LMFDB - Embedded newform 252.4.w.a.5.18

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			5.18
Character	$\chi$	$=$	252.5
Dual form			252.4.w.a.101.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.58371 + 3.76258i) q^{3} +(-1.13691 - 1.96919i) q^{5} +(-14.5181 + 11.4989i) q^{7} +(-1.31403 + 26.9680i) q^{9} +O(q^{10})$	\(q+(3.58371 + 3.76258i) q^{3} +(-1.13691 - 1.96919i) q^{5} +(-14.5181 + 11.4989i) q^{7} +(-1.31403 + 26.9680i) q^{9} +(-31.0776 - 17.9426i) q^{11} +(-70.2337 - 40.5494i) q^{13} +(3.33487 - 11.3347i) q^{15} +(25.8458 + 44.7662i) q^{17} +(-9.61456 - 5.55097i) q^{19} +(-95.2942 - 13.4167i) q^{21} +(-26.4664 + 15.2804i) q^{23} +(59.9149 - 103.776i) q^{25} +(-106.178 + 91.7014i) q^{27} +(-167.883 + 96.9271i) q^{29} +188.005i q^{31} +(-43.8624 - 181.233i) q^{33} +(39.1494 + 15.5156i) q^{35} +(25.3619 - 43.9281i) q^{37} +(-99.1267 - 409.577i) q^{39} +(151.024 - 261.582i) q^{41} +(28.1579 + 48.7709i) q^{43} +(54.5991 - 28.0727i) q^{45} -108.275 q^{47} +(78.5497 - 333.885i) q^{49} +(-75.8126 + 257.676i) q^{51} +(-548.106 + 316.449i) q^{53} +81.5969i q^{55} +(-13.5698 - 56.0686i) q^{57} -686.710 q^{59} +393.545i q^{61} +(-291.026 - 406.634i) q^{63} +184.405i q^{65} +18.8780 q^{67} +(-152.341 - 44.8214i) q^{69} +1116.45i q^{71} +(458.520 - 264.726i) q^{73} +(605.182 - 146.467i) q^{75} +(657.508 - 96.8656i) q^{77} +463.570 q^{79} +(-725.547 - 70.8735i) q^{81} +(212.584 + 368.205i) q^{83} +(58.7688 - 101.791i) q^{85} +(-966.339 - 284.313i) q^{87} +(74.5855 - 129.186i) q^{89} +(1485.93 - 218.911i) q^{91} +(-707.384 + 673.756i) q^{93} +25.2439i q^{95} +(-1059.18 + 611.519i) q^{97} +(524.714 - 814.523i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.58371	+	3.76258i	0.689686	+	0.724109i
$3$	3.58371	+	3.76258i	0.689686	+	0.724109i
$4$		0			0
$5$	−1.13691	−	1.96919i	−0.101689	−	0.176130i	0.810692	−	0.585473i	$-0.199091\pi$
$5$	−1.13691	−	1.96919i	−0.101689	−	0.176130i	−0.912380	+	0.409343i	$0.865758\pi$
$6$		0			0
$7$	−14.5181	+	11.4989i	−0.783903	+	0.620883i
$7$	−14.5181	+	11.4989i	−0.783903	+	0.620883i
$8$		0			0
$9$	−1.31403	+	26.9680i	−0.0486678	+	0.998815i
$10$		0			0
$11$	−31.0776	−	17.9426i	−0.851840	−	0.491810i	0.00943122	−	0.999956i	$-0.496998\pi$
$11$	−31.0776	−	17.9426i	−0.851840	−	0.491810i	−0.861271	+	0.508145i	$0.830331\pi$
$12$		0			0
$13$	−70.2337	−	40.5494i	−1.49841	−	0.865107i	−0.498411	−	0.866941i	$-0.666083\pi$
$13$	−70.2337	−	40.5494i	−1.49841	−	0.865107i	−0.999998	+	0.00183406i	$0.999416\pi$
$14$		0			0
$15$	3.33487	−	11.3347i	0.0574040	−	0.195108i
$16$		0			0
$17$	25.8458	+	44.7662i	0.368737	+	0.638670i	0.989368	−	0.145432i	$-0.0464571\pi$
$17$	25.8458	+	44.7662i	0.368737	+	0.638670i	−0.620632	+	0.784102i	$0.713124\pi$
$18$		0			0
$19$	−9.61456	−	5.55097i	−0.116091	−	0.0670252i	0.440830	−	0.897591i	$-0.354684\pi$
$19$	−9.61456	−	5.55097i	−0.116091	−	0.0670252i	−0.556921	+	0.830565i	$0.688017\pi$
$20$		0			0
$21$	−95.2942	−	13.4167i	−0.990234	−	0.139417i
$22$		0			0
$23$	−26.4664	+	15.2804i	−0.239940	+	0.138529i	−0.615149	−	0.788411i	$-0.710904\pi$
$23$	−26.4664	+	15.2804i	−0.239940	+	0.138529i	0.375209	+	0.926940i	$0.377571\pi$
$24$		0			0
$25$	59.9149	−	103.776i	0.479319	−	0.830205i
$26$		0			0
$27$	−106.178	+	91.7014i	−0.756816	+	0.653627i
$28$		0			0
$29$	−167.883	+	96.9271i	−1.07500	+	0.620652i	−0.929543	−	0.368713i	$-0.879799\pi$
$29$	−167.883	+	96.9271i	−1.07500	+	0.620652i	−0.145457	+	0.989365i	$0.546465\pi$
$30$		0			0
$31$			188.005i			1.08925i	0.838680	+	0.544624i	$0.183328\pi$
$31$			188.005i			1.08925i	−0.838680	+	0.544624i	$0.816672\pi$
$32$		0			0
$33$	−43.8624	−	181.233i	−0.231378	−	0.956019i
$34$		0			0
$35$	39.1494	+	15.5156i	0.189070	+	0.0749319i
$36$		0			0
$37$	25.3619	−	43.9281i	0.112688	−	0.195182i	−0.804165	−	0.594406i	$-0.797387\pi$
$37$	25.3619	−	43.9281i	0.112688	−	0.195182i	0.916853	+	0.399224i	$0.130720\pi$
$38$		0			0
$39$	−99.1267	−	409.577i	−0.406999	−	1.68166i
$40$		0			0
$41$	151.024	−	261.582i	0.575269	−	0.996396i	−0.420743	−	0.907180i	$-0.638231\pi$
$41$	151.024	−	261.582i	0.575269	−	0.996396i	0.996012	−	0.0892157i	$-0.0284360\pi$
$42$		0			0
$43$	28.1579	+	48.7709i	0.0998613	+	0.172965i	0.911627	−	0.411018i	$-0.134827\pi$
$43$	28.1579	+	48.7709i	0.0998613	+	0.172965i	−0.811766	+	0.583983i	$0.801493\pi$
$44$		0			0
$45$	54.5991	−	28.0727i	0.180870	−	0.0929962i
$46$		0			0
$47$	−108.275			−0.336032			−0.168016	−	0.985784i	$-0.553736\pi$
$47$	−108.275			−0.336032			−0.168016	+	0.985784i	$0.553736\pi$
$48$		0			0
$49$	78.5497	−	333.885i	0.229008	−	0.973425i
$50$		0			0
$51$	−75.8126	+	257.676i	−0.208155	+	0.707487i
$52$		0			0
$53$	−548.106	+	316.449i	−1.42053	+	0.820145i	−0.996344	−	0.0854295i	$-0.972774\pi$
$53$	−548.106	+	316.449i	−1.42053	+	0.820145i	−0.424188	+	0.905574i	$0.639440\pi$
$54$		0			0
$55$			81.5969i			0.200046i
$56$		0			0
$57$	−13.5698	−	56.0686i	−0.0315328	−	0.130289i
$58$		0			0
$59$	−686.710			−1.51529			−0.757644	−	0.652668i	$-0.773650\pi$
$59$	−686.710			−1.51529			−0.757644	+	0.652668i	$0.773650\pi$
$60$		0			0
$61$			393.545i			0.826038i	0.910722	+	0.413019i	$0.135526\pi$
$61$			393.545i			0.826038i	−0.910722	+	0.413019i	$0.864474\pi$
$62$		0			0
$63$	−291.026	−	406.634i	−0.581997	−	0.813191i
$64$		0			0
$65$			184.405i			0.351886i
$66$		0			0
$67$	18.8780			0.0344226			0.0172113	−	0.999852i	$-0.494521\pi$
$67$	18.8780			0.0344226			0.0172113	+	0.999852i	$0.494521\pi$
$68$		0			0
$69$	−152.341	−	44.8214i	−0.265793	−	0.0782010i
$70$		0			0
$71$			1116.45i			1.86618i	0.359649	+	0.933088i	$0.382897\pi$
$71$			1116.45i			1.86618i	−0.359649	+	0.933088i	$0.617103\pi$
$72$		0			0
$73$	458.520	−	264.726i	0.735146	−	0.424437i	−0.0851557	−	0.996368i	$-0.527139\pi$
$73$	458.520	−	264.726i	0.735146	−	0.424437i	0.820302	+	0.571931i	$0.193805\pi$
$74$		0			0
$75$	605.182	−	146.467i	0.931738	−	0.225501i
$76$		0			0
$77$	657.508	−	96.8656i	0.973117	−	0.143362i
$78$		0			0
$79$	463.570			0.660199			0.330100	−	0.943946i	$-0.392918\pi$
$79$	463.570			0.660199			0.330100	+	0.943946i	$0.392918\pi$
$80$		0			0
$81$	−725.547	−	70.8735i	−0.995263	−	0.0972202i
$82$		0			0
$83$	212.584	+	368.205i	0.281133	+	0.486937i	0.971664	−	0.236366i	$-0.0759563\pi$
$83$	212.584	+	368.205i	0.281133	+	0.486937i	−0.690531	+	0.723303i	$0.742623\pi$
$84$		0			0
$85$	58.7688	−	101.791i	0.0749926	−	0.129891i
$86$		0			0
$87$	−966.339	−	284.313i	−1.19083	−	0.350363i
$88$		0			0
$89$	74.5855	−	129.186i	0.0888320	−	0.153862i	−0.818186	−	0.574954i	$-0.805020\pi$
$89$	74.5855	−	129.186i	0.0888320	−	0.153862i	0.907018	+	0.421093i	$0.138353\pi$
$90$		0			0
$91$	1485.93	−	218.911i	1.71174	−	0.252177i
$92$		0			0
$93$	−707.384	+	673.756i	−0.788735	+	0.751239i
$94$		0			0
$95$			25.2439i			0.0272628i
$96$		0			0
$97$	−1059.18	+	611.519i	−1.10870	+	0.640106i	−0.938491	−	0.345302i	$-0.887776\pi$
$97$	−1059.18	+	611.519i	−1.10870	+	0.640106i	−0.170205	+	0.985409i	$0.554443\pi$
$98$		0			0
$99$	524.714	−	814.523i	0.532684	−	0.826895i
$100$		0			0
$101$	61.9796	−	107.352i	0.0610614	−	0.105761i	−0.833879	−	0.551948i	$-0.813885\pi$
$101$	61.9796	−	107.352i	0.0610614	−	0.105761i	0.894940	+	0.446186i	$0.147218\pi$
$102$		0			0
$103$	1526.28	−	881.200i	1.46009	−	0.842983i	0.461074	−	0.887362i	$-0.347464\pi$
$103$	1526.28	−	881.200i	1.46009	−	0.842983i	0.999015	+	0.0443790i	$0.0141309\pi$
$104$		0			0
$105$	81.9213	+	202.906i	0.0761400	+	0.188587i
$106$		0			0
$107$	1378.50	+	795.876i	1.24546	+	0.719068i	0.970201	−	0.242301i	$-0.0779023\pi$
$107$	1378.50	+	795.876i	1.24546	+	0.719068i	0.275261	+	0.961369i	$0.411236\pi$
$108$		0			0
$109$	304.355	+	527.159i	0.267449	+	0.463236i	0.968202	−	0.250168i	$-0.0804859\pi$
$109$	304.355	+	527.159i	0.267449	+	0.463236i	−0.700753	+	0.713404i	$0.747153\pi$
$110$		0			0
$111$	256.173	−	61.9994i	0.219053	−	0.0530155i
$112$		0			0
$113$	207.921	+	120.043i	0.173093	+	0.0999354i	0.584044	−	0.811722i	$-0.301470\pi$
$113$	207.921	+	120.043i	0.173093	+	0.0999354i	−0.410950	+	0.911658i	$0.634803\pi$
$114$		0			0
$115$	60.1799	+	34.7449i	0.0487983	+	0.0281737i
$116$		0			0
$117$	1185.83	−	1840.78i	0.937006	−	1.45453i
$118$		0			0
$119$	−889.994	−	352.721i	−0.685593	−	0.271713i
$120$		0			0
$121$	−21.6230	−	37.4521i	−0.0162457	−	0.0281383i
$122$		0			0
$123$	1525.45	−	369.192i	1.11825	−	0.270642i
$124$		0			0
$125$	−556.700			−0.398342
$126$		0			0
$127$	2223.59			1.55364			0.776819	−	0.629724i	$-0.216832\pi$
$127$	2223.59			1.55364			0.776819	+	0.629724i	$0.216832\pi$
$128$		0			0
$129$	−82.5947	+	280.727i	−0.0563725	+	0.191602i
$130$		0			0
$131$	283.660	+	491.313i	0.189187	+	0.327681i	0.944979	−	0.327130i	$-0.106081\pi$
$131$	283.660	+	491.313i	0.189187	+	0.327681i	−0.755792	+	0.654811i	$0.772748\pi$
$132$		0			0
$133$	203.415	−	29.9676i	0.132619	−	0.0195377i
$134$		0			0
$135$	301.293	+	104.829i	0.192083	+	0.0668315i
$136$		0			0
$137$	−266.410	−	153.812i	−0.166139	−	0.0959201i	0.414625	−	0.909992i	$-0.363913\pi$
$137$	−266.410	−	153.812i	−0.166139	−	0.0959201i	−0.580764	+	0.814072i	$0.697246\pi$
$138$		0			0
$139$	505.917	+	292.091i	0.308715	+	0.178237i	0.646351	−	0.763040i	$-0.276294\pi$
$139$	505.917	+	292.091i	0.308715	+	0.178237i	−0.337636	+	0.941277i	$0.609627\pi$
$140$		0			0
$141$	−388.025	−	407.393i	−0.231756	−	0.243324i
$142$		0			0
$143$	1455.13	+	2520.36i	0.850937	+	1.47387i
$144$		0			0
$145$	381.736	+	220.395i	0.218631	+	0.126226i
$146$		0			0
$147$	1537.77	−	900.996i	0.862809	−	0.505530i
$148$		0			0
$149$	−2457.85	+	1419.04i	−1.35137	+	0.780215i	−0.988442	−	0.151601i	$-0.951557\pi$
$149$	−2457.85	+	1419.04i	−1.35137	+	0.780215i	−0.362931	+	0.931816i	$0.618224\pi$
$150$		0			0
$151$	822.227	−	1424.14i	0.443125	−	0.767516i	−0.554794	−	0.831988i	$-0.687203\pi$
$151$	822.227	−	1424.14i	0.443125	−	0.767516i	0.997920	+	0.0644721i	$0.0205363\pi$
$152$		0			0
$153$	−1241.22	+	638.185i	−0.655859	+	0.337217i
$154$		0			0
$155$	370.218	−	213.745i	0.191849	−	0.110764i
$156$		0			0
$157$		−	3358.38i		−	1.70718i	−0.520941	−	0.853592i	$-0.674419\pi$
$157$		−	3358.38i		−	1.70718i	0.520941	−	0.853592i	$-0.325581\pi$
$158$		0			0
$159$	−3154.92	−	928.232i	−1.57359	−	0.462978i
$160$		0			0
$161$	208.533	−	526.176i	0.102079	−	0.257568i
$162$		0			0
$163$	−361.999	+	627.001i	−0.173951	+	0.301292i	−0.939798	−	0.341731i	$-0.888987\pi$
$163$	−361.999	+	627.001i	−0.173951	+	0.301292i	0.765847	+	0.643023i	$0.222320\pi$
$164$		0			0
$165$	−307.015	+	292.420i	−0.144855	+	0.137969i
$166$		0			0
$167$	−1939.60	+	3359.48i	−0.898745	+	1.55667i	−0.0696458	+	0.997572i	$0.522187\pi$
$167$	−1939.60	+	3359.48i	−0.898745	+	1.55667i	−0.829100	+	0.559101i	$0.811146\pi$
$168$		0			0
$169$	2190.01	+	3793.21i	0.996820	+	1.72654i
$170$		0			0
$171$	162.332	−	251.991i	0.0725957	−	0.112692i
$172$		0			0
$173$	−2894.75			−1.27216			−0.636079	−	0.771624i	$-0.719445\pi$
$173$	−2894.75			−1.27216			−0.636079	+	0.771624i	$0.719445\pi$
$174$		0			0
$175$	323.458	+	2195.58i	0.139721	+	0.948401i
$176$		0			0
$177$	−2460.97	−	2583.80i	−1.04507	−	1.09723i
$178$		0			0
$179$	565.314	−	326.384i	0.236053	−	0.136285i	−0.377308	−	0.926088i	$-0.623150\pi$
$179$	565.314	−	326.384i	0.236053	−	0.136285i	0.613361	+	0.789802i	$0.289817\pi$
$180$		0			0
$181$			287.007i			0.117862i	0.998262	+	0.0589310i	$0.0187692\pi$
$181$			287.007i			0.117862i	−0.998262	+	0.0589310i	$0.981231\pi$
$182$		0			0
$183$	−1480.75	+	1410.35i	−0.598141	+	0.569706i
$184$		0			0
$185$	−115.337			−0.0458365
$186$		0			0
$187$		−	1854.97i		−	0.725393i
$188$		0			0
$189$	487.040	−	2552.27i	0.187444	−	0.982275i
$190$		0			0
$191$		−	3650.30i		−	1.38286i	−0.722442	−	0.691431i	$-0.756980\pi$
$191$		−	3650.30i		−	1.38286i	0.722442	−	0.691431i	$-0.243020\pi$
$192$		0			0
$193$	−2895.29			−1.07983			−0.539915	−	0.841719i	$-0.681544\pi$
$193$	−2895.29			−1.07983			−0.539915	+	0.841719i	$0.681544\pi$
$194$		0			0
$195$	−693.838	+	660.853i	−0.254804	+	0.242691i
$196$		0			0
$197$			3842.00i			1.38950i	0.719253	+	0.694748i	$0.244484\pi$
$197$			3842.00i			1.38950i	−0.719253	+	0.694748i	$0.755516\pi$
$198$		0			0
$199$	−2033.43	+	1174.00i	−0.724353	+	0.418205i	−0.816353	−	0.577554i	$-0.804007\pi$
$199$	−2033.43	+	1174.00i	−0.724353	+	0.418205i	0.0920000	+	0.995759i	$0.470674\pi$
$200$		0			0
$201$	67.6534	+	71.0301i	0.0237408	+	0.0249258i
$202$		0			0
$203$	1322.78	−	3337.66i	0.457344	−	1.15398i
$204$		0			0
$205$	−686.806			−0.233993
$206$		0			0
$207$	−377.303	−	733.824i	−0.126688	−	0.246398i
$208$		0			0
$209$	199.198	+	345.021i	0.0659274	+	0.114190i
$210$		0			0
$211$	829.419	−	1436.60i	0.270614	−	0.468717i	−0.698405	−	0.715702i	$-0.746107\pi$
$211$	829.419	−	1436.60i	0.270614	−	0.468717i	0.969019	+	0.246985i	$0.0794400\pi$
$212$		0			0
$213$	−4200.74	+	4001.04i	−1.35131	+	1.28707i
$214$		0			0
$215$	64.0261	−	110.896i	0.0203095	−	0.0351771i
$216$		0			0
$217$	−2161.85	−	2729.47i	−0.676296	−	0.853865i
$218$		0			0
$219$	2639.26	+	776.514i	0.814358	+	0.239598i
$220$		0			0
$221$		−	4192.13i		−	1.27599i
$222$		0			0
$223$	−125.129	+	72.2431i	−0.0375750	+	0.0216940i	−0.518670	−	0.854975i	$-0.673573\pi$
$223$	−125.129	+	72.2431i	−0.0375750	+	0.0216940i	0.481095	+	0.876669i	$0.340239\pi$
$224$		0			0
$225$	2719.89	+	1752.15i	0.805893	+	0.519155i
$226$		0			0
$227$	1419.84	−	2459.23i	0.415146	−	0.719053i	−0.580298	−	0.814404i	$-0.697064\pi$
$227$	1419.84	−	2459.23i	0.415146	−	0.719053i	0.995444	+	0.0953508i	$0.0303973\pi$
$228$		0			0
$229$	−4267.57	+	2463.88i	−1.23148	+	0.710995i	−0.967338	−	0.253489i	$-0.918422\pi$
$229$	−4267.57	+	2463.88i	−1.23148	+	0.710995i	−0.264142	+	0.964484i	$0.585089\pi$
$230$		0			0
$231$	2720.78	+	2126.79i	0.774954	+	0.605768i
$232$		0			0
$233$	3636.65	+	2099.62i	1.02251	+	0.590347i	0.914830	−	0.403839i	$-0.132324\pi$
$233$	3636.65	+	2099.62i	1.02251	+	0.590347i	0.107680	+	0.994186i	$0.465658\pi$
$234$		0			0
$235$	123.099	+	213.214i	0.0341706	+	0.0591852i
$236$		0			0
$237$	1661.30	+	1744.22i	0.455330	+	0.478056i
$238$		0			0
$239$	−2362.56	−	1364.02i	−0.639420	−	0.369169i	0.144971	−	0.989436i	$-0.453691\pi$
$239$	−2362.56	−	1364.02i	−0.639420	−	0.369169i	−0.784391	+	0.620267i	$0.787024\pi$
$240$		0			0
$241$	−3467.42	−	2001.91i	−0.926788	−	0.535081i	−0.0409936	−	0.999159i	$-0.513052\pi$
$241$	−3467.42	−	2001.91i	−0.926788	−	0.535081i	−0.885794	+	0.464078i	$0.846386\pi$
$242$		0			0
$243$	−2333.48	−	2983.92i	−0.616020	−	0.787730i
$244$		0			0
$245$	−746.787	+	224.918i	−0.194737	+	0.0586511i
$246$		0			0
$247$	450.177	+	779.730i	0.115968	+	0.200862i
$248$		0			0
$249$	−623.565	+	2119.40i	−0.158702	+	0.539405i
$250$		0			0
$251$	−4710.33			−1.18452			−0.592258	−	0.805748i	$-0.701763\pi$
$251$	−4710.33			−1.18452			−0.592258	+	0.805748i	$0.701763\pi$
$252$		0			0
$253$	1096.68			0.272521
$254$		0			0
$255$	593.606	−	143.666i	0.145777	−	0.0352811i
$256$		0			0
$257$	−2892.68	−	5010.27i	−0.702102	−	1.21608i	−0.967727	−	0.252001i	$-0.918912\pi$
$257$	−2892.68	−	5010.27i	−0.702102	−	1.21608i	0.265625	−	0.964077i	$-0.414422\pi$
$258$		0			0
$259$	136.919	+	929.387i	0.0328485	+	0.222970i
$260$		0			0
$261$	−2393.33	−	4654.82i	−0.567599	−	1.10393i
$262$		0			0
$263$	6928.86	+	4000.38i	1.62453	+	0.937924i	0.985686	+	0.168589i	$0.0539211\pi$
$263$	6928.86	+	4000.38i	1.62453	+	0.937924i	0.638846	+	0.769335i	$0.279412\pi$
$264$		0			0
$265$	1246.30	+	719.551i	0.288904	+	0.166799i
$266$		0			0
$267$	753.365	−	182.331i	0.172679	−	0.0417920i
$268$		0			0
$269$	−2493.11	−	4318.20i	−0.565084	−	0.978755i	−0.997042	−	0.0768609i	$-0.975510\pi$
$269$	−2493.11	−	4318.20i	−0.565084	−	0.978755i	0.431957	−	0.901894i	$-0.357823\pi$
$270$		0			0
$271$	−6058.94	−	3498.13i	−1.35813	−	0.784119i	−0.368762	−	0.929524i	$-0.620218\pi$
$271$	−6058.94	−	3498.13i	−1.35813	−	0.784119i	−0.989372	+	0.145404i	$0.953552\pi$
$272$		0			0
$273$	6148.83	+	4806.43i	1.36316	+	1.06556i
$274$		0			0
$275$	−3724.02	+	2150.06i	−0.816606	+	0.471468i
$276$		0			0
$277$	2161.68	−	3744.15i	0.468892	−	0.812144i	−0.530476	−	0.847700i	$-0.677987\pi$
$277$	2161.68	−	3744.15i	0.468892	−	0.812144i	0.999368	+	0.0355556i	$0.0113201\pi$
$278$		0			0
$279$	−5070.12	−	247.044i	−1.08796	−	0.0530113i
$280$		0			0
$281$	7203.44	−	4158.91i	1.52926	−	0.882917i	0.529864	−	0.848083i	$-0.322243\pi$
$281$	7203.44	−	4158.91i	1.52926	−	0.882917i	0.999393	−	0.0348341i	$-0.0110903\pi$
$282$		0			0
$283$			2095.20i			0.440094i	0.975489	+	0.220047i	$0.0706210\pi$
$283$			2095.20i			0.440094i	−0.975489	+	0.220047i	$0.929379\pi$
$284$		0			0
$285$	−94.9821	+	90.4667i	−0.0197412	+	0.0188028i
$286$		0			0
$287$	815.324	+	5534.28i	0.167690	+	1.13825i
$288$		0			0
$289$	1120.49	−	1940.75i	0.228067	−	0.395023i
$290$		0			0
$291$	−6096.69	−	1793.75i	−1.22816	−	0.361345i
$292$		0			0
$293$	−1520.43	+	2633.47i	−0.303156	+	0.525081i	−0.976849	−	0.213930i	$-0.931374\pi$
$293$	−1520.43	+	2633.47i	−0.303156	+	0.525081i	0.673693	+	0.739011i	$0.264707\pi$
$294$		0			0
$295$	780.729	+	1352.26i	0.154088	+	0.266887i
$296$		0			0
$297$	4945.13	−	944.735i	0.966147	−	0.184576i
$298$		0			0
$299$	2478.44			0.479371
$300$		0			0
$301$	−969.611	−	384.275i	−0.185673	−	0.0735855i
$302$		0			0
$303$	626.037	−	151.515i	0.118696	−	0.0287270i
$304$		0			0
$305$	774.966	−	447.427i	0.145490	−	0.0839986i
$306$		0			0
$307$			1893.14i			0.351945i	0.984395	+	0.175972i	$0.0563069\pi$
$307$			1893.14i			0.351945i	−0.984395	+	0.175972i	$0.943693\pi$
$308$		0			0
$309$	8785.34	+	2584.80i	1.61741	+	0.475871i
$310$		0			0
$311$	−3217.93			−0.586727			−0.293364	−	0.956001i	$-0.594775\pi$
$311$	−3217.93			−0.586727			−0.293364	+	0.956001i	$0.594775\pi$
$312$		0			0
$313$		−	934.699i		−	0.168793i	−0.996432	−	0.0843967i	$-0.973104\pi$
$313$		−	934.699i		−	0.168793i	0.996432	−	0.0843967i	$-0.0268963\pi$
$314$		0			0
$315$	−469.869	+	1035.39i	−0.0840448	+	0.185199i
$316$		0			0
$317$		−	5054.26i		−	0.895506i	−0.894157	−	0.447753i	$-0.852224\pi$
$317$		−	5054.26i		−	0.895506i	0.894157	−	0.447753i	$-0.147776\pi$
$318$		0			0
$319$	6956.51			1.22097
$320$		0			0
$321$	1945.59	+	8038.90i	0.338294	+	1.39778i
$322$		0			0
$323$		−	573.876i		−	0.0988586i
$324$		0			0
$325$	−8416.08	+	4859.03i	−1.43643	+	0.829324i
$326$		0			0
$327$	−892.757	+	3034.35i	−0.150977	+	0.513149i
$328$		0			0
$329$	1571.94	−	1245.04i	0.263416	−	0.208637i
$330$		0			0
$331$	−2234.40			−0.371038			−0.185519	−	0.982641i	$-0.559397\pi$
$331$	−2234.40			−0.371038			−0.185519	+	0.982641i	$0.559397\pi$
$332$		0			0
$333$	1151.33	+	741.683i	0.189466	+	0.122054i
$334$		0			0
$335$	−21.4627	−	37.1744i	−0.00350039	−	0.00606285i
$336$		0			0
$337$	−4391.12	+	7605.65i	−0.709791	+	1.22939i	0.255143	+	0.966903i	$0.417878\pi$
$337$	−4391.12	+	7605.65i	−0.709791	+	1.22939i	−0.964934	+	0.262492i	$0.915456\pi$
$338$		0			0
$339$	293.456	+	1212.52i	0.0470157	+	0.194262i
$340$		0			0
$341$	3373.31	−	5842.74i	0.535703	−	0.927865i
$342$		0			0
$343$	2698.92	+	5750.60i	0.424863	+	0.905258i
$344$		0			0
$345$	84.9370	+	350.947i	0.0132546	+	0.0547663i
$346$		0			0
$347$			11769.6i			1.82082i	0.413711	+	0.910408i	$0.364232\pi$
$347$			11769.6i			1.82082i	−0.413711	+	0.910408i	$0.635768\pi$
$348$		0			0
$349$	−7683.47	+	4436.06i	−1.17847	+	0.680391i	−0.955661	−	0.294470i	$-0.904857\pi$
$349$	−7683.47	+	4436.06i	−1.17847	+	0.680391i	−0.222812	+	0.974861i	$0.571524\pi$
$350$		0			0
$351$	11175.7	−	2135.05i	1.69948	−	0.324674i
$352$		0			0
$353$	5519.01	−	9559.20i	0.832145	−	1.44132i	−0.0641889	−	0.997938i	$-0.520446\pi$
$353$	5519.01	−	9559.20i	0.832145	−	1.44132i	0.896334	−	0.443380i	$-0.146221\pi$
$354$		0			0
$355$	2198.51	−	1269.31i	0.328689	−	0.189769i
$356$		0			0
$357$	−1862.34	−	4612.73i	−0.276094	−	0.683841i
$358$		0			0
$359$	−3344.50	−	1930.95i	−0.491689	−	0.283877i	0.233586	−	0.972336i	$-0.424954\pi$
$359$	−3344.50	−	1930.95i	−0.491689	−	0.283877i	−0.725275	+	0.688460i	$0.758287\pi$
$360$		0			0
$361$	−3367.87	−	5833.33i	−0.491015	−	0.850463i
$362$		0			0
$363$	63.4261	−	215.576i	0.00917082	−	0.0311702i
$364$		0			0
$365$	−1042.59	−	601.942i	−0.149512	−	0.0863208i
$366$		0			0
$367$	−1584.31	−	914.704i	−0.225342	−	0.130101i	0.383079	−	0.923715i	$-0.374864\pi$
$367$	−1584.31	−	914.704i	−0.225342	−	0.130101i	−0.608421	+	0.793614i	$0.708197\pi$
$368$		0			0
$369$	6855.89	+	4416.55i	0.967218	+	0.623080i
$370$		0			0
$371$	4318.63	−	10896.9i	0.604345	−	1.52490i
$372$		0			0
$373$	80.7854	+	139.924i	0.0112142	+	0.0194236i	0.871578	−	0.490257i	$-0.163097\pi$
$373$	80.7854	+	139.924i	0.0112142	+	0.0194236i	−0.860364	+	0.509680i	$0.829764\pi$
$374$		0			0
$375$	−1995.05	−	2094.63i	−0.274731	−	0.288443i
$376$		0			0
$377$	15721.4			2.14772
$378$		0			0
$379$	3831.91			0.519345			0.259673	−	0.965697i	$-0.416385\pi$
$379$	3831.91			0.519345			0.259673	+	0.965697i	$0.416385\pi$
$380$		0			0
$381$	7968.71	+	8366.45i	1.07152	+	1.12500i
$382$		0			0
$383$	−3501.12	−	6064.13i	−0.467100	−	0.809040i	0.532194	−	0.846622i	$-0.321368\pi$
$383$	−3501.12	−	6064.13i	−0.467100	−	0.809040i	−0.999294	+	0.0375823i	$0.988034\pi$
$384$		0			0
$385$	−938.276	−	1184.63i	−0.124205	−	0.156817i
$386$		0			0
$387$	−1352.25	+	695.275i	−0.177620	+	0.0913252i
$388$		0			0
$389$	3536.26	+	2041.66i	0.460914	+	0.266109i	0.712428	−	0.701745i	$-0.247595\pi$
$389$	3536.26	+	2041.66i	0.460914	+	0.266109i	−0.251515	+	0.967853i	$0.580929\pi$
$390$		0			0
$391$	−1368.09	−	789.866i	−0.176949	−	0.102162i
$392$		0			0
$393$	−832.051	+	2828.02i	−0.106798	+	0.362989i
$394$		0			0
$395$	−527.039	−	912.858i	−0.0671347	−	0.116281i
$396$		0			0
$397$	−922.738	−	532.743i	−0.116652	−	0.0673492i	0.440539	−	0.897734i	$-0.354787\pi$
$397$	−922.738	−	532.743i	−0.116652	−	0.0673492i	−0.557191	+	0.830384i	$0.688121\pi$
$398$		0			0
$399$	841.737	+	657.971i	0.105613	+	0.0825557i
$400$		0			0
$401$	−4363.81	+	2519.45i	−0.543437	+	0.313754i	−0.746471	−	0.665418i	$-0.768253\pi$
$401$	−4363.81	+	2519.45i	−0.543437	+	0.313754i	0.203034	+	0.979172i	$0.434920\pi$
$402$		0			0
$403$	7623.50	−	13204.3i	0.942316	−	1.63214i
$404$		0			0
$405$	685.320	+	1509.32i	0.0840835	+	0.185182i
$406$		0			0
$407$	−1576.37	+	910.119i	−0.191985	+	0.110843i
$408$		0			0
$409$		−	2615.68i		−	0.316228i	−0.987421	−	0.158114i	$-0.949459\pi$
$409$		−	2615.68i		−	0.316228i	0.987421	−	0.158114i	$-0.0505413\pi$
$410$		0			0
$411$	−376.007	−	1553.61i	−0.0451267	−	0.186457i
$412$		0			0
$413$	9969.71	−	7896.42i	1.18784	−	0.940817i
$414$		0			0
$415$	483.378	−	837.235i	0.0571761	−	0.0990320i
$416$		0			0
$417$	714.044	+	2950.33i	0.0838534	+	0.346470i
$418$		0			0
$419$	−2301.75	+	3986.75i	−0.268372	+	0.464834i	−0.968442	−	0.249241i	$-0.919819\pi$
$419$	−2301.75	+	3986.75i	−0.268372	+	0.464834i	0.700070	+	0.714075i	$0.253152\pi$
$420$		0			0
$421$	2846.57	+	4930.40i	0.329532	+	0.570767i	0.982419	−	0.186689i	$-0.0597756\pi$
$421$	2846.57	+	4930.40i	0.329532	+	0.570767i	−0.652887	+	0.757456i	$0.726442\pi$
$422$		0			0
$423$	142.276	−	2919.95i	0.0163539	−	0.335634i
$424$		0			0
$425$	6194.18			0.706970
$426$		0			0
$427$	−4525.35	−	5713.52i	−0.512873	−	0.647534i
$428$		0			0
$429$	−4268.28	+	14507.3i	−0.480361	+	1.63267i
$430$		0			0
$431$	−1672.76	+	965.770i	−0.186947	+	0.107934i	−0.590552	−	0.806999i	$-0.701090\pi$
$431$	−1672.76	+	965.770i	−0.186947	+	0.107934i	0.403606	+	0.914933i	$0.367757\pi$
$432$		0			0
$433$		−	1114.83i		−	0.123731i	−0.998084	−	0.0618655i	$-0.980295\pi$
$433$		−	1114.83i		−	0.123731i	0.998084	−	0.0618655i	$-0.0197050\pi$
$434$		0			0
$435$	538.776	+	2226.15i	0.0593847	+	0.245369i
$436$		0			0
$437$	339.283			0.0371399
$438$		0			0
$439$			556.782i			0.0605324i	0.999542	+	0.0302662i	$0.00963551\pi$
$439$			556.782i			0.0605324i	−0.999542	+	0.0302662i	$0.990364\pi$
$440$		0			0
$441$	8900.99	+	2557.06i	0.961126	+	0.276111i
$442$		0			0
$443$			5441.38i			0.583585i	0.956482	+	0.291792i	$0.0942516\pi$
$443$			5441.38i			0.583585i	−0.956482	+	0.291792i	$0.905748\pi$
$444$		0			0
$445$	−339.189			−0.0361328
$446$		0			0
$447$	−14147.5	−	4162.42i	−1.49698	−	0.440438i
$448$		0			0
$449$			4960.39i			0.521370i	0.965424	+	0.260685i	$0.0839485\pi$
$449$			4960.39i			0.521370i	−0.965424	+	0.260685i	$0.916052\pi$
$450$		0			0
$451$	−9386.94	+	5419.55i	−0.980075	+	0.565846i
$452$		0			0
$453$	8305.07	−	2010.01i	0.861382	−	0.208473i
$454$		0			0
$455$	−2120.46	−	2677.20i	−0.218480	−	0.275845i
$456$		0			0
$457$	7763.43			0.794656			0.397328	−	0.917677i	$-0.369937\pi$
$457$	7763.43			0.794656			0.397328	+	0.917677i	$0.369937\pi$
$458$		0			0
$459$	−6849.39	−	2383.11i	−0.696518	−	0.242340i
$460$		0			0
$461$	623.184	+	1079.39i	0.0629601	+	0.109050i	0.895787	−	0.444483i	$-0.146613\pi$
$461$	623.184	+	1079.39i	0.0629601	+	0.109050i	−0.832827	+	0.553533i	$0.813279\pi$
$462$		0			0
$463$	−3542.90	+	6136.49i	−0.355621	+	0.615954i	−0.987224	−	0.159338i	$-0.949064\pi$
$463$	−3542.90	+	6136.49i	−0.355621	+	0.615954i	0.631603	+	0.775292i	$0.282397\pi$
$464$		0			0
$465$	2130.99	+	626.973i	0.212521	+	0.0625272i
$466$		0			0
$467$	−6642.20	+	11504.6i	−0.658168	+	1.13998i	0.322921	+	0.946426i	$0.395335\pi$
$467$	−6642.20	+	11504.6i	−0.658168	+	1.13998i	−0.981089	+	0.193555i	$0.937998\pi$
$468$		0			0
$469$	−274.073	+	217.077i	−0.0269840	+	0.0213724i
$470$		0			0
$471$	12636.2	−	12035.5i	1.23619	−	1.17742i
$472$		0			0
$473$		−	2020.91i		−	0.196451i
$474$		0			0
$475$	−1152.11	+	665.171i	−0.111289	+	0.0642529i
$476$		0			0
$477$	−7813.78	−	15197.2i	−0.750039	−	1.45876i
$478$		0			0
$479$	6464.43	−	11196.7i	0.616633	−	1.06804i	−0.373462	−	0.927645i	$-0.621830\pi$
$479$	6464.43	−	11196.7i	0.616633	−	1.06804i	0.990096	−	0.140395i	$-0.0448371\pi$
$480$		0			0
$481$	−3562.52	+	2056.82i	−0.337707	+	0.194975i
$482$		0			0
$483$	2727.10	−	1101.04i	0.256910	−	0.103725i
$484$		0			0
$485$	2408.39	+	1390.49i	0.225484	+	0.130183i
$486$		0			0
$487$	−3884.93	−	6728.90i	−0.361485	−	0.626110i	0.626721	−	0.779244i	$-0.284397\pi$
$487$	−3884.93	−	6728.90i	−0.361485	−	0.626110i	−0.988205	+	0.153134i	$0.951063\pi$
$488$		0			0
$489$	−3656.44	+	884.940i	−0.338139	+	0.0818371i
$490$		0			0
$491$	−1821.57	−	1051.68i	−0.167426	−	0.0966636i	0.413945	−	0.910302i	$-0.364150\pi$
$491$	−1821.57	−	1051.68i	−0.167426	−	0.0966636i	−0.581372	+	0.813638i	$0.697484\pi$
$492$		0			0
$493$	−8678.11	−	5010.31i	−0.792784	−	0.457714i
$494$		0			0
$495$	−2200.51	−	107.221i	−0.199809	−	0.00973579i
$496$		0			0
$497$	−12838.0	−	16208.7i	−1.15868	−	1.46290i
$498$		0			0
$499$	2548.60	+	4414.30i	0.228639	+	0.396014i	0.957405	−	0.288749i	$-0.0932392\pi$
$499$	2548.60	+	4414.30i	0.228639	+	0.396014i	−0.728766	+	0.684763i	$0.759906\pi$
$500$		0			0
$501$	−19591.3	+	4741.52i	−1.74705	+	0.422825i
$502$		0			0
$503$	−13933.6			−1.23512			−0.617562	−	0.786523i	$-0.711879\pi$
$503$	−13933.6			−1.23512			−0.617562	+	0.786523i	$0.711879\pi$
$504$		0			0
$505$	−281.862			−0.0248370
$506$		0			0
$507$	−6423.90	+	21833.9i	−0.562713	+	1.91258i
$508$		0			0
$509$	−5311.06	−	9199.03i	−0.462492	−	0.801060i	0.536592	−	0.843842i	$-0.319711\pi$
$509$	−5311.06	−	9199.03i	−0.462492	−	0.801060i	−0.999084	+	0.0427815i	$0.986378\pi$
$510$		0			0
$511$	−3612.76	+	9115.80i	−0.312758	+	0.789157i
$512$		0			0
$513$	1529.89	−	292.276i	0.131669	−	0.0251545i
$514$		0			0
$515$	−3470.50	−	2003.70i	−0.296949	−	0.171443i
$516$		0			0
$517$	3364.92	+	1942.74i	0.286245	+	0.165264i
$518$		0			0
$519$	−10373.9	−	10891.7i	−0.877390	−	0.921182i
$520$		0			0
$521$	5442.58	+	9426.83i	0.457666	+	0.792700i	0.998837	−	0.0482119i	$-0.0153523\pi$
$521$	5442.58	+	9426.83i	0.457666	+	0.792700i	−0.541171	+	0.840912i	$0.682019\pi$
$522$		0			0
$523$	9617.88	+	5552.89i	0.804131	+	0.464265i	0.844914	−	0.534903i	$-0.179652\pi$
$523$	9617.88	+	5552.89i	0.804131	+	0.464265i	−0.0407825	+	0.999168i	$0.512985\pi$
$524$		0			0
$525$	−7101.86	+	9085.36i	−0.590382	+	0.755271i
$526$		0			0
$527$	−8416.27	+	4859.14i	−0.695671	+	0.401646i
$528$		0			0
$529$	−5616.52	+	9728.10i	−0.461619	+	0.799548i
$530$		0			0
$531$	902.357	−	18519.2i	0.0737457	−	1.51349i
$532$		0			0
$533$	−21214.0	+	12247.9i	−1.72398	+	0.995339i
$534$		0			0
$535$		−	3619.37i		−	0.292484i
$536$		0			0
$537$	3253.97	+	957.373i	0.261488	+	0.0769342i
$538$		0			0
$539$	−8431.91	+	8966.93i	−0.673818	+	0.716574i
$540$		0			0
$541$	−3329.27	+	5766.47i	−0.264578	+	0.458262i	−0.967453	−	0.253051i	$-0.918566\pi$
$541$	−3329.27	+	5766.47i	−0.264578	+	0.458262i	0.702875	+	0.711313i	$0.251899\pi$
$542$		0			0
$543$	−1079.89	+	1028.55i	−0.0853450	+	0.0812878i
$544$		0			0
$545$	692.051	−	1198.67i	0.0543931	−	0.0942115i
$546$		0			0
$547$	−2063.26	−	3573.67i	−0.161277	−	0.279340i	0.774050	−	0.633125i	$-0.218228\pi$
$547$	−2063.26	−	3573.67i	−0.161277	−	0.279340i	−0.935327	+	0.353784i	$0.884895\pi$
$548$		0			0
$549$	−10613.1	−	517.130i	−0.825059	−	0.0402014i
$550$		0			0
$551$	2152.16			0.166397
$552$		0			0
$553$	−6730.15	+	5330.56i	−0.517532	+	0.409907i
$554$		0			0
$555$	−413.335	−	433.965i	−0.0316128	−	0.0331906i
$556$		0			0
$557$	11144.8	−	6434.47i	0.847795	−	0.489475i	−0.0121114	−	0.999927i	$-0.503855\pi$
$557$	11144.8	−	6434.47i	0.847795	−	0.489475i	0.859906	+	0.510452i	$0.170522\pi$
$558$		0			0
$559$		−	4567.14i		−	0.345563i
$560$		0			0
$561$	6979.46	−	6647.66i	0.525264	−	0.500293i
$562$		0			0
$563$	15418.4			1.15419			0.577094	−	0.816677i	$-0.304186\pi$
$563$	15418.4			1.15419			0.577094	+	0.816677i	$0.304186\pi$
$564$		0			0
$565$		−	545.914i		−	0.0406492i
$566$		0			0
$567$	11348.5	−	7314.05i	0.840552	−	0.541731i
$568$		0			0
$569$			20866.1i			1.53735i	0.639640	+	0.768674i	$0.279083\pi$
$569$			20866.1i			1.53735i	−0.639640	+	0.768674i	$0.720917\pi$
$570$		0			0
$571$	1450.06			0.106275			0.0531377	−	0.998587i	$-0.483078\pi$
$571$	1450.06			0.106275			0.0531377	+	0.998587i	$0.483078\pi$
$572$		0			0
$573$	13734.6	−	13081.6i	1.00134	−	0.953740i
$574$		0			0
$575$			3662.08i			0.265599i
$576$		0			0
$577$	18532.1	−	10699.5i	1.33709	−	0.771969i	0.350715	−	0.936482i	$-0.385939\pi$
$577$	18532.1	−	10699.5i	1.33709	−	0.771969i	0.986375	+	0.164513i	$0.0526052\pi$
$578$		0			0
$579$	−10375.9	−	10893.8i	−0.744744	−	0.781915i
$580$		0			0
$581$	−7320.27	−	2901.16i	−0.522713	−	0.207161i
$582$		0			0
$583$	22711.8			1.61342
$584$		0			0
$585$	−4973.03	−	242.313i	−0.351469	−	0.0171255i
$586$		0			0
$587$	−859.708	−	1489.06i	−0.0604496	−	0.104702i	0.834217	−	0.551437i	$-0.185920\pi$
$587$	−859.708	−	1489.06i	−0.0604496	−	0.104702i	−0.894666	+	0.446735i	$0.852587\pi$
$588$		0			0
$589$	1043.61	−	1807.59i	0.0730071	−	0.126452i
$590$		0			0
$591$	−14455.8	+	13768.6i	−1.00615	+	0.958316i
$592$		0			0
$593$	−7790.59	+	13493.7i	−0.539496	+	0.934435i	0.459435	+	0.888211i	$0.348052\pi$
$593$	−7790.59	+	13493.7i	−0.539496	+	0.934435i	−0.998931	+	0.0462235i	$0.985281\pi$
$594$		0			0
$595$	317.271	+	2153.58i	0.0218602	+	0.148384i
$596$		0			0
$597$	−11704.5	−	3443.67i	−0.802402	−	0.236080i
$598$		0			0
$599$			21598.0i			1.47324i	0.676308	+	0.736619i	$0.263579\pi$
$599$			21598.0i			1.47324i	−0.676308	+	0.736619i	$0.736421\pi$
$600$		0			0
$601$	23499.2	−	13567.3i	1.59493	−	0.920832i	0.602485	−	0.798131i	$-0.294178\pi$
$601$	23499.2	−	13567.3i	1.59493	−	0.920832i	0.992444	−	0.122702i	$-0.0391558\pi$
$602$		0			0
$603$	−24.8063	+	509.103i	−0.00167527	+	0.0343819i
$604$		0			0
$605$	−49.1669	+	85.1596i	−0.00330400	+	0.00572270i
$606$		0			0
$607$	15348.2	−	8861.30i	1.02630	−	0.592536i	0.110379	−	0.993890i	$-0.464794\pi$
$607$	15348.2	−	8861.30i	1.02630	−	0.592536i	0.915923	+	0.401354i	$0.131460\pi$
$608$		0			0
$609$	17298.7	−	6984.17i	1.15103	−	0.464717i
$610$		0			0
$611$	7604.53	+	4390.48i	0.503513	+	0.290703i
$612$		0			0
$613$	−11100.2	−	19226.2i	−0.731377	−	1.26678i	−0.956295	−	0.292404i	$-0.905545\pi$
$613$	−11100.2	−	19226.2i	−0.731377	−	1.26678i	0.224918	−	0.974378i	$-0.427789\pi$
$614$		0			0
$615$	−2461.31	−	2584.16i	−0.161382	−	0.169437i
$616$		0			0
$617$	−18959.9	−	10946.5i	−1.23711	−	0.714247i	−0.268609	−	0.963249i	$-0.586564\pi$
$617$	−18959.9	−	10946.5i	−1.23711	−	0.714247i	−0.968503	+	0.249003i	$0.919897\pi$
$618$		0			0
$619$	−26566.9	−	15338.4i	−1.72506	−	0.995966i	−0.907397	−	0.420275i	$-0.861933\pi$
$619$	−26566.9	−	15338.4i	−1.72506	−	0.995966i	−0.817668	−	0.575691i	$-0.804733\pi$
$620$		0			0
$621$	1408.93	−	4049.45i	0.0910439	−	0.261673i
$622$		0			0
$623$	402.659	+	2733.19i	0.0258944	+	0.175767i
$624$		0			0
$625$	−6856.44	−	11875.7i	−0.438812	−	0.760045i
$626$		0			0
$627$	−584.302	+	1985.96i	−0.0372165	+	0.126493i
$628$		0			0
$629$	2621.99			0.166209
$630$		0			0
$631$	16086.9			1.01491			0.507454	−	0.861679i	$-0.330587\pi$
$631$	16086.9			1.01491			0.507454	+	0.861679i	$0.330587\pi$
$632$		0			0
$633$	8377.70	−	2027.59i	0.526041	−	0.127313i
$634$		0			0
$635$	−2528.03	−	4378.68i	−0.157987	−	0.273642i
$636$		0			0
$637$	−19055.7	+	20264.8i	−1.18526	+	1.26047i
$638$		0			0
$639$	−30108.5	−	1467.05i	−1.86396	−	0.0908226i
$640$		0			0
$641$	−2678.55	−	1546.46i	−0.165049	−	0.0952909i	0.415200	−	0.909730i	$-0.363711\pi$
$641$	−2678.55	−	1546.46i	−0.165049	−	0.0952909i	−0.580249	+	0.814439i	$0.697045\pi$
$642$		0			0
$643$	6233.64	+	3598.99i	0.382318	+	0.220732i	0.678826	−	0.734299i	$-0.262489\pi$
$643$	6233.64	+	3598.99i	0.382318	+	0.220732i	−0.296508	+	0.955030i	$0.595822\pi$
$644$		0			0
$645$	646.708	−	156.518i	0.0394792	−	0.00955484i
$646$		0			0
$647$	5869.52	+	10166.3i	0.356653	+	0.617742i	0.987399	−	0.158248i	$-0.0505844\pi$
$647$	5869.52	+	10166.3i	0.356653	+	0.617742i	−0.630746	+	0.775989i	$0.717251\pi$
$648$		0			0
$649$	21341.3	+	12321.4i	1.29078	+	0.745234i
$650$		0			0
$651$	2522.40	−	17915.8i	0.151860	−	1.07861i
$652$		0			0
$653$	8444.12	−	4875.21i	0.506040	−	0.292162i	−0.225165	−	0.974321i	$-0.572292\pi$
$653$	8444.12	−	4875.21i	0.506040	−	0.292162i	0.731204	+	0.682159i	$0.238959\pi$
$654$		0			0
$655$	644.993	−	1117.16i	0.0384763	−	0.0666429i
$656$		0			0
$657$	6536.64	+	12713.2i	0.388156	+	0.754931i
$658$		0			0
$659$	−18192.1	+	10503.2i	−1.07536	+	0.620862i	−0.929642	−	0.368464i	$-0.879884\pi$
$659$	−18192.1	+	10503.2i	−1.07536	+	0.620862i	−0.145722	+	0.989326i	$0.546551\pi$
$660$		0			0
$661$		−	13221.4i		−	0.777993i	−0.921239	−	0.388996i	$-0.872822\pi$
$661$		−	13221.4i		−	0.777993i	0.921239	−	0.388996i	$-0.127178\pi$
$662$		0			0
$663$	15773.2	−	15023.4i	0.923953	−	0.880029i
$664$		0			0
$665$	−290.277	−	366.493i	−0.0169270	−	0.0213714i
$666$		0			0
$667$	2962.16	−	5130.62i	0.171957	−	0.297838i
$668$		0			0
$669$	−720.245	−	211.908i	−0.0416238	−	0.0122464i
$670$		0			0
$671$	7061.24	−	12230.4i	0.406254	−	0.703652i
$672$		0			0
$673$	13521.6	+	23420.1i	0.774471	+	1.34142i	0.935091	+	0.354407i	$0.115317\pi$
$673$	13521.6	+	23420.1i	0.774471	+	1.34142i	−0.160620	+	0.987016i	$0.551349\pi$
$674$		0			0
$675$	3154.70	+	16513.0i	0.179888	+	0.941608i
$676$		0			0
$677$	10883.5			0.617851			0.308926	−	0.951086i	$-0.400031\pi$
$677$	10883.5			0.617851			0.308926	+	0.951086i	$0.400031\pi$
$678$		0			0
$679$	8345.48	−	21057.5i	0.471679	−	1.19015i
$680$		0			0
$681$	14341.4	−	3470.92i	0.806993	−	0.195310i
$682$		0			0
$683$	2604.50	−	1503.71i	0.145913	−	0.0842429i	−0.425266	−	0.905068i	$-0.639819\pi$
$683$	2604.50	−	1503.71i	0.145913	−	0.0842429i	0.571179	+	0.820825i	$0.306486\pi$
$684$		0			0
$685$			699.484i			0.0390159i
$686$		0			0
$687$	−24564.3	−	7227.23i	−1.36417	−	0.401363i
$688$		0			0
$689$	51327.4			2.83805
$690$		0			0
$691$			34214.3i			1.88361i	0.336165	+	0.941803i	$0.390870\pi$
$691$			34214.3i			1.88361i	−0.336165	+	0.941803i	$0.609130\pi$
$692$		0			0
$693$	1748.29	+	17859.0i	0.0958325	+	0.978941i
$694$		0			0
$695$		−	1328.33i		−	0.0724985i
$696$		0			0
$697$	15613.4			0.848491
$698$		0			0
$699$	5132.71	+	21207.6i	0.277735	+	1.14756i
$700$		0			0
$701$		−	12333.8i		−	0.664537i	−0.943185	−	0.332268i	$-0.892186\pi$
$701$		−	12333.8i		−	0.664537i	0.943185	−	0.332268i	$-0.107814\pi$
$702$		0			0
$703$	−487.687	+	281.566i	−0.0261642	+	0.0151059i
$704$		0			0
$705$	−361.083	+	1227.27i	−0.0192896	+	0.0655624i
$706$		0			0
$707$	334.604	+	2271.24i	0.0177993	+	0.120819i
$708$		0			0
$709$	−8527.19			−0.451686			−0.225843	−	0.974164i	$-0.572514\pi$
$709$	−8527.19			−0.451686			−0.225843	+	0.974164i	$0.572514\pi$
$710$		0			0
$711$	−609.145	+	12501.6i	−0.0321304	+	0.659417i
$712$		0			0
$713$	−2872.79	−	4975.81i	−0.150893	−	0.261354i
$714$		0			0
$715$	3308.71	−	5730.85i	0.173061	−	0.299751i
$716$		0			0
$717$	−3334.48	−	13777.6i	−0.173680	−	0.717620i
$718$		0			0
$719$	−13463.9	+	23320.1i	−0.698355	+	1.20959i	0.270681	+	0.962669i	$0.412751\pi$
$719$	−13463.9	+	23320.1i	−0.698355	+	1.20959i	−0.969036	+	0.246918i	$0.920582\pi$
$720$		0			0
$721$	−12025.9	+	30343.9i	−0.621174	+	1.56736i
$722$		0			0
$723$	−4893.85	−	20220.7i	−0.251735	−	1.04013i
$724$		0			0
$725$			23229.5i			1.18996i
$726$		0			0
$727$	21031.5	−	12142.6i	1.07293	−	0.619454i	0.143946	−	0.989586i	$-0.454021\pi$
$727$	21031.5	−	12142.6i	1.07293	−	0.619454i	0.928979	+	0.370132i	$0.120687\pi$
$728$		0			0
$729$	2864.71	−	19473.4i	0.145542	−	0.989352i
$730$		0			0
$731$	−1455.52	+	2521.04i	−0.0736450	+	0.127557i
$732$		0			0
$733$	−13243.5	+	7646.14i	−0.667340	+	0.385289i	−0.795068	−	0.606520i	$-0.792565\pi$
$733$	−13243.5	+	7646.14i	−0.667340	+	0.385289i	0.127728	+	0.991809i	$0.459232\pi$
$734$		0			0
$735$	−3522.54	−	2003.80i	−0.176777	−	0.100560i
$736$		0			0
$737$	−586.683	−	338.722i	−0.0293226	−	0.0169294i
$738$		0			0
$739$	12820.2	+	22205.3i	0.638158	+	1.10532i	0.985837	+	0.167709i	$0.0536368\pi$
$739$	12820.2	+	22205.3i	0.638158	+	1.10532i	−0.347678	+	0.937614i	$0.613030\pi$
$740$		0			0
$741$	−1320.49	+	4488.15i	−0.0654649	+	0.222505i
$742$		0			0
$743$	−10166.3	−	5869.52i	−0.501973	−	0.289814i	0.227555	−	0.973765i	$-0.426927\pi$
$743$	−10166.3	−	5869.52i	−0.501973	−	0.289814i	−0.729528	+	0.683951i	$0.760260\pi$
$744$		0			0
$745$	5588.71	+	3226.64i	0.274838	+	0.158678i
$746$		0			0
$747$	−10209.1	+	5249.12i	−0.500043	+	0.257102i
$748$		0			0
$749$	−29164.9	+	4296.64i	−1.42278	+	0.209607i
$750$		0			0
$751$	5827.35	+	10093.3i	0.283147	+	0.490424i	0.972158	−	0.234326i	$-0.0752884\pi$
$751$	5827.35	+	10093.3i	0.283147	+	0.490424i	−0.689011	+	0.724750i	$0.741955\pi$
$752$		0			0
$753$	−16880.5	−	17723.0i	−0.816944	−	0.857719i
$754$		0			0
$755$	−3739.20			−0.180243
$756$		0			0
$757$	28915.3			1.38830			0.694151	−	0.719829i	$-0.255780\pi$
$757$	28915.3			1.38830			0.694151	+	0.719829i	$0.255780\pi$
$758$		0			0
$759$	3930.19	+	4126.35i	0.187954	+	0.197335i
$760$		0			0
$761$	6284.63	+	10885.3i	0.299366	+	0.518517i	0.975991	−	0.217810i	$-0.0698914\pi$
$761$	6284.63	+	10885.3i	0.299366	+	0.518517i	−0.676625	+	0.736328i	$0.736558\pi$
$762$		0			0
$763$	−10480.4	−	4153.58i	−0.497269	−	0.197077i
$764$		0			0
$765$	2667.86	+	1718.63i	0.126087	+	0.0812252i
$766$		0			0
$767$	48230.2	+	27845.7i	2.27052	+	1.31089i
$768$		0			0
$769$	−18621.1	−	10750.9i	−0.873206	−	0.504146i	−0.00479362	−	0.999989i	$-0.501526\pi$
$769$	−18621.1	−	10750.9i	−0.873206	−	0.504146i	−0.868412	+	0.495843i	$0.834859\pi$
$770$		0			0
$771$	8485.01	−	28839.3i	0.396343	−	1.34711i
$772$		0			0
$773$	−15174.1	−	26282.4i	−0.706049	−	1.22291i	−0.966311	−	0.257376i	$-0.917142\pi$
$773$	−15174.1	−	26282.4i	−0.706049	−	1.22291i	0.260262	−	0.965538i	$-0.416191\pi$
$774$		0			0
$775$	19510.3	+	11264.3i	0.904299	+	0.522097i
$776$		0			0
$777$	−3006.21	+	3845.82i	−0.138800	+	0.177565i
$778$		0			0
$779$	−2904.06	+	1676.66i	−0.133567	+	0.0771151i
$780$		0			0
$781$	20032.1	−	34696.6i	0.917804	−	1.58968i
$782$		0			0
$783$	8937.16	−	25686.6i	0.407903	−	1.17237i
$784$		0			0
$785$	−6613.30	+	3818.19i	−0.300686	+	0.173601i
$786$		0			0
$787$			6972.83i			0.315825i	0.987453	+	0.157913i	$0.0504764\pi$
$787$			6972.83i			0.315825i	−0.987453	+	0.157913i	$0.949524\pi$
$788$		0			0
$789$	9779.28	+	40406.6i	0.441257	+	1.82321i
$790$		0			0
$791$	−4398.98	+	648.067i	−0.197736	+	0.0291310i
$792$		0			0
$793$	15958.0	−	27640.1i	0.714611	−	1.23774i
$794$		0			0
$795$	1759.01	+	7267.96i	0.0784723	+	0.324237i
$796$		0			0
$797$	−8953.19	+	15507.4i	−0.397915	+	0.689209i	−0.993469	−	0.114107i	$-0.963599\pi$
$797$	−8953.19	+	15507.4i	−0.397915	+	0.689209i	0.595553	+	0.803316i	$0.296933\pi$
$798$		0			0
$799$	−2798.44	−	4847.05i	−0.123907	−	0.214614i
$800$		0			0
$801$	3385.88	+	2181.18i	0.149356	+	0.0962149i
$802$		0			0
$803$	−18999.6			−0.834969
$804$		0			0
$805$	−1273.23	+	187.575i	−0.0557457	+	0.00821259i
$806$		0			0
$807$	7312.97	−	24855.7i	0.318995	−	1.08422i
$808$		0			0
$809$	−18644.0	+	10764.1i	−0.810245	+	0.467795i	−0.847041	−	0.531528i	$-0.821618\pi$
$809$	−18644.0	+	10764.1i	−0.810245	+	0.467795i	0.0367961	+	0.999323i	$0.488285\pi$
$810$		0			0
$811$		−	23203.9i		−	1.00469i	−0.864669	−	0.502343i	$-0.832472\pi$
$811$		−	23203.9i		−	1.00469i	0.864669	−	0.502343i	$-0.167528\pi$
$812$		0			0
$813$	−8551.49	−	35333.6i	−0.368898	−	1.52423i
$814$		0			0
$815$	1646.25			0.0707552
$816$		0			0
$817$		−	625.214i		−	0.0267729i
$818$		0			0
$819$	3951.04	+	40360.3i	0.168572	+	1.72198i
$820$		0			0
$821$			2085.12i			0.0886371i	0.999017	+	0.0443186i	$0.0141117\pi$
$821$			2085.12i			0.0886371i	−0.999017	+	0.0443186i	$0.985888\pi$
$822$		0			0
$823$	39012.8			1.65237			0.826185	−	0.563398i	$-0.190506\pi$
$823$	39012.8			1.65237			0.826185	+	0.563398i	$0.190506\pi$
$824$		0			0
$825$	−21435.6	−	6306.71i	−0.904595	−	0.266147i
$826$		0			0
$827$		−	8515.43i		−	0.358054i	−0.983844	−	0.179027i	$-0.942705\pi$
$827$		−	8515.43i		−	0.358054i	0.983844	−	0.179027i	$-0.0572949\pi$
$828$		0			0
$829$	−19851.6	+	11461.3i	−0.831696	+	0.480180i	−0.854433	−	0.519562i	$-0.826095\pi$
$829$	−19851.6	+	11461.3i	−0.831696	+	0.480180i	0.0227370	+	0.999741i	$0.492762\pi$
$830$		0			0
$831$	21834.5	−	5284.43i	0.911469	−	0.220595i
$832$		0			0
$833$	16976.9	−	5113.14i	0.706141	−	0.212677i
$834$		0			0
$835$	8820.61			0.365569
$836$		0			0
$837$	−17240.3	−	19962.1i	−0.711963	−	0.824361i
$838$		0			0
$839$	14263.6	+	24705.3i	0.586929	+	1.01659i	0.994632	+	0.103477i	$0.0329967\pi$
$839$	14263.6	+	24705.3i	0.586929	+	1.01659i	−0.407703	+	0.913115i	$0.633670\pi$
$840$		0			0
$841$	6595.22	−	11423.2i	0.270418	−	0.468377i
$842$		0			0
$843$	41463.3	+	12199.2i	1.69403	+	0.498414i
$844$		0			0
$845$	4979.71	−	8625.11i	0.202730	−	0.351139i
$846$		0			0
$847$	744.584	+	295.092i	0.0302057	+	0.0119711i
$848$		0			0
$849$	−7883.35	+	7508.58i	−0.318676	+	0.303526i
$850$		0			0
$851$			1550.16i			0.0624426i
$852$		0			0
$853$	−3816.92	+	2203.70i	−0.153211	+	0.0884563i	−0.574645	−	0.818402i	$-0.694860\pi$
$853$	−3816.92	+	2203.70i	−0.153211	+	0.0884563i	0.421435	+	0.906859i	$0.361527\pi$
$854$		0			0
$855$	−680.777	−	33.1712i	−0.0272305	−	0.00132682i
$856$		0			0
$857$	3570.37	−	6184.07i	0.142312	−	0.246492i	−0.786055	−	0.618157i	$-0.787880\pi$
$857$	3570.37	−	6184.07i	0.142312	−	0.246492i	0.928367	+	0.371665i	$0.121213\pi$
$858$		0			0
$859$	−30809.7	+	17788.0i	−1.22377	+	0.706542i	−0.965719	−	0.259591i	$-0.916412\pi$
$859$	−30809.7	+	17788.0i	−1.22377	+	0.706542i	−0.258047	+	0.966132i	$0.583079\pi$
$860$		0			0
$861$	−17901.3	+	22901.0i	−0.708566	+	0.906462i
$862$		0			0
$863$	10089.3	+	5825.03i	0.397963	+	0.229764i	0.685605	−	0.727974i	$-0.259538\pi$
$863$	10089.3	+	5825.03i	0.397963	+	0.229764i	−0.287642	+	0.957738i	$0.592871\pi$
$864$		0			0
$865$	3291.07	+	5700.31i	0.129364	+	0.224065i
$866$		0			0
$867$	11317.7	−	2739.14i	0.443334	−	0.107297i
$868$		0			0
$869$	−14406.6	−	8317.68i	−0.562384	−	0.324693i
$870$		0			0
$871$	−1325.87	−	765.493i	−0.0515792	−	0.0297793i
$872$		0			0
$873$	−15099.6	−	29367.6i	−0.585390	−	1.13854i
$874$		0			0
$875$	8082.22	−	6401.45i	0.312262	−	0.247324i
$876$		0			0
$877$	6238.51	+	10805.4i	0.240205	+	0.416047i	0.960773	−	0.277338i	$-0.0894521\pi$
$877$	6238.51	+	10805.4i	0.240205	+	0.416047i	−0.720568	+	0.693385i	$0.756119\pi$
$878$		0			0
$879$	−15357.4	+	3716.83i	−0.589298	+	0.142623i
$880$		0			0
$881$	25422.6			0.972203			0.486101	−	0.873902i	$-0.338419\pi$
$881$	25422.6			0.972203			0.486101	+	0.873902i	$0.338419\pi$
$882$		0			0
$883$	−32619.3			−1.24318			−0.621589	−	0.783344i	$-0.713512\pi$
$883$	−32619.3			−1.24318			−0.621589	+	0.783344i	$0.713512\pi$
$884$		0			0
$885$	−2290.09	+	7783.68i	−0.0869837	+	0.295645i
$886$		0			0
$887$	−5206.64	−	9018.17i	−0.197094	−	0.341376i	0.750491	−	0.660880i	$-0.229817\pi$
$887$	−5206.64	−	9018.17i	−0.197094	−	0.341376i	−0.947585	+	0.319504i	$0.896484\pi$
$888$		0			0
$889$	−32282.3	+	25568.9i	−1.21790	+	0.964627i
$890$		0			0
$891$	21276.6	+	15220.8i	0.799991	+	0.572296i
$892$		0			0
$893$	1041.01	+	601.030i	0.0390103	+	0.0225226i
$894$		0			0
$895$	−1285.43	−	742.141i	−0.0480078	−	0.0277173i
$896$		0			0
$897$	8882.01	+	9325.33i	0.330615	+	0.347117i
$898$		0			0
$899$	−18222.8	−	31562.8i	−0.676044	−	1.17094i
$900$		0			0
$901$	−28332.5	−	16357.8i	−1.04760	−	0.604835i
$902$		0			0
$903$	−2028.94	−	5025.37i	−0.0747718	−	0.185198i
$904$		0			0
$905$	565.171	−	326.302i	0.0207590	−	0.0119852i
$906$		0			0
$907$	10139.7	−	17562.5i	0.371206	−	0.642948i	−0.618545	−	0.785749i	$-0.712278\pi$
$907$	10139.7	−	17562.5i	0.371206	−	0.642948i	0.989751	+	0.142801i	$0.0456109\pi$
$908$		0			0
$909$	2813.62	+	1812.53i	0.102664	+	0.0661362i
$910$		0			0
$911$	−37900.7	+	21882.0i	−1.37838	+	0.795810i	−0.991965	−	0.126513i	$-0.959621\pi$
$911$	−37900.7	+	21882.0i	−1.37838	+	0.795810i	−0.386419	+	0.922323i	$0.626288\pi$
$912$		0			0
$913$		−	15257.2i		−	0.553057i
$914$		0			0
$915$	4460.73	+	1312.42i	0.161166	+	0.0474179i
$916$		0			0
$917$	−9767.77	−	3871.15i	−0.351756	−	0.139407i
$918$		0			0
$919$	−669.644	+	1159.86i	−0.0240365	+	0.0416324i	−0.877793	−	0.479039i	$-0.840985\pi$
$919$	−669.644	+	1159.86i	−0.0240365	+	0.0416324i	0.853757	+	0.520672i	$0.174318\pi$
$920$		0			0
$921$	−7123.08	+	6784.46i	−0.254846	+	0.242731i
$922$		0			0
$923$	45271.5	−	78412.5i	1.61444	−	2.79629i
$924$		0			0
$925$	−3039.11	−	5263.89i	−0.108027	−	0.187109i
$926$		0			0
$927$	21758.6	+	42318.7i	0.770924	+	1.49938i
$928$		0			0
$929$	−27477.4			−0.970403			−0.485202	−	0.874402i	$-0.661254\pi$
$929$	−27477.4			−0.970403			−0.485202	+	0.874402i	$0.661254\pi$
$930$		0			0
$931$	−2608.60	+	2774.13i	−0.0918298	+	0.0976566i
$932$		0			0
$933$	−11532.1	−	12107.7i	−0.404657	−	0.424854i
$934$		0			0
$935$	−3652.78	+	2108.94i	−0.127763	+	0.0737642i
$936$		0			0
$937$			7077.24i			0.246749i	0.992360	+	0.123374i	$0.0393716\pi$
$937$			7077.24i			0.246749i	−0.992360	+	0.123374i	$0.960628\pi$
$938$		0			0
$939$	3516.88	−	3349.69i	0.122225	−	0.116414i
$940$		0			0
$941$	29821.2			1.03310			0.516548	−	0.856258i	$-0.327217\pi$
$941$	29821.2			1.03310			0.516548	+	0.856258i	$0.327217\pi$
$942$		0			0
$943$			9230.83i			0.318767i
$944$		0			0
$945$	−5579.62	+	1942.63i	−0.192069	+	0.0668717i
$946$		0			0
$947$		−	37528.4i		−	1.28776i	−0.765126	−	0.643881i	$-0.777323\pi$
$947$		−	37528.4i		−	1.28776i	0.765126	−	0.643881i	$-0.222677\pi$
$948$		0			0
$949$	−42938.0			−1.46873
$950$		0			0
$951$	19017.1	−	18113.0i	0.648444	−	0.617618i
$952$		0			0
$953$		−	32602.0i		−	1.10817i	−0.832462	−	0.554083i	$-0.813069\pi$
$953$		−	32602.0i		−	1.10817i	0.832462	−	0.554083i	$-0.186931\pi$
$954$		0			0
$955$	−7188.15	+	4150.08i	−0.243563	+	0.140621i
$956$		0			0
$957$	24930.1	+	26174.4i	0.842086	+	0.884116i
$958$		0			0
$959$	5636.44	−	830.374i	0.189792	−	0.0279606i
$960$		0			0
$961$	−5554.89			−0.186462
$962$		0			0
$963$	−23274.6	+	36129.5i	−0.778830	+	1.20899i
$964$		0			0
$965$	3291.69	+	5701.37i	0.109806	+	0.190190i
$966$		0			0
$967$	−25441.4	+	44065.9i	−0.846061	+	1.46542i	0.0386347	+	0.999253i	$0.487699\pi$
$967$	−25441.4	+	44065.9i	−0.846061	+	1.46542i	−0.884696	+	0.466168i	$0.845634\pi$
$968$		0			0
$969$	2159.26	−	2056.61i	0.0715844	−	0.0681813i
$970$		0			0
$971$	5033.66	−	8718.55i	0.166362	−	0.288148i	−0.770776	−	0.637106i	$-0.780131\pi$
$971$	5033.66	−	8718.55i	0.166362	−	0.288148i	0.937138	+	0.348958i	$0.113465\pi$
$972$		0			0
$973$	−10703.7	+	1576.89i	−0.352666	+	0.0519557i
$974$		0			0
$975$	−48443.3	−	14252.8i	−1.59121	−	0.468160i
$976$		0			0
$977$			44973.7i			1.47271i	0.676597	+	0.736354i	$0.263454\pi$
$977$			44973.7i			1.47271i	−0.676597	+	0.736354i	$0.736546\pi$
$978$		0			0
$979$	−4635.87	+	2676.52i	−0.151341	+	0.0873770i
$980$		0			0
$981$	−14616.4	+	7515.16i	−0.475703	+	0.244588i
$982$		0			0
$983$	−1419.40	+	2458.48i	−0.0460548	+	0.0797693i	−0.888134	−	0.459585i	$-0.847998\pi$
$983$	−1419.40	+	2458.48i	−0.0460548	+	0.0797693i	0.842079	+	0.539354i	$0.181332\pi$
$984$		0			0
$985$	7565.62	−	4368.02i	0.244732	−	0.141296i
$986$		0			0
$987$	10318.0	+	1452.69i	0.332750	+	0.0468486i
$988$		0			0
$989$	−1490.47	−	860.525i	−0.0479214	−	0.0276675i
$990$		0			0
$991$	−17603.9	−	30490.9i	−0.564285	−	0.977371i	−0.997116	−	0.0758954i	$-0.975818\pi$
$991$	−17603.9	−	30490.9i	−0.564285	−	0.977371i	0.432831	−	0.901475i	$-0.357515\pi$
$992$		0			0
$993$	−8007.44	−	8407.11i	−0.255900	−	0.268672i
$994$		0			0
$995$	4623.67	+	2669.48i	0.147317	+	0.0850534i
$996$		0			0
$997$	−36724.0	−	21202.6i	−1.16656	−	0.673513i	−0.213692	−	0.976901i	$-0.568549\pi$
$997$	−36724.0	−	21202.6i	−1.16656	−	0.673513i	−0.952867	+	0.303388i	$0.901882\pi$
$998$		0			0
$999$	1335.38	+	6989.94i	0.0422919	+	0.221373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.w.a.5.18	✓	48
3.2	odd	2		756.4.w.a.341.13		48
7.3	odd	6		252.4.bm.a.185.9	yes	48
9.2	odd	6		252.4.bm.a.173.9	yes	48
9.7	even	3		756.4.bm.a.89.13		48
21.17	even	6		756.4.bm.a.17.13		48
63.38	even	6	inner	252.4.w.a.101.18	yes	48
63.52	odd	6		756.4.w.a.521.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.18	✓	48	1.1	even	1	trivial
252.4.w.a.101.18	yes	48	63.38	even	6	inner
252.4.bm.a.173.9	yes	48	9.2	odd	6
252.4.bm.a.185.9	yes	48	7.3	odd	6
756.4.w.a.341.13		48	3.2	odd	2
756.4.w.a.521.13		48	63.52	odd	6
756.4.bm.a.17.13		48	21.17	even	6
756.4.bm.a.89.13		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)

\(f(q)\)	\(=\)	\(q+(3.58371 + 3.76258i) q^{3} +(-1.13691 - 1.96919i) q^{5} +(-14.5181 + 11.4989i) q^{7} +(-1.31403 + 26.9680i) q^{9} +O(q^{10})\)	\(q+(3.58371 + 3.76258i) q^{3} +(-1.13691 - 1.96919i) q^{5} +(-14.5181 + 11.4989i) q^{7} +(-1.31403 + 26.9680i) q^{9} +(-31.0776 - 17.9426i) q^{11} +(-70.2337 - 40.5494i) q^{13} +(3.33487 - 11.3347i) q^{15} +(25.8458 + 44.7662i) q^{17} +(-9.61456 - 5.55097i) q^{19} +(-95.2942 - 13.4167i) q^{21} +(-26.4664 + 15.2804i) q^{23} +(59.9149 - 103.776i) q^{25} +(-106.178 + 91.7014i) q^{27} +(-167.883 + 96.9271i) q^{29} +188.005i q^{31} +(-43.8624 - 181.233i) q^{33} +(39.1494 + 15.5156i) q^{35} +(25.3619 - 43.9281i) q^{37} +(-99.1267 - 409.577i) q^{39} +(151.024 - 261.582i) q^{41} +(28.1579 + 48.7709i) q^{43} +(54.5991 - 28.0727i) q^{45} -108.275 q^{47} +(78.5497 - 333.885i) q^{49} +(-75.8126 + 257.676i) q^{51} +(-548.106 + 316.449i) q^{53} +81.5969i q^{55} +(-13.5698 - 56.0686i) q^{57} -686.710 q^{59} +393.545i q^{61} +(-291.026 - 406.634i) q^{63} +184.405i q^{65} +18.8780 q^{67} +(-152.341 - 44.8214i) q^{69} +1116.45i q^{71} +(458.520 - 264.726i) q^{73} +(605.182 - 146.467i) q^{75} +(657.508 - 96.8656i) q^{77} +463.570 q^{79} +(-725.547 - 70.8735i) q^{81} +(212.584 + 368.205i) q^{83} +(58.7688 - 101.791i) q^{85} +(-966.339 - 284.313i) q^{87} +(74.5855 - 129.186i) q^{89} +(1485.93 - 218.911i) q^{91} +(-707.384 + 673.756i) q^{93} +25.2439i q^{95} +(-1059.18 + 611.519i) q^{97} +(524.714 - 814.523i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) \) 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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