LMFDB - Embedded newform 409.3.p.a.21.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [409,3,Mod(21,409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(409, base_ring=CyclotomicField(408)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("409.21"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 409 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	409.p (of order $408$, degree $128$, 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:	$11.1444428123$
Analytic rank:	$0$
Dimension:	$8576$
Relative dimension:	$67$ over $\Q(\zeta_{408})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{408}]$

Embedding invariants

Embedding label			21.15
Character	$\chi$	$=$	409.21
Dual form			409.3.p.a.39.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00582 - 1.46677i) q^{2} +(1.28816 + 1.00430i) q^{3} +(0.659278 + 2.07240i) q^{4} +(4.28592 + 0.801176i) q^{5} +(-1.11075 - 3.90388i) q^{6} +(-4.78569 + 3.67219i) q^{7} +(-1.44137 + 4.30048i) q^{8} +(-1.54447 - 6.14077i) q^{9} +(-7.42163 - 7.89348i) q^{10} +(0.435029 + 3.74973i) q^{11} +(-1.23204 + 3.33170i) q^{12} +(-4.76720 + 3.77604i) q^{13} +(14.9855 - 0.346226i) q^{14} +(4.71635 + 5.33638i) q^{15} +(16.2990 - 11.5378i) q^{16} +(-6.71841 + 10.1391i) q^{17} +(-5.90920 + 14.5827i) q^{18} +(-25.3905 + 24.2437i) q^{19} +(1.16525 + 9.41032i) q^{20} +(-9.85273 - 0.0758673i) q^{21} +(4.62741 - 8.15937i) q^{22} +(-8.65026 - 42.6294i) q^{23} +(-6.17568 + 4.09215i) q^{24} +(-5.58462 - 2.16349i) q^{25} +(15.1007 - 0.581665i) q^{26} +(10.1155 - 22.9094i) q^{27} +(-10.7653 - 7.49687i) q^{28} +(-8.80620 + 10.7726i) q^{29} +(-1.63288 - 17.6216i) q^{30} +(-12.4203 - 5.14467i) q^{31} +(-31.4760 - 0.484768i) q^{32} +(-3.20545 + 5.26716i) q^{33} +(28.3477 - 10.4828i) q^{34} +(-23.4532 + 11.9045i) q^{35} +(11.7079 - 7.24923i) q^{36} +(-17.7259 - 16.4110i) q^{37} +(86.4888 - 11.3865i) q^{38} +(-9.93320 + 0.0764870i) q^{39} +(-9.62305 + 17.2767i) q^{40} +(-16.2117 + 17.2424i) q^{41} +(19.6515 + 14.6039i) q^{42} +(10.9783 - 11.4976i) q^{43} +(-7.48413 + 3.37366i) q^{44} +(-1.69961 - 27.5562i) q^{45} +(-45.1768 + 98.1948i) q^{46} +(-4.48464 + 19.7486i) q^{47} +(32.5832 + 1.50641i) q^{48} +(-3.26426 + 12.1824i) q^{49} +(8.02838 + 12.5309i) q^{50} +(-18.8371 + 6.31355i) q^{51} +(-10.9684 - 7.39007i) q^{52} +(-47.3204 + 81.9614i) q^{53} +(-53.8928 + 31.1150i) q^{54} +(-1.13970 + 16.4195i) q^{55} +(-8.89420 - 25.8738i) q^{56} +(-57.0550 + 5.73035i) q^{57} +(33.4646 - 8.69121i) q^{58} +(-6.11835 + 16.9452i) q^{59} +(-7.94972 + 13.2923i) q^{60} +(-37.2968 + 21.9180i) q^{61} +(17.3669 + 28.5371i) q^{62} +(29.9415 + 23.7163i) q^{63} +(-1.31969 - 0.996581i) q^{64} +(-23.4571 + 12.3644i) q^{65} +(14.1553 - 5.86331i) q^{66} +(47.6366 - 18.8776i) q^{67} +(-25.4416 - 7.23875i) q^{68} +(31.6696 - 63.6011i) q^{69} +(64.5040 + 10.5221i) q^{70} +(5.74018 + 6.69997i) q^{71} +(28.6344 + 2.20921i) q^{72} +(58.1714 + 83.5328i) q^{73} +(11.4838 + 58.9173i) q^{74} +(-5.02112 - 8.39555i) q^{75} +(-66.9821 - 36.6359i) q^{76} +(-15.8516 - 16.3475i) q^{77} +(20.0364 + 14.4163i) q^{78} +(0.421978 + 2.00039i) q^{79} +(79.1000 - 36.3918i) q^{80} +(-14.1690 + 7.60861i) q^{81} +(57.8085 - 10.8063i) q^{82} +(20.8382 + 41.8487i) q^{83} +(-6.33846 - 20.4688i) q^{84} +(-36.9178 + 38.0727i) q^{85} +(-38.8850 + 6.95943i) q^{86} +(-22.1627 + 5.03286i) q^{87} +(-16.7526 - 3.53393i) q^{88} +(-89.8068 + 81.8697i) q^{89} +(-37.0096 + 57.7658i) q^{90} +(8.94799 - 35.5771i) q^{91} +(82.6422 - 46.0314i) q^{92} +(-10.8327 - 19.1009i) q^{93} +(37.9621 - 33.0342i) q^{94} +(-128.245 + 83.5643i) q^{95} +(-40.0595 - 32.2357i) q^{96} +(37.7623 + 12.3340i) q^{97} +(24.4163 - 19.6477i) q^{98} +(22.3543 - 8.46274i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8576 q - 124 q^{2} - 112 q^{3} - 124 q^{4} - 120 q^{5} - 120 q^{6} - 144 q^{7} + 8 q^{8} - 292 q^{9} - 96 q^{10} - 160 q^{11} + 36 q^{12} - 164 q^{13} - 16 q^{14} - 80 q^{15} - 204 q^{16} - 148 q^{17} - 148 q^{18}+ \cdots + 1180 q^{99}+O(q^{100}) $ 8576 * q - 124 * q^2 - 112 * q^3 - 124 * q^4 - 120 * q^5 - 120 * q^6 - 144 * q^7 + 8 * q^8 - 292 * q^9 - 96 * q^10 - 160 * q^11 + 36 * q^12 - 164 * q^13 - 16 * q^14 - 80 * q^15 - 204 * q^16 - 148 * q^17 - 148 * q^18 - 96 * q^19 + 68 * q^20 - 144 * q^21 - 256 * q^22 - 128 * q^23 - 1156 * q^24 - 2496 * q^25 - 280 * q^26 - 100 * q^27 - 92 * q^28 - 80 * q^29 + 672 * q^30 - 168 * q^31 + 2112 * q^32 - 96 * q^33 + 92 * q^34 + 64 * q^35 - 2344 * q^36 - 152 * q^37 - 2972 * q^39 + 112 * q^40 - 196 * q^41 + 488 * q^42 - 452 * q^43 + 92 * q^44 - 244 * q^45 - 124 * q^46 + 16 * q^47 - 188 * q^48 + 16 * q^49 + 96 * q^50 + 8 * q^51 - 828 * q^52 - 256 * q^53 + 240 * q^54 - 1016 * q^55 + 76 * q^56 - 92 * q^57 - 800 * q^58 + 48 * q^59 - 64 * q^60 + 428 * q^61 - 52 * q^62 + 1604 * q^63 - 136 * q^64 + 136 * q^65 + 224 * q^66 + 600 * q^67 - 136 * q^68 + 2808 * q^69 - 20 * q^70 - 188 * q^71 + 560 * q^72 + 144 * q^73 - 996 * q^74 + 1152 * q^75 + 992 * q^76 - 3084 * q^77 - 4900 * q^78 - 560 * q^79 - 292 * q^80 - 3128 * q^81 + 1488 * q^82 + 120 * q^83 + 6560 * q^84 + 288 * q^85 + 3248 * q^86 - 632 * q^87 + 144 * q^88 + 608 * q^89 + 268 * q^90 + 404 * q^91 - 5128 * q^92 - 104 * q^93 - 624 * q^94 + 84 * q^95 + 140 * q^96 - 840 * q^97 - 72 * q^98 + 1180 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/409\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{408}\right)$

Coefficient data

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

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

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

$2$	−2.00582	−	1.46677i	−1.00291	−	0.733387i	−0.0388973	−	0.999243i	$-0.512385\pi$
$2$	−2.00582	−	1.46677i	−1.00291	−	0.733387i	−0.964013	+	0.265856i	$0.914345\pi$
$3$	1.28816	+	1.00430i	0.429388	+	0.334765i	0.806324	−	0.591474i	$-0.201454\pi$
$3$	1.28816	+	1.00430i	0.429388	+	0.334765i	−0.376936	+	0.926239i	$0.623022\pi$
$4$	0.659278	+	2.07240i	0.164819	+	0.518100i
$5$	4.28592	+	0.801176i	0.857183	+	0.160235i	0.593955	−	0.804498i	$-0.297566\pi$
$5$	4.28592	+	0.801176i	0.857183	+	0.160235i	0.263228	+	0.964734i	$0.415213\pi$
$6$	−1.11075	−	3.90388i	−0.185125	−	0.650647i
$7$	−4.78569	+	3.67219i	−0.683671	+	0.524599i	−0.891189	−	0.453632i	$-0.850128\pi$
$7$	−4.78569	+	3.67219i	−0.683671	+	0.524599i	0.207518	+	0.978231i	$0.433461\pi$
$8$	−1.44137	+	4.30048i	−0.180172	+	0.537559i
$9$	−1.54447	−	6.14077i	−0.171607	−	0.682308i
$10$	−7.42163	−	7.89348i	−0.742163	−	0.789348i
$11$	0.435029	+	3.74973i	0.0395481	+	0.340884i	0.998379	+	0.0569082i	$0.0181242\pi$
$11$	0.435029	+	3.74973i	0.0395481	+	0.340884i	−0.958831	+	0.283976i	$0.908346\pi$
$12$	−1.23204	+	3.33170i	−0.102670	+	0.277642i
$13$	−4.76720	+	3.77604i	−0.366707	+	0.290465i	−0.787036	−	0.616907i	$-0.788385\pi$
$13$	−4.76720	+	3.77604i	−0.366707	+	0.290465i	0.420329	+	0.907372i	$0.361915\pi$
$14$	14.9855	−	0.346226i	1.07039	−	0.0247304i
$15$	4.71635	+	5.33638i	0.314423	+	0.355758i
$16$	16.2990	−	11.5378i	1.01869	−	0.721115i
$17$	−6.71841	+	10.1391i	−0.395201	+	0.596418i	−0.976038	−	0.217602i	$-0.930176\pi$
$17$	−6.71841	+	10.1391i	−0.395201	+	0.596418i	0.580837	+	0.814020i	$0.302725\pi$
$18$	−5.90920	+	14.5827i	−0.328289	+	0.810148i
$19$	−25.3905	+	24.2437i	−1.33634	+	1.27599i	−0.403835	+	0.914832i	$0.632323\pi$
$19$	−25.3905	+	24.2437i	−1.33634	+	1.27599i	−0.932506	+	0.361154i	$0.882383\pi$
$20$	1.16525	+	9.41032i	0.0582625	+	0.470516i
$21$	−9.85273	−	0.0758673i	−0.469178	−	0.00361273i
$22$	4.62741	−	8.15937i	0.210337	−	0.370880i
$23$	−8.65026	−	42.6294i	−0.376098	−	1.85345i	−0.506847	−	0.862036i	$-0.669189\pi$
$23$	−8.65026	−	42.6294i	−0.376098	−	1.85345i	0.130749	−	0.991416i	$-0.458262\pi$
$24$	−6.17568	+	4.09215i	−0.257320	+	0.170506i
$25$	−5.58462	−	2.16349i	−0.223385	−	0.0865397i
$26$	15.1007	−	0.581665i	0.580798	−	0.0223717i
$27$	10.1155	−	22.9094i	0.374648	−	0.848497i
$28$	−10.7653	−	7.49687i	−0.384477	−	0.267745i
$29$	−8.80620	+	10.7726i	−0.303662	+	0.371469i	−0.903453	−	0.428688i	$-0.858976\pi$
$29$	−8.80620	+	10.7726i	−0.303662	+	0.371469i	0.599791	+	0.800157i	$0.295251\pi$
$30$	−1.63288	−	17.6216i	−0.0544295	−	0.587387i
$31$	−12.4203	−	5.14467i	−0.400656	−	0.165957i	0.173251	−	0.984878i	$-0.444573\pi$
$31$	−12.4203	−	5.14467i	−0.400656	−	0.165957i	−0.573907	+	0.818921i	$0.694573\pi$
$32$	−31.4760	−	0.484768i	−0.983626	−	0.0151490i
$33$	−3.20545	+	5.26716i	−0.0971348	+	0.159611i
$34$	28.3477	−	10.4828i	0.833756	−	0.308318i
$35$	−23.4532	+	11.9045i	−0.670090	+	0.340129i
$36$	11.7079	−	7.24923i	0.325220	−	0.201367i
$37$	−17.7259	−	16.4110i	−0.479078	−	0.443540i	0.402611	−	0.915371i	$-0.368103\pi$
$37$	−17.7259	−	16.4110i	−0.479078	−	0.443540i	−0.881689	+	0.471831i	$0.843593\pi$
$38$	86.4888	−	11.3865i	2.27602	−	0.299644i
$39$	−9.93320	+	0.0764870i	−0.254697	+	0.00196120i
$40$	−9.62305	+	17.2767i	−0.240576	+	0.431917i
$41$	−16.2117	+	17.2424i	−0.395408	+	0.420547i	−0.895246	−	0.445571i	$-0.853001\pi$
$41$	−16.2117	+	17.2424i	−0.395408	+	0.420547i	0.499839	+	0.866119i	$0.333393\pi$
$42$	19.6515	+	14.6039i	0.467893	+	0.347712i
$43$	10.9783	−	11.4976i	0.255310	−	0.267387i	−0.583132	−	0.812378i	$-0.698173\pi$
$43$	10.9783	−	11.4976i	0.255310	−	0.267387i	0.838442	+	0.544991i	$0.183467\pi$
$44$	−7.48413	+	3.37366i	−0.170094	+	0.0766742i
$45$	−1.69961	−	27.5562i	−0.0377691	−	0.612361i
$46$	−45.1768	+	98.1948i	−0.982104	+	2.13467i
$47$	−4.48464	+	19.7486i	−0.0954179	+	0.420183i	−0.999981	−	0.00615656i	$-0.998040\pi$
$47$	−4.48464	+	19.7486i	−0.0954179	+	0.420183i	0.904563	+	0.426340i	$0.140197\pi$
$48$	32.5832	+	1.50641i	0.678817	+	0.0313836i
$49$	−3.26426	+	12.1824i	−0.0666176	+	0.248620i
$50$	8.02838	+	12.5309i	0.160568	+	0.250619i
$51$	−18.8371	+	6.31355i	−0.369355	+	0.123795i
$52$	−10.9684	−	7.39007i	−0.210930	−	0.142117i
$53$	−47.3204	+	81.9614i	−0.892839	+	1.54644i	−0.0563817	+	0.998409i	$0.517956\pi$
$53$	−47.3204	+	81.9614i	−0.892839	+	1.54644i	−0.836457	+	0.548033i	$0.815377\pi$
$54$	−53.8928	+	31.1150i	−0.998014	+	0.576204i
$55$	−1.13970	+	16.4195i	−0.0207218	+	0.298537i
$56$	−8.89420	−	25.8738i	−0.158825	−	0.462031i
$57$	−57.0550	+	5.73035i	−1.00097	+	0.100532i
$58$	33.4646	−	8.69121i	0.576976	−	0.149848i
$59$	−6.11835	+	16.9452i	−0.103701	+	0.287207i	−0.981391	−	0.192022i	$-0.938496\pi$
$59$	−6.11835	+	16.9452i	−0.103701	+	0.287207i	0.877690	+	0.479229i	$0.159084\pi$
$60$	−7.94972	+	13.2923i	−0.132495	+	0.221538i
$61$	−37.2968	+	21.9180i	−0.611423	+	0.359311i	−0.779443	−	0.626473i	$-0.784498\pi$
$61$	−37.2968	+	21.9180i	−0.611423	+	0.359311i	0.168020	+	0.985784i	$0.446263\pi$
$62$	17.3669	+	28.5371i	0.280111	+	0.460276i
$63$	29.9415	+	23.7163i	0.475261	+	0.376449i
$64$	−1.31969	−	0.996581i	−0.0206201	−	0.0155716i
$65$	−23.4571	+	12.3644i	−0.360878	+	0.190222i
$66$	14.1553	−	5.86331i	0.214474	−	0.0888381i
$67$	47.6366	−	18.8776i	0.710994	−	0.281756i	0.0150853	−	0.999886i	$-0.495198\pi$
$67$	47.6366	−	18.8776i	0.710994	−	0.281756i	0.695908	+	0.718131i	$0.255002\pi$
$68$	−25.4416	−	7.23875i	−0.374141	−	0.106452i
$69$	31.6696	−	63.6011i	0.458979	−	0.921755i
$70$	64.5040	+	10.5221i	0.921486	+	0.150316i
$71$	5.74018	+	6.69997i	0.0808476	+	0.0943657i	0.798362	−	0.602178i	$-0.205700\pi$
$71$	5.74018	+	6.69997i	0.0808476	+	0.0943657i	−0.717514	+	0.696544i	$0.754720\pi$
$72$	28.6344	+	2.20921i	0.397700	+	0.0306835i
$73$	58.1714	+	83.5328i	0.796868	+	1.14428i	0.986713	+	0.162471i	$0.0519464\pi$
$73$	58.1714	+	83.5328i	0.796868	+	1.14428i	−0.189845	+	0.981814i	$0.560799\pi$
$74$	11.4838	+	58.9173i	0.155186	+	0.796180i
$75$	−5.02112	−	8.39555i	−0.0669483	−	0.111941i
$76$	−66.9821	−	36.6359i	−0.881343	−	0.482051i
$77$	−15.8516	−	16.3475i	−0.205865	−	0.212306i
$78$	20.0364	+	14.4163i	0.256877	+	0.184825i
$79$	0.421978	+	2.00039i	0.00534149	+	0.0253214i	0.981055	−	0.193727i	$-0.0620576\pi$
$79$	0.421978	+	2.00039i	0.00534149	+	0.0253214i	−0.975714	+	0.219049i	$0.929705\pi$
$80$	79.1000	−	36.3918i	0.988751	−	0.454897i
$81$	−14.1690	+	7.60861i	−0.174926	+	0.0939335i
$82$	57.8085	−	10.8063i	0.704982	−	0.131784i
$83$	20.8382	+	41.8487i	0.251063	+	0.504202i	0.984462	−	0.175596i	$-0.0561852\pi$
$83$	20.8382	+	41.8487i	0.251063	+	0.504202i	−0.733400	+	0.679798i	$0.762068\pi$
$84$	−6.33846	−	20.4688i	−0.0754578	−	0.243676i
$85$	−36.9178	+	38.0727i	−0.434327	+	0.447914i
$86$	−38.8850	+	6.95943i	−0.452151	+	0.0809236i
$87$	−22.1627	+	5.03286i	−0.254744	+	0.0578489i
$88$	−16.7526	−	3.53393i	−0.190371	−	0.0401583i
$89$	−89.8068	+	81.8697i	−1.00907	+	0.919884i	−0.996792	−	0.0800403i	$-0.974495\pi$
$89$	−89.8068	+	81.8697i	−1.00907	+	0.919884i	−0.0122735	+	0.999925i	$0.503907\pi$
$90$	−37.0096	+	57.7658i	−0.411218	+	0.641842i
$91$	8.94799	−	35.5771i	0.0983295	−	0.390957i
$92$	82.6422	−	46.0314i	0.898284	−	0.500341i
$93$	−10.8327	−	19.1009i	−0.116480	−	0.205386i
$94$	37.9621	−	33.0342i	0.403852	−	0.351428i
$95$	−128.245	+	83.5643i	−1.34995	+	0.879624i
$96$	−40.0595	−	32.2357i	−0.417286	−	0.335789i
$97$	37.7623	+	12.3340i	0.389302	+	0.127155i	0.498553	−	0.866859i	$-0.333865\pi$
$97$	37.7623	+	12.3340i	0.389302	+	0.127155i	−0.109251	+	0.994014i	$0.534845\pi$
$98$	24.4163	−	19.6477i	0.249146	−	0.200487i
$99$	22.3543	−	8.46274i	0.225801	−	0.0854822i
$100$	0.801806	−	12.9999i	0.00801806	−	0.129999i
$101$	−90.2842	−	48.4816i	−0.893903	−	0.480016i	−0.0392580	−	0.999229i	$-0.512499\pi$
$101$	−90.2842	−	48.4816i	−0.893903	−	0.480016i	−0.854645	+	0.519214i	$0.826225\pi$
$102$	47.0444	+	14.9659i	0.461219	+	0.146724i
$103$	161.598	−	110.697i	1.56891	−	1.07473i	0.609472	−	0.792808i	$-0.291382\pi$
$103$	161.598	−	110.697i	1.56891	−	1.07473i	0.959438	−	0.281920i	$-0.0909713\pi$
$104$	−9.36747	−	25.9439i	−0.0900718	−	0.249461i
$105$	−42.1672	−	8.21894i	−0.401592	−	0.0782756i
$106$	215.135	−	94.9915i	2.02958	−	0.896146i
$107$	−5.50696	−	11.2763i	−0.0514669	−	0.105386i	0.871289	−	0.490770i	$-0.163284\pi$
$107$	−5.50696	−	11.2763i	−0.0514669	−	0.105386i	−0.922756	+	0.385385i	$0.874069\pi$
$108$	54.1464	+	5.85968i	0.501355	+	0.0542563i
$109$	0.184597	+	0.163149i	0.00169355	+	0.00149678i	0.663082	−	0.748547i	$-0.269248\pi$
$109$	0.184597	+	0.163149i	0.00169355	+	0.00149678i	−0.661388	+	0.750044i	$0.730032\pi$
$110$	26.3698	−	31.2630i	0.239725	−	0.284209i
$111$	−6.35238	−	38.9421i	−0.0572287	−	0.350830i
$112$	−35.6330	+	115.070i	−0.318151	+	1.02741i
$113$	−53.9267	−	98.5951i	−0.477227	−	0.872523i	−0.999801	−	0.0199297i	$-0.993656\pi$
$113$	−53.9267	−	98.5951i	−0.477227	−	0.872523i	0.522574	−	0.852594i	$-0.324972\pi$
$114$	122.847	+	72.1927i	1.07761	+	0.633270i
$115$	−2.92062	−	189.636i	−0.0253967	−	1.64901i
$116$	−28.1309	−	11.1478i	−0.242508	−	0.0961019i
$117$	30.5506	+	23.4423i	0.261116	+	0.200362i
$118$	37.1271	−	25.0149i	0.314637	−	0.211990i
$119$	−5.08046	−	73.1939i	−0.0426930	−	0.615075i
$120$	−29.7470	+	12.5908i	−0.247891	+	0.104923i
$121$	103.915	−	24.4405i	0.858800	−	0.201988i
$122$	106.959	+	10.7425i	0.876716	+	0.0880534i
$123$	−38.1999	+	5.92972i	−0.310568	+	0.0482091i
$124$	2.47336	−	29.1316i	0.0199465	−	0.234933i
$125$	−114.879	−	71.1300i	−0.919031	−	0.569040i
$126$	−25.2707	−	91.4879i	−0.200561	−	0.726095i
$127$	0.632003	+	11.7142i	0.00497641	+	0.0922374i	0.999970	−	0.00769758i	$-0.00245024\pi$
$127$	0.632003	+	11.7142i	0.00497641	+	0.0922374i	−0.994994	+	0.0999350i	$0.968137\pi$
$128$	37.5057	+	124.502i	0.293013	+	0.972671i
$129$	25.6889	−	3.78533i	0.199139	−	0.0293436i
$130$	65.1865	+	9.60539i	0.501435	+	0.0738876i
$131$	−86.8129	−	26.1520i	−0.662694	−	0.199634i	−0.0607264	−	0.998154i	$-0.519342\pi$
$131$	−86.8129	−	26.1520i	−0.662694	−	0.199634i	−0.601967	+	0.798521i	$0.705616\pi$
$132$	−13.0289	−	3.17045i	−0.0987041	−	0.0240185i
$133$	32.4834	−	209.262i	0.244236	−	1.57340i
$134$	−123.240	−	32.0070i	−0.919699	−	0.238858i
$135$	61.7086	−	90.0835i	0.457101	−	0.667285i
$136$	−33.9192	−	43.5066i	−0.249406	−	0.319902i
$137$	30.9110	−	0.952359i	0.225628	−	0.00695153i	0.0822157	−	0.996615i	$-0.473800\pi$
$137$	30.9110	−	0.952359i	0.225628	−	0.00695153i	0.143412	+	0.989663i	$0.454193\pi$
$138$	−156.812	+	81.1202i	−1.13632	+	0.587828i
$139$	−60.3515	−	171.265i	−0.434183	−	1.23212i	−0.931241	−	0.364405i	$-0.881272\pi$
$139$	−60.3515	−	171.265i	−0.434183	−	1.23212i	0.497057	−	0.867718i	$-0.334414\pi$
$140$	−40.1331	−	40.7559i	−0.286665	−	0.291114i
$141$	−25.6104	+	20.9355i	−0.181634	+	0.148479i
$142$	−1.68643	−	21.8585i	−0.0118763	−	0.153933i
$143$	−16.2330	−	16.2330i	−0.113517	−	0.113517i
$144$	−96.0245	−	82.2688i	−0.666837	−	0.571311i
$145$	−46.3734	+	39.1152i	−0.319817	+	0.269760i
$146$	5.84246	−	252.876i	0.0400168	−	1.73203i
$147$	−16.4396	+	12.4146i	−0.111834	+	0.0844533i
$148$	22.3238	−	47.5545i	0.150837	−	0.321314i
$149$	−166.932	+	169.522i	−1.12035	+	1.13773i	−0.131117	+	0.991367i	$0.541856\pi$
$149$	−166.932	+	169.522i	−1.12035	+	1.13773i	−0.989230	+	0.146368i	$0.953242\pi$
$150$	−2.24291	+	24.2048i	−0.0149527	+	0.161365i
$151$	48.7874	−	92.5566i	0.323096	−	0.612958i	−0.668295	−	0.743896i	$-0.732976\pi$
$151$	48.7874	−	92.5566i	0.323096	−	0.612958i	0.991390	+	0.130939i	$0.0417991\pi$
$152$	−67.6624	−	144.135i	−0.445147	−	0.948259i
$153$	72.6383	+	25.5968i	0.474760	+	0.167299i
$154$	7.81738	+	56.0410i	0.0507622	+	0.363902i
$155$	−49.1107	−	32.0005i	−0.316843	−	0.206455i
$156$	−6.70725	−	20.5351i	−0.0429952	−	0.131635i
$157$	179.858	+	68.0892i	1.14559	+	0.433689i	0.852671	−	0.522448i	$-0.174981\pi$
$157$	179.858	+	68.0892i	1.14559	+	0.433689i	0.292919	+	0.956137i	$0.405373\pi$
$158$	2.08771	−	4.63137i	0.0132134	−	0.0293125i
$159$	−143.270	+	58.0560i	−0.901070	+	0.365132i
$160$	−134.515	−	27.2955i	−0.840720	−	0.170597i
$161$	197.941	+	172.246i	1.22945	+	1.06985i
$162$	39.5807	+	5.52126i	0.244325	+	0.0340819i
$163$	−9.60898	+	18.5749i	−0.0589508	+	0.113957i	−0.915839	−	0.401546i	$-0.868473\pi$
$163$	−9.60898	+	18.5749i	−0.0589508	+	0.113957i	0.856888	+	0.515502i	$0.172395\pi$
$164$	−46.4212	−	22.2296i	−0.283056	−	0.135546i
$165$	−17.9582	+	20.0065i	−0.108838	+	0.121251i
$166$	19.5850	−	114.506i	0.117982	−	0.689795i
$167$	−2.80177	+	6.61944i	−0.0167771	+	0.0396374i	−0.929081	−	0.369877i	$-0.879400\pi$
$167$	−2.80177	+	6.61944i	−0.0167771	+	0.0396374i	0.912304	+	0.409514i	$0.134302\pi$
$168$	14.5277	−	42.2621i	0.0864746	−	0.251560i
$169$	−30.2250	+	128.509i	−0.178846	+	0.760407i
$170$	129.894	−	22.2170i	0.764085	−	0.130688i
$171$	188.090	+	118.474i	1.09994	+	0.692828i
$172$	31.0654	+	15.1714i	0.180613	+	0.0882056i
$173$	6.78841	−	176.236i	0.0392393	−	1.01870i	−0.840078	−	0.542466i	$-0.817491\pi$
$173$	6.78841	−	176.236i	0.0392393	−	1.01870i	0.879317	−	0.476237i	$-0.157999\pi$
$174$	51.8365	+	22.4127i	0.297911	+	0.128809i
$175$	34.6710	−	10.1540i	0.198120	−	0.0580227i
$176$	50.3543	+	56.0976i	0.286104	+	0.318736i
$177$	−24.8995	+	15.6836i	−0.140675	+	0.0886080i
$178$	300.221	−	32.4897i	1.68663	−	0.182526i
$179$	16.2484	+	11.5020i	0.0907735	+	0.0642572i	0.622267	−	0.782805i	$-0.286212\pi$
$179$	16.2484	+	11.5020i	0.0907735	+	0.0642572i	−0.531493	+	0.847063i	$0.678369\pi$
$180$	55.9870	−	21.6895i	0.311039	−	0.120497i
$181$	199.309	−	86.1758i	1.10115	−	0.476110i	0.233037	−	0.972468i	$-0.425134\pi$
$181$	199.309	−	86.1758i	1.10115	−	0.476110i	0.868118	+	0.496358i	$0.165330\pi$
$182$	−70.1315	+	58.2365i	−0.385338	+	0.319981i
$183$	−70.0565	−	9.22312i	−0.382823	−	0.0503996i
$184$	195.795	+	24.2447i	1.06410	+	0.131764i
$185$	−62.8236	−	84.5376i	−0.339587	−	0.456960i
$186$	−6.28830	+	54.2020i	−0.0338081	+	0.291408i
$187$	−40.9416	−	20.7814i	−0.218939	−	0.111131i
$188$	−43.8836	+	3.72585i	−0.233423	+	0.0198183i
$189$	35.7181	+	146.783i	0.188985	+	0.776632i
$190$	379.806	+	20.4914i	1.99898	+	0.107849i
$191$	167.050	−	36.5845i	0.874606	−	0.191542i	0.246004	−	0.969269i	$-0.420882\pi$
$191$	167.050	−	36.5845i	0.874606	−	0.191542i	0.628602	+	0.777727i	$0.283627\pi$
$192$	−0.699111	−	2.60912i	−0.00364120	−	0.0135892i
$193$	−47.7930	+	52.4264i	−0.247632	+	0.271639i	−0.850237	−	0.526400i	$-0.823541\pi$
$193$	−47.7930	+	52.4264i	−0.247632	+	0.271639i	0.602605	+	0.798040i	$0.294130\pi$
$194$	−57.6531	−	80.1286i	−0.297181	−	0.413034i
$195$	−42.6341	−	7.63043i	−0.218637	−	0.0391304i
$196$	−27.3988	+	1.26672i	−0.139790	+	0.00646288i
$197$	39.3361	−	179.614i	0.199676	−	0.911747i	−0.764113	−	0.645082i	$-0.776823\pi$
$197$	39.3361	−	179.614i	0.199676	−	0.911747i	0.963789	−	0.266665i	$-0.0859219\pi$
$198$	−57.2517	−	15.8140i	−0.289150	−	0.0798688i
$199$	−186.154	+	172.345i	−0.935448	+	0.866056i	−0.991198	−	0.132389i	$-0.957735\pi$
$199$	−186.154	+	172.345i	−0.935448	+	0.866056i	0.0557499	+	0.998445i	$0.482245\pi$
$200$	17.3536	−	20.8981i	0.0867679	−	0.104491i
$201$	80.3225	+	23.5238i	0.399614	+	0.117034i
$202$	109.982	+	229.672i	0.544467	+	1.13699i
$203$	2.58470	−	83.8925i	0.0127325	−	0.413263i
$204$	−25.5031	−	34.8756i	−0.125015	−	0.170959i
$205$	−83.2963	+	60.9112i	−0.406323	+	0.297128i
$206$	−486.503	−	14.9890i	−2.36167	−	0.0727622i
$207$	−248.417	+	118.959i	−1.20008	+	0.574681i
$208$	−34.1333	+	116.549i	−0.164102	+	0.560331i
$209$	−101.953	−	84.6607i	−0.487813	−	0.405075i
$210$	72.5245	+	78.3354i	0.345355	+	0.373026i
$211$	89.0326	−	322.326i	0.421955	−	1.52761i	−0.376996	−	0.926215i	$-0.623043\pi$
$211$	89.0326	−	322.326i	0.421955	−	1.52761i	0.798951	−	0.601396i	$-0.205388\pi$
$212$	−201.054	−	44.0315i	−0.948368	−	0.207696i
$213$	0.665544	+	14.3955i	0.00312462	+	0.0675845i
$214$	−5.49373	+	30.6956i	−0.0256717	+	0.143437i
$215$	56.2639	−	40.4823i	0.261692	−	0.188290i
$216$	83.9411	+	76.5224i	0.388616	+	0.354271i
$217$	78.3321	−	20.9890i	0.360978	−	0.0967236i
$218$	−0.130966	−	0.598008i	−0.000600760	−	0.00274316i
$219$	−8.95742	+	166.025i	−0.0409014	+	0.758106i
$220$	−34.7792	+	8.46313i	−0.158087	+	0.0384688i
$221$	−6.25770	−	73.7041i	−0.0283154	−	0.333503i
$222$	−44.3775	+	87.4283i	−0.199899	+	0.393821i
$223$	10.4239	+	1.20934i	0.0467439	+	0.00542305i	0.138583	−	0.990351i	$-0.455745\pi$
$223$	10.4239	+	1.20934i	0.0467439	+	0.00542305i	−0.0918392	+	0.995774i	$0.529275\pi$
$224$	152.415	−	113.266i	0.680424	−	0.505652i
$225$	−4.66026	+	37.6353i	−0.0207123	+	0.167268i
$226$	−36.4496	+	276.862i	−0.161281	+	1.22505i
$227$	−72.2870	−	87.0519i	−0.318445	−	0.383489i	0.585834	−	0.810431i	$-0.300767\pi$
$227$	−72.2870	−	87.0519i	−0.318445	−	0.383489i	−0.904279	+	0.426943i	$0.859591\pi$
$228$	−49.4906	−	114.463i	−0.217064	−	0.502030i
$229$	163.505	+	422.055i	0.713996	+	1.84304i	0.499505	+	0.866311i	$0.333515\pi$
$229$	163.505	+	422.055i	0.713996	+	1.84304i	0.214492	+	0.976726i	$0.431191\pi$
$230$	−272.295	+	384.660i	−1.18389	+	1.67244i
$231$	−4.00174	−	36.9781i	−0.0173235	−	0.160078i
$232$	−33.6343	−	53.3982i	−0.144975	−	0.230165i
$233$	162.677	−	146.022i	0.698184	−	0.626703i	−0.240836	−	0.970566i	$-0.577422\pi$
$233$	162.677	−	146.022i	0.698184	−	0.626703i	0.939020	+	0.343863i	$0.111735\pi$
$234$	−26.8945	−	91.8319i	−0.114934	−	0.392444i
$235$	−35.0429	+	81.0479i	−0.149119	+	0.344885i
$236$	−39.1510	−	1.50805i	−0.165894	−	0.00639006i
$237$	−1.46541	+	3.00062i	−0.00618316	+	0.0126609i
$238$	−97.1684	+	154.266i	−0.408271	+	0.648175i
$239$	77.5456	+	453.380i	0.324459	+	1.89699i	0.430438	+	0.902620i	$0.358359\pi$
$239$	77.5456	+	453.380i	0.324459	+	1.89699i	−0.105979	+	0.994368i	$0.533798\pi$
$240$	138.442	+	32.5613i	0.576842	+	0.135672i
$241$	−335.604	−	115.365i	−1.39255	−	0.478694i	−0.476293	−	0.879287i	$-0.658020\pi$
$241$	−335.604	−	115.365i	−1.39255	−	0.478694i	−0.916256	+	0.400593i	$0.868804\pi$
$242$	−244.283	−	103.396i	−1.00943	−	0.427257i
$243$	−248.056	−	42.4273i	−1.02081	−	0.174598i
$244$	−70.0117	−	62.8439i	−0.286933	−	0.257557i
$245$	−23.7506	+	49.5974i	−0.0969412	+	0.202439i
$246$	85.3196	+	44.1366i	0.346828	+	0.179417i
$247$	29.4960	−	211.450i	0.119417	−	0.856074i
$248$	40.0269	−	45.9979i	0.161399	−	0.185476i
$249$	−15.1855	+	74.8358i	−0.0609860	+	0.300545i
$250$	126.095	+	311.175i	0.504379	+	1.24470i
$251$	222.636	+	100.359i	0.886996	+	0.399837i	0.802545	−	0.596591i	$-0.203479\pi$
$251$	222.636	+	100.359i	0.886996	+	0.399837i	0.0844509	+	0.996428i	$0.473086\pi$
$252$	−29.4099	+	77.6863i	−0.116706	+	0.308279i
$253$	156.085	−	50.9811i	0.616938	−	0.201506i
$254$	15.9143	−	24.4235i	0.0626548	−	0.0961554i
$255$	−85.7924	+	11.9675i	−0.336441	+	0.0469315i
$256$	105.188	−	298.502i	0.410891	−	1.16602i
$257$	141.932	−	66.6281i	0.552265	−	0.259253i	−0.128557	−	0.991702i	$-0.541034\pi$
$257$	141.932	−	66.6281i	0.552265	−	0.259253i	0.680822	+	0.732449i	$0.261623\pi$
$258$	−57.0796	−	30.0872i	−0.221239	−	0.116617i
$259$	145.095	+	13.4450i	0.560212	+	0.0519113i
$260$	−41.0888	−	40.4608i	−0.158034	−	0.155619i
$261$	79.7530	+	37.4390i	0.305567	+	0.143444i
$262$	135.772	+	179.791i	0.518213	+	0.686225i
$263$	−2.53335	−	0.0585306i	−0.00963250	−	0.000222550i	0.0182814	−	0.999833i	$-0.494181\pi$
$263$	−2.53335	−	0.0585306i	−0.00963250	−	0.000222550i	−0.0279139	+	0.999610i	$0.508886\pi$
$264$	−18.0311	−	21.3769i	−0.0682994	−	0.0809731i
$265$	−268.477	+	313.368i	−1.01312	+	1.18252i
$266$	−372.096	+	372.096i	−1.39886	+	1.39886i
$267$	−197.907	+	15.2690i	−0.741226	+	0.0571873i
$268$	70.5277	+	86.2764i	0.263163	+	0.321927i
$269$	−76.7141	+	75.5417i	−0.285182	+	0.280824i	−0.830039	−	0.557705i	$-0.811682\pi$
$269$	−76.7141	+	75.5417i	−0.285182	+	0.280824i	0.544857	+	0.838529i	$0.316584\pi$
$270$	−255.908	+	90.1787i	−0.947809	+	0.333995i
$271$	−130.614	−	252.488i	−0.481971	−	0.931689i	−0.997210	−	0.0746422i	$-0.976219\pi$
$271$	−130.614	−	252.488i	−0.481971	−	0.931689i	0.515239	−	0.857046i	$-0.327703\pi$
$272$	7.47977	+	242.773i	0.0274991	+	0.892549i
$273$	47.2564	−	36.8427i	0.173100	−	0.134955i
$274$	−63.3989	−	43.4292i	−0.231383	−	0.158501i
$275$	5.68304	−	21.8820i	0.0206656	−	0.0795708i
$276$	152.686	+	23.7012i	0.553210	+	0.0858740i
$277$	0.360931	−	1.48324i	0.00130300	−	0.00535467i	−0.970991	−	0.239116i	$-0.923143\pi$
$277$	0.360931	−	1.48324i	0.00130300	−	0.00535467i	0.972294	+	0.233761i	$0.0751033\pi$
$278$	−130.153	+	432.049i	−0.468176	+	1.55413i
$279$	−12.4095	+	84.2162i	−0.0444784	+	0.301850i
$280$	−17.3903	−	118.019i	−0.0621083	−	0.421495i
$281$	−457.562	+	137.839i	−1.62834	+	0.490529i	−0.965971	−	0.258652i	$-0.916722\pi$
$281$	−457.562	+	137.839i	−1.62834	+	0.490529i	−0.662365	+	0.749181i	$0.730447\pi$
$282$	82.0776	−	4.42826i	0.291055	−	0.0157030i
$283$	163.324	−	45.1133i	0.577118	−	0.159411i	0.0345204	−	0.999404i	$-0.489010\pi$
$283$	163.324	−	45.1133i	0.577118	−	0.159411i	0.542597	+	0.839993i	$0.317441\pi$
$284$	−10.1006	+	16.3131i	−0.0355656	+	0.0574404i
$285$	−249.124	−	21.1514i	−0.874119	−	0.0742153i
$286$	8.75034	+	56.3706i	0.0305956	+	0.197100i
$287$	14.2668	−	142.050i	0.0497101	−	0.494946i
$288$	45.6369	+	194.036i	0.158461	+	0.673736i
$289$	54.9838	+	129.904i	0.190255	+	0.449496i
$290$	150.390	−	10.4387i	0.518585	−	0.0359955i
$291$	36.2570	+	53.8128i	0.124595	+	0.184924i
$292$	−134.762	+	175.626i	−0.461514	+	0.601457i
$293$	20.6593	−	52.1325i	0.0705095	−	0.177926i	−0.890142	−	0.455683i	$-0.849395\pi$
$293$	20.6593	−	52.1325i	0.0705095	−	0.177926i	0.960651	+	0.277757i	$0.0895910\pi$
$294$	51.1844	−	0.788300i	0.174097	−	0.00268129i
$295$	−39.7989	+	67.7240i	−0.134911	+	0.229573i
$296$	96.1246	−	52.5754i	0.324745	−	0.177620i
$297$	90.3046	+	27.9641i	0.304056	+	0.0941552i
$298$	583.486	−	95.1805i	1.95801	−	0.319398i
$299$	202.208	+	170.559i	0.676281	+	0.570431i
$300$	14.0886	−	15.9408i	0.0469620	−	0.0531359i
$301$	−10.3175	+	95.3387i	−0.0342774	+	0.316740i
$302$	−233.618	+	114.092i	−0.773571	+	0.377788i
$303$	−67.6110	−	153.124i	−0.223139	−	0.505361i
$304$	−134.120	+	688.100i	−0.441183	+	2.26349i
$305$	−177.411	+	64.0572i	−0.581676	+	0.210024i
$306$	−108.155	−	157.886i	−0.353447	−	0.515969i
$307$	26.9137	−	84.6017i	0.0876669	−	0.275575i	−0.899094	−	0.437755i	$-0.855774\pi$
$307$	26.9137	−	84.6017i	0.0876669	−	0.275575i	0.986761	+	0.162179i	$0.0518523\pi$
$308$	23.4280	−	43.6285i	0.0760649	−	0.141651i
$309$	319.337	+	19.6960i	1.03345	+	0.0637412i
$310$	51.5697	+	136.222i	0.166354	+	0.439424i
$311$	351.207	+	436.446i	1.12928	+	1.40336i	0.903181	+	0.429260i	$0.141226\pi$
$311$	351.207	+	436.446i	1.12928	+	1.40336i	0.226102	+	0.974104i	$0.427402\pi$
$312$	13.9885	−	42.8277i	0.0448350	−	0.137268i
$313$	44.8095	−	55.6849i	0.143161	−	0.177907i	−0.702405	−	0.711777i	$-0.747890\pi$
$313$	44.8095	−	55.6849i	0.143161	−	0.177907i	0.845566	+	0.533870i	$0.179263\pi$
$314$	−260.891	−	400.385i	−0.830861	−	1.27511i
$315$	109.326	+	125.634i	0.347065	+	0.398839i
$316$	−3.86741	+	2.19332i	−0.0122386	+	0.00694088i
$317$	−193.260	−	346.968i	−0.609653	−	1.09454i	−0.985792	−	0.167973i	$-0.946278\pi$
$317$	−193.260	−	346.968i	−0.609653	−	1.09454i	0.376139	−	0.926563i	$-0.377252\pi$
$318$	372.529	+	93.6948i	1.17147	+	0.294638i
$319$	−44.2253	−	28.3345i	−0.138637	−	0.0888228i
$320$	−4.85763	−	5.32856i	−0.0151801	−	0.0166518i
$321$	4.23082	−	20.0563i	0.0131801	−	0.0624807i
$322$	−144.388	−	635.828i	−0.448410	−	1.97462i
$323$	−75.2259	−	420.316i	−0.232898	−	1.30129i
$324$	−25.1094	−	24.3477i	−0.0774982	−	0.0751473i
$325$	34.7924	−	10.7740i	0.107054	−	0.0331507i
$326$	46.5191	−	23.1637i	0.142697	−	0.0710544i
$327$	0.0739415	+	0.395552i	0.000226121	+	0.00120964i
$328$	−50.7835	−	94.5709i	−0.154828	−	0.288326i
$329$	−51.0586	−	110.979i	−0.155193	−	0.337323i
$330$	65.3659	−	13.7888i	0.198079	−	0.0417842i
$331$	9.12463	−	12.6818i	0.0275669	−	0.0383135i	−0.797714	−	0.603035i	$-0.793958\pi$
$331$	9.12463	−	12.6818i	0.0275669	−	0.0383135i	0.825281	+	0.564722i	$0.191017\pi$
$332$	−72.9891	+	70.7750i	−0.219847	+	0.213178i
$333$	−73.3991	+	134.197i	−0.220418	+	0.402994i
$334$	15.3291	−	9.16785i	0.0458954	−	0.0274487i
$335$	219.291	−	42.7426i	0.654599	−	0.127590i
$336$	−161.465	+	112.443i	−0.480551	+	0.334651i
$337$	3.41369	−	44.2461i	0.0101297	−	0.131294i	−0.989809	−	0.142404i	$-0.954517\pi$
$337$	3.41369	−	44.2461i	0.0101297	−	0.131294i	0.999938	+	0.0111098i	$0.00353642\pi$
$338$	249.119	−	213.432i	0.737039	−	0.631456i
$339$	29.5523	−	181.165i	0.0871751	−	0.534410i
$340$	−103.241	−	51.4078i	−0.303650	−	0.151200i
$341$	13.8879	−	48.8109i	0.0407270	−	0.143141i
$342$	−203.501	−	513.522i	−0.595032	−	1.50153i
$343$	−142.228	−	343.368i	−0.414658	−	1.00107i
$344$	33.6214	+	63.7844i	0.0977365	+	0.185420i
$345$	186.689	−	247.216i	0.541127	−	0.716568i
$346$	−272.114	+	343.540i	−0.786456	+	0.992889i
$347$	−251.060	+	152.788i	−0.723516	+	0.440311i	−0.832710	−	0.553709i	$-0.813212\pi$
$347$	−251.060	+	152.788i	−0.723516	+	0.440311i	0.109195	+	0.994020i	$0.465173\pi$
$348$	−25.0415	−	42.6120i	−0.0719583	−	0.122448i
$349$	220.352	+	131.786i	0.631382	+	0.377610i	0.792981	−	0.609246i	$-0.208528\pi$
$349$	220.352	+	131.786i	0.631382	+	0.377610i	−0.161599	+	0.986856i	$0.551665\pi$
$350$	−84.4374	−	30.4875i	−0.241250	−	0.0871072i
$351$	38.2844	+	147.410i	0.109072	+	0.419972i
$352$	−11.8752	−	118.237i	−0.0337365	−	0.335902i
$353$	242.892	−	83.4949i	0.688079	−	0.236529i	0.0412320	−	0.999150i	$-0.486872\pi$
$353$	242.892	−	83.4949i	0.688079	−	0.236529i	0.646847	+	0.762620i	$0.276087\pi$
$354$	72.9482	+	5.06341i	0.206068	+	0.0143034i
$355$	19.2341	+	33.3144i	0.0541805	+	0.0938434i
$356$	−228.874	−	132.141i	−0.642905	−	0.371182i
$357$	66.9639	−	99.3881i	0.187574	−	0.278398i
$358$	−15.7206	−	46.9038i	−0.0439122	−	0.131016i
$359$	220.092	−	141.009i	0.613069	−	0.392784i	−0.195909	−	0.980622i	$-0.562766\pi$
$359$	220.092	−	141.009i	0.613069	−	0.392784i	0.808979	+	0.587838i	$0.200021\pi$
$360$	120.955	+	32.4097i	0.335985	+	0.0900270i
$361$	40.2459	−	870.505i	0.111484	−	2.41137i
$362$	−526.178	−	119.488i	−1.45353	−	0.330077i
$363$	158.405	+	72.8778i	0.436377	+	0.200765i
$364$	79.6291	−	4.91135i	0.218761	−	0.0134927i
$365$	182.393	+	404.620i	0.499707	+	1.10855i
$366$	126.993	+	121.257i	0.346974	+	0.331303i
$367$	−369.437	+	497.128i	−1.00664	+	1.35457i	−0.0726184	+	0.997360i	$0.523136\pi$
$367$	−369.437	+	497.128i	−1.00664	+	1.35457i	−0.934023	+	0.357212i	$0.883727\pi$
$368$	−632.842	−	595.012i	−1.71968	−	1.61688i
$369$	130.920	+	72.9222i	0.354798	+	0.197621i
$370$	2.01524	+	261.715i	0.00544660	+	0.707338i
$371$	−74.5169	−	566.012i	−0.200854	−	1.52564i
$372$	32.4429	−	35.0424i	0.0872121	−	0.0941999i
$373$	−141.447	−	228.444i	−0.379214	−	0.612452i	0.603548	−	0.797327i	$-0.293753\pi$
$373$	−141.447	−	228.444i	−0.379214	−	0.612452i	−0.982762	+	0.184875i	$0.940812\pi$
$374$	51.6398	+	101.736i	0.138074	+	0.272021i
$375$	−76.5473	−	206.999i	−0.204126	−	0.551999i
$376$	−78.4643	−	47.7512i	−0.208682	−	0.126998i
$377$	1.30306	−	84.6078i	0.00345639	−	0.224424i
$378$	143.654	−	346.811i	0.380037	−	0.917491i
$379$	271.794	−	25.1854i	0.717134	−	0.0664523i	0.272489	−	0.962159i	$-0.412153\pi$
$379$	271.794	−	25.1854i	0.717134	−	0.0664523i	0.444645	+	0.895707i	$0.353330\pi$
$380$	−257.728	−	210.683i	−0.678231	−	0.554428i
$381$	−10.9504	+	15.7245i	−0.0287411	+	0.0412716i
$382$	−388.733	−	171.642i	−1.01763	−	0.449326i
$383$	18.3687	+	476.874i	0.0479600	+	1.24510i	0.805612	+	0.592443i	$0.201836\pi$
$383$	18.3687	+	476.874i	0.0479600	+	1.24510i	−0.757652	+	0.652658i	$0.773654\pi$
$384$	−76.7233	+	198.046i	−0.199800	+	0.515744i
$385$	−54.8415	−	82.7641i	−0.142445	−	0.214972i
$386$	172.762	−	35.0564i	0.447570	−	0.0908198i
$387$	−87.5600	−	49.6578i	−0.226253	−	0.128315i
$388$	−0.665216	+	86.3901i	−0.00171447	+	0.222655i
$389$	−370.871	+	45.9238i	−0.953397	+	0.118056i	−0.584482	−	0.811407i	$-0.698702\pi$
$389$	−370.871	+	45.9238i	−0.953397	+	0.118056i	−0.368915	+	0.929463i	$0.620271\pi$
$390$	74.3243	+	77.8399i	0.190575	+	0.199589i
$391$	490.340	+	198.696i	1.25407	+	0.508174i
$392$	−47.6850	−	31.5973i	−0.121646	−	0.0806052i
$393$	−85.5649	−	120.874i	−0.217722	−	0.307567i
$394$	−342.355	+	302.577i	−0.868920	+	0.767961i
$395$	0.205894	+	8.91159i	0.000521250	+	0.0225610i
$396$	32.2759	+	40.7478i	0.0815048	+	0.102899i
$397$	626.174	+	231.556i	1.57726	+	0.583264i	0.976378	−	0.216071i	$-0.0693241\pi$
$397$	626.174	+	231.556i	1.57726	+	0.583264i	0.600887	+	0.799334i	$0.294814\pi$
$398$	626.183	−	72.6473i	1.57332	−	0.182531i
$399$	252.005	−	236.941i	0.631591	−	0.593836i
$400$	−115.986	+	29.1716i	−0.289965	+	0.0729290i
$401$	−414.904	−	139.062i	−1.03467	−	0.346787i	−0.251017	−	0.967983i	$-0.580765\pi$
$401$	−414.904	−	139.062i	−1.03467	−	0.346787i	−0.783656	+	0.621195i	$0.786647\pi$
$402$	−126.608	−	164.999i	−0.314946	−	0.410446i
$403$	78.6367	−	22.3741i	0.195128	−	0.0555188i
$404$	40.9508	−	219.068i	0.101363	−	0.542247i
$405$	−66.8231	+	21.2580i	−0.164995	+	0.0524888i
$406$	−128.236	+	164.482i	−0.315851	+	0.405128i
$407$	53.8254	−	73.6065i	0.132249	−	0.180851i
$408$		−	90.1086i		−	0.220854i
$409$	272.633	+	304.881i	0.666584	+	0.745430i
$409$	272.633	+	304.881i	0.666584	+	0.745430i
$410$	256.420			0.625415
$411$	40.7750	+	29.8170i	0.0992091	+	0.0725476i
$412$	335.946	+	261.915i	0.815403	+	0.635716i
$413$	−32.9456	−	103.562i	−0.0797714	−	0.250757i
$414$	672.766	+	125.762i	1.62504	+	0.303773i
$415$	55.7825	+	196.055i	0.134416	+	0.472422i
$416$	151.883	−	116.544i	0.365103	−	0.280154i
$417$	94.2582	−	281.228i	0.226039	−	0.674409i
$418$	80.3212	+	319.356i	0.192156	+	0.764009i
$419$	−277.617	−	295.268i	−0.662571	−	0.704696i	0.306391	−	0.951906i	$-0.400878\pi$
$419$	−277.617	−	295.268i	−0.662571	−	0.704696i	−0.968962	+	0.247210i	$0.920486\pi$
$420$	−10.7670	−	92.8058i	−0.0256356	−	0.220966i
$421$	245.897	−	664.955i	0.584077	−	1.57946i	−0.213951	−	0.976844i	$-0.568633\pi$
$421$	245.897	−	664.955i	0.584077	−	1.57946i	0.798028	−	0.602620i	$-0.205877\pi$
$422$	−651.362	+	515.937i	−1.54351	+	1.22260i
$423$	128.198	−	2.96190i	0.303069	−	0.00700212i
$424$	−284.267	−	321.637i	−0.670440	−	0.758579i
$425$	59.4557	−	42.0878i	0.139896	−	0.0990301i
$426$	19.7800	−	29.8510i	0.0464319	−	0.0700727i
$427$	98.0042	−	241.854i	0.229518	−	0.566402i
$428$	19.7383	−	18.8468i	0.0461175	−	0.0440346i
$429$	−4.60803	−	37.2135i	−0.0107413	−	0.0867448i
$430$	−172.233	−	1.32622i	−0.400543	−	0.00308423i
$431$	−260.903	+	460.043i	−0.605344	+	1.06738i	0.384213	+	0.923245i	$0.374473\pi$
$431$	−260.903	+	460.043i	−0.605344	+	1.06738i	−0.989557	+	0.144140i	$0.953959\pi$
$432$	−99.4524	−	490.112i	−0.230214	−	1.13452i
$433$	−700.477	+	464.153i	−1.61773	+	1.07195i	−0.675300	+	0.737543i	$0.735986\pi$
$433$	−700.477	+	464.153i	−1.61773	+	1.07195i	−0.942430	+	0.334404i	$0.891465\pi$
$434$	−187.906	−	72.7953i	−0.432964	−	0.167731i
$435$	−99.0198	+	3.81414i	−0.227632	+	0.00876813i
$436$	−0.216408	+	0.490118i	−0.000496349	+	0.00112412i
$437$	1253.13	+	872.666i	2.86757	+	1.99695i
$438$	261.488	−	319.878i	0.597006	−	0.730316i
$439$	−7.61737	−	82.2045i	−0.0173516	−	0.187254i	−0.999998	−	0.00176742i	$-0.999437\pi$
$439$	−7.61737	−	82.2045i	−0.0173516	−	0.187254i	0.982647	−	0.185487i	$-0.0593861\pi$
$440$	−68.9691	−	28.5679i	−0.156748	−	0.0649272i
$441$	79.8509	+	1.22980i	0.181068	+	0.00278866i
$442$	−95.5555	+	157.016i	−0.216189	+	0.355239i
$443$	−389.967	+	144.208i	−0.880286	+	0.325525i	−0.746420	−	0.665475i	$-0.768229\pi$
$443$	−389.967	+	144.208i	−0.880286	+	0.325525i	−0.133865	+	0.991000i	$0.542739\pi$
$444$	76.5156	−	38.8383i	0.172332	−	0.0874737i
$445$	−450.496	+	278.936i	−1.01235	+	0.626822i
$446$	−19.1346	−	17.7152i	−0.0429028	−	0.0397202i
$447$	−385.286	+	50.7239i	−0.861938	+	0.113476i
$448$	9.97525	−	0.0768108i	0.0222662	−	0.000171453i
$449$	−327.362	+	587.727i	−0.729091	+	1.30897i	0.214130	+	0.976805i	$0.431308\pi$
$449$	−327.362	+	587.727i	−0.729091	+	1.30897i	−0.943221	+	0.332164i	$0.892221\pi$
$450$	64.5502	−	68.6541i	0.143445	−	0.152565i
$451$	−71.7070	−	53.2886i	−0.158996	−	0.118156i
$452$	168.776	−	176.759i	0.373398	−	0.391060i
$453$	155.801	−	70.2311i	0.343931	−	0.155036i
$454$	17.3092	+	280.639i	0.0381260	+	0.618148i
$455$	66.8538	−	145.311i	0.146931	−	0.319366i
$456$	57.5944	−	253.623i	0.126304	−	0.556191i
$457$	322.241	+	14.8981i	0.705122	+	0.0325998i	0.395772	−	0.918349i	$-0.370477\pi$
$457$	322.241	+	14.8981i	0.705122	+	0.0325998i	0.309350	+	0.950948i	$0.399889\pi$
$458$	291.098	−	1086.39i	0.635585	−	2.37204i
$459$	164.321	+	256.477i	0.357997	+	0.558773i
$460$	391.077	−	131.076i	0.850167	−	0.284947i
$461$	63.1995	+	42.5814i	0.137092	+	0.0923675i	0.625402	−	0.780303i	$-0.284935\pi$
$461$	63.1995	+	42.5814i	0.137092	+	0.0923675i	−0.488309	+	0.872671i	$0.662386\pi$
$462$	−46.2117	+	80.0410i	−0.100025	+	0.173249i
$463$	310.873	−	179.483i	0.671433	−	0.387652i	−0.125187	−	0.992133i	$-0.539953\pi$
$463$	310.873	−	179.483i	0.671433	−	0.387652i	0.796619	+	0.604481i	$0.206620\pi$
$464$	−19.2399	+	277.187i	−0.0414652	+	0.597387i
$465$	−31.1247	−	90.5436i	−0.0669348	−	0.194717i
$466$	−540.481	+	54.2835i	−1.15983	+	0.116488i
$467$	−31.0097	+	8.05363i	−0.0664020	+	0.0172455i	−0.284427	−	0.958698i	$-0.591803\pi$
$467$	−31.0097	+	8.05363i	−0.0664020	+	0.0172455i	0.218025	+	0.975943i	$0.430039\pi$
$468$	−28.4405	+	78.7681i	−0.0607703	+	0.168308i
$469$	−158.652	+	265.273i	−0.338277	+	0.565615i
$470$	189.169	−	111.167i	0.402486	−	0.236526i
$471$	163.304	+	268.340i	0.346719	+	0.569725i
$472$	−64.0537	−	50.7362i	−0.135707	−	0.107492i
$473$	47.8888	+	36.1640i	0.101245	+	0.0764566i
$474$	7.34058	−	3.86929i	0.0154865	−	0.00816305i
$475$	194.247	−	80.4599i	0.408942	−	0.169389i
$476$	148.338	−	58.7839i	0.311634	−	0.123496i
$477$	576.391	+	163.998i	1.20837	+	0.343810i
$478$	509.464	−	1023.14i	1.06582	−	2.14046i
$479$	−425.156	−	69.3530i	−0.887590	−	0.144787i	−0.299994	−	0.953941i	$-0.596985\pi$
$479$	−425.156	−	69.3530i	−0.887590	−	0.144787i	−0.587597	+	0.809154i	$0.699926\pi$
$480$	−145.865	−	170.254i	−0.303885	−	0.354697i
$481$	146.471	+	11.3006i	0.304514	+	0.0234940i
$482$	503.947	+	723.657i	1.04553	+	1.50136i
$483$	81.9945	+	420.672i	0.169761	+	0.870957i
$484$	119.159	+	199.240i	0.246197	+	0.411653i
$485$	151.964	+	83.1169i	0.313328	+	0.171375i
$486$	435.325	+	448.944i	0.895731	+	0.923753i
$487$	−681.433	−	490.296i	−1.39925	−	1.00677i	−0.995780	−	0.0917742i	$-0.970746\pi$
$487$	−681.433	−	490.296i	−1.39925	−	1.00677i	−0.403467	−	0.914994i	$-0.632195\pi$
$488$	−40.4990	−	191.986i	−0.0829897	−	0.393414i
$489$	−31.0327	+	14.2773i	−0.0634615	+	0.0291969i
$490$	120.388	−	64.6468i	0.245689	−	0.131932i
$491$	449.054	−	83.9428i	0.914571	−	0.170963i	0.294630	−	0.955611i	$-0.404804\pi$
$491$	449.054	−	83.9428i	0.914571	−	0.170963i	0.619941	+	0.784648i	$0.287157\pi$
$492$	−37.4731	−	75.2560i	−0.0761648	−	0.152959i
$493$	−50.0609	−	161.662i	−0.101543	−	0.327914i
$494$	−369.313	+	380.867i	−0.747598	+	0.770986i
$495$	102.589	−	18.3608i	0.207250	−	0.0370926i
$496$	−261.798	+	59.4507i	−0.527818	+	0.119860i
$497$	−52.0743	−	10.9849i	−0.104777	−	0.0221025i
$498$	140.227	−	127.833i	0.281579	−	0.256694i
$499$	−268.685	+	419.371i	−0.538446	+	0.840424i	−0.998882	−	0.0472695i	$-0.984948\pi$
$499$	−268.685	+	419.371i	−0.538446	+	0.840424i	0.460436	+	0.887693i	$0.347693\pi$
$500$	71.6726	−	284.969i	0.143345	−	0.569938i
$501$	−10.2570	+	5.71313i	−0.0204731	+	0.0114034i
$502$	−299.364	−	527.859i	−0.596342	−	1.05151i
$503$	−2.36667	+	2.05945i	−0.00470511	+	0.00409433i	−0.658796	−	0.752322i	$-0.728934\pi$
$503$	−2.36667	+	2.05945i	−0.00470511	+	0.00409433i	0.654091	+	0.756416i	$0.273051\pi$
$504$	−145.148	+	94.5784i	−0.287992	+	0.187656i
$505$	−348.108	−	280.121i	−0.689323	−	0.554696i
$506$	−387.857	−	126.683i	−0.766516	−	0.250362i
$507$	−167.996	+	135.186i	−0.331352	+	0.266638i
$508$	−23.8597	+	9.03264i	−0.0469680	+	0.0177808i
$509$	−1.77960	+	28.8532i	−0.00349627	+	0.0566860i	−0.999449	−	0.0331931i	$-0.989432\pi$
$509$	−1.77960	+	28.8532i	−0.00349627	+	0.0566860i	0.995953	+	0.0898791i	$0.0286481\pi$
$510$	189.638	+	101.833i	0.371839	+	0.199673i
$511$	−585.139	−	186.146i	−1.14509	−	0.364278i
$512$	−219.730	+	150.519i	−0.429161	+	0.293982i
$513$	298.572	+	826.918i	0.582012	+	1.61193i
$514$	−382.419	−	74.5384i	−0.744005	−	0.145016i
$515$	781.282	−	344.970i	1.51705	−	0.669844i
$516$	24.7808	+	50.7421i	0.0480249	+	0.0983375i
$517$	−76.0028	−	8.22497i	−0.147007	−	0.0159090i
$518$	−271.314	−	239.790i	−0.523771	−	0.462915i
$519$	185.737	−	220.203i	0.357875	−	0.424283i
$520$	−19.3625	−	118.698i	−0.0372356	−	0.228266i
$521$	−78.2096	+	252.563i	−0.150114	+	0.484765i	−0.999043	−	0.0437427i	$-0.986072\pi$
$521$	−78.2096	+	252.563i	−0.150114	+	0.484765i	0.848928	+	0.528508i	$0.177248\pi$
$522$	−105.056	−	192.075i	−0.201256	−	0.367961i
$523$	459.034	+	269.757i	0.877694	+	0.515789i	0.874953	−	0.484208i	$-0.160892\pi$
$523$	459.034	+	269.757i	0.877694	+	0.515789i	0.00274135	+	0.999996i	$0.499127\pi$
$524$	−3.03638	−	197.152i	−0.00579462	−	0.376245i
$525$	54.8596	+	21.7400i	0.104494	+	0.0414095i
$526$	4.99559	+	3.83325i	0.00949731	+	0.00728754i
$527$	135.607	−	91.3670i	0.257319	−	0.173372i
$528$	8.52600	+	122.834i	0.0161477	+	0.232639i
$529$	−1255.28	+	531.314i	−2.37293	+	1.00437i
$530$	998.156	−	234.764i	1.88331	−	0.442951i
$531$	113.506	+	11.4001i	0.213760	+	0.0214691i
$532$	455.090	−	70.6430i	0.855432	−	0.132788i
$533$	12.1763	−	143.414i	0.0228448	−	0.269070i
$534$	419.363	+	259.658i	0.785323	+	0.486252i
$535$	−14.5681	−	52.7411i	−0.0272301	−	0.0985815i
$536$	12.5207	+	232.070i	0.0233594	+	0.432966i
$537$	9.37922	+	31.1348i	0.0174660	+	0.0579791i
$538$	264.677	−	39.0008i	0.491965	−	0.0724923i
$539$	−47.1007	−	6.94040i	−0.0873853	−	0.0128764i
$540$	227.372	+	68.4949i	0.421059	+	0.126842i
$541$	−125.377	−	30.5090i	−0.231750	−	0.0563937i	0.118877	−	0.992909i	$-0.462071\pi$
$541$	−125.377	−	30.5090i	−0.231750	−	0.0563937i	−0.350627	+	0.936515i	$0.614031\pi$
$542$	−108.354	+	698.026i	−0.199915	+	1.28787i
$543$	343.289	+	89.1567i	0.632208	+	0.164193i
$544$	216.384	−	315.882i	0.397765	−	0.580665i
$545$	0.660455	+	0.847135i	0.00121184	+	0.00155438i
$546$	−148.828	+	4.58533i	−0.272578	+	0.00839804i
$547$	−223.886	+	115.818i	−0.409298	+	0.211734i	−0.651757	−	0.758428i	$-0.725968\pi$
$547$	−223.886	+	115.818i	−0.409298	+	0.211734i	0.242459	+	0.970162i	$0.422046\pi$
$548$	22.3526	+	63.4321i	0.0407895	+	0.115752i
$549$	192.197	+	195.180i	0.350085	+	0.355519i
$550$	−43.4951	+	35.5556i	−0.0790819	+	0.0646465i
$551$	−37.5745	−	487.017i	−0.0681933	−	0.883878i
$552$	227.867	+	227.867i	0.412803	+	0.412803i
$553$	−9.36528	−	8.02368i	−0.0169354	−	0.0145094i
$554$	−2.89955	+	2.44572i	−0.00523384	+	0.00441465i
$555$	3.97371	−	171.992i	0.00715984	−	0.309895i
$556$	315.141	−	237.984i	0.566801	−	0.428028i
$557$	−180.432	+	384.359i	−0.323936	+	0.690052i	−0.998855	−	0.0478389i	$-0.984767\pi$
$557$	−180.432	+	384.359i	−0.323936	+	0.690052i	0.674919	+	0.737891i	$0.264178\pi$
$558$	148.417	−	150.721i	0.265981	−	0.270109i
$559$	−8.92037	+	96.2661i	−0.0159577	+	0.172211i
$560$	−244.911	+	464.631i	−0.437341	+	0.829697i
$561$	−31.8688	−	67.8873i	−0.0568071	−	0.121011i
$562$	1119.97	+	394.661i	1.99282	+	0.702243i
$563$	−50.3964	−	361.280i	−0.0895140	−	0.641705i	−0.981756	−	0.190147i	$-0.939104\pi$
$563$	−50.3964	−	361.280i	−0.0895140	−	0.641705i	0.892242	−	0.451558i	$-0.149132\pi$
$564$	−60.2712	−	39.2726i	−0.106864	−	0.0696324i
$565$	−152.133	−	465.775i	−0.269262	−	0.824381i
$566$	−393.770	−	149.071i	−0.695707	−	0.263376i
$567$	39.8684	−	88.4439i	0.0703146	−	0.155986i
$568$	−37.0868	+	15.0283i	−0.0652936	+	0.0264584i
$569$	−633.052	−	128.458i	−1.11257	−	0.225760i	−0.392562	−	0.919726i	$-0.628411\pi$
$569$	−633.052	−	128.458i	−1.11257	−	0.225760i	−0.720008	+	0.693966i	$0.755862\pi$
$570$	468.674	+	407.834i	0.822234	+	0.715499i
$571$	−774.102	−	107.983i	−1.35570	−	0.189112i	−0.577119	−	0.816660i	$-0.695823\pi$
$571$	−774.102	−	107.983i	−1.35570	−	0.189112i	−0.778577	+	0.627549i	$0.784058\pi$
$572$	22.9392	−	44.3433i	0.0401035	−	0.0775233i
$573$	251.929	+	120.641i	0.439667	+	0.210542i
$574$	−236.971	+	264.000i	−0.412842	+	0.459930i
$575$	−43.9200	+	256.784i	−0.0763825	+	0.446580i
$576$	−4.08157	+	9.64309i	−0.00708606	+	0.0167415i
$577$	−106.676	+	310.328i	−0.184881	+	0.537830i	−0.999086	−	0.0427477i	$-0.986389\pi$
$577$	−106.676	+	310.328i	−0.184881	+	0.537830i	0.814205	+	0.580577i	$0.197173\pi$
$578$	80.2527	−	341.213i	0.138845	−	0.590335i
$579$	−114.217	+	19.5355i	−0.197266	+	0.0337401i
$580$	−111.635	−	70.3164i	−0.192474	−	0.121235i
$581$	−253.402	−	123.753i	−0.436148	−	0.213001i
$582$	6.20616	−	161.120i	0.0106635	−	0.276838i
$583$	−327.919	−	141.783i	−0.562468	−	0.243196i
$584$	−443.077	+	129.762i	−0.758694	+	0.222196i
$585$	112.156	+	124.948i	0.191720	+	0.213587i
$586$	−117.905	+	74.2658i	−0.201204	+	0.126734i
$587$	602.199	−	65.1695i	1.02589	−	0.111021i	0.420781	−	0.907162i	$-0.361756\pi$
$587$	602.199	−	65.1695i	1.02589	−	0.111021i	0.605111	+	0.796141i	$0.293129\pi$
$588$	−36.5664	−	25.8848i	−0.0621877	−	0.0440218i
$589$	440.084	−	170.490i	0.747172	−	0.289456i
$590$	179.165	−	77.4661i	0.303670	−	0.131299i
$591$	231.057	−	191.868i	0.390960	−	0.324649i
$592$	−478.262	−	62.9644i	−0.807875	−	0.106359i
$593$	−573.675	−	71.0363i	−0.967411	−	0.119791i	−0.376402	−	0.926456i	$-0.622839\pi$
$593$	−573.675	−	71.0363i	−0.967411	−	0.119791i	−0.591009	+	0.806665i	$0.701270\pi$
$594$	−140.118	−	188.547i	−0.235888	−	0.317420i
$595$	36.8668	−	317.773i	0.0619610	−	0.534073i
$596$	−461.373	−	234.187i	−0.774115	−	0.392931i
$597$	−412.883	+	35.0550i	−0.691596	+	0.0587185i
$598$	−155.421	−	638.704i	−0.259902	−	1.06807i
$599$	1008.74	+	54.4238i	1.68404	+	0.0908578i	0.870981	−	0.491317i	$-0.163485\pi$
$599$	1008.74	+	54.4238i	1.68404	+	0.0908578i	0.813063	+	0.582175i	$0.197798\pi$
$600$	43.3422	−	9.49208i	0.0722369	−	0.0158201i
$601$	283.450	+	1057.85i	0.471631	+	1.76015i	0.633911	+	0.773406i	$0.281449\pi$
$601$	283.450	+	1057.85i	0.471631	+	1.76015i	−0.162280	+	0.986745i	$0.551885\pi$
$602$	160.535	−	176.099i	0.266670	−	0.292523i
$603$	−189.496	−	263.370i	−0.314256	−	0.436766i
$604$	223.979	+	40.0865i	0.370826	+	0.0663684i
$605$	464.951	−	21.4960i	0.768514	−	0.0355306i
$606$	−88.9832	+	406.310i	−0.146837	+	0.670478i
$607$	275.320	+	76.0486i	0.453574	+	0.125286i	0.485562	−	0.874202i	$-0.338615\pi$
$607$	275.320	+	76.0486i	0.453574	+	0.125286i	−0.0319876	+	0.999488i	$0.510184\pi$
$608$	810.945	−	750.788i	1.33379	−	1.23485i
$609$	87.5824	−	105.471i	0.143813	−	0.173188i
$610$	449.812	+	131.735i	0.737397	+	0.215959i
$611$	−53.1924	−	111.080i	−0.0870580	−	0.181800i
$612$	−5.15788	+	167.411i	−0.00842790	+	0.273547i
$613$	466.250	+	637.599i	0.760603	+	1.04013i	0.997642	+	0.0686281i	$0.0218622\pi$
$613$	466.250	+	637.599i	0.760603	+	1.04013i	−0.237039	+	0.971500i	$0.576177\pi$
$614$	−178.076	+	130.219i	−0.290025	+	0.212084i
$615$	−168.472	−	5.19057i	−0.273938	−	0.00843995i
$616$	93.1503	−	44.6066i	0.151218	−	0.0724134i
$617$	−234.740	+	801.527i	−0.380454	+	1.29907i	0.516248	+	0.856439i	$0.327328\pi$
$617$	−234.740	+	801.527i	−0.380454	+	1.29907i	−0.896703	+	0.442633i	$0.854044\pi$
$618$	−611.643	−	507.902i	−0.989713	−	0.821847i
$619$	−383.838	−	414.593i	−0.620094	−	0.669778i	0.342878	−	0.939380i	$-0.388598\pi$
$619$	−383.838	−	414.593i	−0.620094	−	0.669778i	−0.962972	+	0.269601i	$0.913108\pi$
$620$	33.9402	−	122.874i	0.0547423	−	0.198184i
$621$	−1064.12	−	233.045i	−1.71355	−	0.375274i
$622$	−64.2901	−	1390.57i	−0.103360	−	2.23565i
$623$	129.147	−	721.591i	0.207298	−	1.15825i
$624$	−161.019	+	115.854i	−0.258043	+	0.185664i
$625$	−324.724	−	296.025i	−0.519559	−	0.473641i
$626$	−171.557	+	45.9685i	−0.274053	+	0.0734322i
$627$	−46.3078	−	211.448i	−0.0738561	−	0.337237i
$628$	−22.5318	+	417.626i	−0.0358787	+	0.665010i
$629$	285.482	−	69.4689i	0.453867	−	0.110443i
$630$	−35.0102	−	412.356i	−0.0555718	−	0.654533i
$631$	385.920	−	760.304i	0.611601	−	1.20492i	−0.351603	−	0.936149i	$-0.614363\pi$
$631$	385.920	−	760.304i	0.611601	−	1.20492i	0.963205	−	0.268770i	$-0.0866170\pi$
$632$	−9.21086	−	1.06861i	−0.0145741	−	0.00169084i
$633$	438.399	−	325.794i	0.692574	−	0.514682i
$634$	−121.279	+	979.424i	−0.191292	+	1.54483i
$635$	−6.67639	+	50.7122i	−0.0105140	+	0.0798617i
$636$	−214.770	−	258.638i	−0.337689	−	0.406663i
$637$	−30.4399	−	70.4018i	−0.0477863	−	0.110521i
$638$	47.1477	+	121.702i	0.0738993	+	0.190756i
$639$	32.2775	−	45.5970i	0.0505125	−	0.0713569i
$640$	60.9981	+	563.653i	0.0953096	+	0.880708i
$641$	505.148	+	801.979i	0.788063	+	1.25114i	0.963780	+	0.266697i	$0.0859322\pi$
$641$	505.148	+	801.979i	0.788063	+	1.25114i	−0.175718	+	0.984441i	$0.556225\pi$
$642$	−37.9043	+	34.0236i	−0.0590410	+	0.0529963i
$643$	−49.0280	−	167.407i	−0.0762489	−	0.260354i	0.912696	−	0.408640i	$-0.133997\pi$
$643$	−49.0280	−	167.407i	−0.0762489	−	0.260354i	−0.988944	+	0.148286i	$0.952624\pi$
$644$	−226.464	+	523.770i	−0.351652	+	0.813308i
$645$	113.133	+	4.35777i	0.175400	+	0.00675624i
$646$	−465.619	+	953.418i	−0.720772	+	1.47588i
$647$	−184.162	+	292.378i	−0.284641	+	0.451899i	−0.957733	−	0.287660i	$-0.907123\pi$
$647$	−184.162	+	292.378i	−0.284641	+	0.451899i	0.673092	+	0.739559i	$0.264966\pi$
$648$	−12.2978	−	71.9005i	−0.0189780	−	0.110957i
$649$	−66.2017	−	15.5705i	−0.102006	−	0.0239915i
$650$	−85.5903	−	29.4220i	−0.131677	−	0.0452646i
$651$	121.984	+	51.6313i	0.187379	+	0.0793108i
$652$	−44.8296	−	7.66761i	−0.0687571	−	0.0117601i
$653$	−274.064	−	246.005i	−0.419700	−	0.376731i	0.431027	−	0.902339i	$-0.358151\pi$
$653$	−274.064	−	246.005i	−0.419700	−	0.376731i	−0.850727	+	0.525608i	$0.823838\pi$
$654$	0.431872	−	0.901861i	0.000660354	−	0.00137899i
$655$	−351.120	−	181.638i	−0.536061	−	0.277310i
$656$	−65.2948	+	468.083i	−0.0995347	+	0.713541i
$657$	423.112	−	486.231i	0.644007	−	0.740077i
$658$	−60.3672	+	297.496i	−0.0917434	+	0.452121i
$659$	143.234	+	353.472i	0.217351	+	0.536377i	0.995823	−	0.0913026i	$-0.0291030\pi$
$659$	143.234	+	353.472i	0.217351	+	0.536377i	−0.778472	+	0.627679i	$0.784005\pi$
$660$	−53.3009	−	24.0267i	−0.0807589	−	0.0364042i
$661$	−268.216	+	708.493i	−0.405773	+	1.07185i	0.563555	+	0.826079i	$0.309433\pi$
$661$	−268.216	+	708.493i	−0.405773	+	1.07185i	−0.969328	+	0.245771i	$0.920959\pi$
$662$	−36.9037	+	12.0536i	−0.0557457	+	0.0182078i
$663$	65.9598	−	101.228i	0.0994869	−	0.152681i
$664$	−210.005	+	29.2945i	−0.316273	+	0.0441182i
$665$	306.877	−	870.853i	0.461469	−	1.30955i
$666$	344.062	−	161.515i	0.516609	−	0.242515i
$667$	535.406	+	282.217i	0.802707	+	0.423114i
$668$	−15.5653	−	1.44234i	−0.0233013	−	0.00215918i
$669$	12.2132	+	12.0265i	0.0182558	+	0.0179768i
$670$	−502.551	−	235.916i	−0.750077	−	0.352113i
$671$	−98.4115	−	130.318i	−0.146664	−	0.194214i
$672$	310.088	+	7.16429i	0.461441	+	0.0106612i
$673$	380.496	+	451.101i	0.565373	+	0.670284i	0.969691	−	0.244334i	$-0.0785694\pi$
$673$	380.496	+	451.101i	0.565373	+	0.670284i	−0.404318	+	0.914619i	$0.632491\pi$
$674$	−71.7463	+	83.7426i	−0.106449	+	0.124247i
$675$	−106.056	+	106.056i	−0.157119	+	0.157119i
$676$	−286.248	+	22.0847i	−0.423444	+	0.0326697i
$677$	541.117	+	661.947i	0.799286	+	0.977765i	0.999998	−	0.00188542i	$-0.000600149\pi$
$677$	541.117	+	661.947i	0.799286	+	0.977765i	−0.200712	+	0.979650i	$0.564326\pi$
$678$	−325.005	+	320.038i	−0.479358	+	0.472032i
$679$	−226.012	+	79.6435i	−0.332860	+	0.117295i
$680$	−110.518	−	213.641i	−0.162527	−	0.314178i
$681$	−5.69162	−	184.735i	−0.00835773	−	0.271270i
$682$	−99.4512	+	77.5355i	−0.145823	+	0.113688i
$683$	−915.318	−	627.007i	−1.34014	−	0.918020i	−0.340391	−	0.940284i	$-0.610560\pi$
$683$	−915.318	−	627.007i	−1.34014	−	0.918020i	−0.999752	+	0.0222641i	$0.992913\pi$
$684$	−121.521	+	467.905i	−0.177662	+	0.684071i
$685$	133.245	+	20.6835i	0.194518	+	0.0301948i
$686$	−218.360	+	897.350i	−0.318309	+	1.30809i
$687$	−213.247	+	707.885i	−0.310404	+	1.03040i
$688$	46.2784	−	314.066i	0.0672652	−	0.456492i
$689$	−83.9040	−	569.410i	−0.121777	−	0.826430i
$690$	−737.074	+	222.040i	−1.06822	+	0.321798i
$691$	207.157	−	11.1765i	0.299792	−	0.0161744i	0.0966329	−	0.995320i	$-0.469193\pi$
$691$	207.157	−	11.1765i	0.299792	−	0.0161744i	0.203160	+	0.979146i	$0.434879\pi$
$692$	369.706	−	102.120i	0.534257	−	0.147572i
$693$	−75.9042	+	122.590i	−0.109530	+	0.176897i
$694$	727.686	+	61.7827i	1.04854	+	0.0890241i
$695$	−121.448	−	782.380i	−0.174745	−	1.12573i
$696$	10.3011	−	102.564i	0.0148004	−	0.147363i
$697$	−65.9057	−	280.214i	−0.0945563	−	0.402029i
$698$	−248.687	−	587.546i	−0.356285	−	0.841756i
$699$	356.204	−	24.7244i	0.509590	−	0.0353712i
$700$	43.9009	+	65.1579i	0.0627156	+	0.0930828i
$701$	299.928	−	390.873i	0.427857	−	0.557594i	−0.528825	−	0.848731i	$-0.677367\pi$
$701$	299.928	−	390.873i	0.427857	−	0.557594i	0.956681	+	0.291137i	$0.0940337\pi$
$702$	139.426	−	351.833i	0.198612	−	0.501186i
$703$	847.932	−	13.0592i	1.20616	−	0.0185763i
$704$	3.16281	−	5.38201i	0.00449262	−	0.00764490i
$705$	−126.537	+	69.2095i	−0.179485	+	0.0981695i
$706$	−609.665	−	188.791i	−0.863548	−	0.267410i
$707$	610.106	−	99.5228i	0.862950	−	0.140768i
$708$	−48.9184	−	41.2618i	−0.0690937	−	0.0582794i
$709$	−192.076	+	217.327i	−0.270911	+	0.306526i	−0.868909	−	0.494971i	$-0.835179\pi$
$709$	−192.076	+	217.327i	−0.270911	+	0.306526i	0.597999	+	0.801497i	$0.295963\pi$
$710$	10.2846	−	95.0347i	0.0144853	−	0.133852i
$711$	11.6322	−	5.68081i	0.0163604	−	0.00798988i
$712$	−222.633	−	504.217i	−0.312687	−	0.708170i
$713$	−111.875	+	573.974i	−0.156907	+	0.805012i
$714$	−280.097	+	101.134i	−0.392293	+	0.141644i
$715$	−56.5678	−	82.5788i	−0.0791158	−	0.115495i
$716$	−13.1246	+	41.2563i	−0.0183304	+	0.0576205i
$717$	−355.437	+	661.907i	−0.495728	+	0.923162i
$718$	−648.293	−	39.9854i	−0.902916	−	0.0556899i
$719$	−476.242	−	1257.99i	−0.662368	−	1.74964i	−0.661840	−	0.749645i	$-0.730224\pi$
$719$	−476.242	−	1257.99i	−0.662368	−	1.74964i	−0.000527200	−	1.00000i	$-0.500168\pi$
$720$	−345.641	−	429.530i	−0.480057	−	0.596569i
$721$	−366.856	+	1123.18i	−0.508816	+	1.55781i
$722$	−1357.56	+	1687.05i	−1.88028	+	2.33663i
$723$	−316.453	−	485.655i	−0.437694	−	0.671723i
$724$	309.991	+	356.234i	0.428164	+	0.492036i
$725$	72.4857	−	41.1088i	0.0999803	−	0.0567017i
$726$	−210.836	−	378.524i	−0.290408	−	0.521383i
$727$	−68.2167	−	17.1572i	−0.0938331	−	0.0236000i	0.196712	−	0.980461i	$-0.436974\pi$
$727$	−68.2167	−	17.1572i	−0.0938331	−	0.0236000i	−0.290545	+	0.956861i	$0.593836\pi$
$728$	140.101	+	89.7604i	0.192446	+	0.123297i
$729$	−179.414	−	196.808i	−0.246110	−	0.269970i
$730$	227.639	−	1079.12i	0.311834	−	1.47825i
$731$	42.8186	+	188.556i	0.0585753	+	0.257943i
$732$	−27.0727	−	151.266i	−0.0369846	−	0.206647i
$733$	−500.995	−	485.797i	−0.683486	−	0.662752i	0.270460	−	0.962731i	$-0.412824\pi$
$733$	−500.995	−	485.797i	−0.683486	−	0.662752i	−0.953946	+	0.299979i	$0.903020\pi$
$734$	1470.20	−	455.268i	2.00300	−	0.620256i
$735$	−80.4052	+	40.0370i	−0.109395	+	0.0544721i
$736$	251.611	+	1346.00i	0.341862	+	1.82880i
$737$	91.5092	+	170.412i	0.124165	+	0.231224i
$738$	−155.642	−	338.299i	−0.210897	−	0.458400i
$739$	−831.480	+	175.399i	−1.12514	+	0.237346i	−0.731449	−	0.681896i	$-0.761156\pi$
$739$	−831.480	+	175.399i	−1.12514	+	0.237346i	−0.393693	+	0.919242i	$0.628803\pi$
$740$	133.778	−	185.929i	0.180780	−	0.251256i
$741$	250.354	−	242.760i	0.337860	−	0.327611i
$742$	−680.744	+	1244.62i	−0.917445	+	1.67738i
$743$	257.521	−	154.015i	0.346596	−	0.207288i	−0.329406	−	0.944188i	$-0.606848\pi$
$743$	257.521	−	154.015i	0.346596	−	0.207288i	0.676002	+	0.736900i	$0.263711\pi$
$744$	97.7568	−	19.0541i	0.131393	−	0.0256103i
$745$	−851.273	+	592.817i	−1.14265	+	0.795728i
$746$	−51.3595	+	665.689i	−0.0688465	+	0.892344i
$747$	224.800	−	192.597i	0.300937	−	0.257827i
$748$	16.0755	−	98.5480i	0.0214913	−	0.131749i
$749$	67.7632	+	33.7421i	0.0904716	+	0.0450495i
$750$	−150.081	+	527.481i	−0.200108	+	0.703308i
$751$	−42.2539	−	106.625i	−0.0562635	−	0.141978i	0.898817	−	0.438324i	$-0.144428\pi$
$751$	−42.2539	−	106.625i	−0.0562635	−	0.141978i	−0.955081	+	0.296346i	$0.904232\pi$
$752$	154.761	+	373.626i	0.205799	+	0.496843i
$753$	186.002	+	352.871i	0.247014	+	0.468621i
$754$	−126.714	+	167.797i	−0.168056	+	0.222542i
$755$	283.253	−	357.603i	0.375170	−	0.473646i
$756$	−280.646	+	170.793i	−0.371225	+	0.225917i
$757$	−485.699	−	826.493i	−0.641611	−	1.09180i	−0.988110	−	0.153750i	$-0.950865\pi$
$757$	−485.699	−	826.493i	−0.641611	−	1.09180i	0.346499	−	0.938050i	$-0.387370\pi$
$758$	−582.111	−	348.143i	−0.767956	−	0.459291i
$759$	252.264	+	91.0840i	0.332363	+	0.120005i
$760$	−174.517	−	671.962i	−0.229628	−	0.884160i
$761$	45.3256	+	451.291i	0.0595606	+	0.593024i	0.979567	+	0.201120i	$0.0644581\pi$
$761$	45.3256	+	451.291i	0.0595606	+	0.593024i	−0.920006	+	0.391904i	$0.871816\pi$
$762$	45.0287	−	15.4788i	0.0590928	−	0.0203133i
$763$	−1.48254	−	0.102904i	−0.00194304	−	0.000134868i
$764$	185.950	+	322.074i	0.243390	+	0.421563i
$765$	290.814	+	167.902i	0.380149	+	0.219479i
$766$	662.622	−	983.465i	0.865041	−	1.28390i
$767$	−34.8186	−	103.884i	−0.0453958	−	0.135443i
$768$	435.284	−	278.880i	0.566776	−	0.363124i
$769$	571.416	+	153.110i	0.743063	+	0.199103i	0.610439	−	0.792063i	$-0.290993\pi$
$769$	571.416	+	153.110i	0.743063	+	0.199103i	0.132624	+	0.991166i	$0.457660\pi$
$770$	−11.3941	+	246.450i	−0.0147975	+	0.320065i
$771$	249.746	+	56.7140i	0.323925	+	0.0735590i
$772$	−140.157	−	64.4826i	−0.181551	−	0.0835267i
$773$	458.147	−	28.2575i	0.592686	−	0.0365556i	0.237558	−	0.971373i	$-0.423653\pi$
$773$	458.147	−	28.2575i	0.592686	−	0.0365556i	0.355128	+	0.934818i	$0.384437\pi$
$774$	102.793	+	228.035i	0.132807	+	0.294619i
$775$	58.2324	+	55.6023i	0.0751385	+	0.0717449i
$776$	−107.472	+	144.618i	−0.138495	+	0.186363i
$777$	173.403	+	163.038i	0.223170	+	0.209830i
$778$	811.261	+	451.869i	1.04275	+	0.580809i
$779$	−6.39747	−	830.826i	−0.00821242	−	1.06653i
$780$	−12.2944	−	93.3855i	−0.0157621	−	0.119725i
$781$	−22.6259	+	24.4388i	−0.0289704	+	0.0312917i
$782$	−692.091	−	1117.77i	−0.885027	−	1.42937i
$783$	157.715	+	310.715i	0.201424	+	0.396826i
$784$	87.3541	+	236.223i	0.111421	+	0.301305i
$785$	716.303	+	435.922i	0.912488	+	0.555315i
$786$	−5.66695	+	367.956i	−0.00720986	+	0.468137i
$787$	119.467	−	288.418i	0.151800	−	0.366478i	−0.829626	−	0.558320i	$-0.811446\pi$
$787$	119.467	−	288.418i	0.151800	−	0.366478i	0.981426	+	0.191842i	$0.0614461\pi$
$788$	398.166	−	36.8955i	0.505287	−	0.0468217i
$789$	−3.20459	−	2.61963i	−0.00406158	−	0.00332019i
$790$	12.6583	−	18.1770i	0.0160232	−	0.0230089i
$791$	620.137	+	273.817i	0.783991	+	0.346166i
$792$	4.17284	+	108.332i	0.00526874	+	0.136783i
$793$	95.0381	−	245.322i	0.119846	−	0.309359i
$794$	−916.352	−	1382.91i	−1.15410	−	1.74171i
$795$	−660.557	+	134.039i	−0.830889	+	0.168602i
$796$	−479.895	−	272.162i	−0.602883	−	0.341913i
$797$	1.14601	−	148.830i	0.00143791	−	0.186738i	−0.994883	−	0.101035i	$-0.967785\pi$
$797$	1.14601	−	148.830i	0.00143791	−	0.186738i	0.996321	−	0.0857027i	$-0.0273135\pi$
$798$	−853.015	+	105.626i	−1.06894	+	0.132364i
$799$	−170.103	−	178.150i	−0.212895	−	0.222966i
$800$	174.733	+	70.8054i	0.218416	+	0.0885068i
$801$	641.447	+	425.038i	0.800808	+	0.530635i
$802$	628.250	+	887.503i	0.783355	+	1.10661i
$803$	−287.919	+	254.466i	−0.358554	+	0.316894i
$804$	4.20422	+	181.969i	0.00522913	+	0.226330i
$805$	710.358	+	896.816i	0.882433	+	1.11406i
$806$	−190.549	−	70.4639i	−0.236413	−	0.0874241i
$807$	−174.687	+	20.2665i	−0.216464	+	0.0251133i
$808$	338.627	−	318.385i	0.419093	−	0.394040i
$809$	400.630	−	100.762i	0.495216	−	0.124552i	0.0117782	−	0.999931i	$-0.496251\pi$
$809$	400.630	−	100.762i	0.495216	−	0.124552i	0.483438	+	0.875379i	$0.339388\pi$
$810$	165.216	+	55.3748i	0.203970	+	0.0683639i
$811$	219.187	+	285.650i	0.270268	+	0.352220i	0.908694	−	0.417463i	$-0.137081\pi$
$811$	219.187	+	285.650i	0.270268	+	0.352220i	−0.638426	+	0.769683i	$0.720414\pi$
$812$	175.563	−	49.9519i	0.216210	−	0.0615171i
$813$	85.3199	−	456.421i	0.104944	−	0.561403i
$814$	−215.928	+	68.6917i	−0.265268	+	0.0843878i
$815$	−56.0651	+	71.9121i	−0.0687915	+	0.0882356i
$816$	−234.181	+	320.244i	−0.286987	+	0.392456i
$817$			558.086i			0.683092i
$818$	−99.6609	−	1011.43i	−0.121835	−	1.23646i
$819$	−232.291			−0.283627
$820$	−181.148	−	132.466i	−0.220912	−	0.161544i
$821$	−448.212	−	349.441i	−0.545934	−	0.425628i	0.303881	−	0.952710i	$-0.401718\pi$
$821$	−448.212	−	349.441i	−0.545934	−	0.425628i	−0.849815	+	0.527082i	$0.823286\pi$
$822$	−38.0523	−	119.615i	−0.0462924	−	0.145517i
$823$	−732.298	−	136.890i	−0.889791	−	0.166331i	−0.281044	−	0.959695i	$-0.590681\pi$
$823$	−732.298	−	136.890i	−0.889791	−	0.166331i	−0.608747	+	0.793364i	$0.708328\pi$
$824$	243.127	+	854.503i	0.295057	+	1.03702i
$825$	29.2967	−	22.4801i	0.0355111	−	0.0272486i
$826$	−85.8198	+	256.051i	−0.103898	+	0.309990i
$827$	31.5492	+	125.439i	0.0381490	+	0.151680i	0.985901	−	0.167327i	$-0.0535135\pi$
$827$	31.5492	+	125.439i	0.0381490	+	0.151680i	−0.947752	+	0.319007i	$0.896651\pi$
$828$	−410.306	−	436.393i	−0.495539	−	0.527045i
$829$	11.7345	+	101.146i	0.0141550	+	0.122009i	0.998540	−	0.0540210i	$-0.0172038\pi$
$829$	11.7345	+	101.146i	0.0141550	+	0.122009i	−0.984385	+	0.176030i	$0.943674\pi$
$830$	175.679	−	475.072i	0.211661	−	0.572376i
$831$	1.95456	−	1.54818i	0.00235205	−	0.00186303i
$832$	10.0543	−	0.232296i	0.0120845	−	0.000279202i
$833$	−101.588	−	114.943i	−0.121954	−	0.137987i
$834$	−601.563	+	425.838i	−0.721299	+	0.510597i
$835$	−17.3115	+	26.1257i	−0.0207323	+	0.0312882i
$836$	108.235	−	267.102i	0.129468	−	0.319500i
$837$	−243.499	+	232.502i	−0.290919	+	0.277780i
$838$	123.759	+	999.455i	0.147684	+	1.19267i
$839$	−342.683	−	2.63870i	−0.408442	−	0.00314506i	−0.196683	−	0.980467i	$-0.563017\pi$
$839$	−342.683	−	2.63870i	−0.408442	−	0.00314506i	−0.211759	+	0.977322i	$0.567919\pi$
$840$	96.1240	−	169.492i	0.114433	−	0.201777i
$841$	128.745	+	634.471i	0.153086	+	0.754425i
$842$	−1468.56	+	973.105i	−1.74414	+	1.15571i
$843$	−727.846	−	281.969i	−0.863400	−	0.334483i
$844$	726.685	−	27.9911i	0.861001	−	0.0331649i
$845$	−232.500	+	526.562i	−0.275148	+	0.623150i
$846$	−261.487	−	182.097i	−0.309086	−	0.215244i
$847$	−407.554	+	498.560i	−0.481174	+	0.588619i
$848$	174.381	+	1881.87i	0.205637	+	2.21918i
$849$	255.696	+	105.913i	0.301173	+	0.124750i
$850$	−180.991	−	2.78747i	−0.212930	−	0.00327937i
$851$	−546.256	+	897.603i	−0.641899	+	1.05476i
$852$	−29.3944	+	10.8699i	−0.0345005	+	0.0127581i
$853$	357.780	−	181.605i	0.419437	−	0.212901i	−0.230203	−	0.973143i	$-0.573939\pi$
$853$	357.780	−	181.605i	0.419437	−	0.212901i	0.649640	+	0.760242i	$0.274919\pi$
$854$	−551.323	+	341.365i	−0.645578	+	0.399725i
$855$	711.220	+	658.461i	0.831836	+	0.770130i
$856$	56.4308	−	7.42926i	0.0659239	−	0.00867904i
$857$	−306.178	+	2.35761i	−0.357267	+	0.00275101i	−0.186210	−	0.982510i	$-0.559620\pi$
$857$	−306.178	+	2.35761i	−0.357267	+	0.00275101i	−0.171058	+	0.985261i	$0.554718\pi$
$858$	−45.3409	+	81.4026i	−0.0528449	+	0.0948748i
$859$	58.4002	−	62.1132i	0.0679862	−	0.0723087i	−0.693656	−	0.720306i	$-0.744001\pi$
$859$	58.4002	−	62.1132i	0.0679862	−	0.0723087i	0.761642	+	0.647998i	$0.224393\pi$
$860$	120.989	+	89.9121i	0.140685	+	0.104549i
$861$	161.038	−	168.655i	0.187036	−	0.195883i
$862$	1198.10	−	540.076i	1.38991	−	0.626539i
$863$	−0.612035	−	9.92309i	−0.000709195	−	0.0114984i	0.997732	−	0.0673091i	$-0.0214414\pi$
$863$	−0.612035	−	9.92309i	−0.000709195	−	0.0114984i	−0.998441	+	0.0558107i	$0.982226\pi$
$864$	−329.501	+	716.194i	−0.381367	+	0.828928i
$865$	170.290	−	749.892i	0.196867	−	0.866927i
$866$	2085.84	+	96.4341i	2.40859	+	0.111356i
$867$	−59.6343	+	222.558i	−0.0687823	+	0.256699i
$868$	95.1403	+	148.498i	0.109609	+	0.171080i
$869$	−7.31735	+	2.45253i	−0.00842043	+	0.00282224i
$870$	204.210	+	137.589i	0.234724	+	0.158148i
$871$	−155.810	+	269.871i	−0.178887	+	0.309841i
$872$	−0.967689	+	0.558695i	−0.00110974	+	0.000640706i
$873$	17.4179	−	250.939i	0.0199518	−	0.287445i
$874$	−1233.55	−	3588.47i	−1.41138	−	4.10580i
$875$	810.978	−	81.4509i	0.926832	−	0.0930868i
$876$	−349.976	+	90.8934i	−0.399516	+	0.103760i
$877$	203.488	−	563.574i	0.232027	−	0.642616i	−0.767971	−	0.640485i	$-0.778733\pi$
$877$	203.488	−	563.574i	0.232027	−	0.642616i	0.999998	−	0.00213091i	$-0.000678291\pi$
$878$	−105.296	+	176.060i	−0.119927	+	0.200524i
$879$	78.9690	−	46.4072i	0.0898396	−	0.0527954i
$880$	170.870	+	280.772i	0.194171	+	0.319059i
$881$	1167.49	+	924.757i	1.32519	+	1.04967i	0.994369	+	0.105974i	$0.0337961\pi$
$881$	1167.49	+	924.757i	1.32519	+	1.04967i	0.330821	+	0.943694i	$0.392675\pi$
$882$	−158.363	−	119.590i	−0.179549	−	0.135589i
$883$	−313.039	+	165.005i	−0.354517	+	0.186869i	−0.634097	−	0.773253i	$-0.718628\pi$
$883$	−313.039	+	165.005i	−0.354517	+	0.186869i	0.279580	+	0.960122i	$0.409805\pi$
$884$	148.619	−	61.5599i	0.168121	−	0.0696379i
$885$	−119.282	+	47.2698i	−0.134782	+	0.0534122i
$886$	993.723	+	282.738i	1.12158	+	0.319118i
$887$	−665.742	+	1336.99i	−0.750554	+	1.50732i	0.107752	+	0.994178i	$0.465635\pi$
$887$	−665.742	+	1336.99i	−0.750554	+	1.50732i	−0.858306	+	0.513138i	$0.828483\pi$
$888$	176.626	+	28.8119i	0.198903	+	0.0324458i
$889$	−46.0412	−	53.7395i	−0.0517899	−	0.0604494i
$890$	1312.75	+	101.282i	1.47500	+	0.113800i
$891$	−34.6942	−	49.8201i	−0.0389385	−	0.0559148i
$892$	4.36601	+	22.3998i	0.00489463	+	0.0251118i
$893$	−364.913	−	610.151i	−0.408637	−	0.683260i
$894$	847.215	+	463.385i	0.947668	+	0.518328i
$895$	60.4243	+	62.3146i	0.0675132	+	0.0696253i
$896$	−636.685	−	458.100i	−0.710586	−	0.511272i
$897$	89.1854	+	422.785i	0.0994263	+	0.471332i
$898$	1518.69	−	698.709i	1.69119	−	0.778073i
$899$	164.797	−	88.4944i	0.183312	−	0.0984365i
$900$	−81.0678	+	15.1542i	−0.0900754	+	0.0168380i
$901$	−513.097	−	1030.44i	−0.569475	−	1.14366i
$902$	65.6690	+	212.065i	0.0728038	+	0.235106i
$903$	−109.039	+	112.450i	−0.120752	+	0.124529i
$904$	501.734	−	89.7977i	0.555016	−	0.0993338i
$905$	923.264	−	209.661i	1.02018	−	0.231669i
$906$	−415.521	−	87.6531i	−0.458632	−	0.0967474i
$907$	−671.839	+	612.462i	−0.740726	+	0.675261i	−0.953348	−	0.301873i	$-0.902388\pi$
$907$	−671.839	+	612.462i	−0.740726	+	0.675261i	0.212622	+	0.977135i	$0.431800\pi$
$908$	132.749	−	207.199i	0.146199	−	0.228193i
$909$	−158.273	+	629.293i	−0.174118	+	0.692291i
$910$	−347.236	+	193.409i	−0.381578	+	0.212537i
$911$	89.3285	+	157.510i	0.0980555	+	0.172898i	0.914571	−	0.404425i	$-0.132529\pi$
$911$	89.3285	+	157.510i	0.0980555	+	0.172898i	−0.816515	+	0.577324i	$0.804097\pi$
$912$	−863.825	+	751.690i	−0.947176	+	0.824222i
$913$	−147.856	+	96.3430i	−0.161945	+	0.105523i
$914$	−624.505	−	502.537i	−0.683266	−	0.549822i
$915$	−292.867	−	95.6572i	−0.320073	−	0.104543i
$916$	−766.872	+	617.100i	−0.837197	+	0.673690i
$917$	511.495	−	193.638i	0.557792	−	0.211165i
$918$	46.5957	−	755.468i	0.0507578	−	0.822950i
$919$	904.585	+	485.752i	0.984314	+	0.528566i	0.884550	−	0.466445i	$-0.154466\pi$
$919$	904.585	+	485.752i	0.984314	+	0.528566i	0.0997644	+	0.995011i	$0.468191\pi$
$920$	819.736	+	260.777i	0.891017	+	0.283453i
$921$	119.634	−	81.9515i	0.129896	−	0.0889810i
$922$	−64.3095	−	178.110i	−0.0697500	−	0.193178i
$923$	−52.6639	−	10.2649i	−0.0570574	−	0.0111212i
$924$	73.9950	−	32.6720i	0.0800812	−	0.0353593i
$925$	63.4873	+	129.999i	0.0686349	+	0.140539i
$926$	−886.817	−	95.9706i	−0.957685	−	0.103640i
$927$	−929.347	−	821.367i	−1.00253	−	0.886049i
$928$	282.407	−	334.810i	0.304317	−	0.360787i
$929$	−12.1353	−	74.3930i	−0.0130627	−	0.0800786i	0.979611	−	0.200903i	$-0.0643875\pi$
$929$	−12.1353	−	74.3930i	−0.0130627	−	0.0800786i	−0.992674	+	0.120824i	$0.961446\pi$
$930$	−70.3765	+	227.267i	−0.0756736	+	0.244373i
$931$	−212.465	−	388.455i	−0.228212	−	0.417244i
$932$	409.865	+	240.862i	0.439769	+	0.258436i
$933$	14.0910	+	914.930i	0.0151029	+	0.980633i
$934$	74.0128	+	29.3301i	0.0792428	+	0.0314027i
$935$	−158.823	−	121.869i	−0.169864	−	0.130341i
$936$	−144.848	+	97.5930i	−0.154752	+	0.104266i
$937$	58.1687	+	838.033i	0.0620797	+	0.894379i	0.922795	+	0.385292i	$0.125899\pi$
$937$	58.1687	+	838.033i	0.0620797	+	0.894379i	−0.860715	+	0.509087i	$0.829983\pi$
$938$	707.323	−	299.384i	0.754075	−	0.319173i
$939$	113.646	−	26.7293i	0.121029	−	0.0284657i
$940$	−191.067	−	19.1898i	−0.203262	−	0.0204147i
$941$	−144.286	+	22.3973i	−0.153332	+	0.0238016i	−0.229595	−	0.973286i	$-0.573740\pi$
$941$	−144.286	+	22.3973i	−0.153332	+	0.0238016i	0.0762632	+	0.997088i	$0.475701\pi$
$942$	66.0352	−	777.773i	0.0701011	−	0.825661i
$943$	875.270	+	541.944i	0.928176	+	0.574702i
$944$	95.7882	+	346.783i	0.101471	+	0.367355i
$945$	35.4853	+	657.718i	0.0375506	+	0.695998i
$946$	−43.0120	−	142.781i	−0.0454673	−	0.150931i
$947$	−558.372	+	82.2775i	−0.589622	+	0.0868823i	−0.433966	−	0.900929i	$-0.642886\pi$
$947$	−558.372	+	82.2775i	−0.589622	+	0.0868823i	−0.155656	+	0.987811i	$0.549749\pi$
$948$	−7.18460	−	1.05867i	−0.00757869	−	0.00111674i
$949$	−592.738	−	178.560i	−0.624592	−	0.188156i
$950$	−507.642	−	123.529i	−0.534359	−	0.130030i
$951$	99.5081	−	641.042i	0.104635	−	0.674072i
$952$	322.092	+	83.6514i	0.338332	+	0.0878692i
$953$	221.264	−	323.005i	0.232176	−	0.338935i	−0.691316	−	0.722552i	$-0.742969\pi$
$953$	221.264	−	323.005i	0.232176	−	0.338935i	0.923492	+	0.383617i	$0.125322\pi$
$954$	−915.590	−	1174.39i	−0.959738	−	1.23101i
$955$	745.272	−	22.9616i	0.780389	−	0.0240435i
$956$	−888.461	+	459.609i	−0.929352	+	0.480762i
$957$	−28.5133	−	80.9147i	−0.0297944	−	0.0845504i
$958$	751.061	+	762.717i	0.783988	+	0.796155i
$959$	−144.434	+	118.069i	−0.150608	+	0.123117i
$960$	−0.905967	−	11.7426i	−0.000943715	−	0.0122318i
$961$	−551.733	−	551.733i	−0.574123	−	0.574123i
$962$	−277.220	−	237.507i	−0.288170	−	0.246889i
$963$	−60.7396	+	51.2328i	−0.0630733	+	0.0532013i
$964$	17.8263	−	771.564i	0.0184920	−	0.800377i
$965$	−246.840	+	186.405i	−0.255792	+	0.193165i
$966$	452.565	−	964.060i	0.468493	−	0.997991i
$967$	330.448	−	335.576i	0.341725	−	0.347028i	−0.520218	−	0.854033i	$-0.674149\pi$
$967$	330.448	−	335.576i	0.341725	−	0.347028i	0.861943	+	0.507005i	$0.169248\pi$
$968$	−44.6742	+	482.111i	−0.0461510	+	0.498049i
$969$	325.219	−	616.985i	0.335623	−	0.636724i
$970$	−182.899	−	389.615i	−0.188556	−	0.401665i
$971$	−901.816	−	317.788i	−0.928750	−	0.327279i	−0.175097	−	0.984551i	$-0.556024\pi$
$971$	−901.816	−	317.788i	−0.928750	−	0.327279i	−0.753653	+	0.657273i	$0.771710\pi$
$972$	−75.6118	−	542.043i	−0.0777899	−	0.557658i
$973$	917.742	+	598.000i	0.943209	+	0.614594i
$974$	647.679	+	1982.95i	0.664968	+	2.03589i
$975$	55.6386	+	21.0633i	0.0570653	+	0.0216033i
$976$	−355.016	+	787.566i	−0.363745	+	0.806932i
$977$	−379.136	+	153.634i	−0.388061	+	0.157250i	−0.561266	−	0.827635i	$-0.689686\pi$
$977$	−379.136	+	153.634i	−0.388061	+	0.157250i	0.173205	+	0.984886i	$0.444588\pi$
$978$	83.1875	+	16.8802i	0.0850588	+	0.0172599i
$979$	−346.058	−	301.135i	−0.353481	−	0.307595i
$980$	−118.444	−	16.5222i	−0.120861	−	0.0168594i
$981$	0.716755	−	1.38554i	0.000730637	−	0.00141238i
$982$	−1023.85	−	490.287i	−1.04261	−	0.499274i
$983$	1060.85	−	1181.85i	1.07920	−	1.20229i	0.100941	−	0.994892i	$-0.467815\pi$
$983$	1060.85	−	1181.85i	1.07920	−	1.20229i	0.978257	−	0.207397i	$-0.0664991\pi$
$984$	29.5597	−	172.825i	0.0300403	−	0.175635i
$985$	312.494	−	738.296i	0.317253	−	0.749539i
$986$	−136.708	+	397.692i	−0.138649	+	0.403339i
$987$	45.6842	−	194.237i	0.0462859	−	0.196796i
$988$	457.655	−	78.2768i	0.463214	−	0.0792275i
$989$	−585.102	−	368.542i	−0.591610	−	0.372641i
$990$	−232.706	−	113.646i	−0.235057	−	0.114794i
$991$	61.5916	−	1599.00i	0.0621510	−	1.61352i	−0.558551	−	0.829470i	$-0.688642\pi$
$991$	61.5916	−	1599.00i	0.0621510	−	1.61352i	0.620702	−	0.784047i	$-0.286848\pi$
$992$	388.449	+	167.955i	0.391582	+	0.169309i
$993$	24.4903	−	7.17238i	0.0246629	−	0.00722294i
$994$	88.3393	+	98.4151i	0.0888725	+	0.0990091i
$995$	−935.920	+	589.514i	−0.940623	+	0.592477i
$996$	−165.101	+	17.8671i	−0.165764	+	0.0179389i
$997$	423.525	+	299.807i	0.424800	+	0.300710i	0.770267	−	0.637721i	$-0.220123\pi$
$997$	423.525	+	299.807i	0.424800	+	0.300710i	−0.345468	+	0.938431i	$0.612280\pi$
$998$	1154.06	−	447.084i	1.15637	−	0.447980i
$999$	−555.272	+	240.085i	−0.555828	+	0.240325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	409.3.p.a.21.15	✓	8576
409.39	odd	408	inner	409.3.p.a.39.15	yes	8576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.3.p.a.21.15	✓	8576	1.1	even	1	trivial
409.3.p.a.39.15	yes	8576	409.39	odd	408	inner

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:	\( N \)	\(=\)	\( 409 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	409.p (of order \(408\), degree \(128\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00582 - 1.46677i) q^{2} +(1.28816 + 1.00430i) q^{3} +(0.659278 + 2.07240i) q^{4} +(4.28592 + 0.801176i) q^{5} +(-1.11075 - 3.90388i) q^{6} +(-4.78569 + 3.67219i) q^{7} +(-1.44137 + 4.30048i) q^{8} +(-1.54447 - 6.14077i) q^{9} +(-7.42163 - 7.89348i) q^{10} +(0.435029 + 3.74973i) q^{11} +(-1.23204 + 3.33170i) q^{12} +(-4.76720 + 3.77604i) q^{13} +(14.9855 - 0.346226i) q^{14} +(4.71635 + 5.33638i) q^{15} +(16.2990 - 11.5378i) q^{16} +(-6.71841 + 10.1391i) q^{17} +(-5.90920 + 14.5827i) q^{18} +(-25.3905 + 24.2437i) q^{19} +(1.16525 + 9.41032i) q^{20} +(-9.85273 - 0.0758673i) q^{21} +(4.62741 - 8.15937i) q^{22} +(-8.65026 - 42.6294i) q^{23} +(-6.17568 + 4.09215i) q^{24} +(-5.58462 - 2.16349i) q^{25} +(15.1007 - 0.581665i) q^{26} +(10.1155 - 22.9094i) q^{27} +(-10.7653 - 7.49687i) q^{28} +(-8.80620 + 10.7726i) q^{29} +(-1.63288 - 17.6216i) q^{30} +(-12.4203 - 5.14467i) q^{31} +(-31.4760 - 0.484768i) q^{32} +(-3.20545 + 5.26716i) q^{33} +(28.3477 - 10.4828i) q^{34} +(-23.4532 + 11.9045i) q^{35} +(11.7079 - 7.24923i) q^{36} +(-17.7259 - 16.4110i) q^{37} +(86.4888 - 11.3865i) q^{38} +(-9.93320 + 0.0764870i) q^{39} +(-9.62305 + 17.2767i) q^{40} +(-16.2117 + 17.2424i) q^{41} +(19.6515 + 14.6039i) q^{42} +(10.9783 - 11.4976i) q^{43} +(-7.48413 + 3.37366i) q^{44} +(-1.69961 - 27.5562i) q^{45} +(-45.1768 + 98.1948i) q^{46} +(-4.48464 + 19.7486i) q^{47} +(32.5832 + 1.50641i) q^{48} +(-3.26426 + 12.1824i) q^{49} +(8.02838 + 12.5309i) q^{50} +(-18.8371 + 6.31355i) q^{51} +(-10.9684 - 7.39007i) q^{52} +(-47.3204 + 81.9614i) q^{53} +(-53.8928 + 31.1150i) q^{54} +(-1.13970 + 16.4195i) q^{55} +(-8.89420 - 25.8738i) q^{56} +(-57.0550 + 5.73035i) q^{57} +(33.4646 - 8.69121i) q^{58} +(-6.11835 + 16.9452i) q^{59} +(-7.94972 + 13.2923i) q^{60} +(-37.2968 + 21.9180i) q^{61} +(17.3669 + 28.5371i) q^{62} +(29.9415 + 23.7163i) q^{63} +(-1.31969 - 0.996581i) q^{64} +(-23.4571 + 12.3644i) q^{65} +(14.1553 - 5.86331i) q^{66} +(47.6366 - 18.8776i) q^{67} +(-25.4416 - 7.23875i) q^{68} +(31.6696 - 63.6011i) q^{69} +(64.5040 + 10.5221i) q^{70} +(5.74018 + 6.69997i) q^{71} +(28.6344 + 2.20921i) q^{72} +(58.1714 + 83.5328i) q^{73} +(11.4838 + 58.9173i) q^{74} +(-5.02112 - 8.39555i) q^{75} +(-66.9821 - 36.6359i) q^{76} +(-15.8516 - 16.3475i) q^{77} +(20.0364 + 14.4163i) q^{78} +(0.421978 + 2.00039i) q^{79} +(79.1000 - 36.3918i) q^{80} +(-14.1690 + 7.60861i) q^{81} +(57.8085 - 10.8063i) q^{82} +(20.8382 + 41.8487i) q^{83} +(-6.33846 - 20.4688i) q^{84} +(-36.9178 + 38.0727i) q^{85} +(-38.8850 + 6.95943i) q^{86} +(-22.1627 + 5.03286i) q^{87} +(-16.7526 - 3.53393i) q^{88} +(-89.8068 + 81.8697i) q^{89} +(-37.0096 + 57.7658i) q^{90} +(8.94799 - 35.5771i) q^{91} +(82.6422 - 46.0314i) q^{92} +(-10.8327 - 19.1009i) q^{93} +(37.9621 - 33.0342i) q^{94} +(-128.245 + 83.5643i) q^{95} +(-40.0595 - 32.2357i) q^{96} +(37.7623 + 12.3340i) q^{97} +(24.4163 - 19.6477i) q^{98} +(22.3543 - 8.46274i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8576 q - 124 q^{2} - 112 q^{3} - 124 q^{4} - 120 q^{5} - 120 q^{6} - 144 q^{7} + 8 q^{8} - 292 q^{9} - 96 q^{10} - 160 q^{11} + 36 q^{12} - 164 q^{13} - 16 q^{14} - 80 q^{15} - 204 q^{16} - 148 q^{17} - 148 q^{18}+ \cdots + 1180 q^{99}+O(q^{100}) \) 8576 * q - 124 * q^2 - 112 * q^3 - 124 * q^4 - 120 * q^5 - 120 * q^6 - 144 * q^7 + 8 * q^8 - 292 * q^9 - 96 * q^10 - 160 * q^11 + 36 * q^12 - 164 * q^13 - 16 * q^14 - 80 * q^15 - 204 * q^16 - 148 * q^17 - 148 * q^18 - 96 * q^19 + 68 * q^20 - 144 * q^21 - 256 * q^22 - 128 * q^23 - 1156 * q^24 - 2496 * q^25 - 280 * q^26 - 100 * q^27 - 92 * q^28 - 80 * q^29 + 672 * q^30 - 168 * q^31 + 2112 * q^32 - 96 * q^33 + 92 * q^34 + 64 * q^35 - 2344 * q^36 - 152 * q^37 - 2972 * q^39 + 112 * q^40 - 196 * q^41 + 488 * q^42 - 452 * q^43 + 92 * q^44 - 244 * q^45 - 124 * q^46 + 16 * q^47 - 188 * q^48 + 16 * q^49 + 96 * q^50 + 8 * q^51 - 828 * q^52 - 256 * q^53 + 240 * q^54 - 1016 * q^55 + 76 * q^56 - 92 * q^57 - 800 * q^58 + 48 * q^59 - 64 * q^60 + 428 * q^61 - 52 * q^62 + 1604 * q^63 - 136 * q^64 + 136 * q^65 + 224 * q^66 + 600 * q^67 - 136 * q^68 + 2808 * q^69 - 20 * q^70 - 188 * q^71 + 560 * q^72 + 144 * q^73 - 996 * q^74 + 1152 * q^75 + 992 * q^76 - 3084 * q^77 - 4900 * q^78 - 560 * q^79 - 292 * q^80 - 3128 * q^81 + 1488 * q^82 + 120 * q^83 + 6560 * q^84 + 288 * q^85 + 3248 * q^86 - 632 * q^87 + 144 * q^88 + 608 * q^89 + 268 * q^90 + 404 * q^91 - 5128 * q^92 - 104 * q^93 - 624 * q^94 + 84 * q^95 + 140 * q^96 - 840 * q^97 - 72 * q^98 + 1180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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