LMFDB - Embedded newform 1003.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 10x^{8} + 34x^{7} + 28x^{6} - 129x^{5} - 3x^{4} + 178x^{3} - 56x^{2} - 56x + 15 $ x^10 - 3x^9 - 10x^8 + 34x^7 + 28x^6 - 129x^5 - 3x^4 + 178x^3 - 56x^2 - 56*x + 15
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.06592$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.755134 q^{2} +0.0659171 q^{3} -1.42977 q^{4} +1.80730 q^{5} +0.0497762 q^{6} -1.15845 q^{7} -2.58994 q^{8} -2.99565 q^{9} +O(q^{10})$	\(q+0.755134 q^{2} +0.0659171 q^{3} -1.42977 q^{4} +1.80730 q^{5} +0.0497762 q^{6} -1.15845 q^{7} -2.58994 q^{8} -2.99565 q^{9} +1.36475 q^{10} +0.520161 q^{11} -0.0942465 q^{12} +0.157108 q^{13} -0.874783 q^{14} +0.119132 q^{15} +0.903798 q^{16} -1.00000 q^{17} -2.26212 q^{18} -7.60523 q^{19} -2.58402 q^{20} -0.0763615 q^{21} +0.392791 q^{22} +3.13485 q^{23} -0.170721 q^{24} -1.73368 q^{25} +0.118638 q^{26} -0.395216 q^{27} +1.65632 q^{28} -3.99936 q^{29} +0.0899603 q^{30} -9.13604 q^{31} +5.86236 q^{32} +0.0342875 q^{33} -0.755134 q^{34} -2.09366 q^{35} +4.28311 q^{36} +1.80409 q^{37} -5.74296 q^{38} +0.0103561 q^{39} -4.68078 q^{40} -11.8682 q^{41} -0.0576631 q^{42} +10.3657 q^{43} -0.743712 q^{44} -5.41404 q^{45} +2.36723 q^{46} -0.794695 q^{47} +0.0595758 q^{48} -5.65800 q^{49} -1.30916 q^{50} -0.0659171 q^{51} -0.224629 q^{52} +11.1437 q^{53} -0.298441 q^{54} +0.940085 q^{55} +3.00031 q^{56} -0.501314 q^{57} -3.02005 q^{58} -1.00000 q^{59} -0.170331 q^{60} -12.2215 q^{61} -6.89893 q^{62} +3.47031 q^{63} +2.61927 q^{64} +0.283941 q^{65} +0.0258916 q^{66} -9.60423 q^{67} +1.42977 q^{68} +0.206640 q^{69} -1.58099 q^{70} +7.46839 q^{71} +7.75856 q^{72} +4.59490 q^{73} +1.36233 q^{74} -0.114279 q^{75} +10.8737 q^{76} -0.602580 q^{77} +0.00782025 q^{78} +3.05080 q^{79} +1.63343 q^{80} +8.96091 q^{81} -8.96209 q^{82} +12.4642 q^{83} +0.109180 q^{84} -1.80730 q^{85} +7.82748 q^{86} -0.263626 q^{87} -1.34718 q^{88} -9.83735 q^{89} -4.08832 q^{90} -0.182002 q^{91} -4.48213 q^{92} -0.602221 q^{93} -0.600101 q^{94} -13.7449 q^{95} +0.386430 q^{96} -5.35933 q^{97} -4.27254 q^{98} -1.55822 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) $ 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9} + 4 q^{10} + 12 q^{11} - 24 q^{12} - 11 q^{13} - 12 q^{14} + 9 q^{15} - 3 q^{16} - 10 q^{17} - 22 q^{18} - 5 q^{19} - 36 q^{20} - 10 q^{21} + 6 q^{22} - 7 q^{23} + 35 q^{24} + 2 q^{25} + q^{26} - 31 q^{27} - 4 q^{28} + 10 q^{29} - 9 q^{30} + 13 q^{31} - 15 q^{32} - 9 q^{33} + q^{34} - 8 q^{35} + 40 q^{36} + 12 q^{37} - 50 q^{38} + 24 q^{39} + 5 q^{40} - 29 q^{41} - 17 q^{42} - 18 q^{43} - 6 q^{44} - 14 q^{45} + 11 q^{46} - 18 q^{47} - 43 q^{48} - 9 q^{49} - 31 q^{50} + 7 q^{51} - 68 q^{52} + 19 q^{54} - 27 q^{55} - 7 q^{56} + 20 q^{57} + 23 q^{58} - 10 q^{59} + 38 q^{60} + 8 q^{61} - 46 q^{62} + 39 q^{63} - 20 q^{64} + 58 q^{65} - 34 q^{66} - 6 q^{67} - 15 q^{68} + 6 q^{69} + 73 q^{70} + 8 q^{71} - 70 q^{72} - 41 q^{73} - 10 q^{74} + 10 q^{75} + 12 q^{76} - 22 q^{77} - 43 q^{78} + 3 q^{79} - 15 q^{80} + 26 q^{81} + 8 q^{82} - 22 q^{84} + 12 q^{85} - 29 q^{86} - 28 q^{87} + 33 q^{88} - 45 q^{89} + 56 q^{90} - 14 q^{91} + 36 q^{92} - 19 q^{93} + 15 q^{94} - 17 q^{95} + 90 q^{96} - 5 q^{97} + 30 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9 + 4 * q^10 + 12 * q^11 - 24 * q^12 - 11 * q^13 - 12 * q^14 + 9 * q^15 - 3 * q^16 - 10 * q^17 - 22 * q^18 - 5 * q^19 - 36 * q^20 - 10 * q^21 + 6 * q^22 - 7 * q^23 + 35 * q^24 + 2 * q^25 + q^26 - 31 * q^27 - 4 * q^28 + 10 * q^29 - 9 * q^30 + 13 * q^31 - 15 * q^32 - 9 * q^33 + q^34 - 8 * q^35 + 40 * q^36 + 12 * q^37 - 50 * q^38 + 24 * q^39 + 5 * q^40 - 29 * q^41 - 17 * q^42 - 18 * q^43 - 6 * q^44 - 14 * q^45 + 11 * q^46 - 18 * q^47 - 43 * q^48 - 9 * q^49 - 31 * q^50 + 7 * q^51 - 68 * q^52 + 19 * q^54 - 27 * q^55 - 7 * q^56 + 20 * q^57 + 23 * q^58 - 10 * q^59 + 38 * q^60 + 8 * q^61 - 46 * q^62 + 39 * q^63 - 20 * q^64 + 58 * q^65 - 34 * q^66 - 6 * q^67 - 15 * q^68 + 6 * q^69 + 73 * q^70 + 8 * q^71 - 70 * q^72 - 41 * q^73 - 10 * q^74 + 10 * q^75 + 12 * q^76 - 22 * q^77 - 43 * q^78 + 3 * q^79 - 15 * q^80 + 26 * q^81 + 8 * q^82 - 22 * q^84 + 12 * q^85 - 29 * q^86 - 28 * q^87 + 33 * q^88 - 45 * q^89 + 56 * q^90 - 14 * q^91 + 36 * q^92 - 19 * q^93 + 15 * q^94 - 17 * q^95 + 90 * q^96 - 5 * q^97 + 30 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.755134	0.533960	0.266980	−	0.963702i	$-0.413974\pi$
$2$	0.755134	0.533960	0.266980	+	0.963702i	$0.413974\pi$
$3$	0.0659171	0.0380572	0.0190286	−	0.999819i	$-0.493943\pi$
$3$	0.0659171	0.0380572	0.0190286	+	0.999819i	$0.493943\pi$
$4$	−1.42977	−0.714887
$5$	1.80730	0.808247	0.404124	−	0.914704i	$-0.367577\pi$
$5$	1.80730	0.808247	0.404124	+	0.914704i	$0.367577\pi$
$6$	0.0497762	0.0203210
$7$	−1.15845	−0.437852	−0.218926	−	0.975741i	$-0.570255\pi$
$7$	−1.15845	−0.437852	−0.218926	+	0.975741i	$0.570255\pi$
$8$	−2.58994	−0.915681
$9$	−2.99565	−0.998552
$10$	1.36475	0.431572
$11$	0.520161	0.156834	0.0784172	−	0.996921i	$-0.475013\pi$
$11$	0.520161	0.156834	0.0784172	+	0.996921i	$0.475013\pi$
$12$	−0.0942465	−0.0272066
$13$	0.157108	0.0435740	0.0217870	−	0.999763i	$-0.493064\pi$
$13$	0.157108	0.0435740	0.0217870	+	0.999763i	$0.493064\pi$
$14$	−0.874783	−0.233796
$15$	0.119132	0.0307597
$16$	0.903798	0.225950
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.26212	−0.533187
$19$	−7.60523	−1.74476	−0.872379	−	0.488830i	$-0.837424\pi$
$19$	−7.60523	−1.74476	−0.872379	+	0.488830i	$0.837424\pi$
$20$	−2.58402	−0.577805
$21$	−0.0763615	−0.0166634
$22$	0.392791	0.0837433
$23$	3.13485	0.653662	0.326831	−	0.945083i	$-0.394019\pi$
$23$	3.13485	0.653662	0.326831	+	0.945083i	$0.394019\pi$
$24$	−0.170721	−0.0348483
$25$	−1.73368	−0.346736
$26$	0.118638	0.0232668
$27$	−0.395216	−0.0760594
$28$	1.65632	0.313015
$29$	−3.99936	−0.742663	−0.371332	−	0.928500i	$-0.621099\pi$
$29$	−3.99936	−0.742663	−0.371332	+	0.928500i	$0.621099\pi$
$30$	0.0899603	0.0164244
$31$	−9.13604	−1.64088	−0.820441	−	0.571732i	$-0.806272\pi$
$31$	−9.13604	−1.64088	−0.820441	+	0.571732i	$0.806272\pi$
$32$	5.86236	1.03633
$33$	0.0342875	0.00596869
$34$	−0.755134	−0.129504
$35$	−2.09366	−0.353893
$36$	4.28311	0.713851
$37$	1.80409	0.296590	0.148295	−	0.988943i	$-0.452621\pi$
$37$	1.80409	0.296590	0.148295	+	0.988943i	$0.452621\pi$
$38$	−5.74296	−0.931631
$39$	0.0103561	0.00165831
$40$	−4.68078	−0.740097
$41$	−11.8682	−1.85350	−0.926752	−	0.375673i	$-0.877412\pi$
$41$	−11.8682	−1.85350	−0.926752	+	0.375673i	$0.877412\pi$
$42$	−0.0576631	−0.00889762
$43$	10.3657	1.58075	0.790377	−	0.612621i	$-0.209885\pi$
$43$	10.3657	1.58075	0.790377	+	0.612621i	$0.209885\pi$
$44$	−0.743712	−0.112119
$45$	−5.41404	−0.807077
$46$	2.36723	0.349029
$47$	−0.794695	−0.115918	−0.0579591	−	0.998319i	$-0.518459\pi$
$47$	−0.794695	−0.115918	−0.0579591	+	0.998319i	$0.518459\pi$
$48$	0.0595758	0.00859902
$49$	−5.65800	−0.808285
$50$	−1.30916	−0.185143
$51$	−0.0659171	−0.00923024
$52$	−0.224629	−0.0311505
$53$	11.1437	1.53071	0.765353	−	0.643611i	$-0.222565\pi$
$53$	11.1437	1.53071	0.765353	+	0.643611i	$0.222565\pi$
$54$	−0.298441	−0.0406127
$55$	0.940085	0.126761
$56$	3.00031	0.400933
$57$	−0.501314	−0.0664007
$58$	−3.02005	−0.396552
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−0.170331	−0.0219897
$61$	−12.2215	−1.56480	−0.782401	−	0.622775i	$-0.786005\pi$
$61$	−12.2215	−1.56480	−0.782401	+	0.622775i	$0.786005\pi$
$62$	−6.89893	−0.876165
$63$	3.47031	0.437218
$64$	2.61927	0.327409
$65$	0.283941	0.0352186
$66$	0.0258916	0.00318704
$67$	−9.60423	−1.17334	−0.586672	−	0.809825i	$-0.699562\pi$
$67$	−9.60423	−1.17334	−0.586672	+	0.809825i	$0.699562\pi$
$68$	1.42977	0.173385
$69$	0.206640	0.0248766
$70$	−1.58099	−0.188965
$71$	7.46839	0.886334	0.443167	−	0.896439i	$-0.353855\pi$
$71$	7.46839	0.886334	0.443167	+	0.896439i	$0.353855\pi$
$72$	7.75856	0.914355
$73$	4.59490	0.537792	0.268896	−	0.963169i	$-0.413341\pi$
$73$	4.59490	0.537792	0.268896	+	0.963169i	$0.413341\pi$
$74$	1.36233	0.158367
$75$	−0.114279	−0.0131958
$76$	10.8737	1.24730
$77$	−0.602580	−0.0686703
$78$	0.00782025	0.000885469 0
$79$	3.05080	0.343242	0.171621	−	0.985163i	$-0.445100\pi$
$79$	3.05080	0.343242	0.171621	+	0.985163i	$0.445100\pi$
$80$	1.63343	0.182623
$81$	8.96091	0.995657
$82$	−8.96209	−0.989697
$83$	12.4642	1.36813	0.684064	−	0.729422i	$-0.260211\pi$
$83$	12.4642	1.36813	0.684064	+	0.729422i	$0.260211\pi$
$84$	0.109180	0.0119125
$85$	−1.80730	−0.196029
$86$	7.82748	0.844059
$87$	−0.263626	−0.0282637
$88$	−1.34718	−0.143610
$89$	−9.83735	−1.04276	−0.521379	−	0.853325i	$-0.674582\pi$
$89$	−9.83735	−1.04276	−0.521379	+	0.853325i	$0.674582\pi$
$90$	−4.08832	−0.430947
$91$	−0.182002	−0.0190790
$92$	−4.48213	−0.467294
$93$	−0.602221	−0.0624474
$94$	−0.600101	−0.0618957
$95$	−13.7449	−1.41020
$96$	0.386430	0.0394398
$97$	−5.35933	−0.544158	−0.272079	−	0.962275i	$-0.587711\pi$
$97$	−5.35933	−0.544158	−0.272079	+	0.962275i	$0.587711\pi$
$98$	−4.27254	−0.431592
$99$	−1.55822	−0.156607
$100$	2.47877	0.247877
$101$	−5.39499	−0.536822	−0.268411	−	0.963305i	$-0.586499\pi$
$101$	−5.39499	−0.536822	−0.268411	+	0.963305i	$0.586499\pi$
$102$	−0.0497762	−0.00492858
$103$	3.11520	0.306950	0.153475	−	0.988153i	$-0.450954\pi$
$103$	3.11520	0.306950	0.153475	+	0.988153i	$0.450954\pi$
$104$	−0.406901	−0.0398999
$105$	−0.138008	−0.0134682
$106$	8.41498	0.817335
$107$	−4.10853	−0.397186	−0.198593	−	0.980082i	$-0.563637\pi$
$107$	−4.10853	−0.397186	−0.198593	+	0.980082i	$0.563637\pi$
$108$	0.565069	0.0543738
$109$	0.444957	0.0426192	0.0213096	−	0.999773i	$-0.493216\pi$
$109$	0.444957	0.0426192	0.0213096	+	0.999773i	$0.493216\pi$
$110$	0.709890	0.0676853
$111$	0.118920	0.0112874
$112$	−1.04700	−0.0989325
$113$	8.40945	0.791095	0.395547	−	0.918446i	$-0.370555\pi$
$113$	8.40945	0.791095	0.395547	+	0.918446i	$0.370555\pi$
$114$	−0.378559	−0.0354553
$115$	5.66560	0.528320
$116$	5.71818	0.530920
$117$	−0.470642	−0.0435109
$118$	−0.755134	−0.0695157
$119$	1.15845	0.106195
$120$	−0.308544	−0.0281660
$121$	−10.7294	−0.975403
$122$	−9.22886	−0.835542
$123$	−0.782318	−0.0705393
$124$	13.0625	1.17304
$125$	−12.1698	−1.08850
$126$	2.62055	0.233457
$127$	−10.2893	−0.913028	−0.456514	−	0.889716i	$-0.650902\pi$
$127$	−10.2893	−0.913028	−0.456514	+	0.889716i	$0.650902\pi$
$128$	−9.74683	−0.861506
$129$	0.683276	0.0601591
$130$	0.214413	0.0188053
$131$	15.3991	1.34542	0.672712	−	0.739905i	$-0.265129\pi$
$131$	15.3991	1.34542	0.672712	+	0.739905i	$0.265129\pi$
$132$	−0.0490233	−0.00426693
$133$	8.81026	0.763946
$134$	−7.25248	−0.626519
$135$	−0.714272	−0.0614748
$136$	2.58994	0.222085
$137$	−3.15396	−0.269461	−0.134731	−	0.990882i	$-0.543017\pi$
$137$	−3.15396	−0.269461	−0.134731	+	0.990882i	$0.543017\pi$
$138$	0.156041	0.0132831
$139$	−9.39769	−0.797102	−0.398551	−	0.917146i	$-0.630487\pi$
$139$	−9.39769	−0.797102	−0.398551	+	0.917146i	$0.630487\pi$
$140$	2.99346	0.252993
$141$	−0.0523840	−0.00441153
$142$	5.63963	0.473267
$143$	0.0817216	0.00683390
$144$	−2.70747	−0.225622
$145$	−7.22803	−0.600256
$146$	3.46976	0.287160
$147$	−0.372959	−0.0307611
$148$	−2.57944	−0.212028
$149$	14.9777	1.22702	0.613508	−	0.789688i	$-0.289758\pi$
$149$	14.9777	1.22702	0.613508	+	0.789688i	$0.289758\pi$
$150$	−0.0862961	−0.00704604
$151$	19.7155	1.60442	0.802212	−	0.597039i	$-0.203656\pi$
$151$	19.7155	1.60442	0.802212	+	0.597039i	$0.203656\pi$
$152$	19.6971	1.59764
$153$	2.99565	0.242184
$154$	−0.455028	−0.0366672
$155$	−16.5115	−1.32624
$156$	−0.0148069	−0.00118550
$157$	20.1204	1.60579	0.802893	−	0.596124i	$-0.203293\pi$
$157$	20.1204	1.60579	0.802893	+	0.596124i	$0.203293\pi$
$158$	2.30376	0.183278
$159$	0.734560	0.0582544
$160$	10.5950	0.837610
$161$	−3.63156	−0.286207
$162$	6.76669	0.531641
$163$	−16.1609	−1.26582	−0.632909	−	0.774226i	$-0.718139\pi$
$163$	−16.1609	−1.26582	−0.632909	+	0.774226i	$0.718139\pi$
$164$	16.9689	1.32505
$165$	0.0619677	0.00482418
$166$	9.41216	0.730525
$167$	15.4520	1.19571	0.597855	−	0.801605i	$-0.296020\pi$
$167$	15.4520	1.19571	0.597855	+	0.801605i	$0.296020\pi$
$168$	0.197771	0.0152584
$169$	−12.9753	−0.998101
$170$	−1.36475	−0.104672
$171$	22.7826	1.74223
$172$	−14.8206	−1.13006
$173$	18.4772	1.40480	0.702399	−	0.711783i	$-0.252112\pi$
$173$	18.4772	1.40480	0.702399	+	0.711783i	$0.252112\pi$
$174$	−0.199073	−0.0150917
$175$	2.00838	0.151819
$176$	0.470121	0.0354367
$177$	−0.0659171	−0.00495463
$178$	−7.42851	−0.556791
$179$	11.0458	0.825603	0.412802	−	0.910821i	$-0.364550\pi$
$179$	11.0458	0.825603	0.412802	+	0.910821i	$0.364550\pi$
$180$	7.74084	0.576968
$181$	17.2913	1.28525	0.642625	−	0.766181i	$-0.277845\pi$
$181$	17.2913	1.28525	0.642625	+	0.766181i	$0.277845\pi$
$182$	−0.137436	−0.0101874
$183$	−0.805605	−0.0595520
$184$	−8.11907	−0.598545
$185$	3.26052	0.239718
$186$	−0.454757	−0.0333444
$187$	−0.520161	−0.0380379
$188$	1.13623	0.0828684
$189$	0.457837	0.0333028
$190$	−10.3792	−0.752989
$191$	4.76645	0.344888	0.172444	−	0.985019i	$-0.444834\pi$
$191$	4.76645	0.344888	0.172444	+	0.985019i	$0.444834\pi$
$192$	0.172655	0.0124603
$193$	1.81160	0.130401	0.0652007	−	0.997872i	$-0.479231\pi$
$193$	1.81160	0.130401	0.0652007	+	0.997872i	$0.479231\pi$
$194$	−4.04701	−0.290558
$195$	0.0187166	0.00134032
$196$	8.08965	0.577832
$197$	−12.2484	−0.872664	−0.436332	−	0.899786i	$-0.643723\pi$
$197$	−12.2484	−0.872664	−0.436332	+	0.899786i	$0.643723\pi$
$198$	−1.17667	−0.0836220
$199$	9.94903	0.705268	0.352634	−	0.935761i	$-0.385286\pi$
$199$	9.94903	0.705268	0.352634	+	0.935761i	$0.385286\pi$
$200$	4.49013	0.317500
$201$	−0.633083	−0.0446542
$202$	−4.07394	−0.286641
$203$	4.63305	0.325177
$204$	0.0942465	0.00659857
$205$	−21.4494	−1.49809
$206$	2.35239	0.163899
$207$	−9.39093	−0.652715
$208$	0.141994	0.00984553
$209$	−3.95594	−0.273638
$210$	−0.104214	−0.00719147
$211$	1.05682	0.0727547	0.0363774	−	0.999338i	$-0.488418\pi$
$211$	1.05682	0.0727547	0.0363774	+	0.999338i	$0.488418\pi$
$212$	−15.9330	−1.09428
$213$	0.492294	0.0337314
$214$	−3.10249	−0.212082
$215$	18.7339	1.27764
$216$	1.02358	0.0696461
$217$	10.5836	0.718464
$218$	0.336002	0.0227569
$219$	0.302882	0.0204669
$220$	−1.34411	−0.0906198
$221$	−0.157108	−0.0105682
$222$	0.0898006	0.00602702
$223$	−16.3020	−1.09166	−0.545830	−	0.837896i	$-0.683786\pi$
$223$	−16.3020	−1.09166	−0.545830	+	0.837896i	$0.683786\pi$
$224$	−6.79124	−0.453759
$225$	5.19351	0.346234
$226$	6.35026	0.422413
$227$	−11.9087	−0.790410	−0.395205	−	0.918593i	$-0.629326\pi$
$227$	−11.9087	−0.790410	−0.395205	+	0.918593i	$0.629326\pi$
$228$	0.716766	0.0474690
$229$	−5.16915	−0.341587	−0.170793	−	0.985307i	$-0.554633\pi$
$229$	−5.16915	−0.341587	−0.170793	+	0.985307i	$0.554633\pi$
$230$	4.27829	0.282102
$231$	−0.0397203	−0.00261340
$232$	10.3581	0.680043
$233$	20.6651	1.35381	0.676907	−	0.736069i	$-0.263320\pi$
$233$	20.6651	1.35381	0.676907	+	0.736069i	$0.263320\pi$
$234$	−0.355398	−0.0232331
$235$	−1.43625	−0.0936906
$236$	1.42977	0.0930703
$237$	0.201100	0.0130629
$238$	0.874783	0.0567038
$239$	4.08295	0.264104	0.132052	−	0.991243i	$-0.457843\pi$
$239$	4.08295	0.264104	0.132052	+	0.991243i	$0.457843\pi$
$240$	0.107671	0.00695013
$241$	−24.9197	−1.60522	−0.802609	−	0.596506i	$-0.796555\pi$
$241$	−24.9197	−1.60522	−0.802609	+	0.596506i	$0.796555\pi$
$242$	−8.10215	−0.520826
$243$	1.77633	0.113951
$244$	17.4740	1.11866
$245$	−10.2257	−0.653295
$246$	−0.590755	−0.0376652
$247$	−1.19484	−0.0760261
$248$	23.6618	1.50252
$249$	0.821606	0.0520672
$250$	−9.18979	−0.581213
$251$	−6.34962	−0.400785	−0.200392	−	0.979716i	$-0.564222\pi$
$251$	−6.34962	−0.400785	−0.200392	+	0.979716i	$0.564222\pi$
$252$	−4.96176	−0.312561
$253$	1.63063	0.102517
$254$	−7.76980	−0.487521
$255$	−0.119132	−0.00746031
$256$	−12.5987	−0.787418
$257$	−20.0257	−1.24917	−0.624583	−	0.780958i	$-0.714731\pi$
$257$	−20.0257	−1.24917	−0.624583	+	0.780958i	$0.714731\pi$
$258$	0.515965	0.0321226
$259$	−2.08994	−0.129863
$260$	−0.405971	−0.0251773
$261$	11.9807	0.741588
$262$	11.6284	0.718402
$263$	−5.45914	−0.336625	−0.168312	−	0.985734i	$-0.553832\pi$
$263$	−5.45914	−0.336625	−0.168312	+	0.985734i	$0.553832\pi$
$264$	−0.0888025	−0.00546541
$265$	20.1400	1.23719
$266$	6.65292	0.407917
$267$	−0.648450	−0.0396845
$268$	13.7319	0.838808
$269$	−5.08636	−0.310121	−0.155060	−	0.987905i	$-0.549557\pi$
$269$	−5.08636	−0.310121	−0.155060	+	0.987905i	$0.549557\pi$
$270$	−0.539371	−0.0328251
$271$	−24.0299	−1.45971	−0.729857	−	0.683600i	$-0.760414\pi$
$271$	−24.0299	−1.45971	−0.729857	+	0.683600i	$0.760414\pi$
$272$	−0.903798	−0.0548008
$273$	−0.0119970	−0.000726093 0
$274$	−2.38166	−0.143881
$275$	−0.901793	−0.0543802
$276$	−0.295449	−0.0177839
$277$	26.5461	1.59500	0.797500	−	0.603319i	$-0.206156\pi$
$277$	26.5461	1.59500	0.797500	+	0.603319i	$0.206156\pi$
$278$	−7.09651	−0.425621
$279$	27.3684	1.63850
$280$	5.42244	0.324053
$281$	−32.3942	−1.93248	−0.966239	−	0.257646i	$-0.917053\pi$
$281$	−32.3942	−1.93248	−0.966239	+	0.257646i	$0.917053\pi$
$282$	−0.0395569	−0.00235558
$283$	3.35943	0.199697	0.0998487	−	0.995003i	$-0.468164\pi$
$283$	3.35943	0.199697	0.0998487	+	0.995003i	$0.468164\pi$
$284$	−10.6781	−0.633629
$285$	−0.906023	−0.0536682
$286$	0.0617107	0.00364903
$287$	13.7487	0.811561
$288$	−17.5616	−1.03483
$289$	1.00000	0.0588235
$290$	−5.45813	−0.320512
$291$	−0.353271	−0.0207091
$292$	−6.56966	−0.384460
$293$	−21.1769	−1.23717	−0.618583	−	0.785719i	$-0.712293\pi$
$293$	−21.1769	−1.23717	−0.618583	+	0.785719i	$0.712293\pi$
$294$	−0.281634	−0.0164252
$295$	−1.80730	−0.105225
$296$	−4.67247	−0.271582
$297$	−0.205576	−0.0119287
$298$	11.3101	0.655178
$299$	0.492511	0.0284826
$300$	0.163393	0.00943352
$301$	−12.0081	−0.692136
$302$	14.8878	0.856699
$303$	−0.355622	−0.0204300
$304$	−6.87359	−0.394228
$305$	−22.0879	−1.26475
$306$	2.26212	0.129317
$307$	14.6227	0.834564	0.417282	−	0.908777i	$-0.362983\pi$
$307$	14.6227	0.834564	0.417282	+	0.908777i	$0.362983\pi$
$308$	0.861552	0.0490915
$309$	0.205345	0.0116817
$310$	−12.4684	−0.708158
$311$	−7.10616	−0.402953	−0.201477	−	0.979493i	$-0.564574\pi$
$311$	−7.10616	−0.402953	−0.201477	+	0.979493i	$0.564574\pi$
$312$	−0.0268217	−0.00151848
$313$	−28.4814	−1.60986	−0.804932	−	0.593367i	$-0.797798\pi$
$313$	−28.4814	−1.60986	−0.804932	+	0.593367i	$0.797798\pi$
$314$	15.1936	0.857425
$315$	6.27188	0.353380
$316$	−4.36196	−0.245379
$317$	−27.4171	−1.53990	−0.769948	−	0.638107i	$-0.779718\pi$
$317$	−27.4171	−1.53990	−0.769948	+	0.638107i	$0.779718\pi$
$318$	0.554691	0.0311055
$319$	−2.08031	−0.116475
$320$	4.73380	0.264627
$321$	−0.270822	−0.0151158
$322$	−2.74231	−0.152823
$323$	7.60523	0.423166
$324$	−12.8121	−0.711782
$325$	−0.272376	−0.0151087
$326$	−12.2036	−0.675896
$327$	0.0293303	0.00162197
$328$	30.7379	1.69722
$329$	0.920613	0.0507551
$330$	0.0467939	0.00257592
$331$	28.8833	1.58757	0.793785	−	0.608199i	$-0.208108\pi$
$331$	28.8833	1.58757	0.793785	+	0.608199i	$0.208108\pi$
$332$	−17.8210	−0.978056
$333$	−5.40442	−0.296160
$334$	11.6683	0.638461
$335$	−17.3577	−0.948352
$336$	−0.0690154	−0.00376510
$337$	−2.65669	−0.144719	−0.0723595	−	0.997379i	$-0.523053\pi$
$337$	−2.65669	−0.144719	−0.0723595	+	0.997379i	$0.523053\pi$
$338$	−9.79810	−0.532946
$339$	0.554327	0.0301069
$340$	2.58402	0.140138
$341$	−4.75221	−0.257347
$342$	17.2039	0.930282
$343$	14.6636	0.791762
$344$	−26.8465	−1.44747
$345$	0.373460	0.0201064
$346$	13.9528	0.750106
$347$	20.3954	1.09488	0.547440	−	0.836845i	$-0.315602\pi$
$347$	20.3954	1.09488	0.547440	+	0.836845i	$0.315602\pi$
$348$	0.376926	0.0202054
$349$	−6.24913	−0.334508	−0.167254	−	0.985914i	$-0.553490\pi$
$349$	−6.24913	−0.334508	−0.167254	+	0.985914i	$0.553490\pi$
$350$	1.51659	0.0810654
$351$	−0.0620917	−0.00331421
$352$	3.04937	0.162532
$353$	−19.1328	−1.01834	−0.509169	−	0.860666i	$-0.670047\pi$
$353$	−19.1328	−1.01834	−0.509169	+	0.860666i	$0.670047\pi$
$354$	−0.0497762	−0.00264558
$355$	13.4976	0.716377
$356$	14.0652	0.745453
$357$	0.0763615	0.00404148
$358$	8.34107	0.440839
$359$	0.907150	0.0478776	0.0239388	−	0.999713i	$-0.492379\pi$
$359$	0.907150	0.0478776	0.0239388	+	0.999713i	$0.492379\pi$
$360$	14.0220	0.739025
$361$	38.8395	2.04418
$362$	13.0572	0.686272
$363$	−0.707253	−0.0371211
$364$	0.260221	0.0136393
$365$	8.30434	0.434669
$366$	−0.608339	−0.0317984
$367$	−4.03647	−0.210702	−0.105351	−	0.994435i	$-0.533597\pi$
$367$	−4.03647	−0.210702	−0.105351	+	0.994435i	$0.533597\pi$
$368$	2.83327	0.147695
$369$	35.5531	1.85082
$370$	2.46213	0.128000
$371$	−12.9094	−0.670223
$372$	0.861040	0.0446428
$373$	11.3853	0.589509	0.294755	−	0.955573i	$-0.404762\pi$
$373$	11.3853	0.589509	0.294755	+	0.955573i	$0.404762\pi$
$374$	−0.392791	−0.0203107
$375$	−0.802195	−0.0414252
$376$	2.05821	0.106144
$377$	−0.628333	−0.0323608
$378$	0.345728	0.0177823
$379$	−16.0445	−0.824151	−0.412075	−	0.911150i	$-0.635196\pi$
$379$	−16.0445	−0.824151	−0.412075	+	0.911150i	$0.635196\pi$
$380$	19.6521	1.00813
$381$	−0.678241	−0.0347473
$382$	3.59931	0.184157
$383$	21.5919	1.10330	0.551648	−	0.834077i	$-0.313999\pi$
$383$	21.5919	1.10330	0.551648	+	0.834077i	$0.313999\pi$
$384$	−0.642482	−0.0327865
$385$	−1.08904	−0.0555026
$386$	1.36800	0.0696292
$387$	−31.0520	−1.57846
$388$	7.66263	0.389011
$389$	−18.9578	−0.961201	−0.480601	−	0.876940i	$-0.659581\pi$
$389$	−18.9578	−0.961201	−0.480601	+	0.876940i	$0.659581\pi$
$390$	0.0141335	0.000715678 0
$391$	−3.13485	−0.158536
$392$	14.6539	0.740132
$393$	1.01506	0.0512031
$394$	−9.24919	−0.465968
$395$	5.51370	0.277425
$396$	2.22791	0.111956
$397$	−29.3043	−1.47074	−0.735370	−	0.677666i	$-0.762991\pi$
$397$	−29.3043	−1.47074	−0.735370	+	0.677666i	$0.762991\pi$
$398$	7.51285	0.376585
$399$	0.580747	0.0290737
$400$	−1.56690	−0.0783449
$401$	−32.1657	−1.60628	−0.803138	−	0.595793i	$-0.796838\pi$
$401$	−32.1657	−1.60628	−0.803138	+	0.595793i	$0.796838\pi$
$402$	−0.478062	−0.0238436
$403$	−1.43535	−0.0714998
$404$	7.71362	0.383767
$405$	16.1950	0.804737
$406$	3.49858	0.173631
$407$	0.938416	0.0465155
$408$	0.170721	0.00845195
$409$	28.8268	1.42539	0.712697	−	0.701472i	$-0.247474\pi$
$409$	28.8268	1.42539	0.712697	+	0.701472i	$0.247474\pi$
$410$	−16.1972	−0.799920
$411$	−0.207900	−0.0102549
$412$	−4.45403	−0.219434
$413$	1.15845	0.0570035
$414$	−7.09141	−0.348524
$415$	22.5266	1.10579
$416$	0.921026	0.0451570
$417$	−0.619468	−0.0303355
$418$	−2.98726	−0.146112
$419$	−3.50120	−0.171045	−0.0855224	−	0.996336i	$-0.527256\pi$
$419$	−3.50120	−0.171045	−0.0855224	+	0.996336i	$0.527256\pi$
$420$	0.197320	0.00962823
$421$	5.96347	0.290642	0.145321	−	0.989385i	$-0.453579\pi$
$421$	5.96347	0.290642	0.145321	+	0.989385i	$0.453579\pi$
$422$	0.798043	0.0388481
$423$	2.38063	0.115750
$424$	−28.8615	−1.40164
$425$	1.73368	0.0840959
$426$	0.371748	0.0180112
$427$	14.1580	0.685152
$428$	5.87426	0.283943
$429$	0.00538685	0.000260080 0
$430$	14.1466	0.682209
$431$	−18.8721	−0.909039	−0.454520	−	0.890737i	$-0.650189\pi$
$431$	−18.8721	−0.909039	−0.454520	+	0.890737i	$0.650189\pi$
$432$	−0.357196	−0.0171856
$433$	−15.8586	−0.762114	−0.381057	−	0.924552i	$-0.624440\pi$
$433$	−15.8586	−0.762114	−0.381057	+	0.924552i	$0.624440\pi$
$434$	7.99205	0.383631
$435$	−0.476451	−0.0228441
$436$	−0.636188	−0.0304679
$437$	−23.8412	−1.14048
$438$	0.228717	0.0109285
$439$	25.8148	1.23207	0.616037	−	0.787717i	$-0.288737\pi$
$439$	25.8148	1.23207	0.616037	+	0.787717i	$0.288737\pi$
$440$	−2.43476	−0.116073
$441$	16.9494	0.807115
$442$	−0.118638	−0.00564302
$443$	−3.35216	−0.159266	−0.0796330	−	0.996824i	$-0.525375\pi$
$443$	−3.35216	−0.159266	−0.0796330	+	0.996824i	$0.525375\pi$
$444$	−0.170029	−0.00806921
$445$	−17.7790	−0.842806
$446$	−12.3102	−0.582903
$447$	0.987283	0.0466969
$448$	−3.03429	−0.143357
$449$	8.48226	0.400303	0.200151	−	0.979765i	$-0.435857\pi$
$449$	8.48226	0.400303	0.200151	+	0.979765i	$0.435857\pi$
$450$	3.92179	0.184875
$451$	−6.17339	−0.290693
$452$	−12.0236	−0.565543
$453$	1.29959	0.0610600
$454$	−8.99268	−0.422047
$455$	−0.328931	−0.0154205
$456$	1.29837	0.0608019
$457$	−25.5124	−1.19342	−0.596710	−	0.802457i	$-0.703526\pi$
$457$	−25.5124	−1.19342	−0.596710	+	0.802457i	$0.703526\pi$
$458$	−3.90340	−0.182394
$459$	0.395216	0.0184471
$460$	−8.10053	−0.377689
$461$	−19.3848	−0.902842	−0.451421	−	0.892311i	$-0.649083\pi$
$461$	−19.3848	−0.902842	−0.451421	+	0.892311i	$0.649083\pi$
$462$	−0.0299941	−0.00139545
$463$	5.78051	0.268643	0.134321	−	0.990938i	$-0.457115\pi$
$463$	5.78051	0.268643	0.134321	+	0.990938i	$0.457115\pi$
$464$	−3.61462	−0.167804
$465$	−1.08839	−0.0504730
$466$	15.6049	0.722882
$467$	21.5654	0.997928	0.498964	−	0.866623i	$-0.333714\pi$
$467$	21.5654	0.997928	0.498964	+	0.866623i	$0.333714\pi$
$468$	0.672912	0.0311054
$469$	11.1260	0.513751
$470$	−1.08456	−0.0500270
$471$	1.32628	0.0611118
$472$	2.58994	0.119212
$473$	5.39183	0.247917
$474$	0.151857	0.00697504
$475$	13.1850	0.604971
$476$	−1.65632	−0.0759172
$477$	−33.3827	−1.52849
$478$	3.08317	0.141021
$479$	−38.8978	−1.77729	−0.888644	−	0.458598i	$-0.848352\pi$
$479$	−38.8978	−1.77729	−0.888644	+	0.458598i	$0.848352\pi$
$480$	0.698393	0.0318771
$481$	0.283437	0.0129236
$482$	−18.8177	−0.857122
$483$	−0.239382	−0.0108923
$484$	15.3407	0.697303
$485$	−9.68590	−0.439814
$486$	1.34136	0.0608455
$487$	−9.02976	−0.409178	−0.204589	−	0.978848i	$-0.565586\pi$
$487$	−9.02976	−0.409178	−0.204589	+	0.978848i	$0.565586\pi$
$488$	31.6529	1.43286
$489$	−1.06528	−0.0481735
$490$	−7.72175	−0.348833
$491$	−35.8042	−1.61582	−0.807910	−	0.589305i	$-0.799401\pi$
$491$	−35.8042	−1.61582	−0.807910	+	0.589305i	$0.799401\pi$
$492$	1.11854	0.0504276
$493$	3.99936	0.180122
$494$	−0.902267	−0.0405949
$495$	−2.81617	−0.126577
$496$	−8.25714	−0.370757
$497$	−8.65174	−0.388083
$498$	0.620422	0.0278018
$499$	−28.7401	−1.28658	−0.643291	−	0.765622i	$-0.722431\pi$
$499$	−28.7401	−1.28658	−0.643291	+	0.765622i	$0.722431\pi$
$500$	17.4000	0.778151
$501$	1.01855	0.0455054
$502$	−4.79481	−0.214003
$503$	−19.6079	−0.874272	−0.437136	−	0.899395i	$-0.644007\pi$
$503$	−19.6079	−0.874272	−0.437136	+	0.899395i	$0.644007\pi$
$504$	−8.98789	−0.400352
$505$	−9.75035	−0.433885
$506$	1.23134	0.0547398
$507$	−0.855295	−0.0379850
$508$	14.7114	0.652712
$509$	−41.0508	−1.81955	−0.909773	−	0.415106i	$-0.863744\pi$
$509$	−41.0508	−1.81955	−0.909773	+	0.415106i	$0.863744\pi$
$510$	−0.0899603	−0.00398351
$511$	−5.32295	−0.235474
$512$	9.97996	0.441056
$513$	3.00571	0.132705
$514$	−15.1220	−0.667005
$515$	5.63009	0.248092
$516$	−0.976930	−0.0430070
$517$	−0.413370	−0.0181800
$518$	−1.57818	−0.0693414
$519$	1.21797	0.0534628
$520$	−0.735390	−0.0322490
$521$	7.90013	0.346111	0.173055	−	0.984912i	$-0.444636\pi$
$521$	7.90013	0.346111	0.173055	+	0.984912i	$0.444636\pi$
$522$	9.04704	0.395978
$523$	−35.0714	−1.53356	−0.766782	−	0.641907i	$-0.778143\pi$
$523$	−35.0714	−1.53356	−0.766782	+	0.641907i	$0.778143\pi$
$524$	−22.0172	−0.961825
$525$	0.132387	0.00577782
$526$	−4.12238	−0.179744
$527$	9.13604	0.397972
$528$	0.0309890	0.00134862
$529$	−13.1727	−0.572727
$530$	15.2084	0.660609
$531$	2.99565	0.130000
$532$	−12.5967	−0.546135
$533$	−1.86460	−0.0807646
$534$	−0.489666	−0.0211899
$535$	−7.42532	−0.321025
$536$	24.8744	1.07441
$537$	0.728108	0.0314202
$538$	−3.84088	−0.165592
$539$	−2.94307	−0.126767
$540$	1.02125	0.0439475
$541$	6.38310	0.274431	0.137215	−	0.990541i	$-0.456185\pi$
$541$	6.38310	0.274431	0.137215	+	0.990541i	$0.456185\pi$
$542$	−18.1458	−0.779429
$543$	1.13979	0.0489131
$544$	−5.86236	−0.251347
$545$	0.804169	0.0344468
$546$	−0.00905936	−0.000387705 0
$547$	28.4365	1.21585	0.607927	−	0.793993i	$-0.292001\pi$
$547$	28.4365	1.21585	0.607927	+	0.793993i	$0.292001\pi$
$548$	4.50945	0.192634
$549$	36.6114	1.56254
$550$	−0.680975	−0.0290369
$551$	30.4161	1.29577
$552$	−0.535185	−0.0227790
$553$	−3.53420	−0.150289
$554$	20.0458	0.851666
$555$	0.214924	0.00912301
$556$	13.4366	0.569838
$557$	40.0404	1.69656	0.848282	−	0.529544i	$-0.177637\pi$
$557$	40.0404	1.69656	0.848282	+	0.529544i	$0.177637\pi$
$558$	20.6668	0.874896
$559$	1.62854	0.0688797
$560$	−1.89225	−0.0799620
$561$	−0.0342875	−0.00144762
$562$	−24.4620	−1.03187
$563$	−42.0319	−1.77143	−0.885717	−	0.464225i	$-0.846333\pi$
$563$	−42.0319	−1.77143	−0.885717	+	0.464225i	$0.846333\pi$
$564$	0.0748973	0.00315374
$565$	15.1984	0.639400
$566$	2.53682	0.106630
$567$	−10.3808	−0.435951
$568$	−19.3427	−0.811600
$569$	−20.6192	−0.864404	−0.432202	−	0.901777i	$-0.642263\pi$
$569$	−20.6192	−0.864404	−0.432202	+	0.901777i	$0.642263\pi$
$570$	−0.684169	−0.0286567
$571$	40.7591	1.70572	0.852858	−	0.522143i	$-0.174867\pi$
$571$	40.7591	1.70572	0.852858	+	0.522143i	$0.174867\pi$
$572$	−0.116843	−0.00488547
$573$	0.314190	0.0131255
$574$	10.3821	0.433341
$575$	−5.43483	−0.226648
$576$	−7.84643	−0.326934
$577$	−7.99810	−0.332965	−0.166483	−	0.986044i	$-0.553241\pi$
$577$	−7.99810	−0.332965	−0.166483	+	0.986044i	$0.553241\pi$
$578$	0.755134	0.0314094
$579$	0.119415	0.00496272
$580$	10.3344	0.429115
$581$	−14.4392	−0.599038
$582$	−0.266767	−0.0110579
$583$	5.79652	0.240067
$584$	−11.9005	−0.492446
$585$	−0.850590	−0.0351676
$586$	−15.9914	−0.660597
$587$	−15.0868	−0.622700	−0.311350	−	0.950295i	$-0.600781\pi$
$587$	−15.0868	−0.622700	−0.311350	+	0.950295i	$0.600781\pi$
$588$	0.533246	0.0219907
$589$	69.4817	2.86294
$590$	−1.36475	−0.0561859
$591$	−0.807380	−0.0332112
$592$	1.63053	0.0670144
$593$	−36.7369	−1.50860	−0.754302	−	0.656527i	$-0.772025\pi$
$593$	−36.7369	−1.50860	−0.754302	+	0.656527i	$0.772025\pi$
$594$	−0.155237	−0.00636946
$595$	2.09366	0.0858316
$596$	−21.4146	−0.877178
$597$	0.655811	0.0268406
$598$	0.371912	0.0152086
$599$	−25.4583	−1.04020	−0.520098	−	0.854106i	$-0.674105\pi$
$599$	−25.4583	−1.04020	−0.520098	+	0.854106i	$0.674105\pi$
$600$	0.295976	0.0120832
$601$	9.46329	0.386016	0.193008	−	0.981197i	$-0.438176\pi$
$601$	9.46329	0.386016	0.193008	+	0.981197i	$0.438176\pi$
$602$	−9.06773	−0.369573
$603$	28.7710	1.17164
$604$	−28.1887	−1.14698
$605$	−19.3913	−0.788367
$606$	−0.268542	−0.0109088
$607$	24.8157	1.00724	0.503620	−	0.863925i	$-0.332001\pi$
$607$	24.8157	1.00724	0.503620	+	0.863925i	$0.332001\pi$
$608$	−44.5846	−1.80814
$609$	0.305397	0.0123753
$610$	−16.6793	−0.675324
$611$	−0.124853	−0.00505102
$612$	−4.28311	−0.173134
$613$	24.5644	0.992146	0.496073	−	0.868281i	$-0.334775\pi$
$613$	24.5644	0.992146	0.496073	+	0.868281i	$0.334775\pi$
$614$	11.0421	0.445624
$615$	−1.41388	−0.0570132
$616$	1.56064	0.0628801
$617$	−25.6561	−1.03288	−0.516438	−	0.856325i	$-0.672742\pi$
$617$	−25.6561	−1.03288	−0.516438	+	0.856325i	$0.672742\pi$
$618$	0.155063	0.00623755
$619$	−2.18208	−0.0877051	−0.0438526	−	0.999038i	$-0.513963\pi$
$619$	−2.18208	−0.0877051	−0.0438526	+	0.999038i	$0.513963\pi$
$620$	23.6077	0.948110
$621$	−1.23894	−0.0497171
$622$	−5.36610	−0.215161
$623$	11.3961	0.456574
$624$	0.00935984	0.000374694 0
$625$	−13.3259	−0.533038
$626$	−21.5073	−0.859603
$627$	−0.260764	−0.0104139
$628$	−28.7677	−1.14795
$629$	−1.80409	−0.0719337
$630$	4.73611	0.188691
$631$	−34.6037	−1.37755	−0.688775	−	0.724975i	$-0.741851\pi$
$631$	−34.6037	−1.37755	−0.688775	+	0.724975i	$0.741851\pi$
$632$	−7.90139	−0.314300
$633$	0.0696627	0.00276884
$634$	−20.7035	−0.822243
$635$	−18.5958	−0.737953
$636$	−1.05025	−0.0416453
$637$	−0.888918	−0.0352202
$638$	−1.57091	−0.0621931
$639$	−22.3727	−0.885051
$640$	−17.6154	−0.696310
$641$	20.8478	0.823437	0.411719	−	0.911311i	$-0.364929\pi$
$641$	20.8478	0.823437	0.411719	+	0.911311i	$0.364929\pi$
$642$	−0.204507	−0.00807124
$643$	7.69091	0.303300	0.151650	−	0.988434i	$-0.451541\pi$
$643$	7.69091	0.303300	0.151650	+	0.988434i	$0.451541\pi$
$644$	5.19231	0.204606
$645$	1.23488	0.0486234
$646$	5.74296	0.225954
$647$	0.0550437	0.00216399	0.00108200	−	0.999999i	$-0.499656\pi$
$647$	0.0550437	0.00216399	0.00108200	+	0.999999i	$0.499656\pi$
$648$	−23.2082	−0.911704
$649$	−0.520161	−0.0204181
$650$	−0.205680	−0.00806743
$651$	0.697642	0.0273427
$652$	23.1064	0.904916
$653$	−23.4144	−0.916277	−0.458139	−	0.888881i	$-0.651484\pi$
$653$	−23.4144	−0.916277	−0.458139	+	0.888881i	$0.651484\pi$
$654$	0.0221483	0.000866066 0
$655$	27.8307	1.08743
$656$	−10.7265	−0.418799
$657$	−13.7647	−0.537013
$658$	0.695186	0.0271012
$659$	30.7548	1.19804	0.599018	−	0.800736i	$-0.295558\pi$
$659$	30.7548	1.19804	0.599018	+	0.800736i	$0.295558\pi$
$660$	−0.0885997	−0.00344874
$661$	48.4980	1.88636	0.943178	−	0.332289i	$-0.107821\pi$
$661$	48.4980	1.88636	0.943178	+	0.332289i	$0.107821\pi$
$662$	21.8107	0.847699
$663$	−0.0103561	−0.000402198 0
$664$	−32.2816	−1.25277
$665$	15.9227	0.617458
$666$	−4.08106	−0.158138
$667$	−12.5374	−0.485450
$668$	−22.0928	−0.854797
$669$	−1.07458	−0.0415456
$670$	−13.1074	−0.506382
$671$	−6.35714	−0.245415
$672$	−0.447659	−0.0172688
$673$	44.8875	1.73029	0.865143	−	0.501525i	$-0.167228\pi$
$673$	44.8875	1.73029	0.865143	+	0.501525i	$0.167228\pi$
$674$	−2.00616	−0.0772742
$675$	0.685179	0.0263725
$676$	18.5518	0.713529
$677$	7.34965	0.282470	0.141235	−	0.989976i	$-0.454893\pi$
$677$	7.34965	0.282470	0.141235	+	0.989976i	$0.454893\pi$
$678$	0.418591	0.0160759
$679$	6.20851	0.238261
$680$	4.68078	0.179500
$681$	−0.784988	−0.0300808
$682$	−3.58855	−0.137413
$683$	34.1717	1.30754	0.653772	−	0.756692i	$-0.273186\pi$
$683$	34.1717	1.30754	0.653772	+	0.756692i	$0.273186\pi$
$684$	−32.5740	−1.24550
$685$	−5.70014	−0.217791
$686$	11.0730	0.422769
$687$	−0.340735	−0.0129999
$688$	9.36850	0.357171
$689$	1.75077	0.0666989
$690$	0.282012	0.0107360
$691$	29.2811	1.11391	0.556953	−	0.830544i	$-0.311971\pi$
$691$	29.2811	1.11391	0.556953	+	0.830544i	$0.311971\pi$
$692$	−26.4183	−1.00427
$693$	1.80512	0.0685709
$694$	15.4012	0.584622
$695$	−16.9844	−0.644256
$696$	0.682776	0.0258805
$697$	11.8682	0.449541
$698$	−4.71893	−0.178614
$699$	1.36218	0.0515224
$700$	−2.87153	−0.108534
$701$	1.39100	0.0525372	0.0262686	−	0.999655i	$-0.491637\pi$
$701$	1.39100	0.0525372	0.0262686	+	0.999655i	$0.491637\pi$
$702$	−0.0468875	−0.00176966
$703$	−13.7205	−0.517478
$704$	1.36244	0.0513490
$705$	−0.0946734	−0.00356561
$706$	−14.4479	−0.543752
$707$	6.24982	0.235049
$708$	0.0942465	0.00354200
$709$	−10.5714	−0.397016	−0.198508	−	0.980099i	$-0.563610\pi$
$709$	−10.5714	−0.397016	−0.198508	+	0.980099i	$0.563610\pi$
$710$	10.1925	0.382517
$711$	−9.13915	−0.342745
$712$	25.4781	0.954833
$713$	−28.6401	−1.07258
$714$	0.0576631	0.00215799
$715$	0.147695	0.00552348
$716$	−15.7930	−0.590213
$717$	0.269136	0.0100511
$718$	0.685020	0.0255647
$719$	19.9639	0.744529	0.372264	−	0.928127i	$-0.378581\pi$
$719$	19.9639	0.744529	0.372264	+	0.928127i	$0.378581\pi$
$720$	−4.89320	−0.182359
$721$	−3.60880	−0.134399
$722$	29.3290	1.09151
$723$	−1.64263	−0.0610902
$724$	−24.7226	−0.918808
$725$	6.93362	0.257508
$726$	−0.534070	−0.0198212
$727$	46.3639	1.71954	0.859770	−	0.510681i	$-0.170607\pi$
$727$	46.3639	1.71954	0.859770	+	0.510681i	$0.170607\pi$
$728$	0.471373	0.0174702
$729$	−26.7656	−0.991320
$730$	6.27089	0.232096
$731$	−10.3657	−0.383389
$732$	1.15183	0.0425730
$733$	9.91306	0.366147	0.183074	−	0.983099i	$-0.441395\pi$
$733$	9.91306	0.366147	0.183074	+	0.983099i	$0.441395\pi$
$734$	−3.04807	−0.112506
$735$	−0.674047	−0.0248626
$736$	18.3776	0.677408
$737$	−4.99575	−0.184021
$738$	26.8473	0.988264
$739$	4.61939	0.169927	0.0849636	−	0.996384i	$-0.472923\pi$
$739$	4.61939	0.169927	0.0849636	+	0.996384i	$0.472923\pi$
$740$	−4.66180	−0.171371
$741$	−0.0787606	−0.00289334
$742$	−9.74832	−0.357872
$743$	25.4219	0.932641	0.466320	−	0.884616i	$-0.345579\pi$
$743$	25.4219	0.932641	0.466320	+	0.884616i	$0.345579\pi$
$744$	1.55971	0.0571819
$745$	27.0690	0.991733
$746$	8.59743	0.314774
$747$	−37.3385	−1.36615
$748$	0.743712	0.0271928
$749$	4.75951	0.173909
$750$	−0.605764	−0.0221194
$751$	−37.4743	−1.36746	−0.683729	−	0.729736i	$-0.739643\pi$
$751$	−37.4743	−1.36746	−0.683729	+	0.729736i	$0.739643\pi$
$752$	−0.718245	−0.0261917
$753$	−0.418549	−0.0152528
$754$	−0.474475	−0.0172794
$755$	35.6317	1.29677
$756$	−0.654603	−0.0238077
$757$	−39.2886	−1.42797	−0.713984	−	0.700162i	$-0.753111\pi$
$757$	−39.2886	−1.42797	−0.713984	+	0.700162i	$0.753111\pi$
$758$	−12.1157	−0.440064
$759$	0.107486	0.00390150
$760$	35.5984	1.29129
$761$	26.1231	0.946963	0.473482	−	0.880804i	$-0.342997\pi$
$761$	26.1231	0.946963	0.473482	+	0.880804i	$0.342997\pi$
$762$	−0.512162	−0.0185537
$763$	−0.515460	−0.0186609
$764$	−6.81494	−0.246556
$765$	5.41404	0.195745
$766$	16.3048	0.589116
$767$	−0.157108	−0.00567285
$768$	−0.830469	−0.0299670
$769$	−47.8509	−1.72555	−0.862774	−	0.505590i	$-0.831275\pi$
$769$	−47.8509	−1.72555	−0.862774	+	0.505590i	$0.831275\pi$
$770$	−0.822370	−0.0296362
$771$	−1.32003	−0.0475398
$772$	−2.59017	−0.0932223
$773$	−0.420600	−0.0151279	−0.00756397	−	0.999971i	$-0.502408\pi$
$773$	−0.420600	−0.0151279	−0.00756397	+	0.999971i	$0.502408\pi$
$774$	−23.4484	−0.842837
$775$	15.8390	0.568953
$776$	13.8803	0.498275
$777$	−0.137763	−0.00494221
$778$	−14.3157	−0.513243
$779$	90.2605	3.23392
$780$	−0.0267605	−0.000958178 0
$781$	3.88476	0.139008
$782$	−2.36723	−0.0846520
$783$	1.58061	0.0564865
$784$	−5.11369	−0.182632
$785$	36.3636	1.29787
$786$	0.766507	0.0273404
$787$	7.11411	0.253591	0.126795	−	0.991929i	$-0.459531\pi$
$787$	7.11411	0.253591	0.126795	+	0.991929i	$0.459531\pi$
$788$	17.5125	0.623856
$789$	−0.359850	−0.0128110
$790$	4.16358	0.148134
$791$	−9.74191	−0.346383
$792$	4.03570	0.143402
$793$	−1.92010	−0.0681847
$794$	−22.1286	−0.785316
$795$	1.32757	0.0470840
$796$	−14.2249	−0.504187
$797$	33.9189	1.20147	0.600734	−	0.799449i	$-0.294875\pi$
$797$	33.9189	1.20147	0.600734	+	0.799449i	$0.294875\pi$
$798$	0.438541	0.0155242
$799$	0.794695	0.0281143
$800$	−10.1635	−0.359333
$801$	29.4693	1.04125
$802$	−24.2894	−0.857687
$803$	2.39009	0.0843444
$804$	0.905165	0.0319227
$805$	−6.56331	−0.231326
$806$	−1.08388	−0.0381780
$807$	−0.335278	−0.0118023
$808$	13.9727	0.491558
$809$	−16.8816	−0.593527	−0.296764	−	0.954951i	$-0.595907\pi$
$809$	−16.8816	−0.593527	−0.296764	+	0.954951i	$0.595907\pi$
$810$	12.2294	0.429697
$811$	30.3778	1.06671	0.533354	−	0.845892i	$-0.320931\pi$
$811$	30.3778	1.06671	0.533354	+	0.845892i	$0.320931\pi$
$812$	−6.62422	−0.232464
$813$	−1.58398	−0.0555527
$814$	0.708629	0.0248374
$815$	−29.2075	−1.02309
$816$	−0.0595758	−0.00208557
$817$	−78.8335	−2.75803
$818$	21.7681	0.761103
$819$	0.545214	0.0190513
$820$	30.6678	1.07096
$821$	−21.1793	−0.739162	−0.369581	−	0.929199i	$-0.620499\pi$
$821$	−21.1793	−0.739162	−0.369581	+	0.929199i	$0.620499\pi$
$822$	−0.156992	−0.00547573
$823$	−53.6953	−1.87170	−0.935851	−	0.352396i	$-0.885367\pi$
$823$	−53.6953	−1.87170	−0.935851	+	0.352396i	$0.885367\pi$
$824$	−8.06818	−0.281068
$825$	−0.0594436	−0.00206956
$826$	0.874783	0.0304376
$827$	−26.3078	−0.914812	−0.457406	−	0.889258i	$-0.651221\pi$
$827$	−26.3078	−0.914812	−0.457406	+	0.889258i	$0.651221\pi$
$828$	13.4269	0.466617
$829$	−11.1846	−0.388456	−0.194228	−	0.980956i	$-0.562220\pi$
$829$	−11.1846	−0.388456	−0.194228	+	0.980956i	$0.562220\pi$
$830$	17.0106	0.590445
$831$	1.74984	0.0607013
$832$	0.411509	0.0142665
$833$	5.65800	0.196038
$834$	−0.467781	−0.0161979
$835$	27.9263	0.966429
$836$	5.65610	0.195620
$837$	3.61071	0.124804
$838$	−2.64387	−0.0913311
$839$	36.9151	1.27445	0.637225	−	0.770678i	$-0.280082\pi$
$839$	36.9151	1.27445	0.637225	+	0.770678i	$0.280082\pi$
$840$	0.357432	0.0123326
$841$	−13.0051	−0.448451
$842$	4.50321	0.155191
$843$	−2.13533	−0.0735448
$844$	−1.51102	−0.0520114
$845$	−23.4502	−0.806713
$846$	1.79770	0.0618061
$847$	12.4295	0.427082
$848$	10.0717	0.345862
$849$	0.221444	0.00759993
$850$	1.30916	0.0449039
$851$	5.65554	0.193870
$852$	−0.703869	−0.0241142
$853$	49.8232	1.70591	0.852957	−	0.521980i	$-0.174807\pi$
$853$	49.8232	1.70591	0.852957	+	0.521980i	$0.174807\pi$
$854$	10.6912	0.365844
$855$	41.1750	1.40815
$856$	10.6408	0.363696
$857$	34.8365	1.18999	0.594996	−	0.803729i	$-0.297154\pi$
$857$	34.8365	1.18999	0.594996	+	0.803729i	$0.297154\pi$
$858$	0.00406779	0.000138872 0
$859$	−52.8534	−1.80333	−0.901667	−	0.432431i	$-0.857656\pi$
$859$	−52.8534	−1.80333	−0.901667	+	0.432431i	$0.857656\pi$
$860$	−26.7852	−0.913368
$861$	0.906275	0.0308858
$862$	−14.2510	−0.485391
$863$	5.20228	0.177088	0.0885438	−	0.996072i	$-0.471779\pi$
$863$	5.20228	0.177088	0.0885438	+	0.996072i	$0.471779\pi$
$864$	−2.31690	−0.0788225
$865$	33.3938	1.13542
$866$	−11.9753	−0.406938
$867$	0.0659171	0.00223866
$868$	−15.1322	−0.513620
$869$	1.58691	0.0538322
$870$	−0.359784	−0.0121978
$871$	−1.50890	−0.0511273
$872$	−1.15241	−0.0390256
$873$	16.0547	0.543369
$874$	−18.0033	−0.608972
$875$	14.0980	0.476600
$876$	−0.433053	−0.0146315
$877$	−34.3183	−1.15885	−0.579423	−	0.815027i	$-0.696722\pi$
$877$	−34.3183	−1.15885	−0.579423	+	0.815027i	$0.696722\pi$
$878$	19.4936	0.657879
$879$	−1.39592	−0.0470831
$880$	0.849647	0.0286416
$881$	42.0124	1.41543	0.707717	−	0.706496i	$-0.249725\pi$
$881$	42.0124	1.41543	0.707717	+	0.706496i	$0.249725\pi$
$882$	12.7991	0.430967
$883$	−23.1916	−0.780459	−0.390230	−	0.920718i	$-0.627604\pi$
$883$	−23.1916	−0.780459	−0.390230	+	0.920718i	$0.627604\pi$
$884$	0.224629	0.00755510
$885$	−0.119132	−0.00400457
$886$	−2.53133	−0.0850417
$887$	−57.3009	−1.92398	−0.961988	−	0.273091i	$-0.911954\pi$
$887$	−57.3009	−1.92398	−0.961988	+	0.273091i	$0.911954\pi$
$888$	−0.307996	−0.0103357
$889$	11.9196	0.399771
$890$	−13.4255	−0.450025
$891$	4.66112	0.156153
$892$	23.3081	0.780413
$893$	6.04384	0.202249
$894$	0.745531	0.0249343
$895$	19.9631	0.667291
$896$	11.2912	0.377212
$897$	0.0324649	0.00108397
$898$	6.40524	0.213746
$899$	36.5383	1.21862
$900$	−7.42554	−0.247518
$901$	−11.1437	−0.371251
$902$	−4.66173	−0.155219
$903$	−0.791540	−0.0263408
$904$	−21.7800	−0.724390
$905$	31.2504	1.03880
$906$	0.981363	0.0326036
$907$	54.2908	1.80270	0.901349	−	0.433093i	$-0.142578\pi$
$907$	54.2908	1.80270	0.901349	+	0.433093i	$0.142578\pi$
$908$	17.0268	0.565053
$909$	16.1615	0.536044
$910$	−0.248387	−0.00823394
$911$	−21.1934	−0.702169	−0.351084	−	0.936344i	$-0.614187\pi$
$911$	−21.1934	−0.702169	−0.351084	+	0.936344i	$0.614187\pi$
$912$	−0.453087	−0.0150032
$913$	6.48341	0.214570
$914$	−19.2653	−0.637239
$915$	−1.45597	−0.0481328
$916$	7.39071	0.244196
$917$	−17.8390	−0.589097
$918$	0.298441	0.00985002
$919$	−27.6557	−0.912278	−0.456139	−	0.889909i	$-0.650768\pi$
$919$	−27.6557	−0.912278	−0.456139	+	0.889909i	$0.650768\pi$
$920$	−14.6736	−0.483773
$921$	0.963889	0.0317612
$922$	−14.6381	−0.482082
$923$	1.17335	0.0386211
$924$	0.0567910	0.00186829
$925$	−3.12771	−0.102839
$926$	4.36505	0.143445
$927$	−9.33207	−0.306505
$928$	−23.4457	−0.769643
$929$	43.2446	1.41881	0.709405	−	0.704801i	$-0.248964\pi$
$929$	43.2446	1.41881	0.709405	+	0.704801i	$0.248964\pi$
$930$	−0.821881	−0.0269505
$931$	43.0304	1.41026
$932$	−29.5464	−0.967823
$933$	−0.468417	−0.0153353
$934$	16.2848	0.532854
$935$	−0.940085	−0.0307441
$936$	1.21893	0.0398421
$937$	17.2614	0.563907	0.281953	−	0.959428i	$-0.409018\pi$
$937$	17.2614	0.563907	0.281953	+	0.959428i	$0.409018\pi$
$938$	8.40162	0.274323
$939$	−1.87741	−0.0612670
$940$	2.05351	0.0669782
$941$	−28.8163	−0.939385	−0.469692	−	0.882830i	$-0.655635\pi$
$941$	−28.8163	−0.939385	−0.469692	+	0.882830i	$0.655635\pi$
$942$	1.00152	0.0326312
$943$	−37.2051	−1.21156
$944$	−0.903798	−0.0294161
$945$	0.827447	0.0269169
$946$	4.07155	0.132378
$947$	54.2389	1.76253	0.881263	−	0.472625i	$-0.156694\pi$
$947$	54.2389	1.76253	0.881263	+	0.472625i	$0.156694\pi$
$948$	−0.287528	−0.00933846
$949$	0.721897	0.0234338
$950$	9.95647	0.323030
$951$	−1.80725	−0.0586042
$952$	−3.00031	−0.0972405
$953$	−15.2601	−0.494323	−0.247162	−	0.968974i	$-0.579498\pi$
$953$	−15.2601	−0.494323	−0.247162	+	0.968974i	$0.579498\pi$
$954$	−25.2084	−0.816152
$955$	8.61439	0.278755
$956$	−5.83770	−0.188805
$957$	−0.137128	−0.00443272
$958$	−29.3731	−0.949001
$959$	3.65370	0.117984
$960$	0.312038	0.0100710
$961$	52.4672	1.69249
$962$	0.214033	0.00690069
$963$	12.3077	0.396611
$964$	35.6295	1.14755
$965$	3.27409	0.105397
$966$	−0.180765	−0.00581603
$967$	3.96802	0.127603	0.0638015	−	0.997963i	$-0.479678\pi$
$967$	3.96802	0.127603	0.0638015	+	0.997963i	$0.479678\pi$
$968$	27.7886	0.893158
$969$	0.501314	0.0161045
$970$	−7.31414	−0.234843
$971$	6.60487	0.211960	0.105980	−	0.994368i	$-0.466202\pi$
$971$	6.60487	0.211960	0.105980	+	0.994368i	$0.466202\pi$
$972$	−2.53974	−0.0814623
$973$	10.8867	0.349013
$974$	−6.81868	−0.218484
$975$	−0.0179542	−0.000574995 0
$976$	−11.0458	−0.353566
$977$	19.0505	0.609480	0.304740	−	0.952436i	$-0.401430\pi$
$977$	19.0505	0.609480	0.304740	+	0.952436i	$0.401430\pi$
$978$	−0.804427	−0.0257227
$979$	−5.11701	−0.163540
$980$	14.6204	0.467032
$981$	−1.33294	−0.0425574
$982$	−27.0369	−0.862784
$983$	−22.2501	−0.709667	−0.354834	−	0.934929i	$-0.615462\pi$
$983$	−22.2501	−0.709667	−0.354834	+	0.934929i	$0.615462\pi$
$984$	2.02616	0.0645915
$985$	−22.1365	−0.705328
$986$	3.02005	0.0961781
$987$	0.0606841	0.00193160
$988$	1.70836	0.0543500
$989$	32.4949	1.03328
$990$	−2.12658	−0.0675873
$991$	31.3686	0.996457	0.498228	−	0.867046i	$-0.333984\pi$
$991$	31.3686	0.996457	0.498228	+	0.867046i	$0.333984\pi$
$992$	−53.5588	−1.70049
$993$	1.90390	0.0604185
$994$	−6.53322	−0.207221
$995$	17.9808	0.570031
$996$	−1.17471	−0.0372221
$997$	17.8451	0.565159	0.282579	−	0.959244i	$-0.408810\pi$
$997$	17.8451	0.565159	0.282579	+	0.959244i	$0.408810\pi$
$998$	−21.7026	−0.686983
$999$	−0.713004	−0.0225585

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.g.1.6	✓	10
3.2	odd	2		9027.2.a.j.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.g.1.6	✓	10	1.1	even	1	trivial
9027.2.a.j.1.5		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q+0.755134 q^{2} +0.0659171 q^{3} -1.42977 q^{4} +1.80730 q^{5} +0.0497762 q^{6} -1.15845 q^{7} -2.58994 q^{8} -2.99565 q^{9} +O(q^{10})\)	\(q+0.755134 q^{2} +0.0659171 q^{3} -1.42977 q^{4} +1.80730 q^{5} +0.0497762 q^{6} -1.15845 q^{7} -2.58994 q^{8} -2.99565 q^{9} +1.36475 q^{10} +0.520161 q^{11} -0.0942465 q^{12} +0.157108 q^{13} -0.874783 q^{14} +0.119132 q^{15} +0.903798 q^{16} -1.00000 q^{17} -2.26212 q^{18} -7.60523 q^{19} -2.58402 q^{20} -0.0763615 q^{21} +0.392791 q^{22} +3.13485 q^{23} -0.170721 q^{24} -1.73368 q^{25} +0.118638 q^{26} -0.395216 q^{27} +1.65632 q^{28} -3.99936 q^{29} +0.0899603 q^{30} -9.13604 q^{31} +5.86236 q^{32} +0.0342875 q^{33} -0.755134 q^{34} -2.09366 q^{35} +4.28311 q^{36} +1.80409 q^{37} -5.74296 q^{38} +0.0103561 q^{39} -4.68078 q^{40} -11.8682 q^{41} -0.0576631 q^{42} +10.3657 q^{43} -0.743712 q^{44} -5.41404 q^{45} +2.36723 q^{46} -0.794695 q^{47} +0.0595758 q^{48} -5.65800 q^{49} -1.30916 q^{50} -0.0659171 q^{51} -0.224629 q^{52} +11.1437 q^{53} -0.298441 q^{54} +0.940085 q^{55} +3.00031 q^{56} -0.501314 q^{57} -3.02005 q^{58} -1.00000 q^{59} -0.170331 q^{60} -12.2215 q^{61} -6.89893 q^{62} +3.47031 q^{63} +2.61927 q^{64} +0.283941 q^{65} +0.0258916 q^{66} -9.60423 q^{67} +1.42977 q^{68} +0.206640 q^{69} -1.58099 q^{70} +7.46839 q^{71} +7.75856 q^{72} +4.59490 q^{73} +1.36233 q^{74} -0.114279 q^{75} +10.8737 q^{76} -0.602580 q^{77} +0.00782025 q^{78} +3.05080 q^{79} +1.63343 q^{80} +8.96091 q^{81} -8.96209 q^{82} +12.4642 q^{83} +0.109180 q^{84} -1.80730 q^{85} +7.82748 q^{86} -0.263626 q^{87} -1.34718 q^{88} -9.83735 q^{89} -4.08832 q^{90} -0.182002 q^{91} -4.48213 q^{92} -0.602221 q^{93} -0.600101 q^{94} -13.7449 q^{95} +0.386430 q^{96} -5.35933 q^{97} -4.27254 q^{98} -1.55822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9} + 4 q^{10} + 12 q^{11} - 24 q^{12} - 11 q^{13} - 12 q^{14} + 9 q^{15} - 3 q^{16} - 10 q^{17} - 22 q^{18} - 5 q^{19} - 36 q^{20} - 10 q^{21} + 6 q^{22} - 7 q^{23} + 35 q^{24} + 2 q^{25} + q^{26} - 31 q^{27} - 4 q^{28} + 10 q^{29} - 9 q^{30} + 13 q^{31} - 15 q^{32} - 9 q^{33} + q^{34} - 8 q^{35} + 40 q^{36} + 12 q^{37} - 50 q^{38} + 24 q^{39} + 5 q^{40} - 29 q^{41} - 17 q^{42} - 18 q^{43} - 6 q^{44} - 14 q^{45} + 11 q^{46} - 18 q^{47} - 43 q^{48} - 9 q^{49} - 31 q^{50} + 7 q^{51} - 68 q^{52} + 19 q^{54} - 27 q^{55} - 7 q^{56} + 20 q^{57} + 23 q^{58} - 10 q^{59} + 38 q^{60} + 8 q^{61} - 46 q^{62} + 39 q^{63} - 20 q^{64} + 58 q^{65} - 34 q^{66} - 6 q^{67} - 15 q^{68} + 6 q^{69} + 73 q^{70} + 8 q^{71} - 70 q^{72} - 41 q^{73} - 10 q^{74} + 10 q^{75} + 12 q^{76} - 22 q^{77} - 43 q^{78} + 3 q^{79} - 15 q^{80} + 26 q^{81} + 8 q^{82} - 22 q^{84} + 12 q^{85} - 29 q^{86} - 28 q^{87} + 33 q^{88} - 45 q^{89} + 56 q^{90} - 14 q^{91} + 36 q^{92} - 19 q^{93} + 15 q^{94} - 17 q^{95} + 90 q^{96} - 5 q^{97} + 30 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9 + 4 * q^10 + 12 * q^11 - 24 * q^12 - 11 * q^13 - 12 * q^14 + 9 * q^15 - 3 * q^16 - 10 * q^17 - 22 * q^18 - 5 * q^19 - 36 * q^20 - 10 * q^21 + 6 * q^22 - 7 * q^23 + 35 * q^24 + 2 * q^25 + q^26 - 31 * q^27 - 4 * q^28 + 10 * q^29 - 9 * q^30 + 13 * q^31 - 15 * q^32 - 9 * q^33 + q^34 - 8 * q^35 + 40 * q^36 + 12 * q^37 - 50 * q^38 + 24 * q^39 + 5 * q^40 - 29 * q^41 - 17 * q^42 - 18 * q^43 - 6 * q^44 - 14 * q^45 + 11 * q^46 - 18 * q^47 - 43 * q^48 - 9 * q^49 - 31 * q^50 + 7 * q^51 - 68 * q^52 + 19 * q^54 - 27 * q^55 - 7 * q^56 + 20 * q^57 + 23 * q^58 - 10 * q^59 + 38 * q^60 + 8 * q^61 - 46 * q^62 + 39 * q^63 - 20 * q^64 + 58 * q^65 - 34 * q^66 - 6 * q^67 - 15 * q^68 + 6 * q^69 + 73 * q^70 + 8 * q^71 - 70 * q^72 - 41 * q^73 - 10 * q^74 + 10 * q^75 + 12 * q^76 - 22 * q^77 - 43 * q^78 + 3 * q^79 - 15 * q^80 + 26 * q^81 + 8 * q^82 - 22 * q^84 + 12 * q^85 - 29 * q^86 - 28 * q^87 + 33 * q^88 - 45 * q^89 + 56 * q^90 - 14 * q^91 + 36 * q^92 - 19 * q^93 + 15 * q^94 - 17 * q^95 + 90 * q^96 - 5 * q^97 + 30 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more