LMFDB - Embedded newform 128.4.g.a.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(17,128)]

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([0, 7]))

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

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

chi := DirichletCharacter("128.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.g (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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	128.49
Dual form			128.4.g.a.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.53310 + 2.29188i) q^{3} +(4.22177 - 10.1923i) q^{5} +(11.6451 + 11.6451i) q^{7} +(6.27055 - 6.27055i) q^{9} +O(q^{10})$	\(q+(-5.53310 + 2.29188i) q^{3} +(4.22177 - 10.1923i) q^{5} +(11.6451 + 11.6451i) q^{7} +(6.27055 - 6.27055i) q^{9} +(-27.7531 - 11.4957i) q^{11} +(15.9612 + 38.5338i) q^{13} +66.0706i q^{15} +131.437i q^{17} +(13.7982 + 33.3119i) q^{19} +(-91.1226 - 37.7442i) q^{21} +(-128.594 + 128.594i) q^{23} +(2.32952 + 2.32952i) q^{25} +(41.5567 - 100.327i) q^{27} +(-192.157 + 79.5938i) q^{29} +215.350 q^{31} +179.908 q^{33} +(167.853 - 69.5268i) q^{35} +(-9.39705 + 22.6865i) q^{37} +(-176.630 - 176.630i) q^{39} +(257.295 - 257.295i) q^{41} +(81.5685 + 33.7868i) q^{43} +(-37.4383 - 90.3840i) q^{45} +113.432i q^{47} -71.7841i q^{49} +(-301.238 - 727.254i) q^{51} +(-11.8996 - 4.92896i) q^{53} +(-234.335 + 234.335i) q^{55} +(-152.694 - 152.694i) q^{57} +(-210.637 + 508.522i) q^{59} +(-251.800 + 104.299i) q^{61} +146.042 q^{63} +460.131 q^{65} +(418.173 - 173.213i) q^{67} +(416.801 - 1006.25i) q^{69} +(28.0923 + 28.0923i) q^{71} +(-333.018 + 333.018i) q^{73} +(-18.2285 - 7.55047i) q^{75} +(-189.319 - 457.056i) q^{77} +38.8621i q^{79} +889.794i q^{81} +(-229.913 - 555.060i) q^{83} +(1339.64 + 554.897i) q^{85} +(880.801 - 880.801i) q^{87} +(-872.568 - 872.568i) q^{89} +(-262.859 + 634.599i) q^{91} +(-1191.55 + 493.557i) q^{93} +397.776 q^{95} -51.1346 q^{97} +(-246.112 + 101.943i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−5.53310	+	2.29188i	−1.06485	+	0.441073i	−0.845169	−	0.534499i	$-0.820500\pi$
$3$	−5.53310	+	2.29188i	−1.06485	+	0.441073i	−0.219676	+	0.975573i	$0.570500\pi$
$4$		0			0
$5$	4.22177	−	10.1923i	0.377607	−	0.911624i	−0.614807	−	0.788678i	$-0.710766\pi$
$5$	4.22177	−	10.1923i	0.377607	−	0.911624i	0.992413	−	0.122946i	$-0.0392341\pi$
$6$		0			0
$7$	11.6451	+	11.6451i	0.628775	+	0.628775i	0.947760	−	0.318985i	$-0.103342\pi$
$7$	11.6451	+	11.6451i	0.628775	+	0.628775i	−0.318985	+	0.947760i	$0.603342\pi$
$8$		0			0
$9$	6.27055	−	6.27055i	0.232243	−	0.232243i
$10$		0			0
$11$	−27.7531	−	11.4957i	−0.760717	−	0.315099i	−0.0316109	−	0.999500i	$-0.510064\pi$
$11$	−27.7531	−	11.4957i	−0.760717	−	0.315099i	−0.729106	+	0.684401i	$0.760064\pi$
$12$		0			0
$13$	15.9612	+	38.5338i	0.340527	+	0.822104i	0.997663	+	0.0683319i	$0.0217677\pi$
$13$	15.9612	+	38.5338i	0.340527	+	0.822104i	−0.657136	+	0.753772i	$0.728232\pi$
$14$		0			0
$15$			66.0706i			1.13729i
$16$		0			0
$17$			131.437i			1.87518i	0.347736	+	0.937592i	$0.386951\pi$
$17$			131.437i			1.87518i	−0.347736	+	0.937592i	$0.613049\pi$
$18$		0			0
$19$	13.7982	+	33.3119i	0.166607	+	0.402224i	0.985028	−	0.172394i	$-0.0551503\pi$
$19$	13.7982	+	33.3119i	0.166607	+	0.402224i	−0.818421	+	0.574619i	$0.805150\pi$
$20$		0			0
$21$	−91.1226	−	37.7442i	−0.946884	−	0.392212i
$22$		0			0
$23$	−128.594	+	128.594i	−1.16582	+	1.16582i	−0.182634	+	0.983181i	$0.558462\pi$
$23$	−128.594	+	128.594i	−1.16582	+	1.16582i	−0.983181	+	0.182634i	$0.941538\pi$
$24$		0			0
$25$	2.32952	+	2.32952i	0.0186362	+	0.0186362i
$26$		0			0
$27$	41.5567	−	100.327i	0.296207	−	0.715106i
$28$		0			0
$29$	−192.157	+	79.5938i	−1.23043	+	0.509662i	−0.900712	−	0.434416i	$-0.856955\pi$
$29$	−192.157	+	79.5938i	−1.23043	+	0.509662i	−0.329721	+	0.944078i	$0.606955\pi$
$30$		0			0
$31$	215.350			1.24768			0.623839	−	0.781553i	$-0.285572\pi$
$31$	215.350			1.24768			0.623839	+	0.781553i	$0.285572\pi$
$32$		0			0
$33$	179.908			0.949027
$34$		0			0
$35$	167.853	−	69.5268i	0.810636	−	0.335777i
$36$		0			0
$37$	−9.39705	+	22.6865i	−0.0417531	+	0.100801i	−0.943380	−	0.331713i	$-0.892373\pi$
$37$	−9.39705	+	22.6865i	−0.0417531	+	0.100801i	0.901627	+	0.432514i	$0.142373\pi$
$38$		0			0
$39$	−176.630	−	176.630i	−0.725216	−	0.725216i
$40$		0			0
$41$	257.295	−	257.295i	0.980067	−	0.980067i	−0.0197381	−	0.999805i	$-0.506283\pi$
$41$	257.295	−	257.295i	0.980067	−	0.980067i	0.999805	+	0.0197381i	$0.00628325\pi$
$42$		0			0
$43$	81.5685	+	33.7868i	0.289281	+	0.119824i	0.522605	−	0.852575i	$-0.324960\pi$
$43$	81.5685	+	33.7868i	0.289281	+	0.119824i	−0.233324	+	0.972399i	$0.574960\pi$
$44$		0			0
$45$	−37.4383	−	90.3840i	−0.124022	−	0.299414i
$46$		0			0
$47$			113.432i			0.352037i	0.984387	+	0.176018i	$0.0563218\pi$
$47$			113.432i			0.352037i	−0.984387	+	0.176018i	$0.943678\pi$
$48$		0			0
$49$		−	71.7841i		−	0.209283i
$50$		0			0
$51$	−301.238	−	727.254i	−0.827094	−	1.99678i
$52$		0			0
$53$	−11.8996	−	4.92896i	−0.0308402	−	0.0127744i	0.367210	−	0.930138i	$-0.380313\pi$
$53$	−11.8996	−	4.92896i	−0.0308402	−	0.0127744i	−0.398050	+	0.917364i	$0.630313\pi$
$54$		0			0
$55$	−234.335	+	234.335i	−0.574504	+	0.574504i
$56$		0			0
$57$	−152.694	−	152.694i	−0.354821	−	0.354821i
$58$		0			0
$59$	−210.637	+	508.522i	−0.464789	+	1.12210i	0.501619	+	0.865088i	$0.332738\pi$
$59$	−210.637	+	508.522i	−0.464789	+	1.12210i	−0.966408	+	0.257011i	$0.917262\pi$
$60$		0			0
$61$	−251.800	+	104.299i	−0.528519	+	0.218920i	−0.630954	−	0.775820i	$-0.717336\pi$
$61$	−251.800	+	104.299i	−0.528519	+	0.218920i	0.102436	+	0.994740i	$0.467336\pi$
$62$		0			0
$63$	146.042			0.292057
$64$		0			0
$65$	460.131			0.878034
$66$		0			0
$67$	418.173	−	173.213i	0.762507	−	0.315841i	0.0326737	−	0.999466i	$-0.489598\pi$
$67$	418.173	−	173.213i	0.762507	−	0.315841i	0.729833	+	0.683625i	$0.239598\pi$
$68$		0			0
$69$	416.801	−	1006.25i	0.727203	−	1.75562i
$70$		0			0
$71$	28.0923	+	28.0923i	0.0469569	+	0.0469569i	0.730195	−	0.683238i	$-0.239429\pi$
$71$	28.0923	+	28.0923i	0.0469569	+	0.0469569i	−0.683238	+	0.730195i	$0.739429\pi$
$72$		0			0
$73$	−333.018	+	333.018i	−0.533928	+	0.533928i	−0.921739	−	0.387811i	$-0.873231\pi$
$73$	−333.018	+	333.018i	−0.533928	+	0.533928i	0.387811	+	0.921739i	$0.373231\pi$
$74$		0			0
$75$	−18.2285	−	7.55047i	−0.0280645	−	0.0116247i
$76$		0			0
$77$	−189.319	−	457.056i	−0.280193	−	0.676446i
$78$		0			0
$79$			38.8621i			0.0553460i	0.999617	+	0.0276730i	$0.00880971\pi$
$79$			38.8621i			0.0553460i	−0.999617	+	0.0276730i	$0.991190\pi$
$80$		0			0
$81$			889.794i			1.22057i
$82$		0			0
$83$	−229.913	−	555.060i	−0.304051	−	0.734045i	−0.999875	−	0.0158320i	$-0.994960\pi$
$83$	−229.913	−	555.060i	−0.304051	−	0.734045i	0.695823	−	0.718213i	$-0.255040\pi$
$84$		0			0
$85$	1339.64	+	554.897i	1.70946	+	0.708083i
$86$		0			0
$87$	880.801	−	880.801i	1.08542	−	1.08542i
$88$		0			0
$89$	−872.568	−	872.568i	−1.03924	−	1.03924i	−0.999198	−	0.0400377i	$-0.987252\pi$
$89$	−872.568	−	872.568i	−1.03924	−	1.03924i	−0.0400377	−	0.999198i	$-0.512748\pi$
$90$		0			0
$91$	−262.859	+	634.599i	−0.302804	+	0.731033i
$92$		0			0
$93$	−1191.55	+	493.557i	−1.32858	+	0.550317i
$94$		0			0
$95$	397.776			0.429589
$96$		0			0
$97$	−51.1346			−0.0535251			−0.0267625	−	0.999642i	$-0.508520\pi$
$97$	−51.1346			−0.0535251			−0.0267625	+	0.999642i	$0.508520\pi$
$98$		0			0
$99$	−246.112	+	101.943i	−0.249850	+	0.103491i
$100$		0			0
$101$	−153.885	+	371.512i	−0.151606	+	0.366008i	−0.981376	−	0.192096i	$-0.938471\pi$
$101$	−153.885	+	371.512i	−0.151606	+	0.366008i	0.829770	+	0.558105i	$0.188471\pi$
$102$		0			0
$103$	−601.189	−	601.189i	−0.575115	−	0.575115i	0.358438	−	0.933553i	$-0.383309\pi$
$103$	−601.189	−	601.189i	−0.575115	−	0.575115i	−0.933553	+	0.358438i	$0.883309\pi$
$104$		0			0
$105$	−769.398	+	769.398i	−0.715100	+	0.715100i
$106$		0			0
$107$	825.321	+	341.859i	0.745671	+	0.308867i	0.722974	−	0.690875i	$-0.242775\pi$
$107$	825.321	+	341.859i	0.745671	+	0.308867i	0.0226969	+	0.999742i	$0.492775\pi$
$108$		0			0
$109$	790.968	+	1909.57i	0.695055	+	1.67801i	0.734338	+	0.678784i	$0.237493\pi$
$109$	790.968	+	1909.57i	0.695055	+	1.67801i	−0.0392828	+	0.999228i	$0.512507\pi$
$110$		0			0
$111$		−	147.064i		−	0.125754i
$112$		0			0
$113$		−	717.104i		−	0.596987i	−0.954412	−	0.298493i	$-0.903516\pi$
$113$		−	717.104i		−	0.596987i	0.954412	−	0.298493i	$-0.0964841\pi$
$114$		0			0
$115$	767.770	+	1853.56i	0.622565	+	1.50300i
$116$		0			0
$117$	341.714	+	141.543i	0.270013	+	0.111843i
$118$		0			0
$119$	−1530.59	+	1530.59i	−1.17907	+	1.17907i
$120$		0			0
$121$	−303.075	−	303.075i	−0.227705	−	0.227705i
$122$		0			0
$123$	−833.948	+	2013.33i	−0.611338	+	1.47590i
$124$		0			0
$125$	1307.61	−	541.630i	0.935650	−	0.387559i
$126$		0			0
$127$	713.424			0.498474			0.249237	−	0.968443i	$-0.419820\pi$
$127$	713.424			0.498474			0.249237	+	0.968443i	$0.419820\pi$
$128$		0			0
$129$	−528.762			−0.360890
$130$		0			0
$131$	−918.787	+	380.574i	−0.612784	+	0.253824i	−0.667419	−	0.744683i	$-0.732601\pi$
$131$	−918.787	+	380.574i	−0.612784	+	0.253824i	0.0546341	+	0.998506i	$0.482601\pi$
$132$		0			0
$133$	−227.238	+	548.601i	−0.148151	+	0.357667i
$134$		0			0
$135$	−847.113	−	847.113i	−0.540058	−	0.540058i
$136$		0			0
$137$	1589.55	−	1589.55i	0.991274	−	0.991274i	−0.00868786	−	0.999962i	$-0.502765\pi$
$137$	1589.55	−	1589.55i	0.991274	−	0.991274i	0.999962	+	0.00868786i	$0.00276547\pi$
$138$		0			0
$139$	−828.901	−	343.342i	−0.505802	−	0.209510i	0.115166	−	0.993346i	$-0.463260\pi$
$139$	−828.901	−	343.342i	−0.505802	−	0.209510i	−0.620967	+	0.783836i	$0.713260\pi$
$140$		0			0
$141$	−259.972	−	627.629i	−0.155274	−	0.374865i
$142$		0			0
$143$		−	1252.92i		−	0.732688i
$144$		0			0
$145$			2294.54i			1.31414i
$146$		0			0
$147$	164.521	+	397.188i	0.0923092	+	0.222854i
$148$		0			0
$149$	−1399.70	−	579.774i	−0.769582	−	0.318771i	−0.0368792	−	0.999320i	$-0.511742\pi$
$149$	−1399.70	−	579.774i	−0.769582	−	0.318771i	−0.732703	+	0.680548i	$0.761742\pi$
$150$		0			0
$151$	521.322	−	521.322i	0.280958	−	0.280958i	−0.552533	−	0.833491i	$-0.686339\pi$
$151$	521.322	−	521.322i	0.280958	−	0.280958i	0.833491	+	0.552533i	$0.186339\pi$
$152$		0			0
$153$	824.183	+	824.183i	0.435498	+	0.435498i
$154$		0			0
$155$	909.159	−	2194.90i	0.471131	−	1.13741i
$156$		0			0
$157$	1501.66	−	622.009i	0.763348	−	0.316189i	0.0331736	−	0.999450i	$-0.489439\pi$
$157$	1501.66	−	622.009i	0.763348	−	0.316189i	0.730175	+	0.683260i	$0.239439\pi$
$158$		0			0
$159$	77.1380			0.0384745
$160$		0			0
$161$	−2994.98			−1.46607
$162$		0			0
$163$	1676.94	−	694.610i	0.805815	−	0.333779i	0.0585321	−	0.998286i	$-0.481358\pi$
$163$	1676.94	−	694.610i	0.805815	−	0.333779i	0.747283	+	0.664506i	$0.231358\pi$
$164$		0			0
$165$	759.529	−	1833.67i	0.358359	−	0.865156i
$166$		0			0
$167$	664.730	+	664.730i	0.308014	+	0.308014i	0.844139	−	0.536125i	$-0.180112\pi$
$167$	664.730	+	664.730i	0.308014	+	0.308014i	−0.536125	+	0.844139i	$0.680112\pi$
$168$		0			0
$169$	323.421	−	323.421i	0.147210	−	0.147210i
$170$		0			0
$171$	295.406	+	122.361i	0.132107	+	0.0547205i
$172$		0			0
$173$	190.687	+	460.359i	0.0838016	+	0.202315i	0.960226	−	0.279225i	$-0.0900776\pi$
$173$	190.687	+	460.359i	0.0838016	+	0.202315i	−0.876424	+	0.481540i	$0.840078\pi$
$174$		0			0
$175$			54.2549i			0.0234359i
$176$		0			0
$177$		−	3296.45i		−	1.39987i
$178$		0			0
$179$	−1230.51	−	2970.71i	−0.513814	−	1.24046i	−0.941648	−	0.336599i	$-0.890723\pi$
$179$	−1230.51	−	2970.71i	−0.513814	−	1.24046i	0.427835	−	0.903857i	$-0.359277\pi$
$180$		0			0
$181$	−1720.96	−	712.847i	−0.706731	−	0.292738i	0.000220198	−	1.00000i	$-0.499930\pi$
$181$	−1720.96	−	712.847i	−0.706731	−	0.292738i	−0.706951	+	0.707262i	$0.749930\pi$
$182$		0			0
$183$	1154.19	−	1154.19i	0.466231	−	0.466231i
$184$		0			0
$185$	191.554	+	191.554i	0.0761263	+	0.0761263i
$186$		0			0
$187$	1510.96	−	3647.79i	0.590869	−	1.42648i
$188$		0			0
$189$	1652.24	−	684.381i	0.635889	−	0.263394i
$190$		0			0
$191$	454.987			0.172365			0.0861825	−	0.996279i	$-0.472533\pi$
$191$	454.987			0.172365			0.0861825	+	0.996279i	$0.472533\pi$
$192$		0			0
$193$	3199.61			1.19333			0.596666	−	0.802490i	$-0.296492\pi$
$193$	3199.61			1.19333			0.596666	+	0.802490i	$0.296492\pi$
$194$		0			0
$195$	−2545.95	+	1054.57i	−0.934971	+	0.387278i
$196$		0			0
$197$	−1023.92	+	2471.95i	−0.370309	+	0.894006i	0.623388	+	0.781912i	$0.285756\pi$
$197$	−1023.92	+	2471.95i	−0.370309	+	0.894006i	−0.993698	+	0.112093i	$0.964244\pi$
$198$		0			0
$199$	2332.44	+	2332.44i	0.830867	+	0.830867i	0.987635	−	0.156768i	$-0.0501077\pi$
$199$	2332.44	+	2332.44i	0.830867	+	0.830867i	−0.156768	+	0.987635i	$0.550108\pi$
$200$		0			0
$201$	−1916.81	+	1916.81i	−0.672643	+	0.672643i
$202$		0			0
$203$	−3164.56	−	1310.80i	−1.09413	−	0.453203i
$204$		0			0
$205$	−1536.18	−	3708.66i	−0.523372	−	1.26353i
$206$		0			0
$207$			1612.71i			0.541504i
$208$		0			0
$209$		−	1083.13i		−	0.358476i
$210$		0			0
$211$	2070.04	+	4997.52i	0.675390	+	1.63054i	0.772311	+	0.635245i	$0.219101\pi$
$211$	2070.04	+	4997.52i	0.675390	+	1.63054i	−0.0969206	+	0.995292i	$0.530899\pi$
$212$		0			0
$213$	−219.822	−	91.0531i	−0.0707133	−	0.0292904i
$214$		0			0
$215$	688.727	−	688.727i	0.218469	−	0.218469i
$216$		0			0
$217$	2507.77	+	2507.77i	0.784509	+	0.784509i
$218$		0			0
$219$	1079.38	−	2605.86i	0.333049	−	0.804052i
$220$		0			0
$221$	−5064.76	+	2097.89i	−1.54160	+	0.638550i
$222$		0			0
$223$	−6620.99			−1.98822			−0.994112	−	0.108357i	$-0.965441\pi$
$223$	−6620.99			−1.98822			−0.994112	+	0.108357i	$0.965441\pi$
$224$		0			0
$225$	29.2148			0.00865623
$226$		0			0
$227$	1044.31	−	432.568i	0.305345	−	0.126478i	−0.224750	−	0.974417i	$-0.572156\pi$
$227$	1044.31	−	432.568i	0.305345	−	0.126478i	0.530095	+	0.847939i	$0.322156\pi$
$228$		0			0
$229$	−986.462	+	2381.53i	−0.284660	+	0.687231i	−0.999933	−	0.0116150i	$-0.996303\pi$
$229$	−986.462	+	2381.53i	−0.284660	+	0.687231i	0.715272	+	0.698846i	$0.246303\pi$
$230$		0			0
$231$	2095.04	+	2095.04i	0.596725	+	0.596725i
$232$		0			0
$233$	978.403	−	978.403i	0.275096	−	0.275096i	−0.556052	−	0.831148i	$-0.687684\pi$
$233$	978.403	−	978.403i	0.275096	−	0.275096i	0.831148	+	0.556052i	$0.187684\pi$
$234$		0			0
$235$	1156.13	+	478.883i	0.320925	+	0.132931i
$236$		0			0
$237$	−89.0675	−	215.028i	−0.0244116	−	0.0589349i
$238$		0			0
$239$			706.309i			0.191160i	0.995422	+	0.0955801i	$0.0304706\pi$
$239$			706.309i			0.191160i	−0.995422	+	0.0955801i	$0.969529\pi$
$240$		0			0
$241$		−	1700.85i		−	0.454611i	−0.973824	−	0.227305i	$-0.927008\pi$
$241$		−	1700.85i		−	0.454611i	0.973824	−	0.227305i	$-0.0729916\pi$
$242$		0			0
$243$	−917.274	−	2214.50i	−0.242153	−	0.584609i
$244$		0			0
$245$	−731.642	−	303.056i	−0.190787	−	0.0790267i
$246$		0			0
$247$	−1063.40	+	1063.40i	−0.273936	+	0.273936i
$248$		0			0
$249$	2544.27	+	2544.27i	0.647535	+	0.647535i
$250$		0			0
$251$	436.343	−	1053.43i	0.109728	−	0.264907i	−0.859472	−	0.511184i	$-0.829207\pi$
$251$	436.343	−	1053.43i	0.109728	−	0.264907i	0.969200	+	0.246277i	$0.0792072\pi$
$252$		0			0
$253$	5047.17	−	2090.61i	1.25420	−	0.519508i
$254$		0			0
$255$	−8684.12			−2.13263
$256$		0			0
$257$	7006.16			1.70052			0.850258	−	0.526366i	$-0.176446\pi$
$257$	7006.16			1.70052			0.850258	+	0.526366i	$0.176446\pi$
$258$		0			0
$259$	−373.616	+	154.757i	−0.0896345	+	0.0371278i
$260$		0			0
$261$	−705.831	+	1704.03i	−0.167394	+	0.404125i
$262$		0			0
$263$	361.548	+	361.548i	0.0847681	+	0.0847681i	0.748219	−	0.663451i	$-0.230909\pi$
$263$	361.548	+	361.548i	0.0847681	+	0.0847681i	−0.663451	+	0.748219i	$0.730909\pi$
$264$		0			0
$265$	−100.474	+	100.474i	−0.0232909	+	0.0232909i
$266$		0			0
$267$	6827.83	+	2828.18i	1.56500	+	0.648246i
$268$		0			0
$269$	45.5340	+	109.929i	0.0103207	+	0.0249163i	0.928956	−	0.370190i	$-0.120708\pi$
$269$	45.5340	+	109.929i	0.0103207	+	0.0249163i	−0.918635	+	0.395107i	$0.870708\pi$
$270$		0			0
$271$			3443.94i			0.771972i	0.922505	+	0.385986i	$0.126139\pi$
$271$			3443.94i			0.771972i	−0.922505	+	0.385986i	$0.873861\pi$
$272$		0			0
$273$		−	4113.74i		−	0.911996i
$274$		0			0
$275$	−37.8720	−	91.4310i	−0.00830460	−	0.0200491i
$276$		0			0
$277$	−2101.15	−	870.326i	−0.455762	−	0.188783i	0.142979	−	0.989726i	$-0.454332\pi$
$277$	−2101.15	−	870.326i	−0.455762	−	0.188783i	−0.598741	+	0.800943i	$0.704332\pi$
$278$		0			0
$279$	1350.36	−	1350.36i	0.289764	−	0.289764i
$280$		0			0
$281$	2252.56	+	2252.56i	0.478207	+	0.478207i	0.904558	−	0.426351i	$-0.140201\pi$
$281$	2252.56	+	2252.56i	0.478207	+	0.478207i	−0.426351	+	0.904558i	$0.640201\pi$
$282$		0			0
$283$	−2659.18	+	6419.84i	−0.558559	+	1.34848i	0.352349	+	0.935869i	$0.385383\pi$
$283$	−2659.18	+	6419.84i	−0.558559	+	1.34848i	−0.910907	+	0.412611i	$0.864617\pi$
$284$		0			0
$285$	−2200.93	+	911.657i	−0.457446	+	0.189480i
$286$		0			0
$287$	5992.45			1.23248
$288$		0			0
$289$	−12362.7			−2.51632
$290$		0			0
$291$	282.933	−	117.195i	0.0569959	−	0.0236085i
$292$		0			0
$293$	−1751.78	+	4229.17i	−0.349284	+	0.843245i	0.647421	+	0.762132i	$0.275847\pi$
$293$	−1751.78	+	4229.17i	−0.349284	+	0.843245i	−0.996705	+	0.0811131i	$0.974153\pi$
$294$		0			0
$295$	4293.73	+	4293.73i	0.847425	+	0.847425i
$296$		0			0
$297$	−2306.65	+	2306.65i	−0.450659	+	0.450659i
$298$		0			0
$299$	−7007.74	−	2902.70i	−1.35541	−	0.561430i
$300$		0			0
$301$	556.422	+	1343.32i	0.106550	+	0.257235i
$302$		0			0
$303$		−	2408.30i		−	0.456612i
$304$		0			0
$305$			3006.73i			0.564476i
$306$		0			0
$307$	172.273	+	415.904i	0.0320265	+	0.0773189i	0.939084	−	0.343689i	$-0.111677\pi$
$307$	172.273	+	415.904i	0.0320265	+	0.0773189i	−0.907057	+	0.421008i	$0.861677\pi$
$308$		0			0
$309$	4704.29	+	1948.58i	0.866077	+	0.358741i
$310$		0			0
$311$	−1586.57	+	1586.57i	−0.289279	+	0.289279i	−0.836795	−	0.547516i	$-0.815574\pi$
$311$	−1586.57	+	1586.57i	−0.289279	+	0.289279i	0.547516	+	0.836795i	$0.315574\pi$
$312$		0			0
$313$	1221.66	+	1221.66i	0.220615	+	0.220615i	0.808757	−	0.588143i	$-0.200141\pi$
$313$	1221.66	+	1221.66i	0.220615	+	0.220615i	−0.588143	+	0.808757i	$0.700141\pi$
$314$		0			0
$315$	616.557	−	1488.50i	0.110283	−	0.266246i
$316$		0			0
$317$	1676.17	−	694.291i	0.296981	−	0.123013i	−0.229218	−	0.973375i	$-0.573617\pi$
$317$	1676.17	−	694.291i	0.296981	−	0.123013i	0.526199	+	0.850362i	$0.323617\pi$
$318$		0			0
$319$	6247.93			1.09661
$320$		0			0
$321$	−5350.08			−0.930257
$322$		0			0
$323$	−4378.41	+	1813.60i	−0.754245	+	0.312419i
$324$		0			0
$325$	−52.5833	+	126.947i	−0.00897475	+	0.0216670i
$326$		0			0
$327$	−8753.01	−	8753.01i	−1.48025	−	1.48025i
$328$		0			0
$329$	−1320.92	+	1320.92i	−0.221352	+	0.221352i
$330$		0			0
$331$	−1687.62	−	699.037i	−0.280242	−	0.116080i	0.238135	−	0.971232i	$-0.423464\pi$
$331$	−1687.62	−	699.037i	−0.280242	−	0.116080i	−0.518378	+	0.855152i	$0.673464\pi$
$332$		0			0
$333$	83.3322	+	201.182i	0.0137134	+	0.0331072i
$334$		0			0
$335$		−	4993.39i		−	0.814383i
$336$		0			0
$337$			7042.63i			1.13839i	0.822203	+	0.569194i	$0.192745\pi$
$337$			7042.63i			1.13839i	−0.822203	+	0.569194i	$0.807255\pi$
$338$		0			0
$339$	1643.52	+	3967.81i	0.263315	+	0.635699i
$340$		0			0
$341$	−5976.63	−	2475.60i	−0.949129	−	0.393142i
$342$		0			0
$343$	4830.20	−	4830.20i	0.760367	−	0.760367i
$344$		0			0
$345$	−8496.30	−	8496.30i	−1.32587	−	1.32587i
$346$		0			0
$347$	1762.67	−	4255.46i	0.272695	−	0.658343i	−0.726902	−	0.686741i	$-0.759041\pi$
$347$	1762.67	−	4255.46i	0.272695	−	0.658343i	0.999597	+	0.0283982i	$0.00904065\pi$
$348$		0			0
$349$	10776.6	−	4463.83i	1.65289	−	0.684651i	0.655392	−	0.755289i	$-0.272503\pi$
$349$	10776.6	−	4463.83i	1.65289	−	0.684651i	0.997502	+	0.0706374i	$0.0225033\pi$
$350$		0			0
$351$	4529.26			0.688758
$352$		0			0
$353$	9544.92			1.43916			0.719582	−	0.694407i	$-0.244333\pi$
$353$	9544.92			1.43916			0.719582	+	0.694407i	$0.244333\pi$
$354$		0			0
$355$	404.923	−	167.725i	0.0605383	−	0.0250758i
$356$		0			0
$357$	4960.98	−	11976.9i	0.735471	−	1.77558i
$358$		0			0
$359$	5623.45	+	5623.45i	0.826725	+	0.826725i	0.987062	−	0.160338i	$-0.0512583\pi$
$359$	5623.45	+	5623.45i	0.826725	+	0.826725i	−0.160338	+	0.987062i	$0.551258\pi$
$360$		0			0
$361$	3930.76	−	3930.76i	0.573080	−	0.573080i
$362$		0			0
$363$	2371.55	+	982.330i	0.342904	+	0.142036i
$364$		0			0
$365$	1988.28	+	4800.13i	0.285127	+	0.688356i
$366$		0			0
$367$		−	5141.87i		−	0.731344i	−0.930744	−	0.365672i	$-0.880839\pi$
$367$		−	5141.87i		−	0.731344i	0.930744	−	0.365672i	$-0.119161\pi$
$368$		0			0
$369$		−	3226.77i		−	0.455227i
$370$		0			0
$371$	−81.1732	−	195.969i	−0.0113593	−	0.0274238i
$372$		0			0
$373$	5767.56	+	2389.00i	0.800625	+	0.331630i	0.745207	−	0.666833i	$-0.232351\pi$
$373$	5767.56	+	2389.00i	0.800625	+	0.331630i	0.0554183	+	0.998463i	$0.482351\pi$
$374$		0			0
$375$	−5993.78	+	5993.78i	−0.825380	+	0.825380i
$376$		0			0
$377$	−6134.10	−	6134.10i	−0.837991	−	0.837991i
$378$		0			0
$379$	961.979	−	2322.42i	0.130379	−	0.314762i	−0.845187	−	0.534471i	$-0.820511\pi$
$379$	961.979	−	2322.42i	0.130379	−	0.314762i	0.975565	+	0.219709i	$0.0705108\pi$
$380$		0			0
$381$	−3947.45	+	1635.09i	−0.530798	+	0.219864i
$382$		0			0
$383$	2634.68			0.351503			0.175752	−	0.984435i	$-0.443764\pi$
$383$	2634.68			0.351503			0.175752	+	0.984435i	$0.443764\pi$
$384$		0			0
$385$	−5457.70			−0.722467
$386$		0			0
$387$	723.341	−	299.618i	0.0950116	−	0.0393551i
$388$		0			0
$389$	4066.54	−	9817.49i	0.530030	−	1.27961i	−0.401473	−	0.915871i	$-0.631502\pi$
$389$	4066.54	−	9817.49i	0.530030	−	1.27961i	0.931503	−	0.363734i	$-0.118498\pi$
$390$		0			0
$391$	−16902.0	−	16902.0i	−2.18612	−	2.18612i
$392$		0			0
$393$	4211.51	−	4211.51i	0.540566	−	0.540566i
$394$		0			0
$395$	396.093	+	164.067i	0.0504547	+	0.0208990i
$396$		0			0
$397$	−1600.83	−	3864.76i	−0.202377	−	0.488581i	0.789809	−	0.613353i	$-0.210180\pi$
$397$	−1600.83	−	3864.76i	−0.202377	−	0.488581i	−0.992185	+	0.124773i	$0.960180\pi$
$398$		0			0
$399$		−	3556.26i		−	0.446205i
$400$		0			0
$401$		−	2096.79i		−	0.261119i	−0.991440	−	0.130560i	$-0.958323\pi$
$401$		−	2096.79i		−	0.261119i	0.991440	−	0.130560i	$-0.0416774\pi$
$402$		0			0
$403$	3437.25	+	8298.25i	0.424867	+	1.02572i
$404$		0			0
$405$	9069.01	+	3756.51i	1.11270	+	0.460895i
$406$		0			0
$407$	521.595	−	521.595i	0.0635246	−	0.0635246i
$408$		0			0
$409$	−2541.72	−	2541.72i	−0.307286	−	0.307286i	0.536570	−	0.843856i	$-0.319720\pi$
$409$	−2541.72	−	2541.72i	−0.307286	−	0.307286i	−0.843856	+	0.536570i	$0.819720\pi$
$410$		0			0
$411$	−5152.08	+	12438.2i	−0.618329	+	1.49278i
$412$		0			0
$413$	−8374.66	+	3468.90i	−0.997796	+	0.413301i
$414$		0			0
$415$	−6627.96			−0.783985
$416$		0			0
$417$	5373.29			0.631010
$418$		0			0
$419$	10221.3	−	4233.80i	1.19175	−	0.493639i	0.303425	−	0.952855i	$-0.401870\pi$
$419$	10221.3	−	4233.80i	1.19175	−	0.493639i	0.888324	+	0.459217i	$0.151870\pi$
$420$		0			0
$421$	−1917.63	+	4629.56i	−0.221994	+	0.535940i	−0.995161	−	0.0982623i	$-0.968672\pi$
$421$	−1917.63	+	4629.56i	−0.221994	+	0.535940i	0.773167	+	0.634203i	$0.218672\pi$
$422$		0			0
$423$	711.280	+	711.280i	0.0817580	+	0.0817580i
$424$		0			0
$425$	−306.185	+	306.185i	−0.0349462	+	0.0349462i
$426$		0			0
$427$	−4146.80	−	1717.66i	−0.469971	−	0.194668i
$428$		0			0
$429$	2871.54	+	6932.52i	0.323169	+	0.780199i
$430$		0			0
$431$			12541.7i			1.40165i	0.713331	+	0.700827i	$0.247186\pi$
$431$			12541.7i			1.40165i	−0.713331	+	0.700827i	$0.752814\pi$
$432$		0			0
$433$			5467.10i			0.606772i	0.952868	+	0.303386i	$0.0981171\pi$
$433$			5467.10i			0.606772i	−0.952868	+	0.303386i	$0.901883\pi$
$434$		0			0
$435$	−5258.81	−	12695.9i	−0.579634	−	1.39936i
$436$		0			0
$437$	−6058.08	−	2509.34i	−0.663152	−	0.274687i
$438$		0			0
$439$	6912.86	−	6912.86i	0.751556	−	0.751556i	−0.223214	−	0.974770i	$-0.571655\pi$
$439$	6912.86	−	6912.86i	0.751556	−	0.751556i	0.974770	+	0.223214i	$0.0716548\pi$
$440$		0			0
$441$	−450.126	−	450.126i	−0.0486045	−	0.0486045i
$442$		0			0
$443$	−5145.53	+	12422.4i	−0.551854	+	1.33229i	0.364230	+	0.931309i	$0.381332\pi$
$443$	−5145.53	+	12422.4i	−0.551854	+	1.33229i	−0.916084	+	0.400985i	$0.868668\pi$
$444$		0			0
$445$	−12577.2	+	5209.66i	−1.33981	+	0.554969i
$446$		0			0
$447$	9073.44			0.960088
$448$		0			0
$449$	4228.21			0.444413			0.222207	−	0.975000i	$-0.428674\pi$
$449$	4228.21			0.444413			0.222207	+	0.975000i	$0.428674\pi$
$450$		0			0
$451$	−10098.5	+	4182.95i	−1.05437	+	0.436735i
$452$		0			0
$453$	−1689.72	+	4079.34i	−0.175253	+	0.423099i
$454$		0			0
$455$	5358.26	+	5358.26i	0.552086	+	0.552086i
$456$		0			0
$457$	−1932.67	+	1932.67i	−0.197826	+	0.197826i	−0.799067	−	0.601242i	$-0.794673\pi$
$457$	−1932.67	+	1932.67i	−0.197826	+	0.197826i	0.601242	+	0.799067i	$0.294673\pi$
$458$		0			0
$459$	13186.6	+	5462.08i	1.34096	+	0.555443i
$460$		0			0
$461$	5203.91	+	12563.3i	0.525749	+	1.26927i	0.934285	+	0.356527i	$0.116039\pi$
$461$	5203.91	+	12563.3i	0.525749	+	1.26927i	−0.408536	+	0.912742i	$0.633961\pi$
$462$		0			0
$463$		−	6800.09i		−	0.682564i	−0.939961	−	0.341282i	$-0.889139\pi$
$463$		−	6800.09i		−	0.682564i	0.939961	−	0.341282i	$-0.110861\pi$
$464$		0			0
$465$			14228.3i			1.41897i
$466$		0			0
$467$	−3594.92	−	8678.90i	−0.356216	−	0.859982i	−0.995825	−	0.0912813i	$-0.970904\pi$
$467$	−3594.92	−	8678.90i	−0.356216	−	0.859982i	0.639609	−	0.768700i	$-0.279096\pi$
$468$		0			0
$469$	6886.74	+	2852.58i	0.678038	+	0.280853i
$470$		0			0
$471$	−6883.27	+	6883.27i	−0.673385	+	0.673385i
$472$		0			0
$473$	−1875.38	−	1875.38i	−0.182304	−	0.182304i
$474$		0			0
$475$	−45.4574	+	109.744i	−0.00439101	+	0.0106008i
$476$		0			0
$477$	−105.524	+	43.7095i	−0.0101292	+	0.00419564i
$478$		0			0
$479$	6129.80			0.584714			0.292357	−	0.956309i	$-0.405561\pi$
$479$	6129.80			0.584714			0.292357	+	0.956309i	$0.405561\pi$
$480$		0			0
$481$	−1024.18			−0.0970869
$482$		0			0
$483$	16571.5	−	6864.15i	1.56114	−	0.646645i
$484$		0			0
$485$	−215.879	+	521.177i	−0.0202114	+	0.0487947i
$486$		0			0
$487$	5985.06	+	5985.06i	0.556897	+	0.556897i	0.928423	−	0.371526i	$-0.121165\pi$
$487$	5985.06	+	5985.06i	0.556897	+	0.556897i	−0.371526	+	0.928423i	$0.621165\pi$
$488$		0			0
$489$	−7686.69	+	7686.69i	−0.710847	+	0.710847i
$490$		0			0
$491$	4495.22	+	1861.98i	0.413170	+	0.171141i	0.579579	−	0.814916i	$-0.303217\pi$
$491$	4495.22	+	1861.98i	0.413170	+	0.171141i	−0.166409	+	0.986057i	$0.553217\pi$
$492$		0			0
$493$	−10461.6	−	25256.5i	−0.955711	−	2.30729i
$494$		0			0
$495$			2938.82i			0.266849i
$496$		0			0
$497$			654.274i			0.0590507i
$498$		0			0
$499$	−6391.46	−	15430.3i	−0.573389	−	1.38428i	−0.898653	−	0.438659i	$-0.855453\pi$
$499$	−6391.46	−	15430.3i	−0.573389	−	1.38428i	0.325265	−	0.945623i	$-0.394547\pi$
$500$		0			0
$501$	−5201.50	−	2154.53i	−0.463844	−	0.192131i
$502$		0			0
$503$	−13536.2	+	13536.2i	−1.19990	+	1.19990i	−0.225706	+	0.974196i	$0.572469\pi$
$503$	−13536.2	+	13536.2i	−1.19990	+	1.19990i	−0.974196	+	0.225706i	$0.927531\pi$
$504$		0			0
$505$	3136.88	+	3136.88i	0.276415	+	0.276415i
$506$		0			0
$507$	−1048.28	+	2530.76i	−0.0918257	+	0.221687i
$508$		0			0
$509$	−6936.01	+	2872.99i	−0.603995	+	0.250183i	−0.663659	−	0.748036i	$-0.730997\pi$
$509$	−6936.01	+	2872.99i	−0.603995	+	0.250183i	0.0596637	+	0.998219i	$0.480997\pi$
$510$		0			0
$511$	−7756.03			−0.671442
$512$		0			0
$513$	3915.48			0.336983
$514$		0			0
$515$	−8665.56	+	3589.39i	−0.741456	+	0.307121i
$516$		0			0
$517$	1303.98	−	3148.09i	0.110926	−	0.267800i
$518$		0			0
$519$	−2110.18	−	2110.18i	−0.178471	−	0.178471i
$520$		0			0
$521$	−513.751	+	513.751i	−0.0432012	+	0.0432012i	−0.728377	−	0.685176i	$-0.759725\pi$
$521$	−513.751	+	513.751i	−0.0432012	+	0.0432012i	0.685176	+	0.728377i	$0.259725\pi$
$522$		0			0
$523$	−10786.8	−	4468.04i	−0.901861	−	0.373563i	−0.116926	−	0.993141i	$-0.537304\pi$
$523$	−10786.8	−	4468.04i	−0.901861	−	0.373563i	−0.784936	+	0.619577i	$0.787304\pi$
$524$		0			0
$525$	−124.346	−	300.198i	−0.0103370	−	0.0249556i
$526$		0			0
$527$			28304.9i			2.33963i
$528$		0			0
$529$		−	20905.9i		−	1.71825i
$530$		0			0
$531$	1867.90	+	4509.52i	0.152656	+	0.368543i
$532$		0			0
$533$	14021.3	+	5807.81i	1.13946	+	0.471978i
$534$		0			0
$535$	6968.63	−	6968.63i	0.563141	−	0.563141i
$536$		0			0
$537$	13617.1	+	13617.1i	1.09426	+	1.09426i
$538$		0			0
$539$	−825.210	+	1992.23i	−0.0659449	+	0.159205i
$540$		0			0
$541$	1012.42	−	419.356i	0.0804568	−	0.0333263i	−0.342092	−	0.939666i	$-0.611135\pi$
$541$	1012.42	−	419.356i	0.0804568	−	0.0333263i	0.422549	+	0.906340i	$0.361135\pi$
$542$		0			0
$543$	11156.0			0.881678
$544$		0			0
$545$	22802.1			1.79217
$546$		0			0
$547$	16637.9	−	6891.62i	1.30052	−	0.538692i	0.378415	−	0.925636i	$-0.376469\pi$
$547$	16637.9	−	6891.62i	1.30052	−	0.538692i	0.922103	+	0.386944i	$0.126469\pi$
$548$		0			0
$549$	−924.912	+	2232.94i	−0.0719022	+	0.173587i
$550$		0			0
$551$	−5302.84	−	5302.84i	−0.409997	−	0.409997i
$552$		0			0
$553$	−452.553	+	452.553i	−0.0348002	+	0.0348002i
$554$		0			0
$555$	−1498.91	−	620.869i	−0.114640	−	0.0474854i
$556$		0			0
$557$	−5219.38	−	12600.7i	−0.397041	−	0.958543i	−0.988364	−	0.152108i	$-0.951394\pi$
$557$	−5219.38	−	12600.7i	−0.397041	−	0.958543i	0.591323	−	0.806435i	$-0.298606\pi$
$558$		0			0
$559$			3682.42i			0.278622i
$560$		0			0
$561$			23646.5i			1.77960i
$562$		0			0
$563$	−7201.62	−	17386.3i	−0.539098	−	1.30150i	−0.925353	−	0.379106i	$-0.876232\pi$
$563$	−7201.62	−	17386.3i	−0.539098	−	1.30150i	0.386255	−	0.922392i	$-0.373768\pi$
$564$		0			0
$565$	−7308.92	−	3027.45i	−0.544227	−	0.225426i
$566$		0			0
$567$	−10361.7	+	10361.7i	−0.767463	+	0.767463i
$568$		0			0
$569$	−2337.98	−	2337.98i	−0.172255	−	0.172255i	0.615714	−	0.787969i	$-0.288868\pi$
$569$	−2337.98	−	2337.98i	−0.172255	−	0.172255i	−0.787969	+	0.615714i	$0.788868\pi$
$570$		0			0
$571$	6423.07	−	15506.7i	0.470748	−	1.13649i	−0.493086	−	0.869981i	$-0.664131\pi$
$571$	6423.07	−	15506.7i	0.470748	−	1.13649i	0.963834	−	0.266505i	$-0.0858688\pi$
$572$		0			0
$573$	−2517.49	+	1042.78i	−0.183542	+	0.0760256i
$574$		0			0
$575$	−599.126			−0.0434526
$576$		0			0
$577$	−15420.1			−1.11256			−0.556279	−	0.830995i	$-0.687772\pi$
$577$	−15420.1			−1.11256			−0.556279	+	0.830995i	$0.687772\pi$
$578$		0			0
$579$	−17703.8	+	7333.13i	−1.27071	+	0.526347i
$580$		0			0
$581$	3786.36	−	9141.08i	0.270369	−	0.652730i
$582$		0			0
$583$	273.588	+	273.588i	0.0194354	+	0.0194354i
$584$		0			0
$585$	2885.28	−	2885.28i	0.203917	−	0.203917i
$586$		0			0
$587$	4807.28	+	1991.24i	0.338020	+	0.140013i	0.545236	−	0.838283i	$-0.316440\pi$
$587$	4807.28	+	1991.24i	0.338020	+	0.140013i	−0.207216	+	0.978295i	$0.566440\pi$
$588$		0			0
$589$	2971.45	+	7173.71i	0.207872	+	0.501846i
$590$		0			0
$591$		−	16024.2i		−	1.11531i
$592$		0			0
$593$		−	7386.71i		−	0.511528i	−0.966739	−	0.255764i	$-0.917673\pi$
$593$		−	7386.71i		−	0.511528i	0.966739	−	0.255764i	$-0.0823269\pi$
$594$		0			0
$595$	9138.40	+	22062.0i	0.629643	+	1.52009i
$596$		0			0
$597$	−18251.3	−	7559.95i	−1.25122	−	0.518271i
$598$		0			0
$599$	14260.6	−	14260.6i	0.972744	−	0.972744i	−0.0268941	−	0.999638i	$-0.508562\pi$
$599$	14260.6	−	14260.6i	0.972744	−	0.972744i	0.999638	+	0.0268941i	$0.00856169\pi$
$600$		0			0
$601$	−849.123	−	849.123i	−0.0576314	−	0.0576314i	0.677704	−	0.735335i	$-0.262975\pi$
$601$	−849.123	−	849.123i	−0.0576314	−	0.0576314i	−0.735335	+	0.677704i	$0.762975\pi$
$602$		0			0
$603$	1536.04	−	3708.32i	0.103735	−	0.250438i
$604$		0			0
$605$	−4368.53	+	1809.50i	−0.293564	+	0.121598i
$606$		0			0
$607$	−24362.0			−1.62904			−0.814518	−	0.580139i	$-0.802998\pi$
$607$	−24362.0			−1.62904			−0.814518	+	0.580139i	$0.802998\pi$
$608$		0			0
$609$	20514.0			1.36497
$610$		0			0
$611$	−4370.96	+	1810.51i	−0.289411	+	0.119878i
$612$		0			0
$613$	−2098.82	+	5066.99i	−0.138288	+	0.333856i	−0.977818	−	0.209457i	$-0.932830\pi$
$613$	−2098.82	+	5066.99i	−0.138288	+	0.333856i	0.839530	+	0.543313i	$0.182830\pi$
$614$		0			0
$615$	16999.6	+	16999.6i	1.11462	+	1.11462i
$616$		0			0
$617$	18585.0	−	18585.0i	1.21265	−	1.21265i	0.242493	−	0.970153i	$-0.422035\pi$
$617$	18585.0	−	18585.0i	1.21265	−	1.21265i	0.970153	−	0.242493i	$-0.0779652\pi$
$618$		0			0
$619$	−5415.72	−	2243.27i	−0.351658	−	0.145662i	0.199860	−	0.979824i	$-0.435951\pi$
$619$	−5415.72	−	2243.27i	−0.351658	−	0.145662i	−0.551518	+	0.834163i	$0.685951\pi$
$620$		0			0
$621$	7557.48	+	18245.4i	0.488360	+	1.17900i
$622$		0			0
$623$		−	20322.2i		−	1.30689i
$624$		0			0
$625$		−	15202.3i		−	0.972950i
$626$		0			0
$627$	2482.41	+	5993.06i	0.158114	+	0.381722i
$628$		0			0
$629$	−2981.84	−	1235.12i	−0.189020	−	0.0782949i
$630$		0			0
$631$	−9326.18	+	9326.18i	−0.588382	+	0.588382i	−0.937193	−	0.348811i	$-0.886586\pi$
$631$	−9326.18	+	9326.18i	−0.588382	+	0.588382i	0.348811	+	0.937193i	$0.386586\pi$
$632$		0			0
$633$	−22907.5	−	22907.5i	−1.43837	−	1.43837i
$634$		0			0
$635$	3011.92	−	7271.41i	0.188227	−	0.454421i
$636$		0			0
$637$	2766.11	−	1145.76i	0.172052	−	0.0712664i
$638$		0			0
$639$	352.309			0.0218108
$640$		0			0
$641$	−24698.6			−1.52189			−0.760947	−	0.648814i	$-0.775265\pi$
$641$	−24698.6			−1.52189			−0.760947	+	0.648814i	$0.775265\pi$
$642$		0			0
$643$	15953.0	−	6607.95i	0.978422	−	0.405276i	0.164581	−	0.986364i	$-0.447373\pi$
$643$	15953.0	−	6607.95i	0.978422	−	0.405276i	0.813841	+	0.581088i	$0.197373\pi$
$644$		0			0
$645$	−2232.31	+	5389.28i	−0.136275	+	0.328996i
$646$		0			0
$647$	−15582.9	−	15582.9i	−0.946874	−	0.946874i	0.0517843	−	0.998658i	$-0.483509\pi$
$647$	−15582.9	−	15582.9i	−0.946874	−	0.946874i	−0.998658	+	0.0517843i	$0.983509\pi$
$648$		0			0
$649$	11691.6	−	11691.6i	0.707145	−	0.707145i
$650$		0			0
$651$	−19623.2	−	8128.21i	−1.18141	−	0.489354i
$652$		0			0
$653$	6341.65	+	15310.1i	0.380043	+	0.917504i	0.991956	+	0.126580i	$0.0403999\pi$
$653$	6341.65	+	15310.1i	0.380043	+	0.917504i	−0.611914	+	0.790924i	$0.709600\pi$
$654$		0			0
$655$			10971.2i			0.654474i
$656$		0			0
$657$			4176.41i			0.248002i
$658$		0			0
$659$	7357.67	+	17763.0i	0.434923	+	1.05000i	0.977679	+	0.210106i	$0.0673810\pi$
$659$	7357.67	+	17763.0i	0.434923	+	1.05000i	−0.542756	+	0.839891i	$0.682619\pi$
$660$		0			0
$661$	−8796.41	−	3643.59i	−0.517611	−	0.214401i	0.108556	−	0.994090i	$-0.465377\pi$
$661$	−8796.41	−	3643.59i	−0.517611	−	0.214401i	−0.626167	+	0.779689i	$0.715377\pi$
$662$		0			0
$663$	23215.7	−	23215.7i	1.35991	−	1.35991i
$664$		0			0
$665$	4632.14	+	4632.14i	0.270115	+	0.270115i
$666$		0			0
$667$	14474.9	−	34945.5i	0.840286	−	2.02863i
$668$		0			0
$669$	36634.6	−	15174.5i	2.11715	−	0.876953i
$670$		0			0
$671$	8187.22			0.471034
$672$		0			0
$673$	−18778.9			−1.07559			−0.537795	−	0.843076i	$-0.680743\pi$
$673$	−18778.9			−1.07559			−0.537795	+	0.843076i	$0.680743\pi$
$674$		0			0
$675$	330.520	−	136.906i	0.0188470	−	0.00780668i
$676$		0			0
$677$	2171.42	−	5242.27i	0.123271	−	0.297603i	−0.850182	−	0.526489i	$-0.823508\pi$
$677$	2171.42	−	5242.27i	0.123271	−	0.297603i	0.973453	+	0.228886i	$0.0735083\pi$
$678$		0			0
$679$	−595.467	−	595.467i	−0.0336552	−	0.0336552i
$680$		0			0
$681$	−4786.88	+	4786.88i	−0.269359	+	0.269359i
$682$		0			0
$683$	25821.4	+	10695.6i	1.44660	+	0.599202i	0.961389	−	0.275195i	$-0.0887423\pi$
$683$	25821.4	+	10695.6i	1.44660	+	0.599202i	0.485212	+	0.874396i	$0.338742\pi$
$684$		0			0
$685$	−9490.40	−	22911.9i	−0.529357	−	1.27798i
$686$		0			0
$687$		−	15438.1i		−	0.857351i
$688$		0			0
$689$		−	537.207i		−	0.0297039i
$690$		0			0
$691$	4070.96	+	9828.16i	0.224120	+	0.541072i	0.995442	−	0.0953726i	$-0.0304042\pi$
$691$	4070.96	+	9828.16i	0.224120	+	0.541072i	−0.771322	+	0.636445i	$0.780404\pi$
$692$		0			0
$693$	−4053.13	−	1678.86i	−0.222173	−	0.0920269i
$694$		0			0
$695$	−6998.86	+	6998.86i	−0.381988	+	0.381988i
$696$		0			0
$697$	33818.1	+	33818.1i	1.83781	+	1.83781i
$698$		0			0
$699$	−3171.21	+	7655.98i	−0.171597	+	0.414272i
$700$		0			0
$701$	1993.12	−	825.577i	0.107388	−	0.0444816i	−0.328343	−	0.944559i	$-0.606490\pi$
$701$	1993.12	−	825.577i	0.107388	−	0.0444816i	0.435731	+	0.900077i	$0.356490\pi$
$702$		0			0
$703$	−885.392			−0.0475010
$704$		0			0
$705$	−7494.50			−0.400368
$706$		0			0
$707$	−6118.30	+	2534.28i	−0.325463	+	0.134811i
$708$		0			0
$709$	−8011.74	+	19342.1i	−0.424383	+	1.02455i	0.556657	+	0.830742i	$0.312084\pi$
$709$	−8011.74	+	19342.1i	−0.424383	+	1.02455i	−0.981040	+	0.193808i	$0.937916\pi$
$710$		0			0
$711$	243.687	+	243.687i	0.0128537	+	0.0128537i
$712$		0			0
$713$	−27692.8	+	27692.8i	−1.45456	+	1.45456i
$714$		0			0
$715$	−12770.1	−	5289.54i	−0.667935	−	0.276668i
$716$		0			0
$717$	−1618.78	−	3908.07i	−0.0843157	−	0.203556i
$718$		0			0
$719$		−	29047.6i		−	1.50667i	−0.657639	−	0.753334i	$-0.728445\pi$
$719$		−	29047.6i		−	1.50667i	0.657639	−	0.753334i	$-0.271555\pi$
$720$		0			0
$721$		−	14001.8i		−	0.723237i
$722$		0			0
$723$	3898.15	+	9410.96i	0.200517	+	0.484090i
$724$		0			0
$725$	−633.048	−	262.217i	−0.0324287	−	0.0134324i
$726$		0			0
$727$	12248.6	−	12248.6i	0.624862	−	0.624862i	−0.321909	−	0.946771i	$-0.604324\pi$
$727$	12248.6	−	12248.6i	0.624862	−	0.624862i	0.946771	+	0.321909i	$0.104324\pi$
$728$		0			0
$729$	−6837.10	−	6837.10i	−0.347361	−	0.347361i
$730$		0			0
$731$	−4440.83	+	10721.1i	−0.224692	+	0.542455i
$732$		0			0
$733$	17288.6	−	7161.19i	0.871174	−	0.360852i	0.0981066	−	0.995176i	$-0.468721\pi$
$733$	17288.6	−	7161.19i	0.871174	−	0.360852i	0.773067	+	0.634324i	$0.218721\pi$
$734$		0			0
$735$	4742.82			0.238016
$736$		0			0
$737$	−13596.8			−0.679573
$738$		0			0
$739$	−31548.5	+	13067.8i	−1.57041	+	0.650483i	−0.986857	−	0.161595i	$-0.948336\pi$
$739$	−31548.5	+	13067.8i	−1.57041	+	0.650483i	−0.583548	+	0.812079i	$0.698336\pi$
$740$		0			0
$741$	3446.69	−	8321.05i	0.170874	−	0.412526i
$742$		0			0
$743$	19385.2	+	19385.2i	0.957163	+	0.957163i	0.999119	−	0.0419563i	$-0.0133590\pi$
$743$	19385.2	+	19385.2i	0.957163	+	0.957163i	−0.0419563	+	0.999119i	$0.513359\pi$
$744$		0			0
$745$	−11818.4	+	11818.4i	−0.581199	+	0.581199i
$746$		0			0
$747$	−4922.22	−	2038.85i	−0.241090	−	0.0998629i
$748$		0			0
$749$	5629.95	+	13591.9i	0.274651	+	0.663067i
$750$		0			0
$751$			32864.8i			1.59688i	0.602078	+	0.798438i	$0.294340\pi$
$751$			32864.8i			1.59688i	−0.602078	+	0.798438i	$0.705660\pi$
$752$		0			0
$753$			6828.75i			0.330483i
$754$		0			0
$755$	−3112.55	−	7514.36i	−0.150036	−	0.362219i
$756$		0			0
$757$	29982.4	+	12419.1i	1.43954	+	0.596275i	0.959686	−	0.281076i	$-0.0906912\pi$
$757$	29982.4	+	12419.1i	1.43954	+	0.596275i	0.479850	+	0.877351i	$0.340691\pi$
$758$		0			0
$759$	−23135.1	+	23135.1i	−1.10639	+	1.10639i
$760$		0			0
$761$	11824.8	+	11824.8i	0.563270	+	0.563270i	0.930235	−	0.366965i	$-0.119603\pi$
$761$	11824.8	+	11824.8i	0.563270	+	0.563270i	−0.366965	+	0.930235i	$0.619603\pi$
$762$		0			0
$763$	−13026.2	+	31448.0i	−0.618059	+	1.49213i
$764$		0			0
$765$	11879.8	−	4920.77i	0.561457	−	0.232563i
$766$		0			0
$767$	−22957.3			−1.08076
$768$		0			0
$769$	−6754.02			−0.316718			−0.158359	−	0.987382i	$-0.550620\pi$
$769$	−6754.02			−0.316718			−0.158359	+	0.987382i	$0.550620\pi$
$770$		0			0
$771$	−38765.8	+	16057.3i	−1.81079	+	0.750052i
$772$		0			0
$773$	−8503.04	+	20528.2i	−0.395644	+	0.955170i	0.593042	+	0.805172i	$0.297927\pi$
$773$	−8503.04	+	20528.2i	−0.395644	+	0.955170i	−0.988686	+	0.149998i	$0.952073\pi$
$774$		0			0
$775$	501.662	+	501.662i	0.0232519	+	0.0232519i
$776$		0			0
$777$	1712.57	−	1712.57i	0.0790708	−	0.0790708i
$778$		0			0
$779$	12121.2	+	5020.76i	0.557493	+	0.230921i
$780$		0			0
$781$	−456.708	−	1102.59i	−0.0209248	−	0.0505170i
$782$		0			0
$783$			22586.1i			1.03086i
$784$		0			0
$785$		−	17931.3i		−	0.815282i
$786$		0			0
$787$	7710.78	+	18615.5i	0.349250	+	0.843164i	0.996709	+	0.0810635i	$0.0258317\pi$
$787$	7710.78	+	18615.5i	0.349250	+	0.843164i	−0.647459	+	0.762100i	$0.724168\pi$
$788$		0			0
$789$	−2829.11	−	1171.86i	−0.127654	−	0.0528760i
$790$		0			0
$791$	8350.74	−	8350.74i	0.375371	−	0.375371i
$792$		0			0
$793$	−8038.06	−	8038.06i	−0.359949	−	0.359949i
$794$		0			0
$795$	325.659	−	786.211i	0.0145282	−	0.0350742i
$796$		0			0
$797$	15755.0	−	6525.92i	0.700213	−	0.290038i	−0.00403511	−	0.999992i	$-0.501284\pi$
$797$	15755.0	−	6525.92i	0.700213	−	0.290038i	0.704248	+	0.709954i	$0.251284\pi$
$798$		0			0
$799$	−14909.1			−0.660134
$800$		0			0
$801$	−10943.0			−0.482710
$802$		0			0
$803$	13070.6	−	5414.00i	0.574408	−	0.237928i
$804$		0			0
$805$	−12644.1	+	30525.6i	−0.553599	+	1.33651i
$806$		0			0
$807$	−503.888	−	503.888i	−0.0219798	−	0.0219798i
$808$		0			0
$809$	−12001.3	+	12001.3i	−0.521561	+	0.521561i	−0.918043	−	0.396482i	$-0.870231\pi$
$809$	−12001.3	+	12001.3i	−0.521561	+	0.521561i	0.396482	+	0.918043i	$0.370231\pi$
$810$		0			0
$811$	850.463	+	352.273i	0.0368234	+	0.0152528i	0.401019	−	0.916070i	$-0.368656\pi$
$811$	850.463	+	352.273i	0.0368234	+	0.0152528i	−0.364196	+	0.931322i	$0.618656\pi$
$812$		0			0
$813$	−7893.11	−	19055.7i	−0.340496	−	0.822031i
$814$		0			0
$815$		−	20024.3i		−	0.860637i
$816$		0			0
$817$			3183.39i			0.136319i
$818$		0			0
$819$	2331.01	+	5627.56i	0.0994532	+	0.240101i
$820$		0			0
$821$	24287.1	+	10060.0i	1.03243	+	0.427647i	0.833589	−	0.552385i	$-0.186282\pi$
$821$	24287.1	+	10060.0i	1.03243	+	0.427647i	0.198842	+	0.980032i	$0.436282\pi$
$822$		0			0
$823$	32502.5	−	32502.5i	1.37663	−	1.37663i	0.526381	−	0.850249i	$-0.323549\pi$
$823$	32502.5	−	32502.5i	1.37663	−	1.37663i	0.850249	−	0.526381i	$-0.176451\pi$
$824$		0			0
$825$	419.098	+	419.098i	0.0176862	+	0.0176862i
$826$		0			0
$827$	709.545	−	1712.99i	0.0298347	−	0.0720273i	−0.908260	−	0.418406i	$-0.862589\pi$
$827$	709.545	−	1712.99i	0.0298347	−	0.0720273i	0.938095	+	0.346379i	$0.112589\pi$
$828$		0			0
$829$	−13491.7	+	5588.43i	−0.565241	+	0.234130i	−0.646959	−	0.762525i	$-0.723959\pi$
$829$	−13491.7	+	5588.43i	−0.565241	+	0.234130i	0.0817180	+	0.996655i	$0.473959\pi$
$830$		0			0
$831$	13620.6			0.568583
$832$		0			0
$833$	9435.08			0.392444
$834$		0			0
$835$	9581.45	−	3968.77i	0.397101	−	0.164485i
$836$		0			0
$837$	8949.23	−	21605.3i	0.369570	−	0.892222i
$838$		0			0
$839$	5631.89	+	5631.89i	0.231745	+	0.231745i	0.813421	−	0.581676i	$-0.197603\pi$
$839$	5631.89	+	5631.89i	0.231745	+	0.231745i	−0.581676	+	0.813421i	$0.697603\pi$
$840$		0			0
$841$	13343.3	−	13343.3i	0.547104	−	0.547104i
$842$		0			0
$843$	−17626.2	−	7301.02i	−0.720141	−	0.298292i
$844$		0			0
$845$	−1930.98	−	4661.80i	−0.0786128	−	0.189788i
$846$		0			0
$847$		−	7058.66i		−	0.286350i
$848$		0			0
$849$		−	41616.1i		−	1.68229i
$850$		0			0
$851$	−1708.95	−	4125.76i	−0.0688389	−	0.166192i
$852$		0			0
$853$	670.402	+	277.690i	0.0269099	+	0.0111464i	0.396098	−	0.918208i	$-0.370364\pi$
$853$	670.402	+	277.690i	0.0269099	+	0.0111464i	−0.369188	+	0.929355i	$0.620364\pi$
$854$		0			0
$855$	2494.28	−	2494.28i	0.0997690	−	0.0997690i
$856$		0			0
$857$	1780.65	+	1780.65i	0.0709754	+	0.0709754i	0.741703	−	0.670728i	$-0.234018\pi$
$857$	1780.65	+	1780.65i	0.0709754	+	0.0709754i	−0.670728	+	0.741703i	$0.734018\pi$
$858$		0			0
$859$	1454.86	−	3512.34i	0.0577871	−	0.139511i	−0.892349	−	0.451346i	$-0.850944\pi$
$859$	1454.86	−	3512.34i	0.0577871	−	0.139511i	0.950136	+	0.311836i	$0.100944\pi$
$860$		0			0
$861$	−33156.8	+	13734.0i	−1.31240	+	0.543616i
$862$		0			0
$863$	−19305.9			−0.761509			−0.380754	−	0.924676i	$-0.624336\pi$
$863$	−19305.9			−0.761509			−0.380754	+	0.924676i	$0.624336\pi$
$864$		0			0
$865$	5497.14			0.216079
$866$		0			0
$867$	68403.9	−	28333.8i	2.67949	−	1.10988i
$868$		0			0
$869$	446.748	−	1078.55i	0.0174395	−	0.0421026i
$870$		0			0
$871$	13349.1	+	13349.1i	0.519308	+	0.519308i
$872$		0			0
$873$	−320.642	+	320.642i	−0.0124308	+	0.0124308i
$874$		0			0
$875$	21534.6	+	8919.91i	0.832001	+	0.344626i
$876$		0			0
$877$	11119.2	+	26844.1i	0.428128	+	1.03359i	0.979880	+	0.199585i	$0.0639595\pi$
$877$	11119.2	+	26844.1i	0.428128	+	1.03359i	−0.551752	+	0.834008i	$0.686041\pi$
$878$		0			0
$879$		−	27415.3i		−	1.05199i
$880$		0			0
$881$			21485.0i			0.821622i	0.911720	+	0.410811i	$0.134754\pi$
$881$			21485.0i			0.821622i	−0.911720	+	0.410811i	$0.865246\pi$
$882$		0			0
$883$	−9972.61	−	24076.0i	−0.380074	−	0.917579i	−0.991951	−	0.126626i	$-0.959585\pi$
$883$	−9972.61	−	24076.0i	−0.380074	−	0.917579i	0.611877	−	0.790953i	$-0.290415\pi$
$884$		0			0
$885$	−33598.3	−	13916.9i	−1.27615	−	0.528600i
$886$		0			0
$887$	−16861.7	+	16861.7i	−0.638286	+	0.638286i	−0.950132	−	0.311847i	$-0.899053\pi$
$887$	−16861.7	+	16861.7i	−0.638286	+	0.638286i	0.311847	+	0.950132i	$0.399053\pi$
$888$		0			0
$889$	8307.89	+	8307.89i	0.313428	+	0.313428i
$890$		0			0
$891$	10228.8	−	24694.6i	0.384600	−	0.928506i
$892$		0			0
$893$	−3778.62	+	1565.16i	−0.141598	+	0.0586517i
$894$		0			0
$895$	−35473.2			−1.32485
$896$		0			0
$897$	45427.2			1.69094
$898$		0			0
$899$	−41380.9	+	17140.5i	−1.53518	+	0.635894i
$900$		0			0
$901$	647.847	−	1564.04i	0.0239544	−	0.0578311i
$902$		0			0
$903$	−6157.47	−	6157.47i	−0.226919	−	0.226919i
$904$		0			0
$905$	−14531.0	+	14531.0i	−0.533733	+	0.533733i
$906$		0			0
$907$	29990.0	+	12422.3i	1.09791	+	0.454767i	0.856757	−	0.515721i	$-0.172476\pi$
$907$	29990.0	+	12422.3i	1.09791	+	0.454767i	0.241149	+	0.970488i	$0.422476\pi$
$908$		0			0
$909$	1364.64	+	3294.54i	0.0497935	+	0.120212i
$910$		0			0
$911$		−	3172.04i		−	0.115362i	−0.998335	−	0.0576809i	$-0.981629\pi$
$911$		−	3172.04i		−	0.115362i	0.998335	−	0.0576809i	$-0.0183706\pi$
$912$		0			0
$913$			18047.7i			0.654207i
$914$		0			0
$915$	−6891.09	−	16636.6i	−0.248975	−	0.601079i
$916$		0			0
$917$	−15131.2	−	6267.53i	−0.544902	−	0.225706i
$918$		0			0
$919$	21688.5	−	21688.5i	0.778494	−	0.778494i	−0.201080	−	0.979575i	$-0.564445\pi$
$919$	21688.5	−	21688.5i	0.778494	−	0.778494i	0.979575	+	0.201080i	$0.0644452\pi$
$920$		0			0
$921$	−1906.41	−	1906.41i	−0.0682066	−	0.0682066i
$922$		0			0
$923$	−634.115	+	1530.89i	−0.0226134	+	0.0545936i
$924$		0			0
$925$	−74.7393	+	30.9580i	−0.00265666	+	0.00110043i
$926$		0			0
$927$	−7539.57			−0.267133
$928$		0			0
$929$	−11367.7			−0.401467			−0.200734	−	0.979646i	$-0.564333\pi$
$929$	−11367.7			−0.401467			−0.200734	+	0.979646i	$0.564333\pi$
$930$		0			0
$931$	2391.26	−	990.493i	0.0841788	−	0.0348680i
$932$		0			0
$933$	5142.40	−	12414.9i	0.180444	−	0.435631i
$934$		0			0
$935$	−30800.3	−	30800.3i	−1.07730	−	1.07730i
$936$		0			0
$937$	23005.0	−	23005.0i	0.802072	−	0.802072i	−0.181347	−	0.983419i	$-0.558046\pi$
$937$	23005.0	−	23005.0i	0.802072	−	0.802072i	0.983419	+	0.181347i	$0.0580456\pi$
$938$		0			0
$939$	−9559.47	−	3959.66i	−0.332228	−	0.137613i
$940$		0			0
$941$	−14177.8	−	34228.4i	−0.491163	−	1.18577i	−0.954129	−	0.299397i	$-0.903215\pi$
$941$	−14177.8	−	34228.4i	−0.491163	−	1.18577i	0.462965	−	0.886376i	$-0.346785\pi$
$942$		0			0
$943$			66173.3i			2.28515i
$944$		0			0
$945$		−	19729.4i		−	0.679151i
$946$		0			0
$947$	−7307.45	−	17641.7i	−0.250750	−	0.605364i	0.747515	−	0.664245i	$-0.231247\pi$
$947$	−7307.45	−	17641.7i	−0.250750	−	0.605364i	−0.998265	+	0.0588811i	$0.981247\pi$
$948$		0			0
$949$	−18147.8	−	7517.06i	−0.620761	−	0.257128i
$950$		0			0
$951$	−7683.16	+	7683.16i	−0.261981	+	0.261981i
$952$		0			0
$953$	−37291.2	−	37291.2i	−1.26756	−	1.26756i	−0.947347	−	0.320209i	$-0.896247\pi$
$953$	−37291.2	−	37291.2i	−1.26756	−	1.26756i	−0.320209	−	0.947347i	$-0.603753\pi$
$954$		0			0
$955$	1920.85	−	4637.35i	0.0650862	−	0.157132i
$956$		0			0
$957$	−34570.4	+	14319.5i	−1.16771	+	0.483683i
$958$		0			0
$959$	37020.9			1.24658
$960$		0			0
$961$	16584.6			0.556698
$962$		0			0
$963$	7318.86	−	3031.57i	0.244909	−	0.101445i
$964$		0			0
$965$	13508.0	−	32611.3i	0.450610	−	1.08787i
$966$		0			0
$967$	21639.9	+	21639.9i	0.719639	+	0.719639i	0.968531	−	0.248892i	$-0.0800664\pi$
$967$	21639.9	+	21639.9i	0.719639	+	0.719639i	−0.248892	+	0.968531i	$0.580066\pi$
$968$		0			0
$969$	20069.6	−	20069.6i	0.665355	−	0.665355i
$970$		0			0
$971$	−15126.7	−	6265.69i	−0.499937	−	0.207081i	0.118441	−	0.992961i	$-0.462210\pi$
$971$	−15126.7	−	6265.69i	−0.499937	−	0.207081i	−0.618379	+	0.785880i	$0.712210\pi$
$972$		0			0
$973$	−5654.37	−	13650.9i	−0.186301	−	0.449770i
$974$		0			0
$975$		−	822.926i		−	0.0270305i
$976$		0			0
$977$			46484.2i			1.52217i	0.648651	+	0.761086i	$0.275333\pi$
$977$			46484.2i			1.52217i	−0.648651	+	0.761086i	$0.724667\pi$
$978$		0			0
$979$	14185.7	+	34247.3i	0.463102	+	1.11803i
$980$		0			0
$981$	16933.9	+	7014.23i	0.551128	+	0.228285i
$982$		0			0
$983$	−31577.7	+	31577.7i	−1.02459	+	1.02459i	−0.0248987	+	0.999690i	$0.507926\pi$
$983$	−31577.7	+	31577.7i	−1.02459	+	1.02459i	−0.999690	+	0.0248987i	$0.992074\pi$
$984$		0			0
$985$	20872.0	+	20872.0i	0.675166	+	0.675166i
$986$		0			0
$987$	4281.39	−	10336.2i	0.138073	−	0.333338i
$988$		0			0
$989$	−14834.0	+	6144.45i	−0.476941	+	0.197555i
$990$		0			0
$991$	38674.2			1.23968			0.619842	−	0.784727i	$-0.287197\pi$
$991$	38674.2			1.23968			0.619842	+	0.784727i	$0.287197\pi$
$992$		0			0
$993$	10939.9			0.349615
$994$		0			0
$995$	33619.9	−	13925.8i	1.07118	−	0.443697i
$996$		0			0
$997$	10556.5	−	25485.6i	0.335333	−	0.809565i	−0.662818	−	0.748780i	$-0.730640\pi$
$997$	10556.5	−	25485.6i	0.335333	−	0.809565i	0.998151	−	0.0607843i	$-0.0193602\pi$
$998$		0			0
$999$	1885.55	+	1885.55i	0.0597159	+	0.0597159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.49.3		44
4.3	odd	2		32.4.g.a.21.4	✓	44
8.3	odd	2		256.4.g.b.97.3		44
8.5	even	2		256.4.g.a.97.9		44
32.3	odd	8		32.4.g.a.29.4	yes	44
32.13	even	8		256.4.g.a.161.9		44
32.19	odd	8		256.4.g.b.161.3		44
32.29	even	8	inner	128.4.g.a.81.3		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.21.4	✓	44	4.3	odd	2
32.4.g.a.29.4	yes	44	32.3	odd	8
128.4.g.a.49.3		44	1.1	even	1	trivial
128.4.g.a.81.3		44	32.29	even	8	inner
256.4.g.a.97.9		44	8.5	even	2
256.4.g.a.161.9		44	32.13	even	8
256.4.g.b.97.3		44	8.3	odd	2
256.4.g.b.161.3		44	32.19	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.53310 + 2.29188i) q^{3} +(4.22177 - 10.1923i) q^{5} +(11.6451 + 11.6451i) q^{7} +(6.27055 - 6.27055i) q^{9} +O(q^{10})\)	\(q+(-5.53310 + 2.29188i) q^{3} +(4.22177 - 10.1923i) q^{5} +(11.6451 + 11.6451i) q^{7} +(6.27055 - 6.27055i) q^{9} +(-27.7531 - 11.4957i) q^{11} +(15.9612 + 38.5338i) q^{13} +66.0706i q^{15} +131.437i q^{17} +(13.7982 + 33.3119i) q^{19} +(-91.1226 - 37.7442i) q^{21} +(-128.594 + 128.594i) q^{23} +(2.32952 + 2.32952i) q^{25} +(41.5567 - 100.327i) q^{27} +(-192.157 + 79.5938i) q^{29} +215.350 q^{31} +179.908 q^{33} +(167.853 - 69.5268i) q^{35} +(-9.39705 + 22.6865i) q^{37} +(-176.630 - 176.630i) q^{39} +(257.295 - 257.295i) q^{41} +(81.5685 + 33.7868i) q^{43} +(-37.4383 - 90.3840i) q^{45} +113.432i q^{47} -71.7841i q^{49} +(-301.238 - 727.254i) q^{51} +(-11.8996 - 4.92896i) q^{53} +(-234.335 + 234.335i) q^{55} +(-152.694 - 152.694i) q^{57} +(-210.637 + 508.522i) q^{59} +(-251.800 + 104.299i) q^{61} +146.042 q^{63} +460.131 q^{65} +(418.173 - 173.213i) q^{67} +(416.801 - 1006.25i) q^{69} +(28.0923 + 28.0923i) q^{71} +(-333.018 + 333.018i) q^{73} +(-18.2285 - 7.55047i) q^{75} +(-189.319 - 457.056i) q^{77} +38.8621i q^{79} +889.794i q^{81} +(-229.913 - 555.060i) q^{83} +(1339.64 + 554.897i) q^{85} +(880.801 - 880.801i) q^{87} +(-872.568 - 872.568i) q^{89} +(-262.859 + 634.599i) q^{91} +(-1191.55 + 493.557i) q^{93} +397.776 q^{95} -51.1346 q^{97} +(-246.112 + 101.943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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