171$	323179.	0.845187
$172$	−331837.	−0.855271
$173$	−45111.6	−0.114597	−0.0572985	−	0.998357i	$-0.518249\pi$
$173$	−45111.6	−0.114597	−0.0572985	+	0.998357i	$0.518249\pi$
$174$	489100.	1.22468
$175$	0	0
$176$	−321229.	−0.781688
$177$	−21714.1	−0.0520966
$178$	926460.	2.19168
$179$	521846.	1.21733	0.608667	−	0.793426i	$-0.291705\pi$
$179$	521846.	1.21733	0.608667	+	0.793426i	$0.291705\pi$
$180$	0	0
$181$	−122780.	−0.278569	−0.139284	−	0.990252i	$-0.544480\pi$
$181$	−122780.	−0.278569	−0.139284	+	0.990252i	$0.544480\pi$
$182$	4181.50	0.00935736
$183$	178934.	0.394970
$184$	−234368.	−0.510334
$185$	0	0
$186$	12893.5	0.0273268
$187$	489140.	1.02289
$188$	−357139.	−0.736957
$189$	−11188.6	−0.0227835
$190$	0	0
$191$	350208.	0.694613	0.347306	−	0.937752i	$-0.387096\pi$
$191$	350208.	0.694613	0.347306	+	0.937752i	$0.387096\pi$
$192$	513238.	1.00477
$193$	−876316.	−1.69343	−0.846716	−	0.532046i	$-0.821423\pi$
$193$	−876316.	−1.69343	−0.846716	+	0.532046i	$0.821423\pi$
$194$	−367186.	−0.700457
$195$	0	0
$196$	−718954.	−1.33678
$197$	−306582.	−0.562835	−0.281418	−	0.959585i	$-0.590805\pi$
$197$	−306582.	−0.562835	−0.281418	+	0.959585i	$0.590805\pi$
$198$	−678277.	−1.22954
$199$	−327849.	−0.586869	−0.293434	−	0.955979i	$-0.594798\pi$
$199$	−327849.	−0.586869	−0.293434	+	0.955979i	$0.594798\pi$
$200$	0	0
$201$	−32106.1	−0.0560528
$202$	−760619.	−1.31156
$203$	15727.7	0.0267871
$204$	−376674.	−0.633709
$205$	0	0
$206$	−837924.	−1.37574
$207$	344272.	0.558439
$208$	94956.6	0.152183
$209$	−1.34690e6	−2.13289
$210$	0	0
$211$	−509483.	−0.787814	−0.393907	−	0.919150i	$-0.628877\pi$
$211$	−509483.	−0.787814	−0.393907	+	0.919150i	$0.628877\pi$
$212$	255769.	0.390849
$213$	−445665.	−0.673069
$214$	−921151.	−1.37498
$215$	0	0
$216$	365223.	0.532627
$217$	414.610	0.000597709 0
$218$	−1.23259e6	−1.75662
$219$	70036.8	0.0986771
$220$	0	0
$221$	−144591.	−0.199142
$222$	−45905.0	−0.0625141
$223$	15061.4	0.0202816	0.0101408	−	0.999949i	$-0.496772\pi$
$223$	15061.4	0.0202816	0.0101408	+	0.999949i	$0.496772\pi$
$224$	22451.6	0.0298969
$225$	0	0
$226$	1.81222e6	2.36016
$227$	−273713.	−0.352558	−0.176279	−	0.984340i	$-0.556406\pi$
$227$	−273713.	−0.352558	−0.176279	+	0.984340i	$0.556406\pi$
$228$	1.03721e6	1.32139
$229$	743056.	0.936339	0.468169	−	0.883639i	$-0.344914\pi$
$229$	743056.	0.936339	0.468169	+	0.883639i	$0.344914\pi$
$230$	0	0
$231$	16825.4	0.0207460
$232$	−513392.	−0.626223
$233$	−1.12122e6	−1.35301	−0.676506	−	0.736437i	$-0.736507\pi$
$233$	−1.12122e6	−1.35301	−0.676506	+	0.736437i	$0.736507\pi$
$234$	200501.	0.239374
$235$	0	0
$236$	90339.5	0.105584
$237$	13175.6	0.0152369
$238$	−21169.0	−0.0242247
$239$	279838.	0.316892	0.158446	−	0.987368i	$-0.449352\pi$
$239$	279838.	0.316892	0.158446	+	0.987368i	$0.449352\pi$
$240$	0	0
$241$	816889.	0.905983	0.452992	−	0.891515i	$-0.350357\pi$
$241$	816889.	0.905983	0.452992	+	0.891515i	$0.350357\pi$
$242$	1.43396e6	1.57398
$243$	−879398.	−0.955366
$244$	−744436.	−0.800484
$245$	0	0
$246$	1.23922e6	1.30560
$247$	398148.	0.415242
$248$	−13533.9	−0.0139731
$249$	73535.7	0.0751623
$250$	0	0
$251$	−766697.	−0.768139	−0.384069	−	0.923304i	$-0.625478\pi$
$251$	−766697.	−0.768139	−0.384069	+	0.923304i	$0.625478\pi$
$252$	16796.1	0.0166612
$253$	−1.43480e6	−1.40926
$254$	471072.	0.458145
$255$	0	0
$256$	36629.4	0.0349325
$257$	1.82413e6	1.72276	0.861379	−	0.507963i	$-0.169601\pi$
$257$	1.82413e6	1.72276	0.861379	+	0.507963i	$0.169601\pi$
$258$	689817.	0.645186
$259$	−1476.14	−0.00136735
$260$	0	0
$261$	754139.	0.685252
$262$	2.23351e6	2.01018
$263$	294257.	0.262323	0.131162	−	0.991361i	$-0.458129\pi$
$263$	294257.	0.262323	0.131162	+	0.991361i	$0.458129\pi$
$264$	−549221.	−0.484995
$265$	0	0
$266$	58291.1	0.0505124
$267$	−1.10197e6	−0.945999
$268$	133574.	0.113602
$269$	289738.	0.244132	0.122066	−	0.992522i	$-0.461048\pi$
$269$	289738.	0.244132	0.122066	+	0.992522i	$0.461048\pi$
$270$	0	0
$271$	1.63179e6	1.34971	0.674855	−	0.737950i	$-0.264206\pi$
$271$	1.63179e6	1.34971	0.674855	+	0.737950i	$0.264206\pi$
$272$	−480722.	−0.393978
$273$	−4973.64	−0.00403894
$274$	−2.54056e6	−2.04434
$275$	0	0
$276$	1.10490e6	0.873076
$277$	−398868.	−0.312341	−0.156171	−	0.987730i	$-0.549915\pi$
$277$	−398868.	−0.312341	−0.156171	+	0.987730i	$0.549915\pi$
$278$	1.56021e6	1.21079
$279$	19880.4	0.0152902
$280$	0	0
$281$	274611.	0.207468	0.103734	−	0.994605i	$-0.466921\pi$
$281$	274611.	0.207468	0.103734	+	0.994605i	$0.466921\pi$
$282$	742414.	0.555934
$283$	794683.	0.589831	0.294916	−	0.955523i	$-0.404708\pi$
$283$	794683.	0.589831	0.294916	+	0.955523i	$0.404708\pi$
$284$	1.85415e6	1.36411
$285$	0	0
$286$	−835619.	−0.604078
$287$	39848.9	0.0285570
$288$	1.07654e6	0.764805
$289$	−687856.	−0.484454
$290$	0	0
$291$	436746.	0.302340
$292$	−291381.	−0.199988
$293$	1.55323e6	1.05698	0.528490	−	0.848940i	$-0.322759\pi$
$293$	1.55323e6	1.05698	0.528490	+	0.848940i	$0.322759\pi$
$294$	1.49455e6	1.00842
$295$	0	0
$296$	48185.0	0.0319656
$297$	2.23590e6	1.47082
$298$	4.46274e6	2.91113
$299$	424133.	0.274362
$300$	0	0
$301$	22182.1	0.0141119
$302$	−2.88664e6	−1.82127
$303$	904711.	0.566113
$304$	1.32372e6	0.821508
$305$	0	0
$306$	−1.01505e6	−0.619702
$307$	−2.07136e6	−1.25433	−0.627163	−	0.778888i	$-0.715784\pi$
$307$	−2.07136e6	−1.25433	−0.627163	+	0.778888i	$0.715784\pi$
$308$	−70000.2	−0.0420458
$309$	996660.	0.593815
$310$	0	0
$311$	−2.50827e6	−1.47053	−0.735263	−	0.677782i	$-0.762941\pi$
$311$	−2.50827e6	−1.47053	−0.735263	+	0.677782i	$0.762941\pi$
$312$	162352.	0.0944215
$313$	−832384.	−0.480245	−0.240123	−	0.970743i	$-0.577188\pi$
$313$	−832384.	−0.480245	−0.240123	+	0.970743i	$0.577188\pi$
$314$	2.29931e6	1.31606
$315$	0	0
$316$	−54815.6	−0.0308806
$317$	1.76537e6	0.986708	0.493354	−	0.869829i	$-0.335771\pi$
$317$	1.76537e6	0.986708	0.493354	+	0.869829i	$0.335771\pi$
$318$	−531689.	−0.294842
$319$	−3.14299e6	−1.72928
$320$	0	0
$321$	1.09565e6	0.593487
$322$	62095.5	0.0333750
$323$	−2.01564e6	−1.07500
$324$	−295165.	−0.156208
$325$	0	0
$326$	2.00143e6	1.04303
$327$	1.46609e6	0.758215
$328$	−1.30077e6	−0.667598
$329$	23873.4	0.0121598
$330$	0	0
$331$	−285068.	−0.143014	−0.0715070	−	0.997440i	$-0.522781\pi$
$331$	−285068.	−0.143014	−0.0715070	+	0.997440i	$0.522781\pi$
$332$	−305938.	−0.152331
$333$	−70780.6	−0.0349787
$334$	5.67542e6	2.78376
$335$	0	0
$336$	−16535.8	−0.00799057
$337$	−1.96932e6	−0.944584	−0.472292	−	0.881442i	$-0.656573\pi$
$337$	−1.96932e6	−0.944584	−0.472292	+	0.881442i	$0.656573\pi$
$338$	247012.	0.117605
$339$	−2.15553e6	−1.01872
$340$	0	0
$341$	−82854.5	−0.0385860
$342$	2.79504e6	1.29218
$343$	96142.4	0.0441245
$344$	−724079.	−0.329906
$345$	0	0
$346$	−390151.	−0.175204
$347$	−1.89753e6	−0.845988	−0.422994	−	0.906133i	$-0.639021\pi$
$347$	−1.89753e6	−0.845988	−0.422994	+	0.906133i	$0.639021\pi$
$348$	2.42033e6	1.07134
$349$	−365808.	−0.160764	−0.0803822	−	0.996764i	$-0.525614\pi$
$349$	−365808.	−0.160764	−0.0803822	+	0.996764i	$0.525614\pi$
$350$	0	0
$351$	−660939.	−0.286348
$352$	−4.48666e6	−1.93004
$353$	−1.56672e6	−0.669196	−0.334598	−	0.942361i	$-0.608601\pi$
$353$	−1.56672e6	−0.669196	−0.334598	+	0.942361i	$0.608601\pi$
$354$	−187796.	−0.0796487
$355$	0	0
$356$	4.58463e6	1.91725
$357$	25179.3	0.0104562
$358$	4.51322e6	1.86114
$359$	−4.03307e6	−1.65158	−0.825789	−	0.563979i	$-0.809270\pi$
$359$	−4.03307e6	−1.65158	−0.825789	+	0.563979i	$0.809270\pi$
$360$	0	0
$361$	3.07418e6	1.24154
$362$	−1.06187e6	−0.425894
$363$	−1.70561e6	−0.679380
$364$	20692.3	0.00818570
$365$	0	0
$366$	1.54752e6	0.603857
$367$	−683844.	−0.265028	−0.132514	−	0.991181i	$-0.542305\pi$
$367$	−683844.	−0.265028	−0.132514	+	0.991181i	$0.542305\pi$
$368$	1.41011e6	0.542793
$369$	1.91074e6	0.730527
$370$	0	0
$371$	−17097.2	−0.00644899
$372$	63804.1	0.0239051
$373$	3.09158e6	1.15056	0.575279	−	0.817957i	$-0.304893\pi$
$373$	3.09158e6	1.15056	0.575279	+	0.817957i	$0.304893\pi$
$374$	4.23036e6	1.56386
$375$	0	0
$376$	−779288.	−0.284268
$377$	929078.	0.336666
$378$	−96765.3	−0.0348329
$379$	−5.24600e6	−1.87599	−0.937995	−	0.346649i	$-0.887319\pi$
$379$	−5.24600e6	−1.87599	−0.937995	+	0.346649i	$0.887319\pi$
$380$	0	0
$381$	−560312.	−0.197751
$382$	3.02880e6	1.06197
$383$	−1.57009e6	−0.546926	−0.273463	−	0.961883i	$-0.588169\pi$
$383$	−1.57009e6	−0.546926	−0.273463	+	0.961883i	$0.588169\pi$
$384$	1.85543e6	0.642120
$385$	0	0
$386$	−7.57889e6	−2.58903
$387$	1.06362e6	0.361003
$388$	−1.81704e6	−0.612751
$389$	1.54482e6	0.517611	0.258805	−	0.965929i	$-0.416671\pi$
$389$	1.54482e6	0.517611	0.258805	+	0.965929i	$0.416671\pi$
$390$	0	0
$391$	−2.14719e6	−0.710280
$392$	−1.56878e6	−0.515640
$393$	−2.65663e6	−0.867659
$394$	−2.65150e6	−0.860500
$395$	0	0
$396$	−3.35649e6	−1.07559
$397$	−5.06711e6	−1.61356	−0.806778	−	0.590855i	$-0.798790\pi$
$397$	−5.06711e6	−1.61356	−0.806778	+	0.590855i	$0.798790\pi$
$398$	−2.83543e6	−0.897244
$399$	−69333.8	−0.0218028
$400$	0	0
$401$	−138120.	−0.0428939	−0.0214469	−	0.999770i	$-0.506827\pi$
$401$	−138120.	−0.0428939	−0.0214469	+	0.999770i	$0.506827\pi$
$402$	−277672.	−0.0856973
$403$	24492.1	0.00751213
$404$	−3.76396e6	−1.14734
$405$	0	0
$406$	136022.	0.0409539
$407$	294989.	0.0882713
$408$	−821914.	−0.244442
$409$	−4.13317e6	−1.22173	−0.610865	−	0.791735i	$-0.709178\pi$
$409$	−4.13317e6	−1.22173	−0.610865	+	0.791735i	$0.709178\pi$
$410$	0	0
$411$	3.02184e6	0.882403
$412$	−4.14651e6	−1.20348
$413$	−6038.87	−0.00174213
$414$	2.97746e6	0.853778
$415$	0	0
$416$	1.32627e6	0.375750
$417$	−1.85577e6	−0.522618
$418$	−1.16487e7	−3.26091
$419$	−2.96703e6	−0.825633	−0.412817	−	0.910814i	$-0.635455\pi$
$419$	−2.96703e6	−0.825633	−0.412817	+	0.910814i	$0.635455\pi$
$420$	0	0
$421$	−2.98125e6	−0.819773	−0.409887	−	0.912137i	$-0.634432\pi$
$421$	−2.98125e6	−0.819773	−0.409887	+	0.912137i	$0.634432\pi$
$422$	−4.40630e6	−1.20446
$423$	1.14472e6	0.311064
$424$	558096.	0.150763
$425$	0	0
$426$	−3.85437e6	−1.02903
$427$	49762.8	0.0132080
$428$	−4.55836e6	−1.20282
$429$	993918.	0.260740
$430$	0	0
$431$	−3.34790e6	−0.868119	−0.434059	−	0.900884i	$-0.642919\pi$
$431$	−3.34790e6	−0.868119	−0.434059	+	0.900884i	$0.642919\pi$
$432$	−2.19742e6	−0.566505
$433$	3.76782e6	0.965764	0.482882	−	0.875686i	$-0.339590\pi$
$433$	3.76782e6	0.965764	0.482882	+	0.875686i	$0.339590\pi$
$434$	3585.78	0.000913818 0
$435$	0	0
$436$	−6.09954e6	−1.53667
$437$	5.91252e6	1.48105
$438$	605719.	0.150864
$439$	5.63075e6	1.39446	0.697228	−	0.716849i	$-0.254416\pi$
$439$	5.63075e6	1.39446	0.697228	+	0.716849i	$0.254416\pi$
$440$	0	0
$441$	2.30444e6	0.564245
$442$	−1.25051e6	−0.304461
$443$	−3.69803e6	−0.895284	−0.447642	−	0.894213i	$-0.647736\pi$
$443$	−3.69803e6	−0.895284	−0.447642	+	0.894213i	$0.647736\pi$
$444$	−227163.	−0.0546865
$445$	0	0
$446$	130260.	0.0310079
$447$	−5.30816e6	−1.25654
$448$	142735.	0.0335998
$449$	−505514.	−0.118336	−0.0591681	−	0.998248i	$-0.518845\pi$
$449$	−505514.	−0.118336	−0.0591681	+	0.998248i	$0.518845\pi$
$450$	0	0
$451$	−7.96330e6	−1.84354
$452$	8.96787e6	2.06464
$453$	3.43348e6	0.786121
$454$	−2.36723e6	−0.539015
$455$	0	0
$456$	2.26323e6	0.509701
$457$	−783627.	−0.175517	−0.0877584	−	0.996142i	$-0.527970\pi$
$457$	−783627.	−0.175517	−0.0877584	+	0.996142i	$0.527970\pi$
$458$	6.42638e6	1.43154
$459$	3.34603e6	0.741308
$460$	0	0
$461$	4.64856e6	1.01875	0.509373	−	0.860546i	$-0.329877\pi$
$461$	4.64856e6	1.01875	0.509373	+	0.860546i	$0.329877\pi$
$462$	145515.	0.0317179
$463$	−2.64872e6	−0.574226	−0.287113	−	0.957897i	$-0.592696\pi$
$463$	−2.64872e6	−0.574226	−0.287113	+	0.957897i	$0.592696\pi$
$464$	3.08890e6	0.666053
$465$	0	0
$466$	−9.69698e6	−2.06858
$467$	2.42172e6	0.513845	0.256923	−	0.966432i	$-0.417291\pi$
$467$	2.42172e6	0.513845	0.256923	+	0.966432i	$0.417291\pi$
$468$	992190.	0.209402
$469$	−8928.96	−0.00187443
$470$	0	0
$471$	−2.73490e6	−0.568052
$472$	197124.	0.0407271
$473$	−4.43281e6	−0.911017
$474$	113950.	0.0232953
$475$	0	0
$476$	−104756.	−0.0211915
$477$	−819807.	−0.164974
$478$	2.42020e6	0.484486
$479$	5.58315e6	1.11184	0.555918	−	0.831237i	$-0.312367\pi$
$479$	5.58315e6	1.11184	0.555918	+	0.831237i	$0.312367\pi$
$480$	0	0
$481$	−87199.7	−0.0171851
$482$	7.06492e6	1.38513
$483$	−73858.9	−0.0144057
$484$	7.09602e6	1.37690
$485$	0	0
$486$	−7.60554e6	−1.46063
$487$	−7.25183e6	−1.38556	−0.692780	−	0.721149i	$-0.743614\pi$
$487$	−7.25183e6	−1.38556	−0.692780	+	0.721149i	$0.743614\pi$
$488$	−1.62438e6	−0.308773
$489$	−2.38058e6	−0.450205
$490$	0	0
$491$	4.17410e6	0.781373	0.390687	−	0.920524i	$-0.372238\pi$
$491$	4.17410e6	0.781373	0.390687	+	0.920524i	$0.372238\pi$
$492$	6.13233e6	1.14212
$493$	−4.70350e6	−0.871574
$494$	3.44341e6	0.634850
$495$	0	0
$496$	81428.7	0.0148619
$497$	−123943.	−0.0225077
$498$	635979.	0.114913
$499$	−7.83551e6	−1.40869	−0.704345	−	0.709857i	$-0.748759\pi$
$499$	−7.83551e6	−1.40869	−0.704345	+	0.709857i	$0.748759\pi$
$500$	0	0
$501$	−6.75057e6	−1.20156
$502$	−6.63084e6	−1.17438
$503$	3.72420e6	0.656315	0.328158	−	0.944623i	$-0.393572\pi$
$503$	3.72420e6	0.656315	0.328158	+	0.944623i	$0.393572\pi$
$504$	36649.6	0.00642678
$505$	0	0
$506$	−1.24090e7	−2.15457
$507$	−293806.	−0.0507622
$508$	2.33112e6	0.400780
$509$	−6.76675e6	−1.15767	−0.578836	−	0.815444i	$-0.696493\pi$
$509$	−6.76675e6	−1.15767	−0.578836	+	0.815444i	$0.696493\pi$
$510$	0	0
$511$	19477.8	0.00329980
$512$	6.08853e6	1.02645
$513$	−9.21366e6	−1.54575
$514$	1.57762e7	2.63387
$515$	0	0
$516$	3.41359e6	0.564401
$517$	−4.77080e6	−0.784992
$518$	−12766.5	−0.00209049
$519$	464062.	0.0756236
$520$	0	0
$521$	9.08380e6	1.46613	0.733066	−	0.680157i	$-0.238088\pi$
$521$	9.08380e6	1.46613	0.733066	+	0.680157i	$0.238088\pi$
$522$	6.52223e6	1.04766
$523$	1.09284e7	1.74703	0.873515	−	0.486796i	$-0.161835\pi$
$523$	1.09284e7	1.74703	0.873515	+	0.486796i	$0.161835\pi$
$524$	1.10526e7	1.75848
$525$	0	0
$526$	2.54490e6	0.401057
$527$	−123992.	−0.0194477
$528$	3.30447e6	0.515843
$529$	−137934.	−0.0214305
$530$	0	0
$531$	−289562.	−0.0445661
$532$	288456.	0.0441877
$533$	2.35398e6	0.358910
$534$	−9.53045e6	−1.44631
$535$	0	0
$536$	291463.	0.0438200
$537$	−5.36821e6	−0.803329
$538$	2.50582e6	0.373245
$539$	−9.60408e6	−1.42391
$540$	0	0
$541$	1.17853e6	0.173120	0.0865598	−	0.996247i	$-0.472413\pi$
$541$	1.17853e6	0.173120	0.0865598	+	0.996247i	$0.472413\pi$
$542$	1.41126e7	2.06353
$543$	1.26304e6	0.183830
$544$	−6.71432e6	−0.972758
$545$	0	0
$546$	−43014.9	−0.00617500
$547$	−9.57702e6	−1.36855	−0.684277	−	0.729222i	$-0.739882\pi$
$547$	−9.57702e6	−1.36855	−0.684277	+	0.729222i	$0.739882\pi$
$548$	−1.25721e7	−1.78836
$549$	2.38611e6	0.337878
$550$	0	0
$551$	1.29516e7	1.81737
$552$	2.41094e6	0.336774
$553$	3664.22	0.000509529 0
$554$	−3.44964e6	−0.477528
$555$	0	0
$556$	7.72075e6	1.05919
$557$	−2.46873e6	−0.337159	−0.168580	−	0.985688i	$-0.553918\pi$
$557$	−2.46873e6	−0.337159	−0.168580	+	0.985688i	$0.553918\pi$
$558$	171937.	0.0233767
$559$	1.31036e6	0.177362
$560$	0	0
$561$	−5.03176e6	−0.675014
$562$	2.37499e6	0.317191
$563$	−7.81681e6	−1.03934	−0.519671	−	0.854367i	$-0.673945\pi$
$563$	−7.81681e6	−1.03934	−0.519671	+	0.854367i	$0.673945\pi$
$564$	3.67387e6	0.486325
$565$	0	0
$566$	6.87288e6	0.901774
$567$	19730.7	0.00257742
$568$	4.04581e6	0.526180
$569$	−9.64303e6	−1.24863	−0.624314	−	0.781174i	$-0.714621\pi$
$569$	−9.64303e6	−1.24863	−0.624314	+	0.781174i	$0.714621\pi$
$570$	0	0
$571$	1.12378e7	1.44242	0.721211	−	0.692715i	$-0.243586\pi$
$571$	1.12378e7	1.44242	0.721211	+	0.692715i	$0.243586\pi$
$572$	−4.13510e6	−0.528440
$573$	−3.60258e6	−0.458381
$574$	344636.	0.0436598
$575$	0	0
$576$	6.84412e6	0.859530
$577$	5.44674e6	0.681078	0.340539	−	0.940230i	$-0.389390\pi$
$577$	5.44674e6	0.681078	0.340539	+	0.940230i	$0.389390\pi$
$578$	−5.94897e6	−0.740666
$579$	9.01463e6	1.11751
$580$	0	0
$581$	20450.9	0.00251346
$582$	3.77723e6	0.462238
$583$	3.41667e6	0.416324
$584$	−635803.	−0.0771420
$585$	0	0
$586$	1.34332e7	1.61598
$587$	−9.96240e6	−1.19335	−0.596676	−	0.802482i	$-0.703512\pi$
$587$	−9.96240e6	−1.19335	−0.596676	+	0.802482i	$0.703512\pi$
$588$	7.39585e6	0.882155
$589$	341426.	0.0405516
$590$	0	0
$591$	3.15380e6	0.371420
$592$	−289912.	−0.0339987
$593$	3.17929e6	0.371273	0.185636	−	0.982619i	$-0.440565\pi$
$593$	3.17929e6	0.371273	0.185636	+	0.982619i	$0.440565\pi$
$594$	1.93373e7	2.24869
$595$	0	0
$596$	2.20841e7	2.54662
$597$	3.37257e6	0.387280
$598$	3.66815e6	0.419463
$599$	−1.66017e7	−1.89054	−0.945271	−	0.326285i	$-0.894203\pi$
$599$	−1.66017e7	−1.89054	−0.945271	+	0.326285i	$0.894203\pi$
$600$	0	0
$601$	1.05771e6	0.119449	0.0597244	−	0.998215i	$-0.480978\pi$
$601$	1.05771e6	0.119449	0.0597244	+	0.998215i	$0.480978\pi$
$602$	191844.	0.0215753
$603$	−428141.	−0.0479505
$604$	−1.42847e7	−1.59323
$605$	0	0
$606$	7.82446e6	0.865512
$607$	−2.42026e6	−0.266619	−0.133309	−	0.991074i	$-0.542560\pi$
$607$	−2.42026e6	−0.266619	−0.133309	+	0.991074i	$0.542560\pi$
$608$	1.84886e7	2.02836
$609$	−161790.	−0.0176770
$610$	0	0
$611$	1.41027e6	0.152826
$612$	−5.02301e6	−0.542108
$613$	−110410.	−0.0118675	−0.00593373	−	0.999982i	$-0.501889\pi$
$613$	−110410.	−0.0118675	−0.00593373	+	0.999982i	$0.501889\pi$
$614$	−1.79144e7	−1.91770
$615$	0	0
$616$	−152743.	−0.0162184
$617$	1.06544e7	1.12672	0.563361	−	0.826211i	$-0.309508\pi$
$617$	1.06544e7	1.12672	0.563361	+	0.826211i	$0.309508\pi$
$618$	8.61969e6	0.907864
$619$	−1.30456e7	−1.36848	−0.684240	−	0.729256i	$-0.739866\pi$
$619$	−1.30456e7	−1.36848	−0.684240	+	0.729256i	$0.739866\pi$
$620$	0	0
$621$	−9.81499e6	−1.02132
$622$	−2.16929e7	−2.24824
$623$	−306466.	−0.0316346
$624$	−976815.	−0.100427
$625$	0	0
$626$	−7.19894e6	−0.734231
$627$	1.38555e7	1.40751
$628$	1.13783e7	1.15127
$629$	441453.	0.0444895
$630$	0	0
$631$	−1.53156e6	−0.153130	−0.0765651	−	0.997065i	$-0.524395\pi$
$631$	−1.53156e6	−0.153130	−0.0765651	+	0.997065i	$0.524395\pi$
$632$	−119609.	−0.0119117
$633$	5.24103e6	0.519885
$634$	1.52680e7	1.50855
$635$	0	0
$636$	−2.63109e6	−0.257924
$637$	2.83900e6	0.277215
$638$	−2.71824e7	−2.64384
$639$	−5.94302e6	−0.575778
$640$	0	0
$641$	8.09995e6	0.778641	0.389321	−	0.921102i	$-0.372710\pi$
$641$	8.09995e6	0.778641	0.389321	+	0.921102i	$0.372710\pi$
$642$	9.47585e6	0.907362
$643$	5.29175e6	0.504745	0.252373	−	0.967630i	$-0.418789\pi$
$643$	5.29175e6	0.504745	0.252373	+	0.967630i	$0.418789\pi$
$644$	307283.	0.0291960
$645$	0	0
$646$	−1.74324e7	−1.64353
$647$	−1.80626e7	−1.69637	−0.848185	−	0.529700i	$-0.822305\pi$
$647$	−1.80626e7	−1.69637	−0.848185	+	0.529700i	$0.822305\pi$
$648$	−644060.	−0.0602544
$649$	1.20679e6	0.112466
$650$	0	0
$651$	−4265.07	−0.000394434 0
$652$	9.90416e6	0.912428
$653$	7.10212e6	0.651786	0.325893	−	0.945407i	$-0.394335\pi$
$653$	7.10212e6	0.651786	0.325893	+	0.945407i	$0.394335\pi$
$654$	1.26796e7	1.15921
$655$	0	0
$656$	7.82627e6	0.710060
$657$	933954.	0.0844135
$658$	206471.	0.0185907
$659$	1.41430e7	1.26861	0.634303	−	0.773084i	$-0.281287\pi$
$659$	1.41430e7	1.26861	0.634303	+	0.773084i	$0.281287\pi$
$660$	0	0
$661$	−675807.	−0.0601615	−0.0300808	−	0.999547i	$-0.509576\pi$
$661$	−675807.	−0.0601615	−0.0300808	+	0.999547i	$0.509576\pi$
$662$	−2.46543e6	−0.218649
$663$	1.48741e6	0.131415
$664$	−667566.	−0.0587590
$665$	0	0
$666$	−612152.	−0.0534778
$667$	1.37969e7	1.20079
$668$	2.80851e7	2.43520
$669$	−154936.	−0.0133840
$670$	0	0
$671$	−9.94447e6	−0.852659
$672$	−230958.	−0.0197292
$673$	−2.66714e6	−0.226991	−0.113496	−	0.993539i	$-0.536205\pi$
$673$	−2.66714e6	−0.226991	−0.113496	+	0.993539i	$0.536205\pi$
$674$	−1.70318e7	−1.44414
$675$	0	0
$676$	1.22235e6	0.102880
$677$	1.20319e7	1.00893	0.504465	−	0.863432i	$-0.331690\pi$
$677$	1.20319e7	1.00893	0.504465	+	0.863432i	$0.331690\pi$
$678$	−1.86423e7	−1.55749
$679$	121462.	0.0101104
$680$	0	0
$681$	2.81568e6	0.232656
$682$	−716573.	−0.0589929
$683$	1.83758e7	1.50728	0.753640	−	0.657287i	$-0.228296\pi$
$683$	1.83758e7	1.50728	0.753640	+	0.657287i	$0.228296\pi$
$684$	1.38314e7	1.13038
$685$	0	0
$686$	831495.	0.0674604
$687$	−7.64379e6	−0.617898
$688$	4.35653e6	0.350889
$689$	−1.00998e6	−0.0810521
$690$	0	0
$691$	1.33412e7	1.06292	0.531459	−	0.847084i	$-0.321644\pi$
$691$	1.33412e7	1.06292	0.531459	+	0.847084i	$0.321644\pi$
$692$	−1.93068e6	−0.153266
$693$	224369.	0.0177472
$694$	−1.64109e7	−1.29340
$695$	0	0
$696$	5.28124e6	0.413250
$697$	−1.19171e7	−0.929159
$698$	−3.16372e6	−0.245787
$699$	1.15340e7	0.892865
$700$	0	0
$701$	2.51952e6	0.193652	0.0968262	−	0.995301i	$-0.469131\pi$
$701$	2.51952e6	0.193652	0.0968262	+	0.995301i	$0.469131\pi$
$702$	−5.71618e6	−0.437787
$703$	−1.21559e6	−0.0927679
$704$	−2.85239e7	−2.16909
$705$	0	0
$706$	−1.35499e7	−1.02311
$707$	251607.	0.0189310
$708$	−929319.	−0.0696757
$709$	2.51441e7	1.87854	0.939272	−	0.343174i	$-0.111502\pi$
$709$	2.51441e7	1.87854	0.939272	+	0.343174i	$0.111502\pi$
$710$	0	0
$711$	175698.	0.0130345
$712$	1.00038e7	0.739546
$713$	363709.	0.0267936
$714$	217765.	0.0159861
$715$	0	0
$716$	2.23339e7	1.62810
$717$	−2.87868e6	−0.209120
$718$	−3.48803e7	−2.52504
$719$	415865.	0.0300006	0.0150003	−	0.999887i	$-0.495225\pi$
$719$	415865.	0.0300006	0.0150003	+	0.999887i	$0.495225\pi$
$720$	0	0
$721$	277179.	0.0198574
$722$	2.65873e7	1.89815
$723$	−8.40330e6	−0.597866
$724$	−5.25474e6	−0.372567
$725$	0	0
$726$	−1.47511e7	−1.03868
$727$	1.53987e7	1.08056	0.540278	−	0.841486i	$-0.318319\pi$
$727$	1.53987e7	1.08056	0.540278	+	0.841486i	$0.318319\pi$
$728$	45151.3	0.00315749
$729$	1.07222e7	0.747251
$730$	0	0
$731$	−6.63374e6	−0.459161
$732$	7.65798e6	0.528246
$733$	1.82125e7	1.25202	0.626008	−	0.779817i	$-0.284688\pi$
$733$	1.82125e7	1.25202	0.626008	+	0.779817i	$0.284688\pi$
$734$	−5.91428e6	−0.405193
$735$	0	0
$736$	1.96953e7	1.34019
$737$	1.78434e6	0.121007
$738$	1.65252e7	1.11688
$739$	−1.88107e7	−1.26705	−0.633524	−	0.773723i	$-0.718392\pi$
$739$	−1.88107e7	−1.26705	−0.633524	+	0.773723i	$0.718392\pi$
$740$	0	0
$741$	−4.09573e6	−0.274022
$742$	−147867.	−0.00985964
$743$	−2.61292e7	−1.73642	−0.868209	−	0.496199i	$-0.834729\pi$
$743$	−2.61292e7	−1.73642	−0.868209	+	0.496199i	$0.834729\pi$
$744$	139223.	0.00922098
$745$	0	0
$746$	2.67378e7	1.75905
$747$	980611.	0.0642977
$748$	2.09341e7	1.36805
$749$	304710.	0.0198464
$750$	0	0
$751$	−1.90282e7	−1.23111	−0.615557	−	0.788092i	$-0.711069\pi$
$751$	−1.90282e7	−1.23111	−0.615557	+	0.788092i	$0.711069\pi$
$752$	4.68871e6	0.302349
$753$	7.88699e6	0.506902
$754$	8.03520e6	0.514717
$755$	0	0
$756$	−478847.	−0.0304714
$757$	1.91639e7	1.21547	0.607734	−	0.794140i	$-0.292079\pi$
$757$	1.91639e7	1.21547	0.607734	+	0.794140i	$0.292079\pi$
$758$	−4.53705e7	−2.86814
$759$	1.47598e7	0.929983
$760$	0	0
$761$	−468091.	−0.0293001	−0.0146500	−	0.999893i	$-0.504663\pi$
$761$	−468091.	−0.0293001	−0.0146500	+	0.999893i	$0.504663\pi$
$762$	−4.84590e6	−0.302334
$763$	407732.	0.0253550
$764$	1.49882e7	0.928999
$765$	0	0
$766$	−1.35791e7	−0.836177
$767$	−356732.	−0.0218954
$768$	−376805.	−0.0230523
$769$	−1.92729e7	−1.17525	−0.587627	−	0.809132i	$-0.699938\pi$
$769$	−1.92729e7	−1.17525	−0.587627	+	0.809132i	$0.699938\pi$
$770$	0	0
$771$	−1.87648e7	−1.13686
$772$	−3.75045e7	−2.26485
$773$	−2.42083e7	−1.45719	−0.728593	−	0.684947i	$-0.759825\pi$
$773$	−2.42083e7	−1.45719	−0.728593	+	0.684947i	$0.759825\pi$
$774$	9.19884e6	0.551926
$775$	0	0
$776$	−3.96483e6	−0.236358
$777$	15185.0	0.000902326 0
$778$	1.33605e7	0.791358
$779$	3.28151e7	1.93745
$780$	0	0
$781$	2.47684e7	1.45302
$782$	−1.85702e7	−1.08592
$783$	−2.15001e7	−1.25324
$784$	9.43881e6	0.548437
$785$	0	0
$786$	−2.29760e7	−1.32653
$787$	1.48087e7	0.852276	0.426138	−	0.904658i	$-0.359874\pi$
$787$	1.48087e7	0.852276	0.426138	+	0.904658i	$0.359874\pi$
$788$	−1.31211e7	−0.752755
$789$	−3.02701e6	−0.173110
$790$	0	0
$791$	−599470.	−0.0340664
$792$	−7.32396e6	−0.414890
$793$	2.93962e6	0.166000
$794$	−4.38233e7	−2.46691
$795$	0	0
$796$	−1.40312e7	−0.784898
$797$	2.90994e7	1.62270	0.811351	−	0.584560i	$-0.198733\pi$
$797$	2.90994e7	1.62270	0.811351	+	0.584560i	$0.198733\pi$
$798$	−599639.	−0.0333336
$799$	−7.13954e6	−0.395643
$800$	0	0
$801$	−1.46949e7	−0.809257
$802$	−1.19454e6	−0.0655790
$803$	−3.89239e6	−0.213023
$804$	−1.37407e6	−0.0749669
$805$	0	0
$806$	211822.	0.0114850
$807$	−2.98052e6	−0.161105
$808$	−8.21308e6	−0.442566
$809$	3.37792e7	1.81459	0.907295	−	0.420496i	$-0.138144\pi$
$809$	3.37792e7	1.81459	0.907295	+	0.420496i	$0.138144\pi$
$810$	0	0
$811$	−2.42986e7	−1.29727	−0.648633	−	0.761101i	$-0.724659\pi$
$811$	−2.42986e7	−1.29727	−0.648633	+	0.761101i	$0.724659\pi$
$812$	673113.	0.0358260
$813$	−1.67861e7	−0.890686
$814$	2.55123e6	0.134955
$815$	0	0
$816$	4.94517e6	0.259990
$817$	1.82667e7	0.957425
$818$	−3.57460e7	−1.86786
$819$	−66324.3	−0.00345512
$820$	0	0
$821$	−7.42442e6	−0.384419	−0.192209	−	0.981354i	$-0.561565\pi$
$821$	−7.42442e6	−0.384419	−0.192209	+	0.981354i	$0.561565\pi$
$822$	2.61346e7	1.34908
$823$	2.98540e7	1.53640	0.768198	−	0.640212i	$-0.221153\pi$
$823$	2.98540e7	1.53640	0.768198	+	0.640212i	$0.221153\pi$
$824$	−9.04781e6	−0.464222
$825$	0	0
$826$	−52227.6	−0.00266348
$827$	−2.47154e7	−1.25662	−0.628311	−	0.777962i	$-0.716253\pi$
$827$	−2.47154e7	−1.25662	−0.628311	+	0.777962i	$0.716253\pi$
$828$	1.47341e7	0.746875
$829$	−1.14800e7	−0.580169	−0.290084	−	0.957001i	$-0.593683\pi$
$829$	−1.14800e7	−0.580169	−0.290084	+	0.957001i	$0.593683\pi$
$830$	0	0
$831$	4.10314e6	0.206117
$832$	8.43176e6	0.422289
$833$	−1.43726e7	−0.717665
$834$	−1.60498e7	−0.799013
$835$	0	0
$836$	−5.76443e7	−2.85260
$837$	−566779.	−0.0279640
$838$	−2.56606e7	−1.26228
$839$	2.41188e7	1.18291	0.591454	−	0.806339i	$-0.298554\pi$
$839$	2.41188e7	1.18291	0.591454	+	0.806339i	$0.298554\pi$
$840$	0	0
$841$	9.71140e6	0.473469
$842$	−2.57836e7	−1.25332
$843$	−2.82491e6	−0.136910
$844$	−2.18048e7	−1.05365
$845$	0	0
$846$	9.90022e6	0.475575
$847$	−474343.	−0.0227187
$848$	−3.35787e6	−0.160352
$849$	−8.17487e6	−0.389235
$850$	0	0
$851$	−1.29492e6	−0.0612943
$852$	−1.90735e7	−0.900186
$853$	2.02681e6	0.0953764	0.0476882	−	0.998862i	$-0.484815\pi$
$853$	2.02681e6	0.0953764	0.0476882	+	0.998862i	$0.484815\pi$
$854$	430378.	0.0201932
$855$	0	0
$856$	−9.94649e6	−0.463965
$857$	−1.52859e7	−0.710950	−0.355475	−	0.934686i	$-0.615681\pi$
$857$	−1.52859e7	−0.710950	−0.355475	+	0.934686i	$0.615681\pi$
$858$	8.59598e6	0.398637
$859$	1.78567e7	0.825693	0.412846	−	0.910801i	$-0.364535\pi$
$859$	1.78567e7	0.825693	0.412846	+	0.910801i	$0.364535\pi$
$860$	0	0
$861$	−409924.	−0.0188450
$862$	−2.89546e7	−1.32724
$863$	1.12315e7	0.513347	0.256673	−	0.966498i	$-0.417374\pi$
$863$	1.12315e7	0.513347	0.256673	+	0.966498i	$0.417374\pi$
$864$	−3.06917e7	−1.39874
$865$	0	0
$866$	3.25863e7	1.47652
$867$	7.07595e6	0.319696
$868$	17744.4	0.000799397 0
$869$	−732249.	−0.0328934
$870$	0	0
$871$	−527457.	−0.0235582
$872$	−1.33094e7	−0.592744
$873$	5.82408e6	0.258638
$874$	5.11349e7	2.26433
$875$	0	0
$876$	2.99743e6	0.131974
$877$	−1.75233e6	−0.0769336	−0.0384668	−	0.999260i	$-0.512247\pi$
$877$	−1.75233e6	−0.0769336	−0.0384668	+	0.999260i	$0.512247\pi$
$878$	4.86980e7	2.13194
$879$	−1.59780e7	−0.697510
$880$	0	0
$881$	−1.04009e7	−0.451474	−0.225737	−	0.974188i	$-0.572479\pi$
$881$	−1.04009e7	−0.451474	−0.225737	+	0.974188i	$0.572479\pi$
$882$	1.99301e7	0.862656
$883$	−4.25645e7	−1.83715	−0.918577	−	0.395241i	$-0.870661\pi$
$883$	−4.25645e7	−1.83715	−0.918577	+	0.395241i	$0.870661\pi$
$884$	−6.18821e6	−0.266339
$885$	0	0
$886$	−3.19827e7	−1.36877
$887$	−201500.	−0.00859935	−0.00429968	−	0.999991i	$-0.501369\pi$
$887$	−201500.	−0.00859935	−0.00429968	+	0.999991i	$0.501369\pi$
$888$	−495677.	−0.0210944
$889$	−155827.	−0.00661285
$890$	0	0
$891$	−3.94294e6	−0.166389
$892$	644596.	0.0271253
$893$	1.96595e7	0.824980
$894$	−4.59081e7	−1.92108
$895$	0	0
$896$	516009.	0.0214727
$897$	−4.36304e6	−0.181054
$898$	−4.37198e6	−0.180920
$899$	796718.	0.0328780
$900$	0	0
$901$	5.11307e6	0.209831
$902$	−6.88712e7	−2.81852
$903$	−228186.	−0.00931259
$904$	1.95682e7	0.796397
$905$	0	0
$906$	2.96947e7	1.20187
$907$	−1.47930e7	−0.597088	−0.298544	−	0.954396i	$-0.596501\pi$
$907$	−1.47930e7	−0.597088	−0.298544	+	0.954396i	$0.596501\pi$
$908$	−1.17143e7	−0.471523
$909$	1.20645e7	0.484283
$910$	0	0
$911$	−3.50070e7	−1.39752	−0.698762	−	0.715354i	$-0.746265\pi$
$911$	−3.50070e7	−1.39752	−0.698762	+	0.715354i	$0.746265\pi$
$912$	−1.36170e7	−0.542121
$913$	−4.08684e6	−0.162260
$914$	−6.77726e6	−0.268342
$915$	0	0
$916$	3.18012e7	1.25229
$917$	−738828.	−0.0290148
$918$	2.89384e7	1.13336
$919$	4.24526e7	1.65812	0.829060	−	0.559160i	$-0.188876\pi$
$919$	4.24526e7	1.65812	0.829060	+	0.559160i	$0.188876\pi$
$920$	0	0
$921$	2.13080e7	0.827741
$922$	4.02034e7	1.55753
$923$	−7.32164e6	−0.282881
$924$	720090.	0.0277464
$925$	0	0
$926$	−2.29076e7	−0.877916
$927$	1.32906e7	0.507980
$928$	4.31431e7	1.64453
$929$	−3.95487e7	−1.50347	−0.751733	−	0.659468i	$-0.770782\pi$
$929$	−3.95487e7	−1.50347	−0.751733	+	0.659468i	$0.770782\pi$
$930$	0	0
$931$	3.95764e7	1.49645
$932$	−4.79859e7	−1.80957
$933$	2.58024e7	0.970413
$934$	2.09445e7	0.785601
$935$	0	0
$936$	2.16499e6	0.0807730
$937$	4.62850e7	1.72223	0.861116	−	0.508409i	$-0.169766\pi$
$937$	4.62850e7	1.72223	0.861116	+	0.508409i	$0.169766\pi$
$938$	−77222.8	−0.00286575
$939$	8.56270e6	0.316918
$940$	0	0
$941$	5.74465e6	0.211490	0.105745	−	0.994393i	$-0.466277\pi$
$941$	5.74465e6	0.211490	0.105745	+	0.994393i	$0.466277\pi$
$942$	−2.36530e7	−0.868477
$943$	3.49568e7	1.28013
$944$	−1.18602e6	−0.0433175
$945$	0	0
$946$	−3.83375e7	−1.39282
$947$	−5.15966e7	−1.86959	−0.934795	−	0.355187i	$-0.884417\pi$
$947$	−5.15966e7	−1.86959	−0.934795	+	0.355187i	$0.884417\pi$
$948$	563886.	0.0203784
$949$	1.15060e6	0.0414725
$950$	0	0
$951$	−1.81603e7	−0.651137
$952$	−228581.	−0.00817424
$953$	2.18333e7	0.778729	0.389365	−	0.921084i	$-0.372695\pi$
$953$	2.18333e7	0.778729	0.389365	+	0.921084i	$0.372695\pi$
$954$	−7.09017e6	−0.252223
$955$	0	0
$956$	1.19765e7	0.423822
$957$	3.23318e7	1.14117
$958$	4.82863e7	1.69985
$959$	840398.	0.0295079
$960$	0	0
$961$	−2.86081e7	−0.999266
$962$	−754154.	−0.0262738
$963$	1.46107e7	0.507699
$964$	3.49611e7	1.21169
$965$	0	0
$966$	−638774.	−0.0220244
$967$	7.30509e6	0.251223	0.125611	−	0.992080i	$-0.459911\pi$
$967$	7.30509e6	0.251223	0.125611	+	0.992080i	$0.459911\pi$
$968$	1.54837e7	0.531114
$969$	2.07348e7	0.709400
$970$	0	0
$971$	−1.62933e6	−0.0554576	−0.0277288	−	0.999615i	$-0.508827\pi$
$971$	−1.62933e6	−0.0554576	−0.0277288	+	0.999615i	$0.508827\pi$
$972$	−3.76364e7	−1.27774
$973$	−516105.	−0.0174765
$974$	−6.27180e7	−2.11834
$975$	0	0
$976$	9.77335e6	0.328412
$977$	2.55515e7	0.856407	0.428204	−	0.903682i	$-0.359147\pi$
$977$	2.55515e7	0.856407	0.428204	+	0.903682i	$0.359147\pi$
$978$	−2.05886e7	−0.688304
$979$	6.12433e7	2.04222
$980$	0	0
$981$	1.95506e7	0.648617
$982$	3.61000e7	1.19462
$983$	8.48095e6	0.279937	0.139969	−	0.990156i	$-0.455300\pi$
$983$	8.48095e6	0.279937	0.139969	+	0.990156i	$0.455300\pi$
$984$	1.33809e7	0.440554
$985$	0	0
$986$	−4.06786e7	−1.33252
$987$	−245585.	−0.00802434
$988$	1.70399e7	0.555359
$989$	1.94589e7	0.632597
$990$	0	0
$991$	−2.74483e7	−0.887833	−0.443916	−	0.896068i	$-0.646411\pi$
$991$	−2.74483e7	−0.887833	−0.443916	+	0.896068i	$0.646411\pi$
$992$	1.13733e6	0.0366949
$993$	2.93248e6	0.0943762
$994$	−1.07193e6	−0.0344113
$995$	0	0
$996$	3.14717e6	0.100525
$997$	2.26765e7	0.722501	0.361251	−	0.932469i	$-0.382350\pi$
$997$	2.26765e7	0.722501	0.361251	+	0.932469i	$0.382350\pi$
$998$	−6.77660e7	−2.15370
$999$	2.01792e6	0.0639719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.6.a.c.1.3		3
5.2	odd	4		325.6.b.c.274.5		6
5.3	odd	4		325.6.b.c.274.2		6
5.4	even	2		13.6.a.b.1.1	✓	3
15.14	odd	2		117.6.a.d.1.3		3
20.19	odd	2		208.6.a.j.1.2		3
35.34	odd	2		637.6.a.b.1.1		3
40.19	odd	2		832.6.a.t.1.2		3
40.29	even	2		832.6.a.s.1.2		3
65.34	odd	4		169.6.b.b.168.2		6
65.44	odd	4		169.6.b.b.168.5		6
65.64	even	2		169.6.a.b.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.6.a.b.1.1	✓	3	5.4	even	2
117.6.a.d.1.3		3	15.14	odd	2
169.6.a.b.1.3		3	65.64	even	2
169.6.b.b.168.2		6	65.34	odd	4
169.6.b.b.168.5		6	65.44	odd	4
208.6.a.j.1.2		3	20.19	odd	2
325.6.a.c.1.3		3	1.1	even	1	trivial
325.6.b.c.274.2		6	5.3	odd	4
325.6.b.c.274.5		6	5.2	odd	4
637.6.a.b.1.1		3	35.34	odd	2
832.6.a.s.1.2		3	40.29	even	2
832.6.a.t.1.2		3	40.19	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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q+8.64858 q^{2} -10.2870 q^{3} +42.7979 q^{4} -88.9676 q^{6} -2.86088 q^{7} +93.3863 q^{8} -137.178 q^{9} +O(q^{10})\)	\(q+8.64858 q^{2} -10.2870 q^{3} +42.7979 q^{4} -88.9676 q^{6} -2.86088 q^{7} +93.3863 q^{8} -137.178 q^{9} +571.711 q^{11} -440.260 q^{12} -169.000 q^{13} -24.7426 q^{14} -561.873 q^{16} +855.571 q^{17} -1186.40 q^{18} -2355.90 q^{19} +29.4298 q^{21} +4944.49 q^{22} -2509.66 q^{23} -960.662 q^{24} -1461.61 q^{26} +3910.88 q^{27} -122.440 q^{28} -5497.50 q^{29} -144.924 q^{31} -7847.77 q^{32} -5881.17 q^{33} +7399.47 q^{34} -5870.95 q^{36} +515.975 q^{37} -20375.2 q^{38} +1738.50 q^{39} -13928.9 q^{41} +254.526 q^{42} -7753.58 q^{43} +24468.0 q^{44} -21705.0 q^{46} -8344.77 q^{47} +5779.97 q^{48} -16798.8 q^{49} -8801.22 q^{51} -7232.84 q^{52} +5976.21 q^{53} +33823.6 q^{54} -267.168 q^{56} +24235.1 q^{57} -47545.6 q^{58} +2110.84 q^{59} -17394.2 q^{61} -1253.38 q^{62} +392.452 q^{63} -49892.1 q^{64} -50863.8 q^{66} +3121.05 q^{67} +36616.6 q^{68} +25816.8 q^{69} +43323.3 q^{71} -12810.6 q^{72} -6808.31 q^{73} +4462.45 q^{74} -100828. q^{76} -1635.60 q^{77} +15035.5 q^{78} -1280.80 q^{79} -6896.72 q^{81} -120465. q^{82} -7148.44 q^{83} +1259.53 q^{84} -67057.5 q^{86} +56552.6 q^{87} +53390.0 q^{88} +107123. q^{89} +483.489 q^{91} -107408. q^{92} +1490.82 q^{93} -72170.4 q^{94} +80729.7 q^{96} -42456.2 q^{97} -145286. q^{98} -78426.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 7 q^{2} - 8 q^{3} + 121 q^{4} - 199 q^{6} + 60 q^{7} - 327 q^{8} - 191 q^{9}+O(q^{10}) \) 3 * q - 7 * q^2 - 8 * q^3 + 121 * q^4 - 199 * q^6 + 60 * q^7 - 327 * q^8 - 191 * q^9	\( 3 q - 7 q^{2} - 8 q^{3} + 121 q^{4} - 199 q^{6} + 60 q^{7} - 327 q^{8} - 191 q^{9} + 556 q^{11} + 1091 q^{12} - 507 q^{13} - 793 q^{14} + 2785 q^{16} - 908 q^{17} - 976 q^{18} + 148 q^{19} + 1390 q^{21} + 3410 q^{22} - 3624 q^{23} - 13377 q^{24} + 1183 q^{26} + 4276 q^{27} + 6661 q^{28} - 8758 q^{29} - 2608 q^{31} - 34871 q^{32} + 1828 q^{33} + 15989 q^{34} - 4678 q^{36} + 20632 q^{37} - 33786 q^{38} + 1352 q^{39} - 10998 q^{41} - 13603 q^{42} - 2032 q^{43} + 49790 q^{44} - 3408 q^{46} - 34260 q^{47} + 76223 q^{48} - 44571 q^{49} + 13468 q^{51} - 20449 q^{52} + 12570 q^{53} + 55595 q^{54} - 49287 q^{56} - 1716 q^{57} + 19126 q^{58} + 63948 q^{59} - 12754 q^{61} + 40340 q^{62} + 1648 q^{63} + 117393 q^{64} - 112354 q^{66} - 56132 q^{67} + 49175 q^{68} - 20112 q^{69} + 77580 q^{71} - 28794 q^{72} + 43026 q^{73} - 131519 q^{74} - 99638 q^{76} + 21052 q^{77} + 33631 q^{78} - 61872 q^{79} - 108221 q^{81} - 142260 q^{82} - 98092 q^{83} + 104723 q^{84} - 69897 q^{86} - 139072 q^{87} - 158010 q^{88} + 33694 q^{89} - 10140 q^{91} - 300864 q^{92} - 105392 q^{93} + 72843 q^{94} - 243641 q^{96} - 76334 q^{97} + 54636 q^{98} - 60332 q^{99}+O(q^{100}) \) 3 * q - 7 * q^2 - 8 * q^3 + 121 * q^4 - 199 * q^6 + 60 * q^7 - 327 * q^8 - 191 * q^9 + 556 * q^11 + 1091 * q^12 - 507 * q^13 - 793 * q^14 + 2785 * q^16 - 908 * q^17 - 976 * q^18 + 148 * q^19 + 1390 * q^21 + 3410 * q^22 - 3624 * q^23 - 13377 * q^24 + 1183 * q^26 + 4276 * q^27 + 6661 * q^28 - 8758 * q^29 - 2608 * q^31 - 34871 * q^32 + 1828 * q^33 + 15989 * q^34 - 4678 * q^36 + 20632 * q^37 - 33786 * q^38 + 1352 * q^39 - 10998 * q^41 - 13603 * q^42 - 2032 * q^43 + 49790 * q^44 - 3408 * q^46 - 34260 * q^47 + 76223 * q^48 - 44571 * q^49 + 13468 * q^51 - 20449 * q^52 + 12570 * q^53 + 55595 * q^54 - 49287 * q^56 - 1716 * q^57 + 19126 * q^58 + 63948 * q^59 - 12754 * q^61 + 40340 * q^62 + 1648 * q^63 + 117393 * q^64 - 112354 * q^66 - 56132 * q^67 + 49175 * q^68 - 20112 * q^69 + 77580 * q^71 - 28794 * q^72 + 43026 * q^73 - 131519 * q^74 - 99638 * q^76 + 21052 * q^77 + 33631 * q^78 - 61872 * q^79 - 108221 * q^81 - 142260 * q^82 - 98092 * q^83 + 104723 * q^84 - 69897 * q^86 - 139072 * q^87 - 158010 * q^88 + 33694 * q^89 - 10140 * q^91 - 300864 * q^92 - 105392 * q^93 + 72843 * q^94 - 243641 * q^96 - 76334 * q^97 + 54636 * q^98 - 60332 * q^99

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