LMFDB - Embedded newform 6027.2.a.bm.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 14 x^{14} + 68 x^{13} + 64 x^{12} - 456 x^{11} - 54 x^{10} + 1532 x^{9} - 400 x^{8} + \cdots - 49 $ x^16 - 4x^15 - 14x^14 + 68x^13 + 64x^12 - 456x^11 - 54x^10 + 1532x^9 - 400x^8 - 2708x^7 + 1218x^6 + 2424x^5 - 1276x^4 - 960x^3 + 500x^2 + 112*x - 49
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.404293$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.404293 q^{2} +1.00000 q^{3} -1.83655 q^{4} -3.62653 q^{5} +0.404293 q^{6} -1.55109 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.404293 q^{2} +1.00000 q^{3} -1.83655 q^{4} -3.62653 q^{5} +0.404293 q^{6} -1.55109 q^{8} +1.00000 q^{9} -1.46618 q^{10} -5.64899 q^{11} -1.83655 q^{12} +4.03783 q^{13} -3.62653 q^{15} +3.04600 q^{16} +2.00918 q^{17} +0.404293 q^{18} -1.50889 q^{19} +6.66029 q^{20} -2.28385 q^{22} +7.05059 q^{23} -1.55109 q^{24} +8.15172 q^{25} +1.63246 q^{26} +1.00000 q^{27} +5.14414 q^{29} -1.46618 q^{30} -3.25825 q^{31} +4.33365 q^{32} -5.64899 q^{33} +0.812296 q^{34} -1.83655 q^{36} +0.612983 q^{37} -0.610033 q^{38} +4.03783 q^{39} +5.62507 q^{40} +1.00000 q^{41} +1.57300 q^{43} +10.3746 q^{44} -3.62653 q^{45} +2.85050 q^{46} +0.256386 q^{47} +3.04600 q^{48} +3.29568 q^{50} +2.00918 q^{51} -7.41566 q^{52} -7.87725 q^{53} +0.404293 q^{54} +20.4862 q^{55} -1.50889 q^{57} +2.07974 q^{58} -4.32499 q^{59} +6.66029 q^{60} +2.81546 q^{61} -1.31729 q^{62} -4.33993 q^{64} -14.6433 q^{65} -2.28385 q^{66} -13.3202 q^{67} -3.68995 q^{68} +7.05059 q^{69} +2.92409 q^{71} -1.55109 q^{72} +5.90098 q^{73} +0.247825 q^{74} +8.15172 q^{75} +2.77114 q^{76} +1.63246 q^{78} -1.04645 q^{79} -11.0464 q^{80} +1.00000 q^{81} +0.404293 q^{82} -10.3790 q^{83} -7.28634 q^{85} +0.635955 q^{86} +5.14414 q^{87} +8.76208 q^{88} +9.74008 q^{89} -1.46618 q^{90} -12.9487 q^{92} -3.25825 q^{93} +0.103655 q^{94} +5.47203 q^{95} +4.33365 q^{96} -8.22998 q^{97} -5.64899 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 16 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 16 * q^3 + 12 * q^4 - 12 * q^5 - 4 * q^6 - 12 * q^8 + 16 * q^9	$ 16 q - 4 q^{2} + 16 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{8} + 16 q^{9} - 4 q^{10} - 4 q^{11} + 12 q^{12} - 12 q^{15} - 8 q^{17} - 4 q^{18} + 4 q^{19} - 20 q^{20} - 16 q^{22} - 12 q^{23} - 12 q^{24} - 8 q^{25} - 8 q^{26} + 16 q^{27} - 16 q^{29} - 4 q^{30} - 4 q^{31} - 48 q^{32} - 4 q^{33} + 16 q^{34} + 12 q^{36} - 48 q^{37} - 4 q^{38} + 56 q^{40} + 16 q^{41} - 16 q^{43} - 12 q^{45} - 4 q^{46} - 36 q^{47} - 8 q^{50} - 8 q^{51} - 60 q^{53} - 4 q^{54} + 8 q^{55} + 4 q^{57} - 36 q^{58} - 36 q^{59} - 20 q^{60} - 4 q^{61} - 12 q^{62} + 52 q^{64} - 36 q^{65} - 16 q^{66} - 52 q^{67} - 8 q^{68} - 12 q^{69} - 12 q^{71} - 12 q^{72} - 16 q^{73} + 4 q^{74} - 8 q^{75} + 16 q^{76} - 8 q^{78} - 36 q^{79} - 68 q^{80} + 16 q^{81} - 4 q^{82} - 32 q^{83} - 28 q^{85} - 8 q^{86} - 16 q^{87} - 36 q^{88} - 12 q^{89} - 4 q^{90} - 36 q^{92} - 4 q^{93} + 24 q^{94} - 20 q^{95} - 48 q^{96} + 48 q^{97} - 4 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 + 16 * q^3 + 12 * q^4 - 12 * q^5 - 4 * q^6 - 12 * q^8 + 16 * q^9 - 4 * q^10 - 4 * q^11 + 12 * q^12 - 12 * q^15 - 8 * q^17 - 4 * q^18 + 4 * q^19 - 20 * q^20 - 16 * q^22 - 12 * q^23 - 12 * q^24 - 8 * q^25 - 8 * q^26 + 16 * q^27 - 16 * q^29 - 4 * q^30 - 4 * q^31 - 48 * q^32 - 4 * q^33 + 16 * q^34 + 12 * q^36 - 48 * q^37 - 4 * q^38 + 56 * q^40 + 16 * q^41 - 16 * q^43 - 12 * q^45 - 4 * q^46 - 36 * q^47 - 8 * q^50 - 8 * q^51 - 60 * q^53 - 4 * q^54 + 8 * q^55 + 4 * q^57 - 36 * q^58 - 36 * q^59 - 20 * q^60 - 4 * q^61 - 12 * q^62 + 52 * q^64 - 36 * q^65 - 16 * q^66 - 52 * q^67 - 8 * q^68 - 12 * q^69 - 12 * q^71 - 12 * q^72 - 16 * q^73 + 4 * q^74 - 8 * q^75 + 16 * q^76 - 8 * q^78 - 36 * q^79 - 68 * q^80 + 16 * q^81 - 4 * q^82 - 32 * q^83 - 28 * q^85 - 8 * q^86 - 16 * q^87 - 36 * q^88 - 12 * q^89 - 4 * q^90 - 36 * q^92 - 4 * q^93 + 24 * q^94 - 20 * q^95 - 48 * q^96 + 48 * q^97 - 4 * 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 $

$2$	0.404293	0.285878	0.142939	−	0.989731i	$-0.454345\pi$
$2$	0.404293	0.285878	0.142939	+	0.989731i	$0.454345\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.83655	−0.918274
$5$	−3.62653	−1.62183	−0.810917	−	0.585162i	$-0.801031\pi$
$5$	−3.62653	−1.62183	−0.810917	+	0.585162i	$0.801031\pi$
$6$	0.404293	0.165052
$7$	0	0
$7$	0	0
$8$	−1.55109	−0.548393
$9$	1.00000	0.333333
$10$	−1.46618	−0.463647
$11$	−5.64899	−1.70323	−0.851617	−	0.524165i	$-0.824377\pi$
$11$	−5.64899	−1.70323	−0.851617	+	0.524165i	$0.824377\pi$
$12$	−1.83655	−0.530166
$13$	4.03783	1.11989	0.559946	−	0.828529i	$-0.310822\pi$
$13$	4.03783	1.11989	0.559946	+	0.828529i	$0.310822\pi$
$14$	0	0
$15$	−3.62653	−0.936366
$16$	3.04600	0.761500
$17$	2.00918	0.487297	0.243649	−	0.969864i	$-0.421656\pi$
$17$	2.00918	0.487297	0.243649	+	0.969864i	$0.421656\pi$
$18$	0.404293	0.0952928
$19$	−1.50889	−0.346163	−0.173081	−	0.984908i	$-0.555372\pi$
$19$	−1.50889	−0.346163	−0.173081	+	0.984908i	$0.555372\pi$
$20$	6.66029	1.48929
$21$	0	0
$22$	−2.28385	−0.486917
$23$	7.05059	1.47015	0.735075	−	0.677986i	$-0.237147\pi$
$23$	7.05059	1.47015	0.735075	+	0.677986i	$0.237147\pi$
$24$	−1.55109	−0.316615
$25$	8.15172	1.63034
$26$	1.63246	0.320153
$27$	1.00000	0.192450
$28$	0	0
$29$	5.14414	0.955242	0.477621	−	0.878566i	$-0.341499\pi$
$29$	5.14414	0.955242	0.477621	+	0.878566i	$0.341499\pi$
$30$	−1.46618	−0.267687
$31$	−3.25825	−0.585199	−0.292600	−	0.956235i	$-0.594520\pi$
$31$	−3.25825	−0.585199	−0.292600	+	0.956235i	$0.594520\pi$
$32$	4.33365	0.766089
$33$	−5.64899	−0.983362
$34$	0.812296	0.139308
$35$	0	0
$36$	−1.83655	−0.306091
$37$	0.612983	0.100774	0.0503869	−	0.998730i	$-0.483955\pi$
$37$	0.612983	0.100774	0.0503869	+	0.998730i	$0.483955\pi$
$38$	−0.610033	−0.0989604
$39$	4.03783	0.646570
$40$	5.62507	0.889402
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	1.57300	0.239881	0.119940	−	0.992781i	$-0.461730\pi$
$43$	1.57300	0.239881	0.119940	+	0.992781i	$0.461730\pi$
$44$	10.3746	1.56403
$45$	−3.62653	−0.540611
$46$	2.85050	0.420284
$47$	0.256386	0.0373977	0.0186989	−	0.999825i	$-0.494048\pi$
$47$	0.256386	0.0373977	0.0186989	+	0.999825i	$0.494048\pi$
$48$	3.04600	0.439652
$49$	0	0
$50$	3.29568	0.466080
$51$	2.00918	0.281341
$52$	−7.41566	−1.02837
$53$	−7.87725	−1.08202	−0.541012	−	0.841015i	$-0.681959\pi$
$53$	−7.87725	−1.08202	−0.541012	+	0.841015i	$0.681959\pi$
$54$	0.404293	0.0550173
$55$	20.4862	2.76236
$56$	0	0
$57$	−1.50889	−0.199857
$58$	2.07974	0.273083
$59$	−4.32499	−0.563066	−0.281533	−	0.959552i	$-0.590843\pi$
$59$	−4.32499	−0.563066	−0.281533	+	0.959552i	$0.590843\pi$
$60$	6.66029	0.859840
$61$	2.81546	0.360483	0.180242	−	0.983622i	$-0.442312\pi$
$61$	2.81546	0.360483	0.180242	+	0.983622i	$0.442312\pi$
$62$	−1.31729	−0.167296
$63$	0	0
$64$	−4.33993	−0.542492
$65$	−14.6433	−1.81628
$66$	−2.28385	−0.281122
$67$	−13.3202	−1.62732	−0.813659	−	0.581342i	$-0.802528\pi$
$67$	−13.3202	−1.62732	−0.813659	+	0.581342i	$0.802528\pi$
$68$	−3.68995	−0.447472
$69$	7.05059	0.848791
$70$	0	0
$71$	2.92409	0.347026	0.173513	−	0.984832i	$-0.444488\pi$
$71$	2.92409	0.347026	0.173513	+	0.984832i	$0.444488\pi$
$72$	−1.55109	−0.182798
$73$	5.90098	0.690657	0.345329	−	0.938482i	$-0.387767\pi$
$73$	5.90098	0.690657	0.345329	+	0.938482i	$0.387767\pi$
$74$	0.247825	0.0288090
$75$	8.15172	0.941280
$76$	2.77114	0.317872
$77$	0	0
$78$	1.63246	0.184840
$79$	−1.04645	−0.117735	−0.0588674	−	0.998266i	$-0.518749\pi$
$79$	−1.04645	−0.117735	−0.0588674	+	0.998266i	$0.518749\pi$
$80$	−11.0464	−1.23503
$81$	1.00000	0.111111
$82$	0.404293	0.0446467
$83$	−10.3790	−1.13925	−0.569623	−	0.821906i	$-0.692911\pi$
$83$	−10.3790	−1.13925	−0.569623	+	0.821906i	$0.692911\pi$
$84$	0	0
$85$	−7.28634	−0.790315
$86$	0.635955	0.0685767
$87$	5.14414	0.551509
$88$	8.76208	0.934041
$89$	9.74008	1.03245	0.516223	−	0.856454i	$-0.327338\pi$
$89$	9.74008	1.03245	0.516223	+	0.856454i	$0.327338\pi$
$90$	−1.46618	−0.154549
$91$	0	0
$92$	−12.9487	−1.35000
$93$	−3.25825	−0.337865
$94$	0.103655	0.0106912
$95$	5.47203	0.561418
$96$	4.33365	0.442302
$97$	−8.22998	−0.835628	−0.417814	−	0.908533i	$-0.637204\pi$
$97$	−8.22998	−0.835628	−0.417814	+	0.908533i	$0.637204\pi$
$98$	0	0
$99$	−5.64899	−0.567744
$100$	−14.9710	−1.49710
$101$	13.1011	1.30361	0.651806	−	0.758386i	$-0.274012\pi$
$101$	13.1011	1.30361	0.651806	+	0.758386i	$0.274012\pi$
$102$	0.812296	0.0804293
$103$	12.0801	1.19029	0.595143	−	0.803620i	$-0.297095\pi$
$103$	12.0801	1.19029	0.595143	+	0.803620i	$0.297095\pi$
$104$	−6.26303	−0.614140
$105$	0	0
$106$	−3.18472	−0.309327
$107$	−10.0504	−0.971613	−0.485806	−	0.874066i	$-0.661474\pi$
$107$	−10.0504	−0.971613	−0.485806	+	0.874066i	$0.661474\pi$
$108$	−1.83655	−0.176722
$109$	−11.8153	−1.13170	−0.565849	−	0.824509i	$-0.691451\pi$
$109$	−11.8153	−1.13170	−0.565849	+	0.824509i	$0.691451\pi$
$110$	8.28243	0.789699
$111$	0.612983	0.0581818
$112$	0	0
$113$	−18.5214	−1.74235	−0.871173	−	0.490976i	$-0.836640\pi$
$113$	−18.5214	−1.74235	−0.871173	+	0.490976i	$0.836640\pi$
$114$	−0.610033	−0.0571348
$115$	−25.5692	−2.38434
$116$	−9.44745	−0.877174
$117$	4.03783	0.373297
$118$	−1.74856	−0.160968
$119$	0	0
$120$	5.62507	0.513496
$121$	20.9110	1.90100
$122$	1.13827	0.103054
$123$	1.00000	0.0901670
$124$	5.98393	0.537373
$125$	−11.4298	−1.02231
$126$	0	0
$127$	8.16826	0.724816	0.362408	−	0.932020i	$-0.381955\pi$
$127$	8.16826	0.724816	0.362408	+	0.932020i	$0.381955\pi$
$128$	−10.4219	−0.921176
$129$	1.57300	0.138495
$130$	−5.92018	−0.519234
$131$	−13.2261	−1.15557	−0.577786	−	0.816188i	$-0.696083\pi$
$131$	−13.2261	−1.15557	−0.577786	+	0.816188i	$0.696083\pi$
$132$	10.3746	0.902996
$133$	0	0
$134$	−5.38525	−0.465215
$135$	−3.62653	−0.312122
$136$	−3.11641	−0.267230
$137$	−17.1227	−1.46289	−0.731447	−	0.681898i	$-0.761155\pi$
$137$	−17.1227	−1.46289	−0.731447	+	0.681898i	$0.761155\pi$
$138$	2.85050	0.242651
$139$	18.7120	1.58713	0.793565	−	0.608485i	$-0.208223\pi$
$139$	18.7120	1.58713	0.793565	+	0.608485i	$0.208223\pi$
$140$	0	0
$141$	0.256386	0.0215916
$142$	1.18219	0.0992071
$143$	−22.8096	−1.90744
$144$	3.04600	0.253833
$145$	−18.6554	−1.54924
$146$	2.38572	0.197444
$147$	0	0
$148$	−1.12577	−0.0925379
$149$	−14.4114	−1.18063	−0.590313	−	0.807175i	$-0.700996\pi$
$149$	−14.4114	−1.18063	−0.590313	+	0.807175i	$0.700996\pi$
$150$	3.29568	0.269091
$151$	−7.70354	−0.626905	−0.313452	−	0.949604i	$-0.601486\pi$
$151$	−7.70354	−0.626905	−0.313452	+	0.949604i	$0.601486\pi$
$152$	2.34042	0.189833
$153$	2.00918	0.162432
$154$	0	0
$155$	11.8161	0.949096
$156$	−7.41566	−0.593728
$157$	0.429607	0.0342864	0.0171432	−	0.999853i	$-0.494543\pi$
$157$	0.429607	0.0342864	0.0171432	+	0.999853i	$0.494543\pi$
$158$	−0.423072	−0.0336578
$159$	−7.87725	−0.624707
$160$	−15.7161	−1.24247
$161$	0	0
$162$	0.404293	0.0317643
$163$	20.8708	1.63472	0.817362	−	0.576125i	$-0.195436\pi$
$163$	20.8708	1.63472	0.817362	+	0.576125i	$0.195436\pi$
$164$	−1.83655	−0.143410
$165$	20.4862	1.59485
$166$	−4.19617	−0.325686
$167$	−15.9352	−1.23310	−0.616552	−	0.787314i	$-0.711471\pi$
$167$	−15.9352	−1.23310	−0.616552	+	0.787314i	$0.711471\pi$
$168$	0	0
$169$	3.30404	0.254157
$170$	−2.94582	−0.225934
$171$	−1.50889	−0.115388
$172$	−2.88890	−0.220276
$173$	−5.12594	−0.389718	−0.194859	−	0.980831i	$-0.562425\pi$
$173$	−5.12594	−0.389718	−0.194859	+	0.980831i	$0.562425\pi$
$174$	2.07974	0.157665
$175$	0	0
$176$	−17.2068	−1.29701
$177$	−4.32499	−0.325086
$178$	3.93785	0.295154
$179$	−5.22886	−0.390823	−0.195412	−	0.980721i	$-0.562604\pi$
$179$	−5.22886	−0.390823	−0.195412	+	0.980721i	$0.562604\pi$
$180$	6.66029	0.496429
$181$	1.60946	0.119630	0.0598150	−	0.998209i	$-0.480949\pi$
$181$	1.60946	0.119630	0.0598150	+	0.998209i	$0.480949\pi$
$182$	0	0
$183$	2.81546	0.208125
$184$	−10.9361	−0.806219
$185$	−2.22300	−0.163438
$186$	−1.31729	−0.0965883
$187$	−11.3498	−0.829981
$188$	−0.470865	−0.0343413
$189$	0	0
$190$	2.21230	0.160497
$191$	−25.0344	−1.81142	−0.905712	−	0.423893i	$-0.860663\pi$
$191$	−25.0344	−1.81142	−0.905712	+	0.423893i	$0.860663\pi$
$192$	−4.33993	−0.313208
$193$	−2.83996	−0.204425	−0.102212	−	0.994763i	$-0.532592\pi$
$193$	−2.83996	−0.204425	−0.102212	+	0.994763i	$0.532592\pi$
$194$	−3.32732	−0.238888
$195$	−14.6433	−1.04863
$196$	0	0
$197$	−26.8159	−1.91056	−0.955278	−	0.295709i	$-0.904444\pi$
$197$	−26.8159	−1.91056	−0.955278	+	0.295709i	$0.904444\pi$
$198$	−2.28385	−0.162306
$199$	−7.39204	−0.524008	−0.262004	−	0.965067i	$-0.584383\pi$
$199$	−7.39204	−0.524008	−0.262004	+	0.965067i	$0.584383\pi$
$200$	−12.6440	−0.894069
$201$	−13.3202	−0.939533
$202$	5.29670	0.372674
$203$	0	0
$204$	−3.68995	−0.258348
$205$	−3.62653	−0.253288
$206$	4.88389	0.340277
$207$	7.05059	0.490050
$208$	12.2992	0.852797
$209$	8.52369	0.589596
$210$	0	0
$211$	22.3498	1.53862	0.769311	−	0.638875i	$-0.220600\pi$
$211$	22.3498	1.53862	0.769311	+	0.638875i	$0.220600\pi$
$212$	14.4669	0.993594
$213$	2.92409	0.200355
$214$	−4.06332	−0.277763
$215$	−5.70455	−0.389047
$216$	−1.55109	−0.105538
$217$	0	0
$218$	−4.77683	−0.323528
$219$	5.90098	0.398751
$220$	−37.6239	−2.53660
$221$	8.11271	0.545720
$222$	0.247825	0.0166329
$223$	28.5254	1.91020	0.955102	−	0.296276i	$-0.0957449\pi$
$223$	28.5254	1.91020	0.955102	+	0.296276i	$0.0957449\pi$
$224$	0	0
$225$	8.15172	0.543448
$226$	−7.48807	−0.498099
$227$	23.9051	1.58664	0.793319	−	0.608807i	$-0.208351\pi$
$227$	23.9051	1.58664	0.793319	+	0.608807i	$0.208351\pi$
$228$	2.77114	0.183524
$229$	−5.21232	−0.344440	−0.172220	−	0.985059i	$-0.555094\pi$
$229$	−5.21232	−0.344440	−0.172220	+	0.985059i	$0.555094\pi$
$230$	−10.3374	−0.681630
$231$	0	0
$232$	−7.97902	−0.523848
$233$	−22.9871	−1.50594	−0.752969	−	0.658056i	$-0.771379\pi$
$233$	−22.9871	−1.50594	−0.752969	+	0.658056i	$0.771379\pi$
$234$	1.63246	0.106718
$235$	−0.929791	−0.0606529
$236$	7.94305	0.517049
$237$	−1.04645	−0.0679742
$238$	0	0
$239$	30.5972	1.97917	0.989584	−	0.143959i	$-0.0459832\pi$
$239$	30.5972	1.97917	0.989584	+	0.143959i	$0.0459832\pi$
$240$	−11.0464	−0.713043
$241$	−14.3324	−0.923232	−0.461616	−	0.887080i	$-0.652730\pi$
$241$	−14.3324	−0.923232	−0.461616	+	0.887080i	$0.652730\pi$
$242$	8.45419	0.543456
$243$	1.00000	0.0641500
$244$	−5.17073	−0.331022
$245$	0	0
$246$	0.404293	0.0257768
$247$	−6.09263	−0.387665
$248$	5.05384	0.320919
$249$	−10.3790	−0.657744
$250$	−4.62099	−0.292257
$251$	−13.7477	−0.867746	−0.433873	−	0.900974i	$-0.642853\pi$
$251$	−13.7477	−0.867746	−0.433873	+	0.900974i	$0.642853\pi$
$252$	0	0
$253$	−39.8287	−2.50401
$254$	3.30237	0.207209
$255$	−7.28634	−0.456289
$256$	4.46636	0.279148
$257$	12.4136	0.774340	0.387170	−	0.922008i	$-0.373453\pi$
$257$	12.4136	0.774340	0.387170	+	0.922008i	$0.373453\pi$
$258$	0.635955	0.0395928
$259$	0	0
$260$	26.8931	1.66784
$261$	5.14414	0.318414
$262$	−5.34723	−0.330353
$263$	21.1795	1.30599	0.652993	−	0.757364i	$-0.273513\pi$
$263$	21.1795	1.30599	0.652993	+	0.757364i	$0.273513\pi$
$264$	8.76208	0.539269
$265$	28.5671	1.75486
$266$	0	0
$267$	9.74008	0.596083
$268$	24.4631	1.49432
$269$	5.56435	0.339264	0.169632	−	0.985507i	$-0.445742\pi$
$269$	5.56435	0.339264	0.169632	+	0.985507i	$0.445742\pi$
$270$	−1.46618	−0.0892289
$271$	11.2067	0.680762	0.340381	−	0.940288i	$-0.389444\pi$
$271$	11.2067	0.680762	0.340381	+	0.940288i	$0.389444\pi$
$272$	6.11996	0.371077
$273$	0	0
$274$	−6.92260	−0.418210
$275$	−46.0489	−2.77686
$276$	−12.9487	−0.779422
$277$	9.16881	0.550900	0.275450	−	0.961315i	$-0.411173\pi$
$277$	9.16881	0.550900	0.275450	+	0.961315i	$0.411173\pi$
$278$	7.56513	0.453726
$279$	−3.25825	−0.195066
$280$	0	0
$281$	21.2196	1.26585	0.632927	−	0.774212i	$-0.281853\pi$
$281$	21.2196	1.26585	0.632927	+	0.774212i	$0.281853\pi$
$282$	0.103655	0.00617256
$283$	4.61530	0.274351	0.137176	−	0.990547i	$-0.456198\pi$
$283$	4.61530	0.274351	0.137176	+	0.990547i	$0.456198\pi$
$284$	−5.37023	−0.318665
$285$	5.47203	0.324135
$286$	−9.22177	−0.545295
$287$	0	0
$288$	4.33365	0.255363
$289$	−12.9632	−0.762541
$290$	−7.54223	−0.442895
$291$	−8.22998	−0.482450
$292$	−10.8374	−0.634212
$293$	−4.86448	−0.284186	−0.142093	−	0.989853i	$-0.545383\pi$
$293$	−4.86448	−0.284186	−0.142093	+	0.989853i	$0.545383\pi$
$294$	0	0
$295$	15.6847	0.913199
$296$	−0.950791	−0.0552636
$297$	−5.64899	−0.327787
$298$	−5.82642	−0.337515
$299$	28.4691	1.64641
$300$	−14.9710	−0.864352
$301$	0	0
$302$	−3.11449	−0.179219
$303$	13.1011	0.752641
$304$	−4.59607	−0.263603
$305$	−10.2104	−0.584644
$306$	0.812296	0.0464359
$307$	−5.00629	−0.285724	−0.142862	−	0.989743i	$-0.545631\pi$
$307$	−5.00629	−0.285724	−0.142862	+	0.989743i	$0.545631\pi$
$308$	0	0
$309$	12.0801	0.687212
$310$	4.77719	0.271326
$311$	−13.3816	−0.758804	−0.379402	−	0.925232i	$-0.623870\pi$
$311$	−13.3816	−0.758804	−0.379402	+	0.925232i	$0.623870\pi$
$312$	−6.26303	−0.354574
$313$	−14.0907	−0.796451	−0.398225	−	0.917288i	$-0.630374\pi$
$313$	−14.0907	−0.796451	−0.398225	+	0.917288i	$0.630374\pi$
$314$	0.173687	0.00980173
$315$	0	0
$316$	1.92185	0.108113
$317$	−0.790011	−0.0443714	−0.0221857	−	0.999754i	$-0.507063\pi$
$317$	−0.790011	−0.0443714	−0.0221857	+	0.999754i	$0.507063\pi$
$318$	−3.18472	−0.178590
$319$	−29.0592	−1.62700
$320$	15.7389	0.879831
$321$	−10.0504	−0.560961
$322$	0	0
$323$	−3.03162	−0.168684
$324$	−1.83655	−0.102030
$325$	32.9152	1.82581
$326$	8.43790	0.467332
$327$	−11.8153	−0.653386
$328$	−1.55109	−0.0856446
$329$	0	0
$330$	8.28243	0.455933
$331$	4.79253	0.263421	0.131711	−	0.991288i	$-0.457953\pi$
$331$	4.79253	0.263421	0.131711	+	0.991288i	$0.457953\pi$
$332$	19.0616	1.04614
$333$	0.612983	0.0335913
$334$	−6.44250	−0.352518
$335$	48.3060	2.63924
$336$	0	0
$337$	−4.66846	−0.254307	−0.127153	−	0.991883i	$-0.540584\pi$
$337$	−4.66846	−0.254307	−0.127153	+	0.991883i	$0.540584\pi$
$338$	1.33580	0.0726580
$339$	−18.5214	−1.00594
$340$	13.3817	0.725725
$341$	18.4058	0.996731
$342$	−0.610033	−0.0329868
$343$	0	0
$344$	−2.43987	−0.131549
$345$	−25.5692	−1.37660
$346$	−2.07238	−0.111412
$347$	−24.1667	−1.29734	−0.648668	−	0.761072i	$-0.724673\pi$
$347$	−24.1667	−1.29734	−0.648668	+	0.761072i	$0.724673\pi$
$348$	−9.44745	−0.506437
$349$	−23.7131	−1.26933	−0.634665	−	0.772787i	$-0.718862\pi$
$349$	−23.7131	−1.26933	−0.634665	+	0.772787i	$0.718862\pi$
$350$	0	0
$351$	4.03783	0.215523
$352$	−24.4808	−1.30483
$353$	−8.89299	−0.473326	−0.236663	−	0.971592i	$-0.576054\pi$
$353$	−8.89299	−0.473326	−0.236663	+	0.971592i	$0.576054\pi$
$354$	−1.74856	−0.0929351
$355$	−10.6043	−0.562818
$356$	−17.8881	−0.948068
$357$	0	0
$358$	−2.11399	−0.111728
$359$	−21.1936	−1.11856	−0.559278	−	0.828980i	$-0.688922\pi$
$359$	−21.1936	−1.11856	−0.559278	+	0.828980i	$0.688922\pi$
$360$	5.62507	0.296467
$361$	−16.7233	−0.880171
$362$	0.650692	0.0341996
$363$	20.9110	1.09754
$364$	0	0
$365$	−21.4001	−1.12013
$366$	1.13827	0.0594984
$367$	21.4776	1.12112	0.560560	−	0.828114i	$-0.310586\pi$
$367$	21.4776	1.12112	0.560560	+	0.828114i	$0.310586\pi$
$368$	21.4761	1.11952
$369$	1.00000	0.0520579
$370$	−0.898743	−0.0467234
$371$	0	0
$372$	5.98393	0.310253
$373$	−37.7164	−1.95288	−0.976442	−	0.215781i	$-0.930770\pi$
$373$	−37.7164	−1.95288	−0.976442	+	0.215781i	$0.930770\pi$
$374$	−4.58865	−0.237273
$375$	−11.4298	−0.590233
$376$	−0.397677	−0.0205086
$377$	20.7711	1.06977
$378$	0	0
$379$	−15.8102	−0.812115	−0.406057	−	0.913848i	$-0.633097\pi$
$379$	−15.8102	−0.812115	−0.406057	+	0.913848i	$0.633097\pi$
$380$	−10.0496	−0.515536
$381$	8.16826	0.418472
$382$	−10.1212	−0.517847
$383$	17.8178	0.910449	0.455225	−	0.890377i	$-0.349559\pi$
$383$	17.8178	0.910449	0.455225	+	0.890377i	$0.349559\pi$
$384$	−10.4219	−0.531841
$385$	0	0
$386$	−1.14818	−0.0584406
$387$	1.57300	0.0799603
$388$	15.1147	0.767335
$389$	−35.3148	−1.79053	−0.895265	−	0.445534i	$-0.853014\pi$
$389$	−35.3148	−1.79053	−0.895265	+	0.445534i	$0.853014\pi$
$390$	−5.92018	−0.299780
$391$	14.1659	0.716400
$392$	0	0
$393$	−13.2261	−0.667170
$394$	−10.8415	−0.546186
$395$	3.79498	0.190946
$396$	10.3746	0.521345
$397$	−5.29392	−0.265694	−0.132847	−	0.991137i	$-0.542412\pi$
$397$	−5.29392	−0.265694	−0.132847	+	0.991137i	$0.542412\pi$
$398$	−2.98855	−0.149802
$399$	0	0
$400$	24.8301	1.24151
$401$	−29.3969	−1.46801	−0.734005	−	0.679144i	$-0.762351\pi$
$401$	−29.3969	−1.46801	−0.734005	+	0.679144i	$0.762351\pi$
$402$	−5.38525	−0.268592
$403$	−13.1563	−0.655360
$404$	−24.0609	−1.19707
$405$	−3.62653	−0.180204
$406$	0	0
$407$	−3.46273	−0.171641
$408$	−3.11641	−0.154285
$409$	−21.6968	−1.07284	−0.536419	−	0.843952i	$-0.680223\pi$
$409$	−21.6968	−1.07284	−0.536419	+	0.843952i	$0.680223\pi$
$410$	−1.46618	−0.0724095
$411$	−17.1227	−0.844602
$412$	−22.1856	−1.09301
$413$	0	0
$414$	2.85050	0.140095
$415$	37.6398	1.84767
$416$	17.4985	0.857937
$417$	18.7120	0.916330
$418$	3.44607	0.168553
$419$	1.07735	0.0526321	0.0263161	−	0.999654i	$-0.491622\pi$
$419$	1.07735	0.0526321	0.0263161	+	0.999654i	$0.491622\pi$
$420$	0	0
$421$	−18.8444	−0.918418	−0.459209	−	0.888328i	$-0.651867\pi$
$421$	−18.8444	−0.918418	−0.459209	+	0.888328i	$0.651867\pi$
$422$	9.03586	0.439859
$423$	0.256386	0.0124659
$424$	12.2183	0.593374
$425$	16.3783	0.794462
$426$	1.18219	0.0572773
$427$	0	0
$428$	18.4581	0.892206
$429$	−22.8096	−1.10126
$430$	−2.30631	−0.111220
$431$	21.2760	1.02483	0.512414	−	0.858739i	$-0.328751\pi$
$431$	21.2760	1.02483	0.512414	+	0.858739i	$0.328751\pi$
$432$	3.04600	0.146551
$433$	36.1242	1.73602	0.868010	−	0.496546i	$-0.165399\pi$
$433$	36.1242	1.73602	0.868010	+	0.496546i	$0.165399\pi$
$434$	0	0
$435$	−18.6554	−0.894457
$436$	21.6993	1.03921
$437$	−10.6385	−0.508911
$438$	2.38572	0.113994
$439$	24.0930	1.14989	0.574947	−	0.818191i	$-0.305023\pi$
$439$	24.0930	1.14989	0.574947	+	0.818191i	$0.305023\pi$
$440$	−31.7759	−1.51486
$441$	0	0
$442$	3.27991	0.156010
$443$	18.9748	0.901519	0.450759	−	0.892645i	$-0.351153\pi$
$443$	18.9748	0.901519	0.450759	+	0.892645i	$0.351153\pi$
$444$	−1.12577	−0.0534268
$445$	−35.3227	−1.67446
$446$	11.5326	0.546086
$447$	−14.4114	−0.681635
$448$	0	0
$449$	14.3690	0.678115	0.339058	−	0.940766i	$-0.389892\pi$
$449$	14.3690	0.678115	0.339058	+	0.940766i	$0.389892\pi$
$450$	3.29568	0.155360
$451$	−5.64899	−0.266000
$452$	34.0154	1.59995
$453$	−7.70354	−0.361944
$454$	9.66466	0.453585
$455$	0	0
$456$	2.34042	0.109600
$457$	8.51958	0.398529	0.199265	−	0.979946i	$-0.436145\pi$
$457$	8.51958	0.398529	0.199265	+	0.979946i	$0.436145\pi$
$458$	−2.10730	−0.0984679
$459$	2.00918	0.0937804
$460$	46.9590	2.18947
$461$	−32.8708	−1.53095	−0.765473	−	0.643468i	$-0.777495\pi$
$461$	−32.8708	−1.53095	−0.765473	+	0.643468i	$0.777495\pi$
$462$	0	0
$463$	32.4709	1.50905	0.754526	−	0.656270i	$-0.227867\pi$
$463$	32.4709	1.50905	0.754526	+	0.656270i	$0.227867\pi$
$464$	15.6690	0.727417
$465$	11.8161	0.547961
$466$	−9.29354	−0.430515
$467$	−28.5450	−1.32091	−0.660453	−	0.750867i	$-0.729636\pi$
$467$	−28.5450	−1.32091	−0.660453	+	0.750867i	$0.729636\pi$
$468$	−7.41566	−0.342789
$469$	0	0
$470$	−0.375908	−0.0173393
$471$	0.429607	0.0197952
$472$	6.70845	0.308781
$473$	−8.88588	−0.408573
$474$	−0.423072	−0.0194323
$475$	−12.3000	−0.564364
$476$	0	0
$477$	−7.87725	−0.360675
$478$	12.3702	0.565801
$479$	−22.9726	−1.04964	−0.524822	−	0.851212i	$-0.675868\pi$
$479$	−22.9726	−1.04964	−0.524822	+	0.851212i	$0.675868\pi$
$480$	−15.7161	−0.717340
$481$	2.47512	0.112856
$482$	−5.79450	−0.263932
$483$	0	0
$484$	−38.4041	−1.74564
$485$	29.8463	1.35525
$486$	0.404293	0.0183391
$487$	10.4709	0.474483	0.237242	−	0.971451i	$-0.423757\pi$
$487$	10.4709	0.474483	0.237242	+	0.971451i	$0.423757\pi$
$488$	−4.36703	−0.197686
$489$	20.8708	0.943808
$490$	0	0
$491$	−24.5729	−1.10896	−0.554479	−	0.832198i	$-0.687082\pi$
$491$	−24.5729	−1.10896	−0.554479	+	0.832198i	$0.687082\pi$
$492$	−1.83655	−0.0827979
$493$	10.3355	0.465487
$494$	−2.46321	−0.110825
$495$	20.4862	0.920787
$496$	−9.92464	−0.445629
$497$	0	0
$498$	−4.19617	−0.188035
$499$	−24.2119	−1.08387	−0.541937	−	0.840419i	$-0.682309\pi$
$499$	−24.2119	−1.08387	−0.541937	+	0.840419i	$0.682309\pi$
$500$	20.9914	0.938763
$501$	−15.9352	−0.711933
$502$	−5.55809	−0.248070
$503$	2.90630	0.129586	0.0647928	−	0.997899i	$-0.479361\pi$
$503$	2.90630	0.129586	0.0647928	+	0.997899i	$0.479361\pi$
$504$	0	0
$505$	−47.5117	−2.11424
$506$	−16.1025	−0.715841
$507$	3.30404	0.146738
$508$	−15.0014	−0.665579
$509$	−2.21101	−0.0980015	−0.0490008	−	0.998799i	$-0.515604\pi$
$509$	−2.21101	−0.0980015	−0.0490008	+	0.998799i	$0.515604\pi$
$510$	−2.94582	−0.130443
$511$	0	0
$512$	22.6495	1.00098
$513$	−1.50889	−0.0666190
$514$	5.01874	0.221367
$515$	−43.8088	−1.93045
$516$	−2.88890	−0.127177
$517$	−1.44832	−0.0636970
$518$	0	0
$519$	−5.12594	−0.225004
$520$	22.7131	0.996034
$521$	7.75309	0.339669	0.169835	−	0.985473i	$-0.445677\pi$
$521$	7.75309	0.339669	0.169835	+	0.985473i	$0.445677\pi$
$522$	2.07974	0.0910277
$523$	−17.8791	−0.781798	−0.390899	−	0.920434i	$-0.627836\pi$
$523$	−17.8791	−0.781798	−0.390899	+	0.920434i	$0.627836\pi$
$524$	24.2904	1.06113
$525$	0	0
$526$	8.56274	0.373353
$527$	−6.54641	−0.285166
$528$	−17.2068	−0.748830
$529$	26.7108	1.16134
$530$	11.5495	0.501677
$531$	−4.32499	−0.187689
$532$	0	0
$533$	4.03783	0.174898
$534$	3.93785	0.170407
$535$	36.4482	1.57579
$536$	20.6608	0.892410
$537$	−5.22886	−0.225642
$538$	2.24963	0.0969883
$539$	0	0
$540$	6.66029	0.286613
$541$	−8.00513	−0.344167	−0.172084	−	0.985082i	$-0.555050\pi$
$541$	−8.00513	−0.344167	−0.172084	+	0.985082i	$0.555050\pi$
$542$	4.53081	0.194615
$543$	1.60946	0.0690684
$544$	8.70708	0.373313
$545$	42.8484	1.83543
$546$	0	0
$547$	17.5624	0.750915	0.375458	−	0.926840i	$-0.377486\pi$
$547$	17.5624	0.750915	0.375458	+	0.926840i	$0.377486\pi$
$548$	31.4467	1.34334
$549$	2.81546	0.120161
$550$	−18.6173	−0.793843
$551$	−7.76193	−0.330669
$552$	−10.9361	−0.465471
$553$	0	0
$554$	3.70688	0.157490
$555$	−2.22300	−0.0943611
$556$	−34.3655	−1.45742
$557$	24.1031	1.02128	0.510640	−	0.859794i	$-0.329408\pi$
$557$	24.1031	1.02128	0.510640	+	0.859794i	$0.329408\pi$
$558$	−1.31729	−0.0557653
$559$	6.35152	0.268641
$560$	0	0
$561$	−11.3498	−0.479190
$562$	8.57892	0.361880
$563$	38.9921	1.64332	0.821662	−	0.569976i	$-0.193047\pi$
$563$	38.9921	1.64332	0.821662	+	0.569976i	$0.193047\pi$
$564$	−0.470865	−0.0198270
$565$	67.1684	2.82580
$566$	1.86593	0.0784311
$567$	0	0
$568$	−4.53553	−0.190306
$569$	10.9127	0.457485	0.228743	−	0.973487i	$-0.426539\pi$
$569$	10.9127	0.457485	0.228743	+	0.973487i	$0.426539\pi$
$570$	2.21230	0.0926631
$571$	−33.5273	−1.40307	−0.701537	−	0.712633i	$-0.747503\pi$
$571$	−33.5273	−1.40307	−0.701537	+	0.712633i	$0.747503\pi$
$572$	41.8910	1.75155
$573$	−25.0344	−1.04583
$574$	0	0
$575$	57.4744	2.39685
$576$	−4.33993	−0.180831
$577$	−34.2097	−1.42417	−0.712084	−	0.702094i	$-0.752248\pi$
$577$	−34.2097	−1.42417	−0.712084	+	0.702094i	$0.752248\pi$
$578$	−5.24093	−0.217994
$579$	−2.83996	−0.118025
$580$	34.2615	1.42263
$581$	0	0
$582$	−3.32732	−0.137922
$583$	44.4985	1.84294
$584$	−9.15294	−0.378751
$585$	−14.6433	−0.605426
$586$	−1.96667	−0.0812426
$587$	34.0227	1.40427	0.702134	−	0.712045i	$-0.252231\pi$
$587$	34.0227	1.40427	0.702134	+	0.712045i	$0.252231\pi$
$588$	0	0
$589$	4.91634	0.202574
$590$	6.34122	0.261064
$591$	−26.8159	−1.10306
$592$	1.86715	0.0767392
$593$	−35.1165	−1.44206	−0.721030	−	0.692904i	$-0.756331\pi$
$593$	−35.1165	−1.44206	−0.721030	+	0.692904i	$0.756331\pi$
$594$	−2.28385	−0.0937073
$595$	0	0
$596$	26.4672	1.08414
$597$	−7.39204	−0.302536
$598$	11.5098	0.470672
$599$	−7.10088	−0.290134	−0.145067	−	0.989422i	$-0.546340\pi$
$599$	−7.10088	−0.290134	−0.145067	+	0.989422i	$0.546340\pi$
$600$	−12.6440	−0.516191
$601$	−1.73551	−0.0707930	−0.0353965	−	0.999373i	$-0.511269\pi$
$601$	−1.73551	−0.0707930	−0.0353965	+	0.999373i	$0.511269\pi$
$602$	0	0
$603$	−13.3202	−0.542439
$604$	14.1479	0.575670
$605$	−75.8345	−3.08311
$606$	5.29670	0.215164
$607$	13.3765	0.542934	0.271467	−	0.962448i	$-0.412491\pi$
$607$	13.3765	0.542934	0.271467	+	0.962448i	$0.412491\pi$
$608$	−6.53900	−0.265191
$609$	0	0
$610$	−4.12798	−0.167137
$611$	1.03524	0.0418814
$612$	−3.68995	−0.149157
$613$	−1.90309	−0.0768652	−0.0384326	−	0.999261i	$-0.512236\pi$
$613$	−1.90309	−0.0768652	−0.0384326	+	0.999261i	$0.512236\pi$
$614$	−2.02401	−0.0816824
$615$	−3.62653	−0.146236
$616$	0	0
$617$	−9.72463	−0.391499	−0.195749	−	0.980654i	$-0.562714\pi$
$617$	−9.72463	−0.391499	−0.195749	+	0.980654i	$0.562714\pi$
$618$	4.88389	0.196459
$619$	−6.45607	−0.259491	−0.129746	−	0.991547i	$-0.541416\pi$
$619$	−6.45607	−0.259491	−0.129746	+	0.991547i	$0.541416\pi$
$620$	−21.7009	−0.871530
$621$	7.05059	0.282930
$622$	−5.41011	−0.216925
$623$	0	0
$624$	12.2992	0.492363
$625$	0.691937	0.0276775
$626$	−5.69675	−0.227688
$627$	8.52369	0.340403
$628$	−0.788993	−0.0314843
$629$	1.23159	0.0491068
$630$	0	0
$631$	−34.1970	−1.36136	−0.680681	−	0.732580i	$-0.738316\pi$
$631$	−34.1970	−1.36136	−0.680681	+	0.732580i	$0.738316\pi$
$632$	1.62314	0.0645649
$633$	22.3498	0.888324
$634$	−0.319396	−0.0126848
$635$	−29.6224	−1.17553
$636$	14.4669	0.573652
$637$	0	0
$638$	−11.7484	−0.465124
$639$	2.92409	0.115675
$640$	37.7954	1.49399
$641$	4.71311	0.186157	0.0930784	−	0.995659i	$-0.470329\pi$
$641$	4.71311	0.186157	0.0930784	+	0.995659i	$0.470329\pi$
$642$	−4.06332	−0.160367
$643$	−15.6912	−0.618800	−0.309400	−	0.950932i	$-0.600128\pi$
$643$	−15.6912	−0.618800	−0.309400	+	0.950932i	$0.600128\pi$
$644$	0	0
$645$	−5.70455	−0.224616
$646$	−1.22566	−0.0482231
$647$	−20.5419	−0.807585	−0.403793	−	0.914851i	$-0.632308\pi$
$647$	−20.5419	−0.807585	−0.403793	+	0.914851i	$0.632308\pi$
$648$	−1.55109	−0.0609325
$649$	24.4318	0.959033
$650$	13.3074	0.521959
$651$	0	0
$652$	−38.3301	−1.50112
$653$	−16.9600	−0.663698	−0.331849	−	0.943333i	$-0.607672\pi$
$653$	−16.9600	−0.663698	−0.331849	+	0.943333i	$0.607672\pi$
$654$	−4.77683	−0.186789
$655$	47.9649	1.87414
$656$	3.04600	0.118926
$657$	5.90098	0.230219
$658$	0	0
$659$	1.00491	0.0391459	0.0195729	−	0.999808i	$-0.493769\pi$
$659$	1.00491	0.0391459	0.0195729	+	0.999808i	$0.493769\pi$
$660$	−37.6239	−1.46451
$661$	−1.53402	−0.0596663	−0.0298332	−	0.999555i	$-0.509498\pi$
$661$	−1.53402	−0.0596663	−0.0298332	+	0.999555i	$0.509498\pi$
$662$	1.93759	0.0753065
$663$	8.11271	0.315072
$664$	16.0988	0.624754
$665$	0	0
$666$	0.247825	0.00960301
$667$	36.2692	1.40435
$668$	29.2658	1.13233
$669$	28.5254	1.10286
$670$	19.5298	0.754501
$671$	−15.9045	−0.613987
$672$	0	0
$673$	−4.78993	−0.184638	−0.0923192	−	0.995729i	$-0.529428\pi$
$673$	−4.78993	−0.184638	−0.0923192	+	0.995729i	$0.529428\pi$
$674$	−1.88742	−0.0727008
$675$	8.15172	0.313760
$676$	−6.06803	−0.233386
$677$	34.0664	1.30928	0.654638	−	0.755942i	$-0.272821\pi$
$677$	34.0664	1.30928	0.654638	+	0.755942i	$0.272821\pi$
$678$	−7.48807	−0.287578
$679$	0	0
$680$	11.3018	0.433403
$681$	23.9051	0.916045
$682$	7.44134	0.284944
$683$	−9.63255	−0.368579	−0.184290	−	0.982872i	$-0.558998\pi$
$683$	−9.63255	−0.368579	−0.184290	+	0.982872i	$0.558998\pi$
$684$	2.77114	0.105957
$685$	62.0961	2.37257
$686$	0	0
$687$	−5.21232	−0.198862
$688$	4.79137	0.182669
$689$	−31.8070	−1.21175
$690$	−10.3374	−0.393539
$691$	42.1141	1.60210	0.801049	−	0.598599i	$-0.204276\pi$
$691$	42.1141	1.60210	0.801049	+	0.598599i	$0.204276\pi$
$692$	9.41403	0.357868
$693$	0	0
$694$	−9.77042	−0.370880
$695$	−67.8596	−2.57406
$696$	−7.97902	−0.302444
$697$	2.00918	0.0761030
$698$	−9.58702	−0.362874
$699$	−22.9871	−0.869453
$700$	0	0
$701$	−30.5053	−1.15217	−0.576084	−	0.817391i	$-0.695420\pi$
$701$	−30.5053	−1.15217	−0.576084	+	0.817391i	$0.695420\pi$
$702$	1.63246	0.0616134
$703$	−0.924922	−0.0348841
$704$	24.5162	0.923990
$705$	−0.929791	−0.0350179
$706$	−3.59537	−0.135314
$707$	0	0
$708$	7.94305	0.298518
$709$	46.4610	1.74488	0.872440	−	0.488721i	$-0.162536\pi$
$709$	46.4610	1.74488	0.872440	+	0.488721i	$0.162536\pi$
$710$	−4.28724	−0.160897
$711$	−1.04645	−0.0392449
$712$	−15.1077	−0.566186
$713$	−22.9726	−0.860330
$714$	0	0
$715$	82.7198	3.09354
$716$	9.60305	0.358883
$717$	30.5972	1.14267
$718$	−8.56843	−0.319771
$719$	−42.8582	−1.59834	−0.799170	−	0.601105i	$-0.794727\pi$
$719$	−42.8582	−1.59834	−0.799170	+	0.601105i	$0.794727\pi$
$720$	−11.0464	−0.411675
$721$	0	0
$722$	−6.76109	−0.251622
$723$	−14.3324	−0.533028
$724$	−2.95584	−0.109853
$725$	41.9336	1.55737
$726$	8.45419	0.313764
$727$	−18.9785	−0.703874	−0.351937	−	0.936024i	$-0.614477\pi$
$727$	−18.9785	−0.703874	−0.351937	+	0.936024i	$0.614477\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−8.65190	−0.320221
$731$	3.16045	0.116893
$732$	−5.17073	−0.191116
$733$	−43.0175	−1.58889	−0.794445	−	0.607337i	$-0.792238\pi$
$733$	−43.0175	−1.58889	−0.794445	+	0.607337i	$0.792238\pi$
$734$	8.68323	0.320504
$735$	0	0
$736$	30.5548	1.12627
$737$	75.2455	2.77170
$738$	0.404293	0.0148822
$739$	−16.2946	−0.599408	−0.299704	−	0.954032i	$-0.596888\pi$
$739$	−16.2946	−0.599408	−0.299704	+	0.954032i	$0.596888\pi$
$740$	4.08265	0.150081
$741$	−6.09263	−0.223818
$742$	0	0
$743$	−24.1083	−0.884449	−0.442224	−	0.896905i	$-0.645810\pi$
$743$	−24.1083	−0.884449	−0.442224	+	0.896905i	$0.645810\pi$
$744$	5.05384	0.185283
$745$	52.2633	1.91478
$746$	−15.2485	−0.558287
$747$	−10.3790	−0.379749
$748$	20.8445	0.762149
$749$	0	0
$750$	−4.62099	−0.168735
$751$	−39.4430	−1.43929	−0.719647	−	0.694340i	$-0.755697\pi$
$751$	−39.4430	−1.43929	−0.719647	+	0.694340i	$0.755697\pi$
$752$	0.780951	0.0284784
$753$	−13.7477	−0.500994
$754$	8.39762	0.305823
$755$	27.9371	1.01674
$756$	0	0
$757$	−3.32835	−0.120971	−0.0604855	−	0.998169i	$-0.519265\pi$
$757$	−3.32835	−0.120971	−0.0604855	+	0.998169i	$0.519265\pi$
$758$	−6.39195	−0.232166
$759$	−39.8287	−1.44569
$760$	−8.48760	−0.307878
$761$	−54.7231	−1.98371	−0.991856	−	0.127364i	$-0.959348\pi$
$761$	−54.7231	−1.98371	−0.991856	+	0.127364i	$0.959348\pi$
$762$	3.30237	0.119632
$763$	0	0
$764$	45.9768	1.66338
$765$	−7.28634	−0.263438
$766$	7.20363	0.260278
$767$	−17.4636	−0.630573
$768$	4.46636	0.161166
$769$	23.7003	0.854655	0.427328	−	0.904097i	$-0.359455\pi$
$769$	23.7003	0.854655	0.427328	+	0.904097i	$0.359455\pi$
$770$	0	0
$771$	12.4136	0.447065
$772$	5.21572	0.187718
$773$	32.7011	1.17618	0.588089	−	0.808796i	$-0.299880\pi$
$773$	32.7011	1.17618	0.588089	+	0.808796i	$0.299880\pi$
$774$	0.635955	0.0228589
$775$	−26.5604	−0.954076
$776$	12.7654	0.458252
$777$	0	0
$778$	−14.2775	−0.511874
$779$	−1.50889	−0.0540615
$780$	26.8931	0.962928
$781$	−16.5181	−0.591066
$782$	5.72717	0.204803
$783$	5.14414	0.183836
$784$	0	0
$785$	−1.55798	−0.0556068
$786$	−5.34723	−0.190729
$787$	−18.2860	−0.651824	−0.325912	−	0.945400i	$-0.605671\pi$
$787$	−18.2860	−0.651824	−0.325912	+	0.945400i	$0.605671\pi$
$788$	49.2487	1.75441
$789$	21.1795	0.754011
$790$	1.53428	0.0545873
$791$	0	0
$792$	8.76208	0.311347
$793$	11.3684	0.403702
$794$	−2.14030	−0.0759563
$795$	28.5671	1.01317
$796$	13.5758	0.481183
$797$	−7.87343	−0.278891	−0.139446	−	0.990230i	$-0.544532\pi$
$797$	−7.87343	−0.278891	−0.139446	+	0.990230i	$0.544532\pi$
$798$	0	0
$799$	0.515125	0.0182238
$800$	35.3267	1.24899
$801$	9.74008	0.344149
$802$	−11.8849	−0.419672
$803$	−33.3345	−1.17635
$804$	24.4631	0.862748
$805$	0	0
$806$	−5.31898	−0.187353
$807$	5.56435	0.195874
$808$	−20.3210	−0.714892
$809$	19.0892	0.671140	0.335570	−	0.942015i	$-0.391071\pi$
$809$	19.0892	0.671140	0.335570	+	0.942015i	$0.391071\pi$
$810$	−1.46618	−0.0515163
$811$	20.5665	0.722186	0.361093	−	0.932530i	$-0.382404\pi$
$811$	20.5665	0.722186	0.361093	+	0.932530i	$0.382404\pi$
$812$	0	0
$813$	11.2067	0.393038
$814$	−1.39996	−0.0490685
$815$	−75.6884	−2.65125
$816$	6.11996	0.214241
$817$	−2.37349	−0.0830378
$818$	−8.77186	−0.306701
$819$	0	0
$820$	6.66029	0.232588
$821$	−2.65350	−0.0926079	−0.0463040	−	0.998927i	$-0.514744\pi$
$821$	−2.65350	−0.0926079	−0.0463040	+	0.998927i	$0.514744\pi$
$822$	−6.92260	−0.241453
$823$	30.8909	1.07679	0.538394	−	0.842693i	$-0.319031\pi$
$823$	30.8909	1.07679	0.538394	+	0.842693i	$0.319031\pi$
$824$	−18.7373	−0.652744
$825$	−46.0489	−1.60322
$826$	0	0
$827$	0.774423	0.0269293	0.0134647	−	0.999909i	$-0.495714\pi$
$827$	0.774423	0.0269293	0.0134647	+	0.999909i	$0.495714\pi$
$828$	−12.9487	−0.450000
$829$	−15.5292	−0.539352	−0.269676	−	0.962951i	$-0.586917\pi$
$829$	−15.5292	−0.539352	−0.269676	+	0.962951i	$0.586917\pi$
$830$	15.2175	0.528208
$831$	9.16881	0.318062
$832$	−17.5239	−0.607532
$833$	0	0
$834$	7.56513	0.261959
$835$	57.7896	1.99989
$836$	−15.6542	−0.541410
$837$	−3.25825	−0.112622
$838$	0.435566	0.0150464
$839$	−2.34091	−0.0808172	−0.0404086	−	0.999183i	$-0.512866\pi$
$839$	−2.34091	−0.0808172	−0.0404086	+	0.999183i	$0.512866\pi$
$840$	0	0
$841$	−2.53785	−0.0875119
$842$	−7.61864	−0.262556
$843$	21.2196	0.730841
$844$	−41.0464	−1.41288
$845$	−11.9822	−0.412201
$846$	0.103655	0.00356373
$847$	0	0
$848$	−23.9941	−0.823961
$849$	4.61530	0.158397
$850$	6.62161	0.227119
$851$	4.32189	0.148152
$852$	−5.37023	−0.183981
$853$	46.7682	1.60131	0.800656	−	0.599125i	$-0.204485\pi$
$853$	46.7682	1.60131	0.800656	+	0.599125i	$0.204485\pi$
$854$	0	0
$855$	5.47203	0.187139
$856$	15.5891	0.532825
$857$	−3.78098	−0.129156	−0.0645778	−	0.997913i	$-0.520570\pi$
$857$	−3.78098	−0.129156	−0.0645778	+	0.997913i	$0.520570\pi$
$858$	−9.22177	−0.314826
$859$	16.9802	0.579357	0.289679	−	0.957124i	$-0.406452\pi$
$859$	16.9802	0.579357	0.289679	+	0.957124i	$0.406452\pi$
$860$	10.4767	0.357251
$861$	0	0
$862$	8.60172	0.292976
$863$	42.9271	1.46125	0.730627	−	0.682776i	$-0.239228\pi$
$863$	42.9271	1.46125	0.730627	+	0.682776i	$0.239228\pi$
$864$	4.33365	0.147434
$865$	18.5894	0.632058
$866$	14.6048	0.496291
$867$	−12.9632	−0.440253
$868$	0	0
$869$	5.91138	0.200530
$870$	−7.54223	−0.255706
$871$	−53.7846	−1.82242
$872$	18.3265	0.620615
$873$	−8.22998	−0.278543
$874$	−4.30109	−0.145487
$875$	0	0
$876$	−10.8374	−0.366163
$877$	−14.8161	−0.500303	−0.250152	−	0.968207i	$-0.580480\pi$
$877$	−14.8161	−0.500303	−0.250152	+	0.968207i	$0.580480\pi$
$878$	9.74061	0.328730
$879$	−4.86448	−0.164075
$880$	62.4010	2.10354
$881$	48.7594	1.64275	0.821373	−	0.570391i	$-0.193208\pi$
$881$	48.7594	1.64275	0.821373	+	0.570391i	$0.193208\pi$
$882$	0	0
$883$	−27.6259	−0.929687	−0.464843	−	0.885393i	$-0.653889\pi$
$883$	−27.6259	−0.929687	−0.464843	+	0.885393i	$0.653889\pi$
$884$	−14.8994	−0.501120
$885$	15.6847	0.527236
$886$	7.67137	0.257725
$887$	−29.6770	−0.996457	−0.498229	−	0.867046i	$-0.666016\pi$
$887$	−29.6770	−0.996457	−0.498229	+	0.867046i	$0.666016\pi$
$888$	−0.950791	−0.0319065
$889$	0	0
$890$	−14.2807	−0.478691
$891$	−5.64899	−0.189248
$892$	−52.3883	−1.75409
$893$	−0.386857	−0.0129457
$894$	−5.82642	−0.194865
$895$	18.9626	0.633850
$896$	0	0
$897$	28.4691	0.950554
$898$	5.80929	0.193858
$899$	−16.7609	−0.559007
$900$	−14.9710	−0.499034
$901$	−15.8268	−0.527267
$902$	−2.28385	−0.0760437
$903$	0	0
$904$	28.7283	0.955490
$905$	−5.83674	−0.194020
$906$	−3.11449	−0.103472
$907$	35.1406	1.16683	0.583413	−	0.812176i	$-0.301717\pi$
$907$	35.1406	1.16683	0.583413	+	0.812176i	$0.301717\pi$
$908$	−43.9028	−1.45697
$909$	13.1011	0.434537
$910$	0	0
$911$	48.9016	1.62018	0.810091	−	0.586305i	$-0.199418\pi$
$911$	48.9016	1.62018	0.810091	+	0.586305i	$0.199418\pi$
$912$	−4.59607	−0.152191
$913$	58.6310	1.94040
$914$	3.44441	0.113931
$915$	−10.2104	−0.337544
$916$	9.57267	0.316290
$917$	0	0
$918$	0.812296	0.0268098
$919$	29.0668	0.958825	0.479412	−	0.877590i	$-0.340850\pi$
$919$	29.0668	0.958825	0.479412	+	0.877590i	$0.340850\pi$
$920$	39.6601	1.30755
$921$	−5.00629	−0.164963
$922$	−13.2894	−0.437664
$923$	11.8070	0.388631
$924$	0	0
$925$	4.99686	0.164296
$926$	13.1278	0.431405
$927$	12.0801	0.396762
$928$	22.2929	0.731801
$929$	4.60405	0.151054	0.0755271	−	0.997144i	$-0.475936\pi$
$929$	4.60405	0.151054	0.0755271	+	0.997144i	$0.475936\pi$
$930$	4.77719	0.156650
$931$	0	0
$932$	42.2170	1.38286
$933$	−13.3816	−0.438095
$934$	−11.5406	−0.377618
$935$	41.1605	1.34609
$936$	−6.26303	−0.204713
$937$	−9.16034	−0.299255	−0.149628	−	0.988742i	$-0.547807\pi$
$937$	−9.16034	−0.299255	−0.149628	+	0.988742i	$0.547807\pi$
$938$	0	0
$939$	−14.0907	−0.459831
$940$	1.70760	0.0556959
$941$	−49.9191	−1.62732	−0.813658	−	0.581344i	$-0.802527\pi$
$941$	−49.9191	−1.62732	−0.813658	+	0.581344i	$0.802527\pi$
$942$	0.173687	0.00565903
$943$	7.05059	0.229599
$944$	−13.1739	−0.428775
$945$	0	0
$946$	−3.59250	−0.116802
$947$	46.5491	1.51264	0.756322	−	0.654200i	$-0.226994\pi$
$947$	46.5491	1.51264	0.756322	+	0.654200i	$0.226994\pi$
$948$	1.92185	0.0624189
$949$	23.8271	0.773461
$950$	−4.97282	−0.161339
$951$	−0.790011	−0.0256179
$952$	0	0
$953$	−11.7321	−0.380041	−0.190020	−	0.981780i	$-0.560855\pi$
$953$	−11.7321	−0.380041	−0.190020	+	0.981780i	$0.560855\pi$
$954$	−3.18472	−0.103109
$955$	90.7880	2.93783
$956$	−56.1932	−1.81742
$957$	−29.0592	−0.939349
$958$	−9.28765	−0.300070
$959$	0	0
$960$	15.7389	0.507971
$961$	−20.3838	−0.657542
$962$	1.00067	0.0322630
$963$	−10.0504	−0.323871
$964$	26.3222	0.847780
$965$	10.2992	0.331543
$966$	0	0
$967$	−57.4991	−1.84905	−0.924523	−	0.381127i	$-0.875536\pi$
$967$	−57.4991	−1.84905	−0.924523	+	0.381127i	$0.875536\pi$
$968$	−32.4349	−1.04250
$969$	−3.03162	−0.0973898
$970$	12.0666	0.387436
$971$	−48.4020	−1.55329	−0.776647	−	0.629936i	$-0.783081\pi$
$971$	−48.4020	−1.55329	−0.776647	+	0.629936i	$0.783081\pi$
$972$	−1.83655	−0.0589073
$973$	0	0
$974$	4.23332	0.135644
$975$	32.9152	1.05413
$976$	8.57590	0.274508
$977$	20.1753	0.645464	0.322732	−	0.946490i	$-0.395399\pi$
$977$	20.1753	0.645464	0.322732	+	0.946490i	$0.395399\pi$
$978$	8.43790	0.269814
$979$	−55.0216	−1.75850
$980$	0	0
$981$	−11.8153	−0.377233
$982$	−9.93463	−0.317027
$983$	−32.6666	−1.04190	−0.520952	−	0.853586i	$-0.674423\pi$
$983$	−32.6666	−1.04190	−0.520952	+	0.853586i	$0.674423\pi$
$984$	−1.55109	−0.0494469
$985$	97.2488	3.09860
$986$	4.17857	0.133073
$987$	0	0
$988$	11.1894	0.355982
$989$	11.0906	0.352661
$990$	8.28243	0.263233
$991$	35.1121	1.11537	0.557686	−	0.830052i	$-0.311689\pi$
$991$	35.1121	1.11537	0.557686	+	0.830052i	$0.311689\pi$
$992$	−14.1201	−0.448315
$993$	4.79253	0.152086
$994$	0	0
$995$	26.8075	0.849854
$996$	19.0616	0.603989
$997$	−12.4124	−0.393104	−0.196552	−	0.980493i	$-0.562974\pi$
$997$	−12.4124	−0.393104	−0.196552	+	0.980493i	$0.562974\pi$
$998$	−9.78870	−0.309856
$999$	0.612983	0.0193939

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bm.1.10	yes	16
7.6	odd	2		6027.2.a.bl.1.10	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bl.1.10	✓	16	7.6	odd	2
6027.2.a.bm.1.10	yes	16	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+0.404293 q^{2} +1.00000 q^{3} -1.83655 q^{4} -3.62653 q^{5} +0.404293 q^{6} -1.55109 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.404293 q^{2} +1.00000 q^{3} -1.83655 q^{4} -3.62653 q^{5} +0.404293 q^{6} -1.55109 q^{8} +1.00000 q^{9} -1.46618 q^{10} -5.64899 q^{11} -1.83655 q^{12} +4.03783 q^{13} -3.62653 q^{15} +3.04600 q^{16} +2.00918 q^{17} +0.404293 q^{18} -1.50889 q^{19} +6.66029 q^{20} -2.28385 q^{22} +7.05059 q^{23} -1.55109 q^{24} +8.15172 q^{25} +1.63246 q^{26} +1.00000 q^{27} +5.14414 q^{29} -1.46618 q^{30} -3.25825 q^{31} +4.33365 q^{32} -5.64899 q^{33} +0.812296 q^{34} -1.83655 q^{36} +0.612983 q^{37} -0.610033 q^{38} +4.03783 q^{39} +5.62507 q^{40} +1.00000 q^{41} +1.57300 q^{43} +10.3746 q^{44} -3.62653 q^{45} +2.85050 q^{46} +0.256386 q^{47} +3.04600 q^{48} +3.29568 q^{50} +2.00918 q^{51} -7.41566 q^{52} -7.87725 q^{53} +0.404293 q^{54} +20.4862 q^{55} -1.50889 q^{57} +2.07974 q^{58} -4.32499 q^{59} +6.66029 q^{60} +2.81546 q^{61} -1.31729 q^{62} -4.33993 q^{64} -14.6433 q^{65} -2.28385 q^{66} -13.3202 q^{67} -3.68995 q^{68} +7.05059 q^{69} +2.92409 q^{71} -1.55109 q^{72} +5.90098 q^{73} +0.247825 q^{74} +8.15172 q^{75} +2.77114 q^{76} +1.63246 q^{78} -1.04645 q^{79} -11.0464 q^{80} +1.00000 q^{81} +0.404293 q^{82} -10.3790 q^{83} -7.28634 q^{85} +0.635955 q^{86} +5.14414 q^{87} +8.76208 q^{88} +9.74008 q^{89} -1.46618 q^{90} -12.9487 q^{92} -3.25825 q^{93} +0.103655 q^{94} +5.47203 q^{95} +4.33365 q^{96} -8.22998 q^{97} -5.64899 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 16 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 16 * q^3 + 12 * q^4 - 12 * q^5 - 4 * q^6 - 12 * q^8 + 16 * q^9	\( 16 q - 4 q^{2} + 16 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 12 q^{8} + 16 q^{9} - 4 q^{10} - 4 q^{11} + 12 q^{12} - 12 q^{15} - 8 q^{17} - 4 q^{18} + 4 q^{19} - 20 q^{20} - 16 q^{22} - 12 q^{23} - 12 q^{24} - 8 q^{25} - 8 q^{26} + 16 q^{27} - 16 q^{29} - 4 q^{30} - 4 q^{31} - 48 q^{32} - 4 q^{33} + 16 q^{34} + 12 q^{36} - 48 q^{37} - 4 q^{38} + 56 q^{40} + 16 q^{41} - 16 q^{43} - 12 q^{45} - 4 q^{46} - 36 q^{47} - 8 q^{50} - 8 q^{51} - 60 q^{53} - 4 q^{54} + 8 q^{55} + 4 q^{57} - 36 q^{58} - 36 q^{59} - 20 q^{60} - 4 q^{61} - 12 q^{62} + 52 q^{64} - 36 q^{65} - 16 q^{66} - 52 q^{67} - 8 q^{68} - 12 q^{69} - 12 q^{71} - 12 q^{72} - 16 q^{73} + 4 q^{74} - 8 q^{75} + 16 q^{76} - 8 q^{78} - 36 q^{79} - 68 q^{80} + 16 q^{81} - 4 q^{82} - 32 q^{83} - 28 q^{85} - 8 q^{86} - 16 q^{87} - 36 q^{88} - 12 q^{89} - 4 q^{90} - 36 q^{92} - 4 q^{93} + 24 q^{94} - 20 q^{95} - 48 q^{96} + 48 q^{97} - 4 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 16 * q^3 + 12 * q^4 - 12 * q^5 - 4 * q^6 - 12 * q^8 + 16 * q^9 - 4 * q^10 - 4 * q^11 + 12 * q^12 - 12 * q^15 - 8 * q^17 - 4 * q^18 + 4 * q^19 - 20 * q^20 - 16 * q^22 - 12 * q^23 - 12 * q^24 - 8 * q^25 - 8 * q^26 + 16 * q^27 - 16 * q^29 - 4 * q^30 - 4 * q^31 - 48 * q^32 - 4 * q^33 + 16 * q^34 + 12 * q^36 - 48 * q^37 - 4 * q^38 + 56 * q^40 + 16 * q^41 - 16 * q^43 - 12 * q^45 - 4 * q^46 - 36 * q^47 - 8 * q^50 - 8 * q^51 - 60 * q^53 - 4 * q^54 + 8 * q^55 + 4 * q^57 - 36 * q^58 - 36 * q^59 - 20 * q^60 - 4 * q^61 - 12 * q^62 + 52 * q^64 - 36 * q^65 - 16 * q^66 - 52 * q^67 - 8 * q^68 - 12 * q^69 - 12 * q^71 - 12 * q^72 - 16 * q^73 + 4 * q^74 - 8 * q^75 + 16 * q^76 - 8 * q^78 - 36 * q^79 - 68 * q^80 + 16 * q^81 - 4 * q^82 - 32 * q^83 - 28 * q^85 - 8 * q^86 - 16 * q^87 - 36 * q^88 - 12 * q^89 - 4 * q^90 - 36 * q^92 - 4 * q^93 + 24 * q^94 - 20 * q^95 - 48 * q^96 + 48 * q^97 - 4 * q^99

Introduction

L-functions

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