LMFDB - Embedded newform 120.4.w.c.77.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [120,4,Mod(53,120)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [128,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			77.18
Character	$\chi$	$=$	120.77
Dual form			120.4.w.c.53.18

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.74392 + 2.22682i) q^{2} +(-4.46520 + 2.65743i) q^{3} +(-1.91749 - 7.76680i) q^{4} +(-10.9958 - 2.02288i) q^{5} +(1.86933 - 14.5776i) q^{6} +(-3.45928 - 3.45928i) q^{7} +(20.6392 + 9.27479i) q^{8} +(12.8761 - 23.7320i) q^{9} +(23.6804 - 20.9580i) q^{10} -18.5170 q^{11} +(29.2017 + 29.5848i) q^{12} +(36.1308 + 36.1308i) q^{13} +(13.7359 - 1.67050i) q^{14} +(54.4742 - 20.1881i) q^{15} +(-56.6465 + 29.7855i) q^{16} +(38.1039 - 38.1039i) q^{17} +(30.3920 + 70.0595i) q^{18} -31.0847 q^{19} +(5.37302 + 89.2812i) q^{20} +(24.6392 + 6.25360i) q^{21} +(32.2922 - 41.2341i) q^{22} +(65.5468 + 65.5468i) q^{23} +(-116.806 + 13.4336i) q^{24} +(116.816 + 44.4864i) q^{25} +(-143.466 + 17.4477i) q^{26} +(5.57160 + 140.185i) q^{27} +(-20.2345 + 33.5007i) q^{28} -80.5549i q^{29} +(-50.0434 + 156.511i) q^{30} +224.617 q^{31} +(32.4600 - 178.085i) q^{32} +(82.6822 - 49.2077i) q^{33} +(18.4005 + 151.301i) q^{34} +(31.0399 + 45.0354i) q^{35} +(-209.011 - 54.5005i) q^{36} +(229.948 - 229.948i) q^{37} +(54.2092 - 69.2201i) q^{38} +(-257.346 - 65.3162i) q^{39} +(-208.184 - 143.734i) q^{40} -458.179i q^{41} +(-56.8945 + 43.9614i) q^{42} +(49.4266 + 49.4266i) q^{43} +(35.5061 + 143.818i) q^{44} +(-189.590 + 234.905i) q^{45} +(-260.270 + 31.6528i) q^{46} +(-270.817 + 270.817i) q^{47} +(173.785 - 283.532i) q^{48} -319.067i q^{49} +(-302.781 + 182.548i) q^{50} +(-68.8831 + 271.400i) q^{51} +(211.340 - 349.901i) q^{52} +(209.692 - 209.692i) q^{53} +(-321.885 - 232.065i) q^{54} +(203.609 + 37.4576i) q^{55} +(-39.3129 - 103.481i) q^{56} +(138.799 - 82.6054i) q^{57} +(179.382 + 140.481i) q^{58} -631.752i q^{59} +(-261.250 - 384.380i) q^{60} +476.481i q^{61} +(-391.714 + 500.182i) q^{62} +(-126.638 + 37.5535i) q^{63} +(339.957 + 382.849i) q^{64} +(-324.199 - 470.375i) q^{65} +(-34.6144 + 269.933i) q^{66} +(503.686 - 503.686i) q^{67} +(-369.009 - 222.882i) q^{68} +(-466.866 - 118.494i) q^{69} +(-154.417 - 9.41759i) q^{70} +954.546i q^{71} +(485.862 - 370.386i) q^{72} +(-436.711 + 436.711i) q^{73} +(111.042 + 913.063i) q^{74} +(-639.827 + 111.790i) q^{75} +(59.6044 + 241.429i) q^{76} +(64.0556 + 64.0556i) q^{77} +(594.239 - 459.159i) q^{78} -87.4699i q^{79} +(683.127 - 212.927i) q^{80} +(-397.412 - 611.151i) q^{81} +(1020.28 + 799.028i) q^{82} +(92.3665 - 92.3665i) q^{83} +(1.32513 - 203.359i) q^{84} +(-496.063 + 341.904i) q^{85} +(-196.260 + 23.8683i) q^{86} +(214.069 + 359.694i) q^{87} +(-382.177 - 171.741i) q^{88} +1255.51 q^{89} +(-192.463 - 831.840i) q^{90} -249.973i q^{91} +(383.404 - 634.775i) q^{92} +(-1002.96 + 596.904i) q^{93} +(-130.778 - 1075.34i) q^{94} +(341.801 + 62.8805i) q^{95} +(328.309 + 881.447i) q^{96} +(-102.475 - 102.475i) q^{97} +(710.505 + 556.427i) q^{98} +(-238.427 + 439.445i) 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 $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$ .

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

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

)

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

$2$	−1.74392	+	2.22682i	−0.616569	+	0.787301i
$2$	−1.74392	+	2.22682i	−0.616569	+	0.787301i
$3$	−4.46520	+	2.65743i	−0.859329	+	0.511423i
$3$	−4.46520	+	2.65743i	−0.859329	+	0.511423i
$4$	−1.91749	−	7.76680i	−0.239686	−	0.970851i
$5$	−10.9958	−	2.02288i	−0.983496	−	0.180932i
$5$	−10.9958	−	2.02288i	−0.983496	−	0.180932i
$6$	1.86933	−	14.5776i	0.127192	−	0.991878i
$7$	−3.45928	−	3.45928i	−0.186784	−	0.186784i	0.607520	−	0.794304i	$-0.292164\pi$
$7$	−3.45928	−	3.45928i	−0.186784	−	0.186784i	−0.794304	+	0.607520i	$0.792164\pi$
$8$	20.6392	+	9.27479i	0.912134	+	0.409891i
$9$	12.8761	−	23.7320i	0.476893	−	0.878961i
$10$	23.6804	−	20.9580i	0.748840	−	0.662750i
$11$	−18.5170			−0.507553			−0.253777	−	0.967263i	$-0.581673\pi$
$11$	−18.5170			−0.507553			−0.253777	+	0.967263i	$0.581673\pi$
$12$	29.2017	+	29.5848i	0.702484	+	0.711699i
$13$	36.1308	+	36.1308i	0.770836	+	0.770836i	0.978253	−	0.207416i	$-0.0665055\pi$
$13$	36.1308	+	36.1308i	0.770836	+	0.770836i	−0.207416	+	0.978253i	$0.566506\pi$
$14$	13.7359	−	1.67050i	0.262220	−	0.0318900i
$15$	54.4742	−	20.1881i	0.937679	−	0.347503i
$16$	−56.6465	+	29.7855i	−0.885102	+	0.465398i
$17$	38.1039	−	38.1039i	0.543620	−	0.543620i	−0.380968	−	0.924588i	$-0.624409\pi$
$17$	38.1039	−	38.1039i	0.543620	−	0.543620i	0.924588	+	0.380968i	$0.124409\pi$
$18$	30.3920	+	70.0595i	0.397970	+	0.917399i
$19$	−31.0847			−0.375332			−0.187666	−	0.982233i	$-0.560092\pi$
$19$	−31.0847			−0.375332			−0.187666	+	0.982233i	$0.560092\pi$
$20$	5.37302	+	89.2812i	0.0600722	+	0.998194i
$21$	24.6392	+	6.25360i	0.256034	+	0.0649832i
$22$	32.2922	−	41.2341i	0.312941	−	0.399597i
$23$	65.5468	+	65.5468i	0.594237	+	0.594237i	0.938773	−	0.344536i	$-0.111964\pi$
$23$	65.5468	+	65.5468i	0.594237	+	0.594237i	−0.344536	+	0.938773i	$0.611964\pi$
$24$	−116.806	+	13.4336i	−0.993451	+	0.114255i
$25$	116.816	+	44.4864i	0.934527	+	0.355891i
$26$	−143.466	+	17.4477i	−1.08215	+	0.131607i
$27$	5.57160	+	140.185i	0.0397131	+	0.999211i
$28$	−20.2345	+	33.5007i	−0.136570	+	0.226109i
$29$		−	80.5549i		−	0.515816i	−0.966169	−	0.257908i	$-0.916967\pi$
$29$		−	80.5549i		−	0.515816i	0.966169	−	0.257908i	$-0.0830332\pi$
$30$	−50.0434	+	156.511i	−0.304555	+	0.952495i
$31$	224.617			1.30137			0.650683	−	0.759350i	$-0.274483\pi$
$31$	224.617			1.30137			0.650683	+	0.759350i	$0.274483\pi$
$32$	32.4600	−	178.085i	0.179318	−	0.983791i
$33$	82.6822	−	49.2077i	0.436155	−	0.259574i
$34$	18.4005	+	151.301i	0.0928134	+	0.763172i
$35$	31.0399	+	45.0354i	0.149906	+	0.217496i
$36$	−209.011	−	54.5005i	−0.967645	−	0.252317i
$37$	229.948	−	229.948i	1.02171	−	1.02171i	0.0219474	−	0.999759i	$-0.493013\pi$
$37$	229.948	−	229.948i	1.02171	−	1.02171i	0.999759	−	0.0219474i	$-0.00698663\pi$
$38$	54.2092	−	69.2201i	0.231418	−	0.295500i
$39$	−257.346	−	65.3162i	−1.05663	−	0.268179i
$40$	−208.184	−	143.734i	−0.822918	−	0.568160i
$41$		−	458.179i		−	1.74526i	−0.488384	−	0.872629i	$-0.662413\pi$
$41$		−	458.179i		−	1.74526i	0.488384	−	0.872629i	$-0.337587\pi$
$42$	−56.8945	+	43.9614i	−0.209024	+	0.161509i
$43$	49.4266	+	49.4266i	0.175290	+	0.175290i	0.789299	−	0.614009i	$-0.210444\pi$
$43$	49.4266	+	49.4266i	0.175290	+	0.175290i	−0.614009	+	0.789299i	$0.710444\pi$
$44$	35.5061	+	143.818i	0.121653	+	0.492758i
$45$	−189.590	+	234.905i	−0.628054	+	0.778170i
$46$	−260.270	+	31.6528i	−0.834232	+	0.101455i
$47$	−270.817	+	270.817i	−0.840482	+	0.840482i	−0.988921	−	0.148440i	$-0.952575\pi$
$47$	−270.817	+	270.817i	−0.840482	+	0.840482i	0.148440	+	0.988921i	$0.452575\pi$
$48$	173.785	−	283.532i	0.522578	−	0.852591i
$49$		−	319.067i		−	0.930224i
$50$	−302.781	+	182.548i	−0.856394	+	0.516323i
$51$	−68.8831	+	271.400i	−0.189129	+	0.745169i
$52$	211.340	−	349.901i	0.563608	−	0.933125i
$53$	209.692	−	209.692i	0.543460	−	0.543460i	−0.381081	−	0.924542i	$-0.624448\pi$
$53$	209.692	−	209.692i	0.543460	−	0.543460i	0.924542	+	0.381081i	$0.124448\pi$
$54$	−321.885	−	232.065i	−0.811166	−	0.584816i
$55$	203.609	+	37.4576i	0.499176	+	0.0918324i
$56$	−39.3129	−	103.481i	−0.0938108	−	0.246933i
$57$	138.799	−	82.6054i	0.322534	−	0.191954i
$58$	179.382	+	140.481i	0.406103	+	0.318036i
$59$		−	631.752i		−	1.39402i	−0.717062	−	0.697010i	$-0.754514\pi$
$59$		−	631.752i		−	1.39402i	0.717062	−	0.697010i	$-0.245486\pi$
$60$	−261.250	−	384.380i	−0.562121	−	0.827055i
$61$			476.481i			1.00012i	0.865992	+	0.500059i	$0.166688\pi$
$61$			476.481i			1.00012i	−0.865992	+	0.500059i	$0.833312\pi$
$62$	−391.714	+	500.182i	−0.802382	+	1.02457i
$63$	−126.638	+	37.5535i	−0.253252	+	0.0750999i
$64$	339.957	+	382.849i	0.663978	+	0.747752i
$65$	−324.199	−	470.375i	−0.618646	−	0.897583i
$66$	−34.6144	+	269.933i	−0.0645565	+	0.503431i
$67$	503.686	−	503.686i	0.918433	−	0.918433i	−0.0784827	−	0.996915i	$-0.525008\pi$
$67$	503.686	−	503.686i	0.918433	−	0.918433i	0.996915	+	0.0784827i	$0.0250075\pi$
$68$	−369.009	−	222.882i	−0.658072	−	0.397476i
$69$	−466.866	−	118.494i	−0.814552	−	0.206739i
$70$	−154.417	−	9.41759i	−0.263662	−	0.0160803i
$71$			954.546i			1.59555i	0.602958	+	0.797773i	$0.293989\pi$
$71$			954.546i			1.59555i	−0.602958	+	0.797773i	$0.706011\pi$
$72$	485.862	−	370.386i	0.795269	−	0.606256i
$73$	−436.711	+	436.711i	−0.700179	+	0.700179i	−0.964449	−	0.264269i	$-0.914869\pi$
$73$	−436.711	+	436.711i	−0.700179	+	0.700179i	0.264269	+	0.964449i	$0.414869\pi$
$74$	111.042	+	913.063i	0.174438	+	1.43434i
$75$	−639.827	+	111.790i	−0.985077	+	0.172111i
$76$	59.6044	+	241.429i	0.0899618	+	0.364392i
$77$	64.0556	+	64.0556i	0.0948027	+	0.0948027i
$78$	594.239	−	459.159i	0.862620	−	0.666532i
$79$		−	87.4699i		−	0.124571i	−0.998058	−	0.0622856i	$-0.980161\pi$
$79$		−	87.4699i		−	0.124571i	0.998058	−	0.0622856i	$-0.0198390\pi$
$80$	683.127	−	212.927i	0.954699	−	0.297574i
$81$	−397.412	−	611.151i	−0.545146	−	0.838341i
$82$	1020.28	+	799.028i	1.37404	+	1.07607i
$83$	92.3665	−	92.3665i	0.122151	−	0.122151i	−0.643389	−	0.765540i	$-0.722472\pi$
$83$	92.3665	−	92.3665i	0.122151	−	0.122151i	0.765540	+	0.643389i	$0.222472\pi$
$84$	1.32513	−	203.359i	0.00172124	−	0.264147i
$85$	−496.063	+	341.904i	−0.633006	+	0.436290i
$86$	−196.260	+	23.8683i	−0.246085	+	0.0299277i
$87$	214.069	+	359.694i	0.263800	+	0.443256i
$88$	−382.177	−	171.741i	−0.462957	−	0.208042i
$89$	1255.51			1.49533			0.747664	−	0.664077i	$-0.231175\pi$
$89$	1255.51			1.49533			0.747664	+	0.664077i	$0.231175\pi$
$90$	−192.463	−	831.840i	−0.225415	−	0.974263i
$91$		−	249.973i		−	0.287959i
$92$	383.404	−	634.775i	0.434486	−	0.719346i
$93$	−1002.96	+	596.904i	−1.11830	+	0.665549i
$94$	−130.778	−	1075.34i	−0.143497	−	1.17993i
$95$	341.801	+	62.8805i	0.369138	+	0.0679095i
$96$	328.309	+	881.447i	0.349040	+	0.937108i
$97$	−102.475	−	102.475i	−0.107266	−	0.107266i	0.651437	−	0.758703i	$-0.274167\pi$
$97$	−102.475	−	102.475i	−0.107266	−	0.107266i	−0.758703	+	0.651437i	$0.774167\pi$
$98$	710.505	+	556.427i	0.732366	+	0.573547i
$99$	−238.427	+	439.445i	−0.242049	+	0.446120i
$100$	121.524	−	992.588i	0.121524	−	0.992588i
$101$	1142.93			1.12599			0.562997	−	0.826459i	$-0.309648\pi$
$101$	1142.93			1.12599			0.562997	+	0.826459i	$0.309648\pi$
$102$	−484.233	−	626.690i	−0.470061	−	0.608349i
$103$	−874.856	+	874.856i	−0.836914	+	0.836914i	−0.988452	−	0.151537i	$-0.951578\pi$
$103$	−874.856	+	874.856i	−0.836914	+	0.836914i	0.151537	+	0.988452i	$0.451578\pi$
$104$	410.607	+	1080.82i	0.387147	+	1.01907i
$105$	−258.278	−	118.606i	−0.240051	−	0.110235i
$106$	101.261	+	832.633i	0.0927861	+	0.762948i
$107$	−191.735	−	191.735i	−0.173231	−	0.173231i	0.615166	−	0.788397i	$-0.289089\pi$
$107$	−191.735	−	191.735i	−0.173231	−	0.173231i	−0.788397	+	0.615166i	$0.789089\pi$
$108$	1078.11	−	312.077i	0.960566	−	0.278052i
$109$	906.599			0.796665			0.398332	−	0.917241i	$-0.369589\pi$
$109$	906.599			0.796665			0.398332	+	0.917241i	$0.369589\pi$
$110$	−438.490	+	388.079i	−0.380076	+	0.336381i
$111$	−415.693	+	1637.83i	−0.355458	+	1.40051i
$112$	298.993	+	92.9200i	0.252251	+	0.0783938i
$113$	765.764	+	765.764i	0.637496	+	0.637496i	0.949937	−	0.312441i	$-0.101147\pi$
$113$	765.764	+	765.764i	0.637496	+	0.637496i	−0.312441	+	0.949937i	$0.601147\pi$
$114$	−58.1075	+	453.139i	−0.0477392	+	0.372284i
$115$	−588.148	−	853.334i	−0.476914	−	0.691946i
$116$	−625.654	+	154.463i	−0.500781	+	0.123634i
$117$	1322.68	−	392.230i	1.04514	−	0.309929i
$118$	1406.80	+	1101.73i	1.09751	+	0.859509i
$119$	−263.624			−0.203079
$120$	1311.55	+	88.5703i	0.997728	+	0.0673777i
$121$	−988.121			−0.742390
$122$	−1061.04	−	830.945i	−0.787393	−	0.616641i
$123$	1217.58	+	2045.86i	0.892565	+	1.49975i
$124$	−430.699	−	1744.55i	−0.311919	−	1.26343i
$125$	−1194.50	−	725.468i	−0.854712	−	0.519103i
$126$	137.221	−	347.490i	0.0970209	−	0.245689i
$127$	−565.279	−	565.279i	−0.394964	−	0.394964i	0.481488	−	0.876452i	$-0.340096\pi$
$127$	−565.279	−	565.279i	−0.394964	−	0.394964i	−0.876452	+	0.481488i	$0.840096\pi$
$128$	−1445.39	+	89.3653i	−0.998094	+	0.0617098i
$129$	−352.047	−	89.3520i	−0.240279	−	0.0609845i
$130$	1612.82	+	98.3628i	1.08811	+	0.0663615i
$131$	2195.99			1.46461			0.732307	−	0.680974i	$-0.238443\pi$
$131$	2195.99			1.46461			0.732307	+	0.680974i	$0.238443\pi$
$132$	−540.728	−	547.821i	−0.356548	−	0.361225i
$133$	107.531	+	107.531i	0.0701060	+	0.0701060i
$134$	243.231	+	2000.01i	0.156806	+	1.28936i
$135$	222.314	−	1552.72i	0.141731	−	0.989905i
$136$	1139.84	−	433.030i	0.718680	−	0.273029i
$137$	−442.876	+	442.876i	−0.276186	+	0.276186i	−0.831584	−	0.555399i	$-0.812566\pi$
$137$	−442.876	+	442.876i	−0.276186	+	0.276186i	0.555399	+	0.831584i	$0.312566\pi$
$138$	1078.04	−	832.985i	0.664993	−	0.513829i
$139$	−2914.23			−1.77829			−0.889144	−	0.457628i	$-0.848699\pi$
$139$	−2914.23			−1.77829			−0.889144	+	0.457628i	$0.848699\pi$
$140$	290.262	−	327.436i	0.175226	−	0.197667i
$141$	489.575	−	1928.93i	0.292409	−	1.15209i
$142$	−2125.61	−	1664.65i	−1.25618	−	0.983764i
$143$	−669.033	−	669.033i	−0.391240	−	0.391240i
$144$	−22.5191	+	1727.85i	−0.0130319	+	0.999915i
$145$	−162.953	+	885.767i	−0.0933275	+	0.507303i
$146$	−210.889	−	1734.07i	−0.119543	−	0.982961i
$147$	847.898	+	1424.70i	0.475738	+	0.799368i
$148$	−2226.88	−	1345.04i	−1.23681	−	0.747036i
$149$		−	2791.54i		−	1.53484i	−0.641142	−	0.767422i	$-0.721539\pi$
$149$		−	2791.54i		−	1.53484i	0.641142	−	0.767422i	$-0.278461\pi$
$150$	866.871	−	1619.73i	0.471865	−	0.881671i
$151$	1375.07			0.741070			0.370535	−	0.928819i	$-0.379174\pi$
$151$	1375.07			0.741070			0.370535	+	0.928819i	$0.379174\pi$
$152$	−641.564	−	288.304i	−0.342354	−	0.153846i
$153$	−413.650	−	1394.91i	−0.218573	−	0.737070i
$154$	−254.348	+	30.9326i	−0.133091	+	0.0161859i
$155$	−2469.84	−	454.372i	−1.27989	−	0.235458i
$156$	−13.8405	+	2124.00i	−0.00710336	+	1.09010i
$157$	213.276	−	213.276i	0.108416	−	0.108416i	−0.650818	−	0.759234i	$-0.725574\pi$
$157$	213.276	−	213.276i	0.108416	−	0.108416i	0.759234	+	0.650818i	$0.225574\pi$
$158$	194.780	+	152.540i	0.0980751	+	0.0768068i
$159$	−379.075	+	1493.56i	−0.189073	+	0.744949i
$160$	−717.169	+	1892.53i	−0.354357	+	0.935110i
$161$		−	453.490i		−	0.221988i
$162$	2053.98	+	180.832i	0.996147	+	0.0877008i
$163$	123.966	+	123.966i	0.0595693	+	0.0595693i	0.736264	−	0.676695i	$-0.236588\pi$
$163$	123.966	+	123.966i	0.0595693	+	0.0595693i	−0.676695	+	0.736264i	$0.736588\pi$
$164$	−3558.59	+	878.552i	−1.69438	+	0.418313i
$165$	−1008.70	+	373.822i	−0.475922	+	0.176376i
$166$	44.6041	+	366.764i	0.0208551	+	0.171484i
$167$	1063.96	−	1063.96i	0.493006	−	0.493006i	−0.416246	−	0.909252i	$-0.636655\pi$
$167$	1063.96	−	1063.96i	0.493006	−	0.493006i	0.909252	+	0.416246i	$0.136655\pi$
$168$	450.534	+	357.593i	0.206902	+	0.164220i
$169$			413.865i			0.188377i
$170$	103.734	−	1700.90i	0.0468004	−	0.767369i
$171$	−400.250	+	737.700i	−0.178993	+	0.329903i
$172$	289.112	−	478.661i	0.128166	−	0.212195i
$173$	−1464.65	+	1464.65i	−0.643673	+	0.643673i	−0.951457	−	0.307783i	$-0.900413\pi$
$173$	−1464.65	+	1464.65i	−0.643673	+	0.643673i	0.307783	+	0.951457i	$0.400413\pi$
$174$	−1174.30	−	150.584i	−0.511627	−	0.0656075i
$175$	−250.209	−	557.991i	−0.108080	−	0.241029i
$176$	1048.92	−	551.537i	0.449236	−	0.236214i
$177$	1678.84	+	2820.90i	0.712933	+	1.19792i
$178$	−2189.52	+	2795.81i	−0.921973	+	1.17727i
$179$		−	2183.04i		−	0.911556i	−0.890094	−	0.455778i	$-0.849361\pi$
$179$		−	2183.04i		−	0.911556i	0.890094	−	0.455778i	$-0.150639\pi$
$180$	2188.00	+	1022.08i	0.906022	+	0.423231i
$181$			3786.44i			1.55494i	0.628921	+	0.777469i	$0.283497\pi$
$181$			3786.44i			1.55494i	−0.628921	+	0.777469i	$0.716503\pi$
$182$	556.646	+	435.933i	0.226711	+	0.177547i
$183$	−1266.22	−	2127.59i	−0.511483	−	0.859430i
$184$	744.904	+	1960.77i	0.298451	+	0.785597i
$185$	−2993.62	+	2063.31i	−1.18970	+	0.819985i
$186$	419.882	−	3274.37i	0.165523	−	1.29080i
$187$	−705.569	+	705.569i	−0.275916	+	0.275916i
$188$	2622.67	+	1584.09i	1.01743	+	0.614531i
$189$	465.668	−	504.215i	0.179219	−	0.194054i
$190$	−736.098	+	651.473i	−0.281064	+	0.248752i
$191$		−	3559.53i		−	1.34848i	−0.738514	−	0.674238i	$-0.764472\pi$
$191$		−	3559.53i		−	1.34848i	0.738514	−	0.674238i	$-0.235528\pi$
$192$	−2535.37	−	806.088i	−0.952993	−	0.302992i
$193$	2856.85	−	2856.85i	1.06550	−	1.06550i	0.0677977	−	0.997699i	$-0.478403\pi$
$193$	2856.85	−	2856.85i	1.06550	−	1.06550i	0.997699	−	0.0677977i	$-0.0215973\pi$
$194$	406.904	−	49.4857i	0.150588	−	0.0183138i
$195$	2697.61	+	1238.79i	0.990665	+	0.454930i
$196$	−2478.13	+	611.806i	−0.903108	+	0.222961i
$197$	774.373	+	774.373i	0.280060	+	0.280060i	0.833133	−	0.553073i	$-0.186545\pi$
$197$	774.373	+	774.373i	0.280060	+	0.280060i	−0.553073	+	0.833133i	$0.686545\pi$
$198$	−562.768	−	1297.29i	−0.201991	−	0.465629i
$199$		−	416.947i		−	0.148526i	−0.997239	−	0.0742628i	$-0.976340\pi$
$199$		−	416.947i		−	0.148526i	0.997239	−	0.0742628i	$-0.0236604\pi$
$200$	1998.39	+	2001.61i	0.706538	+	0.707675i
$201$	−910.549	+	3587.57i	−0.319528	+	1.25894i
$202$	−1993.17	+	2545.10i	−0.694253	+	0.886497i
$203$	−278.662	+	278.662i	−0.0963461	+	0.0963461i
$204$	2239.99	+	14.5963i	0.768779	+	0.00500954i
$205$	−926.841	+	5038.06i	−0.315772	+	1.71645i
$206$	−422.471	−	3473.83i	−0.142888	−	1.17492i
$207$	2399.54	−	711.567i	0.805699	−	0.238924i
$208$	−3122.85	−	970.510i	−1.04101	−	0.323523i
$209$	575.595			0.190501
$210$	714.530	−	368.301i	0.234796	−	0.121025i
$211$		−	5816.14i		−	1.89763i	−0.315835	−	0.948814i	$-0.602285\pi$
$211$		−	5816.14i		−	1.89763i	0.315835	−	0.948814i	$-0.397715\pi$
$212$	−2030.72	−	1226.55i	−0.657878	−	0.397359i
$213$	−2536.64	−	4262.24i	−0.815999	−	1.37110i
$214$	761.330	−	92.5893i	0.243194	−	0.0295761i
$215$	−443.502	−	643.469i	−0.140682	−	0.204113i
$216$	−1185.20	+	2945.00i	−0.373344	+	0.927693i
$217$	−777.013	−	777.013i	−0.243074	−	0.243074i
$218$	−1581.04	+	2018.84i	−0.491199	+	0.627215i
$219$	789.473	−	3110.53i	0.243597	−	0.959772i
$220$	−99.4922	−	1653.22i	−0.0304898	−	0.506637i
$221$	2753.44			0.838084
$222$	−2922.23	−	3781.92i	−0.883456	−	1.14336i
$223$	2791.91	−	2791.91i	0.838386	−	0.838386i	−0.150260	−	0.988646i	$-0.548011\pi$
$223$	2791.91	−	2791.91i	0.838386	−	0.838386i	0.988646	+	0.150260i	$0.0480112\pi$
$224$	−728.336	+	503.759i	−0.217250	+	0.150263i
$225$	2559.88	−	2199.46i	0.758484	−	0.651692i
$226$	−3040.65	+	369.790i	−0.894961	+	0.108841i
$227$	4225.50	+	4225.50i	1.23549	+	1.23549i	0.961825	+	0.273664i	$0.0882355\pi$
$227$	4225.50	+	4225.50i	1.23549	+	1.23549i	0.273664	+	0.961825i	$0.411765\pi$
$228$	−907.726	−	919.634i	−0.263665	−	0.267124i
$229$	1927.71			0.556275			0.278137	−	0.960541i	$-0.410283\pi$
$229$	1927.71			0.556275			0.278137	+	0.960541i	$0.410283\pi$
$230$	2925.91	+	178.445i	0.838820	+	0.0511580i
$231$	−456.244	−	115.798i	−0.129951	−	0.0329824i
$232$	747.130	−	1662.59i	0.211429	−	0.470494i
$233$	506.129	+	506.129i	0.142307	+	0.142307i	0.774671	−	0.632364i	$-0.217915\pi$
$233$	506.129	+	506.129i	0.142307	+	0.142307i	−0.632364	+	0.774671i	$0.717915\pi$
$234$	−1433.22	+	3629.39i	−0.400394	+	1.01393i
$235$	3525.68	−	2430.02i	0.978680	−	0.674541i
$236$	−4906.70	+	1211.38i	−1.35338	+	0.334126i
$237$	232.445	+	390.571i	0.0637086	+	0.107048i
$238$	459.740	−	587.045i	0.125212	−	0.159884i
$239$	3610.68			0.977221			0.488610	−	0.872502i	$-0.337504\pi$
$239$	3610.68			0.977221			0.488610	+	0.872502i	$0.337504\pi$
$240$	−2484.46	+	2766.12i	−0.668214	+	0.743969i
$241$	5542.25			1.48136			0.740679	−	0.671859i	$-0.234504\pi$
$241$	5542.25			1.48136			0.740679	+	0.671859i	$0.234504\pi$
$242$	1723.20	−	2200.37i	0.457734	−	0.584484i
$243$	3398.62	+	1672.82i	0.897207	+	0.441610i
$244$	3700.74	−	913.645i	0.970964	−	0.239714i
$245$	−645.433	+	3508.40i	−0.168307	+	0.914871i
$246$	−6679.14	−	856.488i	−1.73108	−	0.221982i
$247$	−1123.11	−	1123.11i	−0.289320	−	0.289320i
$248$	4635.92	+	2083.27i	1.18702	+	0.533419i
$249$	−166.978	+	657.893i	−0.0424971	+	0.167439i
$250$	3698.60	−	1394.77i	0.935679	−	0.352853i
$251$	−1723.36			−0.433377			−0.216688	−	0.976241i	$-0.569526\pi$
$251$	−1723.36			−0.433377			−0.216688	+	0.976241i	$0.569526\pi$
$252$	534.496	+	911.562i	0.133612	+	0.227869i
$253$	−1213.73	−	1213.73i	−0.301607	−	0.301607i
$254$	2244.58	−	272.975i	0.554478	−	0.0674330i
$255$	1306.44	−	2844.92i	0.320832	−	0.698651i
$256$	2321.65	−	3374.48i	0.566810	−	0.823849i
$257$	−3472.88	+	3472.88i	−0.842928	+	0.842928i	−0.989239	−	0.146311i	$-0.953260\pi$
$257$	−3472.88	+	3472.88i	−0.842928	+	0.842928i	0.146311	+	0.989239i	$0.453260\pi$
$258$	812.914	−	628.125i	0.196162	−	0.151571i
$259$	−1590.91			−0.381676
$260$	−3031.67	+	3419.93i	−0.723138	+	0.815750i
$261$	−1911.73	−	1037.23i	−0.453383	−	0.245989i
$262$	−3829.63	+	4890.08i	−0.903036	+	1.15309i
$263$	2393.44	+	2393.44i	0.561162	+	0.561162i	0.929637	−	0.368476i	$-0.120120\pi$
$263$	2393.44	+	2393.44i	0.561162	+	0.561162i	−0.368476	+	0.929637i	$0.620120\pi$
$264$	2162.89	−	248.749i	0.504229	−	0.0579904i
$265$	−2729.91	+	1881.55i	−0.632820	+	0.436162i
$266$	−426.977	+	51.9270i	−0.0984197	+	0.0119693i
$267$	−5606.13	+	3336.44i	−1.28498	+	0.764745i
$268$	−4877.84	−	2946.22i	−1.11180	−	0.671526i
$269$		−	1421.29i		−	0.322146i	−0.986942	−	0.161073i	$-0.948505\pi$
$269$		−	1421.29i		−	0.322146i	0.986942	−	0.161073i	$-0.0514955\pi$
$270$	3069.94	+	3202.88i	0.691966	+	0.721930i
$271$	−317.487			−0.0711659			−0.0355830	−	0.999367i	$-0.511329\pi$
$271$	−317.487			−0.0711659			−0.0355830	+	0.999367i	$0.511329\pi$
$272$	−1023.51	+	3293.39i	−0.228159	+	0.734159i
$273$	664.287	+	1116.18i	0.147269	+	0.247452i
$274$	−213.866	−	1758.55i	−0.0471537	−	0.387729i
$275$	−2163.08	−	823.754i	−0.474322	−	0.180634i
$276$	−25.1088	+	3853.27i	−0.00547598	+	0.840361i
$277$	2357.75	−	2357.75i	0.511420	−	0.511420i	−0.403541	−	0.914961i	$-0.632221\pi$
$277$	2357.75	−	2357.75i	0.511420	−	0.511420i	0.914961	+	0.403541i	$0.132221\pi$
$278$	5082.19	−	6489.48i	1.09644	−	1.40005i
$279$	2892.19	−	5330.59i	0.620612	−	1.14385i
$280$	222.948	+	1217.38i	0.0475845	+	0.259831i
$281$			2095.66i			0.444899i	0.974944	+	0.222450i	$0.0714053\pi$
$281$			2095.66i			0.444899i	−0.974944	+	0.222450i	$0.928595\pi$
$282$	3441.60	+	4454.09i	0.726753	+	0.940558i
$283$	1062.00	+	1062.00i	0.223071	+	0.223071i	0.809790	−	0.586719i	$-0.199581\pi$
$283$	1062.00	+	1062.00i	0.223071	+	0.223071i	−0.586719	+	0.809790i	$0.699581\pi$
$284$	7413.77	−	1830.33i	1.54904	−	0.382430i
$285$	−1693.31	+	627.540i	−0.351941	+	0.130429i
$286$	2656.56	−	323.078i	0.549251	−	0.0667973i
$287$	−1584.97	+	1584.97i	−0.325986	+	0.325986i
$288$	−3808.35	−	3063.38i	−0.779199	−	0.626777i
$289$			2009.19i			0.408954i
$290$	−1688.27	−	1907.57i	−0.341857	−	0.386264i
$291$	729.895	+	185.252i	0.147035	+	0.0373185i
$292$	4229.23	+	2554.46i	0.847593	+	0.511947i
$293$	−3933.16	+	3933.16i	−0.784224	+	0.784224i	−0.980541	−	0.196317i	$-0.937102\pi$
$293$	−3933.16	+	3933.16i	−0.784224	+	0.784224i	0.196317	+	0.980541i	$0.437102\pi$
$294$	−4651.22	−	596.440i	−0.922668	−	0.118317i
$295$	−1277.96	+	6946.63i	−0.252222	+	1.37101i
$296$	6878.66	−	2613.23i	1.35072	−	0.513145i
$297$	−103.169	−	2595.81i	−0.0201565	−	0.507153i
$298$	6216.26	+	4868.22i	1.20838	+	0.946337i
$299$			4736.52i			0.916120i
$300$	2095.11	+	4755.05i	0.403203	+	0.915110i
$301$		−	341.961i		−	0.0654828i
$302$	−2398.01	+	3062.04i	−0.456921	+	0.583445i
$303$	−5103.40	+	3037.25i	−0.967600	+	0.575860i
$304$	1760.84	−	925.872i	0.332207	−	0.174679i
$305$	963.863	−	5239.30i	0.180953	−	0.983611i
$306$	3827.59	+	1511.48i	0.715061	+	0.282372i
$307$	−4085.25	+	4085.25i	−0.759470	+	0.759470i	−0.976226	−	0.216756i	$-0.930452\pi$
$307$	−4085.25	+	4085.25i	−0.759470	+	0.759470i	0.216756	+	0.976226i	$0.430452\pi$
$308$	374.681	−	620.333i	0.0693164	−	0.114762i
$309$	1581.54	−	6231.28i	0.291168	−	1.14720i
$310$	5319.02	−	4707.52i	0.974515	−	0.862481i
$311$		−	6517.84i		−	1.18840i	−0.804317	−	0.594201i	$-0.797469\pi$
$311$		−	6517.84i		−	1.18840i	0.804317	−	0.594201i	$-0.202531\pi$
$312$	−4705.64	−	3734.91i	−0.853860	−	0.677717i
$313$	−4758.79	+	4758.79i	−0.859370	+	0.859370i	−0.991264	−	0.131894i	$-0.957894\pi$
$313$	−4758.79	+	4758.79i	−0.859370	+	0.859370i	0.131894	+	0.991264i	$0.457894\pi$
$314$	102.992	+	846.864i	0.0185101	+	0.152202i
$315$	1468.45	−	156.758i	0.262660	−	0.0280392i
$316$	−679.361	+	167.722i	−0.120940	+	0.0298579i
$317$	−584.917	−	584.917i	−0.103635	−	0.103635i	0.653388	−	0.757023i	$-0.273347\pi$
$317$	−584.917	−	584.917i	−0.103635	−	0.103635i	−0.757023	+	0.653388i	$0.773347\pi$
$318$	−2664.82	−	3448.78i	−0.469923	−	0.608170i
$319$			1491.64i			0.261804i
$320$	−2963.64	−	4897.43i	−0.517727	−	0.855546i
$321$	1365.66	+	346.613i	0.237457	+	0.0602680i
$322$	1009.84	+	790.851i	0.174771	+	0.136871i
$323$	−1184.45	+	1184.45i	−0.204038	+	0.204038i
$324$	−3984.66	+	4258.49i	−0.683240	+	0.730194i
$325$	2613.32	+	5827.98i	0.446034	+	0.994701i
$326$	−492.238	+	59.8637i	−0.0836275	+	0.0101704i
$327$	−4048.15	+	2409.23i	−0.684597	+	0.407433i
$328$	4249.51	−	9456.47i	0.715366	−	1.59191i
$329$	1873.66			0.313977
$330$	926.654	−	2898.11i	0.154578	−	0.483442i
$331$		−	4354.25i		−	0.723055i	−0.932361	−	0.361528i	$-0.882255\pi$
$331$		−	4354.25i		−	0.723055i	0.932361	−	0.361528i	$-0.117745\pi$
$332$	−894.504	−	540.281i	−0.147868	−	0.0893126i
$333$	−2496.28	−	8417.93i	−0.410796	−	1.38529i
$334$	513.792	+	4224.73i	0.0841719	+	0.692116i
$335$	−6557.33	+	4519.54i	−1.06945	+	0.737101i
$336$	−1581.99	+	379.646i	−0.256859	+	0.0616411i
$337$	−2814.99	−	2814.99i	−0.455022	−	0.455022i	0.441995	−	0.897017i	$-0.354271\pi$
$337$	−2814.99	−	2814.99i	−0.455022	−	0.455022i	−0.897017	+	0.441995i	$0.854271\pi$
$338$	−921.604	−	721.747i	−0.148310	−	0.116148i
$339$	−5454.26	−	1384.33i	−0.873848	−	0.221789i
$340$	3606.69	+	3197.23i	0.575295	+	0.509982i
$341$	−4159.23			−0.660512
$342$	−944.725	−	2177.78i	−0.149371	−	0.344329i
$343$	−2290.28	+	2290.28i	−0.360534	+	0.360534i
$344$	561.706	+	1478.55i	0.0880383	+	0.231738i
$345$	4893.88	+	2247.35i	0.763703	+	0.350705i
$346$	−707.286	−	5815.76i	−0.109896	−	0.903634i
$347$	−561.173	−	561.173i	−0.0868166	−	0.0868166i	0.662365	−	0.749181i	$-0.269553\pi$
$347$	−561.173	−	561.173i	−0.0868166	−	0.0868166i	−0.749181	+	0.662365i	$0.769553\pi$
$348$	2383.20	−	2352.34i	0.367106	−	0.362353i
$349$	9517.18			1.45972			0.729861	−	0.683596i	$-0.239585\pi$
$349$	9517.18			1.45972			0.729861	+	0.683596i	$0.239585\pi$
$350$	1678.89	+	415.921i	0.256401	+	0.0635197i
$351$	−4863.70	+	5266.31i	−0.739616	+	0.800841i
$352$	−601.062	+	3297.60i	−0.0910133	+	0.499326i
$353$	−3863.92	−	3863.92i	−0.582594	−	0.582594i	0.353021	−	0.935615i	$-0.385154\pi$
$353$	−3863.92	−	3863.92i	−0.582594	−	0.582594i	−0.935615	+	0.353021i	$0.885154\pi$
$354$	−9209.41	−	1180.95i	−1.38270	−	0.177308i
$355$	1930.93	−	10496.0i	0.288685	−	1.56921i
$356$	−2407.43	−	9751.33i	−0.358409	−	1.45174i
$357$	1177.14	−	700.563i	0.174512	−	0.103859i
$358$	4861.26	+	3807.06i	0.717669	+	0.562037i
$359$	−5175.82			−0.760917			−0.380459	−	0.924798i	$-0.624234\pi$
$359$	−5175.82			−0.760917			−0.380459	+	0.924798i	$0.624234\pi$
$360$	−6091.70	+	3089.86i	−0.891835	+	0.452361i
$361$	−5892.74			−0.859126
$362$	−8431.73	−	6603.25i	−1.22420	−	0.958726i
$363$	4412.16	−	2625.86i	0.637957	−	0.379675i
$364$	−1941.49	+	479.320i	−0.279566	+	0.0690198i
$365$	5685.40	−	3918.58i	0.815308	−	0.561939i
$366$	6945.94	+	890.700i	0.991994	+	0.127207i
$367$	−4046.98	−	4046.98i	−0.575615	−	0.575615i	0.358077	−	0.933692i	$-0.383432\pi$
$367$	−4046.98	−	4046.98i	−0.575615	−	0.575615i	−0.933692	+	0.358077i	$0.883432\pi$
$368$	−5665.34	−	1760.66i	−0.802517	−	0.249404i
$369$	−10873.5	−	5899.57i	−1.53401	−	0.832301i
$370$	626.012	−	10264.5i	0.0879589	−	1.44223i
$371$	−1450.77			−0.203019
$372$	6559.19	+	6645.24i	0.914189	+	0.926181i
$373$	−5803.41	−	5803.41i	−0.805601	−	0.805601i	0.178364	−	0.983965i	$-0.442920\pi$
$373$	−5803.41	−	5803.41i	−0.805601	−	0.805601i	−0.983965	+	0.178364i	$0.942920\pi$
$374$	−340.722	−	2801.63i	−0.0471077	−	0.387350i
$375$	7261.55	+	65.0724i	0.999960	+	0.00896087i
$376$	−8101.21	+	3077.68i	−1.11114	+	0.422126i
$377$	2910.51	−	2910.51i	0.397610	−	0.397610i
$378$	310.711	+	1916.27i	0.0422784	+	0.260747i
$379$	−5970.93			−0.809251			−0.404626	−	0.914482i	$-0.632598\pi$
$379$	−5970.93			−0.809251			−0.404626	+	0.914482i	$0.632598\pi$
$380$	−167.019	−	2775.28i	−0.0225470	−	0.374655i
$381$	4026.28	+	1021.90i	0.541398	+	0.137410i
$382$	7926.45	+	6207.54i	1.06166	+	0.831428i
$383$	5634.68	+	5634.68i	0.751746	+	0.751746i	0.974805	−	0.223059i	$-0.0716042\pi$
$383$	5634.68	+	5634.68i	0.751746	+	0.751746i	−0.223059	+	0.974805i	$0.571604\pi$
$384$	6216.50	−	4240.07i	0.826131	−	0.563477i
$385$	−574.767	−	833.920i	−0.0760852	−	0.110391i
$386$	1379.58	+	11343.8i	0.181915	+	1.49582i
$387$	1809.41	−	536.567i	0.237668	−	0.0704787i
$388$	−599.411	+	992.402i	−0.0784291	+	0.129849i
$389$			7826.87i			1.02015i	0.860130	+	0.510075i	$0.170382\pi$
$389$			7826.87i			1.02015i	−0.860130	+	0.510075i	$0.829618\pi$
$390$	−7462.97	+	3846.75i	−0.968979	+	0.499456i
$391$	4995.18			0.646079
$392$	2959.28	−	6585.30i	0.381291	−	0.848489i
$393$	−9805.54	+	5835.69i	−1.25859	+	0.749038i
$394$	−3074.84	+	373.947i	−0.393167	+	0.0478152i
$395$	−176.941	+	961.803i	−0.0225389	+	0.122515i
$396$	3870.26	+	1009.19i	0.491131	+	0.128064i
$397$	2459.32	−	2459.32i	0.310906	−	0.310906i	−0.534354	−	0.845261i	$-0.679445\pi$
$397$	2459.32	−	2459.32i	0.310906	−	0.310906i	0.845261	+	0.534354i	$0.179445\pi$
$398$	928.468	+	727.123i	0.116934	+	0.0915763i
$399$	−765.902	−	194.391i	−0.0960980	−	0.0243903i
$400$	−7942.26	+	959.420i	−0.992783	+	0.119927i
$401$		−	2120.72i		−	0.264099i	−0.991243	−	0.132049i	$-0.957844\pi$
$401$		−	2120.72i		−	0.264099i	0.991243	−	0.132049i	$-0.0421558\pi$
$402$	−6400.96	−	8284.07i	−0.794156	−	1.02779i
$403$	8115.57	+	8115.57i	1.00314	+	1.00314i
$404$	−2191.54	−	8876.89i	−0.269885	−	1.09317i
$405$	3133.58	+	7524.01i	0.384467	+	0.923139i
$406$	−134.567	−	1106.50i	−0.0164494	−	0.135257i
$407$	−4257.94	+	4257.94i	−0.518570	+	0.518570i
$408$	−3938.87	+	4962.61i	−0.477949	+	0.602172i
$409$			8011.87i			0.968610i	0.874899	+	0.484305i	$0.160927\pi$
$409$			8011.87i			0.968610i	−0.874899	+	0.484305i	$0.839073\pi$
$410$	−9602.52	−	10849.9i	−1.15667	−	1.30692i
$411$	800.619	−	3154.44i	0.0960866	−	0.378582i
$412$	8472.36	+	5117.31i	1.01311	+	0.611922i
$413$	−2185.41	+	2185.41i	−0.260380	+	0.260380i
$414$	−2600.08	+	6584.27i	−0.308664	+	0.781641i
$415$	−1202.49	+	828.799i	−0.142236	+	0.0980341i
$416$	7607.16	−	5261.55i	0.896567	−	0.620117i
$417$	13012.6	−	7744.37i	1.52813	−	0.909457i
$418$	−1003.79	+	1281.75i	−0.117457	+	0.149982i
$419$			7128.89i			0.831191i	0.909550	+	0.415596i	$0.136427\pi$
$419$			7128.89i			0.831191i	−0.909550	+	0.415596i	$0.863573\pi$
$420$	−425.942	+	2233.42i	−0.0494853	+	0.259476i
$421$			6431.12i			0.744498i	0.928133	+	0.372249i	$0.121413\pi$
$421$			6431.12i			0.744498i	−0.928133	+	0.372249i	$0.878587\pi$
$422$	12951.5	+	10142.9i	1.49400	+	1.17002i
$423$	2939.94	+	9914.07i	0.337931	+	1.13957i
$424$	6272.73	−	2383.03i	0.718469	−	0.272949i
$425$	6146.24	−	2756.04i	0.701498	−	0.314559i
$426$	13915.0	+	1784.36i	1.58259	+	0.202940i
$427$	1648.28	−	1648.28i	0.186806	−	0.186806i
$428$	−1121.52	+	1856.81i	−0.126660	+	0.209702i
$429$	4765.28	+	1209.46i	0.536294	+	0.136115i
$430$	2206.32	+	134.559i	0.247438	+	0.0150908i
$431$			1168.10i			0.130546i	0.997867	+	0.0652729i	$0.0207918\pi$
$431$			1168.10i			0.130546i	−0.997867	+	0.0652729i	$0.979208\pi$
$432$	−4491.10	−	7775.06i	−0.500181	−	0.865921i
$433$	11674.9	−	11674.9i	1.29575	−	1.29575i	0.364580	−	0.931172i	$-0.381213\pi$
$433$	11674.9	−	11674.9i	1.29575	−	1.29575i	0.931172	−	0.364580i	$-0.118787\pi$
$434$	3085.32	−	375.222i	0.341244	−	0.0415005i
$435$	−1626.25	−	4388.17i	−0.179247	−	0.483670i
$436$	−1738.39	−	7041.38i	−0.190949	−	0.773442i
$437$	−2037.50	−	2037.50i	−0.223037	−	0.223037i
$438$	5549.82	+	7182.53i	0.605436	+	0.783550i
$439$			2681.21i			0.291497i	0.989322	+	0.145749i	$0.0465591\pi$
$439$			2681.21i			0.291497i	−0.989322	+	0.145749i	$0.953441\pi$
$440$	3854.93	+	2661.53i	0.417675	+	0.288372i
$441$	−7572.08	−	4108.34i	−0.817631	−	0.443617i
$442$	−4801.79	+	6131.43i	−0.516737	+	0.659825i
$443$	164.199	−	164.199i	0.0176103	−	0.0176103i	−0.698247	−	0.715857i	$-0.746036\pi$
$443$	164.199	−	164.199i	0.0176103	−	0.0176103i	0.715857	+	0.698247i	$0.246036\pi$
$444$	13517.8	+	88.0851i	1.44488	+	0.00941517i
$445$	−13805.4	−	2539.75i	−1.47065	−	0.270552i
$446$	1348.22	+	11086.0i	0.143139	+	1.17698i
$447$	7418.32	+	12464.8i	0.784955	+	1.31894i
$448$	148.377	−	2500.39i	0.0156477	−	0.263688i
$449$	7243.98			0.761391			0.380695	−	0.924700i	$-0.375685\pi$
$449$	7243.98			0.761391			0.380695	+	0.924700i	$0.375685\pi$
$450$	433.575	+	9536.09i	0.0454199	+	0.998968i
$451$			8484.10i			0.885811i
$452$	4479.20	−	7415.88i	0.466114	−	0.771711i
$453$	−6139.97	+	3654.15i	−0.636823	+	0.379000i
$454$	−16778.4	+	2040.51i	−1.73447	+	0.210938i
$455$	−505.665	+	2748.66i	−0.0521010	+	0.283207i
$456$	3630.86	−	417.578i	0.372874	−	0.0428835i
$457$	−5337.97	−	5337.97i	−0.546389	−	0.546389i	0.379005	−	0.925394i	$-0.376266\pi$
$457$	−5337.97	−	5337.97i	−0.546389	−	0.546389i	−0.925394	+	0.379005i	$0.876266\pi$
$458$	−3361.78	+	4292.68i	−0.342982	+	0.437955i
$459$	5553.91	+	5129.31i	0.564780	+	0.521603i
$460$	−5499.92	+	6204.28i	−0.557467	+	0.628861i
$461$	1695.65			0.171311			0.0856553	−	0.996325i	$-0.472702\pi$
$461$	1695.65			0.171311			0.0856553	+	0.996325i	$0.472702\pi$
$462$	1053.52	−	814.034i	0.106091	−	0.0819746i
$463$	11701.3	−	11701.3i	1.17453	−	1.17453i	0.193411	−	0.981118i	$-0.438045\pi$
$463$	11701.3	−	11701.3i	1.17453	−	1.17453i	0.981118	−	0.193411i	$-0.0619552\pi$
$464$	2399.37	+	4563.15i	0.240060	+	0.456550i
$465$	12235.8	−	4534.58i	1.22026	−	0.452228i
$466$	−2009.71	+	244.411i	−0.199781	+	0.0242964i
$467$	−12062.5	−	12062.5i	−1.19526	−	1.19526i	−0.975571	−	0.219686i	$-0.929497\pi$
$467$	−12062.5	−	12062.5i	−1.19526	−	1.19526i	−0.219686	−	0.975571i	$-0.570503\pi$
$468$	−5582.59	−	9520.88i	−0.551400	−	0.940391i
$469$	−3484.78			−0.343097
$470$	−737.274	+	12088.8i	−0.0723573	+	1.18642i
$471$	−385.554	+	1519.09i	−0.0377185	+	0.148611i
$472$	5859.37	−	13038.9i	0.571397	−	1.27153i
$473$	−915.232	−	915.232i	−0.0889691	−	0.0889691i
$474$	−1275.10	−	163.510i	−0.123560	−	0.0158444i
$475$	−3631.19	−	1382.84i	−0.350758	−	0.133577i
$476$	505.495	+	2047.52i	0.0486751	+	0.197159i
$477$	−2276.38	−	7676.42i	−0.218508	−	0.736853i
$478$	−6296.74	+	8040.36i	−0.602524	+	0.769367i
$479$	−5861.63			−0.559133			−0.279567	−	0.960126i	$-0.590191\pi$
$479$	−5861.63			−0.559133			−0.279567	+	0.960126i	$0.590191\pi$
$480$	−1826.96	−	10356.4i	−0.173727	−	0.984794i
$481$	16616.4			1.57514
$482$	−9665.24	+	12341.6i	−0.913360	+	1.16628i
$483$	1205.12	+	2024.93i	0.113530	+	0.190761i
$484$	1894.71	+	7674.54i	0.177940	+	0.720750i
$485$	919.506	+	1334.10i	0.0860878	+	0.124903i
$486$	−9651.98	+	4650.86i	−0.900870	+	0.434089i
$487$	−964.842	−	964.842i	−0.0897765	−	0.0897765i	0.660792	−	0.750569i	$-0.270220\pi$
$487$	−964.842	−	964.842i	−0.0897765	−	0.0897765i	−0.750569	+	0.660792i	$0.770220\pi$
$488$	−4419.26	+	9834.21i	−0.409940	+	0.912241i
$489$	−882.967	−	224.103i	−0.0816547	−	0.0207245i
$490$	−6687.00	−	7555.63i	−0.616506	−	0.696589i
$491$	4731.40			0.434878			0.217439	−	0.976074i	$-0.430230\pi$
$491$	4731.40			0.434878			0.217439	+	0.976074i	$0.430230\pi$
$492$	13555.1	−	13379.6i	1.24210	−	1.22602i
$493$	−3069.45	−	3069.45i	−0.280408	−	0.280408i
$494$	4459.60	−	542.355i	0.406167	−	0.0493962i
$495$	3510.64	−	4349.74i	0.318771	−	0.394962i
$496$	−12723.7	+	6690.31i	−1.15184	+	0.605653i
$497$	3302.05	−	3302.05i	0.298022	−	0.298022i
$498$	−1173.82	−	1519.14i	−0.105622	−	0.136696i
$499$	−5345.28			−0.479534			−0.239767	−	0.970830i	$-0.577071\pi$
$499$	−5345.28			−0.479534			−0.239767	+	0.970830i	$0.577071\pi$
$500$	−3344.14	+	10668.5i	−0.299109	+	0.954219i
$501$	−1923.40	+	7578.23i	−0.171520	+	0.675789i
$502$	3005.40	−	3837.62i	0.267207	−	0.341198i
$503$	894.890	+	894.890i	0.0793264	+	0.0793264i	0.745657	−	0.666330i	$-0.232136\pi$
$503$	894.890	+	894.890i	0.0793264	+	0.0793264i	−0.666330	+	0.745657i	$0.732136\pi$
$504$	−2962.01	−	399.462i	−0.261782	−	0.0353045i
$505$	−12567.4	−	2312.00i	−1.10741	−	0.203728i
$506$	4819.41	−	586.115i	0.423417	−	0.0514940i
$507$	−1099.82	−	1847.99i	−0.0963405	−	0.161878i
$508$	−3306.50	+	5474.33i	−0.288784	+	0.478118i
$509$			12604.8i			1.09763i	0.835942	+	0.548817i	$0.184922\pi$
$509$			12604.8i			1.09763i	−0.835942	+	0.548817i	$0.815078\pi$
$510$	4056.82	+	7870.52i	0.352233	+	0.683358i
$511$	3021.41			0.261564
$512$	3465.61	+	11054.7i	0.299140	+	0.954209i
$513$	−173.191	−	4357.62i	−0.0149056	−	0.375036i
$514$	−1677.07	−	13789.9i	−0.143915	−	1.18336i
$515$	11389.5	−	7850.03i	0.974526	−	0.671677i
$516$	−18.9336	+	2905.62i	−0.00161532	+	0.247893i
$517$	5014.71	−	5014.71i	0.426589	−	0.426589i
$518$	2774.42	−	3542.67i	0.235330	−	0.300494i
$519$	2647.76	−	10432.2i	0.223938	−	0.882317i
$520$	−2328.59	−	12715.1i	−0.196376	−	1.07229i
$521$			1664.43i			0.139962i	0.997548	+	0.0699810i	$0.0222939\pi$
$521$			1664.43i			0.139962i	−0.997548	+	0.0699810i	$0.977706\pi$
$522$	5643.63	−	2448.22i	0.473209	−	0.205279i
$523$	14882.3	+	14882.3i	1.24428	+	1.24428i	0.958208	+	0.286073i	$0.0923499\pi$
$523$	14882.3	+	14882.3i	1.24428	+	1.24428i	0.286073	+	0.958208i	$0.407650\pi$
$524$	−4210.78	−	17055.8i	−0.351047	−	1.42192i
$525$	2600.05	+	1826.63i	0.216144	+	0.151849i
$526$	−9503.72	+	1155.80i	−0.787798	+	0.0958083i
$527$	8558.76	−	8558.76i	0.707449	−	0.707449i
$528$	−3217.98	+	5250.17i	−0.265236	+	0.432735i
$529$		−	3574.22i		−	0.293764i
$530$	570.868	−	9360.32i	0.0467866	−	0.767144i
$531$	−14992.7	−	8134.51i	−1.22529	−	0.664798i
$532$	628.982	−	1041.36i	0.0512590	−	0.0848659i
$533$	16554.4	−	16554.4i	1.34531	−	1.34531i
$534$	2346.97	−	18302.3i	0.190193	−	1.48318i
$535$	1720.42	+	2496.14i	0.139029	+	0.201715i
$536$	15067.3	−	5724.11i	1.21419	−	0.461276i
$537$	5801.29	+	9747.74i	0.466190	+	0.783326i
$538$	3164.95	+	2478.61i	0.253626	+	0.198625i
$539$			5908.16i			0.472138i
$540$	−12486.0	+	1250.66i	−0.995021	+	0.0996662i
$541$			9914.81i			0.787931i	0.919125	+	0.393966i	$0.128897\pi$
$541$			9914.81i			0.787931i	−0.919125	+	0.393966i	$0.871103\pi$
$542$	553.672	−	706.988i	0.0438787	−	0.0560290i
$543$	−10062.2	−	16907.2i	−0.795231	−	1.33620i
$544$	−5548.88	−	8022.59i	−0.437328	−	0.632290i
$545$	−9968.80	−	1833.94i	−0.783516	−	0.144142i
$546$	−3644.00	−	467.282i	−0.285621	−	0.0366261i
$547$	−7769.85	+	7769.85i	−0.607340	+	0.607340i	−0.942250	−	0.334910i	$-0.891294\pi$
$547$	−7769.85	+	7769.85i	−0.607340	+	0.607340i	0.334910	+	0.942250i	$0.391294\pi$
$548$	4288.94	+	2590.52i	0.334333	+	0.201937i
$549$	11307.8	+	6135.22i	0.879064	+	0.476949i
$550$	5606.59	−	3380.24i	0.434665	−	0.262061i
$551$			2504.02i			0.193603i
$552$	−8536.76	−	6775.71i	−0.658241	−	0.522452i
$553$	−302.583	+	302.583i	−0.0232679	+	0.0232679i
$554$	1138.56	+	9362.01i	0.0873158	+	0.717967i
$555$	7884.02	−	17168.4i	0.602987	−	1.31308i
$556$	5588.00	+	22634.3i	0.426230	+	1.72645i
$557$	−11010.7	−	11010.7i	−0.837593	−	0.837593i	0.150948	−	0.988542i	$-0.451767\pi$
$557$	−11010.7	−	11010.7i	−0.837593	−	0.837593i	−0.988542	+	0.150948i	$0.951767\pi$
$558$	6826.54	+	15736.5i	0.517904	+	1.19387i
$559$			3571.64i			0.270240i
$560$	−3099.70	−	1626.56i	−0.233904	−	0.122740i
$561$	1275.51	−	5025.51i	0.0959929	−	0.378213i
$562$	−4666.67	−	3654.67i	−0.350270	−	0.274311i
$563$	9471.63	−	9471.63i	0.709026	−	0.709026i	−0.257304	−	0.966330i	$-0.582834\pi$
$563$	9471.63	−	9471.63i	0.709026	−	0.709026i	0.966330	+	0.257304i	$0.0828343\pi$
$564$	−15920.4	−	103.741i	−1.18860	−	0.00774516i
$565$	−6871.15	−	9969.24i	−0.511631	−	0.742317i
$566$	−4216.91	+	512.841i	−0.313163	+	0.0380854i
$567$	−739.384	+	3488.90i	−0.0547640	+	0.258413i
$568$	−8853.21	+	19701.1i	−0.654001	+	1.45535i
$569$	−1343.84			−0.0990100			−0.0495050	−	0.998774i	$-0.515764\pi$
$569$	−1343.84			−0.0990100			−0.0495050	+	0.998774i	$0.515764\pi$
$570$	1555.58	−	4865.09i	0.114309	−	0.357502i
$571$			1193.06i			0.0874397i	0.999044	+	0.0437199i	$0.0139209\pi$
$571$			1193.06i			0.0874397i	−0.999044	+	0.0437199i	$0.986079\pi$
$572$	−3913.39	+	6479.11i	−0.286061	+	0.473611i
$573$	9459.22	+	15894.0i	0.689641	+	1.15878i
$574$	−765.388	−	6293.52i	−0.0556563	−	0.457642i
$575$	4740.97	+	10572.9i	0.343847	+	0.766815i
$576$	13463.1	−	3138.23i	0.973892	−	0.227013i
$577$	7256.15	+	7256.15i	0.523531	+	0.523531i	0.918636	−	0.395105i	$-0.129292\pi$
$577$	7256.15	+	7256.15i	0.523531	+	0.523531i	−0.395105	+	0.918636i	$0.629292\pi$
$578$	−4474.11	−	3503.87i	−0.321970	−	0.252148i
$579$	−5164.54	+	20348.3i	−0.370693	+	1.46053i
$580$	7192.04	−	432.823i	0.514885	−	0.0309862i
$581$	−639.044			−0.0456317
$582$	−1685.40	+	1302.28i	−0.120038	+	0.0927515i
$583$	−3882.86	+	3882.86i	−0.275835	+	0.275835i
$584$	−13063.8	+	4962.98i	−0.925655	+	0.351660i
$585$	−15337.4	+	1637.28i	−1.08397	+	0.115715i
$586$	−1899.34	−	15617.6i	−0.133892	−	1.10095i
$587$	9401.10	+	9401.10i	0.661030	+	0.661030i	0.955623	−	0.294593i	$-0.0951840\pi$
$587$	9401.10	+	9401.10i	0.661030	+	0.661030i	−0.294593	+	0.955623i	$0.595184\pi$
$588$	9439.52	−	9317.30i	0.662040	−	0.653467i
$589$	−6982.14			−0.488445
$590$	−13240.3	−	14960.2i	−0.923887	−	1.04390i
$591$	−5515.57	−	1399.89i	−0.383892	−	0.0974345i
$592$	−6176.63	+	19874.8i	−0.428814	+	1.37981i
$593$	−4806.34	−	4806.34i	−0.332838	−	0.332838i	0.520826	−	0.853663i	$-0.325624\pi$
$593$	−4806.34	−	4806.34i	−0.332838	−	0.332838i	−0.853663	+	0.520826i	$0.825624\pi$
$594$	5960.34	+	4297.15i	0.411710	+	0.296825i
$595$	2898.76	+	533.279i	0.199727	+	0.0367434i
$596$	−21681.3	+	5352.73i	−1.49010	+	0.367880i
$597$	1108.01	+	1861.75i	0.0759594	+	0.127632i
$598$	−10547.4	−	8260.10i	−0.721262	−	0.564851i
$599$	−10448.4			−0.712704			−0.356352	−	0.934352i	$-0.615980\pi$
$599$	−10448.4			−0.712704			−0.356352	+	0.934352i	$0.615980\pi$
$600$	−14242.4	−	3627.00i	−0.969070	−	0.246786i
$601$	−12023.9			−0.816083			−0.408042	−	0.912963i	$-0.633788\pi$
$601$	−12023.9			−0.816083			−0.408042	+	0.912963i	$0.633788\pi$
$602$	761.487	+	596.353i	0.0515546	+	0.0403746i
$603$	−5467.93	−	18439.0i	−0.369273	−	1.24526i
$604$	−2636.68	−	10679.9i	−0.177624	−	0.719468i
$605$	10865.2	+	1998.85i	0.730137	+	0.134322i
$606$	2136.51	−	16661.1i	0.143217	−	1.11685i
$607$	1211.56	+	1211.56i	0.0810146	+	0.0810146i	0.746453	−	0.665438i	$-0.231755\pi$
$607$	1211.56	+	1211.56i	0.0810146	+	0.0810146i	−0.665438	+	0.746453i	$0.731755\pi$
$608$	−1009.01	+	5535.72i	−0.0673038	+	0.369249i
$609$	503.758	−	1984.81i	0.0335194	−	0.132067i
$610$	9986.09	+	11283.3i	0.662828	+	0.748928i
$611$	−19569.6			−1.29575
$612$	−10040.8	+	5887.45i	−0.663196	+	0.388866i
$613$	−5238.86	−	5238.86i	−0.345181	−	0.345181i	0.513130	−	0.858311i	$-0.328486\pi$
$613$	−5238.86	−	5238.86i	−0.345181	−	0.345181i	−0.858311	+	0.513130i	$0.828486\pi$
$614$	−1972.78	−	16221.5i	−0.129666	−	1.06620i
$615$	−9249.76	−	24959.0i	−0.606482	−	1.63649i
$616$	727.957	+	1916.16i	0.0476140	+	0.125332i
$617$	−15212.0	+	15212.0i	−0.992567	+	0.992567i	−0.999973	−	0.00740595i	$-0.997643\pi$
$617$	−15212.0	+	15212.0i	−0.992567	+	0.992567i	0.00740595	+	0.999973i	$0.497643\pi$
$618$	11117.9	+	14388.7i	0.723668	+	0.936565i
$619$	−8492.91			−0.551468			−0.275734	−	0.961234i	$-0.588921\pi$
$619$	−8492.91			−0.551468			−0.275734	+	0.961234i	$0.588921\pi$
$620$	1206.87	+	20054.0i	0.0781759	+	1.29902i
$621$	−8823.51	+	9553.91i	−0.570170	+	0.617368i
$622$	14514.1	+	11366.6i	0.935629	+	0.732731i
$623$	−4343.18	−	4343.18i	−0.279303	−	0.279303i
$624$	16523.2	−	3965.25i	1.06003	−	0.254386i
$625$	11666.9	+	10393.4i	0.746683	+	0.665180i
$626$	−2298.04	−	18895.9i	−0.146722	−	1.20644i
$627$	−2570.15	+	1529.60i	−0.163703	+	0.0974267i
$628$	−2065.43	−	1247.52i	−0.131241	−	0.0792698i
$629$		−	17523.8i		−	1.11084i
$630$	−2211.79	+	3543.36i	−0.139873	+	0.224080i
$631$	−3175.45			−0.200337			−0.100169	−	0.994970i	$-0.531938\pi$
$631$	−3175.45			−0.200337			−0.100169	+	0.994970i	$0.531938\pi$
$632$	811.264	−	1805.31i	0.0510607	−	0.113626i
$633$	15456.0	+	25970.3i	0.970491	+	1.63069i
$634$	2322.56	−	282.458i	0.145490	−	0.0176938i
$635$	5072.22	+	7359.20i	0.316984	+	0.459907i
$636$	12327.1	+	80.3259i	0.768553	+	0.00500806i
$637$	11528.1	−	11528.1i	0.717050	−	0.717050i
$638$	−3321.61	−	2601.29i	−0.206119	−	0.161420i
$639$	22653.2	+	12290.8i	1.40242	+	0.760905i
$640$	16074.1	+	1941.21i	0.992787	+	0.119895i
$641$			7829.22i			0.482427i	0.970472	+	0.241213i	$0.0775454\pi$
$641$			7829.22i			0.482427i	−0.970472	+	0.241213i	$0.922455\pi$
$642$	−3153.44	+	2436.61i	−0.193857	+	0.149790i
$643$	−1829.67	−	1829.67i	−0.112217	−	0.112217i	0.648769	−	0.760986i	$-0.275284\pi$
$643$	−1829.67	−	1829.67i	−0.112217	−	0.112217i	−0.760986	+	0.648769i	$0.775284\pi$
$644$	−3522.17	+	869.561i	−0.215517	+	0.0532073i
$645$	3690.30	+	1694.65i	0.225280	+	0.103452i
$646$	−571.973	−	4703.13i	−0.0348359	−	0.286443i
$647$	19937.2	−	19937.2i	1.21145	−	1.21145i	0.240905	−	0.970549i	$-0.422556\pi$
$647$	19937.2	−	19937.2i	1.21145	−	1.21145i	0.970549	−	0.240905i	$-0.0774443\pi$
$648$	−2533.98	−	16299.6i	−0.153618	−	0.988130i
$649$			11698.2i			0.707539i
$650$	−17535.3	−	4344.12i	−1.05814	−	0.262139i
$651$	5534.38	+	1404.66i	0.333194	+	0.0845669i
$652$	725.118	−	1200.53i	0.0435549	−	0.0721107i
$653$	4595.08	−	4595.08i	0.275374	−	0.275374i	−0.555885	−	0.831259i	$-0.687621\pi$
$653$	4595.08	−	4595.08i	0.275374	−	0.275374i	0.831259	+	0.555885i	$0.187621\pi$
$654$	1694.73	−	13216.0i	0.101329	−	0.790194i
$655$	−24146.7	−	4442.22i	−1.44044	−	0.264995i
$656$	13647.1	+	25954.3i	0.812240	+	1.54473i
$657$	4740.86	+	15987.1i	0.281520	+	0.949341i
$658$	−3267.52	+	4172.32i	−0.193588	+	0.247194i
$659$		−	22319.0i		−	1.31931i	−0.751569	−	0.659655i	$-0.770703\pi$
$659$		−	22319.0i		−	1.31931i	0.751569	−	0.659655i	$-0.229297\pi$
$660$	4837.57	+	7117.57i	0.285306	+	0.419774i
$661$		−	20965.9i		−	1.23371i	−0.787078	−	0.616854i	$-0.788407\pi$
$661$		−	20965.9i		−	1.23371i	0.787078	−	0.616854i	$-0.211593\pi$
$662$	9696.15	+	7593.47i	0.569262	+	0.445813i
$663$	−12294.7	+	7317.09i	−0.720190	+	0.428616i
$664$	2763.06	−	1049.70i	0.161487	−	0.0613495i
$665$	−964.867	−	1399.91i	−0.0562646	−	0.0816333i
$666$	23098.6	+	9121.44i	1.34392	+	0.530704i
$667$	5280.12	−	5280.12i	0.306517	−	0.306517i
$668$	−10303.7	−	6223.46i	−0.596801	−	0.360469i
$669$	−5047.14	+	19885.8i	−0.291680	+	1.14922i
$670$	1371.24	−	22483.7i	0.0790681	−	1.29645i
$671$		−	8823.00i		−	0.507613i
$672$	1913.46	−	4184.89i	0.109841	−	0.240232i
$673$	12726.5	−	12726.5i	0.728930	−	0.728930i	−0.241477	−	0.970407i	$-0.577632\pi$
$673$	12726.5	−	12726.5i	0.728930	−	0.728930i	0.970407	+	0.241477i	$0.0776318\pi$
$674$	11177.6	−	1359.37i	0.638792	−	0.0776869i
$675$	−5585.49	+	16623.8i	−0.318497	+	0.947924i
$676$	3214.41	−	793.580i	0.182886	−	0.0451513i
$677$	−1788.30	−	1788.30i	−0.101522	−	0.101522i	0.654522	−	0.756043i	$-0.272870\pi$
$677$	−1788.30	−	1788.30i	−0.101522	−	0.101522i	−0.756043	+	0.654522i	$0.772870\pi$
$678$	12594.4	−	9731.51i	0.713402	−	0.551234i
$679$			708.983i			0.0400711i
$680$	−13409.4	+	2455.76i	−0.756218	+	0.138491i
$681$	−30096.7	−	7638.74i	−1.69355	−	0.429834i
$682$	7253.36	−	9261.86i	0.407251	−	0.520022i
$683$	5320.30	−	5320.30i	0.298061	−	0.298061i	−0.542193	−	0.840254i	$-0.682406\pi$
$683$	5320.30	−	5320.30i	0.298061	−	0.298061i	0.840254	+	0.542193i	$0.182406\pi$
$684$	6497.05	+	1694.13i	0.363188	+	0.0947029i
$685$	5765.66	−	3973.90i	0.321598	−	0.221657i
$686$	−1105.98	−	9094.10i	−0.0615548	−	0.506143i
$687$	−8607.63	+	5122.77i	−0.478023	+	0.284492i
$688$	−4272.04	−	1327.65i	−0.236729	−	0.0735700i
$689$	15152.7			0.837838
$690$	−13539.0	+	6978.60i	−0.746986	+	0.385030i
$691$			28284.1i			1.55713i	0.627563	+	0.778566i	$0.284053\pi$
$691$			28284.1i			1.55713i	−0.627563	+	0.778566i	$0.715947\pi$
$692$	14184.1	+	8567.22i	0.779190	+	0.470631i
$693$	2344.95	−	695.377i	0.128539	−	0.0381172i
$694$	2228.28	−	270.992i	0.121879	−	0.0148224i
$695$	32044.4	+	5895.13i	1.74894	+	0.321748i
$696$	1082.14	+	9409.26i	0.0589345	+	0.512438i
$697$	−17458.4	−	17458.4i	−0.948758	−	0.948758i
$698$	−16597.2	+	21193.1i	−0.900019	+	1.14924i
$699$	−3604.97	−	914.966i	−0.195068	−	0.0495095i
$700$	−3854.03	+	3013.26i	−0.208098	+	0.162701i
$701$	−31041.9			−1.67252			−0.836261	−	0.548332i	$-0.815263\pi$
$701$	−31041.9			−1.67252			−0.836261	+	0.548332i	$0.815263\pi$
$702$	−3245.24	−	20014.6i	−0.174478	−	1.07607i
$703$	−7147.85	+	7147.85i	−0.383480	+	0.383480i
$704$	−6294.98	−	7089.22i	−0.337004	−	0.379524i
$705$	−9285.26	+	20219.8i	−0.496033	+	1.08017i
$706$	15342.6	−	1865.90i	0.817886	−	0.0994675i
$707$	−3953.71	−	3953.71i	−0.210318	−	0.210318i
$708$	18690.3	−	18448.2i	0.992122	−	0.979276i
$709$	8883.00			0.470533			0.235267	−	0.971931i	$-0.424404\pi$
$709$	8883.00			0.470533			0.235267	+	0.971931i	$0.424404\pi$
$710$	20005.4	+	22604.0i	1.05745	+	1.19481i
$711$	−2075.83	−	1126.27i	−0.109493	−	0.0594072i
$712$	25912.9	+	11644.6i	1.36394	+	0.612922i
$713$	14722.9	+	14722.9i	0.773320	+	0.773320i
$714$	−492.800	+	3843.00i	−0.0258299	+	0.201430i
$715$	6003.19	+	8709.94i	0.313995	+	0.455571i
$716$	−16955.3	+	4185.96i	−0.884984	+	0.218487i
$717$	−16122.4	+	9595.15i	−0.839754	+	0.499773i
$718$	9026.22	−	11525.6i	0.469158	−	0.599071i
$719$	−15279.2			−0.792517			−0.396258	−	0.918139i	$-0.629692\pi$
$719$	−15279.2			−0.792517			−0.396258	+	0.918139i	$0.629692\pi$
$720$	3742.85	−	18953.6i	0.193733	−	0.981054i
$721$	6052.75			0.312644
$722$	10276.5	−	13122.1i	0.529710	−	0.676390i
$723$	−24747.3	+	14728.1i	−1.27297	+	0.757601i
$724$	29408.5	−	7260.44i	1.50961	−	0.372696i
$725$	3583.60	−	9410.10i	0.183574	−	0.482044i
$726$	−1847.12	+	14404.4i	−0.0944258	+	0.736360i
$727$	−24400.1	−	24400.1i	−1.24477	−	1.24477i	−0.957999	−	0.286772i	$-0.907418\pi$
$727$	−24400.1	−	24400.1i	−1.24477	−	1.24477i	−0.286772	−	0.957999i	$-0.592582\pi$
$728$	2318.45	−	5159.26i	0.118032	−	0.262658i
$729$	−19620.9	+	1562.11i	−0.996846	+	0.0793636i
$730$	−1188.91	+	19494.1i	−0.0602786	+	0.988367i
$731$	3766.69			0.190583
$732$	−14096.6	+	13914.1i	−0.711783	+	0.702567i
$733$	−10881.4	−	10881.4i	−0.548312	−	0.548312i	0.377640	−	0.925952i	$-0.376736\pi$
$733$	−10881.4	−	10881.4i	−0.548312	−	0.548312i	−0.925952	+	0.377640i	$0.876736\pi$
$734$	16069.5	−	1954.30i	0.808088	−	0.0982759i
$735$	−6441.34	−	17380.9i	−0.323255	−	0.872251i
$736$	13800.6	−	9545.27i	0.691163	−	0.478048i
$737$	−9326.75	+	9326.75i	−0.466153	+	0.466153i
$738$	32099.8	−	13925.0i	1.60110	−	0.694560i
$739$	36732.5			1.82845			0.914226	−	0.405205i	$-0.132800\pi$
$739$	36732.5			1.82845			0.914226	+	0.405205i	$0.132800\pi$
$740$	21765.5	+	19294.5i	1.08124	+	0.958485i
$741$	7999.53	+	2030.33i	0.396586	+	0.100656i
$742$	2530.02	−	3230.60i	0.125175	−	0.159837i
$743$	667.180	+	667.180i	0.0329428	+	0.0329428i	0.723386	−	0.690444i	$-0.242585\pi$
$743$	667.180	+	667.180i	0.0329428	+	0.0329428i	−0.690444	+	0.723386i	$0.742585\pi$
$744$	−26236.5	+	3017.40i	−1.29284	+	0.148687i
$745$	−5646.94	+	30695.2i	−0.277702	+	1.50951i
$746$	23043.9	−	2802.49i	1.13096	−	0.137542i
$747$	−1002.72	−	3381.36i	−0.0491131	−	0.165619i
$748$	6832.94	+	4127.10i	0.334007	+	0.201740i
$749$			1326.53i			0.0647134i
$750$	−12808.5	+	16056.7i	−0.623599	+	0.781744i
$751$	5350.59			0.259981			0.129990	−	0.991515i	$-0.458505\pi$
$751$	5350.59			0.259981			0.129990	+	0.991515i	$0.458505\pi$
$752$	7274.41	−	23407.2i	0.352753	−	1.13507i
$753$	7695.16	−	4579.72i	0.372413	−	0.221639i
$754$	1405.50	+	11556.9i	0.0678848	+	0.558193i
$755$	−15120.0	−	2781.60i	−0.728839	−	0.134083i
$756$	−4809.05	−	2649.92i	−0.231354	−	0.127483i
$757$	−12209.3	+	12209.3i	−0.586203	+	0.586203i	−0.936601	−	0.350398i	$-0.886046\pi$
$757$	−12209.3	+	12209.3i	−0.586203	+	0.586203i	0.350398	+	0.936601i	$0.386046\pi$
$758$	10412.8	−	13296.2i	0.498959	−	0.637124i
$759$	8644.96	+	2194.15i	0.413429	+	0.104931i
$760$	6471.32	+	4467.94i	0.308868	+	0.213249i
$761$			23460.9i			1.11755i	0.829319	+	0.558775i	$0.188729\pi$
$761$			23460.9i			1.11755i	−0.829319	+	0.558775i	$0.811271\pi$
$762$	−9297.09	+	7183.71i	−0.441992	+	0.341520i
$763$	−3136.18	−	3136.18i	−0.148804	−	0.148804i
$764$	−27646.2	+	6825.35i	−1.30917	+	0.323210i
$765$	1726.69	+	16174.9i	0.0816059	+	0.764452i
$766$	−22373.9	+	2721.01i	−1.05535	+	0.128347i
$767$	22825.7	−	22825.7i	1.07456	−	1.07456i
$768$	−1399.19	+	21237.4i	−0.0657407	+	0.997837i
$769$		−	20164.4i		−	0.945577i	−0.881176	−	0.472788i	$-0.843248\pi$
$769$		−	20164.4i		−	0.945577i	0.881176	−	0.472788i	$-0.156752\pi$
$770$	2859.34	+	174.386i	0.133823	+	0.00816158i
$771$	6278.18	−	24736.1i	0.293260	−	1.15545i
$772$	−27666.6	−	16710.7i	−1.28982	−	0.779054i
$773$	−20428.0	+	20428.0i	−0.950508	+	0.950508i	−0.998832	−	0.0483241i	$-0.984612\pi$
$773$	−20428.0	+	20428.0i	−0.950508	+	0.950508i	0.0483241	+	0.998832i	$0.484612\pi$
$774$	−1960.63	+	4964.97i	−0.0910508	+	0.230571i
$775$	26238.8	+	9992.38i	1.21616	+	0.463144i
$776$	−1164.58	−	3065.45i	−0.0538736	−	0.141808i
$777$	7103.73	−	4227.73i	0.327986	−	0.195198i
$778$	−17429.1	−	13649.4i	−0.803165	−	0.628993i
$779$			14242.4i			0.655052i
$780$	4448.78	−	23327.1i	0.204220	−	1.07083i
$781$		−	17675.3i		−	0.809825i
$782$	−8711.19	+	11123.4i	−0.398352	+	0.508659i
$783$	11292.6	−	448.820i	0.515409	−	0.0204847i
$784$	9503.55	+	18074.0i	0.432924	+	0.823342i
$785$	−2776.57	+	1913.71i	−0.126242	+	0.0870106i
$786$	4105.03	−	32012.2i	0.186287	−	1.45272i
$787$	12526.6	−	12526.6i	0.567378	−	0.567378i	−0.364015	−	0.931393i	$-0.618594\pi$
$787$	12526.6	−	12526.6i	0.567378	−	0.567378i	0.931393	+	0.364015i	$0.118594\pi$
$788$	4529.55	−	7499.25i	0.204770	−	0.339022i
$789$	−17047.6	−	4326.79i	−0.769214	−	0.195232i
$790$	−1833.19	−	2071.32i	−0.0825596	−	0.0932840i
$791$		−	5297.99i		−	0.238148i
$792$	−8996.70	+	6858.45i	−0.403641	+	0.307707i
$793$	−17215.6	+	17215.6i	−0.770927	+	0.770927i
$794$	1187.61	+	9765.33i	0.0530817	+	0.436472i
$795$	7189.53	−	15656.1i	0.320738	−	0.698445i
$796$	−3238.35	+	799.490i	−0.144196	+	0.0355995i
$797$	14857.7	+	14857.7i	0.660334	+	0.660334i	0.955459	−	0.295125i	$-0.0953612\pi$
$797$	14857.7	+	14857.7i	0.660334	+	0.660334i	−0.295125	+	0.955459i	$0.595361\pi$
$798$	1768.55	−	1366.53i	0.0784535	−	0.0606197i
$799$			20638.3i			0.913806i
$800$	11714.2	−	19359.2i	0.517700	−	0.855562i
$801$	16166.1	−	29795.8i	0.713112	−	1.31434i
$802$	4722.47	+	3698.36i	0.207925	+	0.162835i
$803$	8086.57	−	8086.57i	0.355378	−	0.355378i
$804$	29609.9	+	192.945i	1.29883	+	0.00846348i
$805$	−917.355	+	4986.50i	−0.0401646	+	0.218324i
$806$	−32224.9	+	3919.04i	−1.40828	+	0.171268i
$807$	3776.97	+	6346.33i	0.164753	+	0.276830i
$808$	23589.1	+	10600.4i	1.02706	+	0.461536i
$809$	12005.1			0.521726			0.260863	−	0.965376i	$-0.415993\pi$
$809$	12005.1			0.521726			0.260863	+	0.965376i	$0.415993\pi$
$810$	−22219.4	−	6143.34i	−0.963838	−	0.266488i
$811$		−	13671.8i		−	0.591965i	−0.955193	−	0.295982i	$-0.904353\pi$
$811$		−	13671.8i		−	0.591965i	0.955193	−	0.295982i	$-0.0956470\pi$
$812$	2698.65	+	1629.98i	0.116630	+	0.0704449i
$813$	1417.64	−	843.700i	0.0611549	−	0.0363959i
$814$	−2056.17	−	16907.2i	−0.0885366	−	0.728005i
$815$	−1112.34	−	1613.88i	−0.0478081	−	0.0693641i
$816$	−4181.79	−	17425.6i	−0.179402	−	0.747570i
$817$	−1536.41	−	1536.41i	−0.0657921	−	0.0657921i
$818$	−17841.0	−	13972.1i	−0.762588	−	0.597215i
$819$	−5932.35	−	3218.68i	−0.253105	−	0.137326i
$820$	40906.8	−	2461.81i	1.74211	−	0.104842i
$821$	42878.8			1.82275			0.911376	−	0.411575i	$-0.135021\pi$
$821$	42878.8			1.82275			0.911376	+	0.411575i	$0.135021\pi$
$822$	5628.17	+	7283.93i	0.238814	+	0.309071i
$823$	−9876.45	+	9876.45i	−0.418313	+	0.418313i	−0.884622	−	0.466309i	$-0.845583\pi$
$823$	−9876.45	+	9876.45i	−0.418313	+	0.418313i	0.466309	+	0.884622i	$0.345583\pi$
$824$	−26170.5	+	9942.27i	−1.10642	+	0.420334i
$825$	11847.7	−	2070.01i	0.499979	−	0.0873557i
$826$	−1055.34	−	8677.70i	−0.0444553	−	0.365540i
$827$	−4437.22	−	4437.22i	−0.186575	−	0.186575i	0.607639	−	0.794214i	$-0.292117\pi$
$827$	−4437.22	−	4437.22i	−0.186575	−	0.186575i	−0.794214	+	0.607639i	$0.792117\pi$
$828$	−10127.7	−	17272.4i	−0.425074	−	0.724947i
$829$	−2940.19			−0.123181			−0.0615905	−	0.998102i	$-0.519617\pi$
$829$	−2940.19			−0.123181			−0.0615905	+	0.998102i	$0.519617\pi$
$830$	251.460	−	4123.10i	0.0105160	−	0.172427i
$831$	−4262.27	+	16793.4i	−0.177926	+	0.701030i
$832$	−1549.73	+	26115.5i	−0.0645762	+	1.08821i
$833$	−12157.7	−	12157.7i	−0.505688	−	0.505688i
$834$	−5447.66	+	42482.4i	−0.226183	+	1.76384i
$835$	−13851.4	+	9546.88i	−0.574070	+	0.395669i
$836$	−1103.69	−	4470.53i	−0.0456604	−	0.184948i
$837$	1251.47	+	31488.0i	0.0516813	+	1.30034i
$838$	−15874.8	−	12432.2i	−0.654398	−	0.512487i
$839$	−41157.8			−1.69359			−0.846796	−	0.531917i	$-0.821472\pi$
$839$	−41157.8			−1.69359			−0.846796	+	0.531917i	$0.821472\pi$
$840$	−4230.62	−	4843.40i	−0.173774	−	0.198944i
$841$	17899.9			0.733934
$842$	−14321.0	−	11215.4i	−0.586144	−	0.459035i
$843$	−5569.08	−	9357.56i	−0.227532	−	0.382315i
$844$	−45172.8	+	11152.4i	−1.84231	+	0.454834i
$845$	837.198	−	4550.78i	0.0340834	−	0.185268i
$846$	−27203.9	−	10742.6i	−1.10554	−	0.436570i
$847$	3418.19	+	3418.19i	0.138666	+	0.138666i
$848$	−5632.54	+	18124.1i	−0.228092	+	0.733943i
$849$	−7564.21	−	1919.85i	−0.305775	−	0.0776078i
$850$	−4581.35	+	18492.9i	−0.184869	+	0.746237i
$851$	30144.7			1.21427
$852$	−28240.0	+	27874.4i	−1.13555	+	1.12085i
$853$	17740.4	+	17740.4i	0.712099	+	0.712099i	0.966974	−	0.254875i	$-0.0820343\pi$
$853$	17740.4	+	17740.4i	0.712099	+	0.712099i	−0.254875	+	0.966974i	$0.582034\pi$
$854$	795.962	+	6544.91i	0.0318937	+	0.262251i
$855$	5893.35	−	7301.96i	0.235729	−	0.292072i
$856$	−2178.96	−	5735.56i	−0.0870039	−	0.229016i
$857$	−5027.71	+	5027.71i	−0.200401	+	0.200401i	−0.800172	−	0.599771i	$-0.795258\pi$
$857$	−5027.71	+	5027.71i	−0.200401	+	0.200401i	0.599771	+	0.800172i	$0.295258\pi$
$858$	−11003.5	+	8502.24i	−0.437825	+	0.338300i
$859$	27281.6			1.08363			0.541813	−	0.840499i	$-0.317738\pi$
$859$	27281.6			1.08363			0.541813	+	0.840499i	$0.317738\pi$
$860$	−4147.29	+	4678.43i	−0.164444	+	0.185504i
$861$	2865.27	−	11289.2i	0.113412	−	0.446846i
$862$	−2601.14	−	2037.07i	−0.102779	−	0.0804904i
$863$	−15232.3	−	15232.3i	−0.600828	−	0.600828i	0.339704	−	0.940532i	$-0.389673\pi$
$863$	−15232.3	−	15232.3i	−0.600828	−	0.600828i	−0.940532	+	0.339704i	$0.889673\pi$
$864$	25145.8	+	3558.20i	0.990136	+	0.140107i
$865$	19067.9	−	13142.2i	0.749511	−	0.516589i
$866$	5637.86	+	46358.1i	0.221227	+	1.81907i
$867$	−5339.29	−	8971.45i	−0.209149	−	0.351426i
$868$	−4545.00	+	7524.82i	−0.177727	+	0.294250i
$869$			1619.68i			0.0632265i
$870$	12607.7	+	4031.24i	0.491312	+	0.157094i
$871$	36397.1			1.41592
$872$	18711.5	+	8408.51i	0.726665	+	0.326546i
$873$	−3751.43	+	1112.46i	−0.145437	+	0.0431283i
$874$	8090.40	−	983.917i	0.313114	−	0.0380795i
$875$	1622.50	+	6641.70i	0.0626863	+	0.256606i
$876$	−25672.7	−	167.289i	−0.990182	−	0.00645225i
$877$	−19026.8	+	19026.8i	−0.732598	+	0.732598i	−0.971134	−	0.238535i	$-0.923333\pi$
$877$	−19026.8	+	19026.8i	−0.732598	+	0.732598i	0.238535	+	0.971134i	$0.423333\pi$
$878$	−5970.58	−	4675.82i	−0.229496	−	0.179728i
$879$	7110.26	−	28014.5i	0.272836	−	1.07498i
$880$	−12649.5	+	3942.76i	−0.484560	+	0.151035i
$881$			11104.8i			0.424664i	0.977198	+	0.212332i	$0.0681058\pi$
$881$			11104.8i			0.424664i	−0.977198	+	0.212332i	$0.931894\pi$
$882$	22353.6	−	9697.07i	0.853386	−	0.370201i
$883$	−20205.9	−	20205.9i	−0.770083	−	0.770083i	0.208038	−	0.978121i	$-0.433292\pi$
$883$	−20205.9	−	20205.9i	−0.770083	−	0.770083i	−0.978121	+	0.208038i	$0.933292\pi$
$884$	−5279.69	−	21385.5i	−0.200877	−	0.813655i
$885$	−12753.9	−	34414.2i	−0.484425	−	1.30714i
$886$	79.2925	+	651.994i	0.00300664	+	0.0247225i
$887$	−29931.3	+	29931.3i	−1.13303	+	1.13303i	−0.143356	+	0.989671i	$0.545789\pi$
$887$	−29931.3	+	29931.3i	−1.13303	+	1.13303i	−0.989671	+	0.143356i	$0.954211\pi$
$888$	−23770.1	+	29948.2i	−0.898281	+	1.13175i
$889$			3910.92i			0.147546i
$890$	29731.1	−	26313.1i	1.11976	−	0.991029i
$891$	7358.87	+	11316.7i	0.276691	+	0.425503i
$892$	−27037.7	−	16330.8i	−1.01490	−	0.612998i
$893$	8418.25	−	8418.25i	0.315460	−	0.315460i
$894$	−40693.9	−	5218.30i	−1.52238	−	0.195219i
$895$	−4416.03	+	24004.4i	−0.164929	+	0.896511i
$896$	5309.17	+	4690.89i	0.197954	+	0.174901i
$897$	−12587.0	−	21149.5i	−0.468525	−	0.787248i
$898$	−12632.9	+	16131.1i	−0.469450	+	0.599444i
$899$		−	18094.0i		−	0.671266i
$900$	−21991.3	−	15664.7i	−0.814493	−	0.580173i
$901$		−	15980.1i		−	0.590872i
$902$	−18892.6	−	14795.6i	−0.697400	−	0.546164i
$903$	908.738	+	1526.93i	0.0334894	+	0.0562712i
$904$	8702.49	+	22907.1i	0.320178	+	0.842786i
$905$	7659.50	−	41635.0i	0.281337	−	1.52927i
$906$	2570.46	−	20045.2i	0.0942579	−	0.735051i
$907$	−13344.7	+	13344.7i	−0.488537	+	0.488537i	−0.907844	−	0.419308i	$-0.862273\pi$
$907$	−13344.7	+	13344.7i	−0.488537	+	0.488537i	0.419308	+	0.907844i	$0.362273\pi$
$908$	24716.3	−	40920.9i	0.903346	−	1.49560i
$909$	14716.4	−	27123.9i	0.536979	−	0.989706i
$910$	−5238.94	−	5919.47i	−0.190845	−	0.215636i
$911$			16222.6i			0.589987i	0.955499	+	0.294994i	$0.0953175\pi$
$911$			16222.6i			0.589987i	−0.955499	+	0.294994i	$0.904682\pi$
$912$	−5402.06	+	8813.52i	−0.196141	+	0.320005i
$913$	−1710.35	+	1710.35i	−0.0619982	+	0.0619982i
$914$	21195.7	−	2577.72i	0.767059	−	0.0932862i
$915$	9619.23	+	25955.9i	0.347543	+	0.937789i
$916$	−3696.36	−	14972.2i	−0.133331	−	0.540059i
$917$	−7596.55	−	7596.55i	−0.273566	−	0.273566i
$918$	−21107.6	+	3422.47i	−0.758884	+	0.123048i
$919$		−	39369.4i		−	1.41314i	−0.707643	−	0.706570i	$-0.750241\pi$
$919$		−	39369.4i		−	1.41314i	0.707643	−	0.706570i	$-0.249759\pi$
$920$	−4224.43	−	23067.1i	−0.151386	−	0.826631i
$921$	7385.20	−	29097.7i	0.264224	−	1.04105i
$922$	−2957.08	+	3775.91i	−0.105625	+	0.134873i
$923$	−34488.5	+	34488.5i	−1.22990	+	1.22990i
$924$	−24.5375	+	3765.60i	−0.000873620	+	0.134068i
$925$	37091.1	−	16632.0i	1.31843	−	0.591197i
$926$	5650.61	+	46463.0i	0.200530	+	1.64889i
$927$	9497.31	+	32026.8i	0.336497	+	1.13473i
$928$	−14345.6	−	2614.81i	−0.507456	−	0.0924951i
$929$	−3033.88			−0.107146			−0.0535728	−	0.998564i	$-0.517061\pi$
$929$	−3033.88			−0.107146			−0.0535728	+	0.998564i	$0.517061\pi$
$930$	−11240.6	+	35155.0i	−0.396337	+	1.23954i
$931$			9918.09i			0.349143i
$932$	2960.51	−	4901.50i	0.104050	−	0.172268i
$933$	17320.7	+	29103.5i	0.607776	+	1.02123i
$934$	47897.0	−	5825.01i	1.67798	−	0.204069i
$935$	9185.59	−	6331.03i	0.321284	−	0.221440i
$936$	30936.9	+	4172.22i	1.08035	+	0.145698i
$937$	−609.065	−	609.065i	−0.0212351	−	0.0212351i	0.696410	−	0.717645i	$-0.254780\pi$
$937$	−609.065	−	609.065i	−0.0212351	−	0.0212351i	−0.717645	+	0.696410i	$0.754780\pi$
$938$	6077.18	−	7760.00i	0.211543	−	0.270120i
$939$	8602.81	−	33895.1i	0.298980	−	1.17798i
$940$	−25633.9	−	22723.7i	−0.889454	−	0.788474i
$941$	−11642.3			−0.403326			−0.201663	−	0.979455i	$-0.564635\pi$
$941$	−11642.3			−0.403326			−0.201663	+	0.979455i	$0.564635\pi$
$942$	−2710.36	−	3507.73i	−0.0937456	−	0.121325i
$943$	30032.2	−	30032.2i	1.03710	−	1.03710i
$944$	18817.0	+	35786.5i	0.648774	+	1.23385i
$945$	−6140.36	+	4602.27i	−0.211371	+	0.158425i
$946$	3634.15	−	441.968i	0.124901	−	0.0151899i
$947$	31917.7	+	31917.7i	1.09523	+	1.09523i	0.994960	+	0.100274i	$0.0319719\pi$
$947$	31917.7	+	31917.7i	1.09523	+	1.09523i	0.100274	+	0.994960i	$0.468028\pi$
$948$	2587.78	−	2554.27i	0.0886573	−	0.0875093i
$949$	−31557.4			−1.07945
$950$	9411.85	−	5674.44i	0.321432	−	0.193793i
$951$	4166.15	+	1057.40i	0.142058	+	0.0360552i
$952$	−5441.00	−	2445.06i	−0.185235	−	0.0832403i
$953$	−26760.5	−	26760.5i	−0.909609	−	0.909609i	0.0866316	−	0.996240i	$-0.472390\pi$
$953$	−26760.5	−	26760.5i	−0.909609	−	0.909609i	−0.996240	+	0.0866316i	$0.972390\pi$
$954$	21063.9	+	8317.95i	0.714851	+	0.282289i
$955$	−7200.50	+	39140.0i	−0.243982	+	1.32622i
$956$	−6923.43	−	28043.5i	−0.234226	−	0.948735i
$957$	−3963.92	−	6660.46i	−0.133893	−	0.224976i
$958$	10222.2	−	13052.8i	0.344744	−	0.440206i
$959$	3064.07			0.103174
$960$	26247.9	+	13992.3i	0.882444	+	0.470417i
$961$	20661.6			0.693553
$962$	−28977.6	+	37001.7i	−0.971180	+	1.24011i
$963$	−7019.04	+	2081.44i	−0.234876	+	0.0696506i
$964$	−10627.2	−	43045.5i	−0.355060	−	1.43818i
$965$	−37192.5	+	25634.4i	−1.24069	+	0.855129i
$966$	−6610.79	−	847.722i	−0.220185	−	0.0282350i
$967$	−17748.1	−	17748.1i	−0.590216	−	0.590216i	0.347473	−	0.937690i	$-0.387040\pi$
$967$	−17748.1	−	17748.1i	−0.590216	−	0.590216i	−0.937690	+	0.347473i	$0.887040\pi$
$968$	−20394.1	−	9164.61i	−0.677159	−	0.304299i
$969$	2141.21	−	8436.38i	0.0709861	−	0.279686i
$970$	−4574.34	−	278.980i	−0.151416	−	0.00923455i
$971$	−40785.0			−1.34794			−0.673971	−	0.738758i	$-0.735413\pi$
$971$	−40785.0			−1.34794			−0.673971	+	0.738758i	$0.735413\pi$
$972$	6475.66	−	29604.0i	0.213690	−	0.976902i
$973$	10081.2	+	10081.2i	0.332155	+	0.332155i
$974$	3831.14	−	465.926i	0.126035	−	0.0153277i
$975$	−27156.5	−	19078.4i	−0.892003	−	0.626664i
$976$	−14192.2	−	26991.0i	−0.465452	−	0.885205i
$977$	13491.6	−	13491.6i	0.441795	−	0.441795i	−0.450820	−	0.892615i	$-0.648868\pi$
$977$	13491.6	−	13491.6i	0.441795	−	0.441795i	0.892615	+	0.450820i	$0.148868\pi$
$978$	2038.86	−	1575.39i	0.0666622	−	0.0515087i
$979$	−23248.4			−0.758959
$980$	28486.7	−	1714.35i	0.928544	−	0.0558806i
$981$	11673.5	−	21515.4i	0.379924	−	0.700237i
$982$	−8251.19	+	10536.0i	−0.268132	+	0.342380i
$983$	17965.7	+	17965.7i	0.582925	+	0.582925i	0.935706	−	0.352781i	$-0.114764\pi$
$983$	17965.7	+	17965.7i	0.582925	+	0.582925i	−0.352781	+	0.935706i	$0.614764\pi$
$984$	6154.98	+	53517.9i	0.199404	+	1.73383i
$985$	−6948.40	−	10081.3i	−0.224766	−	0.326109i
$986$	12188.0	−	1482.25i	0.393657	−	0.0478747i
$987$	−8366.29	+	4979.13i	−0.269809	+	0.160575i
$988$	−6569.45	+	10876.6i	−0.211540	+	0.350232i
$989$			6479.51i			0.208328i
$990$	3563.83	+	15403.2i	0.114410	+	0.494490i
$991$	−8487.26			−0.272055			−0.136028	−	0.990705i	$-0.543434\pi$
$991$	−8487.26			−0.272055			−0.136028	+	0.990705i	$0.543434\pi$
$992$	7291.06	−	40000.9i	0.233358	−	1.28027i
$993$	11571.1	+	19442.6i	0.369787	+	0.621342i
$994$	1594.57	+	13111.6i	0.0508820	+	0.418384i
$995$	−843.433	+	4584.67i	−0.0268730	+	0.146074i
$996$	5429.91	+	35.3825i	0.172744	+	0.00112564i
$997$	15358.5	−	15358.5i	0.487872	−	0.487872i	−0.419762	−	0.907634i	$-0.637887\pi$
$997$	15358.5	−	15358.5i	0.487872	−	0.487872i	0.907634	+	0.419762i	$0.137887\pi$
$998$	9321.73	−	11903.0i	0.295666	−	0.377537i
$999$	33516.5	+	30954.1i	1.06148	+	0.980325i

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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up to: 50 250 1000 (See only

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a_p

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.w.c.77.18	yes	128
3.2	odd	2	inner	120.4.w.c.77.47	yes	128
5.3	odd	4	inner	120.4.w.c.53.50	yes	128
8.5	even	2	inner	120.4.w.c.77.15	yes	128
15.8	even	4	inner	120.4.w.c.53.15	✓	128
24.5	odd	2	inner	120.4.w.c.77.50	yes	128
40.13	odd	4	inner	120.4.w.c.53.47	yes	128
120.53	even	4	inner	120.4.w.c.53.18	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.w.c.53.15	✓	128	15.8	even	4	inner
120.4.w.c.53.18	yes	128	120.53	even	4	inner
120.4.w.c.53.47	yes	128	40.13	odd	4	inner
120.4.w.c.53.50	yes	128	5.3	odd	4	inner
120.4.w.c.77.15	yes	128	8.5	even	2	inner
120.4.w.c.77.18	yes	128	1.1	even	1	trivial
120.4.w.c.77.47	yes	128	3.2	odd	2	inner
120.4.w.c.77.50	yes	128	24.5	odd	2	inner

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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	120.4.w.c.77.18

Level	$120$
Weight	$4$
Character	120.77
Analytic conductor	$7.080$
Analytic rank	$0$
Dimension	$128$
Inner twists	$8$