LMFDB - Embedded newform 35.6.a.c.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [35,6,Mod(1,35)] 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("35.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	35.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$5.61343369345$
Analytic rank:	$0$
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:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-8.38673$ of defining polynomial
Character	$\chi$	$=$	35.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-10.3867 q^{2} +27.9421 q^{3} +75.8842 q^{4} -25.0000 q^{5} -290.227 q^{6} +49.0000 q^{7} -455.813 q^{8} +537.760 q^{9} +259.668 q^{10} -132.501 q^{11} +2120.36 q^{12} +802.665 q^{13} -508.950 q^{14} -698.552 q^{15} +2306.11 q^{16} +763.068 q^{17} -5585.57 q^{18} -61.2154 q^{19} -1897.10 q^{20} +1369.16 q^{21} +1376.25 q^{22} +3589.61 q^{23} -12736.4 q^{24} +625.000 q^{25} -8337.06 q^{26} +8236.22 q^{27} +3718.32 q^{28} -4593.21 q^{29} +7255.67 q^{30} -384.018 q^{31} -9366.97 q^{32} -3702.35 q^{33} -7925.78 q^{34} -1225.00 q^{35} +40807.5 q^{36} +5377.28 q^{37} +635.827 q^{38} +22428.1 q^{39} +11395.3 q^{40} -20530.3 q^{41} -14221.1 q^{42} -12175.3 q^{43} -10054.7 q^{44} -13444.0 q^{45} -37284.3 q^{46} -15232.4 q^{47} +64437.7 q^{48} +2401.00 q^{49} -6491.71 q^{50} +21321.7 q^{51} +60909.6 q^{52} +1369.77 q^{53} -85547.4 q^{54} +3312.52 q^{55} -22334.8 q^{56} -1710.48 q^{57} +47708.4 q^{58} +27738.1 q^{59} -53009.1 q^{60} -15708.6 q^{61} +3988.70 q^{62} +26350.3 q^{63} +23496.6 q^{64} -20066.6 q^{65} +38455.3 q^{66} -16813.0 q^{67} +57904.8 q^{68} +100301. q^{69} +12723.7 q^{70} +37925.9 q^{71} -245118. q^{72} -48894.9 q^{73} -55852.3 q^{74} +17463.8 q^{75} -4645.28 q^{76} -6492.54 q^{77} -232955. q^{78} -66582.2 q^{79} -57652.9 q^{80} +99461.4 q^{81} +213243. q^{82} -63358.0 q^{83} +103898. q^{84} -19076.7 q^{85} +126461. q^{86} -128344. q^{87} +60395.6 q^{88} -69175.3 q^{89} +139639. q^{90} +39330.6 q^{91} +272395. q^{92} -10730.3 q^{93} +158215. q^{94} +1530.38 q^{95} -261733. q^{96} -55697.0 q^{97} -24938.5 q^{98} -71253.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6 q^{2} + 26 q^{3} + 112 q^{4} - 75 q^{5} - 96 q^{6} + 147 q^{7} - 120 q^{8} + 489 q^{9} + 150 q^{10} - 194 q^{11} + 2956 q^{12} + 1892 q^{13} - 294 q^{14} - 650 q^{15} + 1496 q^{16} - 184 q^{17}+ \cdots - 60752 q^{99}+O(q^{100}) $ 3 * q - 6 * q^2 + 26 * q^3 + 112 * q^4 - 75 * q^5 - 96 * q^6 + 147 * q^7 - 120 * q^8 + 489 * q^9 + 150 * q^10 - 194 * q^11 + 2956 * q^12 + 1892 * q^13 - 294 * q^14 - 650 * q^15 + 1496 * q^16 - 184 * q^17 - 6078 * q^18 + 1212 * q^19 - 2800 * q^20 + 1274 * q^21 - 872 * q^22 + 3188 * q^23 - 13920 * q^24 + 1875 * q^25 - 9836 * q^26 + 7910 * q^27 + 5488 * q^28 - 11332 * q^29 + 2400 * q^30 + 9200 * q^31 - 20256 * q^32 - 8278 * q^33 - 18492 * q^34 - 3675 * q^35 + 38236 * q^36 + 6042 * q^37 + 25520 * q^38 + 12842 * q^39 + 3000 * q^40 + 10442 * q^41 - 4704 * q^42 + 28112 * q^43 - 20436 * q^44 - 12225 * q^45 - 41856 * q^46 + 2330 * q^47 + 68808 * q^48 + 7203 * q^49 - 3750 * q^50 + 3622 * q^51 + 63524 * q^52 + 7190 * q^53 - 138960 * q^54 + 4850 * q^55 - 5880 * q^56 + 45508 * q^57 + 37260 * q^58 + 23760 * q^59 - 73900 * q^60 + 8722 * q^61 + 24848 * q^62 + 23961 * q^63 + 4976 * q^64 - 47300 * q^65 + 24368 * q^66 - 97572 * q^67 + 3564 * q^68 + 92596 * q^69 + 7350 * q^70 - 52816 * q^71 - 251640 * q^72 + 34870 * q^73 - 241892 * q^74 + 16250 * q^75 + 115256 * q^76 - 9506 * q^77 - 142096 * q^78 - 71546 * q^79 - 37400 * q^80 - 3957 * q^81 + 241908 * q^82 - 20920 * q^83 + 144844 * q^84 + 4600 * q^85 + 266024 * q^86 - 112298 * q^87 + 59200 * q^88 - 192622 * q^89 + 151950 * q^90 + 92708 * q^91 + 248952 * q^92 - 20392 * q^93 + 360128 * q^94 - 30300 * q^95 - 296256 * q^96 + 116320 * q^97 - 14406 * q^98 - 60752 * 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 $

$2$	−10.3867	−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	$-0.146286\pi$
$3$	27.9421	1.79249	0.896243	+	0.443564i	$0.146286\pi$
$4$	75.8842	2.37138
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−290.227	−3.29124
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	−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	$-0.271133\pi$
$13$	802.665	1.31727	0.658637	+	0.752461i	$0.271133\pi$
$14$	−508.950	−0.693993
$15$	−698.552	−0.801624
$16$	2306.11	2.25207
$17$	763.068	0.640385	0.320192	−	0.947353i	$-0.396252\pi$
$17$	763.068	0.640385	0.320192	+	0.947353i	$0.396252\pi$
$18$	−5585.57	−4.06337
$19$	−61.2154	−0.0389024	−0.0194512	−	0.999811i	$-0.506192\pi$
$19$	−61.2154	−0.0389024	−0.0194512	+	0.999811i	$0.506192\pi$
$20$	−1897.10	−1.06051
$21$	1369.16	0.677496
$22$	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
$28$	3718.32	0.896298
$29$	−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	$-0.511425\pi$
$31$	−384.018	−0.0717708	−0.0358854	+	0.999356i	$0.511425\pi$
$32$	−9366.97	−1.61705
$33$	−3702.35	−0.591824
$34$	−7925.78	−1.17583
$35$	−1225.00	−0.169031
$36$	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	$-0.902745\pi$
$41$	−20530.3	−1.90737	−0.953686	+	0.300804i	$0.902745\pi$
$42$	−14221.1	−1.24397
$43$	−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	$-0.667739\pi$
$47$	−15232.4	−1.00583	−0.502915	+	0.864336i	$0.667739\pi$
$48$	64437.7	4.03680
$49$	2401.00	0.142857
$50$	−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
$56$	−22334.8	−0.951728
$57$	−1710.48	−0.0697320
$58$	47708.4	1.86219
$59$	27738.1	1.03740	0.518700	−	0.854956i	$-0.326416\pi$
$59$	27738.1	1.03740	0.518700	+	0.854956i	$0.326416\pi$
$60$	−53009.1	−1.90096
$61$	−15708.6	−0.540523	−0.270261	−	0.962787i	$-0.587110\pi$
$61$	−15708.6	−0.540523	−0.270261	+	0.962787i	$0.587110\pi$
$62$	3988.70	0.131781
$63$	26350.3	0.836437
$64$	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
$70$	12723.7	0.310363
$71$	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	$-0.680420\pi$
$73$	−48894.9	−1.07388	−0.536940	+	0.843620i	$0.680420\pi$
$74$	−55852.3	−1.18566
$75$	17463.8	0.358497
$76$	−4645.28	−0.0922524
$77$	−6492.54	−0.124792
$78$	−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	$-0.668415\pi$
$83$	−63358.0	−1.00950	−0.504750	+	0.863266i	$0.668415\pi$
$84$	103898.	1.60660
$85$	−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	$-0.653175\pi$
$89$	−69175.3	−0.925712	−0.462856	+	0.886434i	$0.653175\pi$
$90$	139639.	1.81719
$91$	39330.6	0.497883
$92$	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	$-0.597160\pi$
$97$	−55697.0	−0.601039	−0.300519	+	0.953776i	$0.597160\pi$
$98$	−24938.5	−0.262305
$99$	−71253.7	−0.730667
$100$	47427.6	0.474276
$101$	29027.0	0.283139	0.141569	−	0.989928i	$-0.454785\pi$
$101$	29027.0	0.283139	0.141569	+	0.989928i	$0.454785\pi$
$102$	−221463.	−2.10766
$103$	86612.7	0.804430	0.402215	−	0.915545i	$-0.368240\pi$
$103$	86612.7	0.804430	0.402215	+	0.915545i	$0.368240\pi$
$104$	−365865.	−3.31694
$105$	−34229.1	−0.302985
$106$	−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
$112$	113000.	0.851201
$113$	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
$119$	37390.3	0.242043
$120$	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
$126$	−273693.	−1.53581
$127$	−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	$-0.448491\pi$
$131$	63290.9	0.322228	0.161114	+	0.986936i	$0.448491\pi$
$132$	−280950.	−1.40344
$133$	−2999.55	−0.0147037
$134$	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	$-0.429195\pi$
$139$	100506.	0.441220	0.220610	+	0.975362i	$0.429195\pi$
$140$	−92958.1	−0.400836
$141$	−425626.	−1.80294
$142$	−393926.	−1.63943
$143$	−106354.	−0.434923
$144$	1.24014e6	4.98383
$145$	114830.	0.453561
$146$	507858.	1.97179
$147$	67089.0	0.256069
$148$	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
$154$	67436.2	0.229135
$155$	9600.46	0.0320969
$156$	1.70194e6	5.59929
$157$	−37131.5	−0.120225	−0.0601123	−	0.998192i	$-0.519146\pi$
$157$	−37131.5	−0.120225	−0.0601123	+	0.998192i	$0.519146\pi$
$158$	691571.	2.20391
$159$	38274.3	0.120065
$160$	234174.	0.723168
$161$	175891.	0.534785
$162$	−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	$-0.399712\pi$
$167$	223362.	0.619752	0.309876	+	0.950777i	$0.399712\pi$
$168$	−624082.	−1.70596
$169$	272978.	0.735209
$170$	198145.	0.525848
$171$	−32919.2	−0.0860912
$172$	−923911.	−2.38127
$173$	482127.	1.22475	0.612374	−	0.790568i	$-0.290215\pi$
$173$	482127.	1.22475	0.612374	+	0.790568i	$0.290215\pi$
$174$	1.33307e6	3.33796
$175$	30625.0	0.0755929
$176$	−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	$-0.565404\pi$
$181$	−179855.	−0.408061	−0.204030	+	0.978965i	$0.565404\pi$
$182$	−408516.	−0.914178
$183$	−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
$189$	403575.	0.821806
$190$	−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
$196$	182198.	0.338769
$197$	−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	$-0.212108\pi$
$199$	878271.	1.57216	0.786078	+	0.618127i	$0.212108\pi$
$200$	−284883.	−0.503607
$201$	−469791.	−0.820190
$202$	−301496.	−0.519880
$203$	−225067.	−0.383329
$204$	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
$210$	355528.	0.556321
$211$	−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
$217$	−18816.9	−0.0271268
$218$	−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	$-0.343703\pi$
$223$	700322.	0.943052	0.471526	+	0.881852i	$0.343703\pi$
$224$	−458982.	−0.611189
$225$	336100.	0.442601
$226$	−433631.	−0.564741
$227$	795250.	1.02433	0.512164	−	0.858888i	$-0.328844\pi$
$227$	795250.	1.02433	0.512164	+	0.858888i	$0.328844\pi$
$228$	−129799.	−0.165361
$229$	−1.18132e6	−1.48860	−0.744301	−	0.667844i	$-0.767217\pi$
$229$	−1.18132e6	−1.48860	−0.744301	+	0.667844i	$0.767217\pi$
$230$	932108.	1.16184
$231$	−181415.	−0.223688
$232$	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
$238$	−388363.	−0.444422
$239$	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	$-0.337247\pi$
$241$	882390.	0.978629	0.489314	+	0.872107i	$0.337247\pi$
$242$	1.49044e6	1.63597
$243$	777759.	0.844946
$244$	−1.19204e6	−1.28179
$245$	−60025.0	−0.0638877
$246$	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	$-0.578819\pi$
$251$	−489271.	−0.490191	−0.245095	+	0.969499i	$0.578819\pi$
$252$	1.99957e6	1.98351
$253$	−475626.	−0.467159
$254$	513248.	0.499163
$255$	−533043.	−0.513348
$256$	−1.33033e6	−1.26871
$257$	−968316.	−0.914502	−0.457251	−	0.889338i	$-0.651166\pi$
$257$	−968316.	−0.914502	−0.457251	+	0.889338i	$0.651166\pi$
$258$	3.53360e6	3.30497
$259$	263487.	0.244067
$260$	−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
$266$	31155.5	0.0269980
$267$	−1.93290e6	−1.65933
$268$	−1.27584e6	−1.08508
$269$	1.91422e6	1.61292	0.806458	−	0.591291i	$-0.201382\pi$
$269$	1.91422e6	1.61292	0.806458	+	0.591291i	$0.201382\pi$
$270$	2.13868e6	1.78541
$271$	648945.	0.536765	0.268383	−	0.963312i	$-0.413511\pi$
$271$	648945.	0.536765	0.268383	+	0.963312i	$0.413511\pi$
$272$	1.75972e6	1.44219
$273$	1.09898e6	0.892447
$274$	−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
$280$	558371.	0.425626
$281$	−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	$-0.484976\pi$
$283$	127141.	0.0943666	0.0471833	+	0.998886i	$0.484976\pi$
$284$	2.87797e6	2.11734
$285$	42762.1	0.0311851
$286$	1.10467e6	0.798576
$287$	−1.00598e6	−0.720919
$288$	−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	$-0.502218\pi$
$293$	−20479.1	−0.0139361	−0.00696805	+	0.999976i	$0.502218\pi$
$294$	−696835.	−0.470177
$295$	−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
$301$	−596589.	−0.379541
$302$	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	$-0.606489\pi$
$307$	−1.08442e6	−0.656676	−0.328338	+	0.944560i	$0.606489\pi$
$308$	−492681.	−0.295930
$309$	2.42014e6	1.44193
$310$	−99717.4	−0.0589341
$311$	−2.13660e6	−1.25263	−0.626314	−	0.779571i	$-0.715437\pi$
$311$	−2.13660e6	−1.25263	−0.626314	+	0.779571i	$0.715437\pi$
$312$	−1.02230e7	−5.94557
$313$	1.79419e6	1.03516	0.517580	−	0.855635i	$-0.326833\pi$
$313$	1.79419e6	1.03516	0.517580	+	0.855635i	$0.326833\pi$
$314$	385675.	0.220748
$315$	−658756.	−0.374066
$316$	−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
$322$	−1.82693e6	−0.981935
$323$	−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
$329$	−746390.	−0.380168
$330$	−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
$336$	3.15745e6	1.52577
$337$	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
$343$	117649.	0.0539949
$344$	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	$-0.238938\pi$
$349$	3.32781e6	1.46250	0.731249	+	0.682110i	$0.238938\pi$
$350$	−318094.	−0.138799
$351$	6.61092e6	2.86414
$352$	1.24113e6	0.533901
$353$	2.21885e6	0.947745	0.473872	−	0.880594i	$-0.342856\pi$
$353$	2.21885e6	0.947745	0.473872	+	0.880594i	$0.342856\pi$
$354$	−8.05034e6	−3.41434
$355$	−948147.	−0.399305
$356$	−5.24931e6	−2.19521
$357$	1.04476e6	0.433858
$358$	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
$364$	2.98457e6	1.18067
$365$	1.22237e6	0.480254
$366$	4.55907e6	1.77899
$367$	98918.7	0.0383366	0.0191683	−	0.999816i	$-0.493898\pi$
$367$	98918.7	0.0383366	0.0191683	+	0.999816i	$0.493898\pi$
$368$	8.27806e6	3.18646
$369$	−1.10404e7	−4.22102
$370$	1.39631e6	0.530245
$371$	67118.9	0.0253169
$372$	−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
$378$	−4.19182e6	−1.50894
$379$	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	$-0.616904\pi$
$383$	−2.06158e6	−0.718130	−0.359065	+	0.933313i	$0.616904\pi$
$384$	1.55612e6	0.538535
$385$	162313.	0.0558088
$386$	−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
$392$	−1.09441e6	−0.359719
$393$	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	$-0.606687\pi$
$397$	−2.06588e6	−0.657853	−0.328926	+	0.944356i	$0.606687\pi$
$398$	−9.12237e6	−2.88669
$399$	−83813.8	−0.0263562
$400$	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
$406$	2.33771e6	0.703843
$407$	−712493.	−0.213204
$408$	−9.71872e6	−2.89040
$409$	6.52308e6	1.92817	0.964084	−	0.265598i	$-0.0855695\pi$
$409$	6.52308e6	1.92817	0.964084	+	0.265598i	$0.0855695\pi$
$410$	−5.33106e6	−1.56623
$411$	1.03003e7	3.00778
$412$	6.57253e6	1.90761
$413$	1.35917e6	0.392101
$414$	−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	$-0.773772\pi$
$419$	−5.44720e6	−1.51579	−0.757894	+	0.652378i	$0.773772\pi$
$420$	−2.59744e6	−0.718494
$421$	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
$427$	−769723.	−0.204298
$428$	−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	$-0.510815\pi$
$433$	−265058.	−0.0679393	−0.0339697	+	0.999423i	$0.510815\pi$
$434$	195446.	0.0498084
$435$	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	$-0.621626\pi$
$439$	−3.01126e6	−0.745738	−0.372869	+	0.927884i	$0.621626\pi$
$440$	−1.50989e6	−0.371804
$441$	1.29116e6	0.316144
$442$	−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
$448$	1.15133e6	0.271022
$449$	−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
$455$	−983265.	−0.222660
$456$	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	$-0.487398\pi$
$461$	361201.	0.0791583	0.0395792	+	0.999216i	$0.487398\pi$
$462$	1.88431e6	0.410721
$463$	−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	$-0.537981\pi$
$467$	−1.12204e6	−0.238077	−0.119038	+	0.992890i	$0.537981\pi$
$468$	3.27548e7	6.91289
$469$	−823838.	−0.172946
$470$	−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
$476$	2.83734e6	0.573975
$477$	736610.	0.148232
$478$	−1.33399e7	−2.67044
$479$	−4.14410e6	−0.825262	−0.412631	−	0.910898i	$-0.635390\pi$
$479$	−4.14410e6	−0.825262	−0.412631	+	0.910898i	$0.635390\pi$
$480$	6.54332e6	1.29627
$481$	4.31615e6	0.850617
$482$	−9.16515e6	−1.79689
$483$	4.91476e6	0.958594
$484$	−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
$490$	623464.	0.117306
$491$	−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
$497$	1.85837e6	0.337474
$498$	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	$-0.396650\pi$
$503$	3.62037e6	0.638018	0.319009	+	0.947752i	$0.396650\pi$
$504$	−1.20108e7	−2.10618
$505$	−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	$-0.435127\pi$
$509$	2.36607e6	0.404792	0.202396	+	0.979304i	$0.435127\pi$
$510$	5.53657e6	0.942575
$511$	−2.39585e6	−0.405889
$512$	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
$518$	−2.73676e6	−0.448139
$519$	1.34716e7	2.19534
$520$	9.14663e6	1.48338
$521$	−120692.	−0.0194798	−0.00973992	−	0.999953i	$-0.503100\pi$
$521$	−120692.	−0.0194798	−0.00973992	+	0.999953i	$0.503100\pi$
$522$	2.56557e7	4.12105
$523$	1.08230e7	1.73018	0.865091	−	0.501615i	$-0.167261\pi$
$523$	1.08230e7	1.73018	0.865091	+	0.501615i	$0.167261\pi$
$524$	4.80278e6	0.764125
$525$	855726.	0.135499
$526$	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
$532$	−227619.	−0.0348681
$533$	−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
$539$	−318134.	−0.0471670
$540$	−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
$546$	−1.14148e7	−1.63865
$547$	−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
$553$	−3.26253e6	−0.453671
$554$	−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
$560$	−2.82499e6	−0.380669
$561$	−2.82514e6	−0.378995
$562$	2.06759e7	2.76137
$563$	6.74502e6	0.896835	0.448417	−	0.893824i	$-0.351988\pi$
$563$	6.74502e6	0.896835	0.448417	+	0.893824i	$0.351988\pi$
$564$	−3.22983e7	−4.27545
$565$	−1.04371e6	−0.137550
$566$	−1.32058e6	−0.173269
$567$	4.87361e6	0.636639
$568$	−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
$574$	1.04489e7	1.32370
$575$	2.24351e6	0.282981
$576$	1.26355e7	1.58685
$577$	5.52053e6	0.690305	0.345153	−	0.938547i	$-0.387827\pi$
$577$	5.52053e6	0.690305	0.345153	+	0.938547i	$0.387827\pi$
$578$	8.69976e6	1.08315
$579$	9.55395e6	1.18437
$580$	8.71379e6	1.07557
$581$	−3.10454e6	−0.381555
$582$	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	$-0.385217\pi$
$587$	5.89116e6	0.705677	0.352838	+	0.935684i	$0.385217\pi$
$588$	5.09099e6	0.607238
$589$	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	$-0.237954\pi$
$593$	1.25597e7	1.46671	0.733354	+	0.679847i	$0.237954\pi$
$594$	1.13351e7	1.31813
$595$	−934759.	−0.108245
$596$	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	$-0.508903\pi$
$601$	−495264.	−0.0559307	−0.0279654	+	0.999609i	$0.508903\pi$
$602$	6.19661e6	0.696888
$603$	−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	$-0.795255\pi$
$607$	−1.45272e7	−1.60033	−0.800165	+	0.599780i	$0.795255\pi$
$608$	573403.	0.0629072
$609$	−6.28885e6	−0.687112
$610$	−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
$616$	2.95938e6	0.314231
$617$	−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	$-0.467888\pi$
$619$	1.92017e6	0.201425	0.100713	+	0.994916i	$0.467888\pi$
$620$	728523.	0.0761139
$621$	2.95648e7	3.07643
$622$	2.21923e7	2.29999
$623$	−3.38959e6	−0.349886
$624$	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
$630$	6.84233e6	0.686835
$631$	−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
$637$	1.92720e6	0.188182
$638$	−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	$-0.447847\pi$
$643$	3.42013e6	0.326223	0.163112	+	0.986608i	$0.447847\pi$
$644$	1.33473e7	1.26818
$645$	8.50507e6	0.804968
$646$	485180.	0.0457426
$647$	−2.21315e6	−0.207850	−0.103925	−	0.994585i	$-0.533140\pi$
$647$	−2.21315e6	−0.207850	−0.103925	+	0.994585i	$0.533140\pi$
$648$	−4.53358e7	−4.24135
$649$	−3.67532e6	−0.342518
$650$	−5.21067e6	−0.483738
$651$	−525784.	−0.0486244
$652$	−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
$658$	7.75255e6	0.698039
$659$	−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	$-0.174737\pi$
$661$	1.91655e7	1.70614	0.853072	+	0.521793i	$0.174737\pi$
$662$	5.59217e6	0.495947
$663$	1.71142e7	1.51207
$664$	2.88794e7	2.54196
$665$	74988.8	0.00657570
$666$	−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
$672$	−1.28249e7	−1.09555
$673$	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	$-0.471628\pi$
$677$	2.12311e6	0.178033	0.0890166	+	0.996030i	$0.471628\pi$
$678$	−1.21166e7	−1.01229
$679$	−2.72915e6	−0.227171
$680$	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
$686$	−1.22199e6	−0.0991418
$687$	−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	$-0.596461\pi$
$691$	−7.49135e6	−0.596850	−0.298425	+	0.954433i	$0.596461\pi$
$692$	3.65858e7	2.90434
$693$	−3.49143e6	−0.276166
$694$	−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
$700$	2.32395e6	0.179260
$701$	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
$707$	1.42232e6	0.107016
$708$	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
$714$	−1.08517e7	−0.796621
$715$	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	$-0.588292\pi$
$719$	−7.59175e6	−0.547671	−0.273835	+	0.961777i	$0.588292\pi$
$720$	−3.10034e7	−2.22884
$721$	4.24402e6	0.304046
$722$	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	$-0.347536\pi$
$727$	1.31356e7	0.921748	0.460874	+	0.887465i	$0.347536\pi$
$728$	−1.79274e7	−1.25369
$729$	−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	$-0.423840\pi$
$733$	6.89469e6	0.473974	0.236987	+	0.971513i	$0.423840\pi$
$734$	−1.02744e6	−0.0703910
$735$	−1.67722e6	−0.114518
$736$	−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
$742$	−697146.	−0.0464851
$743$	−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
$749$	−68248.3	−0.00444516
$750$	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
$756$	3.06249e7	1.94882
$757$	−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	$-0.535503\pi$
$761$	−3.55632e6	−0.222607	−0.111304	+	0.993786i	$0.535503\pi$
$762$	1.43412e7	0.894743
$763$	7.94581e6	0.494113
$764$	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	$-0.199258\pi$
$769$	2.65789e7	1.62077	0.810384	+	0.585899i	$0.199258\pi$
$770$	−1.68591e6	−0.102472
$771$	−2.70568e7	−1.63923
$772$	2.59463e7	1.56687
$773$	3.14386e7	1.89241	0.946204	−	0.323571i	$-0.104883\pi$
$773$	3.14386e7	1.89241	0.946204	+	0.323571i	$0.104883\pi$
$774$	6.80059e7	4.08032
$775$	−240011.	−0.0143542
$776$	2.53874e7	1.51344
$777$	7.36237e6	0.437487
$778$	−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
$784$	5.53698e6	0.321724
$785$	928287.	0.0537660
$786$	−1.83687e7	−1.06053
$787$	−1.42418e7	−0.819647	−0.409823	−	0.912165i	$-0.634410\pi$
$787$	−1.42418e7	−0.819647	−0.409823	+	0.912165i	$0.634410\pi$
$788$	−6.11527e7	−3.50833
$789$	−5.76082e7	−3.29452
$790$	−1.72893e7	−0.985620
$791$	2.04568e6	0.116251
$792$	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	$-0.138750\pi$
$797$	3.25117e7	1.81298	0.906492	+	0.422223i	$0.138750\pi$
$798$	870551.	0.0483935
$799$	−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
$805$	−4.39727e6	−0.239163
$806$	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	$-0.735481\pi$
$811$	−2.52537e7	−1.34826	−0.674130	+	0.738613i	$0.735481\pi$
$812$	−1.70790e7	−0.909020
$813$	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
$819$	2.11504e7	1.10182
$820$	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
$826$	−1.41173e7	−0.719949
$827$	−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	$-0.593217\pi$
$829$	−1.14245e7	−0.577364	−0.288682	+	0.957425i	$0.593217\pi$
$830$	−1.64521e7	−0.828944
$831$	1.70256e7	0.855264
$832$	1.88599e7	0.944561
$833$	1.83213e6	0.0914836
$834$	−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	$-0.620914\pi$
$839$	−1.51205e7	−0.741585	−0.370793	+	0.928716i	$0.620914\pi$
$840$	1.56021e7	0.762928
$841$	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
$847$	−7.03123e6	−0.336762
$848$	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	$-0.311017\pi$
$853$	2.37769e7	1.11888	0.559438	+	0.828872i	$0.311017\pi$
$854$	7.99491e6	0.375119
$855$	822980.	0.0385012
$856$	634866.	0.0296141
$857$	5.58994e6	0.259989	0.129995	−	0.991515i	$-0.458504\pi$
$857$	5.58994e6	0.259989	0.129995	+	0.991515i	$0.458504\pi$
$858$	3.08667e7	1.43144
$859$	−6.57947e6	−0.304234	−0.152117	−	0.988362i	$-0.548609\pi$
$859$	−6.57947e6	−0.304234	−0.152117	+	0.988362i	$0.548609\pi$
$860$	2.30978e7	1.06494
$861$	−2.81093e7	−1.29224
$862$	−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
$868$	−1.42791e6	−0.0643280
$869$	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
$875$	−765625.	−0.0338062
$876$	−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	$-0.478406\pi$
$881$	3.12332e6	0.135574	0.0677871	+	0.997700i	$0.478406\pi$
$882$	−1.34110e7	−0.580481
$883$	−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	$-0.279713\pi$
$887$	2.99048e7	1.27624	0.638118	+	0.769938i	$0.279713\pi$
$888$	−6.84870e7	−2.91458
$889$	−2.42128e6	−0.102752
$890$	−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
$896$	2.72885e6	0.113556
$897$	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
$903$	−1.66699e7	−0.680322
$904$	−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
$910$	1.02129e7	0.408833
$911$	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
$917$	3.10125e6	0.121791
$918$	−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
$924$	−1.37665e7	−0.530450
$925$	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	$-0.581795\pi$
$929$	−1.33708e7	−0.508297	−0.254148	+	0.967165i	$0.581795\pi$
$930$	−2.78631e6	−0.105639
$931$	−146978.	−0.00555748
$932$	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	$-0.738342\pi$
$937$	−3.65899e7	−1.36148	−0.680741	+	0.732524i	$0.738342\pi$
$938$	8.55698e6	0.317551
$939$	5.01334e7	1.85551
$940$	2.88975e7	1.06670
$941$	1.02348e7	0.376795	0.188398	−	0.982093i	$-0.439671\pi$
$941$	1.02348e7	0.376795	0.188398	+	0.982093i	$0.439671\pi$
$942$	1.07766e7	0.395688
$943$	−7.36958e7	−2.69875
$944$	6.39672e7	2.33629
$945$	−1.00894e7	−0.367523
$946$	−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
$952$	−1.70430e7	−0.609472
$953$	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
$959$	1.80629e7	0.634222
$960$	−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
$966$	−5.10483e7	−1.76010
$967$	−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	$-0.528273\pi$
$971$	−5.21222e6	−0.177409	−0.0887043	+	0.996058i	$0.528273\pi$
$972$	5.90196e7	2.00369
$973$	4.92480e6	0.166765
$974$	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
$980$	−4.55495e6	−0.151502
$981$	8.72029e7	2.89307
$982$	1.15941e7	0.383671
$983$	2.60735e7	0.860628	0.430314	−	0.902679i	$-0.358403\pi$
$983$	2.60735e7	0.860628	0.430314	+	0.902679i	$0.358403\pi$
$984$	2.61481e8	8.60901
$985$	2.01467e7	0.661628
$986$	3.64048e7	1.19252
$987$	−2.08557e7	−0.681446
$988$	−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
$994$	−1.93024e7	−0.619647
$995$	−2.19568e7	−0.703090
$996$	−1.34342e8	−4.29105
$997$	−4.53151e7	−1.44379	−0.721896	−	0.692001i	$-0.756729\pi$
$997$	−4.53151e7	−1.44379	−0.721896	+	0.692001i	$0.756729\pi$
$998$	−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	35.6.a.c.1.1	✓	3
3.2	odd	2		315.6.a.i.1.3		3
4.3	odd	2		560.6.a.q.1.1		3
5.2	odd	4		175.6.b.e.99.1		6
5.3	odd	4		175.6.b.e.99.6		6
5.4	even	2		175.6.a.e.1.3		3
7.6	odd	2		245.6.a.d.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.a.c.1.1	✓	3	1.1	even	1	trivial
175.6.a.e.1.3		3	5.4	even	2
175.6.b.e.99.1		6	5.2	odd	4
175.6.b.e.99.6		6	5.3	odd	4
245.6.a.d.1.1		3	7.6	odd	2
315.6.a.i.1.3		3	3.2	odd	2
560.6.a.q.1.1		3	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	35.a (trivial)

\(f(q)\)	\(=\)	\(q-10.3867 q^{2} +27.9421 q^{3} +75.8842 q^{4} -25.0000 q^{5} -290.227 q^{6} +49.0000 q^{7} -455.813 q^{8} +537.760 q^{9} +259.668 q^{10} -132.501 q^{11} +2120.36 q^{12} +802.665 q^{13} -508.950 q^{14} -698.552 q^{15} +2306.11 q^{16} +763.068 q^{17} -5585.57 q^{18} -61.2154 q^{19} -1897.10 q^{20} +1369.16 q^{21} +1376.25 q^{22} +3589.61 q^{23} -12736.4 q^{24} +625.000 q^{25} -8337.06 q^{26} +8236.22 q^{27} +3718.32 q^{28} -4593.21 q^{29} +7255.67 q^{30} -384.018 q^{31} -9366.97 q^{32} -3702.35 q^{33} -7925.78 q^{34} -1225.00 q^{35} +40807.5 q^{36} +5377.28 q^{37} +635.827 q^{38} +22428.1 q^{39} +11395.3 q^{40} -20530.3 q^{41} -14221.1 q^{42} -12175.3 q^{43} -10054.7 q^{44} -13444.0 q^{45} -37284.3 q^{46} -15232.4 q^{47} +64437.7 q^{48} +2401.00 q^{49} -6491.71 q^{50} +21321.7 q^{51} +60909.6 q^{52} +1369.77 q^{53} -85547.4 q^{54} +3312.52 q^{55} -22334.8 q^{56} -1710.48 q^{57} +47708.4 q^{58} +27738.1 q^{59} -53009.1 q^{60} -15708.6 q^{61} +3988.70 q^{62} +26350.3 q^{63} +23496.6 q^{64} -20066.6 q^{65} +38455.3 q^{66} -16813.0 q^{67} +57904.8 q^{68} +100301. q^{69} +12723.7 q^{70} +37925.9 q^{71} -245118. q^{72} -48894.9 q^{73} -55852.3 q^{74} +17463.8 q^{75} -4645.28 q^{76} -6492.54 q^{77} -232955. q^{78} -66582.2 q^{79} -57652.9 q^{80} +99461.4 q^{81} +213243. q^{82} -63358.0 q^{83} +103898. q^{84} -19076.7 q^{85} +126461. q^{86} -128344. q^{87} +60395.6 q^{88} -69175.3 q^{89} +139639. q^{90} +39330.6 q^{91} +272395. q^{92} -10730.3 q^{93} +158215. q^{94} +1530.38 q^{95} -261733. q^{96} -55697.0 q^{97} -24938.5 q^{98} -71253.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} + 26 q^{3} + 112 q^{4} - 75 q^{5} - 96 q^{6} + 147 q^{7} - 120 q^{8} + 489 q^{9} + 150 q^{10} - 194 q^{11} + 2956 q^{12} + 1892 q^{13} - 294 q^{14} - 650 q^{15} + 1496 q^{16} - 184 q^{17}+ \cdots - 60752 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 + 26 * q^3 + 112 * q^4 - 75 * q^5 - 96 * q^6 + 147 * q^7 - 120 * q^8 + 489 * q^9 + 150 * q^10 - 194 * q^11 + 2956 * q^12 + 1892 * q^13 - 294 * q^14 - 650 * q^15 + 1496 * q^16 - 184 * q^17 - 6078 * q^18 + 1212 * q^19 - 2800 * q^20 + 1274 * q^21 - 872 * q^22 + 3188 * q^23 - 13920 * q^24 + 1875 * q^25 - 9836 * q^26 + 7910 * q^27 + 5488 * q^28 - 11332 * q^29 + 2400 * q^30 + 9200 * q^31 - 20256 * q^32 - 8278 * q^33 - 18492 * q^34 - 3675 * q^35 + 38236 * q^36 + 6042 * q^37 + 25520 * q^38 + 12842 * q^39 + 3000 * q^40 + 10442 * q^41 - 4704 * q^42 + 28112 * q^43 - 20436 * q^44 - 12225 * q^45 - 41856 * q^46 + 2330 * q^47 + 68808 * q^48 + 7203 * q^49 - 3750 * q^50 + 3622 * q^51 + 63524 * q^52 + 7190 * q^53 - 138960 * q^54 + 4850 * q^55 - 5880 * q^56 + 45508 * q^57 + 37260 * q^58 + 23760 * q^59 - 73900 * q^60 + 8722 * q^61 + 24848 * q^62 + 23961 * q^63 + 4976 * q^64 - 47300 * q^65 + 24368 * q^66 - 97572 * q^67 + 3564 * q^68 + 92596 * q^69 + 7350 * q^70 - 52816 * q^71 - 251640 * q^72 + 34870 * q^73 - 241892 * q^74 + 16250 * q^75 + 115256 * q^76 - 9506 * q^77 - 142096 * q^78 - 71546 * q^79 - 37400 * q^80 - 3957 * q^81 + 241908 * q^82 - 20920 * q^83 + 144844 * q^84 + 4600 * q^85 + 266024 * q^86 - 112298 * q^87 + 59200 * q^88 - 192622 * q^89 + 151950 * q^90 + 92708 * q^91 + 248952 * q^92 - 20392 * q^93 + 360128 * q^94 - 30300 * q^95 - 296256 * q^96 + 116320 * q^97 - 14406 * q^98 - 60752 * q^99

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