LMFDB - Embedded newform 325.3.g.e.99.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(99,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.99"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	325.g (of order $4$, degree $2$, not 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			99.10
Root			$-2.80071 - 2.80071i$ of defining polynomial
Character	$\chi$	$=$	325.99
Dual form			325.3.g.e.174.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.80071 - 2.80071i) q^{2} +3.72091i q^{3} -11.6880i q^{4} +(10.4212 + 10.4212i) q^{6} +(-4.32223 - 4.32223i) q^{7} +(-21.5319 - 21.5319i) q^{8} -4.84515 q^{9} +(10.1737 - 10.1737i) q^{11} +43.4900 q^{12} +(8.97368 - 9.40601i) q^{13} -24.2107 q^{14} -73.8573 q^{16} -4.58160 q^{17} +(-13.5699 + 13.5699i) q^{18} +(8.66275 + 8.66275i) q^{19} +(16.0826 - 16.0826i) q^{21} -56.9872i q^{22} -4.10253 q^{23} +(80.1182 - 80.1182i) q^{24} +(-1.21085 - 51.4763i) q^{26} +15.4598i q^{27} +(-50.5183 + 50.5183i) q^{28} +21.6657 q^{29} +(18.7114 + 18.7114i) q^{31} +(-120.726 + 120.726i) q^{32} +(37.8553 + 37.8553i) q^{33} +(-12.8317 + 12.8317i) q^{34} +56.6301i q^{36} +(-3.49363 - 3.49363i) q^{37} +48.5237 q^{38} +(34.9989 + 33.3902i) q^{39} +(10.3761 + 10.3761i) q^{41} -90.0857i q^{42} -39.1435 q^{43} +(-118.910 - 118.910i) q^{44} +(-11.4900 + 11.4900i) q^{46} +(12.3768 + 12.3768i) q^{47} -274.816i q^{48} -11.6366i q^{49} -17.0477i q^{51} +(-109.937 - 104.884i) q^{52} +102.477i q^{53} +(43.2985 + 43.2985i) q^{54} +186.132i q^{56} +(-32.2333 + 32.2333i) q^{57} +(60.6796 - 60.6796i) q^{58} +(10.2757 - 10.2757i) q^{59} -0.0733554 q^{61} +104.811 q^{62} +(20.9419 + 20.9419i) q^{63} +380.807i q^{64} +212.044 q^{66} +(-6.11609 + 6.11609i) q^{67} +53.5497i q^{68} -15.2651i q^{69} +(-16.3303 - 16.3303i) q^{71} +(104.325 + 104.325i) q^{72} +(63.9462 + 63.9462i) q^{73} -19.5693 q^{74} +(101.250 - 101.250i) q^{76} -87.9461 q^{77} +(191.538 - 4.50547i) q^{78} +128.156 q^{79} -101.131 q^{81} +58.1208 q^{82} +(-54.7720 + 54.7720i) q^{83} +(-187.974 - 187.974i) q^{84} +(-109.630 + 109.630i) q^{86} +80.6162i q^{87} -438.117 q^{88} +(74.8403 - 74.8403i) q^{89} +(-79.4413 + 1.86866i) q^{91} +47.9504i q^{92} +(-69.6234 + 69.6234i) q^{93} +69.3279 q^{94} +(-449.209 - 449.209i) q^{96} +(97.6532 - 97.6532i) q^{97} +(-32.5907 - 32.5907i) q^{98} +(-49.2930 + 49.2930i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{6} - 20 q^{7} - 18 q^{8} - 72 q^{9} + 6 q^{11} + 120 q^{12} + 18 q^{13} + 24 q^{14} - 128 q^{16} + 16 q^{17} + 58 q^{18} + 20 q^{19} + 90 q^{21} - 28 q^{23} + 28 q^{24} - 278 q^{28} + 40 q^{29}+ \cdots + 410 q^{99}+O(q^{100}) $ 20 * q - 6 * q^6 - 20 * q^7 - 18 * q^8 - 72 * q^9 + 6 * q^11 + 120 * q^12 + 18 * q^13 + 24 * q^14 - 128 * q^16 + 16 * q^17 + 58 * q^18 + 20 * q^19 + 90 * q^21 - 28 * q^23 + 28 * q^24 - 278 * q^28 + 40 * q^29 - 32 * q^31 - 162 * q^32 + 124 * q^33 + 14 * q^34 - 158 * q^37 - 124 * q^38 + 26 * q^39 + 70 * q^41 + 32 * q^43 - 366 * q^44 + 58 * q^46 + 130 * q^47 - 244 * q^52 + 350 * q^54 + 168 * q^57 + 180 * q^58 - 132 * q^59 - 152 * q^61 - 212 * q^62 + 442 * q^63 + 720 * q^66 + 178 * q^67 - 258 * q^71 - 390 * q^72 - 262 * q^73 - 220 * q^74 + 68 * q^76 - 184 * q^77 + 918 * q^78 + 544 * q^79 + 204 * q^81 + 920 * q^82 - 88 * q^83 - 352 * q^84 - 174 * q^86 - 424 * q^88 + 282 * q^89 - 440 * q^91 - 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 $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

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

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	$-0.294595\pi$
$2$	2.80071	−	2.80071i	1.40036	−	1.40036i	0.798921	−	0.601436i	$-0.205405\pi$
$3$			3.72091i			1.24030i	0.784482	+	0.620151i	$0.212929\pi$
$3$			3.72091i			1.24030i	−0.784482	+	0.620151i	$0.787071\pi$
$4$		−	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	−0.0724888	−	0.997369i	$-0.523094\pi$
$11$	10.1737	−	10.1737i	0.924880	−	0.924880i	0.997369	+	0.0724888i	$0.0230942\pi$
$12$	43.4900			3.62416
$13$	8.97368	−	9.40601i	0.690283	−	0.723540i
$13$	8.97368	−	9.40601i	0.690283	−	0.723540i
$14$	−24.2107			−1.72933
$15$		0			0
$16$	−73.8573			−4.61608
$17$	−4.58160			−0.269506			−0.134753	−	0.990879i	$-0.543024\pi$
$17$	−4.58160			−0.269506			−0.134753	+	0.990879i	$0.543024\pi$
$18$	−13.5699	+	13.5699i	−0.753882	+	0.753882i
$19$	8.66275	+	8.66275i	0.455934	+	0.455934i	0.897318	−	0.441384i	$-0.145512\pi$
$19$	8.66275	+	8.66275i	0.455934	+	0.455934i	−0.441384	+	0.897318i	$0.645512\pi$
$20$		0			0
$21$	16.0826	−	16.0826i	0.765840	−	0.765840i
$22$		−	56.9872i		−	2.59033i
$23$	−4.10253			−0.178371			−0.0891855	−	0.996015i	$-0.528426\pi$
$23$	−4.10253			−0.178371			−0.0891855	+	0.996015i	$0.528426\pi$
$24$	80.1182	−	80.1182i	3.33826	−	3.33826i
$25$		0			0
$26$	−1.21085	−	51.4763i	−0.0465712	−	1.97986i
$27$			15.4598i			0.572586i
$28$	−50.5183	+	50.5183i	−1.80422	+	1.80422i
$29$	21.6657			0.747095			0.373547	−	0.927611i	$-0.378141\pi$
$29$	21.6657			0.747095			0.373547	+	0.927611i	$0.378141\pi$
$30$		0			0
$31$	18.7114	+	18.7114i	0.603594	+	0.603594i	0.941264	−	0.337671i	$-0.109639\pi$
$31$	18.7114	+	18.7114i	0.603594	+	0.603594i	−0.337671	+	0.941264i	$0.609639\pi$
$32$	−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	$0.771268\pi$
$38$	48.5237			1.27694
$39$	34.9989	+	33.3902i	0.897408	+	0.856159i
$40$		0			0
$41$	10.3761	+	10.3761i	0.253075	+	0.253075i	0.822230	−	0.569155i	$-0.192730\pi$
$41$	10.3761	+	10.3761i	0.253075	+	0.253075i	−0.569155	+	0.822230i	$0.692730\pi$
$42$		−	90.0857i		−	2.14490i
$43$	−39.1435			−0.910313			−0.455157	−	0.890411i	$-0.650417\pi$
$43$	−39.1435			−0.910313			−0.455157	+	0.890411i	$0.650417\pi$
$44$	−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	$0.690380\pi$
$48$		−	274.816i		−	5.72534i
$49$		−	11.6366i		−	0.237481i
$50$		0			0
$51$		−	17.0477i		−	0.334269i
$52$	−109.937	−	104.884i	−2.11418	−	2.01701i
$53$			102.477i			1.93353i	0.255669	+	0.966764i	$0.417704\pi$
$53$			102.477i			1.93353i	−0.255669	+	0.966764i	$0.582296\pi$
$54$	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	$-0.710699\pi$
$59$	10.2757	−	10.2757i	0.174165	−	0.174165i	0.788807	+	0.614641i	$0.210699\pi$
$60$		0			0
$61$	−0.0733554			−0.00120255			−0.000601274	−	1.00000i	$-0.500191\pi$
$61$	−0.0733554			−0.00120255			−0.000601274		1.00000i	$0.500191\pi$
$62$	104.811			1.69049
$63$	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	−0.751275	−	0.659990i	$-0.770561\pi$
$67$	−6.11609	+	6.11609i	−0.0912849	+	0.0912849i	0.659990	+	0.751275i	$0.270561\pi$
$68$			53.5497i			0.787496i
$69$		−	15.2651i		−	0.221234i
$70$		0			0
$71$	−16.3303	−	16.3303i	−0.230004	−	0.230004i	0.582690	−	0.812694i	$-0.302000\pi$
$71$	−16.3303	−	16.3303i	−0.230004	−	0.230004i	−0.812694	+	0.582690i	$0.802000\pi$
$72$	104.325	+	104.325i	1.44896	+	1.44896i
$73$	63.9462	+	63.9462i	0.875975	+	0.875975i	0.993115	−	0.117140i	$-0.0373727\pi$
$73$	63.9462	+	63.9462i	0.875975	+	0.875975i	−0.117140	+	0.993115i	$0.537373\pi$
$74$	−19.5693			−0.264451
$75$		0			0
$76$	101.250	−	101.250i	1.33224	−	1.33224i
$77$	−87.9461			−1.14216
$78$	191.538	−	4.50547i	2.45562	−	0.0577624i
$79$	128.156			1.62223			0.811114	−	0.584888i	$-0.198862\pi$
$79$	128.156			1.62223			0.811114	+	0.584888i	$0.198862\pi$
$80$		0			0
$81$	−101.131			−1.24853
$82$	58.1208			0.708790
$83$	−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
$87$			80.6162i			0.926623i
$88$	−438.117			−4.97861
$89$	74.8403	−	74.8403i	0.840902	−	0.840902i	−0.148074	−	0.988976i	$-0.547307\pi$
$89$	74.8403	−	74.8403i	0.840902	−	0.840902i	0.988976	+	0.148074i	$0.0473075\pi$
$90$		0			0
$91$	−79.4413	+	1.86866i	−0.872982	+	0.0205347i
$92$			47.9504i			0.521200i
$93$	−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	$-0.497849\pi$
$97$	97.6532	−	97.6532i	1.00673	−	1.00673i	0.999977	−	0.00675648i	$-0.00215067\pi$
$98$	−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	$-0.849039\pi$
$101$		−	92.2491i		−	0.913357i	0.889632	−	0.456679i	$-0.150961\pi$
$102$	−47.7457	−	47.7457i	−0.468095	−	0.468095i
$103$	−8.26839			−0.0802757			−0.0401378	−	0.999194i	$-0.512780\pi$
$103$	−8.26839			−0.0802757			−0.0401378	+	0.999194i	$0.512780\pi$
$104$	−395.750	+	9.30903i	−3.80528	+	0.0895099i
$105$		0			0
$106$	287.009	+	287.009i	2.70763	+	2.70763i
$107$		−	33.2484i		−	0.310732i	−0.987857	−	0.155366i	$-0.950344\pi$
$107$		−	33.2484i		−	0.310732i	0.987857	−	0.155366i	$-0.0496557\pi$
$108$	180.694			1.67310
$109$	48.6760	+	48.6760i	0.446569	+	0.446569i	0.894212	−	0.447643i	$-0.147736\pi$
$109$	48.6760	+	48.6760i	0.446569	+	0.446569i	−0.447643	+	0.894212i	$0.647736\pi$
$110$		0			0
$111$	12.9995	−	12.9995i	0.117112	−	0.117112i
$112$	319.229	+	319.229i	2.85026	+	2.85026i
$113$		−	83.3899i		−	0.737964i	−0.929437	−	0.368982i	$-0.879706\pi$
$113$		−	83.3899i		−	0.737964i	0.929437	−	0.368982i	$-0.120294\pi$
$114$			180.552i			1.58379i
$115$		0			0
$116$		−	253.229i		−	2.18301i
$117$	−43.4788	+	45.5735i	−0.371614	+	0.389517i
$118$		−	57.5589i		−	0.487787i
$119$	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
$127$	25.9910			0.204653			0.102327	−	0.994751i	$-0.467371\pi$
$127$	25.9910			0.204653			0.102327	+	0.994751i	$0.467371\pi$
$128$	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
$133$		−	74.8848i		−	0.563044i
$134$			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	$-0.769192\pi$
$139$	−208.063			−1.49686			−0.748429	+	0.663215i	$0.769192\pi$
$140$		0			0
$141$	−46.0530	+	46.0530i	−0.326617	+	0.326617i
$142$	−91.4731			−0.644177
$143$	−4.39846	−	186.989i	−0.0307584	−	1.30762i
$144$	357.850			2.48507
$145$		0			0
$146$	358.190			2.45336
$147$	43.2986			0.294548
$148$	−40.8336	+	40.8336i	−0.275903	+	0.275903i
$149$	49.5038	+	49.5038i	0.332240	+	0.332240i	0.853437	−	0.521197i	$-0.174514\pi$
$149$	49.5038	+	49.5038i	0.332240	+	0.332240i	−0.521197	+	0.853437i	$0.674514\pi$
$150$		0			0
$151$	−59.0365	+	59.0365i	−0.390970	+	0.390970i	−0.875033	−	0.484063i	$-0.839161\pi$
$151$	−59.0365	+	59.0365i	−0.390970	+	0.390970i	0.484063	+	0.875033i	$0.339161\pi$
$152$		−	373.051i		−	2.45428i
$153$	22.1985			0.145088
$154$	−246.312	+	246.312i	−1.59943	+	1.59943i
$155$		0			0
$156$	390.265	−	409.067i	2.50170	−	2.62223i
$157$		−	151.047i		−	0.962083i	−0.876698	−	0.481041i	$-0.840259\pi$
$157$		−	151.047i		−	0.962083i	0.876698	−	0.481041i	$-0.159741\pi$
$158$	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	0.893103	−	0.449853i	$-0.148524\pi$
$163$	72.2498	+	72.2498i	0.443250	+	0.443250i	−0.449853	+	0.893103i	$0.648524\pi$
$164$	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	$0.477258\pi$
$168$	−692.579			−4.12249
$169$	−7.94622	−	168.813i	−0.0470190	−	0.998894i
$170$		0			0
$171$	−41.9723	−	41.9723i	−0.245452	−	0.245452i
$172$			457.509i			2.65994i
$173$	−165.934			−0.959155			−0.479577	−	0.877500i	$-0.659210\pi$
$173$	−165.934			−0.959155			−0.479577	+	0.877500i	$0.659210\pi$
$174$	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
$178$		−	419.212i		−	2.35513i
$179$			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	$-0.904155\pi$
$181$		−	107.361i		−	0.593154i	0.955009	−	0.296577i	$-0.0958451\pi$
$182$	−217.259	+	227.726i	−1.19373	+	1.25124i
$183$		−	0.272949i		−	0.00149152i
$184$	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	$0.550837\pi$
$192$	−1416.95			−7.37994
$193$	−120.907	−	120.907i	−0.626460	−	0.626460i	0.320715	−	0.947176i	$-0.396077\pi$
$193$	−120.907	−	120.907i	−0.626460	−	0.626460i	−0.947176	+	0.320715i	$0.896077\pi$
$194$		−	546.997i		−	2.81957i
$195$		0			0
$196$	−136.008			−0.693920
$197$	−182.704	+	182.704i	−0.927432	+	0.927432i	−0.997539	−	0.0701072i	$-0.977666\pi$
$197$	−182.704	+	182.704i	−0.927432	+	0.927432i	0.0701072	+	0.997539i	$0.477666\pi$
$198$			276.111i			1.39450i
$199$			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
$207$	19.8774			0.0960260
$208$	−662.772	+	694.703i	−3.18640	+	3.33992i
$209$	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	$0.721294\pi$
$212$	1197.75			5.64977
$213$	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
$217$		−	161.750i		−	0.745393i
$218$	272.655			1.25071
$219$	−237.938	+	237.938i	−1.08647	+	1.08647i
$220$		0			0
$221$	−41.1138	+	43.0946i	−0.186035	+	0.194998i
$222$		−	72.8157i		−	0.327999i
$223$	−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	−0.668016	−	0.744147i	$-0.732856\pi$
$227$	17.2819	−	17.2819i	0.0761315	−	0.0761315i	0.744147	+	0.668016i	$0.232856\pi$
$228$	376.742	+	376.742i	1.65238	+	1.65238i
$229$	−15.3900	+	15.3900i	−0.0672054	+	0.0672054i	−0.739911	−	0.672705i	$-0.765132\pi$
$229$	−15.3900	+	15.3900i	−0.0672054	+	0.0672054i	0.672705	+	0.739911i	$0.265132\pi$
$230$		0			0
$231$		−	327.239i		−	1.41662i
$232$	−466.504	−	466.504i	−2.01079	−	2.01079i
$233$	419.048			1.79849			0.899245	−	0.437445i	$-0.144117\pi$
$233$	419.048			1.79849			0.899245	+	0.437445i	$0.144117\pi$
$234$	5.86676	+	249.410i	0.0250716	+	1.06586i
$235$		0			0
$236$	−120.103	−	120.103i	−0.508911	−	0.508911i
$237$			476.856i			2.01205i
$238$	110.924			0.466066
$239$	210.184	+	210.184i	0.879431	+	0.879431i	0.993476	−	0.114045i	$-0.0363807\pi$
$239$	210.184	+	210.184i	0.879431	+	0.879431i	−0.114045	+	0.993476i	$0.536381\pi$
$240$		0			0
$241$	−149.026	+	149.026i	−0.618364	+	0.618364i	−0.945112	−	0.326747i	$-0.894047\pi$
$241$	−149.026	+	149.026i	−0.618364	+	0.618364i	0.326747	+	0.945112i	$0.394047\pi$
$242$	−240.883	−	240.883i	−0.995384	−	0.995384i
$243$		−	237.160i		−	0.975968i
$244$			0.857378i			0.00351384i
$245$		0			0
$246$			216.262i			0.879114i
$247$	159.219	−	3.74522i	0.644610	−	0.0151628i
$248$		−	805.784i		−	3.24913i
$249$	−203.802	−	203.802i	−0.818480	−	0.818480i
$250$		0			0
$251$			323.149i			1.28745i	0.765258	+	0.643724i	$0.222611\pi$
$251$			323.149i			1.28745i	−0.765258	+	0.643724i	$0.777389\pi$
$252$	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
$257$	84.1773			0.327538			0.163769	−	0.986499i	$-0.447635\pi$
$257$	84.1773			0.327538			0.163769	+	0.986499i	$0.447635\pi$
$258$	−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
$263$		−	173.935i		−	0.661351i	−0.943745	−	0.330675i	$-0.892723\pi$
$263$		−	173.935i		−	0.661351i	0.943745	−	0.330675i	$-0.107277\pi$
$264$		−	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	$-0.307843\pi$
$269$	305.410			1.13535			0.567676	+	0.823252i	$0.307843\pi$
$270$		0			0
$271$	−295.817	+	295.817i	−1.09158	+	1.09158i	−0.0962150	+	0.995361i	$0.530674\pi$
$271$	−295.817	+	295.817i	−1.09158	+	1.09158i	−0.995361	+	0.0962150i	$0.969326\pi$
$272$	338.385			1.24406
$273$	−6.95311	−	295.594i	−0.0254693	−	1.08276i
$274$	−753.435			−2.74976
$275$		0			0
$276$	−178.419			−0.646446
$277$	−205.098			−0.740426			−0.370213	−	0.928947i	$-0.620715\pi$
$277$	−205.098			−0.740426			−0.370213	+	0.928947i	$0.620715\pi$
$278$	−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	−0.512698	−	0.858569i	$-0.671354\pi$
$281$	97.1896	−	97.1896i	0.345870	−	0.345870i	0.858569	+	0.512698i	$0.171354\pi$
$282$			257.963i			0.914762i
$283$	251.591			0.889014			0.444507	−	0.895775i	$-0.353379\pi$
$283$	251.591			0.889014			0.444507	+	0.895775i	$0.353379\pi$
$284$	−190.869	+	190.869i	−0.672073	+	0.672073i
$285$		0			0
$286$	−536.022	−	511.384i	−1.87420	−	1.78806i
$287$		−	89.6955i		−	0.312528i
$288$	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	0.126682	−	0.991943i	$-0.459567\pi$
$293$	−253.522	−	253.522i	−0.865262	−	0.865262i	−0.991943	+	0.126682i	$0.959567\pi$
$294$	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
$298$	277.292			0.930510
$299$	−36.8148	+	38.5885i	−0.123126	+	0.129058i
$300$		0			0
$301$	169.187	+	169.187i	0.562084	+	0.562084i
$302$			330.689i			1.09500i
$303$	343.250			1.13284
$304$	−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	$0.854317\pi$
$308$			1027.91i			3.33738i
$309$		−	30.7659i		−	0.0995661i
$310$		0			0
$311$		−	458.676i		−	1.47484i	−0.675434	−	0.737421i	$-0.736043\pi$
$311$		−	458.676i		−	1.47484i	0.675434	−	0.737421i	$-0.263957\pi$
$312$	−34.6380	−	1472.55i	−0.111019	−	4.71970i
$313$			379.531i			1.21256i	0.795251	+	0.606280i	$0.207339\pi$
$313$			379.531i			1.21256i	−0.795251	+	0.606280i	$0.792661\pi$
$314$	−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	−0.553488	−	0.832857i	$-0.686704\pi$
$317$	88.5600	−	88.5600i	0.279369	−	0.279369i	0.832857	+	0.553488i	$0.186704\pi$
$318$	−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
$322$	99.3251			0.308463
$323$	−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
$328$		−	446.832i		−	1.36229i
$329$		−	106.991i		−	0.325201i
$330$		0			0
$331$	168.982	+	168.982i	0.510521	+	0.510521i	0.914686	−	0.404165i	$-0.132438\pi$
$331$	168.982	+	168.982i	0.510521	+	0.510521i	−0.404165	+	0.914686i	$0.632438\pi$
$332$	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
$337$	−530.169			−1.57320			−0.786601	−	0.617462i	$-0.788161\pi$
$337$	−530.169			−1.57320			−0.786601	+	0.617462i	$0.788161\pi$
$338$	−495.052	−	450.542i	−1.46465	−	1.33296i
$339$	310.286			0.915298
$340$		0			0
$341$	380.728			1.11650
$342$	−235.105			−0.687441
$343$	−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
$347$		−	318.306i		−	0.917308i	−0.888615	−	0.458654i	$-0.848332\pi$
$347$		−	318.306i		−	0.917308i	0.888615	−	0.458654i	$-0.151668\pi$
$348$	942.242			2.70759
$349$	155.842	−	155.842i	0.446539	−	0.446539i	−0.447663	−	0.894202i	$-0.647744\pi$
$349$	155.842	−	155.842i	0.446539	−	0.446539i	0.894202	+	0.447663i	$0.147744\pi$
$350$		0			0
$351$	145.415	+	138.731i	0.414288	+	0.395246i
$352$			2456.45i			6.97855i
$353$	−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	−0.0633515	+	0.997991i	$0.520179\pi$
$359$	−381.022	+	381.022i	−1.06134	+	1.06134i	−0.997991	+	0.0633515i	$0.979821\pi$
$360$		0			0
$361$		−	210.914i		−	0.584248i
$362$	−300.687	−	300.687i	−0.830627	−	0.830627i
$363$	320.027			0.881616
$364$	21.8409	+	928.510i	0.0600025	+	2.55085i
$365$		0			0
$366$	−0.764451	−	0.764451i	−0.00208866	−	0.00208866i
$367$		−	393.203i		−	1.07140i	−0.844409	−	0.535699i	$-0.820048\pi$
$367$		−	393.203i		−	1.07140i	0.844409	−	0.535699i	$-0.179952\pi$
$368$	303.002			0.823375
$369$	−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
$373$		−	346.362i		−	0.928586i	−0.885682	−	0.464293i	$-0.846309\pi$
$373$		−	346.362i		−	0.928586i	0.885682	−	0.464293i	$-0.153691\pi$
$374$			261.092i			0.698108i
$375$		0			0
$376$		−	532.993i		−	1.41754i
$377$	194.421	−	203.788i	0.515707	−	0.540553i
$378$		−	374.293i		−	0.990193i
$379$	−243.538	−	243.538i	−0.642581	−	0.642581i	0.308608	−	0.951189i	$-0.400137\pi$
$379$	−243.538	−	243.538i	−0.642581	−	0.642581i	−0.951189	+	0.308608i	$0.900137\pi$
$380$		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
$387$	189.656			0.490067
$388$	−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
$393$			32.3250i			0.0822519i
$394$			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	−0.944745	−	0.327807i	$-0.893690\pi$
$401$	−247.392	+	247.392i	−0.616937	+	0.616937i	0.327807	+	0.944745i	$0.393690\pi$
$402$	−127.474			−0.317099
$403$	343.910	−	8.08963i	0.853374	−	0.0200735i
$404$	−1078.21			−2.66883
$405$		0			0
$406$	−524.543			−1.29198
$407$	−71.0863			−0.174659
$408$	−367.069	+	367.069i	−0.899679	+	0.899679i
$409$	−330.958	−	330.958i	−0.809189	−	0.809189i	0.175322	−	0.984511i	$-0.443903\pi$
$409$	−330.958	−	330.958i	−0.809189	−	0.809189i	−0.984511	+	0.175322i	$0.943903\pi$
$410$		0			0
$411$	500.490	−	500.490i	1.21774	−	1.21774i
$412$			96.6410i			0.234566i
$413$	−88.8284			−0.215081
$414$	55.6709	−	55.6709i	0.134471	−	0.134471i
$415$		0			0
$416$	52.1942	+	2218.90i	0.125467	+	5.33390i
$417$		−	774.184i		−	1.85656i
$418$	493.665	−	493.665i	1.18102	−	1.18102i
$419$	−27.5079			−0.0656513			−0.0328256	−	0.999461i	$-0.510451\pi$
$419$	−27.5079			−0.0656513			−0.0328256	+	0.999461i	$0.510451\pi$
$420$		0			0
$421$	371.548	+	371.548i	0.882537	+	0.882537i	0.993792	−	0.111255i	$-0.0354871\pi$
$421$	371.548	+	371.548i	0.882537	+	0.882537i	−0.111255	+	0.993792i	$0.535487\pi$
$422$	−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
$428$	−388.607			−0.907960
$429$	695.769	−	16.3663i	1.62184	−	0.0381498i
$430$		0			0
$431$	11.9557	+	11.9557i	0.0277393	+	0.0277393i	0.720840	−	0.693101i	$-0.243756\pi$
$431$	11.9557	+	11.9557i	0.0277393	+	0.0277393i	−0.693101	+	0.720840i	$0.743756\pi$
$432$		−	1141.82i		−	2.64310i
$433$	−213.638			−0.493390			−0.246695	−	0.969093i	$-0.579345\pi$
$433$	−213.638			−0.493390			−0.246695	+	0.969093i	$0.579345\pi$
$434$	−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
$438$			1332.79i			3.04290i
$439$			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
$442$	5.54764	+	235.844i	0.0125512	+	0.533583i
$443$			267.997i			0.604960i	0.953156	+	0.302480i	$0.0978145\pi$
$443$			267.997i			0.604960i	−0.953156	+	0.302480i	$0.902185\pi$
$444$	−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	0.188746	−	0.982026i	$-0.439558\pi$
$449$	525.677	−	525.677i	1.17077	−	1.17077i	0.982026	−	0.188746i	$-0.0604424\pi$
$450$		0			0
$451$	211.126			0.468128
$452$	−974.661			−2.15633
$453$	−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	−0.155934	−	0.987767i	$-0.549839\pi$
$457$	380.148	−	380.148i	0.831833	−	0.831833i	0.987767	+	0.155934i	$0.0498387\pi$
$458$			86.2062i			0.188223i
$459$		−	70.8306i		−	0.154315i
$460$		0			0
$461$	607.424	+	607.424i	1.31762	+	1.31762i	0.915652	+	0.401971i	$0.131675\pi$
$461$	607.424	+	607.424i	1.31762	+	1.31762i	0.401971	+	0.915652i	$0.368325\pi$
$462$	−916.504	−	916.504i	−1.98377	−	1.98377i
$463$	553.304	+	553.304i	1.19504	+	1.19504i	0.975633	+	0.219407i	$0.0704122\pi$
$463$	553.304	+	553.304i	1.19504	+	1.19504i	0.219407	+	0.975633i	$0.429588\pi$
$464$	−1600.17			−3.44865
$465$		0			0
$466$	1173.63	−	1173.63i	2.51853	−	2.51853i
$467$	616.765			1.32070			0.660348	−	0.750960i	$-0.270409\pi$
$467$	616.765			1.32070			0.660348	+	0.750960i	$0.270409\pi$
$468$	532.663	+	508.180i	1.13817	+	1.08586i
$469$	52.8703			0.112730
$470$		0			0
$471$	562.032			1.19327
$472$	−442.513			−0.937527
$473$	−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
$477$		−	496.516i		−	1.04091i
$478$	1177.33			2.46303
$479$	−106.901	+	106.901i	−0.223176	+	0.223176i	−0.809834	−	0.586659i	$-0.800443\pi$
$479$	−106.901	+	106.901i	−0.223176	+	0.223176i	0.586659	+	0.809834i	$0.300443\pi$
$480$		0			0
$481$	−64.2119	+	1.51043i	−0.133497	+	0.00314018i
$482$			834.757i			1.73186i
$483$	−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	−0.905454	−	0.424444i	$-0.860470\pi$
$487$	−234.252	+	234.252i	−0.481010	+	0.481010i	0.424444	+	0.905454i	$0.360470\pi$
$488$	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	$-0.768755\pi$
$491$		−	652.284i		−	1.32848i	0.747519	−	0.664240i	$-0.231245\pi$
$492$	451.254	+	451.254i	0.917184	+	0.917184i
$493$	−99.2637			−0.201346
$494$	435.436	−	456.415i	0.881450	−	0.923917i
$495$		0			0
$496$	−1381.97	−	1381.97i	−2.78624	−	2.78624i
$497$			141.167i			0.284038i
$498$	−1141.58			−2.29233
$499$	−248.398	−	248.398i	−0.497791	−	0.497791i	0.412959	−	0.910750i	$-0.364495\pi$
$499$	−248.398	−	248.398i	−0.497791	−	0.497791i	−0.910750	+	0.412959i	$0.864495\pi$
$500$		0			0
$501$	−664.164	+	664.164i	−1.32568	+	1.32568i
$502$	905.049	+	905.049i	1.80289	+	1.80289i
$503$			185.135i			0.368062i	0.982920	+	0.184031i	$0.0589146\pi$
$503$			185.135i			0.368062i	−0.982920	+	0.184031i	$0.941085\pi$
$504$		−	901.836i		−	1.78936i
$505$		0			0
$506$			233.792i			0.462039i
$507$	628.138	−	29.5671i	1.23893	−	0.0583178i
$508$		−	303.782i		−	0.597997i
$509$	234.707	+	234.707i	0.461114	+	0.461114i	0.899020	−	0.437907i	$-0.144280\pi$
$509$	234.707	+	234.707i	0.461114	+	0.461114i	−0.437907	+	0.899020i	$0.644280\pi$
$510$		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
$517$	251.836			0.487110
$518$	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
$523$			772.536i			1.47712i	0.674185	+	0.738562i	$0.264495\pi$
$523$			772.536i			1.47712i	−0.674185	+	0.738562i	$0.735505\pi$
$524$		−	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
$532$	−875.254			−1.64521
$533$	190.709	−	4.48595i	0.357803	−	0.00841642i
$534$	1559.85			2.92107
$535$		0			0
$536$	263.382			0.491384
$537$	−549.534			−1.02334
$538$	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	−0.957264	−	0.289216i	$-0.906605\pi$
$541$	−361.414	+	361.414i	−0.668047	+	0.668047i	0.289216	+	0.957264i	$0.406605\pi$
$542$			1657.00i			3.05719i
$543$	399.480			0.735690
$544$	553.117	−	553.117i	1.01676	−	1.01676i
$545$		0			0
$546$	−847.348	−	808.400i	−1.55192	−	1.48059i
$547$		−	453.400i		−	0.828884i	−0.910076	−	0.414442i	$-0.863977\pi$
$547$		−	453.400i		−	0.828884i	0.910076	−	0.414442i	$-0.136023\pi$
$548$	−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	$0.554688\pi$
$558$	−507.823			−0.910077
$559$	−351.261	+	368.184i	−0.628374	+	0.658648i
$560$		0			0
$561$	−173.438	−	173.438i	−0.309158	−	0.309158i
$562$		−	544.401i		−	0.968684i
$563$	979.383			1.73958			0.869790	−	0.493423i	$-0.164254\pi$
$563$	979.383			1.73958			0.869790	+	0.493423i	$0.164254\pi$
$564$	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
$568$			703.245i			1.23811i
$569$			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	$0.137077\pi$
$571$			476.731i			0.834905i	−0.908699	+	0.417452i	$0.862923\pi$
$572$	−2185.53	+	51.4092i	−3.82086	+	0.0898762i
$573$		−	226.043i		−	0.394491i
$574$	−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	−0.00529665	−	0.999986i	$-0.501686\pi$
$577$	573.936	−	573.936i	0.994689	−	0.994689i	0.999986	+	0.00529665i	$0.00168598\pi$
$578$	−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
$582$	2035.33			3.49712
$583$	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	−0.992655	−	0.120981i	$-0.961396\pi$
$587$	−511.672	+	511.672i	−0.871673	+	0.871673i	0.120981	+	0.992655i	$0.461396\pi$
$588$		−	506.074i		−	0.860670i
$589$			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	0.819208	−	0.573497i	$-0.194414\pi$
$593$	145.706	+	145.706i	0.245711	+	0.245711i	−0.573497	+	0.819208i	$0.694414\pi$
$594$	881.011			1.48318
$595$		0			0
$596$	578.600	−	578.600i	0.970806	−	0.970806i
$597$	−912.094			−1.52780
$598$	4.96756	+	211.183i	0.00830696	+	0.353149i
$599$	330.589			0.551902			0.275951	−	0.961172i	$-0.411007\pi$
$599$	330.589			0.551902			0.275951	+	0.961172i	$0.411007\pi$
$600$		0			0
$601$	−538.002			−0.895177			−0.447589	−	0.894240i	$-0.647717\pi$
$601$	−538.002			−0.895177			−0.447589	+	0.894240i	$0.647717\pi$
$602$	947.690			1.57424
$603$	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
$607$		−	412.828i		−	0.680111i	−0.940405	−	0.340056i	$-0.889554\pi$
$607$		−	412.828i		−	0.680111i	0.940405	−	0.340056i	$-0.110446\pi$
$608$	−2091.63			−3.44019
$609$	348.442	−	348.442i	0.572155	−	0.572155i
$610$		0			0
$611$	227.482	−	5.35096i	0.372312	−	0.00875771i
$612$		−	259.456i		−	0.423948i
$613$	−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	−0.603028	−	0.797720i	$-0.706039\pi$
$617$	120.125	−	120.125i	0.194691	−	0.194691i	0.797720	+	0.603028i	$0.206039\pi$
$618$	−86.1666	−	86.1666i	−0.139428	−	0.139428i
$619$	−732.097	+	732.097i	−1.18271	+	1.18271i	−0.203669	+	0.979040i	$0.565287\pi$
$619$	−732.097	+	732.097i	−1.18271	+	1.18271i	−0.979040	+	0.203669i	$0.934713\pi$
$620$		0			0
$621$		−	63.4244i		−	0.102133i
$622$	−1284.62	−	1284.62i	−2.06531	−	2.06531i
$623$	−646.954			−1.03845
$624$	−2584.93	−	2466.11i	−4.14251	−	3.95210i
$625$		0			0
$626$	1062.96	+	1062.96i	1.69802	+	1.69802i
$627$			655.862i			1.04603i
$628$	−1765.44			−2.81121
$629$	16.0064	+	16.0064i	0.0254474	+	0.0254474i
$630$		0			0
$631$	−377.611	+	377.611i	−0.598433	+	0.598433i	−0.939895	−	0.341463i	$-0.889078\pi$
$631$	−377.611	+	377.611i	−0.598433	+	0.598433i	0.341463	+	0.939895i	$0.389078\pi$
$632$	−2759.44	−	2759.44i	−4.36620	−	4.36620i
$633$		−	1005.81i		−	1.58895i
$634$		−	496.063i		−	0.782433i
$635$		0			0
$636$			4456.72i			7.00742i
$637$	−109.454	−	104.423i	−0.171827	−	0.163929i
$638$		−	1234.67i		−	1.93522i
$639$	79.1228	+	79.1228i	0.123823	+	0.123823i
$640$		0			0
$641$		−	1125.68i		−	1.75614i	−0.478535	−	0.878068i	$-0.658832\pi$
$641$		−	1125.68i		−	1.75614i	0.478535	−	0.878068i	$-0.341168\pi$
$642$	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
$647$	894.637			1.38275			0.691374	−	0.722498i	$-0.257006\pi$
$647$	894.637			1.38275			0.691374	+	0.722498i	$0.257006\pi$
$648$	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
$653$		−	259.531i		−	0.397444i	−0.980056	−	0.198722i	$-0.936321\pi$
$653$		−	259.531i		−	0.397444i	0.980056	−	0.198722i	$-0.0636791\pi$
$654$			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	$-0.365360\pi$
$659$	541.017			0.820967			0.410483	+	0.911868i	$0.365360\pi$
$660$		0			0
$661$	580.306	−	580.306i	0.877921	−	0.877921i	−0.115398	−	0.993319i	$-0.536814\pi$
$661$	580.306	−	580.306i	0.877921	−	0.877921i	0.993319	+	0.115398i	$0.0368145\pi$
$662$	946.543			1.42982
$663$	−160.351	−	152.981i	−0.241857	−	0.230740i
$664$	2358.69			3.55224
$665$		0			0
$666$	94.8164			0.142367
$667$	−88.8844			−0.133260
$668$	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
$672$			3883.18i			5.77854i
$673$	−965.968			−1.43532			−0.717658	−	0.696396i	$-0.754786\pi$
$673$	−965.968			−1.43532			−0.717658	+	0.696396i	$0.754786\pi$
$674$	−1484.85	+	1484.85i	−2.20304	+	2.20304i
$675$		0			0
$676$	−1973.09	+	92.8754i	−2.91877	+	0.137390i
$677$			813.684i			1.20190i	0.799288	+	0.600948i	$0.205210\pi$
$677$			813.684i			1.20190i	−0.799288	+	0.600948i	$0.794790\pi$
$678$	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	$-0.924116\pi$
$683$	−824.970	−	824.970i	−1.20786	−	1.20786i	−0.236145	−	0.971718i	$-0.575884\pi$
$684$	−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
$688$	2891.03			4.20208
$689$	963.900	+	919.596i	1.39898	+	1.33468i
$690$		0			0
$691$	190.752	+	190.752i	0.276052	+	0.276052i	0.831531	−	0.555479i	$-0.187465\pi$
$691$	190.752	+	190.752i	0.276052	+	0.276052i	−0.555479	+	0.831531i	$0.687465\pi$
$692$			1939.43i			2.80265i
$693$	426.112			0.614880
$694$	−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
$698$		−	872.939i		−	1.25063i
$699$			1559.24i			2.23067i
$700$		0			0
$701$			623.742i			0.889789i	0.895583	+	0.444894i	$0.146759\pi$
$701$			623.742i			0.889789i	−0.895583	+	0.444894i	$0.853241\pi$
$702$	795.814	−	18.7195i	1.13364	−	0.0266660i
$703$		−	60.5289i		−	0.0861009i
$704$	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	$-0.824504\pi$
$709$	−232.551	+	232.551i	−0.327998	+	0.327998i	0.523827	+	0.851825i	$0.324504\pi$
$710$		0			0
$711$	−620.935			−0.873326
$712$	−3222.91			−4.52655
$713$	−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
$718$			2134.27i			2.97252i
$719$		−	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
$727$	−270.298			−0.371799			−0.185899	−	0.982569i	$-0.559520\pi$
$727$	−270.298			−0.371799			−0.185899	+	0.982569i	$0.559520\pi$
$728$	1750.76	+	1670.29i	2.40489	+	2.29435i
$729$	−27.7267			−0.0380339
$730$		0			0
$731$	179.340			0.245335
$732$	−3.19022			−0.00435823
$733$	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
$737$			124.446i			0.168855i
$738$	−281.604			−0.381577
$739$	−0.209620	+	0.209620i	−0.000283653	+	0.000283653i	−0.707249	−	0.706965i	$-0.750064\pi$
$739$	−0.209620	+	0.209620i	−0.000283653	+	0.000283653i	0.706965	+	0.707249i	$0.250064\pi$
$740$		0			0
$741$	13.9356	+	592.438i	0.0188065	+	0.799511i
$742$		−	2481.04i		−	3.34372i
$743$	−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	$-0.906811\pi$
$751$		−	433.472i		−	0.577193i	0.957451	−	0.288596i	$-0.0931886\pi$
$752$	−914.120	−	914.120i	−1.21558	−	1.21558i
$753$	−1202.41			−1.59682
$754$	−26.2340	−	1115.27i	−0.0347931	−	1.47914i
$755$		0			0
$756$	−781.003	−	781.003i	−1.03307	−	1.03307i
$757$			667.177i			0.881343i	0.897668	+	0.440672i	$0.145260\pi$
$757$			667.177i			0.881343i	−0.897668	+	0.440672i	$0.854740\pi$
$758$	−1364.16			−1.79969
$759$	−155.303	−	155.303i	−0.204615	−	0.204615i
$760$		0			0
$761$	−331.781	+	331.781i	−0.435980	+	0.435980i	−0.890657	−	0.454676i	$-0.849755\pi$
$761$	−331.781	+	331.781i	−0.435980	+	0.435980i	0.454676	+	0.890657i	$0.349755\pi$
$762$	270.857	+	270.857i	0.355455	+	0.355455i
$763$		−	420.779i		−	0.551479i
$764$			710.040i			0.929371i
$765$		0			0
$766$		−	1194.81i		−	1.55980i
$767$	−4.44258	−	188.865i	−0.00579216	−	0.246239i
$768$			6496.44i			8.45890i
$769$	−927.008	−	927.008i	−1.20547	−	1.20547i	−0.972478	−	0.232994i	$-0.925148\pi$
$769$	−927.008	−	927.008i	−1.20547	−	1.20547i	−0.232994	−	0.972478i	$-0.574852\pi$
$770$		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
$777$	−112.374			−0.144625
$778$	−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
$783$			334.948i			0.427776i
$784$			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
$792$	2122.74			2.68023
$793$	−0.658268	+	0.689982i	−0.000830098	+	0.000870091i
$794$	−1242.73			−1.56515
$795$		0			0
$796$	2865.04			3.59930
$797$	704.728			0.884226			0.442113	−	0.896959i	$-0.354229\pi$
$797$	704.728			0.884226			0.442113	+	0.896959i	$0.354229\pi$
$798$	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
$802$			1385.75i			1.72786i
$803$	1301.14			1.62034
$804$	−265.988	+	265.988i	−0.330831	+	0.330831i
$805$		0			0
$806$	940.537	−	985.850i	1.16692	−	1.22314i
$807$			1136.40i			1.40818i
$808$	−1986.30	+	1986.30i	−2.45829	+	2.45829i
$809$	−500.209			−0.618305			−0.309153	−	0.951012i	$-0.600045\pi$
$809$	−500.209			−0.618305			−0.309153	+	0.951012i	$0.600045\pi$
$810$		0			0
$811$	−267.269	−	267.269i	−0.329555	−	0.329555i	0.522862	−	0.852417i	$-0.324864\pi$
$811$	−267.269	−	267.269i	−0.329555	−	0.329555i	−0.852417	+	0.522862i	$0.824864\pi$
$812$	−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
$818$	−1853.84			−2.26631
$819$	384.905	−	9.05394i	0.469970	−	0.0110549i
$820$		0			0
$821$	−253.704	−	253.704i	−0.309019	−	0.309019i	0.535510	−	0.844529i	$-0.320119\pi$
$821$	−253.704	−	253.704i	−0.309019	−	0.309019i	−0.844529	+	0.535510i	$0.820119\pi$
$822$		−	2803.46i		−	3.41054i
$823$	−890.680			−1.08224			−0.541118	−	0.840947i	$-0.681999\pi$
$823$	−890.680			−1.08224			−0.541118	+	0.840947i	$0.681999\pi$
$824$	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	$0.878756\pi$
$828$		−	232.327i		−	0.280588i
$829$			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
$832$	3581.88	+	3417.24i	4.30514	+	4.10726i
$833$			53.3141i			0.0640025i
$834$	−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	$-0.923196\pi$
$839$	−614.213	+	614.213i	−0.732078	+	0.732078i	0.238953	+	0.971031i	$0.423196\pi$
$840$		0			0
$841$	−371.596			−0.441850
$842$	2081.20			2.47173
$843$	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
$848$		−	7568.68i		−	8.92533i
$849$			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	0.639062	−	0.769155i	$-0.279323\pi$
$853$	−110.970	−	110.970i	−0.130094	−	0.130094i	−0.769155	+	0.639062i	$0.779323\pi$
$854$	1.77598			0.00207961
$855$		0			0
$856$	−715.900	+	715.900i	−0.836332	+	0.836332i
$857$	797.203			0.930225			0.465113	−	0.885251i	$-0.346014\pi$
$857$	797.203			0.930225			0.465113	+	0.885251i	$0.346014\pi$
$858$	1902.81	−	1994.49i	2.21773	−	2.32458i
$859$	364.974			0.424882			0.212441	−	0.977174i	$-0.431859\pi$
$859$	364.974			0.424882			0.212441	+	0.977174i	$0.431859\pi$
$860$		0			0
$861$	333.749			0.387629
$862$	66.9687			0.0776899
$863$	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
$867$		−	997.236i		−	1.15022i
$868$	−1890.54			−2.17804
$869$	1303.82	−	1303.82i	1.50037	−	1.50037i
$870$		0			0
$871$	2.64421	+	112.412i	0.00303583	+	0.129061i
$872$		−	2096.17i		−	2.40387i
$873$	−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	−0.994732	−	0.102507i	$-0.967314\pi$
$877$	−782.481	+	782.481i	−0.892225	+	0.892225i	0.102507	+	0.994732i	$0.467314\pi$
$878$	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	$0.0327575\pi$
$881$			181.009i			0.205458i	−0.994709	+	0.102729i	$0.967243\pi$
$882$	157.907	+	157.907i	0.179033	+	0.179033i
$883$	−898.698			−1.01778			−0.508889	−	0.860832i	$-0.669944\pi$
$883$	−898.698			−1.01778			−0.508889	+	0.860832i	$0.669944\pi$
$884$	503.689	+	480.538i	0.569784	+	0.543595i
$885$		0			0
$886$	750.584	+	750.584i	0.847160	+	0.847160i
$887$			153.874i			0.173477i	0.996231	+	0.0867387i	$0.0276445\pi$
$887$			153.874i			0.173477i	−0.996231	+	0.0867387i	$0.972355\pi$
$888$	−559.807			−0.630413
$889$	−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
$893$			214.435i			0.240128i
$894$			1031.78i			1.15411i
$895$		0			0
$896$		−	5045.17i		−	5.63077i
$897$	−143.584	−	136.984i	−0.160072	−	0.152714i
$898$		−	2944.54i		−	3.27900i
$899$	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
$907$	636.228			0.701464			0.350732	−	0.936476i	$-0.385933\pi$
$907$	636.228			0.701464			0.350732	+	0.936476i	$0.385933\pi$
$908$	−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
$913$			1114.47i			1.22066i
$914$		−	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	$-0.358292\pi$
$919$	791.494			0.861256			0.430628	+	0.902530i	$0.358292\pi$
$920$		0			0
$921$	520.002	−	520.002i	0.564606	−	0.564606i
$922$	3402.44			3.69029
$923$	−300.146	+	7.06020i	−0.325185	+	0.00764918i
$924$	−3824.77			−4.13936
$925$		0			0
$926$	3099.29			3.34697
$927$	40.0616			0.0432164
$928$	−2615.61	+	2615.61i	−2.81855	+	2.81855i
$929$	−31.5586	−	31.5586i	−0.0339705	−	0.0339705i	0.689918	−	0.723888i	$-0.257647\pi$
$929$	−31.5586	−	31.5586i	−0.0339705	−	0.0339705i	−0.723888	+	0.689918i	$0.757647\pi$
$930$		0			0
$931$	100.805	−	100.805i	0.108276	−	0.108276i
$932$		−	4897.83i		−	5.25519i
$933$	1706.69			1.82925
$934$	1727.38	−	1727.38i	1.84945	−	1.84945i
$935$		0			0
$936$	1917.47	−	45.1036i	2.04857	−	0.0481876i
$937$			602.943i			0.643482i	0.946828	+	0.321741i	$0.104268\pi$
$937$			602.943i			0.643482i	−0.946828	+	0.321741i	$0.895732\pi$
$938$	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	0.0140252	−	0.999902i	$-0.495535\pi$
$941$	−927.710	−	927.710i	−0.985876	−	0.985876i	−0.999902	+	0.0140252i	$0.995535\pi$
$942$	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	$0.767137\pi$
$948$	5573.50			5.87922
$949$	1175.31	−	27.6463i	1.23847	−	0.0291320i
$950$		0			0
$951$	329.524	+	329.524i	0.346502	+	0.346502i
$952$		−	852.781i		−	0.895778i
$953$	870.605			0.913542			0.456771	−	0.889584i	$-0.349006\pi$
$953$	870.605			0.913542			0.456771	+	0.889584i	$0.349006\pi$
$954$	−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
$958$			598.800i			0.625052i
$959$			1162.75i			1.21246i
$960$		0			0
$961$		−	260.767i		−	0.271349i
$962$	−175.609	+	184.069i	−0.182546	+	0.191340i
$963$			161.093i			0.167283i
$964$	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	$0.650144\pi$
$967$	−1300.80	+	1300.80i	−1.34519	+	1.34519i	−0.890802	+	0.454392i	$0.849856\pi$
$968$	−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	$0.562535\pi$
$972$	−2771.93			−2.85178
$973$	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	−0.664917	−	0.746917i	$-0.731533\pi$
$977$	80.1135	−	80.1135i	0.0819995	−	0.0819995i	0.746917	+	0.664917i	$0.231533\pi$
$978$			1505.86i			1.53973i
$979$		−	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	0.312610	−	0.949882i	$-0.398797\pi$
$983$	−626.438	−	626.438i	−0.637272	−	0.637272i	−0.949882	+	0.312610i	$0.898797\pi$
$984$	1662.62			1.68966
$985$		0			0
$986$	−278.009	+	278.009i	−0.281957	+	0.281957i
$987$	398.104			0.403348
$988$	−43.7742	−	1860.95i	−0.0443058	−	1.88355i
$989$	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	$0.613797\pi$
$992$	−4517.90			−4.55433
$993$	−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
$997$			442.915i			0.444247i	0.975019	+	0.222124i	$0.0712989\pi$
$997$			442.915i			0.444247i	−0.975019	+	0.222124i	$0.928701\pi$
$998$	−1391.38			−1.39417
$999$	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.g.e.99.10		20
5.2	odd	4		325.3.j.d.151.10	yes	20
5.3	odd	4		325.3.j.c.151.1	✓	20
5.4	even	2		325.3.g.f.99.1		20
13.5	odd	4		325.3.g.f.174.1		20
65.18	even	4		325.3.j.c.226.1	yes	20
65.44	odd	4	inner	325.3.g.e.174.10		20
65.57	even	4		325.3.j.d.226.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.3.g.e.99.10		20	1.1	even	1	trivial
325.3.g.e.174.10		20	65.44	odd	4	inner
325.3.g.f.99.1		20	5.4	even	2
325.3.g.f.174.1		20	13.5	odd	4
325.3.j.c.151.1	✓	20	5.3	odd	4
325.3.j.c.226.1	yes	20	65.18	even	4
325.3.j.d.151.10	yes	20	5.2	odd	4
325.3.j.d.226.10	yes	20	65.57	even	4

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.g (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.80071 - 2.80071i) q^{2} +3.72091i q^{3} -11.6880i q^{4} +(10.4212 + 10.4212i) q^{6} +(-4.32223 - 4.32223i) q^{7} +(-21.5319 - 21.5319i) q^{8} -4.84515 q^{9} +(10.1737 - 10.1737i) q^{11} +43.4900 q^{12} +(8.97368 - 9.40601i) q^{13} -24.2107 q^{14} -73.8573 q^{16} -4.58160 q^{17} +(-13.5699 + 13.5699i) q^{18} +(8.66275 + 8.66275i) q^{19} +(16.0826 - 16.0826i) q^{21} -56.9872i q^{22} -4.10253 q^{23} +(80.1182 - 80.1182i) q^{24} +(-1.21085 - 51.4763i) q^{26} +15.4598i q^{27} +(-50.5183 + 50.5183i) q^{28} +21.6657 q^{29} +(18.7114 + 18.7114i) q^{31} +(-120.726 + 120.726i) q^{32} +(37.8553 + 37.8553i) q^{33} +(-12.8317 + 12.8317i) q^{34} +56.6301i q^{36} +(-3.49363 - 3.49363i) q^{37} +48.5237 q^{38} +(34.9989 + 33.3902i) q^{39} +(10.3761 + 10.3761i) q^{41} -90.0857i q^{42} -39.1435 q^{43} +(-118.910 - 118.910i) q^{44} +(-11.4900 + 11.4900i) q^{46} +(12.3768 + 12.3768i) q^{47} -274.816i q^{48} -11.6366i q^{49} -17.0477i q^{51} +(-109.937 - 104.884i) q^{52} +102.477i q^{53} +(43.2985 + 43.2985i) q^{54} +186.132i q^{56} +(-32.2333 + 32.2333i) q^{57} +(60.6796 - 60.6796i) q^{58} +(10.2757 - 10.2757i) q^{59} -0.0733554 q^{61} +104.811 q^{62} +(20.9419 + 20.9419i) q^{63} +380.807i q^{64} +212.044 q^{66} +(-6.11609 + 6.11609i) q^{67} +53.5497i q^{68} -15.2651i q^{69} +(-16.3303 - 16.3303i) q^{71} +(104.325 + 104.325i) q^{72} +(63.9462 + 63.9462i) q^{73} -19.5693 q^{74} +(101.250 - 101.250i) q^{76} -87.9461 q^{77} +(191.538 - 4.50547i) q^{78} +128.156 q^{79} -101.131 q^{81} +58.1208 q^{82} +(-54.7720 + 54.7720i) q^{83} +(-187.974 - 187.974i) q^{84} +(-109.630 + 109.630i) q^{86} +80.6162i q^{87} -438.117 q^{88} +(74.8403 - 74.8403i) q^{89} +(-79.4413 + 1.86866i) q^{91} +47.9504i q^{92} +(-69.6234 + 69.6234i) q^{93} +69.3279 q^{94} +(-449.209 - 449.209i) q^{96} +(97.6532 - 97.6532i) q^{97} +(-32.5907 - 32.5907i) q^{98} +(-49.2930 + 49.2930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{6} - 20 q^{7} - 18 q^{8} - 72 q^{9} + 6 q^{11} + 120 q^{12} + 18 q^{13} + 24 q^{14} - 128 q^{16} + 16 q^{17} + 58 q^{18} + 20 q^{19} + 90 q^{21} - 28 q^{23} + 28 q^{24} - 278 q^{28} + 40 q^{29}+ \cdots + 410 q^{99}+O(q^{100}) \) 20 * q - 6 * q^6 - 20 * q^7 - 18 * q^8 - 72 * q^9 + 6 * q^11 + 120 * q^12 + 18 * q^13 + 24 * q^14 - 128 * q^16 + 16 * q^17 + 58 * q^18 + 20 * q^19 + 90 * q^21 - 28 * q^23 + 28 * q^24 - 278 * q^28 + 40 * q^29 - 32 * q^31 - 162 * q^32 + 124 * q^33 + 14 * q^34 - 158 * q^37 - 124 * q^38 + 26 * q^39 + 70 * q^41 + 32 * q^43 - 366 * q^44 + 58 * q^46 + 130 * q^47 - 244 * q^52 + 350 * q^54 + 168 * q^57 + 180 * q^58 - 132 * q^59 - 152 * q^61 - 212 * q^62 + 442 * q^63 + 720 * q^66 + 178 * q^67 - 258 * q^71 - 390 * q^72 - 262 * q^73 - 220 * q^74 + 68 * q^76 - 184 * q^77 + 918 * q^78 + 544 * q^79 + 204 * q^81 + 920 * q^82 - 88 * q^83 - 352 * q^84 - 174 * q^86 - 424 * q^88 + 282 * q^89 - 440 * q^91 - 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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