LMFDB - Embedded newform 136.3.t.a.41.3

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:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			41.3
Character	$\chi$	$=$	136.41
Dual form			136.3.t.a.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.265432 - 0.397247i) q^{3} +(0.373441 + 1.87742i) q^{5} +(-2.10274 + 10.5712i) q^{7} +(3.35680 + 8.10403i) q^{9} +O(q^{10})$	\(q+(0.265432 - 0.397247i) q^{3} +(0.373441 + 1.87742i) q^{5} +(-2.10274 + 10.5712i) q^{7} +(3.35680 + 8.10403i) q^{9} +(5.50678 - 3.67951i) q^{11} +(17.0115 - 17.0115i) q^{13} +(0.844922 + 0.349978i) q^{15} +(-0.468896 + 16.9935i) q^{17} +(-12.7274 + 30.7266i) q^{19} +(3.64124 + 3.64124i) q^{21} +(-14.4543 - 21.6324i) q^{23} +(19.7118 - 8.16488i) q^{25} +(8.32757 + 1.65646i) q^{27} +(3.90826 - 0.777401i) q^{29} +(-30.8342 - 20.6027i) q^{31} -3.16422i q^{33} -20.6318 q^{35} +(-9.24177 + 13.8313i) q^{37} +(-2.24237 - 11.2732i) q^{39} +(13.9213 - 69.9870i) q^{41} +(-0.281866 - 0.680485i) q^{43} +(-13.9611 + 9.32849i) q^{45} +(-9.20162 + 9.20162i) q^{47} +(-62.0583 - 25.7054i) q^{49} +(6.62618 + 4.69690i) q^{51} +(10.1255 - 24.4451i) q^{53} +(8.96444 + 8.96444i) q^{55} +(8.82780 + 13.2117i) q^{57} +(81.0988 - 33.5922i) q^{59} +(-44.2798 - 8.80781i) q^{61} +(-92.7277 + 18.4447i) q^{63} +(38.2904 + 25.5848i) q^{65} -33.0049i q^{67} -12.4300 q^{69} +(49.6401 - 74.2917i) q^{71} +(17.0394 + 85.6629i) q^{73} +(1.98866 - 9.99766i) q^{75} +(27.3175 + 65.9503i) q^{77} +(-17.2534 + 11.5284i) q^{79} +(-52.9546 + 52.9546i) q^{81} +(128.971 + 53.4216i) q^{83} +(-32.0790 + 5.46577i) q^{85} +(0.728557 - 1.75889i) q^{87} +(-67.9449 - 67.9449i) q^{89} +(144.061 + 215.602i) q^{91} +(-16.3688 + 6.78016i) q^{93} +(-62.4395 - 12.4200i) q^{95} +(58.6948 - 11.6751i) q^{97} +(48.3041 + 32.2757i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) $ 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	$ 32 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} + 112 q^{25} - 80 q^{27} + 56 q^{29} - 24 q^{31} - 96 q^{35} + 48 q^{37} - 72 q^{39} - 160 q^{41} + 112 q^{43} - 504 q^{45} + 48 q^{47} + 208 q^{49} - 400 q^{51} + 304 q^{53} - 368 q^{55} - 264 q^{57} + 192 q^{59} - 288 q^{61} + 56 q^{63} + 8 q^{65} + 32 q^{69} + 352 q^{71} - 184 q^{73} + 24 q^{75} + 688 q^{77} - 424 q^{79} + 312 q^{81} + 600 q^{83} - 512 q^{85} + 1336 q^{87} - 144 q^{89} - 24 q^{91} + 944 q^{93} - 256 q^{95} + 416 q^{97} + 128 q^{99}+O(q^{100}) $ 32 * 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 + 112 * q^25 - 80 * q^27 + 56 * q^29 - 24 * q^31 - 96 * q^35 + 48 * q^37 - 72 * q^39 - 160 * q^41 + 112 * q^43 - 504 * q^45 + 48 * q^47 + 208 * q^49 - 400 * q^51 + 304 * q^53 - 368 * q^55 - 264 * q^57 + 192 * q^59 - 288 * q^61 + 56 * q^63 + 8 * q^65 + 32 * q^69 + 352 * q^71 - 184 * q^73 + 24 * q^75 + 688 * q^77 - 424 * q^79 + 312 * q^81 + 600 * q^83 - 512 * q^85 + 1336 * q^87 - 144 * q^89 - 24 * q^91 + 944 * q^93 - 256 * q^95 + 416 * q^97 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{16}\right)$

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
$3$	0.265432	−	0.397247i	0.0884774	−	0.132416i	−0.784591	−	0.620014i	$-0.787127\pi$
$3$	0.265432	−	0.397247i	0.0884774	−	0.132416i	0.873068	+	0.487598i	$0.162127\pi$
$4$		0			0
$5$	0.373441	+	1.87742i	0.0746883	+	0.375483i	0.999993	−	0.00374117i	$-0.00119085\pi$
$5$	0.373441	+	1.87742i	0.0746883	+	0.375483i	−0.925305	+	0.379224i	$0.876191\pi$
$6$		0			0
$7$	−2.10274	+	10.5712i	−0.300391	+	1.51017i	0.475733	+	0.879589i	$0.342183\pi$
$7$	−2.10274	+	10.5712i	−0.300391	+	1.51017i	−0.776125	+	0.630579i	$0.782817\pi$
$8$		0			0
$9$	3.35680	+	8.10403i	0.372978	+	0.900448i
$10$		0			0
$11$	5.50678	−	3.67951i	0.500617	−	0.334501i	−0.279489	−	0.960149i	$-0.590165\pi$
$11$	5.50678	−	3.67951i	0.500617	−	0.334501i	0.780106	+	0.625648i	$0.215165\pi$
$12$		0			0
$13$	17.0115	−	17.0115i	1.30857	−	1.30857i	0.386130	−	0.922444i	$-0.373812\pi$
$13$	17.0115	−	17.0115i	1.30857	−	1.30857i	0.922444	−	0.386130i	$-0.126188\pi$
$14$		0			0
$15$	0.844922	+	0.349978i	0.0563281	+	0.0233319i
$16$		0			0
$17$	−0.468896	+	16.9935i	−0.0275821	+	0.999620i
$17$	−0.468896	+	16.9935i	−0.0275821	+	0.999620i
$18$		0			0
$19$	−12.7274	+	30.7266i	−0.669861	+	1.61719i	0.111979	+	0.993711i	$0.464281\pi$
$19$	−12.7274	+	30.7266i	−0.669861	+	1.61719i	−0.781841	+	0.623478i	$0.785719\pi$
$20$		0			0
$21$	3.64124	+	3.64124i	0.173392	+	0.173392i
$22$		0			0
$23$	−14.4543	−	21.6324i	−0.628447	−	0.940537i	−0.999927	−	0.0120962i	$-0.996150\pi$
$23$	−14.4543	−	21.6324i	−0.628447	−	0.940537i	0.371480	−	0.928441i	$-0.378850\pi$
$24$		0			0
$25$	19.7118	−	8.16488i	0.788470	−	0.326595i
$26$		0			0
$27$	8.32757	+	1.65646i	0.308429	+	0.0613503i
$28$		0			0
$29$	3.90826	−	0.777401i	0.134768	−	0.0268069i	−0.127246	−	0.991871i	$-0.540614\pi$
$29$	3.90826	−	0.777401i	0.134768	−	0.0268069i	0.262013	+	0.965064i	$0.415614\pi$
$30$		0			0
$31$	−30.8342	−	20.6027i	−0.994651	−	0.664604i	−0.0520911	−	0.998642i	$-0.516589\pi$
$31$	−30.8342	−	20.6027i	−0.994651	−	0.664604i	−0.942560	+	0.334038i	$0.891589\pi$
$32$		0			0
$33$		−	3.16422i		−	0.0958853i
$34$		0			0
$35$	−20.6318			−0.589479
$36$		0			0
$37$	−9.24177	+	13.8313i	−0.249777	+	0.373818i	−0.935078	−	0.354442i	$-0.884671\pi$
$37$	−9.24177	+	13.8313i	−0.249777	+	0.373818i	0.685301	+	0.728260i	$0.259671\pi$
$38$		0			0
$39$	−2.24237	−	11.2732i	−0.0574966	−	0.289055i
$40$		0			0
$41$	13.9213	−	69.9870i	0.339543	−	1.70700i	−0.313424	−	0.949613i	$-0.601476\pi$
$41$	13.9213	−	69.9870i	0.339543	−	1.70700i	0.652968	−	0.757386i	$-0.273524\pi$
$42$		0			0
$43$	−0.281866	−	0.680485i	−0.00655502	−	0.0158252i	0.920568	−	0.390582i	$-0.127726\pi$
$43$	−0.281866	−	0.680485i	−0.00655502	−	0.0158252i	−0.927123	+	0.374757i	$0.877726\pi$
$44$		0			0
$45$	−13.9611	+	9.32849i	−0.310246	+	0.207300i
$46$		0			0
$47$	−9.20162	+	9.20162i	−0.195779	+	0.195779i	−0.798188	−	0.602409i	$-0.794208\pi$
$47$	−9.20162	+	9.20162i	−0.195779	+	0.195779i	0.602409	+	0.798188i	$0.294208\pi$
$48$		0			0
$49$	−62.0583	−	25.7054i	−1.26650	−	0.524600i
$50$		0			0
$51$	6.62618	+	4.69690i	0.129925	+	0.0920960i
$52$		0			0
$53$	10.1255	−	24.4451i	0.191047	−	0.461228i	−0.799111	−	0.601184i	$-0.794696\pi$
$53$	10.1255	−	24.4451i	0.191047	−	0.461228i	0.990158	+	0.139956i	$0.0446961\pi$
$54$		0			0
$55$	8.96444	+	8.96444i	0.162990	+	0.162990i
$56$		0			0
$57$	8.82780	+	13.2117i	0.154874	+	0.231785i
$58$		0			0
$59$	81.0988	−	33.5922i	1.37456	−	0.569360i	0.431536	−	0.902096i	$-0.357972\pi$
$59$	81.0988	−	33.5922i	1.37456	−	0.569360i	0.943020	+	0.332736i	$0.107972\pi$
$60$		0			0
$61$	−44.2798	−	8.80781i	−0.725899	−	0.144390i	−0.181709	−	0.983352i	$-0.558163\pi$
$61$	−44.2798	−	8.80781i	−0.725899	−	0.144390i	−0.544190	+	0.838962i	$0.683163\pi$
$62$		0			0
$63$	−92.7277	+	18.4447i	−1.47187	+	0.292773i
$64$		0			0
$65$	38.2904	+	25.5848i	0.589083	+	0.393613i
$66$		0			0
$67$		−	33.0049i		−	0.492611i	−0.969192	−	0.246305i	$-0.920783\pi$
$67$		−	33.0049i		−	0.492611i	0.969192	−	0.246305i	$-0.0792166\pi$
$68$		0			0
$69$	−12.4300			−0.180145
$70$		0			0
$71$	49.6401	−	74.2917i	0.699156	−	1.04636i	−0.296660	−	0.954983i	$-0.595873\pi$
$71$	49.6401	−	74.2917i	0.699156	−	1.04636i	0.995816	−	0.0913783i	$-0.0291272\pi$
$72$		0			0
$73$	17.0394	+	85.6629i	0.233417	+	1.17346i	0.902638	+	0.430401i	$0.141628\pi$
$73$	17.0394	+	85.6629i	0.233417	+	1.17346i	−0.669221	+	0.743063i	$0.733372\pi$
$74$		0			0
$75$	1.98866	−	9.99766i	0.0265155	−	0.133302i
$76$		0			0
$77$	27.3175	+	65.9503i	0.354773	+	0.856497i
$78$		0			0
$79$	−17.2534	+	11.5284i	−0.218397	+	0.145928i	−0.659957	−	0.751304i	$-0.729425\pi$
$79$	−17.2534	+	11.5284i	−0.218397	+	0.145928i	0.441559	+	0.897232i	$0.354425\pi$
$80$		0			0
$81$	−52.9546	+	52.9546i	−0.653760	+	0.653760i
$82$		0			0
$83$	128.971	+	53.4216i	1.55387	+	0.643634i	0.984011	−	0.178110i	$-0.0569981\pi$
$83$	128.971	+	53.4216i	1.55387	+	0.643634i	0.569858	+	0.821743i	$0.306998\pi$
$84$		0			0
$85$	−32.0790	+	5.46577i	−0.377400	+	0.0643032i
$86$		0			0
$87$	0.728557	−	1.75889i	0.00837422	−	0.0202172i
$88$		0			0
$89$	−67.9449	−	67.9449i	−0.763426	−	0.763426i	0.213514	−	0.976940i	$-0.431509\pi$
$89$	−67.9449	−	67.9449i	−0.763426	−	0.763426i	−0.976940	+	0.213514i	$0.931509\pi$
$90$		0			0
$91$	144.061	+	215.602i	1.58308	+	2.36925i
$92$		0			0
$93$	−16.3688	+	6.78016i	−0.176008	+	0.0729050i
$94$		0			0
$95$	−62.4395	−	12.4200i	−0.657258	−	0.130737i
$96$		0			0
$97$	58.6948	−	11.6751i	0.605101	−	0.120362i	0.116975	−	0.993135i	$-0.462680\pi$
$97$	58.6948	−	11.6751i	0.605101	−	0.120362i	0.488127	+	0.872773i	$0.337680\pi$
$98$		0			0
$99$	48.3041	+	32.2757i	0.487920	+	0.326018i
$100$		0			0
$101$		−	103.479i		−	1.02454i	−0.858823	−	0.512272i	$-0.828804\pi$
$101$		−	103.479i		−	1.02454i	0.858823	−	0.512272i	$-0.171196\pi$
$102$		0			0
$103$	78.0109			0.757388			0.378694	−	0.925522i	$-0.376373\pi$
$103$	78.0109			0.757388			0.378694	+	0.925522i	$0.376373\pi$
$104$		0			0
$105$	−5.47633	+	8.19591i	−0.0521555	+	0.0780563i
$106$		0			0
$107$	−16.8408	−	84.6645i	−0.157391	−	0.791257i	−0.976146	−	0.217114i	$-0.930336\pi$
$107$	−16.8408	−	84.6645i	−0.157391	−	0.791257i	0.818755	−	0.574142i	$-0.194664\pi$
$108$		0			0
$109$	−11.2232	+	56.4230i	−0.102965	+	0.517642i	0.894536	+	0.446996i	$0.147506\pi$
$109$	−11.2232	+	56.4230i	−0.102965	+	0.517642i	−0.997501	+	0.0706462i	$0.977494\pi$
$110$		0			0
$111$	3.04138	+	7.34253i	0.0273998	+	0.0661490i
$112$		0			0
$113$	−47.5393	+	31.7647i	−0.420701	+	0.281104i	−0.747848	−	0.663870i	$-0.768913\pi$
$113$	−47.5393	+	31.7647i	−0.420701	+	0.281104i	0.327147	+	0.944974i	$0.393913\pi$
$114$		0			0
$115$	35.2151	−	35.2151i	0.306218	−	0.306218i
$116$		0			0
$117$	194.966	+	80.7574i	1.66637	+	0.690234i
$118$		0			0
$119$	−178.656	−	40.6897i	−1.50131	−	0.341931i
$120$		0			0
$121$	−29.5189	+	71.2649i	−0.243958	+	0.588966i
$122$		0			0
$123$	−24.1070	−	24.1070i	−0.195992	−	0.195992i
$124$		0			0
$125$	49.2768	+	73.7480i	0.394215	+	0.589984i
$126$		0			0
$127$	71.8403	−	29.7572i	0.565672	−	0.234309i	−0.0814737	−	0.996675i	$-0.525963\pi$
$127$	71.8403	−	29.7572i	0.565672	−	0.234309i	0.647145	+	0.762367i	$0.275963\pi$
$128$		0			0
$129$	−0.345137	−	0.0686520i	−0.00267548	−	0.000532186i
$130$		0			0
$131$	−7.88727	+	1.56888i	−0.0602082	+	0.0119762i	−0.225102	−	0.974335i	$-0.572272\pi$
$131$	−7.88727	+	1.56888i	−0.0602082	+	0.0119762i	0.164894	+	0.986311i	$0.447272\pi$
$132$		0			0
$133$	−298.054	−	199.153i	−2.24101	−	1.49739i
$134$		0			0
$135$			16.2529i			0.120392i
$136$		0			0
$137$	23.5715			0.172055			0.0860273	−	0.996293i	$-0.472583\pi$
$137$	23.5715			0.172055			0.0860273	+	0.996293i	$0.472583\pi$
$138$		0			0
$139$	−51.1133	+	76.4965i	−0.367722	+	0.550334i	−0.968478	−	0.249098i	$-0.919866\pi$
$139$	−51.1133	+	76.4965i	−0.367722	+	0.550334i	0.600757	+	0.799432i	$0.294866\pi$
$140$		0			0
$141$	1.21291	+	6.09773i	0.00860222	+	0.0432463i
$142$		0			0
$143$	31.0845	−	156.272i	0.217374	−	1.09281i
$144$		0			0
$145$	2.91901	+	7.04711i	0.0201311	+	0.0486008i
$146$		0			0
$147$	−26.6837	+	17.8295i	−0.181522	+	0.121289i
$148$		0			0
$149$	88.3896	−	88.3896i	0.593219	−	0.593219i	−0.345281	−	0.938500i	$-0.612216\pi$
$149$	88.3896	−	88.3896i	0.593219	−	0.593219i	0.938500	+	0.345281i	$0.112216\pi$
$150$		0			0
$151$	−119.598	−	49.5393i	−0.792042	−	0.328075i	−0.0502780	−	0.998735i	$-0.516011\pi$
$151$	−119.598	−	49.5393i	−0.792042	−	0.328075i	−0.741764	+	0.670661i	$0.766011\pi$
$152$		0			0
$153$	−139.290	+	53.2439i	−0.910393	+	0.348000i
$154$		0			0
$155$	27.1652	−	65.5825i	0.175259	−	0.423113i
$156$		0			0
$157$	57.7710	+	57.7710i	0.367968	+	0.367968i	0.866736	−	0.498767i	$-0.166214\pi$
$157$	57.7710	+	57.7710i	0.367968	+	0.367968i	−0.498767	+	0.866736i	$0.666214\pi$
$158$		0			0
$159$	−7.02311	−	10.5108i	−0.0441705	−	0.0661058i
$160$		0			0
$161$	259.073	−	107.312i	1.60915	−	0.666532i
$162$		0			0
$163$	−46.3909	−	9.22773i	−0.284607	−	0.0566118i	0.0507224	−	0.998713i	$-0.483848\pi$
$163$	−46.3909	−	9.22773i	−0.284607	−	0.0566118i	−0.335329	+	0.942101i	$0.608848\pi$
$164$		0			0
$165$	5.94055	−	1.18165i	0.0360033	−	0.00716151i
$166$		0			0
$167$	−75.3091	−	50.3200i	−0.450953	−	0.301317i	0.309276	−	0.950972i	$-0.399913\pi$
$167$	−75.3091	−	50.3200i	−0.450953	−	0.301317i	−0.760229	+	0.649655i	$0.774913\pi$
$168$		0			0
$169$		−	409.780i		−	2.42473i
$170$		0			0
$171$	−291.732			−1.70604
$172$		0			0
$173$	94.0015	−	140.683i	0.543362	−	0.813198i	−0.453591	−	0.891210i	$-0.649857\pi$
$173$	94.0015	−	140.683i	0.543362	−	0.813198i	0.996952	+	0.0780120i	$0.0248573\pi$
$174$		0			0
$175$	44.8637	+	225.545i	0.256364	+	1.28883i
$176$		0			0
$177$	8.18182	−	41.1328i	0.0462249	−	0.232388i
$178$		0			0
$179$	27.8092	+	67.1373i	0.155359	+	0.375069i	0.982325	−	0.187182i	$-0.0599355\pi$
$179$	27.8092	+	67.1373i	0.155359	+	0.375069i	−0.826967	+	0.562251i	$0.809935\pi$
$180$		0			0
$181$	−236.027	+	157.708i	−1.30402	+	0.871316i	−0.996770	−	0.0803138i	$-0.974408\pi$
$181$	−236.027	+	157.708i	−1.30402	+	0.871316i	−0.307247	+	0.951630i	$0.599408\pi$
$182$		0			0
$183$	−15.2522	+	15.2522i	−0.0833452	+	0.0833452i
$184$		0			0
$185$	−29.4183	−	12.1855i	−0.159018	−	0.0658674i
$186$		0			0
$187$	59.9458	+	95.3050i	0.320566	+	0.509652i
$188$		0			0
$189$	−35.0214	+	84.5492i	−0.185299	+	0.447350i
$190$		0			0
$191$	−37.6324	−	37.6324i	−0.197028	−	0.197028i	0.601696	−	0.798725i	$-0.294492\pi$
$191$	−37.6324	−	37.6324i	−0.197028	−	0.197028i	−0.798725	+	0.601696i	$0.794492\pi$
$192$		0			0
$193$	67.4583	+	100.959i	0.349525	+	0.523101i	0.964024	−	0.265817i	$-0.0856416\pi$
$193$	67.4583	+	100.959i	0.349525	+	0.523101i	−0.614499	+	0.788918i	$0.710642\pi$
$194$		0			0
$195$	20.3270	−	8.41972i	0.104241	−	0.0431780i
$196$		0			0
$197$	−18.9297	−	3.76535i	−0.0960899	−	0.0191135i	0.146811	−	0.989165i	$-0.453099\pi$
$197$	−18.9297	−	3.76535i	−0.0960899	−	0.0191135i	−0.242901	+	0.970051i	$0.578099\pi$
$198$		0			0
$199$	−293.722	+	58.4248i	−1.47599	+	0.293592i	−0.866489	−	0.499195i	$-0.833629\pi$
$199$	−293.722	+	58.4248i	−1.47599	+	0.293592i	−0.609498	+	0.792788i	$0.708629\pi$
$200$		0			0
$201$	−13.1111	−	8.76057i	−0.0652294	−	0.0435849i
$202$		0			0
$203$			42.9496i			0.211574i
$204$		0			0
$205$	136.593			0.666309
$206$		0			0
$207$	126.789	−	189.753i	0.612508	−	0.916683i
$208$		0			0
$209$	42.9721	+	216.035i	0.205608	+	1.03366i
$210$		0			0
$211$	59.3560	−	298.403i	0.281308	−	1.41423i	−0.538998	−	0.842307i	$-0.681197\pi$
$211$	59.3560	−	298.403i	0.281308	−	1.41423i	0.820306	−	0.571925i	$-0.193803\pi$
$212$		0			0
$213$	−16.3361	−	39.4388i	−0.0766952	−	0.185159i
$214$		0			0
$215$	1.17229	−	0.783301i	0.00545252	−	0.00364326i
$216$		0			0
$217$	282.631	−	282.631i	1.30245	−	1.30245i
$218$		0			0
$219$	38.5522	+	15.9688i	0.176037	+	0.0729170i
$220$		0			0
$221$	281.108	+	297.062i	1.27198	+	1.34417i
$222$		0			0
$223$	8.53867	−	20.6142i	0.0382900	−	0.0924402i	−0.903578	−	0.428424i	$-0.859069\pi$
$223$	8.53867	−	20.6142i	0.0382900	−	0.0924402i	0.941868	+	0.335984i	$0.109069\pi$
$224$		0			0
$225$	132.337	+	132.337i	0.588164	+	0.588164i
$226$		0			0
$227$	96.2583	+	144.061i	0.424046	+	0.634629i	0.980562	−	0.196207i	$-0.0628626\pi$
$227$	96.2583	+	144.061i	0.424046	+	0.634629i	−0.556517	+	0.830836i	$0.687863\pi$
$228$		0			0
$229$	178.614	−	73.9844i	0.779975	−	0.323076i	0.0430693	−	0.999072i	$-0.486286\pi$
$229$	178.614	−	73.9844i	0.779975	−	0.323076i	0.736905	+	0.675996i	$0.236286\pi$
$230$		0			0
$231$	33.4495	+	6.65352i	0.144803	+	0.0288031i
$232$		0			0
$233$	−217.735	+	43.3101i	−0.934484	+	0.185880i	−0.638772	−	0.769396i	$-0.720557\pi$
$233$	−217.735	+	43.3101i	−0.934484	+	0.185880i	−0.295713	+	0.955277i	$0.595557\pi$
$234$		0			0
$235$	−20.7115	−	13.8390i	−0.0881342	−	0.0588894i
$236$		0			0
$237$			9.91386i			0.0418306i
$238$		0			0
$239$	−288.072			−1.20532			−0.602662	−	0.797997i	$-0.705893\pi$
$239$	−288.072			−1.20532			−0.602662	+	0.797997i	$0.705893\pi$
$240$		0			0
$241$	−148.653	+	222.476i	−0.616819	+	0.923135i	−1.00000		0.000538115i	$-0.999829\pi$
$241$	−148.653	+	222.476i	−0.616819	+	0.923135i	0.383181	+	0.923673i	$0.374829\pi$
$242$		0			0
$243$	21.8883	+	110.040i	0.0900755	+	0.452840i
$244$		0			0
$245$	25.0846	−	126.109i	0.102386	−	0.514729i
$246$		0			0
$247$	306.193	+	739.215i	1.23965	+	2.99277i
$248$		0			0
$249$	55.4547	−	37.0536i	0.222710	−	0.148810i
$250$		0			0
$251$	−89.2062	+	89.2062i	−0.355403	+	0.355403i	−0.862115	−	0.506712i	$-0.830861\pi$
$251$	−89.2062	+	89.2062i	−0.355403	+	0.355403i	0.506712	+	0.862115i	$0.330861\pi$
$252$		0			0
$253$	−159.193	−	65.9399i	−0.629222	−	0.260632i
$254$		0			0
$255$	−6.34354	+	14.1941i	−0.0248766	+	0.0556632i
$256$		0			0
$257$	−163.366	+	394.401i	−0.635666	+	1.53463i	0.196732	+	0.980457i	$0.436967\pi$
$257$	−163.366	+	394.401i	−0.635666	+	1.53463i	−0.832399	+	0.554177i	$0.813033\pi$
$258$		0			0
$259$	−126.780	−	126.780i	−0.489498	−	0.489498i
$260$		0			0
$261$	19.4193	+	29.0631i	0.0744035	+	0.111353i
$262$		0			0
$263$	295.151	−	122.256i	1.12225	−	0.464851i	0.257109	−	0.966382i	$-0.417230\pi$
$263$	295.151	−	122.256i	1.12225	−	0.464851i	0.865139	+	0.501532i	$0.167230\pi$
$264$		0			0
$265$	49.6748	+	9.88094i	0.187452	+	0.0372866i
$266$		0			0
$267$	−45.0257	+	8.95617i	−0.168636	+	0.0335437i
$268$		0			0
$269$	−203.053	−	135.676i	−0.754845	−	0.504371i	0.117613	−	0.993059i	$-0.462476\pi$
$269$	−203.053	−	135.676i	−0.754845	−	0.504371i	−0.872459	+	0.488688i	$0.837476\pi$
$270$		0			0
$271$			97.8004i			0.360887i	0.983585	+	0.180444i	$0.0577533\pi$
$271$			97.8004i			0.360887i	−0.983585	+	0.180444i	$0.942247\pi$
$272$		0			0
$273$	123.886			0.453794
$274$		0			0
$275$	78.5056	−	117.492i	0.285475	−	0.427243i
$276$		0			0
$277$	−45.1350	−	226.909i	−0.162942	−	0.819165i	−0.972640	−	0.232318i	$-0.925369\pi$
$277$	−45.1350	−	226.909i	−0.162942	−	0.819165i	0.809698	−	0.586847i	$-0.199631\pi$
$278$		0			0
$279$	63.4611	−	319.040i	0.227459	−	1.14351i
$280$		0			0
$281$	−51.6369	−	124.663i	−0.183761	−	0.443639i	0.804975	−	0.593309i	$-0.202179\pi$
$281$	−51.6369	−	124.663i	−0.183761	−	0.443639i	−0.988736	+	0.149670i	$0.952179\pi$
$282$		0			0
$283$	253.922	−	169.665i	0.897250	−	0.599524i	−0.0191367	−	0.999817i	$-0.506092\pi$
$283$	253.922	−	169.665i	0.897250	−	0.599524i	0.916387	+	0.400293i	$0.131092\pi$
$284$		0			0
$285$	−21.5073	+	21.5073i	−0.0754641	+	0.0754641i
$286$		0			0
$287$	710.572	+	294.329i	2.47586	+	1.02554i
$288$		0			0
$289$	−288.560	−	15.9364i	−0.998478	−	0.0551433i
$290$		0			0
$291$	10.9416	−	26.4153i	0.0376000	−	0.0907743i
$292$		0			0
$293$	168.378	+	168.378i	0.574670	+	0.574670i	0.933430	−	0.358760i	$-0.116800\pi$
$293$	168.378	+	168.378i	0.574670	+	0.574670i	−0.358760	+	0.933430i	$0.616800\pi$
$294$		0			0
$295$	93.3523	+	139.712i	0.316448	+	0.473598i
$296$		0			0
$297$	51.9531	−	21.5197i	0.174926	−	0.0724568i
$298$		0			0
$299$	−613.887	−	122.110i	−2.05313	−	0.408393i
$300$		0			0
$301$	7.78622	−	1.54877i	0.0258678	−	0.00514543i
$302$		0			0
$303$	−41.1067	−	27.4667i	−0.135666	−	0.0906490i
$304$		0			0
$305$		−	86.4209i		−	0.283347i
$306$		0			0
$307$	44.6453			0.145424			0.0727122	−	0.997353i	$-0.476835\pi$
$307$	44.6453			0.145424			0.0727122	+	0.997353i	$0.476835\pi$
$308$		0			0
$309$	20.7066	−	30.9896i	0.0670117	−	0.100290i
$310$		0			0
$311$	−62.4353	−	313.883i	−0.200757	−	1.00927i	−0.941379	−	0.337350i	$-0.890469\pi$
$311$	−62.4353	−	313.883i	−0.200757	−	1.00927i	0.740623	−	0.671921i	$-0.234531\pi$
$312$		0			0
$313$	−65.3551	+	328.563i	−0.208802	+	1.04972i	0.724129	+	0.689665i	$0.242242\pi$
$313$	−65.3551	+	328.563i	−0.208802	+	1.04972i	−0.932931	+	0.360055i	$0.882758\pi$
$314$		0			0
$315$	−69.2567	−	167.200i	−0.219862	−	0.530795i
$316$		0			0
$317$	−443.228	+	296.155i	−1.39819	+	0.934244i	−0.398339	+	0.917238i	$0.630413\pi$
$317$	−443.228	+	296.155i	−1.39819	+	0.934244i	−0.999855	+	0.0170055i	$0.994587\pi$
$318$		0			0
$319$	18.6615	−	18.6615i	0.0584999	−	0.0584999i
$320$		0			0
$321$	−38.1028	−	15.7827i	−0.118700	−	0.0491673i
$322$		0			0
$323$	−516.185	−	230.691i	−1.59810	−	0.714212i
$324$		0			0
$325$	196.429	−	474.222i	0.604398	−	1.45915i
$326$		0			0
$327$	19.4349	+	19.4349i	0.0594339	+	0.0594339i
$328$		0			0
$329$	−77.9234	−	116.621i	−0.236849	−	0.354470i
$330$		0			0
$331$	258.006	−	106.869i	0.779474	−	0.322869i	0.0427705	−	0.999085i	$-0.486382\pi$
$331$	258.006	−	106.869i	0.779474	−	0.322869i	0.736703	+	0.676216i	$0.236382\pi$
$332$		0			0
$333$	−143.112	−	28.4667i	−0.429765	−	0.0854857i
$334$		0			0
$335$	61.9640	−	12.3254i	0.184967	−	0.0367922i
$336$		0			0
$337$	−203.212	−	135.782i	−0.603004	−	0.402914i	0.216256	−	0.976337i	$-0.430615\pi$
$337$	−203.212	−	135.782i	−0.603004	−	0.402914i	−0.819260	+	0.573422i	$0.805615\pi$
$338$		0			0
$339$			27.3162i			0.0805788i
$340$		0			0
$341$	−245.605			−0.720250
$342$		0			0
$343$	108.812	−	162.849i	0.317236	−	0.474778i
$344$		0			0
$345$	−4.64188	−	23.3363i	−0.0134547	−	0.0676415i
$346$		0			0
$347$	−36.1831	+	181.905i	−0.104274	+	0.524221i	0.892976	+	0.450105i	$0.148613\pi$
$347$	−36.1831	+	181.905i	−0.104274	+	0.524221i	−0.997250	+	0.0741157i	$0.976387\pi$
$348$		0			0
$349$	66.9162	+	161.550i	0.191737	+	0.462894i	0.990288	−	0.139034i	$-0.0443996\pi$
$349$	66.9162	+	161.550i	0.191737	+	0.462894i	−0.798551	+	0.601928i	$0.794400\pi$
$350$		0			0
$351$	169.843	−	113.485i	0.483883	−	0.323320i
$352$		0			0
$353$	−139.607	+	139.607i	−0.395487	+	0.395487i	−0.876638	−	0.481151i	$-0.840219\pi$
$353$	−139.607	+	139.607i	−0.395487	+	0.395487i	0.481151	+	0.876638i	$0.340219\pi$
$354$		0			0
$355$	158.014	+	65.4516i	0.445110	+	0.184371i
$356$		0			0
$357$	−63.5849	+	60.1702i	−0.178109	+	0.168544i
$358$		0			0
$359$	−129.099	+	311.672i	−0.359607	+	0.868168i	0.635748	+	0.771896i	$0.280692\pi$
$359$	−129.099	+	311.672i	−0.359607	+	0.868168i	−0.995355	+	0.0962713i	$0.969308\pi$
$360$		0			0
$361$	−526.871	−	526.871i	−1.45948	−	1.45948i
$362$		0			0
$363$	20.4745	+	30.6423i	0.0564036	+	0.0844140i
$364$		0			0
$365$	−154.462	+	63.9801i	−0.423183	+	0.175288i
$366$		0			0
$367$	54.7504	+	10.8905i	0.149184	+	0.0296745i	0.269117	−	0.963107i	$-0.413268\pi$
$367$	54.7504	+	10.8905i	0.149184	+	0.0296745i	−0.119933	+	0.992782i	$0.538268\pi$
$368$		0			0
$369$	613.907	−	122.114i	1.66371	−	0.330932i
$370$		0			0
$371$	237.122	+	158.440i	0.639143	+	0.427062i
$372$		0			0
$373$		−	327.522i		−	0.878075i	−0.898469	−	0.439038i	$-0.855319\pi$
$373$		−	327.522i		−	0.878075i	0.898469	−	0.439038i	$-0.144681\pi$
$374$		0			0
$375$	42.3758			0.113002
$376$		0			0
$377$	53.2605	−	79.7099i	0.141274	−	0.211432i
$378$		0			0
$379$	−96.7322	−	486.306i	−0.255230	−	1.28313i	−0.869461	−	0.494002i	$-0.835534\pi$
$379$	−96.7322	−	486.306i	−0.255230	−	1.28313i	0.614231	−	0.789127i	$-0.289466\pi$
$380$		0			0
$381$	7.24775	−	36.4369i	0.0190230	−	0.0956349i
$382$		0			0
$383$	−109.953	−	265.451i	−0.287085	−	0.693084i	0.712882	−	0.701284i	$-0.247390\pi$
$383$	−109.953	−	265.451i	−0.287085	−	0.693084i	−0.999966	+	0.00820042i	$0.997390\pi$
$384$		0			0
$385$	−113.615	+	75.9148i	−0.295103	+	0.197181i
$386$		0			0
$387$	4.56850	−	4.56850i	0.0118049	−	0.0118049i
$388$		0			0
$389$	−439.801	−	182.172i	−1.13059	−	0.468307i	−0.262611	−	0.964902i	$-0.584584\pi$
$389$	−439.801	−	182.172i	−1.13059	−	0.468307i	−0.867983	+	0.496595i	$0.834584\pi$
$390$		0			0
$391$	374.388	−	235.486i	0.957513	−	0.602266i
$392$		0			0
$393$	−1.47030	+	3.54963i	−0.00374123	+	0.00903213i
$394$		0			0
$395$	−28.0866	−	28.0866i	−0.0711054	−	0.0711054i
$396$		0			0
$397$	359.417	+	537.905i	0.905331	+	1.35492i	0.934731	+	0.355356i	$0.115640\pi$
$397$	359.417	+	537.905i	0.905331	+	1.35492i	−0.0293995	+	0.999568i	$0.509360\pi$
$398$		0			0
$399$	−158.226	+	65.5395i	−0.396557	+	0.164259i
$400$		0			0
$401$	330.510	+	65.7426i	0.824215	+	0.163947i	0.589140	−	0.808031i	$-0.299467\pi$
$401$	330.510	+	65.7426i	0.824215	+	0.163947i	0.235075	+	0.971977i	$0.424467\pi$
$402$		0			0
$403$	−875.017	+	174.052i	−2.17126	+	0.431890i
$404$		0			0
$405$	−119.193	−	79.6424i	−0.294304	−	0.196648i
$406$		0			0
$407$			110.171i			0.270691i
$408$		0			0
$409$	290.067			0.709211			0.354606	−	0.935016i	$-0.384615\pi$
$409$	290.067			0.709211			0.354606	+	0.935016i	$0.384615\pi$
$410$		0			0
$411$	6.25663	−	9.36371i	0.0152229	−	0.0227827i
$412$		0			0
$413$	184.580	+	927.946i	0.446925	+	2.24684i
$414$		0			0
$415$	−52.1314	+	262.082i	−0.125618	+	0.631523i
$416$		0			0
$417$	16.8209	+	40.6093i	0.0403379	+	0.0973843i
$418$		0			0
$419$	−414.289	+	276.819i	−0.988757	+	0.660666i	−0.941076	−	0.338196i	$-0.890183\pi$
$419$	−414.289	+	276.819i	−0.988757	+	0.660666i	−0.0476814	+	0.998863i	$0.515183\pi$
$420$		0			0
$421$	−53.7087	+	53.7087i	−0.127574	+	0.127574i	−0.768011	−	0.640437i	$-0.778753\pi$
$421$	−53.7087	+	53.7087i	−0.127574	+	0.127574i	0.640437	+	0.768011i	$0.278753\pi$
$422$		0			0
$423$	−105.458	−	43.6822i	−0.249310	−	0.103268i
$424$		0			0
$425$	129.507	+	338.801i	0.304723	+	0.797178i
$426$		0			0
$427$	186.218	−	449.570i	0.436107	−	1.05286i
$428$		0			0
$429$	−53.8280	−	53.8280i	−0.125473	−	0.125473i
$430$		0			0
$431$	288.768	+	432.172i	0.669995	+	1.00272i	0.998308	+	0.0581497i	$0.0185201\pi$
$431$	288.768	+	432.172i	0.669995	+	1.00272i	−0.328313	+	0.944569i	$0.606480\pi$
$432$		0			0
$433$	12.2561	−	5.07664i	0.0283050	−	0.0117243i	−0.368486	−	0.929633i	$-0.620124\pi$
$433$	12.2561	−	5.07664i	0.0283050	−	0.0117243i	0.396791	+	0.917909i	$0.370124\pi$
$434$		0			0
$435$	3.57425	+	0.710962i	0.00821666	+	0.00163439i
$436$		0			0
$437$	848.653	−	168.808i	1.94200	−	0.386287i
$438$		0			0
$439$	516.086	+	344.838i	1.17560	+	0.785508i	0.980739	−	0.195324i	$-0.0625758\pi$
$439$	516.086	+	344.838i	1.17560	+	0.785508i	0.194857	+	0.980832i	$0.437576\pi$
$440$		0			0
$441$		−	589.210i		−	1.33608i
$442$		0			0
$443$	642.505			1.45035			0.725175	−	0.688564i	$-0.241759\pi$
$443$	642.505			1.45035			0.725175	+	0.688564i	$0.241759\pi$
$444$		0			0
$445$	102.187	−	152.934i	0.229635	−	0.343673i
$446$		0			0
$447$	−11.6511	−	58.5740i	−0.0260651	−	0.131038i
$448$		0			0
$449$	49.3910	−	248.306i	0.110002	−	0.553019i	−0.886000	−	0.463686i	$-0.846527\pi$
$449$	49.3910	−	248.306i	0.110002	−	0.553019i	0.996002	−	0.0893328i	$-0.0284735\pi$
$450$		0			0
$451$	−180.857	−	436.626i	−0.401012	−	0.968130i
$452$		0			0
$453$	−51.4246	+	34.3608i	−0.113520	+	0.0758517i
$454$		0			0
$455$	−350.976	+	350.976i	−0.771377	+	0.771377i
$456$		0			0
$457$	−254.389	−	105.372i	−0.556651	−	0.230572i	0.0865796	−	0.996245i	$-0.472406\pi$
$457$	−254.389	−	105.372i	−0.556651	−	0.230572i	−0.643231	+	0.765673i	$0.722406\pi$
$458$		0			0
$459$	−32.0538	+	140.738i	−0.0698341	+	0.306619i
$460$		0			0
$461$	−25.2863	+	61.0466i	−0.0548510	+	0.132422i	−0.948929	−	0.315488i	$-0.897832\pi$
$461$	−25.2863	+	61.0466i	−0.0548510	+	0.132422i	0.894078	+	0.447910i	$0.147832\pi$
$462$		0			0
$463$	−35.6885	−	35.6885i	−0.0770810	−	0.0770810i	0.667515	−	0.744596i	$-0.267358\pi$
$463$	−35.6885	−	35.6885i	−0.0770810	−	0.0770810i	−0.744596	+	0.667515i	$0.767358\pi$
$464$		0			0
$465$	−18.8420	−	28.1990i	−0.0405203	−	0.0606430i
$466$		0			0
$467$	−420.363	+	174.120i	−0.900134	+	0.372848i	−0.784272	−	0.620418i	$-0.786963\pi$
$467$	−420.363	+	174.120i	−0.900134	+	0.372848i	−0.115862	+	0.993265i	$0.536963\pi$
$468$		0			0
$469$	348.901	+	69.4007i	0.743925	+	0.147976i
$470$		0			0
$471$	38.2837	−	7.61510i	0.0812817	−	0.0161679i
$472$		0			0
$473$	−4.05603	−	2.71015i	−0.00857511	−	0.00572971i
$474$		0			0
$475$			709.592i			1.49388i
$476$		0			0
$477$	232.093			0.486568
$478$		0			0
$479$	−322.559	+	482.744i	−0.673401	+	1.00782i	0.324675	+	0.945825i	$0.394745\pi$
$479$	−322.559	+	482.744i	−0.673401	+	1.00782i	−0.998077	+	0.0619907i	$0.980255\pi$
$480$		0			0
$481$	78.0744	+	392.506i	0.162317	+	0.816021i
$482$		0			0
$483$	26.1371	−	131.400i	0.0541141	−	0.272050i
$484$		0			0
$485$	43.8382	+	105.835i	0.0903879	+	0.218216i
$486$		0			0
$487$	268.281	−	179.260i	0.550886	−	0.368090i	−0.248757	−	0.968566i	$-0.580022\pi$
$487$	268.281	−	179.260i	0.550886	−	0.368090i	0.799643	+	0.600476i	$0.205022\pi$
$488$		0			0
$489$	−15.9793	+	15.9793i	−0.0326776	+	0.0326776i
$490$		0			0
$491$	6.63585	+	2.74866i	0.0135150	+	0.00559809i	0.389431	−	0.921056i	$-0.372672\pi$
$491$	6.63585	+	2.74866i	0.0135150	+	0.00559809i	−0.375916	+	0.926654i	$0.622672\pi$
$492$		0			0
$493$	11.3782	+	66.7796i	0.0230795	+	0.135456i
$494$		0			0
$495$	−42.5563	+	102.740i	−0.0859723	+	0.207555i
$496$		0			0
$497$	680.971	+	680.971i	1.37016	+	1.37016i
$498$		0			0
$499$	−192.793	−	288.536i	−0.386360	−	0.578228i	0.586406	−	0.810017i	$-0.300542\pi$
$499$	−192.793	−	288.536i	−0.386360	−	0.578228i	−0.972766	+	0.231789i	$0.925542\pi$
$500$		0			0
$501$	−39.9789	+	16.5598i	−0.0797983	+	0.0330535i
$502$		0			0
$503$	320.681	+	63.7874i	0.637537	+	0.126814i	0.503267	−	0.864131i	$-0.332131\pi$
$503$	320.681	+	63.7874i	0.637537	+	0.126814i	0.134270	+	0.990945i	$0.457131\pi$
$504$		0			0
$505$	194.273	−	38.6433i	0.384699	−	0.0765214i
$506$		0			0
$507$	−162.784	−	108.769i	−0.321073	−	0.214534i
$508$		0			0
$509$		−	228.751i		−	0.449414i	−0.974426	−	0.224707i	$-0.927858\pi$
$509$		−	228.751i		−	0.449414i	0.974426	−	0.224707i	$-0.0721424\pi$
$510$		0			0
$511$	−941.388			−1.84225
$512$		0			0
$513$	−156.885	+	234.796i	−0.305819	+	0.457691i
$514$		0			0
$515$	29.1325	+	146.459i	0.0565680	+	0.284386i
$516$		0			0
$517$	−16.8138	+	84.5288i	−0.0325219	+	0.163499i
$518$		0			0
$519$	−30.9350	−	74.6837i	−0.0596050	−	0.143899i
$520$		0			0
$521$	149.591	−	99.9538i	0.287124	−	0.191850i	−0.403665	−	0.914907i	$-0.632264\pi$
$521$	149.591	−	99.9538i	0.287124	−	0.191850i	0.690788	+	0.723057i	$0.257264\pi$
$522$		0			0
$523$	4.37150	−	4.37150i	0.00835850	−	0.00835850i	−0.702915	−	0.711274i	$-0.748119\pi$
$523$	4.37150	−	4.37150i	0.00835850	−	0.00835850i	0.711274	+	0.702915i	$0.248119\pi$
$524$		0			0
$525$	101.506	+	42.0450i	0.193344	+	0.0800856i
$526$		0			0
$527$	364.571	−	514.321i	0.691786	−	0.975941i
$528$		0			0
$529$	−56.5931	+	136.628i	−0.106981	+	0.258276i
$530$		0			0
$531$	544.465	+	544.465i	1.02536	+	1.02536i
$532$		0			0
$533$	−953.760	−	1427.40i	−1.78942	−	2.67805i
$534$		0			0
$535$	152.661	−	63.2344i	0.285348	−	0.118195i
$536$		0			0
$537$	34.0516	+	6.77328i	0.0634108	+	0.0126132i
$538$		0			0
$539$	−436.325	+	86.7904i	−0.809508	+	0.161021i
$540$		0			0
$541$	344.826	+	230.405i	0.637386	+	0.425888i	0.831834	−	0.555025i	$-0.187291\pi$
$541$	344.826	+	230.405i	0.637386	+	0.425888i	−0.194447	+	0.980913i	$0.562291\pi$
$542$		0			0
$543$			135.622i			0.249764i
$544$		0			0
$545$	−110.121			−0.202056
$546$		0			0
$547$	232.255	−	347.595i	0.424598	−	0.635456i	−0.556070	−	0.831136i	$-0.687691\pi$
$547$	232.255	−	347.595i	0.424598	−	0.635456i	0.980668	+	0.195679i	$0.0626912\pi$
$548$		0			0
$549$	−77.2598	−	388.411i	−0.140728	−	0.707489i
$550$		0			0
$551$	−25.8550	+	129.982i	−0.0469237	+	0.235901i
$552$		0			0
$553$	−85.5889	−	206.630i	−0.154772	−	0.373653i
$554$		0			0
$555$	−12.6492	+	8.45194i	−0.0227914	+	0.0152287i
$556$		0			0
$557$	678.412	−	678.412i	1.21798	−	1.21798i	0.249635	−	0.968340i	$-0.419689\pi$
$557$	678.412	−	678.412i	1.21798	−	1.21798i	0.968340	−	0.249635i	$-0.0803108\pi$
$558$		0			0
$559$	−16.3710	−	6.78109i	−0.0292862	−	0.0121307i
$560$		0			0
$561$	53.7712	+	1.48369i	0.0958489	+	0.00264472i
$562$		0			0
$563$	40.9909	−	98.9608i	0.0728080	−	0.175774i	−0.883286	−	0.468835i	$-0.844674\pi$
$563$	40.9909	−	98.9608i	0.0728080	−	0.175774i	0.956094	+	0.293061i	$0.0946739\pi$
$564$		0			0
$565$	−77.3887	−	77.3887i	−0.136971	−	0.136971i
$566$		0			0
$567$	−448.443	−	671.142i	−0.790905	−	1.18367i
$568$		0			0
$569$	−438.626	+	181.685i	−0.770872	+	0.319305i	−0.733225	−	0.679986i	$-0.761986\pi$
$569$	−438.626	+	181.685i	−0.770872	+	0.319305i	−0.0376462	+	0.999291i	$0.511986\pi$
$570$		0			0
$571$	−481.393	−	95.7550i	−0.843069	−	0.167697i	−0.245382	−	0.969426i	$-0.578913\pi$
$571$	−481.393	−	95.7550i	−0.843069	−	0.167697i	−0.597687	+	0.801729i	$0.703913\pi$
$572$		0			0
$573$	−24.9382	+	4.96053i	−0.0435223	+	0.00865711i
$574$		0			0
$575$	−461.545	−	308.394i	−0.802686	−	0.536338i
$576$		0			0
$577$			460.619i			0.798300i	0.916886	+	0.399150i	$0.130695\pi$
$577$			460.619i			0.798300i	−0.916886	+	0.399150i	$0.869305\pi$
$578$		0			0
$579$	58.0111			0.100192
$580$		0			0
$581$	−835.922	+	1251.05i	−1.43876	+	2.15326i
$582$		0			0
$583$	−34.1872	−	171.871i	−0.0586401	−	0.294804i
$584$		0			0
$585$	−78.8070	+	396.190i	−0.134713	+	0.677247i
$586$		0			0
$587$	153.696	+	371.056i	0.261834	+	0.632122i	0.999052	−	0.0435322i	$-0.0138611\pi$
$587$	153.696	+	371.056i	0.261834	+	0.632122i	−0.737218	+	0.675655i	$0.763861\pi$
$588$		0			0
$589$	1025.49	−	685.210i	1.74107	−	1.16334i
$590$		0			0
$591$	−6.52033	+	6.52033i	−0.0110327	+	0.0110327i
$592$		0			0
$593$	−285.847	−	118.402i	−0.482036	−	0.199666i	0.128414	−	0.991721i	$-0.459011\pi$
$593$	−285.847	−	118.402i	−0.482036	−	0.199666i	−0.610450	+	0.792055i	$0.709011\pi$
$594$		0			0
$595$	9.67415	−	350.606i	0.0162591	−	0.589254i
$596$		0			0
$597$	−54.7540	+	132.188i	−0.0917153	+	0.221420i
$598$		0			0
$599$	−710.965	−	710.965i	−1.18692	−	1.18692i	−0.977914	−	0.209006i	$-0.932977\pi$
$599$	−710.965	−	710.965i	−1.18692	−	1.18692i	−0.209006	−	0.977914i	$-0.567023\pi$
$600$		0			0
$601$	−215.893	−	323.107i	−0.359224	−	0.537616i	0.607207	−	0.794544i	$-0.292290\pi$
$601$	−215.893	−	323.107i	−0.359224	−	0.537616i	−0.966431	+	0.256927i	$0.917290\pi$
$602$		0			0
$603$	267.473	−	110.791i	0.443570	−	0.183733i
$604$		0			0
$605$	−144.817	−	28.8060i	−0.239368	−	0.0476132i
$606$		0			0
$607$	−341.087	+	67.8463i	−0.561922	+	0.111773i	−0.467875	−	0.883795i	$-0.654980\pi$
$607$	−341.087	+	67.8463i	−0.561922	+	0.111773i	−0.0940468	+	0.995568i	$0.529980\pi$
$608$		0			0
$609$	17.0616	+	11.4002i	0.0280158	+	0.0187195i
$610$		0			0
$611$			313.066i			0.512383i
$612$		0			0
$613$	192.992			0.314832			0.157416	−	0.987532i	$-0.449684\pi$
$613$	192.992			0.314832			0.157416	+	0.987532i	$0.449684\pi$
$614$		0			0
$615$	36.2563	−	54.2614i	0.0589533	−	0.0882299i
$616$		0			0
$617$	−198.328	−	997.060i	−0.321439	−	1.61598i	−0.716679	−	0.697403i	$-0.754339\pi$
$617$	−198.328	−	997.060i	−0.321439	−	1.61598i	0.395241	−	0.918578i	$-0.370661\pi$
$618$		0			0
$619$	43.6399	−	219.393i	0.0705007	−	0.354431i	−0.929392	−	0.369095i	$-0.879668\pi$
$619$	43.6399	−	219.393i	0.0705007	−	0.354431i	0.999892	+	0.0146637i	$0.00466778\pi$
$620$		0			0
$621$	−84.5360	−	204.088i	−0.136129	−	0.328644i
$622$		0			0
$623$	861.129	−	575.388i	1.38223	−	0.923576i
$624$		0			0
$625$	257.114	−	257.114i	0.411383	−	0.411383i
$626$		0			0
$627$	97.2256	+	40.2721i	0.155065	+	0.0642299i
$628$		0			0
$629$	−230.709	−	163.536i	−0.366787	−	0.259993i
$630$		0			0
$631$	−240.805	+	581.354i	−0.381624	+	0.921322i	0.610028	+	0.792380i	$0.291158\pi$
$631$	−240.805	+	581.354i	−0.381624	+	0.921322i	−0.991652	+	0.128942i	$0.958842\pi$
$632$		0			0
$633$	−102.785	−	102.785i	−0.162377	−	0.162377i
$634$		0			0
$635$	82.6948	+	123.762i	0.130228	+	0.194900i
$636$		0			0
$637$	−1492.99	+	618.416i	−2.34378	+	0.970826i
$638$		0			0
$639$	768.694	+	152.903i	1.20296	+	0.239284i
$640$		0			0
$641$	−146.678	+	29.1761i	−0.228827	+	0.0455165i	−0.308172	−	0.951331i	$-0.599717\pi$
$641$	−146.678	+	29.1761i	−0.228827	+	0.0455165i	0.0793449	+	0.996847i	$0.474717\pi$
$642$		0			0
$643$	990.083	+	661.552i	1.53979	+	1.02885i	0.979712	+	0.200410i	$0.0642273\pi$
$643$	990.083	+	661.552i	1.53979	+	1.02885i	0.560074	+	0.828443i	$0.310773\pi$
$644$		0			0
$645$		−	0.673603i		−	0.00104435i
$646$		0			0
$647$	−669.549			−1.03485			−0.517426	−	0.855728i	$-0.673110\pi$
$647$	−669.549			−1.03485			−0.517426	+	0.855728i	$0.673110\pi$
$648$		0			0
$649$	322.991	−	483.389i	0.497674	−	0.744822i
$650$		0			0
$651$	−37.2551	−	187.294i	−0.0572275	−	0.287702i
$652$		0			0
$653$	−149.250	+	750.328i	−0.228560	+	1.14905i	0.680618	+	0.732639i	$0.261712\pi$
$653$	−149.250	+	750.328i	−0.228560	+	1.14905i	−0.909177	+	0.416409i	$0.863288\pi$
$654$		0			0
$655$	−5.89087	−	14.2218i	−0.00899369	−	0.0217127i
$656$		0			0
$657$	−637.017	+	425.641i	−0.969584	+	0.647856i
$658$		0			0
$659$	335.360	−	335.360i	0.508892	−	0.508892i	−0.405295	−	0.914186i	$-0.632831\pi$
$659$	335.360	−	335.360i	0.508892	−	0.508892i	0.914186	+	0.405295i	$0.132831\pi$
$660$		0			0
$661$	308.086	+	127.614i	0.466091	+	0.193061i	0.603354	−	0.797473i	$-0.293831\pi$
$661$	308.086	+	127.614i	0.466091	+	0.193061i	−0.137263	+	0.990535i	$0.543831\pi$
$662$		0			0
$663$	192.622	−	32.8198i	0.290531	−	0.0495020i
$664$		0			0
$665$	262.588	−	633.943i	0.394869	−	0.953298i
$666$		0			0
$667$	−73.3081	−	73.3081i	−0.109907	−	0.109907i
$668$		0			0
$669$	−5.92249	−	8.86363i	−0.00885275	−	0.0132491i
$670$		0			0
$671$	−276.248	+	114.426i	−0.411696	+	0.170530i
$672$		0			0
$673$	−345.950	−	68.8138i	−0.514042	−	0.102249i	−0.0687485	−	0.997634i	$-0.521901\pi$
$673$	−345.950	−	68.8138i	−0.514042	−	0.102249i	−0.445293	+	0.895385i	$0.646901\pi$
$674$		0			0
$675$	177.676	−	35.3419i	0.263224	−	0.0523584i
$676$		0			0
$677$	124.723	+	83.3373i	0.184229	+	0.123098i	0.644265	−	0.764802i	$-0.277163\pi$
$677$	124.723	+	83.3373i	0.184229	+	0.123098i	−0.460036	+	0.887900i	$0.652163\pi$
$678$		0			0
$679$			645.024i			0.949961i
$680$		0			0
$681$	82.7778			0.121553
$682$		0			0
$683$	290.407	−	434.625i	0.425193	−	0.636347i	−0.555588	−	0.831458i	$-0.687507\pi$
$683$	290.407	−	434.625i	0.425193	−	0.636347i	0.980781	+	0.195111i	$0.0625068\pi$
$684$		0			0
$685$	8.80256	+	44.2535i	0.0128505	+	0.0646036i
$686$		0			0
$687$	18.0198	−	90.5918i	0.0262298	−	0.131866i
$688$		0			0
$689$	−243.597	−	588.096i	−0.353552	−	0.853550i
$690$		0			0
$691$	779.506	−	520.849i	1.12808	−	0.753762i	0.155852	−	0.987780i	$-0.450188\pi$
$691$	779.506	−	520.849i	1.12808	−	0.753762i	0.972232	+	0.234019i	$0.0751877\pi$
$692$		0			0
$693$	−442.764	+	442.764i	−0.638909	+	0.638909i
$694$		0			0
$695$	−162.704	−	67.3940i	−0.234106	−	0.0969698i
$696$		0			0
$697$	1182.80	+	269.388i	1.69698	+	0.386497i
$698$		0			0
$699$	−40.5890	+	97.9905i	−0.0580672	+	0.140187i
$700$		0			0
$701$	100.524	+	100.524i	0.143401	+	0.143401i	0.775163	−	0.631762i	$-0.217668\pi$
$701$	100.524	+	100.524i	0.143401	+	0.143401i	−0.631762	+	0.775163i	$0.717668\pi$
$702$		0			0
$703$	−307.365	−	460.004i	−0.437218	−	0.654344i
$704$		0			0
$705$	−10.9950	+	4.55428i	−0.0155958	+	0.00645998i
$706$		0			0
$707$	1093.90	+	217.589i	1.54723	+	0.307764i
$708$		0			0
$709$	−347.794	+	69.1805i	−0.490541	+	0.0975747i	−0.434162	−	0.900835i	$-0.642956\pi$
$709$	−347.794	+	69.1805i	−0.490541	+	0.0975747i	−0.0563790	+	0.998409i	$0.517956\pi$
$710$		0			0
$711$	−151.342	−	101.124i	−0.212858	−	0.142227i
$712$		0			0
$713$			964.813i			1.35317i
$714$		0			0
$715$	304.996			0.426569
$716$		0			0
$717$	−76.4637	+	114.436i	−0.106644	+	0.159604i
$718$		0			0
$719$	186.174	+	935.962i	0.258935	+	1.30175i	0.863156	+	0.504938i	$0.168485\pi$
$719$	186.174	+	935.962i	0.258935	+	1.30175i	−0.604221	+	0.796817i	$0.706515\pi$
$720$		0			0
$721$	−164.037	+	824.668i	−0.227513	+	1.14378i
$722$		0			0
$723$	48.9204	+	118.104i	0.0676631	+	0.163353i
$724$		0			0
$725$	70.6912	−	47.2344i	0.0975052	−	0.0651509i
$726$		0			0
$727$	−829.401	+	829.401i	−1.14085	+	1.14085i	−0.152560	+	0.988294i	$0.548752\pi$
$727$	−829.401	+	829.401i	−1.14085	+	1.14085i	−0.988294	+	0.152560i	$0.951248\pi$
$728$		0			0
$729$	−573.173	−	237.416i	−0.786246	−	0.325674i
$730$		0			0
$731$	11.6960	−	4.47082i	0.0160000	−	0.00611603i
$732$		0			0
$733$	−417.754	+	1008.55i	−0.569924	+	1.37592i	0.331695	+	0.943387i	$0.392380\pi$
$733$	−417.754	+	1008.55i	−0.569924	+	1.37592i	−0.901619	+	0.432532i	$0.857620\pi$
$734$		0			0
$735$	−43.4381	−	43.4381i	−0.0590994	−	0.0590994i
$736$		0			0
$737$	−121.442	−	181.751i	−0.164779	−	0.246609i
$738$		0			0
$739$	−1105.89	+	458.076i	−1.49647	+	0.619859i	−0.972714	−	0.232008i	$-0.925470\pi$
$739$	−1105.89	+	458.076i	−1.49647	+	0.619859i	−0.523758	+	0.851867i	$0.675470\pi$
$740$		0			0
$741$	374.925	+	74.5772i	0.505971	+	0.100644i
$742$		0			0
$743$	1289.35	−	256.468i	1.73533	−	0.345180i	0.776711	−	0.629857i	$-0.216886\pi$
$743$	1289.35	−	256.468i	1.73533	−	0.345180i	0.958623	+	0.284677i	$0.0918864\pi$
$744$		0			0
$745$	198.952	+	132.936i	0.267050	+	0.178437i
$746$		0			0
$747$			1224.51i			1.63924i
$748$		0			0
$749$	930.415			1.24221
$750$		0			0
$751$	359.724	−	538.365i	0.478993	−	0.716864i	−0.510749	−	0.859730i	$-0.670632\pi$
$751$	359.724	−	538.365i	0.478993	−	0.716864i	0.989742	+	0.142866i	$0.0456318\pi$
$752$		0			0
$753$	11.7587	+	59.1151i	0.0156158	+	0.0785061i
$754$		0			0
$755$	48.3429	−	243.036i	0.0640303	−	0.321902i
$756$		0			0
$757$	−242.200	−	584.722i	−0.319947	−	0.772421i	−0.999256	−	0.0385681i	$-0.987720\pi$
$757$	−242.200	−	584.722i	−0.319947	−	0.772421i	0.679309	−	0.733852i	$-0.262280\pi$
$758$		0			0
$759$	−68.4495	+	45.7365i	−0.0901837	+	0.0602588i
$760$		0			0
$761$	−341.821	+	341.821i	−0.449173	+	0.449173i	−0.895080	−	0.445906i	$-0.852881\pi$
$761$	−341.821	+	341.821i	−0.449173	+	0.449173i	0.445906	+	0.895080i	$0.352881\pi$
$762$		0			0
$763$	−572.858	−	237.286i	−0.750797	−	0.310990i
$764$		0			0
$765$	−151.978	−	241.622i	−0.198664	−	0.315846i
$766$		0			0
$767$	808.157	−	1951.06i	1.05366	−	2.54376i
$768$		0			0
$769$	744.788	+	744.788i	0.968515	+	0.968515i	0.999519	−	0.0310039i	$-0.00987042\pi$
$769$	744.788	+	744.788i	0.968515	+	0.968515i	−0.0310039	+	0.999519i	$0.509870\pi$
$770$		0			0
$771$	113.312	+	169.584i	0.146968	+	0.219953i
$772$		0			0
$773$	1086.03	−	449.849i	1.40496	−	0.581952i	0.453924	−	0.891040i	$-0.350024\pi$
$773$	1086.03	−	449.849i	1.40496	−	0.581952i	0.951033	+	0.309088i	$0.100024\pi$
$774$		0			0
$775$	−776.014	−	154.359i	−1.00131	−	0.199173i
$776$		0			0
$777$	−84.0145	+	16.7115i	−0.108127	+	0.0215077i
$778$		0			0
$779$	1973.28	+	1318.50i	2.53309	+	1.69256i
$780$		0			0
$781$		−	591.760i		−	0.757695i
$782$		0			0
$783$	33.8340			0.0432108
$784$		0			0
$785$	−86.8862	+	130.034i	−0.110683	+	0.165649i
$786$		0			0
$787$	−102.066	−	513.122i	−0.129690	−	0.651998i	−0.989867	−	0.142001i	$-0.954646\pi$
$787$	−102.066	−	513.122i	−0.129690	−	0.651998i	0.860176	−	0.509997i	$-0.170354\pi$
$788$		0			0
$789$	29.7769	−	149.699i	0.0377401	−	0.189732i
$790$		0			0
$791$	−235.828	−	569.339i	−0.298139	−	0.719771i
$792$		0			0
$793$	−903.099	+	603.431i	−1.13884	+	0.760947i
$794$		0			0
$795$	17.1105	−	17.1105i	0.0215226	−	0.0215226i
$796$		0			0
$797$	−722.944	−	299.453i	−0.907081	−	0.375725i	−0.120143	−	0.992757i	$-0.538335\pi$
$797$	−722.944	−	299.453i	−0.907081	−	0.375725i	−0.786939	+	0.617031i	$0.788335\pi$
$798$		0			0
$799$	−152.053	−	160.683i	−0.190305	−	0.201105i
$800$		0			0
$801$	322.550	−	778.705i	0.402685	−	0.972167i
$802$		0			0
$803$	409.030	+	409.030i	0.509378	+	0.509378i
$804$		0			0
$805$	298.217	+	446.313i	0.370456	+	0.554427i
$806$		0			0
$807$	−107.794	+	44.6497i	−0.133573	+	0.0553280i
$808$		0			0
$809$	916.549	+	182.313i	1.13294	+	0.225356i	0.725731	−	0.687979i	$-0.241502\pi$
$809$	916.549	+	182.313i	1.13294	+	0.225356i	0.407209	+	0.913335i	$0.366502\pi$
$810$		0			0
$811$	1560.86	−	310.474i	1.92461	−	0.382829i	0.924611	−	0.380913i	$-0.124390\pi$
$811$	1560.86	−	310.474i	1.92461	−	0.382829i	0.999998	−	0.00191501i	$-0.000609567\pi$
$812$		0			0
$813$	38.8510	+	25.9594i	0.0477872	+	0.0319304i
$814$		0			0
$815$		−	90.5411i		−	0.111093i
$816$		0			0
$817$	24.4964			0.0299833
$818$		0			0
$819$	−1263.66	+	1891.20i	−1.54293	+	2.30916i
$820$		0			0
$821$	−114.241	−	574.329i	−0.139149	−	0.699548i	−0.985870	−	0.167511i	$-0.946427\pi$
$821$	−114.241	−	574.329i	−0.139149	−	0.699548i	0.846721	−	0.532037i	$-0.178573\pi$
$822$		0			0
$823$	−234.940	+	1181.12i	−0.285468	+	1.43515i	0.525869	+	0.850566i	$0.323740\pi$
$823$	−234.940	+	1181.12i	−0.285468	+	1.43515i	−0.811337	+	0.584579i	$0.801260\pi$
$824$		0			0
$825$	−25.8354	−	62.3723i	−0.0313157	−	0.0756027i
$826$		0			0
$827$	−1268.38	+	847.508i	−1.53372	+	1.02480i	−0.552136	+	0.833754i	$0.686187\pi$
$827$	−1268.38	+	847.508i	−1.53372	+	1.02480i	−0.981582	+	0.191044i	$0.938813\pi$
$828$		0			0
$829$	−802.324	+	802.324i	−0.967821	+	0.967821i	−0.999498	−	0.0316768i	$-0.989915\pi$
$829$	−802.324	+	802.324i	−0.967821	+	0.967821i	0.0316768	+	0.999498i	$0.489915\pi$
$830$		0			0
$831$	−102.119	−	42.2992i	−0.122887	−	0.0509015i
$832$		0			0
$833$	465.924	−	1042.54i	0.559333	−	1.25154i
$834$		0			0
$835$	66.3480	−	160.178i	0.0794586	−	0.191830i
$836$		0			0
$837$	−222.646	−	222.646i	−0.266005	−	0.266005i
$838$		0			0
$839$	−230.548	−	345.040i	−0.274790	−	0.411252i	0.668248	−	0.743939i	$-0.267045\pi$
$839$	−230.548	−	345.040i	−0.274790	−	0.411252i	−0.943037	+	0.332687i	$0.892045\pi$
$840$		0			0
$841$	−762.313	+	315.760i	−0.906436	+	0.375458i
$842$		0			0
$843$	−63.2280	−	12.5768i	−0.0750035	−	0.0149191i
$844$		0			0
$845$	769.328	−	153.029i	0.910447	−	0.181099i
$846$		0			0
$847$	−691.283	−	461.901i	−0.816155	−	0.545337i
$848$		0			0
$849$		−	145.904i		−	0.171854i
$850$		0			0
$851$	432.786			0.508562
$852$		0			0
$853$	295.138	−	441.705i	0.345999	−	0.517825i	−0.617131	−	0.786861i	$-0.711705\pi$
$853$	295.138	−	441.705i	0.345999	−	0.517825i	0.963130	+	0.269036i	$0.0867050\pi$
$854$		0			0
$855$	−108.945	−	547.703i	−0.127421	−	0.640588i
$856$		0			0
$857$	27.6435	−	138.973i	0.0322561	−	0.162163i	−0.961300	−	0.275504i	$-0.911155\pi$
$857$	27.6435	−	138.973i	0.0322561	−	0.162163i	0.993556	+	0.113341i	$0.0361553\pi$
$858$		0			0
$859$	−295.209	−	712.697i	−0.343666	−	0.829682i	−0.997339	−	0.0729052i	$-0.976773\pi$
$859$	−295.209	−	712.697i	−0.343666	−	0.829682i	0.653673	−	0.756777i	$-0.273227\pi$
$860$		0			0
$861$	305.530	−	204.149i	0.354855	−	0.237106i
$862$		0			0
$863$	−676.655	+	676.655i	−0.784073	+	0.784073i	−0.980515	−	0.196442i	$-0.937061\pi$
$863$	−676.655	+	676.655i	−0.784073	+	0.784073i	0.196442	+	0.980515i	$0.437061\pi$
$864$		0			0
$865$	299.225	+	123.943i	0.345925	+	0.143287i
$866$		0			0
$867$	−82.9239	+	110.400i	−0.0956446	+	0.127335i
$868$		0			0
$869$	−52.5920	+	126.968i	−0.0605201	+	0.146108i
$870$		0			0
$871$	−561.462	−	561.462i	−0.644618	−	0.644618i
$872$		0			0
$873$	291.642	+	436.474i	0.334069	+	0.499970i
$874$		0			0
$875$	−883.220	+	365.842i	−1.00939	+	0.418105i
$876$		0			0
$877$	−174.679	−	34.7459i	−0.199178	−	0.0396190i	0.0944928	−	0.995526i	$-0.469877\pi$
$877$	−174.679	−	34.7459i	−0.199178	−	0.0396190i	−0.293671	+	0.955907i	$0.594877\pi$
$878$		0			0
$879$	111.581	−	22.1948i	0.126941	−	0.0252501i
$880$		0			0
$881$	−1121.60	−	749.432i	−1.27310	−	0.850660i	−0.279127	−	0.960254i	$-0.590045\pi$
$881$	−1121.60	−	749.432i	−1.27310	−	0.850660i	−0.993976	+	0.109594i	$0.965045\pi$
$882$		0			0
$883$		−	968.110i		−	1.09639i	−0.836352	−	0.548194i	$-0.815316\pi$
$883$		−	968.110i		−	1.09639i	0.836352	−	0.548194i	$-0.184684\pi$
$884$		0			0
$885$	80.2787			0.0907104
$886$		0			0
$887$	121.859	−	182.375i	0.137384	−	0.205609i	−0.756398	−	0.654112i	$-0.773043\pi$
$887$	121.859	−	182.375i	0.137384	−	0.205609i	0.893781	+	0.448503i	$0.148043\pi$
$888$		0			0
$889$	163.508	+	822.009i	0.183923	+	0.924644i
$890$		0			0
$891$	−96.7622	+	486.456i	−0.108600	+	0.545967i
$892$		0			0
$893$	−165.622	−	399.847i	−0.185467	−	0.447757i
$894$		0			0
$895$	−115.660	+	77.2813i	−0.129229	+	0.0863478i
$896$		0			0
$897$	−211.453	+	211.453i	−0.235734	+	0.235734i
$898$		0			0
$899$	−136.524	−	56.5503i	−0.151863	−	0.0629035i
$900$		0			0
$901$	410.660	+	183.530i	0.455783	+	0.203696i
$902$		0			0
$903$	1.45147	−	3.50415i	0.00160738	−	0.00388056i
$904$		0			0
$905$	−384.226	−	384.226i	−0.424559	−	0.424559i
$906$		0			0
$907$	−639.883	−	957.653i	−0.705494	−	1.05585i	−0.995117	−	0.0987056i	$-0.968530\pi$
$907$	−639.883	−	957.653i	−0.705494	−	1.05585i	0.289623	−	0.957141i	$-0.406470\pi$
$908$		0			0
$909$	838.597	−	347.358i	0.922549	−	0.382132i
$910$		0			0
$911$	−683.819	−	136.020i	−0.750624	−	0.149308i	−0.195071	−	0.980789i	$-0.562494\pi$
$911$	−683.819	−	136.020i	−0.750624	−	0.149308i	−0.555554	+	0.831481i	$0.687494\pi$
$912$		0			0
$913$	906.781	−	180.370i	0.993189	−	0.197558i
$914$		0			0
$915$	−34.3305	−	22.9389i	−0.0375196	−	0.0250698i
$916$		0			0
$917$		−	86.6767i		−	0.0945221i
$918$		0			0
$919$	783.867			0.852957			0.426478	−	0.904498i	$-0.359754\pi$
$919$	783.867			0.852957			0.426478	+	0.904498i	$0.359754\pi$
$920$		0			0
$921$	11.8503	−	17.7352i	0.0128668	−	0.0192565i
$922$		0			0
$923$	−419.359	−	2108.26i	−0.454344	−	2.28414i
$924$		0			0
$925$	−69.2407	+	348.097i	−0.0748548	+	0.376321i
$926$		0			0
$927$	261.867	+	632.203i	0.282489	+	0.681988i
$928$		0			0
$929$	1264.33	−	844.800i	1.36096	−	0.909365i	0.361228	−	0.932478i	$-0.382358\pi$
$929$	1264.33	−	844.800i	1.36096	−	0.909365i	0.999733	+	0.0231127i	$0.00735764\pi$
$930$		0			0
$931$	1579.68	−	1579.68i	1.69675	−	1.69675i
$932$		0			0
$933$	−141.262	−	58.5125i	−0.151406	−	0.0627144i
$934$		0			0
$935$	−156.541	+	148.134i	−0.167423	+	0.158432i
$936$		0			0
$937$	171.031	−	412.905i	0.182530	−	0.440667i	−0.805956	−	0.591975i	$-0.798348\pi$
$937$	171.031	−	412.905i	0.182530	−	0.440667i	0.988487	+	0.151308i	$0.0483485\pi$
$938$		0			0
$939$	113.173	+	113.173i	0.120525	+	0.120525i
$940$		0			0
$941$	−810.536	−	1213.05i	−0.861355	−	1.28911i	−0.955931	−	0.293592i	$-0.905149\pi$
$941$	−810.536	−	1213.05i	−0.861355	−	1.28911i	0.0945754	−	0.995518i	$-0.469851\pi$
$942$		0			0
$943$	−1715.20	+	710.461i	−1.81888	+	0.753405i
$944$		0			0
$945$	−171.812	−	34.1756i	−0.181812	−	0.0361647i
$946$		0			0
$947$	−920.267	+	183.052i	−0.971771	+	0.193297i	−0.655353	−	0.755323i	$-0.727480\pi$
$947$	−920.267	+	183.052i	−0.971771	+	0.193297i	−0.316418	+	0.948620i	$0.602480\pi$
$948$		0			0
$949$	1747.12	+	1167.39i	1.84101	+	1.23012i
$950$		0			0
$951$			254.680i			0.267802i
$952$		0			0
$953$	−297.586			−0.312263			−0.156131	−	0.987736i	$-0.549902\pi$
$953$	−297.586			−0.312263			−0.156131	+	0.987736i	$0.549902\pi$
$954$		0			0
$955$	56.5982	−	84.7053i	0.0592652	−	0.0886966i
$956$		0			0
$957$	−2.45986	−	12.3666i	−0.00257039	−	0.0129222i
$958$		0			0
$959$	−49.5647	+	249.178i	−0.0516837	+	0.259832i
$960$		0			0
$961$	158.515	+	382.688i	0.164948	+	0.398219i
$962$		0			0
$963$	629.592	−	420.680i	0.653782	−	0.436843i
$964$		0			0
$965$	−164.349	+	164.349i	−0.170310	+	0.170310i
$966$		0			0
$967$	−244.147	−	101.129i	−0.252479	−	0.104580i	0.252855	−	0.967504i	$-0.418630\pi$
$967$	−244.147	−	101.129i	−0.252479	−	0.104580i	−0.505333	+	0.862924i	$0.668630\pi$
$968$		0			0
$969$	−228.653	+	143.821i	−0.235968	+	0.148422i
$970$		0			0
$971$	−323.427	+	780.821i	−0.333086	+	0.804142i	0.665258	+	0.746614i	$0.268322\pi$
$971$	−323.427	+	780.821i	−0.333086	+	0.804142i	−0.998344	+	0.0575276i	$0.981678\pi$
$972$		0			0
$973$	−701.180	−	701.180i	−0.720637	−	0.720637i
$974$		0			0
$975$	−136.245	−	203.905i	−0.139738	−	0.209133i
$976$		0			0
$977$	−1292.13	+	535.217i	−1.32255	+	0.547817i	−0.928520	−	0.371281i	$-0.878919\pi$
$977$	−1292.13	+	535.217i	−1.32255	+	0.547817i	−0.394027	+	0.919099i	$0.628919\pi$
$978$		0			0
$979$	−624.162	−	124.154i	−0.637551	−	0.126817i
$980$		0			0
$981$	−494.928	+	98.4472i	−0.504514	+	0.100354i
$982$		0			0
$983$	−1090.94	−	728.940i	−1.10980	−	0.741546i	−0.141155	−	0.989988i	$-0.545082\pi$
$983$	−1090.94	−	728.940i	−1.10980	−	0.741546i	−0.968647	+	0.248442i	$0.920082\pi$
$984$		0			0
$985$		−	36.9451i		−	0.0375077i
$986$		0			0
$987$	−67.0106			−0.0678932
$988$		0			0
$989$	−10.6463	+	15.9333i	−0.0107647	+	0.0161106i
$990$		0			0
$991$	293.696	+	1476.51i	0.296363	+	1.48992i	0.786129	+	0.618063i	$0.212082\pi$
$991$	293.696	+	1476.51i	0.296363	+	1.48992i	−0.489766	+	0.871854i	$0.662918\pi$
$992$		0			0
$993$	26.0294	−	130.859i	0.0262129	−	0.131781i
$994$		0			0
$995$	−219.375	−	529.619i	−0.220478	−	0.532281i
$996$		0			0
$997$	−327.594	+	218.891i	−0.328580	+	0.219550i	−0.708907	−	0.705302i	$-0.750811\pi$
$997$	−327.594	+	218.891i	−0.328580	+	0.219550i	0.380327	+	0.924852i	$0.375811\pi$
$998$		0			0
$999$	−99.8724	+	99.8724i	−0.0999724	+	0.0999724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.a.41.3	✓	32
4.3	odd	2		272.3.bh.f.177.2		32
17.5	odd	16	inner	136.3.t.a.73.3	yes	32
68.39	even	16		272.3.bh.f.209.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.a.41.3	✓	32	1.1	even	1	trivial
136.3.t.a.73.3	yes	32	17.5	odd	16	inner
272.3.bh.f.177.2		32	4.3	odd	2
272.3.bh.f.209.2		32	68.39	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)

\(f(q)\)	\(=\)	\(q+(0.265432 - 0.397247i) q^{3} +(0.373441 + 1.87742i) q^{5} +(-2.10274 + 10.5712i) q^{7} +(3.35680 + 8.10403i) q^{9} +O(q^{10})\)	\(q+(0.265432 - 0.397247i) q^{3} +(0.373441 + 1.87742i) q^{5} +(-2.10274 + 10.5712i) q^{7} +(3.35680 + 8.10403i) q^{9} +(5.50678 - 3.67951i) q^{11} +(17.0115 - 17.0115i) q^{13} +(0.844922 + 0.349978i) q^{15} +(-0.468896 + 16.9935i) q^{17} +(-12.7274 + 30.7266i) q^{19} +(3.64124 + 3.64124i) q^{21} +(-14.4543 - 21.6324i) q^{23} +(19.7118 - 8.16488i) q^{25} +(8.32757 + 1.65646i) q^{27} +(3.90826 - 0.777401i) q^{29} +(-30.8342 - 20.6027i) q^{31} -3.16422i q^{33} -20.6318 q^{35} +(-9.24177 + 13.8313i) q^{37} +(-2.24237 - 11.2732i) q^{39} +(13.9213 - 69.9870i) q^{41} +(-0.281866 - 0.680485i) q^{43} +(-13.9611 + 9.32849i) q^{45} +(-9.20162 + 9.20162i) q^{47} +(-62.0583 - 25.7054i) q^{49} +(6.62618 + 4.69690i) q^{51} +(10.1255 - 24.4451i) q^{53} +(8.96444 + 8.96444i) q^{55} +(8.82780 + 13.2117i) q^{57} +(81.0988 - 33.5922i) q^{59} +(-44.2798 - 8.80781i) q^{61} +(-92.7277 + 18.4447i) q^{63} +(38.2904 + 25.5848i) q^{65} -33.0049i q^{67} -12.4300 q^{69} +(49.6401 - 74.2917i) q^{71} +(17.0394 + 85.6629i) q^{73} +(1.98866 - 9.99766i) q^{75} +(27.3175 + 65.9503i) q^{77} +(-17.2534 + 11.5284i) q^{79} +(-52.9546 + 52.9546i) q^{81} +(128.971 + 53.4216i) q^{83} +(-32.0790 + 5.46577i) q^{85} +(0.728557 - 1.75889i) q^{87} +(-67.9449 - 67.9449i) q^{89} +(144.061 + 215.602i) q^{91} +(-16.3688 + 6.78016i) q^{93} +(-62.4395 - 12.4200i) q^{95} +(58.6948 - 11.6751i) q^{97} +(48.3041 + 32.2757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9} - 24 q^{11} + 48 q^{13} + 96 q^{15} + 40 q^{19} - 80 q^{21} - 48 q^{23} + 112 q^{25} - 80 q^{27} + 56 q^{29} - 24 q^{31} - 96 q^{35} + 48 q^{37} - 72 q^{39} - 160 q^{41} + 112 q^{43} - 504 q^{45} + 48 q^{47} + 208 q^{49} - 400 q^{51} + 304 q^{53} - 368 q^{55} - 264 q^{57} + 192 q^{59} - 288 q^{61} + 56 q^{63} + 8 q^{65} + 32 q^{69} + 352 q^{71} - 184 q^{73} + 24 q^{75} + 688 q^{77} - 424 q^{79} + 312 q^{81} + 600 q^{83} - 512 q^{85} + 1336 q^{87} - 144 q^{89} - 24 q^{91} + 944 q^{93} - 256 q^{95} + 416 q^{97} + 128 q^{99}+O(q^{100}) \) 32 * 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 + 112 * q^25 - 80 * q^27 + 56 * q^29 - 24 * q^31 - 96 * q^35 + 48 * q^37 - 72 * q^39 - 160 * q^41 + 112 * q^43 - 504 * q^45 + 48 * q^47 + 208 * q^49 - 400 * q^51 + 304 * q^53 - 368 * q^55 - 264 * q^57 + 192 * q^59 - 288 * q^61 + 56 * q^63 + 8 * q^65 + 32 * q^69 + 352 * q^71 - 184 * q^73 + 24 * q^75 + 688 * q^77 - 424 * q^79 + 312 * q^81 + 600 * q^83 - 512 * q^85 + 1336 * q^87 - 144 * q^89 - 24 * q^91 + 944 * q^93 - 256 * q^95 + 416 * q^97 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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