LMFDB - Embedded newform 48.5.l.a.19.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,5,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	48.l (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:	$4.96175822802$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.9
Character	$\chi$	$=$	48.19
Dual form			48.5.l.a.43.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.149438 + 3.99721i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(-15.9553 - 1.19467i) q^{4} +(-0.419719 + 0.419719i) q^{5} +(-14.1376 - 15.2357i) q^{6} -40.4181 q^{7} +(7.15966 - 63.5983i) q^{8} -27.0000i q^{9} +O(q^{10})$	\(q+(-0.149438 + 3.99721i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(-15.9553 - 1.19467i) q^{4} +(-0.419719 + 0.419719i) q^{5} +(-14.1376 - 15.2357i) q^{6} -40.4181 q^{7} +(7.15966 - 63.5983i) q^{8} -27.0000i q^{9} +(-1.61498 - 1.74043i) q^{10} +(-67.0343 - 67.0343i) q^{11} +(63.0131 - 54.2342i) q^{12} +(22.3334 + 22.3334i) q^{13} +(6.03999 - 161.560i) q^{14} -3.08429i q^{15} +(253.146 + 38.1226i) q^{16} -171.480 q^{17} +(107.925 + 4.03482i) q^{18} +(-309.599 + 309.599i) q^{19} +(7.19818 - 6.19533i) q^{20} +(148.506 - 148.506i) q^{21} +(277.968 - 257.933i) q^{22} -763.220 q^{23} +(207.369 + 259.981i) q^{24} +624.648i q^{25} +(-92.6086 + 85.9337i) q^{26} +(99.2043 + 99.2043i) q^{27} +(644.884 + 48.2862i) q^{28} +(16.3995 + 16.3995i) q^{29} +(12.3286 + 0.460909i) q^{30} +1324.73i q^{31} +(-190.214 + 1006.18i) q^{32} +492.600 q^{33} +(25.6256 - 685.443i) q^{34} +(16.9642 - 16.9642i) q^{35} +(-32.2560 + 430.794i) q^{36} +(1412.01 - 1412.01i) q^{37} +(-1191.27 - 1283.80i) q^{38} -164.116 q^{39} +(23.6883 + 29.6984i) q^{40} -388.101i q^{41} +(571.415 + 615.800i) q^{42} +(-611.619 - 611.619i) q^{43} +(989.472 + 1149.64i) q^{44} +(11.3324 + 11.3324i) q^{45} +(114.054 - 3050.75i) q^{46} +317.326i q^{47} +(-1070.19 + 790.045i) q^{48} -767.378 q^{49} +(-2496.85 - 93.3459i) q^{50} +(630.059 - 630.059i) q^{51} +(-329.656 - 383.018i) q^{52} +(2461.50 - 2461.50i) q^{53} +(-411.365 + 381.715i) q^{54} +56.2712 q^{55} +(-289.380 + 2570.52i) q^{56} -2275.08i q^{57} +(-68.0028 + 63.1014i) q^{58} +(-3649.46 - 3649.46i) q^{59} +(-3.68470 + 49.2109i) q^{60} +(2837.11 + 2837.11i) q^{61} +(-5295.24 - 197.965i) q^{62} +1091.29i q^{63} +(-3993.48 - 910.684i) q^{64} -18.7475 q^{65} +(-73.6130 + 1969.02i) q^{66} +(-3391.06 + 3391.06i) q^{67} +(2736.03 + 204.862i) q^{68} +(2804.25 - 2804.25i) q^{69} +(65.2745 + 70.3447i) q^{70} +6501.21 q^{71} +(-1717.15 - 193.311i) q^{72} +710.991i q^{73} +(5433.08 + 5855.09i) q^{74} +(-2295.10 - 2295.10i) q^{75} +(5309.63 - 4569.90i) q^{76} +(2709.40 + 2709.40i) q^{77} +(24.5251 - 656.006i) q^{78} +9854.21i q^{79} +(-122.251 + 90.2492i) q^{80} -729.000 q^{81} +(1551.32 + 57.9969i) q^{82} +(8860.67 - 8860.67i) q^{83} +(-2546.87 + 2192.04i) q^{84} +(71.9736 - 71.9736i) q^{85} +(2536.17 - 2353.37i) q^{86} -120.511 q^{87} +(-4743.21 + 3783.32i) q^{88} +11699.0i q^{89} +(-46.9915 + 43.6045i) q^{90} +(-902.673 - 902.673i) q^{91} +(12177.4 + 911.794i) q^{92} +(-4867.39 - 4867.39i) q^{93} +(-1268.42 - 47.4205i) q^{94} -259.889i q^{95} +(-2998.05 - 4395.82i) q^{96} -17717.7 q^{97} +(114.675 - 3067.37i) q^{98} +(-1809.93 + 1809.93i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} + 180 q^{8}+O(q^{10}) $ 32 * q + 12 * q^4 + 180 * q^8	$ 32 q + 12 q^{4} + 180 q^{8} + 296 q^{10} - 192 q^{11} + 360 q^{12} - 156 q^{14} + 352 q^{16} - 324 q^{18} + 704 q^{19} - 1200 q^{20} - 1568 q^{22} - 2304 q^{23} + 1188 q^{24} + 2700 q^{26} + 4680 q^{28} - 1728 q^{29} + 1512 q^{30} - 3360 q^{32} - 9312 q^{34} - 5184 q^{35} - 756 q^{36} + 3648 q^{37} - 5880 q^{38} + 5232 q^{40} + 4500 q^{42} + 1088 q^{43} + 18840 q^{44} + 680 q^{46} + 2160 q^{48} + 10976 q^{49} - 25884 q^{50} - 4032 q^{51} - 25584 q^{52} + 960 q^{53} + 972 q^{54} + 11776 q^{55} + 15456 q^{56} + 12624 q^{58} + 13056 q^{59} + 7992 q^{60} + 3776 q^{61} + 21852 q^{62} - 8664 q^{64} + 4032 q^{65} - 8856 q^{66} - 896 q^{67} - 17280 q^{68} - 9792 q^{69} - 18240 q^{70} - 39936 q^{71} + 4860 q^{72} + 24204 q^{74} - 1152 q^{75} + 16776 q^{76} + 9408 q^{77} - 3780 q^{78} - 14232 q^{80} - 23328 q^{81} - 33800 q^{82} + 24000 q^{83} - 11448 q^{84} - 11200 q^{85} - 1200 q^{86} - 11424 q^{88} + 4104 q^{90} + 30528 q^{91} - 11664 q^{92} - 8040 q^{94} + 10080 q^{96} + 52968 q^{98} - 5184 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 + 180 * q^8 + 296 * q^10 - 192 * q^11 + 360 * q^12 - 156 * q^14 + 352 * q^16 - 324 * q^18 + 704 * q^19 - 1200 * q^20 - 1568 * q^22 - 2304 * q^23 + 1188 * q^24 + 2700 * q^26 + 4680 * q^28 - 1728 * q^29 + 1512 * q^30 - 3360 * q^32 - 9312 * q^34 - 5184 * q^35 - 756 * q^36 + 3648 * q^37 - 5880 * q^38 + 5232 * q^40 + 4500 * q^42 + 1088 * q^43 + 18840 * q^44 + 680 * q^46 + 2160 * q^48 + 10976 * q^49 - 25884 * q^50 - 4032 * q^51 - 25584 * q^52 + 960 * q^53 + 972 * q^54 + 11776 * q^55 + 15456 * q^56 + 12624 * q^58 + 13056 * q^59 + 7992 * q^60 + 3776 * q^61 + 21852 * q^62 - 8664 * q^64 + 4032 * q^65 - 8856 * q^66 - 896 * q^67 - 17280 * q^68 - 9792 * q^69 - 18240 * q^70 - 39936 * q^71 + 4860 * q^72 + 24204 * q^74 - 1152 * q^75 + 16776 * q^76 + 9408 * q^77 - 3780 * q^78 - 14232 * q^80 - 23328 * q^81 - 33800 * q^82 + 24000 * q^83 - 11448 * q^84 - 11200 * q^85 - 1200 * q^86 - 11424 * q^88 + 4104 * q^90 + 30528 * q^91 - 11664 * q^92 - 8040 * q^94 + 10080 * q^96 + 52968 * q^98 - 5184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.149438	+	3.99721i	−0.0373594	+	0.999302i
$2$	−0.149438	+	3.99721i	−0.0373594	+	0.999302i
$3$	−3.67423	+	3.67423i	−0.408248	+	0.408248i
$3$	−3.67423	+	3.67423i	−0.408248	+	0.408248i
$4$	−15.9553	−	1.19467i	−0.997209	−	0.0746667i
$5$	−0.419719	+	0.419719i	−0.0167888	+	0.0167888i	−0.715451	−	0.698663i	$-0.753779\pi$
$5$	−0.419719	+	0.419719i	−0.0167888	+	0.0167888i	0.698663	+	0.715451i	$0.253779\pi$
$6$	−14.1376	−	15.2357i	−0.392711	−	0.423215i
$7$	−40.4181			−0.824859			−0.412430	−	0.910990i	$-0.635320\pi$
$7$	−40.4181			−0.824859			−0.412430	+	0.910990i	$0.635320\pi$
$8$	7.15966	−	63.5983i	0.111870	−	0.993723i
$9$		−	27.0000i		−	0.333333i
$10$	−1.61498	−	1.74043i	−0.0161498	−	0.0174043i
$11$	−67.0343	−	67.0343i	−0.554003	−	0.554003i	0.373591	−	0.927594i	$-0.378126\pi$
$11$	−67.0343	−	67.0343i	−0.554003	−	0.554003i	−0.927594	+	0.373591i	$0.878126\pi$
$12$	63.0131	−	54.2342i	0.437591	−	0.376626i
$13$	22.3334	+	22.3334i	0.132150	+	0.132150i	0.770088	−	0.637938i	$-0.220212\pi$
$13$	22.3334	+	22.3334i	0.132150	+	0.132150i	−0.637938	+	0.770088i	$0.720212\pi$
$14$	6.03999	−	161.560i	0.0308163	−	0.824283i
$15$		−	3.08429i		−	0.0137080i
$16$	253.146	+	38.1226i	0.988850	+	0.148917i
$17$	−171.480			−0.593358			−0.296679	−	0.954977i	$-0.595879\pi$
$17$	−171.480			−0.593358			−0.296679	+	0.954977i	$0.595879\pi$
$18$	107.925	+	4.03482i	0.333101	+	0.0124531i
$19$	−309.599	+	309.599i	−0.857616	+	0.857616i	−0.991057	−	0.133441i	$-0.957397\pi$
$19$	−309.599	+	309.599i	−0.857616	+	0.857616i	0.133441	+	0.991057i	$0.457397\pi$
$20$	7.19818	−	6.19533i	0.0179955	−	0.0154883i
$21$	148.506	−	148.506i	0.336747	−	0.336747i
$22$	277.968	−	257.933i	0.574313	−	0.532919i
$23$	−763.220			−1.44276			−0.721380	−	0.692539i	$-0.756492\pi$
$23$	−763.220			−1.44276			−0.721380	+	0.692539i	$0.756492\pi$
$24$	207.369	+	259.981i	0.360015	+	0.451356i
$25$			624.648i			0.999436i
$26$	−92.6086	+	85.9337i	−0.136995	+	0.127121i
$27$	99.2043	+	99.2043i	0.136083	+	0.136083i
$28$	644.884	+	48.2862i	0.822556	+	0.0615895i
$29$	16.3995	+	16.3995i	0.0195000	+	0.0195000i	0.716790	−	0.697290i	$-0.245611\pi$
$29$	16.3995	+	16.3995i	0.0195000	+	0.0195000i	−0.697290	+	0.716790i	$0.745611\pi$
$30$	12.3286	+	0.460909i	0.0136984	+	0.000512122i
$31$			1324.73i			1.37850i	0.724525	+	0.689248i	$0.242059\pi$
$31$			1324.73i			1.37850i	−0.724525	+	0.689248i	$0.757941\pi$
$32$	−190.214	+	1006.18i	−0.185755	+	0.982596i
$33$	492.600			0.452341
$34$	25.6256	−	685.443i	0.0221675	−	0.592944i
$35$	16.9642	−	16.9642i	0.0138484	−	0.0138484i
$36$	−32.2560	+	430.794i	−0.0248889	+	0.332403i
$37$	1412.01	−	1412.01i	1.03142	−	1.03142i	0.0319248	−	0.999490i	$-0.489836\pi$
$37$	1412.01	−	1412.01i	1.03142	−	1.03142i	0.999490	−	0.0319248i	$-0.0101637\pi$
$38$	−1191.27	−	1283.80i	−0.824978	−	0.889058i
$39$	−164.116			−0.107900
$40$	23.6883	+	29.6984i	0.0148052	+	0.0185615i
$41$		−	388.101i		−	0.230875i	−0.993315	−	0.115437i	$-0.963173\pi$
$41$		−	388.101i		−	0.230875i	0.993315	−	0.115437i	$-0.0368270\pi$
$42$	571.415	+	615.800i	0.323932	+	0.349093i
$43$	−611.619	−	611.619i	−0.330784	−	0.330784i	0.522100	−	0.852884i	$-0.325149\pi$
$43$	−611.619	−	611.619i	−0.330784	−	0.330784i	−0.852884	+	0.522100i	$0.825149\pi$
$44$	989.472	+	1149.64i	0.511091	+	0.593822i
$45$	11.3324	+	11.3324i	0.00559625	+	0.00559625i
$46$	114.054	−	3050.75i	0.0539007	−	1.44175i
$47$			317.326i			0.143652i	0.997417	+	0.0718258i	$0.0228826\pi$
$47$			317.326i			0.143652i	−0.997417	+	0.0718258i	$0.977117\pi$
$48$	−1070.19	+	790.045i	−0.464491	+	0.342901i
$49$	−767.378			−0.319608
$50$	−2496.85	−	93.3459i	−0.998739	−	0.0373384i
$51$	630.059	−	630.059i	0.242237	−	0.242237i
$52$	−329.656	−	383.018i	−0.121914	−	0.141649i
$53$	2461.50	−	2461.50i	0.876289	−	0.876289i	−0.116859	−	0.993148i	$-0.537283\pi$
$53$	2461.50	−	2461.50i	0.876289	−	0.876289i	0.993148	+	0.116859i	$0.0372827\pi$
$54$	−411.365	+	381.715i	−0.141072	+	0.130904i
$55$	56.2712			0.0186020
$56$	−289.380	+	2570.52i	−0.0922767	+	0.819681i
$57$		−	2275.08i		−	0.700241i
$58$	−68.0028	+	63.1014i	−0.0202149	+	0.0187579i
$59$	−3649.46	−	3649.46i	−1.04839	−	1.04839i	−0.998768	−	0.0496255i	$-0.984197\pi$
$59$	−3649.46	−	3649.46i	−1.04839	−	1.04839i	−0.0496255	−	0.998768i	$-0.515803\pi$
$60$	−3.68470	+	49.2109i	−0.00102353	+	0.0136697i
$61$	2837.11	+	2837.11i	0.762460	+	0.762460i	0.976766	−	0.214307i	$-0.0687492\pi$
$61$	2837.11	+	2837.11i	0.762460	+	0.762460i	−0.214307	+	0.976766i	$0.568749\pi$
$62$	−5295.24	−	197.965i	−1.37753	−	0.0514998i
$63$			1091.29i			0.274953i
$64$	−3993.48	−	910.684i	−0.974970	−	0.222335i
$65$	−18.7475			−0.00443727
$66$	−73.6130	+	1969.02i	−0.0168992	+	0.452026i
$67$	−3391.06	+	3391.06i	−0.755415	+	0.755415i	−0.975484	−	0.220070i	$-0.929372\pi$
$67$	−3391.06	+	3391.06i	−0.755415	+	0.755415i	0.220070	+	0.975484i	$0.429372\pi$
$68$	2736.03	+	204.862i	0.591701	+	0.0443041i
$69$	2804.25	−	2804.25i	0.589004	−	0.589004i
$70$	65.2745	+	70.3447i	0.0133213	+	0.0143561i
$71$	6501.21			1.28967			0.644834	−	0.764323i	$-0.276927\pi$
$71$	6501.21			1.28967			0.644834	+	0.764323i	$0.276927\pi$
$72$	−1717.15	−	193.311i	−0.331241	−	0.0372899i
$73$			710.991i			0.133419i	0.997772	+	0.0667096i	$0.0212501\pi$
$73$			710.991i			0.133419i	−0.997772	+	0.0667096i	$0.978750\pi$
$74$	5433.08	+	5855.09i	0.992162	+	1.06923i
$75$	−2295.10	−	2295.10i	−0.408018	−	0.408018i
$76$	5309.63	−	4569.90i	0.919258	−	0.791187i
$77$	2709.40	+	2709.40i	0.456974	+	0.456974i
$78$	24.5251	−	656.006i	0.00403109	−	0.107825i
$79$			9854.21i			1.57895i	0.613785	+	0.789474i	$0.289646\pi$
$79$			9854.21i			1.57895i	−0.613785	+	0.789474i	$0.710354\pi$
$80$	−122.251	+	90.2492i	−0.0191017	+	0.0141014i
$81$	−729.000			−0.111111
$82$	1551.32	+	57.9969i	0.230714	+	0.00862536i
$83$	8860.67	−	8860.67i	1.28621	−	1.28621i	0.349132	−	0.937074i	$-0.386477\pi$
$83$	8860.67	−	8860.67i	1.28621	−	1.28621i	0.937074	−	0.349132i	$-0.113523\pi$
$84$	−2546.87	+	2192.04i	−0.360951	+	0.310663i
$85$	71.9736	−	71.9736i	0.00996174	−	0.00996174i
$86$	2536.17	−	2353.37i	0.342911	−	0.318195i
$87$	−120.511			−0.0159217
$88$	−4743.21	+	3783.32i	−0.612501	+	0.488549i
$89$			11699.0i			1.47696i	0.674276	+	0.738479i	$0.264456\pi$
$89$			11699.0i			1.47696i	−0.674276	+	0.738479i	$0.735544\pi$
$90$	−46.9915	+	43.6045i	−0.00580142	+	0.00538327i
$91$	−902.673	−	902.673i	−0.109005	−	0.109005i
$92$	12177.4	+	911.794i	1.43873	+	0.107726i
$93$	−4867.39	−	4867.39i	−0.562769	−	0.562769i
$94$	−1268.42	−	47.4205i	−0.143551	−	0.00536674i
$95$		−	259.889i		−	0.0287966i
$96$	−2998.05	−	4395.82i	−0.325309	−	0.476977i
$97$	−17717.7			−1.88306			−0.941529	−	0.336933i	$-0.890610\pi$
$97$	−17717.7			−1.88306			−0.941529	+	0.336933i	$0.890610\pi$
$98$	114.675	−	3067.37i	0.0119404	−	0.319384i
$99$	−1809.93	+	1809.93i	−0.184668	+	0.184668i
$100$	746.246	−	9966.46i	0.0746246	−	0.996646i
$101$	−6415.96	+	6415.96i	−0.628954	+	0.628954i	−0.947805	−	0.318851i	$-0.896703\pi$
$101$	−6415.96	+	6415.96i	−0.628954	+	0.628954i	0.318851	+	0.947805i	$0.396703\pi$
$102$	2424.32	+	2612.63i	0.233018	+	0.251118i
$103$	2249.74			0.212059			0.106030	−	0.994363i	$-0.466186\pi$
$103$	2249.74			0.212059			0.106030	+	0.994363i	$0.466186\pi$
$104$	1580.26	−	1260.46i	0.146104	−	0.116537i
$105$			124.661i			0.0113071i
$106$	9471.27	+	10207.0i	0.842940	+	0.908415i
$107$	−6606.07	−	6606.07i	−0.577000	−	0.577000i	0.357075	−	0.934076i	$-0.383774\pi$
$107$	−6606.07	−	6606.07i	−0.577000	−	0.577000i	−0.934076	+	0.357075i	$0.883774\pi$
$108$	−1464.32	−	1701.35i	−0.125542	−	0.145864i
$109$	−509.087	−	509.087i	−0.0428488	−	0.0428488i	0.685358	−	0.728207i	$-0.259646\pi$
$109$	−509.087	−	509.087i	−0.0428488	−	0.0428488i	−0.728207	+	0.685358i	$0.759646\pi$
$110$	−8.40903	+	224.927i	−0.000694961	+	0.0185890i
$111$			10376.1i			0.842147i
$112$	−10231.7	−	1540.84i	−0.815662	−	0.122835i
$113$	−21863.5			−1.71223			−0.856116	−	0.516783i	$-0.827129\pi$
$113$	−21863.5			−1.71223			−0.856116	+	0.516783i	$0.827129\pi$
$114$	9093.98	+	339.983i	0.699752	+	0.0261606i
$115$	320.338	−	320.338i	0.0242221	−	0.0242221i
$116$	−242.067	−	281.251i	−0.0179895	−	0.0209015i
$117$	603.001	−	603.001i	0.0440501	−	0.0440501i
$118$	15133.0	−	14042.3i	1.08683	−	1.00849i
$119$	6930.91			0.489437
$120$	−196.156	−	22.0825i	−0.0136219	−	0.00153351i
$121$		−	5653.80i		−	0.386162i
$122$	−11764.5	+	10916.6i	−0.790413	+	0.733442i
$123$	1425.97	+	1425.97i	0.0942543	+	0.0942543i
$124$	1582.62	−	21136.6i	0.102928	−	1.37465i
$125$	−524.501	−	524.501i	−0.0335680	−	0.0335680i
$126$	−4362.11	−	163.080i	−0.274761	−	0.0102721i
$127$		−	17711.1i		−	1.09809i	−0.835793	−	0.549044i	$-0.814992\pi$
$127$		−	17711.1i		−	1.09809i	0.835793	−	0.549044i	$-0.185008\pi$
$128$	4236.97	−	15826.7i	0.258604	−	0.965983i
$129$	4494.46			0.270084
$130$	2.80158	−	74.9376i	0.000165774	−	0.00443418i
$131$	12152.8	−	12152.8i	0.708166	−	0.708166i	−0.257983	−	0.966149i	$-0.583058\pi$
$131$	12152.8	−	12152.8i	0.708166	−	0.708166i	0.966149	+	0.257983i	$0.0830579\pi$
$132$	−7859.59	−	588.493i	−0.451079	−	0.0337748i
$133$	12513.4	−	12513.4i	0.707413	−	0.707413i
$134$	−13048.0	−	14061.5i	−0.726665	−	0.783109i
$135$	−83.2759			−0.00456932
$136$	−1227.74	+	10905.9i	−0.0663788	+	0.589633i
$137$			20301.2i			1.08164i	0.841140	+	0.540818i	$0.181885\pi$
$137$			20301.2i			1.08164i	−0.841140	+	0.540818i	$0.818115\pi$
$138$	10790.1	+	11628.2i	0.566588	+	0.610598i
$139$	7512.70	+	7512.70i	0.388836	+	0.388836i	0.874272	−	0.485436i	$-0.161339\pi$
$139$	7512.70	+	7512.70i	0.388836	+	0.388836i	−0.485436	+	0.874272i	$0.661339\pi$
$140$	−290.937	+	250.403i	−0.0148437	+	0.0127757i
$141$	−1165.93	−	1165.93i	−0.0586455	−	0.0586455i
$142$	−971.526	+	25986.7i	−0.0481812	+	1.28877i
$143$		−	2994.21i		−	0.146423i
$144$	1029.31	−	6834.93i	0.0496388	−	0.329617i
$145$	−13.7663			−0.000654761
$146$	−2841.98	−	106.249i	−0.133326	−	0.00498447i
$147$	2819.53	−	2819.53i	0.130479	−	0.130479i
$148$	−24215.9	+	20842.2i	−1.10555	+	0.951524i
$149$	−11075.0	+	11075.0i	−0.498853	+	0.498853i	−0.911081	−	0.412228i	$-0.864751\pi$
$149$	−11075.0	+	11075.0i	−0.498853	+	0.498853i	0.412228	+	0.911081i	$0.364751\pi$
$150$	9516.97	−	8831.02i	0.422977	−	0.392490i
$151$	19086.0			0.837068			0.418534	−	0.908201i	$-0.362544\pi$
$151$	19086.0			0.837068			0.418534	+	0.908201i	$0.362544\pi$
$152$	17473.4	+	21906.6i	0.756292	+	0.948174i
$153$			4629.97i			0.197786i
$154$	−11234.9	+	10425.1i	−0.473727	+	0.439583i
$155$	−556.016	−	556.016i	−0.0231432	−	0.0231432i
$156$	2618.53	+	196.064i	0.107599	+	0.00805655i
$157$	13388.1	+	13388.1i	0.543152	+	0.543152i	0.924451	−	0.381300i	$-0.124523\pi$
$157$	13388.1	+	13388.1i	0.543152	+	0.543152i	−0.381300	+	0.924451i	$0.624523\pi$
$158$	−39389.3	−	1472.59i	−1.57784	−	0.0589886i
$159$			18088.2i			0.715487i
$160$	−342.476	−	502.148i	−0.0133780	−	0.0196152i
$161$	30847.9			1.19007
$162$	108.940	−	2913.96i	0.00415105	−	0.111034i
$163$	−10874.3	+	10874.3i	−0.409285	+	0.409285i	−0.881489	−	0.472204i	$-0.843458\pi$
$163$	−10874.3	+	10874.3i	−0.409285	+	0.409285i	0.472204	+	0.881489i	$0.343458\pi$
$164$	−463.651	+	6192.28i	−0.0172387	+	0.230230i
$165$	−206.753	+	206.753i	−0.00759425	+	0.00759425i
$166$	34093.8	+	36742.1i	1.23726	+	1.33336i
$167$	−27549.9			−0.987841			−0.493920	−	0.869507i	$-0.664437\pi$
$167$	−27549.9			−0.987841			−0.493920	+	0.869507i	$0.664437\pi$
$168$	−8381.45	−	10507.9i	−0.296962	−	0.372305i
$169$		−	27563.4i		−	0.965073i
$170$	276.938	+	298.449i	0.00958262	+	0.0103269i
$171$	8359.19	+	8359.19i	0.285872	+	0.285872i
$172$	9027.91	+	10489.3i	0.305162	+	0.354559i
$173$	−9824.71	−	9824.71i	−0.328267	−	0.328267i	0.523660	−	0.851927i	$-0.324566\pi$
$173$	−9824.71	−	9824.71i	−0.328267	−	0.328267i	−0.851927	+	0.523660i	$0.824566\pi$
$174$	18.0089	−	481.708i	0.000594824	−	0.0159105i
$175$		−	25247.1i		−	0.824394i
$176$	−14413.9	−	19525.0i	−0.465325	−	0.630326i
$177$	26817.9			0.856010
$178$	−46763.3	−	1748.27i	−1.47593	−	0.0551783i
$179$	4614.04	−	4614.04i	0.144004	−	0.144004i	−0.631429	−	0.775433i	$-0.717531\pi$
$179$	4614.04	−	4614.04i	0.144004	−	0.144004i	0.775433	+	0.631429i	$0.217531\pi$
$180$	−167.274	−	194.351i	−0.00516278	−	0.00599848i
$181$	37427.0	−	37427.0i	1.14243	−	1.14243i	0.154422	−	0.988005i	$-0.450649\pi$
$181$	37427.0	−	37427.0i	1.14243	−	1.14243i	0.988005	−	0.154422i	$-0.0493514\pi$
$182$	3743.06	−	3473.28i	0.113002	−	0.104857i
$183$	−20848.4			−0.622546
$184$	−5464.40	+	48539.5i	−0.161401	+	1.43370i
$185$			1185.29i			0.0346323i
$186$	20183.3	−	18728.6i	0.583401	−	0.541351i
$187$	11495.1	+	11495.1i	0.328722	+	0.328722i
$188$	379.099	−	5063.05i	0.0107260	−	0.143251i
$189$	−4009.65	−	4009.65i	−0.112249	−	0.112249i
$190$	1038.83	+	38.8373i	0.0287765	+	0.00107583i
$191$		−	18416.6i		−	0.504827i	−0.967619	−	0.252414i	$-0.918776\pi$
$191$		−	18416.6i		−	0.504827i	0.967619	−	0.252414i	$-0.0812243\pi$
$192$	18019.0	−	11326.9i	0.488798	−	0.307262i
$193$	4067.43			0.109196			0.0545979	−	0.998508i	$-0.482612\pi$
$193$	4067.43			0.109196			0.0545979	+	0.998508i	$0.482612\pi$
$194$	2647.69	−	70821.3i	0.0703499	−	1.88174i
$195$	68.8827	−	68.8827i	0.00181151	−	0.00181151i
$196$	12243.8	+	916.761i	0.318715	+	0.0238640i
$197$	−31178.3	+	31178.3i	−0.803378	+	0.803378i	−0.983622	−	0.180244i	$-0.942311\pi$
$197$	−31178.3	+	31178.3i	−0.803378	+	0.803378i	0.180244	+	0.983622i	$0.442311\pi$
$198$	−6964.18	−	7505.13i	−0.177640	−	0.191438i
$199$	−14783.1			−0.373302			−0.186651	−	0.982426i	$-0.559763\pi$
$199$	−14783.1			−0.373302			−0.186651	+	0.982426i	$0.559763\pi$
$200$	39726.5	+	4472.27i	0.993163	+	0.111807i
$201$		−	24919.1i		−	0.616793i
$202$	−24687.1	−	26604.7i	−0.605017	−	0.652012i
$203$	−662.836	−	662.836i	−0.0160847	−	0.0160847i
$204$	−10805.5	+	9300.10i	−0.259648	+	0.223474i
$205$	162.893	+	162.893i	0.00387610	+	0.00387610i
$206$	−336.196	+	8992.67i	−0.00792242	+	0.211911i
$207$			20606.9i			0.480920i
$208$	4802.19	+	6505.00i	0.110997	+	0.150356i
$209$	41507.6			0.950244
$210$	−498.297	−	18.6291i	−0.0112992	−	0.000422428i
$211$	−50503.2	+	50503.2i	−1.13437	+	1.13437i	−0.144925	+	0.989443i	$0.546294\pi$
$211$	−50503.2	+	50503.2i	−1.13437	+	1.13437i	−0.989443	+	0.144925i	$0.953706\pi$
$212$	−42214.7	+	36333.3i	−0.939273	+	0.808413i
$213$	−23887.0	+	23887.0i	−0.526505	+	0.526505i
$214$	27393.0	−	25418.7i	0.598154	−	0.555041i
$215$	513.416			0.0111069
$216$	7019.49	−	5598.95i	0.150452	−	0.120005i
$217$		−	53543.3i		−	1.13707i
$218$	2111.00	−	1958.85i	0.0444197	−	0.0412181i
$219$	−2612.35	−	2612.35i	−0.0544682	−	0.0544682i
$220$	−897.825	−	67.2253i	−0.0185501	−	0.00138895i
$221$	−3829.74	−	3829.74i	−0.0784123	−	0.0784123i
$222$	−41475.4	−	1550.58i	−0.841559	−	0.0314621i
$223$		−	60108.1i		−	1.20871i	−0.796714	−	0.604356i	$-0.793430\pi$
$223$		−	60108.1i		−	1.20871i	0.796714	−	0.604356i	$-0.206570\pi$
$224$	7688.07	−	40667.8i	0.153222	−	0.810503i
$225$	16865.5			0.333145
$226$	3267.23	−	87392.9i	0.0639680	−	1.71104i
$227$	−33000.0	+	33000.0i	−0.640416	+	0.640416i	−0.950658	−	0.310242i	$-0.899590\pi$
$227$	−33000.0	+	33000.0i	−0.640416	+	0.640416i	0.310242	+	0.950658i	$0.399590\pi$
$228$	−2717.97	+	36299.7i	−0.0522847	+	0.698286i
$229$	−47268.9	+	47268.9i	−0.901372	+	0.901372i	−0.995555	−	0.0941825i	$-0.969976\pi$
$229$	−47268.9	+	47268.9i	−0.901372	+	0.901372i	0.0941825	+	0.995555i	$0.469976\pi$
$230$	1232.59	+	1328.33i	0.0233003	+	0.0251102i
$231$	−19909.9			−0.373118
$232$	1160.39	−	925.564i	0.0215590	−	0.0171961i
$233$		−	24412.3i		−	0.449672i	−0.974397	−	0.224836i	$-0.927815\pi$
$233$		−	24412.3i		−	0.449672i	0.974397	−	0.224836i	$-0.0721847\pi$
$234$	2320.21	+	2500.43i	0.0423736	+	0.0456650i
$235$	−133.188	−	133.188i	−0.00241173	−	0.00241173i
$236$	53868.4	+	62588.2i	0.967187	+	1.12375i
$237$	−36206.7	−	36206.7i	−0.644602	−	0.644602i
$238$	−1035.74	+	27704.3i	−0.0182851	+	0.489095i
$239$			55226.7i			0.966836i	0.875390	+	0.483418i	$0.160605\pi$
$239$			55226.7i			0.966836i	−0.875390	+	0.483418i	$0.839395\pi$
$240$	117.581	−	780.775i	0.00204134	−	0.0135551i
$241$	−21664.1			−0.372999			−0.186499	−	0.982455i	$-0.559714\pi$
$241$	−21664.1			−0.372999			−0.186499	+	0.982455i	$0.559714\pi$
$242$	22599.4	+	844.890i	0.385892	+	0.0144268i
$243$	2678.52	−	2678.52i	0.0453609	−	0.0453609i
$244$	−41877.7	−	48656.5i	−0.703401	−	0.817262i
$245$	322.083	−	322.083i	0.00536581	−	0.00536581i
$246$	−5913.01	+	5486.82i	−0.0977098	+	0.0906672i
$247$	−13828.8			−0.226668
$248$	84250.8	+	9484.65i	1.36984	+	0.154212i
$249$			65112.4i			1.05018i
$250$	2174.92	−	2018.16i	0.0347987	−	0.0322905i
$251$	43801.1	+	43801.1i	0.695244	+	0.695244i	0.963381	−	0.268137i	$-0.0864080\pi$
$251$	43801.1	+	43801.1i	0.695244	+	0.695244i	−0.268137	+	0.963381i	$0.586408\pi$
$252$	1303.73	−	17411.9i	0.0205298	−	0.274185i
$253$	51162.0	+	51162.0i	0.799293	+	0.799293i
$254$	70794.8	+	2646.70i	1.09732	+	0.0410239i
$255$			528.895i			0.00813373i
$256$	62629.3	+	19301.1i	0.955648	+	0.294512i
$257$	84973.1			1.28652			0.643258	−	0.765649i	$-0.277582\pi$
$257$	84973.1			1.28652			0.643258	+	0.765649i	$0.277582\pi$
$258$	−671.642	+	17965.3i	−0.0100902	+	0.269895i
$259$	−57070.6	+	57070.6i	−0.850772	+	0.850772i
$260$	299.122	+	22.3970i	0.00442489	+	0.000331317i
$261$	442.786	−	442.786i	0.00649999	−	0.00649999i
$262$	46761.3	+	50393.5i	0.681215	+	0.734129i
$263$	−56559.6			−0.817701			−0.408851	−	0.912601i	$-0.634070\pi$
$263$	−56559.6			−0.817701			−0.408851	+	0.912601i	$0.634070\pi$
$264$	3526.85	−	31328.5i	0.0506033	−	0.449502i
$265$			2066.27i			0.0294236i
$266$	48148.8	+	51888.7i	0.680490	+	0.733347i
$267$	−42984.8	−	42984.8i	−0.602966	−	0.602966i
$268$	58156.6	−	50054.3i	0.809710	−	0.696902i
$269$	−10449.7	−	10449.7i	−0.144411	−	0.144411i	0.631205	−	0.775616i	$-0.282561\pi$
$269$	−10449.7	−	10449.7i	−0.144411	−	0.144411i	−0.775616	+	0.631205i	$0.782561\pi$
$270$	12.4446	−	332.871i	0.000170707	−	0.00456613i
$271$		−	106853.i		−	1.45494i	−0.686138	−	0.727472i	$-0.740695\pi$
$271$		−	106853.i		−	1.45494i	0.686138	−	0.727472i	$-0.259305\pi$
$272$	−43409.5	−	6537.28i	−0.586742	−	0.0883608i
$273$	6633.26			0.0890024
$274$	−81148.2	−	3033.77i	−1.08088	−	0.0404093i
$275$	41872.8	−	41872.8i	0.553690	−	0.553690i
$276$	−48092.9	+	41392.6i	−0.631339	+	0.543381i
$277$	−25914.8	+	25914.8i	−0.337745	+	0.337745i	−0.855518	−	0.517773i	$-0.826761\pi$
$277$	−25914.8	+	25914.8i	−0.337745	+	0.337745i	0.517773	+	0.855518i	$0.326761\pi$
$278$	−31152.5	+	28907.1i	−0.403091	+	0.374038i
$279$	35767.8			0.459499
$280$	−957.438	−	1200.35i	−0.0122122	−	0.0153106i
$281$		−	39571.3i		−	0.501150i	−0.968097	−	0.250575i	$-0.919380\pi$
$281$		−	39571.3i		−	0.501150i	0.968097	−	0.250575i	$-0.0806197\pi$
$282$	4834.70	−	4486.23i	0.0607955	−	0.0564136i
$283$	107807.	+	107807.i	1.34609	+	1.34609i	0.889865	+	0.456225i	$0.150799\pi$
$283$	107807.	+	107807.i	1.34609	+	1.34609i	0.456225	+	0.889865i	$0.349201\pi$
$284$	−103729.	−	7766.79i	−1.28607	−	0.0962952i
$285$	954.895	+	954.895i	0.0117562	+	0.0117562i
$286$	11968.5	+	447.447i	0.146321	+	0.00547028i
$287$			15686.3i			0.190439i
$288$	27166.8	+	5135.77i	0.327532	+	0.0619185i
$289$	−54115.5			−0.647927
$290$	2.05721	−	55.0269i	2.44615e−5	−	0.000654303i
$291$	65098.9	−	65098.9i	0.768755	−	0.768755i
$292$	849.398	−	11344.1i	0.00996198	−	0.133047i
$293$	27738.4	−	27738.4i	0.323107	−	0.323107i	−0.526851	−	0.849958i	$-0.676627\pi$
$293$	27738.4	−	27738.4i	0.323107	−	0.323107i	0.849958	+	0.526851i	$0.176627\pi$
$294$	10848.9	+	11691.6i	0.125514	+	0.135263i
$295$	3063.49			0.0352024
$296$	−79691.7	−	99910.7i	−0.909557	−	1.14032i
$297$		−	13300.2i		−	0.150780i
$298$	−42614.2	−	45924.2i	−0.479868	−	0.517141i
$299$	−17045.3	−	17045.3i	−0.190661	−	0.190661i
$300$	33877.2	+	39361.0i	0.376414	+	0.437345i
$301$	24720.5	+	24720.5i	0.272850	+	0.272850i
$302$	−2852.17	+	76290.7i	−0.0312724	+	0.836484i
$303$		−	47147.5i		−	0.513539i
$304$	−90176.5	+	66571.0i	−0.975767	+	0.720340i
$305$	−2381.58			−0.0256015
$306$	−18507.0	−	691.892i	−0.197648	−	0.00738917i
$307$	45679.0	−	45679.0i	0.484663	−	0.484663i	−0.421954	−	0.906617i	$-0.638656\pi$
$307$	45679.0	−	45679.0i	0.484663	−	0.484663i	0.906617	+	0.421954i	$0.138656\pi$
$308$	−39992.6	−	46466.2i	−0.421578	−	0.489819i
$309$	−8266.06	+	8266.06i	−0.0865729	+	0.0865729i
$310$	2305.60	−	2139.42i	0.0239917	−	0.0222625i
$311$	53277.8			0.550840			0.275420	−	0.961324i	$-0.411183\pi$
$311$	53277.8			0.550840			0.275420	+	0.961324i	$0.411183\pi$
$312$	−1175.02	+	10437.5i	−0.0120708	+	0.107223i
$313$			142501.i			1.45455i	0.686345	+	0.727276i	$0.259214\pi$
$313$			142501.i			1.45455i	−0.686345	+	0.727276i	$0.740786\pi$
$314$	−55515.9	+	51514.5i	−0.563064	+	0.522481i
$315$	−458.034	−	458.034i	−0.00461612	−	0.00461612i
$316$	11772.5	−	157227.i	0.117895	−	1.57454i
$317$	−139779.	−	139779.i	−1.39098	−	1.39098i	−0.823128	−	0.567855i	$-0.807773\pi$
$317$	−139779.	−	139779.i	−1.39098	−	1.39098i	−0.567855	−	0.823128i	$-0.692227\pi$
$318$	−72302.4	−	2703.06i	−0.714988	−	0.0267302i
$319$		−	2198.66i		−	0.0216061i
$320$	2058.37	−	1293.91i	0.0201013	−	0.0126358i
$321$	48544.5			0.471119
$322$	−4609.84	+	123305.i	−0.0444605	+	1.18924i
$323$	53090.2	−	53090.2i	0.508873	−	0.508873i
$324$	11631.4	+	870.912i	0.110801	+	0.00829630i
$325$	−13950.5	+	13950.5i	−0.132076	+	0.132076i
$326$	−41841.8	−	45091.8i	−0.393709	−	0.424290i
$327$	3741.01			0.0349859
$328$	−24682.5	−	2778.67i	−0.229426	−	0.0258279i
$329$		−	12825.7i		−	0.118492i
$330$	−795.540	−	857.333i	−0.00730523	−	0.00787266i
$331$	−6944.56	−	6944.56i	−0.0633854	−	0.0633854i	0.674704	−	0.738089i	$-0.264271\pi$
$331$	−6944.56	−	6944.56i	−0.0633854	−	0.0633854i	−0.738089	+	0.674704i	$0.764271\pi$
$332$	−151961.	+	130789.i	−1.37865	+	1.18658i
$333$	−38124.2	−	38124.2i	−0.343805	−	0.343805i
$334$	4116.99	−	110123.i	0.0369052	−	0.987151i
$335$		−	2846.58i		−	0.0253649i
$336$	43254.9	−	31932.1i	0.383140	−	0.282845i
$337$	−196971.			−1.73438			−0.867188	−	0.497981i	$-0.834075\pi$
$337$	−196971.			−1.73438			−0.867188	+	0.497981i	$0.834075\pi$
$338$	110177.	+	4119.02i	0.964399	+	0.0360546i
$339$	80331.6	−	80331.6i	0.699016	−	0.699016i
$340$	−1234.35	+	1062.38i	−0.0106777	+	0.00919012i
$341$	88802.7	−	88802.7i	0.763691	−	0.763691i
$342$	−34662.6	+	32164.2i	−0.296353	+	0.274993i
$343$	128060.			1.08849
$344$	−43276.9	+	34518.9i	−0.365712	+	0.291703i
$345$			2353.99i			0.0197773i
$346$	40739.6	−	37803.2i	0.340302	−	0.315774i
$347$	−29232.7	−	29232.7i	−0.242778	−	0.242778i	0.575220	−	0.817998i	$-0.304916\pi$
$347$	−29232.7	−	29232.7i	−0.242778	−	0.242778i	−0.817998	+	0.575220i	$0.804916\pi$
$348$	1922.79	+	143.971i	0.0158772	+	0.00118882i
$349$	133064.	+	133064.i	1.09247	+	1.09247i	0.995264	+	0.0972042i	$0.0309900\pi$
$349$	133064.	+	133064.i	1.09247	+	1.09247i	0.0972042	+	0.995264i	$0.469010\pi$
$350$	100918.	+	3772.86i	0.823819	+	0.0307989i
$351$			4431.14i			0.0359667i
$352$	80199.3	−	54697.7i	0.647270	−	0.441452i
$353$	−59486.0			−0.477381			−0.238691	−	0.971096i	$-0.576718\pi$
$353$	−59486.0			−0.477381			−0.238691	+	0.971096i	$0.576718\pi$
$354$	−4007.61	+	107197.i	−0.0319800	+	0.855412i
$355$	−2728.68	+	2728.68i	−0.0216519	+	0.0216519i
$356$	13976.4	−	186661.i	0.110280	−	1.47284i
$357$	−25465.8	+	25465.8i	−0.199812	+	0.199812i
$358$	17753.8	+	19132.8i	0.138524	+	0.149284i
$359$	52327.2			0.406012			0.203006	−	0.979177i	$-0.434929\pi$
$359$	52327.2			0.406012			0.203006	+	0.979177i	$0.434929\pi$
$360$	801.858	−	639.585i	0.00618717	−	0.00493507i
$361$		−	61382.7i		−	0.471011i
$362$	144011.	+	155197.i	1.09895	+	1.18431i
$363$	20773.4	+	20773.4i	0.157650	+	0.157650i
$364$	13324.1	+	15480.8i	0.100562	+	0.116840i
$365$	−298.417	−	298.417i	−0.00223994	−	0.00223994i
$366$	3115.54	−	83335.5i	0.0232580	−	0.622111i
$367$			20184.1i			0.149857i	0.997189	+	0.0749284i	$0.0238728\pi$
$367$			20184.1i			0.149857i	−0.997189	+	0.0749284i	$0.976127\pi$
$368$	−193206.	−	29096.0i	−1.42667	−	0.214851i
$369$	−10478.7			−0.0769583
$370$	−4737.86	−	177.127i	−0.0346082	−	0.00129384i
$371$	−99489.0	+	99489.0i	−0.722815	+	0.722815i
$372$	71845.9	+	83475.7i	0.519178	+	0.603218i
$373$	24423.7	−	24423.7i	0.175547	−	0.175547i	−0.613864	−	0.789411i	$-0.710386\pi$
$373$	24423.7	−	24423.7i	0.175547	−	0.175547i	0.789411	+	0.613864i	$0.210386\pi$
$374$	−47666.0	+	44230.4i	−0.340773	+	0.316211i
$375$	3854.28			0.0274082
$376$	20181.4	+	2271.95i	0.142750	+	0.0160703i
$377$			732.512i			0.00515385i
$378$	16626.6	−	15428.2i	0.116364	−	0.107977i
$379$	−93864.3	−	93864.3i	−0.653465	−	0.653465i	0.300361	−	0.953826i	$-0.402893\pi$
$379$	−93864.3	−	93864.3i	−0.653465	−	0.653465i	−0.953826	+	0.300361i	$0.902893\pi$
$380$	−310.481	+	4146.62i	−0.00215015	+	0.0287162i
$381$	65074.6	+	65074.6i	0.448293	+	0.448293i
$382$	73615.0	+	2752.13i	0.504475	+	0.0188601i
$383$			176323.i			1.20202i	0.799241	+	0.601011i	$0.205235\pi$
$383$			176323.i			1.20202i	−0.799241	+	0.601011i	$0.794765\pi$
$384$	42583.3	+	73718.5i	0.288786	+	0.499936i
$385$	−2274.37			−0.0153441
$386$	−607.828	+	16258.4i	−0.00407949	+	0.109120i
$387$	−16513.7	+	16513.7i	−0.110261	+	0.110261i
$388$	282692.	+	21166.7i	1.87780	+	0.140602i
$389$	−98110.0	+	98110.0i	−0.648357	+	0.648357i	−0.952596	−	0.304239i	$-0.901598\pi$
$389$	−98110.0	+	98110.0i	−0.648357	+	0.648357i	0.304239	+	0.952596i	$0.401598\pi$
$390$	265.045	+	285.632i	0.00174257	+	0.00187792i
$391$	130877.			0.856073
$392$	−5494.17	+	48803.9i	−0.0357544	+	0.317601i
$393$			89304.8i			0.578215i
$394$	−119967.	−	129285.i	−0.772803	−	0.832830i
$395$	−4136.00	−	4136.00i	−0.0265086	−	0.0265086i
$396$	31040.3	−	26715.7i	0.197941	−	0.170364i
$397$	−62782.5	−	62782.5i	−0.398343	−	0.398343i	0.479305	−	0.877648i	$-0.340889\pi$
$397$	−62782.5	−	62782.5i	−0.398343	−	0.398343i	−0.877648	+	0.479305i	$0.840889\pi$
$398$	2209.16	−	59091.2i	0.0139463	−	0.373041i
$399$			91954.5i			0.577600i
$400$	−23813.2	+	158127.i	−0.148833	+	0.988292i
$401$	−171342.			−1.06555			−0.532776	−	0.846256i	$-0.678851\pi$
$401$	−171342.			−1.06555			−0.532776	+	0.846256i	$0.678851\pi$
$402$	99606.7	+	3723.85i	0.616363	+	0.0230430i
$403$	−29585.8	+	29585.8i	−0.182169	+	0.182169i
$404$	110034.	−	94703.8i	0.674160	−	0.580236i
$405$	305.975	−	305.975i	0.00186542	−	0.00186542i
$406$	2748.54	−	2550.44i	0.0166744	−	0.0154726i
$407$	−189306.			−1.14281
$408$	−35559.7	−	44581.7i	−0.213618	−	0.267816i
$409$			185879.i			1.11118i	0.831458	+	0.555588i	$0.187507\pi$
$409$			185879.i			1.11118i	−0.831458	+	0.555588i	$0.812493\pi$
$410$	−675.460	+	626.776i	−0.00401821	+	0.00372859i
$411$	−74591.5	−	74591.5i	−0.441576	−	0.441576i
$412$	−35895.3	−	2687.69i	−0.211467	−	0.0158338i
$413$	147504.	+	147504.i	0.864777	+	0.864777i
$414$	−82370.2	−	3079.45i	−0.480584	−	0.0179669i
$415$			7437.98i			0.0431876i
$416$	−26719.5	+	18223.3i	−0.154398	+	0.105303i
$417$	−55206.9			−0.317483
$418$	−6202.80	+	165914.i	−0.0355006	+	0.949580i
$419$	8082.59	−	8082.59i	0.0460386	−	0.0460386i	−0.683713	−	0.729751i	$-0.739636\pi$
$419$	8082.59	−	8082.59i	0.0460386	−	0.0460386i	0.729751	+	0.683713i	$0.239636\pi$
$420$	148.929	−	1989.01i	0.000844266	−	0.0112756i
$421$	109813.	−	109813.i	0.619567	−	0.619567i	−0.325853	−	0.945420i	$-0.605652\pi$
$421$	109813.	−	109813.i	0.619567	−	0.619567i	0.945420	+	0.325853i	$0.105652\pi$
$422$	−194325.	−	209419.i	−1.09120	−	1.17596i
$423$	8567.81			0.0478838
$424$	−138923.	−	174170.i	−0.772758	−	0.968819i
$425$		−	107115.i		−	0.593023i
$426$	−91911.6	−	99050.9i	−0.506467	−	0.545807i
$427$	−114671.	−	114671.i	−0.628922	−	0.628922i
$428$	97510.1	+	113294.i	0.532307	+	0.618472i
$429$	11001.4	+	11001.4i	0.0597770	+	0.0597770i
$430$	−76.7237	+	2052.23i	−0.000414947	+	0.0110991i
$431$			298818.i			1.60861i	0.594214	+	0.804307i	$0.297463\pi$
$431$			298818.i			1.60861i	−0.594214	+	0.804307i	$0.702537\pi$
$432$	21331.2	+	28895.1i	0.114300	+	0.154830i
$433$	−81674.5			−0.435623			−0.217811	−	0.975991i	$-0.569892\pi$
$433$	−81674.5			−0.435623			−0.217811	+	0.975991i	$0.569892\pi$
$434$	214024.	+	8001.38i	1.13627	+	0.0424801i
$435$	50.5808	−	50.5808i	0.000267305	−	0.000267305i
$436$	7514.46	+	8730.84i	0.0395298	+	0.0459286i
$437$	236293.	−	236293.i	1.23733	−	1.23733i
$438$	10832.5	−	10051.7i	0.0564651	−	0.0523953i
$439$	−160592.			−0.833289			−0.416645	−	0.909069i	$-0.636794\pi$
$439$	−160592.			−0.833289			−0.416645	+	0.909069i	$0.636794\pi$
$440$	402.882	−	3578.75i	0.00208100	−	0.0184853i
$441$			20719.2i			0.106536i
$442$	15880.6	−	14735.9i	0.0812870	−	0.0754282i
$443$	−155555.	−	155555.i	−0.792640	−	0.792640i	0.189283	−	0.981923i	$-0.439384\pi$
$443$	−155555.	−	155555.i	−0.792640	−	0.792640i	−0.981923	+	0.189283i	$0.939384\pi$
$444$	12396.0	−	165554.i	0.0628803	−	0.839796i
$445$	−4910.29	−	4910.29i	−0.0247963	−	0.0247963i
$446$	240264.	+	8982.41i	1.20787	+	0.0451568i
$447$		−	81384.5i		−	0.407312i
$448$	161409.	+	36808.1i	0.804213	+	0.183395i
$449$	348908.			1.73068			0.865342	−	0.501181i	$-0.167101\pi$
$449$	348908.			1.73068			0.865342	+	0.501181i	$0.167101\pi$
$450$	−2520.34	+	67414.9i	−0.0124461	+	0.332913i
$451$	−26016.1	+	26016.1i	−0.127905	+	0.127905i
$452$	348839.	+	26119.6i	1.70745	+	0.127847i
$453$	−70126.4	+	70126.4i	−0.341732	+	0.341732i
$454$	−126976.	−	136839.i	−0.616043	−	0.663894i
$455$	757.738			0.00366013
$456$	−144691.	−	16288.8i	−0.695845	−	0.0783357i
$457$		−	205846.i		−	0.985619i	−0.870137	−	0.492809i	$-0.835970\pi$
$457$		−	205846.i		−	0.985619i	0.870137	−	0.492809i	$-0.164030\pi$
$458$	−181880.	−	196007.i	−0.867068	−	0.934418i
$459$	−17011.6	−	17011.6i	−0.0807458	−	0.0807458i
$460$	−5493.80	+	4728.40i	−0.0259631	+	0.0223459i
$461$	−110453.	−	110453.i	−0.519729	−	0.519729i	0.397760	−	0.917489i	$-0.369788\pi$
$461$	−110453.	−	110453.i	−0.519729	−	0.519729i	−0.917489	+	0.397760i	$0.869788\pi$
$462$	2975.30	−	79584.2i	0.0139395	−	0.372857i
$463$			132697.i			0.619013i	0.950897	+	0.309506i	$0.100164\pi$
$463$			132697.i			0.619013i	−0.950897	+	0.309506i	$0.899836\pi$
$464$	3526.26	+	4776.65i	0.0163787	+	0.0221864i
$465$	4085.87			0.0188964
$466$	97580.8	+	3648.11i	0.449358	+	0.0167995i
$467$	−39343.3	+	39343.3i	−0.180400	+	0.180400i	−0.791530	−	0.611130i	$-0.790715\pi$
$467$	−39343.3	+	39343.3i	−0.180400	+	0.180400i	0.611130	+	0.791530i	$0.290715\pi$
$468$	−10341.5	+	8900.70i	−0.0472162	+	0.0406380i
$469$	137060.	−	137060.i	0.623111	−	0.623111i
$470$	552.283	−	512.476i	0.00250015	−	0.00231995i
$471$	−98382.4			−0.443481
$472$	−258228.	+	205970.i	−1.15910	+	0.924529i
$473$			81998.9i			0.366510i
$474$	150136.	−	139315.i	0.668234	−	0.620070i
$475$	−193391.	−	193391.i	−0.857133	−	0.857133i
$476$	−110585.	−	8280.13i	−0.488070	−	0.0365446i
$477$	−66460.4	−	66460.4i	−0.292096	−	0.292096i
$478$	−220752.	−	8252.95i	−0.966161	−	0.0361205i
$479$		−	47668.6i		−	0.207760i	−0.994590	−	0.103880i	$-0.966874\pi$
$479$		−	47668.6i		−	0.207760i	0.994590	−	0.103880i	$-0.0331257\pi$
$480$	3103.35	+	586.674i	0.0134694	+	0.00254633i
$481$	63069.8			0.272603
$482$	3237.44	−	86596.0i	0.0139350	−	0.372738i
$483$	−113342.	+	113342.i	−0.485846	+	0.485846i
$484$	−6754.40	+	90208.2i	−0.0288334	+	0.385084i
$485$	7436.45	−	7436.45i	0.0316142	−	0.0316142i
$486$	10306.3	+	11106.9i	0.0436346	+	0.0470239i
$487$	−15296.1			−0.0644946			−0.0322473	−	0.999480i	$-0.510266\pi$
$487$	−15296.1			−0.0644946			−0.0322473	+	0.999480i	$0.510266\pi$
$488$	200748.	−	160123.i	0.842970	−	0.672378i
$489$		−	79909.4i		−	0.334180i
$490$	1239.30	+	1335.56i	0.00516160	+	0.00556253i
$491$	157989.	+	157989.i	0.655335	+	0.655335i	0.954273	−	0.298937i	$-0.0966322\pi$
$491$	157989.	+	157989.i	0.655335	+	0.655335i	−0.298937	+	0.954273i	$0.596632\pi$
$492$	−21048.3	−	24455.4i	−0.0869535	−	0.101029i
$493$	−2812.19	−	2812.19i	−0.0115705	−	0.0115705i
$494$	2066.55	−	55276.6i	0.00846820	−	0.226510i
$495$		−	1519.32i		−	0.00620068i
$496$	−50502.4	+	335351.i	−0.205281	+	1.36313i
$497$	−262767.			−1.06379
$498$	−260268.	−	9730.24i	−1.04945	−	0.0392342i
$499$	131708.	−	131708.i	0.528947	−	0.528947i	−0.391311	−	0.920258i	$-0.627978\pi$
$499$	131708.	−	131708.i	0.528947	−	0.528947i	0.920258	+	0.391311i	$0.127978\pi$
$500$	7741.98	+	8995.19i	0.0309679	+	0.0359808i
$501$	101225.	−	101225.i	0.403284	−	0.403284i
$502$	−181627.	+	168536.i	−0.720732	+	0.668785i
$503$	292355.			1.15551			0.577756	−	0.816209i	$-0.303928\pi$
$503$	292355.			1.15551			0.577756	+	0.816209i	$0.303928\pi$
$504$	69404.1	+	7813.26i	0.273227	+	0.0307589i
$505$		−	5385.80i		−	0.0211187i
$506$	−212150.	+	196859.i	−0.828596	+	0.768874i
$507$	101275.	+	101275.i	0.393989	+	0.393989i
$508$	−21158.8	+	282586.i	−0.0819906	+	1.09502i
$509$	323407.	+	323407.i	1.24829	+	1.24829i	0.956477	+	0.291809i	$0.0942571\pi$
$509$	323407.	+	323407.i	1.24829	+	1.24829i	0.291809	+	0.956477i	$0.405743\pi$
$510$	−2114.11	−	79.0369i	−0.00812805	−	0.000303871i
$511$		−	28736.9i		−	0.110052i
$512$	−86509.9	+	247458.i	−0.330009	+	0.943978i
$513$	−61427.2			−0.233414
$514$	−12698.2	+	339655.i	−0.0480635	+	1.28562i
$515$	−944.257	+	944.257i	−0.00356021	+	0.00356021i
$516$	−71710.7	−	5369.39i	−0.269330	−	0.0201663i
$517$	21271.8	−	21271.8i	0.0795833	−	0.0795833i
$518$	−219595.	−	236652.i	−0.818394	−	0.881962i
$519$	72196.6			0.268029
$520$	−134.226	+	1192.31i	−0.000496397	+	0.00440942i
$521$			66159.8i			0.243735i	0.992546	+	0.121868i	$0.0388884\pi$
$521$			66159.8i			0.243735i	−0.992546	+	0.121868i	$0.961112\pi$
$522$	1703.74	+	1836.08i	0.00625262	+	0.00673829i
$523$	197336.	+	197336.i	0.721444	+	0.721444i	0.968899	−	0.247456i	$-0.0795944\pi$
$523$	197336.	+	197336.i	0.721444	+	0.721444i	−0.247456	+	0.968899i	$0.579594\pi$
$524$	−208421.	+	179384.i	−0.759066	+	0.653313i
$525$	92763.6	+	92763.6i	0.336557	+	0.336557i
$526$	8452.13	−	226080.i	0.0305488	−	0.817130i
$527$		−	227166.i		−	0.817941i
$528$	124699.	+	18779.2i	0.447298	+	0.0673611i
$529$	302664.			1.08156
$530$	−8259.32	−	308.779i	−0.0294031	−	0.00109925i
$531$	−98535.3	+	98535.3i	−0.349464	+	0.349464i
$532$	−214605.	+	184706.i	−0.758258	+	0.652618i
$533$	8667.60	−	8667.60i	0.0305102	−	0.0305102i
$534$	178243.	−	165396.i	0.625071	−	0.580018i
$535$	5545.39			0.0193742
$536$	191386.	+	239944.i	0.666165	+	0.835181i
$537$			33906.1i			0.117579i
$538$	43331.4	−	40208.2i	0.149706	−	0.138915i
$539$	51440.7	+	51440.7i	0.177063	+	0.177063i
$540$	1328.69	+	99.4869i	0.00455657	+	0.000341176i
$541$	−106284.	−	106284.i	−0.363140	−	0.363140i	0.501828	−	0.864968i	$-0.332661\pi$
$541$	−106284.	−	106284.i	−0.363140	−	0.363140i	−0.864968	+	0.501828i	$0.832661\pi$
$542$	427112.	+	15967.8i	1.45393	+	0.0543559i
$543$			275031.i			0.932787i
$544$	32617.9	−	172540.i	0.110219	−	0.583031i
$545$	427.347			0.00143876
$546$	−991.259	+	26514.5i	−0.00332508	+	0.0889403i
$547$	199343.	−	199343.i	0.666235	−	0.666235i	−0.290608	−	0.956842i	$-0.593857\pi$
$547$	199343.	−	199343.i	0.666235	−	0.666235i	0.956842	+	0.290608i	$0.0938575\pi$
$548$	24253.2	−	323913.i	0.0807622	−	1.07862i
$549$	76602.0	−	76602.0i	0.254153	−	0.254153i
$550$	161117.	+	173632.i	0.532618	+	0.573989i
$551$	−10154.5			−0.0334470
$552$	−158268.	−	198423.i	−0.519415	−	0.651199i
$553$		−	398288.i		−	1.30241i
$554$	−99714.3	−	107460.i	−0.324891	−	0.350127i
$555$	−4355.04	−	4355.04i	−0.0141386	−	0.0141386i
$556$	−110892.	−	128843.i	−0.358718	−	0.416784i
$557$	−96984.6	−	96984.6i	−0.312603	−	0.312603i	0.533314	−	0.845917i	$-0.320946\pi$
$557$	−96984.6	−	96984.6i	−0.312603	−	0.312603i	−0.845917	+	0.533314i	$0.820946\pi$
$558$	−5345.06	+	142971.i	−0.0171666	+	0.459178i
$559$		−	27319.0i		−	0.0874262i
$560$	4941.14	−	3647.70i	0.0157562	−	0.0116317i
$561$	−84471.2			−0.268400
$562$	158175.	+	5913.45i	0.500801	+	0.0187227i
$563$	65346.7	−	65346.7i	0.206161	−	0.206161i	−0.596472	−	0.802634i	$-0.703432\pi$
$563$	65346.7	−	65346.7i	0.206161	−	0.206161i	0.802634	+	0.596472i	$0.203432\pi$
$564$	17209.9	+	19995.7i	0.0541029	+	0.0628606i
$565$	9176.52	−	9176.52i	0.0287462	−	0.0287462i
$566$	−447037.	+	414816.i	−1.39544	+	1.29486i
$567$	29464.8			0.0916510
$568$	46546.5	−	413466.i	0.144275	−	1.28157i
$569$			470610.i			1.45357i	0.686864	+	0.726786i	$0.258987\pi$
$569$			470610.i			1.45357i	−0.686864	+	0.726786i	$0.741013\pi$
$570$	−3959.61	+	3674.22i	−0.0121872	+	0.0113088i
$571$	184929.	+	184929.i	0.567196	+	0.567196i	0.931342	−	0.364146i	$-0.118639\pi$
$571$	184929.	+	184929.i	0.567196	+	0.567196i	−0.364146	+	0.931342i	$0.618639\pi$
$572$	−3577.08	+	47773.6i	−0.0109329	+	0.146014i
$573$	67666.9	+	67666.9i	0.206095	+	0.206095i
$574$	−62701.4	−	2344.12i	−0.190306	−	0.00711470i
$575$		−	476744.i		−	1.44195i
$576$	−24588.5	+	107824.i	−0.0741117	+	0.324990i
$577$	537834.			1.61546			0.807731	−	0.589551i	$-0.200695\pi$
$577$	537834.			1.61546			0.807731	+	0.589551i	$0.200695\pi$
$578$	8086.89	−	216311.i	0.0242062	−	0.647474i
$579$	−14944.7	+	14944.7i	−0.0445790	+	0.0445790i
$580$	219.647	+	16.4462i	0.000652933	+	4.88888e-5i
$581$	−358131.	+	358131.i	−1.06094	+	1.06094i
$582$	250486.	+	269942.i	0.739498	+	0.796938i
$583$	−330009.			−0.970933
$584$	45217.8	+	5090.46i	0.132582	+	0.0149256i
$585$			506.182i			0.00147909i
$586$	106731.	+	115021.i	0.310810	+	0.334952i
$587$	−104568.	−	104568.i	−0.303476	−	0.303476i	0.538896	−	0.842372i	$-0.318841\pi$
$587$	−104568.	−	104568.i	−0.303476	−	0.303476i	−0.842372	+	0.538896i	$0.818841\pi$
$588$	−48354.9	+	41618.1i	−0.139857	+	0.120373i
$589$	−410137.	−	410137.i	−1.18222	−	1.18222i
$590$	−457.801	+	12245.4i	−0.00131514	+	0.0351779i
$591$		−	229113.i		−	0.655955i
$592$	411273.	−	303614.i	1.17351	−	0.866320i
$593$	−136845.			−0.389152			−0.194576	−	0.980887i	$-0.562333\pi$
$593$	−136845.			−0.389152			−0.194576	+	0.980887i	$0.562333\pi$
$594$	53163.6	+	1987.55i	0.150675	+	0.00563307i
$595$	−2909.03	+	2909.03i	−0.00821703	+	0.00821703i
$596$	189937.	−	163475.i	0.534708	−	0.460213i
$597$	54316.7	−	54316.7i	0.152400	−	0.152400i
$598$	70680.7	−	65586.3i	0.197651	−	0.183405i
$599$	−204546.			−0.570082			−0.285041	−	0.958515i	$-0.592007\pi$
$599$	−204546.			−0.570082			−0.285041	+	0.958515i	$0.592007\pi$
$600$	−162397.	+	129532.i	−0.451102	+	0.359812i
$601$			179891.i			0.498037i	0.968499	+	0.249018i	$0.0801080\pi$
$601$			179891.i			0.498037i	−0.968499	+	0.249018i	$0.919892\pi$
$602$	−102507.	+	95118.7i	−0.282853	+	0.262466i
$603$	91558.5	+	91558.5i	0.251805	+	0.251805i
$604$	−304523.	−	22801.4i	−0.834731	−	0.0625011i
$605$	2373.00	+	2373.00i	0.00648318	+	0.00648318i
$606$	188458.	+	7045.61i	0.513180	+	0.0191855i
$607$			316721.i			0.859605i	0.902923	+	0.429802i	$0.141417\pi$
$607$			316721.i			0.859605i	−0.902923	+	0.429802i	$0.858583\pi$
$608$	−252622.	−	370402.i	−0.683383	−	1.00200i
$609$	4870.83			0.0131331
$610$	355.898	−	9519.67i	0.000956457	−	0.0255836i
$611$	−7086.97	+	7086.97i	−0.0189836	+	0.0189836i
$612$	5531.27	−	73872.7i	0.0147680	−	0.197234i
$613$	−522223.	+	522223.i	−1.38974	+	1.38974i	−0.563904	+	0.825840i	$0.690701\pi$
$613$	−522223.	+	522223.i	−1.38974	+	1.38974i	−0.825840	+	0.563904i	$0.809299\pi$
$614$	175762.	+	189415.i	0.466218	+	0.502432i
$615$	−1197.02			−0.00316482
$616$	191712.	−	152915.i	0.505227	−	0.402984i
$617$		−	144630.i		−	0.379916i	−0.981792	−	0.189958i	$-0.939165\pi$
$617$		−	144630.i		−	0.379916i	0.981792	−	0.189958i	$-0.0608352\pi$
$618$	−31805.9	−	34276.4i	−0.0832781	−	0.0897467i
$619$	30198.8	+	30198.8i	0.0788150	+	0.0788150i	0.745415	−	0.666600i	$-0.232251\pi$
$619$	30198.8	+	30198.8i	0.0788150	+	0.0788150i	−0.666600	+	0.745415i	$0.732251\pi$
$620$	8207.17	+	9535.68i	0.0213506	+	0.0248067i
$621$	−75714.7	−	75714.7i	−0.196335	−	0.196335i
$622$	−7961.71	+	212962.i	−0.0205791	+	0.550456i
$623$		−	472851.i		−	1.21828i
$624$	−41545.3	−	6256.54i	−0.106697	−	0.0160681i
$625$	−389965.			−0.998309
$626$	−569606.	−	21295.0i	−1.45354	−	0.0543412i
$627$	−152509.	+	152509.i	−0.387935	+	0.387935i
$628$	−197618.	−	229607.i	−0.501080	−	0.582191i
$629$	−242132.	+	242132.i	−0.611998	+	0.611998i
$630$	1899.31	−	1762.41i	0.00478535	−	0.00444044i
$631$	−309926.			−0.778394			−0.389197	−	0.921155i	$-0.627247\pi$
$631$	−309926.			−0.778394			−0.389197	+	0.921155i	$0.627247\pi$
$632$	626711.	+	70552.8i	1.56904	+	0.176636i
$633$		−	371121.i		−	0.926207i
$634$	579612.	−	537836.i	1.44198	−	1.33805i
$635$	7433.67	+	7433.67i	0.0184355	+	0.0184355i
$636$	21609.4	−	288604.i	0.0534230	−	0.713490i
$637$	−17138.1	−	17138.1i	−0.0422362	−	0.0422362i
$638$	8788.48	+	328.562i	0.0215910	+	0.000807191i
$639$		−	175533.i		−	0.429889i
$640$	4864.42	+	8421.09i	0.0118760	+	0.0205593i
$641$	−418638.			−1.01888			−0.509440	−	0.860506i	$-0.670147\pi$
$641$	−418638.			−1.01888			−0.509440	+	0.860506i	$0.670147\pi$
$642$	−7254.38	+	194043.i	−0.0176007	+	0.470790i
$643$	157517.	−	157517.i	0.380983	−	0.380983i	−0.490473	−	0.871456i	$-0.663176\pi$
$643$	157517.	−	157517.i	0.380983	−	0.380983i	0.871456	+	0.490473i	$0.163176\pi$
$644$	−492189.	−	36853.0i	−1.18675	−	0.0888589i
$645$	−1886.41	+	1886.41i	−0.00453437	+	0.00453437i
$646$	204279.	+	220146.i	0.489507	+	0.527529i
$647$	232962.			0.556516			0.278258	−	0.960506i	$-0.410243\pi$
$647$	232962.			0.556516			0.278258	+	0.960506i	$0.410243\pi$
$648$	−5219.39	+	46363.1i	−0.0124300	+	0.110414i
$649$			489278.i			1.16163i
$650$	−53678.3	−	57847.8i	−0.127049	−	0.136918i
$651$	196730.	+	196730.i	0.464205	+	0.464205i
$652$	186494.	−	160512.i	0.438702	−	0.377583i
$653$	−348883.	−	348883.i	−0.818190	−	0.818190i	0.167656	−	0.985846i	$-0.446380\pi$
$653$	−348883.	−	348883.i	−0.818190	−	0.818190i	−0.985846	+	0.167656i	$0.946380\pi$
$654$	−559.048	+	14953.6i	−0.00130705	+	0.0349615i
$655$			10201.6i			0.0237785i
$656$	14795.4	−	98246.0i	0.0343811	−	0.228301i
$657$	19196.8			0.0444731
$658$	51267.1	+	1916.65i	0.118410	+	0.00442680i
$659$	−65269.7	+	65269.7i	−0.150294	+	0.150294i	−0.778249	−	0.627956i	$-0.783892\pi$
$659$	−65269.7	+	65269.7i	−0.150294	+	0.150294i	0.627956	+	0.778249i	$0.283892\pi$
$660$	3545.82	−	3051.82i	0.00814009	−	0.00700601i
$661$	−179961.	+	179961.i	−0.411885	+	0.411885i	−0.882395	−	0.470510i	$-0.844070\pi$
$661$	−179961.	+	179961.i	−0.411885	+	0.411885i	0.470510	+	0.882395i	$0.344070\pi$
$662$	28796.6	−	26721.1i	0.0657091	−	0.0609731i
$663$	28142.7			0.0640234
$664$	−500084.	−	626963.i	−1.13424	−	1.42202i
$665$			10504.2i			0.0237532i
$666$	158088.	−	146693.i	0.356409	−	0.330721i
$667$	−12516.4	−	12516.4i	−0.0281338	−	0.0281338i
$668$	439568.	+	32913.0i	0.985083	+	0.0737588i
$669$	220851.	+	220851.i	0.493455	+	0.493455i
$670$	11378.4	+	425.386i	0.0253472	+	0.000947620i
$671$		−	380368.i		−	0.844810i
$672$	121175.	+	177671.i	0.268334	+	0.393439i
$673$	802675.			1.77219			0.886094	−	0.463506i	$-0.153409\pi$
$673$	802675.			1.77219			0.886094	+	0.463506i	$0.153409\pi$
$674$	29434.9	−	787335.i	0.0647953	−	1.73317i
$675$	−61967.8	+	61967.8i	−0.136006	+	0.136006i
$676$	−32929.1	+	439784.i	−0.0720588	+	0.962379i
$677$	−356689.	+	356689.i	−0.778237	+	0.778237i	−0.979531	−	0.201294i	$-0.935485\pi$
$677$	−356689.	+	356689.i	−0.778237	+	0.778237i	0.201294	+	0.979531i	$0.435485\pi$
$678$	309098.	+	333107.i	0.672413	+	0.724643i
$679$	716115.			1.55326
$680$	−4062.09	−	5092.70i	−0.00878479	−	0.0110136i
$681$		−	242499.i		−	0.522897i
$682$	341692.	+	368233.i	0.734627	+	0.791689i
$683$	288764.	+	288764.i	0.619016	+	0.619016i	0.945279	−	0.326263i	$-0.105790\pi$
$683$	288764.	+	288764.i	0.619016	+	0.619016i	−0.326263	+	0.945279i	$0.605790\pi$
$684$	−123387.	−	143360.i	−0.263729	−	0.306419i
$685$	−8520.81	−	8520.81i	−0.0181593	−	0.0181593i
$686$	−19137.0	+	511882.i	−0.0406654	+	1.08773i
$687$		−	347354.i		−	0.735968i
$688$	−131512.	−	178145.i	−0.277836	−	0.376355i
$689$	109947.			0.231604
$690$	−9409.40	−	351.775i	−0.0197635	−	0.000738869i
$691$	−352595.	+	352595.i	−0.738448	+	0.738448i	−0.972278	−	0.233830i	$-0.924874\pi$
$691$	−352595.	+	352595.i	−0.738448	+	0.738448i	0.233830	+	0.972278i	$0.424874\pi$
$692$	145019.	+	168494.i	0.302840	+	0.351862i
$693$	73153.8	−	73153.8i	0.152325	−	0.152325i
$694$	121217.	−	112481.i	0.251679	−	0.233539i
$695$	−6306.45			−0.0130561
$696$	−862.818	+	7664.29i	−0.00178115	+	0.0158217i
$697$			66551.7i			0.136991i
$698$	−551768.	+	511999.i	−1.13252	+	1.05089i
$699$	89696.4	+	89696.4i	0.183578	+	0.183578i
$700$	−30161.8	+	402825.i	−0.0615548	+	0.822093i
$701$	640273.	+	640273.i	1.30295	+	1.30295i	0.926391	+	0.376563i	$0.122894\pi$
$701$	640273.	+	640273.i	1.30295	+	1.30295i	0.376563	+	0.926391i	$0.377106\pi$
$702$	−17712.2	−	662.179i	−0.0359416	−	0.00134370i
$703$			874313.i			1.76912i
$704$	206653.	+	328747.i	0.416962	+	0.663310i
$705$	978.726			0.00196917
$706$	8889.45	−	237778.i	0.0178347	−	0.477048i
$707$	259321.	−	259321.i	0.518798	−	0.518798i
$708$	−427889.	−	32038.5i	−0.853620	−	0.0639154i
$709$	−448853.	+	448853.i	−0.892918	+	0.892918i	−0.994797	−	0.101879i	$-0.967515\pi$
$709$	−448853.	+	448853.i	−0.892918	+	0.892918i	0.101879	+	0.994797i	$0.467515\pi$
$710$	−10499.3	−	11314.9i	−0.0208279	−	0.0224457i
$711$	266064.			0.526316
$712$	744035.	+	83760.8i	1.46769	+	0.165227i
$713$		−	1.01106e6i		−	1.98884i
$714$	−97986.5	−	105598.i	−0.192207	−	0.207137i
$715$	1256.73	+	1256.73i	0.00245826	+	0.00245826i
$716$	−79130.8	+	68106.3i	−0.154355	+	0.132850i
$717$	−202916.	−	202916.i	−0.394709	−	0.394709i
$718$	−7819.66	+	209163.i	−0.0151684	+	0.405729i
$719$		−	357287.i		−	0.691129i	−0.938395	−	0.345565i	$-0.887687\pi$
$719$		−	357287.i		−	0.691129i	0.938395	−	0.345565i	$-0.112313\pi$
$720$	2436.73	+	3300.77i	0.00470048	+	0.00636723i
$721$	−90930.1			−0.174919
$722$	245359.	+	9172.89i	0.470683	+	0.0175967i
$723$	79599.1	−	79599.1i	0.152276	−	0.152276i
$724$	−641874.	+	552448.i	−1.22454	+	1.05394i
$725$	−10243.9	+	10243.9i	−0.0194890	+	0.0194890i
$726$	−86139.8	+	79931.2i	−0.163430	+	0.151650i
$727$	−156701.			−0.296485			−0.148242	−	0.988951i	$-0.547362\pi$
$727$	−156701.			−0.296485			−0.148242	+	0.988951i	$0.547362\pi$
$728$	−63871.2	+	50945.6i	−0.120515	+	0.0961266i
$729$			19683.0i			0.0370370i
$730$	1237.43	−	1148.24i	0.00232206	−	0.00215470i
$731$	104881.	+	104881.i	0.196273	+	0.196273i
$732$	332644.	+	24906.9i	0.620808	+	0.0464834i
$733$	−365988.	−	365988.i	−0.681175	−	0.681175i	0.279090	−	0.960265i	$-0.409967\pi$
$733$	−365988.	−	365988.i	−0.681175	−	0.681175i	−0.960265	+	0.279090i	$0.909967\pi$
$734$	−80679.9	−	3016.26i	−0.149752	−	0.00559857i
$735$			2366.82i			0.00438117i
$736$	145175.	−	767936.i	0.268001	−	1.41765i
$737$	454634.			0.837004
$738$	1565.92	−	41885.6i	0.00287512	−	0.0769046i
$739$	−95631.5	+	95631.5i	−0.175110	+	0.175110i	−0.789220	−	0.614110i	$-0.789515\pi$
$739$	−95631.5	+	95631.5i	−0.175110	+	0.175110i	0.614110	+	0.789220i	$0.289515\pi$
$740$	1416.03	−	18911.7i	0.00258588	−	0.0345357i
$741$	50810.3	−	50810.3i	0.0925369	−	0.0925369i
$742$	−382811.	−	412545.i	−0.695306	−	0.749314i
$743$	−43596.2			−0.0789716			−0.0394858	−	0.999220i	$-0.512572\pi$
$743$	−43596.2			−0.0789716			−0.0394858	+	0.999220i	$0.512572\pi$
$744$	−344406.	+	274708.i	−0.622193	+	0.496279i
$745$		−	9296.80i		−	0.0167502i
$746$	93976.7	+	101276.i	0.168866	+	0.181983i
$747$	−239238.	−	239238.i	−0.428735	−	0.428735i
$748$	−169675.	−	197141.i	−0.303260	−	0.352349i
$749$	267005.	+	267005.i	0.475944	+	0.475944i
$750$	−575.974	+	15406.3i	−0.00102395	+	0.0273891i
$751$			96159.0i			0.170494i	0.996360	+	0.0852472i	$0.0271680\pi$
$751$			96159.0i			0.170494i	−0.996360	+	0.0852472i	$0.972832\pi$
$752$	−12097.3	+	80329.7i	−0.0213921	+	0.142050i
$753$	−321871.			−0.567664
$754$	−2928.00	−	109.465i	−0.00515025	−	0.000192545i
$755$	−8010.75	+	8010.75i	−0.0140533	+	0.0140533i
$756$	59185.1	+	68765.5i	0.103554	+	0.120317i
$757$	510342.	−	510342.i	0.890573	−	0.890573i	−0.104004	−	0.994577i	$-0.533165\pi$
$757$	510342.	−	510342.i	0.890573	−	0.890573i	0.994577	+	0.104004i	$0.0331655\pi$
$758$	389222.	−	361168.i	0.677422	−	0.628596i
$759$	−375962.			−0.652620
$760$	−16528.5	−	1860.72i	−0.0286159	−	0.00322147i
$761$			644070.i			1.11215i	0.831132	+	0.556075i	$0.187693\pi$
$761$			644070.i			1.11215i	−0.831132	+	0.556075i	$0.812307\pi$
$762$	−269841.	+	250392.i	−0.464728	+	0.431232i
$763$	20576.3	+	20576.3i	0.0353442	+	0.0353442i
$764$	−22001.7	+	293843.i	−0.0376938	+	0.503418i
$765$	−1943.29	−	1943.29i	−0.00332058	−	0.00332058i
$766$	−704801.	−	26349.4i	−1.20118	−	0.0449069i
$767$		−	163009.i		−	0.277091i
$768$	−301032.	+	159198.i	−0.510376	+	0.269907i
$769$	536649.			0.907481			0.453741	−	0.891134i	$-0.350089\pi$
$769$	536649.			0.907481			0.453741	+	0.891134i	$0.350089\pi$
$770$	339.877	−	9091.14i	0.000573245	−	0.0153333i
$771$	−312211.	+	312211.i	−0.525218	+	0.525218i
$772$	−64897.3	−	4859.23i	−0.108891	−	0.00815329i
$773$	418869.	−	418869.i	0.701001	−	0.701001i	−0.263624	−	0.964625i	$-0.584918\pi$
$773$	418869.	−	418869.i	0.701001	−	0.701001i	0.964625	+	0.263624i	$0.0849179\pi$
$774$	−63541.0	−	68476.5i	−0.106065	−	0.114304i
$775$	−827493.			−1.37772
$776$	−126853.	+	1.12681e6i	−0.210657	+	1.87124i
$777$		−	419382.i		−	0.694652i
$778$	−377505.	−	406827.i	−0.623682	−	0.672126i
$779$	120156.	+	120156.i	0.198002	+	0.198002i
$780$	−1181.34	+	1016.75i	−0.00194171	+	0.00167119i
$781$	−435805.	−	435805.i	−0.714479	−	0.714479i
$782$	−19558.0	+	523144.i	−0.0319824	+	0.855475i
$783$			3253.80i			0.00530722i
$784$	−194258.	−	29254.5i	−0.316044	−	0.0475949i
$785$	−11238.5			−0.0182377
$786$	−356970.	−	13345.5i	−0.577812	−	0.0216018i
$787$	588143.	−	588143.i	0.949585	−	0.949585i	−0.0492041	−	0.998789i	$-0.515668\pi$
$787$	588143.	−	588143.i	0.949585	−	0.949585i	0.998789	+	0.0492041i	$0.0156685\pi$
$788$	534708.	−	460212.i	0.861120	−	0.741149i
$789$	207813.	−	207813.i	0.333825	−	0.333825i
$790$	17150.5	−	15914.4i	0.0274804	−	0.0254997i
$791$	883681.			1.41235
$792$	102150.	+	128067.i	0.162850	+	0.204167i
$793$			126725.i			0.201518i
$794$	260337.	−	241573.i	0.412947	−	0.383183i
$795$	−7591.97	−	7591.97i	−0.0120121	−	0.0120121i
$796$	235870.	+	17660.9i	0.372260	+	0.0278732i
$797$	−166304.	−	166304.i	−0.261809	−	0.261809i	0.563980	−	0.825789i	$-0.309270\pi$
$797$	−166304.	−	166304.i	−0.261809	−	0.261809i	−0.825789	+	0.563980i	$0.809270\pi$
$798$	−367561.	−	13741.5i	−0.577197	−	0.0215788i
$799$		−	54415.2i		−	0.0852367i
$800$	−628507.	−	118816.i	−0.982042	−	0.185651i
$801$	315873.			0.492319
$802$	25604.9	−	684889.i	0.0398084	−	1.06481i
$803$	47660.8	−	47660.8i	0.0739147	−	0.0739147i
$804$	−29770.0	+	397592.i	−0.0460539	+	0.615072i
$805$	−12947.4	+	12947.4i	−0.0199799	+	0.0199799i
$806$	−113839.	−	122682.i	−0.175236	−	0.188847i
$807$	76789.6			0.117911
$808$	362108.	+	453980.i	0.554645	+	0.695367i
$809$		−	109516.i		−	0.167333i	−0.996494	−	0.0836666i	$-0.973337\pi$
$809$		−	109516.i		−	0.167333i	0.996494	−	0.0836666i	$-0.0266631\pi$
$810$	1177.32	+	1268.77i	0.00179442	+	0.00193381i
$811$	−400453.	−	400453.i	−0.608849	−	0.608849i	0.333796	−	0.942645i	$-0.391670\pi$
$811$	−400453.	−	400453.i	−0.608849	−	0.608849i	−0.942645	+	0.333796i	$0.891670\pi$
$812$	9783.90	+	11367.6i	0.0148388	+	0.0172408i
$813$	392601.	+	392601.i	0.593978	+	0.593978i
$814$	28289.4	−	756695.i	0.0426949	−	1.14202i
$815$		−	9128.29i		−	0.0137428i
$816$	183516.	−	135477.i	0.275609	−	0.203463i
$817$	378714.			0.567371
$818$	−742996.	−	27777.3i	−1.11040	−	0.0415129i
$819$	−24372.2	+	24372.2i	−0.0363351	+	0.0363351i
$820$	−2404.41	−	2793.62i	−0.00357587	−	0.00415470i
$821$	740450.	−	740450.i	1.09852	−	1.09852i	0.103941	−	0.994584i	$-0.466855\pi$
$821$	740450.	−	740450.i	1.09852	−	1.09852i	0.994584	−	0.103941i	$-0.0331452\pi$
$822$	309304.	−	287011.i	0.457765	−	0.424771i
$823$	−264830.			−0.390991			−0.195496	−	0.980705i	$-0.562632\pi$
$823$	−264830.			−0.390991			−0.195496	+	0.980705i	$0.562632\pi$
$824$	16107.4	−	143079.i	0.0237230	−	0.210728i
$825$			307701.i			0.452086i
$826$	−611647.	+	567562.i	−0.896481	+	0.831865i
$827$	−462984.	−	462984.i	−0.676947	−	0.676947i	0.282361	−	0.959308i	$-0.408882\pi$
$827$	−462984.	−	462984.i	−0.676947	−	0.676947i	−0.959308	+	0.282361i	$0.908882\pi$
$828$	24618.4	−	328791.i	0.0359087	−	0.479578i
$829$	598471.	+	598471.i	0.870831	+	0.870831i	0.992563	−	0.121732i	$-0.0388448\pi$
$829$	598471.	+	598471.i	0.870831	+	0.870831i	−0.121732	+	0.992563i	$0.538845\pi$
$830$	−29731.2	−	1111.51i	−0.0431574	−	0.00161346i
$831$		−	190434.i		−	0.275768i
$832$	−68849.2	−	109527.i	−0.0994609	−	0.158224i
$833$	131590.			0.189642
$834$	8249.99	−	220673.i	0.0118610	−	0.317262i
$835$	11563.2	−	11563.2i	0.0165846	−	0.0165846i
$836$	−662268.	−	49587.8i	−0.947591	−	0.0709515i
$837$	−131419.	+	131419.i	−0.187590	+	0.187590i
$838$	31099.9	+	33515.6i	0.0442865	+	0.0477265i
$839$	−1.11942e6			−1.59027			−0.795133	−	0.606435i	$-0.792599\pi$
$839$	−1.11942e6			−1.59027			−0.795133	+	0.606435i	$0.792599\pi$
$840$	7928.23	+	892.532i	0.0112362	+	0.00126493i
$841$		−	706743.i		−	0.999240i
$842$	422534.	+	455354.i	0.595988	+	0.642281i
$843$	145394.	+	145394.i	0.204594	+	0.204594i
$844$	866130.	−	745461.i	1.21590	−	1.04650i
$845$	11568.9	+	11568.9i	0.0162024	+	0.0162024i
$846$	−1280.35	+	34247.3i	−0.00178891	+	0.0478504i
$847$			228516.i			0.318529i
$848$	716955.	−	529278.i	0.997012	−	0.736024i
$849$	−792216.			−1.09908
$850$	428160.	+	16007.0i	0.592609	+	0.0221550i
$851$	−1.07767e6	+	1.07767e6i	−1.48808	+	1.48808i
$852$	409662.	−	352588.i	0.564347	−	0.485722i
$853$	542412.	−	542412.i	0.745471	−	0.745471i	−0.228154	−	0.973625i	$-0.573269\pi$
$853$	542412.	−	542412.i	0.745471	−	0.745471i	0.973625	+	0.228154i	$0.0732689\pi$
$854$	475499.	−	441226.i	0.651979	−	0.604987i
$855$	−7017.02			−0.00959887
$856$	−467432.	+	372838.i	−0.637927	+	0.508829i
$857$			482232.i			0.656590i	0.944575	+	0.328295i	$0.106474\pi$
$857$			482232.i			0.656590i	−0.944575	+	0.328295i	$0.893526\pi$
$858$	−45619.0	+	42330.9i	−0.0619685	+	0.0575020i
$859$	105103.	+	105103.i	0.142440	+	0.142440i	0.774731	−	0.632291i	$-0.217885\pi$
$859$	105103.	+	105103.i	0.142440	+	0.142440i	−0.632291	+	0.774731i	$0.717885\pi$
$860$	−8191.73	−	613.361i	−0.0110759	−	0.000829315i
$861$	−57635.1	−	57635.1i	−0.0777465	−	0.0777465i
$862$	−1.19444e6	−	44654.6i	−1.60749	−	0.0600969i
$863$			1.22454e6i			1.64419i	0.569348	+	0.822097i	$0.307196\pi$
$863$			1.22454e6i			1.64419i	−0.569348	+	0.822097i	$0.692804\pi$
$864$	−118687.	+	80947.2i	−0.158992	+	0.108436i
$865$	8247.23			0.0110224
$866$	12205.2	−	326470.i	0.0162746	−	0.435319i
$867$	198833.	−	198833.i	0.264515	−	0.264515i
$868$	−63966.4	+	854301.i	−0.0849009	+	1.13389i
$869$	660570.	−	660570.i	0.874741	−	0.874741i
$870$	194.623	+	209.740i	0.000257132	+	0.000277105i
$871$	−151467.			−0.199656
$872$	−36021.9	+	28732.1i	−0.0473733	+	0.0377864i
$873$			478378.i			0.627686i
$874$	909199.	+	979821.i	1.19024	+	1.28270i
$875$	21199.3	+	21199.3i	0.0276889	+	0.0276889i
$876$	38560.0	+	44801.8i	0.0502492	+	0.0583831i
$877$	−311290.	−	311290.i	−0.404731	−	0.404731i	0.475165	−	0.879896i	$-0.342388\pi$
$877$	−311290.	−	311290.i	−0.404731	−	0.404731i	−0.879896	+	0.475165i	$0.842388\pi$
$878$	23998.6	−	641921.i	0.0311312	−	0.832708i
$879$			203835.i			0.263815i
$880$	14244.8	+	2145.20i	0.0183946	+	0.00277015i
$881$	−434458.			−0.559753			−0.279876	−	0.960036i	$-0.590294\pi$
$881$	−434458.			−0.559753			−0.279876	+	0.960036i	$0.590294\pi$
$882$	−82818.9	−	3096.23i	−0.106461	−	0.00398012i
$883$	152798.	−	152798.i	0.195973	−	0.195973i	−0.602298	−	0.798271i	$-0.705748\pi$
$883$	152798.	−	152798.i	0.195973	−	0.195973i	0.798271	+	0.602298i	$0.205748\pi$
$884$	56529.5	+	65680.0i	0.0723387	+	0.0840482i
$885$	−11256.0	+	11256.0i	−0.0143713	+	0.0143713i
$886$	645031.	−	598539.i	0.821699	−	0.762474i
$887$	1704.48			0.00216643			0.00108321	−	0.999999i	$-0.499655\pi$
$887$	1704.48			0.00216643			0.00108321	+	0.999999i	$0.499655\pi$
$888$	659901.	+	74289.3i	0.836861	+	0.0942107i
$889$			715847.i			0.905768i
$890$	20361.2	−	18893.7i	0.0257054	−	0.0238526i
$891$	48868.0	+	48868.0i	0.0615559	+	0.0615559i
$892$	−71809.1	+	959044.i	−0.0902506	+	1.20534i
$893$	−98244.0	−	98244.0i	−0.123198	−	0.123198i
$894$	325311.	+	12161.9i	0.407027	+	0.0152169i
$895$			3873.20i			0.00483530i
$896$	−171250.	+	639684.i	−0.213312	+	0.796800i
$897$	125257.			0.155674
$898$	−52140.0	+	1.39466e6i	−0.0646574	+	1.72948i
$899$	−21725.0	+	21725.0i	−0.0268806	+	0.0268806i
$900$	−269095.	−	20148.6i	−0.332215	−	0.0248749i
$901$	−422098.	+	422098.i	−0.519953	+	0.519953i
$902$	−100104.	−	107879.i	−0.123038	−	0.132595i
$903$	−181658.			−0.222781
$904$	−156535.	+	1.39048e6i	−0.191547	+	1.70148i
$905$			31417.7i			0.0383598i
$906$	−269830.	−	290789.i	−0.328726	−	0.354260i
$907$	−784865.	−	784865.i	−0.954070	−	0.954070i	0.0449202	−	0.998991i	$-0.485697\pi$
$907$	−784865.	−	784865.i	−0.954070	−	0.954070i	−0.998991	+	0.0449202i	$0.985697\pi$
$908$	565950.	−	487102.i	0.686446	−	0.590810i
$909$	173231.	+	173231.i	0.209651	+	0.209651i
$910$	−113.235	+	3028.83i	−0.000136740	+	0.00365757i
$911$			1.55102e6i			1.86888i	0.356125	+	0.934438i	$0.384098\pi$
$911$			1.55102e6i			1.86888i	−0.356125	+	0.934438i	$0.615902\pi$
$912$	86732.1	−	575927.i	0.104277	−	0.692433i
$913$	−1.18794e6			−1.42512
$914$	822807.	+	30761.1i	0.984931	+	0.0368222i
$915$	8750.48	−	8750.48i	0.0104518	−	0.0104518i
$916$	810661.	−	697720.i	0.966159	−	0.831554i
$917$	−491195.	+	491195.i	−0.584137	+	0.584137i
$918$	70541.1	−	65456.7i	0.0837060	−	0.0776728i
$919$	400879.			0.474659			0.237330	−	0.971429i	$-0.423728\pi$
$919$	400879.			0.474659			0.237330	+	0.971429i	$0.423728\pi$
$920$	−18079.4	−	22666.4i	−0.0213604	−	0.0267798i
$921$			335671.i			0.395726i
$922$	458011.	−	424999.i	0.538783	−	0.499949i
$923$	145194.	+	145194.i	0.170430	+	0.170430i
$924$	317670.	+	23785.8i	0.372076	+	0.0278595i
$925$	882007.	+	882007.i	1.03083	+	1.03083i
$926$	−530418.	−	19830.0i	−0.618581	−	0.0231260i
$927$		−	60742.9i		−	0.0706864i
$928$	−19620.2	+	13381.4i	−0.0227828	+	0.0155384i
$929$	−689513.			−0.798934			−0.399467	−	0.916748i	$-0.630805\pi$
$929$	−689513.			−0.798934			−0.399467	+	0.916748i	$0.630805\pi$
$930$	−610.583	+	16332.1i	−0.000705958	+	0.0188832i
$931$	237580.	−	237580.i	0.274101	−	0.274101i
$932$	−29164.5	+	389506.i	−0.0335755	+	0.448417i
$933$	−195755.	+	195755.i	−0.224880	+	0.224880i
$934$	−151384.	−	163143.i	−0.173535	−	0.187014i
$935$	−9649.40			−0.0110377
$936$	−34032.5	−	42667.1i	−0.0388457	−	0.0487014i
$937$			401797.i			0.457643i	0.973468	+	0.228822i	$0.0734873\pi$
$937$			401797.i			0.457643i	−0.973468	+	0.228822i	$0.926513\pi$
$938$	527375.	+	568339.i	0.599396	+	0.645955i
$939$	−523582.	−	523582.i	−0.593818	−	0.593818i
$940$	1965.94	+	2284.17i	0.00222492	+	0.00258507i
$941$	−422620.	−	422620.i	−0.477277	−	0.477277i	0.426983	−	0.904260i	$-0.359577\pi$
$941$	−422620.	−	422620.i	−0.477277	−	0.477277i	−0.904260	+	0.426983i	$0.859577\pi$
$942$	14702.0	−	393255.i	0.0165682	−	0.443172i
$943$			296206.i			0.333097i
$944$	−784717.	−	1.06297e6i	−0.880580	−	1.19283i
$945$	3365.85			0.00376905
$946$	−327767.	−	12253.7i	−0.366254	−	0.0136926i
$947$	−156550.	+	156550.i	−0.174563	+	0.174563i	−0.788981	−	0.614418i	$-0.789391\pi$
$947$	−156550.	+	156550.i	−0.174563	+	0.174563i	0.614418	+	0.788981i	$0.289391\pi$
$948$	534435.	+	620945.i	0.594673	+	0.690933i
$949$	−15878.8	+	15878.8i	−0.0176314	+	0.0176314i
$950$	801922.	−	744122.i	0.888556	−	0.824512i
$951$	1.02716e6			1.13573
$952$	49623.0	−	440794.i	0.0547531	−	0.486364i
$953$		−	1.43959e6i		−	1.58508i	−0.609818	−	0.792541i	$-0.708758\pi$
$953$		−	1.43959e6i		−	1.58508i	0.609818	−	0.792541i	$-0.291242\pi$
$954$	275588.	−	255724.i	0.302805	−	0.280980i
$955$	7729.79	+	7729.79i	0.00847542	+	0.00847542i
$956$	65977.5	−	881160.i	0.0721905	−	0.964138i
$957$	8078.38	+	8078.38i	0.00882064	+	0.00882064i
$958$	190541.	+	7123.49i	0.207615	+	0.00776178i
$959$		−	820537.i		−	0.892198i
$960$	−2808.81	+	12317.1i	−0.00304776	+	0.0133649i
$961$	−831401.			−0.900252
$962$	−9425.00	+	252103.i	−0.0101843	+	0.272413i
$963$	−178364.	+	178364.i	−0.192333	+	0.192333i
$964$	345658.	+	25881.4i	0.371957	+	0.0278506i
$965$	−1707.18	+	1707.18i	−0.00183326	+	0.00183326i
$966$	−436116.	−	469991.i	−0.467355	−	0.503657i
$967$	1.25758e6			1.34488			0.672438	−	0.740153i	$-0.265247\pi$
$967$	1.25758e6			1.34488			0.672438	+	0.740153i	$0.265247\pi$
$968$	−359572.	−	40479.3i	−0.383738	−	0.0431998i
$969$			390132.i			0.415493i
$970$	28613.7	+	30836.3i	0.0304110	+	0.0327732i
$971$	−225668.	−	225668.i	−0.239349	−	0.239349i	0.577232	−	0.816580i	$-0.304133\pi$
$971$	−225668.	−	225668.i	−0.239349	−	0.239349i	−0.816580	+	0.577232i	$0.804133\pi$
$972$	−45936.6	+	39536.7i	−0.0486212	+	0.0418473i
$973$	−303649.	−	303649.i	−0.320735	−	0.320735i
$974$	2285.82	−	61141.8i	0.00240948	−	0.0644496i
$975$		−	102515.i		−	0.107839i
$976$	610044.	+	826361.i	0.640415	+	0.867501i
$977$	−884645.			−0.926787			−0.463393	−	0.886153i	$-0.653368\pi$
$977$	−884645.			−0.926787			−0.463393	+	0.886153i	$0.653368\pi$
$978$	319414.	+	11941.5i	0.333947	+	0.0124848i
$979$	784234.	−	784234.i	0.818239	−	0.818239i
$980$	−5523.72	+	4754.16i	−0.00575148	+	0.00495019i
$981$	−13745.3	+	13745.3i	−0.0142829	+	0.0142829i
$982$	−655124.	+	607905.i	−0.679361	+	0.630395i
$983$	97439.6			0.100839			0.0504195	−	0.998728i	$-0.483944\pi$
$983$	97439.6			0.100839			0.0504195	+	0.998728i	$0.483944\pi$
$984$	100899.	−	80479.9i	0.104207	−	0.0831184i
$985$		−	26172.2i		−	0.0269754i
$986$	11661.1	−	10820.7i	0.0119946	−	0.0111301i
$987$	47124.7	+	47124.7i	0.0483743	+	0.0483743i
$988$	220643.	+	16520.8i	0.226036	+	0.0169246i
$989$	466800.	+	466800.i	0.477241	+	0.477241i
$990$	6073.04	+	227.044i	0.00619635	+	0.000231654i
$991$		−	807885.i		−	0.822626i	−0.911494	−	0.411313i	$-0.865070\pi$
$991$		−	807885.i		−	0.822626i	0.911494	−	0.411313i	$-0.134930\pi$
$992$	−1.33292e6	−	251983.i	−1.35450	−	0.256063i
$993$	51031.9			0.0517539
$994$	39267.2	−	1.05033e6i	0.0397427	−	1.06305i
$995$	6204.76	−	6204.76i	0.00626727	−	0.00626727i
$996$	77787.6	−	1.03889e6i	0.0784136	−	1.04725i
$997$	781589.	−	781589.i	0.786299	−	0.786299i	−0.194586	−	0.980885i	$-0.562336\pi$
$997$	781589.	−	781589.i	0.786299	−	0.786299i	0.980885	+	0.194586i	$0.0623364\pi$
$998$	506783.	+	546148.i	0.508817	+	0.548339i
$999$	280154.			0.280716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.5.l.a.19.9	✓	32
3.2	odd	2		144.5.m.c.19.8		32
4.3	odd	2		192.5.l.a.175.10		32
8.3	odd	2		384.5.l.a.223.7		32
8.5	even	2		384.5.l.b.223.10		32
12.11	even	2		576.5.m.b.559.8		32
16.3	odd	4		384.5.l.b.31.10		32
16.5	even	4		192.5.l.a.79.10		32
16.11	odd	4	inner	48.5.l.a.43.9	yes	32
16.13	even	4		384.5.l.a.31.7		32
48.5	odd	4		576.5.m.b.271.8		32
48.11	even	4		144.5.m.c.91.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.5.l.a.19.9	✓	32	1.1	even	1	trivial
48.5.l.a.43.9	yes	32	16.11	odd	4	inner
144.5.m.c.19.8		32	3.2	odd	2
144.5.m.c.91.8		32	48.11	even	4
192.5.l.a.79.10		32	16.5	even	4
192.5.l.a.175.10		32	4.3	odd	2
384.5.l.a.31.7		32	16.13	even	4
384.5.l.a.223.7		32	8.3	odd	2
384.5.l.b.31.10		32	16.3	odd	4
384.5.l.b.223.10		32	8.5	even	2
576.5.m.b.271.8		32	48.5	odd	4
576.5.m.b.559.8		32	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.149438 + 3.99721i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(-15.9553 - 1.19467i) q^{4} +(-0.419719 + 0.419719i) q^{5} +(-14.1376 - 15.2357i) q^{6} -40.4181 q^{7} +(7.15966 - 63.5983i) q^{8} -27.0000i q^{9} +O(q^{10})\)	\(q+(-0.149438 + 3.99721i) q^{2} +(-3.67423 + 3.67423i) q^{3} +(-15.9553 - 1.19467i) q^{4} +(-0.419719 + 0.419719i) q^{5} +(-14.1376 - 15.2357i) q^{6} -40.4181 q^{7} +(7.15966 - 63.5983i) q^{8} -27.0000i q^{9} +(-1.61498 - 1.74043i) q^{10} +(-67.0343 - 67.0343i) q^{11} +(63.0131 - 54.2342i) q^{12} +(22.3334 + 22.3334i) q^{13} +(6.03999 - 161.560i) q^{14} -3.08429i q^{15} +(253.146 + 38.1226i) q^{16} -171.480 q^{17} +(107.925 + 4.03482i) q^{18} +(-309.599 + 309.599i) q^{19} +(7.19818 - 6.19533i) q^{20} +(148.506 - 148.506i) q^{21} +(277.968 - 257.933i) q^{22} -763.220 q^{23} +(207.369 + 259.981i) q^{24} +624.648i q^{25} +(-92.6086 + 85.9337i) q^{26} +(99.2043 + 99.2043i) q^{27} +(644.884 + 48.2862i) q^{28} +(16.3995 + 16.3995i) q^{29} +(12.3286 + 0.460909i) q^{30} +1324.73i q^{31} +(-190.214 + 1006.18i) q^{32} +492.600 q^{33} +(25.6256 - 685.443i) q^{34} +(16.9642 - 16.9642i) q^{35} +(-32.2560 + 430.794i) q^{36} +(1412.01 - 1412.01i) q^{37} +(-1191.27 - 1283.80i) q^{38} -164.116 q^{39} +(23.6883 + 29.6984i) q^{40} -388.101i q^{41} +(571.415 + 615.800i) q^{42} +(-611.619 - 611.619i) q^{43} +(989.472 + 1149.64i) q^{44} +(11.3324 + 11.3324i) q^{45} +(114.054 - 3050.75i) q^{46} +317.326i q^{47} +(-1070.19 + 790.045i) q^{48} -767.378 q^{49} +(-2496.85 - 93.3459i) q^{50} +(630.059 - 630.059i) q^{51} +(-329.656 - 383.018i) q^{52} +(2461.50 - 2461.50i) q^{53} +(-411.365 + 381.715i) q^{54} +56.2712 q^{55} +(-289.380 + 2570.52i) q^{56} -2275.08i q^{57} +(-68.0028 + 63.1014i) q^{58} +(-3649.46 - 3649.46i) q^{59} +(-3.68470 + 49.2109i) q^{60} +(2837.11 + 2837.11i) q^{61} +(-5295.24 - 197.965i) q^{62} +1091.29i q^{63} +(-3993.48 - 910.684i) q^{64} -18.7475 q^{65} +(-73.6130 + 1969.02i) q^{66} +(-3391.06 + 3391.06i) q^{67} +(2736.03 + 204.862i) q^{68} +(2804.25 - 2804.25i) q^{69} +(65.2745 + 70.3447i) q^{70} +6501.21 q^{71} +(-1717.15 - 193.311i) q^{72} +710.991i q^{73} +(5433.08 + 5855.09i) q^{74} +(-2295.10 - 2295.10i) q^{75} +(5309.63 - 4569.90i) q^{76} +(2709.40 + 2709.40i) q^{77} +(24.5251 - 656.006i) q^{78} +9854.21i q^{79} +(-122.251 + 90.2492i) q^{80} -729.000 q^{81} +(1551.32 + 57.9969i) q^{82} +(8860.67 - 8860.67i) q^{83} +(-2546.87 + 2192.04i) q^{84} +(71.9736 - 71.9736i) q^{85} +(2536.17 - 2353.37i) q^{86} -120.511 q^{87} +(-4743.21 + 3783.32i) q^{88} +11699.0i q^{89} +(-46.9915 + 43.6045i) q^{90} +(-902.673 - 902.673i) q^{91} +(12177.4 + 911.794i) q^{92} +(-4867.39 - 4867.39i) q^{93} +(-1268.42 - 47.4205i) q^{94} -259.889i q^{95} +(-2998.05 - 4395.82i) q^{96} -17717.7 q^{97} +(114.675 - 3067.37i) q^{98} +(-1809.93 + 1809.93i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} + 180 q^{8}+O(q^{10}) \) 32 * q + 12 * q^4 + 180 * q^8	\( 32 q + 12 q^{4} + 180 q^{8} + 296 q^{10} - 192 q^{11} + 360 q^{12} - 156 q^{14} + 352 q^{16} - 324 q^{18} + 704 q^{19} - 1200 q^{20} - 1568 q^{22} - 2304 q^{23} + 1188 q^{24} + 2700 q^{26} + 4680 q^{28} - 1728 q^{29} + 1512 q^{30} - 3360 q^{32} - 9312 q^{34} - 5184 q^{35} - 756 q^{36} + 3648 q^{37} - 5880 q^{38} + 5232 q^{40} + 4500 q^{42} + 1088 q^{43} + 18840 q^{44} + 680 q^{46} + 2160 q^{48} + 10976 q^{49} - 25884 q^{50} - 4032 q^{51} - 25584 q^{52} + 960 q^{53} + 972 q^{54} + 11776 q^{55} + 15456 q^{56} + 12624 q^{58} + 13056 q^{59} + 7992 q^{60} + 3776 q^{61} + 21852 q^{62} - 8664 q^{64} + 4032 q^{65} - 8856 q^{66} - 896 q^{67} - 17280 q^{68} - 9792 q^{69} - 18240 q^{70} - 39936 q^{71} + 4860 q^{72} + 24204 q^{74} - 1152 q^{75} + 16776 q^{76} + 9408 q^{77} - 3780 q^{78} - 14232 q^{80} - 23328 q^{81} - 33800 q^{82} + 24000 q^{83} - 11448 q^{84} - 11200 q^{85} - 1200 q^{86} - 11424 q^{88} + 4104 q^{90} + 30528 q^{91} - 11664 q^{92} - 8040 q^{94} + 10080 q^{96} + 52968 q^{98} - 5184 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 + 180 * q^8 + 296 * q^10 - 192 * q^11 + 360 * q^12 - 156 * q^14 + 352 * q^16 - 324 * q^18 + 704 * q^19 - 1200 * q^20 - 1568 * q^22 - 2304 * q^23 + 1188 * q^24 + 2700 * q^26 + 4680 * q^28 - 1728 * q^29 + 1512 * q^30 - 3360 * q^32 - 9312 * q^34 - 5184 * q^35 - 756 * q^36 + 3648 * q^37 - 5880 * q^38 + 5232 * q^40 + 4500 * q^42 + 1088 * q^43 + 18840 * q^44 + 680 * q^46 + 2160 * q^48 + 10976 * q^49 - 25884 * q^50 - 4032 * q^51 - 25584 * q^52 + 960 * q^53 + 972 * q^54 + 11776 * q^55 + 15456 * q^56 + 12624 * q^58 + 13056 * q^59 + 7992 * q^60 + 3776 * q^61 + 21852 * q^62 - 8664 * q^64 + 4032 * q^65 - 8856 * q^66 - 896 * q^67 - 17280 * q^68 - 9792 * q^69 - 18240 * q^70 - 39936 * q^71 + 4860 * q^72 + 24204 * q^74 - 1152 * q^75 + 16776 * q^76 + 9408 * q^77 - 3780 * q^78 - 14232 * q^80 - 23328 * q^81 - 33800 * q^82 + 24000 * q^83 - 11448 * q^84 - 11200 * q^85 - 1200 * q^86 - 11424 * q^88 + 4104 * q^90 + 30528 * q^91 - 11664 * q^92 - 8040 * q^94 + 10080 * q^96 + 52968 * q^98 - 5184 * q^99

Introduction

L-functions

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