LMFDB - Embedded newform 124.4.e.c.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,4,Mod(5,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("124.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	124.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.31623684071$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 29x^{6} - 58x^{5} + 824x^{4} - 1198x^{3} + 1933x^{2} + 129x + 9 $ x^8 - x^7 + 29x^6 - 58x^5 + 824x^4 - 1198x^3 + 1933x^2 + 129x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			5.4
Root			$0.833026 - 1.44284i$ of defining polynomial
Character	$\chi$	$=$	124.5
Dual form			124.4.e.c.25.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00416 - 6.93540i) q^{3} +(-3.98613 - 6.90419i) q^{5} +(3.19423 - 5.53257i) q^{7} +(-18.5665 - 32.1582i) q^{9} +O(q^{10})$	\(q+(4.00416 - 6.93540i) q^{3} +(-3.98613 - 6.90419i) q^{5} +(3.19423 - 5.53257i) q^{7} +(-18.5665 - 32.1582i) q^{9} +(2.85844 + 4.95096i) q^{11} +(-12.2243 - 21.1730i) q^{13} -63.8444 q^{15} +(-3.04991 + 5.28260i) q^{17} +(-26.3686 + 45.6718i) q^{19} +(-25.5804 - 44.3066i) q^{21} -67.4468 q^{23} +(30.7215 - 53.2111i) q^{25} -81.1488 q^{27} +128.400 q^{29} +(41.5805 - 167.517i) q^{31} +45.7825 q^{33} -50.9305 q^{35} +(119.262 - 206.567i) q^{37} -195.791 q^{39} +(4.18298 + 7.24513i) q^{41} +(-0.491871 + 0.851945i) q^{43} +(-148.017 + 256.374i) q^{45} +513.177 q^{47} +(151.094 + 261.702i) q^{49} +(24.4246 + 42.3047i) q^{51} +(302.794 + 524.455i) q^{53} +(22.7882 - 39.4704i) q^{55} +(211.168 + 365.754i) q^{57} +(-229.385 + 397.306i) q^{59} +16.2670 q^{61} -237.223 q^{63} +(-97.4551 + 168.797i) q^{65} +(-58.8933 - 102.006i) q^{67} +(-270.067 + 467.771i) q^{69} +(-238.899 - 413.785i) q^{71} +(498.097 + 862.728i) q^{73} +(-246.027 - 426.131i) q^{75} +36.5220 q^{77} +(528.137 - 914.759i) q^{79} +(176.364 - 305.472i) q^{81} +(-128.319 - 222.256i) q^{83} +48.6294 q^{85} +(514.133 - 890.504i) q^{87} +393.355 q^{89} -156.188 q^{91} +(-995.306 - 959.143i) q^{93} +420.435 q^{95} +350.552 q^{97} +(106.143 - 183.844i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{5} - 32 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 16 * q^5 - 32 * q^7 - 4 * q^9	$ 8 q - 16 q^{5} - 32 q^{7} - 4 q^{9} - 80 q^{11} - 28 q^{13} - 304 q^{15} - 8 q^{17} - 56 q^{19} - 76 q^{21} - 624 q^{23} - 48 q^{25} - 432 q^{27} - 216 q^{29} + 528 q^{31} + 584 q^{33} + 592 q^{35} + 96 q^{37} + 128 q^{39} + 552 q^{41} - 112 q^{43} + 524 q^{45} - 304 q^{47} - 4 q^{49} - 232 q^{51} + 1316 q^{53} - 208 q^{55} + 464 q^{57} + 224 q^{59} + 2664 q^{61} - 1856 q^{63} + 504 q^{65} - 272 q^{67} + 496 q^{69} + 1120 q^{71} + 248 q^{73} - 912 q^{75} + 624 q^{77} + 824 q^{79} + 104 q^{81} + 1616 q^{83} - 2232 q^{85} + 456 q^{87} + 184 q^{89} - 6928 q^{91} - 1960 q^{93} + 544 q^{95} + 2520 q^{97} + 1336 q^{99}+O(q^{100}) $ 8 * q - 16 * q^5 - 32 * q^7 - 4 * q^9 - 80 * q^11 - 28 * q^13 - 304 * q^15 - 8 * q^17 - 56 * q^19 - 76 * q^21 - 624 * q^23 - 48 * q^25 - 432 * q^27 - 216 * q^29 + 528 * q^31 + 584 * q^33 + 592 * q^35 + 96 * q^37 + 128 * q^39 + 552 * q^41 - 112 * q^43 + 524 * q^45 - 304 * q^47 - 4 * q^49 - 232 * q^51 + 1316 * q^53 - 208 * q^55 + 464 * q^57 + 224 * q^59 + 2664 * q^61 - 1856 * q^63 + 504 * q^65 - 272 * q^67 + 496 * q^69 + 1120 * q^71 + 248 * q^73 - 912 * q^75 + 624 * q^77 + 824 * q^79 + 104 * q^81 + 1616 * q^83 - 2232 * q^85 + 456 * q^87 + 184 * q^89 - 6928 * q^91 - 1960 * q^93 + 544 * q^95 + 2520 * q^97 + 1336 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.00416	−	6.93540i	0.770600	−	1.33472i	−0.166634	−	0.986019i	$-0.553290\pi$
$3$	4.00416	−	6.93540i	0.770600	−	1.33472i	0.937234	−	0.348700i	$-0.113377\pi$
$4$		0			0
$5$	−3.98613	−	6.90419i	−0.356531	−	0.617529i	0.630848	−	0.775906i	$-0.282707\pi$
$5$	−3.98613	−	6.90419i	−0.356531	−	0.617529i	−0.987379	+	0.158377i	$0.949374\pi$
$6$		0			0
$7$	3.19423	−	5.53257i	0.172472	−	0.298731i	−0.766811	−	0.641873i	$-0.778158\pi$
$7$	3.19423	−	5.53257i	0.172472	−	0.298731i	0.939284	+	0.343142i	$0.111491\pi$
$8$		0			0
$9$	−18.5665	−	32.1582i	−0.687649	−	1.19104i
$10$		0			0
$11$	2.85844	+	4.95096i	0.0783501	+	0.135706i	0.902538	−	0.430610i	$-0.141701\pi$
$11$	2.85844	+	4.95096i	0.0783501	+	0.135706i	−0.824188	+	0.566316i	$0.808368\pi$
$12$		0			0
$13$	−12.2243	−	21.1730i	−0.260800	−	0.451719i	0.705655	−	0.708556i	$-0.250653\pi$
$13$	−12.2243	−	21.1730i	−0.260800	−	0.451719i	−0.966455	+	0.256837i	$0.917320\pi$
$14$		0			0
$15$	−63.8444			−1.09897
$16$		0			0
$17$	−3.04991	+	5.28260i	−0.0435124	+	0.0753658i	−0.886961	−	0.461844i	$-0.847188\pi$
$17$	−3.04991	+	5.28260i	−0.0435124	+	0.0753658i	0.843449	+	0.537209i	$0.180521\pi$
$18$		0			0
$19$	−26.3686	+	45.6718i	−0.318388	+	0.551464i	−0.980152	−	0.198248i	$-0.936475\pi$
$19$	−26.3686	+	45.6718i	−0.318388	+	0.551464i	0.661764	+	0.749712i	$0.269808\pi$
$20$		0			0
$21$	−25.5804	−	44.3066i	−0.265814	−	0.460404i
$22$		0			0
$23$	−67.4468			−0.611462			−0.305731	−	0.952118i	$-0.598901\pi$
$23$	−67.4468			−0.611462			−0.305731	+	0.952118i	$0.598901\pi$
$24$		0			0
$25$	30.7215	−	53.2111i	0.245772	−	0.425689i
$26$		0			0
$27$	−81.1488			−0.578411
$28$		0			0
$29$	128.400			0.822181			0.411091	−	0.911595i	$-0.365148\pi$
$29$	128.400			0.822181			0.411091	+	0.911595i	$0.365148\pi$
$30$		0			0
$31$	41.5805	−	167.517i	0.240906	−	0.970549i
$31$	41.5805	−	167.517i	0.240906	−	0.970549i
$32$		0			0
$33$	45.7825			0.241506
$34$		0			0
$35$	−50.9305			−0.245967
$36$		0			0
$37$	119.262	−	206.567i	0.529905	−	0.917822i	−0.469487	−	0.882939i	$-0.655561\pi$
$37$	119.262	−	206.567i	0.529905	−	0.917822i	0.999391	−	0.0348823i	$-0.0111056\pi$
$38$		0			0
$39$	−195.791			−0.803890
$40$		0			0
$41$	4.18298	+	7.24513i	0.0159334	+	0.0275975i	0.873882	−	0.486138i	$-0.161595\pi$
$41$	4.18298	+	7.24513i	0.0159334	+	0.0275975i	−0.857949	+	0.513735i	$0.828261\pi$
$42$		0			0
$43$	−0.491871	+	0.851945i	−0.00174441	+	0.00302140i	−0.866896	−	0.498489i	$-0.833889\pi$
$43$	−0.491871	+	0.851945i	−0.00174441	+	0.00302140i	0.865152	+	0.501510i	$0.167222\pi$
$44$		0			0
$45$	−148.017	+	256.374i	−0.490336	+	0.849287i
$46$		0			0
$47$	513.177			1.59265			0.796324	−	0.604870i	$-0.206775\pi$
$47$	513.177			1.59265			0.796324	+	0.604870i	$0.206775\pi$
$48$		0			0
$49$	151.094	+	261.702i	0.440507	+	0.762980i
$50$		0			0
$51$	24.4246	+	42.3047i	0.0670614	+	0.116154i
$52$		0			0
$53$	302.794	+	524.455i	0.784754	+	1.35923i	0.929146	+	0.369713i	$0.120544\pi$
$53$	302.794	+	524.455i	0.784754	+	1.35923i	−0.144392	+	0.989521i	$0.546123\pi$
$54$		0			0
$55$	22.7882	−	39.4704i	0.0558684	−	0.0967670i
$56$		0			0
$57$	211.168	+	365.754i	0.490700	+	0.849917i
$58$		0			0
$59$	−229.385	+	397.306i	−0.506158	+	0.876691i	0.493817	+	0.869566i	$0.335601\pi$
$59$	−229.385	+	397.306i	−0.506158	+	0.876691i	−0.999975	+	0.00712527i	$0.997732\pi$
$60$		0			0
$61$	16.2670			0.0341440			0.0170720	−	0.999854i	$-0.494566\pi$
$61$	16.2670			0.0341440			0.0170720	+	0.999854i	$0.494566\pi$
$62$		0			0
$63$	−237.223			−0.474402
$64$		0			0
$65$	−97.4551	+	168.797i	−0.185966	+	0.322103i
$66$		0			0
$67$	−58.8933	−	102.006i	−0.107388	−	0.186001i	0.807324	−	0.590109i	$-0.200915\pi$
$67$	−58.8933	−	102.006i	−0.107388	−	0.186001i	−0.914711	+	0.404108i	$0.867582\pi$
$68$		0			0
$69$	−270.067	+	467.771i	−0.471193	+	0.816130i
$70$		0			0
$71$	−238.899	−	413.785i	−0.399325	−	0.691651i	0.594318	−	0.804230i	$-0.297422\pi$
$71$	−238.899	−	413.785i	−0.399325	−	0.691651i	−0.993643	+	0.112579i	$0.964089\pi$
$72$		0			0
$73$	498.097	+	862.728i	0.798600	+	1.38322i	0.920528	+	0.390677i	$0.127759\pi$
$73$	498.097	+	862.728i	0.798600	+	1.38322i	−0.121928	+	0.992539i	$0.538908\pi$
$74$		0			0
$75$	−246.027	−	426.131i	−0.378783	−	0.656072i
$76$		0			0
$77$	36.5220			0.0540529
$78$		0			0
$79$	528.137	−	914.759i	0.752152	−	1.30277i	−0.194626	−	0.980878i	$-0.562349\pi$
$79$	528.137	−	914.759i	0.752152	−	1.30277i	0.946778	−	0.321888i	$-0.104317\pi$
$80$		0			0
$81$	176.364	−	305.472i	0.241926	−	0.419028i
$82$		0			0
$83$	−128.319	−	222.256i	−0.169697	−	0.293924i	0.768616	−	0.639710i	$-0.220946\pi$
$83$	−128.319	−	222.256i	−0.169697	−	0.293924i	−0.938313	+	0.345786i	$0.887612\pi$
$84$		0			0
$85$	48.6294			0.0620541
$86$		0			0
$87$	514.133	−	890.504i	0.633573	−	1.09738i
$88$		0			0
$89$	393.355			0.468489			0.234245	−	0.972178i	$-0.424738\pi$
$89$	393.355			0.468489			0.234245	+	0.972178i	$0.424738\pi$
$90$		0			0
$91$	−156.188			−0.179923
$92$		0			0
$93$	−995.306	−	959.143i	−1.10977	−	1.06945i
$94$		0			0
$95$	420.435			0.454061
$96$		0			0
$97$	350.552			0.366940			0.183470	−	0.983025i	$-0.441267\pi$
$97$	350.552			0.366940			0.183470	+	0.983025i	$0.441267\pi$
$98$		0			0
$99$	106.143	−	183.844i	0.107755	−	0.186637i
$100$		0			0
$101$	−1080.75			−1.06474			−0.532369	−	0.846513i	$-0.678698\pi$
$101$	−1080.75			−1.06474			−0.532369	+	0.846513i	$0.678698\pi$
$102$		0			0
$103$	−683.841	−	1184.45i	−0.654183	−	1.13308i	−0.982098	−	0.188371i	$-0.939679\pi$
$103$	−683.841	−	1184.45i	−0.654183	−	1.13308i	0.327915	−	0.944707i	$-0.393654\pi$
$104$		0			0
$105$	−203.934	+	353.224i	−0.189542	+	0.328296i
$106$		0			0
$107$	−763.256	+	1322.00i	−0.689596	+	1.19442i	0.282373	+	0.959305i	$0.408878\pi$
$107$	−763.256	+	1322.00i	−0.689596	+	1.19442i	−0.971969	+	0.235110i	$0.924455\pi$
$108$		0			0
$109$	278.502			0.244730			0.122365	−	0.992485i	$-0.460952\pi$
$109$	278.502			0.244730			0.122365	+	0.992485i	$0.460952\pi$
$110$		0			0
$111$	−955.083	−	1654.25i	−0.816689	−	1.41455i
$112$		0			0
$113$	167.729	+	290.515i	0.139634	+	0.241852i	0.927358	−	0.374175i	$-0.122074\pi$
$113$	167.729	+	290.515i	0.139634	+	0.241852i	−0.787724	+	0.616028i	$0.788741\pi$
$114$		0			0
$115$	268.852	+	465.665i	0.218005	+	0.377596i
$116$		0			0
$117$	−453.924	+	786.220i	−0.358678	+	0.621248i
$118$		0			0
$119$	19.4842	+	33.7477i	0.0150094	+	0.0259970i
$120$		0			0
$121$	649.159	−	1124.38i	0.487723	−	0.844760i
$122$		0			0
$123$	66.9972			0.0491133
$124$		0			0
$125$	−1486.37			−1.06356
$126$		0			0
$127$	−461.247	+	798.903i	−0.322276	+	0.558198i	−0.980957	−	0.194224i	$-0.937781\pi$
$127$	−461.247	+	798.903i	−0.322276	+	0.558198i	0.658681	+	0.752422i	$0.271115\pi$
$128$		0			0
$129$	3.93905	+	6.82264i	0.00268848	+	0.00465659i
$130$		0			0
$131$	−1063.92	+	1842.76i	−0.709579	+	1.22903i	0.255435	+	0.966826i	$0.417781\pi$
$131$	−1063.92	+	1842.76i	−0.709579	+	1.22903i	−0.965014	+	0.262200i	$0.915552\pi$
$132$		0			0
$133$	168.455	+	291.772i	0.109826	+	0.190225i
$134$		0			0
$135$	323.470	+	560.266i	0.206221	+	0.357186i
$136$		0			0
$137$	588.170	+	1018.74i	0.366794	+	0.635306i	0.989062	−	0.147498i	$-0.0471220\pi$
$137$	588.170	+	1018.74i	0.366794	+	0.635306i	−0.622268	+	0.782804i	$0.713789\pi$
$138$		0			0
$139$	−2110.65			−1.28794			−0.643968	−	0.765053i	$-0.722713\pi$
$139$	−2110.65			−1.28794			−0.643968	+	0.765053i	$0.722713\pi$
$140$		0			0
$141$	2054.84	−	3559.09i	1.22730	−	2.12574i
$142$		0			0
$143$	69.8845	−	121.044i	0.0408674	−	0.0707844i
$144$		0			0
$145$	−511.819	−	886.497i	−0.293133	−	0.507721i
$146$		0			0
$147$	2420.01			1.35782
$148$		0			0
$149$	531.462	−	920.519i	0.292208	−	0.506120i	−0.682123	−	0.731237i	$-0.738943\pi$
$149$	531.462	−	920.519i	0.292208	−	0.506120i	0.974332	+	0.225117i	$0.0722766\pi$
$150$		0			0
$151$	−1427.95			−0.769567			−0.384783	−	0.923007i	$-0.625724\pi$
$151$	−1427.95			−0.769567			−0.384783	+	0.923007i	$0.625724\pi$
$152$		0			0
$153$	226.505			0.119685
$154$		0			0
$155$	−1322.32	+	380.667i	−0.685232	+	0.197264i
$156$		0			0
$157$	2818.55			1.43277			0.716386	−	0.697704i	$-0.245795\pi$
$157$	2818.55			1.43277			0.716386	+	0.697704i	$0.245795\pi$
$158$		0			0
$159$	4849.74			2.41893
$160$		0			0
$161$	−215.441	+	373.154i	−0.105460	+	0.182662i
$162$		0			0
$163$	714.140			0.343164			0.171582	−	0.985170i	$-0.445112\pi$
$163$	714.140			0.343164			0.171582	+	0.985170i	$0.445112\pi$
$164$		0			0
$165$	−182.495	−	316.091i	−0.0861045	−	0.149137i
$166$		0			0
$167$	−1346.24	+	2331.75i	−0.623803	+	1.08046i	0.364968	+	0.931020i	$0.381080\pi$
$167$	−1346.24	+	2331.75i	−0.623803	+	1.08046i	−0.988771	+	0.149438i	$0.952254\pi$
$168$		0			0
$169$	799.635	−	1385.01i	0.363967	−	0.630409i
$170$		0			0
$171$	1958.29			0.875758
$172$		0			0
$173$	−415.219	−	719.181i	−0.182477	−	0.316060i	0.760246	−	0.649635i	$-0.225078\pi$
$173$	−415.219	−	719.181i	−0.182477	−	0.316060i	−0.942723	+	0.333575i	$0.891745\pi$
$174$		0			0
$175$	−196.263	−	339.937i	−0.0847776	−	0.146839i
$176$		0			0
$177$	1836.98	+	3181.75i	0.780091	+	1.35116i
$178$		0			0
$179$	−2302.48	+	3988.01i	−0.961426	+	1.66524i	−0.242501	+	0.970151i	$0.577968\pi$
$179$	−2302.48	+	3988.01i	−0.961426	+	1.66524i	−0.718925	+	0.695088i	$0.755365\pi$
$180$		0			0
$181$	−1772.97	−	3070.87i	−0.728087	−	1.26108i	−0.957691	−	0.287800i	$-0.907076\pi$
$181$	−1772.97	−	3070.87i	−0.728087	−	1.26108i	0.229604	−	0.973284i	$-0.426257\pi$
$182$		0			0
$183$	65.1358	−	112.818i	0.0263113	−	0.0455726i
$184$		0			0
$185$	−1901.57			−0.755709
$186$		0			0
$187$	−34.8719			−0.0136368
$188$		0			0
$189$	−259.208	+	448.961i	−0.0997598	+	0.172789i
$190$		0			0
$191$	838.291	+	1451.96i	0.317574	+	0.550054i	0.979981	−	0.199090i	$-0.0637985\pi$
$191$	838.291	+	1451.96i	0.317574	+	0.550054i	−0.662407	+	0.749144i	$0.730465\pi$
$192$		0			0
$193$	−2506.13	+	4340.75i	−0.934691	+	1.61893i	−0.159508	+	0.987197i	$0.550991\pi$
$193$	−2506.13	+	4340.75i	−0.934691	+	1.61893i	−0.775183	+	0.631736i	$0.782343\pi$
$194$		0			0
$195$	780.451	+	1351.78i	0.286611	+	0.496426i
$196$		0			0
$197$	1779.43	+	3082.07i	0.643549	+	1.11466i	0.984635	+	0.174628i	$0.0558722\pi$
$197$	1779.43	+	3082.07i	0.643549	+	1.11466i	−0.341085	+	0.940032i	$0.610794\pi$
$198$		0			0
$199$	241.222	+	417.809i	0.0859286	+	0.148833i	0.905787	−	0.423734i	$-0.139281\pi$
$199$	241.222	+	417.809i	0.0859286	+	0.148833i	−0.819858	+	0.572567i	$0.805948\pi$
$200$		0			0
$201$	−943.272			−0.331011
$202$		0			0
$203$	410.139	−	710.381i	0.141803	−	0.245611i
$204$		0			0
$205$	33.3478	−	57.7601i	0.0113615	−	0.0196787i
$206$		0			0
$207$	1252.25	+	2168.97i	0.420471	+	0.728278i
$208$		0			0
$209$	−301.492			−0.0997830
$210$		0			0
$211$	2298.97	−	3981.94i	0.750084	−	1.29918i	−0.197697	−	0.980263i	$-0.563346\pi$
$211$	2298.97	−	3981.94i	0.750084	−	1.29918i	0.947781	−	0.318921i	$-0.103321\pi$
$212$		0			0
$213$	−3826.35			−1.23088
$214$		0			0
$215$	7.84265			0.00248774
$216$		0			0
$217$	−793.984	−	765.136i	−0.248383	−	0.239359i
$218$		0			0
$219$	7977.82			2.46160
$220$		0			0
$221$	149.131			0.0453922
$222$		0			0
$223$	−225.767	+	391.040i	−0.0677960	+	0.117426i	−0.897931	−	0.440137i	$-0.854930\pi$
$223$	−225.767	+	391.040i	−0.0677960	+	0.117426i	0.830135	+	0.557563i	$0.188263\pi$
$224$		0			0
$225$	−2281.56			−0.676019
$226$		0			0
$227$	−702.544	−	1216.84i	−0.205416	−	0.355791i	0.744849	−	0.667233i	$-0.232521\pi$
$227$	−702.544	−	1216.84i	−0.205416	−	0.355791i	−0.950265	+	0.311442i	$0.899188\pi$
$228$		0			0
$229$	−837.027	+	1449.77i	−0.241538	+	0.418357i	−0.961153	−	0.276017i	$-0.910985\pi$
$229$	−837.027	+	1449.77i	−0.241538	+	0.418357i	0.719614	+	0.694374i	$0.244319\pi$
$230$		0			0
$231$	146.240	−	253.295i	0.0416532	−	0.0721454i
$232$		0			0
$233$	1318.84			0.370815			0.185408	−	0.982662i	$-0.440639\pi$
$233$	1318.84			0.370815			0.185408	+	0.982662i	$0.440639\pi$
$234$		0			0
$235$	−2045.59	−	3543.07i	−0.567828	−	0.983507i
$236$		0			0
$237$	−4229.48	−	7325.68i	−1.15922	−	2.00782i
$238$		0			0
$239$	931.393	+	1613.22i	0.252079	+	0.436613i	0.964098	−	0.265547i	$-0.0855524\pi$
$239$	931.393	+	1613.22i	0.252079	+	0.436613i	−0.712019	+	0.702160i	$0.752219\pi$
$240$		0			0
$241$	−310.917	+	538.525i	−0.0831035	+	0.143940i	−0.904582	−	0.426301i	$-0.859817\pi$
$241$	−310.917	+	538.525i	−0.0831035	+	0.143940i	0.821478	+	0.570240i	$0.193150\pi$
$242$		0			0
$243$	−2507.89	−	4343.79i	−0.662062	−	1.14672i
$244$		0			0
$245$	1204.56	−	2086.36i	0.314108	−	0.544052i
$246$		0			0
$247$	1289.35			0.332142
$248$		0			0
$249$	−2055.24			−0.523075
$250$		0			0
$251$	−230.902	+	399.934i	−0.0580653	+	0.100572i	−0.893597	−	0.448870i	$-0.851827\pi$
$251$	−230.902	+	399.934i	−0.0580653	+	0.100572i	0.835532	+	0.549442i	$0.185160\pi$
$252$		0			0
$253$	−192.792	−	333.926i	−0.0479081	−	0.0829793i
$254$		0			0
$255$	194.720	−	337.264i	0.0478189	−	0.0828247i
$256$		0			0
$257$	727.099	+	1259.37i	0.176479	+	0.305671i	0.940672	−	0.339317i	$-0.110196\pi$
$257$	727.099	+	1259.37i	0.176479	+	0.305671i	−0.764193	+	0.644988i	$0.776862\pi$
$258$		0			0
$259$	−761.898	−	1319.65i	−0.182788	−	0.316598i
$260$		0			0
$261$	−2383.94	−	4129.10i	−0.565372	−	0.979254i
$262$		0			0
$263$	−5677.68			−1.33118			−0.665591	−	0.746317i	$-0.731820\pi$
$263$	−5677.68			−1.33118			−0.665591	+	0.746317i	$0.731820\pi$
$264$		0			0
$265$	2413.96	−	4181.09i	0.559578	−	0.969217i
$266$		0			0
$267$	1575.05	−	2728.07i	0.361018	−	0.625301i
$268$		0			0
$269$	−1645.37	−	2849.86i	−0.372936	−	0.645945i	0.617079	−	0.786901i	$-0.288316\pi$
$269$	−1645.37	−	2849.86i	−0.372936	−	0.645945i	−0.990016	+	0.140956i	$0.954982\pi$
$270$		0			0
$271$	799.362			0.179180			0.0895900	−	0.995979i	$-0.471444\pi$
$271$	799.362			0.179180			0.0895900	+	0.995979i	$0.471444\pi$
$272$		0			0
$273$	−625.403	+	1083.23i	−0.138649	+	0.240147i
$274$		0			0
$275$	351.261			0.0770250
$276$		0			0
$277$	1497.42			0.324806			0.162403	−	0.986725i	$-0.448076\pi$
$277$	1497.42			0.324806			0.162403	+	0.986725i	$0.448076\pi$
$278$		0			0
$279$	−6159.06	+	1773.06i	−1.32162	+	0.380468i
$280$		0			0
$281$	6084.49			1.29171			0.645855	−	0.763460i	$-0.276501\pi$
$281$	6084.49			1.29171			0.645855	+	0.763460i	$0.276501\pi$
$282$		0			0
$283$	−852.750			−0.179119			−0.0895595	−	0.995981i	$-0.528546\pi$
$283$	−852.750			−0.179119			−0.0895595	+	0.995981i	$0.528546\pi$
$284$		0			0
$285$	1683.49	−	2915.89i	0.349899	−	0.606043i
$286$		0			0
$287$	53.4456			0.0109923
$288$		0			0
$289$	2437.90	+	4222.56i	0.496213	+	0.859467i
$290$		0			0
$291$	1403.67	−	2431.22i	0.282764	−	0.489762i
$292$		0			0
$293$	−3862.14	+	6689.41i	−0.770063	+	1.33379i	0.167465	+	0.985878i	$0.446442\pi$
$293$	−3862.14	+	6689.41i	−0.770063	+	1.33379i	−0.937528	+	0.347910i	$0.886892\pi$
$294$		0			0
$295$	3657.43			0.721843
$296$		0			0
$297$	−231.959	−	401.764i	−0.0453185	−	0.0784940i
$298$		0			0
$299$	824.487	+	1428.05i	0.159469	+	0.276209i
$300$		0			0
$301$	3.14230	+	5.44262i	0.000601724	+	0.00104222i
$302$		0			0
$303$	−4327.48	+	7495.42i	−0.820487	+	1.42112i
$304$		0			0
$305$	−64.8426	−	112.311i	−0.0121734	−	0.0210849i
$306$		0			0
$307$	−2871.50	+	4973.58i	−0.533828	+	0.924617i	0.465391	+	0.885105i	$0.345914\pi$
$307$	−2871.50	+	4973.58i	−0.533828	+	0.924617i	−0.999219	+	0.0395118i	$0.987420\pi$
$308$		0			0
$309$	−10952.8			−2.01646
$310$		0			0
$311$	−2392.04			−0.436142			−0.218071	−	0.975933i	$-0.569977\pi$
$311$	−2392.04			−0.436142			−0.218071	+	0.975933i	$0.569977\pi$
$312$		0			0
$313$	1082.54	−	1875.01i	0.195491	−	0.338600i	−0.751570	−	0.659653i	$-0.770703\pi$
$313$	1082.54	−	1875.01i	0.195491	−	0.338600i	0.947061	+	0.321053i	$0.104037\pi$
$314$		0			0
$315$	945.604	+	1637.83i	0.169139	+	0.292957i
$316$		0			0
$317$	3302.53	−	5720.15i	0.585137	−	1.01349i	−0.409721	−	0.912211i	$-0.634374\pi$
$317$	3302.53	−	5720.15i	0.585137	−	1.01349i	0.994858	−	0.101276i	$-0.0322926\pi$
$318$		0			0
$319$	367.023	+	635.702i	0.0644180	+	0.111575i
$320$		0			0
$321$	6112.39	+	10587.0i	1.06281	+	1.84083i
$322$		0			0
$323$	−160.844	−	278.589i	−0.0277077	−	0.0479911i
$324$		0			0
$325$	−1502.19			−0.256389
$326$		0			0
$327$	1115.16	−	1931.52i	0.188589	−	0.326646i
$328$		0			0
$329$	1639.20	−	2839.19i	0.274688	−	0.475773i
$330$		0			0
$331$	3720.05	+	6443.31i	0.617741	+	1.06996i	0.989897	+	0.141789i	$0.0452854\pi$
$331$	3720.05	+	6443.31i	0.617741	+	1.06996i	−0.372156	+	0.928170i	$0.621381\pi$
$332$		0			0
$333$	−8857.09			−1.45755
$334$		0			0
$335$	−469.513	+	813.221i	−0.0765739	+	0.132630i
$336$		0			0
$337$	8500.92			1.37411			0.687055	−	0.726606i	$-0.258903\pi$
$337$	8500.92			1.37411			0.687055	+	0.726606i	$0.258903\pi$
$338$		0			0
$339$	2686.45			0.430407
$340$		0			0
$341$	948.227	−	272.975i	0.150585	−	0.0433502i
$342$		0			0
$343$	4121.76			0.648845
$344$		0			0
$345$	4306.10			0.671979
$346$		0			0
$347$	3588.74	−	6215.87i	0.555197	−	0.961630i	−0.442691	−	0.896674i	$-0.645976\pi$
$347$	3588.74	−	6215.87i	0.555197	−	0.961630i	0.997888	−	0.0649557i	$-0.0206906\pi$
$348$		0			0
$349$	−2411.06			−0.369802			−0.184901	−	0.982757i	$-0.559196\pi$
$349$	−2411.06			−0.369802			−0.184901	+	0.982757i	$0.559196\pi$
$350$		0			0
$351$	991.983	+	1718.17i	0.150849	+	0.261279i
$352$		0			0
$353$	1123.91	−	1946.67i	0.169461	−	0.293516i	−0.768769	−	0.639526i	$-0.779131\pi$
$353$	1123.91	−	1946.67i	0.169461	−	0.293516i	0.938231	+	0.346011i	$0.112464\pi$
$354$		0			0
$355$	−1904.57	+	3298.80i	−0.284743	+	0.493190i
$356$		0			0
$357$	312.072			0.0462649
$358$		0			0
$359$	3819.15	+	6614.96i	0.561468	+	0.972491i	0.997369	+	0.0724960i	$0.0230965\pi$
$359$	3819.15	+	6614.96i	0.561468	+	0.972491i	−0.435901	+	0.899995i	$0.643570\pi$
$360$		0			0
$361$	2038.89	+	3531.47i	0.297258	+	0.514866i
$362$		0			0
$363$	−5198.67	−	9004.35i	−0.751678	−	1.30194i
$364$		0			0
$365$	3970.96	−	6877.90i	0.569451	−	0.986318i
$366$		0			0
$367$	−1477.65	−	2559.37i	−0.210171	−	0.364028i	0.741597	−	0.670846i	$-0.234069\pi$
$367$	−1477.65	−	2559.37i	−0.210171	−	0.364028i	−0.951768	+	0.306819i	$0.900736\pi$
$368$		0			0
$369$	155.327	−	269.034i	0.0219133	−	0.0379549i
$370$		0			0
$371$	3868.78			0.541393
$372$		0			0
$373$	−2019.14			−0.280288			−0.140144	−	0.990131i	$-0.544756\pi$
$373$	−2019.14			−0.280288			−0.140144	+	0.990131i	$0.544756\pi$
$374$		0			0
$375$	−5951.67	+	10308.6i	−0.819581	+	1.41956i
$376$		0			0
$377$	−1569.59	−	2718.61i	−0.214425	−	0.371395i
$378$		0			0
$379$	4409.28	−	7637.10i	0.597598	−	1.03507i	−0.395577	−	0.918433i	$-0.629455\pi$
$379$	4409.28	−	7637.10i	0.597598	−	1.03507i	0.993175	−	0.116637i	$-0.0372113\pi$
$380$		0			0
$381$	3693.81	+	6397.86i	0.496692	+	0.860295i
$382$		0			0
$383$	621.332	+	1076.18i	0.0828945	+	0.143577i	0.904492	−	0.426490i	$-0.140250\pi$
$383$	621.332	+	1076.18i	0.0828945	+	0.143577i	−0.821598	+	0.570068i	$0.806917\pi$
$384$		0			0
$385$	−145.582	−	252.155i	−0.0192715	−	0.0333792i
$386$		0			0
$387$	36.5293			0.00479817
$388$		0			0
$389$	3420.83	−	5925.04i	0.445868	−	0.772266i	−0.552244	−	0.833683i	$-0.686228\pi$
$389$	3420.83	−	5925.04i	0.445868	−	0.772266i	0.998112	+	0.0614161i	$0.0195617\pi$
$390$		0			0
$391$	205.707	−	356.294i	0.0266062	−	0.0460833i
$392$		0			0
$393$	8520.17	+	14757.4i	1.09360	+	1.89418i
$394$		0			0
$395$	−8420.89			−1.07266
$396$		0			0
$397$	−275.828	+	477.748i	−0.0348700	+	0.0603967i	−0.882934	−	0.469498i	$-0.844435\pi$
$397$	−275.828	+	477.748i	−0.0348700	+	0.0603967i	0.848064	+	0.529894i	$0.177768\pi$
$398$		0			0
$399$	2698.08			0.338528
$400$		0			0
$401$	9005.19			1.12144			0.560720	−	0.828005i	$-0.310524\pi$
$401$	9005.19			1.12144			0.560720	+	0.828005i	$0.310524\pi$
$402$		0			0
$403$	−4055.14	+	1167.39i	−0.501243	+	0.144297i
$404$		0			0
$405$	−2812.04			−0.345016
$406$		0			0
$407$	1363.61			0.166072
$408$		0			0
$409$	1551.97	−	2688.08i	0.187628	−	0.324981i	−0.756831	−	0.653611i	$-0.773253\pi$
$409$	1551.97	−	2688.08i	0.187628	−	0.324981i	0.944459	+	0.328630i	$0.106587\pi$
$410$		0			0
$411$	9420.50			1.13061
$412$		0			0
$413$	1465.41	+	2538.17i	0.174596	+	0.302410i
$414$		0			0
$415$	−1023.00	+	1771.88i	−0.121005	+	0.209586i
$416$		0			0
$417$	−8451.37	+	14638.2i	−0.992483	+	1.71903i
$418$		0			0
$419$	−9848.32			−1.14826			−0.574131	−	0.818764i	$-0.694660\pi$
$419$	−9848.32			−1.14826			−0.574131	+	0.818764i	$0.694660\pi$
$420$		0			0
$421$	6549.07	+	11343.3i	0.758153	+	1.31316i	0.943792	+	0.330541i	$0.107231\pi$
$421$	6549.07	+	11343.3i	0.758153	+	1.31316i	−0.185639	+	0.982618i	$0.559435\pi$
$422$		0			0
$423$	−9527.91	−	16502.8i	−1.09518	−	1.89691i
$424$		0			0
$425$	187.395	+	324.578i	0.0213883	+	0.0370455i
$426$		0			0
$427$	51.9607	−	89.9985i	0.00588888	−	0.0101998i
$428$		0			0
$429$	−559.657	−	969.355i	−0.0629848	−	0.109093i
$430$		0			0
$431$	−2230.30	+	3863.00i	−0.249257	+	0.431726i	−0.963320	−	0.268356i	$-0.913520\pi$
$431$	−2230.30	+	3863.00i	−0.249257	+	0.431726i	0.714063	+	0.700082i	$0.246853\pi$
$432$		0			0
$433$	−13605.8			−1.51005			−0.755025	−	0.655696i	$-0.772375\pi$
$433$	−13605.8			−1.51005			−0.755025	+	0.655696i	$0.772375\pi$
$434$		0			0
$435$	−8197.61			−0.903553
$436$		0			0
$437$	1778.48	−	3080.41i	0.194682	−	0.337200i
$438$		0			0
$439$	1665.65	+	2884.99i	0.181087	+	0.313652i	0.942251	−	0.334908i	$-0.108705\pi$
$439$	1665.65	+	2884.99i	0.181087	+	0.313652i	−0.761164	+	0.648559i	$0.775372\pi$
$440$		0			0
$441$	5610.58	−	9717.80i	0.605828	−	1.04933i
$442$		0			0
$443$	−2496.42	−	4323.92i	−0.267739	−	0.463738i	0.700539	−	0.713614i	$-0.252943\pi$
$443$	−2496.42	−	4323.92i	−0.267739	−	0.463738i	−0.968278	+	0.249877i	$0.919610\pi$
$444$		0			0
$445$	−1567.97	−	2715.80i	−0.167031	−	0.289306i
$446$		0			0
$447$	−4256.11	−	7371.80i	−0.450352	−	0.780032i
$448$		0			0
$449$	−1862.58			−0.195770			−0.0978848	−	0.995198i	$-0.531208\pi$
$449$	−1862.58			−0.195770			−0.0978848	+	0.995198i	$0.531208\pi$
$450$		0			0
$451$	−23.9136	+	41.4195i	−0.00249677	+	0.00432454i
$452$		0			0
$453$	−5717.72	+	9903.38i	−0.593028	+	1.02716i
$454$		0			0
$455$	622.588	+	1078.35i	0.0641481	+	0.111108i
$456$		0			0
$457$	−14770.8			−1.51192			−0.755962	−	0.654615i	$-0.772831\pi$
$457$	−14770.8			−1.51192			−0.755962	+	0.654615i	$0.772831\pi$
$458$		0			0
$459$	247.496	−	428.676i	0.0251681	−	0.0435924i
$460$		0			0
$461$	4555.32			0.460222			0.230111	−	0.973164i	$-0.426091\pi$
$461$	4555.32			0.460222			0.230111	+	0.973164i	$0.426091\pi$
$462$		0			0
$463$	−8678.52			−0.871113			−0.435556	−	0.900161i	$-0.643448\pi$
$463$	−8678.52			−0.871113			−0.435556	+	0.900161i	$0.643448\pi$
$464$		0			0
$465$	−2654.68	+	10695.0i	−0.264748	+	1.06660i
$466$		0			0
$467$	2377.00			0.235534			0.117767	−	0.993041i	$-0.462426\pi$
$467$	2377.00			0.235534			0.117767	+	0.993041i	$0.462426\pi$
$468$		0			0
$469$	−752.475			−0.0740855
$470$		0			0
$471$	11285.9	−	19547.8i	1.10409	−	1.91235i
$472$		0			0
$473$	−5.62393			−0.000546698
$474$		0			0
$475$	1620.16	+	2806.21i	0.156502	+	0.271069i
$476$		0			0
$477$	11243.7	−	19474.6i	1.07927	−	1.86935i
$478$		0			0
$479$	8648.95	−	14980.4i	0.825012	−	1.42896i	−0.0768990	−	0.997039i	$-0.524502\pi$
$479$	8648.95	−	14980.4i	0.825012	−	1.42896i	0.901910	−	0.431923i	$-0.142165\pi$
$480$		0			0
$481$	−5831.53			−0.552796
$482$		0			0
$483$	1725.32	+	2988.33i	0.162535	+	0.281520i
$484$		0			0
$485$	−1397.35	−	2420.28i	−0.130825	−	0.226596i
$486$		0			0
$487$	−5889.88	−	10201.6i	−0.548041	−	0.949234i	−0.998409	−	0.0563912i	$-0.982041\pi$
$487$	−5889.88	−	10201.6i	−0.548041	−	0.949234i	0.450368	−	0.892843i	$-0.351293\pi$
$488$		0			0
$489$	2859.53	−	4952.85i	0.264442	−	0.458028i
$490$		0			0
$491$	−1367.17	−	2368.00i	−0.125661	−	0.217650i	0.796330	−	0.604862i	$-0.206772\pi$
$491$	−1367.17	−	2368.00i	−0.125661	−	0.217650i	−0.921991	+	0.387211i	$0.873438\pi$
$492$		0			0
$493$	−391.608	+	678.284i	−0.0357751	+	0.0619643i
$494$		0			0
$495$	−1692.39			−0.153672
$496$		0			0
$497$	−3052.39			−0.275490
$498$		0			0
$499$	3567.71	−	6179.45i	0.320065	−	0.554369i	−0.660436	−	0.750882i	$-0.729628\pi$
$499$	3567.71	−	6179.45i	0.320065	−	0.554369i	0.980501	+	0.196513i	$0.0629618\pi$
$500$		0			0
$501$	10781.1	+	18673.4i	0.961405	+	1.66520i
$502$		0			0
$503$	10673.8	−	18487.6i	0.946166	−	1.63881i	0.192767	−	0.981245i	$-0.438254\pi$
$503$	10673.8	−	18487.6i	0.946166	−	1.63881i	0.753399	−	0.657563i	$-0.228413\pi$
$504$		0			0
$505$	4308.01	+	7461.69i	0.379612	+	0.657507i
$506$		0			0
$507$	−6403.73	−	11091.6i	−0.560946	−	0.971587i
$508$		0			0
$509$	−9126.42	−	15807.4i	−0.794738	−	1.37653i	−0.923006	−	0.384786i	$-0.874275\pi$
$509$	−9126.42	−	15807.4i	−0.794738	−	1.37653i	0.128268	−	0.991740i	$-0.459058\pi$
$510$		0			0
$511$	6364.14			0.550945
$512$		0			0
$513$	2139.78	−	3706.21i	0.184159	−	0.318973i
$514$		0			0
$515$	−5451.77	+	9442.74i	−0.466473	+	0.807955i
$516$		0			0
$517$	1466.88	+	2540.72i	0.124784	+	0.216133i
$518$		0			0
$519$	−6650.41			−0.562468
$520$		0			0
$521$	3689.47	−	6390.36i	0.310247	−	0.537364i	−0.668169	−	0.744010i	$-0.732922\pi$
$521$	3689.47	−	6390.36i	0.310247	−	0.537364i	0.978416	+	0.206646i	$0.0662548\pi$
$522$		0			0
$523$	−17146.8			−1.43361			−0.716803	−	0.697275i	$-0.754395\pi$
$523$	−17146.8			−1.43361			−0.716803	+	0.697275i	$0.754395\pi$
$524$		0			0
$525$	−3143.47			−0.261319
$526$		0			0
$527$	758.110	+	730.565i	0.0626637	+	0.0603870i
$528$		0			0
$529$	−7617.93			−0.626114
$530$		0			0
$531$	17035.5			1.39224
$532$		0			0
$533$	102.268	−	177.133i	0.00831088	−	0.0143949i
$534$		0			0
$535$	12169.8			0.983448
$536$		0			0
$537$	18439.0	+	31937.2i	1.48175	+	2.56647i
$538$		0			0
$539$	−863.784	+	1496.12i	−0.0690275	+	0.119559i
$540$		0			0
$541$	−6396.74	+	11079.5i	−0.508350	+	0.880488i	0.491603	+	0.870819i	$0.336411\pi$
$541$	−6396.74	+	11079.5i	−0.508350	+	0.880488i	−0.999953	+	0.00966900i	$0.996922\pi$
$542$		0			0
$543$	−28397.0			−2.24426
$544$		0			0
$545$	−1110.15	−	1922.83i	−0.0872539	−	0.151128i
$546$		0			0
$547$	−7907.89	−	13696.9i	−0.618130	−	1.07063i	−0.989827	−	0.142278i	$-0.954557\pi$
$547$	−7907.89	−	13696.9i	−0.618130	−	1.07063i	0.371697	−	0.928354i	$-0.378776\pi$
$548$		0			0
$549$	−302.023	−	523.118i	−0.0234791	−	0.0406669i
$550$		0			0
$551$	−3385.73	+	5864.25i	−0.261773	+	0.453404i
$552$		0			0
$553$	−3373.98	−	5843.91i	−0.259451	−	0.449382i
$554$		0			0
$555$	−7614.18	+	13188.2i	−0.582350	+	1.00866i
$556$		0			0
$557$	805.072			0.0612424			0.0306212	−	0.999531i	$-0.490251\pi$
$557$	805.072			0.0612424			0.0306212	+	0.999531i	$0.490251\pi$
$558$		0			0
$559$	24.0510			0.00181977
$560$		0			0
$561$	−139.632	+	241.851i	−0.0105085	+	0.0182013i
$562$		0			0
$563$	10538.1	+	18252.6i	0.788861	+	1.36635i	0.926665	+	0.375888i	$0.122662\pi$
$563$	10538.1	+	18252.6i	0.788861	+	1.36635i	−0.137804	+	0.990460i	$0.544004\pi$
$564$		0			0
$565$	1337.18	−	2316.06i	0.0995673	−	0.172456i
$566$		0			0
$567$	−1126.70	−	1951.49i	−0.0834511	−	0.144541i
$568$		0			0
$569$	−11782.4	−	20407.6i	−0.868088	−	1.50357i	−0.863948	−	0.503581i	$-0.832015\pi$
$569$	−11782.4	−	20407.6i	−0.868088	−	1.50357i	−0.00414041	−	0.999991i	$-0.501318\pi$
$570$		0			0
$571$	9957.03	+	17246.1i	0.729753	+	1.26397i	0.956988	+	0.290129i	$0.0936982\pi$
$571$	9957.03	+	17246.1i	0.729753	+	1.26397i	−0.227235	+	0.973840i	$0.572968\pi$
$572$		0			0
$573$	13426.6			0.978890
$574$		0			0
$575$	−2072.06	+	3588.92i	−0.150280	+	0.260293i
$576$		0			0
$577$	−10905.0	+	18888.0i	−0.786795	+	1.36277i	0.141125	+	0.989992i	$0.454928\pi$
$577$	−10905.0	+	18888.0i	−0.786795	+	1.36277i	−0.927921	+	0.372778i	$0.878405\pi$
$578$		0			0
$579$	20069.9	+	34762.1i	1.44055	+	2.49510i
$580$		0			0
$581$	−1639.53			−0.117072
$582$		0			0
$583$	−1731.04	+	2998.24i	−0.122971	+	0.212992i
$584$		0			0
$585$	7237.61			0.511519
$586$		0			0
$587$	−17664.9			−1.24210			−0.621048	−	0.783773i	$-0.713293\pi$
$587$	−17664.9			−1.24210			−0.621048	+	0.783773i	$0.713293\pi$
$588$		0			0
$589$	6554.40	+	6316.25i	0.458522	+	0.441862i
$590$		0			0
$591$	28500.5			1.98368
$592$		0			0
$593$	3729.48			0.258265			0.129133	−	0.991627i	$-0.458781\pi$
$593$	3729.48			0.258265			0.129133	+	0.991627i	$0.458781\pi$
$594$		0			0
$595$	155.333	−	269.045i	0.0107026	−	0.0185375i
$596$		0			0
$597$	3863.57			0.264866
$598$		0			0
$599$	5468.33	+	9471.42i	0.373005	+	0.646063i	0.990026	−	0.140883i	$-0.0449942\pi$
$599$	5468.33	+	9471.42i	0.373005	+	0.646063i	−0.617022	+	0.786946i	$0.711661\pi$
$600$		0			0
$601$	4516.36	−	7822.56i	0.306533	−	0.530930i	−0.671069	−	0.741395i	$-0.734164\pi$
$601$	4516.36	−	7822.56i	0.306533	−	0.530930i	0.977601	+	0.210465i	$0.0674978\pi$
$602$		0			0
$603$	−2186.89	+	3787.80i	−0.147690	+	0.255806i
$604$		0			0
$605$	−10350.5			−0.695552
$606$		0			0
$607$	13402.4	+	23213.6i	0.896186	+	1.55224i	0.832330	+	0.554280i	$0.187006\pi$
$607$	13402.4	+	23213.6i	0.896186	+	1.55224i	0.0638559	+	0.997959i	$0.479660\pi$
$608$		0			0
$609$	−3284.52	−	5688.95i	−0.218547	−	0.378535i
$610$		0			0
$611$	−6273.20	−	10865.5i	−0.415363	−	0.719429i
$612$		0			0
$613$	−4016.04	+	6955.99i	−0.264611	+	0.458319i	−0.967462	−	0.253018i	$-0.918577\pi$
$613$	−4016.04	+	6955.99i	−0.264611	+	0.458319i	0.702851	+	0.711337i	$0.251910\pi$
$614$		0			0
$615$	−267.060	−	462.561i	−0.0175104	−	0.0303289i
$616$		0			0
$617$	12428.5	−	21526.8i	0.810943	−	1.40459i	−0.101262	−	0.994860i	$-0.532288\pi$
$617$	12428.5	−	21526.8i	0.810943	−	1.40459i	0.912205	−	0.409735i	$-0.134379\pi$
$618$		0			0
$619$	2722.29			0.176766			0.0883830	−	0.996087i	$-0.471830\pi$
$619$	2722.29			0.176766			0.0883830	+	0.996087i	$0.471830\pi$
$620$		0			0
$621$	5473.22			0.353676
$622$		0			0
$623$	1256.47	−	2176.26i	0.0808014	−	0.139952i
$624$		0			0
$625$	2084.70	+	3610.81i	0.133421	+	0.231092i
$626$		0			0
$627$	−1207.22	+	2090.97i	−0.0768928	+	0.133182i
$628$		0			0
$629$	727.473	+	1260.02i	0.0461149	+	0.0798733i
$630$		0			0
$631$	−9964.92	−	17259.7i	−0.628680	−	1.08891i	−0.987817	−	0.155621i	$-0.950262\pi$
$631$	−9964.92	−	17259.7i	−0.628680	−	1.08891i	0.359137	−	0.933285i	$-0.383071\pi$
$632$		0			0
$633$	−18410.9	−	31888.6i	−1.15603	−	2.00230i
$634$		0			0
$635$	7354.37			0.459605
$636$		0			0
$637$	3694.02	−	6398.23i	0.229768	−	0.397970i
$638$		0			0
$639$	−8871.04	+	15365.1i	−0.549191	+	0.951227i
$640$		0			0
$641$	13859.4	+	24005.2i	0.854001	+	1.47917i	0.877569	+	0.479451i	$0.159164\pi$
$641$	13859.4	+	24005.2i	0.854001	+	1.47917i	−0.0235678	+	0.999722i	$0.507503\pi$
$642$		0			0
$643$	1188.91			0.0729175			0.0364588	−	0.999335i	$-0.488392\pi$
$643$	1188.91			0.0729175			0.0364588	+	0.999335i	$0.488392\pi$
$644$		0			0
$645$	31.4032	−	54.3919i	0.00191705	−	0.00332044i
$646$		0			0
$647$	17927.4			1.08933			0.544665	−	0.838653i	$-0.316657\pi$
$647$	17927.4			1.08933			0.544665	+	0.838653i	$0.316657\pi$
$648$		0			0
$649$	−2622.72			−0.158630
$650$		0			0
$651$	−8485.76	+	2442.87i	−0.510880	+	0.147072i
$652$		0			0
$653$	−18867.8			−1.13071			−0.565355	−	0.824848i	$-0.691261\pi$
$653$	−18867.8			−1.13071			−0.565355	+	0.824848i	$0.691261\pi$
$654$		0			0
$655$	16963.7			1.01195
$656$		0			0
$657$	18495.9	−	32035.8i	1.09831	−	1.90233i
$658$		0			0
$659$	22382.3			1.32305			0.661526	−	0.749922i	$-0.269909\pi$
$659$	22382.3			1.32305			0.661526	+	0.749922i	$0.269909\pi$
$660$		0			0
$661$	2609.82	+	4520.34i	0.153571	+	0.265992i	0.932538	−	0.361073i	$-0.117589\pi$
$661$	2609.82	+	4520.34i	0.153571	+	0.265992i	−0.778967	+	0.627065i	$0.784256\pi$
$662$		0			0
$663$	597.146	−	1034.29i	0.0349792	−	0.0605858i
$664$		0			0
$665$	1342.97	−	2326.09i	0.0783129	−	0.135642i
$666$		0			0
$667$	−8660.16			−0.502732
$668$		0			0
$669$	1808.02	+	3131.57i	0.104487	+	0.180977i
$670$		0			0
$671$	46.4983	+	80.5374i	0.00267518	+	0.00463355i
$672$		0			0
$673$	3532.26	+	6118.05i	0.202316	+	0.350421i	0.949274	−	0.314449i	$-0.101820\pi$
$673$	3532.26	+	6118.05i	0.202316	+	0.350421i	−0.746958	+	0.664871i	$0.768487\pi$
$674$		0			0
$675$	−2493.01	+	4318.02i	−0.142157	+	0.246223i
$676$		0			0
$677$	−12155.9	−	21054.7i	−0.690088	−	1.19527i	−0.971809	−	0.235771i	$-0.924238\pi$
$677$	−12155.9	−	21054.7i	−0.690088	−	1.19527i	0.281720	−	0.959497i	$-0.409095\pi$
$678$		0			0
$679$	1119.74	−	1939.45i	0.0632870	−	0.109616i
$680$		0			0
$681$	−11252.4			−0.633175
$682$		0			0
$683$	−25024.4			−1.40195			−0.700974	−	0.713187i	$-0.747251\pi$
$683$	−25024.4			−1.40195			−0.700974	+	0.713187i	$0.747251\pi$
$684$		0			0
$685$	4689.05	−	8121.68i	0.261547	−	0.453012i
$686$		0			0
$687$	6703.17	+	11610.2i	0.372259	+	0.644772i
$688$		0			0
$689$	7402.86	−	12822.1i	0.409328	−	0.708976i
$690$		0			0
$691$	−1932.73	−	3347.58i	−0.106403	−	0.184295i	0.807908	−	0.589309i	$-0.200600\pi$
$691$	−1932.73	−	3347.58i	−0.106403	−	0.184295i	−0.914310	+	0.405014i	$0.867267\pi$
$692$		0			0
$693$	−678.087	−	1174.48i	−0.0371694	−	0.0643793i
$694$		0			0
$695$	8413.34	+	14572.3i	0.459188	+	0.795338i
$696$		0			0
$697$	−51.0308			−0.00277321
$698$		0			0
$699$	5280.83	−	9146.67i	0.285750	−	0.494934i
$700$		0			0
$701$	3261.00	−	5648.22i	0.175701	−	0.304323i	−0.764703	−	0.644383i	$-0.777114\pi$
$701$	3261.00	−	5648.22i	0.175701	−	0.304323i	0.940404	+	0.340060i	$0.110448\pi$
$702$		0			0
$703$	6289.52	+	10893.8i	0.337431	+	0.584447i
$704$		0			0
$705$	−32763.5			−1.75027
$706$		0			0
$707$	−3452.16	+	5979.32i	−0.183638	+	0.318070i
$708$		0			0
$709$	−21324.8			−1.12958			−0.564789	−	0.825235i	$-0.691042\pi$
$709$	−21324.8			−1.12958			−0.564789	+	0.825235i	$0.691042\pi$
$710$		0			0
$711$	−39222.7			−2.06887
$712$		0			0
$713$	−2804.47	+	11298.5i	−0.147305	+	0.593454i
$714$		0			0
$715$	−1114.28			−0.0582819
$716$		0			0
$717$	14917.8			0.777008
$718$		0			0
$719$	2139.85	−	3706.33i	0.110992	−	0.192243i	−0.805179	−	0.593032i	$-0.797931\pi$
$719$	2139.85	−	3706.33i	0.110992	−	0.192243i	0.916170	+	0.400789i	$0.131264\pi$
$720$		0			0
$721$	−8737.39			−0.451314
$722$		0			0
$723$	2489.92	+	4312.67i	0.128079	+	0.221840i
$724$		0			0
$725$	3944.63	−	6832.30i	0.202069	−	0.349993i
$726$		0			0
$727$	7609.84	−	13180.6i	0.388216	−	0.672410i	−0.603993	−	0.796989i	$-0.706425\pi$
$727$	7609.84	−	13180.6i	0.388216	−	0.672410i	0.992210	+	0.124579i	$0.0397580\pi$
$728$		0			0
$729$	−30644.2			−1.55689
$730$		0			0
$731$	−3.00032	−	5.19671i	−0.000151807	−	0.000262937i
$732$		0			0
$733$	11119.5	+	19259.6i	0.560312	+	0.970489i	0.997469	+	0.0711036i	$0.0226521\pi$
$733$	11119.5	+	19259.6i	0.560312	+	0.970489i	−0.437157	+	0.899385i	$0.644015\pi$
$734$		0			0
$735$	−9646.49	−	16708.2i	−0.484104	−	0.838492i
$736$		0			0
$737$	336.686	−	583.157i	0.0168276	−	0.0291463i
$738$		0			0
$739$	13976.1	+	24207.3i	0.695697	+	1.20498i	0.969945	+	0.243323i	$0.0782375\pi$
$739$	13976.1	+	24207.3i	0.695697	+	1.20498i	−0.274249	+	0.961659i	$0.588429\pi$
$740$		0			0
$741$	5162.75	−	8942.14i	0.255949	−	0.443317i
$742$		0			0
$743$	−25403.2			−1.25431			−0.627156	−	0.778894i	$-0.715781\pi$
$743$	−25403.2			−1.25431			−0.627156	+	0.778894i	$0.715781\pi$
$744$		0			0
$745$	−8473.92			−0.416725
$746$		0			0
$747$	−4764.89	+	8253.03i	−0.233384	+	0.404234i
$748$		0			0
$749$	4876.03	+	8445.54i	0.237872	+	0.412007i
$750$		0			0
$751$	13662.3	−	23663.9i	0.663843	−	1.14981i	−0.315755	−	0.948841i	$-0.602258\pi$
$751$	13662.3	−	23663.9i	0.663843	−	1.14981i	0.979598	−	0.200968i	$-0.0644089\pi$
$752$		0			0
$753$	1849.13	+	3202.79i	0.0894903	+	0.155002i
$754$		0			0
$755$	5691.98	+	9858.81i	0.274374	+	0.475230i
$756$		0			0
$757$	−4681.78	−	8109.09i	−0.224785	−	0.389339i	0.731470	−	0.681874i	$-0.238835\pi$
$757$	−4681.78	−	8109.09i	−0.224785	−	0.389339i	−0.956255	+	0.292535i	$0.905501\pi$
$758$		0			0
$759$	−3087.88			−0.147672
$760$		0			0
$761$	6356.05	−	11009.0i	0.302768	−	0.524410i	−0.673994	−	0.738737i	$-0.735423\pi$
$761$	6356.05	−	11009.0i	0.302768	−	0.524410i	0.976762	+	0.214327i	$0.0687559\pi$
$762$		0			0
$763$	889.599	−	1540.83i	0.0422092	−	0.0731085i
$764$		0			0
$765$	−902.879	−	1563.83i	−0.0426715	−	0.0739091i
$766$		0			0
$767$	11216.2			0.528024
$768$		0			0
$769$	11226.9	−	19445.5i	0.526464	−	0.911863i	−0.473060	−	0.881030i	$-0.656851\pi$
$769$	11226.9	−	19445.5i	0.526464	−	0.911863i	0.999525	−	0.0308331i	$-0.00981603\pi$
$770$		0			0
$771$	11645.7			0.543980
$772$		0			0
$773$	11203.8			0.521309			0.260655	−	0.965432i	$-0.416062\pi$
$773$	11203.8			0.521309			0.260655	+	0.965432i	$0.416062\pi$
$774$		0			0
$775$	−7636.38	−	7358.92i	−0.353944	−	0.341084i
$776$		0			0
$777$	−12203.0			−0.563425
$778$		0			0
$779$	−441.197			−0.0202921
$780$		0			0
$781$	1365.75	−	2365.56i	0.0625743	−	0.108382i
$782$		0			0
$783$	−10419.5			−0.475558
$784$		0			0
$785$	−11235.1	−	19459.8i	−0.510827	−	0.884779i
$786$		0			0
$787$	14796.6	−	25628.5i	0.670195	−	1.16081i	−0.307654	−	0.951498i	$-0.599544\pi$
$787$	14796.6	−	25628.5i	0.670195	−	1.16081i	0.977849	−	0.209313i	$-0.0671227\pi$
$788$		0			0
$789$	−22734.3	+	39377.0i	−1.02581	+	1.77675i
$790$		0			0
$791$	2143.06			0.0963317
$792$		0			0
$793$	−198.852	−	344.423i	−0.00890474	−	0.0154235i
$794$		0			0
$795$	−19331.7	−	33483.5i	−0.862422	−	1.49376i
$796$		0			0
$797$	13040.8	+	22587.4i	0.579586	+	1.00387i	0.995527	+	0.0944807i	$0.0301191\pi$
$797$	13040.8	+	22587.4i	0.579586	+	1.00387i	−0.415941	+	0.909392i	$0.636548\pi$
$798$		0			0
$799$	−1565.14	+	2710.90i	−0.0693000	+	0.120031i
$800$		0			0
$801$	−7303.24	−	12649.6i	−0.322156	−	0.557991i
$802$		0			0
$803$	−2847.55	+	4932.11i	−0.125141	+	0.216750i
$804$		0			0
$805$	3435.10			0.150399
$806$		0			0
$807$	−26353.3			−1.14954
$808$		0			0
$809$	4247.79	−	7357.38i	0.184603	−	0.319743i	−0.758839	−	0.651278i	$-0.774233\pi$
$809$	4247.79	−	7357.38i	0.184603	−	0.319743i	0.943443	+	0.331535i	$0.107567\pi$
$810$		0			0
$811$	−9718.16	−	16832.3i	−0.420778	−	0.728808i	0.575238	−	0.817986i	$-0.304909\pi$
$811$	−9718.16	−	16832.3i	−0.420778	−	0.728808i	−0.996016	+	0.0891777i	$0.971576\pi$
$812$		0			0
$813$	3200.77	−	5543.90i	0.138076	−	0.239155i
$814$		0			0
$815$	−2846.66	−	4930.56i	−0.122349	−	0.211914i
$816$		0			0
$817$	−25.9399	−	44.9292i	−0.00111080	−	0.00192396i
$818$		0			0
$819$	2899.88	+	5022.73i	0.123724	+	0.214296i
$820$		0			0
$821$	−5046.69			−0.214532			−0.107266	−	0.994230i	$-0.534210\pi$
$821$	−5046.69			−0.214532			−0.107266	+	0.994230i	$0.534210\pi$
$822$		0			0
$823$	4748.73	−	8225.04i	0.201130	−	0.348368i	−0.747762	−	0.663966i	$-0.768872\pi$
$823$	4748.73	−	8225.04i	0.201130	−	0.348368i	0.948893	+	0.315598i	$0.102205\pi$
$824$		0			0
$825$	1406.51	−	2436.14i	0.0593554	−	0.102807i
$826$		0			0
$827$	11942.2	+	20684.4i	0.502140	+	0.869731i	0.999997	+	0.00247234i	$0.000786970\pi$
$827$	11942.2	+	20684.4i	0.502140	+	0.869731i	−0.497857	+	0.867259i	$0.665880\pi$
$828$		0			0
$829$	−31447.6			−1.31752			−0.658759	−	0.752354i	$-0.728918\pi$
$829$	−31447.6			−1.31752			−0.658759	+	0.752354i	$0.728918\pi$
$830$		0			0
$831$	5995.90	−	10385.2i	0.250296	−	0.433525i
$832$		0			0
$833$	−1843.29			−0.0766701
$834$		0			0
$835$	21465.1			0.889619
$836$		0			0
$837$	−3374.20	+	13593.8i	−0.139342	+	0.561376i
$838$		0			0
$839$	41693.8			1.71565			0.857825	−	0.513943i	$-0.171816\pi$
$839$	41693.8			1.71565			0.857825	+	0.513943i	$0.171816\pi$
$840$		0			0
$841$	−7902.48			−0.324018
$842$		0			0
$843$	24363.3	−	42198.4i	0.995392	−	1.72407i
$844$		0			0
$845$	−12749.8			−0.519061
$846$		0			0
$847$	−4147.13	−	7183.03i	−0.168237	−	0.291395i
$848$		0			0
$849$	−3414.54	+	5914.16i	−0.138029	+	0.239074i
$850$		0			0
$851$	−8043.81	+	13932.3i	−0.324017	+	0.561213i
$852$		0			0
$853$	42595.7			1.70979			0.854894	−	0.518803i	$-0.173622\pi$
$853$	42595.7			1.70979			0.854894	+	0.518803i	$0.173622\pi$
$854$		0			0
$855$	−7806.03	−	13520.4i	−0.312234	−	0.540806i
$856$		0			0
$857$	3792.94	+	6569.57i	0.151184	+	0.261858i	0.931663	−	0.363324i	$-0.118358\pi$
$857$	3792.94	+	6569.57i	0.151184	+	0.261858i	−0.780479	+	0.625182i	$0.785025\pi$
$858$		0			0
$859$	−11781.5	−	20406.1i	−0.467961	−	0.810532i	0.531369	−	0.847141i	$-0.321678\pi$
$859$	−11781.5	−	20406.1i	−0.467961	−	0.810532i	−0.999330	+	0.0366085i	$0.988345\pi$
$860$		0			0
$861$	214.004	−	370.667i	0.00847068	−	0.0146716i
$862$		0			0
$863$	15676.2	+	27152.1i	0.618338	+	1.07099i	0.989789	+	0.142540i	$0.0455270\pi$
$863$	15676.2	+	27152.1i	0.618338	+	1.07099i	−0.371451	+	0.928452i	$0.621140\pi$
$864$		0			0
$865$	−3310.24	+	5733.50i	−0.130117	+	0.225370i
$866$		0			0
$867$	39046.9			1.52953
$868$		0			0
$869$	6038.58			0.235725
$870$		0			0
$871$	−1439.85	+	2493.90i	−0.0560133	+	0.0970179i
$872$		0			0
$873$	−6508.54	−	11273.1i	−0.252326	−	0.437042i
$874$		0			0
$875$	−4747.82	+	8223.46i	−0.183435	+	0.317719i
$876$		0			0
$877$	20271.4	+	35111.1i	0.780521	+	1.35190i	0.931639	+	0.363386i	$0.118379\pi$
$877$	20271.4	+	35111.1i	0.780521	+	1.35190i	−0.151118	+	0.988516i	$0.548287\pi$
$878$		0			0
$879$	30929.2	+	53570.9i	1.18682	+	2.05563i
$880$		0			0
$881$	−15207.2	−	26339.7i	−0.581549	−	1.00727i	−0.995296	−	0.0968808i	$-0.969113\pi$
$881$	−15207.2	−	26339.7i	−0.581549	−	1.00727i	0.413747	−	0.910392i	$-0.364220\pi$
$882$		0			0
$883$	−21822.0			−0.831675			−0.415838	−	0.909439i	$-0.636512\pi$
$883$	−21822.0			−0.831675			−0.415838	+	0.909439i	$0.636512\pi$
$884$		0			0
$885$	14644.9	−	25365.7i	0.556253	−	0.963458i
$886$		0			0
$887$	−16953.8	+	29364.8i	−0.641773	+	1.11158i	0.343264	+	0.939239i	$0.388467\pi$
$887$	−16953.8	+	29364.8i	−0.641773	+	1.11158i	−0.985037	+	0.172344i	$0.944866\pi$
$888$		0			0
$889$	2946.66	+	5103.76i	0.111167	+	0.192547i
$890$		0			0
$891$	2016.50			0.0758197
$892$		0			0
$893$	−13531.8	+	23437.7i	−0.507080	+	0.878289i
$894$		0			0
$895$	36711.9			1.37111
$896$		0			0
$897$	13205.5			0.491548
$898$		0			0
$899$	5338.92	−	21509.2i	0.198068	−	0.797967i
$900$		0			0
$901$	−3693.98			−0.136586
$902$		0			0
$903$	50.3290			0.00185476
$904$		0			0
$905$	−14134.6	+	24481.8i	−0.519171	+	0.899230i
$906$		0			0
$907$	938.158			0.0343451			0.0171726	−	0.999853i	$-0.494534\pi$
$907$	938.158			0.0343451			0.0171726	+	0.999853i	$0.494534\pi$
$908$		0			0
$909$	20065.7	+	34754.9i	0.732166	+	1.26815i
$910$		0			0
$911$	−19630.5	+	34001.0i	−0.713927	+	1.23656i	0.249445	+	0.968389i	$0.419752\pi$
$911$	−19630.5	+	34001.0i	−0.713927	+	1.23656i	−0.963372	+	0.268169i	$0.913581\pi$
$912$		0			0
$913$	733.585	−	1270.61i	0.0265916	−	0.0460580i
$914$		0			0
$915$	−1038.56			−0.0375232
$916$		0			0
$917$	6796.79	+	11772.4i	0.244765	+	0.423946i
$918$		0			0
$919$	−242.205	−	419.512i	−0.00869381	−	0.0150581i	0.861646	−	0.507510i	$-0.169434\pi$
$919$	−242.205	−	419.512i	−0.00869381	−	0.0150581i	−0.870340	+	0.492452i	$0.836101\pi$
$920$		0			0
$921$	22995.9	+	39830.0i	0.822736	+	1.42502i
$922$		0			0
$923$	−5840.72	+	10116.4i	−0.208288	+	0.360765i
$924$		0			0
$925$	−7327.78	−	12692.1i	−0.260471	−	0.451149i
$926$		0			0
$927$	−25393.1	+	43982.2i	−0.899698	+	1.55832i
$928$		0			0
$929$	−17513.2			−0.618502			−0.309251	−	0.950980i	$-0.600078\pi$
$929$	−17513.2			−0.618502			−0.309251	+	0.950980i	$0.600078\pi$
$930$		0			0
$931$	−15936.5			−0.561008
$932$		0			0
$933$	−9578.11	+	16589.8i	−0.336091	+	0.582128i
$934$		0			0
$935$	139.004	+	240.762i	0.00486194	+	0.00842113i
$936$		0			0
$937$	−8359.06	+	14478.3i	−0.291439	+	0.504788i	−0.974150	−	0.225901i	$-0.927467\pi$
$937$	−8359.06	+	14478.3i	−0.291439	+	0.504788i	0.682711	+	0.730689i	$0.260801\pi$
$938$		0			0
$939$	−8669.31	−	15015.7i	−0.301291	−	0.521851i
$940$		0			0
$941$	8387.45	+	14527.5i	0.290566	+	0.503276i	0.973944	−	0.226790i	$-0.0728229\pi$
$941$	8387.45	+	14527.5i	0.290566	+	0.503276i	−0.683377	+	0.730065i	$0.739490\pi$
$942$		0			0
$943$	−282.128	−	488.661i	−0.00974270	−	0.0168748i
$944$		0			0
$945$	4132.95			0.142270
$946$		0			0
$947$	−21108.3	+	36560.6i	−0.724316	+	1.25455i	0.234938	+	0.972010i	$0.424511\pi$
$947$	−21108.3	+	36560.6i	−0.724316	+	1.25455i	−0.959255	+	0.282542i	$0.908822\pi$
$948$		0			0
$949$	12177.7	−	21092.4i	0.416549	−	0.721485i
$950$		0			0
$951$	−26447.7	−	45808.7i	−0.901813	−	1.56199i
$952$		0			0
$953$	−19260.4			−0.654675			−0.327338	−	0.944907i	$-0.606151\pi$
$953$	−19260.4			−0.654675			−0.327338	+	0.944907i	$0.606151\pi$
$954$		0			0
$955$	6683.08	−	11575.4i	0.226450	−	0.392223i
$956$		0			0
$957$	5878.47			0.198562
$958$		0			0
$959$	7515.01			0.253047
$960$		0			0
$961$	−26333.1	−	13930.9i	−0.883929	−	0.467621i
$962$		0			0
$963$	56684.1			1.89680
$964$		0			0
$965$	39959.1			1.33298
$966$		0			0
$967$	−10573.8	+	18314.4i	−0.351635	+	0.609049i	−0.986536	−	0.163544i	$-0.947707\pi$
$967$	−10573.8	+	18314.4i	−0.351635	+	0.609049i	0.634901	+	0.772593i	$0.281041\pi$
$968$		0			0
$969$	−2576.17			−0.0854062
$970$		0			0
$971$	−11730.7	−	20318.1i	−0.387698	−	0.671513i	0.604441	−	0.796650i	$-0.293396\pi$
$971$	−11730.7	−	20318.1i	−0.387698	−	0.671513i	−0.992140	+	0.125137i	$0.960063\pi$
$972$		0			0
$973$	−6741.90	+	11677.3i	−0.222133	+	0.384746i
$974$		0			0
$975$	−6015.00	+	10418.3i	−0.197573	+	0.342207i
$976$		0			0
$977$	48744.4			1.59618			0.798092	−	0.602535i	$-0.205843\pi$
$977$	48744.4			1.59618			0.798092	+	0.602535i	$0.205843\pi$
$978$		0			0
$979$	1124.38	+	1947.48i	0.0367062	+	0.0635770i
$980$		0			0
$981$	−5170.81	−	8956.11i	−0.168289	−	0.291485i
$982$		0			0
$983$	3521.50	+	6099.42i	0.114261	+	0.197906i	0.917484	−	0.397773i	$-0.130217\pi$
$983$	3521.50	+	6099.42i	0.114261	+	0.197906i	−0.803223	+	0.595678i	$0.796883\pi$
$984$		0			0
$985$	14186.1	−	24571.1i	0.458890	−	0.794821i
$986$		0			0
$987$	−13127.3	−	22737.1i	−0.423349	−	0.733262i
$988$		0			0
$989$	33.1751	−	57.4610i	0.00106664	−	0.00184747i
$990$		0			0
$991$	−29898.6			−0.958386			−0.479193	−	0.877710i	$-0.659071\pi$
$991$	−29898.6			−0.958386			−0.479193	+	0.877710i	$0.659071\pi$
$992$		0			0
$993$	59582.6			1.90413
$994$		0			0
$995$	1923.09	−	3330.89i	0.0612724	−	0.106127i
$996$		0			0
$997$	7605.38	+	13172.9i	0.241589	+	0.418445i	0.961167	−	0.275967i	$-0.0889979\pi$
$997$	7605.38	+	13172.9i	0.241589	+	0.418445i	−0.719578	+	0.694412i	$0.755665\pi$
$998$		0			0
$999$	−9677.92	+	16762.7i	−0.306502	+	0.530878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.4.e.c.5.4	✓	8
3.2	odd	2		1116.4.i.e.253.2		8
4.3	odd	2		496.4.i.e.129.1		8
31.25	even	3	inner	124.4.e.c.25.4	yes	8
93.56	odd	6		1116.4.i.e.397.2		8
124.87	odd	6		496.4.i.e.273.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.4.e.c.5.4	✓	8	1.1	even	1	trivial
124.4.e.c.25.4	yes	8	31.25	even	3	inner
496.4.i.e.129.1		8	4.3	odd	2
496.4.i.e.273.1		8	124.87	odd	6
1116.4.i.e.253.2		8	3.2	odd	2
1116.4.i.e.397.2		8	93.56	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	124.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00416 - 6.93540i) q^{3} +(-3.98613 - 6.90419i) q^{5} +(3.19423 - 5.53257i) q^{7} +(-18.5665 - 32.1582i) q^{9} +O(q^{10})\)	\(q+(4.00416 - 6.93540i) q^{3} +(-3.98613 - 6.90419i) q^{5} +(3.19423 - 5.53257i) q^{7} +(-18.5665 - 32.1582i) q^{9} +(2.85844 + 4.95096i) q^{11} +(-12.2243 - 21.1730i) q^{13} -63.8444 q^{15} +(-3.04991 + 5.28260i) q^{17} +(-26.3686 + 45.6718i) q^{19} +(-25.5804 - 44.3066i) q^{21} -67.4468 q^{23} +(30.7215 - 53.2111i) q^{25} -81.1488 q^{27} +128.400 q^{29} +(41.5805 - 167.517i) q^{31} +45.7825 q^{33} -50.9305 q^{35} +(119.262 - 206.567i) q^{37} -195.791 q^{39} +(4.18298 + 7.24513i) q^{41} +(-0.491871 + 0.851945i) q^{43} +(-148.017 + 256.374i) q^{45} +513.177 q^{47} +(151.094 + 261.702i) q^{49} +(24.4246 + 42.3047i) q^{51} +(302.794 + 524.455i) q^{53} +(22.7882 - 39.4704i) q^{55} +(211.168 + 365.754i) q^{57} +(-229.385 + 397.306i) q^{59} +16.2670 q^{61} -237.223 q^{63} +(-97.4551 + 168.797i) q^{65} +(-58.8933 - 102.006i) q^{67} +(-270.067 + 467.771i) q^{69} +(-238.899 - 413.785i) q^{71} +(498.097 + 862.728i) q^{73} +(-246.027 - 426.131i) q^{75} +36.5220 q^{77} +(528.137 - 914.759i) q^{79} +(176.364 - 305.472i) q^{81} +(-128.319 - 222.256i) q^{83} +48.6294 q^{85} +(514.133 - 890.504i) q^{87} +393.355 q^{89} -156.188 q^{91} +(-995.306 - 959.143i) q^{93} +420.435 q^{95} +350.552 q^{97} +(106.143 - 183.844i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{5} - 32 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 16 * q^5 - 32 * q^7 - 4 * q^9	\( 8 q - 16 q^{5} - 32 q^{7} - 4 q^{9} - 80 q^{11} - 28 q^{13} - 304 q^{15} - 8 q^{17} - 56 q^{19} - 76 q^{21} - 624 q^{23} - 48 q^{25} - 432 q^{27} - 216 q^{29} + 528 q^{31} + 584 q^{33} + 592 q^{35} + 96 q^{37} + 128 q^{39} + 552 q^{41} - 112 q^{43} + 524 q^{45} - 304 q^{47} - 4 q^{49} - 232 q^{51} + 1316 q^{53} - 208 q^{55} + 464 q^{57} + 224 q^{59} + 2664 q^{61} - 1856 q^{63} + 504 q^{65} - 272 q^{67} + 496 q^{69} + 1120 q^{71} + 248 q^{73} - 912 q^{75} + 624 q^{77} + 824 q^{79} + 104 q^{81} + 1616 q^{83} - 2232 q^{85} + 456 q^{87} + 184 q^{89} - 6928 q^{91} - 1960 q^{93} + 544 q^{95} + 2520 q^{97} + 1336 q^{99}+O(q^{100}) \) 8 * q - 16 * q^5 - 32 * q^7 - 4 * q^9 - 80 * q^11 - 28 * q^13 - 304 * q^15 - 8 * q^17 - 56 * q^19 - 76 * q^21 - 624 * q^23 - 48 * q^25 - 432 * q^27 - 216 * q^29 + 528 * q^31 + 584 * q^33 + 592 * q^35 + 96 * q^37 + 128 * q^39 + 552 * q^41 - 112 * q^43 + 524 * q^45 - 304 * q^47 - 4 * q^49 - 232 * q^51 + 1316 * q^53 - 208 * q^55 + 464 * q^57 + 224 * q^59 + 2664 * q^61 - 1856 * q^63 + 504 * q^65 - 272 * q^67 + 496 * q^69 + 1120 * q^71 + 248 * q^73 - 912 * q^75 + 624 * q^77 + 824 * q^79 + 104 * q^81 + 1616 * q^83 - 2232 * q^85 + 456 * q^87 + 184 * q^89 - 6928 * q^91 - 1960 * q^93 + 544 * q^95 + 2520 * q^97 + 1336 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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