LMFDB - Embedded newform 1045.2.b.e.419.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(419,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("1045.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.3
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.e.419.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44393i q^{2} +0.661177i q^{3} -3.97280 q^{4} +(1.55248 + 1.60929i) q^{5} +1.61587 q^{6} -2.05193i q^{7} +4.82139i q^{8} +2.56284 q^{9} +O(q^{10})$	\(q-2.44393i q^{2} +0.661177i q^{3} -3.97280 q^{4} +(1.55248 + 1.60929i) q^{5} +1.61587 q^{6} -2.05193i q^{7} +4.82139i q^{8} +2.56284 q^{9} +(3.93299 - 3.79415i) q^{10} +1.00000 q^{11} -2.62672i q^{12} +7.18384i q^{13} -5.01478 q^{14} +(-1.06403 + 1.02646i) q^{15} +3.83754 q^{16} +3.65397i q^{17} -6.26342i q^{18} -1.00000 q^{19} +(-6.16768 - 6.39338i) q^{20} +1.35669 q^{21} -2.44393i q^{22} +5.65061i q^{23} -3.18779 q^{24} +(-0.179625 + 4.99677i) q^{25} +17.5568 q^{26} +3.67803i q^{27} +8.15191i q^{28} +0.355126 q^{29} +(2.50861 + 2.60041i) q^{30} +3.81095 q^{31} +0.264097i q^{32} +0.661177i q^{33} +8.93004 q^{34} +(3.30215 - 3.18558i) q^{35} -10.1817 q^{36} -3.78219i q^{37} +2.44393i q^{38} -4.74979 q^{39} +(-7.75901 + 7.48509i) q^{40} -6.80938 q^{41} -3.31566i q^{42} +2.39648i q^{43} -3.97280 q^{44} +(3.97876 + 4.12436i) q^{45} +13.8097 q^{46} -9.86457i q^{47} +2.53729i q^{48} +2.78958 q^{49} +(12.2118 + 0.438992i) q^{50} -2.41592 q^{51} -28.5399i q^{52} -11.0140i q^{53} +8.98884 q^{54} +(1.55248 + 1.60929i) q^{55} +9.89315 q^{56} -0.661177i q^{57} -0.867904i q^{58} +12.5732 q^{59} +(4.22716 - 4.07793i) q^{60} +7.64692 q^{61} -9.31371i q^{62} -5.25878i q^{63} +8.32051 q^{64} +(-11.5609 + 11.1527i) q^{65} +1.61587 q^{66} -11.9805i q^{67} -14.5165i q^{68} -3.73605 q^{69} +(-7.78533 - 8.07023i) q^{70} -10.3500 q^{71} +12.3565i q^{72} +15.6395i q^{73} -9.24341 q^{74} +(-3.30375 - 0.118764i) q^{75} +3.97280 q^{76} -2.05193i q^{77} +11.6082i q^{78} -3.96099 q^{79} +(5.95769 + 6.17571i) q^{80} +5.25671 q^{81} +16.6417i q^{82} -9.80243i q^{83} -5.38986 q^{84} +(-5.88029 + 5.67270i) q^{85} +5.85683 q^{86} +0.234801i q^{87} +4.82139i q^{88} +8.04623 q^{89} +(10.0796 - 9.72381i) q^{90} +14.7407 q^{91} -22.4487i q^{92} +2.51972i q^{93} -24.1083 q^{94} +(-1.55248 - 1.60929i) q^{95} -0.174615 q^{96} -5.99744i q^{97} -6.81755i q^{98} +2.56284 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	2.44393i		−	1.72812i	−0.503389	−	0.864060i	$-0.667914\pi$
$2$		−	2.44393i		−	1.72812i	0.503389	−	0.864060i	$-0.332086\pi$
$3$			0.661177i			0.381731i	0.981616	+	0.190865i	$0.0611294\pi$
$3$			0.661177i			0.381731i	−0.981616	+	0.190865i	$0.938871\pi$
$4$	−3.97280			−1.98640
$5$	1.55248	+	1.60929i	0.694289	+	0.719696i
$5$	1.55248	+	1.60929i	0.694289	+	0.719696i
$6$	1.61587			0.659677
$7$		−	2.05193i		−	0.775557i	−0.921753	−	0.387778i	$-0.873243\pi$
$7$		−	2.05193i		−	0.775557i	0.921753	−	0.387778i	$-0.126757\pi$
$8$			4.82139i			1.70462i
$9$	2.56284			0.854282
$10$	3.93299	−	3.79415i	1.24372	−	1.19982i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		−	2.62672i		−	0.758270i
$13$			7.18384i			1.99244i	0.0868761	+	0.996219i	$0.472312\pi$
$13$			7.18384i			1.99244i	−0.0868761	+	0.996219i	$0.527688\pi$
$14$	−5.01478			−1.34026
$15$	−1.06403	+	1.02646i	−0.274730	+	0.265032i
$16$	3.83754			0.959384
$17$			3.65397i			0.886217i	0.896468	+	0.443109i	$0.146124\pi$
$17$			3.65397i			0.886217i	−0.896468	+	0.443109i	$0.853876\pi$
$18$		−	6.26342i		−	1.47630i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−6.16768	−	6.39338i	−1.37914	−	1.42960i
$21$	1.35669			0.296054
$22$		−	2.44393i		−	0.521048i
$23$			5.65061i			1.17823i	0.808048	+	0.589117i	$0.200524\pi$
$23$			5.65061i			1.17823i	−0.808048	+	0.589117i	$0.799476\pi$
$24$	−3.18779			−0.650705
$25$	−0.179625	+	4.99677i	−0.0359251	+	0.999354i
$26$	17.5568			3.44317
$27$			3.67803i			0.707837i
$28$			8.15191i			1.54057i
$29$	0.355126			0.0659453			0.0329726	−	0.999456i	$-0.489503\pi$
$29$	0.355126			0.0659453			0.0329726	+	0.999456i	$0.489503\pi$
$30$	2.50861	+	2.60041i	0.458007	+	0.474767i
$31$	3.81095			0.684467			0.342234	−	0.939615i	$-0.388817\pi$
$31$	3.81095			0.684467			0.342234	+	0.939615i	$0.388817\pi$
$32$			0.264097i			0.0466863i
$33$			0.661177i			0.115096i
$34$	8.93004			1.53149
$35$	3.30215	−	3.18558i	0.558165	−	0.538461i
$36$	−10.1817			−1.69694
$37$		−	3.78219i		−	0.621788i	−0.950445	−	0.310894i	$-0.899372\pi$
$37$		−	3.78219i		−	0.621788i	0.950445	−	0.310894i	$-0.100628\pi$
$38$			2.44393i			0.396458i
$39$	−4.74979			−0.760575
$40$	−7.75901	+	7.48509i	−1.22681	+	1.18350i
$41$	−6.80938			−1.06345			−0.531724	−	0.846918i	$-0.678455\pi$
$41$	−6.80938			−1.06345			−0.531724	+	0.846918i	$0.678455\pi$
$42$		−	3.31566i		−	0.511617i
$43$			2.39648i			0.365460i	0.983163	+	0.182730i	$0.0584934\pi$
$43$			2.39648i			0.365460i	−0.983163	+	0.182730i	$0.941507\pi$
$44$	−3.97280			−0.598922
$45$	3.97876	+	4.12436i	0.593118	+	0.614823i
$46$	13.8097			2.03613
$47$		−	9.86457i		−	1.43890i	−0.694546	−	0.719448i	$-0.744395\pi$
$47$		−	9.86457i		−	1.43890i	0.694546	−	0.719448i	$-0.255605\pi$
$48$			2.53729i			0.366227i
$49$	2.78958			0.398512
$50$	12.2118	+	0.438992i	1.72700	+	0.0620829i
$51$	−2.41592			−0.338297
$52$		−	28.5399i		−	3.95778i
$53$		−	11.0140i		−	1.51289i	−0.654056	−	0.756446i	$-0.726934\pi$
$53$		−	11.0140i		−	1.51289i	0.654056	−	0.756446i	$-0.273066\pi$
$54$	8.98884			1.22323
$55$	1.55248	+	1.60929i	0.209336	+	0.216997i
$56$	9.89315			1.32203
$57$		−	0.661177i		−	0.0875751i
$58$		−	0.867904i		−	0.113961i
$59$	12.5732			1.63689			0.818445	−	0.574584i	$-0.194836\pi$
$59$	12.5732			1.63689			0.818445	+	0.574584i	$0.194836\pi$
$60$	4.22716	−	4.07793i	0.545724	−	0.526459i
$61$	7.64692			0.979088			0.489544	−	0.871978i	$-0.337163\pi$
$61$	7.64692			0.979088			0.489544	+	0.871978i	$0.337163\pi$
$62$		−	9.31371i		−	1.18284i
$63$		−	5.25878i		−	0.662544i
$64$	8.32051			1.04006
$65$	−11.5609	+	11.1527i	−1.43395	+	1.38333i
$66$	1.61587			0.198900
$67$		−	11.9805i		−	1.46365i	−0.681491	−	0.731827i	$-0.738668\pi$
$67$		−	11.9805i		−	1.46365i	0.681491	−	0.731827i	$-0.261332\pi$
$68$		−	14.5165i		−	1.76038i
$69$	−3.73605			−0.449768
$70$	−7.78533	−	8.07023i	−0.930525	−	0.964577i
$71$	−10.3500			−1.22832			−0.614160	−	0.789182i	$-0.710505\pi$
$71$	−10.3500			−1.22832			−0.614160	+	0.789182i	$0.710505\pi$
$72$			12.3565i			1.45622i
$73$			15.6395i			1.83046i	0.402929	+	0.915231i	$0.367992\pi$
$73$			15.6395i			1.83046i	−0.402929	+	0.915231i	$0.632008\pi$
$74$	−9.24341			−1.07453
$75$	−3.30375	−	0.118764i	−0.381485	−	0.0137137i
$76$	3.97280			0.455711
$77$		−	2.05193i		−	0.233839i
$78$			11.6082i			1.31437i
$79$	−3.96099			−0.445646			−0.222823	−	0.974859i	$-0.571527\pi$
$79$	−3.96099			−0.445646			−0.222823	+	0.974859i	$0.571527\pi$
$80$	5.95769	+	6.17571i	0.666090	+	0.690465i
$81$	5.25671			0.584078
$82$			16.6417i			1.83776i
$83$		−	9.80243i		−	1.07596i	−0.842959	−	0.537978i	$-0.819188\pi$
$83$		−	9.80243i		−	1.07596i	0.842959	−	0.537978i	$-0.180812\pi$
$84$	−5.38986			−0.588082
$85$	−5.88029	+	5.67270i	−0.637807	+	0.615291i
$86$	5.85683			0.631559
$87$			0.234801i			0.0251733i
$88$			4.82139i			0.513961i
$89$	8.04623			0.852899			0.426450	−	0.904511i	$-0.359764\pi$
$89$	8.04623			0.852899			0.426450	+	0.904511i	$0.359764\pi$
$90$	10.0796	−	9.72381i	1.06249	−	1.02498i
$91$	14.7407			1.54525
$92$		−	22.4487i		−	2.34044i
$93$			2.51972i			0.261282i
$94$	−24.1083			−2.48659
$95$	−1.55248	−	1.60929i	−0.159281	−	0.165110i
$96$	−0.174615			−0.0178216
$97$		−	5.99744i		−	0.608948i	−0.952521	−	0.304474i	$-0.901519\pi$
$97$		−	5.99744i		−	0.608948i	0.952521	−	0.304474i	$-0.0984807\pi$
$98$		−	6.81755i		−	0.688676i
$99$	2.56284			0.257576
$100$	0.713616	−	19.8512i	0.0713616	−	1.98512i
$101$	4.94647			0.492192			0.246096	−	0.969245i	$-0.420852\pi$
$101$	4.94647			0.492192			0.246096	+	0.969245i	$0.420852\pi$
$102$			5.90434i			0.584617i
$103$			0.481524i			0.0474460i	0.999719	+	0.0237230i	$0.00755197\pi$
$103$			0.481524i			0.0474460i	−0.999719	+	0.0237230i	$0.992448\pi$
$104$	−34.6361			−3.39634
$105$	2.10623	+	2.18331i	0.205547	+	0.213069i
$106$	−26.9175			−2.61446
$107$			14.3212i			1.38448i	0.721667	+	0.692240i	$0.243376\pi$
$107$			14.3212i			1.38448i	−0.721667	+	0.692240i	$0.756624\pi$
$108$		−	14.6121i		−	1.40605i
$109$	−3.22883			−0.309266			−0.154633	−	0.987972i	$-0.549419\pi$
$109$	−3.22883			−0.309266			−0.154633	+	0.987972i	$0.549419\pi$
$110$	3.93299	−	3.79415i	0.374996	−	0.361758i
$111$	2.50070			0.237356
$112$		−	7.87436i		−	0.744057i
$113$			17.2322i			1.62107i	0.585688	+	0.810537i	$0.300825\pi$
$113$			17.2322i			1.62107i	−0.585688	+	0.810537i	$0.699175\pi$
$114$	−1.61587			−0.151340
$115$	−9.09346	+	8.77244i	−0.847970	+	0.818035i
$116$	−1.41084			−0.130994
$117$			18.4111i			1.70210i
$118$		−	30.7280i		−	2.82874i
$119$	7.49769			0.687312
$120$	−4.94897	−	5.13008i	−0.451778	−	0.468310i
$121$	1.00000			0.0909091
$122$		−	18.6886i		−	1.69198i
$123$		−	4.50221i		−	0.405951i
$124$	−15.1401			−1.35963
$125$	−8.32012	+	7.46831i	−0.744174	+	0.667986i
$126$	−12.8521			−1.14496
$127$		−	10.3228i		−	0.916000i	−0.888952	−	0.458000i	$-0.848566\pi$
$127$		−	10.3228i		−	0.916000i	0.888952	−	0.458000i	$-0.151434\pi$
$128$		−	19.8066i		−	1.75067i
$129$	−1.58450			−0.139507
$130$	27.2566	+	28.2540i	2.39056	+	2.47804i
$131$	−11.8458			−1.03497			−0.517487	−	0.855691i	$-0.673133\pi$
$131$	−11.8458			−1.03497			−0.517487	+	0.855691i	$0.673133\pi$
$132$		−	2.62672i		−	0.228627i
$133$			2.05193i			0.177925i
$134$	−29.2796			−2.52937
$135$	−5.91901	+	5.71005i	−0.509427	+	0.491443i
$136$	−17.6172			−1.51066
$137$		−	10.5496i		−	0.901311i	−0.892698	−	0.450656i	$-0.851190\pi$
$137$		−	10.5496i		−	0.901311i	0.892698	−	0.450656i	$-0.148810\pi$
$138$			9.13066i			0.777253i
$139$	−13.6234			−1.15553			−0.577763	−	0.816205i	$-0.696074\pi$
$139$	−13.6234			−1.15553			−0.577763	+	0.816205i	$0.696074\pi$
$140$	−13.1188	+	12.6557i	−1.10874	+	1.06960i
$141$	6.52223			0.549271
$142$			25.2947i			2.12268i
$143$			7.18384i			0.600743i
$144$	9.83501			0.819584
$145$	0.551325	+	0.571501i	0.0457851	+	0.0474606i
$146$	38.2218			3.16326
$147$			1.84441i			0.152124i
$148$			15.0259i			1.23512i
$149$	7.90835			0.647878			0.323939	−	0.946078i	$-0.394993\pi$
$149$	7.90835			0.647878			0.323939	+	0.946078i	$0.394993\pi$
$150$	−0.290252	+	8.07414i	−0.0236989	+	0.659251i
$151$	−3.06001			−0.249020			−0.124510	−	0.992218i	$-0.539736\pi$
$151$	−3.06001			−0.249020			−0.124510	+	0.992218i	$0.539736\pi$
$152$		−	4.82139i		−	0.391066i
$153$			9.36455i			0.757079i
$154$	−5.01478			−0.404102
$155$	5.91642	+	6.13293i	0.475218	+	0.492608i
$156$	18.8700			1.51081
$157$			17.3559i			1.38515i	0.721345	+	0.692575i	$0.243524\pi$
$157$			17.3559i			1.38515i	−0.721345	+	0.692575i	$0.756476\pi$
$158$			9.68038i			0.770129i
$159$	7.28222			0.577518
$160$	−0.425009	+	0.410005i	−0.0335999	+	0.0324138i
$161$	11.5947			0.913787
$162$		−	12.8470i		−	1.00936i
$163$		−	24.5391i		−	1.92205i	−0.276464	−	0.961024i	$-0.589163\pi$
$163$		−	24.5391i		−	1.92205i	0.276464	−	0.961024i	$-0.410837\pi$
$164$	27.0523			2.11243
$165$	−1.06403	+	1.02646i	−0.0828343	+	0.0799100i
$166$	−23.9565			−1.85938
$167$			6.16236i			0.476858i	0.971160	+	0.238429i	$0.0766324\pi$
$167$			6.16236i			0.476858i	−0.971160	+	0.238429i	$0.923368\pi$
$168$			6.54113i			0.504659i
$169$	−38.6075			−2.96981
$170$	13.8637	+	14.3710i	1.06330	+	1.10221i
$171$	−2.56284			−0.195986
$172$		−	9.52074i		−	0.725949i
$173$		−	0.326872i		−	0.0248516i	−0.999923	−	0.0124258i	$-0.996045\pi$
$173$		−	0.326872i		−	0.0248516i	0.999923	−	0.0124258i	$-0.00395535\pi$
$174$	0.573838			0.0435026
$175$	10.2530	+	0.368579i	0.775056	+	0.0278619i
$176$	3.83754			0.289265
$177$			8.31311i			0.624852i
$178$		−	19.6644i		−	1.47391i
$179$	9.52357			0.711825			0.355913	−	0.934519i	$-0.384170\pi$
$179$	9.52357			0.711825			0.355913	+	0.934519i	$0.384170\pi$
$180$	−15.8068	−	16.3852i	−1.17817	−	1.22128i
$181$	−17.3768			−1.29160			−0.645802	−	0.763505i	$-0.723477\pi$
$181$	−17.3768			−1.29160			−0.645802	+	0.763505i	$0.723477\pi$
$182$		−	36.0253i		−	2.67038i
$183$			5.05597i			0.373748i
$184$	−27.2438			−2.00844
$185$	6.08664	−	5.87177i	0.447499	−	0.431701i
$186$	6.15801			0.451527
$187$			3.65397i			0.267205i
$188$			39.1900i			2.85822i
$189$	7.54706			0.548967
$190$	−3.93299	+	3.79415i	−0.285329	+	0.275256i
$191$	5.76344			0.417028			0.208514	−	0.978019i	$-0.433137\pi$
$191$	5.76344			0.417028			0.208514	+	0.978019i	$0.433137\pi$
$192$			5.50133i			0.397024i
$193$		−	12.6327i		−	0.909319i	−0.890665	−	0.454659i	$-0.849761\pi$
$193$		−	12.6327i		−	0.909319i	0.890665	−	0.454659i	$-0.150239\pi$
$194$	−14.6573			−1.05234
$195$	−7.37395	−	7.64379i	−0.528059	−	0.547383i
$196$	−11.0824			−0.791603
$197$			0.551851i			0.0393177i	0.999807	+	0.0196589i	$0.00625801\pi$
$197$			0.551851i			0.0393177i	−0.999807	+	0.0196589i	$0.993742\pi$
$198$		−	6.26342i		−	0.445122i
$199$	18.4893			1.31067			0.655335	−	0.755338i	$-0.272527\pi$
$199$	18.4893			1.31067			0.655335	+	0.755338i	$0.272527\pi$
$200$	−24.0914	−	0.866043i	−1.70352	−	0.0612385i
$201$	7.92125			0.558722
$202$		−	12.0888i		−	0.850567i
$203$		−	0.728694i		−	0.0511443i
$204$	9.59797			0.671992
$205$	−10.5714	−	10.9583i	−0.738340	−	0.765359i
$206$	1.17681			0.0819923
$207$			14.4816i			1.00654i
$208$			27.5682i			1.91151i
$209$	−1.00000			−0.0691714
$210$	5.33585	−	5.14748i	0.368209	−	0.355210i
$211$	−19.4923			−1.34190			−0.670952	−	0.741501i	$-0.734114\pi$
$211$	−19.4923			−1.34190			−0.670952	+	0.741501i	$0.734114\pi$
$212$			43.7565i			3.00521i
$213$		−	6.84319i		−	0.468887i
$214$	35.0000			2.39255
$215$	−3.85663	+	3.72048i	−0.263020	+	0.253735i
$216$	−17.7332			−1.20659
$217$		−	7.81981i		−	0.530843i
$218$			7.89104i			0.534449i
$219$	−10.3405			−0.698744
$220$	−6.16768	−	6.39338i	−0.415825	−	0.431042i
$221$	−26.2495			−1.76573
$222$		−	6.11154i		−	0.410179i
$223$		−	8.38614i		−	0.561578i	−0.959770	−	0.280789i	$-0.909404\pi$
$223$		−	8.38614i		−	0.561578i	0.959770	−	0.280789i	$-0.0905960\pi$
$224$	0.541910			0.0362079
$225$	−0.460352	+	12.8060i	−0.0306901	+	0.853730i
$226$	42.1144			2.80141
$227$		−	3.69908i		−	0.245517i	−0.992437	−	0.122758i	$-0.960826\pi$
$227$		−	3.69908i		−	0.245517i	0.992437	−	0.122758i	$-0.0391740\pi$
$228$			2.62672i			0.173959i
$229$	−13.8060			−0.912325			−0.456163	−	0.889896i	$-0.650776\pi$
$229$	−13.8060			−0.912325			−0.456163	+	0.889896i	$0.650776\pi$
$230$	21.4392	+	22.2238i	1.41366	+	1.46539i
$231$	1.35669			0.0892636
$232$			1.71220i			0.112411i
$233$		−	8.05235i		−	0.527527i	−0.964587	−	0.263763i	$-0.915036\pi$
$233$		−	8.05235i		−	0.527527i	0.964587	−	0.263763i	$-0.0849638\pi$
$234$	44.9954			2.94144
$235$	15.8750	−	15.3145i	1.03557	−	0.999010i
$236$	−49.9508			−3.25152
$237$		−	2.61891i		−	0.170117i
$238$		−	18.3238i		−	1.18776i
$239$	23.4469			1.51666			0.758328	−	0.651874i	$-0.226017\pi$
$239$	23.4469			1.51666			0.758328	+	0.651874i	$0.226017\pi$
$240$	−4.08324	+	3.93909i	−0.263572	+	0.254267i
$241$	4.65798			0.300047			0.150023	−	0.988682i	$-0.452065\pi$
$241$	4.65798			0.300047			0.150023	+	0.988682i	$0.452065\pi$
$242$		−	2.44393i		−	0.157102i
$243$			14.5097i			0.930797i
$244$	−30.3797			−1.94486
$245$	4.33076	+	4.48924i	0.276682	+	0.286807i
$246$	−11.0031			−0.701532
$247$		−	7.18384i		−	0.457097i
$248$			18.3741i			1.16675i
$249$	6.48115			0.410726
$250$	18.2520	+	20.3338i	1.15436	+	1.28602i
$251$	19.3021			1.21834			0.609170	−	0.793040i	$-0.291503\pi$
$251$	19.3021			1.21834			0.609170	+	0.793040i	$0.291503\pi$
$252$			20.8921i			1.31608i
$253$			5.65061i			0.355251i
$254$	−25.2282			−1.58296
$255$	−3.75066	−	3.88792i	−0.234876	−	0.243471i
$256$	−31.7648			−1.98530
$257$		−	16.5508i		−	1.03241i	−0.856465	−	0.516206i	$-0.827344\pi$
$257$		−	16.5508i		−	1.03241i	0.856465	−	0.516206i	$-0.172656\pi$
$258$			3.87241i			0.241085i
$259$	−7.76079			−0.482232
$260$	45.9290	−	44.3076i	2.84840	−	2.74784i
$261$	0.910133			0.0563358
$262$			28.9504i			1.78856i
$263$			10.5451i			0.650238i	0.945673	+	0.325119i	$0.105404\pi$
$263$			10.5451i			0.650238i	−0.945673	+	0.325119i	$0.894596\pi$
$264$	−3.18779			−0.196195
$265$	17.7247	−	17.0990i	1.08882	−	1.05038i
$266$	5.01478			0.307476
$267$			5.31999i			0.325578i
$268$			47.5962i			2.90740i
$269$	7.39386			0.450811			0.225406	−	0.974265i	$-0.427629\pi$
$269$	7.39386			0.450811			0.225406	+	0.974265i	$0.427629\pi$
$270$	13.9550	+	14.4657i	0.849273	+	0.880352i
$271$	11.4813			0.697442			0.348721	−	0.937227i	$-0.386616\pi$
$271$	11.4813			0.697442			0.348721	+	0.937227i	$0.386616\pi$
$272$			14.0222i			0.850223i
$273$			9.74624i			0.589869i
$274$	−25.7824			−1.55757
$275$	−0.179625	+	4.99677i	−0.0108318	+	0.301317i
$276$	14.8426			0.893419
$277$		−	12.1627i		−	0.730787i	−0.930853	−	0.365393i	$-0.880934\pi$
$277$		−	12.1627i		−	0.730787i	0.930853	−	0.365393i	$-0.119066\pi$
$278$			33.2948i			1.99689i
$279$	9.76688			0.584728
$280$	15.3589	+	15.9209i	0.917869	+	0.951458i
$281$	−19.7102			−1.17581			−0.587905	−	0.808930i	$-0.700047\pi$
$281$	−19.7102			−1.17581			−0.587905	+	0.808930i	$0.700047\pi$
$282$		−	15.9399i		−	0.949207i
$283$		−	1.14741i		−	0.0682067i	−0.999418	−	0.0341034i	$-0.989142\pi$
$283$		−	1.14741i		−	0.0682067i	0.999418	−	0.0341034i	$-0.0108575\pi$
$284$	41.1185			2.43993
$285$	1.06403	−	1.02646i	0.0630274	−	0.0608024i
$286$	17.5568			1.03816
$287$			13.9724i			0.824764i
$288$			0.676841i			0.0398832i
$289$	3.64852			0.214619
$290$	1.39671	−	1.34740i	0.0820175	−	0.0791221i
$291$	3.96537			0.232454
$292$		−	62.1325i		−	3.63603i
$293$		−	12.3256i		−	0.720066i	−0.932939	−	0.360033i	$-0.882765\pi$
$293$		−	12.3256i		−	0.720066i	0.932939	−	0.360033i	$-0.117235\pi$
$294$	4.50761			0.262889
$295$	19.5196	+	20.2339i	1.13648	+	1.17806i
$296$	18.2354			1.05991
$297$			3.67803i			0.213421i
$298$		−	19.3275i		−	1.11961i
$299$	−40.5931			−2.34756
$300$	13.1251	+	0.471827i	0.757781	+	0.0272409i
$301$	4.91741			0.283435
$302$			7.47846i			0.430337i
$303$			3.27049i			0.187885i
$304$	−3.83754			−0.220098
$305$	11.8717	+	12.3061i	0.679770	+	0.704646i
$306$	22.8863			1.30832
$307$		−	19.9438i		−	1.13825i	−0.822250	−	0.569127i	$-0.807281\pi$
$307$		−	19.9438i		−	1.13825i	0.822250	−	0.569127i	$-0.192719\pi$
$308$			8.15191i			0.464498i
$309$	−0.318373			−0.0181116
$310$	14.9884	−	14.4593i	0.851287	−	0.821234i
$311$	13.2117			0.749167			0.374584	−	0.927193i	$-0.377786\pi$
$311$	13.2117			0.749167			0.374584	+	0.927193i	$0.377786\pi$
$312$		−	22.9006i		−	1.29649i
$313$		−	16.8574i		−	0.952835i	−0.879219	−	0.476417i	$-0.841935\pi$
$313$		−	16.8574i		−	0.952835i	0.879219	−	0.476417i	$-0.158065\pi$
$314$	42.4166			2.39371
$315$	8.46290	−	8.16414i	0.476830	−	0.459997i
$316$	15.7362			0.885230
$317$			4.62971i			0.260030i	0.991512	+	0.130015i	$0.0415026\pi$
$317$			4.62971i			0.260030i	−0.991512	+	0.130015i	$0.958497\pi$
$318$		−	17.7972i		−	0.998020i
$319$	0.355126			0.0198832
$320$	12.9174	+	13.3901i	0.722105	+	0.748530i
$321$	−9.46884			−0.528499
$322$		−	28.3365i		−	1.57913i
$323$		−	3.65397i		−	0.203312i
$324$	−20.8838			−1.16021
$325$	−35.8960	−	1.29040i	−1.99115	−	0.0715785i
$326$	−59.9718			−3.32153
$327$		−	2.13483i		−	0.118056i
$328$		−	32.8307i		−	1.81277i
$329$	−20.2414			−1.11595
$330$	2.50861	+	2.60041i	0.138094	+	0.143148i
$331$	−0.486396			−0.0267347			−0.0133674	−	0.999911i	$-0.504255\pi$
$331$	−0.486396			−0.0267347			−0.0133674	+	0.999911i	$0.504255\pi$
$332$			38.9431i			2.13728i
$333$		−	9.69317i		−	0.531182i
$334$	15.0604			0.824067
$335$	19.2801	−	18.5995i	1.05339	−	1.01620i
$336$	5.20635			0.284029
$337$			29.7902i			1.62278i	0.584507	+	0.811388i	$0.301288\pi$
$337$			29.7902i			1.62278i	−0.584507	+	0.811388i	$0.698712\pi$
$338$			94.3541i			5.13219i
$339$	−11.3936			−0.618814
$340$	23.3612	−	22.5365i	1.26694	−	1.22221i
$341$	3.81095			0.206375
$342$			6.26342i			0.338687i
$343$		−	20.0875i		−	1.08463i
$344$	−11.5544			−0.622969
$345$	−5.80014	−	6.01239i	−0.312269	−	0.323696i
$346$	−0.798852			−0.0429465
$347$			20.5442i			1.10287i	0.834217	+	0.551436i	$0.185920\pi$
$347$			20.5442i			1.10287i	−0.834217	+	0.551436i	$0.814080\pi$
$348$		−	0.932819i		−	0.0500043i
$349$	0.864399			0.0462702			0.0231351	−	0.999732i	$-0.492635\pi$
$349$	0.864399			0.0462702			0.0231351	+	0.999732i	$0.492635\pi$
$350$	0.900781	−	25.0577i	0.0481488	−	1.33939i
$351$	−26.4223			−1.41032
$352$			0.264097i			0.0140764i
$353$			27.2206i			1.44881i	0.689377	+	0.724403i	$0.257884\pi$
$353$			27.2206i			1.44881i	−0.689377	+	0.724403i	$0.742116\pi$
$354$	20.3167			1.07982
$355$	−16.0681	−	16.6562i	−0.852809	−	0.884017i
$356$	−31.9661			−1.69420
$357$			4.95730i			0.262368i
$358$		−	23.2750i		−	1.23012i
$359$	3.80431			0.200784			0.100392	−	0.994948i	$-0.467990\pi$
$359$	3.80431			0.200784			0.100392	+	0.994948i	$0.467990\pi$
$360$	−19.8851	+	19.1831i	−1.04804	+	1.01104i
$361$	1.00000			0.0526316
$362$			42.4676i			2.23205i
$363$			0.661177i			0.0347028i
$364$	−58.5620			−3.06948
$365$	−25.1684	+	24.2799i	−1.31738	+	1.27087i
$366$	12.3565			0.645882
$367$			10.9378i			0.570947i	0.958387	+	0.285474i	$0.0921509\pi$
$367$			10.9378i			0.570947i	−0.958387	+	0.285474i	$0.907849\pi$
$368$			21.6844i			1.13038i
$369$	−17.4514			−0.908483
$370$	−14.3502	−	14.8753i	−0.746031	−	0.773332i
$371$	−22.6000			−1.17333
$372$		−	10.0103i		−	0.519011i
$373$		−	23.0273i		−	1.19231i	−0.802870	−	0.596155i	$-0.796695\pi$
$373$		−	23.0273i		−	1.19231i	0.802870	−	0.596155i	$-0.203305\pi$
$374$	8.93004			0.461762
$375$	−4.93788	−	5.50107i	−0.254991	−	0.284074i
$376$	47.5609			2.45277
$377$			2.55117i			0.131392i
$378$		−	18.4445i		−	0.948682i
$379$	−19.9159			−1.02301			−0.511506	−	0.859280i	$-0.670912\pi$
$379$	−19.9159			−1.02301			−0.511506	+	0.859280i	$0.670912\pi$
$380$	6.16768	+	6.39338i	0.316395	+	0.327974i
$381$	6.82520			0.349666
$382$		−	14.0854i		−	0.720674i
$383$			5.37720i			0.274762i	0.990518	+	0.137381i	$0.0438685\pi$
$383$			5.37720i			0.274762i	−0.990518	+	0.137381i	$0.956132\pi$
$384$	13.0956			0.668284
$385$	3.30215	−	3.18558i	0.168293	−	0.162352i
$386$	−30.8734			−1.57141
$387$			6.14181i			0.312206i
$388$			23.8266i			1.20961i
$389$	−13.7419			−0.696741			−0.348370	−	0.937357i	$-0.613265\pi$
$389$	−13.7419			−0.696741			−0.348370	+	0.937357i	$0.613265\pi$
$390$	−18.6809	+	18.0214i	−0.945944	+	0.912550i
$391$	−20.6471			−1.04417
$392$			13.4496i			0.679310i
$393$		−	7.83219i		−	0.395082i
$394$	1.34868			0.0679458
$395$	−6.14934	−	6.37437i	−0.309407	−	0.320729i
$396$	−10.1817			−0.511648
$397$		−	3.52041i		−	0.176684i	−0.996090	−	0.0883421i	$-0.971843\pi$
$397$		−	3.52041i		−	0.176684i	0.996090	−	0.0883421i	$-0.0281569\pi$
$398$		−	45.1865i		−	2.26500i
$399$	−1.35669			−0.0679194
$400$	−0.689319	+	19.1753i	−0.0344660	+	0.958765i
$401$	−25.3417			−1.26550			−0.632751	−	0.774355i	$-0.718074\pi$
$401$	−25.3417			−1.26550			−0.632751	+	0.774355i	$0.718074\pi$
$402$		−	19.3590i		−	0.965539i
$403$			27.3773i			1.36376i
$404$	−19.6513			−0.977690
$405$	8.16092	+	8.45956i	0.405519	+	0.420359i
$406$	−1.78088			−0.0883835
$407$		−	3.78219i		−	0.187476i
$408$		−	11.6481i		−	0.576666i
$409$	−15.0936			−0.746332			−0.373166	−	0.927765i	$-0.621728\pi$
$409$	−15.0936			−0.746332			−0.373166	+	0.927765i	$0.621728\pi$
$410$	−26.7813	+	25.8358i	−1.32263	+	1.27594i
$411$	6.97514			0.344058
$412$		−	1.91300i		−	0.0942466i
$413$		−	25.7993i		−	1.26950i
$414$	35.3921			1.73943
$415$	15.7749	−	15.2181i	0.774362	−	0.747025i
$416$	−1.89723			−0.0930195
$417$		−	9.00751i		−	0.441100i
$418$			2.44393i			0.119537i
$419$	27.6709			1.35181			0.675907	−	0.736987i	$-0.263752\pi$
$419$	27.6709			1.35181			0.675907	+	0.736987i	$0.263752\pi$
$420$	−8.36763	−	8.67384i	−0.408299	−	0.423240i
$421$	−11.1983			−0.545772			−0.272886	−	0.962046i	$-0.587978\pi$
$421$	−11.1983			−0.545772			−0.272886	+	0.962046i	$0.587978\pi$
$422$			47.6378i			2.31897i
$423$		−	25.2814i		−	1.22922i
$424$	53.1028			2.57890
$425$	−18.2580	−	0.656345i	−0.885645	−	0.0318374i
$426$	−16.7243			−0.810294
$427$		−	15.6910i		−	0.759339i
$428$		−	56.8952i		−	2.75013i
$429$	−4.74979			−0.229322
$430$	9.09260	+	9.42534i	0.438484	+	0.454530i
$431$	2.75670			0.132786			0.0663928	−	0.997794i	$-0.478851\pi$
$431$	2.75670			0.132786			0.0663928	+	0.997794i	$0.478851\pi$
$432$			14.1146i			0.679087i
$433$		−	36.0623i		−	1.73304i	−0.499138	−	0.866522i	$-0.666350\pi$
$433$		−	36.0623i		−	1.73304i	0.499138	−	0.866522i	$-0.333650\pi$
$434$	−19.1111			−0.917361
$435$	−0.377863	+	0.364524i	−0.0181172	+	0.0174776i
$436$	12.8275			0.614326
$437$		−	5.65061i		−	0.270305i
$438$			25.2714i			1.20751i
$439$	18.5497			0.885330			0.442665	−	0.896687i	$-0.354033\pi$
$439$	18.5497			0.885330			0.442665	+	0.896687i	$0.354033\pi$
$440$	−7.75901	+	7.48509i	−0.369896	+	0.356838i
$441$	7.14926			0.340441
$442$			64.1520i			3.05140i
$443$			31.6783i			1.50508i	0.658547	+	0.752540i	$0.271171\pi$
$443$			31.6783i			1.50508i	−0.658547	+	0.752540i	$0.728829\pi$
$444$	−9.93478			−0.471484
$445$	12.4916	+	12.9487i	0.592159	+	0.613828i
$446$	−20.4952			−0.970474
$447$			5.22882i			0.247315i
$448$		−	17.0731i		−	0.806628i
$449$	3.09352			0.145992			0.0729961	−	0.997332i	$-0.476744\pi$
$449$	3.09352			0.145992			0.0729961	+	0.997332i	$0.476744\pi$
$450$	31.2969	+	1.12507i	1.47535	+	0.0530362i
$451$	−6.80938			−0.320641
$452$		−	68.4603i		−	3.22010i
$453$		−	2.02321i		−	0.0950587i
$454$	−9.04030			−0.424282
$455$	22.8847	+	23.7221i	1.07285	+	1.11211i
$456$	3.18779			0.149282
$457$			34.3303i			1.60590i	0.596045	+	0.802951i	$0.296738\pi$
$457$			34.3303i			1.60590i	−0.596045	+	0.802951i	$0.703262\pi$
$458$			33.7409i			1.57661i
$459$	−13.4394			−0.627297
$460$	36.1265	−	34.8512i	1.68441	−	1.62494i
$461$	4.96910			0.231434			0.115717	−	0.993282i	$-0.463083\pi$
$461$	4.96910			0.231434			0.115717	+	0.993282i	$0.463083\pi$
$462$		−	3.31566i		−	0.154258i
$463$		−	23.6126i		−	1.09737i	−0.836029	−	0.548686i	$-0.815128\pi$
$463$		−	23.6126i		−	1.09737i	0.836029	−	0.548686i	$-0.184872\pi$
$464$	1.36281			0.0632668
$465$	−4.05495	+	3.91180i	−0.188044	+	0.181405i
$466$	−19.6794			−0.911630
$467$			7.65725i			0.354335i	0.984181	+	0.177168i	$0.0566935\pi$
$467$			7.65725i			0.354335i	−0.984181	+	0.177168i	$0.943306\pi$
$468$		−	73.1434i		−	3.38106i
$469$	−24.5832			−1.13515
$470$	−37.4277	−	38.7973i	−1.72641	−	1.78959i
$471$	−11.4753			−0.528755
$472$			60.6202i			2.79027i
$473$			2.39648i			0.110190i
$474$	−6.40045			−0.293982
$475$	0.179625	−	4.99677i	0.00824178	−	0.229268i
$476$	−29.7868			−1.36528
$477$		−	28.2272i		−	1.29244i
$478$		−	57.3027i		−	2.62096i
$479$	21.9643			1.00358			0.501788	−	0.864991i	$-0.332676\pi$
$479$	21.9643			1.00358			0.501788	+	0.864991i	$0.332676\pi$
$480$	−0.271086	−	0.281007i	−0.0123733	−	0.0128261i
$481$	27.1707			1.23888
$482$		−	11.3838i		−	0.518517i
$483$			7.66612i			0.348821i
$484$	−3.97280			−0.180582
$485$	9.65162	−	9.31089i	0.438257	−	0.422786i
$486$	35.4607			1.60853
$487$			15.6417i			0.708795i	0.935095	+	0.354398i	$0.115314\pi$
$487$			15.6417i			0.708795i	−0.935095	+	0.354398i	$0.884686\pi$
$488$			36.8688i			1.66897i
$489$	16.2247			0.733705
$490$	10.9714	−	10.5841i	0.495638	−	0.478140i
$491$	19.5676			0.883071			0.441536	−	0.897244i	$-0.354434\pi$
$491$	19.5676			0.883071			0.441536	+	0.897244i	$0.354434\pi$
$492$			17.8864i			0.806380i
$493$			1.29762i			0.0584418i
$494$	−17.5568			−0.789918
$495$	3.97876	+	4.12436i	0.178832	+	0.185376i
$496$	14.6247			0.656667
$497$			21.2375i			0.952631i
$498$		−	15.8395i		−	0.709784i
$499$	−33.1194			−1.48263			−0.741315	−	0.671157i	$-0.765797\pi$
$499$	−33.1194			−1.48263			−0.741315	+	0.671157i	$0.765797\pi$
$500$	33.0542	−	29.6701i	1.47823	−	1.32689i
$501$	−4.07441			−0.182031
$502$		−	47.1731i		−	2.10544i
$503$		−	28.6793i		−	1.27874i	−0.768897	−	0.639372i	$-0.779194\pi$
$503$		−	28.6793i		−	1.27874i	0.768897	−	0.639372i	$-0.220806\pi$
$504$	25.3546			1.12938
$505$	7.67928	+	7.96030i	0.341723	+	0.354229i
$506$	13.8097			0.613916
$507$		−	25.5264i		−	1.13367i
$508$			41.0104i			1.81954i
$509$	12.8283			0.568604			0.284302	−	0.958735i	$-0.408238\pi$
$509$	12.8283			0.568604			0.284302	+	0.958735i	$0.408238\pi$
$510$	−9.50180	+	9.16636i	−0.420747	+	0.405893i
$511$	32.0911			1.41963
$512$			38.0180i			1.68017i
$513$		−	3.67803i		−	0.162389i
$514$	−40.4490			−1.78413
$515$	−0.774911	+	0.747555i	−0.0341467	+	0.0329412i
$516$	6.29490			0.277117
$517$		−	9.86457i		−	0.433843i
$518$			18.9668i			0.833355i
$519$	0.216120			0.00948662
$520$	−53.7717	−	55.7394i	−2.35805	−	2.44434i
$521$	−7.62421			−0.334023			−0.167011	−	0.985955i	$-0.553412\pi$
$521$	−7.62421			−0.334023			−0.167011	+	0.985955i	$0.553412\pi$
$522$		−	2.22430i		−	0.0973551i
$523$			2.29309i			0.100270i	0.998742	+	0.0501349i	$0.0159651\pi$
$523$			2.29309i			0.100270i	−0.998742	+	0.0501349i	$0.984035\pi$
$524$	47.0611			2.05587
$525$	−0.243696	+	6.77907i	−0.0106358	+	0.295863i
$526$	25.7715			1.12369
$527$			13.9251i			0.606587i
$528$			2.53729i			0.110421i
$529$	−8.92937			−0.388233
$530$	−41.7888	−	43.3181i	−1.81519	−	1.88162i
$531$	32.2231			1.39837
$532$		−	8.15191i		−	0.353430i
$533$		−	48.9175i		−	2.11885i
$534$	13.0017			0.562638
$535$	−23.0469	+	22.2333i	−0.996405	+	0.961230i
$536$	57.7627			2.49497
$537$			6.29677i			0.271726i
$538$		−	18.0701i		−	0.779056i
$539$	2.78958			0.120156
$540$	23.5150	−	22.6849i	1.01193	−	0.976203i
$541$	31.1807			1.34056			0.670282	−	0.742107i	$-0.266173\pi$
$541$	31.1807			1.34056			0.670282	+	0.742107i	$0.266173\pi$
$542$		−	28.0596i		−	1.20526i
$543$		−	11.4891i		−	0.493045i
$544$	−0.965004			−0.0413742
$545$	−5.01269	−	5.19612i	−0.214720	−	0.222577i
$546$	23.8191			1.01937
$547$		−	14.5145i		−	0.620594i	−0.950640	−	0.310297i	$-0.899571\pi$
$547$		−	14.5145i		−	0.620594i	0.950640	−	0.310297i	$-0.100429\pi$
$548$			41.9114i			1.79036i
$549$	19.5979			0.836417
$550$	12.2118	+	0.438992i	0.520712	+	0.0187187i
$551$	−0.355126			−0.0151289
$552$		−	18.0130i		−	0.766682i
$553$			8.12767i			0.345624i
$554$	−29.7248			−1.26289
$555$	3.88228	+	4.02435i	0.164794	+	0.170824i
$556$	54.1232			2.29534
$557$			9.20769i			0.390142i	0.980789	+	0.195071i	$0.0624938\pi$
$557$			9.20769i			0.390142i	−0.980789	+	0.195071i	$0.937506\pi$
$558$		−	23.8696i		−	1.01048i
$559$	−17.2159			−0.728156
$560$	12.6721	−	12.2248i	0.535495	−	0.516591i
$561$	−2.41592			−0.102000
$562$			48.1703i			2.03194i
$563$		−	29.1920i		−	1.23030i	−0.788411	−	0.615149i	$-0.789096\pi$
$563$		−	29.1920i		−	1.23030i	0.788411	−	0.615149i	$-0.210904\pi$
$564$	−25.9115			−1.09107
$565$	−27.7317	+	26.7527i	−1.16668	+	1.12549i
$566$	−2.80420			−0.117869
$567$		−	10.7864i		−	0.452986i
$568$		−	49.9014i		−	2.09381i
$569$	−38.8786			−1.62988			−0.814939	−	0.579547i	$-0.803229\pi$
$569$	−38.8786			−1.62988			−0.814939	+	0.579547i	$0.803229\pi$
$570$	−2.50861	−	2.60041i	−0.105074	−	0.108919i
$571$	4.76443			0.199385			0.0996926	−	0.995018i	$-0.468214\pi$
$571$	4.76443			0.199385			0.0996926	+	0.995018i	$0.468214\pi$
$572$		−	28.5399i		−	1.19332i
$573$			3.81065i			0.159192i
$574$	34.1475			1.42529
$575$	−28.2348	−	1.01499i	−1.17747	−	0.0423281i
$576$	21.3242			0.888507
$577$		−	18.9048i		−	0.787018i	−0.919321	−	0.393509i	$-0.871261\pi$
$577$		−	18.9048i		−	0.787018i	0.919321	−	0.393509i	$-0.128739\pi$
$578$		−	8.91674i		−	0.370887i
$579$	8.35243			0.347115
$580$	−2.19031	−	2.27046i	−0.0909475	−	0.0942756i
$581$	−20.1139			−0.834465
$582$		−	9.69110i		−	0.401709i
$583$		−	11.0140i		−	0.456154i
$584$	−75.4040			−3.12024
$585$	−29.6287	+	28.5828i	−1.22500	+	1.18175i
$586$	−30.1228			−1.24436
$587$		−	10.8509i		−	0.447866i	−0.974605	−	0.223933i	$-0.928110\pi$
$587$		−	10.8509i		−	0.447866i	0.974605	−	0.223933i	$-0.0718896\pi$
$588$		−	7.32746i		−	0.302180i
$589$	−3.81095			−0.157028
$590$	49.4503	−	47.7046i	2.03584	−	1.96397i
$591$	−0.364871			−0.0150088
$592$		−	14.5143i		−	0.596534i
$593$		−	2.57634i		−	0.105798i	−0.998600	−	0.0528988i	$-0.983154\pi$
$593$		−	2.57634i		−	0.105798i	0.998600	−	0.0528988i	$-0.0168461\pi$
$594$	8.98884			0.368817
$595$	11.6400	+	12.0659i	0.477193	+	0.494656i
$596$	−31.4183			−1.28694
$597$			12.2247i			0.500324i
$598$			99.2066i			4.05686i
$599$	3.39709			0.138801			0.0694007	−	0.997589i	$-0.477891\pi$
$599$	3.39709			0.138801			0.0694007	+	0.997589i	$0.477891\pi$
$600$	0.572608	−	15.9287i	0.0233766	−	0.650285i
$601$	14.8796			0.606952			0.303476	−	0.952839i	$-0.401853\pi$
$601$	14.8796			0.606952			0.303476	+	0.952839i	$0.401853\pi$
$602$		−	12.0178i		−	0.489810i
$603$		−	30.7042i		−	1.25037i
$604$	12.1568			0.494654
$605$	1.55248	+	1.60929i	0.0631172	+	0.0654269i
$606$	7.99286			0.324688
$607$			22.4464i			0.911073i	0.890217	+	0.455537i	$0.150553\pi$
$607$			22.4464i			0.911073i	−0.890217	+	0.455537i	$0.849447\pi$
$608$		−	0.264097i		−	0.0107106i
$609$	0.481796			0.0195234
$610$	30.0753	−	29.0136i	1.21771	−	1.17473i
$611$	70.8655			2.86691
$612$		−	37.2035i		−	1.50386i
$613$		−	10.6228i		−	0.429051i	−0.976718	−	0.214526i	$-0.931179\pi$
$613$		−	10.6228i		−	0.429051i	0.976718	−	0.214526i	$-0.0688205\pi$
$614$	−48.7413			−1.96704
$615$	7.24536	−	6.98958i	0.292161	−	0.281847i
$616$	9.89315			0.398606
$617$		−	24.4015i		−	0.982369i	−0.871056	−	0.491184i	$-0.836564\pi$
$617$		−	24.4015i		−	0.982369i	0.871056	−	0.491184i	$-0.163436\pi$
$618$			0.778081i			0.0312990i
$619$	−21.8969			−0.880110			−0.440055	−	0.897971i	$-0.645041\pi$
$619$	−21.8969			−0.880110			−0.440055	+	0.897971i	$0.645041\pi$
$620$	−23.5047	−	24.3649i	−0.943973	−	0.978517i
$621$	−20.7831			−0.833997
$622$		−	32.2885i		−	1.29465i
$623$		−	16.5103i		−	0.661472i
$624$	−18.2275			−0.729684
$625$	−24.9355	−	1.79509i	−0.997419	−	0.0718038i
$626$	−41.1982			−1.64661
$627$		−	0.661177i		−	0.0264049i
$628$		−	68.9515i		−	2.75146i
$629$	13.8200			0.551040
$630$	−19.9526	−	20.6827i	−0.794930	−	0.824020i
$631$	39.9982			1.59230			0.796152	−	0.605097i	$-0.206865\pi$
$631$	39.9982			1.59230			0.796152	+	0.605097i	$0.206865\pi$
$632$		−	19.0974i		−	0.759655i
$633$		−	12.8878i		−	0.512246i
$634$	11.3147			0.449364
$635$	16.6124	−	16.0259i	0.659242	−	0.635969i
$636$	−28.9308			−1.14718
$637$			20.0399i			0.794010i
$638$		−	0.867904i		−	0.0343606i
$639$	−26.5254			−1.04933
$640$	31.8745	−	30.7492i	1.25995	−	1.21547i
$641$	27.9035			1.10212			0.551062	−	0.834465i	$-0.314223\pi$
$641$	27.9035			1.10212			0.551062	+	0.834465i	$0.314223\pi$
$642$			23.1412i			0.913310i
$643$			2.45001i			0.0966191i	0.998832	+	0.0483096i	$0.0153834\pi$
$643$			2.45001i			0.0966191i	−0.998832	+	0.0483096i	$0.984617\pi$
$644$	−46.0632			−1.81515
$645$	−2.45990	−	2.54992i	−0.0968584	−	0.100403i
$646$	−8.93004			−0.351348
$647$			2.23685i			0.0879398i	0.999033	+	0.0439699i	$0.0140006\pi$
$647$			2.23685i			0.0879398i	−0.999033	+	0.0439699i	$0.985999\pi$
$648$			25.3446i			0.995630i
$649$	12.5732			0.493541
$650$	−3.15365	+	87.7274i	−0.123696	+	3.44095i
$651$	5.17028			0.202639
$652$			97.4888i			3.81796i
$653$			47.2782i			1.85014i	0.379797	+	0.925070i	$0.375994\pi$
$653$			47.2782i			1.85014i	−0.379797	+	0.925070i	$0.624006\pi$
$654$	−5.21738			−0.204016
$655$	−18.3904	−	19.0634i	−0.718572	−	0.744867i
$656$	−26.1313			−1.02025
$657$			40.0815i			1.56373i
$658$			49.4686i			1.92849i
$659$	−17.2503			−0.671975			−0.335988	−	0.941866i	$-0.609070\pi$
$659$	−17.2503			−0.671975			−0.335988	+	0.941866i	$0.609070\pi$
$660$	4.22716	−	4.07793i	0.164542	−	0.158733i
$661$	−3.06333			−0.119150			−0.0595749	−	0.998224i	$-0.518975\pi$
$661$	−3.06333			−0.119150			−0.0595749	+	0.998224i	$0.518975\pi$
$662$			1.18872i			0.0462008i
$663$		−	17.3556i		−	0.674035i
$664$	47.2613			1.83409
$665$	−3.30215	+	3.18558i	−0.128052	+	0.123531i
$666$	−23.6894			−0.917947
$667$			2.00668i			0.0776989i
$668$		−	24.4818i		−	0.947230i
$669$	5.54473			0.214372
$670$	−45.4559	−	47.1193i	−1.75611	−	1.82038i
$671$	7.64692			0.295206
$672$			0.358298i			0.0138217i
$673$		−	8.46566i		−	0.326327i	−0.986599	−	0.163164i	$-0.947830\pi$
$673$		−	8.46566i		−	0.326327i	0.986599	−	0.163164i	$-0.0521698\pi$
$674$	72.8052			2.80435
$675$	−18.3783	−	0.660667i	−0.707380	−	0.0254291i
$676$	153.380			5.89923
$677$		−	21.5907i		−	0.829797i	−0.909868	−	0.414899i	$-0.863817\pi$
$677$		−	21.5907i		−	0.829797i	0.909868	−	0.414899i	$-0.136183\pi$
$678$			27.8451i			1.06938i
$679$	−12.3063			−0.472274
$680$	−27.3503	−	28.3512i	−1.04884	−	1.08722i
$681$	2.44575			0.0937213
$682$		−	9.31371i		−	0.356640i
$683$		−	9.54718i		−	0.365313i	−0.983177	−	0.182656i	$-0.941530\pi$
$683$		−	9.54718i		−	0.365313i	0.983177	−	0.182656i	$-0.0584695\pi$
$684$	10.1817			0.389306
$685$	16.9773	−	16.3780i	0.648670	−	0.625771i
$686$	−49.0926			−1.87436
$687$		−	9.12821i		−	0.348263i
$688$			9.19658i			0.350616i
$689$	79.1229			3.01434
$690$	−14.6939	+	14.1751i	−0.559386	+	0.539639i
$691$	−37.5876			−1.42990			−0.714951	−	0.699175i	$-0.753551\pi$
$691$	−37.5876			−1.42990			−0.714951	+	0.699175i	$0.753551\pi$
$692$			1.29860i			0.0493652i
$693$		−	5.25878i		−	0.199764i
$694$	50.2087			1.90590
$695$	−21.1501	−	21.9241i	−0.802269	−	0.831627i
$696$	−1.13207			−0.0429109
$697$		−	24.8813i		−	0.942445i
$698$		−	2.11253i		−	0.0799605i
$699$	5.32403			0.201373
$700$	−40.7332	−	1.46429i	−1.53957	−	0.0553450i
$701$	−3.35187			−0.126598			−0.0632992	−	0.997995i	$-0.520162\pi$
$701$	−3.35187			−0.126598			−0.0632992	+	0.997995i	$0.520162\pi$
$702$			64.5744i			2.43720i
$703$			3.78219i			0.142648i
$704$	8.32051			0.313591
$705$	10.1256	+	10.4962i	0.381353	+	0.395308i
$706$	66.5252			2.50371
$707$		−	10.1498i		−	0.381723i
$708$		−	33.0263i		−	1.24121i
$709$	−25.0089			−0.939227			−0.469614	−	0.882872i	$-0.655607\pi$
$709$	−25.0089			−0.939227			−0.469614	+	0.882872i	$0.655607\pi$
$710$	−40.7065	+	39.2695i	−1.52769	+	1.47376i
$711$	−10.1514			−0.380707
$712$			38.7940i			1.45387i
$713$			21.5342i			0.806462i
$714$	12.1153			0.453404
$715$	−11.5609	+	11.1527i	−0.432352	+	0.417089i
$716$	−37.8353			−1.41397
$717$			15.5026i			0.578954i
$718$		−	9.29748i		−	0.346979i
$719$	−5.33605			−0.199001			−0.0995005	−	0.995038i	$-0.531724\pi$
$719$	−5.33605			−0.199001			−0.0995005	+	0.995038i	$0.531724\pi$
$720$	15.2686	+	15.8274i	0.569028	+	0.589851i
$721$	0.988053			0.0367970
$722$		−	2.44393i		−	0.0909537i
$723$			3.07975i			0.114537i
$724$	69.0344			2.56564
$725$	−0.0637897	+	1.77448i	−0.00236909	+	0.0659027i
$726$	1.61587			0.0599706
$727$			22.9397i			0.850788i	0.905008	+	0.425394i	$0.139864\pi$
$727$			22.9397i			0.850788i	−0.905008	+	0.425394i	$0.860136\pi$
$728$			71.0708i			2.63406i
$729$	6.17663			0.228764
$730$	59.3385	+	61.5099i	2.19622	+	2.27659i
$731$	−8.75666			−0.323877
$732$		−	20.0864i		−	0.742414i
$733$		−	42.2613i		−	1.56096i	−0.625182	−	0.780479i	$-0.714975\pi$
$733$		−	42.2613i		−	1.56096i	0.625182	−	0.780479i	$-0.285025\pi$
$734$	26.7312			0.986665
$735$	−2.96819	+	2.86340i	−0.109483	+	0.105618i
$736$	−1.49231			−0.0550073
$737$		−	11.9805i		−	0.441308i
$738$			42.6500i			1.56997i
$739$	−12.1117			−0.445537			−0.222768	−	0.974871i	$-0.571509\pi$
$739$	−12.1117			−0.445537			−0.222768	+	0.974871i	$0.571509\pi$
$740$	−24.1810	+	23.3274i	−0.888911	+	0.857531i
$741$	4.74979			0.174488
$742$			55.2328i			2.02766i
$743$			25.2981i			0.928096i	0.885810	+	0.464048i	$0.153604\pi$
$743$			25.2981i			0.928096i	−0.885810	+	0.464048i	$0.846396\pi$
$744$	−12.1485			−0.445386
$745$	12.2775	+	12.7268i	0.449814	+	0.466275i
$746$	−56.2772			−2.06045
$747$		−	25.1221i		−	0.919170i
$748$		−	14.5165i		−	0.530775i
$749$	29.3861			1.07374
$750$	−13.4442	+	12.0678i	−0.490914	+	0.440655i
$751$	−4.19248			−0.152986			−0.0764928	−	0.997070i	$-0.524372\pi$
$751$	−4.19248			−0.152986			−0.0764928	+	0.997070i	$0.524372\pi$
$752$		−	37.8557i		−	1.38045i
$753$			12.7621i			0.465078i
$754$	6.23488			0.227061
$755$	−4.75060	−	4.92444i	−0.172892	−	0.179219i
$756$	−29.9829			−1.09047
$757$			7.35769i			0.267420i	0.991021	+	0.133710i	$0.0426890\pi$
$757$			7.35769i			0.267420i	−0.991021	+	0.133710i	$0.957311\pi$
$758$			48.6731i			1.76789i
$759$	−3.73605			−0.135610
$760$	7.75901	−	7.48509i	0.281449	−	0.271513i
$761$	29.4890			1.06898			0.534489	−	0.845176i	$-0.320504\pi$
$761$	29.4890			1.06898			0.534489	+	0.845176i	$0.320504\pi$
$762$		−	16.6803i		−	0.604264i
$763$			6.62533i			0.239853i
$764$	−22.8970			−0.828383
$765$	−15.0703	+	14.5383i	−0.544867	+	0.525632i
$766$	13.1415			0.474822
$767$			90.3238i			3.26140i
$768$		−	21.0022i		−	0.757851i
$769$	42.6293			1.53725			0.768626	−	0.639699i	$-0.220941\pi$
$769$	42.6293			1.53725			0.768626	+	0.639699i	$0.220941\pi$
$770$	−7.78533	−	8.07023i	−0.280564	−	0.290831i
$771$	10.9430			0.394103
$772$			50.1870i			1.80627i
$773$			9.22141i			0.331671i	0.986153	+	0.165836i	$0.0530321\pi$
$773$			9.22141i			0.331671i	−0.986153	+	0.165836i	$0.946968\pi$
$774$	15.0102			0.539529
$775$	−0.684544	+	19.0425i	−0.0245895	+	0.684025i
$776$	28.9160			1.03802
$777$		−	5.13126i		−	0.184083i
$778$			33.5842i			1.20405i
$779$	6.80938			0.243972
$780$	29.2952	+	30.3672i	1.04894	+	1.08732i
$781$	−10.3500			−0.370352
$782$			50.4602i			1.80445i
$783$			1.30616i			0.0466785i
$784$	10.7051			0.382326
$785$	−27.9307	+	26.9446i	−0.996888	+	0.961695i
$786$	−19.1413			−0.682749
$787$		−	31.6768i		−	1.12916i	−0.825380	−	0.564578i	$-0.809039\pi$
$787$		−	31.6768i		−	1.12916i	0.825380	−	0.564578i	$-0.190961\pi$
$788$		−	2.19239i		−	0.0781007i
$789$	−6.97217			−0.248216
$790$	−15.5785	+	15.0286i	−0.554259	+	0.534692i
$791$	35.3594			1.25723
$792$			12.3565i			0.439068i
$793$			54.9343i			1.95077i
$794$	−8.60364			−0.305332
$795$	11.3055	+	11.7192i	0.400964	+	0.415637i
$796$	−73.4542			−2.60352
$797$		−	47.3248i		−	1.67633i	−0.545417	−	0.838165i	$-0.683629\pi$
$797$		−	47.3248i		−	1.67633i	0.545417	−	0.838165i	$-0.316371\pi$
$798$			3.31566i			0.117373i
$799$	36.0448			1.27517
$800$	−1.31964	−	0.0474386i	−0.0466561	−	0.00167721i
$801$	20.6212			0.728616
$802$			61.9333i			2.18694i
$803$			15.6395i			0.551905i
$804$	−31.4695			−1.10985
$805$	18.0004	+	18.6592i	0.634432	+	0.657649i
$806$	66.9082			2.35674
$807$			4.88865i			0.172089i
$808$			23.8488i			0.838999i
$809$	22.6951			0.797917			0.398959	−	0.916969i	$-0.369372\pi$
$809$	22.6951			0.797917			0.398959	+	0.916969i	$0.369372\pi$
$810$	20.6746	−	19.9447i	0.726431	−	0.700786i
$811$	−40.8525			−1.43453			−0.717263	−	0.696802i	$-0.754605\pi$
$811$	−40.8525			−1.43453			−0.717263	+	0.696802i	$0.754605\pi$
$812$			2.89496i			0.101593i
$813$			7.59121i			0.266235i
$814$	−9.24341			−0.323982
$815$	39.4905	−	38.0964i	1.38329	−	1.33446i
$816$	−9.27118			−0.324556
$817$		−	2.39648i		−	0.0838422i
$818$			36.8878i			1.28975i
$819$	37.7782			1.32008
$820$	41.9981	+	43.5350i	1.46664	+	1.52031i
$821$	−13.9521			−0.486932			−0.243466	−	0.969909i	$-0.578284\pi$
$821$	−13.9521			−0.486932			−0.243466	+	0.969909i	$0.578284\pi$
$822$		−	17.0468i		−	0.594574i
$823$		−	39.8195i		−	1.38802i	−0.719965	−	0.694010i	$-0.755842\pi$
$823$		−	39.8195i		−	1.38802i	0.719965	−	0.694010i	$-0.244158\pi$
$824$	−2.32161			−0.0808772
$825$	−3.30375	−	0.118764i	−0.115022	−	0.00413484i
$826$	−63.0518			−2.19385
$827$		−	9.11371i		−	0.316915i	−0.987366	−	0.158457i	$-0.949348\pi$
$827$		−	9.11371i		−	0.316915i	0.987366	−	0.158457i	$-0.0506521\pi$
$828$		−	57.5326i		−	1.99940i
$829$	−30.1084			−1.04571			−0.522854	−	0.852422i	$-0.675133\pi$
$829$	−30.1084			−1.04571			−0.522854	+	0.852422i	$0.675133\pi$
$830$	−37.1919	−	38.5529i	−1.29095	−	1.33819i
$831$	8.04171			0.278964
$832$			59.7732i			2.07226i
$833$			10.1930i			0.353168i
$834$	−22.0137			−0.762273
$835$	−9.91702	+	9.56693i	−0.343193	+	0.331077i
$836$	3.97280			0.137402
$837$			14.0168i			0.484491i
$838$		−	67.6258i		−	2.33610i
$839$	−19.4558			−0.671688			−0.335844	−	0.941918i	$-0.609022\pi$
$839$	−19.4558			−0.671688			−0.335844	+	0.941918i	$0.609022\pi$
$840$	−10.5266	+	10.1550i	−0.363201	+	0.350379i
$841$	−28.8739			−0.995651
$842$			27.3679i			0.943160i
$843$		−	13.0319i		−	0.448843i
$844$	77.4389			2.66556
$845$	−59.9373	−	62.1307i	−2.06191	−	2.13736i
$846$	−61.7859			−2.12424
$847$		−	2.05193i		−	0.0705052i
$848$		−	42.2667i		−	1.45144i
$849$	0.758644			0.0260366
$850$	−1.60406	+	44.6214i	−0.0550189	+	1.53050i
$851$	21.3717			0.732612
$852$			27.1866i			0.931398i
$853$		−	45.6882i		−	1.56433i	−0.623069	−	0.782167i	$-0.714114\pi$
$853$		−	45.6882i		−	1.56433i	0.623069	−	0.782167i	$-0.285886\pi$
$854$	−38.3476			−1.31223
$855$	−3.97876	−	4.12436i	−0.136071	−	0.141050i
$856$	−69.0479			−2.36001
$857$		−	2.36906i		−	0.0809254i	−0.999181	−	0.0404627i	$-0.987117\pi$
$857$		−	2.36906i		−	0.0809254i	0.999181	−	0.0404627i	$-0.0128832\pi$
$858$			11.6082i			0.396296i
$859$	−4.79295			−0.163533			−0.0817667	−	0.996651i	$-0.526056\pi$
$859$	−4.79295			−0.163533			−0.0817667	+	0.996651i	$0.526056\pi$
$860$	15.3216	−	14.7807i	0.522463	−	0.504019i
$861$	−9.23822			−0.314838
$862$		−	6.73719i		−	0.229469i
$863$		−	13.5884i		−	0.462555i	−0.972888	−	0.231278i	$-0.925709\pi$
$863$		−	13.5884i		−	0.462555i	0.972888	−	0.231278i	$-0.0742906\pi$
$864$	−0.971358			−0.0330463
$865$	0.526031	−	0.507461i	0.0178856	−	0.0172542i
$866$	−88.1338			−2.99491
$867$			2.41232i			0.0819267i
$868$			31.0665i			1.05447i
$869$	−3.96099			−0.134367
$870$	0.890871	+	0.923472i	0.0302034	+	0.0313086i
$871$	86.0661			2.91624
$872$		−	15.5674i		−	0.527180i
$873$		−	15.3705i		−	0.520213i
$874$	−13.8097			−0.467120
$875$	15.3245	+	17.0723i	0.518061	+	0.577149i
$876$	41.0806			1.38799
$877$		−	49.4450i		−	1.66964i	−0.550523	−	0.834820i	$-0.685572\pi$
$877$		−	49.4450i		−	1.66964i	0.550523	−	0.834820i	$-0.314428\pi$
$878$		−	45.3342i		−	1.52996i
$879$	8.14938			0.274872
$880$	5.95769	+	6.17571i	0.200834	+	0.208183i
$881$	52.6903			1.77518			0.887591	−	0.460632i	$-0.152377\pi$
$881$	52.6903			1.77518			0.887591	+	0.460632i	$0.152377\pi$
$882$		−	17.4723i		−	0.588323i
$883$			45.4465i			1.52940i	0.644389	+	0.764698i	$0.277112\pi$
$883$			45.4465i			1.52940i	−0.644389	+	0.764698i	$0.722888\pi$
$884$	104.284			3.50745
$885$	−13.3782	+	12.9059i	−0.449703	+	0.433828i
$886$	77.4195			2.60096
$887$			34.3778i			1.15430i	0.816640	+	0.577148i	$0.195834\pi$
$887$			34.3778i			1.15430i	−0.816640	+	0.577148i	$0.804166\pi$
$888$			12.0568i			0.404601i
$889$	−21.1817			−0.710410
$890$	31.6458	−	30.5286i	1.06077	−	1.02332i
$891$	5.25671			0.176106
$892$			33.3165i			1.11552i
$893$			9.86457i			0.330105i
$894$	12.7789			0.427390
$895$	14.7851	+	15.3262i	0.494213	+	0.512298i
$896$	−40.6417			−1.35774
$897$		−	26.8392i		−	0.896135i
$898$		−	7.56035i		−	0.252292i
$899$	1.35337			0.0451374
$900$	1.82889	−	50.8755i	0.0609629	−	1.69585i
$901$	40.2449			1.34075
$902$			16.6417i			0.554107i
$903$			3.25128i			0.108196i
$904$	−83.0833			−2.76331
$905$	−26.9770	−	27.9642i	−0.896747	−	0.929563i
$906$	−4.94459			−0.164273
$907$		−	10.3575i		−	0.343916i	−0.985104	−	0.171958i	$-0.944991\pi$
$907$		−	10.3575i		−	0.343916i	0.985104	−	0.171958i	$-0.0550094\pi$
$908$			14.6957i			0.487694i
$909$	12.6770			0.420470
$910$	57.9752	−	55.9285i	1.92186	−	1.85401i
$911$	38.5589			1.27751			0.638757	−	0.769409i	$-0.279449\pi$
$911$	38.5589			1.27751			0.638757	+	0.769409i	$0.279449\pi$
$912$		−	2.53729i		−	0.0840181i
$913$		−	9.80243i		−	0.324413i
$914$	83.9008			2.77519
$915$	−8.13653	+	7.84929i	−0.268985	+	0.259489i
$916$	54.8484			1.81224
$917$			24.3068i			0.802682i
$918$			32.8449i			1.08404i
$919$	−57.3323			−1.89122			−0.945608	−	0.325307i	$-0.894532\pi$
$919$	−57.3323			−1.89122			−0.945608	+	0.325307i	$0.894532\pi$
$920$	−42.2953	−	43.8431i	−1.39444	−	1.44546i
$921$	13.1864			0.434507
$922$		−	12.1441i		−	0.399946i
$923$		−	74.3527i		−	2.44735i
$924$	−5.38986			−0.177313
$925$	18.8987	+	0.679378i	0.621387	+	0.0223378i
$926$	−57.7076			−1.89639
$927$			1.23407i			0.0405322i
$928$			0.0937879i			0.00307874i
$929$	−20.6900			−0.678818			−0.339409	−	0.940639i	$-0.610227\pi$
$929$	−20.6900			−0.678818			−0.339409	+	0.940639i	$0.610227\pi$
$930$	9.56018	+	9.91002i	0.313490	+	0.324962i
$931$	−2.78958			−0.0914248
$932$			31.9904i			1.04788i
$933$			8.73528i			0.285980i
$934$	18.7138			0.612334
$935$	−5.88029	+	5.67270i	−0.192306	+	0.185517i
$936$	−88.7668			−2.90143
$937$			7.91240i			0.258487i	0.991613	+	0.129243i	$0.0412549\pi$
$937$			7.91240i			0.258487i	−0.991613	+	0.129243i	$0.958745\pi$
$938$			60.0797i			1.96167i
$939$	11.1457			0.363726
$940$	−63.0680	+	60.8416i	−2.05705	+	1.98443i
$941$	9.43095			0.307440			0.153720	−	0.988114i	$-0.450875\pi$
$941$	9.43095			0.307440			0.153720	+	0.988114i	$0.450875\pi$
$942$			28.0449i			0.913752i
$943$		−	38.4772i		−	1.25299i
$944$	48.2501			1.57041
$945$	11.7166	+	12.1454i	0.381142	+	0.395090i
$946$	5.85683			0.190422
$947$			35.3715i			1.14942i	0.818358	+	0.574709i	$0.194885\pi$
$947$			35.3715i			1.14942i	−0.818358	+	0.574709i	$0.805115\pi$
$948$			10.4044i			0.337920i
$949$	−112.351			−3.64708
$950$	−12.2118	−	0.438992i	−0.396202	−	0.0142428i
$951$	−3.06106			−0.0992617
$952$			36.1492i			1.17160i
$953$			47.8242i			1.54918i	0.632466	+	0.774588i	$0.282043\pi$
$953$			47.8242i			1.54918i	−0.632466	+	0.774588i	$0.717957\pi$
$954$	−68.9854			−2.23348
$955$	8.94761	+	9.27504i	0.289538	+	0.300133i
$956$	−93.1499			−3.01268
$957$			0.234801i			0.00759005i
$958$		−	53.6793i		−	1.73430i
$959$	−21.6470			−0.699018
$960$	−8.85324	+	8.54070i	−0.285737	+	0.275650i
$961$	−16.4766			−0.531505
$962$		−	66.4032i		−	2.14093i
$963$			36.7029i			1.18274i
$964$	−18.5052			−0.596013
$965$	20.3296	−	19.6119i	0.654433	−	0.631330i
$966$	18.7355			0.602804
$967$		−	31.2662i		−	1.00545i	−0.864446	−	0.502726i	$-0.832331\pi$
$967$		−	31.2662i		−	1.00545i	0.864446	−	0.502726i	$-0.167669\pi$
$968$			4.82139i			0.154965i
$969$	2.41592			0.0776105
$970$	−22.7552	−	23.5879i	−0.730625	−	0.757362i
$971$	−18.8495			−0.604908			−0.302454	−	0.953164i	$-0.597806\pi$
$971$	−18.8495			−0.604908			−0.302454	+	0.953164i	$0.597806\pi$
$972$		−	57.6441i		−	1.84894i
$973$			27.9544i			0.896176i
$974$	38.2273			1.22488
$975$	0.853183	−	23.7336i	0.0273237	−	0.760084i
$976$	29.3454			0.939322
$977$		−	47.1226i		−	1.50758i	−0.657113	−	0.753792i	$-0.728223\pi$
$977$		−	47.1226i		−	1.50758i	0.657113	−	0.753792i	$-0.271777\pi$
$978$		−	39.6520i		−	1.26793i
$979$	8.04623			0.257159
$980$	−17.2053	−	17.8349i	−0.549602	−	0.569714i
$981$	−8.27499			−0.264200
$982$		−	47.8218i		−	1.52605i
$983$		−	26.6057i		−	0.848591i	−0.905524	−	0.424296i	$-0.860522\pi$
$983$		−	26.6057i		−	0.848591i	0.905524	−	0.424296i	$-0.139478\pi$
$984$	21.7069			0.691991
$985$	−0.888087	+	0.856736i	−0.0282968	+	0.0272979i
$986$	3.17129			0.100995
$987$		−	13.3832i		−	0.425991i
$988$			28.5399i			0.907977i
$989$	−13.5416			−0.430597
$990$	10.0796	−	9.72381i	0.320352	−	0.309043i
$991$	−21.1143			−0.670717			−0.335358	−	0.942091i	$-0.608857\pi$
$991$	−21.1143			−0.670717			−0.335358	+	0.942091i	$0.608857\pi$
$992$			1.00646i			0.0319552i
$993$		−	0.321594i		−	0.0102055i
$994$	51.9030			1.64626
$995$	28.7042	+	29.7546i	0.909984	+	0.943285i
$996$	−25.7483			−0.815866
$997$			24.5780i			0.778394i	0.921154	+	0.389197i	$0.127248\pi$
$997$			24.5780i			0.778394i	−0.921154	+	0.389197i	$0.872752\pi$
$998$			80.9416i			2.56216i
$999$	13.9110			0.440125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.e.419.3	✓	30
5.2	odd	4		5225.2.a.bc.1.28		30
5.3	odd	4		5225.2.a.bc.1.3		30
5.4	even	2	inner	1045.2.b.e.419.28	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.e.419.3	✓	30	1.1	even	1	trivial
1045.2.b.e.419.28	yes	30	5.4	even	2	inner
5225.2.a.bc.1.3		30	5.3	odd	4
5225.2.a.bc.1.28		30	5.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.44393i q^{2} +0.661177i q^{3} -3.97280 q^{4} +(1.55248 + 1.60929i) q^{5} +1.61587 q^{6} -2.05193i q^{7} +4.82139i q^{8} +2.56284 q^{9} +O(q^{10})\)	\(q-2.44393i q^{2} +0.661177i q^{3} -3.97280 q^{4} +(1.55248 + 1.60929i) q^{5} +1.61587 q^{6} -2.05193i q^{7} +4.82139i q^{8} +2.56284 q^{9} +(3.93299 - 3.79415i) q^{10} +1.00000 q^{11} -2.62672i q^{12} +7.18384i q^{13} -5.01478 q^{14} +(-1.06403 + 1.02646i) q^{15} +3.83754 q^{16} +3.65397i q^{17} -6.26342i q^{18} -1.00000 q^{19} +(-6.16768 - 6.39338i) q^{20} +1.35669 q^{21} -2.44393i q^{22} +5.65061i q^{23} -3.18779 q^{24} +(-0.179625 + 4.99677i) q^{25} +17.5568 q^{26} +3.67803i q^{27} +8.15191i q^{28} +0.355126 q^{29} +(2.50861 + 2.60041i) q^{30} +3.81095 q^{31} +0.264097i q^{32} +0.661177i q^{33} +8.93004 q^{34} +(3.30215 - 3.18558i) q^{35} -10.1817 q^{36} -3.78219i q^{37} +2.44393i q^{38} -4.74979 q^{39} +(-7.75901 + 7.48509i) q^{40} -6.80938 q^{41} -3.31566i q^{42} +2.39648i q^{43} -3.97280 q^{44} +(3.97876 + 4.12436i) q^{45} +13.8097 q^{46} -9.86457i q^{47} +2.53729i q^{48} +2.78958 q^{49} +(12.2118 + 0.438992i) q^{50} -2.41592 q^{51} -28.5399i q^{52} -11.0140i q^{53} +8.98884 q^{54} +(1.55248 + 1.60929i) q^{55} +9.89315 q^{56} -0.661177i q^{57} -0.867904i q^{58} +12.5732 q^{59} +(4.22716 - 4.07793i) q^{60} +7.64692 q^{61} -9.31371i q^{62} -5.25878i q^{63} +8.32051 q^{64} +(-11.5609 + 11.1527i) q^{65} +1.61587 q^{66} -11.9805i q^{67} -14.5165i q^{68} -3.73605 q^{69} +(-7.78533 - 8.07023i) q^{70} -10.3500 q^{71} +12.3565i q^{72} +15.6395i q^{73} -9.24341 q^{74} +(-3.30375 - 0.118764i) q^{75} +3.97280 q^{76} -2.05193i q^{77} +11.6082i q^{78} -3.96099 q^{79} +(5.95769 + 6.17571i) q^{80} +5.25671 q^{81} +16.6417i q^{82} -9.80243i q^{83} -5.38986 q^{84} +(-5.88029 + 5.67270i) q^{85} +5.85683 q^{86} +0.234801i q^{87} +4.82139i q^{88} +8.04623 q^{89} +(10.0796 - 9.72381i) q^{90} +14.7407 q^{91} -22.4487i q^{92} +2.51972i q^{93} -24.1083 q^{94} +(-1.55248 - 1.60929i) q^{95} -0.174615 q^{96} -5.99744i q^{97} -6.81755i q^{98} +2.56284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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