LMFDB - Embedded newform 294.5.c.b.97.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,5,Mod(97,294)]

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, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("294.97");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	294.c (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$30.3907691467$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.339738624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			97.8
Root			$1.60021 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	294.97
Dual form			294.5.c.b.97.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843 q^{2} +5.19615i q^{3} +8.00000 q^{4} -12.2936i q^{5} +14.6969i q^{6} +22.6274 q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+2.82843 q^{2} +5.19615i q^{3} +8.00000 q^{4} -12.2936i q^{5} +14.6969i q^{6} +22.6274 q^{8} -27.0000 q^{9} -34.7716i q^{10} -65.1601 q^{11} +41.5692i q^{12} -323.669i q^{13} +63.8796 q^{15} +64.0000 q^{16} +0.752480i q^{17} -76.3675 q^{18} -313.033i q^{19} -98.3490i q^{20} -184.301 q^{22} +293.127 q^{23} +117.576i q^{24} +473.867 q^{25} -915.473i q^{26} -140.296i q^{27} -83.7940 q^{29} +180.679 q^{30} -85.5457i q^{31} +181.019 q^{32} -338.582i q^{33} +2.12834i q^{34} -216.000 q^{36} -2149.07 q^{37} -885.392i q^{38} +1681.83 q^{39} -278.173i q^{40} -1949.77i q^{41} +1061.57 q^{43} -521.281 q^{44} +331.928i q^{45} +829.088 q^{46} -2779.84i q^{47} +332.554i q^{48} +1340.30 q^{50} -3.91000 q^{51} -2589.35i q^{52} +2547.21 q^{53} -396.817i q^{54} +801.055i q^{55} +1626.57 q^{57} -237.005 q^{58} +2345.95i q^{59} +511.037 q^{60} -1574.76i q^{61} -241.960i q^{62} +512.000 q^{64} -3979.06 q^{65} -957.654i q^{66} +5125.07 q^{67} +6.01984i q^{68} +1523.13i q^{69} +9255.69 q^{71} -610.940 q^{72} -4412.55i q^{73} -6078.50 q^{74} +2462.28i q^{75} -2504.27i q^{76} +4756.94 q^{78} -7832.04 q^{79} -786.792i q^{80} +729.000 q^{81} -5514.77i q^{82} +2065.60i q^{83} +9.25071 q^{85} +3002.58 q^{86} -435.407i q^{87} -1474.41 q^{88} -14122.5i q^{89} +938.834i q^{90} +2345.02 q^{92} +444.509 q^{93} -7862.58i q^{94} -3848.32 q^{95} +940.604i q^{96} +16530.2i q^{97} +1759.32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 64 q^{4} - 216 q^{9}+O(q^{10}) $ 8 * q + 64 * q^4 - 216 * q^9	$ 8 q + 64 q^{4} - 216 q^{9} + 512 q^{16} - 1312 q^{22} - 272 q^{23} - 2808 q^{25} + 400 q^{29} + 3168 q^{30} - 1728 q^{36} - 3328 q^{37} + 656 q^{43} - 2400 q^{46} + 800 q^{50} + 7200 q^{51} + 9264 q^{53} + 1152 q^{57} - 11488 q^{58} + 4096 q^{64} - 15696 q^{65} + 26816 q^{67} + 28192 q^{71} - 4512 q^{74} + 9216 q^{78} + 19728 q^{79} + 5832 q^{81} - 49632 q^{85} + 5888 q^{86} - 10496 q^{88} - 2176 q^{92} + 15264 q^{93} - 92752 q^{95}+O(q^{100}) $ 8 * q + 64 * q^4 - 216 * q^9 + 512 * q^16 - 1312 * q^22 - 272 * q^23 - 2808 * q^25 + 400 * q^29 + 3168 * q^30 - 1728 * q^36 - 3328 * q^37 + 656 * q^43 - 2400 * q^46 + 800 * q^50 + 7200 * q^51 + 9264 * q^53 + 1152 * q^57 - 11488 * q^58 + 4096 * q^64 - 15696 * q^65 + 26816 * q^67 + 28192 * q^71 - 4512 * q^74 + 9216 * q^78 + 19728 * q^79 + 5832 * q^81 - 49632 * q^85 + 5888 * q^86 - 10496 * q^88 - 2176 * q^92 + 15264 * q^93 - 92752 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$-1$

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 $

$2$	2.82843	0.707107
$2$	2.82843	0.707107
$3$	5.19615i	0.577350i
$3$	5.19615i	0.577350i
$4$	8.00000	0.500000
$5$	− 12.2936i	− 0.491745i	−0.969302	−	0.245873i	$-0.920926\pi$
$5$	− 12.2936i	− 0.491745i	0.969302	−	0.245873i	$-0.0790745\pi$
$6$	14.6969i	0.408248i
$7$	0	0
$7$	0	0
$8$	22.6274	0.353553
$9$	−27.0000	−0.333333
$10$	− 34.7716i	− 0.347716i
$11$	−65.1601	−0.538513	−0.269257	−	0.963068i	$-0.586778\pi$
$11$	−65.1601	−0.538513	−0.269257	+	0.963068i	$0.586778\pi$
$12$	41.5692i	0.288675i
$13$	− 323.669i	− 1.91520i	−0.288103	−	0.957599i	$-0.593025\pi$
$13$	− 323.669i	− 1.91520i	0.288103	−	0.957599i	$-0.406975\pi$
$14$	0	0
$15$	63.8796	0.283909
$16$	64.0000	0.250000
$17$	0.752480i	0.00260374i	0.999999	+	0.00130187i	$0.000414398\pi$
$17$	0.752480i	0.00260374i	−0.999999	+	0.00130187i	$0.999586\pi$
$18$	−76.3675	−0.235702
$19$	− 313.033i	− 0.867128i	−0.901123	−	0.433564i	$-0.857256\pi$
$19$	− 313.033i	− 0.867128i	0.901123	−	0.433564i	$-0.142744\pi$
$20$	− 98.3490i	− 0.245873i
$21$	0	0
$22$	−184.301	−0.380787
$23$	293.127	0.554115	0.277058	−	0.960853i	$-0.410641\pi$
$23$	293.127	0.554115	0.277058	+	0.960853i	$0.410641\pi$
$24$	117.576i	0.204124i
$25$	473.867	0.758187
$26$	− 915.473i	− 1.35425i
$27$	− 140.296i	− 0.192450i
$28$	0	0
$29$	−83.7940	−0.0996362	−0.0498181	−	0.998758i	$-0.515864\pi$
$29$	−83.7940	−0.0996362	−0.0498181	+	0.998758i	$0.515864\pi$
$30$	180.679	0.200754
$31$	− 85.5457i	− 0.0890174i	−0.999009	−	0.0445087i	$-0.985828\pi$
$31$	− 85.5457i	− 0.0890174i	0.999009	−	0.0445087i	$-0.0141722\pi$
$32$	181.019	0.176777
$33$	− 338.582i	− 0.310911i
$34$	2.12834i	0.00184112i
$35$	0	0
$36$	−216.000	−0.166667
$37$	−2149.07	−1.56981	−0.784907	−	0.619614i	$-0.787289\pi$
$37$	−2149.07	−1.56981	−0.784907	+	0.619614i	$0.787289\pi$
$38$	− 885.392i	− 0.613152i
$39$	1681.83	1.10574
$40$	− 278.173i	− 0.173858i
$41$	− 1949.77i	− 1.15988i	−0.814657	−	0.579942i	$-0.803075\pi$
$41$	− 1949.77i	− 1.15988i	0.814657	−	0.579942i	$-0.196925\pi$
$42$	0	0
$43$	1061.57	0.574132	0.287066	−	0.957911i	$-0.407320\pi$
$43$	1061.57	0.574132	0.287066	+	0.957911i	$0.407320\pi$
$44$	−521.281	−0.269257
$45$	331.928i	0.163915i
$46$	829.088	0.391819
$47$	− 2779.84i	− 1.25842i	−0.777237	−	0.629208i	$-0.783379\pi$
$47$	− 2779.84i	− 1.25842i	0.777237	−	0.629208i	$-0.216621\pi$
$48$	332.554i	0.144338i
$49$	0	0
$50$	1340.30	0.536119
$51$	−3.91000	−0.00150327
$52$	− 2589.35i	− 0.957599i
$53$	2547.21	0.906802	0.453401	−	0.891307i	$-0.350211\pi$
$53$	2547.21	0.906802	0.453401	+	0.891307i	$0.350211\pi$
$54$	− 396.817i	− 0.136083i
$55$	801.055i	0.264811i
$56$	0	0
$57$	1626.57	0.500637
$58$	−237.005	−0.0704534
$59$	2345.95i	0.673931i	0.941517	+	0.336966i	$0.109401\pi$
$59$	2345.95i	0.673931i	−0.941517	+	0.336966i	$0.890599\pi$
$60$	511.037	0.141955
$61$	− 1574.76i	− 0.423210i	−0.977355	−	0.211605i	$-0.932131\pi$
$61$	− 1574.76i	− 0.423210i	0.977355	−	0.211605i	$-0.0678691\pi$
$62$	− 241.960i	− 0.0629448i
$63$	0	0
$64$	512.000	0.125000
$65$	−3979.06	−0.941790
$66$	− 957.654i	− 0.219847i
$67$	5125.07	1.14169	0.570847	−	0.821056i	$-0.306615\pi$
$67$	5125.07	1.14169	0.570847	+	0.821056i	$0.306615\pi$
$68$	6.01984i	0.00130187i
$69$	1523.13i	0.319919i
$70$	0	0
$71$	9255.69	1.83608	0.918042	−	0.396484i	$-0.129770\pi$
$71$	9255.69	1.83608	0.918042	+	0.396484i	$0.129770\pi$
$72$	−610.940	−0.117851
$73$	− 4412.55i	− 0.828027i	−0.910271	−	0.414013i	$-0.864127\pi$
$73$	− 4412.55i	− 0.828027i	0.910271	−	0.414013i	$-0.135873\pi$
$74$	−6078.50	−1.11003
$75$	2462.28i	0.437739i
$76$	− 2504.27i	− 0.433564i
$77$	0	0
$78$	4756.94	0.781877
$79$	−7832.04	−1.25493	−0.627467	−	0.778643i	$-0.715908\pi$
$79$	−7832.04	−1.25493	−0.627467	+	0.778643i	$0.715908\pi$
$80$	− 786.792i	− 0.122936i
$81$	729.000	0.111111
$82$	− 5514.77i	− 0.820162i
$83$	2065.60i	0.299841i	0.988698	+	0.149920i	$0.0479017\pi$
$83$	2065.60i	0.299841i	−0.988698	+	0.149920i	$0.952098\pi$
$84$	0	0
$85$	9.25071	0.00128038
$86$	3002.58	0.405973
$87$	− 435.407i	− 0.0575250i
$88$	−1474.41	−0.190393
$89$	− 14122.5i	− 1.78292i	−0.453102	−	0.891459i	$-0.649683\pi$
$89$	− 14122.5i	− 1.78292i	0.453102	−	0.891459i	$-0.350317\pi$
$90$	938.834i	0.115905i
$91$	0	0
$92$	2345.02	0.277058
$93$	444.509	0.0513942
$94$	− 7862.58i	− 0.889835i
$95$	−3848.32	−0.426406
$96$	940.604i	0.102062i
$97$	16530.2i	1.75685i	0.477882	+	0.878424i	$0.341405\pi$
$97$	16530.2i	1.75685i	−0.477882	+	0.878424i	$0.658595\pi$
$98$	0	0
$99$	1759.32	0.179504
$100$	3790.93	0.379093
$101$	19014.6i	1.86399i	0.362466	+	0.931997i	$0.381935\pi$
$101$	19014.6i	1.86399i	−0.362466	+	0.931997i	$0.618065\pi$
$102$	−11.0592	−0.00106297
$103$	− 4339.23i	− 0.409014i	−0.978865	−	0.204507i	$-0.934441\pi$
$103$	− 4339.23i	− 0.409014i	0.978865	−	0.204507i	$-0.0655592\pi$
$104$	− 7323.78i	− 0.677125i
$105$	0	0
$106$	7204.59	0.641206
$107$	−15448.9	−1.34937	−0.674683	−	0.738108i	$-0.735720\pi$
$107$	−15448.9	−1.34937	−0.674683	+	0.738108i	$0.735720\pi$
$108$	− 1122.37i	− 0.0962250i
$109$	−5774.77	−0.486050	−0.243025	−	0.970020i	$-0.578140\pi$
$109$	−5774.77	−0.486050	−0.243025	+	0.970020i	$0.578140\pi$
$110$	2265.72i	0.187250i
$111$	− 11166.9i	− 0.906332i
$112$	0	0
$113$	−19497.5	−1.52694	−0.763469	−	0.645844i	$-0.776506\pi$
$113$	−19497.5	−1.52694	−0.763469	+	0.645844i	$0.776506\pi$
$114$	4600.63	0.354004
$115$	− 3603.59i	− 0.272483i
$116$	−670.352	−0.0498181
$117$	8739.05i	0.638400i
$118$	6635.36i	0.476541i
$119$	0	0
$120$	1445.43	0.100377
$121$	−10395.2	−0.710003
$122$	− 4454.11i	− 0.299255i
$123$	10131.3	0.669660
$124$	− 684.366i	− 0.0445087i
$125$	− 13509.1i	− 0.864580i
$126$	0	0
$127$	−27028.3	−1.67576	−0.837879	−	0.545856i	$-0.816205\pi$
$127$	−27028.3	−1.67576	−0.837879	+	0.545856i	$0.816205\pi$
$128$	1448.15	0.0883883
$129$	5516.08i	0.331475i
$130$	−11254.5	−0.665946
$131$	21385.1i	1.24615i	0.782163	+	0.623073i	$0.214116\pi$
$131$	21385.1i	1.24615i	−0.782163	+	0.623073i	$0.785884\pi$
$132$	− 2708.66i	− 0.155455i
$133$	0	0
$134$	14495.9	0.807300
$135$	−1724.75	−0.0946364
$136$	17.0267i	0 0.000920560i
$137$	1920.54	0.102325	0.0511625	−	0.998690i	$-0.483707\pi$
$137$	1920.54	0.102325	0.0511625	+	0.998690i	$0.483707\pi$
$138$	4308.07i	0.226217i
$139$	17433.4i	0.902305i	0.892447	+	0.451153i	$0.148987\pi$
$139$	17433.4i	0.902305i	−0.892447	+	0.451153i	$0.851013\pi$
$140$	0	0
$141$	14444.5	0.726547
$142$	26179.1	1.29831
$143$	21090.3i	1.03136i
$144$	−1728.00	−0.0833333
$145$	1030.13i	0.0489956i
$146$	− 12480.6i	− 0.585503i
$147$	0	0
$148$	−17192.6	−0.784907
$149$	32017.4	1.44216	0.721079	−	0.692853i	$-0.243646\pi$
$149$	32017.4	1.44216	0.721079	+	0.692853i	$0.243646\pi$
$150$	6964.39i	0.309528i
$151$	31102.7	1.36409	0.682046	−	0.731309i	$-0.261090\pi$
$151$	31102.7	1.36409	0.682046	+	0.731309i	$0.261090\pi$
$152$	− 7083.14i	− 0.306576i
$153$	− 20.3170i	0 0.000867912i
$154$	0	0
$155$	−1051.67	−0.0437739
$156$	13454.7	0.552870
$157$	− 9929.61i	− 0.402840i	−0.979505	−	0.201420i	$-0.935444\pi$
$157$	− 9929.61i	− 0.402840i	0.979505	−	0.201420i	$-0.0645557\pi$
$158$	−22152.4	−0.887372
$159$	13235.7i	0.523542i
$160$	− 2225.38i	− 0.0869291i
$161$	0	0
$162$	2061.92	0.0785674
$163$	14656.3	0.551631	0.275816	−	0.961211i	$-0.411052\pi$
$163$	14656.3	0.551631	0.275816	+	0.961211i	$0.411052\pi$
$164$	− 15598.1i	− 0.579942i
$165$	−4162.40	−0.152889
$166$	5842.40i	0.212019i
$167$	6891.47i	0.247103i	0.992338	+	0.123552i	$0.0394285\pi$
$167$	6891.47i	0.247103i	−0.992338	+	0.123552i	$0.960572\pi$
$168$	0	0
$169$	−76200.4	−2.66799
$170$	26.1650	0.000905362 0
$171$	8451.90i	0.289043i
$172$	8492.56	0.287066
$173$	37396.8i	1.24952i	0.780819	+	0.624758i	$0.214802\pi$
$173$	37396.8i	1.24952i	−0.780819	+	0.624758i	$0.785198\pi$
$174$	− 1231.52i	− 0.0406763i
$175$	0	0
$176$	−4170.25	−0.134628
$177$	−12189.9	−0.389094
$178$	− 39944.4i	− 1.26071i
$179$	12390.3	0.386702	0.193351	−	0.981130i	$-0.438064\pi$
$179$	12390.3	0.386702	0.193351	+	0.981130i	$0.438064\pi$
$180$	2655.42i	0.0819575i
$181$	− 6840.13i	− 0.208789i	−0.994536	−	0.104394i	$-0.966710\pi$
$181$	− 6840.13i	− 0.208789i	0.994536	−	0.104394i	$-0.0332904\pi$
$182$	0	0
$183$	8182.72	0.244340
$184$	6632.70	0.195909
$185$	26419.9i	0.771948i
$186$	1257.26	0.0363412
$187$	− 49.0317i	− 0.00140215i
$188$	− 22238.7i	− 0.629208i
$189$	0	0
$190$	−10884.7	−0.301515
$191$	47051.6	1.28976	0.644878	−	0.764286i	$-0.276908\pi$
$191$	47051.6	1.28976	0.644878	+	0.764286i	$0.276908\pi$
$192$	2660.43i	0.0721688i
$193$	−51379.0	−1.37934	−0.689670	−	0.724124i	$-0.742244\pi$
$193$	−51379.0	−1.37934	−0.689670	+	0.724124i	$0.742244\pi$
$194$	46754.4i	1.24228i
$195$	− 20675.8i	− 0.543743i
$196$	0	0
$197$	15985.0	0.411889	0.205945	−	0.978564i	$-0.433973\pi$
$197$	15985.0	0.411889	0.205945	+	0.978564i	$0.433973\pi$
$198$	4976.12	0.126929
$199$	− 21625.9i	− 0.546095i	−0.962001	−	0.273048i	$-0.911968\pi$
$199$	− 21625.9i	− 0.546095i	0.962001	−	0.273048i	$-0.0880316\pi$
$200$	10722.4	0.268059
$201$	26630.6i	0.659158i
$202$	53781.4i	1.31804i
$203$	0	0
$204$	−31.2800	−0.000751634 0
$205$	−23969.7	−0.570368
$206$	− 12273.2i	− 0.289217i
$207$	−7914.43	−0.184705
$208$	− 20714.8i	− 0.478800i
$209$	20397.3i	0.466960i
$210$	0	0
$211$	−37768.2	−0.848324	−0.424162	−	0.905586i	$-0.639431\pi$
$211$	−37768.2	−0.848324	−0.424162	+	0.905586i	$0.639431\pi$
$212$	20377.6	0.453401
$213$	48094.0i	1.06006i
$214$	−43696.0	−0.954145
$215$	− 13050.6i	− 0.282327i
$216$	− 3174.54i	− 0.0680414i
$217$	0	0
$218$	−16333.5	−0.343690
$219$	22928.3	0.478061
$220$	6408.44i	0.132406i
$221$	243.554	0.00498667
$222$	− 31584.8i	− 0.640874i
$223$	46676.0i	0.938606i	0.883037	+	0.469303i	$0.155495\pi$
$223$	46676.0i	0.938606i	−0.883037	+	0.469303i	$0.844505\pi$
$224$	0	0
$225$	−12794.4	−0.252729
$226$	−55147.2	−1.07971
$227$	21374.3i	0.414802i	0.978256	+	0.207401i	$0.0665005\pi$
$227$	21374.3i	0.414802i	−0.978256	+	0.207401i	$0.933499\pi$
$228$	13012.6	0.250318
$229$	15682.2i	0.299045i	0.988758	+	0.149523i	$0.0477737\pi$
$229$	15682.2i	0.299045i	−0.988758	+	0.149523i	$0.952226\pi$
$230$	− 10192.5i	− 0.192675i
$231$	0	0
$232$	−1896.04	−0.0352267
$233$	19095.2	0.351733	0.175866	−	0.984414i	$-0.443727\pi$
$233$	19095.2	0.351733	0.175866	+	0.984414i	$0.443727\pi$
$234$	24717.8i	0.451417i
$235$	−34174.4	−0.618820
$236$	18767.6i	0.336966i
$237$	− 40696.5i	− 0.724536i
$238$	0	0
$239$	97743.0	1.71116	0.855579	−	0.517672i	$-0.173201\pi$
$239$	97743.0	1.71116	0.855579	+	0.517672i	$0.173201\pi$
$240$	4088.29	0.0709773
$241$	− 6964.37i	− 0.119908i	−0.998201	−	0.0599539i	$-0.980905\pi$
$241$	− 6964.37i	− 0.119908i	0.998201	−	0.0599539i	$-0.0190954\pi$
$242$	−29401.9	−0.502048
$243$	3788.00i	0.0641500i
$244$	− 12598.1i	− 0.211605i
$245$	0	0
$246$	28655.6	0.473521
$247$	−101319.	−1.66072
$248$	− 1935.68i	− 0.0314724i
$249$	−10733.2	−0.173113
$250$	− 38209.4i	− 0.611350i
$251$	20168.7i	0.320133i	0.987106	+	0.160067i	$0.0511709\pi$
$251$	20168.7i	0.320133i	−0.987106	+	0.160067i	$0.948829\pi$
$252$	0	0
$253$	−19100.2	−0.298398
$254$	−76447.6	−1.18494
$255$	48.0681i	0 0.000739225i
$256$	4096.00	0.0625000
$257$	4937.00i	0.0747475i	0.999301	+	0.0373738i	$0.0118992\pi$
$257$	4937.00i	0.0747475i	−0.999301	+	0.0373738i	$0.988101\pi$
$258$	15601.8i	0.234389i
$259$	0	0
$260$	−31832.5	−0.470895
$261$	2262.44	0.0332121
$262$	60486.3i	0.881159i
$263$	79098.2	1.14355	0.571775	−	0.820410i	$-0.306255\pi$
$263$	79098.2	1.14355	0.571775	+	0.820410i	$0.306255\pi$
$264$	− 7661.24i	− 0.109924i
$265$	− 31314.4i	− 0.445915i
$266$	0	0
$267$	73382.6	1.02937
$268$	41000.5	0.570847
$269$	26116.1i	0.360914i	0.983583	+	0.180457i	$0.0577577\pi$
$269$	26116.1i	0.360914i	−0.983583	+	0.180457i	$0.942242\pi$
$270$	−4878.33	−0.0669181
$271$	− 77580.8i	− 1.05637i	−0.849130	−	0.528184i	$-0.822873\pi$
$271$	− 77580.8i	− 1.05637i	0.849130	−	0.528184i	$-0.177127\pi$
$272$	48.1587i	0 0.000650934i
$273$	0	0
$274$	5432.10	0.0723547
$275$	−30877.2	−0.408294
$276$	12185.1i	0.159959i
$277$	−20681.4	−0.269539	−0.134769	−	0.990877i	$-0.543029\pi$
$277$	−20681.4	−0.269539	−0.134769	+	0.990877i	$0.543029\pi$
$278$	49309.2i	0.638026i
$279$	2309.73i	0.0296725i
$280$	0	0
$281$	61112.5	0.773958	0.386979	−	0.922089i	$-0.373519\pi$
$281$	61112.5	0.773958	0.386979	+	0.922089i	$0.373519\pi$
$282$	40855.2	0.513746
$283$	− 123610.i	− 1.54341i	−0.635980	−	0.771705i	$-0.719404\pi$
$283$	− 123610.i	− 1.54341i	0.635980	−	0.771705i	$-0.280596\pi$
$284$	74045.6	0.918042
$285$	− 19996.4i	− 0.246186i
$286$	59652.3i	0.729282i
$287$	0	0
$288$	−4887.52	−0.0589256
$289$	83520.4	0.999993
$290$	2913.66i	0.0346451i
$291$	−85893.4	−1.01432
$292$	− 35300.4i	− 0.414013i
$293$	95807.9i	1.11601i	0.829839	+	0.558003i	$0.188432\pi$
$293$	95807.9i	1.11601i	−0.829839	+	0.558003i	$0.811568\pi$
$294$	0	0
$295$	28840.3	0.331403
$296$	−48628.0	−0.555013
$297$	9141.71i	0.103637i
$298$	90558.8	1.01976
$299$	− 94876.0i	− 1.06124i
$300$	19698.3i	0.218870i
$301$	0	0
$302$	87971.6	0.964559
$303$	−98802.8	−1.07618
$304$	− 20034.1i	− 0.216782i
$305$	−19359.6	−0.208112
$306$	− 57.4650i	0 0.000613707i
$307$	− 79487.6i	− 0.843378i	−0.906740	−	0.421689i	$-0.861437\pi$
$307$	− 79487.6i	− 0.843378i	0.906740	−	0.421689i	$-0.138563\pi$
$308$	0	0
$309$	22547.3	0.236145
$310$	−2974.57	−0.0309528
$311$	− 154223.i	− 1.59451i	−0.603643	−	0.797255i	$-0.706285\pi$
$311$	− 154223.i	− 1.59451i	0.603643	−	0.797255i	$-0.293715\pi$
$312$	38055.5	0.390938
$313$	− 60321.2i	− 0.615718i	−0.951432	−	0.307859i	$-0.900388\pi$
$313$	− 60321.2i	− 0.615718i	0.951432	−	0.307859i	$-0.0996124\pi$
$314$	− 28085.2i	− 0.284851i
$315$	0	0
$316$	−62656.3	−0.627467
$317$	88142.3	0.877134	0.438567	−	0.898699i	$-0.355486\pi$
$317$	88142.3	0.877134	0.438567	+	0.898699i	$0.355486\pi$
$318$	37436.1i	0.370200i
$319$	5460.03	0.0536554
$320$	− 6294.34i	− 0.0614682i
$321$	− 80274.8i	− 0.779056i
$322$	0	0
$323$	235.551	0.00225777
$324$	5832.00	0.0555556
$325$	− 153376.i	− 1.45208i
$326$	41454.3	0.390062
$327$	− 30006.6i	− 0.280621i
$328$	− 44118.2i	− 0.410081i
$329$	0	0
$330$	−11773.1	−0.108109
$331$	−174376.	−1.59159	−0.795795	−	0.605567i	$-0.792946\pi$
$331$	−174376.	−1.59159	−0.795795	+	0.605567i	$0.792946\pi$
$332$	16524.8i	0.149920i
$333$	58025.0	0.523271
$334$	19492.0i	0.174728i
$335$	− 63005.7i	− 0.561423i
$336$	0	0
$337$	91897.2	0.809175	0.404587	−	0.914499i	$-0.367415\pi$
$337$	91897.2	0.809175	0.404587	+	0.914499i	$0.367415\pi$
$338$	−215527.	−1.88655
$339$	− 101312.i	− 0.881579i
$340$	74.0057	0.000640188 0
$341$	5574.17i	0.0479371i
$342$	23905.6i	0.204384i
$343$	0	0
$344$	24020.6	0.202986
$345$	18724.8	0.157318
$346$	105774.i	0.883541i
$347$	191101.	1.58710	0.793548	−	0.608508i	$-0.208231\pi$
$347$	191101.	1.58710	0.793548	+	0.608508i	$0.208231\pi$
$348$	− 3483.25i	− 0.0287625i
$349$	26923.3i	0.221043i	0.993874	+	0.110522i	$0.0352521\pi$
$349$	26923.3i	0.221043i	−0.993874	+	0.110522i	$0.964748\pi$
$350$	0	0
$351$	−45409.5	−0.368580
$352$	−11795.2	−0.0951966
$353$	12865.7i	0.103248i	0.998667	+	0.0516242i	$0.0164398\pi$
$353$	12865.7i	0.103248i	−0.998667	+	0.0516242i	$0.983560\pi$
$354$	−34478.4	−0.275131
$355$	− 113786.i	− 0.902885i
$356$	− 112980.i	− 0.891459i
$357$	0	0
$358$	35045.1	0.273440
$359$	206380.	1.60132	0.800661	−	0.599118i	$-0.204482\pi$
$359$	206380.	1.60132	0.800661	+	0.599118i	$0.204482\pi$
$360$	7510.67i	0.0579527i
$361$	32331.1	0.248088
$362$	− 19346.8i	− 0.147636i
$363$	− 54014.8i	− 0.409921i
$364$	0	0
$365$	−54246.3	−0.407178
$366$	23144.2	0.172775
$367$	53938.4i	0.400466i	0.979748	+	0.200233i	$0.0641699\pi$
$367$	53938.4i	0.400466i	−0.979748	+	0.200233i	$0.935830\pi$
$368$	18760.1	0.138529
$369$	52643.7i	0.386628i
$370$	74726.8i	0.545850i
$371$	0	0
$372$	3556.07	0.0256971
$373$	130392.	0.937202	0.468601	−	0.883410i	$-0.344758\pi$
$373$	130392.	0.937202	0.468601	+	0.883410i	$0.344758\pi$
$374$	− 138.683i	0 0.000991468i
$375$	70195.1	0.499165
$376$	− 62900.7i	− 0.444917i
$377$	27121.5i	0.190823i
$378$	0	0
$379$	170413.	1.18638	0.593191	−	0.805062i	$-0.297868\pi$
$379$	170413.	1.18638	0.593191	+	0.805062i	$0.297868\pi$
$380$	−30786.5	−0.213203
$381$	− 140443.i	− 0.967499i
$382$	133082.	0.911995
$383$	− 248874.i	− 1.69661i	−0.529510	−	0.848304i	$-0.677624\pi$
$383$	− 248874.i	− 1.69661i	0.529510	−	0.848304i	$-0.322376\pi$
$384$	7524.83i	0.0510310i
$385$	0	0
$386$	−145322.	−0.975340
$387$	−28662.4	−0.191377
$388$	132241.i	0.878424i
$389$	−111254.	−0.735219	−0.367610	−	0.929980i	$-0.619824\pi$
$389$	−111254.	−0.735219	−0.367610	+	0.929980i	$0.619824\pi$
$390$	− 58480.0i	− 0.384484i
$391$	220.572i	0.00144277i
$392$	0	0
$393$	−111120.	−0.719463
$394$	45212.4	0.291250
$395$	96284.2i	0.617108i
$396$	14074.6	0.0897522
$397$	166854.i	1.05866i	0.848417	+	0.529329i	$0.177556\pi$
$397$	166854.i	1.05866i	−0.848417	+	0.529329i	$0.822444\pi$
$398$	− 61167.3i	− 0.386147i
$399$	0	0
$400$	30327.5	0.189547
$401$	4290.63	0.0266829	0.0133414	−	0.999911i	$-0.495753\pi$
$401$	4290.63	0.0266829	0.0133414	+	0.999911i	$0.495753\pi$
$402$	75322.8i	0.466095i
$403$	−27688.5	−0.170486
$404$	152117.i	0.931997i
$405$	− 8962.06i	− 0.0546384i
$406$	0	0
$407$	140034.	0.845366
$408$	−88.4732	−0.000531486 0
$409$	141282.i	0.844580i	0.906461	+	0.422290i	$0.138774\pi$
$409$	141282.i	0.844580i	−0.906461	+	0.422290i	$0.861226\pi$
$410$	−67796.6	−0.403311
$411$	9979.40i	0.0590773i
$412$	− 34713.9i	− 0.204507i
$413$	0	0
$414$	−22385.4	−0.130606
$415$	25393.7	0.147445
$416$	− 58590.3i	− 0.338563i
$417$	−90586.8	−0.520946
$418$	57692.3i	0.330191i
$419$	− 58056.6i	− 0.330692i	−0.986236	−	0.165346i	$-0.947126\pi$
$419$	− 58056.6i	− 0.330692i	0.986236	−	0.165346i	$-0.0528741\pi$
$420$	0	0
$421$	−128665.	−0.725933	−0.362967	−	0.931802i	$-0.618236\pi$
$421$	−128665.	−0.725933	−0.362967	+	0.931802i	$0.618236\pi$
$422$	−106825.	−0.599855
$423$	75055.7i	0.419472i
$424$	57636.7	0.320603
$425$	356.575i	0.00197412i
$426$	136030.i	0.749578i
$427$	0	0
$428$	−123591.	−0.674683
$429$	−109588.	−0.595456
$430$	− 36912.5i	− 0.199635i
$431$	−322471.	−1.73594	−0.867972	−	0.496614i	$-0.834577\pi$
$431$	−322471.	−1.73594	−0.867972	+	0.496614i	$0.834577\pi$
$432$	− 8978.95i	− 0.0481125i
$433$	− 232814.i	− 1.24175i	−0.783911	−	0.620873i	$-0.786778\pi$
$433$	− 232814.i	− 1.24175i	0.783911	−	0.620873i	$-0.213222\pi$
$434$	0	0
$435$	−5352.73	−0.0282876
$436$	−46198.1	−0.243025
$437$	− 91758.5i	− 0.480489i
$438$	64851.0	0.338040
$439$	54468.4i	0.282628i	0.989965	+	0.141314i	$0.0451327\pi$
$439$	54468.4i	0.282628i	−0.989965	+	0.141314i	$0.954867\pi$
$440$	18125.8i	0.0936250i
$441$	0	0
$442$	688.875	0.00352611
$443$	−17821.7	−0.0908117	−0.0454059	−	0.998969i	$-0.514458\pi$
$443$	−17821.7	−0.0908117	−0.0454059	+	0.998969i	$0.514458\pi$
$444$	− 89335.4i	− 0.453166i
$445$	−173617.	−0.876741
$446$	132020.i	0.663695i
$447$	166367.i	0.832630i
$448$	0	0
$449$	−222042.	−1.10139	−0.550696	−	0.834706i	$-0.685638\pi$
$449$	−222042.	−1.10139	−0.550696	+	0.834706i	$0.685638\pi$
$450$	−36188.0	−0.178706
$451$	127047.i	0.624614i
$452$	−155980.	−0.763469
$453$	161614.i	0.787559i
$454$	60455.8i	0.293309i
$455$	0	0
$456$	36805.1	0.177002
$457$	181120.	0.867231	0.433615	−	0.901098i	$-0.357238\pi$
$457$	181120.	0.867231	0.433615	+	0.901098i	$0.357238\pi$
$458$	44356.0i	0.211457i
$459$	105.570	0.000501089 0
$460$	− 28828.8i	− 0.136242i
$461$	329793.i	1.55181i	0.630847	+	0.775907i	$0.282708\pi$
$461$	329793.i	1.55181i	−0.630847	+	0.775907i	$0.717292\pi$
$462$	0	0
$463$	167169.	0.779821	0.389911	−	0.920853i	$-0.372506\pi$
$463$	167169.	0.779821	0.389911	+	0.920853i	$0.372506\pi$
$464$	−5362.82	−0.0249090
$465$	− 5464.63i	− 0.0252729i
$466$	54009.5	0.248713
$467$	− 299794.i	− 1.37464i	−0.726355	−	0.687320i	$-0.758787\pi$
$467$	− 299794.i	− 1.37464i	0.726355	−	0.687320i	$-0.241213\pi$
$468$	69912.4i	0.319200i
$469$	0	0
$470$	−96659.7	−0.437572
$471$	51595.8	0.232580
$472$	53082.9i	0.238271i
$473$	−69172.1	−0.309178
$474$	− 115107.i	− 0.512325i
$475$	− 148336.i	− 0.657445i
$476$	0	0
$477$	−68774.6	−0.302267
$478$	276459.	1.20997
$479$	38224.2i	0.166597i	0.996525	+	0.0832985i	$0.0265455\pi$
$479$	38224.2i	0.166597i	−0.996525	+	0.0832985i	$0.973454\pi$
$480$	11563.4	0.0501885
$481$	695588.i	3.00651i
$482$	− 19698.2i	− 0.0847877i
$483$	0	0
$484$	−83161.3	−0.355002
$485$	203216.	0.863922
$486$	10714.1i	0.0453609i
$487$	185056.	0.780271	0.390135	−	0.920757i	$-0.372428\pi$
$487$	185056.	0.780271	0.390135	+	0.920757i	$0.372428\pi$
$488$	− 35632.9i	− 0.149627i
$489$	76156.3i	0.318484i
$490$	0	0
$491$	40646.5	0.168601	0.0843005	−	0.996440i	$-0.473134\pi$
$491$	40646.5	0.168601	0.0843005	+	0.996440i	$0.473134\pi$
$492$	81050.3	0.334830
$493$	− 63.0533i	0 0.000259426i
$494$	−286574.	−1.17431
$495$	− 21628.5i	− 0.0882705i
$496$	− 5474.93i	− 0.0222544i
$497$	0	0
$498$	−30358.0	−0.122409
$499$	−26222.5	−0.105311	−0.0526555	−	0.998613i	$-0.516769\pi$
$499$	−26222.5	−0.105311	−0.0526555	+	0.998613i	$0.516769\pi$
$500$	− 108072.i	− 0.432290i
$501$	−35809.1	−0.142665
$502$	57045.8i	0.226369i
$503$	86233.7i	0.340832i	0.985372	+	0.170416i	$0.0545112\pi$
$503$	86233.7i	0.340832i	−0.985372	+	0.170416i	$0.945489\pi$
$504$	0	0
$505$	233758.	0.916610
$506$	−54023.5	−0.211000
$507$	− 395949.i	− 1.54036i
$508$	−216226.	−0.837879
$509$	279710.i	1.07962i	0.841785	+	0.539812i	$0.181505\pi$
$509$	279710.i	1.07962i	−0.841785	+	0.539812i	$0.818495\pi$
$510$	135.957i	0 0.000522711i
$511$	0	0
$512$	11585.2	0.0441942
$513$	−43917.4	−0.166879
$514$	13963.9i	0.0528545i
$515$	−53344.9	−0.201131
$516$	44128.7i	0.165738i
$517$	181135.i	0.677674i
$518$	0	0
$519$	−194319.	−0.721408
$520$	−90035.9	−0.332973
$521$	160145.i	0.589981i	0.955500	+	0.294990i	$0.0953164\pi$
$521$	160145.i	0.589981i	−0.955500	+	0.294990i	$0.904684\pi$
$522$	6399.14	0.0234845
$523$	409766.i	1.49807i	0.662530	+	0.749035i	$0.269483\pi$
$523$	409766.i	1.49807i	−0.662530	+	0.749035i	$0.730517\pi$
$524$	171081.i	0.623073i
$525$	0	0
$526$	223724.	0.808612
$527$	64.3715	0.000231778 0
$528$	− 21669.2i	− 0.0777277i
$529$	−193918.	−0.692956
$530$	− 88570.5i	− 0.315310i
$531$	− 63340.8i	− 0.224644i
$532$	0	0
$533$	−631078.	−2.22141
$534$	207557.	0.727873
$535$	189923.i	0.663544i
$536$	115967.	0.403650
$537$	64382.0i	0.223263i
$538$	73867.5i	0.255205i
$539$	0	0
$540$	−13798.0	−0.0473182
$541$	−104834.	−0.358185	−0.179092	−	0.983832i	$-0.557316\pi$
$541$	−104834.	−0.358185	−0.179092	+	0.983832i	$0.557316\pi$
$542$	− 219432.i	− 0.746965i
$543$	35542.4	0.120544
$544$	136.213i	0 0.000460280i
$545$	70992.8i	0.239013i
$546$	0	0
$547$	113968.	0.380898	0.190449	−	0.981697i	$-0.439006\pi$
$547$	113968.	0.380898	0.190449	+	0.981697i	$0.439006\pi$
$548$	15364.3	0.0511625
$549$	42518.7i	0.141070i
$550$	−87333.9	−0.288707
$551$	26230.3i	0.0863974i
$552$	34464.5i	0.113108i
$553$	0	0
$554$	−58495.9	−0.190593
$555$	−137282.	−0.445685
$556$	139467.i	0.451153i
$557$	108516.	0.349772	0.174886	−	0.984589i	$-0.444044\pi$
$557$	108516.	0.349772	0.174886	+	0.984589i	$0.444044\pi$
$558$	6532.92i	0.0209816i
$559$	− 343597.i	− 1.09958i
$560$	0	0
$561$	254.776	0.000809530 0
$562$	172852.	0.547271
$563$	440946.i	1.39113i	0.718462	+	0.695566i	$0.244846\pi$
$563$	440946.i	1.39113i	−0.718462	+	0.695566i	$0.755154\pi$
$564$	115556.	0.363274
$565$	239695.i	0.750865i
$566$	− 349622.i	− 1.09136i
$567$	0	0
$568$	209432.	0.649153
$569$	552837.	1.70755	0.853774	−	0.520644i	$-0.174308\pi$
$569$	552837.	1.70755	0.853774	+	0.520644i	$0.174308\pi$
$570$	− 56558.5i	− 0.174080i
$571$	209257.	0.641812	0.320906	−	0.947111i	$-0.396013\pi$
$571$	209257.	0.641812	0.320906	+	0.947111i	$0.396013\pi$
$572$	168722.i	0.515680i
$573$	244487.i	0.744641i
$574$	0	0
$575$	138903.	0.420123
$576$	−13824.0	−0.0416667
$577$	472723.i	1.41989i	0.704256	+	0.709946i	$0.251281\pi$
$577$	472723.i	1.41989i	−0.704256	+	0.709946i	$0.748719\pi$
$578$	236231.	0.707102
$579$	− 266973.i	− 0.796362i
$580$	8241.06i	0.0244978i
$581$	0	0
$582$	−242943.	−0.717230
$583$	−165976.	−0.488325
$584$	− 99844.7i	− 0.292752i
$585$	107435.	0.313930
$586$	270986.i	0.789135i
$587$	308785.i	0.896148i	0.893997	+	0.448074i	$0.147890\pi$
$587$	308785.i	0.896148i	−0.893997	+	0.448074i	$0.852110\pi$
$588$	0	0
$589$	−26778.7	−0.0771895
$590$	81572.7	0.234337
$591$	83060.6i	0.237804i
$592$	−137541.	−0.392453
$593$	− 349275.i	− 0.993249i	−0.867966	−	0.496624i	$-0.834573\pi$
$593$	− 349275.i	− 0.993249i	0.867966	−	0.496624i	$-0.165427\pi$
$594$	25856.7i	0.0732824i
$595$	0	0
$596$	256139.	0.721079
$597$	112372.	0.315288
$598$	− 268350.i	− 0.750411i
$599$	34714.2	0.0967506	0.0483753	−	0.998829i	$-0.484596\pi$
$599$	34714.2	0.0967506	0.0483753	+	0.998829i	$0.484596\pi$
$600$	55715.1i	0.154764i
$601$	− 183803.i	− 0.508865i	−0.967090	−	0.254433i	$-0.918111\pi$
$601$	− 183803.i	− 0.508865i	0.967090	−	0.254433i	$-0.0818887\pi$
$602$	0	0
$603$	−138377.	−0.380565
$604$	248821.	0.682046
$605$	127794.i	0.349141i
$606$	−279456.	−0.760972
$607$	− 665906.i	− 1.80732i	−0.428249	−	0.903661i	$-0.640870\pi$
$607$	− 665906.i	− 1.80732i	0.428249	−	0.903661i	$-0.359130\pi$
$608$	− 56665.1i	− 0.153288i
$609$	0	0
$610$	−54757.2	−0.147157
$611$	−899748.	−2.41012
$612$	− 162.536i	0 0.000433956i
$613$	464627.	1.23647	0.618235	−	0.785993i	$-0.287848\pi$
$613$	464627.	1.23647	0.618235	+	0.785993i	$0.287848\pi$
$614$	− 224825.i	− 0.596359i
$615$	− 124550.i	− 0.329302i
$616$	0	0
$617$	−671436.	−1.76374	−0.881870	−	0.471493i	$-0.843715\pi$
$617$	−671436.	−1.76374	−0.881870	+	0.471493i	$0.843715\pi$
$618$	63773.5	0.166979
$619$	− 541090.i	− 1.41217i	−0.708125	−	0.706087i	$-0.750459\pi$
$619$	− 541090.i	− 1.41217i	0.708125	−	0.706087i	$-0.249541\pi$
$620$	−8413.34	−0.0218869
$621$	− 41124.6i	− 0.106640i
$622$	− 436207.i	− 1.12749i
$623$	0	0
$624$	107637.	0.276435
$625$	130091.	0.333034
$626$	− 170614.i	− 0.435378i
$627$	−105987.	−0.269600
$628$	− 79436.9i	− 0.201420i
$629$	− 1617.14i	− 0.00408738i
$630$	0	0
$631$	44756.6	0.112408	0.0562041	−	0.998419i	$-0.482100\pi$
$631$	44756.6	0.112408	0.0562041	+	0.998419i	$0.482100\pi$
$632$	−177219.	−0.443686
$633$	− 196249.i	− 0.489780i
$634$	249304.	0.620227
$635$	332276.i	0.824046i
$636$	105885.i	0.261771i
$637$	0	0
$638$	15443.3	0.0379401
$639$	−249904.	−0.612028
$640$	− 17803.1i	− 0.0434645i
$641$	120619.	0.293562	0.146781	−	0.989169i	$-0.453109\pi$
$641$	120619.	0.293562	0.146781	+	0.989169i	$0.453109\pi$
$642$	− 227051.i	− 0.550876i
$643$	− 531715.i	− 1.28605i	−0.765846	−	0.643024i	$-0.777680\pi$
$643$	− 531715.i	− 1.28605i	0.765846	−	0.643024i	$-0.222320\pi$
$644$	0	0
$645$	67812.7	0.163001
$646$	666.240	0.00159649
$647$	− 168582.i	− 0.402719i	−0.979517	−	0.201359i	$-0.935464\pi$
$647$	− 168582.i	− 0.402719i	0.979517	−	0.201359i	$-0.0645359\pi$
$648$	16495.4	0.0392837
$649$	− 152863.i	− 0.362921i
$650$	− 433812.i	− 1.02677i
$651$	0	0
$652$	117250.	0.275816
$653$	−305781.	−0.717107	−0.358553	−	0.933509i	$-0.616730\pi$
$653$	−305781.	−0.717107	−0.358553	+	0.933509i	$0.616730\pi$
$654$	− 84871.4i	− 0.198429i
$655$	262901.	0.612787
$656$	− 124785.i	− 0.289971i
$657$	119139.i	0.276009i
$658$	0	0
$659$	341855.	0.787174	0.393587	−	0.919287i	$-0.371234\pi$
$659$	341855.	0.787174	0.393587	+	0.919287i	$0.371234\pi$
$660$	−33299.2	−0.0764445
$661$	572535.i	1.31039i	0.755462	+	0.655193i	$0.227413\pi$
$661$	572535.i	1.31039i	−0.755462	+	0.655193i	$0.772587\pi$
$662$	−493210.	−1.12542
$663$	1265.54i	0.00287906i
$664$	46739.2i	0.106010i
$665$	0	0
$666$	164120.	0.370009
$667$	−24562.3	−0.0552099
$668$	55131.7i	0.123552i
$669$	−242535.	−0.541905
$670$	− 178207.i	− 0.396986i
$671$	102612.i	0.227904i
$672$	0	0
$673$	−517235.	−1.14198	−0.570989	−	0.820958i	$-0.693440\pi$
$673$	−517235.	−1.14198	−0.570989	+	0.820958i	$0.693440\pi$
$674$	259924.	0.572173
$675$	− 66481.6i	− 0.145913i
$676$	−609603.	−1.33399
$677$	− 298140.i	− 0.650493i	−0.945629	−	0.325246i	$-0.894553\pi$
$677$	− 298140.i	− 0.650493i	0.945629	−	0.325246i	$-0.105447\pi$
$678$	− 286553.i	− 0.623370i
$679$	0	0
$680$	209.320	0.000452681 0
$681$	−111064.	−0.239486
$682$	15766.1i	0.0338966i
$683$	827969.	1.77490	0.887448	−	0.460909i	$-0.152476\pi$
$683$	827969.	1.77490	0.887448	+	0.460909i	$0.152476\pi$
$684$	67615.2i	0.144521i
$685$	− 23610.4i	− 0.0503178i
$686$	0	0
$687$	−81487.2	−0.172654
$688$	67940.5	0.143533
$689$	− 824451.i	− 1.73671i
$690$	52961.8	0.111241
$691$	− 641520.i	− 1.34355i	−0.740755	−	0.671776i	$-0.765532\pi$
$691$	− 641520.i	− 1.34355i	0.740755	−	0.671776i	$-0.234468\pi$
$692$	299174.i	0.624758i
$693$	0	0
$694$	540514.	1.12225
$695$	214320.	0.443704
$696$	− 9852.13i	− 0.0203382i
$697$	1467.16	0.00302004
$698$	76150.5i	0.156301i
$699$	99221.7i	0.203073i
$700$	0	0
$701$	573073.	1.16620	0.583101	−	0.812400i	$-0.301839\pi$
$701$	573073.	1.16620	0.583101	+	0.812400i	$0.301839\pi$
$702$	−128437.	−0.260626
$703$	672732.i	1.36123i
$704$	−33362.0	−0.0673142
$705$	− 177575.i	− 0.357276i
$706$	36389.6i	0.0730077i
$707$	0	0
$708$	−97519.5	−0.194547
$709$	−135203.	−0.268964	−0.134482	−	0.990916i	$-0.542937\pi$
$709$	−135203.	−0.268964	−0.134482	+	0.990916i	$0.542937\pi$
$710$	− 321836.i	− 0.638436i
$711$	211465.	0.418311
$712$	− 319555.i	− 0.630356i
$713$	− 25075.8i	− 0.0493259i
$714$	0	0
$715$	259276.	0.507167
$716$	99122.6	0.193351
$717$	507888.i	0.987937i
$718$	583731.	1.13231
$719$	− 701786.i	− 1.35752i	−0.734359	−	0.678761i	$-0.762517\pi$
$719$	− 701786.i	− 1.35752i	0.734359	−	0.678761i	$-0.237483\pi$
$720$	21243.4i	0.0409788i
$721$	0	0
$722$	91446.2	0.175425
$723$	36187.9	0.0692289
$724$	− 54721.1i	− 0.104394i
$725$	−39707.2	−0.0755428
$726$	− 152777.i	− 0.289858i
$727$	988380.i	1.87006i	0.354571	+	0.935029i	$0.384627\pi$
$727$	988380.i	1.87006i	−0.354571	+	0.935029i	$0.615373\pi$
$728$	0	0
$729$	−19683.0	−0.0370370
$730$	−153432.	−0.287918
$731$	798.811i	0.00149489i
$732$	65461.7	0.122170
$733$	170331.i	0.317019i	0.987357	+	0.158510i	$0.0506689\pi$
$733$	170331.i	0.317019i	−0.987357	+	0.158510i	$0.949331\pi$
$734$	152561.i	0.283172i
$735$	0	0
$736$	53061.6	0.0979546
$737$	−333950.	−0.614818
$738$	148899.i	0.273387i
$739$	−437499.	−0.801103	−0.400551	−	0.916274i	$-0.631181\pi$
$739$	−437499.	−0.801103	−0.400551	+	0.916274i	$0.631181\pi$
$740$	211359.i	0.385974i
$741$	− 526469.i	− 0.958819i
$742$	0	0
$743$	543550.	0.984604	0.492302	−	0.870425i	$-0.336156\pi$
$743$	543550.	0.984604	0.492302	+	0.870425i	$0.336156\pi$
$744$	10058.1	0.0181706
$745$	− 393610.i	− 0.709174i
$746$	368804.	0.662702
$747$	− 55771.2i	− 0.0999468i
$748$	− 392.254i	0 0.000701074i
$749$	0	0
$750$	198542.	0.352963
$751$	−409532.	−0.726119	−0.363060	−	0.931766i	$-0.618268\pi$
$751$	−409532.	−0.726119	−0.363060	+	0.931766i	$0.618268\pi$
$752$	− 177910.i	− 0.314604i
$753$	−104800.	−0.184829
$754$	76711.2i	0.134932i
$755$	− 382365.i	− 0.670786i
$756$	0	0
$757$	853854.	1.49002	0.745009	−	0.667054i	$-0.232445\pi$
$757$	853854.	1.49002	0.745009	+	0.667054i	$0.232445\pi$
$758$	482001.	0.838898
$759$	− 99247.5i	− 0.172280i
$760$	−87077.5	−0.150757
$761$	557851.i	0.963272i	0.876371	+	0.481636i	$0.159957\pi$
$761$	557851.i	0.963272i	−0.876371	+	0.481636i	$0.840043\pi$
$762$	− 397233.i	− 0.684125i
$763$	0	0
$764$	376413.	0.644878
$765$	−249.769	−0.000426792 0
$766$	− 703921.i	− 1.19968i
$767$	759312.	1.29071
$768$	21283.4i	0.0360844i
$769$	− 169329.i	− 0.286338i	−0.989698	−	0.143169i	$-0.954271\pi$
$769$	− 169329.i	− 0.286338i	0.989698	−	0.143169i	$-0.0457293\pi$
$770$	0	0
$771$	−25653.4	−0.0431555
$772$	−411032.	−0.689670
$773$	− 171006.i	− 0.286188i	−0.989709	−	0.143094i	$-0.954295\pi$
$773$	− 171006.i	− 0.286188i	0.989709	−	0.143094i	$-0.0457052\pi$
$774$	−81069.5	−0.135324
$775$	− 40537.3i	− 0.0674918i
$776$	374035.i	0.621140i
$777$	0	0
$778$	−314674.	−0.519878
$779$	−610342.	−1.00577
$780$	− 165407.i	− 0.271871i
$781$	−603102.	−0.988755
$782$	623.872i	0.00102019i
$783$	11756.0i	0.0191750i
$784$	0	0
$785$	−122071.	−0.198095
$786$	−314296.	−0.508737
$787$	− 311272.i	− 0.502564i	−0.967914	−	0.251282i	$-0.919148\pi$
$787$	− 311272.i	− 0.502564i	0.967914	−	0.251282i	$-0.0808521\pi$
$788$	127880.	0.205945
$789$	411006.i	0.660229i
$790$	272333.i	0.436361i
$791$	0	0
$792$	39808.9	0.0634644
$793$	−509702.	−0.810532
$794$	471934.i	0.748584i
$795$	162714.	0.257449
$796$	− 173007.i	− 0.273048i
$797$	− 133867.i	− 0.210745i	−0.994433	−	0.105373i	$-0.966396\pi$
$797$	− 133867.i	− 0.210745i	0.994433	−	0.105373i	$-0.0336036\pi$
$798$	0	0
$799$	2091.78	0.00327659
$800$	85779.0	0.134030
$801$	381307.i	0.594306i
$802$	12135.7	0.0188677
$803$	287523.i	0.445903i
$804$	213045.i	0.329579i
$805$	0	0
$806$	−78314.8	−0.120552
$807$	−135703.	−0.208374
$808$	430251.i	0.659021i
$809$	−192248.	−0.293741	−0.146870	−	0.989156i	$-0.546920\pi$
$809$	−192248.	−0.293741	−0.146870	+	0.989156i	$0.546920\pi$
$810$	− 25348.5i	− 0.0386352i
$811$	947738.i	1.44094i	0.693485	+	0.720471i	$0.256074\pi$
$811$	947738.i	1.44094i	−0.693485	+	0.720471i	$0.743926\pi$
$812$	0	0
$813$	403121.	0.609895
$814$	396076.	0.597764
$815$	− 180179.i	− 0.271262i
$816$	−250.240	−0.000375817 0
$817$	− 332307.i	− 0.497846i
$818$	399606.i	0.597208i
$819$	0	0
$820$	−191758.	−0.285184
$821$	−281860.	−0.418165	−0.209082	−	0.977898i	$-0.567048\pi$
$821$	−281860.	−0.418165	−0.209082	+	0.977898i	$0.567048\pi$
$822$	28226.0i	0.0417740i
$823$	715907.	1.05696	0.528478	−	0.848947i	$-0.322763\pi$
$823$	715907.	1.05696	0.528478	+	0.848947i	$0.322763\pi$
$824$	− 98185.7i	− 0.144608i
$825$	− 160443.i	− 0.235728i
$826$	0	0
$827$	437240.	0.639306	0.319653	−	0.947535i	$-0.396434\pi$
$827$	437240.	0.639306	0.319653	+	0.947535i	$0.396434\pi$
$828$	−63315.4	−0.0923525
$829$	499067.i	0.726190i	0.931752	+	0.363095i	$0.118280\pi$
$829$	499067.i	0.726190i	−0.931752	+	0.363095i	$0.881720\pi$
$830$	71824.4	0.104259
$831$	− 107464.i	− 0.155618i
$832$	− 165718.i	− 0.239400i
$833$	0	0
$834$	−256218.	−0.368364
$835$	84721.1	0.121512
$836$	163178.i	0.233480i
$837$	−12001.7	−0.0171314
$838$	− 164209.i	− 0.233835i
$839$	67860.2i	0.0964031i	0.998838	+	0.0482016i	$0.0153490\pi$
$839$	67860.2i	0.0964031i	−0.998838	+	0.0482016i	$0.984651\pi$
$840$	0	0
$841$	−700260.	−0.990073
$842$	−363920.	−0.513312
$843$	317550.i	0.446845i
$844$	−302146.	−0.424162
$845$	936779.i	1.31197i
$846$	212290.i	0.296612i
$847$	0	0
$848$	163021.	0.226700
$849$	642298.	0.891089
$850$	1008.55i	0.00139591i
$851$	−629952.	−0.869857
$852$	384752.i	0.530032i
$853$	147552.i	0.202790i	0.994846	+	0.101395i	$0.0323306\pi$
$853$	147552.i	0.202790i	−0.994846	+	0.101395i	$0.967669\pi$
$854$	0	0
$855$	103905.	0.142135
$856$	−349568.	−0.477073
$857$	461092.i	0.627806i	0.949455	+	0.313903i	$0.101637\pi$
$857$	461092.i	0.627806i	−0.949455	+	0.313903i	$0.898363\pi$
$858$	−309963.	−0.421051
$859$	− 391343.i	− 0.530361i	−0.964199	−	0.265180i	$-0.914568\pi$
$859$	− 391343.i	− 0.530361i	0.964199	−	0.265180i	$-0.0854315\pi$
$860$	− 104404.i	− 0.141163i
$861$	0	0
$862$	−912085.	−1.22750
$863$	972964.	1.30640	0.653198	−	0.757187i	$-0.273427\pi$
$863$	972964.	1.30640	0.653198	+	0.757187i	$0.273427\pi$
$864$	− 25396.3i	− 0.0340207i
$865$	459742.	0.614443
$866$	− 658496.i	− 0.878047i
$867$	433985.i	0.577346i
$868$	0	0
$869$	510337.	0.675799
$870$	−15139.8	−0.0200024
$871$	− 1.65882e6i	− 2.18657i
$872$	−130668.	−0.171845
$873$	− 446315.i	− 0.585616i
$874$	− 259532.i	− 0.339757i
$875$	0	0
$876$	183426.	0.239031
$877$	444095.	0.577400	0.288700	−	0.957420i	$-0.406777\pi$
$877$	444095.	0.577400	0.288700	+	0.957420i	$0.406777\pi$
$878$	154060.i	0.199848i
$879$	−497833.	−0.644326
$880$	51267.5i	0.0662029i
$881$	623969.i	0.803917i	0.915658	+	0.401959i	$0.131670\pi$
$881$	623969.i	0.803917i	−0.915658	+	0.401959i	$0.868330\pi$
$882$	0	0
$883$	−1.11109e6	−1.42504	−0.712522	−	0.701650i	$-0.752447\pi$
$883$	−1.11109e6	−1.42504	−0.712522	+	0.701650i	$0.752447\pi$
$884$	1948.43	0.00249334
$885$	149859.i	0.191335i
$886$	−50407.4	−0.0642136
$887$	1.35740e6i	1.72528i	0.505814	+	0.862642i	$0.331192\pi$
$887$	1.35740e6i	1.72528i	−0.505814	+	0.862642i	$0.668808\pi$
$888$	− 252679.i	− 0.320437i
$889$	0	0
$890$	−491062.	−0.619949
$891$	−47501.7	−0.0598348
$892$	373408.i	0.469303i
$893$	−870183.	−1.09121
$894$	470557.i	0.588759i
$895$	− 152322.i	− 0.190159i
$896$	0	0
$897$	492990.	0.612708
$898$	−628029.	−0.778802
$899$	7168.22i	0.00886936i
$900$	−102355.	−0.126364
$901$	1916.72i	0.00236107i
$902$	359343.i	0.441669i
$903$	0	0
$904$	−441178.	−0.539854
$905$	−84090.1	−0.102671
$906$	457114.i	0.556888i
$907$	−793450.	−0.964506	−0.482253	−	0.876032i	$-0.660181\pi$
$907$	−793450.	−0.964506	−0.482253	+	0.876032i	$0.660181\pi$
$908$	170995.i	0.207401i
$909$	− 513394.i	− 0.621331i
$910$	0	0
$911$	−116593.	−0.140487	−0.0702437	−	0.997530i	$-0.522378\pi$
$911$	−116593.	−0.140487	−0.0702437	+	0.997530i	$0.522378\pi$
$912$	104100.	0.125159
$913$	− 134595.i	− 0.161468i
$914$	512286.	0.613225
$915$	− 100595.i	− 0.120153i
$916$	125458.i	0.149523i
$917$	0	0
$918$	298.597	0.000354324 0
$919$	768109.	0.909477	0.454738	−	0.890625i	$-0.349733\pi$
$919$	768109.	0.909477	0.454738	+	0.890625i	$0.349733\pi$
$920$	− 81540.0i	− 0.0963375i
$921$	413030.	0.486925
$922$	932796.i	1.09730i
$923$	− 2.99578e6i	− 3.51646i
$924$	0	0
$925$	−1.01837e6	−1.19021
$926$	472827.	0.551417
$927$	117159.i	0.136338i
$928$	−15168.3	−0.0176134
$929$	− 511470.i	− 0.592637i	−0.955089	−	0.296318i	$-0.904241\pi$
$929$	− 511470.i	− 0.592637i	0.955089	−	0.296318i	$-0.0957590\pi$
$930$	− 15456.3i	− 0.0178706i
$931$	0	0
$932$	152762.	0.175866
$933$	801364.	0.920590
$934$	− 847945.i	− 0.972017i
$935$	−602.778	−0.000689499 0
$936$	197742.i	0.225708i
$937$	− 172562.i	− 0.196546i	−0.995159	−	0.0982732i	$-0.968668\pi$
$937$	− 172562.i	− 0.196546i	0.995159	−	0.0982732i	$-0.0313319\pi$
$938$	0	0
$939$	313438.	0.355485
$940$	−273395.	−0.309410
$941$	266447.i	0.300907i	0.988617	+	0.150453i	$0.0480734\pi$
$941$	266447.i	0.300907i	−0.988617	+	0.150453i	$0.951927\pi$
$942$	145935.	0.164459
$943$	− 571529.i	− 0.642710i
$944$	150141.i	0.168483i
$945$	0	0
$946$	−195648.	−0.218622
$947$	1.24479e6	1.38802	0.694011	−	0.719964i	$-0.255842\pi$
$947$	1.24479e6	1.38802	0.694011	+	0.719964i	$0.255842\pi$
$948$	− 325572.i	− 0.362268i
$949$	−1.42821e6	−1.58584
$950$	− 419558.i	− 0.464884i
$951$	458001.i	0.506413i
$952$	0	0
$953$	−1.50615e6	−1.65838	−0.829188	−	0.558970i	$-0.811197\pi$
$953$	−1.50615e6	−1.65838	−0.829188	+	0.558970i	$0.811197\pi$
$954$	−194524.	−0.213735
$955$	− 578435.i	− 0.634231i
$956$	781944.	0.855579
$957$	28371.1i	0.0309780i
$958$	108114.i	0.117802i
$959$	0	0
$960$	32706.3	0.0354887
$961$	916203.	0.992076
$962$	1.96742e6i	2.12592i
$963$	417120.	0.449788
$964$	− 55715.0i	− 0.0599539i
$965$	631635.i	0.678284i
$966$	0	0
$967$	−15303.5	−0.0163659	−0.00818293	−	0.999967i	$-0.502605\pi$
$967$	−15303.5	−0.0163659	−0.00818293	+	0.999967i	$0.502605\pi$
$968$	−235216.	−0.251024
$969$	1223.96i	0.00130353i
$970$	574782.	0.610885
$971$	1.10327e6i	1.17016i	0.810976	+	0.585079i	$0.198937\pi$
$971$	1.10327e6i	1.17016i	−0.810976	+	0.585079i	$0.801063\pi$
$972$	30304.0i	0.0320750i
$973$	0	0
$974$	523418.	0.551735
$975$	796964.	0.838358
$976$	− 100785.i	− 0.105803i
$977$	−477937.	−0.500705	−0.250352	−	0.968155i	$-0.580546\pi$
$977$	−477937.	−0.500705	−0.250352	+	0.968155i	$0.580546\pi$
$978$	215403.i	0.225203i
$979$	920223.i	0.960125i
$980$	0	0
$981$	155919.	0.162017
$982$	114966.	0.119219
$983$	1.21701e6i	1.25947i	0.776811	+	0.629734i	$0.216836\pi$
$983$	1.21701e6i	1.25947i	−0.776811	+	0.629734i	$0.783164\pi$
$984$	229245.	0.236761
$985$	− 196514.i	− 0.202545i
$986$	− 178.342i	0 0.000183442i
$987$	0	0
$988$	−810553.	−0.830362
$989$	311175.	0.318135
$990$	− 61174.6i	− 0.0624167i
$991$	−1.42518e6	−1.45118	−0.725592	−	0.688126i	$-0.758434\pi$
$991$	−1.42518e6	−1.45118	−0.725592	+	0.688126i	$0.758434\pi$
$992$	− 15485.4i	− 0.0157362i
$993$	− 906085.i	− 0.918904i
$994$	0	0
$995$	−265861.	−0.268540
$996$	−85865.4	−0.0865565
$997$	− 376761.i	− 0.379032i	−0.981878	−	0.189516i	$-0.939308\pi$
$997$	− 376761.i	− 0.379032i	0.981878	−	0.189516i	$-0.0606919\pi$
$998$	−74168.5	−0.0744661
$999$	301507.i	0.302111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.5.c.b.97.8	yes	8
3.2	odd	2		882.5.c.f.685.3		8
7.2	even	3		294.5.g.e.31.2		8
7.3	odd	6		294.5.g.e.19.2		8
7.4	even	3		294.5.g.g.19.1		8
7.5	odd	6		294.5.g.g.31.1		8
7.6	odd	2	inner	294.5.c.b.97.5	✓	8
21.20	even	2		882.5.c.f.685.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.5.c.b.97.5	✓	8	7.6	odd	2	inner
294.5.c.b.97.8	yes	8	1.1	even	1	trivial
294.5.g.e.19.2		8	7.3	odd	6
294.5.g.e.31.2		8	7.2	even	3
294.5.g.g.19.1		8	7.4	even	3
294.5.g.g.31.1		8	7.5	odd	6
882.5.c.f.685.2		8	21.20	even	2
882.5.c.f.685.3		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	294.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843 q^{2} +5.19615i q^{3} +8.00000 q^{4} -12.2936i q^{5} +14.6969i q^{6} +22.6274 q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+2.82843 q^{2} +5.19615i q^{3} +8.00000 q^{4} -12.2936i q^{5} +14.6969i q^{6} +22.6274 q^{8} -27.0000 q^{9} -34.7716i q^{10} -65.1601 q^{11} +41.5692i q^{12} -323.669i q^{13} +63.8796 q^{15} +64.0000 q^{16} +0.752480i q^{17} -76.3675 q^{18} -313.033i q^{19} -98.3490i q^{20} -184.301 q^{22} +293.127 q^{23} +117.576i q^{24} +473.867 q^{25} -915.473i q^{26} -140.296i q^{27} -83.7940 q^{29} +180.679 q^{30} -85.5457i q^{31} +181.019 q^{32} -338.582i q^{33} +2.12834i q^{34} -216.000 q^{36} -2149.07 q^{37} -885.392i q^{38} +1681.83 q^{39} -278.173i q^{40} -1949.77i q^{41} +1061.57 q^{43} -521.281 q^{44} +331.928i q^{45} +829.088 q^{46} -2779.84i q^{47} +332.554i q^{48} +1340.30 q^{50} -3.91000 q^{51} -2589.35i q^{52} +2547.21 q^{53} -396.817i q^{54} +801.055i q^{55} +1626.57 q^{57} -237.005 q^{58} +2345.95i q^{59} +511.037 q^{60} -1574.76i q^{61} -241.960i q^{62} +512.000 q^{64} -3979.06 q^{65} -957.654i q^{66} +5125.07 q^{67} +6.01984i q^{68} +1523.13i q^{69} +9255.69 q^{71} -610.940 q^{72} -4412.55i q^{73} -6078.50 q^{74} +2462.28i q^{75} -2504.27i q^{76} +4756.94 q^{78} -7832.04 q^{79} -786.792i q^{80} +729.000 q^{81} -5514.77i q^{82} +2065.60i q^{83} +9.25071 q^{85} +3002.58 q^{86} -435.407i q^{87} -1474.41 q^{88} -14122.5i q^{89} +938.834i q^{90} +2345.02 q^{92} +444.509 q^{93} -7862.58i q^{94} -3848.32 q^{95} +940.604i q^{96} +16530.2i q^{97} +1759.32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 64 q^{4} - 216 q^{9}+O(q^{10}) \) 8 * q + 64 * q^4 - 216 * q^9	\( 8 q + 64 q^{4} - 216 q^{9} + 512 q^{16} - 1312 q^{22} - 272 q^{23} - 2808 q^{25} + 400 q^{29} + 3168 q^{30} - 1728 q^{36} - 3328 q^{37} + 656 q^{43} - 2400 q^{46} + 800 q^{50} + 7200 q^{51} + 9264 q^{53} + 1152 q^{57} - 11488 q^{58} + 4096 q^{64} - 15696 q^{65} + 26816 q^{67} + 28192 q^{71} - 4512 q^{74} + 9216 q^{78} + 19728 q^{79} + 5832 q^{81} - 49632 q^{85} + 5888 q^{86} - 10496 q^{88} - 2176 q^{92} + 15264 q^{93} - 92752 q^{95}+O(q^{100}) \) 8 * q + 64 * q^4 - 216 * q^9 + 512 * q^16 - 1312 * q^22 - 272 * q^23 - 2808 * q^25 + 400 * q^29 + 3168 * q^30 - 1728 * q^36 - 3328 * q^37 + 656 * q^43 - 2400 * q^46 + 800 * q^50 + 7200 * q^51 + 9264 * q^53 + 1152 * q^57 - 11488 * q^58 + 4096 * q^64 - 15696 * q^65 + 26816 * q^67 + 28192 * q^71 - 4512 * q^74 + 9216 * q^78 + 19728 * q^79 + 5832 * q^81 - 49632 * q^85 + 5888 * q^86 - 10496 * q^88 - 2176 * q^92 + 15264 * q^93 - 92752 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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