LMFDB - Embedded newform 252.4.w.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(5,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

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

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

chi := DirichletCharacter("252.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.w (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.7
Character	$\chi$	$=$	252.5
Dual form			252.4.w.a.101.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.44710 + 3.88813i) q^{3} +(-0.950243 - 1.64587i) q^{5} +(14.2951 + 11.7749i) q^{7} +(-3.23505 - 26.8055i) q^{9} +O(q^{10})$	\(q+(-3.44710 + 3.88813i) q^{3} +(-0.950243 - 1.64587i) q^{5} +(14.2951 + 11.7749i) q^{7} +(-3.23505 - 26.8055i) q^{9} +(33.6863 + 19.4488i) q^{11} +(-8.40442 - 4.85229i) q^{13} +(9.67493 + 1.97881i) q^{15} +(22.9025 + 39.6683i) q^{17} +(19.7981 + 11.4305i) q^{19} +(-95.0591 + 14.9920i) q^{21} +(-135.938 + 78.4838i) q^{23} +(60.6941 - 105.125i) q^{25} +(115.375 + 79.8229i) q^{27} +(-187.249 + 108.108i) q^{29} +201.129i q^{31} +(-191.739 + 63.9347i) q^{33} +(5.79612 - 34.7170i) q^{35} +(-146.423 + 253.611i) q^{37} +(47.8372 - 15.9511i) q^{39} +(-119.448 + 206.891i) q^{41} +(-158.939 - 275.290i) q^{43} +(-41.0443 + 30.7962i) q^{45} +152.849 q^{47} +(65.7025 + 336.648i) q^{49} +(-233.182 - 47.6926i) q^{51} +(-26.3084 + 15.1892i) q^{53} -73.9244i q^{55} +(-112.689 + 37.5758i) q^{57} -466.502 q^{59} +506.946i q^{61} +(269.387 - 421.281i) q^{63} +18.4434i q^{65} +630.811 q^{67} +(163.436 - 799.085i) q^{69} -413.018i q^{71} +(276.563 - 159.674i) q^{73} +(199.522 + 598.363i) q^{75} +(252.543 + 674.677i) q^{77} +1005.15 q^{79} +(-708.069 + 173.434i) q^{81} +(415.211 + 719.167i) q^{83} +(43.5259 - 75.3890i) q^{85} +(225.127 - 1100.71i) q^{87} +(-572.009 + 990.749i) q^{89} +(-63.0070 - 168.326i) q^{91} +(-782.013 - 693.310i) q^{93} -43.4469i q^{95} +(1557.30 - 899.106i) q^{97} +(412.358 - 965.896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 12 * q^9	$ 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−3.44710	+	3.88813i	−0.663394	+	0.748270i
$3$	−3.44710	+	3.88813i	−0.663394	+	0.748270i
$4$		0			0
$5$	−0.950243	−	1.64587i	−0.0849923	−	0.147211i	0.820396	−	0.571796i	$-0.193753\pi$
$5$	−0.950243	−	1.64587i	−0.0849923	−	0.147211i	−0.905388	+	0.424585i	$0.860420\pi$
$6$		0			0
$7$	14.2951	+	11.7749i	0.771865	+	0.635786i
$7$	14.2951	+	11.7749i	0.771865	+	0.635786i
$8$		0			0
$9$	−3.23505	−	26.8055i	−0.119817	−	0.992796i
$10$		0			0
$11$	33.6863	+	19.4488i	0.923346	+	0.533094i	0.884701	−	0.466159i	$-0.154363\pi$
$11$	33.6863	+	19.4488i	0.923346	+	0.533094i	0.0386448	+	0.999253i	$0.487696\pi$
$12$		0			0
$13$	−8.40442	−	4.85229i	−0.179305	−	0.103522i	0.407661	−	0.913133i	$-0.366345\pi$
$13$	−8.40442	−	4.85229i	−0.179305	−	0.103522i	−0.586966	+	0.809611i	$0.699678\pi$
$14$		0			0
$15$	9.67493	+	1.97881i	0.166537	+	0.0340617i
$16$		0			0
$17$	22.9025	+	39.6683i	0.326745	+	0.565940i	0.981864	−	0.189586i	$-0.0607147\pi$
$17$	22.9025	+	39.6683i	0.326745	+	0.565940i	−0.655119	+	0.755526i	$0.727381\pi$
$18$		0			0
$19$	19.7981	+	11.4305i	0.239053	+	0.138017i	0.614741	−	0.788729i	$-0.289260\pi$
$19$	19.7981	+	11.4305i	0.239053	+	0.138017i	−0.375688	+	0.926746i	$0.622594\pi$
$20$		0			0
$21$	−95.0591	+	14.9920i	−0.987791	+	0.155787i
$22$		0			0
$23$	−135.938	+	78.4838i	−1.23239	+	0.711522i	−0.967528	−	0.252764i	$-0.918660\pi$
$23$	−135.938	+	78.4838i	−1.23239	+	0.711522i	−0.264864	+	0.964286i	$0.585327\pi$
$24$		0			0
$25$	60.6941	−	105.125i	0.485553	−	0.841002i
$26$		0			0
$27$	115.375	+	79.8229i	0.822365	+	0.568960i
$28$		0			0
$29$	−187.249	+	108.108i	−1.19901	+	0.692248i	−0.960334	−	0.278851i	$-0.910046\pi$
$29$	−187.249	+	108.108i	−1.19901	+	0.692248i	−0.238675	+	0.971100i	$0.576713\pi$
$30$		0			0
$31$			201.129i			1.16528i	0.812729	+	0.582641i	$0.197981\pi$
$31$			201.129i			1.16528i	−0.812729	+	0.582641i	$0.802019\pi$
$32$		0			0
$33$	−191.739	+	63.9347i	−1.01144	+	0.337261i
$34$		0			0
$35$	5.79612	−	34.7170i	0.0279921	−	0.167664i
$36$		0			0
$37$	−146.423	+	253.611i	−0.650587	+	1.12685i	0.332393	+	0.943141i	$0.392144\pi$
$37$	−146.423	+	253.611i	−0.650587	+	1.12685i	−0.982981	+	0.183709i	$0.941190\pi$
$38$		0			0
$39$	47.8372	−	15.9511i	0.196412	−	0.0654929i
$40$		0			0
$41$	−119.448	+	206.891i	−0.454993	+	0.788070i	−0.998688	−	0.0512125i	$-0.983691\pi$
$41$	−119.448	+	206.891i	−0.454993	+	0.788070i	0.543695	+	0.839283i	$0.317025\pi$
$42$		0			0
$43$	−158.939	−	275.290i	−0.563674	−	0.976312i	−0.997172	−	0.0751570i	$-0.976054\pi$
$43$	−158.939	−	275.290i	−0.563674	−	0.976312i	0.433498	−	0.901155i	$-0.357279\pi$
$44$		0			0
$45$	−41.0443	+	30.7962i	−0.135967	+	0.102018i
$46$		0			0
$47$	152.849			0.474369			0.237184	−	0.971465i	$-0.423775\pi$
$47$	152.849			0.474369			0.237184	+	0.971465i	$0.423775\pi$
$48$		0			0
$49$	65.7025	+	336.648i	0.191552	+	0.981482i
$50$		0			0
$51$	−233.182	−	47.6926i	−0.640237	−	0.130947i
$52$		0			0
$53$	−26.3084	+	15.1892i	−0.0681838	+	0.0393659i	−0.533704	−	0.845671i	$-0.679200\pi$
$53$	−26.3084	+	15.1892i	−0.0681838	+	0.0393659i	0.465521	+	0.885037i	$0.345867\pi$
$54$		0			0
$55$		−	73.9244i		−	0.181236i
$56$		0			0
$57$	−112.689	+	37.5758i	−0.261860	+	0.0873163i
$58$		0			0
$59$	−466.502			−1.02938			−0.514690	−	0.857376i	$-0.672093\pi$
$59$	−466.502			−1.02938			−0.514690	+	0.857376i	$0.672093\pi$
$60$		0			0
$61$			506.946i			1.06406i	0.846725	+	0.532031i	$0.178571\pi$
$61$			506.946i			1.06406i	−0.846725	+	0.532031i	$0.821429\pi$
$62$		0			0
$63$	269.387	−	421.281i	0.538724	−	0.842483i
$64$		0			0
$65$			18.4434i			0.0351943i
$66$		0			0
$67$	630.811			1.15024			0.575118	−	0.818071i	$-0.304956\pi$
$67$	630.811			1.15024			0.575118	+	0.818071i	$0.304956\pi$
$68$		0			0
$69$	163.436	−	799.085i	0.285151	−	1.39418i
$70$		0			0
$71$		−	413.018i		−	0.690369i	−0.938535	−	0.345184i	$-0.887816\pi$
$71$		−	413.018i		−	0.690369i	0.938535	−	0.345184i	$-0.112184\pi$
$72$		0			0
$73$	276.563	−	159.674i	0.443414	−	0.256005i	−0.261631	−	0.965168i	$-0.584260\pi$
$73$	276.563	−	159.674i	0.443414	−	0.256005i	0.705045	+	0.709163i	$0.250927\pi$
$74$		0			0
$75$	199.522	+	598.363i	0.307184	+	0.921240i
$76$		0			0
$77$	252.543	+	674.677i	0.373765	+	0.998527i
$78$		0			0
$79$	1005.15			1.43150			0.715750	−	0.698357i	$-0.246085\pi$
$79$	1005.15			1.43150			0.715750	+	0.698357i	$0.246085\pi$
$80$		0			0
$81$	−708.069	+	173.434i	−0.971288	+	0.237907i
$82$		0			0
$83$	415.211	+	719.167i	0.549101	+	0.951071i	0.998336	+	0.0576573i	$0.0183631\pi$
$83$	415.211	+	719.167i	0.549101	+	0.951071i	−0.449236	+	0.893413i	$0.648304\pi$
$84$		0			0
$85$	43.5259	−	75.3890i	0.0555417	−	0.0962011i
$86$		0			0
$87$	225.127	−	1100.71i	0.277427	−	1.35642i
$88$		0			0
$89$	−572.009	+	990.749i	−0.681268	+	1.17999i	0.293326	+	0.956012i	$0.405238\pi$
$89$	−572.009	+	990.749i	−0.681268	+	1.17999i	−0.974594	+	0.223978i	$0.928096\pi$
$90$		0			0
$91$	−63.0070	−	168.326i	−0.0725817	−	0.193905i
$92$		0			0
$93$	−782.013	−	693.310i	−0.871946	−	0.773042i
$94$		0			0
$95$		−	43.4469i		−	0.0469216i
$96$		0			0
$97$	1557.30	−	899.106i	1.63010	−	0.941137i	0.646037	−	0.763306i	$-0.276425\pi$
$97$	1557.30	−	899.106i	1.63010	−	0.941137i	0.984061	−	0.177831i	$-0.0569082\pi$
$98$		0			0
$99$	412.358	−	965.896i	0.418621	−	0.980567i
$100$		0			0
$101$	170.883	−	295.977i	0.168351	−	0.291592i	−0.769489	−	0.638660i	$-0.779489\pi$
$101$	170.883	−	295.977i	0.168351	−	0.291592i	0.937840	+	0.347067i	$0.112822\pi$
$102$		0			0
$103$	408.959	−	236.112i	0.391222	−	0.225872i	−0.291467	−	0.956581i	$-0.594143\pi$
$103$	408.959	−	236.112i	0.391222	−	0.225872i	0.682690	+	0.730709i	$0.260810\pi$
$104$		0			0
$105$	115.004	+	142.209i	0.106888	+	0.132173i
$106$		0			0
$107$	−1358.84	−	784.526i	−1.22770	−	0.708813i	−0.261152	−	0.965298i	$-0.584102\pi$
$107$	−1358.84	−	784.526i	−1.22770	−	0.708813i	−0.966548	+	0.256485i	$0.917436\pi$
$108$		0			0
$109$	−314.661	−	545.009i	−0.276505	−	0.478921i	0.694009	−	0.719967i	$-0.255843\pi$
$109$	−314.661	−	545.009i	−0.276505	−	0.478921i	−0.970514	+	0.241046i	$0.922510\pi$
$110$		0			0
$111$	−481.340	−	1443.53i	−0.411593	−	1.23436i
$112$		0			0
$113$	−1399.29	−	807.883i	−1.16491	−	0.672560i	−0.212432	−	0.977176i	$-0.568138\pi$
$113$	−1399.29	−	807.883i	−1.16491	−	0.672560i	−0.952475	+	0.304616i	$0.901472\pi$
$114$		0			0
$115$	258.348	+	149.157i	0.209488	+	0.120948i
$116$		0			0
$117$	−102.879	+	240.982i	−0.0812924	+	0.190417i
$118$		0			0
$119$	−139.696	+	836.739i	−0.107613	+	0.644569i
$120$		0			0
$121$	91.0114	+	157.636i	0.0683782	+	0.118435i
$122$		0			0
$123$	−392.667	−	1177.60i	−0.287850	−	0.863259i
$124$		0			0
$125$	−468.257			−0.335058
$126$		0			0
$127$	542.510			0.379055			0.189527	−	0.981875i	$-0.439304\pi$
$127$	542.510			0.379055			0.189527	+	0.981875i	$0.439304\pi$
$128$		0			0
$129$	1618.24	+	330.978i	1.10448	+	0.225899i
$130$		0			0
$131$	721.936	+	1250.43i	0.481495	+	0.833974i	0.999774	−	0.0212372i	$-0.00676051\pi$
$131$	721.936	+	1250.43i	0.481495	+	0.833974i	−0.518279	+	0.855211i	$0.673427\pi$
$132$		0			0
$133$	148.425	+	396.522i	0.0967672	+	0.258517i
$134$		0			0
$135$	21.7440	−	265.743i	0.0138624	−	0.169419i
$136$		0			0
$137$	1581.51	+	913.083i	0.986257	+	0.569416i	0.904153	−	0.427208i	$-0.140503\pi$
$137$	1581.51	+	913.083i	0.986257	+	0.569416i	0.0821036	+	0.996624i	$0.473836\pi$
$138$		0			0
$139$	320.792	+	185.209i	0.195750	+	0.113016i	0.594671	−	0.803969i	$-0.297282\pi$
$139$	320.792	+	185.209i	0.195750	+	0.113016i	−0.398922	+	0.916985i	$0.630615\pi$
$140$		0			0
$141$	−526.886	+	594.296i	−0.314693	+	0.354956i
$142$		0			0
$143$	−188.743	−	326.912i	−0.110374	−	0.191173i
$144$		0			0
$145$	355.864	+	205.458i	0.203813	+	0.117672i
$146$		0			0
$147$	−1535.41	−	905.000i	−0.861489	−	0.507777i
$148$		0			0
$149$	−88.0478	+	50.8344i	−0.0484104	+	0.0279498i	−0.524010	−	0.851712i	$-0.675565\pi$
$149$	−88.0478	+	50.8344i	−0.0484104	+	0.0279498i	0.475599	+	0.879662i	$0.342231\pi$
$150$		0			0
$151$	182.836	−	316.681i	0.0985363	−	0.170670i	−0.812543	−	0.582902i	$-0.801917\pi$
$151$	182.836	−	316.681i	0.0985363	−	0.170670i	0.911079	+	0.412232i	$0.135251\pi$
$152$		0			0
$153$	989.237	−	742.241i	0.522713	−	0.392200i
$154$		0			0
$155$	331.032	−	191.121i	0.171543	−	0.0990401i
$156$		0			0
$157$			2990.41i			1.52013i	0.649846	+	0.760066i	$0.274834\pi$
$157$			2990.41i			1.52013i	−0.649846	+	0.760066i	$0.725166\pi$
$158$		0			0
$159$	31.6303	−	154.649i	0.0157764	−	0.0771350i
$160$		0			0
$161$	−2867.39	−	478.721i	−1.40362	−	0.234338i
$162$		0			0
$163$	336.216	−	582.342i	0.161561	−	0.279832i	−0.773868	−	0.633347i	$-0.781680\pi$
$163$	336.216	−	582.342i	0.161561	−	0.279832i	0.935429	+	0.353515i	$0.115014\pi$
$164$		0			0
$165$	287.427	+	254.824i	0.135613	+	0.120231i
$166$		0			0
$167$	1463.64	−	2535.11i	0.678205	−	1.17468i	−0.297316	−	0.954779i	$-0.596092\pi$
$167$	1463.64	−	2535.11i	0.678205	−	1.17468i	0.975521	−	0.219906i	$-0.0705750\pi$
$168$		0			0
$169$	−1051.41	−	1821.10i	−0.478566	−	0.828901i
$170$		0			0
$171$	242.351	−	567.677i	0.108380	−	0.253868i
$172$		0			0
$173$	1549.89			0.681131			0.340566	−	0.940221i	$-0.389381\pi$
$173$	1549.89			0.681131			0.340566	+	0.940221i	$0.389381\pi$
$174$		0			0
$175$	2105.47	−	788.113i	0.909478	−	0.340433i
$176$		0			0
$177$	1608.08	−	1813.82i	0.682885	−	0.770254i
$178$		0			0
$179$	−1680.94	+	970.492i	−0.701897	+	0.405240i	−0.808053	−	0.589109i	$-0.799479\pi$
$179$	−1680.94	+	970.492i	−0.701897	+	0.405240i	0.106157	+	0.994349i	$0.466145\pi$
$180$		0			0
$181$			613.398i			0.251898i	0.992037	+	0.125949i	$0.0401975\pi$
$181$			613.398i			0.251898i	−0.992037	+	0.125949i	$0.959802\pi$
$182$		0			0
$183$	−1971.07	−	1747.49i	−0.796206	−	0.705893i
$184$		0			0
$185$	556.548			0.221180
$186$		0			0
$187$			1781.70i			0.696744i
$188$		0			0
$189$	709.390	+	2499.61i	0.273019	+	0.962009i
$190$		0			0
$191$			3635.29i			1.37717i	0.725154	+	0.688587i	$0.241769\pi$
$191$			3635.29i			1.37717i	−0.725154	+	0.688587i	$0.758231\pi$
$192$		0			0
$193$	−724.878			−0.270352			−0.135176	−	0.990822i	$-0.543160\pi$
$193$	−724.878			−0.270352			−0.135176	+	0.990822i	$0.543160\pi$
$194$		0			0
$195$	−71.7104	−	63.5763i	−0.0263348	−	0.0233477i
$196$		0			0
$197$			1264.97i			0.457488i	0.973487	+	0.228744i	$0.0734619\pi$
$197$			1264.97i			0.457488i	−0.973487	+	0.228744i	$0.926538\pi$
$198$		0			0
$199$	600.872	−	346.914i	0.214044	−	0.123578i	−0.389146	−	0.921176i	$-0.627230\pi$
$199$	600.872	−	346.914i	0.214044	−	0.123578i	0.603189	+	0.797598i	$0.293896\pi$
$200$		0			0
$201$	−2174.47	+	2452.67i	−0.763059	+	0.860687i
$202$		0			0
$203$	−3949.72	−	659.419i	−1.36560	−	0.227991i
$204$		0			0
$205$	454.020			0.154684
$206$		0			0
$207$	2543.56	+	3389.98i	0.854057	+	1.13826i
$208$		0			0
$209$	444.617	+	770.100i	0.147152	+	0.254875i
$210$		0			0
$211$	211.295	−	365.974i	0.0689392	−	0.119406i	−0.829495	−	0.558514i	$-0.811372\pi$
$211$	211.295	−	365.974i	0.0689392	−	0.119406i	0.898435	+	0.439107i	$0.144705\pi$
$212$		0			0
$213$	1605.87	+	1423.71i	0.516582	+	0.457987i
$214$		0			0
$215$	−302.061	+	523.186i	−0.0958159	+	0.165958i
$216$		0			0
$217$	−2368.27	+	2875.16i	−0.740871	+	0.899442i
$218$		0			0
$219$	−332.508	+	1625.72i	−0.102597	+	0.501626i
$220$		0			0
$221$		−	444.519i		−	0.135301i
$222$		0			0
$223$	3523.38	−	2034.22i	1.05804	−	0.610859i	0.133150	−	0.991096i	$-0.457491\pi$
$223$	3523.38	−	2034.22i	1.05804	−	0.610859i	0.924889	+	0.380237i	$0.124157\pi$
$224$		0			0
$225$	−3014.28	−	1286.85i	−0.893120	−	0.381289i
$226$		0			0
$227$	−1674.82	+	2900.87i	−0.489699	+	0.848184i	−0.999930	−	0.0118539i	$-0.996227\pi$
$227$	−1674.82	+	2900.87i	−0.489699	+	0.848184i	0.510231	+	0.860038i	$0.329560\pi$
$228$		0			0
$229$	−2254.04	+	1301.37i	−0.650442	+	0.375533i	−0.788625	−	0.614874i	$-0.789207\pi$
$229$	−2254.04	+	1301.37i	−0.650442	+	0.375533i	0.138184	+	0.990407i	$0.455874\pi$
$230$		0			0
$231$	−3493.77	−	1343.76i	−0.995121	−	0.382740i
$232$		0			0
$233$	3225.72	+	1862.37i	0.906969	+	0.523639i	0.879455	−	0.475982i	$-0.157907\pi$
$233$	3225.72	+	1862.37i	0.906969	+	0.523639i	0.0275144	+	0.999621i	$0.491241\pi$
$234$		0			0
$235$	−145.244	−	251.570i	−0.0403177	−	0.0698323i
$236$		0			0
$237$	−3464.86	+	3908.16i	−0.949648	+	1.07115i
$238$		0			0
$239$	−1000.97	−	577.908i	−0.270908	−	0.156409i	0.358392	−	0.933571i	$-0.383325\pi$
$239$	−1000.97	−	577.908i	−0.270908	−	0.156409i	−0.629300	+	0.777162i	$0.716658\pi$
$240$		0			0
$241$	−1831.90	−	1057.65i	−0.489638	−	0.282693i	0.234786	−	0.972047i	$-0.424561\pi$
$241$	−1831.90	−	1057.65i	−0.489638	−	0.282693i	−0.724424	+	0.689354i	$0.757894\pi$
$242$		0			0
$243$	1766.45	−	3350.91i	0.466328	−	0.884612i
$244$		0			0
$245$	491.646	−	428.036i	0.128205	−	0.111617i
$246$		0			0
$247$	−110.928	−	192.133i	−0.0285756	−	0.0494944i
$248$		0			0
$249$	−4227.49	−	864.645i	−1.07593	−	0.220059i
$250$		0			0
$251$	1100.68			0.276789			0.138394	−	0.990377i	$-0.455806\pi$
$251$	1100.68			0.276789			0.138394	+	0.990377i	$0.455806\pi$
$252$		0			0
$253$	−6105.66			−1.51723
$254$		0			0
$255$	143.084	+	429.107i	0.0351383	+	0.105379i
$256$		0			0
$257$	−966.948	−	1674.80i	−0.234695	−	0.406503i	0.724489	−	0.689286i	$-0.242076\pi$
$257$	−966.948	−	1674.80i	−0.234695	−	0.406503i	−0.959184	+	0.282783i	$0.908742\pi$
$258$		0			0
$259$	−5079.39	+	1901.30i	−1.21860	+	0.456142i
$260$		0			0
$261$	3503.65	+	4669.57i	0.830922	+	1.10743i
$262$		0			0
$263$	1694.21	+	978.155i	0.397223	+	0.229337i	0.685285	−	0.728275i	$-0.259678\pi$
$263$	1694.21	+	978.155i	0.397223	+	0.229337i	−0.288062	+	0.957612i	$0.593011\pi$
$264$		0			0
$265$	49.9988	+	28.8668i	0.0115902	+	0.00669161i
$266$		0			0
$267$	−1880.39	−	5639.25i	−0.431003	−	1.29257i
$268$		0			0
$269$	−1896.71	−	3285.20i	−0.429906	−	0.744618i	0.566959	−	0.823746i	$-0.308120\pi$
$269$	−1896.71	−	3285.20i	−0.429906	−	0.744618i	−0.996864	+	0.0791277i	$0.974787\pi$
$270$		0			0
$271$	5348.41	+	3087.91i	1.19887	+	0.692166i	0.960302	−	0.278961i	$-0.0899901\pi$
$271$	5348.41	+	3087.91i	1.19887	+	0.692166i	0.238564	+	0.971127i	$0.423323\pi$
$272$		0			0
$273$	871.663	+	335.255i	0.193243	+	0.0743245i
$274$		0			0
$275$	4089.12	−	2360.85i	0.896666	−	0.517690i
$276$		0			0
$277$	−4309.11	+	7463.60i	−0.934691	+	1.61893i	−0.159508	+	0.987197i	$0.550991\pi$
$277$	−4309.11	+	7463.60i	−0.934691	+	1.61893i	−0.775183	+	0.631737i	$0.782342\pi$
$278$		0			0
$279$	5391.35	−	650.661i	1.15689	−	0.139620i
$280$		0			0
$281$	784.803	−	453.106i	0.166610	−	0.0961923i	−0.414376	−	0.910106i	$-0.636000\pi$
$281$	784.803	−	453.106i	0.166610	−	0.0961923i	0.580986	+	0.813913i	$0.302667\pi$
$282$		0			0
$283$		−	1395.99i		−	0.293226i	−0.989194	−	0.146613i	$-0.953163\pi$
$283$		−	1395.99i		−	0.293226i	0.989194	−	0.146613i	$-0.0468373\pi$
$284$		0			0
$285$	168.927	+	149.766i	0.0351101	+	0.0311275i
$286$		0			0
$287$	−4143.65	+	1551.04i	−0.852237	+	0.319006i
$288$		0			0
$289$	1407.45	−	2437.78i	0.286475	−	0.496189i
$290$		0			0
$291$	−1872.32	+	9154.27i	−0.377172	+	1.84410i
$292$		0			0
$293$	4611.23	−	7986.88i	0.919422	−	1.59249i	0.119128	−	0.992879i	$-0.461990\pi$
$293$	4611.23	−	7986.88i	0.919422	−	1.59249i	0.800295	−	0.599607i	$-0.204676\pi$
$294$		0			0
$295$	443.291	+	767.802i	0.0874894	+	0.151536i
$296$		0			0
$297$	2334.09	+	4932.84i	0.456018	+	0.963745i
$298$		0			0
$299$	1523.31			0.294632
$300$		0			0
$301$	969.467	−	5806.81i	0.185645	−	1.11196i
$302$		0			0
$303$	561.748	+	1684.68i	0.106507	+	0.319413i
$304$		0			0
$305$	834.367	−	481.722i	0.156642	−	0.0904372i
$306$		0			0
$307$		−	6442.61i		−	1.19772i	−0.800854	−	0.598859i	$-0.795621\pi$
$307$		−	6442.61i		−	1.19772i	0.800854	−	0.598859i	$-0.204379\pi$
$308$		0			0
$309$	−491.685	+	2403.98i	−0.0905210	+	0.442582i
$310$		0			0
$311$	6993.54			1.27514			0.637568	−	0.770394i	$-0.279941\pi$
$311$	6993.54			1.27514			0.637568	+	0.770394i	$0.279941\pi$
$312$		0			0
$313$		−	6023.42i		−	1.08774i	−0.839168	−	0.543872i	$-0.816958\pi$
$313$		−	6023.42i		−	1.08774i	0.839168	−	0.543872i	$-0.183042\pi$
$314$		0			0
$315$	−949.357	−	43.0567i	−0.169810	−	0.00770149i
$316$		0			0
$317$		−	8668.66i		−	1.53590i	−0.640509	−	0.767950i	$-0.721277\pi$
$317$		−	8668.66i		−	1.53590i	0.640509	−	0.767950i	$-0.278723\pi$
$318$		0			0
$319$	−8410.30			−1.47613
$320$		0			0
$321$	7734.38	−	2579.00i	1.34483	−	0.448429i
$322$		0			0
$323$			1047.14i			0.180386i
$324$		0			0
$325$	−1020.20	+	589.011i	−0.174124	+	0.100531i
$326$		0			0
$327$	3203.73	+	655.256i	0.541794	+	0.110813i
$328$		0			0
$329$	2185.00	+	1799.79i	0.366149	+	0.301597i
$330$		0			0
$331$	−1046.29			−0.173745			−0.0868724	−	0.996219i	$-0.527687\pi$
$331$	−1046.29			−0.173745			−0.0868724	+	0.996219i	$0.527687\pi$
$332$		0			0
$333$	7271.86	+	3104.48i	1.19668	+	0.510885i
$334$		0			0
$335$	−599.424	−	1038.23i	−0.0977612	−	0.169327i
$336$		0			0
$337$	3755.97	−	6505.53i	0.607124	−	1.05157i	−0.384588	−	0.923088i	$-0.625657\pi$
$337$	3755.97	−	6505.53i	0.607124	−	1.05157i	0.991712	−	0.128481i	$-0.0410100\pi$
$338$		0			0
$339$	7964.65	−	2655.78i	1.27605	−	0.425493i
$340$		0			0
$341$	−3911.71	+	6775.28i	−0.621205	+	1.07596i
$342$		0			0
$343$	−3024.78	+	5586.08i	−0.476160	+	0.879359i
$344$		0			0
$345$	−1470.49	+	490.330i	−0.229475	+	0.0765174i
$346$		0			0
$347$		−	11746.7i		−	1.81728i	−0.417582	−	0.908639i	$-0.637122\pi$
$347$		−	11746.7i		−	1.81728i	0.417582	−	0.908639i	$-0.362878\pi$
$348$		0			0
$349$	−7738.38	+	4467.75i	−1.18689	+	0.685253i	−0.957599	−	0.288104i	$-0.906975\pi$
$349$	−7738.38	+	4467.75i	−1.18689	+	0.685253i	−0.229294	+	0.973357i	$0.573642\pi$
$350$		0			0
$351$	−582.333	−	1230.70i	−0.0885545	−	0.187150i
$352$		0			0
$353$	5199.46	−	9005.74i	0.783965	−	1.35787i	−0.145651	−	0.989336i	$-0.546528\pi$
$353$	5199.46	−	9005.74i	0.783965	−	1.35787i	0.929616	−	0.368531i	$-0.120139\pi$
$354$		0			0
$355$	−679.773	+	392.467i	−0.101630	+	0.0586761i
$356$		0			0
$357$	−2771.80	−	3427.48i	−0.410922	−	0.508127i
$358$		0			0
$359$	2639.17	+	1523.72i	0.387994	+	0.224008i	0.681291	−	0.732013i	$-0.261419\pi$
$359$	2639.17	+	1523.72i	0.387994	+	0.224008i	−0.293297	+	0.956021i	$0.594752\pi$
$360$		0			0
$361$	−3168.19	−	5487.46i	−0.461902	−	0.800039i
$362$		0			0
$363$	−926.635	−	189.524i	−0.133983	−	0.0274034i
$364$		0			0
$365$	−525.604	−	303.458i	−0.0753736	−	0.0435170i
$366$		0			0
$367$	4936.76	+	2850.24i	0.702170	+	0.405398i	0.808155	−	0.588970i	$-0.200466\pi$
$367$	4936.76	+	2850.24i	0.702170	+	0.405398i	−0.105985	+	0.994368i	$0.533800\pi$
$368$		0			0
$369$	5932.23	+	2532.57i	0.836909	+	0.357291i
$370$		0			0
$371$	−554.934	−	92.6482i	−0.0776570	−	0.0129651i
$372$		0			0
$373$	−5246.24	−	9086.75i	−0.728257	−	1.26138i	−0.957619	−	0.288037i	$-0.906997\pi$
$373$	−5246.24	−	9086.75i	−0.728257	−	1.26138i	0.229362	−	0.973341i	$-0.426336\pi$
$374$		0			0
$375$	1614.13	−	1820.64i	0.222275	−	0.250714i
$376$		0			0
$377$	2098.29			0.286651
$378$		0			0
$379$	14073.9			1.90746			0.953732	−	0.300657i	$-0.0972059\pi$
$379$	14073.9			1.90746			0.953732	+	0.300657i	$0.0972059\pi$
$380$		0			0
$381$	−1870.08	+	2109.35i	−0.251463	+	0.283636i
$382$		0			0
$383$	−1933.55	−	3349.01i	−0.257963	−	0.446805i	0.707733	−	0.706480i	$-0.249718\pi$
$383$	−1933.55	−	3349.01i	−0.257963	−	0.446805i	−0.965696	+	0.259675i	$0.916385\pi$
$384$		0			0
$385$	870.453	−	1056.76i	0.115227	−	0.139889i
$386$		0			0
$387$	−6865.12	+	5151.02i	−0.901741	+	0.676591i
$388$		0			0
$389$	9472.05	+	5468.69i	1.23458	+	0.712786i	0.967982	−	0.251021i	$-0.0807665\pi$
$389$	9472.05	+	5468.69i	1.23458	+	0.712786i	0.266600	+	0.963807i	$0.414100\pi$
$390$		0			0
$391$	−6226.64	−	3594.95i	−0.805357	−	0.464973i
$392$		0			0
$393$	−7350.42	−	1503.38i	−0.943459	−	0.192965i
$394$		0			0
$395$	−955.139	−	1654.35i	−0.121667	−	0.210733i
$396$		0			0
$397$	1745.19	+	1007.59i	0.220626	+	0.127379i	0.606240	−	0.795282i	$-0.292677\pi$
$397$	1745.19	+	1007.59i	0.220626	+	0.127379i	−0.385614	+	0.922660i	$0.626010\pi$
$398$		0			0
$399$	−2053.36	−	789.755i	−0.257636	−	0.0990908i
$400$		0			0
$401$	11131.3	−	6426.64i	1.38621	−	0.800327i	0.393322	−	0.919401i	$-0.371326\pi$
$401$	11131.3	−	6426.64i	1.38621	−	0.800327i	0.992885	+	0.119073i	$0.0379923\pi$
$402$		0			0
$403$	975.935	−	1690.37i	0.120632	−	0.208941i
$404$		0			0
$405$	958.288	+	1000.58i	0.117575	+	0.122764i
$406$		0			0
$407$	−9864.87	+	5695.49i	−1.20143	+	0.693648i
$408$		0			0
$409$			9745.11i			1.17815i	0.808077	+	0.589077i	$0.200508\pi$
$409$			9745.11i			1.17815i	−0.808077	+	0.589077i	$0.799492\pi$
$410$		0			0
$411$	−9001.79	+	3001.61i	−1.08035	+	0.360240i
$412$		0			0
$413$	−6668.72	−	5493.03i	−0.794543	−	0.654465i
$414$		0			0
$415$	789.104	−	1366.77i	0.0933388	−	0.161667i
$416$		0			0
$417$	−1825.92	+	608.845i	−0.214426	+	0.0714995i
$418$		0			0
$419$	4142.47	−	7174.97i	0.482990	−	0.836564i	−0.516819	−	0.856095i	$-0.672884\pi$
$419$	4142.47	−	7174.97i	0.482990	−	0.836564i	0.999809	+	0.0195309i	$0.00621728\pi$
$420$		0			0
$421$	−7400.02	−	12817.2i	−0.856663	−	1.48378i	−0.875094	−	0.483953i	$-0.839201\pi$
$421$	−7400.02	−	12817.2i	−0.856663	−	1.48378i	0.0184314	−	0.999830i	$-0.494133\pi$
$422$		0			0
$423$	−494.474	−	4097.19i	−0.0568372	−	0.470951i
$424$		0			0
$425$	5560.18			0.634608
$426$		0			0
$427$	−5969.25	+	7246.87i	−0.676516	+	0.821313i
$428$		0			0
$429$	1921.69	+	393.041i	0.216270	+	0.0442336i
$430$		0			0
$431$	−384.561	+	222.027i	−0.0429783	+	0.0248136i	−0.521335	−	0.853352i	$-0.674566\pi$
$431$	−384.561	+	222.027i	−0.0429783	+	0.0248136i	0.478357	+	0.878166i	$0.341233\pi$
$432$		0			0
$433$		−	3694.87i		−	0.410079i	−0.978754	−	0.205039i	$-0.934268\pi$
$433$		−	3694.87i		−	0.410079i	0.978754	−	0.205039i	$-0.0657322\pi$
$434$		0			0
$435$	−2025.55	+	675.410i	−0.223259	+	0.0744447i
$436$		0			0
$437$	−3588.42			−0.392809
$438$		0			0
$439$			13415.6i			1.45852i	0.684234	+	0.729262i	$0.260137\pi$
$439$			13415.6i			1.45852i	−0.684234	+	0.729262i	$0.739863\pi$
$440$		0			0
$441$	8811.48	−	2850.26i	0.951461	−	0.307770i
$442$		0			0
$443$			14631.9i			1.56926i	0.619963	+	0.784631i	$0.287148\pi$
$443$			14631.9i			1.56926i	−0.619963	+	0.784631i	$0.712852\pi$
$444$		0			0
$445$	2174.19			0.231610
$446$		0			0
$447$	105.859	−	517.572i	0.0112012	−	0.0547658i
$448$		0			0
$449$		−	983.155i		−	0.103336i	−0.998664	−	0.0516681i	$-0.983546\pi$
$449$		−	983.155i		−	0.103336i	0.998664	−	0.0516681i	$-0.0164538\pi$
$450$		0			0
$451$	−8047.55	+	4646.25i	−0.840231	+	0.485108i
$452$		0			0
$453$	601.043	+	1802.52i	0.0623388	+	0.186953i
$454$		0			0
$455$	−217.170	+	263.652i	−0.0223760	+	0.0271652i
$456$		0			0
$457$	−3666.28			−0.375276			−0.187638	−	0.982238i	$-0.560083\pi$
$457$	−3666.28			−0.375276			−0.187638	+	0.982238i	$0.560083\pi$
$458$		0			0
$459$	−524.068	+	6404.86i	−0.0532928	+	0.651314i
$460$		0			0
$461$	4271.79	+	7398.96i	0.431577	+	0.747514i	0.997009	−	0.0772812i	$-0.0246239\pi$
$461$	4271.79	+	7398.96i	0.431577	+	0.747514i	−0.565432	+	0.824795i	$0.691291\pi$
$462$		0			0
$463$	3109.20	−	5385.29i	0.312088	−	0.540552i	−0.666726	−	0.745303i	$-0.732305\pi$
$463$	3109.20	−	5385.29i	0.312088	−	0.540552i	0.978814	+	0.204751i	$0.0656383\pi$
$464$		0			0
$465$	−397.995	+	1945.91i	−0.0396915	+	0.194063i
$466$		0			0
$467$	−7487.21	+	12968.2i	−0.741899	+	1.28501i	0.209731	+	0.977759i	$0.432741\pi$
$467$	−7487.21	+	12968.2i	−0.741899	+	1.28501i	−0.951630	+	0.307247i	$0.900592\pi$
$468$		0			0
$469$	9017.53	+	7427.75i	0.887827	+	0.731304i
$470$		0			0
$471$	−11627.1	−	10308.2i	−1.13747	−	1.00845i
$472$		0			0
$473$		−	12364.7i		−	1.20196i
$474$		0			0
$475$	2403.26	−	1387.52i	0.232145	−	0.134029i
$476$		0			0
$477$	492.263	+	656.073i	0.0472519	+	0.0629759i
$478$		0			0
$479$	−1024.18	+	1773.94i	−0.0976954	+	0.169213i	−0.910730	−	0.413001i	$-0.864480\pi$
$479$	−1024.18	+	1773.94i	−0.0976954	+	0.169213i	0.813035	+	0.582215i	$0.197814\pi$
$480$		0			0
$481$	2461.19	−	1420.97i	0.233307	−	0.134700i
$482$		0			0
$483$	11745.5	−	9498.59i	1.10650	−	0.894826i
$484$		0			0
$485$	−2959.62	−	1708.74i	−0.277092	−	0.159979i
$486$		0			0
$487$	−3427.55	−	5936.69i	−0.318926	−	0.552396i	0.661338	−	0.750088i	$-0.269989\pi$
$487$	−3427.55	−	5936.69i	−0.318926	−	0.552396i	−0.980264	+	0.197692i	$0.936655\pi$
$488$		0			0
$489$	1105.25	+	3314.64i	0.102211	+	0.306530i
$490$		0			0
$491$	4312.68	+	2489.93i	0.396392	+	0.228857i	0.684926	−	0.728613i	$-0.259835\pi$
$491$	4312.68	+	2489.93i	0.396392	+	0.228857i	−0.288534	+	0.957470i	$0.593168\pi$
$492$		0			0
$493$	−8576.94	−	4951.90i	−0.783541	−	0.452378i
$494$		0			0
$495$	−1981.58	+	239.149i	−0.179930	+	0.0217150i
$496$		0			0
$497$	4863.25	−	5904.15i	0.438927	−	0.532872i
$498$		0			0
$499$	3238.99	+	5610.09i	0.290575	+	0.503291i	0.973946	−	0.226781i	$-0.0728201\pi$
$499$	3238.99	+	5610.09i	0.290575	+	0.503291i	−0.683371	+	0.730071i	$0.739487\pi$
$500$		0			0
$501$	4811.49	+	14429.6i	0.429065	+	1.28676i
$502$		0			0
$503$	−5984.97			−0.530530			−0.265265	−	0.964176i	$-0.585459\pi$
$503$	−5984.97			−0.530530			−0.265265	+	0.964176i	$0.585459\pi$
$504$		0			0
$505$	−649.520			−0.0572342
$506$		0			0
$507$	10705.0	+	2189.48i	0.937720	+	0.191791i
$508$		0			0
$509$	2561.33	+	4436.36i	0.223043	+	0.386322i	0.955731	−	0.294243i	$-0.0950675\pi$
$509$	2561.33	+	4436.36i	0.223043	+	0.386322i	−0.732687	+	0.680565i	$0.761734\pi$
$510$		0			0
$511$	5833.65	+	973.948i	0.505021	+	0.0843149i
$512$		0			0
$513$	1371.79	+	2899.13i	0.118063	+	0.249512i
$514$		0			0
$515$	−777.220	−	448.728i	−0.0665018	−	0.0383948i
$516$		0			0
$517$	5148.92	+	2972.73i	0.438006	+	0.252883i
$518$		0			0
$519$	−5342.61	+	6026.16i	−0.451859	+	0.509670i
$520$		0			0
$521$	−8086.94	−	14007.0i	−0.680029	−	1.17784i	−0.974972	−	0.222330i	$-0.928634\pi$
$521$	−8086.94	−	14007.0i	−0.680029	−	1.17784i	0.294943	−	0.955515i	$-0.404699\pi$
$522$		0			0
$523$	−2114.57	−	1220.85i	−0.176795	−	0.102073i	0.408991	−	0.912538i	$-0.365881\pi$
$523$	−2114.57	−	1220.85i	−0.176795	−	0.102073i	−0.585786	+	0.810466i	$0.699214\pi$
$524$		0			0
$525$	−4193.48	+	10903.0i	−0.348607	+	0.906377i
$526$		0			0
$527$	−7978.43	+	4606.35i	−0.659480	+	0.380751i
$528$		0			0
$529$	6235.91	−	10800.9i	0.512527	−	0.887722i
$530$		0			0
$531$	1509.16	+	12504.8i	0.123337	+	1.02196i
$532$		0			0
$533$	2007.79	−	1159.20i	0.163165	−	0.0942034i
$534$		0			0
$535$			2981.96i			0.240975i
$536$		0			0
$537$	2020.97	−	9881.09i	0.162405	−	0.794042i
$538$		0			0
$539$	−4334.13	+	12618.3i	−0.346353	+	1.00836i
$540$		0			0
$541$	−6556.23	+	11355.7i	−0.521025	+	0.902441i	0.478676	+	0.877991i	$0.341117\pi$
$541$	−6556.23	+	11355.7i	−0.521025	+	0.902441i	−0.999701	+	0.0244500i	$0.992217\pi$
$542$		0			0
$543$	−2384.97	−	2114.44i	−0.188488	−	0.167107i
$544$		0			0
$545$	−598.009	+	1035.78i	−0.0470016	+	0.0814092i
$546$		0			0
$547$	4518.94	+	7827.03i	0.353228	+	0.611809i	0.986813	−	0.161864i	$-0.0517506\pi$
$547$	4518.94	+	7827.03i	0.353228	+	0.611809i	−0.633585	+	0.773673i	$0.718417\pi$
$548$		0			0
$549$	13588.9	−	1640.00i	1.05640	−	0.127492i
$550$		0			0
$551$	−4942.91			−0.382169
$552$		0			0
$553$	14368.8	+	11835.6i	1.10493	+	0.910127i
$554$		0			0
$555$	−1918.48	+	2163.93i	−0.146729	+	0.165502i
$556$		0			0
$557$	14829.3	−	8561.71i	1.12808	−	0.651295i	0.184626	−	0.982809i	$-0.440893\pi$
$557$	14829.3	−	8561.71i	1.12808	−	0.651295i	0.943450	+	0.331514i	$0.107559\pi$
$558$		0			0
$559$			3084.87i			0.233410i
$560$		0			0
$561$	−6927.49	−	6141.71i	−0.521353	−	0.462216i
$562$		0			0
$563$	−24282.9			−1.81777			−0.908884	−	0.417048i	$-0.863065\pi$
$563$	−24282.9			−1.81777			−0.908884	+	0.417048i	$0.863065\pi$
$564$		0			0
$565$			3070.74i			0.228650i
$566$		0			0
$567$	−12164.1	−	5858.19i	−0.900961	−	0.433899i
$568$		0			0
$569$			2572.35i			0.189523i	0.995500	+	0.0947616i	$0.0302089\pi$
$569$			2572.35i			0.189523i	−0.995500	+	0.0947616i	$0.969791\pi$
$570$		0			0
$571$	−16593.3			−1.21613			−0.608064	−	0.793888i	$-0.708054\pi$
$571$	−16593.3			−1.21613			−0.608064	+	0.793888i	$0.708054\pi$
$572$		0			0
$573$	−14134.5	−	12531.2i	−1.03050	−	0.913609i
$574$		0			0
$575$			19054.0i			1.38193i
$576$		0			0
$577$	−20461.9	+	11813.7i	−1.47632	+	0.852356i	−0.999643	−	0.0267211i	$-0.991493\pi$
$577$	−20461.9	+	11813.7i	−1.47632	+	0.852356i	−0.476680	+	0.879077i	$0.658160\pi$
$578$		0			0
$579$	2498.72	−	2818.42i	0.179350	−	0.202296i
$580$		0			0
$581$	−2532.63	+	15169.7i	−0.180845	+	1.08321i
$582$		0			0
$583$	−1181.65			−0.0839430
$584$		0			0
$585$	494.386	−	59.6654i	0.0349407	−	0.00421686i
$586$		0			0
$587$	11765.5	+	20378.5i	0.827284	+	1.43290i	0.900161	+	0.435557i	$0.143449\pi$
$587$	11765.5	+	20378.5i	0.827284	+	1.43290i	−0.0728767	+	0.997341i	$0.523218\pi$
$588$		0			0
$589$	−2298.99	+	3981.97i	−0.160829	+	0.278564i
$590$		0			0
$591$	−4918.35	−	4360.46i	−0.342325	−	0.303495i
$592$		0			0
$593$	3428.18	−	5937.78i	0.237400	−	0.411190i	−0.722567	−	0.691301i	$-0.757038\pi$
$593$	3428.18	−	5937.78i	0.237400	−	0.411190i	0.959968	+	0.280111i	$0.0903713\pi$
$594$		0			0
$595$	1509.91	−	565.184i	0.104034	−	0.0389416i
$596$		0			0
$597$	−722.421	+	3532.11i	−0.0495255	+	0.242144i
$598$		0			0
$599$			3664.27i			0.249947i	0.992160	+	0.124973i	$0.0398845\pi$
$599$			3664.27i			0.249947i	−0.992160	+	0.124973i	$0.960115\pi$
$600$		0			0
$601$	8573.94	−	4950.17i	0.581927	−	0.335976i	−0.179972	−	0.983672i	$-0.557601\pi$
$601$	8573.94	−	4950.17i	0.581927	−	0.335976i	0.761899	+	0.647696i	$0.224267\pi$
$602$		0			0
$603$	−2040.70	−	16909.2i	−0.137817	−	1.14195i
$604$		0			0
$605$	172.966	−	299.586i	0.0116232	−	0.0201321i
$606$		0			0
$607$	18972.6	−	10953.9i	1.26866	−	0.732461i	0.293925	−	0.955829i	$-0.405038\pi$
$607$	18972.6	−	10953.9i	1.26866	−	0.732461i	0.974734	+	0.223368i	$0.0717051\pi$
$608$		0			0
$609$	16179.0	−	13083.9i	1.07653	−	0.870587i
$610$		0			0
$611$	−1284.61	−	741.669i	−0.0850567	−	0.0491075i
$612$		0			0
$613$	−3679.09	−	6372.37i	−0.242409	−	0.419865i	0.718991	−	0.695020i	$-0.244604\pi$
$613$	−3679.09	−	6372.37i	−0.242409	−	0.419865i	−0.961400	+	0.275154i	$0.911271\pi$
$614$		0			0
$615$	−1565.05	+	1765.29i	−0.102616	+	0.115745i
$616$		0			0
$617$	2206.69	+	1274.03i	0.143984	+	0.0831291i	0.570261	−	0.821463i	$-0.306842\pi$
$617$	2206.69	+	1274.03i	0.143984	+	0.0831291i	−0.426277	+	0.904592i	$0.640175\pi$
$618$		0			0
$619$	21105.0	+	12185.0i	1.37041	+	0.791206i	0.990979	−	0.134015i	$-0.0427869\pi$
$619$	21105.0	+	12185.0i	1.37041	+	0.791206i	0.379430	+	0.925221i	$0.376120\pi$
$620$		0			0
$621$	−21948.6	−	1795.91i	−1.41830	−	0.116051i
$622$		0			0
$623$	−19842.9	+	7427.54i	−1.27607	+	0.477653i
$624$		0			0
$625$	−7141.80	−	12370.0i	−0.457075	−	0.791678i
$626$		0			0
$627$	−4526.89	−	925.881i	−0.288336	−	0.0589731i
$628$		0			0
$629$	−13413.8			−0.850305
$630$		0			0
$631$	19187.2			1.21051			0.605254	−	0.796032i	$-0.293072\pi$
$631$	19187.2			1.21051			0.605254	+	0.796032i	$0.293072\pi$
$632$		0			0
$633$	694.599	+	2083.09i	0.0436142	+	0.130799i
$634$		0			0
$635$	−515.517	−	892.901i	−0.0322168	−	0.0558011i
$636$		0			0
$637$	1081.33	−	3148.14i	0.0672586	−	0.195815i
$638$		0			0
$639$	−11071.1	+	1336.13i	−0.685396	+	0.0827176i
$640$		0			0
$641$	8657.25	+	4998.27i	0.533449	+	0.307987i	0.742420	−	0.669935i	$-0.233678\pi$
$641$	8657.25	+	4998.27i	0.533449	+	0.307987i	−0.208971	+	0.977922i	$0.567011\pi$
$642$		0			0
$643$	14185.9	+	8190.25i	0.870044	+	0.502320i	0.867363	−	0.497676i	$-0.165813\pi$
$643$	14185.9	+	8190.25i	0.870044	+	0.502320i	0.00268127	+	0.999996i	$0.499147\pi$
$644$		0			0
$645$	−992.977	−	2977.92i	−0.0606177	−	0.181792i
$646$		0			0
$647$	−13680.6	−	23695.5i	−0.831283	−	1.43982i	−0.897021	−	0.441987i	$-0.854274\pi$
$647$	−13680.6	−	23695.5i	−0.831283	−	1.43982i	0.0657388	−	0.997837i	$-0.479060\pi$
$648$		0			0
$649$	−15714.7	−	9072.91i	−0.950474	−	0.548756i
$650$		0			0
$651$	−3015.33	−	19119.1i	−0.181536	−	1.15106i
$652$		0			0
$653$	−19362.9	+	11179.2i	−1.16038	+	0.669946i	−0.951395	−	0.307973i	$-0.900349\pi$
$653$	−19362.9	+	11179.2i	−1.16038	+	0.669946i	−0.208985	+	0.977919i	$0.567016\pi$
$654$		0			0
$655$	1372.03	−	2376.43i	0.0818468	−	0.141763i
$656$		0			0
$657$	−5174.82	−	6896.85i	−0.307289	−	0.409546i
$658$		0			0
$659$	1570.82	−	906.912i	0.0928533	−	0.0536089i	−0.452854	−	0.891585i	$-0.649594\pi$
$659$	1570.82	−	906.912i	0.0928533	−	0.0536089i	0.545708	+	0.837976i	$0.316261\pi$
$660$		0			0
$661$			16831.1i			0.990397i	0.868780	+	0.495198i	$0.164905\pi$
$661$			16831.1i			0.990397i	−0.868780	+	0.495198i	$0.835095\pi$
$662$		0			0
$663$	1728.34	+	1532.30i	0.101242	+	0.0897580i
$664$		0			0
$665$	511.584	−	621.080i	0.0298321	−	0.0362172i
$666$		0			0
$667$	16969.5	−	29392.0i	0.985099	−	1.70624i
$668$		0			0
$669$	−4236.11	+	20711.5i	−0.244809	+	1.19694i
$670$		0			0
$671$	−9859.49	+	17077.1i	−0.567245	+	0.982498i
$672$		0			0
$673$	7863.55	+	13620.1i	0.450397	+	0.780111i	0.998411	−	0.0563584i	$-0.0179490\pi$
$673$	7863.55	+	13620.1i	0.450397	+	0.780111i	−0.548013	+	0.836470i	$0.684616\pi$
$674$		0			0
$675$	15394.0	−	7284.01i	0.877798	−	0.415351i
$676$		0			0
$677$	1593.96			0.0904888			0.0452444	−	0.998976i	$-0.485593\pi$
$677$	1593.96			0.0904888			0.0452444	+	0.998976i	$0.485593\pi$
$678$		0			0
$679$	32848.7	+	5484.20i	1.85658	+	0.309962i
$680$		0			0
$681$	−5505.69	−	16511.5i	−0.309807	−	0.929107i
$682$		0			0
$683$	26968.4	−	15570.2i	1.51086	−	0.872295i	0.510940	−	0.859616i	$-0.329297\pi$
$683$	26968.4	−	15570.2i	1.51086	−	0.872295i	0.999920	−	0.0126788i	$-0.00403589\pi$
$684$		0			0
$685$		−	3470.60i		−	0.193584i
$686$		0			0
$687$	2710.00	−	13249.9i	0.150499	−	0.735833i
$688$		0			0
$689$	294.810			0.0163009
$690$		0			0
$691$		−	23163.3i		−	1.27521i	−0.770362	−	0.637607i	$-0.779924\pi$
$691$		−	23163.3i		−	1.27521i	0.770362	−	0.637607i	$-0.220076\pi$
$692$		0			0
$693$	17268.1	−	8952.14i	0.946550	−	0.490712i
$694$		0			0
$695$		−	703.976i		−	0.0384221i
$696$		0			0
$697$	−10942.7			−0.594667
$698$		0			0
$699$	−18360.5	+	6122.23i	−0.993501	+	0.331279i
$700$		0			0
$701$			29311.3i			1.57928i	0.613572	+	0.789639i	$0.289732\pi$
$701$			29311.3i			1.57928i	−0.613572	+	0.789639i	$0.710268\pi$
$702$		0			0
$703$	−5797.79	+	3347.36i	−0.311049	+	0.179584i
$704$		0			0
$705$	1478.80	+	302.459i	0.0790000	+	0.0161578i
$706$		0			0
$707$	5927.90	−	2218.91i	0.315335	−	0.118035i
$708$		0			0
$709$	17085.7			0.905028			0.452514	−	0.891757i	$-0.350527\pi$
$709$	17085.7			0.905028			0.452514	+	0.891757i	$0.350527\pi$
$710$		0			0
$711$	−3251.72	−	26943.6i	−0.171517	−	1.42119i
$712$		0			0
$713$	−15785.3	−	27341.0i	−0.829124	−	1.43609i
$714$		0			0
$715$	−358.703	+	621.291i	−0.0187618	+	0.0324965i
$716$		0			0
$717$	5697.41	−	1899.78i	0.296755	−	0.0989518i
$718$		0			0
$719$	−4805.75	+	8323.80i	−0.249269	+	0.431746i	−0.963323	−	0.268344i	$-0.913524\pi$
$719$	−4805.75	+	8323.80i	−0.249269	+	0.431746i	0.714054	+	0.700090i	$0.246857\pi$
$720$		0			0
$721$	8626.33	+	1440.19i	0.445577	+	0.0743906i
$722$		0			0
$723$	10427.0	−	3476.84i	0.536354	−	0.178845i
$724$		0			0
$725$			26246.1i			1.34449i
$726$		0			0
$727$	−12057.5	+	6961.43i	−0.615117	+	0.355138i	−0.774965	−	0.632004i	$-0.782233\pi$
$727$	−12057.5	+	6961.43i	−0.615117	+	0.355138i	0.159849	+	0.987142i	$0.448899\pi$
$728$		0			0
$729$	6939.62	+	18419.1i	0.352569	+	0.935786i
$730$		0			0
$731$	7280.20	−	12609.7i	0.368356	−	0.638010i
$732$		0			0
$733$	2391.14	−	1380.53i	0.120490	−	0.0695646i	−0.438544	−	0.898710i	$-0.644506\pi$
$733$	2391.14	−	1380.53i	0.120490	−	0.0695646i	0.559033	+	0.829145i	$0.311172\pi$
$734$		0			0
$735$	−30.4954	+	3387.06i	−0.00153039	+	0.169978i
$736$		0			0
$737$	21249.7	+	12268.5i	1.06207	+	0.613184i
$738$		0			0
$739$	−6285.08	−	10886.1i	−0.312856	−	0.541882i	0.666124	−	0.745841i	$-0.267952\pi$
$739$	−6285.08	−	10886.1i	−0.312856	−	0.541882i	−0.978979	+	0.203959i	$0.934619\pi$
$740$		0			0
$741$	1129.42	+	230.999i	0.0559921	+	0.0114520i
$742$		0			0
$743$	28569.3	+	16494.5i	1.41064	+	0.814435i	0.995449	−	0.0952981i	$-0.0303804\pi$
$743$	28569.3	+	16494.5i	1.41064	+	0.814435i	0.415194	+	0.909733i	$0.363714\pi$
$744$		0			0
$745$	167.334	+	96.6101i	0.00822903	+	0.00475103i
$746$		0			0
$747$	17934.4	−	13456.5i	0.878428	−	0.659099i
$748$		0			0
$749$	−10187.1	−	27215.1i	−0.496966	−	1.32766i
$750$		0			0
$751$	5990.55	+	10375.9i	0.291076	+	0.504159i	0.974064	−	0.226271i	$-0.0726534\pi$
$751$	5990.55	+	10375.9i	0.291076	+	0.504159i	−0.682988	+	0.730429i	$0.739320\pi$
$752$		0			0
$753$	−3794.13	+	4279.56i	−0.183620	+	0.207113i
$754$		0			0
$755$	−694.954			−0.0334993
$756$		0			0
$757$	34387.9			1.65106			0.825529	−	0.564360i	$-0.190877\pi$
$757$	34387.9			1.65106			0.825529	+	0.564360i	$0.190877\pi$
$758$		0			0
$759$	21046.8	−	23739.6i	1.00652	−	1.13530i
$760$		0			0
$761$	−14406.2	−	24952.3i	−0.686234	−	1.18859i	−0.973047	−	0.230606i	$-0.925929\pi$
$761$	−14406.2	−	24952.3i	−0.686234	−	1.18859i	0.286813	−	0.957987i	$-0.407404\pi$
$762$		0			0
$763$	1919.31	−	11496.1i	0.0910664	−	0.545460i
$764$		0			0
$765$	−2161.65	−	922.846i	−0.102163	−	0.0436151i
$766$		0			0
$767$	3920.68	+	2263.61i	0.184573	+	0.106563i
$768$		0			0
$769$	−17312.9	−	9995.63i	−0.811860	−	0.468728i	0.0357414	−	0.999361i	$-0.488621\pi$
$769$	−17312.9	−	9995.63i	−0.811860	−	0.468728i	−0.847601	+	0.530633i	$0.821954\pi$
$770$		0			0
$771$	9845.01	+	2013.59i	0.459870	+	0.0940568i
$772$		0			0
$773$	−11813.5	−	20461.5i	−0.549677	−	0.952069i	−0.998296	−	0.0583457i	$-0.981417\pi$
$773$	−11813.5	−	20461.5i	−0.549677	−	0.952069i	0.448619	−	0.893723i	$-0.351916\pi$
$774$		0			0
$775$	21143.7	+	12207.3i	0.980005	+	0.565806i
$776$		0			0
$777$	10116.7	−	26303.2i	0.467095	−	1.21445i
$778$		0			0
$779$	−4729.71	+	2730.70i	−0.217535	+	0.125594i
$780$		0			0
$781$	8032.70	−	13913.0i	0.368031	−	0.637449i
$782$		0			0
$783$	−30233.3	−	2473.80i	−1.37988	−	0.112907i
$784$		0			0
$785$	4921.83	−	2841.62i	0.223780	−	0.129200i
$786$		0			0
$787$		−	1687.18i		−	0.0764187i	−0.999270	−	0.0382094i	$-0.987835\pi$
$787$		−	1687.18i		−	0.0764187i	0.999270	−	0.0382094i	$-0.0121654\pi$
$788$		0			0
$789$	−9643.31	+	3215.52i	−0.435121	+	0.145090i
$790$		0			0
$791$	−10490.4	−	28025.4i	−0.471548	−	1.25976i
$792$		0			0
$793$	2459.85	−	4260.59i	0.110154	−	0.190792i
$794$		0			0
$795$	−284.589	+	94.8950i	−0.0126960	+	0.00423343i
$796$		0			0
$797$	−13519.0	+	23415.5i	−0.600836	+	1.04068i	0.391859	+	0.920025i	$0.371832\pi$
$797$	−13519.0	+	23415.5i	−0.600836	+	1.04068i	−0.992695	+	0.120653i	$0.961501\pi$
$798$		0			0
$799$	3500.62	+	6063.26i	0.154998	+	0.268464i
$800$		0			0
$801$	28408.0	+	12127.9i	1.25312	+	0.534978i
$802$		0			0
$803$	12421.8			0.545899
$804$		0			0
$805$	1936.81	+	5174.26i	0.0847994	+	0.226545i
$806$		0			0
$807$	19311.4	+	3949.75i	0.842373	+	0.172290i
$808$		0			0
$809$	4823.45	−	2784.82i	0.209621	−	0.121025i	−0.391514	−	0.920172i	$-0.628049\pi$
$809$	4823.45	−	2784.82i	0.209621	−	0.121025i	0.601135	+	0.799147i	$0.294715\pi$
$810$		0			0
$811$			17975.7i			0.778313i	0.921172	+	0.389157i	$0.127233\pi$
$811$			17975.7i			0.778313i	−0.921172	+	0.389157i	$0.872767\pi$
$812$		0			0
$813$	−30442.7	+	10151.0i	−1.31325	+	0.437897i
$814$		0			0
$815$	−1277.95			−0.0549258
$816$		0			0
$817$		−	7266.98i		−	0.311187i
$818$		0			0
$819$	−4308.22	+	2233.48i	−0.183811	+	0.0952918i
$820$		0			0
$821$		−	15986.3i		−	0.679569i	−0.940503	−	0.339785i	$-0.889646\pi$
$821$		−	15986.3i		−	0.679569i	0.940503	−	0.339785i	$-0.110354\pi$
$822$		0			0
$823$	−32100.2			−1.35959			−0.679794	−	0.733403i	$-0.737931\pi$
$823$	−32100.2			−1.35959			−0.679794	+	0.733403i	$0.737931\pi$
$824$		0			0
$825$	−4916.29	+	24037.1i	−0.207471	+	1.01438i
$826$		0			0
$827$			1963.56i			0.0825632i	0.999148	+	0.0412816i	$0.0131441\pi$
$827$			1963.56i			0.0825632i	−0.999148	+	0.0412816i	$0.986856\pi$
$828$		0			0
$829$	−33297.6	+	19224.4i	−1.39502	+	0.805416i	−0.993866	−	0.110594i	$-0.964725\pi$
$829$	−33297.6	+	19224.4i	−1.39502	+	0.805416i	−0.401156	+	0.916010i	$0.631391\pi$
$830$		0			0
$831$	−14165.5	−	42482.1i	−0.591331	−	1.77339i
$832$		0			0
$833$	−11849.5	+	10316.4i	−0.492871	+	0.429102i
$834$		0			0
$835$	−5563.27			−0.230569
$836$		0			0
$837$	−16054.7	+	23205.1i	−0.662999	+	0.958288i
$838$		0			0
$839$	3023.03	+	5236.05i	0.124394	+	0.215457i	0.921496	−	0.388388i	$-0.126968\pi$
$839$	3023.03	+	5236.05i	0.124394	+	0.215457i	−0.797102	+	0.603845i	$0.793635\pi$
$840$		0			0
$841$	11180.3	−	19364.8i	0.458415	−	0.793998i
$842$		0			0
$843$	−943.558	+	4613.31i	−0.0385502	+	0.188483i
$844$		0			0
$845$	−1998.19	+	3460.97i	−0.0813490	+	0.140901i
$846$		0			0
$847$	−555.134	+	3325.09i	−0.0225202	+	0.134889i
$848$		0			0
$849$	5427.79	+	4812.12i	0.219413	+	0.194525i
$850$		0			0
$851$		−	45967.2i		−	1.85163i
$852$		0			0
$853$	−14223.5	+	8211.95i	−0.570931	+	0.329627i	−0.757521	−	0.652811i	$-0.773590\pi$
$853$	−14223.5	+	8211.95i	−0.570931	+	0.329627i	0.186590	+	0.982438i	$0.440256\pi$
$854$		0			0
$855$	−1164.62	+	140.553i	−0.0465836	+	0.00562199i
$856$		0			0
$857$	−20931.9	+	36255.1i	−0.834330	+	1.44510i	0.0602454	+	0.998184i	$0.480812\pi$
$857$	−20931.9	+	36255.1i	−0.834330	+	1.44510i	−0.894575	+	0.446918i	$0.852522\pi$
$858$		0			0
$859$	−4241.11	+	2448.61i	−0.168457	+	0.0972589i	−0.581858	−	0.813290i	$-0.697674\pi$
$859$	−4241.11	+	2448.61i	−0.168457	+	0.0972589i	0.413401	+	0.910549i	$0.364341\pi$
$860$		0			0
$861$	8252.94	−	21457.6i	0.326666	−	0.849330i
$862$		0			0
$863$	26389.8	+	15236.1i	1.04092	+	0.600978i	0.920095	−	0.391695i	$-0.128111\pi$
$863$	26389.8	+	15236.1i	1.04092	+	0.600978i	0.120829	+	0.992673i	$0.461445\pi$
$864$		0			0
$865$	−1472.77	−	2550.91i	−0.0578910	−	0.100270i
$866$		0			0
$867$	4626.76	+	13875.6i	0.181238	+	0.543530i
$868$		0			0
$869$	33859.9	+	19549.0i	1.32177	+	0.763124i
$870$		0			0
$871$	−5301.60	−	3060.88i	−0.206243	−	0.119075i
$872$		0			0
$873$	−29138.9	−	38835.5i	−1.12967	−	1.50559i
$874$		0			0
$875$	−6693.81	−	5513.69i	−0.258619	−	0.213025i
$876$		0			0
$877$	−1006.72	−	1743.69i	−0.0387623	−	0.0671383i	0.845993	−	0.533193i	$-0.179008\pi$
$877$	−1006.72	−	1743.69i	−0.0387623	−	0.0671383i	−0.884756	+	0.466055i	$0.845675\pi$
$878$		0			0
$879$	15158.6	+	45460.6i	0.581671	+	1.74442i
$880$		0			0
$881$	27298.7			1.04395			0.521974	−	0.852962i	$-0.325196\pi$
$881$	27298.7			1.04395			0.521974	+	0.852962i	$0.325196\pi$
$882$		0			0
$883$	−29319.3			−1.11741			−0.558704	−	0.829367i	$-0.688701\pi$
$883$	−29319.3			−1.11741			−0.558704	+	0.829367i	$0.688701\pi$
$884$		0			0
$885$	−4513.38	−	923.118i	−0.171430	−	0.0350624i
$886$		0			0
$887$	5058.63	+	8761.80i	0.191491	+	0.331671i	0.945744	−	0.324912i	$-0.105335\pi$
$887$	5058.63	+	8761.80i	0.191491	+	0.331671i	−0.754254	+	0.656583i	$0.772001\pi$
$888$		0			0
$889$	7755.26	+	6388.01i	0.292579	+	0.240998i
$890$		0			0
$891$	−27225.3	−	7928.73i	−1.02366	−	0.298117i
$892$		0			0
$893$	3026.13	+	1747.14i	0.113399	+	0.0654711i
$894$		0			0
$895$	3194.61	+	1844.41i	0.119312	+	0.0688846i
$896$		0			0
$897$	−5250.98	+	5922.81i	−0.195457	+	0.220465i
$898$		0			0
$899$	−21743.7	−	37661.1i	−0.806665	−	1.39718i
$900$		0			0
$901$	−1205.06	−	695.740i	−0.0445575	−	0.0257253i
$902$		0			0
$903$	19235.8	+	23786.0i	0.708888	+	0.876578i
$904$		0			0
$905$	1009.57	−	582.877i	0.0370821	−	0.0214094i
$906$		0			0
$907$	−598.218	+	1036.14i	−0.0219002	+	0.0379323i	−0.876768	−	0.480914i	$-0.840305\pi$
$907$	−598.218	+	1036.14i	−0.0219002	+	0.0379323i	0.854868	+	0.518846i	$0.173638\pi$
$908$		0			0
$909$	−8486.63	−	3623.09i	−0.309663	−	0.132201i
$910$		0			0
$911$	−41715.9	+	24084.7i	−1.51713	+	0.875917i	−0.517336	+	0.855783i	$0.673076\pi$
$911$	−41715.9	+	24084.7i	−1.51713	+	0.875917i	−0.999797	+	0.0201344i	$0.993591\pi$
$912$		0			0
$913$			32301.5i			1.17089i
$914$		0			0
$915$	−1003.15	+	4904.67i	−0.0362438	+	0.177206i
$916$		0			0
$917$	−4403.53	+	26375.8i	−0.158580	+	0.949844i
$918$		0			0
$919$	−6221.58	+	10776.1i	−0.223320	+	0.386801i	−0.955814	−	0.293972i	$-0.905023\pi$
$919$	−6221.58	+	10776.1i	−0.223320	+	0.386801i	0.732494	+	0.680773i	$0.238356\pi$
$920$		0			0
$921$	25049.7	+	22208.3i	0.896217	+	0.794559i
$922$		0			0
$923$	−2004.08	+	3471.17i	−0.0714683	+	0.123787i
$924$		0			0
$925$	17774.0	+	30785.4i	0.631789	+	1.09429i
$926$		0			0
$927$	−7652.11	−	10198.5i	−0.271120	−	0.361341i
$928$		0			0
$929$	−21812.3			−0.770333			−0.385166	−	0.922847i	$-0.625856\pi$
$929$	−21812.3			−0.770333			−0.385166	+	0.922847i	$0.625856\pi$
$930$		0			0
$931$	−2547.26	+	7416.02i	−0.0896703	+	0.261064i
$932$		0			0
$933$	−24107.4	+	27191.8i	−0.845918	+	0.954146i
$934$		0			0
$935$	2932.45	−	1693.05i	0.102568	−	0.0592179i
$936$		0			0
$937$		−	18197.9i		−	0.634472i	−0.948347	−	0.317236i	$-0.897245\pi$
$937$		−	18197.9i		−	0.634472i	0.948347	−	0.317236i	$-0.102755\pi$
$938$		0			0
$939$	23419.8	+	20763.3i	0.813927	+	0.721603i
$940$		0			0
$941$	−31875.1			−1.10425			−0.552124	−	0.833762i	$-0.686182\pi$
$941$	−31875.1			−1.10425			−0.552124	+	0.833762i	$0.686182\pi$
$942$		0			0
$943$		−	37499.0i		−	1.29495i
$944$		0			0
$945$	3439.93	−	3542.80i	0.118414	−	0.121955i
$946$		0			0
$947$		−	6215.87i		−	0.213293i	−0.994297	−	0.106647i	$-0.965989\pi$
$947$		−	6215.87i		−	0.213293i	0.994297	−	0.106647i	$-0.0340114\pi$
$948$		0			0
$949$	−3099.13			−0.106009
$950$		0			0
$951$	33704.8	+	29881.7i	1.14927	+	1.01891i
$952$		0			0
$953$			23220.7i			0.789288i	0.918834	+	0.394644i	$0.129132\pi$
$953$			23220.7i			0.789288i	−0.918834	+	0.394644i	$0.870868\pi$
$954$		0			0
$955$	5983.21	−	3454.41i	0.202735	−	0.117049i
$956$		0			0
$957$	28991.1	−	32700.3i	0.979258	−	1.10455i
$958$		0			0
$959$	11856.4	+	31674.8i	0.399231	+	1.06656i
$960$		0			0
$961$	−10661.7			−0.357884
$962$		0			0
$963$	−16633.7	+	38962.3i	−0.556608	+	1.30378i
$964$		0			0
$965$	688.810	+	1193.05i	0.0229778	+	0.0397987i
$966$		0			0
$967$	24314.0	−	42113.0i	0.808567	−	1.40048i	−0.105289	−	0.994442i	$-0.533577\pi$
$967$	24314.0	−	42113.0i	0.808567	−	1.40048i	0.913856	−	0.406038i	$-0.133090\pi$
$968$		0			0
$969$	−4071.43	−	3609.61i	−0.134977	−	0.119667i
$970$		0			0
$971$	26197.2	−	45374.9i	0.865817	−	1.49964i	−0.000416873	−	1.00000i	$-0.500133\pi$
$971$	26197.2	−	45374.9i	0.865817	−	1.49964i	0.866234	−	0.499639i	$-0.166534\pi$
$972$		0			0
$973$	2404.94	+	6424.90i	0.0792384	+	0.211688i
$974$		0			0
$975$	1226.57	−	5997.03i	0.0402889	−	0.196983i
$976$		0			0
$977$		−	965.678i		−	0.0316221i	−0.999875	−	0.0158110i	$-0.994967\pi$
$977$		−	965.678i		−	0.0316221i	0.999875	−	0.0158110i	$-0.00503302\pi$
$978$		0			0
$979$	−38537.7	+	22249.8i	−1.25809	+	0.726360i
$980$		0			0
$981$	−13591.3	+	10197.8i	−0.442341	+	0.331896i
$982$		0			0
$983$	16557.0	−	28677.6i	0.537220	−	0.930492i	−0.461832	−	0.886967i	$-0.652808\pi$
$983$	16557.0	−	28677.6i	0.537220	−	0.930492i	0.999052	−	0.0435249i	$-0.0138588\pi$
$984$		0			0
$985$	2081.97	−	1202.03i	0.0673473	−	0.0388830i
$986$		0			0
$987$	−14529.7	+	2291.52i	−0.468577	+	0.0739006i
$988$		0			0
$989$	43211.7	+	24948.3i	1.38933	+	0.802132i
$990$		0			0
$991$	−19799.9	−	34294.4i	−0.634676	−	1.09929i	−0.986584	−	0.163257i	$-0.947800\pi$
$991$	−19799.9	−	34294.4i	−0.634676	−	1.09929i	0.351907	−	0.936035i	$-0.385533\pi$
$992$		0			0
$993$	3606.68	−	4068.12i	0.115261	−	0.130008i
$994$		0			0
$995$	−1141.95	−	659.305i	−0.0363842	−	0.0210064i
$996$		0			0
$997$	−39506.3	−	22809.0i	−1.25494	−	0.724541i	−0.282855	−	0.959163i	$-0.591282\pi$
$997$	−39506.3	−	22809.0i	−1.25494	−	0.724541i	−0.972087	+	0.234622i	$0.924615\pi$
$998$		0			0
$999$	−37137.4	+	17572.5i	−1.17615	+	0.556524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.w.a.5.7	✓	48
3.2	odd	2		756.4.w.a.341.12		48
7.3	odd	6		252.4.bm.a.185.2	yes	48
9.2	odd	6		252.4.bm.a.173.2	yes	48
9.7	even	3		756.4.bm.a.89.12		48
21.17	even	6		756.4.bm.a.17.12		48
63.38	even	6	inner	252.4.w.a.101.7	yes	48
63.52	odd	6		756.4.w.a.521.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.7	✓	48	1.1	even	1	trivial
252.4.w.a.101.7	yes	48	63.38	even	6	inner
252.4.bm.a.173.2	yes	48	9.2	odd	6
252.4.bm.a.185.2	yes	48	7.3	odd	6
756.4.w.a.341.12		48	3.2	odd	2
756.4.w.a.521.12		48	63.52	odd	6
756.4.bm.a.17.12		48	21.17	even	6
756.4.bm.a.89.12		48	9.7	even	3

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.44710 + 3.88813i) q^{3} +(-0.950243 - 1.64587i) q^{5} +(14.2951 + 11.7749i) q^{7} +(-3.23505 - 26.8055i) q^{9} +O(q^{10})\)	\(q+(-3.44710 + 3.88813i) q^{3} +(-0.950243 - 1.64587i) q^{5} +(14.2951 + 11.7749i) q^{7} +(-3.23505 - 26.8055i) q^{9} +(33.6863 + 19.4488i) q^{11} +(-8.40442 - 4.85229i) q^{13} +(9.67493 + 1.97881i) q^{15} +(22.9025 + 39.6683i) q^{17} +(19.7981 + 11.4305i) q^{19} +(-95.0591 + 14.9920i) q^{21} +(-135.938 + 78.4838i) q^{23} +(60.6941 - 105.125i) q^{25} +(115.375 + 79.8229i) q^{27} +(-187.249 + 108.108i) q^{29} +201.129i q^{31} +(-191.739 + 63.9347i) q^{33} +(5.79612 - 34.7170i) q^{35} +(-146.423 + 253.611i) q^{37} +(47.8372 - 15.9511i) q^{39} +(-119.448 + 206.891i) q^{41} +(-158.939 - 275.290i) q^{43} +(-41.0443 + 30.7962i) q^{45} +152.849 q^{47} +(65.7025 + 336.648i) q^{49} +(-233.182 - 47.6926i) q^{51} +(-26.3084 + 15.1892i) q^{53} -73.9244i q^{55} +(-112.689 + 37.5758i) q^{57} -466.502 q^{59} +506.946i q^{61} +(269.387 - 421.281i) q^{63} +18.4434i q^{65} +630.811 q^{67} +(163.436 - 799.085i) q^{69} -413.018i q^{71} +(276.563 - 159.674i) q^{73} +(199.522 + 598.363i) q^{75} +(252.543 + 674.677i) q^{77} +1005.15 q^{79} +(-708.069 + 173.434i) q^{81} +(415.211 + 719.167i) q^{83} +(43.5259 - 75.3890i) q^{85} +(225.127 - 1100.71i) q^{87} +(-572.009 + 990.749i) q^{89} +(-63.0070 - 168.326i) q^{91} +(-782.013 - 693.310i) q^{93} -43.4469i q^{95} +(1557.30 - 899.106i) q^{97} +(412.358 - 965.896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 12 * q^9	\( 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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