LMFDB - Embedded newform 245.6.a.l.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,6,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, 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("245.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	245.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:	$39.2940358542$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 246 x^{8} - 192 x^{7} + 20336 x^{6} + 25380 x^{5} - 639206 x^{4} - 722920 x^{3} + \cdots - 22888100 $ x^10 - 246x^8 - 192x^7 + 20336x^6 + 25380x^5 - 639206x^4 - 722920x^3 + 7583055x^2 + 5935300x - 22888100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 7^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-6.46320$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.46320 q^{2} +9.93685 q^{3} +23.6994 q^{4} -25.0000 q^{5} +74.1607 q^{6} -61.9494 q^{8} -144.259 q^{9} +O(q^{10})$	\(q+7.46320 q^{2} +9.93685 q^{3} +23.6994 q^{4} -25.0000 q^{5} +74.1607 q^{6} -61.9494 q^{8} -144.259 q^{9} -186.580 q^{10} +239.532 q^{11} +235.497 q^{12} -1145.33 q^{13} -248.421 q^{15} -1220.72 q^{16} -37.5365 q^{17} -1076.63 q^{18} -421.405 q^{19} -592.484 q^{20} +1787.68 q^{22} -118.217 q^{23} -615.582 q^{24} +625.000 q^{25} -8547.84 q^{26} -3848.13 q^{27} +5652.55 q^{29} -1854.02 q^{30} -6290.43 q^{31} -7128.10 q^{32} +2380.19 q^{33} -280.142 q^{34} -3418.85 q^{36} +2166.65 q^{37} -3145.03 q^{38} -11381.0 q^{39} +1548.73 q^{40} -11004.3 q^{41} +11701.4 q^{43} +5676.75 q^{44} +3606.48 q^{45} -882.276 q^{46} +5785.82 q^{47} -12130.1 q^{48} +4664.50 q^{50} -372.994 q^{51} -27143.6 q^{52} -30038.4 q^{53} -28719.4 q^{54} -5988.30 q^{55} -4187.43 q^{57} +42186.1 q^{58} -25256.5 q^{59} -5887.42 q^{60} +14426.1 q^{61} -46946.8 q^{62} -14135.4 q^{64} +28633.3 q^{65} +17763.9 q^{66} +51931.5 q^{67} -889.591 q^{68} -1174.70 q^{69} -48578.4 q^{71} +8936.76 q^{72} -5366.41 q^{73} +16170.1 q^{74} +6210.53 q^{75} -9987.02 q^{76} -84938.6 q^{78} +76732.2 q^{79} +30518.0 q^{80} -3183.39 q^{81} -82127.6 q^{82} +33446.1 q^{83} +938.412 q^{85} +87329.6 q^{86} +56168.6 q^{87} -14838.9 q^{88} -95387.5 q^{89} +26915.8 q^{90} -2801.66 q^{92} -62507.1 q^{93} +43180.8 q^{94} +10535.1 q^{95} -70830.8 q^{96} -124843. q^{97} -34554.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - 58 q^{3} + 182 q^{4} - 250 q^{5} - 144 q^{6} + 270 q^{8} + 700 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - 58 * q^3 + 182 * q^4 - 250 * q^5 - 144 * q^6 + 270 * q^8 + 700 * q^9	\( 10 q + 10 q^{2} - 58 q^{3} + 182 q^{4} - 250 q^{5} - 144 q^{6} + 270 q^{8} + 700 q^{9} - 250 q^{10} + 794 q^{11} - 2560 q^{12} - 474 q^{13} + 1450 q^{15} + 2394 q^{16} - 802 q^{17} + 3702 q^{18} - 7292 q^{19} - 4550 q^{20} + 3948 q^{22} + 3708 q^{23} - 2092 q^{24} + 6250 q^{25} - 6576 q^{26} - 11818 q^{27} - 8866 q^{29} + 3600 q^{30} - 13292 q^{31} + 2590 q^{32} - 9854 q^{33} - 44468 q^{34} - 10690 q^{36} + 16124 q^{37} - 2180 q^{38} - 24982 q^{39} - 6750 q^{40} - 34836 q^{41} - 28604 q^{43} - 31120 q^{44} - 17500 q^{45} - 39732 q^{46} - 18106 q^{47} - 101788 q^{48} + 6250 q^{50} + 31602 q^{51} + 22480 q^{52} + 36440 q^{53} - 80836 q^{54} - 19850 q^{55} + 126988 q^{57} - 100356 q^{58} - 18644 q^{59} + 64000 q^{60} - 68120 q^{61} - 181052 q^{62} - 59358 q^{64} + 11850 q^{65} - 157780 q^{66} + 92328 q^{67} - 288540 q^{68} - 170888 q^{69} + 5044 q^{71} - 61654 q^{72} - 170160 q^{73} - 216584 q^{74} - 36250 q^{75} - 505180 q^{76} - 158008 q^{78} + 26442 q^{79} - 59850 q^{80} - 56314 q^{81} - 353948 q^{82} - 353360 q^{83} + 20050 q^{85} - 52940 q^{86} + 3190 q^{87} - 114916 q^{88} - 90704 q^{89} - 92550 q^{90} + 183520 q^{92} + 188560 q^{93} + 121388 q^{94} + 182300 q^{95} - 442220 q^{96} - 236382 q^{97} + 109024 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 58 * q^3 + 182 * q^4 - 250 * q^5 - 144 * q^6 + 270 * q^8 + 700 * q^9 - 250 * q^10 + 794 * q^11 - 2560 * q^12 - 474 * q^13 + 1450 * q^15 + 2394 * q^16 - 802 * q^17 + 3702 * q^18 - 7292 * q^19 - 4550 * q^20 + 3948 * q^22 + 3708 * q^23 - 2092 * q^24 + 6250 * q^25 - 6576 * q^26 - 11818 * q^27 - 8866 * q^29 + 3600 * q^30 - 13292 * q^31 + 2590 * q^32 - 9854 * q^33 - 44468 * q^34 - 10690 * q^36 + 16124 * q^37 - 2180 * q^38 - 24982 * q^39 - 6750 * q^40 - 34836 * q^41 - 28604 * q^43 - 31120 * q^44 - 17500 * q^45 - 39732 * q^46 - 18106 * q^47 - 101788 * q^48 + 6250 * q^50 + 31602 * q^51 + 22480 * q^52 + 36440 * q^53 - 80836 * q^54 - 19850 * q^55 + 126988 * q^57 - 100356 * q^58 - 18644 * q^59 + 64000 * q^60 - 68120 * q^61 - 181052 * q^62 - 59358 * q^64 + 11850 * q^65 - 157780 * q^66 + 92328 * q^67 - 288540 * q^68 - 170888 * q^69 + 5044 * q^71 - 61654 * q^72 - 170160 * q^73 - 216584 * q^74 - 36250 * q^75 - 505180 * q^76 - 158008 * q^78 + 26442 * q^79 - 59850 * q^80 - 56314 * q^81 - 353948 * q^82 - 353360 * q^83 + 20050 * q^85 - 52940 * q^86 + 3190 * q^87 - 114916 * q^88 - 90704 * q^89 - 92550 * q^90 + 183520 * q^92 + 188560 * q^93 + 121388 * q^94 + 182300 * q^95 - 442220 * q^96 - 236382 * q^97 + 109024 * 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 $

$2$	7.46320	1.31932	0.659660	−	0.751564i	$-0.270700\pi$
$2$	7.46320	1.31932	0.659660	+	0.751564i	$0.270700\pi$
$3$	9.93685	0.637449	0.318725	−	0.947847i	$-0.396745\pi$
$3$	9.93685	0.637449	0.318725	+	0.947847i	$0.396745\pi$
$4$	23.6994	0.740605
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	74.1607	0.840999
$7$	0	0
$7$	0	0
$8$	−61.9494	−0.342225
$9$	−144.259	−0.593659
$10$	−186.580	−0.590018
$11$	239.532	0.596873	0.298436	−	0.954430i	$-0.403535\pi$
$11$	239.532	0.596873	0.298436	+	0.954430i	$0.403535\pi$
$12$	235.497	0.472098
$13$	−1145.33	−1.87963	−0.939816	−	0.341681i	$-0.889004\pi$
$13$	−1145.33	−1.87963	−0.939816	+	0.341681i	$0.889004\pi$
$14$	0	0
$15$	−248.421	−0.285076
$16$	−1220.72	−1.19211
$17$	−37.5365	−0.0315015	−0.0157508	−	0.999876i	$-0.505014\pi$
$17$	−37.5365	−0.0315015	−0.0157508	+	0.999876i	$0.505014\pi$
$18$	−1076.63	−0.783226
$19$	−421.405	−0.267803	−0.133901	−	0.990995i	$-0.542751\pi$
$19$	−421.405	−0.267803	−0.133901	+	0.990995i	$0.542751\pi$
$20$	−592.484	−0.331209
$21$	0	0
$22$	1787.68	0.787466
$23$	−118.217	−0.0465972	−0.0232986	−	0.999729i	$-0.507417\pi$
$23$	−118.217	−0.0465972	−0.0232986	+	0.999729i	$0.507417\pi$
$24$	−615.582	−0.218151
$25$	625.000	0.200000
$26$	−8547.84	−2.47984
$27$	−3848.13	−1.01588
$28$	0	0
$29$	5652.55	1.24810	0.624050	−	0.781384i	$-0.285486\pi$
$29$	5652.55	1.24810	0.624050	+	0.781384i	$0.285486\pi$
$30$	−1854.02	−0.376106
$31$	−6290.43	−1.17565	−0.587823	−	0.808990i	$-0.700015\pi$
$31$	−6290.43	−1.17565	−0.587823	+	0.808990i	$0.700015\pi$
$32$	−7128.10	−1.23055
$33$	2380.19	0.380476
$34$	−280.142	−0.0415606
$35$	0	0
$36$	−3418.85	−0.439666
$37$	2166.65	0.260186	0.130093	−	0.991502i	$-0.458472\pi$
$37$	2166.65	0.260186	0.130093	+	0.991502i	$0.458472\pi$
$38$	−3145.03	−0.353318
$39$	−11381.0	−1.19817
$40$	1548.73	0.153048
$41$	−11004.3	−1.02236	−0.511181	−	0.859473i	$-0.670792\pi$
$41$	−11004.3	−1.02236	−0.511181	+	0.859473i	$0.670792\pi$
$42$	0	0
$43$	11701.4	0.965084	0.482542	−	0.875873i	$-0.339714\pi$
$43$	11701.4	0.965084	0.482542	+	0.875873i	$0.339714\pi$
$44$	5676.75	0.442047
$45$	3606.48	0.265492
$46$	−882.276	−0.0614766
$47$	5785.82	0.382050	0.191025	−	0.981585i	$-0.438819\pi$
$47$	5785.82	0.382050	0.191025	+	0.981585i	$0.438819\pi$
$48$	−12130.1	−0.759909
$49$	0	0
$50$	4664.50	0.263864
$51$	−372.994	−0.0200806
$52$	−27143.6	−1.39206
$53$	−30038.4	−1.46888	−0.734442	−	0.678671i	$-0.762556\pi$
$53$	−30038.4	−1.46888	−0.734442	+	0.678671i	$0.762556\pi$
$54$	−28719.4	−1.34027
$55$	−5988.30	−0.266930
$56$	0	0
$57$	−4187.43	−0.170711
$58$	42186.1	1.64664
$59$	−25256.5	−0.944591	−0.472296	−	0.881440i	$-0.656574\pi$
$59$	−25256.5	−0.944591	−0.472296	+	0.881440i	$0.656574\pi$
$60$	−5887.42	−0.211129
$61$	14426.1	0.496391	0.248196	−	0.968710i	$-0.420162\pi$
$61$	14426.1	0.496391	0.248196	+	0.968710i	$0.420162\pi$
$62$	−46946.8	−1.55105
$63$	0	0
$64$	−14135.4	−0.431378
$65$	28633.3	0.840597
$66$	17763.9	0.501970
$67$	51931.5	1.41333	0.706666	−	0.707547i	$-0.250198\pi$
$67$	51931.5	1.41333	0.706666	+	0.707547i	$0.250198\pi$
$68$	−889.591	−0.0233302
$69$	−1174.70	−0.0297033
$70$	0	0
$71$	−48578.4	−1.14366	−0.571831	−	0.820371i	$-0.693767\pi$
$71$	−48578.4	−1.14366	−0.571831	+	0.820371i	$0.693767\pi$
$72$	8936.76	0.203165
$73$	−5366.41	−0.117863	−0.0589314	−	0.998262i	$-0.518769\pi$
$73$	−5366.41	−0.117863	−0.0589314	+	0.998262i	$0.518769\pi$
$74$	16170.1	0.343268
$75$	6210.53	0.127490
$76$	−9987.02	−0.198336
$77$	0	0
$78$	−84938.6	−1.58077
$79$	76732.2	1.38328	0.691640	−	0.722242i	$-0.256888\pi$
$79$	76732.2	1.38328	0.691640	+	0.722242i	$0.256888\pi$
$80$	30518.0	0.533127
$81$	−3183.39	−0.0539110
$82$	−82127.6	−1.34882
$83$	33446.1	0.532906	0.266453	−	0.963848i	$-0.414148\pi$
$83$	33446.1	0.532906	0.266453	+	0.963848i	$0.414148\pi$
$84$	0	0
$85$	938.412	0.0140879
$86$	87329.6	1.27325
$87$	56168.6	0.795601
$88$	−14838.9	−0.204265
$89$	−95387.5	−1.27649	−0.638243	−	0.769835i	$-0.720339\pi$
$89$	−95387.5	−1.27649	−0.638243	+	0.769835i	$0.720339\pi$
$90$	26915.8	0.350269
$91$	0	0
$92$	−2801.66	−0.0345101
$93$	−62507.1	−0.749414
$94$	43180.8	0.504046
$95$	10535.1	0.119765
$96$	−70830.8	−0.784412
$97$	−124843.	−1.34721	−0.673605	−	0.739091i	$-0.735255\pi$
$97$	−124843.	−1.34721	−0.673605	+	0.739091i	$0.735255\pi$
$98$	0	0
$99$	−34554.7	−0.354339
$100$	14812.1	0.148121
$101$	81191.1	0.791963	0.395981	−	0.918259i	$-0.370404\pi$
$101$	81191.1	0.791963	0.395981	+	0.918259i	$0.370404\pi$
$102$	−2783.73	−0.0264927
$103$	167394.	1.55470	0.777352	−	0.629066i	$-0.216562\pi$
$103$	167394.	1.55470	0.777352	+	0.629066i	$0.216562\pi$
$104$	70952.6	0.643257
$105$	0	0
$106$	−224183.	−1.93793
$107$	104784.	0.884783	0.442392	−	0.896822i	$-0.354130\pi$
$107$	104784.	0.884783	0.442392	+	0.896822i	$0.354130\pi$
$108$	−91198.3	−0.752363
$109$	−185424.	−1.49485	−0.747427	−	0.664344i	$-0.768711\pi$
$109$	−185424.	−1.49485	−0.747427	+	0.664344i	$0.768711\pi$
$110$	−44691.9	−0.352166
$111$	21529.6	0.165855
$112$	0	0
$113$	−181328.	−1.33588	−0.667941	−	0.744214i	$-0.732824\pi$
$113$	−181328.	−1.33588	−0.667941	+	0.744214i	$0.732824\pi$
$114$	−31251.7	−0.225222
$115$	2955.42	0.0208389
$116$	133962.	0.924349
$117$	165224.	1.11586
$118$	−188495.	−1.24622
$119$	0	0
$120$	15389.5	0.0975601
$121$	−103675.	−0.643743
$122$	107665.	0.654899
$123$	−109348.	−0.651703
$124$	−149079.	−0.870689
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	274385.	1.50956	0.754781	−	0.655977i	$-0.227743\pi$
$127$	274385.	1.50956	0.754781	+	0.655977i	$0.227743\pi$
$128$	122604.	0.661423
$129$	116275.	0.615192
$130$	213696.	1.10902
$131$	206164.	1.04963	0.524813	−	0.851217i	$-0.324135\pi$
$131$	206164.	1.04963	0.524813	+	0.851217i	$0.324135\pi$
$132$	56409.0	0.281782
$133$	0	0
$134$	387575.	1.86464
$135$	96203.4	0.454314
$136$	2325.36	0.0107806
$137$	−350675.	−1.59626	−0.798130	−	0.602485i	$-0.794177\pi$
$137$	−350675.	−1.59626	−0.798130	+	0.602485i	$0.794177\pi$
$138$	−8767.04	−0.0391882
$139$	201239.	0.883435	0.441717	−	0.897154i	$-0.354369\pi$
$139$	201239.	0.883435	0.441717	+	0.897154i	$0.354369\pi$
$140$	0	0
$141$	57492.8	0.243538
$142$	−362551.	−1.50886
$143$	−274344.	−1.12190
$144$	176100.	0.707706
$145$	−141314.	−0.558167
$146$	−40050.6	−0.155499
$147$	0	0
$148$	51348.1	0.192695
$149$	169621.	0.625913	0.312956	−	0.949768i	$-0.398681\pi$
$149$	169621.	0.625913	0.312956	+	0.949768i	$0.398681\pi$
$150$	46350.4	0.168200
$151$	−274003.	−0.977943	−0.488972	−	0.872300i	$-0.662628\pi$
$151$	−274003.	−0.977943	−0.488972	+	0.872300i	$0.662628\pi$
$152$	26105.7	0.0916489
$153$	5414.98	0.0187011
$154$	0	0
$155$	157261.	0.525765
$156$	−269722.	−0.887371
$157$	−436835.	−1.41439	−0.707193	−	0.707020i	$-0.750039\pi$
$157$	−436835.	−1.41439	−0.707193	+	0.707020i	$0.750039\pi$
$158$	572668.	1.82499
$159$	−298487.	−0.936339
$160$	178202.	0.550318
$161$	0	0
$162$	−23758.3	−0.0711258
$163$	−615567.	−1.81470	−0.907352	−	0.420371i	$-0.861900\pi$
$163$	−615567.	−1.81470	−0.907352	+	0.420371i	$0.861900\pi$
$164$	−260796.	−0.757166
$165$	−59504.8	−0.170154
$166$	249615.	0.703073
$167$	−315224.	−0.874637	−0.437319	−	0.899307i	$-0.644072\pi$
$167$	−315224.	−0.874637	−0.437319	+	0.899307i	$0.644072\pi$
$168$	0	0
$169$	940492.	2.53302
$170$	7003.56	0.0185865
$171$	60791.4	0.158983
$172$	277315.	0.714746
$173$	526575.	1.33766	0.668829	−	0.743417i	$-0.266796\pi$
$173$	526575.	1.33766	0.668829	+	0.743417i	$0.266796\pi$
$174$	419197.	1.04965
$175$	0	0
$176$	−292401.	−0.711538
$177$	−250970.	−0.602129
$178$	−711896.	−1.68409
$179$	67668.8	0.157854	0.0789271	−	0.996880i	$-0.474851\pi$
$179$	67668.8	0.157854	0.0789271	+	0.996880i	$0.474851\pi$
$180$	85471.2	0.196625
$181$	6373.57	0.0144606	0.00723030	−	0.999974i	$-0.497699\pi$
$181$	6373.57	0.0144606	0.00723030	+	0.999974i	$0.497699\pi$
$182$	0	0
$183$	143350.	0.316424
$184$	7323.46	0.0159467
$185$	−54166.1	−0.116359
$186$	−466503.	−0.988717
$187$	−8991.19	−0.0188024
$188$	137120.	0.282948
$189$	0	0
$190$	78625.7	0.158008
$191$	−197490.	−0.391707	−0.195854	−	0.980633i	$-0.562748\pi$
$191$	−197490.	−0.391707	−0.195854	+	0.980633i	$0.562748\pi$
$192$	−140461.	−0.274981
$193$	77475.9	0.149718	0.0748589	−	0.997194i	$-0.476149\pi$
$193$	77475.9	0.149718	0.0748589	+	0.997194i	$0.476149\pi$
$194$	−931729.	−1.77740
$195$	284525.	0.535838
$196$	0	0
$197$	−181922.	−0.333980	−0.166990	−	0.985959i	$-0.553405\pi$
$197$	−181922.	−0.333980	−0.166990	+	0.985959i	$0.553405\pi$
$198$	−257888.	−0.467486
$199$	893439.	1.59931	0.799654	−	0.600461i	$-0.205016\pi$
$199$	893439.	1.59931	0.799654	+	0.600461i	$0.205016\pi$
$200$	−38718.4	−0.0684450
$201$	516036.	0.900927
$202$	605945.	1.04485
$203$	0	0
$204$	−8839.73	−0.0148718
$205$	275109.	0.457214
$206$	1.24930e6	2.05115
$207$	17053.8	0.0276628
$208$	1.39813e6	2.24073
$209$	−100940.	−0.159844
$210$	0	0
$211$	500047.	0.773224	0.386612	−	0.922243i	$-0.373645\pi$
$211$	500047.	0.773224	0.386612	+	0.922243i	$0.373645\pi$
$212$	−711892.	−1.08786
$213$	−482717.	−0.729026
$214$	782026.	1.16731
$215$	−292534.	−0.431599
$216$	238389.	0.347658
$217$	0	0
$218$	−1.38385e6	−1.97219
$219$	−53325.2	−0.0751316
$220$	−141919.	−0.197689
$221$	42991.7	0.0592113
$222$	160680.	0.218816
$223$	−222203.	−0.299218	−0.149609	−	0.988745i	$-0.547801\pi$
$223$	−222203.	−0.299218	−0.149609	+	0.988745i	$0.547801\pi$
$224$	0	0
$225$	−90161.9	−0.118732
$226$	−1.35328e6	−1.76246
$227$	710491.	0.915154	0.457577	−	0.889170i	$-0.348717\pi$
$227$	710491.	0.915154	0.457577	+	0.889170i	$0.348717\pi$
$228$	−99239.5	−0.126429
$229$	5642.57	0.00711030	0.00355515	−	0.999994i	$-0.498868\pi$
$229$	5642.57	0.00711030	0.00355515	+	0.999994i	$0.498868\pi$
$230$	22056.9	0.0274932
$231$	0	0
$232$	−350172.	−0.427131
$233$	1.08608e6	1.31061	0.655304	−	0.755365i	$-0.272541\pi$
$233$	1.08608e6	1.31061	0.655304	+	0.755365i	$0.272541\pi$
$234$	1.23310e6	1.47218
$235$	−144646.	−0.170858
$236$	−598564.	−0.699569
$237$	762477.	0.881771
$238$	0	0
$239$	1.59144e6	1.80217	0.901087	−	0.433638i	$-0.142770\pi$
$239$	1.59144e6	1.80217	0.901087	+	0.433638i	$0.142770\pi$
$240$	303253.	0.339842
$241$	−145342.	−0.161194	−0.0805971	−	0.996747i	$-0.525683\pi$
$241$	−145342.	−0.161194	−0.0805971	+	0.996747i	$0.525683\pi$
$242$	−773750.	−0.849303
$243$	903464.	0.981511
$244$	341889.	0.367630
$245$	0	0
$246$	−816090.	−0.859805
$247$	482648.	0.503371
$248$	389688.	0.402335
$249$	332349.	0.339700
$250$	−116613.	−0.118004
$251$	−1.60635e6	−1.60937	−0.804685	−	0.593702i	$-0.797666\pi$
$251$	−1.60635e6	−1.60937	−0.804685	+	0.593702i	$0.797666\pi$
$252$	0	0
$253$	−28316.7	−0.0278126
$254$	2.04779e6	1.99160
$255$	9324.86	0.00898032
$256$	1.36735e6	1.30401
$257$	−873353.	−0.824816	−0.412408	−	0.910999i	$-0.635312\pi$
$257$	−873353.	−0.824816	−0.412408	+	0.910999i	$0.635312\pi$
$258$	867781.	0.811635
$259$	0	0
$260$	678591.	0.622550
$261$	−815432.	−0.740945
$262$	1.53864e6	1.38479
$263$	271899.	0.242392	0.121196	−	0.992629i	$-0.461327\pi$
$263$	271899.	0.242392	0.121196	+	0.992629i	$0.461327\pi$
$264$	−147451.	−0.130208
$265$	750961.	0.656905
$266$	0	0
$267$	−947851.	−0.813695
$268$	1.23074e6	1.04672
$269$	−276241.	−0.232759	−0.116380	−	0.993205i	$-0.537129\pi$
$269$	−276241.	−0.232759	−0.116380	+	0.993205i	$0.537129\pi$
$270$	717985.	0.599385
$271$	−1.96301e6	−1.62368	−0.811838	−	0.583883i	$-0.801533\pi$
$271$	−1.96301e6	−1.62368	−0.811838	+	0.583883i	$0.801533\pi$
$272$	45821.5	0.0375532
$273$	0	0
$274$	−2.61716e6	−2.10598
$275$	149707.	0.119375
$276$	−27839.7	−0.0219984
$277$	−785002.	−0.614711	−0.307356	−	0.951595i	$-0.599444\pi$
$277$	−785002.	−0.614711	−0.307356	+	0.951595i	$0.599444\pi$
$278$	1.50188e6	1.16553
$279$	907452.	0.697932
$280$	0	0
$281$	−2.22596e6	−1.68171	−0.840854	−	0.541261i	$-0.817947\pi$
$281$	−2.22596e6	−1.68171	−0.840854	+	0.541261i	$0.817947\pi$
$282$	429081.	0.321304
$283$	−1.86558e6	−1.38468	−0.692338	−	0.721573i	$-0.743419\pi$
$283$	−1.86558e6	−1.38468	−0.692338	+	0.721573i	$0.743419\pi$
$284$	−1.15128e6	−0.847002
$285$	104686.	0.0763442
$286$	−2.04748e6	−1.48015
$287$	0	0
$288$	1.02829e6	0.730526
$289$	−1.41845e6	−0.999008
$290$	−1.05465e6	−0.736401
$291$	−1.24055e6	−0.858778
$292$	−127181.	−0.0872898
$293$	−1.00283e6	−0.682433	−0.341216	−	0.939985i	$-0.610839\pi$
$293$	−1.00283e6	−0.682433	−0.341216	+	0.939985i	$0.610839\pi$
$294$	0	0
$295$	631414.	0.422434
$296$	−134222.	−0.0890421
$297$	−921751.	−0.606349
$298$	1.26591e6	0.825779
$299$	135397.	0.0875856
$300$	147186.	0.0944196
$301$	0	0
$302$	−2.04494e6	−1.29022
$303$	806783.	0.504836
$304$	514417.	0.319250
$305$	−360652.	−0.221993
$306$	40413.1	0.0246728
$307$	−1.95714e6	−1.18516	−0.592578	−	0.805513i	$-0.701890\pi$
$307$	−1.95714e6	−1.18516	−0.592578	+	0.805513i	$0.701890\pi$
$308$	0	0
$309$	1.66337e6	0.991045
$310$	1.17367e6	0.693652
$311$	−2.26547e6	−1.32818	−0.664090	−	0.747653i	$-0.731181\pi$
$311$	−2.26547e6	−1.32818	−0.664090	+	0.747653i	$0.731181\pi$
$312$	705045.	0.410044
$313$	−818015.	−0.471955	−0.235978	−	0.971759i	$-0.575829\pi$
$313$	−818015.	−0.471955	−0.235978	+	0.971759i	$0.575829\pi$
$314$	−3.26019e6	−1.86603
$315$	0	0
$316$	1.81850e6	1.02446
$317$	246269.	0.137646	0.0688228	−	0.997629i	$-0.478076\pi$
$317$	246269.	0.137646	0.0688228	+	0.997629i	$0.478076\pi$
$318$	−2.22767e6	−1.23533
$319$	1.35397e6	0.744957
$320$	353384.	0.192918
$321$	1.04123e6	0.564004
$322$	0	0
$323$	15818.1	0.00843620
$324$	−75444.3	−0.0399267
$325$	−715832.	−0.375926
$326$	−4.59410e6	−2.39418
$327$	−1.84253e6	−0.952893
$328$	681712.	0.349878
$329$	0	0
$330$	−444096.	−0.224488
$331$	−1.69016e6	−0.847925	−0.423963	−	0.905680i	$-0.639361\pi$
$331$	−1.69016e6	−0.847925	−0.423963	+	0.905680i	$0.639361\pi$
$332$	792651.	0.394673
$333$	−312558.	−0.154462
$334$	−2.35258e6	−1.15393
$335$	−1.29829e6	−0.632061
$336$	0	0
$337$	2.67119e6	1.28124	0.640620	−	0.767858i	$-0.278678\pi$
$337$	2.67119e6	1.28124	0.640620	+	0.767858i	$0.278678\pi$
$338$	7.01908e6	3.34186
$339$	−1.80183e6	−0.851557
$340$	22239.8	0.0104336
$341$	−1.50676e6	−0.701711
$342$	453699.	0.209750
$343$	0	0
$344$	−724892.	−0.330276
$345$	29367.6	0.0132837
$346$	3.92993e6	1.76480
$347$	615922.	0.274601	0.137301	−	0.990529i	$-0.456157\pi$
$347$	615922.	0.274601	0.137301	+	0.990529i	$0.456157\pi$
$348$	1.33116e6	0.589226
$349$	16390.7	0.00720332	0.00360166	−	0.999994i	$-0.498854\pi$
$349$	16390.7	0.00720332	0.00360166	+	0.999994i	$0.498854\pi$
$350$	0	0
$351$	4.40739e6	1.90947
$352$	−1.70741e6	−0.734481
$353$	−2.55764e6	−1.09245	−0.546226	−	0.837638i	$-0.683936\pi$
$353$	−2.55764e6	−1.09245	−0.546226	+	0.837638i	$0.683936\pi$
$354$	−1.87304e6	−0.794400
$355$	1.21446e6	0.511461
$356$	−2.26062e6	−0.945372
$357$	0	0
$358$	505026.	0.208260
$359$	756392.	0.309749	0.154875	−	0.987934i	$-0.450503\pi$
$359$	756392.	0.309749	0.154875	+	0.987934i	$0.450503\pi$
$360$	−223419.	−0.0908581
$361$	−2.29852e6	−0.928282
$362$	47567.2	0.0190782
$363$	−1.03021e6	−0.410353
$364$	0	0
$365$	134160.	0.0527099
$366$	1.06985e6	0.417465
$367$	1.59120e6	0.616680	0.308340	−	0.951276i	$-0.400227\pi$
$367$	1.59120e6	0.616680	0.308340	+	0.951276i	$0.400227\pi$
$368$	144310.	0.0555489
$369$	1.58748e6	0.606934
$370$	−404253.	−0.153514
$371$	0	0
$372$	−1.48138e6	−0.555020
$373$	−2.47069e6	−0.919489	−0.459745	−	0.888051i	$-0.652059\pi$
$373$	−2.47069e6	−0.919489	−0.459745	+	0.888051i	$0.652059\pi$
$374$	−67103.1	−0.0248064
$375$	−155263.	−0.0570152
$376$	−358428.	−0.130747
$377$	−6.47405e6	−2.34597
$378$	0	0
$379$	−4.75688e6	−1.70108	−0.850539	−	0.525911i	$-0.823724\pi$
$379$	−4.75688e6	−1.70108	−0.850539	+	0.525911i	$0.823724\pi$
$380$	249675.	0.0886986
$381$	2.72652e6	0.962269
$382$	−1.47391e6	−0.516787
$383$	−3.44209e6	−1.19902	−0.599508	−	0.800369i	$-0.704637\pi$
$383$	−3.44209e6	−1.19902	−0.599508	+	0.800369i	$0.704637\pi$
$384$	1.21830e6	0.421624
$385$	0	0
$386$	578218.	0.197526
$387$	−1.68803e6	−0.572930
$388$	−2.95870e6	−0.997751
$389$	−4.66543e6	−1.56321	−0.781605	−	0.623774i	$-0.785599\pi$
$389$	−4.66543e6	−1.56321	−0.781605	+	0.623774i	$0.785599\pi$
$390$	2.12346e6	0.706942
$391$	4437.44	0.00146788
$392$	0	0
$393$	2.04862e6	0.669083
$394$	−1.35772e6	−0.440626
$395$	−1.91831e6	−0.618622
$396$	−818923.	−0.262425
$397$	−781228.	−0.248772	−0.124386	−	0.992234i	$-0.539696\pi$
$397$	−781228.	−0.248772	−0.124386	+	0.992234i	$0.539696\pi$
$398$	6.66791e6	2.11000
$399$	0	0
$400$	−762950.	−0.238422
$401$	−1.47498e6	−0.458062	−0.229031	−	0.973419i	$-0.573556\pi$
$401$	−1.47498e6	−0.458062	−0.229031	+	0.973419i	$0.573556\pi$
$402$	3.85128e6	1.18861
$403$	7.20463e6	2.20978
$404$	1.92418e6	0.586531
$405$	79584.7	0.0241097
$406$	0	0
$407$	518981.	0.155298
$408$	23106.8	0.00687209
$409$	−1.84853e6	−0.546411	−0.273205	−	0.961956i	$-0.588084\pi$
$409$	−1.84853e6	−0.546411	−0.273205	+	0.961956i	$0.588084\pi$
$410$	2.05319e6	0.603211
$411$	−3.48461e6	−1.01753
$412$	3.96714e6	1.15142
$413$	0	0
$414$	127276.	0.0364961
$415$	−836153.	−0.238323
$416$	8.16404e6	2.31298
$417$	1.99968e6	0.563145
$418$	−753335.	−0.210886
$419$	−2.87435e6	−0.799842	−0.399921	−	0.916550i	$-0.630962\pi$
$419$	−2.87435e6	−0.799842	−0.399921	+	0.916550i	$0.630962\pi$
$420$	0	0
$421$	−4.88009e6	−1.34191	−0.670954	−	0.741499i	$-0.734115\pi$
$421$	−4.88009e6	−1.34191	−0.670954	+	0.741499i	$0.734115\pi$
$422$	3.73195e6	1.02013
$423$	−834657.	−0.226807
$424$	1.86086e6	0.502689
$425$	−23460.3	−0.00630030
$426$	−3.60261e6	−0.961819
$427$	0	0
$428$	2.48332e6	0.655275
$429$	−2.72611e6	−0.715155
$430$	−2.18324e6	−0.569417
$431$	133355.	0.0345792	0.0172896	−	0.999851i	$-0.494496\pi$
$431$	133355.	0.0345792	0.0172896	+	0.999851i	$0.494496\pi$
$432$	4.69749e6	1.21104
$433$	6.52186e6	1.67167	0.835837	−	0.548978i	$-0.184983\pi$
$433$	6.52186e6	1.67167	0.835837	+	0.548978i	$0.184983\pi$
$434$	0	0
$435$	−1.40421e6	−0.355803
$436$	−4.39442e6	−1.10710
$437$	49817.1	0.0124789
$438$	−397977.	−0.0991226
$439$	5.45374e6	1.35062	0.675310	−	0.737534i	$-0.264010\pi$
$439$	5.45374e6	1.35062	0.675310	+	0.737534i	$0.264010\pi$
$440$	370971.	0.0913500
$441$	0	0
$442$	320856.	0.0781186
$443$	4.97544e6	1.20454	0.602272	−	0.798291i	$-0.294262\pi$
$443$	4.97544e6	1.20454	0.602272	+	0.798291i	$0.294262\pi$
$444$	510238.	0.122833
$445$	2.38469e6	0.570862
$446$	−1.65834e6	−0.394764
$447$	1.68550e6	0.398988
$448$	0	0
$449$	−6.92047e6	−1.62002	−0.810009	−	0.586418i	$-0.800538\pi$
$449$	−6.92047e6	−1.62002	−0.810009	+	0.586418i	$0.800538\pi$
$450$	−672896.	−0.156645
$451$	−2.63589e6	−0.610220
$452$	−4.29735e6	−0.989360
$453$	−2.72273e6	−0.623389
$454$	5.30254e6	1.20738
$455$	0	0
$456$	259409.	0.0584215
$457$	−3.15961e6	−0.707690	−0.353845	−	0.935304i	$-0.615126\pi$
$457$	−3.15961e6	−0.707690	−0.353845	+	0.935304i	$0.615126\pi$
$458$	42111.6	0.00938076
$459$	144445.	0.0320016
$460$	70041.6	0.0154334
$461$	6.01476e6	1.31815	0.659077	−	0.752075i	$-0.270947\pi$
$461$	6.01476e6	1.31815	0.659077	+	0.752075i	$0.270947\pi$
$462$	0	0
$463$	1.08987e6	0.236278	0.118139	−	0.992997i	$-0.462307\pi$
$463$	1.08987e6	0.236278	0.118139	+	0.992997i	$0.462307\pi$
$464$	−6.90018e6	−1.48787
$465$	1.56268e6	0.335148
$466$	8.10564e6	1.72911
$467$	4.74234e6	1.00624	0.503118	−	0.864218i	$-0.332186\pi$
$467$	4.74234e6	1.00624	0.503118	+	0.864218i	$0.332186\pi$
$468$	3.91571e6	0.826411
$469$	0	0
$470$	−1.07952e6	−0.225416
$471$	−4.34076e6	−0.901600
$472$	1.56463e6	0.323263
$473$	2.80285e6	0.576032
$474$	5.69052e6	1.16334
$475$	−263378.	−0.0535606
$476$	0	0
$477$	4.33332e6	0.872016
$478$	1.18773e7	2.37764
$479$	1.47206e6	0.293148	0.146574	−	0.989200i	$-0.453175\pi$
$479$	1.47206e6	0.293148	0.146574	+	0.989200i	$0.453175\pi$
$480$	1.77077e6	0.350800
$481$	−2.48153e6	−0.489054
$482$	−1.08472e6	−0.212667
$483$	0	0
$484$	−2.45704e6	−0.476759
$485$	3.12108e6	0.602491
$486$	6.74273e6	1.29493
$487$	8.12335e6	1.55208	0.776038	−	0.630687i	$-0.217227\pi$
$487$	8.12335e6	1.55208	0.776038	+	0.630687i	$0.217227\pi$
$488$	−893687.	−0.169878
$489$	−6.11679e6	−1.15678
$490$	0	0
$491$	−1.35992e6	−0.254572	−0.127286	−	0.991866i	$-0.540627\pi$
$491$	−1.35992e6	−0.254572	−0.127286	+	0.991866i	$0.540627\pi$
$492$	−2.59149e6	−0.482655
$493$	−212177.	−0.0393170
$494$	3.60210e6	0.664107
$495$	863866.	0.158465
$496$	7.67886e6	1.40150
$497$	0	0
$498$	2.48039e6	0.448173
$499$	−2.17413e6	−0.390871	−0.195435	−	0.980717i	$-0.562612\pi$
$499$	−2.17413e6	−0.390871	−0.195435	+	0.980717i	$0.562612\pi$
$500$	−370302.	−0.0662417
$501$	−3.13233e6	−0.557537
$502$	−1.19885e7	−2.12327
$503$	1.49742e6	0.263890	0.131945	−	0.991257i	$-0.457878\pi$
$503$	1.49742e6	0.263890	0.131945	+	0.991257i	$0.457878\pi$
$504$	0	0
$505$	−2.02978e6	−0.354176
$506$	−211333.	−0.0366937
$507$	9.34552e6	1.61467
$508$	6.50275e6	1.11799
$509$	7.50644e6	1.28422	0.642110	−	0.766612i	$-0.278059\pi$
$509$	7.50644e6	1.28422	0.642110	+	0.766612i	$0.278059\pi$
$510$	69593.3	0.0118479
$511$	0	0
$512$	6.28148e6	1.05898
$513$	1.62162e6	0.272055
$514$	−6.51801e6	−1.08820
$515$	−4.18486e6	−0.695285
$516$	2.75563e6	0.455614
$517$	1.38589e6	0.228035
$518$	0	0
$519$	5.23250e6	0.852689
$520$	−1.77381e6	−0.287673
$521$	3.46879e6	0.559865	0.279932	−	0.960020i	$-0.409688\pi$
$521$	3.46879e6	0.559865	0.279932	+	0.960020i	$0.409688\pi$
$522$	−6.08573e6	−0.977544
$523$	6.68012e6	1.06790	0.533949	−	0.845517i	$-0.320707\pi$
$523$	6.68012e6	1.06790	0.533949	+	0.845517i	$0.320707\pi$
$524$	4.88596e6	0.777358
$525$	0	0
$526$	2.02924e6	0.319793
$527$	236121.	0.0370346
$528$	−2.90555e6	−0.453569
$529$	−6.42237e6	−0.997829
$530$	5.60457e6	0.866668
$531$	3.64348e6	0.560765
$532$	0	0
$533$	1.26036e7	1.92166
$534$	−7.07400e6	−1.07352
$535$	−2.61961e6	−0.395687
$536$	−3.21713e6	−0.483678
$537$	672415.	0.100624
$538$	−2.06164e6	−0.307084
$539$	0	0
$540$	2.27996e6	0.336467
$541$	4.89595e6	0.719191	0.359595	−	0.933108i	$-0.382915\pi$
$541$	4.89595e6	0.719191	0.359595	+	0.933108i	$0.382915\pi$
$542$	−1.46503e7	−2.14215
$543$	63333.2	0.00921790
$544$	267564.	0.0387641
$545$	4.63559e6	0.668519
$546$	0	0
$547$	−610243.	−0.0872036	−0.0436018	−	0.999049i	$-0.513883\pi$
$547$	−610243.	−0.0872036	−0.0436018	+	0.999049i	$0.513883\pi$
$548$	−8.31078e6	−1.18220
$549$	−2.08109e6	−0.294687
$550$	1.11730e6	0.157493
$551$	−2.38201e6	−0.334245
$552$	72772.1	0.0101652
$553$	0	0
$554$	−5.85862e6	−0.811001
$555$	−538241.	−0.0741727
$556$	4.76923e6	0.654276
$557$	−3.24366e6	−0.442993	−0.221497	−	0.975161i	$-0.571094\pi$
$557$	−3.24366e6	−0.442993	−0.221497	+	0.975161i	$0.571094\pi$
$558$	6.77249e6	0.920795
$559$	−1.34019e7	−1.81400
$560$	0	0
$561$	−89344.1	−0.0119856
$562$	−1.66128e7	−2.21871
$563$	507536.	0.0674833	0.0337416	−	0.999431i	$-0.489258\pi$
$563$	507536.	0.0674833	0.0337416	+	0.999431i	$0.489258\pi$
$564$	1.36254e6	0.180365
$565$	4.53319e6	0.597424
$566$	−1.39232e7	−1.82683
$567$	0	0
$568$	3.00940e6	0.391390
$569$	4.30204e6	0.557049	0.278525	−	0.960429i	$-0.410155\pi$
$569$	4.30204e6	0.557049	0.278525	+	0.960429i	$0.410155\pi$
$570$	781291.	0.100722
$571$	−3.43783e6	−0.441260	−0.220630	−	0.975358i	$-0.570811\pi$
$571$	−3.43783e6	−0.441260	−0.220630	+	0.975358i	$0.570811\pi$
$572$	−6.50177e6	−0.830886
$573$	−1.96243e6	−0.249693
$574$	0	0
$575$	−73885.5	−0.00931944
$576$	2.03916e6	0.256091
$577$	−9.47815e6	−1.18518	−0.592590	−	0.805505i	$-0.701894\pi$
$577$	−9.47815e6	−1.18518	−0.592590	+	0.805505i	$0.701894\pi$
$578$	−1.05862e7	−1.31801
$579$	769866.	0.0954375
$580$	−3.34905e6	−0.413382
$581$	0	0
$582$	−9.25846e6	−1.13300
$583$	−7.19517e6	−0.876737
$584$	332446.	0.0403356
$585$	−4.13061e6	−0.499028
$586$	−7.48435e6	−0.900347
$587$	8.33003e6	0.997818	0.498909	−	0.866654i	$-0.333734\pi$
$587$	8.33003e6	0.997818	0.498909	+	0.866654i	$0.333734\pi$
$588$	0	0
$589$	2.65082e6	0.314841
$590$	4.71237e6	0.557326
$591$	−1.80773e6	−0.212895
$592$	−2.64487e6	−0.310170
$593$	−2.80365e6	−0.327407	−0.163703	−	0.986510i	$-0.552344\pi$
$593$	−2.80365e6	−0.327407	−0.163703	+	0.986510i	$0.552344\pi$
$594$	−6.87921e6	−0.799968
$595$	0	0
$596$	4.01991e6	0.463554
$597$	8.87797e6	1.01948
$598$	1.01050e6	0.115553
$599$	3.34293e6	0.380680	0.190340	−	0.981718i	$-0.439041\pi$
$599$	3.34293e6	0.380680	0.190340	+	0.981718i	$0.439041\pi$
$600$	−384738.	−0.0436302
$601$	6.35286e6	0.717436	0.358718	−	0.933446i	$-0.383214\pi$
$601$	6.35286e6	0.717436	0.358718	+	0.933446i	$0.383214\pi$
$602$	0	0
$603$	−7.49159e6	−0.839037
$604$	−6.49370e6	−0.724269
$605$	2.59189e6	0.287891
$606$	6.02118e6	0.666040
$607$	−1.22503e7	−1.34950	−0.674752	−	0.738044i	$-0.735750\pi$
$607$	−1.22503e7	−1.34950	−0.674752	+	0.738044i	$0.735750\pi$
$608$	3.00381e6	0.329544
$609$	0	0
$610$	−2.69162e6	−0.292880
$611$	−6.62669e6	−0.718114
$612$	128331.	0.0138502
$613$	−2.95043e6	−0.317127	−0.158564	−	0.987349i	$-0.550686\pi$
$613$	−2.95043e6	−0.317127	−0.158564	+	0.987349i	$0.550686\pi$
$614$	−1.46065e7	−1.56360
$615$	2.73371e6	0.291451
$616$	0	0
$617$	1.16659e7	1.23368	0.616842	−	0.787087i	$-0.288412\pi$
$617$	1.16659e7	1.23368	0.616842	+	0.787087i	$0.288412\pi$
$618$	1.24141e7	1.30751
$619$	3.73232e6	0.391518	0.195759	−	0.980652i	$-0.437283\pi$
$619$	3.73232e6	0.391518	0.195759	+	0.980652i	$0.437283\pi$
$620$	3.72698e6	0.389384
$621$	454914.	0.0473370
$622$	−1.69076e7	−1.75229
$623$	0	0
$624$	1.38930e7	1.42835
$625$	390625.	0.0400000
$626$	−6.10501e6	−0.622660
$627$	−1.00302e6	−0.101893
$628$	−1.03527e7	−1.04750
$629$	−81328.3	−0.00819625
$630$	0	0
$631$	−2.92168e6	−0.292119	−0.146059	−	0.989276i	$-0.546659\pi$
$631$	−2.92168e6	−0.292119	−0.146059	+	0.989276i	$0.546659\pi$
$632$	−4.75351e6	−0.473393
$633$	4.96890e6	0.492891
$634$	1.83796e6	0.181599
$635$	−6.85962e6	−0.675097
$636$	−7.07396e6	−0.693457
$637$	0	0
$638$	1.01049e7	0.982837
$639$	7.00788e6	0.678945
$640$	−3.06510e6	−0.295798
$641$	−583563.	−0.0560974	−0.0280487	−	0.999607i	$-0.508929\pi$
$641$	−583563.	−0.0560974	−0.0280487	+	0.999607i	$0.508929\pi$
$642$	7.77088e6	0.744102
$643$	−6.39772e6	−0.610236	−0.305118	−	0.952315i	$-0.598696\pi$
$643$	−6.39772e6	−0.610236	−0.305118	+	0.952315i	$0.598696\pi$
$644$	0	0
$645$	−2.90687e6	−0.275122
$646$	118053.	0.0111300
$647$	7.06909e6	0.663900	0.331950	−	0.943297i	$-0.392293\pi$
$647$	7.06909e6	0.663900	0.331950	+	0.943297i	$0.392293\pi$
$648$	197209.	0.0184497
$649$	−6.04975e6	−0.563801
$650$	−5.34240e6	−0.495967
$651$	0	0
$652$	−1.45885e7	−1.34398
$653$	1.60843e7	1.47611	0.738055	−	0.674741i	$-0.235745\pi$
$653$	1.60843e7	1.47611	0.738055	+	0.674741i	$0.235745\pi$
$654$	−1.37511e7	−1.25717
$655$	−5.15410e6	−0.469407
$656$	1.34332e7	1.21877
$657$	774153.	0.0699703
$658$	0	0
$659$	−7.03792e6	−0.631293	−0.315646	−	0.948877i	$-0.602221\pi$
$659$	−7.03792e6	−0.631293	−0.315646	+	0.948877i	$0.602221\pi$
$660$	−1.41023e6	−0.126017
$661$	−5.89325e6	−0.524628	−0.262314	−	0.964983i	$-0.584486\pi$
$661$	−5.89325e6	−0.524628	−0.262314	+	0.964983i	$0.584486\pi$
$662$	−1.26140e7	−1.11868
$663$	427202.	0.0377442
$664$	−2.07197e6	−0.182374
$665$	0	0
$666$	−2.33268e6	−0.203784
$667$	−668227.	−0.0581580
$668$	−7.47061e6	−0.647761
$669$	−2.20800e6	−0.190736
$670$	−9.68939e6	−0.833891
$671$	3.45551e6	0.296282
$672$	0	0
$673$	−1.74476e7	−1.48490	−0.742450	−	0.669901i	$-0.766336\pi$
$673$	−1.74476e7	−1.48490	−0.742450	+	0.669901i	$0.766336\pi$
$674$	1.99356e7	1.69036
$675$	−2.40508e6	−0.203175
$676$	2.22890e7	1.87596
$677$	1.95963e7	1.64325	0.821624	−	0.570030i	$-0.193068\pi$
$677$	1.95963e7	1.64325	0.821624	+	0.570030i	$0.193068\pi$
$678$	−1.34474e7	−1.12348
$679$	0	0
$680$	−58134.0	−0.00482123
$681$	7.06005e6	0.583364
$682$	−1.12453e7	−0.925781
$683$	2.32938e6	0.191069	0.0955343	−	0.995426i	$-0.469544\pi$
$683$	2.32938e6	0.191069	0.0955343	+	0.995426i	$0.469544\pi$
$684$	1.44072e6	0.117744
$685$	8.76688e6	0.713869
$686$	0	0
$687$	56069.3	0.00453245
$688$	−1.42841e7	−1.15049
$689$	3.44040e7	2.76096
$690$	219176.	0.0175255
$691$	−8.65367e6	−0.689454	−0.344727	−	0.938703i	$-0.612028\pi$
$691$	−8.65367e6	−0.689454	−0.344727	+	0.938703i	$0.612028\pi$
$692$	1.24795e7	0.990676
$693$	0	0
$694$	4.59675e6	0.362287
$695$	−5.03097e6	−0.395084
$696$	−3.47961e6	−0.272275
$697$	413064.	0.0322059
$698$	122327.	0.00950349
$699$	1.07922e7	0.835446
$700$	0	0
$701$	−2.22670e7	−1.71146	−0.855729	−	0.517425i	$-0.826891\pi$
$701$	−2.22670e7	−1.71146	−0.855729	+	0.517425i	$0.826891\pi$
$702$	3.28932e7	2.51921
$703$	−913035.	−0.0696785
$704$	−3.38588e6	−0.257478
$705$	−1.43732e6	−0.108913
$706$	−1.90882e7	−1.44129
$707$	0	0
$708$	−5.94784e6	−0.445940
$709$	1.59340e7	1.19044	0.595221	−	0.803562i	$-0.297064\pi$
$709$	1.59340e7	1.19044	0.595221	+	0.803562i	$0.297064\pi$
$710$	9.06376e6	0.674781
$711$	−1.10693e7	−0.821196
$712$	5.90919e6	0.436846
$713$	743635.	0.0547818
$714$	0	0
$715$	6.85859e6	0.501730
$716$	1.60371e6	0.116908
$717$	1.58139e7	1.14879
$718$	5.64510e6	0.408659
$719$	1.91403e7	1.38079	0.690393	−	0.723434i	$-0.257438\pi$
$719$	1.91403e7	1.38079	0.690393	+	0.723434i	$0.257438\pi$
$720$	−4.40250e6	−0.316496
$721$	0	0
$722$	−1.71543e7	−1.22470
$723$	−1.44425e6	−0.102753
$724$	151050.	0.0107096
$725$	3.53284e6	0.249620
$726$	−7.68864e6	−0.541387
$727$	−1.63078e7	−1.14435	−0.572177	−	0.820130i	$-0.693901\pi$
$727$	−1.63078e7	−1.14435	−0.572177	+	0.820130i	$0.693901\pi$
$728$	0	0
$729$	9.75115e6	0.679574
$730$	1.00127e6	0.0695412
$731$	−439228.	−0.0304016
$732$	3.39730e6	0.234345
$733$	4.52597e6	0.311137	0.155569	−	0.987825i	$-0.450279\pi$
$733$	4.52597e6	0.311137	0.155569	+	0.987825i	$0.450279\pi$
$734$	1.18755e7	0.813598
$735$	0	0
$736$	842661.	0.0573401
$737$	1.24393e7	0.843579
$738$	1.18476e7	0.800739
$739$	1.77436e7	1.19517	0.597586	−	0.801805i	$-0.296127\pi$
$739$	1.77436e7	1.19517	0.597586	+	0.801805i	$0.296127\pi$
$740$	−1.28370e6	−0.0861758
$741$	4.79600e6	0.320873
$742$	0	0
$743$	−2.11122e7	−1.40301	−0.701505	−	0.712664i	$-0.747488\pi$
$743$	−2.11122e7	−1.40301	−0.701505	+	0.712664i	$0.747488\pi$
$744$	3.87227e6	0.256468
$745$	−4.24052e6	−0.279917
$746$	−1.84393e7	−1.21310
$747$	−4.82490e6	−0.316364
$748$	−213085.	−0.0139251
$749$	0	0
$750$	−1.15876e6	−0.0752213
$751$	2.55449e7	1.65274	0.826371	−	0.563126i	$-0.190402\pi$
$751$	2.55449e7	1.65274	0.826371	+	0.563126i	$0.190402\pi$
$752$	−7.06287e6	−0.455446
$753$	−1.59621e7	−1.02589
$754$	−4.83171e7	−3.09508
$755$	6.85009e6	0.437349
$756$	0	0
$757$	4.07738e6	0.258608	0.129304	−	0.991605i	$-0.458726\pi$
$757$	4.07738e6	0.258608	0.129304	+	0.991605i	$0.458726\pi$
$758$	−3.55016e7	−2.24427
$759$	−281379.	−0.0177291
$760$	−652644.	−0.0409866
$761$	2.76645e7	1.73165	0.865826	−	0.500345i	$-0.166794\pi$
$761$	2.76645e7	1.73165	0.865826	+	0.500345i	$0.166794\pi$
$762$	2.03486e7	1.26954
$763$	0	0
$764$	−4.68038e6	−0.290100
$765$	−135374.	−0.00836340
$766$	−2.56890e7	−1.58189
$767$	2.89271e7	1.77548
$768$	1.35872e7	0.831238
$769$	5.53787e6	0.337697	0.168848	−	0.985642i	$-0.445995\pi$
$769$	5.53787e6	0.337697	0.168848	+	0.985642i	$0.445995\pi$
$770$	0	0
$771$	−8.67838e6	−0.525778
$772$	1.83613e6	0.110882
$773$	1.64644e7	0.991052	0.495526	−	0.868593i	$-0.334975\pi$
$773$	1.64644e7	0.991052	0.495526	+	0.868593i	$0.334975\pi$
$774$	−1.25981e7	−0.755878
$775$	−3.93152e6	−0.235129
$776$	7.73395e6	0.461049
$777$	0	0
$778$	−3.48190e7	−2.06237
$779$	4.63728e6	0.273791
$780$	6.74305e6	0.396844
$781$	−1.16361e7	−0.682621
$782$	33117.5	0.00193661
$783$	−2.17518e7	−1.26792
$784$	0	0
$785$	1.09209e7	0.632533
$786$	1.52893e7	0.882735
$787$	1.46529e7	0.843307	0.421653	−	0.906757i	$-0.361450\pi$
$787$	1.46529e7	0.843307	0.421653	+	0.906757i	$0.361450\pi$
$788$	−4.31144e6	−0.247347
$789$	2.70182e6	0.154513
$790$	−1.43167e7	−0.816160
$791$	0	0
$792$	2.14064e6	0.121264
$793$	−1.65227e7	−0.933033
$794$	−5.83046e6	−0.328210
$795$	7.46219e6	0.418744
$796$	2.11739e7	1.18446
$797$	−4.40489e6	−0.245635	−0.122817	−	0.992429i	$-0.539193\pi$
$797$	−4.40489e6	−0.245635	−0.122817	+	0.992429i	$0.539193\pi$
$798$	0	0
$799$	−217179.	−0.0120352
$800$	−4.45506e6	−0.246110
$801$	1.37605e7	0.757797
$802$	−1.10080e7	−0.604330
$803$	−1.28543e6	−0.0703491
$804$	1.22297e7	0.667231
$805$	0	0
$806$	5.37696e7	2.91541
$807$	−2.74496e6	−0.148372
$808$	−5.02973e6	−0.271030
$809$	7.80578e6	0.419320	0.209660	−	0.977774i	$-0.432764\pi$
$809$	7.80578e6	0.419320	0.209660	+	0.977774i	$0.432764\pi$
$810$	593957.	0.0318084
$811$	1.23076e7	0.657083	0.328541	−	0.944490i	$-0.393443\pi$
$811$	1.23076e7	0.657083	0.328541	+	0.944490i	$0.393443\pi$
$812$	0	0
$813$	−1.95061e7	−1.03501
$814$	3.87326e6	0.204888
$815$	1.53892e7	0.811561
$816$	455322.	0.0239383
$817$	−4.93101e6	−0.258452
$818$	−1.37960e7	−0.720890
$819$	0	0
$820$	6.51990e6	0.338615
$821$	−3.03424e7	−1.57106	−0.785528	−	0.618826i	$-0.787609\pi$
$821$	−3.03424e7	−1.57106	−0.785528	+	0.618826i	$0.787609\pi$
$822$	−2.60063e7	−1.34245
$823$	8.32590e6	0.428481	0.214241	−	0.976781i	$-0.431272\pi$
$823$	8.32590e6	0.428481	0.214241	+	0.976781i	$0.431272\pi$
$824$	−1.03700e7	−0.532059
$825$	1.48762e6	0.0760952
$826$	0	0
$827$	6.91414e6	0.351540	0.175770	−	0.984431i	$-0.443759\pi$
$827$	6.91414e6	0.351540	0.175770	+	0.984431i	$0.443759\pi$
$828$	404165.	0.0204872
$829$	−8.84012e6	−0.446758	−0.223379	−	0.974732i	$-0.571709\pi$
$829$	−8.84012e6	−0.446758	−0.223379	+	0.974732i	$0.571709\pi$
$830$	−6.24038e6	−0.314424
$831$	−7.80044e6	−0.391847
$832$	1.61897e7	0.810831
$833$	0	0
$834$	1.49240e7	0.742968
$835$	7.88060e6	0.391150
$836$	−2.39221e6	−0.118381
$837$	2.42064e7	1.19431
$838$	−2.14518e7	−1.05525
$839$	3.02617e7	1.48419	0.742094	−	0.670296i	$-0.233833\pi$
$839$	3.02617e7	1.48419	0.742094	+	0.670296i	$0.233833\pi$
$840$	0	0
$841$	1.14402e7	0.557755
$842$	−3.64211e7	−1.77041
$843$	−2.21190e7	−1.07200
$844$	1.18508e7	0.572653
$845$	−2.35123e7	−1.13280
$846$	−6.22921e6	−0.299231
$847$	0	0
$848$	3.66685e7	1.75107
$849$	−1.85380e7	−0.882661
$850$	−175089.	−0.00831211
$851$	−256134.	−0.0121239
$852$	−1.14401e7	−0.539920
$853$	−2.67059e7	−1.25671	−0.628353	−	0.777928i	$-0.716271\pi$
$853$	−2.67059e7	−1.25671	−0.628353	+	0.777928i	$0.716271\pi$
$854$	0	0
$855$	−1.51979e6	−0.0710996
$856$	−6.49132e6	−0.302795
$857$	2.47722e7	1.15216	0.576079	−	0.817394i	$-0.304582\pi$
$857$	2.47722e7	1.15216	0.576079	+	0.817394i	$0.304582\pi$
$858$	−2.03455e7	−0.943518
$859$	−3.82296e7	−1.76773	−0.883866	−	0.467740i	$-0.845068\pi$
$859$	−3.82296e7	−1.76773	−0.883866	+	0.467740i	$0.845068\pi$
$860$	−6.93287e6	−0.319644
$861$	0	0
$862$	995253.	0.0456210
$863$	−3.22284e7	−1.47303	−0.736515	−	0.676421i	$-0.763530\pi$
$863$	−3.22284e7	−1.47303	−0.736515	+	0.676421i	$0.763530\pi$
$864$	2.74299e7	1.25008
$865$	−1.31644e7	−0.598219
$866$	4.86739e7	2.20547
$867$	−1.40949e7	−0.636817
$868$	0	0
$869$	1.83798e7	0.825642
$870$	−1.04799e7	−0.469418
$871$	−5.94788e7	−2.65654
$872$	1.14869e7	0.511577
$873$	1.80098e7	0.799783
$874$	371795.	0.0164636
$875$	0	0
$876$	−1.26377e6	−0.0556428
$877$	1.43593e7	0.630426	0.315213	−	0.949021i	$-0.397924\pi$
$877$	1.43593e7	0.630426	0.315213	+	0.949021i	$0.397924\pi$
$878$	4.07023e7	1.78190
$879$	−9.96501e6	−0.435016
$880$	7.31004e6	0.318209
$881$	8.13081e6	0.352935	0.176467	−	0.984307i	$-0.443533\pi$
$881$	8.13081e6	0.352935	0.176467	+	0.984307i	$0.443533\pi$
$882$	0	0
$883$	−1.98192e6	−0.0855428	−0.0427714	−	0.999085i	$-0.513619\pi$
$883$	−1.98192e6	−0.0855428	−0.0427714	+	0.999085i	$0.513619\pi$
$884$	1.01888e6	0.0438521
$885$	6.27426e6	0.269280
$886$	3.71327e7	1.58918
$887$	1.96580e7	0.838937	0.419469	−	0.907770i	$-0.362216\pi$
$887$	1.96580e7	0.838937	0.419469	+	0.907770i	$0.362216\pi$
$888$	−1.33375e6	−0.0567598
$889$	0	0
$890$	1.77974e7	0.753150
$891$	−762524.	−0.0321780
$892$	−5.26606e6	−0.221602
$893$	−2.43817e6	−0.102314
$894$	1.25792e7	0.526392
$895$	−1.69172e6	−0.0705946
$896$	0	0
$897$	1.34542e6	0.0558314
$898$	−5.16488e7	−2.13732
$899$	−3.55570e7	−1.46732
$900$	−2.13678e6	−0.0879333
$901$	1.12754e6	0.0462721
$902$	−1.96722e7	−0.805075
$903$	0	0
$904$	1.12331e7	0.457172
$905$	−159339.	−0.00646698
$906$	−2.03203e7	−0.822450
$907$	2.41241e7	0.973718	0.486859	−	0.873481i	$-0.338143\pi$
$907$	2.41241e7	0.973718	0.486859	+	0.873481i	$0.338143\pi$
$908$	1.68382e7	0.677767
$909$	−1.17125e7	−0.470155
$910$	0	0
$911$	−4.31594e7	−1.72298	−0.861488	−	0.507779i	$-0.830467\pi$
$911$	−4.31594e7	−1.72298	−0.861488	+	0.507779i	$0.830467\pi$
$912$	5.11168e6	0.203506
$913$	8.01141e6	0.318077
$914$	−2.35808e7	−0.933669
$915$	−3.58375e6	−0.141509
$916$	133725.	0.00526592
$917$	0	0
$918$	1.07803e6	0.0422204
$919$	−1.05059e7	−0.410340	−0.205170	−	0.978726i	$-0.565775\pi$
$919$	−1.05059e7	−0.410340	−0.205170	+	0.978726i	$0.565775\pi$
$920$	−183086.	−0.00713159
$921$	−1.94478e7	−0.755477
$922$	4.48894e7	1.73907
$923$	5.56384e7	2.14966
$924$	0	0
$925$	1.35415e6	0.0520372
$926$	8.13395e6	0.311727
$927$	−2.41481e7	−0.922963
$928$	−4.02919e7	−1.53585
$929$	2.35119e7	0.893818	0.446909	−	0.894580i	$-0.352525\pi$
$929$	2.35119e7	0.893818	0.446909	+	0.894580i	$0.352525\pi$
$930$	1.16626e7	0.442168
$931$	0	0
$932$	2.57394e7	0.970642
$933$	−2.25116e7	−0.846647
$934$	3.53930e7	1.32755
$935$	224780.	0.00840869
$936$	−1.02355e7	−0.381875
$937$	−1.08677e6	−0.0404378	−0.0202189	−	0.999796i	$-0.506436\pi$
$937$	−1.08677e6	−0.0404378	−0.0202189	+	0.999796i	$0.506436\pi$
$938$	0	0
$939$	−8.12850e6	−0.300847
$940$	−3.42801e6	−0.126538
$941$	−4.89867e7	−1.80345	−0.901726	−	0.432309i	$-0.857699\pi$
$941$	−4.89867e7	−1.80345	−0.901726	+	0.432309i	$0.857699\pi$
$942$	−3.23960e7	−1.18950
$943$	1.30090e6	0.0476392
$944$	3.08312e7	1.12606
$945$	0	0
$946$	2.09182e7	0.759971
$947$	6.99643e6	0.253514	0.126757	−	0.991934i	$-0.459543\pi$
$947$	6.99643e6	0.253514	0.126757	+	0.991934i	$0.459543\pi$
$948$	1.80702e7	0.653044
$949$	6.14632e6	0.221539
$950$	−1.96564e6	−0.0706635
$951$	2.44714e6	0.0877421
$952$	0	0
$953$	8.86261e6	0.316103	0.158052	−	0.987431i	$-0.449479\pi$
$953$	8.86261e6	0.316103	0.158052	+	0.987431i	$0.449479\pi$
$954$	3.23404e7	1.15047
$955$	4.93725e6	0.175177
$956$	3.77162e7	1.33470
$957$	1.34542e7	0.474872
$958$	1.09863e7	0.386756
$959$	0	0
$960$	3.51153e6	0.122975
$961$	1.09404e7	0.382142
$962$	−1.85201e7	−0.645218
$963$	−1.51161e7	−0.525259
$964$	−3.44452e6	−0.119381
$965$	−1.93690e6	−0.0669558
$966$	0	0
$967$	1.81443e7	0.623986	0.311993	−	0.950084i	$-0.399004\pi$
$967$	1.81443e7	0.623986	0.311993	+	0.950084i	$0.399004\pi$
$968$	6.42263e6	0.220305
$969$	157182.	0.00537765
$970$	2.32932e7	0.794878
$971$	−2.26200e7	−0.769918	−0.384959	−	0.922934i	$-0.625784\pi$
$971$	−2.26200e7	−0.769918	−0.384959	+	0.922934i	$0.625784\pi$
$972$	2.14115e7	0.726912
$973$	0	0
$974$	6.06262e7	2.04768
$975$	−7.11312e6	−0.239634
$976$	−1.76102e7	−0.591753
$977$	4.20930e6	0.141083	0.0705413	−	0.997509i	$-0.477527\pi$
$977$	4.20930e6	0.141083	0.0705413	+	0.997509i	$0.477527\pi$
$978$	−4.56508e7	−1.52617
$979$	−2.28483e7	−0.761900
$980$	0	0
$981$	2.67490e7	0.887433
$982$	−1.01494e7	−0.335862
$983$	2.08839e7	0.689330	0.344665	−	0.938726i	$-0.387992\pi$
$983$	2.08839e7	0.689330	0.344665	+	0.938726i	$0.387992\pi$
$984$	6.77407e6	0.223029
$985$	4.54806e6	0.149360
$986$	−1.58352e6	−0.0518718
$987$	0	0
$988$	1.14384e7	0.372799
$989$	−1.38330e6	−0.0449702
$990$	6.44721e6	0.209066
$991$	5.45752e7	1.76527	0.882636	−	0.470058i	$-0.155767\pi$
$991$	5.45752e7	1.76527	0.882636	+	0.470058i	$0.155767\pi$
$992$	4.48388e7	1.44669
$993$	−1.67948e7	−0.540509
$994$	0	0
$995$	−2.23360e7	−0.715232
$996$	7.87646e6	0.251584
$997$	3.13980e7	1.00038	0.500188	−	0.865917i	$-0.333264\pi$
$997$	3.13980e7	1.00038	0.500188	+	0.865917i	$0.333264\pi$
$998$	−1.62259e7	−0.515684
$999$	−8.33754e6	−0.264317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.l.1.8	✓	10
7.6	odd	2		245.6.a.m.1.8	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.6.a.l.1.8	✓	10	1.1	even	1	trivial
245.6.a.m.1.8	yes	10	7.6	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q+7.46320 q^{2} +9.93685 q^{3} +23.6994 q^{4} -25.0000 q^{5} +74.1607 q^{6} -61.9494 q^{8} -144.259 q^{9} +O(q^{10})\)	\(q+7.46320 q^{2} +9.93685 q^{3} +23.6994 q^{4} -25.0000 q^{5} +74.1607 q^{6} -61.9494 q^{8} -144.259 q^{9} -186.580 q^{10} +239.532 q^{11} +235.497 q^{12} -1145.33 q^{13} -248.421 q^{15} -1220.72 q^{16} -37.5365 q^{17} -1076.63 q^{18} -421.405 q^{19} -592.484 q^{20} +1787.68 q^{22} -118.217 q^{23} -615.582 q^{24} +625.000 q^{25} -8547.84 q^{26} -3848.13 q^{27} +5652.55 q^{29} -1854.02 q^{30} -6290.43 q^{31} -7128.10 q^{32} +2380.19 q^{33} -280.142 q^{34} -3418.85 q^{36} +2166.65 q^{37} -3145.03 q^{38} -11381.0 q^{39} +1548.73 q^{40} -11004.3 q^{41} +11701.4 q^{43} +5676.75 q^{44} +3606.48 q^{45} -882.276 q^{46} +5785.82 q^{47} -12130.1 q^{48} +4664.50 q^{50} -372.994 q^{51} -27143.6 q^{52} -30038.4 q^{53} -28719.4 q^{54} -5988.30 q^{55} -4187.43 q^{57} +42186.1 q^{58} -25256.5 q^{59} -5887.42 q^{60} +14426.1 q^{61} -46946.8 q^{62} -14135.4 q^{64} +28633.3 q^{65} +17763.9 q^{66} +51931.5 q^{67} -889.591 q^{68} -1174.70 q^{69} -48578.4 q^{71} +8936.76 q^{72} -5366.41 q^{73} +16170.1 q^{74} +6210.53 q^{75} -9987.02 q^{76} -84938.6 q^{78} +76732.2 q^{79} +30518.0 q^{80} -3183.39 q^{81} -82127.6 q^{82} +33446.1 q^{83} +938.412 q^{85} +87329.6 q^{86} +56168.6 q^{87} -14838.9 q^{88} -95387.5 q^{89} +26915.8 q^{90} -2801.66 q^{92} -62507.1 q^{93} +43180.8 q^{94} +10535.1 q^{95} -70830.8 q^{96} -124843. q^{97} -34554.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - 58 q^{3} + 182 q^{4} - 250 q^{5} - 144 q^{6} + 270 q^{8} + 700 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - 58 * q^3 + 182 * q^4 - 250 * q^5 - 144 * q^6 + 270 * q^8 + 700 * q^9	\( 10 q + 10 q^{2} - 58 q^{3} + 182 q^{4} - 250 q^{5} - 144 q^{6} + 270 q^{8} + 700 q^{9} - 250 q^{10} + 794 q^{11} - 2560 q^{12} - 474 q^{13} + 1450 q^{15} + 2394 q^{16} - 802 q^{17} + 3702 q^{18} - 7292 q^{19} - 4550 q^{20} + 3948 q^{22} + 3708 q^{23} - 2092 q^{24} + 6250 q^{25} - 6576 q^{26} - 11818 q^{27} - 8866 q^{29} + 3600 q^{30} - 13292 q^{31} + 2590 q^{32} - 9854 q^{33} - 44468 q^{34} - 10690 q^{36} + 16124 q^{37} - 2180 q^{38} - 24982 q^{39} - 6750 q^{40} - 34836 q^{41} - 28604 q^{43} - 31120 q^{44} - 17500 q^{45} - 39732 q^{46} - 18106 q^{47} - 101788 q^{48} + 6250 q^{50} + 31602 q^{51} + 22480 q^{52} + 36440 q^{53} - 80836 q^{54} - 19850 q^{55} + 126988 q^{57} - 100356 q^{58} - 18644 q^{59} + 64000 q^{60} - 68120 q^{61} - 181052 q^{62} - 59358 q^{64} + 11850 q^{65} - 157780 q^{66} + 92328 q^{67} - 288540 q^{68} - 170888 q^{69} + 5044 q^{71} - 61654 q^{72} - 170160 q^{73} - 216584 q^{74} - 36250 q^{75} - 505180 q^{76} - 158008 q^{78} + 26442 q^{79} - 59850 q^{80} - 56314 q^{81} - 353948 q^{82} - 353360 q^{83} + 20050 q^{85} - 52940 q^{86} + 3190 q^{87} - 114916 q^{88} - 90704 q^{89} - 92550 q^{90} + 183520 q^{92} + 188560 q^{93} + 121388 q^{94} + 182300 q^{95} - 442220 q^{96} - 236382 q^{97} + 109024 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 58 * q^3 + 182 * q^4 - 250 * q^5 - 144 * q^6 + 270 * q^8 + 700 * q^9 - 250 * q^10 + 794 * q^11 - 2560 * q^12 - 474 * q^13 + 1450 * q^15 + 2394 * q^16 - 802 * q^17 + 3702 * q^18 - 7292 * q^19 - 4550 * q^20 + 3948 * q^22 + 3708 * q^23 - 2092 * q^24 + 6250 * q^25 - 6576 * q^26 - 11818 * q^27 - 8866 * q^29 + 3600 * q^30 - 13292 * q^31 + 2590 * q^32 - 9854 * q^33 - 44468 * q^34 - 10690 * q^36 + 16124 * q^37 - 2180 * q^38 - 24982 * q^39 - 6750 * q^40 - 34836 * q^41 - 28604 * q^43 - 31120 * q^44 - 17500 * q^45 - 39732 * q^46 - 18106 * q^47 - 101788 * q^48 + 6250 * q^50 + 31602 * q^51 + 22480 * q^52 + 36440 * q^53 - 80836 * q^54 - 19850 * q^55 + 126988 * q^57 - 100356 * q^58 - 18644 * q^59 + 64000 * q^60 - 68120 * q^61 - 181052 * q^62 - 59358 * q^64 + 11850 * q^65 - 157780 * q^66 + 92328 * q^67 - 288540 * q^68 - 170888 * q^69 + 5044 * q^71 - 61654 * q^72 - 170160 * q^73 - 216584 * q^74 - 36250 * q^75 - 505180 * q^76 - 158008 * q^78 + 26442 * q^79 - 59850 * q^80 - 56314 * q^81 - 353948 * q^82 - 353360 * q^83 + 20050 * q^85 - 52940 * q^86 + 3190 * q^87 - 114916 * q^88 - 90704 * q^89 - 92550 * q^90 + 183520 * q^92 + 188560 * q^93 + 121388 * q^94 + 182300 * q^95 - 442220 * q^96 - 236382 * q^97 + 109024 * q^99

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