LMFDB - Embedded newform 252.4.bm.a.173.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(173,252)]

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, 1, 5]))

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

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

chi := DirichletCharacter("252.173");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.bm (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			173.8
Character	$\chi$	$=$	252.173
Dual form			252.4.bm.a.185.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.94236 + 4.28282i) q^{3} -17.3719 q^{5} +(-18.1816 + 3.52543i) q^{7} +(-9.68509 - 25.2032i) q^{9} +O(q^{10})$	\(q+(-2.94236 + 4.28282i) q^{3} -17.3719 q^{5} +(-18.1816 + 3.52543i) q^{7} +(-9.68509 - 25.2032i) q^{9} -10.5210i q^{11} +(11.0151 - 6.35956i) q^{13} +(51.1144 - 74.4008i) q^{15} +(28.9921 + 50.2158i) q^{17} +(56.6851 + 32.7272i) q^{19} +(38.3980 - 88.2417i) q^{21} +36.0738i q^{23} +176.784 q^{25} +(136.438 + 32.6772i) q^{27} +(-230.478 - 133.066i) q^{29} +(140.887 + 81.3410i) q^{31} +(45.0594 + 30.9564i) q^{33} +(315.850 - 61.2435i) q^{35} +(-59.1062 + 102.375i) q^{37} +(-5.17344 + 65.8877i) q^{39} +(-33.7999 - 58.5431i) q^{41} +(136.218 - 235.936i) q^{43} +(168.249 + 437.827i) q^{45} +(-64.8762 - 112.369i) q^{47} +(318.143 - 128.196i) q^{49} +(-300.370 - 23.5848i) q^{51} +(39.3597 - 22.7244i) q^{53} +182.769i q^{55} +(-306.952 + 146.477i) q^{57} +(213.630 - 370.018i) q^{59} +(776.582 - 448.360i) q^{61} +(264.943 + 424.090i) q^{63} +(-191.353 + 110.478i) q^{65} +(36.3149 - 62.8992i) q^{67} +(-154.498 - 106.142i) q^{69} -664.418i q^{71} +(-363.478 + 209.854i) q^{73} +(-520.161 + 757.133i) q^{75} +(37.0909 + 191.288i) q^{77} +(-597.764 - 1035.36i) q^{79} +(-541.398 + 488.190i) q^{81} +(711.970 - 1233.17i) q^{83} +(-503.648 - 872.345i) q^{85} +(1248.05 - 595.566i) q^{87} +(-759.561 + 1315.60i) q^{89} +(-177.852 + 154.460i) q^{91} +(-762.907 + 364.058i) q^{93} +(-984.729 - 568.534i) q^{95} +(1012.75 + 584.714i) q^{97} +(-265.161 + 101.896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 - 30 * q^9	$ 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−2.94236	+	4.28282i	−0.566257	+	0.824229i
$3$	−2.94236	+	4.28282i	−0.566257	+	0.824229i
$4$		0			0
$5$	−17.3719			−1.55379			−0.776896	−	0.629629i	$-0.783207\pi$
$5$	−17.3719			−1.55379			−0.776896	+	0.629629i	$0.783207\pi$
$6$		0			0
$7$	−18.1816	+	3.52543i	−0.981715	+	0.190355i
$7$	−18.1816	+	3.52543i	−0.981715	+	0.190355i
$8$		0			0
$9$	−9.68509	−	25.2032i	−0.358707	−	0.933450i
$10$		0			0
$11$		−	10.5210i		−	0.288381i	−0.989550	−	0.144190i	$-0.953942\pi$
$11$		−	10.5210i		−	0.288381i	0.989550	−	0.144190i	$-0.0460578\pi$
$12$		0			0
$13$	11.0151	−	6.35956i	0.235003	−	0.135679i	−0.377875	−	0.925857i	$-0.623345\pi$
$13$	11.0151	−	6.35956i	0.235003	−	0.135679i	0.612878	+	0.790178i	$0.290012\pi$
$14$		0			0
$15$	51.1144	−	74.4008i	0.879845	−	1.28068i
$16$		0			0
$17$	28.9921	+	50.2158i	0.413624	+	0.716418i	0.995283	−	0.0970146i	$-0.0309294\pi$
$17$	28.9921	+	50.2158i	0.413624	+	0.716418i	−0.581659	+	0.813433i	$0.697596\pi$
$18$		0			0
$19$	56.6851	+	32.7272i	0.684445	+	0.395164i	0.801528	−	0.597958i	$-0.204021\pi$
$19$	56.6851	+	32.7272i	0.684445	+	0.395164i	−0.117083	+	0.993122i	$0.537354\pi$
$20$		0			0
$21$	38.3980	−	88.2417i	0.399006	−	0.916948i
$22$		0			0
$23$			36.0738i			0.327040i	0.986540	+	0.163520i	$0.0522848\pi$
$23$			36.0738i			0.327040i	−0.986540	+	0.163520i	$0.947715\pi$
$24$		0			0
$25$	176.784			1.41427
$26$		0			0
$27$	136.438	+	32.6772i	0.972497	+	0.232916i
$28$		0			0
$29$	−230.478	−	133.066i	−1.47582	−	0.852062i	−0.476187	−	0.879344i	$-0.657982\pi$
$29$	−230.478	−	133.066i	−1.47582	−	0.852062i	−0.999628	+	0.0272817i	$0.991315\pi$
$30$		0			0
$31$	140.887	+	81.3410i	0.816258	+	0.471267i	0.849124	−	0.528193i	$-0.177130\pi$
$31$	140.887	+	81.3410i	0.816258	+	0.471267i	−0.0328665	+	0.999460i	$0.510464\pi$
$32$		0			0
$33$	45.0594	+	30.9564i	0.237692	+	0.163298i
$34$		0			0
$35$	315.850	−	61.2435i	1.52538	−	0.295773i
$36$		0			0
$37$	−59.1062	+	102.375i	−0.262622	+	0.454874i	−0.966938	−	0.255012i	$-0.917920\pi$
$37$	−59.1062	+	102.375i	−0.262622	+	0.454874i	0.704316	+	0.709887i	$0.251254\pi$
$38$		0			0
$39$	−5.17344	+	65.8877i	−0.0212413	+	0.270525i
$40$		0			0
$41$	−33.7999	−	58.5431i	−0.128748	−	0.222998i	0.794444	−	0.607337i	$-0.207762\pi$
$41$	−33.7999	−	58.5431i	−0.128748	−	0.222998i	−0.923192	+	0.384340i	$0.874429\pi$
$42$		0			0
$43$	136.218	−	235.936i	0.483093	−	0.836741i	−0.516719	−	0.856155i	$-0.672847\pi$
$43$	136.218	−	235.936i	0.483093	−	0.836741i	0.999812	+	0.0194142i	$0.00618013\pi$
$44$		0			0
$45$	168.249	+	437.827i	0.557356	+	1.45039i
$46$		0			0
$47$	−64.8762	−	112.369i	−0.201344	−	0.348738i	0.747618	−	0.664129i	$-0.231198\pi$
$47$	−64.8762	−	112.369i	−0.201344	−	0.348738i	−0.948962	+	0.315391i	$0.897864\pi$
$48$		0			0
$49$	318.143	−	128.196i	0.927530	−	0.373750i
$50$		0			0
$51$	−300.370	−	23.5848i	−0.824710	−	0.0647554i
$52$		0			0
$53$	39.3597	−	22.7244i	0.102009	−	0.0588949i	−0.448128	−	0.893970i	$-0.647909\pi$
$53$	39.3597	−	22.7244i	0.102009	−	0.0588949i	0.550137	+	0.835075i	$0.314576\pi$
$54$		0			0
$55$			182.769i			0.448084i
$56$		0			0
$57$	−306.952	+	146.477i	−0.713277	+	0.340375i
$58$		0			0
$59$	213.630	−	370.018i	0.471395	−	0.816480i	−0.528070	−	0.849201i	$-0.677084\pi$
$59$	213.630	−	370.018i	0.471395	−	0.816480i	0.999465	+	0.0327213i	$0.0104174\pi$
$60$		0			0
$61$	776.582	−	448.360i	1.63002	−	0.941092i	0.645934	−	0.763394i	$-0.276468\pi$
$61$	776.582	−	448.360i	1.63002	−	0.941092i	0.984085	−	0.177698i	$-0.0568650\pi$
$62$		0			0
$63$	264.943	+	424.090i	0.529835	+	0.848100i
$64$		0			0
$65$	−191.353	+	110.478i	−0.365145	+	0.210817i
$66$		0			0
$67$	36.3149	−	62.8992i	0.0662174	−	0.114692i	−0.831016	−	0.556249i	$-0.812240\pi$
$67$	36.3149	−	62.8992i	0.0662174	−	0.114692i	0.897233	+	0.441557i	$0.145574\pi$
$68$		0			0
$69$	−154.498	−	106.142i	−0.269555	−	0.185188i
$70$		0			0
$71$		−	664.418i		−	1.11059i	−0.831653	−	0.555295i	$-0.812605\pi$
$71$		−	664.418i		−	1.11059i	0.831653	−	0.555295i	$-0.187395\pi$
$72$		0			0
$73$	−363.478	+	209.854i	−0.582766	+	0.336460i	−0.762232	−	0.647304i	$-0.775896\pi$
$73$	−363.478	+	209.854i	−0.582766	+	0.336460i	0.179466	+	0.983764i	$0.442563\pi$
$74$		0			0
$75$	−520.161	+	757.133i	−0.800840	+	1.16568i
$76$		0			0
$77$	37.0909	+	191.288i	0.0548948	+	0.283108i
$78$		0			0
$79$	−597.764	−	1035.36i	−0.851312	−	1.47452i	−0.880025	−	0.474928i	$-0.842474\pi$
$79$	−597.764	−	1035.36i	−0.851312	−	1.47452i	0.0287127	−	0.999588i	$-0.490859\pi$
$80$		0			0
$81$	−541.398	+	488.190i	−0.742659	+	0.669670i
$82$		0			0
$83$	711.970	−	1233.17i	0.941553	−	1.63082i	0.179042	−	0.983841i	$-0.442700\pi$
$83$	711.970	−	1233.17i	0.941553	−	1.63082i	0.762511	−	0.646975i	$-0.223966\pi$
$84$		0			0
$85$	−503.648	−	872.345i	−0.642686	−	1.11317i
$86$		0			0
$87$	1248.05	−	595.566i	1.53798	−	0.733924i
$88$		0			0
$89$	−759.561	+	1315.60i	−0.904644	+	1.56689i	−0.0832491	+	0.996529i	$0.526530\pi$
$89$	−759.561	+	1315.60i	−0.904644	+	1.56689i	−0.821395	+	0.570360i	$0.806804\pi$
$90$		0			0
$91$	−177.852	+	154.460i	−0.204878	+	0.177932i
$92$		0			0
$93$	−762.907	+	364.058i	−0.850643	+	0.405926i
$94$		0			0
$95$	−984.729	−	568.534i	−1.06349	−	0.614004i
$96$		0			0
$97$	1012.75	+	584.714i	1.06010	+	0.612049i	0.925460	−	0.378846i	$-0.123679\pi$
$97$	1012.75	+	584.714i	1.06010	+	0.612049i	0.134640	+	0.990895i	$0.457012\pi$
$98$		0			0
$99$	−265.161	+	101.896i	−0.269189	+	0.103444i
$100$		0			0
$101$	−1592.82			−1.56922			−0.784611	−	0.619988i	$-0.787137\pi$
$101$	−1592.82			−1.56922			−0.784611	+	0.619988i	$0.787137\pi$
$102$		0			0
$103$			1901.48i			1.81902i	0.415687	+	0.909508i	$0.363541\pi$
$103$			1901.48i			1.81902i	−0.415687	+	0.909508i	$0.636459\pi$
$104$		0			0
$105$	−667.047	+	1532.93i	−0.619973	+	1.42475i
$106$		0			0
$107$	672.583	+	388.316i	0.607674	+	0.350841i	0.772054	−	0.635556i	$-0.219229\pi$
$107$	672.583	+	388.316i	0.607674	+	0.350841i	−0.164381	+	0.986397i	$0.552563\pi$
$108$		0			0
$109$	369.316	+	639.674i	0.324532	+	0.562107i	0.981418	−	0.191884i	$-0.0614597\pi$
$109$	369.316	+	639.674i	0.324532	+	0.562107i	−0.656885	+	0.753991i	$0.728126\pi$
$110$		0			0
$111$	−264.542	−	554.365i	−0.226209	−	0.474036i
$112$		0			0
$113$	−447.624	+	258.436i	−0.372646	+	0.215147i	−0.674614	−	0.738171i	$-0.735690\pi$
$113$	−447.624	+	258.436i	−0.372646	+	0.215147i	0.301968	+	0.953318i	$0.402356\pi$
$114$		0			0
$115$		−	626.672i		−	0.508152i
$116$		0			0
$117$	−266.963	−	216.022i	−0.210946	−	0.170694i
$118$		0			0
$119$	−704.155	−	810.794i	−0.542435	−	0.624583i
$120$		0			0
$121$	1220.31			0.916837
$122$		0			0
$123$	350.181	+	27.4959i	0.256705	+	0.0201562i
$124$		0			0
$125$	−899.585			−0.643691
$126$		0			0
$127$	306.161			0.213916			0.106958	−	0.994264i	$-0.465889\pi$
$127$	306.161			0.213916			0.106958	+	0.994264i	$0.465889\pi$
$128$		0			0
$129$	609.670	+	1277.60i	0.416112	+	0.871989i
$130$		0			0
$131$	−1671.29			−1.11467			−0.557335	−	0.830288i	$-0.688176\pi$
$131$	−1671.29			−1.11467			−0.557335	+	0.830288i	$0.688176\pi$
$132$		0			0
$133$	−1146.00	−	395.193i	−0.747152	−	0.257651i
$134$		0			0
$135$	−2370.18	−	567.665i	−1.51106	−	0.361903i
$136$		0			0
$137$		−	1324.30i		−	0.825856i	−0.910764	−	0.412928i	$-0.864506\pi$
$137$		−	1324.30i		−	0.825856i	0.910764	−	0.412928i	$-0.135494\pi$
$138$		0			0
$139$	523.824	−	302.430i	0.319642	−	0.184545i	−0.331591	−	0.943423i	$-0.607585\pi$
$139$	523.824	−	302.430i	0.319642	−	0.184545i	0.651233	+	0.758878i	$0.274252\pi$
$140$		0			0
$141$	672.145	+	52.7761i	0.401453	+	0.0315217i
$142$		0			0
$143$	−66.9087	−	115.889i	−0.0391272	−	0.0677702i
$144$		0			0
$145$	4003.84	+	2311.62i	2.29311	+	1.32393i
$146$		0			0
$147$	−387.048	+	1739.75i	−0.217165	+	0.976135i
$148$		0			0
$149$			1065.66i			0.585921i	0.956124	+	0.292961i	$0.0946405\pi$
$149$			1065.66i			0.585921i	−0.956124	+	0.292961i	$0.905359\pi$
$150$		0			0
$151$	2808.41			1.51354			0.756772	−	0.653679i	$-0.226775\pi$
$151$	2808.41			1.51354			0.756772	+	0.653679i	$0.226775\pi$
$152$		0			0
$153$	984.805	−	1217.04i	0.520371	−	0.643082i
$154$		0			0
$155$	−2447.47	−	1413.05i	−1.26830	−	0.732251i
$156$		0			0
$157$	−889.938	−	513.806i	−0.452387	−	0.261186i	0.256451	−	0.966557i	$-0.417447\pi$
$157$	−889.938	−	513.806i	−0.452387	−	0.261186i	−0.708838	+	0.705372i	$0.750780\pi$
$158$		0			0
$159$	−18.4860	+	235.434i	−0.00922036	+	0.117428i
$160$		0			0
$161$	−127.176	−	655.880i	−0.0622537	−	0.321060i
$162$		0			0
$163$	1492.45	−	2585.00i	0.717164	−	1.24216i	−0.244955	−	0.969534i	$-0.578773\pi$
$163$	1492.45	−	2585.00i	0.717164	−	1.24216i	0.962119	−	0.272630i	$-0.0878933\pi$
$164$		0			0
$165$	−782.768	−	537.772i	−0.369324	−	0.253730i
$166$		0			0
$167$	−393.810	−	682.099i	−0.182479	−	0.316062i	0.760245	−	0.649636i	$-0.225079\pi$
$167$	−393.810	−	682.099i	−0.182479	−	0.316062i	−0.942724	+	0.333574i	$0.891745\pi$
$168$		0			0
$169$	−1017.61	+	1762.56i	−0.463183	+	0.802256i
$170$		0			0
$171$	275.827	−	1745.61i	0.123351	−	0.780643i
$172$		0			0
$173$	75.8291	+	131.340i	0.0333247	+	0.0577201i	0.882207	−	0.470862i	$-0.156057\pi$
$173$	75.8291	+	131.340i	0.0333247	+	0.0577201i	−0.848882	+	0.528582i	$0.822724\pi$
$174$		0			0
$175$	−3214.22	+	623.239i	−1.38841	+	0.269214i
$176$		0			0
$177$	956.146	+	2003.67i	0.406036	+	0.850874i
$178$		0			0
$179$	66.8949	−	38.6218i	0.0279327	−	0.0161270i	−0.485969	−	0.873976i	$-0.661533\pi$
$179$	66.8949	−	38.6218i	0.0279327	−	0.0161270i	0.513901	+	0.857849i	$0.328200\pi$
$180$		0			0
$181$		−	2643.35i		−	1.08552i	−0.839889	−	0.542759i	$-0.817380\pi$
$181$		−	2643.35i		−	1.08552i	0.839889	−	0.542759i	$-0.182620\pi$
$182$		0			0
$183$	−364.736	+	4645.19i	−0.147334	+	1.87641i
$184$		0			0
$185$	1026.79	−	1778.45i	0.408060	−	0.706780i
$186$		0			0
$187$	528.318	−	305.025i	0.206601	−	0.119281i
$188$		0			0
$189$	−2595.86	−	113.122i	−0.999052	−	0.0435368i
$190$		0			0
$191$	2356.27	−	1360.39i	0.892638	−	0.515365i	0.0178338	−	0.999841i	$-0.494323\pi$
$191$	2356.27	−	1360.39i	0.892638	−	0.515365i	0.874805	+	0.484476i	$0.160990\pi$
$192$		0			0
$193$	879.622	−	1523.55i	0.328065	−	0.568225i	−0.654063	−	0.756440i	$-0.726937\pi$
$193$	879.622	−	1523.55i	0.328065	−	0.568225i	0.982128	+	0.188215i	$0.0602701\pi$
$194$		0			0
$195$	89.8725	−	1144.60i	0.0330046	−	0.420340i
$196$		0			0
$197$		−	1404.67i		−	0.508012i	−0.967203	−	0.254006i	$-0.918252\pi$
$197$		−	1404.67i		−	0.508012i	0.967203	−	0.254006i	$-0.0817483\pi$
$198$		0			0
$199$	−2636.13	+	1521.97i	−0.939048	+	0.542159i	−0.889662	−	0.456620i	$-0.849060\pi$
$199$	−2636.13	+	1521.97i	−0.939048	+	0.542159i	−0.0493861	+	0.998780i	$0.515726\pi$
$200$		0			0
$201$	162.535	+	340.602i	0.0570364	+	0.119523i
$202$		0			0
$203$	4659.57	+	1606.83i	1.61102	+	0.555553i
$204$		0			0
$205$	587.169	+	1017.01i	0.200047	+	0.346492i
$206$		0			0
$207$	909.174	−	349.378i	0.305275	−	0.117311i
$208$		0			0
$209$	344.321	−	596.382i	0.113958	−	0.197381i
$210$		0			0
$211$	−2076.53	−	3596.65i	−0.677507	−	1.17348i	−0.975729	−	0.218980i	$-0.929727\pi$
$211$	−2076.53	−	3596.65i	−0.677507	−	1.17348i	0.298223	−	0.954496i	$-0.403606\pi$
$212$		0			0
$213$	2845.58	+	1954.95i	0.915381	+	0.628879i
$214$		0			0
$215$	−2366.36	+	4098.66i	−0.750626	+	1.30012i
$216$		0			0
$217$	−2848.31	−	982.224i	−0.891041	−	0.307271i
$218$		0			0
$219$	170.714	−	2174.18i	0.0526749	−	0.670856i
$220$		0			0
$221$	638.700	+	368.754i	0.194406	+	0.112240i
$222$		0			0
$223$	4479.35	+	2586.15i	1.34511	+	0.776600i	0.987552	−	0.157292i	$-0.0502762\pi$
$223$	4479.35	+	2586.15i	1.34511	+	0.776600i	0.357558	+	0.933891i	$0.383610\pi$
$224$		0			0
$225$	−1712.17	−	4455.51i	−0.507309	−	1.32015i
$226$		0			0
$227$	972.760			0.284424			0.142212	−	0.989836i	$-0.454578\pi$
$227$	972.760			0.284424			0.142212	+	0.989836i	$0.454578\pi$
$228$		0			0
$229$		−	3585.89i		−	1.03477i	−0.855753	−	0.517385i	$-0.826906\pi$
$229$		−	3585.89i		−	1.03477i	0.855753	−	0.517385i	$-0.173094\pi$
$230$		0			0
$231$	−928.387	−	403.984i	−0.264430	−	0.115066i
$232$		0			0
$233$	5151.33	+	2974.12i	1.44839	+	0.836229i	0.998386	−	0.0567977i	$-0.0180890\pi$
$233$	5151.33	+	2974.12i	1.44839	+	0.836229i	0.450005	+	0.893026i	$0.351422\pi$
$234$		0			0
$235$	1127.03	+	1952.07i	0.312847	+	0.541867i
$236$		0			0
$237$	6193.08	+	486.274i	1.69740	+	0.133278i
$238$		0			0
$239$	4873.83	−	2813.91i	1.31909	−	0.761576i	0.335506	−	0.942038i	$-0.391093\pi$
$239$	4873.83	−	2813.91i	1.31909	−	0.761576i	0.983582	+	0.180462i	$0.0577594\pi$
$240$		0			0
$241$			373.840i			0.0999217i	0.998751	+	0.0499608i	$0.0159097\pi$
$241$			373.840i			0.0999217i	−0.998751	+	0.0499608i	$0.984090\pi$
$242$		0			0
$243$	−497.842	−	3755.14i	−0.131426	−	0.991326i
$244$		0			0
$245$	−5526.75	+	2227.01i	−1.44119	+	0.580729i
$246$		0			0
$247$	832.521			0.214462
$248$		0			0
$249$	3186.57	+	6677.66i	0.811006	+	1.69952i
$250$		0			0
$251$	4536.61			1.14083			0.570415	−	0.821356i	$-0.306782\pi$
$251$	4536.61			1.14083			0.570415	+	0.821356i	$0.306782\pi$
$252$		0			0
$253$	379.531			0.0943119
$254$		0			0
$255$	5218.01	+	409.713i	1.28143	+	0.100616i
$256$		0			0
$257$	7673.08			1.86239			0.931194	−	0.364524i	$-0.118768\pi$
$257$	7673.08			1.86239			0.931194	+	0.364524i	$0.118768\pi$
$258$		0			0
$259$	713.731	−	2069.72i	0.171232	−	0.496549i
$260$		0			0
$261$	−1121.50	+	7097.53i	−0.265972	+	1.68324i
$262$		0			0
$263$			2385.83i			0.559380i	0.960090	+	0.279690i	$0.0902316\pi$
$263$			2385.83i			0.559380i	−0.960090	+	0.279690i	$0.909768\pi$
$264$		0			0
$265$	−683.755	+	394.766i	−0.158501	+	0.0915105i
$266$		0			0
$267$	−3399.57	−	7124.02i	−0.779215	−	1.63289i
$268$		0			0
$269$	1709.27	+	2960.54i	0.387419	+	0.671030i	0.992102	−	0.125437i	$-0.0400332\pi$
$269$	1709.27	+	2960.54i	0.387419	+	0.671030i	−0.604682	+	0.796467i	$0.706700\pi$
$270$		0			0
$271$	793.596	+	458.183i	0.177888	+	0.102703i	0.586300	−	0.810094i	$-0.300584\pi$
$271$	793.596	+	458.183i	0.177888	+	0.102703i	−0.408412	+	0.912798i	$0.633917\pi$
$272$		0			0
$273$	−138.221	−	1216.18i	−0.0306429	−	0.269622i
$274$		0			0
$275$		−	1859.94i		−	0.407849i
$276$		0			0
$277$	−8904.39			−1.93145			−0.965727	−	0.259560i	$-0.916423\pi$
$277$	−8904.39			−1.93145			−0.965727	+	0.259560i	$0.916423\pi$
$278$		0			0
$279$	685.549	−	4338.58i	0.147107	−	0.930983i
$280$		0			0
$281$	−4851.04	−	2800.75i	−1.02985	−	0.594586i	−0.112911	−	0.993605i	$-0.536017\pi$
$281$	−4851.04	−	2800.75i	−1.02985	−	0.594586i	−0.916943	+	0.399019i	$0.869351\pi$
$282$		0			0
$283$	4084.01	+	2357.91i	0.857842	+	0.495275i	0.863289	−	0.504710i	$-0.168401\pi$
$283$	4084.01	+	2357.91i	0.857842	+	0.495275i	−0.00544699	+	0.999985i	$0.501734\pi$
$284$		0			0
$285$	5332.35	−	2544.59i	1.10829	−	0.528872i
$286$		0			0
$287$	820.927	+	945.250i	0.168842	+	0.194412i
$288$		0			0
$289$	775.418	−	1343.06i	0.157830	−	0.273369i
$290$		0			0
$291$	−5484.11	+	2617.01i	−1.10476	+	0.527188i
$292$		0			0
$293$	−3562.65	−	6170.68i	−0.710348	−	1.23036i	−0.964726	−	0.263254i	$-0.915204\pi$
$293$	−3562.65	−	6170.68i	−0.710348	−	1.23036i	0.254378	−	0.967105i	$-0.418129\pi$
$294$		0			0
$295$	−3711.17	+	6427.93i	−0.732450	+	1.26864i
$296$		0			0
$297$	343.795	−	1435.45i	0.0671684	−	0.280449i
$298$		0			0
$299$	229.414	+	397.356i	0.0443723	+	0.0768551i
$300$		0			0
$301$	−1644.88	+	4769.92i	−0.314981	+	0.913401i
$302$		0			0
$303$	4686.64	−	6821.76i	0.888583	−	1.29340i
$304$		0			0
$305$	−13490.7	+	7788.87i	−2.53271	+	1.46226i
$306$		0			0
$307$		−	5631.36i		−	1.04690i	−0.852056	−	0.523450i	$-0.824645\pi$
$307$		−	5631.36i		−	1.04690i	0.852056	−	0.523450i	$-0.175355\pi$
$308$		0			0
$309$	−8143.70	−	5594.84i	−1.49929	−	1.03003i
$310$		0			0
$311$	−1522.32	+	2636.74i	−0.277566	+	0.480758i	−0.970779	−	0.239974i	$-0.922861\pi$
$311$	−1522.32	+	2636.74i	−0.277566	+	0.480758i	0.693213	+	0.720732i	$0.256194\pi$
$312$		0			0
$313$	−5869.32	+	3388.65i	−1.05992	+	0.611943i	−0.925409	−	0.378970i	$-0.876278\pi$
$313$	−5869.32	+	3388.65i	−1.05992	+	0.611943i	−0.134507	+	0.990913i	$0.542945\pi$
$314$		0			0
$315$	−4602.56	−	7367.26i	−0.823254	−	1.31777i
$316$		0			0
$317$	−4423.05	+	2553.65i	−0.783669	+	0.452451i	−0.837729	−	0.546086i	$-0.816117\pi$
$317$	−4423.05	+	2553.65i	−0.783669	+	0.452451i	0.0540602	+	0.998538i	$0.482784\pi$
$318$		0			0
$319$	−1399.99	+	2424.85i	−0.245718	+	0.425597i
$320$		0			0
$321$	−3642.07	+	1737.99i	−0.633272	+	0.302197i
$322$		0			0
$323$			3795.31i			0.653799i
$324$		0			0
$325$	1947.29	−	1124.27i	0.332357	−	0.191887i
$326$		0			0
$327$	−3826.27	−	300.435i	−0.647073	−	0.0508075i
$328$		0			0
$329$	1575.70	+	1814.33i	0.264047	+	0.304035i
$330$		0			0
$331$	−1933.67	−	3349.21i	−0.321099	−	0.556160i	0.659616	−	0.751603i	$-0.270719\pi$
$331$	−1933.67	−	3349.21i	−0.321099	−	0.556160i	−0.980715	+	0.195443i	$0.937386\pi$
$332$		0			0
$333$	3152.62	+	498.153i	0.518807	+	0.0819778i
$334$		0			0
$335$	−630.859	+	1092.68i	−0.102888	+	0.178207i
$336$		0			0
$337$	1460.79	+	2530.17i	0.236126	+	0.408982i	0.959599	−	0.281370i	$-0.0907889\pi$
$337$	1460.79	+	2530.17i	0.236126	+	0.408982i	−0.723473	+	0.690352i	$0.757456\pi$
$338$		0			0
$339$	210.235	−	2677.51i	0.0336826	−	0.428974i
$340$		0			0
$341$	855.785	−	1482.26i	0.135904	−	0.235393i
$342$		0			0
$343$	−5332.40	+	3452.40i	−0.839425	+	0.543476i
$344$		0			0
$345$	2683.92	+	1843.89i	0.418833	+	0.287744i
$346$		0			0
$347$	1943.93	+	1122.33i	0.300736	+	0.173630i	0.642774	−	0.766056i	$-0.277784\pi$
$347$	1943.93	+	1122.33i	0.300736	+	0.173630i	−0.342037	+	0.939686i	$0.611117\pi$
$348$		0			0
$349$	−4363.18	−	2519.08i	−0.669214	−	0.386371i	0.126565	−	0.991958i	$-0.459605\pi$
$349$	−4363.18	−	2519.08i	−0.669214	−	0.386371i	−0.795779	+	0.605588i	$0.792938\pi$
$350$		0			0
$351$	1710.68	−	507.741i	0.260141	−	0.0772115i
$352$		0			0
$353$	2546.17			0.383907			0.191953	−	0.981404i	$-0.438518\pi$
$353$	2546.17			0.383907			0.191953	+	0.981404i	$0.438518\pi$
$354$		0			0
$355$			11542.2i			1.72563i
$356$		0			0
$357$	5544.36	−	630.125i	0.821957	−	0.0934167i
$358$		0			0
$359$	−7218.04	−	4167.34i	−1.06115	−	0.612656i	−0.135401	−	0.990791i	$-0.543232\pi$
$359$	−7218.04	−	4167.34i	−1.06115	−	0.612656i	−0.925751	+	0.378134i	$0.876566\pi$
$360$		0			0
$361$	−1287.37	−	2229.78i	−0.187690	−	0.325089i
$362$		0			0
$363$	−3590.58	+	5226.37i	−0.519165	+	0.755683i
$364$		0			0
$365$	6314.32	−	3645.57i	0.905498	−	0.522789i
$366$		0			0
$367$		−	5913.32i		−	0.841070i	−0.907276	−	0.420535i	$-0.861842\pi$
$367$		−	5913.32i		−	0.841070i	0.907276	−	0.420535i	$-0.138158\pi$
$368$		0			0
$369$	−1148.12	+	1418.86i	−0.161974	+	0.200170i
$370$		0			0
$371$	−635.511	+	551.926i	−0.0889328	+	0.0772360i
$372$		0			0
$373$	12355.4			1.71512			0.857559	−	0.514386i	$-0.171980\pi$
$373$	12355.4			1.71512			0.857559	+	0.514386i	$0.171980\pi$
$374$		0			0
$375$	2646.90	−	3852.76i	0.364494	−	0.530549i
$376$		0			0
$377$	−3384.97			−0.462427
$378$		0			0
$379$	−7619.91			−1.03274			−0.516370	−	0.856365i	$-0.672717\pi$
$379$	−7619.91			−1.03274			−0.516370	+	0.856365i	$0.672717\pi$
$380$		0			0
$381$	−900.834	+	1311.23i	−0.121132	+	0.176316i
$382$		0			0
$383$	8329.02			1.11121			0.555604	−	0.831447i	$-0.312487\pi$
$383$	8329.02			1.11121			0.555604	+	0.831447i	$0.312487\pi$
$384$		0			0
$385$	−644.341	−	3323.04i	−0.0852952	−	0.439891i
$386$		0			0
$387$	−7265.60	−	1148.05i	−0.954345	−	0.150798i
$388$		0			0
$389$			3837.06i			0.500119i	0.968230	+	0.250060i	$0.0804502\pi$
$389$			3837.06i			0.500119i	−0.968230	+	0.250060i	$0.919550\pi$
$390$		0			0
$391$	−1811.47	+	1045.85i	−0.234297	+	0.135272i
$392$		0			0
$393$	4917.54	−	7157.85i	0.631189	−	0.918743i
$394$		0			0
$395$	10384.3	+	17986.1i	1.32276	+	2.29109i
$396$		0			0
$397$	−10910.5	−	6299.16i	−1.37930	−	0.796338i	−0.387222	−	0.921986i	$-0.626565\pi$
$397$	−10910.5	−	6299.16i	−1.37930	−	0.796338i	−0.992075	+	0.125649i	$0.959899\pi$
$398$		0			0
$399$	5064.49	−	3745.33i	0.635443	−	0.469927i
$400$		0			0
$401$		−	13227.8i		−	1.64729i	−0.567102	−	0.823647i	$-0.691936\pi$
$401$		−	13227.8i		−	1.64729i	0.567102	−	0.823647i	$-0.308064\pi$
$402$		0			0
$403$	2069.17			0.255764
$404$		0			0
$405$	9405.13	−	8480.79i	1.15394	−	1.04053i
$406$		0			0
$407$	1077.08	+	621.854i	0.131177	+	0.0757351i
$408$		0			0
$409$	−6840.84	−	3949.56i	−0.827036	−	0.477489i	0.0258011	−	0.999667i	$-0.491786\pi$
$409$	−6840.84	−	3949.56i	−0.827036	−	0.477489i	−0.852837	+	0.522178i	$0.825120\pi$
$410$		0			0
$411$	5671.72	+	3896.55i	0.680694	+	0.467646i
$412$		0			0
$413$	−2579.67	+	7480.67i	−0.307354	+	0.891283i
$414$		0			0
$415$	−12368.3	+	21422.5i	−1.46298	+	2.53395i
$416$		0			0
$417$	−246.024	+	3133.30i	−0.0288917	+	0.367958i
$418$		0			0
$419$	7531.25	+	13044.5i	0.878105	+	1.52092i	0.853418	+	0.521227i	$0.174525\pi$
$419$	7531.25	+	13044.5i	0.878105	+	1.52092i	0.0246862	+	0.999695i	$0.492141\pi$
$420$		0			0
$421$	27.7536	−	48.0706i	0.00321289	−	0.00556489i	−0.864414	−	0.502780i	$-0.832311\pi$
$421$	27.7536	−	48.0706i	0.00321289	−	0.00556489i	0.867627	+	0.497215i	$0.165644\pi$
$422$		0			0
$423$	−2203.72	+	2723.39i	−0.253306	+	0.313040i
$424$		0			0
$425$	5125.33	+	8877.34i	0.584977	+	1.01321i
$426$		0			0
$427$	−12538.9	+	10889.7i	−1.42107	+	1.23417i
$428$		0			0
$429$	693.202	+	54.4295i	0.0780142	+	0.00612560i
$430$		0			0
$431$	2138.30	−	1234.55i	0.238975	−	0.137972i	−0.375731	−	0.926729i	$-0.622608\pi$
$431$	2138.30	−	1234.55i	0.238975	−	0.137972i	0.614705	+	0.788757i	$0.289275\pi$
$432$		0			0
$433$		−	16722.0i		−	1.85591i	−0.372698	−	0.927953i	$-0.621567\pi$
$433$		−	16722.0i		−	1.85591i	0.372698	−	0.927953i	$-0.378433\pi$
$434$		0			0
$435$	−21681.0	+	10346.1i	−2.38971	+	1.14037i
$436$		0			0
$437$	−1180.59	+	2044.85i	−0.129234	+	0.223841i
$438$		0			0
$439$	−9687.68	+	5593.18i	−1.05323	+	0.608082i	−0.923552	−	0.383474i	$-0.874728\pi$
$439$	−9687.68	+	5593.18i	−1.05323	+	0.608082i	−0.129678	+	0.991556i	$0.541394\pi$
$440$		0			0
$441$	−6312.19	−	6776.61i	−0.681588	−	0.731736i
$442$		0			0
$443$	5151.63	−	2974.29i	0.552509	−	0.318991i	−0.197625	−	0.980278i	$-0.563323\pi$
$443$	5151.63	−	2974.29i	0.552509	−	0.318991i	0.750133	+	0.661287i	$0.229989\pi$
$444$		0			0
$445$	13195.0	−	22854.5i	1.40563	−	2.43462i
$446$		0			0
$447$	−4564.03	−	3135.55i	−0.482933	−	0.331782i
$448$		0			0
$449$		−	1653.46i		−	0.173790i	−0.996217	−	0.0868949i	$-0.972306\pi$
$449$		−	1653.46i		−	0.173790i	0.996217	−	0.0868949i	$-0.0276944\pi$
$450$		0			0
$451$	−615.930	+	355.607i	−0.0643082	+	0.0371284i
$452$		0			0
$453$	−8263.34	+	12027.9i	−0.857054	+	1.24751i
$454$		0			0
$455$	3089.63	−	2683.27i	0.318339	−	0.276469i
$456$		0			0
$457$	733.503	+	1270.46i	0.0750806	+	0.130043i	0.901121	−	0.433567i	$-0.142745\pi$
$457$	733.503	+	1270.46i	0.0750806	+	0.130043i	−0.826041	+	0.563610i	$0.809412\pi$
$458$		0			0
$459$	2314.70	+	7798.69i	0.235383	+	0.793054i
$460$		0			0
$461$	3479.03	−	6025.86i	0.351485	−	0.608790i	−0.635025	−	0.772492i	$-0.719010\pi$
$461$	3479.03	−	6025.86i	0.351485	−	0.608790i	0.986510	+	0.163701i	$0.0523434\pi$
$462$		0			0
$463$	−2351.47	−	4072.87i	−0.236031	−	0.408817i	0.723541	−	0.690281i	$-0.242513\pi$
$463$	−2351.47	−	4072.87i	−0.236031	−	0.408817i	−0.959572	+	0.281464i	$0.909180\pi$
$464$		0			0
$465$	13253.2	−	6324.39i	1.32172	−	0.630724i
$466$		0			0
$467$	2332.92	−	4040.74i	0.231167	−	0.400393i	−0.726985	−	0.686653i	$-0.759079\pi$
$467$	2332.92	−	4040.74i	0.231167	−	0.400393i	0.958152	+	0.286261i	$0.0924124\pi$
$468$		0			0
$469$	−438.516	+	1271.63i	−0.0431744	+	0.125200i
$470$		0			0
$471$	4819.05	−	2299.64i	0.471444	−	0.224972i
$472$		0			0
$473$	−2482.27	−	1433.14i	−0.241300	−	0.139315i
$474$		0			0
$475$	10021.0	+	5785.63i	0.967990	+	0.558870i
$476$		0			0
$477$	−953.928	−	771.902i	−0.0915668	−	0.0740943i
$478$		0			0
$479$	−16056.9			−1.53164			−0.765822	−	0.643053i	$-0.777668\pi$
$479$	−16056.9			−1.53164			−0.765822	+	0.643053i	$0.777668\pi$
$480$		0			0
$481$			1503.56i			0.142529i
$482$		0			0
$483$	3183.21	+	1385.16i	0.299878	+	0.130491i
$484$		0			0
$485$	−17593.5	−	10157.6i	−1.64717	−	0.950996i
$486$		0			0
$487$	669.467	+	1159.55i	0.0622925	+	0.107894i	0.895490	−	0.445082i	$-0.146826\pi$
$487$	669.467	+	1159.55i	0.0622925	+	0.107894i	−0.833197	+	0.552976i	$0.813492\pi$
$488$		0			0
$489$	6679.77	+	13997.9i	0.617729	+	1.29449i
$490$		0			0
$491$	12517.4	−	7226.91i	1.15051	−	0.664248i	0.201500	−	0.979489i	$-0.435419\pi$
$491$	12517.4	−	7226.91i	1.15051	−	0.664248i	0.949012	+	0.315240i	$0.102085\pi$
$492$		0			0
$493$		−	15431.5i		−	1.40973i
$494$		0			0
$495$	4606.36	−	1770.14i	0.418264	−	0.160731i
$496$		0			0
$497$	2342.36	+	12080.2i	0.211407	+	1.09028i
$498$		0			0
$499$	7999.24			0.717625			0.358813	−	0.933410i	$-0.383182\pi$
$499$	7999.24			0.717625			0.358813	+	0.933410i	$0.383182\pi$
$500$		0			0
$501$	4080.03	+	320.360i	0.363837	+	0.0285681i
$502$		0			0
$503$	13008.8			1.15315			0.576575	−	0.817044i	$-0.304389\pi$
$503$	13008.8			1.15315			0.576575	+	0.817044i	$0.304389\pi$
$504$		0			0
$505$	27670.3			2.43825
$506$		0			0
$507$	−4554.53	−	9544.31i	−0.398962	−	0.836051i
$508$		0			0
$509$	5393.81			0.469698			0.234849	−	0.972032i	$-0.424540\pi$
$509$	5393.81			0.469698			0.234849	+	0.972032i	$0.424540\pi$
$510$		0			0
$511$	5868.80	−	5096.91i	0.508063	−	0.441241i
$512$		0			0
$513$	6664.54	+	6317.52i	0.573581	+	0.543714i
$514$		0			0
$515$		−	33032.4i		−	2.82637i
$516$		0			0
$517$	−1182.23	+	682.560i	−0.100569	+	0.0580638i
$518$		0			0
$519$	−785.621	−	61.6862i	−0.0664450	−	0.00521719i
$520$		0			0
$521$	927.697	+	1606.82i	0.0780098	+	0.135117i	0.902391	−	0.430918i	$-0.141810\pi$
$521$	927.697	+	1606.82i	0.0780098	+	0.135117i	−0.824381	+	0.566035i	$0.808477\pi$
$522$		0			0
$523$	5031.68	+	2905.04i	0.420688	+	0.242884i	0.695372	−	0.718650i	$-0.255240\pi$
$523$	5031.68	+	2905.04i	0.420688	+	0.242884i	−0.274684	+	0.961535i	$0.588573\pi$
$524$		0			0
$525$	6788.15	−	15599.7i	0.564303	−	1.29681i
$526$		0			0
$527$			9432.98i			0.779709i
$528$		0			0
$529$	10865.7			0.893045
$530$		0			0
$531$	−11394.7	−	1800.50i	−0.931236	−	0.147147i
$532$		0			0
$533$	−744.617	−	429.905i	−0.0605121	−	0.0349367i
$534$		0			0
$535$	−11684.1	−	6745.80i	−0.944199	−	0.545133i
$536$		0			0
$537$	−31.4184	+	400.138i	−0.00252477	+	0.0321550i
$538$		0			0
$539$	−1348.75	−	3347.17i	−0.107782	−	0.267482i
$540$		0			0
$541$	−3807.16	+	6594.20i	−0.302556	+	0.524042i	−0.976714	−	0.214545i	$-0.931173\pi$
$541$	−3807.16	+	6594.20i	−0.302556	+	0.524042i	0.674158	+	0.738587i	$0.264507\pi$
$542$		0			0
$543$	11321.0	+	7777.67i	0.894715	+	0.614681i
$544$		0			0
$545$	−6415.73	−	11112.4i	−0.504256	−	0.873397i
$546$		0			0
$547$	−8625.28	+	14939.4i	−0.674205	+	1.16776i	0.302496	+	0.953151i	$0.402180\pi$
$547$	−8625.28	+	14939.4i	−0.674205	+	1.16776i	−0.976701	+	0.214607i	$0.931153\pi$
$548$		0			0
$549$	−18821.3	−	15229.9i	−1.46316	−	1.18397i
$550$		0			0
$551$	−8709.77	−	15085.8i	−0.673409	−	1.16638i
$552$		0			0
$553$	14518.4	+	16717.1i	1.11643	+	1.28550i
$554$		0			0
$555$	4595.61	+	9630.39i	0.351482	+	0.736554i
$556$		0			0
$557$	6370.51	−	3678.02i	0.484609	−	0.279789i	−0.237726	−	0.971332i	$-0.576402\pi$
$557$	6370.51	−	3678.02i	0.484609	−	0.279789i	0.722335	+	0.691543i	$0.243069\pi$
$558$		0			0
$559$		−	3465.13i		−	0.262182i
$560$		0			0
$561$	−248.134	+	3160.18i	−0.0186742	+	0.237831i
$562$		0			0
$563$	−8406.47	+	14560.4i	−0.629290	+	1.08996i	0.358404	+	0.933567i	$0.383321\pi$
$563$	−8406.47	+	14560.4i	−0.629290	+	1.08996i	−0.987694	+	0.156396i	$0.950012\pi$
$564$		0			0
$565$	7776.10	−	4489.53i	0.579014	−	0.334294i
$566$		0			0
$567$	8122.42	−	10784.7i	0.601604	−	0.798795i
$568$		0			0
$569$	−1432.92	+	827.299i	−0.105573	+	0.0609529i	−0.551857	−	0.833939i	$-0.686081\pi$
$569$	−1432.92	+	827.299i	−0.105573	+	0.0609529i	0.446284	+	0.894892i	$0.352747\pi$
$570$		0			0
$571$	6435.42	−	11146.5i	0.471653	−	0.816927i	−0.527821	−	0.849356i	$-0.676991\pi$
$571$	6435.42	−	11146.5i	0.471653	−	0.816927i	0.999474	+	0.0324288i	$0.0103242\pi$
$572$		0			0
$573$	−1106.67	+	14094.3i	−0.0806836	+	1.02757i
$574$		0			0
$575$			6377.27i			0.462522i
$576$		0			0
$577$	6846.17	−	3952.64i	0.493951	−	0.285183i	−0.232261	−	0.972654i	$-0.574612\pi$
$577$	6846.17	−	3952.64i	0.493951	−	0.285183i	0.726212	+	0.687471i	$0.241279\pi$
$578$		0			0
$579$	3936.93	+	8250.09i	0.282579	+	0.592162i
$580$		0			0
$581$	−8597.32	+	24931.0i	−0.613902	+	1.78023i
$582$		0			0
$583$	−239.082	−	414.102i	−0.0169842	−	0.0294174i
$584$		0			0
$585$	4637.66	+	3752.72i	0.327767	+	0.265223i
$586$		0			0
$587$	−1022.74	+	1771.43i	−0.0719128	+	0.124557i	−0.899740	−	0.436427i	$-0.856244\pi$
$587$	−1022.74	+	1771.43i	−0.0719128	+	0.124557i	0.827827	+	0.560984i	$0.189577\pi$
$588$		0			0
$589$	5324.12	+	9221.64i	0.372456	+	0.645112i
$590$		0			0
$591$	6015.93	+	4133.03i	0.418718	+	0.287665i
$592$		0			0
$593$	5545.60	−	9605.27i	0.384031	−	0.665162i	−0.607603	−	0.794241i	$-0.707869\pi$
$593$	5545.60	−	9605.27i	0.384031	−	0.665162i	0.991634	+	0.129079i	$0.0412021\pi$
$594$		0			0
$595$	12232.5	+	14085.1i	0.842832	+	0.970473i
$596$		0			0
$597$	1238.11	−	15768.3i	0.0848784	−	1.08099i
$598$		0			0
$599$	−19963.1	−	11525.7i	−1.36172	−	0.786190i	−0.371869	−	0.928285i	$-0.621283\pi$
$599$	−19963.1	−	11525.7i	−1.36172	−	0.786190i	−0.989853	+	0.142095i	$0.954616\pi$
$600$		0			0
$601$	18168.5	+	10489.6i	1.23312	+	0.711944i	0.967680	−	0.252183i	$-0.0811485\pi$
$601$	18168.5	+	10489.6i	1.23312	+	0.711944i	0.265443	+	0.964127i	$0.414482\pi$
$602$		0			0
$603$	−1936.97	−	306.065i	−0.130812	−	0.0206699i
$604$		0			0
$605$	−21199.1			−1.42457
$606$		0			0
$607$		−	6801.09i		−	0.454774i	−0.973805	−	0.227387i	$-0.926982\pi$
$607$		−	6801.09i		−	0.454774i	0.973805	−	0.227387i	$-0.0730182\pi$
$608$		0			0
$609$	−20591.9	+	15228.3i	−1.37016	+	1.01327i
$610$		0			0
$611$	−1429.23	−	825.169i	−0.0946328	−	0.0546363i
$612$		0			0
$613$	−2638.29	−	4569.66i	−0.173833	−	0.301088i	0.765924	−	0.642931i	$-0.222282\pi$
$613$	−2638.29	−	4569.66i	−0.173833	−	0.301088i	−0.939757	+	0.341844i	$0.888949\pi$
$614$		0			0
$615$	−6083.32	−	477.656i	−0.398867	−	0.0313186i
$616$		0			0
$617$	−5536.17	+	3196.31i	−0.361228	+	0.208555i	−0.669619	−	0.742704i	$-0.733543\pi$
$617$	−5536.17	+	3196.31i	−0.361228	+	0.208555i	0.308391	+	0.951260i	$0.400209\pi$
$618$		0			0
$619$		−	9073.56i		−	0.589172i	−0.955625	−	0.294586i	$-0.904818\pi$
$619$		−	9073.56i		−	0.589172i	0.955625	−	0.294586i	$-0.0951817\pi$
$620$		0			0
$621$	−1178.79	+	4921.82i	−0.0761726	+	0.318045i
$622$		0			0
$623$	9172.00	−	26597.5i	0.589837	−	1.71044i
$624$		0			0
$625$	−6470.45			−0.414109
$626$		0			0
$627$	1541.08	+	3229.43i	0.0981576	+	0.205696i
$628$		0			0
$629$	−6854.45			−0.434507
$630$		0			0
$631$	23528.6			1.48440			0.742202	−	0.670176i	$-0.233781\pi$
$631$	23528.6			1.48440			0.742202	+	0.670176i	$0.233781\pi$
$632$		0			0
$633$	21513.7	+	1689.23i	1.35086	+	0.106068i
$634$		0			0
$635$	−5318.60			−0.332382
$636$		0			0
$637$	2689.10	−	3435.34i	0.167262	−	0.213678i
$638$		0			0
$639$	−16745.4	+	6434.95i	−1.03668	+	0.398376i
$640$		0			0
$641$			19683.9i			1.21290i	0.795123	+	0.606449i	$0.207406\pi$
$641$			19683.9i			1.21290i	−0.795123	+	0.606449i	$0.792594\pi$
$642$		0			0
$643$	−5839.25	+	3371.29i	−0.358130	+	0.206766i	−0.668260	−	0.743928i	$-0.732961\pi$
$643$	−5839.25	+	3371.29i	−0.358130	+	0.206766i	0.310130	+	0.950694i	$0.399627\pi$
$644$		0			0
$645$	−10591.1	−	22194.4i	−0.646551	−	1.35489i
$646$		0			0
$647$	14790.6	+	25618.1i	0.898732	+	1.55665i	0.829116	+	0.559076i	$0.188844\pi$
$647$	14790.6	+	25618.1i	0.898732	+	1.55665i	0.0696158	+	0.997574i	$0.477823\pi$
$648$		0			0
$649$	−3892.95	−	2247.60i	−0.235457	−	0.135941i
$650$		0			0
$651$	12587.4	−	9308.74i	0.757819	−	0.560428i
$652$		0			0
$653$		−	20802.1i		−	1.24663i	−0.781970	−	0.623316i	$-0.785785\pi$
$653$		−	20802.1i		−	1.24663i	0.781970	−	0.623316i	$-0.214215\pi$
$654$		0			0
$655$	29033.6			1.73196
$656$		0			0
$657$	8809.31	+	7128.34i	0.523111	+	0.423293i
$658$		0			0
$659$	−1400.70	−	808.695i	−0.0827975	−	0.0478032i	0.458030	−	0.888937i	$-0.348555\pi$
$659$	−1400.70	−	808.695i	−0.0827975	−	0.0478032i	−0.540827	+	0.841134i	$0.681889\pi$
$660$		0			0
$661$	−24563.6	−	14181.8i	−1.44541	−	0.834507i	−0.447206	−	0.894431i	$-0.647581\pi$
$661$	−24563.6	−	14181.8i	−1.44541	−	0.834507i	−0.998203	+	0.0599242i	$0.980914\pi$
$662$		0			0
$663$	−3458.59	+	1650.43i	−0.202595	+	0.0966780i
$664$		0			0
$665$	19908.3	+	6865.27i	1.16092	+	0.400336i
$666$		0			0
$667$	4800.21	−	8314.21i	0.278658	−	0.482650i
$668$		0			0
$669$	−24255.9	+	11574.9i	−1.40177	+	0.668924i
$670$		0			0
$671$	−4717.18	−	8170.39i	−0.271393	−	0.470066i
$672$		0			0
$673$	−10413.9	+	18037.4i	−0.596473	+	1.03312i	0.396864	+	0.917878i	$0.370099\pi$
$673$	−10413.9	+	18037.4i	−0.596473	+	1.03312i	−0.993337	+	0.115245i	$0.963235\pi$
$674$		0			0
$675$	24120.0	+	5776.79i	1.37537	+	0.329406i
$676$		0			0
$677$	−2901.21	−	5025.05i	−0.164701	−	0.285271i	0.771848	−	0.635807i	$-0.219333\pi$
$677$	−2901.21	−	5025.05i	−0.164701	−	0.285271i	−0.936549	+	0.350536i	$0.885999\pi$
$678$		0			0
$679$	−20474.9	−	7060.65i	−1.15722	−	0.399062i
$680$		0			0
$681$	−2862.21	+	4166.16i	−0.161057	+	0.234431i
$682$		0			0
$683$	−11625.5	+	6712.01i	−0.651302	+	0.376029i	−0.788955	−	0.614451i	$-0.789377\pi$
$683$	−11625.5	+	6712.01i	−0.651302	+	0.376029i	0.137653	+	0.990481i	$0.456044\pi$
$684$		0			0
$685$			23005.6i			1.28321i
$686$		0			0
$687$	15357.7	+	10551.0i	0.852888	+	0.585945i
$688$		0			0
$689$	289.034	−	500.621i	0.0159816	−	0.0276809i
$690$		0			0
$691$	−9486.07	+	5476.79i	−0.522239	+	0.301515i	−0.737850	−	0.674964i	$-0.764159\pi$
$691$	−9486.07	+	5476.79i	−0.522239	+	0.301515i	0.215611	+	0.976479i	$0.430826\pi$
$692$		0			0
$693$	4461.84	−	2787.45i	0.244576	−	0.152794i
$694$		0			0
$695$	−9099.83	+	5253.79i	−0.496657	+	0.286745i
$696$		0			0
$697$	1959.86	−	3394.58i	0.106506	−	0.184474i
$698$		0			0
$699$	−27894.7	+	13311.3i	−1.50940	+	0.720285i
$700$		0			0
$701$		−	22141.3i		−	1.19296i	−0.802628	−	0.596480i	$-0.796565\pi$
$701$		−	22141.3i		−	1.19296i	0.802628	−	0.596480i	$-0.203435\pi$
$702$		0			0
$703$	−6700.89	+	3868.76i	−0.359500	+	0.207558i
$704$		0			0
$705$	−11676.5	−	916.823i	−0.623774	−	0.0489781i
$706$		0			0
$707$	28960.0	−	5615.38i	1.54053	−	0.298710i
$708$		0			0
$709$	1592.13	+	2757.65i	0.0843352	+	0.146073i	0.905108	−	0.425182i	$-0.139790\pi$
$709$	1592.13	+	2757.65i	0.0843352	+	0.146073i	−0.820773	+	0.571255i	$0.806457\pi$
$710$		0			0
$711$	−20304.9	+	25093.0i	−1.07102	+	1.32358i
$712$		0			0
$713$	−2934.28	+	5082.32i	−0.154123	+	0.266949i
$714$		0			0
$715$	1162.33	+	2013.22i	0.0607955	+	0.105301i
$716$		0			0
$717$	−2289.08	+	29153.3i	−0.119229	+	1.51848i
$718$		0			0
$719$	9037.29	−	15653.0i	0.468754	−	0.811905i	−0.530608	−	0.847617i	$-0.678036\pi$
$719$	9037.29	−	15653.0i	0.468754	−	0.811905i	0.999362	+	0.0357117i	$0.0113698\pi$
$720$		0			0
$721$	−6703.54	−	34572.0i	−0.346259	−	1.78576i
$722$		0			0
$723$	−1601.09	−	1099.97i	−0.0823584	−	0.0565813i
$724$		0			0
$725$	−40744.7	−	23524.0i	−2.08720	−	1.20505i
$726$		0			0
$727$	−11015.0	−	6359.54i	−0.561933	−	0.324432i	0.191988	−	0.981397i	$-0.438507\pi$
$727$	−11015.0	−	6359.54i	−0.561933	−	0.324432i	−0.753921	+	0.656965i	$0.771840\pi$
$728$		0			0
$729$	17547.4	+	8916.78i	0.891501	+	0.453019i
$730$		0			0
$731$	15796.9			0.799275
$732$		0			0
$733$		−	26440.4i		−	1.33233i	−0.745804	−	0.666165i	$-0.767934\pi$
$733$		−	26440.4i		−	1.33233i	0.745804	−	0.666165i	$-0.232066\pi$
$734$		0			0
$735$	6723.77	−	30222.7i	0.337429	−	1.51671i
$736$		0			0
$737$	−661.760	−	382.067i	−0.0330750	−	0.0190958i
$738$		0			0
$739$	3625.92	+	6280.28i	0.180489	+	0.312617i	0.942047	−	0.335480i	$-0.108899\pi$
$739$	3625.92	+	6280.28i	0.180489	+	0.312617i	−0.761558	+	0.648097i	$0.775565\pi$
$740$		0			0
$741$	−2449.57	+	3565.54i	−0.121440	+	0.176766i
$742$		0			0
$743$	20547.0	−	11862.8i	1.01453	−	0.585739i	0.102015	−	0.994783i	$-0.467471\pi$
$743$	20547.0	−	11862.8i	1.01453	−	0.585739i	0.912515	+	0.409044i	$0.134138\pi$
$744$		0			0
$745$		−	18512.6i		−	0.910400i
$746$		0			0
$747$	−37975.2	−	6000.55i	−1.86003	−	0.293907i
$748$		0			0
$749$	−13597.6	−	4689.07i	−0.663347	−	0.228752i
$750$		0			0
$751$	7767.13			0.377399			0.188699	−	0.982035i	$-0.439573\pi$
$751$	7767.13			0.377399			0.188699	+	0.982035i	$0.439573\pi$
$752$		0			0
$753$	−13348.3	+	19429.5i	−0.646003	+	0.940306i
$754$		0			0
$755$	−48787.5			−2.35173
$756$		0			0
$757$	6465.50			0.310426			0.155213	−	0.987881i	$-0.450394\pi$
$757$	6465.50			0.310426			0.155213	+	0.987881i	$0.450394\pi$
$758$		0			0
$759$	−1116.72	+	1625.46i	−0.0534047	+	0.0777346i
$760$		0			0
$761$	−27303.6			−1.30060			−0.650298	−	0.759679i	$-0.725356\pi$
$761$	−27303.6			−1.30060			−0.650298	+	0.759679i	$0.725356\pi$
$762$		0			0
$763$	−8969.89	−	10328.3i	−0.425599	−	0.490052i
$764$		0			0
$765$	−17108.0	+	21142.3i	−0.808548	+	0.999216i
$766$		0			0
$767$		−	5434.38i		−	0.255833i
$768$		0			0
$769$	−22662.8	+	13084.4i	−1.06273	+	0.613569i	−0.926187	−	0.377065i	$-0.876933\pi$
$769$	−22662.8	+	13084.4i	−1.06273	+	0.613569i	−0.136545	+	0.990634i	$0.543600\pi$
$770$		0			0
$771$	−22576.9	+	32862.4i	−1.05459	+	1.53503i
$772$		0			0
$773$	−473.922	−	820.858i	−0.0220515	−	0.0381943i	0.854789	−	0.518976i	$-0.173686\pi$
$773$	−473.922	−	820.858i	−0.0220515	−	0.0381943i	−0.876841	+	0.480781i	$0.840353\pi$
$774$		0			0
$775$	24906.5	+	14379.8i	1.15441	+	0.666499i
$776$		0			0
$777$	6764.18	+	9146.63i	0.312308	+	0.422308i
$778$		0			0
$779$		−	4424.70i		−	0.203506i
$780$		0			0
$781$	−6990.32			−0.320273
$782$		0			0
$783$	−27097.6	−	25686.6i	−1.23677	−	1.17237i
$784$		0			0
$785$	15459.9	+	8925.80i	0.702916	+	0.405828i
$786$		0			0
$787$	3374.18	+	1948.08i	0.152829	+	0.0882360i	0.574464	−	0.818530i	$-0.305210\pi$
$787$	3374.18	+	1948.08i	0.152829	+	0.0882360i	−0.421635	+	0.906766i	$0.638544\pi$
$788$		0			0
$789$	−10218.1	−	7019.97i	−0.461057	−	0.316752i
$790$		0			0
$791$	7227.44	−	6276.86i	0.324878	−	0.282148i
$792$		0			0
$793$	5702.74	−	9877.44i	0.255372	−	0.442318i
$794$		0			0
$795$	321.138	−	4089.94i	0.0143265	−	0.182459i
$796$		0			0
$797$	5483.64	+	9497.94i	0.243715	+	0.422126i	0.961769	−	0.273861i	$-0.0883007\pi$
$797$	5483.64	+	9497.94i	0.243715	+	0.422126i	−0.718055	+	0.695987i	$0.754967\pi$
$798$		0			0
$799$	3761.80	−	6515.62i	0.166562	−	0.288493i
$800$		0			0
$801$	40513.6	+	6401.65i	1.78711	+	0.282386i
$802$		0			0
$803$	2207.87	+	3824.14i	0.0970287	+	0.168059i
$804$		0			0
$805$	2209.29	+	11393.9i	0.0967294	+	0.498860i
$806$		0			0
$807$	−17708.7	−	1390.47i	−0.772461	−	0.0606529i
$808$		0			0
$809$	−17253.4	+	9961.24i	−0.749810	+	0.432903i	−0.825625	−	0.564219i	$-0.809177\pi$
$809$	−17253.4	+	9961.24i	−0.749810	+	0.432903i	0.0758152	+	0.997122i	$0.475844\pi$
$810$		0			0
$811$		−	1565.39i		−	0.0677783i	−0.999426	−	0.0338891i	$-0.989211\pi$
$811$		−	1565.39i		−	0.0677783i	0.999426	−	0.0338891i	$-0.0107893\pi$
$812$		0			0
$813$	−4297.36	+	2050.69i	−0.185381	+	0.0884636i
$814$		0			0
$815$	−25926.7	+	44906.4i	−1.11432	+	1.93006i
$816$		0			0
$817$	15443.0	−	8916.03i	0.661300	−	0.381802i
$818$		0			0
$819$	5615.39	+	2986.47i	0.239582	+	0.127418i
$820$		0			0
$821$	31017.1	−	17907.7i	1.31852	−	0.761248i	0.335030	−	0.942208i	$-0.391254\pi$
$821$	31017.1	−	17907.7i	1.31852	−	0.761248i	0.983491	+	0.180960i	$0.0579203\pi$
$822$		0			0
$823$	11809.0	−	20453.8i	0.500167	−	0.866314i	−0.499833	−	0.866122i	$-0.666605\pi$
$823$	11809.0	−	20453.8i	0.500167	−	0.866314i	1.00000		0.000192357i	$-6.12291e-5\pi$
$824$		0			0
$825$	7965.77	+	5472.59i	0.336161	+	0.230947i
$826$		0			0
$827$		−	18218.7i		−	0.766052i	−0.923738	−	0.383026i	$-0.874882\pi$
$827$		−	18218.7i		−	0.766052i	0.923738	−	0.383026i	$-0.125118\pi$
$828$		0			0
$829$	−31582.0	+	18233.9i	−1.32315	+	0.763920i	−0.984230	−	0.176896i	$-0.943394\pi$
$829$	−31582.0	+	18233.9i	−1.32315	+	0.763920i	−0.338918	+	0.940816i	$0.610061\pi$
$830$		0			0
$831$	26199.9	−	38135.9i	1.09370	−	1.59196i
$832$		0			0
$833$	15661.1	+	12259.1i	0.651410	+	0.509907i
$834$		0			0
$835$	6841.24	+	11849.4i	0.283534	+	0.491095i
$836$		0			0
$837$	16564.2	+	15701.7i	0.684043	+	0.648425i
$838$		0			0
$839$	−10928.0	+	18927.8i	−0.449673	+	0.778857i	−0.998365	−	0.0571682i	$-0.981793\pi$
$839$	−10928.0	+	18927.8i	−0.449673	+	0.778857i	0.548691	+	0.836025i	$0.315126\pi$
$840$		0			0
$841$	23218.8	+	40216.2i	0.952020	+	1.64895i
$842$		0			0
$843$	26268.6	−	12535.3i	1.07324	−	0.512147i
$844$		0			0
$845$	17677.9	−	30619.0i	0.719689	−	1.24654i
$846$		0			0
$847$	−22187.2	+	4302.12i	−0.900072	+	0.174525i
$848$		0			0
$849$	−22115.1	+	10553.3i	−0.893979	+	0.426605i
$850$		0			0
$851$	−3693.06	−	2132.19i	−0.148762	−	0.0858877i
$852$		0			0
$853$	501.872	+	289.756i	0.0201451	+	0.0116308i	0.510039	−	0.860151i	$-0.329631\pi$
$853$	501.872	+	289.756i	0.0201451	+	0.0116308i	−0.489894	+	0.871782i	$0.662964\pi$
$854$		0			0
$855$	−4791.65	+	30324.6i	−0.191662	+	1.21296i
$856$		0			0
$857$	−15123.1			−0.602795			−0.301398	−	0.953499i	$-0.597453\pi$
$857$	−15123.1			−0.602795			−0.301398	+	0.953499i	$0.597453\pi$
$858$		0			0
$859$			5265.45i			0.209144i	0.994517	+	0.104572i	$0.0333473\pi$
$859$			5265.45i			0.209144i	−0.994517	+	0.104572i	$0.966653\pi$
$860$		0			0
$861$	−6463.79	+	734.620i	−0.255848	+	0.0290776i
$862$		0			0
$863$	6243.76	+	3604.83i	0.246280	+	0.142190i	0.618060	−	0.786131i	$-0.287919\pi$
$863$	6243.76	+	3604.83i	0.246280	+	0.142190i	−0.371780	+	0.928321i	$0.621252\pi$
$864$		0			0
$865$	−1317.30	−	2281.63i	−0.0517797	−	0.0896851i
$866$		0			0
$867$	3470.54	+	7272.74i	0.135947	+	0.284885i
$868$		0			0
$869$	−10892.9	+	6289.05i	−0.425222	+	0.245502i
$870$		0			0
$871$		−	923.786i		−	0.0359372i
$872$		0			0
$873$	4928.02	−	31187.6i	0.191052	−	1.20910i
$874$		0			0
$875$	16355.9	−	3171.43i	0.631921	−	0.122530i
$876$		0			0
$877$	21803.7			0.839521			0.419761	−	0.907635i	$-0.362114\pi$
$877$	21803.7			0.839521			0.419761	+	0.907635i	$0.362114\pi$
$878$		0			0
$879$	36910.5	+	2898.18i	1.41634	+	0.111209i
$880$		0			0
$881$	26107.7			0.998402			0.499201	−	0.866486i	$-0.333627\pi$
$881$	26107.7			0.998402			0.499201	+	0.866486i	$0.333627\pi$
$882$		0			0
$883$	20345.4			0.775398			0.387699	−	0.921786i	$-0.373270\pi$
$883$	20345.4			0.775398			0.387699	+	0.921786i	$0.373270\pi$
$884$		0			0
$885$	−16610.1	−	34807.5i	−0.630895	−	1.32208i
$886$		0			0
$887$	−24377.8			−0.922804			−0.461402	−	0.887191i	$-0.652653\pi$
$887$	−24377.8			−0.922804			−0.461402	+	0.887191i	$0.652653\pi$
$888$		0			0
$889$	−5566.50	+	1079.35i	−0.210005	+	0.0407201i
$890$		0			0
$891$	5136.22	+	5696.03i	0.193120	+	0.214168i
$892$		0			0
$893$		−	8492.86i		−	0.318256i
$894$		0			0
$895$	−1162.09	+	670.934i	−0.0434016	+	0.0250579i
$896$		0			0
$897$	−2376.82	−	186.626i	−0.0884724	−	0.00694676i
$898$		0			0
$899$	−21647.5	−	37494.6i	−0.803097	−	1.39100i
$900$		0			0
$901$	2282.24	+	1317.65i	0.0843868	+	0.0487207i
$902$		0			0
$903$	−15588.9	−	21079.5i	−0.574491	−	0.776836i
$904$		0			0
$905$			45920.1i			1.68667i
$906$		0			0
$907$	16204.1			0.593216			0.296608	−	0.954999i	$-0.404144\pi$
$907$	16204.1			0.593216			0.296608	+	0.954999i	$0.404144\pi$
$908$		0			0
$909$	15426.6	+	40144.1i	0.562891	+	1.46479i
$910$		0			0
$911$	43150.7	+	24913.1i	1.56931	+	0.906044i	0.996249	+	0.0865353i	$0.0275795\pi$
$911$	43150.7	+	24913.1i	1.56931	+	0.906044i	0.573066	+	0.819509i	$0.305754\pi$
$912$		0			0
$913$	−12974.1	−	7490.61i	−0.470296	−	0.271526i
$914$		0			0
$915$	6336.17	−	80696.0i	0.228926	−	2.91555i
$916$		0			0
$917$	30386.8	−	5892.03i	1.09429	−	0.212183i
$918$		0			0
$919$	21549.5	−	37324.8i	0.773506	−	1.33975i	−0.162124	−	0.986770i	$-0.551834\pi$
$919$	21549.5	−	37324.8i	0.773506	−	1.33975i	0.935630	−	0.352982i	$-0.114832\pi$
$920$		0			0
$921$	24118.1	+	16569.5i	0.862886	+	0.592814i
$922$		0			0
$923$	−4225.41	−	7318.62i	−0.150684	−	0.260992i
$924$		0			0
$925$	−10449.0	+	18098.2i	−0.371418	+	0.643315i
$926$		0			0
$927$	47923.3	−	18416.0i	1.69796	−	0.652494i
$928$		0			0
$929$	9063.28	+	15698.1i	0.320082	+	0.554399i	0.980505	−	0.196495i	$-0.0629560\pi$
$929$	9063.28	+	15698.1i	0.320082	+	0.554399i	−0.660422	+	0.750894i	$0.729623\pi$
$930$		0			0
$931$	22229.4	+	3145.10i	0.782535	+	0.110716i
$932$		0			0
$933$	−6813.47	−	14278.1i	−0.239081	−	0.501010i
$934$		0			0
$935$	−9177.90	+	5298.87i	−0.321016	+	0.185338i
$936$		0			0
$937$			34444.4i			1.20091i	0.799659	+	0.600454i	$0.205013\pi$
$937$			34444.4i			1.20091i	−0.799659	+	0.600454i	$0.794987\pi$
$938$		0			0
$939$	2756.63	−	35107.9i	0.0958034	−	1.22013i
$940$		0			0
$941$	−2514.81	+	4355.77i	−0.0871205	+	0.150897i	−0.906293	−	0.422650i	$-0.861100\pi$
$941$	−2514.81	+	4355.77i	−0.0871205	+	0.150897i	0.819172	+	0.573547i	$0.194433\pi$
$942$		0			0
$943$	2111.87	−	1219.29i	0.0729290	−	0.0421056i
$944$		0			0
$945$	45095.0	+	1965.16i	1.55232	+	0.0676471i
$946$		0			0
$947$	21610.1	−	12476.6i	0.741535	−	0.428126i	−0.0810921	−	0.996707i	$-0.525841\pi$
$947$	21610.1	−	12476.6i	0.741535	−	0.428126i	0.822627	+	0.568581i	$0.192507\pi$
$948$		0			0
$949$	−2669.16	+	4623.13i	−0.0913010	+	0.158138i
$950$		0			0
$951$	2077.36	−	26456.8i	0.0708340	−	0.902126i
$952$		0			0
$953$			247.996i			0.00842956i	0.999991	+	0.00421478i	$0.00134161\pi$
$953$			247.996i			0.00842956i	−0.999991	+	0.00421478i	$0.998658\pi$
$954$		0			0
$955$	−40933.0	+	23632.7i	−1.38697	+	0.800770i
$956$		0			0
$957$	−6265.93	−	13130.6i	−0.211650	−	0.443525i
$958$		0			0
$959$	4668.71	+	24077.8i	0.157206	+	0.810755i
$960$		0			0
$961$	−1662.80	−	2880.05i	−0.0558155	−	0.0966752i
$962$		0			0
$963$	3272.76	−	20712.1i	0.109515	−	0.693082i
$964$		0			0
$965$	−15280.7	+	26467.0i	−0.509745	+	0.882904i
$966$		0			0
$967$	6168.00	+	10683.3i	0.205118	+	0.355275i	0.950170	−	0.311731i	$-0.100909\pi$
$967$	6168.00	+	10683.3i	0.205118	+	0.355275i	−0.745052	+	0.667006i	$0.767575\pi$
$968$		0			0
$969$	−16254.6	−	11167.2i	−0.538880	−	0.370218i
$970$		0			0
$971$	−9582.24	+	16596.9i	−0.316693	+	0.548528i	−0.979796	−	0.200000i	$-0.935906\pi$
$971$	−9582.24	+	16596.9i	−0.316693	+	0.548528i	0.663103	+	0.748528i	$0.269239\pi$
$972$		0			0
$973$	−8457.77	+	7345.37i	−0.278668	+	0.242016i
$974$		0			0
$975$	−914.580	+	11647.9i	−0.0300410	+	0.382596i
$976$		0			0
$977$	−13924.5	−	8039.31i	−0.455972	−	0.263255i	0.254377	−	0.967105i	$-0.418129\pi$
$977$	−13924.5	−	8039.31i	−0.455972	−	0.263255i	−0.710349	+	0.703850i	$0.751463\pi$
$978$		0			0
$979$	13841.4	+	7991.31i	0.451861	+	0.260882i
$980$		0			0
$981$	12544.9	−	15503.2i	0.408287	−	0.504567i
$982$		0			0
$983$	−11267.2			−0.365583			−0.182791	−	0.983152i	$-0.558513\pi$
$983$	−11267.2			−0.365583			−0.182791	+	0.983152i	$0.558513\pi$
$984$		0			0
$985$			24401.8i			0.789345i
$986$		0			0
$987$	−12406.7	+	1410.04i	−0.400112	+	0.0454734i
$988$		0			0
$989$	8511.10	+	4913.89i	0.273647	+	0.157990i
$990$		0			0
$991$	−17932.4	−	31059.9i	−0.574816	−	0.995611i	−0.996062	−	0.0886640i	$-0.971740\pi$
$991$	−17932.4	−	31059.9i	−0.574816	−	0.995611i	0.421245	−	0.906947i	$-0.361593\pi$
$992$		0			0
$993$	20033.6	+	1573.02i	0.640228	+	0.0502701i
$994$		0			0
$995$	45794.7	−	26439.6i	1.45909	−	0.842403i
$996$		0			0
$997$		−	27670.9i		−	0.878984i	−0.898247	−	0.439492i	$-0.855158\pi$
$997$		−	27670.9i		−	0.878984i	0.898247	−	0.439492i	$-0.144842\pi$
$998$		0			0
$999$	−11409.6	+	12036.4i	−0.361346	+	0.381195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.bm.a.173.8	yes	48
3.2	odd	2		756.4.bm.a.89.22		48
7.3	odd	6		252.4.w.a.101.1	yes	48
9.4	even	3		756.4.w.a.341.22		48
9.5	odd	6		252.4.w.a.5.1	✓	48
21.17	even	6		756.4.w.a.521.22		48
63.31	odd	6		756.4.bm.a.17.22		48
63.59	even	6	inner	252.4.bm.a.185.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.1	✓	48	9.5	odd	6
252.4.w.a.101.1	yes	48	7.3	odd	6
252.4.bm.a.173.8	yes	48	1.1	even	1	trivial
252.4.bm.a.185.8	yes	48	63.59	even	6	inner
756.4.w.a.341.22		48	9.4	even	3
756.4.w.a.521.22		48	21.17	even	6
756.4.bm.a.17.22		48	63.31	odd	6
756.4.bm.a.89.22		48	3.2	odd	2

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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.94236 + 4.28282i) q^{3} -17.3719 q^{5} +(-18.1816 + 3.52543i) q^{7} +(-9.68509 - 25.2032i) q^{9} +O(q^{10})\)	\(q+(-2.94236 + 4.28282i) q^{3} -17.3719 q^{5} +(-18.1816 + 3.52543i) q^{7} +(-9.68509 - 25.2032i) q^{9} -10.5210i q^{11} +(11.0151 - 6.35956i) q^{13} +(51.1144 - 74.4008i) q^{15} +(28.9921 + 50.2158i) q^{17} +(56.6851 + 32.7272i) q^{19} +(38.3980 - 88.2417i) q^{21} +36.0738i q^{23} +176.784 q^{25} +(136.438 + 32.6772i) q^{27} +(-230.478 - 133.066i) q^{29} +(140.887 + 81.3410i) q^{31} +(45.0594 + 30.9564i) q^{33} +(315.850 - 61.2435i) q^{35} +(-59.1062 + 102.375i) q^{37} +(-5.17344 + 65.8877i) q^{39} +(-33.7999 - 58.5431i) q^{41} +(136.218 - 235.936i) q^{43} +(168.249 + 437.827i) q^{45} +(-64.8762 - 112.369i) q^{47} +(318.143 - 128.196i) q^{49} +(-300.370 - 23.5848i) q^{51} +(39.3597 - 22.7244i) q^{53} +182.769i q^{55} +(-306.952 + 146.477i) q^{57} +(213.630 - 370.018i) q^{59} +(776.582 - 448.360i) q^{61} +(264.943 + 424.090i) q^{63} +(-191.353 + 110.478i) q^{65} +(36.3149 - 62.8992i) q^{67} +(-154.498 - 106.142i) q^{69} -664.418i q^{71} +(-363.478 + 209.854i) q^{73} +(-520.161 + 757.133i) q^{75} +(37.0909 + 191.288i) q^{77} +(-597.764 - 1035.36i) q^{79} +(-541.398 + 488.190i) q^{81} +(711.970 - 1233.17i) q^{83} +(-503.648 - 872.345i) q^{85} +(1248.05 - 595.566i) q^{87} +(-759.561 + 1315.60i) q^{89} +(-177.852 + 154.460i) q^{91} +(-762.907 + 364.058i) q^{93} +(-984.729 - 568.534i) q^{95} +(1012.75 + 584.714i) q^{97} +(-265.161 + 101.896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 - 30 * q^9	\( 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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