LMFDB - Embedded newform 1003.2.a.g.1.7

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			1.7
Root			$2.16584$ 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)

$f(q)$	$=$	$q+1.26414 q^{2} +1.16584 q^{3} -0.401948 q^{4} -0.0160405 q^{5} +1.47379 q^{6} -4.37637 q^{7} -3.03640 q^{8} -1.64081 q^{9} +O(q^{10})$	\(q+1.26414 q^{2} +1.16584 q^{3} -0.401948 q^{4} -0.0160405 q^{5} +1.47379 q^{6} -4.37637 q^{7} -3.03640 q^{8} -1.64081 q^{9} -0.0202774 q^{10} +0.663918 q^{11} -0.468609 q^{12} +1.57500 q^{13} -5.53235 q^{14} -0.0187007 q^{15} -3.03454 q^{16} -1.00000 q^{17} -2.07421 q^{18} +0.0656888 q^{19} +0.00644743 q^{20} -5.10216 q^{21} +0.839286 q^{22} -2.93400 q^{23} -3.53997 q^{24} -4.99974 q^{25} +1.99102 q^{26} -5.41046 q^{27} +1.75907 q^{28} -1.44206 q^{29} -0.0236403 q^{30} +4.16584 q^{31} +2.23671 q^{32} +0.774025 q^{33} -1.26414 q^{34} +0.0701990 q^{35} +0.659520 q^{36} -9.93621 q^{37} +0.0830399 q^{38} +1.83620 q^{39} +0.0487053 q^{40} +4.78704 q^{41} -6.44985 q^{42} -8.46387 q^{43} -0.266861 q^{44} +0.0263193 q^{45} -3.70899 q^{46} -2.38278 q^{47} -3.53780 q^{48} +12.1526 q^{49} -6.32038 q^{50} -1.16584 q^{51} -0.633067 q^{52} -7.47636 q^{53} -6.83958 q^{54} -0.0106496 q^{55} +13.2884 q^{56} +0.0765829 q^{57} -1.82296 q^{58} -1.00000 q^{59} +0.00751670 q^{60} +12.7312 q^{61} +5.26621 q^{62} +7.18078 q^{63} +8.89660 q^{64} -0.0252637 q^{65} +0.978476 q^{66} +11.6837 q^{67} +0.401948 q^{68} -3.42059 q^{69} +0.0887414 q^{70} +9.79270 q^{71} +4.98215 q^{72} -7.48558 q^{73} -12.5608 q^{74} -5.82892 q^{75} -0.0264035 q^{76} -2.90555 q^{77} +2.32122 q^{78} -0.452397 q^{79} +0.0486754 q^{80} -1.38532 q^{81} +6.05149 q^{82} +12.2586 q^{83} +2.05080 q^{84} +0.0160405 q^{85} -10.6995 q^{86} -1.68121 q^{87} -2.01592 q^{88} +1.86002 q^{89} +0.0332713 q^{90} -6.89277 q^{91} +1.17932 q^{92} +4.85672 q^{93} -3.01217 q^{94} -0.00105368 q^{95} +2.60766 q^{96} +9.33415 q^{97} +15.3626 q^{98} -1.08936 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.26414	0.893883	0.446941	−	0.894563i	$-0.352513\pi$
$2$	1.26414	0.893883	0.446941	+	0.894563i	$0.352513\pi$
$3$	1.16584	0.673100	0.336550	−	0.941666i	$-0.390740\pi$
$3$	1.16584	0.673100	0.336550	+	0.941666i	$0.390740\pi$
$4$	−0.401948	−0.200974
$5$	−0.0160405	−0.00717351	−0.00358676	−	0.999994i	$-0.501142\pi$
$5$	−0.0160405	−0.00717351	−0.00358676	+	0.999994i	$0.501142\pi$
$6$	1.47379	0.601672
$7$	−4.37637	−1.65411	−0.827056	−	0.562119i	$-0.809986\pi$
$7$	−4.37637	−1.65411	−0.827056	+	0.562119i	$0.809986\pi$
$8$	−3.03640	−1.07353
$9$	−1.64081	−0.546936
$10$	−0.0202774	−0.00641228
$11$	0.663918	0.200179	0.100089	−	0.994978i	$-0.468087\pi$
$11$	0.663918	0.200179	0.100089	+	0.994978i	$0.468087\pi$
$12$	−0.468609	−0.135276
$13$	1.57500	0.436826	0.218413	−	0.975856i	$-0.429912\pi$
$13$	1.57500	0.436826	0.218413	+	0.975856i	$0.429912\pi$
$14$	−5.53235	−1.47858
$15$	−0.0187007	−0.00482849
$16$	−3.03454	−0.758635
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.07421	−0.488897
$19$	0.0656888	0.0150701	0.00753503	−	0.999972i	$-0.497602\pi$
$19$	0.0656888	0.0150701	0.00753503	+	0.999972i	$0.497602\pi$
$20$	0.00644743	0.00144169
$21$	−5.10216	−1.11338
$22$	0.839286	0.178936
$23$	−2.93400	−0.611781	−0.305891	−	0.952067i	$-0.598954\pi$
$23$	−2.93400	−0.611781	−0.305891	+	0.952067i	$0.598954\pi$
$24$	−3.53997	−0.722593
$25$	−4.99974	−0.999949
$26$	1.99102	0.390471
$27$	−5.41046	−1.04124
$28$	1.75907	0.332434
$29$	−1.44206	−0.267783	−0.133892	−	0.990996i	$-0.542747\pi$
$29$	−1.44206	−0.267783	−0.133892	+	0.990996i	$0.542747\pi$
$30$	−0.0236403	−0.00431610
$31$	4.16584	0.748207	0.374104	−	0.927387i	$-0.377950\pi$
$31$	4.16584	0.748207	0.374104	+	0.927387i	$0.377950\pi$
$32$	2.23671	0.395399
$33$	0.774025	0.134740
$34$	−1.26414	−0.216798
$35$	0.0701990	0.0118658
$36$	0.659520	0.109920
$37$	−9.93621	−1.63350	−0.816751	−	0.576990i	$-0.804227\pi$
$37$	−9.93621	−1.63350	−0.816751	+	0.576990i	$0.804227\pi$
$38$	0.0830399	0.0134709
$39$	1.83620	0.294028
$40$	0.0487053	0.00770098
$41$	4.78704	0.747610	0.373805	−	0.927507i	$-0.378053\pi$
$41$	4.78704	0.747610	0.373805	+	0.927507i	$0.378053\pi$
$42$	−6.44985	−0.995234
$43$	−8.46387	−1.29073	−0.645364	−	0.763875i	$-0.723294\pi$
$43$	−8.46387	−1.29073	−0.645364	+	0.763875i	$0.723294\pi$
$44$	−0.266861	−0.0402308
$45$	0.0263193	0.00392345
$46$	−3.70899	−0.546861
$47$	−2.38278	−0.347565	−0.173782	−	0.984784i	$-0.555599\pi$
$47$	−2.38278	−0.347565	−0.173782	+	0.984784i	$0.555599\pi$
$48$	−3.53780	−0.510638
$49$	12.1526	1.73609
$50$	−6.32038	−0.893837
$51$	−1.16584	−0.163251
$52$	−0.633067	−0.0877907
$53$	−7.47636	−1.02696	−0.513478	−	0.858102i	$-0.671643\pi$
$53$	−7.47636	−1.02696	−0.513478	+	0.858102i	$0.671643\pi$
$54$	−6.83958	−0.930749
$55$	−0.0106496	−0.00143599
$56$	13.2884	1.77574
$57$	0.0765829	0.0101437
$58$	−1.82296	−0.239367
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	0.00751670	0.000970401 0
$61$	12.7312	1.63006	0.815032	−	0.579416i	$-0.196719\pi$
$61$	12.7312	1.63006	0.815032	+	0.579416i	$0.196719\pi$
$62$	5.26621	0.668810
$63$	7.18078	0.904694
$64$	8.89660	1.11208
$65$	−0.0252637	−0.00313357
$66$	0.978476	0.120442
$67$	11.6837	1.42740	0.713698	−	0.700453i	$-0.247019\pi$
$67$	11.6837	1.42740	0.713698	+	0.700453i	$0.247019\pi$
$68$	0.401948	0.0487434
$69$	−3.42059	−0.411790
$70$	0.0887414	0.0106066
$71$	9.79270	1.16218	0.581090	−	0.813840i	$-0.302627\pi$
$71$	9.79270	1.16218	0.581090	+	0.813840i	$0.302627\pi$
$72$	4.98215	0.587152
$73$	−7.48558	−0.876121	−0.438060	−	0.898946i	$-0.644334\pi$
$73$	−7.48558	−0.876121	−0.438060	+	0.898946i	$0.644334\pi$
$74$	−12.5608	−1.46016
$75$	−5.82892	−0.673066
$76$	−0.0264035	−0.00302869
$77$	−2.90555	−0.331118
$78$	2.32122	0.262826
$79$	−0.452397	−0.0508987	−0.0254493	−	0.999676i	$-0.508102\pi$
$79$	−0.452397	−0.0508987	−0.0254493	+	0.999676i	$0.508102\pi$
$80$	0.0486754	0.00544208
$81$	−1.38532	−0.153925
$82$	6.05149	0.668276
$83$	12.2586	1.34556	0.672780	−	0.739842i	$-0.265100\pi$
$83$	12.2586	1.34556	0.672780	+	0.739842i	$0.265100\pi$
$84$	2.05080	0.223761
$85$	0.0160405	0.00173983
$86$	−10.6995	−1.15376
$87$	−1.68121	−0.180245
$88$	−2.01592	−0.214898
$89$	1.86002	0.197162	0.0985810	−	0.995129i	$-0.468570\pi$
$89$	1.86002	0.197162	0.0985810	+	0.995129i	$0.468570\pi$
$90$	0.0332713	0.00350711
$91$	−6.89277	−0.722559
$92$	1.17932	0.122952
$93$	4.85672	0.503619
$94$	−3.01217	−0.310682
$95$	−0.00105368	−0.000108105 0
$96$	2.60766	0.266143
$97$	9.33415	0.947739	0.473870	−	0.880595i	$-0.342857\pi$
$97$	9.33415	0.947739	0.473870	+	0.880595i	$0.342857\pi$
$98$	15.3626	1.55186
$99$	−1.08936	−0.109485
$100$	2.00964	0.200964
$101$	5.81958	0.579070	0.289535	−	0.957167i	$-0.406499\pi$
$101$	5.81958	0.579070	0.289535	+	0.957167i	$0.406499\pi$
$102$	−1.47379	−0.145927
$103$	0.159802	0.0157457	0.00787287	−	0.999969i	$-0.497494\pi$
$103$	0.159802	0.0157457	0.00787287	+	0.999969i	$0.497494\pi$
$104$	−4.78232	−0.468945
$105$	0.0818410	0.00798687
$106$	−9.45117	−0.917979
$107$	0.431732	0.0417371	0.0208685	−	0.999782i	$-0.493357\pi$
$107$	0.431732	0.0417371	0.0208685	+	0.999782i	$0.493357\pi$
$108$	2.17472	0.209263
$109$	−14.8582	−1.42315	−0.711577	−	0.702608i	$-0.752019\pi$
$109$	−14.8582	−1.42315	−0.711577	+	0.702608i	$0.752019\pi$
$110$	−0.0134625	−0.00128360
$111$	−11.5841	−1.09951
$112$	13.2803	1.25487
$113$	−3.79808	−0.357293	−0.178647	−	0.983913i	$-0.557172\pi$
$113$	−3.79808	−0.357293	−0.178647	+	0.983913i	$0.557172\pi$
$114$	0.0968116	0.00906724
$115$	0.0470627	0.00438862
$116$	0.579632	0.0538175
$117$	−2.58427	−0.238916
$118$	−1.26414	−0.116374
$119$	4.37637	0.401181
$120$	0.0567827	0.00518353
$121$	−10.5592	−0.959928
$122$	16.0940	1.45709
$123$	5.58094	0.503217
$124$	−1.67445	−0.150370
$125$	0.160400	0.0143467
$126$	9.07752	0.808690
$127$	−19.9081	−1.76656	−0.883278	−	0.468849i	$-0.844669\pi$
$127$	−19.9081	−1.76656	−0.883278	+	0.468849i	$0.844669\pi$
$128$	6.77313	0.598666
$129$	−9.86755	−0.868790
$130$	−0.0319369	−0.00280105
$131$	6.36569	0.556173	0.278086	−	0.960556i	$-0.410300\pi$
$131$	6.36569	0.556173	0.278086	+	0.960556i	$0.410300\pi$
$132$	−0.311118	−0.0270793
$133$	−0.287479	−0.0249276
$134$	14.7699	1.27592
$135$	0.0867862	0.00746937
$136$	3.03640	0.260369
$137$	−10.1421	−0.866496	−0.433248	−	0.901275i	$-0.642632\pi$
$137$	−10.1421	−0.866496	−0.433248	+	0.901275i	$0.642632\pi$
$138$	−4.32410	−0.368092
$139$	−4.09938	−0.347705	−0.173853	−	0.984772i	$-0.555622\pi$
$139$	−4.09938	−0.347705	−0.173853	+	0.984772i	$0.555622\pi$
$140$	−0.0282163	−0.00238472
$141$	−2.77795	−0.233946
$142$	12.3793	1.03885
$143$	1.04567	0.0874433
$144$	4.97910	0.414925
$145$	0.0231313	0.00192095
$146$	−9.46283	−0.783149
$147$	14.1680	1.16856
$148$	3.99384	0.328292
$149$	−6.31881	−0.517657	−0.258829	−	0.965923i	$-0.583337\pi$
$149$	−6.31881	−0.517657	−0.258829	+	0.965923i	$0.583337\pi$
$150$	−7.36857	−0.601642
$151$	−4.92486	−0.400779	−0.200390	−	0.979716i	$-0.564221\pi$
$151$	−4.92486	−0.400779	−0.200390	+	0.979716i	$0.564221\pi$
$152$	−0.199458	−0.0161781
$153$	1.64081	0.132651
$154$	−3.67303	−0.295981
$155$	−0.0668220	−0.00536727
$156$	−0.738058	−0.0590919
$157$	−9.80978	−0.782905	−0.391453	−	0.920198i	$-0.628027\pi$
$157$	−9.80978	−0.782905	−0.391453	+	0.920198i	$0.628027\pi$
$158$	−0.571894	−0.0454974
$159$	−8.71627	−0.691245
$160$	−0.0358779	−0.00283640
$161$	12.8403	1.01196
$162$	−1.75124	−0.137591
$163$	−4.44373	−0.348060	−0.174030	−	0.984740i	$-0.555679\pi$
$163$	−4.44373	−0.348060	−0.174030	+	0.984740i	$0.555679\pi$
$164$	−1.92414	−0.150250
$165$	−0.0124157	−0.000966562 0
$166$	15.4966	1.20277
$167$	−4.19121	−0.324326	−0.162163	−	0.986764i	$-0.551847\pi$
$167$	−4.19121	−0.324326	−0.162163	+	0.986764i	$0.551847\pi$
$168$	15.4922	1.19525
$169$	−10.5194	−0.809183
$170$	0.0202774	0.00155521
$171$	−0.107783	−0.00824236
$172$	3.40204	0.259403
$173$	−9.56395	−0.727134	−0.363567	−	0.931568i	$-0.618441\pi$
$173$	−9.56395	−0.727134	−0.363567	+	0.931568i	$0.618441\pi$
$174$	−2.12529	−0.161118
$175$	21.8807	1.65403
$176$	−2.01469	−0.151863
$177$	−1.16584	−0.0876302
$178$	2.35133	0.176240
$179$	−5.94316	−0.444213	−0.222106	−	0.975022i	$-0.571293\pi$
$179$	−5.94316	−0.444213	−0.222106	+	0.975022i	$0.571293\pi$
$180$	−0.0105790	−0.000788512 0
$181$	1.53964	0.114440	0.0572202	−	0.998362i	$-0.481776\pi$
$181$	1.53964	0.114440	0.0572202	+	0.998362i	$0.481776\pi$
$182$	−8.71343	−0.645883
$183$	14.8426	1.09720
$184$	8.90880	0.656766
$185$	0.159381	0.0117179
$186$	6.13958	0.450176
$187$	−0.663918	−0.0485505
$188$	0.957756	0.0698515
$189$	23.6782	1.72233
$190$	−0.00133200	−9.66333e−5 0
$191$	16.0455	1.16101	0.580506	−	0.814256i	$-0.302855\pi$
$191$	16.0455	1.16101	0.580506	+	0.814256i	$0.302855\pi$
$192$	10.3720	0.748538
$193$	4.68069	0.336923	0.168462	−	0.985708i	$-0.446120\pi$
$193$	4.68069	0.336923	0.168462	+	0.985708i	$0.446120\pi$
$194$	11.7997	0.847167
$195$	−0.0294535	−0.00210921
$196$	−4.88472	−0.348908
$197$	−20.1672	−1.43685	−0.718425	−	0.695604i	$-0.755137\pi$
$197$	−20.1672	−1.43685	−0.718425	+	0.695604i	$0.755137\pi$
$198$	−1.37711	−0.0978668
$199$	−2.68031	−0.190002	−0.0950009	−	0.995477i	$-0.530285\pi$
$199$	−2.68031	−0.190002	−0.0950009	+	0.995477i	$0.530285\pi$
$200$	15.1812	1.07347
$201$	13.6214	0.960781
$202$	7.35677	0.517620
$203$	6.31098	0.442944
$204$	0.468609	0.0328092
$205$	−0.0767863	−0.00536299
$206$	0.202012	0.0140748
$207$	4.81413	0.334605
$208$	−4.77940	−0.331391
$209$	0.0436120	0.00301671
$210$	0.103459	0.00713932
$211$	11.2933	0.777463	0.388732	−	0.921351i	$-0.372913\pi$
$211$	11.2933	0.777463	0.388732	+	0.921351i	$0.372913\pi$
$212$	3.00511	0.206392
$213$	11.4168	0.782263
$214$	0.545770	0.0373081
$215$	0.135764	0.00925906
$216$	16.4283	1.11781
$217$	−18.2313	−1.23762
$218$	−18.7828	−1.27213
$219$	−8.72702	−0.589717
$220$	0.00428057	0.000288596 0
$221$	−1.57500	−0.105946
$222$	−14.6439	−0.982833
$223$	−3.38287	−0.226534	−0.113267	−	0.993565i	$-0.536132\pi$
$223$	−3.38287	−0.226534	−0.113267	+	0.993565i	$0.536132\pi$
$224$	−9.78868	−0.654034
$225$	8.20362	0.546908
$226$	−4.80130	−0.319378
$227$	−10.1641	−0.674618	−0.337309	−	0.941394i	$-0.609517\pi$
$227$	−10.1641	−0.674618	−0.337309	+	0.941394i	$0.609517\pi$
$228$	−0.0307824	−0.00203861
$229$	−7.84463	−0.518388	−0.259194	−	0.965825i	$-0.583457\pi$
$229$	−7.84463	−0.518388	−0.259194	+	0.965825i	$0.583457\pi$
$230$	0.0594939	0.00392291
$231$	−3.38742	−0.222876
$232$	4.37866	0.287473
$233$	−6.76367	−0.443103	−0.221551	−	0.975149i	$-0.571112\pi$
$233$	−6.76367	−0.443103	−0.221551	+	0.975149i	$0.571112\pi$
$234$	−3.26688	−0.213563
$235$	0.0382209	0.00249326
$236$	0.401948	0.0261646
$237$	−0.527425	−0.0342599
$238$	5.53235	0.358609
$239$	1.63604	0.105826	0.0529132	−	0.998599i	$-0.483149\pi$
$239$	1.63604	0.105826	0.0529132	+	0.998599i	$0.483149\pi$
$240$	0.0567479	0.00366306
$241$	6.40962	0.412880	0.206440	−	0.978459i	$-0.433812\pi$
$241$	6.40962	0.412880	0.206440	+	0.978459i	$0.433812\pi$
$242$	−13.3483	−0.858063
$243$	14.6163	0.937636
$244$	−5.11728	−0.327600
$245$	−0.194933	−0.0124538
$246$	7.05510	0.449817
$247$	0.103460	0.00658299
$248$	−12.6492	−0.803223
$249$	14.2917	0.905697
$250$	0.202769	0.0128242
$251$	22.7415	1.43543	0.717717	−	0.696335i	$-0.245187\pi$
$251$	22.7415	1.43543	0.717717	+	0.696335i	$0.245187\pi$
$252$	−2.88630	−0.181820
$253$	−1.94794	−0.122466
$254$	−25.1666	−1.57909
$255$	0.0187007	0.00117108
$256$	−9.23101	−0.576938
$257$	−28.9878	−1.80821	−0.904106	−	0.427308i	$-0.859462\pi$
$257$	−28.9878	−1.80821	−0.904106	+	0.427308i	$0.859462\pi$
$258$	−12.4740	−0.776596
$259$	43.4845	2.70200
$260$	0.0101547	0.000629767 0
$261$	2.36614	0.146460
$262$	8.04713	0.497153
$263$	−24.3327	−1.50042	−0.750209	−	0.661201i	$-0.770047\pi$
$263$	−24.3327	−1.50042	−0.750209	+	0.661201i	$0.770047\pi$
$264$	−2.35025	−0.144648
$265$	0.119924	0.00736689
$266$	−0.363413	−0.0222823
$267$	2.16849	0.132710
$268$	−4.69626	−0.286870
$269$	24.1463	1.47223	0.736114	−	0.676857i	$-0.236659\pi$
$269$	24.1463	1.47223	0.736114	+	0.676857i	$0.236659\pi$
$270$	0.109710	0.00667674
$271$	−31.5174	−1.91454	−0.957272	−	0.289188i	$-0.906615\pi$
$271$	−31.5174	−1.91454	−0.957272	+	0.289188i	$0.906615\pi$
$272$	3.03454	0.183996
$273$	−8.03590	−0.486355
$274$	−12.8210	−0.774545
$275$	−3.31942	−0.200169
$276$	1.37490	0.0827592
$277$	−17.2074	−1.03390	−0.516948	−	0.856017i	$-0.672932\pi$
$277$	−17.2074	−1.03390	−0.516948	+	0.856017i	$0.672932\pi$
$278$	−5.18220	−0.310808
$279$	−6.83535	−0.409222
$280$	−0.213152	−0.0127383
$281$	−15.9872	−0.953717	−0.476858	−	0.878980i	$-0.658225\pi$
$281$	−15.9872	−0.953717	−0.476858	+	0.878980i	$0.658225\pi$
$282$	−3.51173	−0.209120
$283$	−3.54428	−0.210685	−0.105343	−	0.994436i	$-0.533594\pi$
$283$	−3.54428	−0.210685	−0.105343	+	0.994436i	$0.533594\pi$
$284$	−3.93616	−0.233568
$285$	−0.00122843	−7.27656e−5 0
$286$	1.32187	0.0781640
$287$	−20.9499	−1.23663
$288$	−3.67002	−0.216258
$289$	1.00000	0.0588235
$290$	0.0292412	0.00171710
$291$	10.8822	0.637923
$292$	3.00881	0.176078
$293$	17.5670	1.02628	0.513139	−	0.858306i	$-0.328483\pi$
$293$	17.5670	1.02628	0.513139	+	0.858306i	$0.328483\pi$
$294$	17.9104	1.04456
$295$	0.0160405	0.000933911 0
$296$	30.1703	1.75361
$297$	−3.59210	−0.208435
$298$	−7.98787	−0.462725
$299$	−4.62105	−0.267242
$300$	2.34292	0.135269
$301$	37.0410	2.13501
$302$	−6.22572	−0.358250
$303$	6.78472	0.389772
$304$	−0.199336	−0.0114327
$305$	−0.204214	−0.0116933
$306$	2.07421	0.118575
$307$	20.5423	1.17241	0.586207	−	0.810161i	$-0.300621\pi$
$307$	20.5423	1.17241	0.586207	+	0.810161i	$0.300621\pi$
$308$	1.16788	0.0665462
$309$	0.186304	0.0105985
$310$	−0.0844724	−0.00479771
$311$	−18.2074	−1.03245	−0.516224	−	0.856453i	$-0.672663\pi$
$311$	−18.2074	−1.03245	−0.516224	+	0.856453i	$0.672663\pi$
$312$	−5.57544	−0.315647
$313$	8.75659	0.494952	0.247476	−	0.968894i	$-0.420399\pi$
$313$	8.75659	0.494952	0.247476	+	0.968894i	$0.420399\pi$
$314$	−12.4009	−0.699825
$315$	−0.115183	−0.00648983
$316$	0.181840	0.0102293
$317$	15.1754	0.852337	0.426169	−	0.904644i	$-0.359863\pi$
$317$	15.1754	0.852337	0.426169	+	0.904644i	$0.359863\pi$
$318$	−11.0186	−0.617892
$319$	−0.957408	−0.0536046
$320$	−0.142706	−0.00797748
$321$	0.503332	0.0280932
$322$	16.2319	0.904569
$323$	−0.0656888	−0.00365502
$324$	0.556828	0.0309349
$325$	−7.87458	−0.436803
$326$	−5.61750	−0.311125
$327$	−17.3223	−0.957926
$328$	−14.5354	−0.802582
$329$	10.4279	0.574911
$330$	−0.0156952	−0.000863993 0
$331$	0.440688	0.0242224	0.0121112	−	0.999927i	$-0.496145\pi$
$331$	0.440688	0.0242224	0.0121112	+	0.999927i	$0.496145\pi$
$332$	−4.92734	−0.270423
$333$	16.3034	0.893422
$334$	−5.29828	−0.289909
$335$	−0.187413	−0.0102394
$336$	15.4827	0.844652
$337$	6.93351	0.377692	0.188846	−	0.982007i	$-0.439525\pi$
$337$	6.93351	0.377692	0.188846	+	0.982007i	$0.439525\pi$
$338$	−13.2980	−0.723315
$339$	−4.42796	−0.240494
$340$	−0.00644743	−0.000349661 0
$341$	2.76578	0.149775
$342$	−0.136253	−0.00736770
$343$	−22.5497	−1.21757
$344$	25.6997	1.38564
$345$	0.0548678	0.00295398
$346$	−12.0902	−0.649972
$347$	5.17603	0.277864	0.138932	−	0.990302i	$-0.455633\pi$
$347$	5.17603	0.277864	0.138932	+	0.990302i	$0.455633\pi$
$348$	0.675761	0.0362246
$349$	17.6743	0.946084	0.473042	−	0.881040i	$-0.343156\pi$
$349$	17.6743	0.946084	0.473042	+	0.881040i	$0.343156\pi$
$350$	27.6603	1.47851
$351$	−8.52146	−0.454842
$352$	1.48499	0.0791505
$353$	14.5115	0.772372	0.386186	−	0.922421i	$-0.373792\pi$
$353$	14.5115	0.772372	0.386186	+	0.922421i	$0.373792\pi$
$354$	−1.47379	−0.0783311
$355$	−0.157079	−0.00833691
$356$	−0.747632	−0.0396244
$357$	5.10216	0.270035
$358$	−7.51300	−0.397074
$359$	−33.3465	−1.75996	−0.879981	−	0.475009i	$-0.842445\pi$
$359$	−33.3465	−1.75996	−0.879981	+	0.475009i	$0.842445\pi$
$360$	−0.0799160	−0.00421194
$361$	−18.9957	−0.999773
$362$	1.94632	0.102296
$363$	−12.3104	−0.646128
$364$	2.77054	0.145216
$365$	0.120072	0.00628486
$366$	18.7631	0.980764
$367$	31.8033	1.66012	0.830059	−	0.557676i	$-0.188307\pi$
$367$	31.8033	1.66012	0.830059	+	0.557676i	$0.188307\pi$
$368$	8.90335	0.464119
$369$	−7.85462	−0.408895
$370$	0.201480	0.0104745
$371$	32.7193	1.69870
$372$	−1.95215	−0.101214
$373$	−4.79332	−0.248189	−0.124094	−	0.992270i	$-0.539603\pi$
$373$	−4.79332	−0.248189	−0.124094	+	0.992270i	$0.539603\pi$
$374$	−0.839286	−0.0433985
$375$	0.187002	0.00965673
$376$	7.23509	0.373121
$377$	−2.27124	−0.116975
$378$	29.9325	1.53956
$379$	21.0121	1.07932	0.539660	−	0.841883i	$-0.318553\pi$
$379$	21.0121	1.07932	0.539660	+	0.841883i	$0.318553\pi$
$380$	0.000423524 0	2.17263e−5 0
$381$	−23.2097	−1.18907
$382$	20.2838	1.03781
$383$	−8.02038	−0.409822	−0.204911	−	0.978781i	$-0.565691\pi$
$383$	−8.02038	−0.409822	−0.204911	+	0.978781i	$0.565691\pi$
$384$	7.89641	0.402962
$385$	0.0466064	0.00237528
$386$	5.91705	0.301170
$387$	13.8876	0.705946
$388$	−3.75184	−0.190471
$389$	−20.0310	−1.01561	−0.507807	−	0.861471i	$-0.669544\pi$
$389$	−20.0310	−1.01561	−0.507807	+	0.861471i	$0.669544\pi$
$390$	−0.0372334	−0.00188539
$391$	2.93400	0.148379
$392$	−36.9002	−1.86374
$393$	7.42140	0.374360
$394$	−25.4941	−1.28438
$395$	0.00725666	0.000365122 0
$396$	0.437867	0.0220037
$397$	13.4825	0.676670	0.338335	−	0.941026i	$-0.390136\pi$
$397$	13.4825	0.676670	0.338335	+	0.941026i	$0.390136\pi$
$398$	−3.38828	−0.169839
$399$	−0.335155	−0.0167787
$400$	15.1719	0.758596
$401$	−33.7190	−1.68384	−0.841922	−	0.539599i	$-0.818576\pi$
$401$	−33.7190	−1.68384	−0.841922	+	0.539599i	$0.818576\pi$
$402$	17.2194	0.858825
$403$	6.56119	0.326836
$404$	−2.33917	−0.116378
$405$	0.0222212	0.00110418
$406$	7.97796	0.395940
$407$	−6.59683	−0.326993
$408$	3.53997	0.175255
$409$	1.78961	0.0884906	0.0442453	−	0.999021i	$-0.485912\pi$
$409$	1.78961	0.0884906	0.0442453	+	0.999021i	$0.485912\pi$
$410$	−0.0970687	−0.00479388
$411$	−11.8241	−0.583238
$412$	−0.0642320	−0.00316449
$413$	4.37637	0.215347
$414$	6.08574	0.299098
$415$	−0.196634	−0.00965239
$416$	3.52282	0.172720
$417$	−4.77924	−0.234041
$418$	0.0551317	0.00269658
$419$	−10.8173	−0.528458	−0.264229	−	0.964460i	$-0.585118\pi$
$419$	−10.8173	−0.528458	−0.264229	+	0.964460i	$0.585118\pi$
$420$	−0.0328958	−0.00160515
$421$	16.7842	0.818014	0.409007	−	0.912531i	$-0.365875\pi$
$421$	16.7842	0.818014	0.409007	+	0.912531i	$0.365875\pi$
$422$	14.2763	0.694961
$423$	3.90969	0.190096
$424$	22.7012	1.10247
$425$	4.99974	0.242523
$426$	14.4324	0.699251
$427$	−55.7164	−2.69631
$428$	−0.173534	−0.00838807
$429$	1.21909	0.0588581
$430$	0.171625	0.00827651
$431$	4.19752	0.202187	0.101094	−	0.994877i	$-0.467766\pi$
$431$	4.19752	0.202187	0.101094	+	0.994877i	$0.467766\pi$
$432$	16.4183	0.789924
$433$	20.7949	0.999341	0.499670	−	0.866216i	$-0.333455\pi$
$433$	20.7949	0.999341	0.499670	+	0.866216i	$0.333455\pi$
$434$	−23.0469	−1.10629
$435$	0.0269674	0.00129299
$436$	5.97222	0.286017
$437$	−0.192731	−0.00921958
$438$	−11.0322	−0.527138
$439$	−3.02172	−0.144219	−0.0721094	−	0.997397i	$-0.522973\pi$
$439$	−3.02172	−0.144219	−0.0721094	+	0.997397i	$0.522973\pi$
$440$	0.0323363	0.00154157
$441$	−19.9401	−0.949529
$442$	−1.99102	−0.0947031
$443$	26.3313	1.25104	0.625518	−	0.780209i	$-0.284888\pi$
$443$	26.3313	1.25104	0.625518	+	0.780209i	$0.284888\pi$
$444$	4.65619	0.220973
$445$	−0.0298356	−0.00141434
$446$	−4.27643	−0.202495
$447$	−7.36675	−0.348435
$448$	−38.9348	−1.83950
$449$	−22.6977	−1.07117	−0.535585	−	0.844481i	$-0.679909\pi$
$449$	−22.6977	−1.07117	−0.535585	+	0.844481i	$0.679909\pi$
$450$	10.3705	0.488871
$451$	3.17820	0.149656
$452$	1.52663	0.0718066
$453$	−5.74162	−0.269765
$454$	−12.8489	−0.603029
$455$	0.110563	0.00518328
$456$	−0.232536	−0.0108895
$457$	32.3543	1.51347	0.756734	−	0.653722i	$-0.226794\pi$
$457$	32.3543	1.51347	0.756734	+	0.653722i	$0.226794\pi$
$458$	−9.91672	−0.463378
$459$	5.41046	0.252539
$460$	−0.0189168	−0.000881999 0
$461$	−27.3252	−1.27266	−0.636331	−	0.771416i	$-0.719549\pi$
$461$	−27.3252	−1.27266	−0.636331	+	0.771416i	$0.719549\pi$
$462$	−4.28217	−0.199225
$463$	−26.2441	−1.21967	−0.609833	−	0.792530i	$-0.708764\pi$
$463$	−26.2441	−1.21967	−0.609833	+	0.792530i	$0.708764\pi$
$464$	4.37598	0.203150
$465$	−0.0779040	−0.00361271
$466$	−8.55023	−0.396082
$467$	−26.2990	−1.21697	−0.608486	−	0.793565i	$-0.708223\pi$
$467$	−26.2990	−1.21697	−0.608486	+	0.793565i	$0.708223\pi$
$468$	1.03874	0.0480159
$469$	−51.1324	−2.36107
$470$	0.0483167	0.00222868
$471$	−11.4367	−0.526974
$472$	3.03640	0.139762
$473$	−5.61932	−0.258377
$474$	−0.666739	−0.0306243
$475$	−0.328427	−0.0150693
$476$	−1.75907	−0.0806270
$477$	12.2673	0.561680
$478$	2.06818	0.0945964
$479$	27.6497	1.26335	0.631673	−	0.775235i	$-0.282369\pi$
$479$	27.6497	1.26335	0.631673	+	0.775235i	$0.282369\pi$
$480$	−0.0418280	−0.00190918
$481$	−15.6495	−0.713556
$482$	8.10266	0.369066
$483$	14.9698	0.681147
$484$	4.24426	0.192921
$485$	−0.149724	−0.00679862
$486$	18.4771	0.838137
$487$	40.0762	1.81603	0.908013	−	0.418943i	$-0.137599\pi$
$487$	40.0762	1.81603	0.908013	+	0.418943i	$0.137599\pi$
$488$	−38.6570	−1.74992
$489$	−5.18070	−0.234279
$490$	−0.246423	−0.0111323
$491$	−7.13626	−0.322055	−0.161028	−	0.986950i	$-0.551481\pi$
$491$	−7.13626	−0.322055	−0.161028	+	0.986950i	$0.551481\pi$
$492$	−2.24325	−0.101133
$493$	1.44206	0.0649470
$494$	0.130788	0.00588442
$495$	0.0174739	0.000785392 0
$496$	−12.6414	−0.567617
$497$	−42.8565	−1.92238
$498$	18.0667	0.809587
$499$	38.8964	1.74124	0.870621	−	0.491954i	$-0.163717\pi$
$499$	38.8964	1.74124	0.870621	+	0.491954i	$0.163717\pi$
$500$	−0.0644727	−0.00288330
$501$	−4.88630	−0.218304
$502$	28.7485	1.28311
$503$	6.13589	0.273586	0.136793	−	0.990600i	$-0.456321\pi$
$503$	6.13589	0.273586	0.136793	+	0.990600i	$0.456321\pi$
$504$	−21.8037	−0.971216
$505$	−0.0933487	−0.00415396
$506$	−2.46247	−0.109470
$507$	−12.2640	−0.544661
$508$	8.00202	0.355032
$509$	−34.1015	−1.51152	−0.755762	−	0.654847i	$-0.772733\pi$
$509$	−34.1015	−1.51152	−0.755762	+	0.654847i	$0.772733\pi$
$510$	0.0236403	0.00104681
$511$	32.7597	1.44920
$512$	−25.2156	−1.11438
$513$	−0.355407	−0.0156916
$514$	−36.6447	−1.61633
$515$	−0.00256329	−0.000112952 0
$516$	3.96624	0.174604
$517$	−1.58197	−0.0695751
$518$	54.9705	2.41527
$519$	−11.1501	−0.489434
$520$	0.0767107	0.00336399
$521$	6.95070	0.304516	0.152258	−	0.988341i	$-0.451346\pi$
$521$	6.95070	0.304516	0.152258	+	0.988341i	$0.451346\pi$
$522$	2.99113	0.130918
$523$	3.29866	0.144240	0.0721201	−	0.997396i	$-0.477024\pi$
$523$	3.29866	0.144240	0.0721201	+	0.997396i	$0.477024\pi$
$524$	−2.55868	−0.111776
$525$	25.5095	1.11333
$526$	−30.7599	−1.34120
$527$	−4.16584	−0.181467
$528$	−2.34881	−0.102219
$529$	−14.3916	−0.625723
$530$	0.151601	0.00658513
$531$	1.64081	0.0712050
$532$	0.115551	0.00500979
$533$	7.53958	0.326575
$534$	2.74128	0.118627
$535$	−0.00692518	−0.000299401 0
$536$	−35.4765	−1.53235
$537$	−6.92880	−0.299000
$538$	30.5244	1.31600
$539$	8.06834	0.347528
$540$	−0.0348836	−0.00150115
$541$	−6.50728	−0.279770	−0.139885	−	0.990168i	$-0.544673\pi$
$541$	−6.50728	−0.279770	−0.139885	+	0.990168i	$0.544673\pi$
$542$	−39.8424	−1.71138
$543$	1.79498	0.0770298
$544$	−2.23671	−0.0958983
$545$	0.238332	0.0102090
$546$	−10.1585	−0.434744
$547$	−38.4717	−1.64493	−0.822466	−	0.568814i	$-0.807402\pi$
$547$	−38.4717	−1.64493	−0.822466	+	0.568814i	$0.807402\pi$
$548$	4.07659	0.174143
$549$	−20.8895	−0.891541
$550$	−4.19621	−0.178927
$551$	−0.0947271	−0.00403551
$552$	10.3863	0.442069
$553$	1.97986	0.0841921
$554$	−21.7526	−0.924181
$555$	0.185814	0.00788735
$556$	1.64774	0.0698797
$557$	−21.5320	−0.912340	−0.456170	−	0.889893i	$-0.650779\pi$
$557$	−21.5320	−0.912340	−0.456170	+	0.889893i	$0.650779\pi$
$558$	−8.64084	−0.365796
$559$	−13.3306	−0.563824
$560$	−0.213022	−0.00900181
$561$	−0.774025	−0.0326794
$562$	−20.2101	−0.852511
$563$	20.3102	0.855974	0.427987	−	0.903785i	$-0.359223\pi$
$563$	20.3102	0.855974	0.427987	+	0.903785i	$0.359223\pi$
$564$	1.11659	0.0470171
$565$	0.0609229	0.00256305
$566$	−4.48046	−0.188328
$567$	6.06268	0.254609
$568$	−29.7346	−1.24763
$569$	40.9880	1.71831	0.859154	−	0.511717i	$-0.170990\pi$
$569$	40.9880	1.71831	0.859154	+	0.511717i	$0.170990\pi$
$570$	−0.00155290	−6.50439e−5 0
$571$	14.8862	0.622968	0.311484	−	0.950251i	$-0.399174\pi$
$571$	14.8862	0.622968	0.311484	+	0.950251i	$0.399174\pi$
$572$	−0.420305	−0.0175738
$573$	18.7066	0.781477
$574$	−26.4836	−1.10540
$575$	14.6693	0.611750
$576$	−14.5976	−0.608234
$577$	−23.0870	−0.961123	−0.480561	−	0.876961i	$-0.659567\pi$
$577$	−23.0870	−0.961123	−0.480561	+	0.876961i	$0.659567\pi$
$578$	1.26414	0.0525813
$579$	5.45695	0.226783
$580$	−0.00929757	−0.000386060 0
$581$	−53.6483	−2.22571
$582$	13.7566	0.570228
$583$	−4.96369	−0.205575
$584$	22.7292	0.940542
$585$	0.0414529	0.00171386
$586$	22.2072	0.917371
$587$	−30.7702	−1.27002	−0.635011	−	0.772503i	$-0.719004\pi$
$587$	−30.7702	−1.27002	−0.635011	+	0.772503i	$0.719004\pi$
$588$	−5.69482	−0.234850
$589$	0.273649	0.0112755
$590$	0.0202774	0.000834807 0
$591$	−23.5117	−0.967144
$592$	30.1518	1.23923
$593$	27.8779	1.14481	0.572404	−	0.819972i	$-0.306011\pi$
$593$	27.8779	1.14481	0.572404	+	0.819972i	$0.306011\pi$
$594$	−4.54092	−0.186316
$595$	−0.0701990	−0.00287788
$596$	2.53983	0.104036
$597$	−3.12482	−0.127890
$598$	−5.84165	−0.238883
$599$	−17.4483	−0.712920	−0.356460	−	0.934311i	$-0.616016\pi$
$599$	−17.4483	−0.712920	−0.356460	+	0.934311i	$0.616016\pi$
$600$	17.6989	0.722556
$601$	36.6746	1.49599	0.747993	−	0.663706i	$-0.231018\pi$
$601$	36.6746	1.49599	0.747993	+	0.663706i	$0.231018\pi$
$602$	46.8251	1.90845
$603$	−19.1708	−0.780695
$604$	1.97954	0.0805463
$605$	0.169375	0.00688606
$606$	8.57684	0.348410
$607$	−29.0684	−1.17985	−0.589925	−	0.807458i	$-0.700843\pi$
$607$	−29.0684	−1.17985	−0.589925	+	0.807458i	$0.700843\pi$
$608$	0.146927	0.00595868
$609$	7.35761	0.298145
$610$	−0.258156	−0.0104524
$611$	−3.75288	−0.151825
$612$	−0.659520	−0.0266595
$613$	−33.3491	−1.34696	−0.673479	−	0.739207i	$-0.735201\pi$
$613$	−33.3491	−1.34696	−0.673479	+	0.739207i	$0.735201\pi$
$614$	25.9684	1.04800
$615$	−0.0895209	−0.00360983
$616$	8.82242	0.355465
$617$	−18.7082	−0.753163	−0.376582	−	0.926383i	$-0.622901\pi$
$617$	−18.7082	−0.753163	−0.376582	+	0.926383i	$0.622901\pi$
$618$	0.235514	0.00947378
$619$	6.02285	0.242079	0.121039	−	0.992648i	$-0.461377\pi$
$619$	6.02285	0.242079	0.121039	+	0.992648i	$0.461377\pi$
$620$	0.0268590	0.00107868
$621$	15.8743	0.637013
$622$	−23.0168	−0.922888
$623$	−8.14014	−0.326128
$624$	−5.57203	−0.223060
$625$	24.9961	0.999846
$626$	11.0696	0.442429
$627$	0.0508448	0.00203055
$628$	3.94302	0.157344
$629$	9.93621	0.396183
$630$	−0.145608	−0.00580115
$631$	0.779774	0.0310423	0.0155212	−	0.999880i	$-0.495059\pi$
$631$	0.779774	0.0310423	0.0155212	+	0.999880i	$0.495059\pi$
$632$	1.37366	0.0546412
$633$	13.1662	0.523311
$634$	19.1839	0.761889
$635$	0.319335	0.0126724
$636$	3.50349	0.138922
$637$	19.1403	0.758368
$638$	−1.21030	−0.0479162
$639$	−16.0679	−0.635638
$640$	−0.108644	−0.00429454
$641$	−32.2889	−1.27533	−0.637667	−	0.770312i	$-0.720100\pi$
$641$	−32.2889	−1.27533	−0.637667	+	0.770312i	$0.720100\pi$
$642$	0.636282	0.0251121
$643$	44.2624	1.74554	0.872770	−	0.488131i	$-0.162321\pi$
$643$	44.2624	1.74554	0.872770	+	0.488131i	$0.162321\pi$
$644$	−5.16112	−0.203377
$645$	0.158280	0.00623227
$646$	−0.0830399	−0.00326716
$647$	6.71247	0.263895	0.131947	−	0.991257i	$-0.457877\pi$
$647$	6.71247	0.263895	0.131947	+	0.991257i	$0.457877\pi$
$648$	4.20639	0.165243
$649$	−0.663918	−0.0260611
$650$	−9.95458	−0.390451
$651$	−21.2548	−0.833042
$652$	1.78615	0.0699510
$653$	−3.01456	−0.117969	−0.0589843	−	0.998259i	$-0.518786\pi$
$653$	−3.01456	−0.117969	−0.0589843	+	0.998259i	$0.518786\pi$
$654$	−21.8978	−0.856273
$655$	−0.102109	−0.00398971
$656$	−14.5265	−0.567164
$657$	12.2824	0.479182
$658$	13.1824	0.513903
$659$	1.67978	0.0654350	0.0327175	−	0.999465i	$-0.489584\pi$
$659$	1.67978	0.0654350	0.0327175	+	0.999465i	$0.489584\pi$
$660$	0.00499047	0.000194254 0
$661$	−5.33802	−0.207625	−0.103812	−	0.994597i	$-0.533104\pi$
$661$	−5.33802	−0.207625	−0.103812	+	0.994597i	$0.533104\pi$
$662$	0.557091	0.0216520
$663$	−1.83620	−0.0713121
$664$	−37.2221	−1.44450
$665$	0.00461129	0.000178818 0
$666$	20.6098	0.798614
$667$	4.23100	0.163825
$668$	1.68465	0.0651810
$669$	−3.94390	−0.152480
$670$	−0.236916	−0.00915286
$671$	8.45248	0.326304
$672$	−11.4121	−0.440230
$673$	−1.73843	−0.0670117	−0.0335059	−	0.999439i	$-0.510667\pi$
$673$	−1.73843	−0.0670117	−0.0335059	+	0.999439i	$0.510667\pi$
$674$	8.76494	0.337613
$675$	27.0509	1.04119
$676$	4.22825	0.162625
$677$	44.3489	1.70447	0.852234	−	0.523160i	$-0.175247\pi$
$677$	44.3489	1.70447	0.852234	+	0.523160i	$0.175247\pi$
$678$	−5.59757	−0.214973
$679$	−40.8497	−1.56767
$680$	−0.0487053	−0.00186776
$681$	−11.8498	−0.454085
$682$	3.49633	0.133882
$683$	44.2569	1.69344	0.846721	−	0.532038i	$-0.178574\pi$
$683$	44.2569	1.69344	0.846721	+	0.532038i	$0.178574\pi$
$684$	0.0433231	0.00165650
$685$	0.162683	0.00621581
$686$	−28.5060	−1.08837
$687$	−9.14562	−0.348927
$688$	25.6840	0.979192
$689$	−11.7752	−0.448601
$690$	0.0693606	0.00264051
$691$	−26.2748	−0.999540	−0.499770	−	0.866158i	$-0.666582\pi$
$691$	−26.2748	−0.999540	−0.499770	+	0.866158i	$0.666582\pi$
$692$	3.84421	0.146135
$693$	4.76745	0.181101
$694$	6.54324	0.248378
$695$	0.0657560	0.00249427
$696$	5.10484	0.193498
$697$	−4.78704	−0.181322
$698$	22.3428	0.845688
$699$	−7.88538	−0.298252
$700$	−8.79491	−0.332417
$701$	−12.3588	−0.466786	−0.233393	−	0.972382i	$-0.574983\pi$
$701$	−12.3588	−0.466786	−0.233393	+	0.972382i	$0.574983\pi$
$702$	−10.7723	−0.406575
$703$	−0.652698	−0.0246170
$704$	5.90662	0.222614
$705$	0.0445597	0.00167821
$706$	18.3446	0.690409
$707$	−25.4686	−0.957847
$708$	0.468609	0.0176114
$709$	35.7507	1.34264	0.671322	−	0.741166i	$-0.265727\pi$
$709$	35.7507	1.34264	0.671322	+	0.741166i	$0.265727\pi$
$710$	−0.198570	−0.00745221
$711$	0.742297	0.0278383
$712$	−5.64777	−0.211659
$713$	−12.2226	−0.457739
$714$	6.44985	0.241380
$715$	−0.0167730	−0.000627275 0
$716$	2.38884	0.0892753
$717$	1.90736	0.0712318
$718$	−42.1547	−1.57320
$719$	36.7805	1.37168	0.685840	−	0.727753i	$-0.259435\pi$
$719$	36.7805	1.37168	0.685840	+	0.727753i	$0.259435\pi$
$720$	−0.0798671	−0.00297647
$721$	−0.699352	−0.0260452
$722$	−24.0132	−0.893680
$723$	7.47261	0.277909
$724$	−0.618854	−0.0229995
$725$	7.20992	0.267770
$726$	−15.5621	−0.577563
$727$	−10.0680	−0.373401	−0.186700	−	0.982417i	$-0.559779\pi$
$727$	−10.0680	−0.373401	−0.186700	+	0.982417i	$0.559779\pi$
$728$	20.9292	0.775688
$729$	21.1963	0.785048
$730$	0.151788	0.00561793
$731$	8.46387	0.313048
$732$	−5.96595	−0.220508
$733$	−30.1704	−1.11437	−0.557185	−	0.830388i	$-0.688119\pi$
$733$	−30.1704	−1.11437	−0.557185	+	0.830388i	$0.688119\pi$
$734$	40.2038	1.48395
$735$	−0.227262	−0.00838268
$736$	−6.56252	−0.241898
$737$	7.75705	0.285735
$738$	−9.92934	−0.365504
$739$	44.7925	1.64772	0.823860	−	0.566793i	$-0.191816\pi$
$739$	44.7925	1.64772	0.823860	+	0.566793i	$0.191816\pi$
$740$	−0.0640630	−0.00235500
$741$	0.120618	0.00443101
$742$	41.3618	1.51844
$743$	13.6677	0.501419	0.250710	−	0.968062i	$-0.419336\pi$
$743$	13.6677	0.501419	0.250710	+	0.968062i	$0.419336\pi$
$744$	−14.7470	−0.540649
$745$	0.101357	0.00371342
$746$	−6.05943	−0.221852
$747$	−20.1141	−0.735936
$748$	0.266861	0.00975739
$749$	−1.88942	−0.0690378
$750$	0.236397	0.00863199
$751$	−29.9666	−1.09350	−0.546748	−	0.837297i	$-0.684134\pi$
$751$	−29.9666	−1.09350	−0.546748	+	0.837297i	$0.684134\pi$
$752$	7.23066	0.263675
$753$	26.5131	0.966191
$754$	−2.87116	−0.104562
$755$	0.0789970	0.00287500
$756$	−9.51739	−0.346144
$757$	10.1245	0.367982	0.183991	−	0.982928i	$-0.441098\pi$
$757$	10.1245	0.367982	0.183991	+	0.982928i	$0.441098\pi$
$758$	26.5623	0.964785
$759$	−2.27099	−0.0824317
$760$	0.00319939	0.000116054 0
$761$	32.0714	1.16259	0.581294	−	0.813694i	$-0.302547\pi$
$761$	32.0714	1.16259	0.581294	+	0.813694i	$0.302547\pi$
$762$	−29.3403	−1.06289
$763$	65.0249	2.35406
$764$	−6.44946	−0.233333
$765$	−0.0263193	−0.000951577 0
$766$	−10.1389	−0.366333
$767$	−1.57500	−0.0568699
$768$	−10.7619	−0.388337
$769$	8.42278	0.303733	0.151867	−	0.988401i	$-0.451472\pi$
$769$	8.42278	0.303733	0.151867	+	0.988401i	$0.451472\pi$
$770$	0.0589170	0.00212322
$771$	−33.7953	−1.21711
$772$	−1.88139	−0.0677129
$773$	−22.8030	−0.820167	−0.410084	−	0.912048i	$-0.634501\pi$
$773$	−22.8030	−0.820167	−0.410084	+	0.912048i	$0.634501\pi$
$774$	17.5559	0.631033
$775$	−20.8281	−0.748169
$776$	−28.3422	−1.01743
$777$	50.6961	1.81871
$778$	−25.3221	−0.907840
$779$	0.314455	0.0112665
$780$	0.0118388	0.000423896 0
$781$	6.50155	0.232644
$782$	3.70899	0.132633
$783$	7.80219	0.278828
$784$	−36.8776	−1.31706
$785$	0.157353	0.00561618
$786$	9.38169	0.334634
$787$	33.3769	1.18976	0.594878	−	0.803816i	$-0.297200\pi$
$787$	33.3769	1.18976	0.594878	+	0.803816i	$0.297200\pi$
$788$	8.10615	0.288770
$789$	−28.3681	−1.00993
$790$	0.00917344	0.000326376 0
$791$	16.6218	0.591003
$792$	3.30774	0.117535
$793$	20.0516	0.712054
$794$	17.0438	0.604863
$795$	0.139813	0.00495865
$796$	1.07734	0.0381854
$797$	−51.4465	−1.82233	−0.911164	−	0.412044i	$-0.864815\pi$
$797$	−51.4465	−1.82233	−0.911164	+	0.412044i	$0.864815\pi$
$798$	−0.423683	−0.0149982
$799$	2.38278	0.0842968
$800$	−11.1830	−0.395378
$801$	−3.05194	−0.107835
$802$	−42.6255	−1.50516
$803$	−4.96981	−0.175381
$804$	−5.47510	−0.193092
$805$	−0.205964	−0.00725927
$806$	8.29427	0.292153
$807$	28.1509	0.990957
$808$	−17.6706	−0.621649
$809$	−10.8536	−0.381594	−0.190797	−	0.981630i	$-0.561107\pi$
$809$	−10.8536	−0.381594	−0.190797	+	0.981630i	$0.561107\pi$
$810$	0.0280907	0.000987008 0
$811$	42.5334	1.49355	0.746774	−	0.665078i	$-0.231602\pi$
$811$	42.5334	1.49355	0.746774	+	0.665078i	$0.231602\pi$
$812$	−2.53668	−0.0890202
$813$	−36.7443	−1.28868
$814$	−8.33932	−0.292293
$815$	0.0712795	0.00249681
$816$	3.53780	0.123848
$817$	−0.555982	−0.0194513
$818$	2.26232	0.0791002
$819$	11.3097	0.395194
$820$	0.0308641	0.00107782
$821$	−47.2085	−1.64759	−0.823794	−	0.566889i	$-0.808147\pi$
$821$	−47.2085	−1.64759	−0.823794	+	0.566889i	$0.808147\pi$
$822$	−14.9473	−0.521347
$823$	28.2543	0.984884	0.492442	−	0.870345i	$-0.336104\pi$
$823$	28.2543	0.984884	0.492442	+	0.870345i	$0.336104\pi$
$824$	−0.485222	−0.0169035
$825$	−3.86993	−0.134734
$826$	5.53235	0.192495
$827$	30.7826	1.07042	0.535208	−	0.844720i	$-0.320233\pi$
$827$	30.7826	1.07042	0.535208	+	0.844720i	$0.320233\pi$
$828$	−1.93503	−0.0672470
$829$	2.03623	0.0707213	0.0353606	−	0.999375i	$-0.488742\pi$
$829$	2.03623	0.0707213	0.0353606	+	0.999375i	$0.488742\pi$
$830$	−0.248573	−0.00862811
$831$	−20.0612	−0.695915
$832$	14.0121	0.485783
$833$	−12.1526	−0.421063
$834$	−6.04164	−0.209205
$835$	0.0672289	0.00232655
$836$	−0.0175298	−0.000606280 0
$837$	−22.5391	−0.779066
$838$	−13.6746	−0.472380
$839$	−41.4428	−1.43077	−0.715383	−	0.698733i	$-0.753748\pi$
$839$	−41.4428	−1.43077	−0.715383	+	0.698733i	$0.753748\pi$
$840$	−0.248502	−0.00857414
$841$	−26.9205	−0.928292
$842$	21.2176	0.731208
$843$	−18.6386	−0.641947
$844$	−4.53932	−0.156250
$845$	0.168736	0.00580468
$846$	4.94240	0.169923
$847$	46.2110	1.58783
$848$	22.6873	0.779086
$849$	−4.13207	−0.141812
$850$	6.32038	0.216787
$851$	29.1528	0.999347
$852$	−4.58894	−0.157215
$853$	28.7371	0.983939	0.491969	−	0.870613i	$-0.336277\pi$
$853$	28.7371	0.983939	0.491969	+	0.870613i	$0.336277\pi$
$854$	−70.4334	−2.41018
$855$	0.00172889	5.91266e−5 0
$856$	−1.31091	−0.0448060
$857$	−14.5101	−0.495656	−0.247828	−	0.968804i	$-0.579717\pi$
$857$	−14.5101	−0.495656	−0.247828	+	0.968804i	$0.579717\pi$
$858$	1.54110	0.0526122
$859$	−17.2661	−0.589113	−0.294556	−	0.955634i	$-0.595172\pi$
$859$	−17.2661	−0.589113	−0.294556	+	0.955634i	$0.595172\pi$
$860$	−0.0545702	−0.00186083
$861$	−24.4243	−0.832377
$862$	5.30625	0.180732
$863$	−22.1066	−0.752516	−0.376258	−	0.926515i	$-0.622789\pi$
$863$	−22.1066	−0.752516	−0.376258	+	0.926515i	$0.622789\pi$
$864$	−12.1016	−0.411706
$865$	0.153410	0.00521610
$866$	26.2877	0.893293
$867$	1.16584	0.0395941
$868$	7.32802	0.248729
$869$	−0.300355	−0.0101888
$870$	0.0340906	0.00115578
$871$	18.4019	0.623524
$872$	45.1154	1.52780
$873$	−15.3155	−0.518353
$874$	−0.243639	−0.00824122
$875$	−0.701972	−0.0237310
$876$	3.50781	0.118518
$877$	−2.28900	−0.0772941	−0.0386471	−	0.999253i	$-0.512305\pi$
$877$	−2.28900	−0.0772941	−0.0386471	+	0.999253i	$0.512305\pi$
$878$	−3.81988	−0.128915
$879$	20.4804	0.690788
$880$	0.0323165	0.00108939
$881$	−5.02326	−0.169238	−0.0846190	−	0.996413i	$-0.526967\pi$
$881$	−5.02326	−0.169238	−0.0846190	+	0.996413i	$0.526967\pi$
$882$	−25.2071	−0.848767
$883$	−21.7402	−0.731617	−0.365809	−	0.930690i	$-0.619208\pi$
$883$	−21.7402	−0.731617	−0.365809	+	0.930690i	$0.619208\pi$
$884$	0.633067	0.0212924
$885$	0.0187007	0.000628616 0
$886$	33.2864	1.11828
$887$	14.2820	0.479544	0.239772	−	0.970829i	$-0.422927\pi$
$887$	14.2820	0.479544	0.239772	+	0.970829i	$0.422927\pi$
$888$	35.1739	1.18036
$889$	87.1251	2.92208
$890$	−0.0377164	−0.00126426
$891$	−0.919741	−0.0308125
$892$	1.35974	0.0455274
$893$	−0.156522	−0.00523782
$894$	−9.31261	−0.311460
$895$	0.0953311	0.00318657
$896$	−29.6417	−0.990261
$897$	−5.38742	−0.179881
$898$	−28.6931	−0.957500
$899$	−6.00738	−0.200357
$900$	−3.29743	−0.109914
$901$	7.47636	0.249074
$902$	4.01770	0.133775
$903$	43.1841	1.43708
$904$	11.5325	0.383565
$905$	−0.0246965	−0.000820939 0
$906$	−7.25821	−0.241138
$907$	18.6983	0.620868	0.310434	−	0.950595i	$-0.399526\pi$
$907$	18.6983	0.620868	0.310434	+	0.950595i	$0.399526\pi$
$908$	4.08546	0.135581
$909$	−9.54882	−0.316714
$910$	0.139767	0.00463325
$911$	−5.75441	−0.190652	−0.0953260	−	0.995446i	$-0.530389\pi$
$911$	−5.75441	−0.190652	−0.0953260	+	0.995446i	$0.530389\pi$
$912$	−0.232394	−0.00769534
$913$	8.13874	0.269353
$914$	40.9003	1.35286
$915$	−0.238082	−0.00787075
$916$	3.15314	0.104183
$917$	−27.8586	−0.919972
$918$	6.83958	0.225740
$919$	13.1118	0.432518	0.216259	−	0.976336i	$-0.430614\pi$
$919$	13.1118	0.432518	0.216259	+	0.976336i	$0.430614\pi$
$920$	−0.142901	−0.00471131
$921$	23.9492	0.789152
$922$	−34.5429	−1.13761
$923$	15.4235	0.507670
$924$	1.36157	0.0447923
$925$	49.6785	1.63342
$926$	−33.1762	−1.09024
$927$	−0.262204	−0.00861191
$928$	−3.22547	−0.105881
$929$	12.3402	0.404868	0.202434	−	0.979296i	$-0.435115\pi$
$929$	12.3402	0.404868	0.202434	+	0.979296i	$0.435115\pi$
$930$	−0.0984817	−0.00322934
$931$	0.798291	0.0261629
$932$	2.71864	0.0890521
$933$	−21.2270	−0.694942
$934$	−33.2456	−1.08783
$935$	0.0106496	0.000348278 0
$936$	7.84688	0.256483
$937$	42.4974	1.38833	0.694165	−	0.719816i	$-0.255774\pi$
$937$	42.4974	1.38833	0.694165	+	0.719816i	$0.255774\pi$
$938$	−64.6385	−2.11052
$939$	10.2088	0.333152
$940$	−0.0153628	−0.000501081 0
$941$	−36.9505	−1.20455	−0.602277	−	0.798287i	$-0.705740\pi$
$941$	−36.9505	−1.20455	−0.602277	+	0.798287i	$0.705740\pi$
$942$	−14.4576	−0.471053
$943$	−14.0452	−0.457374
$944$	3.03454	0.0987659
$945$	−0.379809	−0.0123552
$946$	−7.10361	−0.230958
$947$	−50.8334	−1.65186	−0.825932	−	0.563769i	$-0.809351\pi$
$947$	−50.8334	−1.65186	−0.825932	+	0.563769i	$0.809351\pi$
$948$	0.211997	0.00688535
$949$	−11.7898	−0.382712
$950$	−0.415178	−0.0134702
$951$	17.6922	0.573708
$952$	−13.2884	−0.430680
$953$	−16.4985	−0.534438	−0.267219	−	0.963636i	$-0.586105\pi$
$953$	−16.4985	−0.534438	−0.267219	+	0.963636i	$0.586105\pi$
$954$	15.5076	0.502076
$955$	−0.257377	−0.00832853
$956$	−0.657602	−0.0212684
$957$	−1.11619	−0.0360812
$958$	34.9531	1.12928
$959$	44.3854	1.43328
$960$	−0.166372	−0.00536965
$961$	−13.6458	−0.440186
$962$	−19.7832	−0.637835
$963$	−0.708389	−0.0228275
$964$	−2.57633	−0.0829781
$965$	−0.0750804	−0.00241692
$966$	18.9239	0.608866
$967$	57.3959	1.84573	0.922864	−	0.385125i	$-0.125842\pi$
$967$	57.3959	1.84573	0.922864	+	0.385125i	$0.125842\pi$
$968$	32.0620	1.03051
$969$	−0.0765829	−0.00246020
$970$	−0.189272	−0.00607716
$971$	−0.800357	−0.0256847	−0.0128423	−	0.999918i	$-0.504088\pi$
$971$	−0.800357	−0.0256847	−0.0128423	+	0.999918i	$0.504088\pi$
$972$	−5.87500	−0.188441
$973$	17.9404	0.575144
$974$	50.6619	1.62331
$975$	−9.18053	−0.294012
$976$	−38.6334	−1.23662
$977$	−33.3321	−1.06639	−0.533194	−	0.845993i	$-0.679008\pi$
$977$	−33.3321	−1.06639	−0.533194	+	0.845993i	$0.679008\pi$
$978$	−6.54913	−0.209418
$979$	1.23490	0.0394677
$980$	0.0783531	0.00250290
$981$	24.3794	0.778375
$982$	−9.02124	−0.287879
$983$	22.3446	0.712682	0.356341	−	0.934356i	$-0.384024\pi$
$983$	22.3446	0.712682	0.356341	+	0.934356i	$0.384024\pi$
$984$	−16.9460	−0.540218
$985$	0.323490	0.0103073
$986$	1.82296	0.0580550
$987$	12.1574	0.386973
$988$	−0.0415855	−0.00132301
$989$	24.8330	0.789644
$990$	0.0220894	0.000702048 0
$991$	49.5893	1.57526	0.787628	−	0.616151i	$-0.211309\pi$
$991$	49.5893	1.57526	0.787628	+	0.616151i	$0.211309\pi$
$992$	9.31780	0.295840
$993$	0.513773	0.0163041
$994$	−54.1766	−1.71838
$995$	0.0429933	0.00136298
$996$	−5.74451	−0.182022
$997$	12.2305	0.387344	0.193672	−	0.981066i	$-0.437960\pi$
$997$	12.2305	0.387344	0.193672	+	0.981066i	$0.437960\pi$
$998$	49.1705	1.55647
$999$	53.7594	1.70087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.g.1.7	✓	10
3.2	odd	2		9027.2.a.j.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.g.1.7	✓	10	1.1	even	1	trivial
9027.2.a.j.1.4		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)

\(f(q)\)	\(=\)	\(q+1.26414 q^{2} +1.16584 q^{3} -0.401948 q^{4} -0.0160405 q^{5} +1.47379 q^{6} -4.37637 q^{7} -3.03640 q^{8} -1.64081 q^{9} +O(q^{10})\)	\(q+1.26414 q^{2} +1.16584 q^{3} -0.401948 q^{4} -0.0160405 q^{5} +1.47379 q^{6} -4.37637 q^{7} -3.03640 q^{8} -1.64081 q^{9} -0.0202774 q^{10} +0.663918 q^{11} -0.468609 q^{12} +1.57500 q^{13} -5.53235 q^{14} -0.0187007 q^{15} -3.03454 q^{16} -1.00000 q^{17} -2.07421 q^{18} +0.0656888 q^{19} +0.00644743 q^{20} -5.10216 q^{21} +0.839286 q^{22} -2.93400 q^{23} -3.53997 q^{24} -4.99974 q^{25} +1.99102 q^{26} -5.41046 q^{27} +1.75907 q^{28} -1.44206 q^{29} -0.0236403 q^{30} +4.16584 q^{31} +2.23671 q^{32} +0.774025 q^{33} -1.26414 q^{34} +0.0701990 q^{35} +0.659520 q^{36} -9.93621 q^{37} +0.0830399 q^{38} +1.83620 q^{39} +0.0487053 q^{40} +4.78704 q^{41} -6.44985 q^{42} -8.46387 q^{43} -0.266861 q^{44} +0.0263193 q^{45} -3.70899 q^{46} -2.38278 q^{47} -3.53780 q^{48} +12.1526 q^{49} -6.32038 q^{50} -1.16584 q^{51} -0.633067 q^{52} -7.47636 q^{53} -6.83958 q^{54} -0.0106496 q^{55} +13.2884 q^{56} +0.0765829 q^{57} -1.82296 q^{58} -1.00000 q^{59} +0.00751670 q^{60} +12.7312 q^{61} +5.26621 q^{62} +7.18078 q^{63} +8.89660 q^{64} -0.0252637 q^{65} +0.978476 q^{66} +11.6837 q^{67} +0.401948 q^{68} -3.42059 q^{69} +0.0887414 q^{70} +9.79270 q^{71} +4.98215 q^{72} -7.48558 q^{73} -12.5608 q^{74} -5.82892 q^{75} -0.0264035 q^{76} -2.90555 q^{77} +2.32122 q^{78} -0.452397 q^{79} +0.0486754 q^{80} -1.38532 q^{81} +6.05149 q^{82} +12.2586 q^{83} +2.05080 q^{84} +0.0160405 q^{85} -10.6995 q^{86} -1.68121 q^{87} -2.01592 q^{88} +1.86002 q^{89} +0.0332713 q^{90} -6.89277 q^{91} +1.17932 q^{92} +4.85672 q^{93} -3.01217 q^{94} -0.00105368 q^{95} +2.60766 q^{96} +9.33415 q^{97} +15.3626 q^{98} -1.08936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) \) 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

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