LMFDB - Embedded newform 245.6.a.d.1.1

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:	$3$
Coefficient field:	3.3.577880.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 98x - 232 $ x^3 - 98*x - 232
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-8.38673$ 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)

$f(q)$	$=$	$q-10.3867 q^{2} -27.9421 q^{3} +75.8842 q^{4} +25.0000 q^{5} +290.227 q^{6} -455.813 q^{8} +537.760 q^{9} +O(q^{10})$	\(q-10.3867 q^{2} -27.9421 q^{3} +75.8842 q^{4} +25.0000 q^{5} +290.227 q^{6} -455.813 q^{8} +537.760 q^{9} -259.668 q^{10} -132.501 q^{11} -2120.36 q^{12} -802.665 q^{13} -698.552 q^{15} +2306.11 q^{16} -763.068 q^{17} -5585.57 q^{18} +61.2154 q^{19} +1897.10 q^{20} +1376.25 q^{22} +3589.61 q^{23} +12736.4 q^{24} +625.000 q^{25} +8337.06 q^{26} -8236.22 q^{27} -4593.21 q^{29} +7255.67 q^{30} +384.018 q^{31} -9366.97 q^{32} +3702.35 q^{33} +7925.78 q^{34} +40807.5 q^{36} +5377.28 q^{37} -635.827 q^{38} +22428.1 q^{39} -11395.3 q^{40} +20530.3 q^{41} -12175.3 q^{43} -10054.7 q^{44} +13444.0 q^{45} -37284.3 q^{46} +15232.4 q^{47} -64437.7 q^{48} -6491.71 q^{50} +21321.7 q^{51} -60909.6 q^{52} +1369.77 q^{53} +85547.4 q^{54} -3312.52 q^{55} -1710.48 q^{57} +47708.4 q^{58} -27738.1 q^{59} -53009.1 q^{60} +15708.6 q^{61} -3988.70 q^{62} +23496.6 q^{64} -20066.6 q^{65} -38455.3 q^{66} -16813.0 q^{67} -57904.8 q^{68} -100301. q^{69} +37925.9 q^{71} -245118. q^{72} +48894.9 q^{73} -55852.3 q^{74} -17463.8 q^{75} +4645.28 q^{76} -232955. q^{78} -66582.2 q^{79} +57652.9 q^{80} +99461.4 q^{81} -213243. q^{82} +63358.0 q^{83} -19076.7 q^{85} +126461. q^{86} +128344. q^{87} +60395.6 q^{88} +69175.3 q^{89} -139639. q^{90} +272395. q^{92} -10730.3 q^{93} -158215. q^{94} +1530.38 q^{95} +261733. q^{96} +55697.0 q^{97} -71253.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6 q^{2} - 26 q^{3} + 112 q^{4} + 75 q^{5} + 96 q^{6} - 120 q^{8} + 489 q^{9}+O(q^{10}) $ 3 * q - 6 * q^2 - 26 * q^3 + 112 * q^4 + 75 * q^5 + 96 * q^6 - 120 * q^8 + 489 * q^9	\( 3 q - 6 q^{2} - 26 q^{3} + 112 q^{4} + 75 q^{5} + 96 q^{6} - 120 q^{8} + 489 q^{9} - 150 q^{10} - 194 q^{11} - 2956 q^{12} - 1892 q^{13} - 650 q^{15} + 1496 q^{16} + 184 q^{17} - 6078 q^{18} - 1212 q^{19} + 2800 q^{20} - 872 q^{22} + 3188 q^{23} + 13920 q^{24} + 1875 q^{25} + 9836 q^{26} - 7910 q^{27} - 11332 q^{29} + 2400 q^{30} - 9200 q^{31} - 20256 q^{32} + 8278 q^{33} + 18492 q^{34} + 38236 q^{36} + 6042 q^{37} - 25520 q^{38} + 12842 q^{39} - 3000 q^{40} - 10442 q^{41} + 28112 q^{43} - 20436 q^{44} + 12225 q^{45} - 41856 q^{46} - 2330 q^{47} - 68808 q^{48} - 3750 q^{50} + 3622 q^{51} - 63524 q^{52} + 7190 q^{53} + 138960 q^{54} - 4850 q^{55} + 45508 q^{57} + 37260 q^{58} - 23760 q^{59} - 73900 q^{60} - 8722 q^{61} - 24848 q^{62} + 4976 q^{64} - 47300 q^{65} - 24368 q^{66} - 97572 q^{67} - 3564 q^{68} - 92596 q^{69} - 52816 q^{71} - 251640 q^{72} - 34870 q^{73} - 241892 q^{74} - 16250 q^{75} - 115256 q^{76} - 142096 q^{78} - 71546 q^{79} + 37400 q^{80} - 3957 q^{81} - 241908 q^{82} + 20920 q^{83} + 4600 q^{85} + 266024 q^{86} + 112298 q^{87} + 59200 q^{88} + 192622 q^{89} - 151950 q^{90} + 248952 q^{92} - 20392 q^{93} - 360128 q^{94} - 30300 q^{95} + 296256 q^{96} - 116320 q^{97} - 60752 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 - 26 * q^3 + 112 * q^4 + 75 * q^5 + 96 * q^6 - 120 * q^8 + 489 * q^9 - 150 * q^10 - 194 * q^11 - 2956 * q^12 - 1892 * q^13 - 650 * q^15 + 1496 * q^16 + 184 * q^17 - 6078 * q^18 - 1212 * q^19 + 2800 * q^20 - 872 * q^22 + 3188 * q^23 + 13920 * q^24 + 1875 * q^25 + 9836 * q^26 - 7910 * q^27 - 11332 * q^29 + 2400 * q^30 - 9200 * q^31 - 20256 * q^32 + 8278 * q^33 + 18492 * q^34 + 38236 * q^36 + 6042 * q^37 - 25520 * q^38 + 12842 * q^39 - 3000 * q^40 - 10442 * q^41 + 28112 * q^43 - 20436 * q^44 + 12225 * q^45 - 41856 * q^46 - 2330 * q^47 - 68808 * q^48 - 3750 * q^50 + 3622 * q^51 - 63524 * q^52 + 7190 * q^53 + 138960 * q^54 - 4850 * q^55 + 45508 * q^57 + 37260 * q^58 - 23760 * q^59 - 73900 * q^60 - 8722 * q^61 - 24848 * q^62 + 4976 * q^64 - 47300 * q^65 - 24368 * q^66 - 97572 * q^67 - 3564 * q^68 - 92596 * q^69 - 52816 * q^71 - 251640 * q^72 - 34870 * q^73 - 241892 * q^74 - 16250 * q^75 - 115256 * q^76 - 142096 * q^78 - 71546 * q^79 + 37400 * q^80 - 3957 * q^81 - 241908 * q^82 + 20920 * q^83 + 4600 * q^85 + 266024 * q^86 + 112298 * q^87 + 59200 * q^88 + 192622 * q^89 - 151950 * q^90 + 248952 * q^92 - 20392 * q^93 - 360128 * q^94 - 30300 * q^95 + 296256 * q^96 - 116320 * q^97 - 60752 * 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 $

$2$	−10.3867	−1.83613	−0.918066	−	0.396428i	$-0.870250\pi$
$2$	−10.3867	−1.83613	−0.918066	+	0.396428i	$0.870250\pi$
$3$	−27.9421	−1.79249	−0.896243	−	0.443564i	$-0.853714\pi$
$3$	−27.9421	−1.79249	−0.896243	+	0.443564i	$0.853714\pi$
$4$	75.8842	2.37138
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	290.227	3.29124
$7$	0	0
$7$	0	0
$8$	−455.813	−2.51804
$9$	537.760	2.21301
$10$	−259.668	−0.821143
$11$	−132.501	−0.330169	−0.165085	−	0.986279i	$-0.552790\pi$
$11$	−132.501	−0.330169	−0.165085	+	0.986279i	$0.552790\pi$
$12$	−2120.36	−4.25067
$13$	−802.665	−1.31727	−0.658637	−	0.752461i	$-0.728867\pi$
$13$	−802.665	−1.31727	−0.658637	+	0.752461i	$0.728867\pi$
$14$	0	0
$15$	−698.552	−0.801624
$16$	2306.11	2.25207
$17$	−763.068	−0.640385	−0.320192	−	0.947353i	$-0.603748\pi$
$17$	−763.068	−0.640385	−0.320192	+	0.947353i	$0.603748\pi$
$18$	−5585.57	−4.06337
$19$	61.2154	0.0389024	0.0194512	−	0.999811i	$-0.493808\pi$
$19$	61.2154	0.0389024	0.0194512	+	0.999811i	$0.493808\pi$
$20$	1897.10	1.06051
$21$	0	0
$22$	1376.25	0.606234
$23$	3589.61	1.41491	0.707454	−	0.706760i	$-0.249844\pi$
$23$	3589.61	1.41491	0.707454	+	0.706760i	$0.249844\pi$
$24$	12736.4	4.51354
$25$	625.000	0.200000
$26$	8337.06	2.41869
$27$	−8236.22	−2.17430
$28$	0	0
$29$	−4593.21	−1.01419	−0.507097	−	0.861889i	$-0.669281\pi$
$29$	−4593.21	−1.01419	−0.507097	+	0.861889i	$0.669281\pi$
$30$	7255.67	1.47189
$31$	384.018	0.0717708	0.0358854	−	0.999356i	$-0.488575\pi$
$31$	384.018	0.0717708	0.0358854	+	0.999356i	$0.488575\pi$
$32$	−9366.97	−1.61705
$33$	3702.35	0.591824
$34$	7925.78	1.17583
$35$	0	0
$36$	40807.5	5.24788
$37$	5377.28	0.645741	0.322870	−	0.946443i	$-0.395352\pi$
$37$	5377.28	0.645741	0.322870	+	0.946443i	$0.395352\pi$
$38$	−635.827	−0.0714299
$39$	22428.1	2.36119
$40$	−11395.3	−1.12610
$41$	20530.3	1.90737	0.953686	−	0.300804i	$-0.0972549\pi$
$41$	20530.3	1.90737	0.953686	+	0.300804i	$0.0972549\pi$
$42$	0	0
$43$	−12175.3	−1.00417	−0.502086	−	0.864818i	$-0.667434\pi$
$43$	−12175.3	−1.00417	−0.502086	+	0.864818i	$0.667434\pi$
$44$	−10054.7	−0.782957
$45$	13444.0	0.989686
$46$	−37284.3	−2.59796
$47$	15232.4	1.00583	0.502915	−	0.864336i	$-0.332261\pi$
$47$	15232.4	1.00583	0.502915	+	0.864336i	$0.332261\pi$
$48$	−64437.7	−4.03680
$49$	0	0
$50$	−6491.71	−0.367226
$51$	21321.7	1.14788
$52$	−60909.6	−3.12376
$53$	1369.77	0.0669821	0.0334911	−	0.999439i	$-0.489337\pi$
$53$	1369.77	0.0669821	0.0334911	+	0.999439i	$0.489337\pi$
$54$	85547.4	3.99229
$55$	−3312.52	−0.147656
$56$	0	0
$57$	−1710.48	−0.0697320
$58$	47708.4	1.86219
$59$	−27738.1	−1.03740	−0.518700	−	0.854956i	$-0.673584\pi$
$59$	−27738.1	−1.03740	−0.518700	+	0.854956i	$0.673584\pi$
$60$	−53009.1	−1.90096
$61$	15708.6	0.540523	0.270261	−	0.962787i	$-0.412890\pi$
$61$	15708.6	0.540523	0.270261	+	0.962787i	$0.412890\pi$
$62$	−3988.70	−0.131781
$63$	0	0
$64$	23496.6	0.717058
$65$	−20066.6	−0.589103
$66$	−38455.3	−1.08667
$67$	−16813.0	−0.457571	−0.228786	−	0.973477i	$-0.573475\pi$
$67$	−16813.0	−0.457571	−0.228786	+	0.973477i	$0.573475\pi$
$68$	−57904.8	−1.51860
$69$	−100301.	−2.53620
$70$	0	0
$71$	37925.9	0.892873	0.446437	−	0.894815i	$-0.352693\pi$
$71$	37925.9	0.892873	0.446437	+	0.894815i	$0.352693\pi$
$72$	−245118.	−5.57243
$73$	48894.9	1.07388	0.536940	−	0.843620i	$-0.319580\pi$
$73$	48894.9	1.07388	0.536940	+	0.843620i	$0.319580\pi$
$74$	−55852.3	−1.18566
$75$	−17463.8	−0.358497
$76$	4645.28	0.0922524
$77$	0	0
$78$	−232955.	−4.33546
$79$	−66582.2	−1.20030	−0.600151	−	0.799887i	$-0.704893\pi$
$79$	−66582.2	−1.20030	−0.600151	+	0.799887i	$0.704893\pi$
$80$	57652.9	1.00715
$81$	99461.4	1.68439
$82$	−213243.	−3.50219
$83$	63358.0	1.00950	0.504750	−	0.863266i	$-0.331585\pi$
$83$	63358.0	1.00950	0.504750	+	0.863266i	$0.331585\pi$
$84$	0	0
$85$	−19076.7	−0.286389
$86$	126461.	1.84379
$87$	128344.	1.81793
$88$	60395.6	0.831378
$89$	69175.3	0.925712	0.462856	−	0.886434i	$-0.346825\pi$
$89$	69175.3	0.925712	0.462856	+	0.886434i	$0.346825\pi$
$90$	−139639.	−1.81719
$91$	0	0
$92$	272395.	3.35528
$93$	−10730.3	−0.128648
$94$	−158215.	−1.84684
$95$	1530.38	0.0173977
$96$	261733.	2.89855
$97$	55697.0	0.601039	0.300519	−	0.953776i	$-0.402840\pi$
$97$	55697.0	0.601039	0.300519	+	0.953776i	$0.402840\pi$
$98$	0	0
$99$	−71253.7	−0.730667
$100$	47427.6	0.474276
$101$	−29027.0	−0.283139	−0.141569	−	0.989928i	$-0.545215\pi$
$101$	−29027.0	−0.283139	−0.141569	+	0.989928i	$0.545215\pi$
$102$	−221463.	−2.10766
$103$	−86612.7	−0.804430	−0.402215	−	0.915545i	$-0.631760\pi$
$103$	−86612.7	−0.804430	−0.402215	+	0.915545i	$0.631760\pi$
$104$	365865.	3.31694
$105$	0	0
$106$	−14227.5	−0.122988
$107$	−1392.82	−0.0117608	−0.00588039	−	0.999983i	$-0.501872\pi$
$107$	−1392.82	−0.0117608	−0.00588039	+	0.999983i	$0.501872\pi$
$108$	−624999.	−5.15608
$109$	162159.	1.30730	0.653651	−	0.756796i	$-0.273237\pi$
$109$	162159.	1.30730	0.653651	+	0.756796i	$0.273237\pi$
$110$	34406.2	0.271116
$111$	−150252.	−1.15748
$112$	0	0
$113$	41748.6	0.307571	0.153786	−	0.988104i	$-0.450853\pi$
$113$	41748.6	0.307571	0.153786	+	0.988104i	$0.450853\pi$
$114$	17766.3	0.128037
$115$	89740.3	0.632766
$116$	−348552.	−2.40504
$117$	−431641.	−2.91513
$118$	288108.	1.90480
$119$	0	0
$120$	318409.	2.01852
$121$	−143495.	−0.890988
$122$	−163161.	−0.992471
$123$	−573659.	−3.41894
$124$	29140.9	0.170196
$125$	15625.0	0.0894427
$126$	0	0
$127$	−49413.8	−0.271856	−0.135928	−	0.990719i	$-0.543402\pi$
$127$	−49413.8	−0.271856	−0.135928	+	0.990719i	$0.543402\pi$
$128$	55690.8	0.300440
$129$	340203.	1.79996
$130$	208427.	1.08167
$131$	−63290.9	−0.322228	−0.161114	−	0.986936i	$-0.551509\pi$
$131$	−63290.9	−0.322228	−0.161114	+	0.986936i	$0.551509\pi$
$132$	280950.	1.40344
$133$	0	0
$134$	174632.	0.840161
$135$	−205905.	−0.972374
$136$	347817.	1.61251
$137$	368631.	1.67799	0.838997	−	0.544137i	$-0.183143\pi$
$137$	368631.	1.67799	0.838997	+	0.544137i	$0.183143\pi$
$138$	1.04180e6	4.65680
$139$	−100506.	−0.441220	−0.220610	−	0.975362i	$-0.570805\pi$
$139$	−100506.	−0.441220	−0.220610	+	0.975362i	$0.570805\pi$
$140$	0	0
$141$	−425626.	−1.80294
$142$	−393926.	−1.63943
$143$	106354.	0.434923
$144$	1.24014e6	4.98383
$145$	−114830.	−0.453561
$146$	−507858.	−1.97179
$147$	0	0
$148$	408050.	1.53130
$149$	289797.	1.06937	0.534685	−	0.845052i	$-0.320430\pi$
$149$	289797.	1.06937	0.534685	+	0.845052i	$0.320430\pi$
$150$	181392.	0.658248
$151$	−475852.	−1.69836	−0.849180	−	0.528104i	$-0.822903\pi$
$151$	−475852.	−1.69836	−0.849180	+	0.528104i	$0.822903\pi$
$152$	−27902.8	−0.0979576
$153$	−410348.	−1.41718
$154$	0	0
$155$	9600.46	0.0320969
$156$	1.70194e6	5.59929
$157$	37131.5	0.120225	0.0601123	−	0.998192i	$-0.480854\pi$
$157$	37131.5	0.120225	0.0601123	+	0.998192i	$0.480854\pi$
$158$	691571.	2.20391
$159$	−38274.3	−0.120065
$160$	−234174.	−0.723168
$161$	0	0
$162$	−1.03308e6	−3.09276
$163$	−453030.	−1.33554	−0.667771	−	0.744367i	$-0.732751\pi$
$163$	−453030.	−1.33554	−0.667771	+	0.744367i	$0.732751\pi$
$164$	1.55792e6	4.52311
$165$	92558.7	0.264672
$166$	−658082.	−1.85357
$167$	−223362.	−0.619752	−0.309876	−	0.950777i	$-0.600288\pi$
$167$	−223362.	−0.619752	−0.309876	+	0.950777i	$0.600288\pi$
$168$	0	0
$169$	272978.	0.735209
$170$	198145.	0.525848
$171$	32919.2	0.0860912
$172$	−923911.	−2.38127
$173$	−482127.	−1.22475	−0.612374	−	0.790568i	$-0.709785\pi$
$173$	−482127.	−1.22475	−0.612374	+	0.790568i	$0.709785\pi$
$174$	−1.33307e6	−3.33796
$175$	0	0
$176$	−305562.	−0.743563
$177$	775060.	1.85953
$178$	−718505.	−1.69973
$179$	−653347.	−1.52409	−0.762046	−	0.647523i	$-0.775805\pi$
$179$	−653347.	−1.52409	−0.762046	+	0.647523i	$0.775805\pi$
$180$	1.02019e6	2.34692
$181$	179855.	0.408061	0.204030	−	0.978965i	$-0.434596\pi$
$181$	179855.	0.408061	0.204030	+	0.978965i	$0.434596\pi$
$182$	0	0
$183$	−438932.	−0.968879
$184$	−1.63619e6	−3.56279
$185$	134432.	0.288784
$186$	111452.	0.236215
$187$	101107.	0.211435
$188$	1.15590e6	2.38521
$189$	0	0
$190$	−15895.7	−0.0319444
$191$	516528.	1.02450	0.512249	−	0.858837i	$-0.328813\pi$
$191$	516528.	1.02450	0.512249	+	0.858837i	$0.328813\pi$
$192$	−656543.	−1.28532
$193$	341920.	0.660740	0.330370	−	0.943851i	$-0.392826\pi$
$193$	341920.	0.660740	0.330370	+	0.943851i	$0.392826\pi$
$194$	−578510.	−1.10359
$195$	560703.	1.05596
$196$	0	0
$197$	−805869.	−1.47944	−0.739722	−	0.672912i	$-0.765043\pi$
$197$	−805869.	−1.47944	−0.739722	+	0.672912i	$0.765043\pi$
$198$	740093.	1.34160
$199$	−878271.	−1.57216	−0.786078	−	0.618127i	$-0.787892\pi$
$199$	−878271.	−1.57216	−0.786078	+	0.618127i	$0.787892\pi$
$200$	−284883.	−0.503607
$201$	469791.	0.820190
$202$	301496.	0.519880
$203$	0	0
$204$	1.61798e6	2.72206
$205$	513257.	0.853003
$206$	899623.	1.47704
$207$	1.93035e6	3.13120
$208$	−1.85104e6	−2.96659
$209$	−8111.08	−0.0128444
$210$	0	0
$211$	−848810.	−1.31251	−0.656257	−	0.754537i	$-0.727861\pi$
$211$	−848810.	−1.31251	−0.656257	+	0.754537i	$0.727861\pi$
$212$	103944.	0.158840
$213$	−1.05973e6	−1.60046
$214$	14466.9	0.0215943
$215$	−304382.	−0.449079
$216$	3.75418e6	5.47495
$217$	0	0
$218$	−1.68431e6	−2.40038
$219$	−1.36622e6	−1.92492
$220$	−251368.	−0.350149
$221$	612488.	0.843562
$222$	1.56063e6	2.12529
$223$	−700322.	−0.943052	−0.471526	−	0.881852i	$-0.656297\pi$
$223$	−700322.	−0.943052	−0.471526	+	0.881852i	$0.656297\pi$
$224$	0	0
$225$	336100.	0.442601
$226$	−433631.	−0.564741
$227$	−795250.	−1.02433	−0.512164	−	0.858888i	$-0.671156\pi$
$227$	−795250.	−1.02433	−0.512164	+	0.858888i	$0.671156\pi$
$228$	−129799.	−0.165361
$229$	1.18132e6	1.48860	0.744301	−	0.667844i	$-0.232783\pi$
$229$	1.18132e6	1.48860	0.744301	+	0.667844i	$0.232783\pi$
$230$	−932108.	−1.16184
$231$	0	0
$232$	2.09364e6	2.55378
$233$	89303.7	0.107765	0.0538827	−	0.998547i	$-0.482840\pi$
$233$	89303.7	0.107765	0.0538827	+	0.998547i	$0.482840\pi$
$234$	4.48334e6	5.35257
$235$	380811.	0.449821
$236$	−2.10488e6	−2.46007
$237$	1.86045e6	2.15152
$238$	0	0
$239$	1.28432e6	1.45438	0.727191	−	0.686436i	$-0.240826\pi$
$239$	1.28432e6	1.45438	0.727191	+	0.686436i	$0.240826\pi$
$240$	−1.61094e6	−1.80531
$241$	−882390.	−0.978629	−0.489314	−	0.872107i	$-0.662753\pi$
$241$	−882390.	−0.978629	−0.489314	+	0.872107i	$0.662753\pi$
$242$	1.49044e6	1.63597
$243$	−777759.	−0.844946
$244$	1.19204e6	1.28179
$245$	0	0
$246$	5.95844e6	6.27762
$247$	−49135.4	−0.0512451
$248$	−175041.	−0.180721
$249$	−1.77035e6	−1.80951
$250$	−162293.	−0.164229
$251$	489271.	0.490191	0.245095	−	0.969499i	$-0.421181\pi$
$251$	489271.	0.490191	0.245095	+	0.969499i	$0.421181\pi$
$252$	0	0
$253$	−475626.	−0.467159
$254$	513248.	0.499163
$255$	533043.	0.513348
$256$	−1.33033e6	−1.26871
$257$	968316.	0.914502	0.457251	−	0.889338i	$-0.348834\pi$
$257$	968316.	0.914502	0.457251	+	0.889338i	$0.348834\pi$
$258$	−3.53360e6	−3.30497
$259$	0	0
$260$	−1.52274e6	−1.39699
$261$	−2.47004e6	−2.24442
$262$	657386.	0.591653
$263$	−2.06170e6	−1.83796	−0.918980	−	0.394303i	$-0.870986\pi$
$263$	−2.06170e6	−1.83796	−0.918980	+	0.394303i	$0.870986\pi$
$264$	−1.68758e6	−1.49023
$265$	34244.3	0.0299553
$266$	0	0
$267$	−1.93290e6	−1.65933
$268$	−1.27584e6	−1.08508
$269$	−1.91422e6	−1.61292	−0.806458	−	0.591291i	$-0.798618\pi$
$269$	−1.91422e6	−1.61292	−0.806458	+	0.591291i	$0.798618\pi$
$270$	2.13868e6	1.78541
$271$	−648945.	−0.536765	−0.268383	−	0.963312i	$-0.586489\pi$
$271$	−648945.	−0.536765	−0.268383	+	0.963312i	$0.586489\pi$
$272$	−1.75972e6	−1.44219
$273$	0	0
$274$	−3.82887e6	−3.08102
$275$	−82813.0	−0.0660339
$276$	−7.61128e6	−6.01430
$277$	609318.	0.477139	0.238569	−	0.971125i	$-0.423322\pi$
$277$	609318.	0.477139	0.238569	+	0.971125i	$0.423322\pi$
$278$	1.04393e6	0.810138
$279$	206510.	0.158829
$280$	0	0
$281$	−1.99061e6	−1.50390	−0.751952	−	0.659217i	$-0.770888\pi$
$281$	−1.99061e6	−1.50390	−0.751952	+	0.659217i	$0.770888\pi$
$282$	4.42086e6	3.31043
$283$	−127141.	−0.0943666	−0.0471833	−	0.998886i	$-0.515024\pi$
$283$	−127141.	−0.0943666	−0.0471833	+	0.998886i	$0.515024\pi$
$284$	2.87797e6	2.11734
$285$	−42762.1	−0.0311851
$286$	−1.10467e6	−0.798576
$287$	0	0
$288$	−5.03719e6	−3.57855
$289$	−837584.	−0.589907
$290$	1.19271e6	0.832799
$291$	−1.55629e6	−1.07735
$292$	3.71035e6	2.54658
$293$	20479.1	0.0139361	0.00696805	−	0.999976i	$-0.497782\pi$
$293$	20479.1	0.0139361	0.00696805	+	0.999976i	$0.497782\pi$
$294$	0	0
$295$	−693452.	−0.463940
$296$	−2.45103e6	−1.62600
$297$	1.09131e6	0.717886
$298$	−3.01004e6	−1.96350
$299$	−2.88126e6	−1.86382
$300$	−1.32523e6	−0.850133
$301$	0	0
$302$	4.94255e6	3.11841
$303$	811076.	0.507522
$304$	141170.	0.0876107
$305$	392716.	0.241729
$306$	4.26217e6	2.60212
$307$	1.08442e6	0.656676	0.328338	−	0.944560i	$-0.393511\pi$
$307$	1.08442e6	0.656676	0.328338	+	0.944560i	$0.393511\pi$
$308$	0	0
$309$	2.42014e6	1.44193
$310$	−99717.4	−0.0589341
$311$	2.13660e6	1.25263	0.626314	−	0.779571i	$-0.284563\pi$
$311$	2.13660e6	1.25263	0.626314	+	0.779571i	$0.284563\pi$
$312$	−1.02230e7	−5.94557
$313$	−1.79419e6	−1.03516	−0.517580	−	0.855635i	$-0.673167\pi$
$313$	−1.79419e6	−1.03516	−0.517580	+	0.855635i	$0.673167\pi$
$314$	−385675.	−0.220748
$315$	0	0
$316$	−5.05254e6	−2.84637
$317$	607762.	0.339692	0.169846	−	0.985471i	$-0.445673\pi$
$317$	607762.	0.339692	0.169846	+	0.985471i	$0.445673\pi$
$318$	397545.	0.220454
$319$	608604.	0.334856
$320$	587414.	0.320678
$321$	38918.3	0.0210810
$322$	0	0
$323$	−46711.5	−0.0249125
$324$	7.54755e6	3.99432
$325$	−501666.	−0.263455
$326$	4.70550e6	2.45223
$327$	−4.53107e6	−2.34332
$328$	−9.35798e6	−4.80283
$329$	0	0
$330$	−961382.	−0.485972
$331$	−538396.	−0.270104	−0.135052	−	0.990838i	$-0.543120\pi$
$331$	−538396.	−0.270104	−0.135052	+	0.990838i	$0.543120\pi$
$332$	4.80787e6	2.39391
$333$	2.89169e6	1.42903
$334$	2.32000e6	1.13795
$335$	−420326.	−0.204632
$336$	0	0
$337$	1.72106e6	0.825510	0.412755	−	0.910842i	$-0.364567\pi$
$337$	1.72106e6	0.825510	0.412755	+	0.910842i	$0.364567\pi$
$338$	−2.83535e6	−1.34994
$339$	−1.16654e6	−0.551317
$340$	−1.44762e6	−0.679137
$341$	−50882.7	−0.0236965
$342$	−341923.	−0.158075
$343$	0	0
$344$	5.54965e6	2.52854
$345$	−2.50753e6	−1.13422
$346$	5.00773e6	2.24880
$347$	2.74378e6	1.22328	0.611640	−	0.791136i	$-0.290510\pi$
$347$	2.74378e6	1.22328	0.611640	+	0.791136i	$0.290510\pi$
$348$	9.73927e6	4.31100
$349$	−3.32781e6	−1.46250	−0.731249	−	0.682110i	$-0.761062\pi$
$349$	−3.32781e6	−1.46250	−0.731249	+	0.682110i	$0.761062\pi$
$350$	0	0
$351$	6.61092e6	2.86414
$352$	1.24113e6	0.533901
$353$	−2.21885e6	−0.947745	−0.473872	−	0.880594i	$-0.657144\pi$
$353$	−2.21885e6	−0.947745	−0.473872	+	0.880594i	$0.657144\pi$
$354$	−8.05034e6	−3.41434
$355$	948147.	0.399305
$356$	5.24931e6	2.19521
$357$	0	0
$358$	6.78614e6	2.79843
$359$	−2.19557e6	−0.899109	−0.449554	−	0.893253i	$-0.648417\pi$
$359$	−2.19557e6	−0.899109	−0.449554	+	0.893253i	$0.648417\pi$
$360$	−6.12796e6	−2.49207
$361$	−2.47235e6	−0.998487
$362$	−1.86810e6	−0.749254
$363$	4.00954e6	1.59708
$364$	0	0
$365$	1.22237e6	0.480254
$366$	4.55907e6	1.77899
$367$	−98918.7	−0.0383366	−0.0191683	−	0.999816i	$-0.506102\pi$
$367$	−98918.7	−0.0383366	−0.0191683	+	0.999816i	$0.506102\pi$
$368$	8.27806e6	3.18646
$369$	1.10404e7	4.22102
$370$	−1.39631e6	−0.530245
$371$	0	0
$372$	−814258.	−0.305074
$373$	2.39481e6	0.891251	0.445625	−	0.895220i	$-0.352981\pi$
$373$	2.39481e6	0.891251	0.445625	+	0.895220i	$0.352981\pi$
$374$	−1.05017e6	−0.388223
$375$	−436595.	−0.160325
$376$	−6.94315e6	−2.53272
$377$	3.68681e6	1.33597
$378$	0	0
$379$	2.74448e6	0.981436	0.490718	−	0.871318i	$-0.336734\pi$
$379$	2.74448e6	0.981436	0.490718	+	0.871318i	$0.336734\pi$
$380$	116132.	0.0412565
$381$	1.38072e6	0.487298
$382$	−5.36504e6	−1.88111
$383$	2.06158e6	0.718130	0.359065	−	0.933313i	$-0.383096\pi$
$383$	2.06158e6	0.718130	0.359065	+	0.933313i	$0.383096\pi$
$384$	−1.55612e6	−0.538535
$385$	0	0
$386$	−3.55143e6	−1.21321
$387$	−6.54739e6	−2.22224
$388$	4.22652e6	1.42529
$389$	2.64856e6	0.887433	0.443717	−	0.896167i	$-0.353660\pi$
$389$	2.64856e6	0.887433	0.443717	+	0.896167i	$0.353660\pi$
$390$	−5.82388e6	−1.93888
$391$	−2.73912e6	−0.906085
$392$	0	0
$393$	1.76848e6	0.577589
$394$	8.37034e6	2.71645
$395$	−1.66456e6	−0.536791
$396$	−5.40703e6	−1.73269
$397$	2.06588e6	0.657853	0.328926	−	0.944356i	$-0.393313\pi$
$397$	2.06588e6	0.657853	0.328926	+	0.944356i	$0.393313\pi$
$398$	9.12237e6	2.88669
$399$	0	0
$400$	1.44132e6	0.450413
$401$	−1.84739e6	−0.573718	−0.286859	−	0.957973i	$-0.592611\pi$
$401$	−1.84739e6	−0.573718	−0.286859	+	0.957973i	$0.592611\pi$
$402$	−4.87959e6	−1.50598
$403$	−308238.	−0.0945418
$404$	−2.20269e6	−0.671430
$405$	2.48654e6	0.753281
$406$	0	0
$407$	−712493.	−0.213204
$408$	−9.71872e6	−2.89040
$409$	−6.52308e6	−1.92817	−0.964084	−	0.265598i	$-0.914430\pi$
$409$	−6.52308e6	−1.92817	−0.964084	+	0.265598i	$0.914430\pi$
$410$	−5.33106e6	−1.56623
$411$	−1.03003e7	−3.00778
$412$	−6.57253e6	−1.90761
$413$	0	0
$414$	−2.00500e7	−5.74929
$415$	1.58395e6	0.451462
$416$	7.51854e6	2.13010
$417$	2.80835e6	0.790880
$418$	84247.6	0.0235840
$419$	5.44720e6	1.51579	0.757894	−	0.652378i	$-0.226228\pi$
$419$	5.44720e6	1.51579	0.757894	+	0.652378i	$0.226228\pi$
$420$	0	0
$421$	1.64211e6	0.451541	0.225771	−	0.974180i	$-0.427510\pi$
$421$	1.64211e6	0.451541	0.225771	+	0.974180i	$0.427510\pi$
$422$	8.81636e6	2.40995
$423$	8.19140e6	2.22591
$424$	−624361.	−0.168663
$425$	−476918.	−0.128077
$426$	1.10071e7	2.93866
$427$	0	0
$428$	−105693.	−0.0278893
$429$	−2.97175e6	−0.779594
$430$	3.16154e6	0.824569
$431$	421002.	0.109167	0.0545835	−	0.998509i	$-0.482617\pi$
$431$	421002.	0.109167	0.0545835	+	0.998509i	$0.482617\pi$
$432$	−1.89937e7	−4.89665
$433$	265058.	0.0679393	0.0339697	−	0.999423i	$-0.489185\pi$
$433$	265058.	0.0679393	0.0339697	+	0.999423i	$0.489185\pi$
$434$	0	0
$435$	3.20860e6	0.813002
$436$	1.23053e7	3.10011
$437$	219739.	0.0550433
$438$	1.41906e7	3.53440
$439$	3.01126e6	0.745738	0.372869	−	0.927884i	$-0.378374\pi$
$439$	3.01126e6	0.745738	0.372869	+	0.927884i	$0.378374\pi$
$440$	1.50989e6	0.371804
$441$	0	0
$442$	−6.36175e6	−1.54889
$443$	−3.68381e6	−0.891841	−0.445921	−	0.895072i	$-0.647124\pi$
$443$	−3.68381e6	−0.891841	−0.445921	+	0.895072i	$0.647124\pi$
$444$	−1.14018e7	−2.74483
$445$	1.72938e6	0.413991
$446$	7.27405e6	1.73157
$447$	−8.09752e6	−1.91683
$448$	0	0
$449$	−5.63615e6	−1.31937	−0.659685	−	0.751542i	$-0.729310\pi$
$449$	−5.63615e6	−1.31937	−0.659685	+	0.751542i	$0.729310\pi$
$450$	−3.49098e6	−0.812674
$451$	−2.72028e6	−0.629756
$452$	3.16806e6	0.729368
$453$	1.32963e7	3.04428
$454$	8.26004e6	1.88080
$455$	0	0
$456$	779661.	0.175588
$457$	5.45504e6	1.22182	0.610910	−	0.791700i	$-0.290804\pi$
$457$	5.45504e6	1.22182	0.610910	+	0.791700i	$0.290804\pi$
$458$	−1.22700e7	−2.73327
$459$	6.28480e6	1.39239
$460$	6.80987e6	1.50053
$461$	−361201.	−0.0791583	−0.0395792	−	0.999216i	$-0.512602\pi$
$461$	−361201.	−0.0791583	−0.0395792	+	0.999216i	$0.512602\pi$
$462$	0	0
$463$	−4.05569e6	−0.879251	−0.439625	−	0.898181i	$-0.644889\pi$
$463$	−4.05569e6	−0.879251	−0.439625	+	0.898181i	$0.644889\pi$
$464$	−1.05925e7	−2.28403
$465$	−268257.	−0.0575332
$466$	−927574.	−0.197872
$467$	1.12204e6	0.238077	0.119038	−	0.992890i	$-0.462019\pi$
$467$	1.12204e6	0.238077	0.119038	+	0.992890i	$0.462019\pi$
$468$	−3.27548e7	−6.91289
$469$	0	0
$470$	−3.95538e6	−0.825931
$471$	−1.03753e6	−0.215501
$472$	1.26434e7	2.61221
$473$	1.61323e6	0.331547
$474$	−1.93240e7	−3.95048
$475$	38259.6	0.00778048
$476$	0	0
$477$	736610.	0.148232
$478$	−1.33399e7	−2.67044
$479$	4.14410e6	0.825262	0.412631	−	0.910898i	$-0.364610\pi$
$479$	4.14410e6	0.825262	0.412631	+	0.910898i	$0.364610\pi$
$480$	6.54332e6	1.29627
$481$	−4.31615e6	−0.850617
$482$	9.16515e6	1.79689
$483$	0	0
$484$	−1.08890e7	−2.11287
$485$	1.39242e6	0.268793
$486$	8.07837e6	1.55143
$487$	−6.17446e6	−1.17971	−0.589857	−	0.807508i	$-0.700816\pi$
$487$	−6.17446e6	−1.17971	−0.589857	+	0.807508i	$0.700816\pi$
$488$	−7.16020e6	−1.36106
$489$	1.26586e7	2.39394
$490$	0	0
$491$	−1.11624e6	−0.208956	−0.104478	−	0.994527i	$-0.533317\pi$
$491$	−1.11624e6	−0.208956	−0.104478	+	0.994527i	$0.533317\pi$
$492$	−4.35317e7	−8.10760
$493$	3.50493e6	0.649475
$494$	510356.	0.0940927
$495$	−1.78134e6	−0.326764
$496$	885590.	0.161633
$497$	0	0
$498$	1.83882e7	3.32251
$499$	9.53803e6	1.71478	0.857388	−	0.514671i	$-0.172086\pi$
$499$	9.53803e6	1.71478	0.857388	+	0.514671i	$0.172086\pi$
$500$	1.18569e6	0.212103
$501$	6.24120e6	1.11090
$502$	−5.08193e6	−0.900055
$503$	−3.62037e6	−0.638018	−0.319009	−	0.947752i	$-0.603350\pi$
$503$	−3.62037e6	−0.638018	−0.319009	+	0.947752i	$0.603350\pi$
$504$	0	0
$505$	−725676.	−0.126623
$506$	4.94020e6	0.857765
$507$	−7.62758e6	−1.31785
$508$	−3.74973e6	−0.644674
$509$	−2.36607e6	−0.404792	−0.202396	−	0.979304i	$-0.564873\pi$
$509$	−2.36607e6	−0.404792	−0.202396	+	0.979304i	$0.564873\pi$
$510$	−5.53657e6	−0.942575
$511$	0	0
$512$	1.20357e7	2.02907
$513$	−504183.	−0.0845853
$514$	−1.00576e7	−1.67915
$515$	−2.16532e6	−0.359752
$516$	2.58160e7	4.26840
$517$	−2.01831e6	−0.332094
$518$	0	0
$519$	1.34716e7	2.19534
$520$	9.14663e6	1.48338
$521$	120692.	0.0194798	0.00973992	−	0.999953i	$-0.496900\pi$
$521$	120692.	0.0194798	0.00973992	+	0.999953i	$0.496900\pi$
$522$	2.56557e7	4.12105
$523$	−1.08230e7	−1.73018	−0.865091	−	0.501615i	$-0.832739\pi$
$523$	−1.08230e7	−1.73018	−0.865091	+	0.501615i	$0.832739\pi$
$524$	−4.80278e6	−0.764125
$525$	0	0
$526$	2.14143e7	3.37474
$527$	−293032.	−0.0459609
$528$	8.53804e6	1.33283
$529$	6.44897e6	1.00196
$530$	−355687.	−0.0550019
$531$	−1.49164e7	−2.29577
$532$	0	0
$533$	−1.64789e7	−2.51253
$534$	2.00765e7	3.04674
$535$	−34820.5	−0.00525958
$536$	7.66360e6	1.15218
$537$	1.82559e7	2.73191
$538$	1.98825e7	2.96153
$539$	0	0
$540$	−1.56250e7	−2.30587
$541$	−2.08816e6	−0.306740	−0.153370	−	0.988169i	$-0.549013\pi$
$541$	−2.08816e6	−0.306740	−0.153370	+	0.988169i	$0.549013\pi$
$542$	6.74041e6	0.985572
$543$	−5.02551e6	−0.731443
$544$	7.14764e6	1.03554
$545$	4.05398e6	0.584643
$546$	0	0
$547$	−4.45529e6	−0.636660	−0.318330	−	0.947980i	$-0.603122\pi$
$547$	−4.45529e6	−0.636660	−0.318330	+	0.947980i	$0.603122\pi$
$548$	2.79732e7	3.97916
$549$	8.44748e6	1.19618
$550$	860156.	0.121247
$551$	−281175.	−0.0394546
$552$	4.57186e7	6.38624
$553$	0	0
$554$	−6.32882e6	−0.876090
$555$	−3.75631e6	−0.517641
$556$	−7.62682e6	−1.04630
$557$	−1.36327e7	−1.86185	−0.930924	−	0.365214i	$-0.880996\pi$
$557$	−1.36327e7	−1.86185	−0.930924	+	0.365214i	$0.880996\pi$
$558$	−2.14496e6	−0.291631
$559$	9.77267e6	1.32277
$560$	0	0
$561$	−2.82514e6	−0.378995
$562$	2.06759e7	2.76137
$563$	−6.74502e6	−0.896835	−0.448417	−	0.893824i	$-0.648012\pi$
$563$	−6.74502e6	−0.896835	−0.448417	+	0.893824i	$0.648012\pi$
$564$	−3.22983e7	−4.27545
$565$	1.04371e6	0.137550
$566$	1.32058e6	0.173269
$567$	0	0
$568$	−1.72871e7	−2.24829
$569$	−1.02524e7	−1.32753	−0.663763	−	0.747943i	$-0.731042\pi$
$569$	−1.02524e7	−1.32753	−0.663763	+	0.747943i	$0.731042\pi$
$570$	444159.	0.0572599
$571$	−1.29295e7	−1.65955	−0.829775	−	0.558098i	$-0.811531\pi$
$571$	−1.29295e7	−1.65955	−0.829775	+	0.558098i	$0.811531\pi$
$572$	8.07057e6	1.03137
$573$	−1.44329e7	−1.83640
$574$	0	0
$575$	2.24351e6	0.282981
$576$	1.26355e7	1.58685
$577$	−5.52053e6	−0.690305	−0.345153	−	0.938547i	$-0.612173\pi$
$577$	−5.52053e6	−0.690305	−0.345153	+	0.938547i	$0.612173\pi$
$578$	8.69976e6	1.08315
$579$	−9.55395e6	−1.18437
$580$	−8.71379e6	−1.07557
$581$	0	0
$582$	1.61648e7	1.97816
$583$	−181496.	−0.0221154
$584$	−2.22869e7	−2.70407
$585$	−1.07910e7	−1.30369
$586$	−212711.	−0.0255885
$587$	−5.89116e6	−0.705677	−0.352838	−	0.935684i	$-0.614783\pi$
$587$	−5.89116e6	−0.705677	−0.352838	+	0.935684i	$0.614783\pi$
$588$	0	0
$589$	23507.8	0.00279206
$590$	7.20270e6	0.851855
$591$	2.25176e7	2.65188
$592$	1.24006e7	1.45425
$593$	−1.25597e7	−1.46671	−0.733354	−	0.679847i	$-0.762046\pi$
$593$	−1.25597e7	−1.46671	−0.733354	+	0.679847i	$0.762046\pi$
$594$	−1.13351e7	−1.31813
$595$	0	0
$596$	2.19910e7	2.53588
$597$	2.45407e7	2.81807
$598$	2.99268e7	3.42222
$599$	−9.59347e6	−1.09247	−0.546234	−	0.837633i	$-0.683939\pi$
$599$	−9.59347e6	−1.09247	−0.546234	+	0.837633i	$0.683939\pi$
$600$	7.96023e6	0.902709
$601$	495264.	0.0559307	0.0279654	−	0.999609i	$-0.491097\pi$
$601$	495264.	0.0559307	0.0279654	+	0.999609i	$0.491097\pi$
$602$	0	0
$603$	−9.04138e6	−1.01261
$604$	−3.61096e7	−4.02746
$605$	−3.58736e6	−0.398462
$606$	−8.42443e6	−0.931877
$607$	1.45272e7	1.60033	0.800165	−	0.599780i	$-0.204745\pi$
$607$	1.45272e7	1.60033	0.800165	+	0.599780i	$0.204745\pi$
$608$	−573403.	−0.0629072
$609$	0	0
$610$	−4.07904e6	−0.443847
$611$	−1.22265e7	−1.32495
$612$	−3.11389e7	−3.36066
$613$	1.11108e7	1.19425	0.597126	−	0.802148i	$-0.296309\pi$
$613$	1.11108e7	1.19425	0.597126	+	0.802148i	$0.296309\pi$
$614$	−1.12636e7	−1.20574
$615$	−1.43415e7	−1.52900
$616$	0	0
$617$	−325507.	−0.0344229	−0.0172115	−	0.999852i	$-0.505479\pi$
$617$	−325507.	−0.0344229	−0.0172115	+	0.999852i	$0.505479\pi$
$618$	−2.51373e7	−2.64757
$619$	−1.92017e6	−0.201425	−0.100713	−	0.994916i	$-0.532112\pi$
$619$	−1.92017e6	−0.201425	−0.100713	+	0.994916i	$0.532112\pi$
$620$	728523.	0.0761139
$621$	−2.95648e7	−3.07643
$622$	−2.21923e7	−2.29999
$623$	0	0
$624$	5.17219e7	5.31756
$625$	390625.	0.0400000
$626$	1.86358e7	1.90069
$627$	226641.	0.0230234
$628$	2.81769e6	0.285098
$629$	−4.10323e6	−0.413523
$630$	0	0
$631$	−7.23818e6	−0.723696	−0.361848	−	0.932237i	$-0.617854\pi$
$631$	−7.23818e6	−0.723696	−0.361848	+	0.932237i	$0.617854\pi$
$632$	3.03490e7	3.02240
$633$	2.37175e7	2.35266
$634$	−6.31266e6	−0.623720
$635$	−1.23534e6	−0.121578
$636$	−2.90442e6	−0.284719
$637$	0	0
$638$	−6.32140e6	−0.614839
$639$	2.03950e7	1.97593
$640$	1.39227e6	0.134361
$641$	7.66338e6	0.736674	0.368337	−	0.929692i	$-0.379927\pi$
$641$	7.66338e6	0.736674	0.368337	+	0.929692i	$0.379927\pi$
$642$	−404234.	−0.0387076
$643$	−3.42013e6	−0.326223	−0.163112	−	0.986608i	$-0.552153\pi$
$643$	−3.42013e6	−0.326223	−0.163112	+	0.986608i	$0.552153\pi$
$644$	0	0
$645$	8.50507e6	0.804968
$646$	485180.	0.0457426
$647$	2.21315e6	0.207850	0.103925	−	0.994585i	$-0.466860\pi$
$647$	2.21315e6	0.207850	0.103925	+	0.994585i	$0.466860\pi$
$648$	−4.53358e7	−4.24135
$649$	3.67532e6	0.342518
$650$	5.21067e6	0.483738
$651$	0	0
$652$	−3.43778e7	−3.16708
$653$	1.68516e7	1.54653	0.773264	−	0.634084i	$-0.218623\pi$
$653$	1.68516e7	1.54653	0.773264	+	0.634084i	$0.218623\pi$
$654$	4.70630e7	4.30264
$655$	−1.58227e6	−0.144105
$656$	4.73452e7	4.29553
$657$	2.62937e7	2.37650
$658$	0	0
$659$	−4.37802e6	−0.392703	−0.196351	−	0.980534i	$-0.562909\pi$
$659$	−4.37802e6	−0.392703	−0.196351	+	0.980534i	$0.562909\pi$
$660$	7.02374e6	0.627637
$661$	−1.91655e7	−1.70614	−0.853072	−	0.521793i	$-0.825263\pi$
$661$	−1.91655e7	−1.70614	−0.853072	+	0.521793i	$0.825263\pi$
$662$	5.59217e6	0.495947
$663$	−1.71142e7	−1.51207
$664$	−2.88794e7	−2.54196
$665$	0	0
$666$	−3.00352e7	−2.62388
$667$	−1.64878e7	−1.43499
$668$	−1.69496e7	−1.46967
$669$	1.95685e7	1.69041
$670$	4.36581e6	0.375732
$671$	−2.08141e6	−0.178464
$672$	0	0
$673$	1.32590e7	1.12842	0.564212	−	0.825630i	$-0.309180\pi$
$673$	1.32590e7	1.12842	0.564212	+	0.825630i	$0.309180\pi$
$674$	−1.78762e7	−1.51575
$675$	−5.14764e6	−0.434859
$676$	2.07147e7	1.74346
$677$	−2.12311e6	−0.178033	−0.0890166	−	0.996030i	$-0.528372\pi$
$677$	−2.12311e6	−0.178033	−0.0890166	+	0.996030i	$0.528372\pi$
$678$	1.21166e7	1.01229
$679$	0	0
$680$	8.69541e6	0.721137
$681$	2.22209e7	1.83609
$682$	528505.	0.0435099
$683$	−3.82921e6	−0.314092	−0.157046	−	0.987591i	$-0.550197\pi$
$683$	−3.82921e6	−0.314092	−0.157046	+	0.987591i	$0.550197\pi$
$684$	2.49805e6	0.204155
$685$	9.21577e6	0.750421
$686$	0	0
$687$	−3.30085e7	−2.66830
$688$	−2.80776e7	−2.26146
$689$	−1.09947e6	−0.0882338
$690$	2.60451e7	2.08258
$691$	7.49135e6	0.596850	0.298425	−	0.954433i	$-0.403539\pi$
$691$	7.49135e6	0.596850	0.298425	+	0.954433i	$0.403539\pi$
$692$	−3.65858e7	−2.90434
$693$	0	0
$694$	−2.84989e7	−2.24611
$695$	−2.51265e6	−0.197320
$696$	−5.85008e7	−4.57761
$697$	−1.56660e7	−1.22145
$698$	3.45651e7	2.68534
$699$	−2.49533e6	−0.193168
$700$	0	0
$701$	1.94223e7	1.49281	0.746405	−	0.665492i	$-0.231778\pi$
$701$	1.94223e7	1.49281	0.746405	+	0.665492i	$0.231778\pi$
$702$	−6.86659e7	−5.25894
$703$	329172.	0.0251209
$704$	−3.11331e6	−0.236751
$705$	−1.06407e7	−0.806298
$706$	2.30466e7	1.74018
$707$	0	0
$708$	5.88148e7	4.40964
$709$	−8.21902e6	−0.614051	−0.307025	−	0.951701i	$-0.599334\pi$
$709$	−8.21902e6	−0.614051	−0.307025	+	0.951701i	$0.599334\pi$
$710$	−9.84815e6	−0.733177
$711$	−3.58053e7	−2.65627
$712$	−3.15310e7	−2.33097
$713$	1.37848e6	0.101549
$714$	0	0
$715$	2.65884e6	0.194504
$716$	−4.95787e7	−3.61420
$717$	−3.58866e7	−2.60696
$718$	2.28048e7	1.65088
$719$	7.59175e6	0.547671	0.273835	−	0.961777i	$-0.411708\pi$
$719$	7.59175e6	0.547671	0.273835	+	0.961777i	$0.411708\pi$
$720$	3.10034e7	2.22884
$721$	0	0
$722$	2.56797e7	1.83335
$723$	2.46558e7	1.75418
$724$	1.36481e7	0.967668
$725$	−2.87075e6	−0.202839
$726$	−4.16460e7	−2.93246
$727$	−1.31356e7	−0.921748	−0.460874	−	0.887465i	$-0.652464\pi$
$727$	−1.31356e7	−0.921748	−0.460874	+	0.887465i	$0.652464\pi$
$728$	0	0
$729$	−2.43693e6	−0.169834
$730$	−1.26964e7	−0.881810
$731$	9.29057e6	0.643056
$732$	−3.33080e7	−2.29758
$733$	−6.89469e6	−0.473974	−0.236987	−	0.971513i	$-0.576160\pi$
$733$	−6.89469e6	−0.473974	−0.236987	+	0.971513i	$0.576160\pi$
$734$	1.02744e6	0.0703910
$735$	0	0
$736$	−3.36238e7	−2.28798
$737$	2.22774e6	0.151076
$738$	−1.14673e8	−7.75036
$739$	2.67404e7	1.80118	0.900590	−	0.434670i	$-0.143135\pi$
$739$	2.67404e7	1.80118	0.900590	+	0.434670i	$0.143135\pi$
$740$	1.02013e7	0.684817
$741$	1.37295e6	0.0918561
$742$	0	0
$743$	−5.90356e6	−0.392321	−0.196161	−	0.980572i	$-0.562847\pi$
$743$	−5.90356e6	−0.392321	−0.196161	+	0.980572i	$0.562847\pi$
$744$	4.89100e6	0.323941
$745$	7.24492e6	0.478236
$746$	−2.48743e7	−1.63645
$747$	3.40714e7	2.23403
$748$	7.67243e6	0.501394
$749$	0	0
$750$	4.53480e6	0.294378
$751$	1.95022e7	1.26178	0.630892	−	0.775871i	$-0.282689\pi$
$751$	1.95022e7	1.26178	0.630892	+	0.775871i	$0.282689\pi$
$752$	3.51278e7	2.26520
$753$	−1.36713e7	−0.878660
$754$	−3.82939e7	−2.45302
$755$	−1.18963e7	−0.759529
$756$	0	0
$757$	−8.03409e6	−0.509562	−0.254781	−	0.966999i	$-0.582003\pi$
$757$	−8.03409e6	−0.509562	−0.254781	+	0.966999i	$0.582003\pi$
$758$	−2.85062e7	−1.80205
$759$	1.32900e7	0.837376
$760$	−697569.	−0.0438080
$761$	3.55632e6	0.222607	0.111304	−	0.993786i	$-0.464497\pi$
$761$	3.55632e6	0.222607	0.111304	+	0.993786i	$0.464497\pi$
$762$	−1.43412e7	−0.894743
$763$	0	0
$764$	3.91963e7	2.42947
$765$	−1.02587e7	−0.633780
$766$	−2.14131e7	−1.31858
$767$	2.22644e7	1.36654
$768$	3.71723e7	2.27414
$769$	−2.65789e7	−1.62077	−0.810384	−	0.585899i	$-0.800742\pi$
$769$	−2.65789e7	−1.62077	−0.810384	+	0.585899i	$0.800742\pi$
$770$	0	0
$771$	−2.70568e7	−1.63923
$772$	2.59463e7	1.56687
$773$	−3.14386e7	−1.89241	−0.946204	−	0.323571i	$-0.895117\pi$
$773$	−3.14386e7	−1.89241	−0.946204	+	0.323571i	$0.895117\pi$
$774$	6.80059e7	4.08032
$775$	240011.	0.0143542
$776$	−2.53874e7	−1.51344
$777$	0	0
$778$	−2.75099e7	−1.62944
$779$	1.25677e6	0.0742013
$780$	4.25485e7	2.50408
$781$	−5.02521e6	−0.294799
$782$	2.84505e7	1.66369
$783$	3.78307e7	2.20516
$784$	0	0
$785$	928287.	0.0537660
$786$	−1.83687e7	−1.06053
$787$	1.42418e7	0.819647	0.409823	−	0.912165i	$-0.365590\pi$
$787$	1.42418e7	0.819647	0.409823	+	0.912165i	$0.365590\pi$
$788$	−6.11527e7	−3.50833
$789$	5.76082e7	3.29452
$790$	1.72893e7	0.985620
$791$	0	0
$792$	3.24784e7	1.83984
$793$	−1.26088e7	−0.712016
$794$	−2.14577e7	−1.20790
$795$	−956858.	−0.0536945
$796$	−6.66469e7	−3.72818
$797$	−3.25117e7	−1.81298	−0.906492	−	0.422223i	$-0.861250\pi$
$797$	−3.25117e7	−1.81298	−0.906492	+	0.422223i	$0.861250\pi$
$798$	0	0
$799$	−1.16234e7	−0.644119
$800$	−5.85436e6	−0.323411
$801$	3.71997e7	2.04861
$802$	1.91884e7	1.05342
$803$	−6.47861e6	−0.354562
$804$	3.56497e7	1.94498
$805$	0	0
$806$	3.20159e6	0.173591
$807$	5.34874e7	2.89113
$808$	1.32309e7	0.712953
$809$	8.75841e6	0.470494	0.235247	−	0.971936i	$-0.424410\pi$
$809$	8.75841e6	0.470494	0.235247	+	0.971936i	$0.424410\pi$
$810$	−2.58270e7	−1.38312
$811$	2.52537e7	1.34826	0.674130	−	0.738613i	$-0.264519\pi$
$811$	2.52537e7	1.34826	0.674130	+	0.738613i	$0.264519\pi$
$812$	0	0
$813$	1.81329e7	0.962144
$814$	7.40048e6	0.391470
$815$	−1.13257e7	−0.597273
$816$	4.91703e7	2.58510
$817$	−745314.	−0.0390647
$818$	6.77535e7	3.54037
$819$	0	0
$820$	3.89481e7	2.02279
$821$	−2.60982e7	−1.35130	−0.675651	−	0.737221i	$-0.736138\pi$
$821$	−2.60982e7	−1.35130	−0.675651	+	0.737221i	$0.736138\pi$
$822$	1.06987e8	5.52268
$823$	1.43570e7	0.738863	0.369432	−	0.929258i	$-0.379552\pi$
$823$	1.43570e7	0.738863	0.369432	+	0.929258i	$0.379552\pi$
$824$	3.94792e7	2.02558
$825$	2.31397e6	0.118365
$826$	0	0
$827$	−1.34784e7	−0.685290	−0.342645	−	0.939465i	$-0.611323\pi$
$827$	−1.34784e7	−0.685290	−0.342645	+	0.939465i	$0.611323\pi$
$828$	1.46483e8	7.42526
$829$	1.14245e7	0.577364	0.288682	−	0.957425i	$-0.406783\pi$
$829$	1.14245e7	0.577364	0.288682	+	0.957425i	$0.406783\pi$
$830$	−1.64521e7	−0.828944
$831$	−1.70256e7	−0.855264
$832$	−1.88599e7	−0.944561
$833$	0	0
$834$	−2.91696e7	−1.45216
$835$	−5.58405e6	−0.277162
$836$	−615503.	−0.0304589
$837$	−3.16286e6	−0.156051
$838$	−5.65786e7	−2.78319
$839$	1.51205e7	0.741585	0.370793	−	0.928716i	$-0.379086\pi$
$839$	1.51205e7	0.741585	0.370793	+	0.928716i	$0.379086\pi$
$840$	0	0
$841$	586407.	0.0285897
$842$	−1.70562e7	−0.829089
$843$	5.56218e7	2.69573
$844$	−6.44112e7	−3.11247
$845$	6.82445e6	0.328796
$846$	−8.50819e7	−4.08706
$847$	0	0
$848$	3.15885e6	0.150848
$849$	3.55257e6	0.169151
$850$	4.95362e6	0.235166
$851$	1.93023e7	0.913663
$852$	−8.04166e7	−3.79531
$853$	−2.37769e7	−1.11888	−0.559438	−	0.828872i	$-0.688983\pi$
$853$	−2.37769e7	−1.11888	−0.559438	+	0.828872i	$0.688983\pi$
$854$	0	0
$855$	822980.	0.0385012
$856$	634866.	0.0296141
$857$	−5.58994e6	−0.259989	−0.129995	−	0.991515i	$-0.541496\pi$
$857$	−5.58994e6	−0.259989	−0.129995	+	0.991515i	$0.541496\pi$
$858$	3.08667e7	1.43144
$859$	6.57947e6	0.304234	0.152117	−	0.988362i	$-0.451391\pi$
$859$	6.57947e6	0.304234	0.152117	+	0.988362i	$0.451391\pi$
$860$	−2.30978e7	−1.06494
$861$	0	0
$862$	−4.37284e6	−0.200445
$863$	221099.	0.0101055	0.00505277	−	0.999987i	$-0.498392\pi$
$863$	221099.	0.0101055	0.00505277	+	0.999987i	$0.498392\pi$
$864$	7.71484e7	3.51595
$865$	−1.20532e7	−0.547724
$866$	−2.75309e6	−0.124746
$867$	2.34038e7	1.05740
$868$	0	0
$869$	8.82219e6	0.396303
$870$	−3.33268e7	−1.49278
$871$	1.34952e7	0.602746
$872$	−7.39144e7	−3.29183
$873$	2.99516e7	1.33010
$874$	−2.28237e6	−0.101067
$875$	0	0
$876$	−1.03675e8	−4.56471
$877$	−4.40848e6	−0.193548	−0.0967742	−	0.995306i	$-0.530852\pi$
$877$	−4.40848e6	−0.193548	−0.0967742	+	0.995306i	$0.530852\pi$
$878$	−3.12771e7	−1.36927
$879$	−572228.	−0.0249803
$880$	−7.63905e6	−0.332531
$881$	−3.12332e6	−0.135574	−0.0677871	−	0.997700i	$-0.521594\pi$
$881$	−3.12332e6	−0.135574	−0.0677871	+	0.997700i	$0.521594\pi$
$882$	0	0
$883$	−5.91201e6	−0.255172	−0.127586	−	0.991827i	$-0.540723\pi$
$883$	−5.91201e6	−0.255172	−0.127586	+	0.991827i	$0.540723\pi$
$884$	4.64782e7	2.00041
$885$	1.93765e7	0.831605
$886$	3.82627e7	1.63754
$887$	−2.99048e7	−1.27624	−0.638118	−	0.769938i	$-0.720287\pi$
$887$	−2.99048e7	−1.27624	−0.638118	+	0.769938i	$0.720287\pi$
$888$	6.84870e7	2.91458
$889$	0	0
$890$	−1.79626e7	−0.760142
$891$	−1.31787e7	−0.556133
$892$	−5.31433e7	−2.23633
$893$	932459.	0.0391292
$894$	8.41068e7	3.51955
$895$	−1.63337e7	−0.681595
$896$	0	0
$897$	8.05083e7	3.34087
$898$	5.85412e7	2.42254
$899$	−1.76388e6	−0.0727895
$900$	2.55047e7	1.04958
$901$	−1.04523e6	−0.0428943
$902$	2.82548e7	1.15631
$903$	0	0
$904$	−1.90296e7	−0.774475
$905$	4.49636e6	0.182490
$906$	−1.38105e8	−5.58971
$907$	1.14372e7	0.461637	0.230819	−	0.972997i	$-0.425860\pi$
$907$	1.14372e7	0.461637	0.230819	+	0.972997i	$0.425860\pi$
$908$	−6.03469e7	−2.42907
$909$	−1.56096e7	−0.626587
$910$	0	0
$911$	3.69307e7	1.47432	0.737160	−	0.675719i	$-0.236167\pi$
$911$	3.69307e7	1.47432	0.737160	+	0.675719i	$0.236167\pi$
$912$	−3.94457e6	−0.157041
$913$	−8.39498e6	−0.333306
$914$	−5.66600e7	−2.24342
$915$	−1.09733e7	−0.433296
$916$	8.96435e7	3.53004
$917$	0	0
$918$	−6.52785e7	−2.55660
$919$	−4.03035e6	−0.157418	−0.0787089	−	0.996898i	$-0.525080\pi$
$919$	−4.03035e6	−0.157418	−0.0787089	+	0.996898i	$0.525080\pi$
$920$	−4.09048e7	−1.59333
$921$	−3.03010e7	−1.17708
$922$	3.75170e6	0.145345
$923$	−3.04418e7	−1.17616
$924$	0	0
$925$	3.36080e6	0.129148
$926$	4.21254e7	1.61442
$927$	−4.65769e7	−1.78021
$928$	4.30245e7	1.64001
$929$	1.33708e7	0.508297	0.254148	−	0.967165i	$-0.418205\pi$
$929$	1.33708e7	0.508297	0.254148	+	0.967165i	$0.418205\pi$
$930$	2.78631e6	0.105639
$931$	0	0
$932$	6.77674e6	0.255553
$933$	−5.97010e7	−2.24532
$934$	−1.16543e7	−0.437140
$935$	2.52768e6	0.0945568
$936$	1.96748e8	7.34041
$937$	3.65899e7	1.36148	0.680741	−	0.732524i	$-0.261658\pi$
$937$	3.65899e7	1.36148	0.680741	+	0.732524i	$0.261658\pi$
$938$	0	0
$939$	5.01334e7	1.85551
$940$	2.88975e7	1.06670
$941$	−1.02348e7	−0.376795	−0.188398	−	0.982093i	$-0.560329\pi$
$941$	−1.02348e7	−0.376795	−0.188398	+	0.982093i	$0.560329\pi$
$942$	1.07766e7	0.395688
$943$	7.36958e7	2.69875
$944$	−6.39672e7	−2.33629
$945$	0	0
$946$	−1.67562e7	−0.608763
$947$	1.01364e7	0.367291	0.183645	−	0.982993i	$-0.441210\pi$
$947$	1.01364e7	0.367291	0.183645	+	0.982993i	$0.441210\pi$
$948$	1.41178e8	5.10208
$949$	−3.92462e7	−1.41459
$950$	−397392.	−0.0142860
$951$	−1.69821e7	−0.608893
$952$	0	0
$953$	2.70615e6	0.0965206	0.0482603	−	0.998835i	$-0.484632\pi$
$953$	2.70615e6	0.0965206	0.0482603	+	0.998835i	$0.484632\pi$
$954$	−7.65097e6	−0.272173
$955$	1.29132e7	0.458169
$956$	9.74595e7	3.44889
$957$	−1.70057e7	−0.600224
$958$	−4.30437e7	−1.51529
$959$	0	0
$960$	−1.64136e7	−0.574811
$961$	−2.84817e7	−0.994849
$962$	4.48307e7	1.56184
$963$	−749004.	−0.0260267
$964$	−6.69594e7	−2.32070
$965$	8.54799e6	0.295492
$966$	0	0
$967$	−8.48268e6	−0.291720	−0.145860	−	0.989305i	$-0.546595\pi$
$967$	−8.48268e6	−0.291720	−0.145860	+	0.989305i	$0.546595\pi$
$968$	6.54067e7	2.24354
$969$	1.30522e6	0.0446553
$970$	−1.44627e7	−0.493539
$971$	5.21222e6	0.177409	0.0887043	−	0.996058i	$-0.471727\pi$
$971$	5.21222e6	0.177409	0.0887043	+	0.996058i	$0.471727\pi$
$972$	−5.90196e7	−2.00369
$973$	0	0
$974$	6.41325e7	2.16611
$975$	1.40176e7	0.472239
$976$	3.62259e7	1.21729
$977$	1.79936e7	0.603090	0.301545	−	0.953452i	$-0.402498\pi$
$977$	1.79936e7	0.603090	0.301545	+	0.953452i	$0.402498\pi$
$978$	−1.31481e8	−4.39559
$979$	−9.16577e6	−0.305642
$980$	0	0
$981$	8.72029e7	2.89307
$982$	1.15941e7	0.383671
$983$	−2.60735e7	−0.860628	−0.430314	−	0.902679i	$-0.641597\pi$
$983$	−2.60735e7	−0.860628	−0.430314	+	0.902679i	$0.641597\pi$
$984$	2.61481e8	8.60901
$985$	−2.01467e7	−0.661628
$986$	−3.64048e7	−1.19252
$987$	0	0
$988$	−3.72860e6	−0.121522
$989$	−4.37045e7	−1.42081
$990$	1.85023e7	0.599982
$991$	−8.44686e6	−0.273219	−0.136610	−	0.990625i	$-0.543621\pi$
$991$	−8.44686e6	−0.273219	−0.136610	+	0.990625i	$0.543621\pi$
$992$	−3.59709e6	−0.116057
$993$	1.50439e7	0.484158
$994$	0	0
$995$	−2.19568e7	−0.703090
$996$	−1.34342e8	−4.29105
$997$	4.53151e7	1.44379	0.721896	−	0.692001i	$-0.243271\pi$
$997$	4.53151e7	1.44379	0.721896	+	0.692001i	$0.243271\pi$
$998$	−9.90689e7	−3.14855
$999$	−4.42884e7	−1.40403

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.d.1.1		3
7.6	odd	2		35.6.a.c.1.1	✓	3
21.20	even	2		315.6.a.i.1.3		3
28.27	even	2		560.6.a.q.1.1		3
35.13	even	4		175.6.b.e.99.6		6
35.27	even	4		175.6.b.e.99.1		6
35.34	odd	2		175.6.a.e.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.a.c.1.1	✓	3	7.6	odd	2
175.6.a.e.1.3		3	35.34	odd	2
175.6.b.e.99.1		6	35.27	even	4
175.6.b.e.99.6		6	35.13	even	4
245.6.a.d.1.1		3	1.1	even	1	trivial
315.6.a.i.1.3		3	21.20	even	2
560.6.a.q.1.1		3	28.27	even	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)

\(f(q)\)	\(=\)	\(q-10.3867 q^{2} -27.9421 q^{3} +75.8842 q^{4} +25.0000 q^{5} +290.227 q^{6} -455.813 q^{8} +537.760 q^{9} +O(q^{10})\)	\(q-10.3867 q^{2} -27.9421 q^{3} +75.8842 q^{4} +25.0000 q^{5} +290.227 q^{6} -455.813 q^{8} +537.760 q^{9} -259.668 q^{10} -132.501 q^{11} -2120.36 q^{12} -802.665 q^{13} -698.552 q^{15} +2306.11 q^{16} -763.068 q^{17} -5585.57 q^{18} +61.2154 q^{19} +1897.10 q^{20} +1376.25 q^{22} +3589.61 q^{23} +12736.4 q^{24} +625.000 q^{25} +8337.06 q^{26} -8236.22 q^{27} -4593.21 q^{29} +7255.67 q^{30} +384.018 q^{31} -9366.97 q^{32} +3702.35 q^{33} +7925.78 q^{34} +40807.5 q^{36} +5377.28 q^{37} -635.827 q^{38} +22428.1 q^{39} -11395.3 q^{40} +20530.3 q^{41} -12175.3 q^{43} -10054.7 q^{44} +13444.0 q^{45} -37284.3 q^{46} +15232.4 q^{47} -64437.7 q^{48} -6491.71 q^{50} +21321.7 q^{51} -60909.6 q^{52} +1369.77 q^{53} +85547.4 q^{54} -3312.52 q^{55} -1710.48 q^{57} +47708.4 q^{58} -27738.1 q^{59} -53009.1 q^{60} +15708.6 q^{61} -3988.70 q^{62} +23496.6 q^{64} -20066.6 q^{65} -38455.3 q^{66} -16813.0 q^{67} -57904.8 q^{68} -100301. q^{69} +37925.9 q^{71} -245118. q^{72} +48894.9 q^{73} -55852.3 q^{74} -17463.8 q^{75} +4645.28 q^{76} -232955. q^{78} -66582.2 q^{79} +57652.9 q^{80} +99461.4 q^{81} -213243. q^{82} +63358.0 q^{83} -19076.7 q^{85} +126461. q^{86} +128344. q^{87} +60395.6 q^{88} +69175.3 q^{89} -139639. q^{90} +272395. q^{92} -10730.3 q^{93} -158215. q^{94} +1530.38 q^{95} +261733. q^{96} +55697.0 q^{97} -71253.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} - 26 q^{3} + 112 q^{4} + 75 q^{5} + 96 q^{6} - 120 q^{8} + 489 q^{9}+O(q^{10}) \) 3 * q - 6 * q^2 - 26 * q^3 + 112 * q^4 + 75 * q^5 + 96 * q^6 - 120 * q^8 + 489 * q^9	\( 3 q - 6 q^{2} - 26 q^{3} + 112 q^{4} + 75 q^{5} + 96 q^{6} - 120 q^{8} + 489 q^{9} - 150 q^{10} - 194 q^{11} - 2956 q^{12} - 1892 q^{13} - 650 q^{15} + 1496 q^{16} + 184 q^{17} - 6078 q^{18} - 1212 q^{19} + 2800 q^{20} - 872 q^{22} + 3188 q^{23} + 13920 q^{24} + 1875 q^{25} + 9836 q^{26} - 7910 q^{27} - 11332 q^{29} + 2400 q^{30} - 9200 q^{31} - 20256 q^{32} + 8278 q^{33} + 18492 q^{34} + 38236 q^{36} + 6042 q^{37} - 25520 q^{38} + 12842 q^{39} - 3000 q^{40} - 10442 q^{41} + 28112 q^{43} - 20436 q^{44} + 12225 q^{45} - 41856 q^{46} - 2330 q^{47} - 68808 q^{48} - 3750 q^{50} + 3622 q^{51} - 63524 q^{52} + 7190 q^{53} + 138960 q^{54} - 4850 q^{55} + 45508 q^{57} + 37260 q^{58} - 23760 q^{59} - 73900 q^{60} - 8722 q^{61} - 24848 q^{62} + 4976 q^{64} - 47300 q^{65} - 24368 q^{66} - 97572 q^{67} - 3564 q^{68} - 92596 q^{69} - 52816 q^{71} - 251640 q^{72} - 34870 q^{73} - 241892 q^{74} - 16250 q^{75} - 115256 q^{76} - 142096 q^{78} - 71546 q^{79} + 37400 q^{80} - 3957 q^{81} - 241908 q^{82} + 20920 q^{83} + 4600 q^{85} + 266024 q^{86} + 112298 q^{87} + 59200 q^{88} + 192622 q^{89} - 151950 q^{90} + 248952 q^{92} - 20392 q^{93} - 360128 q^{94} - 30300 q^{95} + 296256 q^{96} - 116320 q^{97} - 60752 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 - 26 * q^3 + 112 * q^4 + 75 * q^5 + 96 * q^6 - 120 * q^8 + 489 * q^9 - 150 * q^10 - 194 * q^11 - 2956 * q^12 - 1892 * q^13 - 650 * q^15 + 1496 * q^16 + 184 * q^17 - 6078 * q^18 - 1212 * q^19 + 2800 * q^20 - 872 * q^22 + 3188 * q^23 + 13920 * q^24 + 1875 * q^25 + 9836 * q^26 - 7910 * q^27 - 11332 * q^29 + 2400 * q^30 - 9200 * q^31 - 20256 * q^32 + 8278 * q^33 + 18492 * q^34 + 38236 * q^36 + 6042 * q^37 - 25520 * q^38 + 12842 * q^39 - 3000 * q^40 - 10442 * q^41 + 28112 * q^43 - 20436 * q^44 + 12225 * q^45 - 41856 * q^46 - 2330 * q^47 - 68808 * q^48 - 3750 * q^50 + 3622 * q^51 - 63524 * q^52 + 7190 * q^53 + 138960 * q^54 - 4850 * q^55 + 45508 * q^57 + 37260 * q^58 - 23760 * q^59 - 73900 * q^60 - 8722 * q^61 - 24848 * q^62 + 4976 * q^64 - 47300 * q^65 - 24368 * q^66 - 97572 * q^67 - 3564 * q^68 - 92596 * q^69 - 52816 * q^71 - 251640 * q^72 - 34870 * q^73 - 241892 * q^74 - 16250 * q^75 - 115256 * q^76 - 142096 * q^78 - 71546 * q^79 + 37400 * q^80 - 3957 * q^81 - 241908 * q^82 + 20920 * q^83 + 4600 * q^85 + 266024 * q^86 + 112298 * q^87 + 59200 * q^88 + 192622 * q^89 - 151950 * q^90 + 248952 * q^92 - 20392 * q^93 - 360128 * q^94 - 30300 * q^95 + 296256 * q^96 - 116320 * q^97 - 60752 * q^99

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