LMFDB - Embedded newform 1003.2.d.d.237.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(237,1003)]

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([1, 0]))

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

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

chi := DirichletCharacter("1003.237");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.d (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$8.00899532273$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			237.5
Character	$\chi$	$=$	1003.237
Dual form			1003.2.d.d.237.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49154 q^{2} -1.56691i q^{3} +4.20776 q^{4} +2.43371i q^{5} +3.90401i q^{6} -4.19592i q^{7} -5.50071 q^{8} +0.544794 q^{9} +O(q^{10})$	\(q-2.49154 q^{2} -1.56691i q^{3} +4.20776 q^{4} +2.43371i q^{5} +3.90401i q^{6} -4.19592i q^{7} -5.50071 q^{8} +0.544794 q^{9} -6.06369i q^{10} -5.11774i q^{11} -6.59318i q^{12} +0.796443 q^{13} +10.4543i q^{14} +3.81341 q^{15} +5.28972 q^{16} +(3.46154 - 2.24004i) q^{17} -1.35738 q^{18} -6.96207 q^{19} +10.2405i q^{20} -6.57462 q^{21} +12.7511i q^{22} +3.86110i q^{23} +8.61912i q^{24} -0.922958 q^{25} -1.98437 q^{26} -5.55437i q^{27} -17.6554i q^{28} +4.39028i q^{29} -9.50125 q^{30} -5.41606i q^{31} -2.17810 q^{32} -8.01904 q^{33} +(-8.62454 + 5.58114i) q^{34} +10.2117 q^{35} +2.29236 q^{36} -4.75760i q^{37} +17.3463 q^{38} -1.24795i q^{39} -13.3872i q^{40} +5.85982i q^{41} +16.3809 q^{42} -5.22841 q^{43} -21.5342i q^{44} +1.32587i q^{45} -9.62008i q^{46} +8.11140 q^{47} -8.28851i q^{48} -10.6057 q^{49} +2.29958 q^{50} +(-3.50994 - 5.42391i) q^{51} +3.35124 q^{52} +5.58786 q^{53} +13.8389i q^{54} +12.4551 q^{55} +23.0805i q^{56} +10.9089i q^{57} -10.9386i q^{58} -1.00000 q^{59} +16.0459 q^{60} -6.64568i q^{61} +13.4943i q^{62} -2.28591i q^{63} -5.15261 q^{64} +1.93831i q^{65} +19.9797 q^{66} -0.297022 q^{67} +(14.5653 - 9.42554i) q^{68} +6.05000 q^{69} -25.4427 q^{70} -2.56185i q^{71} -2.99676 q^{72} -2.90736i q^{73} +11.8537i q^{74} +1.44619i q^{75} -29.2947 q^{76} -21.4736 q^{77} +3.10933i q^{78} +14.1427i q^{79} +12.8737i q^{80} -7.06882 q^{81} -14.6000i q^{82} -18.0332 q^{83} -27.6644 q^{84} +(5.45161 + 8.42438i) q^{85} +13.0268 q^{86} +6.87918 q^{87} +28.1512i q^{88} -6.01554 q^{89} -3.30346i q^{90} -3.34181i q^{91} +16.2466i q^{92} -8.48647 q^{93} -20.2099 q^{94} -16.9437i q^{95} +3.41289i q^{96} -8.40407i q^{97} +26.4245 q^{98} -2.78812i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 8 q^{2} + 60 q^{4} - 6 q^{8} - 62 q^{9}+O(q^{10}) $ 44 * q - 8 * q^2 + 60 * q^4 - 6 * q^8 - 62 * q^9	$ 44 q - 8 q^{2} + 60 q^{4} - 6 q^{8} - 62 q^{9} + 26 q^{13} + 84 q^{16} - 13 q^{17} + 22 q^{18} - 30 q^{19} + 66 q^{21} - 96 q^{25} - 6 q^{26} + 14 q^{30} + 20 q^{32} + 18 q^{33} - 26 q^{34} + 10 q^{35} - 130 q^{36} + 72 q^{38} - 10 q^{42} - 72 q^{43} + 8 q^{47} - 70 q^{49} + 4 q^{50} - 14 q^{51} - 48 q^{52} + 4 q^{53} + 70 q^{55} - 44 q^{59} - 52 q^{60} + 74 q^{64} + 116 q^{66} + 92 q^{67} - 54 q^{68} + 76 q^{69} - 38 q^{70} + 118 q^{72} - 76 q^{76} + 32 q^{77} + 60 q^{81} + 20 q^{83} + 168 q^{84} - 36 q^{85} - 46 q^{86} - 166 q^{87} + 18 q^{89} - 2 q^{93} - 54 q^{94} - 34 q^{98}+O(q^{100}) $ 44 * q - 8 * q^2 + 60 * q^4 - 6 * q^8 - 62 * q^9 + 26 * q^13 + 84 * q^16 - 13 * q^17 + 22 * q^18 - 30 * q^19 + 66 * q^21 - 96 * q^25 - 6 * q^26 + 14 * q^30 + 20 * q^32 + 18 * q^33 - 26 * q^34 + 10 * q^35 - 130 * q^36 + 72 * q^38 - 10 * q^42 - 72 * q^43 + 8 * q^47 - 70 * q^49 + 4 * q^50 - 14 * q^51 - 48 * q^52 + 4 * q^53 + 70 * q^55 - 44 * q^59 - 52 * q^60 + 74 * q^64 + 116 * q^66 + 92 * q^67 - 54 * q^68 + 76 * q^69 - 38 * q^70 + 118 * q^72 - 76 * q^76 + 32 * q^77 + 60 * q^81 + 20 * q^83 + 168 * q^84 - 36 * q^85 - 46 * q^86 - 166 * q^87 + 18 * q^89 - 2 * q^93 - 54 * q^94 - 34 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1003\mathbb{Z}\right)^\times$.

$n$	$120$	$768$
$\chi(n)$	$1$	$-1$

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 $

$2$	−2.49154			−1.76178			−0.880892	−	0.473318i	$-0.843056\pi$
$2$	−2.49154			−1.76178			−0.880892	+	0.473318i	$0.843056\pi$
$3$		−	1.56691i		−	0.904656i	−0.891852	−	0.452328i	$-0.850594\pi$
$3$		−	1.56691i		−	0.904656i	0.891852	−	0.452328i	$-0.149406\pi$
$4$	4.20776			2.10388
$5$			2.43371i			1.08839i	0.838959	+	0.544195i	$0.183165\pi$
$5$			2.43371i			1.08839i	−0.838959	+	0.544195i	$0.816835\pi$
$6$			3.90401i			1.59381i
$7$		−	4.19592i		−	1.58591i	−0.609282	−	0.792953i	$-0.708542\pi$
$7$		−	4.19592i		−	1.58591i	0.609282	−	0.792953i	$-0.291458\pi$
$8$	−5.50071			−1.94480
$9$	0.544794			0.181598
$10$		−	6.06369i		−	1.91751i
$11$		−	5.11774i		−	1.54306i	−0.636194	−	0.771529i	$-0.719492\pi$
$11$		−	5.11774i		−	1.54306i	0.636194	−	0.771529i	$-0.280508\pi$
$12$		−	6.59318i		−	1.90329i
$13$	0.796443			0.220894			0.110447	−	0.993882i	$-0.464772\pi$
$13$	0.796443			0.220894			0.110447	+	0.993882i	$0.464772\pi$
$14$			10.4543i			2.79402i
$15$	3.81341			0.984618
$16$	5.28972			1.32243
$17$	3.46154	−	2.24004i	0.839546	−	0.543289i
$17$	3.46154	−	2.24004i	0.839546	−	0.543289i
$18$	−1.35738			−0.319936
$19$	−6.96207			−1.59721			−0.798605	−	0.601856i	$-0.794428\pi$
$19$	−6.96207			−1.59721			−0.798605	+	0.601856i	$0.794428\pi$
$20$			10.2405i			2.28984i
$21$	−6.57462			−1.43470
$22$			12.7511i			2.71853i
$23$			3.86110i			0.805095i	0.915399	+	0.402548i	$0.131875\pi$
$23$			3.86110i			0.805095i	−0.915399	+	0.402548i	$0.868125\pi$
$24$			8.61912i			1.75937i
$25$	−0.922958			−0.184592
$26$	−1.98437			−0.389167
$27$		−	5.55437i		−	1.06894i
$28$		−	17.6554i		−	3.33656i
$29$			4.39028i			0.815255i	0.913148	+	0.407628i	$0.133644\pi$
$29$			4.39028i			0.815255i	−0.913148	+	0.407628i	$0.866356\pi$
$30$	−9.50125			−1.73468
$31$		−	5.41606i		−	0.972753i	−0.873749	−	0.486376i	$-0.838318\pi$
$31$		−	5.41606i		−	0.972753i	0.873749	−	0.486376i	$-0.161682\pi$
$32$	−2.17810			−0.385038
$33$	−8.01904			−1.39594
$34$	−8.62454	+	5.58114i	−1.47910	+	0.957158i
$35$	10.2117			1.72608
$36$	2.29236			0.382061
$37$		−	4.75760i		−	0.782145i	−0.920360	−	0.391072i	$-0.872104\pi$
$37$		−	4.75760i		−	0.782145i	0.920360	−	0.391072i	$-0.127896\pi$
$38$	17.3463			2.81394
$39$		−	1.24795i		−	0.199833i
$40$		−	13.3872i		−	2.11670i
$41$			5.85982i			0.915150i	0.889171	+	0.457575i	$0.151282\pi$
$41$			5.85982i			0.915150i	−0.889171	+	0.457575i	$0.848718\pi$
$42$	16.3809			2.52763
$43$	−5.22841			−0.797325			−0.398663	−	0.917098i	$-0.630526\pi$
$43$	−5.22841			−0.797325			−0.398663	+	0.917098i	$0.630526\pi$
$44$		−	21.5342i		−	3.24641i
$45$			1.32587i			0.197649i
$46$		−	9.62008i		−	1.41840i
$47$	8.11140			1.18317			0.591585	−	0.806243i	$-0.298503\pi$
$47$	8.11140			1.18317			0.591585	+	0.806243i	$0.298503\pi$
$48$		−	8.28851i		−	1.19634i
$49$	−10.6057			−1.51510
$50$	2.29958			0.325210
$51$	−3.50994	−	5.42391i	−0.491490	−	0.759500i
$52$	3.35124			0.464733
$53$	5.58786			0.767552			0.383776	−	0.923426i	$-0.374623\pi$
$53$	5.58786			0.767552			0.383776	+	0.923426i	$0.374623\pi$
$54$			13.8389i			1.88324i
$55$	12.4551			1.67945
$56$			23.0805i			3.08427i
$57$			10.9089i			1.44492i
$58$		−	10.9386i		−	1.43630i
$59$	−1.00000			−0.130189
$59$	−1.00000			−0.130189
$60$	16.0459			2.07152
$61$		−	6.64568i		−	0.850892i	−0.904984	−	0.425446i	$-0.860117\pi$
$61$		−	6.64568i		−	0.850892i	0.904984	−	0.425446i	$-0.139883\pi$
$62$			13.4943i			1.71378i
$63$		−	2.28591i		−	0.287998i
$64$	−5.15261			−0.644077
$65$			1.93831i			0.240418i
$66$	19.9797			2.45934
$67$	−0.297022			−0.0362870			−0.0181435	−	0.999835i	$-0.505776\pi$
$67$	−0.297022			−0.0362870			−0.0181435	+	0.999835i	$0.505776\pi$
$68$	14.5653	−	9.42554i	1.76630	−	1.14302i
$69$	6.05000			0.728334
$70$	−25.4427			−3.04099
$71$		−	2.56185i		−	0.304036i	−0.988378	−	0.152018i	$-0.951423\pi$
$71$		−	2.56185i		−	0.304036i	0.988378	−	0.152018i	$-0.0485772\pi$
$72$	−2.99676			−0.353171
$73$		−	2.90736i		−	0.340281i	−0.985420	−	0.170140i	$-0.945578\pi$
$73$		−	2.90736i		−	0.340281i	0.985420	−	0.170140i	$-0.0544222\pi$
$74$			11.8537i			1.37797i
$75$			1.44619i			0.166992i
$76$	−29.2947			−3.36034
$77$	−21.4736			−2.44715
$78$			3.10933i			0.352062i
$79$			14.1427i			1.59117i	0.605839	+	0.795587i	$0.292838\pi$
$79$			14.1427i			1.59117i	−0.605839	+	0.795587i	$0.707162\pi$
$80$			12.8737i			1.43932i
$81$	−7.06882			−0.785424
$82$		−	14.6000i		−	1.61230i
$83$	−18.0332			−1.97940			−0.989700	−	0.143154i	$-0.954275\pi$
$83$	−18.0332			−1.97940			−0.989700	+	0.143154i	$0.954275\pi$
$84$	−27.6644			−3.01844
$85$	5.45161	+	8.42438i	0.591310	+	0.913753i
$86$	13.0268			1.40471
$87$	6.87918			0.737525
$88$			28.1512i			3.00093i
$89$	−6.01554			−0.637646			−0.318823	−	0.947814i	$-0.603287\pi$
$89$	−6.01554			−0.637646			−0.318823	+	0.947814i	$0.603287\pi$
$90$		−	3.30346i		−	0.348215i
$91$		−	3.34181i		−	0.350317i
$92$			16.2466i			1.69382i
$93$	−8.48647			−0.880006
$94$	−20.2099			−2.08449
$95$		−	16.9437i		−	1.73839i
$96$			3.41289i			0.348327i
$97$		−	8.40407i		−	0.853304i	−0.904416	−	0.426652i	$-0.859693\pi$
$97$		−	8.40407i		−	0.853304i	0.904416	−	0.426652i	$-0.140307\pi$
$98$	26.4245			2.66928
$99$		−	2.78812i		−	0.280216i
$100$	−3.88358			−0.388358
$101$	−16.3118			−1.62309			−0.811543	−	0.584292i	$-0.801372\pi$
$101$	−16.3118			−1.62309			−0.811543	+	0.584292i	$0.801372\pi$
$102$	8.74514	+	13.5139i	0.865898	+	1.33807i
$103$	19.4846			1.91987			0.959936	−	0.280220i	$-0.0904075\pi$
$103$	19.4846			1.91987			0.959936	+	0.280220i	$0.0904075\pi$
$104$	−4.38101			−0.429593
$105$		−	16.0007i		−	1.56151i
$106$	−13.9224			−1.35226
$107$		−	2.84970i		−	0.275491i	−0.990468	−	0.137746i	$-0.956014\pi$
$107$		−	2.84970i		−	0.275491i	0.990468	−	0.137746i	$-0.0439857\pi$
$108$		−	23.3715i		−	2.24892i
$109$		−	13.9531i		−	1.33646i	−0.743954	−	0.668231i	$-0.767052\pi$
$109$		−	13.9531i		−	1.33646i	0.743954	−	0.668231i	$-0.232948\pi$
$110$	−31.0324			−2.95882
$111$	−7.45473			−0.707572
$112$		−	22.1952i		−	2.09725i
$113$			3.51898i			0.331038i	0.986207	+	0.165519i	$0.0529300\pi$
$113$			3.51898i			0.331038i	−0.986207	+	0.165519i	$0.947070\pi$
$114$		−	27.1800i		−	2.54564i
$115$	−9.39681			−0.876257
$116$			18.4733i			1.71520i
$117$	0.433898			0.0401138
$118$	2.49154			0.229365
$119$	−9.39901	−	14.5243i	−0.861606	−	1.33144i
$120$	−20.9765			−1.91488
$121$	−15.1913			−1.38103
$122$			16.5580i			1.49909i
$123$	9.18181			0.827896
$124$		−	22.7895i		−	2.04655i
$125$			9.92235i			0.887482i
$126$			5.69543i			0.507389i
$127$	−7.93742			−0.704332			−0.352166	−	0.935938i	$-0.614555\pi$
$127$	−7.93742			−0.704332			−0.352166	+	0.935938i	$0.614555\pi$
$128$	17.1941			1.51976
$129$			8.19245i			0.721305i
$130$		−	4.82938i		−	0.423565i
$131$		−	9.94432i		−	0.868839i	−0.900711	−	0.434419i	$-0.856954\pi$
$131$		−	9.94432i		−	0.868839i	0.900711	−	0.434419i	$-0.143046\pi$
$132$	−33.7422			−2.93688
$133$			29.2123i			2.53302i
$134$	0.740042			0.0639299
$135$	13.5177			1.16342
$136$	−19.0409	+	12.3218i	−1.63275	+	1.05659i
$137$	2.06965			0.176822			0.0884109	−	0.996084i	$-0.471821\pi$
$137$	2.06965			0.176822			0.0884109	+	0.996084i	$0.471821\pi$
$138$	−15.0738			−1.28317
$139$			0.827153i			0.0701582i	0.999385	+	0.0350791i	$0.0111683\pi$
$139$			0.827153i			0.0701582i	−0.999385	+	0.0350791i	$0.988832\pi$
$140$	42.9682			3.63147
$141$		−	12.7098i		−	1.07036i
$142$			6.38296i			0.535646i
$143$		−	4.07599i		−	0.340852i
$144$	2.88181			0.240151
$145$	−10.6847			−0.887315
$146$			7.24380i			0.599501i
$147$			16.6182i			1.37064i
$148$		−	20.0188i		−	1.64554i
$149$	−19.7394			−1.61711			−0.808557	−	0.588417i	$-0.799751\pi$
$149$	−19.7394			−1.61711			−0.808557	+	0.588417i	$0.799751\pi$
$150$		−	3.60324i		−	0.294203i
$151$	−7.23125			−0.588471			−0.294235	−	0.955733i	$-0.595065\pi$
$151$	−7.23125			−0.588471			−0.294235	+	0.955733i	$0.595065\pi$
$152$	38.2964			3.10625
$153$	1.88582	−	1.22036i	0.152460	−	0.0986603i
$154$	53.5023			4.31134
$155$	13.1811			1.05873
$156$		−	5.25109i		−	0.420424i
$157$	0.616693			0.0492174			0.0246087	−	0.999697i	$-0.492166\pi$
$157$	0.616693			0.0492174			0.0246087	+	0.999697i	$0.492166\pi$
$158$		−	35.2370i		−	2.80330i
$159$		−	8.75568i		−	0.694371i
$160$		−	5.30088i		−	0.419071i
$161$	16.2009			1.27681
$162$	17.6122			1.38375
$163$		−	5.14459i		−	0.402956i	−0.979493	−	0.201478i	$-0.935426\pi$
$163$		−	5.14459i		−	0.402956i	0.979493	−	0.201478i	$-0.0645744\pi$
$164$			24.6567i			1.92537i
$165$		−	19.5160i		−	1.51932i
$166$	44.9304			3.48727
$167$		−	9.14854i		−	0.707936i	−0.935258	−	0.353968i	$-0.884832\pi$
$167$		−	9.14854i		−	0.707936i	0.935258	−	0.353968i	$-0.115168\pi$
$168$	36.1651			2.79020
$169$	−12.3657			−0.951206
$170$	−13.5829	−	20.9897i	−1.04176	−	1.60983i
$171$	−3.79290			−0.290050
$172$	−21.9999			−1.67748
$173$		−	8.72402i		−	0.663275i	−0.943407	−	0.331638i	$-0.892399\pi$
$173$		−	8.72402i		−	0.663275i	0.943407	−	0.331638i	$-0.107601\pi$
$174$	−17.1397			−1.29936
$175$			3.87265i			0.292745i
$176$		−	27.0714i		−	2.04059i
$177$			1.56691i			0.117776i
$178$	14.9879			1.12339
$179$	8.72533			0.652162			0.326081	−	0.945342i	$-0.394272\pi$
$179$	8.72533			0.652162			0.326081	+	0.945342i	$0.394272\pi$
$180$			5.57895i			0.415831i
$181$			11.8991i			0.884453i	0.896903	+	0.442226i	$0.145811\pi$
$181$			11.8991i			0.884453i	−0.896903	+	0.442226i	$0.854189\pi$
$182$			8.32624i			0.617182i
$183$	−10.4132			−0.769765
$184$		−	21.2388i		−	1.56575i
$185$	11.5786			0.851278
$186$	21.1444			1.55038
$187$	−11.4639	−	17.7153i	−0.838327	−	1.29547i
$188$	34.1308			2.48925
$189$	−23.3057			−1.69524
$190$			42.2158i			3.06266i
$191$	−0.776326			−0.0561730			−0.0280865	−	0.999605i	$-0.508941\pi$
$191$	−0.776326			−0.0561730			−0.0280865	+	0.999605i	$0.508941\pi$
$192$			8.07368i			0.582667i
$193$			2.08577i			0.150137i	0.997178	+	0.0750685i	$0.0239175\pi$
$193$			2.08577i			0.150137i	−0.997178	+	0.0750685i	$0.976082\pi$
$194$			20.9391i			1.50334i
$195$	3.03716			0.217496
$196$	−44.6262			−3.18759
$197$			4.64917i			0.331240i	0.986190	+	0.165620i	$0.0529625\pi$
$197$			4.64917i			0.331240i	−0.986190	+	0.165620i	$0.947038\pi$
$198$			6.94670i			0.493680i
$199$		−	20.0984i		−	1.42474i	−0.701806	−	0.712368i	$-0.747623\pi$
$199$		−	20.0984i		−	1.42474i	0.701806	−	0.712368i	$-0.252377\pi$
$200$	5.07693			0.358993
$201$			0.465407i			0.0328273i
$202$	40.6415			2.85953
$203$	18.4213			1.29292
$204$	−14.7690	−	22.8225i	−1.03404	−	1.59790i
$205$	−14.2611			−0.996040
$206$	−48.5465			−3.38240
$207$			2.10351i			0.146204i
$208$	4.21296			0.292116
$209$			35.6301i			2.46459i
$210$			39.8664i			2.75105i
$211$		−	6.30636i		−	0.434148i	−0.976155	−	0.217074i	$-0.930349\pi$
$211$		−	6.30636i		−	0.434148i	0.976155	−	0.217074i	$-0.0696512\pi$
$212$	23.5124			1.61484
$213$	−4.01419			−0.275048
$214$			7.10015i			0.485356i
$215$		−	12.7245i		−	0.867800i
$216$			30.5530i			2.07887i
$217$	−22.7253			−1.54270
$218$			34.7646i			2.35456i
$219$	−4.55557			−0.307837
$220$	52.4081			3.53336
$221$	2.75692	−	1.78406i	0.185450	−	0.120009i
$222$	18.5737			1.24659
$223$	7.60240			0.509094			0.254547	−	0.967060i	$-0.418074\pi$
$223$	7.60240			0.509094			0.254547	+	0.967060i	$0.418074\pi$
$224$			9.13913i			0.610634i
$225$	−0.502822			−0.0335215
$226$		−	8.76768i		−	0.583218i
$227$			2.13548i			0.141737i	0.997486	+	0.0708685i	$0.0225771\pi$
$227$			2.13548i			0.141737i	−0.997486	+	0.0708685i	$0.977423\pi$
$228$			45.9022i			3.03995i
$229$	8.82712			0.583312			0.291656	−	0.956523i	$-0.405794\pi$
$229$	8.82712			0.583312			0.291656	+	0.956523i	$0.405794\pi$
$230$	23.4125			1.54378
$231$			33.6472i			2.21382i
$232$		−	24.1497i		−	1.58551i
$233$			25.5718i			1.67526i	0.546235	+	0.837632i	$0.316060\pi$
$233$			25.5718i			1.67526i	−0.546235	+	0.837632i	$0.683940\pi$
$234$	−1.08107			−0.0706719
$235$			19.7408i			1.28775i
$236$	−4.20776			−0.273902
$237$	22.1603			1.43947
$238$	23.4180	+	36.1879i	1.51796	+	2.34571i
$239$	−15.7020			−1.01568			−0.507839	−	0.861452i	$-0.669555\pi$
$239$	−15.7020			−1.01568			−0.507839	+	0.861452i	$0.669555\pi$
$240$	20.1719			1.30209
$241$			22.2645i			1.43418i	0.696980	+	0.717090i	$0.254526\pi$
$241$			22.2645i			1.43418i	−0.696980	+	0.717090i	$0.745474\pi$
$242$	37.8497			2.43307
$243$		−	5.58692i		−	0.358401i
$244$		−	27.9634i		−	1.79018i
$245$		−	25.8112i		−	1.64902i
$246$	−22.8768			−1.45857
$247$	−5.54490			−0.352813
$248$			29.7922i			1.89181i
$249$			28.2564i			1.79068i
$250$		−	24.7219i		−	1.56355i
$251$	20.3898			1.28699			0.643495	−	0.765450i	$-0.277484\pi$
$251$	20.3898			1.28699			0.643495	+	0.765450i	$0.277484\pi$
$252$		−	9.61856i		−	0.605912i
$253$	19.7601			1.24231
$254$	19.7764			1.24088
$255$	13.2002	−	8.54218i	0.826631	−	0.534932i
$256$	−32.5346			−2.03341
$257$	23.5068			1.46631			0.733156	−	0.680060i	$-0.238046\pi$
$257$	23.5068			1.46631			0.733156	+	0.680060i	$0.238046\pi$
$258$		−	20.4118i		−	1.27078i
$259$	−19.9625			−1.24041
$260$			8.15596i			0.505811i
$261$			2.39180i			0.148049i
$262$			24.7766i			1.53071i
$263$	−20.5951			−1.26995			−0.634974	−	0.772533i	$-0.718989\pi$
$263$	−20.5951			−1.26995			−0.634974	+	0.772533i	$0.718989\pi$
$264$	44.1105			2.71481
$265$			13.5993i			0.835396i
$266$		−	72.7835i		−	4.46264i
$267$			9.42580i			0.576850i
$268$	−1.24980			−0.0763436
$269$		−	25.2099i		−	1.53707i	−0.639806	−	0.768536i	$-0.720985\pi$
$269$		−	25.2099i		−	1.53707i	0.639806	−	0.768536i	$-0.279015\pi$
$270$	−33.6800			−2.04970
$271$	27.5579			1.67402			0.837012	−	0.547185i	$-0.184301\pi$
$271$	27.5579			1.67402			0.837012	+	0.547185i	$0.184301\pi$
$272$	18.3105	−	11.8492i	1.11024	−	0.718462i
$273$	−5.23631			−0.316916
$274$	−5.15660			−0.311522
$275$			4.72346i			0.284835i
$276$	25.4569			1.53233
$277$		−	31.2202i		−	1.87584i	−0.346852	−	0.937920i	$-0.612749\pi$
$277$		−	31.2202i		−	1.87584i	0.346852	−	0.937920i	$-0.387251\pi$
$278$		−	2.06088i		−	0.123604i
$279$		−	2.95064i		−	0.176650i
$280$	−56.1714			−3.35688
$281$	17.2113			1.02674			0.513371	−	0.858167i	$-0.328397\pi$
$281$	17.2113			1.02674			0.513371	+	0.858167i	$0.328397\pi$
$282$			31.6670i			1.88574i
$283$		−	8.32509i		−	0.494875i	−0.968904	−	0.247438i	$-0.920411\pi$
$283$		−	8.32509i		−	0.494875i	0.968904	−	0.247438i	$-0.0795886\pi$
$284$		−	10.7797i		−	0.639655i
$285$	−26.5492			−1.57264
$286$			10.1555i			0.600507i
$287$	24.5873			1.45134
$288$	−1.18662			−0.0699221
$289$	6.96445	−	15.5079i	0.409674	−	0.912232i
$290$	26.6213			1.56326
$291$	−13.1684			−0.771947
$292$		−	12.2335i		−	0.715910i
$293$	29.8859			1.74595			0.872977	−	0.487762i	$-0.162187\pi$
$293$	29.8859			1.74595			0.872977	+	0.487762i	$0.162187\pi$
$294$		−	41.4048i		−	2.41478i
$295$		−	2.43371i		−	0.141696i
$296$			26.1702i			1.52111i
$297$	−28.4259			−1.64944
$298$	49.1815			2.84901
$299$			3.07515i			0.177840i
$300$			6.08523i			0.351331i
$301$			21.9380i			1.26448i
$302$	18.0169			1.03676
$303$			25.5591i			1.46833i
$304$	−36.8274			−2.11220
$305$	16.1737			0.926102
$306$	−4.69860	+	3.04057i	−0.268601	+	0.173818i
$307$	20.2127			1.15360			0.576800	−	0.816886i	$-0.304301\pi$
$307$	20.2127			1.15360			0.576800	+	0.816886i	$0.304301\pi$
$308$	−90.3558			−5.14850
$309$		−	30.5306i		−	1.73682i
$310$	−32.8413			−1.86526
$311$			14.5852i			0.827049i	0.910493	+	0.413525i	$0.135702\pi$
$311$			14.5852i			0.827049i	−0.910493	+	0.413525i	$0.864298\pi$
$312$			6.86464i			0.388634i
$313$			24.9246i			1.40882i	0.709792	+	0.704412i	$0.248789\pi$
$313$			24.9246i			1.40882i	−0.709792	+	0.704412i	$0.751211\pi$
$314$	−1.53651			−0.0867105
$315$	5.56325			0.313454
$316$			59.5089i			3.34764i
$317$		−	15.4355i		−	0.866944i	−0.901167	−	0.433472i	$-0.857288\pi$
$317$		−	15.4355i		−	0.866944i	0.901167	−	0.433472i	$-0.142712\pi$
$318$			21.8151i			1.22333i
$319$	22.4683			1.25799
$320$		−	12.5400i		−	0.701006i
$321$	−4.46523			−0.249225
$322$	−40.3650			−2.24946
$323$	−24.0995	+	15.5953i	−1.34093	+	0.867747i
$324$	−29.7439			−1.65244
$325$	−0.735083			−0.0407751
$326$			12.8179i			0.709921i
$327$	−21.8632			−1.20904
$328$		−	32.2332i		−	1.77978i
$329$		−	34.0348i		−	1.87640i
$330$			48.6250i			2.67672i
$331$	12.9990			0.714488			0.357244	−	0.934011i	$-0.383716\pi$
$331$	12.9990			0.714488			0.357244	+	0.934011i	$0.383716\pi$
$332$	−75.8794			−4.16442
$333$		−	2.59191i		−	0.142036i
$334$			22.7939i			1.24723i
$335$		−	0.722867i		−	0.0394944i
$336$	−34.7779			−1.89729
$337$			0.680306i			0.0370586i	0.999828	+	0.0185293i	$0.00589840\pi$
$337$			0.680306i			0.0370586i	−0.999828	+	0.0185293i	$0.994102\pi$
$338$	30.8096			1.67582
$339$	5.51393			0.299476
$340$	22.9391	+	35.4478i	1.24405	+	1.92243i
$341$	−27.7180			−1.50101
$342$	9.45015			0.511005
$343$			15.1292i			0.816901i
$344$	28.7600			1.55064
$345$			14.7240i			0.792711i
$346$			21.7362i			1.16855i
$347$		−	19.2130i		−	1.03141i	−0.856767	−	0.515704i	$-0.827530\pi$
$347$		−	19.2130i		−	1.03141i	0.856767	−	0.515704i	$-0.172470\pi$
$348$	28.9459			1.55166
$349$	26.2867			1.40709			0.703547	−	0.710649i	$-0.251598\pi$
$349$	26.2867			1.40709			0.703547	+	0.710649i	$0.251598\pi$
$350$		−	9.64886i		−	0.515753i
$351$		−	4.42374i		−	0.236122i
$352$			11.1470i			0.594136i
$353$	−21.2226			−1.12957			−0.564783	−	0.825239i	$-0.691040\pi$
$353$	−21.2226			−1.12957			−0.564783	+	0.825239i	$0.691040\pi$
$354$		−	3.90401i		−	0.207496i
$355$	6.23482			0.330910
$356$	−25.3119			−1.34153
$357$	−22.7583	+	14.7274i	−1.20450	+	0.779457i
$358$	−21.7395			−1.14897
$359$	−1.85616			−0.0979642			−0.0489821	−	0.998800i	$-0.515598\pi$
$359$	−1.85616			−0.0979642			−0.0489821	+	0.998800i	$0.515598\pi$
$360$		−	7.29325i		−	0.384388i
$361$	29.4705			1.55108
$362$		−	29.6470i		−	1.55821i
$363$			23.8034i			1.24935i
$364$		−	14.0615i		−	0.737024i
$365$	7.07568			0.370358
$366$	25.9448			1.35616
$367$		−	11.5122i		−	0.600931i	−0.953793	−	0.300465i	$-0.902858\pi$
$367$		−	11.5122i		−	0.600931i	0.953793	−	0.300465i	$-0.0971420\pi$
$368$			20.4241i			1.06468i
$369$			3.19240i			0.166190i
$370$	−28.8486			−1.49977
$371$		−	23.4462i		−	1.21727i
$372$	−35.7090			−1.85143
$373$	−12.5543			−0.650036			−0.325018	−	0.945708i	$-0.605370\pi$
$373$	−12.5543			−0.650036			−0.325018	+	0.945708i	$0.605370\pi$
$374$	28.5629	+	44.1382i	1.47695	+	2.28233i
$375$	15.5474			0.802866
$376$	−44.6185			−2.30102
$377$			3.49661i			0.180085i
$378$	58.0670			2.98664
$379$		−	1.91620i		−	0.0984288i	−0.998788	−	0.0492144i	$-0.984328\pi$
$379$		−	1.91620i		−	0.0984288i	0.998788	−	0.0492144i	$-0.0156718\pi$
$380$		−	71.2950i		−	3.65735i
$381$			12.4372i			0.637178i
$382$	1.93425			0.0989647
$383$	−3.74351			−0.191284			−0.0956422	−	0.995416i	$-0.530490\pi$
$383$	−3.74351			−0.191284			−0.0956422	+	0.995416i	$0.530490\pi$
$384$		−	26.9417i		−	1.37486i
$385$		−	52.2606i		−	2.66345i
$386$		−	5.19677i		−	0.264509i
$387$	−2.84841			−0.144793
$388$		−	35.3623i		−	1.79525i
$389$	−14.3108			−0.725586			−0.362793	−	0.931870i	$-0.618177\pi$
$389$	−14.3108			−0.725586			−0.362793	+	0.931870i	$0.618177\pi$
$390$	−7.56720			−0.383180
$391$	8.64902	+	13.3653i	0.437400	+	0.675914i
$392$	58.3389			2.94656
$393$	−15.5818			−0.786000
$394$		−	11.5836i		−	0.583573i
$395$	−34.4192			−1.73182
$396$		−	11.7317i		−	0.589541i
$397$		−	20.2347i		−	1.01555i	−0.861489	−	0.507776i	$-0.830468\pi$
$397$		−	20.2347i		−	1.01555i	0.861489	−	0.507776i	$-0.169532\pi$
$398$			50.0758i			2.51008i
$399$	45.7730			2.29152
$400$	−4.88219			−0.244109
$401$		−	16.5869i		−	0.828309i	−0.910207	−	0.414155i	$-0.864077\pi$
$401$		−	16.5869i		−	0.828309i	0.910207	−	0.414155i	$-0.135923\pi$
$402$		−	1.15958i		−	0.0578345i
$403$		−	4.31358i		−	0.214875i
$404$	−68.6362			−3.41478
$405$		−	17.2035i		−	0.854847i
$406$	−45.8972			−2.27784
$407$	−24.3482			−1.20689
$408$	19.3072	+	29.8354i	0.955847	+	1.47707i
$409$	28.3030			1.39949			0.699746	−	0.714392i	$-0.253297\pi$
$409$	28.3030			1.39949			0.699746	+	0.714392i	$0.253297\pi$
$410$	35.5321			1.75481
$411$		−	3.24295i		−	0.159963i
$412$	81.9864			4.03918
$413$			4.19592i			0.206467i
$414$		−	5.24096i		−	0.257579i
$415$		−	43.8876i		−	2.15436i
$416$	−1.73473			−0.0850524
$417$	1.29607			0.0634690
$418$		−	88.7737i		−	4.34207i
$419$			37.3611i			1.82521i	0.408841	+	0.912606i	$0.365933\pi$
$419$			37.3611i			1.82521i	−0.408841	+	0.912606i	$0.634067\pi$
$420$		−	67.3272i		−	3.28523i
$421$	−16.5946			−0.808770			−0.404385	−	0.914589i	$-0.632514\pi$
$421$	−16.5946			−0.808770			−0.404385	+	0.914589i	$0.632514\pi$
$422$			15.7125i			0.764874i
$423$	4.41905			0.214861
$424$	−30.7372			−1.49273
$425$	−3.19485	+	2.06746i	−0.154973	+	0.100287i
$426$	10.0015			0.484575
$427$	−27.8847			−1.34944
$428$		−	11.9909i		−	0.579601i
$429$	−6.38671			−0.308353
$430$			31.7034i			1.52888i
$431$		−	0.641133i		−	0.0308823i	−0.999881	−	0.0154411i	$-0.995085\pi$
$431$		−	0.641133i		−	0.0308823i	0.999881	−	0.0154411i	$-0.00491526\pi$
$432$		−	29.3811i		−	1.41360i
$433$	−21.3342			−1.02525			−0.512627	−	0.858611i	$-0.671328\pi$
$433$	−21.3342			−1.02525			−0.512627	+	0.858611i	$0.671328\pi$
$434$	56.6210			2.71789
$435$			16.7419i			0.802715i
$436$		−	58.7112i		−	2.81176i
$437$		−	26.8813i		−	1.28591i
$438$	11.3504			0.542342
$439$			35.2383i			1.68183i	0.541164	+	0.840917i	$0.317984\pi$
$439$			35.2383i			1.68183i	−0.541164	+	0.840917i	$0.682016\pi$
$440$	−68.5121			−3.26618
$441$	−5.77793			−0.275139
$442$	−6.86896	+	4.44506i	−0.326723	+	0.211430i
$443$	21.9270			1.04178			0.520892	−	0.853622i	$-0.325599\pi$
$443$	21.9270			1.04178			0.520892	+	0.853622i	$0.325599\pi$
$444$	−31.3677			−1.48865
$445$		−	14.6401i		−	0.694007i
$446$	−18.9417			−0.896914
$447$			30.9299i			1.46293i
$448$			21.6199i			1.02145i
$449$		−	2.82597i		−	0.133366i	−0.997774	−	0.0666829i	$-0.978758\pi$
$449$		−	2.82597i		−	0.133366i	0.997774	−	0.0666829i	$-0.0212416\pi$
$450$	1.25280			0.0590576
$451$	29.9891			1.41213
$452$			14.8070i			0.696465i
$453$			11.3307i			0.532364i
$454$		−	5.32064i		−	0.249710i
$455$	8.13300			0.381281
$456$		−	60.0070i		−	2.81008i
$457$	11.5564			0.540588			0.270294	−	0.962778i	$-0.412879\pi$
$457$	11.5564			0.540588			0.270294	+	0.962778i	$0.412879\pi$
$458$	−21.9931			−1.02767
$459$	−12.4420	−	19.2267i	−0.580743	−	0.897423i
$460$	−39.5395			−1.84354
$461$	33.3572			1.55360			0.776799	−	0.629748i	$-0.216842\pi$
$461$	33.3572			1.55360			0.776799	+	0.629748i	$0.216842\pi$
$462$		−	83.8333i		−	3.90028i
$463$	−4.46501			−0.207507			−0.103753	−	0.994603i	$-0.533085\pi$
$463$	−4.46501			−0.207507			−0.103753	+	0.994603i	$0.533085\pi$
$464$			23.2234i			1.07812i
$465$		−	20.6536i		−	0.957789i
$466$		−	63.7131i		−	2.95145i
$467$	1.85920			0.0860336			0.0430168	−	0.999074i	$-0.486303\pi$
$467$	1.85920			0.0860336			0.0430168	+	0.999074i	$0.486303\pi$
$468$	1.82574			0.0843947
$469$			1.24628i			0.0575479i
$470$		−	49.1850i		−	2.26873i
$471$		−	0.966302i		−	0.0445248i
$472$	5.50071			0.253191
$473$			26.7577i			1.23032i
$474$	−55.2132			−2.53603
$475$	6.42570			0.294831
$476$	−39.5488	−	61.1148i	−1.81272	−	2.80119i
$477$	3.04424			0.139386
$478$	39.1221			1.78940
$479$			13.0113i			0.594501i	0.954800	+	0.297250i	$0.0960696\pi$
$479$			13.0113i			0.594501i	−0.954800	+	0.297250i	$0.903930\pi$
$480$	−8.30599			−0.379115
$481$		−	3.78916i		−	0.172771i
$482$		−	55.4728i		−	2.52672i
$483$		−	25.3853i		−	1.15507i
$484$	−63.9213			−2.90552
$485$	20.4531			0.928728
$486$			13.9200i			0.631425i
$487$			33.6015i			1.52263i	0.648382	+	0.761316i	$0.275446\pi$
$487$			33.6015i			1.52263i	−0.648382	+	0.761316i	$0.724554\pi$
$488$			36.5560i			1.65481i
$489$	−8.06111			−0.364536
$490$			64.3097i			2.90521i
$491$	−18.9856			−0.856807			−0.428404	−	0.903587i	$-0.640924\pi$
$491$	−18.9856			−0.856807			−0.428404	+	0.903587i	$0.640924\pi$
$492$	38.6349			1.74179
$493$	9.83440	+	15.1971i	0.442919	+	0.684444i
$494$	13.8153			0.621580
$495$	6.78548			0.304985
$496$		−	28.6494i		−	1.28640i
$497$	−10.7493			−0.482173
$498$		−	70.4019i		−	3.15478i
$499$			25.4197i			1.13794i	0.822357	+	0.568972i	$0.192659\pi$
$499$			25.4197i			1.13794i	−0.822357	+	0.568972i	$0.807341\pi$
$500$			41.7509i			1.86716i
$501$	−14.3349			−0.640438
$502$	−50.8019			−2.26740
$503$			37.6291i			1.67780i	0.544287	+	0.838899i	$0.316800\pi$
$503$			37.6291i			1.67780i	−0.544287	+	0.838899i	$0.683200\pi$
$504$			12.5741i			0.560097i
$505$		−	39.6983i		−	1.76655i
$506$	−49.2331			−2.18868
$507$			19.3759i			0.860514i
$508$	−33.3987			−1.48183
$509$	−33.6175			−1.49007			−0.745036	−	0.667025i	$-0.767567\pi$
$509$	−33.6175			−1.49007			−0.745036	+	0.667025i	$0.767567\pi$
$510$	−32.8889	+	21.2832i	−1.45635	+	0.942434i
$511$	−12.1990			−0.539654
$512$	46.6729			2.06267
$513$			38.6699i			1.70732i
$514$	−58.5680			−2.58332
$515$			47.4198i			2.08957i
$516$			34.4718i			1.51754i
$517$		−	41.5121i		−	1.82570i
$518$	49.7373			2.18533
$519$	−13.6698			−0.600036
$520$		−	10.6621i		−	0.467564i
$521$			22.7304i			0.995835i	0.867224	+	0.497917i	$0.165902\pi$
$521$			22.7304i			0.995835i	−0.867224	+	0.497917i	$0.834098\pi$
$522$		−	5.95926i		−	0.260830i
$523$	30.6944			1.34217			0.671087	−	0.741379i	$-0.265828\pi$
$523$	30.6944			1.34217			0.671087	+	0.741379i	$0.265828\pi$
$524$		−	41.8433i		−	1.82793i
$525$	6.06810			0.264833
$526$	51.3135			2.23737
$527$	−12.1322	−	18.7479i	−0.528486	−	0.816670i
$528$	−42.4185			−1.84603
$529$	8.09189			0.351821
$530$		−	33.8831i		−	1.47179i
$531$	−0.544794			−0.0236421
$532$			122.918i			5.32918i
$533$			4.66701i			0.202151i
$534$		−	23.4847i		−	1.01628i
$535$	6.93536			0.299842
$536$	1.63383			0.0705709
$537$		−	13.6718i		−	0.589982i
$538$			62.8113i			2.70799i
$539$			54.2773i			2.33789i
$540$	56.8794			2.44770
$541$		−	24.2782i		−	1.04380i	−0.853006	−	0.521900i	$-0.825223\pi$
$541$		−	24.2782i		−	1.04380i	0.853006	−	0.521900i	$-0.174777\pi$
$542$	−68.6616			−2.94927
$543$	18.6448			0.800125
$544$	−7.53958	+	4.87904i	−0.323257	+	0.209187i
$545$	33.9578			1.45459
$546$	13.0465			0.558337
$547$		−	2.96724i		−	0.126870i	−0.997986	−	0.0634350i	$-0.979794\pi$
$547$		−	2.96724i		−	0.126870i	0.997986	−	0.0634350i	$-0.0202056\pi$
$548$	8.70857			0.372012
$549$		−	3.62053i		−	0.154520i
$550$		−	11.7687i		−	0.501818i
$551$		−	30.5655i		−	1.30213i
$552$	−33.2793			−1.41646
$553$	59.3414			2.52345
$554$			77.7863i			3.30482i
$555$		−	18.1427i		−	0.770113i
$556$			3.48046i			0.147604i
$557$	36.6482			1.55284			0.776418	−	0.630219i	$-0.217035\pi$
$557$	36.6482			1.55284			0.776418	+	0.630219i	$0.217035\pi$
$558$			7.35162i			0.311219i
$559$	−4.16413			−0.176124
$560$	54.0168			2.28262
$561$	−27.7582	+	17.9630i	−1.17195	+	0.758397i
$562$	−42.8827			−1.80890
$563$	−23.0627			−0.971977			−0.485988	−	0.873965i	$-0.661540\pi$
$563$	−23.0627			−0.971977			−0.485988	+	0.873965i	$0.661540\pi$
$564$		−	53.4799i		−	2.25191i
$565$	−8.56420			−0.360298
$566$			20.7423i			0.871863i
$567$			29.6602i			1.24561i
$568$			14.0920i			0.591288i
$569$	41.2593			1.72968			0.864840	−	0.502047i	$-0.167420\pi$
$569$	41.2593			1.72968			0.864840	+	0.502047i	$0.167420\pi$
$570$	66.1484			2.77065
$571$			7.64487i			0.319928i	0.987123	+	0.159964i	$0.0511378\pi$
$571$			7.64487i			0.319928i	−0.987123	+	0.159964i	$0.948862\pi$
$572$		−	17.1508i		−	0.717111i
$573$			1.21643i			0.0508172i
$574$	−61.2602			−2.55695
$575$		−	3.56363i		−	0.148614i
$576$	−2.80711			−0.116963
$577$	7.64493			0.318263			0.159131	−	0.987257i	$-0.449131\pi$
$577$	7.64493			0.318263			0.159131	+	0.987257i	$0.449131\pi$
$578$	−17.3522	+	38.6386i	−0.721756	+	1.60716i
$579$	3.26821			0.135822
$580$	−44.9586			−1.86680
$581$			75.6658i			3.13915i
$582$	32.8096			1.36000
$583$		−	28.5973i		−	1.18438i
$584$			15.9926i			0.661777i
$585$			1.05598i			0.0436595i
$586$	−74.4619			−3.07599
$587$	−28.0989			−1.15976			−0.579882	−	0.814700i	$-0.696901\pi$
$587$	−28.0989			−1.15976			−0.579882	+	0.814700i	$0.696901\pi$
$588$			69.9253i			2.88367i
$589$			37.7070i			1.55369i
$590$			6.06369i			0.249638i
$591$	7.28483			0.299658
$592$		−	25.1664i		−	1.03433i
$593$	−37.7815			−1.55150			−0.775750	−	0.631040i	$-0.782628\pi$
$593$	−37.7815			−1.55150			−0.775750	+	0.631040i	$0.782628\pi$
$594$	70.8241			2.90595
$595$	35.3480	−	22.8745i	1.44913	−	0.937763i
$596$	−83.0586			−3.40221
$597$	−31.4923			−1.28890
$598$		−	7.66185i		−	0.313316i
$599$	28.1728			1.15111			0.575555	−	0.817763i	$-0.304786\pi$
$599$	28.1728			1.15111			0.575555	+	0.817763i	$0.304786\pi$
$600$		−	7.95509i		−	0.324765i
$601$			5.68859i			0.232042i	0.993247	+	0.116021i	$0.0370141\pi$
$601$			5.68859i			0.232042i	−0.993247	+	0.116021i	$0.962986\pi$
$602$		−	54.6593i		−	2.22775i
$603$	−0.161816			−0.00658966
$604$	−30.4274			−1.23807
$605$		−	36.9713i		−	1.50310i
$606$		−	63.6816i		−	2.58689i
$607$			29.0426i			1.17880i	0.807841	+	0.589401i	$0.200636\pi$
$607$			29.0426i			1.17880i	−0.807841	+	0.589401i	$0.799364\pi$
$608$	15.1641			0.614986
$609$		−	28.8644i		−	1.16965i
$610$	−40.2973			−1.63159
$611$	6.46027			0.261355
$612$	7.93510	−	5.13498i	0.320757	−	0.207569i
$613$	34.0804			1.37650			0.688248	−	0.725476i	$-0.258380\pi$
$613$	34.0804			1.37650			0.688248	+	0.725476i	$0.258380\pi$
$614$	−50.3607			−2.03239
$615$			22.3459i			0.901073i
$616$	118.120			4.75920
$617$		−	20.7723i		−	0.836260i	−0.908387	−	0.418130i	$-0.862686\pi$
$617$		−	20.7723i		−	0.836260i	0.908387	−	0.418130i	$-0.137314\pi$
$618$			76.0680i			3.05990i
$619$		−	15.6711i		−	0.629874i	−0.949113	−	0.314937i	$-0.898017\pi$
$619$		−	15.6711i		−	0.629874i	0.949113	−	0.314937i	$-0.101983\pi$
$620$	55.4630			2.22745
$621$	21.4460			0.860598
$622$		−	36.3395i		−	1.45708i
$623$			25.2407i			1.01125i
$624$		−	6.60133i		−	0.264265i
$625$	−28.7629			−1.15052
$626$		−	62.1007i		−	2.48204i
$627$	55.8292			2.22960
$628$	2.59489			0.103548
$629$	−10.6572	−	16.4686i	−0.424931	−	0.656646i
$630$	−13.8610			−0.552237
$631$	−19.1074			−0.760653			−0.380327	−	0.924852i	$-0.624188\pi$
$631$	−19.1074			−0.760653			−0.380327	+	0.924852i	$0.624188\pi$
$632$		−	77.7948i		−	3.09451i
$633$	−9.88149			−0.392754
$634$			38.4581i			1.52737i
$635$		−	19.3174i		−	0.766587i
$636$		−	36.8418i		−	1.46087i
$637$	−8.44684			−0.334676
$638$	−55.9807			−2.21630
$639$		−	1.39568i		−	0.0552124i
$640$			41.8456i			1.65409i
$641$			9.90754i			0.391324i	0.980671	+	0.195662i	$0.0626856\pi$
$641$			9.90754i			0.391324i	−0.980671	+	0.195662i	$0.937314\pi$
$642$	11.1253			0.439080
$643$		−	5.99792i		−	0.236535i	−0.992982	−	0.118267i	$-0.962266\pi$
$643$		−	5.99792i		−	0.236535i	0.992982	−	0.118267i	$-0.0377340\pi$
$644$	68.1693			2.68625
$645$	−19.9381			−0.785061
$646$	60.0447	−	38.8563i	2.36243	−	1.52878i
$647$	11.9529			0.469918			0.234959	−	0.972005i	$-0.424504\pi$
$647$	11.9529			0.469918			0.234959	+	0.972005i	$0.424504\pi$
$648$	38.8835			1.52749
$649$			5.11774i			0.200889i
$650$	1.83149			0.0718369
$651$			35.6085i			1.39561i
$652$		−	21.6472i		−	0.847770i
$653$			29.6195i			1.15910i	0.814936	+	0.579551i	$0.196772\pi$
$653$			29.6195i			1.15910i	−0.814936	+	0.579551i	$0.803228\pi$
$654$	54.4730			2.13006
$655$	24.2016			0.945635
$656$			30.9968i			1.21022i
$657$		−	1.58391i		−	0.0617944i
$658$			84.7989i			3.30580i
$659$	11.0235			0.429415			0.214708	−	0.976678i	$-0.431120\pi$
$659$	11.0235			0.429415			0.214708	+	0.976678i	$0.431120\pi$
$660$		−	82.1188i		−	3.19647i
$661$	−1.13326			−0.0440787			−0.0220394	−	0.999757i	$-0.507016\pi$
$661$	−1.13326			−0.0440787			−0.0220394	+	0.999757i	$0.507016\pi$
$662$	−32.3874			−1.25877
$663$	−2.79547	−	4.31984i	−0.108567	−	0.167769i
$664$	99.1955			3.84953
$665$	−71.0943			−2.75692
$666$			6.45785i			0.250237i
$667$	−16.9513			−0.656358
$668$		−	38.4949i		−	1.48941i
$669$		−	11.9123i		−	0.460555i
$670$			1.80105i			0.0695806i
$671$	−34.0109			−1.31298
$672$	14.3202			0.552414
$673$		−	15.7006i		−	0.605215i	−0.953115	−	0.302608i	$-0.902143\pi$
$673$		−	15.7006i		−	0.605215i	0.953115	−	0.302608i	$-0.0978572\pi$
$674$		−	1.69501i		−	0.0652892i
$675$			5.12645i			0.197317i
$676$	−52.0318			−2.00122
$677$		−	17.8922i		−	0.687652i	−0.939033	−	0.343826i	$-0.888277\pi$
$677$		−	17.8922i		−	0.687652i	0.939033	−	0.343826i	$-0.111723\pi$
$678$	−13.7382			−0.527611
$679$	−35.2628			−1.35326
$680$	−29.9878	−	46.3401i	−1.14998	−	1.77706i
$681$	3.34611			0.128223
$682$	69.0604			2.64446
$683$		−	7.65132i		−	0.292770i	−0.989228	−	0.146385i	$-0.953236\pi$
$683$		−	7.65132i		−	0.292770i	0.989228	−	0.146385i	$-0.0467638\pi$
$684$	−15.9596			−0.610231
$685$			5.03692i			0.192451i
$686$		−	37.6950i		−	1.43920i
$687$		−	13.8313i		−	0.527697i
$688$	−27.6568			−1.05441
$689$	4.45042			0.169547
$690$		−	36.6853i		−	1.39659i
$691$			35.2690i			1.34169i	0.741596	+	0.670847i	$0.234069\pi$
$691$			35.2690i			1.34169i	−0.741596	+	0.670847i	$0.765931\pi$
$692$		−	36.7086i		−	1.39545i
$693$	−11.6987			−0.444397
$694$			47.8699i			1.81712i
$695$	−2.01305			−0.0763595
$696$	−37.8404			−1.43434
$697$	13.1262	+	20.2840i	0.497191	+	0.768311i
$698$	−65.4943			−2.47899
$699$	40.0687			1.51554
$700$			16.2952i			0.615900i
$701$	45.3446			1.71264			0.856321	−	0.516445i	$-0.172745\pi$
$701$	45.3446			1.71264			0.856321	+	0.516445i	$0.172745\pi$
$702$			11.0219i			0.415995i
$703$			33.1228i			1.24925i
$704$			26.3697i			0.993847i
$705$	30.9321			1.16497
$706$	52.8770			1.99005
$707$			68.4430i			2.57406i
$708$			6.59318i			0.247787i
$709$			24.2829i			0.911963i	0.889989	+	0.455982i	$0.150712\pi$
$709$			24.2829i			0.911963i	−0.889989	+	0.455982i	$0.849288\pi$
$710$	−15.5343			−0.582991
$711$			7.70485i			0.288954i
$712$	33.0897			1.24009
$713$	20.9120			0.783159
$714$	56.7031	−	36.6939i	2.12206	−	1.37323i
$715$	9.91979			0.370979
$716$	36.7141			1.37207
$717$			24.6036i			0.918839i
$718$	4.62468			0.172592
$719$			32.3570i			1.20671i	0.797471	+	0.603357i	$0.206171\pi$
$719$			32.3570i			1.20671i	−0.797471	+	0.603357i	$0.793829\pi$
$720$			7.01349i			0.261377i
$721$		−	81.7556i		−	3.04474i
$722$	−73.4268			−2.73266
$723$	34.8864			1.29744
$724$			50.0685i			1.86078i
$725$		−	4.05205i		−	0.150489i
$726$		−	59.3071i		−	2.20109i
$727$	4.28843			0.159049			0.0795246	−	0.996833i	$-0.474660\pi$
$727$	4.28843			0.159049			0.0795246	+	0.996833i	$0.474660\pi$
$728$			18.3823i			0.681294i
$729$	−29.9606			−1.10965
$730$	−17.6293			−0.652491
$731$	−18.0983	+	11.7118i	−0.669391	+	0.433178i
$732$	−43.8162			−1.61949
$733$	15.8035			0.583715			0.291857	−	0.956462i	$-0.405727\pi$
$733$	15.8035			0.583715			0.291857	+	0.956462i	$0.405727\pi$
$734$			28.6830i			1.05871i
$735$	−40.4439			−1.49179
$736$		−	8.40988i		−	0.309992i
$737$			1.52008i			0.0559930i
$738$		−	7.95398i		−	0.292790i
$739$	1.81560			0.0667879			0.0333939	−	0.999442i	$-0.489368\pi$
$739$	1.81560			0.0667879			0.0333939	+	0.999442i	$0.489368\pi$
$740$	48.7201			1.79099
$741$			8.68835i			0.319174i
$742$			58.4171i			2.14456i
$743$		−	29.7962i		−	1.09312i	−0.837421	−	0.546559i	$-0.815937\pi$
$743$		−	29.7962i		−	1.09312i	0.837421	−	0.546559i	$-0.184063\pi$
$744$	46.6817			1.71143
$745$		−	48.0400i		−	1.76005i
$746$	31.2795			1.14522
$747$	−9.82438			−0.359455
$748$	−48.2375	−	74.5415i	−1.76374	−	2.72551i
$749$	−11.9571			−0.436904
$750$	−38.7370			−1.41447
$751$		−	22.2757i		−	0.812853i	−0.913683	−	0.406427i	$-0.866775\pi$
$751$		−	22.2757i		−	0.812853i	0.913683	−	0.406427i	$-0.133225\pi$
$752$	42.9070			1.56466
$753$		−	31.9489i		−	1.16428i
$754$		−	8.71194i		−	0.317270i
$755$		−	17.5988i		−	0.640486i
$756$	−98.0647			−3.56658
$757$	−27.3236			−0.993094			−0.496547	−	0.868010i	$-0.665399\pi$
$757$	−27.3236			−0.993094			−0.496547	+	0.868010i	$0.665399\pi$
$758$			4.77429i			0.173410i
$759$		−	30.9623i		−	1.12386i
$760$			93.2024i			3.38081i
$761$	−32.2187			−1.16793			−0.583963	−	0.811780i	$-0.698499\pi$
$761$	−32.2187			−1.16793			−0.583963	+	0.811780i	$0.698499\pi$
$762$		−	30.9878i		−	1.12257i
$763$	−58.5459			−2.11950
$764$	−3.26659			−0.118181
$765$	2.97001	+	4.58956i	0.107381	+	0.165936i
$766$	9.32710			0.337002
$767$	−0.796443			−0.0287579
$768$			50.9788i			1.83954i
$769$	−6.20013			−0.223582			−0.111791	−	0.993732i	$-0.535659\pi$
$769$	−6.20013			−0.223582			−0.111791	+	0.993732i	$0.535659\pi$
$770$			130.209i			4.69242i
$771$		−	36.8330i		−	1.32651i
$772$			8.77641i			0.315870i
$773$	48.2116			1.73405			0.867026	−	0.498263i	$-0.166029\pi$
$773$	48.2116			1.73405			0.867026	+	0.498263i	$0.166029\pi$
$774$	7.09692			0.255093
$775$			4.99879i			0.179562i
$776$			46.2284i			1.65950i
$777$			31.2794i			1.12214i
$778$	35.6559			1.27832
$779$		−	40.7965i		−	1.46169i
$780$	12.7796			0.457585
$781$	−13.1109			−0.469145
$782$	−21.5494	−	33.3002i	−0.770603	−	1.19081i
$783$	24.3853			0.871458
$784$	−56.1012			−2.00361
$785$			1.50085i			0.0535677i
$786$	38.8227			1.38476
$787$		−	20.3495i		−	0.725380i	−0.931910	−	0.362690i	$-0.881858\pi$
$787$		−	20.3495i		−	0.725380i	0.931910	−	0.362690i	$-0.118142\pi$
$788$			19.5626i			0.696889i
$789$			32.2707i			1.14887i
$790$	85.7567			3.05109
$791$	14.7654			0.524996
$792$			15.3366i			0.544964i
$793$		−	5.29291i		−	0.187957i
$794$			50.4156i			1.78918i
$795$	21.3088			0.755746
$796$		−	84.5691i		−	2.99747i
$797$	−2.49079			−0.0882282			−0.0441141	−	0.999026i	$-0.514047\pi$
$797$	−2.49079			−0.0882282			−0.0441141	+	0.999026i	$0.514047\pi$
$798$	−114.045			−4.03715
$799$	28.0779	−	18.1699i	0.993325	−	0.642803i
$800$	2.01030			0.0710747
$801$	−3.27723			−0.115795
$802$			41.3268i			1.45930i
$803$	−14.8791			−0.525073
$804$			1.95832i			0.0690646i
$805$			39.4282i			1.38966i
$806$			10.7475i			0.378563i
$807$	−39.5016			−1.39052
$808$	89.7267			3.15657
$809$		−	33.6024i		−	1.18140i	−0.806892	−	0.590699i	$-0.798852\pi$
$809$		−	33.6024i		−	1.18140i	0.806892	−	0.590699i	$-0.201148\pi$
$810$			42.8631i			1.50606i
$811$		−	26.6762i		−	0.936728i	−0.883536	−	0.468364i	$-0.844844\pi$
$811$		−	26.6762i		−	0.936728i	0.883536	−	0.468364i	$-0.155156\pi$
$812$	77.5122			2.72015
$813$		−	43.1807i		−	1.51441i
$814$	60.6644			2.12629
$815$	12.5205			0.438573
$816$	−18.5666	−	28.6910i	−0.649961	−	1.00438i
$817$	36.4006			1.27350
$818$	−70.5179			−2.46560
$819$		−	1.82060i		−	0.0636168i
$820$	−60.0074			−2.09555
$821$			8.00457i			0.279362i	0.990197	+	0.139681i	$0.0446076\pi$
$821$			8.00457i			0.279362i	−0.990197	+	0.139681i	$0.955392\pi$
$822$			8.07993i			0.281820i
$823$		−	47.4477i		−	1.65392i	−0.562257	−	0.826962i	$-0.690067\pi$
$823$		−	47.4477i		−	1.65392i	0.562257	−	0.826962i	$-0.309933\pi$
$824$	−107.179			−3.73376
$825$	7.40124			0.257678
$826$		−	10.4543i		−	0.363751i
$827$		−	28.0638i		−	0.975874i	−0.872879	−	0.487937i	$-0.837749\pi$
$827$		−	28.0638i		−	0.975874i	0.872879	−	0.487937i	$-0.162251\pi$
$828$			8.85105i			0.307595i
$829$	41.5734			1.44390			0.721951	−	0.691944i	$-0.243245\pi$
$829$	41.5734			1.44390			0.721951	+	0.691944i	$0.243245\pi$
$830$			109.348i			3.79551i
$831$	−48.9192			−1.69699
$832$	−4.10376			−0.142272
$833$	−36.7120	+	23.7572i	−1.27200	+	0.823138i
$834$	−3.22922			−0.111819
$835$	22.2649			0.770510
$836$			149.923i			5.18519i
$837$	−30.0828			−1.03981
$838$		−	93.0867i		−	3.21563i
$839$		−	36.0378i		−	1.24416i	−0.782953	−	0.622081i	$-0.786287\pi$
$839$		−	36.0378i		−	1.24416i	0.782953	−	0.622081i	$-0.213713\pi$
$840$			88.0155i			3.03682i
$841$	9.72541			0.335359
$842$	41.3460			1.42488
$843$		−	26.9686i		−	0.928848i
$844$		−	26.5356i		−	0.913394i
$845$		−	30.0945i		−	1.03528i
$846$	−11.0102			−0.378539
$847$			63.7414i			2.19018i
$848$	29.5582			1.01503
$849$	−13.0447			−0.447692
$850$	7.96009	−	5.15116i	0.273029	−	0.176683i
$851$	18.3696			0.629701
$852$	−16.8908			−0.578668
$853$		−	47.6429i		−	1.63126i	−0.578573	−	0.815631i	$-0.696390\pi$
$853$		−	47.6429i		−	1.63126i	0.578573	−	0.815631i	$-0.303610\pi$
$854$	69.4758			2.37741
$855$		−	9.23082i		−	0.315687i
$856$			15.6754i			0.535775i
$857$			4.11818i			0.140674i	0.997523	+	0.0703372i	$0.0224075\pi$
$857$			4.11818i			0.140674i	−0.997523	+	0.0703372i	$0.977592\pi$
$858$	15.9127			0.543252
$859$	32.3689			1.10441			0.552206	−	0.833708i	$-0.313786\pi$
$859$	32.3689			1.10441			0.552206	+	0.833708i	$0.313786\pi$
$860$		−	53.5414i		−	1.82575i
$861$		−	38.5261i		−	1.31297i
$862$			1.59741i			0.0544079i
$863$	−6.31821			−0.215074			−0.107537	−	0.994201i	$-0.534296\pi$
$863$	−6.31821			−0.215074			−0.107537	+	0.994201i	$0.534296\pi$
$864$			12.0980i			0.411582i
$865$	21.2318			0.721902
$866$	53.1549			1.80628
$867$	−24.2996	−	10.9127i	−0.825256	−	0.370614i
$868$	−95.6227			−3.24564
$869$	72.3786			2.45527
$870$		−	41.7132i		−	1.41421i
$871$	−0.236561			−0.00801557
$872$			76.7519i			2.59915i
$873$		−	4.57849i		−	0.154958i
$874$			66.9757i			2.26549i
$875$	41.6333			1.40746
$876$	−19.1688			−0.647652
$877$			19.8041i			0.668736i	0.942443	+	0.334368i	$0.108523\pi$
$877$			19.8041i			0.668736i	−0.942443	+	0.334368i	$0.891477\pi$
$878$		−	87.7977i		−	2.96303i
$879$		−	46.8285i		−	1.57949i
$880$	65.8841			2.22095
$881$			42.7712i			1.44100i	0.693455	+	0.720500i	$0.256088\pi$
$881$			42.7712i			1.44100i	−0.693455	+	0.720500i	$0.743912\pi$
$882$	14.3959			0.484736
$883$	17.0313			0.573148			0.286574	−	0.958058i	$-0.407484\pi$
$883$	17.0313			0.573148			0.286574	+	0.958058i	$0.407484\pi$
$884$	11.6004	−	7.50691i	0.390165	−	0.252485i
$885$	−3.81341			−0.128186
$886$	−54.6320			−1.83540
$887$			10.9675i			0.368254i	0.982902	+	0.184127i	$0.0589458\pi$
$887$			10.9675i			0.368254i	−0.982902	+	0.184127i	$0.941054\pi$
$888$	41.0063			1.37608
$889$			33.3047i			1.11700i
$890$			36.4763i			1.22269i
$891$			36.1764i			1.21195i
$892$	31.9891			1.07107
$893$	−56.4722			−1.88977
$894$		−	77.0629i		−	2.57737i
$895$			21.2349i			0.709806i
$896$		−	72.1451i		−	2.41020i
$897$	4.81848			0.160884
$898$			7.04101i			0.234962i
$899$	23.7780			0.793042
$900$	−2.11575			−0.0705251
$901$	19.3426	−	12.5170i	0.644395	−	0.417003i
$902$	−74.7189			−2.48787
$903$	34.3748			1.14392
$904$		−	19.3569i		−	0.643802i
$905$	−28.9590			−0.962629
$906$		−	28.2309i		−	0.937909i
$907$		−	4.89349i		−	0.162486i	−0.996694	−	0.0812428i	$-0.974111\pi$
$907$		−	4.89349i		−	0.162486i	0.996694	−	0.0812428i	$-0.0258889\pi$
$908$			8.98560i			0.298198i
$909$	−8.88659			−0.294749
$910$	−20.2637			−0.671734
$911$		−	37.1570i		−	1.23107i	−0.788111	−	0.615533i	$-0.788941\pi$
$911$		−	37.1570i		−	1.23107i	0.788111	−	0.615533i	$-0.211059\pi$
$912$			57.7052i			1.91081i
$913$			92.2893i			3.05433i
$914$	−28.7933			−0.952398
$915$		−	25.3427i		−	0.837804i
$916$	37.1424			1.22722
$917$	−41.7255			−1.37790
$918$	30.9997	+	47.9039i	1.02314	+	1.58107i
$919$	35.7429			1.17905			0.589524	−	0.807751i	$-0.299315\pi$
$919$	35.7429			1.17905			0.589524	+	0.807751i	$0.299315\pi$
$920$	51.6892			1.70414
$921$		−	31.6715i		−	1.04361i
$922$	−83.1106			−2.73710
$923$		−	2.04037i		−	0.0671596i
$924$			141.579i			4.65762i
$925$			4.39106i			0.144377i
$926$	11.1247			0.365582
$927$	10.6151			0.348645
$928$		−	9.56249i		−	0.313904i
$929$		−	1.05296i		−	0.0345464i	−0.999851	−	0.0172732i	$-0.994502\pi$
$929$		−	1.05296i		−	0.0345464i	0.999851	−	0.0172732i	$-0.00549850\pi$
$930$			51.4593i			1.68742i
$931$	73.8377			2.41993
$932$			107.600i			3.52455i
$933$	22.8536			0.748195
$934$	−4.63227			−0.151573
$935$	43.1138	−	27.9000i	1.40997	−	0.912426i
$936$	−2.38675			−0.0780133
$937$	−2.68417			−0.0876879			−0.0438440	−	0.999038i	$-0.513960\pi$
$937$	−2.68417			−0.0876879			−0.0438440	+	0.999038i	$0.513960\pi$
$938$		−	3.10515i		−	0.101387i
$939$	39.0546			1.27450
$940$			83.0646i			2.70927i
$941$			26.7946i			0.873480i	0.899588	+	0.436740i	$0.143867\pi$
$941$			26.7946i			0.873480i	−0.899588	+	0.436740i	$0.856133\pi$
$942$			2.40758i			0.0784431i
$943$	−22.6254			−0.736783
$944$	−5.28972			−0.172166
$945$		−	56.7193i		−	1.84508i
$946$		−	66.6677i		−	2.16756i
$947$			49.7535i			1.61677i	0.588653	+	0.808386i	$0.299659\pi$
$947$			49.7535i			1.61677i	−0.588653	+	0.808386i	$0.700341\pi$
$948$	93.2451			3.02846
$949$		−	2.31555i		−	0.0751659i
$950$	−16.0099			−0.519429
$951$	−24.1860			−0.784286
$952$	51.7013	+	79.8941i	1.67565	+	2.58938i
$953$	−6.24626			−0.202336			−0.101168	−	0.994869i	$-0.532258\pi$
$953$	−6.24626			−0.202336			−0.101168	+	0.994869i	$0.532258\pi$
$954$	−7.58483			−0.245568
$955$		−	1.88936i		−	0.0611381i
$956$	−66.0702			−2.13686
$957$		−	35.2059i		−	1.13804i
$958$		−	32.4181i		−	1.04738i
$959$		−	8.68406i		−	0.280423i
$960$	−19.6490			−0.634169
$961$	1.66632			0.0537523
$962$			9.44083i			0.304385i
$963$		−	1.55250i		−	0.0500287i
$964$			93.6835i			3.01734i
$965$	−5.07616			−0.163407
$966$			63.2484i			2.03498i
$967$	−4.45625			−0.143303			−0.0716517	−	0.997430i	$-0.522827\pi$
$967$	−4.45625			−0.143303			−0.0716517	+	0.997430i	$0.522827\pi$
$968$	83.5630			2.68582
$969$	24.4364	+	37.7617i	0.785012	+	1.21308i
$970$	−50.9597			−1.63622
$971$	4.33366			0.139074			0.0695369	−	0.997579i	$-0.477848\pi$
$971$	4.33366			0.139074			0.0695369	+	0.997579i	$0.477848\pi$
$972$		−	23.5084i		−	0.754033i
$973$	3.47066			0.111264
$974$		−	83.7195i		−	2.68255i
$975$			1.15181i			0.0368874i
$976$		−	35.1538i		−	1.12525i
$977$	−22.0640			−0.705889			−0.352945	−	0.935644i	$-0.614820\pi$
$977$	−22.0640			−0.705889			−0.352945	+	0.935644i	$0.614820\pi$
$978$	20.0846			0.642234
$979$			30.7860i			0.983924i
$980$		−	108.607i		−	3.46934i
$981$		−	7.60155i		−	0.242699i
$982$	47.3033			1.50951
$983$		−	19.5426i		−	0.623312i	−0.950195	−	0.311656i	$-0.899116\pi$
$983$		−	19.5426i		−	0.623312i	0.950195	−	0.311656i	$-0.100884\pi$
$984$	−50.5065			−1.61009
$985$	−11.3147			−0.360518
$986$	−24.5028	−	37.8642i	−0.780328	−	1.20584i
$987$	−53.3294			−1.69749
$988$	−23.3316			−0.742277
$989$		−	20.1874i		−	0.641923i
$990$	−16.9063			−0.537317
$991$			27.7544i			0.881648i	0.897594	+	0.440824i	$0.145314\pi$
$991$			27.7544i			0.881648i	−0.897594	+	0.440824i	$0.854686\pi$
$992$			11.7967i			0.374547i
$993$		−	20.3682i		−	0.646366i
$994$	26.7823			0.849484
$995$	48.9137			1.55067
$996$			118.896i			3.76737i
$997$		−	18.9455i		−	0.600010i	−0.953938	−	0.300005i	$-0.903012\pi$
$997$		−	18.9455i		−	0.600010i	0.953938	−	0.300005i	$-0.0969884\pi$
$998$		−	63.3342i		−	2.00481i
$999$	−26.4255			−0.836065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.d.d.237.5	✓	44
17.16	even	2	inner	1003.2.d.d.237.6	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.d.d.237.5	✓	44	1.1	even	1	trivial
1003.2.d.d.237.6	yes	44	17.16	even	2	inner

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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.49154 q^{2} -1.56691i q^{3} +4.20776 q^{4} +2.43371i q^{5} +3.90401i q^{6} -4.19592i q^{7} -5.50071 q^{8} +0.544794 q^{9} +O(q^{10})\)	\(q-2.49154 q^{2} -1.56691i q^{3} +4.20776 q^{4} +2.43371i q^{5} +3.90401i q^{6} -4.19592i q^{7} -5.50071 q^{8} +0.544794 q^{9} -6.06369i q^{10} -5.11774i q^{11} -6.59318i q^{12} +0.796443 q^{13} +10.4543i q^{14} +3.81341 q^{15} +5.28972 q^{16} +(3.46154 - 2.24004i) q^{17} -1.35738 q^{18} -6.96207 q^{19} +10.2405i q^{20} -6.57462 q^{21} +12.7511i q^{22} +3.86110i q^{23} +8.61912i q^{24} -0.922958 q^{25} -1.98437 q^{26} -5.55437i q^{27} -17.6554i q^{28} +4.39028i q^{29} -9.50125 q^{30} -5.41606i q^{31} -2.17810 q^{32} -8.01904 q^{33} +(-8.62454 + 5.58114i) q^{34} +10.2117 q^{35} +2.29236 q^{36} -4.75760i q^{37} +17.3463 q^{38} -1.24795i q^{39} -13.3872i q^{40} +5.85982i q^{41} +16.3809 q^{42} -5.22841 q^{43} -21.5342i q^{44} +1.32587i q^{45} -9.62008i q^{46} +8.11140 q^{47} -8.28851i q^{48} -10.6057 q^{49} +2.29958 q^{50} +(-3.50994 - 5.42391i) q^{51} +3.35124 q^{52} +5.58786 q^{53} +13.8389i q^{54} +12.4551 q^{55} +23.0805i q^{56} +10.9089i q^{57} -10.9386i q^{58} -1.00000 q^{59} +16.0459 q^{60} -6.64568i q^{61} +13.4943i q^{62} -2.28591i q^{63} -5.15261 q^{64} +1.93831i q^{65} +19.9797 q^{66} -0.297022 q^{67} +(14.5653 - 9.42554i) q^{68} +6.05000 q^{69} -25.4427 q^{70} -2.56185i q^{71} -2.99676 q^{72} -2.90736i q^{73} +11.8537i q^{74} +1.44619i q^{75} -29.2947 q^{76} -21.4736 q^{77} +3.10933i q^{78} +14.1427i q^{79} +12.8737i q^{80} -7.06882 q^{81} -14.6000i q^{82} -18.0332 q^{83} -27.6644 q^{84} +(5.45161 + 8.42438i) q^{85} +13.0268 q^{86} +6.87918 q^{87} +28.1512i q^{88} -6.01554 q^{89} -3.30346i q^{90} -3.34181i q^{91} +16.2466i q^{92} -8.48647 q^{93} -20.2099 q^{94} -16.9437i q^{95} +3.41289i q^{96} -8.40407i q^{97} +26.4245 q^{98} -2.78812i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 8 q^{2} + 60 q^{4} - 6 q^{8} - 62 q^{9}+O(q^{10}) \) 44 * q - 8 * q^2 + 60 * q^4 - 6 * q^8 - 62 * q^9	\( 44 q - 8 q^{2} + 60 q^{4} - 6 q^{8} - 62 q^{9} + 26 q^{13} + 84 q^{16} - 13 q^{17} + 22 q^{18} - 30 q^{19} + 66 q^{21} - 96 q^{25} - 6 q^{26} + 14 q^{30} + 20 q^{32} + 18 q^{33} - 26 q^{34} + 10 q^{35} - 130 q^{36} + 72 q^{38} - 10 q^{42} - 72 q^{43} + 8 q^{47} - 70 q^{49} + 4 q^{50} - 14 q^{51} - 48 q^{52} + 4 q^{53} + 70 q^{55} - 44 q^{59} - 52 q^{60} + 74 q^{64} + 116 q^{66} + 92 q^{67} - 54 q^{68} + 76 q^{69} - 38 q^{70} + 118 q^{72} - 76 q^{76} + 32 q^{77} + 60 q^{81} + 20 q^{83} + 168 q^{84} - 36 q^{85} - 46 q^{86} - 166 q^{87} + 18 q^{89} - 2 q^{93} - 54 q^{94} - 34 q^{98}+O(q^{100}) \) 44 * q - 8 * q^2 + 60 * q^4 - 6 * q^8 - 62 * q^9 + 26 * q^13 + 84 * q^16 - 13 * q^17 + 22 * q^18 - 30 * q^19 + 66 * q^21 - 96 * q^25 - 6 * q^26 + 14 * q^30 + 20 * q^32 + 18 * q^33 - 26 * q^34 + 10 * q^35 - 130 * q^36 + 72 * q^38 - 10 * q^42 - 72 * q^43 + 8 * q^47 - 70 * q^49 + 4 * q^50 - 14 * q^51 - 48 * q^52 + 4 * q^53 + 70 * q^55 - 44 * q^59 - 52 * q^60 + 74 * q^64 + 116 * q^66 + 92 * q^67 - 54 * q^68 + 76 * q^69 - 38 * q^70 + 118 * q^72 - 76 * q^76 + 32 * q^77 + 60 * q^81 + 20 * q^83 + 168 * q^84 - 36 * q^85 - 46 * q^86 - 166 * q^87 + 18 * q^89 - 2 * q^93 - 54 * q^94 - 34 * q^98

Introduction

L-functions

Modular forms

Varieties

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