LMFDB - Embedded newform 349.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(1,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("349.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 5 x^{16} - 14 x^{15} + 102 x^{14} + 26 x^{13} - 792 x^{12} + 474 x^{11} + 2887 x^{10} + \cdots - 4 $ x^17 - 5x^16 - 14x^15 + 102x^14 + 26x^13 - 792x^12 + 474x^11 + 2887x^10 - 3021x^9 - 4835x^8 + 6673x^7 + 2880x^6 - 5373x^5 - 164x^4 + 1075x^3 + 75x^2 - 41x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.36348$ of defining polynomial
Character	$\chi$	$=$	349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36348 q^{2} -2.15844 q^{3} +3.58604 q^{4} -0.000712583 q^{5} +5.10144 q^{6} -2.22015 q^{7} -3.74859 q^{8} +1.65887 q^{9} +O(q^{10})$	\(q-2.36348 q^{2} -2.15844 q^{3} +3.58604 q^{4} -0.000712583 q^{5} +5.10144 q^{6} -2.22015 q^{7} -3.74859 q^{8} +1.65887 q^{9} +0.00168418 q^{10} +1.81733 q^{11} -7.74027 q^{12} -7.18222 q^{13} +5.24729 q^{14} +0.00153807 q^{15} +1.68763 q^{16} +0.564039 q^{17} -3.92070 q^{18} +0.104168 q^{19} -0.00255536 q^{20} +4.79207 q^{21} -4.29522 q^{22} +4.03075 q^{23} +8.09111 q^{24} -5.00000 q^{25} +16.9750 q^{26} +2.89476 q^{27} -7.96156 q^{28} +5.42192 q^{29} -0.00363520 q^{30} +5.46720 q^{31} +3.50850 q^{32} -3.92260 q^{33} -1.33310 q^{34} +0.00158204 q^{35} +5.94877 q^{36} +5.22495 q^{37} -0.246200 q^{38} +15.5024 q^{39} +0.00267118 q^{40} -0.936170 q^{41} -11.3260 q^{42} +9.72594 q^{43} +6.51702 q^{44} -0.00118208 q^{45} -9.52659 q^{46} +1.65290 q^{47} -3.64265 q^{48} -2.07093 q^{49} +11.8174 q^{50} -1.21744 q^{51} -25.7558 q^{52} +3.03585 q^{53} -6.84170 q^{54} -0.00129500 q^{55} +8.32243 q^{56} -0.224842 q^{57} -12.8146 q^{58} +3.09600 q^{59} +0.00551558 q^{60} +0.192503 q^{61} -12.9216 q^{62} -3.68294 q^{63} -11.6675 q^{64} +0.00511793 q^{65} +9.27099 q^{66} +7.11892 q^{67} +2.02267 q^{68} -8.70013 q^{69} -0.00373913 q^{70} -2.42557 q^{71} -6.21841 q^{72} -4.52712 q^{73} -12.3491 q^{74} +10.7922 q^{75} +0.373553 q^{76} -4.03475 q^{77} -36.6396 q^{78} +2.63989 q^{79} -0.00120258 q^{80} -11.2248 q^{81} +2.21262 q^{82} -13.9736 q^{83} +17.1846 q^{84} -0.000401925 q^{85} -22.9871 q^{86} -11.7029 q^{87} -6.81242 q^{88} +14.6317 q^{89} +0.00279383 q^{90} +15.9456 q^{91} +14.4544 q^{92} -11.8006 q^{93} -3.90659 q^{94} -7.42287e-5 q^{95} -7.57288 q^{96} +7.84243 q^{97} +4.89460 q^{98} +3.01471 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) $ 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9} - 6 q^{10} + 39 q^{11} + 4 q^{12} - 6 q^{13} + 11 q^{14} + 12 q^{15} + 23 q^{16} + q^{17} + 7 q^{19} + 8 q^{20} - 3 q^{21} - q^{22} + 8 q^{23} - 21 q^{24} + 14 q^{25} + q^{26} + 9 q^{27} - 23 q^{28} + 9 q^{29} - 27 q^{30} - 2 q^{31} + 23 q^{32} - 5 q^{33} - 12 q^{34} + 16 q^{35} + 10 q^{36} - 7 q^{37} - 8 q^{38} - 39 q^{40} + 3 q^{41} - 30 q^{42} + q^{43} + 56 q^{44} - 21 q^{45} - q^{46} + 16 q^{47} - 31 q^{48} + 6 q^{49} - 5 q^{50} + 29 q^{51} - 37 q^{52} + 27 q^{53} - 36 q^{54} - 16 q^{55} + 14 q^{56} - 21 q^{57} - 44 q^{58} + 74 q^{59} - 27 q^{60} - 30 q^{61} - 18 q^{62} - 9 q^{63} - 17 q^{64} - 3 q^{65} - 66 q^{66} + 9 q^{67} - 51 q^{68} - 23 q^{69} - 77 q^{70} + 70 q^{71} - 55 q^{72} - 38 q^{73} + 26 q^{74} + 22 q^{75} - 50 q^{76} - 38 q^{77} - 75 q^{78} + 7 q^{79} - 28 q^{80} + 5 q^{81} - 56 q^{82} + 47 q^{83} - 69 q^{84} - 49 q^{85} + 17 q^{86} - 37 q^{87} - 30 q^{88} + 23 q^{89} - 64 q^{90} + 6 q^{91} + 17 q^{92} - 31 q^{93} - 40 q^{94} - 11 q^{95} - 49 q^{96} - 14 q^{97} + 5 q^{98} + 79 q^{99}+O(q^{100}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9 - 6 * q^10 + 39 * q^11 + 4 * q^12 - 6 * q^13 + 11 * q^14 + 12 * q^15 + 23 * q^16 + q^17 + 7 * q^19 + 8 * q^20 - 3 * q^21 - q^22 + 8 * q^23 - 21 * q^24 + 14 * q^25 + q^26 + 9 * q^27 - 23 * q^28 + 9 * q^29 - 27 * q^30 - 2 * q^31 + 23 * q^32 - 5 * q^33 - 12 * q^34 + 16 * q^35 + 10 * q^36 - 7 * q^37 - 8 * q^38 - 39 * q^40 + 3 * q^41 - 30 * q^42 + q^43 + 56 * q^44 - 21 * q^45 - q^46 + 16 * q^47 - 31 * q^48 + 6 * q^49 - 5 * q^50 + 29 * q^51 - 37 * q^52 + 27 * q^53 - 36 * q^54 - 16 * q^55 + 14 * q^56 - 21 * q^57 - 44 * q^58 + 74 * q^59 - 27 * q^60 - 30 * q^61 - 18 * q^62 - 9 * q^63 - 17 * q^64 - 3 * q^65 - 66 * q^66 + 9 * q^67 - 51 * q^68 - 23 * q^69 - 77 * q^70 + 70 * q^71 - 55 * q^72 - 38 * q^73 + 26 * q^74 + 22 * q^75 - 50 * q^76 - 38 * q^77 - 75 * q^78 + 7 * q^79 - 28 * q^80 + 5 * q^81 - 56 * q^82 + 47 * q^83 - 69 * q^84 - 49 * q^85 + 17 * q^86 - 37 * q^87 - 30 * q^88 + 23 * q^89 - 64 * q^90 + 6 * q^91 + 17 * q^92 - 31 * q^93 - 40 * q^94 - 11 * q^95 - 49 * q^96 - 14 * q^97 + 5 * q^98 + 79 * 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 $

$2$	−2.36348	−1.67123	−0.835617	−	0.549313i	$-0.814890\pi$
$2$	−2.36348	−1.67123	−0.835617	+	0.549313i	$0.814890\pi$
$3$	−2.15844	−1.24618	−0.623088	−	0.782152i	$-0.714122\pi$
$3$	−2.15844	−1.24618	−0.623088	+	0.782152i	$0.714122\pi$
$4$	3.58604	1.79302
$5$	−0.000712583 0	−0.000318677 0	−0.000159338	−	1.00000i	$-0.500051\pi$
$5$	−0.000712583 0	−0.000318677 0	−0.000159338		1.00000i	$0.500051\pi$
$6$	5.10144	2.08265
$7$	−2.22015	−0.839138	−0.419569	−	0.907723i	$-0.637819\pi$
$7$	−2.22015	−0.839138	−0.419569	+	0.907723i	$0.637819\pi$
$8$	−3.74859	−1.32533
$9$	1.65887	0.552956
$10$	0.00168418	0.000532584 0
$11$	1.81733	0.547945	0.273973	−	0.961737i	$-0.411662\pi$
$11$	1.81733	0.547945	0.273973	+	0.961737i	$0.411662\pi$
$12$	−7.74027	−2.23442
$13$	−7.18222	−1.99199	−0.995995	−	0.0894090i	$-0.971502\pi$
$13$	−7.18222	−1.99199	−0.995995	+	0.0894090i	$0.971502\pi$
$14$	5.24729	1.40240
$15$	0.00153807	0.000397128 0
$16$	1.68763	0.421907
$17$	0.564039	0.136800	0.0683998	−	0.997658i	$-0.478211\pi$
$17$	0.564039	0.136800	0.0683998	+	0.997658i	$0.478211\pi$
$18$	−3.92070	−0.924118
$19$	0.104168	0.0238979	0.0119489	−	0.999929i	$-0.496196\pi$
$19$	0.104168	0.0238979	0.0119489	+	0.999929i	$0.496196\pi$
$20$	−0.00255536	−0.000571395 0
$21$	4.79207	1.04571
$22$	−4.29522	−0.915745
$23$	4.03075	0.840469	0.420234	−	0.907416i	$-0.361948\pi$
$23$	4.03075	0.840469	0.420234	+	0.907416i	$0.361948\pi$
$24$	8.09111	1.65159
$25$	−5.00000	−1.00000
$26$	16.9750	3.32908
$27$	2.89476	0.557096
$28$	−7.96156	−1.50459
$29$	5.42192	1.00682	0.503412	−	0.864046i	$-0.332078\pi$
$29$	5.42192	1.00682	0.503412	+	0.864046i	$0.332078\pi$
$30$	−0.00363520	−0.000663693 0
$31$	5.46720	0.981938	0.490969	−	0.871177i	$-0.336643\pi$
$31$	5.46720	0.981938	0.490969	+	0.871177i	$0.336643\pi$
$32$	3.50850	0.620221
$33$	−3.92260	−0.682837
$34$	−1.33310	−0.228624
$35$	0.00158204	0.000267414 0
$36$	5.94877	0.991462
$37$	5.22495	0.858977	0.429489	−	0.903072i	$-0.358694\pi$
$37$	5.22495	0.858977	0.429489	+	0.903072i	$0.358694\pi$
$38$	−0.246200	−0.0399390
$39$	15.5024	2.48237
$40$	0.00267118	0.000422351 0
$41$	−0.936170	−0.146205	−0.0731026	−	0.997324i	$-0.523290\pi$
$41$	−0.936170	−0.146205	−0.0731026	+	0.997324i	$0.523290\pi$
$42$	−11.3260	−1.74763
$43$	9.72594	1.48319	0.741596	−	0.670846i	$-0.234069\pi$
$43$	9.72594	1.48319	0.741596	+	0.670846i	$0.234069\pi$
$44$	6.51702	0.982478
$45$	−0.00118208	−0.000176214 0
$46$	−9.52659	−1.40462
$47$	1.65290	0.241100	0.120550	−	0.992707i	$-0.461534\pi$
$47$	1.65290	0.241100	0.120550	+	0.992707i	$0.461534\pi$
$48$	−3.64265	−0.525771
$49$	−2.07093	−0.295847
$50$	11.8174	1.67123
$51$	−1.21744	−0.170476
$52$	−25.7558	−3.57168
$53$	3.03585	0.417006	0.208503	−	0.978022i	$-0.433141\pi$
$53$	3.03585	0.417006	0.208503	+	0.978022i	$0.433141\pi$
$54$	−6.84170	−0.931038
$55$	−0.00129500	−0.000174618 0
$56$	8.32243	1.11213
$57$	−0.224842	−0.0297810
$58$	−12.8146	−1.68264
$59$	3.09600	0.403065	0.201533	−	0.979482i	$-0.435408\pi$
$59$	3.09600	0.403065	0.201533	+	0.979482i	$0.435408\pi$
$60$	0.00551558	0.000712059 0
$61$	0.192503	0.0246475	0.0123238	−	0.999924i	$-0.496077\pi$
$61$	0.192503	0.0246475	0.0123238	+	0.999924i	$0.496077\pi$
$62$	−12.9216	−1.64105
$63$	−3.68294	−0.464006
$64$	−11.6675	−1.45844
$65$	0.00511793	0.000634801 0
$66$	9.27099	1.14118
$67$	7.11892	0.869715	0.434857	−	0.900499i	$-0.356799\pi$
$67$	7.11892	0.869715	0.434857	+	0.900499i	$0.356799\pi$
$68$	2.02267	0.245285
$69$	−8.70013	−1.04737
$70$	−0.00373913	−0.000446911 0
$71$	−2.42557	−0.287862	−0.143931	−	0.989588i	$-0.545974\pi$
$71$	−2.42557	−0.287862	−0.143931	+	0.989588i	$0.545974\pi$
$72$	−6.21841	−0.732847
$73$	−4.52712	−0.529860	−0.264930	−	0.964268i	$-0.585349\pi$
$73$	−4.52712	−0.529860	−0.264930	+	0.964268i	$0.585349\pi$
$74$	−12.3491	−1.43555
$75$	10.7922	1.24618
$76$	0.373553	0.0428495
$77$	−4.03475	−0.459802
$78$	−36.6396	−4.14862
$79$	2.63989	0.297010	0.148505	−	0.988912i	$-0.452554\pi$
$79$	2.63989	0.297010	0.148505	+	0.988912i	$0.452554\pi$
$80$	−0.00120258	−0.000134452 0
$81$	−11.2248	−1.24720
$82$	2.21262	0.244343
$83$	−13.9736	−1.53380	−0.766901	−	0.641765i	$-0.778202\pi$
$83$	−13.9736	−1.53380	−0.766901	+	0.641765i	$0.778202\pi$
$84$	17.1846	1.87499
$85$	−0.000401925 0	−4.35948e−5 0
$86$	−22.9871	−2.47876
$87$	−11.7029	−1.25468
$88$	−6.81242	−0.726206
$89$	14.6317	1.55096	0.775478	−	0.631375i	$-0.217509\pi$
$89$	14.6317	1.55096	0.775478	+	0.631375i	$0.217509\pi$
$90$	0.00279383	0.000294495 0
$91$	15.9456	1.67156
$92$	14.4544	1.50698
$93$	−11.8006	−1.22367
$94$	−3.90659	−0.402934
$95$	−7.42287e−5 0	−7.61570e−6 0
$96$	−7.57288	−0.772904
$97$	7.84243	0.796278	0.398139	−	0.917325i	$-0.369656\pi$
$97$	7.84243	0.796278	0.398139	+	0.917325i	$0.369656\pi$
$98$	4.89460	0.494429
$99$	3.01471	0.302990
$100$	−17.9302	−1.79302
$101$	−9.54293	−0.949557	−0.474778	−	0.880105i	$-0.657472\pi$
$101$	−9.54293	−0.949557	−0.474778	+	0.880105i	$0.657472\pi$
$102$	2.87741	0.284906
$103$	15.0891	1.48677	0.743387	−	0.668862i	$-0.233218\pi$
$103$	15.0891	1.48677	0.743387	+	0.668862i	$0.233218\pi$
$104$	26.9232	2.64004
$105$	−0.00341474	−0.000333245 0
$106$	−7.17518	−0.696915
$107$	19.8308	1.91711	0.958556	−	0.284906i	$-0.0919622\pi$
$107$	19.8308	1.91711	0.958556	+	0.284906i	$0.0919622\pi$
$108$	10.3807	0.998886
$109$	11.4038	1.09229	0.546143	−	0.837692i	$-0.316095\pi$
$109$	11.4038	1.09229	0.546143	+	0.837692i	$0.316095\pi$
$110$	0.00306070	0.000291827 0
$111$	−11.2778	−1.07044
$112$	−3.74679	−0.354038
$113$	3.61741	0.340298	0.170149	−	0.985418i	$-0.445575\pi$
$113$	3.61741	0.340298	0.170149	+	0.985418i	$0.445575\pi$
$114$	0.531409	0.0497710
$115$	−0.00287224	−0.000267838 0
$116$	19.4432	1.80526
$117$	−11.9144	−1.10148
$118$	−7.31734	−0.673616
$119$	−1.25225	−0.114794
$120$	−0.00576559	−0.000526324 0
$121$	−7.69731	−0.699756
$122$	−0.454978	−0.0411917
$123$	2.02067	0.182198
$124$	19.6056	1.76064
$125$	0.00712583	0.000637354 0
$126$	8.70455	0.775463
$127$	−17.7418	−1.57433	−0.787167	−	0.616740i	$-0.788453\pi$
$127$	−17.7418	−1.57433	−0.787167	+	0.616740i	$0.788453\pi$
$128$	20.5590	1.81717
$129$	−20.9929	−1.84832
$130$	−0.0120961	−0.00106090
$131$	18.5943	1.62459	0.812295	−	0.583247i	$-0.198218\pi$
$131$	18.5943	1.62459	0.812295	+	0.583247i	$0.198218\pi$
$132$	−14.0666	−1.22434
$133$	−0.231270	−0.0200536
$134$	−16.8254	−1.45350
$135$	−0.00206275	−0.000177534 0
$136$	−2.11435	−0.181304
$137$	−7.60219	−0.649499	−0.324749	−	0.945800i	$-0.605280\pi$
$137$	−7.60219	−0.649499	−0.324749	+	0.945800i	$0.605280\pi$
$138$	20.5626	1.75040
$139$	−9.15299	−0.776346	−0.388173	−	0.921586i	$-0.626894\pi$
$139$	−9.15299	−0.776346	−0.388173	+	0.921586i	$0.626894\pi$
$140$	0.00567328	0.000479479 0
$141$	−3.56768	−0.300453
$142$	5.73278	0.481084
$143$	−13.0525	−1.09150
$144$	2.79955	0.233296
$145$	−0.00386357	−0.000320852 0
$146$	10.6998	0.885519
$147$	4.46998	0.368677
$148$	18.7369	1.54017
$149$	−6.12081	−0.501436	−0.250718	−	0.968060i	$-0.580667\pi$
$149$	−6.12081	−0.501436	−0.250718	+	0.968060i	$0.580667\pi$
$150$	−25.5072	−2.08265
$151$	−5.10193	−0.415190	−0.207595	−	0.978215i	$-0.566564\pi$
$151$	−5.10193	−0.415190	−0.207595	+	0.978215i	$0.566564\pi$
$152$	−0.390485	−0.0316725
$153$	0.935666	0.0756441
$154$	9.53605	0.768437
$155$	−0.00389583	−0.000312921 0
$156$	55.5923	4.45095
$157$	−16.4741	−1.31478	−0.657390	−	0.753551i	$-0.728339\pi$
$157$	−16.4741	−1.31478	−0.657390	+	0.753551i	$0.728339\pi$
$158$	−6.23932	−0.496374
$159$	−6.55271	−0.519663
$160$	−0.00250010	−0.000197650 0
$161$	−8.94887	−0.705270
$162$	26.5295	2.08436
$163$	7.68992	0.602321	0.301160	−	0.953574i	$-0.402626\pi$
$163$	7.68992	0.602321	0.301160	+	0.953574i	$0.402626\pi$
$164$	−3.35715	−0.262149
$165$	0.00279518	0.000217604 0
$166$	33.0264	2.56334
$167$	2.57519	0.199274	0.0996370	−	0.995024i	$-0.468232\pi$
$167$	2.57519	0.199274	0.0996370	+	0.995024i	$0.468232\pi$
$168$	−17.9635	−1.38591
$169$	38.5843	2.96802
$170$	0.000949941 0	7.28572e−5 0
$171$	0.172802	0.0132145
$172$	34.8777	2.65940
$173$	−10.9374	−0.831557	−0.415779	−	0.909466i	$-0.636491\pi$
$173$	−10.9374	−0.831557	−0.415779	+	0.909466i	$0.636491\pi$
$174$	27.6596	2.09687
$175$	11.1008	0.839138
$176$	3.06698	0.231182
$177$	−6.68254	−0.502290
$178$	−34.5817	−2.59201
$179$	16.3932	1.22529	0.612643	−	0.790360i	$-0.290106\pi$
$179$	16.3932	1.22529	0.612643	+	0.790360i	$0.290106\pi$
$180$	−0.00423899	−0.000315956 0
$181$	6.17213	0.458771	0.229386	−	0.973336i	$-0.426328\pi$
$181$	6.17213	0.458771	0.229386	+	0.973336i	$0.426328\pi$
$182$	−37.6872	−2.79356
$183$	−0.415507	−0.0307151
$184$	−15.1096	−1.11389
$185$	−0.00372321	−0.000273736 0
$186$	27.8906	2.04504
$187$	1.02504	0.0749587
$188$	5.92737	0.432298
$189$	−6.42680	−0.467481
$190$	0.000175438 0	1.27276e−5 0
$191$	−5.68451	−0.411317	−0.205658	−	0.978624i	$-0.565934\pi$
$191$	−5.68451	−0.411317	−0.205658	+	0.978624i	$0.565934\pi$
$192$	25.1837	1.81747
$193$	4.60788	0.331683	0.165841	−	0.986152i	$-0.446966\pi$
$193$	4.60788	0.331683	0.165841	+	0.986152i	$0.446966\pi$
$194$	−18.5354	−1.33077
$195$	−0.0110467	−0.000791074 0
$196$	−7.42644	−0.530460
$197$	23.9940	1.70950	0.854750	−	0.519039i	$-0.173710\pi$
$197$	23.9940	1.70950	0.854750	+	0.519039i	$0.173710\pi$
$198$	−7.12521	−0.506366
$199$	−20.4836	−1.45204	−0.726022	−	0.687672i	$-0.758633\pi$
$199$	−20.4836	−1.45204	−0.726022	+	0.687672i	$0.758633\pi$
$200$	18.7429	1.32533
$201$	−15.3658	−1.08382
$202$	22.5545	1.58693
$203$	−12.0375	−0.844865
$204$	−4.36581	−0.305668
$205$	0.000667099 0	4.65922e−5 0
$206$	−35.6628	−2.48475
$207$	6.68647	0.464742
$208$	−12.1209	−0.840435
$209$	0.189308	0.0130947
$210$	0.00807069	0.000556930 0
$211$	−8.69942	−0.598893	−0.299446	−	0.954113i	$-0.596802\pi$
$211$	−8.69942	−0.598893	−0.299446	+	0.954113i	$0.596802\pi$
$212$	10.8867	0.747702
$213$	5.23544	0.358726
$214$	−46.8696	−3.20394
$215$	−0.00693054	−0.000472659 0
$216$	−10.8512	−0.738334
$217$	−12.1380	−0.823982
$218$	−26.9527	−1.82547
$219$	9.77153	0.660299
$220$	−0.00464392	−0.000313093 0
$221$	−4.05105	−0.272503
$222$	26.6548	1.78895
$223$	−24.9388	−1.67003	−0.835014	−	0.550228i	$-0.814541\pi$
$223$	−24.9388	−1.67003	−0.835014	+	0.550228i	$0.814541\pi$
$224$	−7.78940	−0.520451
$225$	−8.29433	−0.552956
$226$	−8.54969	−0.568717
$227$	−13.7708	−0.913997	−0.456999	−	0.889467i	$-0.651076\pi$
$227$	−13.7708	−0.913997	−0.456999	+	0.889467i	$0.651076\pi$
$228$	−0.806292	−0.0533980
$229$	26.7467	1.76747	0.883737	−	0.467984i	$-0.155019\pi$
$229$	26.7467	1.76747	0.883737	+	0.467984i	$0.155019\pi$
$230$	0.00678849	0.000447620 0
$231$	8.70876	0.572994
$232$	−20.3245	−1.33437
$233$	11.3980	0.746707	0.373353	−	0.927689i	$-0.378208\pi$
$233$	11.3980	0.746707	0.373353	+	0.927689i	$0.378208\pi$
$234$	28.1594	1.84083
$235$	−0.00117783	−7.68330e−5 0
$236$	11.1024	0.722705
$237$	−5.69804	−0.370127
$238$	2.95967	0.191847
$239$	6.18876	0.400317	0.200159	−	0.979763i	$-0.435854\pi$
$239$	6.18876	0.400317	0.200159	+	0.979763i	$0.435854\pi$
$240$	0.00259569	0.000167551 0
$241$	−16.5553	−1.06642	−0.533209	−	0.845984i	$-0.679014\pi$
$241$	−16.5553	−1.06642	−0.533209	+	0.845984i	$0.679014\pi$
$242$	18.1925	1.16946
$243$	15.5437	0.997130
$244$	0.690325	0.0441935
$245$	0.00147571	9.42795e−5 0
$246$	−4.77581	−0.304495
$247$	−0.748161	−0.0476044
$248$	−20.4943	−1.30139
$249$	30.1612	1.91139
$250$	−0.0168418	−0.00106517
$251$	18.2346	1.15096	0.575480	−	0.817816i	$-0.304815\pi$
$251$	18.2346	1.15096	0.575480	+	0.817816i	$0.304815\pi$
$252$	−13.2072	−0.831974
$253$	7.32519	0.460531
$254$	41.9325	2.63108
$255$	0.000867531 0	5.43269e−5 0
$256$	−25.2557	−1.57848
$257$	17.1536	1.07001	0.535006	−	0.844848i	$-0.320309\pi$
$257$	17.1536	1.07001	0.535006	+	0.844848i	$0.320309\pi$
$258$	49.6163	3.08897
$259$	−11.6002	−0.720801
$260$	0.0183531	0.00113821
$261$	8.99424	0.556730
$262$	−43.9472	−2.71507
$263$	−18.7412	−1.15563	−0.577817	−	0.816166i	$-0.696095\pi$
$263$	−18.7412	−1.15563	−0.577817	+	0.816166i	$0.696095\pi$
$264$	14.7042	0.904981
$265$	−0.00216330	−0.000132890 0
$266$	0.546602	0.0335143
$267$	−31.5816	−1.93276
$268$	25.5288	1.55942
$269$	−5.76871	−0.351725	−0.175862	−	0.984415i	$-0.556271\pi$
$269$	−5.76871	−0.351725	−0.175862	+	0.984415i	$0.556271\pi$
$270$	0.00487528	0.000296700 0
$271$	16.8569	1.02398	0.511992	−	0.858990i	$-0.328908\pi$
$271$	16.8569	1.02398	0.511992	+	0.858990i	$0.328908\pi$
$272$	0.951888	0.0577167
$273$	−34.4177	−2.08305
$274$	17.9676	1.08546
$275$	−9.08665	−0.547945
$276$	−31.1990	−1.87796
$277$	3.05058	0.183292	0.0916458	−	0.995792i	$-0.470787\pi$
$277$	3.05058	0.183292	0.0916458	+	0.995792i	$0.470787\pi$
$278$	21.6329	1.29746
$279$	9.06936	0.542968
$280$	−0.00593042	−0.000354411 0
$281$	−23.1463	−1.38079	−0.690396	−	0.723431i	$-0.742564\pi$
$281$	−23.1463	−1.38079	−0.690396	+	0.723431i	$0.742564\pi$
$282$	8.43215	0.502127
$283$	0.859303	0.0510803	0.0255401	−	0.999674i	$-0.491869\pi$
$283$	0.859303	0.0510803	0.0255401	+	0.999674i	$0.491869\pi$
$284$	−8.69819	−0.516142
$285$	0.000160218 0	9.49051e−6 0
$286$	30.8493	1.82415
$287$	2.07844	0.122686
$288$	5.82013	0.342954
$289$	−16.6819	−0.981286
$290$	0.00913147	0.000536218 0
$291$	−16.9274	−0.992303
$292$	−16.2345	−0.950050
$293$	−23.8876	−1.39553	−0.697765	−	0.716327i	$-0.745822\pi$
$293$	−23.8876	−1.39553	−0.697765	+	0.716327i	$0.745822\pi$
$294$	−10.5647	−0.616146
$295$	−0.00220616	−0.000128448 0
$296$	−19.5862	−1.13842
$297$	5.26073	0.305258
$298$	14.4664	0.838017
$299$	−28.9497	−1.67421
$300$	38.7013	2.23442
$301$	−21.5931	−1.24460
$302$	12.0583	0.693879
$303$	20.5978	1.18332
$304$	0.175798	0.0100827
$305$	−0.000137174 0	−7.85459e−6 0
$306$	−2.21143	−0.126419
$307$	30.8393	1.76009	0.880045	−	0.474889i	$-0.157512\pi$
$307$	30.8393	1.76009	0.880045	+	0.474889i	$0.157512\pi$
$308$	−14.4688	−0.824435
$309$	−32.5689	−1.85278
$310$	0.00920773	0.000522964 0
$311$	6.96151	0.394751	0.197375	−	0.980328i	$-0.436758\pi$
$311$	6.96151	0.394751	0.197375	+	0.980328i	$0.436758\pi$
$312$	−58.1121	−3.28995
$313$	5.86215	0.331348	0.165674	−	0.986181i	$-0.447020\pi$
$313$	5.86215	0.331348	0.165674	+	0.986181i	$0.447020\pi$
$314$	38.9363	2.19730
$315$	0.00262440	0.000147868 0
$316$	9.46675	0.532546
$317$	23.0117	1.29246	0.646232	−	0.763141i	$-0.276344\pi$
$317$	23.0117	1.29246	0.646232	+	0.763141i	$0.276344\pi$
$318$	15.4872	0.868479
$319$	9.85341	0.551685
$320$	0.00831408	0.000464771 0
$321$	−42.8035	−2.38906
$322$	21.1505	1.17867
$323$	0.0587551	0.00326922
$324$	−40.2525	−2.23625
$325$	35.9111	1.99199
$326$	−18.1750	−1.00662
$327$	−24.6144	−1.36118
$328$	3.50932	0.193770
$329$	−3.66968	−0.202316
$330$	−0.00660635	−0.000363668 0
$331$	−29.6028	−1.62712	−0.813560	−	0.581482i	$-0.802473\pi$
$331$	−29.6028	−1.62712	−0.813560	+	0.581482i	$0.802473\pi$
$332$	−50.1100	−2.75014
$333$	8.66750	0.474976
$334$	−6.08641	−0.333034
$335$	−0.00507282	−0.000277158 0
$336$	8.08723	0.441194
$337$	−0.400718	−0.0218285	−0.0109143	−	0.999940i	$-0.503474\pi$
$337$	−0.400718	−0.0218285	−0.0109143	+	0.999940i	$0.503474\pi$
$338$	−91.1933	−4.96026
$339$	−7.80797	−0.424071
$340$	−0.00144132	−7.81665e−5 0
$341$	9.93570	0.538048
$342$	−0.408414	−0.0220845
$343$	20.1388	1.08739
$344$	−36.4586	−1.96571
$345$	0.00619956	0.000333773 0
$346$	25.8504	1.38973
$347$	32.4725	1.74321	0.871606	−	0.490207i	$-0.163079\pi$
$347$	32.4725	1.74321	0.871606	+	0.490207i	$0.163079\pi$
$348$	−41.9671	−2.24967
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−26.2364	−1.40240
$351$	−20.7908	−1.10973
$352$	6.37610	0.339847
$353$	17.8716	0.951210	0.475605	−	0.879659i	$-0.342229\pi$
$353$	17.8716	0.951210	0.475605	+	0.879659i	$0.342229\pi$
$354$	15.7941	0.839445
$355$	0.00172842	9.17349e−5 0
$356$	52.4699	2.78090
$357$	2.70291	0.143053
$358$	−38.7450	−2.04774
$359$	23.7600	1.25401	0.627003	−	0.779017i	$-0.284281\pi$
$359$	23.7600	1.25401	0.627003	+	0.779017i	$0.284281\pi$
$360$	0.00443113	0.000233541 0
$361$	−18.9891	−0.999429
$362$	−14.5877	−0.766714
$363$	16.6142	0.872019
$364$	57.1817	2.99714
$365$	0.00322595	0.000168854 0
$366$	0.982042	0.0513322
$367$	−8.32300	−0.434457	−0.217228	−	0.976121i	$-0.569702\pi$
$367$	−8.32300	−0.434457	−0.217228	+	0.976121i	$0.569702\pi$
$368$	6.80240	0.354600
$369$	−1.55298	−0.0808450
$370$	0.00879975	0.000457477 0
$371$	−6.74005	−0.349926
$372$	−42.3176	−2.19406
$373$	−4.49825	−0.232911	−0.116455	−	0.993196i	$-0.537153\pi$
$373$	−4.49825	−0.232911	−0.116455	+	0.993196i	$0.537153\pi$
$374$	−2.42267	−0.125273
$375$	−0.0153807	−0.000794255 0
$376$	−6.19603	−0.319536
$377$	−38.9414	−2.00558
$378$	15.1896	0.781270
$379$	23.8781	1.22654	0.613268	−	0.789875i	$-0.289855\pi$
$379$	23.8781	1.22654	0.613268	+	0.789875i	$0.289855\pi$
$380$	−0.000266187 0	−1.36551e−5 0
$381$	38.2947	1.96190
$382$	13.4352	0.687407
$383$	−11.9542	−0.610829	−0.305414	−	0.952220i	$-0.598795\pi$
$383$	−11.9542	−0.610829	−0.305414	+	0.952220i	$0.598795\pi$
$384$	−44.3754	−2.26452
$385$	0.00287509	0.000146528 0
$386$	−10.8906	−0.554319
$387$	16.1340	0.820140
$388$	28.1233	1.42775
$389$	1.52178	0.0771573	0.0385787	−	0.999256i	$-0.487717\pi$
$389$	1.52178	0.0771573	0.0385787	+	0.999256i	$0.487717\pi$
$390$	0.0261088	0.00132207
$391$	2.27350	0.114976
$392$	7.76305	0.392093
$393$	−40.1346	−2.02453
$394$	−56.7093	−2.85698
$395$	−0.00188114	−9.46503e−5 0
$396$	10.8109	0.543267
$397$	22.2889	1.11865	0.559323	−	0.828950i	$-0.311061\pi$
$397$	22.2889	1.11865	0.559323	+	0.828950i	$0.311061\pi$
$398$	48.4126	2.42670
$399$	0.499182	0.0249904
$400$	−8.43814	−0.421907
$401$	32.6387	1.62990	0.814949	−	0.579532i	$-0.196765\pi$
$401$	32.6387	1.62990	0.814949	+	0.579532i	$0.196765\pi$
$402$	36.3167	1.81131
$403$	−39.2666	−1.95601
$404$	−34.2214	−1.70258
$405$	0.00799858	0.000397452 0
$406$	28.4504	1.41197
$407$	9.49546	0.470673
$408$	4.56370	0.225937
$409$	34.9424	1.72779	0.863896	−	0.503671i	$-0.168018\pi$
$409$	34.9424	1.72779	0.863896	+	0.503671i	$0.168018\pi$
$410$	−0.00157668	−7.78665e−5 0
$411$	16.4089	0.809390
$412$	54.1102	2.66582
$413$	−6.87359	−0.338227
$414$	−15.8034	−0.776692
$415$	0.00995736	0.000488787 0
$416$	−25.1988	−1.23547
$417$	19.7562	0.967464
$418$	−0.447427	−0.0218844
$419$	24.7557	1.20940	0.604698	−	0.796455i	$-0.293294\pi$
$419$	24.7557	1.20940	0.604698	+	0.796455i	$0.293294\pi$
$420$	−0.0122454	−0.000597516 0
$421$	7.39907	0.360609	0.180304	−	0.983611i	$-0.442292\pi$
$421$	7.39907	0.360609	0.180304	+	0.983611i	$0.442292\pi$
$422$	20.5609	1.00089
$423$	2.74194	0.133318
$424$	−11.3802	−0.552669
$425$	−2.82019	−0.136800
$426$	−12.3739	−0.599516
$427$	−0.427386	−0.0206827
$428$	71.1140	3.43742
$429$	28.1730	1.36020
$430$	0.0163802	0.000789924 0
$431$	14.3653	0.691952	0.345976	−	0.938243i	$-0.387548\pi$
$431$	14.3653	0.691952	0.345976	+	0.938243i	$0.387548\pi$
$432$	4.88527	0.235043
$433$	−16.6018	−0.797830	−0.398915	−	0.916988i	$-0.630613\pi$
$433$	−16.6018	−0.797830	−0.398915	+	0.916988i	$0.630613\pi$
$434$	28.6880	1.37707
$435$	0.00833928	0.000399838 0
$436$	40.8946	1.95849
$437$	0.419877	0.0200854
$438$	−23.0948	−1.10351
$439$	15.6329	0.746120	0.373060	−	0.927807i	$-0.378309\pi$
$439$	15.6329	0.746120	0.373060	+	0.927807i	$0.378309\pi$
$440$	0.00485441	0.000231425 0
$441$	−3.43539	−0.163590
$442$	9.57459	0.455417
$443$	8.09253	0.384488	0.192244	−	0.981347i	$-0.438424\pi$
$443$	8.09253	0.384488	0.192244	+	0.981347i	$0.438424\pi$
$444$	−40.4425	−1.91932
$445$	−0.0104263	−0.000494254 0
$446$	58.9425	2.79101
$447$	13.2114	0.624878
$448$	25.9037	1.22383
$449$	−18.8431	−0.889262	−0.444631	−	0.895714i	$-0.646665\pi$
$449$	−18.8431	−0.889262	−0.444631	+	0.895714i	$0.646665\pi$
$450$	19.6035	0.924118
$451$	−1.70133	−0.0801125
$452$	12.9722	0.610161
$453$	11.0122	0.517399
$454$	32.5469	1.52750
$455$	−0.0113626	−0.000532686 0
$456$	0.842838	0.0394695
$457$	33.2552	1.55561	0.777805	−	0.628505i	$-0.216333\pi$
$457$	33.2552	1.55561	0.777805	+	0.628505i	$0.216333\pi$
$458$	−63.2154	−2.95386
$459$	1.63276	0.0762105
$460$	−0.0103000	−0.000480239 0
$461$	−30.0427	−1.39923	−0.699613	−	0.714522i	$-0.746644\pi$
$461$	−30.0427	−1.39923	−0.699613	+	0.714522i	$0.746644\pi$
$462$	−20.5830	−0.957608
$463$	2.30680	0.107206	0.0536030	−	0.998562i	$-0.482929\pi$
$463$	2.30680	0.107206	0.0536030	+	0.998562i	$0.482929\pi$
$464$	9.15018	0.424787
$465$	0.00840893	0.000389955 0
$466$	−26.9389	−1.24792
$467$	−0.369357	−0.0170918	−0.00854589	−	0.999963i	$-0.502720\pi$
$467$	−0.369357	−0.0170918	−0.00854589	+	0.999963i	$0.502720\pi$
$468$	−42.7254	−1.97498
$469$	−15.8051	−0.729811
$470$	0.00278377	0.000128406 0
$471$	35.5585	1.63845
$472$	−11.6056	−0.534193
$473$	17.6752	0.812709
$474$	13.4672	0.618569
$475$	−0.520842	−0.0238979
$476$	−4.49063	−0.205828
$477$	5.03607	0.230586
$478$	−14.6270	−0.669024
$479$	4.38013	0.200133	0.100067	−	0.994981i	$-0.468094\pi$
$479$	4.38013	0.200133	0.100067	+	0.994981i	$0.468094\pi$
$480$	0.00539631	0.000246307 0
$481$	−37.5268	−1.71107
$482$	39.1280	1.78223
$483$	19.3156	0.878890
$484$	−27.6029	−1.25468
$485$	−0.00558839	−0.000253756 0
$486$	−36.7373	−1.66644
$487$	37.3600	1.69294	0.846471	−	0.532435i	$-0.178723\pi$
$487$	37.3600	1.69294	0.846471	+	0.532435i	$0.178723\pi$
$488$	−0.721615	−0.0326660
$489$	−16.5982	−0.750598
$490$	−0.00348781	−0.000157563 0
$491$	36.5622	1.65003	0.825014	−	0.565112i	$-0.191167\pi$
$491$	36.5622	1.65003	0.825014	+	0.565112i	$0.191167\pi$
$492$	7.24621	0.326684
$493$	3.05817	0.137733
$494$	1.76827	0.0795580
$495$	−0.00214823	−9.65558e−5 0
$496$	9.22660	0.414287
$497$	5.38512	0.241556
$498$	−71.2854	−3.19438
$499$	−6.78842	−0.303891	−0.151946	−	0.988389i	$-0.548554\pi$
$499$	−6.78842	−0.303891	−0.151946	+	0.988389i	$0.548554\pi$
$500$	0.0255535	0.00114279
$501$	−5.55839	−0.248331
$502$	−43.0972	−1.92352
$503$	−35.2059	−1.56975	−0.784877	−	0.619652i	$-0.787274\pi$
$503$	−35.2059	−1.56975	−0.784877	+	0.619652i	$0.787274\pi$
$504$	13.8058	0.614960
$505$	0.00680013	0.000302602 0
$506$	−17.3130	−0.769655
$507$	−83.2820	−3.69868
$508$	−63.6230	−2.82282
$509$	−15.7186	−0.696716	−0.348358	−	0.937362i	$-0.613261\pi$
$509$	−15.7186	−0.696716	−0.348358	+	0.937362i	$0.613261\pi$
$510$	−0.00205039	−9.07929e−5 0
$511$	10.0509	0.444626
$512$	18.5735	0.820840
$513$	0.301542	0.0133134
$514$	−40.5422	−1.78824
$515$	−0.0107522	−0.000473800 0
$516$	−75.2814	−3.31408
$517$	3.00386	0.132110
$518$	27.4168	1.20463
$519$	23.6078	1.03627
$520$	−0.0191850	−0.000841318 0
$521$	13.5882	0.595312	0.297656	−	0.954673i	$-0.403795\pi$
$521$	13.5882	0.595312	0.297656	+	0.954673i	$0.403795\pi$
$522$	−21.2577	−0.930425
$523$	−13.7532	−0.601385	−0.300692	−	0.953721i	$-0.597218\pi$
$523$	−13.7532	−0.601385	−0.300692	+	0.953721i	$0.597218\pi$
$524$	66.6799	2.91293
$525$	−23.9603	−1.04571
$526$	44.2946	1.93134
$527$	3.08371	0.134329
$528$	−6.61989	−0.288094
$529$	−6.75308	−0.293612
$530$	0.00511291	0.000222091 0
$531$	5.13586	0.222877
$532$	−0.829344	−0.0359566
$533$	6.72378	0.291239
$534$	74.6426	3.23010
$535$	−0.0141311	−0.000610939 0
$536$	−26.6859	−1.15266
$537$	−35.3838	−1.52692
$538$	13.6342	0.587814
$539$	−3.76356	−0.162108
$540$	−0.00739713	−0.000318322 0
$541$	8.21089	0.353014	0.176507	−	0.984299i	$-0.443520\pi$
$541$	8.21089	0.353014	0.176507	+	0.984299i	$0.443520\pi$
$542$	−39.8410	−1.71132
$543$	−13.3222	−0.571710
$544$	1.97893	0.0848459
$545$	−0.00812616	−0.000348086 0
$546$	81.3455	3.48127
$547$	−21.2884	−0.910227	−0.455113	−	0.890433i	$-0.650401\pi$
$547$	−21.2884	−0.910227	−0.455113	+	0.890433i	$0.650401\pi$
$548$	−27.2618	−1.16457
$549$	0.319337	0.0136290
$550$	21.4761	0.915745
$551$	0.564793	0.0240610
$552$	32.6132	1.38811
$553$	−5.86094	−0.249233
$554$	−7.20999	−0.306323
$555$	0.00803634	0.000341124 0
$556$	−32.8230	−1.39201
$557$	−17.0387	−0.721952	−0.360976	−	0.932575i	$-0.617556\pi$
$557$	−17.0387	−0.721952	−0.360976	+	0.932575i	$0.617556\pi$
$558$	−21.4353	−0.907427
$559$	−69.8539	−2.95450
$560$	0.00266990	0.000112824 0
$561$	−2.21250	−0.0934117
$562$	54.7058	2.30763
$563$	−0.784415	−0.0330591	−0.0165296	−	0.999863i	$-0.505262\pi$
$563$	−0.784415	−0.0330591	−0.0165296	+	0.999863i	$0.505262\pi$
$564$	−12.7939	−0.538719
$565$	−0.00257771	−0.000108445 0
$566$	−2.03095	−0.0853671
$567$	24.9207	1.04657
$568$	9.09245	0.381511
$569$	−10.2873	−0.431267	−0.215634	−	0.976474i	$-0.569182\pi$
$569$	−10.2873	−0.431267	−0.215634	+	0.976474i	$0.569182\pi$
$570$	−0.000378673 0	−1.58609e−5 0
$571$	−42.5986	−1.78270	−0.891348	−	0.453320i	$-0.850240\pi$
$571$	−42.5986	−1.78270	−0.891348	+	0.453320i	$0.850240\pi$
$572$	−46.8067	−1.95709
$573$	12.2697	0.512573
$574$	−4.91236	−0.205038
$575$	−20.1537	−0.840469
$576$	−19.3549	−0.806453
$577$	45.6865	1.90195	0.950977	−	0.309261i	$-0.100082\pi$
$577$	45.6865	1.90195	0.950977	+	0.309261i	$0.100082\pi$
$578$	39.4273	1.63996
$579$	−9.94584	−0.413335
$580$	−0.0138549	−0.000575294 0
$581$	31.0235	1.28707
$582$	40.0077	1.65837
$583$	5.51714	0.228497
$584$	16.9703	0.702237
$585$	0.00848997	0.000351017 0
$586$	56.4580	2.33226
$587$	40.4543	1.66973	0.834863	−	0.550458i	$-0.185547\pi$
$587$	40.4543	1.66973	0.834863	+	0.550458i	$0.185547\pi$
$588$	16.0295	0.661047
$589$	0.569510	0.0234662
$590$	0.00521422	0.000214666 0
$591$	−51.7896	−2.13034
$592$	8.81778	0.362409
$593$	−19.7391	−0.810589	−0.405295	−	0.914186i	$-0.632831\pi$
$593$	−19.7391	−0.810589	−0.405295	+	0.914186i	$0.632831\pi$
$594$	−12.4336	−0.510158
$595$	0.000892333 0	3.65821e−5 0
$596$	−21.9495	−0.899086
$597$	44.2126	1.80950
$598$	68.4221	2.79799
$599$	19.4564	0.794966	0.397483	−	0.917610i	$-0.369884\pi$
$599$	19.4564	0.794966	0.397483	+	0.917610i	$0.369884\pi$
$600$	−40.4555	−1.65159
$601$	8.55170	0.348831	0.174415	−	0.984672i	$-0.444196\pi$
$601$	8.55170	0.348831	0.174415	+	0.984672i	$0.444196\pi$
$602$	51.0348	2.08002
$603$	11.8093	0.480914
$604$	−18.2958	−0.744444
$605$	0.00548498	0.000222996 0
$606$	−48.6826	−1.97760
$607$	−12.5811	−0.510649	−0.255325	−	0.966855i	$-0.582182\pi$
$607$	−12.5811	−0.510649	−0.255325	+	0.966855i	$0.582182\pi$
$608$	0.365475	0.0148220
$609$	25.9822	1.05285
$610$	0.000324209 0	1.31269e−5 0
$611$	−11.8715	−0.480269
$612$	3.35534	0.135632
$613$	−5.24500	−0.211844	−0.105922	−	0.994374i	$-0.533779\pi$
$613$	−5.24500	−0.211844	−0.105922	+	0.994374i	$0.533779\pi$
$614$	−72.8881	−2.94152
$615$	−0.00143989	−5.80621e−5 0
$616$	15.1246	0.609388
$617$	3.60746	0.145231	0.0726153	−	0.997360i	$-0.476865\pi$
$617$	3.60746	0.145231	0.0726153	+	0.997360i	$0.476865\pi$
$618$	76.9761	3.09643
$619$	19.2384	0.773259	0.386629	−	0.922235i	$-0.373639\pi$
$619$	19.2384	0.773259	0.386629	+	0.922235i	$0.373639\pi$
$620$	−0.0139706	−0.000561074 0
$621$	11.6680	0.468222
$622$	−16.4534	−0.659721
$623$	−32.4846	−1.30147
$624$	26.1623	1.04733
$625$	25.0000	1.00000
$626$	−13.8551	−0.553761
$627$	−0.408611	−0.0163184
$628$	−59.0770	−2.35743
$629$	2.94708	0.117508
$630$	−0.00620272	−0.000247122 0
$631$	−23.7473	−0.945363	−0.472682	−	0.881233i	$-0.656714\pi$
$631$	−23.7473	−0.945363	−0.472682	+	0.881233i	$0.656714\pi$
$632$	−9.89584	−0.393635
$633$	18.7772	0.746326
$634$	−54.3876	−2.16001
$635$	0.0126425	0.000501704 0
$636$	−23.4983	−0.931768
$637$	14.8739	0.589324
$638$	−23.2884	−0.921995
$639$	−4.02369	−0.159175
$640$	−0.0146500	−0.000579092 0
$641$	−42.2589	−1.66913	−0.834564	−	0.550911i	$-0.814280\pi$
$641$	−42.2589	−1.66913	−0.834564	+	0.550911i	$0.814280\pi$
$642$	101.165	3.99268
$643$	−21.3297	−0.841160	−0.420580	−	0.907256i	$-0.638173\pi$
$643$	−21.3297	−0.841160	−0.420580	+	0.907256i	$0.638173\pi$
$644$	−32.0910	−1.26456
$645$	0.0149592	0.000589017 0
$646$	−0.138867	−0.00546363
$647$	−13.7728	−0.541467	−0.270733	−	0.962654i	$-0.587266\pi$
$647$	−13.7728	−0.541467	−0.270733	+	0.962654i	$0.587266\pi$
$648$	42.0770	1.65294
$649$	5.62646	0.220858
$650$	−84.8752	−3.32908
$651$	26.1992	1.02683
$652$	27.5764	1.07997
$653$	−37.3288	−1.46079	−0.730395	−	0.683025i	$-0.760664\pi$
$653$	−37.3288	−1.46079	−0.730395	+	0.683025i	$0.760664\pi$
$654$	58.1758	2.27485
$655$	−0.0132500	−0.000517719 0
$656$	−1.57991	−0.0616850
$657$	−7.50990	−0.292989
$658$	8.67323	0.338118
$659$	33.0194	1.28625	0.643126	−	0.765760i	$-0.277637\pi$
$659$	33.0194	1.28625	0.643126	+	0.765760i	$0.277637\pi$
$660$	0.0100236	0.000390169 0
$661$	−21.6072	−0.840423	−0.420211	−	0.907426i	$-0.638044\pi$
$661$	−21.6072	−0.840423	−0.420211	+	0.907426i	$0.638044\pi$
$662$	69.9658	2.71930
$663$	8.74396	0.339587
$664$	52.3813	2.03279
$665$	0.000164799 0	6.39063e−6 0
$666$	−20.4855	−0.793796
$667$	21.8544	0.846205
$668$	9.23474	0.357303
$669$	53.8290	2.08115
$670$	0.0119895	0.000463196 0
$671$	0.349842	0.0135055
$672$	16.8129	0.648574
$673$	23.9814	0.924416	0.462208	−	0.886772i	$-0.347057\pi$
$673$	23.9814	0.924416	0.462208	+	0.886772i	$0.347057\pi$
$674$	0.947090	0.0364805
$675$	−14.4738	−0.557096
$676$	138.365	5.32173
$677$	26.9804	1.03694	0.518471	−	0.855095i	$-0.326502\pi$
$677$	26.9804	1.03694	0.518471	+	0.855095i	$0.326502\pi$
$678$	18.4540	0.708721
$679$	−17.4114	−0.668188
$680$	0.00150665	5.77774e−5 0
$681$	29.7234	1.13900
$682$	−23.4828	−0.899205
$683$	34.4648	1.31876	0.659379	−	0.751811i	$-0.270819\pi$
$683$	34.4648	1.31876	0.659379	+	0.751811i	$0.270819\pi$
$684$	0.619675	0.0236938
$685$	0.00541719	0.000206980 0
$686$	−47.5978	−1.81729
$687$	−57.7313	−2.20258
$688$	16.4138	0.625770
$689$	−21.8042	−0.830672
$690$	−0.0146526	−0.000557813 0
$691$	38.1496	1.45128	0.725640	−	0.688074i	$-0.241544\pi$
$691$	38.1496	1.45128	0.725640	+	0.688074i	$0.241544\pi$
$692$	−39.2221	−1.49100
$693$	−6.69311	−0.254250
$694$	−76.7480	−2.91332
$695$	0.00652226	0.000247404 0
$696$	43.8693	1.66286
$697$	−0.528037	−0.0200008
$698$	−2.36348	−0.0894591
$699$	−24.6019	−0.930529
$700$	39.8078	1.50459
$701$	47.7815	1.80468	0.902340	−	0.431024i	$-0.141848\pi$
$701$	47.7815	1.80468	0.902340	+	0.431024i	$0.141848\pi$
$702$	49.1386	1.85462
$703$	0.544276	0.0205277
$704$	−21.2037	−0.799146
$705$	0.00254227	9.57474e−5 0
$706$	−42.2392	−1.58969
$707$	21.1867	0.796809
$708$	−23.9639	−0.900618
$709$	−28.4048	−1.06676	−0.533382	−	0.845874i	$-0.679079\pi$
$709$	−28.4048	−1.06676	−0.533382	+	0.845874i	$0.679079\pi$
$710$	−0.00408508	−0.000153310 0
$711$	4.37922	0.164234
$712$	−54.8482	−2.05552
$713$	22.0369	0.825288
$714$	−6.38828	−0.239075
$715$	0.00930096	0.000347836 0
$716$	58.7868	2.19697
$717$	−13.3581	−0.498866
$718$	−56.1564	−2.09574
$719$	−51.1820	−1.90877	−0.954383	−	0.298586i	$-0.903485\pi$
$719$	−51.1820	−1.90877	−0.954383	+	0.298586i	$0.903485\pi$
$720$	−0.00199491	−7.43460e−5 0
$721$	−33.5001	−1.24761
$722$	44.8805	1.67028
$723$	35.7335	1.32894
$724$	22.1335	0.822587
$725$	−27.1096	−1.00682
$726$	−39.2673	−1.45735
$727$	−18.1494	−0.673123	−0.336561	−	0.941662i	$-0.609264\pi$
$727$	−18.1494	−0.673123	−0.336561	+	0.941662i	$0.609264\pi$
$728$	−59.7736	−2.21536
$729$	0.124093	0.00459603
$730$	−0.00762448	−0.000282195 0
$731$	5.48581	0.202900
$732$	−1.49003	−0.0550729
$733$	23.2955	0.860438	0.430219	−	0.902724i	$-0.358436\pi$
$733$	23.2955	0.860438	0.430219	+	0.902724i	$0.358436\pi$
$734$	19.6712	0.726079
$735$	−0.00318523	−0.000117489 0
$736$	14.1419	0.521276
$737$	12.9374	0.476556
$738$	3.67045	0.135111
$739$	−37.1673	−1.36722	−0.683610	−	0.729847i	$-0.739591\pi$
$739$	−37.1673	−1.36722	−0.683610	+	0.729847i	$0.739591\pi$
$740$	−0.0133516	−0.000490815 0
$741$	1.61486	0.0593234
$742$	15.9300	0.584808
$743$	−41.9300	−1.53826	−0.769131	−	0.639092i	$-0.779311\pi$
$743$	−41.9300	−1.53826	−0.769131	+	0.639092i	$0.779311\pi$
$744$	44.2357	1.62176
$745$	0.00436159	0.000159796 0
$746$	10.6315	0.389248
$747$	−23.1804	−0.848125
$748$	3.67586	0.134403
$749$	−44.0273	−1.60872
$750$	0.0363520	0.00132739
$751$	8.71994	0.318195	0.159098	−	0.987263i	$-0.449142\pi$
$751$	8.71994	0.318195	0.159098	+	0.987263i	$0.449142\pi$
$752$	2.78948	0.101722
$753$	−39.3584	−1.43430
$754$	92.0373	3.35180
$755$	0.00363555	0.000132311 0
$756$	−23.0468	−0.838203
$757$	−20.3670	−0.740251	−0.370125	−	0.928982i	$-0.620685\pi$
$757$	−20.3670	−0.740251	−0.370125	+	0.928982i	$0.620685\pi$
$758$	−56.4354	−2.04983
$759$	−15.8110	−0.573903
$760$	0.000278253 0	1.00933e−5 0
$761$	−34.5731	−1.25327	−0.626637	−	0.779311i	$-0.715569\pi$
$761$	−34.5731	−1.25327	−0.626637	+	0.779311i	$0.715569\pi$
$762$	−90.5088	−3.27879
$763$	−25.3182	−0.916579
$764$	−20.3849	−0.737501
$765$	−0.000666740 0	−2.41060e−5 0
$766$	28.2534	1.02084
$767$	−22.2362	−0.802902
$768$	54.5130	1.96707
$769$	−38.2705	−1.38007	−0.690034	−	0.723777i	$-0.742405\pi$
$769$	−38.2705	−1.38007	−0.690034	+	0.723777i	$0.742405\pi$
$770$	−0.00679523	−0.000244883 0
$771$	−37.0250	−1.33342
$772$	16.5241	0.594714
$773$	25.4557	0.915577	0.457788	−	0.889061i	$-0.348642\pi$
$773$	25.4557	0.915577	0.457788	+	0.889061i	$0.348642\pi$
$774$	−38.1325	−1.37065
$775$	−27.3360	−0.981938
$776$	−29.3981	−1.05533
$777$	25.0383	0.898245
$778$	−3.59670	−0.128948
$779$	−0.0975195	−0.00349400
$780$	−0.0396141	−0.00141841
$781$	−4.40805	−0.157732
$782$	−5.37337	−0.192151
$783$	15.6951	0.560898
$784$	−3.49496	−0.124820
$785$	0.0117392	0.000418990 0
$786$	94.8575	3.38345
$787$	27.2348	0.970816	0.485408	−	0.874288i	$-0.338671\pi$
$787$	27.2348	0.970816	0.485408	+	0.874288i	$0.338671\pi$
$788$	86.0435	3.06517
$789$	40.4519	1.44012
$790$	0.00444603	0.000158183 0
$791$	−8.03120	−0.285557
$792$	−11.3009	−0.401560
$793$	−1.38260	−0.0490976
$794$	−52.6793	−1.86952
$795$	0.00466935	0.000165605 0
$796$	−73.4551	−2.60355
$797$	17.7783	0.629741	0.314871	−	0.949135i	$-0.398039\pi$
$797$	17.7783	0.629741	0.314871	+	0.949135i	$0.398039\pi$
$798$	−1.17981	−0.0417647
$799$	0.932299	0.0329824
$800$	−17.5425	−0.620220
$801$	24.2720	0.857610
$802$	−77.1410	−2.72394
$803$	−8.22727	−0.290334
$804$	−55.1024	−1.94331
$805$	0.00637681	0.000224753 0
$806$	92.8060	3.26895
$807$	12.4514	0.438311
$808$	35.7725	1.25847
$809$	−21.8912	−0.769652	−0.384826	−	0.922989i	$-0.625739\pi$
$809$	−21.8912	−0.769652	−0.384826	+	0.922989i	$0.625739\pi$
$810$	−0.0189045	−0.000664236 0
$811$	2.87360	0.100906	0.0504528	−	0.998726i	$-0.483934\pi$
$811$	2.87360	0.100906	0.0504528	+	0.998726i	$0.483934\pi$
$812$	−43.1669	−1.51486
$813$	−36.3846	−1.27606
$814$	−22.4423	−0.786604
$815$	−0.00547970	−0.000191946 0
$816$	−2.05459	−0.0719252
$817$	1.01314	0.0354452
$818$	−82.5857	−2.88754
$819$	26.4517	0.924296
$820$	0.00239225	8.35409e−5 0
$821$	11.5915	0.404546	0.202273	−	0.979329i	$-0.435167\pi$
$821$	11.5915	0.404546	0.202273	+	0.979329i	$0.435167\pi$
$822$	−38.7821	−1.35268
$823$	55.3892	1.93075	0.965373	−	0.260872i	$-0.0840101\pi$
$823$	55.3892	1.93075	0.965373	+	0.260872i	$0.0840101\pi$
$824$	−56.5628	−1.97046
$825$	19.6130	0.682837
$826$	16.2456	0.565257
$827$	15.7077	0.546212	0.273106	−	0.961984i	$-0.411949\pi$
$827$	15.7077	0.546212	0.273106	+	0.961984i	$0.411949\pi$
$828$	23.9780	0.833293
$829$	17.8082	0.618505	0.309252	−	0.950980i	$-0.399921\pi$
$829$	17.8082	0.618505	0.309252	+	0.950980i	$0.399921\pi$
$830$	−0.0235340	−0.000816878 0
$831$	−6.58450	−0.228414
$832$	83.7988	2.90520
$833$	−1.16808	−0.0404717
$834$	−46.6934	−1.61686
$835$	−0.00183504	−6.35040e−5 0
$836$	0.678869	0.0234792
$837$	15.8262	0.547034
$838$	−58.5097	−2.02118
$839$	13.3547	0.461055	0.230527	−	0.973066i	$-0.425955\pi$
$839$	13.3547	0.461055	0.230527	+	0.973066i	$0.425955\pi$
$840$	0.0128005	0.000441658 0
$841$	0.397188	0.0136962
$842$	−17.4876	−0.602661
$843$	49.9599	1.72071
$844$	−31.1965	−1.07383
$845$	−0.0274945	−0.000945841 0
$846$	−6.48052	−0.222805
$847$	17.0892	0.587192
$848$	5.12339	0.175938
$849$	−1.85475	−0.0636550
$850$	6.66548	0.228624
$851$	21.0605	0.721943
$852$	18.7745	0.643205
$853$	−21.6954	−0.742835	−0.371418	−	0.928466i	$-0.621128\pi$
$853$	−21.6954	−0.742835	−0.371418	+	0.928466i	$0.621128\pi$
$854$	1.01012	0.0345656
$855$	−0.000123136 0	−4.21115e−6 0
$856$	−74.3373	−2.54080
$857$	−46.4520	−1.58677	−0.793385	−	0.608720i	$-0.791683\pi$
$857$	−46.4520	−1.58677	−0.793385	+	0.608720i	$0.791683\pi$
$858$	−66.5863	−2.27322
$859$	10.7617	0.367186	0.183593	−	0.983002i	$-0.441227\pi$
$859$	10.7617	0.367186	0.183593	+	0.983002i	$0.441227\pi$
$860$	−0.0248532	−0.000847489 0
$861$	−4.48619	−0.152889
$862$	−33.9521	−1.15641
$863$	40.9666	1.39452	0.697260	−	0.716818i	$-0.254402\pi$
$863$	40.9666	1.39452	0.697260	+	0.716818i	$0.254402\pi$
$864$	10.1562	0.345522
$865$	0.00779383	0.000264998 0
$866$	39.2380	1.33336
$867$	36.0068	1.22286
$868$	−43.5275	−1.47742
$869$	4.79754	0.162745
$870$	−0.0197097	−0.000668223 0
$871$	−51.1297	−1.73246
$872$	−42.7482	−1.44764
$873$	13.0096	0.440307
$874$	−0.992371	−0.0335674
$875$	−0.0158204	−0.000534828 0
$876$	35.0411	1.18393
$877$	−16.0253	−0.541135	−0.270568	−	0.962701i	$-0.587211\pi$
$877$	−16.0253	−0.541135	−0.270568	+	0.962701i	$0.587211\pi$
$878$	−36.9482	−1.24694
$879$	51.5600	1.73908
$880$	−0.00218548	−7.36724e−5 0
$881$	51.7821	1.74458	0.872292	−	0.488985i	$-0.162633\pi$
$881$	51.7821	1.74458	0.872292	+	0.488985i	$0.162633\pi$
$882$	8.11949	0.273397
$883$	39.5968	1.33254	0.666269	−	0.745711i	$-0.267890\pi$
$883$	39.5968	1.33254	0.666269	+	0.745711i	$0.267890\pi$
$884$	−14.5273	−0.488605
$885$	0.00476186	0.000160068 0
$886$	−19.1265	−0.642569
$887$	3.22730	0.108362	0.0541811	−	0.998531i	$-0.482745\pi$
$887$	3.22730	0.108362	0.0541811	+	0.998531i	$0.482745\pi$
$888$	42.2757	1.41868
$889$	39.3896	1.32108
$890$	0.0246423	0.000826013 0
$891$	−20.3991	−0.683395
$892$	−89.4318	−2.99440
$893$	0.172180	0.00576178
$894$	−31.2249	−1.04432
$895$	−0.0116815	−0.000390470 0
$896$	−45.6441	−1.52486
$897$	62.4862	2.08636
$898$	44.5354	1.48617
$899$	29.6427	0.988640
$900$	−29.7439	−0.991462
$901$	1.71234	0.0570463
$902$	4.02106	0.133887
$903$	46.6074	1.55100
$904$	−13.5602	−0.451005
$905$	−0.00439816	−0.000146200 0
$906$	−26.0272	−0.864695
$907$	−14.1035	−0.468299	−0.234150	−	0.972201i	$-0.575231\pi$
$907$	−14.1035	−0.468299	−0.234150	+	0.972201i	$0.575231\pi$
$908$	−49.3826	−1.63882
$909$	−15.8304	−0.525063
$910$	0.0268552	0.000890243 0
$911$	−21.2499	−0.704039	−0.352020	−	0.935993i	$-0.614505\pi$
$911$	−21.2499	−0.704039	−0.352020	+	0.935993i	$0.614505\pi$
$912$	−0.379449	−0.0125648
$913$	−25.3946	−0.840440
$914$	−78.5979	−2.59979
$915$	0.000296083 0	9.78820e−6 0
$916$	95.9150	3.16912
$917$	−41.2821	−1.36326
$918$	−3.85899	−0.127366
$919$	1.10227	0.0363604	0.0181802	−	0.999835i	$-0.494213\pi$
$919$	1.10227	0.0363604	0.0181802	+	0.999835i	$0.494213\pi$
$920$	0.0107669	0.000354973 0
$921$	−66.5648	−2.19338
$922$	71.0053	2.33843
$923$	17.4210	0.573418
$924$	31.2300	1.02739
$925$	−26.1248	−0.858977
$926$	−5.45207	−0.179166
$927$	25.0308	0.822120
$928$	19.0228	0.624453
$929$	11.1560	0.366017	0.183009	−	0.983111i	$-0.441416\pi$
$929$	11.1560	0.366017	0.183009	+	0.983111i	$0.441416\pi$
$930$	−0.0198743	−0.000651705 0
$931$	−0.215725	−0.00707011
$932$	40.8737	1.33886
$933$	−15.0260	−0.491929
$934$	0.872968	0.0285644
$935$	−0.000730429 0	−2.38876e−5 0
$936$	44.6620	1.45982
$937$	−51.1035	−1.66948	−0.834740	−	0.550645i	$-0.814382\pi$
$937$	−51.1035	−1.66948	−0.834740	+	0.550645i	$0.814382\pi$
$938$	37.3550	1.21969
$939$	−12.6531	−0.412919
$940$	−0.00422374	−0.000137763 0
$941$	46.0295	1.50052	0.750260	−	0.661143i	$-0.229928\pi$
$941$	46.0295	1.50052	0.750260	+	0.661143i	$0.229928\pi$
$942$	−84.0418	−2.73823
$943$	−3.77347	−0.122881
$944$	5.22490	0.170056
$945$	0.00457963	0.000148975 0
$946$	−41.7751	−1.35823
$947$	42.1159	1.36858	0.684291	−	0.729209i	$-0.260112\pi$
$947$	42.1159	1.36858	0.684291	+	0.729209i	$0.260112\pi$
$948$	−20.4334	−0.663646
$949$	32.5148	1.05548
$950$	1.23100	0.0399390
$951$	−49.6693	−1.61064
$952$	4.69418	0.152139
$953$	−27.2878	−0.883939	−0.441970	−	0.897030i	$-0.645720\pi$
$953$	−27.2878	−0.883939	−0.441970	+	0.897030i	$0.645720\pi$
$954$	−11.9027	−0.385363
$955$	0.00405069	0.000131077 0
$956$	22.1932	0.717778
$957$	−21.2680	−0.687497
$958$	−10.3524	−0.334469
$959$	16.8780	0.545019
$960$	−0.0179455	−0.000579187 0
$961$	−1.10973	−0.0357978
$962$	88.6939	2.85960
$963$	32.8966	1.06008
$964$	−59.3679	−1.91211
$965$	−0.00328350	−0.000105700 0
$966$	−45.6521	−1.46883
$967$	−23.8279	−0.766252	−0.383126	−	0.923696i	$-0.625153\pi$
$967$	−23.8279	−0.766252	−0.383126	+	0.923696i	$0.625153\pi$
$968$	28.8541	0.927405
$969$	−0.126819	−0.00407402
$970$	0.0132080	0.000424085 0
$971$	16.5938	0.532519	0.266260	−	0.963901i	$-0.414212\pi$
$971$	16.5938	0.532519	0.266260	+	0.963901i	$0.414212\pi$
$972$	55.7405	1.78788
$973$	20.3210	0.651462
$974$	−88.2996	−2.82930
$975$	−77.5120	−2.48237
$976$	0.324874	0.0103990
$977$	35.3393	1.13060	0.565302	−	0.824884i	$-0.308760\pi$
$977$	35.3393	1.13060	0.565302	+	0.824884i	$0.308760\pi$
$978$	39.2296	1.25442
$979$	26.5906	0.849839
$980$	0.00529196	0.000169045 0
$981$	18.9174	0.603986
$982$	−86.4141	−2.75758
$983$	−37.5905	−1.19895	−0.599475	−	0.800394i	$-0.704624\pi$
$983$	−37.5905	−1.19895	−0.599475	+	0.800394i	$0.704624\pi$
$984$	−7.57465	−0.241471
$985$	−0.0170977	−0.000544778 0
$986$	−7.22793	−0.230184
$987$	7.92079	0.252122
$988$	−2.68294	−0.0853557
$989$	39.2028	1.24658
$990$	0.00507730	0.000161367 0
$991$	23.8676	0.758181	0.379090	−	0.925360i	$-0.376237\pi$
$991$	23.8676	0.758181	0.379090	+	0.925360i	$0.376237\pi$
$992$	19.1817	0.609018
$993$	63.8960	2.02768
$994$	−12.7276	−0.403696
$995$	0.0145963	0.000462733 0
$996$	108.159	3.42716
$997$	0.731419	0.0231643	0.0115821	−	0.999933i	$-0.496313\pi$
$997$	0.731419	0.0231643	0.0115821	+	0.999933i	$0.496313\pi$
$998$	16.0443	0.507874
$999$	15.1250	0.478533

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.b.1.2	✓	17
3.2	odd	2		3141.2.a.e.1.16		17
4.3	odd	2		5584.2.a.m.1.15		17
5.4	even	2		8725.2.a.m.1.16		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.b.1.2	✓	17	1.1	even	1	trivial
3141.2.a.e.1.16		17	3.2	odd	2
5584.2.a.m.1.15		17	4.3	odd	2
8725.2.a.m.1.16		17	5.4	even	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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36348 q^{2} -2.15844 q^{3} +3.58604 q^{4} -0.000712583 q^{5} +5.10144 q^{6} -2.22015 q^{7} -3.74859 q^{8} +1.65887 q^{9} +O(q^{10})\)	\(q-2.36348 q^{2} -2.15844 q^{3} +3.58604 q^{4} -0.000712583 q^{5} +5.10144 q^{6} -2.22015 q^{7} -3.74859 q^{8} +1.65887 q^{9} +0.00168418 q^{10} +1.81733 q^{11} -7.74027 q^{12} -7.18222 q^{13} +5.24729 q^{14} +0.00153807 q^{15} +1.68763 q^{16} +0.564039 q^{17} -3.92070 q^{18} +0.104168 q^{19} -0.00255536 q^{20} +4.79207 q^{21} -4.29522 q^{22} +4.03075 q^{23} +8.09111 q^{24} -5.00000 q^{25} +16.9750 q^{26} +2.89476 q^{27} -7.96156 q^{28} +5.42192 q^{29} -0.00363520 q^{30} +5.46720 q^{31} +3.50850 q^{32} -3.92260 q^{33} -1.33310 q^{34} +0.00158204 q^{35} +5.94877 q^{36} +5.22495 q^{37} -0.246200 q^{38} +15.5024 q^{39} +0.00267118 q^{40} -0.936170 q^{41} -11.3260 q^{42} +9.72594 q^{43} +6.51702 q^{44} -0.00118208 q^{45} -9.52659 q^{46} +1.65290 q^{47} -3.64265 q^{48} -2.07093 q^{49} +11.8174 q^{50} -1.21744 q^{51} -25.7558 q^{52} +3.03585 q^{53} -6.84170 q^{54} -0.00129500 q^{55} +8.32243 q^{56} -0.224842 q^{57} -12.8146 q^{58} +3.09600 q^{59} +0.00551558 q^{60} +0.192503 q^{61} -12.9216 q^{62} -3.68294 q^{63} -11.6675 q^{64} +0.00511793 q^{65} +9.27099 q^{66} +7.11892 q^{67} +2.02267 q^{68} -8.70013 q^{69} -0.00373913 q^{70} -2.42557 q^{71} -6.21841 q^{72} -4.52712 q^{73} -12.3491 q^{74} +10.7922 q^{75} +0.373553 q^{76} -4.03475 q^{77} -36.6396 q^{78} +2.63989 q^{79} -0.00120258 q^{80} -11.2248 q^{81} +2.21262 q^{82} -13.9736 q^{83} +17.1846 q^{84} -0.000401925 q^{85} -22.9871 q^{86} -11.7029 q^{87} -6.81242 q^{88} +14.6317 q^{89} +0.00279383 q^{90} +15.9456 q^{91} +14.4544 q^{92} -11.8006 q^{93} -3.90659 q^{94} -7.42287e-5 q^{95} -7.57288 q^{96} +7.84243 q^{97} +4.89460 q^{98} +3.01471 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9} - 6 q^{10} + 39 q^{11} + 4 q^{12} - 6 q^{13} + 11 q^{14} + 12 q^{15} + 23 q^{16} + q^{17} + 7 q^{19} + 8 q^{20} - 3 q^{21} - q^{22} + 8 q^{23} - 21 q^{24} + 14 q^{25} + q^{26} + 9 q^{27} - 23 q^{28} + 9 q^{29} - 27 q^{30} - 2 q^{31} + 23 q^{32} - 5 q^{33} - 12 q^{34} + 16 q^{35} + 10 q^{36} - 7 q^{37} - 8 q^{38} - 39 q^{40} + 3 q^{41} - 30 q^{42} + q^{43} + 56 q^{44} - 21 q^{45} - q^{46} + 16 q^{47} - 31 q^{48} + 6 q^{49} - 5 q^{50} + 29 q^{51} - 37 q^{52} + 27 q^{53} - 36 q^{54} - 16 q^{55} + 14 q^{56} - 21 q^{57} - 44 q^{58} + 74 q^{59} - 27 q^{60} - 30 q^{61} - 18 q^{62} - 9 q^{63} - 17 q^{64} - 3 q^{65} - 66 q^{66} + 9 q^{67} - 51 q^{68} - 23 q^{69} - 77 q^{70} + 70 q^{71} - 55 q^{72} - 38 q^{73} + 26 q^{74} + 22 q^{75} - 50 q^{76} - 38 q^{77} - 75 q^{78} + 7 q^{79} - 28 q^{80} + 5 q^{81} - 56 q^{82} + 47 q^{83} - 69 q^{84} - 49 q^{85} + 17 q^{86} - 37 q^{87} - 30 q^{88} + 23 q^{89} - 64 q^{90} + 6 q^{91} + 17 q^{92} - 31 q^{93} - 40 q^{94} - 11 q^{95} - 49 q^{96} - 14 q^{97} + 5 q^{98} + 79 q^{99}+O(q^{100}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9 - 6 * q^10 + 39 * q^11 + 4 * q^12 - 6 * q^13 + 11 * q^14 + 12 * q^15 + 23 * q^16 + q^17 + 7 * q^19 + 8 * q^20 - 3 * q^21 - q^22 + 8 * q^23 - 21 * q^24 + 14 * q^25 + q^26 + 9 * q^27 - 23 * q^28 + 9 * q^29 - 27 * q^30 - 2 * q^31 + 23 * q^32 - 5 * q^33 - 12 * q^34 + 16 * q^35 + 10 * q^36 - 7 * q^37 - 8 * q^38 - 39 * q^40 + 3 * q^41 - 30 * q^42 + q^43 + 56 * q^44 - 21 * q^45 - q^46 + 16 * q^47 - 31 * q^48 + 6 * q^49 - 5 * q^50 + 29 * q^51 - 37 * q^52 + 27 * q^53 - 36 * q^54 - 16 * q^55 + 14 * q^56 - 21 * q^57 - 44 * q^58 + 74 * q^59 - 27 * q^60 - 30 * q^61 - 18 * q^62 - 9 * q^63 - 17 * q^64 - 3 * q^65 - 66 * q^66 + 9 * q^67 - 51 * q^68 - 23 * q^69 - 77 * q^70 + 70 * q^71 - 55 * q^72 - 38 * q^73 + 26 * q^74 + 22 * q^75 - 50 * q^76 - 38 * q^77 - 75 * q^78 + 7 * q^79 - 28 * q^80 + 5 * q^81 - 56 * q^82 + 47 * q^83 - 69 * q^84 - 49 * q^85 + 17 * q^86 - 37 * q^87 - 30 * q^88 + 23 * q^89 - 64 * q^90 + 6 * q^91 + 17 * q^92 - 31 * q^93 - 40 * q^94 - 11 * q^95 - 49 * q^96 - 14 * q^97 + 5 * q^98 + 79 * q^99

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