LMFDB - Embedded newform 684.3.t.a.265.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(265,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("684.265");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			265.14
Character	$\chi$	$=$	684.265
Dual form			684.3.t.a.493.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21404 - 2.74338i) q^{3} +(-3.81342 + 6.60503i) q^{5} +(1.86164 + 3.22446i) q^{7} +(-6.05222 + 6.66113i) q^{9} +O(q^{10})$	\(q+(-1.21404 - 2.74338i) q^{3} +(-3.81342 + 6.60503i) q^{5} +(1.86164 + 3.22446i) q^{7} +(-6.05222 + 6.66113i) q^{9} +(4.51751 + 7.82455i) q^{11} +(-14.3462 - 8.28281i) q^{13} +(22.7497 + 2.44287i) q^{15} -17.8798 q^{17} +(16.8247 - 8.82771i) q^{19} +(6.58580 - 9.02181i) q^{21} +(11.1954 - 19.3911i) q^{23} +(-16.5843 - 28.7249i) q^{25} +(25.6216 + 8.51665i) q^{27} +(6.74845 - 3.89622i) q^{29} +(-16.7284 - 9.65812i) q^{31} +(15.9813 - 21.8925i) q^{33} -28.3969 q^{35} -36.8348i q^{37} +(-5.30596 + 49.4128i) q^{39} +(36.8467 + 21.2734i) q^{41} +(-18.1721 - 31.4750i) q^{43} +(-20.9173 - 65.3768i) q^{45} +(-26.7261 - 46.2909i) q^{47} +(17.5686 - 30.4296i) q^{49} +(21.7068 + 49.0511i) q^{51} +11.8904i q^{53} -68.9085 q^{55} +(-44.6436 - 35.4394i) q^{57} +(-40.6788 - 23.4859i) q^{59} +(10.0255 + 17.3646i) q^{61} +(-32.7456 - 7.11451i) q^{63} +(109.416 - 63.1716i) q^{65} +(-77.5915 - 44.7975i) q^{67} +(-66.7887 - 7.17179i) q^{69} +81.2577i q^{71} -72.6229 q^{73} +(-58.6691 + 80.3701i) q^{75} +(-16.8200 + 29.1331i) q^{77} +(-17.5298 + 10.1208i) q^{79} +(-7.74126 - 80.6292i) q^{81} +(6.41240 + 11.1066i) q^{83} +(68.1833 - 118.097i) q^{85} +(-18.8817 - 13.7834i) q^{87} -80.1144i q^{89} -61.6786i q^{91} +(-6.18698 + 57.6175i) q^{93} +(-5.85240 + 144.792i) q^{95} +(-147.549 + 85.1873i) q^{97} +(-79.4613 - 17.2642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 2 * q^7 + 4 * q^9	$ 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) $ 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.21404	−	2.74338i	−0.404680	−	0.914459i
$3$	−1.21404	−	2.74338i	−0.404680	−	0.914459i
$4$		0			0
$5$	−3.81342	+	6.60503i	−0.762684	+	1.32101i	0.178779	+	0.983889i	$0.442785\pi$
$5$	−3.81342	+	6.60503i	−0.762684	+	1.32101i	−0.941463	+	0.337117i	$0.890548\pi$
$6$		0			0
$7$	1.86164	+	3.22446i	0.265949	+	0.460638i	0.967812	−	0.251675i	$-0.0809813\pi$
$7$	1.86164	+	3.22446i	0.265949	+	0.460638i	−0.701863	+	0.712312i	$0.747648\pi$
$8$		0			0
$9$	−6.05222	+	6.66113i	−0.672469	+	0.740125i
$10$		0			0
$11$	4.51751	+	7.82455i	0.410682	+	0.711323i	0.994965	−	0.100228i	$-0.0319572\pi$
$11$	4.51751	+	7.82455i	0.410682	+	0.711323i	−0.584282	+	0.811551i	$0.698624\pi$
$12$		0			0
$13$	−14.3462	−	8.28281i	−1.10356	−	0.637139i	−0.166404	−	0.986058i	$-0.553216\pi$
$13$	−14.3462	−	8.28281i	−1.10356	−	0.637139i	−0.937153	+	0.348918i	$0.886549\pi$
$14$		0			0
$15$	22.7497	+	2.44287i	1.51665	+	0.162858i
$16$		0			0
$17$	−17.8798			−1.05176			−0.525878	−	0.850560i	$-0.676263\pi$
$17$	−17.8798			−1.05176			−0.525878	+	0.850560i	$0.676263\pi$
$18$		0			0
$19$	16.8247	−	8.82771i	0.885512	−	0.464616i
$19$	16.8247	−	8.82771i	0.885512	−	0.464616i
$20$		0			0
$21$	6.58580	−	9.02181i	0.313610	−	0.429610i
$22$		0			0
$23$	11.1954	−	19.3911i	0.486758	−	0.843090i	−0.513126	−	0.858313i	$-0.671513\pi$
$23$	11.1954	−	19.3911i	0.486758	−	0.843090i	0.999884	+	0.0152232i	$0.00484588\pi$
$24$		0			0
$25$	−16.5843	−	28.7249i	−0.663372	−	1.14899i
$26$		0			0
$27$	25.6216	+	8.51665i	0.948948	+	0.315431i
$28$		0			0
$29$	6.74845	−	3.89622i	0.232705	−	0.134352i	−0.379114	−	0.925350i	$-0.623771\pi$
$29$	6.74845	−	3.89622i	0.232705	−	0.134352i	0.611819	+	0.790997i	$0.290438\pi$
$30$		0			0
$31$	−16.7284	−	9.65812i	−0.539625	−	0.311552i	0.205302	−	0.978699i	$-0.434182\pi$
$31$	−16.7284	−	9.65812i	−0.539625	−	0.311552i	−0.744927	+	0.667146i	$0.767516\pi$
$32$		0			0
$33$	15.9813	−	21.8925i	0.484280	−	0.663410i
$34$		0			0
$35$	−28.3969			−0.811340
$36$		0			0
$37$		−	36.8348i		−	0.995535i	−0.867310	−	0.497768i	$-0.834153\pi$
$37$		−	36.8348i		−	0.995535i	0.867310	−	0.497768i	$-0.165847\pi$
$38$		0			0
$39$	−5.30596	+	49.4128i	−0.136050	+	1.26699i
$40$		0			0
$41$	36.8467	+	21.2734i	0.898700	+	0.518865i	0.876778	−	0.480895i	$-0.159688\pi$
$41$	36.8467	+	21.2734i	0.898700	+	0.518865i	0.0219217	+	0.999760i	$0.493022\pi$
$42$		0			0
$43$	−18.1721	−	31.4750i	−0.422607	−	0.731977i	0.573587	−	0.819145i	$-0.305552\pi$
$43$	−18.1721	−	31.4750i	−0.422607	−	0.731977i	−0.996194	+	0.0871681i	$0.972218\pi$
$44$		0			0
$45$	−20.9173	−	65.3768i	−0.464830	−	1.45282i
$46$		0			0
$47$	−26.7261	−	46.2909i	−0.568639	−	0.984912i	−0.996701	−	0.0811628i	$-0.974137\pi$
$47$	−26.7261	−	46.2909i	−0.568639	−	0.984912i	0.428061	−	0.903750i	$-0.359197\pi$
$48$		0			0
$49$	17.5686	−	30.4296i	0.358542	−	0.621013i
$50$		0			0
$51$	21.7068	+	49.0511i	0.425624	+	0.961787i
$52$		0			0
$53$			11.8904i			0.224347i	0.993689	+	0.112174i	$0.0357813\pi$
$53$			11.8904i			0.224347i	−0.993689	+	0.112174i	$0.964219\pi$
$54$		0			0
$55$	−68.9085			−1.25288
$56$		0			0
$57$	−44.6436	−	35.4394i	−0.783221	−	0.621743i
$58$		0			0
$59$	−40.6788	−	23.4859i	−0.689470	−	0.398066i	0.113943	−	0.993487i	$-0.463652\pi$
$59$	−40.6788	−	23.4859i	−0.689470	−	0.398066i	−0.803414	+	0.595421i	$0.796985\pi$
$60$		0			0
$61$	10.0255	+	17.3646i	0.164352	+	0.284666i	0.936425	−	0.350868i	$-0.114113\pi$
$61$	10.0255	+	17.3646i	0.164352	+	0.284666i	−0.772073	+	0.635534i	$0.780780\pi$
$62$		0			0
$63$	−32.7456	−	7.11451i	−0.519772	−	0.112929i
$64$		0			0
$65$	109.416	−	63.1716i	1.68333	−	0.971871i
$66$		0			0
$67$	−77.5915	−	44.7975i	−1.15808	−	0.668619i	−0.207238	−	0.978291i	$-0.566447\pi$
$67$	−77.5915	−	44.7975i	−1.15808	−	0.668619i	−0.950844	+	0.309672i	$0.899781\pi$
$68$		0			0
$69$	−66.7887	−	7.17179i	−0.967952	−	0.103939i
$70$		0			0
$71$			81.2577i			1.14447i	0.820088	+	0.572237i	$0.193924\pi$
$71$			81.2577i			1.14447i	−0.820088	+	0.572237i	$0.806076\pi$
$72$		0			0
$73$	−72.6229			−0.994835			−0.497417	−	0.867511i	$-0.665718\pi$
$73$	−72.6229			−0.994835			−0.497417	+	0.867511i	$0.665718\pi$
$74$		0			0
$75$	−58.6691	+	80.3701i	−0.782255	+	1.07160i
$76$		0			0
$77$	−16.8200	+	29.1331i	−0.218441	+	0.378351i
$78$		0			0
$79$	−17.5298	+	10.1208i	−0.221896	+	0.128111i	−0.606828	−	0.794833i	$-0.707558\pi$
$79$	−17.5298	+	10.1208i	−0.221896	+	0.128111i	0.384932	+	0.922945i	$0.374225\pi$
$80$		0			0
$81$	−7.74126	−	80.6292i	−0.0955711	−	0.995423i
$82$		0			0
$83$	6.41240	+	11.1066i	0.0772579	+	0.133815i	0.902066	−	0.431598i	$-0.142050\pi$
$83$	6.41240	+	11.1066i	0.0772579	+	0.133815i	−0.824808	+	0.565413i	$0.808717\pi$
$84$		0			0
$85$	68.1833	−	118.097i	0.802157	−	1.38938i
$86$		0			0
$87$	−18.8817	−	13.7834i	−0.217031	−	0.158430i
$88$		0			0
$89$		−	80.1144i		−	0.900161i	−0.892988	−	0.450081i	$-0.851395\pi$
$89$		−	80.1144i		−	0.900161i	0.892988	−	0.450081i	$-0.148605\pi$
$90$		0			0
$91$		−	61.6786i		−	0.677787i
$92$		0			0
$93$	−6.18698	+	57.6175i	−0.0665267	+	0.619543i
$94$		0			0
$95$	−5.85240	+	144.792i	−0.0616042	+	1.52412i
$96$		0			0
$97$	−147.549	+	85.1873i	−1.52112	+	0.878220i	−0.521432	+	0.853293i	$0.674602\pi$
$97$	−147.549	+	85.1873i	−1.52112	+	0.878220i	−0.999689	+	0.0249270i	$0.992065\pi$
$98$		0			0
$99$	−79.4613	−	17.2642i	−0.802639	−	0.174386i
$100$		0			0
$101$	17.7581	+	30.7579i	0.175822	+	0.304533i	0.940446	−	0.339944i	$-0.110408\pi$
$101$	17.7581	+	30.7579i	0.175822	+	0.304533i	−0.764623	+	0.644478i	$0.777075\pi$
$102$		0			0
$103$	122.861	+	70.9339i	1.19283	+	0.688678i	0.958946	−	0.283587i	$-0.0915246\pi$
$103$	122.861	+	70.9339i	1.19283	+	0.688678i	0.233879	+	0.972266i	$0.424858\pi$
$104$		0			0
$105$	34.4749	+	77.9034i	0.328333	+	0.741937i
$106$		0			0
$107$		−	145.743i		−	1.36209i	−0.732244	−	0.681043i	$-0.761527\pi$
$107$		−	145.743i		−	1.36209i	0.732244	−	0.681043i	$-0.238473\pi$
$108$		0			0
$109$		−	91.0129i		−	0.834981i	−0.908681	−	0.417491i	$-0.862910\pi$
$109$		−	91.0129i		−	0.834981i	0.908681	−	0.417491i	$-0.137090\pi$
$110$		0			0
$111$	−101.052	+	44.7189i	−0.910376	+	0.402873i
$112$		0			0
$113$	−7.80242	−	4.50473i	−0.0690480	−	0.0398649i	0.465079	−	0.885269i	$-0.346026\pi$
$113$	−7.80242	−	4.50473i	−0.0690480	−	0.0398649i	−0.534127	+	0.845405i	$0.679359\pi$
$114$		0			0
$115$	85.3858	+	147.893i	0.742485	+	1.28602i
$116$		0			0
$117$	142.000	−	45.4328i	1.21367	−	0.388315i
$118$		0			0
$119$	−33.2859	−	57.6529i	−0.279714	−	0.484478i
$120$		0			0
$121$	19.6843	−	34.0942i	0.162680	−	0.281770i
$122$		0			0
$123$	13.6277	−	126.911i	0.110795	−	1.03180i
$124$		0			0
$125$	62.3007			0.498405
$126$		0			0
$127$		−	87.4413i		−	0.688514i	−0.938875	−	0.344257i	$-0.888131\pi$
$127$		−	87.4413i		−	0.688514i	0.938875	−	0.344257i	$-0.111869\pi$
$128$		0			0
$129$	−64.2861	+	88.0648i	−0.498342	+	0.682673i
$130$		0			0
$131$	−0.294493	+	0.510076i	−0.00224803	+	0.00389371i	−0.867147	−	0.498052i	$-0.834049\pi$
$131$	−0.294493	+	0.510076i	−0.00224803	+	0.00389371i	0.864899	+	0.501946i	$0.167382\pi$
$132$		0			0
$133$	59.7863	+	37.8167i	0.449521	+	0.284336i
$134$		0			0
$135$	−153.959	+	136.754i	−1.14043	+	1.01299i
$136$		0			0
$137$	111.009	+	192.273i	0.810282	+	1.40345i	0.912667	+	0.408704i	$0.134019\pi$
$137$	111.009	+	192.273i	0.810282	+	1.40345i	−0.102385	+	0.994745i	$0.532647\pi$
$138$		0			0
$139$	−61.3054	+	106.184i	−0.441046	+	0.763914i	−0.997767	−	0.0667853i	$-0.978726\pi$
$139$	−61.3054	+	106.184i	−0.441046	+	0.763914i	0.556721	+	0.830699i	$0.312059\pi$
$140$		0			0
$141$	−94.5468	+	129.519i	−0.670545	+	0.918571i
$142$		0			0
$143$		−	149.671i		−	1.04665i
$144$		0			0
$145$			59.4317i			0.409874i
$146$		0			0
$147$	−104.809	−	11.2544i	−0.712985	−	0.0765606i
$148$		0			0
$149$	130.305	−	225.695i	0.874531	−	1.51473i	0.0172690	−	0.999851i	$-0.494503\pi$
$149$	130.305	−	225.695i	0.874531	−	1.51473i	0.857262	−	0.514881i	$-0.172164\pi$
$150$		0			0
$151$	192.731	−	111.273i	1.27636	−	0.736908i	0.300184	−	0.953881i	$-0.402952\pi$
$151$	192.731	−	111.273i	1.27636	−	0.736908i	0.976177	+	0.216974i	$0.0696186\pi$
$152$		0			0
$153$	108.213	−	119.100i	0.707273	−	0.778431i
$154$		0			0
$155$	127.584	−	73.6609i	0.823125	−	0.475232i
$156$		0			0
$157$	118.508	−	205.261i	0.754825	−	1.30740i	−0.190636	−	0.981661i	$-0.561055\pi$
$157$	118.508	−	205.261i	0.754825	−	1.30740i	0.945461	−	0.325735i	$-0.105612\pi$
$158$		0			0
$159$	32.6198	−	14.4354i	0.205156	−	0.0907887i
$160$		0			0
$161$	83.3677			0.517812
$162$		0			0
$163$	−18.4073			−0.112928			−0.0564642	−	0.998405i	$-0.517983\pi$
$163$	−18.4073			−0.112928			−0.0564642	+	0.998405i	$0.517983\pi$
$164$		0			0
$165$	83.6576	+	189.042i	0.507016	+	1.14571i
$166$		0			0
$167$	50.3588	+	29.0747i	0.301550	+	0.174100i	0.643139	−	0.765750i	$-0.277632\pi$
$167$	50.3588	+	29.0747i	0.301550	+	0.174100i	−0.341589	+	0.939849i	$0.610965\pi$
$168$		0			0
$169$	52.7099	+	91.2962i	0.311893	+	0.540214i
$170$		0			0
$171$	−43.0245	+	165.499i	−0.251605	+	0.967830i
$172$		0			0
$173$	200.436	−	115.722i	1.15859	−	0.668913i	0.207625	−	0.978209i	$-0.433427\pi$
$173$	200.436	−	115.722i	1.15859	−	0.668913i	0.950966	+	0.309296i	$0.100093\pi$
$174$		0			0
$175$	61.7482	−	106.951i	0.352847	−	0.611148i
$176$		0			0
$177$	−15.0450	+	140.110i	−0.0850002	+	0.791581i
$178$		0			0
$179$		−	250.792i		−	1.40107i	−0.713618	−	0.700535i	$-0.752945\pi$
$179$		−	250.792i		−	1.40107i	0.713618	−	0.700535i	$-0.247055\pi$
$180$		0			0
$181$		−	1.43574i		−	0.00793226i	−0.999992	−	0.00396613i	$-0.998738\pi$
$181$		−	1.43574i		−	0.00793226i	0.999992	−	0.00396613i	$-0.00126246\pi$
$182$		0			0
$183$	35.4664	−	48.5850i	0.193805	−	0.265492i
$184$		0			0
$185$	243.295	+	140.466i	1.31511	+	0.759278i
$186$		0			0
$187$	−80.7723	−	139.902i	−0.431937	−	0.748138i
$188$		0			0
$189$	20.2367	+	98.4709i	0.107073	+	0.521010i
$190$		0			0
$191$	176.303	+	305.365i	0.923051	+	1.59877i	0.794666	+	0.607047i	$0.207646\pi$
$191$	176.303	+	305.365i	0.923051	+	1.59877i	0.128385	+	0.991724i	$0.459021\pi$
$192$		0			0
$193$	−281.473	−	162.508i	−1.45841	−	0.842013i	−0.459476	−	0.888190i	$-0.651963\pi$
$193$	−281.473	−	162.508i	−1.45841	−	0.842013i	−0.998933	+	0.0461773i	$0.985296\pi$
$194$		0			0
$195$	−306.139	−	223.478i	−1.56995	−	1.14604i
$196$		0			0
$197$	7.20610			0.0365792			0.0182896	−	0.999833i	$-0.494178\pi$
$197$	7.20610			0.0365792			0.0182896	+	0.999833i	$0.494178\pi$
$198$		0			0
$199$	−132.210			−0.664371			−0.332186	−	0.943214i	$-0.607786\pi$
$199$	−132.210			−0.664371			−0.332186	+	0.943214i	$0.607786\pi$
$200$		0			0
$201$	−28.6972	+	267.248i	−0.142772	+	1.32959i
$202$		0			0
$203$	25.1264	+	14.5068i	0.123776	+	0.0714619i
$204$		0			0
$205$	−281.024	+	162.249i	−1.37085	+	0.791459i
$206$		0			0
$207$	61.4092	+	191.933i	0.296663	+	0.927214i
$208$		0			0
$209$	145.079	+	91.7667i	0.694156	+	0.439075i
$210$		0			0
$211$	−61.1573	−	35.3092i	−0.289845	−	0.167342i	0.348027	−	0.937485i	$-0.386852\pi$
$211$	−61.1573	−	35.3092i	−0.289845	−	0.167342i	−0.637872	+	0.770142i	$0.720185\pi$
$212$		0			0
$213$	222.920	−	98.6500i	1.04657	−	0.463145i
$214$		0			0
$215$	277.191			1.28926
$216$		0			0
$217$		−	71.9200i		−	0.331428i
$218$		0			0
$219$	88.1670	+	199.232i	0.402589	+	0.909735i
$220$		0			0
$221$	256.509	+	148.095i	1.16067	+	0.670115i
$222$		0			0
$223$	−307.104	+	177.307i	−1.37715	+	0.795098i	−0.991816	−	0.127679i	$-0.959247\pi$
$223$	−307.104	+	177.307i	−1.37715	+	0.795098i	−0.385334	+	0.922777i	$0.625914\pi$
$224$		0			0
$225$	291.712	+	63.3790i	1.29650	+	0.281684i
$226$		0			0
$227$	−351.305	+	202.826i	−1.54760	+	0.893507i	−0.549275	+	0.835642i	$0.685096\pi$
$227$	−351.305	+	202.826i	−1.54760	+	0.893507i	−0.998324	+	0.0578650i	$0.981571\pi$
$228$		0			0
$229$	76.6908	−	132.832i	0.334894	−	0.580054i	−0.648570	−	0.761155i	$-0.724633\pi$
$229$	76.6908	−	132.832i	0.334894	−	0.580054i	0.983465	+	0.181101i	$0.0579660\pi$
$230$		0			0
$231$	100.343	+	10.7749i	0.434385	+	0.0466444i
$232$		0			0
$233$	−206.442			−0.886017			−0.443009	−	0.896517i	$-0.646089\pi$
$233$	−206.442			−0.886017			−0.443009	+	0.896517i	$0.646089\pi$
$234$		0			0
$235$	407.670			1.73477
$236$		0			0
$237$	49.0470	+	35.8036i	0.206949	+	0.151070i
$238$		0			0
$239$	−63.8827	+	110.648i	−0.267292	+	0.462962i	−0.968161	−	0.250327i	$-0.919462\pi$
$239$	−63.8827	+	110.648i	−0.267292	+	0.462962i	0.700870	+	0.713289i	$0.252795\pi$
$240$		0			0
$241$	−340.457	+	196.563i	−1.41269	+	0.815614i	−0.995641	−	0.0932720i	$-0.970267\pi$
$241$	−340.457	+	196.563i	−1.41269	+	0.815614i	−0.417044	+	0.908886i	$0.636934\pi$
$242$		0			0
$243$	−211.798	+	119.124i	−0.871597	+	0.490223i
$244$		0			0
$245$	133.993	+	232.082i	0.546908	+	0.947273i
$246$		0			0
$247$	−314.490	−	12.7115i	−1.27324	−	0.0514636i
$248$		0			0
$249$	22.6847	−	31.0755i	0.0911032	−	0.124801i
$250$		0			0
$251$	−341.990			−1.36251			−0.681254	−	0.732047i	$-0.738565\pi$
$251$	−341.990			−1.36251			−0.681254	+	0.732047i	$0.738565\pi$
$252$		0			0
$253$	202.302			0.799612
$254$		0			0
$255$	−406.762	−	43.6782i	−1.59514	−	0.171287i
$256$		0			0
$257$	−87.1628	−	50.3235i	−0.339155	−	0.195811i	0.320743	−	0.947166i	$-0.396067\pi$
$257$	−87.1628	−	50.3235i	−0.339155	−	0.195811i	−0.659898	+	0.751355i	$0.729401\pi$
$258$		0			0
$259$	118.772	−	68.5733i	0.458581	−	0.264762i
$260$		0			0
$261$	−14.8899	+	68.5331i	−0.0570494	+	0.262579i
$262$		0			0
$263$	46.7435	+	80.9621i	0.177732	+	0.307841i	0.941103	−	0.338119i	$-0.109791\pi$
$263$	46.7435	+	80.9621i	0.177732	+	0.307841i	−0.763371	+	0.645960i	$0.776457\pi$
$264$		0			0
$265$	−78.5365	−	45.3431i	−0.296364	−	0.171106i
$266$		0			0
$267$	−219.784	+	97.2619i	−0.823160	+	0.364277i
$268$		0			0
$269$			268.259i			0.997246i	0.866819	+	0.498623i	$0.166161\pi$
$269$			268.259i			0.997246i	−0.866819	+	0.498623i	$0.833839\pi$
$270$		0			0
$271$	167.498			0.618076			0.309038	−	0.951050i	$-0.399993\pi$
$271$	167.498			0.618076			0.309038	+	0.951050i	$0.399993\pi$
$272$		0			0
$273$	−169.208	+	74.8802i	−0.619808	+	0.274286i
$274$		0			0
$275$	149.839	−	259.529i	0.544871	−	0.943743i
$276$		0			0
$277$	97.9992	+	169.740i	0.353788	+	0.612778i	0.986910	−	0.161274i	$-0.0515602\pi$
$277$	97.9992	+	169.740i	0.353788	+	0.612778i	−0.633122	+	0.774052i	$0.718227\pi$
$278$		0			0
$279$	165.578	−	52.9767i	0.593469	−	0.189881i
$280$		0			0
$281$	−57.9792	+	33.4743i	−0.206332	+	0.119126i	−0.599605	−	0.800296i	$-0.704676\pi$
$281$	−57.9792	+	33.4743i	−0.206332	+	0.119126i	0.393274	+	0.919421i	$0.371342\pi$
$282$		0			0
$283$	−58.3410	+	101.050i	−0.206152	+	0.357066i	−0.950499	−	0.310727i	$-0.899427\pi$
$283$	−58.3410	+	101.050i	−0.206152	+	0.357066i	0.744347	+	0.667793i	$0.232761\pi$
$284$		0			0
$285$	404.323	−	159.727i	1.41868	−	0.560447i
$286$		0			0
$287$			158.414i			0.551966i
$288$		0			0
$289$	30.6889			0.106190
$290$		0			0
$291$	412.831	+	301.361i	1.41866	+	1.03560i
$292$		0			0
$293$	18.5988	+	10.7380i	0.0634773	+	0.0366486i	0.531403	−	0.847119i	$-0.321665\pi$
$293$	18.5988	+	10.7380i	0.0634773	+	0.0366486i	−0.467925	+	0.883768i	$0.654998\pi$
$294$		0			0
$295$	310.250	−	179.123i	1.05170	−	0.607197i
$296$		0			0
$297$	49.1068	+	238.952i	0.165343	+	0.804551i
$298$		0			0
$299$	−321.225	+	185.459i	−1.07433	+	0.620266i
$300$		0			0
$301$	67.6600	−	117.191i	0.224784	−	0.389337i
$302$		0			0
$303$	62.8214	−	86.0582i	0.207331	−	0.284021i
$304$		0			0
$305$	−152.925			−0.501394
$306$		0			0
$307$		−	331.464i		−	1.07969i	−0.841766	−	0.539843i	$-0.818484\pi$
$307$		−	331.464i		−	1.07969i	0.841766	−	0.539843i	$-0.181516\pi$
$308$		0			0
$309$	45.4402	−	423.170i	0.147056	−	1.36948i
$310$		0			0
$311$	−107.164	+	185.613i	−0.344578	+	0.596826i	−0.985277	−	0.170966i	$-0.945311\pi$
$311$	−107.164	+	185.613i	−0.344578	+	0.596826i	0.640699	+	0.767792i	$0.278645\pi$
$312$		0			0
$313$	−220.175	−	381.354i	−0.703433	−	1.21838i	−0.967254	−	0.253810i	$-0.918316\pi$
$313$	−220.175	−	381.354i	−0.703433	−	1.21838i	0.263821	−	0.964572i	$-0.415017\pi$
$314$		0			0
$315$	171.864	−	189.155i	0.545601	−	0.600494i
$316$		0			0
$317$	−132.234	+	76.3455i	−0.417143	+	0.240838i	−0.693854	−	0.720116i	$-0.744089\pi$
$317$	−132.234	+	76.3455i	−0.417143	+	0.240838i	0.276711	+	0.960953i	$0.410755\pi$
$318$		0			0
$319$	60.9723	+	35.2024i	0.191136	+	0.110352i
$320$		0			0
$321$	−399.828	+	176.938i	−1.24557	+	0.551208i
$322$		0			0
$323$	−300.824	+	157.838i	−0.931342	+	0.488663i
$324$		0			0
$325$			549.459i			1.69064i
$326$		0			0
$327$	−249.683	+	110.493i	−0.763556	+	0.337900i
$328$		0			0
$329$	99.5088	−	172.354i	0.302458	−	0.523873i
$330$		0			0
$331$	256.950	−	148.350i	0.776285	−	0.448189i	−0.0588268	−	0.998268i	$-0.518736\pi$
$331$	256.950	−	148.350i	0.776285	−	0.448189i	0.835112	+	0.550080i	$0.185403\pi$
$332$		0			0
$333$	245.361	+	222.932i	0.736821	+	0.669466i
$334$		0			0
$335$	591.777	−	341.663i	1.76650	−	1.01989i
$336$		0			0
$337$	−350.090	−	202.125i	−1.03884	−	0.599776i	−0.119338	−	0.992854i	$-0.538077\pi$
$337$	−350.090	−	202.125i	−1.03884	−	0.599776i	−0.919505	+	0.393077i	$0.871410\pi$
$338$		0			0
$339$	−2.88572	+	26.8739i	−0.00851246	+	0.0792740i
$340$		0			0
$341$		−	174.523i		−	0.511796i
$342$		0			0
$343$	313.267			0.913314
$344$		0			0
$345$	302.063	−	413.793i	0.875545	−	1.19940i
$346$		0			0
$347$	67.7568	−	117.358i	0.195265	−	0.338208i	−0.751723	−	0.659479i	$-0.770777\pi$
$347$	67.7568	−	117.358i	0.195265	−	0.338208i	0.946987	+	0.321271i	$0.104110\pi$
$348$		0			0
$349$	−97.7502	−	169.308i	−0.280087	−	0.485124i	0.691319	−	0.722549i	$-0.257030\pi$
$349$	−97.7502	−	169.308i	−0.280087	−	0.485124i	−0.971406	+	0.237425i	$0.923697\pi$
$350$		0			0
$351$	−297.032	−	334.401i	−0.846245	−	0.952709i
$352$		0			0
$353$	116.483	+	201.755i	0.329982	+	0.571545i	0.982508	−	0.186221i	$-0.0596241\pi$
$353$	116.483	+	201.755i	0.329982	+	0.571545i	−0.652526	+	0.757766i	$0.726291\pi$
$354$		0			0
$355$	−536.710	−	309.869i	−1.51186	−	0.872872i
$356$		0			0
$357$	−117.753	+	161.309i	−0.329841	+	0.451845i
$358$		0			0
$359$	−139.728			−0.389213			−0.194607	−	0.980881i	$-0.562343\pi$
$359$	−139.728			−0.389213			−0.194607	+	0.980881i	$0.562343\pi$
$360$		0			0
$361$	205.143	−	297.048i	0.568263	−	0.822847i
$362$		0			0
$363$	−117.431	−	12.6097i	−0.323500	−	0.0347376i
$364$		0			0
$365$	276.942	−	479.677i	0.758744	−	1.31418i
$366$		0			0
$367$	−175.834	−	304.554i	−0.479113	−	0.829847i	0.520600	−	0.853800i	$-0.325708\pi$
$367$	−175.834	−	304.554i	−0.479113	−	0.829847i	−0.999713	+	0.0239530i	$0.992375\pi$
$368$		0			0
$369$	−364.709	+	116.689i	−0.988372	+	0.316230i
$370$		0			0
$371$	−38.3402	+	22.1357i	−0.103343	+	0.0596650i
$372$		0			0
$373$	223.111	+	128.813i	0.598152	+	0.345343i	0.768314	−	0.640073i	$-0.221096\pi$
$373$	223.111	+	128.813i	0.598152	+	0.345343i	−0.170162	+	0.985416i	$0.554429\pi$
$374$		0			0
$375$	−75.6354	−	170.914i	−0.201694	−	0.455771i
$376$		0			0
$377$	−129.087			−0.342405
$378$		0			0
$379$		−	286.620i		−	0.756253i	−0.925754	−	0.378126i	$-0.876568\pi$
$379$		−	286.620i		−	0.756253i	0.925754	−	0.378126i	$-0.123432\pi$
$380$		0			0
$381$	−239.884	+	106.157i	−0.629618	+	0.278628i
$382$		0			0
$383$	196.496	+	113.447i	0.513045	+	0.296207i	0.734084	−	0.679058i	$-0.237612\pi$
$383$	196.496	+	113.447i	0.513045	+	0.296207i	−0.221039	+	0.975265i	$0.570945\pi$
$384$		0			0
$385$	−128.283	−	222.193i	−0.333203	−	0.577125i
$386$		0			0
$387$	319.641	+	69.4470i	0.825945	+	0.179450i
$388$		0			0
$389$	−245.371	−	424.995i	−0.630774	−	1.09253i	−0.987394	−	0.158283i	$-0.949404\pi$
$389$	−245.371	−	424.995i	−0.630774	−	1.09253i	0.356619	−	0.934250i	$-0.383929\pi$
$390$		0			0
$391$	−200.173	+	346.709i	−0.511951	+	0.886725i
$392$		0			0
$393$	1.75686	+	0.188652i	0.00447037	+	0.000480030i
$394$		0			0
$395$		−	154.379i		−	0.390834i
$396$		0			0
$397$	−602.483			−1.51759			−0.758794	−	0.651330i	$-0.774211\pi$
$397$	−602.483			−1.51759			−0.758794	+	0.651330i	$0.774211\pi$
$398$		0			0
$399$	31.1624	−	209.927i	0.0781013	−	0.526133i
$400$		0			0
$401$	−99.4967	−	57.4444i	−0.248121	−	0.143253i	0.370782	−	0.928720i	$-0.379090\pi$
$401$	−99.4967	−	57.4444i	−0.248121	−	0.143253i	−0.618904	+	0.785467i	$0.712423\pi$
$402$		0			0
$403$	159.993	+	277.116i	0.397004	+	0.687632i
$404$		0			0
$405$	562.079	+	256.342i	1.38785	+	0.632942i
$406$		0			0
$407$	288.216	−	166.401i	0.708147	−	0.408849i
$408$		0			0
$409$	538.504	+	310.905i	1.31664	+	0.760160i	0.983186	−	0.182608i	$-0.0584539\pi$
$409$	538.504	+	310.905i	1.31664	+	0.760160i	0.333450	+	0.942768i	$0.391787\pi$
$410$		0			0
$411$	392.707	−	537.965i	0.955492	−	1.30892i
$412$		0			0
$413$		−	174.890i		−	0.423461i
$414$		0			0
$415$	−97.8127			−0.235693
$416$		0			0
$417$	365.730	+	39.2722i	0.877050	+	0.0941779i
$418$		0			0
$419$	−200.920	+	348.004i	−0.479524	+	0.830560i	−0.999724	−	0.0234847i	$-0.992524\pi$
$419$	−200.920	+	348.004i	−0.479524	+	0.830560i	0.520200	+	0.854044i	$0.325857\pi$
$420$		0			0
$421$	527.759	−	304.702i	1.25358	−	0.723757i	0.281765	−	0.959484i	$-0.409080\pi$
$421$	527.759	−	304.702i	1.25358	−	0.723757i	0.971819	+	0.235726i	$0.0757469\pi$
$422$		0			0
$423$	470.101	+	102.137i	1.11135	+	0.241459i
$424$		0			0
$425$	296.525	+	513.596i	0.697706	+	1.20846i
$426$		0			0
$427$	−37.3277	+	64.6535i	−0.0874185	+	0.151413i
$428$		0			0
$429$	−410.603	+	181.706i	−0.957116	+	0.423557i
$430$		0			0
$431$			754.616i			1.75085i	0.483356	+	0.875424i	$0.339418\pi$
$431$			754.616i			1.75085i	−0.483356	+	0.875424i	$0.660582\pi$
$432$		0			0
$433$			460.695i			1.06396i	0.846756	+	0.531981i	$0.178552\pi$
$433$			460.695i			1.06396i	−0.846756	+	0.531981i	$0.821448\pi$
$434$		0			0
$435$	163.043	−	72.1523i	0.374812	−	0.165867i
$436$		0			0
$437$	17.1815	−	425.080i	0.0393169	−	0.972723i
$438$		0			0
$439$	338.757	−	195.582i	0.771656	−	0.445516i	−0.0618088	−	0.998088i	$-0.519687\pi$
$439$	338.757	−	195.582i	0.771656	−	0.445516i	0.833465	+	0.552572i	$0.186354\pi$
$440$		0			0
$441$	96.3669	+	301.193i	0.218519	+	0.682978i
$442$		0			0
$443$	−74.0782	−	128.307i	−0.167219	−	0.289633i	0.770222	−	0.637776i	$-0.220146\pi$
$443$	−74.0782	−	128.307i	−0.167219	−	0.289633i	−0.937441	+	0.348144i	$0.886812\pi$
$444$		0			0
$445$	529.158	+	305.509i	1.18912	+	0.686538i
$446$		0			0
$447$	−777.362	−	83.4733i	−1.73906	−	0.186741i
$448$		0			0
$449$		−	700.485i		−	1.56010i	−0.625717	−	0.780050i	$-0.715193\pi$
$449$		−	700.485i		−	1.56010i	0.625717	−	0.780050i	$-0.284807\pi$
$450$		0			0
$451$			384.412i			0.852354i
$452$		0			0
$453$	−539.246	−	393.643i	−1.19039	−	0.868968i
$454$		0			0
$455$	407.389	+	235.206i	0.895361	+	0.516937i
$456$		0			0
$457$	172.502	+	298.782i	0.377466	+	0.653791i	0.990693	−	0.136116i	$-0.0434621\pi$
$457$	172.502	+	298.782i	0.377466	+	0.653791i	−0.613227	+	0.789907i	$0.710129\pi$
$458$		0			0
$459$	−458.110	−	152.276i	−0.998062	−	0.331757i
$460$		0			0
$461$	221.815	+	384.195i	0.481161	+	0.833395i	0.999766	−	0.0216184i	$-0.00688190\pi$
$461$	221.815	+	384.195i	0.481161	+	0.833395i	−0.518605	+	0.855014i	$0.673549\pi$
$462$		0			0
$463$	−331.416	+	574.030i	−0.715802	+	1.23980i	0.246848	+	0.969054i	$0.420605\pi$
$463$	−331.416	+	574.030i	−0.715802	+	1.23980i	−0.962650	+	0.270751i	$0.912728\pi$
$464$		0			0
$465$	−356.972	−	260.585i	−0.767682	−	0.560398i
$466$		0			0
$467$	−436.002			−0.933622			−0.466811	−	0.884357i	$-0.654597\pi$
$467$	−436.002			−0.933622			−0.466811	+	0.884357i	$0.654597\pi$
$468$		0			0
$469$		−	333.588i		−	0.711275i
$470$		0			0
$471$	−706.981	−	75.9158i	−1.50102	−	0.161180i
$472$		0			0
$473$	164.185	−	284.377i	0.347114	−	0.601220i
$474$		0			0
$475$	−532.601	−	336.887i	−1.12127	−	0.709235i
$476$		0			0
$477$	−79.2035	−	71.9633i	−0.166045	−	0.150866i
$478$		0			0
$479$	152.200	+	263.619i	0.317746	+	0.550352i	0.980017	−	0.198912i	$-0.0637408\pi$
$479$	152.200	+	263.619i	0.317746	+	0.550352i	−0.662271	+	0.749264i	$0.730407\pi$
$480$		0			0
$481$	−305.096	+	528.441i	−0.634294	+	1.09863i
$482$		0			0
$483$	−101.212	−	228.709i	−0.209548	−	0.473518i
$484$		0			0
$485$		−	1299.42i		−	2.67922i
$486$		0			0
$487$			594.476i			1.22069i	0.792136	+	0.610345i	$0.208969\pi$
$487$			594.476i			1.22069i	−0.792136	+	0.610345i	$0.791031\pi$
$488$		0			0
$489$	22.3472	+	50.4983i	0.0456998	+	0.103268i
$490$		0			0
$491$	253.549	−	439.159i	0.516392	−	0.894418i	−0.483427	−	0.875385i	$-0.660608\pi$
$491$	253.549	−	439.159i	0.516392	−	0.894418i	0.999819	−	0.0190327i	$-0.00605866\pi$
$492$		0			0
$493$	−120.661	+	69.6638i	−0.244749	+	0.141306i
$494$		0			0
$495$	417.050	−	459.009i	0.842525	−	0.927290i
$496$		0			0
$497$	−262.012	+	151.273i	−0.527188	+	0.304372i
$498$		0			0
$499$	−293.818	+	508.907i	−0.588813	+	1.01985i	0.405575	+	0.914062i	$0.367071\pi$
$499$	−293.818	+	508.907i	−0.588813	+	1.01985i	−0.994388	+	0.105792i	$0.966262\pi$
$500$		0			0
$501$	18.6252	−	173.451i	0.0371761	−	0.346209i
$502$		0			0
$503$	−858.585			−1.70693			−0.853464	−	0.521151i	$-0.825503\pi$
$503$	−858.585			−1.70693			−0.853464	+	0.521151i	$0.825503\pi$
$504$		0			0
$505$	−270.876			−0.536387
$506$		0			0
$507$	186.468	−	255.440i	0.367787	−	0.503827i
$508$		0			0
$509$	−831.158	−	479.869i	−1.63292	−	0.942769i	−0.983185	−	0.182610i	$-0.941545\pi$
$509$	−831.158	−	479.869i	−1.63292	−	0.942769i	−0.649738	−	0.760159i	$-0.725121\pi$
$510$		0			0
$511$	−135.198	−	234.170i	−0.264575	−	0.458258i
$512$		0			0
$513$	506.259	−	82.8899i	0.986860	−	0.161579i
$514$		0			0
$515$	−937.041	+	541.001i	−1.81950	+	1.05049i
$516$		0			0
$517$	241.470	−	418.239i	0.467060	−	0.808972i
$518$		0			0
$519$	−560.806	−	409.381i	−1.08055	−	0.788788i
$520$		0			0
$521$		−	959.314i		−	1.84129i	−0.390397	−	0.920647i	$-0.627662\pi$
$521$		−	959.314i		−	1.84129i	0.390397	−	0.920647i	$-0.372338\pi$
$522$		0			0
$523$			105.431i			0.201589i	0.994907	+	0.100794i	$0.0321384\pi$
$523$			105.431i			0.201589i	−0.994907	+	0.100794i	$0.967862\pi$
$524$		0			0
$525$	−368.371	−	39.5558i	−0.701660	−	0.0753444i
$526$		0			0
$527$	299.100	+	172.686i	0.567553	+	0.327677i
$528$		0			0
$529$	13.8241	+	23.9441i	0.0261326	+	0.0452629i
$530$		0			0
$531$	402.639	−	128.825i	0.758266	−	0.242608i
$532$		0			0
$533$	−352.408	−	610.388i	−0.661178	−	1.14519i
$534$		0			0
$535$	962.639	+	555.780i	1.79932	+	1.03884i
$536$		0			0
$537$	−688.016	+	304.471i	−1.28122	+	0.566985i
$538$		0			0
$539$	317.464			0.588987
$540$		0			0
$541$	−751.836			−1.38971			−0.694857	−	0.719148i	$-0.744533\pi$
$541$	−751.836			−1.38971			−0.694857	+	0.719148i	$0.744533\pi$
$542$		0			0
$543$	−3.93877	+	1.74304i	−0.00725372	+	0.00321002i
$544$		0			0
$545$	601.143	+	347.070i	1.10302	+	0.636826i
$546$		0			0
$547$	705.032	−	407.050i	1.28891	−	0.744151i	0.310448	−	0.950591i	$-0.399521\pi$
$547$	705.032	−	407.050i	1.28891	−	0.744151i	0.978459	+	0.206440i	$0.0661878\pi$
$548$		0			0
$549$	−176.344	−	38.3136i	−0.321210	−	0.0697879i
$550$		0			0
$551$	79.1462	−	125.126i	0.143641	−	0.227089i
$552$		0			0
$553$	−65.2683	−	37.6827i	−0.118026	−	0.0681423i
$554$		0			0
$555$	89.9827	−	837.981i	0.162131	−	1.50988i
$556$		0			0
$557$	199.780			0.358671			0.179336	−	0.983788i	$-0.442605\pi$
$557$	199.780			0.358671			0.179336	+	0.983788i	$0.442605\pi$
$558$		0			0
$559$			602.064i			1.07704i
$560$		0			0
$561$	−285.742	+	391.435i	−0.509345	+	0.697745i
$562$		0			0
$563$	−940.331	−	542.901i	−1.67022	−	0.964299i	−0.967515	−	0.252814i	$-0.918644\pi$
$563$	−940.331	−	542.901i	−1.67022	−	0.964299i	−0.702701	−	0.711486i	$-0.748023\pi$
$564$		0			0
$565$	59.5078	−	34.3568i	0.105323	−	0.0608085i
$566$		0			0
$567$	245.574	−	175.064i	0.433112	−	0.308756i
$568$		0			0
$569$	−718.678	+	414.929i	−1.26305	+	0.729225i	−0.973664	−	0.227987i	$-0.926786\pi$
$569$	−718.678	+	414.929i	−1.26305	+	0.729225i	−0.289390	+	0.957211i	$0.593452\pi$
$570$		0			0
$571$	262.023	−	453.838i	0.458885	−	0.794813i	−0.540017	−	0.841654i	$-0.681582\pi$
$571$	262.023	−	453.838i	0.458885	−	0.794813i	0.998902	+	0.0468415i	$0.0149156\pi$
$572$		0			0
$573$	623.693	−	854.390i	1.08847	−	1.49108i
$574$		0			0
$575$	−742.675			−1.29161
$576$		0			0
$577$	806.213			1.39725			0.698625	−	0.715488i	$-0.253796\pi$
$577$	806.213			1.39725			0.698625	+	0.715488i	$0.253796\pi$
$578$		0			0
$579$	−104.103	+	969.478i	−0.179798	+	1.67440i
$580$		0			0
$581$	−23.8752	+	41.3531i	−0.0410934	+	0.0711758i
$582$		0			0
$583$	−93.0370	+	53.7149i	−0.159583	+	0.0921354i
$584$		0			0
$585$	−241.418	+	1111.17i	−0.412681	+	1.89943i
$586$		0			0
$587$	−407.231	−	705.344i	−0.693749	−	1.20161i	−0.970601	−	0.240696i	$-0.922624\pi$
$587$	−407.231	−	705.344i	−0.693749	−	1.20161i	0.276851	−	0.960913i	$-0.410709\pi$
$588$		0			0
$589$	−366.709	−	14.8222i	−0.622596	−	0.0251650i
$590$		0			0
$591$	−8.74849	−	19.7690i	−0.0148029	−	0.0334502i
$592$		0			0
$593$	218.675			0.368760			0.184380	−	0.982855i	$-0.440972\pi$
$593$	218.675			0.368760			0.184380	+	0.982855i	$0.440972\pi$
$594$		0			0
$595$	507.732			0.853332
$596$		0			0
$597$	160.508	+	362.701i	0.268857	+	0.607540i
$598$		0			0
$599$	340.763	+	196.740i	0.568886	+	0.328447i	0.756704	−	0.653757i	$-0.226808\pi$
$599$	340.763	+	196.740i	0.568886	+	0.328447i	−0.187818	+	0.982204i	$0.560142\pi$
$600$		0			0
$601$	−283.595	+	163.733i	−0.471871	+	0.272435i	−0.717023	−	0.697050i	$-0.754496\pi$
$601$	−283.595	+	163.733i	−0.471871	+	0.272435i	0.245152	+	0.969485i	$0.421162\pi$
$602$		0			0
$603$	768.002	−	245.723i	1.27364	−	0.407500i
$604$		0			0
$605$	150.129	+	260.031i	0.248147	+	0.429803i
$606$		0			0
$607$	37.8064	+	21.8276i	0.0622841	+	0.0359597i	0.530819	−	0.847485i	$-0.321885\pi$
$607$	37.8064	+	21.8276i	0.0622841	+	0.0359597i	−0.468535	+	0.883445i	$0.655218\pi$
$608$		0			0
$609$	9.29301	−	86.5430i	0.0152595	−	0.142107i
$610$		0			0
$611$			885.467i			1.44921i
$612$		0			0
$613$	293.743			0.479189			0.239594	−	0.970873i	$-0.422986\pi$
$613$	293.743			0.479189			0.239594	+	0.970873i	$0.422986\pi$
$614$		0			0
$615$	786.284	+	573.977i	1.27851	+	0.933296i
$616$		0			0
$617$	−88.0423	+	152.494i	−0.142694	+	0.247154i	−0.928510	−	0.371307i	$-0.878910\pi$
$617$	−88.0423	+	152.494i	−0.142694	+	0.247154i	0.785816	+	0.618460i	$0.212243\pi$
$618$		0			0
$619$	−201.297	−	348.657i	−0.325197	−	0.563258i	0.656355	−	0.754452i	$-0.272097\pi$
$619$	−201.297	−	348.657i	−0.325197	−	0.563258i	−0.981552	+	0.191194i	$0.938764\pi$
$620$		0			0
$621$	451.992	−	401.483i	0.727846	−	0.646510i
$622$		0			0
$623$	258.326	−	149.144i	0.414648	−	0.239397i
$624$		0			0
$625$	177.029	−	306.624i	0.283247	−	0.490598i
$626$		0			0
$627$	75.6194	−	509.414i	0.120605	−	0.812462i
$628$		0			0
$629$			658.600i			1.04706i
$630$		0			0
$631$	−589.071			−0.933551			−0.466775	−	0.884376i	$-0.654584\pi$
$631$	−589.071			−0.933551			−0.466775	+	0.884376i	$0.654584\pi$
$632$		0			0
$633$	−22.6190	+	210.644i	−0.0357331	+	0.332771i
$634$		0			0
$635$	577.553	+	333.450i	0.909532	+	0.525118i
$636$		0			0
$637$	−504.086	+	291.034i	−0.791344	+	0.456882i
$638$		0			0
$639$	−541.268	−	491.789i	−0.847054	−	0.769623i
$640$		0			0
$641$	−515.698	+	297.739i	−0.804521	+	0.464491i	−0.845050	−	0.534688i	$-0.820429\pi$
$641$	−515.698	+	297.739i	−0.804521	+	0.464491i	0.0405283	+	0.999178i	$0.487096\pi$
$642$		0			0
$643$	−150.324	+	260.368i	−0.233785	+	0.404927i	−0.958919	−	0.283681i	$-0.908444\pi$
$643$	−150.324	+	260.368i	−0.233785	+	0.404927i	0.725134	+	0.688608i	$0.241778\pi$
$644$		0			0
$645$	−336.521	−	760.440i	−0.521738	−	1.17898i
$646$		0			0
$647$	1004.09			1.55191			0.775956	−	0.630786i	$-0.217268\pi$
$647$	1004.09			1.55191			0.775956	+	0.630786i	$0.217268\pi$
$648$		0			0
$649$		−	424.391i		−	0.653915i
$650$		0			0
$651$	−197.303	+	87.3136i	−0.303078	+	0.134122i
$652$		0			0
$653$	521.151	−	902.660i	0.798088	−	1.38233i	−0.122772	−	0.992435i	$-0.539179\pi$
$653$	521.151	−	902.660i	0.798088	−	1.38233i	0.920860	−	0.389893i	$-0.127488\pi$
$654$		0			0
$655$	−2.24605	−	3.89027i	−0.00342908	−	0.00593934i
$656$		0			0
$657$	439.530	−	483.751i	0.668995	−	0.736302i
$658$		0			0
$659$	−968.515	+	559.172i	−1.46967	+	0.848516i	−0.999421	−	0.0340158i	$-0.989170\pi$
$659$	−968.515	+	559.172i	−1.46967	+	0.848516i	−0.470252	+	0.882532i	$0.655837\pi$
$660$		0			0
$661$	777.393	+	448.828i	1.17609	+	0.679013i	0.955106	−	0.296265i	$-0.0957411\pi$
$661$	777.393	+	448.828i	1.17609	+	0.679013i	0.220980	+	0.975278i	$0.429074\pi$
$662$		0			0
$663$	94.8697	−	883.493i	0.143092	−	1.33257i
$664$		0			0
$665$	−477.770	+	250.680i	−0.718452	+	0.376962i
$666$		0			0
$667$		−	174.480i		−	0.261589i
$668$		0			0
$669$	859.256	+	627.245i	1.28439	+	0.937587i
$670$		0			0
$671$	−90.5802	+	156.890i	−0.134993	+	0.233815i
$672$		0			0
$673$	591.889	−	341.727i	0.879478	−	0.507767i	0.00899163	−	0.999960i	$-0.497138\pi$
$673$	591.889	−	341.727i	0.879478	−	0.507767i	0.870486	+	0.492193i	$0.163805\pi$
$674$		0			0
$675$	−180.277	−	877.220i	−0.267077	−	1.29958i
$676$		0			0
$677$	−498.032	+	287.539i	−0.735645	+	0.424725i	−0.820484	−	0.571670i	$-0.806296\pi$
$677$	−498.032	+	287.539i	−0.735645	+	0.424725i	0.0848386	+	0.996395i	$0.472963\pi$
$678$		0			0
$679$	−549.367	−	317.177i	−0.809082	−	0.467124i
$680$		0			0
$681$	982.926	+	717.523i	1.44336	+	1.05363i
$682$		0			0
$683$			1073.68i			1.57201i	0.618220	+	0.786005i	$0.287854\pi$
$683$			1073.68i			1.57201i	−0.618220	+	0.786005i	$0.712146\pi$
$684$		0			0
$685$	−1693.29			−2.47195
$686$		0			0
$687$	−457.515	−	49.1281i	−0.665960	−	0.0715110i
$688$		0			0
$689$	98.4859	−	170.583i	0.142940	−	0.247580i
$690$		0			0
$691$	339.324	+	587.726i	0.491062	+	0.850544i	0.999947	−	0.0102903i	$-0.00327556\pi$
$691$	339.324	+	587.726i	0.491062	+	0.850544i	−0.508885	+	0.860834i	$0.669942\pi$
$692$		0			0
$693$	−92.2608	−	288.360i	−0.133132	−	0.416103i
$694$		0			0
$695$	−467.566	−	809.848i	−0.672757	−	1.16525i
$696$		0			0
$697$	−658.813	−	380.366i	−0.945213	−	0.545719i
$698$		0			0
$699$	250.629	+	566.348i	0.358553	+	0.810226i
$700$		0			0
$701$	−1181.19			−1.68501			−0.842504	−	0.538691i	$-0.818919\pi$
$701$	−1181.19			−1.68501			−0.842504	+	0.538691i	$0.818919\pi$
$702$		0			0
$703$	−325.167	−	619.735i	−0.462542	−	0.881558i
$704$		0			0
$705$	−494.928	−	1118.39i	−0.702025	−	1.58637i
$706$		0			0
$707$	−66.1184	+	114.520i	−0.0935196	+	0.161981i
$708$		0			0
$709$	530.811	+	919.391i	0.748675	+	1.29674i	0.948458	+	0.316903i	$0.102643\pi$
$709$	530.811	+	919.391i	0.748675	+	1.29674i	−0.199783	+	0.979840i	$0.564024\pi$
$710$		0			0
$711$	38.6779	−	178.021i	0.0543993	−	0.250382i
$712$		0			0
$713$	−374.563	+	216.254i	−0.525334	+	0.303301i
$714$		0			0
$715$	988.579	+	570.756i	1.38263	+	0.798261i
$716$		0			0
$717$	381.105	+	40.9232i	0.531527	+	0.0570756i
$718$		0			0
$719$	−528.734			−0.735374			−0.367687	−	0.929950i	$-0.619850\pi$
$719$	−528.734			−0.735374			−0.367687	+	0.929950i	$0.619850\pi$
$720$		0			0
$721$			528.214i			0.732614i
$722$		0			0
$723$	952.574	+	695.367i	1.31753	+	0.961780i
$724$		0			0
$725$	−223.837	−	129.232i	−0.308740	−	0.178251i
$726$		0			0
$727$	−26.8882	−	46.5717i	−0.0369851	−	0.0640601i	0.846940	−	0.531688i	$-0.178442\pi$
$727$	−26.8882	−	46.5717i	−0.0369851	−	0.0640601i	−0.883925	+	0.467628i	$0.845109\pi$
$728$		0			0
$729$	583.933	+	436.420i	0.801006	+	0.598656i
$730$		0			0
$731$	324.914	+	562.768i	0.444479	+	0.769861i
$732$		0			0
$733$	582.773	−	1009.39i	0.795052	−	1.37707i	−0.127755	−	0.991806i	$-0.540777\pi$
$733$	582.773	−	1009.39i	0.795052	−	1.37707i	0.922806	−	0.385264i	$-0.125890\pi$
$734$		0			0
$735$	474.016	−	649.348i	0.644919	−	0.883467i
$736$		0			0
$737$		−	809.491i		−	1.09836i
$738$		0			0
$739$	617.863			0.836080			0.418040	−	0.908429i	$-0.362717\pi$
$739$	617.863			0.836080			0.418040	+	0.908429i	$0.362717\pi$
$740$		0			0
$741$	346.931	+	878.196i	0.468192	+	1.18515i
$742$		0			0
$743$	−909.905	−	525.334i	−1.22464	−	0.707045i	−0.258734	−	0.965949i	$-0.583305\pi$
$743$	−909.905	−	525.334i	−1.22464	−	0.707045i	−0.965903	+	0.258904i	$0.916639\pi$
$744$		0			0
$745$	993.815	+	1721.34i	1.33398	+	2.31052i
$746$		0			0
$747$	−112.792	−	24.5058i	−0.150993	−	0.0328056i
$748$		0			0
$749$	469.943	−	271.322i	0.627428	−	0.362246i
$750$		0			0
$751$	489.308	+	282.502i	0.651542	+	0.376168i	0.789047	−	0.614333i	$-0.210575\pi$
$751$	489.308	+	282.502i	0.651542	+	0.376168i	−0.137504	+	0.990501i	$0.543908\pi$
$752$		0			0
$753$	415.189	+	938.206i	0.551379	+	1.24596i
$754$		0			0
$755$			1697.32i			2.24811i
$756$		0			0
$757$	222.464			0.293876			0.146938	−	0.989146i	$-0.453058\pi$
$757$	222.464			0.293876			0.146938	+	0.989146i	$0.453058\pi$
$758$		0			0
$759$	−245.602	−	554.990i	−0.323587	−	0.731212i
$760$		0			0
$761$	350.343	−	606.811i	0.460371	−	0.797387i	−0.538608	−	0.842557i	$-0.681050\pi$
$761$	350.343	−	606.811i	0.460371	−	0.797387i	0.998979	+	0.0451698i	$0.0143829\pi$
$762$		0			0
$763$	293.468	−	169.434i	0.384624	−	0.222063i
$764$		0			0
$765$	373.999	+	1168.93i	0.488887	+	1.52801i
$766$		0			0
$767$	389.058	+	673.869i	0.507247	+	0.878577i
$768$		0			0
$769$	−301.484	+	522.186i	−0.392047	+	0.679045i	−0.992719	−	0.120450i	$-0.961566\pi$
$769$	−301.484	+	522.186i	−0.392047	+	0.679045i	0.600672	+	0.799495i	$0.294900\pi$
$770$		0			0
$771$	−32.2372	+	300.215i	−0.0418121	+	0.389384i
$772$		0			0
$773$			359.661i			0.465279i	0.972563	+	0.232640i	$0.0747363\pi$
$773$			359.661i			0.465279i	−0.972563	+	0.232640i	$0.925264\pi$
$774$		0			0
$775$			640.693i			0.826701i
$776$		0			0
$777$	−332.317	−	242.587i	−0.427692	−	0.312209i
$778$		0			0
$779$	807.731	+	32.6480i	1.03688	+	0.0419102i
$780$		0			0
$781$	−635.805	+	367.082i	−0.814090	+	0.470015i
$782$		0			0
$783$	206.089	−	42.3533i	0.263204	−	0.0540910i
$784$		0			0
$785$	903.838	+	1565.49i	1.15139	+	1.99426i
$786$		0			0
$787$	608.257	+	351.177i	0.772881	+	0.446223i	0.833901	−	0.551914i	$-0.186102\pi$
$787$	608.257	+	351.177i	0.772881	+	0.446223i	−0.0610206	+	0.998137i	$0.519436\pi$
$788$		0			0
$789$	165.361	−	226.526i	0.209583	−	0.287105i
$790$		0			0
$791$		−	33.5448i		−	0.0424081i
$792$		0			0
$793$		−	332.156i		−	0.418860i
$794$		0			0
$795$	−29.0467	+	270.503i	−0.0365368	+	0.340256i
$796$		0			0
$797$	−48.8648	−	28.2121i	−0.0613109	−	0.0353979i	0.469031	−	0.883182i	$-0.344603\pi$
$797$	−48.8648	−	28.2121i	−0.0613109	−	0.0353979i	−0.530342	+	0.847784i	$0.677937\pi$
$798$		0			0
$799$	477.858	+	827.674i	0.598070	+	1.03589i
$800$		0			0
$801$	533.652	+	484.870i	0.666232	+	0.605330i
$802$		0			0
$803$	−328.074	−	568.242i	−0.408561	−	0.707648i
$804$		0			0
$805$	−317.916	+	550.647i	−0.394927	+	0.684033i
$806$		0			0
$807$	735.936	−	325.677i	0.911940	−	0.403565i
$808$		0			0
$809$	708.319			0.875549			0.437774	−	0.899085i	$-0.355767\pi$
$809$	708.319			0.875549			0.437774	+	0.899085i	$0.355767\pi$
$810$		0			0
$811$		−	485.623i		−	0.598795i	−0.954128	−	0.299397i	$-0.903214\pi$
$811$		−	485.623i		−	0.598795i	0.954128	−	0.299397i	$-0.0967857\pi$
$812$		0			0
$813$	−203.350	−	459.511i	−0.250123	−	0.565204i
$814$		0			0
$815$	70.1949	−	121.581i	0.0861287	−	0.149179i
$816$		0			0
$817$	−583.593	−	369.140i	−0.714312	−	0.451824i
$818$		0			0
$819$	410.849	+	373.292i	0.501647	+	0.455791i
$820$		0			0
$821$	592.879	+	1026.90i	0.722143	+	1.25079i	0.960139	+	0.279522i	$0.0901760\pi$
$821$	592.879	+	1026.90i	0.722143	+	1.25079i	−0.237997	+	0.971266i	$0.576491\pi$
$822$		0			0
$823$	457.793	−	792.920i	0.556249	−	0.963451i	−0.441556	−	0.897234i	$-0.645573\pi$
$823$	457.793	−	792.920i	0.556249	−	0.963451i	0.997805	−	0.0662178i	$-0.0210932\pi$
$824$		0			0
$825$	−893.898	−	95.9870i	−1.08351	−	0.116348i
$826$		0			0
$827$		−	608.294i		−	0.735543i	−0.929916	−	0.367771i	$-0.880121\pi$
$827$		−	608.294i		−	0.735543i	0.929916	−	0.367771i	$-0.119879\pi$
$828$		0			0
$829$		−	834.975i		−	1.00721i	−0.863935	−	0.503604i	$-0.832007\pi$
$829$		−	834.975i		−	1.00721i	0.863935	−	0.503604i	$-0.167993\pi$
$830$		0			0
$831$	346.685	−	474.919i	0.417190	−	0.571503i
$832$		0			0
$833$	−314.123	+	544.077i	−0.377099	+	0.653154i
$834$		0			0
$835$	−384.078	+	221.748i	−0.459974	+	0.265566i
$836$		0			0
$837$	−346.353	−	389.926i	−0.413802	−	0.465862i
$838$		0			0
$839$	−601.061	+	347.023i	−0.716402	+	0.413615i	−0.813427	−	0.581667i	$-0.802401\pi$
$839$	−601.061	+	347.023i	−0.716402	+	0.413615i	0.0970249	+	0.995282i	$0.469067\pi$
$840$		0			0
$841$	−390.139	+	675.740i	−0.463899	+	0.803496i
$842$		0			0
$843$	162.222	+	118.420i	0.192434	+	0.140474i
$844$		0			0
$845$	−804.019			−0.951502
$846$		0			0
$847$	146.581			0.173059
$848$		0			0
$849$	348.045	+	37.3732i	0.409947	+	0.0440203i
$850$		0			0
$851$	−714.266	−	412.382i	−0.839326	−	0.484585i
$852$		0			0
$853$	−638.926	−	1106.65i	−0.749034	−	1.29736i	−0.948286	−	0.317417i	$-0.897185\pi$
$853$	−638.926	−	1106.65i	−0.749034	−	1.29736i	0.199252	−	0.979948i	$-0.436149\pi$
$854$		0			0
$855$	−929.056	−	915.294i	−1.08661	−	1.07052i
$856$		0			0
$857$	−30.9483	+	17.8680i	−0.0361123	+	0.0208495i	−0.517947	−	0.855412i	$-0.673304\pi$
$857$	−30.9483	+	17.8680i	−0.0361123	+	0.0208495i	0.481835	+	0.876262i	$0.339970\pi$
$858$		0			0
$859$	646.051	−	1118.99i	0.752097	−	1.30267i	−0.194708	−	0.980861i	$-0.562376\pi$
$859$	646.051	−	1118.99i	0.752097	−	1.30267i	0.946805	−	0.321808i	$-0.104291\pi$
$860$		0			0
$861$	434.590	−	192.321i	0.504750	−	0.223370i
$862$		0			0
$863$		−	48.1378i		−	0.0557796i	−0.999611	−	0.0278898i	$-0.991121\pi$
$863$		−	48.1378i		−	0.0557796i	0.999611	−	0.0278898i	$-0.00887874\pi$
$864$		0			0
$865$			1765.18i			2.04067i
$866$		0			0
$867$	−37.2575	−	84.1911i	−0.0429729	−	0.0971062i
$868$		0			0
$869$	−158.382	−	91.4416i	−0.182257	−	0.105226i
$870$		0			0
$871$	742.098	+	1285.35i	0.852006	+	1.47572i
$872$		0			0
$873$	325.554	−	1498.41i	0.372914	−	1.71640i
$874$		0			0
$875$	115.982	+	200.886i	0.132551	+	0.229584i
$876$		0			0
$877$	−1256.58	−	725.485i	−1.43281	−	0.827235i	−0.435478	−	0.900200i	$-0.643421\pi$
$877$	−1256.58	−	725.485i	−1.43281	−	0.827235i	−0.997335	+	0.0729650i	$0.976754\pi$
$878$		0			0
$879$	6.87878	−	64.0600i	0.00782569	−	0.0728783i
$880$		0			0
$881$	−381.805			−0.433377			−0.216689	−	0.976241i	$-0.569526\pi$
$881$	−381.805			−0.433377			−0.216689	+	0.976241i	$0.569526\pi$
$882$		0			0
$883$	480.250			0.543884			0.271942	−	0.962314i	$-0.412334\pi$
$883$	480.250			0.543884			0.271942	+	0.962314i	$0.412334\pi$
$884$		0			0
$885$	−868.057	−	633.671i	−0.980856	−	0.716012i
$886$		0			0
$887$	927.572	+	535.534i	1.04574	+	0.603758i	0.921454	−	0.388488i	$-0.127003\pi$
$887$	927.572	+	535.534i	1.04574	+	0.603758i	0.124286	+	0.992246i	$0.460336\pi$
$888$		0			0
$889$	281.951	−	162.785i	0.317156	−	0.183110i
$890$		0			0
$891$	595.916	−	424.815i	0.668817	−	0.476784i
$892$		0			0
$893$	−858.301	−	542.902i	−0.961144	−	0.607953i
$894$		0			0
$895$	1656.49	+	956.373i	1.85082	+	1.06857i
$896$		0			0
$897$	898.765	+	656.086i	1.00197	+	0.731423i
$898$		0			0
$899$	−150.521			−0.167431
$900$		0			0
$901$		−	212.599i		−	0.235958i
$902$		0			0
$903$	−403.640	−	43.3429i	−0.446998	−	0.0479988i
$904$		0			0
$905$	9.48310	+	5.47507i	0.0104786	+	0.00604980i
$906$		0			0
$907$	−205.998	+	118.933i	−0.227120	+	0.131128i	−0.609243	−	0.792984i	$-0.708526\pi$
$907$	−205.998	+	118.933i	−0.227120	+	0.131128i	0.382123	+	0.924112i	$0.375193\pi$
$908$		0			0
$909$	−312.358	−	67.8646i	−0.343628	−	0.0746585i
$910$		0			0
$911$	−992.153	+	572.820i	−1.08908	+	0.628781i	−0.933332	−	0.359015i	$-0.883113\pi$
$911$	−992.153	+	572.820i	−1.08908	+	0.628781i	−0.155749	+	0.987797i	$0.549779\pi$
$912$		0			0
$913$	−57.9361	+	100.348i	−0.0634569	+	0.109911i
$914$		0			0
$915$	185.657	+	419.531i	0.202904	+	0.458504i
$916$		0			0
$917$	−2.19296			−0.00239145
$918$		0			0
$919$	1114.40			1.21263			0.606313	−	0.795226i	$-0.292648\pi$
$919$	1114.40			1.21263			0.606313	+	0.795226i	$0.292648\pi$
$920$		0			0
$921$	−909.329	+	402.410i	−0.987328	+	0.436927i
$922$		0			0
$923$	673.042	−	1165.74i	0.729189	−	1.26299i
$924$		0			0
$925$	−1058.07	+	610.880i	−1.14386	+	0.660410i
$926$		0			0
$927$	−1216.08	+	389.086i	−1.31185	+	0.419726i
$928$		0			0
$929$	−558.424	−	967.219i	−0.601102	−	1.04114i	−0.992654	−	0.120984i	$-0.961395\pi$
$929$	−558.424	−	967.219i	−0.601102	−	1.04114i	0.391552	−	0.920156i	$-0.371938\pi$
$930$		0			0
$931$	26.9622	−	667.061i	0.0289605	−	0.716499i
$932$		0			0
$933$	639.307	+	68.6490i	0.685217	+	0.0735788i
$934$		0			0
$935$	1232.07			1.31773
$936$		0			0
$937$	817.150			0.872092			0.436046	−	0.899924i	$-0.356379\pi$
$937$	817.150			0.872092			0.436046	+	0.899924i	$0.356379\pi$
$938$		0			0
$939$	−778.896	+	1067.00i	−0.829495	+	1.13631i
$940$		0			0
$941$	496.357	+	286.572i	0.527478	+	0.304539i	0.739989	−	0.672619i	$-0.234831\pi$
$941$	496.357	+	286.572i	0.527478	+	0.304539i	−0.212511	+	0.977159i	$0.568164\pi$
$942$		0			0
$943$	825.030	−	476.331i	0.874899	−	0.505123i
$944$		0			0
$945$	−727.575	−	241.846i	−0.769920	−	0.255922i
$946$		0			0
$947$	616.105	+	1067.13i	0.650586	+	1.12685i	0.982981	+	0.183708i	$0.0588100\pi$
$947$	616.105	+	1067.13i	0.650586	+	1.12685i	−0.332395	+	0.943140i	$0.607857\pi$
$948$		0			0
$949$	1041.87	+	601.522i	1.09786	+	0.633848i
$950$		0			0
$951$	369.982	+	270.082i	0.389045	+	0.283998i
$952$		0			0
$953$			172.723i			0.181241i	0.995885	+	0.0906206i	$0.0288851\pi$
$953$			172.723i			0.181241i	−0.995885	+	0.0906206i	$0.971115\pi$
$954$		0			0
$955$	−2689.26			−2.81598
$956$		0			0
$957$	22.5506	−	210.007i	0.0235639	−	0.219443i
$958$		0			0
$959$	−413.317	+	715.886i	−0.430988	+	0.746492i
$960$		0			0
$961$	−293.941	−	509.121i	−0.305870	−	0.529783i
$962$		0			0
$963$	970.814	+	882.070i	1.00811	+	0.915960i
$964$		0			0
$965$	2146.75	−	1239.43i	2.22461	−	1.28438i
$966$		0			0
$967$	−131.833	+	228.342i	−0.136332	+	0.236135i	−0.926106	−	0.377264i	$-0.876865\pi$
$967$	−131.833	+	228.342i	−0.136332	+	0.236135i	0.789773	+	0.613399i	$0.210198\pi$
$968$		0			0
$969$	798.221	+	633.650i	0.823757	+	0.653922i
$970$		0			0
$971$		−	822.120i		−	0.846673i	−0.905972	−	0.423337i	$-0.860859\pi$
$971$		−	822.120i		−	0.846673i	0.905972	−	0.423337i	$-0.139141\pi$
$972$		0			0
$973$	−456.515			−0.469183
$974$		0			0
$975$	1507.37	−	667.064i	1.54602	−	0.684168i
$976$		0			0
$977$	−904.278	−	522.085i	−0.925566	−	0.534376i	−0.0401597	−	0.999193i	$-0.512787\pi$
$977$	−904.278	−	522.085i	−0.925566	−	0.534376i	−0.885407	+	0.464817i	$0.846120\pi$
$978$		0			0
$979$	626.859	−	361.917i	0.640305	−	0.369680i
$980$		0			0
$981$	606.249	+	550.830i	0.617991	+	0.561499i
$982$		0			0
$983$	2.41785	−	1.39595i	0.00245966	−	0.00142009i	−0.498770	−	0.866735i	$-0.666215\pi$
$983$	2.41785	−	1.39595i	0.00245966	−	0.00142009i	0.501229	+	0.865314i	$0.332881\pi$
$984$		0			0
$985$	−27.4799	+	47.5965i	−0.0278984	+	0.0483214i
$986$		0			0
$987$	−593.640	−	63.7453i	−0.601459	−	0.0645849i
$988$		0			0
$989$	−813.779			−0.822830
$990$		0			0
$991$			307.080i			0.309869i	0.987925	+	0.154935i	$0.0495167\pi$
$991$			307.080i			0.309869i	−0.987925	+	0.154935i	$0.950483\pi$
$992$		0			0
$993$	−718.929	−	524.809i	−0.723997	−	0.528508i
$994$		0			0
$995$	504.171	−	873.250i	0.506705	−	0.877639i
$996$		0			0
$997$	275.923	+	477.913i	0.276753	+	0.479351i	0.970576	−	0.240795i	$-0.0774081\pi$
$997$	275.923	+	477.913i	0.276753	+	0.479351i	−0.693823	+	0.720146i	$0.744075\pi$
$998$		0			0
$999$	313.709	−	943.767i	0.314023	−	0.944711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.t.a.265.14	✓	80
3.2	odd	2		2052.3.t.a.37.37		80
9.2	odd	6		2052.3.t.a.721.38		80
9.7	even	3	inner	684.3.t.a.493.27	yes	80
19.18	odd	2	inner	684.3.t.a.265.27	yes	80
57.56	even	2		2052.3.t.a.37.38		80
171.56	even	6		2052.3.t.a.721.37		80
171.151	odd	6	inner	684.3.t.a.493.14	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.t.a.265.14	✓	80	1.1	even	1	trivial
684.3.t.a.265.27	yes	80	19.18	odd	2	inner
684.3.t.a.493.14	yes	80	171.151	odd	6	inner
684.3.t.a.493.27	yes	80	9.7	even	3	inner
2052.3.t.a.37.37		80	3.2	odd	2
2052.3.t.a.37.38		80	57.56	even	2
2052.3.t.a.721.37		80	171.56	even	6
2052.3.t.a.721.38		80	9.2	odd	6

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21404 - 2.74338i) q^{3} +(-3.81342 + 6.60503i) q^{5} +(1.86164 + 3.22446i) q^{7} +(-6.05222 + 6.66113i) q^{9} +O(q^{10})\)	\(q+(-1.21404 - 2.74338i) q^{3} +(-3.81342 + 6.60503i) q^{5} +(1.86164 + 3.22446i) q^{7} +(-6.05222 + 6.66113i) q^{9} +(4.51751 + 7.82455i) q^{11} +(-14.3462 - 8.28281i) q^{13} +(22.7497 + 2.44287i) q^{15} -17.8798 q^{17} +(16.8247 - 8.82771i) q^{19} +(6.58580 - 9.02181i) q^{21} +(11.1954 - 19.3911i) q^{23} +(-16.5843 - 28.7249i) q^{25} +(25.6216 + 8.51665i) q^{27} +(6.74845 - 3.89622i) q^{29} +(-16.7284 - 9.65812i) q^{31} +(15.9813 - 21.8925i) q^{33} -28.3969 q^{35} -36.8348i q^{37} +(-5.30596 + 49.4128i) q^{39} +(36.8467 + 21.2734i) q^{41} +(-18.1721 - 31.4750i) q^{43} +(-20.9173 - 65.3768i) q^{45} +(-26.7261 - 46.2909i) q^{47} +(17.5686 - 30.4296i) q^{49} +(21.7068 + 49.0511i) q^{51} +11.8904i q^{53} -68.9085 q^{55} +(-44.6436 - 35.4394i) q^{57} +(-40.6788 - 23.4859i) q^{59} +(10.0255 + 17.3646i) q^{61} +(-32.7456 - 7.11451i) q^{63} +(109.416 - 63.1716i) q^{65} +(-77.5915 - 44.7975i) q^{67} +(-66.7887 - 7.17179i) q^{69} +81.2577i q^{71} -72.6229 q^{73} +(-58.6691 + 80.3701i) q^{75} +(-16.8200 + 29.1331i) q^{77} +(-17.5298 + 10.1208i) q^{79} +(-7.74126 - 80.6292i) q^{81} +(6.41240 + 11.1066i) q^{83} +(68.1833 - 118.097i) q^{85} +(-18.8817 - 13.7834i) q^{87} -80.1144i q^{89} -61.6786i q^{91} +(-6.18698 + 57.6175i) q^{93} +(-5.85240 + 144.792i) q^{95} +(-147.549 + 85.1873i) q^{97} +(-79.4613 - 17.2642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 2 * q^7 + 4 * q^9	\( 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) \) 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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