LMFDB - Embedded newform 120.4.b.b.11.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(11,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("120.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	120.11
Dual form			120.4.b.b.11.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.40201 - 1.49343i) q^{2} +(-1.49310 - 4.97701i) q^{3} +(3.53933 - 7.17448i) q^{4} -5.00000 q^{5} +(-11.0193 - 9.72502i) q^{6} -14.5956i q^{7} +(-2.21306 - 22.5189i) q^{8} +(-22.5413 + 14.8623i) q^{9} +O(q^{10})$	\(q+(2.40201 - 1.49343i) q^{2} +(-1.49310 - 4.97701i) q^{3} +(3.53933 - 7.17448i) q^{4} -5.00000 q^{5} +(-11.0193 - 9.72502i) q^{6} -14.5956i q^{7} +(-2.21306 - 22.5189i) q^{8} +(-22.5413 + 14.8623i) q^{9} +(-12.0101 + 7.46715i) q^{10} +58.0556i q^{11} +(-40.9920 - 6.90313i) q^{12} -43.9441i q^{13} +(-21.7975 - 35.0588i) q^{14} +(7.46548 + 24.8851i) q^{15} +(-38.9462 - 50.7857i) q^{16} -78.8045i q^{17} +(-31.9487 + 69.3634i) q^{18} +103.306 q^{19} +(-17.6967 + 35.8724i) q^{20} +(-72.6425 + 21.7926i) q^{21} +(86.7019 + 139.450i) q^{22} -163.945 q^{23} +(-108.773 + 44.6373i) q^{24} +25.0000 q^{25} +(-65.6275 - 105.554i) q^{26} +(107.626 + 89.9977i) q^{27} +(-104.716 - 51.6587i) q^{28} +247.735 q^{29} +(55.0963 + 48.6251i) q^{30} -153.271i q^{31} +(-169.394 - 63.8245i) q^{32} +(288.943 - 86.6825i) q^{33} +(-117.689 - 189.289i) q^{34} +72.9780i q^{35} +(26.8480 + 214.325i) q^{36} -153.638i q^{37} +(248.143 - 154.281i) q^{38} +(-218.711 + 65.6128i) q^{39} +(11.0653 + 112.595i) q^{40} -27.0586i q^{41} +(-141.943 + 160.833i) q^{42} +246.934 q^{43} +(416.518 + 205.478i) q^{44} +(112.707 - 74.3116i) q^{45} +(-393.799 + 244.841i) q^{46} +411.901 q^{47} +(-194.611 + 269.664i) q^{48} +129.968 q^{49} +(60.0503 - 37.3358i) q^{50} +(-392.211 + 117.663i) q^{51} +(-315.276 - 155.533i) q^{52} +80.1737 q^{53} +(392.925 + 55.4432i) q^{54} -290.278i q^{55} +(-328.678 + 32.3009i) q^{56} +(-154.246 - 514.157i) q^{57} +(595.063 - 369.975i) q^{58} +513.612i q^{59} +(204.960 + 34.5157i) q^{60} -27.0460i q^{61} +(-228.899 - 368.159i) q^{62} +(216.924 + 329.004i) q^{63} +(-502.205 + 99.6713i) q^{64} +219.721i q^{65} +(564.592 - 639.729i) q^{66} -453.089 q^{67} +(-565.381 - 278.915i) q^{68} +(244.786 + 815.958i) q^{69} +(108.988 + 175.294i) q^{70} -446.258 q^{71} +(384.569 + 474.716i) q^{72} +524.821 q^{73} +(-229.447 - 369.040i) q^{74} +(-37.3274 - 124.425i) q^{75} +(365.636 - 741.169i) q^{76} +847.356 q^{77} +(-427.358 + 484.232i) q^{78} +93.4259i q^{79} +(194.731 + 253.929i) q^{80} +(287.223 - 670.033i) q^{81} +(-40.4102 - 64.9952i) q^{82} +1249.95i q^{83} +(-100.755 + 598.304i) q^{84} +394.023i q^{85} +(593.139 - 368.779i) q^{86} +(-369.892 - 1232.98i) q^{87} +(1307.35 - 128.480i) q^{88} +267.674i q^{89} +(159.744 - 346.817i) q^{90} -641.391 q^{91} +(-580.257 + 1176.22i) q^{92} +(-762.832 + 228.848i) q^{93} +(989.392 - 615.146i) q^{94} -516.532 q^{95} +(-64.7335 + 938.374i) q^{96} -897.223 q^{97} +(312.185 - 194.098i) q^{98} +(-862.840 - 1308.65i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8}+O(q^{10}) $ 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8	$ 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8} - 15 q^{10} - 33 q^{12} + 54 q^{14} + 153 q^{16} + 59 q^{18} + 12 q^{19} + 15 q^{20} + 4 q^{21} - 102 q^{22} - 228 q^{23} - 27 q^{24} + 600 q^{25} - 336 q^{26} + 132 q^{27} - 186 q^{28} - 55 q^{30} - 177 q^{32} + 116 q^{33} + 408 q^{34} + 641 q^{36} - 312 q^{38} + 656 q^{39} + 105 q^{40} - 1042 q^{42} + 450 q^{44} - 1104 q^{46} + 924 q^{47} - 717 q^{48} - 816 q^{49} + 75 q^{50} - 700 q^{51} - 1548 q^{52} - 528 q^{53} + 987 q^{54} + 390 q^{56} - 172 q^{57} + 1410 q^{58} + 165 q^{60} + 978 q^{62} - 476 q^{63} + 1137 q^{64} - 582 q^{66} + 1632 q^{67} + 1608 q^{68} - 980 q^{69} - 270 q^{70} - 216 q^{71} - 589 q^{72} - 216 q^{73} - 768 q^{74} - 1812 q^{76} - 324 q^{78} - 765 q^{80} + 152 q^{81} + 2244 q^{82} - 134 q^{84} + 2808 q^{86} - 252 q^{87} + 2622 q^{88} - 295 q^{90} - 1800 q^{91} + 1836 q^{92} - 1968 q^{94} - 60 q^{95} + 1445 q^{96} + 792 q^{97} - 4851 q^{98} - 1328 q^{99}+O(q^{100}) $ 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8 - 15 * q^10 - 33 * q^12 + 54 * q^14 + 153 * q^16 + 59 * q^18 + 12 * q^19 + 15 * q^20 + 4 * q^21 - 102 * q^22 - 228 * q^23 - 27 * q^24 + 600 * q^25 - 336 * q^26 + 132 * q^27 - 186 * q^28 - 55 * q^30 - 177 * q^32 + 116 * q^33 + 408 * q^34 + 641 * q^36 - 312 * q^38 + 656 * q^39 + 105 * q^40 - 1042 * q^42 + 450 * q^44 - 1104 * q^46 + 924 * q^47 - 717 * q^48 - 816 * q^49 + 75 * q^50 - 700 * q^51 - 1548 * q^52 - 528 * q^53 + 987 * q^54 + 390 * q^56 - 172 * q^57 + 1410 * q^58 + 165 * q^60 + 978 * q^62 - 476 * q^63 + 1137 * q^64 - 582 * q^66 + 1632 * q^67 + 1608 * q^68 - 980 * q^69 - 270 * q^70 - 216 * q^71 - 589 * q^72 - 216 * q^73 - 768 * q^74 - 1812 * q^76 - 324 * q^78 - 765 * q^80 + 152 * q^81 + 2244 * q^82 - 134 * q^84 + 2808 * q^86 - 252 * q^87 + 2622 * q^88 - 295 * q^90 - 1800 * q^91 + 1836 * q^92 - 1968 * q^94 - 60 * q^95 + 1445 * q^96 + 792 * q^97 - 4851 * q^98 - 1328 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	2.40201	−	1.49343i	0.849240	−	0.528007i
$2$	2.40201	−	1.49343i	0.849240	−	0.528007i
$3$	−1.49310	−	4.97701i	−0.287346	−	0.957827i
$3$	−1.49310	−	4.97701i	−0.287346	−	0.957827i
$4$	3.53933	−	7.17448i	0.442417	−	0.896810i
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	−11.0193	−	9.72502i	−0.749765	−	0.661704i
$7$		−	14.5956i		−	0.788089i	−0.919091	−	0.394044i	$-0.871076\pi$
$7$		−	14.5956i		−	0.788089i	0.919091	−	0.394044i	$-0.128924\pi$
$8$	−2.21306	−	22.5189i	−0.0978042	−	0.995206i
$9$	−22.5413	+	14.8623i	−0.834864	+	0.550456i
$10$	−12.0101	+	7.46715i	−0.379792	+	0.236132i
$11$			58.0556i			1.59131i	0.605750	+	0.795655i	$0.292873\pi$
$11$			58.0556i			1.59131i	−0.605750	+	0.795655i	$0.707127\pi$
$12$	−40.9920	−	6.90313i	−0.986115	−	0.166064i
$13$		−	43.9441i		−	0.937532i	−0.883322	−	0.468766i	$-0.844699\pi$
$13$		−	43.9441i		−	0.937532i	0.883322	−	0.468766i	$-0.155301\pi$
$14$	−21.7975	−	35.0588i	−0.416117	−	0.669276i
$15$	7.46548	+	24.8851i	0.128505	+	0.428353i
$16$	−38.9462	−	50.7857i	−0.608535	−	0.793527i
$17$		−	78.8045i		−	1.12429i	−0.827039	−	0.562144i	$-0.809977\pi$
$17$		−	78.8045i		−	1.12429i	0.827039	−	0.562144i	$-0.190023\pi$
$18$	−31.9487	+	69.3634i	−0.418355	+	0.908284i
$19$	103.306			1.24737			0.623687	−	0.781674i	$-0.285634\pi$
$19$	103.306			1.24737			0.623687	+	0.781674i	$0.285634\pi$
$20$	−17.6967	+	35.8724i	−0.197855	+	0.401065i
$21$	−72.6425	+	21.7926i	−0.754852	+	0.226454i
$22$	86.7019	+	139.450i	0.840223	+	1.35140i
$23$	−163.945			−1.48630			−0.743151	−	0.669123i	$-0.766670\pi$
$23$	−163.945			−1.48630			−0.743151	+	0.669123i	$0.766670\pi$
$24$	−108.773	+	44.6373i	−0.925131	+	0.379648i
$25$	25.0000			0.200000
$26$	−65.6275	−	105.554i	−0.495024	−	0.796189i
$27$	107.626	+	89.9977i	0.767137	+	0.641484i
$28$	−104.716	−	51.6587i	−0.706766	−	0.348664i
$29$	247.735			1.58632			0.793160	−	0.609013i	$-0.208434\pi$
$29$	247.735			1.58632			0.793160	+	0.609013i	$0.208434\pi$
$30$	55.0963	+	48.6251i	0.335305	+	0.295923i
$31$		−	153.271i		−	0.888009i	−0.896025	−	0.444004i	$-0.853557\pi$
$31$		−	153.271i		−	0.888009i	0.896025	−	0.444004i	$-0.146443\pi$
$32$	−169.394	−	63.8245i	−0.935780	−	0.352584i
$33$	288.943	−	86.6825i	1.52420	−	0.457257i
$34$	−117.689	−	189.289i	−0.593632	−	0.954790i
$35$			72.9780i			0.352444i
$36$	26.8480	+	214.325i	0.124296	+	0.992245i
$37$		−	153.638i		−	0.682646i	−0.939946	−	0.341323i	$-0.889125\pi$
$37$		−	153.638i		−	0.682646i	0.939946	−	0.341323i	$-0.110875\pi$
$38$	248.143	−	154.281i	1.05932	−	0.658623i
$39$	−218.711	+	65.6128i	−0.897993	+	0.269396i
$40$	11.0653	+	112.595i	0.0437394	+	0.445070i
$41$		−	27.0586i		−	0.103070i	−0.998671	−	0.0515348i	$-0.983589\pi$
$41$		−	27.0586i		−	0.103070i	0.998671	−	0.0515348i	$-0.0164113\pi$
$42$	−141.943	+	160.833i	−0.521481	+	0.590882i
$43$	246.934			0.875746			0.437873	−	0.899037i	$-0.355732\pi$
$43$	246.934			0.875746			0.437873	+	0.899037i	$0.355732\pi$
$44$	416.518	+	205.478i	1.42710	+	0.704022i
$45$	112.707	−	74.3116i	0.373363	−	0.246171i
$46$	−393.799	+	244.841i	−1.26223	+	0.784779i
$47$	411.901			1.27834			0.639170	−	0.769065i	$-0.279278\pi$
$47$	411.901			1.27834			0.639170	+	0.769065i	$0.279278\pi$
$48$	−194.611	+	269.664i	−0.585201	+	0.810888i
$49$	129.968			0.378916
$50$	60.0503	−	37.3358i	0.169848	−	0.105601i
$51$	−392.211	+	117.663i	−1.07687	+	0.323060i
$52$	−315.276	−	155.533i	−0.840788	−	0.414780i
$53$	80.1737			0.207787			0.103893	−	0.994588i	$-0.466870\pi$
$53$	80.1737			0.207787			0.103893	+	0.994588i	$0.466870\pi$
$54$	392.925	+	55.4432i	0.990191	+	0.139720i
$55$		−	290.278i		−	0.711656i
$56$	−328.678	+	32.3009i	−0.784310	+	0.0770784i
$57$	−154.246	−	514.157i	−0.358428	−	1.19477i
$58$	595.063	−	369.975i	1.34717	−	0.837589i
$59$			513.612i			1.13333i	0.823947	+	0.566666i	$0.191767\pi$
$59$			513.612i			1.13333i	−0.823947	+	0.566666i	$0.808233\pi$
$60$	204.960	+	34.5157i	0.441004	+	0.0742659i
$61$		−	27.0460i		−	0.0567686i	−0.999597	−	0.0283843i	$-0.990964\pi$
$61$		−	27.0460i		−	0.0567686i	0.999597	−	0.0283843i	$-0.00903622\pi$
$62$	−228.899	−	368.159i	−0.468875	−	0.754133i
$63$	216.924	+	329.004i	0.433808	+	0.657947i
$64$	−502.205	+	99.6713i	−0.980869	+	0.194671i
$65$			219.721i			0.419277i
$66$	564.592	−	639.729i	1.05298	−	1.19311i
$67$	−453.089			−0.826173			−0.413087	−	0.910692i	$-0.635549\pi$
$67$	−453.089			−0.826173			−0.413087	+	0.910692i	$0.635549\pi$
$68$	−565.381	−	278.915i	−1.00827	−	0.497404i
$69$	244.786	+	815.958i	0.427084	+	1.42362i
$70$	108.988	+	175.294i	0.186093	+	0.299309i
$71$	−446.258			−0.745930			−0.372965	−	0.927845i	$-0.621659\pi$
$71$	−446.258			−0.745930			−0.372965	+	0.927845i	$0.621659\pi$
$72$	384.569	+	474.716i	0.629470	+	0.777025i
$73$	524.821			0.841447			0.420724	−	0.907189i	$-0.361776\pi$
$73$	524.821			0.841447			0.420724	+	0.907189i	$0.361776\pi$
$74$	−229.447	−	369.040i	−0.360442	−	0.579730i
$75$	−37.3274	−	124.425i	−0.0574693	−	0.191565i
$76$	365.636	−	741.169i	0.551859	−	1.11866i
$77$	847.356			1.25409
$78$	−427.358	+	484.232i	−0.620368	+	0.702929i
$79$			93.4259i			0.133054i	0.997785	+	0.0665268i	$0.0211918\pi$
$79$			93.4259i			0.133054i	−0.997785	+	0.0665268i	$0.978808\pi$
$80$	194.731	+	253.929i	0.272145	+	0.354876i
$81$	287.223	−	670.033i	0.393996	−	0.919112i
$82$	−40.4102	−	64.9952i	−0.0544215	−	0.0875308i
$83$			1249.95i			1.65301i	0.562933	+	0.826503i	$0.309673\pi$
$83$			1249.95i			1.65301i	−0.562933	+	0.826503i	$0.690327\pi$
$84$	−100.755	+	598.304i	−0.130873	+	0.777146i
$85$			394.023i			0.502797i
$86$	593.139	−	368.779i	0.743719	−	0.462400i
$87$	−369.892	−	1232.98i	−0.455823	−	1.51942i
$88$	1307.35	−	128.480i	1.58368	−	0.155637i
$89$			267.674i			0.318803i	0.987214	+	0.159401i	$0.0509564\pi$
$89$			267.674i			0.318803i	−0.987214	+	0.159401i	$0.949044\pi$
$90$	159.744	−	346.817i	0.187094	−	0.406197i
$91$	−641.391			−0.738858
$92$	−580.257	+	1176.22i	−0.657565	+	1.33293i
$93$	−762.832	+	228.848i	−0.850559	+	0.255166i
$94$	989.392	−	615.146i	1.08562	−	0.674973i
$95$	−516.532			−0.557843
$96$	−64.7335	+	938.374i	−0.0688212	+	0.997629i
$97$	−897.223			−0.939167			−0.469584	−	0.882888i	$-0.655596\pi$
$97$	−897.223			−0.939167			−0.469584	+	0.882888i	$0.655596\pi$
$98$	312.185	−	194.098i	0.321791	−	0.200070i
$99$	−862.840	−	1308.65i	−0.875946	−	1.32853i
$100$	88.4833	−	179.362i	0.0884833	−	0.179362i
$101$	−1086.03			−1.06994			−0.534972	−	0.844870i	$-0.679678\pi$
$101$	−1086.03			−1.06994			−0.534972	+	0.844870i	$0.679678\pi$
$102$	−766.375	+	868.367i	−0.743946	+	0.842952i
$103$			602.598i			0.576464i	0.957561	+	0.288232i	$0.0930674\pi$
$103$			602.598i			0.576464i	−0.957561	+	0.288232i	$0.906933\pi$
$104$	−989.575	+	97.2509i	−0.933037	+	0.0916945i
$105$	363.213	−	108.963i	0.337580	−	0.101273i
$106$	192.578	−	119.734i	0.176461	−	0.109713i
$107$		−	209.243i		−	0.189050i	−0.995522	−	0.0945249i	$-0.969867\pi$
$107$		−	209.243i		−	0.189050i	0.995522	−	0.0945249i	$-0.0301332\pi$
$108$	1026.61	−	453.631i	0.914683	−	0.404173i
$109$		−	866.438i		−	0.761374i	−0.924704	−	0.380687i	$-0.875688\pi$
$109$		−	866.438i		−	0.761374i	0.924704	−	0.380687i	$-0.124312\pi$
$110$	−433.510	−	697.251i	−0.375759	−	0.604366i
$111$	−764.657	+	229.396i	−0.653856	+	0.196156i
$112$	−741.249	+	568.444i	−0.625370	+	0.479580i
$113$		−	1455.92i		−	1.21205i	−0.795445	−	0.606026i	$-0.792763\pi$
$113$		−	1455.92i		−	1.21205i	0.795445	−	0.606026i	$-0.207237\pi$
$114$	−1138.36	−	1004.66i	−0.935238	−	0.825392i
$115$	819.727			0.664695
$116$	876.818	−	1777.37i	0.701814	−	1.42263i
$117$	653.112	+	990.560i	0.516070	+	0.782712i
$118$	767.044	+	1233.70i	0.598408	+	0.962471i
$119$	−1150.20			−0.886039
$120$	543.864	−	223.187i	0.413731	−	0.169784i
$121$	−2039.45			−1.53227
$122$	−40.3913	−	64.9648i	−0.0299742	−	0.0482102i
$123$	−134.671	+	40.4011i	−0.0987228	+	0.0296167i
$124$	−1099.64	−	542.477i	−0.796375	−	0.392870i
$125$	−125.000			−0.0894427
$126$	1012.40	+	466.311i	0.715808	+	0.329701i
$127$			1710.12i			1.19487i	0.801917	+	0.597435i	$0.203814\pi$
$127$			1710.12i			1.19487i	−0.801917	+	0.597435i	$0.796186\pi$
$128$	−1057.45	+	989.420i	−0.730205	+	0.683228i
$129$	−368.696	−	1228.99i	−0.251642	−	0.838813i
$130$	328.138	+	527.772i	0.221381	+	0.356067i
$131$			994.011i			0.662955i	0.943463	+	0.331478i	$0.107547\pi$
$131$			994.011i			0.662955i	−0.943463	+	0.331478i	$0.892453\pi$
$132$	400.765	−	2379.82i	0.264259	−	1.56922i
$133$		−	1507.82i		−	0.983041i
$134$	−1088.33	+	676.656i	−0.701619	+	0.436225i
$135$	−538.131	−	449.988i	−0.343074	−	0.286880i
$136$	−1774.59	+	174.399i	−1.11890	+	0.109960i
$137$		−	218.135i		−	0.136033i	−0.997684	−	0.0680166i	$-0.978333\pi$
$137$		−	218.135i		−	0.136033i	0.997684	−	0.0680166i	$-0.0216671\pi$
$138$	1806.56	+	1594.37i	1.11438	+	0.983492i
$139$	871.961			0.532078			0.266039	−	0.963962i	$-0.414285\pi$
$139$	871.961			0.532078			0.266039	+	0.963962i	$0.414285\pi$
$140$	523.579	+	258.294i	0.316075	+	0.155927i
$141$	−615.008	−	2050.04i	−0.367326	−	1.22443i
$142$	−1071.92	+	666.455i	−0.633474	+	0.393857i
$143$	2551.20			1.49190
$144$	1632.69	+	565.947i	0.944846	+	0.327515i
$145$	−1238.68			−0.709424
$146$	1260.63	−	783.783i	0.714590	−	0.444290i
$147$	−194.055	−	646.854i	−0.108880	−	0.362936i
$148$	−1102.27	−	543.775i	−0.612203	−	0.302014i
$149$	2649.54			1.45677			0.728385	−	0.685168i	$-0.240271\pi$
$149$	2649.54			1.45677			0.728385	+	0.685168i	$0.240271\pi$
$150$	−275.481	−	243.125i	−0.149953	−	0.132341i
$151$			717.633i			0.386756i	0.981124	+	0.193378i	$0.0619443\pi$
$151$			717.633i			0.386756i	−0.981124	+	0.193378i	$0.938056\pi$
$152$	−228.623	−	2326.35i	−0.121998	−	1.24139i
$153$	1171.22	+	1776.36i	0.618871	+	0.938628i
$154$	2035.36	−	1265.47i	1.06503	−	0.662171i
$155$			766.355i			0.397130i
$156$	−303.352	+	1801.36i	−0.155690	+	0.924514i
$157$			3251.75i			1.65298i	0.562951	+	0.826490i	$0.309666\pi$
$157$			3251.75i			1.65298i	−0.562951	+	0.826490i	$0.690334\pi$
$158$	139.525	+	224.410i	0.0702533	+	0.112994i
$159$	−119.707	−	399.026i	−0.0597068	−	0.199024i
$160$	846.972	+	319.122i	0.418494	+	0.157680i
$161$			2392.88i			1.17134i
$162$	−310.733	−	2038.38i	−0.150700	−	0.988579i
$163$	−180.616			−0.0867912			−0.0433956	−	0.999058i	$-0.513818\pi$
$163$	−180.616			−0.0867912			−0.0433956	+	0.999058i	$0.513818\pi$
$164$	−194.132	−	95.7696i	−0.0924338	−	0.0455997i
$165$	−1444.72	+	433.413i	−0.681643	+	0.204492i
$166$	1866.71	+	3002.39i	0.872799	+	1.40380i
$167$	3583.90			1.66066			0.830332	−	0.557269i	$-0.188151\pi$
$167$	3583.90			1.66066			0.830332	+	0.557269i	$0.188151\pi$
$168$	651.509	+	1587.60i	0.299196	+	0.729085i
$169$	265.912			0.121034
$170$	588.445	+	946.447i	0.265480	+	0.426995i
$171$	−2328.66	+	1535.37i	−1.04139	+	0.686625i
$172$	873.982	−	1771.62i	0.387445	−	0.785378i
$173$	529.974			0.232909			0.116454	−	0.993196i	$-0.462847\pi$
$173$	529.974			0.232909			0.116454	+	0.993196i	$0.462847\pi$
$174$	−2729.86	−	2409.23i	−1.18937	−	1.04967i
$175$		−	364.890i		−	0.157618i
$176$	2948.39	−	2261.05i	1.26275	−	0.968368i
$177$	2556.26	−	766.872i	1.08554	−	0.325659i
$178$	399.753	+	642.957i	0.168330	+	0.270740i
$179$		−	2272.25i		−	0.948805i	−0.880308	−	0.474402i	$-0.842664\pi$
$179$		−	2272.25i		−	0.948805i	0.880308	−	0.474402i	$-0.157336\pi$
$180$	−134.240	−	1071.62i	−0.0555871	−	0.443746i
$181$		−	768.299i		−	0.315509i	−0.987478	−	0.157755i	$-0.949574\pi$
$181$		−	768.299i		−	0.315509i	0.987478	−	0.157755i	$-0.0504255\pi$
$182$	−1540.63	+	957.873i	−0.627468	+	0.390123i
$183$	−134.608	+	40.3823i	−0.0543745	+	0.0163123i
$184$	362.820	+	3691.87i	0.145367	+	1.47918i
$185$			768.189i			0.305288i
$186$	−1490.56	+	1688.93i	−0.587599	+	0.665798i
$187$	4575.04			1.78909
$188$	1457.86	−	2955.18i	0.565559	−	1.14643i
$189$	1313.57	−	1570.87i	0.505546	−	0.604572i
$190$	−1240.72	+	771.404i	−0.473742	+	0.294545i
$191$	−1338.21			−0.506962			−0.253481	−	0.967340i	$-0.581576\pi$
$191$	−1338.21			−0.506962			−0.253481	+	0.967340i	$0.581576\pi$
$192$	1245.91	+	2350.66i	0.468310	+	0.883564i
$193$	−858.809			−0.320303			−0.160151	−	0.987092i	$-0.551198\pi$
$193$	−858.809			−0.320303			−0.160151	+	0.987092i	$0.551198\pi$
$194$	−2155.14	+	1339.94i	−0.797578	+	0.495887i
$195$	1093.55	−	328.064i	0.401595	−	0.120478i
$196$	460.001	−	932.454i	0.167639	−	0.339816i
$197$	−3040.41			−1.09960			−0.549798	−	0.835298i	$-0.685295\pi$
$197$	−3040.41			−1.09960			−0.549798	+	0.835298i	$0.685295\pi$
$198$	−4026.93	−	1854.80i	−1.44536	−	0.665733i
$199$			1636.95i			0.583118i	0.956553	+	0.291559i	$0.0941740\pi$
$199$			1636.95i			0.583118i	−0.956553	+	0.291559i	$0.905826\pi$
$200$	−55.3264	−	562.973i	−0.0195608	−	0.199041i
$201$	676.505	+	2255.03i	0.237398	+	0.791331i
$202$	−2608.67	+	1621.92i	−0.908639	+	0.564938i
$203$		−	3615.85i		−	1.25016i
$204$	−543.998	+	3230.36i	−0.186703	+	1.10868i
$205$			135.293i			0.0460941i
$206$	899.938	+	1447.45i	0.304377	+	0.489556i
$207$	3695.55	−	2436.61i	1.24086	−	0.818144i
$208$	−2231.74	+	1711.46i	−0.743957	+	0.570521i
$209$			5997.51i			1.98496i
$210$	709.713	−	804.164i	0.233213	−	0.264250i
$211$	6036.05			1.96938			0.984689	−	0.174322i	$-0.0557734\pi$
$211$	6036.05			1.96938			0.984689	+	0.174322i	$0.0557734\pi$
$212$	283.762	−	575.205i	0.0919284	−	0.186345i
$213$	666.305	+	2221.03i	0.214340	+	0.714472i
$214$	−312.490	−	502.605i	−0.0998196	−	0.160549i
$215$	−1234.67			−0.391646
$216$	1788.47	−	2622.80i	0.563379	−	0.826199i
$217$	−2237.08			−0.699830
$218$	−1293.97	−	2081.20i	−0.402011	−	0.646589i
$219$	−783.608	−	2612.04i	−0.241787	−	0.805961i
$220$	−2082.59	−	1027.39i	−0.638220	−	0.314848i
$221$	−3463.00			−1.05406
$222$	−1494.13	+	1692.97i	−0.451709	+	0.511824i
$223$			1524.61i			0.457828i	0.973447	+	0.228914i	$0.0735175\pi$
$223$			1524.61i			0.457828i	−0.973447	+	0.228914i	$0.926483\pi$
$224$	−931.557	+	2472.41i	−0.277867	+	0.737478i
$225$	−563.533	+	371.558i	−0.166973	+	0.110091i
$226$	−2174.32	−	3497.15i	−0.639972	−	1.02932i
$227$		−	472.571i		−	0.138174i	−0.997611	−	0.0690872i	$-0.977991\pi$
$227$		−	472.571i		−	0.138174i	0.997611	−	0.0690872i	$-0.0220087\pi$
$228$	−4234.74	−	713.137i	−1.23005	−	0.207143i
$229$		−	3068.70i		−	0.885526i	−0.896639	−	0.442763i	$-0.853998\pi$
$229$		−	3068.70i		−	0.885526i	0.896639	−	0.442763i	$-0.146002\pi$
$230$	1968.99	−	1224.20i	0.564485	−	0.350964i
$231$	−1265.18	−	4217.30i	−0.360359	−	1.20120i
$232$	−548.252	−	5578.73i	−0.155149	−	1.57871i
$233$		−	141.515i		−	0.0397895i	−0.999802	−	0.0198947i	$-0.993667\pi$
$233$		−	141.515i		−	0.0397895i	0.999802	−	0.0198947i	$-0.00633311\pi$
$234$	3048.11	+	1403.96i	0.851545	+	0.392221i
$235$	−2059.51			−0.571691
$236$	3684.90	+	1817.85i	1.01638	+	0.501405i
$237$	464.982	−	139.494i	0.127442	−	0.0382325i
$238$	−2762.79	+	1717.74i	−0.752460	+	0.467835i
$239$	3911.18			1.05855			0.529274	−	0.848451i	$-0.322464\pi$
$239$	3911.18			1.05855			0.529274	+	0.848451i	$0.322464\pi$
$240$	973.054	−	1348.32i	0.261710	−	0.362640i
$241$	4114.37			1.09971			0.549855	−	0.835260i	$-0.314683\pi$
$241$	4114.37			1.09971			0.549855	+	0.835260i	$0.314683\pi$
$242$	−4898.79	+	3045.78i	−1.30126	+	0.809049i
$243$	−3763.61	−	429.092i	−0.993563	−	0.113277i
$244$	−194.041	−	95.7248i	−0.0509106	−	0.0251154i
$245$	−649.841			−0.169456
$246$	−263.146	+	298.166i	−0.0682015	+	0.0772780i
$247$		−	4539.71i		−	1.16945i
$248$	−3451.50	+	339.197i	−0.883751	+	0.0868510i
$249$	6221.00	−	1866.29i	1.58329	−	0.474985i
$250$	−300.252	+	186.679i	−0.0759583	+	0.0472264i
$251$		−	5279.91i		−	1.32775i	−0.747844	−	0.663874i	$-0.768911\pi$
$251$		−	5279.91i		−	1.32775i	0.747844	−	0.663874i	$-0.231089\pi$
$252$	3128.20	−	391.863i	0.781977	−	0.0979567i
$253$		−	9517.94i		−	2.36517i
$254$	2553.94	+	4107.73i	0.630901	+	1.01473i
$255$	1961.06	−	588.313i	0.481592	−	0.144477i
$256$	−1062.38	+	3955.83i	−0.259370	+	0.965778i
$257$		−	2278.07i		−	0.552928i	−0.961024	−	0.276464i	$-0.910837\pi$
$257$		−	2278.07i		−	0.552928i	0.961024	−	0.276464i	$-0.0891626\pi$
$258$	−2721.03	−	2401.44i	−0.656604	−	0.579484i
$259$	−2242.44			−0.537985
$260$	1576.38	+	777.665i	0.376012	+	0.185495i
$261$	−5584.28	+	3681.92i	−1.32436	+	0.873199i
$262$	1484.49	+	2387.63i	0.350045	+	0.563008i
$263$	−6017.98			−1.41097			−0.705484	−	0.708726i	$-0.749270\pi$
$263$	−6017.98			−1.41097			−0.705484	+	0.708726i	$0.749270\pi$
$264$	−2591.45	−	6314.86i	−0.604138	−	1.47217i
$265$	−400.869			−0.0929252
$266$	−2251.82	−	3621.80i	−0.519053	−	0.834838i
$267$	1332.22	−	399.663i	0.305358	−	0.0916067i
$268$	−1603.63	+	3250.67i	−0.365513	+	0.740920i
$269$	−3008.84			−0.681979			−0.340989	−	0.940067i	$-0.610762\pi$
$269$	−3008.84			−0.681979			−0.340989	+	0.940067i	$0.610762\pi$
$270$	−1964.62	−	277.216i	−0.442827	−	0.0624846i
$271$			2907.26i			0.651673i	0.945426	+	0.325836i	$0.105646\pi$
$271$			2907.26i			0.651673i	−0.945426	+	0.325836i	$0.894354\pi$
$272$	−4002.14	+	3069.14i	−0.892153	+	0.684169i
$273$	957.659	+	3192.21i	0.212308	+	0.707698i
$274$	−325.770	−	523.963i	−0.0718265	−	0.115525i
$275$			1451.39i			0.318262i
$276$	6720.45	+	1131.74i	1.46567	+	0.246821i
$277$			7971.57i			1.72912i	0.502532	+	0.864558i	$0.332402\pi$
$277$			7971.57i			1.72912i	−0.502532	+	0.864558i	$0.667598\pi$
$278$	2094.46	−	1302.21i	0.451861	−	0.280941i
$279$	2277.96	+	3454.93i	0.488810	+	0.741367i
$280$	1643.39	−	161.505i	0.350754	−	0.0344705i
$281$		−	913.436i		−	0.193918i	−0.995288	−	0.0969591i	$-0.969088\pi$
$281$		−	913.436i		−	0.193918i	0.995288	−	0.0969591i	$-0.0309116\pi$
$282$	−4538.85	−	4005.75i	−0.958455	−	0.845882i
$283$	−1838.40			−0.386154			−0.193077	−	0.981184i	$-0.561847\pi$
$283$	−1838.40			−0.386154			−0.193077	+	0.981184i	$0.561847\pi$
$284$	−1579.45	+	3201.67i	−0.330012	+	0.668957i
$285$	771.231	+	2570.79i	0.160294	+	0.534317i
$286$	6128.02	−	3810.04i	1.26698	−	0.787736i
$287$	−394.937			−0.0812279
$288$	4766.95	−	1078.90i	0.975331	−	0.220746i
$289$	−1297.15			−0.264024
$290$	−2975.32	+	1849.88i	−0.602471	+	0.374581i
$291$	1339.64	+	4465.49i	0.269866	+	0.899559i
$292$	1857.52	−	3765.32i	0.372270	−	0.754618i
$293$	−742.598			−0.148065			−0.0740324	−	0.997256i	$-0.523587\pi$
$293$	−742.598			−0.148065			−0.0740324	+	0.997256i	$0.523587\pi$
$294$	−1432.15	−	1263.94i	−0.284098	−	0.250730i
$295$		−	2568.06i		−	0.506842i
$296$	−3459.76	+	340.009i	−0.679373	+	0.0667656i
$297$	−5224.87	+	6248.31i	−1.02080	+	1.22075i
$298$	6364.23	−	3956.90i	1.23715	−	0.769185i
$299$			7204.44i			1.39346i
$300$	−1024.80	−	172.578i	−0.197223	−	0.0332127i
$301$		−	3604.15i		−	0.690166i
$302$	1071.73	+	1723.76i	0.204210	+	0.328448i
$303$	1621.55	+	5405.20i	0.307445	+	1.02482i
$304$	−4023.40	−	5246.49i	−0.759071	−	0.989825i
$305$			135.230i			0.0253877i
$306$	5466.15	+	2517.71i	1.02117	+	0.470352i
$307$	8317.65			1.54630			0.773149	−	0.634225i	$-0.218681\pi$
$307$	8317.65			1.54630			0.773149	+	0.634225i	$0.218681\pi$
$308$	2999.08	−	6079.34i	0.554832	−	1.12468i
$309$	2999.14	−	899.736i	0.552152	−	0.165645i
$310$	1144.50	+	1840.79i	0.209687	+	0.337258i
$311$	−3016.33			−0.549970			−0.274985	−	0.961449i	$-0.588673\pi$
$311$	−3016.33			−0.549970			−0.274985	+	0.961449i	$0.588673\pi$
$312$	1961.55	+	4779.93i	0.355932	+	0.867340i
$313$	−9400.48			−1.69759			−0.848797	−	0.528720i	$-0.822672\pi$
$313$	−9400.48			−1.69759			−0.848797	+	0.528720i	$0.822672\pi$
$314$	4856.26	+	7810.74i	0.872785	+	1.40378i
$315$	−1084.62	−	1645.02i	−0.194005	−	0.294243i
$316$	670.282	+	330.665i	0.119324	+	0.0588651i
$317$	5801.88			1.02797			0.513985	−	0.857799i	$-0.328169\pi$
$317$	5801.88			1.02797			0.513985	+	0.857799i	$0.328169\pi$
$318$	−883.455	−	779.691i	−0.155791	−	0.137493i
$319$			14382.4i			2.52433i
$320$	2511.02	−	498.357i	0.438658	−	0.0870593i
$321$	−1041.41	+	312.420i	−0.181077	+	0.0543228i
$322$	3573.60	+	5747.73i	0.618475	+	0.994747i
$323$		−	8141.01i		−	1.40241i
$324$	−3790.56	−	4432.15i	−0.649958	−	0.759970i
$325$		−	1098.60i		−	0.187506i
$326$	−433.843	+	269.738i	−0.0737066	+	0.0458264i
$327$	−4312.28	+	1293.68i	−0.729264	+	0.218778i
$328$	−609.332	+	59.8823i	−0.102575	+	0.0100806i
$329$		−	6011.95i		−	1.00745i
$330$	−2822.96	+	3198.65i	−0.470905	+	0.533575i
$331$	−5997.26			−0.995888			−0.497944	−	0.867209i	$-0.665912\pi$
$331$	−5997.26			−0.995888			−0.497944	+	0.867209i	$0.665912\pi$
$332$	8967.71	+	4423.98i	1.48243	+	0.731317i
$333$	2283.41	+	3463.20i	0.375766	+	0.569916i
$334$	8608.58	−	5352.31i	1.41030	−	0.876842i
$335$	2265.44			0.369476
$336$	3935.91	+	2840.46i	0.639052	+	0.461190i
$337$	−8013.40			−1.29531			−0.647653	−	0.761936i	$-0.724249\pi$
$337$	−8013.40			−1.29531			−0.647653	+	0.761936i	$0.724249\pi$
$338$	638.724	−	397.121i	0.102787	−	0.0639069i
$339$	−7246.16	+	2173.83i	−1.16094	+	0.348279i
$340$	2826.91	+	1394.58i	0.450913	+	0.222446i
$341$	8898.23			1.41310
$342$	−3300.51	+	7165.68i	−0.521845	+	1.13297i
$343$		−	6903.26i		−	1.08671i
$344$	−546.479	−	5560.69i	−0.0856516	−	0.871548i
$345$	−1223.93	−	4079.79i	−0.190998	−	0.636663i
$346$	1273.00	−	791.479i	0.197795	−	0.122977i
$347$			249.070i			0.0385325i	0.999814	+	0.0192662i	$0.00613301\pi$
$347$			249.070i			0.0385325i	−0.999814	+	0.0192662i	$0.993867\pi$
$348$	−10155.2	−	1710.15i	−1.56429	−	0.263430i
$349$		−	8681.38i		−	1.33153i	−0.746162	−	0.665764i	$-0.768106\pi$
$349$		−	8681.38i		−	1.33153i	0.746162	−	0.665764i	$-0.231894\pi$
$350$	−544.938	−	876.471i	−0.0832233	−	0.133855i
$351$	3954.87	−	4729.55i	0.601411	−	0.719215i
$352$	3705.37	−	9834.28i	0.561070	−	1.48912i
$353$		−	6747.03i		−	1.01730i	−0.860972	−	0.508652i	$-0.830144\pi$
$353$		−	6747.03i		−	1.01730i	0.860972	−	0.508652i	$-0.169856\pi$
$354$	4994.89	−	5659.63i	0.749930	−	0.849734i
$355$	2231.29			0.333590
$356$	1920.42	+	947.389i	0.285905	+	0.141044i
$357$	1717.36	+	5724.56i	0.254600	+	0.848672i
$358$	−3393.45	−	5457.98i	−0.500976	−	0.805763i
$359$	−1559.98			−0.229339			−0.114669	−	0.993404i	$-0.536581\pi$
$359$	−1559.98			−0.229339			−0.114669	+	0.993404i	$0.536581\pi$
$360$	−1922.84	−	2373.58i	−0.281508	−	0.347496i
$361$	3813.21			0.555942
$362$	−1147.40	−	1845.46i	−0.166591	−	0.267943i
$363$	3045.09	+	10150.4i	0.440292	+	1.46765i
$364$	−2270.10	+	4601.65i	−0.326883	+	0.662615i
$365$	−2624.10			−0.376307
$366$	−263.023	+	298.027i	−0.0375640	+	0.0425631i
$367$		−	13670.5i		−	1.94440i	−0.234144	−	0.972202i	$-0.575229\pi$
$367$		−	13670.5i		−	1.94440i	0.234144	−	0.972202i	$-0.424771\pi$
$368$	6385.06	+	8326.08i	0.904467	+	1.17942i
$369$	402.154	+	609.938i	0.0567352	+	0.0860491i
$370$	1147.24	+	1845.20i	0.161195	+	0.259263i
$371$		−	1170.18i		−	0.163755i
$372$	−1058.05	+	6282.89i	−0.147466	+	0.875679i
$373$			10962.3i			1.52173i	0.648909	+	0.760866i	$0.275226\pi$
$373$			10962.3i			1.52173i	−0.648909	+	0.760866i	$0.724774\pi$
$374$	10989.3	−	6832.50i	1.51937	−	0.944653i
$375$	186.637	+	622.127i	0.0257010	+	0.0856706i
$376$	−911.561	−	9275.58i	−0.125027	−	1.27221i
$377$		−	10886.5i		−	1.48723i
$378$	809.228	−	5734.98i	0.110112	−	0.780358i
$379$	−221.741			−0.0300529			−0.0150265	−	0.999887i	$-0.504783\pi$
$379$	−221.741			−0.0300529			−0.0150265	+	0.999887i	$0.504783\pi$
$380$	−1828.18	+	3705.85i	−0.246799	+	0.500279i
$381$	8511.29	−	2553.37i	1.14448	−	0.343342i
$382$	−3214.41	+	1998.53i	−0.430532	+	0.267680i
$383$	−567.176			−0.0756694			−0.0378347	−	0.999284i	$-0.512046\pi$
$383$	−567.176			−0.0756694			−0.0378347	+	0.999284i	$0.512046\pi$
$384$	6503.23	+	3785.65i	0.864236	+	0.503087i
$385$	−4236.78			−0.560848
$386$	−2062.87	+	1282.57i	−0.272014	+	0.169122i
$387$	−5566.22	+	3670.01i	−0.731129	+	0.482060i
$388$	−3175.57	+	6437.11i	−0.415503	+	0.842254i
$389$	−10143.0			−1.32204			−0.661019	−	0.750369i	$-0.729876\pi$
$389$	−10143.0			−1.32204			−0.661019	+	0.750369i	$0.729876\pi$
$390$	2136.79	−	2421.16i	0.277437	−	0.314359i
$391$			12919.6i			1.67103i
$392$	−287.627	−	2926.75i	−0.0370596	−	0.377100i
$393$	4947.21	−	1484.15i	0.634996	−	0.190498i
$394$	−7303.11	+	4540.64i	−0.933821	+	0.580595i
$395$		−	467.129i		−	0.0595034i
$396$	−12442.8	+	1558.68i	−1.57897	+	0.197794i
$397$		−	4548.29i		−	0.574992i	−0.957782	−	0.287496i	$-0.907177\pi$
$397$		−	4548.29i		−	0.574992i	0.957782	−	0.287496i	$-0.0928228\pi$
$398$	2444.67	+	3931.98i	0.307891	+	0.495207i
$399$	−7504.44	+	2251.32i	−0.941583	+	0.282473i
$400$	−973.656	−	1269.64i	−0.121707	−	0.158705i
$401$			141.751i			0.0176526i	0.999961	+	0.00882632i	$0.00280954\pi$
$401$			141.751i			0.0176526i	−0.999961	+	0.00882632i	$0.997190\pi$
$402$	4992.70	+	4406.30i	0.619436	+	0.546682i
$403$	−6735.36			−0.832537
$404$	−3843.83	+	7791.72i	−0.473361	+	0.959536i
$405$	−1436.12	+	3350.16i	−0.176201	+	0.411039i
$406$	−5400.01	−	8685.31i	−0.660094	−	1.06169i
$407$	8919.53			1.08630
$408$	3517.62	+	8571.78i	0.426834	+	1.04011i
$409$	10767.4			1.30175			0.650873	−	0.759186i	$-0.274403\pi$
$409$	10767.4			1.30175			0.650873	+	0.759186i	$0.274403\pi$
$410$	202.051	+	324.976i	0.0243380	+	0.0391449i
$411$	−1085.66	+	325.697i	−0.130296	+	0.0390886i
$412$	4323.33	+	2132.80i	0.516978	+	0.255037i
$413$	7496.48			0.893167
$414$	5237.85	−	11371.8i	0.621802	−	1.34998i
$415$		−	6249.73i		−	0.739246i
$416$	−2804.71	+	7443.89i	−0.330559	+	0.877324i
$417$	−1301.92	−	4339.76i	−0.152891	−	0.509638i
$418$	8956.86	+	14406.1i	1.04807	+	1.68571i
$419$			1276.55i			0.148840i	0.997227	+	0.0744198i	$0.0237105\pi$
$419$			1276.55i			0.148840i	−0.997227	+	0.0744198i	$0.976290\pi$
$420$	503.777	−	2991.52i	0.0585281	−	0.347550i
$421$			14268.0i			1.65173i	0.563869	+	0.825864i	$0.309312\pi$
$421$			14268.0i			1.65173i	−0.563869	+	0.825864i	$0.690688\pi$
$422$	14498.7	−	9014.41i	1.67247	−	1.03985i
$423$	−9284.81	+	6121.81i	−1.06724	+	0.703670i
$424$	−177.429	−	1805.43i	−0.0203224	−	0.206791i
$425$		−	1970.11i		−	0.224858i
$426$	4917.43	+	4339.86i	0.559273	+	0.493585i
$427$	−394.753			−0.0447387
$428$	−1501.21	−	740.582i	−0.169542	−	0.0836388i
$429$	−3809.19	−	12697.4i	−0.428693	−	1.42899i
$430$	−2965.69	+	1843.89i	−0.332601	+	0.206792i
$431$	−15402.6			−1.72139			−0.860695	−	0.509120i	$-0.829971\pi$
$431$	−15402.6			−1.72139			−0.860695	+	0.509120i	$0.829971\pi$
$432$	378.957	−	8970.95i	0.0422051	−	0.999109i
$433$	9528.41			1.05752			0.528760	−	0.848771i	$-0.322657\pi$
$433$	9528.41			1.05752			0.528760	+	0.848771i	$0.322657\pi$
$434$	−5373.50	+	3340.93i	−0.594323	+	0.369515i
$435$	1849.46	+	6164.91i	0.203850	+	0.679505i
$436$	−6216.24	−	3066.61i	−0.682807	−	0.336844i
$437$	−16936.6			−1.85398
$438$	−5783.14	−	5103.89i	−0.630888	−	0.556789i
$439$			2811.08i			0.305616i	0.988256	+	0.152808i	$0.0488317\pi$
$439$			2811.08i			0.305616i	−0.988256	+	0.152808i	$0.951168\pi$
$440$	−6536.75	+	642.401i	−0.708244	+	0.0696029i
$441$	−2929.66	+	1931.63i	−0.316344	+	0.208577i
$442$	−8318.16	+	5171.74i	−0.895146	+	0.556549i
$443$			4207.40i			0.451241i	0.974215	+	0.225620i	$0.0724409\pi$
$443$			4207.40i			0.451241i	−0.974215	+	0.225620i	$0.927559\pi$
$444$	−1060.58	+	6297.92i	−0.113363	+	0.673167i
$445$		−	1338.37i		−	0.142573i
$446$	2276.90	+	3662.14i	0.241737	+	0.388806i
$447$	−3956.02	−	13186.8i	−0.418598	−	1.39533i
$448$	1454.76	+	7329.98i	0.153418	+	0.773012i
$449$		−	5099.95i		−	0.536040i	−0.963413	−	0.268020i	$-0.913631\pi$
$449$		−	5099.95i		−	0.536040i	0.963413	−	0.268020i	$-0.0863693\pi$
$450$	−798.719	+	1734.08i	−0.0836710	+	0.181657i
$451$	1570.91			0.164016
$452$	−10445.5	−	5153.00i	−1.08698	−	0.536232i
$453$	3571.67	−	1071.49i	0.370445	−	0.111133i
$454$	−705.751	−	1135.12i	−0.0729571	−	0.117343i
$455$	3206.96			0.330427
$456$	−11236.9	+	4611.32i	−1.15398	+	0.473563i
$457$	8660.31			0.886460			0.443230	−	0.896408i	$-0.353833\pi$
$457$	8660.31			0.886460			0.443230	+	0.896408i	$0.353833\pi$
$458$	−4582.89	−	7371.06i	−0.467564	−	0.752024i
$459$	7092.22	−	8481.44i	0.721213	−	0.862483i
$460$	2901.29	−	5881.11i	0.294072	−	0.596105i
$461$	11202.5			1.13179			0.565893	−	0.824479i	$-0.308532\pi$
$461$	11202.5			1.13179			0.565893	+	0.824479i	$0.308532\pi$
$462$	−9337.24	−	8240.56i	−0.940276	−	0.829838i
$463$		−	2975.15i		−	0.298633i	−0.988789	−	0.149316i	$-0.952293\pi$
$463$		−	2975.15i		−	0.298633i	0.988789	−	0.149316i	$-0.0477073\pi$
$464$	−9648.36	−	12581.4i	−0.965331	−	1.25879i
$465$	3814.16	−	1144.24i	0.380381	−	0.114114i
$466$	−211.342	−	339.920i	−0.0210091	−	0.0337908i
$467$			13454.8i			1.33322i	0.745406	+	0.666611i	$0.232256\pi$
$467$			13454.8i			1.33322i	−0.745406	+	0.666611i	$0.767744\pi$
$468$	9418.33	−	1179.81i	0.930261	−	0.116532i
$469$			6613.11i			0.651098i
$470$	−4946.96	+	3075.73i	−0.485503	+	0.301857i
$471$	16184.0	−	4855.17i	1.58327	−	0.474978i
$472$	11566.0	−	1136.65i	1.12790	−	0.110845i
$473$			14335.9i			1.39358i
$474$	908.569	−	1029.48i	0.0880421	−	0.0997590i
$475$	2582.66			0.249475
$476$	−4070.94	+	8252.08i	−0.391998	+	0.794608i
$477$	−1807.22	+	1191.57i	−0.173474	+	0.114378i
$478$	9394.70	−	5841.07i	0.898961	−	0.558921i
$479$	−11128.5			−1.06153			−0.530765	−	0.847519i	$-0.678095\pi$
$479$	−11128.5			−1.06153			−0.530765	+	0.847519i	$0.678095\pi$
$480$	323.667	−	4691.87i	0.0307778	−	0.446153i
$481$	−6751.48			−0.640002
$482$	9882.78	−	6144.53i	0.933918	−	0.580655i
$483$	11909.4	−	3572.80i	1.12194	−	0.336580i
$484$	−7218.29	+	14632.0i	−0.677901	+	1.37415i
$485$	4486.12			0.420008
$486$	−9681.07	+	4590.01i	−0.903585	+	0.428410i
$487$		−	2167.65i		−	0.201695i	−0.994902	−	0.100848i	$-0.967845\pi$
$487$		−	2167.65i		−	0.201695i	0.994902	−	0.100848i	$-0.0321555\pi$
$488$	−609.047	+	59.8543i	−0.0564964	+	0.00555221i
$489$	269.677	+	898.930i	0.0249391	+	0.0831309i
$490$	−1560.93	+	970.492i	−0.143909	+	0.0894742i
$491$			4706.59i			0.432597i	0.976327	+	0.216299i	$0.0693985\pi$
$491$			4706.59i			0.432597i	−0.976327	+	0.216299i	$0.930601\pi$
$492$	−186.789	+	1109.19i	−0.0171161	+	0.101638i
$493$		−	19522.7i		−	1.78348i
$494$	−6779.74	−	10904.4i	−0.617480	−	0.993146i
$495$	4314.20	+	6543.25i	0.391735	+	0.594136i
$496$	−7783.98	+	5969.33i	−0.704659	+	0.540385i
$497$			6513.40i			0.587859i
$498$	12155.8	−	13773.5i	1.09380	−	1.23937i
$499$	−21594.1			−1.93724			−0.968620	−	0.248546i	$-0.920047\pi$
$499$	−21594.1			−1.93724			−0.968620	+	0.248546i	$0.920047\pi$
$500$	−442.417	+	896.810i	−0.0395709	+	0.0802131i
$501$	−5351.11	−	17837.1i	−0.477186	−	1.59063i
$502$	−7885.17	−	12682.4i	−0.701061	−	1.12758i
$503$	3910.09			0.346605			0.173303	−	0.984869i	$-0.444556\pi$
$503$	3910.09			0.346605			0.173303	+	0.984869i	$0.444556\pi$
$504$	6928.76	−	5613.01i	0.612364	−	0.496078i
$505$	5430.17			0.478494
$506$	−14214.4	−	22862.2i	−1.24883	−	2.00860i
$507$	−397.032	−	1323.45i	−0.0347787	−	0.115930i
$508$	12269.2	+	6052.68i	1.07157	+	0.528631i
$509$	18113.4			1.57733			0.788667	−	0.614821i	$-0.210772\pi$
$509$	18113.4			1.57733			0.788667	+	0.614821i	$0.210772\pi$
$510$	3831.88	−	4341.84i	0.332703	−	0.376980i
$511$		−	7660.08i		−	0.663135i
$512$	3355.90	+	11088.5i	0.289670	+	0.957126i
$513$	11118.5	+	9297.33i	0.956906	+	0.800170i
$514$	−3402.15	−	5471.97i	−0.291950	−	0.469568i
$515$		−	3012.99i		−	0.257802i
$516$	−10122.3	−	1704.62i	−0.863586	−	0.145429i
$517$			23913.2i			2.03424i
$518$	−5386.36	+	3348.92i	−0.456879	+	0.284060i
$519$	−791.302	−	2637.69i	−0.0669254	−	0.223086i
$520$	4947.88	−	486.254i	0.417267	−	0.0410070i
$521$		−	16469.0i		−	1.38487i	−0.721480	−	0.692436i	$-0.756538\pi$
$521$		−	16469.0i		−	1.38487i	0.721480	−	0.692436i	$-0.243462\pi$
$522$	−7914.83	+	17183.8i	−0.663645	+	1.44083i
$523$	380.198			0.0317876			0.0158938	−	0.999874i	$-0.494941\pi$
$523$	380.198			0.0317876			0.0158938	+	0.999874i	$0.494941\pi$
$524$	7131.51	+	3518.14i	0.594545	+	0.293303i
$525$	−1816.06	+	544.816i	−0.150970	+	0.0452909i
$526$	−14455.3	+	8987.43i	−1.19825	+	0.745001i
$527$	−12078.4			−0.998378
$528$	−15655.5	−	11298.2i	−1.29037	−	0.931237i
$529$	14711.1			1.20910
$530$	−962.892	+	598.669i	−0.0789157	+	0.0490652i
$531$	−7633.47	−	11577.5i	−0.623850	−	0.946179i
$532$	−10817.8	−	5336.67i	−0.881601	−	0.434914i
$533$	−1189.07			−0.0966310
$534$	2603.14	−	2949.57i	0.210953	−	0.239027i
$535$			1046.22i			0.0845456i
$536$	1002.71	+	10203.1i	0.0808032	+	0.822212i
$537$	−11309.0	+	3392.69i	−0.908791	+	0.272636i
$538$	−7227.28	+	4493.49i	−0.579164	+	0.360090i
$539$			7545.38i			0.602973i
$540$	−5133.06	+	2268.15i	−0.409059	+	0.180751i
$541$			5985.34i			0.475656i	0.971307	+	0.237828i	$0.0764354\pi$
$541$			5985.34i			0.475656i	−0.971307	+	0.237828i	$0.923565\pi$
$542$	4341.79	+	6983.27i	0.344088	+	0.553427i
$543$	−3823.83	+	1147.14i	−0.302203	+	0.0906605i
$544$	−5029.66	+	13349.0i	−0.396406	+	1.05209i
$545$			4332.19i			0.340497i
$546$	7067.66	+	6237.54i	0.553970	+	0.488905i
$547$	6496.76			0.507827			0.253914	−	0.967227i	$-0.418282\pi$
$547$	6496.76			0.507827			0.253914	+	0.967227i	$0.418282\pi$
$548$	−1565.01	−	772.053i	−0.121996	−	0.0601833i
$549$	401.966	+	609.653i	0.0312486	+	0.0473941i
$550$	2167.55	+	3486.26i	0.168045	+	0.270281i
$551$	25592.6			1.97873
$552$	17832.8	−	7318.08i	1.37502	−	0.564272i
$553$	1363.61			0.104858
$554$	11905.0	+	19147.8i	0.912986	+	1.46843i
$555$	3823.29	−	1146.98i	0.292413	−	0.0877235i
$556$	3086.16	−	6255.87i	0.235400	−	0.477172i
$557$	−22280.1			−1.69486			−0.847431	−	0.530905i	$-0.821852\pi$
$557$	−22280.1			−1.69486			−0.847431	+	0.530905i	$0.821852\pi$
$558$	10631.4	+	4896.81i	0.806564	+	0.371503i
$559$		−	10851.3i		−	0.821040i
$560$	3706.24	−	2842.22i	0.279674	−	0.214475i
$561$	−6830.97	−	22770.0i	−0.514089	−	1.71364i
$562$	−1364.15	−	2194.08i	−0.102390	−	0.164683i
$563$			10370.5i			0.776317i	0.921593	+	0.388158i	$0.126889\pi$
$563$			10370.5i			0.776317i	−0.921593	+	0.388158i	$0.873111\pi$
$564$	−16884.7	−	2843.41i	−1.26059	−	0.212286i
$565$			7279.62i			0.542046i
$566$	−4415.86	+	2745.52i	−0.327937	+	0.203892i
$567$	−9779.53	−	4192.20i	−0.724342	−	0.310504i
$568$	987.593	+	10049.2i	0.0729551	+	0.742354i
$569$			15791.9i			1.16350i	0.813368	+	0.581750i	$0.197632\pi$
$569$			15791.9i			1.16350i	−0.813368	+	0.581750i	$0.802368\pi$
$570$	5691.80	+	5023.28i	0.418251	+	0.369127i
$571$	14459.2			1.05972			0.529858	−	0.848087i	$-0.322245\pi$
$571$	14459.2			1.05972			0.529858	+	0.848087i	$0.322245\pi$
$572$	9029.56	−	18303.5i	0.660043	−	1.33795i
$573$	1998.08	+	6660.31i	0.145674	+	0.485582i
$574$	−948.645	+	589.811i	−0.0689820	+	0.0428889i
$575$	−4098.63			−0.297261
$576$	9839.02	−	9710.65i	0.711735	−	0.702449i
$577$	−1179.27			−0.0850845			−0.0425423	−	0.999095i	$-0.513546\pi$
$577$	−1179.27			−0.0850845			−0.0425423	+	0.999095i	$0.513546\pi$
$578$	−3115.77	+	1937.20i	−0.224220	+	0.139407i
$579$	1282.28	+	4274.30i	0.0920378	+	0.306795i
$580$	−4384.09	+	8886.85i	−0.313861	+	0.636218i
$581$	18243.7			1.30271
$582$	9886.73	+	8725.51i	0.704155	+	0.621450i
$583$			4654.53i			0.330654i
$584$	−1161.46	−	11818.4i	−0.0822971	−	0.837413i
$585$	−3265.56	−	4952.80i	−0.230794	−	0.350039i
$586$	−1783.73	+	1109.02i	−0.125743	+	0.0781793i
$587$			3761.00i			0.264451i	0.991220	+	0.132226i	$0.0422124\pi$
$587$			3761.00i			0.264451i	−0.991220	+	0.132226i	$0.957788\pi$
$588$	−5327.66	−	897.188i	−0.373655	−	0.0629241i
$589$		−	15833.9i		−	1.10768i
$590$	−3835.22	−	6168.52i	−0.267616	−	0.430430i
$591$	4539.63	+	15132.2i	0.315965	+	1.05322i
$592$	−7802.61	+	5983.61i	−0.541698	+	0.415414i
$593$		−	7912.85i		−	0.547962i	−0.961735	−	0.273981i	$-0.911659\pi$
$593$		−	7912.85i		−	0.547962i	0.961735	−	0.273981i	$-0.0883406\pi$
$594$	−3218.79	+	22811.5i	−0.222338	+	1.57570i
$595$	5751.00			0.396249
$596$	9377.60	−	19009.1i	0.644499	−	1.30645i
$597$	8147.14	−	2444.13i	0.558526	−	0.167557i
$598$	10759.3	+	17305.2i	0.735755	+	1.18338i
$599$	13018.4			0.888012			0.444006	−	0.896024i	$-0.353557\pi$
$599$	13018.4			0.888012			0.444006	+	0.896024i	$0.353557\pi$
$600$	−2719.32	+	1115.93i	−0.185026	+	0.0759296i
$601$	6784.23			0.460457			0.230228	−	0.973137i	$-0.426053\pi$
$601$	6784.23			0.460457			0.230228	+	0.973137i	$0.426053\pi$
$602$	−5382.55	−	8657.22i	−0.364412	−	0.586116i
$603$	10213.2	−	6733.95i	0.689742	−	0.454772i
$604$	5148.64	+	2539.94i	0.346846	+	0.171107i
$605$	10197.2			0.685251
$606$	11967.3	+	10561.7i	0.802207	+	0.707986i
$607$			16589.8i			1.10932i	0.832077	+	0.554661i	$0.187152\pi$
$607$			16589.8i			1.10932i	−0.832077	+	0.554661i	$0.812848\pi$
$608$	−17499.5	−	6593.48i	−1.16727	−	0.439804i
$609$	−17996.1	+	5398.80i	−1.19744	+	0.359229i
$610$	201.957	+	324.824i	0.0134049	+	0.0215602i
$611$		−	18100.7i		−	1.19848i
$612$	16889.8	−	2115.75i	1.11557	−	0.139745i
$613$		−	16207.7i		−	1.06790i	−0.845516	−	0.533950i	$-0.820707\pi$
$613$		−	16207.7i		−	1.06790i	0.845516	−	0.533950i	$-0.179293\pi$
$614$	19979.1	−	12421.8i	1.31318	−	0.816456i
$615$	673.356	−	202.006i	0.0441502	−	0.0132450i
$616$	−1875.25	−	19081.6i	−0.122656	−	1.24808i
$617$			17461.9i			1.13936i	0.821865	+	0.569682i	$0.192934\pi$
$617$			17461.9i			1.13936i	−0.821865	+	0.569682i	$0.807066\pi$
$618$	5860.28	−	6640.18i	0.381448	−	0.432212i
$619$	5700.52			0.370151			0.185075	−	0.982724i	$-0.440747\pi$
$619$	5700.52			0.370151			0.185075	+	0.982724i	$0.440747\pi$
$620$	5498.19	+	2712.38i	0.356150	+	0.175697i
$621$	−17644.8	−	14754.7i	−1.14020	−	0.953439i
$622$	−7245.27	+	4504.68i	−0.467056	+	0.290388i
$623$	3906.87			0.251245
$624$	11850.2	+	8552.01i	0.760233	+	0.548645i
$625$	625.000			0.0400000
$626$	−22580.1	+	14039.0i	−1.44166	+	0.896342i
$627$	29849.7	−	8954.86i	1.90125	−	0.570371i
$628$	23329.6	+	11509.0i	1.48241	+	0.731306i
$629$	−12107.3			−0.767491
$630$	−5062.00	−	2331.56i	−0.320119	−	0.147447i
$631$			8186.74i			0.516496i	0.966079	+	0.258248i	$0.0831452\pi$
$631$			8186.74i			0.516496i	−0.966079	+	0.258248i	$0.916855\pi$
$632$	2103.85	−	206.757i	0.132416	−	0.0130132i
$633$	−9012.39	−	30041.5i	−0.565893	−	1.88632i
$634$	13936.2	−	8664.71i	0.872992	−	0.542775i
$635$		−	8550.60i		−	0.534363i
$636$	−3286.48	−	553.450i	−0.204902	−	0.0345058i
$637$		−	5711.34i		−	0.355246i
$638$	21479.1	+	34546.7i	1.33286	+	2.14376i
$639$	10059.2	−	6632.42i	0.622750	−	0.410602i
$640$	5287.25	−	4947.10i	0.326558	−	0.305549i
$641$			27307.8i			1.68267i	0.540510	+	0.841337i	$0.318231\pi$
$641$			27307.8i			1.68267i	−0.540510	+	0.841337i	$0.681769\pi$
$642$	−2034.90	+	2305.71i	−0.125095	+	0.141743i
$643$	−11306.2			−0.693427			−0.346714	−	0.937971i	$-0.612702\pi$
$643$	−11306.2			−0.693427			−0.346714	+	0.937971i	$0.612702\pi$
$644$	17167.7	+	8469.21i	1.05047	+	0.518220i
$645$	1843.48	+	6144.97i	0.112538	+	0.375129i
$646$	−12158.0	−	19554.8i	−0.740482	−	1.19098i
$647$	4998.32			0.303716			0.151858	−	0.988402i	$-0.451474\pi$
$647$	4998.32			0.303716			0.151858	+	0.988402i	$0.451474\pi$
$648$	−15724.1	−	4985.14i	−0.953240	−	0.302214i
$649$	−29818.1			−1.80348
$650$	−1640.69	−	2638.86i	−0.0990047	−	0.159238i
$651$	3340.18	+	11134.0i	0.201094	+	0.670316i
$652$	−639.262	+	1295.83i	−0.0383979	+	0.0778352i
$653$	−23047.6			−1.38120			−0.690599	−	0.723238i	$-0.742653\pi$
$653$	−23047.6			−1.38120			−0.690599	+	0.723238i	$0.742653\pi$
$654$	−8426.13	+	9547.51i	−0.503804	+	0.570852i
$655$		−	4970.06i		−	0.296483i
$656$	−1374.19	+	1053.83i	−0.0817885	+	0.0627214i
$657$	−11830.2	+	7800.05i	−0.702494	+	0.463180i
$658$	−8978.43	−	14440.8i	−0.531939	−	0.855563i
$659$		−	18811.4i		−	1.11197i	−0.831191	−	0.555986i	$-0.812341\pi$
$659$		−	18811.4i		−	1.11197i	0.831191	−	0.555986i	$-0.187659\pi$
$660$	−2003.83	+	11899.1i	−0.118180	+	0.701774i
$661$			30855.3i			1.81563i	0.419370	+	0.907815i	$0.362251\pi$
$661$			30855.3i			1.81563i	−0.419370	+	0.907815i	$0.637749\pi$
$662$	−14405.5	+	8956.48i	−0.845748	+	0.525836i
$663$	5170.58	+	17235.4i	0.302879	+	1.00960i
$664$	28147.5	−	2766.20i	1.64508	−	0.161671i
$665$			7539.10i			0.439629i
$666$	10656.8	+	4908.53i	0.620036	+	0.285588i
$667$	−40615.0			−2.35775
$668$	12684.6	−	25712.6i	0.734705	−	1.48930i
$669$	7588.02	−	2276.39i	0.438520	−	0.131555i
$670$	5441.63	−	3383.28i	0.313774	−	0.195086i
$671$	1570.17			0.0903365
$672$	13696.1	+	944.824i	0.786220	+	0.0542372i
$673$	12293.3			0.704117			0.352058	−	0.935978i	$-0.385482\pi$
$673$	12293.3			0.704117			0.352058	+	0.935978i	$0.385482\pi$
$674$	−19248.3	+	11967.5i	−1.10002	+	0.683931i
$675$	2690.66	+	2249.94i	0.153427	+	0.128297i
$676$	941.152	−	1907.78i	0.0535475	−	0.108545i
$677$	296.947			0.0168576			0.00842881	−	0.999964i	$-0.497317\pi$
$677$	296.947			0.0168576			0.00842881	+	0.999964i	$0.497317\pi$
$678$	−14158.9	+	16043.2i	−0.802019	+	0.908755i
$679$			13095.5i			0.740147i
$680$	8872.97	−	871.994i	0.500386	−	0.0491757i
$681$	−2351.99	+	705.593i	−0.132347	+	0.0397039i
$682$	21373.7	−	13288.9i	1.20006	−	0.746126i
$683$		−	6305.85i		−	0.353275i	−0.984276	−	0.176638i	$-0.943478\pi$
$683$		−	6305.85i		−	0.353275i	0.984276	−	0.176638i	$-0.0565220\pi$
$684$	2773.57	+	22141.1i	0.155044	+	1.23770i
$685$			1090.68i			0.0608359i
$686$	−10309.5	−	16581.7i	−0.573790	−	0.922876i
$687$	−15273.0	+	4581.86i	−0.848181	+	0.254453i
$688$	−9617.15	−	12540.7i	−0.532922	−	0.694928i
$689$		−	3523.17i		−	0.194807i
$690$	−9032.78	−	7971.86i	−0.498365	−	0.439831i
$691$	−27248.7			−1.50013			−0.750064	−	0.661365i	$-0.769978\pi$
$691$	−27248.7			−1.50013			−0.750064	+	0.661365i	$0.769978\pi$
$692$	1875.75	−	3802.29i	0.103043	−	0.208875i
$693$	−19100.5	+	12593.7i	−1.04700	+	0.690323i
$694$	371.968	+	598.269i	0.0203454	+	0.0327233i
$695$	−4359.81			−0.237952
$696$	−26946.8	+	11058.2i	−1.46755	+	0.602244i
$697$	−2132.34			−0.115880
$698$	−12965.0	−	20852.8i	−0.703057	−	1.13079i
$699$	−704.321	+	211.295i	−0.0381114	+	0.0114334i
$700$	−2617.90	−	1291.47i	−0.141353	−	0.0697327i
$701$	17919.3			0.965481			0.482741	−	0.875763i	$-0.339641\pi$
$701$	17919.3			0.965481			0.482741	+	0.875763i	$0.339641\pi$
$702$	2436.41	−	17266.8i	0.130992	−	0.928336i
$703$		−	15871.8i		−	0.851515i
$704$	−5786.48	−	29155.8i	−0.309781	−	1.56087i
$705$	3075.04	+	10250.2i	0.164273	+	0.547581i
$706$	−10076.2	−	16206.5i	−0.537144	−	0.863935i
$707$			15851.3i			0.843211i
$708$	3545.53	−	21054.0i	0.188205	−	1.11760i
$709$			12485.0i			0.661329i	0.943748	+	0.330665i	$0.107273\pi$
$709$			12485.0i			0.661329i	−0.943748	+	0.330665i	$0.892727\pi$
$710$	5359.58	−	3332.27i	0.283298	−	0.176138i
$711$	−1388.52	−	2105.94i	−0.0732402	−	0.111082i
$712$	6027.74	−	592.378i	0.317274	−	0.0311802i
$713$			25128.1i			1.31985i
$714$	12674.3	+	11185.7i	0.664321	+	0.586295i
$715$	−12756.0			−0.667200
$716$	−16302.2	−	8042.26i	−0.850897	−	0.419767i
$717$	−5839.76	−	19466.0i	−0.304170	−	1.01391i
$718$	−3747.09	+	2329.72i	−0.194763	+	0.121092i
$719$	−7727.83			−0.400834			−0.200417	−	0.979711i	$-0.564230\pi$
$719$	−7727.83			−0.400834			−0.200417	+	0.979711i	$0.564230\pi$
$720$	−8163.47	−	2829.73i	−0.422548	−	0.146469i
$721$	8795.28			0.454304
$722$	9159.37	−	5694.76i	0.472128	−	0.293541i
$723$	−6143.15	−	20477.3i	−0.315998	−	1.05333i
$724$	−5512.14	−	2719.27i	−0.282952	−	0.139587i
$725$	6193.38			0.317264
$726$	22473.2	+	19833.7i	1.14884	+	1.01391i
$727$		−	12917.1i		−	0.658964i	−0.944162	−	0.329482i	$-0.893126\pi$
$727$		−	12917.1i		−	0.658964i	0.944162	−	0.329482i	$-0.106874\pi$
$728$	1419.44	+	14443.5i	0.0722634	+	0.735316i
$729$	3483.84	+	19372.2i	0.176997	+	0.984211i
$730$	−6303.13	+	3918.92i	−0.319575	+	0.198693i
$731$		−	19459.5i		−	0.984591i
$732$	−186.702	+	1108.67i	−0.00942719	+	0.0559804i
$733$		−	5574.53i		−	0.280900i	−0.990088	−	0.140450i	$-0.955145\pi$
$733$		−	5574.53i		−	0.280900i	0.990088	−	0.140450i	$-0.0448550\pi$
$734$	−20416.0	−	32836.8i	−1.02666	−	1.65127i
$735$	970.275	+	3234.27i	0.0486927	+	0.162310i
$736$	27771.4	+	10463.7i	1.39085	+	0.524046i
$737$		−	26304.3i		−	1.31470i
$738$	1876.88	+	864.490i	0.0936164	+	0.0431197i
$739$	17289.1			0.860607			0.430304	−	0.902684i	$-0.358406\pi$
$739$	17289.1			0.860607			0.430304	+	0.902684i	$0.358406\pi$
$740$	5511.35	+	2718.88i	0.273786	+	0.135065i
$741$	−22594.2	+	6778.22i	−1.12013	+	0.336038i
$742$	−1747.59	−	2810.80i	−0.0864636	−	0.139067i
$743$	13359.7			0.659649			0.329824	−	0.944042i	$-0.393010\pi$
$743$	13359.7			0.659649			0.329824	+	0.944042i	$0.393010\pi$
$744$	6841.61	+	16671.7i	0.337131	+	0.821524i
$745$	−13247.7			−0.651487
$746$	16371.4	+	26331.6i	0.803486	+	1.29232i
$747$	−18577.1	−	28175.5i	−0.909907	−	1.38003i
$748$	16192.6	−	32823.5i	0.791524	−	1.60447i
$749$	−3054.03			−0.148988
$750$	1377.41	+	1215.63i	0.0670611	+	0.0591846i
$751$		−	8468.05i		−	0.411456i	−0.978609	−	0.205728i	$-0.934044\pi$
$751$		−	8468.05i		−	0.411456i	0.978609	−	0.205728i	$-0.0659563\pi$
$752$	−16042.0	−	20918.7i	−0.777915	−	1.01440i
$753$	−26278.2	+	7883.41i	−1.27175	+	0.381524i
$754$	−16258.2	−	26149.5i	−0.785266	−	1.26301i
$755$		−	3588.16i		−	0.172962i
$756$	−6621.02	−	14984.0i	−0.318524	−	0.720851i
$757$		−	6277.34i		−	0.301392i	−0.988580	−	0.150696i	$-0.951849\pi$
$757$		−	6277.34i		−	0.301392i	0.988580	−	0.150696i	$-0.0481515\pi$
$758$	−532.624	+	331.154i	−0.0255221	+	0.0158682i
$759$	−47370.9	+	14211.2i	−2.26542	+	0.679623i
$760$	1143.11	+	11631.7i	0.0545594	+	0.555168i
$761$			11037.7i			0.525778i	0.964826	+	0.262889i	$0.0846752\pi$
$761$			11037.7i			0.525778i	−0.964826	+	0.262889i	$0.915325\pi$
$762$	16630.9	−	18844.3i	0.790651	−	0.895873i
$763$	−12646.2			−0.600030
$764$	−4736.38	+	9600.99i	−0.224288	+	0.454649i
$765$	−5856.09	−	8881.79i	−0.276768	−	0.419767i
$766$	−1362.37	+	847.038i	−0.0642614	+	0.0399540i
$767$	22570.3			1.06254
$768$	21274.4	−	618.946i	0.999577	−	0.0290811i
$769$	5492.77			0.257574			0.128787	−	0.991672i	$-0.458892\pi$
$769$	5492.77			0.257574			0.128787	+	0.991672i	$0.458892\pi$
$770$	−10176.8	+	6327.34i	−0.476294	+	0.296132i
$771$	−11338.0	+	3401.38i	−0.529609	+	0.158882i
$772$	−3039.61	+	6161.51i	−0.141707	+	0.287251i
$773$	−21115.4			−0.982497			−0.491248	−	0.871020i	$-0.663459\pi$
$773$	−21115.4			−0.982497			−0.491248	+	0.871020i	$0.663459\pi$
$774$	−7889.23	+	17128.2i	−0.366373	+	0.795426i
$775$		−	3831.77i		−	0.177602i
$776$	1985.61	+	20204.5i	0.0918545	+	0.934665i
$777$	3348.17	+	11160.6i	0.154588	+	0.515297i
$778$	−24363.7	+	15147.9i	−1.12273	+	0.698045i
$779$		−	2795.33i		−	0.128566i
$780$	1516.76	−	9006.80i	0.0696266	−	0.413455i
$781$		−	25907.7i		−	1.18701i
$782$	19294.6	+	31033.1i	0.882318	+	1.41911i
$783$	26662.8	+	22295.6i	1.21692	+	1.01760i
$784$	−5061.78	−	6600.53i	−0.230584	−	0.300680i
$785$		−	16258.7i		−	0.739235i
$786$	9666.78	−	10953.3i	0.438680	−	0.497061i
$787$	38018.5			1.72200			0.861000	−	0.508605i	$-0.169839\pi$
$787$	38018.5			1.72200			0.861000	+	0.508605i	$0.169839\pi$
$788$	−10761.0	+	21813.4i	−0.486480	+	0.986128i
$789$	8985.42	+	29951.6i	0.405436	+	1.35146i
$790$	−697.625	−	1122.05i	−0.0314182	−	0.0505326i
$791$	−21250.1			−0.955205
$792$	−27559.9	+	22326.4i	−1.23649	+	1.00168i
$793$	−1188.51			−0.0532224
$794$	−6792.55	−	10925.0i	−0.303600	−	0.488306i
$795$	598.535	+	1995.13i	0.0267017	+	0.0890062i
$796$	11744.3	+	5793.72i	0.522946	+	0.257981i
$797$	−5023.82			−0.223278			−0.111639	−	0.993749i	$-0.535610\pi$
$797$	−5023.82			−0.223278			−0.111639	+	0.993749i	$0.535610\pi$
$798$	−14663.6	+	16615.0i	−0.650482	+	0.737051i
$799$		−	32459.7i		−	1.43722i
$800$	−4234.86	−	1595.61i	−0.187156	−	0.0705168i
$801$	−3978.26	−	6033.74i	−0.175487	−	0.266157i
$802$	211.695	+	340.488i	0.00932072	+	0.0149913i
$803$			30468.8i			1.33900i
$804$	18573.0	+	3127.73i	0.814702	+	0.137197i
$805$		−	11964.4i		−	0.523839i
$806$	−16178.4	+	10058.8i	−0.707023	+	0.439585i
$807$	4492.49	+	14975.0i	0.195964	+	0.653218i
$808$	2403.45	+	24456.3i	0.104645	+	1.06481i
$809$		−	9928.57i		−	0.431483i	−0.976450	−	0.215742i	$-0.930783\pi$
$809$		−	9928.57i		−	0.431483i	0.976450	−	0.215742i	$-0.0692169\pi$
$810$	1553.66	+	10191.9i	0.0673953	+	0.442106i
$811$	16918.7			0.732549			0.366274	−	0.930507i	$-0.380633\pi$
$811$	16918.7			0.732549			0.366274	+	0.930507i	$0.380633\pi$
$812$	−25941.8	−	12797.7i	−1.12116	−	0.553092i
$813$	14469.5	−	4340.81i	0.624190	−	0.187256i
$814$	21424.8	−	13320.7i	0.922530	−	0.573575i
$815$	903.082			0.0388142
$816$	21250.7	+	15336.2i	0.911672	+	0.657935i
$817$	25509.9			1.09238
$818$	25863.5	−	16080.4i	1.10550	−	0.687332i
$819$	14457.8	−	9532.56i	0.616846	−	0.406709i
$820$	970.658	+	478.848i	0.0413376	+	0.0203928i
$821$	−18362.5			−0.780579			−0.390289	−	0.920692i	$-0.627625\pi$
$821$	−18362.5			−0.780579			−0.390289	+	0.920692i	$0.627625\pi$
$822$	−2121.37	+	2403.69i	−0.0900136	+	0.101993i
$823$		−	35007.5i		−	1.48273i	−0.671103	−	0.741364i	$-0.734179\pi$
$823$		−	35007.5i		−	1.48273i	0.671103	−	0.741364i	$-0.265821\pi$
$824$	13569.9	−	1333.58i	0.573700	−	0.0563806i
$825$	7223.59	−	2167.06i	0.304840	−	0.0914514i
$826$	18006.7	−	11195.5i	0.758513	−	0.471599i
$827$		−	21104.7i		−	0.887404i	−0.896174	−	0.443702i	$-0.853665\pi$
$827$		−	21104.7i		−	0.887404i	0.896174	−	0.443702i	$-0.146335\pi$
$828$	−4401.61	−	35137.6i	−0.184742	−	1.47478i
$829$			44840.3i			1.87861i	0.343085	+	0.939304i	$0.388528\pi$
$829$			44840.3i			1.87861i	−0.343085	+	0.939304i	$0.611472\pi$
$830$	−9333.54	−	15011.9i	−0.390327	−	0.627797i
$831$	39674.6	−	11902.3i	1.65619	−	0.496855i
$832$	4379.97	+	22069.0i	0.182510	+	0.919596i
$833$		−	10242.1i		−	0.426011i
$834$	−9608.36	−	8479.84i	−0.398933	−	0.352078i
$835$	−17919.5			−0.742671
$836$	43029.0	+	21227.2i	1.78013	+	0.878179i
$837$	13794.0	−	16496.0i	0.569643	−	0.681224i
$838$	1906.44	+	3066.30i	0.0785883	+	0.126400i
$839$	19998.2			0.822900			0.411450	−	0.911432i	$-0.365022\pi$
$839$	19998.2			0.822900			0.411450	+	0.911432i	$0.365022\pi$
$840$	−3257.54	−	7938.02i	−0.133805	−	0.326057i
$841$	36983.8			1.51641
$842$	21308.2	+	34271.8i	0.872125	+	1.40271i
$843$	−4546.18	+	1363.85i	−0.185740	+	0.0557217i
$844$	21363.6	−	43305.5i	0.871285	−	1.76616i
$845$	−1329.56			−0.0541281
$846$	−13159.7	+	28570.9i	−0.534800	+	1.16110i
$847$			29767.0i			1.20756i
$848$	−3122.47	−	4071.68i	−0.126446	−	0.164885i
$849$	2744.91	+	9149.75i	0.110960	+	0.369869i
$850$	−2942.23	−	4732.24i	−0.118726	−	0.190958i
$851$			25188.2i			1.01462i
$852$	18293.0	+	3080.58i	0.735573	+	0.123872i
$853$			27500.9i			1.10388i	0.833882	+	0.551942i	$0.186113\pi$
$853$			27500.9i			1.10388i	−0.833882	+	0.551942i	$0.813887\pi$
$854$	−948.201	+	589.536i	−0.0379939	+	0.0236224i
$855$	11643.3	−	7676.86i	0.465723	−	0.307068i
$856$	−4711.94	+	463.067i	−0.188143	+	0.0184899i
$857$			1250.31i			0.0498365i	0.999689	+	0.0249183i	$0.00793255\pi$
$857$			1250.31i			0.0498365i	−0.999689	+	0.0249183i	$0.992067\pi$
$858$	−28112.4	−	24810.5i	−1.11858	−	0.987198i
$859$	15260.3			0.606142			0.303071	−	0.952968i	$-0.401988\pi$
$859$	15260.3			0.606142			0.303071	+	0.952968i	$0.401988\pi$
$860$	−4369.91	+	8858.11i	−0.173271	+	0.351232i
$861$	589.679	+	1965.61i	0.0233406	+	0.0778023i
$862$	−36997.4	+	23002.8i	−1.46187	+	0.908907i
$863$	−15513.7			−0.611926			−0.305963	−	0.952043i	$-0.598978\pi$
$863$	−15513.7			−0.611926			−0.305963	+	0.952043i	$0.598978\pi$
$864$	−12487.2	−	22114.3i	−0.491695	−	0.870768i
$865$	−2649.87			−0.104160
$866$	22887.4	−	14230.0i	0.898088	−	0.558378i
$867$	1936.77	+	6455.93i	0.0758664	+	0.252889i
$868$	−7917.78	+	16049.9i	−0.309616	+	0.627614i
$869$	−5423.89			−0.211730
$870$	13649.3	+	12046.1i	0.531902	+	0.469428i
$871$			19910.6i			0.774564i
$872$	−19511.3	+	1917.48i	−0.757724	+	0.0744656i
$873$	20224.6	−	13334.8i	0.784077	−	0.516970i
$874$	−40681.9	+	25293.6i	−1.57447	+	0.978913i
$875$			1824.45i			0.0704888i
$876$	−21513.5	−	3622.91i	−0.829764	−	0.139734i
$877$		−	17948.8i		−	0.691091i	−0.938402	−	0.345545i	$-0.887694\pi$
$877$		−	17948.8i		−	0.691091i	0.938402	−	0.345545i	$-0.112306\pi$
$878$	4198.15	+	6752.25i	0.161368	+	0.259542i
$879$	1108.77	+	3695.92i	0.0425459	+	0.141821i
$880$	−14742.0	+	11305.2i	−0.564718	+	0.433067i
$881$			50006.7i			1.91234i	0.292817	+	0.956169i	$0.405407\pi$
$881$			50006.7i			1.91234i	−0.292817	+	0.956169i	$0.594593\pi$
$882$	−4152.32	+	9015.04i	−0.158522	+	0.344163i
$883$	−2670.53			−0.101779			−0.0508894	−	0.998704i	$-0.516206\pi$
$883$	−2670.53			−0.101779			−0.0508894	+	0.998704i	$0.516206\pi$
$884$	−12256.7	+	24845.2i	−0.466332	+	0.945288i
$885$	−12781.3	+	3834.36i	−0.485467	+	0.145639i
$886$	6283.46	+	10106.2i	0.238258	+	0.383212i
$887$	27123.1			1.02672			0.513362	−	0.858172i	$-0.328400\pi$
$887$	27123.1			1.02672			0.513362	+	0.858172i	$0.328400\pi$
$888$	6857.98	+	16711.6i	0.259165	+	0.631537i
$889$	24960.2			0.941664
$890$	−1998.76	−	3214.79i	−0.0752795	−	0.121079i
$891$	38899.1	+	16674.9i	1.46259	+	0.626970i
$892$	10938.3	+	5396.11i	0.410585	+	0.202551i
$893$	42552.0			1.59457
$894$	−29196.0	−	25766.8i	−1.09224	−	0.963950i
$895$			11361.3i			0.424318i
$896$	14441.2	+	15434.1i	0.538444	+	0.575467i
$897$	35856.6	−	10756.9i	1.33469	−	0.400405i
$898$	−7616.43	−	12250.2i	−0.283033	−	0.455226i
$899$		−	37970.6i		−	1.40867i
$900$	671.201	+	5358.12i	0.0248593	+	0.198449i
$901$		−	6318.05i		−	0.233612i
$902$	3773.34	−	2346.04i	0.139289	−	0.0866014i
$903$	−17937.9	+	5381.34i	−0.661059	+	0.198317i
$904$	−32785.9	+	3222.04i	−1.20624	+	0.118544i
$905$			3841.49i			0.141100i
$906$	6978.99	−	7907.78i	0.255918	−	0.289976i
$907$	−33013.5			−1.20860			−0.604298	−	0.796759i	$-0.706546\pi$
$907$	−33013.5			−1.20860			−0.604298	+	0.796759i	$0.706546\pi$
$908$	−3390.45	−	1672.58i	−0.123916	−	0.0611307i
$909$	24480.6	−	16141.0i	0.893258	−	0.588957i
$910$	7703.15	−	4789.37i	0.280612	−	0.174468i
$911$	−47241.1			−1.71808			−0.859038	−	0.511912i	$-0.828938\pi$
$911$	−47241.1			−1.71808			−0.859038	+	0.511912i	$0.828938\pi$
$912$	−20104.5	+	27858.0i	−0.729965	+	1.01148i
$913$	−72566.3			−2.63044
$914$	20802.2	−	12933.6i	0.752817	−	0.468057i
$915$	673.041	−	201.911i	0.0243170	−	0.00729506i
$916$	−22016.3	−	10861.2i	−0.794148	−	0.391772i
$917$	14508.2			0.522468
$918$	4369.18	−	30964.3i	0.157085	−	1.11326i
$919$		−	50644.8i		−	1.81787i	−0.416942	−	0.908933i	$-0.636898\pi$
$919$		−	50644.8i		−	1.81787i	0.416942	−	0.908933i	$-0.363102\pi$
$920$	−1814.10	−	18459.4i	−0.0650099	−	0.661508i
$921$	−12419.0	−	41397.1i	−0.444323	−	1.48108i
$922$	26908.6	−	16730.2i	0.961157	−	0.597591i
$923$			19610.4i			0.699333i
$924$	−34734.9	−	5849.41i	−1.23668	−	0.208259i
$925$		−	3840.94i		−	0.136529i
$926$	−4443.18	−	7146.35i	−0.157680	−	0.253611i
$927$	−8956.00	−	13583.4i	−0.317318	−	0.481269i
$928$	−41964.9	−	15811.6i	−1.48445	−	0.559311i
$929$		−	36463.1i		−	1.28774i	−0.765133	−	0.643872i	$-0.777327\pi$
$929$		−	36463.1i		−	1.28774i	0.765133	−	0.643872i	$-0.222673\pi$
$930$	7452.81	−	8444.66i	0.262782	−	0.297754i
$931$	13426.5			0.472650
$932$	−1015.29	−	500.868i	−0.0356836	−	0.0176035i
$933$	4503.67	+	15012.3i	0.158032	+	0.526776i
$934$	20093.8	+	32318.6i	0.703950	+	1.13222i
$935$	−22875.2			−0.800106
$936$	20861.0	−	16899.5i	0.728485	−	0.590148i
$937$	−1429.44			−0.0498376			−0.0249188	−	0.999689i	$-0.507933\pi$
$937$	−1429.44			−0.0498376			−0.0249188	+	0.999689i	$0.507933\pi$
$938$	9876.21	+	15884.8i	0.343784	+	0.552938i
$939$	14035.8	+	46786.3i	0.487797	+	1.62600i
$940$	−7289.28	+	14775.9i	−0.252926	+	0.512698i
$941$	8397.60			0.290918			0.145459	−	0.989364i	$-0.453534\pi$
$941$	8397.60			0.290918			0.145459	+	0.989364i	$0.453534\pi$
$942$	31623.3	−	35831.9i	1.09378	−	1.23935i
$943$			4436.14i			0.153193i
$944$	26084.2	−	20003.3i	0.899330	−	0.689673i
$945$	−6567.85	+	7854.36i	−0.226087	+	0.270373i
$946$	21409.7	+	34435.0i	0.735822	+	1.18349i
$947$			43156.1i			1.48087i	0.672127	+	0.740436i	$0.265381\pi$
$947$			43156.1i			1.48087i	−0.672127	+	0.740436i	$0.734619\pi$
$948$	644.931	−	3829.72i	0.0220953	−	0.131206i
$949$		−	23062.8i		−	0.788883i
$950$	6203.58	−	3857.02i	0.211864	−	0.131725i
$951$	−8662.77	−	28876.1i	−0.295383	−	0.984616i
$952$	2545.46	+	25901.3i	0.0866583	+	0.881791i
$953$		−	20652.4i		−	0.701991i	−0.936377	−	0.350995i	$-0.885843\pi$
$953$		−	20652.4i		−	0.701991i	0.936377	−	0.350995i	$-0.114157\pi$
$954$	−2561.45	+	5561.12i	−0.0869287	+	0.188729i
$955$	6691.07			0.226720
$956$	13843.0	−	28060.6i	0.468319	−	0.949316i
$957$	71581.5	−	21474.3i	2.41787	−	0.725356i
$958$	−26730.7	+	16619.6i	−0.901493	+	0.560495i
$959$	−3183.81			−0.107206
$960$	−6229.53	−	11753.3i	−0.209434	−	0.395142i
$961$	6299.02			0.211440
$962$	−16217.1	+	10082.9i	−0.543515	+	0.337926i
$963$	3109.84	+	4716.63i	0.104064	+	0.157831i
$964$	14562.1	−	29518.5i	0.486530	−	0.986231i
$965$	4294.05			0.143244
$966$	23270.8	−	26367.8i	0.775079	−	0.878229i
$967$			27587.9i			0.917443i	0.888580	+	0.458721i	$0.151692\pi$
$967$			27587.9i			0.917443i	−0.888580	+	0.458721i	$0.848308\pi$
$968$	4513.42	+	45926.2i	0.149862	+	1.52492i
$969$	−40517.9	+	12155.3i	−1.34326	+	0.402977i
$970$	10775.7	−	6699.70i	0.356688	−	0.221767i
$971$			13285.7i			0.439093i	0.975602	+	0.219547i	$0.0704578\pi$
$971$			13285.7i			0.439093i	−0.975602	+	0.219547i	$0.929542\pi$
$972$	−16399.2	+	25483.3i	−0.541157	+	0.840922i
$973$		−	12726.8i		−	0.419324i
$974$	−3237.24	−	5206.73i	−0.106497	−	0.171288i
$975$	−5467.77	+	1640.32i	−0.179599	+	0.0538793i
$976$	−1373.55	+	1053.34i	−0.0450474	+	0.0345457i
$977$		−	20541.2i		−	0.672642i	−0.941747	−	0.336321i	$-0.890817\pi$
$977$		−	20541.2i		−	0.672642i	0.941747	−	0.336321i	$-0.109183\pi$
$978$	1990.26	+	1756.50i	0.0650731	+	0.0574301i
$979$	−15540.0			−0.507314
$980$	−2300.00	+	4662.27i	−0.0749704	+	0.151970i
$981$	12877.3	+	19530.7i	0.419103	+	0.635644i
$982$	7028.96	+	11305.3i	0.228415	+	0.367379i
$983$	28203.9			0.915123			0.457562	−	0.889178i	$-0.348723\pi$
$983$	28203.9			0.915123			0.457562	+	0.889178i	$0.348723\pi$
$984$	1207.83	+	2943.24i	0.0391302	+	0.0953528i
$985$	15202.1			0.491754
$986$	−29155.7	−	46893.7i	−0.941691	−	1.51460i
$987$	−29921.6	+	8976.42i	−0.964958	+	0.289486i
$988$	−32570.0	−	16067.5i	−1.04878	−	0.517385i
$989$	−40483.7			−1.30162
$990$	20134.7	+	9274.01i	0.646385	+	0.297725i
$991$			30236.1i			0.969206i	0.874734	+	0.484603i	$0.161036\pi$
$991$			30236.1i			0.969206i	−0.874734	+	0.484603i	$0.838964\pi$
$992$	−9782.44	+	25963.2i	−0.313098	+	0.830981i
$993$	8954.48	+	29848.4i	0.286165	+	0.953888i
$994$	9727.31	+	15645.3i	0.310394	+	0.499233i
$995$		−	8184.76i		−	0.260778i
$996$	8628.54	−	51237.8i	0.274504	−	1.63005i
$997$			848.710i			0.0269598i	0.999909	+	0.0134799i	$0.00429091\pi$
$997$			848.710i			0.0269598i	−0.999909	+	0.0134799i	$0.995709\pi$
$998$	−51869.2	+	32249.2i	−1.64518	+	1.02288i
$999$	13827.0	−	16535.5i	0.437906	−	0.523683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.b.b.11.19	yes	24
3.2	odd	2		120.4.b.a.11.6	yes	24
4.3	odd	2		480.4.b.a.431.16		24
8.3	odd	2		120.4.b.a.11.5	✓	24
8.5	even	2		480.4.b.b.431.16		24
12.11	even	2		480.4.b.b.431.15		24
24.5	odd	2		480.4.b.a.431.15		24
24.11	even	2	inner	120.4.b.b.11.20	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.b.a.11.5	✓	24	8.3	odd	2
120.4.b.a.11.6	yes	24	3.2	odd	2
120.4.b.b.11.19	yes	24	1.1	even	1	trivial
120.4.b.b.11.20	yes	24	24.11	even	2	inner
480.4.b.a.431.15		24	24.5	odd	2
480.4.b.a.431.16		24	4.3	odd	2
480.4.b.b.431.15		24	12.11	even	2
480.4.b.b.431.16		24	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.40201 - 1.49343i) q^{2} +(-1.49310 - 4.97701i) q^{3} +(3.53933 - 7.17448i) q^{4} -5.00000 q^{5} +(-11.0193 - 9.72502i) q^{6} -14.5956i q^{7} +(-2.21306 - 22.5189i) q^{8} +(-22.5413 + 14.8623i) q^{9} +O(q^{10})\)	\(q+(2.40201 - 1.49343i) q^{2} +(-1.49310 - 4.97701i) q^{3} +(3.53933 - 7.17448i) q^{4} -5.00000 q^{5} +(-11.0193 - 9.72502i) q^{6} -14.5956i q^{7} +(-2.21306 - 22.5189i) q^{8} +(-22.5413 + 14.8623i) q^{9} +(-12.0101 + 7.46715i) q^{10} +58.0556i q^{11} +(-40.9920 - 6.90313i) q^{12} -43.9441i q^{13} +(-21.7975 - 35.0588i) q^{14} +(7.46548 + 24.8851i) q^{15} +(-38.9462 - 50.7857i) q^{16} -78.8045i q^{17} +(-31.9487 + 69.3634i) q^{18} +103.306 q^{19} +(-17.6967 + 35.8724i) q^{20} +(-72.6425 + 21.7926i) q^{21} +(86.7019 + 139.450i) q^{22} -163.945 q^{23} +(-108.773 + 44.6373i) q^{24} +25.0000 q^{25} +(-65.6275 - 105.554i) q^{26} +(107.626 + 89.9977i) q^{27} +(-104.716 - 51.6587i) q^{28} +247.735 q^{29} +(55.0963 + 48.6251i) q^{30} -153.271i q^{31} +(-169.394 - 63.8245i) q^{32} +(288.943 - 86.6825i) q^{33} +(-117.689 - 189.289i) q^{34} +72.9780i q^{35} +(26.8480 + 214.325i) q^{36} -153.638i q^{37} +(248.143 - 154.281i) q^{38} +(-218.711 + 65.6128i) q^{39} +(11.0653 + 112.595i) q^{40} -27.0586i q^{41} +(-141.943 + 160.833i) q^{42} +246.934 q^{43} +(416.518 + 205.478i) q^{44} +(112.707 - 74.3116i) q^{45} +(-393.799 + 244.841i) q^{46} +411.901 q^{47} +(-194.611 + 269.664i) q^{48} +129.968 q^{49} +(60.0503 - 37.3358i) q^{50} +(-392.211 + 117.663i) q^{51} +(-315.276 - 155.533i) q^{52} +80.1737 q^{53} +(392.925 + 55.4432i) q^{54} -290.278i q^{55} +(-328.678 + 32.3009i) q^{56} +(-154.246 - 514.157i) q^{57} +(595.063 - 369.975i) q^{58} +513.612i q^{59} +(204.960 + 34.5157i) q^{60} -27.0460i q^{61} +(-228.899 - 368.159i) q^{62} +(216.924 + 329.004i) q^{63} +(-502.205 + 99.6713i) q^{64} +219.721i q^{65} +(564.592 - 639.729i) q^{66} -453.089 q^{67} +(-565.381 - 278.915i) q^{68} +(244.786 + 815.958i) q^{69} +(108.988 + 175.294i) q^{70} -446.258 q^{71} +(384.569 + 474.716i) q^{72} +524.821 q^{73} +(-229.447 - 369.040i) q^{74} +(-37.3274 - 124.425i) q^{75} +(365.636 - 741.169i) q^{76} +847.356 q^{77} +(-427.358 + 484.232i) q^{78} +93.4259i q^{79} +(194.731 + 253.929i) q^{80} +(287.223 - 670.033i) q^{81} +(-40.4102 - 64.9952i) q^{82} +1249.95i q^{83} +(-100.755 + 598.304i) q^{84} +394.023i q^{85} +(593.139 - 368.779i) q^{86} +(-369.892 - 1232.98i) q^{87} +(1307.35 - 128.480i) q^{88} +267.674i q^{89} +(159.744 - 346.817i) q^{90} -641.391 q^{91} +(-580.257 + 1176.22i) q^{92} +(-762.832 + 228.848i) q^{93} +(989.392 - 615.146i) q^{94} -516.532 q^{95} +(-64.7335 + 938.374i) q^{96} -897.223 q^{97} +(312.185 - 194.098i) q^{98} +(-862.840 - 1308.65i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8}+O(q^{10}) \) 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8	\( 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8} - 15 q^{10} - 33 q^{12} + 54 q^{14} + 153 q^{16} + 59 q^{18} + 12 q^{19} + 15 q^{20} + 4 q^{21} - 102 q^{22} - 228 q^{23} - 27 q^{24} + 600 q^{25} - 336 q^{26} + 132 q^{27} - 186 q^{28} - 55 q^{30} - 177 q^{32} + 116 q^{33} + 408 q^{34} + 641 q^{36} - 312 q^{38} + 656 q^{39} + 105 q^{40} - 1042 q^{42} + 450 q^{44} - 1104 q^{46} + 924 q^{47} - 717 q^{48} - 816 q^{49} + 75 q^{50} - 700 q^{51} - 1548 q^{52} - 528 q^{53} + 987 q^{54} + 390 q^{56} - 172 q^{57} + 1410 q^{58} + 165 q^{60} + 978 q^{62} - 476 q^{63} + 1137 q^{64} - 582 q^{66} + 1632 q^{67} + 1608 q^{68} - 980 q^{69} - 270 q^{70} - 216 q^{71} - 589 q^{72} - 216 q^{73} - 768 q^{74} - 1812 q^{76} - 324 q^{78} - 765 q^{80} + 152 q^{81} + 2244 q^{82} - 134 q^{84} + 2808 q^{86} - 252 q^{87} + 2622 q^{88} - 295 q^{90} - 1800 q^{91} + 1836 q^{92} - 1968 q^{94} - 60 q^{95} + 1445 q^{96} + 792 q^{97} - 4851 q^{98} - 1328 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8 - 15 * q^10 - 33 * q^12 + 54 * q^14 + 153 * q^16 + 59 * q^18 + 12 * q^19 + 15 * q^20 + 4 * q^21 - 102 * q^22 - 228 * q^23 - 27 * q^24 + 600 * q^25 - 336 * q^26 + 132 * q^27 - 186 * q^28 - 55 * q^30 - 177 * q^32 + 116 * q^33 + 408 * q^34 + 641 * q^36 - 312 * q^38 + 656 * q^39 + 105 * q^40 - 1042 * q^42 + 450 * q^44 - 1104 * q^46 + 924 * q^47 - 717 * q^48 - 816 * q^49 + 75 * q^50 - 700 * q^51 - 1548 * q^52 - 528 * q^53 + 987 * q^54 + 390 * q^56 - 172 * q^57 + 1410 * q^58 + 165 * q^60 + 978 * q^62 - 476 * q^63 + 1137 * q^64 - 582 * q^66 + 1632 * q^67 + 1608 * q^68 - 980 * q^69 - 270 * q^70 - 216 * q^71 - 589 * q^72 - 216 * q^73 - 768 * q^74 - 1812 * q^76 - 324 * q^78 - 765 * q^80 + 152 * q^81 + 2244 * q^82 - 134 * q^84 + 2808 * q^86 - 252 * q^87 + 2622 * q^88 - 295 * q^90 - 1800 * q^91 + 1836 * q^92 - 1968 * q^94 - 60 * q^95 + 1445 * q^96 + 792 * q^97 - 4851 * q^98 - 1328 * q^99

Introduction

L-functions

Modular forms

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