LMFDB - Embedded newform 136.3.t.b.57.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,3,Mod(41,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 0, 11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("136.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	136.t (of order $16$, degree $8$, 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:	$3.70573159530$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			57.4
Character	$\chi$	$=$	136.57
Dual form			136.3.t.b.105.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67722 - 0.333620i) q^{3} +(3.22552 - 4.82733i) q^{5} +(5.51299 + 8.25077i) q^{7} +(-5.61314 + 2.32504i) q^{9} +O(q^{10})$	\(q+(1.67722 - 0.333620i) q^{3} +(3.22552 - 4.82733i) q^{5} +(5.51299 + 8.25077i) q^{7} +(-5.61314 + 2.32504i) q^{9} +(3.92006 - 19.7075i) q^{11} +(6.04210 - 6.04210i) q^{13} +(3.79942 - 9.17260i) q^{15} +(-9.53691 + 14.0729i) q^{17} +(30.9271 + 12.8104i) q^{19} +(11.9991 + 11.9991i) q^{21} +(-2.39325 - 0.476047i) q^{23} +(-3.33203 - 8.04424i) q^{25} +(-21.4357 + 14.3229i) q^{27} +(-40.2359 - 26.8848i) q^{29} +(1.14641 + 5.76339i) q^{31} -34.3617i q^{33} +57.6114 q^{35} +(-70.9963 + 14.1221i) q^{37} +(8.11818 - 12.1497i) q^{39} +(17.1190 + 25.6203i) q^{41} +(-32.5769 + 13.4938i) q^{43} +(-6.88155 + 34.5959i) q^{45} +(-23.9254 + 23.9254i) q^{47} +(-18.9307 + 45.7027i) q^{49} +(-11.3005 + 26.7852i) q^{51} +(-15.3566 - 6.36093i) q^{53} +(-82.4902 - 82.4902i) q^{55} +(56.1455 + 11.1680i) q^{57} +(12.7032 + 30.6683i) q^{59} +(42.9508 - 28.6988i) q^{61} +(-50.1285 - 33.4948i) q^{63} +(-9.67829 - 48.6561i) q^{65} +45.9884i q^{67} -4.17283 q^{69} +(18.0674 - 3.59383i) q^{71} +(-11.7344 + 17.5617i) q^{73} +(-8.27228 - 12.3803i) q^{75} +(184.213 - 76.3036i) q^{77} +(6.09511 - 30.6422i) q^{79} +(7.49089 - 7.49089i) q^{81} +(-12.0724 + 29.1454i) q^{83} +(37.1731 + 91.4302i) q^{85} +(-76.4539 - 31.6683i) q^{87} +(2.49113 + 2.49113i) q^{89} +(83.1620 + 16.5419i) q^{91} +(3.84557 + 9.28402i) q^{93} +(161.596 - 107.975i) q^{95} +(50.5412 + 33.7705i) q^{97} +(23.8168 + 119.735i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9 + 24 * q^11 - 48 * q^13 - 96 * q^15 - 40 * q^19 + 80 * q^21 + 48 * q^23 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{15}{16}\right)$

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			0
$2$		0			0
$3$	1.67722	−	0.333620i	0.559074	−	0.111207i	0.0925386	−	0.995709i	$-0.470502\pi$
$3$	1.67722	−	0.333620i	0.559074	−	0.111207i	0.466536	+	0.884502i	$0.345502\pi$
$4$		0			0
$5$	3.22552	−	4.82733i	0.645103	−	0.965465i	−0.354435	−	0.935081i	$-0.615327\pi$
$5$	3.22552	−	4.82733i	0.645103	−	0.965465i	0.999538	−	0.0303845i	$-0.00967316\pi$
$6$		0			0
$7$	5.51299	+	8.25077i	0.787570	+	1.17868i	0.980316	+	0.197433i	$0.0632604\pi$
$7$	5.51299	+	8.25077i	0.787570	+	1.17868i	−0.192747	+	0.981249i	$0.561740\pi$
$8$		0			0
$9$	−5.61314	+	2.32504i	−0.623682	+	0.258338i
$10$		0			0
$11$	3.92006	−	19.7075i	0.356369	−	1.79159i	−0.221178	−	0.975233i	$-0.570990\pi$
$11$	3.92006	−	19.7075i	0.356369	−	1.79159i	0.577548	−	0.816357i	$-0.304010\pi$
$12$		0			0
$13$	6.04210	−	6.04210i	0.464777	−	0.464777i	−0.435441	−	0.900217i	$-0.643407\pi$
$13$	6.04210	−	6.04210i	0.464777	−	0.464777i	0.900217	+	0.435441i	$0.143407\pi$
$14$		0			0
$15$	3.79942	−	9.17260i	0.253294	−	0.611507i
$16$		0			0
$17$	−9.53691	+	14.0729i	−0.560995	+	0.827819i
$17$	−9.53691	+	14.0729i	−0.560995	+	0.827819i
$18$		0			0
$19$	30.9271	+	12.8104i	1.62774	+	0.674233i	0.994977	−	0.100109i	$-0.0319191\pi$
$19$	30.9271	+	12.8104i	1.62774	+	0.674233i	0.632767	+	0.774342i	$0.281919\pi$
$20$		0			0
$21$	11.9991	+	11.9991i	0.571387	+	0.571387i
$22$		0			0
$23$	−2.39325	−	0.476047i	−0.104054	−	0.0206977i	0.142788	−	0.989753i	$-0.454393\pi$
$23$	−2.39325	−	0.476047i	−0.104054	−	0.0206977i	−0.246843	+	0.969056i	$0.579393\pi$
$24$		0			0
$25$	−3.33203	−	8.04424i	−0.133281	−	0.321770i
$26$		0			0
$27$	−21.4357	+	14.3229i	−0.793916	+	0.530478i
$28$		0			0
$29$	−40.2359	−	26.8848i	−1.38745	−	0.927062i	−0.999987	−	0.00517471i	$-0.998353\pi$
$29$	−40.2359	−	26.8848i	−1.38745	−	0.927062i	−0.387459	−	0.921887i	$-0.626647\pi$
$30$		0			0
$31$	1.14641	+	5.76339i	0.0369809	+	0.185916i	0.994861	−	0.101254i	$-0.0322856\pi$
$31$	1.14641	+	5.76339i	0.0369809	+	0.185916i	−0.957880	+	0.287170i	$0.907286\pi$
$32$		0			0
$33$		−	34.3617i		−	1.04126i
$34$		0			0
$35$	57.6114			1.64604
$36$		0			0
$37$	−70.9963	+	14.1221i	−1.91882	+	0.381677i	−0.999918	−	0.0128082i	$-0.995923\pi$
$37$	−70.9963	+	14.1221i	−1.91882	+	0.381677i	−0.918902	+	0.394485i	$0.870923\pi$
$38$		0			0
$39$	8.11818	−	12.1497i	0.208158	−	0.311531i
$40$		0			0
$41$	17.1190	+	25.6203i	0.417536	+	0.624886i	0.979301	−	0.202411i	$-0.0648775\pi$
$41$	17.1190	+	25.6203i	0.417536	+	0.624886i	−0.561765	+	0.827297i	$0.689878\pi$
$42$		0			0
$43$	−32.5769	+	13.4938i	−0.757602	+	0.313809i	−0.727839	−	0.685748i	$-0.759475\pi$
$43$	−32.5769	+	13.4938i	−0.757602	+	0.313809i	−0.0297630	+	0.999557i	$0.509475\pi$
$44$		0			0
$45$	−6.88155	+	34.5959i	−0.152923	+	0.768798i
$46$		0			0
$47$	−23.9254	+	23.9254i	−0.509051	+	0.509051i	−0.914235	−	0.405184i	$-0.867207\pi$
$47$	−23.9254	+	23.9254i	−0.509051	+	0.509051i	0.405184	+	0.914235i	$0.367207\pi$
$48$		0			0
$49$	−18.9307	+	45.7027i	−0.386340	+	0.932708i
$50$		0			0
$51$	−11.3005	+	26.7852i	−0.221579	+	0.525199i
$52$		0			0
$53$	−15.3566	−	6.36093i	−0.289748	−	0.120018i	0.233075	−	0.972459i	$-0.425121\pi$
$53$	−15.3566	−	6.36093i	−0.289748	−	0.120018i	−0.522823	+	0.852441i	$0.675121\pi$
$54$		0			0
$55$	−82.4902	−	82.4902i	−1.49982	−	1.49982i
$56$		0			0
$57$	56.1455	+	11.1680i	0.985009	+	0.195931i
$58$		0			0
$59$	12.7032	+	30.6683i	0.215309	+	0.519802i	0.994224	−	0.107328i	$-0.0342294\pi$
$59$	12.7032	+	30.6683i	0.215309	+	0.519802i	−0.778915	+	0.627130i	$0.784229\pi$
$60$		0			0
$61$	42.9508	−	28.6988i	0.704111	−	0.470472i	−0.151256	−	0.988495i	$-0.548332\pi$
$61$	42.9508	−	28.6988i	0.704111	−	0.470472i	0.855367	+	0.518023i	$0.173332\pi$
$62$		0			0
$63$	−50.1285	−	33.4948i	−0.795691	−	0.531664i
$64$		0			0
$65$	−9.67829	−	48.6561i	−0.148897	−	0.748555i
$66$		0			0
$67$			45.9884i			0.686395i	0.939263	+	0.343197i	$0.111510\pi$
$67$			45.9884i			0.686395i	−0.939263	+	0.343197i	$0.888490\pi$
$68$		0			0
$69$	−4.17283			−0.0604758
$70$		0			0
$71$	18.0674	−	3.59383i	0.254471	−	0.0506174i	−0.0662064	−	0.997806i	$-0.521090\pi$
$71$	18.0674	−	3.59383i	0.254471	−	0.0506174i	0.320677	+	0.947189i	$0.396090\pi$
$72$		0			0
$73$	−11.7344	+	17.5617i	−0.160745	+	0.240571i	−0.903095	−	0.429440i	$-0.858711\pi$
$73$	−11.7344	+	17.5617i	−0.160745	+	0.240571i	0.742351	+	0.670012i	$0.233711\pi$
$74$		0			0
$75$	−8.27228	−	12.3803i	−0.110297	−	0.165071i
$76$		0			0
$77$	184.213	−	76.3036i	2.39238	−	0.990956i
$78$		0			0
$79$	6.09511	−	30.6422i	0.0771532	−	0.387876i	−0.922843	−	0.385176i	$-0.874141\pi$
$79$	6.09511	−	30.6422i	0.0771532	−	0.387876i	0.999996	−	0.00269950i	$-0.000859277\pi$
$80$		0			0
$81$	7.49089	−	7.49089i	0.0924802	−	0.0924802i
$82$		0			0
$83$	−12.0724	+	29.1454i	−0.145451	+	0.351149i	−0.979768	−	0.200135i	$-0.935862\pi$
$83$	−12.0724	+	29.1454i	−0.145451	+	0.351149i	0.834318	+	0.551284i	$0.185862\pi$
$84$		0			0
$85$	37.1731	+	91.4302i	0.437331	+	1.07565i
$86$		0			0
$87$	−76.4539	−	31.6683i	−0.878781	−	0.364003i
$88$		0			0
$89$	2.49113	+	2.49113i	0.0279903	+	0.0279903i	0.720963	−	0.692973i	$-0.243700\pi$
$89$	2.49113	+	2.49113i	0.0279903	+	0.0279903i	−0.692973	+	0.720963i	$0.743700\pi$
$90$		0			0
$91$	83.1620	+	16.5419i	0.913868	+	0.181780i
$92$		0			0
$93$	3.84557	+	9.28402i	0.0413502	+	0.0998282i
$94$		0			0
$95$	161.596	−	107.975i	1.70101	−	1.13658i
$96$		0			0
$97$	50.5412	+	33.7705i	0.521043	+	0.348150i	0.788116	−	0.615526i	$-0.211057\pi$
$97$	50.5412	+	33.7705i	0.521043	+	0.348150i	−0.267073	+	0.963676i	$0.586057\pi$
$98$		0			0
$99$	23.8168	+	119.735i	0.240574	+	1.20945i
$100$		0			0
$101$		−	33.0424i		−	0.327153i	−0.986531	−	0.163576i	$-0.947697\pi$
$101$		−	33.0424i		−	0.327153i	0.986531	−	0.163576i	$-0.0523030\pi$
$102$		0			0
$103$	0.998817			0.00969725			0.00484863	−	0.999988i	$-0.498457\pi$
$103$	0.998817			0.00969725			0.00484863	+	0.999988i	$0.498457\pi$
$104$		0			0
$105$	96.6271	−	19.2203i	0.920258	−	0.183051i
$106$		0			0
$107$	54.7435	−	81.9294i	0.511621	−	0.765695i	−0.482274	−	0.876020i	$-0.660189\pi$
$107$	54.7435	−	81.9294i	0.511621	−	0.765695i	0.993896	+	0.110325i	$0.0351891\pi$
$108$		0			0
$109$	−68.4299	−	102.413i	−0.627797	−	0.939565i	−0.999935	−	0.0113873i	$-0.996375\pi$
$109$	−68.4299	−	102.413i	−0.627797	−	0.939565i	0.372138	−	0.928177i	$-0.378625\pi$
$110$		0			0
$111$	−114.365	+	47.3717i	−1.03032	+	0.426772i
$112$		0			0
$113$	23.1545	−	116.405i	0.204907	−	1.03014i	−0.732199	−	0.681091i	$-0.761506\pi$
$113$	23.1545	−	116.405i	0.204907	−	1.03014i	0.937106	−	0.349045i	$-0.113494\pi$
$114$		0			0
$115$	−10.0175	+	10.0175i	−0.0871087	+	0.0871087i
$116$		0			0
$117$	−19.8670	+	47.9633i	−0.169804	+	0.409942i
$118$		0			0
$119$	−168.689	−	1.10299i	−1.41756	−	0.00926883i
$120$		0			0
$121$	−261.229	−	108.205i	−2.15892	−	0.894253i
$122$		0			0
$123$	37.2598	+	37.2598i	0.302925	+	0.302925i
$124$		0			0
$125$	92.7758	+	18.4543i	0.742206	+	0.147634i
$126$		0			0
$127$	−8.17027	−	19.7248i	−0.0643329	−	0.155313i	0.888444	−	0.458986i	$-0.151787\pi$
$127$	−8.17027	−	19.7248i	−0.0643329	−	0.155313i	−0.952776	+	0.303673i	$0.901787\pi$
$128$		0			0
$129$	−50.1369	+	33.5004i	−0.388658	+	0.259693i
$130$		0			0
$131$	−100.260	−	66.9917i	−0.765345	−	0.511387i	0.110561	−	0.993869i	$-0.464735\pi$
$131$	−100.260	−	66.9917i	−0.765345	−	0.511387i	−0.875906	+	0.482482i	$0.839735\pi$
$132$		0			0
$133$	64.8049	+	325.796i	0.487255	+	2.44960i
$134$		0			0
$135$			149.676i			1.10871i
$136$		0			0
$137$	261.140			1.90613			0.953064	−	0.302768i	$-0.0979107\pi$
$137$	261.140			1.90613			0.953064	+	0.302768i	$0.0979107\pi$
$138$		0			0
$139$	161.900	−	32.2040i	1.16475	−	0.231683i	0.425400	−	0.905005i	$-0.360133\pi$
$139$	161.900	−	32.2040i	1.16475	−	0.231683i	0.739349	+	0.673322i	$0.235133\pi$
$140$		0			0
$141$	−32.1462	+	48.1102i	−0.227987	+	0.341207i
$142$		0			0
$143$	−95.3892	−	142.760i	−0.667057	−	0.998322i
$144$		0			0
$145$	−259.563	+	107.515i	−1.79009	+	0.741480i
$146$		0			0
$147$	−16.5036	+	82.9692i	−0.112269	+	0.564417i
$148$		0			0
$149$	73.1923	−	73.1923i	0.491223	−	0.491223i	−0.417468	−	0.908692i	$-0.637082\pi$
$149$	73.1923	−	73.1923i	0.491223	−	0.491223i	0.908692	+	0.417468i	$0.137082\pi$
$150$		0			0
$151$	13.0434	−	31.4895i	0.0863799	−	0.208540i	−0.874787	−	0.484508i	$-0.838999\pi$
$151$	13.0434	−	31.4895i	0.0863799	−	0.208540i	0.961167	+	0.275969i	$0.0889986\pi$
$152$		0			0
$153$	20.8119	−	101.167i	0.136026	−	0.661222i
$154$		0			0
$155$	31.5195	+	13.0558i	0.203352	+	0.0842310i
$156$		0			0
$157$	−56.2052	−	56.2052i	−0.357995	−	0.357995i	0.505079	−	0.863073i	$-0.331464\pi$
$157$	−56.2052	−	56.2052i	−0.357995	−	0.357995i	−0.863073	+	0.505079i	$0.831464\pi$
$158$		0			0
$159$	−27.8787	−	5.54541i	−0.175337	−	0.0348768i
$160$		0			0
$161$	−9.26620	−	22.3706i	−0.0575540	−	0.138948i
$162$		0			0
$163$	102.155	−	68.2578i	0.626718	−	0.418759i	−0.201246	−	0.979541i	$-0.564499\pi$
$163$	102.155	−	68.2578i	0.626718	−	0.418759i	0.827964	+	0.560781i	$0.189499\pi$
$164$		0			0
$165$	−165.875	−	110.834i	−1.00530	−	0.671722i
$166$		0			0
$167$	38.0692	+	191.387i	0.227959	+	1.14603i	0.909966	+	0.414683i	$0.136108\pi$
$167$	38.0692	+	191.387i	0.227959	+	1.14603i	−0.682006	+	0.731346i	$0.738892\pi$
$168$		0			0
$169$			95.9861i			0.567965i
$170$		0			0
$171$	−203.383			−1.18937
$172$		0			0
$173$	−228.556	+	45.4627i	−1.32113	+	0.262790i	−0.804774	−	0.593581i	$-0.797714\pi$
$173$	−228.556	+	45.4627i	−1.32113	+	0.262790i	−0.516361	+	0.856371i	$0.672714\pi$
$174$		0			0
$175$	48.0017	−	71.8396i	0.274295	−	0.410512i
$176$		0			0
$177$	31.5378	+	47.1996i	0.178179	+	0.266664i
$178$		0			0
$179$	−128.601	+	53.2684i	−0.718443	+	0.297589i	−0.711793	−	0.702389i	$-0.752117\pi$
$179$	−128.601	+	53.2684i	−0.718443	+	0.297589i	−0.00664989	+	0.999978i	$0.502117\pi$
$180$		0			0
$181$	42.8707	−	215.526i	0.236855	−	1.19075i	−0.660975	−	0.750408i	$-0.729857\pi$
$181$	42.8707	−	215.526i	0.236855	−	1.19075i	0.897830	−	0.440342i	$-0.145143\pi$
$182$		0			0
$183$	62.4635	−	62.4635i	0.341331	−	0.341331i
$184$		0			0
$185$	−160.828	+	388.273i	−0.869341	+	2.09877i
$186$		0			0
$187$	239.957	+	243.115i	1.28319	+	1.30008i
$188$		0			0
$189$	−236.350	−	97.8994i	−1.25053	−	0.517986i
$190$		0			0
$191$	52.0086	+	52.0086i	0.272296	+	0.272296i	0.830024	−	0.557728i	$-0.188327\pi$
$191$	52.0086	+	52.0086i	0.272296	+	0.272296i	−0.557728	+	0.830024i	$0.688327\pi$
$192$		0			0
$193$	−151.016	−	30.0390i	−0.782468	−	0.155643i	−0.212337	−	0.977196i	$-0.568108\pi$
$193$	−151.016	−	30.0390i	−0.782468	−	0.155643i	−0.570131	+	0.821554i	$0.693108\pi$
$194$		0			0
$195$	−32.4653	−	78.3782i	−0.166489	−	0.401939i
$196$		0			0
$197$	−154.132	+	102.988i	−0.782395	+	0.522780i	−0.881436	−	0.472304i	$-0.843423\pi$
$197$	−154.132	+	102.988i	−0.782395	+	0.522780i	0.0990406	+	0.995083i	$0.468423\pi$
$198$		0			0
$199$	86.6204	+	57.8779i	0.435278	+	0.290844i	0.753840	−	0.657059i	$-0.228200\pi$
$199$	86.6204	+	57.8779i	0.435278	+	0.290844i	−0.318561	+	0.947902i	$0.603200\pi$
$200$		0			0
$201$	15.3427	+	77.1329i	0.0763318	+	0.383746i
$202$		0			0
$203$		−	480.193i		−	2.36548i
$204$		0			0
$205$	178.895			0.872659
$206$		0			0
$207$	14.5405	−	2.89228i	0.0702438	−	0.0139724i
$208$		0			0
$209$	373.698	−	559.278i	1.78803	−	2.67597i
$210$		0			0
$211$	126.132	+	188.770i	0.597781	+	0.894642i	0.999780	−	0.0209979i	$-0.00668432\pi$
$211$	126.132	+	188.770i	0.597781	+	0.894642i	−0.401999	+	0.915640i	$0.631684\pi$
$212$		0			0
$213$	29.1041	−	12.0553i	0.136639	−	0.0565977i
$214$		0			0
$215$	−39.9384	+	200.784i	−0.185760	+	0.933878i
$216$		0			0
$217$	−41.2322	+	41.2322i	−0.190010	+	0.190010i
$218$		0			0
$219$	−13.8222	+	33.3697i	−0.0631151	+	0.152373i
$220$		0			0
$221$	27.4070	+	142.653i	0.124014	+	0.645489i
$222$		0			0
$223$	−237.789	−	98.4956i	−1.06632	−	0.441684i	−0.220629	−	0.975358i	$-0.570811\pi$
$223$	−237.789	−	98.4956i	−1.06632	−	0.441684i	−0.845691	+	0.533673i	$0.820811\pi$
$224$		0			0
$225$	37.4063	+	37.4063i	0.166250	+	0.166250i
$226$		0			0
$227$	253.304	+	50.3854i	1.11588	+	0.221962i	0.718387	−	0.695644i	$-0.244881\pi$
$227$	253.304	+	50.3854i	1.11588	+	0.221962i	0.397492	+	0.917606i	$0.369881\pi$
$228$		0			0
$229$	−49.6689	−	119.911i	−0.216895	−	0.523631i	0.777558	−	0.628811i	$-0.216458\pi$
$229$	−49.6689	−	119.911i	−0.216895	−	0.523631i	−0.994453	+	0.105180i	$0.966458\pi$
$230$		0			0
$231$	283.510	−	189.436i	1.22732	−	0.820067i
$232$		0			0
$233$	−48.7775	−	32.5921i	−0.209345	−	0.139880i	0.446478	−	0.894795i	$-0.352678\pi$
$233$	−48.7775	−	32.5921i	−0.209345	−	0.139880i	−0.655823	+	0.754915i	$0.727678\pi$
$234$		0			0
$235$	38.3239	+	192.667i	0.163080	+	0.819861i
$236$		0			0
$237$		−	53.4272i		−	0.225431i
$238$		0			0
$239$	227.826			0.953245			0.476622	−	0.879108i	$-0.341861\pi$
$239$	227.826			0.953245			0.476622	+	0.879108i	$0.341861\pi$
$240$		0			0
$241$	174.585	−	34.7271i	0.724419	−	0.144096i	0.180911	−	0.983500i	$-0.442095\pi$
$241$	174.585	−	34.7271i	0.724419	−	0.144096i	0.543509	+	0.839404i	$0.317095\pi$
$242$		0			0
$243$	138.971	−	207.985i	0.571897	−	0.855904i
$244$		0			0
$245$	159.561	+	238.799i	0.651267	+	0.974690i
$246$		0			0
$247$	264.267	−	109.463i	1.06991	−	0.443169i
$248$		0			0
$249$	−10.5246	+	52.9109i	−0.0422676	+	0.212494i
$250$		0			0
$251$	−206.647	+	206.647i	−0.823295	+	0.823295i	−0.986579	−	0.163284i	$-0.947791\pi$
$251$	−206.647	+	206.647i	−0.823295	+	0.823295i	0.163284	+	0.986579i	$0.447791\pi$
$252$		0			0
$253$	−18.7634	+	45.2988i	−0.0741636	+	0.179047i
$254$		0			0
$255$	92.8506	+	140.947i	0.364120	+	0.552734i
$256$		0			0
$257$	54.5850	+	22.6099i	0.212393	+	0.0879761i	0.486343	−	0.873768i	$-0.338330\pi$
$257$	54.5850	+	22.6099i	0.212393	+	0.0879761i	−0.273950	+	0.961744i	$0.588330\pi$
$258$		0			0
$259$	−507.920	−	507.920i	−1.96108	−	1.96108i
$260$		0			0
$261$	288.358	+	57.3580i	1.10482	+	0.219762i
$262$		0			0
$263$	−24.2964	−	58.6566i	−0.0923817	−	0.223029i	0.870934	−	0.491400i	$-0.163515\pi$
$263$	−24.2964	−	58.6566i	−0.0923817	−	0.223029i	−0.963316	+	0.268371i	$0.913515\pi$
$264$		0			0
$265$	−80.2394	+	53.6142i	−0.302790	+	0.202318i
$266$		0			0
$267$	5.00928	+	3.34710i	0.0187614	+	0.0125359i
$268$		0			0
$269$	−63.0185	−	316.816i	−0.234270	−	1.17775i	−0.901459	−	0.432865i	$-0.857503\pi$
$269$	−63.0185	−	316.816i	−0.234270	−	1.17775i	0.667189	−	0.744888i	$-0.267497\pi$
$270$		0			0
$271$		−	354.193i		−	1.30699i	−0.756933	−	0.653493i	$-0.773303\pi$
$271$		−	354.193i		−	1.30699i	0.756933	−	0.653493i	$-0.226697\pi$
$272$		0			0
$273$	145.000			0.531135
$274$		0			0
$275$	−171.594	+	34.1321i	−0.623976	+	0.124117i
$276$		0			0
$277$	−57.3515	+	85.8327i	−0.207045	+	0.309865i	−0.920430	−	0.390907i	$-0.872161\pi$
$277$	−57.3515	+	85.8327i	−0.207045	+	0.309865i	0.713385	+	0.700773i	$0.247161\pi$
$278$		0			0
$279$	−19.8351	−	29.6853i	−0.0710934	−	0.106399i
$280$		0			0
$281$	−218.735	+	90.6028i	−0.778415	+	0.322430i	−0.736276	−	0.676682i	$-0.763417\pi$
$281$	−218.735	+	90.6028i	−0.778415	+	0.322430i	−0.0421392	+	0.999112i	$0.513417\pi$
$282$		0			0
$283$	−31.7224	+	159.479i	−0.112093	+	0.563531i	0.883394	+	0.468632i	$0.155253\pi$
$283$	−31.7224	+	159.479i	−0.112093	+	0.563531i	−0.995487	+	0.0948994i	$0.969747\pi$
$284$		0			0
$285$	235.010	−	235.010i	0.824597	−	0.824597i
$286$		0			0
$287$	−117.011	+	282.489i	−0.407703	+	0.984283i
$288$		0			0
$289$	−107.095	−	268.425i	−0.370569	−	0.928805i
$290$		0			0
$291$	96.0354	+	39.7792i	0.330019	+	0.136698i
$292$		0			0
$293$	291.879	+	291.879i	0.996173	+	0.996173i	0.999993	−	0.00381961i	$-0.00121582\pi$
$293$	291.879	+	291.879i	0.996173	+	0.996173i	−0.00381961	+	0.999993i	$0.501216\pi$
$294$		0			0
$295$	189.021	+	37.5985i	0.640748	+	0.127453i
$296$		0			0
$297$	198.239	+	478.591i	0.667472	+	1.61142i
$298$		0			0
$299$	−17.3366	+	11.5839i	−0.0579818	+	0.0387422i
$300$		0			0
$301$	−290.930	−	194.393i	−0.966545	−	0.645825i
$302$		0			0
$303$	−11.0236	−	55.4196i	−0.0363816	−	0.182903i
$304$		0			0
$305$		−	299.906i		−	0.983297i
$306$		0			0
$307$	171.144			0.557472			0.278736	−	0.960368i	$-0.410085\pi$
$307$	171.144			0.557472			0.278736	+	0.960368i	$0.410085\pi$
$308$		0			0
$309$	1.67524	−	0.333226i	0.00542148	−	0.00107840i
$310$		0			0
$311$	−110.967	+	166.074i	−0.356808	+	0.534001i	−0.965838	−	0.259146i	$-0.916559\pi$
$311$	−110.967	+	166.074i	−0.356808	+	0.534001i	0.609030	+	0.793147i	$0.291559\pi$
$312$		0			0
$313$	95.7078	+	143.237i	0.305776	+	0.457626i	0.952254	−	0.305307i	$-0.0987589\pi$
$313$	95.7078	+	143.237i	0.305776	+	0.457626i	−0.646478	+	0.762932i	$0.723759\pi$
$314$		0			0
$315$	−323.381	+	133.949i	−1.02661	+	0.425234i
$316$		0			0
$317$	35.1894	−	176.909i	0.111007	−	0.558072i	−0.884751	−	0.466064i	$-0.845672\pi$
$317$	35.1894	−	176.909i	0.111007	−	0.558072i	0.995758	−	0.0920078i	$-0.0293285\pi$
$318$		0			0
$319$	−687.559	+	687.559i	−2.15536	+	2.15536i
$320$		0			0
$321$	64.4837	−	155.677i	0.200884	−	0.484976i
$322$		0			0
$323$	−475.230	+	313.063i	−1.47130	+	0.969236i
$324$		0			0
$325$	−68.7365	−	28.4716i	−0.211497	−	0.0876049i
$326$		0			0
$327$	−148.939	−	148.939i	−0.455471	−	0.455471i
$328$		0			0
$329$	−329.303	−	65.5025i	−1.00092	−	0.199096i
$330$		0			0
$331$	−114.757	−	277.047i	−0.346697	−	0.837001i	−0.997006	−	0.0773306i	$-0.975360\pi$
$331$	−114.757	−	277.047i	−0.346697	−	0.837001i	0.650308	−	0.759670i	$-0.274640\pi$
$332$		0			0
$333$	365.678	−	244.338i	1.09813	−	0.733749i
$334$		0			0
$335$	222.001	+	148.336i	0.662690	+	0.442795i
$336$		0			0
$337$	101.839	+	511.977i	0.302192	+	1.51922i	0.771525	+	0.636199i	$0.219494\pi$
$337$	101.839	+	511.977i	0.302192	+	1.51922i	−0.469334	+	0.883021i	$0.655506\pi$
$338$		0			0
$339$		−	202.963i		−	0.598710i
$340$		0			0
$341$	118.076			0.346264
$342$		0			0
$343$	−4.55689	+	0.906423i	−0.0132854	+	0.00264263i
$344$		0			0
$345$	−13.4595	+	20.1436i	−0.0390132	+	0.0583873i
$346$		0			0
$347$	−316.377	−	473.491i	−0.911749	−	1.36453i	−0.931119	−	0.364716i	$-0.881166\pi$
$347$	−316.377	−	473.491i	−0.911749	−	1.36453i	0.0193697	−	0.999812i	$-0.493834\pi$
$348$		0			0
$349$	−243.001	+	100.654i	−0.696277	+	0.288407i	−0.702612	−	0.711573i	$-0.747983\pi$
$349$	−243.001	+	100.654i	−0.696277	+	0.288407i	0.00633587	+	0.999980i	$0.497983\pi$
$350$		0			0
$351$	−42.9765	+	216.057i	−0.122440	+	0.615548i
$352$		0			0
$353$	−103.511	+	103.511i	−0.293232	+	0.293232i	−0.838356	−	0.545124i	$-0.816483\pi$
$353$	−103.511	+	103.511i	−0.293232	+	0.293232i	0.545124	+	0.838356i	$0.316483\pi$
$354$		0			0
$355$	40.9281	−	98.8093i	0.115291	−	0.278336i
$356$		0			0
$357$	−283.298	+	54.4283i	−0.793551	+	0.152460i
$358$		0			0
$359$	−262.596	−	108.771i	−0.731465	−	0.302983i	−0.0143110	−	0.999898i	$-0.504555\pi$
$359$	−262.596	−	108.771i	−0.731465	−	0.302983i	−0.717154	+	0.696915i	$0.754555\pi$
$360$		0			0
$361$	537.114	+	537.114i	1.48785	+	1.48785i
$362$		0			0
$363$	−474.239	−	94.3319i	−1.30644	−	0.259868i
$364$		0			0
$365$	46.9267	+	113.291i	0.128566	+	0.310387i
$366$		0			0
$367$	498.212	−	332.894i	1.35753	−	0.907069i	0.357882	−	0.933767i	$-0.383499\pi$
$367$	498.212	−	332.894i	1.35753	−	0.907069i	0.999644	+	0.0266975i	$0.00849910\pi$
$368$		0			0
$369$	−155.659	−	104.008i	−0.421841	−	0.281865i
$370$		0			0
$371$	−32.1784	−	161.772i	−0.0867343	−	0.436043i
$372$		0			0
$373$			424.142i			1.13711i	0.822646	+	0.568554i	$0.192497\pi$
$373$			424.142i			1.13711i	−0.822646	+	0.568554i	$0.807503\pi$
$374$		0			0
$375$	161.762			0.431366
$376$		0			0
$377$	−405.550	+	80.6689i	−1.07573	+	0.213976i
$378$		0			0
$379$	160.811	−	240.671i	0.424303	−	0.635015i	−0.556308	−	0.830976i	$-0.687783\pi$
$379$	160.811	−	240.671i	0.424303	−	0.635015i	0.980612	+	0.195961i	$0.0627826\pi$
$380$		0			0
$381$	−20.2840	−	30.3571i	−0.0532388	−	0.0796774i
$382$		0			0
$383$	184.602	−	76.4647i	0.481990	−	0.199647i	−0.128439	−	0.991717i	$-0.540997\pi$
$383$	184.602	−	76.4647i	0.481990	−	0.199647i	0.610430	+	0.792070i	$0.290997\pi$
$384$		0			0
$385$	225.840	−	1135.38i	0.586598	−	2.94903i
$386$		0			0
$387$	151.485	−	151.485i	0.391434	−	0.391434i
$388$		0			0
$389$	−142.794	+	344.735i	−0.367080	+	0.886209i	0.627146	+	0.778902i	$0.284223\pi$
$389$	−142.794	+	344.735i	−0.367080	+	0.886209i	−0.994226	+	0.107308i	$0.965777\pi$
$390$		0			0
$391$	29.5236	−	29.1400i	0.0755079	−	0.0745269i
$392$		0			0
$393$	−190.508	−	78.9112i	−0.484754	−	0.200792i
$394$		0			0
$395$	−128.260	−	128.260i	−0.324708	−	0.324708i
$396$		0			0
$397$	139.988	+	27.8453i	0.352614	+	0.0701393i	0.368220	−	0.929739i	$-0.379967\pi$
$397$	139.988	+	27.8453i	0.352614	+	0.0701393i	−0.0156052	+	0.999878i	$0.504967\pi$
$398$		0			0
$399$	217.385	+	524.813i	0.544824	+	1.31532i
$400$		0			0
$401$	6.54768	−	4.37502i	0.0163284	−	0.0109103i	−0.547379	−	0.836885i	$-0.684374\pi$
$401$	6.54768	−	4.37502i	0.0163284	−	0.0109103i	0.563708	+	0.825974i	$0.309374\pi$
$402$		0			0
$403$	41.7497	+	27.8962i	0.103597	+	0.0692214i
$404$		0			0
$405$	−11.9990	−	60.3230i	−0.0296271	−	0.148946i
$406$		0			0
$407$			1454.52i			3.57376i
$408$		0			0
$409$	34.6917			0.0848209			0.0424104	−	0.999100i	$-0.486496\pi$
$409$	34.6917			0.0848209			0.0424104	+	0.999100i	$0.486496\pi$
$410$		0			0
$411$	437.989	−	87.1215i	1.06567	−	0.211975i
$412$		0			0
$413$	−183.005	+	273.886i	−0.443110	+	0.663161i
$414$		0			0
$415$	101.754	+	152.286i	0.245191	+	0.366955i
$416$		0			0
$417$	260.799	−	108.026i	0.625417	−	0.259056i
$418$		0			0
$419$	−4.80253	+	24.1439i	−0.0114619	+	0.0576227i	−0.986093	−	0.166195i	$-0.946852\pi$
$419$	−4.80253	+	24.1439i	−0.0114619	+	0.0576227i	0.974631	+	0.223818i	$0.0718520\pi$
$420$		0			0
$421$	−0.753481	+	0.753481i	−0.00178974	+	0.00178974i	−0.708001	−	0.706211i	$-0.750403\pi$
$421$	−0.753481	+	0.753481i	−0.00178974	+	0.00178974i	0.706211	+	0.708001i	$0.250403\pi$
$422$		0			0
$423$	78.6691	−	189.924i	0.185979	−	0.448993i
$424$		0			0
$425$	144.983	+	29.8257i	0.341137	+	0.0701782i
$426$		0			0
$427$	473.574	+	196.161i	1.10907	+	0.459393i
$428$		0			0
$429$	−207.617	−	207.617i	−0.483955	−	0.483955i
$430$		0			0
$431$	−7.61852	−	1.51542i	−0.0176764	−	0.00351605i	0.186244	−	0.982503i	$-0.440368\pi$
$431$	−7.61852	−	1.51542i	−0.0176764	−	0.00351605i	−0.203921	+	0.978987i	$0.565368\pi$
$432$		0			0
$433$	−82.4729	−	199.107i	−0.190469	−	0.459832i	0.799580	−	0.600560i	$-0.205056\pi$
$433$	−82.4729	−	199.107i	−0.190469	−	0.459832i	−0.990048	+	0.140728i	$0.955056\pi$
$434$		0			0
$435$	−399.476	+	266.922i	−0.918337	+	0.613613i
$436$		0			0
$437$	−67.9180	−	45.3813i	−0.155419	−	0.103847i
$438$		0			0
$439$	−116.315	−	584.756i	−0.264955	−	1.33202i	−0.852458	−	0.522796i	$-0.824889\pi$
$439$	−116.315	−	584.756i	−0.264955	−	1.33202i	0.587503	−	0.809222i	$-0.300111\pi$
$440$		0			0
$441$		−	300.550i		−	0.681519i
$442$		0			0
$443$	−402.677			−0.908977			−0.454489	−	0.890753i	$-0.650178\pi$
$443$	−402.677			−0.908977			−0.454489	+	0.890753i	$0.650178\pi$
$444$		0			0
$445$	20.0607	−	3.99032i	0.0450803	−	0.00896702i
$446$		0			0
$447$	98.3414	−	147.178i	0.220003	−	0.329258i
$448$		0			0
$449$	−91.6560	−	137.173i	−0.204134	−	0.305508i	0.715251	−	0.698868i	$-0.246313\pi$
$449$	−91.6560	−	137.173i	−0.204134	−	0.305508i	−0.919384	+	0.393360i	$0.871313\pi$
$450$		0			0
$451$	572.020	−	236.938i	1.26834	−	0.525362i
$452$		0			0
$453$	11.3711	−	57.1664i	0.0251018	−	0.126195i
$454$		0			0
$455$	348.094	−	348.094i	0.765041	−	0.765041i
$456$		0			0
$457$	297.601	−	718.473i	0.651206	−	1.57215i	−0.159824	−	0.987146i	$-0.551093\pi$
$457$	297.601	−	718.473i	0.651206	−	1.57215i	0.811030	−	0.585005i	$-0.198907\pi$
$458$		0			0
$459$	2.86560	−	438.260i	0.00624314	−	0.954815i
$460$		0			0
$461$	−407.125	−	168.637i	−0.883135	−	0.365807i	−0.105423	−	0.994427i	$-0.533620\pi$
$461$	−407.125	−	168.637i	−0.883135	−	0.365807i	−0.777712	+	0.628621i	$0.783620\pi$
$462$		0			0
$463$	52.1776	+	52.1776i	0.112695	+	0.112695i	0.761205	−	0.648511i	$-0.224608\pi$
$463$	52.1776	+	52.1776i	0.112695	+	0.112695i	−0.648511	+	0.761205i	$0.724608\pi$
$464$		0			0
$465$	57.2209	+	11.3819i	0.123056	+	0.0244773i
$466$		0			0
$467$	−46.0844	−	111.258i	−0.0986818	−	0.238239i	0.866827	−	0.498609i	$-0.166156\pi$
$467$	−46.0844	−	111.258i	−0.0986818	−	0.238239i	−0.965509	+	0.260370i	$0.916156\pi$
$468$		0			0
$469$	−379.440	+	253.534i	−0.809040	+	0.540584i
$470$		0			0
$471$	−113.020	−	75.5174i	−0.239957	−	0.160334i
$472$		0			0
$473$	138.225	+	694.905i	0.292231	+	1.46914i
$474$		0			0
$475$		−	291.470i		−	0.613621i
$476$		0			0
$477$	100.988			0.211716
$478$		0			0
$479$	820.903	−	163.288i	1.71379	−	0.340893i	0.761981	−	0.647599i	$-0.224227\pi$
$479$	820.903	−	163.288i	1.71379	−	0.340893i	0.951804	+	0.306706i	$0.0992270\pi$
$480$		0			0
$481$	−343.640	+	514.294i	−0.714428	+	1.06922i
$482$		0			0
$483$	−23.0048	−	34.4291i	−0.0476289	−	0.0712817i
$484$		0			0
$485$	326.043	−	135.051i	0.672253	−	0.278456i
$486$		0			0
$487$	−66.0116	+	331.863i	−0.135548	+	0.681443i	0.851926	+	0.523661i	$0.175434\pi$
$487$	−66.0116	+	331.863i	−0.135548	+	0.681443i	−0.987474	+	0.157782i	$0.949566\pi$
$488$		0			0
$489$	148.565	−	148.565i	0.303813	−	0.303813i
$490$		0			0
$491$	−190.468	+	459.831i	−0.387919	+	0.936519i	0.602462	+	0.798148i	$0.294187\pi$
$491$	−190.468	+	459.831i	−0.387919	+	0.936519i	−0.990380	+	0.138371i	$0.955813\pi$
$492$		0			0
$493$	762.074	−	309.839i	1.54579	−	0.628477i
$494$		0			0
$495$	654.822	+	271.236i	1.32287	+	0.547952i
$496$		0			0
$497$	129.257	+	129.257i	0.260075	+	0.260075i
$498$		0			0
$499$	609.078	+	121.153i	1.22060	+	0.242792i	0.763018	−	0.646377i	$-0.223717\pi$
$499$	609.078	+	121.153i	1.22060	+	0.242792i	0.457579	+	0.889169i	$0.348717\pi$
$500$		0			0
$501$	127.701	+	308.298i	0.254893	+	0.615365i
$502$		0			0
$503$	226.901	−	151.610i	0.451095	−	0.301412i	−0.309192	−	0.951000i	$-0.600058\pi$
$503$	226.901	−	151.610i	0.451095	−	0.301412i	0.760287	+	0.649588i	$0.225058\pi$
$504$		0			0
$505$	−159.507	−	106.579i	−0.315855	−	0.211047i
$506$		0			0
$507$	32.0229	+	160.990i	0.0631616	+	0.317535i
$508$		0			0
$509$		−	329.950i		−	0.648232i	−0.946017	−	0.324116i	$-0.894933\pi$
$509$		−	329.950i		−	0.648232i	0.946017	−	0.324116i	$-0.105067\pi$
$510$		0			0
$511$	−209.589			−0.410155
$512$		0			0
$513$	−846.429	+	168.365i	−1.64996	+	0.328197i
$514$		0			0
$515$	3.22170	−	4.82161i	0.00625573	−	0.00936236i
$516$		0			0
$517$	377.720	+	565.298i	0.730600	+	1.09342i
$518$		0			0
$519$	−368.173	+	152.502i	−0.709389	+	0.293838i
$520$		0			0
$521$	−138.553	+	696.553i	−0.265937	+	1.33695i	0.584721	+	0.811235i	$0.301204\pi$
$521$	−138.553	+	696.553i	−0.265937	+	1.33695i	−0.850658	+	0.525720i	$0.823796\pi$
$522$		0			0
$523$	360.855	−	360.855i	0.689971	−	0.689971i	−0.272255	−	0.962225i	$-0.587769\pi$
$523$	360.855	−	360.855i	0.689971	−	0.689971i	0.962225	+	0.272255i	$0.0877693\pi$
$524$		0			0
$525$	56.5424	−	136.505i	0.107700	−	0.260010i
$526$		0			0
$527$	−92.0409	−	38.8316i	−0.174651	−	0.0736842i
$528$		0			0
$529$	−483.231	−	200.161i	−0.913481	−	0.378376i
$530$		0			0
$531$	−142.610	−	142.610i	−0.268569	−	0.268569i
$532$		0			0
$533$	258.235	+	51.3661i	0.484493	+	0.0963717i
$534$		0			0
$535$	−218.924	−	528.529i	−0.409204	−	0.987905i
$536$		0			0
$537$	−197.922	+	132.247i	−0.368569	+	0.246270i
$538$		0			0
$539$	826.476	+	552.233i	1.53335	+	1.02455i
$540$		0			0
$541$	−80.7678	−	406.047i	−0.149294	−	0.750549i	−0.980797	−	0.195030i	$-0.937520\pi$
$541$	−80.7678	−	406.047i	−0.149294	−	0.750549i	0.831504	−	0.555519i	$-0.187480\pi$
$542$		0			0
$543$		−	375.787i		−	0.692058i
$544$		0			0
$545$	−715.100			−1.31211
$546$		0			0
$547$	−444.550	+	88.4265i	−0.812706	+	0.161657i	−0.583911	−	0.811817i	$-0.698478\pi$
$547$	−444.550	+	88.4265i	−0.812706	+	0.161657i	−0.228795	+	0.973475i	$0.573478\pi$
$548$		0			0
$549$	−174.363	+	260.952i	−0.317601	+	0.475323i
$550$		0			0
$551$	−899.976	−	1346.91i	−1.63335	−	2.44448i
$552$		0			0
$553$	286.424	−	118.641i	0.517945	−	0.214540i
$554$		0			0
$555$	−140.209	+	704.877i	−0.252628	+	1.27005i
$556$		0			0
$557$	645.774	−	645.774i	1.15938	−	1.15938i	0.174770	−	0.984609i	$-0.444082\pi$
$557$	645.774	−	645.774i	1.15938	−	1.15938i	0.984609	−	0.174770i	$-0.0559183\pi$
$558$		0			0
$559$	−115.302	+	278.364i	−0.206265	+	0.497967i
$560$		0			0
$561$	483.569	+	327.704i	0.861978	+	0.584143i
$562$		0			0
$563$	283.794	+	117.551i	0.504075	+	0.208795i	0.620205	−	0.784439i	$-0.287049\pi$
$563$	283.794	+	117.551i	0.504075	+	0.208795i	−0.116131	+	0.993234i	$0.537049\pi$
$564$		0			0
$565$	−487.241	−	487.241i	−0.862374	−	0.862374i
$566$		0			0
$567$	103.103	+	20.5084i	0.181839	+	0.0361701i
$568$		0			0
$569$	−312.374	−	754.138i	−0.548988	−	1.32537i	−0.918232	−	0.396042i	$-0.870383\pi$
$569$	−312.374	−	754.138i	−0.548988	−	1.32537i	0.369244	−	0.929332i	$-0.379617\pi$
$570$		0			0
$571$	−665.589	+	444.733i	−1.16566	+	0.778866i	−0.979060	−	0.203571i	$-0.934745\pi$
$571$	−665.589	+	444.733i	−1.16566	+	0.778866i	−0.186595	+	0.982437i	$0.559745\pi$
$572$		0			0
$573$	104.581	+	69.8788i	0.182515	+	0.121953i
$574$		0			0
$575$	4.14495	+	20.8381i	0.00720861	+	0.0362401i
$576$		0			0
$577$			796.009i			1.37957i	0.724016	+	0.689783i	$0.242294\pi$
$577$			796.009i			1.37957i	−0.724016	+	0.689783i	$0.757706\pi$
$578$		0			0
$579$	−263.310			−0.454766
$580$		0			0
$581$	−307.027	+	61.0714i	−0.528445	+	0.105114i
$582$		0			0
$583$	−185.557	+	277.706i	−0.318280	+	0.476339i
$584$		0			0
$585$	167.453	+	250.611i	0.286244	+	0.428395i
$586$		0			0
$587$	−268.910	+	111.386i	−0.458109	+	0.189755i	−0.599790	−	0.800157i	$-0.704749\pi$
$587$	−268.910	+	111.386i	−0.458109	+	0.189755i	0.141681	+	0.989912i	$0.454749\pi$
$588$		0			0
$589$	−38.3764	+	192.931i	−0.0651551	+	0.327557i
$590$		0			0
$591$	−224.155	+	224.155i	−0.379281	+	0.379281i
$592$		0			0
$593$	119.623	−	288.795i	0.201725	−	0.487007i	−0.790350	−	0.612656i	$-0.790101\pi$
$593$	119.623	−	288.795i	0.201725	−	0.487007i	0.992075	+	0.125649i	$0.0401013\pi$
$594$		0			0
$595$	−549.435	+	810.761i	−0.923420	+	1.36262i
$596$		0			0
$597$	164.591	+	68.1758i	0.275697	+	0.114197i
$598$		0			0
$599$	−22.6736	−	22.6736i	−0.0378523	−	0.0378523i	0.687927	−	0.725780i	$-0.258521\pi$
$599$	−22.6736	−	22.6736i	−0.0378523	−	0.0378523i	−0.725780	+	0.687927i	$0.758521\pi$
$600$		0			0
$601$	−464.993	−	92.4928i	−0.773698	−	0.153898i	−0.207575	−	0.978219i	$-0.566557\pi$
$601$	−464.993	−	92.4928i	−0.773698	−	0.153898i	−0.566123	+	0.824321i	$0.691557\pi$
$602$		0			0
$603$	−106.925	−	258.140i	−0.177322	−	0.428092i
$604$		0			0
$605$	−1364.94	+	912.022i	−2.25609	+	1.50747i
$606$		0			0
$607$	−443.123	−	296.085i	−0.730022	−	0.487785i	0.134163	−	0.990959i	$-0.457165\pi$
$607$	−443.123	−	296.085i	−0.730022	−	0.487785i	−0.864185	+	0.503174i	$0.832165\pi$
$608$		0			0
$609$	−160.202	−	805.391i	−0.263058	−	1.32248i
$610$		0			0
$611$			289.119i			0.473190i
$612$		0			0
$613$	−994.853			−1.62292			−0.811462	−	0.584405i	$-0.801328\pi$
$613$	−994.853			−1.62292			−0.811462	+	0.584405i	$0.801328\pi$
$614$		0			0
$615$	300.047	−	59.6831i	0.487882	−	0.0970457i
$616$		0			0
$617$	−498.348	+	745.830i	−0.807695	+	1.20880i	0.167153	+	0.985931i	$0.446543\pi$
$617$	−498.348	+	745.830i	−0.807695	+	1.20880i	−0.974848	+	0.222870i	$0.928457\pi$
$618$		0			0
$619$	560.353	+	838.627i	0.905255	+	1.35481i	0.934773	+	0.355246i	$0.115603\pi$
$619$	560.353	+	838.627i	0.905255	+	1.35481i	−0.0295177	+	0.999564i	$0.509397\pi$
$620$		0			0
$621$	58.1194	−	24.0739i	0.0935901	−	0.0387663i
$622$		0			0
$623$	−6.82018	+	34.2874i	−0.0109473	+	0.0550359i
$624$		0			0
$625$	542.254	−	542.254i	0.867607	−	0.867607i
$626$		0			0
$627$	440.188	−	1062.71i	0.702054	−	1.69491i
$628$		0			0
$629$	478.347	−	1133.81i	0.760489	−	1.80256i
$630$		0			0
$631$	929.574	+	385.042i	1.47318	+	0.610209i	0.967581	−	0.252561i	$-0.0812730\pi$
$631$	929.574	+	385.042i	1.47318	+	0.610209i	0.505595	+	0.862771i	$0.331273\pi$
$632$		0			0
$633$	274.529	+	274.529i	0.433694	+	0.433694i
$634$		0			0
$635$	−121.571	−	24.1820i	−0.191451	−	0.0380819i
$636$		0			0
$637$	161.759	+	390.521i	0.253939	+	0.613063i
$638$		0			0
$639$	−93.0591	+	62.1801i	−0.145632	+	0.0973085i
$640$		0			0
$641$	161.558	+	107.949i	0.252040	+	0.168408i	0.675172	−	0.737660i	$-0.264069\pi$
$641$	161.558	+	107.949i	0.252040	+	0.168408i	−0.423132	+	0.906068i	$0.639069\pi$
$642$		0			0
$643$	−59.5737	−	299.497i	−0.0926497	−	0.465781i	−0.999059	−	0.0433801i	$-0.986187\pi$
$643$	−59.5737	−	299.497i	−0.0926497	−	0.465781i	0.906409	−	0.422401i	$-0.138813\pi$
$644$		0			0
$645$			350.083i			0.542765i
$646$		0			0
$647$	−373.337			−0.577028			−0.288514	−	0.957476i	$-0.593161\pi$
$647$	−373.337			−0.577028			−0.288514	+	0.957476i	$0.593161\pi$
$648$		0			0
$649$	654.194	−	130.127i	1.00800	−	0.200504i
$650$		0			0
$651$	−55.3997	+	82.9116i	−0.0850995	+	0.127360i
$652$		0			0
$653$	57.9999	+	86.8030i	0.0888207	+	0.132930i	0.873219	−	0.487328i	$-0.162028\pi$
$653$	57.9999	+	86.8030i	0.0888207	+	0.132930i	−0.784399	+	0.620257i	$0.787028\pi$
$654$		0			0
$655$	−646.781	+	267.906i	−0.987452	+	0.409016i
$656$		0			0
$657$	25.0350	−	125.859i	0.0381050	−	0.191567i
$658$		0			0
$659$	−167.790	+	167.790i	−0.254612	+	0.254612i	−0.822859	−	0.568246i	$-0.807622\pi$
$659$	−167.790	+	167.790i	−0.254612	+	0.254612i	0.568246	+	0.822859i	$0.307622\pi$
$660$		0			0
$661$	−242.652	+	585.814i	−0.367099	+	0.886255i	0.627124	+	0.778919i	$0.284232\pi$
$661$	−242.652	+	585.814i	−0.367099	+	0.886255i	−0.994223	+	0.107335i	$0.965768\pi$
$662$		0			0
$663$	93.5597	+	230.117i	0.141116	+	0.347085i
$664$		0			0
$665$	1781.75	+	738.027i	2.67933	+	1.10981i
$666$		0			0
$667$	83.4962	+	83.4962i	0.125182	+	0.125182i
$668$		0			0
$669$	−431.686	−	85.8677i	−0.645271	−	0.128352i
$670$		0			0
$671$	−397.211	−	958.953i	−0.591969	−	1.42914i
$672$		0			0
$673$	745.985	−	498.451i	1.10845	−	0.740641i	0.140072	−	0.990141i	$-0.455266\pi$
$673$	745.985	−	498.451i	1.10845	−	0.740641i	0.968375	+	0.249501i	$0.0802665\pi$
$674$		0			0
$675$	186.641	+	124.710i	0.276506	+	0.184755i
$676$		0			0
$677$	−126.191	−	634.406i	−0.186398	−	0.937084i	−0.954830	−	0.297153i	$-0.903963\pi$
$677$	−126.191	−	634.406i	−0.186398	−	0.937084i	0.768432	−	0.639931i	$-0.221037\pi$
$678$		0			0
$679$			603.180i			0.888336i
$680$		0			0
$681$	441.658			0.648543
$682$		0			0
$683$	690.247	−	137.299i	1.01061	−	0.201023i	0.338100	−	0.941110i	$-0.390216\pi$
$683$	690.247	−	137.299i	1.01061	−	0.201023i	0.672511	+	0.740087i	$0.265216\pi$
$684$		0			0
$685$	842.310	−	1260.61i	1.22965	−	1.84030i
$686$		0			0
$687$	−123.311	−	184.548i	−0.179492	−	0.268628i
$688$		0			0
$689$	−131.220	+	54.3530i	−0.190450	+	0.0788868i
$690$		0			0
$691$	212.680	−	1069.22i	0.307786	−	1.54735i	−0.448908	−	0.893578i	$-0.648187\pi$
$691$	212.680	−	1069.22i	0.307786	−	1.54735i	0.756694	−	0.653769i	$-0.226813\pi$
$692$		0			0
$693$	−856.606	+	856.606i	−1.23608	+	1.23608i
$694$		0			0
$695$	366.753	−	885.419i	0.527702	−	1.27398i
$696$		0			0
$697$	−523.815	−	3.42501i	−0.751528	−	0.00491394i
$698$		0			0
$699$	−92.6841	−	38.3910i	−0.132595	−	0.0549228i
$700$		0			0
$701$	195.485	+	195.485i	0.278866	+	0.278866i	0.832656	−	0.553790i	$-0.186819\pi$
$701$	195.485	+	195.485i	0.278866	+	0.278866i	−0.553790	+	0.832656i	$0.686819\pi$
$702$		0			0
$703$	−2376.62	−	472.740i	−3.38069	−	0.672460i
$704$		0			0
$705$	128.556	+	310.360i	0.182348	+	0.440228i
$706$		0			0
$707$	272.626	−	182.163i	0.385609	−	0.257656i
$708$		0			0
$709$	670.471	+	447.995i	0.945658	+	0.631868i	0.929823	−	0.368006i	$-0.119960\pi$
$709$	670.471	+	447.995i	0.945658	+	0.631868i	0.0158344	+	0.999875i	$0.494960\pi$
$710$		0			0
$711$	37.0315	+	186.170i	0.0520837	+	0.261843i
$712$		0			0
$713$		−	14.3390i		−	0.0201108i
$714$		0			0
$715$	−996.828			−1.39417
$716$		0			0
$717$	382.114	−	76.0073i	0.532935	−	0.106007i
$718$		0			0
$719$	−165.532	+	247.736i	−0.230225	+	0.344557i	−0.928539	−	0.371236i	$-0.878934\pi$
$719$	−165.532	+	247.736i	−0.230225	+	0.344557i	0.698313	+	0.715792i	$0.253934\pi$
$720$		0			0
$721$	5.50646	+	8.24101i	0.00763726	+	0.0114300i
$722$		0			0
$723$	281.233	−	116.490i	0.388980	−	0.161121i
$724$		0			0
$725$	−82.2002	+	413.248i	−0.113380	+	0.569998i
$726$		0			0
$727$	−216.741	+	216.741i	−0.298130	+	0.298130i	−0.840281	−	0.542151i	$-0.817610\pi$
$727$	−216.741	+	216.741i	−0.298130	+	0.298130i	0.542151	+	0.840281i	$0.317610\pi$
$728$		0			0
$729$	127.211	−	307.114i	0.174501	−	0.421282i
$730$		0			0
$731$	120.786	−	587.141i	0.165234	−	0.803203i
$732$		0			0
$733$	69.4620	+	28.7721i	0.0947639	+	0.0392525i	0.429562	−	0.903037i	$-0.358668\pi$
$733$	69.4620	+	28.7721i	0.0947639	+	0.0392525i	−0.334798	+	0.942290i	$0.608668\pi$
$734$		0			0
$735$	347.287	+	347.287i	0.472499	+	0.472499i
$736$		0			0
$737$	906.317	+	180.278i	1.22974	+	0.244610i
$738$		0			0
$739$	557.583	+	1346.12i	0.754510	+	1.82155i	0.532315	+	0.846547i	$0.321322\pi$
$739$	557.583	+	1346.12i	0.754510	+	1.82155i	0.222196	+	0.975002i	$0.428678\pi$
$740$		0			0
$741$	406.715	−	271.758i	0.548873	−	0.366745i
$742$		0			0
$743$	333.191	+	222.631i	0.448440	+	0.299638i	0.759208	−	0.650848i	$-0.225586\pi$
$743$	333.191	+	222.631i	0.448440	+	0.299638i	−0.310769	+	0.950486i	$0.600586\pi$
$744$		0			0
$745$	−117.240	−	589.406i	−0.157369	−	0.791149i
$746$		0			0
$747$		−	191.666i		−	0.256581i
$748$		0			0
$749$	977.781			1.30545
$750$		0			0
$751$	−1177.82	+	234.284i	−1.56834	+	0.311962i	−0.901346	−	0.433100i	$-0.857420\pi$
$751$	−1177.82	+	234.284i	−1.56834	+	0.311962i	−0.666995	+	0.745062i	$0.732420\pi$
$752$		0			0
$753$	−277.652	+	415.535i	−0.368727	+	0.551839i
$754$		0			0
$755$	−109.938	−	164.534i	−0.145614	−	0.217926i
$756$		0			0
$757$	1020.22	−	422.587i	1.34771	−	0.558239i	0.412055	−	0.911159i	$-0.364811\pi$
$757$	1020.22	−	422.587i	1.34771	−	0.558239i	0.935654	+	0.352919i	$0.114811\pi$
$758$		0			0
$759$	−16.3578	+	82.2361i	−0.0215517	+	0.108348i
$760$		0			0
$761$	444.531	−	444.531i	0.584140	−	0.584140i	−0.351898	−	0.936038i	$-0.614464\pi$
$761$	444.531	−	444.531i	0.584140	−	0.584140i	0.936038	+	0.351898i	$0.114464\pi$
$762$		0			0
$763$	467.729	−	1129.20i	0.613013	−	1.47995i
$764$		0			0
$765$	−421.237	−	426.782i	−0.550636	−	0.557885i
$766$		0			0
$767$	262.055	+	108.547i	0.341663	+	0.141521i
$768$		0			0
$769$	618.353	+	618.353i	0.804100	+	0.804100i	0.983734	−	0.179634i	$-0.0574913\pi$
$769$	618.353	+	618.353i	0.804100	+	0.804100i	−0.179634	+	0.983734i	$0.557491\pi$
$770$		0			0
$771$	99.0944	+	19.7111i	0.128527	+	0.0255656i
$772$		0			0
$773$	93.0009	+	224.524i	0.120312	+	0.290458i	0.972549	−	0.232697i	$-0.0747550\pi$
$773$	93.0009	+	224.524i	0.120312	+	0.290458i	−0.852238	+	0.523155i	$0.824755\pi$
$774$		0			0
$775$	42.5422	−	28.4258i	0.0548931	−	0.0366784i
$776$		0			0
$777$	−1021.35	−	682.442i	−1.31448	−	0.878304i
$778$		0			0
$779$	201.233	+	1011.66i	0.258322	+	1.29867i
$780$		0			0
$781$		−	370.152i		−	0.473946i
$782$		0			0
$783$	1247.56			1.59330
$784$		0			0
$785$	−452.611	+	90.0300i	−0.576575	+	0.114688i
$786$		0			0
$787$	−547.093	+	818.783i	−0.695163	+	1.04038i	0.301064	+	0.953604i	$0.402658\pi$
$787$	−547.093	+	818.783i	−0.695163	+	1.04038i	−0.996227	+	0.0867812i	$0.972342\pi$
$788$		0			0
$789$	−60.3195	−	90.2745i	−0.0764506	−	0.114416i
$790$		0			0
$791$	1088.08	−	450.699i	1.37558	−	0.569784i
$792$		0			0
$793$	86.1119	−	432.914i	0.108590	−	0.545919i
$794$		0			0
$795$	−116.693	+	116.693i	−0.146783	+	0.146783i
$796$		0			0
$797$	191.175	−	461.538i	0.239869	−	0.579094i	−0.757400	−	0.652951i	$-0.773531\pi$
$797$	191.175	−	461.538i	0.239869	−	0.579094i	0.997269	+	0.0738567i	$0.0235308\pi$
$798$		0			0
$799$	−108.526	−	564.875i	−0.135827	−	0.706977i
$800$		0			0
$801$	−19.7751	−	8.19110i	−0.0246880	−	0.0102261i
$802$		0			0
$803$	300.098	+	300.098i	0.373721	+	0.373721i
$804$		0			0
$805$	−137.878	−	27.4257i	−0.171277	−	0.0340692i
$806$		0			0
$807$	−211.392	−	510.346i	−0.261948	−	0.632399i
$808$		0			0
$809$	−799.034	+	533.897i	−0.987681	+	0.659947i	−0.940803	−	0.338953i	$-0.889927\pi$
$809$	−799.034	+	533.897i	−0.987681	+	0.659947i	−0.0468778	+	0.998901i	$0.514927\pi$
$810$		0			0
$811$	1262.52	+	843.591i	1.55675	+	1.04019i	0.973724	+	0.227731i	$0.0731308\pi$
$811$	1262.52	+	843.591i	1.55675	+	1.04019i	0.583024	+	0.812455i	$0.301869\pi$
$812$		0			0
$813$	−118.166	−	594.061i	−0.145346	−	0.730702i
$814$		0			0
$815$		−	713.302i		−	0.875217i
$816$		0			0
$817$	−1180.37			−1.44476
$818$		0			0
$819$	−505.260	+	100.503i	−0.616924	+	0.122714i
$820$		0			0
$821$	−271.716	+	406.652i	−0.330958	+	0.495313i	−0.959209	−	0.282697i	$-0.908771\pi$
$821$	−271.716	+	406.652i	−0.330958	+	0.495313i	0.628252	+	0.778010i	$0.283771\pi$
$822$		0			0
$823$	−0.222234	−	0.332597i	−0.000270030	−	0.000404128i	0.831335	−	0.555772i	$-0.187577\pi$
$823$	−0.222234	−	0.332597i	−0.000270030	−	0.000404128i	−0.831605	+	0.555368i	$0.812577\pi$
$824$		0			0
$825$	−276.414	+	114.494i	−0.335047	+	0.138781i
$826$		0			0
$827$	69.7382	−	350.598i	0.0843267	−	0.423939i	−0.915442	−	0.402449i	$-0.868159\pi$
$827$	69.7382	−	350.598i	0.0843267	−	0.423939i	0.999769	−	0.0214899i	$-0.00684098\pi$
$828$		0			0
$829$	−577.656	+	577.656i	−0.696810	+	0.696810i	−0.963721	−	0.266911i	$-0.913997\pi$
$829$	−577.656	+	577.656i	−0.696810	+	0.696810i	0.266911	+	0.963721i	$0.413997\pi$
$830$		0			0
$831$	−67.5558	+	163.094i	−0.0812946	+	0.196263i
$832$		0			0
$833$	−462.630	−	702.272i	−0.555378	−	0.843064i
$834$		0			0
$835$	1046.68	+	433.549i	1.25351	+	0.519220i
$836$		0			0
$837$	−107.123	−	107.123i	−0.127984	−	0.127984i
$838$		0			0
$839$	−227.105	−	45.1740i	−0.270685	−	0.0538426i	0.0578813	−	0.998323i	$-0.481566\pi$
$839$	−227.105	−	45.1740i	−0.270685	−	0.0538426i	−0.328567	+	0.944481i	$0.606566\pi$
$840$		0			0
$841$	574.301	+	1386.49i	0.682879	+	1.64862i
$842$		0			0
$843$	−336.640	+	224.936i	−0.399335	+	0.266827i
$844$		0			0
$845$	463.356	+	309.605i	0.548350	+	0.366396i
$846$		0			0
$847$	−547.381	−	2751.87i	−0.646259	−	3.24896i
$848$		0			0
$849$			278.066i			0.327522i
$850$		0			0
$851$	176.635			0.207561
$852$		0			0
$853$	318.630	−	63.3795i	0.373540	−	0.0743018i	−0.00475011	−	0.999989i	$-0.501512\pi$
$853$	318.630	−	63.3795i	0.373540	−	0.0743018i	0.378291	+	0.925687i	$0.376512\pi$
$854$		0			0
$855$	−656.015	+	981.796i	−0.767269	+	1.14830i
$856$		0			0
$857$	−56.3685	−	84.3614i	−0.0657742	−	0.0984380i	0.797124	−	0.603815i	$-0.206353\pi$
$857$	−56.3685	−	84.3614i	−0.0657742	−	0.0984380i	−0.862899	+	0.505377i	$0.831353\pi$
$858$		0			0
$859$	514.687	−	213.191i	0.599170	−	0.248185i	−0.0624199	−	0.998050i	$-0.519882\pi$
$859$	514.687	−	213.191i	0.599170	−	0.248185i	0.661590	+	0.749865i	$0.269882\pi$
$860$		0			0
$861$	−102.009	+	512.835i	−0.118478	+	0.595627i
$862$		0			0
$863$	−283.466	+	283.466i	−0.328466	+	0.328466i	−0.852003	−	0.523537i	$-0.824612\pi$
$863$	−283.466	+	283.466i	−0.328466	+	0.328466i	0.523537	+	0.852003i	$0.324612\pi$
$864$		0			0
$865$	−517.749	+	1249.96i	−0.598554	+	1.44504i
$866$		0			0
$867$	−269.173	−	414.479i	−0.310465	−	0.478061i
$868$		0			0
$869$	−579.987	−	240.239i	−0.667419	−	0.276454i
$870$		0			0
$871$	277.867	+	277.867i	0.319020	+	0.319020i
$872$		0			0
$873$	−362.213	−	72.0486i	−0.414906	−	0.0825298i
$874$		0			0
$875$	359.210	+	867.210i	0.410526	+	0.991097i
$876$		0			0
$877$	−66.0596	+	44.1396i	−0.0753245	+	0.0503302i	−0.592662	−	0.805451i	$-0.701923\pi$
$877$	−66.0596	+	44.1396i	−0.0753245	+	0.0503302i	0.517338	+	0.855781i	$0.326923\pi$
$878$		0			0
$879$	586.923	+	392.169i	0.667716	+	0.446154i
$880$		0			0
$881$	−251.665	−	1265.20i	−0.285658	−	1.43610i	−0.810919	−	0.585158i	$-0.801032\pi$
$881$	−251.665	−	1265.20i	−0.285658	−	1.43610i	0.525261	−	0.850941i	$-0.323968\pi$
$882$		0			0
$883$			364.218i			0.412478i	0.978502	+	0.206239i	$0.0661224\pi$
$883$			364.218i			0.412478i	−0.978502	+	0.206239i	$0.933878\pi$
$884$		0			0
$885$	329.573			0.372399
$886$		0			0
$887$	−742.498	+	147.692i	−0.837089	+	0.166507i	−0.594979	−	0.803741i	$-0.702840\pi$
$887$	−742.498	+	147.692i	−0.837089	+	0.166507i	−0.242110	+	0.970249i	$0.577840\pi$
$888$		0			0
$889$	117.702	−	176.154i	0.132398	−	0.198148i
$890$		0			0
$891$	−118.262	−	176.992i	−0.132729	−	0.198644i
$892$		0			0
$893$	−1046.44	+	433.449i	−1.17182	+	0.485385i
$894$		0			0
$895$	−157.662	+	792.619i	−0.176158	+	0.885607i
$896$		0			0
$897$	−25.2127	+	25.2127i	−0.0281078	+	0.0281078i
$898$		0			0
$899$	108.821	−	262.716i	0.121046	−	0.292232i
$900$		0			0
$901$	235.972	−	155.449i	0.261900	−	0.172530i
$902$		0			0
$903$	−552.808	−	228.981i	−0.612191	−	0.253578i
$904$		0			0
$905$	−902.133	−	902.133i	−0.996832	−	0.996832i
$906$		0			0
$907$	728.789	+	144.965i	0.803516	+	0.159829i	0.579729	−	0.814809i	$-0.303158\pi$
$907$	728.789	+	144.965i	0.803516	+	0.159829i	0.223786	+	0.974638i	$0.428158\pi$
$908$		0			0
$909$	76.8250	+	185.472i	0.0845159	+	0.204039i
$910$		0			0
$911$	785.215	−	524.664i	0.861926	−	0.575921i	−0.0441550	−	0.999025i	$-0.514060\pi$
$911$	785.215	−	524.664i	0.861926	−	0.575921i	0.906081	+	0.423104i	$0.139060\pi$
$912$		0			0
$913$	527.058	+	352.169i	0.577281	+	0.385727i
$914$		0			0
$915$	−100.055	−	503.009i	−0.109349	−	0.549736i
$916$		0			0
$917$		−	1196.55i		−	1.30485i
$918$		0			0
$919$	−1608.59			−1.75037			−0.875187	−	0.483785i	$-0.839262\pi$
$919$	−1608.59			−1.75037			−0.875187	+	0.483785i	$0.839262\pi$
$920$		0			0
$921$	287.047	−	57.0971i	0.311668	−	0.0619947i
$922$		0			0
$923$	87.4508	−	130.879i	0.0947463	−	0.141798i
$924$		0			0
$925$	350.163	+	524.056i	0.378555	+	0.566547i
$926$		0			0
$927$	−5.60650	+	2.32229i	−0.00604800	+	0.00250516i
$928$		0			0
$929$	150.549	−	756.860i	0.162055	−	0.814704i	−0.811163	−	0.584820i	$-0.801165\pi$
$929$	150.549	−	756.860i	0.162055	−	0.814704i	0.973218	−	0.229884i	$-0.0738348\pi$
$930$		0			0
$931$	−1170.94	+	1170.94i	−1.25773	+	1.25773i
$932$		0			0
$933$	−130.711	+	315.564i	−0.140098	+	0.338226i
$934$		0			0
$935$	1947.58	−	374.177i	2.08297	−	0.400189i
$936$		0			0
$937$	−1068.74	−	442.688i	−1.14060	−	0.472453i	−0.269230	−	0.963076i	$-0.586769\pi$
$937$	−1068.74	−	442.688i	−1.14060	−	0.472453i	−0.871372	+	0.490623i	$0.836769\pi$
$938$		0			0
$939$	208.310	+	208.310i	0.221842	+	0.221842i
$940$		0			0
$941$	−1520.83	−	302.511i	−1.61618	−	0.321479i	−0.697533	−	0.716552i	$-0.745719\pi$
$941$	−1520.83	−	302.511i	−1.61618	−	0.321479i	−0.918649	+	0.395074i	$0.870719\pi$
$942$		0			0
$943$	−28.7735	−	69.4653i	−0.0305127	−	0.0736641i
$944$		0			0
$945$	−1234.94	+	825.162i	−1.30682	+	0.873187i
$946$		0			0
$947$	−678.583	−	453.415i	−0.716561	−	0.478790i	0.143066	−	0.989713i	$-0.454304\pi$
$947$	−678.583	−	453.415i	−0.716561	−	0.478790i	−0.859627	+	0.510923i	$0.829304\pi$
$948$		0			0
$949$	35.2094	+	177.010i	0.0371016	+	0.186522i
$950$		0			0
$951$		−	308.456i		−	0.324349i
$952$		0			0
$953$	80.9644			0.0849574			0.0424787	−	0.999097i	$-0.486475\pi$
$953$	80.9644			0.0849574			0.0424787	+	0.999097i	$0.486475\pi$
$954$		0			0
$955$	418.817	−	83.3078i	0.438551	−	0.0872333i
$956$		0			0
$957$	−923.806	+	1382.57i	−0.965315	+	1.44470i
$958$		0			0
$959$	1439.66	+	2154.60i	1.50121	+	2.24672i
$960$		0			0
$961$	855.946	−	354.544i	0.890682	−	0.368933i
$962$		0			0
$963$	−116.794	+	587.162i	−0.121281	+	0.609722i
$964$		0			0
$965$	−632.114	+	632.114i	−0.655040	+	0.655040i
$966$		0			0
$967$	−527.015	+	1272.33i	−0.545000	+	1.31575i	0.376157	+	0.926556i	$0.377245\pi$
$967$	−527.015	+	1272.33i	−0.545000	+	1.31575i	−0.921157	+	0.389190i	$0.872755\pi$
$968$		0			0
$969$	−692.622	+	683.623i	−0.714780	+	0.705494i
$970$		0			0
$971$	−1375.40	−	569.711i	−1.41648	−	0.586726i	−0.462507	−	0.886616i	$-0.653050\pi$
$971$	−1375.40	−	569.711i	−1.41648	−	0.586726i	−0.953974	+	0.299890i	$0.903050\pi$
$972$		0			0
$973$	1158.26	+	1158.26i	1.19040	+	1.19040i
$974$		0			0
$975$	−124.785	−	24.8213i	−0.127985	−	0.0254578i
$976$		0			0
$977$	−475.498	−	1147.95i	−0.486692	−	1.17498i	−0.956375	−	0.292142i	$-0.905632\pi$
$977$	−475.498	−	1147.95i	−0.486692	−	1.17498i	0.469683	−	0.882835i	$-0.344368\pi$
$978$		0			0
$979$	58.8594	−	39.3286i	0.0601220	−	0.0401722i
$980$		0			0
$981$	622.220	+	415.754i	0.634271	+	0.423806i
$982$		0			0
$983$	43.2834	+	217.600i	0.0440319	+	0.221364i	0.996536	−	0.0831623i	$-0.0265020\pi$
$983$	43.2834	+	217.600i	0.0440319	+	0.221364i	−0.952504	+	0.304526i	$0.901502\pi$
$984$		0			0
$985$			1076.23i			1.09262i
$986$		0			0
$987$	−574.168			−0.581730
$988$		0			0
$989$	84.3883	−	16.7859i	0.0853269	−	0.0169726i
$990$		0			0
$991$	975.692	−	1460.23i	0.984553	−	1.47349i	0.106854	−	0.994275i	$-0.465922\pi$
$991$	975.692	−	1460.23i	0.984553	−	1.47349i	0.877699	−	0.479212i	$-0.159078\pi$
$992$		0			0
$993$	−284.901	−	426.385i	−0.286910	−	0.429391i
$994$		0			0
$995$	558.791	−	231.459i	0.561599	−	0.232622i
$996$		0			0
$997$	−100.262	+	504.050i	−0.100563	+	0.505567i	0.897368	+	0.441283i	$0.145476\pi$
$997$	−100.262	+	504.050i	−0.100563	+	0.505567i	−0.997932	+	0.0642840i	$0.979524\pi$
$998$		0			0
$999$	1319.59	−	1319.59i	1.32091	−	1.32091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.b.57.4	✓	40
4.3	odd	2		272.3.bh.g.193.2		40
17.3	odd	16	inner	136.3.t.b.105.4	yes	40
68.3	even	16		272.3.bh.g.241.2		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.b.57.4	✓	40	1.1	even	1	trivial
136.3.t.b.105.4	yes	40	17.3	odd	16	inner
272.3.bh.g.193.2		40	4.3	odd	2
272.3.bh.g.241.2		40	68.3	even	16

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	136.t (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.67722 - 0.333620i) q^{3} +(3.22552 - 4.82733i) q^{5} +(5.51299 + 8.25077i) q^{7} +(-5.61314 + 2.32504i) q^{9} +O(q^{10})\)	\(q+(1.67722 - 0.333620i) q^{3} +(3.22552 - 4.82733i) q^{5} +(5.51299 + 8.25077i) q^{7} +(-5.61314 + 2.32504i) q^{9} +(3.92006 - 19.7075i) q^{11} +(6.04210 - 6.04210i) q^{13} +(3.79942 - 9.17260i) q^{15} +(-9.53691 + 14.0729i) q^{17} +(30.9271 + 12.8104i) q^{19} +(11.9991 + 11.9991i) q^{21} +(-2.39325 - 0.476047i) q^{23} +(-3.33203 - 8.04424i) q^{25} +(-21.4357 + 14.3229i) q^{27} +(-40.2359 - 26.8848i) q^{29} +(1.14641 + 5.76339i) q^{31} -34.3617i q^{33} +57.6114 q^{35} +(-70.9963 + 14.1221i) q^{37} +(8.11818 - 12.1497i) q^{39} +(17.1190 + 25.6203i) q^{41} +(-32.5769 + 13.4938i) q^{43} +(-6.88155 + 34.5959i) q^{45} +(-23.9254 + 23.9254i) q^{47} +(-18.9307 + 45.7027i) q^{49} +(-11.3005 + 26.7852i) q^{51} +(-15.3566 - 6.36093i) q^{53} +(-82.4902 - 82.4902i) q^{55} +(56.1455 + 11.1680i) q^{57} +(12.7032 + 30.6683i) q^{59} +(42.9508 - 28.6988i) q^{61} +(-50.1285 - 33.4948i) q^{63} +(-9.67829 - 48.6561i) q^{65} +45.9884i q^{67} -4.17283 q^{69} +(18.0674 - 3.59383i) q^{71} +(-11.7344 + 17.5617i) q^{73} +(-8.27228 - 12.3803i) q^{75} +(184.213 - 76.3036i) q^{77} +(6.09511 - 30.6422i) q^{79} +(7.49089 - 7.49089i) q^{81} +(-12.0724 + 29.1454i) q^{83} +(37.1731 + 91.4302i) q^{85} +(-76.4539 - 31.6683i) q^{87} +(2.49113 + 2.49113i) q^{89} +(83.1620 + 16.5419i) q^{91} +(3.84557 + 9.28402i) q^{93} +(161.596 - 107.975i) q^{95} +(50.5412 + 33.7705i) q^{97} +(23.8168 + 119.735i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9 + 24 * q^11 - 48 * q^13 - 96 * q^15 - 40 * q^19 + 80 * q^21 + 48 * q^23 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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