LMFDB - Embedded newform 1680.2.cz.f.433.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1680,2,Mod(97,1680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1680.97"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.cz (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 840)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.8
Character	$\chi$	$=$	1680.433
Dual form			1680.2.cz.f.97.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{3} +(-0.793022 + 2.09072i) q^{5} +(-2.38904 - 1.13687i) q^{7} -1.00000i q^{9} -1.83199 q^{11} +(1.48628 - 1.48628i) q^{13} +(0.917612 + 2.03911i) q^{15} +(4.65516 + 4.65516i) q^{17} +3.78446 q^{19} +(-2.49320 + 0.885417i) q^{21} +(-0.980552 - 0.980552i) q^{23} +(-3.74223 - 3.31598i) q^{25} +(-0.707107 - 0.707107i) q^{27} +3.98517i q^{29} -0.418991i q^{31} +(-1.29541 + 1.29541i) q^{33} +(4.27145 - 4.09326i) q^{35} +(-3.70069 + 3.70069i) q^{37} -2.10191i q^{39} +10.3583i q^{41} +(6.57302 + 6.57302i) q^{43} +(2.09072 + 0.793022i) q^{45} +(5.32205 + 5.32205i) q^{47} +(4.41504 + 5.43207i) q^{49} +6.58339 q^{51} +(3.94238 + 3.94238i) q^{53} +(1.45281 - 3.83017i) q^{55} +(2.67602 - 2.67602i) q^{57} +7.45184 q^{59} +9.97493i q^{61} +(-1.13687 + 2.38904i) q^{63} +(1.92874 + 4.28604i) q^{65} +(-5.40365 + 5.40365i) q^{67} -1.38671 q^{69} -12.5907 q^{71} +(5.08337 - 5.08337i) q^{73} +(-4.99091 + 0.301408i) q^{75} +(4.37669 + 2.08274i) q^{77} -6.33742i q^{79} -1.00000 q^{81} +(5.50407 - 5.50407i) q^{83} +(-13.4243 + 6.04100i) q^{85} +(2.81794 + 2.81794i) q^{87} -6.27930 q^{89} +(-5.24049 + 1.86107i) q^{91} +(-0.296271 - 0.296271i) q^{93} +(-3.00116 + 7.91226i) q^{95} +(2.50605 + 2.50605i) q^{97} +1.83199i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{7} + 8 q^{11} + 16 q^{13} - 4 q^{15} + 20 q^{17} - 8 q^{19} - 24 q^{23} - 4 q^{25} + 4 q^{37} + 16 q^{43} - 4 q^{45} + 24 q^{47} + 36 q^{49} + 16 q^{53} - 28 q^{55} + 4 q^{57} - 8 q^{59} + 24 q^{65}+ \cdots - 28 q^{97}+O(q^{100}) $ 24 * q + 4 * q^7 + 8 * q^11 + 16 * q^13 - 4 * q^15 + 20 * q^17 - 8 * q^19 - 24 * q^23 - 4 * q^25 + 4 * q^37 + 16 * q^43 - 4 * q^45 + 24 * q^47 + 36 * q^49 + 16 * q^53 - 28 * q^55 + 4 * q^57 - 8 * q^59 + 24 * q^65 - 16 * q^67 - 8 * q^69 - 8 * q^71 - 28 * q^73 + 20 * q^77 - 24 * q^81 - 64 * q^83 - 20 * q^85 - 20 * q^87 + 16 * q^89 - 24 * q^91 - 12 * q^93 - 24 * q^95 - 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	−0.793022	+	2.09072i	−0.354650	+	0.934999i
$5$	−0.793022	+	2.09072i	−0.354650	+	0.934999i
$6$		0			0
$7$	−2.38904	−	1.13687i	−0.902973	−	0.429697i
$7$	−2.38904	−	1.13687i	−0.902973	−	0.429697i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−1.83199			−0.552365			−0.276182	−	0.961105i	$-0.589069\pi$
$11$	−1.83199			−0.552365			−0.276182	+	0.961105i	$0.589069\pi$
$12$		0			0
$13$	1.48628	−	1.48628i	0.412219	−	0.412219i	−0.470292	−	0.882511i	$-0.655851\pi$
$13$	1.48628	−	1.48628i	0.412219	−	0.412219i	0.882511	+	0.470292i	$0.155851\pi$
$14$		0			0
$15$	0.917612	+	2.03911i	0.236926	+	0.526497i
$16$		0			0
$17$	4.65516	+	4.65516i	1.12904	+	1.12904i	0.990333	+	0.138709i	$0.0442953\pi$
$17$	4.65516	+	4.65516i	1.12904	+	1.12904i	0.138709	+	0.990333i	$0.455705\pi$
$18$		0			0
$19$	3.78446			0.868215			0.434108	−	0.900861i	$-0.357064\pi$
$19$	3.78446			0.868215			0.434108	+	0.900861i	$0.357064\pi$
$20$		0			0
$21$	−2.49320	+	0.885417i	−0.544060	+	0.193214i
$22$		0			0
$23$	−0.980552	−	0.980552i	−0.204459	−	0.204459i	0.597448	−	0.801908i	$-0.296181\pi$
$23$	−0.980552	−	0.980552i	−0.204459	−	0.204459i	−0.801908	+	0.597448i	$0.796181\pi$
$24$		0			0
$25$	−3.74223	−	3.31598i	−0.748446	−	0.663195i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			3.98517i			0.740028i	0.929026	+	0.370014i	$0.120647\pi$
$29$			3.98517i			0.740028i	−0.929026	+	0.370014i	$0.879353\pi$
$30$		0			0
$31$		−	0.418991i		−	0.0752529i	−0.999292	−	0.0376265i	$-0.988020\pi$
$31$		−	0.418991i		−	0.0752529i	0.999292	−	0.0376265i	$-0.0119797\pi$
$32$		0			0
$33$	−1.29541	+	1.29541i	−0.225502	+	0.225502i
$34$		0			0
$35$	4.27145	−	4.09326i	0.722006	−	0.691887i
$36$		0			0
$37$	−3.70069	+	3.70069i	−0.608390	+	0.608390i	−0.942525	−	0.334135i	$-0.891556\pi$
$37$	−3.70069	+	3.70069i	−0.608390	+	0.608390i	0.334135	+	0.942525i	$0.391556\pi$
$38$		0			0
$39$		−	2.10191i		−	0.336576i
$40$		0			0
$41$			10.3583i			1.61769i	0.588021	+	0.808846i	$0.299907\pi$
$41$			10.3583i			1.61769i	−0.588021	+	0.808846i	$0.700093\pi$
$42$		0			0
$43$	6.57302	+	6.57302i	1.00238	+	1.00238i	0.999997	+	0.00237930i	$0.000757355\pi$
$43$	6.57302	+	6.57302i	1.00238	+	1.00238i	0.00237930	+	0.999997i	$0.499243\pi$
$44$		0			0
$45$	2.09072	+	0.793022i	0.311666	+	0.118217i
$46$		0			0
$47$	5.32205	+	5.32205i	0.776301	+	0.776301i	0.979200	−	0.202899i	$-0.0650363\pi$
$47$	5.32205	+	5.32205i	0.776301	+	0.776301i	−0.202899	+	0.979200i	$0.565036\pi$
$48$		0			0
$49$	4.41504	+	5.43207i	0.630720	+	0.776010i
$50$		0			0
$51$	6.58339			0.921859
$52$		0			0
$53$	3.94238	+	3.94238i	0.541528	+	0.541528i	0.923977	−	0.382449i	$-0.124919\pi$
$53$	3.94238	+	3.94238i	0.541528	+	0.541528i	−0.382449	+	0.923977i	$0.624919\pi$
$54$		0			0
$55$	1.45281	−	3.83017i	0.195896	−	0.516461i
$56$		0			0
$57$	2.67602	−	2.67602i	0.354447	−	0.354447i
$58$		0			0
$59$	7.45184			0.970147			0.485073	−	0.874473i	$-0.338793\pi$
$59$	7.45184			0.970147			0.485073	+	0.874473i	$0.338793\pi$
$60$		0			0
$61$			9.97493i			1.27716i	0.769556	+	0.638579i	$0.220478\pi$
$61$			9.97493i			1.27716i	−0.769556	+	0.638579i	$0.779522\pi$
$62$		0			0
$63$	−1.13687	+	2.38904i	−0.143232	+	0.300991i
$64$		0			0
$65$	1.92874	+	4.28604i	0.239231	+	0.531618i
$66$		0			0
$67$	−5.40365	+	5.40365i	−0.660160	+	0.660160i	−0.955418	−	0.295257i	$-0.904595\pi$
$67$	−5.40365	+	5.40365i	−0.660160	+	0.660160i	0.295257	+	0.955418i	$0.404595\pi$
$68$		0			0
$69$	−1.38671			−0.166940
$70$		0			0
$71$	−12.5907			−1.49424			−0.747121	−	0.664689i	$-0.768564\pi$
$71$	−12.5907			−1.49424			−0.747121	+	0.664689i	$0.768564\pi$
$72$		0			0
$73$	5.08337	−	5.08337i	0.594963	−	0.594963i	−0.344005	−	0.938968i	$-0.611784\pi$
$73$	5.08337	−	5.08337i	0.594963	−	0.594963i	0.938968	+	0.344005i	$0.111784\pi$
$74$		0			0
$75$	−4.99091	+	0.301408i	−0.576300	+	0.0348036i
$76$		0			0
$77$	4.37669	+	2.08274i	0.498771	+	0.237350i
$78$		0			0
$79$		−	6.33742i		−	0.713016i	−0.934292	−	0.356508i	$-0.883967\pi$
$79$		−	6.33742i		−	0.713016i	0.934292	−	0.356508i	$-0.116033\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	5.50407	−	5.50407i	0.604151	−	0.604151i	−0.337261	−	0.941411i	$-0.609500\pi$
$83$	5.50407	−	5.50407i	0.604151	−	0.604151i	0.941411	+	0.337261i	$0.109500\pi$
$84$		0			0
$85$	−13.4243	+	6.04100i	−1.45607	+	0.655238i
$86$		0			0
$87$	2.81794	+	2.81794i	0.302115	+	0.302115i
$88$		0			0
$89$	−6.27930			−0.665604			−0.332802	−	0.942997i	$-0.607994\pi$
$89$	−6.27930			−0.665604			−0.332802	+	0.942997i	$0.607994\pi$
$90$		0			0
$91$	−5.24049	+	1.86107i	−0.549352	+	0.195093i
$92$		0			0
$93$	−0.296271	−	0.296271i	−0.0307219	−	0.0307219i
$94$		0			0
$95$	−3.00116	+	7.91226i	−0.307913	+	0.811781i
$96$		0			0
$97$	2.50605	+	2.50605i	0.254450	+	0.254450i	0.822792	−	0.568342i	$-0.192415\pi$
$97$	2.50605	+	2.50605i	0.254450	+	0.254450i	−0.568342	+	0.822792i	$0.692415\pi$
$98$		0			0
$99$			1.83199i			0.184122i
$100$		0			0
$101$		−	2.35631i		−	0.234462i	−0.993105	−	0.117231i	$-0.962598\pi$
$101$		−	2.35631i		−	0.234462i	0.993105	−	0.117231i	$-0.0374017\pi$
$102$		0			0
$103$	−5.78700	+	5.78700i	−0.570210	+	0.570210i	−0.932187	−	0.361977i	$-0.882102\pi$
$103$	−5.78700	+	5.78700i	−0.570210	+	0.570210i	0.361977	+	0.932187i	$0.382102\pi$
$104$		0			0
$105$	0.126000	−	5.91474i	0.0122963	−	0.577219i
$106$		0			0
$107$	−1.37319	+	1.37319i	−0.132751	+	0.132751i	−0.770360	−	0.637609i	$-0.779924\pi$
$107$	−1.37319	+	1.37319i	−0.132751	+	0.132751i	0.637609	+	0.770360i	$0.279924\pi$
$108$		0			0
$109$		−	19.0097i		−	1.82080i	−0.413730	−	0.910400i	$-0.635774\pi$
$109$		−	19.0097i		−	1.82080i	0.413730	−	0.910400i	$-0.364226\pi$
$110$		0			0
$111$			5.23357i			0.496748i
$112$		0			0
$113$	4.32972	+	4.32972i	0.407305	+	0.407305i	0.880798	−	0.473492i	$-0.157007\pi$
$113$	4.32972	+	4.32972i	0.407305	+	0.407305i	−0.473492	+	0.880798i	$0.657007\pi$
$114$		0			0
$115$	2.82766	−	1.27246i	0.263681	−	0.118658i
$116$		0			0
$117$	−1.48628	−	1.48628i	−0.137406	−	0.137406i
$118$		0			0
$119$	−5.82905	−	16.4137i	−0.534348	−	1.50464i
$120$		0			0
$121$	−7.64382			−0.694893
$122$		0			0
$123$	7.32441	+	7.32441i	0.660420	+	0.660420i
$124$		0			0
$125$	9.90046	−	5.19432i	0.885524	−	0.464594i
$126$		0			0
$127$	−2.53070	+	2.53070i	−0.224563	+	0.224563i	−0.810417	−	0.585853i	$-0.800759\pi$
$127$	−2.53070	+	2.53070i	−0.224563	+	0.224563i	0.585853	+	0.810417i	$0.300759\pi$
$128$		0			0
$129$	9.29566			0.818437
$130$		0			0
$131$			7.81417i			0.682727i	0.939931	+	0.341364i	$0.110889\pi$
$131$			7.81417i			0.682727i	−0.939931	+	0.341364i	$0.889111\pi$
$132$		0			0
$133$	−9.04124	−	4.30245i	−0.783975	−	0.373070i
$134$		0			0
$135$	2.03911	−	0.917612i	0.175499	−	0.0789755i
$136$		0			0
$137$	15.5825	−	15.5825i	1.33130	−	1.33130i	0.427098	−	0.904205i	$-0.359536\pi$
$137$	15.5825	−	15.5825i	1.33130	−	1.33130i	0.904205	−	0.427098i	$-0.140464\pi$
$138$		0			0
$139$	17.0665			1.44756			0.723780	−	0.690031i	$-0.242403\pi$
$139$	17.0665			1.44756			0.723780	+	0.690031i	$0.242403\pi$
$140$		0			0
$141$	7.52652			0.633847
$142$		0			0
$143$	−2.72284	+	2.72284i	−0.227696	+	0.227696i
$144$		0			0
$145$	−8.33189	−	3.16033i	−0.691925	−	0.262451i
$146$		0			0
$147$	6.96296	+	0.719149i	0.574295	+	0.0593144i
$148$		0			0
$149$			18.8606i			1.54512i	0.634939	+	0.772562i	$0.281025\pi$
$149$			18.8606i			1.54512i	−0.634939	+	0.772562i	$0.718975\pi$
$150$		0			0
$151$	−20.6451			−1.68008			−0.840038	−	0.542527i	$-0.817468\pi$
$151$	−20.6451			−1.68008			−0.840038	+	0.542527i	$0.817468\pi$
$152$		0			0
$153$	4.65516	−	4.65516i	0.376347	−	0.376347i
$154$		0			0
$155$	0.875993	+	0.332269i	0.0703614	+	0.0266885i
$156$		0			0
$157$	0.595458	+	0.595458i	0.0475227	+	0.0475227i	0.730469	−	0.682946i	$-0.239302\pi$
$157$	0.595458	+	0.595458i	0.0475227	+	0.0475227i	−0.682946	+	0.730469i	$0.739302\pi$
$158$		0			0
$159$	5.57537			0.442156
$160$		0			0
$161$	1.22782	+	3.45734i	0.0967656	+	0.272477i
$162$		0			0
$163$	2.87052	+	2.87052i	0.224836	+	0.224836i	0.810531	−	0.585695i	$-0.199178\pi$
$163$	2.87052	+	2.87052i	0.224836	+	0.224836i	−0.585695	+	0.810531i	$0.699178\pi$
$164$		0			0
$165$	−1.68105	−	3.73563i	−0.130870	−	0.290819i
$166$		0			0
$167$	12.7912	+	12.7912i	0.989811	+	0.989811i	0.999949	−	0.0101379i	$-0.00322704\pi$
$167$	12.7912	+	12.7912i	0.989811	+	0.989811i	−0.0101379	+	0.999949i	$0.503227\pi$
$168$		0			0
$169$			8.58196i			0.660150i
$170$		0			0
$171$		−	3.78446i		−	0.289405i
$172$		0			0
$173$	3.91765	−	3.91765i	0.297853	−	0.297853i	−0.542319	−	0.840173i	$-0.682454\pi$
$173$	3.91765	−	3.91765i	0.297853	−	0.297853i	0.840173	+	0.542319i	$0.182454\pi$
$174$		0			0
$175$	5.17051	+	12.1764i	0.390854	+	0.920453i
$176$		0			0
$177$	5.26925	−	5.26925i	0.396061	−	0.396061i
$178$		0			0
$179$		−	21.1175i		−	1.57840i	−0.614137	−	0.789200i	$-0.710496\pi$
$179$		−	21.1175i		−	1.57840i	0.614137	−	0.789200i	$-0.289504\pi$
$180$		0			0
$181$		−	24.1970i		−	1.79855i	−0.437382	−	0.899276i	$-0.644094\pi$
$181$		−	24.1970i		−	1.79855i	0.437382	−	0.899276i	$-0.355906\pi$
$182$		0			0
$183$	7.05334	+	7.05334i	0.521398	+	0.521398i
$184$		0			0
$185$	−4.80238	−	10.6718i	−0.353078	−	0.784609i
$186$		0			0
$187$	−8.52819	−	8.52819i	−0.623643	−	0.623643i
$188$		0			0
$189$	0.885417	+	2.49320i	0.0644046	+	0.181353i
$190$		0			0
$191$	1.56938			0.113556			0.0567780	−	0.998387i	$-0.481917\pi$
$191$	1.56938			0.113556			0.0567780	+	0.998387i	$0.481917\pi$
$192$		0			0
$193$	2.32792	+	2.32792i	0.167567	+	0.167567i	0.785909	−	0.618342i	$-0.212195\pi$
$193$	2.32792	+	2.32792i	0.167567	+	0.167567i	−0.618342	+	0.785909i	$0.712195\pi$
$194$		0			0
$195$	4.39452	+	1.66686i	0.314698	+	0.119367i
$196$		0			0
$197$	14.6194	−	14.6194i	1.04159	−	1.04159i	0.0424939	−	0.999097i	$-0.486470\pi$
$197$	14.6194	−	14.6194i	1.04159	−	1.04159i	0.999097	−	0.0424939i	$-0.0135303\pi$
$198$		0			0
$199$	−5.93362			−0.420623			−0.210312	−	0.977634i	$-0.567448\pi$
$199$	−5.93362			−0.420623			−0.210312	+	0.977634i	$0.567448\pi$
$200$		0			0
$201$			7.64191i			0.539019i
$202$		0			0
$203$	4.53063	−	9.52074i	0.317988	−	0.668225i
$204$		0			0
$205$	−21.6563	−	8.21434i	−1.51254	−	0.573715i
$206$		0			0
$207$	−0.980552	+	0.980552i	−0.0681531	+	0.0681531i
$208$		0			0
$209$	−6.93309			−0.479572
$210$		0			0
$211$	−6.16052			−0.424108			−0.212054	−	0.977258i	$-0.568015\pi$
$211$	−6.16052			−0.424108			−0.212054	+	0.977258i	$0.568015\pi$
$212$		0			0
$213$	−8.90297	+	8.90297i	−0.610021	+	0.610021i
$214$		0			0
$215$	−18.9549	+	8.52981i	−1.29271	+	0.581728i
$216$		0			0
$217$	−0.476339	+	1.00099i	−0.0323360	+	0.0679514i
$218$		0			0
$219$		−	7.18897i		−	0.485785i
$220$		0			0
$221$	13.8377			0.930826
$222$		0			0
$223$	−17.0970	+	17.0970i	−1.14490	+	1.14490i	−0.157361	+	0.987541i	$0.550299\pi$
$223$	−17.0970	+	17.0970i	−1.14490	+	1.14490i	−0.987541	+	0.157361i	$0.949701\pi$
$224$		0			0
$225$	−3.31598	+	3.74223i	−0.221065	+	0.249482i
$226$		0			0
$227$	−4.16552	−	4.16552i	−0.276475	−	0.276475i	0.555225	−	0.831700i	$-0.312632\pi$
$227$	−4.16552	−	4.16552i	−0.276475	−	0.276475i	−0.831700	+	0.555225i	$0.812632\pi$
$228$		0			0
$229$	6.76436			0.447001			0.223501	−	0.974704i	$-0.428252\pi$
$229$	6.76436			0.447001			0.223501	+	0.974704i	$0.428252\pi$
$230$		0			0
$231$	4.56751	−	1.62207i	0.300520	−	0.106725i
$232$		0			0
$233$	8.50439	+	8.50439i	0.557141	+	0.557141i	0.928492	−	0.371351i	$-0.121105\pi$
$233$	8.50439	+	8.50439i	0.557141	+	0.557141i	−0.371351	+	0.928492i	$0.621105\pi$
$234$		0			0
$235$	−15.3474	+	6.90642i	−1.00116	+	0.450525i
$236$		0			0
$237$	−4.48123	−	4.48123i	−0.291087	−	0.291087i
$238$		0			0
$239$			10.0210i			0.648202i	0.946022	+	0.324101i	$0.105062\pi$
$239$			10.0210i			0.648202i	−0.946022	+	0.324101i	$0.894938\pi$
$240$		0			0
$241$		−	8.24673i		−	0.531219i	−0.964081	−	0.265609i	$-0.914427\pi$
$241$		−	8.24673i		−	0.531219i	0.964081	−	0.265609i	$-0.0855732\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−14.8582	+	4.92287i	−0.949254	+	0.314511i
$246$		0			0
$247$	5.62476	−	5.62476i	0.357895	−	0.357895i
$248$		0			0
$249$		−	7.78394i		−	0.493287i
$250$		0			0
$251$		−	27.2141i		−	1.71774i	−0.512194	−	0.858870i	$-0.671167\pi$
$251$		−	27.2141i		−	1.71774i	0.512194	−	0.858870i	$-0.328833\pi$
$252$		0			0
$253$	1.79636	+	1.79636i	0.112936	+	0.112936i
$254$		0			0
$255$	−5.22077	+	13.7640i	−0.326938	+	0.861937i
$256$		0			0
$257$	−11.2946	−	11.2946i	−0.704538	−	0.704538i	0.260843	−	0.965381i	$-0.415999\pi$
$257$	−11.2946	−	11.2946i	−0.704538	−	0.704538i	−0.965381	+	0.260843i	$0.915999\pi$
$258$		0			0
$259$	13.0483	−	4.63389i	0.810783	−	0.287936i
$260$		0			0
$261$	3.98517			0.246676
$262$		0			0
$263$	13.4333	+	13.4333i	0.828334	+	0.828334i	0.987286	−	0.158952i	$-0.0508116\pi$
$263$	13.4333	+	13.4333i	0.828334	+	0.828334i	−0.158952	+	0.987286i	$0.550812\pi$
$264$		0			0
$265$	−11.3688	+	5.11603i	−0.698381	+	0.314275i
$266$		0			0
$267$	−4.44013	+	4.44013i	−0.271732	+	0.271732i
$268$		0			0
$269$	9.83354			0.599561			0.299781	−	0.954008i	$-0.403087\pi$
$269$	9.83354			0.599561			0.299781	+	0.954008i	$0.403087\pi$
$270$		0			0
$271$			11.3225i			0.687790i	0.939008	+	0.343895i	$0.111747\pi$
$271$			11.3225i			0.687790i	−0.939008	+	0.343895i	$0.888253\pi$
$272$		0			0
$273$	−2.38961	+	5.02156i	−0.144626	+	0.303919i
$274$		0			0
$275$	6.85572	+	6.07483i	0.413416	+	0.366326i
$276$		0			0
$277$	18.5572	−	18.5572i	1.11500	−	1.11500i	0.122532	−	0.992465i	$-0.460899\pi$
$277$	18.5572	−	18.5572i	1.11500	−	1.11500i	0.992465	−	0.122532i	$-0.0391014\pi$
$278$		0			0
$279$	−0.418991			−0.0250843
$280$		0			0
$281$	7.80892			0.465841			0.232921	−	0.972496i	$-0.425172\pi$
$281$	7.80892			0.465841			0.232921	+	0.972496i	$0.425172\pi$
$282$		0			0
$283$	1.14863	−	1.14863i	0.0682792	−	0.0682792i	−0.672143	−	0.740422i	$-0.734626\pi$
$283$	1.14863	−	1.14863i	0.0682792	−	0.0682792i	0.740422	+	0.672143i	$0.234626\pi$
$284$		0			0
$285$	3.47267	+	7.71695i	0.205703	+	0.457113i
$286$		0			0
$287$	11.7760	−	24.7464i	0.695118	−	1.46073i
$288$		0			0
$289$			26.3410i			1.54947i
$290$		0			0
$291$	3.54408			0.207758
$292$		0			0
$293$	−3.97738	+	3.97738i	−0.232361	+	0.232361i	−0.813677	−	0.581317i	$-0.802538\pi$
$293$	−3.97738	+	3.97738i	−0.232361	+	0.232361i	0.581317	+	0.813677i	$0.302538\pi$
$294$		0			0
$295$	−5.90947	+	15.5797i	−0.344063	+	0.907086i
$296$		0			0
$297$	1.29541	+	1.29541i	0.0751673	+	0.0751673i
$298$		0			0
$299$	−2.91475			−0.168564
$300$		0			0
$301$	−8.23054	−	23.1759i	−0.474400	−	1.33584i
$302$		0			0
$303$	−1.66616	−	1.66616i	−0.0957185	−	0.0957185i
$304$		0			0
$305$	−20.8548	−	7.91034i	−1.19414	−	0.452945i
$306$		0			0
$307$	−13.8073	−	13.8073i	−0.788026	−	0.788026i	0.193144	−	0.981170i	$-0.438132\pi$
$307$	−13.8073	−	13.8073i	−0.788026	−	0.788026i	−0.981170	+	0.193144i	$0.938132\pi$
$308$		0			0
$309$			8.18405i			0.465574i
$310$		0			0
$311$			15.4188i			0.874320i	0.899384	+	0.437160i	$0.144016\pi$
$311$			15.4188i			0.874320i	−0.899384	+	0.437160i	$0.855984\pi$
$312$		0			0
$313$	3.89720	−	3.89720i	0.220283	−	0.220283i	−0.588335	−	0.808618i	$-0.700216\pi$
$313$	3.89720	−	3.89720i	0.220283	−	0.220283i	0.808618	+	0.588335i	$0.200216\pi$
$314$		0			0
$315$	−4.09326	−	4.27145i	−0.230629	−	0.240669i
$316$		0			0
$317$	−9.98823	+	9.98823i	−0.560995	+	0.560995i	−0.929590	−	0.368595i	$-0.879839\pi$
$317$	−9.98823	+	9.98823i	−0.560995	+	0.560995i	0.368595	+	0.929590i	$0.379839\pi$
$318$		0			0
$319$		−	7.30079i		−	0.408766i
$320$		0			0
$321$			1.94198i			0.108391i
$322$		0			0
$323$	17.6173	+	17.6173i	0.980252	+	0.980252i
$324$		0			0
$325$	−10.4905	+	0.633534i	−0.581906	+	0.0351422i
$326$		0			0
$327$	−13.4419	−	13.4419i	−0.743338	−	0.743338i
$328$		0			0
$329$	−6.66411	−	18.7651i	−0.367404	−	1.03455i
$330$		0			0
$331$	−7.76207			−0.426642			−0.213321	−	0.976982i	$-0.568428\pi$
$331$	−7.76207			−0.426642			−0.213321	+	0.976982i	$0.568428\pi$
$332$		0			0
$333$	3.70069	+	3.70069i	0.202797	+	0.202797i
$334$		0			0
$335$	−7.01231	−	15.5827i	−0.383123	−	0.851375i
$336$		0			0
$337$	−20.7009	+	20.7009i	−1.12765	+	1.12765i	−0.137094	+	0.990558i	$0.543776\pi$
$337$	−20.7009	+	20.7009i	−1.12765	+	1.12765i	−0.990558	+	0.137094i	$0.956224\pi$
$338$		0			0
$339$	6.12314			0.332563
$340$		0			0
$341$			0.767585i			0.0415671i
$342$		0			0
$343$	−4.37215	−	17.9968i	−0.236074	−	0.971735i
$344$		0			0
$345$	1.09969	−	2.89923i	0.0592054	−	0.156089i
$346$		0			0
$347$	−16.8422	+	16.8422i	−0.904138	+	0.904138i	−0.995791	−	0.0916528i	$-0.970785\pi$
$347$	−16.8422	+	16.8422i	−0.904138	+	0.904138i	0.0916528	+	0.995791i	$0.470785\pi$
$348$		0			0
$349$	−14.5075			−0.776567			−0.388284	−	0.921540i	$-0.626932\pi$
$349$	−14.5075			−0.776567			−0.388284	+	0.921540i	$0.626932\pi$
$350$		0			0
$351$	−2.10191			−0.112192
$352$		0			0
$353$	−13.1207	+	13.1207i	−0.698344	+	0.698344i	−0.964053	−	0.265709i	$-0.914394\pi$
$353$	−13.1207	+	13.1207i	−0.698344	+	0.698344i	0.265709	+	0.964053i	$0.414394\pi$
$354$		0			0
$355$	9.98470	−	26.3236i	0.529933	−	1.39711i
$356$		0			0
$357$	−15.7280	−	7.48448i	−0.832414	−	0.396120i
$358$		0			0
$359$		−	15.8826i		−	0.838251i	−0.907928	−	0.419126i	$-0.862337\pi$
$359$		−	15.8826i		−	0.838251i	0.907928	−	0.419126i	$-0.137663\pi$
$360$		0			0
$361$	−4.67784			−0.246202
$362$		0			0
$363$	−5.40500	+	5.40500i	−0.283689	+	0.283689i
$364$		0			0
$365$	6.59668	+	14.6591i	0.345286	+	0.767294i
$366$		0			0
$367$	−26.1316	−	26.1316i	−1.36406	−	1.36406i	−0.868672	−	0.495388i	$-0.835026\pi$
$367$	−26.1316	−	26.1316i	−1.36406	−	1.36406i	−0.495388	−	0.868672i	$-0.664974\pi$
$368$		0			0
$369$	10.3583			0.539230
$370$		0			0
$371$	−4.93653	−	13.9005i	−0.256292	−	0.721678i
$372$		0			0
$373$	11.6475	+	11.6475i	0.603086	+	0.603086i	0.941130	−	0.338044i	$-0.109765\pi$
$373$	11.6475	+	11.6475i	0.603086	+	0.603086i	−0.338044	+	0.941130i	$0.609765\pi$
$374$		0			0
$375$	3.32774	−	10.6736i	0.171844	−	0.551183i
$376$		0			0
$377$	5.92307	+	5.92307i	0.305054	+	0.305054i
$378$		0			0
$379$			11.1749i			0.574018i	0.957928	+	0.287009i	$0.0926610\pi$
$379$			11.1749i			0.574018i	−0.957928	+	0.287009i	$0.907339\pi$
$380$		0			0
$381$			3.57895i			0.183355i
$382$		0			0
$383$	−3.94634	+	3.94634i	−0.201649	+	0.201649i	−0.800706	−	0.599057i	$-0.795542\pi$
$383$	−3.94634	+	3.94634i	−0.201649	+	0.201649i	0.599057	+	0.800706i	$0.295542\pi$
$384$		0			0
$385$	−7.82524	+	7.49879i	−0.398811	+	0.382174i
$386$		0			0
$387$	6.57302	−	6.57302i	0.334125	−	0.334125i
$388$		0			0
$389$		−	23.9327i		−	1.21344i	−0.794917	−	0.606719i	$-0.792485\pi$
$389$		−	23.9327i		−	1.21344i	0.794917	−	0.606719i	$-0.207515\pi$
$390$		0			0
$391$		−	9.12926i		−	0.461686i
$392$		0			0
$393$	5.52545	+	5.52545i	0.278722	+	0.278722i
$394$		0			0
$395$	13.2498	+	5.02572i	0.666669	+	0.252871i
$396$		0			0
$397$	26.4416	+	26.4416i	1.32707	+	1.32707i	0.907917	+	0.419150i	$0.137672\pi$
$397$	26.4416	+	26.4416i	1.32707	+	1.32707i	0.419150	+	0.907917i	$0.362328\pi$
$398$		0			0
$399$	−9.43542	+	3.35083i	−0.472362	+	0.167751i
$400$		0			0
$401$	−22.6400			−1.13059			−0.565293	−	0.824890i	$-0.691237\pi$
$401$	−22.6400			−1.13059			−0.565293	+	0.824890i	$0.691237\pi$
$402$		0			0
$403$	−0.622737	−	0.622737i	−0.0310207	−	0.0310207i
$404$		0			0
$405$	0.793022	−	2.09072i	0.0394056	−	0.103889i
$406$		0			0
$407$	6.77962	−	6.77962i	0.336053	−	0.336053i
$408$		0			0
$409$	−31.0267			−1.53417			−0.767086	−	0.641544i	$-0.778294\pi$
$409$	−31.0267			−1.53417			−0.767086	+	0.641544i	$0.778294\pi$
$410$		0			0
$411$		−	22.0370i		−	1.08700i
$412$		0			0
$413$	−17.8028	−	8.47179i	−0.876016	−	0.416870i
$414$		0			0
$415$	7.14263	+	15.8723i	0.350618	+	0.779143i
$416$		0			0
$417$	12.0678	−	12.0678i	0.590964	−	0.590964i
$418$		0			0
$419$	−27.9504			−1.36547			−0.682733	−	0.730668i	$-0.739209\pi$
$419$	−27.9504			−1.36547			−0.682733	+	0.730668i	$0.739209\pi$
$420$		0			0
$421$	7.38882			0.360109			0.180054	−	0.983657i	$-0.442373\pi$
$421$	7.38882			0.360109			0.180054	+	0.983657i	$0.442373\pi$
$422$		0			0
$423$	5.32205	−	5.32205i	0.258767	−	0.258767i
$424$		0			0
$425$	−1.98429	−	32.8571i	−0.0962521	−	1.59380i
$426$		0			0
$427$	11.3402	−	23.8305i	0.548792	−	1.15324i
$428$		0			0
$429$			3.85068i			0.185913i
$430$		0			0
$431$	−12.4443			−0.599420			−0.299710	−	0.954030i	$-0.596890\pi$
$431$	−12.4443			−0.599420			−0.299710	+	0.954030i	$0.596890\pi$
$432$		0			0
$433$	12.6923	−	12.6923i	0.609951	−	0.609951i	−0.332982	−	0.942933i	$-0.608055\pi$
$433$	12.6923	−	12.6923i	0.609951	−	0.609951i	0.942933	+	0.332982i	$0.108055\pi$
$434$		0			0
$435$	−8.12622	+	3.65684i	−0.389623	+	0.175332i
$436$		0			0
$437$	−3.71086	−	3.71086i	−0.177515	−	0.177515i
$438$		0			0
$439$	2.02052			0.0964342			0.0482171	−	0.998837i	$-0.484646\pi$
$439$	2.02052			0.0964342			0.0482171	+	0.998837i	$0.484646\pi$
$440$		0			0
$441$	5.43207	−	4.41504i	0.258670	−	0.210240i
$442$		0			0
$443$	20.9380	+	20.9380i	0.994796	+	0.994796i	0.999987	−	0.00519085i	$-0.00165231\pi$
$443$	20.9380	+	20.9380i	0.994796	+	0.994796i	−0.00519085	+	0.999987i	$0.501652\pi$
$444$		0			0
$445$	4.97962	−	13.1283i	0.236057	−	0.622339i
$446$		0			0
$447$	13.3365	+	13.3365i	0.630794	+	0.630794i
$448$		0			0
$449$		−	16.4487i		−	0.776264i	−0.921604	−	0.388132i	$-0.873121\pi$
$449$		−	16.4487i		−	0.776264i	0.921604	−	0.388132i	$-0.126879\pi$
$450$		0			0
$451$		−	18.9762i		−	0.893556i
$452$		0			0
$453$	−14.5983	+	14.5983i	−0.685888	+	0.685888i
$454$		0			0
$455$	0.264841	−	12.4323i	0.0124159	−	0.582834i
$456$		0			0
$457$	21.1469	−	21.1469i	0.989208	−	0.989208i	−0.0107342	−	0.999942i	$-0.503417\pi$
$457$	21.1469	−	21.1469i	0.989208	−	0.989208i	0.999942	+	0.0107342i	$0.00341688\pi$
$458$		0			0
$459$		−	6.58339i		−	0.307286i
$460$		0			0
$461$			21.3492i			0.994333i	0.867655	+	0.497167i	$0.165626\pi$
$461$			21.3492i			0.994333i	−0.867655	+	0.497167i	$0.834374\pi$
$462$		0			0
$463$	4.82602	+	4.82602i	0.224284	+	0.224284i	0.810300	−	0.586016i	$-0.199304\pi$
$463$	4.82602	+	4.82602i	0.224284	+	0.224284i	−0.586016	+	0.810300i	$0.699304\pi$
$464$		0			0
$465$	0.854370	−	0.384471i	0.0396205	−	0.0178294i
$466$		0			0
$467$	18.7364	+	18.7364i	0.867016	+	0.867016i	0.992141	−	0.125125i	$-0.0399333\pi$
$467$	18.7364	+	18.7364i	0.867016	+	0.867016i	−0.125125	+	0.992141i	$0.539933\pi$
$468$		0			0
$469$	19.0528	−	6.76628i	0.879776	−	0.312438i
$470$		0			0
$471$	0.842105			0.0388022
$472$		0			0
$473$	−12.0417	−	12.0417i	−0.553678	−	0.553678i
$474$		0			0
$475$	−14.1623	−	12.5492i	−0.649813	−	0.575796i
$476$		0			0
$477$	3.94238	−	3.94238i	0.180509	−	0.180509i
$478$		0			0
$479$	−26.7428			−1.22191			−0.610954	−	0.791666i	$-0.709214\pi$
$479$	−26.7428			−1.22191			−0.610954	+	0.791666i	$0.709214\pi$
$480$		0			0
$481$			11.0005i			0.501580i
$482$		0			0
$483$	3.31291	+	1.57651i	0.150743	+	0.0717338i
$484$		0			0
$485$	−7.22679	+	3.25209i	−0.328152	+	0.147670i
$486$		0			0
$487$	13.0281	−	13.0281i	0.590359	−	0.590359i	−0.347370	−	0.937728i	$-0.612925\pi$
$487$	13.0281	−	13.0281i	0.590359	−	0.590359i	0.937728	+	0.347370i	$0.112925\pi$
$488$		0			0
$489$	4.05953			0.183578
$490$		0			0
$491$	34.2448			1.54544			0.772722	−	0.634745i	$-0.218895\pi$
$491$	34.2448			1.54544			0.772722	+	0.634745i	$0.218895\pi$
$492$		0			0
$493$	−18.5516	+	18.5516i	−0.835523	+	0.835523i
$494$		0			0
$495$	−3.83017	−	1.45281i	−0.172154	−	0.0652988i
$496$		0			0
$497$	30.0797	+	14.3140i	1.34926	+	0.642072i
$498$		0			0
$499$		−	38.0422i		−	1.70300i	−0.524352	−	0.851502i	$-0.675692\pi$
$499$		−	38.0422i		−	1.70300i	0.524352	−	0.851502i	$-0.324308\pi$
$500$		0			0
$501$	18.0895			0.808177
$502$		0			0
$503$	−17.0324	+	17.0324i	−0.759439	+	0.759439i	−0.976220	−	0.216781i	$-0.930444\pi$
$503$	−17.0324	+	17.0324i	−0.759439	+	0.759439i	0.216781	+	0.976220i	$0.430444\pi$
$504$		0			0
$505$	4.92639	+	1.86861i	0.219221	+	0.0831519i
$506$		0			0
$507$	6.06836	+	6.06836i	0.269505	+	0.269505i
$508$		0			0
$509$	−0.424186			−0.0188017			−0.00940085	−	0.999956i	$-0.502992\pi$
$509$	−0.424186			−0.0188017			−0.00940085	+	0.999956i	$0.502992\pi$
$510$		0			0
$511$	−17.9235	+	6.36524i	−0.792890	+	0.281581i
$512$		0			0
$513$	−2.67602	−	2.67602i	−0.118149	−	0.118149i
$514$		0			0
$515$	−7.50978	−	16.6882i	−0.330921	−	0.735371i
$516$		0			0
$517$	−9.74993	−	9.74993i	−0.428801	−	0.428801i
$518$		0			0
$519$		−	5.54039i		−	0.243196i
$520$		0			0
$521$			10.0586i			0.440674i	0.975424	+	0.220337i	$0.0707157\pi$
$521$			10.0586i			0.440674i	−0.975424	+	0.220337i	$0.929284\pi$
$522$		0			0
$523$	20.4023	−	20.4023i	0.892132	−	0.892132i	−0.102591	−	0.994724i	$-0.532713\pi$
$523$	20.4023	−	20.4023i	0.892132	−	0.892132i	0.994724	+	0.102591i	$0.0327134\pi$
$524$		0			0
$525$	12.2661	+	4.95395i	0.535339	+	0.216208i
$526$		0			0
$527$	1.95047	−	1.95047i	0.0849637	−	0.0849637i
$528$		0			0
$529$		−	21.0770i		−	0.916393i
$530$		0			0
$531$		−	7.45184i		−	0.323382i
$532$		0			0
$533$	15.3953	+	15.3953i	0.666844	+	0.666844i
$534$		0			0
$535$	−1.78199	−	3.95992i	−0.0770420	−	0.171202i
$536$		0			0
$537$	−14.9324	−	14.9324i	−0.644379	−	0.644379i
$538$		0			0
$539$	−8.08830	−	9.95149i	−0.348388	−	0.428641i
$540$		0			0
$541$	−10.8989			−0.468582			−0.234291	−	0.972167i	$-0.575277\pi$
$541$	−10.8989			−0.468582			−0.234291	+	0.972167i	$0.575277\pi$
$542$		0			0
$543$	−17.1099	−	17.1099i	−0.734256	−	0.734256i
$544$		0			0
$545$	39.7440	+	15.0751i	1.70245	+	0.645747i
$546$		0			0
$547$	−20.6904	+	20.6904i	−0.884658	+	0.884658i	−0.994004	−	0.109345i	$-0.965125\pi$
$547$	−20.6904	+	20.6904i	−0.884658	+	0.884658i	0.109345	+	0.994004i	$0.465125\pi$
$548$		0			0
$549$	9.97493			0.425720
$550$		0			0
$551$			15.0817i			0.642504i
$552$		0			0
$553$	−7.20484	+	15.1404i	−0.306381	+	0.643834i
$554$		0			0
$555$	−10.9419	−	4.15033i	−0.464459	−	0.176172i
$556$		0			0
$557$	0.997840	−	0.997840i	0.0422799	−	0.0422799i	−0.685651	−	0.727931i	$-0.740482\pi$
$557$	0.997840	−	0.997840i	0.0422799	−	0.0422799i	0.727931	+	0.685651i	$0.240482\pi$
$558$		0			0
$559$	19.5387			0.826398
$560$		0			0
$561$	−12.0607			−0.509203
$562$		0			0
$563$	14.4588	−	14.4588i	0.609368	−	0.609368i	−0.333413	−	0.942781i	$-0.608200\pi$
$563$	14.4588	−	14.4588i	0.609368	−	0.609368i	0.942781	+	0.333413i	$0.108200\pi$
$564$		0			0
$565$	−12.4858	+	5.61867i	−0.525281	+	0.236379i
$566$		0			0
$567$	2.38904	+	1.13687i	0.100330	+	0.0477442i
$568$		0			0
$569$		−	18.6912i		−	0.783574i	−0.920056	−	0.391787i	$-0.871857\pi$
$569$		−	18.6912i		−	0.783574i	0.920056	−	0.391787i	$-0.128143\pi$
$570$		0			0
$571$	31.7294			1.32783			0.663917	−	0.747806i	$-0.268893\pi$
$571$	31.7294			1.32783			0.663917	+	0.747806i	$0.268893\pi$
$572$		0			0
$573$	1.10972	−	1.10972i	0.0463590	−	0.0463590i
$574$		0			0
$575$	0.417966	+	6.92094i	0.0174304	+	0.288623i
$576$		0			0
$577$	4.01321	+	4.01321i	0.167072	+	0.167072i	0.785691	−	0.618619i	$-0.212307\pi$
$577$	4.01321	+	4.01321i	0.167072	+	0.167072i	−0.618619	+	0.785691i	$0.712307\pi$
$578$		0			0
$579$	3.29217			0.136818
$580$		0			0
$581$	−19.4069	+	6.89203i	−0.805134	+	0.285930i
$582$		0			0
$583$	−7.22240	−	7.22240i	−0.299121	−	0.299121i
$584$		0			0
$585$	4.28604	−	1.92874i	0.177206	−	0.0797437i
$586$		0			0
$587$	9.30224	+	9.30224i	0.383945	+	0.383945i	0.872521	−	0.488576i	$-0.162484\pi$
$587$	9.30224	+	9.30224i	0.383945	+	0.383945i	−0.488576	+	0.872521i	$0.662484\pi$
$588$		0			0
$589$		−	1.58565i		−	0.0653358i
$590$		0			0
$591$		−	20.6750i		−	0.850455i
$592$		0			0
$593$	21.9584	−	21.9584i	0.901725	−	0.901725i	−0.0938604	−	0.995585i	$-0.529921\pi$
$593$	21.9584	−	21.9584i	0.901725	−	0.901725i	0.995585	+	0.0938604i	$0.0299207\pi$
$594$		0			0
$595$	38.9390	+	0.829506i	1.59634	+	0.0340064i
$596$		0			0
$597$	−4.19570	+	4.19570i	−0.171719	+	0.171719i
$598$		0			0
$599$			3.67685i			0.150232i	0.997175	+	0.0751160i	$0.0239327\pi$
$599$			3.67685i			0.150232i	−0.997175	+	0.0751160i	$0.976067\pi$
$600$		0			0
$601$		−	7.54954i		−	0.307952i	−0.988075	−	0.153976i	$-0.950792\pi$
$601$		−	7.54954i		−	0.307952i	0.988075	−	0.153976i	$-0.0492079\pi$
$602$		0			0
$603$	5.40365	+	5.40365i	0.220053	+	0.220053i
$604$		0			0
$605$	6.06172	−	15.9811i	0.246444	−	0.649724i
$606$		0			0
$607$	6.40919	+	6.40919i	0.260141	+	0.260141i	0.825111	−	0.564970i	$-0.191112\pi$
$607$	6.40919	+	6.40919i	0.260141	+	0.260141i	−0.564970	+	0.825111i	$0.691112\pi$
$608$		0			0
$609$	−3.52854	−	9.93582i	−0.142984	−	0.402620i
$610$		0			0
$611$	15.8201			0.640012
$612$		0			0
$613$	−1.26803	−	1.26803i	−0.0512153	−	0.0512153i	0.681035	−	0.732251i	$-0.261530\pi$
$613$	−1.26803	−	1.26803i	−0.0512153	−	0.0512153i	−0.732251	+	0.681035i	$0.761530\pi$
$614$		0			0
$615$	−21.1217	+	9.50488i	−0.851710	+	0.383274i
$616$		0			0
$617$	−29.8460	+	29.8460i	−1.20155	+	1.20155i	−0.227861	+	0.973694i	$0.573173\pi$
$617$	−29.8460	+	29.8460i	−1.20155	+	1.20155i	−0.973694	+	0.227861i	$0.926827\pi$
$618$		0			0
$619$	−15.0957			−0.606747			−0.303374	−	0.952872i	$-0.598113\pi$
$619$	−15.0957			−0.606747			−0.303374	+	0.952872i	$0.598113\pi$
$620$		0			0
$621$			1.38671i			0.0556468i
$622$		0			0
$623$	15.0015	+	7.13876i	0.601023	+	0.286008i
$624$		0			0
$625$	3.00860	+	24.8183i	0.120344	+	0.992732i
$626$		0			0
$627$	−4.90243	+	4.90243i	−0.195784	+	0.195784i
$628$		0			0
$629$	−34.4546			−1.37380
$630$		0			0
$631$	−18.9855			−0.755801			−0.377900	−	0.925846i	$-0.623354\pi$
$631$	−18.9855			−0.755801			−0.377900	+	0.925846i	$0.623354\pi$
$632$		0			0
$633$	−4.35615	+	4.35615i	−0.173141	+	0.173141i
$634$		0			0
$635$	−3.28409	−	7.29790i	−0.130325	−	0.289608i
$636$		0			0
$637$	14.6355	+	1.51159i	0.579882	+	0.0598913i
$638$		0			0
$639$			12.5907i			0.498080i
$640$		0			0
$641$	−19.8604			−0.784438			−0.392219	−	0.919872i	$-0.628292\pi$
$641$	−19.8604			−0.784438			−0.392219	+	0.919872i	$0.628292\pi$
$642$		0			0
$643$	−34.3590	+	34.3590i	−1.35499	+	1.35499i	−0.475002	+	0.879985i	$0.657553\pi$
$643$	−34.3590	+	34.3590i	−1.35499	+	1.35499i	−0.879985	+	0.475002i	$0.842447\pi$
$644$		0			0
$645$	−7.37166	+	19.4346i	−0.290259	+	0.765238i
$646$		0			0
$647$	27.0162	+	27.0162i	1.06212	+	1.06212i	0.997938	+	0.0641784i	$0.0204427\pi$
$647$	27.0162	+	27.0162i	1.06212	+	1.06212i	0.0641784	+	0.997938i	$0.479557\pi$
$648$		0			0
$649$	−13.6517			−0.535875
$650$		0			0
$651$	0.370982	+	1.04463i	0.0145399	+	0.0409421i
$652$		0			0
$653$	11.1822	+	11.1822i	0.437593	+	0.437593i	0.891201	−	0.453608i	$-0.149864\pi$
$653$	11.1822	+	11.1822i	0.437593	+	0.437593i	−0.453608	+	0.891201i	$0.649864\pi$
$654$		0			0
$655$	−16.3372	−	6.19681i	−0.638349	−	0.242129i
$656$		0			0
$657$	−5.08337	−	5.08337i	−0.198321	−	0.198321i
$658$		0			0
$659$			6.74496i			0.262746i	0.991333	+	0.131373i	$0.0419386\pi$
$659$			6.74496i			0.262746i	−0.991333	+	0.131373i	$0.958061\pi$
$660$		0			0
$661$		−	43.4695i		−	1.69077i	−0.534159	−	0.845384i	$-0.679372\pi$
$661$		−	43.4695i		−	1.69077i	0.534159	−	0.845384i	$-0.320628\pi$
$662$		0			0
$663$	9.78475	−	9.78475i	0.380008	−	0.380008i
$664$		0			0
$665$	16.1651	−	15.4908i	0.626857	−	0.600707i
$666$		0			0
$667$	3.90767	−	3.90767i	0.151306	−	0.151306i
$668$		0			0
$669$			24.1789i			0.934809i
$670$		0			0
$671$		−	18.2739i		−	0.705458i
$672$		0			0
$673$	33.9579	+	33.9579i	1.30898	+	1.30898i	0.922151	+	0.386831i	$0.126430\pi$
$673$	33.9579	+	33.9579i	1.30898	+	1.30898i	0.386831	+	0.922151i	$0.373570\pi$
$674$		0			0
$675$	0.301408	+	4.99091i	0.0116012	+	0.192100i
$676$		0			0
$677$	−25.7087	−	25.7087i	−0.988065	−	0.988065i	0.0118642	−	0.999930i	$-0.496223\pi$
$677$	−25.7087	−	25.7087i	−0.988065	−	0.988065i	−0.999930	+	0.0118642i	$0.996223\pi$
$678$		0			0
$679$	−3.13799	−	8.83610i	−0.120425	−	0.339098i
$680$		0			0
$681$	−5.89093			−0.225741
$682$		0			0
$683$	−3.23539	−	3.23539i	−0.123799	−	0.123799i	0.642493	−	0.766292i	$-0.277900\pi$
$683$	−3.23539	−	3.23539i	−0.123799	−	0.123799i	−0.766292	+	0.642493i	$0.777900\pi$
$684$		0			0
$685$	20.2214	+	44.9360i	0.772620	+	1.71691i
$686$		0			0
$687$	4.78312	−	4.78312i	0.182488	−	0.182488i
$688$		0			0
$689$	11.7190			0.446457
$690$		0			0
$691$			20.4287i			0.777146i	0.921418	+	0.388573i	$0.127032\pi$
$691$			20.4287i			0.777146i	−0.921418	+	0.388573i	$0.872968\pi$
$692$		0			0
$693$	2.08274	−	4.37669i	0.0791166	−	0.166257i
$694$		0			0
$695$	−13.5341	+	35.6812i	−0.513377	+	1.35347i
$696$		0			0
$697$	−48.2195	+	48.2195i	−1.82644	+	1.82644i
$698$		0			0
$699$	12.0270			0.454904
$700$		0			0
$701$	−19.0180			−0.718299			−0.359149	−	0.933280i	$-0.616933\pi$
$701$	−19.0180			−0.718299			−0.359149	+	0.933280i	$0.616933\pi$
$702$		0			0
$703$	−14.0051	+	14.0051i	−0.528213	+	0.528213i
$704$		0			0
$705$	−5.96869	+	15.7358i	−0.224794	+	0.592646i
$706$		0			0
$707$	−2.67882	+	5.62932i	−0.100748	+	0.211712i
$708$		0			0
$709$		−	43.1544i		−	1.62070i	−0.585948	−	0.810349i	$-0.699278\pi$
$709$		−	43.1544i		−	1.62070i	0.585948	−	0.810349i	$-0.300722\pi$
$710$		0			0
$711$	−6.33742			−0.237672
$712$		0			0
$713$	−0.410842	+	0.410842i	−0.0153862	+	0.0153862i
$714$		0			0
$715$	−3.53343	−	7.85198i	−0.132143	−	0.293647i
$716$		0			0
$717$	7.08589	+	7.08589i	0.264627	+	0.264627i
$718$		0			0
$719$	22.2054			0.828120			0.414060	−	0.910250i	$-0.364110\pi$
$719$	22.2054			0.828120			0.414060	+	0.910250i	$0.364110\pi$
$720$		0			0
$721$	20.4045	−	7.24630i	0.759902	−	0.269866i
$722$		0			0
$723$	−5.83132	−	5.83132i	−0.216869	−	0.216869i
$724$		0			0
$725$	13.2147	−	14.9134i	0.490783	−	0.553871i
$726$		0			0
$727$	22.2068	+	22.2068i	0.823605	+	0.823605i	0.986623	−	0.163018i	$-0.0521230\pi$
$727$	22.2068	+	22.2068i	0.823605	+	0.823605i	−0.163018	+	0.986623i	$0.552123\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$			61.1969i			2.26345i
$732$		0			0
$733$	23.8751	−	23.8751i	0.881848	−	0.881848i	−0.111874	−	0.993722i	$-0.535685\pi$
$733$	23.8751	−	23.8751i	0.881848	−	0.881848i	0.993722	+	0.111874i	$0.0356854\pi$
$734$		0			0
$735$	−7.02532	+	13.9873i	−0.259133	+	0.515930i
$736$		0			0
$737$	9.89941	−	9.89941i	0.364649	−	0.364649i
$738$		0			0
$739$			15.7638i			0.579882i	0.957045	+	0.289941i	$0.0936357\pi$
$739$			15.7638i			0.579882i	−0.957045	+	0.289941i	$0.906364\pi$
$740$		0			0
$741$		−	7.95462i		−	0.292220i
$742$		0			0
$743$	12.8208	+	12.8208i	0.470350	+	0.470350i	0.902028	−	0.431678i	$-0.142078\pi$
$743$	12.8208	+	12.8208i	0.470350	+	0.470350i	−0.431678	+	0.902028i	$0.642078\pi$
$744$		0			0
$745$	−39.4324	−	14.9569i	−1.44469	−	0.547979i
$746$		0			0
$747$	−5.50407	−	5.50407i	−0.201384	−	0.201384i
$748$		0			0
$749$	4.84174	−	1.71946i	0.176913	−	0.0628279i
$750$		0			0
$751$	2.25311			0.0822172			0.0411086	−	0.999155i	$-0.486911\pi$
$751$	2.25311			0.0822172			0.0411086	+	0.999155i	$0.486911\pi$
$752$		0			0
$753$	−19.2433	−	19.2433i	−0.701264	−	0.701264i
$754$		0			0
$755$	16.3720	−	43.1632i	0.595840	−	1.57087i
$756$		0			0
$757$	11.4332	−	11.4332i	0.415546	−	0.415546i	−0.468120	−	0.883665i	$-0.655068\pi$
$757$	11.4332	−	11.4332i	0.415546	−	0.415546i	0.883665	+	0.468120i	$0.155068\pi$
$758$		0			0
$759$	2.54044			0.0922120
$760$		0			0
$761$		−	46.4983i		−	1.68556i	−0.538256	−	0.842781i	$-0.680917\pi$
$761$		−	46.4983i		−	1.68556i	0.538256	−	0.842781i	$-0.319083\pi$
$762$		0			0
$763$	−21.6116	+	45.4150i	−0.782393	+	1.64413i
$764$		0			0
$765$	6.04100	+	13.4243i	0.218413	+	0.485356i
$766$		0			0
$767$	11.0755	−	11.0755i	0.399913	−	0.399913i
$768$		0			0
$769$	1.59057			0.0573576			0.0286788	−	0.999589i	$-0.490870\pi$
$769$	1.59057			0.0573576			0.0286788	+	0.999589i	$0.490870\pi$
$770$		0			0
$771$	−15.9730			−0.575253
$772$		0			0
$773$	4.44860	−	4.44860i	0.160005	−	0.160005i	−0.622564	−	0.782569i	$-0.713909\pi$
$773$	4.44860	−	4.44860i	0.160005	−	0.160005i	0.782569	+	0.622564i	$0.213909\pi$
$774$		0			0
$775$	−1.38936	+	1.56796i	−0.0499074	+	0.0563228i
$776$		0			0
$777$	5.94990	−	12.5032i	0.213451	−	0.448550i
$778$		0			0
$779$			39.2005i			1.40450i
$780$		0			0
$781$	23.0660			0.825366
$782$		0			0
$783$	2.81794	−	2.81794i	0.100705	−	0.100705i
$784$		0			0
$785$	−1.71715	+	0.772726i	−0.0612877	+	0.0275798i
$786$		0			0
$787$	−7.11882	−	7.11882i	−0.253759	−	0.253759i	0.568751	−	0.822510i	$-0.307427\pi$
$787$	−7.11882	−	7.11882i	−0.253759	−	0.253759i	−0.822510	+	0.568751i	$0.807427\pi$
$788$		0			0
$789$	18.9976			0.676332
$790$		0			0
$791$	−5.42154	−	15.2662i	−0.192768	−	0.542804i
$792$		0			0
$793$	14.8255	+	14.8255i	0.526470	+	0.526470i
$794$		0			0
$795$	−4.42139	+	11.6565i	−0.156811	+	0.413415i
$796$		0			0
$797$	10.4565	+	10.4565i	0.370390	+	0.370390i	0.867619	−	0.497229i	$-0.165649\pi$
$797$	10.4565	+	10.4565i	0.370390	+	0.370390i	−0.497229	+	0.867619i	$0.665649\pi$
$798$		0			0
$799$			49.5500i			1.75295i
$800$		0			0
$801$			6.27930i			0.221868i
$802$		0			0
$803$	−9.31266	+	9.31266i	−0.328637	+	0.328637i
$804$		0			0
$805$	−8.20203	−	0.174725i	−0.289084	−	0.00615825i
$806$		0			0
$807$	6.95336	−	6.95336i	0.244770	−	0.244770i
$808$		0			0
$809$		−	17.8967i		−	0.629214i	−0.949222	−	0.314607i	$-0.898127\pi$
$809$		−	17.8967i		−	0.629214i	0.949222	−	0.314607i	$-0.101873\pi$
$810$		0			0
$811$			12.3372i			0.433216i	0.976259	+	0.216608i	$0.0694994\pi$
$811$			12.3372i			0.433216i	−0.976259	+	0.216608i	$0.930501\pi$
$812$		0			0
$813$	8.00619	+	8.00619i	0.280789	+	0.280789i
$814$		0			0
$815$	−8.27784	+	3.72507i	−0.289960	+	0.130483i
$816$		0			0
$817$	24.8754	+	24.8754i	0.870279	+	0.870279i
$818$		0			0
$819$	1.86107	+	5.24049i	0.0650311	+	0.183117i
$820$		0			0
$821$	−39.9421			−1.39399			−0.696995	−	0.717076i	$-0.745480\pi$
$821$	−39.9421			−1.39399			−0.696995	+	0.717076i	$0.745480\pi$
$822$		0			0
$823$	−30.8158	−	30.8158i	−1.07417	−	1.07417i	−0.997019	−	0.0771513i	$-0.975418\pi$
$823$	−30.8158	−	30.8158i	−1.07417	−	1.07417i	−0.0771513	−	0.997019i	$-0.524582\pi$
$824$		0			0
$825$	9.14328	−	0.552176i	0.318328	−	0.0192243i
$826$		0			0
$827$	−29.7898	+	29.7898i	−1.03589	+	1.03589i	−0.0365603	+	0.999331i	$0.511640\pi$
$827$	−29.7898	+	29.7898i	−1.03589	+	1.03589i	−0.999331	+	0.0365603i	$0.988360\pi$
$828$		0			0
$829$	38.2648			1.32899			0.664496	−	0.747292i	$-0.268646\pi$
$829$	38.2648			1.32899			0.664496	+	0.747292i	$0.268646\pi$
$830$		0			0
$831$		−	26.2439i		−	0.910391i
$832$		0			0
$833$	−4.73444	+	45.8399i	−0.164039	+	1.58826i
$834$		0			0
$835$	−36.8865	+	16.5991i	−1.27651	+	0.574435i
$836$		0			0
$837$	−0.296271	+	0.296271i	−0.0102406	+	0.0102406i
$838$		0			0
$839$	0.632232			0.0218271			0.0109135	−	0.999940i	$-0.496526\pi$
$839$	0.632232			0.0218271			0.0109135	+	0.999940i	$0.496526\pi$
$840$		0			0
$841$	13.1184			0.452359
$842$		0			0
$843$	5.52174	−	5.52174i	0.190179	−	0.190179i
$844$		0			0
$845$	−17.9425	−	6.80568i	−0.617240	−	0.234123i
$846$		0			0
$847$	18.2614	+	8.69005i	0.627470	+	0.298594i
$848$		0			0
$849$		−	1.62441i		−	0.0557498i
$850$		0			0
$851$	7.25744			0.248782
$852$		0			0
$853$	22.4320	−	22.4320i	0.768056	−	0.768056i	−0.209708	−	0.977764i	$-0.567251\pi$
$853$	22.4320	−	22.4320i	0.768056	−	0.768056i	0.977764	+	0.209708i	$0.0672514\pi$
$854$		0			0
$855$	7.91226	+	3.00116i	0.270594	+	0.102638i
$856$		0			0
$857$	7.26136	+	7.26136i	0.248043	+	0.248043i	0.820167	−	0.572124i	$-0.193880\pi$
$857$	7.26136	+	7.26136i	0.248043	+	0.248043i	−0.572124	+	0.820167i	$0.693880\pi$
$858$		0			0
$859$	46.5049			1.58673			0.793364	−	0.608748i	$-0.208328\pi$
$859$	46.5049			1.58673			0.793364	+	0.608748i	$0.208328\pi$
$860$		0			0
$861$	−9.17140	−	25.8252i	−0.312561	−	0.880122i
$862$		0			0
$863$	−35.2803	−	35.2803i	−1.20095	−	1.20095i	−0.973877	−	0.227077i	$-0.927083\pi$
$863$	−35.2803	−	35.2803i	−1.20095	−	1.20095i	−0.227077	−	0.973877i	$-0.572917\pi$
$864$		0			0
$865$	5.08393	+	11.2975i	0.172859	+	0.384126i
$866$		0			0
$867$	18.6259	+	18.6259i	0.632570	+	0.632570i
$868$		0			0
$869$			11.6101i			0.393845i
$870$		0			0
$871$			16.0626i			0.544262i
$872$		0			0
$873$	2.50605	−	2.50605i	0.0848168	−	0.0848168i
$874$		0			0
$875$	−29.5579	+	1.15390i	−0.999239	+	0.0390089i
$876$		0			0
$877$	−2.65411	+	2.65411i	−0.0896229	+	0.0896229i	−0.750497	−	0.660874i	$-0.770186\pi$
$877$	−2.65411	+	2.65411i	−0.0896229	+	0.0896229i	0.660874	+	0.750497i	$0.270186\pi$
$878$		0			0
$879$			5.62486i			0.189722i
$880$		0			0
$881$			13.4692i			0.453790i	0.973919	+	0.226895i	$0.0728574\pi$
$881$			13.4692i			0.453790i	−0.973919	+	0.226895i	$0.927143\pi$
$882$		0			0
$883$	7.95368	+	7.95368i	0.267662	+	0.267662i	0.828158	−	0.560495i	$-0.189389\pi$
$883$	7.95368	+	7.95368i	0.267662	+	0.267662i	−0.560495	+	0.828158i	$0.689389\pi$
$884$		0			0
$885$	6.83790	+	15.1952i	0.229853	+	0.510780i
$886$		0			0
$887$	13.1591	+	13.1591i	0.441838	+	0.441838i	0.892629	−	0.450791i	$-0.148858\pi$
$887$	13.1591	+	13.1591i	0.441838	+	0.441838i	−0.450791	+	0.892629i	$0.648858\pi$
$888$		0			0
$889$	8.92304	−	3.16887i	0.299269	−	0.106280i
$890$		0			0
$891$	1.83199			0.0613739
$892$		0			0
$893$	20.1411	+	20.1411i	0.673996	+	0.673996i
$894$		0			0
$895$	44.1509	+	16.7467i	1.47580	+	0.559780i
$896$		0			0
$897$	−2.06104	+	2.06104i	−0.0688160	+	0.0688160i
$898$		0			0
$899$	1.66975			0.0556893
$900$		0			0
$901$			36.7049i			1.22282i
$902$		0			0
$903$	−22.2077	−	10.5680i	−0.739026	−	0.351680i
$904$		0			0
$905$	50.5893	+	19.1888i	1.68164	+	0.637857i
$906$		0			0
$907$	27.3862	−	27.3862i	0.909344	−	0.909344i	−0.0868752	−	0.996219i	$-0.527688\pi$
$907$	27.3862	−	27.3862i	0.909344	−	0.909344i	0.996219	+	0.0868752i	$0.0276881\pi$
$908$		0			0
$909$	−2.35631			−0.0781539
$910$		0			0
$911$	−28.2418			−0.935691			−0.467846	−	0.883810i	$-0.654970\pi$
$911$	−28.2418			−0.935691			−0.467846	+	0.883810i	$0.654970\pi$
$912$		0			0
$913$	−10.0834	+	10.0834i	−0.333712	+	0.333712i
$914$		0			0
$915$	−20.3400	+	9.15311i	−0.672420	+	0.302593i
$916$		0			0
$917$	8.88371	−	18.6684i	0.293366	−	0.616484i
$918$		0			0
$919$			44.4983i			1.46786i	0.679224	+	0.733931i	$0.262317\pi$
$919$			44.4983i			1.46786i	−0.679224	+	0.733931i	$0.737683\pi$
$920$		0			0
$921$	−19.5265			−0.643421
$922$		0			0
$923$	−18.7133	+	18.7133i	−0.615955	+	0.615955i
$924$		0			0
$925$	26.1202	−	1.57744i	0.858828	−	0.0518659i
$926$		0			0
$927$	5.78700	+	5.78700i	0.190070	+	0.190070i
$928$		0			0
$929$	10.5215			0.345200			0.172600	−	0.984992i	$-0.444783\pi$
$929$	10.5215			0.345200			0.172600	+	0.984992i	$0.444783\pi$
$930$		0			0
$931$	16.7086	+	20.5575i	0.547601	+	0.673744i
$932$		0			0
$933$	10.9027	+	10.9027i	0.356940	+	0.356940i
$934$		0			0
$935$	24.5931	−	11.0670i	0.804281	−	0.361931i
$936$		0			0
$937$	−32.2864	−	32.2864i	−1.05475	−	1.05475i	−0.998412	−	0.0563380i	$-0.982058\pi$
$937$	−32.2864	−	32.2864i	−1.05475	−	1.05475i	−0.0563380	−	0.998412i	$-0.517942\pi$
$938$		0			0
$939$		−	5.51147i		−	0.179860i
$940$		0			0
$941$			44.5075i			1.45090i	0.688273	+	0.725452i	$0.258369\pi$
$941$			44.5075i			1.45090i	−0.688273	+	0.725452i	$0.741631\pi$
$942$		0			0
$943$	10.1568	−	10.1568i	0.330752	−	0.330752i
$944$		0			0
$945$	−5.91474	−	0.126000i	−0.192406	−	0.00409877i
$946$		0			0
$947$	−3.96469	+	3.96469i	−0.128835	+	0.128835i	−0.768584	−	0.639749i	$-0.779038\pi$
$947$	−3.96469	+	3.96469i	−0.128835	+	0.128835i	0.639749	+	0.768584i	$0.279038\pi$
$948$		0			0
$949$		−	15.1106i		−	0.490511i
$950$		0			0
$951$			14.1255i			0.458050i
$952$		0			0
$953$	−32.3886	−	32.3886i	−1.04917	−	1.04917i	−0.998727	−	0.0504422i	$-0.983937\pi$
$953$	−32.3886	−	32.3886i	−1.04917	−	1.04917i	−0.0504422	−	0.998727i	$-0.516063\pi$
$954$		0			0
$955$	−1.24455	+	3.28113i	−0.0402727	+	0.106175i
$956$		0			0
$957$	−5.16243	−	5.16243i	−0.166878	−	0.166878i
$958$		0			0
$959$	−54.9426	+	19.5119i	−1.77419	+	0.630073i
$960$		0			0
$961$	30.8244			0.994337
$962$		0			0
$963$	1.37319	+	1.37319i	0.0442504	+	0.0442504i
$964$		0			0
$965$	−6.71312	+	3.02094i	−0.216103	+	0.0972474i
$966$		0			0
$967$	40.0486	−	40.0486i	1.28788	−	1.28788i	0.351800	−	0.936075i	$-0.385570\pi$
$967$	40.0486	−	40.0486i	1.28788	−	1.28788i	0.936075	−	0.351800i	$-0.114430\pi$
$968$		0			0
$969$	24.9146			0.800372
$970$		0			0
$971$			47.0594i			1.51021i	0.655604	+	0.755105i	$0.272414\pi$
$971$			47.0594i			1.51021i	−0.655604	+	0.755105i	$0.727586\pi$
$972$		0			0
$973$	−40.7725	−	19.4024i	−1.30711	−	0.622012i
$974$		0			0
$975$	−6.96990	+	7.86585i	−0.223215	+	0.251909i
$976$		0			0
$977$	−30.2303	+	30.2303i	−0.967153	+	0.967153i	−0.999477	−	0.0323246i	$-0.989709\pi$
$977$	−30.2303	+	30.2303i	−0.967153	+	0.967153i	0.0323246	+	0.999477i	$0.489709\pi$
$978$		0			0
$979$	11.5036			0.367656
$980$		0			0
$981$	−19.0097			−0.606933
$982$		0			0
$983$	41.1744	−	41.1744i	1.31326	−	1.31326i	0.394261	−	0.918999i	$-0.371001\pi$
$983$	41.1744	−	41.1744i	1.31326	−	1.31326i	0.918999	−	0.394261i	$-0.128999\pi$
$984$		0			0
$985$	18.9716	+	42.1587i	0.604486	+	1.34329i
$986$		0			0
$987$	−17.9812	−	8.55669i	−0.572347	−	0.272362i
$988$		0			0
$989$		−	12.8904i		−	0.409890i
$990$		0			0
$991$	57.0948			1.81368			0.906839	−	0.421478i	$-0.138488\pi$
$991$	57.0948			1.81368			0.906839	+	0.421478i	$0.138488\pi$
$992$		0			0
$993$	−5.48861	+	5.48861i	−0.174176	+	0.174176i
$994$		0			0
$995$	4.70549	−	12.4055i	0.149174	−	0.393282i
$996$		0			0
$997$	2.86425	+	2.86425i	0.0907118	+	0.0907118i	0.751007	−	0.660295i	$-0.229569\pi$
$997$	2.86425	+	2.86425i	0.0907118	+	0.0907118i	−0.660295	+	0.751007i	$0.729569\pi$
$998$		0			0
$999$	5.23357			0.165583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.cz.f.433.8		24
4.3	odd	2		840.2.bt.a.433.3	yes	24
5.2	odd	4		1680.2.cz.e.97.5		24
7.6	odd	2		1680.2.cz.e.433.5		24
20.7	even	4		840.2.bt.b.97.10	yes	24
28.27	even	2		840.2.bt.b.433.10	yes	24
35.27	even	4	inner	1680.2.cz.f.97.8		24
140.27	odd	4		840.2.bt.a.97.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bt.a.97.3	✓	24	140.27	odd	4
840.2.bt.a.433.3	yes	24	4.3	odd	2
840.2.bt.b.97.10	yes	24	20.7	even	4
840.2.bt.b.433.10	yes	24	28.27	even	2
1680.2.cz.e.97.5		24	5.2	odd	4
1680.2.cz.e.433.5		24	7.6	odd	2
1680.2.cz.f.97.8		24	35.27	even	4	inner
1680.2.cz.f.433.8		24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.cz (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-0.793022 + 2.09072i) q^{5} +(-2.38904 - 1.13687i) q^{7} -1.00000i q^{9} -1.83199 q^{11} +(1.48628 - 1.48628i) q^{13} +(0.917612 + 2.03911i) q^{15} +(4.65516 + 4.65516i) q^{17} +3.78446 q^{19} +(-2.49320 + 0.885417i) q^{21} +(-0.980552 - 0.980552i) q^{23} +(-3.74223 - 3.31598i) q^{25} +(-0.707107 - 0.707107i) q^{27} +3.98517i q^{29} -0.418991i q^{31} +(-1.29541 + 1.29541i) q^{33} +(4.27145 - 4.09326i) q^{35} +(-3.70069 + 3.70069i) q^{37} -2.10191i q^{39} +10.3583i q^{41} +(6.57302 + 6.57302i) q^{43} +(2.09072 + 0.793022i) q^{45} +(5.32205 + 5.32205i) q^{47} +(4.41504 + 5.43207i) q^{49} +6.58339 q^{51} +(3.94238 + 3.94238i) q^{53} +(1.45281 - 3.83017i) q^{55} +(2.67602 - 2.67602i) q^{57} +7.45184 q^{59} +9.97493i q^{61} +(-1.13687 + 2.38904i) q^{63} +(1.92874 + 4.28604i) q^{65} +(-5.40365 + 5.40365i) q^{67} -1.38671 q^{69} -12.5907 q^{71} +(5.08337 - 5.08337i) q^{73} +(-4.99091 + 0.301408i) q^{75} +(4.37669 + 2.08274i) q^{77} -6.33742i q^{79} -1.00000 q^{81} +(5.50407 - 5.50407i) q^{83} +(-13.4243 + 6.04100i) q^{85} +(2.81794 + 2.81794i) q^{87} -6.27930 q^{89} +(-5.24049 + 1.86107i) q^{91} +(-0.296271 - 0.296271i) q^{93} +(-3.00116 + 7.91226i) q^{95} +(2.50605 + 2.50605i) q^{97} +1.83199i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{7} + 8 q^{11} + 16 q^{13} - 4 q^{15} + 20 q^{17} - 8 q^{19} - 24 q^{23} - 4 q^{25} + 4 q^{37} + 16 q^{43} - 4 q^{45} + 24 q^{47} + 36 q^{49} + 16 q^{53} - 28 q^{55} + 4 q^{57} - 8 q^{59} + 24 q^{65}+ \cdots - 28 q^{97}+O(q^{100}) \) 24 * q + 4 * q^7 + 8 * q^11 + 16 * q^13 - 4 * q^15 + 20 * q^17 - 8 * q^19 - 24 * q^23 - 4 * q^25 + 4 * q^37 + 16 * q^43 - 4 * q^45 + 24 * q^47 + 36 * q^49 + 16 * q^53 - 28 * q^55 + 4 * q^57 - 8 * q^59 + 24 * q^65 - 16 * q^67 - 8 * q^69 - 8 * q^71 - 28 * q^73 + 20 * q^77 - 24 * q^81 - 64 * q^83 - 20 * q^85 - 20 * q^87 + 16 * q^89 - 24 * q^91 - 12 * q^93 - 24 * q^95 - 28 * q^97

Introduction

L-functions

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Database

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