LMFDB - Embedded newform 120.4.w.c.53.37

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			53.37
Character	$\chi$	$=$	120.53
Dual form			120.4.w.c.77.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.626941 - 2.75807i) q^{2} +(-0.195243 + 5.19248i) q^{3} +(-7.21389 - 3.45829i) q^{4} +(10.6250 + 3.47979i) q^{5} +(14.1988 + 3.79387i) q^{6} +(-17.6061 + 17.6061i) q^{7} +(-14.0609 + 17.7283i) q^{8} +(-26.9238 - 2.02759i) q^{9} +(16.2588 - 27.1229i) q^{10} -56.4191 q^{11} +(19.3656 - 36.7828i) q^{12} +(-0.217514 + 0.217514i) q^{13} +(37.5210 + 59.5970i) q^{14} +(-20.1432 + 54.4908i) q^{15} +(40.0804 + 49.8955i) q^{16} +(75.4592 + 75.4592i) q^{17} +(-22.4718 + 72.9864i) q^{18} +36.8594 q^{19} +(-64.6136 - 61.8473i) q^{20} +(-87.9821 - 94.8571i) q^{21} +(-35.3714 + 155.608i) q^{22} +(-74.5235 + 74.5235i) q^{23} +(-89.3084 - 76.4722i) q^{24} +(100.782 + 73.9457i) q^{25} +(0.463550 + 0.736287i) q^{26} +(15.7849 - 139.405i) q^{27} +(187.896 - 66.1216i) q^{28} -16.5840i q^{29} +(137.661 + 89.7189i) q^{30} -20.7734 q^{31} +(162.743 - 79.2632i) q^{32} +(11.0154 - 292.955i) q^{33} +(255.430 - 160.813i) q^{34} +(-248.331 + 125.800i) q^{35} +(187.213 + 107.737i) q^{36} +(-79.9565 - 79.9565i) q^{37} +(23.1087 - 101.661i) q^{38} +(-1.08697 - 1.17191i) q^{39} +(-211.088 + 139.434i) q^{40} +276.664i q^{41} +(-316.782 + 183.191i) q^{42} +(286.448 - 286.448i) q^{43} +(407.001 + 195.114i) q^{44} +(-279.010 - 115.232i) q^{45} +(158.819 + 252.263i) q^{46} +(-229.786 - 229.786i) q^{47} +(-266.907 + 198.375i) q^{48} -276.953i q^{49} +(267.132 - 231.604i) q^{50} +(-406.553 + 377.088i) q^{51} +(2.32135 - 0.816895i) q^{52} +(25.1531 + 25.1531i) q^{53} +(-374.593 - 130.935i) q^{54} +(-599.454 - 196.327i) q^{55} +(-64.5684 - 559.684i) q^{56} +(-7.19654 + 191.392i) q^{57} +(-45.7397 - 10.3972i) q^{58} +431.866i q^{59} +(333.756 - 323.430i) q^{60} -745.120i q^{61} +(-13.0237 + 57.2944i) q^{62} +(509.722 - 438.325i) q^{63} +(-116.583 - 498.550i) q^{64} +(-3.06799 + 1.55419i) q^{65} +(-801.085 - 214.047i) q^{66} +(583.852 + 583.852i) q^{67} +(-283.395 - 805.314i) q^{68} +(-372.412 - 401.512i) q^{69} +(191.276 + 763.784i) q^{70} +295.657i q^{71} +(414.518 - 448.802i) q^{72} +(26.9724 + 26.9724i) q^{73} +(-270.653 + 170.398i) q^{74} +(-403.639 + 508.872i) q^{75} +(-265.900 - 127.471i) q^{76} +(993.323 - 993.323i) q^{77} +(-3.91366 + 2.26322i) q^{78} +1137.70i q^{79} +(252.230 + 669.612i) q^{80} +(720.778 + 109.181i) q^{81} +(763.058 + 173.452i) q^{82} +(275.299 + 275.299i) q^{83} +(306.650 + 988.556i) q^{84} +(539.173 + 1064.34i) q^{85} +(-610.458 - 969.631i) q^{86} +(86.1119 + 3.23790i) q^{87} +(793.303 - 1000.21i) q^{88} -756.706 q^{89} +(-492.741 + 697.285i) q^{90} -7.65916i q^{91} +(795.328 - 279.880i) q^{92} +(4.05585 - 107.865i) q^{93} +(-777.828 + 489.703i) q^{94} +(391.632 + 128.263i) q^{95} +(379.798 + 860.517i) q^{96} +(575.441 - 575.441i) q^{97} +(-763.854 - 173.633i) q^{98} +(1519.01 + 114.395i) 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 $

$2$	0.626941	−	2.75807i	0.221657	−	0.975125i
$2$	0.626941	−	2.75807i	0.221657	−	0.975125i
$3$	−0.195243	+	5.19248i	−0.0375745	+	0.999294i
$3$	−0.195243	+	5.19248i	−0.0375745	+	0.999294i
$4$	−7.21389	−	3.45829i	−0.901736	−	0.432286i
$5$	10.6250	+	3.47979i	0.950331	+	0.311242i
$5$	10.6250	+	3.47979i	0.950331	+	0.311242i
$6$	14.1988	+	3.79387i	0.966107	+	0.258140i
$7$	−17.6061	+	17.6061i	−0.950642	+	0.950642i	−0.998838	−	0.0481956i	$-0.984653\pi$
$7$	−17.6061	+	17.6061i	−0.950642	+	0.950642i	0.0481956	+	0.998838i	$0.484653\pi$
$8$	−14.0609	+	17.7283i	−0.621409	+	0.783486i
$9$	−26.9238	−	2.02759i	−0.997176	−	0.0750960i
$10$	16.2588	−	27.1229i	0.514147	−	0.857702i
$11$	−56.4191			−1.54645			−0.773227	−	0.634129i	$-0.781359\pi$
$11$	−56.4191			−1.54645			−0.773227	+	0.634129i	$0.781359\pi$
$12$	19.3656	−	36.7828i	0.465863	−	0.884857i
$13$	−0.217514	+	0.217514i	−0.00464058	+	0.00464058i	−0.709423	−	0.704783i	$-0.751044\pi$
$13$	−0.217514	+	0.217514i	−0.00464058	+	0.00464058i	0.704783	+	0.709423i	$0.251044\pi$
$14$	37.5210	+	59.5970i	0.716278	+	1.13771i
$15$	−20.1432	+	54.4908i	−0.346731	+	0.937965i
$16$	40.0804	+	49.8955i	0.626257	+	0.779617i
$17$	75.4592	+	75.4592i	1.07656	+	1.07656i	0.996815	+	0.0797460i	$0.0254109\pi$
$17$	75.4592	+	75.4592i	1.07656	+	1.07656i	0.0797460	+	0.996815i	$0.474589\pi$
$18$	−22.4718	+	72.9864i	−0.294259	+	0.955726i
$19$	36.8594			0.445060			0.222530	−	0.974926i	$-0.428569\pi$
$19$	36.8594			0.445060			0.222530	+	0.974926i	$0.428569\pi$
$20$	−64.6136	−	61.8473i	−0.722402	−	0.691473i
$21$	−87.9821	−	94.8571i	−0.914251	−	0.985691i
$22$	−35.3714	+	155.608i	−0.342782	+	1.50799i
$23$	−74.5235	+	74.5235i	−0.675618	+	0.675618i	−0.959006	−	0.283387i	$-0.908542\pi$
$23$	−74.5235	+	74.5235i	−0.675618	+	0.675618i	0.283387	+	0.959006i	$0.408542\pi$
$24$	−89.3084	−	76.4722i	−0.759584	−	0.650410i
$25$	100.782	+	73.9457i	0.806257	+	0.591566i
$26$	0.463550	+	0.736287i	0.00349653	+	0.00555376i
$27$	15.7849	−	139.405i	0.112511	−	0.993650i
$28$	187.896	−	66.1216i	1.26818	−	0.446279i
$29$		−	16.5840i		−	0.106192i	−0.998589	−	0.0530959i	$-0.983091\pi$
$29$		−	16.5840i		−	0.106192i	0.998589	−	0.0530959i	$-0.0169089\pi$
$30$	137.661	+	89.7189i	0.837777	+	0.546012i
$31$	−20.7734			−0.120355			−0.0601775	−	0.998188i	$-0.519167\pi$
$31$	−20.7734			−0.120355			−0.0601775	+	0.998188i	$0.519167\pi$
$32$	162.743	−	79.2632i	0.899038	−	0.437871i
$33$	11.0154	−	292.955i	0.0581073	−	1.54536i
$34$	255.430	−	160.813i	1.28841	−	0.811154i
$35$	−248.331	+	125.800i	−1.19930	+	0.607545i
$36$	187.213	+	107.737i	0.866727	+	0.498783i
$37$	−79.9565	−	79.9565i	−0.355264	−	0.355264i	0.506800	−	0.862064i	$-0.330828\pi$
$37$	−79.9565	−	79.9565i	−0.355264	−	0.355264i	−0.862064	+	0.506800i	$0.830828\pi$
$38$	23.1087	−	101.661i	0.0986506	−	0.433989i
$39$	−1.08697	−	1.17191i	−0.00446293	−	0.00481167i
$40$	−211.088	+	139.434i	−0.834398	+	0.551162i
$41$			276.664i			1.05384i	0.849914	+	0.526922i	$0.176654\pi$
$41$			276.664i			1.05384i	−0.849914	+	0.526922i	$0.823346\pi$
$42$	−316.782	+	183.191i	−1.16382	+	0.673024i
$43$	286.448	−	286.448i	1.01588	−	1.01588i	0.0160113	−	0.999872i	$-0.494903\pi$
$43$	286.448	−	286.448i	1.01588	−	1.01588i	0.999872	−	0.0160113i	$-0.00509677\pi$
$44$	407.001	+	195.114i	1.39449	+	0.668511i
$45$	−279.010	−	115.232i	−0.924274	−	0.381729i
$46$	158.819	+	252.263i	0.509056	+	0.808567i
$47$	−229.786	−	229.786i	−0.713143	−	0.713143i	0.254048	−	0.967191i	$-0.418238\pi$
$47$	−229.786	−	229.786i	−0.713143	−	0.713143i	−0.967191	+	0.254048i	$0.918238\pi$
$48$	−266.907	+	198.375i	−0.802597	+	0.596521i
$49$		−	276.953i		−	0.807442i
$50$	267.132	−	231.604i	0.755563	−	0.655076i
$51$	−406.553	+	377.088i	−1.11625	+	1.03535i
$52$	2.32135	−	0.816895i	0.00619064	−	0.00217852i
$53$	25.1531	+	25.1531i	0.0651896	+	0.0651896i	0.738950	−	0.673760i	$-0.235322\pi$
$53$	25.1531	+	25.1531i	0.0651896	+	0.0651896i	−0.673760	+	0.738950i	$0.735322\pi$
$54$	−374.593	−	130.935i	−0.943994	−	0.329962i
$55$	−599.454	−	196.327i	−1.46964	−	0.481322i
$56$	−64.5684	−	559.684i	−0.154077	−	1.33555i
$57$	−7.19654	+	191.392i	−0.0167229	+	0.444745i
$58$	−45.7397	−	10.3972i	−0.103550	−	0.0235382i
$59$			431.866i			0.952953i	0.879187	+	0.476476i	$0.158086\pi$
$59$			431.866i			0.952953i	−0.879187	+	0.476476i	$0.841914\pi$
$60$	333.756	−	323.430i	0.718129	−	0.695910i
$61$		−	745.120i		−	1.56398i	−0.623290	−	0.781991i	$-0.714204\pi$
$61$		−	745.120i		−	1.56398i	0.623290	−	0.781991i	$-0.285796\pi$
$62$	−13.0237	+	57.2944i	−0.0266775	+	0.117361i
$63$	509.722	−	438.325i	1.01935	−	0.876569i
$64$	−116.583	−	498.550i	−0.227701	−	0.973731i
$65$	−3.06799	+	1.55419i	−0.00585443	+	0.00296574i
$66$	−801.085	−	214.047i	−1.49404	−	0.399202i
$67$	583.852	+	583.852i	1.06461	+	1.06461i	0.997763	+	0.0668464i	$0.0212937\pi$
$67$	583.852	+	583.852i	1.06461	+	1.06461i	0.0668464	+	0.997763i	$0.478706\pi$
$68$	−283.395	−	805.314i	−0.505392	−	1.43616i
$69$	−372.412	−	401.512i	−0.649755	−	0.700527i
$70$	191.276	+	763.784i	0.326598	+	1.30414i
$71$			295.657i			0.494198i	0.968990	+	0.247099i	$0.0794772\pi$
$71$			295.657i			0.494198i	−0.968990	+	0.247099i	$0.920523\pi$
$72$	414.518	−	448.802i	0.678491	−	0.734608i
$73$	26.9724	+	26.9724i	0.0432450	+	0.0432450i	0.728399	−	0.685154i	$-0.240265\pi$
$73$	26.9724	+	26.9724i	0.0432450	+	0.0432450i	−0.685154	+	0.728399i	$0.740265\pi$
$74$	−270.653	+	170.398i	−0.425173	+	0.267680i
$75$	−403.639	+	508.872i	−0.621443	+	0.783459i
$76$	−265.900	−	127.471i	−0.401326	−	0.192393i
$77$	993.323	−	993.323i	1.47013	−	1.47013i
$78$	−3.91366	+	2.26322i	−0.00568122	+	0.00328538i
$79$			1137.70i			1.62028i	0.586239	+	0.810138i	$0.300608\pi$
$79$			1137.70i			1.62028i	−0.586239	+	0.810138i	$0.699392\pi$
$80$	252.230	+	669.612i	0.352502	+	0.935811i
$81$	720.778	+	109.181i	0.988721	+	0.149768i
$82$	763.058	+	173.452i	1.02763	+	0.233592i
$83$	275.299	+	275.299i	0.364073	+	0.364073i	0.865310	−	0.501237i	$-0.167122\pi$
$83$	275.299	+	275.299i	0.364073	+	0.364073i	−0.501237	+	0.865310i	$0.667122\pi$
$84$	306.650	+	988.556i	0.398313	+	1.28405i
$85$	539.173	+	1064.34i	0.688018	+	1.35816i
$86$	−610.458	−	969.631i	−0.765435	−	1.21579i
$87$	86.1119	+	3.23790i	0.106117	+	0.00399011i
$88$	793.303	−	1000.21i	0.960981	−	1.21163i
$89$	−756.706			−0.901244			−0.450622	−	0.892715i	$-0.648798\pi$
$89$	−756.706			−0.901244			−0.450622	+	0.892715i	$0.648798\pi$
$90$	−492.741	+	697.285i	−0.577105	+	0.816670i
$91$		−	7.65916i		−	0.00882306i
$92$	795.328	−	279.880i	0.901290	−	0.317169i
$93$	4.05585	−	107.865i	0.00452229	−	0.120270i
$94$	−777.828	+	489.703i	−0.853477	+	0.537330i
$95$	391.632	+	128.263i	0.422954	+	0.138521i
$96$	379.798	+	860.517i	0.403781	+	0.914856i
$97$	575.441	−	575.441i	0.602342	−	0.602342i	−0.338592	−	0.940933i	$-0.609951\pi$
$97$	575.441	−	575.441i	0.602342	−	0.602342i	0.940933	+	0.338592i	$0.109951\pi$
$98$	−763.854	−	173.633i	−0.787356	−	0.178975i
$99$	1519.01	+	114.395i	1.54209	+	0.116133i
$100$	−471.305	−	881.970i	−0.471305	−	0.881970i
$101$	−52.2236			−0.0514499			−0.0257249	−	0.999669i	$-0.508189\pi$
$101$	−52.2236			−0.0514499			−0.0257249	+	0.999669i	$0.508189\pi$
$102$	785.149	+	1357.71i	0.762170	+	1.31798i
$103$	206.494	+	206.494i	0.197538	+	0.197538i	0.798944	−	0.601406i	$-0.205392\pi$
$103$	206.494	+	206.494i	0.197538	+	0.197538i	−0.601406	+	0.798944i	$0.705392\pi$
$104$	−0.797707	−	6.91459i	−0.000752130	−	0.00651953i
$105$	−604.729	−	1314.02i	−0.562052	−	1.22129i
$106$	85.1436	−	53.6046i	0.0780178	−	0.0491183i
$107$	198.623	−	198.623i	0.179454	−	0.179454i	−0.611664	−	0.791118i	$-0.709499\pi$
$107$	198.623	−	198.623i	0.179454	−	0.179454i	0.791118	+	0.611664i	$0.209499\pi$
$108$	−595.975	+	951.066i	−0.530997	+	0.847374i
$109$	−1206.68			−1.06036			−0.530181	−	0.847885i	$-0.677876\pi$
$109$	−1206.68			−1.06036			−0.530181	+	0.847885i	$0.677876\pi$
$110$	−917.305	+	1530.25i	−0.795105	+	1.32640i
$111$	430.784	−	399.562i	0.368362	−	0.341664i
$112$	−1584.13	−	172.805i	−1.33648	−	0.145790i
$113$	−652.264	+	652.264i	−0.543007	+	0.543007i	−0.924409	−	0.381402i	$-0.875441\pi$
$113$	−652.264	+	652.264i	−0.543007	+	0.543007i	0.381402	+	0.924409i	$0.375441\pi$
$114$	523.360	+	139.840i	0.429975	+	0.114888i
$115$	−1051.14	+	532.487i	−0.852341	+	0.431780i
$116$	−57.3521	+	119.635i	−0.0459053	+	0.0957570i
$117$	6.29732	−	5.41526i	0.00497596	−	0.00427899i
$118$	1191.12	+	270.755i	0.929248	+	0.211229i
$119$	−2657.09			−2.04685
$120$	−682.796	−	1123.29i	−0.519421	−	0.854519i
$121$	1852.11			1.39152
$122$	−2055.09	−	467.146i	−1.52508	−	0.346667i
$123$	−1436.57	−	54.0166i	−1.05310	−	0.0395977i
$124$	149.857	+	71.8404i	0.108529	+	0.0520279i
$125$	813.496	+	1136.38i	0.582090	+	0.813124i
$126$	−889.367	−	1680.65i	−0.628818	−	1.18829i
$127$	1196.61	−	1196.61i	0.836076	−	0.836076i	−0.152264	−	0.988340i	$-0.548656\pi$
$127$	1196.61	−	1196.61i	0.836076	−	0.836076i	0.988340	+	0.152264i	$0.0486565\pi$
$128$	−1448.13	+	8.98236i	−0.999981	+	0.00620263i
$129$	1431.45	+	1543.31i	0.976994	+	1.05334i
$130$	2.36310	+	9.43612i	0.00159429	+	0.00636617i
$131$	1286.84			0.858256			0.429128	−	0.903244i	$-0.358821\pi$
$131$	1286.84			0.858256			0.429128	+	0.903244i	$0.358821\pi$
$132$	−1092.59	+	2075.25i	−0.720437	+	1.36839i
$133$	−648.952	+	648.952i	−0.423092	+	0.423092i
$134$	1976.34	−	1244.26i	1.27411	−	0.802149i
$135$	652.817	−	1426.26i	0.416189	−	0.909278i
$136$	−2398.78	+	276.738i	−1.51246	+	0.174486i
$137$	1743.72	+	1743.72i	1.08742	+	1.08742i	0.995794	+	0.0916244i	$0.0292059\pi$
$137$	1743.72	+	1743.72i	1.08742	+	1.08742i	0.0916244	+	0.995794i	$0.470794\pi$
$138$	−1340.88	+	775.413i	−0.827124	+	0.478315i
$139$	37.5643			0.0229220			0.0114610	−	0.999934i	$-0.496352\pi$
$139$	37.5643			0.0229220			0.0114610	+	0.999934i	$0.496352\pi$
$140$	2226.49	−	48.7046i	1.34409	−	0.0294021i
$141$	1238.02	−	1148.30i	0.739435	−	0.685843i
$142$	815.442	+	185.359i	0.481904	+	0.109542i
$143$	12.2719	−	12.2719i	0.00717644	−	0.00717644i
$144$	−977.949	−	1424.64i	−0.565943	−	0.824445i
$145$	57.7087	−	176.205i	0.0330514	−	0.100917i
$146$	91.3020	−	57.4817i	0.0517548	−	0.0325837i
$147$	1438.07	+	54.0730i	0.806872	+	0.0303392i
$148$	300.285	+	853.310i	0.166779	+	0.473930i
$149$			2725.02i			1.49827i	0.662417	+	0.749135i	$0.269531\pi$
$149$			2725.02i			1.49827i	−0.662417	+	0.749135i	$0.730469\pi$
$150$	1150.45	+	1432.30i	0.626224	+	0.779644i
$151$	−3087.06			−1.66372			−0.831858	−	0.554988i	$-0.812723\pi$
$151$	−3087.06			−1.66372			−0.831858	+	0.554988i	$0.812723\pi$
$152$	−518.276	+	653.454i	−0.276564	+	0.348698i
$153$	−1878.64	−	2184.65i	−0.992676	−	1.15437i
$154$	−2116.90	−	3362.41i	−1.10769	−	1.75942i
$155$	−220.717	−	72.2870i	−0.114377	−	0.0374596i
$156$	3.78849	+	12.2131i	0.00194437	+	0.00626812i
$157$	1053.69	+	1053.69i	0.535627	+	0.535627i	0.922241	−	0.386615i	$-0.126356\pi$
$157$	1053.69	+	1053.69i	0.535627	+	0.535627i	−0.386615	+	0.922241i	$0.626356\pi$
$158$	3137.87	+	713.273i	1.57997	+	0.359145i
$159$	−135.518	+	125.696i	−0.0675931	+	0.0626941i
$160$	2004.97	−	275.860i	0.990667	−	0.136304i
$161$		−	2624.14i		−	1.28454i
$162$	753.013	−	1919.51i	0.365199	−	0.930929i
$163$	983.357	−	983.357i	0.472531	−	0.472531i	−0.430202	−	0.902733i	$-0.641558\pi$
$163$	983.357	−	983.357i	0.472531	−	0.472531i	0.902733	+	0.430202i	$0.141558\pi$
$164$	956.783	−	1995.82i	0.455562	−	0.950289i
$165$	1136.46	−	3074.32i	0.536203	−	1.45052i
$166$	931.891	−	586.698i	0.435715	−	0.274317i
$167$	1914.23	+	1914.23i	0.886993	+	0.886993i	0.994233	−	0.107240i	$-0.0342014\pi$
$167$	1914.23	+	1914.23i	0.886993	+	0.886993i	−0.107240	+	0.994233i	$0.534201\pi$
$168$	2918.76	−	225.996i	1.34040	−	0.103786i
$169$			2196.91i			0.999957i
$170$	3273.55	−	819.800i	1.47688	−	0.369858i
$171$	−992.394	−	74.7359i	−0.443803	−	0.0334222i
$172$	−3057.03	+	1075.79i	−1.35521	+	0.476906i
$173$	−2695.49	−	2695.49i	−1.18459	−	1.18459i	−0.978541	−	0.206051i	$-0.933939\pi$
$173$	−2695.49	−	2695.49i	−1.18459	−	1.18459i	−0.206051	−	0.978541i	$-0.566061\pi$
$174$	62.9174	−	235.473i	0.0274124	−	0.102593i
$175$	−3076.28	+	472.484i	−1.32883	+	0.204094i
$176$	−2261.30	−	2815.06i	−0.968478	−	1.20564i
$177$	−2242.46	−	84.3189i	−0.952280	−	0.0358068i
$178$	−474.410	+	2087.05i	−0.199767	+	0.878825i
$179$		−	1585.21i		−	0.661924i	−0.943644	−	0.330962i	$-0.892627\pi$
$179$		−	1585.21i		−	0.661924i	0.943644	−	0.330962i	$-0.107373\pi$
$180$	1614.24	+	1796.17i	0.668435	+	0.743770i
$181$			373.208i			0.153262i	0.997060	+	0.0766308i	$0.0244163\pi$
$181$			373.208i			0.153262i	−0.997060	+	0.0766308i	$0.975584\pi$
$182$	−21.1245	−	4.80184i	−0.00860358	−	0.00195569i
$183$	3869.02	+	145.479i	1.56288	+	0.0587659i
$184$	−273.306	−	2369.04i	−0.109502	−	0.949173i
$185$	−571.307	−	1127.77i	−0.227045	−	0.448191i
$186$	−294.957	−	78.8115i	−0.116276	−	0.0310685i
$187$	−4257.34	−	4257.34i	−1.66485	−	1.66485i
$188$	862.984	+	2452.32i	0.334785	+	0.951349i
$189$	2176.48	+	2732.30i	0.837648	+	1.05156i
$190$	599.289	−	999.735i	0.228826	−	0.381728i
$191$			2401.11i			0.909624i	0.890587	+	0.454812i	$0.150294\pi$
$191$			2401.11i			0.909624i	−0.890587	+	0.454812i	$0.849706\pi$
$192$	2611.48	−	508.016i	0.981599	−	0.190953i
$193$	−820.303	−	820.303i	−0.305941	−	0.305941i	0.537392	−	0.843333i	$-0.319410\pi$
$193$	−820.303	−	820.303i	−0.305941	−	0.305941i	−0.843333	+	0.537392i	$0.819410\pi$
$194$	−1226.34	−	1947.87i	−0.453845	−	0.720871i
$195$	−7.47108	−	16.2339i	−0.00274367	−	0.00596173i
$196$	−957.782	+	1997.91i	−0.349046	+	0.728100i
$197$	−2611.04	+	2611.04i	−0.944308	+	0.944308i	−0.998529	−	0.0542212i	$-0.982732\pi$
$197$	−2611.04	+	2611.04i	−0.944308	+	0.944308i	0.0542212	+	0.998529i	$0.482732\pi$
$198$	1267.84	−	4117.83i	0.455058	−	1.47799i
$199$		−	2091.43i		−	0.745014i	−0.928029	−	0.372507i	$-0.878498\pi$
$199$		−	2091.43i		−	0.745014i	0.928029	−	0.372507i	$-0.121502\pi$
$200$	−2728.02	+	746.949i	−0.964499	+	0.264086i
$201$	−3145.63	+	2917.65i	−1.10386	+	1.02386i
$202$	−32.7411	+	144.036i	−0.0114042	+	0.0501701i
$203$	291.980	+	291.980i	0.100950	+	0.100950i
$204$	4236.91	−	1314.29i	1.45413	−	0.451072i
$205$	−962.732	+	2939.56i	−0.328001	+	1.00150i
$206$	698.983	−	440.065i	0.236410	−	0.148839i
$207$	2157.55	−	1855.35i	0.724447	−	0.622974i
$208$	−19.5710	−	2.13490i	−0.00652407	−	0.000711678i
$209$	−2079.58			−0.688264
$210$	−4003.28	+	844.073i	−1.31549	+	0.277365i
$211$		−	2674.91i		−	0.872740i	−0.899767	−	0.436370i	$-0.856264\pi$
$211$		−	2674.91i		−	0.872740i	0.899767	−	0.436370i	$-0.143736\pi$
$212$	−94.4652	−	268.439i	−0.0306033	−	0.0869644i
$213$	−1535.19	−	57.7249i	−0.493849	−	0.0185692i
$214$	−423.291	−	672.340i	−0.135213	−	0.214767i
$215$	4040.30	−	2046.74i	1.28161	−	0.649239i
$216$	2249.46	+	2240.00i	0.708596	+	0.705615i
$217$	365.739	−	365.739i	0.114415	−	0.114415i
$218$	−756.519	+	3328.12i	−0.235037	+	1.03398i
$219$	−145.320	+	134.788i	−0.0448394	+	0.0415896i
$220$	3645.44	+	3489.37i	1.11716	+	1.06933i
$221$	−32.8269			−0.00999173
$222$	−831.943	−	1438.63i	−0.251515	−	0.434931i
$223$	−550.676	−	550.676i	−0.165363	−	0.165363i	0.619575	−	0.784938i	$-0.287305\pi$
$223$	−550.676	−	550.676i	−0.165363	−	0.165363i	−0.784938	+	0.619575i	$0.787305\pi$
$224$	−1469.76	+	4260.80i	−0.438404	+	1.27092i
$225$	−2563.50	−	2195.24i	−0.759556	−	0.650442i
$226$	1390.06	+	2207.92i	0.409138	+	0.649861i
$227$	−842.165	+	842.165i	−0.246240	+	0.246240i	−0.819426	−	0.573186i	$-0.805707\pi$
$227$	−842.165	+	842.165i	−0.246240	+	0.246240i	0.573186	+	0.819426i	$0.305707\pi$
$228$	713.804	−	1355.79i	0.207337	−	0.393814i
$229$	1434.13			0.413842			0.206921	−	0.978358i	$-0.433656\pi$
$229$	1434.13			0.413842			0.206921	+	0.978358i	$0.433656\pi$
$230$	809.634	+	3232.95i	0.232112	+	0.926846i
$231$	4963.87	+	5351.75i	1.41385	+	1.52433i
$232$	294.005	+	233.185i	0.0831998	+	0.0659886i
$233$	−2771.41	+	2771.41i	−0.779232	+	0.779232i	−0.979700	−	0.200468i	$-0.935754\pi$
$233$	−2771.41	+	2771.41i	−0.779232	+	0.779232i	0.200468	+	0.979700i	$0.435754\pi$
$234$	−10.9876	−	20.7635i	−0.00306959	−	0.00580065i
$235$	−1641.87	−	3241.09i	−0.455762	−	0.899682i
$236$	1493.52	−	3115.44i	0.411949	−	0.859312i
$237$	−5907.51	−	222.129i	−1.61913	−	0.0608811i
$238$	−1665.84	+	7328.44i	−0.453698	+	1.99593i
$239$	−794.482			−0.215024			−0.107512	−	0.994204i	$-0.534288\pi$
$239$	−794.482			−0.215024			−0.107512	+	0.994204i	$0.534288\pi$
$240$	−3526.19	+	1178.96i	−0.948395	+	0.317090i
$241$	5158.76			1.37886			0.689430	−	0.724353i	$-0.257861\pi$
$241$	5158.76			1.37886			0.689430	+	0.724353i	$0.257861\pi$
$242$	1161.17	−	5108.26i	0.308440	−	1.35691i
$243$	−707.646	+	3721.31i	−0.186813	+	0.982396i
$244$	−2576.84	+	5375.22i	−0.676088	+	1.41030i
$245$	963.737	−	2942.63i	0.251310	−	0.767337i
$246$	−1049.63	+	3928.30i	−0.272040	+	1.01813i
$247$	−8.01744	+	8.01744i	−0.00206533	+	0.00206533i
$248$	292.092	−	368.276i	0.0747898	−	0.0942965i
$249$	−1483.24	+	1375.74i	−0.377495	+	0.350136i
$250$	3644.22	−	1531.24i	0.921922	−	0.387376i
$251$	783.842			0.197114			0.0985571	−	0.995131i	$-0.468577\pi$
$251$	783.842			0.197114			0.0985571	+	0.995131i	$0.468577\pi$
$252$	−5192.93	+	1399.27i	−1.29811	+	0.349784i
$253$	4204.55	−	4204.55i	1.04481	−	1.04481i
$254$	−2550.12	−	4050.52i	−0.629956	−	1.00060i
$255$	−5631.82	+	2591.84i	−1.38305	+	0.636500i
$256$	−883.115	+	3999.67i	−0.215604	+	0.976481i
$257$	1459.00	+	1459.00i	0.354125	+	0.354125i	0.861642	−	0.507517i	$-0.169437\pi$
$257$	1459.00	+	1459.00i	0.354125	+	0.354125i	−0.507517	+	0.861642i	$0.669437\pi$
$258$	5153.98	−	2980.48i	1.24369	−	0.719212i
$259$	2815.45			0.675458
$260$	27.5070	−	0.601718i	0.00656120	−	0.000143527i
$261$	−33.6255	+	446.502i	−0.00797458	+	0.105892i
$262$	806.771	−	3549.19i	0.190239	−	0.836907i
$263$	1593.30	−	1593.30i	0.373562	−	0.373562i	−0.495211	−	0.868773i	$-0.664909\pi$
$263$	1593.30	−	1593.30i	0.373562	−	0.373562i	0.868773	+	0.495211i	$0.164909\pi$
$264$	5038.70	+	4314.49i	1.17466	+	1.00583i
$265$	179.725	+	354.780i	0.0416619	+	0.0822415i
$266$	1383.00	+	2196.71i	0.318787	+	0.506349i
$267$	147.742	−	3929.19i	0.0338638	−	0.900608i
$268$	−2192.71	−	6230.97i	−0.499781	−	1.42021i
$269$		−	2716.62i		−	0.615745i	−0.951428	−	0.307873i	$-0.900383\pi$
$269$		−	2716.62i		−	0.615745i	0.951428	−	0.307873i	$-0.0996170\pi$
$270$	−3524.43	−	2694.69i	−0.794408	−	0.607384i
$271$	2356.20			0.528151			0.264075	−	0.964502i	$-0.414933\pi$
$271$	2356.20			0.528151			0.264075	+	0.964502i	$0.414933\pi$
$272$	−740.633	+	6789.51i	−0.165101	+	1.51351i
$273$	39.7701	+	1.49540i	0.00881683	+	0.000331522i
$274$	5902.52	−	3716.10i	1.30140	−	0.819334i
$275$	−5686.03	−	4171.95i	−1.24684	−	0.914830i
$276$	1297.99	+	4184.37i	0.283079	+	0.912571i
$277$	364.520	+	364.520i	0.0790683	+	0.0790683i	0.745535	−	0.666467i	$-0.232194\pi$
$277$	364.520	+	364.520i	0.0790683	+	0.0790683i	−0.666467	+	0.745535i	$0.732194\pi$
$278$	23.5506	−	103.605i	0.00508083	−	0.0223518i
$279$	559.297	+	42.1199i	0.120015	+	0.00903818i
$280$	1261.54	−	6171.34i	0.269256	−	1.31717i
$281$		−	1026.00i		−	0.217815i	−0.994052	−	0.108908i	$-0.965265\pi$
$281$		−	1026.00i		−	0.217815i	0.994052	−	0.108908i	$-0.0347353\pi$
$282$	−2390.91	−	4134.47i	−0.504882	−	0.873064i
$283$	−3337.85	+	3337.85i	−0.701111	+	0.701111i	−0.964649	−	0.263538i	$-0.915111\pi$
$283$	−3337.85	+	3337.85i	−0.701111	+	0.701111i	0.263538	+	0.964649i	$0.415111\pi$
$284$	1022.47	−	2132.84i	0.213635	−	0.445636i
$285$	−742.468	+	2008.50i	−0.154316	+	0.417450i
$286$	−26.1531	−	41.5406i	−0.00540722	−	0.00858864i
$287$	−4870.98	−	4870.98i	−1.00183	−	1.00183i
$288$	−4542.37	+	1804.09i	−0.929381	+	0.369121i
$289$			6475.18i			1.31797i
$290$	−449.805	−	269.635i	−0.0910809	−	0.0545983i
$291$	2875.61	+	3100.32i	0.579284	+	0.624549i
$292$	−101.298	−	287.855i	−0.0203014	−	0.0576898i
$293$	4222.18	+	4222.18i	0.841850	+	0.841850i	0.989099	−	0.147249i	$-0.0470419\pi$
$293$	4222.18	+	4222.18i	0.841850	+	0.841850i	−0.147249	+	0.989099i	$0.547042\pi$
$294$	1050.72	−	3932.40i	0.208433	−	0.780075i
$295$	−1502.81	+	4588.59i	−0.296599	+	0.905620i
$296$	2541.75	−	293.231i	0.499109	−	0.0575801i
$297$	−890.570	+	7865.12i	−0.173994	+	1.53664i
$298$	7515.79	+	1708.43i	1.46100	+	0.332102i
$299$		−	32.4198i		−	0.00627052i
$300$	4671.63	−	2275.05i	0.899056	−	0.437833i
$301$			10086.5i			1.93148i
$302$	−1935.40	+	8514.32i	−0.368774	+	1.62233i
$303$	10.1963	−	271.170i	0.00193321	−	0.0514136i
$304$	1477.34	+	1839.12i	0.278722	+	0.346976i
$305$	2592.86	−	7916.92i	0.486777	−	1.48630i
$306$	−7203.20	+	3811.79i	−1.34569	+	0.712109i
$307$	6882.82	+	6882.82i	1.27956	+	1.27956i	0.940916	+	0.338639i	$0.109966\pi$
$307$	6882.82	+	6882.82i	1.27956	+	1.27956i	0.338639	+	0.940916i	$0.390034\pi$
$308$	−10600.9	+	3730.52i	−1.96118	+	0.690150i
$309$	−1112.53	+	1031.90i	−0.204821	+	0.189976i
$310$	−337.749	+	563.434i	−0.0618802	+	0.103229i
$311$		−	5232.29i		−	0.954007i	−0.878901	−	0.477004i	$-0.841723\pi$
$311$		−	5232.29i		−	0.954007i	0.878901	−	0.477004i	$-0.158277\pi$
$312$	36.0596	−	2.79205i	0.00654318	−	0.000506631i
$313$	−4673.43	−	4673.43i	−0.843955	−	0.843955i	0.145416	−	0.989371i	$-0.453548\pi$
$313$	−4673.43	−	4673.43i	−0.843955	−	0.843955i	−0.989371	+	0.145416i	$0.953548\pi$
$314$	3566.74	−	2245.54i	0.641028	−	0.403577i
$315$	6941.08	−	2883.49i	1.24154	−	0.515766i
$316$	3934.51	−	8207.28i	0.700423	−	1.46106i
$317$	−1016.10	+	1016.10i	−0.180032	+	0.180032i	−0.791370	−	0.611338i	$-0.790632\pi$
$317$	−1016.10	+	1016.10i	−0.180032	+	0.180032i	0.611338	+	0.791370i	$0.290632\pi$
$318$	261.717	+	452.573i	0.0461521	+	0.0798083i
$319$			935.652i			0.164221i
$320$	496.156	−	5702.79i	0.0866749	−	0.996237i
$321$	992.566	+	1070.13i	0.172584	+	0.186070i
$322$	−7237.56	−	1645.18i	−1.25259	−	0.284728i
$323$	2781.38	+	2781.38i	0.479134	+	0.479134i
$324$	−4822.03	−	3280.28i	−0.826823	−	0.562462i
$325$	−38.0057	+	5.83728i	−0.00648671	+	0.000996289i
$326$	−2095.66	−	3328.67i	−0.356037	−	0.565516i
$327$	235.597	−	6265.69i	0.0398426	−	1.05961i
$328$	−4904.77	−	3890.14i	−0.825672	−	0.654868i
$329$	8091.29			1.35589
$330$	−7766.70	−	5061.86i	−1.29558	−	0.844383i
$331$		−	6010.66i		−	0.998114i	−0.866569	−	0.499057i	$-0.833680\pi$
$331$		−	6010.66i		−	0.998114i	0.866569	−	0.499057i	$-0.166320\pi$
$332$	−1033.91	−	2938.04i	−0.170914	−	0.485681i
$333$	1990.61	+	2314.85i	0.327582	+	0.380940i
$334$	6479.70	−	4079.48i	1.06154	−	0.668321i
$335$	4171.75	+	8235.12i	0.680380	+	1.34308i
$336$	1206.58	−	8191.82i	0.195905	−	1.33006i
$337$	4962.27	−	4962.27i	0.802114	−	0.802114i	−0.181312	−	0.983426i	$-0.558034\pi$
$337$	4962.27	−	4962.27i	0.802114	−	0.802114i	0.983426	+	0.181312i	$0.0580344\pi$
$338$	6059.22	+	1377.33i	0.975083	+	0.221647i
$339$	−3259.52	−	3514.22i	−0.522221	−	0.563027i
$340$	−208.746	−	9542.63i	−0.0332966	−	1.52212i
$341$	1172.01			0.186124
$342$	−828.299	+	2690.24i	−0.130963	+	0.425355i
$343$	−1162.84	−	1162.84i	−0.183054	−	0.183054i
$344$	1050.52	+	9105.95i	0.164651	+	1.42721i
$345$	−2559.70	−	5561.99i	−0.399448	−	0.867963i
$346$	−9124.26	+	5744.44i	−1.41770	+	0.892552i
$347$	6201.12	−	6201.12i	0.959347	−	0.959347i	−0.0398580	−	0.999205i	$-0.512691\pi$
$347$	6201.12	−	6201.12i	0.959347	−	0.959347i	0.999205	+	0.0398580i	$0.0126906\pi$
$348$	−610.004	−	321.158i	−0.0939646	−	0.0494709i
$349$	1670.38			0.256198			0.128099	−	0.991761i	$-0.459112\pi$
$349$	1670.38			0.256198			0.128099	+	0.991761i	$0.459112\pi$
$350$	−625.502	+	8780.82i	−0.0955271	+	1.34101i
$351$	26.8892	+	33.7560i	0.00408900	+	0.00513323i
$352$	−9181.83	+	4471.96i	−1.39032	+	0.677148i
$353$	1598.52	−	1598.52i	0.241022	−	0.241022i	−0.576251	−	0.817273i	$-0.695485\pi$
$353$	1598.52	−	1598.52i	0.241022	−	0.241022i	0.817273	+	0.576251i	$0.195485\pi$
$354$	−1638.45	+	6131.99i	−0.245996	+	0.920655i
$355$	−1028.82	+	3141.36i	−0.153815	+	0.469651i
$356$	5458.80	+	2616.91i	0.812684	+	0.389595i
$357$	518.778	−	13796.9i	0.0769094	−	2.04540i
$358$	−4372.13	−	993.834i	−0.645458	−	0.146720i
$359$	−8007.82			−1.17726			−0.588630	−	0.808402i	$-0.700333\pi$
$359$	−8007.82			−1.17726			−0.588630	+	0.808402i	$0.700333\pi$
$360$	5966.00	−	3326.09i	0.873432	−	0.486946i
$361$	−5500.38			−0.801922
$362$	1029.33	+	233.979i	0.149449	+	0.0339715i
$363$	−361.612	+	9617.07i	−0.0522857	+	1.39054i
$364$	−26.4876	+	55.2524i	−0.00381409	+	0.00795607i
$365$	192.724	+	380.441i	0.0276374	+	0.0545567i
$366$	2826.89	−	10579.8i	0.403727	−	1.51097i
$367$	939.139	−	939.139i	0.133577	−	0.133577i	−0.637157	−	0.770734i	$-0.719890\pi$
$367$	939.139	−	939.139i	0.133577	−	0.133577i	0.770734	+	0.637157i	$0.219890\pi$
$368$	−6705.32	−	731.449i	−0.949834	−	0.103613i
$369$	560.961	−	7448.83i	0.0791395	−	1.05087i
$370$	−3468.65	+	868.659i	−0.487368	+	0.122053i
$371$	−885.700			−0.123944
$372$	−402.288	+	764.103i	−0.0560690	+	0.106497i
$373$	521.645	−	521.645i	0.0724122	−	0.0724122i	−0.669973	−	0.742385i	$-0.733694\pi$
$373$	521.645	−	521.645i	0.0724122	−	0.0724122i	0.742385	+	0.669973i	$0.233694\pi$
$374$	−14411.1	+	9072.94i	−1.99247	+	1.25441i
$375$	−6059.44	+	4002.19i	−0.834422	+	0.551126i
$376$	7304.70	−	842.713i	1.00189	−	0.115584i
$377$	3.60724	+	3.60724i	0.000492792	+	0.000492792i
$378$	8900.40	−	4289.89i	1.21108	−	0.583725i
$379$	1425.57			0.193210			0.0966052	−	0.995323i	$-0.469202\pi$
$379$	1425.57			0.193210			0.0966052	+	0.995323i	$0.469202\pi$
$380$	−2381.62	−	2279.65i	−0.321512	−	0.307747i
$381$	5979.73	+	6446.98i	0.804070	+	0.866900i
$382$	6622.43	+	1505.35i	0.886997	+	0.201625i
$383$	10135.4	−	10135.4i	1.35220	−	1.35220i	0.469013	−	0.883191i	$-0.344610\pi$
$383$	10135.4	−	10135.4i	1.35220	−	1.35220i	0.883191	−	0.469013i	$-0.155390\pi$
$384$	236.096	−	7521.13i	0.0313756	−	0.999508i
$385$	14010.6	−	7097.52i	1.85467	−	0.939540i
$386$	−2776.73	+	1748.17i	−0.366145	+	0.230517i
$387$	−8293.07	+	7131.47i	−1.08930	+	0.936726i
$388$	−6141.21	+	2161.12i	−0.803537	+	0.282769i
$389$		−	5444.15i		−	0.709588i	−0.934945	−	0.354794i	$-0.884551\pi$
$389$		−	5444.15i		−	0.709588i	0.934945	−	0.354794i	$-0.115449\pi$
$390$	−49.4583	+	10.4280i	−0.00642158	+	0.00135396i
$391$	−11247.0			−1.45469
$392$	4909.89	+	3894.20i	0.632619	+	0.501752i
$393$	−251.246	+	6681.89i	−0.0322486	+	0.857650i
$394$	5564.45	+	8838.38i	0.711505	+	1.13013i
$395$	−3958.98	+	12088.1i	−0.504298	+	1.53980i
$396$	−10562.4	−	6078.43i	−1.34035	−	0.771344i
$397$	−2532.02	−	2532.02i	−0.320097	−	0.320097i	0.528707	−	0.848804i	$-0.322677\pi$
$397$	−2532.02	−	2532.02i	−0.320097	−	0.320097i	−0.848804	+	0.528707i	$0.822677\pi$
$398$	−5768.32	−	1311.21i	−0.726482	−	0.165138i
$399$	−3242.97	−	3496.38i	−0.406896	−	0.438691i
$400$	349.834	+	7992.35i	0.0437292	+	0.999043i
$401$		−	11326.9i		−	1.41056i	−0.708927	−	0.705282i	$-0.750820\pi$
$401$		−	11326.9i		−	1.41056i	0.708927	−	0.705282i	$-0.249180\pi$
$402$	6074.95	+	10505.1i	0.753709	+	1.30335i
$403$	4.51850	−	4.51850i	0.000558517	−	0.000558517i
$404$	376.735	+	180.604i	0.0463942	+	0.0222411i
$405$	7278.35	+	3668.21i	0.892998	+	0.450061i
$406$	988.353	−	622.246i	0.120816	−	0.0760629i
$407$	4511.07	+	4511.07i	0.549399	+	0.549399i
$408$	−968.609	−	12509.7i	−0.117533	−	1.51794i
$409$			1259.94i			0.152323i	0.997096	+	0.0761614i	$0.0242664\pi$
$409$			1259.94i			0.152323i	−0.997096	+	0.0761614i	$0.975734\pi$
$410$	7503.93	+	4498.21i	0.903884	+	0.541831i
$411$	−9394.70	+	8713.80i	−1.12751	+	1.04579i
$412$	−775.508	−	2203.74i	−0.0927343	−	0.263520i
$413$	−7603.50	−	7603.50i	−0.905917	−	0.905917i
$414$	−3764.52	−	7113.88i	−0.446899	−	0.844512i
$415$	1967.08	+	3883.05i	0.232675	+	0.459304i
$416$	−18.1581	+	52.6398i	−0.00214008	+	0.00620403i
$417$	−7.33417	+	195.052i	−0.000861285	+	0.0229059i
$418$	−1303.77	+	5735.61i	−0.152559	+	0.671144i
$419$			331.702i			0.0386747i	0.999813	+	0.0193374i	$0.00615566\pi$
$419$			331.702i			0.0386747i	−0.999813	+	0.0193374i	$0.993844\pi$
$420$	−181.808	+	11570.5i	−0.0211222	+	1.34425i
$421$		−	12107.7i		−	1.40165i	−0.713333	−	0.700826i	$-0.752815\pi$
$421$		−	12107.7i		−	1.40165i	0.713333	−	0.700826i	$-0.247185\pi$
$422$	−7377.58	−	1677.01i	−0.851031	−	0.193449i
$423$	5720.79	+	6652.61i	0.657575	+	0.764684i
$424$	−799.597	+	92.2462i	−0.0915846	+	0.0105657i
$425$	2025.05	+	13184.8i	0.231128	+	1.50484i
$426$	−1121.68	+	4197.98i	−0.127572	+	0.477448i
$427$	13118.7	+	13118.7i	1.48679	+	1.48679i
$428$	−2119.74	+	745.948i	−0.239396	+	0.0842447i
$429$	61.3258	+	66.1179i	0.00690172	+	0.00744103i
$430$	−3112.02	−	12426.6i	−0.349011	−	1.39364i
$431$		−	1910.95i		−	0.213567i	−0.994282	−	0.106783i	$-0.965945\pi$
$431$		−	1910.95i		−	0.213567i	0.994282	−	0.106783i	$-0.0340551\pi$
$432$	7588.36	−	4799.83i	0.845128	−	0.534565i
$433$	3673.40	+	3673.40i	0.407696	+	0.407696i	0.880934	−	0.473238i	$-0.156915\pi$
$433$	3673.40	+	3673.40i	0.407696	+	0.407696i	−0.473238	+	0.880934i	$0.656915\pi$
$434$	−779.437	−	1238.03i	−0.0862077	−	0.136929i
$435$	903.674	+	334.054i	0.0996042	+	0.0368200i
$436$	8704.89	+	4173.07i	0.956167	+	0.458380i
$437$	−2746.89	+	2746.89i	−0.300690	+	0.300690i
$438$	280.647	+	485.307i	0.0306160	+	0.0529426i
$439$		−	11326.6i		−	1.23141i	−0.787978	−	0.615703i	$-0.788872\pi$
$439$		−	11326.6i		−	1.23141i	0.787978	−	0.615703i	$-0.211128\pi$
$440$	11909.4	−	7866.75i	1.29036	−	0.852347i
$441$	−561.547	+	7456.60i	−0.0606356	+	0.805162i
$442$	−20.5805	+	90.5387i	−0.00221474	+	0.00974319i
$443$	−2204.49	−	2204.49i	−0.236430	−	0.236430i	0.578940	−	0.815370i	$-0.303467\pi$
$443$	−2204.49	−	2204.49i	−0.236430	−	0.236430i	−0.815370	+	0.578940i	$0.803467\pi$
$444$	−4489.43	+	1392.62i	−0.479862	+	0.148853i
$445$	−8040.02	−	2633.18i	−0.856480	−	0.280505i
$446$	−1864.04	+	1173.56i	−0.197904	+	0.124596i
$447$	−14149.6	−	532.041i	−1.49721	−	0.0562968i
$448$	10830.1	+	6724.97i	1.14213	+	0.709208i
$449$	6801.14			0.714845			0.357423	−	0.933943i	$-0.383656\pi$
$449$	6801.14			0.714845			0.357423	+	0.933943i	$0.383656\pi$
$450$	−7661.79	+	5694.03i	−0.802623	+	0.596487i
$451$		−	15609.1i		−	1.62972i
$452$	6961.08	−	2449.64i	0.724384	−	0.254915i
$453$	602.726	−	16029.5i	0.0625134	−	1.66254i
$454$	1794.76	+	2850.74i	0.185534	+	0.294695i
$455$	26.6523	−	81.3788i	0.00274611	−	0.00838483i
$456$	−3291.86	−	2818.72i	−0.338060	−	0.289471i
$457$	−10269.0	+	10269.0i	−1.05113	+	1.05113i	−0.0525049	+	0.998621i	$0.516721\pi$
$457$	−10269.0	+	10269.0i	−1.05113	+	1.05113i	−0.998621	+	0.0525049i	$0.983279\pi$
$458$	899.113	−	3955.42i	0.0917310	−	0.403548i
$459$	11710.5	−	9328.29i	1.19085	−	0.948600i
$460$	9424.30	−	206.157i	0.955240	−	0.0208959i
$461$	4556.03			0.460294			0.230147	−	0.973156i	$-0.426079\pi$
$461$	4556.03			0.460294			0.230147	+	0.973156i	$0.426079\pi$
$462$	17872.6	−	10335.5i	1.79980	−	1.04080i
$463$	10449.2	+	10449.2i	1.04885	+	1.04885i	0.998744	+	0.0501054i	$0.0159557\pi$
$463$	10449.2	+	10449.2i	1.04885	+	1.04885i	0.0501054	+	0.998744i	$0.484044\pi$
$464$	827.464	−	664.692i	0.0827889	−	0.0665034i
$465$	418.443	−	1131.96i	0.0417308	−	0.112889i
$466$	5906.23	+	9381.25i	0.587127	+	0.932571i
$467$	257.763	−	257.763i	0.0255415	−	0.0255415i	−0.694221	−	0.719762i	$-0.744251\pi$
$467$	257.763	−	257.763i	0.0255415	−	0.0255415i	0.719762	+	0.694221i	$0.244251\pi$
$468$	−64.1558	+	17.2872i	−0.00633675	+	0.00170748i
$469$	−20558.8			−2.02413
$470$	−9968.50	+	2496.43i	−0.978325	+	0.245004i
$471$	−5676.98	+	5265.53i	−0.555374	+	0.515122i
$472$	−7656.24	−	6072.42i	−0.746625	−	0.592174i
$473$	−16161.2	+	16161.2i	−1.57102	+	1.57102i
$474$	−4316.31	+	16154.1i	−0.418259	+	1.56536i
$475$	3714.77	+	2725.60i	0.358832	+	0.263282i
$476$	19168.0	+	9188.99i	1.84572	+	0.884825i
$477$	−626.217	−	728.218i	−0.0601101	−	0.0699010i
$478$	−498.093	+	2191.24i	−0.0476616	+	0.209675i
$479$	−6094.09			−0.581307			−0.290653	−	0.956828i	$-0.593873\pi$
$479$	−6094.09			−0.581307			−0.290653	+	0.956828i	$0.593873\pi$
$480$	1040.94	+	10464.6i	0.0989839	+	0.995089i
$481$	34.7833			0.00329726
$482$	3234.24	−	14228.2i	0.305634	−	1.34456i
$483$	13625.8	+	512.345i	1.28364	+	0.0482661i
$484$	−13361.0	−	6405.15i	−1.25479	−	0.601536i
$485$	8116.48	−	4111.65i	0.759898	−	0.384950i
$486$	9819.98	+	4284.78i	0.916550	+	0.399921i
$487$	−2682.68	+	2682.68i	−0.249617	+	0.249617i	−0.820814	−	0.571196i	$-0.806480\pi$
$487$	−2682.68	+	2682.68i	−0.249617	+	0.249617i	0.571196	+	0.820814i	$0.306480\pi$
$488$	13209.7	+	10477.0i	1.22536	+	0.971872i
$489$	4914.07	+	5298.06i	0.454442	+	0.489952i
$490$	−7511.76	−	4502.91i	−0.692544	−	0.415144i
$491$	−11967.9			−1.10000			−0.550002	−	0.835163i	$-0.685373\pi$
$491$	−11967.9			−1.10000			−0.550002	+	0.835163i	$0.685373\pi$
$492$	10176.5	+	5357.75i	0.932501	+	0.490947i
$493$	1251.41	−	1251.41i	0.114322	−	0.114322i
$494$	17.0862	+	27.1391i	0.00155616	+	0.00247175i
$495$	15741.5	+	6501.30i	1.42935	+	0.590327i
$496$	−832.606	−	1036.50i	−0.0753732	−	0.0938308i
$497$	−5205.38	−	5205.38i	−0.469805	−	0.469805i
$498$	2864.48	+	4953.38i	0.257751	+	0.445715i
$499$	−18392.6			−1.65003			−0.825016	−	0.565110i	$-0.808834\pi$
$499$	−18392.6			−1.65003			−0.825016	+	0.565110i	$0.808834\pi$
$500$	−1938.55	−	11011.0i	−0.173389	−	0.984853i
$501$	−10313.4	+	9565.88i	−0.919695	+	0.853038i
$502$	491.422	−	2161.89i	0.0436917	−	0.192211i
$503$	−10849.6	+	10849.6i	−0.961751	+	0.961751i	−0.999295	−	0.0375436i	$-0.988047\pi$
$503$	−10849.6	+	10849.6i	−0.961751	+	0.961751i	0.0375436	+	0.999295i	$0.488047\pi$
$504$	603.614	+	15199.7i	0.0533474	+	1.34335i
$505$	−554.876	−	181.727i	−0.0488944	−	0.0160134i
$506$	−8960.43	−	14232.4i	−0.787233	−	1.25041i
$507$	−11407.4	−	428.930i	−0.999251	−	0.0375729i
$508$	−12770.4	+	4493.97i	−1.11534	+	0.392496i
$509$			1536.80i			0.133826i	0.997759	+	0.0669129i	$0.0213150\pi$
$509$			1536.80i			0.133826i	−0.997759	+	0.0669129i	$0.978685\pi$
$510$	3617.66	+	17157.9i	0.314103	+	1.48973i
$511$	−949.761			−0.0822211
$512$	10477.7	+	4943.25i	0.904400	+	0.426685i
$513$	581.823	−	5138.40i	0.0500743	−	0.442234i
$514$	4938.74	−	3109.32i	0.423810	−	0.266822i
$515$	1475.44	+	2912.55i	0.126244	+	0.249209i
$516$	−4989.14	−	16083.6i	−0.425648	−	1.37217i
$517$	12964.3	+	12964.3i	1.10284	+	1.10284i
$518$	1765.12	−	7765.21i	0.149720	−	0.658656i
$519$	14522.6	−	13470.0i	1.22827	−	1.13924i
$520$	15.5857	−	76.2435i	0.00131438	−	0.00642980i
$521$			1220.87i			0.102662i	0.998682	+	0.0513312i	$0.0163464\pi$
$521$			1220.87i			0.102662i	−0.998682	+	0.0513312i	$0.983654\pi$
$522$	1210.40	+	372.672i	0.101490	+	0.0312479i
$523$	−1647.09	+	1647.09i	−0.137710	+	0.137710i	−0.772601	−	0.634891i	$-0.781045\pi$
$523$	−1647.09	+	1647.09i	−0.137710	+	0.137710i	0.634891	+	0.772601i	$0.281045\pi$
$524$	−9283.11	−	4450.26i	−0.773921	−	0.371013i
$525$	−1852.75	−	16065.8i	−0.154020	−	1.33556i
$526$	−3395.52	−	5393.32i	−0.281467	−	0.447072i
$527$	−1567.54	−	1567.54i	−0.129570	−	0.129570i
$528$	15058.6	−	11192.2i	1.24118	−	0.922493i
$529$			1059.51i			0.0870805i
$530$	1091.19	−	273.268i	0.0894303	−	0.0223962i
$531$	875.649	−	11627.5i	0.0715629	−	0.950262i
$532$	6925.74	−	2437.21i	0.564415	−	0.198621i
$533$	−60.1782	−	60.1782i	−0.00489045	−	0.00489045i
$534$	−10744.3	−	2870.85i	−0.870699	−	0.232647i
$535$	2801.54	−	1419.20i	0.226394	−	0.114687i
$536$	−18560.2	+	2141.21i	−1.49567	+	0.172549i
$537$	8231.19	+	309.502i	0.661456	+	0.0248715i
$538$	−7492.63	−	1703.16i	−0.600428	−	0.136484i
$539$			15625.4i			1.24867i
$540$	−9641.75	+	8031.22i	−0.768361	+	0.640016i
$541$		−	21483.9i		−	1.70733i	−0.520821	−	0.853666i	$-0.674374\pi$
$541$		−	21483.9i		−	1.70733i	0.520821	−	0.853666i	$-0.325626\pi$
$542$	1477.20	−	6498.55i	0.117068	−	0.515013i
$543$	−1937.88	−	72.8663i	−0.153153	−	0.00575873i
$544$	18261.6	+	6299.34i	1.43926	+	0.496474i
$545$	−12821.0	−	4199.01i	−1.00769	−	0.330029i
$546$	29.0579	−	108.751i	0.00227759	−	0.00852402i
$547$	2833.73	+	2833.73i	0.221502	+	0.221502i	0.809131	−	0.587629i	$-0.199938\pi$
$547$	2833.73	+	2833.73i	0.221502	+	0.221502i	−0.587629	+	0.809131i	$0.699938\pi$
$548$	−6548.72	−	18609.3i	−0.510488	−	1.45064i
$549$	−1510.80	+	20061.4i	−0.117449	+	1.55957i
$550$	−15071.3	+	13066.9i	−1.16844	+	1.01305i
$551$		−	611.275i		−	0.0472617i
$552$	12354.5	−	956.598i	0.952617	−	0.0737600i
$553$	−20030.6	−	20030.6i	−1.54030	−	1.54030i
$554$	1233.91	−	776.840i	0.0946275	−	0.0595754i
$555$	5967.48	−	2746.31i	0.456406	−	0.210044i
$556$	−270.985	−	129.908i	−0.0206696	−	0.00990889i
$557$	−5474.08	+	5474.08i	−0.416417	+	0.416417i	−0.883967	−	0.467550i	$-0.845137\pi$
$557$	−5474.08	+	5474.08i	−0.416417	+	0.416417i	0.467550	+	0.883967i	$0.345137\pi$
$558$	466.816	−	1516.17i	0.0354156	−	0.115026i
$559$			124.613i			0.00942857i
$560$	−16230.1	−	7348.49i	−1.22472	−	0.554519i
$561$	22937.4	−	21274.9i	1.72623	−	1.60112i
$562$	−2829.78	−	643.242i	−0.212397	−	0.0482803i
$563$	−8739.40	−	8739.40i	−0.654213	−	0.654213i	0.299792	−	0.954005i	$-0.403083\pi$
$563$	−8739.40	−	8739.40i	−0.654213	−	0.654213i	−0.954005	+	0.299792i	$0.903083\pi$
$564$	−12902.1	+	4002.23i	−0.963257	+	0.298802i
$565$	−9200.06	+	4660.57i	−0.685043	+	0.347030i
$566$	7113.38	+	11298.6i	0.528265	+	0.839077i
$567$	−14612.4	+	10767.9i	−1.08230	+	0.797545i
$568$	−5241.49	−	4157.20i	−0.387197	−	0.307099i
$569$	19460.4			1.43378			0.716890	−	0.697186i	$-0.245565\pi$
$569$	19460.4			1.43378			0.716890	+	0.697186i	$0.245565\pi$
$570$	5074.10	+	3306.99i	0.372861	+	0.243008i
$571$			18416.3i			1.34974i	0.737938	+	0.674868i	$0.235800\pi$
$571$			18416.3i			1.34974i	−0.737938	+	0.674868i	$0.764200\pi$
$572$	−130.968	+	46.0885i	−0.00957354	+	0.00336898i
$573$	−12467.7	−	468.800i	−0.908982	−	0.0341787i
$574$	−16488.3	+	10380.7i	−1.19897	+	0.754846i
$575$	−13021.3	+	1999.94i	−0.944394	+	0.145049i
$576$	2127.99	+	13659.2i	0.153935	+	0.988081i
$577$	−428.158	+	428.158i	−0.0308916	+	0.0308916i	−0.722384	−	0.691492i	$-0.756954\pi$
$577$	−428.158	+	428.158i	−0.0308916	+	0.0308916i	0.691492	+	0.722384i	$0.256954\pi$
$578$	17859.0	+	4059.55i	1.28518	+	0.292137i
$579$	4419.57	−	4099.25i	0.317221	−	0.294230i
$580$	−1025.67	+	1071.55i	−0.0734288	+	0.0767132i
$581$	−9693.92			−0.692206
$582$	10353.7	−	5987.43i	0.737415	−	0.426438i
$583$	−1419.12	−	1419.12i	−0.100813	−	0.100813i
$584$	−857.431	+	98.9182i	−0.0607547	+	0.00700901i
$585$	85.7532	−	35.6239i	0.00606061	−	0.00251772i
$586$	14292.1	−	8998.00i	1.00751	−	0.634307i
$587$	10405.3	−	10405.3i	0.731637	−	0.731637i	−0.239307	−	0.970944i	$-0.576920\pi$
$587$	10405.3	−	10405.3i	0.731637	−	0.731637i	0.970944	+	0.239307i	$0.0769202\pi$
$588$	−10187.1	−	5363.35i	−0.714470	−	0.376158i
$589$	−765.695			−0.0535652
$590$	11713.5	+	7021.62i	0.817349	+	0.489958i
$591$	−13048.0	−	14067.5i	−0.908159	−	0.979123i
$592$	784.774	−	7194.16i	0.0544832	−	0.499456i
$593$	−1677.44	+	1677.44i	−0.116162	+	0.116162i	−0.762799	−	0.646636i	$-0.776175\pi$
$593$	−1677.44	+	1677.44i	−0.116162	+	0.116162i	0.646636	+	0.762799i	$0.276175\pi$
$594$	21134.2	+	7387.22i	1.45984	+	0.510271i
$595$	−28231.6	−	9246.12i	−1.94518	−	0.637066i
$596$	9423.91	−	19658.0i	0.647682	−	1.35104i
$597$	10859.7	+	408.338i	0.744488	+	0.0279936i
$598$	−89.4160	−	20.3253i	−0.00611454	−	0.00138990i
$599$	11567.1			0.789011			0.394506	−	0.918894i	$-0.370916\pi$
$599$	11567.1			0.789011			0.394506	+	0.918894i	$0.370916\pi$
$600$	−3345.89	−	14311.0i	−0.227659	−	0.973741i
$601$	−23523.8			−1.59660			−0.798300	−	0.602260i	$-0.794267\pi$
$601$	−23523.8			−1.59660			−0.798300	+	0.602260i	$0.794267\pi$
$602$	27819.3	+	6323.64i	1.88344	+	0.428127i
$603$	−14535.7	−	16903.3i	−0.981656	−	1.14155i
$604$	22269.7	+	10675.9i	1.50023	+	0.719202i
$605$	19678.8	+	6444.98i	1.32241	+	0.433100i
$606$	−741.513	−	198.130i	−0.0497061	−	0.0132813i
$607$	14760.8	−	14760.8i	0.987021	−	0.987021i	−0.0128957	−	0.999917i	$-0.504105\pi$
$607$	14760.8	−	14760.8i	0.987021	−	0.987021i	0.999917	+	0.0128957i	$0.00410493\pi$
$608$	5998.62	−	2921.59i	0.400125	−	0.194879i
$609$	−1573.11	+	1459.09i	−0.104672	+	0.0970860i
$610$	−20209.8	−	12114.7i	−1.34143	−	0.804117i
$611$	99.9633			0.00661879
$612$	5997.20	+	22256.7i	0.396115	+	1.47005i
$613$	19044.7	−	19044.7i	1.25483	−	1.25483i	0.301294	−	0.953531i	$-0.402581\pi$
$613$	19044.7	−	19044.7i	1.25483	−	1.25483i	0.953531	−	0.301294i	$-0.0974185\pi$
$614$	23298.4	−	14668.2i	1.53135	−	0.964104i
$615$	−15075.6	−	5572.90i	−0.988469	−	0.365400i
$616$	3642.89	+	31576.9i	0.238273	+	2.06537i
$617$	6519.56	+	6519.56i	0.425393	+	0.425393i	0.887056	−	0.461662i	$-0.152747\pi$
$617$	6519.56	+	6519.56i	0.425393	+	0.425393i	−0.461662	+	0.887056i	$0.652747\pi$
$618$	2148.56	+	3715.38i	0.139851	+	0.241836i
$619$	11016.2			0.715315			0.357657	−	0.933853i	$-0.383576\pi$
$619$	11016.2			0.715315			0.357657	+	0.933853i	$0.383576\pi$
$620$	1342.24	+	1284.78i	0.0869448	+	0.0832223i
$621$	9212.62	+	11565.3i	0.595313	+	0.747343i
$622$	−14431.0	−	3280.34i	−0.930276	−	0.211462i
$623$	13322.7	−	13322.7i	0.856761	−	0.856761i
$624$	14.9066	−	101.205i	0.000956314	−	0.00649272i
$625$	4689.06	+	14904.8i	0.300100	+	0.953908i
$626$	−15819.6	+	9959.68i	−1.01003	+	0.635893i
$627$	406.022	−	10798.2i	0.0258612	−	0.687778i
$628$	−3957.23	−	11245.1i	−0.251450	−	0.714538i
$629$		−	12066.9i		−	0.764927i
$630$	−3601.22	−	20951.8i	−0.227740	−	1.32498i
$631$	21365.5			1.34794			0.673969	−	0.738760i	$-0.264588\pi$
$631$	21365.5			1.34794			0.673969	+	0.738760i	$0.264588\pi$
$632$	−20169.5	−	15997.1i	−1.26946	−	1.00685i
$633$	13889.4	+	522.257i	0.872124	+	0.0327928i
$634$	2165.45	+	3439.52i	0.135648	+	0.215459i
$635$	16877.9	−	8550.02i	1.05477	−	0.534326i
$636$	1412.31	−	438.098i	0.0880529	−	0.0273140i
$637$	60.2410	+	60.2410i	0.00374700	+	0.00374700i
$638$	2580.59	+	586.598i	0.160136	+	0.0364007i
$639$	599.472	−	7960.20i	0.0371122	−	0.492802i
$640$	−15417.6	−	4943.74i	−0.952243	−	0.305342i
$641$		−	963.186i		−	0.0593503i	−0.999560	−	0.0296751i	$-0.990553\pi$
$641$		−	963.186i		−	0.0593503i	0.999560	−	0.0296751i	$-0.00944728\pi$
$642$	3573.76	−	2066.66i	0.219696	−	0.127048i
$643$	4715.22	−	4715.22i	0.289191	−	0.289191i	−0.547569	−	0.836761i	$-0.684447\pi$
$643$	4715.22	−	4715.22i	0.289191	−	0.289191i	0.836761	+	0.547569i	$0.184447\pi$
$644$	−9075.04	+	18930.3i	−0.555290	+	1.15832i
$645$	9838.82	+	21378.8i	0.600625	+	1.30510i
$646$	9415.01	−	5927.48i	0.573419	−	0.361012i
$647$	−3929.10	−	3929.10i	−0.238746	−	0.238746i	0.577585	−	0.816331i	$-0.303995\pi$
$647$	−3929.10	−	3929.10i	−0.238746	−	0.238746i	−0.816331	+	0.577585i	$0.803995\pi$
$648$	−12070.4	+	11243.0i	−0.731742	+	0.681582i
$649$		−	24365.5i		−	1.47370i
$650$	−7.72772	+	108.482i	−0.000466317	+	0.00654618i
$651$	1827.69	+	1970.50i	0.110035	+	0.118633i
$652$	−10494.6	+	3693.10i	−0.630367	+	0.221830i
$653$	19013.2	+	19013.2i	1.13942	+	1.13942i	0.988554	+	0.150870i	$0.0482076\pi$
$653$	19013.2	+	19013.2i	1.13942	+	1.13942i	0.150870	+	0.988554i	$0.451792\pi$
$654$	−17133.5	−	4578.01i	−1.02442	−	0.273722i
$655$	13672.7	+	4477.93i	0.815627	+	0.267126i
$656$	−13804.3	+	11088.8i	−0.821594	+	0.659977i
$657$	−671.510	−	780.889i	−0.0398754	−	0.0463704i
$658$	5072.76	−	22316.3i	0.300542	−	1.32216i
$659$		−	5159.16i		−	0.304966i	−0.988306	−	0.152483i	$-0.951273\pi$
$659$		−	5159.16i		−	0.304966i	0.988306	−	0.152483i	$-0.0487269\pi$
$660$	−18830.2	+	18247.6i	−1.11055	+	1.07619i
$661$			12528.0i			0.737189i	0.929590	+	0.368594i	$0.120161\pi$
$661$			12528.0i			0.737189i	−0.929590	+	0.368594i	$0.879839\pi$
$662$	−16577.8	−	3768.33i	−0.973286	−	0.221239i
$663$	6.40921	−	170.453i	0.000375435	−	0.00998468i
$664$	−8751.53	+	1009.63i	−0.511484	+	0.0590078i
$665$	−9153.35	+	4636.91i	−0.533762	+	0.270394i
$666$	7632.50	−	4038.97i	0.444074	−	0.234995i
$667$	1235.89	+	1235.89i	0.0717451	+	0.0717451i
$668$	−7189.09	−	20429.0i	−0.416399	−	1.18327i
$669$	2966.89	−	2751.86i	0.171460	−	0.159033i
$670$	25328.5	−	6343.05i	1.46048	−	0.365752i
$671$			42039.0i			2.41863i
$672$	−21837.2	−	8463.60i	−1.25355	−	0.485849i
$673$	16189.2	+	16189.2i	0.927263	+	0.927263i	0.997528	−	0.0702654i	$-0.0223846\pi$
$673$	16189.2	+	16189.2i	0.927263	+	0.927263i	−0.0702654	+	0.997528i	$0.522385\pi$
$674$	−10575.2	−	16797.3i	−0.604367	−	0.959955i
$675$	11899.3	−	12882.3i	0.678523	−	0.734579i
$676$	7597.54	−	15848.2i	0.432268	−	0.901698i
$677$	−16242.7	+	16242.7i	−0.922094	+	0.922094i	−0.997177	−	0.0750831i	$-0.976078\pi$
$677$	−16242.7	+	16242.7i	−0.922094	+	0.922094i	0.0750831	+	0.997177i	$0.476078\pi$
$678$	−11736.0	+	6786.77i	−0.664775	+	0.384431i
$679$			20262.6i			1.14522i
$680$	−26450.1	−	5406.93i	−1.49164	−	0.304921i
$681$	−4208.50	−	4537.35i	−0.236814	−	0.255318i
$682$	734.784	−	3232.50i	0.0412556	−	0.181494i
$683$	10542.2	+	10542.2i	0.590608	+	0.590608i	0.937796	−	0.347188i	$-0.112863\pi$
$683$	10542.2	+	10542.2i	0.590608	+	0.590608i	−0.347188	+	0.937796i	$0.612863\pi$
$684$	6900.57	+	3971.12i	0.385745	+	0.221988i
$685$	12459.3	+	24594.9i	0.694956	+	1.37186i
$686$	−3936.23	+	2478.17i	−0.219076	+	0.137925i
$687$	−280.003	+	7446.69i	−0.0155499	+	0.413550i
$688$	25773.5	+	2811.50i	1.42820	+	0.155796i
$689$	−10.9423			−0.000605035
$690$	−16945.1	+	3572.80i	−0.934913	+	0.197122i
$691$			18865.6i			1.03861i	0.854588	+	0.519307i	$0.173810\pi$
$691$			18865.6i			1.03861i	−0.854588	+	0.519307i	$0.826190\pi$
$692$	10123.2	+	28766.8i	0.556107	+	1.58027i
$693$	−28758.0	+	24729.9i	−1.57637	+	1.35557i
$694$	−13215.4	−	20990.8i	−0.722837	−	1.14813i
$695$	399.122	+	130.716i	0.0217835	+	0.00713431i
$696$	−1268.21	+	1481.09i	−0.0690682	+	0.0806616i
$697$	−20876.8	+	20876.8i	−1.13453	+	1.13453i
$698$	1047.23	−	4607.01i	0.0567881	−	0.249825i
$699$	−13849.4	−	14931.6i	−0.749403	−	0.807962i
$700$	23826.0	+	7230.23i	1.28648	+	0.390396i
$701$	−19145.8			−1.03156			−0.515782	−	0.856720i	$-0.672499\pi$
$701$	−19145.8			−1.03156			−0.515782	+	0.856720i	$0.672499\pi$
$702$	109.959	−	52.9991i	0.00591189	−	0.00284946i
$703$	−2947.15	−	2947.15i	−0.158114	−	0.158114i
$704$	6577.50	+	28127.8i	0.352129	+	1.50583i
$705$	17149.9	−	7892.60i	0.916172	−	0.421635i
$706$	−3406.66	−	5411.01i	−0.181602	−	0.288451i
$707$	919.455	−	919.455i	0.0489104	−	0.0489104i
$708$	15885.3	+	8363.34i	0.843227	+	0.443946i
$709$	8859.33			0.469279			0.234640	−	0.972082i	$-0.424609\pi$
$709$	8859.33			0.469279			0.234640	+	0.972082i	$0.424609\pi$
$710$	8019.08	+	4807.02i	0.423874	+	0.254090i
$711$	2306.80	−	30631.3i	0.121676	−	1.61570i
$712$	10640.0	−	13415.1i	0.560041	−	0.706112i
$713$	1548.10	−	1548.10i	0.0813141	−	0.0813141i
$714$	−37727.6	−	10080.7i	−1.97748	−	0.528374i
$715$	173.093	−	87.6858i	0.00905361	−	0.00458638i
$716$	−5482.13	+	11435.6i	−0.286141	+	0.596881i
$717$	155.117	−	4125.34i	0.00807943	−	0.214872i
$718$	−5020.43	+	22086.1i	−0.260948	+	1.14798i
$719$	−12578.1			−0.652413			−0.326206	−	0.945299i	$-0.605770\pi$
$719$	−12578.1			−0.652413			−0.326206	+	0.945299i	$0.605770\pi$
$720$	−5433.27	−	18539.9i	−0.281231	−	0.959640i
$721$	−7271.11			−0.375576
$722$	−3448.41	+	15170.4i	−0.177752	+	0.781974i
$723$	−1007.21	+	26786.8i	−0.0518100	+	1.37789i
$724$	1290.66	−	2692.28i	0.0662529	−	0.138202i
$725$	1226.31	−	1671.37i	0.0628195	−	0.0856179i
$726$	26297.8	+	7026.69i	1.34436	+	0.359208i
$727$	25898.4	−	25898.4i	1.32121	−	1.32121i	0.408406	−	0.912800i	$-0.366085\pi$
$727$	25898.4	−	25898.4i	1.32121	−	1.32121i	0.912800	−	0.408406i	$-0.133915\pi$
$728$	135.784	+	107.695i	0.00691275	+	0.00548273i
$729$	−19184.7	−	4401.00i	−0.974682	−	0.223594i
$730$	1170.11	−	293.033i	0.0593256	−	0.0148570i
$731$	43230.3			2.18732
$732$	−27407.6	−	14429.7i	−1.38390	−	0.728602i
$733$	−1525.46	+	1525.46i	−0.0768678	+	0.0768678i	−0.744495	−	0.667628i	$-0.767310\pi$
$733$	−1525.46	+	1525.46i	−0.0768678	+	0.0768678i	0.667628	+	0.744495i	$0.267310\pi$
$734$	−2001.43	−	3178.99i	−0.100646	−	0.159862i
$735$	15091.4	+	5578.72i	0.757352	+	0.279965i
$736$	−6221.22	+	18035.2i	−0.311572	+	0.903240i
$737$	−32940.4	−	32940.4i	−1.64637	−	1.64637i
$738$	−20192.7	−	6217.14i	−1.00719	−	0.310103i
$739$	−2500.36			−0.124462			−0.0622309	−	0.998062i	$-0.519822\pi$
$739$	−2500.36			−0.124462			−0.0622309	+	0.998062i	$0.519822\pi$
$740$	221.187	+	10111.4i	0.0109878	+	0.502299i
$741$	−40.0651	−	43.1958i	−0.00198627	−	0.00214148i
$742$	−555.281	+	2442.82i	−0.0274731	+	0.120861i
$743$	−14554.7	+	14554.7i	−0.718652	+	0.718652i	−0.968329	−	0.249677i	$-0.919676\pi$
$743$	−14554.7	+	14554.7i	−0.718652	+	0.718652i	0.249677	+	0.968329i	$0.419676\pi$
$744$	1855.24	+	1588.59i	0.0914198	+	0.0782801i
$745$	−9482.50	+	28953.4i	−0.466325	+	1.42385i
$746$	−1111.69	−	1765.77i	−0.0545603	−	0.0866616i
$747$	−6853.90	−	7970.29i	−0.335704	−	0.390385i
$748$	15988.9	+	45435.1i	0.781565	+	2.22095i
$749$			6993.96i			0.341193i
$750$	7239.42	+	19221.5i	0.352462	+	0.935826i
$751$	−14265.0			−0.693124			−0.346562	−	0.938027i	$-0.612651\pi$
$751$	−14265.0			−0.693124			−0.346562	+	0.938027i	$0.612651\pi$
$752$	2255.35	−	20675.2i	0.109367	−	1.00259i
$753$	−153.040	+	4070.09i	−0.00740647	+	0.196975i
$754$	12.2106	−	7.68750i	0.000589764	−	0.000371303i
$755$	−32800.0	−	10742.3i	−1.58108	−	0.517819i
$756$	−6251.78	−	27237.4i	−0.300761	−	1.31034i
$757$	10388.6	+	10388.6i	0.498784	+	0.498784i	0.911059	−	0.412275i	$-0.135266\pi$
$757$	10388.6	+	10388.6i	0.498784	+	0.498784i	−0.412275	+	0.911059i	$0.635266\pi$
$758$	893.749	−	3931.83i	0.0428264	−	0.188404i
$759$	21011.1	+	22652.9i	1.00482	+	1.08333i
$760$	−7780.58	+	5139.46i	−0.371357	+	0.245300i
$761$			32985.9i			1.57127i	0.618689	+	0.785636i	$0.287664\pi$
$761$			32985.9i			1.57127i	−0.618689	+	0.785636i	$0.712336\pi$
$762$	21530.2	−	12450.6i	1.02356	−	0.591914i
$763$	21245.1	−	21245.1i	1.00802	−	1.00802i
$764$	8303.74	−	17321.3i	0.393218	−	0.820241i
$765$	−12358.5	−	29749.2i	−0.584083	−	1.40599i
$766$	−21599.8	−	34308.4i	−1.01884	−	1.61829i
$767$	−93.9370	−	93.9370i	−0.00442225	−	0.00442225i
$768$	−20595.8	−	5366.47i	−0.967690	−	0.252143i
$769$		−	9528.24i		−	0.446810i	−0.974726	−	0.223405i	$-0.928283\pi$
$769$		−	9528.24i		−	0.446810i	0.974726	−	0.223405i	$-0.0717173\pi$
$770$	−10791.6	−	43092.0i	−0.505068	−	2.01679i
$771$	−7860.71	+	7290.99i	−0.367181	+	0.340569i
$772$	3080.73	+	8754.42i	0.143624	+	0.408133i
$773$	4885.11	+	4885.11i	0.227303	+	0.227303i	0.811565	−	0.584262i	$-0.198616\pi$
$773$	4885.11	+	4885.11i	0.227303	+	0.227303i	−0.584262	+	0.811565i	$0.698616\pi$
$774$	14469.8	+	27343.9i	0.671973	+	1.26984i
$775$	−2093.58	−	1536.10i	−0.0970371	−	0.0711980i
$776$	2110.36	+	18292.8i	0.0976256	+	0.846227i
$777$	−549.697	+	14619.2i	−0.0253800	+	0.674981i
$778$	−15015.4	−	3413.16i	−0.691936	−	0.157285i
$779$			10197.7i			0.469023i
$780$	−2.24614	+	142.947i	−0.000103109	+	0.00656196i
$781$		−	16680.7i		−	0.764254i
$782$	−7051.17	+	31019.9i	−0.322442	+	1.41850i
$783$	−2311.89	−	261.776i	−0.105518	−	0.0119478i
$784$	13818.7	−	11100.4i	0.629495	−	0.505666i
$785$	7528.83	+	14862.1i	0.342313	+	0.675732i
$786$	18271.6	+	4882.10i	0.829168	+	0.221551i
$787$	−3024.18	−	3024.18i	−0.136976	−	0.136976i	0.635294	−	0.772270i	$-0.280879\pi$
$787$	−3024.18	−	3024.18i	−0.136976	−	0.136976i	−0.772270	+	0.635294i	$0.780879\pi$
$788$	27865.5	−	9806.01i	1.25973	−	0.443305i
$789$	7962.08	+	8584.24i	0.359262	+	0.387335i
$790$	30857.9	+	18497.7i	1.38971	+	0.833061i
$791$		−	22967.7i		−	1.03241i
$792$	−23386.7	+	25321.0i	−1.04926	+	1.13604i
$793$	162.074	+	162.074i	0.00725778	+	0.00725778i
$794$	−8570.91	+	5396.06i	−0.383086	+	0.241182i
$795$	−1877.28	+	863.950i	−0.0837488	+	0.0385423i
$796$	−7232.79	+	15087.4i	−0.322060	+	0.671807i
$797$	15081.3	−	15081.3i	0.670274	−	0.670274i	−0.287505	−	0.957779i	$-0.592826\pi$
$797$	15081.3	−	15081.3i	0.670274	−	0.670274i	0.957779	+	0.287505i	$0.0928259\pi$
$798$	−11676.4	+	6752.32i	−0.517970	+	0.299536i
$799$		−	34678.9i		−	1.53548i
$800$	22262.8	+	4045.86i	0.983885	+	0.178803i
$801$	20373.4	+	1534.29i	0.898699	+	0.0676798i
$802$	−31240.2	−	7101.26i	−1.37548	−	0.312661i
$803$	−1521.76	−	1521.76i	−0.0668764	−	0.0668764i
$804$	32782.3	−	10169.1i	1.43799	−	0.446064i
$805$	9131.47	−	27881.6i	0.399804	−	1.22074i
$806$	−9.62950	−	15.2952i	−0.000420825	−	0.000668423i
$807$	14106.0	+	530.401i	0.615310	+	0.0231363i
$808$	734.310	−	925.833i	0.0319714	−	0.0403103i
$809$	−38667.7			−1.68045			−0.840225	−	0.542238i	$-0.817577\pi$
$809$	−38667.7			−1.68045			−0.840225	+	0.542238i	$0.817577\pi$
$810$	14680.3	−	17774.4i	0.636805	−	0.771025i
$811$			1042.09i			0.0451205i	0.999745	+	0.0225602i	$0.00718175\pi$
$811$			1042.09i			0.0451205i	−0.999745	+	0.0225602i	$0.992818\pi$
$812$	−1096.56	−	3116.06i	−0.0473912	−	0.134670i
$813$	−460.031	+	12234.5i	−0.0198450	+	0.527778i
$814$	15270.0	−	9613.67i	0.657511	−	0.413955i
$815$	13870.1	−	7026.31i	0.596132	−	0.301989i
$816$	−35109.8	−	5171.33i	−1.50624	−	0.221854i
$817$	10558.3	−	10558.3i	0.452129	−	0.452129i
$818$	3475.00	+	789.908i	0.148534	+	0.0337634i
$819$	−15.5297	+	206.213i	−0.000662576	+	0.00879815i
$820$	17110.9	−	17876.2i	0.728705	−	0.761299i
$821$	7134.89			0.303300			0.151650	−	0.988434i	$-0.451541\pi$
$821$	7134.89			0.303300			0.151650	+	0.988434i	$0.451541\pi$
$822$	18143.3	+	31374.3i	0.769856	+	1.33127i
$823$	15626.7	+	15626.7i	0.661861	+	0.661861i	0.955818	−	0.293958i	$-0.0949725\pi$
$823$	15626.7	+	15626.7i	0.661861	+	0.661861i	−0.293958	+	0.955818i	$0.594972\pi$
$824$	−6564.26	+	757.291i	−0.277520	+	0.0320164i
$825$	22772.9	−	28710.1i	0.961033	−	1.21158i
$826$	−25737.9	+	16204.0i	−1.08419	+	0.682579i
$827$	−4429.66	+	4429.66i	−0.186257	+	0.186257i	−0.794076	−	0.607819i	$-0.792045\pi$
$827$	−4429.66	+	4429.66i	−0.186257	+	0.186257i	0.607819	+	0.794076i	$0.292045\pi$
$828$	−21980.7	+	5922.83i	−0.922563	+	0.248590i
$829$	2178.63			0.0912748			0.0456374	−	0.998958i	$-0.485468\pi$
$829$	2178.63			0.0912748			0.0456374	+	0.998958i	$0.485468\pi$
$830$	11942.9	−	2990.89i	0.499453	−	0.125079i
$831$	−1963.94	+	1821.60i	−0.0819834	+	0.0760415i
$832$	133.800	+	83.0832i	0.00557534	+	0.00346201i
$833$	20898.6	−	20898.6i	0.869260	−	0.869260i
$834$	533.369	+	142.514i	0.0221452	+	0.00591710i
$835$	13677.6	+	26999.9i	0.566867	+	1.11901i
$836$	15001.8	+	7191.78i	0.620633	+	0.297527i
$837$	−327.906	+	2895.92i	−0.0135413	+	0.119591i
$838$	914.858	+	207.958i	0.0377127	+	0.00857252i
$839$	39382.4			1.62054			0.810270	−	0.586057i	$-0.199321\pi$
$839$	39382.4			1.62054			0.810270	+	0.586057i	$0.199321\pi$
$840$	31798.3	+	7755.46i	1.30612	+	0.318558i
$841$	24114.0			0.988723
$842$	−33394.0	−	7590.83i	−1.36678	−	0.310686i
$843$	5327.49	+	200.319i	0.217661	+	0.00818430i
$844$	−9250.61	+	19296.5i	−0.377274	+	0.786982i
$845$	−7644.78	+	23342.2i	−0.311229	+	0.950290i
$846$	21935.0	−	11607.5i	0.891418	−	0.471720i
$847$	−32608.6	+	32608.6i	−1.32284	+	1.32284i
$848$	−246.879	+	2263.18i	−0.00999746	+	0.0916484i
$849$	−16680.0	−	17983.4i	−0.674272	−	0.726960i
$850$	37634.2	+	2680.87i	1.51864	+	0.108180i
$851$	11917.3			0.480045
$852$	10875.1	+	5725.57i	0.437294	+	0.230229i
$853$	−22195.8	+	22195.8i	−0.890936	+	0.890936i	−0.994611	−	0.103676i	$-0.966940\pi$
$853$	−22195.8	+	22195.8i	−0.890936	+	0.890936i	0.103676	+	0.994611i	$0.466940\pi$
$854$	44406.9	−	27957.6i	1.77936	−	1.12025i
$855$	−10284.1	−	4247.40i	−0.411357	−	0.169892i
$856$	728.425	+	6314.05i	0.0290854	+	0.252114i
$857$	3062.33	+	3062.33i	0.122062	+	0.122062i	0.765499	−	0.643437i	$-0.222492\pi$
$857$	3062.33	+	3062.33i	0.122062	+	0.122062i	−0.643437	+	0.765499i	$0.722492\pi$
$858$	220.805	−	127.689i	0.00878574	−	0.00508069i
$859$	−17983.8			−0.714319			−0.357159	−	0.934043i	$-0.616255\pi$
$859$	−17983.8			−0.714319			−0.357159	+	0.934043i	$0.616255\pi$
$860$	−36224.5	+	792.414i	−1.43633	+	0.0314199i
$861$	26243.5	−	24341.5i	1.03876	−	0.963478i
$862$	−5270.53	−	1198.05i	−0.208254	−	0.0473385i
$863$	14696.3	−	14696.3i	0.579685	−	0.579685i	−0.355131	−	0.934816i	$-0.615564\pi$
$863$	14696.3	−	14696.3i	0.579685	−	0.579685i	0.934816	+	0.355131i	$0.115564\pi$
$864$	−8480.82	−	23938.4i	−0.333939	−	0.942595i
$865$	−19259.9	−	38019.4i	−0.757059	−	1.49445i
$866$	12434.5	−	7828.49i	0.487923	−	0.307186i
$867$	−33622.2	−	1264.23i	−1.31704	−	0.0495220i
$868$	−3903.23	+	1373.57i	−0.152632	+	0.0537120i
$869$		−	64188.3i		−	2.50568i
$870$	1487.89	−	2282.96i	0.0579820	−	0.0889651i
$871$	−253.992			−0.00988081
$872$	16967.1	−	21392.4i	0.658919	−	0.830779i
$873$	−16659.8	+	14326.3i	−0.645874	+	0.555407i
$874$	5853.98	+	9298.26i	0.226560	+	0.359861i
$875$	−34329.7	−	5684.67i	−1.32635	−	0.219631i
$876$	1514.46	−	469.785i	0.0584119	−	0.0181194i
$877$	−9324.85	−	9324.85i	−0.359040	−	0.359040i	0.504419	−	0.863459i	$-0.331707\pi$
$877$	−9324.85	−	9324.85i	−0.359040	−	0.359040i	−0.863459	+	0.504419i	$0.831707\pi$
$878$	−31239.4	−	7101.08i	−1.20077	−	0.272950i
$879$	−22747.9	+	21099.2i	−0.872888	+	0.809624i
$880$	−14230.6	−	37778.9i	−0.545128	−	1.44719i
$881$		−	28980.3i		−	1.10825i	−0.832433	−	0.554126i	$-0.813053\pi$
$881$		−	28980.3i		−	1.10825i	0.832433	−	0.554126i	$-0.186947\pi$
$882$	20213.8	+	6223.63i	0.771693	+	0.237597i
$883$	13718.9	−	13718.9i	0.522851	−	0.522851i	−0.395581	−	0.918431i	$-0.629457\pi$
$883$	13718.9	−	13718.9i	0.522851	−	0.522851i	0.918431	+	0.395581i	$0.129457\pi$
$884$	236.809	+	113.525i	0.00900991	+	0.00431929i
$885$	−23532.8	−	8699.18i	−0.893836	−	0.330418i
$886$	−7462.23	+	4698.06i	−0.282956	+	0.178143i
$887$	19735.8	+	19735.8i	0.747084	+	0.747084i	0.973930	−	0.226847i	$-0.0728416\pi$
$887$	19735.8	+	19735.8i	0.747084	+	0.747084i	−0.226847	+	0.973930i	$0.572842\pi$
$888$	1026.34	+	13255.2i	0.0387856	+	0.500920i
$889$			42135.2i			1.58962i
$890$	−12303.1	+	20524.1i	−0.463372	+	0.772999i
$891$	−40665.6	−	6159.88i	−1.52901	−	0.231609i
$892$	2068.12	+	5876.91i	0.0776297	+	0.220598i
$893$	−8469.78	−	8469.78i	−0.317391	−	0.317391i
$894$	−10338.4	+	38692.1i	−0.386764	+	1.44749i
$895$	5516.21	−	16842.9i	0.206019	−	0.629046i
$896$	25337.8	−	25654.1i	0.944728	−	0.956521i
$897$	168.339	+	6.32974i	0.00626609	+	0.000235612i
$898$	4263.91	−	18758.0i	0.158450	−	0.697063i
$899$			344.505i			0.0127807i
$900$	10901.0	+	24701.6i	0.403742	+	0.914873i
$901$			3796.07i			0.140361i
$902$	−43051.0	−	9785.99i	−1.58918	−	0.361239i
$903$	−52374.0	−	1969.32i	−1.93012	−	0.0725746i
$904$	−2392.10	−	20734.9i	−0.0880089	−	0.762868i
$905$	−1298.69	+	3965.34i	−0.0477015	+	0.145649i
$906$	−43832.6	−	11711.9i	−1.60733	−	0.429472i
$907$	−15544.7	−	15544.7i	−0.569077	−	0.569077i	0.362793	−	0.931870i	$-0.381823\pi$
$907$	−15544.7	−	15544.7i	−0.569077	−	0.569077i	−0.931870	+	0.362793i	$0.881823\pi$
$908$	8987.74	−	3162.83i	0.328490	−	0.115597i
$909$	1406.05	+	105.888i	0.0513046	+	0.00386368i
$910$	−207.739	−	124.529i	−0.00756756	−	0.00453635i
$911$			22364.3i			0.813350i	0.913573	+	0.406675i	$0.133312\pi$
$911$			22364.3i			0.813350i	−0.913573	+	0.406675i	$0.866688\pi$
$912$	−9838.03	+	7312.00i	−0.357204	+	0.265487i
$913$	−15532.1	−	15532.1i	−0.563022	−	0.563022i
$914$	21884.6	+	34760.7i	0.791989	+	1.25797i
$915$	40602.2	+	15009.1i	1.46696	+	0.542280i
$916$	−10345.6	−	4959.63i	−0.373177	−	0.178898i
$917$	−22656.3	+	22656.3i	−0.815895	+	0.815895i
$918$	−18386.3	−	38146.7i	−0.661043	−	1.37149i
$919$			29829.7i			1.07072i	0.844624	+	0.535360i	$0.179824\pi$
$919$			29829.7i			1.07072i	−0.844624	+	0.535360i	$0.820176\pi$
$920$	5339.88	−	26122.1i	0.191359	−	0.936110i
$921$	−37082.8	+	34395.1i	−1.32673	+	1.23057i
$922$	2856.36	−	12565.9i	0.102027	−	0.448844i
$923$	−64.3095	−	64.3095i	−0.00229336	−	0.00229336i
$924$	−17300.9	−	55773.5i	−0.615972	−	1.98573i
$925$	−2145.74	−	13970.6i	−0.0762719	−	0.496596i
$926$	35370.8	−	22268.7i	1.25524	−	0.790274i
$927$	−5140.90	−	5978.27i	−0.182146	−	0.211815i
$928$	−1314.50	−	2698.93i	−0.0464983	−	0.0954705i
$929$	45227.2			1.59726			0.798631	−	0.601821i	$-0.205558\pi$
$929$	45227.2			1.59726			0.798631	+	0.601821i	$0.205558\pi$
$930$	−2859.68	−	1863.76i	−0.100831	−	0.0657153i
$931$		−	10208.3i		−	0.359360i
$932$	29577.0	−	10408.3i	1.03951	−	0.365811i
$933$	27168.6	+	1021.57i	0.953333	+	0.0358464i
$934$	−549.327	−	872.531i	−0.0192447	−	0.0305675i
$935$	−30419.7	−	60049.0i	−1.06399	−	2.10033i
$936$	7.45731	+	187.784i	0.000260416	+	0.00655760i
$937$	38060.2	−	38060.2i	1.32697	−	1.32697i	0.418974	−	0.907998i	$-0.362390\pi$
$937$	38060.2	−	38060.2i	1.32697	−	1.32697i	0.907998	−	0.418974i	$-0.137610\pi$
$938$	−12889.1	+	56702.5i	−0.448662	+	1.97378i
$939$	25179.2	−	23354.2i	0.875070	−	0.811648i
$940$	635.666	+	29058.9i	0.0220565	+	1.00830i
$941$	−45892.4			−1.58985			−0.794925	−	0.606707i	$-0.792490\pi$
$941$	−45892.4			−1.58985			−0.794925	+	0.606707i	$0.792490\pi$
$942$	10963.6	+	18958.7i	0.379206	+	0.655740i
$943$	−20617.9	−	20617.9i	−0.711996	−	0.711996i
$944$	−21548.2	+	17309.4i	−0.742938	+	0.596793i
$945$	13617.3	+	36604.4i	0.468752	+	1.26005i
$946$	34441.5	+	54705.7i	1.18371	+	1.88016i
$947$	3233.14	−	3233.14i	0.110943	−	0.110943i	−0.649456	−	0.760399i	$-0.725003\pi$
$947$	3233.14	−	3233.14i	0.110943	−	0.110943i	0.760399	+	0.649456i	$0.225003\pi$
$948$	41848.0	+	22032.3i	1.43371	+	0.754827i
$949$	−11.7338			−0.000401364
$950$	9846.33	−	8536.80i	0.336271	−	0.291548i
$951$	−5077.71	−	5474.48i	−0.173140	−	0.186669i
$952$	37361.0	−	47105.6i	1.27193	−	1.60368i
$953$	28661.7	−	28661.7i	0.974232	−	0.974232i	−0.0254438	−	0.999676i	$-0.508100\pi$
$953$	28661.7	−	28661.7i	0.974232	−	0.974232i	0.999676	+	0.0254438i	$0.00809989\pi$
$954$	−2401.08	+	1270.60i	−0.0814860	+	0.0431208i
$955$	−8355.37	+	25511.8i	−0.283113	+	0.864444i
$956$	5731.31	+	2747.55i	0.193895	+	0.0929520i
$957$	−4858.36	−	182.679i	−0.164105	−	0.00617052i
$958$	−3820.63	+	16807.9i	−0.128851	+	0.566847i
$959$	−61400.5			−2.06749
$960$	29514.8	+	3689.71i	0.992276	+	0.124047i
$961$	−29359.5			−0.985515
$962$	21.8071	−	95.9347i	0.000730861	−	0.00321524i
$963$	−5750.40	+	4944.95i	−0.192424	+	0.165471i
$964$	−37214.8	−	17840.5i	−1.24337	−	0.596062i
$965$	−5861.25	−	11570.2i	−0.195524	−	0.385967i
$966$	9955.66	−	37259.7i	0.331592	−	1.24101i
$967$	−5022.89	+	5022.89i	−0.167038	+	0.167038i	−0.785676	−	0.618638i	$-0.787685\pi$
$967$	−5022.89	+	5022.89i	−0.167038	+	0.167038i	0.618638	+	0.785676i	$0.287685\pi$
$968$	−26042.4	+	32834.8i	−0.864704	+	1.09024i
$969$	−14985.3	+	13899.2i	−0.496799	+	0.460792i
$970$	−6251.67	−	24963.6i	−0.206937	−	0.826322i
$971$	3437.95			0.113624			0.0568121	−	0.998385i	$-0.481906\pi$
$971$	3437.95			0.113624			0.0568121	+	0.998385i	$0.481906\pi$
$972$	17974.3	−	24397.9i	0.593132	−	0.805105i
$973$	−661.363	+	661.363i	−0.0217907	+	0.0217907i
$974$	5717.13	+	9080.89i	0.188079	+	0.298738i
$975$	−22.8896	−	198.484i	−0.000751851	−	0.00651956i
$976$	37178.1	−	29864.7i	1.21931	−	0.979454i
$977$	23653.5	+	23653.5i	0.774558	+	0.774558i	0.978900	−	0.204341i	$-0.0655053\pi$
$977$	23653.5	+	23653.5i	0.774558	+	0.774558i	−0.204341	+	0.978900i	$0.565505\pi$
$978$	17693.3	−	10231.8i	0.578495	−	0.334536i
$979$	42692.7			1.39373
$980$	−17128.8	+	17894.9i	−0.558324	+	0.583297i
$981$	32488.5	+	2446.66i	1.05737	+	0.0796289i
$982$	−7503.14	+	33008.2i	−0.243824	+	1.07264i
$983$	−18513.5	+	18513.5i	−0.600701	+	0.600701i	−0.940499	−	0.339797i	$-0.889641\pi$
$983$	−18513.5	+	18513.5i	−0.600701	+	0.600701i	0.339797	+	0.940499i	$0.389641\pi$
$984$	21157.1	−	24708.4i	0.685430	−	0.800483i
$985$	−36828.2	+	18656.4i	−1.19131	+	0.603496i
$986$	−2666.92	−	4236.04i	−0.0861380	−	0.136818i
$987$	−1579.77	+	42013.9i	−0.0509468	+	1.35493i
$988$	85.5636	−	30.1103i	0.00275520	−	0.000969571i
$989$			42694.3i			1.37270i
$990$	27800.0	−	39340.2i	0.892467	−	1.26294i
$991$	12092.6			0.387622			0.193811	−	0.981039i	$-0.437915\pi$
$991$	12092.6			0.387622			0.193811	+	0.981039i	$0.437915\pi$
$992$	−3380.73	+	1646.56i	−0.108204	+	0.0527000i
$993$	31210.3	+	1173.54i	0.997409	+	0.0375037i
$994$	−17620.3	+	11093.3i	−0.562254	+	0.353983i
$995$	7277.76	−	22221.5i	0.231880	−	0.708010i
$996$	15457.6	−	4794.95i	0.491760	−	0.152544i
$997$	−40548.9	−	40548.9i	−1.28806	−	1.28806i	−0.935964	−	0.352095i	$-0.885469\pi$
$997$	−40548.9	−	40548.9i	−1.28806	−	1.28806i	−0.352095	−	0.935964i	$-0.614531\pi$
$998$	−11531.1	+	50728.0i	−0.365741	+	1.60899i
$999$	−12408.5	+	9884.25i	−0.392979	+	0.313037i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.w.c.53.37	yes	128
3.2	odd	2	inner	120.4.w.c.53.28	yes	128
5.2	odd	4	inner	120.4.w.c.77.60	yes	128
8.5	even	2	inner	120.4.w.c.53.5	✓	128
15.2	even	4	inner	120.4.w.c.77.5	yes	128
24.5	odd	2	inner	120.4.w.c.53.60	yes	128
40.37	odd	4	inner	120.4.w.c.77.28	yes	128
120.77	even	4	inner	120.4.w.c.77.37	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.w.c.53.5	✓	128	8.5	even	2	inner
120.4.w.c.53.28	yes	128	3.2	odd	2	inner
120.4.w.c.53.37	yes	128	1.1	even	1	trivial
120.4.w.c.53.60	yes	128	24.5	odd	2	inner
120.4.w.c.77.5	yes	128	15.2	even	4	inner
120.4.w.c.77.28	yes	128	40.37	odd	4	inner
120.4.w.c.77.37	yes	128	120.77	even	4	inner
120.4.w.c.77.60	yes	128	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.626941 - 2.75807i) q^{2} +(-0.195243 + 5.19248i) q^{3} +(-7.21389 - 3.45829i) q^{4} +(10.6250 + 3.47979i) q^{5} +(14.1988 + 3.79387i) q^{6} +(-17.6061 + 17.6061i) q^{7} +(-14.0609 + 17.7283i) q^{8} +(-26.9238 - 2.02759i) q^{9} +(16.2588 - 27.1229i) q^{10} -56.4191 q^{11} +(19.3656 - 36.7828i) q^{12} +(-0.217514 + 0.217514i) q^{13} +(37.5210 + 59.5970i) q^{14} +(-20.1432 + 54.4908i) q^{15} +(40.0804 + 49.8955i) q^{16} +(75.4592 + 75.4592i) q^{17} +(-22.4718 + 72.9864i) q^{18} +36.8594 q^{19} +(-64.6136 - 61.8473i) q^{20} +(-87.9821 - 94.8571i) q^{21} +(-35.3714 + 155.608i) q^{22} +(-74.5235 + 74.5235i) q^{23} +(-89.3084 - 76.4722i) q^{24} +(100.782 + 73.9457i) q^{25} +(0.463550 + 0.736287i) q^{26} +(15.7849 - 139.405i) q^{27} +(187.896 - 66.1216i) q^{28} -16.5840i q^{29} +(137.661 + 89.7189i) q^{30} -20.7734 q^{31} +(162.743 - 79.2632i) q^{32} +(11.0154 - 292.955i) q^{33} +(255.430 - 160.813i) q^{34} +(-248.331 + 125.800i) q^{35} +(187.213 + 107.737i) q^{36} +(-79.9565 - 79.9565i) q^{37} +(23.1087 - 101.661i) q^{38} +(-1.08697 - 1.17191i) q^{39} +(-211.088 + 139.434i) q^{40} +276.664i q^{41} +(-316.782 + 183.191i) q^{42} +(286.448 - 286.448i) q^{43} +(407.001 + 195.114i) q^{44} +(-279.010 - 115.232i) q^{45} +(158.819 + 252.263i) q^{46} +(-229.786 - 229.786i) q^{47} +(-266.907 + 198.375i) q^{48} -276.953i q^{49} +(267.132 - 231.604i) q^{50} +(-406.553 + 377.088i) q^{51} +(2.32135 - 0.816895i) q^{52} +(25.1531 + 25.1531i) q^{53} +(-374.593 - 130.935i) q^{54} +(-599.454 - 196.327i) q^{55} +(-64.5684 - 559.684i) q^{56} +(-7.19654 + 191.392i) q^{57} +(-45.7397 - 10.3972i) q^{58} +431.866i q^{59} +(333.756 - 323.430i) q^{60} -745.120i q^{61} +(-13.0237 + 57.2944i) q^{62} +(509.722 - 438.325i) q^{63} +(-116.583 - 498.550i) q^{64} +(-3.06799 + 1.55419i) q^{65} +(-801.085 - 214.047i) q^{66} +(583.852 + 583.852i) q^{67} +(-283.395 - 805.314i) q^{68} +(-372.412 - 401.512i) q^{69} +(191.276 + 763.784i) q^{70} +295.657i q^{71} +(414.518 - 448.802i) q^{72} +(26.9724 + 26.9724i) q^{73} +(-270.653 + 170.398i) q^{74} +(-403.639 + 508.872i) q^{75} +(-265.900 - 127.471i) q^{76} +(993.323 - 993.323i) q^{77} +(-3.91366 + 2.26322i) q^{78} +1137.70i q^{79} +(252.230 + 669.612i) q^{80} +(720.778 + 109.181i) q^{81} +(763.058 + 173.452i) q^{82} +(275.299 + 275.299i) q^{83} +(306.650 + 988.556i) q^{84} +(539.173 + 1064.34i) q^{85} +(-610.458 - 969.631i) q^{86} +(86.1119 + 3.23790i) q^{87} +(793.303 - 1000.21i) q^{88} -756.706 q^{89} +(-492.741 + 697.285i) q^{90} -7.65916i q^{91} +(795.328 - 279.880i) q^{92} +(4.05585 - 107.865i) q^{93} +(-777.828 + 489.703i) q^{94} +(391.632 + 128.263i) q^{95} +(379.798 + 860.517i) q^{96} +(575.441 - 575.441i) q^{97} +(-763.854 - 173.633i) q^{98} +(1519.01 + 114.395i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{6} - 144 q^{7} - 156 q^{10} - 56 q^{12} + 212 q^{15} + 636 q^{16} + 220 q^{18} - 188 q^{22} - 8 q^{25} + 908 q^{28} + 328 q^{30} - 544 q^{31} - 1624 q^{33} - 1268 q^{36} - 136 q^{40} + 328 q^{42}+ \cdots - 3792 q^{97}+O(q^{100}) \) 128 * q - 4 * q^6 - 144 * q^7 - 156 * q^10 - 56 * q^12 + 212 * q^15 + 636 * q^16 + 220 * q^18 - 188 * q^22 - 8 * q^25 + 908 * q^28 + 328 * q^30 - 544 * q^31 - 1624 * q^33 - 1268 * q^36 - 136 * q^40 + 328 * q^42 + 568 * q^46 - 148 * q^48 + 616 * q^52 + 728 * q^55 - 112 * q^57 + 2196 * q^58 - 424 * q^60 - 2304 * q^63 + 304 * q^66 - 4740 * q^70 + 224 * q^72 + 1280 * q^73 - 1624 * q^76 - 1448 * q^78 + 7056 * q^81 - 1472 * q^82 - 5720 * q^87 + 1516 * q^88 - 996 * q^90 + 2732 * q^96 - 3792 * q^97

Introduction

L-functions

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