LMFDB - Embedded newform 120.4.w.c.53.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(53,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("120.53");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.w (of order $4$, degree $2$, 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:	$128$
Relative dimension:	$64$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.8
Character	$\chi$	$=$	120.53
Dual form			120.4.w.c.77.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.68461 - 0.890420i) q^{2} +(-4.50848 + 2.58334i) q^{3} +(6.41430 + 4.78087i) q^{4} +(-7.39959 - 8.38130i) q^{5} +(14.4038 - 2.92083i) q^{6} +(8.77577 - 8.77577i) q^{7} +(-12.9629 - 18.5462i) q^{8} +(13.6527 - 23.2938i) q^{9} +(12.4022 + 29.0893i) q^{10} +2.95255 q^{11} +(-41.2693 - 4.98412i) q^{12} +(-54.7622 + 54.7622i) q^{13} +(-31.3737 + 15.7454i) q^{14} +(55.0126 + 18.6712i) q^{15} +(18.2866 + 61.3319i) q^{16} +(28.5815 + 28.5815i) q^{17} +(-57.3936 + 50.3783i) q^{18} +80.3420 q^{19} +(-7.39330 - 89.1366i) q^{20} +(-16.8946 + 62.2362i) q^{21} +(-7.92646 - 2.62901i) q^{22} +(-73.2914 + 73.2914i) q^{23} +(106.354 + 50.1275i) q^{24} +(-15.4922 + 124.036i) q^{25} +(195.777 - 98.2540i) q^{26} +(-1.37709 + 140.289i) q^{27} +(98.2463 - 14.3346i) q^{28} +240.870i q^{29} +(-131.062 - 99.1094i) q^{30} +131.509 q^{31} +(5.51879 - 180.935i) q^{32} +(-13.3115 + 7.62744i) q^{33} +(-51.2807 - 102.180i) q^{34} +(-138.489 - 8.61527i) q^{35} +(198.938 - 84.1419i) q^{36} +(-53.0074 - 53.0074i) q^{37} +(-215.687 - 71.5382i) q^{38} +(105.425 - 388.364i) q^{39} +(-59.5209 + 245.881i) q^{40} +251.827i q^{41} +(100.772 - 152.037i) q^{42} +(100.289 - 100.289i) q^{43} +(18.9385 + 14.1158i) q^{44} +(-296.257 + 57.9373i) q^{45} +(262.019 - 131.499i) q^{46} +(-111.559 - 111.559i) q^{47} +(-240.886 - 229.273i) q^{48} +188.972i q^{49} +(152.035 - 319.195i) q^{50} +(-202.695 - 55.0233i) q^{51} +(-613.073 + 89.4504i) q^{52} +(-100.811 - 100.811i) q^{53} +(128.613 - 375.397i) q^{54} +(-21.8476 - 24.7462i) q^{55} +(-276.517 - 48.9975i) q^{56} +(-362.220 + 207.551i) q^{57} +(214.476 - 646.643i) q^{58} -270.848i q^{59} +(263.603 + 382.771i) q^{60} -286.796i q^{61} +(-353.050 - 117.098i) q^{62} +(-84.6083 - 324.235i) q^{63} +(-175.924 + 480.827i) q^{64} +(864.196 + 53.7606i) q^{65} +(42.5279 - 8.62389i) q^{66} +(326.692 + 326.692i) q^{67} +(46.6859 + 319.975i) q^{68} +(141.096 - 519.769i) q^{69} +(364.120 + 146.442i) q^{70} +986.927i q^{71} +(-608.992 + 48.7504i) q^{72} +(778.110 + 778.110i) q^{73} +(95.1056 + 189.503i) q^{74} +(-250.581 - 599.236i) q^{75} +(515.338 + 384.105i) q^{76} +(25.9109 - 25.9109i) q^{77} +(-628.832 + 948.734i) q^{78} -1224.19i q^{79} +(378.728 - 607.096i) q^{80} +(-356.206 - 636.049i) q^{81} +(224.231 - 676.057i) q^{82} +(978.764 + 978.764i) q^{83} +(-405.910 + 318.431i) q^{84} +(28.0587 - 451.041i) q^{85} +(-358.538 + 179.939i) q^{86} +(-622.249 - 1085.96i) q^{87} +(-38.2737 - 54.7586i) q^{88} -556.133 q^{89} +(846.924 + 108.254i) q^{90} +961.162i q^{91} +(-820.510 + 119.717i) q^{92} +(-592.903 + 339.731i) q^{93} +(200.158 + 398.827i) q^{94} +(-594.498 - 673.370i) q^{95} +(442.536 + 829.999i) q^{96} +(-514.604 + 514.604i) q^{97} +(168.264 - 507.316i) q^{98} +(40.3103 - 68.7762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 4 q^{6} - 144 q^{7} - 156 q^{10} - 56 q^{12} + 212 q^{15} + 636 q^{16} + 220 q^{18} - 188 q^{22} - 8 q^{25} + 908 q^{28} + 328 q^{30} - 544 q^{31} - 1624 q^{33} - 1268 q^{36} - 136 q^{40} + 328 q^{42}+ \cdots - 3792 q^{97}+O(q^{100}) $ 128 * q - 4 * q^6 - 144 * q^7 - 156 * q^10 - 56 * q^12 + 212 * q^15 + 636 * q^16 + 220 * q^18 - 188 * q^22 - 8 * q^25 + 908 * q^28 + 328 * q^30 - 544 * q^31 - 1624 * q^33 - 1268 * q^36 - 136 * q^40 + 328 * q^42 + 568 * q^46 - 148 * q^48 + 616 * q^52 + 728 * q^55 - 112 * q^57 + 2196 * q^58 - 424 * q^60 - 2304 * q^63 + 304 * q^66 - 4740 * q^70 + 224 * q^72 + 1280 * q^73 - 1624 * q^76 - 1448 * q^78 + 7056 * q^81 - 1472 * q^82 - 5720 * q^87 + 1516 * q^88 - 996 * q^90 + 2732 * q^96 - 3792 * q^97

Character values

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

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−2.68461	−	0.890420i	−0.949154	−	0.314811i
$2$	−2.68461	−	0.890420i	−0.949154	−	0.314811i
$3$	−4.50848	+	2.58334i	−0.867657	+	0.497164i
$3$	−4.50848	+	2.58334i	−0.867657	+	0.497164i
$4$	6.41430	+	4.78087i	0.801788	+	0.597609i
$5$	−7.39959	−	8.38130i	−0.661839	−	0.749646i
$5$	−7.39959	−	8.38130i	−0.661839	−	0.749646i
$6$	14.4038	−	2.92083i	0.980053	−	0.198737i
$7$	8.77577	−	8.77577i	0.473847	−	0.473847i	−0.429310	−	0.903157i	$-0.641243\pi$
$7$	8.77577	−	8.77577i	0.473847	−	0.473847i	0.903157	+	0.429310i	$0.141243\pi$
$8$	−12.9629	−	18.5462i	−0.572887	−	0.819635i
$9$	13.6527	−	23.2938i	0.505656	−	0.862735i
$10$	12.4022	+	29.0893i	0.392191	+	0.919884i
$11$	2.95255			0.0809297			0.0404649	−	0.999181i	$-0.487116\pi$
$11$	2.95255			0.0809297			0.0404649	+	0.999181i	$0.487116\pi$
$12$	−41.2693	−	4.98412i	−0.992786	−	0.119899i
$13$	−54.7622	+	54.7622i	−1.16833	+	1.16833i	−0.185731	+	0.982601i	$0.559465\pi$
$13$	−54.7622	+	54.7622i	−1.16833	+	1.16833i	−0.982601	+	0.185731i	$0.940535\pi$
$14$	−31.3737	+	15.7454i	−0.598927	+	0.300582i
$15$	55.0126	+	18.6712i	0.946946	+	0.321393i
$16$	18.2866	+	61.3319i	0.285728	+	0.958311i
$17$	28.5815	+	28.5815i	0.407766	+	0.407766i	0.880959	−	0.473193i	$-0.156899\pi$
$17$	28.5815	+	28.5815i	0.407766	+	0.407766i	−0.473193	+	0.880959i	$0.656899\pi$
$18$	−57.3936	+	50.3783i	−0.751545	+	0.659682i
$19$	80.3420			0.970091			0.485045	−	0.874489i	$-0.338803\pi$
$19$	80.3420			0.970091			0.485045	+	0.874489i	$0.338803\pi$
$20$	−7.39330	−	89.1366i	−0.0826596	−	0.996578i
$21$	−16.8946	+	62.2362i	−0.175557	+	0.646716i
$22$	−7.92646	−	2.62901i	−0.0768148	−	0.0254776i
$23$	−73.2914	+	73.2914i	−0.664448	+	0.664448i	−0.956425	−	0.291977i	$-0.905687\pi$
$23$	−73.2914	+	73.2914i	−0.664448	+	0.664448i	0.291977	+	0.956425i	$0.405687\pi$
$24$	106.354	+	50.1275i	0.904562	+	0.426343i
$25$	−15.4922	+	124.036i	−0.123938	+	0.992290i
$26$	195.777	−	98.2540i	1.47673	−	0.741123i
$27$	−1.37709	+	140.289i	−0.00981561	+	0.999952i
$28$	98.2463	−	14.3346i	0.663100	−	0.0967497i
$29$			240.870i			1.54236i	0.636616	+	0.771181i	$0.280333\pi$
$29$			240.870i			1.54236i	−0.636616	+	0.771181i	$0.719667\pi$
$30$	−131.062	−	99.1094i	−0.797620	−	0.603161i
$31$	131.509			0.761924			0.380962	−	0.924591i	$-0.375593\pi$
$31$	131.509			0.761924			0.380962	+	0.924591i	$0.375593\pi$
$32$	5.51879	−	180.935i	0.0304873	−	0.999535i
$33$	−13.3115	+	7.62744i	−0.0702192	+	0.0402353i
$34$	−51.2807	−	102.180i	−0.258664	−	0.515402i
$35$	−138.489	−	8.61527i	−0.668828	−	0.0416070i
$36$	198.938	−	84.1419i	0.921007	−	0.389546i
$37$	−53.0074	−	53.0074i	−0.235524	−	0.235524i	0.579470	−	0.814994i	$-0.303260\pi$
$37$	−53.0074	−	53.0074i	−0.235524	−	0.235524i	−0.814994	+	0.579470i	$0.803260\pi$
$38$	−215.687	−	71.5382i	−0.920766	−	0.305395i
$39$	105.425	−	388.364i	0.432859	−	1.59456i
$40$	−59.5209	+	245.881i	−0.235277	+	0.971928i
$41$			251.827i			0.959236i	0.877477	+	0.479618i	$0.159225\pi$
$41$			251.827i			0.959236i	−0.877477	+	0.479618i	$0.840775\pi$
$42$	100.772	−	152.037i	0.370224	−	0.558566i
$43$	100.289	−	100.289i	0.355674	−	0.355674i	−0.506541	−	0.862216i	$-0.669076\pi$
$43$	100.289	−	100.289i	0.355674	−	0.355674i	0.862216	+	0.506541i	$0.169076\pi$
$44$	18.9385	+	14.1158i	0.0648885	+	0.0483643i
$45$	−296.257	+	57.9373i	−0.981409	+	0.191928i
$46$	262.019	−	131.499i	0.839839	−	0.421488i
$47$	−111.559	−	111.559i	−0.346224	−	0.346224i	0.512477	−	0.858701i	$-0.328728\pi$
$47$	−111.559	−	111.559i	−0.346224	−	0.346224i	−0.858701	+	0.512477i	$0.828728\pi$
$48$	−240.886	−	229.273i	−0.724351	−	0.689431i
$49$			188.972i			0.550938i
$50$	152.035	−	319.195i	0.430020	−	0.902819i
$51$	−202.695	−	55.0233i	−0.556528	−	0.151075i
$52$	−613.073	+	89.4504i	−1.63496	+	0.238549i
$53$	−100.811	−	100.811i	−0.261272	−	0.261272i	0.564299	−	0.825571i	$-0.309147\pi$
$53$	−100.811	−	100.811i	−0.261272	−	0.261272i	−0.825571	+	0.564299i	$0.809147\pi$
$54$	128.613	−	375.397i	0.324113	−	0.946019i
$55$	−21.8476	−	24.7462i	−0.0535625	−	0.0606687i
$56$	−276.517	−	48.9975i	−0.659842	−	0.116921i
$57$	−362.220	+	207.551i	−0.841706	+	0.482294i
$58$	214.476	−	646.643i	0.485552	−	1.46394i
$59$		−	270.848i		−	0.597652i	−0.954308	−	0.298826i	$-0.903405\pi$
$59$		−	270.848i		−	0.597652i	0.954308	−	0.298826i	$-0.0965950\pi$
$60$	263.603	+	382.771i	0.567183	+	0.823592i
$61$		−	286.796i		−	0.601975i	−0.953628	−	0.300988i	$-0.902684\pi$
$61$		−	286.796i		−	0.601975i	0.953628	−	0.300988i	$-0.0973163\pi$
$62$	−353.050	−	117.098i	−0.723183	−	0.239862i
$63$	−84.6083	−	324.235i	−0.169201	−	0.648409i
$64$	−175.924	+	480.827i	−0.343602	+	0.939115i
$65$	864.196	+	53.7606i	1.64908	+	0.102587i
$66$	42.5279	−	8.62389i	0.0793154	−	0.0160837i
$67$	326.692	+	326.692i	0.595698	+	0.595698i	0.939165	−	0.343467i	$-0.111601\pi$
$67$	326.692	+	326.692i	0.595698	+	0.595698i	−0.343467	+	0.939165i	$0.611601\pi$
$68$	46.6859	+	319.975i	0.0832574	+	0.570627i
$69$	141.096	−	519.769i	0.246173	−	0.906852i
$70$	364.120	+	146.442i	0.621723	+	0.250046i
$71$			986.927i			1.64967i	0.565372	+	0.824836i	$0.308733\pi$
$71$			986.927i			1.64967i	−0.565372	+	0.824836i	$0.691267\pi$
$72$	−608.992	+	48.7504i	−0.996811	+	0.0797958i
$73$	778.110	+	778.110i	1.24755	+	1.24755i	0.956800	+	0.290747i	$0.0939038\pi$
$73$	778.110	+	778.110i	1.24755	+	1.24755i	0.290747	+	0.956800i	$0.406096\pi$
$74$	95.1056	+	189.503i	0.149403	+	0.297694i
$75$	−250.581	−	599.236i	−0.385795	−	0.922585i
$76$	515.338	+	384.105i	0.777807	+	0.579735i
$77$	25.9109	−	25.9109i	0.0383483	−	0.0383483i
$78$	−628.832	+	948.734i	−0.912836	+	1.37722i
$79$		−	1224.19i		−	1.74345i	−0.489994	−	0.871726i	$-0.663001\pi$
$79$		−	1224.19i		−	1.74345i	0.489994	−	0.871726i	$-0.336999\pi$
$80$	378.728	−	607.096i	0.529288	−	0.848442i
$81$	−356.206	−	636.049i	−0.488623	−	0.872495i
$82$	224.231	−	676.057i	0.301978	−	0.910463i
$83$	978.764	+	978.764i	1.29438	+	1.29438i	0.932051	+	0.362326i	$0.118017\pi$
$83$	978.764	+	978.764i	1.29438	+	1.29438i	0.362326	+	0.932051i	$0.381983\pi$
$84$	−405.910	+	318.431i	−0.527243	+	0.413615i
$85$	28.0587	−	451.041i	0.0358046	−	0.575556i
$86$	−358.538	+	179.939i	−0.449560	+	0.225620i
$87$	−622.249	−	1085.96i	−0.766806	−	1.33824i
$88$	−38.2737	−	54.7586i	−0.0463636	−	0.0663328i
$89$	−556.133			−0.662360			−0.331180	−	0.943568i	$-0.607447\pi$
$89$	−556.133			−0.662360			−0.331180	+	0.943568i	$0.607447\pi$
$90$	846.924	+	108.254i	0.991930	+	0.126789i
$91$			961.162i			1.10722i
$92$	−820.510	+	119.717i	−0.929826	+	0.135666i
$93$	−592.903	+	339.731i	−0.661088	+	0.378801i
$94$	200.158	+	398.827i	0.219625	+	0.437615i
$95$	−594.498	−	673.370i	−0.642044	−	0.727225i
$96$	442.536	+	829.999i	0.470480	+	0.882411i
$97$	−514.604	+	514.604i	−0.538661	+	0.538661i	−0.923136	−	0.384475i	$-0.874383\pi$
$97$	−514.604	+	514.604i	−0.538661	+	0.538661i	0.384475	+	0.923136i	$0.374383\pi$
$98$	168.264	−	507.316i	0.173441	−	0.522925i
$99$	40.3103	−	68.7762i	0.0409226	−	0.0698209i
$100$	−692.373	+	721.540i	−0.692373	+	0.721540i
$101$	1171.44			1.15408			0.577041	−	0.816715i	$-0.304207\pi$
$101$	1171.44			1.15408			0.577041	+	0.816715i	$0.304207\pi$
$102$	495.163	+	328.200i	0.480671	+	0.318594i
$103$	256.427	+	256.427i	0.245306	+	0.245306i	0.819041	−	0.573735i	$-0.194506\pi$
$103$	256.427	+	256.427i	0.245306	+	0.245306i	−0.573735	+	0.819041i	$0.694506\pi$
$104$	1725.51	+	305.752i	1.62693	+	0.288284i
$105$	646.633	−	318.923i	0.600999	−	0.296417i
$106$	180.874	+	360.401i	0.165736	+	0.330238i
$107$	1109.46	−	1109.46i	1.00239	−	1.00239i	0.00238868	−	0.999997i	$-0.499240\pi$
$107$	1109.46	−	1109.46i	1.00239	−	1.00239i	0.999997	−	0.00238868i	$-0.000760342\pi$
$108$	−679.538	+	893.275i	−0.605450	+	0.795883i
$109$	−2112.92			−1.85671			−0.928355	−	0.371696i	$-0.878776\pi$
$109$	−2112.92			−1.85671			−0.928355	+	0.371696i	$0.878776\pi$
$110$	36.6180	+	85.8876i	0.0317399	+	0.0744460i
$111$	375.919	+	102.047i	0.321447	+	0.0872598i
$112$	698.714	+	377.756i	0.589484	+	0.318702i
$113$	−855.116	+	855.116i	−0.711881	+	0.711881i	−0.966929	−	0.255047i	$-0.917909\pi$
$113$	−855.116	+	855.116i	−0.711881	+	0.711881i	0.255047	+	0.966929i	$0.417909\pi$
$114$	1157.23	−	234.665i	0.950740	−	0.192793i
$115$	1156.60	+	71.9509i	0.937859	+	0.0583431i
$116$	−1151.57	+	1545.01i	−0.921728	+	1.23665i
$117$	527.969	+	2023.28i	0.417186	+	1.59873i
$118$	−241.169	+	727.123i	−0.188147	+	0.567264i
$119$	501.649			0.386438
$120$	−366.844	−	1262.31i	−0.279068	−	0.960271i
$121$	−1322.28			−0.993450
$122$	−255.369	+	769.937i	−0.189509	+	0.571368i
$123$	−650.553	−	1135.35i	−0.476898	−	0.832288i
$124$	843.536	+	628.725i	0.610901	+	0.455332i
$125$	1154.22	−	787.972i	0.825893	−	0.563827i
$126$	−61.5646	+	945.782i	−0.0435286	+	0.668706i
$127$	−1012.30	+	1012.30i	−0.707298	+	0.707298i	−0.965966	−	0.258668i	$-0.916716\pi$
$127$	−1012.30	+	1012.30i	−0.707298	+	0.707298i	0.258668	+	0.965966i	$0.416716\pi$
$128$	900.427	−	1134.19i	0.621775	−	0.783196i
$129$	−193.071	+	711.234i	−0.131775	+	0.485432i
$130$	−2272.16	−	913.824i	−1.53294	−	0.616521i
$131$	−818.107			−0.545636			−0.272818	−	0.962066i	$-0.587956\pi$
$131$	−818.107			−0.545636			−0.272818	+	0.962066i	$0.587956\pi$
$132$	−121.850	−	14.7159i	−0.0803459	−	0.00970342i
$133$	705.064	−	705.064i	0.459675	−	0.459675i
$134$	−586.148	−	1167.93i	−0.377877	−	0.752941i
$135$	1186.00	−	1026.54i	0.756106	−	0.654449i
$136$	159.578	−	900.578i	0.100616	−	0.567823i
$137$	−1039.96	−	1039.96i	−0.648539	−	0.648539i	0.304101	−	0.952640i	$-0.401644\pi$
$137$	−1039.96	−	1039.96i	−0.648539	−	0.648539i	−0.952640	+	0.304101i	$0.901644\pi$
$138$	−841.601	+	1269.74i	−0.519144	+	0.783245i
$139$	−1018.34			−0.621399			−0.310699	−	0.950508i	$-0.600563\pi$
$139$	−1018.34			−0.621399			−0.310699	+	0.950508i	$0.600563\pi$
$140$	−847.125	−	717.361i	−0.511394	−	0.433058i
$141$	791.155	+	214.766i	0.472534	+	0.128274i
$142$	878.780	−	2649.52i	0.519335	−	1.56579i
$143$	−161.688	+	161.688i	−0.0945528	+	0.0945528i
$144$	1678.32	+	411.383i	0.971248	+	0.238069i
$145$	2018.80	−	1782.34i	1.15622	−	1.02079i
$146$	−1396.08	−	2781.77i	−0.791373	−	1.57686i
$147$	−488.178	−	851.974i	−0.273906	−	0.478025i
$148$	−86.5841	−	593.427i	−0.0480890	−	0.329591i
$149$			1288.60i			0.708496i	0.935151	+	0.354248i	$0.115263\pi$
$149$			1288.60i			0.708496i	−0.935151	+	0.354248i	$0.884737\pi$
$150$	139.142	+	1831.84i	0.0757391	+	0.997128i
$151$	−2038.28			−1.09849			−0.549247	−	0.835660i	$-0.685085\pi$
$151$	−2038.28			−1.09849			−0.549247	+	0.835660i	$0.685085\pi$
$152$	−1041.47	−	1490.04i	−0.555752	−	0.795120i
$153$	1055.99	−	275.557i	0.557984	−	0.145605i
$154$	−92.6324	+	46.4892i	−0.0484710	+	0.0243260i
$155$	−973.109	−	1102.21i	−0.504271	−	0.571173i
$156$	2532.94	−	1987.06i	1.29999	−	1.01982i
$157$	−979.292	−	979.292i	−0.497809	−	0.497809i	0.412946	−	0.910755i	$-0.364500\pi$
$157$	−979.292	−	979.292i	−0.497809	−	0.497809i	−0.910755	+	0.412946i	$0.864500\pi$
$158$	−1090.05	+	3286.49i	−0.548858	+	1.65480i
$159$	714.930	+	194.074i	0.356589	+	0.0967993i
$160$	−1557.31	+	1292.59i	−0.769475	+	0.638677i
$161$			1286.38i			0.629694i
$162$	389.926	+	2024.72i	0.189108	+	0.981956i
$163$	1186.14	−	1186.14i	0.569975	−	0.569975i	−0.362146	−	0.932121i	$-0.617956\pi$
$163$	1186.14	−	1186.14i	0.569975	−	0.569975i	0.932121	+	0.362146i	$0.117956\pi$
$164$	−1203.95	+	1615.29i	−0.573248	+	0.769104i
$165$	162.427	+	55.1278i	0.0766361	+	0.0260102i
$166$	−1756.09	−	3499.12i	−0.821080	−	1.63605i
$167$	1556.58	+	1556.58i	0.721269	+	0.721269i	0.968864	−	0.247595i	$-0.0796401\pi$
$167$	1556.58	+	1556.58i	0.721269	+	0.721269i	−0.247595	+	0.968864i	$0.579640\pi$
$168$	1373.25	−	493.433i	0.630646	−	0.226603i
$169$		−	3800.80i		−	1.73000i
$170$	−476.943	+	1185.89i	−0.215176	+	0.535020i
$171$	1096.89	−	1871.47i	0.490533	−	0.836931i
$172$	1122.76	−	163.816i	0.497730	−	0.0726213i
$173$	−1264.74	−	1264.74i	−0.555817	−	0.555817i	0.372297	−	0.928114i	$-0.378570\pi$
$173$	−1264.74	−	1264.74i	−0.555817	−	0.555817i	−0.928114	+	0.372297i	$0.878570\pi$
$174$	703.540	+	3469.44i	0.306524	+	1.51160i
$175$	952.558	+	1224.47i	0.411466	+	0.528922i
$176$	53.9920	+	181.085i	0.0231239	+	0.0775559i
$177$	699.693	+	1221.11i	0.297131	+	0.518557i
$178$	1493.00	+	495.192i	0.628682	+	0.208518i
$179$			1786.21i			0.745851i	0.927861	+	0.372925i	$0.121645\pi$
$179$			1786.21i			0.745851i	−0.927861	+	0.372925i	$0.878355\pi$
$180$	−2177.27	−	1044.74i	−0.901580	−	0.432613i
$181$			758.404i			0.311446i	0.987801	+	0.155723i	$0.0497707\pi$
$181$			758.404i			0.311446i	−0.987801	+	0.155723i	$0.950229\pi$
$182$	855.838	−	2580.35i	0.348566	−	1.05092i
$183$	740.892	+	1293.01i	0.299280	+	0.522308i
$184$	2309.35	+	409.206i	0.925258	+	0.163951i
$185$	−52.0379	+	836.504i	−0.0206806	+	0.332438i
$186$	1894.22	−	384.114i	0.746726	−	0.151423i
$187$	84.3882	+	84.3882i	0.0330004	+	0.0330004i
$188$	−182.224	−	1248.92i	−0.0706917	−	0.484505i
$189$	1219.06	+	1243.23i	0.469173	+	0.478476i
$190$	996.414	+	2337.09i	0.380460	+	0.892371i
$191$			374.208i			0.141763i	0.997485	+	0.0708814i	$0.0225812\pi$
$191$			374.208i			0.141763i	−0.997485	+	0.0708814i	$0.977419\pi$
$192$	−448.989	−	2622.27i	−0.168766	−	0.985656i
$193$	−1234.40	−	1234.40i	−0.460383	−	0.460383i	0.438398	−	0.898781i	$-0.355546\pi$
$193$	−1234.40	−	1234.40i	−0.460383	−	0.460383i	−0.898781	+	0.438398i	$0.855546\pi$
$194$	1839.73	−	923.299i	0.680849	−	0.341696i
$195$	−4035.09	+	1990.13i	−1.48184	+	0.730853i
$196$	−903.448	+	1212.12i	−0.329245	+	0.441735i
$197$	−668.199	+	668.199i	−0.241661	+	0.241661i	−0.817537	−	0.575876i	$-0.804661\pi$
$197$	−668.199	+	668.199i	−0.241661	+	0.241661i	0.575876	+	0.817537i	$0.304661\pi$
$198$	−169.457	+	148.744i	−0.0608223	+	0.0533879i
$199$			254.399i			0.0906226i	0.998973	+	0.0453113i	$0.0144280\pi$
$199$			254.399i			0.0906226i	−0.998973	+	0.0453113i	$0.985572\pi$
$200$	2501.23	−	1320.55i	0.884318	−	0.466886i
$201$	−2316.84	−	628.927i	−0.813020	−	0.220702i
$202$	−3144.85	−	1043.07i	−1.09540	−	0.363318i
$203$	2113.82	+	2113.82i	0.730844	+	0.730844i
$204$	−1037.09	−	1321.99i	−0.355934	−	0.453716i
$205$	2110.63	−	1863.41i	0.719088	−	0.634860i
$206$	−460.080	−	916.735i	−0.155608	−	0.310058i
$207$	706.611	+	2707.86i	0.237260	+	0.909225i
$208$	−4360.08	−	2357.26i	−1.45345	−	0.785800i
$209$	237.214			0.0785092
$210$	−2019.93	+	280.411i	−0.663756	+	0.0921439i
$211$			5979.07i			1.95079i	0.220472	+	0.975393i	$0.429240\pi$
$211$			5979.07i			1.95079i	−0.220472	+	0.975393i	$0.570760\pi$
$212$	−164.667	−	1128.59i	−0.0533462	−	0.365623i
$213$	−2549.57	−	4449.54i	−0.820157	−	1.43135i
$214$	−3966.35	+	1990.58i	−1.26698	+	0.635857i
$215$	−1582.66	−	98.4552i	−0.502029	−	0.0312306i
$216$	2619.69	−	1793.02i	0.825218	−	0.564814i
$217$	1154.09	−	1154.09i	0.361036	−	0.361036i
$218$	5672.38	+	1881.39i	1.76230	+	0.584513i
$219$	−5518.22	−	1497.97i	−1.70268	−	0.462207i
$220$	−21.8291	−	263.180i	−0.00668962	−	0.0806528i
$221$	−3130.37			−0.952812
$222$	−918.333	−	608.682i	−0.277633	−	0.184018i
$223$	661.694	+	661.694i	0.198701	+	0.198701i	0.799443	−	0.600742i	$-0.205128\pi$
$223$	661.694	+	661.694i	0.198701	+	0.198701i	−0.600742	+	0.799443i	$0.705128\pi$
$224$	−1539.41	−	1636.28i	−0.459181	−	0.488073i
$225$	2677.77	+	2054.31i	0.793413	+	0.608683i
$226$	3057.07	−	1534.24i	0.899793	−	0.451577i
$227$	−778.379	+	778.379i	−0.227590	+	0.227590i	−0.811685	−	0.584095i	$-0.801449\pi$
$227$	−778.379	+	778.379i	−0.227590	+	0.227590i	0.584095	+	0.811685i	$0.301449\pi$
$228$	−3315.66	−	400.435i	−0.963093	−	0.116313i
$229$	806.325			0.232679			0.116339	−	0.993210i	$-0.462884\pi$
$229$	806.325			0.232679			0.116339	+	0.993210i	$0.462884\pi$
$230$	−3040.96	−	1223.02i	−0.871805	−	0.350625i
$231$	−49.8821	+	183.755i	−0.0142078	+	0.0523386i
$232$	4467.23	−	3122.39i	1.26417	−	0.883598i
$233$	2208.00	−	2208.00i	0.620820	−	0.620820i	−0.324921	−	0.945741i	$-0.605338\pi$
$233$	2208.00	−	2208.00i	0.620820	−	0.620820i	0.945741	+	0.324921i	$0.105338\pi$
$234$	384.173	−	5901.83i	0.107325	−	1.64878i
$235$	−109.518	+	1760.50i	−0.0304008	+	0.488690i
$236$	1294.89	−	1737.30i	0.357162	−	0.479190i
$237$	3162.51	+	5519.25i	0.866781	+	1.51272i
$238$	−1346.73	−	446.679i	−0.366789	−	0.121655i
$239$	71.0867			0.0192394			0.00961969	−	0.999954i	$-0.496938\pi$
$239$	71.0867			0.0192394			0.00961969	+	0.999954i	$0.496938\pi$
$240$	−139.151	+	3715.46i	−0.0374257	+	0.999299i
$241$	4908.67			1.31201			0.656007	−	0.754755i	$-0.272244\pi$
$241$	4908.67			1.31201			0.656007	+	0.754755i	$0.272244\pi$
$242$	3549.82	+	1177.39i	0.942938	+	0.312749i
$243$	3249.08	+	1947.41i	0.857730	+	0.514100i
$244$	1371.14	−	1839.60i	0.359746	−	0.482657i
$245$	1583.83	−	1398.31i	0.413008	−	0.364632i
$246$	735.542	+	3627.25i	0.190636	+	0.940102i
$247$	−4399.71	+	4399.71i	−1.13339	+	1.13339i
$248$	−1704.74	−	2438.99i	−0.436496	−	0.624499i
$249$	−6941.22	−	1884.26i	−1.76659	−	0.479558i
$250$	−3800.26	+	1087.66i	−0.961399	+	0.275158i
$251$	−5374.31			−1.35149			−0.675745	−	0.737136i	$-0.736178\pi$
$251$	−5374.31			−1.35149			−0.675745	+	0.737136i	$0.736178\pi$
$252$	1007.42	−	2484.24i	0.251832	−	0.621002i
$253$	−216.396	+	216.396i	−0.0537736	+	0.0537736i
$254$	3619.00	−	1816.26i	0.894000	−	0.448670i
$255$	1038.69	+	2105.99i	0.255079	+	0.517186i
$256$	−3427.20	+	2243.10i	−0.836719	+	0.547632i
$257$	2707.98	+	2707.98i	0.657274	+	0.657274i	0.954734	−	0.297460i	$-0.0961396\pi$
$257$	2707.98	+	2707.98i	0.657274	+	0.657274i	−0.297460	+	0.954734i	$0.596140\pi$
$258$	1151.62	−	1737.48i	0.277894	−	0.419265i
$259$	−930.363			−0.223204
$260$	5286.19	+	4476.45i	1.26091	+	1.06776i
$261$	5610.79	+	3288.53i	1.33065	+	0.779905i
$262$	2196.30	+	728.459i	0.517893	+	0.171772i
$263$	1447.81	−	1447.81i	0.339452	−	0.339452i	−0.516709	−	0.856161i	$-0.672843\pi$
$263$	1447.81	−	1447.81i	0.339452	−	0.339452i	0.856161	+	0.516709i	$0.172843\pi$
$264$	314.016	+	148.004i	0.0732059	+	0.0345038i
$265$	−98.9667	+	1590.88i	−0.0229414	+	0.368781i
$266$	−2520.63	+	1265.02i	−0.581013	+	0.291592i
$267$	2507.31	−	1436.68i	0.574701	−	0.329301i
$268$	533.629	+	3657.37i	0.121629	+	0.833617i
$269$			5530.40i			1.25351i	0.779216	+	0.626756i	$0.215618\pi$
$269$			5530.40i			1.25351i	−0.779216	+	0.626756i	$0.784382\pi$
$270$	−4098.00	+	1699.83i	−0.923689	+	0.383142i
$271$	1262.45			0.282983			0.141492	−	0.989939i	$-0.454810\pi$
$271$	1262.45			0.282983			0.141492	+	0.989939i	$0.454810\pi$
$272$	−1230.30	+	2275.61i	−0.274257	+	0.507277i
$273$	−2483.01	−	4333.38i	−0.550470	−	0.960688i
$274$	1865.89	+	3717.89i	0.411396	+	0.819731i
$275$	−45.7416	+	366.223i	−0.0100303	+	0.0803058i
$276$	3389.98	−	2659.39i	0.739322	−	0.579988i
$277$	−1992.51	−	1992.51i	−0.432196	−	0.432196i	0.457178	−	0.889375i	$-0.348860\pi$
$277$	−1992.51	−	1992.51i	−0.432196	−	0.432196i	−0.889375	+	0.457178i	$0.848860\pi$
$278$	2733.85	+	906.750i	0.589803	+	0.195623i
$279$	1795.45	−	3063.34i	0.385272	−	0.657338i
$280$	1635.45	+	2680.13i	0.349060	+	0.572031i
$281$		−	5669.33i		−	1.20357i	−0.798657	−	0.601786i	$-0.794456\pi$
$281$		−	5669.33i		−	1.20357i	0.798657	−	0.601786i	$-0.205544\pi$
$282$	−1932.71	−	1281.02i	−0.408125	−	0.270510i
$283$	−796.860	+	796.860i	−0.167379	+	0.167379i	−0.785826	−	0.618447i	$-0.787762\pi$
$283$	−796.860	+	796.860i	−0.167379	+	0.167379i	0.618447	+	0.785826i	$0.287762\pi$
$284$	−4718.37	+	6330.45i	−0.985858	+	1.32269i
$285$	4419.82	+	1500.09i	0.918624	+	0.311780i
$286$	578.041	−	290.100i	0.119511	−	0.0599789i
$287$	2209.97	+	2209.97i	0.454532	+	0.454532i
$288$	−4139.33	−	2598.81i	−0.846918	−	0.531724i
$289$		−	3279.20i		−	0.667453i
$290$	−7006.74	+	2987.31i	−1.41879	+	0.604899i
$291$	990.684	−	3649.48i	0.199570	−	0.735176i
$292$	1270.99	+	8711.08i	0.254723	+	1.74581i
$293$	−1686.12	−	1686.12i	−0.336192	−	0.336192i	0.518740	−	0.854932i	$-0.326401\pi$
$293$	−1686.12	−	1686.12i	−0.336192	−	0.336192i	−0.854932	+	0.518740i	$0.826401\pi$
$294$	551.953	+	2721.90i	0.109492	+	0.539948i
$295$	−2270.06	+	2004.17i	−0.448027	+	0.395549i
$296$	−295.955	+	1670.22i	−0.0581150	+	0.327971i
$297$	−4.06593	+	414.211i	−0.000794375	+	0.0809258i
$298$	1147.39	−	3459.38i	0.223042	−	0.672472i
$299$		−	8027.20i		−	1.55259i
$300$	1257.57	−	5041.68i	0.242019	−	0.970272i
$301$		−	1760.24i		−	0.337071i
$302$	5471.99	+	1814.92i	1.04264	+	0.345818i
$303$	−5281.39	+	3026.22i	−1.00135	+	0.573768i
$304$	1469.18	+	4927.53i	0.277182	+	0.929649i
$305$	−2403.72	+	2122.17i	−0.451268	+	0.398411i
$306$	−3080.28	−	200.507i	−0.575451	−	0.0374583i
$307$	762.633	+	762.633i	0.141778	+	0.141778i	0.774433	−	0.632656i	$-0.218035\pi$
$307$	762.633	+	762.633i	0.141778	+	0.141778i	−0.632656	+	0.774433i	$0.718035\pi$
$308$	290.077	−	42.3237i	0.0536645	−	0.00782993i
$309$	−1818.53	−	493.657i	−0.334798	−	0.0908841i
$310$	1630.99	+	3825.49i	0.298819	+	0.700882i
$311$		−	8701.71i		−	1.58659i	−0.608839	−	0.793294i	$-0.708364\pi$
$311$		−	8701.71i		−	1.58659i	0.608839	−	0.793294i	$-0.291636\pi$
$312$	−8569.29	+	3079.10i	−1.55494	+	0.558718i
$313$	1971.93	+	1971.93i	0.356103	+	0.356103i	0.862374	−	0.506271i	$-0.168977\pi$
$313$	1971.93	+	1971.93i	0.356103	+	0.356103i	−0.506271	+	0.862374i	$0.668977\pi$
$314$	1757.04	+	3501.00i	0.315782	+	0.629214i
$315$	−2091.44	+	3108.33i	−0.374093	+	0.555983i
$316$	5852.71	−	7852.36i	1.04190	−	1.39788i
$317$	1852.35	−	1852.35i	0.328196	−	0.328196i	−0.523704	−	0.851900i	$-0.675450\pi$
$317$	1852.35	−	1852.35i	0.328196	−	0.328196i	0.851900	+	0.523704i	$0.175450\pi$
$318$	−1746.50	−	1157.60i	−0.307984	−	0.204136i
$319$			711.181i			0.124823i
$320$	5331.72	−	2083.45i	0.931413	−	0.363963i
$321$	−2135.86	+	7868.07i	−0.371377	+	1.36808i
$322$	1145.42	−	3453.43i	0.198235	−	0.597677i
$323$	2296.29	+	2296.29i	0.395570	+	0.395570i
$324$	756.051	−	5782.79i	0.129638	−	0.991561i
$325$	−5944.11	−	7640.89i	−1.01452	−	1.30412i
$326$	−4240.50	+	2128.17i	−0.720428	+	0.361560i
$327$	9526.06	−	5458.39i	1.61099	−	0.923088i
$328$	4670.43	−	3264.41i	0.786223	−	0.549534i
$329$	−1958.03			−0.328115
$330$	−386.968	−	292.625i	−0.0645512	−	0.0488136i
$331$		−	2022.13i		−	0.335790i	−0.985805	−	0.167895i	$-0.946303\pi$
$331$		−	2022.13i		−	0.335790i	0.985805	−	0.167895i	$-0.0536969\pi$
$332$	1598.75	+	10957.4i	0.264285	+	1.81135i
$333$	−1958.44	+	511.051i	−0.322288	+	0.0841004i
$334$	−2792.81	−	5564.84i	−0.457532	−	0.911659i
$335$	320.716	−	5155.48i	0.0523063	−	0.840818i
$336$	−4126.01	+	101.910i	−0.669917	+	0.0165465i
$337$	−3248.61	+	3248.61i	−0.525112	+	0.525112i	−0.919111	−	0.393999i	$-0.871091\pi$
$337$	−3248.61	+	3248.61i	−0.525112	+	0.525112i	0.393999	+	0.919111i	$0.371091\pi$
$338$	−3384.31	+	10203.7i	−0.544622	+	1.64203i
$339$	1646.22	−	6064.33i	0.263747	−	0.971590i
$340$	2336.34	−	2758.97i	0.372665	−	0.440077i
$341$	388.286			0.0616623
$342$	−4611.12	+	4047.50i	−0.729066	+	0.639952i
$343$	4668.46	+	4668.46i	0.734908	+	0.734908i
$344$	−3160.04	−	559.943i	−0.495284	−	0.0877620i
$345$	−5400.39	+	2663.51i	−0.842745	+	0.415648i
$346$	2269.19	+	4521.49i	0.352579	+	0.702534i
$347$	5387.71	−	5387.71i	0.833509	−	0.833509i	−0.154486	−	0.987995i	$-0.549372\pi$
$347$	5387.71	−	5387.71i	0.833509	−	0.833509i	0.987995	+	0.154486i	$0.0493722\pi$
$348$	1200.53	−	9940.55i	0.184928	−	1.53123i
$349$	4293.21			0.658481			0.329241	−	0.944246i	$-0.393207\pi$
$349$	4293.21			0.658481			0.329241	+	0.944246i	$0.393207\pi$
$350$	−1466.96	−	4135.41i	−0.224035	−	0.631562i
$351$	−7607.14	−	7757.97i	−1.15681	−	1.17974i
$352$	16.2945	−	534.220i	0.00246733	−	0.0808921i
$353$	7436.95	−	7436.95i	1.12133	−	1.12133i	0.129787	−	0.991542i	$-0.458571\pi$
$353$	7436.95	−	7436.95i	1.12133	−	1.12133i	0.991542	−	0.129787i	$-0.0414292\pi$
$354$	−791.101	−	3901.24i	−0.118776	−	0.585730i
$355$	8271.73	−	7302.85i	1.23667	−	1.09182i
$356$	−3567.21	−	2658.80i	−0.531072	−	0.395832i
$357$	−2261.67	+	1295.93i	−0.335295	+	0.192123i
$358$	1590.47	−	4795.27i	0.234802	−	0.707927i
$359$	−7022.70			−1.03243			−0.516217	−	0.856458i	$-0.672660\pi$
$359$	−7022.70			−1.03243			−0.516217	+	0.856458i	$0.672660\pi$
$360$	4914.88	+	4743.41i	0.719547	+	0.694444i
$361$	−404.158			−0.0589237
$362$	675.298	−	2036.02i	0.0980467	−	0.295610i
$363$	5961.48	−	3415.90i	0.861974	−	0.493908i
$364$	−4595.19	+	6165.18i	−0.661685	+	0.887757i
$365$	763.879	−	12279.3i	0.109543	−	1.76089i
$366$	−837.682	−	4130.95i	−0.119635	−	0.589968i
$367$	4218.02	−	4218.02i	0.599943	−	0.599943i	−0.340355	−	0.940297i	$-0.610547\pi$
$367$	4218.02	−	4218.02i	0.599943	−	0.599943i	0.940297	+	0.340355i	$0.110547\pi$
$368$	−5835.35	−	3154.85i	−0.826599	−	0.446897i
$369$	5866.01	+	3438.12i	0.827567	+	0.485044i
$370$	884.542	−	2199.36i	0.124284	−	0.309024i
$371$	−1769.38			−0.247606
$372$	−5427.27	−	655.455i	−0.756427	−	0.0913542i
$373$	−7234.45	+	7234.45i	−1.00425	+	1.00425i	−0.00425978	+	0.999991i	$0.501356\pi$
$373$	−7234.45	+	7234.45i	−1.00425	+	1.00425i	−0.999991	+	0.00425978i	$0.998644\pi$
$374$	−151.409	−	301.691i	−0.0209336	−	0.0417114i
$375$	−3168.18	+	6534.30i	−0.436278	+	0.899812i
$376$	−622.863	+	3515.13i	−0.0854301	+	0.482124i
$377$	−13190.6	−	13190.6i	−1.80199	−	1.80199i
$378$	−2165.71	−	4423.08i	−0.294688	−	0.601848i
$379$	9113.88			1.23522			0.617610	−	0.786484i	$-0.288101\pi$
$379$	9113.88			1.23522			0.617610	+	0.786484i	$0.288101\pi$
$380$	−593.993	−	7161.42i	−0.0801874	−	0.966771i
$381$	1948.81	−	7179.03i	0.262049	−	0.965335i
$382$	333.202	−	1004.60i	0.0446285	−	0.134555i
$383$	−2991.35	+	2991.35i	−0.399088	+	0.399088i	−0.877911	−	0.478823i	$-0.841064\pi$
$383$	−2991.35	+	2991.35i	−0.399088	+	0.399088i	0.478823	+	0.877911i	$0.341064\pi$
$384$	−1129.56	+	7439.57i	−0.150111	+	0.988669i
$385$	−408.897	−	25.4370i	−0.0541281	−	0.00336725i
$386$	2214.75	+	4413.02i	0.292041	+	0.581908i
$387$	−966.903	−	3705.35i	−0.127004	−	0.486702i
$388$	−5761.08	+	840.571i	−0.753800	+	0.109983i
$389$			8563.25i			1.11613i	0.829798	+	0.558064i	$0.188456\pi$
$389$			8563.25i			1.11613i	−0.829798	+	0.558064i	$0.811544\pi$
$390$	12604.7	−	1749.81i	1.63658	−	0.227193i
$391$	−4189.55			−0.541879
$392$	3504.71	−	2449.63i	0.451567	−	0.315625i
$393$	3688.41	−	2113.45i	0.473425	−	0.271270i
$394$	2388.83	−	1198.88i	0.305451	−	0.153296i
$395$	−10260.3	+	9058.53i	−1.30697	+	1.15388i
$396$	587.373	−	248.433i	0.0745369	−	0.0315258i
$397$	−1106.78	−	1106.78i	−0.139918	−	0.139918i	0.633678	−	0.773597i	$-0.281544\pi$
$397$	−1106.78	−	1106.78i	−0.139918	−	0.139918i	−0.773597	+	0.633678i	$0.781544\pi$
$398$	226.522	−	682.964i	0.0285290	−	0.0860149i
$399$	−1357.34	+	5000.18i	−0.170306	+	0.627374i
$400$	−7890.68	+	1318.03i	−0.986335	+	0.164754i
$401$			12705.4i			1.58224i	0.611664	+	0.791118i	$0.290500\pi$
$401$			12705.4i			1.58224i	−0.611664	+	0.791118i	$0.709500\pi$
$402$	5659.80	+	3751.38i	0.702202	+	0.465428i
$403$	−7201.70	+	7201.70i	−0.890180	+	0.890180i
$404$	7513.95	+	5600.49i	0.925329	+	0.689690i
$405$	−2695.13	+	7691.97i	−0.330672	+	0.943746i
$406$	−3792.61	−	7556.99i	−0.463606	−	0.923761i
$407$	−156.507	−	156.507i	−0.0190609	−	0.0190609i
$408$	1607.04	+	4472.48i	0.195001	+	0.542698i
$409$			13738.3i			1.66092i	0.557081	+	0.830458i	$0.311921\pi$
$409$			13738.3i			1.66092i	−0.557081	+	0.830458i	$0.688079\pi$
$410$	−7325.45	+	3123.19i	−0.882386	+	0.376203i
$411$	7375.21	+	2002.07i	0.885139	+	0.240279i
$412$	418.856	+	2870.74i	0.0500863	+	0.343280i
$413$	−2376.90	−	2376.90i	−0.283196	−	0.283196i
$414$	514.160	−	7898.75i	0.0610376	−	0.937687i
$415$	960.863	−	15445.8i	0.113655	−	1.82699i
$416$	9606.19	+	10210.6i	1.13217	+	1.20341i
$417$	4591.16	−	2630.72i	0.539161	−	0.308937i
$418$	−636.828	−	211.220i	−0.0745174	−	0.0247156i
$419$		−	4553.17i		−	0.530876i	−0.964128	−	0.265438i	$-0.914483\pi$
$419$		−	4553.17i		−	0.530876i	0.964128	−	0.265438i	$-0.0855165\pi$
$420$	5672.43	+	1045.79i	0.659015	+	0.121499i
$421$			402.412i			0.0465851i	0.999729	+	0.0232926i	$0.00741493\pi$
$421$			402.412i			0.0465851i	−0.999729	+	0.0232926i	$0.992585\pi$
$422$	5323.88	−	16051.5i	0.614129	−	1.85160i
$423$	−4121.72	+	1075.55i	−0.473770	+	0.123629i
$424$	−562.853	+	3176.46i	−0.0644683	+	0.363826i
$425$	−3987.93	+	3102.35i	−0.455160	+	0.354085i
$426$	2882.64	+	14215.5i	0.327851	+	1.61677i
$427$	−2516.86	−	2516.86i	−0.285244	−	0.285244i
$428$	12420.6	−	1812.22i	1.40274	−	0.204666i
$429$	311.272	−	1146.66i	0.0350311	−	0.129048i
$430$	4161.15	+	1673.54i	0.466671	+	0.187687i
$431$			3649.85i			0.407905i	0.978981	+	0.203953i	$0.0653789\pi$
$431$			3649.85i			0.407905i	−0.978981	+	0.203953i	$0.934621\pi$
$432$	−8629.39	+	2480.95i	−0.961069	+	0.276307i
$433$	1855.68	+	1855.68i	0.205954	+	0.205954i	0.802545	−	0.596591i	$-0.203479\pi$
$433$	1855.68	+	1855.68i	0.205954	+	0.205954i	−0.596591	+	0.802545i	$0.703479\pi$
$434$	−4125.91	+	2070.66i	−0.456336	+	0.229020i
$435$	−4497.35	+	13250.9i	−0.495704	+	1.46053i
$436$	−13552.9	−	10101.6i	−1.48869	−	1.10959i
$437$	−5888.38	+	5888.38i	−0.644575	+	0.644575i
$438$	13480.5	+	8935.00i	1.47060	+	0.974728i
$439$		−	7826.71i		−	0.850908i	−0.904980	−	0.425454i	$-0.860114\pi$
$439$		−	7826.71i		−	0.850908i	0.904980	−	0.425454i	$-0.139886\pi$
$440$	−175.738	+	725.975i	−0.0190409	+	0.0786579i
$441$	4401.87	+	2579.98i	0.475313	+	0.278585i
$442$	8403.83	+	2787.35i	0.904366	+	0.299956i
$443$	8020.06	+	8020.06i	0.860146	+	0.860146i	0.991355	−	0.131209i	$-0.0418859\pi$
$443$	8020.06	+	8020.06i	0.860146	+	0.860146i	−0.131209	+	0.991355i	$0.541886\pi$
$444$	1923.39	+	2451.78i	0.205585	+	0.262064i
$445$	4115.16	+	4661.12i	0.438376	+	0.496535i
$446$	−1187.21	−	2365.58i	−0.126045	−	0.251151i
$447$	−3328.88	−	5809.61i	−0.352239	−	0.614731i
$448$	2675.76	+	5763.50i	0.282182	+	0.607812i
$449$	8962.08			0.941975			0.470987	−	0.882140i	$-0.343898\pi$
$449$	8962.08			0.941975			0.470987	+	0.882140i	$0.343898\pi$
$450$	−5359.58	−	7899.36i	−0.561451	−	0.827510i
$451$			743.530i			0.0776308i
$452$	−9573.18	+	1396.78i	−0.996204	+	0.145351i
$453$	9189.53	−	5265.56i	0.953116	−	0.546132i
$454$	2782.73	−	1396.56i	0.287665	−	0.144370i
$455$	8055.78	−	7112.20i	0.830024	−	0.732802i
$456$	8544.72	+	4027.35i	0.877507	+	0.413592i
$457$	−7293.00	+	7293.00i	−0.746503	+	0.746503i	−0.973821	−	0.227317i	$-0.927005\pi$
$457$	−7293.00	+	7293.00i	−0.746503	+	0.746503i	0.227317	+	0.973821i	$0.427005\pi$
$458$	−2164.67	−	717.968i	−0.220848	−	0.0732499i
$459$	−4049.04	+	3970.32i	−0.411749	+	0.403744i
$460$	7074.81	+	5991.08i	0.717097	+	0.607251i
$461$	1390.84			0.140516			0.0702578	−	0.997529i	$-0.477618\pi$
$461$	1390.84			0.140516			0.0702578	+	0.997529i	$0.477618\pi$
$462$	297.534	−	448.896i	0.0299622	−	0.0452046i
$463$	−4381.43	−	4381.43i	−0.439789	−	0.439789i	0.452152	−	0.891941i	$-0.350656\pi$
$463$	−4381.43	−	4381.43i	−0.439789	−	0.439789i	−0.891941	+	0.452152i	$0.850656\pi$
$464$	−14773.0	+	4404.69i	−1.47806	+	0.440695i
$465$	7234.63	+	2455.43i	0.721501	+	0.244877i
$466$	−7893.69	+	3961.58i	−0.784695	+	0.393813i
$467$	4599.72	−	4599.72i	0.455781	−	0.455781i	−0.441487	−	0.897268i	$-0.645549\pi$
$467$	4599.72	−	4599.72i	0.455781	−	0.455781i	0.897268	+	0.441487i	$0.145549\pi$
$468$	−6286.46	+	15502.1i	−0.620923	+	1.53116i
$469$	5733.94			0.564539
$470$	1861.60	−	4628.74i	0.182700	−	0.454272i
$471$	6944.96	+	1885.27i	0.679420	+	0.184435i
$472$	−5023.21	+	3510.99i	−0.489856	+	0.342387i
$473$	296.110	−	296.110i	0.0287846	−	0.0287846i
$474$	−3575.66	−	17633.0i	−0.346489	−	1.70867i
$475$	−1244.68	+	9965.32i	−0.120231	+	0.962611i
$476$	3217.73	+	2398.32i	0.309841	+	0.230939i
$477$	−3724.60	+	971.927i	−0.357522	+	0.0932945i
$478$	−190.840	−	63.2970i	−0.0182611	−	0.00605677i
$479$	10999.8			1.04925			0.524627	−	0.851332i	$-0.324205\pi$
$479$	10999.8			1.04925			0.524627	+	0.851332i	$0.324205\pi$
$480$	3681.89	−	9850.67i	0.350113	−	0.936707i
$481$	5805.61			0.550339
$482$	−13177.9	−	4370.78i	−1.24530	−	0.413036i
$483$	−3323.15	−	5799.60i	−0.313061	−	0.546358i
$484$	−8481.52	−	6321.66i	−0.796536	−	0.593695i
$485$	8120.90	+	505.192i	0.760312	+	0.0472981i
$486$	−6988.50	−	8121.09i	−0.652274	−	0.757984i
$487$	7033.89	−	7033.89i	0.654488	−	0.654488i	−0.299582	−	0.954071i	$-0.596847\pi$
$487$	7033.89	−	7033.89i	0.654488	−	0.654488i	0.954071	+	0.299582i	$0.0968473\pi$
$488$	−5318.99	+	3717.72i	−0.493400	+	0.344864i
$489$	−2283.49	+	8411.91i	−0.211172	+	0.777913i
$490$	−5497.05	+	2343.65i	−0.506799	+	0.216073i
$491$	−13060.8			−1.20046			−0.600230	−	0.799827i	$-0.704924\pi$
$491$	−13060.8			−1.20046			−0.600230	+	0.799827i	$0.704924\pi$
$492$	1255.13	−	10392.7i	0.115012	−	0.952317i
$493$	−6884.43	+	6884.43i	−0.628923	+	0.628923i
$494$	15729.1	−	7893.93i	1.43256	−	0.718957i
$495$	−874.714	+	171.063i	−0.0794252	+	0.0155327i
$496$	2404.84	+	8065.67i	0.217703	+	0.730160i
$497$	8661.05	+	8661.05i	0.781693	+	0.781693i
$498$	16956.7	+	11239.1i	1.52580	+	1.01132i
$499$	−631.672			−0.0566684			−0.0283342	−	0.999599i	$-0.509020\pi$
$499$	−631.672			−0.0566684			−0.0283342	+	0.999599i	$0.509020\pi$
$500$	11170.7	+	463.889i	0.999139	+	0.0414915i
$501$	−11039.0	−	2996.64i	−0.984403	−	0.267225i
$502$	14428.0	+	4785.40i	1.28277	+	0.425464i
$503$	−8586.92	+	8586.92i	−0.761177	+	0.761177i	−0.976535	−	0.215358i	$-0.930908\pi$
$503$	−8586.92	+	8586.92i	−0.761177	+	0.761177i	0.215358	+	0.976535i	$0.430908\pi$
$504$	−4916.55	+	5772.20i	−0.434525	+	0.510147i
$505$	−8668.15	−	9818.16i	−0.763817	−	0.865153i
$506$	773.624	−	388.257i	0.0679680	−	0.0341109i
$507$	9818.76	+	17135.8i	0.860092	+	1.50104i
$508$	−11332.8	+	1653.52i	−0.989791	+	0.144416i
$509$			5407.55i			0.470895i	0.971887	+	0.235448i	$0.0756556\pi$
$509$			5407.55i			0.470895i	−0.971887	+	0.235448i	$0.924344\pi$
$510$	−913.261	−	6578.65i	−0.0792939	−	0.571191i
$511$	13657.0			1.18229
$512$	11198.0	−	2970.21i	0.966576	−	0.256378i
$513$	−110.638	+	11271.1i	−0.00952203	+	0.970044i
$514$	−4858.65	−	9681.13i	−0.416937	−	0.830771i
$515$	251.737	−	4046.64i	0.0215395	−	0.346245i
$516$	−4638.73	+	3639.02i	−0.395754	+	0.310463i
$517$	−329.383	−	329.383i	−0.0280198	−	0.0280198i
$518$	2497.66	+	828.414i	0.211855	+	0.0702672i
$519$	8969.30	+	2434.80i	0.758591	+	0.205926i
$520$	−10205.5	−	16724.5i	−0.860653	−	1.41042i
$521$		−	12452.0i		−	1.04709i	−0.851998	−	0.523545i	$-0.824609\pi$
$521$		−	12452.0i		−	1.04709i	0.851998	−	0.523545i	$-0.175391\pi$
$522$	−12134.6	−	13824.4i	−1.01747	−	1.15915i
$523$	2438.51	−	2438.51i	0.203879	−	0.203879i	−0.597781	−	0.801660i	$-0.703951\pi$
$523$	2438.51	−	2438.51i	0.203879	−	0.203879i	0.801660	+	0.597781i	$0.203951\pi$
$524$	−5247.58	−	3911.26i	−0.437484	−	0.326077i
$525$	−7457.81	−	3059.72i	−0.619972	−	0.254356i
$526$	−5175.98	+	2597.66i	−0.429056	+	0.215329i
$527$	3758.71	+	3758.71i	0.310687	+	0.310687i
$528$	−711.227	−	676.940i	−0.0586215	−	0.0557955i
$529$			1423.75i			0.117017i
$530$	1682.24	−	4182.78i	0.137871	−	0.342808i
$531$	−6309.10	−	3697.82i	−0.515615	−	0.302206i
$532$	7893.31	−	1151.67i	0.643268	−	0.0938560i
$533$	−13790.6	−	13790.6i	−1.12071	−	1.12071i
$534$	−8010.42	+	1624.37i	−0.649147	+	0.131635i
$535$	−17508.2	−	1089.17i	−1.41485	−	0.0880163i
$536$	1824.01	−	10293.8i	0.146987	−	0.829522i
$537$	−4614.37	−	8053.07i	−0.370810	−	0.647142i
$538$	4924.38	−	14847.0i	0.394619	−	1.18978i
$539$			557.948i			0.0445872i
$540$	12515.1	−	914.452i	0.997341	−	0.0728736i
$541$			3308.79i			0.262950i	0.991319	+	0.131475i	$0.0419714\pi$
$541$			3308.79i			0.262950i	−0.991319	+	0.131475i	$0.958029\pi$
$542$	−3389.19	−	1124.11i	−0.268595	−	0.0890862i
$543$	−1959.21	−	3419.25i	−0.154840	−	0.270228i
$544$	5329.13	−	5013.66i	0.420008	−	0.395145i
$545$	15634.8	+	17709.0i	1.22884	+	1.39187i
$546$	2807.39	+	13844.4i	0.220046	+	1.08514i
$547$	−16055.5	−	16055.5i	−1.25500	−	1.25500i	−0.953451	−	0.301549i	$-0.902496\pi$
$547$	−16055.5	−	16055.5i	−1.25500	−	1.25500i	−0.301549	−	0.953451i	$-0.597504\pi$
$548$	−1698.71	−	11642.5i	−0.132418	−	0.907563i
$549$	−6680.59	−	3915.55i	−0.519345	−	0.304393i
$550$	448.891	−	942.438i	0.0348014	−	0.0730649i
$551$			19352.0i			1.49623i
$552$	−11468.8	+	4120.94i	−0.884317	+	0.317751i
$553$	−10743.3	−	10743.3i	−0.826130	−	0.826130i
$554$	3574.95	+	7123.30i	0.274161	+	0.546281i
$555$	−1926.36	−	3905.79i	−0.147332	−	0.298724i
$556$	−6531.94	−	4868.55i	−0.498230	−	0.371353i
$557$	−13123.8	+	13123.8i	−0.998338	+	0.998338i	−0.999999	−	0.00166067i	$-0.999471\pi$
$557$	−13123.8	+	13123.8i	−0.998338	+	0.998338i	0.00166067	+	0.999999i	$0.499471\pi$
$558$	−7547.75	+	6625.18i	−0.572620	+	0.502628i
$559$			10984.1i			0.831091i
$560$	−2004.11	−	8651.36i	−0.151230	−	0.652834i
$561$	−598.466	−	162.459i	−0.0450396	−	0.0122264i
$562$	−5048.08	+	15220.0i	−0.378898	+	1.14238i
$563$	7631.61	+	7631.61i	0.571286	+	0.571286i	0.932488	−	0.361202i	$-0.117633\pi$
$563$	7631.61	+	7631.61i	0.571286	+	0.571286i	−0.361202	+	0.932488i	$0.617633\pi$
$564$	4047.94	+	5159.98i	0.302214	+	0.385238i
$565$	13494.5	+	839.476i	1.00481	+	0.0625080i
$566$	2848.80	−	1429.72i	0.211562	−	0.106176i
$567$	−8707.81	−	2455.83i	−0.644962	−	0.181897i
$568$	18303.8	−	12793.5i	1.35213	−	0.945075i
$569$	4352.87			0.320706			0.160353	−	0.987060i	$-0.448737\pi$
$569$	4352.87			0.320706			0.160353	+	0.987060i	$0.448737\pi$
$570$	−10529.8	−	7962.65i	−0.773764	−	0.585121i
$571$		−	9873.22i		−	0.723610i	−0.932254	−	0.361805i	$-0.882161\pi$
$571$		−	9873.22i		−	0.723610i	0.932254	−	0.361805i	$-0.117839\pi$
$572$	−1810.13	+	264.107i	−0.132317	+	0.0193057i
$573$	−966.705	−	1687.11i	−0.0704794	−	0.123001i
$574$	−3965.12	−	7900.73i	−0.288329	−	0.574512i
$575$	−7955.34	−	10226.2i	−0.576975	−	0.741676i
$576$	8798.47	+	10662.5i	0.636463	+	0.771307i
$577$	6780.91	−	6780.91i	0.489242	−	0.489242i	−0.418825	−	0.908067i	$-0.637558\pi$
$577$	6780.91	−	6780.91i	0.489242	−	0.489242i	0.908067	+	0.418825i	$0.137558\pi$
$578$	−2919.87	+	8803.38i	−0.210122	+	0.633516i
$579$	8754.12	+	2376.39i	0.628340	+	0.170569i
$580$	21470.4	−	1780.83i	1.53708	−	0.127491i
$581$	17178.8			1.22667
$582$	−5909.17	+	8915.31i	−0.420864	+	0.634968i
$583$	−297.648	−	297.648i	−0.0211446	−	0.0211446i
$584$	4344.40	−	24517.6i	0.307830	−	1.73724i
$585$	13050.9	−	19396.5i	0.922375	−	1.37085i
$586$	3025.22	+	6027.93i	0.213261	+	0.424935i
$587$	−12940.0	+	12940.0i	−0.909865	+	0.909865i	−0.996261	−	0.0863956i	$-0.972465\pi$
$587$	−12940.0	+	12940.0i	−0.909865	+	0.909865i	0.0863956	+	0.996261i	$0.472465\pi$
$588$	941.857	−	7798.73i	0.0660570	−	0.546963i
$589$	10565.7			0.739135
$590$	7878.79	−	3359.10i	0.549770	−	0.234393i
$591$	1286.37	−	4738.74i	0.0895336	−	0.329824i
$592$	2281.72	−	4220.37i	0.158409	−	0.293000i
$593$	−16321.6	+	16321.6i	−1.13027	+	1.13027i	−0.140134	+	0.990133i	$0.544753\pi$
$593$	−16321.6	+	16321.6i	−1.13027	+	1.13027i	−0.990133	+	0.140134i	$0.955247\pi$
$594$	379.738	−	1108.38i	0.0262303	−	0.0765610i
$595$	−3712.00	−	4204.47i	−0.255760	−	0.289692i
$596$	−6160.61	+	8265.45i	−0.423403	+	0.568064i
$597$	−657.200	−	1146.95i	−0.0450543	−	0.0786293i
$598$	−7147.58	+	21549.9i	−0.488773	+	1.47365i
$599$	−1598.73			−0.109052			−0.0545260	−	0.998512i	$-0.517365\pi$
$599$	−1598.73			−0.109052			−0.0545260	+	0.998512i	$0.517365\pi$
$600$	−7865.29	+	12415.2i	−0.535166	+	0.844747i
$601$	6858.48			0.465496			0.232748	−	0.972537i	$-0.425228\pi$
$601$	6858.48			0.465496			0.232748	+	0.972537i	$0.425228\pi$
$602$	−1567.35	+	4725.55i	−0.106114	+	0.319932i
$603$	12070.1	−	3149.67i	0.815147	−	0.212711i
$604$	−13074.1	−	9744.74i	−0.880760	−	0.656470i
$605$	9784.34	+	11082.4i	0.657504	+	0.744736i
$606$	16873.1	−	3421.56i	1.13106	−	0.229359i
$607$	−12784.0	+	12784.0i	−0.854838	+	0.854838i	−0.990724	−	0.135886i	$-0.956612\pi$
$607$	−12784.0	+	12784.0i	−0.854838	+	0.854838i	0.135886	+	0.990724i	$0.456612\pi$
$608$	443.391	−	14536.7i	0.0295755	−	0.969640i
$609$	−14990.8	−	4069.40i	−0.997470	−	0.270772i
$610$	8342.70	−	3556.89i	0.553748	−	0.236089i
$611$	12218.4			0.809009
$612$	8090.83	+	3281.03i	0.534399	+	0.216712i
$613$	496.176	−	496.176i	0.0326922	−	0.0326922i	−0.690572	−	0.723264i	$-0.742641\pi$
$613$	496.176	−	496.176i	0.0326922	−	0.0326922i	0.723264	+	0.690572i	$0.242641\pi$
$614$	−1368.31	−	2726.44i	−0.0899357	−	0.179202i
$615$	−4701.91	+	13853.6i	−0.308292	+	0.908345i
$616$	−816.431	−	144.668i	−0.0534009	−	0.00946238i
$617$	−15213.3	−	15213.3i	−0.992647	−	0.992647i	0.00732619	−	0.999973i	$-0.497668\pi$
$617$	−15213.3	−	15213.3i	−0.992647	−	0.992647i	−0.999973	+	0.00732619i	$0.997668\pi$
$618$	4442.50	+	2944.54i	0.289164	+	0.191661i
$619$	3703.30			0.240466			0.120233	−	0.992746i	$-0.461636\pi$
$619$	3703.30			0.240466			0.120233	+	0.992746i	$0.461636\pi$
$620$	−972.283	−	11722.2i	−0.0629804	−	0.759316i
$621$	−10181.1	−	10382.9i	−0.657894	−	0.670938i
$622$	−7748.18	+	23360.7i	−0.499476	+	1.50592i
$623$	−4880.50	+	4880.50i	−0.313857	+	0.313857i
$624$	25746.9	−	635.932i	1.65177	−	0.0407975i
$625$	−15145.0	−	3843.20i	−0.969279	−	0.245965i
$626$	−3538.03	−	7049.73i	−0.225892	−	0.450102i
$627$	−1069.47	+	612.804i	−0.0681190	+	0.0390319i
$628$	−1599.61	−	10963.3i	−0.101642	−	0.696632i
$629$		−	3030.06i		−	0.192077i
$630$	8382.43	−	6482.40i	0.530102	−	0.409945i
$631$	20282.5			1.27961			0.639804	−	0.768538i	$-0.279015\pi$
$631$	20282.5			1.27961			0.639804	+	0.768538i	$0.279015\pi$
$632$	−22704.2	+	15869.2i	−1.42899	+	0.998800i
$633$	−15446.0	−	26956.5i	−0.969860	−	1.69261i
$634$	−6622.21	+	3323.47i	−0.414829	+	0.208189i
$635$	15974.9	+	993.782i	0.998341	+	0.0621056i
$636$	3657.93	+	4662.84i	0.228061	+	0.290713i
$637$	−10348.5	−	10348.5i	−0.643678	−	0.643678i
$638$	633.250	−	1909.25i	0.0392956	−	0.118476i
$639$	22989.3	+	13474.2i	1.42323	+	0.834167i
$640$	−16168.8	+	845.782i	−0.998635	+	0.0522382i
$641$			4260.12i			0.262503i	0.991349	+	0.131252i	$0.0418996\pi$
$641$			4260.12i			0.262503i	−0.991349	+	0.131252i	$0.958100\pi$
$642$	12739.8	−	19220.9i	0.783180	−	1.18160i
$643$	7755.58	−	7755.58i	0.475662	−	0.475662i	−0.428080	−	0.903741i	$-0.640810\pi$
$643$	7755.58	−	7755.58i	0.475662	−	0.475662i	0.903741	+	0.428080i	$0.140810\pi$
$644$	−6150.00	+	8251.21i	−0.376311	+	0.504881i
$645$	7389.71	−	3644.65i	0.451116	−	0.222493i
$646$	−4120.00	−	8209.33i	−0.250927	−	0.499987i
$647$	−6857.20	−	6857.20i	−0.416668	−	0.416668i	0.467386	−	0.884054i	$-0.345196\pi$
$647$	−6857.20	−	6857.20i	−0.416668	−	0.416668i	−0.884054	+	0.467386i	$0.845196\pi$
$648$	−7178.82	+	14851.3i	−0.435201	+	0.900333i
$649$		−	799.693i		−	0.0483678i
$650$	9154.04	+	25805.6i	0.552386	+	1.55720i
$651$	−2221.78	+	8184.59i	−0.133761	+	0.492749i
$652$	13279.1	−	1937.49i	0.797621	−	0.116377i
$653$	5826.10	+	5826.10i	0.349147	+	0.349147i	0.859792	−	0.510645i	$-0.170593\pi$
$653$	5826.10	+	5826.10i	0.349147	+	0.349147i	−0.510645	+	0.859792i	$0.670593\pi$
$654$	−30434.1	+	6171.48i	−1.81967	+	0.368997i
$655$	6053.65	+	6856.79i	0.361123	+	0.409034i
$656$	−15445.0	+	4605.04i	−0.919247	+	0.274080i
$657$	28748.5	−	7501.86i	1.70713	−	0.445472i
$658$	5256.56	+	1743.47i	0.311431	+	0.103294i
$659$		−	30709.8i		−	1.81530i	−0.419727	−	0.907650i	$-0.637874\pi$
$659$		−	30709.8i		−	1.81530i	0.419727	−	0.907650i	$-0.362126\pi$
$660$	778.300	+	1130.15i	0.0459019	+	0.0666531i
$661$			21773.7i			1.28124i	0.767858	+	0.640620i	$0.221323\pi$
$661$			21773.7i			1.28124i	−0.767858	+	0.640620i	$0.778677\pi$
$662$	−1800.55	+	5428.65i	−0.105710	+	0.318716i
$663$	14113.2	−	8086.81i	0.826714	−	0.473704i
$664$	5464.71	−	30840.0i	0.319385	−	1.80245i
$665$	−11126.5	−	692.168i	−0.648824	−	0.0403626i
$666$	5712.71	+	371.862i	0.332377	+	0.0216357i
$667$	−17653.7	−	17653.7i	−1.02482	−	1.02482i
$668$	2542.57	+	17426.2i	0.147268	+	1.00934i
$669$	−4692.61	−	1273.85i	−0.271191	−	0.0736173i
$670$	−5451.55	+	13554.9i	−0.314346	+	0.781600i
$671$		−	846.780i		−	0.0487177i
$672$	11167.5	+	3400.29i	0.641064	+	0.195192i
$673$	5146.58	+	5146.58i	0.294779	+	0.294779i	0.838965	−	0.544186i	$-0.183161\pi$
$673$	5146.58	+	5146.58i	0.294779	+	0.294779i	−0.544186	+	0.838965i	$0.683161\pi$
$674$	11613.9	−	5828.63i	0.663724	−	0.333101i
$675$	−17379.6	−	2344.21i	−0.991026	−	0.133672i
$676$	18171.1	−	24379.5i	1.03386	−	1.38709i
$677$	20066.2	−	20066.2i	1.13915	−	1.13915i	0.150551	−	0.988602i	$-0.451895\pi$
$677$	20066.2	−	20066.2i	1.13915	−	1.13915i	0.988602	−	0.150551i	$-0.0481048\pi$
$678$	−9819.26	+	14814.6i	−0.556204	+	0.839159i
$679$			9032.10i			0.510486i
$680$	−8728.82	+	5326.43i	−0.492258	+	0.300382i
$681$	1498.49	−	5520.12i	0.0843204	−	0.310619i
$682$	−1042.40	−	345.737i	−0.0585270	−	0.0194120i
$683$	−8516.25	−	8516.25i	−0.477109	−	0.477109i	0.427097	−	0.904206i	$-0.359536\pi$
$683$	−8516.25	−	8516.25i	−0.477109	−	0.477109i	−0.904206	+	0.427097i	$0.859536\pi$
$684$	15983.0	−	6760.13i	0.893461	−	0.377895i
$685$	−1020.94	+	16411.5i	−0.0569461	+	0.915403i
$686$	−8376.12	−	16689.9i	−0.466184	−	0.928898i
$687$	−3635.30	+	2083.01i	−0.201885	+	0.115679i
$688$	7984.89	+	4316.99i	0.442473	+	0.239221i
$689$	11041.2			0.610504
$690$	16869.6	−	2341.87i	0.930746	−	0.129208i
$691$			12867.4i			0.708391i	0.935171	+	0.354196i	$0.115245\pi$
$691$			12867.4i			0.708391i	−0.935171	+	0.354196i	$0.884755\pi$
$692$	−2065.87	−	14159.0i	−0.113486	−	0.777809i
$693$	−249.810	−	957.319i	−0.0136934	−	0.0524755i
$694$	−19261.3	+	9666.60i	−1.05353	+	0.528731i
$695$	7535.29	+	8535.00i	0.411266	+	0.465829i
$696$	−12074.2	+	25617.6i	−0.657575	+	1.39516i
$697$	−7197.57	+	7197.57i	−0.391144	+	0.391144i
$698$	−11525.6	−	3822.76i	−0.625000	−	0.207297i
$699$	−4250.71	+	15658.7i	−0.230009	+	0.847308i
$700$	255.959	+	12408.2i	0.0138205	+	0.669979i
$701$	23310.0			1.25593			0.627964	−	0.778243i	$-0.283889\pi$
$701$	23310.0			1.25593			0.627964	+	0.778243i	$0.283889\pi$
$702$	13514.4	+	27600.7i	0.726592	+	1.48393i
$703$	−4258.73	−	4258.73i	−0.228479	−	0.228479i
$704$	−519.425	+	1419.67i	−0.0278076	+	0.0760024i
$705$	−4054.20	−	8220.08i	−0.216582	−	0.439129i
$706$	−26587.4	+	13343.3i	−1.41732	+	0.711307i
$707$	10280.3	−	10280.3i	0.546859	−	0.546859i
$708$	−1349.94	+	11177.7i	−0.0716581	+	0.593340i
$709$	21246.2			1.12541			0.562707	−	0.826656i	$-0.309760\pi$
$709$	21246.2			1.12541			0.562707	+	0.826656i	$0.309760\pi$
$710$	−28709.0	+	12240.0i	−1.51751	+	0.646986i
$711$	−28516.2	−	16713.6i	−1.50414	−	0.881587i
$712$	7209.12	+	10314.2i	0.379457	+	0.542893i
$713$	−9638.44	+	9638.44i	−0.506259	+	0.506259i
$714$	7225.64	−	1465.23i	0.378729	−	0.0767995i
$715$	2551.58	+	158.731i	0.133460	+	0.00830238i
$716$	−8539.62	+	11457.3i	−0.445727	+	0.598014i
$717$	−320.493	+	183.641i	−0.0166932	+	0.00956513i
$718$	18853.2	+	6253.16i	0.979940	+	0.325022i
$719$	−21983.8			−1.14028			−0.570138	−	0.821549i	$-0.693110\pi$
$719$	−21983.8			−1.14028			−0.570138	+	0.821549i	$0.693110\pi$
$720$	−8970.93	−	17110.5i	−0.464343	−	0.885656i
$721$	4500.69			0.232475
$722$	1085.01	+	359.870i	0.0559277	+	0.0185498i
$723$	−22130.6	+	12680.8i	−1.13838	+	0.652286i
$724$	−3625.83	+	4864.63i	−0.186123	+	0.249714i
$725$	−29876.6	−	3731.62i	−1.53047	−	0.191157i
$726$	−19045.9	+	3862.16i	−0.973634	+	0.197435i
$727$	1652.04	−	1652.04i	0.0842790	−	0.0842790i	−0.663711	−	0.747990i	$-0.731019\pi$
$727$	1652.04	−	1652.04i	0.0842790	−	0.0842790i	0.747990	+	0.663711i	$0.231019\pi$
$728$	17825.9	−	12459.5i	0.907517	−	0.634312i
$729$	−19679.2	−	386.383i	−0.999807	−	0.0196303i
$730$	−12984.4	+	32284.9i	−0.658322	+	1.63687i
$731$	5732.84			0.290064
$732$	−1429.43	+	11835.9i	−0.0721765	+	0.597633i
$733$	4353.35	−	4353.35i	0.219365	−	0.219365i	−0.588866	−	0.808231i	$-0.700425\pi$
$733$	4353.35	−	4353.35i	0.219365	−	0.219365i	0.808231	+	0.588866i	$0.200425\pi$
$734$	−15079.6	+	7567.95i	−0.758307	+	0.380569i
$735$	−3528.33	+	10395.8i	−0.177067	+	0.521708i
$736$	12856.5	+	13665.5i	0.643882	+	0.684396i
$737$	964.573	+	964.573i	0.0482097	+	0.0482097i
$738$	−12686.6	−	14453.2i	−0.632791	−	0.720909i
$739$	−27070.7			−1.34751			−0.673757	−	0.738953i	$-0.735321\pi$
$739$	−27070.7			−1.34751			−0.673757	+	0.738953i	$0.735321\pi$
$740$	−4333.00	+	5116.80i	−0.215249	+	0.254186i
$741$	8470.05	−	31201.9i	0.419912	−	1.54687i
$742$	4750.11	+	1575.49i	0.235016	+	0.0779490i
$743$	23857.9	−	23857.9i	1.17801	−	1.17801i	0.197761	−	0.980250i	$-0.436633\pi$
$743$	23857.9	−	23857.9i	1.17801	−	1.17801i	0.980250	−	0.197761i	$-0.0633671\pi$
$744$	13986.5	+	6592.20i	0.689207	+	0.324841i
$745$	10800.1	−	9535.08i	0.531121	−	0.468910i
$746$	25863.4	−	12980.0i	1.26934	−	0.637040i
$747$	36162.0	−	9436.39i	1.77122	−	0.462194i
$748$	137.843	+	944.741i	0.00673800	+	0.0461807i
$749$		−	19472.7i		−	0.949956i
$750$	14323.6	−	14721.0i	0.697366	−	0.716716i
$751$	11331.7			0.550601			0.275300	−	0.961358i	$-0.411223\pi$
$751$	11331.7			0.550601			0.275300	+	0.961358i	$0.411223\pi$
$752$	4802.09	−	8882.14i	0.232864	−	0.430716i
$753$	24230.0	−	13883.7i	1.17263	−	0.671911i
$754$	23666.5	+	47156.8i	1.14308	+	2.27765i
$755$	15082.4	+	17083.4i	0.727027	+	0.823482i
$756$	1875.70	+	13802.7i	0.0902363	+	0.664018i
$757$	20807.8	+	20807.8i	0.999039	+	0.999039i	1.00000		0.000960377i	$-0.000305698\pi$
$757$	20807.8	+	20807.8i	0.999039	+	0.999039i	−0.000960377		1.00000i	$0.500306\pi$
$758$	−24467.2	−	8115.18i	−1.17241	−	0.388861i
$759$	416.593	−	1534.64i	0.0199227	−	0.0733913i
$760$	−4782.03	+	19754.5i	−0.228240	+	0.942859i
$761$		−	38732.1i		−	1.84499i	−0.386011	−	0.922494i	$-0.626147\pi$
$761$		−	38732.1i		−	1.84499i	0.386011	−	0.922494i	$-0.373853\pi$
$762$	−11624.2	+	17537.7i	−0.552623	+	0.833756i
$763$	−18542.5	+	18542.5i	−0.879796	+	0.879796i
$764$	−1789.04	+	2400.28i	−0.0847187	+	0.113664i
$765$	−10123.4	−	6811.53i	−0.478447	−	0.321923i
$766$	10694.2	−	5367.06i	0.504434	−	0.253159i
$767$	14832.3	+	14832.3i	0.698255	+	0.698255i
$768$	9656.78	−	18966.6i	0.453723	−	0.891143i
$769$		−	16310.3i		−	0.764842i	−0.923988	−	0.382421i	$-0.875090\pi$
$769$		−	16310.3i		−	0.764842i	0.923988	−	0.382421i	$-0.124910\pi$
$770$	1075.08	+	432.379i	0.0503159	+	0.0202362i
$771$	−19204.5	−	5213.24i	−0.897061	−	0.243515i
$772$	−2016.31	−	13819.3i	−0.0940006	−	0.644258i
$773$	12398.7	+	12398.7i	0.576907	+	0.576907i	0.934050	−	0.357143i	$-0.116249\pi$
$773$	12398.7	+	12398.7i	0.576907	+	0.576907i	−0.357143	+	0.934050i	$0.616249\pi$
$774$	−703.559	+	10808.4i	−0.0326730	+	0.501937i
$775$	−2037.36	+	16311.8i	−0.0944313	+	0.756049i
$776$	16214.7	+	2873.17i	0.750097	+	0.132914i
$777$	4194.52	−	2403.44i	0.193665	−	0.110969i
$778$	7624.89	−	22989.0i	0.351370	−	1.05938i
$779$			20232.3i			0.930547i
$780$	−35396.9	−	6525.92i	−1.62489	−	0.299571i
$781$			2913.95i			0.133508i
$782$	11247.3	+	3730.46i	0.514327	+	0.170590i
$783$	−33791.5	−	331.700i	−1.54229	−	0.0151392i
$784$	−11590.0	+	3455.64i	−0.527969	+	0.157418i
$785$	−961.381	+	15454.1i	−0.0437110	+	0.702650i
$786$	−11783.8	+	2389.55i	−0.534752	+	0.108438i
$787$	−3751.32	−	3751.32i	−0.169911	−	0.169911i	0.617029	−	0.786940i	$-0.288336\pi$
$787$	−3751.32	−	3751.32i	−0.169911	−	0.169911i	−0.786940	+	0.617029i	$0.788336\pi$
$788$	−7480.60	+	1091.46i	−0.338179	+	0.0493421i
$789$	−2787.24	+	10267.6i	−0.125765	+	0.463291i
$790$	35610.9	−	15182.7i	1.60377	−	0.683765i
$791$			15008.6i			0.674646i
$792$	−1798.08	+	143.938i	−0.0806717	+	0.00645785i
$793$	15705.6	+	15705.6i	0.703307	+	0.703307i
$794$	1985.77	+	3956.76i	0.0887560	+	0.176852i
$795$	−3663.59	−	7428.11i	−0.163439	−	0.331381i
$796$	−1216.25	+	1631.80i	−0.0541569	+	0.0726601i
$797$	16226.9	−	16226.9i	0.721189	−	0.721189i	−0.247659	−	0.968847i	$-0.579661\pi$
$797$	16226.9	−	16226.9i	0.721189	−	0.721189i	0.968847	+	0.247659i	$0.0796611\pi$
$798$	8096.21	−	12214.9i	0.359151	−	0.541860i
$799$		−	6377.03i		−	0.282357i
$800$	22357.0	+	3487.62i	0.988050	+	0.154133i
$801$	−7592.73	+	12954.5i	−0.334926	+	0.571441i
$802$	11313.1	−	34109.0i	0.498105	−	1.50179i
$803$	2297.41	+	2297.41i	0.100964	+	0.100964i
$804$	−11854.1	−	15110.6i	−0.519977	−	0.662824i
$805$	10781.5	−	9518.66i	0.472047	−	0.416756i
$806$	25746.3	−	12921.2i	1.12516	−	0.564679i
$807$	−14286.9	−	24933.7i	−0.623200	−	1.08762i
$808$	−15185.3	−	21725.7i	−0.661158	−	0.945926i
$809$	−17188.7			−0.746997			−0.373499	−	0.927631i	$-0.621842\pi$
$809$	−17188.7			−0.746997			−0.373499	+	0.927631i	$0.621842\pi$
$810$	14084.5	−	18250.2i	0.610961	−	0.791661i
$811$		−	13269.2i		−	0.574532i	−0.957851	−	0.287266i	$-0.907254\pi$
$811$		−	13269.2i		−	0.574532i	0.957851	−	0.287266i	$-0.0927464\pi$
$812$	3452.79	+	23664.6i	0.149223	+	1.02274i
$813$	−5691.73	+	3261.34i	−0.245532	+	0.140689i
$814$	280.804	+	559.518i	0.0120911	+	0.0240923i
$815$	−18718.4	−	1164.45i	−0.804511	−	0.0500477i
$816$	−331.905	−	13437.8i	−0.0142390	−	0.576493i
$817$	8057.46	−	8057.46i	0.345036	−	0.345036i
$818$	12232.9	−	36882.0i	0.522875	−	1.57647i
$819$	22389.2	+	13122.5i	0.955239	+	0.559874i
$820$	22447.0	−	1861.83i	0.955954	−	0.0792901i
$821$	−23600.7			−1.00325			−0.501626	−	0.865084i	$-0.667265\pi$
$821$	−23600.7			−1.00325			−0.501626	+	0.865084i	$0.667265\pi$
$822$	−18016.9	−	11941.8i	−0.764491	−	0.506714i
$823$	30822.7	+	30822.7i	1.30548	+	1.30548i	0.924641	+	0.380839i	$0.124365\pi$
$823$	30822.7	+	30822.7i	1.30548	+	1.30548i	0.380839	+	0.924641i	$0.375635\pi$
$824$	1431.70	−	8079.80i	0.0605287	−	0.341594i
$825$	−739.853	−	1769.27i	−0.0312223	−	0.0746645i
$826$	4264.63	+	8497.51i	0.179643	+	0.357950i
$827$	−25914.9	+	25914.9i	−1.08966	+	1.08966i	−0.0940970	+	0.995563i	$0.529996\pi$
$827$	−25914.9	+	25914.9i	−1.08966	+	1.08966i	−0.995563	+	0.0940970i	$0.970004\pi$
$828$	−8413.53	+	20747.3i	−0.353128	+	0.870794i
$829$	−3666.33			−0.153603			−0.0768014	−	0.997046i	$-0.524471\pi$
$829$	−3666.33			−0.153603			−0.0768014	+	0.997046i	$0.524471\pi$
$830$	−16332.8	+	40610.3i	−0.683035	+	1.69832i
$831$	14130.5	+	3835.86i	0.589871	+	0.160126i
$832$	−16697.2	−	35965.2i	−0.695757	−	1.49864i
$833$	−5401.09	+	5401.09i	−0.224654	+	0.224654i
$834$	−14667.9	+	2974.39i	−0.609004	+	0.123495i
$835$	1528.11	−	24564.2i	0.0633323	−	1.01806i
$836$	1521.56	+	1134.09i	0.0629477	+	0.0469178i
$837$	−181.099	+	18449.3i	−0.00747875	+	0.761887i
$838$	−4054.24	+	12223.5i	−0.167126	+	0.503883i
$839$	−14960.2			−0.615595			−0.307797	−	0.951452i	$-0.599592\pi$
$839$	−14960.2			−0.615595			−0.307797	+	0.951452i	$0.599592\pi$
$840$	−14297.1	−	7858.40i	−0.587258	−	0.322786i
$841$	−33629.4			−1.37888
$842$	358.316	−	1080.32i	0.0146655	−	0.0442165i
$843$	14645.8	+	25560.0i	0.598372	+	1.04429i
$844$	−28585.1	+	38351.6i	−1.16581	+	1.56412i
$845$	−31855.6	+	28124.4i	−1.29688	+	1.14498i
$846$	12022.9	+	782.617i	0.488601	+	0.0318049i
$847$	−11604.1	+	11604.1i	−0.470744	+	0.470744i
$848$	4339.42	−	8026.38i	0.175727	−	0.325032i
$849$	1534.06	−	5651.18i	0.0620129	−	0.228443i
$850$	13468.4	−	4777.67i	0.543487	−	0.192791i
$851$	7769.98			0.312986
$852$	4918.97	−	40729.8i	0.197795	−	1.63777i
$853$	7182.93	−	7182.93i	0.288322	−	0.288322i	−0.548094	−	0.836416i	$-0.684647\pi$
$853$	7182.93	−	7182.93i	0.288322	−	0.288322i	0.836416	+	0.548094i	$0.184647\pi$
$854$	4515.73	+	8997.86i	0.180943	+	0.360539i
$855$	−23801.9	+	4654.80i	−0.952056	+	0.186188i
$856$	−34958.1	−	6194.40i	−1.39584	−	0.247337i
$857$	15618.0	+	15618.0i	0.622523	+	0.622523i	0.946176	−	0.323653i	$-0.104911\pi$
$857$	15618.0	+	15618.0i	0.622523	+	0.622523i	−0.323653	+	0.946176i	$0.604911\pi$
$858$	−1856.66	+	2801.18i	−0.0738756	+	0.111458i
$859$	27534.0			1.09365			0.546826	−	0.837246i	$-0.315836\pi$
$859$	27534.0			1.09365			0.546826	+	0.837246i	$0.315836\pi$
$860$	−9680.93	−	8197.99i	−0.383857	−	0.325057i
$861$	−15672.7	−	4254.50i	−0.620354	−	0.168401i
$862$	3249.90	−	9798.44i	0.128413	−	0.387165i
$863$	29314.9	−	29314.9i	1.15630	−	1.15630i	0.171041	−	0.985264i	$-0.445287\pi$
$863$	29314.9	−	29314.9i	1.15630	−	1.15630i	0.985264	−	0.171041i	$-0.0547129\pi$
$864$	25375.7	+	1023.39i	0.999188	+	0.0402969i
$865$	−1241.61	+	19958.7i	−0.0488045	+	0.784528i
$866$	−3329.44	−	6634.11i	−0.130646	−	0.260319i
$867$	8471.28	+	14784.2i	0.331834	+	0.579120i
$868$	12920.2	−	1885.13i	0.505232	−	0.0737159i
$869$		−	3614.50i		−	0.141097i
$870$	23872.5	−	31569.0i	0.930291	−	1.23022i
$871$	−35780.7			−1.39194
$872$	27389.7	+	39186.7i	1.06368	+	1.52182i
$873$	4961.36	+	19012.8i	0.192344	+	0.737099i
$874$	21051.2	−	10564.9i	0.814721	−	0.408882i
$875$	3214.12	−	17044.2i	0.124179	−	0.658515i
$876$	−28233.9	−	35990.3i	−1.08897	−	1.38813i
$877$	−8080.35	−	8080.35i	−0.311122	−	0.311122i	0.534222	−	0.845344i	$-0.320605\pi$
$877$	−8080.35	−	8080.35i	−0.311122	−	0.311122i	−0.845344	+	0.534222i	$0.820605\pi$
$878$	−6969.07	+	21011.7i	−0.267875	+	0.807643i
$879$	11957.6	+	3246.01i	0.458841	+	0.124557i
$880$	1118.21	−	1792.48i	0.0428352	−	0.0686642i
$881$		−	8552.35i		−	0.327056i	−0.986539	−	0.163528i	$-0.947713\pi$
$881$		−	8552.35i		−	0.327056i	0.986539	−	0.163528i	$-0.0522873\pi$
$882$	−9520.07	−	10845.8i	−0.363444	−	0.414054i
$883$	13269.8	−	13269.8i	0.505736	−	0.505736i	−0.407479	−	0.913215i	$-0.633592\pi$
$883$	13269.8	−	13269.8i	0.505736	−	0.505736i	0.913215	+	0.407479i	$0.133592\pi$
$884$	−20079.1	−	14965.9i	−0.763953	−	0.569409i
$885$	5057.08	−	14900.1i	0.192081	−	0.565944i
$886$	−14389.5	−	28672.0i	−0.545628	−	1.08719i
$887$	28025.2	+	28025.2i	1.06087	+	1.06087i	0.998023	+	0.0628495i	$0.0200188\pi$
$887$	28025.2	+	28025.2i	1.06087	+	1.06087i	0.0628495	+	0.998023i	$0.479981\pi$
$888$	−2980.44	−	8294.70i	−0.112632	−	0.313459i
$889$			17767.4i			0.670303i
$890$	−6897.25	−	16177.5i	−0.259771	−	0.609294i
$891$	−1051.72	−	1877.97i	−0.0395442	−	0.0706108i
$892$	1080.83	+	7407.78i	0.0405706	+	0.278061i
$893$	−8962.86	−	8962.86i	−0.335869	−	0.335869i
$894$	3763.77	+	18560.7i	0.140804	+	0.694364i
$895$	14970.7	−	13217.2i	0.559124	−	0.493633i
$896$	−2051.44	−	17855.3i	−0.0764886	−	0.665742i
$897$	20737.0	+	36190.4i	0.771892	+	1.34712i
$898$	−24059.7	−	7980.02i	−0.894079	−	0.296544i
$899$			31676.5i			1.17516i
$900$	7354.65	+	25979.0i	0.272395	+	0.962186i
$901$		−	5762.63i		−	0.213075i
$902$	662.054	−	1996.09i	0.0244390	−	0.0736836i
$903$	4547.28	+	7935.98i	0.167579	+	0.292462i
$904$	26944.0	+	4774.35i	0.991310	+	0.175655i
$905$	6356.41	−	5611.88i	0.233474	−	0.206127i
$906$	−29358.9	+	5953.46i	−1.07658	+	0.218312i
$907$	−1455.61	−	1455.61i	−0.0532887	−	0.0532887i	0.679960	−	0.733249i	$-0.261997\pi$
$907$	−1455.61	−	1455.61i	−0.0532887	−	0.0532887i	−0.733249	+	0.679960i	$0.761997\pi$
$908$	−8714.09	+	1271.43i	−0.318488	+	0.0464691i
$909$	15993.3	−	27287.3i	0.583569	−	0.995667i
$910$	−27959.5	+	11920.5i	−1.01852	+	0.434242i
$911$			10513.9i			0.382374i	0.981554	+	0.191187i	$0.0612336\pi$
$911$			10513.9i			0.382374i	−0.981554	+	0.191187i	$0.938766\pi$
$912$	−19353.2	−	18420.3i	−0.702686	−	0.668811i
$913$	2889.85	+	2889.85i	0.104754	+	0.104754i
$914$	26072.7	−	13085.0i	0.943554	−	0.473539i
$915$	5354.84	−	15777.4i	0.193471	−	0.570038i
$916$	5172.01	+	3854.94i	0.186559	+	0.139051i
$917$	−7179.52	+	7179.52i	−0.258548	+	0.258548i
$918$	14405.3	−	7053.42i	0.517917	−	0.253592i
$919$		−	52430.9i		−	1.88197i	−0.338442	−	0.940987i	$-0.609900\pi$
$919$		−	52430.9i		−	1.88197i	0.338442	−	0.940987i	$-0.390100\pi$
$920$	−13658.6	−	22383.3i	−0.489467	−	0.802125i
$921$	−5408.45	−	1468.17i	−0.193501	−	0.0525276i
$922$	−3733.86	−	1238.43i	−0.133371	−	0.0442359i
$923$	−54046.3	−	54046.3i	−1.92736	−	1.92736i
$924$	−1198.47	+	940.183i	−0.0426696	+	0.0334738i
$925$	7396.05	−	5753.64i	0.262898	−	0.204517i
$926$	7861.13	+	15663.8i	0.278977	+	0.555878i
$927$	9474.10	−	2472.24i	0.335674	−	0.0875935i
$928$	43581.9	+	1329.31i	1.54164	+	0.0470225i
$929$	43896.0			1.55025			0.775124	−	0.631810i	$-0.217688\pi$
$929$	43896.0			1.55025			0.775124	+	0.631810i	$0.217688\pi$
$930$	−17235.8	−	13033.7i	−0.607726	−	0.459562i
$931$			15182.4i			0.534459i
$932$	24719.0	−	3606.63i	0.868773	−	0.126759i
$933$	22479.5	+	39231.5i	0.788794	+	1.37661i
$934$	−16444.1	+	8252.78i	−0.576091	+	0.289121i
$935$	82.8448	−	1331.72i	0.00289766	−	0.0465796i
$936$	30680.1	−	36019.4i	1.07138	−	1.25783i
$937$	−8786.53	+	8786.53i	−0.306343	+	0.306343i	−0.843489	−	0.537146i	$-0.819502\pi$
$937$	−8786.53	+	8786.53i	−0.306343	+	0.306343i	0.537146	+	0.843489i	$0.319502\pi$
$938$	−15393.4	−	5105.62i	−0.535835	−	0.177723i
$939$	−13984.6	−	3796.24i	−0.486017	−	0.131934i
$940$	−9119.19	+	10768.8i	−0.316420	+	0.373658i
$941$	−1471.41			−0.0509740			−0.0254870	−	0.999675i	$-0.508114\pi$
$941$	−1471.41			−0.0509740			−0.0254870	+	0.999675i	$0.508114\pi$
$942$	−16965.8	−	11245.2i	−0.586812	−	0.388946i
$943$	−18456.7	−	18456.7i	−0.637363	−	0.637363i
$944$	16611.6	−	4952.89i	0.572736	−	0.170766i
$945$	1399.34	−	19416.7i	0.0481700	−	0.668388i
$946$	−1058.60	+	531.278i	−0.0363828	+	0.0182593i
$947$	−22482.0	+	22482.0i	−0.771454	+	0.771454i	−0.978361	−	0.206907i	$-0.933660\pi$
$947$	−22482.0	+	22482.0i	−0.771454	+	0.771454i	0.206907	+	0.978361i	$0.433660\pi$
$948$	−6101.54	+	50521.7i	−0.209039	+	1.73087i
$949$	−85222.1			−2.91510
$950$	12214.8	−	25644.8i	0.417159	−	0.875817i
$951$	−3566.02	+	13136.5i	−0.121594	+	0.447929i
$952$	−6502.85	−	9303.69i	−0.221385	−	0.316738i
$953$	−4887.41	+	4887.41i	−0.166127	+	0.166127i	−0.785274	−	0.619148i	$-0.787478\pi$
$953$	−4887.41	+	4887.41i	−0.166127	+	0.166127i	0.619148	+	0.785274i	$0.287478\pi$
$954$	10864.5	+	707.215i	0.368714	+	0.0240010i
$955$	3136.34	−	2768.98i	0.106272	−	0.0938242i
$956$	455.971	+	339.856i	0.0154259	+	0.0114976i
$957$	−1837.22	−	3206.34i	−0.0620574	−	0.108303i
$958$	−29530.2	−	9794.43i	−0.995904	−	0.330317i
$959$	−18252.9			−0.614617
$960$	−18655.7	+	23166.8i	−0.627198	+	0.778860i
$961$	−12496.5			−0.419472
$962$	−15585.8	−	5169.43i	−0.522357	−	0.173253i
$963$	−10696.4	−	40990.6i	−0.357931	−	1.37166i
$964$	31485.7	+	23467.7i	1.05196	+	0.784071i
$965$	−1211.82	+	19479.9i	−0.0404248	+	0.649824i
$966$	3757.29	+	18528.7i	0.125144	+	0.617133i
$967$	35645.9	−	35645.9i	1.18541	−	1.18541i	0.207092	−	0.978322i	$-0.433600\pi$
$967$	35645.9	−	35645.9i	1.18541	−	1.18541i	0.978322	−	0.207092i	$-0.0663998\pi$
$968$	17140.7	+	24523.3i	0.569134	+	0.814266i
$969$	−16284.9	−	4420.68i	−0.539882	−	0.146556i
$970$	−21351.7	−	8587.26i	−0.706763	−	0.284248i
$971$	−1819.84			−0.0601456			−0.0300728	−	0.999548i	$-0.509574\pi$
$971$	−1819.84			−0.0601456			−0.0300728	+	0.999548i	$0.509574\pi$
$972$	11530.3	+	28024.7i	0.380487	+	0.924786i
$973$	−8936.72	+	8936.72i	−0.294448	+	0.294448i
$974$	−25146.4	+	12620.2i	−0.827251	+	0.415170i
$975$	46537.9	+	19093.1i	1.52862	+	0.627148i
$976$	17589.8	−	5244.52i	0.576880	−	0.172001i
$977$	−3639.86	−	3639.86i	−0.119191	−	0.119191i	0.644996	−	0.764186i	$-0.276859\pi$
$977$	−3639.86	−	3639.86i	−0.119191	−	0.119191i	−0.764186	+	0.644996i	$0.776859\pi$
$978$	13620.4	−	20549.5i	0.445330	−	0.671881i
$979$	−1642.01			−0.0536046
$980$	16844.3	−	1397.12i	0.549052	−	0.0455403i
$981$	−28847.1	+	49218.1i	−0.938857	+	1.60185i
$982$	35063.2	+	11629.6i	1.13942	+	0.377918i
$983$	25003.9	−	25003.9i	0.811294	−	0.811294i	−0.173534	−	0.984828i	$-0.555519\pi$
$983$	25003.9	−	25003.9i	0.811294	−	0.811294i	0.984828	+	0.173534i	$0.0555186\pi$
$984$	−12623.4	+	26782.8i	−0.408964	+	0.867688i
$985$	10544.8	+	655.977i	0.341101	+	0.0212195i
$986$	24612.1	−	12352.0i	0.794937	−	0.398953i
$987$	8827.74	−	5058.26i	0.284691	−	0.163127i
$988$	−49255.5	+	7186.63i	−1.58606	+	0.231414i
$989$			14700.7i			0.472654i
$990$	2500.59	+	319.626i	0.0802766	+	0.0102610i
$991$	−8481.76			−0.271879			−0.135939	−	0.990717i	$-0.543405\pi$
$991$	−8481.76			−0.271879			−0.135939	+	0.990717i	$0.543405\pi$
$992$	725.769	−	23794.5i	0.0232290	−	0.761570i
$993$	5223.85	+	9116.74i	0.166943	+	0.291350i
$994$	−15539.6	−	30963.6i	−0.495861	−	0.988032i
$995$	2132.20	−	1882.45i	0.0679349	−	0.0599776i
$996$	−35514.7	−	45271.2i	−1.12984	−	1.44023i
$997$	−14916.6	−	14916.6i	−0.473834	−	0.473834i	0.429319	−	0.903153i	$-0.358754\pi$
$997$	−14916.6	−	14916.6i	−0.473834	−	0.473834i	−0.903153	+	0.429319i	$0.858754\pi$
$998$	1695.80	+	562.454i	0.0537870	+	0.0178398i
$999$	7509.38	−	7363.38i	0.237824	−	0.233200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.w.c.53.8	✓	128
3.2	odd	2	inner	120.4.w.c.53.57	yes	128
5.2	odd	4	inner	120.4.w.c.77.40	yes	128
8.5	even	2	inner	120.4.w.c.53.25	yes	128
15.2	even	4	inner	120.4.w.c.77.25	yes	128
24.5	odd	2	inner	120.4.w.c.53.40	yes	128
40.37	odd	4	inner	120.4.w.c.77.57	yes	128
120.77	even	4	inner	120.4.w.c.77.8	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.w.c.53.8	✓	128	1.1	even	1	trivial
120.4.w.c.53.25	yes	128	8.5	even	2	inner
120.4.w.c.53.40	yes	128	24.5	odd	2	inner
120.4.w.c.53.57	yes	128	3.2	odd	2	inner
120.4.w.c.77.8	yes	128	120.77	even	4	inner
120.4.w.c.77.25	yes	128	15.2	even	4	inner
120.4.w.c.77.40	yes	128	5.2	odd	4	inner
120.4.w.c.77.57	yes	128	40.37	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.68461 - 0.890420i) q^{2} +(-4.50848 + 2.58334i) q^{3} +(6.41430 + 4.78087i) q^{4} +(-7.39959 - 8.38130i) q^{5} +(14.4038 - 2.92083i) q^{6} +(8.77577 - 8.77577i) q^{7} +(-12.9629 - 18.5462i) q^{8} +(13.6527 - 23.2938i) q^{9} +(12.4022 + 29.0893i) q^{10} +2.95255 q^{11} +(-41.2693 - 4.98412i) q^{12} +(-54.7622 + 54.7622i) q^{13} +(-31.3737 + 15.7454i) q^{14} +(55.0126 + 18.6712i) q^{15} +(18.2866 + 61.3319i) q^{16} +(28.5815 + 28.5815i) q^{17} +(-57.3936 + 50.3783i) q^{18} +80.3420 q^{19} +(-7.39330 - 89.1366i) q^{20} +(-16.8946 + 62.2362i) q^{21} +(-7.92646 - 2.62901i) q^{22} +(-73.2914 + 73.2914i) q^{23} +(106.354 + 50.1275i) q^{24} +(-15.4922 + 124.036i) q^{25} +(195.777 - 98.2540i) q^{26} +(-1.37709 + 140.289i) q^{27} +(98.2463 - 14.3346i) q^{28} +240.870i q^{29} +(-131.062 - 99.1094i) q^{30} +131.509 q^{31} +(5.51879 - 180.935i) q^{32} +(-13.3115 + 7.62744i) q^{33} +(-51.2807 - 102.180i) q^{34} +(-138.489 - 8.61527i) q^{35} +(198.938 - 84.1419i) q^{36} +(-53.0074 - 53.0074i) q^{37} +(-215.687 - 71.5382i) q^{38} +(105.425 - 388.364i) q^{39} +(-59.5209 + 245.881i) q^{40} +251.827i q^{41} +(100.772 - 152.037i) q^{42} +(100.289 - 100.289i) q^{43} +(18.9385 + 14.1158i) q^{44} +(-296.257 + 57.9373i) q^{45} +(262.019 - 131.499i) q^{46} +(-111.559 - 111.559i) q^{47} +(-240.886 - 229.273i) q^{48} +188.972i q^{49} +(152.035 - 319.195i) q^{50} +(-202.695 - 55.0233i) q^{51} +(-613.073 + 89.4504i) q^{52} +(-100.811 - 100.811i) q^{53} +(128.613 - 375.397i) q^{54} +(-21.8476 - 24.7462i) q^{55} +(-276.517 - 48.9975i) q^{56} +(-362.220 + 207.551i) q^{57} +(214.476 - 646.643i) q^{58} -270.848i q^{59} +(263.603 + 382.771i) q^{60} -286.796i q^{61} +(-353.050 - 117.098i) q^{62} +(-84.6083 - 324.235i) q^{63} +(-175.924 + 480.827i) q^{64} +(864.196 + 53.7606i) q^{65} +(42.5279 - 8.62389i) q^{66} +(326.692 + 326.692i) q^{67} +(46.6859 + 319.975i) q^{68} +(141.096 - 519.769i) q^{69} +(364.120 + 146.442i) q^{70} +986.927i q^{71} +(-608.992 + 48.7504i) q^{72} +(778.110 + 778.110i) q^{73} +(95.1056 + 189.503i) q^{74} +(-250.581 - 599.236i) q^{75} +(515.338 + 384.105i) q^{76} +(25.9109 - 25.9109i) q^{77} +(-628.832 + 948.734i) q^{78} -1224.19i q^{79} +(378.728 - 607.096i) q^{80} +(-356.206 - 636.049i) q^{81} +(224.231 - 676.057i) q^{82} +(978.764 + 978.764i) q^{83} +(-405.910 + 318.431i) q^{84} +(28.0587 - 451.041i) q^{85} +(-358.538 + 179.939i) q^{86} +(-622.249 - 1085.96i) q^{87} +(-38.2737 - 54.7586i) q^{88} -556.133 q^{89} +(846.924 + 108.254i) q^{90} +961.162i q^{91} +(-820.510 + 119.717i) q^{92} +(-592.903 + 339.731i) q^{93} +(200.158 + 398.827i) q^{94} +(-594.498 - 673.370i) q^{95} +(442.536 + 829.999i) q^{96} +(-514.604 + 514.604i) q^{97} +(168.264 - 507.316i) q^{98} +(40.3103 - 68.7762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{6} - 144 q^{7} - 156 q^{10} - 56 q^{12} + 212 q^{15} + 636 q^{16} + 220 q^{18} - 188 q^{22} - 8 q^{25} + 908 q^{28} + 328 q^{30} - 544 q^{31} - 1624 q^{33} - 1268 q^{36} - 136 q^{40} + 328 q^{42}+ \cdots - 3792 q^{97}+O(q^{100}) \) 128 * q - 4 * q^6 - 144 * q^7 - 156 * q^10 - 56 * q^12 + 212 * q^15 + 636 * q^16 + 220 * q^18 - 188 * q^22 - 8 * q^25 + 908 * q^28 + 328 * q^30 - 544 * q^31 - 1624 * q^33 - 1268 * q^36 - 136 * q^40 + 328 * q^42 + 568 * q^46 - 148 * q^48 + 616 * q^52 + 728 * q^55 - 112 * q^57 + 2196 * q^58 - 424 * q^60 - 2304 * q^63 + 304 * q^66 - 4740 * q^70 + 224 * q^72 + 1280 * q^73 - 1624 * q^76 - 1448 * q^78 + 7056 * q^81 - 1472 * q^82 - 5720 * q^87 + 1516 * q^88 - 996 * q^90 + 2732 * q^96 - 3792 * q^97

Introduction

L-functions

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