LMFDB - Embedded newform 153.4.l.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,4,Mod(19,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("153.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.l (of order $8$, degree $4$, 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:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	153.19
Dual form			153.4.l.b.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.22560 - 3.22560i) q^{2} +12.8090i q^{4} +(-2.92988 - 7.07335i) q^{5} +(-4.41551 + 10.6600i) q^{7} +(15.5118 - 15.5118i) q^{8} +O(q^{10})$	\(q+(-3.22560 - 3.22560i) q^{2} +12.8090i q^{4} +(-2.92988 - 7.07335i) q^{5} +(-4.41551 + 10.6600i) q^{7} +(15.5118 - 15.5118i) q^{8} +(-13.3652 + 32.2664i) q^{10} +(1.96204 + 0.812704i) q^{11} +36.3279i q^{13} +(48.6275 - 20.1422i) q^{14} +2.40210 q^{16} +(57.0466 + 40.7270i) q^{17} +(20.7525 + 20.7525i) q^{19} +(90.6023 - 37.5287i) q^{20} +(-3.70730 - 8.95021i) q^{22} +(6.04603 + 2.50435i) q^{23} +(46.9403 - 46.9403i) q^{25} +(117.179 - 117.179i) q^{26} +(-136.543 - 56.5581i) q^{28} +(-41.3275 - 99.7734i) q^{29} +(70.8666 - 29.3539i) q^{31} +(-131.843 - 131.843i) q^{32} +(-52.6407 - 315.378i) q^{34} +88.3386 q^{35} +(260.040 - 107.712i) q^{37} -133.879i q^{38} +(-155.168 - 64.2727i) q^{40} +(-27.5977 + 66.6267i) q^{41} +(152.810 - 152.810i) q^{43} +(-10.4099 + 25.1317i) q^{44} +(-11.4241 - 27.5801i) q^{46} +173.041i q^{47} +(148.399 + 148.399i) q^{49} -302.821 q^{50} -465.322 q^{52} +(432.514 + 432.514i) q^{53} -16.2593i q^{55} +(96.8630 + 233.848i) q^{56} +(-188.523 + 455.135i) q^{58} +(-455.659 + 455.659i) q^{59} +(-179.555 + 433.485i) q^{61} +(-323.271 - 133.903i) q^{62} +831.326i q^{64} +(256.960 - 106.436i) q^{65} +1001.77 q^{67} +(-521.670 + 730.708i) q^{68} +(-284.945 - 284.945i) q^{70} +(446.936 - 185.127i) q^{71} +(433.977 + 1047.71i) q^{73} +(-1186.22 - 491.348i) q^{74} +(-265.818 + 265.818i) q^{76} +(-17.3268 + 17.3268i) q^{77} +(-1023.08 - 423.774i) q^{79} +(-7.03787 - 16.9909i) q^{80} +(303.930 - 125.892i) q^{82} +(-369.115 - 369.115i) q^{83} +(120.936 - 522.835i) q^{85} -985.810 q^{86} +(43.0413 - 17.8283i) q^{88} +469.598i q^{89} +(-387.254 - 160.406i) q^{91} +(-32.0781 + 77.4435i) q^{92} +(558.162 - 558.162i) q^{94} +(85.9875 - 207.592i) q^{95} +(-470.826 - 1136.68i) q^{97} -957.352i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 80 q^{10} - 128 q^{16} + 128 q^{19} + 280 q^{22} + 16 q^{25} + 184 q^{28} - 192 q^{31} + 24 q^{34} - 416 q^{37} - 488 q^{40} + 672 q^{43} - 384 q^{46} + 944 q^{49} - 4032 q^{52} - 1576 q^{58} + 4816 q^{61} + 2464 q^{67} + 5944 q^{70} + 3024 q^{73} - 3384 q^{76} - 4992 q^{79} - 1176 q^{82} - 2544 q^{85} - 1480 q^{88} - 4016 q^{91} + 4672 q^{94} + 1008 q^{97}+O(q^{100}) $ 32 * q - 80 * q^10 - 128 * q^16 + 128 * q^19 + 280 * q^22 + 16 * q^25 + 184 * q^28 - 192 * q^31 + 24 * q^34 - 416 * q^37 - 488 * q^40 + 672 * q^43 - 384 * q^46 + 944 * q^49 - 4032 * q^52 - 1576 * q^58 + 4816 * q^61 + 2464 * q^67 + 5944 * q^70 + 3024 * q^73 - 3384 * q^76 - 4992 * q^79 - 1176 * q^82 - 2544 * q^85 - 1480 * q^88 - 4016 * q^91 + 4672 * q^94 + 1008 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	−3.22560	−	3.22560i	−1.14042	−	1.14042i	−0.988373	−	0.152048i	$-0.951413\pi$
$2$	−3.22560	−	3.22560i	−1.14042	−	1.14042i	−0.152048	−	0.988373i	$-0.548587\pi$
$3$		0			0
$3$		0			0
$4$			12.8090i			1.60112i
$5$	−2.92988	−	7.07335i	−0.262056	−	0.632660i	0.737009	−	0.675883i	$-0.236237\pi$
$5$	−2.92988	−	7.07335i	−0.262056	−	0.632660i	−0.999065	+	0.0432231i	$0.986237\pi$
$6$		0			0
$7$	−4.41551	+	10.6600i	−0.238415	+	0.575585i	−0.997119	−	0.0758505i	$-0.975833\pi$
$7$	−4.41551	+	10.6600i	−0.238415	+	0.575585i	0.758704	+	0.651435i	$0.225833\pi$
$8$	15.5118	−	15.5118i	0.685531	−	0.685531i
$9$		0			0
$10$	−13.3652	+	32.2664i	−0.422644	+	1.02035i
$11$	1.96204	+	0.812704i	0.0537798	+	0.0222763i	0.409411	−	0.912350i	$-0.365734\pi$
$11$	1.96204	+	0.812704i	0.0537798	+	0.0222763i	−0.355631	+	0.934626i	$0.615734\pi$
$12$		0			0
$13$			36.3279i			0.775041i	0.921861	+	0.387521i	$0.126668\pi$
$13$			36.3279i			0.775041i	−0.921861	+	0.387521i	$0.873332\pi$
$14$	48.6275	−	20.1422i	0.928303	−	0.384516i
$15$		0			0
$16$	2.40210			0.0375329
$17$	57.0466	+	40.7270i	0.813873	+	0.581043i
$17$	57.0466	+	40.7270i	0.813873	+	0.581043i
$18$		0			0
$19$	20.7525	+	20.7525i	0.250577	+	0.250577i	0.821207	−	0.570630i	$-0.193301\pi$
$19$	20.7525	+	20.7525i	0.250577	+	0.250577i	−0.570630	+	0.821207i	$0.693301\pi$
$20$	90.6023	−	37.5287i	1.01296	−	0.419584i
$21$		0			0
$22$	−3.70730	−	8.95021i	−0.0359272	−	0.0867360i
$23$	6.04603	+	2.50435i	0.0548124	+	0.0227040i	0.409921	−	0.912121i	$-0.365556\pi$
$23$	6.04603	+	2.50435i	0.0548124	+	0.0227040i	−0.355109	+	0.934825i	$0.615556\pi$
$24$		0			0
$25$	46.9403	−	46.9403i	0.375522	−	0.375522i
$26$	117.179	−	117.179i	0.883873	−	0.883873i
$27$		0			0
$28$	−136.543	−	56.5581i	−0.921581	−	0.381731i
$29$	−41.3275	−	99.7734i	−0.264632	−	0.638878i	0.734582	−	0.678520i	$-0.237378\pi$
$29$	−41.3275	−	99.7734i	−0.264632	−	0.638878i	−0.999214	+	0.0396420i	$0.987378\pi$
$30$		0			0
$31$	70.8666	−	29.3539i	0.410581	−	0.170068i	−0.167826	−	0.985817i	$-0.553675\pi$
$31$	70.8666	−	29.3539i	0.410581	−	0.170068i	0.578407	+	0.815748i	$0.303675\pi$
$32$	−131.843	−	131.843i	−0.728334	−	0.728334i
$33$		0			0
$34$	−52.6407	−	315.378i	−0.265523	−	1.59079i
$35$	88.3386			0.426627
$36$		0			0
$37$	260.040	−	107.712i	1.15541	−	0.478587i	0.279067	−	0.960272i	$-0.409975\pi$
$37$	260.040	−	107.712i	1.15541	−	0.478587i	0.876345	+	0.481684i	$0.159975\pi$
$38$		−	133.879i		−	0.571526i
$39$		0			0
$40$	−155.168	−	64.2727i	−0.613355	−	0.254060i
$41$	−27.5977	+	66.6267i	−0.105123	+	0.253789i	−0.967685	−	0.252162i	$-0.918858\pi$
$41$	−27.5977	+	66.6267i	−0.105123	+	0.253789i	0.862562	+	0.505951i	$0.168858\pi$
$42$		0			0
$43$	152.810	−	152.810i	0.541939	−	0.541939i	−0.382158	−	0.924097i	$-0.624819\pi$
$43$	152.810	−	152.810i	0.541939	−	0.541939i	0.924097	+	0.382158i	$0.124819\pi$
$44$	−10.4099	+	25.1317i	−0.0356671	+	0.0861079i
$45$		0			0
$46$	−11.4241	−	27.5801i	−0.0366171	−	0.0884014i
$47$			173.041i			0.537036i	0.963275	+	0.268518i	$0.0865338\pi$
$47$			173.041i			0.537036i	−0.963275	+	0.268518i	$0.913466\pi$
$48$		0			0
$49$	148.399	+	148.399i	0.432651	+	0.432651i
$50$	−302.821			−0.856507
$51$		0			0
$52$	−465.322			−1.24093
$53$	432.514	+	432.514i	1.12095	+	1.12095i	0.991599	+	0.129352i	$0.0412896\pi$
$53$	432.514	+	432.514i	1.12095	+	1.12095i	0.129352	+	0.991599i	$0.458710\pi$
$54$		0			0
$55$		−	16.2593i		−	0.0398619i
$56$	96.8630	+	233.848i	0.231140	+	0.558022i
$57$		0			0
$58$	−188.523	+	455.135i	−0.426798	+	1.03038i
$59$	−455.659	+	455.659i	−1.00545	+	1.00545i	−0.00546913	+	0.999985i	$0.501741\pi$
$59$	−455.659	+	455.659i	−1.00545	+	1.00545i	−0.999985	+	0.00546913i	$0.998259\pi$
$60$		0			0
$61$	−179.555	+	433.485i	−0.376880	+	0.909869i	0.615667	+	0.788006i	$0.288887\pi$
$61$	−179.555	+	433.485i	−0.376880	+	0.909869i	−0.992547	+	0.121862i	$0.961113\pi$
$62$	−323.271	−	133.903i	−0.662185	−	0.274286i
$63$		0			0
$64$			831.326i			1.62368i
$65$	256.960	−	106.436i	0.490337	−	0.203104i
$66$		0			0
$67$	1001.77			1.82666			0.913329	−	0.407223i	$-0.133503\pi$
$67$	1001.77			1.82666			0.913329	+	0.407223i	$0.133503\pi$
$68$	−521.670	+	730.708i	−0.930321	+	1.30311i
$69$		0			0
$70$	−284.945	−	284.945i	−0.486535	−	0.486535i
$71$	446.936	−	185.127i	0.747064	−	0.309444i	0.0235211	−	0.999723i	$-0.492512\pi$
$71$	446.936	−	185.127i	0.747064	−	0.309444i	0.723543	+	0.690279i	$0.242512\pi$
$72$		0			0
$73$	433.977	+	1047.71i	0.695797	+	1.67980i	0.732761	+	0.680486i	$0.238231\pi$
$73$	433.977	+	1047.71i	0.695797	+	1.67980i	−0.0369641	+	0.999317i	$0.511769\pi$
$74$	−1186.22	−	491.348i	−1.86345	−	0.771865i
$75$		0			0
$76$	−265.818	+	265.818i	−0.401204	+	0.401204i
$77$	−17.3268	+	17.3268i	−0.0256438	+	0.0256438i
$78$		0			0
$79$	−1023.08	−	423.774i	−1.45703	−	0.603523i	−0.493173	−	0.869931i	$-0.664163\pi$
$79$	−1023.08	−	423.774i	−1.45703	−	0.603523i	−0.963860	+	0.266409i	$0.914163\pi$
$80$	−7.03787	−	16.9909i	−0.00983572	−	0.0237455i
$81$		0			0
$82$	303.930	−	125.892i	0.409310	−	0.169542i
$83$	−369.115	−	369.115i	−0.488141	−	0.488141i	0.419578	−	0.907719i	$-0.362178\pi$
$83$	−369.115	−	369.115i	−0.488141	−	0.488141i	−0.907719	+	0.419578i	$0.862178\pi$
$84$		0			0
$85$	120.936	−	522.835i	0.154322	−	0.667170i
$86$	−985.810			−1.23608
$87$		0			0
$88$	43.0413	−	17.8283i	0.0521388	−	0.0215966i
$89$			469.598i			0.559295i	0.960103	+	0.279647i	$0.0902176\pi$
$89$			469.598i			0.559295i	−0.960103	+	0.279647i	$0.909782\pi$
$90$		0			0
$91$	−387.254	−	160.406i	−0.446102	−	0.184781i
$92$	−32.0781	+	77.4435i	−0.0363519	+	0.0877613i
$93$		0			0
$94$	558.162	−	558.162i	0.612447	−	0.612447i
$95$	85.9875	−	207.592i	0.0928646	−	0.224195i
$96$		0			0
$97$	−470.826	−	1136.68i	−0.492837	−	1.18981i	−0.953270	−	0.302119i	$-0.902306\pi$
$97$	−470.826	−	1136.68i	−0.492837	−	1.18981i	0.460433	−	0.887694i	$-0.347694\pi$
$98$		−	957.352i		−	0.986808i
$99$		0			0
$100$	601.256	+	601.256i	0.601256	+	0.601256i
$101$	962.308			0.948052			0.474026	−	0.880511i	$-0.342800\pi$
$101$	962.308			0.948052			0.474026	+	0.880511i	$0.342800\pi$
$102$		0			0
$103$	−346.736			−0.331698			−0.165849	−	0.986151i	$-0.553036\pi$
$103$	−346.736			−0.331698			−0.165849	+	0.986151i	$0.553036\pi$
$104$	563.510	+	563.510i	0.531315	+	0.531315i
$105$		0			0
$106$		−	2790.23i		−	2.55671i
$107$	613.689	+	1481.58i	0.554463	+	1.33859i	0.914096	+	0.405499i	$0.132902\pi$
$107$	613.689	+	1481.58i	0.554463	+	1.33859i	−0.359632	+	0.933094i	$0.617098\pi$
$108$		0			0
$109$	−259.876	+	627.395i	−0.228363	+	0.551317i	−0.995978	−	0.0895936i	$-0.971443\pi$
$109$	−259.876	+	627.395i	−0.228363	+	0.551317i	0.767615	+	0.640911i	$0.221443\pi$
$110$	−52.4460	+	52.4460i	−0.0454594	+	0.0454594i
$111$		0			0
$112$	−10.6065	+	25.6064i	−0.00894840	+	0.0216033i
$113$	1567.16	+	649.137i	1.30465	+	0.540404i	0.923319	−	0.384034i	$-0.125465\pi$
$113$	1567.16	+	649.137i	1.30465	+	0.540404i	0.381332	+	0.924438i	$0.375465\pi$
$114$		0			0
$115$		−	50.1031i		−	0.0406273i
$116$	1277.99	−	529.363i	1.02292	−	0.423708i
$117$		0			0
$118$	2939.55			2.29328
$119$	−686.038	+	428.285i	−0.528479	+	0.329923i
$120$		0			0
$121$	−937.970	−	937.970i	−0.704711	−	0.704711i
$122$	1977.42	−	819.074i	1.46744	−	0.607832i
$123$		0			0
$124$	375.993	+	907.728i	0.272300	+	0.657390i
$125$	−1353.72	−	560.730i	−0.968645	−	0.401226i
$126$		0			0
$127$	−336.837	+	336.837i	−0.235350	+	0.235350i	−0.814922	−	0.579571i	$-0.803220\pi$
$127$	−336.837	+	336.837i	−0.235350	+	0.235350i	0.579571	+	0.814922i	$0.303220\pi$
$128$	1626.78	−	1626.78i	1.12335	−	1.12335i
$129$		0			0
$130$	−1172.17	−	485.528i	−0.790815	−	0.327566i
$131$	459.699	+	1109.81i	0.306596	+	0.740189i	0.999811	+	0.0194573i	$0.00619386\pi$
$131$	459.699	+	1109.81i	0.306596	+	0.740189i	−0.693214	+	0.720731i	$0.743806\pi$
$132$		0			0
$133$	−312.854	+	129.589i	−0.203969	+	0.0844869i
$134$	−3231.32	−	3231.32i	−2.08316	−	2.08316i
$135$		0			0
$136$	1516.64	−	253.147i	0.956258	−	0.159612i
$137$	−743.547			−0.463690			−0.231845	−	0.972753i	$-0.574476\pi$
$137$	−743.547			−0.463690			−0.231845	+	0.972753i	$0.574476\pi$
$138$		0			0
$139$	−829.604	+	343.633i	−0.506231	+	0.209688i	−0.621157	−	0.783686i	$-0.713337\pi$
$139$	−829.604	+	343.633i	−0.506231	+	0.209688i	0.114926	+	0.993374i	$0.463337\pi$
$140$			1131.53i			0.683082i
$141$		0			0
$142$	−2038.78	−	844.491i	−1.20486	−	0.499071i
$143$	−29.5238	+	71.2768i	−0.0172651	+	0.0416816i
$144$		0			0
$145$	−584.648	+	584.648i	−0.334844	+	0.334844i
$146$	1979.67	−	4779.34i	1.12218	−	2.70918i
$147$		0			0
$148$	1379.68	+	3330.84i	0.766276	+	1.84995i
$149$		−	1271.78i		−	0.699253i	−0.936889	−	0.349626i	$-0.886309\pi$
$149$		−	1271.78i		−	0.699253i	0.936889	−	0.349626i	$-0.113691\pi$
$150$		0			0
$151$	−448.413	−	448.413i	−0.241665	−	0.241665i	0.575874	−	0.817539i	$-0.304662\pi$
$151$	−448.413	−	448.413i	−0.241665	−	0.241665i	−0.817539	+	0.575874i	$0.804662\pi$
$152$	643.818			0.343556
$153$		0			0
$154$	111.779			0.0584895
$155$	−415.261	−	415.261i	−0.215191	−	0.215191i
$156$		0			0
$157$			41.3631i			0.0210263i	0.999945	+	0.0105132i	$0.00334650\pi$
$157$			41.3631i			0.0210263i	−0.999945	+	0.0105132i	$0.996653\pi$
$158$	1933.12	+	4666.97i	0.973361	+	2.34990i
$159$		0			0
$160$	−546.286	+	1318.85i	−0.269923	+	0.651652i
$161$	−53.3926	+	53.3926i	−0.0261362	+	0.0261362i
$162$		0			0
$163$	−486.094	+	1173.53i	−0.233582	+	0.563916i	−0.996594	−	0.0824682i	$-0.973720\pi$
$163$	−486.094	+	1173.53i	−0.233582	+	0.563916i	0.763012	+	0.646384i	$0.223720\pi$
$164$	−853.419	−	353.498i	−0.406346	−	0.168314i
$165$		0			0
$166$			2381.24i			1.11337i
$167$	1412.99	−	585.279i	0.654732	−	0.271199i	−0.0304879	−	0.999535i	$-0.509706\pi$
$167$	1412.99	−	585.279i	0.654732	−	0.271199i	0.685220	+	0.728336i	$0.259706\pi$
$168$		0			0
$169$	877.287			0.399311
$170$	−2076.55	+	1296.36i	−0.936847	+	0.584863i
$171$		0			0
$172$	1957.34	+	1957.34i	0.867710	+	0.867710i
$173$	3258.49	−	1349.71i	1.43202	−	0.593160i	0.474167	−	0.880435i	$-0.342749\pi$
$173$	3258.49	−	1349.71i	1.43202	−	0.593160i	0.957848	+	0.287275i	$0.0927492\pi$
$174$		0			0
$175$	293.117	+	707.647i	0.126615	+	0.305675i
$176$	4.71303	+	1.95220i	0.00201851	+	0.000836094i
$177$		0			0
$178$	1514.73	−	1514.73i	0.637832	−	0.637832i
$179$	−1836.59	+	1836.59i	−0.766888	+	0.766888i	−0.977557	−	0.210669i	$-0.932436\pi$
$179$	−1836.59	+	1836.59i	−0.766888	+	0.766888i	0.210669	+	0.977557i	$0.432436\pi$
$180$		0			0
$181$	−1936.82	−	802.258i	−0.795375	−	0.329455i	−0.0522726	−	0.998633i	$-0.516646\pi$
$181$	−1936.82	−	802.258i	−0.795375	−	0.329455i	−0.743102	+	0.669178i	$0.766646\pi$
$182$	731.721	+	1766.53i	0.298015	+	0.719473i
$183$		0			0
$184$	132.632	−	54.9379i	0.0531399	−	0.0220113i
$185$	−1523.77	−	1523.77i	−0.605566	−	0.605566i
$186$		0			0
$187$	78.8288	+	126.270i	0.0308264	+	0.0493785i
$188$	−2216.48			−0.859859
$189$		0			0
$190$	−946.970	+	392.248i	−0.361581	+	0.149772i
$191$			2678.09i			1.01455i	0.861783	+	0.507277i	$0.169348\pi$
$191$			2678.09i			1.01455i	−0.861783	+	0.507277i	$0.830652\pi$
$192$		0			0
$193$	484.837	+	200.826i	0.180826	+	0.0749005i	0.471259	−	0.881995i	$-0.343800\pi$
$193$	484.837	+	200.826i	0.180826	+	0.0749005i	−0.290434	+	0.956895i	$0.593800\pi$
$194$	−2147.76	+	5185.15i	−0.794847	+	1.91893i
$195$		0			0
$196$	−1900.84	+	1900.84i	−0.692726	+	0.692726i
$197$	1128.39	−	2724.17i	0.408093	−	0.985224i	−0.577546	−	0.816358i	$-0.695989\pi$
$197$	1128.39	−	2724.17i	0.408093	−	0.985224i	0.985639	−	0.168866i	$-0.0540105\pi$
$198$		0			0
$199$	−226.992	−	548.008i	−0.0808596	−	0.195212i	0.878279	−	0.478148i	$-0.158692\pi$
$199$	−226.992	−	548.008i	−0.0808596	−	0.195212i	−0.959139	+	0.282936i	$0.908692\pi$
$200$		−	1456.26i		−	0.514864i
$201$		0			0
$202$	−3104.02	−	3104.02i	−1.08118	−	1.08118i
$203$	1246.06			0.430821
$204$		0			0
$205$	552.132			0.188110
$206$	1118.43	+	1118.43i	0.378276	+	0.378276i
$207$		0			0
$208$			87.2632i			0.0290895i
$209$	23.8517	+	57.5830i	0.00789404	+	0.0190579i
$210$		0			0
$211$	1892.59	−	4569.12i	0.617495	−	1.49076i	−0.237109	−	0.971483i	$-0.576200\pi$
$211$	1892.59	−	4569.12i	0.617495	−	1.49076i	0.854603	−	0.519281i	$-0.173800\pi$
$212$	−5540.06	+	5540.06i	−1.79478	+	1.79478i
$213$		0			0
$214$	2799.46	−	6758.49i	0.894238	−	2.15888i
$215$	−1528.60	−	633.166i	−0.484881	−	0.200844i
$216$		0			0
$217$			885.049i			0.276871i
$218$	2861.98	−	1185.47i	0.889164	−	0.368304i
$219$		0			0
$220$	208.265			0.0638238
$221$	−1479.52	+	2072.38i	−0.450332	+	0.630785i
$222$		0			0
$223$	3181.09	+	3181.09i	0.955254	+	0.955254i	0.999041	−	0.0437864i	$-0.0139421\pi$
$223$	3181.09	+	3181.09i	0.955254	+	0.955254i	−0.0437864	+	0.999041i	$0.513942\pi$
$224$	1987.59	−	823.287i	0.592864	−	0.245572i
$225$		0			0
$226$	−2961.16	−	7148.87i	−0.871563	−	2.10414i
$227$	−4701.77	−	1947.54i	−1.37475	−	0.569439i	−0.431675	−	0.902029i	$-0.642077\pi$
$227$	−4701.77	−	1947.54i	−1.37475	−	0.569439i	−0.943071	+	0.332591i	$0.892077\pi$
$228$		0			0
$229$	2789.40	−	2789.40i	0.804928	−	0.804928i	−0.178933	−	0.983861i	$-0.557265\pi$
$229$	2789.40	−	2789.40i	0.804928	−	0.804928i	0.983861	+	0.178933i	$0.0572646\pi$
$230$	−161.613	+	161.613i	−0.0463323	+	0.0463323i
$231$		0			0
$232$	−2188.73	−	906.601i	−0.619384	−	0.256557i
$233$	−686.693	−	1657.82i	−0.193076	−	0.466127i	0.797461	−	0.603370i	$-0.206176\pi$
$233$	−686.693	−	1657.82i	−0.193076	−	0.466127i	−0.990537	+	0.137243i	$0.956176\pi$
$234$		0			0
$235$	1223.98	−	506.990i	0.339761	−	0.140734i
$236$	−5836.53	−	5836.53i	−1.60985	−	1.60985i
$237$		0			0
$238$	3594.36	+	831.407i	0.978940	+	0.226437i
$239$	−4691.46			−1.26973			−0.634865	−	0.772623i	$-0.718944\pi$
$239$	−4691.46			−1.26973			−0.634865	+	0.772623i	$0.718944\pi$
$240$		0			0
$241$	−1282.92	+	531.402i	−0.342904	+	0.142036i	−0.547488	−	0.836813i	$-0.684416\pi$
$241$	−1282.92	+	531.402i	−0.342904	+	0.142036i	0.204584	+	0.978849i	$0.434416\pi$
$242$			6051.03i			1.60733i
$243$		0			0
$244$	−5552.49	−	2299.92i	−1.45681	−	0.603431i
$245$	614.888	−	1484.47i	0.160342	−	0.387099i
$246$		0			0
$247$	−753.895	+	753.895i	−0.194207	+	0.194207i
$248$	643.936	−	1554.60i	0.164879	−	0.398053i
$249$		0			0
$250$	2557.87	+	6175.26i	0.647097	+	1.56223i
$251$		−	2711.02i		−	0.681745i	−0.940109	−	0.340873i	$-0.889277\pi$
$251$		−	2711.02i		−	0.681745i	0.940109	−	0.340873i	$-0.110723\pi$
$252$		0			0
$253$	9.82728	+	9.82728i	0.00244204	+	0.00244204i
$254$	2173.00			0.536797
$255$		0			0
$256$	−3844.08			−0.938497
$257$	1887.33	+	1887.33i	0.458087	+	0.458087i	0.898027	−	0.439940i	$-0.145000\pi$
$257$	1887.33	+	1887.33i	0.458087	+	0.458087i	−0.439940	+	0.898027i	$0.645000\pi$
$258$		0			0
$259$			3247.62i			0.779140i
$260$	1363.34	+	3291.39i	0.325195	+	0.785089i
$261$		0			0
$262$	2097.00	−	5062.61i	0.494478	−	1.19378i
$263$	−5316.18	+	5316.18i	−1.24642	+	1.24642i	−0.289137	+	0.957288i	$0.593368\pi$
$263$	−5316.18	+	5316.18i	−1.24642	+	1.24642i	−0.957288	+	0.289137i	$0.906632\pi$
$264$		0			0
$265$	1792.11	−	4326.54i	0.415428	−	1.00293i
$266$	1427.14	+	591.142i	0.328962	+	0.136260i
$267$		0			0
$268$			12831.7i			2.92470i
$269$	6307.34	−	2612.59i	1.42961	−	0.592165i	0.472356	−	0.881408i	$-0.343404\pi$
$269$	6307.34	−	2612.59i	1.42961	−	0.592165i	0.957256	+	0.289243i	$0.0934036\pi$
$270$		0			0
$271$	−6314.39			−1.41539			−0.707697	−	0.706516i	$-0.750266\pi$
$271$	−6314.39			−1.41539			−0.707697	+	0.706516i	$0.750266\pi$
$272$	137.032	+	97.8303i	0.0305470	+	0.0218082i
$273$		0			0
$274$	2398.38	+	2398.38i	0.528802	+	0.528802i
$275$	130.247	−	53.9502i	0.0285608	−	0.0118303i
$276$		0			0
$277$	−238.865	−	576.672i	−0.0518124	−	0.125086i	0.895854	−	0.444349i	$-0.146565\pi$
$277$	−238.865	−	576.672i	−0.0518124	−	0.125086i	−0.947666	+	0.319262i	$0.896565\pi$
$278$	3784.39	+	1567.55i	0.816449	+	0.338184i
$279$		0			0
$280$	1370.29	−	1370.29i	0.292466	−	0.292466i
$281$	2332.32	−	2332.32i	0.495141	−	0.495141i	−0.414780	−	0.909922i	$-0.636142\pi$
$281$	2332.32	−	2332.32i	0.495141	−	0.495141i	0.909922	+	0.414780i	$0.136142\pi$
$282$		0			0
$283$	7605.06	+	3150.12i	1.59743	+	0.661679i	0.991050	−	0.133493i	$-0.0426193\pi$
$283$	7605.06	+	3150.12i	1.59743	+	0.661679i	0.606384	+	0.795172i	$0.292619\pi$
$284$	2371.29	+	5724.79i	0.495457	+	1.19614i
$285$		0			0
$286$	325.142	−	134.678i	0.0672240	−	0.0278451i
$287$	−588.381	−	588.381i	−0.121014	−	0.121014i
$288$		0			0
$289$	1595.63	+	4646.67i	0.324777	+	0.945791i
$290$	3771.68			0.763726
$291$		0			0
$292$	−13420.1	+	5558.80i	−2.68957	+	1.11406i
$293$		−	2825.12i		−	0.563295i	−0.959518	−	0.281647i	$-0.909119\pi$
$293$		−	2825.12i		−	0.563295i	0.959518	−	0.281647i	$-0.0908808\pi$
$294$		0			0
$295$	4558.06	+	1888.01i	0.899596	+	0.372625i
$296$	2362.88	−	5704.49i	0.463984	−	1.12016i
$297$		0			0
$298$	−4102.27	+	4102.27i	−0.797442	+	0.797442i
$299$	−90.9777	+	219.639i	−0.0175966	+	0.0424819i
$300$		0			0
$301$	954.220	+	2303.69i	0.182725	+	0.441138i
$302$			2892.80i			0.551199i
$303$		0			0
$304$	49.8497	+	49.8497i	0.00940486	+	0.00940486i
$305$	3592.26			0.674401
$306$		0			0
$307$	−1075.21			−0.199888			−0.0999442	−	0.994993i	$-0.531866\pi$
$307$	−1075.21			−0.199888			−0.0999442	+	0.994993i	$0.531866\pi$
$308$	−221.939	−	221.939i	−0.0410589	−	0.0410589i
$309$		0			0
$310$			2678.93i			0.490816i
$311$	−2719.27	−	6564.91i	−0.495806	−	1.19698i	−0.951722	−	0.306960i	$-0.900688\pi$
$311$	−2719.27	−	6564.91i	−0.495806	−	1.19698i	0.455916	−	0.890023i	$-0.349312\pi$
$312$		0			0
$313$	416.075	−	1004.49i	0.0751372	−	0.181397i	−0.881848	−	0.471534i	$-0.843701\pi$
$313$	416.075	−	1004.49i	0.0751372	−	0.181397i	0.956985	+	0.290136i	$0.0937006\pi$
$314$	133.421	−	133.421i	0.0239789	−	0.0239789i
$315$		0			0
$316$	5428.11	−	13104.6i	0.966313	−	2.33289i
$317$	−4224.51	−	1749.85i	−0.748492	−	0.310036i	−0.0243662	−	0.999703i	$-0.507757\pi$
$317$	−4224.51	−	1749.85i	−0.748492	−	0.310036i	−0.724126	+	0.689667i	$0.757757\pi$
$318$		0			0
$319$		−	229.347i		−	0.0402537i
$320$	5880.25	−	2435.68i	1.02724	−	0.425496i
$321$		0			0
$322$	344.446			0.0596126
$323$	338.674	+	2029.05i	0.0583416	+	0.349533i
$324$		0			0
$325$	1705.24	+	1705.24i	0.291045	+	0.291045i
$326$	5353.30	−	2217.41i	0.909484	−	0.376720i
$327$		0			0
$328$	605.410	+	1461.59i	0.101915	+	0.246045i
$329$	−1844.62	−	764.066i	−0.309110	−	0.128037i
$330$		0			0
$331$	1124.08	−	1124.08i	0.186662	−	0.186662i	−0.607589	−	0.794251i	$-0.707863\pi$
$331$	1124.08	−	1124.08i	0.186662	−	0.186662i	0.794251	+	0.607589i	$0.207863\pi$
$332$	4727.99	−	4727.99i	0.781572	−	0.781572i
$333$		0			0
$334$	−6445.60	−	2669.86i	−1.05595	−	0.437389i
$335$	−2935.07	−	7085.89i	−0.478687	−	1.15565i
$336$		0			0
$337$	3311.22	−	1371.55i	0.535233	−	0.221701i	−0.0986602	−	0.995121i	$-0.531456\pi$
$337$	3311.22	−	1371.55i	0.535233	−	0.221701i	0.633894	+	0.773420i	$0.281456\pi$
$338$	−2829.77	−	2829.77i	−0.455383	−	0.455383i
$339$		0			0
$340$	6696.98	+	1549.07i	1.06822	+	0.247089i
$341$	162.899			0.0258695
$342$		0			0
$343$	−5893.56	+	2441.19i	−0.927762	+	0.384292i
$344$		−	4740.73i		−	0.743032i
$345$		0			0
$346$	−14864.2	−	6156.96i	−2.30955	−	0.956648i
$347$	−2884.13	+	6962.91i	−0.446191	+	1.07720i	0.527546	+	0.849526i	$0.323112\pi$
$347$	−2884.13	+	6962.91i	−0.446191	+	1.07720i	−0.973737	+	0.227675i	$0.926888\pi$
$348$		0			0
$349$	−2312.06	+	2312.06i	−0.354619	+	0.354619i	−0.861825	−	0.507206i	$-0.830678\pi$
$349$	−2312.06	+	2312.06i	−0.354619	+	0.354619i	0.507206	+	0.861825i	$0.330678\pi$
$350$	1337.11	−	3228.06i	0.204204	−	0.492992i
$351$		0			0
$352$	−151.532	−	365.830i	−0.0229451	−	0.0553943i
$353$		−	7031.32i		−	1.06017i	−0.847945	−	0.530084i	$-0.822160\pi$
$353$		−	7031.32i		−	1.06017i	0.847945	−	0.530084i	$-0.177840\pi$
$354$		0			0
$355$	−2618.94	−	2618.94i	−0.391546	−	0.391546i
$356$	−6015.06			−0.895499
$357$		0			0
$358$	11848.2			1.74915
$359$	2012.48	+	2012.48i	0.295862	+	0.295862i	0.839391	−	0.543529i	$-0.182912\pi$
$359$	2012.48	+	2012.48i	0.295862	+	0.295862i	−0.543529	+	0.839391i	$0.682912\pi$
$360$		0			0
$361$		−	5997.67i		−	0.874423i
$362$	3659.65	+	8835.17i	0.531345	+	1.28278i
$363$		0			0
$364$	2054.63	−	4960.33i	0.295857	−	0.714263i
$365$	6139.34	−	6139.34i	0.880405	−	0.880405i
$366$		0			0
$367$	3992.86	−	9639.62i	0.567917	−	1.37107i	−0.335390	−	0.942079i	$-0.608868\pi$
$367$	3992.86	−	9639.62i	0.567917	−	1.37107i	0.903307	−	0.428994i	$-0.141132\pi$
$368$	14.5232	+	6.01571i	0.00205727	+	0.000852148i
$369$		0			0
$370$			9830.13i			1.38120i
$371$	−6520.36	+	2700.82i	−0.912454	+	0.377951i
$372$		0			0
$373$	1145.22			0.158973			0.0794866	−	0.996836i	$-0.474672\pi$
$373$	1145.22			0.158973			0.0794866	+	0.996836i	$0.474672\pi$
$374$	153.026	−	661.566i	0.0211572	−	0.0914673i
$375$		0			0
$376$	2684.18	+	2684.18i	0.368155	+	0.368155i
$377$	3624.55	−	1501.34i	0.495157	−	0.205101i
$378$		0			0
$379$	−2970.99	−	7172.60i	−0.402663	−	0.972115i	−0.987017	−	0.160616i	$-0.948652\pi$
$379$	−2970.99	−	7172.60i	−0.402663	−	0.972115i	0.584354	−	0.811499i	$-0.301348\pi$
$380$	2659.04	+	1101.41i	0.358963	+	0.148687i
$381$		0			0
$382$	8638.44	−	8638.44i	1.15702	−	1.15702i
$383$	−8532.56	+	8532.56i	−1.13836	+	1.13836i	−0.149620	+	0.988744i	$0.547805\pi$
$383$	−8532.56	+	8532.56i	−1.13836	+	1.13836i	−0.988744	+	0.149620i	$0.952195\pi$
$384$		0			0
$385$	173.324	+	71.7932i	0.0229439	+	0.00950369i
$386$	−916.106	−	2211.68i	−0.120799	−	0.291636i
$387$		0			0
$388$	14559.6	−	6030.80i	1.90503	−	0.789091i
$389$	9867.71	+	9867.71i	1.28615	+	1.28615i	0.937106	+	0.349045i	$0.113494\pi$
$389$	9867.71	+	9867.71i	1.28615	+	1.28615i	0.349045	+	0.937106i	$0.386506\pi$
$390$		0			0
$391$	242.911	+	389.101i	0.0314183	+	0.0503266i
$392$	4603.88			0.593191
$393$		0			0
$394$	−12426.8	+	5147.35i	−1.58897	+	0.658173i
$395$			8478.21i			1.07996i
$396$		0			0
$397$	−4617.99	−	1912.83i	−0.583804	−	0.241820i	0.0711784	−	0.997464i	$-0.477324\pi$
$397$	−4617.99	−	1912.83i	−0.583804	−	0.241820i	−0.654983	+	0.755644i	$0.727324\pi$
$398$	−1035.47	+	2499.84i	−0.130410	+	0.314838i
$399$		0			0
$400$	112.755	−	112.755i	0.0140944	−	0.0140944i
$401$	364.859	−	880.848i	0.0454369	−	0.109694i	−0.899532	−	0.436856i	$-0.856092\pi$
$401$	364.859	−	880.848i	0.0454369	−	0.109694i	0.944969	+	0.327161i	$0.106092\pi$
$402$		0			0
$403$	1066.36	+	2574.43i	0.131810	+	0.318217i
$404$			12326.2i			1.51795i
$405$		0			0
$406$	−4019.30	−	4019.30i	−0.491317	−	0.491317i
$407$	597.746			0.0727990
$408$		0			0
$409$	−7862.57			−0.950559			−0.475280	−	0.879835i	$-0.657653\pi$
$409$	−7862.57			−0.950559			−0.475280	+	0.879835i	$0.657653\pi$
$410$	−1780.95	−	1780.95i	−0.214525	−	0.214525i
$411$		0			0
$412$		−	4441.33i		−	0.531089i
$413$	−2845.35	−	6869.29i	−0.339009	−	0.818440i
$414$		0			0
$415$	−1529.42	+	3692.34i	−0.180907	+	0.436747i
$416$	4789.56	−	4789.56i	0.564489	−	0.564489i
$417$		0			0
$418$	108.804	−	262.675i	0.0127315	−	0.0307365i
$419$	9465.70	+	3920.82i	1.10365	+	0.457147i	0.858747	−	0.512400i	$-0.171244\pi$
$419$	9465.70	+	3920.82i	1.10365	+	0.457147i	0.244904	+	0.969547i	$0.421244\pi$
$420$		0			0
$421$			805.452i			0.0932431i	0.998913	+	0.0466215i	$0.0148455\pi$
$421$			805.452i			0.0932431i	−0.998913	+	0.0466215i	$0.985155\pi$
$422$	−20842.9	+	8633.41i	−2.40430	+	0.995895i
$423$		0			0
$424$	13418.1			1.53689
$425$	4589.52	−	766.049i	0.523822	−	0.0874326i
$426$		0			0
$427$	−3828.11	−	3828.11i	−0.433853	−	0.433853i
$428$	−18977.5	+	7860.73i	−2.14325	+	0.887763i
$429$		0			0
$430$	2888.30	+	6972.98i	0.323922	+	0.782016i
$431$	−6150.35	−	2547.56i	−0.687359	−	0.284713i	0.0115404	−	0.999933i	$-0.496326\pi$
$431$	−6150.35	−	2547.56i	−0.687359	−	0.284713i	−0.698899	+	0.715220i	$0.746326\pi$
$432$		0			0
$433$	−12250.2	+	12250.2i	−1.35960	+	1.35960i	−0.485191	+	0.874408i	$0.661250\pi$
$433$	−12250.2	+	12250.2i	−1.35960	+	1.35960i	−0.874408	+	0.485191i	$0.838750\pi$
$434$	2854.81	−	2854.81i	0.315750	−	0.315750i
$435$		0			0
$436$	−8036.29	−	3328.74i	−0.882726	−	0.365637i
$437$	73.4989	+	177.442i	0.00804561	+	0.0194238i
$438$		0			0
$439$	−7159.21	+	2965.44i	−0.778339	+	0.322398i	−0.736245	−	0.676715i	$-0.763403\pi$
$439$	−7159.21	+	2965.44i	−0.778339	+	0.322398i	−0.0420937	+	0.999114i	$0.513403\pi$
$440$	−252.211	−	252.211i	−0.0273266	−	0.0273266i
$441$		0			0
$442$	11457.0	−	1912.32i	1.23293	−	0.205792i
$443$	−5866.35			−0.629161			−0.314581	−	0.949231i	$-0.601864\pi$
$443$	−5866.35			−0.629161			−0.314581	+	0.949231i	$0.601864\pi$
$444$		0			0
$445$	3321.63	−	1375.86i	0.353843	−	0.146567i
$446$		−	20521.9i		−	2.17878i
$447$		0			0
$448$	−8861.91	−	3670.72i	−0.934567	−	0.387110i
$449$	522.340	−	1261.04i	0.0549015	−	0.132544i	−0.894049	−	0.447970i	$-0.852147\pi$
$449$	522.340	−	1261.04i	0.0549015	−	0.132544i	0.948950	+	0.315426i	$0.102147\pi$
$450$		0			0
$451$	−108.296	+	108.296i	−0.0113070	+	0.0113070i
$452$	−8314.77	+	20073.6i	−0.865252	+	2.08890i
$453$		0			0
$454$	8884.05	+	21448.0i	0.918390	+	2.21719i
$455$			3209.15i			0.330654i
$456$		0			0
$457$	3715.24	+	3715.24i	0.380288	+	0.380288i	0.871206	−	0.490918i	$-0.163338\pi$
$457$	3715.24	+	3715.24i	0.380288	+	0.380288i	−0.490918	+	0.871206i	$0.663338\pi$
$458$	−17994.9			−1.83591
$459$		0			0
$460$	641.770			0.0650493
$461$	−6964.00	−	6964.00i	−0.703571	−	0.703571i	0.261605	−	0.965175i	$-0.415748\pi$
$461$	−6964.00	−	6964.00i	−0.703571	−	0.703571i	−0.965175	+	0.261605i	$0.915748\pi$
$462$		0			0
$463$		−	3872.95i		−	0.388750i	−0.980927	−	0.194375i	$-0.937732\pi$
$463$		−	3872.95i		−	0.388750i	0.980927	−	0.194375i	$-0.0622679\pi$
$464$	−99.2729	−	239.666i	−0.00993239	−	0.0239789i
$465$		0			0
$466$	−3132.48	+	7562.47i	−0.311393	+	0.751770i
$467$	7610.65	−	7610.65i	0.754131	−	0.754131i	−0.221117	−	0.975247i	$-0.570970\pi$
$467$	7610.65	−	7610.65i	0.754131	−	0.754131i	0.975247	+	0.221117i	$0.0709702\pi$
$468$		0			0
$469$	−4423.34	+	10678.9i	−0.435503	+	1.05140i
$470$	−5583.42	−	2312.73i	−0.547966	−	0.226975i
$471$		0			0
$472$			14136.2i			1.37854i
$473$	424.010	−	175.631i	0.0412178	−	0.0170730i
$474$		0			0
$475$	1948.26			0.188194
$476$	−5485.89	−	8787.44i	−0.528247	−	0.846159i
$477$		0			0
$478$	15132.8	+	15132.8i	1.44803	+	1.44803i
$479$	−3055.73	+	1265.73i	−0.291482	+	0.120736i	−0.523633	−	0.851944i	$-0.675424\pi$
$479$	−3055.73	+	1265.73i	−0.291482	+	0.120736i	0.232151	+	0.972680i	$0.425424\pi$
$480$		0			0
$481$	3912.94	+	9446.68i	0.370925	+	0.895492i
$482$	5852.26	+	2424.09i	0.553036	+	0.229075i
$483$		0			0
$484$	12014.4	−	12014.4i	1.12833	−	1.12833i
$485$	−6660.64	+	6660.64i	−0.623596	+	0.623596i
$486$		0			0
$487$	−11598.5	−	4804.27i	−1.07922	−	0.447027i	−0.228983	−	0.973430i	$-0.573540\pi$
$487$	−11598.5	−	4804.27i	−1.07922	−	0.447027i	−0.850235	+	0.526403i	$0.823540\pi$
$488$	3938.90	+	9509.35i	0.365380	+	0.882106i
$489$		0			0
$490$	−6771.69	+	2804.92i	−0.624313	+	0.258599i
$491$	10896.9	+	10896.9i	1.00157	+	1.00157i	0.999999	+	0.00157069i	$0.000499966\pi$
$491$	10896.9	+	10896.9i	1.00157	+	1.00157i	0.00157069	+	0.999999i	$0.499500\pi$
$492$		0			0
$493$	1705.87	−	7374.88i	0.155839	−	0.673728i
$494$	4863.52			0.442956
$495$		0			0
$496$	170.229	−	70.5111i	0.0154103	−	0.00638315i
$497$			5581.76i			0.503775i
$498$		0			0
$499$	−1673.50	−	693.186i	−0.150132	−	0.0621869i	0.306352	−	0.951918i	$-0.400892\pi$
$499$	−1673.50	−	693.186i	−0.150132	−	0.0621869i	−0.456484	+	0.889731i	$0.650892\pi$
$500$	7182.38	−	17339.8i	0.642411	−	1.55092i
$501$		0			0
$502$	−8744.66	+	8744.66i	−0.777477	+	0.777477i
$503$	−5095.16	+	12300.8i	−0.451654	+	1.09039i	0.520039	+	0.854143i	$0.325917\pi$
$503$	−5095.16	+	12300.8i	−0.451654	+	1.09039i	−0.971693	+	0.236247i	$0.924083\pi$
$504$		0			0
$505$	−2819.44	−	6806.74i	−0.248443	−	0.599794i
$506$		−	63.3977i		−	0.00556990i
$507$		0			0
$508$	−4314.54	−	4314.54i	−0.376824	−	0.376824i
$509$	12877.9			1.12142			0.560711	−	0.828011i	$-0.310528\pi$
$509$	12877.9			1.12142			0.560711	+	0.828011i	$0.310528\pi$
$510$		0			0
$511$	−13084.8			−1.13276
$512$	−614.787	−	614.787i	−0.0530664	−	0.0530664i
$513$		0			0
$514$		−	12175.5i		−	1.04482i
$515$	1015.89	+	2452.58i	0.0869236	+	0.209852i
$516$		0			0
$517$	−140.631	+	339.514i	−0.0119632	+	0.0288817i
$518$	10475.5	−	10475.5i	0.888548	−	0.888548i
$519$		0			0
$520$	2334.89	−	5636.92i	0.196907	−	0.475376i
$521$	11183.8	+	4632.47i	0.940441	+	0.389543i	0.799630	−	0.600493i	$-0.205029\pi$
$521$	11183.8	+	4632.47i	0.940441	+	0.389543i	0.140811	+	0.990037i	$0.455029\pi$
$522$		0			0
$523$			16809.9i			1.40544i	0.711465	+	0.702722i	$0.248032\pi$
$523$			16809.9i			1.40544i	−0.711465	+	0.702722i	$0.751968\pi$
$524$	−14215.5	+	5888.27i	−1.18513	+	0.490898i
$525$		0			0
$526$	34295.7			2.84290
$527$	5238.19	+	1211.64i	0.432978	+	0.100152i
$528$		0			0
$529$	−8573.09	−	8573.09i	−0.704618	−	0.704618i
$530$	−19736.3	+	8175.04i	−1.61753	+	0.670002i
$531$		0			0
$532$	−1659.90	−	4007.34i	−0.135274	−	0.326580i
$533$	−2420.40	−	1002.56i	−0.196697	−	0.0814745i
$534$		0			0
$535$	8681.68	−	8681.68i	0.701573	−	0.701573i
$536$	15539.3	−	15539.3i	1.25223	−	1.25223i
$537$		0			0
$538$	−28772.1	−	11917.8i	−2.30568	−	0.955042i
$539$	170.561	+	411.770i	0.0136300	+	0.0329057i
$540$		0			0
$541$	−1215.15	+	503.334i	−0.0965686	+	0.0400000i	−0.430445	−	0.902617i	$-0.641643\pi$
$541$	−1215.15	+	503.334i	−0.0965686	+	0.0400000i	0.333876	+	0.942617i	$0.391643\pi$
$542$	20367.7	+	20367.7i	1.61415	+	1.61415i
$543$		0			0
$544$	−2151.63	−	12890.7i	−0.169578	−	1.01597i
$545$	5199.19			0.408640
$546$		0			0
$547$	17822.8	−	7382.43i	1.39314	−	0.577056i	0.445176	−	0.895443i	$-0.353141\pi$
$547$	17822.8	−	7382.43i	1.39314	−	0.577056i	0.947961	+	0.318387i	$0.103141\pi$
$548$		−	9524.07i		−	0.742424i
$549$		0			0
$550$	−594.147	−	246.104i	−0.0460628	−	0.0190798i
$551$	1212.90	−	2928.20i	0.0937773	−	0.226398i
$552$		0			0
$553$	9034.85	−	9034.85i	0.694757	−	0.694757i
$554$	−1089.63	+	2630.59i	−0.0835629	+	0.201739i
$555$		0			0
$556$	−4401.59	−	10626.4i	−0.335735	−	0.810537i
$557$			798.500i			0.0607424i	0.999539	+	0.0303712i	$0.00966895\pi$
$557$			798.500i			0.0607424i	−0.999539	+	0.0303712i	$0.990331\pi$
$558$		0			0
$559$	5551.28	+	5551.28i	0.420025	+	0.420025i
$560$	212.199			0.0160125
$561$		0			0
$562$	−15046.3			−1.12934
$563$	−3469.50	−	3469.50i	−0.259719	−	0.259719i	0.565221	−	0.824940i	$-0.308791\pi$
$563$	−3469.50	−	3469.50i	−0.259719	−	0.259719i	−0.824940	+	0.565221i	$0.808791\pi$
$564$		0			0
$565$		−	12986.9i		−	0.967016i
$566$	−14369.8	−	34691.9i	−1.06716	−	2.57634i
$567$		0			0
$568$	4061.13	−	9804.43i	0.300002	−	0.724269i
$569$	5187.75	−	5187.75i	0.382218	−	0.382218i	−0.489683	−	0.871901i	$-0.662887\pi$
$569$	5187.75	−	5187.75i	0.382218	−	0.382218i	0.871901	+	0.489683i	$0.162887\pi$
$570$		0			0
$571$	1381.72	−	3335.76i	0.101266	−	0.244479i	−0.865124	−	0.501558i	$-0.832760\pi$
$571$	1381.72	−	3335.76i	0.101266	−	0.244479i	0.966390	+	0.257080i	$0.0827603\pi$
$572$	−912.982	−	378.169i	−0.0667372	−	0.0276435i
$573$		0			0
$574$			3795.76i			0.276014i
$575$	401.357	−	166.248i	0.0291091	−	0.0120574i
$576$		0			0
$577$	21558.2			1.55542			0.777712	−	0.628621i	$-0.216380\pi$
$577$	21558.2			1.55542			0.777712	+	0.628621i	$0.216380\pi$
$578$	9841.42	−	20135.2i	0.708217	−	1.44898i
$579$		0			0
$580$	−7488.73	−	7488.73i	−0.536125	−	0.536125i
$581$	5564.60	−	2304.93i	0.397346	−	0.164586i
$582$		0			0
$583$	497.105	+	1200.12i	0.0353138	+	0.0852551i
$584$	22983.7	+	9520.15i	1.62855	+	0.674566i
$585$		0			0
$586$	−9112.71	+	9112.71i	−0.642393	+	0.642393i
$587$	−15618.8	+	15618.8i	−1.09823	+	1.09823i	−0.103607	+	0.994618i	$0.533039\pi$
$587$	−15618.8	+	15618.8i	−1.09823	+	1.09823i	−0.994618	+	0.103607i	$0.966961\pi$
$588$		0			0
$589$	2079.83	+	861.493i	0.145497	+	0.0602669i
$590$	−8612.51	−	20792.4i	−0.600969	−	1.45087i
$591$		0			0
$592$	624.642	−	258.735i	0.0433659	−	0.0179628i
$593$	17239.3	+	17239.3i	1.19382	+	1.19382i	0.975987	+	0.217831i	$0.0698980\pi$
$593$	17239.3	+	17239.3i	1.19382	+	1.19382i	0.217831	+	0.975987i	$0.430102\pi$
$594$		0			0
$595$	5039.42	+	3597.76i	0.347220	+	0.247889i
$596$	16290.2			1.11959
$597$		0			0
$598$	1001.93	−	415.011i	0.0685147	−	0.0283797i
$599$		−	14748.3i		−	1.00601i	−0.864283	−	0.503005i	$-0.832228\pi$
$599$		−	14748.3i		−	1.00601i	0.864283	−	0.503005i	$-0.167772\pi$
$600$		0			0
$601$	2061.05	+	853.713i	0.139887	+	0.0579429i	0.451528	−	0.892257i	$-0.350879\pi$
$601$	2061.05	+	853.713i	0.139887	+	0.0579429i	−0.311642	+	0.950200i	$0.600879\pi$
$602$	4352.85	−	10508.7i	0.294699	−	0.711467i
$603$		0			0
$604$	5743.71	−	5743.71i	0.386934	−	0.386934i
$605$	−3886.45	+	9382.73i	−0.261168	+	0.630516i
$606$		0			0
$607$	1898.96	+	4584.49i	0.126979	+	0.306555i	0.974566	−	0.224103i	$-0.0719451\pi$
$607$	1898.96	+	4584.49i	0.126979	+	0.306555i	−0.847586	+	0.530658i	$0.821945\pi$
$608$		−	5472.13i		−	0.365007i
$609$		0			0
$610$	−11587.2	−	11587.2i	−0.769101	−	0.769101i
$611$	−6286.22			−0.416225
$612$		0			0
$613$	1562.65			0.102960			0.0514801	−	0.998674i	$-0.483606\pi$
$613$	1562.65			0.102960			0.0514801	+	0.998674i	$0.483606\pi$
$614$	3468.21	+	3468.21i	0.227957	+	0.227957i
$615$		0			0
$616$			537.540i			0.0351593i
$617$	−10460.4	−	25253.5i	−0.682525	−	1.64776i	−0.759322	−	0.650715i	$-0.774469\pi$
$617$	−10460.4	−	25253.5i	−0.682525	−	1.64776i	0.0767966	−	0.997047i	$-0.475531\pi$
$618$		0			0
$619$	241.334	−	582.633i	0.0156705	−	0.0378320i	−0.915851	−	0.401519i	$-0.868482\pi$
$619$	241.334	−	582.633i	0.0156705	−	0.0378320i	0.931521	+	0.363687i	$0.118482\pi$
$620$	5319.06	−	5319.06i	0.344546	−	0.344546i
$621$		0			0
$622$	−12404.5	+	29947.0i	−0.799636	+	1.93049i
$623$	−5005.90	−	2073.51i	−0.321922	−	0.133344i
$624$		0			0
$625$			2920.28i			0.186898i
$626$	−4582.18	+	1898.00i	−0.292557	+	0.121181i
$627$		0			0
$628$	−529.818			−0.0336657
$629$	19221.2	+	4446.02i	1.21844	+	0.281835i
$630$		0			0
$631$	10916.3	+	10916.3i	0.688703	+	0.688703i	0.961945	−	0.273242i	$-0.0880960\pi$
$631$	10916.3	+	10916.3i	0.688703	+	0.688703i	−0.273242	+	0.961945i	$0.588096\pi$
$632$	−22443.3	+	9296.33i	−1.41257	+	0.585108i
$633$		0			0
$634$	7982.26	+	19270.9i	0.500025	+	1.20717i
$635$	3369.46	+	1395.68i	0.210572	+	0.0872216i
$636$		0			0
$637$	−5391.02	+	5391.02i	−0.335322	+	0.335322i
$638$	−739.780	+	739.780i	−0.0459062	+	0.0459062i
$639$		0			0
$640$	−16273.1	−	6740.52i	−1.00508	−	0.416316i
$641$	−10488.5	−	25321.4i	−0.646286	−	1.56027i	−0.818058	−	0.575136i	$-0.804949\pi$
$641$	−10488.5	−	25321.4i	−0.646286	−	1.56027i	0.171771	−	0.985137i	$-0.445051\pi$
$642$		0			0
$643$	−11761.8	+	4871.92i	−0.721372	+	0.298802i	−0.713001	−	0.701163i	$-0.752665\pi$
$643$	−11761.8	+	4871.92i	−0.721372	+	0.298802i	−0.00837074	+	0.999965i	$0.502665\pi$
$644$	−683.904	−	683.904i	−0.0418472	−	0.0418472i
$645$		0			0
$646$	5452.47	−	7637.32i	0.332081	−	0.465149i
$647$	15446.1			0.938558			0.469279	−	0.883050i	$-0.344514\pi$
$647$	15446.1			0.938558			0.469279	+	0.883050i	$0.344514\pi$
$648$		0			0
$649$	−1264.34	+	523.706i	−0.0764709	+	0.0316753i
$650$		−	11000.8i		−	0.663828i
$651$		0			0
$652$	−15031.8	−	6226.36i	−0.902898	−	0.373993i
$653$	−5354.13	+	12926.0i	−0.320863	+	0.774631i	0.678342	+	0.734747i	$0.262699\pi$
$653$	−5354.13	+	12926.0i	−0.320863	+	0.774631i	−0.999204	+	0.0398843i	$0.987301\pi$
$654$		0			0
$655$	6503.22	−	6503.22i	0.387942	−	0.387942i
$656$	−66.2925	+	160.044i	−0.00394556	+	0.00952542i
$657$		0			0
$658$	3485.43	+	8414.56i	0.206499	+	0.498532i
$659$			27427.8i			1.62130i	0.585533	+	0.810648i	$0.300885\pi$
$659$			27427.8i			1.62130i	−0.585533	+	0.810648i	$0.699115\pi$
$660$		0			0
$661$	15260.7	+	15260.7i	0.897992	+	0.897992i	0.995258	−	0.0972668i	$-0.0310100\pi$
$661$	15260.7	+	15260.7i	0.897992	+	0.897992i	−0.0972668	+	0.995258i	$0.531010\pi$
$662$	−7251.67			−0.425746
$663$		0			0
$664$	−11451.3			−0.669271
$665$	1833.25	+	1833.25i	0.106903	+	0.106903i
$666$		0			0
$667$		−	706.732i		−	0.0410266i
$668$	7496.81	+	18098.9i	0.434222	+	1.04831i
$669$		0			0
$670$	−13388.9	+	32323.6i	−0.772026	+	1.86383i
$671$	−704.589	+	704.589i	−0.0405371	+	0.0405371i
$672$		0			0
$673$	1952.53	−	4713.84i	0.111835	−	0.269993i	−0.858046	−	0.513572i	$-0.828322\pi$
$673$	1952.53	−	4713.84i	0.111835	−	0.269993i	0.969881	+	0.243580i	$0.0783218\pi$
$674$	−15104.7	−	6256.59i	−0.863224	−	0.357559i
$675$		0			0
$676$			11237.1i			0.639346i
$677$	−3216.94	+	1332.50i	−0.182625	+	0.0756458i	−0.472122	−	0.881533i	$-0.656512\pi$
$677$	−3216.94	+	1332.50i	−0.182625	+	0.0756458i	0.289497	+	0.957179i	$0.406512\pi$
$678$		0			0
$679$	14195.9			0.802338
$680$	−6234.18	−	9986.06i	−0.351573	−	0.563159i
$681$		0			0
$682$	−525.447	−	525.447i	−0.0295021	−	0.0295021i
$683$	19205.9	−	7955.34i	1.07598	−	0.445684i	0.226881	−	0.973922i	$-0.427147\pi$
$683$	19205.9	−	7955.34i	1.07598	−	0.445684i	0.849096	+	0.528238i	$0.177147\pi$
$684$		0			0
$685$	2178.50	+	5259.37i	0.121513	+	0.293358i
$686$	26884.6	+	11136.0i	1.49629	+	0.619785i
$687$		0			0
$688$	367.066	−	367.066i	0.0203405	−	0.0203405i
$689$	−15712.3	+	15712.3i	−0.868783	+	0.868783i
$690$		0			0
$691$	6535.76	+	2707.20i	0.359815	+	0.149040i	0.555265	−	0.831673i	$-0.312617\pi$
$691$	6535.76	+	2707.20i	0.359815	+	0.149040i	−0.195450	+	0.980714i	$0.562617\pi$
$692$	17288.4	+	41737.9i	0.949721	+	2.29283i
$693$		0			0
$694$	31762.6	−	13156.5i	1.73731	−	0.719617i
$695$	4861.28	+	4861.28i	0.265322	+	0.265322i
$696$		0			0
$697$	−4287.86	+	2676.86i	−0.233019	+	0.145471i
$698$	14915.6			0.808829
$699$		0			0
$700$	−9064.23	+	3754.53i	−0.489423	+	0.202725i
$701$			15109.3i			0.814082i	0.913410	+	0.407041i	$0.133439\pi$
$701$			15109.3i			0.814082i	−0.913410	+	0.407041i	$0.866561\pi$
$702$		0			0
$703$	7631.77	+	3161.18i	0.409442	+	0.169596i
$704$	−675.622	+	1631.10i	−0.0361697	+	0.0873213i
$705$		0			0
$706$	−22680.2	+	22680.2i	−1.20904	+	1.20904i
$707$	−4249.08	+	10258.2i	−0.226030	+	0.545684i
$708$		0			0
$709$	−1608.98	−	3884.42i	−0.0852277	−	0.205758i	0.875520	−	0.483182i	$-0.160519\pi$
$709$	−1608.98	−	3884.42i	−0.0852277	−	0.205758i	−0.960747	+	0.277424i	$0.910519\pi$
$710$			16895.3i			0.893054i
$711$		0			0
$712$	7284.30	+	7284.30i	0.383414	+	0.383414i
$713$	501.974			0.0263662
$714$		0			0
$715$	590.666			0.0308946
$716$	−23524.8	−	23524.8i	−1.22788	−	1.22788i
$717$		0			0
$718$		−	12982.9i		−	0.674814i
$719$	−10584.8	−	25554.1i	−0.549024	−	1.32546i	−0.918206	−	0.396104i	$-0.870362\pi$
$719$	−10584.8	−	25554.1i	−0.549024	−	1.32546i	0.369182	−	0.929357i	$-0.379638\pi$
$720$		0			0
$721$	1531.02	−	3696.20i	0.0790818	−	0.190920i
$722$	−19346.1	+	19346.1i	−0.997210	+	0.997210i
$723$		0			0
$724$	10276.1	−	24808.7i	0.527497	−	1.27349i
$725$	−6623.31	−	2743.47i	−0.339288	−	0.140538i
$726$		0			0
$727$			2032.63i			0.103695i	0.998655	+	0.0518474i	$0.0165109\pi$
$727$			2032.63i			0.103695i	−0.998655	+	0.0518474i	$0.983489\pi$
$728$	−8495.19	+	3518.82i	−0.432490	+	0.179143i
$729$		0			0
$730$	−39606.1			−2.00807
$731$	14940.8	−	2493.81i	0.755959	−	0.126179i
$732$		0			0
$733$	−17736.7	−	17736.7i	−0.893750	−	0.893750i	0.101124	−	0.994874i	$-0.467756\pi$
$733$	−17736.7	−	17736.7i	−0.893750	−	0.893750i	−0.994874	+	0.101124i	$0.967756\pi$
$734$	−43972.9	+	18214.2i	−2.21127	+	0.915936i
$735$		0			0
$736$	−466.945	−	1127.30i	−0.0233856	−	0.0564579i
$737$	1965.52	+	814.145i	0.0982372	+	0.0406912i
$738$		0			0
$739$	−15432.3	+	15432.3i	−0.768180	+	0.768180i	−0.977786	−	0.209606i	$-0.932782\pi$
$739$	−15432.3	+	15432.3i	−0.768180	+	0.768180i	0.209606	+	0.977786i	$0.432782\pi$
$740$	19517.9	−	19517.9i	0.969584	−	0.969584i
$741$		0			0
$742$	29743.8	+	12320.3i	1.47160	+	0.609558i
$743$	−12847.0	−	31015.3i	−0.634333	−	1.53142i	−0.834124	−	0.551578i	$-0.814026\pi$
$743$	−12847.0	−	31015.3i	−0.634333	−	1.53142i	0.199790	−	0.979839i	$-0.435974\pi$
$744$		0			0
$745$	−8995.77	+	3726.17i	−0.442389	+	0.183243i
$746$	−3694.00	−	3694.00i	−0.181296	−	0.181296i
$747$		0			0
$748$	−1617.39	+	1009.72i	−0.0790609	+	0.0493568i
$749$	−18503.3			−0.902666
$750$		0			0
$751$	−3428.00	+	1419.92i	−0.166564	+	0.0689931i	−0.464407	−	0.885622i	$-0.653733\pi$
$751$	−3428.00	+	1419.92i	−0.166564	+	0.0689931i	0.297843	+	0.954615i	$0.403733\pi$
$752$			415.663i			0.0201565i
$753$		0			0
$754$	−16534.1	−	6848.64i	−0.798588	−	0.330786i
$755$	−1857.99	+	4485.58i	−0.0895618	+	0.216221i
$756$		0			0
$757$	17517.0	−	17517.0i	0.841038	−	0.841038i	−0.147956	−	0.988994i	$-0.547270\pi$
$757$	17517.0	−	17517.0i	0.841038	−	0.841038i	0.988994	+	0.147956i	$0.0472695\pi$
$758$	−13552.7	+	32719.1i	−0.649415	+	1.56783i
$759$		0			0
$760$	−1886.31	−	4553.95i	−0.0900310	−	0.217354i
$761$		−	14733.8i		−	0.701841i	−0.936405	−	0.350921i	$-0.885869\pi$
$761$		−	14733.8i		−	0.701841i	0.936405	−	0.350921i	$-0.114131\pi$
$762$		0			0
$763$	−5540.54	−	5540.54i	−0.262885	−	0.262885i
$764$	−34303.6			−1.62442
$765$		0			0
$766$	55045.2			2.59643
$767$	−16553.1	−	16553.1i	−0.779268	−	0.779268i
$768$		0			0
$769$			15639.0i			0.733366i	0.930346	+	0.366683i	$0.119507\pi$
$769$			15639.0i			0.733366i	−0.930346	+	0.366683i	$0.880493\pi$
$770$	−327.498	−	790.650i	−0.0153275	−	0.0370039i
$771$		0			0
$772$	−2572.38	+	6210.27i	−0.119925	+	0.289524i
$773$	6719.67	−	6719.67i	0.312664	−	0.312664i	−0.533277	−	0.845941i	$-0.679039\pi$
$773$	6719.67	−	6719.67i	0.312664	−	0.312664i	0.845941	+	0.533277i	$0.179039\pi$
$774$		0			0
$775$	1948.62	−	4704.38i	0.0903179	−	0.218047i
$776$	−24935.2	−	10328.5i	−1.15351	−	0.477799i
$777$		0			0
$778$		−	63658.5i		−	2.93351i
$779$	−1955.39	+	809.951i	−0.0899349	+	0.0372522i
$780$		0			0
$781$	1027.36			0.0470702
$782$	471.550	−	2038.62i	0.0215634	−	0.0932236i
$783$		0			0
$784$	356.470	+	356.470i	0.0162386	+	0.0162386i
$785$	292.575	−	121.189i	0.0133025	−	0.00551008i
$786$		0			0
$787$	755.319	+	1823.50i	0.0342112	+	0.0825932i	0.940062	−	0.341004i	$-0.110767\pi$
$787$	755.319	+	1823.50i	0.0342112	+	0.0825932i	−0.905851	+	0.423598i	$0.860767\pi$
$788$	34893.8	+	14453.5i	1.57746	+	0.653407i
$789$		0			0
$790$	27347.3	−	27347.3i	1.23161	−	1.23161i
$791$	−13839.6	+	13839.6i	−0.622097	+	0.622097i
$792$		0			0
$793$	−15747.6	−	6522.85i	−0.705186	−	0.292098i
$794$	8725.75	+	21065.8i	0.390006	+	0.941559i
$795$		0			0
$796$	7019.41	−	2907.54i	0.312558	−	0.129466i
$797$	−3559.83	−	3559.83i	−0.158213	−	0.158213i	0.623561	−	0.781774i	$-0.285685\pi$
$797$	−3559.83	−	3559.83i	−0.158213	−	0.158213i	−0.781774	+	0.623561i	$0.785685\pi$
$798$		0			0
$799$	−7047.45	+	9871.42i	−0.312041	+	0.437079i
$800$	−12377.5			−0.547011
$801$		0			0
$802$	−4018.15	+	1664.37i	−0.176915	+	0.0732806i
$803$			2408.35i			0.105839i
$804$		0			0
$805$	534.099	+	221.231i	0.0233845	+	0.00968616i
$806$	4864.42	−	11743.7i	0.212583	−	0.513220i
$807$		0			0
$808$	14927.1	−	14927.1i	0.649919	−	0.649919i
$809$	8411.12	−	20306.2i	0.365537	−	0.882484i	−0.628933	−	0.777459i	$-0.716508\pi$
$809$	8411.12	−	20306.2i	0.365537	−	0.882484i	0.994470	−	0.105024i	$-0.0334920\pi$
$810$		0			0
$811$	−13318.9	−	32154.7i	−0.576684	−	1.39224i	−0.895773	−	0.444513i	$-0.853377\pi$
$811$	−13318.9	−	32154.7i	−0.576684	−	1.39224i	0.319089	−	0.947725i	$-0.396623\pi$
$812$			15960.8i			0.689796i
$813$		0			0
$814$	−1928.09	−	1928.09i	−0.0830215	−	0.0830215i
$815$	9725.02			0.417978
$816$		0			0
$817$	6342.41			0.271594
$818$	25361.5	+	25361.5i	1.08404	+	1.08404i
$819$		0			0
$820$			7072.23i			0.301187i
$821$	−2219.90	−	5359.32i	−0.0943669	−	0.227822i	0.869647	−	0.493674i	$-0.164347\pi$
$821$	−2219.90	−	5359.32i	−0.0943669	−	0.227822i	−0.964014	+	0.265853i	$0.914347\pi$
$822$		0			0
$823$	12209.1	−	29475.3i	0.517109	−	1.24841i	−0.422562	−	0.906334i	$-0.638869\pi$
$823$	12209.1	−	29475.3i	0.517109	−	1.24841i	0.939671	−	0.342078i	$-0.111131\pi$
$824$	−5378.50	+	5378.50i	−0.227389	+	0.227389i
$825$		0			0
$826$	−12979.6	+	31335.5i	−0.546753	+	1.31998i
$827$	35321.9	+	14630.8i	1.48520	+	0.615191i	0.970267	−	0.242039i	$-0.0778161\pi$
$827$	35321.9	+	14630.8i	1.48520	+	0.615191i	0.514935	+	0.857229i	$0.327816\pi$
$828$		0			0
$829$			6622.89i			0.277470i	0.990330	+	0.138735i	$0.0443036\pi$
$829$			6622.89i			0.277470i	−0.990330	+	0.138735i	$0.955696\pi$
$830$	16843.3	−	6976.73i	0.704385	−	0.291766i
$831$		0			0
$832$	−30200.3			−1.25842
$833$	2421.82	+	14509.5i	0.100734	+	0.603511i
$834$		0			0
$835$	−8279.76	−	8279.76i	−0.343153	−	0.343153i
$836$	−737.579	+	305.515i	−0.0305140	+	0.0126393i
$837$		0			0
$838$	−17885.5	−	43179.5i	−0.737286	−	1.77997i
$839$	−43704.6	−	18103.0i	−1.79839	−	0.744918i	−0.987064	−	0.160324i	$-0.948746\pi$
$839$	−43704.6	−	18103.0i	−1.79839	−	0.744918i	−0.811326	−	0.584594i	$-0.801254\pi$
$840$		0			0
$841$	8998.86	−	8998.86i	0.368972	−	0.368972i
$842$	2598.07	−	2598.07i	0.106336	−	0.106336i
$843$		0			0
$844$	58525.7	+	24242.1i	2.38689	+	0.988684i
$845$	−2570.34	−	6205.36i	−0.104642	−	0.252628i
$846$		0			0
$847$	14140.4	−	5857.13i	0.573634	−	0.237607i
$848$	1038.94	+	1038.94i	0.0420725	+	0.0420725i
$849$		0			0
$850$	−17274.9	−	12333.0i	−0.697087	−	0.497668i
$851$	1841.96			0.0741968
$852$		0			0
$853$	−41437.3	+	17163.9i	−1.66329	+	0.688957i	−0.998321	−	0.0579157i	$-0.981555\pi$
$853$	−41437.3	+	17163.9i	−1.66329	+	0.688957i	−0.664967	+	0.746872i	$0.731555\pi$
$854$			24695.9i			0.989550i
$855$		0			0
$856$	32501.3	+	13462.5i	1.29775	+	0.537545i
$857$	−17462.6	+	42158.5i	−0.696047	+	1.68041i	0.0361809	+	0.999345i	$0.488481\pi$
$857$	−17462.6	+	42158.5i	−0.696047	+	1.68041i	−0.732228	+	0.681060i	$0.761519\pi$
$858$		0			0
$859$	−29194.9	+	29194.9i	−1.15963	+	1.15963i	−0.175070	+	0.984556i	$0.556015\pi$
$859$	−29194.9	+	29194.9i	−1.15963	+	1.15963i	−0.984556	+	0.175070i	$0.943985\pi$
$860$	8110.20	−	19579.7i	0.321576	−	0.776353i
$861$		0			0
$862$	11621.1	+	28055.9i	0.459186	+	1.10857i
$863$		−	40572.4i		−	1.60035i	−0.599767	−	0.800174i	$-0.704740\pi$
$863$		−	40572.4i		−	1.60035i	0.599767	−	0.800174i	$-0.295260\pi$
$864$		0			0
$865$	−19094.0	−	19094.0i	−0.750537	−	0.750537i
$866$	79028.4			3.10103
$867$		0			0
$868$	−11336.6			−0.443304
$869$	−1662.92	−	1662.92i	−0.0649147	−	0.0649147i
$870$		0			0
$871$			36392.3i			1.41573i
$872$	5700.89	+	13763.2i	0.221395	+	0.534495i
$873$		0			0
$874$	335.279	−	809.435i	0.0129759	−	0.0313267i
$875$	11954.7	−	11954.7i	0.461879	−	0.461879i
$876$		0			0
$877$	16770.3	−	40487.1i	0.645716	−	1.55890i	−0.173141	−	0.984897i	$-0.555392\pi$
$877$	16770.3	−	40487.1i	0.645716	−	1.55890i	0.818857	−	0.573998i	$-0.194608\pi$
$878$	32658.1	+	13527.4i	1.25530	+	0.519964i
$879$		0			0
$880$		−	39.0566i		−	0.00149613i
$881$	−5459.41	+	2261.36i	−0.208777	+	0.0864781i	−0.484621	−	0.874724i	$-0.661043\pi$
$881$	−5459.41	+	2261.36i	−0.208777	+	0.0864781i	0.275844	+	0.961202i	$0.411043\pi$
$882$		0			0
$883$	−39579.8			−1.50846			−0.754228	−	0.656613i	$-0.771989\pi$
$883$	−39579.8			−1.50846			−0.754228	+	0.656613i	$0.771989\pi$
$884$	−26545.1	−	18951.2i	−1.00996	−	0.721037i
$885$		0			0
$886$	18922.5	+	18922.5i	0.717509	+	0.717509i
$887$	26957.4	−	11166.1i	1.02045	−	0.422684i	0.191194	−	0.981552i	$-0.438764\pi$
$887$	26957.4	−	11166.1i	1.02045	−	0.422684i	0.829257	+	0.558868i	$0.188764\pi$
$888$		0			0
$889$	−2103.37	−	5077.99i	−0.0793530	−	0.191575i
$890$	−15152.2	−	6276.25i	−0.570678	−	0.236383i
$891$		0			0
$892$	−40746.5	+	40746.5i	−1.52948	+	1.52948i
$893$	−3591.05	+	3591.05i	−0.134569	+	0.134569i
$894$		0			0
$895$	18371.8	+	7609.85i	0.686147	+	0.284211i
$896$	10158.4	+	24524.5i	0.378759	+	0.914405i
$897$		0			0
$898$	−5752.47	+	2382.75i	−0.213767	+	0.0885450i
$899$	−5857.48	−	5857.48i	−0.217306	−	0.217306i
$900$		0			0
$901$	7058.48	+	42288.4i	0.260990	+	1.56363i
$902$	698.636			0.0257894
$903$		0			0
$904$	34378.7	−	14240.1i	1.26484	−	0.523915i
$905$			16050.3i			0.589537i
$906$		0			0
$907$	28776.6	+	11919.7i	1.05349	+	0.436368i	0.841135	−	0.540826i	$-0.181888\pi$
$907$	28776.6	+	11919.7i	1.05349	+	0.436368i	0.212351	+	0.977194i	$0.431888\pi$
$908$	24945.9	−	60224.8i	0.911740	−	2.20113i
$909$		0			0
$910$	10351.4	−	10351.4i	0.377084	−	0.377084i
$911$	9913.08	−	23932.3i	0.360521	−	0.870376i	−0.634702	−	0.772757i	$-0.718877\pi$
$911$	9913.08	−	23932.3i	0.360521	−	0.870376i	0.995224	−	0.0976191i	$-0.0311227\pi$
$912$		0			0
$913$	−424.238	−	1024.20i	−0.0153781	−	0.0371261i
$914$		−	23967.8i		−	0.867378i
$915$		0			0
$916$	35729.3	+	35729.3i	1.28879	+	1.28879i
$917$	−13860.4			−0.499138
$918$		0			0
$919$	−25856.2			−0.928094			−0.464047	−	0.885811i	$-0.653603\pi$
$919$	−25856.2			−0.928094			−0.464047	+	0.885811i	$0.653603\pi$
$920$	−777.190	−	777.190i	−0.0278513	−	0.0278513i
$921$		0			0
$922$			44926.2i			1.60473i
$923$	6725.27	+	16236.2i	0.239832	+	0.579006i
$924$		0			0
$925$	7150.30	−	17262.4i	0.254163	−	0.613603i
$926$	−12492.6	+	12492.6i	−0.443339	+	0.443339i
$927$		0			0
$928$	−7705.66	+	18603.1i	−0.272576	+	0.658057i
$929$	−31553.2	−	13069.8i	−1.11434	−	0.461577i	−0.251913	−	0.967750i	$-0.581060\pi$
$929$	−31553.2	−	13069.8i	−1.11434	−	0.461577i	−0.862432	+	0.506173i	$0.831060\pi$
$930$		0			0
$931$			6159.32i			0.216824i
$932$	21235.0	−	8795.83i	0.746326	−	0.309138i
$933$		0			0
$934$	−49097.8			−1.72005
$935$	662.193	−	927.539i	0.0231615	−	0.0324425i
$936$		0			0
$937$	16857.4	+	16857.4i	0.587734	+	0.587734i	0.937017	−	0.349283i	$-0.113575\pi$
$937$	16857.4	+	16857.4i	0.587734	+	0.587734i	−0.349283	+	0.937017i	$0.613575\pi$
$938$	48713.7	−	20177.9i	1.69569	−	0.702378i
$939$		0			0
$940$	6494.02	+	15677.9i	0.225331	+	0.543998i
$941$	−21020.1	−	8706.79i	−0.728198	−	0.301630i	−0.0123868	−	0.999923i	$-0.503943\pi$
$941$	−21020.1	−	8706.79i	−0.728198	−	0.301630i	−0.715811	+	0.698294i	$0.753943\pi$
$942$		0			0
$943$	−333.713	+	333.713i	−0.0115241	+	0.0115241i
$944$	−1094.54	+	1094.54i	−0.0377376	+	0.0377376i
$945$		0			0
$946$	−1934.20	−	801.172i	−0.0664760	−	0.0275352i
$947$	−7555.31	−	18240.1i	−0.259255	−	0.625897i	0.739635	−	0.673009i	$-0.234998\pi$
$947$	−7555.31	−	18240.1i	−0.259255	−	0.625897i	−0.998890	+	0.0471117i	$0.984998\pi$
$948$		0			0
$949$	−38061.2	+	15765.5i	−1.30192	+	0.539271i
$950$	−6284.30	−	6284.30i	−0.214621	−	0.214621i
$951$		0			0
$952$	−3998.21	+	17285.2i	−0.136116	+	0.588461i
$953$	−32415.5			−1.10183			−0.550914	−	0.834562i	$-0.685721\pi$
$953$	−32415.5			−1.10183			−0.550914	+	0.834562i	$0.685721\pi$
$954$		0			0
$955$	18943.1	−	7846.47i	0.641867	−	0.265870i
$956$		−	60092.7i		−	2.03299i
$957$		0			0
$958$	13939.3	+	5773.85i	0.470103	+	0.194723i
$959$	3283.14	−	7926.20i	0.110551	−	0.266893i
$960$		0			0
$961$	−16905.0	+	16905.0i	−0.567453	+	0.567453i
$962$	17849.6	−	43092.8i	0.598227	−	1.44425i
$963$		0			0
$964$	−6806.71	−	16432.8i	−0.227416	−	0.549031i
$965$		−	4017.82i		−	0.134029i
$966$		0			0
$967$	−3356.24	−	3356.24i	−0.111612	−	0.111612i	0.649095	−	0.760707i	$-0.275148\pi$
$967$	−3356.24	−	3356.24i	−0.111612	−	0.111612i	−0.760707	+	0.649095i	$0.775148\pi$
$968$	−29099.2			−0.966202
$969$		0			0
$970$	42969.1			1.42232
$971$	2899.63	+	2899.63i	0.0958326	+	0.0958326i	0.753398	−	0.657565i	$-0.228414\pi$
$971$	2899.63	+	2899.63i	0.0958326	+	0.0958326i	−0.657565	+	0.753398i	$0.728414\pi$
$972$		0			0
$973$		−	10360.9i		−	0.341372i
$974$	21915.5	+	52908.8i	0.720965	+	1.74056i
$975$		0			0
$976$	−431.310	+	1041.27i	−0.0141454	+	0.0341500i
$977$	14226.5	−	14226.5i	0.465860	−	0.465860i	−0.434710	−	0.900570i	$-0.643149\pi$
$977$	14226.5	−	14226.5i	0.465860	−	0.465860i	0.900570	+	0.434710i	$0.143149\pi$
$978$		0			0
$979$	−381.644	+	921.370i	−0.0124590	+	0.0300788i
$980$	19014.5	+	7876.08i	0.619793	+	0.256727i
$981$		0			0
$982$		−	70298.1i		−	2.28442i
$983$	12545.0	−	5196.32i	0.407044	−	0.168603i	−0.169760	−	0.985485i	$-0.554299\pi$
$983$	12545.0	−	5196.32i	0.407044	−	0.168603i	0.576805	+	0.816882i	$0.304299\pi$
$984$		0			0
$985$	−22575.1			−0.730255
$986$	−29290.9	+	18285.9i	−0.946056	+	0.590611i
$987$		0			0
$988$	−9656.61	−	9656.61i	−0.310949	−	0.310949i
$989$	1306.59	−	541.206i	0.0420092	−	0.0174008i
$990$		0			0
$991$	−19882.4	−	48000.3i	−0.637320	−	1.53863i	−0.830236	−	0.557412i	$-0.811794\pi$
$991$	−19882.4	−	48000.3i	−0.637320	−	1.53863i	0.192915	−	0.981215i	$-0.438206\pi$
$992$	−13213.3	−	5473.14i	−0.422907	−	0.175174i
$993$		0			0
$994$	18004.5	−	18004.5i	0.574516	−	0.574516i
$995$	−3211.19	+	3211.19i	−0.102313	+	0.102313i
$996$		0			0
$997$	39806.6	+	16488.4i	1.26448	+	0.523766i	0.911282	−	0.411782i	$-0.135094\pi$
$997$	39806.6	+	16488.4i	1.26448	+	0.523766i	0.353200	+	0.935548i	$0.385094\pi$
$998$	3162.09	+	7633.97i	0.100295	+	0.242133i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.l.b.19.1	✓	32
3.2	odd	2	inner	153.4.l.b.19.8	yes	32
17.9	even	8	inner	153.4.l.b.145.1	yes	32
51.26	odd	8	inner	153.4.l.b.145.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.4.l.b.19.1	✓	32	1.1	even	1	trivial
153.4.l.b.19.8	yes	32	3.2	odd	2	inner
153.4.l.b.145.1	yes	32	17.9	even	8	inner
153.4.l.b.145.8	yes	32	51.26	odd	8	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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.22560 - 3.22560i) q^{2} +12.8090i q^{4} +(-2.92988 - 7.07335i) q^{5} +(-4.41551 + 10.6600i) q^{7} +(15.5118 - 15.5118i) q^{8} +O(q^{10})\)	\(q+(-3.22560 - 3.22560i) q^{2} +12.8090i q^{4} +(-2.92988 - 7.07335i) q^{5} +(-4.41551 + 10.6600i) q^{7} +(15.5118 - 15.5118i) q^{8} +(-13.3652 + 32.2664i) q^{10} +(1.96204 + 0.812704i) q^{11} +36.3279i q^{13} +(48.6275 - 20.1422i) q^{14} +2.40210 q^{16} +(57.0466 + 40.7270i) q^{17} +(20.7525 + 20.7525i) q^{19} +(90.6023 - 37.5287i) q^{20} +(-3.70730 - 8.95021i) q^{22} +(6.04603 + 2.50435i) q^{23} +(46.9403 - 46.9403i) q^{25} +(117.179 - 117.179i) q^{26} +(-136.543 - 56.5581i) q^{28} +(-41.3275 - 99.7734i) q^{29} +(70.8666 - 29.3539i) q^{31} +(-131.843 - 131.843i) q^{32} +(-52.6407 - 315.378i) q^{34} +88.3386 q^{35} +(260.040 - 107.712i) q^{37} -133.879i q^{38} +(-155.168 - 64.2727i) q^{40} +(-27.5977 + 66.6267i) q^{41} +(152.810 - 152.810i) q^{43} +(-10.4099 + 25.1317i) q^{44} +(-11.4241 - 27.5801i) q^{46} +173.041i q^{47} +(148.399 + 148.399i) q^{49} -302.821 q^{50} -465.322 q^{52} +(432.514 + 432.514i) q^{53} -16.2593i q^{55} +(96.8630 + 233.848i) q^{56} +(-188.523 + 455.135i) q^{58} +(-455.659 + 455.659i) q^{59} +(-179.555 + 433.485i) q^{61} +(-323.271 - 133.903i) q^{62} +831.326i q^{64} +(256.960 - 106.436i) q^{65} +1001.77 q^{67} +(-521.670 + 730.708i) q^{68} +(-284.945 - 284.945i) q^{70} +(446.936 - 185.127i) q^{71} +(433.977 + 1047.71i) q^{73} +(-1186.22 - 491.348i) q^{74} +(-265.818 + 265.818i) q^{76} +(-17.3268 + 17.3268i) q^{77} +(-1023.08 - 423.774i) q^{79} +(-7.03787 - 16.9909i) q^{80} +(303.930 - 125.892i) q^{82} +(-369.115 - 369.115i) q^{83} +(120.936 - 522.835i) q^{85} -985.810 q^{86} +(43.0413 - 17.8283i) q^{88} +469.598i q^{89} +(-387.254 - 160.406i) q^{91} +(-32.0781 + 77.4435i) q^{92} +(558.162 - 558.162i) q^{94} +(85.9875 - 207.592i) q^{95} +(-470.826 - 1136.68i) q^{97} -957.352i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 80 q^{10} - 128 q^{16} + 128 q^{19} + 280 q^{22} + 16 q^{25} + 184 q^{28} - 192 q^{31} + 24 q^{34} - 416 q^{37} - 488 q^{40} + 672 q^{43} - 384 q^{46} + 944 q^{49} - 4032 q^{52} - 1576 q^{58} + 4816 q^{61} + 2464 q^{67} + 5944 q^{70} + 3024 q^{73} - 3384 q^{76} - 4992 q^{79} - 1176 q^{82} - 2544 q^{85} - 1480 q^{88} - 4016 q^{91} + 4672 q^{94} + 1008 q^{97}+O(q^{100}) \) 32 * q - 80 * q^10 - 128 * q^16 + 128 * q^19 + 280 * q^22 + 16 * q^25 + 184 * q^28 - 192 * q^31 + 24 * q^34 - 416 * q^37 - 488 * q^40 + 672 * q^43 - 384 * q^46 + 944 * q^49 - 4032 * q^52 - 1576 * q^58 + 4816 * q^61 + 2464 * q^67 + 5944 * q^70 + 3024 * q^73 - 3384 * q^76 - 4992 * q^79 - 1176 * q^82 - 2544 * q^85 - 1480 * q^88 - 4016 * q^91 + 4672 * q^94 + 1008 * q^97

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