LMFDB - Embedded newform 145.6.a.c.1.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [145,6,Mod(1,145)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("145.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(145, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	145.a (trivial)

Newform invariants

comment:select newform

sage:traces = [13,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$23.2556538729$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 6 x^{12} - 296 x^{11} + 1238 x^{10} + 33250 x^{9} - 78360 x^{8} - 1708024 x^{7} + \cdots + 251513192 $ x^13 - 6x^12 - 296x^11 + 1238x^10 + 33250x^9 - 78360x^8 - 1708024x^7 + 1285720x^6 + 37751885x^5 + 19686342x^4 - 252219704x^3 - 352125886x^2 + 108510888x + 251513192
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-9.63745$ of defining polynomial
Character	$\chi$	$=$	145.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+10.6375 q^{2} +7.90198 q^{3} +81.1554 q^{4} -25.0000 q^{5} +84.0569 q^{6} +171.117 q^{7} +522.888 q^{8} -180.559 q^{9} -265.936 q^{10} +349.035 q^{11} +641.288 q^{12} -367.714 q^{13} +1820.25 q^{14} -197.550 q^{15} +2965.22 q^{16} -79.3079 q^{17} -1920.68 q^{18} -1922.95 q^{19} -2028.88 q^{20} +1352.16 q^{21} +3712.85 q^{22} +3602.40 q^{23} +4131.85 q^{24} +625.000 q^{25} -3911.54 q^{26} -3346.95 q^{27} +13887.0 q^{28} +841.000 q^{29} -2101.42 q^{30} -773.522 q^{31} +14810.0 q^{32} +2758.07 q^{33} -843.633 q^{34} -4277.92 q^{35} -14653.3 q^{36} -2307.63 q^{37} -20455.3 q^{38} -2905.67 q^{39} -13072.2 q^{40} -17859.0 q^{41} +14383.6 q^{42} +20958.8 q^{43} +28326.1 q^{44} +4513.97 q^{45} +38320.3 q^{46} -25263.7 q^{47} +23431.1 q^{48} +12474.0 q^{49} +6648.41 q^{50} -626.689 q^{51} -29842.0 q^{52} -5065.18 q^{53} -35603.0 q^{54} -8725.88 q^{55} +89474.9 q^{56} -15195.1 q^{57} +8946.10 q^{58} -16380.0 q^{59} -16032.2 q^{60} +9332.80 q^{61} -8228.30 q^{62} -30896.6 q^{63} +62653.4 q^{64} +9192.86 q^{65} +29338.8 q^{66} -72265.4 q^{67} -6436.26 q^{68} +28466.1 q^{69} -45506.2 q^{70} -34216.5 q^{71} -94411.9 q^{72} +64735.5 q^{73} -24547.3 q^{74} +4938.74 q^{75} -156058. q^{76} +59725.8 q^{77} -30909.0 q^{78} -35527.2 q^{79} -74130.5 q^{80} +17428.2 q^{81} -189974. q^{82} +74144.2 q^{83} +109735. q^{84} +1982.70 q^{85} +222948. q^{86} +6645.57 q^{87} +182506. q^{88} -33510.8 q^{89} +48017.1 q^{90} -62922.1 q^{91} +292354. q^{92} -6112.35 q^{93} -268742. q^{94} +48073.7 q^{95} +117028. q^{96} +165247. q^{97} +132691. q^{98} -63021.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 7 q^{2} + 2 q^{3} + 213 q^{4} - 325 q^{5} - 3 q^{6} - 18 q^{7} - 399 q^{8} + 1155 q^{9} - 175 q^{10} + 844 q^{11} + 167 q^{12} - 704 q^{13} + 4425 q^{14} - 50 q^{15} + 5805 q^{16} - 210 q^{17} + 7378 q^{18}+ \cdots - 3872 q^{99}+O(q^{100}) $ 13 * q + 7 * q^2 + 2 * q^3 + 213 * q^4 - 325 * q^5 - 3 * q^6 - 18 * q^7 - 399 * q^8 + 1155 * q^9 - 175 * q^10 + 844 * q^11 + 167 * q^12 - 704 * q^13 + 4425 * q^14 - 50 * q^15 + 5805 * q^16 - 210 * q^17 + 7378 * q^18 + 2524 * q^19 - 5325 * q^20 + 7088 * q^21 - 3772 * q^22 + 10806 * q^23 + 11131 * q^24 + 8125 * q^25 + 15003 * q^26 - 2872 * q^27 + 6007 * q^28 + 10933 * q^29 + 75 * q^30 + 6820 * q^31 - 9761 * q^32 + 9416 * q^33 + 18557 * q^34 + 450 * q^35 + 28284 * q^36 - 7784 * q^37 + 43872 * q^38 + 30524 * q^39 + 9975 * q^40 + 17950 * q^41 + 104284 * q^42 + 24570 * q^43 + 101386 * q^44 - 28875 * q^45 + 71703 * q^46 + 26242 * q^47 + 96475 * q^48 + 45423 * q^49 + 4375 * q^50 - 5632 * q^51 - 2925 * q^52 + 50580 * q^53 + 61352 * q^54 - 21100 * q^55 + 172651 * q^56 + 71600 * q^57 + 5887 * q^58 + 50712 * q^59 - 4175 * q^60 - 24104 * q^61 + 82941 * q^62 - 1298 * q^63 + 75673 * q^64 + 17600 * q^65 - 7632 * q^66 - 93110 * q^67 - 113909 * q^68 + 116878 * q^69 - 110625 * q^70 + 253344 * q^71 - 206562 * q^72 - 11006 * q^73 - 171316 * q^74 + 1250 * q^75 - 275002 * q^76 + 106744 * q^77 - 84017 * q^78 - 23792 * q^79 - 145125 * q^80 + 229097 * q^81 - 461156 * q^82 + 115802 * q^83 - 224096 * q^84 + 5250 * q^85 + 31283 * q^86 + 1682 * q^87 - 635028 * q^88 + 87446 * q^89 - 184450 * q^90 - 33904 * q^91 + 197053 * q^92 - 168912 * q^93 - 464496 * q^94 - 63100 * q^95 - 186929 * q^96 + 27766 * q^97 - 166558 * q^98 - 3872 * q^99

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 $

$2$	10.6375	1.88045	0.940227	−	0.340549i	$-0.110613\pi$
$2$	10.6375	1.88045	0.940227	+	0.340549i	$0.110613\pi$
$3$	7.90198	0.506912	0.253456	−	0.967347i	$-0.418433\pi$
$3$	7.90198	0.506912	0.253456	+	0.967347i	$0.418433\pi$
$4$	81.1554	2.53610
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	84.0569	0.953225
$7$	171.117	1.31992	0.659960	−	0.751301i	$-0.270573\pi$
$7$	171.117	1.31992	0.659960	+	0.751301i	$0.270573\pi$
$8$	522.888	2.88857
$9$	−180.559	−0.743040
$10$	−265.936	−0.840964
$11$	349.035	0.869736	0.434868	−	0.900494i	$-0.356795\pi$
$11$	349.035	0.869736	0.434868	+	0.900494i	$0.356795\pi$
$12$	641.288	1.28558
$13$	−367.714	−0.603465	−0.301733	−	0.953393i	$-0.597565\pi$
$13$	−367.714	−0.603465	−0.301733	+	0.953393i	$0.597565\pi$
$14$	1820.25	2.48205
$15$	−197.550	−0.226698
$16$	2965.22	2.89572
$17$	−79.3079	−0.0665570	−0.0332785	−	0.999446i	$-0.510595\pi$
$17$	−79.3079	−0.0665570	−0.0332785	+	0.999446i	$0.510595\pi$
$18$	−1920.68	−1.39725
$19$	−1922.95	−1.22204	−0.611018	−	0.791617i	$-0.709240\pi$
$19$	−1922.95	−1.22204	−0.611018	+	0.791617i	$0.709240\pi$
$20$	−2028.88	−1.13418
$21$	1352.16	0.669084
$22$	3712.85	1.63550
$23$	3602.40	1.41995	0.709973	−	0.704229i	$-0.248707\pi$
$23$	3602.40	1.41995	0.709973	+	0.704229i	$0.248707\pi$
$24$	4131.85	1.46425
$25$	625.000	0.200000
$26$	−3911.54	−1.13479
$27$	−3346.95	−0.883568
$28$	13887.0	3.34746
$29$	841.000	0.185695
$29$	841.000	0.185695
$30$	−2101.42	−0.426295
$31$	−773.522	−0.144567	−0.0722834	−	0.997384i	$-0.523029\pi$
$31$	−773.522	−0.144567	−0.0722834	+	0.997384i	$0.523029\pi$
$32$	14810.0	2.55670
$33$	2758.07	0.440880
$34$	−843.633	−0.125157
$35$	−4277.92	−0.590286
$36$	−14653.3	−1.88443
$37$	−2307.63	−0.277117	−0.138558	−	0.990354i	$-0.544247\pi$
$37$	−2307.63	−0.277117	−0.138558	+	0.990354i	$0.544247\pi$
$38$	−20455.3	−2.29798
$39$	−2905.67	−0.305904
$40$	−13072.2	−1.29181
$41$	−17859.0	−1.65920	−0.829598	−	0.558361i	$-0.811430\pi$
$41$	−17859.0	−1.65920	−0.829598	+	0.558361i	$0.811430\pi$
$42$	14383.6	1.25818
$43$	20958.8	1.72860	0.864300	−	0.502977i	$-0.167762\pi$
$43$	20958.8	1.72860	0.864300	+	0.502977i	$0.167762\pi$
$44$	28326.1	2.20574
$45$	4513.97	0.332298
$46$	38320.3	2.67014
$47$	−25263.7	−1.66822	−0.834109	−	0.551599i	$-0.814018\pi$
$47$	−25263.7	−1.66822	−0.834109	+	0.551599i	$0.814018\pi$
$48$	23431.1	1.46788
$49$	12474.0	0.742188
$50$	6648.41	0.376091
$51$	−626.689	−0.0337386
$52$	−29842.0	−1.53045
$53$	−5065.18	−0.247688	−0.123844	−	0.992302i	$-0.539522\pi$
$53$	−5065.18	−0.247688	−0.123844	+	0.992302i	$0.539522\pi$
$54$	−35603.0	−1.66151
$55$	−8725.88	−0.388958
$56$	89474.9	3.81269
$57$	−15195.1	−0.619465
$58$	8946.10	0.349191
$59$	−16380.0	−0.612610	−0.306305	−	0.951933i	$-0.599093\pi$
$59$	−16380.0	−0.612610	−0.306305	+	0.951933i	$0.599093\pi$
$60$	−16032.2	−0.574930
$61$	9332.80	0.321135	0.160567	−	0.987025i	$-0.448668\pi$
$61$	9332.80	0.321135	0.160567	+	0.987025i	$0.448668\pi$
$62$	−8228.30	−0.271851
$63$	−30896.6	−0.980753
$64$	62653.4	1.91203
$65$	9192.86	0.269878
$66$	29338.8	0.829054
$67$	−72265.4	−1.96672	−0.983362	−	0.181659i	$-0.941853\pi$
$67$	−72265.4	−1.96672	−0.983362	+	0.181659i	$0.941853\pi$
$68$	−6436.26	−0.168796
$69$	28466.1	0.719788
$70$	−45506.2	−1.11001
$71$	−34216.5	−0.805545	−0.402773	−	0.915300i	$-0.631953\pi$
$71$	−34216.5	−0.805545	−0.402773	+	0.915300i	$0.631953\pi$
$72$	−94411.9	−2.14633
$73$	64735.5	1.42179	0.710895	−	0.703298i	$-0.248290\pi$
$73$	64735.5	1.42179	0.710895	+	0.703298i	$0.248290\pi$
$74$	−24547.3	−0.521105
$75$	4938.74	0.101382
$76$	−156058.	−3.09921
$77$	59725.8	1.14798
$78$	−30909.0	−0.575238
$79$	−35527.2	−0.640462	−0.320231	−	0.947340i	$-0.603760\pi$
$79$	−35527.2	−0.640462	−0.320231	+	0.947340i	$0.603760\pi$
$80$	−74130.5	−1.29501
$81$	17428.2	0.295148
$82$	−189974.	−3.12004
$83$	74144.2	1.18136	0.590680	−	0.806906i	$-0.298860\pi$
$83$	74144.2	1.18136	0.590680	+	0.806906i	$0.298860\pi$
$84$	109735.	1.69687
$85$	1982.70	0.0297652
$86$	222948.	3.25055
$87$	6645.57	0.0941313
$88$	182506.	2.51230
$89$	−33510.8	−0.448446	−0.224223	−	0.974538i	$-0.571984\pi$
$89$	−33510.8	−0.448446	−0.224223	+	0.974538i	$0.571984\pi$
$90$	48017.1	0.624870
$91$	−62922.1	−0.796526
$92$	292354.	3.60113
$93$	−6112.35	−0.0732827
$94$	−268742.	−3.13701
$95$	48073.7	0.546511
$96$	117028.	1.29602
$97$	165247.	1.78322	0.891610	−	0.452804i	$-0.149576\pi$
$97$	165247.	1.78322	0.891610	+	0.452804i	$0.149576\pi$
$98$	132691.	1.39565
$99$	−63021.4	−0.646249
$100$	50722.1	0.507221
$101$	−110741.	−1.08020	−0.540099	−	0.841602i	$-0.681613\pi$
$101$	−110741.	−1.08020	−0.540099	+	0.841602i	$0.681613\pi$
$102$	−6666.38	−0.0634438
$103$	6335.82	0.0588450	0.0294225	−	0.999567i	$-0.490633\pi$
$103$	6335.82	0.0588450	0.0294225	+	0.999567i	$0.490633\pi$
$104$	−192273.	−1.74315
$105$	−33804.0	−0.299223
$106$	−53880.7	−0.465766
$107$	16569.9	0.139914	0.0699569	−	0.997550i	$-0.477714\pi$
$107$	16569.9	0.139914	0.0699569	+	0.997550i	$0.477714\pi$
$108$	−271623.	−2.24082
$109$	−8467.39	−0.0682627	−0.0341313	−	0.999417i	$-0.510866\pi$
$109$	−8467.39	−0.0682627	−0.0341313	+	0.999417i	$0.510866\pi$
$110$	−92821.1	−0.731417
$111$	−18234.9	−0.140474
$112$	507399.	3.82212
$113$	89180.8	0.657015	0.328508	−	0.944501i	$-0.393454\pi$
$113$	89180.8	0.657015	0.328508	+	0.944501i	$0.393454\pi$
$114$	−161637.	−1.16487
$115$	−90059.9	−0.635019
$116$	68251.7	0.470943
$117$	66394.0	0.448399
$118$	−174242.	−1.15199
$119$	−13570.9	−0.0878499
$120$	−103296.	−0.654834
$121$	−39225.4	−0.243559
$122$	99277.2	0.603879
$123$	−141122.	−0.841067
$124$	−62775.4	−0.366636
$125$	−15625.0	−0.0894427
$126$	−328661.	−1.84426
$127$	−233526.	−1.28477	−0.642385	−	0.766382i	$-0.722055\pi$
$127$	−233526.	−1.28477	−0.642385	+	0.766382i	$0.722055\pi$
$128$	192553.	1.03878
$129$	165616.	0.876249
$130$	97788.6	0.507493
$131$	83915.3	0.427231	0.213616	−	0.976918i	$-0.431476\pi$
$131$	83915.3	0.427231	0.213616	+	0.976918i	$0.431476\pi$
$132$	223832.	1.11812
$133$	−329049.	−1.61299
$134$	−768719.	−3.69833
$135$	83673.8	0.395144
$136$	−41469.1	−0.192255
$137$	316971.	1.44284	0.721420	−	0.692498i	$-0.243490\pi$
$137$	316971.	1.44284	0.721420	+	0.692498i	$0.243490\pi$
$138$	302806.	1.35353
$139$	40266.1	0.176768	0.0883838	−	0.996086i	$-0.471830\pi$
$139$	40266.1	0.176768	0.0883838	+	0.996086i	$0.471830\pi$
$140$	−347176.	−1.49703
$141$	−199634.	−0.845641
$142$	−363977.	−1.51479
$143$	−128345.	−0.524856
$144$	−535396.	−2.15164
$145$	−21025.0	−0.0830455
$146$	688621.	2.67361
$147$	98569.0	0.376224
$148$	−187277.	−0.702797
$149$	−6919.79	−0.0255345	−0.0127673	−	0.999918i	$-0.504064\pi$
$149$	−6919.79	−0.0255345	−0.0127673	+	0.999918i	$0.504064\pi$
$150$	52535.6	0.190645
$151$	−25767.0	−0.0919647	−0.0459823	−	0.998942i	$-0.514642\pi$
$151$	−25767.0	−0.0919647	−0.0459823	+	0.998942i	$0.514642\pi$
$152$	−1.00549e6	−3.52994
$153$	14319.7	0.0494545
$154$	635330.	2.15873
$155$	19338.0	0.0646522
$156$	−235811.	−0.775805
$157$	−118398.	−0.383351	−0.191676	−	0.981458i	$-0.561392\pi$
$157$	−118398.	−0.383351	−0.191676	+	0.981458i	$0.561392\pi$
$158$	−377919.	−1.20436
$159$	−40025.0	−0.125556
$160$	−370249.	−1.14339
$161$	616430.	1.87421
$162$	185392.	0.555012
$163$	270076.	0.796190	0.398095	−	0.917344i	$-0.369671\pi$
$163$	270076.	0.796190	0.398095	+	0.917344i	$0.369671\pi$
$164$	−1.44935e6	−4.20790
$165$	−68951.8	−0.197168
$166$	788706.	2.22149
$167$	471170.	1.30733	0.653667	−	0.756782i	$-0.273230\pi$
$167$	471170.	1.30733	0.653667	+	0.756782i	$0.273230\pi$
$168$	707029.	1.93270
$169$	−236079.	−0.635830
$170$	21090.8	0.0559721
$171$	347205.	0.908021
$172$	1.70092e6	4.38391
$173$	420463.	1.06810	0.534051	−	0.845452i	$-0.320669\pi$
$173$	420463.	1.06810	0.534051	+	0.845452i	$0.320669\pi$
$174$	70691.9	0.177009
$175$	106948.	0.263984
$176$	1.03497e6	2.51852
$177$	−129435.	−0.310540
$178$	−356470.	−0.843282
$179$	−718345.	−1.67572	−0.837858	−	0.545888i	$-0.816192\pi$
$179$	−718345.	−1.67572	−0.837858	+	0.545888i	$0.816192\pi$
$180$	366333.	0.842741
$181$	−12784.7	−0.0290064	−0.0145032	−	0.999895i	$-0.504617\pi$
$181$	−12784.7	−0.0290064	−0.0145032	+	0.999895i	$0.504617\pi$
$182$	−669331.	−1.49783
$183$	73747.6	0.162787
$184$	1.88365e6	4.10162
$185$	57690.8	0.123930
$186$	−65019.9	−0.137805
$187$	−27681.2	−0.0578871
$188$	−2.05029e6	−4.23078
$189$	−572720.	−1.16624
$190$	511382.	1.02769
$191$	659494.	1.30806	0.654030	−	0.756469i	$-0.273077\pi$
$191$	659494.	1.30806	0.654030	+	0.756469i	$0.273077\pi$
$192$	495086.	0.969231
$193$	653003.	1.26189	0.630946	−	0.775827i	$-0.282667\pi$
$193$	653003.	1.26189	0.630946	+	0.775827i	$0.282667\pi$
$194$	1.75781e6	3.35326
$195$	72641.8	0.136804
$196$	1.01233e6	1.88227
$197$	498950.	0.915991	0.457996	−	0.888954i	$-0.348568\pi$
$197$	498950.	0.915991	0.457996	+	0.888954i	$0.348568\pi$
$198$	−670387.	−1.21524
$199$	552109.	0.988308	0.494154	−	0.869374i	$-0.335478\pi$
$199$	552109.	0.988308	0.494154	+	0.869374i	$0.335478\pi$
$200$	326805.	0.577715
$201$	−571040.	−0.996956
$202$	−1.17800e6	−2.03126
$203$	143909.	0.245103
$204$	−50859.2	−0.0855646
$205$	446475.	0.742015
$206$	67397.0	0.110655
$207$	−650444.	−1.05508
$208$	−1.09035e6	−1.74747
$209$	−671177.	−1.06285
$210$	−359589.	−0.562675
$211$	654995.	1.01282	0.506409	−	0.862293i	$-0.330972\pi$
$211$	654995.	1.01282	0.506409	+	0.862293i	$0.330972\pi$
$212$	−411067.	−0.628164
$213$	−270378.	−0.408341
$214$	176261.	0.263101
$215$	−523969.	−0.773053
$216$	−1.75008e6	−2.55225
$217$	−132363.	−0.190816
$218$	−90071.4	−0.128365
$219$	511539.	0.720723
$220$	−708152.	−0.986438
$221$	29162.6	0.0401649
$222$	−193973.	−0.264154
$223$	−374428.	−0.504204	−0.252102	−	0.967701i	$-0.581122\pi$
$223$	−374428.	−0.504204	−0.252102	+	0.967701i	$0.581122\pi$
$224$	2.53424e6	3.37464
$225$	−112849.	−0.148608
$226$	948657.	1.23549
$227$	608292.	0.783516	0.391758	−	0.920068i	$-0.371867\pi$
$227$	608292.	0.783516	0.391758	+	0.920068i	$0.371867\pi$
$228$	−1.23316e6	−1.57103
$229$	848366.	1.06904	0.534521	−	0.845155i	$-0.320492\pi$
$229$	848366.	1.06904	0.534521	+	0.845155i	$0.320492\pi$
$230$	−958008.	−1.19412
$231$	471952.	0.581926
$232$	439749.	0.536395
$233$	742679.	0.896214	0.448107	−	0.893980i	$-0.352098\pi$
$233$	742679.	0.896214	0.448107	+	0.893980i	$0.352098\pi$
$234$	706263.	0.843193
$235$	631594.	0.746050
$236$	−1.32933e6	−1.55364
$237$	−280735.	−0.324658
$238$	−144360.	−0.165198
$239$	1.38563e6	1.56911	0.784553	−	0.620062i	$-0.212893\pi$
$239$	1.38563e6	1.56911	0.784553	+	0.620062i	$0.212893\pi$
$240$	−585778.	−0.656455
$241$	1.17901e6	1.30760	0.653801	−	0.756666i	$-0.273173\pi$
$241$	1.17901e6	1.30760	0.653801	+	0.756666i	$0.273173\pi$
$242$	−417258.	−0.458001
$243$	951027.	1.03318
$244$	757407.	0.814431
$245$	−311849.	−0.331917
$246$	−1.50117e6	−1.58159
$247$	707096.	0.737456
$248$	−404465.	−0.417592
$249$	585886.	0.598846
$250$	−166210.	−0.168193
$251$	−861676.	−0.863296	−0.431648	−	0.902042i	$-0.642068\pi$
$251$	−861676.	−0.863296	−0.431648	+	0.902042i	$0.642068\pi$
$252$	−2.50743e6	−2.48729
$253$	1.25736e6	1.23498
$254$	−2.48412e6	−2.41595
$255$	15667.2	0.0150884
$256$	43362.8	0.0413540
$257$	−227140.	−0.214517	−0.107258	−	0.994231i	$-0.534207\pi$
$257$	−227140.	−0.214517	−0.107258	+	0.994231i	$0.534207\pi$
$258$	1.76173e6	1.64774
$259$	−394875.	−0.365772
$260$	746050.	0.684439
$261$	−151850.	−0.137979
$262$	892645.	0.803388
$263$	1.57114e6	1.40063	0.700316	−	0.713833i	$-0.253042\pi$
$263$	1.57114e6	1.40063	0.700316	+	0.713833i	$0.253042\pi$
$264$	1.44216e6	1.27351
$265$	126630.	0.110770
$266$	−3.50024e6	−3.03315
$267$	−264802.	−0.227323
$268$	−5.86472e6	−4.98782
$269$	1.95463e6	1.64697	0.823483	−	0.567340i	$-0.192028\pi$
$269$	1.95463e6	1.64697	0.823483	+	0.567340i	$0.192028\pi$
$270$	890076.	0.743050
$271$	−2.03350e6	−1.68198	−0.840991	−	0.541049i	$-0.818027\pi$
$271$	−2.03350e6	−1.68198	−0.840991	+	0.541049i	$0.818027\pi$
$272$	−235165.	−0.192731
$273$	−497209.	−0.403769
$274$	3.37176e6	2.71319
$275$	218147.	0.173947
$276$	2.31017e6	1.82546
$277$	1.06404e6	0.833217	0.416609	−	0.909086i	$-0.363219\pi$
$277$	1.06404e6	0.833217	0.416609	+	0.909086i	$0.363219\pi$
$278$	428329.	0.332403
$279$	139666.	0.107419
$280$	−2.23687e6	−1.70508
$281$	−716996.	−0.541690	−0.270845	−	0.962623i	$-0.587303\pi$
$281$	−716996.	−0.541690	−0.270845	+	0.962623i	$0.587303\pi$
$282$	−2.12359e6	−1.59019
$283$	−1.62722e6	−1.20776	−0.603878	−	0.797077i	$-0.706379\pi$
$283$	−1.62722e6	−1.20776	−0.603878	+	0.797077i	$0.706379\pi$
$284$	−2.77685e6	−2.04295
$285$	379878.	0.277033
$286$	−1.36527e6	−0.986967
$287$	−3.05598e6	−2.19001
$288$	−2.67407e6	−1.89973
$289$	−1.41357e6	−0.995570
$290$	−223652.	−0.156163
$291$	1.30578e6	0.903936
$292$	5.25363e6	3.60581
$293$	−2.15555e6	−1.46686	−0.733430	−	0.679765i	$-0.762082\pi$
$293$	−2.15555e6	−1.46686	−0.733430	+	0.679765i	$0.762082\pi$
$294$	1.04852e6	0.707473
$295$	409501.	0.273968
$296$	−1.20663e6	−0.800472
$297$	−1.16820e6	−0.768472
$298$	−73609.0	−0.0480164
$299$	−1.32465e6	−0.856888
$300$	400805.	0.257117
$301$	3.58640e6	2.28161
$302$	−274095.	−0.172935
$303$	−875069.	−0.547565
$304$	−5.70197e6	−3.53868
$305$	−233320.	−0.143616
$306$	152325.	0.0929969
$307$	−2.75274e6	−1.66694	−0.833469	−	0.552567i	$-0.813648\pi$
$307$	−2.75274e6	−1.66694	−0.833469	+	0.552567i	$0.813648\pi$
$308$	4.84707e6	2.91140
$309$	50065.5	0.0298293
$310$	205707.	0.121575
$311$	1.43353e6	0.840437	0.420218	−	0.907423i	$-0.361953\pi$
$311$	1.43353e6	0.840437	0.420218	+	0.907423i	$0.361953\pi$
$312$	−1.51934e6	−0.883626
$313$	−987882.	−0.569960	−0.284980	−	0.958533i	$-0.591987\pi$
$313$	−987882.	−0.569960	−0.284980	+	0.958533i	$0.591987\pi$
$314$	−1.25946e6	−0.720874
$315$	772416.	0.438606
$316$	−2.88322e6	−1.62428
$317$	−1.61385e6	−0.902017	−0.451009	−	0.892520i	$-0.648936\pi$
$317$	−1.61385e6	−0.902017	−0.451009	+	0.892520i	$0.648936\pi$
$318$	−425764.	−0.236103
$319$	293539.	0.161506
$320$	−1.56633e6	−0.855085
$321$	130935.	0.0709240
$322$	6.55725e6	3.52437
$323$	152505.	0.0813351
$324$	1.41439e6	0.748527
$325$	−229822.	−0.120693
$326$	2.87292e6	1.49720
$327$	−66909.2	−0.0346032
$328$	−9.33826e6	−4.79271
$329$	−4.32305e6	−2.20192
$330$	−733471.	−0.370764
$331$	1.84401e6	0.925109	0.462555	−	0.886591i	$-0.346933\pi$
$331$	1.84401e6	0.925109	0.462555	+	0.886591i	$0.346933\pi$
$332$	6.01720e6	2.99605
$333$	416663.	0.205909
$334$	5.01205e6	2.45838
$335$	1.80663e6	0.879545
$336$	4.00946e6	1.93748
$337$	−3.81514e6	−1.82993	−0.914967	−	0.403528i	$-0.867784\pi$
$337$	−3.81514e6	−1.82993	−0.914967	+	0.403528i	$0.867784\pi$
$338$	−2.51128e6	−1.19565
$339$	704705.	0.333049
$340$	160906.	0.0754877
$341$	−269986.	−0.125735
$342$	3.69338e6	1.70749
$343$	−741456.	−0.340291
$344$	1.09591e7	4.99319
$345$	−711652.	−0.321899
$346$	4.47266e6	2.00852
$347$	2.85411e6	1.27247	0.636235	−	0.771495i	$-0.280491\pi$
$347$	2.85411e6	1.27247	0.636235	+	0.771495i	$0.280491\pi$
$348$	539323.	0.238727
$349$	−3.16307e6	−1.39010	−0.695049	−	0.718962i	$-0.744617\pi$
$349$	−3.16307e6	−1.39010	−0.695049	+	0.718962i	$0.744617\pi$
$350$	1.13765e6	0.496410
$351$	1.23072e6	0.533203
$352$	5.16920e6	2.22365
$353$	2.41123e6	1.02992	0.514959	−	0.857215i	$-0.327807\pi$
$353$	2.41123e6	1.02992	0.514959	+	0.857215i	$0.327807\pi$
$354$	−1.37685e6	−0.583956
$355$	855413.	0.360251
$356$	−2.71958e6	−1.13731
$357$	−107237.	−0.0445322
$358$	−7.64136e6	−3.15111
$359$	1.18835e6	0.486639	0.243320	−	0.969946i	$-0.421764\pi$
$359$	1.18835e6	0.486639	0.243320	+	0.969946i	$0.421764\pi$
$360$	2.36030e6	0.959866
$361$	1.22164e6	0.493371
$362$	−135996.	−0.0545451
$363$	−309958.	−0.123463
$364$	−5.10647e6	−2.02007
$365$	−1.61839e6	−0.635844
$366$	784486.	0.306114
$367$	−3.48335e6	−1.34999	−0.674997	−	0.737820i	$-0.735855\pi$
$367$	−3.48335e6	−1.34999	−0.674997	+	0.737820i	$0.735855\pi$
$368$	1.06819e7	4.11177
$369$	3.22460e6	1.23285
$370$	613683.	0.233045
$371$	−866738.	−0.326929
$372$	−496050.	−0.185852
$373$	−1.08921e6	−0.405360	−0.202680	−	0.979245i	$-0.564965\pi$
$373$	−1.08921e6	−0.405360	−0.202680	+	0.979245i	$0.564965\pi$
$374$	−294458.	−0.108854
$375$	−123468.	−0.0453396
$376$	−1.32101e7	−4.81877
$377$	−309248.	−0.112061
$378$	−6.09228e6	−2.19306
$379$	−645382.	−0.230791	−0.115396	−	0.993320i	$-0.536814\pi$
$379$	−645382.	−0.230791	−0.115396	+	0.993320i	$0.536814\pi$
$380$	3.90144e6	1.38601
$381$	−1.84532e6	−0.651266
$382$	7.01534e6	2.45974
$383$	2.07721e6	0.723577	0.361788	−	0.932260i	$-0.382166\pi$
$383$	2.07721e6	0.723577	0.361788	+	0.932260i	$0.382166\pi$
$384$	1.52155e6	0.526572
$385$	−1.49315e6	−0.513393
$386$	6.94629e6	2.37293
$387$	−3.78429e6	−1.28442
$388$	1.34107e7	4.52243
$389$	−879297.	−0.294620	−0.147310	−	0.989090i	$-0.547061\pi$
$389$	−879297.	−0.294620	−0.147310	+	0.989090i	$0.547061\pi$
$390$	772724.	0.257254
$391$	−285698.	−0.0945074
$392$	6.52248e6	2.14387
$393$	663097.	0.216569
$394$	5.30755e6	1.72248
$395$	888180.	0.286423
$396$	−5.11452e6	−1.63895
$397$	−3.05951e6	−0.974262	−0.487131	−	0.873329i	$-0.661957\pi$
$397$	−3.05951e6	−0.974262	−0.487131	+	0.873329i	$0.661957\pi$
$398$	5.87303e6	1.85847
$399$	−2.60014e6	−0.817644
$400$	1.85326e6	0.579145
$401$	5.07268e6	1.57535	0.787674	−	0.616092i	$-0.211285\pi$
$401$	5.07268e6	1.57535	0.787674	+	0.616092i	$0.211285\pi$
$402$	−6.07441e6	−1.87473
$403$	284435.	0.0872410
$404$	−8.98718e6	−2.73949
$405$	−435705.	−0.131994
$406$	1.53083e6	0.460905
$407$	−805445.	−0.241018
$408$	−327688.	−0.0974564
$409$	3.26444e6	0.964941	0.482471	−	0.875912i	$-0.339740\pi$
$409$	3.26444e6	0.964941	0.482471	+	0.875912i	$0.339740\pi$
$410$	4.74936e6	1.39532
$411$	2.50470e6	0.731393
$412$	514186.	0.149237
$413$	−2.80290e6	−0.808597
$414$	−6.91906e6	−1.98402
$415$	−1.85361e6	−0.528320
$416$	−5.44584e6	−1.54288
$417$	318182.	0.0896057
$418$	−7.13961e6	−1.99864
$419$	−5.95132e6	−1.65607	−0.828033	−	0.560679i	$-0.810540\pi$
$419$	−5.95132e6	−1.65607	−0.828033	+	0.560679i	$0.810540\pi$
$420$	−2.74338e6	−0.758862
$421$	1.63805e6	0.450426	0.225213	−	0.974310i	$-0.427692\pi$
$421$	1.63805e6	0.450426	0.225213	+	0.974310i	$0.427692\pi$
$422$	6.96747e6	1.90456
$423$	4.56159e6	1.23955
$424$	−2.64852e6	−0.715466
$425$	−49567.4	−0.0133114
$426$	−2.87614e6	−0.767866
$427$	1.59700e6	0.423872
$428$	1.34474e6	0.354836
$429$	−1.01418e6	−0.266056
$430$	−5.57369e6	−1.45369
$431$	−1.95855e6	−0.507856	−0.253928	−	0.967223i	$-0.581723\pi$
$431$	−1.95855e6	−0.507856	−0.253928	+	0.967223i	$0.581723\pi$
$432$	−9.92445e6	−2.55857
$433$	−5.83591e6	−1.49585	−0.747927	−	0.663781i	$-0.768951\pi$
$433$	−5.83591e6	−1.49585	−0.747927	+	0.663781i	$0.768951\pi$
$434$	−1.40800e6	−0.358821
$435$	−166139.	−0.0420968
$436$	−687174.	−0.173121
$437$	−6.92722e6	−1.73522
$438$	5.44147e6	1.35529
$439$	−1.14265e6	−0.282978	−0.141489	−	0.989940i	$-0.545189\pi$
$439$	−1.14265e6	−0.282978	−0.141489	+	0.989940i	$0.545189\pi$
$440$	−4.56266e6	−1.12353
$441$	−2.25228e6	−0.551476
$442$	310216.	0.0755281
$443$	−6.01198e6	−1.45549	−0.727744	−	0.685849i	$-0.759431\pi$
$443$	−6.01198e6	−1.45549	−0.727744	+	0.685849i	$0.759431\pi$
$444$	−1.47986e6	−0.356256
$445$	837770.	0.200551
$446$	−3.98296e6	−0.948132
$447$	−54680.1	−0.0129438
$448$	1.07210e7	2.52372
$449$	−1.99042e6	−0.465938	−0.232969	−	0.972484i	$-0.574844\pi$
$449$	−1.99042e6	−0.465938	−0.232969	+	0.972484i	$0.574844\pi$
$450$	−1.20043e6	−0.279450
$451$	−6.23342e6	−1.44306
$452$	7.23750e6	1.66626
$453$	−203610.	−0.0466180
$454$	6.47068e6	1.47336
$455$	1.57305e6	0.356217
$456$	−7.94534e6	−1.78937
$457$	−797270.	−0.178573	−0.0892863	−	0.996006i	$-0.528459\pi$
$457$	−797270.	−0.178573	−0.0892863	+	0.996006i	$0.528459\pi$
$458$	9.02445e6	2.01028
$459$	265440.	0.0588077
$460$	−7.30884e6	−1.61048
$461$	4.15965e6	0.911601	0.455801	−	0.890082i	$-0.349353\pi$
$461$	4.15965e6	0.911601	0.455801	+	0.890082i	$0.349353\pi$
$462$	5.02037e6	1.09429
$463$	−7.65502e6	−1.65956	−0.829781	−	0.558089i	$-0.811535\pi$
$463$	−7.65502e6	−1.65956	−0.829781	+	0.558089i	$0.811535\pi$
$464$	2.49375e6	0.537722
$465$	152809.	0.0327730
$466$	7.90022e6	1.68529
$467$	7.73628e6	1.64150	0.820749	−	0.571289i	$-0.193557\pi$
$467$	7.73628e6	1.64150	0.820749	+	0.571289i	$0.193557\pi$
$468$	5.38823e6	1.13719
$469$	−1.23658e7	−2.59592
$470$	6.71855e6	1.40291
$471$	−935582.	−0.194326
$472$	−8.56491e6	−1.76957
$473$	7.31535e6	1.50343
$474$	−2.98631e6	−0.610504
$475$	−1.20184e6	−0.244407
$476$	−1.10135e6	−0.222797
$477$	914563.	0.184042
$478$	1.47396e7	2.95063
$479$	9.01260e6	1.79478	0.897390	−	0.441238i	$-0.145461\pi$
$479$	9.01260e6	1.79478	0.897390	+	0.441238i	$0.145461\pi$
$480$	−2.92570e6	−0.579599
$481$	848550.	0.167230
$482$	1.25417e7	2.45889
$483$	4.87102e6	0.950063
$484$	−3.18335e6	−0.617690
$485$	−4.13118e6	−0.797480
$486$	1.01165e7	1.94285
$487$	−2.33104e6	−0.445377	−0.222688	−	0.974890i	$-0.571483\pi$
$487$	−2.33104e6	−0.445377	−0.222688	+	0.974890i	$0.571483\pi$
$488$	4.88000e6	0.927621
$489$	2.13414e6	0.403599
$490$	−3.31728e6	−0.624154
$491$	−5.19866e6	−0.973168	−0.486584	−	0.873634i	$-0.661757\pi$
$491$	−5.19866e6	−0.973168	−0.486584	+	0.873634i	$0.661757\pi$
$492$	−1.14528e7	−2.13303
$493$	−66697.9	−0.0123593
$494$	7.52170e6	1.38675
$495$	1.57553e6	0.289011
$496$	−2.29366e6	−0.418625
$497$	−5.85502e6	−1.06326
$498$	6.23234e6	1.12610
$499$	4.69918e6	0.844833	0.422416	−	0.906402i	$-0.361182\pi$
$499$	4.69918e6	0.844833	0.422416	+	0.906402i	$0.361182\pi$
$500$	−1.26805e6	−0.226836
$501$	3.72318e6	0.662704
$502$	−9.16604e6	−1.62339
$503$	2.31325e6	0.407664	0.203832	−	0.979006i	$-0.434660\pi$
$503$	2.31325e6	0.407664	0.203832	+	0.979006i	$0.434660\pi$
$504$	−1.61555e7	−2.83298
$505$	2.76851e6	0.483079
$506$	1.33751e7	2.32232
$507$	−1.86549e6	−0.322310
$508$	−1.89519e7	−3.25831
$509$	−2.54650e6	−0.435661	−0.217831	−	0.975987i	$-0.569898\pi$
$509$	−2.54650e6	−0.435661	−0.217831	+	0.975987i	$0.569898\pi$
$510$	166659.	0.0283729
$511$	1.10773e7	1.87665
$512$	−5.70042e6	−0.961019
$513$	6.43602e6	1.07975
$514$	−2.41619e6	−0.403389
$515$	−158396.	−0.0263163
$516$	1.34406e7	2.22226
$517$	−8.81794e6	−1.45091
$518$	−4.20046e6	−0.687817
$519$	3.32249e6	0.541434
$520$	4.80683e6	0.779562
$521$	804949.	0.129919	0.0649597	−	0.997888i	$-0.479308\pi$
$521$	804949.	0.129919	0.0649597	+	0.997888i	$0.479308\pi$
$522$	−1.61530e6	−0.259463
$523$	302757.	0.0483994	0.0241997	−	0.999707i	$-0.492296\pi$
$523$	302757.	0.0483994	0.0241997	+	0.999707i	$0.492296\pi$
$524$	6.81018e6	1.08350
$525$	845101.	0.133817
$526$	1.67129e7	2.63382
$527$	61346.4	0.00962193
$528$	8.17829e6	1.27667
$529$	6.54091e6	1.01625
$530$	1.34702e6	0.208297
$531$	2.95755e6	0.455194
$532$	−2.67041e7	−4.09071
$533$	6.56702e6	1.00127
$534$	−2.81682e6	−0.427470
$535$	−414247.	−0.0625713
$536$	−3.77867e7	−5.68102
$537$	−5.67635e6	−0.849441
$538$	2.07923e7	3.09704
$539$	4.35385e6	0.645508
$540$	6.79058e6	1.00213
$541$	−2.32952e6	−0.342194	−0.171097	−	0.985254i	$-0.554731\pi$
$541$	−2.32952e6	−0.342194	−0.171097	+	0.985254i	$0.554731\pi$
$542$	−2.16313e7	−3.16289
$543$	−101024.	−0.0147037
$544$	−1.17455e6	−0.170166
$545$	211685.	0.0305280
$546$	−5.28904e6	−0.759268
$547$	4.12008e6	0.588758	0.294379	−	0.955689i	$-0.404887\pi$
$547$	4.12008e6	0.588758	0.294379	+	0.955689i	$0.404887\pi$
$548$	2.57239e7	3.65919
$549$	−1.68512e6	−0.238616
$550$	2.32053e6	0.327100
$551$	−1.61720e6	−0.226926
$552$	1.48846e7	2.07916
$553$	−6.07930e6	−0.845358
$554$	1.13187e7	1.56683
$555$	455872.	0.0628218
$556$	3.26781e6	0.448301
$557$	646181.	0.0882503	0.0441252	−	0.999026i	$-0.485950\pi$
$557$	646181.	0.0882503	0.0441252	+	0.999026i	$0.485950\pi$
$558$	1.48569e6	0.201996
$559$	−7.70684e6	−1.04315
$560$	−1.26850e7	−1.70930
$561$	−218737.	−0.0293437
$562$	−7.62701e6	−1.01862
$563$	−5.89375e6	−0.783647	−0.391824	−	0.920040i	$-0.628156\pi$
$563$	−5.89375e6	−0.783647	−0.391824	+	0.920040i	$0.628156\pi$
$564$	−1.62013e7	−2.14463
$565$	−2.22952e6	−0.293826
$566$	−1.73094e7	−2.27113
$567$	2.98226e6	0.389572
$568$	−1.78914e7	−2.32688
$569$	899415.	0.116461	0.0582303	−	0.998303i	$-0.481454\pi$
$569$	899415.	0.116461	0.0582303	+	0.998303i	$0.481454\pi$
$570$	4.04093e6	0.520948
$571$	9.70241e6	1.24534	0.622672	−	0.782483i	$-0.286047\pi$
$571$	9.70241e6	1.24534	0.622672	+	0.782483i	$0.286047\pi$
$572$	−1.04159e7	−1.33109
$573$	5.21131e6	0.663071
$574$	−3.25078e7	−4.11820
$575$	2.25150e6	0.283989
$576$	−1.13126e7	−1.42071
$577$	−1.76362e6	−0.220528	−0.110264	−	0.993902i	$-0.535170\pi$
$577$	−1.76362e6	−0.220528	−0.110264	+	0.993902i	$0.535170\pi$
$578$	−1.50368e7	−1.87212
$579$	5.16002e6	0.639669
$580$	−1.70629e6	−0.210612
$581$	1.26873e7	1.55930
$582$	1.38902e7	1.69981
$583$	−1.76793e6	−0.215424
$584$	3.38494e7	4.10694
$585$	−1.65985e6	−0.200530
$586$	−2.29295e7	−2.75836
$587$	6.01294e6	0.720264	0.360132	−	0.932901i	$-0.382732\pi$
$587$	6.01294e6	0.720264	0.360132	+	0.932901i	$0.382732\pi$
$588$	7.99940e6	0.954145
$589$	1.48744e6	0.176666
$590$	4.35604e6	0.515184
$591$	3.94269e6	0.464327
$592$	−6.84264e6	−0.802453
$593$	−9.48290e6	−1.10740	−0.553700	−	0.832716i	$-0.686784\pi$
$593$	−9.48290e6	−1.10740	−0.553700	+	0.832716i	$0.686784\pi$
$594$	−1.24267e7	−1.44507
$595$	339273.	0.0392877
$596$	−561578.	−0.0647582
$597$	4.36276e6	0.500985
$598$	−1.40909e7	−1.61134
$599$	4.63972e6	0.528354	0.264177	−	0.964474i	$-0.414900\pi$
$599$	4.63972e6	0.528354	0.264177	+	0.964474i	$0.414900\pi$
$600$	2.58241e6	0.292851
$601$	−989899.	−0.111790	−0.0558952	−	0.998437i	$-0.517801\pi$
$601$	−989899.	−0.111790	−0.0558952	+	0.998437i	$0.517801\pi$
$602$	3.81501e7	4.29047
$603$	1.30481e7	1.46135
$604$	−2.09113e6	−0.233232
$605$	980634.	0.108923
$606$	−9.30851e6	−1.02967
$607$	−5.93495e6	−0.653801	−0.326901	−	0.945059i	$-0.606004\pi$
$607$	−5.93495e6	−0.653801	−0.326901	+	0.945059i	$0.606004\pi$
$608$	−2.84788e7	−3.12438
$609$	1.13717e6	0.124246
$610$	−2.48193e6	−0.270063
$611$	9.28984e6	1.00671
$612$	1.16212e6	0.125422
$613$	3.63601e6	0.390817	0.195409	−	0.980722i	$-0.437397\pi$
$613$	3.63601e6	0.390817	0.195409	+	0.980722i	$0.437397\pi$
$614$	−2.92821e7	−3.13460
$615$	3.52804e6	0.376137
$616$	3.12299e7	3.31603
$617$	1.24047e7	1.31182	0.655910	−	0.754839i	$-0.272285\pi$
$617$	1.24047e7	1.31182	0.655910	+	0.754839i	$0.272285\pi$
$618$	532570.	0.0560926
$619$	2.09019e6	0.219260	0.109630	−	0.993972i	$-0.465033\pi$
$619$	2.09019e6	0.219260	0.109630	+	0.993972i	$0.465033\pi$
$620$	1.56939e6	0.163965
$621$	−1.20570e7	−1.25462
$622$	1.52491e7	1.58040
$623$	−5.73426e6	−0.591913
$624$	−8.61596e6	−0.885813
$625$	390625.	0.0400000
$626$	−1.05085e7	−1.07178
$627$	−5.30363e6	−0.538771
$628$	−9.60867e6	−0.972219
$629$	183013.	0.0184441
$630$	8.21653e6	0.824778
$631$	1.33502e7	1.33480	0.667399	−	0.744700i	$-0.267408\pi$
$631$	1.33502e7	1.33480	0.667399	+	0.744700i	$0.267408\pi$
$632$	−1.85767e7	−1.85002
$633$	5.17576e6	0.513410
$634$	−1.71672e7	−1.69620
$635$	5.83815e6	0.574567
$636$	−3.24824e6	−0.318424
$637$	−4.58686e6	−0.447885
$638$	3.12250e6	0.303704
$639$	6.17809e6	0.598552
$640$	−4.81382e6	−0.464558
$641$	−1.63488e7	−1.57159	−0.785797	−	0.618484i	$-0.787747\pi$
$641$	−1.63488e7	−1.57159	−0.785797	+	0.618484i	$0.787747\pi$
$642$	1.39281e6	0.133369
$643$	5.37759e6	0.512933	0.256466	−	0.966553i	$-0.417442\pi$
$643$	5.37759e6	0.512933	0.256466	+	0.966553i	$0.417442\pi$
$644$	5.00266e7	4.75321
$645$	−4.14039e6	−0.391870
$646$	1.62226e6	0.152947
$647$	9.73809e6	0.914562	0.457281	−	0.889322i	$-0.348823\pi$
$647$	9.73809e6	0.914562	0.457281	+	0.889322i	$0.348823\pi$
$648$	9.11299e6	0.852557
$649$	−5.71720e6	−0.532810
$650$	−2.44472e6	−0.226958
$651$	−1.04593e6	−0.0967272
$652$	2.19181e7	2.01922
$653$	−1.59165e7	−1.46071	−0.730357	−	0.683065i	$-0.760646\pi$
$653$	−1.59165e7	−1.46071	−0.730357	+	0.683065i	$0.760646\pi$
$654$	−711743.	−0.0650697
$655$	−2.09788e6	−0.191064
$656$	−5.29559e7	−4.80457
$657$	−1.16886e7	−1.05645
$658$	−4.59862e7	−4.14060
$659$	−5.28648e6	−0.474191	−0.237096	−	0.971486i	$-0.576195\pi$
$659$	−5.28648e6	−0.474191	−0.237096	+	0.971486i	$0.576195\pi$
$660$	−5.59580e6	−0.500038
$661$	−2.05506e7	−1.82945	−0.914725	−	0.404076i	$-0.867593\pi$
$661$	−2.05506e7	−1.82945	−0.914725	+	0.404076i	$0.867593\pi$
$662$	1.96156e7	1.73962
$663$	230443.	0.0203601
$664$	3.87691e7	3.41244
$665$	8.22622e6	0.721351
$666$	4.43223e6	0.387202
$667$	3.02961e6	0.263677
$668$	3.82380e7	3.31554
$669$	−2.95872e6	−0.255587
$670$	1.92180e7	1.65394
$671$	3.25748e6	0.279303
$672$	2.00255e7	1.71065
$673$	9.36052e6	0.796641	0.398320	−	0.917246i	$-0.369593\pi$
$673$	9.36052e6	0.796641	0.398320	+	0.917246i	$0.369593\pi$
$674$	−4.05834e7	−3.44111
$675$	−2.09185e6	−0.176714
$676$	−1.91591e7	−1.61253
$677$	6.38062e6	0.535046	0.267523	−	0.963551i	$-0.413795\pi$
$677$	6.38062e6	0.535046	0.267523	+	0.963551i	$0.413795\pi$
$678$	7.49627e6	0.626283
$679$	2.82766e7	2.35371
$680$	1.03673e6	0.0859790
$681$	4.80672e6	0.397174
$682$	−2.87197e6	−0.236439
$683$	−2.06286e7	−1.69207	−0.846035	−	0.533127i	$-0.821017\pi$
$683$	−2.06286e7	−1.69207	−0.846035	+	0.533127i	$0.821017\pi$
$684$	2.81776e7	2.30284
$685$	−7.92427e6	−0.645257
$686$	−7.88720e6	−0.639901
$687$	6.70377e6	0.541910
$688$	6.21473e7	5.00555
$689$	1.86254e6	0.149471
$690$	−7.57016e6	−0.605316
$691$	7.08478e6	0.564457	0.282229	−	0.959347i	$-0.408926\pi$
$691$	7.08478e6	0.564457	0.282229	+	0.959347i	$0.408926\pi$
$692$	3.41228e7	2.70882
$693$	−1.07840e7	−0.852997
$694$	3.03605e7	2.39282
$695$	−1.00665e6	−0.0790529
$696$	3.47488e6	0.271905
$697$	1.41636e6	0.110431
$698$	−3.36470e7	−2.61401
$699$	5.86864e6	0.454302
$700$	8.67940e6	0.669491
$701$	−4.01930e6	−0.308927	−0.154463	−	0.987999i	$-0.549365\pi$
$701$	−4.01930e6	−0.308927	−0.154463	+	0.987999i	$0.549365\pi$
$702$	1.30918e7	1.00266
$703$	4.43746e6	0.338646
$704$	2.18682e7	1.66296
$705$	4.99084e6	0.378182
$706$	2.56494e7	1.93671
$707$	−1.89496e7	−1.42577
$708$	−1.05043e7	−0.787562
$709$	−8.62373e6	−0.644288	−0.322144	−	0.946691i	$-0.604403\pi$
$709$	−8.62373e6	−0.644288	−0.322144	+	0.946691i	$0.604403\pi$
$710$	9.09941e6	0.677435
$711$	6.41474e6	0.475889
$712$	−1.75224e7	−1.29537
$713$	−2.78653e6	−0.205277
$714$	−1.14073e6	−0.0837408
$715$	3.20863e6	0.234723
$716$	−5.82975e7	−4.24979
$717$	1.09492e7	0.795399
$718$	1.26410e7	0.915103
$719$	−1.00415e7	−0.724397	−0.362199	−	0.932101i	$-0.617974\pi$
$719$	−1.00415e7	−0.724397	−0.362199	+	0.932101i	$0.617974\pi$
$720$	1.33849e7	0.962242
$721$	1.08417e6	0.0776707
$722$	1.29951e7	0.927761
$723$	9.31654e6	0.662840
$724$	−1.03755e6	−0.0735632
$725$	525625.	0.0371391
$726$	−3.29717e6	−0.232166
$727$	−2.23153e7	−1.56591	−0.782955	−	0.622079i	$-0.786288\pi$
$727$	−2.23153e7	−1.56591	−0.782955	+	0.622079i	$0.786288\pi$
$728$	−3.29012e7	−2.30082
$729$	3.27994e6	0.228585
$730$	−1.72155e7	−1.19567
$731$	−1.66219e6	−0.115050
$732$	5.98501e6	0.412845
$733$	1.12459e7	0.773101	0.386550	−	0.922268i	$-0.373667\pi$
$733$	1.12459e7	0.773101	0.386550	+	0.922268i	$0.373667\pi$
$734$	−3.70540e7	−2.53860
$735$	−2.46423e6	−0.168253
$736$	5.33514e7	3.63037
$737$	−2.52232e7	−1.71053
$738$	3.43015e7	2.31831
$739$	−2.50044e7	−1.68424	−0.842122	−	0.539288i	$-0.818694\pi$
$739$	−2.50044e7	−1.68424	−0.842122	+	0.539288i	$0.818694\pi$
$740$	4.68192e6	0.314300
$741$	5.58746e6	0.373826
$742$	−9.21989e6	−0.614774
$743$	−2.10485e7	−1.39878	−0.699388	−	0.714742i	$-0.746544\pi$
$743$	−2.10485e7	−1.39878	−0.699388	+	0.714742i	$0.746544\pi$
$744$	−3.19607e6	−0.211682
$745$	172995.	0.0114194
$746$	−1.15865e7	−0.762261
$747$	−1.33874e7	−0.877797
$748$	−2.24648e6	−0.146808
$749$	2.83539e6	0.184675
$750$	−1.31339e6	−0.0852590
$751$	8.36257e6	0.541053	0.270527	−	0.962712i	$-0.412802\pi$
$751$	8.36257e6	0.541053	0.270527	+	0.962712i	$0.412802\pi$
$752$	−7.49126e7	−4.83070
$753$	−6.80895e6	−0.437615
$754$	−3.28961e6	−0.210725
$755$	644174.	0.0411278
$756$	−4.64793e7	−2.95771
$757$	7.51817e6	0.476840	0.238420	−	0.971162i	$-0.423371\pi$
$757$	7.51817e6	0.476840	0.238420	+	0.971162i	$0.423371\pi$
$758$	−6.86522e6	−0.433992
$759$	9.93566e6	0.626026
$760$	2.51372e7	1.57864
$761$	2.73916e6	0.171457	0.0857287	−	0.996319i	$-0.472678\pi$
$761$	2.73916e6	0.171457	0.0857287	+	0.996319i	$0.472678\pi$
$762$	−1.96295e7	−1.22468
$763$	−1.44891e6	−0.0901013
$764$	5.35215e7	3.31738
$765$	−357993.	−0.0221167
$766$	2.20963e7	1.36065
$767$	6.02317e6	0.369689
$768$	342652.	0.0209628
$769$	−1.27116e7	−0.775150	−0.387575	−	0.921838i	$-0.626687\pi$
$769$	−1.27116e7	−0.775150	−0.387575	+	0.921838i	$0.626687\pi$
$770$	−1.58833e7	−0.965412
$771$	−1.79486e6	−0.108741
$772$	5.29947e7	3.20029
$773$	1.13751e7	0.684712	0.342356	−	0.939570i	$-0.388775\pi$
$773$	1.13751e7	0.684712	0.342356	+	0.939570i	$0.388775\pi$
$774$	−4.02552e7	−2.41529
$775$	−483451.	−0.0289133
$776$	8.64058e7	5.15096
$777$	−3.12029e6	−0.185414
$778$	−9.35348e6	−0.554019
$779$	3.43420e7	2.02760
$780$	5.89527e6	0.346950
$781$	−1.19428e7	−0.700612
$782$	−3.03910e6	−0.177717
$783$	−2.81479e6	−0.164075
$784$	3.69880e7	2.14917
$785$	2.95996e6	0.171440
$786$	7.05366e6	0.407247
$787$	7.85917e6	0.452314	0.226157	−	0.974091i	$-0.427384\pi$
$787$	7.85917e6	0.452314	0.226157	+	0.974091i	$0.427384\pi$
$788$	4.04925e7	2.32305
$789$	1.24151e7	0.709998
$790$	9.44797e6	0.538606
$791$	1.52603e7	0.867207
$792$	−3.29531e7	−1.86674
$793$	−3.43180e6	−0.193794
$794$	−3.25454e7	−1.83205
$795$	1.00062e6	0.0561505
$796$	4.48066e7	2.50645
$797$	2.28740e7	1.27555	0.637774	−	0.770223i	$-0.279855\pi$
$797$	2.28740e7	1.27555	0.637774	+	0.770223i	$0.279855\pi$
$798$	−2.76588e7	−1.53754
$799$	2.00361e6	0.111032
$800$	9.25624e6	0.511340
$801$	6.05067e6	0.333213
$802$	5.39604e7	2.96237
$803$	2.25950e7	1.23658
$804$	−4.63429e7	−2.52839
$805$	−1.54108e7	−0.838174
$806$	3.02566e6	0.164053
$807$	1.54455e7	0.834868
$808$	−5.79048e7	−3.12023
$809$	3.37257e7	1.81171	0.905856	−	0.423585i	$-0.139229\pi$
$809$	3.37257e7	1.81171	0.905856	+	0.423585i	$0.139229\pi$
$810$	−4.63479e6	−0.248209
$811$	−5.02984e6	−0.268536	−0.134268	−	0.990945i	$-0.542868\pi$
$811$	−5.02984e6	−0.268536	−0.134268	+	0.990945i	$0.542868\pi$
$812$	1.16790e7	0.621607
$813$	−1.60687e7	−0.852618
$814$	−8.56789e6	−0.453224
$815$	−6.75190e6	−0.356067
$816$	−1.85827e6	−0.0976976
$817$	−4.03026e7	−2.11241
$818$	3.47254e7	1.81453
$819$	1.13611e7	0.591850
$820$	3.62339e7	1.88183
$821$	9.57604e6	0.495824	0.247912	−	0.968783i	$-0.420256\pi$
$821$	9.57604e6	0.495824	0.247912	+	0.968783i	$0.420256\pi$
$822$	2.66436e7	1.37535
$823$	8.52616e6	0.438787	0.219394	−	0.975636i	$-0.429592\pi$
$823$	8.52616e6	0.438787	0.219394	+	0.975636i	$0.429592\pi$
$824$	3.31292e6	0.169978
$825$	1.72379e6	0.0881760
$826$	−2.98157e7	−1.52053
$827$	−3.34200e7	−1.69919	−0.849597	−	0.527432i	$-0.823155\pi$
$827$	−3.34200e7	−1.69919	−0.849597	+	0.527432i	$0.823155\pi$
$828$	−5.27870e7	−2.67578
$829$	−9.56877e6	−0.483582	−0.241791	−	0.970328i	$-0.577735\pi$
$829$	−9.56877e6	−0.483582	−0.241791	+	0.970328i	$0.577735\pi$
$830$	−1.97176e7	−0.993481
$831$	8.40802e6	0.422368
$832$	−2.30385e7	−1.15384
$833$	−989283.	−0.0493979
$834$	3.38465e6	0.168499
$835$	−1.17793e7	−0.584657
$836$	−5.44696e7	−2.69550
$837$	2.58894e6	0.127735
$838$	−6.33068e7	−3.11416
$839$	2.43662e7	1.19504	0.597520	−	0.801854i	$-0.296153\pi$
$839$	2.43662e7	1.19504	0.597520	+	0.801854i	$0.296153\pi$
$840$	−1.76757e7	−0.864329
$841$	707281.	0.0344828
$842$	1.74247e7	0.847005
$843$	−5.66569e6	−0.274589
$844$	5.31563e7	2.56861
$845$	5.90198e6	0.284352
$846$	4.85237e7	2.33092
$847$	−6.71212e6	−0.321478
$848$	−1.50194e7	−0.717237
$849$	−1.28582e7	−0.612226
$850$	−527271.	−0.0250315
$851$	−8.31301e6	−0.393491
$852$	−2.19427e7	−1.03560
$853$	−4.13664e6	−0.194659	−0.0973296	−	0.995252i	$-0.531030\pi$
$853$	−4.13664e6	−0.194659	−0.0973296	+	0.995252i	$0.531030\pi$
$854$	1.69880e7	0.797072
$855$	−8.68013e6	−0.406079
$856$	8.66419e6	0.404151
$857$	−3.90275e7	−1.81518	−0.907588	−	0.419861i	$-0.862079\pi$
$857$	−3.90275e7	−1.81518	−0.907588	+	0.419861i	$0.862079\pi$
$858$	−1.07883e7	−0.500306
$859$	1.49365e7	0.690664	0.345332	−	0.938481i	$-0.387766\pi$
$859$	1.49365e7	0.690664	0.345332	+	0.938481i	$0.387766\pi$
$860$	−4.25229e7	−1.96054
$861$	−2.41483e7	−1.11014
$862$	−2.08339e7	−0.954999
$863$	3.17777e7	1.45243	0.726217	−	0.687466i	$-0.241277\pi$
$863$	3.17777e7	1.45243	0.726217	+	0.687466i	$0.241277\pi$
$864$	−4.95683e7	−2.25902
$865$	−1.05116e7	−0.477670
$866$	−6.20793e7	−2.81288
$867$	−1.11700e7	−0.504667
$868$	−1.07419e7	−0.483931
$869$	−1.24002e7	−0.557033
$870$	−1.76730e6	−0.0791610
$871$	2.65730e7	1.18685
$872$	−4.42749e6	−0.197182
$873$	−2.98368e7	−1.32500
$874$	−7.36880e7	−3.26301
$875$	−2.67370e6	−0.118057
$876$	4.15141e7	1.82783
$877$	2.98135e7	1.30892	0.654462	−	0.756095i	$-0.272895\pi$
$877$	2.98135e7	1.30892	0.654462	+	0.756095i	$0.272895\pi$
$878$	−1.21549e7	−0.532126
$879$	−1.70331e7	−0.743569
$880$	−2.58742e7	−1.12631
$881$	−6.93236e6	−0.300913	−0.150457	−	0.988617i	$-0.548074\pi$
$881$	−6.93236e6	−0.300913	−0.150457	+	0.988617i	$0.548074\pi$
$882$	−2.39585e7	−1.03702
$883$	4.25865e6	0.183810	0.0919052	−	0.995768i	$-0.470704\pi$
$883$	4.25865e6	0.183810	0.0919052	+	0.995768i	$0.470704\pi$
$884$	2.36670e6	0.101862
$885$	3.23587e6	0.138878
$886$	−6.39522e7	−2.73698
$887$	3.61329e7	1.54203	0.771017	−	0.636815i	$-0.219749\pi$
$887$	3.61329e7	1.54203	0.771017	+	0.636815i	$0.219749\pi$
$888$	−9.53479e6	−0.405769
$889$	−3.99602e7	−1.69579
$890$	8.91174e6	0.377127
$891$	6.08306e6	0.256701
$892$	−3.03868e7	−1.27871
$893$	4.85809e7	2.03862
$894$	−581657.	−0.0243401
$895$	1.79586e7	0.749403
$896$	3.29490e7	1.37111
$897$	−1.04674e7	−0.434367
$898$	−2.11730e7	−0.876175
$899$	−650532.	−0.0268454
$900$	−9.15832e6	−0.376885
$901$	401709.	0.0164854
$902$	−6.63077e7	−2.71361
$903$	2.83396e7	1.15658
$904$	4.66316e7	1.89784
$905$	319617.	0.0129720
$906$	−2.16589e6	−0.0876630
$907$	−4.55741e7	−1.83950	−0.919751	−	0.392503i	$-0.871609\pi$
$907$	−4.55741e7	−1.83950	−0.919751	+	0.392503i	$0.871609\pi$
$908$	4.93662e7	1.98708
$909$	1.99952e7	0.802630
$910$	1.67333e7	0.669850
$911$	−4.41937e7	−1.76427	−0.882135	−	0.470997i	$-0.843894\pi$
$911$	−4.41937e7	−1.76427	−0.882135	+	0.470997i	$0.843894\pi$
$912$	−4.50568e7	−1.79380
$913$	2.58790e7	1.02747
$914$	−8.48092e6	−0.335798
$915$	−1.84369e6	−0.0728006
$916$	6.88494e7	2.71120
$917$	1.43593e7	0.563911
$918$	2.82360e6	0.110585
$919$	2.96916e7	1.15970	0.579849	−	0.814724i	$-0.303112\pi$
$919$	2.96916e7	1.15970	0.579849	+	0.814724i	$0.303112\pi$
$920$	−4.70912e7	−1.83430
$921$	−2.17521e7	−0.844991
$922$	4.42481e7	1.71422
$923$	1.25819e7	0.486119
$924$	3.83014e7	1.47583
$925$	−1.44227e6	−0.0554233
$926$	−8.14299e7	−3.12073
$927$	−1.14399e6	−0.0437242
$928$	1.24552e7	0.474767
$929$	6.64036e6	0.252437	0.126218	−	0.992002i	$-0.459716\pi$
$929$	6.64036e6	0.252437	0.126218	+	0.992002i	$0.459716\pi$
$930$	1.62550e6	0.0616281
$931$	−2.39868e7	−0.906981
$932$	6.02724e7	2.27289
$933$	1.13277e7	0.426028
$934$	8.22943e7	3.08676
$935$	692031.	0.0258879
$936$	3.47166e7	1.29523
$937$	−1.51548e7	−0.563899	−0.281950	−	0.959429i	$-0.590981\pi$
$937$	−1.51548e7	−0.563899	−0.281950	+	0.959429i	$0.590981\pi$
$938$	−1.31541e8	−4.88150
$939$	−7.80623e6	−0.288920
$940$	5.12572e7	1.89206
$941$	8.67923e6	0.319527	0.159763	−	0.987155i	$-0.448927\pi$
$941$	8.67923e6	0.319527	0.159763	+	0.987155i	$0.448927\pi$
$942$	−9.95221e6	−0.365420
$943$	−6.43352e7	−2.35597
$944$	−4.85704e7	−1.77395
$945$	1.43180e7	0.521558
$946$	7.78166e7	2.82712
$947$	2.91427e7	1.05598	0.527989	−	0.849251i	$-0.322946\pi$
$947$	2.91427e7	1.05598	0.527989	+	0.849251i	$0.322946\pi$
$948$	−2.27832e7	−0.823367
$949$	−2.38042e7	−0.858001
$950$	−1.27845e7	−0.459596
$951$	−1.27526e7	−0.457244
$952$	−7.09606e6	−0.253761
$953$	−1.95808e6	−0.0698390	−0.0349195	−	0.999390i	$-0.511117\pi$
$953$	−1.95808e6	−0.0698390	−0.0349195	+	0.999390i	$0.511117\pi$
$954$	9.72862e6	0.346083
$955$	−1.64874e7	−0.584982
$956$	1.12451e8	3.97942
$957$	2.31954e6	0.0818694
$958$	9.58711e7	3.37500
$959$	5.42390e7	1.90443
$960$	−1.23771e7	−0.433453
$961$	−2.80308e7	−0.979100
$962$	9.02641e6	0.314469
$963$	−2.99184e6	−0.103961
$964$	9.56832e7	3.31622
$965$	−1.63251e7	−0.564335
$966$	5.18153e7	1.78655
$967$	1.07841e7	0.370867	0.185434	−	0.982657i	$-0.440631\pi$
$967$	1.07841e7	0.370867	0.185434	+	0.982657i	$0.440631\pi$
$968$	−2.05105e7	−0.703537
$969$	1.20509e6	0.0412297
$970$	−4.39452e7	−1.49962
$971$	3.44324e7	1.17198	0.585989	−	0.810319i	$-0.300706\pi$
$971$	3.44324e7	1.17198	0.585989	+	0.810319i	$0.300706\pi$
$972$	7.71809e7	2.62026
$973$	6.89021e6	0.233319
$974$	−2.47963e7	−0.837510
$975$	−1.81605e6	−0.0611808
$976$	2.76738e7	0.929917
$977$	3.72128e7	1.24726	0.623628	−	0.781721i	$-0.285658\pi$
$977$	3.72128e7	1.24726	0.623628	+	0.781721i	$0.285658\pi$
$978$	2.27018e7	0.758949
$979$	−1.16965e7	−0.390030
$980$	−2.53082e7	−0.841776
$981$	1.52886e6	0.0507219
$982$	−5.53005e7	−1.83000
$983$	−6.16022e6	−0.203335	−0.101668	−	0.994818i	$-0.532418\pi$
$983$	−6.16022e6	−0.203335	−0.101668	+	0.994818i	$0.532418\pi$
$984$	−7.37907e7	−2.42948
$985$	−1.24737e7	−0.409644
$986$	−709496.	−0.0232411
$987$	−3.41607e7	−1.11618
$988$	5.73846e7	1.87027
$989$	7.55017e7	2.45452
$990$	1.67597e7	0.543472
$991$	−2.58975e7	−0.837671	−0.418835	−	0.908062i	$-0.637562\pi$
$991$	−2.58975e7	−0.837671	−0.418835	+	0.908062i	$0.637562\pi$
$992$	−1.14558e7	−0.369613
$993$	1.45713e7	0.468949
$994$	−6.22825e7	−1.99940
$995$	−1.38027e7	−0.441985
$996$	4.75478e7	1.51874
$997$	5.78618e6	0.184355	0.0921773	−	0.995743i	$-0.470617\pi$
$997$	5.78618e6	0.184355	0.0921773	+	0.995743i	$0.470617\pi$
$998$	4.99873e7	1.58867
$999$	7.72354e6	0.244851

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.6.a.c.1.13	✓	13
5.4	even	2		725.6.a.f.1.1		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.6.a.c.1.13	✓	13	1.1	even	1	trivial
725.6.a.f.1.1		13	5.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	145.a (trivial)

\(f(q)\)	\(=\)	\(q+10.6375 q^{2} +7.90198 q^{3} +81.1554 q^{4} -25.0000 q^{5} +84.0569 q^{6} +171.117 q^{7} +522.888 q^{8} -180.559 q^{9} -265.936 q^{10} +349.035 q^{11} +641.288 q^{12} -367.714 q^{13} +1820.25 q^{14} -197.550 q^{15} +2965.22 q^{16} -79.3079 q^{17} -1920.68 q^{18} -1922.95 q^{19} -2028.88 q^{20} +1352.16 q^{21} +3712.85 q^{22} +3602.40 q^{23} +4131.85 q^{24} +625.000 q^{25} -3911.54 q^{26} -3346.95 q^{27} +13887.0 q^{28} +841.000 q^{29} -2101.42 q^{30} -773.522 q^{31} +14810.0 q^{32} +2758.07 q^{33} -843.633 q^{34} -4277.92 q^{35} -14653.3 q^{36} -2307.63 q^{37} -20455.3 q^{38} -2905.67 q^{39} -13072.2 q^{40} -17859.0 q^{41} +14383.6 q^{42} +20958.8 q^{43} +28326.1 q^{44} +4513.97 q^{45} +38320.3 q^{46} -25263.7 q^{47} +23431.1 q^{48} +12474.0 q^{49} +6648.41 q^{50} -626.689 q^{51} -29842.0 q^{52} -5065.18 q^{53} -35603.0 q^{54} -8725.88 q^{55} +89474.9 q^{56} -15195.1 q^{57} +8946.10 q^{58} -16380.0 q^{59} -16032.2 q^{60} +9332.80 q^{61} -8228.30 q^{62} -30896.6 q^{63} +62653.4 q^{64} +9192.86 q^{65} +29338.8 q^{66} -72265.4 q^{67} -6436.26 q^{68} +28466.1 q^{69} -45506.2 q^{70} -34216.5 q^{71} -94411.9 q^{72} +64735.5 q^{73} -24547.3 q^{74} +4938.74 q^{75} -156058. q^{76} +59725.8 q^{77} -30909.0 q^{78} -35527.2 q^{79} -74130.5 q^{80} +17428.2 q^{81} -189974. q^{82} +74144.2 q^{83} +109735. q^{84} +1982.70 q^{85} +222948. q^{86} +6645.57 q^{87} +182506. q^{88} -33510.8 q^{89} +48017.1 q^{90} -62922.1 q^{91} +292354. q^{92} -6112.35 q^{93} -268742. q^{94} +48073.7 q^{95} +117028. q^{96} +165247. q^{97} +132691. q^{98} -63021.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 7 q^{2} + 2 q^{3} + 213 q^{4} - 325 q^{5} - 3 q^{6} - 18 q^{7} - 399 q^{8} + 1155 q^{9} - 175 q^{10} + 844 q^{11} + 167 q^{12} - 704 q^{13} + 4425 q^{14} - 50 q^{15} + 5805 q^{16} - 210 q^{17} + 7378 q^{18}+ \cdots - 3872 q^{99}+O(q^{100}) \) 13 * q + 7 * q^2 + 2 * q^3 + 213 * q^4 - 325 * q^5 - 3 * q^6 - 18 * q^7 - 399 * q^8 + 1155 * q^9 - 175 * q^10 + 844 * q^11 + 167 * q^12 - 704 * q^13 + 4425 * q^14 - 50 * q^15 + 5805 * q^16 - 210 * q^17 + 7378 * q^18 + 2524 * q^19 - 5325 * q^20 + 7088 * q^21 - 3772 * q^22 + 10806 * q^23 + 11131 * q^24 + 8125 * q^25 + 15003 * q^26 - 2872 * q^27 + 6007 * q^28 + 10933 * q^29 + 75 * q^30 + 6820 * q^31 - 9761 * q^32 + 9416 * q^33 + 18557 * q^34 + 450 * q^35 + 28284 * q^36 - 7784 * q^37 + 43872 * q^38 + 30524 * q^39 + 9975 * q^40 + 17950 * q^41 + 104284 * q^42 + 24570 * q^43 + 101386 * q^44 - 28875 * q^45 + 71703 * q^46 + 26242 * q^47 + 96475 * q^48 + 45423 * q^49 + 4375 * q^50 - 5632 * q^51 - 2925 * q^52 + 50580 * q^53 + 61352 * q^54 - 21100 * q^55 + 172651 * q^56 + 71600 * q^57 + 5887 * q^58 + 50712 * q^59 - 4175 * q^60 - 24104 * q^61 + 82941 * q^62 - 1298 * q^63 + 75673 * q^64 + 17600 * q^65 - 7632 * q^66 - 93110 * q^67 - 113909 * q^68 + 116878 * q^69 - 110625 * q^70 + 253344 * q^71 - 206562 * q^72 - 11006 * q^73 - 171316 * q^74 + 1250 * q^75 - 275002 * q^76 + 106744 * q^77 - 84017 * q^78 - 23792 * q^79 - 145125 * q^80 + 229097 * q^81 - 461156 * q^82 + 115802 * q^83 - 224096 * q^84 + 5250 * q^85 + 31283 * q^86 + 1682 * q^87 - 635028 * q^88 + 87446 * q^89 - 184450 * q^90 - 33904 * q^91 + 197053 * q^92 - 168912 * q^93 - 464496 * q^94 - 63100 * q^95 - 186929 * q^96 + 27766 * q^97 - 166558 * q^98 - 3872 * q^99

Introduction

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