LMFDB - Embedded newform 128.3.h.a.111.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,Mod(15,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("128.15");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	128.h (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			111.7
Character	$\chi$	$=$	128.111
Dual form			128.3.h.a.15.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.68670 + 1.94129i) q^{3} +(-4.51028 + 1.86822i) q^{5} +(3.85317 + 3.85317i) q^{7} +(11.8326 + 11.8326i) q^{9} +O(q^{10})$	\(q+(4.68670 + 1.94129i) q^{3} +(-4.51028 + 1.86822i) q^{5} +(3.85317 + 3.85317i) q^{7} +(11.8326 + 11.8326i) q^{9} +(4.56441 - 1.89064i) q^{11} +(-5.58307 - 2.31258i) q^{13} -24.7651 q^{15} -25.0539i q^{17} +(-6.43433 + 15.5338i) q^{19} +(10.5785 + 25.5388i) q^{21} +(26.9024 - 26.9024i) q^{23} +(-0.825315 + 0.825315i) q^{25} +(15.0136 + 36.2460i) q^{27} +(-0.210028 + 0.507052i) q^{29} -15.8372i q^{31} +25.0623 q^{33} +(-24.5774 - 10.1803i) q^{35} +(-2.18606 + 0.905498i) q^{37} +(-21.6768 - 21.6768i) q^{39} +(-31.1517 - 31.1517i) q^{41} +(-12.9078 + 5.34659i) q^{43} +(-75.4740 - 31.2624i) q^{45} -15.0033 q^{47} -19.3062i q^{49} +(48.6370 - 117.420i) q^{51} +(-15.4409 - 37.2776i) q^{53} +(-17.0546 + 17.0546i) q^{55} +(-60.3115 + 60.3115i) q^{57} +(14.7242 + 35.5473i) q^{59} +(-15.4603 + 37.3243i) q^{61} +91.1858i q^{63} +29.5016 q^{65} +(-61.3598 - 25.4161i) q^{67} +(178.309 - 73.8579i) q^{69} +(51.7789 + 51.7789i) q^{71} +(64.9440 + 64.9440i) q^{73} +(-5.47018 + 2.26582i) q^{75} +(24.8724 + 10.3025i) q^{77} +38.1202 q^{79} +48.4156i q^{81} +(-15.9782 + 38.5748i) q^{83} +(46.8061 + 113.000i) q^{85} +(-1.96868 + 1.96868i) q^{87} +(23.7666 - 23.7666i) q^{89} +(-12.6017 - 30.4233i) q^{91} +(30.7446 - 74.2241i) q^{93} -82.0827i q^{95} -118.710 q^{97} +(76.3798 + 31.6376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	4.68670	+	1.94129i	1.56223	+	0.647098i	0.985476	−	0.169817i	$-0.0543176\pi$
$3$	4.68670	+	1.94129i	1.56223	+	0.647098i	0.576758	+	0.816915i	$0.304318\pi$
$4$		0			0
$5$	−4.51028	+	1.86822i	−0.902055	+	0.373644i	−0.785010	−	0.619483i	$-0.787342\pi$
$5$	−4.51028	+	1.86822i	−0.902055	+	0.373644i	−0.117045	+	0.993127i	$0.537342\pi$
$6$		0			0
$7$	3.85317	+	3.85317i	0.550453	+	0.550453i	0.926571	−	0.376119i	$-0.122742\pi$
$7$	3.85317	+	3.85317i	0.550453	+	0.550453i	−0.376119	+	0.926571i	$0.622742\pi$
$8$		0			0
$9$	11.8326	+	11.8326i	1.31473	+	1.31473i
$10$		0			0
$11$	4.56441	−	1.89064i	0.414946	−	0.171876i	−0.165436	−	0.986221i	$-0.552903\pi$
$11$	4.56441	−	1.89064i	0.414946	−	0.171876i	0.580382	+	0.814344i	$0.302903\pi$
$12$		0			0
$13$	−5.58307	−	2.31258i	−0.429467	−	0.177891i	0.157470	−	0.987524i	$-0.449666\pi$
$13$	−5.58307	−	2.31258i	−0.429467	−	0.177891i	−0.586937	+	0.809633i	$0.699666\pi$
$14$		0			0
$15$	−24.7651			−1.65101
$16$		0			0
$17$		−	25.0539i		−	1.47376i	−0.676025	−	0.736879i	$-0.736299\pi$
$17$		−	25.0539i		−	1.47376i	0.676025	−	0.736879i	$-0.263701\pi$
$18$		0			0
$19$	−6.43433	+	15.5338i	−0.338649	+	0.817571i	0.659197	+	0.751970i	$0.270896\pi$
$19$	−6.43433	+	15.5338i	−0.338649	+	0.817571i	−0.997846	+	0.0656005i	$0.979104\pi$
$20$		0			0
$21$	10.5785	+	25.5388i	0.503739	+	1.21613i
$22$		0			0
$23$	26.9024	−	26.9024i	1.16967	−	1.16967i	0.187381	−	0.982287i	$-0.440000\pi$
$23$	26.9024	−	26.9024i	1.16967	−	1.16967i	0.982287	−	0.187381i	$-0.0600000\pi$
$24$		0			0
$25$	−0.825315	+	0.825315i	−0.0330126	+	0.0330126i
$26$		0			0
$27$	15.0136	+	36.2460i	0.556058	+	1.34244i
$28$		0			0
$29$	−0.210028	+	0.507052i	−0.00724234	+	0.0174846i	−0.927459	−	0.373924i	$-0.878012\pi$
$29$	−0.210028	+	0.507052i	−0.00724234	+	0.0174846i	0.920217	+	0.391409i	$0.128012\pi$
$30$		0			0
$31$		−	15.8372i		−	0.510877i	−0.966825	−	0.255438i	$-0.917780\pi$
$31$		−	15.8372i		−	0.510877i	0.966825	−	0.255438i	$-0.0822198\pi$
$32$		0			0
$33$	25.0623			0.759464
$34$		0			0
$35$	−24.5774	−	10.1803i	−0.702212	−	0.290866i
$36$		0			0
$37$	−2.18606	+	0.905498i	−0.0590828	+	0.0244729i	−0.412029	−	0.911171i	$-0.635180\pi$
$37$	−2.18606	+	0.905498i	−0.0590828	+	0.0244729i	0.352946	+	0.935644i	$0.385180\pi$
$38$		0			0
$39$	−21.6768	−	21.6768i	−0.555814	−	0.555814i
$40$		0			0
$41$	−31.1517	−	31.1517i	−0.759798	−	0.759798i	0.216488	−	0.976285i	$-0.430540\pi$
$41$	−31.1517	−	31.1517i	−0.759798	−	0.759798i	−0.976285	+	0.216488i	$0.930540\pi$
$42$		0			0
$43$	−12.9078	+	5.34659i	−0.300182	+	0.124339i	−0.527691	−	0.849437i	$-0.676942\pi$
$43$	−12.9078	+	5.34659i	−0.300182	+	0.124339i	0.227509	+	0.973776i	$0.426942\pi$
$44$		0			0
$45$	−75.4740	−	31.2624i	−1.67720	−	0.694719i
$46$		0			0
$47$	−15.0033			−0.319220			−0.159610	−	0.987180i	$-0.551024\pi$
$47$	−15.0033			−0.319220			−0.159610	+	0.987180i	$0.551024\pi$
$48$		0			0
$49$		−	19.3062i		−	0.394004i
$50$		0			0
$51$	48.6370	−	117.420i	0.953666	−	2.30235i
$52$		0			0
$53$	−15.4409	−	37.2776i	−0.291338	−	0.703352i	0.708660	−	0.705550i	$-0.249300\pi$
$53$	−15.4409	−	37.2776i	−0.291338	−	0.703352i	−0.999998	+	0.00219873i	$0.999300\pi$
$54$		0			0
$55$	−17.0546	+	17.0546i	−0.310084	+	0.310084i
$56$		0			0
$57$	−60.3115	+	60.3115i	−1.05810	+	1.05810i
$58$		0			0
$59$	14.7242	+	35.5473i	0.249562	+	0.602496i	0.998167	−	0.0605202i	$-0.0192760\pi$
$59$	14.7242	+	35.5473i	0.249562	+	0.602496i	−0.748605	+	0.663016i	$0.769276\pi$
$60$		0			0
$61$	−15.4603	+	37.3243i	−0.253447	+	0.611875i	−0.998478	−	0.0551552i	$-0.982435\pi$
$61$	−15.4603	+	37.3243i	−0.253447	+	0.611875i	0.745031	+	0.667030i	$0.232435\pi$
$62$		0			0
$63$			91.1858i			1.44739i
$64$		0			0
$65$	29.5016			0.453870
$66$		0			0
$67$	−61.3598	−	25.4161i	−0.915818	−	0.379344i	−0.125537	−	0.992089i	$-0.540065\pi$
$67$	−61.3598	−	25.4161i	−0.915818	−	0.379344i	−0.790281	+	0.612745i	$0.790065\pi$
$68$		0			0
$69$	178.309	−	73.8579i	2.58419	−	1.07040i
$70$		0			0
$71$	51.7789	+	51.7789i	0.729281	+	0.729281i	0.970477	−	0.241196i	$-0.0775395\pi$
$71$	51.7789	+	51.7789i	0.729281	+	0.729281i	−0.241196	+	0.970477i	$0.577540\pi$
$72$		0			0
$73$	64.9440	+	64.9440i	0.889643	+	0.889643i	0.994489	−	0.104845i	$-0.0334347\pi$
$73$	64.9440	+	64.9440i	0.889643	+	0.889643i	−0.104845	+	0.994489i	$0.533435\pi$
$74$		0			0
$75$	−5.47018	+	2.26582i	−0.0729358	+	0.0302110i
$76$		0			0
$77$	24.8724	+	10.3025i	0.323018	+	0.133798i
$78$		0			0
$79$	38.1202			0.482535			0.241267	−	0.970459i	$-0.422437\pi$
$79$	38.1202			0.482535			0.241267	+	0.970459i	$0.422437\pi$
$80$		0			0
$81$			48.4156i			0.597724i
$82$		0			0
$83$	−15.9782	+	38.5748i	−0.192509	+	0.464757i	−0.990432	−	0.138002i	$-0.955932\pi$
$83$	−15.9782	+	38.5748i	−0.192509	+	0.464757i	0.797923	+	0.602759i	$0.205932\pi$
$84$		0			0
$85$	46.8061	+	113.000i	0.550660	+	1.32941i
$86$		0			0
$87$	−1.96868	+	1.96868i	−0.0226285	+	0.0226285i
$88$		0			0
$89$	23.7666	−	23.7666i	0.267040	−	0.267040i	−0.560866	−	0.827906i	$-0.689532\pi$
$89$	23.7666	−	23.7666i	0.267040	−	0.267040i	0.827906	+	0.560866i	$0.189532\pi$
$90$		0			0
$91$	−12.6017	−	30.4233i	−0.138481	−	0.334322i
$92$		0			0
$93$	30.7446	−	74.2241i	0.330587	−	0.798109i
$94$		0			0
$95$		−	82.0827i		−	0.864028i
$96$		0			0
$97$	−118.710			−1.22382			−0.611908	−	0.790929i	$-0.709598\pi$
$97$	−118.710			−1.22382			−0.611908	+	0.790929i	$0.709598\pi$
$98$		0			0
$99$	76.3798	+	31.6376i	0.771514	+	0.319571i
$100$		0			0
$101$	−182.236	+	75.4846i	−1.80432	+	0.747372i	−0.819665	+	0.572844i	$0.805840\pi$
$101$	−182.236	+	75.4846i	−1.80432	+	0.747372i	−0.984652	+	0.174529i	$0.944160\pi$
$102$		0			0
$103$	80.3171	+	80.3171i	0.779777	+	0.779777i	0.979793	−	0.200016i	$-0.0640993\pi$
$103$	80.3171	+	80.3171i	0.779777	+	0.779777i	−0.200016	+	0.979793i	$0.564099\pi$
$104$		0			0
$105$	−95.4240	−	95.4240i	−0.908800	−	0.908800i
$106$		0			0
$107$	−22.6854	+	9.39659i	−0.212013	+	0.0878186i	−0.486162	−	0.873868i	$-0.661604\pi$
$107$	−22.6854	+	9.39659i	−0.212013	+	0.0878186i	0.274150	+	0.961687i	$0.411604\pi$
$108$		0			0
$109$	181.428	+	75.1501i	1.66448	+	0.689450i	0.998406	−	0.0564360i	$-0.0179737\pi$
$109$	181.428	+	75.1501i	1.66448	+	0.689450i	0.666074	+	0.745886i	$0.267974\pi$
$110$		0			0
$111$	−12.0033			−0.108138
$112$		0			0
$113$		−	32.7876i		−	0.290156i	−0.989420	−	0.145078i	$-0.953657\pi$
$113$		−	32.7876i		−	0.290156i	0.989420	−	0.145078i	$-0.0463433\pi$
$114$		0			0
$115$	−71.0777	+	171.597i	−0.618067	+	1.49214i
$116$		0			0
$117$	−38.6983	−	93.4259i	−0.330754	−	0.798512i
$118$		0			0
$119$	96.5368	−	96.5368i	0.811234	−	0.811234i
$120$		0			0
$121$	−68.3006	+	68.3006i	−0.564468	+	0.564468i
$122$		0			0
$123$	−85.5241	−	206.473i	−0.695318	−	1.67865i
$124$		0			0
$125$	48.8860	−	118.021i	0.391088	−	0.944169i
$126$		0			0
$127$			130.165i			1.02492i	0.858710	+	0.512462i	$0.171266\pi$
$127$			130.165i			1.02492i	−0.858710	+	0.512462i	$0.828734\pi$
$128$		0			0
$129$	−70.8744			−0.549414
$130$		0			0
$131$	−24.3356	−	10.0801i	−0.185768	−	0.0769476i	0.287861	−	0.957672i	$-0.407056\pi$
$131$	−24.3356	−	10.0801i	−0.185768	−	0.0769476i	−0.473628	+	0.880725i	$0.657056\pi$
$132$		0			0
$133$	−84.6471	+	35.0620i	−0.636444	+	0.263624i
$134$		0			0
$135$	−135.431	−	135.431i	−1.00319	−	1.00319i
$136$		0			0
$137$	147.886	+	147.886i	1.07946	+	1.07946i	0.996557	+	0.0829047i	$0.0264197\pi$
$137$	147.886	+	147.886i	1.07946	+	1.07946i	0.0829047	+	0.996557i	$0.473580\pi$
$138$		0			0
$139$	206.929	−	85.7129i	1.48870	−	0.616639i	0.517666	−	0.855583i	$-0.326801\pi$
$139$	206.929	−	85.7129i	1.48870	−	0.616639i	0.971033	+	0.238944i	$0.0768011\pi$
$140$		0			0
$141$	−70.3162	−	29.1259i	−0.498696	−	0.206567i
$142$		0			0
$143$	−29.8556			−0.208781
$144$		0			0
$145$		−	2.67932i		−	0.0184781i
$146$		0			0
$147$	37.4790	−	90.4823i	0.254959	−	0.615526i
$148$		0			0
$149$	−20.4247	−	49.3095i	−0.137078	−	0.330936i	0.840402	−	0.541964i	$-0.182319\pi$
$149$	−20.4247	−	49.3095i	−0.137078	−	0.330936i	−0.977480	+	0.211028i	$0.932319\pi$
$150$		0			0
$151$	−180.137	+	180.137i	−1.19296	+	1.19296i	−0.216726	+	0.976232i	$0.569538\pi$
$151$	−180.137	+	180.137i	−1.19296	+	1.19296i	−0.976232	+	0.216726i	$0.930462\pi$
$152$		0			0
$153$	296.452	−	296.452i	1.93759	−	1.93759i
$154$		0			0
$155$	29.5873	+	71.4300i	0.190886	+	0.460839i
$156$		0			0
$157$	−60.3999	+	145.818i	−0.384713	+	0.928779i	0.606327	+	0.795215i	$0.292642\pi$
$157$	−60.3999	+	145.818i	−0.384713	+	0.928779i	−0.991040	+	0.133564i	$0.957358\pi$
$158$		0			0
$159$		−	204.684i		−	1.28732i
$160$		0			0
$161$	207.319			1.28769
$162$		0			0
$163$	152.162	+	63.0277i	0.933512	+	0.386673i	0.797010	−	0.603966i	$-0.206414\pi$
$163$	152.162	+	63.0277i	0.933512	+	0.386673i	0.136502	+	0.990640i	$0.456414\pi$
$164$		0			0
$165$	−113.038	+	46.8218i	−0.685078	+	0.283769i
$166$		0			0
$167$	−94.8188	−	94.8188i	−0.567777	−	0.567777i	0.363728	−	0.931505i	$-0.381504\pi$
$167$	−94.8188	−	94.8188i	−0.567777	−	0.567777i	−0.931505	+	0.363728i	$0.881504\pi$
$168$		0			0
$169$	−93.6785	−	93.6785i	−0.554310	−	0.554310i
$170$		0			0
$171$	−259.940	+	107.671i	−1.52012	+	0.629653i
$172$		0			0
$173$	−107.416	−	44.4930i	−0.620900	−	0.257185i	0.0499813	−	0.998750i	$-0.484084\pi$
$173$	−107.416	−	44.4930i	−0.620900	−	0.257185i	−0.670881	+	0.741565i	$0.734084\pi$
$174$		0			0
$175$	−6.36016			−0.0363437
$176$		0			0
$177$			195.183i			1.10273i
$178$		0			0
$179$	−54.7154	+	132.095i	−0.305673	+	0.737959i	0.694163	+	0.719818i	$0.255775\pi$
$179$	−54.7154	+	132.095i	−0.305673	+	0.737959i	−0.999835	+	0.0181410i	$0.994225\pi$
$180$		0			0
$181$	−128.496	−	310.218i	−0.709925	−	1.71391i	−0.700189	−	0.713957i	$-0.746901\pi$
$181$	−128.496	−	310.218i	−0.709925	−	1.71391i	−0.00973575	−	0.999953i	$-0.503099\pi$
$182$		0			0
$183$	−144.915	+	144.915i	−0.791886	+	0.791886i
$184$		0			0
$185$	8.16809	−	8.16809i	0.0441518	−	0.0441518i
$186$		0			0
$187$	−47.3678	−	114.356i	−0.253304	−	0.611530i
$188$		0			0
$189$	−81.8120	+	197.512i	−0.432868	+	1.04503i
$190$		0			0
$191$		−	312.806i		−	1.63773i	−0.573986	−	0.818865i	$-0.694604\pi$
$191$		−	312.806i		−	1.63773i	0.573986	−	0.818865i	$-0.305396\pi$
$192$		0			0
$193$	−70.6708			−0.366170			−0.183085	−	0.983097i	$-0.558608\pi$
$193$	−70.6708			−0.366170			−0.183085	+	0.983097i	$0.558608\pi$
$194$		0			0
$195$	138.265	+	57.2713i	0.709052	+	0.293699i
$196$		0			0
$197$	81.5762	−	33.7900i	0.414092	−	0.171523i	−0.165904	−	0.986142i	$-0.553054\pi$
$197$	81.5762	−	33.7900i	0.414092	−	0.171523i	0.579996	+	0.814619i	$0.303054\pi$
$198$		0			0
$199$	−102.666	−	102.666i	−0.515910	−	0.515910i	0.400421	−	0.916331i	$-0.368864\pi$
$199$	−102.666	−	102.666i	−0.515910	−	0.515910i	−0.916331	+	0.400421i	$0.868864\pi$
$200$		0			0
$201$	−238.235	−	238.235i	−1.18525	−	1.18525i
$202$		0			0
$203$	−2.76303	+	1.14449i	−0.0136110	+	0.00563786i
$204$		0			0
$205$	198.701	+	82.3046i	0.969273	+	0.401486i
$206$		0			0
$207$	636.649			3.07560
$208$		0			0
$209$			83.0678i			0.397454i
$210$		0			0
$211$	−8.35160	+	20.1625i	−0.0395810	+	0.0955571i	−0.942434	−	0.334393i	$-0.891469\pi$
$211$	−8.35160	+	20.1625i	−0.0395810	+	0.0955571i	0.902853	+	0.429950i	$0.141469\pi$
$212$		0			0
$213$	142.154	+	343.191i	0.667391	+	1.61122i
$214$		0			0
$215$	48.2292	−	48.2292i	0.224322	−	0.224322i
$216$		0			0
$217$	61.0233	−	61.0233i	0.281213	−	0.281213i
$218$		0			0
$219$	178.298	+	430.448i	0.814144	+	1.96552i
$220$		0			0
$221$	−57.9391	+	139.877i	−0.262168	+	0.632930i
$222$		0			0
$223$			131.685i			0.590516i	0.955418	+	0.295258i	$0.0954056\pi$
$223$			131.685i			0.590516i	−0.955418	+	0.295258i	$0.904594\pi$
$224$		0			0
$225$	−19.5312			−0.0868054
$226$		0			0
$227$	−60.7552	−	25.1656i	−0.267644	−	0.110862i	0.244825	−	0.969567i	$-0.421269\pi$
$227$	−60.7552	−	25.1656i	−0.267644	−	0.110862i	−0.512470	+	0.858705i	$0.671269\pi$
$228$		0			0
$229$	123.210	−	51.0352i	0.538035	−	0.222861i	−0.0970835	−	0.995276i	$-0.530951\pi$
$229$	123.210	−	51.0352i	0.538035	−	0.222861i	0.635118	+	0.772415i	$0.280951\pi$
$230$		0			0
$231$	96.5693	+	96.5693i	0.418049	+	0.418049i
$232$		0			0
$233$	110.005	+	110.005i	0.472124	+	0.472124i	0.902601	−	0.430477i	$-0.141655\pi$
$233$	110.005	+	110.005i	0.472124	+	0.472124i	−0.430477	+	0.902601i	$0.641655\pi$
$234$		0			0
$235$	67.6692	−	28.0295i	0.287954	−	0.119274i
$236$		0			0
$237$	178.658	+	74.0026i	0.753832	+	0.312247i
$238$		0			0
$239$	−277.831			−1.16247			−0.581236	−	0.813735i	$-0.697431\pi$
$239$	−277.831			−1.16247			−0.581236	+	0.813735i	$0.697431\pi$
$240$		0			0
$241$			52.0006i			0.215770i	0.994163	+	0.107885i	$0.0344079\pi$
$241$			52.0006i			0.215770i	−0.994163	+	0.107885i	$0.965592\pi$
$242$		0			0
$243$	41.1331	−	99.3041i	0.169272	−	0.408659i
$244$		0			0
$245$	36.0681	+	87.0762i	0.147217	+	0.355413i
$246$		0			0
$247$	71.8466	−	71.8466i	0.290877	−	0.290877i
$248$		0			0
$249$	−149.770	+	149.770i	−0.601487	+	0.601487i
$250$		0			0
$251$	−28.7912	−	69.5080i	−0.114706	−	0.276924i	0.856092	−	0.516823i	$-0.172886\pi$
$251$	−28.7912	−	69.5080i	−0.114706	−	0.276924i	−0.970798	+	0.239899i	$0.922886\pi$
$252$		0			0
$253$	71.9307	−	173.656i	0.284311	−	0.686388i
$254$		0			0
$255$			620.461i			2.43318i
$256$		0			0
$257$	241.501			0.939692			0.469846	−	0.882748i	$-0.344309\pi$
$257$	241.501			0.939692			0.469846	+	0.882748i	$0.344309\pi$
$258$		0			0
$259$	−11.9123	−	4.93424i	−0.0459935	−	0.0190511i
$260$		0			0
$261$	−8.48491	+	3.51456i	−0.0325092	+	0.0134658i
$262$		0			0
$263$	118.637	+	118.637i	0.451090	+	0.451090i	0.895716	−	0.444626i	$-0.146664\pi$
$263$	118.637	+	118.637i	0.451090	+	0.451090i	−0.444626	+	0.895716i	$0.646664\pi$
$264$		0			0
$265$	139.285	+	139.285i	0.525606	+	0.525606i
$266$		0			0
$267$	157.525	−	65.2489i	0.589981	−	0.244378i
$268$		0			0
$269$	−231.194	−	95.7638i	−0.859459	−	0.355999i	−0.0909629	−	0.995854i	$-0.528994\pi$
$269$	−231.194	−	95.7638i	−0.859459	−	0.355999i	−0.768496	+	0.639855i	$0.778994\pi$
$270$		0			0
$271$	2.13724			0.00788650			0.00394325	−	0.999992i	$-0.498745\pi$
$271$	2.13724			0.00788650			0.00394325	+	0.999992i	$0.498745\pi$
$272$		0			0
$273$		−	167.048i		−	0.611899i
$274$		0			0
$275$	−2.20670	+	5.32745i	−0.00802437	+	0.0193725i
$276$		0			0
$277$	−177.679	−	428.955i	−0.641441	−	1.54857i	−0.824737	−	0.565517i	$-0.808677\pi$
$277$	−177.679	−	428.955i	−0.641441	−	1.54857i	0.183296	−	0.983058i	$-0.441323\pi$
$278$		0			0
$279$	187.395	−	187.395i	0.671665	−	0.671665i
$280$		0			0
$281$	−261.664	+	261.664i	−0.931188	+	0.931188i	−0.997780	−	0.0665922i	$-0.978787\pi$
$281$	−261.664	+	261.664i	−0.931188	+	0.931188i	0.0665922	+	0.997780i	$0.478787\pi$
$282$		0			0
$283$	−160.904	−	388.456i	−0.568564	−	1.37264i	−0.902765	−	0.430134i	$-0.858466\pi$
$283$	−160.904	−	388.456i	−0.568564	−	1.37264i	0.334201	−	0.942502i	$-0.391534\pi$
$284$		0			0
$285$	159.347	−	384.697i	0.559111	−	1.34981i
$286$		0			0
$287$		−	240.066i		−	0.836465i
$288$		0			0
$289$	−338.697			−1.17196
$290$		0			0
$291$	−556.359	−	230.452i	−1.91189	−	0.791930i
$292$		0			0
$293$	−141.895	+	58.7749i	−0.484284	+	0.200597i	−0.611448	−	0.791285i	$-0.709413\pi$
$293$	−141.895	+	58.7749i	−0.484284	+	0.200597i	0.127164	+	0.991882i	$0.459413\pi$
$294$		0			0
$295$	−132.820	−	132.820i	−0.450238	−	0.450238i
$296$		0			0
$297$	137.056	+	137.056i	0.461468	+	0.461468i
$298$		0			0
$299$	−212.412	+	87.9838i	−0.710407	+	0.294260i
$300$		0			0
$301$	−70.3373	−	29.1347i	−0.233679	−	0.0967929i
$302$		0			0
$303$	−1000.62			−3.30239
$304$		0			0
$305$		−	197.226i		−	0.646643i
$306$		0			0
$307$	36.1806	−	87.3476i	0.117852	−	0.284520i	−0.853935	−	0.520379i	$-0.825791\pi$
$307$	36.1806	−	87.3476i	0.117852	−	0.284520i	0.971787	+	0.235860i	$0.0757905\pi$
$308$		0			0
$309$	220.503	+	532.341i	0.713602	+	1.72279i
$310$		0			0
$311$	−221.462	+	221.462i	−0.712098	+	0.712098i	−0.966974	−	0.254876i	$-0.917965\pi$
$311$	−221.462	+	221.462i	−0.712098	+	0.712098i	0.254876	+	0.966974i	$0.417965\pi$
$312$		0			0
$313$	280.384	−	280.384i	0.895795	−	0.895795i	−0.0992662	−	0.995061i	$-0.531650\pi$
$313$	280.384	−	280.384i	0.895795	−	0.895795i	0.995061	+	0.0992662i	$0.0316495\pi$
$314$		0			0
$315$	−170.355	−	411.273i	−0.540809	−	1.30563i
$316$		0			0
$317$	155.972	−	376.549i	0.492024	−	1.18785i	−0.461665	−	0.887055i	$-0.652748\pi$
$317$	155.972	−	376.549i	0.492024	−	1.18785i	0.953688	−	0.300796i	$-0.0972524\pi$
$318$		0			0
$319$			2.71148i			0.00849994i
$320$		0			0
$321$	−124.561			−0.388041
$322$		0			0
$323$	389.183	+	161.205i	1.20490	+	0.499086i
$324$		0			0
$325$	6.51640	−	2.69918i	0.0200505	−	0.00830517i
$326$		0			0
$327$	704.412	+	704.412i	2.15416	+	2.15416i
$328$		0			0
$329$	−57.8104	−	57.8104i	−0.175715	−	0.175715i
$330$		0			0
$331$	418.148	−	173.202i	1.26329	−	0.523270i	0.352370	−	0.935861i	$-0.385376\pi$
$331$	418.148	−	173.202i	1.26329	−	0.523270i	0.910917	+	0.412591i	$0.135376\pi$
$332$		0			0
$333$	−36.5812	−	15.1524i	−0.109853	−	0.0455027i
$334$		0			0
$335$	324.232			0.967857
$336$		0			0
$337$		−	38.1203i		−	0.113116i	−0.998399	−	0.0565582i	$-0.981987\pi$
$337$		−	38.1203i		−	0.113116i	0.998399	−	0.0565582i	$-0.0180127\pi$
$338$		0			0
$339$	63.6504	−	153.666i	0.187759	−	0.453291i
$340$		0			0
$341$	−29.9424	−	72.2873i	−0.0878076	−	0.211986i
$342$		0			0
$343$	263.195	−	263.195i	0.767333	−	0.767333i
$344$		0			0
$345$	−666.239	+	666.239i	−1.93113	+	1.93113i
$346$		0			0
$347$	201.452	+	486.348i	0.580553	+	1.40158i	0.892313	+	0.451418i	$0.149082\pi$
$347$	201.452	+	486.348i	0.580553	+	1.40158i	−0.311760	+	0.950161i	$0.600918\pi$
$348$		0			0
$349$	−53.2160	+	128.475i	−0.152481	+	0.368122i	−0.981600	−	0.190951i	$-0.938843\pi$
$349$	−53.2160	+	128.475i	−0.152481	+	0.368122i	0.829118	+	0.559073i	$0.188843\pi$
$350$		0			0
$351$		−	237.084i		−	0.675452i
$352$		0			0
$353$	−223.875			−0.634208			−0.317104	−	0.948391i	$-0.602710\pi$
$353$	−223.875			−0.634208			−0.317104	+	0.948391i	$0.602710\pi$
$354$		0			0
$355$	−330.272	−	136.803i	−0.930343	−	0.385361i
$356$		0			0
$357$	639.846	−	265.033i	1.79228	−	0.742389i
$358$		0			0
$359$	44.5652	+	44.5652i	0.124137	+	0.124137i	0.766446	−	0.642309i	$-0.222023\pi$
$359$	44.5652	+	44.5652i	0.124137	+	0.124137i	−0.642309	+	0.766446i	$0.722023\pi$
$360$		0			0
$361$	55.3658	+	55.3658i	0.153368	+	0.153368i
$362$		0			0
$363$	−452.696	+	187.513i	−1.24710	+	0.516565i
$364$		0			0
$365$	−414.245	−	171.586i	−1.13492	−	0.470098i
$366$		0			0
$367$	294.972			0.803739			0.401869	−	0.915697i	$-0.368361\pi$
$367$	294.972			0.803739			0.401869	+	0.915697i	$0.368361\pi$
$368$		0			0
$369$		−	737.210i		−	1.99786i
$370$		0			0
$371$	84.1406	−	203.133i	0.226794	−	0.547529i
$372$		0			0
$373$	96.5187	+	233.017i	0.258763	+	0.624710i	0.998857	−	0.0477936i	$-0.0152190\pi$
$373$	96.5187	+	233.017i	0.258763	+	0.624710i	−0.740094	+	0.672504i	$0.765219\pi$
$374$		0			0
$375$	458.228	−	458.228i	1.22194	−	1.22194i
$376$		0			0
$377$	2.34520	−	2.34520i	0.00622069	−	0.00622069i
$378$		0			0
$379$	70.2002	+	169.478i	0.185225	+	0.447172i	0.989029	−	0.147722i	$-0.0471941\pi$
$379$	70.2002	+	169.478i	0.185225	+	0.447172i	−0.803804	+	0.594894i	$0.797194\pi$
$380$		0			0
$381$	−252.689	+	610.046i	−0.663227	+	1.60117i
$382$		0			0
$383$			519.043i			1.35520i	0.735429	+	0.677602i	$0.236981\pi$
$383$			519.043i			1.35520i	−0.735429	+	0.677602i	$0.763019\pi$
$384$		0			0
$385$	−131.429			−0.341373
$386$		0			0
$387$	−215.997	−	89.4688i	−0.558131	−	0.231185i
$388$		0			0
$389$	52.0121	−	21.5441i	0.133707	−	0.0553834i	−0.314827	−	0.949149i	$-0.601946\pi$
$389$	52.0121	−	21.5441i	0.133707	−	0.0553834i	0.448534	+	0.893766i	$0.351946\pi$
$390$		0			0
$391$	−674.009	−	674.009i	−1.72381	−	1.72381i
$392$		0			0
$393$	−94.4851	−	94.4851i	−0.240420	−	0.240420i
$394$		0			0
$395$	−171.933	+	71.2169i	−0.435273	+	0.180296i
$396$		0			0
$397$	138.533	+	57.3823i	0.348950	+	0.144540i	0.550272	−	0.834985i	$-0.314524\pi$
$397$	138.533	+	57.3823i	0.348950	+	0.144540i	−0.201322	+	0.979525i	$0.564524\pi$
$398$		0			0
$399$	−464.781			−1.16487
$400$		0			0
$401$		−	11.3014i		−	0.0281830i	−0.999901	−	0.0140915i	$-0.995514\pi$
$401$		−	11.3014i		−	0.0281830i	0.999901	−	0.0140915i	$-0.00448560\pi$
$402$		0			0
$403$	−36.6248	+	88.4200i	−0.0908803	+	0.219404i
$404$		0			0
$405$	−90.4509	−	218.368i	−0.223336	−	0.539180i
$406$		0			0
$407$	−8.26612	+	8.26612i	−0.0203099	+	0.0203099i
$408$		0			0
$409$	188.958	−	188.958i	0.462001	−	0.462001i	−0.437310	−	0.899311i	$-0.644069\pi$
$409$	188.958	−	188.958i	0.462001	−	0.462001i	0.899311	+	0.437310i	$0.144069\pi$
$410$		0			0
$411$	406.008	+	980.190i	0.987854	+	2.38489i
$412$		0			0
$413$	−80.2350	+	193.704i	−0.194274	+	0.469018i
$414$		0			0
$415$		−	203.834i		−	0.491166i
$416$		0			0
$417$	1136.21			2.72472
$418$		0			0
$419$	238.026	+	98.5936i	0.568081	+	0.235307i	0.648189	−	0.761479i	$-0.275527\pi$
$419$	238.026	+	98.5936i	0.568081	+	0.235307i	−0.0801080	+	0.996786i	$0.525527\pi$
$420$		0			0
$421$	324.923	−	134.588i	0.771790	−	0.319686i	0.0381925	−	0.999270i	$-0.487840\pi$
$421$	324.923	−	134.588i	0.771790	−	0.319686i	0.733597	+	0.679585i	$0.237840\pi$
$422$		0			0
$423$	−177.528	−	177.528i	−0.419688	−	0.419688i
$424$		0			0
$425$	20.6773	+	20.6773i	0.0486526	+	0.0486526i
$426$		0			0
$427$	−203.388	+	84.2461i	−0.476318	+	0.197298i
$428$		0			0
$429$	−139.924	−	57.9586i	−0.326164	−	0.135102i
$430$		0			0
$431$	16.1400			0.0374479			0.0187239	−	0.999825i	$-0.494040\pi$
$431$	16.1400			0.0374479			0.0187239	+	0.999825i	$0.494040\pi$
$432$		0			0
$433$			732.781i			1.69233i	0.532918	+	0.846167i	$0.321095\pi$
$433$			732.781i			1.69233i	−0.532918	+	0.846167i	$0.678905\pi$
$434$		0			0
$435$	5.20136	−	12.5572i	0.0119571	−	0.0288671i
$436$		0			0
$437$	244.799	+	590.996i	0.560180	+	1.35239i
$438$		0			0
$439$	−460.630	+	460.630i	−1.04927	+	1.04927i	−0.0505487	+	0.998722i	$0.516097\pi$
$439$	−460.630	+	460.630i	−1.04927	+	1.04927i	−0.998722	+	0.0505487i	$0.983903\pi$
$440$		0			0
$441$	228.442	−	228.442i	0.518009	−	0.518009i
$442$		0			0
$443$	55.5453	+	134.098i	0.125384	+	0.302705i	0.974090	−	0.226161i	$-0.0726175\pi$
$443$	55.5453	+	134.098i	0.125384	+	0.302705i	−0.848705	+	0.528866i	$0.822618\pi$
$444$		0			0
$445$	−62.7927	+	151.595i	−0.141107	+	0.340663i
$446$		0			0
$447$		−	270.749i		−	0.605703i
$448$		0			0
$449$	731.262			1.62865			0.814323	−	0.580412i	$-0.197108\pi$
$449$	731.262			1.62865			0.814323	+	0.580412i	$0.197108\pi$
$450$		0			0
$451$	−201.086	−	83.2924i	−0.445866	−	0.184684i
$452$		0			0
$453$	−1193.95	+	494.549i	−2.63564	+	1.09172i
$454$		0			0
$455$	113.675	+	113.675i	0.249834	+	0.249834i
$456$		0			0
$457$	−332.873	−	332.873i	−0.728388	−	0.728388i	0.241911	−	0.970298i	$-0.422226\pi$
$457$	−332.873	−	332.873i	−0.728388	−	0.728388i	−0.970298	+	0.241911i	$0.922226\pi$
$458$		0			0
$459$	908.102	−	376.148i	1.97844	−	0.819495i
$460$		0			0
$461$	−132.650	−	54.9455i	−0.287744	−	0.119188i	0.234143	−	0.972202i	$-0.424772\pi$
$461$	−132.650	−	54.9455i	−0.287744	−	0.119188i	−0.521887	+	0.853015i	$0.674772\pi$
$462$		0			0
$463$	873.591			1.88680			0.943402	−	0.331650i	$-0.107605\pi$
$463$	873.591			1.88680			0.943402	+	0.331650i	$0.107605\pi$
$464$		0			0
$465$			392.209i			0.843460i
$466$		0			0
$467$	135.550	−	327.247i	0.290258	−	0.700744i	−0.709735	−	0.704468i	$-0.751186\pi$
$467$	135.550	−	327.247i	0.290258	−	0.700744i	0.999993	+	0.00372448i	$0.00118554\pi$
$468$		0			0
$469$	−138.497	−	334.362i	−0.295303	−	0.712925i
$470$		0			0
$471$	−566.153	+	566.153i	−1.20202	+	1.20202i
$472$		0			0
$473$	−48.8081	+	48.8081i	−0.103188	+	0.103188i
$474$		0			0
$475$	−7.50997	−	18.1307i	−0.0158105	−	0.0381698i
$476$		0			0
$477$	258.385	−	623.796i	0.541687	−	1.30775i
$478$		0			0
$479$			296.032i			0.618021i	0.951059	+	0.309011i	$0.0999979\pi$
$479$			296.032i			0.618021i	−0.951059	+	0.309011i	$0.900002\pi$
$480$		0			0
$481$	14.2990			0.0297276
$482$		0			0
$483$	971.641	+	402.467i	2.01168	+	0.833265i
$484$		0			0
$485$	535.416	−	221.777i	1.10395	−	0.457271i
$486$		0			0
$487$	232.632	+	232.632i	0.477683	+	0.477683i	0.904390	−	0.426707i	$-0.140326\pi$
$487$	232.632	+	232.632i	0.477683	+	0.477683i	−0.426707	+	0.904390i	$0.640326\pi$
$488$		0			0
$489$	590.784	+	590.784i	1.20815	+	1.20815i
$490$		0			0
$491$	−217.435	+	90.0644i	−0.442840	+	0.183430i	−0.592951	−	0.805239i	$-0.702037\pi$
$491$	−217.435	+	90.0644i	−0.442840	+	0.183430i	0.150110	+	0.988669i	$0.452037\pi$
$492$		0			0
$493$	12.7036	+	5.26201i	0.0257680	+	0.0106735i
$494$		0			0
$495$	−403.600			−0.815354
$496$		0			0
$497$			399.026i			0.802869i
$498$		0			0
$499$	−64.7699	+	156.368i	−0.129799	+	0.313364i	−0.975396	−	0.220458i	$-0.929245\pi$
$499$	−64.7699	+	156.368i	−0.129799	+	0.313364i	0.845597	+	0.533822i	$0.179245\pi$
$500$		0			0
$501$	−260.316	−	628.458i	−0.519593	−	1.25441i
$502$		0			0
$503$	612.203	−	612.203i	1.21710	−	1.21710i	0.248460	−	0.968642i	$-0.420075\pi$
$503$	612.203	−	612.203i	1.21710	−	1.21710i	0.968642	−	0.248460i	$-0.0799246\pi$
$504$		0			0
$505$	680.913	−	680.913i	1.34834	−	1.34834i
$506$		0			0
$507$	−257.185	−	620.900i	−0.507269	−	1.22466i
$508$		0			0
$509$	−273.870	+	661.182i	−0.538056	+	1.29898i	0.388022	+	0.921650i	$0.373158\pi$
$509$	−273.870	+	661.182i	−0.538056	+	1.29898i	−0.926078	+	0.377332i	$0.876842\pi$
$510$		0			0
$511$			500.480i			0.979413i
$512$		0			0
$513$	−659.641			−1.28585
$514$		0			0
$515$	−512.302	−	212.202i	−0.994761	−	0.412043i
$516$		0			0
$517$	−68.4813	+	28.3659i	−0.132459	+	0.0548663i
$518$		0			0
$519$	−417.051	−	417.051i	−0.803566	−	0.803566i
$520$		0			0
$521$	−527.816	−	527.816i	−1.01308	−	1.01308i	−0.999913	−	0.0131690i	$-0.995808\pi$
$521$	−527.816	−	527.816i	−1.01308	−	1.01308i	−0.0131690	−	0.999913i	$-0.504192\pi$
$522$		0			0
$523$	−5.01268	+	2.07632i	−0.00958447	+	0.00397002i	−0.387471	−	0.921882i	$-0.626651\pi$
$523$	−5.01268	+	2.07632i	−0.00958447	+	0.00397002i	0.377886	+	0.925852i	$0.376651\pi$
$524$		0			0
$525$	−29.8081	−	12.3469i	−0.0567774	−	0.0235180i
$526$		0			0
$527$	−396.783			−0.752908
$528$		0			0
$529$		−	918.476i		−	1.73625i
$530$		0			0
$531$	−246.391	+	594.841i	−0.464013	+	1.12023i
$532$		0			0
$533$	101.881	+	245.963i	0.191147	+	0.461469i
$534$		0			0
$535$	84.7624	−	84.7624i	0.158434	−	0.158434i
$536$		0			0
$537$	−512.869	+	512.869i	−0.955064	+	0.955064i
$538$		0			0
$539$	−36.5010	−	88.1213i	−0.0677199	−	0.163490i
$540$		0			0
$541$	−229.279	+	553.528i	−0.423806	+	1.02316i	0.557409	+	0.830238i	$0.311796\pi$
$541$	−229.279	+	553.528i	−0.423806	+	1.02316i	−0.981215	+	0.192919i	$0.938204\pi$
$542$		0			0
$543$		−	1703.35i		−	3.13692i
$544$		0			0
$545$	−958.688			−1.75906
$546$		0			0
$547$	391.381	+	162.115i	0.715504	+	0.296371i	0.710580	−	0.703617i	$-0.248433\pi$
$547$	391.381	+	162.115i	0.715504	+	0.296371i	0.00492387	+	0.999988i	$0.498433\pi$
$548$		0			0
$549$	−624.578	+	258.709i	−1.13766	+	0.471236i
$550$		0			0
$551$	−6.52508	−	6.52508i	−0.0118423	−	0.0118423i
$552$		0			0
$553$	146.884	+	146.884i	0.265613	+	0.265613i
$554$		0			0
$555$	54.1381	−	22.4247i	0.0975461	−	0.0404049i
$556$		0			0
$557$	364.486	+	150.975i	0.654374	+	0.271050i	0.685069	−	0.728478i	$-0.259772\pi$
$557$	364.486	+	150.975i	0.654374	+	0.271050i	−0.0306953	+	0.999529i	$0.509772\pi$
$558$		0			0
$559$	84.4296			0.151037
$560$		0			0
$561$		−	627.908i		−	1.11927i
$562$		0			0
$563$	−114.762	+	277.059i	−0.203840	+	0.492113i	−0.992431	−	0.122805i	$-0.960811\pi$
$563$	−114.762	+	277.059i	−0.203840	+	0.492113i	0.788591	+	0.614918i	$0.210811\pi$
$564$		0			0
$565$	61.2544	+	147.881i	0.108415	+	0.261736i
$566$		0			0
$567$	−186.554	+	186.554i	−0.329019	+	0.329019i
$568$		0			0
$569$	172.424	−	172.424i	0.303029	−	0.303029i	−0.539169	−	0.842198i	$-0.681261\pi$
$569$	172.424	−	172.424i	0.303029	−	0.303029i	0.842198	+	0.539169i	$0.181261\pi$
$570$		0			0
$571$	−295.206	−	712.690i	−0.516998	−	1.24814i	−0.939739	−	0.341894i	$-0.888932\pi$
$571$	−295.206	−	712.690i	−0.516998	−	1.24814i	0.422740	−	0.906251i	$-0.361068\pi$
$572$		0			0
$573$	607.250	−	1466.03i	1.05977	−	2.55852i
$574$		0			0
$575$			44.4059i			0.0772276i
$576$		0			0
$577$	−756.330			−1.31080			−0.655398	−	0.755283i	$-0.727499\pi$
$577$	−756.330			−1.31080			−0.655398	+	0.755283i	$0.727499\pi$
$578$		0			0
$579$	−331.213	−	137.193i	−0.572043	−	0.236948i
$580$		0			0
$581$	−210.202	+	87.0686i	−0.361794	+	0.149860i
$582$		0			0
$583$	−140.957	−	140.957i	−0.241779	−	0.241779i
$584$		0			0
$585$	349.080	+	349.080i	0.596717	+	0.596717i
$586$		0			0
$587$	−736.720	+	305.159i	−1.25506	+	0.519863i	−0.908390	−	0.418125i	$-0.862688\pi$
$587$	−736.720	+	305.159i	−1.25506	+	0.519863i	−0.346670	+	0.937987i	$0.612688\pi$
$588$		0			0
$589$	246.012	+	101.902i	0.417678	+	0.173008i
$590$		0			0
$591$	447.919			0.757901
$592$		0			0
$593$			76.7003i			0.129343i	0.997907	+	0.0646714i	$0.0205999\pi$
$593$			76.7003i			0.129343i	−0.997907	+	0.0646714i	$0.979400\pi$
$594$		0			0
$595$	−255.056	+	615.759i	−0.428665	+	1.03489i
$596$		0			0
$597$	−281.860	−	680.470i	−0.472127	−	1.13982i
$598$		0			0
$599$	−34.1251	+	34.1251i	−0.0569702	+	0.0569702i	−0.735018	−	0.678048i	$-0.762826\pi$
$599$	−34.1251	+	34.1251i	−0.0569702	+	0.0569702i	0.678048	+	0.735018i	$0.262826\pi$
$600$		0			0
$601$	212.552	−	212.552i	0.353664	−	0.353664i	−0.507807	−	0.861471i	$-0.669544\pi$
$601$	212.552	−	212.552i	0.353664	−	0.353664i	0.861471	+	0.507807i	$0.169544\pi$
$602$		0			0
$603$	−425.307	−	1026.78i	−0.705318	−	1.70279i
$604$		0			0
$605$	180.454	−	435.655i	0.298271	−	0.720091i
$606$		0			0
$607$		−	56.8377i		−	0.0936371i	−0.998903	−	0.0468186i	$-0.985092\pi$
$607$		−	56.8377i		−	0.0936371i	0.998903	−	0.0468186i	$-0.0149083\pi$
$608$		0			0
$609$	−15.1713			−0.0249118
$610$		0			0
$611$	83.7646	+	34.6964i	0.137094	+	0.0567863i
$612$		0			0
$613$	−7.45320	+	3.08722i	−0.0121586	+	0.00503624i	−0.388754	−	0.921341i	$-0.627095\pi$
$613$	−7.45320	+	3.08722i	−0.0121586	+	0.00503624i	0.376596	+	0.926378i	$0.377095\pi$
$614$		0			0
$615$	771.474	+	771.474i	1.25443	+	1.25443i
$616$		0			0
$617$	−325.733	−	325.733i	−0.527931	−	0.527931i	0.392024	−	0.919955i	$-0.371775\pi$
$617$	−325.733	−	325.733i	−0.527931	−	0.527931i	−0.919955	+	0.392024i	$0.871775\pi$
$618$		0			0
$619$	−76.1643	+	31.5483i	−0.123044	+	0.0509665i	−0.443356	−	0.896346i	$-0.646212\pi$
$619$	−76.1643	+	31.5483i	−0.123044	+	0.0509665i	0.320312	+	0.947312i	$0.396212\pi$
$620$		0			0
$621$	1379.00	+	571.202i	2.22062	+	0.919810i
$622$		0			0
$623$	183.153			0.293986
$624$		0			0
$625$			594.458i			0.951133i
$626$		0			0
$627$	−161.259	+	389.314i	−0.257192	+	0.620915i
$628$		0			0
$629$	22.6862	+	54.7694i	0.0360671	+	0.0870738i
$630$		0			0
$631$	−70.1301	+	70.1301i	−0.111141	+	0.111141i	−0.760490	−	0.649349i	$-0.775041\pi$
$631$	−70.1301	+	70.1301i	−0.111141	+	0.111141i	0.649349	+	0.760490i	$0.275041\pi$
$632$		0			0
$633$	−78.2829	+	78.2829i	−0.123670	+	0.123670i
$634$		0			0
$635$	−243.177	−	587.082i	−0.382956	−	0.924538i
$636$		0			0
$637$	−44.6471	+	107.788i	−0.0700897	+	0.169211i
$638$		0			0
$639$			1225.36i			1.91762i
$640$		0			0
$641$	458.396			0.715126			0.357563	−	0.933889i	$-0.383608\pi$
$641$	458.396			0.715126			0.357563	+	0.933889i	$0.383608\pi$
$642$		0			0
$643$	882.443	+	365.520i	1.37238	+	0.568460i	0.942434	−	0.334393i	$-0.108531\pi$
$643$	882.443	+	365.520i	1.37238	+	0.568460i	0.429950	+	0.902853i	$0.358531\pi$
$644$		0			0
$645$	319.663	−	132.409i	0.495602	−	0.205285i
$646$		0			0
$647$	130.433	+	130.433i	0.201597	+	0.201597i	0.800684	−	0.599087i	$-0.204470\pi$
$647$	130.433	+	130.433i	0.201597	+	0.201597i	−0.599087	+	0.800684i	$0.704470\pi$
$648$		0			0
$649$	134.414	+	134.414i	0.207110	+	0.207110i
$650$		0			0
$651$	404.462	−	167.534i	0.621294	−	0.257348i
$652$		0			0
$653$	989.811	+	409.993i	1.51579	+	0.627861i	0.976743	−	0.214415i	$-0.0687844\pi$
$653$	989.811	+	409.993i	1.51579	+	0.627861i	0.539047	+	0.842275i	$0.318784\pi$
$654$		0			0
$655$	128.592			0.196324
$656$		0			0
$657$			1536.91i			2.33928i
$658$		0			0
$659$	457.745	−	1105.09i	0.694605	−	1.67693i	−0.0406841	−	0.999172i	$-0.512954\pi$
$659$	457.745	−	1105.09i	0.694605	−	1.67693i	0.735289	−	0.677753i	$-0.237046\pi$
$660$		0			0
$661$	−96.2729	−	232.423i	−0.145647	−	0.351624i	0.834173	−	0.551502i	$-0.185945\pi$
$661$	−96.2729	−	232.423i	−0.145647	−	0.351624i	−0.979821	+	0.199879i	$0.935945\pi$
$662$		0			0
$663$	−543.087	+	543.087i	−0.819135	+	0.819135i
$664$		0			0
$665$	316.278	−	316.278i	0.475607	−	0.475607i
$666$		0			0
$667$	7.99066	+	19.2912i	0.0119800	+	0.0289223i
$668$		0			0
$669$	−255.640	+	617.168i	−0.382122	+	0.922524i
$670$		0			0
$671$			199.593i			0.297456i
$672$		0			0
$673$	−135.640			−0.201545			−0.100772	−	0.994910i	$-0.532131\pi$
$673$	−135.640			−0.201545			−0.100772	+	0.994910i	$0.532131\pi$
$674$		0			0
$675$	−42.3053	−	17.5234i	−0.0626745	−	0.0259606i
$676$		0			0
$677$	−348.196	+	144.228i	−0.514322	+	0.213039i	−0.624721	−	0.780848i	$-0.714787\pi$
$677$	−348.196	+	144.228i	−0.514322	+	0.213039i	0.110399	+	0.993887i	$0.464787\pi$
$678$		0			0
$679$	−457.411	−	457.411i	−0.673653	−	0.673653i
$680$		0			0
$681$	−235.888	−	235.888i	−0.346384	−	0.346384i
$682$		0			0
$683$	812.940	−	336.731i	1.19025	−	0.493017i	0.302413	−	0.953177i	$-0.402208\pi$
$683$	812.940	−	336.731i	1.19025	−	0.493017i	0.887836	+	0.460159i	$0.152208\pi$
$684$		0			0
$685$	−943.292	−	390.724i	−1.37707	−	0.570400i
$686$		0			0
$687$	676.523			0.984749
$688$		0			0
$689$			243.832i			0.353892i
$690$		0			0
$691$	78.3893	−	189.249i	0.113443	−	0.273876i	−0.856953	−	0.515395i	$-0.827645\pi$
$691$	78.3893	−	189.249i	0.113443	−	0.273876i	0.970396	+	0.241518i	$0.0776454\pi$
$692$		0			0
$693$	172.400	+	416.209i	0.248773	+	0.600591i
$694$		0			0
$695$	−773.177	+	773.177i	−1.11249	+	1.11249i
$696$		0			0
$697$	−780.471	+	780.471i	−1.11976	+	1.11976i
$698$		0			0
$699$	302.008	+	729.112i	0.432057	+	1.04308i
$700$		0			0
$701$	432.140	−	1043.28i	0.616463	−	1.48827i	−0.239322	−	0.970940i	$-0.576925\pi$
$701$	432.140	−	1043.28i	0.616463	−	1.48827i	0.855785	−	0.517332i	$-0.173075\pi$
$702$		0			0
$703$		−	39.7843i		−	0.0565921i
$704$		0			0
$705$	371.559			0.527034
$706$		0			0
$707$	−993.041	−	411.331i	−1.40458	−	0.581798i
$708$		0			0
$709$	367.507	−	152.226i	0.518345	−	0.214706i	−0.108145	−	0.994135i	$-0.534491\pi$
$709$	367.507	−	152.226i	0.518345	−	0.214706i	0.626490	+	0.779430i	$0.284491\pi$
$710$		0			0
$711$	451.061	+	451.061i	0.634403	+	0.634403i
$712$		0			0
$713$	−426.058	−	426.058i	−0.597556	−	0.597556i
$714$		0			0
$715$	134.657	−	55.7768i	0.188332	−	0.0780096i
$716$		0			0
$717$	−1302.11	−	539.352i	−1.81605	−	0.752234i
$718$		0			0
$719$	100.566			0.139869			0.0699344	−	0.997552i	$-0.477721\pi$
$719$	100.566			0.139869			0.0699344	+	0.997552i	$0.477721\pi$
$720$		0			0
$721$			618.950i			0.858461i
$722$		0			0
$723$	−100.949	+	243.711i	−0.139625	+	0.337084i
$724$		0			0
$725$	−0.245139	−	0.591817i	−0.000338122	−	0.000816300i
$726$		0			0
$727$	332.402	−	332.402i	0.457224	−	0.457224i	−0.440519	−	0.897743i	$-0.645206\pi$
$727$	332.402	−	332.402i	0.457224	−	0.457224i	0.897743	+	0.440519i	$0.145206\pi$
$728$		0			0
$729$	693.672	−	693.672i	0.951540	−	0.951540i
$730$		0			0
$731$	133.953	+	323.391i	0.183246	+	0.442395i
$732$		0			0
$733$	−166.189	+	401.215i	−0.226724	+	0.547360i	−0.995775	−	0.0918276i	$-0.970729\pi$
$733$	−166.189	+	401.215i	−0.226724	+	0.547360i	0.769051	+	0.639187i	$0.220729\pi$
$734$		0			0
$735$			478.119i			0.650502i
$736$		0			0
$737$	−328.124			−0.445215
$738$		0			0
$739$	−1011.25	−	418.874i	−1.36840	−	0.566812i	−0.427049	−	0.904229i	$-0.640447\pi$
$739$	−1011.25	−	418.874i	−1.36840	−	0.566812i	−0.941355	+	0.337417i	$0.890447\pi$
$740$		0			0
$741$	476.199	−	197.248i	0.642643	−	0.266192i
$742$		0			0
$743$	−458.897	−	458.897i	−0.617627	−	0.617627i	0.327295	−	0.944922i	$-0.393863\pi$
$743$	−458.897	−	458.897i	−0.617627	−	0.617627i	−0.944922	+	0.327295i	$0.893863\pi$
$744$		0			0
$745$	184.242	+	184.242i	0.247304	+	0.247304i
$746$		0			0
$747$	−645.503	+	267.376i	−0.864128	+	0.357933i
$748$		0			0
$749$	−123.617	−	51.2039i	−0.165043	−	0.0683630i
$750$		0			0
$751$	636.920			0.848096			0.424048	−	0.905640i	$-0.360609\pi$
$751$	636.920			0.848096			0.424048	+	0.905640i	$0.360609\pi$
$752$		0			0
$753$		−	381.656i		−	0.506847i
$754$		0			0
$755$	475.932	−	1149.00i	0.630373	−	1.52186i
$756$		0			0
$757$	−414.804	−	1001.43i	−0.547958	−	1.32289i	−0.918995	−	0.394269i	$-0.870998\pi$
$757$	−414.804	−	1001.43i	−0.547958	−	1.32289i	0.371038	−	0.928618i	$-0.379002\pi$
$758$		0			0
$759$	674.236	−	674.236i	0.888321	−	0.888321i
$760$		0			0
$761$	−520.779	+	520.779i	−0.684334	+	0.684334i	−0.960974	−	0.276639i	$-0.910779\pi$
$761$	−520.779	+	520.779i	−0.684334	+	0.684334i	0.276639	+	0.960974i	$0.410779\pi$
$762$		0			0
$763$	409.508	+	988.640i	0.536708	+	1.29573i
$764$		0			0
$765$	−783.243	+	1890.92i	−1.02385	+	2.47179i
$766$		0			0
$767$		−	232.514i		−	0.303147i
$768$		0			0
$769$	973.035			1.26533			0.632663	−	0.774427i	$-0.281962\pi$
$769$	973.035			1.26533			0.632663	+	0.774427i	$0.281962\pi$
$770$		0			0
$771$	1131.84	+	468.825i	1.46802	+	0.608073i
$772$		0			0
$773$	959.578	−	397.470i	1.24137	−	0.514192i	0.337227	−	0.941423i	$-0.390511\pi$
$773$	959.578	−	397.470i	1.24137	−	0.514192i	0.904142	+	0.427232i	$0.140511\pi$
$774$		0			0
$775$	13.0707	+	13.0707i	0.0168654	+	0.0168654i
$776$		0			0
$777$	−46.2506	−	46.2506i	−0.0595246	−	0.0595246i
$778$		0			0
$779$	684.346	−	283.465i	0.878493	−	0.363884i
$780$		0			0
$781$	334.236	+	138.445i	0.427958	+	0.177266i
$782$		0			0
$783$	−21.5319			−0.0274992
$784$		0			0
$785$		−	770.521i		−	0.981556i
$786$		0			0
$787$	−412.612	+	996.133i	−0.524284	+	1.26573i	0.410935	+	0.911665i	$0.365202\pi$
$787$	−412.612	+	996.133i	−0.524284	+	1.26573i	−0.935219	+	0.354070i	$0.884798\pi$
$788$		0			0
$789$	325.706	+	786.323i	0.412808	+	0.996607i
$790$		0			0
$791$	126.336	−	126.336i	0.159717	−	0.159717i
$792$		0			0
$793$	172.631	−	172.631i	0.217694	−	0.217694i
$794$		0			0
$795$	382.395	+	923.183i	0.481000	+	1.16124i
$796$		0			0
$797$	−46.5600	+	112.406i	−0.0584191	+	0.141036i	−0.950394	−	0.311049i	$-0.899320\pi$
$797$	−46.5600	+	112.406i	−0.0584191	+	0.141036i	0.891975	+	0.452085i	$0.149320\pi$
$798$		0			0
$799$			375.892i			0.470453i
$800$		0			0
$801$	562.440			0.702172
$802$		0			0
$803$	419.216	+	173.645i	0.522063	+	0.216245i
$804$		0			0
$805$	−935.065	+	387.317i	−1.16157	+	0.481139i
$806$		0			0
$807$	−897.633	−	897.633i	−1.11231	−	1.11231i
$808$		0			0
$809$	−80.8371	−	80.8371i	−0.0999222	−	0.0999222i	0.655378	−	0.755301i	$-0.272509\pi$
$809$	−80.8371	−	80.8371i	−0.0999222	−	0.0999222i	−0.755301	+	0.655378i	$0.772509\pi$
$810$		0			0
$811$	−1277.99	+	529.360i	−1.57582	+	0.652725i	−0.987744	−	0.156082i	$-0.950114\pi$
$811$	−1277.99	+	529.360i	−1.57582	+	0.652725i	−0.588074	+	0.808807i	$0.700114\pi$
$812$		0			0
$813$	10.0166	+	4.14902i	0.0123206	+	0.00510334i
$814$		0			0
$815$	−804.044			−0.986557
$816$		0			0
$817$		−	234.910i		−	0.287527i
$818$		0			0
$819$	210.875	−	509.096i	0.257478	−	0.621607i
$820$		0			0
$821$	83.7084	+	202.090i	0.101959	+	0.246151i	0.966625	−	0.256197i	$-0.0824696\pi$
$821$	83.7084	+	202.090i	0.101959	+	0.246151i	−0.864666	+	0.502348i	$0.832470\pi$
$822$		0			0
$823$	−588.539	+	588.539i	−0.715114	+	0.715114i	−0.967601	−	0.252486i	$-0.918752\pi$
$823$	−588.539	+	588.539i	−0.715114	+	0.715114i	0.252486	+	0.967601i	$0.418752\pi$
$824$		0			0
$825$	−20.6843	+	20.6843i	−0.0250719	+	0.0250719i
$826$		0			0
$827$	−281.470	−	679.529i	−0.340351	−	0.821679i	−0.997680	−	0.0680759i	$-0.978314\pi$
$827$	−281.470	−	679.529i	−0.340351	−	0.821679i	0.657329	−	0.753603i	$-0.271686\pi$
$828$		0			0
$829$	6.83745	−	16.5071i	0.00824783	−	0.0199120i	−0.919702	−	0.392617i	$-0.871570\pi$
$829$	6.83745	−	16.5071i	0.00824783	−	0.0199120i	0.927950	+	0.372705i	$0.121570\pi$
$830$		0			0
$831$		−	2355.31i		−	2.83431i
$832$		0			0
$833$	−483.695			−0.580666
$834$		0			0
$835$	604.801	+	250.517i	0.724313	+	0.300020i
$836$		0			0
$837$	574.034	−	237.773i	0.685823	−	0.284077i
$838$		0			0
$839$	358.991	+	358.991i	0.427879	+	0.427879i	0.887905	−	0.460026i	$-0.152160\pi$
$839$	358.991	+	358.991i	0.427879	+	0.427879i	−0.460026	+	0.887905i	$0.652160\pi$
$840$		0			0
$841$	594.464	+	594.464i	0.706854	+	0.706854i
$842$		0			0
$843$	−1734.31	+	718.373i	−2.05730	+	0.852163i
$844$		0			0
$845$	597.527	+	247.504i	0.707133	+	0.292904i
$846$		0			0
$847$	−526.348			−0.621426
$848$		0			0
$849$		−	2132.94i		−	2.51229i
$850$		0			0
$851$	−34.4503	+	83.1704i	−0.0404821	+	0.0977325i
$852$		0			0
$853$	545.396	+	1316.70i	0.639386	+	1.54361i	0.827499	+	0.561467i	$0.189763\pi$
$853$	545.396	+	1316.70i	0.639386	+	1.54361i	−0.188114	+	0.982147i	$0.560237\pi$
$854$		0			0
$855$	971.249	−	971.249i	1.13596	−	1.13596i
$856$		0			0
$857$	157.052	−	157.052i	0.183258	−	0.183258i	−0.609516	−	0.792774i	$-0.708636\pi$
$857$	157.052	−	157.052i	0.183258	−	0.183258i	0.792774	+	0.609516i	$0.208636\pi$
$858$		0			0
$859$	−17.7307	−	42.8057i	−0.0206411	−	0.0498321i	0.913223	−	0.407460i	$-0.133586\pi$
$859$	−17.7307	−	42.8057i	−0.0206411	−	0.0498321i	−0.933864	+	0.357628i	$0.883586\pi$
$860$		0			0
$861$	466.038	−	1125.12i	0.541275	−	1.30675i
$862$		0			0
$863$		−	186.088i		−	0.215629i	−0.994171	−	0.107815i	$-0.965615\pi$
$863$		−	186.088i		−	0.215629i	0.994171	−	0.107815i	$-0.0343853\pi$
$864$		0			0
$865$	567.597			0.656181
$866$		0			0
$867$	−1587.37	−	657.510i	−1.83088	−	0.758374i
$868$		0			0
$869$	173.996	−	72.0716i	0.200226	−	0.0829363i
$870$		0			0
$871$	283.799	+	283.799i	0.325831	+	0.325831i
$872$		0			0
$873$	−1404.65	−	1404.65i	−1.60899	−	1.60899i
$874$		0			0
$875$	643.121	−	266.390i	0.734996	−	0.304445i
$876$		0			0
$877$	−216.654	−	89.7412i	−0.247040	−	0.102328i	0.255728	−	0.966749i	$-0.417685\pi$
$877$	−216.654	−	89.7412i	−0.247040	−	0.102328i	−0.502768	+	0.864421i	$0.667685\pi$
$878$		0			0
$879$	−779.119			−0.886370
$880$		0			0
$881$			47.9671i			0.0544462i	0.999629	+	0.0272231i	$0.00866645\pi$
$881$			47.9671i			0.0544462i	−0.999629	+	0.0272231i	$0.991334\pi$
$882$		0			0
$883$	−115.380	+	278.551i	−0.130668	+	0.315460i	−0.975650	−	0.219335i	$-0.929611\pi$
$883$	−115.380	+	278.551i	−0.130668	+	0.315460i	0.844982	+	0.534795i	$0.179611\pi$
$884$		0			0
$885$	−364.645	−	880.331i	−0.412028	−	0.994724i
$886$		0			0
$887$	−233.227	+	233.227i	−0.262939	+	0.262939i	−0.826247	−	0.563308i	$-0.809528\pi$
$887$	−233.227	+	233.227i	−0.262939	+	0.262939i	0.563308	+	0.826247i	$0.309528\pi$
$888$		0			0
$889$	−501.549	+	501.549i	−0.564172	+	0.564172i
$890$		0			0
$891$	91.5365	+	220.989i	0.102735	+	0.248023i
$892$		0			0
$893$	96.5364	−	233.059i	0.108103	−	0.260985i
$894$		0			0
$895$		−	698.004i		−	0.779892i
$896$		0			0
$897$	−1166.31			−1.30024
$898$		0			0
$899$	8.03028	+	3.32625i	0.00893246	+	0.00369994i
$900$		0			0
$901$	−933.949	+	386.854i	−1.03657	+	0.429361i
$902$		0			0
$903$	−273.091	−	273.091i	−0.302426	−	0.302426i
$904$		0			0
$905$	1159.11	+	1159.11i	1.28078	+	1.28078i
$906$		0			0
$907$	827.946	−	342.947i	0.912841	−	0.378111i	0.123697	−	0.992320i	$-0.460525\pi$
$907$	827.946	−	342.947i	0.912841	−	0.378111i	0.789143	+	0.614209i	$0.210525\pi$
$908$		0			0
$909$	−3049.50	−	1263.14i	−3.35478	−	1.38960i
$910$		0			0
$911$	−1321.92			−1.45107			−0.725534	−	0.688186i	$-0.758407\pi$
$911$	−1321.92			−1.45107			−0.725534	+	0.688186i	$0.758407\pi$
$912$		0			0
$913$			206.280i			0.225937i
$914$		0			0
$915$	382.874	−	924.340i	0.418442	−	1.01021i
$916$		0			0
$917$	−54.9287	−	132.610i	−0.0599004	−	0.144612i
$918$		0			0
$919$	717.026	−	717.026i	0.780224	−	0.780224i	−0.199645	−	0.979868i	$-0.563979\pi$
$919$	717.026	−	717.026i	0.780224	−	0.780224i	0.979868	+	0.199645i	$0.0639788\pi$
$920$		0			0
$921$	339.135	−	339.135i	0.368225	−	0.368225i
$922$		0			0
$923$	−169.342	−	408.828i	−0.183469	−	0.442934i
$924$		0			0
$925$	1.05687	−	2.55151i	0.00114256	−	0.00275839i
$926$		0			0
$927$			1900.72i			2.05039i
$928$		0			0
$929$	−430.578			−0.463485			−0.231743	−	0.972777i	$-0.574443\pi$
$929$	−430.578			−0.463485			−0.231743	+	0.972777i	$0.574443\pi$
$930$		0			0
$931$	299.899	+	124.222i	0.322126	+	0.133429i
$932$		0			0
$933$	−1467.85	+	608.004i	−1.57326	+	0.651666i
$934$		0			0
$935$	427.284	+	427.284i	0.456988	+	0.456988i
$936$		0			0
$937$	752.850	+	752.850i	0.803469	+	0.803469i	0.983636	−	0.180167i	$-0.0576639\pi$
$937$	752.850	+	752.850i	0.803469	+	0.803469i	−0.180167	+	0.983636i	$0.557664\pi$
$938$		0			0
$939$	1858.38	−	769.767i	1.97911	−	0.819773i
$940$		0			0
$941$	−1482.20	−	613.948i	−1.57513	−	0.652442i	−0.587501	−	0.809223i	$-0.699888\pi$
$941$	−1482.20	−	613.948i	−1.57513	−	0.652442i	−0.987633	+	0.156781i	$0.949888\pi$
$942$		0			0
$943$	−1676.11			−1.77742
$944$		0			0
$945$		−	1043.67i		−	1.10442i
$946$		0			0
$947$	−528.730	+	1276.47i	−0.558321	+	1.34791i	0.352773	+	0.935709i	$0.385239\pi$
$947$	−528.730	+	1276.47i	−0.558321	+	1.34791i	−0.911094	+	0.412198i	$0.864761\pi$
$948$		0			0
$949$	−212.398	−	512.775i	−0.223813	−	0.540332i
$950$		0			0
$951$	1461.98	−	1461.98i	1.53731	−	1.53731i
$952$		0			0
$953$	−538.112	+	538.112i	−0.564650	+	0.564650i	−0.930625	−	0.365975i	$-0.880736\pi$
$953$	−538.112	+	538.112i	−0.564650	+	0.564650i	0.365975	+	0.930625i	$0.380736\pi$
$954$		0			0
$955$	584.391	+	1410.84i	0.611927	+	1.47732i
$956$		0			0
$957$	−5.26378	+	12.7079i	−0.00550030	+	0.0132789i
$958$		0			0
$959$			1139.66i			1.18839i
$960$		0			0
$961$	710.184			0.739005
$962$		0			0
$963$	−379.612	−	157.240i	−0.394197	−	0.163282i
$964$		0			0
$965$	318.745	−	132.028i	0.330306	−	0.136817i
$966$		0			0
$967$	380.769	+	380.769i	0.393763	+	0.393763i	0.876026	−	0.482263i	$-0.160185\pi$
$967$	380.769	+	380.769i	0.393763	+	0.393763i	−0.482263	+	0.876026i	$0.660185\pi$
$968$		0			0
$969$	1511.04	+	1511.04i	1.55938	+	1.55938i
$970$		0			0
$971$	1000.67	−	414.490i	1.03055	−	0.426869i	0.197642	−	0.980274i	$-0.436672\pi$
$971$	1000.67	−	414.490i	1.03055	−	0.426869i	0.832912	+	0.553405i	$0.186672\pi$
$972$		0			0
$973$	1127.60	+	467.067i	1.15889	+	0.480028i
$974$		0			0
$975$	35.7803			0.0366977
$976$		0			0
$977$		−	920.476i		−	0.942145i	−0.882095	−	0.471072i	$-0.843867\pi$
$977$		−	920.476i		−	0.942145i	0.882095	−	0.471072i	$-0.156133\pi$
$978$		0			0
$979$	63.5463	−	153.414i	0.0649094	−	0.156705i
$980$		0			0
$981$	1257.55	+	3035.98i	1.28190	+	3.09478i
$982$		0			0
$983$	−465.265	+	465.265i	−0.473312	+	0.473312i	−0.902985	−	0.429673i	$-0.858629\pi$
$983$	−465.265	+	465.265i	−0.473312	+	0.473312i	0.429673	+	0.902985i	$0.358629\pi$
$984$		0			0
$985$	−304.804	+	304.804i	−0.309446	+	0.309446i
$986$		0			0
$987$	−158.713	−	383.167i	−0.160803	−	0.388214i
$988$		0			0
$989$	−203.415	+	491.087i	−0.205677	+	0.496549i
$990$		0			0
$991$			365.984i			0.369307i	0.982804	+	0.184654i	$0.0591164\pi$
$991$			365.984i			0.369307i	−0.982804	+	0.184654i	$0.940884\pi$
$992$		0			0
$993$	2295.97			2.31216
$994$		0			0
$995$	654.855	+	271.250i	0.658146	+	0.272613i
$996$		0			0
$997$	−77.3922	+	32.0569i	−0.0776251	+	0.0321534i	−0.421158	−	0.906987i	$-0.638376\pi$
$997$	−77.3922	+	32.0569i	−0.0776251	+	0.0321534i	0.343533	+	0.939141i	$0.388376\pi$
$998$		0			0
$999$	−65.6413	−	65.6413i	−0.0657070	−	0.0657070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.h.a.111.7		28
4.3	odd	2		32.3.h.a.19.2	✓	28
8.3	odd	2		256.3.h.b.223.7		28
8.5	even	2		256.3.h.a.223.1		28
12.11	even	2		288.3.u.a.19.6		28
32.5	even	8		32.3.h.a.27.2	yes	28
32.11	odd	8		256.3.h.a.31.1		28
32.21	even	8		256.3.h.b.31.7		28
32.27	odd	8	inner	128.3.h.a.15.7		28
96.5	odd	8		288.3.u.a.91.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.2	✓	28	4.3	odd	2
32.3.h.a.27.2	yes	28	32.5	even	8
128.3.h.a.15.7		28	32.27	odd	8	inner
128.3.h.a.111.7		28	1.1	even	1	trivial
256.3.h.a.31.1		28	32.11	odd	8
256.3.h.a.223.1		28	8.5	even	2
256.3.h.b.31.7		28	32.21	even	8
256.3.h.b.223.7		28	8.3	odd	2
288.3.u.a.19.6		28	12.11	even	2
288.3.u.a.91.6		28	96.5	odd	8

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.68670 + 1.94129i) q^{3} +(-4.51028 + 1.86822i) q^{5} +(3.85317 + 3.85317i) q^{7} +(11.8326 + 11.8326i) q^{9} +O(q^{10})\)	\(q+(4.68670 + 1.94129i) q^{3} +(-4.51028 + 1.86822i) q^{5} +(3.85317 + 3.85317i) q^{7} +(11.8326 + 11.8326i) q^{9} +(4.56441 - 1.89064i) q^{11} +(-5.58307 - 2.31258i) q^{13} -24.7651 q^{15} -25.0539i q^{17} +(-6.43433 + 15.5338i) q^{19} +(10.5785 + 25.5388i) q^{21} +(26.9024 - 26.9024i) q^{23} +(-0.825315 + 0.825315i) q^{25} +(15.0136 + 36.2460i) q^{27} +(-0.210028 + 0.507052i) q^{29} -15.8372i q^{31} +25.0623 q^{33} +(-24.5774 - 10.1803i) q^{35} +(-2.18606 + 0.905498i) q^{37} +(-21.6768 - 21.6768i) q^{39} +(-31.1517 - 31.1517i) q^{41} +(-12.9078 + 5.34659i) q^{43} +(-75.4740 - 31.2624i) q^{45} -15.0033 q^{47} -19.3062i q^{49} +(48.6370 - 117.420i) q^{51} +(-15.4409 - 37.2776i) q^{53} +(-17.0546 + 17.0546i) q^{55} +(-60.3115 + 60.3115i) q^{57} +(14.7242 + 35.5473i) q^{59} +(-15.4603 + 37.3243i) q^{61} +91.1858i q^{63} +29.5016 q^{65} +(-61.3598 - 25.4161i) q^{67} +(178.309 - 73.8579i) q^{69} +(51.7789 + 51.7789i) q^{71} +(64.9440 + 64.9440i) q^{73} +(-5.47018 + 2.26582i) q^{75} +(24.8724 + 10.3025i) q^{77} +38.1202 q^{79} +48.4156i q^{81} +(-15.9782 + 38.5748i) q^{83} +(46.8061 + 113.000i) q^{85} +(-1.96868 + 1.96868i) q^{87} +(23.7666 - 23.7666i) q^{89} +(-12.6017 - 30.4233i) q^{91} +(30.7446 - 74.2241i) q^{93} -82.0827i q^{95} -118.710 q^{97} +(76.3798 + 31.6376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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