LMFDB - Embedded newform 136.4.n.a.49.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(9,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("136.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	136.n (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.02425976078$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.6
Character	$\chi$	$=$	136.49
Dual form			136.4.n.a.25.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.26351 + 7.87882i) q^{3} +(-8.68823 + 3.59878i) q^{5} +(3.82290 + 1.58350i) q^{7} +(-32.3334 + 32.3334i) q^{9} +(-0.766960 + 1.85161i) q^{11} +58.7886i q^{13} +(-56.7083 - 56.7083i) q^{15} +(-29.9582 - 63.3680i) q^{17} +(-59.0083 - 59.0083i) q^{19} +35.2877i q^{21} +(-15.0348 + 36.2971i) q^{23} +(-25.8542 + 25.8542i) q^{25} +(-147.541 - 61.1136i) q^{27} +(145.881 - 60.4258i) q^{29} +(46.0004 + 111.055i) q^{31} -17.0915 q^{33} -38.9129 q^{35} +(129.260 + 312.061i) q^{37} +(-463.185 + 191.857i) q^{39} +(251.128 + 104.021i) q^{41} +(-169.157 + 169.157i) q^{43} +(164.559 - 397.281i) q^{45} +150.254i q^{47} +(-230.431 - 230.431i) q^{49} +(401.496 - 442.838i) q^{51} +(513.595 + 513.595i) q^{53} -18.8473i q^{55} +(272.341 - 657.490i) q^{57} +(448.507 - 448.507i) q^{59} +(570.476 + 236.299i) q^{61} +(-174.807 + 72.4075i) q^{63} +(-211.567 - 510.769i) q^{65} +712.549 q^{67} -335.045 q^{69} +(-317.730 - 767.069i) q^{71} +(-471.406 + 195.263i) q^{73} +(-288.077 - 119.325i) q^{75} +(-5.86403 + 5.86403i) q^{77} +(114.686 - 276.878i) q^{79} -127.286i q^{81} +(-434.347 - 434.347i) q^{83} +(488.332 + 442.743i) q^{85} +(952.167 + 952.167i) q^{87} +1268.61i q^{89} +(-93.0916 + 224.743i) q^{91} +(-724.857 + 724.857i) q^{93} +(725.035 + 300.319i) q^{95} +(-949.678 + 393.369i) q^{97} +(-35.0703 - 84.6671i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 28 q^{5} - 16 q^{9} + 140 q^{11} - 60 q^{15} - 164 q^{17} - 124 q^{19} - 72 q^{23} + 52 q^{25} - 360 q^{27} + 44 q^{29} - 120 q^{31} + 520 q^{33} + 512 q^{35} + 196 q^{37} - 232 q^{39} + 20 q^{41}+ \cdots + 5244 q^{99}+O(q^{100}) $ 24 * q - 28 * q^5 - 16 * q^9 + 140 * q^11 - 60 * q^15 - 164 * q^17 - 124 * q^19 - 72 * q^23 + 52 * q^25 - 360 * q^27 + 44 * q^29 - 120 * q^31 + 520 * q^33 + 512 * q^35 + 196 * q^37 - 232 * q^39 + 20 * q^41 - 160 * q^43 + 1412 * q^45 - 1020 * q^49 - 248 * q^51 + 92 * q^53 + 28 * q^57 + 656 * q^59 - 1028 * q^61 - 2356 * q^63 + 1392 * q^65 + 1960 * q^67 - 2408 * q^69 - 264 * q^71 + 548 * q^73 - 2356 * q^75 + 492 * q^77 + 2496 * q^79 - 536 * q^83 - 972 * q^85 + 3508 * q^87 + 1320 * q^91 + 2684 * q^93 - 5972 * q^95 - 4936 * q^97 + 5244 * q^99

Character values

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

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

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
$3$	3.26351	+	7.87882i	0.628064	+	1.51628i	0.842026	+	0.539438i	$0.181363\pi$
$3$	3.26351	+	7.87882i	0.628064	+	1.51628i	−0.213962	+	0.976842i	$0.568637\pi$
$4$		0			0
$5$	−8.68823	+	3.59878i	−0.777099	+	0.321885i	−0.735744	−	0.677260i	$-0.763167\pi$
$5$	−8.68823	+	3.59878i	−0.777099	+	0.321885i	−0.0413548	+	0.999145i	$0.513167\pi$
$6$		0			0
$7$	3.82290	+	1.58350i	0.206417	+	0.0855009i	0.483497	−	0.875346i	$-0.339367\pi$
$7$	3.82290	+	1.58350i	0.206417	+	0.0855009i	−0.277079	+	0.960847i	$0.589367\pi$
$8$		0			0
$9$	−32.3334	+	32.3334i	−1.19753	+	1.19753i
$10$		0			0
$11$	−0.766960	+	1.85161i	−0.0210225	+	0.0507527i	−0.934042	−	0.357163i	$-0.883744\pi$
$11$	−0.766960	+	1.85161i	−0.0210225	+	0.0507527i	0.913020	+	0.407915i	$0.133744\pi$
$12$		0			0
$13$			58.7886i			1.25423i	0.778926	+	0.627116i	$0.215765\pi$
$13$			58.7886i			1.25423i	−0.778926	+	0.627116i	$0.784235\pi$
$14$		0			0
$15$	−56.7083	−	56.7083i	−0.976135	−	0.976135i
$16$		0			0
$17$	−29.9582	−	63.3680i	−0.427408	−	0.904059i
$17$	−29.9582	−	63.3680i	−0.427408	−	0.904059i
$18$		0			0
$19$	−59.0083	−	59.0083i	−0.712496	−	0.712496i	0.254561	−	0.967057i	$-0.418069\pi$
$19$	−59.0083	−	59.0083i	−0.712496	−	0.712496i	−0.967057	+	0.254561i	$0.918069\pi$
$20$		0			0
$21$			35.2877i			0.366686i
$22$		0			0
$23$	−15.0348	+	36.2971i	−0.136303	+	0.329064i	−0.977262	−	0.212034i	$-0.931991\pi$
$23$	−15.0348	+	36.2971i	−0.136303	+	0.329064i	0.840960	+	0.541098i	$0.181991\pi$
$24$		0			0
$25$	−25.8542	+	25.8542i	−0.206834	+	0.206834i
$26$		0			0
$27$	−147.541	−	61.1136i	−1.05164	−	0.435605i
$28$		0			0
$29$	145.881	−	60.4258i	0.934116	−	0.386923i	0.136877	−	0.990588i	$-0.456293\pi$
$29$	145.881	−	60.4258i	0.934116	−	0.386923i	0.797238	+	0.603664i	$0.206293\pi$
$30$		0			0
$31$	46.0004	+	111.055i	0.266513	+	0.643420i	0.999314	−	0.0370230i	$-0.0117875\pi$
$31$	46.0004	+	111.055i	0.266513	+	0.643420i	−0.732801	+	0.680443i	$0.761787\pi$
$32$		0			0
$33$	−17.0915			−0.0901588
$34$		0			0
$35$	−38.9129			−0.187928
$36$		0			0
$37$	129.260	+	312.061i	0.574330	+	1.38655i	0.897837	+	0.440329i	$0.145138\pi$
$37$	129.260	+	312.061i	0.574330	+	1.38655i	−0.323507	+	0.946226i	$0.604862\pi$
$38$		0			0
$39$	−463.185	+	191.857i	−1.90177	+	0.787738i
$40$		0			0
$41$	251.128	+	104.021i	0.956575	+	0.396226i	0.805698	−	0.592326i	$-0.201790\pi$
$41$	251.128	+	104.021i	0.956575	+	0.396226i	0.150877	+	0.988553i	$0.451790\pi$
$42$		0			0
$43$	−169.157	+	169.157i	−0.599913	+	0.599913i	−0.940289	−	0.340376i	$-0.889446\pi$
$43$	−169.157	+	169.157i	−0.599913	+	0.599913i	0.340376	+	0.940289i	$0.389446\pi$
$44$		0			0
$45$	164.559	−	397.281i	0.545134	−	1.31607i
$46$		0			0
$47$			150.254i			0.466314i	0.972439	+	0.233157i	$0.0749056\pi$
$47$			150.254i			0.466314i	−0.972439	+	0.233157i	$0.925094\pi$
$48$		0			0
$49$	−230.431	−	230.431i	−0.671809	−	0.671809i
$50$		0			0
$51$	401.496	−	442.838i	1.10237	−	1.21588i
$52$		0			0
$53$	513.595	+	513.595i	1.33109	+	1.33109i	0.904397	+	0.426693i	$0.140321\pi$
$53$	513.595	+	513.595i	1.33109	+	1.33109i	0.426693	+	0.904397i	$0.359679\pi$
$54$		0			0
$55$		−	18.8473i		−	0.0462067i
$56$		0			0
$57$	272.341	−	657.490i	0.632850	−	1.52784i
$58$		0			0
$59$	448.507	−	448.507i	0.989671	−	0.989671i	−0.0102762	−	0.999947i	$-0.503271\pi$
$59$	448.507	−	448.507i	0.989671	−	0.989671i	0.999947	+	0.0102762i	$0.00327106\pi$
$60$		0			0
$61$	570.476	+	236.299i	1.19741	+	0.495983i	0.890161	−	0.455647i	$-0.150592\pi$
$61$	570.476	+	236.299i	1.19741	+	0.495983i	0.307248	+	0.951630i	$0.400592\pi$
$62$		0			0
$63$	−174.807	+	72.4075i	−0.349582	+	0.144801i
$64$		0			0
$65$	−211.567	−	510.769i	−0.403718	−	0.974662i
$66$		0			0
$67$	712.549			1.29928			0.649640	−	0.760242i	$-0.274920\pi$
$67$	712.549			1.29928			0.649640	+	0.760242i	$0.274920\pi$
$68$		0			0
$69$	−335.045			−0.584560
$70$		0			0
$71$	−317.730	−	767.069i	−0.531094	−	1.28217i	−0.930800	−	0.365530i	$-0.880888\pi$
$71$	−317.730	−	767.069i	−0.531094	−	1.28217i	0.399706	−	0.916643i	$-0.369112\pi$
$72$		0			0
$73$	−471.406	+	195.263i	−0.755807	+	0.313066i	−0.727109	−	0.686522i	$-0.759136\pi$
$73$	−471.406	+	195.263i	−0.755807	+	0.313066i	−0.0286987	+	0.999588i	$0.509136\pi$
$74$		0			0
$75$	−288.077	−	119.325i	−0.443523	−	0.183713i
$76$		0			0
$77$	−5.86403	+	5.86403i	−0.00867881	+	0.00867881i
$78$		0			0
$79$	114.686	−	276.878i	0.163332	−	0.394319i	−0.820931	−	0.571027i	$-0.806545\pi$
$79$	114.686	−	276.878i	0.163332	−	0.394319i	0.984263	+	0.176709i	$0.0565451\pi$
$80$		0			0
$81$		−	127.286i		−	0.174604i
$82$		0			0
$83$	−434.347	−	434.347i	−0.574407	−	0.574407i	0.358950	−	0.933357i	$-0.383135\pi$
$83$	−434.347	−	434.347i	−0.574407	−	0.574407i	−0.933357	+	0.358950i	$0.883135\pi$
$84$		0			0
$85$	488.332	+	442.743i	0.623141	+	0.564967i
$86$		0			0
$87$	952.167	+	952.167i	1.17337	+	1.17337i
$88$		0			0
$89$			1268.61i			1.51093i	0.655188	+	0.755466i	$0.272589\pi$
$89$			1268.61i			1.51093i	−0.655188	+	0.755466i	$0.727411\pi$
$90$		0			0
$91$	−93.0916	+	224.743i	−0.107238	+	0.258895i
$92$		0			0
$93$	−724.857	+	724.857i	−0.808217	+	0.808217i
$94$		0			0
$95$	725.035	+	300.319i	0.783022	+	0.324338i
$96$		0			0
$97$	−949.678	+	393.369i	−0.994074	+	0.411759i	−0.819621	−	0.572906i	$-0.805816\pi$
$97$	−949.678	+	393.369i	−0.994074	+	0.411759i	−0.174453	+	0.984665i	$0.555816\pi$
$98$		0			0
$99$	−35.0703	−	84.6671i	−0.0356030	−	0.0859532i
$100$		0			0
$101$	53.5154			0.0527226			0.0263613	−	0.999652i	$-0.491608\pi$
$101$	53.5154			0.0527226			0.0263613	+	0.999652i	$0.491608\pi$
$102$		0			0
$103$	1364.04			1.30488			0.652442	−	0.757839i	$-0.273745\pi$
$103$	1364.04			1.30488			0.652442	+	0.757839i	$0.273745\pi$
$104$		0			0
$105$	−126.993	−	306.588i	−0.118031	−	0.284952i
$106$		0			0
$107$	−495.658	+	205.308i	−0.447823	+	0.185494i	−0.595186	−	0.803588i	$-0.702922\pi$
$107$	−495.658	+	205.308i	−0.447823	+	0.185494i	0.147363	+	0.989083i	$0.452922\pi$
$108$		0			0
$109$	−1256.14	−	520.310i	−1.10382	−	0.457217i	−0.245015	−	0.969519i	$-0.578793\pi$
$109$	−1256.14	−	520.310i	−1.10382	−	0.457217i	−0.858805	+	0.512302i	$0.828793\pi$
$110$		0			0
$111$	−2036.83	+	2036.83i	−1.74169	+	1.74169i
$112$		0			0
$113$	493.616	−	1191.69i	0.410933	−	0.992080i	−0.573955	−	0.818887i	$-0.694591\pi$
$113$	493.616	−	1191.69i	0.410933	−	0.992080i	0.984888	−	0.173193i	$-0.0554085\pi$
$114$		0			0
$115$		−	369.465i		−	0.299589i
$116$		0			0
$117$	−1900.83	−	1900.83i	−1.50198	−	1.50198i
$118$		0			0
$119$	−14.1842	−	289.689i	−0.0109266	−	0.223157i
$120$		0			0
$121$	938.319	+	938.319i	0.704973	+	0.704973i
$122$		0			0
$123$			2318.06i			1.69929i
$124$		0			0
$125$	581.432	−	1403.70i	0.416039	−	1.00441i
$126$		0			0
$127$	−750.398	+	750.398i	−0.524307	+	0.524307i	−0.918869	−	0.394562i	$-0.870896\pi$
$127$	−750.398	+	750.398i	−0.524307	+	0.524307i	0.394562	+	0.918869i	$0.370896\pi$
$128$		0			0
$129$	−1884.81	−	780.713i	−1.28642	−	0.532852i
$130$		0			0
$131$	1.06830	−	0.442504i	0.000712501	−	0.000295128i	−0.382327	−	0.924027i	$-0.624877\pi$
$131$	1.06830	−	0.442504i	0.000712501	−	0.000295128i	0.383040	+	0.923732i	$0.374877\pi$
$132$		0			0
$133$	−132.143	−	319.022i	−0.0861525	−	0.207991i
$134$		0			0
$135$	1501.81			0.957445
$136$		0			0
$137$	581.471			0.362616			0.181308	−	0.983426i	$-0.441967\pi$
$137$	581.471			0.362616			0.181308	+	0.983426i	$0.441967\pi$
$138$		0			0
$139$	−964.808	−	2329.25i	−0.588733	−	1.42133i	−0.884714	−	0.466134i	$-0.845646\pi$
$139$	−964.808	−	2329.25i	−0.588733	−	1.42133i	0.295981	−	0.955194i	$-0.404354\pi$
$140$		0			0
$141$	−1183.82	+	490.355i	−0.707063	+	0.292875i
$142$		0			0
$143$	−108.853	−	45.0885i	−0.0636557	−	0.0263671i
$144$		0			0
$145$	−1049.99	+	1049.99i	−0.601356	+	0.601356i
$146$		0			0
$147$	1063.51	−	2567.53i	0.596712	−	1.44059i
$148$		0			0
$149$		−	1889.71i		−	1.03900i	−0.854470	−	0.519501i	$-0.826118\pi$
$149$		−	1889.71i		−	1.03900i	0.854470	−	0.519501i	$-0.173882\pi$
$150$		0			0
$151$	−798.283	−	798.283i	−0.430221	−	0.430221i	0.458483	−	0.888703i	$-0.348393\pi$
$151$	−798.283	−	798.283i	−0.430221	−	0.430221i	−0.888703	+	0.458483i	$0.848393\pi$
$152$		0			0
$153$	3017.55	+	1080.25i	1.59448	+	0.570805i
$154$		0			0
$155$	−799.324	−	799.324i	−0.414214	−	0.414214i
$156$		0			0
$157$			2012.97i			1.02327i	0.859204	+	0.511633i	$0.170959\pi$
$157$			2012.97i			1.02327i	−0.859204	+	0.511633i	$0.829041\pi$
$158$		0			0
$159$	−2370.40	+	5722.65i	−1.18229	+	2.85431i
$160$		0			0
$161$	−114.953	+	114.953i	−0.0562705	+	0.0562705i
$162$		0			0
$163$	2587.43	+	1071.75i	1.24333	+	0.515005i	0.904754	−	0.425934i	$-0.140054\pi$
$163$	2587.43	+	1071.75i	1.24333	+	0.515005i	0.338577	+	0.940939i	$0.390054\pi$
$164$		0			0
$165$	148.494	−	61.5084i	0.0700623	−	0.0290208i
$166$		0			0
$167$	−799.170	−	1929.37i	−0.370309	−	0.894006i	−0.993698	−	0.112093i	$-0.964244\pi$
$167$	−799.170	−	1929.37i	−0.370309	−	0.894006i	0.623388	−	0.781912i	$-0.285756\pi$
$168$		0			0
$169$	−1259.10			−0.573098
$170$		0			0
$171$	3815.87			1.70647
$172$		0			0
$173$	366.123	+	883.898i	0.160901	+	0.388448i	0.983684	−	0.179907i	$-0.0575798\pi$
$173$	366.123	+	883.898i	0.160901	+	0.388448i	−0.822783	+	0.568356i	$0.807580\pi$
$174$		0			0
$175$	−139.778	+	57.8981i	−0.0603786	+	0.0250096i
$176$		0			0
$177$	4997.41	+	2070.00i	2.12219	+	0.879042i
$178$		0			0
$179$	2960.01	−	2960.01i	1.23599	−	1.23599i	0.274359	−	0.961627i	$-0.411534\pi$
$179$	2960.01	−	2960.01i	1.23599	−	1.23599i	0.961627	−	0.274359i	$-0.0884658\pi$
$180$		0			0
$181$	−178.074	+	429.907i	−0.0731276	+	0.176546i	−0.956217	−	0.292660i	$-0.905460\pi$
$181$	−178.074	+	429.907i	−0.0731276	+	0.176546i	0.883089	+	0.469206i	$0.155460\pi$
$182$		0			0
$183$			5265.84i			2.12711i
$184$		0			0
$185$	−2246.08	−	2246.08i	−0.892622	−	0.892622i
$186$		0			0
$187$	140.309	−	6.87008i	0.0548686	−	0.00268658i
$188$		0			0
$189$	−467.263	−	467.263i	−0.179833	−	0.179833i
$190$		0			0
$191$		−	2273.42i		−	0.861249i	−0.902531	−	0.430625i	$-0.858293\pi$
$191$		−	2273.42i		−	0.861249i	0.902531	−	0.430625i	$-0.141707\pi$
$192$		0			0
$193$	401.207	−	968.600i	0.149635	−	0.361250i	−0.831233	−	0.555924i	$-0.812365\pi$
$193$	401.207	−	968.600i	0.149635	−	0.361250i	0.980868	+	0.194673i	$0.0623647\pi$
$194$		0			0
$195$	3333.80	−	3333.80i	1.22430	−	1.22430i
$196$		0			0
$197$	−2918.69	−	1208.96i	−1.05557	−	0.437233i	−0.213695	−	0.976900i	$-0.568550\pi$
$197$	−2918.69	−	1208.96i	−1.05557	−	0.437233i	−0.841878	+	0.539668i	$0.818550\pi$
$198$		0			0
$199$	−879.632	+	364.356i	−0.313344	+	0.129791i	−0.533813	−	0.845603i	$-0.679241\pi$
$199$	−879.632	+	364.356i	−0.313344	+	0.129791i	0.220469	+	0.975394i	$0.429241\pi$
$200$		0			0
$201$	2325.41	+	5614.05i	0.816030	+	1.97007i
$202$		0			0
$203$	653.372			0.225900
$204$		0			0
$205$	−2556.20			−0.870892
$206$		0			0
$207$	−687.484	−	1659.73i	−0.230838	−	0.557292i
$208$		0			0
$209$	154.517	−	64.0030i	0.0511395	−	0.0211827i
$210$		0			0
$211$	−4359.11	−	1805.60i	−1.42224	−	0.589113i	−0.466821	−	0.884352i	$-0.654601\pi$
$211$	−4359.11	−	1805.60i	−1.42224	−	0.589113i	−0.955423	+	0.295239i	$0.904601\pi$
$212$		0			0
$213$	5006.68	−	5006.68i	1.61057	−	1.61057i
$214$		0			0
$215$	860.917	−	2078.44i	0.273089	−	0.659295i
$216$		0			0
$217$			497.393i			0.155600i
$218$		0			0
$219$	−3076.88	−	3076.88i	−0.949390	−	0.949390i
$220$		0			0
$221$	3725.32	−	1761.20i	1.13390	−	0.536069i
$222$		0			0
$223$	2751.96	+	2751.96i	0.826390	+	0.826390i	0.987015	−	0.160625i	$-0.0513511\pi$
$223$	2751.96	+	2751.96i	0.826390	+	0.826390i	−0.160625	+	0.987015i	$0.551351\pi$
$224$		0			0
$225$		−	1671.91i		−	0.495381i
$226$		0			0
$227$	1146.57	−	2768.07i	0.335245	−	0.809354i	−0.662913	−	0.748696i	$-0.730680\pi$
$227$	1146.57	−	2768.07i	0.335245	−	0.809354i	0.998159	−	0.0606576i	$-0.0193198\pi$
$228$		0			0
$229$	−2777.16	+	2777.16i	−0.801398	+	0.801398i	−0.983314	−	0.181916i	$-0.941770\pi$
$229$	−2777.16	+	2777.16i	−0.801398	+	0.801398i	0.181916	+	0.983314i	$0.441770\pi$
$230$		0			0
$231$	−65.3390	−	27.0643i	−0.0186103	−	0.00770865i
$232$		0			0
$233$	2603.32	−	1078.33i	0.731970	−	0.303192i	0.0146085	−	0.999893i	$-0.495350\pi$
$233$	2603.32	−	1078.33i	0.731970	−	0.303192i	0.717361	+	0.696702i	$0.245350\pi$
$234$		0			0
$235$	−540.731	−	1305.44i	−0.150100	−	0.362372i
$236$		0			0
$237$	2555.75			0.700480
$238$		0			0
$239$	−4737.45			−1.28218			−0.641089	−	0.767467i	$-0.721517\pi$
$239$	−4737.45			−1.28218			−0.641089	+	0.767467i	$0.721517\pi$
$240$		0			0
$241$	1529.50	+	3692.53i	0.408811	+	0.986958i	0.985451	+	0.169959i	$0.0543637\pi$
$241$	1529.50	+	3692.53i	0.408811	+	0.986958i	−0.576640	+	0.816999i	$0.695636\pi$
$242$		0			0
$243$	−2980.75	+	1234.67i	−0.786894	+	0.325942i
$244$		0			0
$245$	2831.30	+	1172.76i	0.738307	+	0.305817i
$246$		0			0
$247$	3469.01	−	3469.01i	0.893635	−	0.893635i
$248$		0			0
$249$	2004.64	−	4839.64i	0.510197	−	1.23172i
$250$		0			0
$251$			6549.14i			1.64693i	0.567370	+	0.823463i	$0.307961\pi$
$251$			6549.14i			1.64693i	−0.567370	+	0.823463i	$0.692039\pi$
$252$		0			0
$253$	−55.6769	−	55.6769i	−0.0138355	−	0.0138355i
$254$		0			0
$255$	−1894.61	+	5292.37i	−0.465276	+	1.29969i
$256$		0			0
$257$	−724.767	−	724.767i	−0.175913	−	0.175913i	0.613658	−	0.789572i	$-0.289697\pi$
$257$	−724.767	−	724.767i	−0.175913	−	0.175913i	−0.789572	+	0.613658i	$0.789697\pi$
$258$		0			0
$259$			1397.66i			0.335315i
$260$		0			0
$261$	−2763.05	+	6670.59i	−0.655281	+	1.58199i
$262$		0			0
$263$	−1014.00	+	1014.00i	−0.237741	+	0.237741i	−0.815914	−	0.578173i	$-0.803766\pi$
$263$	−1014.00	+	1014.00i	−0.237741	+	0.237741i	0.578173	+	0.815914i	$0.303766\pi$
$264$		0			0
$265$	−6310.55	−	2613.92i	−1.46285	−	0.605931i
$266$		0			0
$267$	−9995.19	+	4140.14i	−2.29099	+	0.948961i
$268$		0			0
$269$	482.139	+	1163.99i	0.109281	+	0.263827i	0.969054	−	0.246849i	$-0.0793951\pi$
$269$	482.139	+	1163.99i	0.109281	+	0.263827i	−0.859773	+	0.510676i	$0.829395\pi$
$270$		0			0
$271$	−546.986			−0.122609			−0.0613044	−	0.998119i	$-0.519526\pi$
$271$	−546.986			−0.122609			−0.0613044	+	0.998119i	$0.519526\pi$
$272$		0			0
$273$	−2074.52			−0.459910
$274$		0			0
$275$	−28.0427	−	67.7010i	−0.00614923	−	0.0148455i
$276$		0			0
$277$	6894.80	−	2855.92i	1.49555	−	0.619479i	0.523037	−	0.852310i	$-0.324799\pi$
$277$	6894.80	−	2855.92i	1.49555	−	0.619479i	0.972517	+	0.232831i	$0.0747990\pi$
$278$		0			0
$279$	−5078.12	−	2103.43i	−1.08967	−	0.451358i
$280$		0			0
$281$	3156.53	−	3156.53i	0.670116	−	0.670116i	−0.287626	−	0.957743i	$-0.592866\pi$
$281$	3156.53	−	3156.53i	0.670116	−	0.670116i	0.957743	+	0.287626i	$0.0928662\pi$
$282$		0			0
$283$	−2271.60	+	5484.13i	−0.477147	+	1.15193i	0.483794	+	0.875182i	$0.339258\pi$
$283$	−2271.60	+	5484.13i	−0.477147	+	1.15193i	−0.960941	+	0.276753i	$0.910742\pi$
$284$		0			0
$285$			6692.52i			1.39098i
$286$		0			0
$287$	795.321	+	795.321i	0.163576	+	0.163576i
$288$		0			0
$289$	−3118.01	+	3796.79i	−0.634645	+	0.772804i
$290$		0			0
$291$	−6198.57	−	6198.57i	−1.24868	−	1.24868i
$292$		0			0
$293$			670.673i			0.133724i	0.997762	+	0.0668620i	$0.0212987\pi$
$293$			670.673i			0.133724i	−0.997762	+	0.0668620i	$0.978701\pi$
$294$		0			0
$295$	−2282.65	+	5510.81i	−0.450512	+	1.08763i
$296$		0			0
$297$	226.317	−	226.317i	0.0442162	−	0.0442162i
$298$		0			0
$299$	−2133.86	−	883.872i	−0.412723	−	0.170955i
$300$		0			0
$301$	−914.532	+	378.812i	−0.175125	+	0.0725394i
$302$		0			0
$303$	174.648	+	421.638i	0.0331132	+	0.0799422i
$304$		0			0
$305$	−5806.81			−1.09015
$306$		0			0
$307$	9301.80			1.72926			0.864628	−	0.502412i	$-0.167554\pi$
$307$	9301.80			1.72926			0.864628	+	0.502412i	$0.167554\pi$
$308$		0			0
$309$	4451.57	+	10747.0i	0.819550	+	1.97857i
$310$		0			0
$311$	8381.82	−	3471.86i	1.52826	−	0.633027i	0.549036	−	0.835799i	$-0.314995\pi$
$311$	8381.82	−	3471.86i	1.52826	−	0.633027i	0.979226	+	0.202772i	$0.0649951\pi$
$312$		0			0
$313$	−3184.82	−	1319.20i	−0.575133	−	0.238228i	0.0761069	−	0.997100i	$-0.475751\pi$
$313$	−3184.82	−	1319.20i	−0.575133	−	0.238228i	−0.651240	+	0.758872i	$0.725751\pi$
$314$		0			0
$315$	1258.19	−	1258.19i	0.225050	−	0.225050i
$316$		0			0
$317$	2319.16	−	5598.96i	0.410906	−	0.992015i	−0.573989	−	0.818863i	$-0.694605\pi$
$317$	2319.16	−	5598.96i	0.410906	−	0.992015i	0.984895	−	0.173152i	$-0.0553952\pi$
$318$		0			0
$319$			316.458i			0.0555430i
$320$		0			0
$321$	−3235.17	−	3235.17i	−0.562523	−	0.562523i
$322$		0			0
$323$	−1971.45	+	5507.02i	−0.339612	+	0.948665i
$324$		0			0
$325$	−1519.93	−	1519.93i	−0.259418	−	0.259418i
$326$		0			0
$327$		−	11594.9i		−	1.96086i
$328$		0			0
$329$	−237.927	+	574.406i	−0.0398703	+	0.0962553i
$330$		0			0
$331$	7711.44	−	7711.44i	1.28054	−	1.28054i	0.340181	−	0.940360i	$-0.389512\pi$
$331$	7711.44	−	7711.44i	1.28054	−	1.28054i	0.940360	−	0.340181i	$-0.110488\pi$
$332$		0			0
$333$	−14269.4	−	5910.58i	−2.34822	−	0.972666i
$334$		0			0
$335$	−6190.79	+	2564.31i	−1.00967	+	0.418219i
$336$		0			0
$337$	−1371.34	−	3310.71i	−0.221667	−	0.535151i	0.773450	−	0.633858i	$-0.218529\pi$
$337$	−1371.34	−	3310.71i	−0.221667	−	0.535151i	−0.995117	+	0.0987066i	$0.968529\pi$
$338$		0			0
$339$	11000.1			1.76236
$340$		0			0
$341$	−240.910			−0.0382581
$342$		0			0
$343$	−1059.17	−	2557.06i	−0.166734	−	0.402531i
$344$		0			0
$345$	2910.94	−	1205.75i	0.454261	−	0.188161i
$346$		0			0
$347$	−4688.70	−	1942.12i	−0.725368	−	0.300457i	−0.0107211	−	0.999943i	$-0.503413\pi$
$347$	−4688.70	−	1942.12i	−0.725368	−	0.300457i	−0.714647	+	0.699485i	$0.753413\pi$
$348$		0			0
$349$	−135.360	+	135.360i	−0.0207612	+	0.0207612i	−0.717411	−	0.696650i	$-0.754673\pi$
$349$	−135.360	+	135.360i	−0.0207612	+	0.0207612i	0.696650	+	0.717411i	$0.254673\pi$
$350$		0			0
$351$	3592.78	−	8673.75i	0.546349	−	1.31900i
$352$		0			0
$353$		−	2272.17i		−	0.342594i	−0.985219	−	0.171297i	$-0.945204\pi$
$353$		−	2272.17i		−	0.342594i	0.985219	−	0.171297i	$-0.0547958\pi$
$354$		0			0
$355$	5521.03	+	5521.03i	0.825425	+	0.825425i
$356$		0			0
$357$	2236.11	−	1057.16i	0.331506	−	0.156725i
$358$		0			0
$359$	6256.65	+	6256.65i	0.919814	+	0.919814i	0.997015	−	0.0772017i	$-0.0245985\pi$
$359$	6256.65	+	6256.65i	0.919814	+	0.919814i	−0.0772017	+	0.997015i	$0.524599\pi$
$360$		0			0
$361$			104.949i			0.0153009i
$362$		0			0
$363$	−4330.63	+	10455.1i	−0.626168	+	1.51170i
$364$		0			0
$365$	3392.98	−	3392.98i	0.486566	−	0.486566i
$366$		0			0
$367$	−2199.50	−	911.061i	−0.312841	−	0.129583i	0.220738	−	0.975333i	$-0.429153\pi$
$367$	−2199.50	−	911.061i	−0.312841	−	0.129583i	−0.533579	+	0.845750i	$0.679153\pi$
$368$		0			0
$369$	−11483.1	+	4756.48i	−1.62002	+	0.671036i
$370$		0			0
$371$	1150.15	+	2776.70i	0.160951	+	0.388569i
$372$		0			0
$373$	6927.12			0.961589			0.480794	−	0.876833i	$-0.340348\pi$
$373$	6927.12			0.961589			0.480794	+	0.876833i	$0.340348\pi$
$374$		0			0
$375$	12957.0			1.78426
$376$		0			0
$377$	3552.34	+	8576.12i	0.485292	+	1.17160i
$378$		0			0
$379$	11598.2	−	4804.15i	1.57193	−	0.651115i	0.584821	−	0.811162i	$-0.301165\pi$
$379$	11598.2	−	4804.15i	1.57193	−	0.651115i	0.987109	+	0.160047i	$0.0511646\pi$
$380$		0			0
$381$	−8361.18	−	3463.32i	−1.12429	−	0.465698i
$382$		0			0
$383$	−3611.03	+	3611.03i	−0.481763	+	0.481763i	−0.905694	−	0.423931i	$-0.860650\pi$
$383$	−3611.03	+	3611.03i	−0.481763	+	0.481763i	0.423931	+	0.905694i	$0.360650\pi$
$384$		0			0
$385$	29.8447	−	72.0514i	0.00395071	−	0.00953787i
$386$		0			0
$387$		−	10938.9i		−	1.43683i
$388$		0			0
$389$	7057.17	+	7057.17i	0.919827	+	0.919827i	0.997016	−	0.0771892i	$-0.0245946\pi$
$389$	7057.17	+	7057.17i	0.919827	+	0.919827i	−0.0771892	+	0.997016i	$0.524595\pi$
$390$		0			0
$391$	2750.49	−	134.674i	0.355750	−	0.0174189i
$392$		0			0
$393$	6.97281	+	6.97281i	0.000894992	+	0.000894992i
$394$		0			0
$395$			2818.31i			0.358999i
$396$		0			0
$397$	−1268.43	+	3062.27i	−0.160355	+	0.387130i	−0.983552	−	0.180625i	$-0.942188\pi$
$397$	−1268.43	+	3062.27i	−0.160355	+	0.387130i	0.823197	+	0.567755i	$0.192188\pi$
$398$		0			0
$399$	2082.27	−	2082.27i	0.261263	−	0.261263i
$400$		0			0
$401$	−7808.06	−	3234.20i	−0.972359	−	0.402764i	−0.160769	−	0.986992i	$-0.551397\pi$
$401$	−7808.06	−	3234.20i	−0.972359	−	0.402764i	−0.811590	+	0.584228i	$0.801397\pi$
$402$		0			0
$403$	−6528.75	+	2704.30i	−0.806998	+	0.334269i
$404$		0			0
$405$	458.075	+	1105.89i	0.0562023	+	0.135684i
$406$		0			0
$407$	−676.951			−0.0824453
$408$		0			0
$409$	−44.1623			−0.00533908			−0.00266954	−	0.999996i	$-0.500850\pi$
$409$	−44.1623			−0.00533908			−0.00266954	+	0.999996i	$0.500850\pi$
$410$		0			0
$411$	1897.64	+	4581.30i	0.227746	+	0.549827i
$412$		0			0
$413$	2424.81	−	1004.39i	0.288903	−	0.119668i
$414$		0			0
$415$	5336.82	+	2210.58i	0.631263	+	0.261478i
$416$		0			0
$417$	15203.1	−	15203.1i	1.78537	−	1.78537i
$418$		0			0
$419$	−4406.74	+	10638.8i	−0.513803	+	1.24043i	0.427851	+	0.903849i	$0.359271\pi$
$419$	−4406.74	+	10638.8i	−0.513803	+	1.24043i	−0.941654	+	0.336582i	$0.890729\pi$
$420$		0			0
$421$			10857.1i			1.25688i	0.777860	+	0.628438i	$0.216305\pi$
$421$			10857.1i			1.25688i	−0.777860	+	0.628438i	$0.783695\pi$
$422$		0			0
$423$	−4858.22	−	4858.22i	−0.558427	−	0.558427i
$424$		0			0
$425$	2412.88	+	863.785i	0.275393	+	0.0985876i
$426$		0			0
$427$	1806.69	+	1806.69i	0.204759	+	0.204759i
$428$		0			0
$429$		−	1004.78i		−	0.113080i
$430$		0			0
$431$	659.646	−	1592.53i	0.0737217	−	0.177980i	−0.882723	−	0.469894i	$-0.844292\pi$
$431$	659.646	−	1592.53i	0.0737217	−	0.177980i	0.956445	+	0.291914i	$0.0942921\pi$
$432$		0			0
$433$	1599.38	−	1599.38i	0.177509	−	0.177509i	−0.612760	−	0.790269i	$-0.709941\pi$
$433$	1599.38	−	1599.38i	0.177509	−	0.177509i	0.790269	+	0.612760i	$0.209941\pi$
$434$		0			0
$435$	−11699.3	−	4846.01i	−1.28951	−	0.534134i
$436$		0			0
$437$	3029.00	−	1254.65i	0.331572	−	0.137342i
$438$		0			0
$439$	2989.68	+	7217.72i	0.325033	+	0.784700i	0.998947	+	0.0458893i	$0.0146121\pi$
$439$	2989.68	+	7217.72i	0.325033	+	0.784700i	−0.673913	+	0.738810i	$0.735388\pi$
$440$		0			0
$441$	14901.2			1.60903
$442$		0			0
$443$	4323.15			0.463654			0.231827	−	0.972757i	$-0.425530\pi$
$443$	4323.15			0.463654			0.231827	+	0.972757i	$0.425530\pi$
$444$		0			0
$445$	−4565.47	−	11022.0i	−0.486346	−	1.17414i
$446$		0			0
$447$	14888.7	−	6167.10i	1.57542	−	0.652559i
$448$		0			0
$449$	1417.69	+	587.227i	0.149009	+	0.0617215i	0.455941	−	0.890010i	$-0.349303\pi$
$449$	1417.69	+	587.227i	0.149009	+	0.0617215i	−0.306933	+	0.951731i	$0.599303\pi$
$450$		0			0
$451$	−385.210	+	385.210i	−0.0402191	+	0.0402191i
$452$		0			0
$453$	3684.32	−	8894.74i	0.382129	−	0.922541i
$454$		0			0
$455$		−	2287.64i		−	0.235705i
$456$		0			0
$457$	−8699.98	−	8699.98i	−0.890521	−	0.890521i	0.104051	−	0.994572i	$-0.466819\pi$
$457$	−8699.98	−	8699.98i	−0.890521	−	0.890521i	−0.994572	+	0.104051i	$0.966819\pi$
$458$		0			0
$459$	547.428	+	11180.3i	0.0556683	+	1.13693i
$460$		0			0
$461$	−1886.57	−	1886.57i	−0.190600	−	0.190600i	0.605356	−	0.795955i	$-0.293031\pi$
$461$	−1886.57	−	1886.57i	−0.190600	−	0.190600i	−0.795955	+	0.605356i	$0.793031\pi$
$462$		0			0
$463$		−	15499.8i		−	1.55580i	−0.628388	−	0.777900i	$-0.716285\pi$
$463$		−	15499.8i		−	1.55580i	0.628388	−	0.777900i	$-0.283715\pi$
$464$		0			0
$465$	3689.12	−	8906.33i	0.367912	−	0.888218i
$466$		0			0
$467$	−8780.53	+	8780.53i	−0.870053	+	0.870053i	−0.992478	−	0.122425i	$-0.960933\pi$
$467$	−8780.53	+	8780.53i	−0.870053	+	0.870053i	0.122425	+	0.992478i	$0.460933\pi$
$468$		0			0
$469$	2724.01	+	1128.32i	0.268194	+	0.111090i
$470$		0			0
$471$	−15859.8	+	6569.36i	−1.55156	+	0.642676i
$472$		0			0
$473$	−183.476	−	442.950i	−0.0178356	−	0.0430589i
$474$		0			0
$475$	3051.23			0.294737
$476$		0			0
$477$	−33212.6			−3.18805
$478$		0			0
$479$	2853.09	+	6887.97i	0.272153	+	0.657035i	0.999575	−	0.0291555i	$-0.00928180\pi$
$479$	2853.09	+	6887.97i	0.272153	+	0.657035i	−0.727422	+	0.686190i	$0.759282\pi$
$480$		0			0
$481$	−18345.6	+	7599.01i	−1.73906	+	0.720343i
$482$		0			0
$483$	−1280.84	−	530.542i	−0.120663	−	0.0499804i
$484$		0			0
$485$	6835.37	−	6835.37i	0.639955	−	0.639955i
$486$		0			0
$487$	4184.79	−	10103.0i	0.389386	−	0.940060i	−0.600684	−	0.799486i	$-0.705105\pi$
$487$	4184.79	−	10103.0i	0.389386	−	0.940060i	0.990070	−	0.140574i	$-0.0448948\pi$
$488$		0			0
$489$			23883.5i			2.20869i
$490$		0			0
$491$	−3887.69	−	3887.69i	−0.357330	−	0.357330i	0.505498	−	0.862828i	$-0.331309\pi$
$491$	−3887.69	−	3887.69i	−0.357330	−	0.357330i	−0.862828	+	0.505498i	$0.831309\pi$
$492$		0			0
$493$	−8199.39	−	7433.92i	−0.749050	−	0.679122i
$494$		0			0
$495$	609.397	+	609.397i	0.0553341	+	0.0553341i
$496$		0			0
$497$		−	3435.55i		−	0.310072i
$498$		0			0
$499$	−321.208	+	775.465i	−0.0288161	+	0.0695683i	−0.937633	−	0.347628i	$-0.886987\pi$
$499$	−321.208	+	775.465i	−0.0288161	+	0.0695683i	0.908816	+	0.417196i	$0.136987\pi$
$500$		0			0
$501$	12593.0	−	12593.0i	1.12298	−	1.12298i
$502$		0			0
$503$	−10146.9	−	4202.98i	−0.899458	−	0.372568i	−0.115446	−	0.993314i	$-0.536830\pi$
$503$	−10146.9	−	4202.98i	−0.899458	−	0.372568i	−0.784012	+	0.620746i	$0.786830\pi$
$504$		0			0
$505$	−464.954	+	192.590i	−0.0409707	+	0.0169706i
$506$		0			0
$507$	−4109.08	−	9920.20i	−0.359942	−	0.868977i
$508$		0			0
$509$	−2774.81			−0.241633			−0.120817	−	0.992675i	$-0.538551\pi$
$509$	−2774.81			−0.241633			−0.120817	+	0.992675i	$0.538551\pi$
$510$		0			0
$511$	−2111.34			−0.182779
$512$		0			0
$513$	5099.95	+	12312.4i	0.438924	+	1.05966i
$514$		0			0
$515$	−11851.1	+	4908.89i	−1.01402	+	0.420022i
$516$		0			0
$517$	−278.211	−	115.239i	−0.0236667	−	0.00980308i
$518$		0			0
$519$	−5769.23	+	5769.23i	−0.487940	+	0.487940i
$520$		0			0
$521$	−6004.69	+	14496.6i	−0.504933	+	1.21902i	0.441834	+	0.897097i	$0.354328\pi$
$521$	−6004.69	+	14496.6i	−0.504933	+	1.21902i	−0.946767	+	0.321919i	$0.895672\pi$
$522$		0			0
$523$			5670.76i			0.474121i	0.971495	+	0.237060i	$0.0761839\pi$
$523$			5670.76i			0.474121i	−0.971495	+	0.237060i	$0.923816\pi$
$524$		0			0
$525$	−912.337	−	912.337i	−0.0758432	−	0.0758432i
$526$		0			0
$527$	5659.23	−	6241.95i	0.467779	−	0.515946i
$528$		0			0
$529$	7511.93	+	7511.93i	0.617402	+	0.617402i
$530$		0			0
$531$			29003.5i			2.37033i
$532$		0			0
$533$	−6115.22	+	14763.4i	−0.496960	+	1.19977i
$534$		0			0
$535$	3567.53	−	3567.53i	0.288295	−	0.288295i
$536$		0			0
$537$	32981.4	+	13661.4i	2.65038	+	1.09782i
$538$		0			0
$539$	603.397	−	249.935i	0.0482192	−	0.0199731i
$540$		0			0
$541$	−290.049	−	700.240i	−0.0230502	−	0.0556482i	0.911935	−	0.410334i	$-0.134588\pi$
$541$	−290.049	−	700.240i	−0.0230502	−	0.0556482i	−0.934986	+	0.354686i	$0.884588\pi$
$542$		0			0
$543$	−3968.31			−0.313621
$544$		0			0
$545$	12786.1			1.00495
$546$		0			0
$547$	−972.432	−	2347.66i	−0.0760113	−	0.183508i	0.881306	−	0.472545i	$-0.156665\pi$
$547$	−972.432	−	2347.66i	−0.0760113	−	0.183508i	−0.957318	+	0.289038i	$0.906665\pi$
$548$		0			0
$549$	−26085.8	+	10805.1i	−2.02789	+	0.839980i
$550$		0			0
$551$	−12173.8	−	5042.55i	−0.941235	−	0.389872i
$552$		0			0
$553$	876.870	−	876.870i	0.0674292	−	0.0674292i
$554$		0			0
$555$	10366.3	−	25026.6i	0.792841	−	1.91409i
$556$		0			0
$557$			17606.6i			1.33934i	0.742657	+	0.669672i	$0.233565\pi$
$557$			17606.6i			1.33934i	−0.742657	+	0.669672i	$0.766435\pi$
$558$		0			0
$559$	−9944.52	−	9944.52i	−0.752430	−	0.752430i
$560$		0			0
$561$	512.030	+	1083.05i	0.0385346	+	0.0815089i
$562$		0			0
$563$	5286.50	+	5286.50i	0.395736	+	0.395736i	0.876726	−	0.480990i	$-0.159723\pi$
$563$	5286.50	+	5286.50i	0.395736	+	0.395736i	−0.480990	+	0.876726i	$0.659723\pi$
$564$		0			0
$565$			12130.1i			0.903218i
$566$		0			0
$567$	201.557	−	486.602i	0.0149288	−	0.0360412i
$568$		0			0
$569$	−12145.4	+	12145.4i	−0.894833	+	0.894833i	−0.994973	−	0.100141i	$-0.968071\pi$
$569$	−12145.4	+	12145.4i	−0.894833	+	0.894833i	0.100141	+	0.994973i	$0.468071\pi$
$570$		0			0
$571$	−13625.2	−	5643.73i	−0.998591	−	0.413630i	−0.177311	−	0.984155i	$-0.556740\pi$
$571$	−13625.2	−	5643.73i	−0.998591	−	0.413630i	−0.821280	+	0.570525i	$0.806740\pi$
$572$		0			0
$573$	17911.8	−	7419.32i	1.30589	−	0.540919i
$574$		0			0
$575$	−549.722	−	1327.15i	−0.0398696	−	0.0962536i
$576$		0			0
$577$	−21154.7			−1.52631			−0.763156	−	0.646214i	$-0.776351\pi$
$577$	−21154.7			−1.52631			−0.763156	+	0.646214i	$0.776351\pi$
$578$		0			0
$579$	8940.77			0.641737
$580$		0			0
$581$	−972.678	−	2348.25i	−0.0694552	−	0.167680i
$582$		0			0
$583$	−1344.88	+	557.069i	−0.0955392	+	0.0395736i
$584$		0			0
$585$	23355.6	+	9674.20i	1.65066	+	0.683724i
$586$		0			0
$587$	199.666	−	199.666i	0.0140393	−	0.0140393i	−0.700052	−	0.714092i	$-0.746840\pi$
$587$	199.666	−	199.666i	0.0140393	−	0.0140393i	0.714092	+	0.700052i	$0.246840\pi$
$588$		0			0
$589$	3838.74	−	9267.55i	0.268544	−	0.648324i
$590$		0			0
$591$		−	26941.3i		−	1.87515i
$592$		0			0
$593$	−18956.7	−	18956.7i	−1.31275	−	1.31275i	−0.919382	−	0.393365i	$-0.871311\pi$
$593$	−18956.7	−	18956.7i	−1.31275	−	1.31275i	−0.393365	−	0.919382i	$-0.628689\pi$
$594$		0			0
$595$	1165.76	+	2465.83i	0.0803220	+	0.169898i
$596$		0			0
$597$	−5741.38	−	5741.38i	−0.393600	−	0.393600i
$598$		0			0
$599$			24971.8i			1.70337i	0.524050	+	0.851687i	$0.324420\pi$
$599$			24971.8i			1.70337i	−0.524050	+	0.851687i	$0.675580\pi$
$600$		0			0
$601$	5017.08	−	12112.3i	0.340518	−	0.822082i	−0.657146	−	0.753763i	$-0.728236\pi$
$601$	5017.08	−	12112.3i	0.340518	−	0.822082i	0.997664	−	0.0683189i	$-0.0217635\pi$
$602$		0			0
$603$	−23039.1	+	23039.1i	−1.55593	+	1.55593i
$604$		0			0
$605$	−11529.1	−	4775.52i	−0.774754	−	0.320914i
$606$		0			0
$607$	20011.0	−	8288.83i	1.33809	−	0.554256i	0.405139	−	0.914255i	$-0.367223\pi$
$607$	20011.0	−	8288.83i	1.33809	−	0.554256i	0.932952	+	0.360000i	$0.117223\pi$
$608$		0			0
$609$	2132.29	+	5147.80i	0.141880	+	0.342528i
$610$		0			0
$611$	−8833.21			−0.584866
$612$		0			0
$613$	13819.3			0.910535			0.455268	−	0.890355i	$-0.349544\pi$
$613$	13819.3			0.910535			0.455268	+	0.890355i	$0.349544\pi$
$614$		0			0
$615$	−8342.20	−	20139.9i	−0.546976	−	1.32052i
$616$		0			0
$617$	6287.22	−	2604.25i	0.410233	−	0.169924i	−0.168016	−	0.985784i	$-0.553736\pi$
$617$	6287.22	−	2604.25i	0.410233	−	0.169924i	0.578249	+	0.815860i	$0.303736\pi$
$618$		0			0
$619$	9034.41	+	3742.17i	0.586629	+	0.242990i	0.656200	−	0.754587i	$-0.272163\pi$
$619$	9034.41	+	3742.17i	0.586629	+	0.242990i	−0.0695706	+	0.997577i	$0.522163\pi$
$620$		0			0
$621$	4436.50	−	4436.50i	0.286684	−	0.286684i
$622$		0			0
$623$	−2008.85	+	4849.79i	−0.129186	+	0.311882i
$624$		0			0
$625$			9717.69i			0.621932i
$626$		0			0
$627$	1008.54	+	1008.54i	0.0642378	+	0.0642378i
$628$		0			0
$629$	15902.3	−	17539.7i	1.00805	−	1.11185i
$630$		0			0
$631$	−10905.1	−	10905.1i	−0.687993	−	0.687993i	0.273795	−	0.961788i	$-0.411721\pi$
$631$	−10905.1	−	10905.1i	−0.687993	−	0.687993i	−0.961788	+	0.273795i	$0.911721\pi$
$632$		0			0
$633$		−	40237.3i		−	2.52652i
$634$		0			0
$635$	3819.11	−	9220.15i	0.238672	−	0.576205i
$636$		0			0
$637$	13546.7	−	13546.7i	0.842605	−	0.842605i
$638$		0			0
$639$	35075.2	+	14528.6i	2.17145	+	0.899443i
$640$		0			0
$641$	−68.6209	+	28.4237i	−0.00422833	+	0.00175143i	−0.384797	−	0.923001i	$-0.625728\pi$
$641$	−68.6209	+	28.4237i	−0.00422833	+	0.00175143i	0.380568	+	0.924753i	$0.375728\pi$
$642$		0			0
$643$	−2711.95	−	6547.22i	−0.166328	−	0.401551i	0.818636	−	0.574313i	$-0.194731\pi$
$643$	−2711.95	−	6547.22i	−0.166328	−	0.401551i	−0.984964	+	0.172762i	$0.944731\pi$
$644$		0			0
$645$	19185.3			1.17119
$646$		0			0
$647$	−11222.7			−0.681932			−0.340966	−	0.940076i	$-0.610754\pi$
$647$	−11222.7			−0.681932			−0.340966	+	0.940076i	$0.610754\pi$
$648$		0			0
$649$	486.471	+	1174.44i	0.0294232	+	0.0710338i
$650$		0			0
$651$	−3918.87	+	1623.25i	−0.235933	+	0.0977268i
$652$		0			0
$653$	17536.7	+	7263.94i	1.05094	+	0.435314i	0.840228	−	0.542234i	$-0.182421\pi$
$653$	17536.7	+	7263.94i	1.05094	+	0.435314i	0.210714	+	0.977548i	$0.432421\pi$
$654$		0			0
$655$	−7.68915	+	7.68915i	−0.000458687	+	0.000458687i
$656$		0			0
$657$	8928.65	−	21555.7i	0.530198	−	1.28001i
$658$		0			0
$659$		−	26196.7i		−	1.54853i	−0.632864	−	0.774263i	$-0.718121\pi$
$659$		−	26196.7i		−	1.54853i	0.632864	−	0.774263i	$-0.281879\pi$
$660$		0			0
$661$	−4766.21	−	4766.21i	−0.280460	−	0.280460i	0.552832	−	0.833292i	$-0.313547\pi$
$661$	−4766.21	−	4766.21i	−0.280460	−	0.280460i	−0.833292	+	0.552832i	$0.813547\pi$
$662$		0			0
$663$	26033.8	+	23603.4i	1.52499	+	1.38262i
$664$		0			0
$665$	2296.18	+	2296.18i	0.133898	+	0.133898i
$666$		0			0
$667$			6203.54i			0.360123i
$668$		0			0
$669$	−12701.1	+	30663.3i	−0.734013	+	1.77206i
$670$		0			0
$671$	−875.064	+	875.064i	−0.0503450	+	0.0503450i
$672$		0			0
$673$	6588.41	+	2729.01i	0.377362	+	0.156308i	0.563299	−	0.826253i	$-0.309532\pi$
$673$	6588.41	+	2729.01i	0.377362	+	0.156308i	−0.185937	+	0.982562i	$0.559532\pi$
$674$		0			0
$675$	5394.62	−	2234.52i	0.307613	−	0.127418i
$676$		0			0
$677$	−1644.09	−	3969.19i	−0.0933346	−	0.225330i	0.870317	−	0.492492i	$-0.163914\pi$
$677$	−1644.09	−	3969.19i	−0.0933346	−	0.225330i	−0.963652	+	0.267162i	$0.913914\pi$
$678$		0			0
$679$	−4253.43			−0.240400
$680$		0			0
$681$	25551.0			1.43776
$682$		0			0
$683$	−4718.94	−	11392.5i	−0.264371	−	0.638248i	0.734829	−	0.678253i	$-0.237263\pi$
$683$	−4718.94	−	11392.5i	−0.264371	−	0.638248i	−0.999199	+	0.0400051i	$0.987263\pi$
$684$		0			0
$685$	−5051.95	+	2092.59i	−0.281789	+	0.116721i
$686$		0			0
$687$	−30944.1	−	12817.5i	−1.71847	−	0.711815i
$688$		0			0
$689$	−30193.5	+	30193.5i	−1.66950	+	1.66950i
$690$		0			0
$691$	−9124.08	+	22027.5i	−0.502310	+	1.21268i	0.445912	+	0.895077i	$0.352879\pi$
$691$	−9124.08	+	22027.5i	−0.502310	+	1.21268i	−0.948222	+	0.317607i	$0.897121\pi$
$692$		0			0
$693$		−	379.208i		−	0.0207863i
$694$		0			0
$695$	16764.9	+	16764.9i	0.915008	+	0.915008i
$696$		0			0
$697$	−931.768	−	19029.7i	−0.0506359	−	1.03415i
$698$		0			0
$699$	16991.9	+	16991.9i	0.919447	+	0.919447i
$700$		0			0
$701$			33388.6i			1.79896i	0.436964	+	0.899479i	$0.356054\pi$
$701$			33388.6i			1.79896i	−0.436964	+	0.899479i	$0.643946\pi$
$702$		0			0
$703$	10786.8	−	26041.6i	0.578707	−	1.39712i
$704$		0			0
$705$	8520.64	−	8520.64i	0.455186	−	0.455186i
$706$		0			0
$707$	204.584	+	84.7416i	0.0108829	+	0.00450783i
$708$		0			0
$709$	17467.0	−	7235.08i	0.925231	−	0.383243i	0.131363	−	0.991334i	$-0.458065\pi$
$709$	17467.0	−	7235.08i	0.925231	−	0.383243i	0.793867	+	0.608091i	$0.208065\pi$
$710$		0			0
$711$	5244.19	+	12660.6i	0.276614	+	0.667805i
$712$		0			0
$713$	−4722.57			−0.248053
$714$		0			0
$715$	1108.01			0.0579539
$716$		0			0
$717$	−15460.7	−	37325.5i	−0.805289	−	1.94414i
$718$		0			0
$719$	23990.8	−	9937.31i	1.24437	−	0.515437i	0.339296	−	0.940680i	$-0.389811\pi$
$719$	23990.8	−	9937.31i	1.24437	−	0.515437i	0.905079	+	0.425243i	$0.139811\pi$
$720$		0			0
$721$	5214.60	+	2159.96i	0.269351	+	0.111569i
$722$		0			0
$723$	−24101.3	+	24101.3i	−1.23974	+	1.23974i
$724$		0			0
$725$	−2209.37	+	5333.90i	−0.113178	+	0.273236i
$726$		0			0
$727$		−	3980.23i		−	0.203052i	−0.994833	−	0.101526i	$-0.967628\pi$
$727$		−	3980.23i		−	0.203052i	0.994833	−	0.101526i	$-0.0323724\pi$
$728$		0			0
$729$	−21885.6	−	21885.6i	−1.11190	−	1.11190i
$730$		0			0
$731$	15786.8	+	5651.51i	0.798764	+	0.285949i
$732$		0			0
$733$	5827.96	+	5827.96i	0.293671	+	0.293671i	0.838528	−	0.544858i	$-0.183416\pi$
$733$	5827.96	+	5827.96i	0.293671	+	0.293671i	−0.544858	+	0.838528i	$0.683416\pi$
$734$		0			0
$735$			26134.7i			1.31155i
$736$		0			0
$737$	−546.497	+	1319.36i	−0.0273141	+	0.0659420i
$738$		0			0
$739$	−16134.4	+	16134.4i	−0.803133	+	0.803133i	−0.983584	−	0.180451i	$-0.942244\pi$
$739$	−16134.4	+	16134.4i	−0.803133	+	0.803133i	0.180451	+	0.983584i	$0.442244\pi$
$740$		0			0
$741$	38652.9	+	16010.5i	1.91626	+	0.793741i
$742$		0			0
$743$	−14701.2	+	6089.46i	−0.725890	+	0.300674i	−0.714862	−	0.699266i	$-0.753510\pi$
$743$	−14701.2	+	6089.46i	−0.725890	+	0.300674i	−0.0110283	+	0.999939i	$0.503510\pi$
$744$		0			0
$745$	6800.66	+	16418.3i	0.334439	+	0.807407i
$746$		0			0
$747$	28087.8			1.37574
$748$		0			0
$749$	−2219.96			−0.108298
$750$		0			0
$751$	−12914.0	−	31177.2i	−0.627483	−	1.51488i	−0.842740	−	0.538321i	$-0.819059\pi$
$751$	−12914.0	−	31177.2i	−0.627483	−	1.51488i	0.215257	−	0.976557i	$-0.430941\pi$
$752$		0			0
$753$	−51599.5	+	21373.2i	−2.49720	+	1.03437i
$754$		0			0
$755$	9808.51	+	4062.82i	0.472806	+	0.195843i
$756$		0			0
$757$	−12625.8	+	12625.8i	−0.606200	+	0.606200i	−0.941951	−	0.335750i	$-0.891010\pi$
$757$	−12625.8	+	12625.8i	−0.606200	+	0.606200i	0.335750	+	0.941951i	$0.391010\pi$
$758$		0			0
$759$	256.966	−	620.370i	0.0122889	−	0.0296680i
$760$		0			0
$761$		−	15100.8i		−	0.719322i	−0.933083	−	0.359661i	$-0.882892\pi$
$761$		−	15100.8i		−	0.719322i	0.933083	−	0.359661i	$-0.117108\pi$
$762$		0			0
$763$	−3978.19	−	3978.19i	−0.188755	−	0.188755i
$764$		0			0
$765$	−30104.8	+	1474.04i	−1.42280	+	0.0696656i
$766$		0			0
$767$	26367.1	+	26367.1i	1.24128	+	1.24128i
$768$		0			0
$769$		−	22563.7i		−	1.05809i	−0.848595	−	0.529044i	$-0.822551\pi$
$769$		−	22563.7i		−	1.05809i	0.848595	−	0.529044i	$-0.177449\pi$
$770$		0			0
$771$	3345.02	−	8075.59i	0.156249	−	0.377218i
$772$		0			0
$773$	−8908.54	+	8908.54i	−0.414512	+	0.414512i	−0.883307	−	0.468795i	$-0.844688\pi$
$773$	−8908.54	+	8908.54i	−0.414512	+	0.414512i	0.468795	+	0.883307i	$0.344688\pi$
$774$		0			0
$775$	−4060.54	−	1681.93i	−0.188205	−	0.0779571i
$776$		0			0
$777$	−11011.9	+	4561.29i	−0.508431	+	0.210599i
$778$		0			0
$779$	−8680.54	−	20956.7i	−0.399246	−	0.963865i
$780$		0			0
$781$	1664.00			0.0762387
$782$		0			0
$783$	−25216.3			−1.15090
$784$		0			0
$785$	−7244.25	−	17489.2i	−0.329374	−	0.795179i
$786$		0			0
$787$	31383.8	−	12999.6i	1.42149	−	0.588800i	0.466255	−	0.884650i	$-0.345603\pi$
$787$	31383.8	−	12999.6i	1.42149	−	0.588800i	0.955234	+	0.295850i	$0.0956030\pi$
$788$		0			0
$789$	−11298.3	−	4679.92i	−0.509799	−	0.211166i
$790$		0			0
$791$	3774.09	−	3774.09i	0.169647	−	0.169647i
$792$		0			0
$793$	−13891.7	+	33537.4i	−0.622078	+	1.50183i
$794$		0			0
$795$		−	58250.3i		−	2.59865i
$796$		0			0
$797$	1470.00	+	1470.00i	0.0653325	+	0.0653325i	0.739018	−	0.673686i	$-0.235290\pi$
$797$	1470.00	+	1470.00i	0.0653325	+	0.0653325i	−0.673686	+	0.739018i	$0.735290\pi$
$798$		0			0
$799$	9521.28	−	4501.34i	0.421576	−	0.199306i
$800$		0			0
$801$	−41018.6	−	41018.6i	−1.80939	−	1.80939i
$802$		0			0
$803$		−	1022.62i		−	0.0449407i
$804$		0			0
$805$	585.046	−	1412.43i	0.0256151	−	0.0618404i
$806$		0			0
$807$	−7597.37	+	7597.37i	−0.331401	+	0.331401i
$808$		0			0
$809$	−2085.08	−	863.668i	−0.0906150	−	0.0375339i	0.336916	−	0.941535i	$-0.390616\pi$
$809$	−2085.08	−	863.668i	−0.0906150	−	0.0375339i	−0.427530	+	0.904001i	$0.640616\pi$
$810$		0			0
$811$	8282.53	−	3430.74i	0.358618	−	0.148544i	−0.196098	−	0.980584i	$-0.562827\pi$
$811$	8282.53	−	3430.74i	0.358618	−	0.148544i	0.554716	+	0.832040i	$0.312827\pi$
$812$		0			0
$813$	−1785.10	−	4309.60i	−0.0770062	−	0.185909i
$814$		0			0
$815$	−26337.2			−1.13196
$816$		0			0
$817$	19963.4			0.854871
$818$		0			0
$819$	−4256.74	−	10276.7i	−0.181615	−	0.438457i
$820$		0			0
$821$	−12850.2	+	5322.71i	−0.546253	+	0.226265i	−0.638705	−	0.769452i	$-0.720529\pi$
$821$	−12850.2	+	5322.71i	−0.546253	+	0.226265i	0.0924522	+	0.995717i	$0.470529\pi$
$822$		0			0
$823$	−16743.5	−	6935.37i	−0.709162	−	0.293745i	−0.00120448	−	0.999999i	$-0.500383\pi$
$823$	−16743.5	−	6935.37i	−0.709162	−	0.293745i	−0.707958	+	0.706255i	$0.750383\pi$
$824$		0			0
$825$	441.887	−	441.887i	0.0186479	−	0.0186479i
$826$		0			0
$827$	8981.88	−	21684.2i	0.377667	−	0.911768i	−0.614736	−	0.788733i	$-0.710737\pi$
$827$	8981.88	−	21684.2i	0.377667	−	0.911768i	0.992402	−	0.123035i	$-0.0392628\pi$
$828$		0			0
$829$			43790.8i			1.83464i	0.398149	+	0.917321i	$0.369653\pi$
$829$			43790.8i			1.83464i	−0.398149	+	0.917321i	$0.630347\pi$
$830$		0			0
$831$	45002.6	+	45002.6i	1.87861	+	1.87861i
$832$		0			0
$833$	−7698.63	+	21505.2i	−0.320218	+	0.894492i
$834$		0			0
$835$	13886.7	+	13886.7i	0.575534	+	0.575534i
$836$		0			0
$837$		−	19196.4i		−	0.792742i
$838$		0			0
$839$	4927.55	−	11896.2i	0.202763	−	0.489512i	−0.789488	−	0.613766i	$-0.789654\pi$
$839$	4927.55	−	11896.2i	0.202763	−	0.489512i	0.992250	+	0.124254i	$0.0396537\pi$
$840$		0			0
$841$	384.274	−	384.274i	0.0157560	−	0.0157560i
$842$		0			0
$843$	35171.1	+	14568.3i	1.43696	+	0.595208i
$844$		0			0
$845$	10939.3	−	4531.22i	0.445354	−	0.184472i
$846$		0			0
$847$	2101.28	+	5072.93i	0.0852428	+	0.205794i
$848$		0			0
$849$	−50621.8			−2.04633
$850$		0			0
$851$	−13270.3			−0.534548
$852$		0			0
$853$	9881.85	+	23856.9i	0.396657	+	0.957614i	0.988453	+	0.151526i	$0.0484189\pi$
$853$	9881.85	+	23856.9i	0.396657	+	0.957614i	−0.591797	+	0.806087i	$0.701581\pi$
$854$		0			0
$855$	−33153.2	+	13732.5i	−1.32610	+	0.549289i
$856$		0			0
$857$	15661.0	+	6487.02i	0.624237	+	0.258567i	0.672302	−	0.740277i	$-0.265306\pi$
$857$	15661.0	+	6487.02i	0.624237	+	0.258567i	−0.0480652	+	0.998844i	$0.515306\pi$
$858$		0			0
$859$	9024.56	−	9024.56i	0.358456	−	0.358456i	−0.504787	−	0.863244i	$-0.668429\pi$
$859$	9024.56	−	9024.56i	0.358456	−	0.358456i	0.863244	+	0.504787i	$0.168429\pi$
$860$		0			0
$861$	−3670.65	+	8861.73i	−0.145291	+	0.350763i
$862$		0			0
$863$		−	894.306i		−	0.0352752i	−0.999844	−	0.0176376i	$-0.994385\pi$
$863$		−	894.306i		−	0.0352752i	0.999844	−	0.0176376i	$-0.00561452\pi$
$864$		0			0
$865$	−6361.92	−	6361.92i	−0.250071	−	0.250071i
$866$		0			0
$867$	−40089.9	−	12175.4i	−1.57038	−	0.476929i
$868$		0			0
$869$	424.708	+	424.708i	0.0165791	+	0.0165791i
$870$		0			0
$871$			41889.8i			1.62960i
$872$		0			0
$873$	17987.3	−	43425.3i	0.697342	−	1.68353i
$874$		0			0
$875$	4445.51	−	4445.51i	0.171755	−	0.171755i
$876$		0			0
$877$	−2758.12	−	1142.45i	−0.106198	−	0.0439885i	0.328952	−	0.944347i	$-0.393305\pi$
$877$	−2758.12	−	1142.45i	−0.106198	−	0.0439885i	−0.435150	+	0.900358i	$0.643305\pi$
$878$		0			0
$879$	−5284.11	+	2188.75i	−0.202763	+	0.0839872i
$880$		0			0
$881$	−771.440	−	1862.42i	−0.0295011	−	0.0712219i	0.908442	−	0.418010i	$-0.137272\pi$
$881$	−771.440	−	1862.42i	−0.0295011	−	0.0712219i	−0.937944	+	0.346788i	$0.887272\pi$
$882$		0			0
$883$	−14631.2			−0.557620			−0.278810	−	0.960346i	$-0.589940\pi$
$883$	−14631.2			−0.557620			−0.278810	+	0.960346i	$0.589940\pi$
$884$		0			0
$885$	−50868.1			−1.93211
$886$		0			0
$887$	15773.5	+	38080.5i	0.597092	+	1.44151i	0.876531	+	0.481345i	$0.159851\pi$
$887$	15773.5	+	38080.5i	0.597092	+	1.44151i	−0.279439	+	0.960163i	$0.590149\pi$
$888$		0			0
$889$	−4056.95	+	1680.44i	−0.153055	+	0.0633974i
$890$		0			0
$891$	235.684	+	97.6234i	0.00886161	+	0.00367060i
$892$		0			0
$893$	8866.22	−	8866.22i	0.332247	−	0.332247i
$894$		0			0
$895$	−15064.8	+	36369.7i	−0.562638	+	1.35833i
$896$		0			0
$897$		−	19696.8i		−	0.733174i
$898$		0			0
$899$	13421.1	+	13421.1i	0.497909	+	0.497909i
$900$		0			0
$901$	17159.1	−	47931.9i	0.634465	−	1.77230i
$902$		0			0
$903$	−5969.18	−	5969.18i	−0.219980	−	0.219980i
$904$		0			0
$905$		−	4375.98i		−	0.160732i
$906$		0			0
$907$	−17837.3	+	43063.1i	−0.653008	+	1.57650i	0.155382	+	0.987854i	$0.450339\pi$
$907$	−17837.3	+	43063.1i	−0.653008	+	1.57650i	−0.808390	+	0.588647i	$0.799661\pi$
$908$		0			0
$909$	−1730.34	+	1730.34i	−0.0631371	+	0.0631371i
$910$		0			0
$911$	−28055.3	−	11620.9i	−1.02032	−	0.422631i	−0.191111	−	0.981568i	$-0.561209\pi$
$911$	−28055.3	−	11620.9i	−1.02032	−	0.422631i	−0.829210	+	0.558937i	$0.811209\pi$
$912$		0			0
$913$	1137.37	−	471.112i	0.0412281	−	0.0170773i
$914$		0			0
$915$	−18950.6	−	45750.8i	−0.684686	−	1.65298i
$916$		0			0
$917$	4.78470			0.000172306
$918$		0			0
$919$	−4035.91			−0.144867			−0.0724333	−	0.997373i	$-0.523076\pi$
$919$	−4035.91			−0.144867			−0.0724333	+	0.997373i	$0.523076\pi$
$920$		0			0
$921$	30356.5	+	73287.2i	1.08608	+	2.62204i
$922$		0			0
$923$	45094.9	−	18678.9i	1.60814	−	0.666115i
$924$		0			0
$925$	−11410.0	−	4726.18i	−0.405577	−	0.167996i
$926$		0			0
$927$	−44104.1	+	44104.1i	−1.56264	+	1.56264i
$928$		0			0
$929$	−2340.54	+	5650.57i	−0.0826595	+	0.199558i	−0.959805	−	0.280666i	$-0.909445\pi$
$929$	−2340.54	+	5650.57i	−0.0826595	+	0.199558i	0.877146	+	0.480224i	$0.159445\pi$
$930$		0			0
$931$			27194.6i			0.957322i
$932$		0			0
$933$	54708.4	+	54708.4i	1.91969	+	1.91969i
$934$		0			0
$935$	−1194.32	+	564.632i	−0.0417736	+	0.0197491i
$936$		0			0
$937$	22483.0	+	22483.0i	0.783873	+	0.783873i	0.980482	−	0.196609i	$-0.0629931\pi$
$937$	22483.0	+	22483.0i	0.783873	+	0.783873i	−0.196609	+	0.980482i	$0.562993\pi$
$938$		0			0
$939$		−	29397.8i		−	1.02169i
$940$		0			0
$941$	15721.8	−	37955.9i	0.544652	−	1.31491i	−0.376757	−	0.926312i	$-0.622961\pi$
$941$	15721.8	−	37955.9i	0.544652	−	1.31491i	0.921409	−	0.388594i	$-0.127039\pi$
$942$		0			0
$943$	−7551.29	+	7551.29i	−0.260768	+	0.260768i
$944$		0			0
$945$	5741.26	+	2378.11i	0.197633	+	0.0818623i
$946$		0			0
$947$	37104.1	−	15369.0i	1.27320	−	0.527377i	0.359266	−	0.933235i	$-0.383027\pi$
$947$	37104.1	−	15369.0i	1.27320	−	0.527377i	0.913936	+	0.405858i	$0.133027\pi$
$948$		0			0
$949$	−11479.2	−	27713.3i	−0.392657	−	0.947958i
$950$		0			0
$951$	51681.8			1.76225
$952$		0			0
$953$	34421.2			1.17000			0.585002	−	0.811032i	$-0.301094\pi$
$953$	34421.2			1.17000			0.585002	+	0.811032i	$0.301094\pi$
$954$		0			0
$955$	8181.53	+	19752.0i	0.277223	+	0.669276i
$956$		0			0
$957$	−2493.31	+	1032.76i	−0.0842188	+	0.0348846i
$958$		0			0
$959$	2222.91	+	920.758i	0.0748502	+	0.0310040i
$960$		0			0
$961$	10848.3	−	10848.3i	0.364147	−	0.364147i
$962$		0			0
$963$	9387.99	−	22664.6i	0.314147	−	0.758419i
$964$		0			0
$965$			9859.27i			0.328892i
$966$		0			0
$967$	−15110.4	−	15110.4i	−0.502500	−	0.502500i	0.409714	−	0.912214i	$-0.365628\pi$
$967$	−15110.4	−	15110.4i	−0.502500	−	0.502500i	−0.912214	+	0.409714i	$0.865628\pi$
$968$		0			0
$969$	−49822.7	+	2439.51i	−1.65174	+	0.0808754i
$970$		0			0
$971$	−28513.3	−	28513.3i	−0.942362	−	0.942362i	0.0560648	−	0.998427i	$-0.482145\pi$
$971$	−28513.3	−	28513.3i	−0.942362	−	0.942362i	−0.998427	+	0.0560648i	$0.982145\pi$
$972$		0			0
$973$		−	10432.3i		−	0.343724i
$974$		0			0
$975$	7014.96	−	16935.6i	0.230419	−	0.556281i
$976$		0			0
$977$	30873.7	−	30873.7i	1.01099	−	1.01099i	0.0110496	−	0.999939i	$-0.496483\pi$
$977$	30873.7	−	30873.7i	1.01099	−	1.01099i	0.999939	−	0.0110496i	$-0.00351728\pi$
$978$		0			0
$979$	−2348.97	−	972.977i	−0.0766839	−	0.0317635i
$980$		0			0
$981$	57438.7	−	23791.9i	1.86939	−	0.774328i
$982$		0			0
$983$	1772.57	+	4279.37i	0.0575140	+	0.138851i	0.950024	−	0.312176i	$-0.101058\pi$
$983$	1772.57	+	4279.37i	0.0575140	+	0.138851i	−0.892510	+	0.451027i	$0.851058\pi$
$984$		0			0
$985$	29709.0			0.961023
$986$		0			0
$987$	−5302.12			−0.170991
$988$		0			0
$989$	−3596.68	−	8683.16i	−0.115640	−	0.279180i
$990$		0			0
$991$	−8173.02	+	3385.38i	−0.261982	+	0.108517i	−0.509809	−	0.860288i	$-0.670284\pi$
$991$	−8173.02	+	3385.38i	−0.261982	+	0.108517i	0.247826	+	0.968805i	$0.420284\pi$
$992$		0			0
$993$	85923.5	+	35590.7i	2.74592	+	1.13740i
$994$		0			0
$995$	6331.21	−	6331.21i	0.201721	−	0.201721i
$996$		0			0
$997$	−6197.31	+	14961.6i	−0.196861	+	0.475265i	−0.991226	−	0.132175i	$-0.957804\pi$
$997$	−6197.31	+	14961.6i	−0.196861	+	0.475265i	0.794365	+	0.607441i	$0.207804\pi$
$998$		0			0
$999$		−	53941.4i		−	1.70834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.n.a.49.6	yes	24
17.5	odd	16		2312.4.a.r.1.2		24
17.8	even	8	inner	136.4.n.a.25.6	✓	24
17.12	odd	16		2312.4.a.r.1.23		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.n.a.25.6	✓	24	17.8	even	8	inner
136.4.n.a.49.6	yes	24	1.1	even	1	trivial
2312.4.a.r.1.2		24	17.5	odd	16
2312.4.a.r.1.23		24	17.12	odd	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.26351 + 7.87882i) q^{3} +(-8.68823 + 3.59878i) q^{5} +(3.82290 + 1.58350i) q^{7} +(-32.3334 + 32.3334i) q^{9} +(-0.766960 + 1.85161i) q^{11} +58.7886i q^{13} +(-56.7083 - 56.7083i) q^{15} +(-29.9582 - 63.3680i) q^{17} +(-59.0083 - 59.0083i) q^{19} +35.2877i q^{21} +(-15.0348 + 36.2971i) q^{23} +(-25.8542 + 25.8542i) q^{25} +(-147.541 - 61.1136i) q^{27} +(145.881 - 60.4258i) q^{29} +(46.0004 + 111.055i) q^{31} -17.0915 q^{33} -38.9129 q^{35} +(129.260 + 312.061i) q^{37} +(-463.185 + 191.857i) q^{39} +(251.128 + 104.021i) q^{41} +(-169.157 + 169.157i) q^{43} +(164.559 - 397.281i) q^{45} +150.254i q^{47} +(-230.431 - 230.431i) q^{49} +(401.496 - 442.838i) q^{51} +(513.595 + 513.595i) q^{53} -18.8473i q^{55} +(272.341 - 657.490i) q^{57} +(448.507 - 448.507i) q^{59} +(570.476 + 236.299i) q^{61} +(-174.807 + 72.4075i) q^{63} +(-211.567 - 510.769i) q^{65} +712.549 q^{67} -335.045 q^{69} +(-317.730 - 767.069i) q^{71} +(-471.406 + 195.263i) q^{73} +(-288.077 - 119.325i) q^{75} +(-5.86403 + 5.86403i) q^{77} +(114.686 - 276.878i) q^{79} -127.286i q^{81} +(-434.347 - 434.347i) q^{83} +(488.332 + 442.743i) q^{85} +(952.167 + 952.167i) q^{87} +1268.61i q^{89} +(-93.0916 + 224.743i) q^{91} +(-724.857 + 724.857i) q^{93} +(725.035 + 300.319i) q^{95} +(-949.678 + 393.369i) q^{97} +(-35.0703 - 84.6671i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 28 q^{5} - 16 q^{9} + 140 q^{11} - 60 q^{15} - 164 q^{17} - 124 q^{19} - 72 q^{23} + 52 q^{25} - 360 q^{27} + 44 q^{29} - 120 q^{31} + 520 q^{33} + 512 q^{35} + 196 q^{37} - 232 q^{39} + 20 q^{41}+ \cdots + 5244 q^{99}+O(q^{100}) \) 24 * q - 28 * q^5 - 16 * q^9 + 140 * q^11 - 60 * q^15 - 164 * q^17 - 124 * q^19 - 72 * q^23 + 52 * q^25 - 360 * q^27 + 44 * q^29 - 120 * q^31 + 520 * q^33 + 512 * q^35 + 196 * q^37 - 232 * q^39 + 20 * q^41 - 160 * q^43 + 1412 * q^45 - 1020 * q^49 - 248 * q^51 + 92 * q^53 + 28 * q^57 + 656 * q^59 - 1028 * q^61 - 2356 * q^63 + 1392 * q^65 + 1960 * q^67 - 2408 * q^69 - 264 * q^71 + 548 * q^73 - 2356 * q^75 + 492 * q^77 + 2496 * q^79 - 536 * q^83 - 972 * q^85 + 3508 * q^87 + 1320 * q^91 + 2684 * q^93 - 5972 * q^95 - 4936 * q^97 + 5244 * q^99

Introduction

L-functions

Modular forms

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Database

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