LMFDB - Embedded newform 6027.2.a.u.1.1

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:	$0$
Dimension:	$4$
Coefficient field:	4.4.8468.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + 3x + 4 $ x^4 - x^3 - 5x^2 + 3x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.89122$ 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)

$f(q)$	$=$	$q-1.89122 q^{2} +1.00000 q^{3} +1.57671 q^{4} +1.57671 q^{5} -1.89122 q^{6} +0.800530 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.89122 q^{2} +1.00000 q^{3} +1.57671 q^{4} +1.57671 q^{5} -1.89122 q^{6} +0.800530 q^{8} +1.00000 q^{9} -2.98191 q^{10} +1.66740 q^{11} +1.57671 q^{12} +5.04464 q^{13} +1.57671 q^{15} -4.66740 q^{16} -6.35915 q^{17} -1.89122 q^{18} -0.691750 q^{19} +2.48602 q^{20} -3.15343 q^{22} +8.82708 q^{23} +0.800530 q^{24} -2.51398 q^{25} -9.54053 q^{26} +1.00000 q^{27} -6.64931 q^{29} -2.98191 q^{30} -2.35915 q^{31} +7.22603 q^{32} +1.66740 q^{33} +12.0266 q^{34} +1.57671 q^{36} +9.02655 q^{37} +1.30825 q^{38} +5.04464 q^{39} +1.26221 q^{40} +1.00000 q^{41} -9.96021 q^{43} +2.62901 q^{44} +1.57671 q^{45} -16.6940 q^{46} +1.33621 q^{47} -4.66740 q^{48} +4.75448 q^{50} -6.35915 q^{51} +7.95395 q^{52} +1.66115 q^{53} -1.89122 q^{54} +2.62901 q^{55} -0.691750 q^{57} +12.5753 q^{58} +12.0266 q^{59} +2.48602 q^{60} +11.9602 q^{61} +4.46168 q^{62} -4.33120 q^{64} +7.95395 q^{65} -3.15343 q^{66} -0.870922 q^{67} -10.0266 q^{68} +8.82708 q^{69} -10.8961 q^{71} +0.800530 q^{72} +2.79427 q^{73} -17.0712 q^{74} -2.51398 q^{75} -1.09069 q^{76} -9.54053 q^{78} +12.2463 q^{79} -7.35915 q^{80} +1.00000 q^{81} -1.89122 q^{82} +2.62901 q^{83} -10.0266 q^{85} +18.8369 q^{86} -6.64931 q^{87} +1.33481 q^{88} +12.7183 q^{89} -2.98191 q^{90} +13.9178 q^{92} -2.35915 q^{93} -2.52706 q^{94} -1.09069 q^{95} +7.22603 q^{96} +3.21198 q^{97} +1.66740 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 4 q^{3} + 3 q^{4} + 3 q^{5} + q^{6} + 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + q^2 + 4 * q^3 + 3 * q^4 + 3 * q^5 + q^6 + 3 * q^8 + 4 * q^9	$ 4 q + q^{2} + 4 q^{3} + 3 q^{4} + 3 q^{5} + q^{6} + 3 q^{8} + 4 q^{9} + 5 q^{10} - 5 q^{11} + 3 q^{12} + 5 q^{13} + 3 q^{15} - 7 q^{16} - 5 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 6 q^{22} + 3 q^{23} + 3 q^{24} - 5 q^{25} - q^{26} + 4 q^{27} + 2 q^{29} + 5 q^{30} + 11 q^{31} - 3 q^{32} - 5 q^{33} + 16 q^{34} + 3 q^{36} + 4 q^{37} + 14 q^{38} + 5 q^{39} + 7 q^{40} + 4 q^{41} - 19 q^{43} + 3 q^{45} - 23 q^{46} + 4 q^{47} - 7 q^{48} + 12 q^{50} - 5 q^{51} + 25 q^{52} + 9 q^{53} + q^{54} + 6 q^{57} + 25 q^{58} + 16 q^{59} + 15 q^{60} + 27 q^{61} + 20 q^{62} - 7 q^{64} + 25 q^{65} - 6 q^{66} - 13 q^{67} - 8 q^{68} + 3 q^{69} + q^{71} + 3 q^{72} + 25 q^{73} - 21 q^{74} - 5 q^{75} + 4 q^{76} - q^{78} - q^{79} - 9 q^{80} + 4 q^{81} + q^{82} - 8 q^{85} + 16 q^{86} + 2 q^{87} - 18 q^{88} + 10 q^{89} + 5 q^{90} + 15 q^{92} + 11 q^{93} - 13 q^{94} + 4 q^{95} - 3 q^{96} - 15 q^{97} - 5 q^{99}+O(q^{100}) $ 4 * q + q^2 + 4 * q^3 + 3 * q^4 + 3 * q^5 + q^6 + 3 * q^8 + 4 * q^9 + 5 * q^10 - 5 * q^11 + 3 * q^12 + 5 * q^13 + 3 * q^15 - 7 * q^16 - 5 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 6 * q^22 + 3 * q^23 + 3 * q^24 - 5 * q^25 - q^26 + 4 * q^27 + 2 * q^29 + 5 * q^30 + 11 * q^31 - 3 * q^32 - 5 * q^33 + 16 * q^34 + 3 * q^36 + 4 * q^37 + 14 * q^38 + 5 * q^39 + 7 * q^40 + 4 * q^41 - 19 * q^43 + 3 * q^45 - 23 * q^46 + 4 * q^47 - 7 * q^48 + 12 * q^50 - 5 * q^51 + 25 * q^52 + 9 * q^53 + q^54 + 6 * q^57 + 25 * q^58 + 16 * q^59 + 15 * q^60 + 27 * q^61 + 20 * q^62 - 7 * q^64 + 25 * q^65 - 6 * q^66 - 13 * q^67 - 8 * q^68 + 3 * q^69 + q^71 + 3 * q^72 + 25 * q^73 - 21 * q^74 - 5 * q^75 + 4 * q^76 - q^78 - q^79 - 9 * q^80 + 4 * q^81 + q^82 - 8 * q^85 + 16 * q^86 + 2 * q^87 - 18 * q^88 + 10 * q^89 + 5 * q^90 + 15 * q^92 + 11 * q^93 - 13 * q^94 + 4 * q^95 - 3 * q^96 - 15 * q^97 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.89122	−1.33729	−0.668647	−	0.743580i	$-0.733126\pi$
$2$	−1.89122	−1.33729	−0.668647	+	0.743580i	$0.733126\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.57671	0.788356
$5$	1.57671	0.705127	0.352564	−	0.935788i	$-0.385310\pi$
$5$	1.57671	0.705127	0.352564	+	0.935788i	$0.385310\pi$
$6$	−1.89122	−0.772087
$7$	0	0
$7$	0	0
$8$	0.800530	0.283030
$9$	1.00000	0.333333
$10$	−2.98191	−0.942963
$11$	1.66740	0.502741	0.251370	−	0.967891i	$-0.419119\pi$
$11$	1.66740	0.502741	0.251370	+	0.967891i	$0.419119\pi$
$12$	1.57671	0.455158
$13$	5.04464	1.39913	0.699566	−	0.714568i	$-0.253377\pi$
$13$	5.04464	1.39913	0.699566	+	0.714568i	$0.253377\pi$
$14$	0	0
$15$	1.57671	0.407105
$16$	−4.66740	−1.16685
$17$	−6.35915	−1.54232	−0.771160	−	0.636641i	$-0.780323\pi$
$17$	−6.35915	−1.54232	−0.771160	+	0.636641i	$0.780323\pi$
$18$	−1.89122	−0.445765
$19$	−0.691750	−0.158698	−0.0793491	−	0.996847i	$-0.525284\pi$
$19$	−0.691750	−0.158698	−0.0793491	+	0.996847i	$0.525284\pi$
$20$	2.48602	0.555891
$21$	0	0
$22$	−3.15343	−0.672312
$23$	8.82708	1.84057	0.920287	−	0.391244i	$-0.127955\pi$
$23$	8.82708	1.84057	0.920287	+	0.391244i	$0.127955\pi$
$24$	0.800530	0.163407
$25$	−2.51398	−0.502796
$26$	−9.54053	−1.87105
$27$	1.00000	0.192450
$28$	0	0
$29$	−6.64931	−1.23475	−0.617373	−	0.786670i	$-0.711803\pi$
$29$	−6.64931	−1.23475	−0.617373	+	0.786670i	$0.711803\pi$
$30$	−2.98191	−0.544420
$31$	−2.35915	−0.423716	−0.211858	−	0.977300i	$-0.567951\pi$
$31$	−2.35915	−0.423716	−0.211858	+	0.977300i	$0.567951\pi$
$32$	7.22603	1.27739
$33$	1.66740	0.290258
$34$	12.0266	2.06254
$35$	0	0
$36$	1.57671	0.262785
$37$	9.02655	1.48396	0.741978	−	0.670424i	$-0.233888\pi$
$37$	9.02655	1.48396	0.741978	+	0.670424i	$0.233888\pi$
$38$	1.30825	0.212226
$39$	5.04464	0.807790
$40$	1.26221	0.199572
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−9.96021	−1.51892	−0.759459	−	0.650555i	$-0.774536\pi$
$43$	−9.96021	−1.51892	−0.759459	+	0.650555i	$0.774536\pi$
$44$	2.62901	0.396339
$45$	1.57671	0.235042
$46$	−16.6940	−2.46139
$47$	1.33621	0.194906	0.0974528	−	0.995240i	$-0.468930\pi$
$47$	1.33621	0.194906	0.0974528	+	0.995240i	$0.468930\pi$
$48$	−4.66740	−0.673682
$49$	0	0
$50$	4.75448	0.672386
$51$	−6.35915	−0.890459
$52$	7.95395	1.10302
$53$	1.66115	0.228176	0.114088	−	0.993471i	$-0.463605\pi$
$53$	1.66115	0.228176	0.114088	+	0.993471i	$0.463605\pi$
$54$	−1.89122	−0.257362
$55$	2.62901	0.354496
$56$	0	0
$57$	−0.691750	−0.0916245
$58$	12.5753	1.65122
$59$	12.0266	1.56572	0.782862	−	0.622195i	$-0.213759\pi$
$59$	12.0266	1.56572	0.782862	+	0.622195i	$0.213759\pi$
$60$	2.48602	0.320944
$61$	11.9602	1.53135	0.765674	−	0.643229i	$-0.222406\pi$
$61$	11.9602	1.53135	0.765674	+	0.643229i	$0.222406\pi$
$62$	4.46168	0.566633
$63$	0	0
$64$	−4.33120	−0.541400
$65$	7.95395	0.986567
$66$	−3.15343	−0.388160
$67$	−0.870922	−0.106400	−0.0532000	−	0.998584i	$-0.516942\pi$
$67$	−0.870922	−0.106400	−0.0532000	+	0.998584i	$0.516942\pi$
$68$	−10.0266	−1.21590
$69$	8.82708	1.06266
$70$	0	0
$71$	−10.8961	−1.29313	−0.646563	−	0.762860i	$-0.723794\pi$
$71$	−10.8961	−1.29313	−0.646563	+	0.762860i	$0.723794\pi$
$72$	0.800530	0.0943433
$73$	2.79427	0.327045	0.163522	−	0.986540i	$-0.447714\pi$
$73$	2.79427	0.327045	0.163522	+	0.986540i	$0.447714\pi$
$74$	−17.0712	−1.98449
$75$	−2.51398	−0.290289
$76$	−1.09069	−0.125111
$77$	0	0
$78$	−9.54053	−1.08025
$79$	12.2463	1.37782	0.688910	−	0.724847i	$-0.258090\pi$
$79$	12.2463	1.37782	0.688910	+	0.724847i	$0.258090\pi$
$80$	−7.35915	−0.822778
$81$	1.00000	0.111111
$82$	−1.89122	−0.208850
$83$	2.62901	0.288572	0.144286	−	0.989536i	$-0.453911\pi$
$83$	2.62901	0.288572	0.144286	+	0.989536i	$0.453911\pi$
$84$	0	0
$85$	−10.0266	−1.08753
$86$	18.8369	2.03124
$87$	−6.64931	−0.712881
$88$	1.33481	0.142291
$89$	12.7183	1.34814	0.674069	−	0.738669i	$-0.264545\pi$
$89$	12.7183	1.34814	0.674069	+	0.738669i	$0.264545\pi$
$90$	−2.98191	−0.314321
$91$	0	0
$92$	13.9178	1.45103
$93$	−2.35915	−0.244633
$94$	−2.52706	−0.260646
$95$	−1.09069	−0.111902
$96$	7.22603	0.737503
$97$	3.21198	0.326128	0.163064	−	0.986616i	$-0.447862\pi$
$97$	3.21198	0.326128	0.163064	+	0.986616i	$0.447862\pi$
$98$	0	0
$99$	1.66740	0.167580
$100$	−3.96382	−0.396382
$101$	7.97425	0.793468	0.396734	−	0.917934i	$-0.370144\pi$
$101$	7.97425	0.793468	0.396734	+	0.917934i	$0.370144\pi$
$102$	12.0266	1.19081
$103$	6.34246	0.624941	0.312471	−	0.949927i	$-0.398843\pi$
$103$	6.34246	0.624941	0.312471	+	0.949927i	$0.398843\pi$
$104$	4.03839	0.395997
$105$	0	0
$106$	−3.14159	−0.305138
$107$	−11.2401	−1.08662	−0.543309	−	0.839533i	$-0.682829\pi$
$107$	−11.2401	−1.08662	−0.543309	+	0.839533i	$0.682829\pi$
$108$	1.57671	0.151719
$109$	−7.48963	−0.717377	−0.358688	−	0.933457i	$-0.616776\pi$
$109$	−7.48963	−0.717377	−0.358688	+	0.933457i	$0.616776\pi$
$110$	−4.97204	−0.474066
$111$	9.02655	0.856763
$112$	0	0
$113$	15.3348	1.44258	0.721289	−	0.692635i	$-0.243550\pi$
$113$	15.3348	1.44258	0.721289	+	0.692635i	$0.243550\pi$
$114$	1.30825	0.122529
$115$	13.9178	1.29784
$116$	−10.4841	−0.973420
$117$	5.04464	0.466378
$118$	−22.7449	−2.09383
$119$	0	0
$120$	1.26221	0.115223
$121$	−8.21977	−0.747252
$122$	−22.6194	−2.04786
$123$	1.00000	0.0901670
$124$	−3.71970	−0.334039
$125$	−11.8474	−1.05966
$126$	0	0
$127$	−15.4241	−1.36867	−0.684334	−	0.729169i	$-0.739907\pi$
$127$	−15.4241	−1.36867	−0.684334	+	0.729169i	$0.739907\pi$
$128$	−6.26080	−0.553382
$129$	−9.96021	−0.876948
$130$	−15.0427	−1.31933
$131$	15.9345	1.39220	0.696100	−	0.717945i	$-0.254917\pi$
$131$	15.9345	1.39220	0.696100	+	0.717945i	$0.254917\pi$
$132$	2.62901	0.228826
$133$	0	0
$134$	1.64710	0.142288
$135$	1.57671	0.135702
$136$	−5.09069	−0.436523
$137$	3.13313	0.267681	0.133841	−	0.991003i	$-0.457269\pi$
$137$	3.13313	0.267681	0.133841	+	0.991003i	$0.457269\pi$
$138$	−16.6940	−1.42108
$139$	12.9192	1.09579	0.547895	−	0.836547i	$-0.315429\pi$
$139$	12.9192	1.09579	0.547895	+	0.836547i	$0.315429\pi$
$140$	0	0
$141$	1.33621	0.112529
$142$	20.6069	1.72929
$143$	8.41145	0.703401
$144$	−4.66740	−0.388950
$145$	−10.4841	−0.870653
$146$	−5.28458	−0.437355
$147$	0	0
$148$	14.2323	1.16989
$149$	17.0545	1.39716	0.698580	−	0.715532i	$-0.253816\pi$
$149$	17.0545	1.39716	0.698580	+	0.715532i	$0.253816\pi$
$150$	4.75448	0.388202
$151$	−4.62901	−0.376704	−0.188352	−	0.982102i	$-0.560315\pi$
$151$	−4.62901	−0.376704	−0.188352	+	0.982102i	$0.560315\pi$
$152$	−0.553766	−0.0449164
$153$	−6.35915	−0.514107
$154$	0	0
$155$	−3.71970	−0.298774
$156$	7.95395	0.636826
$157$	−18.4380	−1.47151	−0.735757	−	0.677246i	$-0.763173\pi$
$157$	−18.4380	−1.47151	−0.735757	+	0.677246i	$0.763173\pi$
$158$	−23.1605	−1.84255
$159$	1.66115	0.131737
$160$	11.3934	0.900725
$161$	0	0
$162$	−1.89122	−0.148588
$163$	−17.6019	−1.37868	−0.689342	−	0.724436i	$-0.742100\pi$
$163$	−17.6019	−1.37868	−0.689342	+	0.724436i	$0.742100\pi$
$164$	1.57671	0.123121
$165$	2.62901	0.204669
$166$	−4.97204	−0.385906
$167$	0.255948	0.0198059	0.00990294	−	0.999951i	$-0.496848\pi$
$167$	0.255948	0.0198059	0.00990294	+	0.999951i	$0.496848\pi$
$168$	0	0
$169$	12.4484	0.957572
$170$	18.9624	1.45435
$171$	−0.691750	−0.0528994
$172$	−15.7044	−1.19745
$173$	−21.9173	−1.66634	−0.833172	−	0.553014i	$-0.813478\pi$
$173$	−21.9173	−1.66634	−0.833172	+	0.553014i	$0.813478\pi$
$174$	12.5753	0.953332
$175$	0	0
$176$	−7.78244	−0.586623
$177$	12.0266	0.903971
$178$	−24.0531	−1.80286
$179$	15.5685	1.16364	0.581822	−	0.813316i	$-0.302340\pi$
$179$	15.5685	1.16364	0.581822	+	0.813316i	$0.302340\pi$
$180$	2.48602	0.185297
$181$	22.5707	1.67767	0.838833	−	0.544388i	$-0.183238\pi$
$181$	22.5707	1.67767	0.838833	+	0.544388i	$0.183238\pi$
$182$	0	0
$183$	11.9602	0.884124
$184$	7.06634	0.520938
$185$	14.2323	1.04638
$186$	4.46168	0.327146
$187$	−10.6033	−0.775388
$188$	2.10681	0.153655
$189$	0	0
$190$	2.06273	0.149647
$191$	20.0797	1.45291	0.726457	−	0.687212i	$-0.241166\pi$
$191$	20.0797	1.45291	0.726457	+	0.687212i	$0.241166\pi$
$192$	−4.33120	−0.312577
$193$	2.56628	0.184725	0.0923624	−	0.995725i	$-0.470558\pi$
$193$	2.56628	0.184725	0.0923624	+	0.995725i	$0.470558\pi$
$194$	−6.07457	−0.436129
$195$	7.95395	0.569595
$196$	0	0
$197$	25.4241	1.81139	0.905696	−	0.423928i	$-0.139349\pi$
$197$	25.4241	1.81139	0.905696	+	0.423928i	$0.139349\pi$
$198$	−3.15343	−0.224104
$199$	−15.8215	−1.12156	−0.560778	−	0.827966i	$-0.689498\pi$
$199$	−15.8215	−1.12156	−0.560778	+	0.827966i	$0.689498\pi$
$200$	−2.01251	−0.142306
$201$	−0.870922	−0.0614301
$202$	−15.0811	−1.06110
$203$	0	0
$204$	−10.0266	−0.701999
$205$	1.57671	0.110122
$206$	−11.9950	−0.835731
$207$	8.82708	0.613525
$208$	−23.5454	−1.63258
$209$	−1.15343	−0.0797841
$210$	0	0
$211$	5.63262	0.387766	0.193883	−	0.981025i	$-0.437892\pi$
$211$	5.63262	0.387766	0.193883	+	0.981025i	$0.437892\pi$
$212$	2.61915	0.179884
$213$	−10.8961	−0.746587
$214$	21.2574	1.45313
$215$	−15.7044	−1.07103
$216$	0.800530	0.0544691
$217$	0	0
$218$	14.1645	0.959344
$219$	2.79427	0.188819
$220$	4.14520	0.279469
$221$	−32.0797	−2.15791
$222$	−17.0712	−1.14574
$223$	14.7909	0.990472	0.495236	−	0.868758i	$-0.335082\pi$
$223$	14.7909	0.990472	0.495236	+	0.868758i	$0.335082\pi$
$224$	0	0
$225$	−2.51398	−0.167599
$226$	−29.0015	−1.92915
$227$	5.41298	0.359272	0.179636	−	0.983733i	$-0.442508\pi$
$227$	5.41298	0.359272	0.179636	+	0.983733i	$0.442508\pi$
$228$	−1.09069	−0.0722327
$229$	−0.527059	−0.0348290	−0.0174145	−	0.999848i	$-0.505543\pi$
$229$	−0.527059	−0.0348290	−0.0174145	+	0.999848i	$0.505543\pi$
$230$	−26.3216	−1.73559
$231$	0	0
$232$	−5.32297	−0.349470
$233$	−16.7449	−1.09699	−0.548496	−	0.836153i	$-0.684799\pi$
$233$	−16.7449	−1.09699	−0.548496	+	0.836153i	$0.684799\pi$
$234$	−9.54053	−0.623684
$235$	2.10681	0.137433
$236$	18.9624	1.23435
$237$	12.2463	0.795484
$238$	0	0
$239$	1.42690	0.0922982	0.0461491	−	0.998935i	$-0.485305\pi$
$239$	1.42690	0.0922982	0.0461491	+	0.998935i	$0.485305\pi$
$240$	−7.35915	−0.475031
$241$	−12.8767	−0.829464	−0.414732	−	0.909944i	$-0.636125\pi$
$241$	−12.8767	−0.829464	−0.414732	+	0.909944i	$0.636125\pi$
$242$	15.5454	0.999295
$243$	1.00000	0.0641500
$244$	18.8578	1.20725
$245$	0	0
$246$	−1.89122	−0.120580
$247$	−3.48963	−0.222040
$248$	−1.88857	−0.119924
$249$	2.62901	0.166607
$250$	22.4060	1.41708
$251$	20.8104	1.31354	0.656770	−	0.754091i	$-0.271922\pi$
$251$	20.8104	1.31354	0.656770	+	0.754091i	$0.271922\pi$
$252$	0	0
$253$	14.7183	0.925332
$254$	29.1704	1.83031
$255$	−10.0266	−0.627887
$256$	20.5030	1.28143
$257$	24.4388	1.52445	0.762226	−	0.647311i	$-0.224107\pi$
$257$	24.4388	1.52445	0.762226	+	0.647311i	$0.224107\pi$
$258$	18.8369	1.17274
$259$	0	0
$260$	12.5411	0.777766
$261$	−6.64931	−0.411582
$262$	−30.1356	−1.86178
$263$	−15.0147	−0.925847	−0.462924	−	0.886398i	$-0.653200\pi$
$263$	−15.0147	−0.925847	−0.462924	+	0.886398i	$0.653200\pi$
$264$	1.33481	0.0821516
$265$	2.61915	0.160893
$266$	0	0
$267$	12.7183	0.778348
$268$	−1.37319	−0.0838811
$269$	−4.84598	−0.295465	−0.147732	−	0.989027i	$-0.547197\pi$
$269$	−4.84598	−0.295465	−0.147732	+	0.989027i	$0.547197\pi$
$270$	−2.98191	−0.181473
$271$	−15.3411	−0.931903	−0.465952	−	0.884810i	$-0.654288\pi$
$271$	−15.3411	−0.931903	−0.465952	+	0.884810i	$0.654288\pi$
$272$	29.6807	1.79966
$273$	0	0
$274$	−5.92543	−0.357968
$275$	−4.19181	−0.252776
$276$	13.9178	0.837752
$277$	−4.75741	−0.285845	−0.142923	−	0.989734i	$-0.545650\pi$
$277$	−4.75741	−0.285845	−0.142923	+	0.989734i	$0.545650\pi$
$278$	−24.4330	−1.46539
$279$	−2.35915	−0.141239
$280$	0	0
$281$	−29.6242	−1.76723	−0.883617	−	0.468210i	$-0.844899\pi$
$281$	−29.6242	−1.76723	−0.883617	+	0.468210i	$0.844899\pi$
$282$	−2.52706	−0.150484
$283$	4.78176	0.284246	0.142123	−	0.989849i	$-0.454607\pi$
$283$	4.78176	0.284246	0.142123	+	0.989849i	$0.454607\pi$
$284$	−17.1800	−1.01944
$285$	−1.09069	−0.0646069
$286$	−15.9079	−0.940654
$287$	0	0
$288$	7.22603	0.425798
$289$	23.4388	1.37875
$290$	19.8277	1.16432
$291$	3.21198	0.188290
$292$	4.40576	0.257828
$293$	−15.6380	−0.913584	−0.456792	−	0.889573i	$-0.651002\pi$
$293$	−15.6380	−0.913584	−0.456792	+	0.889573i	$0.651002\pi$
$294$	0	0
$295$	18.9624	1.10403
$296$	7.22603	0.420004
$297$	1.66740	0.0967525
$298$	−32.2538	−1.86841
$299$	44.5295	2.57521
$300$	−3.96382	−0.228851
$301$	0	0
$302$	8.75448	0.503764
$303$	7.97425	0.458109
$304$	3.22867	0.185177
$305$	18.8578	1.07980
$306$	12.0266	0.687512
$307$	21.2711	1.21401	0.607003	−	0.794699i	$-0.292372\pi$
$307$	21.2711	1.21401	0.607003	+	0.794699i	$0.292372\pi$
$308$	0	0
$309$	6.34246	0.360810
$310$	7.03478	0.399549
$311$	−2.85031	−0.161626	−0.0808131	−	0.996729i	$-0.525752\pi$
$311$	−2.85031	−0.161626	−0.0808131	+	0.996729i	$0.525752\pi$
$312$	4.03839	0.228629
$313$	13.3306	0.753492	0.376746	−	0.926317i	$-0.377043\pi$
$313$	13.3306	0.753492	0.376746	+	0.926317i	$0.377043\pi$
$314$	34.8703	1.96785
$315$	0	0
$316$	19.3089	1.08621
$317$	8.50980	0.477958	0.238979	−	0.971025i	$-0.423187\pi$
$317$	8.50980	0.477958	0.238979	+	0.971025i	$0.423187\pi$
$318$	−3.14159	−0.176172
$319$	−11.0871	−0.620757
$320$	−6.82905	−0.381756
$321$	−11.2401	−0.627359
$322$	0	0
$323$	4.39894	0.244764
$324$	1.57671	0.0875951
$325$	−12.6821	−0.703478
$326$	33.2890	1.84371
$327$	−7.48963	−0.414178
$328$	0.800530	0.0442019
$329$	0	0
$330$	−4.97204	−0.273702
$331$	−29.9173	−1.64441	−0.822203	−	0.569195i	$-0.807255\pi$
$331$	−29.9173	−1.64441	−0.822203	+	0.569195i	$0.807255\pi$
$332$	4.14520	0.227497
$333$	9.02655	0.494652
$334$	−0.484055	−0.0264863
$335$	−1.37319	−0.0750256
$336$	0	0
$337$	−6.71161	−0.365605	−0.182802	−	0.983150i	$-0.558517\pi$
$337$	−6.71161	−0.365605	−0.182802	+	0.983150i	$0.558517\pi$
$338$	−23.5427	−1.28056
$339$	15.3348	0.832872
$340$	−15.8090	−0.857363
$341$	−3.93366	−0.213019
$342$	1.30825	0.0707421
$343$	0	0
$344$	−7.97345	−0.429899
$345$	13.9178	0.749308
$346$	41.4505	2.22839
$347$	34.5656	1.85558	0.927788	−	0.373107i	$-0.121708\pi$
$347$	34.5656	1.85558	0.927788	+	0.373107i	$0.121708\pi$
$348$	−10.4841	−0.562004
$349$	−9.95211	−0.532724	−0.266362	−	0.963873i	$-0.585822\pi$
$349$	−9.95211	−0.532724	−0.266362	+	0.963873i	$0.585822\pi$
$350$	0	0
$351$	5.04464	0.269263
$352$	12.0487	0.642198
$353$	7.57739	0.403304	0.201652	−	0.979457i	$-0.435369\pi$
$353$	7.57739	0.403304	0.201652	+	0.979457i	$0.435369\pi$
$354$	−22.7449	−1.20888
$355$	−17.1800	−0.911819
$356$	20.0531	1.06281
$357$	0	0
$358$	−29.4434	−1.55613
$359$	−6.47307	−0.341635	−0.170818	−	0.985303i	$-0.554641\pi$
$359$	−6.47307	−0.341635	−0.170818	+	0.985303i	$0.554641\pi$
$360$	1.26221	0.0665241
$361$	−18.5215	−0.974815
$362$	−42.6861	−2.24353
$363$	−8.21977	−0.431426
$364$	0	0
$365$	4.40576	0.230608
$366$	−22.6194	−1.18233
$367$	11.1250	0.580722	0.290361	−	0.956917i	$-0.406225\pi$
$367$	11.1250	0.580722	0.290361	+	0.956917i	$0.406225\pi$
$368$	−41.1996	−2.14768
$369$	1.00000	0.0520579
$370$	−26.9164	−1.39932
$371$	0	0
$372$	−3.71970	−0.192858
$373$	−25.1437	−1.30189	−0.650945	−	0.759125i	$-0.725627\pi$
$373$	−25.1437	−1.30189	−0.650945	+	0.759125i	$0.725627\pi$
$374$	20.0531	1.03692
$375$	−11.8474	−0.611796
$376$	1.06967	0.0551641
$377$	−33.5434	−1.72757
$378$	0	0
$379$	−24.8289	−1.27537	−0.637686	−	0.770296i	$-0.720108\pi$
$379$	−24.8289	−1.27537	−0.637686	+	0.770296i	$0.720108\pi$
$380$	−1.71970	−0.0882190
$381$	−15.4241	−0.790200
$382$	−37.9751	−1.94297
$383$	18.1410	0.926962	0.463481	−	0.886107i	$-0.346600\pi$
$383$	18.1410	0.926962	0.463481	+	0.886107i	$0.346600\pi$
$384$	−6.26080	−0.319495
$385$	0	0
$386$	−4.85340	−0.247032
$387$	−9.96021	−0.506306
$388$	5.06438	0.257105
$389$	−28.8703	−1.46378	−0.731892	−	0.681421i	$-0.761362\pi$
$389$	−28.8703	−1.46378	−0.731892	+	0.681421i	$0.761362\pi$
$390$	−15.0427	−0.761716
$391$	−56.1328	−2.83876
$392$	0	0
$393$	15.9345	0.803787
$394$	−48.0826	−2.42236
$395$	19.3089	0.971538
$396$	2.62901	0.132113
$397$	−26.5988	−1.33495	−0.667477	−	0.744630i	$-0.732626\pi$
$397$	−26.5988	−1.33495	−0.667477	+	0.744630i	$0.732626\pi$
$398$	29.9220	1.49985
$399$	0	0
$400$	11.7337	0.586687
$401$	7.07665	0.353391	0.176695	−	0.984266i	$-0.443459\pi$
$401$	7.07665	0.353391	0.176695	+	0.984266i	$0.443459\pi$
$402$	1.64710	0.0821501
$403$	−11.9011	−0.592835
$404$	12.5731	0.625535
$405$	1.57671	0.0783475
$406$	0	0
$407$	15.0509	0.746046
$408$	−5.09069	−0.252027
$409$	9.14019	0.451953	0.225977	−	0.974133i	$-0.427443\pi$
$409$	9.14019	0.451953	0.225977	+	0.974133i	$0.427443\pi$
$410$	−2.98191	−0.147266
$411$	3.13313	0.154546
$412$	10.0002	0.492676
$413$	0	0
$414$	−16.6940	−0.820463
$415$	4.14520	0.203480
$416$	36.4527	1.78724
$417$	12.9192	0.632655
$418$	2.18138	0.106695
$419$	23.3208	1.13929	0.569647	−	0.821890i	$-0.307080\pi$
$419$	23.3208	1.13929	0.569647	+	0.821890i	$0.307080\pi$
$420$	0	0
$421$	−7.23309	−0.352519	−0.176260	−	0.984344i	$-0.556400\pi$
$421$	−7.23309	−0.352519	−0.176260	+	0.984344i	$0.556400\pi$
$422$	−10.6525	−0.518557
$423$	1.33621	0.0649685
$424$	1.32980	0.0645806
$425$	15.9868	0.775472
$426$	20.6069	0.998406
$427$	0	0
$428$	−17.7224	−0.856642
$429$	8.41145	0.406109
$430$	29.7005	1.43228
$431$	9.75308	0.469790	0.234895	−	0.972021i	$-0.424525\pi$
$431$	9.75308	0.469790	0.234895	+	0.972021i	$0.424525\pi$
$432$	−4.66740	−0.224561
$433$	−14.8459	−0.713446	−0.356723	−	0.934210i	$-0.616106\pi$
$433$	−14.8459	−0.713446	−0.356723	+	0.934210i	$0.616106\pi$
$434$	0	0
$435$	−10.4841	−0.502672
$436$	−11.8090	−0.565548
$437$	−6.10613	−0.292096
$438$	−5.28458	−0.252507
$439$	0.686453	0.0327626	0.0163813	−	0.999866i	$-0.494785\pi$
$439$	0.686453	0.0327626	0.0163813	+	0.999866i	$0.494785\pi$
$440$	2.10460	0.100333
$441$	0	0
$442$	60.6697	2.88576
$443$	14.2413	0.676625	0.338313	−	0.941034i	$-0.390144\pi$
$443$	14.2413	0.676625	0.338313	+	0.941034i	$0.390144\pi$
$444$	14.2323	0.675434
$445$	20.0531	0.950609
$446$	−27.9729	−1.32455
$447$	17.0545	0.806651
$448$	0	0
$449$	21.0517	0.993492	0.496746	−	0.867896i	$-0.334528\pi$
$449$	21.0517	0.993492	0.496746	+	0.867896i	$0.334528\pi$
$450$	4.75448	0.224129
$451$	1.66740	0.0785149
$452$	24.1786	1.13726
$453$	−4.62901	−0.217490
$454$	−10.2371	−0.480453
$455$	0	0
$456$	−0.553766	−0.0259325
$457$	−29.4366	−1.37699	−0.688493	−	0.725243i	$-0.741728\pi$
$457$	−29.4366	−1.37699	−0.688493	+	0.725243i	$0.741728\pi$
$458$	0.996784	0.0465767
$459$	−6.35915	−0.296820
$460$	21.9443	1.02316
$461$	−12.8388	−0.597961	−0.298980	−	0.954259i	$-0.596647\pi$
$461$	−12.8388	−0.597961	−0.298980	+	0.954259i	$0.596647\pi$
$462$	0	0
$463$	−12.2308	−0.568411	−0.284206	−	0.958763i	$-0.591730\pi$
$463$	−12.2308	−0.568411	−0.284206	+	0.958763i	$0.591730\pi$
$464$	31.0350	1.44076
$465$	−3.71970	−0.172497
$466$	31.6682	1.46700
$467$	22.4867	1.04056	0.520280	−	0.853996i	$-0.325827\pi$
$467$	22.4867	1.04056	0.520280	+	0.853996i	$0.325827\pi$
$468$	7.95395	0.367672
$469$	0	0
$470$	−3.98445	−0.183789
$471$	−18.4380	−0.849579
$472$	9.62761	0.443147
$473$	−16.6077	−0.763622
$474$	−23.1605	−1.06380
$475$	1.73904	0.0797928
$476$	0	0
$477$	1.66115	0.0760586
$478$	−2.69857	−0.123430
$479$	−0.0510288	−0.00233156	−0.00116578	−	0.999999i	$-0.500371\pi$
$479$	−0.0510288	−0.00233156	−0.00116578	+	0.999999i	$0.500371\pi$
$480$	11.3934	0.520034
$481$	45.5358	2.07625
$482$	24.3527	1.10924
$483$	0	0
$484$	−12.9602	−0.589101
$485$	5.06438	0.229961
$486$	−1.89122	−0.0857875
$487$	21.9309	0.993782	0.496891	−	0.867813i	$-0.334475\pi$
$487$	21.9309	0.993782	0.496891	+	0.867813i	$0.334475\pi$
$488$	9.57450	0.433417
$489$	−17.6019	−0.795984
$490$	0	0
$491$	−22.7657	−1.02740	−0.513701	−	0.857969i	$-0.671726\pi$
$491$	−22.7657	−1.02740	−0.513701	+	0.857969i	$0.671726\pi$
$492$	1.57671	0.0710837
$493$	42.2840	1.90438
$494$	6.59966	0.296933
$495$	2.62901	0.118165
$496$	11.0111	0.494414
$497$	0	0
$498$	−4.97204	−0.222803
$499$	25.0730	1.12242	0.561210	−	0.827673i	$-0.310336\pi$
$499$	25.0730	1.12242	0.561210	+	0.827673i	$0.310336\pi$
$500$	−18.6799	−0.835391
$501$	0.255948	0.0114349
$502$	−39.3570	−1.75659
$503$	29.4448	1.31288	0.656440	−	0.754378i	$-0.272061\pi$
$503$	29.4448	1.31288	0.656440	+	0.754378i	$0.272061\pi$
$504$	0	0
$505$	12.5731	0.559496
$506$	−27.8355	−1.23744
$507$	12.4484	0.552855
$508$	−24.3194	−1.07900
$509$	−8.94477	−0.396470	−0.198235	−	0.980155i	$-0.563521\pi$
$509$	−8.94477	−0.396470	−0.198235	+	0.980155i	$0.563521\pi$
$510$	18.9624	0.839670
$511$	0	0
$512$	−26.2540	−1.16027
$513$	−0.691750	−0.0305415
$514$	−46.2192	−2.03864
$515$	10.0002	0.440663
$516$	−15.7044	−0.691347
$517$	2.22799	0.0979870
$518$	0	0
$519$	−21.9173	−0.962064
$520$	6.36738	0.279228
$521$	1.13578	0.0497592	0.0248796	−	0.999690i	$-0.492080\pi$
$521$	1.13578	0.0497592	0.0248796	+	0.999690i	$0.492080\pi$
$522$	12.5753	0.550406
$523$	−24.2249	−1.05928	−0.529640	−	0.848223i	$-0.677673\pi$
$523$	−24.2249	−1.05928	−0.529640	+	0.848223i	$0.677673\pi$
$524$	25.1241	1.09755
$525$	0	0
$526$	28.3961	1.23813
$527$	15.0022	0.653506
$528$	−7.78244	−0.338687
$529$	54.9174	2.38771
$530$	−4.95339	−0.215161
$531$	12.0266	0.521908
$532$	0	0
$533$	5.04464	0.218508
$534$	−24.0531	−1.04088
$535$	−17.7224	−0.766204
$536$	−0.697199	−0.0301144
$537$	15.5685	0.671830
$538$	9.16482	0.395123
$539$	0	0
$540$	2.48602	0.106981
$541$	15.5016	0.666464	0.333232	−	0.942845i	$-0.391861\pi$
$541$	15.5016	0.666464	0.333232	+	0.942845i	$0.391861\pi$
$542$	29.0133	1.24623
$543$	22.5707	0.968601
$544$	−45.9514	−1.97015
$545$	−11.8090	−0.505842
$546$	0	0
$547$	33.5952	1.43643	0.718213	−	0.695823i	$-0.244960\pi$
$547$	33.5952	1.43643	0.718213	+	0.695823i	$0.244960\pi$
$548$	4.94004	0.211028
$549$	11.9602	0.510449
$550$	7.92764	0.338036
$551$	4.59966	0.195952
$552$	7.06634	0.300764
$553$	0	0
$554$	8.99731	0.382259
$555$	14.2323	0.604127
$556$	20.3698	0.863873
$557$	12.7050	0.538327	0.269164	−	0.963094i	$-0.413253\pi$
$557$	12.7050	0.538327	0.269164	+	0.963094i	$0.413253\pi$
$558$	4.46168	0.188878
$559$	−50.2457	−2.12517
$560$	0	0
$561$	−10.6033	−0.447670
$562$	56.0260	2.36331
$563$	17.0531	0.718703	0.359351	−	0.933202i	$-0.382998\pi$
$563$	17.0531	0.718703	0.359351	+	0.933202i	$0.382998\pi$
$564$	2.10681	0.0887128
$565$	24.1786	1.01720
$566$	−9.04336	−0.380121
$567$	0	0
$568$	−8.72263	−0.365994
$569$	28.0319	1.17516	0.587578	−	0.809167i	$-0.300081\pi$
$569$	28.0319	1.17516	0.587578	+	0.809167i	$0.300081\pi$
$570$	2.06273	0.0863985
$571$	−30.4034	−1.27234	−0.636170	−	0.771549i	$-0.719482\pi$
$571$	−30.4034	−1.27234	−0.636170	+	0.771549i	$0.719482\pi$
$572$	13.2624	0.554531
$573$	20.0797	0.838840
$574$	0	0
$575$	−22.1911	−0.925433
$576$	−4.33120	−0.180467
$577$	−32.6653	−1.35987	−0.679937	−	0.733271i	$-0.737993\pi$
$577$	−32.6653	−1.35987	−0.679937	+	0.733271i	$0.737993\pi$
$578$	−44.3280	−1.84380
$579$	2.56628	0.106651
$580$	−16.5303	−0.686385
$581$	0	0
$582$	−6.07457	−0.251799
$583$	2.76980	0.114713
$584$	2.23690	0.0925635
$585$	7.95395	0.328856
$586$	29.5750	1.22173
$587$	−4.70346	−0.194132	−0.0970662	−	0.995278i	$-0.530946\pi$
$587$	−4.70346	−0.194132	−0.0970662	+	0.995278i	$0.530946\pi$
$588$	0	0
$589$	1.63194	0.0672430
$590$	−35.8621	−1.47642
$591$	25.4241	1.04581
$592$	−42.1306	−1.73156
$593$	−22.8333	−0.937653	−0.468826	−	0.883290i	$-0.655323\pi$
$593$	−22.8333	−0.937653	−0.468826	+	0.883290i	$0.655323\pi$
$594$	−3.15343	−0.129387
$595$	0	0
$596$	26.8901	1.10146
$597$	−15.8215	−0.647531
$598$	−84.2151	−3.44381
$599$	−28.2078	−1.15254	−0.576269	−	0.817260i	$-0.695492\pi$
$599$	−28.2078	−1.15254	−0.576269	+	0.817260i	$0.695492\pi$
$600$	−2.01251	−0.0821605
$601$	46.0212	1.87724	0.938622	−	0.344948i	$-0.112103\pi$
$601$	46.0212	1.87724	0.938622	+	0.344948i	$0.112103\pi$
$602$	0	0
$603$	−0.870922	−0.0354667
$604$	−7.29863	−0.296977
$605$	−12.9602	−0.526908
$606$	−15.0811	−0.612626
$607$	48.3754	1.96350	0.981748	−	0.190188i	$-0.0609098\pi$
$607$	48.3754	1.96350	0.981748	+	0.190188i	$0.0609098\pi$
$608$	−4.99860	−0.202720
$609$	0	0
$610$	−35.6643	−1.44400
$611$	6.74068	0.272699
$612$	−10.0266	−0.405299
$613$	30.5767	1.23498	0.617490	−	0.786579i	$-0.288150\pi$
$613$	30.5767	1.23498	0.617490	+	0.786579i	$0.288150\pi$
$614$	−40.2283	−1.62348
$615$	1.57671	0.0635792
$616$	0	0
$617$	38.6874	1.55750	0.778748	−	0.627336i	$-0.215855\pi$
$617$	38.6874	1.55750	0.778748	+	0.627336i	$0.215855\pi$
$618$	−11.9950	−0.482509
$619$	−0.413942	−0.0166377	−0.00831886	−	0.999965i	$-0.502648\pi$
$619$	−0.413942	−0.0166377	−0.00831886	+	0.999965i	$0.502648\pi$
$620$	−5.86491	−0.235540
$621$	8.82708	0.354219
$622$	5.39056	0.216142
$623$	0	0
$624$	−23.5454	−0.942570
$625$	−6.11003	−0.244401
$626$	−25.2112	−1.00764
$627$	−1.15343	−0.0460634
$628$	−29.0714	−1.16008
$629$	−57.4012	−2.28874
$630$	0	0
$631$	2.84144	0.113116	0.0565580	−	0.998399i	$-0.481987\pi$
$631$	2.84144	0.113116	0.0565580	+	0.998399i	$0.481987\pi$
$632$	9.80355	0.389964
$633$	5.63262	0.223877
$634$	−16.0939	−0.639171
$635$	−24.3194	−0.965085
$636$	2.61915	0.103856
$637$	0	0
$638$	20.9681	0.830135
$639$	−10.8961	−0.431042
$640$	−9.87149	−0.390205
$641$	−9.25354	−0.365493	−0.182746	−	0.983160i	$-0.558499\pi$
$641$	−9.25354	−0.365493	−0.182746	+	0.983160i	$0.558499\pi$
$642$	21.2574	0.838964
$643$	−8.80165	−0.347103	−0.173552	−	0.984825i	$-0.555524\pi$
$643$	−8.80165	−0.347103	−0.173552	+	0.984825i	$0.555524\pi$
$644$	0	0
$645$	−15.7044	−0.618360
$646$	−8.31936	−0.327321
$647$	30.1439	1.18508	0.592540	−	0.805541i	$-0.298125\pi$
$647$	30.1439	1.18508	0.592540	+	0.805541i	$0.298125\pi$
$648$	0.800530	0.0314478
$649$	20.0531	0.787153
$650$	23.9847	0.940757
$651$	0	0
$652$	−27.7531	−1.08689
$653$	3.42858	0.134171	0.0670854	−	0.997747i	$-0.478630\pi$
$653$	3.42858	0.134171	0.0670854	+	0.997747i	$0.478630\pi$
$654$	14.1645	0.553877
$655$	25.1241	0.981679
$656$	−4.66740	−0.182231
$657$	2.79427	0.109015
$658$	0	0
$659$	5.84806	0.227808	0.113904	−	0.993492i	$-0.463664\pi$
$659$	5.84806	0.227808	0.113904	+	0.993492i	$0.463664\pi$
$660$	4.14520	0.161352
$661$	10.8716	0.422856	0.211428	−	0.977394i	$-0.432189\pi$
$661$	10.8716	0.422856	0.211428	+	0.977394i	$0.432189\pi$
$662$	56.5803	2.19905
$663$	−32.0797	−1.24587
$664$	2.10460	0.0816745
$665$	0	0
$666$	−17.0712	−0.661496
$667$	−58.6940	−2.27264
$668$	0.403557	0.0156141
$669$	14.7909	0.571849
$670$	2.59701	0.100331
$671$	19.9425	0.769871
$672$	0	0
$673$	22.8775	0.881865	0.440932	−	0.897540i	$-0.354648\pi$
$673$	22.8775	0.881865	0.440932	+	0.897540i	$0.354648\pi$
$674$	12.6931	0.488921
$675$	−2.51398	−0.0967630
$676$	19.6276	0.754908
$677$	16.2635	0.625055	0.312528	−	0.949909i	$-0.398824\pi$
$677$	16.2635	0.625055	0.312528	+	0.949909i	$0.398824\pi$
$678$	−29.0015	−1.11380
$679$	0	0
$680$	−8.02655	−0.307804
$681$	5.41298	0.207426
$682$	7.43941	0.284870
$683$	7.01794	0.268534	0.134267	−	0.990945i	$-0.457132\pi$
$683$	7.01794	0.268534	0.134267	+	0.990945i	$0.457132\pi$
$684$	−1.09069	−0.0417036
$685$	4.94004	0.188749
$686$	0	0
$687$	−0.527059	−0.0201085
$688$	46.4883	1.77235
$689$	8.37989	0.319248
$690$	−26.3216	−1.00205
$691$	−47.3364	−1.80076	−0.900381	−	0.435102i	$-0.856712\pi$
$691$	−47.3364	−1.80076	−0.900381	+	0.435102i	$0.856712\pi$
$692$	−34.5573	−1.31367
$693$	0	0
$694$	−65.3711	−2.48145
$695$	20.3698	0.772672
$696$	−5.32297	−0.201767
$697$	−6.35915	−0.240870
$698$	18.8216	0.712409
$699$	−16.7449	−0.633349
$700$	0	0
$701$	2.65268	0.100190	0.0500952	−	0.998744i	$-0.484048\pi$
$701$	2.65268	0.100190	0.0500952	+	0.998744i	$0.484048\pi$
$702$	−9.54053	−0.360084
$703$	−6.24412	−0.235501
$704$	−7.22185	−0.272184
$705$	2.10681	0.0793471
$706$	−14.3305	−0.539336
$707$	0	0
$708$	18.9624	0.712651
$709$	−28.8201	−1.08236	−0.541181	−	0.840906i	$-0.682023\pi$
$709$	−28.8201	−1.08236	−0.541181	+	0.840906i	$0.682023\pi$
$710$	32.4911	1.21937
$711$	12.2463	0.459273
$712$	10.1814	0.381563
$713$	−20.8244	−0.779881
$714$	0	0
$715$	13.2624	0.495987
$716$	24.5470	0.917366
$717$	1.42690	0.0532884
$718$	12.2420	0.456867
$719$	−23.3900	−0.872300	−0.436150	−	0.899874i	$-0.643658\pi$
$719$	−23.3900	−0.872300	−0.436150	+	0.899874i	$0.643658\pi$
$720$	−7.35915	−0.274259
$721$	0	0
$722$	35.0282	1.30361
$723$	−12.8767	−0.478891
$724$	35.5875	1.32260
$725$	16.7162	0.620825
$726$	15.5454	0.576943
$727$	−24.6218	−0.913172	−0.456586	−	0.889679i	$-0.650928\pi$
$727$	−24.6218	−0.913172	−0.456586	+	0.889679i	$0.650928\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−8.33227	−0.308391
$731$	63.3385	2.34266
$732$	18.8578	0.697005
$733$	47.1181	1.74035	0.870174	−	0.492744i	$-0.164006\pi$
$733$	47.1181	1.74035	0.870174	+	0.492744i	$0.164006\pi$
$734$	−21.0399	−0.776596
$735$	0	0
$736$	63.7847	2.35114
$737$	−1.45218	−0.0534916
$738$	−1.89122	−0.0696168
$739$	−2.83767	−0.104385	−0.0521927	−	0.998637i	$-0.516621\pi$
$739$	−2.83767	−0.104385	−0.0521927	+	0.998637i	$0.516621\pi$
$740$	22.4402	0.824919
$741$	−3.48963	−0.128195
$742$	0	0
$743$	−15.6763	−0.575108	−0.287554	−	0.957764i	$-0.592842\pi$
$743$	−15.6763	−0.575108	−0.287554	+	0.957764i	$0.592842\pi$
$744$	−1.88857	−0.0692384
$745$	26.8901	0.985176
$746$	47.5522	1.74101
$747$	2.62901	0.0961906
$748$	−16.7183	−0.611282
$749$	0	0
$750$	22.4060	0.818152
$751$	−26.2001	−0.956056	−0.478028	−	0.878345i	$-0.658648\pi$
$751$	−26.2001	−0.956056	−0.478028	+	0.878345i	$0.658648\pi$
$752$	−6.23661	−0.227426
$753$	20.8104	0.758373
$754$	63.4380	2.31028
$755$	−7.29863	−0.265624
$756$	0	0
$757$	36.9359	1.34246	0.671228	−	0.741251i	$-0.265767\pi$
$757$	36.9359	1.34246	0.671228	+	0.741251i	$0.265767\pi$
$758$	46.9568	1.70555
$759$	14.7183	0.534241
$760$	−0.873130	−0.0316717
$761$	4.64085	0.168231	0.0841153	−	0.996456i	$-0.473194\pi$
$761$	4.64085	0.168231	0.0841153	+	0.996456i	$0.473194\pi$
$762$	29.1704	1.05673
$763$	0	0
$764$	31.6599	1.14541
$765$	−10.0266	−0.362511
$766$	−34.3086	−1.23962
$767$	60.6697	2.19066
$768$	20.5030	0.739837
$769$	37.9759	1.36944	0.684722	−	0.728804i	$-0.259923\pi$
$769$	37.9759	1.36944	0.684722	+	0.728804i	$0.259923\pi$
$770$	0	0
$771$	24.4388	0.880142
$772$	4.04629	0.145629
$773$	35.0191	1.25955	0.629775	−	0.776777i	$-0.283147\pi$
$773$	35.0191	1.25955	0.629775	+	0.776777i	$0.283147\pi$
$774$	18.8369	0.677080
$775$	5.93086	0.213043
$776$	2.57129	0.0923039
$777$	0	0
$778$	54.6001	1.95751
$779$	−0.691750	−0.0247845
$780$	12.5411	0.449043
$781$	−18.1681	−0.650107
$782$	106.159	3.79625
$783$	−6.64931	−0.237627
$784$	0	0
$785$	−29.0714	−1.03760
$786$	−30.1356	−1.07490
$787$	−30.4583	−1.08572	−0.542861	−	0.839823i	$-0.682659\pi$
$787$	−30.4583	−1.08572	−0.542861	+	0.839823i	$0.682659\pi$
$788$	40.0865	1.42802
$789$	−15.0147	−0.534538
$790$	−36.5174	−1.29923
$791$	0	0
$792$	1.33481	0.0474302
$793$	60.3350	2.14256
$794$	50.3041	1.78523
$795$	2.61915	0.0928917
$796$	−24.9460	−0.884186
$797$	−14.9234	−0.528612	−0.264306	−	0.964439i	$-0.585143\pi$
$797$	−14.9234	−0.528612	−0.264306	+	0.964439i	$0.585143\pi$
$798$	0	0
$799$	−8.49714	−0.300607
$800$	−18.1661	−0.642267
$801$	12.7183	0.449379
$802$	−13.3835	−0.472588
$803$	4.65918	0.164419
$804$	−1.37319	−0.0484288
$805$	0	0
$806$	22.5076	0.792795
$807$	−4.84598	−0.170587
$808$	6.38363	0.224575
$809$	40.8287	1.43546	0.717730	−	0.696321i	$-0.245181\pi$
$809$	40.8287	1.43546	0.717730	+	0.696321i	$0.245181\pi$
$810$	−2.98191	−0.104774
$811$	−11.4066	−0.400540	−0.200270	−	0.979741i	$-0.564182\pi$
$811$	−11.4066	−0.400540	−0.200270	+	0.979741i	$0.564182\pi$
$812$	0	0
$813$	−15.3411	−0.538035
$814$	−28.4646	−0.997682
$815$	−27.7531	−0.972148
$816$	29.6807	1.03903
$817$	6.88997	0.241050
$818$	−17.2861	−0.604395
$819$	0	0
$820$	2.48602	0.0868157
$821$	42.0952	1.46913	0.734567	−	0.678536i	$-0.237385\pi$
$821$	42.0952	1.46913	0.734567	+	0.678536i	$0.237385\pi$
$822$	−5.92543	−0.206673
$823$	−17.7641	−0.619217	−0.309608	−	0.950864i	$-0.600198\pi$
$823$	−17.7641	−0.619217	−0.309608	+	0.950864i	$0.600198\pi$
$824$	5.07733	0.176877
$825$	−4.19181	−0.145940
$826$	0	0
$827$	−24.3092	−0.845313	−0.422657	−	0.906290i	$-0.638902\pi$
$827$	−24.3092	−0.845313	−0.422657	+	0.906290i	$0.638902\pi$
$828$	13.9178	0.483676
$829$	−20.3379	−0.706364	−0.353182	−	0.935555i	$-0.614900\pi$
$829$	−20.3379	−0.706364	−0.353182	+	0.935555i	$0.614900\pi$
$830$	−7.83949	−0.272113
$831$	−4.75741	−0.165033
$832$	−21.8494	−0.757490
$833$	0	0
$834$	−24.4330	−0.846046
$835$	0.403557	0.0139657
$836$	−1.81862	−0.0628983
$837$	−2.35915	−0.0815442
$838$	−44.1047	−1.52357
$839$	−7.52649	−0.259843	−0.129922	−	0.991524i	$-0.541473\pi$
$839$	−7.52649	−0.259843	−0.129922	+	0.991524i	$0.541473\pi$
$840$	0	0
$841$	15.2134	0.524599
$842$	13.6794	0.471422
$843$	−29.6242	−1.02031
$844$	8.88103	0.305698
$845$	19.6276	0.675210
$846$	−2.52706	−0.0868821
$847$	0	0
$848$	−7.75324	−0.266247
$849$	4.78176	0.164110
$850$	−30.2345	−1.03703
$851$	79.6782	2.73133
$852$	−17.1800	−0.588576
$853$	30.5664	1.04657	0.523286	−	0.852157i	$-0.324706\pi$
$853$	30.5664	1.04657	0.523286	+	0.852157i	$0.324706\pi$
$854$	0	0
$855$	−1.09069	−0.0373008
$856$	−8.99801	−0.307546
$857$	−23.2562	−0.794415	−0.397208	−	0.917729i	$-0.630021\pi$
$857$	−23.2562	−0.794415	−0.397208	+	0.917729i	$0.630021\pi$
$858$	−15.9079	−0.543087
$859$	15.2284	0.519585	0.259792	−	0.965664i	$-0.416346\pi$
$859$	15.2284	0.519585	0.259792	+	0.965664i	$0.416346\pi$
$860$	−24.7613	−0.844354
$861$	0	0
$862$	−18.4452	−0.628247
$863$	−31.1449	−1.06019	−0.530093	−	0.847940i	$-0.677843\pi$
$863$	−31.1449	−1.06019	−0.530093	+	0.847940i	$0.677843\pi$
$864$	7.22603	0.245834
$865$	−34.5573	−1.17498
$866$	28.0768	0.954088
$867$	23.4388	0.796024
$868$	0	0
$869$	20.4196	0.692686
$870$	19.8277	0.672220
$871$	−4.39349	−0.148868
$872$	−5.99567	−0.203039
$873$	3.21198	0.108709
$874$	11.5480	0.390618
$875$	0	0
$876$	4.40576	0.148857
$877$	11.7539	0.396901	0.198450	−	0.980111i	$-0.436409\pi$
$877$	11.7539	0.396901	0.198450	+	0.980111i	$0.436409\pi$
$878$	−1.29823	−0.0438132
$879$	−15.6380	−0.527458
$880$	−12.2707	−0.413644
$881$	47.4654	1.59915	0.799575	−	0.600567i	$-0.205058\pi$
$881$	47.4654	1.59915	0.799575	+	0.600567i	$0.205058\pi$
$882$	0	0
$883$	10.4218	0.350720	0.175360	−	0.984504i	$-0.443891\pi$
$883$	10.4218	0.350720	0.175360	+	0.984504i	$0.443891\pi$
$884$	−50.5804	−1.70120
$885$	18.9624	0.637415
$886$	−26.9335	−0.904847
$887$	4.31114	0.144754	0.0723769	−	0.997377i	$-0.476942\pi$
$887$	4.31114	0.144754	0.0723769	+	0.997377i	$0.476942\pi$
$888$	7.22603	0.242490
$889$	0	0
$890$	−37.9248	−1.27124
$891$	1.66740	0.0558601
$892$	23.3210	0.780845
$893$	−0.924320	−0.0309312
$894$	−32.2538	−1.07873
$895$	24.5470	0.820517
$896$	0	0
$897$	44.5295	1.48680
$898$	−39.8134	−1.32859
$899$	15.6867	0.523182
$900$	−3.96382	−0.132127
$901$	−10.5635	−0.351921
$902$	−3.15343	−0.104998
$903$	0	0
$904$	12.2760	0.408293
$905$	35.5875	1.18297
$906$	8.75448	0.290848
$907$	−7.31924	−0.243031	−0.121516	−	0.992590i	$-0.538775\pi$
$907$	−7.31924	−0.243031	−0.121516	+	0.992590i	$0.538775\pi$
$908$	8.53472	0.283235
$909$	7.97425	0.264489
$910$	0	0
$911$	−13.5987	−0.450543	−0.225272	−	0.974296i	$-0.572327\pi$
$911$	−13.5987	−0.450543	−0.225272	+	0.974296i	$0.572327\pi$
$912$	3.22867	0.106912
$913$	4.38363	0.145077
$914$	55.6711	1.84144
$915$	18.8578	0.623420
$916$	−0.831020	−0.0274577
$917$	0	0
$918$	12.0266	0.396935
$919$	−21.2143	−0.699797	−0.349898	−	0.936788i	$-0.613784\pi$
$919$	−21.2143	−0.699797	−0.349898	+	0.936788i	$0.613784\pi$
$920$	11.1416	0.367327
$921$	21.2711	0.700907
$922$	24.2809	0.799650
$923$	−54.9668	−1.80926
$924$	0	0
$925$	−22.6926	−0.746127
$926$	23.1310	0.760133
$927$	6.34246	0.208314
$928$	−48.0481	−1.57726
$929$	−30.5044	−1.00082	−0.500408	−	0.865790i	$-0.666817\pi$
$929$	−30.5044	−1.00082	−0.500408	+	0.865790i	$0.666817\pi$
$930$	7.03478	0.230680
$931$	0	0
$932$	−26.4018	−0.864821
$933$	−2.85031	−0.0933150
$934$	−42.5273	−1.39154
$935$	−16.7183	−0.546747
$936$	4.03839	0.131999
$937$	21.5636	0.704452	0.352226	−	0.935915i	$-0.385425\pi$
$937$	21.5636	0.704452	0.352226	+	0.935915i	$0.385425\pi$
$938$	0	0
$939$	13.3306	0.435029
$940$	3.32184	0.108346
$941$	−21.3467	−0.695883	−0.347942	−	0.937516i	$-0.613119\pi$
$941$	−21.3467	−0.695883	−0.347942	+	0.937516i	$0.613119\pi$
$942$	34.8703	1.13614
$943$	8.82708	0.287449
$944$	−56.1328	−1.82697
$945$	0	0
$946$	31.4088	1.02119
$947$	40.6083	1.31959	0.659795	−	0.751445i	$-0.270643\pi$
$947$	40.6083	1.31959	0.659795	+	0.751445i	$0.270643\pi$
$948$	19.3089	0.627125
$949$	14.0961	0.457579
$950$	−3.28891	−0.106706
$951$	8.50980	0.275949
$952$	0	0
$953$	13.4968	0.437206	0.218603	−	0.975814i	$-0.429850\pi$
$953$	13.4968	0.437206	0.218603	+	0.975814i	$0.429850\pi$
$954$	−3.14159	−0.101713
$955$	31.6599	1.02449
$956$	2.24980	0.0727639
$957$	−11.0871	−0.358394
$958$	0.0965066	0.00311799
$959$	0	0
$960$	−6.82905	−0.220407
$961$	−25.4344	−0.820465
$962$	−86.1181	−2.77656
$963$	−11.2401	−0.362206
$964$	−20.3029	−0.653913
$965$	4.04629	0.130255
$966$	0	0
$967$	−26.7592	−0.860517	−0.430259	−	0.902706i	$-0.641578\pi$
$967$	−26.7592	−0.860517	−0.430259	+	0.902706i	$0.641578\pi$
$968$	−6.58017	−0.211495
$969$	4.39894	0.141314
$970$	−9.57785	−0.307526
$971$	−37.6519	−1.20831	−0.604153	−	0.796868i	$-0.706489\pi$
$971$	−37.6519	−1.20831	−0.604153	+	0.796868i	$0.706489\pi$
$972$	1.57671	0.0505731
$973$	0	0
$974$	−41.4761	−1.32898
$975$	−12.6821	−0.406153
$976$	−55.8231	−1.78685
$977$	48.0278	1.53654	0.768272	−	0.640124i	$-0.221117\pi$
$977$	48.0278	1.53654	0.768272	+	0.640124i	$0.221117\pi$
$978$	33.2890	1.06446
$979$	21.2065	0.677764
$980$	0	0
$981$	−7.48963	−0.239126
$982$	43.0550	1.37394
$983$	−21.5525	−0.687417	−0.343708	−	0.939076i	$-0.611683\pi$
$983$	−21.5525	−0.687417	−0.343708	+	0.939076i	$0.611683\pi$
$984$	0.800530	0.0255200
$985$	40.0865	1.27726
$986$	−79.9683	−2.54671
$987$	0	0
$988$	−5.50214	−0.175047
$989$	−87.9196	−2.79568
$990$	−4.97204	−0.158022
$991$	3.92823	0.124784	0.0623922	−	0.998052i	$-0.480127\pi$
$991$	3.92823	0.124784	0.0623922	+	0.998052i	$0.480127\pi$
$992$	−17.0473	−0.541252
$993$	−29.9173	−0.949398
$994$	0	0
$995$	−24.9460	−0.790840
$996$	4.14520	0.131346
$997$	−51.0675	−1.61732	−0.808662	−	0.588273i	$-0.799808\pi$
$997$	−51.0675	−1.61732	−0.808662	+	0.588273i	$0.799808\pi$
$998$	−47.4185	−1.50101
$999$	9.02655	0.285588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.u.1.1		4
7.6	odd	2		861.2.a.i.1.1	✓	4
21.20	even	2		2583.2.a.o.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.a.i.1.1	✓	4	7.6	odd	2
2583.2.a.o.1.4		4	21.20	even	2
6027.2.a.u.1.1		4	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)

\(f(q)\)	\(=\)	\(q-1.89122 q^{2} +1.00000 q^{3} +1.57671 q^{4} +1.57671 q^{5} -1.89122 q^{6} +0.800530 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.89122 q^{2} +1.00000 q^{3} +1.57671 q^{4} +1.57671 q^{5} -1.89122 q^{6} +0.800530 q^{8} +1.00000 q^{9} -2.98191 q^{10} +1.66740 q^{11} +1.57671 q^{12} +5.04464 q^{13} +1.57671 q^{15} -4.66740 q^{16} -6.35915 q^{17} -1.89122 q^{18} -0.691750 q^{19} +2.48602 q^{20} -3.15343 q^{22} +8.82708 q^{23} +0.800530 q^{24} -2.51398 q^{25} -9.54053 q^{26} +1.00000 q^{27} -6.64931 q^{29} -2.98191 q^{30} -2.35915 q^{31} +7.22603 q^{32} +1.66740 q^{33} +12.0266 q^{34} +1.57671 q^{36} +9.02655 q^{37} +1.30825 q^{38} +5.04464 q^{39} +1.26221 q^{40} +1.00000 q^{41} -9.96021 q^{43} +2.62901 q^{44} +1.57671 q^{45} -16.6940 q^{46} +1.33621 q^{47} -4.66740 q^{48} +4.75448 q^{50} -6.35915 q^{51} +7.95395 q^{52} +1.66115 q^{53} -1.89122 q^{54} +2.62901 q^{55} -0.691750 q^{57} +12.5753 q^{58} +12.0266 q^{59} +2.48602 q^{60} +11.9602 q^{61} +4.46168 q^{62} -4.33120 q^{64} +7.95395 q^{65} -3.15343 q^{66} -0.870922 q^{67} -10.0266 q^{68} +8.82708 q^{69} -10.8961 q^{71} +0.800530 q^{72} +2.79427 q^{73} -17.0712 q^{74} -2.51398 q^{75} -1.09069 q^{76} -9.54053 q^{78} +12.2463 q^{79} -7.35915 q^{80} +1.00000 q^{81} -1.89122 q^{82} +2.62901 q^{83} -10.0266 q^{85} +18.8369 q^{86} -6.64931 q^{87} +1.33481 q^{88} +12.7183 q^{89} -2.98191 q^{90} +13.9178 q^{92} -2.35915 q^{93} -2.52706 q^{94} -1.09069 q^{95} +7.22603 q^{96} +3.21198 q^{97} +1.66740 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 4 q^{3} + 3 q^{4} + 3 q^{5} + q^{6} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + q^2 + 4 * q^3 + 3 * q^4 + 3 * q^5 + q^6 + 3 * q^8 + 4 * q^9	\( 4 q + q^{2} + 4 q^{3} + 3 q^{4} + 3 q^{5} + q^{6} + 3 q^{8} + 4 q^{9} + 5 q^{10} - 5 q^{11} + 3 q^{12} + 5 q^{13} + 3 q^{15} - 7 q^{16} - 5 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 6 q^{22} + 3 q^{23} + 3 q^{24} - 5 q^{25} - q^{26} + 4 q^{27} + 2 q^{29} + 5 q^{30} + 11 q^{31} - 3 q^{32} - 5 q^{33} + 16 q^{34} + 3 q^{36} + 4 q^{37} + 14 q^{38} + 5 q^{39} + 7 q^{40} + 4 q^{41} - 19 q^{43} + 3 q^{45} - 23 q^{46} + 4 q^{47} - 7 q^{48} + 12 q^{50} - 5 q^{51} + 25 q^{52} + 9 q^{53} + q^{54} + 6 q^{57} + 25 q^{58} + 16 q^{59} + 15 q^{60} + 27 q^{61} + 20 q^{62} - 7 q^{64} + 25 q^{65} - 6 q^{66} - 13 q^{67} - 8 q^{68} + 3 q^{69} + q^{71} + 3 q^{72} + 25 q^{73} - 21 q^{74} - 5 q^{75} + 4 q^{76} - q^{78} - q^{79} - 9 q^{80} + 4 q^{81} + q^{82} - 8 q^{85} + 16 q^{86} + 2 q^{87} - 18 q^{88} + 10 q^{89} + 5 q^{90} + 15 q^{92} + 11 q^{93} - 13 q^{94} + 4 q^{95} - 3 q^{96} - 15 q^{97} - 5 q^{99}+O(q^{100}) \) 4 * q + q^2 + 4 * q^3 + 3 * q^4 + 3 * q^5 + q^6 + 3 * q^8 + 4 * q^9 + 5 * q^10 - 5 * q^11 + 3 * q^12 + 5 * q^13 + 3 * q^15 - 7 * q^16 - 5 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 6 * q^22 + 3 * q^23 + 3 * q^24 - 5 * q^25 - q^26 + 4 * q^27 + 2 * q^29 + 5 * q^30 + 11 * q^31 - 3 * q^32 - 5 * q^33 + 16 * q^34 + 3 * q^36 + 4 * q^37 + 14 * q^38 + 5 * q^39 + 7 * q^40 + 4 * q^41 - 19 * q^43 + 3 * q^45 - 23 * q^46 + 4 * q^47 - 7 * q^48 + 12 * q^50 - 5 * q^51 + 25 * q^52 + 9 * q^53 + q^54 + 6 * q^57 + 25 * q^58 + 16 * q^59 + 15 * q^60 + 27 * q^61 + 20 * q^62 - 7 * q^64 + 25 * q^65 - 6 * q^66 - 13 * q^67 - 8 * q^68 + 3 * q^69 + q^71 + 3 * q^72 + 25 * q^73 - 21 * q^74 - 5 * q^75 + 4 * q^76 - q^78 - q^79 - 9 * q^80 + 4 * q^81 + q^82 - 8 * q^85 + 16 * q^86 + 2 * q^87 - 18 * q^88 + 10 * q^89 + 5 * q^90 + 15 * q^92 + 11 * q^93 - 13 * q^94 + 4 * q^95 - 3 * q^96 - 15 * q^97 - 5 * q^99

Introduction

L-functions

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