LMFDB - Embedded newform 325.3.j.c.226.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(151,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.151"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	325.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,0,0,-6,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.85560859171$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{17} + 336 x^{16} - 90 x^{15} + 18 x^{14} - 654 x^{13} + 30550 x^{12} - 9690 x^{11} + \cdots + 46656 $ x^20 - 6x^17 + 336x^16 - 90x^15 + 18x^14 - 654x^13 + 30550x^12 - 9690x^11 + 1926x^10 - 32442x^9 + 812544x^8 - 376230x^7 + 83574x^6 + 45630x^5 + 2633913x^4 - 1039590x^3 + 206082x^2 + 138672*x + 46656
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			226.1
Root			$-2.80071 - 2.80071i$ of defining polynomial
Character	$\chi$	$=$	325.226
Dual form			325.3.j.c.151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.80071 + 2.80071i) q^{2} -3.72091 q^{3} -11.6880i q^{4} +(10.4212 - 10.4212i) q^{6} +(-4.32223 - 4.32223i) q^{7} +(21.5319 + 21.5319i) q^{8} +4.84515 q^{9} +(10.1737 + 10.1737i) q^{11} +43.4900i q^{12} +(9.40601 - 8.97368i) q^{13} +24.2107 q^{14} -73.8573 q^{16} -4.58160i q^{17} +(-13.5699 + 13.5699i) q^{18} +(-8.66275 + 8.66275i) q^{19} +(16.0826 + 16.0826i) q^{21} -56.9872 q^{22} +4.10253i q^{23} +(-80.1182 - 80.1182i) q^{24} +(-1.21085 + 51.4763i) q^{26} +15.4598 q^{27} +(-50.5183 + 50.5183i) q^{28} -21.6657 q^{29} +(18.7114 - 18.7114i) q^{31} +(120.726 - 120.726i) q^{32} +(-37.8553 - 37.8553i) q^{33} +(12.8317 + 12.8317i) q^{34} -56.6301i q^{36} +(-3.49363 - 3.49363i) q^{37} -48.5237i q^{38} +(-34.9989 + 33.3902i) q^{39} +(10.3761 - 10.3761i) q^{41} -90.0857 q^{42} +39.1435i q^{43} +(118.910 - 118.910i) q^{44} +(-11.4900 - 11.4900i) q^{46} +(12.3768 + 12.3768i) q^{47} +274.816 q^{48} -11.6366i q^{49} +17.0477i q^{51} +(-104.884 - 109.937i) q^{52} -102.477 q^{53} +(-43.2985 + 43.2985i) q^{54} -186.132i q^{56} +(32.2333 - 32.2333i) q^{57} +(60.6796 - 60.6796i) q^{58} +(-10.2757 - 10.2757i) q^{59} -0.0733554 q^{61} +104.811i q^{62} +(-20.9419 - 20.9419i) q^{63} +380.807i q^{64} +212.044 q^{66} +(6.11609 - 6.11609i) q^{67} -53.5497 q^{68} -15.2651i q^{69} +(-16.3303 + 16.3303i) q^{71} +(104.325 + 104.325i) q^{72} +(-63.9462 - 63.9462i) q^{73} +19.5693 q^{74} +(101.250 + 101.250i) q^{76} -87.9461i q^{77} +(4.50547 - 191.538i) q^{78} -128.156 q^{79} -101.131 q^{81} +58.1208i q^{82} +(-54.7720 + 54.7720i) q^{83} +(187.974 - 187.974i) q^{84} +(-109.630 - 109.630i) q^{86} +80.6162 q^{87} +438.117i q^{88} +(-74.8403 - 74.8403i) q^{89} +(-79.4413 - 1.86866i) q^{91} +47.9504 q^{92} +(-69.6234 + 69.6234i) q^{93} -69.3279 q^{94} +(-449.209 + 449.209i) q^{96} +(-97.6532 + 97.6532i) q^{97} +(32.5907 + 32.5907i) q^{98} +(49.2930 + 49.2930i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{6} - 20 q^{7} + 18 q^{8} + 72 q^{9} + 6 q^{11} - 6 q^{13} - 24 q^{14} - 128 q^{16} + 58 q^{18} - 20 q^{19} + 90 q^{21} - 24 q^{22} - 28 q^{24} + 12 q^{27} - 278 q^{28} - 40 q^{29} - 32 q^{31}+ \cdots - 410 q^{99}+O(q^{100}) $ 20 * q - 6 * q^6 - 20 * q^7 + 18 * q^8 + 72 * q^9 + 6 * q^11 - 6 * q^13 - 24 * q^14 - 128 * q^16 + 58 * q^18 - 20 * q^19 + 90 * q^21 - 24 * q^22 - 28 * q^24 + 12 * q^27 - 278 * q^28 - 40 * q^29 - 32 * q^31 + 162 * q^32 - 124 * q^33 - 14 * q^34 - 158 * q^37 - 26 * q^39 + 70 * q^41 + 320 * q^42 + 366 * q^44 + 58 * q^46 + 130 * q^47 + 716 * q^48 - 300 * q^52 - 216 * q^53 - 350 * q^54 - 168 * q^57 + 180 * q^58 + 132 * q^59 - 152 * q^61 - 442 * q^63 + 720 * q^66 - 178 * q^67 + 216 * q^68 - 258 * q^71 - 390 * q^72 + 262 * q^73 + 220 * q^74 + 68 * q^76 - 102 * q^78 - 544 * q^79 + 204 * q^81 - 88 * q^83 + 352 * q^84 - 174 * q^86 + 976 * q^87 - 282 * q^89 - 440 * q^91 + 992 * q^92 - 522 * q^93 - 544 * q^94 - 1216 * q^96 - 6 * q^97 - 78 * q^98 - 410 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.80071	+	2.80071i	−1.40036	+	1.40036i	−0.601436	+	0.798921i	$0.705405\pi$
$2$	−2.80071	+	2.80071i	−1.40036	+	1.40036i	−0.798921	+	0.601436i	$0.794595\pi$
$3$	−3.72091			−1.24030			−0.620151	−	0.784482i	$-0.712929\pi$
$3$	−3.72091			−1.24030			−0.620151	+	0.784482i	$0.712929\pi$
$4$		−	11.6880i		−	2.92200i
$5$		0			0
$5$		0			0
$6$	10.4212	−	10.4212i	1.73687	−	1.73687i
$7$	−4.32223	−	4.32223i	−0.617462	−	0.617462i	0.327418	−	0.944880i	$-0.393822\pi$
$7$	−4.32223	−	4.32223i	−0.617462	−	0.617462i	−0.944880	+	0.327418i	$0.893822\pi$
$8$	21.5319	+	21.5319i	2.69149	+	2.69149i
$9$	4.84515			0.538350
$10$		0			0
$11$	10.1737	+	10.1737i	0.924880	+	0.924880i	0.997369	−	0.0724888i	$-0.0230942\pi$
$11$	10.1737	+	10.1737i	0.924880	+	0.924880i	−0.0724888	+	0.997369i	$0.523094\pi$
$12$			43.4900i			3.62416i
$13$	9.40601	−	8.97368i	0.723540	−	0.690283i
$13$	9.40601	−	8.97368i	0.723540	−	0.690283i
$14$	24.2107			1.72933
$15$		0			0
$16$	−73.8573			−4.61608
$17$		−	4.58160i		−	0.269506i	−0.990879	−	0.134753i	$-0.956976\pi$
$17$		−	4.58160i		−	0.269506i	0.990879	−	0.134753i	$-0.0430240\pi$
$18$	−13.5699	+	13.5699i	−0.753882	+	0.753882i
$19$	−8.66275	+	8.66275i	−0.455934	+	0.455934i	−0.897318	−	0.441384i	$-0.854488\pi$
$19$	−8.66275	+	8.66275i	−0.455934	+	0.455934i	0.441384	+	0.897318i	$0.354488\pi$
$20$		0			0
$21$	16.0826	+	16.0826i	0.765840	+	0.765840i
$22$	−56.9872			−2.59033
$23$			4.10253i			0.178371i	0.996015	+	0.0891855i	$0.0284264\pi$
$23$			4.10253i			0.178371i	−0.996015	+	0.0891855i	$0.971574\pi$
$24$	−80.1182	−	80.1182i	−3.33826	−	3.33826i
$25$		0			0
$26$	−1.21085	+	51.4763i	−0.0465712	+	1.97986i
$27$	15.4598			0.572586
$28$	−50.5183	+	50.5183i	−1.80422	+	1.80422i
$29$	−21.6657			−0.747095			−0.373547	−	0.927611i	$-0.621859\pi$
$29$	−21.6657			−0.747095			−0.373547	+	0.927611i	$0.621859\pi$
$30$		0			0
$31$	18.7114	−	18.7114i	0.603594	−	0.603594i	−0.337671	−	0.941264i	$-0.609639\pi$
$31$	18.7114	−	18.7114i	0.603594	−	0.603594i	0.941264	+	0.337671i	$0.109639\pi$
$32$	120.726	−	120.726i	3.77268	−	3.77268i
$33$	−37.8553	−	37.8553i	−1.14713	−	1.14713i
$34$	12.8317	+	12.8317i	0.377404	+	0.377404i
$35$		0			0
$36$		−	56.6301i		−	1.57306i
$37$	−3.49363	−	3.49363i	−0.0944225	−	0.0944225i	0.658318	−	0.752740i	$-0.271268\pi$
$37$	−3.49363	−	3.49363i	−0.0944225	−	0.0944225i	−0.752740	+	0.658318i	$0.771268\pi$
$38$		−	48.5237i		−	1.27694i
$39$	−34.9989	+	33.3902i	−0.897408	+	0.856159i
$40$		0			0
$41$	10.3761	−	10.3761i	0.253075	−	0.253075i	−0.569155	−	0.822230i	$-0.692730\pi$
$41$	10.3761	−	10.3761i	0.253075	−	0.253075i	0.822230	+	0.569155i	$0.192730\pi$
$42$	−90.0857			−2.14490
$43$			39.1435i			0.910313i	0.890411	+	0.455157i	$0.150417\pi$
$43$			39.1435i			0.910313i	−0.890411	+	0.455157i	$0.849583\pi$
$44$	118.910	−	118.910i	2.70250	−	2.70250i
$45$		0			0
$46$	−11.4900	−	11.4900i	−0.249783	−	0.249783i
$47$	12.3768	+	12.3768i	0.263337	+	0.263337i	0.826408	−	0.563071i	$-0.190380\pi$
$47$	12.3768	+	12.3768i	0.263337	+	0.263337i	−0.563071	+	0.826408i	$0.690380\pi$
$48$	274.816			5.72534
$49$		−	11.6366i		−	0.237481i
$50$		0			0
$51$			17.0477i			0.334269i
$52$	−104.884	−	109.937i	−2.01701	−	2.11418i
$53$	−102.477			−1.93353			−0.966764	−	0.255669i	$-0.917704\pi$
$53$	−102.477			−1.93353			−0.966764	+	0.255669i	$0.917704\pi$
$54$	−43.2985	+	43.2985i	−0.801825	+	0.801825i
$55$		0			0
$56$		−	186.132i		−	3.32378i
$57$	32.2333	−	32.2333i	0.565496	−	0.565496i
$58$	60.6796	−	60.6796i	1.04620	−	1.04620i
$59$	−10.2757	−	10.2757i	−0.174165	−	0.174165i	0.614641	−	0.788807i	$-0.289301\pi$
$59$	−10.2757	−	10.2757i	−0.174165	−	0.174165i	−0.788807	+	0.614641i	$0.789301\pi$
$60$		0			0
$61$	−0.0733554			−0.00120255			−0.000601274	−	1.00000i	$-0.500191\pi$
$61$	−0.0733554			−0.00120255			−0.000601274		1.00000i	$0.500191\pi$
$62$			104.811i			1.69049i
$63$	−20.9419	−	20.9419i	−0.332411	−	0.332411i
$64$			380.807i			5.95011i
$65$		0			0
$66$	212.044			3.21279
$67$	6.11609	−	6.11609i	0.0912849	−	0.0912849i	−0.659990	−	0.751275i	$-0.729439\pi$
$67$	6.11609	−	6.11609i	0.0912849	−	0.0912849i	0.751275	+	0.659990i	$0.229439\pi$
$68$	−53.5497			−0.787496
$69$		−	15.2651i		−	0.221234i
$70$		0			0
$71$	−16.3303	+	16.3303i	−0.230004	+	0.230004i	−0.812694	−	0.582690i	$-0.802000\pi$
$71$	−16.3303	+	16.3303i	−0.230004	+	0.230004i	0.582690	+	0.812694i	$0.302000\pi$
$72$	104.325	+	104.325i	1.44896	+	1.44896i
$73$	−63.9462	−	63.9462i	−0.875975	−	0.875975i	0.117140	−	0.993115i	$-0.462627\pi$
$73$	−63.9462	−	63.9462i	−0.875975	−	0.875975i	−0.993115	+	0.117140i	$0.962627\pi$
$74$	19.5693			0.264451
$75$		0			0
$76$	101.250	+	101.250i	1.33224	+	1.33224i
$77$		−	87.9461i		−	1.14216i
$78$	4.50547	−	191.538i	0.0577624	−	2.45562i
$79$	−128.156			−1.62223			−0.811114	−	0.584888i	$-0.801138\pi$
$79$	−128.156			−1.62223			−0.811114	+	0.584888i	$0.801138\pi$
$80$		0			0
$81$	−101.131			−1.24853
$82$			58.1208i			0.708790i
$83$	−54.7720	+	54.7720i	−0.659904	+	0.659904i	−0.955357	−	0.295453i	$-0.904529\pi$
$83$	−54.7720	+	54.7720i	−0.659904	+	0.659904i	0.295453	+	0.955357i	$0.404529\pi$
$84$	187.974	−	187.974i	2.23778	−	2.23778i
$85$		0			0
$86$	−109.630	−	109.630i	−1.27476	−	1.27476i
$87$	80.6162			0.926623
$88$			438.117i			4.97861i
$89$	−74.8403	−	74.8403i	−0.840902	−	0.840902i	0.148074	−	0.988976i	$-0.452693\pi$
$89$	−74.8403	−	74.8403i	−0.840902	−	0.840902i	−0.988976	+	0.148074i	$0.952693\pi$
$90$		0			0
$91$	−79.4413	−	1.86866i	−0.872982	−	0.0205347i
$92$	47.9504			0.521200
$93$	−69.6234	+	69.6234i	−0.748639	+	0.748639i
$94$	−69.3279			−0.737531
$95$		0			0
$96$	−449.209	+	449.209i	−4.67926	+	4.67926i
$97$	−97.6532	+	97.6532i	−1.00673	+	1.00673i	−0.00675648	+	0.999977i	$0.502151\pi$
$97$	−97.6532	+	97.6532i	−1.00673	+	1.00673i	−0.999977	+	0.00675648i	$0.997849\pi$
$98$	32.5907	+	32.5907i	0.332558	+	0.332558i
$99$	49.2930	+	49.2930i	0.497909	+	0.497909i
$100$		0			0
$101$			92.2491i			0.913357i	0.889632	+	0.456679i	$0.150961\pi$
$101$			92.2491i			0.913357i	−0.889632	+	0.456679i	$0.849039\pi$
$102$	−47.7457	−	47.7457i	−0.468095	−	0.468095i
$103$			8.26839i			0.0802757i	0.999194	+	0.0401378i	$0.0127797\pi$
$103$			8.26839i			0.0802757i	−0.999194	+	0.0401378i	$0.987220\pi$
$104$	395.750	+	9.30903i	3.80528	+	0.0895099i
$105$		0			0
$106$	287.009	−	287.009i	2.70763	−	2.70763i
$107$	−33.2484			−0.310732			−0.155366	−	0.987857i	$-0.549656\pi$
$107$	−33.2484			−0.310732			−0.155366	+	0.987857i	$0.549656\pi$
$108$		−	180.694i		−	1.67310i
$109$	−48.6760	+	48.6760i	−0.446569	+	0.446569i	−0.894212	−	0.447643i	$-0.852264\pi$
$109$	−48.6760	+	48.6760i	−0.446569	+	0.446569i	0.447643	+	0.894212i	$0.352264\pi$
$110$		0			0
$111$	12.9995	+	12.9995i	0.117112	+	0.117112i
$112$	319.229	+	319.229i	2.85026	+	2.85026i
$113$	83.3899			0.737964			0.368982	−	0.929437i	$-0.379706\pi$
$113$	83.3899			0.737964			0.368982	+	0.929437i	$0.379706\pi$
$114$			180.552i			1.58379i
$115$		0			0
$116$			253.229i			2.18301i
$117$	45.5735	−	43.4788i	0.389517	−	0.371614i
$118$	57.5589			0.487787
$119$	−19.8027	+	19.8027i	−0.166410	+	0.166410i
$120$		0			0
$121$			86.0077i			0.710807i
$122$	0.205448	−	0.205448i	0.00168400	−	0.00168400i
$123$	−38.6084	+	38.6084i	−0.313889	+	0.313889i
$124$	−218.699	−	218.699i	−1.76370	−	1.76370i
$125$		0			0
$126$	117.304			0.930987
$127$			25.9910i			0.204653i	0.994751	+	0.102327i	$0.0326287\pi$
$127$			25.9910i			0.204653i	−0.994751	+	0.102327i	$0.967371\pi$
$128$	−583.629	−	583.629i	−4.55960	−	4.55960i
$129$		−	145.649i		−	1.12906i
$130$		0			0
$131$	8.68740			0.0663160			0.0331580	−	0.999450i	$-0.489444\pi$
$131$	8.68740			0.0663160			0.0331580	+	0.999450i	$0.489444\pi$
$132$	−442.453	+	442.453i	−3.35192	+	3.35192i
$133$	74.8848			0.563044
$134$			34.2588i			0.255663i
$135$		0			0
$136$	98.6504	−	98.6504i	0.725371	−	0.725371i
$137$	−134.508	−	134.508i	−0.981808	−	0.981808i	0.0180299	−	0.999837i	$-0.494261\pi$
$137$	−134.508	−	134.508i	−0.981808	−	0.981808i	−0.999837	+	0.0180299i	$0.994261\pi$
$138$	42.7533	+	42.7533i	0.309807	+	0.309807i
$139$	208.063			1.49686			0.748429	−	0.663215i	$-0.230808\pi$
$139$	208.063			1.49686			0.748429	+	0.663215i	$0.230808\pi$
$140$		0			0
$141$	−46.0530	−	46.0530i	−0.326617	−	0.326617i
$142$		−	91.4731i		−	0.644177i
$143$	186.989	+	4.39846i	1.30762	+	0.0307584i
$144$	−357.850			−2.48507
$145$		0			0
$146$	358.190			2.45336
$147$			43.2986i			0.294548i
$148$	−40.8336	+	40.8336i	−0.275903	+	0.275903i
$149$	−49.5038	+	49.5038i	−0.332240	+	0.332240i	−0.853437	−	0.521197i	$-0.825486\pi$
$149$	−49.5038	+	49.5038i	−0.332240	+	0.332240i	0.521197	+	0.853437i	$0.325486\pi$
$150$		0			0
$151$	−59.0365	−	59.0365i	−0.390970	−	0.390970i	0.484063	−	0.875033i	$-0.339161\pi$
$151$	−59.0365	−	59.0365i	−0.390970	−	0.390970i	−0.875033	+	0.484063i	$0.839161\pi$
$152$	−373.051			−2.45428
$153$		−	22.1985i		−	0.145088i
$154$	246.312	+	246.312i	1.59943	+	1.59943i
$155$		0			0
$156$	390.265	+	409.067i	2.50170	+	2.62223i
$157$	−151.047			−0.962083			−0.481041	−	0.876698i	$-0.659741\pi$
$157$	−151.047			−0.962083			−0.481041	+	0.876698i	$0.659741\pi$
$158$	358.928	−	358.928i	2.27170	−	2.27170i
$159$	381.307			2.39816
$160$		0			0
$161$	17.7321	−	17.7321i	0.110137	−	0.110137i
$162$	283.239	−	283.239i	1.74839	−	1.74839i
$163$	−72.2498	−	72.2498i	−0.443250	−	0.443250i	0.449853	−	0.893103i	$-0.351476\pi$
$163$	−72.2498	−	72.2498i	−0.443250	−	0.443250i	−0.893103	+	0.449853i	$0.851476\pi$
$164$	−121.275	−	121.275i	−0.739484	−	0.739484i
$165$		0			0
$166$		−	306.802i		−	1.84820i
$167$	178.495	+	178.495i	1.06883	+	1.06883i	0.997449	+	0.0713849i	$0.0227419\pi$
$167$	178.495	+	178.495i	1.06883	+	1.06883i	0.0713849	+	0.997449i	$0.477258\pi$
$168$			692.579i			4.12249i
$169$	7.94622	−	168.813i	0.0470190	−	0.998894i
$170$		0			0
$171$	−41.9723	+	41.9723i	−0.245452	+	0.245452i
$172$	457.509			2.65994
$173$			165.934i			0.959155i	0.877500	+	0.479577i	$0.159210\pi$
$173$			165.934i			0.959155i	−0.877500	+	0.479577i	$0.840790\pi$
$174$	−225.783	+	225.783i	−1.29760	+	1.29760i
$175$		0			0
$176$	−751.401	−	751.401i	−4.26933	−	4.26933i
$177$	38.2351	+	38.2351i	0.216018	+	0.216018i
$178$	419.212			2.35513
$179$			147.688i			0.825073i	0.910941	+	0.412537i	$0.135357\pi$
$179$			147.688i			0.825073i	−0.910941	+	0.412537i	$0.864643\pi$
$180$		0			0
$181$			107.361i			0.593154i	0.955009	+	0.296577i	$0.0958451\pi$
$181$			107.361i			0.593154i	−0.955009	+	0.296577i	$0.904155\pi$
$182$	227.726	−	217.259i	1.25124	−	1.19373i
$183$	0.272949			0.00149152
$184$	−88.3353	+	88.3353i	−0.480083	+	0.480083i
$185$		0			0
$186$		−	389.990i		−	2.09672i
$187$	46.6117	−	46.6117i	0.249261	−	0.249261i
$188$	144.660	−	144.660i	0.769470	−	0.769470i
$189$	−66.8210	−	66.8210i	−0.353550	−	0.353550i
$190$		0			0
$191$	−60.7495			−0.318060			−0.159030	−	0.987274i	$-0.550837\pi$
$191$	−60.7495			−0.318060			−0.159030	+	0.987274i	$0.550837\pi$
$192$		−	1416.95i		−	7.37994i
$193$	120.907	+	120.907i	0.626460	+	0.626460i	0.947176	−	0.320715i	$-0.103923\pi$
$193$	120.907	+	120.907i	0.626460	+	0.626460i	−0.320715	+	0.947176i	$0.603923\pi$
$194$		−	546.997i		−	2.81957i
$195$		0			0
$196$	−136.008			−0.693920
$197$	182.704	−	182.704i	0.927432	−	0.927432i	−0.0701072	−	0.997539i	$-0.522334\pi$
$197$	182.704	−	182.704i	0.927432	−	0.927432i	0.997539	+	0.0701072i	$0.0223341\pi$
$198$	−276.111			−1.39450
$199$			245.127i			1.23179i	0.787827	+	0.615897i	$0.211206\pi$
$199$			245.127i			1.23179i	−0.787827	+	0.615897i	$0.788794\pi$
$200$		0			0
$201$	−22.7574	+	22.7574i	−0.113221	+	0.113221i
$202$	−258.363	−	258.363i	−1.27903	−	1.27903i
$203$	93.6444	+	93.6444i	0.461303	+	0.461303i
$204$	199.253			0.976733
$205$		0			0
$206$	−23.1574	−	23.1574i	−0.112415	−	0.112415i
$207$			19.8774i			0.0960260i
$208$	−694.703	+	662.772i	−3.33992	+	3.18640i
$209$	−176.264			−0.843369
$210$		0			0
$211$	−270.312			−1.28110			−0.640550	−	0.767916i	$-0.721294\pi$
$211$	−270.312			−1.28110			−0.640550	+	0.767916i	$0.721294\pi$
$212$			1197.75i			5.64977i
$213$	60.7636	−	60.7636i	0.285275	−	0.285275i
$214$	93.1191	−	93.1191i	0.435136	−	0.435136i
$215$		0			0
$216$	332.879	+	332.879i	1.54111	+	1.54111i
$217$	−161.750			−0.745393
$218$		−	272.655i		−	1.25071i
$219$	237.938	+	237.938i	1.08647	+	1.08647i
$220$		0			0
$221$	−41.1138	−	43.0946i	−0.186035	−	0.194998i
$222$	−72.8157			−0.327999
$223$	−268.392	+	268.392i	−1.20355	+	1.20355i	−0.230475	+	0.973078i	$0.574028\pi$
$223$	−268.392	+	268.392i	−1.20355	+	1.20355i	−0.973078	+	0.230475i	$0.925972\pi$
$224$	−1043.61			−4.65897
$225$		0			0
$226$	−233.551	+	233.551i	−1.03341	+	1.03341i
$227$	−17.2819	+	17.2819i	−0.0761315	+	0.0761315i	−0.744147	−	0.668016i	$-0.767144\pi$
$227$	−17.2819	+	17.2819i	−0.0761315	+	0.0761315i	0.668016	+	0.744147i	$0.267144\pi$
$228$	−376.742	−	376.742i	−1.65238	−	1.65238i
$229$	15.3900	+	15.3900i	0.0672054	+	0.0672054i	0.739911	−	0.672705i	$-0.234868\pi$
$229$	15.3900	+	15.3900i	0.0672054	+	0.0672054i	−0.672705	+	0.739911i	$0.734868\pi$
$230$		0			0
$231$			327.239i			1.41662i
$232$	−466.504	−	466.504i	−2.01079	−	2.01079i
$233$		−	419.048i		−	1.79849i	−0.437445	−	0.899245i	$-0.644117\pi$
$233$		−	419.048i		−	1.79849i	0.437445	−	0.899245i	$-0.355883\pi$
$234$	−5.86676	+	249.410i	−0.0250716	+	1.06586i
$235$		0			0
$236$	−120.103	+	120.103i	−0.508911	+	0.508911i
$237$	476.856			2.01205
$238$		−	110.924i		−	0.466066i
$239$	−210.184	+	210.184i	−0.879431	+	0.879431i	−0.993476	−	0.114045i	$-0.963619\pi$
$239$	−210.184	+	210.184i	−0.879431	+	0.879431i	0.114045	+	0.993476i	$0.463619\pi$
$240$		0			0
$241$	−149.026	−	149.026i	−0.618364	−	0.618364i	0.326747	−	0.945112i	$-0.394047\pi$
$241$	−149.026	−	149.026i	−0.618364	−	0.618364i	−0.945112	+	0.326747i	$0.894047\pi$
$242$	−240.883	−	240.883i	−0.995384	−	0.995384i
$243$	237.160			0.975968
$244$			0.857378i			0.00351384i
$245$		0			0
$246$		−	216.262i		−	0.879114i
$247$	−3.74522	+	159.219i	−0.0151628	+	0.644610i
$248$	805.784			3.24913
$249$	203.802	−	203.802i	0.818480	−	0.818480i
$250$		0			0
$251$		−	323.149i		−	1.28745i	−0.765258	−	0.643724i	$-0.777389\pi$
$251$		−	323.149i		−	1.28745i	0.765258	−	0.643724i	$-0.222611\pi$
$252$	−244.769	+	244.769i	−0.971304	+	0.971304i
$253$	−41.7379	+	41.7379i	−0.164972	+	0.164972i
$254$	−72.7933	−	72.7933i	−0.286588	−	0.286588i
$255$		0			0
$256$	1745.93			6.82003
$257$			84.1773i			0.327538i	0.986499	+	0.163769i	$0.0523652\pi$
$257$			84.1773i			0.327538i	−0.986499	+	0.163769i	$0.947635\pi$
$258$	407.922	+	407.922i	1.58109	+	1.58109i
$259$			30.2006i			0.116605i
$260$		0			0
$261$	−104.974			−0.402198
$262$	−24.3309	+	24.3309i	−0.0928661	+	0.0928661i
$263$	173.935			0.661351			0.330675	−	0.943745i	$-0.392723\pi$
$263$	173.935			0.661351			0.330675	+	0.943745i	$0.392723\pi$
$264$		−	1630.19i		−	6.17498i
$265$		0			0
$266$	−209.731	+	209.731i	−0.788463	+	0.788463i
$267$	278.474	+	278.474i	1.04297	+	1.04297i
$268$	−71.4848	−	71.4848i	−0.266734	−	0.266734i
$269$	−305.410			−1.13535			−0.567676	−	0.823252i	$-0.692157\pi$
$269$	−305.410			−1.13535			−0.567676	+	0.823252i	$0.692157\pi$
$270$		0			0
$271$	−295.817	−	295.817i	−1.09158	−	1.09158i	−0.995361	−	0.0962150i	$-0.969326\pi$
$271$	−295.817	−	295.817i	−1.09158	−	1.09158i	−0.0962150	−	0.995361i	$-0.530674\pi$
$272$			338.385i			1.24406i
$273$	295.594	+	6.95311i	1.08276	+	0.0254693i
$274$	753.435			2.74976
$275$		0			0
$276$	−178.419			−0.646446
$277$		−	205.098i		−	0.740426i	−0.928947	−	0.370213i	$-0.879285\pi$
$277$		−	205.098i		−	0.740426i	0.928947	−	0.370213i	$-0.120715\pi$
$278$	−582.726	+	582.726i	−2.09614	+	2.09614i
$279$	90.6595	−	90.6595i	0.324945	−	0.324945i
$280$		0			0
$281$	97.1896	+	97.1896i	0.345870	+	0.345870i	0.858569	−	0.512698i	$-0.171354\pi$
$281$	97.1896	+	97.1896i	0.345870	+	0.345870i	−0.512698	+	0.858569i	$0.671354\pi$
$282$	257.963			0.914762
$283$		−	251.591i		−	0.889014i	−0.895775	−	0.444507i	$-0.853379\pi$
$283$		−	251.591i		−	0.889014i	0.895775	−	0.444507i	$-0.146621\pi$
$284$	190.869	+	190.869i	0.672073	+	0.672073i
$285$		0			0
$286$	−536.022	+	511.384i	−1.87420	+	1.78806i
$287$	−89.6955			−0.312528
$288$	584.934	−	584.934i	2.03102	−	2.03102i
$289$	268.009			0.927367
$290$		0			0
$291$	363.358	−	363.358i	1.24865	−	1.24865i
$292$	−747.403	+	747.403i	−2.55960	+	2.55960i
$293$	253.522	+	253.522i	0.865262	+	0.865262i	0.991943	−	0.126682i	$-0.0404327\pi$
$293$	253.522	+	253.522i	0.865262	+	0.865262i	−0.126682	+	0.991943i	$0.540433\pi$
$294$	−121.267	−	121.267i	−0.412473	−	0.412473i
$295$		0			0
$296$		−	150.449i		−	0.508274i
$297$	157.283	+	157.283i	0.529573	+	0.529573i
$298$		−	277.292i		−	0.930510i
$299$	36.8148	+	38.5885i	0.123126	+	0.129058i
$300$		0			0
$301$	169.187	−	169.187i	0.562084	−	0.562084i
$302$	330.689			1.09500
$303$		−	343.250i		−	1.13284i
$304$	639.807	−	639.807i	2.10463	−	2.10463i
$305$		0			0
$306$	62.1717	+	62.1717i	0.203176	+	0.203176i
$307$	−139.751	−	139.751i	−0.455216	−	0.455216i	0.441865	−	0.897081i	$-0.354317\pi$
$307$	−139.751	−	139.751i	−0.455216	−	0.455216i	−0.897081	+	0.441865i	$0.854317\pi$
$308$	−1027.91			−3.33738
$309$		−	30.7659i		−	0.0995661i
$310$		0			0
$311$			458.676i			1.47484i	0.675434	+	0.737421i	$0.263957\pi$
$311$			458.676i			1.47484i	−0.675434	+	0.737421i	$0.736043\pi$
$312$	−1472.55	−	34.6380i	−4.71970	−	0.111019i
$313$	−379.531			−1.21256			−0.606280	−	0.795251i	$-0.707339\pi$
$313$	−379.531			−1.21256			−0.606280	+	0.795251i	$0.707339\pi$
$314$	423.039	−	423.039i	1.34726	−	1.34726i
$315$		0			0
$316$			1497.89i			4.74015i
$317$	−88.5600	+	88.5600i	−0.279369	+	0.279369i	−0.832857	−	0.553488i	$-0.813296\pi$
$317$	−88.5600	+	88.5600i	−0.279369	+	0.279369i	0.553488	+	0.832857i	$0.313296\pi$
$318$	−1067.93	+	1067.93i	−3.35828	+	3.35828i
$319$	−220.420	−	220.420i	−0.690973	−	0.690973i
$320$		0			0
$321$	123.714			0.385402
$322$			99.3251i			0.308463i
$323$	39.6892	+	39.6892i	0.122877	+	0.122877i
$324$			1182.02i			3.64820i
$325$		0			0
$326$	404.702			1.24142
$327$	181.119	−	181.119i	0.553881	−	0.553881i
$328$	446.832			1.36229
$329$		−	106.991i		−	0.325201i
$330$		0			0
$331$	168.982	−	168.982i	0.510521	−	0.510521i	−0.404165	−	0.914686i	$-0.632438\pi$
$331$	168.982	−	168.982i	0.510521	−	0.510521i	0.914686	+	0.404165i	$0.132438\pi$
$332$	640.175	+	640.175i	1.92824	+	1.92824i
$333$	−16.9272	−	16.9272i	−0.0508324	−	0.0508324i
$334$	−999.828			−2.99350
$335$		0			0
$336$	−1187.82	−	1187.82i	−3.53518	−	3.53518i
$337$		−	530.169i		−	1.57320i	−0.617462	−	0.786601i	$-0.711839\pi$
$337$		−	530.169i		−	1.57320i	0.617462	−	0.786601i	$-0.288161\pi$
$338$	450.542	+	495.052i	1.33296	+	1.46465i
$339$	−310.286			−0.915298
$340$		0			0
$341$	380.728			1.11650
$342$		−	235.105i		−	0.687441i
$343$	−262.086	+	262.086i	−0.764098	+	0.764098i
$344$	−842.833	+	842.833i	−2.45010	+	2.45010i
$345$		0			0
$346$	−464.733	−	464.733i	−1.34316	−	1.34316i
$347$	−318.306			−0.917308			−0.458654	−	0.888615i	$-0.651668\pi$
$347$	−318.306			−0.917308			−0.458654	+	0.888615i	$0.651668\pi$
$348$		−	942.242i		−	2.70759i
$349$	−155.842	−	155.842i	−0.446539	−	0.446539i	0.447663	−	0.894202i	$-0.352256\pi$
$349$	−155.842	−	155.842i	−0.446539	−	0.446539i	−0.894202	+	0.447663i	$0.852256\pi$
$350$		0			0
$351$	145.415	−	138.731i	0.414288	−	0.395246i
$352$	2456.45			6.97855
$353$	−128.784	+	128.784i	−0.364827	+	0.364827i	−0.865587	−	0.500759i	$-0.833054\pi$
$353$	−128.784	+	128.784i	−0.364827	+	0.364827i	0.500759	+	0.865587i	$0.333054\pi$
$354$	−214.171			−0.605003
$355$		0			0
$356$	−874.733	+	874.733i	−2.45712	+	2.45712i
$357$	73.6841	−	73.6841i	0.206398	−	0.206398i
$358$	−413.632	−	413.632i	−1.15540	−	1.15540i
$359$	381.022	+	381.022i	1.06134	+	1.06134i	0.997991	+	0.0633515i	$0.0201789\pi$
$359$	381.022	+	381.022i	1.06134	+	1.06134i	0.0633515	+	0.997991i	$0.479821\pi$
$360$		0			0
$361$			210.914i			0.584248i
$362$	−300.687	−	300.687i	−0.830627	−	0.830627i
$363$		−	320.027i		−	0.881616i
$364$	−21.8409	+	928.510i	−0.0600025	+	2.55085i
$365$		0			0
$366$	−0.764451	+	0.764451i	−0.00208866	+	0.00208866i
$367$	−393.203			−1.07140			−0.535699	−	0.844409i	$-0.679952\pi$
$367$	−393.203			−1.07140			−0.535699	+	0.844409i	$0.679952\pi$
$368$		−	303.002i		−	0.823375i
$369$	50.2736	−	50.2736i	0.136243	−	0.136243i
$370$		0			0
$371$	442.930	+	442.930i	1.19388	+	1.19388i
$372$	813.758	+	813.758i	2.18752	+	2.18752i
$373$	346.362			0.928586			0.464293	−	0.885682i	$-0.346309\pi$
$373$	346.362			0.928586			0.464293	+	0.885682i	$0.346309\pi$
$374$			261.092i			0.698108i
$375$		0			0
$376$			532.993i			1.41754i
$377$	−203.788	+	194.421i	−0.540553	+	0.515707i
$378$	374.293			0.990193
$379$	243.538	−	243.538i	0.642581	−	0.642581i	−0.308608	−	0.951189i	$-0.599863\pi$
$379$	243.538	−	243.538i	0.642581	−	0.642581i	0.951189	+	0.308608i	$0.0998631\pi$
$380$		0			0
$381$		−	96.7100i		−	0.253832i
$382$	170.142	−	170.142i	0.445398	−	0.445398i
$383$	213.304	−	213.304i	0.556929	−	0.556929i	−0.371502	−	0.928432i	$-0.621157\pi$
$383$	213.304	−	213.304i	0.556929	−	0.556929i	0.928432	+	0.371502i	$0.121157\pi$
$384$	2171.63	+	2171.63i	5.65529	+	5.65529i
$385$		0			0
$386$	−677.251			−1.75454
$387$			189.656i			0.490067i
$388$	1141.37	+	1141.37i	2.94168	+	2.94168i
$389$		−	183.135i		−	0.470783i	−0.971901	−	0.235392i	$-0.924363\pi$
$389$		−	183.135i		−	0.470783i	0.971901	−	0.235392i	$-0.0756372\pi$
$390$		0			0
$391$	18.7962			0.0480720
$392$	250.557	−	250.557i	0.639177	−	0.639177i
$393$	−32.3250			−0.0822519
$394$			1023.40i			2.59747i
$395$		0			0
$396$	576.137	−	576.137i	1.45489	−	1.45489i
$397$	−221.860	−	221.860i	−0.558840	−	0.558840i	0.370137	−	0.928977i	$-0.379311\pi$
$397$	−221.860	−	221.860i	−0.558840	−	0.558840i	−0.928977	+	0.370137i	$0.879311\pi$
$398$	−686.530	−	686.530i	−1.72495	−	1.72495i
$399$	−278.640			−0.698345
$400$		0			0
$401$	−247.392	−	247.392i	−0.616937	−	0.616937i	0.327807	−	0.944745i	$-0.393690\pi$
$401$	−247.392	−	247.392i	−0.616937	−	0.616937i	−0.944745	+	0.327807i	$0.893690\pi$
$402$		−	127.474i		−	0.317099i
$403$	8.08963	−	343.910i	0.0200735	−	0.853374i
$404$	1078.21			2.66883
$405$		0			0
$406$	−524.543			−1.29198
$407$		−	71.0863i		−	0.174659i
$408$	−367.069	+	367.069i	−0.899679	+	0.899679i
$409$	330.958	−	330.958i	0.809189	−	0.809189i	−0.175322	−	0.984511i	$-0.556097\pi$
$409$	330.958	−	330.958i	0.809189	−	0.809189i	0.984511	+	0.175322i	$0.0560968\pi$
$410$		0			0
$411$	500.490	+	500.490i	1.21774	+	1.21774i
$412$	96.6410			0.234566
$413$			88.8284i			0.215081i
$414$	−55.6709	−	55.6709i	−0.134471	−	0.134471i
$415$		0			0
$416$	52.1942	−	2218.90i	0.125467	−	5.33390i
$417$	−774.184			−1.85656
$418$	493.665	−	493.665i	1.18102	−	1.18102i
$419$	27.5079			0.0656513			0.0328256	−	0.999461i	$-0.489549\pi$
$419$	27.5079			0.0656513			0.0328256	+	0.999461i	$0.489549\pi$
$420$		0			0
$421$	371.548	−	371.548i	0.882537	−	0.882537i	−0.111255	−	0.993792i	$-0.535487\pi$
$421$	371.548	−	371.548i	0.882537	−	0.882537i	0.993792	+	0.111255i	$0.0354871\pi$
$422$	757.067	−	757.067i	1.79400	−	1.79400i
$423$	59.9676	+	59.9676i	0.141767	+	0.141767i
$424$	−2206.52	−	2206.52i	−5.20407	−	5.20407i
$425$		0			0
$426$			340.363i			0.798974i
$427$	0.317059	+	0.317059i	0.000742528	+	0.000742528i
$428$			388.607i			0.907960i
$429$	−695.769	−	16.3663i	−1.62184	−	0.0381498i
$430$		0			0
$431$	11.9557	−	11.9557i	0.0277393	−	0.0277393i	−0.693101	−	0.720840i	$-0.743756\pi$
$431$	11.9557	−	11.9557i	0.0277393	−	0.0277393i	0.720840	+	0.693101i	$0.243756\pi$
$432$	−1141.82			−2.64310
$433$			213.638i			0.493390i	0.969093	+	0.246695i	$0.0793445\pi$
$433$			213.638i			0.493390i	−0.969093	+	0.246695i	$0.920655\pi$
$434$	453.016	−	453.016i	1.04382	−	1.04382i
$435$		0			0
$436$	568.926	+	568.926i	1.30488	+	1.30488i
$437$	−35.5392	−	35.5392i	−0.0813254	−	0.0813254i
$438$	−1332.79			−3.04290
$439$			715.658i			1.63020i	0.579320	+	0.815101i	$0.303318\pi$
$439$			715.658i			1.63020i	−0.579320	+	0.815101i	$0.696682\pi$
$440$		0			0
$441$		−	56.3809i		−	0.127848i
$442$	235.844	+	5.54764i	0.533583	+	0.0125512i
$443$	−267.997			−0.604960			−0.302480	−	0.953156i	$-0.597815\pi$
$443$	−267.997			−0.604960			−0.302480	+	0.953156i	$0.597815\pi$
$444$	151.938	−	151.938i	0.342203	−	0.342203i
$445$		0			0
$446$		−	1503.38i		−	3.37081i
$447$	184.199	−	184.199i	0.412078	−	0.412078i
$448$	1645.94	−	1645.94i	3.67397	−	3.67397i
$449$	−525.677	−	525.677i	−1.17077	−	1.17077i	−0.982026	−	0.188746i	$-0.939558\pi$
$449$	−525.677	−	525.677i	−1.17077	−	1.17077i	−0.188746	−	0.982026i	$-0.560442\pi$
$450$		0			0
$451$	211.126			0.468128
$452$		−	974.661i		−	2.15633i
$453$	219.669	+	219.669i	0.484921	+	0.484921i
$454$		−	96.8031i		−	0.213223i
$455$		0			0
$456$	1388.09			3.04405
$457$	−380.148	+	380.148i	−0.831833	+	0.831833i	−0.987767	−	0.155934i	$-0.950161\pi$
$457$	−380.148	+	380.148i	−0.831833	+	0.831833i	0.155934	+	0.987767i	$0.450161\pi$
$458$	−86.2062			−0.188223
$459$		−	70.8306i		−	0.154315i
$460$		0			0
$461$	607.424	−	607.424i	1.31762	−	1.31762i	0.401971	−	0.915652i	$-0.368325\pi$
$461$	607.424	−	607.424i	1.31762	−	1.31762i	0.915652	−	0.401971i	$-0.131675\pi$
$462$	−916.504	−	916.504i	−1.98377	−	1.98377i
$463$	−553.304	−	553.304i	−1.19504	−	1.19504i	−0.975633	−	0.219407i	$-0.929588\pi$
$463$	−553.304	−	553.304i	−1.19504	−	1.19504i	−0.219407	−	0.975633i	$-0.570412\pi$
$464$	1600.17			3.44865
$465$		0			0
$466$	1173.63	+	1173.63i	2.51853	+	2.51853i
$467$			616.765i			1.32070i	0.750960	+	0.660348i	$0.229591\pi$
$467$			616.765i			1.32070i	−0.750960	+	0.660348i	$0.770409\pi$
$468$	−508.180	−	532.663i	−1.08586	−	1.13817i
$469$	−52.8703			−0.112730
$470$		0			0
$471$	562.032			1.19327
$472$		−	442.513i		−	0.937527i
$473$	−398.233	+	398.233i	−0.841931	+	0.841931i
$474$	−1335.54	+	1335.54i	−2.81759	+	2.81759i
$475$		0			0
$476$	231.454	+	231.454i	0.486249	+	0.486249i
$477$	−496.516			−1.04091
$478$		−	1177.33i		−	2.46303i
$479$	106.901	+	106.901i	0.223176	+	0.223176i	0.809834	−	0.586659i	$-0.199557\pi$
$479$	106.901	+	106.901i	0.223176	+	0.223176i	−0.586659	+	0.809834i	$0.699557\pi$
$480$		0			0
$481$	−64.2119	−	1.51043i	−0.133497	−	0.00314018i
$482$	834.757			1.73186
$483$	−65.9795	+	65.9795i	−0.136604	+	0.136604i
$484$	1005.26			2.07698
$485$		0			0
$486$	−664.218	+	664.218i	−1.36670	+	1.36670i
$487$	234.252	−	234.252i	0.481010	−	0.481010i	−0.424444	−	0.905454i	$-0.639530\pi$
$487$	234.252	−	234.252i	0.481010	−	0.481010i	0.905454	+	0.424444i	$0.139530\pi$
$488$	−1.57948	−	1.57948i	−0.00323664	−	0.00323664i
$489$	268.835	+	268.835i	0.549764	+	0.549764i
$490$		0			0
$491$			652.284i			1.32848i	0.747519	+	0.664240i	$0.231245\pi$
$491$			652.284i			1.32848i	−0.747519	+	0.664240i	$0.768755\pi$
$492$	451.254	+	451.254i	0.917184	+	0.917184i
$493$			99.2637i			0.201346i
$494$	−435.436	−	456.415i	−0.881450	−	0.923917i
$495$		0			0
$496$	−1381.97	+	1381.97i	−2.78624	+	2.78624i
$497$	141.167			0.284038
$498$			1141.58i			2.29233i
$499$	248.398	−	248.398i	0.497791	−	0.497791i	−0.412959	−	0.910750i	$-0.635505\pi$
$499$	248.398	−	248.398i	0.497791	−	0.497791i	0.910750	+	0.412959i	$0.135505\pi$
$500$		0			0
$501$	−664.164	−	664.164i	−1.32568	−	1.32568i
$502$	905.049	+	905.049i	1.80289	+	1.80289i
$503$	−185.135			−0.368062			−0.184031	−	0.982920i	$-0.558915\pi$
$503$	−185.135			−0.368062			−0.184031	+	0.982920i	$0.558915\pi$
$504$		−	901.836i		−	1.78936i
$505$		0			0
$506$		−	233.792i		−	0.462039i
$507$	−29.5671	+	628.138i	−0.0583178	+	1.23893i
$508$	303.782			0.597997
$509$	−234.707	+	234.707i	−0.461114	+	0.461114i	−0.899020	−	0.437907i	$-0.855720\pi$
$509$	−234.707	+	234.707i	−0.461114	+	0.461114i	0.437907	+	0.899020i	$0.355720\pi$
$510$		0			0
$511$			552.781i			1.08176i
$512$	−2555.33	+	2555.33i	−4.99088	+	4.99088i
$513$	−133.924	+	133.924i	−0.261061	+	0.261061i
$514$	−235.756	−	235.756i	−0.458670	−	0.458670i
$515$		0			0
$516$	−1702.35			−3.29912
$517$			251.836i			0.487110i
$518$	−84.5833	−	84.5833i	−0.163288	−	0.163288i
$519$		−	617.424i		−	1.18964i
$520$		0			0
$521$	−749.963			−1.43947			−0.719735	−	0.694249i	$-0.755737\pi$
$521$	−749.963			−1.43947			−0.719735	+	0.694249i	$0.755737\pi$
$522$	294.001	−	294.001i	0.563221	−	0.563221i
$523$	−772.536			−1.47712			−0.738562	−	0.674185i	$-0.764495\pi$
$523$	−772.536			−1.47712			−0.738562	+	0.674185i	$0.764495\pi$
$524$		−	101.538i		−	0.193775i
$525$		0			0
$526$	−487.143	+	487.143i	−0.926127	+	0.926127i
$527$	−85.7281	−	85.7281i	−0.162672	−	0.162672i
$528$	2795.89	+	2795.89i	5.29525	+	5.29525i
$529$	512.169			0.968184
$530$		0			0
$531$	−49.7875	−	49.7875i	−0.0937618	−	0.0937618i
$532$		−	875.254i		−	1.64521i
$533$	4.48595	−	190.709i	0.00841642	−	0.357803i
$534$	−1559.85			−2.92107
$535$		0			0
$536$	263.382			0.491384
$537$		−	549.534i		−	1.02334i
$538$	855.366	−	855.366i	1.58990	−	1.58990i
$539$	118.387	−	118.387i	0.219642	−	0.219642i
$540$		0			0
$541$	−361.414	−	361.414i	−0.668047	−	0.668047i	0.289216	−	0.957264i	$-0.406605\pi$
$541$	−361.414	−	361.414i	−0.668047	−	0.668047i	−0.957264	+	0.289216i	$0.906605\pi$
$542$	1657.00			3.05719
$543$		−	399.480i		−	0.735690i
$544$	−553.117	−	553.117i	−1.01676	−	1.01676i
$545$		0			0
$546$	−847.348	+	808.400i	−1.55192	+	1.48059i
$547$	−453.400			−0.828884			−0.414442	−	0.910076i	$-0.636023\pi$
$547$	−453.400			−0.828884			−0.414442	+	0.910076i	$0.636023\pi$
$548$	−1572.13	+	1572.13i	−2.86884	+	2.86884i
$549$	−0.355418			−0.000647391
$550$		0			0
$551$	187.685	−	187.685i	0.340626	−	0.340626i
$552$	328.687	−	328.687i	0.595448	−	0.595448i
$553$	553.920	+	553.920i	1.00166	+	1.00166i
$554$	574.421	+	574.421i	1.03686	+	1.03686i
$555$		0			0
$556$		−	2431.84i		−	4.37382i
$557$	453.573	+	453.573i	0.814315	+	0.814315i	0.985277	−	0.170963i	$-0.0546878\pi$
$557$	453.573	+	453.573i	0.814315	+	0.814315i	−0.170963	+	0.985277i	$0.554688\pi$
$558$			507.823i			0.910077i
$559$	351.261	+	368.184i	0.628374	+	0.658648i
$560$		0			0
$561$	−173.438	+	173.438i	−0.309158	+	0.309158i
$562$	−544.401			−0.968684
$563$		−	979.383i		−	1.73958i	−0.493423	−	0.869790i	$-0.664254\pi$
$563$		−	979.383i		−	1.73958i	0.493423	−	0.869790i	$-0.335746\pi$
$564$	−538.268	+	538.268i	−0.954376	+	0.954376i
$565$		0			0
$566$	704.634	+	704.634i	1.24494	+	1.24494i
$567$	437.111	+	437.111i	0.770920	+	0.770920i
$568$	−703.245			−1.23811
$569$			31.3304i			0.0550622i	0.999621	+	0.0275311i	$0.00876453\pi$
$569$			31.3304i			0.0550622i	−0.999621	+	0.0275311i	$0.991235\pi$
$570$		0			0
$571$		−	476.731i		−	0.834905i	−0.908699	−	0.417452i	$-0.862923\pi$
$571$		−	476.731i		−	0.834905i	0.908699	−	0.417452i	$-0.137077\pi$
$572$	51.4092	−	2185.53i	0.0898762	−	3.82086i
$573$	226.043			0.394491
$574$	251.212	−	251.212i	0.437651	−	0.437651i
$575$		0			0
$576$			1845.07i			3.20324i
$577$	−573.936	+	573.936i	−0.994689	+	0.994689i	−0.999986	−	0.00529665i	$-0.998314\pi$
$577$	−573.936	+	573.936i	−0.994689	+	0.994689i	0.00529665	+	0.999986i	$0.498314\pi$
$578$	−750.617	+	750.617i	−1.29864	+	1.29864i
$579$	−449.883	−	449.883i	−0.777000	−	0.777000i
$580$		0			0
$581$	473.475			0.814931
$582$			2035.33i			3.49712i
$583$	−1042.57	−	1042.57i	−1.78828	−	1.78828i
$584$		−	2753.76i		−	4.71535i
$585$		0			0
$586$	−1420.08			−2.42335
$587$	511.672	−	511.672i	0.871673	−	0.871673i	−0.120981	−	0.992655i	$-0.538604\pi$
$587$	511.672	−	511.672i	0.871673	−	0.871673i	0.992655	+	0.120981i	$0.0386041\pi$
$588$	506.074			0.860670
$589$			324.184i			0.550398i
$590$		0			0
$591$	−679.825	+	679.825i	−1.15030	+	1.15030i
$592$	258.031	+	258.031i	0.435862	+	0.435862i
$593$	−145.706	−	145.706i	−0.245711	−	0.245711i	0.573497	−	0.819208i	$-0.305586\pi$
$593$	−145.706	−	145.706i	−0.245711	−	0.245711i	−0.819208	+	0.573497i	$0.805586\pi$
$594$	−881.011			−1.48318
$595$		0			0
$596$	578.600	+	578.600i	0.970806	+	0.970806i
$597$		−	912.094i		−	1.52780i
$598$	−211.183	−	4.96756i	−0.353149	−	0.00830696i
$599$	−330.589			−0.551902			−0.275951	−	0.961172i	$-0.588993\pi$
$599$	−330.589			−0.551902			−0.275951	+	0.961172i	$0.588993\pi$
$600$		0			0
$601$	−538.002			−0.895177			−0.447589	−	0.894240i	$-0.647717\pi$
$601$	−538.002			−0.895177			−0.447589	+	0.894240i	$0.647717\pi$
$602$			947.690i			1.57424i
$603$	29.6333	−	29.6333i	0.0491432	−	0.0491432i
$604$	−690.019	+	690.019i	−1.14242	+	1.14242i
$605$		0			0
$606$	961.346	+	961.346i	1.58638	+	1.58638i
$607$	−412.828			−0.680111			−0.340056	−	0.940405i	$-0.610446\pi$
$607$	−412.828			−0.680111			−0.340056	+	0.940405i	$0.610446\pi$
$608$			2091.63i			3.44019i
$609$	−348.442	−	348.442i	−0.572155	−	0.572155i
$610$		0			0
$611$	227.482	+	5.35096i	0.372312	+	0.00875771i
$612$	−259.456			−0.423948
$613$	−452.991	+	452.991i	−0.738973	+	0.738973i	−0.972379	−	0.233406i	$-0.925013\pi$
$613$	−452.991	+	452.991i	−0.738973	+	0.738973i	0.233406	+	0.972379i	$0.425013\pi$
$614$	782.807			1.27493
$615$		0			0
$616$	1893.65	−	1893.65i	3.07410	−	3.07410i
$617$	−120.125	+	120.125i	−0.194691	+	0.194691i	−0.797720	−	0.603028i	$-0.793961\pi$
$617$	−120.125	+	120.125i	−0.194691	+	0.194691i	0.603028	+	0.797720i	$0.293961\pi$
$618$	86.1666	+	86.1666i	0.139428	+	0.139428i
$619$	732.097	+	732.097i	1.18271	+	1.18271i	0.979040	+	0.203669i	$0.0652868\pi$
$619$	732.097	+	732.097i	1.18271	+	1.18271i	0.203669	+	0.979040i	$0.434713\pi$
$620$		0			0
$621$			63.4244i			0.102133i
$622$	−1284.62	−	1284.62i	−2.06531	−	2.06531i
$623$			646.954i			1.03845i
$624$	2584.93	−	2466.11i	4.14251	−	3.95210i
$625$		0			0
$626$	1062.96	−	1062.96i	1.69802	−	1.69802i
$627$	655.862			1.04603
$628$			1765.44i			2.81121i
$629$	−16.0064	+	16.0064i	−0.0254474	+	0.0254474i
$630$		0			0
$631$	−377.611	−	377.611i	−0.598433	−	0.598433i	0.341463	−	0.939895i	$-0.389078\pi$
$631$	−377.611	−	377.611i	−0.598433	−	0.598433i	−0.939895	+	0.341463i	$0.889078\pi$
$632$	−2759.44	−	2759.44i	−4.36620	−	4.36620i
$633$	1005.81			1.58895
$634$		−	496.063i		−	0.782433i
$635$		0			0
$636$		−	4456.72i		−	7.00742i
$637$	−104.423	−	109.454i	−0.163929	−	0.171827i
$638$	1234.67			1.93522
$639$	−79.1228	+	79.1228i	−0.123823	+	0.123823i
$640$		0			0
$641$			1125.68i			1.75614i	0.478535	+	0.878068i	$0.341168\pi$
$641$			1125.68i			1.75614i	−0.478535	+	0.878068i	$0.658832\pi$
$642$	−346.488	+	346.488i	−0.539700	+	0.539700i
$643$	687.121	−	687.121i	1.06862	−	1.06862i	0.0711525	−	0.997465i	$-0.477332\pi$
$643$	687.121	−	687.121i	1.06862	−	1.06862i	0.997465	−	0.0711525i	$-0.0226677\pi$
$644$	−207.253	−	207.253i	−0.321821	−	0.321821i
$645$		0			0
$646$	−222.316			−0.344143
$647$			894.637i			1.38275i	0.722498	+	0.691374i	$0.242994\pi$
$647$			894.637i			1.38275i	−0.722498	+	0.691374i	$0.757006\pi$
$648$	−2177.54	−	2177.54i	−3.36040	−	3.36040i
$649$		−	209.084i		−	0.322164i
$650$		0			0
$651$	601.857			0.924512
$652$	−844.455	+	844.455i	−1.29518	+	1.29518i
$653$	259.531			0.397444			0.198722	−	0.980056i	$-0.436321\pi$
$653$	259.531			0.397444			0.198722	+	0.980056i	$0.436321\pi$
$654$			1014.53i			1.55126i
$655$		0			0
$656$	−766.348	+	766.348i	−1.16821	+	1.16821i
$657$	−309.829	−	309.829i	−0.471581	−	0.471581i
$658$	299.652	+	299.652i	0.455398	+	0.455398i
$659$	−541.017			−0.820967			−0.410483	−	0.911868i	$-0.634640\pi$
$659$	−541.017			−0.820967			−0.410483	+	0.911868i	$0.634640\pi$
$660$		0			0
$661$	580.306	+	580.306i	0.877921	+	0.877921i	0.993319	−	0.115398i	$-0.0368145\pi$
$661$	580.306	+	580.306i	0.877921	+	0.877921i	−0.115398	+	0.993319i	$0.536814\pi$
$662$			946.543i			1.42982i
$663$	152.981	+	160.351i	0.230740	+	0.241857i
$664$	−2358.69			−3.55224
$665$		0			0
$666$	94.8164			0.142367
$667$		−	88.8844i		−	0.133260i
$668$	2086.25	−	2086.25i	3.12313	−	3.12313i
$669$	998.663	−	998.663i	1.49277	−	1.49277i
$670$		0			0
$671$	−0.746295	−	0.746295i	−0.00111221	−	0.00111221i
$672$	3883.18			5.77854
$673$			965.968i			1.43532i	0.696396	+	0.717658i	$0.254786\pi$
$673$			965.968i			1.43532i	−0.696396	+	0.717658i	$0.745214\pi$
$674$	1484.85	+	1484.85i	2.20304	+	2.20304i
$675$		0			0
$676$	−1973.09	−	92.8754i	−2.91877	−	0.137390i
$677$	813.684			1.20190			0.600948	−	0.799288i	$-0.294790\pi$
$677$	813.684			1.20190			0.600948	+	0.799288i	$0.294790\pi$
$678$	869.022	−	869.022i	1.28174	−	1.28174i
$679$	844.160			1.24324
$680$		0			0
$681$	64.3042	−	64.3042i	0.0944261	−	0.0944261i
$682$	−1066.31	+	1066.31i	−1.56350	+	1.56350i
$683$	824.970	+	824.970i	1.20786	+	1.20786i	0.971718	+	0.236145i	$0.0758839\pi$
$683$	824.970	+	824.970i	1.20786	+	1.20786i	0.236145	+	0.971718i	$0.424116\pi$
$684$	490.572	+	490.572i	0.717211	+	0.717211i
$685$		0			0
$686$		−	1468.05i		−	2.14002i
$687$	−57.2649	−	57.2649i	−0.0833550	−	0.0833550i
$688$		−	2891.03i		−	4.20208i
$689$	−963.900	+	919.596i	−1.39898	+	1.33468i
$690$		0			0
$691$	190.752	−	190.752i	0.276052	−	0.276052i	−0.555479	−	0.831531i	$-0.687465\pi$
$691$	190.752	−	190.752i	0.276052	−	0.276052i	0.831531	+	0.555479i	$0.187465\pi$
$692$	1939.43			2.80265
$693$		−	426.112i		−	0.614880i
$694$	891.484	−	891.484i	1.28456	−	1.28456i
$695$		0			0
$696$	1735.82	+	1735.82i	2.49399	+	2.49399i
$697$	−47.5389	−	47.5389i	−0.0682051	−	0.0682051i
$698$	872.939			1.25063
$699$			1559.24i			2.23067i
$700$		0			0
$701$		−	623.742i		−	0.889789i	−0.895583	−	0.444894i	$-0.853241\pi$
$701$		−	623.742i		−	0.889789i	0.895583	−	0.444894i	$-0.146759\pi$
$702$	−18.7195	+	795.814i	−0.0266660	+	1.13364i
$703$	60.5289			0.0861009
$704$	−3874.21	+	3874.21i	−5.50314	+	5.50314i
$705$		0			0
$706$		−	721.374i		−	1.02178i
$707$	398.722	−	398.722i	0.563963	−	0.563963i
$708$	446.892	−	446.892i	0.631203	−	0.631203i
$709$	232.551	+	232.551i	0.327998	+	0.327998i	0.851825	−	0.523827i	$-0.175496\pi$
$709$	232.551	+	232.551i	0.327998	+	0.327998i	−0.523827	+	0.851825i	$0.675496\pi$
$710$		0			0
$711$	−620.935			−0.873326
$712$		−	3222.91i		−	4.52655i
$713$	76.7642	+	76.7642i	0.107664	+	0.107664i
$714$			412.736i			0.578062i
$715$		0			0
$716$	1726.18			2.41086
$717$	782.075	−	782.075i	1.09076	−	1.09076i
$718$	−2134.27			−2.97252
$719$		−	604.087i		−	0.840176i	−0.907483	−	0.420088i	$-0.861999\pi$
$719$		−	604.087i		−	0.840176i	0.907483	−	0.420088i	$-0.138001\pi$
$720$		0			0
$721$	35.7379	−	35.7379i	0.0495672	−	0.0495672i
$722$	−590.709	−	590.709i	−0.818156	−	0.818156i
$723$	554.511	+	554.511i	0.766959	+	0.766959i
$724$	1254.83			1.73320
$725$		0			0
$726$	896.303	+	896.303i	1.23458	+	1.23458i
$727$		−	270.298i		−	0.371799i	−0.982569	−	0.185899i	$-0.940480\pi$
$727$		−	270.298i		−	0.371799i	0.982569	−	0.185899i	$-0.0595198\pi$
$728$	−1670.29	−	1750.76i	−2.29435	−	2.40489i
$729$	27.7267			0.0380339
$730$		0			0
$731$	179.340			0.245335
$732$		−	3.19022i		−	0.00435823i
$733$	769.944	−	769.944i	1.05040	−	1.05040i	0.0517401	−	0.998661i	$-0.483523\pi$
$733$	769.944	−	769.944i	1.05040	−	1.05040i	0.998661	−	0.0517401i	$-0.0164767\pi$
$734$	1101.25	−	1101.25i	1.50034	−	1.50034i
$735$		0			0
$736$	495.281	+	495.281i	0.672937	+	0.672937i
$737$	124.446			0.168855
$738$			281.604i			0.381577i
$739$	0.209620	+	0.209620i	0.000283653	+	0.000283653i	0.707249	−	0.706965i	$-0.249936\pi$
$739$	0.209620	+	0.209620i	0.000283653	+	0.000283653i	−0.706965	+	0.707249i	$0.749936\pi$
$740$		0			0
$741$	13.9356	−	592.438i	0.0188065	−	0.799511i
$742$	−2481.04			−3.34372
$743$	−215.520	+	215.520i	−0.290068	+	0.290068i	−0.837107	−	0.547039i	$-0.815755\pi$
$743$	−215.520	+	215.520i	−0.290068	+	0.290068i	0.547039	+	0.837107i	$0.315755\pi$
$744$	−2998.25			−4.02990
$745$		0			0
$746$	−970.062	+	970.062i	−1.30035	+	1.30035i
$747$	−265.379	+	265.379i	−0.355259	+	0.355259i
$748$	−544.798	−	544.798i	−0.728339	−	0.728339i
$749$	143.707	+	143.707i	0.191865	+	0.191865i
$750$		0			0
$751$			433.472i			0.577193i	0.957451	+	0.288596i	$0.0931886\pi$
$751$			433.472i			0.577193i	−0.957451	+	0.288596i	$0.906811\pi$
$752$	−914.120	−	914.120i	−1.21558	−	1.21558i
$753$			1202.41i			1.59682i
$754$	26.2340	−	1115.27i	0.0347931	−	1.47914i
$755$		0			0
$756$	−781.003	+	781.003i	−1.03307	+	1.03307i
$757$	667.177			0.881343			0.440672	−	0.897668i	$-0.354740\pi$
$757$	667.177			0.881343			0.440672	+	0.897668i	$0.354740\pi$
$758$			1364.16i			1.79969i
$759$	155.303	−	155.303i	0.204615	−	0.204615i
$760$		0			0
$761$	−331.781	−	331.781i	−0.435980	−	0.435980i	0.454676	−	0.890657i	$-0.349755\pi$
$761$	−331.781	−	331.781i	−0.435980	−	0.435980i	−0.890657	+	0.454676i	$0.849755\pi$
$762$	270.857	+	270.857i	0.355455	+	0.355455i
$763$	420.779			0.551479
$764$			710.040i			0.929371i
$765$		0			0
$766$			1194.81i			1.55980i
$767$	−188.865	−	4.44258i	−0.246239	−	0.00579216i
$768$	−6496.44			−8.45890
$769$	927.008	−	927.008i	1.20547	−	1.20547i	0.232994	−	0.972478i	$-0.425148\pi$
$769$	927.008	−	927.008i	1.20547	−	1.20547i	0.972478	−	0.232994i	$-0.0748522\pi$
$770$		0			0
$771$		−	313.216i		−	0.406246i
$772$	1413.16	−	1413.16i	1.83052	−	1.83052i
$773$	398.507	−	398.507i	0.515533	−	0.515533i	−0.400684	−	0.916216i	$-0.631227\pi$
$773$	398.507	−	398.507i	0.515533	−	0.515533i	0.916216	+	0.400684i	$0.131227\pi$
$774$	−531.172	−	531.172i	−0.686269	−	0.686269i
$775$		0			0
$776$	−4205.31			−5.41922
$777$		−	112.374i		−	0.144625i
$778$	512.908	+	512.908i	0.659264	+	0.659264i
$779$			179.770i			0.230771i
$780$		0			0
$781$	−332.279			−0.425453
$782$	−52.6426	+	52.6426i	−0.0673180	+	0.0673180i
$783$	−334.948			−0.427776
$784$			859.446i			1.09623i
$785$		0			0
$786$	90.5331	−	90.5331i	0.115182	−	0.115182i
$787$	−119.609	−	119.609i	−0.151981	−	0.151981i	0.627021	−	0.779002i	$-0.284274\pi$
$787$	−119.609	−	119.609i	−0.151981	−	0.151981i	−0.779002	+	0.627021i	$0.784274\pi$
$788$	−2135.45	−	2135.45i	−2.70996	−	2.70996i
$789$	−647.197			−0.820275
$790$		0			0
$791$	−360.431	−	360.431i	−0.455665	−	0.455665i
$792$			2122.74i			2.68023i
$793$	−0.689982	+	0.658268i	−0.000870091	+	0.000830098i
$794$	1242.73			1.56515
$795$		0			0
$796$	2865.04			3.59930
$797$			704.728i			0.884226i	0.896959	+	0.442113i	$0.145771\pi$
$797$			704.728i			0.884226i	−0.896959	+	0.442113i	$0.854229\pi$
$798$	780.390	−	780.390i	0.977932	−	0.977932i
$799$	56.7057	−	56.7057i	0.0709708	−	0.0709708i
$800$		0			0
$801$	−362.612	−	362.612i	−0.452699	−	0.452699i
$802$	1385.75			1.72786
$803$		−	1301.14i		−	1.62034i
$804$	265.988	+	265.988i	0.330831	+	0.330831i
$805$		0			0
$806$	940.537	+	985.850i	1.16692	+	1.22314i
$807$	1136.40			1.40818
$808$	−1986.30	+	1986.30i	−2.45829	+	2.45829i
$809$	500.209			0.618305			0.309153	−	0.951012i	$-0.399955\pi$
$809$	500.209			0.618305			0.309153	+	0.951012i	$0.399955\pi$
$810$		0			0
$811$	−267.269	+	267.269i	−0.329555	+	0.329555i	−0.852417	−	0.522862i	$-0.824864\pi$
$811$	−267.269	+	267.269i	−0.329555	+	0.329555i	0.522862	+	0.852417i	$0.324864\pi$
$812$	1094.52	−	1094.52i	1.34793	−	1.34793i
$813$	1100.71	+	1100.71i	1.35388	+	1.35388i
$814$	199.092	+	199.092i	0.244585	+	0.244585i
$815$		0			0
$816$		−	1259.10i		−	1.54301i
$817$	−339.090	−	339.090i	−0.415043	−	0.415043i
$818$			1853.84i			2.26631i
$819$	−384.905	−	9.05394i	−0.469970	−	0.0110549i
$820$		0			0
$821$	−253.704	+	253.704i	−0.309019	+	0.309019i	−0.844529	−	0.535510i	$-0.820119\pi$
$821$	−253.704	+	253.704i	−0.309019	+	0.309019i	0.535510	+	0.844529i	$0.320119\pi$
$822$	−2803.46			−3.41054
$823$			890.680i			1.08224i	0.840947	+	0.541118i	$0.181999\pi$
$823$			890.680i			1.08224i	−0.840947	+	0.541118i	$0.818001\pi$
$824$	−178.034	+	178.034i	−0.216061	+	0.216061i
$825$		0			0
$826$	−248.783	−	248.783i	−0.301190	−	0.301190i
$827$	−460.288	−	460.288i	−0.556576	−	0.556576i	0.371755	−	0.928331i	$-0.378756\pi$
$827$	−460.288	−	460.288i	−0.556576	−	0.556576i	−0.928331	+	0.371755i	$0.878756\pi$
$828$	232.327			0.280588
$829$			680.292i			0.820618i	0.911947	+	0.410309i	$0.134579\pi$
$829$			680.292i			0.820618i	−0.911947	+	0.410309i	$0.865421\pi$
$830$		0			0
$831$			763.151i			0.918352i
$832$	3417.24	+	3581.88i	4.10726	+	4.30514i
$833$	−53.3141			−0.0640025
$834$	2168.27	−	2168.27i	2.59984	−	2.59984i
$835$		0			0
$836$			2060.17i			2.46432i
$837$	289.275	−	289.275i	0.345609	−	0.345609i
$838$	−77.0417	+	77.0417i	−0.0919353	+	0.0919353i
$839$	614.213	+	614.213i	0.732078	+	0.732078i	0.971031	−	0.238953i	$-0.0768043\pi$
$839$	614.213	+	614.213i	0.732078	+	0.732078i	−0.238953	+	0.971031i	$0.576804\pi$
$840$		0			0
$841$	−371.596			−0.441850
$842$			2081.20i			2.47173i
$843$	−361.633	−	361.633i	−0.428984	−	0.428984i
$844$			3159.41i			3.74338i
$845$		0			0
$846$	−335.904			−0.397050
$847$	371.745	−	371.745i	0.438897	−	0.438897i
$848$	7568.68			8.92533
$849$			936.147i			1.10265i
$850$		0			0
$851$	14.3327	−	14.3327i	0.0168422	−	0.0168422i
$852$	−710.205	−	710.205i	−0.833574	−	0.833574i
$853$	110.970	+	110.970i	0.130094	+	0.130094i	0.769155	−	0.639062i	$-0.220677\pi$
$853$	110.970	+	110.970i	0.130094	+	0.130094i	−0.639062	+	0.769155i	$0.720677\pi$
$854$	−1.77598			−0.00207961
$855$		0			0
$856$	−715.900	−	715.900i	−0.836332	−	0.836332i
$857$			797.203i			0.930225i	0.885251	+	0.465113i	$0.153986\pi$
$857$			797.203i			0.930225i	−0.885251	+	0.465113i	$0.846014\pi$
$858$	1994.49	−	1902.81i	2.32458	−	2.21773i
$859$	−364.974			−0.424882			−0.212441	−	0.977174i	$-0.568141\pi$
$859$	−364.974			−0.424882			−0.212441	+	0.977174i	$0.568141\pi$
$860$		0			0
$861$	333.749			0.387629
$862$			66.9687i			0.0776899i
$863$	462.068	−	462.068i	0.535420	−	0.535420i	−0.386760	−	0.922180i	$-0.626406\pi$
$863$	462.068	−	462.068i	0.535420	−	0.535420i	0.922180	+	0.386760i	$0.126406\pi$
$864$	1866.40	−	1866.40i	2.16018	−	2.16018i
$865$		0			0
$866$	−598.338	−	598.338i	−0.690922	−	0.690922i
$867$	−997.236			−1.15022
$868$			1890.54i			2.17804i
$869$	−1303.82	−	1303.82i	−1.50037	−	1.50037i
$870$		0			0
$871$	2.64421	−	112.412i	0.00303583	−	0.129061i
$872$	−2096.17			−2.40387
$873$	−473.144	+	473.144i	−0.541975	+	0.541975i
$874$	199.070			0.227769
$875$		0			0
$876$	2781.02	−	2781.02i	3.17468	−	3.17468i
$877$	782.481	−	782.481i	0.892225	−	0.892225i	−0.102507	−	0.994732i	$-0.532686\pi$
$877$	782.481	−	782.481i	0.892225	−	0.892225i	0.994732	+	0.102507i	$0.0326864\pi$
$878$	−2004.35	−	2004.35i	−2.28286	−	2.28286i
$879$	−943.331	−	943.331i	−1.07319	−	1.07319i
$880$		0			0
$881$		−	181.009i		−	0.205458i	−0.994709	−	0.102729i	$-0.967243\pi$
$881$		−	181.009i		−	0.205458i	0.994709	−	0.102729i	$-0.0327575\pi$
$882$	157.907	+	157.907i	0.179033	+	0.179033i
$883$			898.698i			1.01778i	0.860832	+	0.508889i	$0.169944\pi$
$883$			898.698i			1.01778i	−0.860832	+	0.508889i	$0.830056\pi$
$884$	−503.689	+	480.538i	−0.569784	+	0.543595i
$885$		0			0
$886$	750.584	−	750.584i	0.847160	−	0.847160i
$887$	153.874			0.173477			0.0867387	−	0.996231i	$-0.472355\pi$
$887$	153.874			0.173477			0.0867387	+	0.996231i	$0.472355\pi$
$888$			559.807i			0.630413i
$889$	112.339	−	112.339i	0.126366	−	0.126366i
$890$		0			0
$891$	−1028.87	−	1028.87i	−1.15474	−	1.15474i
$892$	3136.97	+	3136.97i	3.51678	+	3.51678i
$893$	−214.435			−0.240128
$894$			1031.78i			1.15411i
$895$		0			0
$896$			5045.17i			5.63077i
$897$	−136.984	−	143.584i	−0.152714	−	0.160072i
$898$	2944.54			3.27900
$899$	−405.397	+	405.397i	−0.450942	+	0.450942i
$900$		0			0
$901$			469.508i			0.521097i
$902$	−591.302	+	591.302i	−0.655546	+	0.655546i
$903$	−629.530	+	629.530i	−0.697154	+	0.697154i
$904$	1795.54	+	1795.54i	1.98622	+	1.98622i
$905$		0			0
$906$	−1230.46			−1.35813
$907$			636.228i			0.701464i	0.936476	+	0.350732i	$0.114067\pi$
$907$			636.228i			0.701464i	−0.936476	+	0.350732i	$0.885933\pi$
$908$	201.990	+	201.990i	0.222456	+	0.222456i
$909$			446.960i			0.491706i
$910$		0			0
$911$	−1415.45			−1.55374			−0.776868	−	0.629664i	$-0.783193\pi$
$911$	−1415.45			−1.55374			−0.776868	+	0.629664i	$0.783193\pi$
$912$	−2380.66	+	2380.66i	−2.61038	+	2.61038i
$913$	−1114.47			−1.22066
$914$		−	2129.37i		−	2.32973i
$915$		0			0
$916$	179.879	−	179.879i	0.196374	−	0.196374i
$917$	−37.5490	−	37.5490i	−0.0409476	−	0.0409476i
$918$	198.376	+	198.376i	0.216096	+	0.216096i
$919$	−791.494			−0.861256			−0.430628	−	0.902530i	$-0.641708\pi$
$919$	−791.494			−0.861256			−0.430628	+	0.902530i	$0.641708\pi$
$920$		0			0
$921$	520.002	+	520.002i	0.564606	+	0.564606i
$922$			3402.44i			3.69029i
$923$	−7.06020	+	300.146i	−0.00764918	+	0.325185i
$924$	3824.77			4.13936
$925$		0			0
$926$	3099.29			3.34697
$927$			40.0616i			0.0432164i
$928$	−2615.61	+	2615.61i	−2.81855	+	2.81855i
$929$	31.5586	−	31.5586i	0.0339705	−	0.0339705i	−0.689918	−	0.723888i	$-0.742353\pi$
$929$	31.5586	−	31.5586i	0.0339705	−	0.0339705i	0.723888	+	0.689918i	$0.242353\pi$
$930$		0			0
$931$	100.805	+	100.805i	0.108276	+	0.108276i
$932$	−4897.83			−5.25519
$933$		−	1706.69i		−	1.82925i
$934$	−1727.38	−	1727.38i	−1.84945	−	1.84945i
$935$		0			0
$936$	1917.47	+	45.1036i	2.04857	+	0.0481876i
$937$	602.943			0.643482			0.321741	−	0.946828i	$-0.395732\pi$
$937$	602.943			0.643482			0.321741	+	0.946828i	$0.395732\pi$
$938$	148.075	−	148.075i	0.157862	−	0.157862i
$939$	1412.20			1.50394
$940$		0			0
$941$	−927.710	+	927.710i	−0.985876	+	0.985876i	−0.999902	−	0.0140252i	$-0.995535\pi$
$941$	−927.710	+	927.710i	−0.985876	+	0.985876i	0.0140252	+	0.999902i	$0.495535\pi$
$942$	−1574.09	+	1574.09i	−1.67101	+	1.67101i
$943$	42.5681	+	42.5681i	0.0451412	+	0.0451412i
$944$	758.940	+	758.940i	0.803961	+	0.803961i
$945$		0			0
$946$		−	2230.68i		−	2.35801i
$947$	−72.0662	−	72.0662i	−0.0760994	−	0.0760994i	0.668033	−	0.744132i	$-0.267137\pi$
$947$	−72.0662	−	72.0662i	−0.0760994	−	0.0760994i	−0.744132	+	0.668033i	$0.767137\pi$
$948$		−	5573.50i		−	5.87922i
$949$	−1175.31	−	27.6463i	−1.23847	−	0.0291320i
$950$		0			0
$951$	329.524	−	329.524i	0.346502	−	0.346502i
$952$	−852.781			−0.895778
$953$		−	870.605i		−	0.913542i	−0.889584	−	0.456771i	$-0.849006\pi$
$953$		−	870.605i		−	0.913542i	0.889584	−	0.456771i	$-0.150994\pi$
$954$	1390.60	−	1390.60i	1.45765	−	1.45765i
$955$		0			0
$956$	2456.63	+	2456.63i	2.56970	+	2.56970i
$957$	820.164	+	820.164i	0.857016	+	0.857016i
$958$	−598.800			−0.625052
$959$			1162.75i			1.21246i
$960$		0			0
$961$			260.767i			0.271349i
$962$	184.069	−	175.609i	0.191340	−	0.182546i
$963$	−161.093			−0.167283
$964$	−1741.81	+	1741.81i	−1.80686	+	1.80686i
$965$		0			0
$966$		−	369.580i		−	0.382588i
$967$	1300.80	−	1300.80i	1.34519	−	1.34519i	0.454392	−	0.890802i	$-0.349856\pi$
$967$	1300.80	−	1300.80i	1.34519	−	1.34519i	0.890802	−	0.454392i	$-0.150144\pi$
$968$	−1851.91	+	1851.91i	−1.91313	+	1.91313i
$969$	−147.680	−	147.680i	−0.152404	−	0.152404i
$970$		0			0
$971$	−379.072			−0.390394			−0.195197	−	0.980764i	$-0.562535\pi$
$971$	−379.072			−0.390394			−0.195197	+	0.980764i	$0.562535\pi$
$972$		−	2771.93i		−	2.85178i
$973$	−899.298	−	899.298i	−0.924253	−	0.924253i
$974$			1312.15i			1.34717i
$975$		0			0
$976$	5.41784			0.00555106
$977$	−80.1135	+	80.1135i	−0.0819995	+	0.0819995i	−0.746917	−	0.664917i	$-0.768467\pi$
$977$	−80.1135	+	80.1135i	−0.0819995	+	0.0819995i	0.664917	+	0.746917i	$0.268467\pi$
$978$	−1505.86			−1.53973
$979$		−	1522.80i		−	1.55547i
$980$		0			0
$981$	−235.843	+	235.843i	−0.240410	+	0.240410i
$982$	−1826.86	−	1826.86i	−1.86035	−	1.86035i
$983$	626.438	+	626.438i	0.637272	+	0.637272i	0.949882	−	0.312610i	$-0.101203\pi$
$983$	626.438	+	626.438i	0.637272	+	0.637272i	−0.312610	+	0.949882i	$0.601203\pi$
$984$	−1662.62			−1.68966
$985$		0			0
$986$	−278.009	−	278.009i	−0.281957	−	0.281957i
$987$			398.104i			0.403348i
$988$	1860.95	+	43.7742i	1.88355	+	0.0443058i
$989$	−160.587			−0.162373
$990$		0			0
$991$	−693.576			−0.699875			−0.349937	−	0.936773i	$-0.613797\pi$
$991$	−693.576			−0.699875			−0.349937	+	0.936773i	$0.613797\pi$
$992$		−	4517.90i		−	4.55433i
$993$	−628.768	+	628.768i	−0.633200	+	0.633200i
$994$	−395.368	+	395.368i	−0.397755	+	0.397755i
$995$		0			0
$996$	−2382.03	−	2382.03i	−2.39160	−	2.39160i
$997$	442.915			0.444247			0.222124	−	0.975019i	$-0.428701\pi$
$997$	442.915			0.444247			0.222124	+	0.975019i	$0.428701\pi$
$998$			1391.38i			1.39417i
$999$	−54.0109	−	54.0109i	−0.0540650	−	0.0540650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.3.j.c.226.1	yes	20
5.2	odd	4		325.3.g.f.174.1		20
5.3	odd	4		325.3.g.e.174.10		20
5.4	even	2		325.3.j.d.226.10	yes	20
13.8	odd	4	inner	325.3.j.c.151.1	✓	20
65.8	even	4		325.3.g.f.99.1		20
65.34	odd	4		325.3.j.d.151.10	yes	20
65.47	even	4		325.3.g.e.99.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.3.g.e.99.10		20	65.47	even	4
325.3.g.e.174.10		20	5.3	odd	4
325.3.g.f.99.1		20	65.8	even	4
325.3.g.f.174.1		20	5.2	odd	4
325.3.j.c.151.1	✓	20	13.8	odd	4	inner
325.3.j.c.226.1	yes	20	1.1	even	1	trivial
325.3.j.d.151.10	yes	20	65.34	odd	4
325.3.j.d.226.10	yes	20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	325.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.80071 + 2.80071i) q^{2} -3.72091 q^{3} -11.6880i q^{4} +(10.4212 - 10.4212i) q^{6} +(-4.32223 - 4.32223i) q^{7} +(21.5319 + 21.5319i) q^{8} +4.84515 q^{9} +(10.1737 + 10.1737i) q^{11} +43.4900i q^{12} +(9.40601 - 8.97368i) q^{13} +24.2107 q^{14} -73.8573 q^{16} -4.58160i q^{17} +(-13.5699 + 13.5699i) q^{18} +(-8.66275 + 8.66275i) q^{19} +(16.0826 + 16.0826i) q^{21} -56.9872 q^{22} +4.10253i q^{23} +(-80.1182 - 80.1182i) q^{24} +(-1.21085 + 51.4763i) q^{26} +15.4598 q^{27} +(-50.5183 + 50.5183i) q^{28} -21.6657 q^{29} +(18.7114 - 18.7114i) q^{31} +(120.726 - 120.726i) q^{32} +(-37.8553 - 37.8553i) q^{33} +(12.8317 + 12.8317i) q^{34} -56.6301i q^{36} +(-3.49363 - 3.49363i) q^{37} -48.5237i q^{38} +(-34.9989 + 33.3902i) q^{39} +(10.3761 - 10.3761i) q^{41} -90.0857 q^{42} +39.1435i q^{43} +(118.910 - 118.910i) q^{44} +(-11.4900 - 11.4900i) q^{46} +(12.3768 + 12.3768i) q^{47} +274.816 q^{48} -11.6366i q^{49} +17.0477i q^{51} +(-104.884 - 109.937i) q^{52} -102.477 q^{53} +(-43.2985 + 43.2985i) q^{54} -186.132i q^{56} +(32.2333 - 32.2333i) q^{57} +(60.6796 - 60.6796i) q^{58} +(-10.2757 - 10.2757i) q^{59} -0.0733554 q^{61} +104.811i q^{62} +(-20.9419 - 20.9419i) q^{63} +380.807i q^{64} +212.044 q^{66} +(6.11609 - 6.11609i) q^{67} -53.5497 q^{68} -15.2651i q^{69} +(-16.3303 + 16.3303i) q^{71} +(104.325 + 104.325i) q^{72} +(-63.9462 - 63.9462i) q^{73} +19.5693 q^{74} +(101.250 + 101.250i) q^{76} -87.9461i q^{77} +(4.50547 - 191.538i) q^{78} -128.156 q^{79} -101.131 q^{81} +58.1208i q^{82} +(-54.7720 + 54.7720i) q^{83} +(187.974 - 187.974i) q^{84} +(-109.630 - 109.630i) q^{86} +80.6162 q^{87} +438.117i q^{88} +(-74.8403 - 74.8403i) q^{89} +(-79.4413 - 1.86866i) q^{91} +47.9504 q^{92} +(-69.6234 + 69.6234i) q^{93} -69.3279 q^{94} +(-449.209 + 449.209i) q^{96} +(-97.6532 + 97.6532i) q^{97} +(32.5907 + 32.5907i) q^{98} +(49.2930 + 49.2930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{6} - 20 q^{7} + 18 q^{8} + 72 q^{9} + 6 q^{11} - 6 q^{13} - 24 q^{14} - 128 q^{16} + 58 q^{18} - 20 q^{19} + 90 q^{21} - 24 q^{22} - 28 q^{24} + 12 q^{27} - 278 q^{28} - 40 q^{29} - 32 q^{31}+ \cdots - 410 q^{99}+O(q^{100}) \) 20 * q - 6 * q^6 - 20 * q^7 + 18 * q^8 + 72 * q^9 + 6 * q^11 - 6 * q^13 - 24 * q^14 - 128 * q^16 + 58 * q^18 - 20 * q^19 + 90 * q^21 - 24 * q^22 - 28 * q^24 + 12 * q^27 - 278 * q^28 - 40 * q^29 - 32 * q^31 + 162 * q^32 - 124 * q^33 - 14 * q^34 - 158 * q^37 - 26 * q^39 + 70 * q^41 + 320 * q^42 + 366 * q^44 + 58 * q^46 + 130 * q^47 + 716 * q^48 - 300 * q^52 - 216 * q^53 - 350 * q^54 - 168 * q^57 + 180 * q^58 + 132 * q^59 - 152 * q^61 - 442 * q^63 + 720 * q^66 - 178 * q^67 + 216 * q^68 - 258 * q^71 - 390 * q^72 + 262 * q^73 + 220 * q^74 + 68 * q^76 - 102 * q^78 - 544 * q^79 + 204 * q^81 - 88 * q^83 + 352 * q^84 - 174 * q^86 + 976 * q^87 - 282 * q^89 - 440 * q^91 + 992 * q^92 - 522 * q^93 - 544 * q^94 - 1216 * q^96 - 6 * q^97 - 78 * q^98 - 410 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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