LMFDB - Embedded newform 595.2.a.j.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [595,2,Mod(1,595)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("595.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(595, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 595 = 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	595.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,2,2,2,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$4.75109892027$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
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			1.4
Root			$0.825785$ of defining polynomial
Character	$\chi$	$=$	595.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.59615 q^{2} +0.452290 q^{3} +4.74002 q^{4} +1.00000 q^{5} +1.17422 q^{6} -1.00000 q^{7} +7.11351 q^{8} -2.79543 q^{9} +2.59615 q^{10} -2.86579 q^{11} +2.14386 q^{12} +5.59615 q^{13} -2.59615 q^{14} +0.452290 q^{15} +8.98774 q^{16} -1.00000 q^{17} -7.25738 q^{18} -1.21422 q^{19} +4.74002 q^{20} -0.452290 q^{21} -7.44003 q^{22} -8.48004 q^{23} +3.21737 q^{24} +1.00000 q^{25} +14.5285 q^{26} -2.62122 q^{27} -4.74002 q^{28} +9.11351 q^{29} +1.17422 q^{30} -4.04844 q^{31} +9.10654 q^{32} -1.29617 q^{33} -2.59615 q^{34} -1.00000 q^{35} -13.2504 q^{36} -3.22266 q^{37} -3.15230 q^{38} +2.53109 q^{39} +7.11351 q^{40} +7.53545 q^{41} -1.17422 q^{42} -12.7511 q^{43} -13.5839 q^{44} -2.79543 q^{45} -22.0155 q^{46} +8.13858 q^{47} +4.06507 q^{48} +1.00000 q^{49} +2.59615 q^{50} -0.452290 q^{51} +26.5259 q^{52} -6.40968 q^{53} -6.80509 q^{54} -2.86579 q^{55} -7.11351 q^{56} -0.549180 q^{57} +23.6601 q^{58} +11.3374 q^{59} +2.14386 q^{60} -14.8716 q^{61} -10.5104 q^{62} +2.79543 q^{63} +5.66651 q^{64} +5.59615 q^{65} -3.36505 q^{66} +12.6574 q^{67} -4.74002 q^{68} -3.83544 q^{69} -2.59615 q^{70} -4.76193 q^{71} -19.8854 q^{72} +3.46891 q^{73} -8.36652 q^{74} +0.452290 q^{75} -5.75543 q^{76} +2.86579 q^{77} +6.57109 q^{78} +2.68989 q^{79} +8.98774 q^{80} +7.20075 q^{81} +19.5632 q^{82} +4.35808 q^{83} -2.14386 q^{84} -1.00000 q^{85} -33.1039 q^{86} +4.12195 q^{87} -20.3858 q^{88} -3.31111 q^{89} -7.25738 q^{90} -5.59615 q^{91} -40.1955 q^{92} -1.83107 q^{93} +21.1290 q^{94} -1.21422 q^{95} +4.11880 q^{96} +11.7015 q^{97} +2.59615 q^{98} +8.01112 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} + 7 q^{6} - 4 q^{7} + 9 q^{8} + 2 q^{9} + 2 q^{10} - 5 q^{11} + 14 q^{13} - 2 q^{14} + 2 q^{15} + 6 q^{16} - 4 q^{17} - q^{18} - 3 q^{19} + 2 q^{20} - 2 q^{21}+ \cdots + q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 + 7 * q^6 - 4 * q^7 + 9 * q^8 + 2 * q^9 + 2 * q^10 - 5 * q^11 + 14 * q^13 - 2 * q^14 + 2 * q^15 + 6 * q^16 - 4 * q^17 - q^18 - 3 * q^19 + 2 * q^20 - 2 * q^21 - 11 * q^24 + 4 * q^25 + 16 * q^26 + 5 * q^27 - 2 * q^28 + 17 * q^29 + 7 * q^30 - 8 * q^31 + 5 * q^32 + 16 * q^33 - 2 * q^34 - 4 * q^35 - 13 * q^36 - 7 * q^37 + 13 * q^39 + 9 * q^40 - 7 * q^42 - 3 * q^43 - 16 * q^44 + 2 * q^45 - 24 * q^46 + 6 * q^47 + 5 * q^48 + 4 * q^49 + 2 * q^50 - 2 * q^51 + 19 * q^52 + 15 * q^53 + q^54 - 5 * q^55 - 9 * q^56 + 14 * q^57 + 14 * q^58 + 9 * q^59 - 4 * q^61 - 19 * q^62 - 2 * q^63 + 21 * q^64 + 14 * q^65 - 15 * q^66 - 3 * q^67 - 2 * q^68 + 2 * q^69 - 2 * q^70 - 17 * q^71 - 38 * q^72 + 11 * q^73 - 19 * q^74 + 2 * q^75 - 14 * q^76 + 5 * q^77 + 25 * q^78 + 8 * q^79 + 6 * q^80 + 8 * q^81 + 14 * q^82 + 7 * q^83 - 4 * q^85 - 56 * q^86 - 7 * q^87 - 37 * q^88 + 5 * q^89 - q^90 - 14 * q^91 - 50 * q^92 - 23 * q^93 + q^94 - 3 * q^95 + 15 * q^96 + 18 * q^97 + 2 * q^98 + q^99

Coefficient data

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

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

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

$2$	2.59615	1.83576	0.917879	−	0.396860i	$-0.129900\pi$
$2$	2.59615	1.83576	0.917879	+	0.396860i	$0.129900\pi$
$3$	0.452290	0.261130	0.130565	−	0.991440i	$-0.458321\pi$
$3$	0.452290	0.261130	0.130565	+	0.991440i	$0.458321\pi$
$4$	4.74002	2.37001
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.17422	0.479371
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	7.11351	2.51501
$9$	−2.79543	−0.931811
$10$	2.59615	0.820976
$11$	−2.86579	−0.864068	−0.432034	−	0.901857i	$-0.642204\pi$
$11$	−2.86579	−0.864068	−0.432034	+	0.901857i	$0.642204\pi$
$12$	2.14386	0.618880
$13$	5.59615	1.55209	0.776047	−	0.630675i	$-0.217222\pi$
$13$	5.59615	1.55209	0.776047	+	0.630675i	$0.217222\pi$
$14$	−2.59615	−0.693852
$15$	0.452290	0.116781
$16$	8.98774	2.24694
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−7.25738	−1.71058
$19$	−1.21422	−0.278561	−0.139281	−	0.990253i	$-0.544479\pi$
$19$	−1.21422	−0.278561	−0.139281	+	0.990253i	$0.544479\pi$
$20$	4.74002	1.05990
$21$	−0.452290	−0.0986978
$22$	−7.44003	−1.58622
$23$	−8.48004	−1.76821	−0.884105	−	0.467288i	$-0.845231\pi$
$23$	−8.48004	−1.76821	−0.884105	+	0.467288i	$0.845231\pi$
$24$	3.21737	0.656743
$25$	1.00000	0.200000
$26$	14.5285	2.84927
$27$	−2.62122	−0.504454
$28$	−4.74002	−0.895779
$29$	9.11351	1.69234	0.846168	−	0.532915i	$-0.178904\pi$
$29$	9.11351	1.69234	0.846168	+	0.532915i	$0.178904\pi$
$30$	1.17422	0.214381
$31$	−4.04844	−0.727122	−0.363561	−	0.931570i	$-0.618439\pi$
$31$	−4.04844	−0.727122	−0.363561	+	0.931570i	$0.618439\pi$
$32$	9.10654	1.60982
$33$	−1.29617	−0.225634
$34$	−2.59615	−0.445237
$35$	−1.00000	−0.169031
$36$	−13.2504	−2.20840
$37$	−3.22266	−0.529802	−0.264901	−	0.964276i	$-0.585339\pi$
$37$	−3.22266	−0.529802	−0.264901	+	0.964276i	$0.585339\pi$
$38$	−3.15230	−0.511371
$39$	2.53109	0.405298
$40$	7.11351	1.12475
$41$	7.53545	1.17684	0.588420	−	0.808555i	$-0.299750\pi$
$41$	7.53545	1.17684	0.588420	+	0.808555i	$0.299750\pi$
$42$	−1.17422	−0.181185
$43$	−12.7511	−1.94453	−0.972266	−	0.233880i	$-0.924858\pi$
$43$	−12.7511	−1.94453	−0.972266	+	0.233880i	$0.924858\pi$
$44$	−13.5839	−2.04785
$45$	−2.79543	−0.416719
$46$	−22.0155	−3.24601
$47$	8.13858	1.18713	0.593567	−	0.804785i	$-0.297719\pi$
$47$	8.13858	1.18713	0.593567	+	0.804785i	$0.297719\pi$
$48$	4.06507	0.586742
$49$	1.00000	0.142857
$50$	2.59615	0.367152
$51$	−0.452290	−0.0633333
$52$	26.5259	3.67848
$53$	−6.40968	−0.880438	−0.440219	−	0.897891i	$-0.645099\pi$
$53$	−6.40968	−0.880438	−0.440219	+	0.897891i	$0.645099\pi$
$54$	−6.80509	−0.926055
$55$	−2.86579	−0.386423
$56$	−7.11351	−0.950583
$57$	−0.549180	−0.0727407
$58$	23.6601	3.10672
$59$	11.3374	1.47600	0.738001	−	0.674800i	$-0.235770\pi$
$59$	11.3374	1.47600	0.738001	+	0.674800i	$0.235770\pi$
$60$	2.14386	0.276772
$61$	−14.8716	−1.90412	−0.952058	−	0.305917i	$-0.901037\pi$
$61$	−14.8716	−1.90412	−0.952058	+	0.305917i	$0.901037\pi$
$62$	−10.5104	−1.33482
$63$	2.79543	0.352192
$64$	5.66651	0.708314
$65$	5.59615	0.694118
$66$	−3.36505	−0.414210
$67$	12.6574	1.54635	0.773174	−	0.634194i	$-0.218668\pi$
$67$	12.6574	1.54635	0.773174	+	0.634194i	$0.218668\pi$
$68$	−4.74002	−0.574812
$69$	−3.83544	−0.461733
$70$	−2.59615	−0.310300
$71$	−4.76193	−0.565137	−0.282569	−	0.959247i	$-0.591186\pi$
$71$	−4.76193	−0.565137	−0.282569	+	0.959247i	$0.591186\pi$
$72$	−19.8854	−2.34351
$73$	3.46891	0.406006	0.203003	−	0.979178i	$-0.434930\pi$
$73$	3.46891	0.406006	0.203003	+	0.979178i	$0.434930\pi$
$74$	−8.36652	−0.972589
$75$	0.452290	0.0522260
$76$	−5.75543	−0.660193
$77$	2.86579	0.326587
$78$	6.57109	0.744030
$79$	2.68989	0.302637	0.151318	−	0.988485i	$-0.451648\pi$
$79$	2.68989	0.302637	0.151318	+	0.988485i	$0.451648\pi$
$80$	8.98774	1.00486
$81$	7.20075	0.800083
$82$	19.5632	2.16039
$83$	4.35808	0.478362	0.239181	−	0.970975i	$-0.423121\pi$
$83$	4.35808	0.478362	0.239181	+	0.970975i	$0.423121\pi$
$84$	−2.14386	−0.233915
$85$	−1.00000	−0.108465
$86$	−33.1039	−3.56969
$87$	4.12195	0.441920
$88$	−20.3858	−2.17314
$89$	−3.31111	−0.350977	−0.175488	−	0.984481i	$-0.556150\pi$
$89$	−3.31111	−0.350977	−0.175488	+	0.984481i	$0.556150\pi$
$90$	−7.25738	−0.764995
$91$	−5.59615	−0.586636
$92$	−40.1955	−4.19068
$93$	−1.83107	−0.189873
$94$	21.1290	2.17929
$95$	−1.21422	−0.124576
$96$	4.11880	0.420373
$97$	11.7015	1.18811	0.594053	−	0.804426i	$-0.297527\pi$
$97$	11.7015	1.18811	0.594053	+	0.804426i	$0.297527\pi$
$98$	2.59615	0.262251
$99$	8.01112	0.805148
$100$	4.74002	0.474002
$101$	1.43373	0.142661	0.0713307	−	0.997453i	$-0.477275\pi$
$101$	1.43373	0.142661	0.0713307	+	0.997453i	$0.477275\pi$
$102$	−1.17422	−0.116265
$103$	5.51568	0.543476	0.271738	−	0.962371i	$-0.412402\pi$
$103$	5.51568	0.543476	0.271738	+	0.962371i	$0.412402\pi$
$104$	39.8083	3.90353
$105$	−0.452290	−0.0441390
$106$	−16.6405	−1.61627
$107$	5.66122	0.547291	0.273646	−	0.961831i	$-0.411770\pi$
$107$	5.66122	0.547291	0.273646	+	0.961831i	$0.411770\pi$
$108$	−12.4246	−1.19556
$109$	5.20343	0.498399	0.249199	−	0.968452i	$-0.419833\pi$
$109$	5.20343	0.498399	0.249199	+	0.968452i	$0.419833\pi$
$110$	−7.44003	−0.709379
$111$	−1.45758	−0.138347
$112$	−8.98774	−0.849262
$113$	−7.29041	−0.685824	−0.342912	−	0.939367i	$-0.611413\pi$
$113$	−7.29041	−0.685824	−0.342912	+	0.939367i	$0.611413\pi$
$114$	−1.42576	−0.133534
$115$	−8.48004	−0.790768
$116$	43.1982	4.01085
$117$	−15.6437	−1.44626
$118$	29.4336	2.70958
$119$	1.00000	0.0916698
$120$	3.21737	0.293705
$121$	−2.78725	−0.253386
$122$	−38.6090	−3.49550
$123$	3.40821	0.307308
$124$	−19.1897	−1.72329
$125$	1.00000	0.0894427
$126$	7.25738	0.646539
$127$	−2.22963	−0.197848	−0.0989238	−	0.995095i	$-0.531540\pi$
$127$	−2.22963	−0.197848	−0.0989238	+	0.995095i	$0.531540\pi$
$128$	−3.50195	−0.309532
$129$	−5.76722	−0.507775
$130$	14.5285	1.27423
$131$	−14.5013	−1.26698	−0.633492	−	0.773750i	$-0.718379\pi$
$131$	−14.5013	−1.26698	−0.633492	+	0.773750i	$0.718379\pi$
$132$	−6.14386	−0.534755
$133$	1.21422	0.105286
$134$	32.8606	2.83872
$135$	−2.62122	−0.225599
$136$	−7.11351	−0.609979
$137$	19.8078	1.69229	0.846146	−	0.532951i	$-0.178917\pi$
$137$	19.8078	1.69229	0.846146	+	0.532951i	$0.178917\pi$
$138$	−9.95739	−0.847629
$139$	−15.5083	−1.31539	−0.657696	−	0.753283i	$-0.728469\pi$
$139$	−15.5083	−1.31539	−0.657696	+	0.753283i	$0.728469\pi$
$140$	−4.74002	−0.400605
$141$	3.68100	0.309996
$142$	−12.3627	−1.03746
$143$	−16.0374	−1.34111
$144$	−25.1246	−2.09372
$145$	9.11351	0.756836
$146$	9.00584	0.745328
$147$	0.452290	0.0373043
$148$	−15.2755	−1.25564
$149$	−11.5767	−0.948398	−0.474199	−	0.880418i	$-0.657262\pi$
$149$	−11.5767	−0.948398	−0.474199	+	0.880418i	$0.657262\pi$
$150$	1.17422	0.0958743
$151$	−0.712271	−0.0579638	−0.0289819	−	0.999580i	$-0.509227\pi$
$151$	−0.712271	−0.0579638	−0.0289819	+	0.999580i	$0.509227\pi$
$152$	−8.63737	−0.700584
$153$	2.79543	0.225997
$154$	7.44003	0.599535
$155$	−4.04844	−0.325179
$156$	11.9974	0.960561
$157$	−15.0058	−1.19760	−0.598798	−	0.800900i	$-0.704355\pi$
$157$	−15.0058	−1.19760	−0.598798	+	0.800900i	$0.704355\pi$
$158$	6.98338	0.555568
$159$	−2.89904	−0.229909
$160$	9.10654	0.719936
$161$	8.48004	0.668321
$162$	18.6943	1.46876
$163$	7.40271	0.579825	0.289913	−	0.957053i	$-0.406374\pi$
$163$	7.40271	0.579825	0.289913	+	0.957053i	$0.406374\pi$
$164$	35.7182	2.78912
$165$	−1.29617	−0.100907
$166$	11.3143	0.878157
$167$	8.85761	0.685422	0.342711	−	0.939441i	$-0.388655\pi$
$167$	8.85761	0.685422	0.342711	+	0.939441i	$0.388655\pi$
$168$	−3.21737	−0.248226
$169$	18.3169	1.40900
$170$	−2.59615	−0.199116
$171$	3.39427	0.259567
$172$	−60.4407	−4.60856
$173$	15.5978	1.18588	0.592941	−	0.805246i	$-0.297967\pi$
$173$	15.5978	1.18588	0.592941	+	0.805246i	$0.297967\pi$
$174$	10.7012	0.811258
$175$	−1.00000	−0.0755929
$176$	−25.7570	−1.94151
$177$	5.12779	0.385428
$178$	−8.59615	−0.644309
$179$	0.215435	0.0161023	0.00805117	−	0.999968i	$-0.497437\pi$
$179$	0.215435	0.0161023	0.00805117	+	0.999968i	$0.497437\pi$
$180$	−13.2504	−0.987627
$181$	−7.85567	−0.583907	−0.291954	−	0.956432i	$-0.594305\pi$
$181$	−7.85567	−0.583907	−0.291954	+	0.956432i	$0.594305\pi$
$182$	−14.5285	−1.07692
$183$	−6.72629	−0.497222
$184$	−60.3229	−4.44706
$185$	−3.22266	−0.236935
$186$	−4.75375	−0.348562
$187$	2.86579	0.209567
$188$	38.5770	2.81352
$189$	2.62122	0.190666
$190$	−3.15230	−0.228692
$191$	11.8121	0.854690	0.427345	−	0.904089i	$-0.359449\pi$
$191$	11.8121	0.854690	0.427345	+	0.904089i	$0.359449\pi$
$192$	2.56291	0.184962
$193$	14.3704	1.03441	0.517203	−	0.855863i	$-0.326973\pi$
$193$	14.3704	1.03441	0.517203	+	0.855863i	$0.326973\pi$
$194$	30.3789	2.18108
$195$	2.53109	0.181255
$196$	4.74002	0.338573
$197$	12.7581	0.908978	0.454489	−	0.890752i	$-0.349822\pi$
$197$	12.7581	0.908978	0.454489	+	0.890752i	$0.349822\pi$
$198$	20.7981	1.47806
$199$	−8.53109	−0.604753	−0.302376	−	0.953189i	$-0.597780\pi$
$199$	−8.53109	−0.604753	−0.302376	+	0.953189i	$0.597780\pi$
$200$	7.11351	0.503001
$201$	5.72482	0.403798
$202$	3.72218	0.261892
$203$	−9.11351	−0.639643
$204$	−2.14386	−0.150101
$205$	7.53545	0.526299
$206$	14.3196	0.997690
$207$	23.7054	1.64764
$208$	50.2968	3.48746
$209$	3.47970	0.240696
$210$	−1.17422	−0.0810286
$211$	−3.65732	−0.251781	−0.125890	−	0.992044i	$-0.540179\pi$
$211$	−3.65732	−0.251781	−0.125890	+	0.992044i	$0.540179\pi$
$212$	−30.3820	−2.08665
$213$	−2.15377	−0.147574
$214$	14.6974	1.00469
$215$	−12.7511	−0.869621
$216$	−18.6461	−1.26870
$217$	4.04844	0.274826
$218$	13.5089	0.914939
$219$	1.56896	0.106020
$220$	−13.5839	−0.915826
$221$	−5.59615	−0.376438
$222$	−3.78410	−0.253972
$223$	16.0234	1.07300	0.536502	−	0.843899i	$-0.319745\pi$
$223$	16.0234	1.07300	0.536502	+	0.843899i	$0.319745\pi$
$224$	−9.10654	−0.608457
$225$	−2.79543	−0.186362
$226$	−18.9270	−1.25901
$227$	−4.86558	−0.322940	−0.161470	−	0.986878i	$-0.551623\pi$
$227$	−4.86558	−0.322940	−0.161470	+	0.986878i	$0.551623\pi$
$228$	−2.60312	−0.172396
$229$	14.0018	0.925263	0.462631	−	0.886551i	$-0.346905\pi$
$229$	14.0018	0.925263	0.462631	+	0.886551i	$0.346905\pi$
$230$	−22.0155	−1.45166
$231$	1.29617	0.0852816
$232$	64.8291	4.25624
$233$	−2.49398	−0.163386	−0.0816929	−	0.996658i	$-0.526033\pi$
$233$	−2.49398	−0.163386	−0.0816929	+	0.996658i	$0.526033\pi$
$234$	−40.6134	−2.65498
$235$	8.13858	0.530902
$236$	53.7394	3.49814
$237$	1.21661	0.0790274
$238$	2.59615	0.168284
$239$	5.20075	0.336409	0.168204	−	0.985752i	$-0.446203\pi$
$239$	5.20075	0.336409	0.168204	+	0.985752i	$0.446203\pi$
$240$	4.06507	0.262399
$241$	3.84703	0.247809	0.123905	−	0.992294i	$-0.460458\pi$
$241$	3.84703	0.247809	0.123905	+	0.992294i	$0.460458\pi$
$242$	−7.23613	−0.465156
$243$	11.1205	0.713379
$244$	−70.4918	−4.51277
$245$	1.00000	0.0638877
$246$	8.84824	0.564143
$247$	−6.79497	−0.432353
$248$	−28.7987	−1.82872
$249$	1.97112	0.124915
$250$	2.59615	0.164195
$251$	21.3372	1.34679	0.673395	−	0.739283i	$-0.264835\pi$
$251$	21.3372	1.34679	0.673395	+	0.739283i	$0.264835\pi$
$252$	13.2504	0.834697
$253$	24.3020	1.52785
$254$	−5.78846	−0.363201
$255$	−0.452290	−0.0283235
$256$	−20.4246	−1.27654
$257$	2.61538	0.163143	0.0815715	−	0.996667i	$-0.474006\pi$
$257$	2.61538	0.163143	0.0815715	+	0.996667i	$0.474006\pi$
$258$	−14.9726	−0.932153
$259$	3.22266	0.200246
$260$	26.5259	1.64507
$261$	−25.4762	−1.57694
$262$	−37.6476	−2.32588
$263$	13.9618	0.860919	0.430459	−	0.902610i	$-0.358352\pi$
$263$	13.9618	0.860919	0.430459	+	0.902610i	$0.358352\pi$
$264$	−9.22031	−0.567471
$265$	−6.40968	−0.393744
$266$	3.15230	0.193280
$267$	−1.49758	−0.0916506
$268$	59.9963	3.66486
$269$	12.5795	0.766988	0.383494	−	0.923543i	$-0.374721\pi$
$269$	12.5795	0.766988	0.383494	+	0.923543i	$0.374721\pi$
$270$	−6.80509	−0.414144
$271$	11.3099	0.687027	0.343514	−	0.939148i	$-0.388383\pi$
$271$	11.3099	0.687027	0.343514	+	0.939148i	$0.388383\pi$
$272$	−8.98774	−0.544962
$273$	−2.53109	−0.153188
$274$	51.4240	3.10664
$275$	−2.86579	−0.172814
$276$	−18.1801	−1.09431
$277$	−26.7970	−1.61007	−0.805037	−	0.593224i	$-0.797855\pi$
$277$	−26.7970	−1.61007	−0.805037	+	0.593224i	$0.797855\pi$
$278$	−40.2618	−2.41474
$279$	11.3172	0.677541
$280$	−7.11351	−0.425114
$281$	−17.6986	−1.05581	−0.527906	−	0.849303i	$-0.677023\pi$
$281$	−17.6986	−1.05581	−0.527906	+	0.849303i	$0.677023\pi$
$282$	9.55644	0.569078
$283$	−21.2046	−1.26049	−0.630243	−	0.776398i	$-0.717045\pi$
$283$	−21.2046	−1.26049	−0.630243	+	0.776398i	$0.717045\pi$
$284$	−22.5716	−1.33938
$285$	−0.549180	−0.0325306
$286$	−41.6356	−2.46196
$287$	−7.53545	−0.444804
$288$	−25.4567	−1.50005
$289$	1.00000	0.0588235
$290$	23.6601	1.38937
$291$	5.29247	0.310250
$292$	16.4427	0.962237
$293$	2.82142	0.164829	0.0824145	−	0.996598i	$-0.473737\pi$
$293$	2.82142	0.164829	0.0824145	+	0.996598i	$0.473737\pi$
$294$	1.17422	0.0684816
$295$	11.3374	0.660088
$296$	−22.9244	−1.33246
$297$	7.51186	0.435882
$298$	−30.0548	−1.74103
$299$	−47.4556	−2.74443
$300$	2.14386	0.123776
$301$	12.7511	0.734964
$302$	−1.84917	−0.106408
$303$	0.648461	0.0372531
$304$	−10.9131	−0.625909
$305$	−14.8716	−0.851547
$306$	7.25738	0.414877
$307$	8.10646	0.462660	0.231330	−	0.972875i	$-0.425692\pi$
$307$	8.10646	0.462660	0.231330	+	0.972875i	$0.425692\pi$
$308$	13.5839	0.774014
$309$	2.49469	0.141918
$310$	−10.5104	−0.596950
$311$	−28.8370	−1.63520	−0.817598	−	0.575790i	$-0.804695\pi$
$311$	−28.8370	−1.63520	−0.817598	+	0.575790i	$0.804695\pi$
$312$	18.0049	1.01933
$313$	2.55736	0.144551	0.0722754	−	0.997385i	$-0.476974\pi$
$313$	2.55736	0.144551	0.0722754	+	0.997385i	$0.476974\pi$
$314$	−38.9575	−2.19850
$315$	2.79543	0.157505
$316$	12.7501	0.717251
$317$	13.4615	0.756072	0.378036	−	0.925791i	$-0.376600\pi$
$317$	13.4615	0.756072	0.378036	+	0.925791i	$0.376600\pi$
$318$	−7.52635	−0.422057
$319$	−26.1174	−1.46229
$320$	5.66651	0.316768
$321$	2.56052	0.142914
$322$	22.0155	1.22688
$323$	1.21422	0.0675610
$324$	34.1317	1.89620
$325$	5.59615	0.310419
$326$	19.2186	1.06442
$327$	2.35346	0.130147
$328$	53.6035	2.95976
$329$	−8.13858	−0.448694
$330$	−3.36505	−0.185240
$331$	−33.7428	−1.85467	−0.927336	−	0.374231i	$-0.877907\pi$
$331$	−33.7428	−1.85467	−0.927336	+	0.374231i	$0.877907\pi$
$332$	20.6574	1.13372
$333$	9.00873	0.493676
$334$	22.9957	1.25827
$335$	12.6574	0.691548
$336$	−4.06507	−0.221768
$337$	−2.83115	−0.154223	−0.0771114	−	0.997022i	$-0.524570\pi$
$337$	−2.83115	−0.154223	−0.0771114	+	0.997022i	$0.524570\pi$
$338$	47.5536	2.58658
$339$	−3.29738	−0.179089
$340$	−4.74002	−0.257064
$341$	11.6020	0.628283
$342$	8.81206	0.476501
$343$	−1.00000	−0.0539949
$344$	−90.7054	−4.89051
$345$	−3.83544	−0.206493
$346$	40.4944	2.17699
$347$	18.7953	1.00898	0.504492	−	0.863416i	$-0.331680\pi$
$347$	18.7953	1.00898	0.504492	+	0.863416i	$0.331680\pi$
$348$	19.5381	1.04735
$349$	20.5856	1.10192	0.550960	−	0.834531i	$-0.314262\pi$
$349$	20.5856	1.10192	0.550960	+	0.834531i	$0.314262\pi$
$350$	−2.59615	−0.138770
$351$	−14.6687	−0.782960
$352$	−26.0974	−1.39100
$353$	−10.4218	−0.554695	−0.277347	−	0.960770i	$-0.589455\pi$
$353$	−10.4218	−0.554695	−0.277347	+	0.960770i	$0.589455\pi$
$354$	13.3125	0.707553
$355$	−4.76193	−0.252737
$356$	−15.6947	−0.831819
$357$	0.452290	0.0239377
$358$	0.559302	0.0295600
$359$	−20.7363	−1.09442	−0.547210	−	0.836996i	$-0.684310\pi$
$359$	−20.7363	−1.09442	−0.547210	+	0.836996i	$0.684310\pi$
$360$	−19.8854	−1.04805
$361$	−17.5257	−0.922404
$362$	−20.3945	−1.07191
$363$	−1.26065	−0.0661668
$364$	−26.5259	−1.39033
$365$	3.46891	0.181571
$366$	−17.4625	−0.912779
$367$	15.1547	0.791071	0.395535	−	0.918451i	$-0.370559\pi$
$367$	15.1547	0.791071	0.395535	+	0.918451i	$0.370559\pi$
$368$	−76.2164	−3.97305
$369$	−21.0649	−1.09659
$370$	−8.36652	−0.434955
$371$	6.40968	0.332774
$372$	−8.67932	−0.450002
$373$	13.7652	0.712733	0.356367	−	0.934346i	$-0.384015\pi$
$373$	13.7652	0.712733	0.356367	+	0.934346i	$0.384015\pi$
$374$	7.44003	0.384715
$375$	0.452290	0.0233562
$376$	57.8939	2.98565
$377$	51.0006	2.62667
$378$	6.80509	0.350016
$379$	−4.27518	−0.219601	−0.109801	−	0.993954i	$-0.535021\pi$
$379$	−4.27518	−0.219601	−0.109801	+	0.993954i	$0.535021\pi$
$380$	−5.75543	−0.295247
$381$	−1.00844	−0.0516639
$382$	30.6659	1.56901
$383$	−25.4774	−1.30184	−0.650918	−	0.759148i	$-0.725616\pi$
$383$	−25.4774	−1.30184	−0.650918	+	0.759148i	$0.725616\pi$
$384$	−1.58390	−0.0808279
$385$	2.86579	0.146054
$386$	37.3078	1.89892
$387$	35.6450	1.81194
$388$	55.4653	2.81582
$389$	15.7776	0.799958	0.399979	−	0.916524i	$-0.369017\pi$
$389$	15.7776	0.799958	0.399979	+	0.916524i	$0.369017\pi$
$390$	6.57109	0.332740
$391$	8.48004	0.428854
$392$	7.11351	0.359287
$393$	−6.55879	−0.330847
$394$	33.1220	1.66866
$395$	2.68989	0.135343
$396$	37.9729	1.90821
$397$	25.9120	1.30048	0.650242	−	0.759727i	$-0.274667\pi$
$397$	25.9120	1.30048	0.650242	+	0.759727i	$0.274667\pi$
$398$	−22.1480	−1.11018
$399$	0.549180	0.0274934
$400$	8.98774	0.449387
$401$	−5.66169	−0.282731	−0.141366	−	0.989957i	$-0.545149\pi$
$401$	−5.66169	−0.282731	−0.141366	+	0.989957i	$0.545149\pi$
$402$	14.8625	0.741275
$403$	−22.6557	−1.12856
$404$	6.79590	0.338109
$405$	7.20075	0.357808
$406$	−23.6601	−1.17423
$407$	9.23547	0.457785
$408$	−3.21737	−0.159284
$409$	−29.0408	−1.43598	−0.717988	−	0.696056i	$-0.754937\pi$
$409$	−29.0408	−1.43598	−0.717988	+	0.696056i	$0.754937\pi$
$410$	19.5632	0.966158
$411$	8.95886	0.441908
$412$	26.1444	1.28804
$413$	−11.3374	−0.557876
$414$	61.5428	3.02467
$415$	4.35808	0.213930
$416$	50.9616	2.49860
$417$	−7.01423	−0.343488
$418$	9.03384	0.441860
$419$	18.9910	0.927770	0.463885	−	0.885895i	$-0.346455\pi$
$419$	18.9910	0.927770	0.463885	+	0.885895i	$0.346455\pi$
$420$	−2.14386	−0.104610
$421$	−9.05643	−0.441383	−0.220692	−	0.975344i	$-0.570831\pi$
$421$	−9.05643	−0.441383	−0.220692	+	0.975344i	$0.570831\pi$
$422$	−9.49498	−0.462208
$423$	−22.7509	−1.10618
$424$	−45.5954	−2.21431
$425$	−1.00000	−0.0485071
$426$	−5.59153	−0.270911
$427$	14.8716	0.719688
$428$	26.8343	1.29709
$429$	−7.25356	−0.350205
$430$	−33.1039	−1.59641
$431$	12.8182	0.617429	0.308714	−	0.951155i	$-0.400101\pi$
$431$	12.8182	0.617429	0.308714	+	0.951155i	$0.400101\pi$
$432$	−23.5588	−1.13347
$433$	−34.1671	−1.64197	−0.820984	−	0.570952i	$-0.806574\pi$
$433$	−34.1671	−1.64197	−0.820984	+	0.570952i	$0.806574\pi$
$434$	10.5104	0.504515
$435$	4.12195	0.197633
$436$	24.6644	1.18121
$437$	10.2966	0.492555
$438$	4.07325	0.194628
$439$	−24.1152	−1.15096	−0.575478	−	0.817817i	$-0.695184\pi$
$439$	−24.1152	−1.15096	−0.575478	+	0.817817i	$0.695184\pi$
$440$	−20.3858	−0.971856
$441$	−2.79543	−0.133116
$442$	−14.5285	−0.691049
$443$	−32.5868	−1.54825	−0.774123	−	0.633036i	$-0.781809\pi$
$443$	−32.5868	−1.54825	−0.774123	+	0.633036i	$0.781809\pi$
$444$	−6.90895	−0.327884
$445$	−3.31111	−0.156962
$446$	41.5992	1.96978
$447$	−5.23602	−0.247655
$448$	−5.66651	−0.267717
$449$	3.22153	0.152033	0.0760166	−	0.997107i	$-0.475780\pi$
$449$	3.22153	0.152033	0.0760166	+	0.997107i	$0.475780\pi$
$450$	−7.25738	−0.342116
$451$	−21.5950	−1.01687
$452$	−34.5567	−1.62541
$453$	−0.322153	−0.0151361
$454$	−12.6318	−0.592839
$455$	−5.59615	−0.262352
$456$	−3.90660	−0.182943
$457$	−11.9868	−0.560720	−0.280360	−	0.959895i	$-0.590454\pi$
$457$	−11.9868	−0.560720	−0.280360	+	0.959895i	$0.590454\pi$
$458$	36.3507	1.69856
$459$	2.62122	0.122348
$460$	−40.1955	−1.87413
$461$	−13.9659	−0.650457	−0.325229	−	0.945635i	$-0.605441\pi$
$461$	−13.9659	−0.650457	−0.325229	+	0.945635i	$0.605441\pi$
$462$	3.36505	0.156557
$463$	−18.8041	−0.873900	−0.436950	−	0.899486i	$-0.643941\pi$
$463$	−18.8041	−0.873900	−0.436950	+	0.899486i	$0.643941\pi$
$464$	81.9099	3.80257
$465$	−1.83107	−0.0849139
$466$	−6.47475	−0.299937
$467$	−5.91415	−0.273674	−0.136837	−	0.990594i	$-0.543694\pi$
$467$	−5.91415	−0.273674	−0.136837	+	0.990594i	$0.543694\pi$
$468$	−74.1513	−3.42765
$469$	−12.6574	−0.584465
$470$	21.1290	0.974608
$471$	−6.78699	−0.312728
$472$	80.6487	3.71216
$473$	36.5421	1.68021
$474$	3.15851	0.145075
$475$	−1.21422	−0.0557123
$476$	4.74002	0.217258
$477$	17.9178	0.820402
$478$	13.5019	0.617565
$479$	10.9586	0.500711	0.250356	−	0.968154i	$-0.419452\pi$
$479$	10.9586	0.500711	0.250356	+	0.968154i	$0.419452\pi$
$480$	4.11880	0.187997
$481$	−18.0345	−0.822303
$482$	9.98749	0.454918
$483$	3.83544	0.174518
$484$	−13.2116	−0.600528
$485$	11.7015	0.531337
$486$	28.8705	1.30959
$487$	−22.6589	−1.02677	−0.513386	−	0.858158i	$-0.671609\pi$
$487$	−22.6589	−1.02677	−0.513386	+	0.858158i	$0.671609\pi$
$488$	−105.790	−4.78887
$489$	3.34817	0.151410
$490$	2.59615	0.117282
$491$	4.50992	0.203530	0.101765	−	0.994808i	$-0.467551\pi$
$491$	4.50992	0.203530	0.101765	+	0.994808i	$0.467551\pi$
$492$	16.1550	0.728323
$493$	−9.11351	−0.410452
$494$	−17.6408	−0.793696
$495$	8.01112	0.360073
$496$	−36.3864	−1.63380
$497$	4.76193	0.213602
$498$	5.11733	0.229313
$499$	11.2510	0.503662	0.251831	−	0.967771i	$-0.418967\pi$
$499$	11.2510	0.503662	0.251831	+	0.967771i	$0.418967\pi$
$500$	4.74002	0.211980
$501$	4.00621	0.178984
$502$	55.3946	2.47238
$503$	15.4671	0.689644	0.344822	−	0.938668i	$-0.387939\pi$
$503$	15.4671	0.689644	0.344822	+	0.938668i	$0.387939\pi$
$504$	19.8854	0.885764
$505$	1.43373	0.0638001
$506$	63.0918	2.80477
$507$	8.28458	0.367931
$508$	−10.5685	−0.468901
$509$	−4.81621	−0.213475	−0.106737	−	0.994287i	$-0.534040\pi$
$509$	−4.81621	−0.213475	−0.106737	+	0.994287i	$0.534040\pi$
$510$	−1.17422	−0.0519951
$511$	−3.46891	−0.153456
$512$	−46.0216	−2.03389
$513$	3.18274	0.140521
$514$	6.78993	0.299491
$515$	5.51568	0.243050
$516$	−27.3367	−1.20343
$517$	−23.3234	−1.02576
$518$	8.36652	0.367604
$519$	7.05475	0.309669
$520$	39.8083	1.74571
$521$	18.5828	0.814126	0.407063	−	0.913400i	$-0.366553\pi$
$521$	18.5828	0.814126	0.407063	+	0.913400i	$0.366553\pi$
$522$	−66.1402	−2.89488
$523$	21.8117	0.953758	0.476879	−	0.878969i	$-0.341768\pi$
$523$	21.8117	0.953758	0.476879	+	0.878969i	$0.341768\pi$
$524$	−68.7364	−3.00276
$525$	−0.452290	−0.0197396
$526$	36.2469	1.58044
$527$	4.04844	0.176353
$528$	−11.6496	−0.506985
$529$	48.9110	2.12657
$530$	−16.6405	−0.722818
$531$	−31.6929	−1.37536
$532$	5.75543	0.249529
$533$	42.1696	1.82657
$534$	−3.88796	−0.168248
$535$	5.66122	0.244756
$536$	90.0386	3.88908
$537$	0.0974390	0.00420480
$538$	32.6584	1.40800
$539$	−2.86579	−0.123438
$540$	−12.4246	−0.534671
$541$	−21.2276	−0.912644	−0.456322	−	0.889815i	$-0.650834\pi$
$541$	−21.2276	−0.912644	−0.456322	+	0.889815i	$0.650834\pi$
$542$	29.3622	1.26122
$543$	−3.55304	−0.152476
$544$	−9.10654	−0.390440
$545$	5.20343	0.222891
$546$	−6.57109	−0.281217
$547$	−42.2300	−1.80563	−0.902813	−	0.430033i	$-0.858502\pi$
$547$	−42.2300	−1.80563	−0.902813	+	0.430033i	$0.858502\pi$
$548$	93.8892	4.01075
$549$	41.5726	1.77428
$550$	−7.44003	−0.317244
$551$	−11.0658	−0.471420
$552$	−27.2834	−1.16126
$553$	−2.68989	−0.114386
$554$	−69.5691	−2.95571
$555$	−1.45758	−0.0618707
$556$	−73.5094	−3.11749
$557$	−15.5181	−0.657523	−0.328762	−	0.944413i	$-0.606631\pi$
$557$	−15.5181	−0.657523	−0.328762	+	0.944413i	$0.606631\pi$
$558$	29.3811	1.24380
$559$	−71.3574	−3.01810
$560$	−8.98774	−0.379801
$561$	1.29617	0.0547243
$562$	−45.9484	−1.93821
$563$	3.55636	0.149883	0.0749414	−	0.997188i	$-0.476123\pi$
$563$	3.55636	0.149883	0.0749414	+	0.997188i	$0.476123\pi$
$564$	17.4480	0.734694
$565$	−7.29041	−0.306710
$566$	−55.0505	−2.31395
$567$	−7.20075	−0.302403
$568$	−33.8741	−1.42132
$569$	−34.4148	−1.44274	−0.721372	−	0.692548i	$-0.756488\pi$
$569$	−34.4148	−1.44274	−0.721372	+	0.692548i	$0.756488\pi$
$570$	−1.42576	−0.0597184
$571$	−1.83262	−0.0766929	−0.0383465	−	0.999265i	$-0.512209\pi$
$571$	−1.83262	−0.0766929	−0.0383465	+	0.999265i	$0.512209\pi$
$572$	−76.0176	−3.17846
$573$	5.34248	0.223185
$574$	−19.5632	−0.816552
$575$	−8.48004	−0.353642
$576$	−15.8404	−0.660015
$577$	−23.4428	−0.975936	−0.487968	−	0.872861i	$-0.662262\pi$
$577$	−23.4428	−0.975936	−0.487968	+	0.872861i	$0.662262\pi$
$578$	2.59615	0.107986
$579$	6.49960	0.270114
$580$	43.1982	1.79371
$581$	−4.35808	−0.180804
$582$	13.7401	0.569544
$583$	18.3688	0.760758
$584$	24.6762	1.02111
$585$	−15.6437	−0.646787
$586$	7.32484	0.302586
$587$	−22.1098	−0.912568	−0.456284	−	0.889834i	$-0.650820\pi$
$587$	−22.1098	−0.912568	−0.456284	+	0.889834i	$0.650820\pi$
$588$	2.14386	0.0884115
$589$	4.91570	0.202548
$590$	29.4336	1.21176
$591$	5.77037	0.237361
$592$	−28.9644	−1.19043
$593$	15.8819	0.652193	0.326097	−	0.945336i	$-0.394267\pi$
$593$	15.8819	0.652193	0.326097	+	0.945336i	$0.394267\pi$
$594$	19.5019	0.800175
$595$	1.00000	0.0409960
$596$	−54.8736	−2.24771
$597$	−3.85853	−0.157919
$598$	−123.202	−5.03811
$599$	−21.3918	−0.874047	−0.437024	−	0.899450i	$-0.643967\pi$
$599$	−21.3918	−0.874047	−0.437024	+	0.899450i	$0.643967\pi$
$600$	3.21737	0.131349
$601$	−37.0490	−1.51126	−0.755630	−	0.654999i	$-0.772669\pi$
$601$	−37.0490	−1.51126	−0.755630	+	0.654999i	$0.772669\pi$
$602$	33.1039	1.34922
$603$	−35.3829	−1.44090
$604$	−3.37618	−0.137375
$605$	−2.78725	−0.113318
$606$	1.68351	0.0683878
$607$	−2.60573	−0.105763	−0.0528816	−	0.998601i	$-0.516841\pi$
$607$	−2.60573	−0.105763	−0.0528816	+	0.998601i	$0.516841\pi$
$608$	−11.0574	−0.448435
$609$	−4.12195	−0.167030
$610$	−38.6090	−1.56323
$611$	45.5447	1.84254
$612$	13.2504	0.535616
$613$	−40.9542	−1.65412	−0.827062	−	0.562110i	$-0.809990\pi$
$613$	−40.9542	−1.65412	−0.827062	+	0.562110i	$0.809990\pi$
$614$	21.0456	0.849333
$615$	3.40821	0.137432
$616$	20.3858	0.821369
$617$	9.24097	0.372027	0.186014	−	0.982547i	$-0.440443\pi$
$617$	9.24097	0.372027	0.186014	+	0.982547i	$0.440443\pi$
$618$	6.47659	0.260527
$619$	32.5908	1.30993	0.654967	−	0.755658i	$-0.272683\pi$
$619$	32.5908	1.30993	0.654967	+	0.755658i	$0.272683\pi$
$620$	−19.1897	−0.770677
$621$	22.2280	0.891980
$622$	−74.8653	−3.00182
$623$	3.31111	0.132657
$624$	22.7488	0.910679
$625$	1.00000	0.0400000
$626$	6.63931	0.265360
$627$	1.57383	0.0628529
$628$	−71.1280	−2.83831
$629$	3.22266	0.128496
$630$	7.25738	0.289141
$631$	11.4959	0.457645	0.228823	−	0.973468i	$-0.426512\pi$
$631$	11.4959	0.457645	0.228823	+	0.973468i	$0.426512\pi$
$632$	19.1346	0.761133
$633$	−1.65417	−0.0657474
$634$	34.9481	1.38797
$635$	−2.22963	−0.0884802
$636$	−13.7415	−0.544886
$637$	5.59615	0.221728
$638$	−67.8048	−2.68442
$639$	13.3117	0.526601
$640$	−3.50195	−0.138427
$641$	13.1161	0.518055	0.259028	−	0.965870i	$-0.416598\pi$
$641$	13.1161	0.518055	0.259028	+	0.965870i	$0.416598\pi$
$642$	6.64750	0.262356
$643$	−33.4191	−1.31792	−0.658961	−	0.752177i	$-0.729004\pi$
$643$	−33.4191	−1.31792	−0.658961	+	0.752177i	$0.729004\pi$
$644$	40.1955	1.58393
$645$	−5.76722	−0.227084
$646$	3.15230	0.124026
$647$	−28.0465	−1.10262	−0.551310	−	0.834300i	$-0.685872\pi$
$647$	−28.0465	−1.10262	−0.551310	+	0.834300i	$0.685872\pi$
$648$	51.2226	2.01221
$649$	−32.4906	−1.27537
$650$	14.5285	0.569854
$651$	1.83107	0.0717654
$652$	35.0890	1.37419
$653$	15.4213	0.603481	0.301740	−	0.953390i	$-0.402432\pi$
$653$	15.4213	0.603481	0.301740	+	0.953390i	$0.402432\pi$
$654$	6.10995	0.238918
$655$	−14.5013	−0.566612
$656$	67.7267	2.64428
$657$	−9.69712	−0.378321
$658$	−21.1290	−0.823694
$659$	6.27300	0.244361	0.122181	−	0.992508i	$-0.461011\pi$
$659$	6.27300	0.244361	0.122181	+	0.992508i	$0.461011\pi$
$660$	−6.14386	−0.239150
$661$	−37.0627	−1.44157	−0.720786	−	0.693157i	$-0.756219\pi$
$661$	−37.0627	−1.44157	−0.720786	+	0.693157i	$0.756219\pi$
$662$	−87.6015	−3.40473
$663$	−2.53109	−0.0982992
$664$	31.0013	1.20308
$665$	1.21422	0.0470855
$666$	23.3881	0.906269
$667$	−77.2829	−2.99241
$668$	41.9852	1.62446
$669$	7.24722	0.280194
$670$	32.8606	1.26952
$671$	42.6190	1.64529
$672$	−4.11880	−0.158886
$673$	19.0649	0.734898	0.367449	−	0.930044i	$-0.380231\pi$
$673$	19.0649	0.734898	0.367449	+	0.930044i	$0.380231\pi$
$674$	−7.35011	−0.283116
$675$	−2.62122	−0.100891
$676$	86.8227	3.33933
$677$	30.8522	1.18575	0.592873	−	0.805296i	$-0.297994\pi$
$677$	30.8522	1.18575	0.592873	+	0.805296i	$0.297994\pi$
$678$	−8.56052	−0.328765
$679$	−11.7015	−0.449062
$680$	−7.11351	−0.272791
$681$	−2.20065	−0.0843292
$682$	30.1206	1.15338
$683$	−44.3013	−1.69514	−0.847572	−	0.530681i	$-0.821936\pi$
$683$	−44.3013	−1.69514	−0.847572	+	0.530681i	$0.821936\pi$
$684$	16.0889	0.615175
$685$	19.8078	0.756816
$686$	−2.59615	−0.0991216
$687$	6.33286	0.241614
$688$	−114.604	−4.36924
$689$	−35.8696	−1.36652
$690$	−9.95739	−0.379071
$691$	−8.94782	−0.340391	−0.170196	−	0.985410i	$-0.554440\pi$
$691$	−8.94782	−0.340391	−0.170196	+	0.985410i	$0.554440\pi$
$692$	73.9340	2.81055
$693$	−8.01112	−0.304317
$694$	48.7955	1.85225
$695$	−15.5083	−0.588262
$696$	29.3216	1.11143
$697$	−7.53545	−0.285426
$698$	53.4433	2.02286
$699$	−1.12800	−0.0426649
$700$	−4.74002	−0.179156
$701$	−21.5436	−0.813692	−0.406846	−	0.913497i	$-0.633371\pi$
$701$	−21.5436	−0.813692	−0.406846	+	0.913497i	$0.633371\pi$
$702$	−38.0823	−1.43732
$703$	3.91302	0.147582
$704$	−16.2390	−0.612031
$705$	3.68100	0.138634
$706$	−27.0565	−1.01829
$707$	−1.43373	−0.0539209
$708$	24.3058	0.913469
$709$	16.7160	0.627782	0.313891	−	0.949459i	$-0.398367\pi$
$709$	16.7160	0.627782	0.313891	+	0.949459i	$0.398367\pi$
$710$	−12.3627	−0.463964
$711$	−7.51942	−0.282000
$712$	−23.5536	−0.882710
$713$	34.3310	1.28570
$714$	1.17422	0.0439439
$715$	−16.0374	−0.599765
$716$	1.02116	0.0381627
$717$	2.35225	0.0878463
$718$	−53.8346	−2.00909
$719$	−13.8420	−0.516219	−0.258110	−	0.966116i	$-0.583100\pi$
$719$	−13.8420	−0.516219	−0.258110	+	0.966116i	$0.583100\pi$
$720$	−25.1246	−0.936340
$721$	−5.51568	−0.205415
$722$	−45.4993	−1.69331
$723$	1.73997	0.0647103
$724$	−37.2360	−1.38387
$725$	9.11351	0.338467
$726$	−3.27283	−0.121466
$727$	32.8280	1.21752	0.608762	−	0.793353i	$-0.291666\pi$
$727$	32.8280	1.21752	0.608762	+	0.793353i	$0.291666\pi$
$728$	−39.8083	−1.47539
$729$	−16.5726	−0.613799
$730$	9.00584	0.333321
$731$	12.7511	0.471618
$732$	−31.8828	−1.17842
$733$	−38.5618	−1.42431	−0.712157	−	0.702021i	$-0.752281\pi$
$733$	−38.5618	−1.42431	−0.712157	+	0.702021i	$0.752281\pi$
$734$	39.3440	1.45221
$735$	0.452290	0.0166830
$736$	−77.2238	−2.84651
$737$	−36.2735	−1.33615
$738$	−54.6876	−2.01308
$739$	−1.21373	−0.0446478	−0.0223239	−	0.999751i	$-0.507107\pi$
$739$	−1.21373	−0.0446478	−0.0223239	+	0.999751i	$0.507107\pi$
$740$	−15.2755	−0.561538
$741$	−3.07330	−0.112900
$742$	16.6405	0.610893
$743$	39.2459	1.43979	0.719897	−	0.694081i	$-0.244189\pi$
$743$	39.2459	1.43979	0.719897	+	0.694081i	$0.244189\pi$
$744$	−13.0254	−0.477533
$745$	−11.5767	−0.424136
$746$	35.7365	1.30841
$747$	−12.1827	−0.445743
$748$	13.5839	0.496676
$749$	−5.66122	−0.206857
$750$	1.17422	0.0428763
$751$	13.1726	0.480676	0.240338	−	0.970689i	$-0.422742\pi$
$751$	13.1726	0.480676	0.240338	+	0.970689i	$0.422742\pi$
$752$	73.1474	2.66741
$753$	9.65060	0.351687
$754$	132.406	4.82192
$755$	−0.712271	−0.0259222
$756$	12.4246	0.451879
$757$	16.9841	0.617298	0.308649	−	0.951176i	$-0.400123\pi$
$757$	16.9841	0.617298	0.308649	+	0.951176i	$0.400123\pi$
$758$	−11.0990	−0.403135
$759$	10.9916	0.398968
$760$	−8.63737	−0.313310
$761$	−42.8792	−1.55437	−0.777185	−	0.629273i	$-0.783353\pi$
$761$	−42.8792	−1.55437	−0.777185	+	0.629273i	$0.783353\pi$
$762$	−2.61807	−0.0948425
$763$	−5.20343	−0.188377
$764$	55.9894	2.02562
$765$	2.79543	0.101069
$766$	−66.1434	−2.38986
$767$	63.4458	2.29089
$768$	−9.23786	−0.333342
$769$	5.93648	0.214075	0.107038	−	0.994255i	$-0.465863\pi$
$769$	5.93648	0.214075	0.107038	+	0.994255i	$0.465863\pi$
$770$	7.44003	0.268120
$771$	1.18291	0.0426015
$772$	68.1161	2.45155
$773$	50.6181	1.82061	0.910304	−	0.413940i	$-0.135848\pi$
$773$	50.6181	1.82061	0.910304	+	0.413940i	$0.135848\pi$
$774$	92.5399	3.32628
$775$	−4.04844	−0.145424
$776$	83.2387	2.98809
$777$	1.45758	0.0522903
$778$	40.9612	1.46853
$779$	−9.14970	−0.327822
$780$	11.9974	0.429576
$781$	13.6467	0.488317
$782$	22.0155	0.787272
$783$	−23.8885	−0.853706
$784$	8.98774	0.320991
$785$	−15.0058	−0.535581
$786$	−17.0276	−0.607356
$787$	22.9203	0.817020	0.408510	−	0.912754i	$-0.366049\pi$
$787$	22.9203	0.817020	0.408510	+	0.912754i	$0.366049\pi$
$788$	60.4737	2.15429
$789$	6.31477	0.224812
$790$	6.98338	0.248457
$791$	7.29041	0.259217
$792$	56.9872	2.02495
$793$	−83.2239	−2.95537
$794$	67.2715	2.38738
$795$	−2.89904	−0.102818
$796$	−40.4375	−1.43327
$797$	27.4169	0.971155	0.485578	−	0.874194i	$-0.338609\pi$
$797$	27.4169	0.971155	0.485578	+	0.874194i	$0.338609\pi$
$798$	1.42576	0.0504712
$799$	−8.13858	−0.287922
$800$	9.10654	0.321965
$801$	9.25599	0.327044
$802$	−14.6986	−0.519026
$803$	−9.94118	−0.350817
$804$	27.1358	0.957005
$805$	8.48004	0.298882
$806$	−58.8178	−2.07177
$807$	5.68960	0.200283
$808$	10.1988	0.358794
$809$	14.3764	0.505449	0.252724	−	0.967538i	$-0.418673\pi$
$809$	14.3764	0.505449	0.252724	+	0.967538i	$0.418673\pi$
$810$	18.6943	0.656849
$811$	5.55958	0.195223	0.0976116	−	0.995225i	$-0.468880\pi$
$811$	5.55958	0.195223	0.0976116	+	0.995225i	$0.468880\pi$
$812$	−43.1982	−1.51596
$813$	5.11536	0.179403
$814$	23.9767	0.840383
$815$	7.40271	0.259306
$816$	−4.06507	−0.142306
$817$	15.4827	0.541671
$818$	−75.3944	−2.63610
$819$	15.6437	0.546634
$820$	35.7182	1.24733
$821$	−42.2108	−1.47317	−0.736584	−	0.676346i	$-0.763562\pi$
$821$	−42.2108	−1.47317	−0.736584	+	0.676346i	$0.763562\pi$
$822$	23.2586	0.811237
$823$	50.4347	1.75804	0.879022	−	0.476782i	$-0.158197\pi$
$823$	50.4347	1.75804	0.879022	+	0.476782i	$0.158197\pi$
$824$	39.2358	1.36685
$825$	−1.29617	−0.0451268
$826$	−29.4336	−1.02413
$827$	−40.7726	−1.41780	−0.708902	−	0.705307i	$-0.750809\pi$
$827$	−40.7726	−1.41780	−0.708902	+	0.705307i	$0.750809\pi$
$828$	112.364	3.90492
$829$	−55.6516	−1.93286	−0.966429	−	0.256933i	$-0.917288\pi$
$829$	−55.6516	−1.93286	−0.966429	+	0.256933i	$0.917288\pi$
$830$	11.3143	0.392724
$831$	−12.1200	−0.420439
$832$	31.7107	1.09937
$833$	−1.00000	−0.0346479
$834$	−18.2100	−0.630562
$835$	8.85761	0.306530
$836$	16.4938	0.570452
$837$	10.6119	0.366799
$838$	49.3035	1.70316
$839$	38.7562	1.33801	0.669007	−	0.743256i	$-0.266720\pi$
$839$	38.7562	1.33801	0.669007	+	0.743256i	$0.266720\pi$
$840$	−3.21737	−0.111010
$841$	54.0561	1.86400
$842$	−23.5119	−0.810273
$843$	−8.00492	−0.275704
$844$	−17.3358	−0.596722
$845$	18.3169	0.630122
$846$	−59.0647	−2.03069
$847$	2.78725	0.0957710
$848$	−57.6086	−1.97829
$849$	−9.59066	−0.329150
$850$	−2.59615	−0.0890474
$851$	27.3283	0.936801
$852$	−10.2089	−0.349752
$853$	30.2359	1.03526	0.517629	−	0.855605i	$-0.326815\pi$
$853$	30.2359	1.03526	0.517629	+	0.855605i	$0.326815\pi$
$854$	38.6090	1.32117
$855$	3.39427	0.116082
$856$	40.2712	1.37644
$857$	−17.1033	−0.584237	−0.292118	−	0.956382i	$-0.594360\pi$
$857$	−17.1033	−0.584237	−0.292118	+	0.956382i	$0.594360\pi$
$858$	−18.8314	−0.642892
$859$	12.8854	0.439645	0.219823	−	0.975540i	$-0.429452\pi$
$859$	12.8854	0.439645	0.219823	+	0.975540i	$0.429452\pi$
$860$	−60.4407	−2.06101
$861$	−3.40821	−0.116152
$862$	33.2779	1.13345
$863$	7.98942	0.271963	0.135982	−	0.990711i	$-0.456581\pi$
$863$	7.98942	0.271963	0.135982	+	0.990711i	$0.456581\pi$
$864$	−23.8702	−0.812082
$865$	15.5978	0.530342
$866$	−88.7032	−3.01426
$867$	0.452290	0.0153606
$868$	19.1897	0.651341
$869$	−7.70867	−0.261499
$870$	10.7012	0.362806
$871$	70.8328	2.40008
$872$	37.0147	1.25348
$873$	−32.7107	−1.10709
$874$	26.7317	0.904212
$875$	−1.00000	−0.0338062
$876$	7.43688	0.251269
$877$	33.7493	1.13963	0.569816	−	0.821772i	$-0.307014\pi$
$877$	33.7493	1.13963	0.569816	+	0.821772i	$0.307014\pi$
$878$	−62.6068	−2.11288
$879$	1.27610	0.0430418
$880$	−25.7570	−0.868268
$881$	51.3850	1.73121	0.865603	−	0.500731i	$-0.166935\pi$
$881$	51.3850	1.73121	0.865603	+	0.500731i	$0.166935\pi$
$882$	−7.25738	−0.244369
$883$	18.5775	0.625181	0.312591	−	0.949888i	$-0.398803\pi$
$883$	18.5775	0.625181	0.312591	+	0.949888i	$0.398803\pi$
$884$	−26.5259	−0.892162
$885$	5.12779	0.172369
$886$	−84.6004	−2.84220
$887$	5.88342	0.197546	0.0987729	−	0.995110i	$-0.468508\pi$
$887$	5.88342	0.197546	0.0987729	+	0.995110i	$0.468508\pi$
$888$	−10.3685	−0.347944
$889$	2.22963	0.0747794
$890$	−8.59615	−0.288144
$891$	−20.6358	−0.691326
$892$	75.9511	2.54303
$893$	−9.88203	−0.330689
$894$	−13.5935	−0.454635
$895$	0.215435	0.00720119
$896$	3.50195	0.116992
$897$	−21.4637	−0.716652
$898$	8.36358	0.279096
$899$	−36.8956	−1.23054
$900$	−13.2504	−0.441680
$901$	6.40968	0.213537
$902$	−56.0640	−1.86673
$903$	5.76722	0.191921
$904$	−51.8605	−1.72485
$905$	−7.85567	−0.261131
$906$	−0.836360	−0.0277862
$907$	−13.1073	−0.435220	−0.217610	−	0.976036i	$-0.569826\pi$
$907$	−13.1073	−0.435220	−0.217610	+	0.976036i	$0.569826\pi$
$908$	−23.0629	−0.765370
$909$	−4.00789	−0.132933
$910$	−14.5285	−0.481615
$911$	−28.4645	−0.943071	−0.471536	−	0.881847i	$-0.656300\pi$
$911$	−28.4645	−0.943071	−0.471536	+	0.881847i	$0.656300\pi$
$912$	−4.93589	−0.163444
$913$	−12.4894	−0.413337
$914$	−31.1196	−1.02935
$915$	−6.72629	−0.222364
$916$	66.3686	2.19288
$917$	14.5013	0.478875
$918$	6.80509	0.224601
$919$	−7.63166	−0.251745	−0.125873	−	0.992046i	$-0.540173\pi$
$919$	−7.63166	−0.251745	−0.125873	+	0.992046i	$0.540173\pi$
$920$	−60.3229	−1.98879
$921$	3.66647	0.120814
$922$	−36.2577	−1.19408
$923$	−26.6485	−0.877146
$924$	6.14386	0.202118
$925$	−3.22266	−0.105960
$926$	−48.8183	−1.60427
$927$	−15.4187	−0.506417
$928$	82.9926	2.72437
$929$	−13.9684	−0.458289	−0.229145	−	0.973392i	$-0.573593\pi$
$929$	−13.9684	−0.458289	−0.229145	+	0.973392i	$0.573593\pi$
$930$	−4.75375	−0.155881
$931$	−1.21422	−0.0397945
$932$	−11.8215	−0.387226
$933$	−13.0427	−0.426998
$934$	−15.3541	−0.502400
$935$	2.86579	0.0937213
$936$	−111.282	−3.63735
$937$	37.8268	1.23575	0.617874	−	0.786277i	$-0.287994\pi$
$937$	37.8268	1.23575	0.617874	+	0.786277i	$0.287994\pi$
$938$	−32.8606	−1.07294
$939$	1.15667	0.0377465
$940$	38.5770	1.25824
$941$	21.7798	0.710003	0.355001	−	0.934866i	$-0.384480\pi$
$941$	21.7798	0.710003	0.355001	+	0.934866i	$0.384480\pi$
$942$	−17.6201	−0.574093
$943$	−63.9009	−2.08090
$944$	101.898	3.31648
$945$	2.62122	0.0852682
$946$	94.8689	3.08445
$947$	−16.2268	−0.527299	−0.263650	−	0.964619i	$-0.584926\pi$
$947$	−16.2268	−0.527299	−0.263650	+	0.964619i	$0.584926\pi$
$948$	5.76676	0.187296
$949$	19.4126	0.630159
$950$	−3.15230	−0.102274
$951$	6.08849	0.197433
$952$	7.11351	0.230550
$953$	46.2440	1.49799	0.748995	−	0.662576i	$-0.230537\pi$
$953$	46.2440	1.49799	0.748995	+	0.662576i	$0.230537\pi$
$954$	46.5175	1.50606
$955$	11.8121	0.382229
$956$	24.6517	0.797291
$957$	−11.8127	−0.381849
$958$	28.4502	0.919185
$959$	−19.8078	−0.639626
$960$	2.56291	0.0827175
$961$	−14.6101	−0.471293
$962$	−46.8204	−1.50955
$963$	−15.8256	−0.509972
$964$	18.2350	0.587310
$965$	14.3704	0.462600
$966$	9.95739	0.320374
$967$	−26.0444	−0.837532	−0.418766	−	0.908094i	$-0.637537\pi$
$967$	−26.0444	−0.837532	−0.418766	+	0.908094i	$0.637537\pi$
$968$	−19.8271	−0.637268
$969$	0.549180	0.0176422
$970$	30.3789	0.975407
$971$	54.9208	1.76249	0.881247	−	0.472657i	$-0.156705\pi$
$971$	54.9208	1.76249	0.881247	+	0.472657i	$0.156705\pi$
$972$	52.7113	1.69072
$973$	15.5083	0.497172
$974$	−58.8259	−1.88490
$975$	2.53109	0.0810596
$976$	−133.662	−4.27843
$977$	−28.7675	−0.920354	−0.460177	−	0.887827i	$-0.652214\pi$
$977$	−28.7675	−0.920354	−0.460177	+	0.887827i	$0.652214\pi$
$978$	8.69238	0.277952
$979$	9.48895	0.303268
$980$	4.74002	0.151414
$981$	−14.5459	−0.464413
$982$	11.7085	0.373632
$983$	49.4927	1.57857	0.789286	−	0.614025i	$-0.210451\pi$
$983$	49.4927	1.57857	0.789286	+	0.614025i	$0.210451\pi$
$984$	24.2444	0.772882
$985$	12.7581	0.406507
$986$	−23.6601	−0.753491
$987$	−3.68100	−0.117167
$988$	−32.2083	−1.02468
$989$	108.130	3.43834
$990$	20.7981	0.661008
$991$	−31.9271	−1.01420	−0.507099	−	0.861888i	$-0.669282\pi$
$991$	−31.9271	−1.01420	−0.507099	+	0.861888i	$0.669282\pi$
$992$	−36.8673	−1.17054
$993$	−15.2615	−0.484310
$994$	12.3627	0.392121
$995$	−8.53109	−0.270454
$996$	9.34314	0.296049
$997$	16.2094	0.513358	0.256679	−	0.966497i	$-0.417372\pi$
$997$	16.2094	0.513358	0.256679	+	0.966497i	$0.417372\pi$
$998$	29.2092	0.924602
$999$	8.44730	0.267261

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	595.2.a.j.1.4	✓	4
3.2	odd	2		5355.2.a.bi.1.1		4
4.3	odd	2		9520.2.a.bh.1.3		4
5.4	even	2		2975.2.a.i.1.1		4
7.6	odd	2		4165.2.a.be.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
595.2.a.j.1.4	✓	4	1.1	even	1	trivial
2975.2.a.i.1.1		4	5.4	even	2
4165.2.a.be.1.4		4	7.6	odd	2
5355.2.a.bi.1.1		4	3.2	odd	2
9520.2.a.bh.1.3		4	4.3	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 595 = 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	595.a (trivial)

\(f(q)\)	\(=\)	\(q+2.59615 q^{2} +0.452290 q^{3} +4.74002 q^{4} +1.00000 q^{5} +1.17422 q^{6} -1.00000 q^{7} +7.11351 q^{8} -2.79543 q^{9} +2.59615 q^{10} -2.86579 q^{11} +2.14386 q^{12} +5.59615 q^{13} -2.59615 q^{14} +0.452290 q^{15} +8.98774 q^{16} -1.00000 q^{17} -7.25738 q^{18} -1.21422 q^{19} +4.74002 q^{20} -0.452290 q^{21} -7.44003 q^{22} -8.48004 q^{23} +3.21737 q^{24} +1.00000 q^{25} +14.5285 q^{26} -2.62122 q^{27} -4.74002 q^{28} +9.11351 q^{29} +1.17422 q^{30} -4.04844 q^{31} +9.10654 q^{32} -1.29617 q^{33} -2.59615 q^{34} -1.00000 q^{35} -13.2504 q^{36} -3.22266 q^{37} -3.15230 q^{38} +2.53109 q^{39} +7.11351 q^{40} +7.53545 q^{41} -1.17422 q^{42} -12.7511 q^{43} -13.5839 q^{44} -2.79543 q^{45} -22.0155 q^{46} +8.13858 q^{47} +4.06507 q^{48} +1.00000 q^{49} +2.59615 q^{50} -0.452290 q^{51} +26.5259 q^{52} -6.40968 q^{53} -6.80509 q^{54} -2.86579 q^{55} -7.11351 q^{56} -0.549180 q^{57} +23.6601 q^{58} +11.3374 q^{59} +2.14386 q^{60} -14.8716 q^{61} -10.5104 q^{62} +2.79543 q^{63} +5.66651 q^{64} +5.59615 q^{65} -3.36505 q^{66} +12.6574 q^{67} -4.74002 q^{68} -3.83544 q^{69} -2.59615 q^{70} -4.76193 q^{71} -19.8854 q^{72} +3.46891 q^{73} -8.36652 q^{74} +0.452290 q^{75} -5.75543 q^{76} +2.86579 q^{77} +6.57109 q^{78} +2.68989 q^{79} +8.98774 q^{80} +7.20075 q^{81} +19.5632 q^{82} +4.35808 q^{83} -2.14386 q^{84} -1.00000 q^{85} -33.1039 q^{86} +4.12195 q^{87} -20.3858 q^{88} -3.31111 q^{89} -7.25738 q^{90} -5.59615 q^{91} -40.1955 q^{92} -1.83107 q^{93} +21.1290 q^{94} -1.21422 q^{95} +4.11880 q^{96} +11.7015 q^{97} +2.59615 q^{98} +8.01112 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} + 7 q^{6} - 4 q^{7} + 9 q^{8} + 2 q^{9} + 2 q^{10} - 5 q^{11} + 14 q^{13} - 2 q^{14} + 2 q^{15} + 6 q^{16} - 4 q^{17} - q^{18} - 3 q^{19} + 2 q^{20} - 2 q^{21}+ \cdots + q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 + 7 * q^6 - 4 * q^7 + 9 * q^8 + 2 * q^9 + 2 * q^10 - 5 * q^11 + 14 * q^13 - 2 * q^14 + 2 * q^15 + 6 * q^16 - 4 * q^17 - q^18 - 3 * q^19 + 2 * q^20 - 2 * q^21 - 11 * q^24 + 4 * q^25 + 16 * q^26 + 5 * q^27 - 2 * q^28 + 17 * q^29 + 7 * q^30 - 8 * q^31 + 5 * q^32 + 16 * q^33 - 2 * q^34 - 4 * q^35 - 13 * q^36 - 7 * q^37 + 13 * q^39 + 9 * q^40 - 7 * q^42 - 3 * q^43 - 16 * q^44 + 2 * q^45 - 24 * q^46 + 6 * q^47 + 5 * q^48 + 4 * q^49 + 2 * q^50 - 2 * q^51 + 19 * q^52 + 15 * q^53 + q^54 - 5 * q^55 - 9 * q^56 + 14 * q^57 + 14 * q^58 + 9 * q^59 - 4 * q^61 - 19 * q^62 - 2 * q^63 + 21 * q^64 + 14 * q^65 - 15 * q^66 - 3 * q^67 - 2 * q^68 + 2 * q^69 - 2 * q^70 - 17 * q^71 - 38 * q^72 + 11 * q^73 - 19 * q^74 + 2 * q^75 - 14 * q^76 + 5 * q^77 + 25 * q^78 + 8 * q^79 + 6 * q^80 + 8 * q^81 + 14 * q^82 + 7 * q^83 - 4 * q^85 - 56 * q^86 - 7 * q^87 - 37 * q^88 + 5 * q^89 - q^90 - 14 * q^91 - 50 * q^92 - 23 * q^93 + q^94 - 3 * q^95 + 15 * q^96 + 18 * q^97 + 2 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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