LMFDB - Embedded newform 294.6.a.v.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(1,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("294.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$47.1528430250$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{4705}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1176 $ x^2 - x - 1176
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$34.7965$ of defining polynomial
Character	$\chi$	$=$	294.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -59.5930 q^{5} +36.0000 q^{6} +64.0000 q^{8} +81.0000 q^{9} -238.372 q^{10} -616.337 q^{11} +144.000 q^{12} +418.372 q^{13} -536.337 q^{15} +256.000 q^{16} +1793.90 q^{17} +324.000 q^{18} +1279.93 q^{19} -953.488 q^{20} -2465.35 q^{22} +4781.69 q^{23} +576.000 q^{24} +426.326 q^{25} +1673.49 q^{26} +729.000 q^{27} +1716.02 q^{29} -2145.35 q^{30} +642.722 q^{31} +1024.00 q^{32} -5547.03 q^{33} +7175.58 q^{34} +1296.00 q^{36} -2360.02 q^{37} +5119.72 q^{38} +3765.35 q^{39} -3813.95 q^{40} +15639.9 q^{41} -1638.61 q^{43} -9861.39 q^{44} -4827.03 q^{45} +19126.7 q^{46} +20735.5 q^{47} +2304.00 q^{48} +1705.30 q^{50} +16145.1 q^{51} +6693.95 q^{52} -5347.93 q^{53} +2916.00 q^{54} +36729.4 q^{55} +11519.4 q^{57} +6864.09 q^{58} +16824.9 q^{59} -8581.39 q^{60} -13527.2 q^{61} +2570.89 q^{62} +4096.00 q^{64} -24932.0 q^{65} -22188.1 q^{66} -46483.5 q^{67} +28702.3 q^{68} +43035.2 q^{69} -3273.91 q^{71} +5184.00 q^{72} -76758.4 q^{73} -9440.09 q^{74} +3836.93 q^{75} +20478.9 q^{76} +15061.4 q^{78} -17731.4 q^{79} -15255.8 q^{80} +6561.00 q^{81} +62559.5 q^{82} +78846.7 q^{83} -106904. q^{85} -6554.43 q^{86} +15444.2 q^{87} -39445.6 q^{88} +74160.4 q^{89} -19308.1 q^{90} +76507.0 q^{92} +5784.50 q^{93} +82942.1 q^{94} -76274.9 q^{95} +9216.00 q^{96} +24360.2 q^{97} -49923.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} + 18 q^{3} + 32 q^{4} + 18 q^{5} + 72 q^{6} + 128 q^{8} + 162 q^{9} + 72 q^{10} + 2 q^{11} + 288 q^{12} + 288 q^{13} + 162 q^{15} + 512 q^{16} + 1530 q^{17} + 648 q^{18} + 1188 q^{19} + 288 q^{20}+ \cdots + 162 q^{99}+O(q^{100}) $ 2 * q + 8 * q^2 + 18 * q^3 + 32 * q^4 + 18 * q^5 + 72 * q^6 + 128 * q^8 + 162 * q^9 + 72 * q^10 + 2 * q^11 + 288 * q^12 + 288 * q^13 + 162 * q^15 + 512 * q^16 + 1530 * q^17 + 648 * q^18 + 1188 * q^19 + 288 * q^20 + 8 * q^22 + 3390 * q^23 + 1152 * q^24 + 3322 * q^25 + 1152 * q^26 + 1458 * q^27 - 3976 * q^29 + 648 * q^30 + 7596 * q^31 + 2048 * q^32 + 18 * q^33 + 6120 * q^34 + 2592 * q^36 + 2688 * q^37 + 4752 * q^38 + 2592 * q^39 + 1152 * q^40 + 36630 * q^41 - 23032 * q^43 + 32 * q^44 + 1458 * q^45 + 13560 * q^46 + 864 * q^47 + 4608 * q^48 + 13288 * q^50 + 13770 * q^51 + 4608 * q^52 - 32920 * q^53 + 5832 * q^54 + 84708 * q^55 + 10692 * q^57 - 15904 * q^58 - 26712 * q^59 + 2592 * q^60 + 20412 * q^61 + 30384 * q^62 + 8192 * q^64 - 35048 * q^65 + 72 * q^66 - 36172 * q^67 + 24480 * q^68 + 30510 * q^69 + 73706 * q^71 + 10368 * q^72 - 74772 * q^73 + 10752 * q^74 + 29898 * q^75 + 19008 * q^76 + 10368 * q^78 - 23116 * q^79 + 4608 * q^80 + 13122 * q^81 + 146520 * q^82 + 147816 * q^83 - 127380 * q^85 - 92128 * q^86 - 35784 * q^87 + 128 * q^88 + 164646 * q^89 + 5832 * q^90 + 54240 * q^92 + 68364 * q^93 + 3456 * q^94 - 83408 * q^95 + 18432 * q^96 + 162036 * q^97 + 162 * 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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	−59.5930	−1.06603	−0.533016	−	0.846105i	$-0.678941\pi$
$5$	−59.5930	−1.06603	−0.533016	+	0.846105i	$0.678941\pi$
$6$	36.0000	0.408248
$7$	0	0
$7$	0	0
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−238.372	−0.753798
$11$	−616.337	−1.53581	−0.767903	−	0.640566i	$-0.778700\pi$
$11$	−616.337	−1.53581	−0.767903	+	0.640566i	$0.778700\pi$
$12$	144.000	0.288675
$13$	418.372	0.686601	0.343300	−	0.939226i	$-0.388455\pi$
$13$	418.372	0.686601	0.343300	+	0.939226i	$0.388455\pi$
$14$	0	0
$15$	−536.337	−0.615474
$16$	256.000	0.250000
$17$	1793.90	1.50548	0.752740	−	0.658318i	$-0.228732\pi$
$17$	1793.90	1.50548	0.752740	+	0.658318i	$0.228732\pi$
$18$	324.000	0.235702
$19$	1279.93	0.813396	0.406698	−	0.913563i	$-0.366680\pi$
$19$	1279.93	0.813396	0.406698	+	0.913563i	$0.366680\pi$
$20$	−953.488	−0.533016
$21$	0	0
$22$	−2465.35	−1.08598
$23$	4781.69	1.88478	0.942392	−	0.334512i	$-0.108571\pi$
$23$	4781.69	1.88478	0.942392	+	0.334512i	$0.108571\pi$
$24$	576.000	0.204124
$25$	426.326	0.136424
$26$	1673.49	0.485500
$27$	729.000	0.192450
$28$	0	0
$29$	1716.02	0.378903	0.189451	−	0.981890i	$-0.439329\pi$
$29$	1716.02	0.378903	0.189451	+	0.981890i	$0.439329\pi$
$30$	−2145.35	−0.435206
$31$	642.722	0.120121	0.0600605	−	0.998195i	$-0.480871\pi$
$31$	642.722	0.120121	0.0600605	+	0.998195i	$0.480871\pi$
$32$	1024.00	0.176777
$33$	−5547.03	−0.886698
$34$	7175.58	1.06453
$35$	0	0
$36$	1296.00	0.166667
$37$	−2360.02	−0.283408	−0.141704	−	0.989909i	$-0.545258\pi$
$37$	−2360.02	−0.283408	−0.141704	+	0.989909i	$0.545258\pi$
$38$	5119.72	0.575158
$39$	3765.35	0.396409
$40$	−3813.95	−0.376899
$41$	15639.9	1.45303	0.726513	−	0.687152i	$-0.241140\pi$
$41$	15639.9	1.45303	0.726513	+	0.687152i	$0.241140\pi$
$42$	0	0
$43$	−1638.61	−0.135146	−0.0675731	−	0.997714i	$-0.521526\pi$
$43$	−1638.61	−0.135146	−0.0675731	+	0.997714i	$0.521526\pi$
$44$	−9861.39	−0.767903
$45$	−4827.03	−0.355344
$46$	19126.7	1.33274
$47$	20735.5	1.36921	0.684606	−	0.728914i	$-0.259974\pi$
$47$	20735.5	1.36921	0.684606	+	0.728914i	$0.259974\pi$
$48$	2304.00	0.144338
$49$	0	0
$50$	1705.30	0.0964666
$51$	16145.1	0.869189
$52$	6693.95	0.343300
$53$	−5347.93	−0.261515	−0.130757	−	0.991414i	$-0.541741\pi$
$53$	−5347.93	−0.261515	−0.130757	+	0.991414i	$0.541741\pi$
$54$	2916.00	0.136083
$55$	36729.4	1.63722
$56$	0	0
$57$	11519.4	0.469615
$58$	6864.09	0.267925
$59$	16824.9	0.629250	0.314625	−	0.949216i	$-0.398121\pi$
$59$	16824.9	0.629250	0.314625	+	0.949216i	$0.398121\pi$
$60$	−8581.39	−0.307737
$61$	−13527.2	−0.465460	−0.232730	−	0.972541i	$-0.574766\pi$
$61$	−13527.2	−0.465460	−0.232730	+	0.972541i	$0.574766\pi$
$62$	2570.89	0.0849384
$63$	0	0
$64$	4096.00	0.125000
$65$	−24932.0	−0.731938
$66$	−22188.1	−0.626990
$67$	−46483.5	−1.26506	−0.632531	−	0.774535i	$-0.717984\pi$
$67$	−46483.5	−1.26506	−0.632531	+	0.774535i	$0.717984\pi$
$68$	28702.3	0.752740
$69$	43035.2	1.08818
$70$	0	0
$71$	−3273.91	−0.0770762	−0.0385381	−	0.999257i	$-0.512270\pi$
$71$	−3273.91	−0.0770762	−0.0385381	+	0.999257i	$0.512270\pi$
$72$	5184.00	0.117851
$73$	−76758.4	−1.68585	−0.842924	−	0.538032i	$-0.819168\pi$
$73$	−76758.4	−1.68585	−0.842924	+	0.538032i	$0.819168\pi$
$74$	−9440.09	−0.200400
$75$	3836.93	0.0787646
$76$	20478.9	0.406698
$77$	0	0
$78$	15061.4	0.280304
$79$	−17731.4	−0.319650	−0.159825	−	0.987145i	$-0.551093\pi$
$79$	−17731.4	−0.319650	−0.159825	+	0.987145i	$0.551093\pi$
$80$	−15255.8	−0.266508
$81$	6561.00	0.111111
$82$	62559.5	1.02744
$83$	78846.7	1.25629	0.628143	−	0.778098i	$-0.283815\pi$
$83$	78846.7	1.25629	0.628143	+	0.778098i	$0.283815\pi$
$84$	0	0
$85$	−106904.	−1.60489
$86$	−6554.43	−0.0955628
$87$	15444.2	0.218760
$88$	−39445.6	−0.542990
$89$	74160.4	0.992424	0.496212	−	0.868201i	$-0.334724\pi$
$89$	74160.4	0.992424	0.496212	+	0.868201i	$0.334724\pi$
$90$	−19308.1	−0.251266
$91$	0	0
$92$	76507.0	0.942392
$93$	5784.50	0.0693519
$94$	82942.1	0.968179
$95$	−76274.9	−0.867107
$96$	9216.00	0.102062
$97$	24360.2	0.262876	0.131438	−	0.991324i	$-0.458041\pi$
$97$	24360.2	0.262876	0.131438	+	0.991324i	$0.458041\pi$
$98$	0	0
$99$	−49923.3	−0.511936
$100$	6821.22	0.0682122
$101$	−148780.	−1.45124	−0.725622	−	0.688093i	$-0.758448\pi$
$101$	−148780.	−1.45124	−0.725622	+	0.688093i	$0.758448\pi$
$102$	64580.2	0.614609
$103$	205516.	1.90877	0.954383	−	0.298584i	$-0.0965143\pi$
$103$	205516.	1.90877	0.954383	+	0.298584i	$0.0965143\pi$
$104$	26775.8	0.242750
$105$	0	0
$106$	−21391.7	−0.184919
$107$	−104578.	−0.883038	−0.441519	−	0.897252i	$-0.645560\pi$
$107$	−104578.	−0.883038	−0.441519	+	0.897252i	$0.645560\pi$
$108$	11664.0	0.0962250
$109$	212746.	1.71512	0.857560	−	0.514383i	$-0.171979\pi$
$109$	212746.	1.71512	0.857560	+	0.514383i	$0.171979\pi$
$110$	146917.	1.15769
$111$	−21240.2	−0.163626
$112$	0	0
$113$	224886.	1.65678	0.828391	−	0.560150i	$-0.189256\pi$
$113$	224886.	1.65678	0.828391	+	0.560150i	$0.189256\pi$
$114$	46077.5	0.332068
$115$	−284955.	−2.00924
$116$	27456.4	0.189451
$117$	33888.1	0.228867
$118$	67299.7	0.444947
$119$	0	0
$120$	−34325.6	−0.217603
$121$	218820.	1.35870
$122$	−54108.7	−0.329130
$123$	140759.	0.838905
$124$	10283.6	0.0600605
$125$	160822.	0.920599
$126$	0	0
$127$	−44027.2	−0.242221	−0.121110	−	0.992639i	$-0.538646\pi$
$127$	−44027.2	−0.242221	−0.121110	+	0.992639i	$0.538646\pi$
$128$	16384.0	0.0883883
$129$	−14747.5	−0.0780267
$130$	−99728.2	−0.517559
$131$	−391132.	−1.99134	−0.995668	−	0.0929748i	$-0.970362\pi$
$131$	−391132.	−1.99134	−0.995668	+	0.0929748i	$0.970362\pi$
$132$	−88752.5	−0.443349
$133$	0	0
$134$	−185934.	−0.894534
$135$	−43443.3	−0.205158
$136$	114809.	0.532267
$137$	70982.2	0.323108	0.161554	−	0.986864i	$-0.448349\pi$
$137$	70982.2	0.323108	0.161554	+	0.986864i	$0.448349\pi$
$138$	172141.	0.769459
$139$	102764.	0.451133	0.225567	−	0.974228i	$-0.427577\pi$
$139$	102764.	0.451133	0.225567	+	0.974228i	$0.427577\pi$
$140$	0	0
$141$	186620.	0.790515
$142$	−13095.6	−0.0545011
$143$	−257858.	−1.05449
$144$	20736.0	0.0833333
$145$	−102263.	−0.403923
$146$	−307034.	−1.19208
$147$	0	0
$148$	−37760.4	−0.141704
$149$	−226298.	−0.835053	−0.417527	−	0.908665i	$-0.637103\pi$
$149$	−226298.	−0.835053	−0.417527	+	0.908665i	$0.637103\pi$
$150$	15347.7	0.0556950
$151$	−548224.	−1.95666	−0.978330	−	0.207051i	$-0.933613\pi$
$151$	−548224.	−1.95666	−0.978330	+	0.207051i	$0.933613\pi$
$152$	81915.5	0.287579
$153$	145305.	0.501826
$154$	0	0
$155$	−38301.7	−0.128053
$156$	60245.6	0.198205
$157$	241144.	0.780778	0.390389	−	0.920650i	$-0.372341\pi$
$157$	241144.	0.780778	0.390389	+	0.920650i	$0.372341\pi$
$158$	−70925.5	−0.226027
$159$	−48131.4	−0.150986
$160$	−61023.2	−0.188450
$161$	0	0
$162$	26244.0	0.0785674
$163$	630902.	1.85991	0.929957	−	0.367668i	$-0.119844\pi$
$163$	630902.	1.85991	0.929957	+	0.367668i	$0.119844\pi$
$164$	250238.	0.726513
$165$	330564.	0.945249
$166$	315387.	0.888328
$167$	239113.	0.663456	0.331728	−	0.943375i	$-0.392368\pi$
$167$	239113.	0.663456	0.331728	+	0.943375i	$0.392368\pi$
$168$	0	0
$169$	−196258.	−0.528579
$170$	−427614.	−1.13483
$171$	103674.	0.271132
$172$	−26217.7	−0.0675731
$173$	−302939.	−0.769556	−0.384778	−	0.923009i	$-0.625722\pi$
$173$	−302939.	−0.769556	−0.384778	+	0.923009i	$0.625722\pi$
$174$	61776.8	0.154686
$175$	0	0
$176$	−157782.	−0.383952
$177$	151424.	0.363297
$178$	296642.	0.701750
$179$	−105990.	−0.247247	−0.123623	−	0.992329i	$-0.539451\pi$
$179$	−105990.	−0.247247	−0.123623	+	0.992329i	$0.539451\pi$
$180$	−77232.5	−0.177672
$181$	−473727.	−1.07481	−0.537405	−	0.843324i	$-0.680595\pi$
$181$	−473727.	−1.07481	−0.537405	+	0.843324i	$0.680595\pi$
$182$	0	0
$183$	−121745.	−0.268734
$184$	306028.	0.666371
$185$	140641.	0.302122
$186$	23138.0	0.0490392
$187$	−1.10564e6	−2.31212
$188$	331768.	0.684606
$189$	0	0
$190$	−305099.	−0.613137
$191$	−587813.	−1.16589	−0.582943	−	0.812513i	$-0.698099\pi$
$191$	−587813.	−1.16589	−0.582943	+	0.812513i	$0.698099\pi$
$192$	36864.0	0.0721688
$193$	−366861.	−0.708938	−0.354469	−	0.935068i	$-0.615338\pi$
$193$	−366861.	−0.708938	−0.354469	+	0.935068i	$0.615338\pi$
$194$	97440.7	0.185881
$195$	−224388.	−0.422585
$196$	0	0
$197$	727471.	1.33552	0.667760	−	0.744377i	$-0.267253\pi$
$197$	727471.	1.33552	0.667760	+	0.744377i	$0.267253\pi$
$198$	−199693.	−0.361993
$199$	−234812.	−0.420327	−0.210163	−	0.977666i	$-0.567400\pi$
$199$	−234812.	−0.420327	−0.210163	+	0.977666i	$0.567400\pi$
$200$	27284.9	0.0482333
$201$	−418352.	−0.730384
$202$	−595119.	−1.02619
$203$	0	0
$204$	258321.	0.434594
$205$	−932027.	−1.54897
$206$	822065.	1.34970
$207$	387316.	0.628261
$208$	107103.	0.171650
$209$	−788868.	−1.24922
$210$	0	0
$211$	−308050.	−0.476337	−0.238169	−	0.971224i	$-0.576547\pi$
$211$	−308050.	−0.476337	−0.238169	+	0.971224i	$0.576547\pi$
$212$	−85566.9	−0.130757
$213$	−29465.2	−0.0445000
$214$	−418311.	−0.624402
$215$	97649.5	0.144070
$216$	46656.0	0.0680414
$217$	0	0
$218$	850983.	1.21277
$219$	−690825.	−0.973325
$220$	587670.	0.818610
$221$	750515.	1.03366
$222$	−84960.8	−0.115701
$223$	510190.	0.687021	0.343510	−	0.939149i	$-0.388384\pi$
$223$	510190.	0.687021	0.343510	+	0.939149i	$0.388384\pi$
$224$	0	0
$225$	34532.4	0.0454748
$226$	899542.	1.17152
$227$	1.03803e6	1.33705	0.668523	−	0.743692i	$-0.266927\pi$
$227$	1.03803e6	1.33705	0.668523	+	0.743692i	$0.266927\pi$
$228$	184310.	0.234807
$229$	−1.03849e6	−1.30862	−0.654310	−	0.756226i	$-0.727041\pi$
$229$	−1.03849e6	−1.30862	−0.654310	+	0.756226i	$0.727041\pi$
$230$	−1.13982e6	−1.42075
$231$	0	0
$232$	109825.	0.133962
$233$	1.31745e6	1.58981	0.794905	−	0.606734i	$-0.207521\pi$
$233$	1.31745e6	1.58981	0.794905	+	0.606734i	$0.207521\pi$
$234$	135553.	0.161833
$235$	−1.23569e6	−1.45962
$236$	269199.	0.314625
$237$	−159582.	−0.184550
$238$	0	0
$239$	800669.	0.906689	0.453345	−	0.891335i	$-0.350231\pi$
$239$	800669.	0.906689	0.453345	+	0.891335i	$0.350231\pi$
$240$	−137302.	−0.153868
$241$	402307.	0.446185	0.223093	−	0.974797i	$-0.428385\pi$
$241$	402307.	0.446185	0.223093	+	0.974797i	$0.428385\pi$
$242$	875281.	0.960747
$243$	59049.0	0.0641500
$244$	−216435.	−0.232730
$245$	0	0
$246$	563035.	0.593196
$247$	535487.	0.558479
$248$	41134.2	0.0424692
$249$	709620.	0.725317
$250$	643288.	0.650962
$251$	−1.29078e6	−1.29320	−0.646601	−	0.762828i	$-0.723810\pi$
$251$	−1.29078e6	−1.29320	−0.646601	+	0.762828i	$0.723810\pi$
$252$	0	0
$253$	−2.94713e6	−2.89466
$254$	−176109.	−0.171276
$255$	−962132.	−0.926583
$256$	65536.0	0.0625000
$257$	−1.76435e6	−1.66629	−0.833146	−	0.553053i	$-0.813463\pi$
$257$	−1.76435e6	−1.66629	−0.833146	+	0.553053i	$0.813463\pi$
$258$	−58989.9	−0.0551732
$259$	0	0
$260$	−398913.	−0.365969
$261$	138998.	0.126301
$262$	−1.56453e6	−1.40809
$263$	427745.	0.381325	0.190663	−	0.981656i	$-0.438936\pi$
$263$	427745.	0.381325	0.190663	+	0.981656i	$0.438936\pi$
$264$	−355010.	−0.313495
$265$	318699.	0.278783
$266$	0	0
$267$	667444.	0.572976
$268$	−743736.	−0.632531
$269$	−1.26691e6	−1.06749	−0.533744	−	0.845646i	$-0.679216\pi$
$269$	−1.26691e6	−1.06749	−0.533744	+	0.845646i	$0.679216\pi$
$270$	−173773.	−0.145069
$271$	−312034.	−0.258095	−0.129047	−	0.991638i	$-0.541192\pi$
$271$	−312034.	−0.258095	−0.129047	+	0.991638i	$0.541192\pi$
$272$	459237.	0.376370
$273$	0	0
$274$	283929.	0.228472
$275$	−262760.	−0.209521
$276$	688563.	0.544090
$277$	−1.67860e6	−1.31446	−0.657229	−	0.753691i	$-0.728271\pi$
$277$	−1.67860e6	−1.31446	−0.657229	+	0.753691i	$0.728271\pi$
$278$	411057.	0.319000
$279$	52060.5	0.0400403
$280$	0	0
$281$	−765001.	−0.577958	−0.288979	−	0.957335i	$-0.593316\pi$
$281$	−765001.	−0.577958	−0.288979	+	0.957335i	$0.593316\pi$
$282$	746479.	0.558978
$283$	−85831.7	−0.0637062	−0.0318531	−	0.999493i	$-0.510141\pi$
$283$	−85831.7	−0.0637062	−0.0318531	+	0.999493i	$0.510141\pi$
$284$	−52382.5	−0.0385381
$285$	−686474.	−0.500624
$286$	−1.03143e6	−0.745634
$287$	0	0
$288$	82944.0	0.0589256
$289$	1.79820e6	1.26647
$290$	−409052.	−0.285616
$291$	219242.	0.151772
$292$	−1.22813e6	−0.842924
$293$	−97784.7	−0.0665429	−0.0332715	−	0.999446i	$-0.510593\pi$
$293$	−97784.7	−0.0665429	−0.0332715	+	0.999446i	$0.510593\pi$
$294$	0	0
$295$	−1.00265e6	−0.670800
$296$	−151041.	−0.100200
$297$	−449310.	−0.295566
$298$	−905190.	−0.590472
$299$	2.00052e6	1.29409
$300$	61390.9	0.0393823
$301$	0	0
$302$	−2.19289e6	−1.38357
$303$	−1.33902e6	−0.837877
$304$	327662.	0.203349
$305$	806125.	0.496196
$306$	581222.	0.354845
$307$	−1.75546e6	−1.06303	−0.531514	−	0.847050i	$-0.678377\pi$
$307$	−1.75546e6	−1.06303	−0.531514	+	0.847050i	$0.678377\pi$
$308$	0	0
$309$	1.84965e6	1.10203
$310$	−153207.	−0.0905470
$311$	−1.80396e6	−1.05761	−0.528804	−	0.848744i	$-0.677359\pi$
$311$	−1.80396e6	−1.05761	−0.528804	+	0.848744i	$0.677359\pi$
$312$	240982.	0.140152
$313$	2.46429e6	1.42178	0.710888	−	0.703305i	$-0.248293\pi$
$313$	2.46429e6	1.42178	0.710888	+	0.703305i	$0.248293\pi$
$314$	964576.	0.552093
$315$	0	0
$316$	−283702.	−0.159825
$317$	1.65286e6	0.923822	0.461911	−	0.886926i	$-0.347164\pi$
$317$	1.65286e6	0.923822	0.461911	+	0.886926i	$0.347164\pi$
$318$	−192526.	−0.106763
$319$	−1.05765e6	−0.581922
$320$	−244093.	−0.133254
$321$	−941199.	−0.509822
$322$	0	0
$323$	2.29606e6	1.22455
$324$	104976.	0.0555556
$325$	178363.	0.0936690
$326$	2.52361e6	1.31516
$327$	1.91471e6	0.990226
$328$	1.00095e6	0.513722
$329$	0	0
$330$	1.32226e6	0.668392
$331$	−1.66814e6	−0.836881	−0.418440	−	0.908244i	$-0.637423\pi$
$331$	−1.66814e6	−0.836881	−0.418440	+	0.908244i	$0.637423\pi$
$332$	1.26155e6	0.628143
$333$	−191162.	−0.0944693
$334$	956452.	0.469134
$335$	2.77009e6	1.34860
$336$	0	0
$337$	−524769.	−0.251706	−0.125853	−	0.992049i	$-0.540167\pi$
$337$	−524769.	−0.251706	−0.125853	+	0.992049i	$0.540167\pi$
$338$	−785031.	−0.373762
$339$	2.02397e6	0.956544
$340$	−1.71046e6	−0.802444
$341$	−396133.	−0.184483
$342$	414697.	0.191719
$343$	0	0
$344$	−104871.	−0.0477814
$345$	−2.56459e6	−1.16003
$346$	−1.21176e6	−0.544158
$347$	1.92637e6	0.858846	0.429423	−	0.903103i	$-0.358717\pi$
$347$	1.92637e6	0.858846	0.429423	+	0.903103i	$0.358717\pi$
$348$	247107.	0.109380
$349$	340342.	0.149573	0.0747864	−	0.997200i	$-0.476173\pi$
$349$	340342.	0.149573	0.0747864	+	0.997200i	$0.476173\pi$
$350$	0	0
$351$	304993.	0.132136
$352$	−631129.	−0.271495
$353$	−74791.2	−0.0319458	−0.0159729	−	0.999872i	$-0.505085\pi$
$353$	−74791.2	−0.0319458	−0.0159729	+	0.999872i	$0.505085\pi$
$354$	605697.	0.256890
$355$	195102.	0.0821657
$356$	1.18657e6	0.496212
$357$	0	0
$358$	−423958.	−0.174830
$359$	2.41754e6	0.990004	0.495002	−	0.868892i	$-0.335167\pi$
$359$	2.41754e6	0.990004	0.495002	+	0.868892i	$0.335167\pi$
$360$	−308930.	−0.125633
$361$	−837878.	−0.338386
$362$	−1.89491e6	−0.760005
$363$	1.96938e6	0.784447
$364$	0	0
$365$	4.57426e6	1.79717
$366$	−486978.	−0.190023
$367$	161864.	0.0627314	0.0313657	−	0.999508i	$-0.490014\pi$
$367$	161864.	0.0627314	0.0313657	+	0.999508i	$0.490014\pi$
$368$	1.22411e6	0.471196
$369$	1.26683e6	0.484342
$370$	562563.	0.213632
$371$	0	0
$372$	92552.0	0.0346759
$373$	77002.5	0.0286571	0.0143286	−	0.999897i	$-0.495439\pi$
$373$	77002.5	0.0286571	0.0143286	+	0.999897i	$0.495439\pi$
$374$	−4.42258e6	−1.63492
$375$	1.44740e6	0.531508
$376$	1.32707e6	0.484089
$377$	717936.	0.260155
$378$	0	0
$379$	−774165.	−0.276844	−0.138422	−	0.990373i	$-0.544203\pi$
$379$	−774165.	−0.276844	−0.138422	+	0.990373i	$0.544203\pi$
$380$	−1.22040e6	−0.433553
$381$	−396245.	−0.139846
$382$	−2.35125e6	−0.824406
$383$	3.63328e6	1.26561	0.632807	−	0.774309i	$-0.281902\pi$
$383$	3.63328e6	1.26561	0.632807	+	0.774309i	$0.281902\pi$
$384$	147456.	0.0510310
$385$	0	0
$386$	−1.46744e6	−0.501295
$387$	−132727.	−0.0450487
$388$	389763.	0.131438
$389$	−2.51908e6	−0.844048	−0.422024	−	0.906585i	$-0.638680\pi$
$389$	−2.51908e6	−0.844048	−0.422024	+	0.906585i	$0.638680\pi$
$390$	−897554.	−0.298813
$391$	8.57784e6	2.83750
$392$	0	0
$393$	−3.52019e6	−1.14970
$394$	2.90989e6	0.944355
$395$	1.05667e6	0.340757
$396$	−798773.	−0.255968
$397$	5.59278e6	1.78095	0.890474	−	0.455034i	$-0.150373\pi$
$397$	5.59278e6	1.78095	0.890474	+	0.455034i	$0.150373\pi$
$398$	−939246.	−0.297216
$399$	0	0
$400$	109139.	0.0341061
$401$	−191062.	−0.0593353	−0.0296676	−	0.999560i	$-0.509445\pi$
$401$	−191062.	−0.0593353	−0.0296676	+	0.999560i	$0.509445\pi$
$402$	−1.67341e6	−0.516459
$403$	268897.	0.0824751
$404$	−2.38048e6	−0.725622
$405$	−390990.	−0.118448
$406$	0	0
$407$	1.45457e6	0.435260
$408$	1.03328e6	0.307305
$409$	4.45805e6	1.31776	0.658880	−	0.752248i	$-0.271030\pi$
$409$	4.45805e6	1.31776	0.658880	+	0.752248i	$0.271030\pi$
$410$	−3.72811e6	−1.09529
$411$	638840.	0.186547
$412$	3.28826e6	0.954383
$413$	0	0
$414$	1.54927e6	0.444248
$415$	−4.69871e6	−1.33924
$416$	428413.	0.121375
$417$	924878.	0.260462
$418$	−3.15547e6	−0.883332
$419$	4.76120e6	1.32489	0.662447	−	0.749109i	$-0.269518\pi$
$419$	4.76120e6	1.32489	0.662447	+	0.749109i	$0.269518\pi$
$420$	0	0
$421$	−1.38498e6	−0.380835	−0.190418	−	0.981703i	$-0.560984\pi$
$421$	−1.38498e6	−0.380835	−0.190418	+	0.981703i	$0.560984\pi$
$422$	−1.23220e6	−0.336821
$423$	1.67958e6	0.456404
$424$	−342268.	−0.0924595
$425$	764784.	0.205384
$426$	−117861.	−0.0314662
$427$	0	0
$428$	−1.67324e6	−0.441519
$429$	−2.32072e6	−0.608808
$430$	390598.	0.101873
$431$	4.55891e6	1.18214	0.591069	−	0.806621i	$-0.298706\pi$
$431$	4.55891e6	1.18214	0.591069	+	0.806621i	$0.298706\pi$
$432$	186624.	0.0481125
$433$	−6.00870e6	−1.54014	−0.770071	−	0.637958i	$-0.779779\pi$
$433$	−6.00870e6	−1.54014	−0.770071	+	0.637958i	$0.779779\pi$
$434$	0	0
$435$	−920366.	−0.233205
$436$	3.40393e6	0.857560
$437$	6.12022e6	1.53308
$438$	−2.76330e6	−0.688245
$439$	560503.	0.138809	0.0694044	−	0.997589i	$-0.477890\pi$
$439$	560503.	0.138809	0.0694044	+	0.997589i	$0.477890\pi$
$440$	2.35068e6	0.578844
$441$	0	0
$442$	3.00206e6	0.730910
$443$	3.34074e6	0.808786	0.404393	−	0.914585i	$-0.367483\pi$
$443$	3.34074e6	0.808786	0.404393	+	0.914585i	$0.367483\pi$
$444$	−339843.	−0.0818128
$445$	−4.41944e6	−1.05796
$446$	2.04076e6	0.485797
$447$	−2.03668e6	−0.482118
$448$	0	0
$449$	−6.47842e6	−1.51654	−0.758269	−	0.651942i	$-0.773955\pi$
$449$	−6.47842e6	−1.51654	−0.758269	+	0.651942i	$0.773955\pi$
$450$	138130.	0.0321555
$451$	−9.63943e6	−2.23157
$452$	3.59817e6	0.828391
$453$	−4.93401e6	−1.12968
$454$	4.15213e6	0.945434
$455$	0	0
$456$	737240.	0.166034
$457$	4.31138e6	0.965663	0.482831	−	0.875713i	$-0.339608\pi$
$457$	4.31138e6	0.965663	0.482831	+	0.875713i	$0.339608\pi$
$458$	−4.15396e6	−0.925334
$459$	1.30775e6	0.289730
$460$	−4.55928e6	−1.00462
$461$	−320951.	−0.0703374	−0.0351687	−	0.999381i	$-0.511197\pi$
$461$	−320951.	−0.0703374	−0.0351687	+	0.999381i	$0.511197\pi$
$462$	0	0
$463$	−3.14239e6	−0.681251	−0.340626	−	0.940199i	$-0.610639\pi$
$463$	−3.14239e6	−0.681251	−0.340626	+	0.940199i	$0.610639\pi$
$464$	439302.	0.0947257
$465$	−344716.	−0.0739313
$466$	5.26981e6	1.12417
$467$	4.14587e6	0.879677	0.439839	−	0.898077i	$-0.355036\pi$
$467$	4.14587e6	0.879677	0.439839	+	0.898077i	$0.355036\pi$
$468$	542210.	0.114433
$469$	0	0
$470$	−4.94277e6	−1.03211
$471$	2.17030e6	0.450782
$472$	1.07679e6	0.222473
$473$	1.00993e6	0.207558
$474$	−638329.	−0.130497
$475$	545667.	0.110967
$476$	0	0
$477$	−433183.	−0.0871716
$478$	3.20268e6	0.641126
$479$	−257678.	−0.0513142	−0.0256571	−	0.999671i	$-0.508168\pi$
$479$	−257678.	−0.0513142	−0.0256571	+	0.999671i	$0.508168\pi$
$480$	−549209.	−0.108801
$481$	−987367.	−0.194588
$482$	1.60923e6	0.315501
$483$	0	0
$484$	3.50113e6	0.679351
$485$	−1.45170e6	−0.280234
$486$	236196.	0.0453609
$487$	1.72033e6	0.328692	0.164346	−	0.986403i	$-0.447449\pi$
$487$	1.72033e6	0.328692	0.164346	+	0.986403i	$0.447449\pi$
$488$	−865739.	−0.164565
$489$	5.67812e6	1.07382
$490$	0	0
$491$	6.49101e6	1.21509	0.607546	−	0.794285i	$-0.292154\pi$
$491$	6.49101e6	1.21509	0.607546	+	0.794285i	$0.292154\pi$
$492$	2.25214e6	0.419453
$493$	3.07836e6	0.570430
$494$	2.14195e6	0.394904
$495$	2.97508e6	0.545740
$496$	164537.	0.0300302
$497$	0	0
$498$	2.83848e6	0.512876
$499$	379631.	0.0682512	0.0341256	−	0.999418i	$-0.489135\pi$
$499$	379631.	0.0682512	0.0341256	+	0.999418i	$0.489135\pi$
$500$	2.57315e6	0.460300
$501$	2.15202e6	0.383047
$502$	−5.16311e6	−0.914433
$503$	−8.60340e6	−1.51618	−0.758089	−	0.652151i	$-0.773867\pi$
$503$	−8.60340e6	−1.51618	−0.758089	+	0.652151i	$0.773867\pi$
$504$	0	0
$505$	8.86624e6	1.54707
$506$	−1.17885e7	−2.04684
$507$	−1.76632e6	−0.305176
$508$	−704435.	−0.121110
$509$	1.03543e6	0.177144	0.0885718	−	0.996070i	$-0.471770\pi$
$509$	1.03543e6	0.177144	0.0885718	+	0.996070i	$0.471770\pi$
$510$	−3.84853e6	−0.655193
$511$	0	0
$512$	262144.	0.0441942
$513$	933069.	0.156538
$514$	−7.05739e6	−1.17825
$515$	−1.22473e7	−2.03481
$516$	−235959.	−0.0390133
$517$	−1.27801e7	−2.10284
$518$	0	0
$519$	−2.72645e6	−0.444303
$520$	−1.59565e6	−0.258779
$521$	6.42373e6	1.03680	0.518398	−	0.855140i	$-0.326529\pi$
$521$	6.42373e6	1.03680	0.518398	+	0.855140i	$0.326529\pi$
$522$	555991.	0.0893083
$523$	8.06384e6	1.28910	0.644551	−	0.764561i	$-0.277044\pi$
$523$	8.06384e6	1.28910	0.644551	+	0.764561i	$0.277044\pi$
$524$	−6.25811e6	−0.995668
$525$	0	0
$526$	1.71098e6	0.269638
$527$	1.15298e6	0.180840
$528$	−1.42004e6	−0.221675
$529$	1.64282e7	2.55241
$530$	1.27480e6	0.197129
$531$	1.36282e6	0.209750
$532$	0	0
$533$	6.54329e6	0.997649
$534$	2.66978e6	0.405155
$535$	6.23210e6	0.941347
$536$	−2.97494e6	−0.447267
$537$	−953906.	−0.142748
$538$	−5.06762e6	−0.754829
$539$	0	0
$540$	−695093.	−0.102579
$541$	−8.62213e6	−1.26655	−0.633274	−	0.773928i	$-0.718289\pi$
$541$	−8.62213e6	−1.26655	−0.633274	+	0.773928i	$0.718289\pi$
$542$	−1.24814e6	−0.182500
$543$	−4.26354e6	−0.620542
$544$	1.83695e6	0.266134
$545$	−1.26782e7	−1.82837
$546$	0	0
$547$	−3.51266e6	−0.501958	−0.250979	−	0.967993i	$-0.580753\pi$
$547$	−3.51266e6	−0.501958	−0.250979	+	0.967993i	$0.580753\pi$
$548$	1.13571e6	0.161554
$549$	−1.09570e6	−0.155153
$550$	−1.05104e6	−0.148154
$551$	2.19639e6	0.308198
$552$	2.75425e6	0.384730
$553$	0	0
$554$	−6.71438e6	−0.929462
$555$	1.26577e6	0.174430
$556$	1.64423e6	0.225567
$557$	−1.22183e7	−1.66868	−0.834340	−	0.551251i	$-0.814151\pi$
$557$	−1.22183e7	−1.66868	−0.834340	+	0.551251i	$0.814151\pi$
$558$	208242.	0.0283128
$559$	−685548.	−0.0927915
$560$	0	0
$561$	−9.95080e6	−1.33491
$562$	−3.06000e6	−0.408678
$563$	1.48761e6	0.197796	0.0988980	−	0.995098i	$-0.468468\pi$
$563$	1.48761e6	0.197796	0.0988980	+	0.995098i	$0.468468\pi$
$564$	2.98592e6	0.395257
$565$	−1.34016e7	−1.76618
$566$	−343327.	−0.0450471
$567$	0	0
$568$	−209530.	−0.0272506
$569$	5.83501e6	0.755547	0.377773	−	0.925898i	$-0.376690\pi$
$569$	5.83501e6	0.755547	0.377773	+	0.925898i	$0.376690\pi$
$570$	−2.74590e6	−0.353995
$571$	9.83227e6	1.26201	0.631006	−	0.775778i	$-0.282642\pi$
$571$	9.83227e6	1.26201	0.631006	+	0.775778i	$0.282642\pi$
$572$	−4.12573e6	−0.527243
$573$	−5.29032e6	−0.673125
$574$	0	0
$575$	2.03856e6	0.257130
$576$	331776.	0.0416667
$577$	324006.	0.0405147	0.0202574	−	0.999795i	$-0.493551\pi$
$577$	324006.	0.0405147	0.0202574	+	0.999795i	$0.493551\pi$
$578$	7.19281e6	0.895528
$579$	−3.30175e6	−0.409305
$580$	−1.63621e6	−0.201961
$581$	0	0
$582$	876966.	0.107319
$583$	3.29613e6	0.401636
$584$	−4.91254e6	−0.596038
$585$	−2.01950e6	−0.243979
$586$	−391139.	−0.0470530
$587$	4.27646e6	0.512258	0.256129	−	0.966643i	$-0.417553\pi$
$587$	4.27646e6	0.512258	0.256129	+	0.966643i	$0.417553\pi$
$588$	0	0
$589$	822639.	0.0977060
$590$	−4.01059e6	−0.474327
$591$	6.54724e6	0.771063
$592$	−604166.	−0.0708519
$593$	−1.58930e7	−1.85596	−0.927982	−	0.372625i	$-0.878458\pi$
$593$	−1.58930e7	−1.85596	−0.927982	+	0.372625i	$0.878458\pi$
$594$	−1.79724e6	−0.208997
$595$	0	0
$596$	−3.62076e6	−0.417527
$597$	−2.11330e6	−0.242676
$598$	8.00209e6	0.915062
$599$	−1.75061e7	−1.99353	−0.996766	−	0.0803623i	$-0.974392\pi$
$599$	−1.75061e7	−1.99353	−0.996766	+	0.0803623i	$0.974392\pi$
$600$	245564.	0.0278475
$601$	−5.98914e6	−0.676361	−0.338180	−	0.941081i	$-0.609811\pi$
$601$	−5.98914e6	−0.676361	−0.338180	+	0.941081i	$0.609811\pi$
$602$	0	0
$603$	−3.76516e6	−0.421687
$604$	−8.77158e6	−0.978330
$605$	−1.30402e7	−1.44842
$606$	−5.35607e6	−0.592468
$607$	−3.27501e6	−0.360778	−0.180389	−	0.983595i	$-0.557736\pi$
$607$	−3.27501e6	−0.360778	−0.180389	+	0.983595i	$0.557736\pi$
$608$	1.31065e6	0.143790
$609$	0	0
$610$	3.22450e6	0.350863
$611$	8.67516e6	0.940101
$612$	2.32489e6	0.250913
$613$	−7.62114e6	−0.819160	−0.409580	−	0.912274i	$-0.634325\pi$
$613$	−7.62114e6	−0.819160	−0.409580	+	0.912274i	$0.634325\pi$
$614$	−7.02183e6	−0.751674
$615$	−8.38824e6	−0.894300
$616$	0	0
$617$	1.28554e7	1.35948	0.679741	−	0.733453i	$-0.262092\pi$
$617$	1.28554e7	1.35948	0.679741	+	0.733453i	$0.262092\pi$
$618$	7.39858e6	0.779251
$619$	−8.52350e6	−0.894111	−0.447055	−	0.894506i	$-0.647527\pi$
$619$	−8.52350e6	−0.894111	−0.447055	+	0.894506i	$0.647527\pi$
$620$	−612828.	−0.0640264
$621$	3.48585e6	0.362727
$622$	−7.21582e6	−0.747842
$623$	0	0
$624$	963929.	0.0991023
$625$	−1.09161e7	−1.11781
$626$	9.85716e6	1.00535
$627$	−7.09981e6	−0.721237
$628$	3.85831e6	0.390389
$629$	−4.23363e6	−0.426664
$630$	0	0
$631$	−1.37373e7	−1.37350	−0.686750	−	0.726894i	$-0.740963\pi$
$631$	−1.37373e7	−1.37350	−0.686750	+	0.726894i	$0.740963\pi$
$632$	−1.13481e6	−0.113013
$633$	−2.77245e6	−0.275013
$634$	6.61144e6	0.653241
$635$	2.62371e6	0.258215
$636$	−770102.	−0.0754928
$637$	0	0
$638$	−4.23059e6	−0.411481
$639$	−265186.	−0.0256921
$640$	−976372.	−0.0942248
$641$	−5.04466e6	−0.484939	−0.242470	−	0.970159i	$-0.577957\pi$
$641$	−5.04466e6	−0.484939	−0.242470	+	0.970159i	$0.577957\pi$
$642$	−3.76480e6	−0.360499
$643$	9.94759e6	0.948835	0.474417	−	0.880300i	$-0.342659\pi$
$643$	9.94759e6	0.948835	0.474417	+	0.880300i	$0.342659\pi$
$644$	0	0
$645$	878846.	0.0831790
$646$	9.18424e6	0.865888
$647$	1.26276e6	0.118593	0.0592966	−	0.998240i	$-0.481114\pi$
$647$	1.26276e6	0.118593	0.0592966	+	0.998240i	$0.481114\pi$
$648$	419904.	0.0392837
$649$	−1.03698e7	−0.966406
$650$	713451.	0.0662340
$651$	0	0
$652$	1.00944e7	0.929957
$653$	−1.28147e7	−1.17605	−0.588026	−	0.808842i	$-0.700095\pi$
$653$	−1.28147e7	−1.17605	−0.588026	+	0.808842i	$0.700095\pi$
$654$	7.65885e6	0.700195
$655$	2.33087e7	2.12283
$656$	4.00381e6	0.363257
$657$	−6.21743e6	−0.561950
$658$	0	0
$659$	−3.81355e6	−0.342071	−0.171035	−	0.985265i	$-0.554711\pi$
$659$	−3.81355e6	−0.342071	−0.171035	+	0.985265i	$0.554711\pi$
$660$	5.28903e6	0.472624
$661$	1.66244e7	1.47994	0.739968	−	0.672642i	$-0.234841\pi$
$661$	1.66244e7	1.47994	0.739968	+	0.672642i	$0.234841\pi$
$662$	−6.67257e6	−0.591764
$663$	6.75464e6	0.596786
$664$	5.04619e6	0.444164
$665$	0	0
$666$	−764647.	−0.0667999
$667$	8.20548e6	0.714150
$668$	3.82581e6	0.331728
$669$	4.59171e6	0.396652
$670$	1.10804e7	0.953602
$671$	8.33730e6	0.714857
$672$	0	0
$673$	1.76139e7	1.49905	0.749527	−	0.661974i	$-0.230281\pi$
$673$	1.76139e7	1.49905	0.749527	+	0.661974i	$0.230281\pi$
$674$	−2.09908e6	−0.177983
$675$	310792.	0.0262549
$676$	−3.14013e6	−0.264290
$677$	−1.78430e7	−1.49622	−0.748112	−	0.663573i	$-0.769039\pi$
$677$	−1.78430e7	−1.49622	−0.748112	+	0.663573i	$0.769039\pi$
$678$	8.09588e6	0.676379
$679$	0	0
$680$	−6.84183e6	−0.567414
$681$	9.34229e6	0.771943
$682$	−1.58453e6	−0.130449
$683$	1.41532e7	1.16092	0.580459	−	0.814289i	$-0.302873\pi$
$683$	1.41532e7	1.16092	0.580459	+	0.814289i	$0.302873\pi$
$684$	1.65879e6	0.135566
$685$	−4.23004e6	−0.344444
$686$	0	0
$687$	−9.34641e6	−0.755532
$688$	−419484.	−0.0337865
$689$	−2.23743e6	−0.179556
$690$	−1.02584e7	−0.820268
$691$	2.22535e6	0.177297	0.0886487	−	0.996063i	$-0.471745\pi$
$691$	2.22535e6	0.177297	0.0886487	+	0.996063i	$0.471745\pi$
$692$	−4.84703e6	−0.384778
$693$	0	0
$694$	7.70547e6	0.607296
$695$	−6.12403e6	−0.480923
$696$	988429.	0.0773432
$697$	2.80563e7	2.18750
$698$	1.36137e6	0.105764
$699$	1.18571e7	0.917877
$700$	0	0
$701$	−4.49378e6	−0.345396	−0.172698	−	0.984975i	$-0.555248\pi$
$701$	−4.49378e6	−0.345396	−0.172698	+	0.984975i	$0.555248\pi$
$702$	1.21997e6	0.0934345
$703$	−3.02066e6	−0.230523
$704$	−2.52452e6	−0.191976
$705$	−1.11212e7	−0.842714
$706$	−299165.	−0.0225891
$707$	0	0
$708$	2.42279e6	0.181649
$709$	−1.54232e7	−1.15228	−0.576141	−	0.817350i	$-0.695442\pi$
$709$	−1.54232e7	−1.15228	−0.576141	+	0.817350i	$0.695442\pi$
$710$	780408.	0.0580999
$711$	−1.43624e6	−0.106550
$712$	4.74627e6	0.350875
$713$	3.07329e6	0.226402
$714$	0	0
$715$	1.53665e7	1.12412
$716$	−1.69583e6	−0.123623
$717$	7.20602e6	0.523477
$718$	9.67014e6	0.700038
$719$	−1.07276e7	−0.773890	−0.386945	−	0.922103i	$-0.626470\pi$
$719$	−1.07276e7	−0.773890	−0.386945	+	0.922103i	$0.626470\pi$
$720$	−1.23572e6	−0.0888360
$721$	0	0
$722$	−3.35151e6	−0.239275
$723$	3.62076e6	0.257605
$724$	−7.57963e6	−0.537405
$725$	731585.	0.0516916
$726$	7.87753e6	0.554688
$727$	2.05652e7	1.44310	0.721551	−	0.692362i	$-0.243430\pi$
$727$	2.05652e7	1.44310	0.721551	+	0.692362i	$0.243430\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	1.82971e7	1.27079
$731$	−2.93949e6	−0.203460
$732$	−1.94791e6	−0.134367
$733$	3.29322e6	0.226392	0.113196	−	0.993573i	$-0.463891\pi$
$733$	3.29322e6	0.226392	0.113196	+	0.993573i	$0.463891\pi$
$734$	647455.	0.0443578
$735$	0	0
$736$	4.89645e6	0.333186
$737$	2.86495e7	1.94289
$738$	5.06732e6	0.342482
$739$	−7.71767e6	−0.519847	−0.259923	−	0.965629i	$-0.583697\pi$
$739$	−7.71767e6	−0.519847	−0.259923	+	0.965629i	$0.583697\pi$
$740$	2.25025e6	0.151061
$741$	4.81938e6	0.322438
$742$	0	0
$743$	−8.33553e6	−0.553938	−0.276969	−	0.960879i	$-0.589330\pi$
$743$	−8.33553e6	−0.553938	−0.276969	+	0.960879i	$0.589330\pi$
$744$	370208.	0.0245196
$745$	1.34857e7	0.890193
$746$	308010.	0.0202636
$747$	6.38658e6	0.418762
$748$	−1.76903e7	−1.15606
$749$	0	0
$750$	5.78960e6	0.375833
$751$	−1.80694e7	−1.16908	−0.584539	−	0.811366i	$-0.698725\pi$
$751$	−1.80694e7	−1.16908	−0.584539	+	0.811366i	$0.698725\pi$
$752$	5.30830e6	0.342303
$753$	−1.16170e7	−0.746631
$754$	2.87174e6	0.183957
$755$	3.26703e7	2.08586
$756$	0	0
$757$	−8.13311e6	−0.515842	−0.257921	−	0.966166i	$-0.583037\pi$
$757$	−8.13311e6	−0.515842	−0.257921	+	0.966166i	$0.583037\pi$
$758$	−3.09666e6	−0.195758
$759$	−2.65242e7	−1.67123
$760$	−4.88159e6	−0.306568
$761$	2.01691e6	0.126248	0.0631239	−	0.998006i	$-0.479894\pi$
$761$	2.01691e6	0.126248	0.0631239	+	0.998006i	$0.479894\pi$
$762$	−1.58498e6	−0.0988863
$763$	0	0
$764$	−9.40501e6	−0.582943
$765$	−8.65919e6	−0.534963
$766$	1.45331e7	0.894925
$767$	7.03908e6	0.432043
$768$	589824.	0.0360844
$769$	1.18971e7	0.725478	0.362739	−	0.931891i	$-0.381842\pi$
$769$	1.18971e7	0.725478	0.362739	+	0.931891i	$0.381842\pi$
$770$	0	0
$771$	−1.58791e7	−0.962034
$772$	−5.86977e6	−0.354469
$773$	172292.	0.0103709	0.00518545	−	0.999987i	$-0.498349\pi$
$773$	172292.	0.0103709	0.00518545	+	0.999987i	$0.498349\pi$
$774$	−530909.	−0.0318543
$775$	274009.	0.0163874
$776$	1.55905e6	0.0929407
$777$	0	0
$778$	−1.00763e7	−0.596832
$779$	2.00179e7	1.18189
$780$	−3.59021e6	−0.211292
$781$	2.01783e6	0.118374
$782$	3.43114e7	2.00642
$783$	1.25098e6	0.0729199
$784$	0	0
$785$	−1.43705e7	−0.832334
$786$	−1.40807e7	−0.812960
$787$	−1.09131e7	−0.628075	−0.314037	−	0.949411i	$-0.601682\pi$
$787$	−1.09131e7	−0.628075	−0.314037	+	0.949411i	$0.601682\pi$
$788$	1.16395e7	0.667760
$789$	3.84971e6	0.220158
$790$	4.22666e6	0.240952
$791$	0	0
$792$	−3.19509e6	−0.180997
$793$	−5.65939e6	−0.319585
$794$	2.23711e7	1.25932
$795$	2.86829e6	0.160956
$796$	−3.75699e6	−0.210163
$797$	−2.45403e7	−1.36847	−0.684234	−	0.729263i	$-0.739863\pi$
$797$	−2.45403e7	−1.36847	−0.684234	+	0.729263i	$0.739863\pi$
$798$	0	0
$799$	3.71974e7	2.06132
$800$	436558.	0.0241166
$801$	6.00700e6	0.330808
$802$	−764247.	−0.0419564
$803$	4.73090e7	2.58914
$804$	−6.69362e6	−0.365192
$805$	0	0
$806$	1.07559e6	0.0583187
$807$	−1.14021e7	−0.616315
$808$	−9.52191e6	−0.513093
$809$	−3.07074e7	−1.64958	−0.824788	−	0.565442i	$-0.808706\pi$
$809$	−3.07074e7	−1.64958	−0.824788	+	0.565442i	$0.808706\pi$
$810$	−1.56396e6	−0.0837554
$811$	1.51675e7	0.809771	0.404886	−	0.914367i	$-0.367311\pi$
$811$	1.51675e7	0.809771	0.404886	+	0.914367i	$0.367311\pi$
$812$	0	0
$813$	−2.80831e6	−0.149011
$814$	5.81828e6	0.307775
$815$	−3.75974e7	−1.98273
$816$	4.13313e6	0.217297
$817$	−2.09730e6	−0.109927
$818$	1.78322e7	0.931797
$819$	0	0
$820$	−1.49124e7	−0.774486
$821$	3.48574e6	0.180483	0.0902416	−	0.995920i	$-0.471236\pi$
$821$	3.48574e6	0.180483	0.0902416	+	0.995920i	$0.471236\pi$
$822$	2.55536e6	0.131908
$823$	−2.20822e7	−1.13643	−0.568214	−	0.822881i	$-0.692365\pi$
$823$	−2.20822e7	−1.13643	−0.568214	+	0.822881i	$0.692365\pi$
$824$	1.31530e7	0.674851
$825$	−2.36484e6	−0.120967
$826$	0	0
$827$	2.28055e7	1.15951	0.579757	−	0.814789i	$-0.303147\pi$
$827$	2.28055e7	1.15951	0.579757	+	0.814789i	$0.303147\pi$
$828$	6.19706e6	0.314131
$829$	−3.56532e7	−1.80182	−0.900912	−	0.434002i	$-0.857101\pi$
$829$	−3.56532e7	−1.80182	−0.900912	+	0.434002i	$0.857101\pi$
$830$	−1.87948e7	−0.946986
$831$	−1.51074e7	−0.758902
$832$	1.71365e6	0.0858251
$833$	0	0
$834$	3.69951e6	0.184174
$835$	−1.42495e7	−0.707266
$836$	−1.26219e7	−0.624610
$837$	468544.	0.0231173
$838$	1.90448e7	0.936842
$839$	2.55545e7	1.25332	0.626662	−	0.779291i	$-0.284421\pi$
$839$	2.55545e7	1.25332	0.626662	+	0.779291i	$0.284421\pi$
$840$	0	0
$841$	−1.75664e7	−0.856433
$842$	−5.53990e6	−0.269291
$843$	−6.88501e6	−0.333684
$844$	−4.92879e6	−0.238169
$845$	1.16956e7	0.563483
$846$	6.71831e6	0.322726
$847$	0	0
$848$	−1.36907e6	−0.0653787
$849$	−772485.	−0.0367808
$850$	3.05914e6	0.145228
$851$	−1.12849e7	−0.534162
$852$	−471443.	−0.0222500
$853$	2.55946e6	0.120441	0.0602206	−	0.998185i	$-0.480820\pi$
$853$	2.55946e6	0.120441	0.0602206	+	0.998185i	$0.480820\pi$
$854$	0	0
$855$	−6.17826e6	−0.289036
$856$	−6.69297e6	−0.312201
$857$	4.96836e6	0.231079	0.115540	−	0.993303i	$-0.463140\pi$
$857$	4.96836e6	0.231079	0.115540	+	0.993303i	$0.463140\pi$
$858$	−9.28289e6	−0.430492
$859$	−1.11897e7	−0.517411	−0.258706	−	0.965956i	$-0.583296\pi$
$859$	−1.11897e7	−0.517411	−0.258706	+	0.965956i	$0.583296\pi$
$860$	1.56239e6	0.0720351
$861$	0	0
$862$	1.82356e7	0.835897
$863$	−2.97620e6	−0.136030	−0.0680151	−	0.997684i	$-0.521667\pi$
$863$	−2.97620e6	−0.136030	−0.0680151	+	0.997684i	$0.521667\pi$
$864$	746496.	0.0340207
$865$	1.80530e7	0.820371
$866$	−2.40348e7	−1.08905
$867$	1.61838e7	0.731195
$868$	0	0
$869$	1.09285e7	0.490920
$870$	−3.68146e6	−0.164901
$871$	−1.94474e7	−0.868593
$872$	1.36157e7	0.606387
$873$	1.97317e6	0.0876254
$874$	2.44809e7	1.08405
$875$	0	0
$876$	−1.10532e7	−0.486663
$877$	2.84689e7	1.24989	0.624945	−	0.780669i	$-0.285121\pi$
$877$	2.84689e7	1.24989	0.624945	+	0.780669i	$0.285121\pi$
$878$	2.24201e6	0.0981526
$879$	−880063.	−0.0384186
$880$	9.40272e6	0.409305
$881$	−1.97744e7	−0.858346	−0.429173	−	0.903222i	$-0.641195\pi$
$881$	−1.97744e7	−0.858346	−0.429173	+	0.903222i	$0.641195\pi$
$882$	0	0
$883$	1.88722e7	0.814556	0.407278	−	0.913304i	$-0.366478\pi$
$883$	1.88722e7	0.814556	0.407278	+	0.913304i	$0.366478\pi$
$884$	1.20082e7	0.516831
$885$	−9.02383e6	−0.387287
$886$	1.33630e7	0.571898
$887$	−1.71526e7	−0.732016	−0.366008	−	0.930612i	$-0.619276\pi$
$887$	−1.71526e7	−0.732016	−0.366008	+	0.930612i	$0.619276\pi$
$888$	−1.35937e6	−0.0578504
$889$	0	0
$890$	−1.76778e7	−0.748088
$891$	−4.04379e6	−0.170645
$892$	8.16304e6	0.343510
$893$	2.65400e7	1.11371
$894$	−8.14671e6	−0.340909
$895$	6.31624e6	0.263573
$896$	0	0
$897$	1.80047e7	0.747145
$898$	−2.59137e7	−1.07235
$899$	1.10292e6	0.0455142
$900$	552518.	0.0227374
$901$	−9.59363e6	−0.393705
$902$	−3.85577e7	−1.57796
$903$	0	0
$904$	1.43927e7	0.585761
$905$	2.82308e7	1.14578
$906$	−1.97361e7	−0.798803
$907$	−2.02760e7	−0.818399	−0.409199	−	0.912445i	$-0.634192\pi$
$907$	−2.02760e7	−0.818399	−0.409199	+	0.912445i	$0.634192\pi$
$908$	1.66085e7	0.668523
$909$	−1.20512e7	−0.483748
$910$	0	0
$911$	−1.53633e7	−0.613322	−0.306661	−	0.951819i	$-0.599212\pi$
$911$	−1.53633e7	−0.613322	−0.306661	+	0.951819i	$0.599212\pi$
$912$	2.94896e6	0.117404
$913$	−4.85961e7	−1.92941
$914$	1.72455e7	0.682827
$915$	7.25513e6	0.286479
$916$	−1.66158e7	−0.654310
$917$	0	0
$918$	5.23100e6	0.204870
$919$	2.10973e7	0.824021	0.412010	−	0.911179i	$-0.364827\pi$
$919$	2.10973e7	0.824021	0.412010	+	0.911179i	$0.364827\pi$
$920$	−1.82371e7	−0.710373
$921$	−1.57991e7	−0.613739
$922$	−1.28380e6	−0.0497360
$923$	−1.36971e6	−0.0529206
$924$	0	0
$925$	−1.00614e6	−0.0386637
$926$	−1.25695e7	−0.481717
$927$	1.66468e7	0.636256
$928$	1.75721e6	0.0669812
$929$	−1.17648e7	−0.447244	−0.223622	−	0.974676i	$-0.571788\pi$
$929$	−1.17648e7	−0.447244	−0.223622	+	0.974676i	$0.571788\pi$
$930$	−1.37886e6	−0.0522773
$931$	0	0
$932$	2.10792e7	0.794905
$933$	−1.62356e7	−0.610611
$934$	1.65835e7	0.622026
$935$	6.58886e7	2.46480
$936$	2.16884e6	0.0809167
$937$	7.83051e6	0.291367	0.145684	−	0.989331i	$-0.453462\pi$
$937$	7.83051e6	0.291367	0.145684	+	0.989331i	$0.453462\pi$
$938$	0	0
$939$	2.21786e7	0.820863
$940$	−1.97711e7	−0.729812
$941$	3.39315e7	1.24919	0.624595	−	0.780948i	$-0.285264\pi$
$941$	3.39315e7	1.24919	0.624595	+	0.780948i	$0.285264\pi$
$942$	8.68119e6	0.318751
$943$	7.47849e7	2.73864
$944$	4.30718e6	0.157312
$945$	0	0
$946$	4.03974e6	0.146766
$947$	−4.08599e7	−1.48055	−0.740274	−	0.672305i	$-0.765304\pi$
$947$	−4.08599e7	−1.48055	−0.740274	+	0.672305i	$0.765304\pi$
$948$	−2.55332e6	−0.0922750
$949$	−3.21136e7	−1.15751
$950$	2.18267e6	0.0784655
$951$	1.48757e7	0.533369
$952$	0	0
$953$	−3.53837e7	−1.26203	−0.631016	−	0.775770i	$-0.717362\pi$
$953$	−3.53837e7	−1.26203	−0.631016	+	0.775770i	$0.717362\pi$
$954$	−1.73273e6	−0.0616396
$955$	3.50296e7	1.24287
$956$	1.28107e7	0.453345
$957$	−9.51883e6	−0.335973
$958$	−1.03071e6	−0.0362846
$959$	0	0
$960$	−2.19684e6	−0.0769342
$961$	−2.82161e7	−0.985571
$962$	−3.94947e6	−0.137594
$963$	−8.47079e6	−0.294346
$964$	6.43691e6	0.223093
$965$	2.18623e7	0.755750
$966$	0	0
$967$	−4.37744e7	−1.50541	−0.752703	−	0.658360i	$-0.771250\pi$
$967$	−4.37744e7	−1.50541	−0.752703	+	0.658360i	$0.771250\pi$
$968$	1.40045e7	0.480374
$969$	2.06645e7	0.706995
$970$	−5.80679e6	−0.198156
$971$	−7.16196e6	−0.243772	−0.121886	−	0.992544i	$-0.538894\pi$
$971$	−7.16196e6	−0.243772	−0.121886	+	0.992544i	$0.538894\pi$
$972$	944784.	0.0320750
$973$	0	0
$974$	6.88132e6	0.232421
$975$	1.60527e6	0.0540798
$976$	−3.46296e6	−0.116365
$977$	−2.68803e7	−0.900945	−0.450473	−	0.892790i	$-0.648745\pi$
$977$	−2.68803e7	−0.900945	−0.450473	+	0.892790i	$0.648745\pi$
$978$	2.27125e7	0.759307
$979$	−4.57078e7	−1.52417
$980$	0	0
$981$	1.72324e7	0.571707
$982$	2.59641e7	0.859199
$983$	1.06207e6	0.0350565	0.0175283	−	0.999846i	$-0.494420\pi$
$983$	1.06207e6	0.0350565	0.0175283	+	0.999846i	$0.494420\pi$
$984$	9.00857e6	0.296598
$985$	−4.33522e7	−1.42371
$986$	1.23135e7	0.403355
$987$	0	0
$988$	8.56779e6	0.279239
$989$	−7.83531e6	−0.254721
$990$	1.19003e7	0.385896
$991$	−7.39380e6	−0.239157	−0.119579	−	0.992825i	$-0.538154\pi$
$991$	−7.39380e6	−0.239157	−0.119579	+	0.992825i	$0.538154\pi$
$992$	658147.	0.0212346
$993$	−1.50133e7	−0.483173
$994$	0	0
$995$	1.39931e7	0.448082
$996$	1.13539e7	0.362658
$997$	2.41365e7	0.769019	0.384510	−	0.923121i	$-0.374371\pi$
$997$	2.41365e7	0.769019	0.384510	+	0.923121i	$0.374371\pi$
$998$	1.51852e6	0.0482609
$999$	−1.72046e6	−0.0545419

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.6.a.v.1.1	yes	2
3.2	odd	2		882.6.a.bc.1.2		2
7.2	even	3		294.6.e.t.67.2		4
7.3	odd	6		294.6.e.w.79.1		4
7.4	even	3		294.6.e.t.79.2		4
7.5	odd	6		294.6.e.w.67.1		4
7.6	odd	2		294.6.a.s.1.2	✓	2
21.20	even	2		882.6.a.bg.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.6.a.s.1.2	✓	2	7.6	odd	2
294.6.a.v.1.1	yes	2	1.1	even	1	trivial
294.6.e.t.67.2		4	7.2	even	3
294.6.e.t.79.2		4	7.4	even	3
294.6.e.w.67.1		4	7.5	odd	6
294.6.e.w.79.1		4	7.3	odd	6
882.6.a.bc.1.2		2	3.2	odd	2
882.6.a.bg.1.1		2	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	294.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -59.5930 q^{5} +36.0000 q^{6} +64.0000 q^{8} +81.0000 q^{9} -238.372 q^{10} -616.337 q^{11} +144.000 q^{12} +418.372 q^{13} -536.337 q^{15} +256.000 q^{16} +1793.90 q^{17} +324.000 q^{18} +1279.93 q^{19} -953.488 q^{20} -2465.35 q^{22} +4781.69 q^{23} +576.000 q^{24} +426.326 q^{25} +1673.49 q^{26} +729.000 q^{27} +1716.02 q^{29} -2145.35 q^{30} +642.722 q^{31} +1024.00 q^{32} -5547.03 q^{33} +7175.58 q^{34} +1296.00 q^{36} -2360.02 q^{37} +5119.72 q^{38} +3765.35 q^{39} -3813.95 q^{40} +15639.9 q^{41} -1638.61 q^{43} -9861.39 q^{44} -4827.03 q^{45} +19126.7 q^{46} +20735.5 q^{47} +2304.00 q^{48} +1705.30 q^{50} +16145.1 q^{51} +6693.95 q^{52} -5347.93 q^{53} +2916.00 q^{54} +36729.4 q^{55} +11519.4 q^{57} +6864.09 q^{58} +16824.9 q^{59} -8581.39 q^{60} -13527.2 q^{61} +2570.89 q^{62} +4096.00 q^{64} -24932.0 q^{65} -22188.1 q^{66} -46483.5 q^{67} +28702.3 q^{68} +43035.2 q^{69} -3273.91 q^{71} +5184.00 q^{72} -76758.4 q^{73} -9440.09 q^{74} +3836.93 q^{75} +20478.9 q^{76} +15061.4 q^{78} -17731.4 q^{79} -15255.8 q^{80} +6561.00 q^{81} +62559.5 q^{82} +78846.7 q^{83} -106904. q^{85} -6554.43 q^{86} +15444.2 q^{87} -39445.6 q^{88} +74160.4 q^{89} -19308.1 q^{90} +76507.0 q^{92} +5784.50 q^{93} +82942.1 q^{94} -76274.9 q^{95} +9216.00 q^{96} +24360.2 q^{97} -49923.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} + 18 q^{3} + 32 q^{4} + 18 q^{5} + 72 q^{6} + 128 q^{8} + 162 q^{9} + 72 q^{10} + 2 q^{11} + 288 q^{12} + 288 q^{13} + 162 q^{15} + 512 q^{16} + 1530 q^{17} + 648 q^{18} + 1188 q^{19} + 288 q^{20}+ \cdots + 162 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 + 18 * q^3 + 32 * q^4 + 18 * q^5 + 72 * q^6 + 128 * q^8 + 162 * q^9 + 72 * q^10 + 2 * q^11 + 288 * q^12 + 288 * q^13 + 162 * q^15 + 512 * q^16 + 1530 * q^17 + 648 * q^18 + 1188 * q^19 + 288 * q^20 + 8 * q^22 + 3390 * q^23 + 1152 * q^24 + 3322 * q^25 + 1152 * q^26 + 1458 * q^27 - 3976 * q^29 + 648 * q^30 + 7596 * q^31 + 2048 * q^32 + 18 * q^33 + 6120 * q^34 + 2592 * q^36 + 2688 * q^37 + 4752 * q^38 + 2592 * q^39 + 1152 * q^40 + 36630 * q^41 - 23032 * q^43 + 32 * q^44 + 1458 * q^45 + 13560 * q^46 + 864 * q^47 + 4608 * q^48 + 13288 * q^50 + 13770 * q^51 + 4608 * q^52 - 32920 * q^53 + 5832 * q^54 + 84708 * q^55 + 10692 * q^57 - 15904 * q^58 - 26712 * q^59 + 2592 * q^60 + 20412 * q^61 + 30384 * q^62 + 8192 * q^64 - 35048 * q^65 + 72 * q^66 - 36172 * q^67 + 24480 * q^68 + 30510 * q^69 + 73706 * q^71 + 10368 * q^72 - 74772 * q^73 + 10752 * q^74 + 29898 * q^75 + 19008 * q^76 + 10368 * q^78 - 23116 * q^79 + 4608 * q^80 + 13122 * q^81 + 146520 * q^82 + 147816 * q^83 - 127380 * q^85 - 92128 * q^86 - 35784 * q^87 + 128 * q^88 + 164646 * q^89 + 5832 * q^90 + 54240 * q^92 + 68364 * q^93 + 3456 * q^94 - 83408 * q^95 + 18432 * q^96 + 162036 * q^97 + 162 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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