LMFDB - Embedded newform 680.2.cf.a.37.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(37,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 8, 4, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.cf (of order $16$, degree $8$, 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:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$104$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.21
Character	$\chi$	$=$	680.37
Dual form			680.2.cf.a.533.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14887 - 0.824675i) q^{2} +(-1.00008 - 1.49673i) q^{3} +(0.639823 + 1.89489i) q^{4} +(-1.25943 + 1.84765i) q^{5} +(-0.0853459 + 2.54430i) q^{6} +(-0.346855 + 0.0689937i) q^{7} +(0.827595 - 2.70464i) q^{8} +(-0.0919848 + 0.222071i) q^{9} +(2.97064 - 1.08410i) q^{10} +(1.00197 - 0.199305i) q^{11} +(2.19627 - 2.85270i) q^{12} -5.05949i q^{13} +(0.455390 + 0.206777i) q^{14} +(4.02498 + 0.0372228i) q^{15} +(-3.18125 + 2.42480i) q^{16} +(3.95447 - 1.16713i) q^{17} +(0.288815 - 0.179274i) q^{18} +(-5.52633 + 2.28908i) q^{19} +(-4.30693 - 1.20432i) q^{20} +(0.450148 + 0.450148i) q^{21} +(-1.31550 - 0.597326i) q^{22} +(-2.32647 + 3.48181i) q^{23} +(-4.87578 + 1.46618i) q^{24} +(-1.82766 - 4.65399i) q^{25} +(-4.17243 + 5.81272i) q^{26} +(-4.87217 + 0.969135i) q^{27} +(-0.352661 - 0.613109i) q^{28} +(-2.83574 + 1.89478i) q^{29} +(-4.59350 - 3.36206i) q^{30} +(-1.22775 + 6.17234i) q^{31} +(5.65453 - 0.162287i) q^{32} +(-1.30036 - 1.30036i) q^{33} +(-5.50568 - 1.92027i) q^{34} +(0.309364 - 0.727760i) q^{35} +(-0.479655 - 0.0322153i) q^{36} +(-5.77512 + 3.85882i) q^{37} +(8.23680 + 1.92756i) q^{38} +(-7.57269 + 5.05991i) q^{39} +(3.95494 + 4.93543i) q^{40} +(4.58964 - 6.86888i) q^{41} +(-0.145938 - 0.888390i) q^{42} +(-2.48116 - 5.99005i) q^{43} +(1.01875 + 1.77111i) q^{44} +(-0.294462 - 0.449639i) q^{45} +(5.54418 - 2.08158i) q^{46} +4.18729i q^{47} +(6.81078 + 2.33648i) q^{48} +(-6.35161 + 2.63092i) q^{49} +(-1.73828 + 6.85408i) q^{50} +(-5.70167 - 4.75155i) q^{51} +(9.58720 - 3.23718i) q^{52} +(1.73696 + 0.719472i) q^{53} +(6.39673 + 2.90454i) q^{54} +(-0.893672 + 2.10231i) q^{55} +(-0.100452 + 0.995216i) q^{56} +(8.95292 + 5.98215i) q^{57} +(4.82048 + 0.161698i) q^{58} +(-4.26567 + 10.2982i) q^{59} +(2.50474 + 7.65073i) q^{60} +(-1.42679 + 2.13534i) q^{61} +(6.50071 - 6.07874i) q^{62} +(0.0165839 - 0.0833726i) q^{63} +(-6.63017 - 4.47670i) q^{64} +(9.34819 + 6.37209i) q^{65} +(0.421577 + 2.56633i) q^{66} +(-4.31620 - 4.31620i) q^{67} +(4.74174 + 6.74655i) q^{68} +7.53799 q^{69} +(-0.955585 + 0.580981i) q^{70} +(-8.21116 - 1.63330i) q^{71} +(0.524496 + 0.432571i) q^{72} +(-4.08301 - 0.812162i) q^{73} +(9.81716 + 0.329307i) q^{74} +(-5.13797 + 7.38989i) q^{75} +(-7.87344 - 9.00720i) q^{76} +(-0.333788 + 0.138260i) q^{77} +(12.8729 + 0.431807i) q^{78} +(2.33914 - 0.465284i) q^{79} +(-0.473612 - 8.93172i) q^{80} +(6.83300 + 6.83300i) q^{81} +(-10.9375 + 4.10652i) q^{82} +(1.68057 - 4.05726i) q^{83} +(-0.564968 + 1.14100i) q^{84} +(-2.82394 + 8.77641i) q^{85} +(-2.08930 + 8.92797i) q^{86} +(5.67194 + 2.34940i) q^{87} +(0.290180 - 2.87492i) q^{88} +(1.76667 + 1.76667i) q^{89} +(-0.0325069 + 0.759414i) q^{90} +(0.349073 + 1.75491i) q^{91} +(-8.08619 - 2.18067i) q^{92} +(10.4662 - 4.33523i) q^{93} +(3.45315 - 4.81066i) q^{94} +(2.73061 - 13.0937i) q^{95} +(-5.89790 - 8.30100i) q^{96} +(-17.7692 - 3.53451i) q^{97} +(9.46685 + 2.21541i) q^{98} +(-0.0479065 + 0.240842i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 8 q^{2} - 16 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{10} - 32 q^{12} - 32 q^{14} - 16 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 8 q^{22} - 16 q^{23} - 16 q^{25} - 48 q^{26} - 40 q^{28} - 72 q^{30} - 32 q^{31}+ \cdots - 16 q^{98}+O(q^{100}) $ 832 * q - 8 * q^2 - 16 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^10 - 32 * q^12 - 32 * q^14 - 16 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^20 - 8 * q^22 - 16 * q^23 - 16 * q^25 - 48 * q^26 - 40 * q^28 - 72 * q^30 - 32 * q^31 - 8 * q^32 + 48 * q^36 + 96 * q^39 + 48 * q^40 - 32 * q^41 + 8 * q^42 - 32 * q^46 + 72 * q^48 - 16 * q^52 - 64 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 - 64 * q^58 - 8 * q^60 - 8 * q^62 - 64 * q^63 + 64 * q^65 - 16 * q^66 - 128 * q^68 - 72 * q^70 - 32 * q^71 - 16 * q^72 - 96 * q^73 - 16 * q^76 - 64 * q^78 - 136 * q^80 - 32 * q^81 - 8 * q^82 - 96 * q^84 - 32 * q^86 - 16 * q^87 + 80 * q^88 + 136 * q^90 + 104 * q^92 + 48 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$1$

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 $

$2$	−1.14887	−	0.824675i	−0.812377	−	0.583133i
$2$	−1.14887	−	0.824675i	−0.812377	−	0.583133i
$3$	−1.00008	−	1.49673i	−0.577398	−	0.864138i	0.421694	−	0.906738i	$-0.361436\pi$
$3$	−1.00008	−	1.49673i	−0.577398	−	0.864138i	−0.999092	+	0.0426006i	$0.986436\pi$
$4$	0.639823	+	1.89489i	0.319912	+	0.947447i
$5$	−1.25943	+	1.84765i	−0.563236	+	0.826296i
$5$	−1.25943	+	1.84765i	−0.563236	+	0.826296i
$6$	−0.0853459	+	2.54430i	−0.0348423	+	1.03871i
$7$	−0.346855	+	0.0689937i	−0.131099	+	0.0260772i	−0.260203	−	0.965554i	$-0.583790\pi$
$7$	−0.346855	+	0.0689937i	−0.131099	+	0.0260772i	0.129105	+	0.991631i	$0.458790\pi$
$8$	0.827595	−	2.70464i	0.292599	−	0.956235i
$9$	−0.0919848	+	0.222071i	−0.0306616	+	0.0740236i
$10$	2.97064	−	1.08410i	0.939400	−	0.342823i
$11$	1.00197	−	0.199305i	0.302106	−	0.0600927i	−0.0417095	−	0.999130i	$-0.513280\pi$
$11$	1.00197	−	0.199305i	0.302106	−	0.0600927i	0.343816	+	0.939037i	$0.388280\pi$
$12$	2.19627	−	2.85270i	0.634008	−	0.823502i
$13$		−	5.05949i		−	1.40325i	−0.712546	−	0.701625i	$-0.752458\pi$
$13$		−	5.05949i		−	1.40325i	0.712546	−	0.701625i	$-0.247542\pi$
$14$	0.455390	+	0.206777i	0.121708	+	0.0552635i
$15$	4.02498	+	0.0372228i	1.03925	+	0.00961088i
$16$	−3.18125	+	2.42480i	−0.795313	+	0.606199i
$17$	3.95447	−	1.16713i	0.959099	−	0.283070i
$17$	3.95447	−	1.16713i	0.959099	−	0.283070i
$18$	0.288815	−	0.179274i	0.0680744	−	0.0422553i
$19$	−5.52633	+	2.28908i	−1.26783	+	0.525151i	−0.912303	−	0.409516i	$-0.865698\pi$
$19$	−5.52633	+	2.28908i	−1.26783	+	0.525151i	−0.355524	+	0.934667i	$0.615698\pi$
$20$	−4.30693	−	1.20432i	−0.963058	−	0.269294i
$21$	0.450148	+	0.450148i	0.0982304	+	0.0982304i
$22$	−1.31550	−	0.597326i	−0.280466	−	0.127350i
$23$	−2.32647	+	3.48181i	−0.485102	+	0.726007i	−0.990595	−	0.136824i	$-0.956311\pi$
$23$	−2.32647	+	3.48181i	−0.485102	+	0.726007i	0.505493	+	0.862831i	$0.331311\pi$
$24$	−4.87578	+	1.46618i	−0.995265	+	0.299283i
$25$	−1.82766	−	4.65399i	−0.365531	−	0.930799i
$26$	−4.17243	+	5.81272i	−0.818282	+	1.13997i
$27$	−4.87217	+	0.969135i	−0.937649	+	0.186510i
$28$	−0.352661	−	0.613109i	−0.0666467	−	0.115867i
$29$	−2.83574	+	1.89478i	−0.526583	+	0.351851i	−0.790272	−	0.612756i	$-0.790061\pi$
$29$	−2.83574	+	1.89478i	−0.526583	+	0.351851i	0.263689	+	0.964608i	$0.415061\pi$
$30$	−4.59350	−	3.36206i	−0.838654	−	0.613826i
$31$	−1.22775	+	6.17234i	−0.220511	+	1.10858i	0.698880	+	0.715239i	$0.253682\pi$
$31$	−1.22775	+	6.17234i	−0.220511	+	1.10858i	−0.919391	+	0.393345i	$0.871318\pi$
$32$	5.65453	−	0.162287i	0.999588	−	0.0286886i
$33$	−1.30036	−	1.30036i	−0.226364	−	0.226364i
$34$	−5.50568	−	1.92027i	−0.944217	−	0.329323i
$35$	0.309364	−	0.727760i	0.0522920	−	0.123014i
$36$	−0.479655	−	0.0322153i	−0.0799425	−	0.00536922i
$37$	−5.77512	+	3.85882i	−0.949425	+	0.634385i	−0.930834	−	0.365442i	$-0.880918\pi$
$37$	−5.77512	+	3.85882i	−0.949425	+	0.634385i	−0.0185905	+	0.999827i	$0.505918\pi$
$38$	8.23680	+	1.92756i	1.33619	+	0.312691i
$39$	−7.57269	+	5.05991i	−1.21260	+	0.810234i
$40$	3.95494	+	4.93543i	0.625331	+	0.780359i
$41$	4.58964	−	6.86888i	0.716782	−	1.07274i	−0.276943	−	0.960886i	$-0.589321\pi$
$41$	4.58964	−	6.86888i	0.716782	−	1.07274i	0.993725	−	0.111853i	$-0.0356786\pi$
$42$	−0.145938	−	0.888390i	−0.0225187	−	0.137081i
$43$	−2.48116	−	5.99005i	−0.378374	−	0.913475i	−0.992271	−	0.124089i	$-0.960399\pi$
$43$	−2.48116	−	5.99005i	−0.378374	−	0.913475i	0.613898	−	0.789386i	$-0.289601\pi$
$44$	1.01875	+	1.77111i	0.153582	+	0.267006i
$45$	−0.294462	−	0.449639i	−0.0438958	−	0.0670283i
$46$	5.54418	−	2.08158i	0.817445	−	0.306912i
$47$			4.18729i			0.610778i	0.952228	+	0.305389i	$0.0987865\pi$
$47$			4.18729i			0.610778i	−0.952228	+	0.305389i	$0.901213\pi$
$48$	6.81078	+	2.33648i	0.983052	+	0.337242i
$49$	−6.35161	+	2.63092i	−0.907373	+	0.375846i
$50$	−1.73828	+	6.85408i	−0.245830	+	0.969313i
$51$	−5.70167	−	4.75155i	−0.798393	−	0.665350i
$52$	9.58720	−	3.23718i	1.32951	−	0.448916i
$53$	1.73696	+	0.719472i	0.238590	+	0.0988271i	0.498775	−	0.866732i	$-0.333784\pi$
$53$	1.73696	+	0.719472i	0.238590	+	0.0988271i	−0.260185	+	0.965559i	$0.583784\pi$
$54$	6.39673	+	2.90454i	0.870485	+	0.395258i
$55$	−0.893672	+	2.10231i	−0.120503	+	0.283476i
$56$	−0.100452	+	0.995216i	−0.0134235	+	0.132991i
$57$	8.95292	+	5.98215i	1.18584	+	0.792355i
$58$	4.82048	+	0.161698i	0.632960	+	0.0212320i
$59$	−4.26567	+	10.2982i	−0.555343	+	1.34072i	0.358075	+	0.933693i	$0.383433\pi$
$59$	−4.26567	+	10.2982i	−0.555343	+	1.34072i	−0.913418	+	0.407023i	$0.866567\pi$
$60$	2.50474	+	7.65073i	0.323361	+	0.987705i
$61$	−1.42679	+	2.13534i	−0.182681	+	0.273402i	−0.911496	−	0.411309i	$-0.865072\pi$
$61$	−1.42679	+	2.13534i	−0.182681	+	0.273402i	0.728814	+	0.684711i	$0.240072\pi$
$62$	6.50071	−	6.07874i	0.825590	−	0.772001i
$63$	0.0165839	−	0.0833726i	0.00208937	−	0.0105040i
$64$	−6.63017	−	4.47670i	−0.828772	−	0.559587i
$65$	9.34819	+	6.37209i	1.15950	+	0.790360i
$66$	0.421577	+	2.56633i	0.0518925	+	0.315893i
$67$	−4.31620	−	4.31620i	−0.527308	−	0.527308i	0.392461	−	0.919769i	$-0.371624\pi$
$67$	−4.31620	−	4.31620i	−0.527308	−	0.527308i	−0.919769	+	0.392461i	$0.871624\pi$
$68$	4.74174	+	6.74655i	0.575021	+	0.818139i
$69$	7.53799			0.907467
$70$	−0.955585	+	0.580981i	−0.114214	+	0.0694405i
$71$	−8.21116	−	1.63330i	−0.974486	−	0.193837i	−0.317930	−	0.948114i	$-0.602988\pi$
$71$	−8.21116	−	1.63330i	−0.974486	−	0.193837i	−0.656556	+	0.754277i	$0.727988\pi$
$72$	0.524496	+	0.432571i	0.0618124	+	0.0509789i
$73$	−4.08301	−	0.812162i	−0.477880	−	0.0950563i	−0.0497279	−	0.998763i	$-0.515835\pi$
$73$	−4.08301	−	0.812162i	−0.477880	−	0.0950563i	−0.428153	+	0.903706i	$0.640835\pi$
$74$	9.81716	+	0.329307i	1.14122	+	0.0382811i
$75$	−5.13797	+	7.38989i	−0.593281	+	0.853311i
$76$	−7.87344	−	9.00720i	−0.903146	−	1.03320i
$77$	−0.333788	+	0.138260i	−0.0380387	+	0.0157561i
$78$	12.8729	+	0.431807i	1.45756	+	0.0488925i
$79$	2.33914	−	0.465284i	0.263174	−	0.0523485i	−0.0617396	−	0.998092i	$-0.519665\pi$
$79$	2.33914	−	0.465284i	0.263174	−	0.0523485i	0.324913	+	0.945744i	$0.394665\pi$
$80$	−0.473612	−	8.93172i	−0.0529514	−	0.998597i
$81$	6.83300	+	6.83300i	0.759223	+	0.759223i
$82$	−10.9375	+	4.10652i	−1.20785	+	0.453489i
$83$	1.68057	−	4.05726i	0.184467	−	0.445343i	−0.804411	−	0.594074i	$-0.797519\pi$
$83$	1.68057	−	4.05726i	0.184467	−	0.445343i	0.988878	+	0.148731i	$0.0475188\pi$
$84$	−0.564968	+	1.14100i	−0.0616431	+	0.124493i
$85$	−2.82394	+	8.77641i	−0.306300	+	0.951935i
$86$	−2.08930	+	8.92797i	−0.225295	+	0.962728i
$87$	5.67194	+	2.34940i	0.608096	+	0.251882i
$88$	0.290180	−	2.87492i	0.0309333	−	0.306468i
$89$	1.76667	+	1.76667i	0.187267	+	0.187267i	0.794513	−	0.607247i	$-0.207726\pi$
$89$	1.76667	+	1.76667i	0.187267	+	0.187267i	−0.607247	+	0.794513i	$0.707726\pi$
$90$	−0.0325069	+	0.759414i	−0.00342653	+	0.0800493i
$91$	0.349073	+	1.75491i	0.0365928	+	0.183964i
$92$	−8.08619	−	2.18067i	−0.843044	−	0.227351i
$93$	10.4662	−	4.33523i	1.08529	−	0.449543i
$94$	3.45315	−	4.81066i	0.356165	−	0.496182i
$95$	2.73061	−	13.0937i	0.280155	−	1.34338i
$96$	−5.89790	−	8.30100i	−0.601951	−	0.847217i
$97$	−17.7692	−	3.53451i	−1.80419	−	0.358875i	−0.825528	−	0.564360i	$-0.809123\pi$
$97$	−17.7692	−	3.53451i	−1.80419	−	0.358875i	−0.978660	+	0.205485i	$0.934123\pi$
$98$	9.46685	+	2.21541i	0.956297	+	0.223790i
$99$	−0.0479065	+	0.240842i	−0.00481478	+	0.0242055i
$100$	7.64945	−	6.44095i	0.764945	−	0.644095i
$101$	1.04145			0.103628			0.0518142	−	0.998657i	$-0.483500\pi$
$101$	1.04145			0.103628			0.0518142	+	0.998657i	$0.483500\pi$
$102$	2.63202	+	10.1610i	0.260609	+	1.00608i
$103$	−9.45589	+	9.45589i	−0.931717	+	0.931717i	−0.997813	−	0.0660967i	$-0.978945\pi$
$103$	−9.45589	+	9.45589i	−0.931717	+	0.931717i	0.0660967	+	0.997813i	$0.478945\pi$
$104$	−13.6841	−	4.18721i	−1.34184	−	0.410590i
$105$	−1.39865	+	0.264787i	−0.136494	+	0.0258406i
$106$	−1.40222	−	2.25901i	−0.136195	−	0.219414i
$107$	−5.59497	−	1.11291i	−0.540886	−	0.107589i	−0.0829160	−	0.996557i	$-0.526423\pi$
$107$	−5.59497	−	1.11291i	−0.540886	−	0.107589i	−0.457970	+	0.888968i	$0.651423\pi$
$108$	−4.95374	−	8.61217i	−0.476673	−	0.828707i
$109$	−2.90056	+	4.34100i	−0.277824	+	0.415792i	−0.943971	−	0.330027i	$-0.892942\pi$
$109$	−2.90056	+	4.34100i	−0.277824	+	0.415792i	0.666148	+	0.745820i	$0.267942\pi$
$110$	2.76044	−	1.67830i	0.263198	−	0.160020i
$111$	11.5512	+	4.78467i	1.09639	+	0.454141i
$112$	0.936136	−	1.06054i	0.0884566	−	0.100211i
$113$	14.6248	+	9.77200i	1.37579	+	0.919272i	0.999972	−	0.00742181i	$-0.00236246\pi$
$113$	14.6248	+	9.77200i	1.37579	+	0.919272i	0.375816	+	0.926694i	$0.377362\pi$
$114$	−5.35245	−	14.2560i	−0.501303	−	1.33520i
$115$	−3.50315	−	8.68362i	−0.326670	−	0.809751i
$116$	−5.40477	−	4.16110i	−0.501821	−	0.386348i
$117$	1.12357	+	0.465396i	0.103874	+	0.0430259i
$118$	13.3934	−	8.31359i	1.23296	−	0.765328i
$119$	−1.29110	+	0.677656i	−0.118355	+	0.0621206i
$120$	3.43173	−	10.8553i	0.313272	−	0.990951i
$121$	−9.19845	+	3.81012i	−0.836222	+	0.346375i
$122$	3.40016	−	1.27660i	0.307836	−	0.115578i
$123$	−14.8709			−1.34086
$124$	−12.4815	+	1.62274i	−1.12087	+	0.145726i
$125$	10.9008	+	2.48451i	0.974996	+	0.222222i
$126$	−0.0878081	+	0.0821084i	−0.00782256	+	0.00731480i
$127$	4.38339	−	1.81566i	0.388963	−	0.161114i	−0.179627	−	0.983735i	$-0.557489\pi$
$127$	4.38339	−	1.81566i	0.388963	−	0.161114i	0.568590	+	0.822621i	$0.307489\pi$
$128$	3.92541	+	10.6109i	0.346961	+	0.937880i
$129$	−6.48413	+	9.70418i	−0.570896	+	0.854406i
$130$	−5.48500	−	15.0299i	−0.481066	−	1.31821i
$131$	−5.46557	−	8.17980i	−0.477529	−	0.714673i	0.512003	−	0.858983i	$-0.328904\pi$
$131$	−5.46557	−	8.17980i	−0.477529	−	0.714673i	−0.989532	+	0.144311i	$0.953904\pi$
$132$	1.63205	−	3.29605i	0.142052	−	0.286885i
$133$	1.75890	−	1.17526i	0.152516	−	0.101908i
$134$	1.39931	+	8.51824i	0.120882	+	0.735864i
$135$	4.34554	−	10.2226i	0.374005	−	0.879825i
$136$	0.116043	−	11.6613i	0.00995056	−	0.999950i
$137$	−15.3372	−	15.3372i	−1.31035	−	1.31035i	−0.921156	−	0.389194i	$-0.872754\pi$
$137$	−15.3372	−	15.3372i	−1.31035	−	1.31035i	−0.389194	−	0.921156i	$-0.627246\pi$
$138$	−8.66020	−	6.21639i	−0.737205	−	0.529174i
$139$	17.5589	+	3.49268i	1.48933	+	0.296245i	0.871627	−	0.490169i	$-0.163065\pi$
$139$	17.5589	+	3.49268i	1.48933	+	0.296245i	0.617699	+	0.786415i	$0.288065\pi$
$140$	1.57697	+	0.120573i	0.133278	+	0.0101903i
$141$	6.26724	−	4.18763i	0.527796	−	0.352662i
$142$	8.08665	+	8.64800i	0.678617	+	0.725724i
$143$	−1.00838	−	5.06948i	−0.0843251	−	0.423931i
$144$	−0.245850	−	0.929508i	−0.0204875	−	0.0774590i
$145$	0.0705230	−	7.62581i	0.00585662	−	0.633289i
$146$	4.02110	+	4.30023i	0.332788	+	0.355889i
$147$	10.2899	+	6.87550i	0.848698	+	0.567082i
$148$	−11.0071	−	8.47429i	−0.904779	−	0.696583i
$149$	−5.51284	−	5.51284i	−0.451629	−	0.451629i	0.444266	−	0.895895i	$-0.353465\pi$
$149$	−5.51284	−	5.51284i	−0.451629	−	0.451629i	−0.895895	+	0.444266i	$0.853465\pi$
$150$	11.9971	−	4.25291i	0.979562	−	0.347248i
$151$	−7.52249	−	18.1609i	−0.612172	−	1.47791i	−0.860610	−	0.509265i	$-0.829917\pi$
$151$	−7.52249	−	18.1609i	−0.612172	−	1.47791i	0.248438	−	0.968648i	$-0.420083\pi$
$152$	1.61758	+	16.8412i	0.131203	+	1.36600i
$153$	−0.104566	+	0.985530i	−0.00845368	+	0.0796754i
$154$	0.497500	+	0.116424i	0.0400897	+	0.00938170i
$155$	−9.85807	−	10.0421i	−0.791820	−	0.806602i
$156$	−14.4332	−	11.1120i	−1.15558	−	0.889672i
$157$		−	4.52318i		−	0.360989i	−0.983576	−	0.180494i	$-0.942230\pi$
$157$		−	4.52318i		−	0.360989i	0.983576	−	0.180494i	$-0.0577698\pi$
$158$	−3.07109	−	1.39448i	−0.244322	−	0.110939i
$159$	−0.660248	−	3.31929i	−0.0523611	−	0.263237i
$160$	−6.82165	+	10.6520i	−0.539298	+	0.842115i
$161$	0.566724	−	1.36819i	0.0446641	−	0.107829i
$162$	−2.21526	−	13.4853i	−0.174047	−	1.05950i
$163$	−1.85310	−	9.31617i	−0.145146	−	0.729699i	−0.982971	−	0.183760i	$-0.941173\pi$
$163$	−1.85310	−	9.31617i	−0.145146	−	0.729699i	0.837825	−	0.545939i	$-0.183827\pi$
$164$	15.9524	+	4.30202i	1.24567	+	0.335931i
$165$	4.04034	−	0.764902i	0.314540	−	0.0595475i
$166$	−5.27669	+	3.27536i	−0.409551	+	0.254217i
$167$	−11.3043	+	7.55328i	−0.874752	+	0.584490i	−0.909870	−	0.414893i	$-0.863819\pi$
$167$	−11.3043	+	7.55328i	−0.874752	+	0.584490i	0.0351186	+	0.999383i	$0.488819\pi$
$168$	1.59003	−	0.844949i	0.122674	−	0.0651893i
$169$	−12.5984			−0.969111
$170$	10.4820	−	7.75416i	0.803935	−	0.594717i
$171$		−	1.43780i		−	0.109951i
$172$	9.76302	−	8.53412i	0.744423	−	0.650720i
$173$	9.13148	+	13.6662i	0.694253	+	1.03902i	0.996318	+	0.0857362i	$0.0273242\pi$
$173$	9.13148	+	13.6662i	0.694253	+	1.03902i	−0.302064	+	0.953288i	$0.597676\pi$
$174$	−4.57886	−	7.37667i	−0.347123	−	0.559224i
$175$	0.955027	+	1.48816i	0.0721933	+	0.112495i
$176$	−2.70426	+	3.06362i	−0.203841	+	0.230929i
$177$	19.6797	−	3.91454i	1.47922	−	0.294235i
$178$	−0.572753	−	3.48661i	−0.0429297	−	0.261332i
$179$	14.6378	+	6.06317i	1.09408	+	0.453183i	0.855427	−	0.517923i	$-0.173294\pi$
$179$	14.6378	+	6.06317i	1.09408	+	0.453183i	0.238652	+	0.971105i	$0.423294\pi$
$180$	0.663616	−	0.845664i	0.0494630	−	0.0630320i
$181$	21.7562	−	4.32757i	1.61712	−	0.321666i	0.698140	−	0.715961i	$-0.254011\pi$
$181$	21.7562	−	4.32757i	1.61712	−	0.321666i	0.918984	+	0.394295i	$0.129011\pi$
$182$	1.04619	−	2.30404i	0.0775485	−	0.170787i
$183$	4.62293			0.341737
$184$	7.49167	+	9.17379i	0.552293	+	0.676301i
$185$	0.143624	−	15.5304i	0.0105594	−	1.14181i
$186$	−15.5995	−	3.65056i	−1.14381	−	0.267672i
$187$	3.72966	−	1.95757i	0.272740	−	0.143152i
$188$	−7.93446	+	2.67912i	−0.578680	+	0.195395i
$189$	1.62307	−	0.672298i	0.118061	−	0.0489024i
$190$	−13.9352	+	12.7911i	−1.01096	+	0.927967i
$191$	3.39565	−	3.39565i	0.245701	−	0.245701i	−0.573503	−	0.819203i	$-0.694416\pi$
$191$	3.39565	−	3.39565i	0.245701	−	0.245701i	0.819203	+	0.573503i	$0.194416\pi$
$192$	−0.0696841	+	14.4006i	−0.00502902	+	1.03928i
$193$	2.09745	−	3.13905i	0.150977	−	0.225954i	−0.748270	−	0.663395i	$-0.769115\pi$
$193$	2.09745	−	3.13905i	0.150977	−	0.225954i	0.899247	+	0.437441i	$0.144115\pi$
$194$	17.4997	+	18.7145i	1.25641	+	1.34362i
$195$	0.188328	−	20.3643i	0.0134865	−	1.45832i
$196$	−9.04923	−	10.3523i	−0.646373	−	0.739450i
$197$	17.6053	−	3.50191i	1.25433	−	0.249501i	0.477171	−	0.878811i	$-0.341662\pi$
$197$	17.6053	−	3.50191i	1.25433	−	0.249501i	0.777155	+	0.629310i	$0.216662\pi$
$198$	0.253655	−	0.237190i	0.0180265	−	0.0168564i
$199$	−0.869525	−	1.30134i	−0.0616390	−	0.0922493i	0.799370	−	0.600839i	$-0.205167\pi$
$199$	−0.869525	−	1.30134i	−0.0616390	−	0.0922493i	−0.861009	+	0.508590i	$0.830167\pi$
$200$	−14.0999	+	1.09153i	−0.997017	+	0.0771831i
$201$	−2.14363	+	10.7768i	−0.151200	+	0.760134i
$202$	−1.19650	−	0.858859i	−0.0841852	−	0.0604291i
$203$	0.852860	−	0.852860i	0.0598590	−	0.0598590i
$204$	5.35562	−	13.8442i	0.374969	−	0.969289i
$205$	6.91098	+	17.1310i	0.482684	+	1.19648i
$206$	18.6617	−	3.06559i	1.30022	−	0.213590i
$207$	−0.559208	−	0.836914i	−0.0388677	−	0.0581696i
$208$	12.2682	+	16.0955i	0.850649	+	1.11602i
$209$	−5.08101	+	3.39502i	−0.351461	+	0.234839i
$210$	1.82524	+	0.849224i	0.125953	+	0.0586021i
$211$	−4.25948	−	2.84609i	−0.293235	−	0.195933i	0.400247	−	0.916407i	$-0.368924\pi$
$211$	−4.25948	−	2.84609i	−0.293235	−	0.195933i	−0.693482	+	0.720474i	$0.743924\pi$
$212$	−0.251977	+	3.75169i	−0.0173058	+	0.257667i
$213$	5.76723	+	13.9233i	0.395164	+	0.954011i
$214$	5.51013	+	5.89262i	0.376665	+	0.402811i
$215$	14.1924	+	2.95974i	0.967914	+	0.201853i
$216$	−1.41102	+	13.9795i	−0.0960079	+	0.951186i
$217$		−	2.22561i		−	0.151084i
$218$	6.91230	−	2.59524i	0.468160	−	0.175772i
$219$	2.86776	+	6.92340i	0.193786	+	0.467840i
$220$	−4.55545	−	0.348305i	−0.307129	−	0.0234827i
$221$	−5.90506	−	20.0076i	−0.397217	−	1.34586i
$222$	−9.32509	−	15.0230i	−0.625859	−	1.00828i
$223$	−5.24797	+	12.6697i	−0.351430	+	0.848428i	0.645014	+	0.764171i	$0.276852\pi$
$223$	−5.24797	+	12.6697i	−0.351430	+	0.848428i	−0.996444	+	0.0842569i	$0.973148\pi$
$224$	−1.95010	+	0.446416i	−0.130297	+	0.0298275i
$225$	1.20163	+	0.0222272i	0.0801089	+	0.00148181i
$226$	−8.74337	−	23.2875i	−0.581600	−	1.54906i
$227$	−13.4098	+	20.0692i	−0.890040	+	1.33204i	0.0527342	+	0.998609i	$0.483206\pi$
$227$	−13.4098	+	20.0692i	−0.890040	+	1.33204i	−0.942775	+	0.333431i	$0.891794\pi$
$228$	−5.60726	+	20.7924i	−0.371350	+	1.37701i
$229$	−3.01312	+	7.27431i	−0.199113	+	0.480700i	−0.991624	−	0.129157i	$-0.958773\pi$
$229$	−3.01312	+	7.27431i	−0.199113	+	0.480700i	0.792512	+	0.609857i	$0.208773\pi$
$230$	−3.13648	+	12.8653i	−0.206814	+	0.848315i
$231$	0.540753	+	0.361320i	0.0355790	+	0.0237731i
$232$	2.77785	+	9.23776i	0.182375	+	0.606488i
$233$	3.18587	−	16.0164i	0.208713	−	1.04927i	−0.724315	−	0.689469i	$-0.757844\pi$
$233$	3.18587	−	16.0164i	0.208713	−	1.04927i	0.933028	−	0.359803i	$-0.117156\pi$
$234$	−0.907035	−	1.46126i	−0.0592947	−	0.0955254i
$235$	−7.73666	−	5.27360i	−0.504684	−	0.344012i
$236$	−22.2433	−	1.49394i	−1.44792	−	0.0972473i
$237$	−3.03574	−	3.03574i	−0.197192	−	0.197192i
$238$	2.04216	+	0.286197i	0.132373	+	0.0185514i
$239$		−	21.3607i		−	1.38171i	−0.722995	−	0.690853i	$-0.757235\pi$
$239$		−	21.3607i		−	1.38171i	0.722995	−	0.690853i	$-0.242765\pi$
$240$	−12.8947	+	9.64134i	−0.832351	+	0.622346i
$241$	17.3503	+	3.45120i	1.11763	+	0.222311i	0.719144	−	0.694862i	$-0.244534\pi$
$241$	17.3503	+	3.45120i	1.11763	+	0.222311i	0.398490	+	0.917173i	$0.369534\pi$
$242$	13.7100	+	3.20838i	0.881310	+	0.206242i
$243$	0.486188	−	2.44423i	0.0311889	−	0.156797i
$244$	−4.95913	−	1.33737i	−0.317476	−	0.0856165i
$245$	3.13839	−	15.0491i	0.200504	−	0.961449i
$246$	17.0848	+	12.2636i	1.08929	+	0.781902i
$247$	11.5816	+	27.9604i	0.736918	+	1.77908i
$248$	15.6779	+	8.42883i	0.995546	+	0.535231i
$249$	−7.75334	+	1.54224i	−0.491348	+	0.0977352i
$250$	−10.4747	−	11.8440i	−0.662479	−	0.749080i
$251$	7.78734	−	7.78734i	0.491532	−	0.491532i	−0.417256	−	0.908789i	$-0.637008\pi$
$251$	7.78734	−	7.78734i	0.491532	−	0.491532i	0.908789	+	0.417256i	$0.137008\pi$
$252$	0.168593	−	0.0219191i	0.0106204	−	0.00138077i
$253$	−1.63712	+	3.95236i	−0.102925	+	0.248483i
$254$	−6.53329	−	1.52891i	−0.409935	−	0.0959320i
$255$	15.9601	−	4.55046i	0.999460	−	0.284961i
$256$	4.24073	−	15.4278i	0.265046	−	0.964236i
$257$	−24.6382	−	10.2055i	−1.53689	−	0.636601i	−0.556004	−	0.831179i	$-0.687666\pi$
$257$	−24.6382	−	10.2055i	−1.53689	−	0.636601i	−0.980887	+	0.194578i	$0.937666\pi$
$258$	15.4522	−	5.80159i	0.962014	−	0.361191i
$259$	1.73689	−	1.73689i	0.107925	−	0.107925i
$260$	−6.09325	+	21.7909i	−0.377887	+	1.35141i
$261$	−0.159930	−	0.804025i	−0.00989945	−	0.0497679i
$262$	−0.466425	+	13.9049i	−0.0288158	+	0.859046i
$263$	−6.05054	−	14.6073i	−0.373092	−	0.900725i	−0.993223	−	0.116226i	$-0.962920\pi$
$263$	−6.05054	−	14.6073i	−0.373092	−	0.900725i	0.620130	−	0.784499i	$-0.287080\pi$
$264$	−4.59319	+	2.44084i	−0.282691	+	0.150223i
$265$	−3.51692	+	2.30317i	−0.216043	+	0.141483i
$266$	−2.98996	−	0.100295i	−0.183326	−	0.00614949i
$267$	0.877411	−	4.41104i	0.0536967	−	0.269951i
$268$	5.41714	−	10.9404i	0.330905	−	0.668289i
$269$	−0.652091	+	3.27828i	−0.0397587	+	0.199880i	−0.995559	−	0.0941347i	$-0.969992\pi$
$269$	−0.652091	+	3.27828i	−0.0397587	+	0.199880i	0.955801	+	0.294015i	$0.0949916\pi$
$270$	−13.4228	+	8.16087i	−0.816888	+	0.496655i
$271$		−	15.3023i		−	0.929549i	−0.885429	−	0.464775i	$-0.846135\pi$
$271$		−	15.3023i		−	0.929549i	0.885429	−	0.464775i	$-0.153865\pi$
$272$	−9.75012	+	13.3017i	−0.591188	+	0.806534i
$273$	2.27752	−	2.27752i	0.137842	−	0.137842i
$274$	4.97233	+	30.2688i	0.300389	+	1.82861i
$275$	−2.75883	−	4.29892i	−0.166364	−	0.259235i
$276$	4.82298	+	14.2837i	0.290309	+	0.859778i
$277$	−26.9185	−	5.35442i	−1.61737	−	0.321716i	−0.698301	−	0.715804i	$-0.746060\pi$
$277$	−26.9185	−	5.35442i	−1.61737	−	0.321716i	−0.919073	+	0.394088i	$0.871060\pi$
$278$	−17.2926	−	18.4930i	−1.03714	−	1.10914i
$279$	−1.25776	−	0.840409i	−0.0753002	−	0.0503140i
$280$	−1.71230	−	1.43901i	−0.102330	−	0.0859972i
$281$	2.90134	+	1.20178i	0.173080	+	0.0716919i	0.467541	−	0.883972i	$-0.345140\pi$
$281$	2.90134	+	1.20178i	0.173080	+	0.0716919i	−0.294461	+	0.955663i	$0.595140\pi$
$282$	−10.6537	−	0.357368i	−0.634419	−	0.0212809i
$283$	−3.63158	+	5.43504i	−0.215875	+	0.323080i	−0.923564	−	0.383444i	$-0.874738\pi$
$283$	−3.63158	+	5.43504i	−0.215875	+	0.323080i	0.707689	+	0.706524i	$0.249738\pi$
$284$	−2.15876	−	16.6043i	−0.128099	−	0.985285i
$285$	−22.3286	+	9.00779i	−1.32263	+	0.533576i
$286$	−3.02216	+	6.65578i	−0.178704	+	0.393564i
$287$	−1.11803	+	2.69916i	−0.0659951	+	0.159326i
$288$	−0.484091	+	1.27063i	−0.0285253	+	0.0748728i
$289$	14.2756	−	9.23072i	0.839743	−	0.542984i
$290$	−6.36983	+	8.70293i	−0.374049	+	0.511054i
$291$	12.4805	+	30.1305i	0.731618	+	1.76628i
$292$	−1.07345	−	8.25652i	−0.0628187	−	0.483176i
$293$	−7.83256			−0.457583			−0.228792	−	0.973475i	$-0.573477\pi$
$293$	−7.83256			−0.457583			−0.228792	+	0.973475i	$0.573477\pi$
$294$	−6.15177	−	16.3849i	−0.358778	−	0.955588i
$295$	−13.6553	−	20.8514i	−0.795040	−	1.21402i
$296$	5.65725	+	18.8132i	0.328821	+	1.09349i
$297$	−4.68863	+	1.94209i	−0.272062	+	0.112692i
$298$	1.78726	+	10.8799i	0.103533	+	0.630253i
$299$	17.6162	+	11.7708i	1.01877	+	0.680720i
$300$	−17.2905	−	5.00768i	−0.998265	−	0.289118i
$301$	1.27388	+	1.90649i	0.0734251	+	0.109888i
$302$	−6.33444	+	27.0682i	−0.364506	+	1.55760i
$303$	−1.04154	−	1.55877i	−0.0598348	−	0.0895491i
$304$	12.0301	−	20.6824i	0.689973	−	1.18621i
$305$	−2.14843	−	5.32553i	−0.123018	−	0.304939i
$306$	0.932875	−	1.04602i	0.0533289	−	0.0597968i
$307$	2.32774	−	2.32774i	0.132851	−	0.132851i	−0.637554	−	0.770405i	$-0.720054\pi$
$307$	2.32774	−	2.32774i	0.132851	−	0.132851i	0.770405	+	0.637554i	$0.220054\pi$
$308$	−0.475553	−	0.544032i	−0.0270971	−	0.0309991i
$309$	23.6096	+	4.69624i	1.34310	+	0.267160i
$310$	3.04421	+	19.6668i	0.172900	+	1.11700i
$311$	13.9606	+	20.8935i	0.791632	+	1.18476i	0.979277	+	0.202524i	$0.0649143\pi$
$311$	13.9606	+	20.8935i	0.791632	+	1.18476i	−0.187646	+	0.982237i	$0.560086\pi$
$312$	7.41812	+	24.6690i	0.419968	+	1.39661i
$313$	−1.85414	−	9.32139i	−0.104802	−	0.526876i	−0.997145	−	0.0755170i	$-0.975939\pi$
$313$	−1.85414	−	9.32139i	−0.104802	−	0.526876i	0.892342	−	0.451359i	$-0.149061\pi$
$314$	−3.73015	+	5.19656i	−0.210504	+	0.293259i
$315$	0.133158	+	0.135643i	0.00750258	+	0.00764265i
$316$	2.37830	+	4.13472i	0.133790	+	0.232596i
$317$	24.2171	+	16.1813i	1.36017	+	0.908835i	0.999713	−	0.0239418i	$-0.00762165\pi$
$317$	24.2171	+	16.1813i	1.36017	+	0.908835i	0.360454	+	0.932777i	$0.382622\pi$
$318$	−1.97879	+	4.35794i	−0.110965	+	0.244381i
$319$	−2.46369	+	2.46369i	−0.137940	+	0.137940i
$320$	16.6216	−	6.61217i	0.929178	−	0.369632i
$321$	3.92971	+	9.48716i	0.219335	+	0.529522i
$322$	−1.77941	+	1.10452i	−0.0991626	+	0.0615524i
$323$	−19.1820	+	15.5020i	−1.06732	+	0.862555i
$324$	−8.57591	+	17.3197i	−0.476439	+	0.962208i
$325$	−23.5468	+	9.24702i	−1.30614	+	0.512932i
$326$	−5.55383	+	12.2313i	−0.307598	+	0.677430i
$327$	9.39811			0.519717
$328$	−14.7795	−	18.0980i	−0.816062	−	0.999294i
$329$	−0.288896	−	1.45238i	−0.0159274	−	0.0800722i
$330$	−5.27264	−	2.45319i	−0.290249	−	0.135044i
$331$	−1.82918	−	0.757669i	−0.100541	−	0.0416453i	0.331846	−	0.943333i	$-0.392328\pi$
$331$	−1.82918	−	0.757669i	−0.100541	−	0.0416453i	−0.432387	+	0.901688i	$0.642328\pi$
$332$	8.76336	+	0.588578i	0.480952	+	0.0323024i
$333$	−0.325707	−	1.63744i	−0.0178486	−	0.0897311i
$334$	19.2162	+	0.644588i	1.05146	+	0.0352703i
$335$	13.4108	−	2.53889i	0.732711	−	0.138714i
$336$	−2.52355	−	0.340518i	−0.137671	−	0.0185768i
$337$	5.30570	−	3.54516i	0.289020	−	0.193117i	−0.402605	−	0.915374i	$-0.631895\pi$
$337$	5.30570	−	3.54516i	0.289020	−	0.193117i	0.691625	+	0.722257i	$0.256895\pi$
$338$	14.4740	+	10.3896i	0.787283	+	0.565121i
$339$		−	31.6622i		−	1.71966i
$340$	−18.4372	+	0.264278i	−0.999897	+	0.0143325i
$341$			6.42922i			0.348162i
$342$	−1.18571	+	1.65185i	−0.0641161	+	0.0893217i
$343$	4.07991	−	2.72611i	0.220295	−	0.147196i
$344$	−18.2543	+	1.75331i	−0.984208	+	0.0945323i
$345$	−9.49359	+	13.9276i	−0.511118	+	0.749837i
$346$	0.779269	−	23.2313i	0.0418938	−	1.24892i
$347$	−0.758191	−	3.81169i	−0.0407018	−	0.204622i	0.955083	−	0.296337i	$-0.0957651\pi$
$347$	−0.758191	−	3.81169i	−0.0407018	−	0.204622i	−0.995785	+	0.0917150i	$0.970765\pi$
$348$	−0.822816	+	12.2509i	−0.0441076	+	0.656719i
$349$	−12.8030	−	5.30318i	−0.685329	−	0.283873i	0.0127234	−	0.999919i	$-0.495950\pi$
$349$	−12.8030	−	5.30318i	−0.685329	−	0.283873i	−0.698053	+	0.716046i	$0.745950\pi$
$350$	0.130044	−	2.49730i	0.00695113	−	0.133486i
$351$	4.90333	+	24.6507i	0.261720	+	1.31576i
$352$	5.63334	−	1.28958i	0.300258	−	0.0687350i
$353$	−4.28015			−0.227809			−0.113905	−	0.993492i	$-0.536336\pi$
$353$	−4.28015			−0.227809			−0.113905	+	0.993492i	$0.536336\pi$
$354$	−25.8377	−	11.7320i	−1.37326	−	0.623551i
$355$	13.3592	−	13.1144i	0.709032	−	0.696038i
$356$	−2.21730	+	4.47801i	−0.117516	+	0.237334i
$357$	2.30548	+	1.25472i	0.122019	+	0.0664067i
$358$	−11.8168	−	19.0372i	−0.624539	−	1.00615i
$359$	12.8794	+	31.0937i	0.679750	+	1.64106i	0.764473	+	0.644656i	$0.222999\pi$
$359$	12.8794	+	31.0937i	0.679750	+	1.64106i	−0.0847229	+	0.996405i	$0.527001\pi$
$360$	−1.45981	+	0.424294i	−0.0769387	+	0.0223622i
$361$	11.8654	−	11.8654i	0.624494	−	0.624494i
$362$	−28.5640	−	12.9699i	−1.50129	−	0.681685i
$363$	14.9019	+	9.95715i	0.782149	+	0.522615i
$364$	−3.10202	+	1.78429i	−0.162590	+	0.0935220i
$365$	6.64287	−	6.52113i	0.347704	−	0.341332i
$366$	−5.31117	−	3.81241i	−0.277619	−	0.199278i
$367$	−3.96818	−	19.9494i	−0.207137	−	1.04135i	−0.934735	−	0.355346i	$-0.884363\pi$
$367$	−3.96818	−	19.9494i	−0.207137	−	1.04135i	0.727598	−	0.686004i	$-0.240637\pi$
$368$	−1.04159	−	16.7177i	−0.0542965	−	0.871472i
$369$	1.10320	+	1.65106i	0.0574304	+	0.0859507i
$370$	−12.9725	+	17.7240i	−0.674408	+	0.921426i
$371$	−0.652111	−	0.129713i	−0.0338559	−	0.00673436i
$372$	14.9113	+	17.0585i	0.773116	+	0.884443i
$373$	19.9125	−	19.9125i	1.03103	−	1.03103i	0.0315254	−	0.999503i	$-0.489964\pi$
$373$	19.9125	−	19.9125i	1.03103	−	1.03103i	0.999503	−	0.0315254i	$-0.0100365\pi$
$374$	−5.89927	−	0.826749i	−0.305044	−	0.0427502i
$375$	−7.18305	−	18.8003i	−0.370931	−	0.970841i
$376$	11.3251	+	3.46538i	0.584048	+	0.178713i
$377$	9.58661	+	14.3474i	0.493736	+	0.738928i
$378$	−2.41913	−	0.566119i	−0.124427	−	0.0291180i
$379$	1.80663	+	2.70381i	0.0928001	+	0.138885i	0.874965	−	0.484187i	$-0.160884\pi$
$379$	1.80663	+	2.70381i	0.0928001	+	0.138885i	−0.782165	+	0.623072i	$0.785884\pi$
$380$	26.5583	−	3.20343i	1.36241	−	0.164333i
$381$	−7.10130	−	4.74494i	−0.363811	−	0.243091i
$382$	−6.70148	+	1.10087i	−0.342877	+	0.0563253i
$383$	−25.2025	+	10.4392i	−1.28779	+	0.533420i	−0.918326	−	0.395826i	$-0.870458\pi$
$383$	−25.2025	+	10.4392i	−1.28779	+	0.533420i	−0.369463	+	0.929245i	$0.620458\pi$
$384$	11.9559	−	16.4871i	0.610122	−	0.841352i
$385$	0.164928	−	0.790854i	0.00840550	−	0.0403057i
$386$	−4.99840	+	1.87666i	−0.254412	+	0.0955196i
$387$	1.55845			0.0792202
$388$	−4.67162	−	35.9322i	−0.237165	−	1.82418i
$389$	−5.83137	−	14.0782i	−0.295662	−	0.713792i	−0.999992	−	0.00391920i	$-0.998752\pi$
$389$	−5.83137	−	14.0782i	−0.295662	−	0.713792i	0.704330	−	0.709873i	$-0.251248\pi$
$390$	−17.0103	+	23.2408i	−0.861351	+	1.17684i
$391$	−5.13624	+	16.4840i	−0.259751	+	0.833631i
$392$	1.85914	+	19.3562i	0.0939008	+	0.977634i
$393$	−6.77693	+	16.3610i	−0.341851	+	0.825302i
$394$	−23.1142	−	10.4954i	−1.16448	−	0.528750i
$395$	−2.08631	+	4.90792i	−0.104973	+	0.246944i
$396$	−0.487022	+	0.0633187i	−0.0244738	+	0.00318188i
$397$	3.04301	−	4.55419i	0.152724	−	0.228568i	−0.747216	−	0.664581i	$-0.768610\pi$
$397$	3.04301	−	4.55419i	0.152724	−	0.228568i	0.899940	+	0.436013i	$0.143610\pi$
$398$	−0.0742042	+	2.21215i	−0.00371952	+	0.110885i
$399$	−3.51809	−	1.45724i	−0.176125	−	0.0729533i
$400$	17.0992	+	10.3738i	0.854961	+	0.518692i
$401$	22.0024	+	14.7015i	1.09875	+	0.734159i	0.966400	−	0.257045i	$-0.0827488\pi$
$401$	22.0024	+	14.7015i	1.09875	+	0.734159i	0.132347	+	0.991203i	$0.457749\pi$
$402$	11.3501	−	10.6133i	0.566090	−	0.529345i
$403$	31.2289	+	6.21181i	1.55562	+	0.309432i
$404$	0.666345	+	1.97344i	0.0331519	+	0.0981824i
$405$	−21.2307	+	4.01932i	−1.05496	+	0.199722i
$406$	−1.68316	+	0.276497i	−0.0835339	+	0.0137223i
$407$	−5.01744	+	5.01744i	−0.248705	+	0.248705i
$408$	−17.5699	+	11.4886i	−0.869840	+	0.568771i
$409$			32.1531i			1.58987i	0.606697	+	0.794933i	$0.292494\pi$
$409$			32.1531i			1.58987i	−0.606697	+	0.794933i	$0.707506\pi$
$410$	6.18763	−	25.3806i	0.305585	−	1.25346i
$411$	−7.61720	+	38.2942i	−0.375729	+	1.88892i
$412$	−23.9680	−	11.8678i	−1.18082	−	0.584685i
$413$	0.769054	−	3.86629i	0.0378427	−	0.190248i
$414$	−0.0477222	+	1.42267i	−0.00234542	+	0.0699206i
$415$	5.37985	+	8.21497i	0.264087	+	0.403257i
$416$	−0.821089	−	28.6090i	−0.0402572	−	1.40267i
$417$	−12.3328	−	29.7739i	−0.603938	−	1.45803i
$418$	8.63723	+	0.289727i	0.422461	+	0.0141710i
$419$	−5.12363	−	25.7582i	−0.250306	−	1.25837i	−0.877526	−	0.479530i	$-0.840807\pi$
$419$	−5.12363	−	25.7582i	−0.250306	−	1.25837i	0.627220	−	0.778842i	$-0.284193\pi$
$420$	−1.39663	−	2.48088i	−0.0681487	−	0.121054i
$421$	1.23168	−	1.23168i	0.0600283	−	0.0600283i	−0.676455	−	0.736484i	$-0.736485\pi$
$421$	1.23168	−	1.23168i	0.0600283	−	0.0600283i	0.736484	+	0.676455i	$0.236485\pi$
$422$	2.54650	+	6.78249i	0.123962	+	0.330166i
$423$	−0.929874	−	0.385166i	−0.0452120	−	0.0187274i
$424$	3.38341	−	4.10242i	0.164313	−	0.199231i
$425$	−12.6592	−	16.2710i	−0.614062	−	0.789258i
$426$	4.85640	−	20.7522i	0.235293	−	1.00545i
$427$	0.347563	−	0.839091i	0.0168198	−	0.0406065i
$428$	−1.47095	−	11.3139i	−0.0711009	−	0.546880i
$429$	−6.57917	+	6.57917i	−0.317645	+	0.317645i
$430$	−13.8645	−	15.1045i	−0.668604	−	0.728403i
$431$	−35.3909	+	7.03969i	−1.70472	+	0.339090i	−0.948873	−	0.315658i	$-0.897775\pi$
$431$	−35.3909	+	7.03969i	−1.70472	+	0.339090i	−0.755847	+	0.654748i	$0.772775\pi$
$432$	13.1496	−	14.8971i	0.632663	−	0.716736i
$433$	1.61138	+	3.89022i	0.0774381	+	0.186952i	0.957858	−	0.287244i	$-0.0927389\pi$
$433$	1.61138	+	3.89022i	0.0774381	+	0.186952i	−0.880419	+	0.474196i	$0.842739\pi$
$434$	−1.83540	+	2.55695i	−0.0881022	+	0.122737i
$435$	−11.4843	+	7.52089i	−0.550630	+	0.360599i
$436$	−10.0816	−	2.71879i	−0.482820	−	0.130206i
$437$	4.88670	−	24.5671i	0.233762	−	1.17520i
$438$	2.41485	−	10.3191i	0.115386	−	0.493065i
$439$	−6.52998	−	1.29889i	−0.311659	−	0.0619928i	0.0367827	−	0.999323i	$-0.488289\pi$
$439$	−6.52998	−	1.29889i	−0.311659	−	0.0619928i	−0.348442	+	0.937330i	$0.613289\pi$
$440$	4.94640	+	4.15693i	0.235811	+	0.198174i
$441$		−	1.65251i		−	0.0786910i
$442$	−9.71558	+	27.8560i	−0.462123	+	1.32497i
$443$	19.8973	+	19.8973i	0.945348	+	0.945348i	0.998582	−	0.0532342i	$-0.0169530\pi$
$443$	19.8973	+	19.8973i	0.945348	+	0.945348i	−0.0532342	+	0.998582i	$0.516953\pi$
$444$	−1.67571	+	24.9497i	−0.0795256	+	1.18406i
$445$	−5.48920	+	1.03919i	−0.260213	+	0.0492625i
$446$	16.4777	−	10.2281i	0.780240	−	0.484312i
$447$	−2.73794	+	13.7645i	−0.129500	+	0.651040i
$448$	2.60857	+	1.09532i	0.123243	+	0.0517491i
$449$	19.1197	+	12.7754i	0.902314	+	0.602907i	0.917831	−	0.396972i	$-0.129939\pi$
$449$	19.1197	+	12.7754i	0.902314	+	0.602907i	−0.0155162	+	0.999880i	$0.504939\pi$
$450$	−1.36220	−	1.01649i	−0.0642145	−	0.0479179i
$451$	3.22970	−	7.79718i	0.152080	−	0.367155i
$452$	−9.15960	+	33.9649i	−0.430831	+	1.59757i
$453$	−19.6588	+	29.4215i	−0.923653	+	1.38234i
$454$	31.9567	−	11.9983i	1.49980	−	0.563106i
$455$	−3.68210	−	1.56522i	−0.172619	−	0.0733787i
$456$	23.5890	−	19.2636i	1.10465	−	0.902103i
$457$	13.4112	−	32.3775i	0.627349	−	1.51455i	−0.215557	−	0.976491i	$-0.569157\pi$
$457$	13.4112	−	32.3775i	0.627349	−	1.51455i	0.842905	−	0.538062i	$-0.180843\pi$
$458$	9.46064	−	5.87243i	0.442067	−	0.274401i
$459$	−18.1357	+	9.51884i	−0.846504	+	0.444302i
$460$	14.2131	−	12.1941i	0.662691	−	0.568552i
$461$	−0.380963	−	0.919727i	−0.0177432	−	0.0428360i	0.914760	−	0.403999i	$-0.132380\pi$
$461$	−0.380963	−	0.919727i	−0.0177432	−	0.0428360i	−0.932503	+	0.361163i	$0.882380\pi$
$462$	−0.323286	−	0.861057i	−0.0150406	−	0.0400600i
$463$			11.2982i			0.525071i	0.964922	+	0.262536i	$0.0845587\pi$
$463$			11.2982i			0.525071i	−0.964922	+	0.262536i	$0.915441\pi$
$464$	4.42674	−	12.9038i	0.205506	−	0.599046i
$465$	−5.17144	+	24.7978i	−0.239820	+	1.14997i
$466$	−16.8685	+	15.7736i	−0.781419	+	0.730696i
$467$	−6.50295	−	15.6995i	−0.300920	−	0.726486i	−0.999935	−	0.0113791i	$-0.996378\pi$
$467$	−6.50295	−	15.6995i	−0.300920	−	0.726486i	0.699015	−	0.715107i	$-0.253622\pi$
$468$	−0.162993	+	2.42681i	−0.00753436	+	0.112179i
$469$	1.79489	+	1.19930i	0.0828801	+	0.0553787i
$470$	4.53944	+	12.4389i	0.209389	+	0.573765i
$471$	−6.76997	+	4.52355i	−0.311944	+	0.208434i
$472$	24.3228	+	20.0599i	1.11955	+	0.923331i
$473$	−3.67991	−	5.50737i	−0.169202	−	0.253229i
$474$	0.984185	+	5.99118i	0.0452051	+	0.275184i
$475$	20.7536	+	21.5359i	0.952241	+	0.988133i
$476$	−2.11016	−	2.01292i	−0.0967192	−	0.0922621i
$477$	−0.319547	+	0.319547i	−0.0146311	+	0.0146311i
$478$	−17.6156	+	24.5407i	−0.805719	+	1.12247i
$479$	3.70087	−	18.6055i	0.169097	−	0.850109i	−0.799345	−	0.600872i	$-0.794820\pi$
$479$	3.70087	−	18.6055i	0.169097	−	0.850109i	0.968443	−	0.249237i	$-0.0801798\pi$
$480$	22.7654	−	0.442724i	1.03909	−	0.0202075i
$481$	19.5236	+	29.2192i	0.890201	+	1.33228i
$482$	−17.0872	−	18.2734i	−0.778302	−	0.832329i
$483$	−2.61459	+	0.520074i	−0.118968	+	0.0236642i
$484$	−13.1052	−	14.9923i	−0.595689	−	0.681467i
$485$	28.9097	−	28.3799i	1.31272	−	1.28866i
$486$	−2.57426	+	2.40717i	−0.116771	+	0.109191i
$487$	8.48568	−	12.6997i	0.384523	−	0.575479i	−0.587833	−	0.808982i	$-0.700019\pi$
$487$	8.48568	−	12.6997i	0.384523	−	0.575479i	0.972356	+	0.233503i	$0.0750189\pi$
$488$	4.59452	+	5.62614i	0.207984	+	0.254684i
$489$	−12.0905	+	12.0905i	−0.546753	+	0.546753i
$490$	−16.0162	+	14.7013i	−0.723537	+	0.664138i
$491$	28.8814	−	11.9631i	1.30340	−	0.539886i	0.380449	−	0.924802i	$-0.375770\pi$
$491$	28.8814	−	11.9631i	1.30340	−	0.539886i	0.922952	+	0.384916i	$0.125770\pi$
$492$	−9.51474	−	28.1788i	−0.428958	−	1.27040i
$493$	−9.00238	+	10.8025i	−0.405447	+	0.486520i
$494$	9.75246	−	41.6740i	0.438784	−	1.87500i
$495$	−0.384658	−	0.391839i	−0.0172891	−	0.0176119i
$496$	−11.0609	−	22.6128i	−0.496647	−	1.01535i
$497$	2.96077			0.132809
$498$	10.1795	+	4.62215i	0.456152	+	0.207124i
$499$	6.89612	−	1.37172i	0.308713	−	0.0614068i	−0.0383027	−	0.999266i	$-0.512195\pi$
$499$	6.89612	−	1.37172i	0.308713	−	0.0614068i	0.347016	+	0.937859i	$0.387195\pi$
$500$	2.26669	+	22.2455i	0.101369	+	0.994849i
$501$	22.6104	+	9.36555i	1.01016	+	0.418422i
$502$	−15.3687	+	2.52465i	−0.685938	+	0.112681i
$503$	−18.0933	+	3.59898i	−0.806741	+	0.160471i	−0.581198	−	0.813762i	$-0.697416\pi$
$503$	−18.0933	+	3.59898i	−0.806741	+	0.160471i	−0.225543	+	0.974233i	$0.572416\pi$
$504$	−0.211768	−	0.113852i	−0.00943292	−	0.00507138i
$505$	−1.31164	+	1.92424i	−0.0583672	+	0.0856277i
$506$	5.14025	−	3.19067i	0.228512	−	0.141843i
$507$	12.5995	+	18.8565i	0.559563	+	0.837445i
$508$	6.24507	+	7.14436i	0.277080	+	0.316980i
$509$		−	0.792404i		−	0.0351227i	−0.999846	−	0.0175613i	$-0.994410\pi$
$509$		−	0.792404i		−	0.0351227i	0.999846	−	0.0175613i	$-0.00559024\pi$
$510$	−22.0888	−	7.93398i	−0.978108	−	0.351323i
$511$	1.47225			0.0651283
$512$	−17.5950	+	14.2273i	−0.777595	+	0.628766i
$513$	24.7068	−	16.5085i	1.09083	−	0.728870i
$514$	19.8900	+	32.0434i	0.877311	+	1.41337i
$515$	−5.56216	−	29.3803i	−0.245098	−	1.29465i
$516$	−22.5371	−	6.07778i	−0.992140	−	0.267559i
$517$	0.834546	+	4.19555i	0.0367033	+	0.184520i
$518$	−3.42785	+	0.563100i	−0.150611	+	0.0247412i
$519$	11.3224	−	27.3347i	0.496999	−	1.19986i
$520$	24.9707	−	20.0100i	1.09504	−	0.877497i
$521$	2.06912	+	10.4022i	0.0906497	+	0.455727i	0.999274	+	0.0381112i	$0.0121341\pi$
$521$	2.06912	+	10.4022i	0.0906497	+	0.455727i	−0.908624	+	0.417616i	$0.862866\pi$
$522$	−0.479319	+	1.05561i	−0.0209792	+	0.0462030i
$523$			20.3746i			0.890921i	0.895302	+	0.445460i	$0.146960\pi$
$523$			20.3746i			0.890921i	−0.895302	+	0.445460i	$0.853040\pi$
$524$	12.0029	−	15.5903i	0.524348	−	0.681066i
$525$	1.27227	−	2.91770i	0.0555265	−	0.127339i
$526$	−5.09496	+	21.7717i	−0.222151	+	0.949290i
$527$	2.34878	+	25.8413i	0.102314	+	1.12566i
$528$	7.28989	+	0.983667i	0.317252	+	0.0428086i
$529$	2.09119	+	5.04859i	0.0909214	+	0.219504i
$530$	5.93987	+	0.254257i	0.258011	+	0.0110442i
$531$	−1.89456	−	1.89456i	−0.0822170	−	0.0822170i
$532$	3.35238	+	2.58097i	0.145344	+	0.111899i
$533$	−34.7531	−	23.2212i	−1.50532	−	1.00582i
$534$	−4.64571	+	4.34415i	−0.201040	+	0.187990i
$535$	9.10276	−	8.93594i	0.393547	−	0.386334i
$536$	−15.2459	+	8.10171i	−0.658520	+	0.349941i
$537$	−5.56407	−	27.9725i	−0.240108	−	1.20710i
$538$	3.45268	−	3.22857i	0.148856	−	0.139193i
$539$	−5.83979	+	3.90202i	−0.251537	+	0.168072i
$540$	22.1512	+	1.69366i	0.953237	+	0.0728835i
$541$	−20.2680	−	4.03156i	−0.871390	−	0.173330i	−0.260911	−	0.965363i	$-0.584023\pi$
$541$	−20.2680	−	4.03156i	−0.871390	−	0.173330i	−0.610479	+	0.792032i	$0.709023\pi$
$542$	−12.6194	+	17.5804i	−0.542051	+	0.755144i
$543$	−28.2352	−	28.2352i	−1.21169	−	1.21169i
$544$	22.1712	−	7.24130i	0.950584	−	0.310468i
$545$	−4.36761	−	10.8264i	−0.187088	−	0.463754i
$546$	−4.49480	+	0.738371i	−0.192360	+	0.0315994i
$547$	29.8328	−	19.9336i	1.27556	−	0.852301i	0.281332	−	0.959610i	$-0.409224\pi$
$547$	29.8328	−	19.9336i	1.27556	−	0.852301i	0.994226	+	0.107310i	$0.0342237\pi$
$548$	19.2493	−	38.8756i	0.822291	−	1.66068i
$549$	−0.342954	−	0.513266i	−0.0146369	−	0.0219057i
$550$	−0.375663	+	7.21405i	−0.0160183	+	0.307608i
$551$	11.3339	−	16.9624i	0.482841	−	0.722622i
$552$	6.23841	−	20.3876i	0.265524	−	0.867752i
$553$	−0.779240	+	0.322772i	−0.0331366	+	0.0137256i
$554$	26.5103	+	28.3505i	1.12631	+	1.20450i
$555$	−23.3884	+	15.3167i	−0.992782	+	0.650157i
$556$	4.61633	+	35.5070i	0.195776	+	1.50583i
$557$	−1.96658			−0.0833268			−0.0416634	−	0.999132i	$-0.513266\pi$
$557$	−1.96658			−0.0833268			−0.0416634	+	0.999132i	$0.513266\pi$
$558$	0.751945	+	2.00277i	0.0318324	+	0.0847840i
$559$	−30.3066	+	12.5534i	−1.28183	+	0.530953i
$560$	0.780507	+	3.06533i	0.0329824	+	0.129534i
$561$	−6.65993	−	3.62456i	−0.281182	−	0.153029i
$562$	−2.34220	−	3.77335i	−0.0987999	−	0.159169i
$563$	23.2279	+	9.62130i	0.978938	+	0.405489i	0.814032	−	0.580820i	$-0.197268\pi$
$563$	23.2279	+	9.62130i	0.978938	+	0.405489i	0.164906	+	0.986309i	$0.447268\pi$
$564$	11.9450	+	9.19641i	0.502977	+	0.387239i
$565$	−36.4743	+	14.7145i	−1.53448	+	0.619042i
$566$	8.65437	−	3.24931i	0.363770	−	0.136579i
$567$	−2.84149	−	1.89862i	−0.119331	−	0.0797347i
$568$	−11.2130	+	20.8565i	−0.470488	+	0.875121i
$569$	−35.4285	−	14.6750i	−1.48524	−	0.615206i	−0.514964	−	0.857212i	$-0.672195\pi$
$569$	−35.4285	−	14.6750i	−1.48524	−	0.615206i	−0.970275	+	0.242005i	$0.922195\pi$
$570$	33.0812	+	8.06498i	1.38562	+	0.337805i
$571$	−0.0543284	+	0.0813082i	−0.00227357	+	0.00340264i	−0.832605	−	0.553868i	$-0.813151\pi$
$571$	−0.0543284	+	0.0813082i	−0.00227357	+	0.00340264i	0.830331	+	0.557270i	$0.188151\pi$
$572$	8.96094	−	5.15435i	0.374676	−	0.215514i
$573$	−8.47830	−	1.68644i	−0.354186	−	0.0704520i
$574$	3.51040	−	2.17899i	0.146521	−	0.0909491i
$575$	20.4563	+	4.46383i	0.853087	+	0.186154i
$576$	1.60402	−	1.06058i	0.0668341	−	0.0441908i
$577$	−6.13086	+	6.13086i	−0.255231	+	0.255231i	−0.823111	−	0.567880i	$-0.807764\pi$
$577$	−6.13086	+	6.13086i	−0.255231	+	0.255231i	0.567880	+	0.823111i	$0.307764\pi$
$578$	−24.0133	−	1.16782i	−0.998820	−	0.0485748i
$579$	−6.79593			−0.282429
$580$	14.4952	−	4.74554i	0.601881	−	0.197048i
$581$	−0.302989	+	1.52323i	−0.0125701	+	0.0631942i
$582$	10.5094	−	44.9085i	0.435628	−	1.86152i
$583$	1.88378	+	0.374707i	0.0780182	+	0.0155188i
$584$	−5.57569	+	10.3709i	−0.230724	+	0.429153i
$585$	−2.27495	+	1.48983i	−0.0940575	+	0.0615967i
$586$	8.99863	+	6.45931i	0.371730	+	0.266832i
$587$	6.59645	−	2.73234i	0.272265	−	0.112776i	−0.242374	−	0.970183i	$-0.577926\pi$
$587$	6.59645	−	2.73234i	0.272265	−	0.112776i	0.514639	+	0.857407i	$0.327926\pi$
$588$	−6.44463	+	23.8974i	−0.265772	+	0.985513i
$589$	−7.34400	−	36.9208i	−0.302604	−	1.52129i
$590$	−1.50746	+	35.2168i	−0.0620612	+	1.44985i
$591$	−22.8482	−	22.8482i	−0.939849	−	0.939849i
$592$	9.01529	−	26.2794i	0.370526	−	1.08008i
$593$	7.30594	+	3.02622i	0.300019	+	0.124272i	0.527615	−	0.849484i	$-0.323087\pi$
$593$	7.30594	+	3.02622i	0.300019	+	0.124272i	−0.227596	+	0.973756i	$0.573087\pi$
$594$	6.98824	+	1.63537i	0.286731	+	0.0671002i
$595$	0.373981	−	3.23897i	0.0153317	−	0.132785i
$596$	6.91901	−	13.9735i	0.283414	−	0.572377i
$597$	−1.07815	+	2.60289i	−0.0441258	+	0.106529i
$598$	−10.5317	−	28.0507i	−0.430674	−	1.14708i
$599$	5.10336	+	5.10336i	0.208518	+	0.208518i	0.803637	−	0.595120i	$-0.202895\pi$
$599$	5.10336	+	5.10336i	0.208518	+	0.208518i	−0.595120	+	0.803637i	$0.702895\pi$
$600$	15.7349	+	20.0122i	0.642373	+	0.816994i
$601$	10.7784	−	2.14397i	0.439662	−	0.0874542i	0.0297041	−	0.999559i	$-0.490543\pi$
$601$	10.7784	−	2.14397i	0.439662	−	0.0874542i	0.409958	+	0.912105i	$0.365543\pi$
$602$	0.108711	−	3.24086i	0.00443074	−	0.132087i
$603$	1.35553	−	0.561478i	0.0552014	−	0.0228651i
$604$	29.5999	−	25.8741i	1.20440	−	1.05280i
$605$	4.54504	−	21.7941i	0.184782	−	0.886058i
$606$	−0.0888836	+	2.64976i	−0.00361065	+	0.107639i
$607$	7.49089	+	1.49003i	0.304046	+	0.0604785i	0.344755	−	0.938693i	$-0.387962\pi$
$607$	7.49089	+	1.49003i	0.304046	+	0.0604785i	−0.0407096	+	0.999171i	$0.512962\pi$
$608$	−30.8773	+	13.8405i	−1.25224	+	0.561307i
$609$	−2.12943	−	0.423570i	−0.0862890	−	0.0171639i
$610$	−1.92356	+	7.89011i	−0.0778825	+	0.319461i
$611$	21.1855			0.857075
$612$	−1.93438	+	0.432423i	−0.0781926	+	0.0174797i
$613$	−1.98632	−	1.98632i	−0.0802268	−	0.0802268i	0.665855	−	0.746081i	$-0.268067\pi$
$613$	−1.98632	−	1.98632i	−0.0802268	−	0.0802268i	−0.746081	+	0.665855i	$0.768067\pi$
$614$	−4.59390	+	0.754650i	−0.185395	+	0.0304552i
$615$	18.7289	−	27.4763i	0.755222	−	1.10795i
$616$	0.0977012	+	1.01720i	0.00393649	+	0.0409842i
$617$	1.29586	−	6.51473i	0.0521694	−	0.262273i	−0.945894	−	0.324475i	$-0.894812\pi$
$617$	1.29586	−	6.51473i	0.0521694	−	0.262273i	0.998064	+	0.0622021i	$0.0198123\pi$
$618$	−23.2516	−	24.8656i	−0.935316	−	1.00024i
$619$	−0.230669	+	0.345220i	−0.00927135	+	0.0138756i	−0.836076	−	0.548613i	$-0.815156\pi$
$619$	−0.230669	+	0.345220i	−0.00927135	+	0.0138756i	0.826805	+	0.562489i	$0.190156\pi$
$620$	12.7213	−	25.1052i	0.510900	−	1.00825i
$621$	7.96061	−	19.2186i	0.319448	−	0.771217i
$622$	1.19138	−	35.5169i	0.0477699	−	1.42410i
$623$	−0.734666	−	0.490888i	−0.0294338	−	0.0196670i
$624$	11.8214	−	34.4591i	0.473234	−	1.37947i
$625$	−18.3193	+	17.0118i	−0.732773	+	0.680473i
$626$	−5.55694	+	12.2382i	−0.222100	+	0.489136i
$627$	10.1629	+	4.20960i	0.405866	+	0.168115i
$628$	8.57094	−	2.89403i	0.342018	−	0.115485i
$629$	−18.3338	+	21.9999i	−0.731017	+	0.877192i
$630$	−0.0411196	−	0.265649i	−0.00163824	−	0.0105837i
$631$	37.8119	−	15.6622i	1.50527	−	0.623502i	0.530692	−	0.847565i	$-0.321932\pi$
$631$	37.8119	−	15.6622i	1.50527	−	0.623502i	0.974575	+	0.224063i	$0.0719321\pi$
$632$	0.677435	−	6.71160i	0.0269469	−	0.266973i
$633$			9.22162i			0.366527i
$634$	−14.4780	−	38.5616i	−0.574997	−	1.53148i
$635$	−2.16587	+	10.3857i	−0.0859500	+	0.412143i
$636$	5.86726	−	3.37486i	0.232652	−	0.133822i
$637$	13.3111	+	32.1359i	0.527406	+	1.27327i
$638$	4.86222	−	0.798728i	0.192497	−	0.0316219i
$639$	1.11801	−	1.67322i	0.0442278	−	0.0661916i
$640$	−24.5491	−	6.11090i	−0.970387	−	0.241555i
$641$	−32.6725	+	21.8311i	−1.29049	+	0.862275i	−0.995641	−	0.0932706i	$-0.970268\pi$
$641$	−32.6725	+	21.8311i	−1.29049	+	0.862275i	−0.294844	+	0.955545i	$0.595268\pi$
$642$	3.30908	−	14.1403i	0.130599	−	0.558073i
$643$	−6.19256	+	4.13774i	−0.244211	+	0.163176i	−0.671652	−	0.740867i	$-0.734415\pi$
$643$	−6.19256	+	4.13774i	−0.244211	+	0.163176i	0.427441	+	0.904043i	$0.359415\pi$
$644$	2.95518	+	0.198481i	0.116451	+	0.00782123i
$645$	−9.76366	−	24.2022i	−0.384444	−	0.952960i
$646$	34.8219	−	1.99092i	1.37005	−	0.0783315i
$647$	−35.2785	−	35.2785i	−1.38694	−	1.38694i	−0.831670	−	0.555271i	$-0.812615\pi$
$647$	−35.2785	−	35.2785i	−1.38694	−	1.38694i	−0.555271	−	0.831670i	$-0.687385\pi$
$648$	24.1358	−	12.8259i	0.948143	−	0.503848i
$649$	−2.22160	+	11.1687i	−0.0872053	+	0.438411i
$650$	34.6781	+	8.79483i	1.36019	+	0.344962i
$651$	−3.33114	+	2.22580i	−0.130558	+	0.0872358i
$652$	16.4675	−	9.47213i	0.644917	−	0.370957i
$653$	−36.7982	+	7.31962i	−1.44003	+	0.286439i	−0.852483	−	0.522754i	$-0.824905\pi$
$653$	−36.7982	+	7.31962i	−1.44003	+	0.286439i	−0.587543	+	0.809193i	$0.699905\pi$
$654$	−10.7972	−	7.75038i	−0.422206	−	0.303064i
$655$	21.9970	+	0.203427i	0.859493	+	0.00794854i
$656$	2.05483	+	32.9806i	0.0802278	+	1.28768i
$657$	0.555932	−	0.832011i	0.0216890	−	0.0324599i
$658$	−0.865835	+	1.90685i	−0.0337538	+	0.0743366i
$659$	−23.2005	−	23.2005i	−0.903762	−	0.903762i	0.0919975	−	0.995759i	$-0.470675\pi$
$659$	−23.2005	−	23.2005i	−0.903762	−	0.903762i	−0.995759	+	0.0919975i	$0.970675\pi$
$660$	4.03451	+	7.16662i	0.157043	+	0.278960i
$661$	−34.8891	+	14.4515i	−1.35703	+	0.562100i	−0.938240	−	0.345984i	$-0.887545\pi$
$661$	−34.8891	+	14.4515i	−1.35703	+	0.562100i	−0.418789	+	0.908084i	$0.637545\pi$
$662$	1.47666	+	2.37894i	0.0573921	+	0.0924602i
$663$	−24.0404	+	28.8475i	−0.933653	+	1.12035i
$664$	−9.58261	−	7.90312i	−0.371877	−	0.306701i
$665$	−0.0437428	+	4.73000i	−0.00169627	+	0.183422i
$666$	−0.976158	+	2.14981i	−0.0378254	+	0.0833036i
$667$		−	14.2816i		−	0.552987i
$668$	−21.5454	−	16.5877i	−0.833617	−	0.641796i
$669$	24.2116	−	4.81598i	0.936074	−	0.186197i
$670$	−17.5011	−	8.14271i	−0.676126	−	0.314580i
$671$	−1.00402	+	2.42392i	−0.0387598	+	0.0935743i
$672$	2.61843	+	2.47232i	0.101008	+	0.0953719i
$673$	2.09188	−	0.416101i	0.0806360	−	0.0160395i	−0.154607	−	0.987976i	$-0.549411\pi$
$673$	2.09188	−	0.416101i	0.0806360	−	0.0160395i	0.235243	+	0.971936i	$0.424411\pi$
$674$	−9.01918	−	0.302539i	−0.347406	−	0.0116534i
$675$	13.4150	+	20.9038i	0.516344	+	0.804588i
$676$	−8.06078	−	23.8727i	−0.310030	−	0.918182i
$677$	−9.04907	−	13.5429i	−0.347784	−	0.520496i	0.615799	−	0.787903i	$-0.288833\pi$
$677$	−9.04907	−	13.5429i	−0.347784	−	0.520496i	−0.963584	+	0.267407i	$0.913833\pi$
$678$	−26.1110	+	36.3759i	−1.00279	+	1.39701i
$679$	6.40719			0.245885
$680$	21.4000	+	14.9011i	0.820651	+	0.571430i
$681$	43.4491			1.66497
$682$	5.30201	−	7.38636i	0.203025	−	0.282838i
$683$	−9.84426	−	14.7330i	−0.376680	−	0.563741i	0.593894	−	0.804543i	$-0.297590\pi$
$683$	−9.84426	−	14.7330i	−0.376680	−	0.563741i	−0.970574	+	0.240802i	$0.922590\pi$
$684$	2.72447	−	0.919936i	0.104173	−	0.0351746i
$685$	47.6542	−	9.02171i	1.82077	−	0.344702i
$686$	−6.93546	−	0.232643i	−0.264797	−	0.00888235i
$687$	13.9011	−	2.76509i	0.530358	−	0.105495i
$688$	22.4179	+	13.0396i	0.854673	+	0.497129i
$689$	3.64016	−	8.78813i	0.138679	−	0.334801i
$690$	22.3927	−	8.17194i	0.852475	−	0.311100i
$691$	−48.9321	+	9.73319i	−1.86146	+	0.370268i	−0.992259	−	0.124185i	$-0.960368\pi$
$691$	−48.9321	+	9.73319i	−1.86146	+	0.370268i	−0.869204	+	0.494453i	$0.835368\pi$
$692$	−20.0535	+	26.0472i	−0.762321	+	0.990164i
$693$		−	0.0868424i		−	0.00329887i
$694$	−2.27233	+	5.00441i	−0.0862566	+	0.189965i
$695$	−28.5675	+	28.0440i	−1.08363	+	1.06377i
$696$	11.0483	−	13.3962i	0.418786	−	0.507783i
$697$	10.1327	−	32.5195i	0.383805	−	1.23176i
$698$	10.3356	+	16.6510i	0.391210	+	0.630250i
$699$	−27.1584	+	11.2494i	−1.02723	+	0.425491i
$700$	−2.20886	+	2.76184i	−0.0834872	+	0.104388i
$701$	−10.0358	−	10.0358i	−0.379046	−	0.379046i	0.491712	−	0.870758i	$-0.336371\pi$
$701$	−10.0358	−	10.0358i	−0.379046	−	0.379046i	−0.870758	+	0.491712i	$0.836371\pi$
$702$	14.6955	−	32.3642i	0.554646	−	1.22151i
$703$	23.0821	−	34.5448i	0.870558	−	1.30288i
$704$	−7.53548	−	3.16411i	−0.284004	−	0.119252i
$705$	−0.155862	+	16.8537i	−0.00587012	+	0.634748i
$706$	4.91735	+	3.52973i	0.185067	+	0.132843i
$707$	−0.361232	+	0.0718536i	−0.0135855	+	0.00270233i
$708$	20.0092	+	34.7864i	0.751991	+	1.30735i
$709$	−11.3757	+	7.60103i	−0.427225	+	0.285463i	−0.750535	−	0.660830i	$-0.770204\pi$
$709$	−11.3757	+	7.60103i	−0.427225	+	0.285463i	0.323310	+	0.946293i	$0.395204\pi$
$710$	−26.1631	+	4.04977i	−0.981884	+	0.151985i
$711$	−0.111839	+	0.562254i	−0.00419430	+	0.0210862i
$712$	6.24029	−	3.31612i	0.233865	−	0.124277i
$713$	−18.6346	−	18.6346i	−0.697870	−	0.697870i
$714$	−1.61397	−	3.34278i	−0.0604013	−	0.125100i
$715$	10.6366	+	4.52152i	0.397787	+	0.169095i
$716$	−2.12347	+	31.6164i	−0.0793578	+	1.18156i
$717$	−31.9712	+	21.3624i	−1.19398	+	0.797795i
$718$	10.8453	−	46.3440i	0.404744	−	1.72954i
$719$	26.5486	−	17.7392i	0.990097	−	0.661562i	0.0486830	−	0.998814i	$-0.484498\pi$
$719$	26.5486	−	17.7392i	0.990097	−	0.661562i	0.941414	+	0.337252i	$0.109498\pi$
$720$	2.02704	+	0.716407i	0.0755433	+	0.0266989i
$721$	2.62742	−	3.93222i	0.0978503	−	0.146443i
$722$	−23.4169	+	3.84675i	−0.871488	+	0.143161i
$723$	−12.1863	−	29.4203i	−0.453212	−	1.09415i
$724$	22.1204	+	38.4568i	0.822099	+	1.42924i
$725$	14.0010	+	9.73449i	0.519986	+	0.361530i
$726$	−8.90903	−	23.7288i	−0.330645	−	0.880657i
$727$			33.7644i			1.25225i	0.779722	+	0.626125i	$0.215360\pi$
$727$			33.7644i			1.25225i	−0.779722	+	0.626125i	$0.784640\pi$
$728$	5.03529	+	0.508236i	0.186620	+	0.0188365i
$729$	22.6387	−	9.37724i	0.838469	−	0.347305i
$730$	−13.0096	+	2.01375i	−0.481508	+	0.0745323i
$731$	−16.8028	−	20.7916i	−0.621475	−	0.769007i
$732$	2.95786	+	8.75997i	0.109326	+	0.323778i
$733$	−40.1465	−	16.6292i	−1.48285	−	0.614215i	−0.513099	−	0.858329i	$-0.671503\pi$
$733$	−40.1465	−	16.6292i	−1.48285	−	0.614215i	−0.969746	+	0.244115i	$0.921503\pi$
$734$	−11.8928	+	26.1918i	−0.438972	+	0.966757i
$735$	−25.6630	+	10.3530i	−0.946595	+	0.381876i
$736$	−12.5900	+	20.0655i	−0.464075	+	0.739625i
$737$	−5.18496	−	3.46448i	−0.190991	−	0.127616i
$738$	0.0941459	−	2.80664i	0.00346556	−	0.103314i
$739$	15.4365	−	37.2670i	0.567840	−	1.37089i	−0.335531	−	0.942029i	$-0.608916\pi$
$739$	15.4365	−	37.2670i	0.567840	−	1.37089i	0.903372	−	0.428859i	$-0.141084\pi$
$740$	29.5203	−	9.66453i	1.08519	−	0.355275i
$741$	30.2666	−	45.2972i	1.11187	−	1.66404i
$742$	0.642223	+	0.686803i	0.0235767	+	0.0252133i
$743$	0.299221	−	1.50429i	0.0109774	−	0.0551869i	−0.974908	−	0.222607i	$-0.928543\pi$
$743$	0.299221	−	1.50429i	0.0109774	−	0.0551869i	0.985886	+	0.167420i	$0.0535435\pi$
$744$	−3.06349	−	31.8951i	−0.112313	−	1.16933i
$745$	17.1289	−	3.24277i	0.627554	−	0.118806i
$746$	−39.2982	+	6.45561i	−1.43881	+	0.236357i
$747$	0.746413	+	0.746413i	0.0273098	+	0.0273098i
$748$	6.09572	+	5.81481i	0.222882	+	0.212610i
$749$	2.01742			0.0737151
$750$	−7.25168	+	27.5228i	−0.264794	+	1.00499i
$751$	−10.5220	−	2.09295i	−0.383953	−	0.0763729i	−0.000659731	−	1.00000i	$-0.500210\pi$
$751$	−10.5220	−	2.09295i	−0.383953	−	0.0763729i	−0.383293	+	0.923627i	$0.625210\pi$
$752$	−10.1533	−	13.3208i	−0.370253	−	0.485760i
$753$	−19.4435	−	3.86756i	−0.708561	−	0.140942i
$754$	0.818110	−	24.3892i	0.0297938	−	0.888201i
$755$	43.0291	+	8.97347i	1.56599	+	0.326578i
$756$	2.31241	+	2.64539i	0.0841016	+	0.0962121i
$757$	−36.0970	+	14.9519i	−1.31197	+	0.543436i	−0.925458	−	0.378849i	$-0.876320\pi$
$757$	−36.0970	+	14.9519i	−1.31197	+	0.543436i	−0.386511	+	0.922285i	$0.626320\pi$
$758$	0.154175	−	4.59621i	0.00559990	−	0.166942i
$759$	7.55287	−	1.50236i	0.274152	−	0.0545322i
$760$	−33.1539	−	18.2216i	−1.20262	−	0.660967i
$761$	−2.66407	−	2.66407i	−0.0965724	−	0.0965724i	0.657170	−	0.753742i	$-0.271753\pi$
$761$	−2.66407	−	2.66407i	−0.0965724	−	0.0965724i	−0.753742	+	0.657170i	$0.771753\pi$
$762$	4.24547	+	11.3076i	0.153797	+	0.409631i
$763$	0.706572	−	1.70582i	0.0255796	−	0.0617547i
$764$	8.60701	+	4.26178i	0.311391	+	0.154186i
$765$	−1.68922	−	1.43441i	−0.0610741	−	0.0518612i
$766$	37.5635	+	8.79052i	1.35722	+	0.317615i
$767$	52.1038	+	21.5821i	1.88136	+	0.779285i
$768$	−27.3323	+	9.08183i	−0.986269	+	0.327712i
$769$	−8.99709	−	8.99709i	−0.324443	−	0.324443i	0.526026	−	0.850469i	$-0.323682\pi$
$769$	−8.99709	−	8.99709i	−0.324443	−	0.324443i	−0.850469	+	0.526026i	$0.823682\pi$
$770$	−0.841679	+	0.772580i	−0.0303320	+	0.0278419i
$771$	9.36542	+	47.0831i	0.337287	+	1.69566i
$772$	7.29016	+	1.96600i	0.262379	+	0.0707579i
$773$	38.2375	−	15.8385i	1.37531	−	0.569671i	0.432086	−	0.901833i	$-0.357778\pi$
$773$	38.2375	−	15.8385i	1.37531	−	0.569671i	0.943223	+	0.332161i	$0.107778\pi$
$774$	−1.79046	−	1.28521i	−0.0643567	−	0.0461959i
$775$	30.9699	−	5.56696i	1.11247	−	0.199971i
$776$	−24.2653	+	45.1342i	−0.871073	+	1.62022i
$777$	−4.33670	−	0.862624i	−0.155578	−	0.0309464i
$778$	−4.91040	+	20.9830i	−0.176047	+	0.752278i
$779$	−9.64044	+	48.4658i	−0.345405	+	1.73647i
$780$	38.7088	−	12.6727i	1.38600	−	0.453756i
$781$	−8.55289			−0.306047
$782$	19.4948	−	14.7023i	0.697133	−	0.525753i
$783$	11.9799	−	11.9799i	0.428126	−	0.428126i
$784$	13.8266	−	23.7710i	0.493808	−	0.848964i
$785$	8.35727	+	5.69664i	0.298284	+	0.203322i
$786$	21.2783	−	13.2079i	0.758972	−	0.471111i
$787$	−29.4996	−	5.86784i	−1.05155	−	0.209166i	−0.361085	−	0.932533i	$-0.617594\pi$
$787$	−29.4996	−	5.86784i	−1.05155	−	0.209166i	−0.690464	+	0.723367i	$0.742594\pi$
$788$	17.9000	+	31.1196i	0.637662	+	1.10859i
$789$	−15.8121	+	23.6645i	−0.562927	+	0.842480i
$790$	6.44434	−	3.91806i	0.229279	−	0.139398i
$791$	−5.74690	−	2.38044i	−0.204336	−	0.0846388i
$792$	0.611744	+	0.328890i	0.0217374	+	0.0116866i
$793$	10.8037	+	7.21882i	0.383652	+	0.256348i
$794$	−7.25176	+	2.72270i	−0.257355	+	0.0966249i
$795$	6.96444	+	2.96051i	0.247003	+	0.104999i
$796$	1.90955	−	2.48028i	0.0676823	−	0.0879113i
$797$	−6.62238	−	2.74308i	−0.234577	−	0.0971649i	0.262299	−	0.964987i	$-0.415519\pi$
$797$	−6.62238	−	2.74308i	−0.234577	−	0.0971649i	−0.496876	+	0.867822i	$0.665519\pi$
$798$	2.84010	+	4.57547i	0.100538	+	0.161970i
$799$	4.88709	+	16.5585i	0.172893	+	0.585797i
$800$	−11.0898	−	26.0195i	−0.392084	−	0.919929i
$801$	−0.554832	+	0.229819i	−0.0196040	+	0.00812026i
$802$	−13.1540	−	35.0350i	−0.464484	−	1.23713i
$803$	−4.25294			−0.150083
$804$	−21.7924	+	2.83327i	−0.768557	+	0.0999216i
$805$	1.81420	+	2.77026i	0.0639420	+	0.0976387i
$806$	−30.7553	−	32.8903i	−1.08331	−	1.15851i
$807$	5.55885	−	2.30255i	0.195681	−	0.0810536i
$808$	0.861901	−	2.81675i	0.0303216	−	0.0990931i
$809$	−4.06234	+	6.07972i	−0.142824	+	0.213752i	−0.895984	−	0.444086i	$-0.853529\pi$
$809$	−4.06234	+	6.07972i	−0.142824	+	0.213752i	0.753160	+	0.657837i	$0.228529\pi$
$810$	27.7061	+	12.8908i	0.973493	+	0.452935i
$811$	4.28040	+	6.40607i	0.150305	+	0.224947i	0.898980	−	0.437990i	$-0.144310\pi$
$811$	4.28040	+	6.40607i	0.150305	+	0.224947i	−0.748675	+	0.662937i	$0.769310\pi$
$812$	2.16176	+	1.07040i	0.0758629	+	0.0375637i
$813$	−22.9034	+	15.3036i	−0.803259	+	0.536720i
$814$	9.90216	−	1.62665i	0.347071	−	0.0570141i
$815$	19.5469	+	8.30920i	0.684699	+	0.291058i
$816$	29.6600	+	1.29049i	1.03831	+	0.0451763i
$817$	27.4234	+	27.4234i	0.959424	+	0.959424i
$818$	26.5158	−	36.9398i	0.927104	−	1.29157i
$819$	−0.421823	−	0.0839058i	−0.0147397	−	0.00293191i
$820$	−28.0396	+	24.0564i	−0.979185	+	0.840085i
$821$	−31.6365	+	21.1388i	−1.10412	+	0.737749i	−0.967499	−	0.252874i	$-0.918624\pi$
$821$	−31.6365	+	21.1388i	−1.10412	+	0.737749i	−0.136621	+	0.990623i	$0.543624\pi$
$822$	40.3315	−	37.7136i	1.40672	−	1.31541i
$823$	2.85905	+	14.3734i	0.0996602	+	0.501026i	0.998083	+	0.0618938i	$0.0197140\pi$
$823$	2.85905	+	14.3734i	0.0996602	+	0.501026i	−0.898422	+	0.439132i	$0.855286\pi$
$824$	17.7491	+	33.4004i	0.618321	+	1.16356i
$825$	−3.67526	+	8.42850i	−0.127956	+	0.293443i
$826$	−4.07198	+	3.80767i	−0.141682	+	0.132486i
$827$	41.8950	+	27.9933i	1.45683	+	0.973423i	0.996315	+	0.0857715i	$0.0273355\pi$
$827$	41.8950	+	27.9933i	1.45683	+	0.973423i	0.460516	+	0.887652i	$0.347665\pi$
$828$	1.22807	−	1.59512i	0.0426784	−	0.0554342i
$829$	14.6798	+	14.6798i	0.509850	+	0.509850i	0.914480	−	0.404630i	$-0.132600\pi$
$829$	14.6798	+	14.6798i	0.509850	+	0.509850i	−0.404630	+	0.914480i	$0.632600\pi$
$830$	0.593905	−	13.8746i	0.0206147	−	0.481594i
$831$	18.9066	+	45.6445i	0.655862	+	1.58339i
$832$	−22.6498	+	33.5453i	−0.785241	+	1.16297i
$833$	−22.0466	+	17.8170i	−0.763870	+	0.617323i
$834$	−10.3850	+	44.3770i	−0.359603	+	1.53665i
$835$	0.281131	−	30.3993i	0.00972893	−	1.05201i
$836$	−9.68416	−	7.45576i	−0.334934	−	0.257863i
$837$		−	31.2625i		−	1.08059i
$838$	−15.3558	+	33.8183i	−0.530456	+	1.16823i
$839$	0.393631	+	1.97892i	0.0135897	+	0.0683198i	0.986985	−	0.160812i	$-0.0514113\pi$
$839$	0.393631	+	1.97892i	0.0135897	+	0.0683198i	−0.973395	+	0.229132i	$0.926411\pi$
$840$	−0.441362	+	4.00198i	−0.0152284	+	0.138082i
$841$	−6.64661	+	16.0463i	−0.229193	+	0.553322i
$842$	−2.43078	+	0.399309i	−0.0837701	+	0.0137611i
$843$	−1.10285	−	5.54440i	−0.0379842	−	0.190959i
$844$	2.66773	−	9.89226i	0.0918272	−	0.340506i
$845$	15.8669	−	23.2776i	0.545838	−	0.800773i
$846$	0.750671	+	1.20935i	0.0258086	+	0.0415783i
$847$	2.92765	−	1.95619i	0.100595	−	0.0672156i
$848$	−7.27028	+	1.92295i	−0.249662	+	0.0660343i
$849$	11.7667			0.403831
$850$	1.12558	+	29.1330i	0.0386071	+	0.999254i
$851$		−	29.0853i		−	0.997031i
$852$	−22.6932	+	19.8368i	−0.777458	+	0.679597i
$853$	26.4163	+	39.5349i	0.904478	+	1.35365i	0.935200	+	0.354120i	$0.115219\pi$
$853$	26.4163	+	39.5349i	0.904478	+	1.35365i	−0.0307218	+	0.999528i	$0.509781\pi$
$854$	−1.09128	+	0.677384i	−0.0373429	+	0.0231796i
$855$	2.65655	+	1.81081i	0.0908522	+	0.0619284i
$856$	−7.64039	+	14.2113i	−0.261143	+	0.485734i
$857$	−31.6360	+	6.29279i	−1.08066	+	0.214958i	−0.703147	−	0.711045i	$-0.748222\pi$
$857$	−31.6360	+	6.29279i	−1.08066	+	0.214958i	−0.377518	+	0.926002i	$0.623222\pi$
$858$	12.9843	−	2.13296i	0.443277	−	0.0728182i
$859$	15.7116	+	6.50797i	0.536074	+	0.222049i	0.634261	−	0.773119i	$-0.281304\pi$
$859$	15.7116	+	6.50797i	0.536074	+	0.222049i	−0.0981874	+	0.995168i	$0.531304\pi$
$860$	3.47224	+	28.7868i	0.118402	+	0.981623i
$861$	5.15804	−	1.02600i	0.175785	−	0.0349659i
$862$	46.4651	+	21.0983i	1.58261	+	0.718610i
$863$	−47.6025			−1.62041			−0.810204	−	0.586149i	$-0.800643\pi$
$863$	−47.6025			−1.62041			−0.810204	+	0.586149i	$0.800643\pi$
$864$	−27.3925	+	6.27069i	−0.931913	+	0.213333i
$865$	−36.7510	−	0.339871i	−1.24957	−	0.0115560i
$866$	1.35689	−	5.79824i	0.0461090	−	0.197032i
$867$	−28.0927	−	12.1353i	−0.954079	−	0.412136i
$868$	4.21730	−	1.42400i	0.143144	−	0.0483336i
$869$	2.25102	−	0.932404i	0.0763607	−	0.0316296i
$870$	19.3963	+	0.830263i	0.657596	+	0.0281485i
$871$	−21.8378	+	21.8378i	−0.739945	+	0.739945i
$872$	9.34036	+	11.4376i	0.316304	+	0.387325i
$873$	2.41941	−	3.62090i	0.0818845	−	0.122549i
$874$	−25.8741	+	24.1946i	−0.875203	+	0.818393i
$875$	−3.95240	−	0.109680i	−0.133616	−	0.00370786i
$876$	−11.2842	+	9.86386i	−0.381259	+	0.333269i
$877$	−44.2026	+	8.79244i	−1.49262	+	0.296900i	−0.872889	−	0.487918i	$-0.837756\pi$
$877$	−44.2026	+	8.79244i	−1.49262	+	0.296900i	−0.619726	+	0.784818i	$0.712756\pi$
$878$	6.43096	+	6.87737i	0.217034	+	0.232100i
$879$	7.83321	+	11.7232i	0.264208	+	0.395415i
$880$	−2.25468	−	8.85496i	−0.0760054	−	0.298501i
$881$	0.880215	−	4.42514i	0.0296552	−	0.149087i	−0.963121	−	0.269069i	$-0.913284\pi$
$881$	0.880215	−	4.42514i	0.0296552	−	0.149087i	0.992776	+	0.119983i	$0.0382839\pi$
$882$	−1.36278	+	1.89853i	−0.0458873	+	0.0639268i
$883$	25.1294	−	25.1294i	0.845673	−	0.845673i	−0.143917	−	0.989590i	$-0.545970\pi$
$883$	25.1294	−	25.1294i	0.845673	−	0.845673i	0.989590	+	0.143917i	$0.0459699\pi$
$884$	34.1341	−	23.9908i	1.14805	−	0.806898i
$885$	−17.5526	+	41.2914i	−0.590023	+	1.38800i
$886$	−6.45068	−	39.2682i	−0.216715	−	1.31924i
$887$	21.1106	+	31.5943i	0.708826	+	1.06083i	0.994725	+	0.102573i	$0.0327076\pi$
$887$	21.1106	+	31.5943i	0.708826	+	1.06083i	−0.285900	+	0.958260i	$0.592292\pi$
$888$	22.5005	−	27.2821i	0.755069	−	0.915528i
$889$	−1.39513	+	0.932195i	−0.0467911	+	0.0312648i
$890$	7.16339	+	3.33290i	0.240117	+	0.111719i
$891$	8.20834	+	5.48464i	0.274990	+	0.183742i
$892$	−27.3656	−	1.83797i	−0.916267	−	0.0615398i
$893$	−9.58503	−	23.1403i	−0.320751	−	0.774361i
$894$	14.4968	−	13.5558i	0.484846	−	0.453374i
$895$	−29.6380	+	19.4094i	−0.990688	+	0.648785i
$896$	−2.09363	−	3.40961i	−0.0699434	−	0.113907i
$897$		−	38.1384i		−	1.27340i
$898$	−11.4306	−	30.4448i	−0.381444	−	1.01596i
$899$	−8.21362	−	19.8294i	−0.273940	−	0.661349i
$900$	0.726715	+	2.29119i	0.0242238	+	0.0763730i
$901$	7.70846	+	0.817880i	0.256806	+	0.0272475i
$902$	−10.1407	+	6.29453i	−0.337647	+	0.209585i
$903$	1.57952	−	3.81330i	0.0525632	−	0.126899i
$904$	38.5332	−	31.4677i	1.28160	−	1.04660i
$905$	−19.4046	+	45.6482i	−0.645030	+	1.51740i
$906$	46.8487	−	17.5895i	1.55645	−	0.584372i
$907$	−11.9601	+	17.8995i	−0.397128	+	0.594344i	−0.975114	−	0.221703i	$-0.928839\pi$
$907$	−11.9601	+	17.8995i	−0.397128	+	0.594344i	0.577987	+	0.816046i	$0.303839\pi$
$908$	−46.6089	−	12.5694i	−1.54677	−	0.417131i
$909$	−0.0957977	+	0.231276i	−0.00317741	+	0.00767094i
$910$	2.93947	+	4.83478i	0.0974424	+	0.160271i
$911$	−20.3249	−	13.5807i	−0.673395	−	0.449948i	0.171284	−	0.985222i	$-0.445209\pi$
$911$	−20.3249	−	13.5807i	−0.673395	−	0.449948i	−0.844679	+	0.535273i	$0.820209\pi$
$912$	−42.9870	+	2.67828i	−1.42344	+	0.0886866i
$913$	0.875258	−	4.40022i	0.0289668	−	0.145626i
$914$	−42.1086	+	26.1378i	−1.39283	+	0.864560i
$915$	−5.82227	+	8.54158i	−0.192478	+	0.282376i
$916$	−15.7119	−	1.05527i	−0.519137	−	0.0348670i
$917$	2.46011	+	2.46011i	0.0812401	+	0.0812401i
$918$	28.6856	+	4.02013i	0.946767	+	0.132684i
$919$			15.3418i			0.506078i	0.967456	+	0.253039i	$0.0814301\pi$
$919$			15.3418i			0.506078i	−0.967456	+	0.253039i	$0.918570\pi$
$920$	−26.3853	+	2.28824i	−0.869896	+	0.0754410i
$921$	−5.81192	−	1.15606i	−0.191509	−	0.0380936i
$922$	−0.320797	+	1.37082i	−0.0105649	+	0.0451456i
$923$	−8.26368	+	41.5443i	−0.272002	+	1.36745i
$924$	−0.338676	+	1.25585i	−0.0111416	+	0.0413145i
$925$	28.5139	+	19.8248i	0.937530	+	0.651836i
$926$	9.31732	−	12.9802i	0.306186	−	0.426555i
$927$	−1.23008	−	2.96968i	−0.0404011	−	0.0975369i
$928$	−15.7272	+	11.1743i	−0.516272	+	0.366813i
$929$	−8.78351	+	1.74715i	−0.288178	+	0.0573221i	−0.337062	−	0.941482i	$-0.609433\pi$
$929$	−8.78351	+	1.74715i	−0.288178	+	0.0573221i	0.0488847	+	0.998804i	$0.484433\pi$
$930$	26.3915	−	24.2248i	0.865410	−	0.794363i
$931$	29.0787	−	29.0787i	0.953015	−	0.953015i
$932$	32.3879	−	4.21081i	1.06090	−	0.137930i
$933$	17.3102	−	41.7904i	0.566709	−	1.36816i
$934$	−5.47591	+	23.3996i	−0.179177	+	0.765657i
$935$	−1.08033	+	9.35655i	−0.0353307	+	0.305992i
$936$	2.18859	−	2.65368i	0.0715362	−	0.0867383i
$937$	−15.0910	−	6.25091i	−0.493003	−	0.204208i	0.122309	−	0.992492i	$-0.460970\pi$
$937$	−15.0910	−	6.25091i	−0.493003	−	0.204208i	−0.615312	+	0.788284i	$0.710970\pi$
$938$	−1.07306	−	2.85805i	−0.0350367	−	0.0933185i
$939$	−12.0973	+	12.0973i	−0.394781	+	0.394781i
$940$	5.04283	−	18.0343i	0.164479	−	0.588215i
$941$	−4.69614	−	23.6091i	−0.153090	−	0.769634i	−0.978684	−	0.205370i	$-0.934160\pi$
$941$	−4.69614	−	23.6091i	−0.153090	−	0.769634i	0.825595	−	0.564264i	$-0.190840\pi$
$942$	11.5083	+	0.386034i	0.374961	+	0.0125777i
$943$	13.2385	+	31.9605i	0.431104	+	1.04078i
$944$	−11.4009	−	43.1047i	−0.371069	−	1.40294i
$945$	−0.801974	+	3.84559i	−0.0260882	+	0.125097i
$946$	−0.314039	+	9.36200i	−0.0102103	+	0.304385i
$947$	1.22674	−	6.16723i	0.0398637	−	0.200408i	−0.955721	−	0.294274i	$-0.904922\pi$
$947$	1.22674	−	6.16723i	0.0398637	−	0.200408i	0.995585	+	0.0938654i	$0.0299223\pi$
$948$	3.81007	−	7.69474i	0.123745	−	0.249914i
$949$	−4.10912	+	20.6580i	−0.133388	+	0.670586i
$950$	−6.08321	−	41.8570i	−0.197365	−	1.35802i
$951$		−	52.4292i		−	1.70013i
$952$	0.764308	+	4.05279i	0.0247714	+	0.131352i
$953$	−6.74183	+	6.74183i	−0.218389	+	0.218389i	−0.807819	−	0.589430i	$-0.799352\pi$
$953$	−6.74183	+	6.74183i	−0.218389	+	0.218389i	0.589430	+	0.807819i	$0.299352\pi$
$954$	0.630643	−	0.103597i	0.0204178	−	0.00335408i
$955$	1.99740	+	10.5506i	0.0646342	+	0.341409i
$956$	40.4762	−	13.6671i	1.30909	−	0.442024i
$957$	6.15138	+	1.22359i	0.198846	+	0.0395529i
$958$	−19.5953	+	18.3234i	−0.633097	+	0.592002i
$959$	6.37797	+	4.26162i	0.205955	+	0.137615i
$960$	−26.5197	−	18.2654i	−0.855919	−	0.589513i
$961$	−7.95010	−	3.29304i	−0.256455	−	0.106227i
$962$	1.66612	−	49.6698i	0.0537180	−	1.60142i
$963$	0.761796	−	1.14011i	0.0245485	−	0.0367395i
$964$	4.56150	+	35.0852i	0.146916	+	1.13002i
$965$	3.15829	+	7.82878i	0.101669	+	0.252017i
$966$	3.43272	+	1.55868i	0.110446	+	0.0501498i
$967$	7.44070	−	17.9634i	0.239277	−	0.577665i	−0.757932	−	0.652334i	$-0.773790\pi$
$967$	7.44070	−	17.9634i	0.239277	−	0.577665i	0.997208	+	0.0746689i	$0.0237900\pi$
$968$	2.69242	+	28.0317i	0.0865377	+	0.900974i
$969$	42.3860	+	13.2070i	1.36163	+	0.424271i
$970$	−56.6177	+	8.76381i	−1.81789	+	0.281389i
$971$	0.725965	+	1.75263i	0.0232973	+	0.0562447i	0.935100	−	0.354384i	$-0.115309\pi$
$971$	0.725965	+	1.75263i	0.0232973	+	0.0562447i	−0.911803	+	0.410628i	$0.865309\pi$
$972$	4.94263	−	0.642601i	0.158535	−	0.0206114i
$973$	−6.33136			−0.202974
$974$	−20.2221	+	7.59245i	−0.647958	+	0.243278i
$975$	37.3891	+	25.9955i	1.19741	+	0.832522i
$976$	−0.638789	−	10.2527i	−0.0204471	−	0.328182i
$977$	−0.834852	+	0.345807i	−0.0267093	+	0.0110633i	−0.395998	−	0.918251i	$-0.629601\pi$
$977$	−0.834852	+	0.345807i	−0.0267093	+	0.0110633i	0.369289	+	0.929315i	$0.379601\pi$
$978$	23.8613	−	3.91974i	0.762999	−	0.125340i
$979$	2.12226	+	1.41805i	0.0678278	+	0.0453211i
$980$	30.5244	−	3.68182i	0.975066	−	0.117611i
$981$	−0.697202	−	1.04344i	−0.0222599	−	0.0333144i
$982$	−43.0468	−	10.0737i	−1.37368	−	0.321465i
$983$	−6.99373	−	10.4669i	−0.223065	−	0.333841i	0.703010	−	0.711180i	$-0.251839\pi$
$983$	−6.99373	−	10.4669i	−0.223065	−	0.333841i	−0.926075	+	0.377339i	$0.876839\pi$
$984$	−12.3071	+	40.2204i	−0.392335	+	1.28218i
$985$	−15.7024	+	36.9389i	−0.500319	+	1.17697i
$986$	19.2511	−	4.98667i	0.613082	−	0.158808i
$987$	−1.88490	+	1.88490i	−0.0599970	+	0.0599970i
$988$	−45.5719	+	39.8356i	−1.44983	+	1.26734i
$989$	26.6286	+	5.29675i	0.846739	+	0.168427i
$990$	0.118784	+	0.767392i	0.00377520	+	0.0243893i
$991$	−30.9412	−	46.3068i	−0.982881	−	1.47099i	−0.879245	−	0.476370i	$-0.841952\pi$
$991$	−30.9412	−	46.3068i	−0.982881	−	1.47099i	−0.103636	−	0.994615i	$-0.533048\pi$
$992$	−5.94068	+	35.1009i	−0.188617	+	1.11445i
$993$	0.695301	+	3.49551i	0.0220647	+	0.110927i
$994$	−3.40155	−	2.44167i	−0.107891	−	0.0774450i
$995$	3.49953	+	0.0323634i	0.110943	+	0.00102599i
$996$	−7.88315	−	13.7050i	−0.249787	−	0.434260i
$997$	6.39893	+	4.27563i	0.202656	+	0.135410i	0.652757	−	0.757567i	$-0.273612\pi$
$997$	6.39893	+	4.27563i	0.202656	+	0.135410i	−0.450101	+	0.892977i	$0.648612\pi$
$998$	−9.05400	−	4.11112i	−0.286600	−	0.130135i
$999$	24.3977	−	24.3977i	0.771908	−	0.771908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.cf.a.37.21	yes	832
5.3	odd	4		680.2.ct.a.173.34	yes	832
8.5	even	2	inner	680.2.cf.a.37.5	✓	832
17.6	odd	16		680.2.ct.a.397.49	yes	832
40.13	odd	4		680.2.ct.a.173.49	yes	832
85.23	even	16	inner	680.2.cf.a.533.5	yes	832
136.125	odd	16		680.2.ct.a.397.34	yes	832
680.533	even	16	inner	680.2.cf.a.533.21	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.cf.a.37.5	✓	832	8.5	even	2	inner
680.2.cf.a.37.21	yes	832	1.1	even	1	trivial
680.2.cf.a.533.5	yes	832	85.23	even	16	inner
680.2.cf.a.533.21	yes	832	680.533	even	16	inner
680.2.ct.a.173.34	yes	832	5.3	odd	4
680.2.ct.a.173.49	yes	832	40.13	odd	4
680.2.ct.a.397.34	yes	832	136.125	odd	16
680.2.ct.a.397.49	yes	832	17.6	odd	16

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.cf (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14887 - 0.824675i) q^{2} +(-1.00008 - 1.49673i) q^{3} +(0.639823 + 1.89489i) q^{4} +(-1.25943 + 1.84765i) q^{5} +(-0.0853459 + 2.54430i) q^{6} +(-0.346855 + 0.0689937i) q^{7} +(0.827595 - 2.70464i) q^{8} +(-0.0919848 + 0.222071i) q^{9} +(2.97064 - 1.08410i) q^{10} +(1.00197 - 0.199305i) q^{11} +(2.19627 - 2.85270i) q^{12} -5.05949i q^{13} +(0.455390 + 0.206777i) q^{14} +(4.02498 + 0.0372228i) q^{15} +(-3.18125 + 2.42480i) q^{16} +(3.95447 - 1.16713i) q^{17} +(0.288815 - 0.179274i) q^{18} +(-5.52633 + 2.28908i) q^{19} +(-4.30693 - 1.20432i) q^{20} +(0.450148 + 0.450148i) q^{21} +(-1.31550 - 0.597326i) q^{22} +(-2.32647 + 3.48181i) q^{23} +(-4.87578 + 1.46618i) q^{24} +(-1.82766 - 4.65399i) q^{25} +(-4.17243 + 5.81272i) q^{26} +(-4.87217 + 0.969135i) q^{27} +(-0.352661 - 0.613109i) q^{28} +(-2.83574 + 1.89478i) q^{29} +(-4.59350 - 3.36206i) q^{30} +(-1.22775 + 6.17234i) q^{31} +(5.65453 - 0.162287i) q^{32} +(-1.30036 - 1.30036i) q^{33} +(-5.50568 - 1.92027i) q^{34} +(0.309364 - 0.727760i) q^{35} +(-0.479655 - 0.0322153i) q^{36} +(-5.77512 + 3.85882i) q^{37} +(8.23680 + 1.92756i) q^{38} +(-7.57269 + 5.05991i) q^{39} +(3.95494 + 4.93543i) q^{40} +(4.58964 - 6.86888i) q^{41} +(-0.145938 - 0.888390i) q^{42} +(-2.48116 - 5.99005i) q^{43} +(1.01875 + 1.77111i) q^{44} +(-0.294462 - 0.449639i) q^{45} +(5.54418 - 2.08158i) q^{46} +4.18729i q^{47} +(6.81078 + 2.33648i) q^{48} +(-6.35161 + 2.63092i) q^{49} +(-1.73828 + 6.85408i) q^{50} +(-5.70167 - 4.75155i) q^{51} +(9.58720 - 3.23718i) q^{52} +(1.73696 + 0.719472i) q^{53} +(6.39673 + 2.90454i) q^{54} +(-0.893672 + 2.10231i) q^{55} +(-0.100452 + 0.995216i) q^{56} +(8.95292 + 5.98215i) q^{57} +(4.82048 + 0.161698i) q^{58} +(-4.26567 + 10.2982i) q^{59} +(2.50474 + 7.65073i) q^{60} +(-1.42679 + 2.13534i) q^{61} +(6.50071 - 6.07874i) q^{62} +(0.0165839 - 0.0833726i) q^{63} +(-6.63017 - 4.47670i) q^{64} +(9.34819 + 6.37209i) q^{65} +(0.421577 + 2.56633i) q^{66} +(-4.31620 - 4.31620i) q^{67} +(4.74174 + 6.74655i) q^{68} +7.53799 q^{69} +(-0.955585 + 0.580981i) q^{70} +(-8.21116 - 1.63330i) q^{71} +(0.524496 + 0.432571i) q^{72} +(-4.08301 - 0.812162i) q^{73} +(9.81716 + 0.329307i) q^{74} +(-5.13797 + 7.38989i) q^{75} +(-7.87344 - 9.00720i) q^{76} +(-0.333788 + 0.138260i) q^{77} +(12.8729 + 0.431807i) q^{78} +(2.33914 - 0.465284i) q^{79} +(-0.473612 - 8.93172i) q^{80} +(6.83300 + 6.83300i) q^{81} +(-10.9375 + 4.10652i) q^{82} +(1.68057 - 4.05726i) q^{83} +(-0.564968 + 1.14100i) q^{84} +(-2.82394 + 8.77641i) q^{85} +(-2.08930 + 8.92797i) q^{86} +(5.67194 + 2.34940i) q^{87} +(0.290180 - 2.87492i) q^{88} +(1.76667 + 1.76667i) q^{89} +(-0.0325069 + 0.759414i) q^{90} +(0.349073 + 1.75491i) q^{91} +(-8.08619 - 2.18067i) q^{92} +(10.4662 - 4.33523i) q^{93} +(3.45315 - 4.81066i) q^{94} +(2.73061 - 13.0937i) q^{95} +(-5.89790 - 8.30100i) q^{96} +(-17.7692 - 3.53451i) q^{97} +(9.46685 + 2.21541i) q^{98} +(-0.0479065 + 0.240842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 8 q^{2} - 16 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{10} - 32 q^{12} - 32 q^{14} - 16 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 8 q^{22} - 16 q^{23} - 16 q^{25} - 48 q^{26} - 40 q^{28} - 72 q^{30} - 32 q^{31}+ \cdots - 16 q^{98}+O(q^{100}) \) 832 * q - 8 * q^2 - 16 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^10 - 32 * q^12 - 32 * q^14 - 16 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^20 - 8 * q^22 - 16 * q^23 - 16 * q^25 - 48 * q^26 - 40 * q^28 - 72 * q^30 - 32 * q^31 - 8 * q^32 + 48 * q^36 + 96 * q^39 + 48 * q^40 - 32 * q^41 + 8 * q^42 - 32 * q^46 + 72 * q^48 - 16 * q^52 - 64 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 - 64 * q^58 - 8 * q^60 - 8 * q^62 - 64 * q^63 + 64 * q^65 - 16 * q^66 - 128 * q^68 - 72 * q^70 - 32 * q^71 - 16 * q^72 - 96 * q^73 - 16 * q^76 - 64 * q^78 - 136 * q^80 - 32 * q^81 - 8 * q^82 - 96 * q^84 - 32 * q^86 - 16 * q^87 + 80 * q^88 + 136 * q^90 + 104 * q^92 + 48 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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