LMFDB - Embedded newform 3549.2.a.bh.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + \cdots + 281 $ x^15 - 2x^14 - 27x^13 + 51x^12 + 290x^11 - 510x^10 - 1575x^9 + 2522x^8 + 4553x^7 - 6393x^6 - 6785x^5 + 7806x^4 + 4632x^3 - 3811x^2 - 1041x + 281
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.89376$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.89376 q^{2} +1.00000 q^{3} +1.58633 q^{4} +0.892462 q^{5} -1.89376 q^{6} -1.00000 q^{7} +0.783390 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.89376 q^{2} +1.00000 q^{3} +1.58633 q^{4} +0.892462 q^{5} -1.89376 q^{6} -1.00000 q^{7} +0.783390 q^{8} +1.00000 q^{9} -1.69011 q^{10} -5.27707 q^{11} +1.58633 q^{12} +1.89376 q^{14} +0.892462 q^{15} -4.65622 q^{16} +4.75966 q^{17} -1.89376 q^{18} +0.639234 q^{19} +1.41574 q^{20} -1.00000 q^{21} +9.99350 q^{22} +4.64933 q^{23} +0.783390 q^{24} -4.20351 q^{25} +1.00000 q^{27} -1.58633 q^{28} -3.84995 q^{29} -1.69011 q^{30} +2.03627 q^{31} +7.25098 q^{32} -5.27707 q^{33} -9.01366 q^{34} -0.892462 q^{35} +1.58633 q^{36} +0.645805 q^{37} -1.21056 q^{38} +0.699146 q^{40} -7.73993 q^{41} +1.89376 q^{42} +10.5241 q^{43} -8.37118 q^{44} +0.892462 q^{45} -8.80472 q^{46} -7.04313 q^{47} -4.65622 q^{48} +1.00000 q^{49} +7.96045 q^{50} +4.75966 q^{51} +8.06403 q^{53} -1.89376 q^{54} -4.70958 q^{55} -0.783390 q^{56} +0.639234 q^{57} +7.29089 q^{58} -11.1500 q^{59} +1.41574 q^{60} +0.832403 q^{61} -3.85621 q^{62} -1.00000 q^{63} -4.41919 q^{64} +9.99350 q^{66} +11.8274 q^{67} +7.55039 q^{68} +4.64933 q^{69} +1.69011 q^{70} +7.42431 q^{71} +0.783390 q^{72} +9.57578 q^{73} -1.22300 q^{74} -4.20351 q^{75} +1.01404 q^{76} +5.27707 q^{77} -0.136717 q^{79} -4.15549 q^{80} +1.00000 q^{81} +14.6576 q^{82} +14.7716 q^{83} -1.58633 q^{84} +4.24781 q^{85} -19.9301 q^{86} -3.84995 q^{87} -4.13400 q^{88} -5.50508 q^{89} -1.69011 q^{90} +7.37537 q^{92} +2.03627 q^{93} +13.3380 q^{94} +0.570492 q^{95} +7.25098 q^{96} +7.63761 q^{97} -1.89376 q^{98} -5.27707 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9} + 21 q^{10} + 5 q^{11} + 28 q^{12} - 2 q^{14} - 9 q^{15} + 50 q^{16} - q^{17} + 2 q^{18} + 3 q^{19} - 23 q^{20} - 15 q^{21} + 21 q^{22} + 4 q^{23} + 9 q^{24} + 50 q^{25} + 15 q^{27} - 28 q^{28} + 9 q^{29} + 21 q^{30} + 7 q^{31} + 35 q^{32} + 5 q^{33} - 2 q^{34} + 9 q^{35} + 28 q^{36} + 17 q^{37} - 12 q^{38} + 46 q^{40} - 22 q^{41} - 2 q^{42} + 36 q^{43} + 29 q^{44} - 9 q^{45} - q^{46} - 12 q^{47} + 50 q^{48} + 15 q^{49} + 53 q^{50} - q^{51} - 5 q^{53} + 2 q^{54} + 43 q^{55} - 9 q^{56} + 3 q^{57} + 29 q^{58} - 29 q^{59} - 23 q^{60} + 12 q^{61} + 14 q^{62} - 15 q^{63} + 95 q^{64} + 21 q^{66} - 12 q^{67} - 16 q^{68} + 4 q^{69} - 21 q^{70} + 36 q^{71} + 9 q^{72} - 29 q^{73} - 5 q^{74} + 50 q^{75} + 25 q^{76} - 5 q^{77} + 35 q^{79} - 89 q^{80} + 15 q^{81} + 51 q^{82} - 10 q^{83} - 28 q^{84} + 23 q^{85} + 19 q^{86} + 9 q^{87} + 73 q^{88} + 25 q^{89} + 21 q^{90} - 31 q^{92} + 7 q^{93} - 19 q^{94} - 7 q^{95} + 35 q^{96} - 26 q^{97} + 2 q^{98} + 5 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9 + 21 * q^10 + 5 * q^11 + 28 * q^12 - 2 * q^14 - 9 * q^15 + 50 * q^16 - q^17 + 2 * q^18 + 3 * q^19 - 23 * q^20 - 15 * q^21 + 21 * q^22 + 4 * q^23 + 9 * q^24 + 50 * q^25 + 15 * q^27 - 28 * q^28 + 9 * q^29 + 21 * q^30 + 7 * q^31 + 35 * q^32 + 5 * q^33 - 2 * q^34 + 9 * q^35 + 28 * q^36 + 17 * q^37 - 12 * q^38 + 46 * q^40 - 22 * q^41 - 2 * q^42 + 36 * q^43 + 29 * q^44 - 9 * q^45 - q^46 - 12 * q^47 + 50 * q^48 + 15 * q^49 + 53 * q^50 - q^51 - 5 * q^53 + 2 * q^54 + 43 * q^55 - 9 * q^56 + 3 * q^57 + 29 * q^58 - 29 * q^59 - 23 * q^60 + 12 * q^61 + 14 * q^62 - 15 * q^63 + 95 * q^64 + 21 * q^66 - 12 * q^67 - 16 * q^68 + 4 * q^69 - 21 * q^70 + 36 * q^71 + 9 * q^72 - 29 * q^73 - 5 * q^74 + 50 * q^75 + 25 * q^76 - 5 * q^77 + 35 * q^79 - 89 * q^80 + 15 * q^81 + 51 * q^82 - 10 * q^83 - 28 * q^84 + 23 * q^85 + 19 * q^86 + 9 * q^87 + 73 * q^88 + 25 * q^89 + 21 * q^90 - 31 * q^92 + 7 * q^93 - 19 * q^94 - 7 * q^95 + 35 * q^96 - 26 * q^97 + 2 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.89376	−1.33909	−0.669546	−	0.742771i	$-0.733511\pi$
$2$	−1.89376	−1.33909	−0.669546	+	0.742771i	$0.733511\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.58633	0.793165
$5$	0.892462	0.399121	0.199561	−	0.979886i	$-0.436049\pi$
$5$	0.892462	0.399121	0.199561	+	0.979886i	$0.436049\pi$
$6$	−1.89376	−0.773125
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.783390	0.276970
$9$	1.00000	0.333333
$10$	−1.69011	−0.534459
$11$	−5.27707	−1.59110	−0.795548	−	0.605891i	$-0.792817\pi$
$11$	−5.27707	−1.59110	−0.795548	+	0.605891i	$0.792817\pi$
$12$	1.58633	0.457934
$13$	0	0
$13$	0	0
$14$	1.89376	0.506129
$15$	0.892462	0.230433
$16$	−4.65622	−1.16405
$17$	4.75966	1.15439	0.577193	−	0.816608i	$-0.304148\pi$
$17$	4.75966	1.15439	0.577193	+	0.816608i	$0.304148\pi$
$18$	−1.89376	−0.446364
$19$	0.639234	0.146650	0.0733251	−	0.997308i	$-0.476639\pi$
$19$	0.639234	0.146650	0.0733251	+	0.997308i	$0.476639\pi$
$20$	1.41574	0.316569
$21$	−1.00000	−0.218218
$22$	9.99350	2.13062
$23$	4.64933	0.969452	0.484726	−	0.874666i	$-0.338919\pi$
$23$	4.64933	0.969452	0.484726	+	0.874666i	$0.338919\pi$
$24$	0.783390	0.159909
$25$	−4.20351	−0.840702
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.58633	−0.299788
$29$	−3.84995	−0.714918	−0.357459	−	0.933929i	$-0.616357\pi$
$29$	−3.84995	−0.714918	−0.357459	+	0.933929i	$0.616357\pi$
$30$	−1.69011	−0.308570
$31$	2.03627	0.365725	0.182862	−	0.983139i	$-0.441464\pi$
$31$	2.03627	0.365725	0.182862	+	0.983139i	$0.441464\pi$
$32$	7.25098	1.28180
$33$	−5.27707	−0.918619
$34$	−9.01366	−1.54583
$35$	−0.892462	−0.150854
$36$	1.58633	0.264388
$37$	0.645805	0.106170	0.0530849	−	0.998590i	$-0.483095\pi$
$37$	0.645805	0.106170	0.0530849	+	0.998590i	$0.483095\pi$
$38$	−1.21056	−0.196378
$39$	0	0
$40$	0.699146	0.110545
$41$	−7.73993	−1.20877	−0.604387	−	0.796691i	$-0.706582\pi$
$41$	−7.73993	−1.20877	−0.604387	+	0.796691i	$0.706582\pi$
$42$	1.89376	0.292214
$43$	10.5241	1.60491	0.802454	−	0.596713i	$-0.203527\pi$
$43$	10.5241	1.60491	0.802454	+	0.596713i	$0.203527\pi$
$44$	−8.37118	−1.26200
$45$	0.892462	0.133040
$46$	−8.80472	−1.29818
$47$	−7.04313	−1.02735	−0.513673	−	0.857986i	$-0.671716\pi$
$47$	−7.04313	−1.02735	−0.513673	+	0.857986i	$0.671716\pi$
$48$	−4.65622	−0.672067
$49$	1.00000	0.142857
$50$	7.96045	1.12578
$51$	4.75966	0.666485
$52$	0	0
$53$	8.06403	1.10768	0.553840	−	0.832623i	$-0.313162\pi$
$53$	8.06403	1.10768	0.553840	+	0.832623i	$0.313162\pi$
$54$	−1.89376	−0.257708
$55$	−4.70958	−0.635040
$56$	−0.783390	−0.104685
$57$	0.639234	0.0846686
$58$	7.29089	0.957340
$59$	−11.1500	−1.45161	−0.725805	−	0.687900i	$-0.758533\pi$
$59$	−11.1500	−1.45161	−0.725805	+	0.687900i	$0.758533\pi$
$60$	1.41574	0.182771
$61$	0.832403	0.106578	0.0532891	−	0.998579i	$-0.483030\pi$
$61$	0.832403	0.106578	0.0532891	+	0.998579i	$0.483030\pi$
$62$	−3.85621	−0.489739
$63$	−1.00000	−0.125988
$64$	−4.41919	−0.552399
$65$	0	0
$66$	9.99350	1.23012
$67$	11.8274	1.44495	0.722476	−	0.691396i	$-0.243004\pi$
$67$	11.8274	1.44495	0.722476	+	0.691396i	$0.243004\pi$
$68$	7.55039	0.915620
$69$	4.64933	0.559713
$70$	1.69011	0.202007
$71$	7.42431	0.881103	0.440552	−	0.897727i	$-0.354783\pi$
$71$	7.42431	0.881103	0.440552	+	0.897727i	$0.354783\pi$
$72$	0.783390	0.0923234
$73$	9.57578	1.12076	0.560380	−	0.828236i	$-0.310655\pi$
$73$	9.57578	1.12076	0.560380	+	0.828236i	$0.310655\pi$
$74$	−1.22300	−0.142171
$75$	−4.20351	−0.485380
$76$	1.01404	0.116318
$77$	5.27707	0.601378
$78$	0	0
$79$	−0.136717	−0.0153819	−0.00769094	−	0.999970i	$-0.502448\pi$
$79$	−0.136717	−0.0153819	−0.00769094	+	0.999970i	$0.502448\pi$
$80$	−4.15549	−0.464598
$81$	1.00000	0.111111
$82$	14.6576	1.61866
$83$	14.7716	1.62139	0.810696	−	0.585468i	$-0.199089\pi$
$83$	14.7716	1.62139	0.810696	+	0.585468i	$0.199089\pi$
$84$	−1.58633	−0.173083
$85$	4.24781	0.460740
$86$	−19.9301	−2.14912
$87$	−3.84995	−0.412758
$88$	−4.13400	−0.440686
$89$	−5.50508	−0.583537	−0.291769	−	0.956489i	$-0.594244\pi$
$89$	−5.50508	−0.583537	−0.291769	+	0.956489i	$0.594244\pi$
$90$	−1.69011	−0.178153
$91$	0	0
$92$	7.37537	0.768936
$93$	2.03627	0.211151
$94$	13.3380	1.37571
$95$	0.570492	0.0585312
$96$	7.25098	0.740050
$97$	7.63761	0.775482	0.387741	−	0.921768i	$-0.373256\pi$
$97$	7.63761	0.775482	0.387741	+	0.921768i	$0.373256\pi$
$98$	−1.89376	−0.191299
$99$	−5.27707	−0.530365
$100$	−6.66816	−0.666816
$101$	13.9998	1.39303	0.696516	−	0.717541i	$-0.254732\pi$
$101$	13.9998	1.39303	0.696516	+	0.717541i	$0.254732\pi$
$102$	−9.01366	−0.892485
$103$	13.6978	1.34968	0.674841	−	0.737963i	$-0.264212\pi$
$103$	13.6978	1.34968	0.674841	+	0.737963i	$0.264212\pi$
$104$	0	0
$105$	−0.892462	−0.0870953
$106$	−15.2713	−1.48328
$107$	−14.0091	−1.35432	−0.677158	−	0.735838i	$-0.736788\pi$
$107$	−14.0091	−1.35432	−0.677158	+	0.735838i	$0.736788\pi$
$108$	1.58633	0.152645
$109$	−14.7520	−1.41298	−0.706492	−	0.707721i	$-0.749723\pi$
$109$	−14.7520	−1.41298	−0.706492	+	0.707721i	$0.749723\pi$
$110$	8.91882	0.850376
$111$	0.645805	0.0612971
$112$	4.65622	0.439971
$113$	−5.81164	−0.546713	−0.273356	−	0.961913i	$-0.588134\pi$
$113$	−5.81164	−0.546713	−0.273356	+	0.961913i	$0.588134\pi$
$114$	−1.21056	−0.113379
$115$	4.14935	0.386929
$116$	−6.10730	−0.567048
$117$	0	0
$118$	21.1155	1.94384
$119$	−4.75966	−0.436317
$120$	0.699146	0.0638230
$121$	16.8474	1.53159
$122$	−1.57637	−0.142718
$123$	−7.73993	−0.697886
$124$	3.23020	0.290080
$125$	−8.21378	−0.734663
$126$	1.89376	0.168710
$127$	−1.69886	−0.150750	−0.0753748	−	0.997155i	$-0.524015\pi$
$127$	−1.69886	−0.150750	−0.0753748	+	0.997155i	$0.524015\pi$
$128$	−6.13307	−0.542092
$129$	10.5241	0.926594
$130$	0	0
$131$	1.19269	0.104206	0.0521030	−	0.998642i	$-0.483408\pi$
$131$	1.19269	0.104206	0.0521030	+	0.998642i	$0.483408\pi$
$132$	−8.37118	−0.728617
$133$	−0.639234	−0.0554286
$134$	−22.3983	−1.93492
$135$	0.892462	0.0768109
$136$	3.72867	0.319731
$137$	4.03058	0.344356	0.172178	−	0.985066i	$-0.444920\pi$
$137$	4.03058	0.344356	0.172178	+	0.985066i	$0.444920\pi$
$138$	−8.80472	−0.749507
$139$	7.79669	0.661307	0.330653	−	0.943752i	$-0.392731\pi$
$139$	7.79669	0.661307	0.330653	+	0.943752i	$0.392731\pi$
$140$	−1.41574	−0.119652
$141$	−7.04313	−0.593139
$142$	−14.0599	−1.17988
$143$	0	0
$144$	−4.65622	−0.388018
$145$	−3.43593	−0.285339
$146$	−18.1342	−1.50080
$147$	1.00000	0.0824786
$148$	1.02446	0.0842102
$149$	15.8997	1.30255	0.651277	−	0.758840i	$-0.274233\pi$
$149$	15.8997	1.30255	0.651277	+	0.758840i	$0.274233\pi$
$150$	7.96045	0.649968
$151$	−5.74035	−0.467143	−0.233571	−	0.972340i	$-0.575041\pi$
$151$	−5.74035	−0.467143	−0.233571	+	0.972340i	$0.575041\pi$
$152$	0.500769	0.0406178
$153$	4.75966	0.384796
$154$	−9.99350	−0.805300
$155$	1.81729	0.145968
$156$	0	0
$157$	18.2220	1.45427	0.727135	−	0.686494i	$-0.240851\pi$
$157$	18.2220	1.45427	0.727135	+	0.686494i	$0.240851\pi$
$158$	0.258909	0.0205977
$159$	8.06403	0.639519
$160$	6.47122	0.511595
$161$	−4.64933	−0.366418
$162$	−1.89376	−0.148788
$163$	17.2611	1.35200	0.675998	−	0.736904i	$-0.263713\pi$
$163$	17.2611	1.35200	0.675998	+	0.736904i	$0.263713\pi$
$164$	−12.2781	−0.958758
$165$	−4.70958	−0.366640
$166$	−27.9738	−2.17119
$167$	12.7165	0.984032	0.492016	−	0.870586i	$-0.336260\pi$
$167$	12.7165	0.984032	0.492016	+	0.870586i	$0.336260\pi$
$168$	−0.783390	−0.0604399
$169$	0	0
$170$	−8.04434	−0.616973
$171$	0.639234	0.0488834
$172$	16.6947	1.27296
$173$	−14.1113	−1.07286	−0.536432	−	0.843944i	$-0.680228\pi$
$173$	−14.1113	−1.07286	−0.536432	+	0.843944i	$0.680228\pi$
$174$	7.29089	0.552721
$175$	4.20351	0.317756
$176$	24.5712	1.85212
$177$	−11.1500	−0.838088
$178$	10.4253	0.781410
$179$	−22.2581	−1.66365	−0.831824	−	0.555039i	$-0.812703\pi$
$179$	−22.2581	−1.66365	−0.831824	+	0.555039i	$0.812703\pi$
$180$	1.41574	0.105523
$181$	−7.25474	−0.539241	−0.269620	−	0.962967i	$-0.586898\pi$
$181$	−7.25474	−0.539241	−0.269620	+	0.962967i	$0.586898\pi$
$182$	0	0
$183$	0.832403	0.0615330
$184$	3.64224	0.268509
$185$	0.576356	0.0423746
$186$	−3.85621	−0.282751
$187$	−25.1170	−1.83674
$188$	−11.1727	−0.814856
$189$	−1.00000	−0.0727393
$190$	−1.08037	−0.0783786
$191$	−4.31005	−0.311864	−0.155932	−	0.987768i	$-0.549838\pi$
$191$	−4.31005	−0.311864	−0.155932	+	0.987768i	$0.549838\pi$
$192$	−4.41919	−0.318928
$193$	−12.3043	−0.885684	−0.442842	−	0.896600i	$-0.646030\pi$
$193$	−12.3043	−0.885684	−0.442842	+	0.896600i	$0.646030\pi$
$194$	−14.4638	−1.03844
$195$	0	0
$196$	1.58633	0.113309
$197$	3.20784	0.228549	0.114275	−	0.993449i	$-0.463546\pi$
$197$	3.20784	0.228549	0.114275	+	0.993449i	$0.463546\pi$
$198$	9.99350	0.710207
$199$	2.13013	0.151001	0.0755005	−	0.997146i	$-0.475945\pi$
$199$	2.13013	0.151001	0.0755005	+	0.997146i	$0.475945\pi$
$200$	−3.29299	−0.232850
$201$	11.8274	0.834243
$202$	−26.5123	−1.86540
$203$	3.84995	0.270214
$204$	7.55039	0.528633
$205$	−6.90759	−0.482447
$206$	−25.9403	−1.80735
$207$	4.64933	0.323151
$208$	0	0
$209$	−3.37328	−0.233335
$210$	1.69011	0.116629
$211$	12.9048	0.888404	0.444202	−	0.895927i	$-0.353487\pi$
$211$	12.9048	0.888404	0.444202	+	0.895927i	$0.353487\pi$
$212$	12.7922	0.878573
$213$	7.42431	0.508705
$214$	26.5300	1.81355
$215$	9.39235	0.640553
$216$	0.783390	0.0533030
$217$	−2.03627	−0.138231
$218$	27.9367	1.89211
$219$	9.57578	0.647071
$220$	−7.47095	−0.503692
$221$	0	0
$222$	−1.22300	−0.0820824
$223$	25.4618	1.70505	0.852524	−	0.522688i	$-0.175071\pi$
$223$	25.4618	1.70505	0.852524	+	0.522688i	$0.175071\pi$
$224$	−7.25098	−0.484476
$225$	−4.20351	−0.280234
$226$	11.0059	0.732098
$227$	−20.5447	−1.36360	−0.681799	−	0.731540i	$-0.738802\pi$
$227$	−20.5447	−1.36360	−0.681799	+	0.731540i	$0.738802\pi$
$228$	1.01404	0.0671562
$229$	13.1613	0.869722	0.434861	−	0.900498i	$-0.356798\pi$
$229$	13.1613	0.869722	0.434861	+	0.900498i	$0.356798\pi$
$230$	−7.85787	−0.518133
$231$	5.27707	0.347206
$232$	−3.01601	−0.198011
$233$	5.59262	0.366385	0.183192	−	0.983077i	$-0.441357\pi$
$233$	5.59262	0.366385	0.183192	+	0.983077i	$0.441357\pi$
$234$	0	0
$235$	−6.28573	−0.410036
$236$	−17.6876	−1.15137
$237$	−0.136717	−0.00888073
$238$	9.01366	0.584268
$239$	25.9477	1.67842	0.839210	−	0.543808i	$-0.183018\pi$
$239$	25.9477	1.67842	0.839210	+	0.543808i	$0.183018\pi$
$240$	−4.15549	−0.268236
$241$	−0.242505	−0.0156211	−0.00781056	−	0.999969i	$-0.502486\pi$
$241$	−0.242505	−0.0156211	−0.00781056	+	0.999969i	$0.502486\pi$
$242$	−31.9050	−2.05093
$243$	1.00000	0.0641500
$244$	1.32047	0.0845342
$245$	0.892462	0.0570173
$246$	14.6576	0.934534
$247$	0	0
$248$	1.59519	0.101295
$249$	14.7716	0.936111
$250$	15.5549	0.983781
$251$	16.9718	1.07125	0.535626	−	0.844455i	$-0.320076\pi$
$251$	16.9718	1.07125	0.535626	+	0.844455i	$0.320076\pi$
$252$	−1.58633	−0.0999295
$253$	−24.5348	−1.54249
$254$	3.21724	0.201867
$255$	4.24781	0.266008
$256$	20.4529	1.27831
$257$	−1.57975	−0.0985419	−0.0492710	−	0.998785i	$-0.515690\pi$
$257$	−1.57975	−0.0985419	−0.0492710	+	0.998785i	$0.515690\pi$
$258$	−19.9301	−1.24079
$259$	−0.645805	−0.0401284
$260$	0	0
$261$	−3.84995	−0.238306
$262$	−2.25868	−0.139541
$263$	9.40336	0.579836	0.289918	−	0.957052i	$-0.406372\pi$
$263$	9.40336	0.579836	0.289918	+	0.957052i	$0.406372\pi$
$264$	−4.13400	−0.254430
$265$	7.19684	0.442098
$266$	1.21056	0.0742239
$267$	−5.50508	−0.336905
$268$	18.7622	1.14609
$269$	−28.4573	−1.73507	−0.867535	−	0.497376i	$-0.834297\pi$
$269$	−28.4573	−1.73507	−0.867535	+	0.497376i	$0.834297\pi$
$270$	−1.69011	−0.102857
$271$	7.15660	0.434733	0.217366	−	0.976090i	$-0.430253\pi$
$271$	7.15660	0.434733	0.217366	+	0.976090i	$0.430253\pi$
$272$	−22.1620	−1.34377
$273$	0	0
$274$	−7.63295	−0.461124
$275$	22.1822	1.33764
$276$	7.37537	0.443945
$277$	−30.4598	−1.83015	−0.915075	−	0.403283i	$-0.867869\pi$
$277$	−30.4598	−1.83015	−0.915075	+	0.403283i	$0.867869\pi$
$278$	−14.7651	−0.885550
$279$	2.03627	0.121908
$280$	−0.699146	−0.0417820
$281$	8.06012	0.480827	0.240413	−	0.970671i	$-0.422717\pi$
$281$	8.06012	0.480827	0.240413	+	0.970671i	$0.422717\pi$
$282$	13.3380	0.794267
$283$	19.6060	1.16546	0.582729	−	0.812666i	$-0.301985\pi$
$283$	19.6060	1.16546	0.582729	+	0.812666i	$0.301985\pi$
$284$	11.7774	0.698861
$285$	0.570492	0.0337930
$286$	0	0
$287$	7.73993	0.456874
$288$	7.25098	0.427268
$289$	5.65435	0.332609
$290$	6.50684	0.382095
$291$	7.63761	0.447724
$292$	15.1904	0.888948
$293$	22.0402	1.28760	0.643801	−	0.765193i	$-0.277356\pi$
$293$	22.0402	1.28760	0.643801	+	0.765193i	$0.277356\pi$
$294$	−1.89376	−0.110446
$295$	−9.95098	−0.579368
$296$	0.505918	0.0294059
$297$	−5.27707	−0.306206
$298$	−30.1103	−1.74424
$299$	0	0
$300$	−6.66816	−0.384986
$301$	−10.5241	−0.606598
$302$	10.8708	0.625547
$303$	13.9998	0.804268
$304$	−2.97641	−0.170709
$305$	0.742888	0.0425376
$306$	−9.01366	−0.515276
$307$	31.2987	1.78631	0.893154	−	0.449750i	$-0.148487\pi$
$307$	31.2987	1.78631	0.893154	+	0.449750i	$0.148487\pi$
$308$	8.37118	0.476992
$309$	13.6978	0.779239
$310$	−3.44152	−0.195465
$311$	−14.2805	−0.809771	−0.404886	−	0.914367i	$-0.632689\pi$
$311$	−14.2805	−0.809771	−0.404886	+	0.914367i	$0.632689\pi$
$312$	0	0
$313$	30.3102	1.71323	0.856617	−	0.515953i	$-0.172562\pi$
$313$	30.3102	1.71323	0.856617	+	0.515953i	$0.172562\pi$
$314$	−34.5080	−1.94740
$315$	−0.892462	−0.0502845
$316$	−0.216879	−0.0122004
$317$	−6.17539	−0.346845	−0.173422	−	0.984848i	$-0.555483\pi$
$317$	−6.17539	−0.346845	−0.173422	+	0.984848i	$0.555483\pi$
$318$	−15.2713	−0.856374
$319$	20.3164	1.13750
$320$	−3.94396	−0.220474
$321$	−14.0091	−0.781914
$322$	8.80472	0.490668
$323$	3.04253	0.169291
$324$	1.58633	0.0881295
$325$	0	0
$326$	−32.6885	−1.81045
$327$	−14.7520	−0.815787
$328$	−6.06339	−0.334795
$329$	7.04313	0.388301
$330$	8.91882	0.490965
$331$	10.5567	0.580249	0.290125	−	0.956989i	$-0.406303\pi$
$331$	10.5567	0.580249	0.290125	+	0.956989i	$0.406303\pi$
$332$	23.4326	1.28603
$333$	0.645805	0.0353899
$334$	−24.0820	−1.31771
$335$	10.5555	0.576711
$336$	4.65622	0.254017
$337$	−14.9855	−0.816313	−0.408157	−	0.912912i	$-0.633828\pi$
$337$	−14.9855	−0.816313	−0.408157	+	0.912912i	$0.633828\pi$
$338$	0	0
$339$	−5.81164	−0.315645
$340$	6.73844	0.365443
$341$	−10.7455	−0.581903
$342$	−1.21056	−0.0654594
$343$	−1.00000	−0.0539949
$344$	8.24447	0.444512
$345$	4.14935	0.223393
$346$	26.7235	1.43666
$347$	−29.4048	−1.57853	−0.789266	−	0.614052i	$-0.789538\pi$
$347$	−29.4048	−1.57853	−0.789266	+	0.614052i	$0.789538\pi$
$348$	−6.10730	−0.327385
$349$	10.4048	0.556955	0.278477	−	0.960443i	$-0.410170\pi$
$349$	10.4048	0.556955	0.278477	+	0.960443i	$0.410170\pi$
$350$	−7.96045	−0.425504
$351$	0	0
$352$	−38.2639	−2.03947
$353$	15.0595	0.801537	0.400769	−	0.916179i	$-0.368743\pi$
$353$	15.0595	0.801537	0.400769	+	0.916179i	$0.368743\pi$
$354$	21.1155	1.12228
$355$	6.62591	0.351667
$356$	−8.73288	−0.462842
$357$	−4.75966	−0.251908
$358$	42.1515	2.22778
$359$	−16.3983	−0.865471	−0.432736	−	0.901521i	$-0.642452\pi$
$359$	−16.3983	−0.865471	−0.432736	+	0.901521i	$0.642452\pi$
$360$	0.699146	0.0368482
$361$	−18.5914	−0.978494
$362$	13.7387	0.722092
$363$	16.8474	0.884261
$364$	0	0
$365$	8.54602	0.447319
$366$	−1.57637	−0.0823983
$367$	−12.9004	−0.673393	−0.336697	−	0.941613i	$-0.609310\pi$
$367$	−12.9004	−0.673393	−0.336697	+	0.941613i	$0.609310\pi$
$368$	−21.6483	−1.12849
$369$	−7.73993	−0.402925
$370$	−1.09148	−0.0567434
$371$	−8.06403	−0.418664
$372$	3.23020	0.167478
$373$	28.8685	1.49475	0.747377	−	0.664400i	$-0.231313\pi$
$373$	28.8685	1.49475	0.747377	+	0.664400i	$0.231313\pi$
$374$	47.5657	2.45956
$375$	−8.21378	−0.424158
$376$	−5.51752	−0.284545
$377$	0	0
$378$	1.89376	0.0974046
$379$	12.3485	0.634300	0.317150	−	0.948375i	$-0.397274\pi$
$379$	12.3485	0.634300	0.317150	+	0.948375i	$0.397274\pi$
$380$	0.904989	0.0464249
$381$	−1.69886	−0.0870353
$382$	8.16221	0.417615
$383$	−3.75999	−0.192127	−0.0960633	−	0.995375i	$-0.530625\pi$
$383$	−3.75999	−0.192127	−0.0960633	+	0.995375i	$0.530625\pi$
$384$	−6.13307	−0.312977
$385$	4.70958	0.240022
$386$	23.3014	1.18601
$387$	10.5241	0.534970
$388$	12.1158	0.615085
$389$	−16.7332	−0.848407	−0.424203	−	0.905567i	$-0.639446\pi$
$389$	−16.7332	−0.848407	−0.424203	+	0.905567i	$0.639446\pi$
$390$	0	0
$391$	22.1292	1.11912
$392$	0.783390	0.0395672
$393$	1.19269	0.0601634
$394$	−6.07488	−0.306048
$395$	−0.122015	−0.00613923
$396$	−8.37118	−0.420667
$397$	4.04515	0.203021	0.101510	−	0.994834i	$-0.467633\pi$
$397$	4.04515	0.203021	0.101510	+	0.994834i	$0.467633\pi$
$398$	−4.03396	−0.202204
$399$	−0.639234	−0.0320017
$400$	19.5725	0.978623
$401$	−8.62134	−0.430529	−0.215265	−	0.976556i	$-0.569061\pi$
$401$	−8.62134	−0.430529	−0.215265	+	0.976556i	$0.569061\pi$
$402$	−22.3983	−1.11713
$403$	0	0
$404$	22.2083	1.10491
$405$	0.892462	0.0443468
$406$	−7.29089	−0.361841
$407$	−3.40796	−0.168926
$408$	3.72867	0.184597
$409$	−25.0049	−1.23641	−0.618206	−	0.786016i	$-0.712140\pi$
$409$	−25.0049	−1.23641	−0.618206	+	0.786016i	$0.712140\pi$
$410$	13.0813	0.646041
$411$	4.03058	0.198814
$412$	21.7292	1.07052
$413$	11.1500	0.548657
$414$	−8.80472	−0.432728
$415$	13.1831	0.647131
$416$	0	0
$417$	7.79669	0.381806
$418$	6.38818	0.312456
$419$	5.95683	0.291010	0.145505	−	0.989358i	$-0.453519\pi$
$419$	5.95683	0.291010	0.145505	+	0.989358i	$0.453519\pi$
$420$	−1.41574	−0.0690810
$421$	5.52313	0.269181	0.134591	−	0.990901i	$-0.457028\pi$
$421$	5.52313	0.269181	0.134591	+	0.990901i	$0.457028\pi$
$422$	−24.4386	−1.18965
$423$	−7.04313	−0.342449
$424$	6.31728	0.306794
$425$	−20.0073	−0.970496
$426$	−14.0599	−0.681203
$427$	−0.832403	−0.0402828
$428$	−22.2231	−1.07420
$429$	0	0
$430$	−17.7869	−0.857759
$431$	24.0748	1.15964	0.579821	−	0.814744i	$-0.303122\pi$
$431$	24.0748	1.15964	0.579821	+	0.814744i	$0.303122\pi$
$432$	−4.65622	−0.224022
$433$	36.8690	1.77181	0.885906	−	0.463865i	$-0.153538\pi$
$433$	36.8690	1.77181	0.885906	+	0.463865i	$0.153538\pi$
$434$	3.85621	0.185104
$435$	−3.43593	−0.164740
$436$	−23.4015	−1.12073
$437$	2.97201	0.142170
$438$	−18.1342	−0.866487
$439$	−16.6516	−0.794736	−0.397368	−	0.917659i	$-0.630076\pi$
$439$	−16.6516	−0.794736	−0.397368	+	0.917659i	$0.630076\pi$
$440$	−3.68944	−0.175887
$441$	1.00000	0.0476190
$442$	0	0
$443$	15.0276	0.713983	0.356991	−	0.934108i	$-0.383803\pi$
$443$	15.0276	0.713983	0.356991	+	0.934108i	$0.383803\pi$
$444$	1.02446	0.0486188
$445$	−4.91307	−0.232902
$446$	−48.2185	−2.28321
$447$	15.8997	0.752030
$448$	4.41919	0.208787
$449$	5.93074	0.279889	0.139944	−	0.990159i	$-0.455308\pi$
$449$	5.93074	0.279889	0.139944	+	0.990159i	$0.455308\pi$
$450$	7.96045	0.375259
$451$	40.8442	1.92328
$452$	−9.21918	−0.433634
$453$	−5.74035	−0.269705
$454$	38.9067	1.82598
$455$	0	0
$456$	0.500769	0.0234507
$457$	−0.542892	−0.0253954	−0.0126977	−	0.999919i	$-0.504042\pi$
$457$	−0.542892	−0.0253954	−0.0126977	+	0.999919i	$0.504042\pi$
$458$	−24.9243	−1.16464
$459$	4.75966	0.222162
$460$	6.58224	0.306898
$461$	−12.9687	−0.604015	−0.302007	−	0.953306i	$-0.597657\pi$
$461$	−12.9687	−0.604015	−0.302007	+	0.953306i	$0.597657\pi$
$462$	−9.99350	−0.464940
$463$	41.0461	1.90758	0.953788	−	0.300481i	$-0.0971472\pi$
$463$	41.0461	1.90758	0.953788	+	0.300481i	$0.0971472\pi$
$464$	17.9262	0.832203
$465$	1.81729	0.0842749
$466$	−10.5911	−0.490623
$467$	39.9232	1.84743	0.923714	−	0.383083i	$-0.125138\pi$
$467$	39.9232	1.84743	0.923714	+	0.383083i	$0.125138\pi$
$468$	0	0
$469$	−11.8274	−0.546141
$470$	11.9037	0.549075
$471$	18.2220	0.839623
$472$	−8.73483	−0.402053
$473$	−55.5363	−2.55356
$474$	0.258909	0.0118921
$475$	−2.68703	−0.123289
$476$	−7.55039	−0.346072
$477$	8.06403	0.369227
$478$	−49.1388	−2.24756
$479$	40.2182	1.83762	0.918808	−	0.394705i	$-0.129153\pi$
$479$	40.2182	1.83762	0.918808	+	0.394705i	$0.129153\pi$
$480$	6.47122	0.295370
$481$	0	0
$482$	0.459246	0.0209181
$483$	−4.64933	−0.211552
$484$	26.7256	1.21480
$485$	6.81627	0.309511
$486$	−1.89376	−0.0859027
$487$	17.2531	0.781813	0.390906	−	0.920430i	$-0.372162\pi$
$487$	17.2531	0.781813	0.390906	+	0.920430i	$0.372162\pi$
$488$	0.652096	0.0295190
$489$	17.2611	0.780575
$490$	−1.69011	−0.0763514
$491$	31.2955	1.41235	0.706173	−	0.708039i	$-0.250420\pi$
$491$	31.2955	1.41235	0.706173	+	0.708039i	$0.250420\pi$
$492$	−12.2781	−0.553539
$493$	−18.3244	−0.825292
$494$	0	0
$495$	−4.70958	−0.211680
$496$	−9.48131	−0.425724
$497$	−7.42431	−0.333026
$498$	−27.9738	−1.25354
$499$	16.8461	0.754134	0.377067	−	0.926186i	$-0.376933\pi$
$499$	16.8461	0.754134	0.377067	+	0.926186i	$0.376933\pi$
$500$	−13.0298	−0.582709
$501$	12.7165	0.568131
$502$	−32.1406	−1.43450
$503$	20.8858	0.931252	0.465626	−	0.884982i	$-0.345829\pi$
$503$	20.8858	0.931252	0.465626	+	0.884982i	$0.345829\pi$
$504$	−0.783390	−0.0348950
$505$	12.4943	0.555988
$506$	46.4631	2.06554
$507$	0	0
$508$	−2.69496	−0.119569
$509$	36.3074	1.60930	0.804650	−	0.593750i	$-0.202353\pi$
$509$	36.3074	1.60930	0.804650	+	0.593750i	$0.202353\pi$
$510$	−8.04434	−0.356209
$511$	−9.57578	−0.423607
$512$	−26.4669	−1.16968
$513$	0.639234	0.0282229
$514$	2.99166	0.131957
$515$	12.2247	0.538687
$516$	16.6947	0.734943
$517$	37.1671	1.63461
$518$	1.22300	0.0537356
$519$	−14.1113	−0.619418
$520$	0	0
$521$	19.2511	0.843408	0.421704	−	0.906734i	$-0.361432\pi$
$521$	19.2511	0.843408	0.421704	+	0.906734i	$0.361432\pi$
$522$	7.29089	0.319113
$523$	14.6001	0.638419	0.319210	−	0.947684i	$-0.396583\pi$
$523$	14.6001	0.638419	0.319210	+	0.947684i	$0.396583\pi$
$524$	1.89201	0.0826527
$525$	4.20351	0.183456
$526$	−17.8077	−0.776453
$527$	9.69195	0.422188
$528$	24.5712	1.06932
$529$	−1.38376	−0.0601633
$530$	−13.6291	−0.592010
$531$	−11.1500	−0.483870
$532$	−1.01404	−0.0439640
$533$	0	0
$534$	10.4253	0.451147
$535$	−12.5026	−0.540536
$536$	9.26550	0.400209
$537$	−22.2581	−0.960508
$538$	53.8913	2.32342
$539$	−5.27707	−0.227299
$540$	1.41574	0.0609237
$541$	−21.6960	−0.932783	−0.466392	−	0.884578i	$-0.654446\pi$
$541$	−21.6960	−0.932783	−0.466392	+	0.884578i	$0.654446\pi$
$542$	−13.5529	−0.582147
$543$	−7.25474	−0.311331
$544$	34.5122	1.47970
$545$	−13.1656	−0.563952
$546$	0	0
$547$	18.1297	0.775170	0.387585	−	0.921834i	$-0.373309\pi$
$547$	18.1297	0.775170	0.387585	+	0.921834i	$0.373309\pi$
$548$	6.39383	0.273131
$549$	0.832403	0.0355261
$550$	−42.0078	−1.79122
$551$	−2.46102	−0.104843
$552$	3.64224	0.155024
$553$	0.136717	0.00581380
$554$	57.6835	2.45074
$555$	0.576356	0.0244650
$556$	12.3681	0.524526
$557$	30.1341	1.27682	0.638412	−	0.769695i	$-0.279592\pi$
$557$	30.1341	1.27682	0.638412	+	0.769695i	$0.279592\pi$
$558$	−3.85621	−0.163246
$559$	0	0
$560$	4.15549	0.175602
$561$	−25.1170	−1.06044
$562$	−15.2639	−0.643871
$563$	−34.5589	−1.45648	−0.728242	−	0.685320i	$-0.759662\pi$
$563$	−34.5589	−1.45648	−0.728242	+	0.685320i	$0.759662\pi$
$564$	−11.1727	−0.470457
$565$	−5.18666	−0.218205
$566$	−37.1292	−1.56066
$567$	−1.00000	−0.0419961
$568$	5.81613	0.244039
$569$	4.59779	0.192749	0.0963746	−	0.995345i	$-0.469275\pi$
$569$	4.59779	0.192749	0.0963746	+	0.995345i	$0.469275\pi$
$570$	−1.08037	−0.0452519
$571$	19.8023	0.828699	0.414349	−	0.910118i	$-0.364009\pi$
$571$	19.8023	0.828699	0.414349	+	0.910118i	$0.364009\pi$
$572$	0	0
$573$	−4.31005	−0.180055
$574$	−14.6576	−0.611796
$575$	−19.5435	−0.815020
$576$	−4.41919	−0.184133
$577$	−20.8218	−0.866822	−0.433411	−	0.901196i	$-0.642690\pi$
$577$	−20.8218	−0.866822	−0.433411	+	0.901196i	$0.642690\pi$
$578$	−10.7080	−0.445393
$579$	−12.3043	−0.511350
$580$	−5.45053	−0.226321
$581$	−14.7716	−0.612828
$582$	−14.4638	−0.599544
$583$	−42.5544	−1.76242
$584$	7.50157	0.310417
$585$	0	0
$586$	−41.7389	−1.72422
$587$	−40.6743	−1.67881	−0.839404	−	0.543508i	$-0.817096\pi$
$587$	−40.6743	−1.67881	−0.839404	+	0.543508i	$0.817096\pi$
$588$	1.58633	0.0654192
$589$	1.30165	0.0536337
$590$	18.8448	0.775827
$591$	3.20784	0.131953
$592$	−3.00701	−0.123587
$593$	−22.3890	−0.919405	−0.459702	−	0.888073i	$-0.652044\pi$
$593$	−22.3890	−0.919405	−0.459702	+	0.888073i	$0.652044\pi$
$594$	9.99350	0.410038
$595$	−4.24781	−0.174143
$596$	25.2222	1.03314
$597$	2.13013	0.0871805
$598$	0	0
$599$	−40.4388	−1.65229	−0.826143	−	0.563461i	$-0.809470\pi$
$599$	−40.4388	−1.65229	−0.826143	+	0.563461i	$0.809470\pi$
$600$	−3.29299	−0.134436
$601$	−20.2325	−0.825301	−0.412650	−	0.910890i	$-0.635397\pi$
$601$	−20.2325	−0.825301	−0.412650	+	0.910890i	$0.635397\pi$
$602$	19.9301	0.812291
$603$	11.8274	0.481651
$604$	−9.10609	−0.370522
$605$	15.0357	0.611288
$606$	−26.5123	−1.07699
$607$	−31.5200	−1.27936	−0.639680	−	0.768642i	$-0.720933\pi$
$607$	−31.5200	−1.27936	−0.639680	+	0.768642i	$0.720933\pi$
$608$	4.63507	0.187977
$609$	3.84995	0.156008
$610$	−1.40685	−0.0569618
$611$	0	0
$612$	7.55039	0.305207
$613$	30.1560	1.21799	0.608994	−	0.793175i	$-0.291573\pi$
$613$	30.1560	1.21799	0.608994	+	0.793175i	$0.291573\pi$
$614$	−59.2722	−2.39203
$615$	−6.90759	−0.278541
$616$	4.13400	0.166564
$617$	−21.0232	−0.846361	−0.423180	−	0.906045i	$-0.639086\pi$
$617$	−21.0232	−0.846361	−0.423180	+	0.906045i	$0.639086\pi$
$618$	−25.9403	−1.04347
$619$	26.2525	1.05518	0.527589	−	0.849500i	$-0.323096\pi$
$619$	26.2525	1.05518	0.527589	+	0.849500i	$0.323096\pi$
$620$	2.88283	0.115777
$621$	4.64933	0.186571
$622$	27.0438	1.08436
$623$	5.50508	0.220556
$624$	0	0
$625$	13.6871	0.547483
$626$	−57.4003	−2.29418
$627$	−3.37328	−0.134716
$628$	28.9061	1.15348
$629$	3.07381	0.122561
$630$	1.69011	0.0673356
$631$	3.88077	0.154491	0.0772455	−	0.997012i	$-0.475387\pi$
$631$	3.88077	0.154491	0.0772455	+	0.997012i	$0.475387\pi$
$632$	−0.107103	−0.00426032
$633$	12.9048	0.512920
$634$	11.6947	0.464457
$635$	−1.51617	−0.0601673
$636$	12.7922	0.507244
$637$	0	0
$638$	−38.4745	−1.52322
$639$	7.42431	0.293701
$640$	−5.47353	−0.216360
$641$	11.2641	0.444905	0.222452	−	0.974944i	$-0.428594\pi$
$641$	11.2641	0.444905	0.222452	+	0.974944i	$0.428594\pi$
$642$	26.5300	1.04705
$643$	−30.1300	−1.18821	−0.594106	−	0.804386i	$-0.702494\pi$
$643$	−30.1300	−1.18821	−0.594106	+	0.804386i	$0.702494\pi$
$644$	−7.37537	−0.290630
$645$	9.39235	0.369823
$646$	−5.76183	−0.226696
$647$	1.03066	0.0405193	0.0202596	−	0.999795i	$-0.493551\pi$
$647$	1.03066	0.0405193	0.0202596	+	0.999795i	$0.493551\pi$
$648$	0.783390	0.0307745
$649$	58.8395	2.30965
$650$	0	0
$651$	−2.03627	−0.0798077
$652$	27.3819	1.07236
$653$	3.88842	0.152165	0.0760827	−	0.997102i	$-0.475759\pi$
$653$	3.88842	0.152165	0.0760827	+	0.997102i	$0.475759\pi$
$654$	27.9367	1.09241
$655$	1.06443	0.0415908
$656$	36.0388	1.40708
$657$	9.57578	0.373587
$658$	−13.3380	−0.519970
$659$	−11.5306	−0.449169	−0.224584	−	0.974455i	$-0.572102\pi$
$659$	−11.5306	−0.449169	−0.224584	+	0.974455i	$0.572102\pi$
$660$	−7.47095	−0.290806
$661$	−9.54278	−0.371171	−0.185586	−	0.982628i	$-0.559418\pi$
$661$	−9.54278	−0.371171	−0.185586	+	0.982628i	$0.559418\pi$
$662$	−19.9919	−0.777007
$663$	0	0
$664$	11.5719	0.449077
$665$	−0.570492	−0.0221227
$666$	−1.22300	−0.0473903
$667$	−17.8997	−0.693078
$668$	20.1726	0.780501
$669$	25.4618	0.984410
$670$	−19.9897	−0.772268
$671$	−4.39265	−0.169576
$672$	−7.25098	−0.279713
$673$	−35.1621	−1.35540	−0.677700	−	0.735339i	$-0.737023\pi$
$673$	−35.1621	−1.35540	−0.677700	+	0.735339i	$0.737023\pi$
$674$	28.3790	1.09312
$675$	−4.20351	−0.161793
$676$	0	0
$677$	−29.3436	−1.12777	−0.563884	−	0.825854i	$-0.690693\pi$
$677$	−29.3436	−1.12777	−0.563884	+	0.825854i	$0.690693\pi$
$678$	11.0059	0.422677
$679$	−7.63761	−0.293104
$680$	3.32770	0.127611
$681$	−20.5447	−0.787274
$682$	20.3495	0.779222
$683$	−23.3475	−0.893369	−0.446685	−	0.894692i	$-0.647395\pi$
$683$	−23.3475	−0.893369	−0.446685	+	0.894692i	$0.647395\pi$
$684$	1.01404	0.0387726
$685$	3.59714	0.137440
$686$	1.89376	0.0723041
$687$	13.1613	0.502134
$688$	−49.0024	−1.86820
$689$	0	0
$690$	−7.85787	−0.299144
$691$	25.1221	0.955692	0.477846	−	0.878444i	$-0.341418\pi$
$691$	25.1221	0.955692	0.477846	+	0.878444i	$0.341418\pi$
$692$	−22.3852	−0.850958
$693$	5.27707	0.200459
$694$	55.6856	2.11380
$695$	6.95825	0.263942
$696$	−3.01601	−0.114322
$697$	−36.8394	−1.39539
$698$	−19.7042	−0.745813
$699$	5.59262	0.211532
$700$	6.66816	0.252033
$701$	−21.1109	−0.797347	−0.398673	−	0.917093i	$-0.630529\pi$
$701$	−21.1109	−0.797347	−0.398673	+	0.917093i	$0.630529\pi$
$702$	0	0
$703$	0.412820	0.0155698
$704$	23.3204	0.878920
$705$	−6.28573	−0.236734
$706$	−28.5191	−1.07333
$707$	−13.9998	−0.526517
$708$	−17.6876	−0.664742
$709$	−43.9044	−1.64886	−0.824431	−	0.565962i	$-0.808505\pi$
$709$	−43.9044	−1.64886	−0.824431	+	0.565962i	$0.808505\pi$
$710$	−12.5479	−0.470914
$711$	−0.136717	−0.00512729
$712$	−4.31263	−0.161622
$713$	9.46729	0.354553
$714$	9.01366	0.337328
$715$	0	0
$716$	−35.3087	−1.31955
$717$	25.9477	0.969036
$718$	31.0545	1.15895
$719$	20.6551	0.770305	0.385152	−	0.922853i	$-0.374149\pi$
$719$	20.6551	0.770305	0.385152	+	0.922853i	$0.374149\pi$
$720$	−4.15549	−0.154866
$721$	−13.6978	−0.510132
$722$	35.2076	1.31029
$723$	−0.242505	−0.00901885
$724$	−11.5084	−0.427707
$725$	16.1833	0.601033
$726$	−31.9050	−1.18411
$727$	39.8996	1.47979	0.739897	−	0.672720i	$-0.234874\pi$
$727$	39.8996	1.47979	0.739897	+	0.672720i	$0.234874\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−16.1841	−0.599001
$731$	50.0911	1.85269
$732$	1.32047	0.0488058
$733$	−40.2926	−1.48824	−0.744120	−	0.668046i	$-0.767131\pi$
$733$	−40.2926	−1.48824	−0.744120	+	0.668046i	$0.767131\pi$
$734$	24.4302	0.901735
$735$	0.892462	0.0329189
$736$	33.7122	1.24265
$737$	−62.4142	−2.29906
$738$	14.6576	0.539553
$739$	−34.8101	−1.28051	−0.640255	−	0.768162i	$-0.721171\pi$
$739$	−34.8101	−1.28051	−0.640255	+	0.768162i	$0.721171\pi$
$740$	0.914292	0.0336100
$741$	0	0
$742$	15.2713	0.560629
$743$	36.6389	1.34415	0.672076	−	0.740483i	$-0.265403\pi$
$743$	36.6389	1.34415	0.672076	+	0.740483i	$0.265403\pi$
$744$	1.59519	0.0584827
$745$	14.1899	0.519877
$746$	−54.6700	−2.00161
$747$	14.7716	0.540464
$748$	−39.8439	−1.45684
$749$	14.0091	0.511883
$750$	15.5549	0.567986
$751$	−23.6488	−0.862958	−0.431479	−	0.902123i	$-0.642008\pi$
$751$	−23.6488	−0.862958	−0.431479	+	0.902123i	$0.642008\pi$
$752$	32.7944	1.19589
$753$	16.9718	0.618487
$754$	0	0
$755$	−5.12304	−0.186447
$756$	−1.58633	−0.0576943
$757$	31.0041	1.12686	0.563432	−	0.826163i	$-0.309481\pi$
$757$	31.0041	1.12686	0.563432	+	0.826163i	$0.309481\pi$
$758$	−23.3851	−0.849385
$759$	−24.5348	−0.890557
$760$	0.446918	0.0162114
$761$	−25.6436	−0.929579	−0.464790	−	0.885421i	$-0.653870\pi$
$761$	−25.6436	−0.929579	−0.464790	+	0.885421i	$0.653870\pi$
$762$	3.21724	0.116548
$763$	14.7520	0.534058
$764$	−6.83717	−0.247360
$765$	4.24781	0.153580
$766$	7.12053	0.257275
$767$	0	0
$768$	20.4529	0.738032
$769$	−28.8868	−1.04169	−0.520843	−	0.853653i	$-0.674382\pi$
$769$	−28.8868	−1.04169	−0.520843	+	0.853653i	$0.674382\pi$
$770$	−8.91882	−0.321412
$771$	−1.57975	−0.0568932
$772$	−19.5187	−0.702494
$773$	−28.1876	−1.01384	−0.506919	−	0.861993i	$-0.669216\pi$
$773$	−28.1876	−1.01384	−0.506919	+	0.861993i	$0.669216\pi$
$774$	−19.9301	−0.716373
$775$	−8.55949	−0.307466
$776$	5.98323	0.214785
$777$	−0.645805	−0.0231681
$778$	31.6887	1.13609
$779$	−4.94763	−0.177267
$780$	0	0
$781$	−39.1786	−1.40192
$782$	−41.9074	−1.49861
$783$	−3.84995	−0.137586
$784$	−4.65622	−0.166293
$785$	16.2624	0.580430
$786$	−2.25868	−0.0805643
$787$	−8.76865	−0.312569	−0.156284	−	0.987712i	$-0.549952\pi$
$787$	−8.76865	−0.312569	−0.156284	+	0.987712i	$0.549952\pi$
$788$	5.08869	0.181277
$789$	9.40336	0.334768
$790$	0.231067	0.00822099
$791$	5.81164	0.206638
$792$	−4.13400	−0.146895
$793$	0	0
$794$	−7.66056	−0.271863
$795$	7.19684	0.255246
$796$	3.37909	0.119769
$797$	41.2911	1.46261	0.731304	−	0.682052i	$-0.238912\pi$
$797$	41.2911	1.46261	0.731304	+	0.682052i	$0.238912\pi$
$798$	1.21056	0.0428532
$799$	−33.5229	−1.18596
$800$	−30.4796	−1.07762
$801$	−5.50508	−0.194512
$802$	16.3268	0.576518
$803$	−50.5320	−1.78324
$804$	18.7622	0.661693
$805$	−4.14935	−0.146245
$806$	0	0
$807$	−28.4573	−1.00174
$808$	10.9673	0.385829
$809$	14.9921	0.527094	0.263547	−	0.964647i	$-0.415108\pi$
$809$	14.9921	0.527094	0.263547	+	0.964647i	$0.415108\pi$
$810$	−1.69011	−0.0593844
$811$	−51.5182	−1.80905	−0.904525	−	0.426421i	$-0.859774\pi$
$811$	−51.5182	−1.80905	−0.904525	+	0.426421i	$0.859774\pi$
$812$	6.10730	0.214324
$813$	7.15660	0.250993
$814$	6.45386	0.226208
$815$	15.4049	0.539610
$816$	−22.1620	−0.775825
$817$	6.72735	0.235360
$818$	47.3533	1.65567
$819$	0	0
$820$	−10.9577	−0.382661
$821$	19.1154	0.667133	0.333567	−	0.942727i	$-0.391748\pi$
$821$	19.1154	0.667133	0.333567	+	0.942727i	$0.391748\pi$
$822$	−7.63295	−0.266230
$823$	−35.2300	−1.22804	−0.614021	−	0.789290i	$-0.710449\pi$
$823$	−35.2300	−1.22804	−0.614021	+	0.789290i	$0.710449\pi$
$824$	10.7307	0.373822
$825$	22.1822	0.772286
$826$	−21.1155	−0.734702
$827$	−0.921236	−0.0320345	−0.0160173	−	0.999872i	$-0.505099\pi$
$827$	−0.921236	−0.0320345	−0.0160173	+	0.999872i	$0.505099\pi$
$828$	7.37537	0.256312
$829$	3.57666	0.124222	0.0621112	−	0.998069i	$-0.480217\pi$
$829$	3.57666	0.124222	0.0621112	+	0.998069i	$0.480217\pi$
$830$	−24.9656	−0.866568
$831$	−30.4598	−1.05664
$832$	0	0
$833$	4.75966	0.164912
$834$	−14.7651	−0.511273
$835$	11.3490	0.392748
$836$	−5.35114	−0.185073
$837$	2.03627	0.0703838
$838$	−11.2808	−0.389689
$839$	−46.3478	−1.60010	−0.800052	−	0.599930i	$-0.795195\pi$
$839$	−46.3478	−1.60010	−0.800052	+	0.599930i	$0.795195\pi$
$840$	−0.699146	−0.0241228
$841$	−14.1779	−0.488893
$842$	−10.4595	−0.360458
$843$	8.06012	0.277605
$844$	20.4713	0.704651
$845$	0	0
$846$	13.3380	0.458570
$847$	−16.8474	−0.578885
$848$	−37.5479	−1.28940
$849$	19.6060	0.672878
$850$	37.8890	1.29958
$851$	3.00256	0.102926
$852$	11.7774	0.403487
$853$	−57.5650	−1.97099	−0.985495	−	0.169706i	$-0.945718\pi$
$853$	−57.5650	−1.97099	−0.985495	+	0.169706i	$0.945718\pi$
$854$	1.57637	0.0539423
$855$	0.570492	0.0195104
$856$	−10.9746	−0.375105
$857$	34.8463	1.19033	0.595164	−	0.803604i	$-0.297087\pi$
$857$	34.8463	1.19033	0.595164	+	0.803604i	$0.297087\pi$
$858$	0	0
$859$	−32.4716	−1.10792	−0.553959	−	0.832544i	$-0.686883\pi$
$859$	−32.4716	−1.10792	−0.553959	+	0.832544i	$0.686883\pi$
$860$	14.8994	0.508064
$861$	7.73993	0.263776
$862$	−45.5919	−1.55287
$863$	−24.8269	−0.845117	−0.422559	−	0.906336i	$-0.638868\pi$
$863$	−24.8269	−0.845117	−0.422559	+	0.906336i	$0.638868\pi$
$864$	7.25098	0.246683
$865$	−12.5938	−0.428202
$866$	−69.8211	−2.37262
$867$	5.65435	0.192032
$868$	−3.23020	−0.109640
$869$	0.721465	0.0244740
$870$	6.50684	0.220602
$871$	0	0
$872$	−11.5566	−0.391355
$873$	7.63761	0.258494
$874$	−5.62827	−0.190379
$875$	8.21378	0.277677
$876$	15.1904	0.513235
$877$	9.37789	0.316669	0.158334	−	0.987386i	$-0.449388\pi$
$877$	9.37789	0.316669	0.158334	+	0.987386i	$0.449388\pi$
$878$	31.5341	1.06422
$879$	22.0402	0.743398
$880$	21.9288	0.739220
$881$	−36.4979	−1.22964	−0.614822	−	0.788666i	$-0.710772\pi$
$881$	−36.4979	−1.22964	−0.614822	+	0.788666i	$0.710772\pi$
$882$	−1.89376	−0.0637663
$883$	43.9023	1.47743	0.738716	−	0.674017i	$-0.235433\pi$
$883$	43.9023	1.47743	0.738716	+	0.674017i	$0.235433\pi$
$884$	0	0
$885$	−9.95098	−0.334498
$886$	−28.4587	−0.956088
$887$	−35.1542	−1.18036	−0.590181	−	0.807271i	$-0.700944\pi$
$887$	−35.1542	−1.18036	−0.590181	+	0.807271i	$0.700944\pi$
$888$	0.505918	0.0169775
$889$	1.69886	0.0569780
$890$	9.30419	0.311877
$891$	−5.27707	−0.176788
$892$	40.3908	1.35238
$893$	−4.50221	−0.150661
$894$	−30.1103	−1.00704
$895$	−19.8645	−0.663997
$896$	6.13307	0.204891
$897$	0	0
$898$	−11.2314	−0.374797
$899$	−7.83954	−0.261463
$900$	−6.66816	−0.222272
$901$	38.3820	1.27869
$902$	−77.3491	−2.57544
$903$	−10.5241	−0.350220
$904$	−4.55278	−0.151423
$905$	−6.47458	−0.215222
$906$	10.8708	0.361160
$907$	−50.8281	−1.68772	−0.843859	−	0.536564i	$-0.819722\pi$
$907$	−50.8281	−1.68772	−0.843859	+	0.536564i	$0.819722\pi$
$908$	−32.5907	−1.08156
$909$	13.9998	0.464344
$910$	0	0
$911$	30.5332	1.01161	0.505806	−	0.862647i	$-0.331195\pi$
$911$	30.5332	1.01161	0.505806	+	0.862647i	$0.331195\pi$
$912$	−2.97641	−0.0985588
$913$	−77.9506	−2.57979
$914$	1.02811	0.0340068
$915$	0.742888	0.0245591
$916$	20.8781	0.689833
$917$	−1.19269	−0.0393862
$918$	−9.01366	−0.297495
$919$	−10.1569	−0.335046	−0.167523	−	0.985868i	$-0.553577\pi$
$919$	−10.1569	−0.335046	−0.167523	+	0.985868i	$0.553577\pi$
$920$	3.25056	0.107168
$921$	31.2987	1.03133
$922$	24.5597	0.808831
$923$	0	0
$924$	8.37118	0.275391
$925$	−2.71465	−0.0892571
$926$	−77.7316	−2.55442
$927$	13.6978	0.449894
$928$	−27.9159	−0.916385
$929$	30.9183	1.01440	0.507198	−	0.861829i	$-0.330681\pi$
$929$	30.9183	1.01440	0.507198	+	0.861829i	$0.330681\pi$
$930$	−3.44152	−0.112852
$931$	0.639234	0.0209500
$932$	8.87175	0.290604
$933$	−14.2805	−0.467522
$934$	−75.6051	−2.47387
$935$	−22.4160	−0.733081
$936$	0	0
$937$	−25.1820	−0.822660	−0.411330	−	0.911487i	$-0.634936\pi$
$937$	−25.1820	−0.822660	−0.411330	+	0.911487i	$0.634936\pi$
$938$	22.3983	0.731332
$939$	30.3102	0.989136
$940$	−9.97125	−0.325226
$941$	21.4880	0.700488	0.350244	−	0.936659i	$-0.386099\pi$
$941$	21.4880	0.700488	0.350244	+	0.936659i	$0.386099\pi$
$942$	−34.5080	−1.12433
$943$	−35.9855	−1.17185
$944$	51.9170	1.68975
$945$	−0.892462	−0.0290318
$946$	105.173	3.41945
$947$	6.75721	0.219580	0.109790	−	0.993955i	$-0.464982\pi$
$947$	6.75721	0.219580	0.109790	+	0.993955i	$0.464982\pi$
$948$	−0.216879	−0.00704389
$949$	0	0
$950$	5.08859	0.165096
$951$	−6.17539	−0.200251
$952$	−3.72867	−0.120847
$953$	12.7022	0.411465	0.205733	−	0.978608i	$-0.434042\pi$
$953$	12.7022	0.411465	0.205733	+	0.978608i	$0.434042\pi$
$954$	−15.2713	−0.494428
$955$	−3.84656	−0.124472
$956$	41.1617	1.33126
$957$	20.3164	0.656737
$958$	−76.1636	−2.46074
$959$	−4.03058	−0.130154
$960$	−3.94396	−0.127291
$961$	−26.8536	−0.866245
$962$	0	0
$963$	−14.0091	−0.451438
$964$	−0.384693	−0.0123901
$965$	−10.9811	−0.353495
$966$	8.80472	0.283287
$967$	−30.7402	−0.988537	−0.494268	−	0.869309i	$-0.664564\pi$
$967$	−30.7402	−0.988537	−0.494268	+	0.869309i	$0.664564\pi$
$968$	13.1981	0.424204
$969$	3.04253	0.0977403
$970$	−12.9084	−0.414463
$971$	39.8444	1.27867	0.639333	−	0.768930i	$-0.279210\pi$
$971$	39.8444	1.27867	0.639333	+	0.768930i	$0.279210\pi$
$972$	1.58633	0.0508816
$973$	−7.79669	−0.249951
$974$	−32.6733	−1.04692
$975$	0	0
$976$	−3.87585	−0.124063
$977$	41.5811	1.33030	0.665149	−	0.746711i	$-0.268368\pi$
$977$	41.5811	1.33030	0.665149	+	0.746711i	$0.268368\pi$
$978$	−32.6885	−1.04526
$979$	29.0507	0.928464
$980$	1.41574	0.0452241
$981$	−14.7520	−0.470995
$982$	−59.2662	−1.89126
$983$	−18.8221	−0.600332	−0.300166	−	0.953887i	$-0.597042\pi$
$983$	−18.8221	−0.600332	−0.300166	+	0.953887i	$0.597042\pi$
$984$	−6.06339	−0.193294
$985$	2.86287	0.0912187
$986$	34.7021	1.10514
$987$	7.04313	0.224185
$988$	0	0
$989$	48.9299	1.55588
$990$	8.91882	0.283459
$991$	−42.2885	−1.34334	−0.671669	−	0.740851i	$-0.734422\pi$
$991$	−42.2885	−1.34334	−0.671669	+	0.740851i	$0.734422\pi$
$992$	14.7650	0.468788
$993$	10.5567	0.335007
$994$	14.0599	0.445952
$995$	1.90106	0.0602677
$996$	23.4326	0.742491
$997$	3.60346	0.114123	0.0570614	−	0.998371i	$-0.481827\pi$
$997$	3.60346	0.114123	0.0570614	+	0.998371i	$0.481827\pi$
$998$	−31.9024	−1.00985
$999$	0.645805	0.0204324

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bh.1.4	yes	15
13.12	even	2		3549.2.a.bg.1.12	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.bg.1.12	✓	15	13.12	even	2
3549.2.a.bh.1.4	yes	15	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q-1.89376 q^{2} +1.00000 q^{3} +1.58633 q^{4} +0.892462 q^{5} -1.89376 q^{6} -1.00000 q^{7} +0.783390 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.89376 q^{2} +1.00000 q^{3} +1.58633 q^{4} +0.892462 q^{5} -1.89376 q^{6} -1.00000 q^{7} +0.783390 q^{8} +1.00000 q^{9} -1.69011 q^{10} -5.27707 q^{11} +1.58633 q^{12} +1.89376 q^{14} +0.892462 q^{15} -4.65622 q^{16} +4.75966 q^{17} -1.89376 q^{18} +0.639234 q^{19} +1.41574 q^{20} -1.00000 q^{21} +9.99350 q^{22} +4.64933 q^{23} +0.783390 q^{24} -4.20351 q^{25} +1.00000 q^{27} -1.58633 q^{28} -3.84995 q^{29} -1.69011 q^{30} +2.03627 q^{31} +7.25098 q^{32} -5.27707 q^{33} -9.01366 q^{34} -0.892462 q^{35} +1.58633 q^{36} +0.645805 q^{37} -1.21056 q^{38} +0.699146 q^{40} -7.73993 q^{41} +1.89376 q^{42} +10.5241 q^{43} -8.37118 q^{44} +0.892462 q^{45} -8.80472 q^{46} -7.04313 q^{47} -4.65622 q^{48} +1.00000 q^{49} +7.96045 q^{50} +4.75966 q^{51} +8.06403 q^{53} -1.89376 q^{54} -4.70958 q^{55} -0.783390 q^{56} +0.639234 q^{57} +7.29089 q^{58} -11.1500 q^{59} +1.41574 q^{60} +0.832403 q^{61} -3.85621 q^{62} -1.00000 q^{63} -4.41919 q^{64} +9.99350 q^{66} +11.8274 q^{67} +7.55039 q^{68} +4.64933 q^{69} +1.69011 q^{70} +7.42431 q^{71} +0.783390 q^{72} +9.57578 q^{73} -1.22300 q^{74} -4.20351 q^{75} +1.01404 q^{76} +5.27707 q^{77} -0.136717 q^{79} -4.15549 q^{80} +1.00000 q^{81} +14.6576 q^{82} +14.7716 q^{83} -1.58633 q^{84} +4.24781 q^{85} -19.9301 q^{86} -3.84995 q^{87} -4.13400 q^{88} -5.50508 q^{89} -1.69011 q^{90} +7.37537 q^{92} +2.03627 q^{93} +13.3380 q^{94} +0.570492 q^{95} +7.25098 q^{96} +7.63761 q^{97} -1.89376 q^{98} -5.27707 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9} + 21 q^{10} + 5 q^{11} + 28 q^{12} - 2 q^{14} - 9 q^{15} + 50 q^{16} - q^{17} + 2 q^{18} + 3 q^{19} - 23 q^{20} - 15 q^{21} + 21 q^{22} + 4 q^{23} + 9 q^{24} + 50 q^{25} + 15 q^{27} - 28 q^{28} + 9 q^{29} + 21 q^{30} + 7 q^{31} + 35 q^{32} + 5 q^{33} - 2 q^{34} + 9 q^{35} + 28 q^{36} + 17 q^{37} - 12 q^{38} + 46 q^{40} - 22 q^{41} - 2 q^{42} + 36 q^{43} + 29 q^{44} - 9 q^{45} - q^{46} - 12 q^{47} + 50 q^{48} + 15 q^{49} + 53 q^{50} - q^{51} - 5 q^{53} + 2 q^{54} + 43 q^{55} - 9 q^{56} + 3 q^{57} + 29 q^{58} - 29 q^{59} - 23 q^{60} + 12 q^{61} + 14 q^{62} - 15 q^{63} + 95 q^{64} + 21 q^{66} - 12 q^{67} - 16 q^{68} + 4 q^{69} - 21 q^{70} + 36 q^{71} + 9 q^{72} - 29 q^{73} - 5 q^{74} + 50 q^{75} + 25 q^{76} - 5 q^{77} + 35 q^{79} - 89 q^{80} + 15 q^{81} + 51 q^{82} - 10 q^{83} - 28 q^{84} + 23 q^{85} + 19 q^{86} + 9 q^{87} + 73 q^{88} + 25 q^{89} + 21 q^{90} - 31 q^{92} + 7 q^{93} - 19 q^{94} - 7 q^{95} + 35 q^{96} - 26 q^{97} + 2 q^{98} + 5 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9 + 21 * q^10 + 5 * q^11 + 28 * q^12 - 2 * q^14 - 9 * q^15 + 50 * q^16 - q^17 + 2 * q^18 + 3 * q^19 - 23 * q^20 - 15 * q^21 + 21 * q^22 + 4 * q^23 + 9 * q^24 + 50 * q^25 + 15 * q^27 - 28 * q^28 + 9 * q^29 + 21 * q^30 + 7 * q^31 + 35 * q^32 + 5 * q^33 - 2 * q^34 + 9 * q^35 + 28 * q^36 + 17 * q^37 - 12 * q^38 + 46 * q^40 - 22 * q^41 - 2 * q^42 + 36 * q^43 + 29 * q^44 - 9 * q^45 - q^46 - 12 * q^47 + 50 * q^48 + 15 * q^49 + 53 * q^50 - q^51 - 5 * q^53 + 2 * q^54 + 43 * q^55 - 9 * q^56 + 3 * q^57 + 29 * q^58 - 29 * q^59 - 23 * q^60 + 12 * q^61 + 14 * q^62 - 15 * q^63 + 95 * q^64 + 21 * q^66 - 12 * q^67 - 16 * q^68 + 4 * q^69 - 21 * q^70 + 36 * q^71 + 9 * q^72 - 29 * q^73 - 5 * q^74 + 50 * q^75 + 25 * q^76 - 5 * q^77 + 35 * q^79 - 89 * q^80 + 15 * q^81 + 51 * q^82 - 10 * q^83 - 28 * q^84 + 23 * q^85 + 19 * q^86 + 9 * q^87 + 73 * q^88 + 25 * q^89 + 21 * q^90 - 31 * q^92 + 7 * q^93 - 19 * q^94 - 7 * q^95 + 35 * q^96 - 26 * q^97 + 2 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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