LMFDB - Embedded newform 120.4.w.c.53.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("120.53");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.3
Character	$\chi$	$=$	120.53
Dual form			120.4.w.c.77.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.79977 + 0.401606i) q^{2} +(4.62659 - 2.36530i) q^{3} +(7.67742 - 2.24881i) q^{4} +(3.00421 - 10.7692i) q^{5} +(-12.0035 + 8.48037i) q^{6} +(13.4333 - 13.4333i) q^{7} +(-20.5919 + 9.37945i) q^{8} +(15.8107 - 21.8866i) q^{9} +(-4.08613 + 31.3577i) q^{10} -30.2559 q^{11} +(30.2012 - 28.5637i) q^{12} +(-25.9300 + 25.9300i) q^{13} +(-32.2154 + 43.0052i) q^{14} +(-11.5730 - 56.9303i) q^{15} +(53.8857 - 34.5301i) q^{16} +(26.6415 + 26.6415i) q^{17} +(-35.4766 + 67.6270i) q^{18} -48.6369 q^{19} +(-1.15320 - 89.4353i) q^{20} +(30.3767 - 93.9245i) q^{21} +(84.7095 - 12.1510i) q^{22} +(59.4674 - 59.4674i) q^{23} +(-73.0850 + 92.1009i) q^{24} +(-106.949 - 64.7056i) q^{25} +(62.1843 - 83.0116i) q^{26} +(21.3814 - 138.657i) q^{27} +(72.9244 - 133.343i) q^{28} -254.245i q^{29} +(55.2654 + 154.744i) q^{30} +240.108 q^{31} +(-137.000 + 118.317i) q^{32} +(-139.982 + 71.5642i) q^{33} +(-85.2896 - 63.8908i) q^{34} +(-104.309 - 185.022i) q^{35} +(72.1668 - 203.588i) q^{36} +(177.892 + 177.892i) q^{37} +(136.172 - 19.5329i) q^{38} +(-58.6353 + 181.300i) q^{39} +(39.1465 + 249.935i) q^{40} -88.8734i q^{41} +(-47.3271 + 275.166i) q^{42} +(-335.874 + 335.874i) q^{43} +(-232.287 + 68.0397i) q^{44} +(-188.201 - 236.020i) q^{45} +(-142.613 + 190.378i) q^{46} +(316.269 + 316.269i) q^{47} +(167.633 - 287.213i) q^{48} -17.9094i q^{49} +(325.420 + 138.209i) q^{50} +(186.275 + 60.2443i) q^{51} +(-140.764 + 257.387i) q^{52} +(53.4606 + 53.4606i) q^{53} +(-4.17744 + 396.795i) q^{54} +(-90.8950 + 325.830i) q^{55} +(-150.620 + 402.615i) q^{56} +(-225.023 + 115.041i) q^{57} +(102.106 + 711.826i) q^{58} +26.0455i q^{59} +(-216.877 - 411.053i) q^{60} -685.352i q^{61} +(-672.246 + 96.4287i) q^{62} +(-81.6190 - 506.400i) q^{63} +(336.052 - 386.281i) q^{64} +(201.345 + 357.143i) q^{65} +(363.176 - 256.581i) q^{66} +(429.061 + 429.061i) q^{67} +(264.450 + 144.627i) q^{68} +(134.473 - 415.790i) q^{69} +(366.348 + 476.129i) q^{70} -2.66287i q^{71} +(-120.288 + 598.981i) q^{72} +(-417.292 - 417.292i) q^{73} +(-569.499 - 426.614i) q^{74} +(-647.860 - 46.3988i) q^{75} +(-373.406 + 109.375i) q^{76} +(-406.438 + 406.438i) q^{77} +(91.3542 - 531.146i) q^{78} +662.246i q^{79} +(-209.977 - 684.039i) q^{80} +(-229.043 - 692.084i) q^{81} +(35.6921 + 248.825i) q^{82} +(915.217 + 915.217i) q^{83} +(21.9966 - 789.410i) q^{84} +(366.944 - 206.870i) q^{85} +(805.481 - 1075.26i) q^{86} +(-601.365 - 1176.29i) q^{87} +(623.026 - 283.784i) q^{88} +470.541 q^{89} +(621.707 + 585.218i) q^{90} +696.653i q^{91} +(322.826 - 590.288i) q^{92} +(1110.88 - 567.927i) q^{93} +(-1012.49 - 758.464i) q^{94} +(-146.115 + 523.779i) q^{95} +(-353.987 + 871.452i) q^{96} +(1209.33 - 1209.33i) q^{97} +(7.19253 + 50.1422i) q^{98} +(-478.367 + 662.197i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$128 q - 4 q^{6} - 144 q^{7} - 156 q^{10} - 56 q^{12} + 212 q^{15} + 636 q^{16} + 220 q^{18} - 188 q^{22} - 8 q^{25} + 908 q^{28} + 328 q^{30} - 544 q^{31} - 1624 q^{33} - 1268 q^{36} - 136 q^{40} + 328 q^{42}+ \cdots - 3792 q^{97}+O(q^{100})$ 128 * q - 4 * q^6 - 144 * q^7 - 156 * q^10 - 56 * q^12 + 212 * q^15 + 636 * q^16 + 220 * q^18 - 188 * q^22 - 8 * q^25 + 908 * q^28 + 328 * q^30 - 544 * q^31 - 1624 * q^33 - 1268 * q^36 - 136 * q^40 + 328 * q^42 + 568 * q^46 - 148 * q^48 + 616 * q^52 + 728 * q^55 - 112 * q^57 + 2196 * q^58 - 424 * q^60 - 2304 * q^63 + 304 * q^66 - 4740 * q^70 + 224 * q^72 + 1280 * q^73 - 1624 * q^76 - 1448 * q^78 + 7056 * q^81 - 1472 * q^82 - 5720 * q^87 + 1516 * q^88 - 996 * q^90 + 2732 * q^96 - 3792 * q^97

Character values

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

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

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−2.79977	+	0.401606i	−0.989868	+	0.141989i
$2$	−2.79977	+	0.401606i	−0.989868	+	0.141989i
$3$	4.62659	−	2.36530i	0.890388	−	0.455202i
$3$	4.62659	−	2.36530i	0.890388	−	0.455202i
$4$	7.67742	−	2.24881i	0.959678	−	0.281101i
$5$	3.00421	−	10.7692i	0.268705	−	0.963223i
$5$	3.00421	−	10.7692i	0.268705	−	0.963223i
$6$	−12.0035	+	8.48037i	−0.816733	+	0.577016i
$7$	13.4333	−	13.4333i	0.725332	−	0.725332i	−0.244354	−	0.969686i	$-0.578576\pi$
$7$	13.4333	−	13.4333i	0.725332	−	0.725332i	0.969686	+	0.244354i	$0.0785758\pi$
$8$	−20.5919	+	9.37945i	−0.910041	+	0.414517i
$9$	15.8107	−	21.8866i	0.585582	−	0.810613i
$10$	−4.08613	+	31.3577i	−0.129215	+	0.991617i
$11$	−30.2559			−0.829317			−0.414659	−	0.909977i	$-0.636099\pi$
$11$	−30.2559			−0.829317			−0.414659	+	0.909977i	$0.636099\pi$
$12$	30.2012	−	28.5637i	0.726528	−	0.687137i
$13$	−25.9300	+	25.9300i	−0.553206	+	0.553206i	−0.927365	−	0.374158i	$-0.877932\pi$
$13$	−25.9300	+	25.9300i	−0.553206	+	0.553206i	0.374158	+	0.927365i	$0.377932\pi$
$14$	−32.2154	+	43.0052i	−0.614994	+	0.820973i
$15$	−11.5730	−	56.9303i	−0.199210	−	0.979957i
$16$	53.8857	−	34.5301i	0.841964	−	0.539533i
$17$	26.6415	+	26.6415i	0.380090	+	0.380090i	0.871134	−	0.491045i	$-0.163385\pi$
$17$	26.6415	+	26.6415i	0.380090	+	0.380090i	−0.491045	+	0.871134i	$0.663385\pi$
$18$	−35.4766	+	67.6270i	−0.464550	+	0.885547i
$19$	−48.6369			−0.587267			−0.293633	−	0.955918i	$-0.594865\pi$
$19$	−48.6369			−0.587267			−0.293633	+	0.955918i	$0.594865\pi$
$20$	−1.15320	−	89.4353i	−0.0128932	−	0.999917i
$21$	30.3767	−	93.9245i	0.315654	−	0.976000i
$22$	84.7095	−	12.1510i	0.820915	−	0.117754i
$23$	59.4674	−	59.4674i	0.539122	−	0.539122i	−0.384149	−	0.923271i	$-0.625505\pi$
$23$	59.4674	−	59.4674i	0.539122	−	0.539122i	0.923271	+	0.384149i	$0.125505\pi$
$24$	−73.0850	+	92.1009i	−0.621601	+	0.783334i
$25$	−106.949	−	64.7056i	−0.855596	−	0.517645i
$26$	62.1843	−	83.0116i	0.469052	−	0.626151i
$27$	21.3814	−	138.657i	0.152402	−	0.988319i
$28$	72.9244	−	133.343i	0.492194	−	0.899977i
$29$		−	254.245i		−	1.62800i	−0.580864	−	0.814001i	$-0.697285\pi$
$29$		−	254.245i		−	1.62800i	0.580864	−	0.814001i	$-0.302715\pi$
$30$	55.2654	+	154.744i	0.336335	+	0.941743i
$31$	240.108			1.39112			0.695558	−	0.718470i	$-0.255157\pi$
$31$	240.108			1.39112			0.695558	+	0.718470i	$0.255157\pi$
$32$	−137.000	+	118.317i	−0.756826	+	0.653617i
$33$	−139.982	+	71.5642i	−0.738414	+	0.377507i
$34$	−85.2896	−	63.8908i	−0.430207	−	0.322270i
$35$	−104.309	−	185.022i	−0.503756	−	0.893557i
$36$	72.1668	−	203.588i	0.334106	−	0.942536i
$37$	177.892	+	177.892i	0.790412	+	0.790412i	0.981561	−	0.191149i	$-0.0612215\pi$
$37$	177.892	+	177.892i	0.790412	+	0.790412i	−0.191149	+	0.981561i	$0.561221\pi$
$38$	136.172	−	19.5329i	0.581317	−	0.0833856i
$39$	−58.6353	+	181.300i	−0.240748	+	0.744389i
$40$	39.1465	+	249.935i	0.154740	+	0.987955i
$41$		−	88.8734i		−	0.338529i	−0.985571	−	0.169265i	$-0.945861\pi$
$41$		−	88.8734i		−	0.338529i	0.985571	−	0.169265i	$-0.0541392\pi$
$42$	−47.3271	+	275.166i	−0.173875	+	1.01093i
$43$	−335.874	+	335.874i	−1.19117	+	1.19117i	−0.214430	+	0.976739i	$0.568789\pi$
$43$	−335.874	+	335.874i	−1.19117	+	1.19117i	−0.976739	+	0.214430i	$0.931211\pi$
$44$	−232.287	+	68.0397i	−0.795878	+	0.233122i
$45$	−188.201	−	236.020i	−0.623453	−	0.781861i
$46$	−142.613	+	190.378i	−0.457111	+	0.610210i
$47$	316.269	+	316.269i	0.981543	+	0.981543i	0.999833	−	0.0182899i	$-0.00582219\pi$
$47$	316.269	+	316.269i	0.981543	+	0.981543i	−0.0182899	+	0.999833i	$0.505822\pi$
$48$	167.633	−	287.213i	0.504078	−	0.863658i
$49$		−	17.9094i		−	0.0522140i
$50$	325.420	+	138.209i	0.920427	+	0.390915i
$51$	186.275	+	60.2443i	0.511445	+	0.165410i
$52$	−140.764	+	257.387i	−0.375393	+	0.686407i
$53$	53.4606	+	53.4606i	0.138554	+	0.138554i	0.772982	−	0.634428i	$-0.218764\pi$
$53$	53.4606	+	53.4606i	0.138554	+	0.138554i	−0.634428	+	0.772982i	$0.718764\pi$
$54$	−4.17744	+	396.795i	−0.0105274	+	0.999945i
$55$	−90.8950	+	325.830i	−0.222841	+	0.798817i
$56$	−150.620	+	402.615i	−0.359420	+	0.960745i
$57$	−225.023	+	115.041i	−0.522896	+	0.267325i
$58$	102.106	+	711.826i	0.231159	+	1.61151i
$59$			26.0455i			0.0574718i	0.999587	+	0.0287359i	$0.00914818\pi$
$59$			26.0455i			0.0574718i	−0.999587	+	0.0287359i	$0.990852\pi$
$60$	−216.877	−	411.053i	−0.466644	−	0.884445i
$61$		−	685.352i		−	1.43853i	−0.694735	−	0.719266i	$-0.744478\pi$
$61$		−	685.352i		−	1.43853i	0.694735	−	0.719266i	$-0.255522\pi$
$62$	−672.246	+	96.4287i	−1.37702	+	0.197524i
$63$	−81.6190	−	506.400i	−0.163223	−	1.01271i
$64$	336.052	−	386.281i	0.656351	−	0.754456i
$65$	201.345	+	357.143i	0.384212	+	0.681510i
$66$	363.176	−	256.581i	0.677331	−	0.478529i
$67$	429.061	+	429.061i	0.782361	+	0.782361i	0.980229	−	0.197868i	$-0.0634017\pi$
$67$	429.061	+	429.061i	0.782361	+	0.782361i	−0.197868	+	0.980229i	$0.563402\pi$
$68$	264.450	+	144.627i	0.471607	+	0.257920i
$69$	134.473	−	415.790i	0.234618	−	0.725438i
$70$	366.348	+	476.129i	0.625528	+	0.812975i
$71$		−	2.66287i		−	0.00445105i	−0.999998	−	0.00222553i	$-0.999292\pi$
$71$		−	2.66287i		−	0.00445105i	0.999998	−	0.00222553i	$-0.000708408\pi$
$72$	−120.288	+	598.981i	−0.196891	+	0.980425i
$73$	−417.292	−	417.292i	−0.669046	−	0.669046i	0.288449	−	0.957495i	$-0.406860\pi$
$73$	−417.292	−	417.292i	−0.669046	−	0.669046i	−0.957495	+	0.288449i	$0.906860\pi$
$74$	−569.499	−	426.614i	−0.894633	−	0.670173i
$75$	−647.860	−	46.3988i	−0.997445	−	0.0714356i
$76$	−373.406	+	109.375i	−0.563587	+	0.165081i
$77$	−406.438	+	406.438i	−0.601531	+	0.601531i
$78$	91.3542	−	531.146i	0.132613	−	0.771031i
$79$			662.246i			0.943146i	0.881827	+	0.471573i	$0.156314\pi$
$79$			662.246i			0.943146i	−0.881827	+	0.471573i	$0.843686\pi$
$80$	−209.977	−	684.039i	−0.293451	−	0.955974i
$81$	−229.043	−	692.084i	−0.314188	−	0.949361i
$82$	35.6921	+	248.825i	0.0480675	+	0.335099i
$83$	915.217	+	915.217i	1.21034	+	1.21034i	0.970915	+	0.239424i	$0.0769587\pi$
$83$	915.217	+	915.217i	1.21034	+	1.21034i	0.239424	+	0.970915i	$0.423041\pi$
$84$	21.9966	−	789.410i	0.0285717	−	1.02538i
$85$	366.944	−	206.870i	0.468243	−	0.263979i
$86$	805.481	−	1075.26i	1.00997	−	1.34823i
$87$	−601.365	−	1176.29i	−0.741070	−	1.44955i
$88$	623.026	−	283.784i	0.754713	−	0.343766i
$89$	470.541			0.560418			0.280209	−	0.959939i	$-0.409596\pi$
$89$	470.541			0.560418			0.280209	+	0.959939i	$0.409596\pi$
$90$	621.707	+	585.218i	0.728152	+	0.685416i
$91$			696.653i			0.802517i
$92$	322.826	−	590.288i	0.365836	−	0.668932i
$93$	1110.88	−	567.927i	1.23863	−	0.633239i
$94$	−1012.49	−	758.464i	−1.11097	−	0.832229i
$95$	−146.115	+	523.779i	−0.157801	+	0.565669i
$96$	−353.987	+	871.452i	−0.376341	+	0.926481i
$97$	1209.33	−	1209.33i	1.26586	−	1.26586i	0.317659	−	0.948205i	$-0.397103\pi$
$97$	1209.33	−	1209.33i	1.26586	−	1.26586i	0.948205	−	0.317659i	$-0.102897\pi$
$98$	7.19253	+	50.1422i	0.00741383	+	0.0516850i
$99$	−478.367	+	662.197i	−0.485633	+	0.672256i
$100$	−966.607	−	256.263i	−0.966607	−	0.256263i
$101$	252.030			0.248296			0.124148	−	0.992264i	$-0.460380\pi$
$101$	252.030			0.248296			0.124148	+	0.992264i	$0.460380\pi$
$102$	−545.721	−	93.8611i	−0.529749	−	0.0911140i
$103$	524.072	+	524.072i	0.501343	+	0.501343i	0.911855	−	0.410512i	$-0.134650\pi$
$103$	524.072	+	524.072i	0.501343	+	0.501343i	−0.410512	+	0.911855i	$0.634650\pi$
$104$	290.738	−	777.156i	0.274127	−	0.732754i
$105$	−920.230	−	609.300i	−0.855288	−	0.566301i
$106$	−171.148	−	128.207i	−0.156824	−	0.117477i
$107$	−1004.13	+	1004.13i	−0.907227	+	0.907227i	−0.996048	−	0.0888208i	$-0.971690\pi$
$107$	−1004.13	+	1004.13i	−0.907227	+	0.907227i	0.0888208	+	0.996048i	$0.471690\pi$
$108$	−147.660	−	1112.61i	−0.131561	−	0.991308i
$109$	−360.617			−0.316888			−0.158444	−	0.987368i	$-0.550648\pi$
$109$	−360.617			−0.316888			−0.158444	+	0.987368i	$0.550648\pi$
$110$	123.630	−	948.754i	0.107160	−	0.822365i
$111$	1243.80	+	402.265i	1.06357	+	0.343976i
$112$	260.010	−	1187.72i	0.219363	−	1.00204i
$113$	−1187.24	+	1187.24i	−0.988377	+	0.988377i	−0.999933	−	0.0115562i	$-0.996321\pi$
$113$	−1187.24	+	1187.24i	−0.988377	+	0.988377i	0.0115562	+	0.999933i	$0.496321\pi$
$114$	583.812	−	412.459i	0.479640	−	0.338862i
$115$	−461.761	−	819.067i	−0.374430	−	0.664160i
$116$	−571.748	−	1951.94i	−0.457633	−	1.56236i
$117$	157.547	+	977.489i	0.124489	+	0.772384i
$118$	−10.4600	−	72.9214i	−0.00816038	−	0.0568895i
$119$	715.770			0.551383
$120$	772.286	+	1063.75i	0.587498	+	0.809226i
$121$	−415.582			−0.312233
$122$	275.242	+	1918.83i	0.204256	+	1.42396i
$123$	−210.212	−	411.181i	−0.154099	−	0.301422i
$124$	1843.41	−	539.957i	1.33502	−	0.391045i
$125$	−1018.12	+	957.366i	−0.728510	+	0.685036i
$126$	431.888	+	1385.03i	0.305362	+	0.979269i
$127$	12.4897	−	12.4897i	0.00872659	−	0.00872659i	−0.702730	−	0.711457i	$-0.748036\pi$
$127$	12.4897	−	12.4897i	0.00872659	−	0.00872659i	0.711457	+	0.702730i	$0.248036\pi$
$128$	−785.735	+	1216.46i	−0.542576	+	0.840006i
$129$	−759.509	+	2348.39i	−0.518380	+	1.60283i
$130$	−707.150	−	919.057i	−0.477086	−	0.620051i
$131$	141.062			0.0940813			0.0470407	−	0.998893i	$-0.485021\pi$
$131$	141.062			0.0940813			0.0470407	+	0.998893i	$0.485021\pi$
$132$	−913.764	+	864.221i	−0.602522	+	0.569855i
$133$	−653.356	+	653.356i	−0.425964	+	0.425964i
$134$	−1373.59	−	1028.96i	−0.885521	−	0.663347i
$135$	−1428.99	−	646.815i	−0.911020	−	0.412363i
$136$	−798.483	−	298.717i	−0.503451	−	0.188344i
$137$	1404.82	+	1404.82i	0.876073	+	0.876073i	0.993126	−	0.117053i	$-0.0373447\pi$
$137$	1404.82	+	1404.82i	0.876073	+	0.876073i	−0.117053	+	0.993126i	$0.537345\pi$
$138$	−209.510	+	1218.12i	−0.129237	+	0.751401i
$139$	1017.67			0.620990			0.310495	−	0.950575i	$-0.399505\pi$
$139$	1017.67			0.620990			0.310495	+	0.950575i	$0.399505\pi$
$140$	−1216.91	−	1185.92i	−0.734624	−	0.715920i
$141$	2211.32	+	715.176i	1.32075	+	0.427154i
$142$	1.06943	+	7.45543i	0.000632002	+	0.00440596i
$143$	784.534	−	784.534i	0.458784	−	0.458784i
$144$	96.2252	−	1725.32i	0.0556859	−	0.998448i
$145$	−2738.00	−	763.804i	−1.56813	−	0.437451i
$146$	1335.91	+	1000.74i	0.757265	+	0.567270i
$147$	−42.3611	−	82.8595i	−0.0237679	−	0.0464907i
$148$	1765.80	+	965.706i	0.980726	+	0.536355i
$149$			799.958i			0.439833i	0.975519	+	0.219916i	$0.0705785\pi$
$149$			799.958i			0.439833i	−0.975519	+	0.219916i	$0.929422\pi$
$150$	1832.49	−	130.279i	0.997482	−	0.0709147i
$151$	703.514			0.379147			0.189574	−	0.981867i	$-0.439289\pi$
$151$	703.514			0.379147			0.189574	+	0.981867i	$0.439289\pi$
$152$	1001.53	−	456.188i	0.534437	−	0.243432i
$153$	1004.31	−	161.870i	0.530679	−	0.0855321i
$154$	974.704	−	1301.16i	0.510025	−	0.680847i
$155$	721.334	−	2585.76i	0.373799	−	1.33996i
$156$	−42.4593	+	1523.77i	−0.0217914	+	0.782048i
$157$	−1231.09	−	1231.09i	−0.625807	−	0.625807i	0.321203	−	0.947010i	$-0.395913\pi$
$157$	−1231.09	−	1231.09i	−0.625807	−	0.625807i	−0.947010	+	0.321203i	$0.895913\pi$
$158$	−265.962	−	1854.14i	−0.133917	−	0.933590i
$159$	373.791	+	120.890i	0.186437	+	0.0602969i
$160$	862.601	+	1830.82i	0.426216	+	0.904621i
$161$		−	1597.69i		−	0.782086i
$162$	919.213	+	1845.69i	0.445804	+	0.895131i
$163$	2547.34	−	2547.34i	1.22407	−	1.22407i	0.257893	−	0.966173i	$-0.416972\pi$
$163$	2547.34	−	2547.34i	1.22407	−	1.22407i	0.966173	−	0.257893i	$-0.0830283\pi$
$164$	−199.859	−	682.319i	−0.0951609	−	0.324879i
$165$	350.153	+	1722.48i	0.165208	+	0.812695i
$166$	−2929.96	−	2194.84i	−1.36993	−	1.02622i
$167$	−703.709	−	703.709i	−0.326076	−	0.326076i	0.525016	−	0.851092i	$-0.324059\pi$
$167$	−703.709	−	703.709i	−0.326076	−	0.326076i	−0.851092	+	0.525016i	$0.824059\pi$
$168$	255.447	+	2219.00i	0.117310	+	1.01904i
$169$			852.272i			0.387926i
$170$	−944.278	+	726.556i	−0.426016	+	0.327790i
$171$	−768.984	+	1064.49i	−0.343893	+	0.476046i
$172$	−1823.33	+	3333.96i	−0.808300	+	1.47798i
$173$	−678.942	−	678.942i	−0.298376	−	0.298376i	0.542002	−	0.840377i	$-0.317667\pi$
$173$	−678.942	−	678.942i	−0.298376	−	0.298376i	−0.840377	+	0.542002i	$0.817667\pi$
$174$	2156.09	+	3051.82i	0.939382	+	1.32964i
$175$	−2305.90	+	567.476i	−0.996056	+	0.245127i
$176$	−1630.36	+	1044.74i	−0.698255	+	0.447444i
$177$	61.6054	+	120.502i	0.0261613	+	0.0511722i
$178$	−1317.41	+	188.972i	−0.554740	+	0.0795733i
$179$			1618.12i			0.675664i	0.941206	+	0.337832i	$0.109694\pi$
$179$			1618.12i			0.675664i	−0.941206	+	0.337832i	$0.890306\pi$
$180$	−1975.66	−	1388.80i	−0.818096	−	0.575082i
$181$			1993.07i			0.818474i	0.912428	+	0.409237i	$0.134205\pi$
$181$			1993.07i			0.818474i	−0.912428	+	0.409237i	$0.865795\pi$
$182$	−279.780	−	1950.47i	−0.113949	−	0.794386i
$183$	−1621.06	−	3170.85i	−0.654823	−	1.28085i
$184$	−666.775	+	1782.32i	−0.267148	+	0.714099i
$185$	2450.17	−	1381.32i	0.973730	−	0.548955i
$186$	−2882.13	+	2036.20i	−1.13617	+	0.802696i
$187$	−806.063	−	806.063i	−0.315215	−	0.315215i
$188$	3139.36	+	1716.90i	1.21788	+	0.666052i
$189$	−1575.41	−	2149.85i	−0.606317	−	0.827402i
$190$	198.737	−	1525.14i	0.0758836	−	0.582344i
$191$			248.208i			0.0940300i	0.998894	+	0.0470150i	$0.0149709\pi$
$191$			248.208i			0.0940300i	−0.998894	+	0.0470150i	$0.985029\pi$
$192$	641.103	−	2582.03i	0.240977	−	0.970531i
$193$	1092.35	+	1092.35i	0.407405	+	0.407405i	0.880833	−	0.473428i	$-0.156984\pi$
$193$	1092.35	+	1092.35i	0.407405	+	0.407405i	−0.473428	+	0.880833i	$0.656984\pi$
$194$	−2900.17	+	3871.52i	−1.07330	+	1.43278i
$195$	1776.29	+	1176.11i	0.652322	+	0.431914i
$196$	−40.2749	−	137.498i	−0.0146774	−	0.0501086i
$197$	3304.03	−	3304.03i	1.19493	−	1.19493i	0.219271	−	0.975664i	$-0.429632\pi$
$197$	3304.03	−	3304.03i	1.19493	−	1.19493i	0.975664	−	0.219271i	$-0.0703678\pi$
$198$	1073.37	−	2046.11i	0.385260	−	0.734399i
$199$			3866.21i			1.37723i	0.725128	+	0.688614i	$0.241780\pi$
$199$			3866.21i			1.37723i	−0.725128	+	0.688614i	$0.758220\pi$
$200$	2809.19	+	329.283i	0.993200	+	0.116419i
$201$	2999.95	+	970.233i	1.05274	+	0.340472i
$202$	−705.626	+	101.217i	−0.245781	+	0.0352554i
$203$	−3415.36	−	3415.36i	−1.18084	−	1.18084i
$204$	1565.59	+	43.6244i	0.537319	+	0.0149722i
$205$	−957.091	−	266.994i	−0.326079	−	0.0909643i
$206$	−1677.75	−	1256.81i	−0.567449	−	0.425078i
$207$	−361.315	−	2241.76i	−0.121320	−	0.752720i
$208$	−501.889	+	2292.62i	−0.167307	+	0.764253i
$209$	1471.55			0.487031
$210$	2821.13	+	1336.33i	0.927031	+	0.439122i
$211$		−	575.392i		−	0.187733i	−0.995585	−	0.0938664i	$-0.970077\pi$
$211$		−	575.392i		−	0.187733i	0.995585	−	0.0938664i	$-0.0299226\pi$
$212$	530.663	+	290.217i	0.171915	+	0.0940198i
$213$	−6.29849	−	12.3200i	−0.00202613	−	0.00396316i
$214$	2408.08	−	3214.61i	0.769218	−	1.02685i
$215$	2608.04	+	4626.11i	0.827289	+	1.46743i
$216$	860.245	+	3055.76i	0.270983	+	0.962584i
$217$	3225.45	−	3225.45i	1.00902	−	1.00902i
$218$	1009.64	−	144.826i	0.313678	−	0.0449947i
$219$	−2917.66	−	943.620i	−0.900262	−	0.291159i
$220$	34.8911	+	2705.94i	0.0106925	+	0.829248i
$221$	−1381.63			−0.420536
$222$	−3643.91	−	626.732i	−1.10164	−	0.189475i
$223$	−3008.11	−	3008.11i	−0.903310	−	0.903310i	0.0924111	−	0.995721i	$-0.470543\pi$
$223$	−3008.11	−	3008.11i	−0.903310	−	0.903310i	−0.995721	+	0.0924111i	$0.970543\pi$
$224$	−250.972	+	3429.77i	−0.0748606	+	1.02304i
$225$	−3107.13	+	1317.71i	−0.920631	+	0.390434i
$226$	2847.21	−	3800.82i	0.838024	−	1.11870i
$227$	997.323	−	997.323i	0.291606	−	0.291606i	−0.546108	−	0.837715i	$-0.683891\pi$
$227$	997.323	−	997.323i	0.291606	−	0.291606i	0.837715	+	0.546108i	$0.183891\pi$
$228$	−1468.89	+	1389.25i	−0.426666	+	0.403533i
$229$	−5420.46			−1.56417			−0.782084	−	0.623173i	$-0.785843\pi$
$229$	−5420.46			−1.56417			−0.782084	+	0.623173i	$0.785843\pi$
$230$	1621.77	+	2107.75i	0.464940	+	0.604265i
$231$	−919.074	+	2841.77i	−0.261778	+	0.809414i
$232$	2384.68	+	5235.38i	0.674835	+	1.48155i
$233$	−3153.68	+	3153.68i	−0.886714	+	0.886714i	−0.994206	−	0.107492i	$-0.965718\pi$
$233$	−3153.68	+	3153.68i	−0.886714	+	0.886714i	0.107492	+	0.994206i	$0.465718\pi$
$234$	−833.660	−	2673.47i	−0.232898	−	0.746882i
$235$	4356.08	−	2455.81i	1.20919	−	0.681699i
$236$	58.5714	+	199.962i	0.0161554	+	0.0551544i
$237$	1566.41	+	3063.94i	0.429322	+	0.839766i
$238$	−2003.99	+	287.458i	−0.545796	+	0.0782904i
$239$	−6261.43			−1.69464			−0.847318	−	0.531085i	$-0.821784\pi$
$239$	−6261.43			−1.69464			−0.847318	+	0.531085i	$0.821784\pi$
$240$	−2589.43	−	2668.11i	−0.696447	−	0.717608i
$241$	3262.64			0.872055			0.436027	−	0.899933i	$-0.356385\pi$
$241$	3262.64			0.872055			0.436027	+	0.899933i	$0.356385\pi$
$242$	1163.53	−	166.900i	0.309069	−	0.0443337i
$243$	−2696.67	−	2660.24i	−0.711900	−	0.702281i
$244$	−1541.23	−	5261.74i	−0.404373	−	1.38053i
$245$	−192.869	−	53.8036i	−0.0502937	−	0.0140301i
$246$	753.679	+	1066.79i	0.195337	+	0.276488i
$247$	1261.15	−	1261.15i	0.324880	−	0.324880i
$248$	−4944.27	+	2252.08i	−1.26597	+	0.576642i
$249$	6399.10	+	2069.57i	1.62862	+	0.526723i
$250$	2466.03	−	3089.29i	0.623861	−	0.781535i
$251$	−647.505			−0.162829			−0.0814147	−	0.996680i	$-0.525944\pi$
$251$	−647.505			−0.162829			−0.0814147	+	0.996680i	$0.525944\pi$
$252$	−1765.42	−	3704.30i	−0.441314	−	0.925989i
$253$	−1799.24	+	1799.24i	−0.447104	+	0.447104i
$254$	−29.9522	+	39.9841i	−0.00739910	+	0.00987726i
$255$	1208.39	−	1825.04i	0.296754	−	0.448189i
$256$	1711.34	−	3721.36i	0.417807	−	0.908536i
$257$	−3097.71	−	3097.71i	−0.751868	−	0.751868i	0.222960	−	0.974828i	$-0.428428\pi$
$257$	−3097.71	−	3097.71i	−0.751868	−	0.751868i	−0.974828	+	0.222960i	$0.928428\pi$
$258$	1183.32	−	6879.99i	0.285544	−	1.66019i
$259$	4779.36			1.14662
$260$	2348.96	+	2289.15i	0.560293	+	0.546028i
$261$	−5564.54	−	4019.79i	−1.31968	−	0.953328i
$262$	−394.941	+	56.6514i	−0.0931281	+	0.0133585i
$263$	1274.72	−	1274.72i	0.298870	−	0.298870i	−0.541701	−	0.840571i	$-0.682220\pi$
$263$	1274.72	−	1274.72i	0.298870	−	0.298870i	0.840571	+	0.541701i	$0.182220\pi$
$264$	2211.25	−	2786.59i	0.515504	−	0.649633i
$265$	736.333	−	415.119i	0.170689	−	0.0962285i
$266$	1566.86	−	2091.64i	0.361166	−	0.482130i
$267$	2177.00	−	1112.97i	0.498990	−	0.255104i
$268$	4258.96	+	2329.21i	0.970737	+	0.530892i
$269$			58.0615i			0.0131601i	0.999978	+	0.00658006i	$0.00209451\pi$
$269$			58.0615i			0.0131601i	−0.999978	+	0.00658006i	$0.997905\pi$
$270$	4260.60	+	1237.04i	0.960341	+	0.278830i
$271$	274.262			0.0614769			0.0307385	−	0.999527i	$-0.490214\pi$
$271$	274.262			0.0614769			0.0307385	+	0.999527i	$0.490214\pi$
$272$	2355.53	+	515.662i	0.525093	+	0.114951i
$273$	1647.79	+	3223.13i	0.365307	+	0.714551i
$274$	−4497.36	−	3368.99i	−0.991590	−	0.742804i
$275$	3235.85	+	1957.72i	0.709560	+	0.429292i
$276$	97.3755	−	3494.60i	0.0212366	−	0.762138i
$277$	−2739.97	−	2739.97i	−0.594328	−	0.594328i	0.344470	−	0.938797i	$-0.388059\pi$
$277$	−2739.97	−	2739.97i	−0.594328	−	0.594328i	−0.938797	+	0.344470i	$0.888059\pi$
$278$	−2849.24	+	408.703i	−0.614699	+	0.0881739i
$279$	3796.27	−	5255.13i	0.814613	−	1.12766i
$280$	3883.33	+	2831.60i	0.828834	+	0.604358i
$281$		−	7305.95i		−	1.55102i	−0.631336	−	0.775510i	$-0.717493\pi$
$281$		−	7305.95i		−	1.55102i	0.631336	−	0.775510i	$-0.282507\pi$
$282$	−6478.39	−	1114.25i	−1.36802	−	0.235293i
$283$	−4572.61	+	4572.61i	−0.960472	+	0.960472i	−0.999248	−	0.0387764i	$-0.987654\pi$
$283$	−4572.61	+	4572.61i	−0.960472	+	0.960472i	0.0387764	+	0.999248i	$0.487654\pi$
$284$	−5.98829	−	20.4440i	−0.00125120	−	0.00427158i
$285$	562.877	+	2768.92i	0.116989	+	0.575496i
$286$	−1881.44	+	2511.59i	−0.388993	+	0.519278i
$287$	−1193.87	−	1193.87i	−0.245546	−	0.245546i
$288$	423.490	+	4869.14i	0.0866472	+	0.996239i
$289$		−	3493.46i		−	0.711064i
$290$	7972.52	+	1038.88i	1.61435	+	0.210362i
$291$	2734.65	−	8455.50i	0.550886	−	1.70333i
$292$	−4142.14	−	2265.32i	−0.830139	−	0.453999i
$293$	6490.04	+	6490.04i	1.29404	+	1.29404i	0.932269	+	0.361766i	$0.117826\pi$
$293$	6490.04	+	6490.04i	1.29404	+	1.29404i	0.361766	+	0.932269i	$0.382174\pi$
$294$	151.878	+	214.975i	0.0301283	+	0.0426449i
$295$	280.488	+	78.2461i	0.0553581	+	0.0154429i
$296$	−5331.66	−	1994.60i	−1.04695	−	0.391668i
$297$	−646.914	+	4195.20i	−0.126390	+	0.819630i
$298$	−321.268	−	2239.70i	−0.0624516	−	0.435377i
$299$			3083.98i			0.596492i
$300$	−5078.24	+	1100.69i	−0.977307	+	0.211828i
$301$			9023.82i			1.72799i
$302$	−1969.68	+	282.536i	−0.375306	+	0.0538348i
$303$	1166.04	−	596.127i	0.221080	−	0.113025i
$304$	−2620.83	+	1679.44i	−0.494458	+	0.316850i
$305$	−7380.67	−	2058.94i	−1.38563	−	0.386540i
$306$	−2746.84	+	856.537i	−0.513158	+	0.160016i
$307$	1998.75	+	1998.75i	0.371579	+	0.371579i	0.868052	−	0.496473i	$-0.165372\pi$
$307$	1998.75	+	1998.75i	0.371579	+	0.371579i	−0.496473	+	0.868052i	$0.665372\pi$
$308$	−2206.39	+	4034.40i	−0.408185	+	0.746367i
$309$	3664.26	+	1185.08i	0.674603	+	0.218177i
$310$	−981.112	+	7529.22i	−0.179753	+	1.37945i
$311$		−	3963.38i		−	0.722646i	−0.932441	−	0.361323i	$-0.882325\pi$
$311$		−	3963.38i		−	0.722646i	0.932441	−	0.361323i	$-0.117675\pi$
$312$	−493.081	−	4283.27i	−0.0894718	−	0.777219i
$313$	−4183.58	−	4183.58i	−0.755495	−	0.755495i	0.220004	−	0.975499i	$-0.429393\pi$
$313$	−4183.58	−	4183.58i	−0.755495	−	0.755495i	−0.975499	+	0.220004i	$0.929393\pi$
$314$	3941.19	+	2952.36i	0.708325	+	0.530609i
$315$	−5698.70	−	642.365i	−1.01932	−	0.114899i
$316$	1489.27	+	5084.34i	0.265119	+	0.905116i
$317$	4334.50	−	4334.50i	0.767980	−	0.767980i	−0.209771	−	0.977751i	$-0.567272\pi$
$317$	4334.50	−	4334.50i	0.767980	−	0.767980i	0.977751	+	0.209771i	$0.0672718\pi$
$318$	−1095.08	−	188.348i	−0.193110	−	0.0332139i
$319$			7692.39i			1.35013i
$320$	−3150.35	−	4779.46i	−0.550344	−	0.834938i
$321$	−2270.64	+	7020.79i	−0.394812	+	1.22076i
$322$	641.643	+	4473.17i	0.111048	+	0.774162i
$323$	−1295.76	−	1295.76i	−0.223214	−	0.223214i
$324$	−3314.83	−	4798.35i	−0.568386	−	0.822762i
$325$	4451.01	−	1095.38i	0.759685	−	0.186957i
$326$	−6108.93	+	8154.99i	−1.03786	+	1.38547i
$327$	−1668.43	+	852.967i	−0.282153	+	0.144248i
$328$	833.584	+	1830.07i	0.140326	+	0.308075i
$329$	8497.09			1.42389
$330$	−1672.10	−	4681.92i	−0.278928	−	0.781003i
$331$			2943.97i			0.488868i	0.969666	+	0.244434i	$0.0786021\pi$
$331$			2943.97i			0.488868i	−0.969666	+	0.244434i	$0.921398\pi$
$332$	9084.66	+	4968.36i	1.50176	+	0.821308i
$333$	6706.03	−	1080.84i	1.10357	−	0.177867i
$334$	2252.84	+	1687.61i	0.369071	+	0.276473i
$335$	5909.62	−	3331.64i	0.963811	−	0.543364i
$336$	−1606.36	−	6110.10i	−0.260815	−	0.992063i
$337$	−3030.00	+	3030.00i	−0.489776	+	0.489776i	−0.908236	−	0.418459i	$-0.862570\pi$
$337$	−3030.00	+	3030.00i	−0.489776	+	0.489776i	0.418459	+	0.908236i	$0.362570\pi$
$338$	−342.278	−	2386.17i	−0.0550813	−	0.383995i
$339$	−2684.71	+	8301.09i	−0.430128	+	1.32995i
$340$	2351.97	−	2413.42i	0.375157	−	0.384959i
$341$	−7264.67			−1.15368
$342$	1725.47	−	3289.17i	0.272815	−	0.520052i
$343$	4367.05	+	4367.05i	0.687460	+	0.687460i
$344$	3765.96	−	10066.6i	0.590253	−	1.57777i
$345$	−4073.72	−	2697.28i	−0.635715	−	0.420918i
$346$	2173.55	+	1628.21i	0.337719	+	0.252986i
$347$	−3686.74	+	3686.74i	−0.570359	+	0.570359i	−0.932229	−	0.361869i	$-0.882139\pi$
$347$	−3686.74	+	3686.74i	−0.570359	+	0.570359i	0.361869	+	0.932229i	$0.382139\pi$
$348$	−7262.18	−	7678.49i	−1.11866	−	1.18279i
$349$	6117.27			0.938252			0.469126	−	0.883131i	$-0.344569\pi$
$349$	6117.27			0.938252			0.469126	+	0.883131i	$0.344569\pi$
$350$	6228.09	−	2514.87i	0.951158	−	0.384072i
$351$	3040.96	+	4149.80i	0.462434	+	0.631054i
$352$	4145.06	−	3579.79i	0.627649	−	0.542056i
$353$	−8370.24	+	8370.24i	−1.26205	+	1.26205i	−0.311949	+	0.950099i	$0.600982\pi$
$353$	−8370.24	+	8370.24i	−1.26205	+	1.26205i	−0.950099	+	0.311949i	$0.899018\pi$
$354$	−220.875	−	312.637i	−0.0331621	−	0.0469391i
$355$	−28.6769	−	7.99982i	−0.00428736	−	0.00119602i
$356$	3612.54	−	1058.16i	0.537821	−	0.157534i
$357$	3311.58	−	1693.01i	0.490945	−	0.250991i
$358$	−649.847	−	4530.36i	−0.0959371	−	0.668819i
$359$	−12878.7			−1.89334			−0.946672	−	0.322199i	$-0.895578\pi$
$359$	−12878.7			−1.89334			−0.946672	+	0.322199i	$0.895578\pi$
$360$	6089.15	+	3094.87i	0.891463	+	0.453094i
$361$	−4493.45			−0.655117
$362$	−800.430	−	5580.14i	−0.116215	−	0.810182i
$363$	−1922.73	+	982.976i	−0.278008	+	0.142129i
$364$	1566.64	+	5348.50i	0.225589	+	0.770158i
$365$	−5747.52	+	3240.25i	−0.824216	+	0.464665i
$366$	5812.04	+	8226.61i	0.830055	+	1.17490i
$367$	−4022.31	+	4022.31i	−0.572107	+	0.572107i	−0.932717	−	0.360610i	$-0.882568\pi$
$367$	−4022.31	+	4022.31i	−0.572107	+	0.572107i	0.360610	+	0.932717i	$0.382568\pi$
$368$	1151.03	−	5257.86i	0.163047	−	0.744796i
$369$	−1945.13	−	1405.15i	−0.274416	−	0.198236i
$370$	−6305.16	+	4851.38i	−0.885918	+	0.681652i
$371$	1436.31			0.200996
$372$	7251.54	−	6858.37i	1.01069	−	0.955888i
$373$	1615.59	−	1615.59i	0.224268	−	0.224268i	−0.586025	−	0.810293i	$-0.699308\pi$
$373$	1615.59	−	1615.59i	0.224268	−	0.224268i	0.810293	+	0.586025i	$0.199308\pi$
$374$	2580.51	+	1933.07i	0.356778	+	0.267264i
$375$	−2445.98	+	6837.51i	−0.336827	+	0.941567i
$376$	−9478.99	−	3546.14i	−1.30011	−	0.486378i
$377$	6592.56	+	6592.56i	0.900621	+	0.900621i
$378$	5274.17	+	5386.40i	0.717656	+	0.732928i
$379$	3781.63			0.512531			0.256265	−	0.966606i	$-0.417508\pi$
$379$	3781.63			0.512531			0.256265	+	0.966606i	$0.417508\pi$
$380$	56.0882	+	4349.86i	0.00757174	+	0.587218i
$381$	28.2428	−	87.3263i	0.00379769	−	0.0117424i
$382$	−99.6820	−	694.926i	−0.0133512	−	0.0930773i
$383$	1479.01	−	1479.01i	0.197321	−	0.197321i	−0.601529	−	0.798851i	$-0.705442\pi$
$383$	1479.01	−	1479.01i	0.197321	−	0.197321i	0.798851	+	0.601529i	$0.205442\pi$
$384$	−757.982	+	7486.56i	−0.100731	+	0.994914i
$385$	3155.97	+	5598.01i	0.417774	+	0.741042i
$386$	−3497.02	−	2619.64i	−0.461124	−	0.345430i
$387$	2040.72	+	12661.5i	0.268051	+	1.66310i
$388$	6564.98	−	12004.1i	0.858986	−	1.57066i
$389$		−	2696.62i		−	0.351476i	−0.984437	−	0.175738i	$-0.943769\pi$
$389$		−	2696.62i		−	0.351476i	0.984437	−	0.175738i	$-0.0562312\pi$
$390$	−5445.54	−	2579.48i	−0.707040	−	0.334915i
$391$	3168.61			0.409830
$392$	167.980	+	368.788i	0.0216436	+	0.0475169i
$393$	652.637	−	333.654i	0.0837689	−	0.0428260i
$394$	−7923.60	+	10577.4i	−1.01316	+	1.35250i
$395$	7131.83	+	1989.53i	0.908459	+	0.253428i
$396$	−2183.47	+	6159.73i	−0.277080	+	0.781661i
$397$	−2574.69	−	2574.69i	−0.325491	−	0.325491i	0.525378	−	0.850869i	$-0.323924\pi$
$397$	−2574.69	−	2574.69i	−0.325491	−	0.325491i	−0.850869	+	0.525378i	$0.823924\pi$
$398$	−1552.69	−	10824.5i	−0.195551	−	1.36327i
$399$	−1477.43	+	4568.20i	−0.185373	+	0.573173i
$400$	−7997.34	+	206.274i	−0.999668	+	0.0257842i
$401$		−	2739.10i		−	0.341108i	−0.985348	−	0.170554i	$-0.945444\pi$
$401$		−	2739.10i		−	0.341108i	0.985348	−	0.170554i	$-0.0545557\pi$
$402$	−8788.82	−	1511.63i	−1.09041	−	0.187545i
$403$	−6225.99	+	6225.99i	−0.769575	+	0.769575i
$404$	1934.94	−	566.768i	0.238285	−	0.0697964i
$405$	−8141.25	+	387.434i	−0.998870	+	0.0475352i
$406$	10933.8	+	8190.58i	1.33654	+	1.00121i
$407$	−5382.27	−	5382.27i	−0.655502	−	0.655502i
$408$	−4400.81	+	506.612i	−0.534001	+	0.0614731i
$409$		−	5821.12i		−	0.703755i	−0.936046	−	0.351878i	$-0.885543\pi$
$409$		−	5821.12i		−	0.703755i	0.936046	−	0.351878i	$-0.114457\pi$
$410$	2786.86	+	363.148i	0.335691	+	0.0437430i
$411$	9822.36	+	3176.71i	1.17884	+	0.381255i
$412$	5202.06	+	2844.99i	0.622056	+	0.340200i
$413$	349.878	+	349.878i	0.0416862	+	0.0416862i
$414$	1911.90	+	6131.30i	0.226968	+	0.727868i
$415$	12605.6	−	7106.62i	1.49105	−	0.840603i
$416$	484.444	−	6620.37i	0.0570957	−	0.780266i
$417$	4708.34	−	2407.10i	0.552922	−	0.282676i
$418$	−4120.01	+	590.985i	−0.482096	+	0.0691531i
$419$		−	9092.51i		−	1.06014i	−0.847954	−	0.530070i	$-0.822166\pi$
$419$		−	9092.51i		−	1.06014i	0.847954	−	0.530070i	$-0.177834\pi$
$420$	−8435.19	−	2608.44i	−0.979989	−	0.303044i
$421$		−	7744.62i		−	0.896555i	−0.893894	−	0.448277i	$-0.852038\pi$
$421$		−	7744.62i		−	0.896555i	0.893894	−	0.448277i	$-0.147962\pi$
$422$	231.081	+	1610.97i	0.0266560	+	0.185831i
$423$	11922.5	−	1921.60i	1.37043	−	0.220878i
$424$	−1602.29	−	599.424i	−0.183523	−	0.0686571i
$425$	−1125.44	−	4573.16i	−0.128452	−	0.521954i
$426$	22.5821	+	31.9637i	0.00256833	+	0.00363532i
$427$	−9206.57	−	9206.57i	−1.04341	−	1.04341i
$428$	−5451.05	+	9967.27i	−0.615623	+	1.12567i
$429$	1774.06	−	5485.38i	0.199656	−	0.617335i
$430$	−9159.80	−	11904.6i	−1.02727	−	1.33510i
$431$			3051.77i			0.341064i	0.985352	+	0.170532i	$0.0545486\pi$
$431$			3051.77i			0.341064i	−0.985352	+	0.170532i	$0.945451\pi$
$432$	−3635.70	−	8209.95i	−0.404914	−	0.914355i
$433$	−254.202	−	254.202i	−0.0282128	−	0.0282128i	0.692860	−	0.721072i	$-0.256351\pi$
$433$	−254.202	−	254.202i	−0.0282128	−	0.0282128i	−0.721072	+	0.692860i	$0.756351\pi$
$434$	−7735.16	+	10325.9i	−0.855528	+	1.14207i
$435$	−14474.2	+	2942.38i	−1.59537	+	0.324314i
$436$	−2768.61	+	810.958i	−0.304111	+	0.0890777i
$437$	−2892.31	+	2892.31i	−0.316609	+	0.316609i
$438$	8547.75	+	1470.17i	0.932482	+	0.160382i
$439$		−	4489.42i		−	0.488082i	−0.969765	−	0.244041i	$-0.921527\pi$
$439$		−	4489.42i		−	0.488082i	0.969765	−	0.244041i	$-0.0784732\pi$
$440$	−1184.41	−	7562.01i	−0.128329	−	0.819328i
$441$	−391.975	−	283.160i	−0.0423254	−	0.0305756i
$442$	3868.24	−	554.871i	0.416275	−	0.0597116i
$443$	1869.97	+	1869.97i	0.200553	+	0.200553i	0.800237	−	0.599684i	$-0.204707\pi$
$443$	1869.97	+	1869.97i	0.200553	+	0.200553i	−0.599684	+	0.800237i	$0.704707\pi$
$444$	10453.8	+	291.291i	1.11738	+	0.0311352i
$445$	1413.60	−	5067.33i	0.150587	−	0.539807i
$446$	9630.10	+	7213.95i	1.02242	+	0.765897i
$447$	1892.14	+	3701.08i	0.200213	+	0.391622i
$448$	−674.751	−	9703.35i	−0.0711585	−	1.02330i
$449$	−14145.1			−1.48674			−0.743370	−	0.668880i	$-0.766774\pi$
$449$	−14145.1			−1.48674			−0.743370	+	0.668880i	$0.766774\pi$
$450$	8170.05	−	4937.14i	0.855866	−	0.517198i
$451$			2688.94i			0.280748i
$452$	−6445.09	+	11784.9i	−0.670690	+	1.22636i
$453$	3254.87	−	1664.02i	0.337588	−	0.172589i
$454$	−2391.74	+	3192.81i	−0.247247	+	0.330057i
$455$	7502.36	+	2092.89i	0.773002	+	0.215640i
$456$	3554.63	−	4479.50i	0.365046	−	0.460026i
$457$	3229.66	−	3229.66i	0.330584	−	0.330584i	−0.522224	−	0.852808i	$-0.674898\pi$
$457$	3229.66	−	3229.66i	0.330584	−	0.330584i	0.852808	+	0.522224i	$0.174898\pi$
$458$	15176.1	−	2176.89i	1.54832	−	0.222095i
$459$	4263.68	−	3124.41i	0.433576	−	0.317723i
$460$	−5387.06	−	5249.91i	−0.546029	−	0.532127i
$461$	2185.14			0.220764			0.110382	−	0.993889i	$-0.464793\pi$
$461$	2185.14			0.220764			0.110382	+	0.993889i	$0.464793\pi$
$462$	1431.92	−	8325.40i	0.144197	−	0.838383i
$463$	−6587.78	−	6587.78i	−0.661253	−	0.661253i	0.294422	−	0.955675i	$-0.404873\pi$
$463$	−6587.78	−	6587.78i	−0.661253	−	0.661253i	−0.955675	+	0.294422i	$0.904873\pi$
$464$	−8779.10	−	13700.2i	−0.878361	−	1.37072i
$465$	−2778.78	−	13669.4i	−0.277124	−	1.36323i
$466$	7563.04	−	10096.1i	0.751826	−	1.00363i
$467$	−170.835	+	170.835i	−0.0169279	+	0.0169279i	−0.715520	−	0.698592i	$-0.753810\pi$
$467$	−170.835	+	170.835i	−0.0169279	+	0.0169279i	0.698592	+	0.715520i	$0.253810\pi$
$468$	3407.74	+	7150.31i	0.336587	+	0.706246i
$469$	11527.5			1.13494
$470$	−11209.8	+	8625.13i	−1.10014	+	0.846484i
$471$	−8607.66	−	2783.86i	−0.842080	−	0.272342i
$472$	−244.293	−	536.326i	−0.0238230	−	0.0523017i
$473$	10162.2	−	10162.2i	0.987858	−	0.987858i
$474$	−5616.09	−	7949.25i	−0.544210	−	0.770298i
$475$	5201.69	+	3147.08i	0.502463	+	0.303996i
$476$	5495.27	−	1609.63i	0.529150	−	0.154994i
$477$	2015.32	−	324.819i	0.193449	−	0.0311791i
$478$	17530.6	−	2514.63i	1.67747	−	0.240620i
$479$	6714.14			0.640452			0.320226	−	0.947341i	$-0.396241\pi$
$479$	6714.14			0.640452			0.320226	+	0.947341i	$0.396241\pi$
$480$	8321.35	+	6430.17i	0.791283	+	0.611450i
$481$	−9225.46			−0.874521
$482$	−9134.65	+	1310.30i	−0.863219	+	0.123822i
$483$	−3779.02	−	7391.87i	−0.356007	−	0.696360i
$484$	−3190.60	+	934.564i	−0.299643	+	0.0877690i
$485$	−9390.38	−	16656.5i	−0.879165	−	1.55945i
$486$	8618.44	+	6365.05i	0.804404	+	0.594083i
$487$	−713.044	+	713.044i	−0.0663472	+	0.0663472i	−0.739502	−	0.673155i	$-0.764939\pi$
$487$	−713.044	+	713.044i	−0.0663472	+	0.0663472i	0.673155	+	0.739502i	$0.264939\pi$
$488$	6428.23	+	14112.7i	0.596296	+	1.30912i
$489$	5760.27	−	17810.7i	0.532696	−	1.64709i
$490$	561.597	+	73.1802i	0.0517763	+	0.00674683i
$491$	4905.98			0.450924			0.225462	−	0.974252i	$-0.427611\pi$
$491$	4905.98			0.450924			0.225462	+	0.974252i	$0.427611\pi$
$492$	−2538.56	−	2684.08i	−0.232616	−	0.245951i
$493$	6773.47	−	6773.47i	0.618786	−	0.618786i
$494$	−3024.45	+	4037.43i	−0.275459	+	0.367718i
$495$	5694.19	+	7140.99i	0.517040	+	0.648411i
$496$	12938.4	−	8290.95i	1.17127	−	0.750554i
$497$	−35.7713	−	35.7713i	−0.00322849	−	0.00322849i
$498$	−18747.2	−	3224.41i	−1.68691	−	0.290139i
$499$	−21912.1			−1.96577			−0.982887	−	0.184209i	$-0.941028\pi$
$499$	−21912.1			−1.96577			−0.982887	+	0.184209i	$0.941028\pi$
$500$	−5663.63	+	9639.67i	−0.506570	+	0.862199i
$501$	−4920.26	−	1591.29i	−0.438764	−	0.141904i
$502$	1812.87	−	260.042i	0.161180	−	0.0231200i
$503$	5722.83	−	5722.83i	0.507293	−	0.507293i	−0.406402	−	0.913695i	$-0.633217\pi$
$503$	5722.83	−	5722.83i	0.507293	−	0.507293i	0.913695	+	0.406402i	$0.133217\pi$
$504$	6430.45	+	9662.20i	0.568323	+	0.853945i
$505$	757.151	−	2714.15i	0.0667184	−	0.239165i
$506$	4314.87	−	5760.04i	0.379090	−	0.506058i
$507$	2015.88	+	3943.12i	0.176585	+	0.345404i
$508$	67.8015	−	123.975i	0.00592166	−	0.0108278i
$509$		−	1543.58i		−	0.134417i	−0.997739	−	0.0672084i	$-0.978591\pi$
$509$		−	1543.58i		−	0.134417i	0.997739	−	0.0672084i	$-0.0214092\pi$
$510$	−2650.26	+	5594.98i	−0.230109	+	0.485784i
$511$	−11211.3			−0.970562
$512$	−3296.83	+	11106.2i	−0.284572	+	0.958655i
$513$	−1039.93	+	6743.86i	−0.0895007	+	0.580407i
$514$	9916.95	+	7428.82i	0.851007	+	0.637493i
$515$	7218.24	−	4069.39i	0.617618	−	0.348192i
$516$	−549.980	+	19737.6i	−0.0469215	+	1.68391i
$517$	−9568.98	−	9568.98i	−0.814010	−	0.814010i
$518$	−13381.1	+	1919.42i	−1.13500	+	0.162808i
$519$	−4747.09	−	1535.29i	−0.401491	−	0.129849i
$520$	−7495.88	−	5465.74i	−0.632146	−	0.460940i
$521$			9459.55i			0.795452i	0.917504	+	0.397726i	$0.130201\pi$
$521$			9459.55i			0.795452i	−0.917504	+	0.397726i	$0.869799\pi$
$522$	17193.8	+	9019.73i	1.44167	+	0.756289i
$523$	−1824.61	+	1824.61i	−0.152552	+	0.152552i	−0.779257	−	0.626705i	$-0.784403\pi$
$523$	−1824.61	+	1824.61i	−0.152552	+	0.152552i	0.626705	+	0.779257i	$0.284403\pi$
$524$	1082.99	−	317.222i	0.0902878	−	0.0264464i
$525$	−9326.21	+	8079.63i	−0.775294	+	0.671665i
$526$	−3056.99	+	4080.87i	−0.253405	+	0.338278i
$527$	6396.84	+	6396.84i	0.528749	+	0.528749i
$528$	−5071.88	+	8689.87i	−0.418041	+	0.716247i
$529$			5094.25i			0.418694i
$530$	−1894.85	+	1457.95i	−0.155296	+	0.119490i
$531$	570.046	+	411.798i	0.0465874	+	0.0336544i
$532$	−3546.82	+	6485.37i	−0.289049	+	0.528527i
$533$	2304.48	+	2304.48i	0.187276	+	0.187276i
$534$	−5648.12	+	3990.36i	−0.457712	+	0.323370i
$535$	7797.05	+	13830.3i	0.630085	+	1.11764i
$536$	−12859.5	−	4810.82i	−1.03628	−	0.387679i
$537$	3827.34	+	7486.38i	0.307564	+	0.601604i
$538$	−23.3178	−	162.559i	−0.00186859	−	0.0130268i
$539$			541.865i			0.0433020i
$540$	−12425.5	−	1752.35i	−0.990201	−	0.139647i
$541$			421.668i			0.0335100i	0.999860	+	0.0167550i	$0.00533354\pi$
$541$			421.668i			0.0335100i	−0.999860	+	0.0167550i	$0.994666\pi$
$542$	−767.871	+	110.145i	−0.0608540	+	0.00872906i
$543$	4714.21	+	9221.13i	0.372571	+	0.728760i
$544$	−6802.05	−	497.738i	−0.536095	−	0.0392286i
$545$	−1083.37	+	3883.54i	−0.0851493	+	0.305234i
$546$	−5907.87	−	8362.25i	−0.463065	−	0.655442i
$547$	−987.491	−	987.491i	−0.0771884	−	0.0771884i	0.667459	−	0.744647i	$-0.267382\pi$
$547$	−987.491	−	987.491i	−0.0771884	−	0.0771884i	−0.744647	+	0.667459i	$0.767382\pi$
$548$	13944.6	+	7626.23i	1.08701	+	0.594483i
$549$	−15000.0	−	10835.9i	−1.16609	−	0.842378i
$550$	−9845.87	−	4181.64i	−0.763326	−	0.324192i
$551$			12365.7i			0.956071i
$552$	1130.82	+	9823.18i	0.0871940	+	0.757432i
$553$	8896.18	+	8896.18i	0.684094	+	0.684094i
$554$	8771.67	+	6570.90i	0.672694	+	0.503918i
$555$	8068.69	−	12186.2i	0.617112	−	0.932027i
$556$	7813.09	−	2288.55i	0.595951	−	0.174561i
$557$	297.033	−	297.033i	0.0225955	−	0.0225955i	−0.695719	−	0.718314i	$-0.744914\pi$
$557$	297.033	−	297.033i	0.0225955	−	0.0225955i	0.718314	+	0.695719i	$0.244914\pi$
$558$	−8518.20	+	16237.8i	−0.646244	+	1.23190i
$559$		−	17418.4i		−	1.31792i
$560$	−12009.6	−	6368.25i	−0.906249	−	0.480549i
$561$	−5635.91	−	1822.74i	−0.424150	−	0.137177i
$562$	2934.12	+	20455.0i	0.220228	+	1.53530i
$563$	−8916.90	−	8916.90i	−0.667500	−	0.667500i	0.289637	−	0.957137i	$-0.406465\pi$
$563$	−8916.90	−	8916.90i	−0.667500	−	0.667500i	−0.957137	+	0.289637i	$0.906465\pi$
$564$	18585.5	+	517.877i	1.38757	+	0.0386641i
$565$	9218.89	+	16352.4i	0.686446	+	1.21761i
$566$	10965.9	−	14638.6i	0.814364	−	1.08712i
$567$	−12373.8	−	6220.19i	−0.916493	−	0.460712i
$568$	24.9763	+	54.8336i	0.00184504	+	0.00405064i
$569$	26385.7			1.94401			0.972007	−	0.234952i	$-0.0754932\pi$
$569$	26385.7			1.94401			0.972007	+	0.234952i	$0.0754932\pi$
$570$	−2687.94	−	7526.27i	−0.197518	−	0.553054i
$571$		−	2486.35i		−	0.182225i	−0.995841	−	0.0911127i	$-0.970958\pi$
$571$		−	2486.35i		−	0.182225i	0.995841	−	0.0911127i	$-0.0290423\pi$
$572$	4258.93	−	7787.47i	0.311320	−	0.569249i
$573$	587.087	+	1148.36i	0.0428026	+	0.0837232i
$574$	3822.02	+	2863.09i	0.277923	+	0.208193i
$575$	−10207.9	+	2512.13i	−0.740345	+	0.182197i
$576$	−3141.15	−	13462.4i	−0.227225	−	0.973842i
$577$	−12978.8	+	12978.8i	−0.936422	+	0.936422i	−0.998096	−	0.0616742i	$-0.980356\pi$
$577$	−12978.8	+	12978.8i	−0.936422	+	0.936422i	0.0616742	+	0.998096i	$0.480356\pi$
$578$	1402.99	+	9780.87i	0.100963	+	0.703859i
$579$	7637.60	+	2470.12i	0.548200	+	0.177297i
$580$	−22738.4	+	293.195i	−1.62787	+	0.0209901i
$581$	24588.9			1.75580
$582$	−4260.60	+	24771.7i	−0.303449	+	1.76430i
$583$	−1617.50	−	1617.50i	−0.114906	−	0.114906i
$584$	12506.8	+	4678.86i	0.886191	+	0.331529i
$585$	11000.0	+	1239.94i	0.777428	+	0.0876327i
$586$	−20777.1	−	15564.2i	−1.46466	−	1.09719i
$587$	−15756.0	+	15756.0i	−1.10787	+	1.10787i	−0.114437	+	0.993430i	$0.536507\pi$
$587$	−15756.0	+	15756.0i	−1.10787	+	1.10787i	−0.993430	+	0.114437i	$0.963493\pi$
$588$	−511.560	−	540.886i	−0.0358782	−	0.0379349i
$589$	−11678.1			−0.816957
$590$	−816.726	−	106.425i	−0.0569900	−	0.00742621i
$591$	7471.37	−	23101.4i	0.520019	−	1.60789i
$592$	15728.5	+	3443.20i	1.09195	+	0.239045i
$593$	−15388.7	+	15388.7i	−1.06567	+	1.06567i	−0.0679791	+	0.997687i	$0.521655\pi$
$593$	−15388.7	+	15388.7i	−1.06567	+	1.06567i	−0.997687	+	0.0679791i	$0.978345\pi$
$594$	126.392	−	12005.4i	0.00873052	−	0.829271i
$595$	2150.32	−	7708.24i	0.148159	−	0.531104i
$596$	1798.95	+	6141.62i	0.123638	+	0.422098i
$597$	9144.74	+	17887.4i	0.626917	+	1.22627i
$598$	−1238.54	−	8634.43i	−0.0846954	−	0.590448i
$599$	−9297.02			−0.634167			−0.317083	−	0.948398i	$-0.602704\pi$
$599$	−9297.02			−0.634167			−0.317083	+	0.948398i	$0.602704\pi$
$600$	13775.8	−	5121.13i	0.937328	−	0.348449i
$601$	−629.406			−0.0427188			−0.0213594	−	0.999772i	$-0.506799\pi$
$601$	−629.406			−0.0427188			−0.0213594	+	0.999772i	$0.506799\pi$
$602$	−3624.02	−	25264.6i	−0.245356	−	1.71048i
$603$	16174.4	−	2606.91i	1.09233	−	0.176056i
$604$	5401.18	−	1582.07i	0.363859	−	0.106579i
$605$	−1248.49	+	4475.46i	−0.0838984	+	0.300750i
$606$	−3025.24	+	2137.31i	−0.202792	+	0.143271i
$607$	−1092.66	+	1092.66i	−0.0730636	+	0.0730636i	−0.742694	−	0.669631i	$-0.766452\pi$
$607$	−1092.66	+	1092.66i	−0.0730636	+	0.0730636i	0.669631	+	0.742694i	$0.266452\pi$
$608$	6663.26	−	5754.59i	0.444459	−	0.383848i
$609$	−23879.8	−	7723.11i	−1.58893	−	0.513886i
$610$	21491.1	+	2800.44i	1.42647	+	0.185880i
$611$	−16401.7			−1.08599
$612$	7346.53	−	3501.26i	0.485238	−	0.231258i
$613$	−8968.39	+	8968.39i	−0.590914	+	0.590914i	−0.937878	−	0.346965i	$-0.887212\pi$
$613$	−8968.39	+	8968.39i	−0.590914	+	0.590914i	0.346965	+	0.937878i	$0.387212\pi$
$614$	−6398.75	−	4793.33i	−0.420574	−	0.315054i
$615$	−5059.59	+	1028.54i	−0.331744	+	0.0674383i
$616$	4557.16	−	12181.5i	0.298073	−	0.796763i
$617$	9216.27	+	9216.27i	0.601350	+	0.601350i	0.940671	−	0.339321i	$-0.110197\pi$
$617$	9216.27	+	9216.27i	0.601350	+	0.601350i	−0.339321	+	0.940671i	$0.610197\pi$
$618$	−10735.0	−	1846.36i	−0.698747	−	0.120181i
$619$	24944.1			1.61969			0.809846	−	0.586642i	$-0.199551\pi$
$619$	24944.1			1.61969			0.809846	+	0.586642i	$0.199551\pi$
$620$	−276.893	−	21474.1i	−0.0179359	−	1.39100i
$621$	−6974.09	−	9517.09i	−0.450661	−	0.614988i
$622$	1591.72	+	11096.6i	0.102608	+	0.715324i
$623$	6320.93	−	6320.93i	0.406489	−	0.406489i
$624$	3100.70	+	11794.1i	0.198922	+	0.756640i
$625$	7251.37	+	13840.5i	0.464088	+	0.885789i
$626$	13393.2	+	10032.9i	0.855112	+	0.640568i
$627$	6808.27	−	3480.66i	0.433646	−	0.221697i
$628$	−12220.1	−	6683.12i	−0.776489	−	0.424658i
$629$			9478.62i			0.600855i
$630$	16213.0	−	490.162i	1.02531	−	0.0309976i
$631$	−13548.3			−0.854751			−0.427376	−	0.904074i	$-0.640562\pi$
$631$	−13548.3			−0.854751			−0.427376	+	0.904074i	$0.640562\pi$
$632$	−6211.51	−	13636.9i	−0.390950	−	0.858302i
$633$	−1360.97	−	2662.10i	−0.0854564	−	0.167155i
$634$	−10394.8	+	13876.4i	−0.651154	+	0.869244i
$635$	−96.9815	−	172.025i	−0.00606078	−	0.0107505i
$636$	3141.61	+	87.5396i	0.195869	+	0.00545782i
$637$	464.391	+	464.391i	0.0288851	+	0.0288851i
$638$	−3089.31	−	21536.9i	−0.191704	−	1.33645i
$639$	−58.2811	−	42.1019i	−0.00360808	−	0.00260646i
$640$	10739.7	+	12116.2i	0.663320	+	0.748335i
$641$		−	19719.3i		−	1.21508i	−0.794290	−	0.607538i	$-0.792157\pi$
$641$		−	19719.3i		−	1.21508i	0.794290	−	0.607538i	$-0.207843\pi$
$642$	3537.67	−	20568.5i	0.217478	−	1.26445i
$643$	3973.80	−	3973.80i	0.243719	−	0.243719i	−0.574668	−	0.818387i	$-0.694869\pi$
$643$	3973.80	−	3973.80i	0.243719	−	0.243719i	0.818387	+	0.574668i	$0.194869\pi$
$644$	−3592.91	−	12266.2i	−0.219845	−	0.750551i
$645$	23008.5	+	15234.3i	1.40459	+	0.930002i
$646$	4148.22	+	3107.45i	0.252647	+	0.189259i
$647$	11028.1	+	11028.1i	0.670107	+	0.670107i	0.957741	−	0.287633i	$-0.0928684\pi$
$647$	11028.1	+	11028.1i	0.670107	+	0.670107i	−0.287633	+	0.957741i	$0.592868\pi$
$648$	11207.8	+	12103.0i	0.679450	+	0.733721i
$649$		−	788.030i		−	0.0476624i
$650$	−12021.9	+	4854.37i	−0.725442	+	0.292930i
$651$	7293.68	−	22552.0i	0.439112	−	1.35773i
$652$	13828.5	−	25285.5i	0.830623	−	1.51880i
$653$	−2459.57	−	2459.57i	−0.147397	−	0.147397i	0.629557	−	0.776954i	$-0.283236\pi$
$653$	−2459.57	−	2459.57i	−0.147397	−	0.147397i	−0.776954	+	0.629557i	$0.783236\pi$
$654$	4328.65	−	3058.16i	0.258813	−	0.182849i
$655$	423.780	−	1519.12i	0.0252801	−	0.0906213i
$656$	−3068.81	−	4789.00i	−0.182648	−	0.285029i
$657$	−15730.8	+	2535.41i	−0.934119	+	0.150556i
$658$	−23789.9	+	3412.48i	−1.40946	+	0.202177i
$659$		−	1120.64i		−	0.0662427i	−0.999451	−	0.0331213i	$-0.989455\pi$
$659$		−	1120.64i		−	0.0662427i	0.999451	−	0.0331213i	$-0.0105448\pi$
$660$	6561.80	+	12436.8i	0.386996	+	0.733486i
$661$			16677.3i			0.981348i	0.871343	+	0.490674i	$0.163249\pi$
$661$			16677.3i			0.981348i	−0.871343	+	0.490674i	$0.836751\pi$
$662$	−1182.32	−	8242.44i	−0.0694140	−	0.483915i
$663$	−6392.24	+	3267.97i	−0.374440	+	0.191429i
$664$	−27430.3	−	10261.8i	−1.60317	−	0.599753i
$665$	5073.28	+	8998.91i	0.295839	+	0.524756i
$666$	−18341.3	+	5719.30i	−1.06713	+	0.332760i
$667$	−15119.3	−	15119.3i	−0.877692	−	0.877692i
$668$	−6985.18	−	3820.17i	−0.404588	−	0.221267i
$669$	−21032.4	−	6802.22i	−1.21548	−	0.393108i
$670$	−15207.6	+	11701.2i	−0.876895	+	0.674709i
$671$			20735.9i			1.19300i
$672$	6951.28	+	16461.8i	0.399035	+	0.944979i
$673$	8421.00	+	8421.00i	0.482326	+	0.482326i	0.905874	−	0.423547i	$-0.139215\pi$
$673$	8421.00	+	8421.00i	0.482326	+	0.482326i	−0.423547	+	0.905874i	$0.639215\pi$
$674$	7266.44	−	9700.17i	0.415271	−	0.554357i
$675$	−11258.6	+	13445.8i	−0.641992	+	0.766711i
$676$	1916.60	+	6543.26i	0.109046	+	0.372284i
$677$	−7237.67	+	7237.67i	−0.410881	+	0.410881i	−0.882045	−	0.471165i	$-0.843834\pi$
$677$	−7237.67	+	7237.67i	−0.410881	+	0.410881i	0.471165	+	0.882045i	$0.343834\pi$
$678$	4182.79	−	24319.3i	0.236931	−	1.37755i
$679$		−	32490.7i		−	1.83634i
$680$	−5615.73	+	7701.58i	−0.316696	+	0.434327i
$681$	2255.24	−	6973.17i	0.126903	−	0.392383i
$682$	20339.4	−	2917.54i	1.14199	−	0.163810i
$683$	13293.6	+	13293.6i	0.744754	+	0.744754i	0.973489	−	0.228734i	$-0.0734588\pi$
$683$	13293.6	+	13293.6i	0.744754	+	0.744754i	−0.228734	+	0.973489i	$0.573459\pi$
$684$	−3509.97	+	9901.88i	−0.196209	+	0.553520i
$685$	19349.1	−	10908.4i	1.07926	−	0.608448i
$686$	−13980.6	−	10472.9i	−0.778107	−	0.582883i
$687$	−25078.3	+	12821.0i	−1.39272	+	0.712012i
$688$	−6501.03	+	29696.6i	−0.360246	+	1.64560i
$689$	−2772.47			−0.153298
$690$	12488.7	+	5915.74i	0.689040	+	0.326389i
$691$			7443.72i			0.409801i	0.978783	+	0.204900i	$0.0656871\pi$
$691$			7443.72i			0.409801i	−0.978783	+	0.204900i	$0.934313\pi$
$692$	−6739.34	−	3685.71i	−0.370218	−	0.202471i
$693$	2469.45	+	15321.6i	0.135363	+	0.839854i
$694$	8841.41	−	11802.6i	0.483596	−	0.645565i
$695$	3057.29	−	10959.4i	0.166863	−	0.598152i
$696$	23416.2	+	18581.5i	1.27527	+	1.01197i
$697$	2367.72	−	2367.72i	0.128671	−	0.128671i
$698$	−17126.9	+	2456.73i	−0.928746	+	0.133222i
$699$	−7131.39	+	22050.2i	−0.385885	+	1.19315i
$700$	−16427.2	+	9542.29i	−0.886987	+	0.515235i
$701$	8377.43			0.451371			0.225686	−	0.974200i	$-0.427538\pi$
$701$	8377.43			0.451371			0.225686	+	0.974200i	$0.427538\pi$
$702$	−10180.6	−	10397.2i	−0.547352	−	0.558999i
$703$	−8652.11	−	8652.11i	−0.464183	−	0.464183i
$704$	−10167.5	+	11687.3i	−0.544323	+	0.625683i
$705$	14345.1	−	21665.5i	0.766337	−	1.15740i
$706$	20073.2	−	26796.3i	1.07006	−	1.42846i
$707$	3385.61	−	3385.61i	0.180097	−	0.180097i
$708$	743.957	+	786.606i	0.0394910	+	0.0417549i
$709$	19615.7			1.03905			0.519523	−	0.854456i	$-0.326110\pi$
$709$	19615.7			1.03905			0.519523	+	0.854456i	$0.326110\pi$
$710$	83.5015	+	10.8809i	0.00441374	+	0.000575142i
$711$	14494.3	+	10470.6i	0.764526	+	0.552289i
$712$	−9689.32	+	4413.41i	−0.510004	+	0.232303i
$713$	14278.6	−	14278.6i	0.749982	−	0.749982i
$714$	−8591.73	+	6069.99i	−0.450332	+	0.318156i
$715$	−6091.87	−	10805.7i	−0.318634	−	0.565188i
$716$	3638.84	+	12423.0i	0.189930	+	0.648420i
$717$	−28969.1	+	14810.2i	−1.50888	+	0.771402i
$718$	36057.3	−	5172.16i	1.87416	−	0.268834i
$719$	−2748.07			−0.142539			−0.0712695	−	0.997457i	$-0.522705\pi$
$719$	−2748.07			−0.142539			−0.0712695	+	0.997457i	$0.522705\pi$
$720$	−18291.1	−	6219.48i	−0.946765	−	0.321926i
$721$	14080.1			0.727281
$722$	12580.6	−	1804.60i	0.648480	−	0.0930196i
$723$	15094.9	−	7717.13i	0.776467	−	0.396961i
$724$	4482.04	+	15301.7i	0.230074	+	0.785472i
$725$	−16451.0	+	27191.3i	−0.842726	+	1.39291i
$726$	4988.42	−	3524.28i	0.255011	−	0.180163i
$727$	16151.9	−	16151.9i	0.823991	−	0.823991i	−0.162687	−	0.986678i	$-0.552016\pi$
$727$	16151.9	−	16151.9i	0.823991	−	0.823991i	0.986678	+	0.162687i	$0.0520160\pi$
$728$	−6534.22	−	14345.4i	−0.332657	−	0.730324i
$729$	−18768.7	−	5929.38i	−0.953547	−	0.301244i
$730$	14790.4	−	11380.2i	0.749888	−	0.576987i
$731$	−17896.4			−0.905502
$732$	−19576.2	−	20698.5i	−0.988468	−	1.04513i
$733$	−17142.4	+	17142.4i	−0.863803	+	0.863803i	−0.991777	−	0.127975i	$-0.959152\pi$
$733$	−17142.4	+	17142.4i	−0.863803	+	0.863803i	0.127975	+	0.991777i	$0.459152\pi$
$734$	9646.17	−	12876.9i	0.485077	−	0.647543i
$735$	−1019.59	+	207.266i	−0.0511675	+	0.0104015i
$736$	−1111.02	+	15183.1i	−0.0556421	+	0.760401i
$737$	−12981.6	−	12981.6i	−0.648825	−	0.648825i
$738$	6010.24	+	3152.92i	0.299783	+	0.157264i
$739$	14346.2			0.714121			0.357060	−	0.934081i	$-0.383779\pi$
$739$	14346.2			0.714121			0.357060	+	0.934081i	$0.383779\pi$
$740$	15704.7	−	16114.9i	0.780155	−	0.800537i
$741$	2851.84	−	8817.85i	0.141383	−	0.437155i
$742$	−4021.34	+	576.831i	−0.198959	+	0.0285393i
$743$	14271.7	−	14271.7i	0.704681	−	0.704681i	−0.260730	−	0.965412i	$-0.583963\pi$
$743$	14271.7	−	14271.7i	0.704681	−	0.704681i	0.965412	+	0.260730i	$0.0839634\pi$
$744$	−17548.3	+	22114.1i	−0.864719	+	1.08971i
$745$	8614.87	+	2403.24i	0.423657	+	0.118185i
$746$	−3874.44	+	5172.10i	−0.190152	+	0.253839i
$747$	34501.2	−	5560.72i	1.68987	−	0.272364i
$748$	−8001.17	−	4375.81i	−0.391112	−	0.213898i
$749$			26977.7i			1.31608i
$750$	4102.20	−	20125.8i	0.199721	−	0.979853i
$751$	16913.8			0.821827			0.410913	−	0.911674i	$-0.365210\pi$
$751$	16913.8			0.821827			0.410913	+	0.911674i	$0.365210\pi$
$752$	27963.2	+	6121.56i	1.35600	+	0.296849i
$753$	−2995.74	+	1531.54i	−0.144981	+	0.0741203i
$754$	−21105.3	−	15810.0i	−1.01937	−	0.763617i
$755$	2113.50	−	7576.26i	0.101879	−	0.365203i
$756$	−16929.7	−	12962.6i	−0.814453	−	0.623603i
$757$	3972.33	+	3972.33i	0.190722	+	0.190722i	0.796008	−	0.605286i	$-0.206941\pi$
$757$	3972.33	+	3972.33i	0.190722	+	0.190722i	−0.605286	+	0.796008i	$0.706941\pi$
$758$	−10587.7	+	1518.73i	−0.507338	+	0.0727739i
$759$	−4068.61	+	12580.1i	−0.194573	+	0.601618i
$760$	−1903.96	−	12156.1i	−0.0908737	−	0.580193i
$761$			3452.52i			0.164459i	0.996613	+	0.0822297i	$0.0262041\pi$
$761$			3452.52i			0.164459i	−0.996613	+	0.0822297i	$0.973796\pi$
$762$	−44.0024	+	255.836i	−0.00209192	+	0.0121627i
$763$	−4844.29	+	4844.29i	−0.229849	+	0.229849i
$764$	558.173	+	1905.60i	0.0264319	+	0.0902385i
$765$	1273.96	−	11301.9i	0.0602095	−	0.534145i
$766$	−3546.92	+	4734.88i	−0.167305	+	0.223340i
$767$	−675.359	−	675.359i	−0.0317938	−	0.0317938i
$768$	−884.474	−	21265.1i	−0.0415569	−	0.999136i
$769$			26820.9i			1.25772i	0.777519	+	0.628860i	$0.216478\pi$
$769$			26820.9i			1.25772i	−0.777519	+	0.628860i	$0.783522\pi$
$770$	−11084.2	−	14405.7i	−0.518761	−	0.674215i
$771$	−21658.9	−	7004.83i	−1.01171	−	0.327202i
$772$	10842.9	+	5929.95i	0.505499	+	0.276455i
$773$	−18959.4	−	18959.4i	−0.882177	−	0.882177i	0.111578	−	0.993756i	$-0.464409\pi$
$773$	−18959.4	−	18959.4i	−0.882177	−	0.882177i	−0.993756	+	0.111578i	$0.964409\pi$
$774$	−10798.5	−	34629.8i	−0.501478	−	1.60819i
$775$	−25679.4	−	15536.3i	−1.19023	−	0.720104i
$776$	−13559.5	+	36245.2i	−0.627266	+	1.67671i
$777$	22112.2	−	11304.6i	1.02094	−	0.521945i
$778$	1082.98	+	7549.92i	0.0499058	+	0.347915i
$779$			4322.53i			0.198807i
$780$	16282.2	+	5034.99i	0.747431	+	0.231130i
$781$			80.5675i			0.00369134i
$782$	−8871.37	+	1272.53i	−0.405677	+	0.0581914i
$783$	−35252.9	−	5436.11i	−1.60898	−	0.248111i
$784$	−618.414	−	965.061i	−0.0281712	−	0.0439623i
$785$	−16956.3	+	9559.36i	−0.770949	+	0.434634i
$786$	−1693.24	+	1196.26i	−0.0768393	+	0.0542864i
$787$	301.044	+	301.044i	0.0136354	+	0.0136354i	0.713892	−	0.700256i	$-0.246931\pi$
$787$	301.044	+	301.044i	0.0136354	+	0.0136354i	−0.700256	+	0.713892i	$0.746931\pi$
$788$	17936.3	−	32796.5i	0.810855	−	1.48265i
$789$	2882.52	−	8912.72i	0.130064	−	0.402156i
$790$	−20766.5	−	2706.03i	−0.935239	−	0.121868i
$791$			31897.3i			1.43380i
$792$	3639.43	−	18122.7i	0.163285	−	0.813084i
$793$	17771.2	+	17771.2i	0.795804	+	0.795804i
$794$	8242.56	+	6174.53i	0.368410	+	0.275977i
$795$	2424.83	−	3662.23i	0.108176	−	0.163379i
$796$	8694.37	+	29682.5i	0.387140	+	1.32169i
$797$	26720.4	−	26720.4i	1.18756	−	1.18756i	0.209819	−	0.977740i	$-0.432713\pi$
$797$	26720.4	−	26720.4i	1.18756	−	1.18756i	0.977740	−	0.209819i	$-0.0672874\pi$
$798$	2301.85	−	13383.2i	0.102111	−	0.593686i
$799$			16851.8i			0.746148i
$800$	22307.9	−	3789.30i	0.985878	−	0.167465i
$801$	7439.58	−	10298.5i	0.328171	−	0.454282i
$802$	1100.04	+	7668.86i	0.0484337	+	0.337652i
$803$	12625.5	+	12625.5i	0.554852	+	0.554852i
$804$	25213.8	+	702.570i	1.10600	+	0.0308181i
$805$	−17205.8	−	4799.80i	−0.753323	−	0.210150i
$806$	14930.9	−	19931.7i	0.652506	−	0.871049i
$807$	137.333	+	268.627i	0.00599051	+	0.0117176i
$808$	−5189.77	+	2363.90i	−0.225960	+	0.102923i
$809$	20135.6			0.875067			0.437533	−	0.899202i	$-0.355852\pi$
$809$	20135.6			0.875067			0.437533	+	0.899202i	$0.355852\pi$
$810$	22638.0	−	4354.31i	0.982000	−	0.188882i
$811$			22929.3i			0.992796i	0.868095	+	0.496398i	$0.165344\pi$
$811$			22929.3i			0.992796i	−0.868095	+	0.496398i	$0.834656\pi$
$812$	−33901.6	−	18540.6i	−1.46516	−	0.801292i
$813$	1268.90	−	648.713i	0.0547383	−	0.0279844i
$814$	17230.7	+	12907.6i	0.741935	+	0.555786i
$815$	−19779.9	−	35085.4i	−0.850136	−	1.50796i
$816$	12117.8	−	3185.79i	0.519862	−	0.136673i
$817$	16335.9	−	16335.9i	0.699534	−	0.699534i
$818$	2337.80	+	16297.8i	0.0999257	+	0.696625i
$819$	15247.3	+	11014.6i	0.650531	+	0.469939i
$820$	−7948.42	+	102.489i	−0.338501	+	0.00436472i
$821$	−12030.9			−0.511428			−0.255714	−	0.966752i	$-0.582311\pi$
$821$	−12030.9			−0.511428			−0.255714	+	0.966752i	$0.582311\pi$
$822$	−28776.1	−	4949.34i	−1.22103	−	0.210010i
$823$	10863.2	+	10863.2i	0.460105	+	0.460105i	0.898690	−	0.438585i	$-0.144520\pi$
$823$	10863.2	+	10863.2i	0.460105	+	0.460105i	−0.438585	+	0.898690i	$0.644520\pi$
$824$	−15707.1	−	5876.12i	−0.664059	−	0.248428i
$825$	19601.6	+	1403.84i	0.827199	+	0.0592428i
$826$	−1120.09	−	839.065i	−0.0471828	−	0.0353448i
$827$	9005.54	−	9005.54i	0.378662	−	0.378662i	−0.491957	−	0.870619i	$-0.663718\pi$
$827$	9005.54	−	9005.54i	0.378662	−	0.378662i	0.870619	+	0.491957i	$0.163718\pi$
$828$	−7815.26	−	16398.4i	−0.328018	−	0.688266i
$829$	8550.46			0.358227			0.179113	−	0.983828i	$-0.442677\pi$
$829$	8550.46			0.358227			0.179113	+	0.983828i	$0.442677\pi$
$830$	−32438.8	+	24959.4i	−1.35659	+	1.04380i
$831$	−19157.6	−	6195.87i	−0.799722	−	0.258643i
$832$	1302.45	+	18730.1i	0.0542721	+	0.780467i
$833$	477.134	−	477.134i	0.0198460	−	0.0198460i
$834$	−12215.6	+	8630.21i	−0.507183	+	0.358321i
$835$	−9692.44	+	5464.26i	−0.401702	+	0.226465i
$836$	11297.7	−	3309.24i	0.467393	−	0.136905i
$837$	5133.84	−	33292.7i	0.212009	−	1.37487i
$838$	3651.61	+	25456.9i	0.150528	+	1.04940i
$839$	5509.51			0.226710			0.113355	−	0.993555i	$-0.463840\pi$
$839$	5509.51			0.226710			0.113355	+	0.993555i	$0.463840\pi$
$840$	24664.2	+	3915.39i	1.01309	+	0.160826i
$841$	−40251.3			−1.65039
$842$	3110.29	+	21683.2i	0.127301	+	0.887471i
$843$	−17280.8	−	33801.7i	−0.706028	−	1.38101i
$844$	−1293.95	−	4417.53i	−0.0527719	−	0.180163i
$845$	9178.25	+	2560.40i	0.373659	+	0.104237i
$846$	−32608.4	+	10168.2i	−1.32518	+	0.413226i
$847$	−5582.65	+	5582.65i	−0.226472	+	0.226472i
$848$	4726.77	+	1034.76i	0.191413	+	0.0419031i
$849$	−10340.0	+	31971.2i	−0.417984	+	1.29240i
$850$	4987.59	+	12351.8i	0.201262	+	0.498427i
$851$	21157.5			0.852257
$852$	−76.0616	−	80.4219i	−0.00305848	−	0.00323381i
$853$	−4754.17	+	4754.17i	−0.190832	+	0.190832i	−0.796056	−	0.605224i	$-0.793084\pi$
$853$	−4754.17	+	4754.17i	−0.190832	+	0.190832i	0.605224	+	0.796056i	$0.293084\pi$
$854$	29473.7	+	22078.9i	1.18099	+	0.884688i
$855$	9153.52	+	11479.3i	0.366133	+	0.459161i
$856$	11258.8	−	30095.2i	0.449553	−	1.20168i
$857$	−14870.9	−	14870.9i	−0.592741	−	0.592741i	0.345630	−	0.938371i	$-0.387665\pi$
$857$	−14870.9	−	14870.9i	−0.592741	−	0.592741i	−0.938371	+	0.345630i	$0.887665\pi$
$858$	−2764.00	+	16070.3i	−0.109978	+	0.639429i
$859$	−12178.8			−0.483741			−0.241871	−	0.970309i	$-0.577761\pi$
$859$	−12178.8			−0.483741			−0.241871	+	0.970309i	$0.577761\pi$
$860$	30426.3	+	29651.6i	1.20643	+	1.17571i
$861$	−8347.39	−	2699.68i	−0.330404	−	0.106858i
$862$	−1225.61	−	8544.25i	−0.0484274	−	0.337608i
$863$	−30687.7	+	30687.7i	−1.21045	+	1.21045i	−0.239576	+	0.970878i	$0.577008\pi$
$863$	−30687.7	+	30687.7i	−1.21045	+	1.21045i	−0.970878	+	0.239576i	$0.922992\pi$
$864$	13476.3	+	21525.8i	0.530640	+	0.847597i
$865$	−9351.31	+	5271.95i	−0.367577	+	0.207227i
$866$	813.795	+	609.617i	0.0319329	+	0.0239211i
$867$	−8263.07	−	16162.8i	−0.323678	−	0.633123i
$868$	17509.7	−	32016.6i	0.684699	−	1.25197i
$869$		−	20036.8i		−	0.782167i
$870$	39342.8	−	14050.9i	1.53316	−	0.547553i
$871$	−22251.1			−0.865614
$872$	7425.78	−	3382.39i	0.288381	−	0.131356i
$873$	−7347.71	−	45588.4i	−0.284859	−	1.76739i
$874$	6936.24	−	9259.38i	0.268446	−	0.358356i
$875$	−816.166	+	26537.4i	−0.0315331	+	1.02529i
$876$	−24522.2	−	683.299i	−0.945807	−	0.0263545i
$877$	16811.3	+	16811.3i	0.647295	+	0.647295i	0.952339	−	0.305043i	$-0.0986709\pi$
$877$	16811.3	+	16811.3i	0.647295	+	0.647295i	−0.305043	+	0.952339i	$0.598671\pi$
$878$	1802.98	+	12569.3i	0.0693025	+	0.483137i
$879$	45377.7	+	14675.9i	1.74124	+	0.563146i
$880$	6353.03	+	20696.2i	0.243364	+	0.792806i
$881$			47957.4i			1.83397i	0.398923	+	0.916984i	$0.369384\pi$
$881$			47957.4i			1.83397i	−0.398923	+	0.916984i	$0.630616\pi$
$882$	1211.16	+	635.364i	0.0462379	+	0.0242560i
$883$	−11808.6	+	11808.6i	−0.450045	+	0.450045i	−0.895369	−	0.445324i	$-0.853088\pi$
$883$	−11808.6	+	11808.6i	−0.450045	+	0.450045i	0.445324	+	0.895369i	$0.353088\pi$
$884$	−10607.4	+	3107.02i	−0.403579	+	0.118213i
$885$	1482.78	−	301.426i	0.0563199	−	0.0114489i
$886$	−5986.49	−	4484.50i	−0.226998	−	0.170045i
$887$	2191.50	+	2191.50i	0.0829577	+	0.0829577i	0.747368	−	0.664410i	$-0.231317\pi$
$887$	2191.50	+	2191.50i	0.0829577	+	0.0829577i	−0.664410	+	0.747368i	$0.731317\pi$
$888$	−29385.2	+	3382.77i	−1.11048	+	0.127836i
$889$		−	335.556i		−	0.0126594i
$890$	−1922.69	+	14755.1i	−0.0724144	+	0.555720i
$891$	6929.90	+	20939.6i	0.260561	+	0.787321i
$892$	−29859.2	−	16329.9i	−1.12081	−	0.612965i
$893$	−15382.3	−	15382.3i	−0.576428	−	0.576428i
$894$	−6783.94	−	9602.28i	−0.253791	−	0.359226i
$895$	17425.8	+	4861.17i	0.650815	+	0.181554i
$896$	5786.07	+	26896.2i	0.215736	+	1.00283i
$897$	7294.53	+	14268.3i	0.271524	+	0.531109i
$898$	39602.9	−	5680.74i	1.47168	−	0.211101i
$899$		−	61046.1i		−	2.26474i
$900$	−20891.5	+	17104.0i	−0.773758	+	0.633481i
$901$			2848.55i			0.105326i
$902$	−1079.90	−	7528.42i	−0.0398632	−	0.277904i
$903$	21344.0	+	41749.5i	0.786584	+	1.53858i
$904$	13311.9	−	35583.3i	0.489765	−	1.30916i
$905$	21463.7	+	5987.60i	0.788373	+	0.219928i
$906$	−8444.62	+	5966.06i	−0.309662	+	0.218774i
$907$	1161.58	+	1161.58i	0.0425244	+	0.0425244i	0.728049	−	0.685525i	$-0.240427\pi$
$907$	1161.58	+	1161.58i	0.0425244	+	0.0425244i	−0.685525	+	0.728049i	$0.740427\pi$
$908$	5414.08	−	9899.66i	0.197877	−	0.361819i
$909$	3984.77	−	5516.07i	0.145398	−	0.201272i
$910$	−21845.4	−	2846.62i	−0.795789	−	0.103697i
$911$		−	49207.5i		−	1.78959i	−0.446478	−	0.894794i	$-0.647322\pi$
$911$		−	49207.5i		−	1.78959i	0.446478	−	0.894794i	$-0.352678\pi$
$912$	−8153.15	+	13969.1i	−0.296028	+	0.507198i
$913$	−27690.7	−	27690.7i	−1.00376	−	1.00376i
$914$	−7745.25	+	10339.4i	−0.280296	+	0.374174i
$915$	−39017.4	+	7931.61i	−1.40970	+	0.286569i
$916$	−41615.2	+	12189.6i	−1.50110	+	0.439689i
$917$	1894.94	−	1894.94i	0.0682402	−	0.0682402i
$918$	−10682.5	+	10459.9i	−0.384070	+	0.376067i
$919$			12161.6i			0.436532i	0.975889	+	0.218266i	$0.0700401\pi$
$919$			12161.6i			0.436532i	−0.975889	+	0.218266i	$0.929960\pi$
$920$	17190.9	+	12535.1i	0.616053	+	0.449205i
$921$	13975.0	+	4519.75i	0.499993	+	0.161706i
$922$	−6117.90	+	877.568i	−0.218528	+	0.0313461i
$923$	69.0482	+	69.0482i	0.00246235	+	0.00246235i
$924$	−665.525	+	23884.3i	−0.0236950	+	0.850363i
$925$	−7514.84	−	30536.0i	−0.267120	−	1.08543i
$926$	21090.0	+	15798.6i	0.748444	+	0.560663i
$927$	19756.1	−	3184.18i	0.699973	−	0.112818i
$928$	30081.5	+	34831.5i	1.06409	+	1.23211i
$929$	13041.6			0.460584			0.230292	−	0.973122i	$-0.426032\pi$
$929$	13041.6			0.460584			0.230292	+	0.973122i	$0.426032\pi$
$930$	13269.7	+	37155.2i	0.467881	+	1.31007i
$931$			871.058i			0.0306636i
$932$	−17120.1	+	31304.2i	−0.601703	+	1.10022i
$933$	−9374.59	−	18337.0i	−0.328950	−	0.643435i
$934$	409.691	−	546.908i	0.0143528	−	0.0191599i
$935$	−11102.2	+	6259.04i	−0.388322	+	0.218922i
$936$	−12412.5	−	18650.7i	−0.433456	−	0.651299i
$937$	−16193.7	+	16193.7i	−0.564593	+	0.564593i	−0.930609	−	0.366016i	$-0.880722\pi$
$937$	−16193.7	+	16193.7i	−0.564593	+	0.564593i	0.366016	+	0.930609i	$0.380722\pi$
$938$	−32274.2	+	4629.50i	−1.12344	+	0.161150i
$939$	−29251.1	−	9460.29i	−1.01659	−	0.328781i
$940$	27920.8	−	28650.3i	0.968806	−	0.994116i
$941$	199.184			0.00690035			0.00345017	−	0.999994i	$-0.498902\pi$
$941$	199.184			0.00690035			0.00345017	+	0.999994i	$0.498902\pi$
$942$	25217.5	+	4337.27i	0.872218	+	0.150017i
$943$	−5285.07	−	5285.07i	−0.182509	−	0.182509i
$944$	899.355	+	1403.48i	0.0310080	+	0.0483892i
$945$	−27885.0	+	10507.2i	−0.959892	+	0.361692i
$946$	−24370.5	+	32532.9i	−0.837584	+	1.11811i
$947$	4630.34	−	4630.34i	0.158887	−	0.158887i	−0.623187	−	0.782073i	$-0.714162\pi$
$947$	4630.34	−	4630.34i	0.158887	−	0.158887i	0.782073	+	0.623187i	$0.214162\pi$
$948$	18916.2	+	20000.6i	0.648070	+	0.685222i
$949$	21640.8			0.740241
$950$	−15827.4	−	6722.07i	−0.540536	−	0.229571i
$951$	9801.56	−	30306.3i	0.334214	−	1.03339i
$952$	−14739.1	+	6713.53i	−0.501781	+	0.228558i
$953$	−12481.4	+	12481.4i	−0.424251	+	0.424251i	−0.886665	−	0.462413i	$-0.846984\pi$
$953$	−12481.4	+	12481.4i	−0.424251	+	0.424251i	0.462413	+	0.886665i	$0.346984\pi$
$954$	−5511.98	+	1718.78i	−0.187062	+	0.0583309i
$955$	2672.99	+	745.670i	0.0905718	+	0.0252663i
$956$	−48071.7	+	14080.8i	−1.62631	+	0.476365i
$957$	18194.8	+	35589.6i	0.614582	+	1.20214i
$958$	−18798.0	+	2696.44i	−0.633964	+	0.0909374i
$959$	37742.9			1.27089
$960$	−25880.3	−	14661.1i	−0.870086	−	0.492901i
$961$	27860.7			0.935205
$962$	25829.2	−	3705.00i	0.865661	−	0.124173i
$963$	6100.97	+	37853.1i	0.204155	+	1.26667i
$964$	25048.7	−	7337.06i	0.836892	−	0.245136i
$965$	15045.3	−	8482.04i	0.501893	−	0.282950i
$966$	13549.0	+	19177.9i	0.451276	+	0.638755i
$967$	20215.1	−	20215.1i	0.672258	−	0.672258i	−0.285978	−	0.958236i	$-0.592318\pi$
$967$	20215.1	−	20215.1i	0.672258	−	0.672258i	0.958236	+	0.285978i	$0.0923185\pi$
$968$	8557.61	−	3897.93i	0.284145	−	0.129426i
$969$	−9059.83	−	2930.10i	−0.300355	−	0.0971396i
$970$	32980.3	+	42863.2i	1.09168	+	1.41882i
$971$	−48021.2			−1.58710			−0.793549	−	0.608506i	$-0.791769\pi$
$971$	−48021.2			−1.58710			−0.793549	+	0.608506i	$0.791769\pi$
$972$	−26685.9	−	14359.4i	−0.880607	−	0.473847i
$973$	13670.7	−	13670.7i	0.450424	−	0.450424i
$974$	1710.00	−	2282.72i	0.0562544	−	0.0750956i
$975$	18002.1	−	15595.9i	0.591312	−	0.512274i
$976$	−23665.3	−	36930.7i	−0.776136	−	1.21119i
$977$	−42560.9	−	42560.9i	−1.39370	−	1.39370i	−0.816850	−	0.576850i	$-0.804282\pi$
$977$	−42560.9	−	42560.9i	−1.39370	−	1.39370i	−0.576850	−	0.816850i	$-0.695718\pi$
$978$	−8974.55	+	52179.2i	−0.293430	+	1.70604i
$979$	−14236.6			−0.464764
$980$	−1601.73	+	20.6532i	−0.0522097	+	0.000673205i
$981$	−5701.60	+	7892.66i	−0.185564	+	0.256874i
$982$	−13735.6	+	1970.27i	−0.446356	+	0.0640264i
$983$	18050.1	−	18050.1i	0.585665	−	0.585665i	−0.350790	−	0.936454i	$-0.614087\pi$
$983$	18050.1	−	18050.1i	0.585665	−	0.585665i	0.936454	+	0.350790i	$0.114087\pi$
$984$	8185.32	+	6495.31i	0.265181	+	0.210430i
$985$	−25655.6	−	45507.6i	−0.829904	−	1.47207i
$986$	−16243.9	+	21684.4i	−0.524656	+	0.700378i
$987$	39312.6	−	20098.2i	1.26781	−	0.648158i
$988$	6846.32	−	12518.5i	0.220456	−	0.403104i
$989$			39947.1i			1.28437i
$990$	−18810.3	−	17706.3i	−0.603869	−	0.568427i
$991$	59114.0			1.89487			0.947435	−	0.319947i	$-0.103665\pi$
$991$	59114.0			1.89487			0.947435	+	0.319947i	$0.103665\pi$
$992$	−32894.8	+	28408.9i	−1.05283	+	0.909257i
$993$	6963.38	+	13620.6i	0.222534	+	0.435282i
$994$	114.517	+	85.7854i	0.00365419	+	0.00273737i
$995$	41635.8	+	11614.9i	1.32658	+	0.370067i
$996$	53782.7	+	1498.63i	1.71101	+	0.0476767i
$997$	−25620.6	−	25620.6i	−0.813853	−	0.813853i	0.171356	−	0.985209i	$-0.445185\pi$
$997$	−25620.6	−	25620.6i	−0.813853	−	0.813853i	−0.985209	+	0.171356i	$0.945185\pi$
$998$	61348.9	−	8800.05i	1.94586	−	0.279119i
$999$	28469.6	−	20862.4i	0.901639	−	0.660718i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.w.c.53.3	✓	128
3.2	odd	2	inner	120.4.w.c.53.62	yes	128
5.2	odd	4	inner	120.4.w.c.77.30	yes	128
8.5	even	2	inner	120.4.w.c.53.35	yes	128
15.2	even	4	inner	120.4.w.c.77.35	yes	128
24.5	odd	2	inner	120.4.w.c.53.30	yes	128
40.37	odd	4	inner	120.4.w.c.77.62	yes	128
120.77	even	4	inner	120.4.w.c.77.3	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.w.c.53.3	✓	128	1.1	even	1	trivial
120.4.w.c.53.30	yes	128	24.5	odd	2	inner
120.4.w.c.53.35	yes	128	8.5	even	2	inner
120.4.w.c.53.62	yes	128	3.2	odd	2	inner
120.4.w.c.77.3	yes	128	120.77	even	4	inner
120.4.w.c.77.30	yes	128	5.2	odd	4	inner
120.4.w.c.77.35	yes	128	15.2	even	4	inner
120.4.w.c.77.62	yes	128	40.37	odd	4	inner

Overview	Random
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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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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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.53.3

Level	$120$
Weight	$4$
Character	120.53
Analytic conductor	$7.080$
Analytic rank	$0$
Dimension	$128$
Inner twists	$8$