LMFDB - Embedded newform 65.4.c.a.51.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [65,4,Mod(51,65)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(65, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("65.51"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	65.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.83512415037$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 84x^{12} + 2674x^{10} + 40048x^{8} + 278769x^{6} + 727552x^{4} + 339456x^{2} + 9216 $ x^14 + 84x^12 + 2674x^10 + 40048x^8 + 278769x^6 + 727552x^4 + 339456x^2 + 9216
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.11
Root			$3.65500i$ of defining polynomial
Character	$\chi$	$=$	65.51
Dual form			65.4.c.a.51.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.65500i q^{2} +8.59394 q^{3} -5.35901 q^{4} +5.00000i q^{5} +31.4108i q^{6} -19.4590i q^{7} +9.65282i q^{8} +46.8559 q^{9} -18.2750 q^{10} -20.0770i q^{11} -46.0550 q^{12} +(-46.8676 + 0.655046i) q^{13} +71.1227 q^{14} +42.9697i q^{15} -78.1531 q^{16} -89.4229 q^{17} +171.258i q^{18} -11.7815i q^{19} -26.7950i q^{20} -167.230i q^{21} +73.3816 q^{22} +157.627 q^{23} +82.9558i q^{24} -25.0000 q^{25} +(-2.39419 - 171.301i) q^{26} +170.640 q^{27} +104.281i q^{28} +116.112 q^{29} -157.054 q^{30} -245.999i q^{31} -208.427i q^{32} -172.541i q^{33} -326.840i q^{34} +97.2951 q^{35} -251.101 q^{36} +213.834i q^{37} +43.0613 q^{38} +(-402.777 + 5.62943i) q^{39} -48.2641 q^{40} +442.192i q^{41} +611.224 q^{42} +184.625 q^{43} +107.593i q^{44} +234.279i q^{45} +576.126i q^{46} -247.157i q^{47} -671.643 q^{48} -35.6534 q^{49} -91.3749i q^{50} -768.495 q^{51} +(251.164 - 3.51040i) q^{52} +14.9253 q^{53} +623.689i q^{54} +100.385 q^{55} +187.834 q^{56} -101.250i q^{57} +424.389i q^{58} -416.520i q^{59} -230.275i q^{60} -898.135 q^{61} +899.127 q^{62} -911.769i q^{63} +136.575 q^{64} +(-3.27523 - 234.338i) q^{65} +630.637 q^{66} +847.535i q^{67} +479.218 q^{68} +1354.64 q^{69} +355.613i q^{70} -512.385i q^{71} +452.291i q^{72} +533.502i q^{73} -781.564 q^{74} -214.849 q^{75} +63.1371i q^{76} -390.680 q^{77} +(-20.5756 - 1472.15i) q^{78} -90.0657 q^{79} -390.766i q^{80} +201.363 q^{81} -1616.21 q^{82} +1092.74i q^{83} +896.185i q^{84} -447.114i q^{85} +674.804i q^{86} +997.859 q^{87} +193.800 q^{88} -117.323i q^{89} -856.290 q^{90} +(12.7466 + 911.997i) q^{91} -844.724 q^{92} -2114.11i q^{93} +903.360 q^{94} +58.9075 q^{95} -1791.21i q^{96} +895.447i q^{97} -130.313i q^{98} -940.727i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 56 q^{4} + 158 q^{9} - 20 q^{10} - 108 q^{12} - 4 q^{13} - 152 q^{14} + 280 q^{16} - 100 q^{17} + 648 q^{22} - 532 q^{23} - 350 q^{25} - 344 q^{26} - 48 q^{27} + 588 q^{29} - 200 q^{30} + 540 q^{35}+ \cdots - 3120 q^{95}+O(q^{100}) $ 14 * q - 56 * q^4 + 158 * q^9 - 20 * q^10 - 108 * q^12 - 4 * q^13 - 152 * q^14 + 280 * q^16 - 100 * q^17 + 648 * q^22 - 532 * q^23 - 350 * q^25 - 344 * q^26 - 48 * q^27 + 588 * q^29 - 200 * q^30 + 540 * q^35 + 496 * q^36 + 148 * q^38 - 260 * q^39 + 240 * q^40 - 620 * q^42 + 728 * q^43 - 2008 * q^48 - 1302 * q^49 + 176 * q^51 - 528 * q^52 + 1040 * q^53 - 40 * q^55 + 512 * q^56 - 1460 * q^61 + 2964 * q^62 + 1296 * q^64 - 30 * q^65 - 600 * q^66 + 1604 * q^68 + 4160 * q^69 - 5928 * q^74 - 3568 * q^77 + 2560 * q^78 - 1024 * q^79 - 2890 * q^81 - 6660 * q^82 + 5256 * q^87 + 1132 * q^88 + 1360 * q^90 + 916 * q^91 + 6044 * q^92 + 2656 * q^94 - 3120 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$			3.65500i			1.29224i	0.763237	+	0.646118i	$0.223609\pi$
$2$			3.65500i			1.29224i	−0.763237	+	0.646118i	$0.776391\pi$
$3$	8.59394			1.65391			0.826953	−	0.562272i	$-0.190072\pi$
$3$	8.59394			1.65391			0.826953	+	0.562272i	$0.190072\pi$
$4$	−5.35901			−0.669876
$5$			5.00000i			0.447214i
$5$			5.00000i			0.447214i
$6$			31.4108i			2.13724i
$7$		−	19.4590i		−	1.05069i	−0.850890	−	0.525344i	$-0.823937\pi$
$7$		−	19.4590i		−	1.05069i	0.850890	−	0.525344i	$-0.176063\pi$
$8$			9.65282i			0.426599i
$9$	46.8559			1.73540
$10$	−18.2750			−0.577906
$11$		−	20.0770i		−	0.550314i	−0.961399	−	0.275157i	$-0.911270\pi$
$11$		−	20.0770i		−	0.550314i	0.961399	−	0.275157i	$-0.0887299\pi$
$12$	−46.0550			−1.10791
$13$	−46.8676	+	0.655046i	−0.999902	+	0.0139752i
$13$	−46.8676	+	0.655046i	−0.999902	+	0.0139752i
$14$	71.1227			1.35774
$15$			42.9697i			0.739649i
$16$	−78.1531			−1.22114
$17$	−89.4229			−1.27578			−0.637889	−	0.770128i	$-0.720192\pi$
$17$	−89.4229			−1.27578			−0.637889	+	0.770128i	$0.720192\pi$
$18$			171.258i			2.24255i
$19$		−	11.7815i		−	0.142256i	−0.997467	−	0.0711279i	$-0.977340\pi$
$19$		−	11.7815i		−	0.142256i	0.997467	−	0.0711279i	$-0.0226599\pi$
$20$		−	26.7950i		−	0.299578i
$21$		−	167.230i		−	1.73774i
$22$	73.3816			0.711136
$23$	157.627			1.42902			0.714511	−	0.699624i	$-0.246649\pi$
$23$	157.627			1.42902			0.714511	+	0.699624i	$0.246649\pi$
$24$			82.9558i			0.705554i
$25$	−25.0000			−0.200000
$26$	−2.39419	−	171.301i	−0.0180592	−	1.29211i
$27$	170.640			1.21629
$28$			104.281i			0.703831i
$29$	116.112			0.743498			0.371749	−	0.928333i	$-0.378758\pi$
$29$	116.112			0.743498			0.371749	+	0.928333i	$0.378758\pi$
$30$	−157.054			−0.955801
$31$		−	245.999i		−	1.42525i	−0.701544	−	0.712626i	$-0.747506\pi$
$31$		−	245.999i		−	1.42525i	0.701544	−	0.712626i	$-0.252494\pi$
$32$		−	208.427i		−	1.15141i
$33$		−	172.541i		−	0.910168i
$34$		−	326.840i		−	1.64861i
$35$	97.2951			0.469882
$36$	−251.101			−1.16250
$37$			213.834i			0.950112i	0.879956	+	0.475056i	$0.157572\pi$
$37$			213.834i			0.950112i	−0.879956	+	0.475056i	$0.842428\pi$
$38$	43.0613			0.183828
$39$	−402.777	+	5.62943i	−1.65374	+	0.0231136i
$40$	−48.2641			−0.190781
$41$			442.192i			1.68436i	0.539196	+	0.842180i	$0.318728\pi$
$41$			442.192i			1.68436i	−0.539196	+	0.842180i	$0.681272\pi$
$42$	611.224			2.24557
$43$	184.625			0.654768			0.327384	−	0.944891i	$-0.393833\pi$
$43$	184.625			0.654768			0.327384	+	0.944891i	$0.393833\pi$
$44$			107.593i			0.368642i
$45$			234.279i			0.776095i
$46$			576.126i			1.84663i
$47$		−	247.157i		−	0.767056i	−0.923529	−	0.383528i	$-0.874709\pi$
$47$		−	247.157i		−	0.767056i	0.923529	−	0.383528i	$-0.125291\pi$
$48$	−671.643			−2.01965
$49$	−35.6534			−0.103946
$50$		−	91.3749i		−	0.258447i
$51$	−768.495			−2.11002
$52$	251.164	−	3.51040i	0.669810	−	0.00936162i
$53$	14.9253			0.0386821			0.0193410	−	0.999813i	$-0.493843\pi$
$53$	14.9253			0.0386821			0.0193410	+	0.999813i	$0.493843\pi$
$54$			623.689i			1.57173i
$55$	100.385			0.246108
$56$	187.834			0.448222
$57$		−	101.250i		−	0.235278i
$58$			424.389i			0.960776i
$59$		−	416.520i		−	0.919090i	−0.888155	−	0.459545i	$-0.848013\pi$
$59$		−	416.520i		−	0.919090i	0.888155	−	0.459545i	$-0.151987\pi$
$60$		−	230.275i		−	0.495473i
$61$	−898.135			−1.88515			−0.942577	−	0.333989i	$-0.891605\pi$
$61$	−898.135			−1.88515			−0.942577	+	0.333989i	$0.891605\pi$
$62$	899.127			1.84176
$63$		−	911.769i		−	1.82337i
$64$	136.575			0.266747
$65$	−3.27523	−	234.338i	−0.00624988	−	0.447170i
$66$	630.637			1.17615
$67$			847.535i			1.54542i	0.634761	+	0.772708i	$0.281098\pi$
$67$			847.535i			1.54542i	−0.634761	+	0.772708i	$0.718902\pi$
$68$	479.218			0.854613
$69$	1354.64			2.36347
$70$			355.613i			0.607199i
$71$		−	512.385i		−	0.856463i	−0.903669	−	0.428232i	$-0.859137\pi$
$71$		−	512.385i		−	0.856463i	0.903669	−	0.428232i	$-0.140863\pi$
$72$			452.291i			0.740320i
$73$			533.502i			0.855365i	0.903929	+	0.427683i	$0.140670\pi$
$73$			533.502i			0.855365i	−0.903929	+	0.427683i	$0.859330\pi$
$74$	−781.564			−1.22777
$75$	−214.849			−0.330781
$76$			63.1371i			0.0952938i
$77$	−390.680			−0.578209
$78$	−20.5756	−	1472.15i	−0.0298682	−	2.13703i
$79$	−90.0657			−0.128268			−0.0641341	−	0.997941i	$-0.520429\pi$
$79$	−90.0657			−0.128268			−0.0641341	+	0.997941i	$0.520429\pi$
$80$		−	390.766i		−	0.546111i
$81$	201.363			0.276218
$82$	−1616.21			−2.17659
$83$			1092.74i			1.44510i	0.691318	+	0.722551i	$0.257030\pi$
$83$			1092.74i			1.44510i	−0.691318	+	0.722551i	$0.742970\pi$
$84$			896.185i			1.16407i
$85$		−	447.114i		−	0.570546i
$86$			674.804i			0.846116i
$87$	997.859			1.22968
$88$	193.800			0.234763
$89$		−	117.323i		−	0.139733i	−0.997556	−	0.0698666i	$-0.977743\pi$
$89$		−	117.323i		−	0.139733i	0.997556	−	0.0698666i	$-0.0222574\pi$
$90$	−856.290			−1.00290
$91$	12.7466	+	911.997i	0.0146835	+	1.05059i
$92$	−844.724			−0.957267
$93$		−	2114.11i		−	2.35723i
$94$	903.360			0.991217
$95$	58.9075			0.0636188
$96$		−	1791.21i		−	1.90432i
$97$			895.447i			0.937308i	0.883382	+	0.468654i	$0.155261\pi$
$97$			895.447i			0.937308i	−0.883382	+	0.468654i	$0.844739\pi$
$98$		−	130.313i		−	0.134323i
$99$		−	940.727i		−	0.955017i
$100$	133.975			0.133975
$101$	−240.227			−0.236668			−0.118334	−	0.992974i	$-0.537755\pi$
$101$	−240.227			−0.236668			−0.118334	+	0.992974i	$0.537755\pi$
$102$		−	2808.85i		−	2.72664i
$103$	−123.954			−0.118578			−0.0592891	−	0.998241i	$-0.518883\pi$
$103$	−123.954			−0.118578			−0.0592891	+	0.998241i	$0.518883\pi$
$104$	−6.32305	−	452.405i	−0.00596178	−	0.426557i
$105$	836.148			0.777140
$106$			54.5520i			0.0499864i
$107$	−1223.36			−1.10530			−0.552649	−	0.833414i	$-0.686383\pi$
$107$	−1223.36			−1.10530			−0.552649	+	0.833414i	$0.686383\pi$
$108$	−914.461			−0.814760
$109$		−	1738.02i		−	1.52727i	−0.645648	−	0.763635i	$-0.723413\pi$
$109$		−	1738.02i		−	1.52727i	0.645648	−	0.763635i	$-0.276587\pi$
$110$			366.908i			0.318030i
$111$			1837.68i			1.57139i
$112$			1520.78i			1.28304i
$113$	633.634			0.527498			0.263749	−	0.964591i	$-0.415041\pi$
$113$	633.634			0.527498			0.263749	+	0.964591i	$0.415041\pi$
$114$	370.067			0.304034
$115$			788.135i			0.639078i
$116$	−622.245			−0.498051
$117$	−2196.02	+	30.6927i	−1.73523	+	0.0242525i
$118$	1522.38			1.18768
$119$			1740.08i			1.34045i
$120$	−414.779			−0.315533
$121$	927.912			0.697154
$122$		−	3282.68i		−	2.43607i
$123$			3800.17i			2.78577i
$124$			1318.31i			0.954742i
$125$		−	125.000i		−	0.0894427i
$126$	3332.51			2.35622
$127$	1731.65			1.20991			0.604955	−	0.796259i	$-0.293191\pi$
$127$	1731.65			1.20991			0.604955	+	0.796259i	$0.293191\pi$
$128$		−	1168.23i		−	0.806706i
$129$	1586.66			1.08292
$130$	856.505	−	11.9710i	0.577849	−	0.00807633i
$131$	2334.08			1.55671			0.778357	−	0.627822i	$-0.216053\pi$
$131$	2334.08			1.55671			0.778357	+	0.627822i	$0.216053\pi$
$132$			924.648i			0.609699i
$133$	−229.256			−0.149467
$134$	−3097.74			−1.99704
$135$			853.200i			0.543939i
$136$		−	863.183i		−	0.544245i
$137$			1528.05i			0.952922i	0.879196	+	0.476461i	$0.158081\pi$
$137$			1528.05i			0.952922i	−0.879196	+	0.476461i	$0.841919\pi$
$138$			4951.20i			3.05416i
$139$	−2246.04			−1.37055			−0.685274	−	0.728285i	$-0.740318\pi$
$139$	−2246.04			−1.37055			−0.685274	+	0.728285i	$0.740318\pi$
$140$	−521.405			−0.314763
$141$		−	2124.06i		−	1.26864i
$142$	1872.77			1.10675
$143$	13.1514	+	940.963i	0.00769073	+	0.550261i
$144$	−3661.93			−2.11917
$145$			580.560i			0.332502i
$146$	−1949.95			−1.10533
$147$	−306.403			−0.171917
$148$		−	1145.94i		−	0.636457i
$149$			710.547i			0.390673i	0.980736	+	0.195337i	$0.0625799\pi$
$149$			710.547i			0.390673i	−0.980736	+	0.195337i	$0.937420\pi$
$150$		−	785.271i		−	0.427447i
$151$		−	1201.89i		−	0.647738i	−0.946102	−	0.323869i	$-0.895016\pi$
$151$		−	1201.89i		−	0.647738i	0.946102	−	0.323869i	$-0.104984\pi$
$152$	113.725			0.0606861
$153$	−4189.99			−2.21399
$154$		−	1427.93i		−	0.747183i
$155$	1230.00			0.637392
$156$	2158.49	−	30.1682i	1.10780	−	0.0154832i
$157$	−677.363			−0.344328			−0.172164	−	0.985068i	$-0.555076\pi$
$157$	−677.363			−0.344328			−0.172164	+	0.985068i	$0.555076\pi$
$158$		−	329.190i		−	0.165753i
$159$	128.267			0.0639765
$160$	1042.13			0.514925
$161$		−	3067.27i		−	1.50146i
$162$			735.981i			0.356939i
$163$		−	2043.08i		−	0.981756i	−0.871228	−	0.490878i	$-0.836676\pi$
$163$		−	2043.08i		−	0.981756i	0.871228	−	0.490878i	$-0.163324\pi$
$164$		−	2369.71i		−	1.12831i
$165$	862.705			0.407039
$166$	−3993.95			−1.86741
$167$			2590.58i			1.20039i	0.799854	+	0.600195i	$0.204910\pi$
$167$			2590.58i			1.20039i	−0.799854	+	0.600195i	$0.795090\pi$
$168$	1614.24			0.741317
$169$	2196.14	−	61.4009i	0.999609	−	0.0279476i
$170$	1634.20			0.737280
$171$		−	552.032i		−	0.246871i
$172$	−989.407			−0.438614
$173$	1092.54			0.480140			0.240070	−	0.970756i	$-0.422830\pi$
$173$	1092.54			0.480140			0.240070	+	0.970756i	$0.422830\pi$
$174$			3647.17i			1.58903i
$175$			486.475i			0.210138i
$176$			1569.08i			0.672012i
$177$		−	3579.55i		−	1.52009i
$178$	428.817			0.180568
$179$	2643.64			1.10388			0.551942	−	0.833883i	$-0.313887\pi$
$179$	2643.64			1.10388			0.551942	+	0.833883i	$0.313887\pi$
$180$		−	1255.50i		−	0.519888i
$181$	113.656			0.0466739			0.0233370	−	0.999728i	$-0.492571\pi$
$181$	113.656			0.0466739			0.0233370	+	0.999728i	$0.492571\pi$
$182$	−3333.35	+	46.5886i	−1.35761	+	0.0189746i
$183$	−7718.52			−3.11787
$184$			1521.55i			0.609619i
$185$	−1069.17			−0.424903
$186$	7727.05			3.04610
$187$			1795.35i			0.702079i
$188$			1324.52i			0.513832i
$189$		−	3320.49i		−	1.27794i
$190$			215.307i			0.0822105i
$191$	−1586.92			−0.601181			−0.300590	−	0.953753i	$-0.597184\pi$
$191$	−1586.92			−0.601181			−0.300590	+	0.953753i	$0.597184\pi$
$192$	1173.71			0.441175
$193$		−	2480.87i		−	0.925270i	−0.886549	−	0.462635i	$-0.846904\pi$
$193$		−	2480.87i		−	0.925270i	0.886549	−	0.462635i	$-0.153096\pi$
$194$	−3272.86			−1.21122
$195$	−28.1471	−	2013.89i	−0.0103367	−	0.739577i
$196$	191.067			0.0696308
$197$		−	4720.28i		−	1.70714i	−0.520981	−	0.853568i	$-0.674434\pi$
$197$		−	4720.28i		−	1.70714i	0.520981	−	0.853568i	$-0.325566\pi$
$198$	3438.36			1.23411
$199$	849.011			0.302436			0.151218	−	0.988500i	$-0.451680\pi$
$199$	849.011			0.302436			0.151218	+	0.988500i	$0.451680\pi$
$200$		−	241.321i		−	0.0853197i
$201$			7283.67i			2.55597i
$202$		−	878.028i		−	0.305831i
$203$		−	2259.42i		−	0.781185i
$204$	4118.37			1.41345
$205$	−2210.96			−0.753269
$206$		−	453.051i		−	0.153231i
$207$	7385.75			2.47993
$208$	3662.85	−	51.1939i	1.22102	−	0.0170657i
$209$	−236.538			−0.0782854
$210$			3056.12i			1.00425i
$211$	−3094.07			−1.00950			−0.504751	−	0.863265i	$-0.668416\pi$
$211$	−3094.07			−1.00950			−0.504751	+	0.863265i	$0.668416\pi$
$212$	−79.9849			−0.0259122
$213$		−	4403.41i		−	1.41651i
$214$		−	4471.38i		−	1.42831i
$215$			923.125i			0.292821i
$216$			1647.16i			0.518865i
$217$	−4786.91			−1.49750
$218$	6352.47			1.97359
$219$			4584.88i			1.41469i
$220$	−537.965			−0.164862
$221$	4191.04	−	58.5761i	1.27565	−	0.0178292i
$222$	−6716.71			−2.03061
$223$			923.125i			0.277206i	0.990348	+	0.138603i	$0.0442613\pi$
$223$			923.125i			0.277206i	−0.990348	+	0.138603i	$0.955739\pi$
$224$	−4055.78			−1.20977
$225$	−1171.40			−0.347080
$226$			2315.93i			0.681652i
$227$		−	652.853i		−	0.190887i	−0.995435	−	0.0954435i	$-0.969573\pi$
$227$		−	652.853i		−	0.190887i	0.995435	−	0.0954435i	$-0.0304269\pi$
$228$			542.597i			0.157607i
$229$		−	3450.44i		−	0.995685i	−0.867268	−	0.497842i	$-0.834126\pi$
$229$		−	3450.44i		−	0.995685i	0.867268	−	0.497842i	$-0.165874\pi$
$230$	−2880.63			−0.825840
$231$	−3357.48			−0.956302
$232$			1120.81i			0.317175i
$233$	2746.83			0.772320			0.386160	−	0.922432i	$-0.373801\pi$
$233$	2746.83			0.772320			0.386160	+	0.922432i	$0.373801\pi$
$234$	−112.182	−	8026.45i	−0.0313400	−	2.24233i
$235$	1235.79			0.343038
$236$			2232.13i			0.615676i
$237$	−774.020			−0.212143
$238$	−6359.99			−1.73217
$239$			6624.49i			1.79290i	0.443148	+	0.896448i	$0.353862\pi$
$239$			6624.49i			1.79290i	−0.443148	+	0.896448i	$0.646138\pi$
$240$		−	3358.22i		−	0.903216i
$241$		−	3220.25i		−	0.860725i	−0.902656	−	0.430362i	$-0.858386\pi$
$241$		−	3220.25i		−	0.860725i	0.902656	−	0.430362i	$-0.141614\pi$
$242$			3391.52i			0.900888i
$243$	−2876.78			−0.759447
$244$	4813.11			1.26282
$245$		−	178.267i		−	0.0464860i
$246$	−13889.6			−3.59988
$247$	7.71743	+	552.170i	0.00198805	+	0.142242i
$248$	2374.59			0.608010
$249$			9390.91i			2.39006i
$250$	456.875			0.115581
$251$	−410.078			−0.103123			−0.0515615	−	0.998670i	$-0.516420\pi$
$251$	−410.078			−0.103123			−0.0515615	+	0.998670i	$0.516420\pi$
$252$			4886.18i			1.22143i
$253$		−	3164.68i		−	0.786411i
$254$			6329.16i			1.56349i
$255$		−	3842.48i		−	0.943628i
$256$	5362.49			1.30920
$257$	117.117			0.0284262			0.0142131	−	0.999899i	$-0.495476\pi$
$257$	117.117			0.0284262			0.0142131	+	0.999899i	$0.495476\pi$
$258$			5799.23i			1.39940i
$259$	4161.00			0.998271
$260$	17.5520	+	1255.82i	0.00418665	+	0.299548i
$261$	5440.52			1.29027
$262$			8531.06i			2.01164i
$263$	2511.96			0.588950			0.294475	−	0.955659i	$-0.404855\pi$
$263$	2511.96			0.588950			0.294475	+	0.955659i	$0.404855\pi$
$264$	1665.51			0.388276
$265$			74.6266i			0.0172992i
$266$		−	837.932i		−	0.193146i
$267$		−	1008.27i		−	0.231105i
$268$		−	4541.95i		−	1.03524i
$269$	5896.91			1.33658			0.668292	−	0.743899i	$-0.267026\pi$
$269$	5896.91			1.33658			0.668292	+	0.743899i	$0.267026\pi$
$270$	−3118.45			−0.702898
$271$		−	3452.44i		−	0.773877i	−0.922106	−	0.386938i	$-0.873533\pi$
$271$		−	3452.44i		−	0.773877i	0.922106	−	0.386938i	$-0.126467\pi$
$272$	6988.68			1.55791
$273$	109.543	+	7837.65i	0.0242852	+	1.73757i
$274$	−5585.03			−1.23140
$275$			501.926i			0.110063i
$276$	−7259.51			−1.58323
$277$	−2430.98			−0.527304			−0.263652	−	0.964618i	$-0.584927\pi$
$277$	−2430.98			−0.527304			−0.263652	+	0.964618i	$0.584927\pi$
$278$		−	8209.26i		−	1.77107i
$279$		−	11526.5i		−	2.47338i
$280$			939.172i			0.200451i
$281$			3512.86i			0.745763i	0.927879	+	0.372882i	$0.121630\pi$
$281$			3512.86i			0.745763i	−0.927879	+	0.372882i	$0.878370\pi$
$282$	7763.42			1.63938
$283$	−3590.13			−0.754103			−0.377051	−	0.926192i	$-0.623062\pi$
$283$	−3590.13			−0.754103			−0.377051	+	0.926192i	$0.623062\pi$
$284$			2745.87i			0.573724i
$285$	506.248			0.105219
$286$	−3439.22	+	48.0683i	−0.711067	+	0.00993825i
$287$	8604.62			1.76974
$288$		−	9766.02i		−	1.99815i
$289$	3083.45			0.627611
$290$	−2121.94			−0.429672
$291$			7695.42i			1.55022i
$292$		−	2859.04i		−	0.572989i
$293$			9311.11i			1.85652i	0.371931	+	0.928260i	$0.378696\pi$
$293$			9311.11i			1.85652i	−0.371931	+	0.928260i	$0.621304\pi$
$294$		−	1119.90i		−	0.222157i
$295$	2082.60			0.411029
$296$	−2064.10			−0.405316
$297$		−	3425.95i		−	0.669339i
$298$	−2597.05			−0.504842
$299$	−7387.60	+	103.253i	−1.42888	+	0.0199708i
$300$	1151.37			0.221582
$301$		−	3592.62i		−	0.687958i
$302$	4392.90			0.837030
$303$	−2064.49			−0.391426
$304$			920.761i			0.173715i
$305$		−	4490.67i		−	0.843067i
$306$		−	15314.4i		−	2.86100i
$307$		−	2634.13i		−	0.489699i	−0.969561	−	0.244849i	$-0.921261\pi$
$307$		−	2634.13i		−	0.489699i	0.969561	−	0.244849i	$-0.0787385\pi$
$308$	2093.65			0.387328
$309$	−1065.25			−0.196117
$310$			4495.64i			0.823661i
$311$	−1976.39			−0.360356			−0.180178	−	0.983634i	$-0.557667\pi$
$311$	−1976.39			−0.360356			−0.180178	+	0.983634i	$0.557667\pi$
$312$	−54.3399	−	3887.94i	−0.00986023	−	0.705485i
$313$	4099.30			0.740276			0.370138	−	0.928977i	$-0.379310\pi$
$313$	4099.30			0.740276			0.370138	+	0.928977i	$0.379310\pi$
$314$		−	2475.76i		−	0.444953i
$315$	4558.84			0.815434
$316$	482.663			0.0859238
$317$		−	619.492i		−	0.109761i	−0.998493	−	0.0548804i	$-0.982522\pi$
$317$		−	619.492i		−	0.109761i	0.998493	−	0.0548804i	$-0.0174777\pi$
$318$			468.817i			0.0826728i
$319$		−	2331.18i		−	0.409158i
$320$			682.873i			0.119293i
$321$	−10513.5			−1.82806
$322$	11210.9			1.94024
$323$			1053.54i			0.181487i
$324$	−1079.11			−0.185032
$325$	1171.69	−	16.3762i	0.199980	−	0.00279503i
$326$	7467.45			1.26866
$327$		−	14936.5i		−	2.52596i
$328$	−4268.40			−0.718546
$329$	−4809.44			−0.805936
$330$			3153.18i			0.525991i
$331$		−	4249.98i		−	0.705741i	−0.935672	−	0.352870i	$-0.885206\pi$
$331$		−	4249.98i		−	0.705741i	0.935672	−	0.352870i	$-0.114794\pi$
$332$		−	5855.98i		−	0.968038i
$333$			10019.4i			1.64883i
$334$	−9468.56			−1.55119
$335$	−4237.68			−0.691131
$336$			13069.5i			2.12203i
$337$	−6965.45			−1.12591			−0.562956	−	0.826487i	$-0.690336\pi$
$337$	−6965.45			−1.12591			−0.562956	+	0.826487i	$0.690336\pi$
$338$	224.420	+	8026.89i	0.0361149	+	1.29173i
$339$	5445.41			0.872431
$340$			2396.09i			0.382195i
$341$	−4938.94			−0.784336
$342$	2017.68			0.319016
$343$		−	5980.66i		−	0.941474i
$344$			1782.15i			0.279323i
$345$			6773.19i			1.05697i
$346$			3993.22i			0.620454i
$347$	−4287.03			−0.663227			−0.331613	−	0.943415i	$-0.607593\pi$
$347$	−4287.03			−0.663227			−0.331613	+	0.943415i	$0.607593\pi$
$348$	−5347.53			−0.823730
$349$		−	10344.2i		−	1.58657i	−0.608848	−	0.793287i	$-0.708368\pi$
$349$		−	10344.2i		−	1.58657i	0.608848	−	0.793287i	$-0.291632\pi$
$350$	−1778.07			−0.271548
$351$	−7997.49	+	111.777i	−1.21617	+	0.0169978i
$352$	−4184.59			−0.633635
$353$			1570.76i			0.236835i	0.992964	+	0.118418i	$0.0377822\pi$
$353$			1570.76i			0.236835i	−0.992964	+	0.118418i	$0.962218\pi$
$354$	13083.2			1.96431
$355$	2561.92			0.383022
$356$			628.737i			0.0936039i
$357$			14954.2i			2.21697i
$358$			9662.51i			1.42648i
$359$		−	4580.91i		−	0.673458i	−0.941602	−	0.336729i	$-0.890679\pi$
$359$		−	4580.91i		−	0.673458i	0.941602	−	0.336729i	$-0.109321\pi$
$360$	−2261.46			−0.331081
$361$	6720.20			0.979763
$362$			415.412i			0.0603138i
$363$	7974.42			1.15303
$364$	−68.3089	−	4887.40i	−0.00983615	−	0.703762i
$365$	−2667.51			−0.382531
$366$		−	28211.2i		−	4.02902i
$367$	7725.22			1.09878			0.549392	−	0.835565i	$-0.314860\pi$
$367$	7725.22			1.09878			0.549392	+	0.835565i	$0.314860\pi$
$368$	−12319.0			−1.74504
$369$			20719.3i			2.92304i
$370$		−	3907.82i		−	0.549075i
$371$		−	290.432i		−	0.0406428i
$372$			11329.5i			1.57905i
$373$	−8286.80			−1.15033			−0.575166	−	0.818036i	$-0.695063\pi$
$373$	−8286.80			−1.15033			−0.575166	+	0.818036i	$0.695063\pi$
$374$	−6561.99			−0.907253
$375$		−	1074.24i		−	0.147930i
$376$	2385.77			0.327225
$377$	−5441.89	+	76.0587i	−0.743425	+	0.0103905i
$378$	12136.4			1.65140
$379$			8496.27i			1.15151i	0.817621	+	0.575757i	$0.195293\pi$
$379$			8496.27i			1.15151i	−0.817621	+	0.575757i	$0.804707\pi$
$380$	−315.686			−0.0426167
$381$	14881.7			2.00108
$382$		−	5800.19i		−	0.776868i
$383$		−	2814.87i		−	0.375544i	−0.982213	−	0.187772i	$-0.939873\pi$
$383$		−	2814.87i		−	0.375544i	0.982213	−	0.187772i	$-0.0601266\pi$
$384$		−	10039.7i		−	1.33421i
$385$		−	1953.40i		−	0.258583i
$386$	9067.58			1.19567
$387$	8650.76			1.13629
$388$		−	4798.70i		−	0.627880i
$389$	−1795.14			−0.233977			−0.116989	−	0.993133i	$-0.537324\pi$
$389$	−1795.14			−0.233977			−0.116989	+	0.993133i	$0.537324\pi$
$390$	7360.75	−	102.878i	0.955708	−	0.0133575i
$391$	−14095.5			−1.82312
$392$		−	344.156i		−	0.0443431i
$393$	20059.0			2.57466
$394$	17252.6			2.20602
$395$		−	450.329i		−	0.0573633i
$396$			5041.36i			0.639743i
$397$			3046.79i			0.385174i	0.981280	+	0.192587i	$0.0616877\pi$
$397$			3046.79i			0.385174i	−0.981280	+	0.192587i	$0.938312\pi$
$398$			3103.13i			0.390819i
$399$	−1970.22			−0.247203
$400$	1953.83			0.244228
$401$		−	6060.07i		−	0.754677i	−0.926075	−	0.377339i	$-0.876839\pi$
$401$		−	6060.07i		−	0.754677i	0.926075	−	0.377339i	$-0.123161\pi$
$402$	−26621.8			−3.30292
$403$	161.141	+	11529.4i	0.0199181	+	1.42511i
$404$	1287.38			0.158538
$405$			1006.82i			0.123529i
$406$	8258.19			1.00948
$407$	4293.16			0.522860
$408$		−	7418.15i		−	0.900130i
$409$		−	5020.20i		−	0.606927i	−0.952843	−	0.303463i	$-0.901857\pi$
$409$		−	5020.20i		−	0.606927i	0.952843	−	0.303463i	$-0.0981430\pi$
$410$		−	8081.05i		−	0.973402i
$411$			13132.0i			1.57604i
$412$	664.270			0.0794326
$413$	−8105.07			−0.965677
$414$			26994.9i			3.20465i
$415$	−5463.68			−0.646269
$416$	136.529	+	9768.46i	0.0160911	+	1.15129i
$417$	−19302.3			−2.26676
$418$		−	864.545i		−	0.101163i
$419$	−9083.45			−1.05908			−0.529541	−	0.848284i	$-0.677636\pi$
$419$	−9083.45			−1.05908			−0.529541	+	0.848284i	$0.677636\pi$
$420$	−4480.93			−0.520588
$421$		−	1928.90i		−	0.223299i	−0.993748	−	0.111650i	$-0.964387\pi$
$421$		−	1928.90i		−	0.223299i	0.993748	−	0.111650i	$-0.0356135\pi$
$422$		−	11308.8i		−	1.30452i
$423$		−	11580.8i		−	1.33115i
$424$			144.072i			0.0165017i
$425$	2235.57			0.255156
$426$	16094.4			1.83047
$427$			17476.8i			1.98071i
$428$	6556.00			0.740412
$429$	113.022	+	8086.58i	0.0127197	+	0.910079i
$430$	−3374.02			−0.378395
$431$		−	3177.44i		−	0.355109i	−0.984111	−	0.177554i	$-0.943181\pi$
$431$		−	3177.44i		−	0.355109i	0.984111	−	0.177554i	$-0.0568185\pi$
$432$	−13336.1			−1.48526
$433$	9465.37			1.05052			0.525262	−	0.850941i	$-0.323967\pi$
$433$	9465.37			1.05052			0.525262	+	0.850941i	$0.323967\pi$
$434$		−	17496.1i		−	1.93512i
$435$			4989.30i			0.549927i
$436$			9314.08i			1.02308i
$437$		−	1857.08i		−	0.203287i
$438$	−16757.7			−1.82812
$439$	−768.174			−0.0835146			−0.0417573	−	0.999128i	$-0.513296\pi$
$439$	−768.174			−0.0835146			−0.0417573	+	0.999128i	$0.513296\pi$
$440$			969.001i			0.104989i
$441$	−1670.57			−0.180388
$442$	214.096	+	15318.2i	0.0230396	+	1.64845i
$443$	1368.96			0.146820			0.0734099	−	0.997302i	$-0.476612\pi$
$443$	1368.96			0.146820			0.0734099	+	0.997302i	$0.476612\pi$
$444$		−	9848.14i		−	1.05264i
$445$	586.617			0.0624906
$446$	−3374.02			−0.358216
$447$			6106.40i			0.646136i
$448$		−	2657.61i		−	0.280268i
$449$			2152.16i			0.226206i	0.993583	+	0.113103i	$0.0360790\pi$
$449$			2152.16i			0.226206i	−0.993583	+	0.113103i	$0.963921\pi$
$450$		−	4281.45i		−	0.448510i
$451$	8877.91			0.926927
$452$	−3395.65			−0.353358
$453$		−	10329.0i		−	1.07130i
$454$	2386.18			0.246671
$455$	−4559.99	+	63.7328i	−0.469836	+	0.00656668i
$456$	977.344			0.100369
$457$		−	10468.5i		−	1.07154i	−0.844363	−	0.535771i	$-0.820021\pi$
$457$		−	10468.5i		−	1.07154i	0.844363	−	0.535771i	$-0.179979\pi$
$458$	12611.4			1.28666
$459$	−15259.1			−1.55171
$460$		−	4223.62i		−	0.428103i
$461$			6737.46i			0.680683i	0.940302	+	0.340341i	$0.110543\pi$
$461$			6737.46i			0.680683i	−0.940302	+	0.340341i	$0.889457\pi$
$462$		−	12271.6i		−	1.23577i
$463$			6896.27i			0.692218i	0.938194	+	0.346109i	$0.112497\pi$
$463$			6896.27i			0.692218i	−0.938194	+	0.346109i	$0.887503\pi$
$464$	−9074.51			−0.907917
$465$	10570.5			1.05419
$466$			10039.6i			0.998021i
$467$	−11356.8			−1.12533			−0.562664	−	0.826685i	$-0.690224\pi$
$467$	−11356.8			−1.12533			−0.562664	+	0.826685i	$0.690224\pi$
$468$	11768.5	−	164.483i	1.16239	−	0.0162462i
$469$	16492.2			1.62375
$470$			4516.80i			0.443286i
$471$	−5821.22			−0.569485
$472$	4020.59			0.392082
$473$		−	3706.72i		−	0.360328i
$474$		−	2829.04i		−	0.274139i
$475$			294.537i			0.0284512i
$476$		−	9325.11i		−	0.897932i
$477$	699.339			0.0671290
$478$	−24212.5			−2.31685
$479$		−	7739.00i		−	0.738213i	−0.929387	−	0.369106i	$-0.879664\pi$
$479$		−	7739.00i		−	0.738213i	0.929387	−	0.369106i	$-0.120336\pi$
$480$	8956.04			0.851636
$481$	−140.071	−	10021.9i	−0.0132780	−	0.950019i
$482$	11770.0			1.11226
$483$		−	26359.9i		−	2.48327i
$484$	−4972.69			−0.467007
$485$	−4477.23			−0.419177
$486$		−	10514.6i		−	0.981385i
$487$		−	21347.3i		−	1.98632i	−0.116748	−	0.993162i	$-0.537247\pi$
$487$		−	21347.3i		−	1.98632i	0.116748	−	0.993162i	$-0.462753\pi$
$488$		−	8669.54i		−	0.804204i
$489$		−	17558.1i		−	1.62373i
$490$	651.566			0.0600709
$491$	11452.5			1.05264			0.526319	−	0.850287i	$-0.323572\pi$
$491$	11452.5			1.05264			0.526319	+	0.850287i	$0.323572\pi$
$492$		−	20365.1i		−	1.86612i
$493$	−10383.1			−0.948539
$494$	−2018.18	+	28.2072i	−0.183810	+	0.00256903i
$495$	4703.64			0.427096
$496$			19225.6i			1.74043i
$497$	−9970.51			−0.899876
$498$	−34323.8			−3.08852
$499$			8778.37i			0.787522i	0.919213	+	0.393761i	$0.128826\pi$
$499$			8778.37i			0.787522i	−0.919213	+	0.393761i	$0.871174\pi$
$500$			669.876i			0.0599155i
$501$			22263.3i			1.98533i
$502$		−	1498.83i		−	0.133259i
$503$	20459.6			1.81362			0.906810	−	0.421540i	$-0.138510\pi$
$503$	20459.6			1.81362			0.906810	+	0.421540i	$0.138510\pi$
$504$	8801.14			0.777846
$505$		−	1201.13i		−	0.105841i
$506$	11566.9			1.01623
$507$	18873.5	−	527.676i	1.65326	−	0.0462227i
$508$	−9279.90			−0.810490
$509$			6203.63i			0.540218i	0.962830	+	0.270109i	$0.0870598\pi$
$509$			6203.63i			0.540218i	−0.962830	+	0.270109i	$0.912940\pi$
$510$	14044.2			1.21939
$511$	10381.4			0.898722
$512$			10254.0i			0.885093i
$513$		−	2010.40i		−	0.173024i
$514$			428.062i			0.0367334i
$515$		−	619.770i		−	0.0530297i
$516$	−8502.90			−0.725425
$517$	−4962.19			−0.422122
$518$			15208.5i			1.29000i
$519$	9389.21			0.794105
$520$	2262.02	−	31.6152i	0.190762	−	0.00266619i
$521$	9308.04			0.782711			0.391356	−	0.920240i	$-0.372006\pi$
$521$	9308.04			0.782711			0.391356	+	0.920240i	$0.372006\pi$
$522$			19885.1i			1.66733i
$523$	1285.95			0.107515			0.0537577	−	0.998554i	$-0.482880\pi$
$523$	1285.95			0.107515			0.0537577	+	0.998554i	$0.482880\pi$
$524$	−12508.4			−1.04281
$525$			4180.74i			0.347548i
$526$			9181.20i			0.761063i
$527$			21998.0i			1.81831i
$528$			13484.6i			1.11144i
$529$	12679.3			1.04210
$530$	−272.760			−0.0223546
$531$		−	19516.4i		−	1.59499i
$532$	1228.59			0.100124
$533$	−289.656	−	20724.5i	−0.0235392	−	1.68420i
$534$	3685.23			0.298643
$535$		−	6116.81i		−	0.494304i
$536$	−8181.11			−0.659272
$537$	22719.3			1.82572
$538$			21553.2i			1.72718i
$539$			715.815i			0.0572029i
$540$		−	4572.31i		−	0.364372i
$541$		−	10504.9i		−	0.834824i	−0.908717	−	0.417412i	$-0.862937\pi$
$541$		−	10504.9i		−	0.834824i	0.908717	−	0.417412i	$-0.137063\pi$
$542$	12618.6			1.00003
$543$	976.753			0.0771943
$544$			18638.1i			1.46894i
$545$	8690.11			0.683016
$546$	−28646.6	+	400.380i	−2.24535	+	0.0313822i
$547$	1017.35			0.0795227			0.0397614	−	0.999209i	$-0.487340\pi$
$547$	1017.35			0.0795227			0.0397614	+	0.999209i	$0.487340\pi$
$548$		−	8188.84i		−	0.638339i
$549$	−42082.9			−3.27150
$550$	−1834.54			−0.142227
$551$		−	1367.97i		−	0.105767i
$552$			13076.1i			1.00825i
$553$			1752.59i			0.134770i
$554$		−	8885.21i		−	0.681401i
$555$	−9188.40			−0.702749
$556$	12036.5			0.918098
$557$			15058.6i			1.14551i	0.819725	+	0.572757i	$0.194126\pi$
$557$			15058.6i			1.14551i	−0.819725	+	0.572757i	$0.805874\pi$
$558$	42129.4			3.19620
$559$	−8652.93	+	120.938i	−0.654705	+	0.00915050i
$560$	−7603.91			−0.573793
$561$			15429.1i			1.16117i
$562$	−12839.5			−0.963703
$563$	−6892.23			−0.515938			−0.257969	−	0.966153i	$-0.583053\pi$
$563$	−6892.23			−0.515938			−0.257969	+	0.966153i	$0.583053\pi$
$564$			11382.8i			0.849829i
$565$			3168.17i			0.235904i
$566$		−	13121.9i		−	0.974479i
$567$		−	3918.33i		−	0.290219i
$568$	4945.96			0.365366
$569$	−23546.3			−1.73482			−0.867409	−	0.497595i	$-0.834217\pi$
$569$	−23546.3			−1.73482			−0.867409	+	0.497595i	$0.834217\pi$
$570$			1850.33i			0.135968i
$571$	−4737.30			−0.347198			−0.173599	−	0.984816i	$-0.555540\pi$
$571$	−4737.30			−0.347198			−0.173599	+	0.984816i	$0.555540\pi$
$572$	−70.4784	−	5042.63i	−0.00515184	−	0.368606i
$573$	−13637.9			−0.994296
$574$			31449.9i			2.28692i
$575$	−3940.68			−0.285804
$576$	6399.32			0.462914
$577$		−	2000.42i		−	0.144330i	−0.997393	−	0.0721652i	$-0.977009\pi$
$577$		−	2000.42i		−	0.144330i	0.997393	−	0.0721652i	$-0.0229909\pi$
$578$			11270.0i			0.811022i
$579$		−	21320.5i		−	1.53031i
$580$		−	3111.22i		−	0.222735i
$581$	21263.6			1.51835
$582$	−28126.7			−2.00325
$583$		−	299.656i		−	0.0212873i
$584$	−5149.80			−0.364898
$585$	−153.464	−	10980.1i	−0.0108461	−	0.776020i
$586$	−34032.1			−2.39906
$587$		−	5961.64i		−	0.419188i	−0.977789	−	0.209594i	$-0.932786\pi$
$587$		−	5961.64i		−	0.419188i	0.977789	−	0.209594i	$-0.0672142\pi$
$588$	1642.02			0.115163
$589$	−2898.24			−0.202750
$590$			7611.90i			0.531147i
$591$		−	40565.8i		−	2.82344i
$592$		−	16711.8i		−	1.16022i
$593$			9517.01i			0.659050i	0.944147	+	0.329525i	$0.106889\pi$
$593$			9517.01i			0.659050i	−0.944147	+	0.329525i	$0.893111\pi$
$594$	12521.8			0.864945
$595$	−8700.41			−0.599465
$596$		−	3807.83i		−	0.261703i
$597$	7296.35			0.500201
$598$	−377.389	−	27001.7i	−0.0258070	−	1.84645i
$599$	8822.25			0.601782			0.300891	−	0.953659i	$-0.402716\pi$
$599$	8822.25			0.601782			0.300891	+	0.953659i	$0.402716\pi$
$600$		−	2073.90i		−	0.141111i
$601$	−388.522			−0.0263696			−0.0131848	−	0.999913i	$-0.504197\pi$
$601$	−388.522			−0.0263696			−0.0131848	+	0.999913i	$0.504197\pi$
$602$	13131.0			0.889004
$603$			39712.0i			2.68192i
$604$			6440.93i			0.433904i
$605$			4639.56i			0.311777i
$606$		−	7545.72i		−	0.505815i
$607$	−2729.75			−0.182532			−0.0912662	−	0.995827i	$-0.529091\pi$
$607$	−2729.75			−0.182532			−0.0912662	+	0.995827i	$0.529091\pi$
$608$	−2455.58			−0.163794
$609$		−	19417.4i		−	1.29201i
$610$	16413.4			1.08944
$611$	161.900	+	11583.7i	0.0107197	+	0.766981i
$612$	22454.2			1.48310
$613$			27578.2i			1.81708i	0.417794	+	0.908542i	$0.362803\pi$
$613$			27578.2i			1.81708i	−0.417794	+	0.908542i	$0.637197\pi$
$614$	9627.72			0.632807
$615$	−19000.9			−1.24583
$616$		−	3771.16i		−	0.246663i
$617$		−	247.197i		−	0.0161293i	−0.999967	−	0.00806464i	$-0.997433\pi$
$617$		−	247.197i		−	0.0161293i	0.999967	−	0.00806464i	$-0.00256708\pi$
$618$		−	3893.50i		−	0.253430i
$619$			6035.92i			0.391929i	0.980611	+	0.195965i	$0.0627838\pi$
$619$			6035.92i			0.391929i	−0.980611	+	0.195965i	$0.937216\pi$
$620$	−6591.56			−0.426973
$621$	26897.5			1.73810
$622$		−	7223.70i		−	0.465665i
$623$	−2283.00			−0.146816
$624$	31478.3	−	439.957i	2.01946	−	0.0282250i
$625$	625.000			0.0400000
$626$			14982.9i			0.956611i
$627$	−2032.79			−0.129477
$628$	3629.99			0.230657
$629$		−	19121.7i		−	1.21213i
$630$			16662.6i			1.05373i
$631$			16570.3i			1.04541i	0.852514	+	0.522705i	$0.175077\pi$
$631$			16570.3i			1.04541i	−0.852514	+	0.522705i	$0.824923\pi$
$632$		−	869.389i		−	0.0547190i
$633$	−26590.3			−1.66962
$634$	2264.24			0.141837
$635$			8658.23i			0.541089i
$636$	−687.386			−0.0428563
$637$	1670.99	−	23.3546i	0.103936	−	0.00145266i
$638$	8520.47			0.528729
$639$		−	24008.2i		−	1.48631i
$640$	5841.17			0.360770
$641$	−7610.28			−0.468936			−0.234468	−	0.972124i	$-0.575335\pi$
$641$	−7610.28			−0.468936			−0.234468	+	0.972124i	$0.575335\pi$
$642$		−	38426.8i		−	2.36228i
$643$			15468.4i			0.948699i	0.880337	+	0.474350i	$0.157317\pi$
$643$			15468.4i			0.948699i	−0.880337	+	0.474350i	$0.842683\pi$
$644$			16437.5i			1.00579i
$645$			7933.28i			0.484299i
$646$	−3850.67			−0.234524
$647$	−25669.6			−1.55978			−0.779889	−	0.625917i	$-0.784725\pi$
$647$	−25669.6			−1.55978			−0.779889	+	0.625917i	$0.784725\pi$
$648$			1943.72i			0.117834i
$649$	−8362.49			−0.505788
$650$	59.8548	+	4282.52i	0.00361184	+	0.258422i
$651$	−41138.4			−2.47671
$652$			10948.9i			0.657655i
$653$	3691.09			0.221200			0.110600	−	0.993865i	$-0.464723\pi$
$653$	3691.09			0.221200			0.110600	+	0.993865i	$0.464723\pi$
$654$	54592.8			3.26414
$655$			11670.4i			0.696184i
$656$		−	34558.7i		−	2.05684i
$657$			24997.7i			1.48440i
$658$		−	17578.5i		−	1.04146i
$659$	23260.7			1.37497			0.687487	−	0.726197i	$-0.258714\pi$
$659$	23260.7			1.37497			0.687487	+	0.726197i	$0.258714\pi$
$660$	−4623.24			−0.272666
$661$			93.6601i			0.00551128i	0.999996	+	0.00275564i	$0.000877149\pi$
$661$			93.6601i			0.00551128i	−0.999996	+	0.00275564i	$0.999123\pi$
$662$	15533.7			0.911984
$663$	36017.5	−	503.400i	2.10981	−	0.0294878i
$664$	−10548.0			−0.616478
$665$		−	1146.28i		−	0.0668435i
$666$	−36620.8			−2.13067
$667$	18302.4			1.06247
$668$		−	13882.9i		−	0.804112i
$669$			7933.29i			0.458473i
$670$		−	15488.7i		−	0.893105i
$671$			18031.9i			1.03743i
$672$	−34855.2			−2.00084
$673$	15681.6			0.898191			0.449096	−	0.893484i	$-0.351746\pi$
$673$	15681.6			0.898191			0.449096	+	0.893484i	$0.351746\pi$
$674$		−	25458.7i		−	1.45494i
$675$	−4266.00			−0.243257
$676$	−11769.1	+	329.048i	−0.669614	+	0.0187214i
$677$	6692.61			0.379938			0.189969	−	0.981790i	$-0.439161\pi$
$677$	6692.61			0.379938			0.189969	+	0.981790i	$0.439161\pi$
$678$			19903.0i			1.12739i
$679$	17424.5			0.984818
$680$	4315.92			0.243394
$681$		−	5610.58i		−	0.315709i
$682$		−	18051.8i		−	1.01355i
$683$		−	5093.28i		−	0.285342i	−0.989770	−	0.142671i	$-0.954431\pi$
$683$		−	5093.28i		−	0.285342i	0.989770	−	0.142671i	$-0.0455691\pi$
$684$			2958.34i			0.165373i
$685$	−7640.26			−0.426160
$686$	21859.3			1.21661
$687$		−	29652.9i		−	1.64677i
$688$	−14429.0			−0.799565
$689$	−699.514	+	9.77678i	−0.0386783	+	0.000540589i
$690$	−24756.0			−1.36586
$691$		−	16747.8i		−	0.922020i	−0.887395	−	0.461010i	$-0.847487\pi$
$691$		−	16747.8i		−	0.922020i	0.887395	−	0.461010i	$-0.152513\pi$
$692$	−5854.92			−0.321634
$693$	−18305.6			−1.00342
$694$		−	15669.1i		−	0.857046i
$695$		−	11230.2i		−	0.612928i
$696$			9632.16i			0.524578i
$697$		−	39542.1i		−	2.14887i
$698$	37808.2			2.05023
$699$	23606.1			1.27734
$700$		−	2607.03i		−	0.140766i
$701$	18385.1			0.990580			0.495290	−	0.868728i	$-0.335062\pi$
$701$	18385.1			0.990580			0.495290	+	0.868728i	$0.335062\pi$
$702$	−408.545	−	29230.8i	−0.0219652	−	1.57157i
$703$	2519.29			0.135159
$704$		−	2742.02i		−	0.146795i
$705$	10620.3			0.567352
$706$	−5741.11			−0.306047
$707$			4674.58i			0.248664i
$708$			19182.8i			1.01827i
$709$			18930.7i			1.00276i	0.865227	+	0.501380i	$0.167174\pi$
$709$			18930.7i			1.00276i	−0.865227	+	0.501380i	$0.832826\pi$
$710$			9363.83i			0.494955i
$711$	−4220.11			−0.222597
$712$	1132.50			0.0596100
$713$		−	38776.2i		−	2.03672i
$714$	−54657.4			−2.86485
$715$	−4704.81	+	65.7570i	−0.246084	+	0.00343940i
$716$	−14167.3			−0.739465
$717$			56930.5i			2.96528i
$718$	16743.2			0.870267
$719$	−12492.1			−0.647951			−0.323975	−	0.946066i	$-0.605019\pi$
$719$	−12492.1			−0.647951			−0.323975	+	0.946066i	$0.605019\pi$
$720$		−	18309.7i		−	0.947723i
$721$			2412.02i			0.124589i
$722$			24562.3i			1.26609i
$723$		−	27674.7i		−	1.42356i
$724$	−609.083			−0.0312657
$725$	−2902.80			−0.148700
$726$			29146.5i			1.48998i
$727$	−20599.5			−1.05088			−0.525442	−	0.850829i	$-0.676100\pi$
$727$	−20599.5			−1.05088			−0.525442	+	0.850829i	$0.676100\pi$
$728$	−8803.35	+	123.040i	−0.448178	+	0.00626398i
$729$	−30159.7			−1.53227
$730$		−	9749.74i		−	0.494321i
$731$	−16509.7			−0.835340
$732$	41363.6			2.08858
$733$			10452.1i			0.526683i	0.964703	+	0.263342i	$0.0848247\pi$
$733$			10452.1i			0.526683i	−0.964703	+	0.263342i	$0.915175\pi$
$734$			28235.7i			1.41989i
$735$		−	1532.02i		−	0.0768834i
$736$		−	32853.7i		−	1.64538i
$737$	17016.0			0.850465
$738$	−75728.9			−3.77726
$739$			15791.4i			0.786059i	0.919526	+	0.393030i	$0.128573\pi$
$739$			15791.4i			0.786059i	−0.919526	+	0.393030i	$0.871427\pi$
$740$	5729.70			0.284632
$741$	66.3231	+	4745.32i	0.00328804	+	0.235255i
$742$	1061.53			0.0525201
$743$		−	16295.2i		−	0.804592i	−0.915510	−	0.402296i	$-0.868212\pi$
$743$		−	16295.2i		−	0.804592i	0.915510	−	0.402296i	$-0.131788\pi$
$744$	20407.1			1.00559
$745$	−3552.74			−0.174714
$746$		−	30288.2i		−	1.48650i
$747$			51201.1i			2.50783i
$748$		−	9621.28i		−	0.470306i
$749$			23805.4i			1.16132i
$750$	3926.35			0.191160
$751$	−2781.04			−0.135129			−0.0675643	−	0.997715i	$-0.521523\pi$
$751$	−2781.04			−0.135129			−0.0675643	+	0.997715i	$0.521523\pi$
$752$			19316.1i			0.936684i
$753$	−3524.19			−0.170556
$754$	−277.994	−	19890.1i	−0.0134270	−	0.960682i
$755$	6009.45			0.289677
$756$			17794.5i			0.856059i
$757$	25968.3			1.24681			0.623403	−	0.781901i	$-0.285750\pi$
$757$	25968.3			1.24681			0.623403	+	0.781901i	$0.285750\pi$
$758$	−31053.8			−1.48803
$759$		−	27197.1i		−	1.30065i
$760$			568.624i			0.0271397i
$761$			6582.16i			0.313539i	0.987635	+	0.156769i	$0.0501080\pi$
$761$			6582.16i			0.313539i	−0.987635	+	0.156769i	$0.949892\pi$
$762$			54392.4i			2.58587i
$763$	−33820.2			−1.60468
$764$	8504.32			0.402716
$765$		−	20949.9i		−	0.990126i
$766$	10288.4			0.485292
$767$	272.840	+	19521.3i	0.0128444	+	0.919000i
$768$	46084.9			2.16530
$769$			7980.32i			0.374223i	0.982339	+	0.187112i	$0.0599126\pi$
$769$			7980.32i			0.374223i	−0.982339	+	0.187112i	$0.940087\pi$
$770$	7139.67			0.334150
$771$	1006.49			0.0470143
$772$			13295.0i			0.619816i
$773$			14633.6i			0.680899i	0.940263	+	0.340450i	$0.110579\pi$
$773$			14633.6i			0.680899i	−0.940263	+	0.340450i	$0.889421\pi$
$774$			31618.5i			1.46835i
$775$			6149.99i			0.285050i
$776$	−8643.59			−0.399854
$777$	35759.4			1.65105
$778$		−	6561.23i		−	0.302354i
$779$	5209.68			0.239610
$780$	150.841	+	10792.4i	0.00692431	+	0.495425i
$781$	−10287.2			−0.471324
$782$		−	51518.9i		−	2.35590i
$783$	19813.3			0.904306
$784$	2786.43			0.126933
$785$		−	3386.81i		−	0.153988i
$786$			73315.4i			3.32707i
$787$		−	32406.4i		−	1.46780i	−0.679255	−	0.733902i	$-0.737697\pi$
$787$		−	32406.4i		−	1.46780i	0.679255	−	0.733902i	$-0.262303\pi$
$788$			25296.0i			1.14357i
$789$	21587.6			0.974068
$790$	1645.95			0.0741269
$791$		−	12329.9i		−	0.554236i
$792$	9080.67			0.407409
$793$	42093.4	−	588.320i	1.88497	−	0.0263453i
$794$	−11136.0			−0.497736
$795$			641.337i			0.0286112i
$796$	−4549.85			−0.202595
$797$	−43761.2			−1.94492			−0.972461	−	0.233066i	$-0.925124\pi$
$797$	−43761.2			−1.94492			−0.972461	+	0.233066i	$0.925124\pi$
$798$		−	7201.14i		−	0.319445i
$799$			22101.5i			0.978593i
$800$			5210.67i			0.230281i
$801$		−	5497.29i		−	0.242493i
$802$	22149.6			0.975222
$803$	10711.1			0.470720
$804$		−	39033.2i		−	1.71218i
$805$	15336.3			0.671472
$806$	−42139.9	+	588.970i	−1.84158	+	0.0257389i
$807$	50677.7			2.21058
$808$		−	2318.87i		−	0.100962i
$809$	−20194.7			−0.877638			−0.438819	−	0.898576i	$-0.644603\pi$
$809$	−20194.7			−0.877638			−0.438819	+	0.898576i	$0.644603\pi$
$810$	−3679.91			−0.159628
$811$			35223.5i			1.52511i	0.646924	+	0.762554i	$0.276055\pi$
$811$			35223.5i			1.52511i	−0.646924	+	0.762554i	$0.723945\pi$
$812$			12108.3i			0.523297i
$813$		−	29670.0i		−	1.27992i
$814$			15691.5i			0.675659i
$815$	10215.4			0.439055
$816$	60060.3			2.57663
$817$		−	2175.16i		−	0.0931446i
$818$	18348.8			0.784293
$819$	597.251	+	42732.4i	0.0254818	+	1.82319i
$820$	11848.5			0.504597
$821$			21772.3i			0.925527i	0.886482	+	0.462764i	$0.153142\pi$
$821$			21772.3i			0.925527i	−0.886482	+	0.462764i	$0.846858\pi$
$822$	−47997.4			−2.03662
$823$	−12117.3			−0.513224			−0.256612	−	0.966514i	$-0.582606\pi$
$823$	−12117.3			−0.513224			−0.256612	+	0.966514i	$0.582606\pi$
$824$		−	1196.51i		−	0.0505852i
$825$			4313.52i			0.182034i
$826$		−	29624.0i		−	1.24788i
$827$		−	17732.9i		−	0.745628i	−0.927906	−	0.372814i	$-0.878393\pi$
$827$		−	17732.9i		−	0.745628i	0.927906	−	0.372814i	$-0.121607\pi$
$828$	−39580.3			−1.66124
$829$	−42202.5			−1.76810			−0.884050	−	0.467392i	$-0.845194\pi$
$829$	−42202.5			−1.76810			−0.884050	+	0.467392i	$0.845194\pi$
$830$		−	19969.7i		−	0.835133i
$831$	−20891.7			−0.872110
$832$	−6400.92	+	89.4627i	−0.266721	+	0.00372784i
$833$	3188.23			0.132612
$834$		−	70549.9i		−	2.92919i
$835$	−12952.9			−0.536830
$836$	1267.61			0.0524415
$837$		−	41977.4i		−	1.73351i
$838$		−	33200.0i		−	1.36859i
$839$		−	24334.6i		−	1.00134i	−0.865639	−	0.500669i	$-0.833087\pi$
$839$		−	24334.6i		−	1.00134i	0.865639	−	0.500669i	$-0.166913\pi$
$840$			8071.19i			0.331527i
$841$	−10907.0			−0.447211
$842$	7050.14			0.288556
$843$			30189.3i			1.23342i
$844$	16581.2			0.676241
$845$	307.004	+	10980.7i	0.0124985	+	0.447039i
$846$	42327.7			1.72016
$847$		−	18056.3i		−	0.732492i
$848$	−1166.46			−0.0472363
$849$	−30853.4			−1.24721
$850$			8171.01i			0.329722i
$851$			33706.0i			1.35773i
$852$			23597.9i			0.948885i
$853$		−	40903.4i		−	1.64186i	−0.571031	−	0.820929i	$-0.693456\pi$
$853$		−	40903.4i		−	1.64186i	0.571031	−	0.820929i	$-0.306544\pi$
$854$	−63877.8			−2.55955
$855$	2760.16			0.110404
$856$		−	11808.9i		−	0.471518i
$857$	−34239.0			−1.36474			−0.682370	−	0.731007i	$-0.739051\pi$
$857$	−34239.0			−1.36474			−0.682370	+	0.731007i	$0.739051\pi$
$858$	−29556.4	+	413.096i	−1.17604	+	0.0164369i
$859$	46008.6			1.82747			0.913734	−	0.406314i	$-0.133186\pi$
$859$	46008.6			1.82747			0.913734	+	0.406314i	$0.133186\pi$
$860$		−	4947.03i		−	0.196154i
$861$	73947.6			2.92698
$862$	11613.5			0.458884
$863$			1552.40i			0.0612331i	0.999531	+	0.0306166i	$0.00974708\pi$
$863$			1552.40i			0.0612331i	−0.999531	+	0.0306166i	$0.990253\pi$
$864$		−	35566.0i		−	1.40044i
$865$			5462.69i			0.214725i
$866$			34595.9i			1.35752i
$867$	26499.0			1.03801
$868$	25653.1			1.00314
$869$			1808.25i			0.0705878i
$870$	−18235.9			−0.710637
$871$	−555.175	−	39721.9i	−0.0215974	−	1.54527i
$872$	16776.8			0.651531
$873$			41956.9i			1.62661i
$874$	6787.63			0.262695
$875$	−2432.38			−0.0939764
$876$		−	24570.4i		−	0.947669i
$877$		−	5802.07i		−	0.223400i	−0.993742	−	0.111700i	$-0.964370\pi$
$877$		−	5802.07i		−	0.223400i	0.993742	−	0.111700i	$-0.0356296\pi$
$878$		−	2807.67i		−	0.107921i
$879$			80019.1i			3.07051i
$880$	−7845.42			−0.300533
$881$	−991.228			−0.0379062			−0.0189531	−	0.999820i	$-0.506033\pi$
$881$	−991.228			−0.0379062			−0.0189531	+	0.999820i	$0.506033\pi$
$882$		−	6105.93i		−	0.233104i
$883$	17576.6			0.669874			0.334937	−	0.942241i	$-0.391285\pi$
$883$	17576.6			0.669874			0.334937	+	0.942241i	$0.391285\pi$
$884$	−22459.8	+	313.910i	−0.854530	+	0.0119434i
$885$	17897.7			0.679804
$886$			5003.54i			0.189726i
$887$	−27370.0			−1.03607			−0.518035	−	0.855360i	$-0.673336\pi$
$887$	−27370.0			−1.03607			−0.518035	+	0.855360i	$0.673336\pi$
$888$	−17738.8			−0.670355
$889$		−	33696.1i		−	1.27124i
$890$			2144.08i			0.0807526i
$891$		−	4042.78i		−	0.152007i
$892$		−	4947.03i		−	0.185694i
$893$	−2911.88			−0.109118
$894$	−22318.9			−0.834961
$895$			13218.2i			0.493672i
$896$	−22732.7			−0.847596
$897$	−63488.6	+	887.350i	−2.36324	+	0.0330298i
$898$	−7866.13			−0.292312
$899$		−	28563.5i		−	1.05967i
$900$	6277.52			0.232501
$901$	−1334.67			−0.0493498
$902$			32448.7i			1.19781i
$903$		−	30874.8i		−	1.13782i
$904$			6116.35i			0.225030i
$905$			568.280i			0.0208732i
$906$	37752.4			1.38437
$907$	−28779.1			−1.05358			−0.526788	−	0.849997i	$-0.676604\pi$
$907$	−28779.1			−1.05358			−0.526788	+	0.849997i	$0.676604\pi$
$908$			3498.64i			0.127871i
$909$	−11256.0			−0.410714
$910$	−232.943	−	16666.7i	−0.00848570	−	0.607140i
$911$	812.241			0.0295398			0.0147699	−	0.999891i	$-0.495298\pi$
$911$	812.241			0.0295398			0.0147699	+	0.999891i	$0.495298\pi$
$912$			7912.96i			0.287307i
$913$	21938.9			0.795260
$914$	38262.3			1.38469
$915$		−	38592.6i		−	1.39435i
$916$			18491.0i			0.666985i
$917$		−	45418.9i		−	1.63562i
$918$		−	55772.1i		−	2.00518i
$919$	−7982.53			−0.286528			−0.143264	−	0.989685i	$-0.545760\pi$
$919$	−7982.53			−0.286528			−0.143264	+	0.989685i	$0.545760\pi$
$920$	−7607.73			−0.272630
$921$		−	22637.5i		−	0.809915i
$922$	−24625.4			−0.879604
$923$	335.636	+	24014.2i	0.0119692	+	0.856380i
$924$	17992.8			0.640604
$925$		−	5345.86i		−	0.190022i
$926$	−25205.9			−0.894510
$927$	−5807.97			−0.205781
$928$		−	24200.8i		−	0.856068i
$929$			52612.3i			1.85808i	0.369984	+	0.929038i	$0.379363\pi$
$929$			52612.3i			1.85808i	−0.369984	+	0.929038i	$0.620637\pi$
$930$			38635.2i			1.36226i
$931$			420.051i			0.0147869i
$932$	−14720.3			−0.517359
$933$	−16985.0			−0.595995
$934$		−	41509.0i		−	1.45419i
$935$	−8976.74			−0.313979
$936$	−296.272	−	21197.8i	−0.0103461	−	0.740248i
$937$	−34900.3			−1.21680			−0.608401	−	0.793630i	$-0.708189\pi$
$937$	−34900.3			−1.21680			−0.608401	+	0.793630i	$0.708189\pi$
$938$			60279.0i			2.09827i
$939$	35229.2			1.22435
$940$	−6622.59			−0.229793
$941$			4626.31i			0.160269i	0.996784	+	0.0801346i	$0.0255350\pi$
$941$			4626.31i			0.160269i	−0.996784	+	0.0801346i	$0.974465\pi$
$942$		−	21276.5i		−	0.735909i
$943$			69701.4i			2.40699i
$944$			32552.3i			1.12234i
$945$	16602.4			0.571511
$946$	13548.1			0.465630
$947$			22103.4i			0.758463i	0.925302	+	0.379232i	$0.123812\pi$
$947$			22103.4i			0.758463i	−0.925302	+	0.379232i	$0.876188\pi$
$948$	4147.98			0.142110
$949$	−349.468	−	25003.9i	−0.0119539	−	0.855282i
$950$	−1076.53			−0.0367656
$951$		−	5323.88i		−	0.181534i
$952$	−16796.7			−0.571832
$953$	41498.1			1.41055			0.705276	−	0.708933i	$-0.250823\pi$
$953$	41498.1			1.41055			0.705276	+	0.708933i	$0.250823\pi$
$954$			2556.08i			0.0867465i
$955$		−	7934.60i		−	0.268856i
$956$		−	35500.7i		−	1.20102i
$957$		−	20034.1i		−	0.676708i
$958$	28286.0			0.953946
$959$	29734.4			1.00122
$960$			5868.57i			0.197299i
$961$	−30724.7			−1.03134
$962$	36630.0	−	511.960i	1.22765	−	0.0171583i
$963$	−57321.7			−1.91814
$964$			17257.4i			0.576579i
$965$	12404.4			0.413793
$966$	96345.4			3.20897
$967$			42191.4i			1.40309i	0.712627	+	0.701543i	$0.247505\pi$
$967$			42191.4i			1.40309i	−0.712627	+	0.701543i	$0.752495\pi$
$968$			8956.97i			0.297405i
$969$			9054.03i			0.300162i
$970$		−	16364.3i		−	0.541676i
$971$	−10472.7			−0.346123			−0.173061	−	0.984911i	$-0.555366\pi$
$971$	−10472.7			−0.346123			−0.173061	+	0.984911i	$0.555366\pi$
$972$	15416.7			0.508735
$973$			43705.7i			1.44002i
$974$	78024.4			2.56680
$975$	10069.4	−	140.736i	0.330749	−	0.00462272i
$976$	70192.0			2.30204
$977$		−	34586.0i		−	1.13255i	−0.824216	−	0.566276i	$-0.808384\pi$
$977$		−	34586.0i		−	1.13255i	0.824216	−	0.566276i	$-0.191616\pi$
$978$	64174.8			2.09825
$979$	−2355.51			−0.0768972
$980$			955.335i			0.0311398i
$981$		−	81436.5i		−	2.65043i
$982$			41858.9i			1.36026i
$983$		−	53923.9i		−	1.74965i	−0.484439	−	0.874825i	$-0.660976\pi$
$983$		−	53923.9i		−	1.74965i	0.484439	−	0.874825i	$-0.339024\pi$
$984$	−36682.4			−1.18841
$985$	23601.4			0.763455
$986$		−	37950.1i		−	1.22574i
$987$	−41332.1			−1.33294
$988$	−41.3577	−	2959.09i	−0.00133175	−	0.0952845i
$989$	29101.9			0.935678
$990$			17191.8i			0.551910i
$991$	−2349.40			−0.0753090			−0.0376545	−	0.999291i	$-0.511989\pi$
$991$	−2349.40			−0.0753090			−0.0376545	+	0.999291i	$0.511989\pi$
$992$	−51272.9			−1.64104
$993$		−	36524.1i		−	1.16723i
$994$		−	36442.2i		−	1.16285i
$995$			4245.05i			0.135254i
$996$		−	50326.0i		−	1.60104i
$997$	−10949.2			−0.347807			−0.173903	−	0.984763i	$-0.555638\pi$
$997$	−10949.2			−0.347807			−0.173903	+	0.984763i	$0.555638\pi$
$998$	−32084.9			−1.01767
$999$			36488.7i			1.15561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.4.c.a.51.11	yes	14
3.2	odd	2		585.4.b.e.181.4		14
4.3	odd	2		1040.4.k.d.961.2		14
5.2	odd	4		325.4.d.c.324.3		14
5.3	odd	4		325.4.d.d.324.12		14
5.4	even	2		325.4.c.e.51.4		14
13.5	odd	4		845.4.a.l.1.6		7
13.8	odd	4		845.4.a.i.1.2		7
13.12	even	2	inner	65.4.c.a.51.4	✓	14
39.38	odd	2		585.4.b.e.181.11		14
52.51	odd	2		1040.4.k.d.961.1		14
65.12	odd	4		325.4.d.d.324.11		14
65.38	odd	4		325.4.d.c.324.4		14
65.64	even	2		325.4.c.e.51.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.c.a.51.4	✓	14	13.12	even	2	inner
65.4.c.a.51.11	yes	14	1.1	even	1	trivial
325.4.c.e.51.4		14	5.4	even	2
325.4.c.e.51.11		14	65.64	even	2
325.4.d.c.324.3		14	5.2	odd	4
325.4.d.c.324.4		14	65.38	odd	4
325.4.d.d.324.11		14	65.12	odd	4
325.4.d.d.324.12		14	5.3	odd	4
585.4.b.e.181.4		14	3.2	odd	2
585.4.b.e.181.11		14	39.38	odd	2
845.4.a.i.1.2		7	13.8	odd	4
845.4.a.l.1.6		7	13.5	odd	4
1040.4.k.d.961.1		14	52.51	odd	2
1040.4.k.d.961.2		14	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	65.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.65500i q^{2} +8.59394 q^{3} -5.35901 q^{4} +5.00000i q^{5} +31.4108i q^{6} -19.4590i q^{7} +9.65282i q^{8} +46.8559 q^{9} -18.2750 q^{10} -20.0770i q^{11} -46.0550 q^{12} +(-46.8676 + 0.655046i) q^{13} +71.1227 q^{14} +42.9697i q^{15} -78.1531 q^{16} -89.4229 q^{17} +171.258i q^{18} -11.7815i q^{19} -26.7950i q^{20} -167.230i q^{21} +73.3816 q^{22} +157.627 q^{23} +82.9558i q^{24} -25.0000 q^{25} +(-2.39419 - 171.301i) q^{26} +170.640 q^{27} +104.281i q^{28} +116.112 q^{29} -157.054 q^{30} -245.999i q^{31} -208.427i q^{32} -172.541i q^{33} -326.840i q^{34} +97.2951 q^{35} -251.101 q^{36} +213.834i q^{37} +43.0613 q^{38} +(-402.777 + 5.62943i) q^{39} -48.2641 q^{40} +442.192i q^{41} +611.224 q^{42} +184.625 q^{43} +107.593i q^{44} +234.279i q^{45} +576.126i q^{46} -247.157i q^{47} -671.643 q^{48} -35.6534 q^{49} -91.3749i q^{50} -768.495 q^{51} +(251.164 - 3.51040i) q^{52} +14.9253 q^{53} +623.689i q^{54} +100.385 q^{55} +187.834 q^{56} -101.250i q^{57} +424.389i q^{58} -416.520i q^{59} -230.275i q^{60} -898.135 q^{61} +899.127 q^{62} -911.769i q^{63} +136.575 q^{64} +(-3.27523 - 234.338i) q^{65} +630.637 q^{66} +847.535i q^{67} +479.218 q^{68} +1354.64 q^{69} +355.613i q^{70} -512.385i q^{71} +452.291i q^{72} +533.502i q^{73} -781.564 q^{74} -214.849 q^{75} +63.1371i q^{76} -390.680 q^{77} +(-20.5756 - 1472.15i) q^{78} -90.0657 q^{79} -390.766i q^{80} +201.363 q^{81} -1616.21 q^{82} +1092.74i q^{83} +896.185i q^{84} -447.114i q^{85} +674.804i q^{86} +997.859 q^{87} +193.800 q^{88} -117.323i q^{89} -856.290 q^{90} +(12.7466 + 911.997i) q^{91} -844.724 q^{92} -2114.11i q^{93} +903.360 q^{94} +58.9075 q^{95} -1791.21i q^{96} +895.447i q^{97} -130.313i q^{98} -940.727i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 56 q^{4} + 158 q^{9} - 20 q^{10} - 108 q^{12} - 4 q^{13} - 152 q^{14} + 280 q^{16} - 100 q^{17} + 648 q^{22} - 532 q^{23} - 350 q^{25} - 344 q^{26} - 48 q^{27} + 588 q^{29} - 200 q^{30} + 540 q^{35}+ \cdots - 3120 q^{95}+O(q^{100}) \) 14 * q - 56 * q^4 + 158 * q^9 - 20 * q^10 - 108 * q^12 - 4 * q^13 - 152 * q^14 + 280 * q^16 - 100 * q^17 + 648 * q^22 - 532 * q^23 - 350 * q^25 - 344 * q^26 - 48 * q^27 + 588 * q^29 - 200 * q^30 + 540 * q^35 + 496 * q^36 + 148 * q^38 - 260 * q^39 + 240 * q^40 - 620 * q^42 + 728 * q^43 - 2008 * q^48 - 1302 * q^49 + 176 * q^51 - 528 * q^52 + 1040 * q^53 - 40 * q^55 + 512 * q^56 - 1460 * q^61 + 2964 * q^62 + 1296 * q^64 - 30 * q^65 - 600 * q^66 + 1604 * q^68 + 4160 * q^69 - 5928 * q^74 - 3568 * q^77 + 2560 * q^78 - 1024 * q^79 - 2890 * q^81 - 6660 * q^82 + 5256 * q^87 + 1132 * q^88 + 1360 * q^90 + 916 * q^91 + 6044 * q^92 + 2656 * q^94 - 3120 * q^95

Introduction

L-functions

Modular forms

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Database

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