LMFDB - Embedded newform 4235.2.a.bc.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.288385.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 7x^{3} - 2x^{2} + 10x + 3 $ x^5 - 7x^3 - 2x^2 + 10*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.90452$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.90452 q^{2} +0.214998 q^{3} +1.62718 q^{4} +1.00000 q^{5} +0.409467 q^{6} -1.00000 q^{7} -0.710046 q^{8} -2.95378 q^{9} +O(q^{10})$	\(q+1.90452 q^{2} +0.214998 q^{3} +1.62718 q^{4} +1.00000 q^{5} +0.409467 q^{6} -1.00000 q^{7} -0.710046 q^{8} -2.95378 q^{9} +1.90452 q^{10} +0.349840 q^{12} +4.56834 q^{13} -1.90452 q^{14} +0.214998 q^{15} -4.60665 q^{16} -3.25164 q^{17} -5.62551 q^{18} -5.02403 q^{19} +1.62718 q^{20} -0.214998 q^{21} +0.292666 q^{23} -0.152659 q^{24} +1.00000 q^{25} +8.70047 q^{26} -1.28005 q^{27} -1.62718 q^{28} -1.00271 q^{29} +0.409467 q^{30} -6.62551 q^{31} -7.35334 q^{32} -6.19280 q^{34} -1.00000 q^{35} -4.80632 q^{36} -4.62822 q^{37} -9.56834 q^{38} +0.982183 q^{39} -0.710046 q^{40} -2.69743 q^{41} -0.409467 q^{42} -0.193423 q^{43} -2.95378 q^{45} +0.557388 q^{46} -4.29620 q^{47} -0.990420 q^{48} +1.00000 q^{49} +1.90452 q^{50} -0.699097 q^{51} +7.43350 q^{52} +2.78333 q^{53} -2.43787 q^{54} +0.710046 q^{56} -1.08016 q^{57} -1.90968 q^{58} -0.846879 q^{59} +0.349840 q^{60} -0.963356 q^{61} -12.6184 q^{62} +2.95378 q^{63} -4.79125 q^{64} +4.56834 q^{65} +3.95848 q^{67} -5.29100 q^{68} +0.0629227 q^{69} -1.90452 q^{70} +5.54264 q^{71} +2.09732 q^{72} -11.7502 q^{73} -8.81452 q^{74} +0.214998 q^{75} -8.17499 q^{76} +1.87058 q^{78} +9.39619 q^{79} -4.60665 q^{80} +8.58612 q^{81} -5.13730 q^{82} -9.07799 q^{83} -0.349840 q^{84} -3.25164 q^{85} -0.368378 q^{86} -0.215581 q^{87} +4.30633 q^{89} -5.62551 q^{90} -4.56834 q^{91} +0.476220 q^{92} -1.42447 q^{93} -8.18218 q^{94} -5.02403 q^{95} -1.58095 q^{96} +1.09820 q^{97} +1.90452 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	$ 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{12} - 6 q^{13} + 2 q^{15} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 5 q^{23} - 8 q^{24} + 5 q^{25} + 9 q^{26} - 7 q^{27} - 4 q^{28} - 11 q^{29} - 9 q^{30} - 2 q^{31} - 7 q^{32} + 8 q^{34} - 5 q^{35} + q^{36} + 2 q^{37} - 19 q^{38} - 2 q^{39} - 6 q^{40} - 13 q^{41} + 9 q^{42} - 10 q^{43} + 7 q^{45} - 2 q^{46} - 2 q^{47} + 32 q^{48} + 5 q^{49} - 30 q^{51} + 8 q^{52} - 14 q^{53} - 16 q^{54} + 6 q^{56} - 6 q^{57} + 4 q^{58} + 6 q^{59} + 3 q^{60} - 20 q^{61} + 15 q^{62} - 7 q^{63} - 6 q^{64} - 6 q^{65} - 9 q^{67} - 3 q^{68} - 30 q^{69} - 10 q^{71} - 38 q^{72} - 15 q^{73} + 19 q^{74} + 2 q^{75} + 5 q^{76} + 21 q^{78} - 23 q^{79} - 6 q^{80} + 13 q^{81} - 16 q^{82} - 8 q^{83} - 3 q^{84} - 2 q^{85} - 29 q^{86} + 22 q^{87} + 7 q^{89} + 3 q^{90} + 6 q^{91} + 26 q^{92} - 45 q^{93} + 14 q^{94} - 7 q^{95} + 18 q^{96} + 21 q^{97}+O(q^{100}) $ 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^12 - 6 * q^13 + 2 * q^15 - 6 * q^16 - 2 * q^17 + 3 * q^18 - 7 * q^19 + 4 * q^20 - 2 * q^21 + 5 * q^23 - 8 * q^24 + 5 * q^25 + 9 * q^26 - 7 * q^27 - 4 * q^28 - 11 * q^29 - 9 * q^30 - 2 * q^31 - 7 * q^32 + 8 * q^34 - 5 * q^35 + q^36 + 2 * q^37 - 19 * q^38 - 2 * q^39 - 6 * q^40 - 13 * q^41 + 9 * q^42 - 10 * q^43 + 7 * q^45 - 2 * q^46 - 2 * q^47 + 32 * q^48 + 5 * q^49 - 30 * q^51 + 8 * q^52 - 14 * q^53 - 16 * q^54 + 6 * q^56 - 6 * q^57 + 4 * q^58 + 6 * q^59 + 3 * q^60 - 20 * q^61 + 15 * q^62 - 7 * q^63 - 6 * q^64 - 6 * q^65 - 9 * q^67 - 3 * q^68 - 30 * q^69 - 10 * q^71 - 38 * q^72 - 15 * q^73 + 19 * q^74 + 2 * q^75 + 5 * q^76 + 21 * q^78 - 23 * q^79 - 6 * q^80 + 13 * q^81 - 16 * q^82 - 8 * q^83 - 3 * q^84 - 2 * q^85 - 29 * q^86 + 22 * q^87 + 7 * q^89 + 3 * q^90 + 6 * q^91 + 26 * q^92 - 45 * q^93 + 14 * q^94 - 7 * q^95 + 18 * q^96 + 21 * q^97

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 $

$2$	1.90452	1.34670	0.673348	−	0.739326i	$-0.264856\pi$
$2$	1.90452	1.34670	0.673348	+	0.739326i	$0.264856\pi$
$3$	0.214998	0.124129	0.0620646	−	0.998072i	$-0.480232\pi$
$3$	0.214998	0.124129	0.0620646	+	0.998072i	$0.480232\pi$
$4$	1.62718	0.813589
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.409467	0.167164
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.710046	−0.251039
$9$	−2.95378	−0.984592
$10$	1.90452	0.602261
$11$	0	0
$11$	0	0
$12$	0.349840	0.100990
$13$	4.56834	1.26703	0.633514	−	0.773731i	$-0.281612\pi$
$13$	4.56834	1.26703	0.633514	+	0.773731i	$0.281612\pi$
$14$	−1.90452	−0.509003
$15$	0.214998	0.0555123
$16$	−4.60665	−1.15166
$17$	−3.25164	−0.788639	−0.394320	−	0.918973i	$-0.629020\pi$
$17$	−3.25164	−0.788639	−0.394320	+	0.918973i	$0.629020\pi$
$18$	−5.62551	−1.32595
$19$	−5.02403	−1.15259	−0.576296	−	0.817241i	$-0.695502\pi$
$19$	−5.02403	−1.15259	−0.576296	+	0.817241i	$0.695502\pi$
$20$	1.62718	0.363848
$21$	−0.214998	−0.0469164
$22$	0	0
$23$	0.292666	0.0610252	0.0305126	−	0.999534i	$-0.490286\pi$
$23$	0.292666	0.0610252	0.0305126	+	0.999534i	$0.490286\pi$
$24$	−0.152659	−0.0311613
$25$	1.00000	0.200000
$26$	8.70047	1.70630
$27$	−1.28005	−0.246346
$28$	−1.62718	−0.307508
$29$	−1.00271	−0.186199	−0.0930995	−	0.995657i	$-0.529677\pi$
$29$	−1.00271	−0.186199	−0.0930995	+	0.995657i	$0.529677\pi$
$30$	0.409467	0.0747581
$31$	−6.62551	−1.18998	−0.594988	−	0.803734i	$-0.702843\pi$
$31$	−6.62551	−1.18998	−0.594988	+	0.803734i	$0.702843\pi$
$32$	−7.35334	−1.29990
$33$	0	0
$34$	−6.19280	−1.06206
$35$	−1.00000	−0.169031
$36$	−4.80632	−0.801053
$37$	−4.62822	−0.760875	−0.380438	−	0.924807i	$-0.624227\pi$
$37$	−4.62822	−0.760875	−0.380438	+	0.924807i	$0.624227\pi$
$38$	−9.56834	−1.55219
$39$	0.982183	0.157275
$40$	−0.710046	−0.112268
$41$	−2.69743	−0.421268	−0.210634	−	0.977565i	$-0.567553\pi$
$41$	−2.69743	−0.421268	−0.210634	+	0.977565i	$0.567553\pi$
$42$	−0.409467	−0.0631821
$43$	−0.193423	−0.0294968	−0.0147484	−	0.999891i	$-0.504695\pi$
$43$	−0.193423	−0.0294968	−0.0147484	+	0.999891i	$0.504695\pi$
$44$	0	0
$45$	−2.95378	−0.440323
$46$	0.557388	0.0821823
$47$	−4.29620	−0.626665	−0.313333	−	0.949643i	$-0.601445\pi$
$47$	−4.29620	−0.626665	−0.313333	+	0.949643i	$0.601445\pi$
$48$	−0.990420	−0.142955
$49$	1.00000	0.142857
$50$	1.90452	0.269339
$51$	−0.699097	−0.0978931
$52$	7.43350	1.03084
$53$	2.78333	0.382320	0.191160	−	0.981559i	$-0.438775\pi$
$53$	2.78333	0.382320	0.191160	+	0.981559i	$0.438775\pi$
$54$	−2.43787	−0.331753
$55$	0	0
$56$	0.710046	0.0948839
$57$	−1.08016	−0.143070
$58$	−1.90968	−0.250753
$59$	−0.846879	−0.110254	−0.0551271	−	0.998479i	$-0.517556\pi$
$59$	−0.846879	−0.110254	−0.0551271	+	0.998479i	$0.517556\pi$
$60$	0.349840	0.0451641
$61$	−0.963356	−0.123345	−0.0616725	−	0.998096i	$-0.519643\pi$
$61$	−0.963356	−0.123345	−0.0616725	+	0.998096i	$0.519643\pi$
$62$	−12.6184	−1.60254
$63$	2.95378	0.372141
$64$	−4.79125	−0.598906
$65$	4.56834	0.566632
$66$	0	0
$67$	3.95848	0.483605	0.241803	−	0.970325i	$-0.422261\pi$
$67$	3.95848	0.483605	0.241803	+	0.970325i	$0.422261\pi$
$68$	−5.29100	−0.641628
$69$	0.0629227	0.00757500
$70$	−1.90452	−0.227633
$71$	5.54264	0.657791	0.328895	−	0.944366i	$-0.393324\pi$
$71$	5.54264	0.657791	0.328895	+	0.944366i	$0.393324\pi$
$72$	2.09732	0.247171
$73$	−11.7502	−1.37526	−0.687628	−	0.726063i	$-0.741348\pi$
$73$	−11.7502	−1.37526	−0.687628	+	0.726063i	$0.741348\pi$
$74$	−8.81452	−1.02467
$75$	0.214998	0.0248258
$76$	−8.17499	−0.937735
$77$	0	0
$78$	1.87058	0.211802
$79$	9.39619	1.05715	0.528577	−	0.848885i	$-0.322726\pi$
$79$	9.39619	1.05715	0.528577	+	0.848885i	$0.322726\pi$
$80$	−4.60665	−0.515039
$81$	8.58612	0.954013
$82$	−5.13730	−0.567319
$83$	−9.07799	−0.996439	−0.498220	−	0.867051i	$-0.666013\pi$
$83$	−9.07799	−0.996439	−0.498220	+	0.867051i	$0.666013\pi$
$84$	−0.349840	−0.0381707
$85$	−3.25164	−0.352690
$86$	−0.368378	−0.0397232
$87$	−0.215581	−0.0231127
$88$	0	0
$89$	4.30633	0.456470	0.228235	−	0.973606i	$-0.426705\pi$
$89$	4.30633	0.456470	0.228235	+	0.973606i	$0.426705\pi$
$90$	−5.62551	−0.592981
$91$	−4.56834	−0.478892
$92$	0.476220	0.0496494
$93$	−1.42447	−0.147711
$94$	−8.18218	−0.843927
$95$	−5.02403	−0.515454
$96$	−1.58095	−0.161355
$97$	1.09820	0.111505	0.0557525	−	0.998445i	$-0.482244\pi$
$97$	1.09820	0.111505	0.0557525	+	0.998445i	$0.482244\pi$
$98$	1.90452	0.192385
$99$	0	0
$100$	1.62718	0.162718
$101$	−4.61577	−0.459286	−0.229643	−	0.973275i	$-0.573756\pi$
$101$	−4.61577	−0.459286	−0.229643	+	0.973275i	$0.573756\pi$
$102$	−1.33144	−0.131832
$103$	13.8643	1.36609	0.683044	−	0.730377i	$-0.260656\pi$
$103$	13.8643	1.36609	0.683044	+	0.730377i	$0.260656\pi$
$104$	−3.24373	−0.318074
$105$	−0.214998	−0.0209817
$106$	5.30090	0.514869
$107$	−14.5598	−1.40755	−0.703775	−	0.710423i	$-0.748504\pi$
$107$	−14.5598	−1.40755	−0.703775	+	0.710423i	$0.748504\pi$
$108$	−2.08287	−0.200424
$109$	−19.4350	−1.86154	−0.930768	−	0.365611i	$-0.880860\pi$
$109$	−19.4350	−1.86154	−0.930768	+	0.365611i	$0.880860\pi$
$110$	0	0
$111$	−0.995059	−0.0944468
$112$	4.60665	0.435287
$113$	−17.1884	−1.61695	−0.808474	−	0.588532i	$-0.799706\pi$
$113$	−17.1884	−1.61695	−0.808474	+	0.588532i	$0.799706\pi$
$114$	−2.05717	−0.192672
$115$	0.292666	0.0272913
$116$	−1.63159	−0.151489
$117$	−13.4938	−1.24751
$118$	−1.61289	−0.148479
$119$	3.25164	0.298078
$120$	−0.152659	−0.0139358
$121$	0	0
$122$	−1.83473	−0.166108
$123$	−0.579942	−0.0522916
$124$	−10.7809	−0.968152
$125$	1.00000	0.0894427
$126$	5.62551	0.501160
$127$	−3.06459	−0.271938	−0.135969	−	0.990713i	$-0.543415\pi$
$127$	−3.06459	−0.271938	−0.135969	+	0.990713i	$0.543415\pi$
$128$	5.58167	0.493355
$129$	−0.0415857	−0.00366141
$130$	8.70047	0.763081
$131$	14.6745	1.28212	0.641059	−	0.767492i	$-0.278495\pi$
$131$	14.6745	1.28212	0.641059	+	0.767492i	$0.278495\pi$
$132$	0	0
$133$	5.02403	0.435638
$134$	7.53898	0.651269
$135$	−1.28005	−0.110169
$136$	2.30882	0.197979
$137$	−15.7705	−1.34737	−0.673683	−	0.739020i	$-0.735289\pi$
$137$	−15.7705	−1.34737	−0.673683	+	0.739020i	$0.735289\pi$
$138$	0.119837	0.0102012
$139$	9.60769	0.814914	0.407457	−	0.913224i	$-0.366416\pi$
$139$	9.60769	0.814914	0.407457	+	0.913224i	$0.366416\pi$
$140$	−1.62718	−0.137522
$141$	−0.923674	−0.0777874
$142$	10.5560	0.885844
$143$	0	0
$144$	13.6070	1.13392
$145$	−1.00271	−0.0832707
$146$	−22.3784	−1.85205
$147$	0.214998	0.0177327
$148$	−7.53094	−0.619039
$149$	−1.39502	−0.114284	−0.0571422	−	0.998366i	$-0.518199\pi$
$149$	−1.39502	−0.114284	−0.0571422	+	0.998366i	$0.518199\pi$
$150$	0.409467	0.0334328
$151$	−11.9950	−0.976136	−0.488068	−	0.872805i	$-0.662298\pi$
$151$	−11.9950	−0.976136	−0.488068	+	0.872805i	$0.662298\pi$
$152$	3.56729	0.289346
$153$	9.60462	0.776488
$154$	0	0
$155$	−6.62551	−0.532174
$156$	1.59819	0.127957
$157$	−24.4749	−1.95331	−0.976657	−	0.214807i	$-0.931088\pi$
$157$	−24.4749	−1.95331	−0.976657	+	0.214807i	$0.931088\pi$
$158$	17.8952	1.42367
$159$	0.598412	0.0474571
$160$	−7.35334	−0.581332
$161$	−0.292666	−0.0230653
$162$	16.3524	1.28477
$163$	1.83205	0.143497	0.0717485	−	0.997423i	$-0.477142\pi$
$163$	1.83205	0.143497	0.0717485	+	0.997423i	$0.477142\pi$
$164$	−4.38920	−0.342739
$165$	0	0
$166$	−17.2892	−1.34190
$167$	6.88977	0.533146	0.266573	−	0.963815i	$-0.414109\pi$
$167$	6.88977	0.533146	0.266573	+	0.963815i	$0.414109\pi$
$168$	0.152659	0.0117779
$169$	7.86970	0.605362
$170$	−6.19280	−0.474966
$171$	14.8399	1.13483
$172$	−0.314734	−0.0239983
$173$	8.34496	0.634456	0.317228	−	0.948349i	$-0.397248\pi$
$173$	8.34496	0.634456	0.317228	+	0.948349i	$0.397248\pi$
$174$	−0.410578	−0.0311258
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−0.182077	−0.0136858
$178$	8.20147	0.614726
$179$	7.34255	0.548808	0.274404	−	0.961614i	$-0.411519\pi$
$179$	7.34255	0.548808	0.274404	+	0.961614i	$0.411519\pi$
$180$	−4.80632	−0.358242
$181$	0.127426	0.00947148	0.00473574	−	0.999989i	$-0.498493\pi$
$181$	0.127426	0.00947148	0.00473574	+	0.999989i	$0.498493\pi$
$182$	−8.70047	−0.644921
$183$	−0.207120	−0.0153107
$184$	−0.207807	−0.0153197
$185$	−4.62822	−0.340274
$186$	−2.71293	−0.198922
$187$	0	0
$188$	−6.99068	−0.509848
$189$	1.28005	0.0931099
$190$	−9.56834	−0.694160
$191$	23.0237	1.66594	0.832968	−	0.553321i	$-0.186640\pi$
$191$	23.0237	1.66594	0.832968	+	0.553321i	$0.186640\pi$
$192$	−1.03011	−0.0743417
$193$	17.8948	1.28809	0.644047	−	0.764986i	$-0.277254\pi$
$193$	17.8948	1.28809	0.644047	+	0.764986i	$0.277254\pi$
$194$	2.09153	0.150163
$195$	0.982183	0.0703356
$196$	1.62718	0.116227
$197$	21.6655	1.54360	0.771801	−	0.635864i	$-0.219356\pi$
$197$	21.6655	1.54360	0.771801	+	0.635864i	$0.219356\pi$
$198$	0	0
$199$	24.8072	1.75853	0.879267	−	0.476330i	$-0.158033\pi$
$199$	24.8072	1.75853	0.879267	+	0.476330i	$0.158033\pi$
$200$	−0.710046	−0.0502078
$201$	0.851065	0.0600295
$202$	−8.79080	−0.618518
$203$	1.00271	0.0703766
$204$	−1.13755	−0.0796447
$205$	−2.69743	−0.188397
$206$	26.4047	1.83970
$207$	−0.864471	−0.0600849
$208$	−21.0447	−1.45919
$209$	0	0
$210$	−0.409467	−0.0282559
$211$	−21.0959	−1.45230	−0.726150	−	0.687536i	$-0.758692\pi$
$211$	−21.0959	−1.45230	−0.726150	+	0.687536i	$0.758692\pi$
$212$	4.52898	0.311052
$213$	1.19166	0.0816510
$214$	−27.7294	−1.89554
$215$	−0.193423	−0.0131914
$216$	0.908895	0.0618424
$217$	6.62551	0.449769
$218$	−37.0143	−2.50692
$219$	−2.52627	−0.170709
$220$	0	0
$221$	−14.8546	−0.999228
$222$	−1.89510	−0.127191
$223$	13.0233	0.872105	0.436053	−	0.899921i	$-0.356376\pi$
$223$	13.0233	0.872105	0.436053	+	0.899921i	$0.356376\pi$
$224$	7.35334	0.491316
$225$	−2.95378	−0.196918
$226$	−32.7355	−2.17754
$227$	−12.1441	−0.806032	−0.403016	−	0.915193i	$-0.632038\pi$
$227$	−12.1441	−0.806032	−0.403016	+	0.915193i	$0.632038\pi$
$228$	−1.75761	−0.116400
$229$	18.8096	1.24297	0.621487	−	0.783424i	$-0.286529\pi$
$229$	18.8096	1.24297	0.621487	+	0.783424i	$0.286529\pi$
$230$	0.557388	0.0367530
$231$	0	0
$232$	0.711972	0.0467433
$233$	−23.4069	−1.53344	−0.766719	−	0.641983i	$-0.778112\pi$
$233$	−23.4069	−1.53344	−0.766719	+	0.641983i	$0.778112\pi$
$234$	−25.6992	−1.68001
$235$	−4.29620	−0.280253
$236$	−1.37802	−0.0897016
$237$	2.02016	0.131224
$238$	6.19280	0.401420
$239$	−15.0841	−0.975710	−0.487855	−	0.872925i	$-0.662221\pi$
$239$	−15.0841	−0.975710	−0.487855	+	0.872925i	$0.662221\pi$
$240$	−0.990420	−0.0639314
$241$	0.499627	0.0321838	0.0160919	−	0.999871i	$-0.494878\pi$
$241$	0.499627	0.0321838	0.0160919	+	0.999871i	$0.494878\pi$
$242$	0	0
$243$	5.68615	0.364767
$244$	−1.56755	−0.100352
$245$	1.00000	0.0638877
$246$	−1.10451	−0.0704209
$247$	−22.9515	−1.46037
$248$	4.70442	0.298731
$249$	−1.95175	−0.123687
$250$	1.90452	0.120452
$251$	−20.8388	−1.31533	−0.657666	−	0.753310i	$-0.728456\pi$
$251$	−20.8388	−1.31533	−0.657666	+	0.753310i	$0.728456\pi$
$252$	4.80632	0.302770
$253$	0	0
$254$	−5.83656	−0.366218
$255$	−0.699097	−0.0437791
$256$	20.2129	1.26330
$257$	−9.23887	−0.576305	−0.288152	−	0.957585i	$-0.593041\pi$
$257$	−9.23887	−0.576305	−0.288152	+	0.957585i	$0.593041\pi$
$258$	−0.0792005	−0.00493081
$259$	4.62822	0.287584
$260$	7.43350	0.461006
$261$	2.96179	0.183330
$262$	27.9478	1.72662
$263$	−3.90063	−0.240523	−0.120262	−	0.992742i	$-0.538373\pi$
$263$	−3.90063	−0.240523	−0.120262	+	0.992742i	$0.538373\pi$
$264$	0	0
$265$	2.78333	0.170979
$266$	9.56834	0.586672
$267$	0.925852	0.0566612
$268$	6.44115	0.393456
$269$	27.9577	1.70461	0.852307	−	0.523043i	$-0.175203\pi$
$269$	27.9577	1.70461	0.852307	+	0.523043i	$0.175203\pi$
$270$	−2.43787	−0.148364
$271$	−24.0897	−1.46335	−0.731673	−	0.681655i	$-0.761260\pi$
$271$	−24.0897	−1.46335	−0.731673	+	0.681655i	$0.761260\pi$
$272$	14.9792	0.908246
$273$	−0.982183	−0.0594444
$274$	−30.0352	−1.81449
$275$	0	0
$276$	0.102386	0.00616294
$277$	−27.1882	−1.63358	−0.816790	−	0.576935i	$-0.804249\pi$
$277$	−27.1882	−1.63358	−0.816790	+	0.576935i	$0.804249\pi$
$278$	18.2980	1.09744
$279$	19.5703	1.17164
$280$	0.710046	0.0424334
$281$	−19.4935	−1.16289	−0.581443	−	0.813587i	$-0.697512\pi$
$281$	−19.4935	−1.16289	−0.581443	+	0.813587i	$0.697512\pi$
$282$	−1.75915	−0.104756
$283$	2.43412	0.144693	0.0723466	−	0.997380i	$-0.476951\pi$
$283$	2.43412	0.144693	0.0723466	+	0.997380i	$0.476951\pi$
$284$	9.01886	0.535171
$285$	−1.08016	−0.0639829
$286$	0	0
$287$	2.69743	0.159224
$288$	21.7201	1.27987
$289$	−6.42682	−0.378048
$290$	−1.90968	−0.112140
$291$	0.236110	0.0138410
$292$	−19.1196	−1.11889
$293$	24.4918	1.43083	0.715413	−	0.698702i	$-0.246239\pi$
$293$	24.4918	1.43083	0.715413	+	0.698702i	$0.246239\pi$
$294$	0.409467	0.0238806
$295$	−0.846879	−0.0493072
$296$	3.28625	0.191009
$297$	0	0
$298$	−2.65683	−0.153906
$299$	1.33700	0.0773206
$300$	0.349840	0.0201980
$301$	0.193423	0.0111487
$302$	−22.8446	−1.31456
$303$	−0.992381	−0.0570108
$304$	23.1439	1.32740
$305$	−0.963356	−0.0551616
$306$	18.2921	1.04569
$307$	23.0511	1.31559	0.657797	−	0.753195i	$-0.271488\pi$
$307$	23.0511	1.31559	0.657797	+	0.753195i	$0.271488\pi$
$308$	0	0
$309$	2.98079	0.169571
$310$	−12.6184	−0.716676
$311$	18.7222	1.06164	0.530819	−	0.847485i	$-0.321884\pi$
$311$	18.7222	1.06164	0.530819	+	0.847485i	$0.321884\pi$
$312$	−0.697395	−0.0394822
$313$	15.4725	0.874555	0.437277	−	0.899327i	$-0.355943\pi$
$313$	15.4725	0.874555	0.437277	+	0.899327i	$0.355943\pi$
$314$	−46.6129	−2.63052
$315$	2.95378	0.166426
$316$	15.2893	0.860089
$317$	12.8989	0.724476	0.362238	−	0.932086i	$-0.382013\pi$
$317$	12.8989	0.724476	0.362238	+	0.932086i	$0.382013\pi$
$318$	1.13968	0.0639103
$319$	0	0
$320$	−4.79125	−0.267839
$321$	−3.13033	−0.174718
$322$	−0.557388	−0.0310620
$323$	16.3363	0.908978
$324$	13.9711	0.776174
$325$	4.56834	0.253406
$326$	3.48916	0.193247
$327$	−4.17849	−0.231071
$328$	1.91530	0.105755
$329$	4.29620	0.236857
$330$	0	0
$331$	−8.28642	−0.455463	−0.227731	−	0.973724i	$-0.573131\pi$
$331$	−8.28642	−0.455463	−0.227731	+	0.973724i	$0.573131\pi$
$332$	−14.7715	−0.810692
$333$	13.6707	0.749152
$334$	13.1217	0.717986
$335$	3.95848	0.216275
$336$	0.990420	0.0540319
$337$	33.6591	1.83353	0.916763	−	0.399431i	$-0.130792\pi$
$337$	33.6591	1.83353	0.916763	+	0.399431i	$0.130792\pi$
$338$	14.9880	0.815238
$339$	−3.69547	−0.200710
$340$	−5.29100	−0.286945
$341$	0	0
$342$	28.2627	1.52827
$343$	−1.00000	−0.0539949
$344$	0.137340	0.00740485
$345$	0.0629227	0.00338764
$346$	15.8931	0.854419
$347$	19.8757	1.06698	0.533492	−	0.845805i	$-0.320879\pi$
$347$	19.8757	1.06698	0.533492	+	0.845805i	$0.320879\pi$
$348$	−0.350789	−0.0188043
$349$	−18.7227	−1.00221	−0.501103	−	0.865388i	$-0.667072\pi$
$349$	−18.7227	−1.00221	−0.501103	+	0.865388i	$0.667072\pi$
$350$	−1.90452	−0.101801
$351$	−5.84770	−0.312127
$352$	0	0
$353$	13.9588	0.742951	0.371476	−	0.928443i	$-0.378852\pi$
$353$	13.9588	0.742951	0.371476	+	0.928443i	$0.378852\pi$
$354$	−0.346769	−0.0184306
$355$	5.54264	0.294173
$356$	7.00716	0.371379
$357$	0.699097	0.0370001
$358$	13.9840	0.739078
$359$	30.4147	1.60523	0.802613	−	0.596501i	$-0.203443\pi$
$359$	30.4147	1.60523	0.802613	+	0.596501i	$0.203443\pi$
$360$	2.09732	0.110538
$361$	6.24086	0.328466
$362$	0.242684	0.0127552
$363$	0	0
$364$	−7.43350	−0.389621
$365$	−11.7502	−0.615033
$366$	−0.394462	−0.0206189
$367$	−22.8152	−1.19094	−0.595471	−	0.803377i	$-0.703035\pi$
$367$	−22.8152	−1.19094	−0.595471	+	0.803377i	$0.703035\pi$
$368$	−1.34821	−0.0702804
$369$	7.96760	0.414777
$370$	−8.81452	−0.458245
$371$	−2.78333	−0.144504
$372$	−2.31787	−0.120176
$373$	−25.0369	−1.29636	−0.648180	−	0.761487i	$-0.724470\pi$
$373$	−25.0369	−1.29636	−0.648180	+	0.761487i	$0.724470\pi$
$374$	0	0
$375$	0.214998	0.0111025
$376$	3.05050	0.157318
$377$	−4.58073	−0.235920
$378$	2.43787	0.125391
$379$	24.0173	1.23369	0.616843	−	0.787086i	$-0.288411\pi$
$379$	24.0173	1.23369	0.616843	+	0.787086i	$0.288411\pi$
$380$	−8.17499	−0.419368
$381$	−0.658881	−0.0337555
$382$	43.8490	2.24351
$383$	7.78788	0.397942	0.198971	−	0.980005i	$-0.436240\pi$
$383$	7.78788	0.397942	0.198971	+	0.980005i	$0.436240\pi$
$384$	1.20005	0.0612397
$385$	0	0
$386$	34.0809	1.73467
$387$	0.571329	0.0290423
$388$	1.78696	0.0907193
$389$	12.4598	0.631735	0.315867	−	0.948803i	$-0.397705\pi$
$389$	12.4598	0.631735	0.315867	+	0.948803i	$0.397705\pi$
$390$	1.87058	0.0947207
$391$	−0.951647	−0.0481268
$392$	−0.710046	−0.0358627
$393$	3.15499	0.159148
$394$	41.2623	2.07876
$395$	9.39619	0.472774
$396$	0	0
$397$	−1.78212	−0.0894419	−0.0447209	−	0.999000i	$-0.514240\pi$
$397$	−1.78212	−0.0894419	−0.0447209	+	0.999000i	$0.514240\pi$
$398$	47.2456	2.36821
$399$	1.08016	0.0540754
$400$	−4.60665	−0.230332
$401$	−32.5153	−1.62373	−0.811867	−	0.583842i	$-0.801549\pi$
$401$	−32.5153	−1.62373	−0.811867	+	0.583842i	$0.801549\pi$
$402$	1.62087	0.0808415
$403$	−30.2676	−1.50773
$404$	−7.51067	−0.373670
$405$	8.58612	0.426648
$406$	1.90968	0.0947759
$407$	0	0
$408$	0.496391	0.0245750
$409$	−25.7104	−1.27130	−0.635648	−	0.771979i	$-0.719267\pi$
$409$	−25.7104	−1.27130	−0.635648	+	0.771979i	$0.719267\pi$
$410$	−5.13730	−0.253713
$411$	−3.39063	−0.167248
$412$	22.5596	1.11143
$413$	0.846879	0.0416722
$414$	−1.64640	−0.0809160
$415$	−9.07799	−0.445621
$416$	−33.5925	−1.64701
$417$	2.06564	0.101155
$418$	0	0
$419$	18.6850	0.912822	0.456411	−	0.889769i	$-0.349135\pi$
$419$	18.6850	0.912822	0.456411	+	0.889769i	$0.349135\pi$
$420$	−0.349840	−0.0170704
$421$	8.91435	0.434459	0.217229	−	0.976121i	$-0.430298\pi$
$421$	8.91435	0.434459	0.217229	+	0.976121i	$0.430298\pi$
$422$	−40.1774	−1.95581
$423$	12.6900	0.617009
$424$	−1.97630	−0.0959774
$425$	−3.25164	−0.157728
$426$	2.26953	0.109959
$427$	0.963356	0.0466200
$428$	−23.6914	−1.14517
$429$	0	0
$430$	−0.368378	−0.0177648
$431$	−25.5710	−1.23171	−0.615856	−	0.787859i	$-0.711190\pi$
$431$	−25.5710	−1.23171	−0.615856	+	0.787859i	$0.711190\pi$
$432$	5.89674	0.283707
$433$	21.0251	1.01040	0.505201	−	0.863002i	$-0.331418\pi$
$433$	21.0251	1.01040	0.505201	+	0.863002i	$0.331418\pi$
$434$	12.6184	0.605702
$435$	−0.215581	−0.0103363
$436$	−31.6242	−1.51452
$437$	−1.47036	−0.0703371
$438$	−4.81131	−0.229893
$439$	−23.6556	−1.12902	−0.564510	−	0.825426i	$-0.690935\pi$
$439$	−23.6556	−1.12902	−0.564510	+	0.825426i	$0.690935\pi$
$440$	0	0
$441$	−2.95378	−0.140656
$442$	−28.2908	−1.34566
$443$	33.3347	1.58378	0.791889	−	0.610665i	$-0.209098\pi$
$443$	33.3347	1.58378	0.791889	+	0.610665i	$0.209098\pi$
$444$	−1.61914	−0.0768409
$445$	4.30633	0.204140
$446$	24.8031	1.17446
$447$	−0.299926	−0.0141860
$448$	4.79125	0.226365
$449$	−27.5835	−1.30175	−0.650873	−	0.759187i	$-0.725597\pi$
$449$	−27.5835	−1.30175	−0.650873	+	0.759187i	$0.725597\pi$
$450$	−5.62551	−0.265189
$451$	0	0
$452$	−27.9686	−1.31553
$453$	−2.57889	−0.121167
$454$	−23.1286	−1.08548
$455$	−4.56834	−0.214167
$456$	0.766961	0.0359162
$457$	−12.8605	−0.601591	−0.300795	−	0.953689i	$-0.597252\pi$
$457$	−12.8605	−0.601591	−0.300795	+	0.953689i	$0.597252\pi$
$458$	35.8232	1.67391
$459$	4.16227	0.194278
$460$	0.476220	0.0222039
$461$	26.6291	1.24024	0.620119	−	0.784507i	$-0.287084\pi$
$461$	26.6291	1.24024	0.620119	+	0.784507i	$0.287084\pi$
$462$	0	0
$463$	19.2976	0.896836	0.448418	−	0.893824i	$-0.351988\pi$
$463$	19.2976	0.896836	0.448418	+	0.893824i	$0.351988\pi$
$464$	4.61914	0.214438
$465$	−1.42447	−0.0660583
$466$	−44.5788	−2.06507
$467$	−35.9799	−1.66495	−0.832475	−	0.554063i	$-0.813077\pi$
$467$	−35.9799	−1.66495	−0.832475	+	0.554063i	$0.813077\pi$
$468$	−21.9569	−1.01496
$469$	−3.95848	−0.182786
$470$	−8.18218	−0.377416
$471$	−5.26206	−0.242463
$472$	0.601323	0.0276781
$473$	0	0
$474$	3.84743	0.176718
$475$	−5.02403	−0.230518
$476$	5.29100	0.242513
$477$	−8.22135	−0.376430
$478$	−28.7279	−1.31398
$479$	−27.9003	−1.27480	−0.637399	−	0.770534i	$-0.719990\pi$
$479$	−27.9003	−1.27480	−0.637399	+	0.770534i	$0.719990\pi$
$480$	−1.58095	−0.0721603
$481$	−21.1433	−0.964051
$482$	0.951547	0.0433418
$483$	−0.0629227	−0.00286308
$484$	0	0
$485$	1.09820	0.0498666
$486$	10.8294	0.491230
$487$	23.1099	1.04721	0.523606	−	0.851961i	$-0.324586\pi$
$487$	23.1099	1.04721	0.523606	+	0.851961i	$0.324586\pi$
$488$	0.684027	0.0309644
$489$	0.393886	0.0178122
$490$	1.90452	0.0860372
$491$	16.1116	0.727107	0.363553	−	0.931573i	$-0.381563\pi$
$491$	16.1116	0.727107	0.363553	+	0.931573i	$0.381563\pi$
$492$	−0.943669	−0.0425439
$493$	3.26046	0.146844
$494$	−43.7114	−1.96667
$495$	0	0
$496$	30.5214	1.37045
$497$	−5.54264	−0.248621
$498$	−3.71714	−0.166569
$499$	−16.4187	−0.735003	−0.367501	−	0.930023i	$-0.619787\pi$
$499$	−16.4187	−0.735003	−0.367501	+	0.930023i	$0.619787\pi$
$500$	1.62718	0.0727696
$501$	1.48129	0.0661790
$502$	−39.6878	−1.77135
$503$	11.4726	0.511536	0.255768	−	0.966738i	$-0.417672\pi$
$503$	11.4726	0.511536	0.255768	+	0.966738i	$0.417672\pi$
$504$	−2.09732	−0.0934219
$505$	−4.61577	−0.205399
$506$	0	0
$507$	1.69197	0.0751430
$508$	−4.98663	−0.221246
$509$	30.6084	1.35669	0.678346	−	0.734743i	$-0.262697\pi$
$509$	30.6084	1.35669	0.678346	+	0.734743i	$0.262697\pi$
$510$	−1.33144	−0.0589572
$511$	11.7502	0.519798
$512$	27.3324	1.20793
$513$	6.43101	0.283936
$514$	−17.5956	−0.776107
$515$	13.8643	0.610933
$516$	−0.0676672	−0.00297888
$517$	0	0
$518$	8.81452	0.387288
$519$	1.79415	0.0787545
$520$	−3.24373	−0.142247
$521$	−7.28080	−0.318978	−0.159489	−	0.987200i	$-0.550985\pi$
$521$	−7.28080	−0.318978	−0.159489	+	0.987200i	$0.550985\pi$
$522$	5.64077	0.246890
$523$	−18.5202	−0.809832	−0.404916	−	0.914354i	$-0.632699\pi$
$523$	−18.5202	−0.809832	−0.404916	+	0.914354i	$0.632699\pi$
$524$	23.8780	1.04312
$525$	−0.214998	−0.00938328
$526$	−7.42881	−0.323912
$527$	21.5438	0.938462
$528$	0	0
$529$	−22.9143	−0.996276
$530$	5.30090	0.230257
$531$	2.50149	0.108555
$532$	8.17499	0.354431
$533$	−12.3228	−0.533758
$534$	1.76330	0.0763054
$535$	−14.5598	−0.629475
$536$	−2.81070	−0.121404
$537$	1.57863	0.0681231
$538$	53.2459	2.29559
$539$	0	0
$540$	−2.08287	−0.0896324
$541$	−13.2331	−0.568933	−0.284467	−	0.958686i	$-0.591817\pi$
$541$	−13.2331	−0.568933	−0.284467	+	0.958686i	$0.591817\pi$
$542$	−45.8792	−1.97068
$543$	0.0273963	0.00117569
$544$	23.9104	1.02515
$545$	−19.4350	−0.832504
$546$	−1.87058	−0.0800536
$547$	21.7449	0.929745	0.464872	−	0.885378i	$-0.346100\pi$
$547$	21.7449	0.929745	0.464872	+	0.885378i	$0.346100\pi$
$548$	−25.6614	−1.09620
$549$	2.84554	0.121445
$550$	0	0
$551$	5.03766	0.214611
$552$	−0.0446780	−0.00190162
$553$	−9.39619	−0.399567
$554$	−51.7803	−2.19994
$555$	−0.995059	−0.0422379
$556$	15.6334	0.663005
$557$	−22.5249	−0.954412	−0.477206	−	0.878792i	$-0.658350\pi$
$557$	−22.5249	−0.954412	−0.477206	+	0.878792i	$0.658350\pi$
$558$	37.2719	1.57784
$559$	−0.883623	−0.0373733
$560$	4.60665	0.194666
$561$	0	0
$562$	−37.1257	−1.56605
$563$	−2.07905	−0.0876213	−0.0438107	−	0.999040i	$-0.513950\pi$
$563$	−2.07905	−0.0876213	−0.0438107	+	0.999040i	$0.513950\pi$
$564$	−1.50298	−0.0632870
$565$	−17.1884	−0.723121
$566$	4.63581	0.194858
$567$	−8.58612	−0.360583
$568$	−3.93553	−0.165131
$569$	−40.5323	−1.69920	−0.849602	−	0.527425i	$-0.823158\pi$
$569$	−40.5323	−1.69920	−0.849602	+	0.527425i	$0.823158\pi$
$570$	−2.05717	−0.0861655
$571$	−45.1005	−1.88740	−0.943698	−	0.330807i	$-0.892679\pi$
$571$	−45.1005	−1.88740	−0.943698	+	0.330807i	$0.892679\pi$
$572$	0	0
$573$	4.95005	0.206791
$574$	5.13730	0.214427
$575$	0.292666	0.0122050
$576$	14.1523	0.589678
$577$	11.0837	0.461420	0.230710	−	0.973023i	$-0.425895\pi$
$577$	11.0837	0.461420	0.230710	+	0.973023i	$0.425895\pi$
$578$	−12.2400	−0.509116
$579$	3.84734	0.159890
$580$	−1.63159	−0.0677481
$581$	9.07799	0.376619
$582$	0.449676	0.0186397
$583$	0	0
$584$	8.34318	0.345243
$585$	−13.4938	−0.557902
$586$	46.6450	1.92689
$587$	−25.9005	−1.06903	−0.534513	−	0.845160i	$-0.679505\pi$
$587$	−25.9005	−1.06903	−0.534513	+	0.845160i	$0.679505\pi$
$588$	0.349840	0.0144272
$589$	33.2868	1.37156
$590$	−1.61289	−0.0664018
$591$	4.65804	0.191606
$592$	21.3206	0.876271
$593$	−2.48445	−0.102024	−0.0510122	−	0.998698i	$-0.516245\pi$
$593$	−2.48445	−0.102024	−0.0510122	+	0.998698i	$0.516245\pi$
$594$	0	0
$595$	3.25164	0.133304
$596$	−2.26994	−0.0929805
$597$	5.33349	0.218285
$598$	2.54633	0.104127
$599$	−5.73493	−0.234323	−0.117161	−	0.993113i	$-0.537379\pi$
$599$	−5.73493	−0.234323	−0.117161	+	0.993113i	$0.537379\pi$
$600$	−0.152659	−0.00623226
$601$	25.8331	1.05375	0.526877	−	0.849942i	$-0.323363\pi$
$601$	25.8331	1.05375	0.526877	+	0.849942i	$0.323363\pi$
$602$	0.368378	0.0150140
$603$	−11.6925	−0.476154
$604$	−19.5179	−0.794174
$605$	0	0
$606$	−1.89000	−0.0767761
$607$	−13.1269	−0.532804	−0.266402	−	0.963862i	$-0.585835\pi$
$607$	−13.1269	−0.532804	−0.266402	+	0.963862i	$0.585835\pi$
$608$	36.9434	1.49825
$609$	0.215581	0.00873579
$610$	−1.83473	−0.0742858
$611$	−19.6265	−0.794003
$612$	15.6284	0.631742
$613$	−13.8513	−0.559450	−0.279725	−	0.960080i	$-0.590243\pi$
$613$	−13.8513	−0.559450	−0.279725	+	0.960080i	$0.590243\pi$
$614$	43.9011	1.77170
$615$	−0.579942	−0.0233855
$616$	0	0
$617$	−0.619693	−0.0249479	−0.0124739	−	0.999922i	$-0.503971\pi$
$617$	−0.619693	−0.0249479	−0.0124739	+	0.999922i	$0.503971\pi$
$618$	5.67696	0.228361
$619$	29.7025	1.19385	0.596923	−	0.802299i	$-0.296390\pi$
$619$	29.7025	1.19385	0.596923	+	0.802299i	$0.296390\pi$
$620$	−10.7809	−0.432971
$621$	−0.374628	−0.0150333
$622$	35.6567	1.42970
$623$	−4.30633	−0.172529
$624$	−4.52457	−0.181128
$625$	1.00000	0.0400000
$626$	29.4675	1.17776
$627$	0	0
$628$	−39.8251	−1.58919
$629$	15.0493	0.600056
$630$	5.62551	0.224126
$631$	20.4025	0.812212	0.406106	−	0.913826i	$-0.366886\pi$
$631$	20.4025	0.812212	0.406106	+	0.913826i	$0.366886\pi$
$632$	−6.67173	−0.265387
$633$	−4.53557	−0.180273
$634$	24.5662	0.975649
$635$	−3.06459	−0.121615
$636$	0.973722	0.0386106
$637$	4.56834	0.181004
$638$	0	0
$639$	−16.3717	−0.647655
$640$	5.58167	0.220635
$641$	−0.905192	−0.0357529	−0.0178765	−	0.999840i	$-0.505691\pi$
$641$	−0.905192	−0.0357529	−0.0178765	+	0.999840i	$0.505691\pi$
$642$	−5.96176	−0.235292
$643$	34.8958	1.37616	0.688078	−	0.725637i	$-0.258455\pi$
$643$	34.8958	1.37616	0.688078	+	0.725637i	$0.258455\pi$
$644$	−0.476220	−0.0187657
$645$	−0.0415857	−0.00163743
$646$	31.1128	1.22412
$647$	−44.8587	−1.76358	−0.881788	−	0.471646i	$-0.843660\pi$
$647$	−44.8587	−1.76358	−0.881788	+	0.471646i	$0.843660\pi$
$648$	−6.09654	−0.239495
$649$	0	0
$650$	8.70047	0.341260
$651$	1.42447	0.0558294
$652$	2.98107	0.116748
$653$	42.4290	1.66037	0.830187	−	0.557485i	$-0.188233\pi$
$653$	42.4290	1.66037	0.830187	+	0.557485i	$0.188233\pi$
$654$	−7.95799	−0.311182
$655$	14.6745	0.573381
$656$	12.4261	0.485158
$657$	34.7074	1.35407
$658$	8.18218	0.318974
$659$	12.8671	0.501232	0.250616	−	0.968087i	$-0.419367\pi$
$659$	12.8671	0.501232	0.250616	+	0.968087i	$0.419367\pi$
$660$	0	0
$661$	24.4320	0.950293	0.475147	−	0.879907i	$-0.342395\pi$
$661$	24.4320	0.950293	0.475147	+	0.879907i	$0.342395\pi$
$662$	−15.7816	−0.613370
$663$	−3.19371	−0.124033
$664$	6.44579	0.250145
$665$	5.02403	0.194823
$666$	26.0361	1.00888
$667$	−0.293460	−0.0113628
$668$	11.2109	0.433762
$669$	2.79999	0.108254
$670$	7.53898	0.291256
$671$	0	0
$672$	1.58095	0.0609866
$673$	−24.1166	−0.929628	−0.464814	−	0.885408i	$-0.653879\pi$
$673$	−24.1166	−0.929628	−0.464814	+	0.885408i	$0.653879\pi$
$674$	64.1042	2.46920
$675$	−1.28005	−0.0492691
$676$	12.8054	0.492515
$677$	−8.27910	−0.318192	−0.159096	−	0.987263i	$-0.550858\pi$
$677$	−8.27910	−0.318192	−0.159096	+	0.987263i	$0.550858\pi$
$678$	−7.03808	−0.270296
$679$	−1.09820	−0.0421450
$680$	2.30882	0.0885391
$681$	−2.61096	−0.100052
$682$	0	0
$683$	−33.6483	−1.28752	−0.643758	−	0.765229i	$-0.722626\pi$
$683$	−33.6483	−1.28752	−0.643758	+	0.765229i	$0.722626\pi$
$684$	24.1471	0.923286
$685$	−15.7705	−0.602561
$686$	−1.90452	−0.0727147
$687$	4.04403	0.154289
$688$	0.891034	0.0339703
$689$	12.7152	0.484411
$690$	0.119837	0.00456213
$691$	−9.01062	−0.342780	−0.171390	−	0.985203i	$-0.554826\pi$
$691$	−9.01062	−0.342780	−0.171390	+	0.985203i	$0.554826\pi$
$692$	13.5787	0.516186
$693$	0	0
$694$	37.8536	1.43690
$695$	9.60769	0.364441
$696$	0.153073	0.00580220
$697$	8.77108	0.332228
$698$	−35.6578	−1.34967
$699$	−5.03244	−0.190344
$700$	−1.62718	−0.0615015
$701$	−38.6147	−1.45846	−0.729228	−	0.684271i	$-0.760121\pi$
$701$	−38.6147	−1.45846	−0.729228	+	0.684271i	$0.760121\pi$
$702$	−11.1370	−0.420340
$703$	23.2523	0.876978
$704$	0	0
$705$	−0.923674	−0.0347876
$706$	26.5847	1.00053
$707$	4.61577	0.173594
$708$	−0.296272	−0.0111346
$709$	45.5575	1.71095	0.855475	−	0.517845i	$-0.173265\pi$
$709$	45.5575	1.71095	0.855475	+	0.517845i	$0.173265\pi$
$710$	10.5560	0.396161
$711$	−27.7543	−1.04087
$712$	−3.05769	−0.114592
$713$	−1.93906	−0.0726185
$714$	1.33144	0.0498279
$715$	0	0
$716$	11.9476	0.446504
$717$	−3.24306	−0.121114
$718$	57.9252	2.16175
$719$	−9.27727	−0.345984	−0.172992	−	0.984923i	$-0.555343\pi$
$719$	−9.27727	−0.345984	−0.172992	+	0.984923i	$0.555343\pi$
$720$	13.6070	0.507103
$721$	−13.8643	−0.516333
$722$	11.8858	0.442344
$723$	0.107419	0.00399495
$724$	0.207344	0.00770589
$725$	−1.00271	−0.0372398
$726$	0	0
$727$	−9.13982	−0.338977	−0.169489	−	0.985532i	$-0.554212\pi$
$727$	−9.13982	−0.338977	−0.169489	+	0.985532i	$0.554212\pi$
$728$	3.24373	0.120221
$729$	−24.5358	−0.908735
$730$	−22.3784	−0.828262
$731$	0.628944	0.0232623
$732$	−0.337020	−0.0124566
$733$	−29.5930	−1.09304	−0.546520	−	0.837446i	$-0.684048\pi$
$733$	−29.5930	−1.09304	−0.546520	+	0.837446i	$0.684048\pi$
$734$	−43.4519	−1.60384
$735$	0.214998	0.00793032
$736$	−2.15208	−0.0793265
$737$	0	0
$738$	15.1744	0.558578
$739$	18.9094	0.695594	0.347797	−	0.937570i	$-0.386930\pi$
$739$	18.9094	0.695594	0.347797	+	0.937570i	$0.386930\pi$
$740$	−7.53094	−0.276843
$741$	−4.93452	−0.181274
$742$	−5.30090	−0.194602
$743$	15.0087	0.550617	0.275309	−	0.961356i	$-0.411220\pi$
$743$	15.0087	0.550617	0.275309	+	0.961356i	$0.411220\pi$
$744$	1.01144	0.0370812
$745$	−1.39502	−0.0511095
$746$	−47.6831	−1.74580
$747$	26.8144	0.981086
$748$	0	0
$749$	14.5598	0.532004
$750$	0.409467	0.0149516
$751$	15.7351	0.574182	0.287091	−	0.957903i	$-0.407312\pi$
$751$	15.7351	0.574182	0.287091	+	0.957903i	$0.407312\pi$
$752$	19.7911	0.721706
$753$	−4.48030	−0.163271
$754$	−8.72407	−0.317712
$755$	−11.9950	−0.436541
$756$	2.08287	0.0757532
$757$	−16.8017	−0.610668	−0.305334	−	0.952245i	$-0.598768\pi$
$757$	−16.8017	−0.610668	−0.305334	+	0.952245i	$0.598768\pi$
$758$	45.7413	1.66140
$759$	0	0
$760$	3.56729	0.129399
$761$	7.79540	0.282583	0.141292	−	0.989968i	$-0.454875\pi$
$761$	7.79540	0.282583	0.141292	+	0.989968i	$0.454875\pi$
$762$	−1.25485	−0.0454584
$763$	19.4350	0.703594
$764$	37.4636	1.35539
$765$	9.60462	0.347256
$766$	14.8321	0.535907
$767$	−3.86883	−0.139695
$768$	4.34573	0.156813
$769$	16.8739	0.608490	0.304245	−	0.952594i	$-0.401596\pi$
$769$	16.8739	0.608490	0.304245	+	0.952594i	$0.401596\pi$
$770$	0	0
$771$	−1.98634	−0.0715362
$772$	29.1180	1.04798
$773$	9.22274	0.331719	0.165859	−	0.986149i	$-0.446960\pi$
$773$	9.22274	0.331719	0.165859	+	0.986149i	$0.446960\pi$
$774$	1.08811	0.0391111
$775$	−6.62551	−0.237995
$776$	−0.779771	−0.0279921
$777$	0.995059	0.0356975
$778$	23.7298	0.850754
$779$	13.5520	0.485549
$780$	1.59819	0.0572243
$781$	0	0
$782$	−1.81243	−0.0648122
$783$	1.28352	0.0458693
$784$	−4.60665	−0.164523
$785$	−24.4749	−0.873548
$786$	6.00873	0.214324
$787$	30.9722	1.10404	0.552020	−	0.833831i	$-0.313857\pi$
$787$	30.9722	1.10404	0.552020	+	0.833831i	$0.313857\pi$
$788$	35.2536	1.25586
$789$	−0.838628	−0.0298560
$790$	17.8952	0.636682
$791$	17.1884	0.611149
$792$	0	0
$793$	−4.40093	−0.156282
$794$	−3.39407	−0.120451
$795$	0.598412	0.0212235
$796$	40.3657	1.43072
$797$	34.4892	1.22167	0.610835	−	0.791758i	$-0.290834\pi$
$797$	34.4892	1.22167	0.610835	+	0.791758i	$0.290834\pi$
$798$	2.05717	0.0728232
$799$	13.9697	0.494213
$800$	−7.35334	−0.259980
$801$	−12.7199	−0.449437
$802$	−61.9258	−2.18668
$803$	0	0
$804$	1.38483	0.0488393
$805$	−0.292666	−0.0103151
$806$	−57.6450	−2.03046
$807$	6.01086	0.211592
$808$	3.27741	0.115299
$809$	−28.9150	−1.01660	−0.508298	−	0.861181i	$-0.669725\pi$
$809$	−28.9150	−1.01660	−0.508298	+	0.861181i	$0.669725\pi$
$810$	16.3524	0.574565
$811$	−4.85554	−0.170501	−0.0852506	−	0.996360i	$-0.527169\pi$
$811$	−4.85554	−0.170501	−0.0852506	+	0.996360i	$0.527169\pi$
$812$	1.63159	0.0572576
$813$	−5.17924	−0.181644
$814$	0	0
$815$	1.83205	0.0641738
$816$	3.22049	0.112740
$817$	0.971765	0.0339977
$818$	−48.9658	−1.71205
$819$	13.4938	0.471513
$820$	−4.38920	−0.153277
$821$	18.6341	0.650335	0.325167	−	0.945656i	$-0.394579\pi$
$821$	18.6341	0.650335	0.325167	+	0.945656i	$0.394579\pi$
$822$	−6.45751	−0.225231
$823$	−17.9622	−0.626122	−0.313061	−	0.949733i	$-0.601354\pi$
$823$	−17.9622	−0.626122	−0.313061	+	0.949733i	$0.601354\pi$
$824$	−9.84428	−0.342942
$825$	0	0
$826$	1.61289	0.0561198
$827$	−24.9389	−0.867212	−0.433606	−	0.901103i	$-0.642759\pi$
$827$	−24.9389	−0.867212	−0.433606	+	0.901103i	$0.642759\pi$
$828$	−1.40665	−0.0488844
$829$	−8.99336	−0.312352	−0.156176	−	0.987729i	$-0.549917\pi$
$829$	−8.99336	−0.312352	−0.156176	+	0.987729i	$0.549917\pi$
$830$	−17.2892	−0.600116
$831$	−5.84541	−0.202775
$832$	−21.8880	−0.758831
$833$	−3.25164	−0.112663
$834$	3.93403	0.136224
$835$	6.88977	0.238430
$836$	0	0
$837$	8.48098	0.293146
$838$	35.5859	1.22929
$839$	−46.9822	−1.62201	−0.811003	−	0.585041i	$-0.801078\pi$
$839$	−46.9822	−1.62201	−0.811003	+	0.585041i	$0.801078\pi$
$840$	0.152659	0.00526722
$841$	−27.9946	−0.965330
$842$	16.9775	0.585084
$843$	−4.19107	−0.144348
$844$	−34.3267	−1.18157
$845$	7.86970	0.270726
$846$	24.1683	0.830924
$847$	0	0
$848$	−12.8218	−0.440304
$849$	0.523330	0.0179606
$850$	−6.19280	−0.212411
$851$	−1.35453	−0.0464325
$852$	1.93904	0.0664303
$853$	49.4824	1.69425	0.847123	−	0.531397i	$-0.178333\pi$
$853$	49.4824	1.69425	0.847123	+	0.531397i	$0.178333\pi$
$854$	1.83473	0.0627830
$855$	14.8399	0.507512
$856$	10.3381	0.353350
$857$	29.2713	0.999890	0.499945	−	0.866057i	$-0.333354\pi$
$857$	29.2713	0.999890	0.499945	+	0.866057i	$0.333354\pi$
$858$	0	0
$859$	−41.2734	−1.40823	−0.704115	−	0.710086i	$-0.748656\pi$
$859$	−41.2734	−1.40823	−0.704115	+	0.710086i	$0.748656\pi$
$860$	−0.314734	−0.0107323
$861$	0.579942	0.0197644
$862$	−48.7003	−1.65874
$863$	29.3160	0.997928	0.498964	−	0.866623i	$-0.333714\pi$
$863$	29.3160	0.997928	0.498964	+	0.866623i	$0.333714\pi$
$864$	9.41264	0.320225
$865$	8.34496	0.283737
$866$	40.0426	1.36070
$867$	−1.38175	−0.0469268
$868$	10.7809	0.365927
$869$	0	0
$870$	−0.410578	−0.0139199
$871$	18.0837	0.612742
$872$	13.7997	0.467318
$873$	−3.24383	−0.109787
$874$	−2.80033	−0.0947226
$875$	−1.00000	−0.0338062
$876$	−4.11069	−0.138887
$877$	−21.1875	−0.715450	−0.357725	−	0.933827i	$-0.616447\pi$
$877$	−21.1875	−0.715450	−0.357725	+	0.933827i	$0.616447\pi$
$878$	−45.0524	−1.52045
$879$	5.26568	0.177607
$880$	0	0
$881$	−24.9158	−0.839435	−0.419717	−	0.907655i	$-0.637871\pi$
$881$	−24.9158	−0.839435	−0.419717	+	0.907655i	$0.637871\pi$
$882$	−5.62551	−0.189421
$883$	−36.1441	−1.21635	−0.608174	−	0.793804i	$-0.708098\pi$
$883$	−36.1441	−1.21635	−0.608174	+	0.793804i	$0.708098\pi$
$884$	−24.1711	−0.812961
$885$	−0.182077	−0.00612046
$886$	63.4864	2.13287
$887$	12.2613	0.411694	0.205847	−	0.978584i	$-0.434005\pi$
$887$	12.2613	0.411694	0.205847	+	0.978584i	$0.434005\pi$
$888$	0.706538	0.0237098
$889$	3.06459	0.102783
$890$	8.20147	0.274914
$891$	0	0
$892$	21.1912	0.709535
$893$	21.5842	0.722289
$894$	−0.571214	−0.0191043
$895$	7.34255	0.245435
$896$	−5.58167	−0.186471
$897$	0.287452	0.00959775
$898$	−52.5332	−1.75306
$899$	6.64348	0.221573
$900$	−4.80632	−0.160211
$901$	−9.05041	−0.301513
$902$	0	0
$903$	0.0415857	0.00138388
$904$	12.2045	0.405917
$905$	0.127426	0.00423578
$906$	−4.91154	−0.163175
$907$	−3.37290	−0.111995	−0.0559977	−	0.998431i	$-0.517834\pi$
$907$	−3.37290	−0.111995	−0.0559977	+	0.998431i	$0.517834\pi$
$908$	−19.7606	−0.655778
$909$	13.6339	0.452209
$910$	−8.70047	−0.288418
$911$	−9.30964	−0.308442	−0.154221	−	0.988036i	$-0.549287\pi$
$911$	−9.30964	−0.308442	−0.154221	+	0.988036i	$0.549287\pi$
$912$	4.97590	0.164768
$913$	0	0
$914$	−24.4931	−0.810160
$915$	−0.207120	−0.00684716
$916$	30.6066	1.01127
$917$	−14.6745	−0.484595
$918$	7.92710	0.261633
$919$	57.5454	1.89825	0.949123	−	0.314905i	$-0.101973\pi$
$919$	57.5454	1.89825	0.949123	+	0.314905i	$0.101973\pi$
$920$	−0.207807	−0.00685118
$921$	4.95593	0.163304
$922$	50.7154	1.67022
$923$	25.3207	0.833440
$924$	0	0
$925$	−4.62822	−0.152175
$926$	36.7526	1.20776
$927$	−40.9520	−1.34504
$928$	7.37328	0.242040
$929$	3.71259	0.121806	0.0609031	−	0.998144i	$-0.480602\pi$
$929$	3.71259	0.121806	0.0609031	+	0.998144i	$0.480602\pi$
$930$	−2.71293	−0.0889604
$931$	−5.02403	−0.164656
$932$	−38.0872	−1.24759
$933$	4.02524	0.131780
$934$	−68.5242	−2.24218
$935$	0	0
$936$	9.58125	0.313173
$937$	−35.7607	−1.16825	−0.584126	−	0.811663i	$-0.698562\pi$
$937$	−35.7607	−1.16825	−0.584126	+	0.811663i	$0.698562\pi$
$938$	−7.53898	−0.246157
$939$	3.32655	0.108558
$940$	−6.99068	−0.228011
$941$	−2.30778	−0.0752316	−0.0376158	−	0.999292i	$-0.511976\pi$
$941$	−2.30778	−0.0752316	−0.0376158	+	0.999292i	$0.511976\pi$
$942$	−10.0217	−0.326524
$943$	−0.789447	−0.0257079
$944$	3.90127	0.126976
$945$	1.28005	0.0416400
$946$	0	0
$947$	−55.9447	−1.81796	−0.908979	−	0.416842i	$-0.863137\pi$
$947$	−55.9447	−1.81796	−0.908979	+	0.416842i	$0.863137\pi$
$948$	3.28716	0.106762
$949$	−53.6788	−1.74249
$950$	−9.56834	−0.310438
$951$	2.77324	0.0899286
$952$	−2.30882	−0.0748292
$953$	21.2762	0.689203	0.344602	−	0.938749i	$-0.388014\pi$
$953$	21.2762	0.689203	0.344602	+	0.938749i	$0.388014\pi$
$954$	−15.6577	−0.506936
$955$	23.0237	0.745029
$956$	−24.5445	−0.793827
$957$	0	0
$958$	−53.1365	−1.71676
$959$	15.7705	0.509257
$960$	−1.03011	−0.0332466
$961$	12.8974	0.416045
$962$	−40.2677	−1.29828
$963$	43.0064	1.38586
$964$	0.812981	0.0261844
$965$	17.8948	0.576053
$966$	−0.119837	−0.00385570
$967$	−1.52052	−0.0488966	−0.0244483	−	0.999701i	$-0.507783\pi$
$967$	−1.52052	−0.0488966	−0.0244483	+	0.999701i	$0.507783\pi$
$968$	0	0
$969$	3.51228	0.112831
$970$	2.09153	0.0671551
$971$	−0.577620	−0.0185367	−0.00926835	−	0.999957i	$-0.502950\pi$
$971$	−0.577620	−0.0185367	−0.00926835	+	0.999957i	$0.502950\pi$
$972$	9.25237	0.296770
$973$	−9.60769	−0.308009
$974$	44.0132	1.41028
$975$	0.982183	0.0314550
$976$	4.43784	0.142052
$977$	14.1855	0.453836	0.226918	−	0.973914i	$-0.427135\pi$
$977$	14.1855	0.453836	0.226918	+	0.973914i	$0.427135\pi$
$978$	0.750163	0.0239876
$979$	0	0
$980$	1.62718	0.0519783
$981$	57.4066	1.83285
$982$	30.6848	0.979192
$983$	10.1642	0.324186	0.162093	−	0.986775i	$-0.448175\pi$
$983$	10.1642	0.324186	0.162093	+	0.986775i	$0.448175\pi$
$984$	0.411786	0.0131272
$985$	21.6655	0.690320
$986$	6.20960	0.197754
$987$	0.923674	0.0294009
$988$	−37.3461	−1.18814
$989$	−0.0566085	−0.00180005
$990$	0	0
$991$	−56.0016	−1.77895	−0.889475	−	0.456983i	$-0.848930\pi$
$991$	−56.0016	−1.77895	−0.889475	+	0.456983i	$0.848930\pi$
$992$	48.7196	1.54685
$993$	−1.78156	−0.0565362
$994$	−10.5560	−0.334817
$995$	24.8072	0.786440
$996$	−3.17584	−0.100630
$997$	−38.8222	−1.22951	−0.614756	−	0.788717i	$-0.710746\pi$
$997$	−38.8222	−1.22951	−0.614756	+	0.788717i	$0.710746\pi$
$998$	−31.2697	−0.989825
$999$	5.92436	0.187438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bc.1.5	✓	5
11.10	odd	2		4235.2.a.bd.1.1	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.bc.1.5	✓	5	1.1	even	1	trivial
4235.2.a.bd.1.1	yes	5	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+1.90452 q^{2} +0.214998 q^{3} +1.62718 q^{4} +1.00000 q^{5} +0.409467 q^{6} -1.00000 q^{7} -0.710046 q^{8} -2.95378 q^{9} +O(q^{10})\)	\(q+1.90452 q^{2} +0.214998 q^{3} +1.62718 q^{4} +1.00000 q^{5} +0.409467 q^{6} -1.00000 q^{7} -0.710046 q^{8} -2.95378 q^{9} +1.90452 q^{10} +0.349840 q^{12} +4.56834 q^{13} -1.90452 q^{14} +0.214998 q^{15} -4.60665 q^{16} -3.25164 q^{17} -5.62551 q^{18} -5.02403 q^{19} +1.62718 q^{20} -0.214998 q^{21} +0.292666 q^{23} -0.152659 q^{24} +1.00000 q^{25} +8.70047 q^{26} -1.28005 q^{27} -1.62718 q^{28} -1.00271 q^{29} +0.409467 q^{30} -6.62551 q^{31} -7.35334 q^{32} -6.19280 q^{34} -1.00000 q^{35} -4.80632 q^{36} -4.62822 q^{37} -9.56834 q^{38} +0.982183 q^{39} -0.710046 q^{40} -2.69743 q^{41} -0.409467 q^{42} -0.193423 q^{43} -2.95378 q^{45} +0.557388 q^{46} -4.29620 q^{47} -0.990420 q^{48} +1.00000 q^{49} +1.90452 q^{50} -0.699097 q^{51} +7.43350 q^{52} +2.78333 q^{53} -2.43787 q^{54} +0.710046 q^{56} -1.08016 q^{57} -1.90968 q^{58} -0.846879 q^{59} +0.349840 q^{60} -0.963356 q^{61} -12.6184 q^{62} +2.95378 q^{63} -4.79125 q^{64} +4.56834 q^{65} +3.95848 q^{67} -5.29100 q^{68} +0.0629227 q^{69} -1.90452 q^{70} +5.54264 q^{71} +2.09732 q^{72} -11.7502 q^{73} -8.81452 q^{74} +0.214998 q^{75} -8.17499 q^{76} +1.87058 q^{78} +9.39619 q^{79} -4.60665 q^{80} +8.58612 q^{81} -5.13730 q^{82} -9.07799 q^{83} -0.349840 q^{84} -3.25164 q^{85} -0.368378 q^{86} -0.215581 q^{87} +4.30633 q^{89} -5.62551 q^{90} -4.56834 q^{91} +0.476220 q^{92} -1.42447 q^{93} -8.18218 q^{94} -5.02403 q^{95} -1.58095 q^{96} +1.09820 q^{97} +1.90452 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	\( 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{12} - 6 q^{13} + 2 q^{15} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 5 q^{23} - 8 q^{24} + 5 q^{25} + 9 q^{26} - 7 q^{27} - 4 q^{28} - 11 q^{29} - 9 q^{30} - 2 q^{31} - 7 q^{32} + 8 q^{34} - 5 q^{35} + q^{36} + 2 q^{37} - 19 q^{38} - 2 q^{39} - 6 q^{40} - 13 q^{41} + 9 q^{42} - 10 q^{43} + 7 q^{45} - 2 q^{46} - 2 q^{47} + 32 q^{48} + 5 q^{49} - 30 q^{51} + 8 q^{52} - 14 q^{53} - 16 q^{54} + 6 q^{56} - 6 q^{57} + 4 q^{58} + 6 q^{59} + 3 q^{60} - 20 q^{61} + 15 q^{62} - 7 q^{63} - 6 q^{64} - 6 q^{65} - 9 q^{67} - 3 q^{68} - 30 q^{69} - 10 q^{71} - 38 q^{72} - 15 q^{73} + 19 q^{74} + 2 q^{75} + 5 q^{76} + 21 q^{78} - 23 q^{79} - 6 q^{80} + 13 q^{81} - 16 q^{82} - 8 q^{83} - 3 q^{84} - 2 q^{85} - 29 q^{86} + 22 q^{87} + 7 q^{89} + 3 q^{90} + 6 q^{91} + 26 q^{92} - 45 q^{93} + 14 q^{94} - 7 q^{95} + 18 q^{96} + 21 q^{97}+O(q^{100}) \) 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^12 - 6 * q^13 + 2 * q^15 - 6 * q^16 - 2 * q^17 + 3 * q^18 - 7 * q^19 + 4 * q^20 - 2 * q^21 + 5 * q^23 - 8 * q^24 + 5 * q^25 + 9 * q^26 - 7 * q^27 - 4 * q^28 - 11 * q^29 - 9 * q^30 - 2 * q^31 - 7 * q^32 + 8 * q^34 - 5 * q^35 + q^36 + 2 * q^37 - 19 * q^38 - 2 * q^39 - 6 * q^40 - 13 * q^41 + 9 * q^42 - 10 * q^43 + 7 * q^45 - 2 * q^46 - 2 * q^47 + 32 * q^48 + 5 * q^49 - 30 * q^51 + 8 * q^52 - 14 * q^53 - 16 * q^54 + 6 * q^56 - 6 * q^57 + 4 * q^58 + 6 * q^59 + 3 * q^60 - 20 * q^61 + 15 * q^62 - 7 * q^63 - 6 * q^64 - 6 * q^65 - 9 * q^67 - 3 * q^68 - 30 * q^69 - 10 * q^71 - 38 * q^72 - 15 * q^73 + 19 * q^74 + 2 * q^75 + 5 * q^76 + 21 * q^78 - 23 * q^79 - 6 * q^80 + 13 * q^81 - 16 * q^82 - 8 * q^83 - 3 * q^84 - 2 * q^85 - 29 * q^86 + 22 * q^87 + 7 * q^89 + 3 * q^90 + 6 * q^91 + 26 * q^92 - 45 * q^93 + 14 * q^94 - 7 * q^95 + 18 * q^96 + 21 * q^97

Introduction

L-functions

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Database

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