LMFDB - Embedded newform 354.3.b.a.119.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,3,Mod(119,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.119");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	354.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.64580135835$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.12
Character	$\chi$	$=$	354.119
Dual form			354.3.b.a.119.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(0.306491 + 2.98430i) q^{3} -2.00000 q^{4} +9.44498i q^{5} +(4.22044 - 0.433443i) q^{6} +10.5753 q^{7} +2.82843i q^{8} +(-8.81213 + 1.82932i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(0.306491 + 2.98430i) q^{3} -2.00000 q^{4} +9.44498i q^{5} +(4.22044 - 0.433443i) q^{6} +10.5753 q^{7} +2.82843i q^{8} +(-8.81213 + 1.82932i) q^{9} +13.3572 q^{10} -10.4132i q^{11} +(-0.612981 - 5.96861i) q^{12} +8.73176 q^{13} -14.9558i q^{14} +(-28.1867 + 2.89480i) q^{15} +4.00000 q^{16} +27.6767i q^{17} +(2.58705 + 12.4622i) q^{18} -17.5610 q^{19} -18.8900i q^{20} +(3.24124 + 31.5600i) q^{21} -14.7265 q^{22} -9.29706i q^{23} +(-8.44088 + 0.866887i) q^{24} -64.2076 q^{25} -12.3486i q^{26} +(-8.16009 - 25.7374i) q^{27} -21.1507 q^{28} +43.5272i q^{29} +(4.09386 + 39.8620i) q^{30} +27.2593 q^{31} -5.65685i q^{32} +(31.0762 - 3.19155i) q^{33} +39.1407 q^{34} +99.8839i q^{35} +(17.6243 - 3.65864i) q^{36} +3.68559 q^{37} +24.8350i q^{38} +(2.67620 + 26.0582i) q^{39} -26.7144 q^{40} -24.7738i q^{41} +(44.6326 - 4.58381i) q^{42} -46.7065 q^{43} +20.8264i q^{44} +(-17.2779 - 83.2303i) q^{45} -13.1480 q^{46} -81.8610i q^{47} +(1.22596 + 11.9372i) q^{48} +62.8379 q^{49} +90.8033i q^{50} +(-82.5955 + 8.48264i) q^{51} -17.4635 q^{52} +18.2800i q^{53} +(-36.3982 + 11.5401i) q^{54} +98.3525 q^{55} +29.9116i q^{56} +(-5.38228 - 52.4073i) q^{57} +61.5568 q^{58} +7.68115i q^{59} +(56.3733 - 5.78960i) q^{60} +91.4059 q^{61} -38.5505i q^{62} +(-93.1913 + 19.3457i) q^{63} -8.00000 q^{64} +82.4713i q^{65} +(-4.51353 - 43.9483i) q^{66} -44.2676 q^{67} -55.3533i q^{68} +(27.7452 - 2.84946i) q^{69} +141.257 q^{70} +11.0731i q^{71} +(-5.17410 - 24.9245i) q^{72} -36.8281 q^{73} -5.21221i q^{74} +(-19.6790 - 191.615i) q^{75} +35.1220 q^{76} -110.123i q^{77} +(36.8519 - 3.78472i) q^{78} +126.618 q^{79} +37.7799i q^{80} +(74.3072 - 32.2404i) q^{81} -35.0354 q^{82} +97.0505i q^{83} +(-6.48249 - 63.1201i) q^{84} -261.405 q^{85} +66.0529i q^{86} +(-129.898 + 13.3407i) q^{87} +29.4530 q^{88} +142.982i q^{89} +(-117.705 + 24.4347i) q^{90} +92.3414 q^{91} +18.5941i q^{92} +(8.35473 + 81.3500i) q^{93} -115.769 q^{94} -165.863i q^{95} +(16.8818 - 1.73377i) q^{96} +55.0720 q^{97} -88.8662i q^{98} +(19.0491 + 91.7625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9}+O(q^{10}) $ 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9	$ 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9} - 16 q^{10} + 34 q^{15} + 160 q^{16} + 16 q^{18} + 24 q^{19} - 18 q^{21} - 16 q^{22} - 16 q^{24} - 216 q^{25} - 30 q^{27} - 16 q^{28} - 64 q^{30} + 96 q^{31} + 76 q^{33} + 80 q^{34} + 48 q^{36} - 200 q^{37} - 28 q^{39} + 32 q^{40} + 48 q^{42} - 104 q^{43} + 58 q^{45} + 32 q^{46} + 288 q^{49} - 176 q^{51} - 40 q^{54} + 360 q^{55} + 214 q^{57} - 128 q^{58} - 68 q^{60} - 32 q^{61} - 132 q^{63} - 320 q^{64} - 112 q^{66} - 344 q^{67} + 88 q^{69} + 192 q^{70} - 32 q^{72} + 40 q^{73} + 28 q^{75} - 48 q^{76} + 96 q^{78} + 32 q^{79} + 336 q^{81} - 80 q^{82} + 36 q^{84} + 168 q^{85} - 162 q^{87} + 32 q^{88} + 112 q^{90} + 88 q^{91} - 316 q^{93} - 400 q^{94} + 32 q^{96} - 184 q^{97} - 148 q^{99}+O(q^{100}) $ 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9 - 16 * q^10 + 34 * q^15 + 160 * q^16 + 16 * q^18 + 24 * q^19 - 18 * q^21 - 16 * q^22 - 16 * q^24 - 216 * q^25 - 30 * q^27 - 16 * q^28 - 64 * q^30 + 96 * q^31 + 76 * q^33 + 80 * q^34 + 48 * q^36 - 200 * q^37 - 28 * q^39 + 32 * q^40 + 48 * q^42 - 104 * q^43 + 58 * q^45 + 32 * q^46 + 288 * q^49 - 176 * q^51 - 40 * q^54 + 360 * q^55 + 214 * q^57 - 128 * q^58 - 68 * q^60 - 32 * q^61 - 132 * q^63 - 320 * q^64 - 112 * q^66 - 344 * q^67 + 88 * q^69 + 192 * q^70 - 32 * q^72 + 40 * q^73 + 28 * q^75 - 48 * q^76 + 96 * q^78 + 32 * q^79 + 336 * q^81 - 80 * q^82 + 36 * q^84 + 168 * q^85 - 162 * q^87 + 32 * q^88 + 112 * q^90 + 88 * q^91 - 316 * q^93 - 400 * q^94 + 32 * q^96 - 184 * q^97 - 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	0.306491	+	2.98430i	0.102164	+	0.994768i
$3$	0.306491	+	2.98430i	0.102164	+	0.994768i
$4$	−2.00000			−0.500000
$5$			9.44498i			1.88900i	0.328518	+	0.944498i	$0.393451\pi$
$5$			9.44498i			1.88900i	−0.328518	+	0.944498i	$0.606549\pi$
$6$	4.22044	−	0.433443i	0.703407	−	0.0722406i
$7$	10.5753			1.51076			0.755382	−	0.655285i	$-0.227452\pi$
$7$	10.5753			1.51076			0.755382	+	0.655285i	$0.227452\pi$
$8$			2.82843i			0.353553i
$9$	−8.81213	+	1.82932i	−0.979125	+	0.203258i
$10$	13.3572			1.33572
$11$		−	10.4132i		−	0.946655i	−0.880887	−	0.473328i	$-0.843053\pi$
$11$		−	10.4132i		−	0.946655i	0.880887	−	0.473328i	$-0.156947\pi$
$12$	−0.612981	−	5.96861i	−0.0510818	−	0.497384i
$13$	8.73176			0.671674			0.335837	−	0.941920i	$-0.390981\pi$
$13$	8.73176			0.671674			0.335837	+	0.941920i	$0.390981\pi$
$14$		−	14.9558i		−	1.06827i
$15$	−28.1867	+	2.89480i	−1.87911	+	0.192987i
$16$	4.00000			0.250000
$17$			27.6767i			1.62804i	0.580838	+	0.814019i	$0.302725\pi$
$17$			27.6767i			1.62804i	−0.580838	+	0.814019i	$0.697275\pi$
$18$	2.58705	+	12.4622i	0.143725	+	0.692346i
$19$	−17.5610			−0.924262			−0.462131	−	0.886812i	$-0.652915\pi$
$19$	−17.5610			−0.924262			−0.462131	+	0.886812i	$0.652915\pi$
$20$		−	18.8900i		−	0.944498i
$21$	3.24124	+	31.5600i	0.154345	+	1.50286i
$22$	−14.7265			−0.669386
$23$		−	9.29706i		−	0.404220i	−0.979363	−	0.202110i	$-0.935220\pi$
$23$		−	9.29706i		−	0.404220i	0.979363	−	0.202110i	$-0.0647798\pi$
$24$	−8.44088	+	0.866887i	−0.351703	+	0.0361203i
$25$	−64.2076			−2.56830
$26$		−	12.3486i		−	0.474945i
$27$	−8.16009	−	25.7374i	−0.302225	−	0.953236i
$28$	−21.1507			−0.755382
$29$			43.5272i			1.50094i	0.660905	+	0.750469i	$0.270172\pi$
$29$			43.5272i			1.50094i	−0.660905	+	0.750469i	$0.729828\pi$
$30$	4.09386	+	39.8620i	0.136462	+	1.32873i
$31$	27.2593			0.879332			0.439666	−	0.898161i	$-0.355097\pi$
$31$	27.2593			0.879332			0.439666	+	0.898161i	$0.355097\pi$
$32$		−	5.65685i		−	0.176777i
$33$	31.0762	−	3.19155i	0.941702	−	0.0967137i
$34$	39.1407			1.15120
$35$			99.8839i			2.85383i
$36$	17.6243	−	3.65864i	0.489563	−	0.101629i
$37$	3.68559			0.0996106			0.0498053	−	0.998759i	$-0.484140\pi$
$37$	3.68559			0.0996106			0.0498053	+	0.998759i	$0.484140\pi$
$38$			24.8350i			0.653552i
$39$	2.67620	+	26.0582i	0.0686206	+	0.668160i
$40$	−26.7144			−0.667861
$41$		−	24.7738i		−	0.604238i	−0.953270	−	0.302119i	$-0.902306\pi$
$41$		−	24.7738i		−	0.604238i	0.953270	−	0.302119i	$-0.0976940\pi$
$42$	44.6326	−	4.58381i	1.06268	−	0.109138i
$43$	−46.7065			−1.08620			−0.543098	−	0.839669i	$-0.682749\pi$
$43$	−46.7065			−1.08620			−0.543098	+	0.839669i	$0.682749\pi$
$44$			20.8264i			0.473328i
$45$	−17.2779	−	83.2303i	−0.383954	−	1.84956i
$46$	−13.1480			−0.285827
$47$		−	81.8610i		−	1.74172i	−0.491529	−	0.870861i	$-0.663562\pi$
$47$		−	81.8610i		−	1.74172i	0.491529	−	0.870861i	$-0.336438\pi$
$48$	1.22596	+	11.9372i	0.0255409	+	0.248692i
$49$	62.8379			1.28241
$50$			90.8033i			1.81607i
$51$	−82.5955	+	8.48264i	−1.61952	+	0.166326i
$52$	−17.4635			−0.335837
$53$			18.2800i			0.344906i	0.985018	+	0.172453i	$0.0551693\pi$
$53$			18.2800i			0.344906i	−0.985018	+	0.172453i	$0.944831\pi$
$54$	−36.3982	+	11.5401i	−0.674040	+	0.213706i
$55$	98.3525			1.78823
$56$			29.9116i			0.534135i
$57$	−5.38228	−	52.4073i	−0.0944260	−	0.919426i
$58$	61.5568			1.06132
$59$			7.68115i			0.130189i
$59$			7.68115i			0.130189i
$60$	56.3733	−	5.78960i	0.939556	−	0.0964933i
$61$	91.4059			1.49846			0.749229	−	0.662311i	$-0.230424\pi$
$61$	91.4059			1.49846			0.749229	+	0.662311i	$0.230424\pi$
$62$		−	38.5505i		−	0.621782i
$63$	−93.1913	+	19.3457i	−1.47923	+	0.307075i
$64$	−8.00000			−0.125000
$65$			82.4713i			1.26879i
$66$	−4.51353	−	43.9483i	−0.0683869	−	0.665884i
$67$	−44.2676			−0.660711			−0.330355	−	0.943857i	$-0.607169\pi$
$67$	−44.2676			−0.660711			−0.330355	+	0.943857i	$0.607169\pi$
$68$		−	55.3533i		−	0.814019i
$69$	27.7452	−	2.84946i	0.402105	−	0.0412966i
$70$	141.257			2.01796
$71$			11.0731i			0.155959i	0.996955	+	0.0779797i	$0.0248469\pi$
$71$			11.0731i			0.155959i	−0.996955	+	0.0779797i	$0.975153\pi$
$72$	−5.17410	−	24.9245i	−0.0718626	−	0.346173i
$73$	−36.8281			−0.504494			−0.252247	−	0.967663i	$-0.581170\pi$
$73$	−36.8281			−0.504494			−0.252247	+	0.967663i	$0.581170\pi$
$74$		−	5.21221i		−	0.0704353i
$75$	−19.6790	−	191.615i	−0.262387	−	2.55487i
$76$	35.1220			0.462131
$77$		−	110.123i		−	1.43017i
$78$	36.8519	−	3.78472i	0.472460	−	0.0485221i
$79$	126.618			1.60277			0.801383	−	0.598152i	$-0.204098\pi$
$79$	126.618			1.60277			0.801383	+	0.598152i	$0.204098\pi$
$80$			37.7799i			0.472249i
$81$	74.3072	−	32.2404i	0.917372	−	0.398030i
$82$	−35.0354			−0.427261
$83$			97.0505i			1.16928i	0.811292	+	0.584642i	$0.198765\pi$
$83$			97.0505i			1.16928i	−0.811292	+	0.584642i	$0.801235\pi$
$84$	−6.48249	−	63.1201i	−0.0771725	−	0.751429i
$85$	−261.405			−3.07536
$86$			66.0529i			0.768057i
$87$	−129.898	+	13.3407i	−1.49308	+	0.153341i
$88$	29.4530			0.334693
$89$			142.982i			1.60654i	0.595615	+	0.803270i	$0.296908\pi$
$89$			142.982i			1.60654i	−0.595615	+	0.803270i	$0.703092\pi$
$90$	−117.705	+	24.4347i	−1.30784	+	0.271496i
$91$	92.3414			1.01474
$92$			18.5941i			0.202110i
$93$	8.35473	+	81.3500i	0.0898358	+	0.874731i
$94$	−115.769			−1.23158
$95$		−	165.863i		−	1.74593i
$96$	16.8818	−	1.73377i	0.175852	−	0.0180601i
$97$	55.0720			0.567753			0.283876	−	0.958861i	$-0.408379\pi$
$97$	55.0720			0.567753			0.283876	+	0.958861i	$0.408379\pi$
$98$		−	88.8662i		−	0.906798i
$99$	19.0491	+	91.7625i	0.192415	+	0.926894i
$100$	128.415			1.28415
$101$		−	50.6884i		−	0.501865i	−0.968005	−	0.250932i	$-0.919263\pi$
$101$		−	50.6884i		−	0.501865i	0.968005	−	0.250932i	$-0.0807372\pi$
$102$	11.9963	+	116.808i	0.117610	+	1.14517i
$103$	99.4790			0.965816			0.482908	−	0.875671i	$-0.339581\pi$
$103$	99.4790			0.965816			0.482908	+	0.875671i	$0.339581\pi$
$104$			24.6972i			0.237473i
$105$	−298.084	+	30.6135i	−2.83889	+	0.291557i
$106$	25.8518			0.243885
$107$		−	15.6573i		−	0.146330i	−0.997320	−	0.0731648i	$-0.976690\pi$
$107$		−	15.6573i		−	0.146330i	0.997320	−	0.0731648i	$-0.0233099\pi$
$108$	16.3202	+	51.4748i	0.151113	+	0.476618i
$109$	−46.7787			−0.429162			−0.214581	−	0.976706i	$-0.568839\pi$
$109$	−46.7787			−0.429162			−0.214581	+	0.976706i	$0.568839\pi$
$110$		−	139.091i		−	1.26447i
$111$	1.12960	+	10.9989i	0.0101766	+	0.0990894i
$112$	42.3014			0.377691
$113$		−	115.004i		−	1.01773i	−0.860845	−	0.508867i	$-0.830065\pi$
$113$		−	115.004i		−	1.01773i	0.860845	−	0.508867i	$-0.169935\pi$
$114$	−74.1151	+	7.61169i	−0.650133	+	0.0667692i
$115$	87.8105			0.763570
$116$		−	87.0544i		−	0.750469i
$117$	−76.9454	+	15.9732i	−0.657653	+	0.136523i
$118$	10.8628			0.0920575
$119$			292.690i			2.45958i
$120$	−8.18773	−	79.7240i	−0.0682310	−	0.664366i
$121$	12.5651			0.103844
$122$		−	129.267i		−	1.05957i
$123$	73.9324	−	7.59293i	0.601076	−	0.0617311i
$124$	−54.5186			−0.439666
$125$		−	370.315i		−	2.96252i
$126$	27.3590	+	131.792i	0.217135	+	1.04597i
$127$	158.357			1.24691			0.623454	−	0.781860i	$-0.285729\pi$
$127$	158.357			1.24691			0.623454	+	0.781860i	$0.285729\pi$
$128$			11.3137i			0.0883883i
$129$	−14.3151	−	139.386i	−0.110970	−	1.08051i
$130$	116.632			0.897170
$131$		−	79.6304i		−	0.607865i	−0.952694	−	0.303933i	$-0.901700\pi$
$131$		−	79.6304i		−	0.607865i	0.952694	−	0.303933i	$-0.0982998\pi$
$132$	−62.1523	+	6.38310i	−0.470851	+	0.0483568i
$133$	−185.713			−1.39634
$134$			62.6039i			0.467193i
$135$	243.089	−	77.0718i	1.80066	−	0.570903i
$136$	−78.2814			−0.575598
$137$		−	62.0764i		−	0.453112i	−0.973998	−	0.226556i	$-0.927253\pi$
$137$		−	62.0764i		−	0.453112i	0.973998	−	0.226556i	$-0.0727467\pi$
$138$	−4.02975	−	39.2377i	−0.0292011	−	0.284331i
$139$	−10.0887			−0.0725807			−0.0362903	−	0.999341i	$-0.511554\pi$
$139$	−10.0887			−0.0725807			−0.0362903	+	0.999341i	$0.511554\pi$
$140$		−	199.768i		−	1.42691i
$141$	244.298	−	25.0896i	1.73261	−	0.177941i
$142$	15.6597			0.110280
$143$		−	90.9256i		−	0.635844i
$144$	−35.2485	+	7.31729i	−0.244781	+	0.0508145i
$145$	−411.114			−2.83527
$146$			52.0828i			0.356731i
$147$	19.2592	+	187.527i	0.131015	+	1.27570i
$148$	−7.37118			−0.0498053
$149$		−	58.8986i		−	0.395292i	−0.980273	−	0.197646i	$-0.936670\pi$
$149$		−	58.8986i		−	0.395292i	0.980273	−	0.197646i	$-0.0633297\pi$
$150$	−270.984	+	27.8304i	−1.80656	+	0.185536i
$151$	167.310			1.10801			0.554007	−	0.832512i	$-0.313098\pi$
$151$	167.310			1.10801			0.554007	+	0.832512i	$0.313098\pi$
$152$		−	49.6700i		−	0.326776i
$153$	−50.6295	−	243.890i	−0.330912	−	1.59405i
$154$	−155.738			−1.01128
$155$			257.464i			1.66106i
$156$	−5.35241	−	52.1164i	−0.0343103	−	0.334080i
$157$	88.6484			0.564640			0.282320	−	0.959320i	$-0.408896\pi$
$157$	88.6484			0.564640			0.282320	+	0.959320i	$0.408896\pi$
$158$		−	179.066i		−	1.13333i
$159$	−54.5531	+	5.60265i	−0.343101	+	0.0352368i
$160$	53.4289			0.333930
$161$		−	98.3196i		−	0.610681i
$162$	−45.5949	−	105.086i	−0.281450	−	0.648680i
$163$	91.9663			0.564210			0.282105	−	0.959383i	$-0.408967\pi$
$163$	91.9663			0.564210			0.282105	+	0.959383i	$0.408967\pi$
$164$			49.5475i			0.302119i
$165$	30.1441	+	293.514i	0.182692	+	1.77887i
$166$	137.250			0.826808
$167$		−	151.561i		−	0.907553i	−0.891116	−	0.453776i	$-0.850077\pi$
$167$		−	151.561i		−	0.907553i	0.891116	−	0.453776i	$-0.149923\pi$
$168$	−89.2652	+	9.16762i	−0.531341	+	0.0545692i
$169$	−92.7563			−0.548854
$170$			369.683i			2.17461i
$171$	154.750	−	32.1247i	0.904969	−	0.187864i
$172$	93.4129			0.543098
$173$			231.086i			1.33576i	0.744271	+	0.667878i	$0.232797\pi$
$173$			231.086i			1.33576i	−0.744271	+	0.667878i	$0.767203\pi$
$174$	18.8666	+	183.704i	0.108429	+	1.05577i
$175$	−679.018			−3.88010
$176$		−	41.6528i		−	0.236664i
$177$	−22.9229	+	2.35420i	−0.129508	+	0.0133006i
$178$	202.207			1.13600
$179$		−	90.4226i		−	0.505154i	−0.967577	−	0.252577i	$-0.918722\pi$
$179$		−	90.4226i		−	0.505154i	0.967577	−	0.252577i	$-0.0812782\pi$
$180$	34.5558	+	166.461i	0.191977	+	0.924782i
$181$	118.913			0.656978			0.328489	−	0.944508i	$-0.393461\pi$
$181$	118.913			0.656978			0.328489	+	0.944508i	$0.393461\pi$
$182$		−	130.590i		−	0.717530i
$183$	28.0151	+	272.783i	0.153088	+	1.49062i
$184$	26.2961			0.142913
$185$			34.8103i			0.188164i
$186$	115.046	−	11.8154i	0.618529	−	0.0635235i
$187$	288.203			1.54119
$188$			163.722i			0.870861i
$189$	−86.2957	−	272.182i	−0.456591	−	1.44011i
$190$	−234.566			−1.23456
$191$		−	197.398i		−	1.03349i	−0.856138	−	0.516747i	$-0.827143\pi$
$191$		−	197.398i		−	1.03349i	0.856138	−	0.516747i	$-0.172857\pi$
$192$	−2.45193	−	23.8744i	−0.0127704	−	0.124346i
$193$	−2.72111			−0.0140990			−0.00704952	−	0.999975i	$-0.502244\pi$
$193$	−2.72111			−0.0140990			−0.00704952	+	0.999975i	$0.502244\pi$
$194$		−	77.8836i		−	0.401462i
$195$	−246.119	+	25.2767i	−1.26215	+	0.129624i
$196$	−125.676			−0.641203
$197$			338.589i			1.71873i	0.511366	+	0.859363i	$0.329140\pi$
$197$			338.589i			1.71873i	−0.511366	+	0.859363i	$0.670860\pi$
$198$	129.772	−	26.9395i	0.655413	−	0.136058i
$199$	−122.298			−0.614562			−0.307281	−	0.951619i	$-0.599419\pi$
$199$	−122.298			−0.614562			−0.307281	+	0.951619i	$0.599419\pi$
$200$		−	181.607i		−	0.908033i
$201$	−13.5676	−	132.108i	−0.0675006	−	0.657254i
$202$	−71.6842			−0.354872
$203$			460.315i			2.26756i
$204$	165.191	−	16.9653i	0.809760	−	0.0831631i
$205$	233.988			1.14140
$206$		−	140.685i		−	0.682935i
$207$	17.0073	+	81.9269i	0.0821609	+	0.395782i
$208$	34.9270			0.167919
$209$			182.866i			0.874958i
$210$	43.2940	+	421.554i	0.206162	+	2.00740i
$211$	−89.5449			−0.424384			−0.212192	−	0.977228i	$-0.568060\pi$
$211$	−89.5449			−0.424384			−0.212192	+	0.977228i	$0.568060\pi$
$212$		−	36.5600i		−	0.172453i
$213$	−33.0455	+	3.39381i	−0.155143	+	0.0159334i
$214$	−22.1427			−0.103471
$215$		−	441.141i		−	2.05182i
$216$	72.7963	−	23.0802i	0.337020	−	0.106853i
$217$	288.277			1.32846
$218$			66.1550i			0.303463i
$219$	−11.2875	−	109.906i	−0.0515409	−	0.501855i
$220$	−196.705			−0.894114
$221$			241.666i			1.09351i
$222$	15.5548	−	1.59750i	0.0700668	−	0.00719592i
$223$	204.559			0.917305			0.458652	−	0.888616i	$-0.348332\pi$
$223$	204.559			0.917305			0.458652	+	0.888616i	$0.348332\pi$
$224$		−	59.8232i		−	0.267068i
$225$	565.806	−	117.456i	2.51469	−	0.522029i
$226$	−162.640			−0.719646
$227$			84.1028i			0.370497i	0.982692	+	0.185248i	$0.0593090\pi$
$227$			84.1028i			0.370497i	−0.982692	+	0.185248i	$0.940691\pi$
$228$	10.7646	+	104.815i	0.0472130	+	0.459713i
$229$	264.087			1.15322			0.576609	−	0.817020i	$-0.304376\pi$
$229$	264.087			1.15322			0.576609	+	0.817020i	$0.304376\pi$
$230$		−	124.183i		−	0.539925i
$231$	328.641	−	33.7517i	1.42269	−	0.146111i
$232$	−123.114			−0.530662
$233$		−	249.194i		−	1.06950i	−0.845009	−	0.534752i	$-0.820405\pi$
$233$		−	249.194i		−	1.06950i	0.845009	−	0.534752i	$-0.179595\pi$
$234$	22.5895	+	108.817i	0.0965364	+	0.465031i
$235$	773.175			3.29011
$236$		−	15.3623i		−	0.0650945i
$237$	38.8074	+	377.868i	0.163744	+	1.59438i
$238$	413.926			1.73919
$239$			300.941i			1.25917i	0.776933	+	0.629583i	$0.216774\pi$
$239$			300.941i			1.25917i	−0.776933	+	0.629583i	$0.783226\pi$
$240$	−112.747	+	11.5792i	−0.469778	+	0.0482466i
$241$	91.9310			0.381456			0.190728	−	0.981643i	$-0.438915\pi$
$241$	91.9310			0.381456			0.190728	+	0.981643i	$0.438915\pi$
$242$		−	17.7698i		−	0.0734289i
$243$	118.990	+	211.874i	0.489670	+	0.871908i
$244$	−182.812			−0.749229
$245$			593.502i			2.42246i
$246$	−10.7380	−	104.556i	−0.0436505	−	0.425025i
$247$	−153.338			−0.620803
$248$			77.1010i			0.310891i
$249$	−289.628	+	29.7451i	−1.16317	+	0.119458i
$250$	−523.705			−2.09482
$251$			360.014i			1.43432i	0.696908	+	0.717160i	$0.254558\pi$
$251$			360.014i			1.43432i	−0.696908	+	0.717160i	$0.745442\pi$
$252$	186.383	−	38.6914i	0.739613	−	0.153537i
$253$	−96.8122			−0.382657
$254$		−	223.951i		−	0.881698i
$255$	−80.1183	−	780.113i	−0.314190	−	3.05927i
$256$	16.0000			0.0625000
$257$		−	379.092i		−	1.47507i	−0.675310	−	0.737534i	$-0.735990\pi$
$257$		−	379.092i		−	1.47507i	0.675310	−	0.737534i	$-0.264010\pi$
$258$	−197.122	+	20.2446i	−0.764038	+	0.0784675i
$259$	38.9764			0.150488
$260$		−	164.943i		−	0.634395i
$261$	−79.6253	−	383.567i	−0.305078	−	1.46961i
$262$	−112.614			−0.429826
$263$			406.957i			1.54736i	0.633574	+	0.773682i	$0.281587\pi$
$263$			406.957i			1.54736i	−0.633574	+	0.773682i	$0.718413\pi$
$264$	9.02707	+	87.8967i	0.0341934	+	0.332942i
$265$	−172.654			−0.651526
$266$			262.638i			0.987363i
$267$	−426.702	+	43.8227i	−1.59813	+	0.164130i
$268$	88.5353			0.330355
$269$		−	101.340i		−	0.376728i	−0.982099	−	0.188364i	$-0.939681\pi$
$269$		−	101.340i		−	0.376728i	0.982099	−	0.188364i	$-0.0603185\pi$
$270$	−108.996	−	343.780i	−0.403689	−	1.27326i
$271$	152.540			0.562880			0.281440	−	0.959579i	$-0.409188\pi$
$271$	152.540			0.562880			0.281440	+	0.959579i	$0.409188\pi$
$272$			110.707i			0.407010i
$273$	28.3018	+	275.575i	0.103670	+	1.00943i
$274$	−87.7893			−0.320399
$275$			668.607i			2.43130i
$276$	−55.4905	+	5.69892i	−0.201052	+	0.0206483i
$277$	135.906			0.490635			0.245317	−	0.969443i	$-0.421108\pi$
$277$	135.906			0.490635			0.245317	+	0.969443i	$0.421108\pi$
$278$			14.2676i			0.0513223i
$279$	−240.212	+	49.8661i	−0.860977	+	0.178731i
$280$	−282.514			−1.00898
$281$			126.325i			0.449553i	0.974410	+	0.224777i	$0.0721653\pi$
$281$			126.325i			0.449553i	−0.974410	+	0.224777i	$0.927835\pi$
$282$	−35.4821	−	345.489i	−0.125823	−	1.22514i
$283$	58.2988			0.206003			0.103001	−	0.994681i	$-0.467155\pi$
$283$	58.2988			0.206003			0.103001	+	0.994681i	$0.467155\pi$
$284$		−	22.1462i		−	0.0779797i
$285$	494.986	−	50.8355i	1.73679	−	0.178370i
$286$	−128.588			−0.449609
$287$		−	261.991i		−	0.912861i
$288$	10.3482	+	49.8489i	0.0359313	+	0.173087i
$289$	−476.997			−1.65051
$290$			581.402i			2.00484i
$291$	16.8791	+	164.352i	0.0580037	+	0.564782i
$292$	73.6562			0.252247
$293$		−	308.560i		−	1.05311i	−0.850142	−	0.526554i	$-0.823484\pi$
$293$		−	308.560i		−	1.05311i	0.850142	−	0.526554i	$-0.176516\pi$
$294$	265.204	−	27.2367i	0.902053	−	0.0926417i
$295$	−72.5483			−0.245926
$296$			10.4244i			0.0352177i
$297$	−268.009	+	84.9727i	−0.902386	+	0.286103i
$298$	−83.2952			−0.279514
$299$		−	81.1797i		−	0.271504i
$300$	39.3581	+	383.230i	0.131194	+	1.27743i
$301$	−493.937			−1.64099
$302$		−	236.612i		−	0.783484i
$303$	151.269	−	15.5355i	0.499239	−	0.0512723i
$304$	−70.2439			−0.231066
$305$			863.327i			2.83058i
$306$	−344.913	+	71.6010i	−1.12717	+	0.233990i
$307$	−218.921			−0.713097			−0.356548	−	0.934277i	$-0.616046\pi$
$307$	−218.921			−0.713097			−0.356548	+	0.934277i	$0.616046\pi$
$308$			220.246i			0.715086i
$309$	30.4894	+	296.876i	0.0986712	+	0.960762i
$310$	364.108			1.17454
$311$		−	254.471i		−	0.818235i	−0.912482	−	0.409117i	$-0.865837\pi$
$311$		−	254.471i		−	0.818235i	0.912482	−	0.409117i	$-0.134163\pi$
$312$	−73.7038	+	7.56945i	−0.236230	+	0.0242611i
$313$	−513.360			−1.64013			−0.820065	−	0.572271i	$-0.806063\pi$
$313$	−513.360			−1.64013			−0.820065	+	0.572271i	$0.806063\pi$
$314$		−	125.368i		−	0.399261i
$315$	−182.720	−	880.189i	−0.580063	−	2.79425i
$316$	−253.237			−0.801383
$317$			250.219i			0.789335i	0.918824	+	0.394668i	$0.129140\pi$
$317$			250.219i			0.789335i	−0.918824	+	0.394668i	$0.870860\pi$
$318$	7.92335	+	77.1497i	0.0249162	+	0.242609i
$319$	453.258			1.42087
$320$		−	75.5598i		−	0.236124i
$321$	46.7260	−	4.79880i	0.145564	−	0.0149495i
$322$	−139.045			−0.431816
$323$		−	486.029i		−	1.50473i
$324$	−148.614	+	64.4809i	−0.458686	+	0.199015i
$325$	−560.646			−1.72506
$326$		−	130.060i		−	0.398957i
$327$	−14.3372	−	139.602i	−0.0438447	−	0.426916i
$328$	70.0708			0.213630
$329$		−	865.708i		−	2.63133i
$330$	415.091	−	42.6302i	1.25785	−	0.129183i
$331$	−52.2322			−0.157801			−0.0789006	−	0.996882i	$-0.525141\pi$
$331$	−52.2322			−0.157801			−0.0789006	+	0.996882i	$0.525141\pi$
$332$		−	194.101i		−	0.584642i
$333$	−32.4779	+	6.74213i	−0.0975312	+	0.0202467i
$334$	−214.340			−0.641737
$335$		−	418.107i		−	1.24808i
$336$	12.9650	+	126.240i	0.0385862	+	0.375715i
$337$	−94.4989			−0.280412			−0.140206	−	0.990122i	$-0.544777\pi$
$337$	−94.4989			−0.280412			−0.140206	+	0.990122i	$0.544777\pi$
$338$			131.177i			0.388098i
$339$	343.206	−	35.2476i	1.01241	−	0.103975i
$340$	522.811			1.53768
$341$		−	283.857i		−	0.832425i
$342$	−45.4312	−	218.849i	−0.132840	−	0.639909i
$343$	146.340			0.426648
$344$		−	132.106i		−	0.384028i
$345$	26.9131	+	262.053i	0.0780090	+	0.759574i
$346$	326.805			0.944522
$347$			25.2803i			0.0728539i	0.999336	+	0.0364269i	$0.0115976\pi$
$347$			25.2803i			0.0728539i	−0.999336	+	0.0364269i	$0.988402\pi$
$348$	259.797	−	26.6814i	0.746542	−	0.0766706i
$349$	−243.624			−0.698064			−0.349032	−	0.937111i	$-0.613490\pi$
$349$	−243.624			−0.698064			−0.349032	+	0.937111i	$0.613490\pi$
$350$			960.276i			2.74365i
$351$	−71.2519	−	224.733i	−0.202997	−	0.640264i
$352$	−58.9060			−0.167347
$353$		−	490.990i		−	1.39091i	−0.718571	−	0.695454i	$-0.755203\pi$
$353$		−	490.990i		−	1.39091i	0.718571	−	0.695454i	$-0.244797\pi$
$354$	3.32934	+	32.4178i	0.00940492	+	0.0915758i
$355$	−104.585			−0.294607
$356$		−	285.964i		−	0.803270i
$357$	−873.476	+	89.7068i	−2.44671	+	0.251280i
$358$	−127.877			−0.357198
$359$		−	546.448i		−	1.52214i	−0.648670	−	0.761069i	$-0.724675\pi$
$359$		−	546.448i		−	1.52214i	0.648670	−	0.761069i	$-0.275325\pi$
$360$	235.411	−	48.8693i	0.653919	−	0.135748i
$361$	−52.6118			−0.145739
$362$		−	168.168i		−	0.464553i
$363$	3.85110	+	37.4982i	0.0106091	+	0.103301i
$364$	−184.683			−0.507370
$365$		−	347.840i		−	0.952988i
$366$	385.773	−	39.6193i	1.05403	−	0.108249i
$367$	−705.131			−1.92134			−0.960669	−	0.277696i	$-0.910429\pi$
$367$	−705.131			−1.92134			−0.960669	+	0.277696i	$0.910429\pi$
$368$		−	37.1882i		−	0.101055i
$369$	45.3192	+	218.309i	0.122816	+	0.591625i
$370$	49.2292			0.133052
$371$			193.317i			0.521071i
$372$	−16.7095	−	162.700i	−0.0449179	−	0.437366i
$373$	179.259			0.480587			0.240293	−	0.970700i	$-0.422756\pi$
$373$	179.259			0.480587			0.240293	+	0.970700i	$0.422756\pi$
$374$		−	407.580i		−	1.08979i
$375$	1105.13	−	113.498i	2.94702	−	0.302662i
$376$	231.538			0.615792
$377$			380.069i			1.00814i
$378$	−384.923	+	122.041i	−1.01831	+	0.322859i
$379$	71.5076			0.188674			0.0943372	−	0.995540i	$-0.469927\pi$
$379$	71.5076			0.188674			0.0943372	+	0.995540i	$0.469927\pi$
$380$			331.726i			0.872964i
$381$	48.5351	+	472.587i	0.127389	+	1.24038i
$382$	−279.162			−0.730791
$383$			221.732i			0.578935i	0.957188	+	0.289468i	$0.0934782\pi$
$383$			221.732i			0.578935i	−0.957188	+	0.289468i	$0.906522\pi$
$384$	−33.7635	+	3.46755i	−0.0879259	+	0.00903007i
$385$	1040.11			2.70159
$386$			3.84823i			0.00996952i
$387$	411.583	−	85.4412i	1.06352	−	0.220778i
$388$	−110.144			−0.283876
$389$			417.420i			1.07306i	0.843881	+	0.536530i	$0.180265\pi$
$389$			417.420i			1.07306i	−0.843881	+	0.536530i	$0.819735\pi$
$390$	35.7466	+	348.065i	0.0916580	+	0.892475i
$391$	257.311			0.658086
$392$			177.732i			0.453399i
$393$	237.641	−	24.4060i	0.604685	−	0.0621017i
$394$	478.837			1.21532
$395$			1195.91i			3.02762i
$396$	−38.0982	−	183.525i	−0.0962076	−	0.463447i
$397$	393.995			0.992431			0.496216	−	0.868199i	$-0.334723\pi$
$397$	393.995			0.992431			0.496216	+	0.868199i	$0.334723\pi$
$398$			172.955i			0.434561i
$399$	−56.9195	−	554.225i	−0.142655	−	1.38904i
$400$	−256.830			−0.642076
$401$		−	380.151i		−	0.948007i	−0.880523	−	0.474003i	$-0.842808\pi$
$401$		−	380.151i		−	0.948007i	0.880523	−	0.474003i	$-0.157192\pi$
$402$	−186.829	+	19.1875i	−0.464749	+	0.0477301i
$403$	238.022			0.590625
$404$			101.377i			0.250932i
$405$	304.510	+	701.829i	0.751877	+	1.73291i
$406$	650.984			1.60341
$407$		−	38.3788i		−	0.0942969i
$408$	−23.9925	−	233.615i	−0.0588052	−	0.572587i
$409$	33.5892			0.0821251			0.0410625	−	0.999157i	$-0.486926\pi$
$409$	33.5892			0.0821251			0.0410625	+	0.999157i	$0.486926\pi$
$410$		−	330.908i		−	0.807094i
$411$	185.255	−	19.0258i	0.450741	−	0.0462916i
$412$	−198.958			−0.482908
$413$			81.2308i			0.196685i
$414$	115.862	−	24.0520i	0.279860	−	0.0580966i
$415$	−916.640			−2.20877
$416$		−	49.3943i		−	0.118736i
$417$	−3.09210	−	30.1078i	−0.00741510	−	0.0722009i
$418$	258.612			0.618689
$419$		−	129.069i		−	0.308040i	−0.988068	−	0.154020i	$-0.950778\pi$
$419$		−	129.069i		−	0.308040i	0.988068	−	0.154020i	$-0.0492220\pi$
$420$	596.168	−	61.2270i	1.41945	−	0.145779i
$421$	344.526			0.818353			0.409176	−	0.912455i	$-0.365816\pi$
$421$	344.526			0.818353			0.409176	+	0.912455i	$0.365816\pi$
$422$			126.636i			0.300085i
$423$	149.750	+	721.369i	0.354019	+	1.70536i
$424$	−51.7037			−0.121943
$425$		−	1777.05i		−	4.18130i
$426$	4.79957	+	46.7334i	0.0112666	+	0.109703i
$427$	966.649			2.26381
$428$			31.3145i			0.0731648i
$429$	271.350	−	27.8679i	0.632517	−	0.0649601i
$430$	−623.868			−1.45086
$431$			280.676i			0.651220i	0.945504	+	0.325610i	$0.105570\pi$
$431$			280.676i			0.651220i	−0.945504	+	0.325610i	$0.894430\pi$
$432$	−32.6403	−	102.950i	−0.0755564	−	0.238309i
$433$	−189.491			−0.437623			−0.218812	−	0.975767i	$-0.570218\pi$
$433$	−189.491			−0.437623			−0.218812	+	0.975767i	$0.570218\pi$
$434$		−	407.685i		−	0.939365i
$435$	−126.002	−	1226.89i	−0.289661	−	2.82043i
$436$	93.5573			0.214581
$437$			163.266i			0.373605i
$438$	−155.431	+	15.9629i	−0.354865	+	0.0364450i
$439$	−504.700			−1.14966			−0.574829	−	0.818274i	$-0.694931\pi$
$439$	−504.700			−1.14966			−0.574829	+	0.818274i	$0.694931\pi$
$440$			278.183i			0.632234i
$441$	−553.735	+	114.951i	−1.25564	+	0.260659i
$442$	341.767			0.773229
$443$		−	642.968i		−	1.45139i	−0.688014	−	0.725697i	$-0.741517\pi$
$443$		−	642.968i		−	1.45139i	0.688014	−	0.725697i	$-0.258483\pi$
$444$	−2.25920	−	21.9978i	−0.00508829	−	0.0495447i
$445$	−1350.46			−3.03475
$446$		−	289.290i		−	0.648632i
$447$	175.771	−	18.0519i	0.393224	−	0.0403845i
$448$	−84.6027			−0.188845
$449$			82.6577i			0.184093i	0.995755	+	0.0920464i	$0.0293408\pi$
$449$			82.6577i			0.184093i	−0.995755	+	0.0920464i	$0.970659\pi$
$450$	−166.108	−	800.170i	−0.369130	−	1.77816i
$451$	−257.974			−0.572005
$452$			230.008i			0.508867i
$453$	51.2790	+	499.304i	0.113199	+	1.10222i
$454$	118.939			0.261981
$455$			872.162i			1.91684i
$456$	148.230	−	15.2234i	0.325066	−	0.0333846i
$457$	282.006			0.617080			0.308540	−	0.951211i	$-0.400160\pi$
$457$	282.006			0.617080			0.308540	+	0.951211i	$0.400160\pi$
$458$		−	373.475i		−	0.815448i
$459$	712.325	−	225.844i	1.55191	−	0.492035i
$460$	−175.621			−0.381785
$461$		−	189.776i		−	0.411661i	−0.978588	−	0.205830i	$-0.934010\pi$
$461$		−	189.776i		−	0.411661i	0.978588	−	0.205830i	$-0.0659895\pi$
$462$	−47.7322	−	464.769i	−0.103316	−	1.00599i
$463$	−815.401			−1.76113			−0.880563	−	0.473929i	$-0.842835\pi$
$463$	−815.401			−1.76113			−0.880563	+	0.473929i	$0.842835\pi$
$464$			174.109i			0.375235i
$465$	−768.349	+	78.9102i	−1.65236	+	0.169699i
$466$	−352.414			−0.756253
$467$		−	635.483i		−	1.36078i	−0.732851	−	0.680389i	$-0.761811\pi$
$467$		−	635.483i		−	1.36078i	0.732851	−	0.680389i	$-0.238189\pi$
$468$	153.891	−	31.9464i	0.328826	−	0.0682616i
$469$	−468.145			−0.998178
$470$		−	1093.43i		−	2.32646i
$471$	27.1699	+	264.554i	0.0576856	+	0.561685i
$472$	−21.7256			−0.0460287
$473$			486.364i			1.02825i
$474$	534.386	−	54.8819i	1.12740	−	0.115785i
$475$	1127.55			2.37379
$476$		−	585.380i		−	1.22979i
$477$	−33.4400	−	161.086i	−0.0701049	−	0.337706i
$478$	425.594			0.890365
$479$		−	623.143i		−	1.30093i	−0.759538	−	0.650463i	$-0.774575\pi$
$479$		−	623.143i		−	1.30093i	0.759538	−	0.650463i	$-0.225425\pi$
$480$	16.3755	+	159.448i	0.0341155	+	0.332183i
$481$	32.1817			0.0669058
$482$		−	130.010i		−	0.269730i
$483$	293.415	−	30.1340i	0.607485	−	0.0623893i
$484$	−25.1303			−0.0519221
$485$			520.154i			1.07248i
$486$	299.635	−	168.277i	0.616532	−	0.346249i
$487$	−322.669			−0.662565			−0.331283	−	0.943532i	$-0.607481\pi$
$487$	−322.669			−0.662565			−0.331283	+	0.943532i	$0.607481\pi$
$488$			258.535i			0.529785i
$489$	28.1868	+	274.455i	0.0576417	+	0.561258i
$490$	839.339			1.71294
$491$		−	270.909i		−	0.551749i	−0.961194	−	0.275874i	$-0.911033\pi$
$491$		−	270.909i		−	0.551749i	0.961194	−	0.275874i	$-0.0889674\pi$
$492$	−147.865	+	15.1859i	−0.300538	+	0.0308656i
$493$	−1204.69			−2.44359
$494$			216.853i			0.438974i
$495$	−866.695	+	179.918i	−1.75090	+	0.363472i
$496$	109.037			0.219833
$497$			117.102i			0.235618i
$498$	42.0659	+	409.596i	0.0844697	+	0.822482i
$499$	39.0129			0.0781823			0.0390911	−	0.999236i	$-0.487554\pi$
$499$	39.0129			0.0781823			0.0390911	+	0.999236i	$0.487554\pi$
$500$			740.630i			1.48126i
$501$	452.305	−	46.4521i	0.902804	−	0.0927188i
$502$	509.137			1.01422
$503$			201.046i			0.399693i	0.979827	+	0.199847i	$0.0640444\pi$
$503$			201.046i			0.399693i	−0.979827	+	0.199847i	$0.935956\pi$
$504$	−54.7179	−	263.585i	−0.108567	−	0.522986i
$505$	478.750			0.948021
$506$			136.913i			0.270579i
$507$	−28.4290	−	276.813i	−0.0560729	−	0.545982i
$508$	−316.715			−0.623454
$509$		−	317.601i		−	0.623971i	−0.950087	−	0.311986i	$-0.899006\pi$
$509$		−	317.601i		−	0.623971i	0.950087	−	0.311986i	$-0.100994\pi$
$510$	−1103.25	+	113.304i	−2.16323	+	0.222166i
$511$	−389.470			−0.762172
$512$		−	22.6274i		−	0.0441942i
$513$	143.299	+	451.974i	0.279336	+	0.881041i
$514$	−536.118			−1.04303
$515$			939.577i			1.82442i
$516$	28.6302	+	278.772i	0.0554849	+	0.540257i
$517$	−852.435			−1.64881
$518$		−	55.1209i		−	0.106411i
$519$	−689.630	+	70.8257i	−1.32877	+	0.136466i
$520$	−233.264			−0.448585
$521$			922.893i			1.77139i	0.464270	+	0.885694i	$0.346317\pi$
$521$			922.893i			1.77139i	−0.464270	+	0.885694i	$0.653683\pi$
$522$	−542.446	+	112.607i	−1.03917	+	0.215723i
$523$	−354.858			−0.678506			−0.339253	−	0.940695i	$-0.610174\pi$
$523$	−354.858			−0.678506			−0.339253	+	0.940695i	$0.610174\pi$
$524$			159.261i			0.303933i
$525$	−208.113	−	2026.39i	−0.396405	−	3.85980i
$526$	575.524			1.09415
$527$			754.446i			1.43159i
$528$	124.305	−	12.7662i	0.235425	−	0.0241784i
$529$	442.565			0.836606
$530$			244.170i			0.460698i
$531$	−14.0513	−	67.6872i	−0.0264619	−	0.127471i
$532$	371.427			0.698171
$533$		−	216.319i		−	0.405851i
$534$	61.9746	+	603.447i	0.116057	+	1.13005i
$535$	147.882			0.276416
$536$		−	125.208i		−	0.233597i
$537$	269.849	−	27.7137i	0.502511	−	0.0516084i
$538$	−143.316			−0.266387
$539$		−	654.344i		−	1.21400i
$540$	−486.178	+	154.144i	−0.900330	+	0.285451i
$541$	−408.170			−0.754474			−0.377237	−	0.926117i	$-0.623126\pi$
$541$	−408.170			−0.754474			−0.377237	+	0.926117i	$0.623126\pi$
$542$		−	215.725i		−	0.398016i
$543$	36.4457	+	354.872i	0.0671192	+	0.653540i
$544$	156.563			0.287799
$545$		−	441.823i		−	0.810685i
$546$	389.721	−	40.0248i	0.713775	−	0.0733054i
$547$	−14.7496			−0.0269645			−0.0134822	−	0.999909i	$-0.504292\pi$
$547$	−14.7496			−0.0269645			−0.0134822	+	0.999909i	$0.504292\pi$
$548$			124.153i			0.226556i
$549$	−805.481	+	167.211i	−1.46718	+	0.304574i
$550$	945.553			1.71919
$551$		−	764.381i		−	1.38726i
$552$	8.05950	+	78.4754i	0.0146005	+	0.142166i
$553$	1339.03			2.42140
$554$		−	192.200i		−	0.346931i
$555$	−103.885	+	10.6690i	−0.187179	+	0.0192235i
$556$	20.1774			0.0362903
$557$			379.303i			0.680975i	0.940249	+	0.340487i	$0.110592\pi$
$557$			379.303i			0.680975i	−0.940249	+	0.340487i	$0.889408\pi$
$558$	70.5213	+	339.712i	0.126382	+	0.608802i
$559$	−407.830			−0.729570
$560$			399.536i			0.713456i
$561$	88.3315	+	860.084i	0.157454	+	1.53313i
$562$	178.650			0.317882
$563$			133.699i			0.237476i	0.992926	+	0.118738i	$0.0378849\pi$
$563$			133.699i			0.237476i	−0.992926	+	0.118738i	$0.962115\pi$
$564$	−488.596	+	50.1793i	−0.866305	+	0.0889703i
$565$	1086.21			1.92249
$566$		−	82.4469i		−	0.145666i
$567$	785.824	−	340.954i	1.38593	−	0.601329i
$568$	−31.3195			−0.0551400
$569$		−	966.171i		−	1.69802i	−0.528381	−	0.849008i	$-0.677201\pi$
$569$		−	966.171i		−	1.69802i	0.528381	−	0.849008i	$-0.322799\pi$
$570$	−71.8923	−	700.016i	−0.126127	−	1.22810i
$571$	739.118			1.29443			0.647214	−	0.762308i	$-0.275934\pi$
$571$	739.118			1.29443			0.647214	+	0.762308i	$0.275934\pi$
$572$			181.851i			0.317922i
$573$	589.094	−	60.5005i	1.02809	−	0.105586i
$574$	−370.511			−0.645490
$575$			596.942i			1.03816i
$576$	70.4970	−	14.6346i	0.122391	−	0.0254073i
$577$	178.030			0.308544			0.154272	−	0.988028i	$-0.450697\pi$
$577$	178.030			0.308544			0.154272	+	0.988028i	$0.450697\pi$
$578$			674.576i			1.16709i
$579$	−0.833996	−	8.12063i	−0.00144041	−	0.0140253i
$580$	822.227			1.41763
$581$			1026.34i			1.76651i
$582$	232.428	−	23.8706i	0.399361	−	0.0410148i
$583$	190.353			0.326507
$584$		−	104.166i		−	0.178366i
$585$	−150.867	−	726.748i	−0.257892	−	1.24230i
$586$	−436.370			−0.744659
$587$		−	108.771i		−	0.185301i	−0.995699	−	0.0926503i	$-0.970466\pi$
$587$		−	108.771i		−	0.185301i	0.995699	−	0.0926503i	$-0.0295338\pi$
$588$	−38.5185	−	375.055i	−0.0655076	−	0.637848i
$589$	−478.700			−0.812734
$590$			102.599i			0.173896i
$591$	−1010.45	+	103.774i	−1.70973	+	0.175591i
$592$	14.7424			0.0249026
$593$			6.90091i			0.0116373i	0.999983	+	0.00581864i	$0.00185214\pi$
$593$			6.90091i			0.0116373i	−0.999983	+	0.00581864i	$0.998148\pi$
$594$	120.170	+	379.022i	0.202306	+	0.638083i
$595$	−2764.45			−4.64614
$596$			117.797i			0.197646i
$597$	−37.4832	−	364.974i	−0.0627859	−	0.611347i
$598$	−114.805			−0.191982
$599$		−	78.1849i		−	0.130526i	−0.997868	−	0.0652628i	$-0.979211\pi$
$599$		−	78.1849i		−	0.130526i	0.997868	−	0.0652628i	$-0.0207886\pi$
$600$	541.969	−	55.6607i	0.903282	−	0.0927679i
$601$	457.153			0.760654			0.380327	−	0.924852i	$-0.375812\pi$
$601$	457.153			0.760654			0.380327	+	0.924852i	$0.375812\pi$
$602$			698.532i			1.16035i
$603$	390.092	−	80.9798i	0.646919	−	0.134295i
$604$	−334.620			−0.554007
$605$			118.677i			0.196161i
$606$	−21.9705	−	213.927i	−0.0362550	−	0.353015i
$607$	−71.1307			−0.117184			−0.0585920	−	0.998282i	$-0.518661\pi$
$607$	−71.1307			−0.117184			−0.0585920	+	0.998282i	$0.518661\pi$
$608$			99.3399i			0.163388i
$609$	−1373.72	+	141.082i	−2.25570	+	0.231662i
$610$	1220.93			2.00152
$611$		−	714.791i		−	1.16987i
$612$	101.259	+	487.780i	0.165456	+	0.797027i
$613$	−817.203			−1.33312			−0.666560	−	0.745451i	$-0.732234\pi$
$613$	−817.203			−1.33312			−0.666560	+	0.745451i	$0.732234\pi$
$614$			309.601i			0.504236i
$615$	71.7150	+	698.290i	0.116610	+	1.13543i
$616$	311.476			0.505642
$617$		−	149.587i		−	0.242442i	−0.992626	−	0.121221i	$-0.961319\pi$
$617$		−	149.587i		−	0.242442i	0.992626	−	0.121221i	$-0.0386809\pi$
$618$	419.845	−	43.1185i	0.679362	−	0.0697711i
$619$	−727.750			−1.17569			−0.587843	−	0.808975i	$-0.700023\pi$
$619$	−727.750			−1.17569			−0.587843	+	0.808975i	$0.700023\pi$
$620$		−	514.927i		−	0.830528i
$621$	−239.282	+	75.8648i	−0.385317	+	0.122166i
$622$	−359.876			−0.578579
$623$			1512.08i			2.42710i
$624$	10.7048	+	104.233i	0.0171552	+	0.167040i
$625$	1892.43			3.02788
$626$			726.001i			1.15975i
$627$	−545.728	+	56.0468i	−0.870380	+	0.0893888i
$628$	−177.297			−0.282320
$629$			102.005i			0.162170i
$630$	−1244.78	+	258.405i	−1.97583	+	0.410166i
$631$	137.461			0.217846			0.108923	−	0.994050i	$-0.465260\pi$
$631$	137.461			0.217846			0.108923	+	0.994050i	$0.465260\pi$
$632$			358.131i			0.566663i
$633$	−27.4447	−	267.229i	−0.0433566	−	0.422163i
$634$	353.864			0.558144
$635$			1495.68i			2.35541i
$636$	109.106	−	11.2053i	0.171551	−	0.0176184i
$637$	548.685			0.861359
$638$		−	641.003i		−	1.00471i
$639$	−20.2563	−	97.5777i	−0.0317000	−	0.152704i
$640$	−106.858			−0.166965
$641$		−	1171.99i		−	1.82838i	−0.405286	−	0.914190i	$-0.632828\pi$
$641$		−	1171.99i		−	1.82838i	0.405286	−	0.914190i	$-0.367172\pi$
$642$	−6.78653	−	66.0805i	−0.0105709	−	0.102929i
$643$	911.038			1.41686			0.708428	−	0.705783i	$-0.249405\pi$
$643$	911.038			1.41686			0.708428	+	0.705783i	$0.249405\pi$
$644$			196.639i			0.305340i
$645$	1316.50	−	135.206i	2.04108	−	0.209621i
$646$	−687.349			−1.06401
$647$			1064.47i			1.64523i	0.568596	+	0.822617i	$0.307487\pi$
$647$			1064.47i			1.64523i	−0.568596	+	0.822617i	$0.692513\pi$
$648$	91.1897	+	210.172i	0.140725	+	0.324340i
$649$	79.9854			0.123244
$650$			792.873i			1.21980i
$651$	88.3541	+	860.304i	0.135721	+	1.32151i
$652$	−183.933			−0.282105
$653$		−	1166.06i		−	1.78570i	−0.450353	−	0.892851i	$-0.648702\pi$
$653$		−	1166.06i		−	1.78570i	0.450353	−	0.892851i	$-0.351298\pi$
$654$	−197.427	+	20.2759i	−0.301876	+	0.0310029i
$655$	752.107			1.14825
$656$		−	99.0950i		−	0.151059i
$657$	324.534	−	67.3704i	0.493963	−	0.102543i
$658$	−1224.30			−1.86063
$659$			103.195i			0.156593i	0.996930	+	0.0782965i	$0.0249481\pi$
$659$			103.195i			0.156593i	−0.996930	+	0.0782965i	$0.975052\pi$
$660$	−60.2883	−	587.027i	−0.0913459	−	0.889435i
$661$	−640.314			−0.968705			−0.484352	−	0.874873i	$-0.660945\pi$
$661$	−640.314			−0.968705			−0.484352	+	0.874873i	$0.660945\pi$
$662$			73.8675i			0.111582i
$663$	−721.204	+	74.0684i	−1.08779	+	0.111717i
$664$	−274.500			−0.413404
$665$		−	1754.06i		−	2.63768i
$666$	9.53482	+	45.9307i	0.0143165	+	0.0689650i
$667$	404.675			0.606709
$668$			303.123i			0.453776i
$669$	62.6954	+	610.466i	0.0937151	+	0.912505i
$670$	−591.292			−0.882526
$671$		−	951.829i		−	1.41852i
$672$	178.530	−	18.3352i	0.265670	−	0.0272846i
$673$	−194.513			−0.289023			−0.144512	−	0.989503i	$-0.546161\pi$
$673$	−194.513			−0.289023			−0.144512	+	0.989503i	$0.546161\pi$
$674$			133.642i			0.198281i
$675$	523.940	+	1652.54i	0.776207	+	2.44820i
$676$	185.513			0.274427
$677$		−	465.169i		−	0.687104i	−0.939134	−	0.343552i	$-0.888370\pi$
$677$		−	465.169i		−	0.687104i	0.939134	−	0.343552i	$-0.111630\pi$
$678$	−49.8477	−	485.367i	−0.0735216	−	0.715881i
$679$	582.406			0.857740
$680$		−	739.366i		−	1.08730i
$681$	−250.988	+	25.7767i	−0.368558	+	0.0378513i
$682$	−401.434			−0.588613
$683$		−	170.875i		−	0.250184i	−0.992145	−	0.125092i	$-0.960077\pi$
$683$		−	170.875i		−	0.250184i	0.992145	−	0.125092i	$-0.0399226\pi$
$684$	−309.499	+	64.2494i	−0.452484	+	0.0939319i
$685$	586.310			0.855927
$686$		−	206.957i		−	0.301686i
$687$	80.9402	+	788.115i	0.117817	+	1.14718i
$688$	−186.826			−0.271549
$689$			159.617i			0.231664i
$690$	370.599	−	38.0609i	0.537100	−	0.0551607i
$691$	−664.382			−0.961480			−0.480740	−	0.876863i	$-0.659632\pi$
$691$	−664.382			−0.961480			−0.480740	+	0.876863i	$0.659632\pi$
$692$		−	462.172i		−	0.667878i
$693$	201.451	+	970.420i	0.290694	+	1.40032i
$694$	35.7517			0.0515155
$695$		−	95.2877i		−	0.137105i
$696$	−37.7332	−	367.408i	−0.0542143	−	0.527885i
$697$	685.655			0.983723
$698$			344.537i			0.493606i
$699$	743.671	−	76.3758i	1.06391	−	0.109264i
$700$	1358.04			1.94005
$701$		−	760.377i		−	1.08470i	−0.840151	−	0.542352i	$-0.817534\pi$
$701$		−	760.377i		−	1.08470i	0.840151	−	0.542352i	$-0.182466\pi$
$702$	−317.820	+	100.765i	−0.452735	+	0.143541i
$703$	−64.7226			−0.0920663
$704$			83.3056i			0.118332i
$705$	236.971	+	2307.39i	0.336129	+	3.27289i
$706$	−694.365			−0.983520
$707$		−	536.047i		−	0.758199i
$708$	45.8457	−	4.70840i	0.0647539	−	0.00665028i
$709$	−692.772			−0.977111			−0.488556	−	0.872533i	$-0.662476\pi$
$709$	−692.772			−0.977111			−0.488556	+	0.872533i	$0.662476\pi$
$710$			147.906i			0.208318i
$711$	−1115.78	+	231.626i	−1.56931	+	0.325775i
$712$	−404.414			−0.567998
$713$		−	253.431i		−	0.355444i
$714$	126.865	+	1235.28i	0.177681	+	1.73009i
$715$	858.791			1.20111
$716$			180.845i			0.252577i
$717$	−898.098	+	92.2355i	−1.25258	+	0.128641i
$718$	−772.794			−1.07631
$719$			97.8693i			0.136119i	0.997681	+	0.0680593i	$0.0216807\pi$
$719$			97.8693i			0.136119i	−0.997681	+	0.0680593i	$0.978319\pi$
$720$	−69.1116	−	332.921i	−0.0959884	−	0.462391i
$721$	1052.02			1.45912
$722$			74.4043i			0.103053i
$723$	28.1760	+	274.350i	0.0389709	+	0.379460i
$724$	−237.826			−0.328489
$725$		−	2794.78i		−	3.85487i
$726$	53.0304	−	5.44628i	0.0730447	−	0.00750176i
$727$	−117.758			−0.161979			−0.0809893	−	0.996715i	$-0.525808\pi$
$727$	−117.758			−0.161979			−0.0809893	+	0.996715i	$0.525808\pi$
$728$			261.181i			0.358765i
$729$	−595.826	+	420.039i	−0.817320	+	0.576185i
$730$	−491.921			−0.673864
$731$		−	1292.68i		−	1.76837i
$732$	−56.0301	−	545.566i	−0.0765439	−	0.745309i
$733$	1113.64			1.51930			0.759648	−	0.650334i	$-0.225371\pi$
$733$	1113.64			1.51930			0.759648	+	0.650334i	$0.225371\pi$
$734$			997.206i			1.35859i
$735$	−1771.19	+	181.903i	−2.40978	+	0.247487i
$736$	−52.5921			−0.0714567
$737$			460.968i			0.625465i
$738$	308.736	−	64.0910i	0.418342	−	0.0868442i
$739$	549.432			0.743480			0.371740	−	0.928337i	$-0.378761\pi$
$739$	549.432			0.743480			0.371740	+	0.928337i	$0.378761\pi$
$740$		−	69.6207i		−	0.0940820i
$741$	−46.9968	−	457.608i	−0.0634235	−	0.617555i
$742$	273.392			0.368453
$743$			1005.27i			1.35299i	0.736446	+	0.676496i	$0.236503\pi$
$743$			1005.27i			1.35299i	−0.736446	+	0.676496i	$0.763497\pi$
$744$	−230.093	+	23.6307i	−0.309264	+	0.0317617i
$745$	556.296			0.746706
$746$		−	253.510i		−	0.339826i
$747$	−177.537	−	855.221i	−0.237666	−	1.14487i
$748$	−576.405			−0.770595
$749$		−	165.581i		−	0.221069i
$750$	−160.511	−	1562.89i	−0.214014	−	2.08386i
$751$	−952.027			−1.26768			−0.633840	−	0.773464i	$-0.718522\pi$
$751$	−952.027			−1.26768			−0.633840	+	0.773464i	$0.718522\pi$
$752$		−	327.444i		−	0.435431i
$753$	−1074.39	+	110.341i	−1.42682	+	0.146535i
$754$	537.499			0.712864
$755$			1580.24i			2.09303i
$756$	172.591	+	544.363i	0.228296	+	0.720057i
$757$	641.896			0.847947			0.423974	−	0.905675i	$-0.360635\pi$
$757$	641.896			0.847947			0.423974	+	0.905675i	$0.360635\pi$
$758$		−	101.127i		−	0.133413i
$759$	−29.6720	−	288.917i	−0.0390936	−	0.380655i
$760$	469.132			0.617279
$761$		−	301.135i		−	0.395709i	−0.980231	−	0.197855i	$-0.936603\pi$
$761$		−	301.135i		−	0.395709i	0.980231	−	0.197855i	$-0.0633974\pi$
$762$	668.338	−	68.6390i	0.877084	−	0.0900774i
$763$	−494.700			−0.648362
$764$			394.795i			0.516747i
$765$	2303.54	−	478.195i	3.01116	−	0.625091i
$766$	313.577			0.409369
$767$			67.0699i			0.0874445i
$768$	4.90385	+	47.7488i	0.00638522	+	0.0621730i
$769$	−464.905			−0.604558			−0.302279	−	0.953219i	$-0.597747\pi$
$769$	−464.905			−0.604558			−0.302279	+	0.953219i	$0.597747\pi$
$770$		−	1470.94i		−	1.91031i
$771$	1131.33	−	116.188i	1.46735	−	0.150698i
$772$	5.44223			0.00704952
$773$			995.530i			1.28788i	0.765077	+	0.643939i	$0.222701\pi$
$773$			995.530i			1.28788i	−0.765077	+	0.643939i	$0.777299\pi$
$774$	−120.832	−	582.067i	−0.156114	−	0.752024i
$775$	−1750.25			−2.25839
$776$			155.767i			0.200731i
$777$	11.9459	+	116.317i	0.0153744	+	0.149701i
$778$	590.322			0.758768
$779$			435.052i			0.558474i
$780$	492.239	−	50.5534i	0.631075	−	0.0648120i
$781$	115.307			0.147640
$782$		−	363.893i		−	0.465337i
$783$	1120.28	−	355.186i	1.43075	−	0.453622i
$784$	251.352			0.320601
$785$			837.282i			1.06660i
$786$	−34.5152	−	336.075i	−0.0439125	−	0.427577i
$787$	−103.405			−0.131392			−0.0656959	−	0.997840i	$-0.520927\pi$
$787$	−103.405			−0.131392			−0.0656959	+	0.997840i	$0.520927\pi$
$788$		−	677.178i		−	0.859363i
$789$	−1214.48	+	124.728i	−1.53927	+	0.158084i
$790$	1691.27			2.14085
$791$		−	1216.21i		−	1.53755i
$792$	−259.544	+	53.8790i	−0.327706	+	0.0680291i
$793$	798.135			1.00648
$794$		−	557.193i		−	0.701755i
$795$	−52.9169	−	515.253i	−0.0665622	−	0.648117i
$796$	244.596			0.307281
$797$			957.971i			1.20197i	0.799260	+	0.600986i	$0.205225\pi$
$797$			957.971i			1.20197i	−0.799260	+	0.600986i	$0.794775\pi$
$798$	−783.793	+	80.4963i	−0.982196	+	0.100873i
$799$	2265.64			2.83559
$800$			363.213i			0.454016i
$801$	−261.560	−	1259.98i	−0.326542	−	1.57300i
$802$	−537.614			−0.670342
$803$			383.498i			0.477582i
$804$	27.1352	+	264.216i	0.0337503	+	0.328627i
$805$	928.626			1.15357
$806$		−	336.614i		−	0.417635i
$807$	302.429	−	31.0597i	0.374757	−	0.0384879i
$808$	143.368			0.177436
$809$			1332.93i			1.64762i	0.566865	+	0.823811i	$0.308156\pi$
$809$			1332.93i			1.64762i	−0.566865	+	0.823811i	$0.691844\pi$
$810$	992.537	−	430.643i	1.22535	−	0.531657i
$811$	−1371.95			−1.69168			−0.845841	−	0.533435i	$-0.820901\pi$
$811$	−1371.95			−1.69168			−0.845841	+	0.533435i	$0.820901\pi$
$812$		−	920.630i		−	1.13378i
$813$	46.7522	+	455.227i	0.0575058	+	0.559935i
$814$	−54.2758			−0.0666779
$815$			868.619i			1.06579i
$816$	−330.382	+	33.9306i	−0.404880	+	0.0415816i
$817$	820.211			1.00393
$818$		−	47.5022i		−	0.0580712i
$819$	−813.724	+	168.922i	−0.993558	+	0.206254i
$820$	−467.975			−0.570701
$821$			998.702i			1.21645i	0.793766	+	0.608223i	$0.208117\pi$
$821$			998.702i			1.21645i	−0.793766	+	0.608223i	$0.791883\pi$
$822$	−26.9066	−	261.990i	−0.0327331	−	0.318722i
$823$	−337.947			−0.410628			−0.205314	−	0.978696i	$-0.565822\pi$
$823$	−337.947			−0.410628			−0.205314	+	0.978696i	$0.565822\pi$
$824$			281.369i			0.341467i
$825$	−1995.33	+	204.922i	−2.41858	+	0.248390i
$826$	114.878			0.139077
$827$			157.877i			0.190904i	0.995434	+	0.0954519i	$0.0304296\pi$
$827$			157.877i			0.190904i	−0.995434	+	0.0954519i	$0.969570\pi$
$828$	−34.0146	−	163.854i	−0.0410805	−	0.197891i
$829$	1455.92			1.75624			0.878118	−	0.478444i	$-0.158799\pi$
$829$	1455.92			1.75624			0.878118	+	0.478444i	$0.158799\pi$
$830$			1296.32i			1.56184i
$831$	41.6539	+	405.584i	0.0501250	+	0.488068i
$832$	−69.8541			−0.0839593
$833$			1739.14i			2.08781i
$834$	−42.5788	+	4.37289i	−0.0510537	+	0.00524327i
$835$	1431.49			1.71436
$836$		−	365.732i		−	0.437479i
$837$	−222.438	−	701.583i	−0.265757	−	0.838212i
$838$	−182.531			−0.217817
$839$		−	325.879i		−	0.388414i	−0.980961	−	0.194207i	$-0.937787\pi$
$839$		−	325.879i		−	0.388414i	0.980961	−	0.194207i	$-0.0622134\pi$
$840$	−86.5880	−	843.108i	−0.103081	−	1.00370i
$841$	−1053.62			−1.25282
$842$		−	487.234i		−	0.578663i
$843$	−376.991	+	38.7173i	−0.447201	+	0.0459280i
$844$	179.090			0.212192
$845$		−	876.081i		−	1.03678i
$846$	1020.17	−	211.779i	1.20587	−	0.250329i
$847$	132.881			0.156884
$848$			73.1200i			0.0862265i
$849$	17.8680	+	173.981i	0.0210460	+	0.204925i
$850$	−2513.13			−2.95662
$851$		−	34.2652i		−	0.0402646i
$852$	66.0911	−	6.78761i	0.0775717	−	0.00796668i
$853$	944.450			1.10721			0.553605	−	0.832779i	$-0.313252\pi$
$853$	944.450			1.10721			0.553605	+	0.832779i	$0.313252\pi$
$854$		−	1367.05i		−	1.60076i
$855$	303.417	+	1461.61i	0.354874	+	1.70948i
$856$	44.2854			0.0517353
$857$		−	1264.68i		−	1.47571i	−0.674961	−	0.737853i	$-0.735840\pi$
$857$		−	1264.68i		−	1.47571i	0.674961	−	0.737853i	$-0.264160\pi$
$858$	−39.4111	−	383.746i	−0.0459337	−	0.447257i
$859$	367.258			0.427541			0.213771	−	0.976884i	$-0.431425\pi$
$859$	367.258			0.427541			0.213771	+	0.976884i	$0.431425\pi$
$860$			882.283i			1.02591i
$861$	781.860	−	80.2978i	0.908084	−	0.0932611i
$862$	396.936			0.460482
$863$		−	779.436i		−	0.903171i	−0.892228	−	0.451585i	$-0.850859\pi$
$863$		−	779.436i		−	0.903171i	0.892228	−	0.451585i	$-0.149141\pi$
$864$	−145.593	+	46.1604i	−0.168510	+	0.0534264i
$865$	−2182.60			−2.52324
$866$			267.981i			0.309446i
$867$	−146.195	−	1423.50i	−0.168622	−	1.64187i
$868$	−576.553			−0.664232
$869$		−	1318.50i		−	1.51727i
$870$	−1735.08	+	178.194i	−1.99435	+	0.204821i
$871$	−386.534			−0.443782
$872$		−	132.310i		−	0.151732i
$873$	−485.302	+	100.744i	−0.555901	+	0.115400i
$874$	230.892			0.264179
$875$		−	3916.21i		−	4.47567i
$876$	22.5749	+	219.812i	0.0257705	+	0.250927i
$877$	814.527			0.928765			0.464382	−	0.885635i	$-0.346276\pi$
$877$	814.527			0.928765			0.464382	+	0.885635i	$0.346276\pi$
$878$			713.753i			0.812931i
$879$	920.838	−	94.5709i	1.04760	−	0.107589i
$880$	393.410			0.447057
$881$			264.110i			0.299785i	0.988702	+	0.149892i	$0.0478927\pi$
$881$			264.110i			0.299785i	−0.988702	+	0.149892i	$0.952107\pi$
$882$	162.565	+	783.100i	0.184314	+	0.887869i
$883$	129.745			0.146937			0.0734683	−	0.997298i	$-0.476593\pi$
$883$	129.745			0.146937			0.0734683	+	0.997298i	$0.476593\pi$
$884$		−	483.332i		−	0.546756i
$885$	−22.2354	−	216.506i	−0.0251247	−	0.244640i
$886$	−909.293			−1.02629
$887$		−	558.068i		−	0.629163i	−0.949230	−	0.314582i	$-0.898136\pi$
$887$		−	558.068i		−	0.629163i	0.949230	−	0.314582i	$-0.101864\pi$
$888$	−31.1096	+	3.19499i	−0.0350334	+	0.00359796i
$889$	1674.68			1.88378
$890$			1909.84i			2.14589i
$891$	−335.726	−	773.776i	−0.376797	−	0.868435i
$892$	−409.118			−0.458652
$893$			1437.56i			1.60981i
$894$	−25.5292	−	248.578i	−0.0285561	−	0.278051i
$895$	854.040			0.954235
$896$			119.646i			0.133534i
$897$	242.265	−	24.8808i	0.270083	−	0.0277378i
$898$	116.896			0.130173
$899$			1186.52i			1.31982i
$900$	−1131.61	+	234.913i	−1.25735	+	0.261014i
$901$	−505.929			−0.561520
$902$			364.831i			0.404469i
$903$	−151.387	−	1474.06i	−0.167649	−	1.63240i
$904$	325.280			0.359823
$905$			1123.13i			1.24103i
$906$	706.123	−	72.5195i	0.779385	−	0.0800436i
$907$	−1622.69			−1.78907			−0.894536	−	0.446997i	$-0.852494\pi$
$907$	−1622.69			−1.78907			−0.894536	+	0.446997i	$0.852494\pi$
$908$		−	168.206i		−	0.185248i
$909$	92.7253	+	446.672i	0.102008	+	0.491389i
$910$	1233.42			1.35541
$911$		−	1428.73i		−	1.56831i	−0.620567	−	0.784153i	$-0.713098\pi$
$911$		−	1428.73i		−	1.56831i	0.620567	−	0.784153i	$-0.286902\pi$
$912$	−21.5291	−	209.629i	−0.0236065	−	0.229857i
$913$	1010.61			1.10691
$914$		−	398.816i		−	0.436342i
$915$	−2576.43	+	264.602i	−2.81577	+	0.289182i
$916$	−528.174			−0.576609
$917$		−	842.118i		−	0.918341i
$918$	−319.391	−	1007.38i	−0.347921	−	1.09736i
$919$	1068.11			1.16225			0.581125	−	0.813814i	$-0.302613\pi$
$919$	1068.11			1.16225			0.581125	+	0.813814i	$0.302613\pi$
$920$			248.366i			0.269963i
$921$	−67.0972	−	653.326i	−0.0728525	−	0.709366i
$922$	−268.383			−0.291088
$923$			96.6878i			0.104754i
$924$	−657.282	+	67.5035i	−0.711344	+	0.0730557i
$925$	−236.643			−0.255830
$926$			1153.15i			1.24530i
$927$	−876.622	+	181.979i	−0.945655	+	0.196310i
$928$	246.227			0.265331
$929$			302.054i			0.325139i	0.986697	+	0.162570i	$0.0519782\pi$
$929$			302.054i			0.325139i	−0.986697	+	0.162570i	$0.948022\pi$
$930$	111.596	+	1086.61i	0.119996	+	1.16840i
$931$	−1103.50			−1.18528
$932$			498.389i			0.534752i
$933$	759.419	−	77.9930i	0.813954	−	0.0835938i
$934$	−898.709			−0.962215
$935$			2722.07i			2.91130i
$936$	−45.1791	−	217.634i	−0.0482682	−	0.232515i
$937$	666.814			0.711648			0.355824	−	0.934553i	$-0.384200\pi$
$937$	666.814			0.711648			0.355824	+	0.934553i	$0.384200\pi$
$938$			662.058i			0.705818i
$939$	−157.340	−	1532.02i	−0.167561	−	1.63155i
$940$	−1546.35			−1.64505
$941$		−	1618.77i		−	1.72026i	−0.510074	−	0.860131i	$-0.670382\pi$
$941$		−	1618.77i		−	1.72026i	0.510074	−	0.860131i	$-0.329618\pi$
$942$	374.136	−	38.4241i	0.397171	−	0.0407899i
$943$	−230.323			−0.244245
$944$			30.7246i			0.0325472i
$945$	2570.75	−	815.061i	2.72037	−	0.862499i
$946$	687.822			0.727085
$947$			593.141i			0.626337i	0.949698	+	0.313169i	$0.101390\pi$
$947$			593.141i			0.626337i	−0.949698	+	0.313169i	$0.898610\pi$
$948$	−77.6148	−	755.736i	−0.0818721	−	0.797189i
$949$	−321.574			−0.338856
$950$		−	1594.60i		−	1.67852i
$951$	−746.730	+	76.6899i	−0.785205	+	0.0806413i
$952$	−827.853			−0.869593
$953$		−	1570.71i		−	1.64817i	−0.566463	−	0.824087i	$-0.691689\pi$
$953$		−	1570.71i		−	1.64817i	0.566463	−	0.824087i	$-0.308311\pi$
$954$	−227.810	+	47.2913i	−0.238794	+	0.0495716i
$955$	1864.42			1.95227
$956$		−	601.881i		−	0.629583i
$957$	138.919	+	1352.66i	0.145161	+	1.41344i
$958$	−881.257			−0.919893
$959$		−	656.479i		−	0.684545i
$960$	225.493	−	23.1584i	0.234889	−	0.0241233i
$961$	−217.930			−0.226774
$962$		−	45.5118i		−	0.0473096i
$963$	28.6422	+	137.974i	0.0297426	+	0.143275i
$964$	−183.862			−0.190728
$965$		−	25.7009i		−	0.0266330i
$966$	−42.6160	−	414.952i	−0.0441159	−	0.429557i
$967$	−1688.51			−1.74613			−0.873066	−	0.487602i	$-0.837872\pi$
$967$	−1688.51			−1.74613			−0.873066	+	0.487602i	$0.837872\pi$
$968$			35.5396i			0.0367144i
$969$	1450.46	−	148.963i	1.49686	−	0.153729i
$970$	735.609			0.758360
$971$		−	163.410i		−	0.168290i	−0.996454	−	0.0841451i	$-0.973184\pi$
$971$		−	163.410i		−	0.168290i	0.996454	−	0.0841451i	$-0.0268159\pi$
$972$	−237.979	−	423.747i	−0.244835	−	0.435954i
$973$	−106.692			−0.109652
$974$			456.323i			0.468504i
$975$	−171.833	−	1673.14i	−0.176239	−	1.71604i
$976$	365.624			0.374614
$977$			950.064i			0.972429i	0.873839	+	0.486215i	$0.161623\pi$
$977$			950.064i			0.972429i	−0.873839	+	0.486215i	$0.838377\pi$
$978$	388.138	−	39.8622i	0.396869	−	0.0407589i
$979$	1488.90			1.52084
$980$		−	1187.00i		−	1.21123i
$981$	412.219	−	85.5732i	0.420203	−	0.0872306i
$982$	−383.123			−0.390145
$983$			1112.82i			1.13207i	0.824382	+	0.566034i	$0.191523\pi$
$983$			1112.82i			1.13207i	−0.824382	+	0.566034i	$0.808477\pi$
$984$	21.4760	+	209.112i	0.0218252	+	0.212513i
$985$	−3197.97			−3.24667
$986$			1703.69i			1.72788i
$987$	2583.53	−	265.331i	2.61756	−	0.268826i
$988$	306.677			0.310402
$989$			434.233i			0.439062i
$990$	254.443	+	1225.69i	0.257013	+	1.23807i
$991$	1226.72			1.23786			0.618932	−	0.785444i	$-0.287565\pi$
$991$	1226.72			1.23786			0.618932	+	0.785444i	$0.287565\pi$
$992$		−	154.202i		−	0.155445i
$993$	−16.0087	−	155.877i	−0.0161215	−	0.156976i
$994$	165.607			0.166607
$995$		−	1155.10i		−	1.16091i
$996$	579.256	−	59.4902i	0.581583	−	0.0597291i
$997$	612.386			0.614228			0.307114	−	0.951673i	$-0.400637\pi$
$997$	612.386			0.614228			0.307114	+	0.951673i	$0.400637\pi$
$998$		−	55.1726i		−	0.0552832i
$999$	−30.0747	−	94.8575i	−0.0301049	−	0.0949524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.b.a.119.12	✓	40
3.2	odd	2	inner	354.3.b.a.119.32	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.b.a.119.12	✓	40	1.1	even	1	trivial
354.3.b.a.119.32	yes	40	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	354.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(0.306491 + 2.98430i) q^{3} -2.00000 q^{4} +9.44498i q^{5} +(4.22044 - 0.433443i) q^{6} +10.5753 q^{7} +2.82843i q^{8} +(-8.81213 + 1.82932i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(0.306491 + 2.98430i) q^{3} -2.00000 q^{4} +9.44498i q^{5} +(4.22044 - 0.433443i) q^{6} +10.5753 q^{7} +2.82843i q^{8} +(-8.81213 + 1.82932i) q^{9} +13.3572 q^{10} -10.4132i q^{11} +(-0.612981 - 5.96861i) q^{12} +8.73176 q^{13} -14.9558i q^{14} +(-28.1867 + 2.89480i) q^{15} +4.00000 q^{16} +27.6767i q^{17} +(2.58705 + 12.4622i) q^{18} -17.5610 q^{19} -18.8900i q^{20} +(3.24124 + 31.5600i) q^{21} -14.7265 q^{22} -9.29706i q^{23} +(-8.44088 + 0.866887i) q^{24} -64.2076 q^{25} -12.3486i q^{26} +(-8.16009 - 25.7374i) q^{27} -21.1507 q^{28} +43.5272i q^{29} +(4.09386 + 39.8620i) q^{30} +27.2593 q^{31} -5.65685i q^{32} +(31.0762 - 3.19155i) q^{33} +39.1407 q^{34} +99.8839i q^{35} +(17.6243 - 3.65864i) q^{36} +3.68559 q^{37} +24.8350i q^{38} +(2.67620 + 26.0582i) q^{39} -26.7144 q^{40} -24.7738i q^{41} +(44.6326 - 4.58381i) q^{42} -46.7065 q^{43} +20.8264i q^{44} +(-17.2779 - 83.2303i) q^{45} -13.1480 q^{46} -81.8610i q^{47} +(1.22596 + 11.9372i) q^{48} +62.8379 q^{49} +90.8033i q^{50} +(-82.5955 + 8.48264i) q^{51} -17.4635 q^{52} +18.2800i q^{53} +(-36.3982 + 11.5401i) q^{54} +98.3525 q^{55} +29.9116i q^{56} +(-5.38228 - 52.4073i) q^{57} +61.5568 q^{58} +7.68115i q^{59} +(56.3733 - 5.78960i) q^{60} +91.4059 q^{61} -38.5505i q^{62} +(-93.1913 + 19.3457i) q^{63} -8.00000 q^{64} +82.4713i q^{65} +(-4.51353 - 43.9483i) q^{66} -44.2676 q^{67} -55.3533i q^{68} +(27.7452 - 2.84946i) q^{69} +141.257 q^{70} +11.0731i q^{71} +(-5.17410 - 24.9245i) q^{72} -36.8281 q^{73} -5.21221i q^{74} +(-19.6790 - 191.615i) q^{75} +35.1220 q^{76} -110.123i q^{77} +(36.8519 - 3.78472i) q^{78} +126.618 q^{79} +37.7799i q^{80} +(74.3072 - 32.2404i) q^{81} -35.0354 q^{82} +97.0505i q^{83} +(-6.48249 - 63.1201i) q^{84} -261.405 q^{85} +66.0529i q^{86} +(-129.898 + 13.3407i) q^{87} +29.4530 q^{88} +142.982i q^{89} +(-117.705 + 24.4347i) q^{90} +92.3414 q^{91} +18.5941i q^{92} +(8.35473 + 81.3500i) q^{93} -115.769 q^{94} -165.863i q^{95} +(16.8818 - 1.73377i) q^{96} +55.0720 q^{97} -88.8662i q^{98} +(19.0491 + 91.7625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9}+O(q^{10}) \) 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9	\( 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9} - 16 q^{10} + 34 q^{15} + 160 q^{16} + 16 q^{18} + 24 q^{19} - 18 q^{21} - 16 q^{22} - 16 q^{24} - 216 q^{25} - 30 q^{27} - 16 q^{28} - 64 q^{30} + 96 q^{31} + 76 q^{33} + 80 q^{34} + 48 q^{36} - 200 q^{37} - 28 q^{39} + 32 q^{40} + 48 q^{42} - 104 q^{43} + 58 q^{45} + 32 q^{46} + 288 q^{49} - 176 q^{51} - 40 q^{54} + 360 q^{55} + 214 q^{57} - 128 q^{58} - 68 q^{60} - 32 q^{61} - 132 q^{63} - 320 q^{64} - 112 q^{66} - 344 q^{67} + 88 q^{69} + 192 q^{70} - 32 q^{72} + 40 q^{73} + 28 q^{75} - 48 q^{76} + 96 q^{78} + 32 q^{79} + 336 q^{81} - 80 q^{82} + 36 q^{84} + 168 q^{85} - 162 q^{87} + 32 q^{88} + 112 q^{90} + 88 q^{91} - 316 q^{93} - 400 q^{94} + 32 q^{96} - 184 q^{97} - 148 q^{99}+O(q^{100}) \) 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9 - 16 * q^10 + 34 * q^15 + 160 * q^16 + 16 * q^18 + 24 * q^19 - 18 * q^21 - 16 * q^22 - 16 * q^24 - 216 * q^25 - 30 * q^27 - 16 * q^28 - 64 * q^30 + 96 * q^31 + 76 * q^33 + 80 * q^34 + 48 * q^36 - 200 * q^37 - 28 * q^39 + 32 * q^40 + 48 * q^42 - 104 * q^43 + 58 * q^45 + 32 * q^46 + 288 * q^49 - 176 * q^51 - 40 * q^54 + 360 * q^55 + 214 * q^57 - 128 * q^58 - 68 * q^60 - 32 * q^61 - 132 * q^63 - 320 * q^64 - 112 * q^66 - 344 * q^67 + 88 * q^69 + 192 * q^70 - 32 * q^72 + 40 * q^73 + 28 * q^75 - 48 * q^76 + 96 * q^78 + 32 * q^79 + 336 * q^81 - 80 * q^82 + 36 * q^84 + 168 * q^85 - 162 * q^87 + 32 * q^88 + 112 * q^90 + 88 * q^91 - 316 * q^93 - 400 * q^94 + 32 * q^96 - 184 * q^97 - 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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