LMFDB - Embedded newform 120.4.b.a.11.6

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			11.6
Character	$\chi$	$=$	120.11
Dual form			120.4.b.a.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.40201 + 1.49343i) q^{2} +(-1.49310 + 4.97701i) q^{3} +(3.53933 - 7.17448i) q^{4} +5.00000 q^{5} +(-3.84639 - 14.1847i) q^{6} -14.5956i q^{7} +(2.21306 + 22.5189i) q^{8} +(-22.5413 - 14.8623i) q^{9} +O(q^{10})$	\(q+(-2.40201 + 1.49343i) q^{2} +(-1.49310 + 4.97701i) q^{3} +(3.53933 - 7.17448i) q^{4} +5.00000 q^{5} +(-3.84639 - 14.1847i) 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} +(30.4229 + 28.3275i) 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} +(76.3404 + 2.03556i) 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} +(-115.381 - 22.6085i) 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} +(-19.2319 - 70.9234i) 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} +(-186.411 + 109.120i) 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} +(-207.034 + 56.1404i) 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} +(310.912 - 118.008i) 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} +(-124.115 + 376.908i) 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} +(152.115 + 141.637i) 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} +(-823.500 + 223.304i) 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} +(284.798 - 540.498i) 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} +(-623.334 + 169.026i) 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} +(413.457 - 444.041i) 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} +(381.702 + 10.1778i) 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} +(-570.577 + 747.782i) 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} + 19 q^{6} + 21 q^{8}+O(q^{10}) $ 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8	$ 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8} - 15 q^{10} + 65 q^{12} - 54 q^{14} + 153 q^{16} - 175 q^{18} + 12 q^{19} - 15 q^{20} - 4 q^{21} - 102 q^{22} + 228 q^{23} - 407 q^{24} + 600 q^{25} + 336 q^{26} + 132 q^{27} - 186 q^{28} + 95 q^{30} + 177 q^{32} + 116 q^{33} + 408 q^{34} + 673 q^{36} + 312 q^{38} - 656 q^{39} + 105 q^{40} - 990 q^{42} - 450 q^{44} - 1104 q^{46} - 924 q^{47} - 535 q^{48} - 816 q^{49} - 75 q^{50} - 700 q^{51} - 1548 q^{52} + 528 q^{53} + 1331 q^{54} - 390 q^{56} - 172 q^{57} + 1410 q^{58} + 325 q^{60} - 978 q^{62} + 476 q^{63} + 1137 q^{64} - 2794 q^{66} + 1632 q^{67} - 1608 q^{68} + 980 q^{69} - 270 q^{70} + 216 q^{71} - 3699 q^{72} - 216 q^{73} + 768 q^{74} - 1812 q^{76} + 4140 q^{78} + 765 q^{80} + 152 q^{81} + 2244 q^{82} + 5086 q^{84} - 2808 q^{86} + 252 q^{87} + 2622 q^{88} - 875 q^{90} - 1800 q^{91} - 1836 q^{92} - 1968 q^{94} + 60 q^{95} - 5455 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 + 19 * q^6 + 21 * q^8 - 15 * q^10 + 65 * q^12 - 54 * q^14 + 153 * q^16 - 175 * q^18 + 12 * q^19 - 15 * q^20 - 4 * q^21 - 102 * q^22 + 228 * q^23 - 407 * q^24 + 600 * q^25 + 336 * q^26 + 132 * q^27 - 186 * q^28 + 95 * q^30 + 177 * q^32 + 116 * q^33 + 408 * q^34 + 673 * q^36 + 312 * q^38 - 656 * q^39 + 105 * q^40 - 990 * q^42 - 450 * q^44 - 1104 * q^46 - 924 * q^47 - 535 * q^48 - 816 * q^49 - 75 * q^50 - 700 * q^51 - 1548 * q^52 + 528 * q^53 + 1331 * q^54 - 390 * q^56 - 172 * q^57 + 1410 * q^58 + 325 * q^60 - 978 * q^62 + 476 * q^63 + 1137 * q^64 - 2794 * q^66 + 1632 * q^67 - 1608 * q^68 + 980 * q^69 - 270 * q^70 + 216 * q^71 - 3699 * q^72 - 216 * q^73 + 768 * q^74 - 1812 * q^76 + 4140 * q^78 + 765 * q^80 + 152 * q^81 + 2244 * q^82 + 5086 * q^84 - 2808 * q^86 + 252 * q^87 + 2622 * q^88 - 875 * q^90 - 1800 * q^91 - 1836 * q^92 - 1968 * q^94 + 60 * q^95 - 5455 * 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
$6$	−3.84639	−	14.1847i	−0.261714	−	0.965146i
$7$		−	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	$-0.707127\pi$
$11$		−	58.0556i		−	1.59131i	0.605750	−	0.795655i	$-0.292873\pi$
$12$	30.4229	+	28.3275i	0.731861	+	0.681453i
$13$		−	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	$0.190023\pi$
$17$			78.8045i			1.12429i	−0.827039	+	0.562144i	$0.809977\pi$
$18$	76.3404	+	2.03556i	0.999645	+	0.0266548i
$19$	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	$-0.233330\pi$
$23$	163.945			1.48630			0.743151	+	0.669123i	$0.233330\pi$
$24$	−115.381	−	22.6085i	−0.981338	−	0.192289i
$25$	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	$-0.791566\pi$
$29$	−247.735			−1.58632			−0.793160	+	0.609013i	$0.791566\pi$
$30$	−19.2319	−	70.9234i	−0.117042	−	0.431626i
$31$		−	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
$36$	−186.411	+	109.120i	−0.863012	+	0.505183i
$37$		−	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	$0.0164113\pi$
$41$			27.0586i			0.103070i	−0.998671	+	0.0515348i	$0.983589\pi$
$42$	−207.034	+	56.1404i	−0.760620	+	0.206253i
$43$	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	$-0.720722\pi$
$47$	−411.901			−1.27834			−0.639170	+	0.769065i	$0.720722\pi$
$48$	310.912	−	118.008i	0.934922	−	0.354854i
$49$	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	$-0.533130\pi$
$53$	−80.1737			−0.207787			−0.103893	+	0.994588i	$0.533130\pi$
$54$	−124.115	+	376.908i	−0.312775	+	0.949827i
$55$		−	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	$-0.808233\pi$
$59$		−	513.612i		−	1.13333i	0.823947	−	0.566666i	$-0.191767\pi$
$60$	152.115	+	141.637i	0.327298	+	0.304755i
$61$		−	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
$66$	−823.500	+	223.304i	−1.53585	+	0.416467i
$67$	−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	$-0.378341\pi$
$71$	446.258			0.745930			0.372965	+	0.927845i	$0.378341\pi$
$72$	284.798	−	540.498i	0.466164	−	0.884698i
$73$	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
$78$	−623.334	+	169.026i	−0.904855	+	0.245365i
$79$			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	$-0.690327\pi$
$83$		−	1249.95i		−	1.65301i	0.562933	−	0.826503i	$-0.309673\pi$
$84$	413.457	−	444.041i	0.537046	−	0.576772i
$85$			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	$-0.949044\pi$
$89$		−	267.674i		−	0.318803i	0.987214	−	0.159401i	$-0.0509564\pi$
$90$	381.702	+	10.1778i	0.447055	+	0.0119204i
$91$	−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
$96$	−570.577	+	747.782i	−0.606607	+	0.795002i
$97$	−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	$-0.320322\pi$
$101$	1086.03			1.06994			0.534972	+	0.844870i	$0.320322\pi$
$102$	1117.82	−	303.113i	1.08510	−	0.294241i
$103$			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	$0.0301332\pi$
$107$			209.243i			0.189050i	−0.995522	+	0.0945249i	$0.969867\pi$
$108$	−264.761	−	1090.69i	−0.235895	−	0.971779i
$109$		−	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	$0.207237\pi$
$113$			1455.92i			1.21205i	−0.795445	+	0.606026i	$0.792763\pi$
$114$	−397.356	−	1465.37i	−0.326455	−	1.20390i
$115$	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
$120$	−576.907	−	113.043i	−0.438868	−	0.0859944i
$121$	−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
$126$	29.7103	−	1114.23i	0.0210064	−	0.787809i
$127$			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	$-0.892453\pi$
$131$		−	994.011i		−	0.662955i	0.943463	−	0.331478i	$-0.107547\pi$
$132$	1644.57	−	1766.22i	1.08440	−	1.16462i
$133$		−	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	$0.0216671\pi$
$137$			218.135i			0.136033i	−0.997684	+	0.0680166i	$0.978333\pi$
$138$	−630.597	−	2325.51i	−0.388986	−	1.43450i
$139$	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
$144$	123.107	+	1723.61i	0.0712424	+	0.997459i
$145$	−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	$-0.759729\pi$
$149$	−2649.54			−1.45677			−0.728385	+	0.685168i	$0.759729\pi$
$150$	−96.1597	−	354.617i	−0.0523427	−	0.193029i
$151$			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
$156$	1244.83	−	1336.91i	0.638884	−	0.686143i
$157$			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
$162$	−1690.56	−	1180.48i	−0.819895	−	0.572514i
$163$	−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	$-0.811849\pi$
$167$	−3583.90			−1.66066			−0.830332	+	0.557269i	$0.811849\pi$
$168$	−329.985	+	1684.06i	−0.151541	+	0.773382i
$169$	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	$-0.537153\pi$
$173$	−529.974			−0.232909			−0.116454	+	0.993196i	$0.537153\pi$
$174$	952.886	+	3514.05i	0.415161	+	1.53103i
$175$		−	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	$0.157336\pi$
$179$			2272.25i			0.948805i	−0.880308	+	0.474402i	$0.842664\pi$
$180$	−932.053	+	545.598i	−0.385951	+	0.225925i
$181$		−	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
$186$	−2174.10	+	589.539i	−0.857058	+	0.232404i
$187$	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	$-0.418424\pi$
$191$	1338.21			0.506962			0.253481	+	0.967340i	$0.418424\pi$
$192$	253.774	−	2648.30i	0.0953883	−	0.995440i
$193$	−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	$-0.314705\pi$
$197$	3040.41			1.09960			0.549798	+	0.835298i	$0.314705\pi$
$198$	118.176	−	4431.99i	0.0424161	−	1.59075i
$199$			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
$204$	−2232.33	+	2397.46i	−0.766150	+	0.822823i
$205$			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
$210$	−1035.17	+	280.702i	−0.340160	+	0.0922394i
$211$	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
$216$	2264.83	+	2224.46i	0.713437	+	0.700719i
$217$	−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
$222$	−2179.30	+	590.950i	−0.658853	+	0.178658i
$223$			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	$0.0220087\pi$
$227$			472.571i			0.138174i	−0.997611	+	0.0690872i	$0.977991\pi$
$228$	3142.88	+	2926.41i	0.912905	+	0.850027i
$229$		−	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	$0.00633311\pi$
$233$			141.515i			0.0397895i	−0.999802	+	0.0198947i	$0.993667\pi$
$234$	89.4511	−	3354.71i	0.0249898	−	0.937199i
$235$	−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	$-0.677536\pi$
$239$	−3911.18			−1.05855			−0.529274	+	0.848451i	$0.677536\pi$
$240$	1554.56	−	590.040i	0.418110	−	0.158696i
$241$	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
$246$	383.818	−	104.078i	0.0994771	−	0.0269747i
$247$		−	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	$0.231089\pi$
$251$			5279.91i			1.32775i	−0.747844	+	0.663874i	$0.768911\pi$
$252$	1592.67	+	2720.78i	0.398129	+	0.680130i
$253$		−	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	$0.0891626\pi$
$257$			2278.07i			0.552928i	−0.961024	+	0.276464i	$0.910837\pi$
$258$	−949.804	−	3502.68i	−0.229195	−	0.845223i
$259$	−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	$-0.250730\pi$
$263$	6017.98			1.41097			0.705484	+	0.708726i	$0.250730\pi$
$264$	−1312.55	+	6698.53i	−0.305992	+	1.56161i
$265$	−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	$-0.389238\pi$
$269$	3008.84			0.681979			0.340989	+	0.940067i	$0.389238\pi$
$270$	−620.573	+	1884.54i	−0.139877	+	0.424776i
$271$			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
$276$	4987.69	+	4644.16i	1.08777	+	1.01285i
$277$			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	$0.0309116\pi$
$281$			913.436i			0.193918i	−0.995288	+	0.0969591i	$0.969088\pi$
$282$	1584.33	+	5842.69i	0.334559	+	1.23378i
$283$	−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
$288$	−2869.79	−	3956.28i	−0.587168	−	0.809465i
$289$	−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	$-0.476413\pi$
$293$	742.598			0.148065			0.0740324	+	0.997256i	$0.476413\pi$
$294$	−499.908	−	1843.56i	−0.0991675	−	0.365709i
$295$		−	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
$300$	760.573	+	708.187i	0.146372	+	0.136291i
$301$		−	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
$306$	−160.412	+	6015.97i	−0.0299677	+	1.12389i
$307$	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	$-0.411327\pi$
$311$	3016.33			0.549970			0.274985	+	0.961449i	$0.411327\pi$
$312$	−993.511	+	5070.33i	−0.180277	+	0.920036i
$313$	−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	$-0.671831\pi$
$317$	−5801.88			−1.02797			−0.513985	+	0.857799i	$0.671831\pi$
$318$	308.379	+	1137.24i	0.0543807	+	0.200545i
$319$			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
$324$	5823.71	+	310.792i	0.998579	+	0.0532907i
$325$		−	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
$330$	−4117.50	+	1116.52i	−0.686851	+	0.186250i
$331$	−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
$336$	−1722.40	−	4537.95i	−0.279656	−	0.736801i
$337$	−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
$342$	7886.45	+	210.287i	1.24693	+	0.0332486i
$343$		−	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	$-0.993867\pi$
$347$		−	249.070i		−	0.0385325i	0.999814	−	0.0192662i	$-0.00613301\pi$
$348$	−7536.83	−	7017.72i	−1.16097	−	1.08100i
$349$		−	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	$0.169856\pi$
$353$			6747.03i			1.01730i	−0.860972	+	0.508652i	$0.830144\pi$
$354$	−7285.43	+	1975.55i	−1.09383	+	0.296609i
$355$	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	$-0.463419\pi$
$359$	1559.98			0.229339			0.114669	+	0.993404i	$0.463419\pi$
$360$	1423.99	−	2702.49i	0.208475	−	0.395649i
$361$	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
$366$	−383.639	+	104.029i	−0.0547900	+	0.0148571i
$367$		−	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
$372$	4341.78	−	4662.95i	0.605137	−	0.649899i
$373$			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
$378$	5501.20	+	1811.53i	0.748548	+	0.246494i
$379$	−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	$-0.487954\pi$
$383$	567.176			0.0756694			0.0378347	+	0.999284i	$0.487954\pi$
$384$	3345.48	+	6740.24i	0.444592	+	0.895733i
$385$	−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	$-0.270124\pi$
$389$	10143.0			1.32204			0.661019	+	0.750369i	$0.270124\pi$
$390$	−3116.67	+	845.131i	−0.404663	+	0.109730i
$391$			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
$396$	6335.00	+	10822.2i	0.803903	+	1.37332i
$397$		−	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	$-0.997190\pi$
$401$		−	141.751i		−	0.0176526i	0.999961	−	0.00882632i	$-0.00280954\pi$
$402$	1742.75	+	6426.92i	0.216221	+	0.797377i
$403$	−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
$408$	1781.65	−	9092.57i	0.216189	−	1.10331i
$409$	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
$414$	12515.7	+	333.721i	1.48577	+	0.0396172i
$415$		−	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	$-0.976290\pi$
$419$		−	1276.55i		−	0.148840i	0.997227	−	0.0744198i	$-0.0237105\pi$
$420$	2067.28	−	2220.20i	0.240174	−	0.257940i
$421$			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
$426$	−1716.48	−	6330.03i	−0.195220	−	0.719931i
$427$	−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	$-0.170029\pi$
$431$	15402.6			1.72139			0.860695	+	0.509120i	$0.170029\pi$
$432$	−8762.24	−	1960.81i	−0.975864	−	0.218378i
$433$	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
$438$	−2018.66	−	7444.42i	−0.220218	−	0.812119i
$439$			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	$-0.927559\pi$
$443$		−	4207.40i		−	0.451241i	0.974215	−	0.225620i	$-0.0724409\pi$
$444$	4352.17	−	4674.11i	0.465191	−	0.499602i
$445$		−	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	$0.0863693\pi$
$449$			5099.95i			0.536040i	−0.963413	+	0.268020i	$0.913631\pi$
$450$	1908.51	+	50.8891i	0.199929	+	0.00533097i
$451$	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
$456$	−11919.6	−	2335.60i	−1.22410	−	0.239857i
$457$	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	$-0.691468\pi$
$461$	−11202.5			−1.13179			−0.565893	+	0.824479i	$0.691468\pi$
$462$	3259.26	+	12019.5i	0.328213	+	1.21038i
$463$		−	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	$-0.767744\pi$
$467$		−	13454.8i		−	1.33322i	0.745406	−	0.666611i	$-0.232256\pi$
$468$	4795.17	+	8191.65i	0.473625	+	0.809101i
$469$			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
$474$	1325.22	−	359.352i	0.128416	−	0.0348219i
$475$	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	$-0.321905\pi$
$479$	11128.5			1.06153			0.530765	+	0.847519i	$0.321905\pi$
$480$	−2852.89	+	3738.91i	−0.271283	+	0.355536i
$481$	−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
$486$	8399.43	−	6651.38i	0.783963	−	0.620808i
$487$		−	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	$-0.930601\pi$
$491$		−	4706.59i		−	0.432597i	0.976327	−	0.216299i	$-0.0693985\pi$
$492$	−766.504	+	823.203i	−0.0702371	+	0.0754326i
$493$		−	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
$498$	−17730.1	+	4807.78i	−1.59539	+	0.432614i
$499$	−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	$-0.555444\pi$
$503$	−3910.09			−0.346605			−0.173303	+	0.984869i	$0.555444\pi$
$504$	−7888.90	−	4156.80i	−0.697221	−	0.367378i
$505$	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	$-0.789228\pi$
$509$	−18113.4			−1.57733			−0.788667	+	0.614821i	$0.789228\pi$
$510$	5589.09	−	1515.56i	0.485272	−	0.131589i
$511$		−	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
$516$	7512.45	+	6995.02i	0.640925	+	0.596780i
$517$			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	$0.243462\pi$
$521$			16469.0i			1.38487i	−0.721480	+	0.692436i	$0.756538\pi$
$522$	−18912.2	−	504.281i	−1.58576	−	0.0422831i
$523$	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
$528$	−6851.03	−	18050.2i	−0.564683	−	1.48775i
$529$	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
$534$	−3796.88	+	1029.58i	−0.307691	+	0.0834349i
$535$			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
$540$	−1323.80	−	5453.47i	−0.105495	−	0.434593i
$541$			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
$546$	2467.04	+	9097.94i	0.193369	+	0.713106i
$547$	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
$552$	−18916.2	−	3706.56i	−1.45857	−	0.285800i
$553$	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	$-0.178148\pi$
$557$	22280.1			1.69486			0.847431	+	0.530905i	$0.178148\pi$
$558$	311.993	−	11700.8i	0.0236697	−	0.887693i
$559$		−	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	$-0.873111\pi$
$563$		−	10370.5i		−	0.776317i	0.921593	−	0.388158i	$-0.126889\pi$
$564$	−12531.2	−	11668.1i	−0.935568	−	0.871129i
$565$			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	$-0.802368\pi$
$569$		−	15791.9i		−	1.16350i	0.813368	−	0.581750i	$-0.197632\pi$
$570$	−1986.78	−	7326.84i	−0.145995	−	0.538399i
$571$	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
$576$	12801.7	+	5217.20i	0.926050	+	0.377402i
$577$	−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
$582$	3451.07	+	12726.8i	0.245793	+	0.906433i
$583$			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	$-0.957788\pi$
$587$		−	3761.00i		−	0.264451i	0.991220	−	0.132226i	$-0.0422124\pi$
$588$	3954.01	+	3681.67i	0.277314	+	0.258214i
$589$		−	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	$0.0883406\pi$
$593$			7912.85i			0.547962i	−0.961735	+	0.273981i	$0.911659\pi$
$594$	21881.6	+	7205.54i	1.51147	+	0.497722i
$595$	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	$-0.646443\pi$
$599$	−13018.4			−0.888012			−0.444006	+	0.896024i	$0.646443\pi$
$600$	−2884.53	−	565.213i	−0.196268	−	0.0384578i
$601$	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
$606$	−4177.31	−	15405.0i	−0.280019	−	1.03265i
$607$			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
$612$	−8599.12	−	14690.0i	−0.567972	−	0.970274i
$613$		−	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	$-0.807066\pi$
$617$		−	17461.9i		−	1.13936i	0.821865	−	0.569682i	$-0.192934\pi$
$618$	8547.66	−	2317.83i	0.556371	−	0.150868i
$619$	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
$624$	−5185.76	−	13662.7i	−0.332687	−	0.876519i
$625$	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
$630$	148.551	−	5571.17i	0.00939434	−	0.352319i
$631$			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
$636$	−2439.12	−	2271.12i	−0.152071	−	0.141597i
$637$		−	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	$-0.681769\pi$
$641$		−	27307.8i		−	1.68267i	0.540510	−	0.841337i	$-0.318231\pi$
$642$	2968.05	−	804.831i	0.182461	−	0.0494769i
$643$	−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	$-0.548526\pi$
$647$	−4998.32			−0.303716			−0.151858	+	0.988402i	$0.548526\pi$
$648$	−14452.8	+	7950.78i	−0.876171	+	0.482000i
$649$	−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	$-0.257347\pi$
$653$	23047.6			1.38120			0.690599	+	0.723238i	$0.257347\pi$
$654$	−12290.2	+	3332.66i	−0.734837	+	0.199262i
$655$		−	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	$0.187659\pi$
$659$			18811.4i			1.11197i	−0.831191	+	0.555986i	$0.812341\pi$
$660$	8222.84	−	8831.10i	0.484960	−	0.520833i
$661$			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
$666$	312.740	−	11728.8i	0.0181958	−	0.682403i
$667$	−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
$672$	10914.3	+	8327.92i	0.626532	+	0.478060i
$673$	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	$-0.502683\pi$
$677$	−296.947			−0.0168576			−0.00842881	+	0.999964i	$0.502683\pi$
$678$	20651.8	−	5600.05i	1.16981	−	0.317210i
$679$			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	$0.0565220\pi$
$683$			6305.85i			0.353275i	−0.984276	+	0.176638i	$0.943478\pi$
$684$	−19257.4	+	11272.7i	−1.07650	+	0.630153i
$685$			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
$690$	−3152.99	−	11627.6i	−0.173960	−	0.641527i
$691$	−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
$696$	28584.0	+	5600.92i	1.55672	+	0.305032i
$697$	−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	$-0.660359\pi$
$701$	−17919.3			−0.965481			−0.482741	+	0.875763i	$0.660359\pi$
$702$	16562.9	+	5454.11i	0.890493	+	0.293236i
$703$		−	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
$708$	14549.3	−	15625.6i	0.772313	−	0.829443i
$709$			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
$714$	−4424.11	−	16315.2i	−0.231888	−	0.855157i
$715$	−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	$-0.435770\pi$
$719$	7727.83			0.400834			0.200417	+	0.979711i	$0.435770\pi$
$720$	615.534	+	8618.05i	0.0318606	+	0.446077i
$721$	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
$726$	7844.51	+	28929.0i	0.401015	+	1.47886i
$727$		−	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
$732$	766.145	−	822.818i	0.0386852	−	0.0415468i
$733$		−	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
$738$	−55.0796	+	2065.67i	−0.00274730	+	0.103033i
$739$	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	$-0.606990\pi$
$743$	−13359.7			−0.659649			−0.329824	+	0.944042i	$0.606990\pi$
$744$	−3465.23	+	17684.6i	−0.170755	+	0.871437i
$745$	−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
$750$	−480.798	−	1773.09i	−0.0234084	−	0.0863252i
$751$		−	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
$756$	−15919.3	+	3864.35i	−0.765848	+	0.185906i
$757$		−	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	$-0.915325\pi$
$761$		−	11037.7i		−	0.525778i	0.964826	−	0.262889i	$-0.0846752\pi$
$762$	24257.5	−	6577.78i	1.15322	−	0.312714i
$763$	−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
$768$	−18102.0	−	11193.9i	−0.850519	−	0.525944i
$769$	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	$-0.336541\pi$
$773$	21115.4			0.982497			0.491248	+	0.871020i	$0.336541\pi$
$774$	18851.0	+	502.650i	0.875435	+	0.0233429i
$775$		−	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
$780$	6224.14	−	6684.54i	0.285718	−	0.306853i
$781$		−	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
$786$	−14099.7	+	3823.35i	−0.639849	+	0.173504i
$787$	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
$792$	−31378.9	−	16534.1i	−1.40783	−	0.741811i
$793$	−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	$-0.464390\pi$
$797$	5023.82			0.223278			0.111639	+	0.993749i	$0.464390\pi$
$798$	−21387.9	+	5799.66i	−0.948778	+	0.257275i
$799$		−	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
$804$	−13784.3	−	12834.9i	−0.604644	−	0.562999i
$805$		−	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	$0.0692169\pi$
$809$			9928.57i			0.431483i	−0.976450	+	0.215742i	$0.930783\pi$
$810$	−8452.81	−	5902.40i	−0.366668	−	0.256036i
$811$	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
$816$	9299.57	+	24501.2i	0.398958	+	1.05112i
$817$	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	$-0.372375\pi$
$821$	18362.5			0.780579			0.390289	+	0.920692i	$0.372375\pi$
$822$	3094.18	−	839.032i	0.131292	−	0.0356017i
$823$		−	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	$0.146335\pi$
$827$			21104.7i			0.887404i	−0.896174	+	0.443702i	$0.853665\pi$
$828$	−30561.2	+	17889.7i	−1.28270	+	0.750855i
$829$			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
$834$	−3353.90	−	12368.5i	−0.139252	−	0.513532i
$835$	−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	$-0.634978\pi$
$839$	−19998.2			−0.822900			−0.411450	+	0.911432i	$0.634978\pi$
$840$	−1649.92	+	8420.30i	−0.0677712	+	0.345867i
$841$	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
$846$	−31444.7	−	838.452i	−1.27789	−	0.0340740i
$847$			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
$852$	13576.5	+	12641.4i	0.545918	+	0.508317i
$853$			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	$-0.992067\pi$
$857$		−	1250.31i		−	0.0498365i	0.999689	−	0.0249183i	$-0.00793255\pi$
$858$	9812.91	+	36188.0i	0.390451	+	1.43990i
$859$	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	$-0.401022\pi$
$863$	15513.7			0.611926			0.305963	+	0.952043i	$0.401022\pi$
$864$	23975.3	−	8375.90i	0.944048	−	0.329808i
$865$	−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
$870$	4764.43	+	17570.2i	0.185666	+	0.684697i
$871$			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
$876$	15966.6	+	14866.9i	0.615823	+	0.573407i
$877$		−	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	$-0.594593\pi$
$881$		−	50006.7i		−	1.91234i	0.292817	−	0.956169i	$-0.405407\pi$
$882$	9921.83	+	264.559i	0.378782	+	0.0100999i
$883$	−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	$-0.671600\pi$
$887$	−27123.1			−1.02672			−0.513362	+	0.858172i	$0.671600\pi$
$888$	−3473.52	+	17726.9i	−0.131265	+	0.669906i
$889$	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
$894$	10191.2	+	37582.9i	0.381256	+	1.40600i
$895$			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
$900$	−4660.27	+	2727.99i	−0.172602	+	0.101037i
$901$		−	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
$906$	10179.4	−	2760.29i	0.373276	−	0.101219i
$907$	−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	$-0.171062\pi$
$911$	47241.1			1.71808			0.859038	+	0.511912i	$0.171062\pi$
$912$	32119.2	−	12191.0i	1.16620	−	0.442636i
$913$	−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
$918$	−29702.0	−	9780.78i	−1.06788	−	0.351649i
$919$		−	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
$924$	−25779.0	−	24003.5i	−0.917823	−	0.854607i
$925$		−	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	$0.222673\pi$
$929$			36463.1i			1.28774i	−0.765133	+	0.643872i	$0.777327\pi$
$930$	−10870.5	+	2947.70i	−0.383288	+	0.103934i
$931$	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
$936$	−23751.7	−	12515.2i	−0.829433	−	0.437043i
$937$	−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	$-0.546466\pi$
$941$	−8397.60			−0.290918			−0.145459	+	0.989364i	$0.546466\pi$
$942$	46125.0	−	12507.5i	1.59537	−	0.432607i
$943$			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	$-0.734619\pi$
$947$		−	43156.1i		−	1.48087i	0.672127	−	0.740436i	$-0.265381\pi$
$948$	−2646.52	+	2842.29i	−0.0906698	+	0.0973768i
$949$		−	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	$0.114157\pi$
$953$			20652.4i			0.701991i	−0.936377	+	0.350995i	$0.885843\pi$
$954$	−6120.49	−	163.199i	−0.207713	−	0.00553853i
$955$	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
$960$	1268.87	−	13241.5i	0.0426590	−	0.445174i
$961$	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
$966$	−33942.3	+	9203.95i	−1.13051	+	0.306555i
$967$			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	$-0.929542\pi$
$971$		−	13285.7i		−	0.439093i	0.975602	−	0.219547i	$-0.0704578\pi$
$972$	−10242.2	+	28520.7i	−0.337981	+	0.941153i
$973$		−	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	$0.109183\pi$
$977$			20541.2i			0.672642i	−0.941747	+	0.336321i	$0.890817\pi$
$978$	694.721	+	2561.99i	0.0227144	+	0.0837662i
$979$	−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	$-0.651277\pi$
$983$	−28203.9			−0.915123			−0.457562	+	0.889178i	$0.651277\pi$
$984$	611.756	−	3122.06i	0.0198192	−	0.101146i
$985$	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
$990$	590.879	−	22159.9i	0.0189691	−	0.711403i
$991$			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
$996$	35407.8	−	38027.0i	1.12645	−	1.20977i
$997$			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.a.11.6	yes	24
3.2	odd	2		120.4.b.b.11.19	yes	24
4.3	odd	2		480.4.b.b.431.15		24
8.3	odd	2		120.4.b.b.11.20	yes	24
8.5	even	2		480.4.b.a.431.15		24
12.11	even	2		480.4.b.a.431.16		24
24.5	odd	2		480.4.b.b.431.16		24
24.11	even	2	inner	120.4.b.a.11.5	✓	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.40201 + 1.49343i) q^{2} +(-1.49310 + 4.97701i) q^{3} +(3.53933 - 7.17448i) q^{4} +5.00000 q^{5} +(-3.84639 - 14.1847i) q^{6} -14.5956i q^{7} +(2.21306 + 22.5189i) q^{8} +(-22.5413 - 14.8623i) q^{9} +O(q^{10})\)	\(q+(-2.40201 + 1.49343i) q^{2} +(-1.49310 + 4.97701i) q^{3} +(3.53933 - 7.17448i) q^{4} +5.00000 q^{5} +(-3.84639 - 14.1847i) 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} +(30.4229 + 28.3275i) 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} +(76.3404 + 2.03556i) 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} +(-115.381 - 22.6085i) 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} +(-19.2319 - 70.9234i) 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} +(-186.411 + 109.120i) 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} +(-207.034 + 56.1404i) 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} +(310.912 - 118.008i) 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} +(-124.115 + 376.908i) 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} +(152.115 + 141.637i) 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} +(-823.500 + 223.304i) 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} +(284.798 - 540.498i) 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} +(-623.334 + 169.026i) 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} +(413.457 - 444.041i) 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} +(381.702 + 10.1778i) 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} +(-570.577 + 747.782i) q^{96} -897.223 q^{97} +(-312.185 + 194.098i) q^{98} +(-862.840 + 1308.65i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8}+O(q^{10}) \) 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8	\( 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8} - 15 q^{10} + 65 q^{12} - 54 q^{14} + 153 q^{16} - 175 q^{18} + 12 q^{19} - 15 q^{20} - 4 q^{21} - 102 q^{22} + 228 q^{23} - 407 q^{24} + 600 q^{25} + 336 q^{26} + 132 q^{27} - 186 q^{28} + 95 q^{30} + 177 q^{32} + 116 q^{33} + 408 q^{34} + 673 q^{36} + 312 q^{38} - 656 q^{39} + 105 q^{40} - 990 q^{42} - 450 q^{44} - 1104 q^{46} - 924 q^{47} - 535 q^{48} - 816 q^{49} - 75 q^{50} - 700 q^{51} - 1548 q^{52} + 528 q^{53} + 1331 q^{54} - 390 q^{56} - 172 q^{57} + 1410 q^{58} + 325 q^{60} - 978 q^{62} + 476 q^{63} + 1137 q^{64} - 2794 q^{66} + 1632 q^{67} - 1608 q^{68} + 980 q^{69} - 270 q^{70} + 216 q^{71} - 3699 q^{72} - 216 q^{73} + 768 q^{74} - 1812 q^{76} + 4140 q^{78} + 765 q^{80} + 152 q^{81} + 2244 q^{82} + 5086 q^{84} - 2808 q^{86} + 252 q^{87} + 2622 q^{88} - 875 q^{90} - 1800 q^{91} - 1836 q^{92} - 1968 q^{94} + 60 q^{95} - 5455 q^{96} + 792 q^{97} + 4851 q^{98} - 1328 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8 - 15 * q^10 + 65 * q^12 - 54 * q^14 + 153 * q^16 - 175 * q^18 + 12 * q^19 - 15 * q^20 - 4 * q^21 - 102 * q^22 + 228 * q^23 - 407 * q^24 + 600 * q^25 + 336 * q^26 + 132 * q^27 - 186 * q^28 + 95 * q^30 + 177 * q^32 + 116 * q^33 + 408 * q^34 + 673 * q^36 + 312 * q^38 - 656 * q^39 + 105 * q^40 - 990 * q^42 - 450 * q^44 - 1104 * q^46 - 924 * q^47 - 535 * q^48 - 816 * q^49 - 75 * q^50 - 700 * q^51 - 1548 * q^52 + 528 * q^53 + 1331 * q^54 - 390 * q^56 - 172 * q^57 + 1410 * q^58 + 325 * q^60 - 978 * q^62 + 476 * q^63 + 1137 * q^64 - 2794 * q^66 + 1632 * q^67 - 1608 * q^68 + 980 * q^69 - 270 * q^70 + 216 * q^71 - 3699 * q^72 - 216 * q^73 + 768 * q^74 - 1812 * q^76 + 4140 * q^78 + 765 * q^80 + 152 * q^81 + 2244 * q^82 + 5086 * q^84 - 2808 * q^86 + 252 * q^87 + 2622 * q^88 - 875 * q^90 - 1800 * q^91 - 1836 * q^92 - 1968 * q^94 + 60 * q^95 - 5455 * q^96 + 792 * q^97 + 4851 * q^98 - 1328 * q^99

Introduction

L-functions

Modular forms

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