LMFDB - Embedded newform 252.4.j.b.169.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(85,252)]

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, 2, 0]))

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

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

chi := DirichletCharacter("252.85");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 7 x^{17} + 81 x^{16} - 470 x^{15} + 2687 x^{14} - 12243 x^{13} + 43732 x^{12} + \cdots + 5500612092612 $ x^18 - 7x^17 + 81x^16 - 470x^15 + 2687x^14 - 12243x^13 + 43732x^12 - 169303x^11 + 166449x^10 - 57172x^9 - 3758051x^8 + 73649097x^7 + 358194386x^6 + 3599409199x^5 + 26802380109x^4 + 114591208112x^3 + 655546044172x^2 + 1324018291596*x + 5500612092612
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.4
Root			$0.0652281 - 5.11138i$ of defining polynomial
Character	$\chi$	$=$	252.169
Dual form			252.4.j.b.85.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.934772 - 5.11138i) q^{3} +(-7.13443 - 12.3572i) q^{5} +(-3.50000 + 6.06218i) q^{7} +(-25.2524 - 9.55595i) q^{9} +O(q^{10})$	\(q+(0.934772 - 5.11138i) q^{3} +(-7.13443 - 12.3572i) q^{5} +(-3.50000 + 6.06218i) q^{7} +(-25.2524 - 9.55595i) q^{9} +(-27.6768 + 47.9377i) q^{11} +(-20.0994 - 34.8132i) q^{13} +(-69.8314 + 24.9156i) q^{15} +33.2927 q^{17} +31.2031 q^{19} +(27.7144 + 23.5566i) q^{21} +(73.6336 + 127.537i) q^{23} +(-39.3002 + 68.0699i) q^{25} +(-72.4493 + 120.142i) q^{27} +(-87.4261 + 151.426i) q^{29} +(-122.171 - 211.606i) q^{31} +(219.156 + 186.278i) q^{33} +99.8820 q^{35} +48.6354 q^{37} +(-196.732 + 70.1933i) q^{39} +(-52.7429 - 91.3534i) q^{41} +(-48.0539 + 83.2317i) q^{43} +(62.0768 + 380.225i) q^{45} +(-70.1146 + 121.442i) q^{47} +(-24.5000 - 42.4352i) q^{49} +(31.1211 - 170.172i) q^{51} -739.997 q^{53} +789.833 q^{55} +(29.1677 - 159.491i) q^{57} +(-170.504 - 295.321i) q^{59} +(-317.394 + 549.743i) q^{61} +(146.313 - 119.639i) q^{63} +(-286.796 + 496.745i) q^{65} +(-41.9510 - 72.6613i) q^{67} +(720.721 - 257.151i) q^{69} -632.468 q^{71} -877.601 q^{73} +(311.195 + 264.508i) q^{75} +(-193.738 - 335.564i) q^{77} +(473.921 - 820.855i) q^{79} +(546.368 + 482.621i) q^{81} +(-325.237 + 563.326i) q^{83} +(-237.525 - 411.405i) q^{85} +(692.274 + 588.417i) q^{87} +399.833 q^{89} +281.392 q^{91} +(-1195.80 + 426.658i) q^{93} +(-222.616 - 385.582i) q^{95} +(723.363 - 1252.90i) q^{97} +(1157.00 - 946.063i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9}+O(q^{10}) $ 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9	$ 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9} - 93 q^{11} - 18 q^{13} + 162 q^{15} - 54 q^{17} - 90 q^{19} - 49 q^{21} - 246 q^{23} - 315 q^{25} - 394 q^{27} - 318 q^{29} - 18 q^{31} + 33 q^{33} + 84 q^{35} - 72 q^{37} + 268 q^{39} - 57 q^{41} - 171 q^{43} - 318 q^{45} - 1056 q^{47} - 441 q^{49} + 705 q^{51} + 1512 q^{53} - 1800 q^{55} - 1271 q^{57} - 411 q^{59} - 198 q^{61} + 308 q^{63} - 1326 q^{65} - 441 q^{67} + 642 q^{69} + 3516 q^{71} + 54 q^{73} - 2497 q^{75} - 651 q^{77} + 72 q^{79} + 1163 q^{81} - 558 q^{83} - 1008 q^{85} + 2766 q^{87} + 2784 q^{89} + 252 q^{91} - 2618 q^{93} - 156 q^{95} + 909 q^{97} + 6318 q^{99}+O(q^{100}) $ 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9 - 93 * q^11 - 18 * q^13 + 162 * q^15 - 54 * q^17 - 90 * q^19 - 49 * q^21 - 246 * q^23 - 315 * q^25 - 394 * q^27 - 318 * q^29 - 18 * q^31 + 33 * q^33 + 84 * q^35 - 72 * q^37 + 268 * q^39 - 57 * q^41 - 171 * q^43 - 318 * q^45 - 1056 * q^47 - 441 * q^49 + 705 * q^51 + 1512 * q^53 - 1800 * q^55 - 1271 * q^57 - 411 * q^59 - 198 * q^61 + 308 * q^63 - 1326 * q^65 - 441 * q^67 + 642 * q^69 + 3516 * q^71 + 54 * q^73 - 2497 * q^75 - 651 * q^77 + 72 * q^79 + 1163 * q^81 - 558 * q^83 - 1008 * q^85 + 2766 * q^87 + 2784 * q^89 + 252 * q^91 - 2618 * q^93 - 156 * q^95 + 909 * q^97 + 6318 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	0.934772	−	5.11138i	0.179897	−	0.983685i
$3$	0.934772	−	5.11138i	0.179897	−	0.983685i
$4$		0			0
$5$	−7.13443	−	12.3572i	−0.638123	−	1.10526i	−0.985844	−	0.167663i	$-0.946378\pi$
$5$	−7.13443	−	12.3572i	−0.638123	−	1.10526i	0.347721	−	0.937598i	$-0.386955\pi$
$6$		0			0
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$8$		0			0
$9$	−25.2524	−	9.55595i	−0.935274	−	0.353924i
$10$		0			0
$11$	−27.6768	+	47.9377i	−0.758625	+	1.31398i	0.184927	+	0.982752i	$0.440795\pi$
$11$	−27.6768	+	47.9377i	−0.758625	+	1.31398i	−0.943552	+	0.331225i	$0.892538\pi$
$12$		0			0
$13$	−20.0994	−	34.8132i	−0.428813	−	0.742727i	0.567955	−	0.823060i	$-0.307735\pi$
$13$	−20.0994	−	34.8132i	−0.428813	−	0.742727i	−0.996768	+	0.0803331i	$0.974402\pi$
$14$		0			0
$15$	−69.8314	+	24.9156i	−1.20203	+	0.428879i
$16$		0			0
$17$	33.2927			0.474981			0.237491	−	0.971390i	$-0.423675\pi$
$17$	33.2927			0.474981			0.237491	+	0.971390i	$0.423675\pi$
$18$		0			0
$19$	31.2031			0.376762			0.188381	−	0.982096i	$-0.439676\pi$
$19$	31.2031			0.376762			0.188381	+	0.982096i	$0.439676\pi$
$20$		0			0
$21$	27.7144	+	23.5566i	0.287989	+	0.244784i
$22$		0			0
$23$	73.6336	+	127.537i	0.667550	+	1.15623i	0.978587	+	0.205833i	$0.0659904\pi$
$23$	73.6336	+	127.537i	0.667550	+	1.15623i	−0.311037	+	0.950398i	$0.600676\pi$
$24$		0			0
$25$	−39.3002	+	68.0699i	−0.314402	+	0.544559i
$26$		0			0
$27$	−72.4493	+	120.142i	−0.516403	+	0.856346i
$28$		0			0
$29$	−87.4261	+	151.426i	−0.559814	+	0.969627i	0.437697	+	0.899122i	$0.355794\pi$
$29$	−87.4261	+	151.426i	−0.559814	+	0.969627i	−0.997511	+	0.0705042i	$0.977539\pi$
$30$		0			0
$31$	−122.171	−	211.606i	−0.707823	−	1.22599i	−0.965663	−	0.259798i	$-0.916344\pi$
$31$	−122.171	−	211.606i	−0.707823	−	1.22599i	0.257840	−	0.966188i	$-0.416989\pi$
$32$		0			0
$33$	219.156	+	186.278i	1.15607	+	0.982629i
$34$		0			0
$35$	99.8820			0.482376
$36$		0			0
$37$	48.6354			0.216098			0.108049	−	0.994146i	$-0.465540\pi$
$37$	48.6354			0.216098			0.108049	+	0.994146i	$0.465540\pi$
$38$		0			0
$39$	−196.732	+	70.1933i	−0.807752	+	0.288203i
$40$		0			0
$41$	−52.7429	−	91.3534i	−0.200904	−	0.347976i	0.747916	−	0.663793i	$-0.231055\pi$
$41$	−52.7429	−	91.3534i	−0.200904	−	0.347976i	−0.948820	+	0.315818i	$0.897721\pi$
$42$		0			0
$43$	−48.0539	+	83.2317i	−0.170422	+	0.295180i	−0.938567	−	0.345096i	$-0.887846\pi$
$43$	−48.0539	+	83.2317i	−0.170422	+	0.295180i	0.768145	+	0.640275i	$0.221180\pi$
$44$		0			0
$45$	62.0768	+	380.225i	0.205641	+	1.25957i
$46$		0			0
$47$	−70.1146	+	121.442i	−0.217601	+	0.376897i	−0.954074	−	0.299571i	$-0.903157\pi$
$47$	−70.1146	+	121.442i	−0.217601	+	0.376897i	0.736473	+	0.676467i	$0.236490\pi$
$48$		0			0
$49$	−24.5000	−	42.4352i	−0.0714286	−	0.123718i
$50$		0			0
$51$	31.1211	−	170.172i	0.0854476	−	0.467232i
$52$		0			0
$53$	−739.997			−1.91786			−0.958929	−	0.283647i	$-0.908456\pi$
$53$	−739.997			−1.91786			−0.958929	+	0.283647i	$0.908456\pi$
$54$		0			0
$55$	789.833			1.93638
$56$		0			0
$57$	29.1677	−	159.491i	0.0677783	−	0.370615i
$58$		0			0
$59$	−170.504	−	295.321i	−0.376232	−	0.651653i	0.614279	−	0.789089i	$-0.289447\pi$
$59$	−170.504	−	295.321i	−0.376232	−	0.651653i	−0.990511	+	0.137436i	$0.956114\pi$
$60$		0			0
$61$	−317.394	+	549.743i	−0.666199	+	1.15389i	0.312759	+	0.949832i	$0.398747\pi$
$61$	−317.394	+	549.743i	−0.666199	+	1.15389i	−0.978959	+	0.204059i	$0.934587\pi$
$62$		0			0
$63$	146.313	−	119.639i	0.292599	−	0.239255i
$64$		0			0
$65$	−286.796	+	496.745i	−0.547271	+	0.947902i
$66$		0			0
$67$	−41.9510	−	72.6613i	−0.0764946	−	0.132492i	0.825241	−	0.564781i	$-0.191039\pi$
$67$	−41.9510	−	72.6613i	−0.0764946	−	0.132492i	−0.901735	+	0.432289i	$0.857706\pi$
$68$		0			0
$69$	720.721	−	257.151i	1.25746	−	0.448657i
$70$		0			0
$71$	−632.468			−1.05719			−0.528593	−	0.848876i	$-0.677280\pi$
$71$	−632.468			−1.05719			−0.528593	+	0.848876i	$0.677280\pi$
$72$		0			0
$73$	−877.601			−1.40706			−0.703531	−	0.710665i	$-0.748394\pi$
$73$	−877.601			−1.40706			−0.703531	+	0.710665i	$0.748394\pi$
$74$		0			0
$75$	311.195	+	264.508i	0.479115	+	0.407237i
$76$		0			0
$77$	−193.738	−	335.564i	−0.286733	−	0.496637i
$78$		0			0
$79$	473.921	−	820.855i	0.674940	−	1.16903i	−0.301547	−	0.953451i	$-0.597503\pi$
$79$	473.921	−	820.855i	0.674940	−	1.16903i	0.976487	−	0.215578i	$-0.0691637\pi$
$80$		0			0
$81$	546.368	+	482.621i	0.749476	+	0.662032i
$82$		0			0
$83$	−325.237	+	563.326i	−0.430113	+	0.744977i	−0.996883	−	0.0788992i	$-0.974859\pi$
$83$	−325.237	+	563.326i	−0.430113	+	0.744977i	0.566770	+	0.823876i	$0.308193\pi$
$84$		0			0
$85$	−237.525	−	411.405i	−0.303096	−	0.524978i
$86$		0			0
$87$	692.274	+	588.417i	0.853099	+	0.725114i
$88$		0			0
$89$	399.833			0.476205			0.238102	−	0.971240i	$-0.423475\pi$
$89$	399.833			0.476205			0.238102	+	0.971240i	$0.423475\pi$
$90$		0			0
$91$	281.392			0.324153
$92$		0			0
$93$	−1195.80	+	426.658i	−1.33332	+	0.475724i
$94$		0			0
$95$	−222.616	−	385.582i	−0.240420	−	0.416420i
$96$		0			0
$97$	723.363	−	1252.90i	0.757180	−	1.31147i	−0.187104	−	0.982340i	$-0.559910\pi$
$97$	723.363	−	1252.90i	0.757180	−	1.31147i	0.944283	−	0.329133i	$-0.106757\pi$
$98$		0			0
$99$	1157.00	−	946.063i	1.17457	−	0.960433i
$100$		0			0
$101$	584.050	−	1011.60i	0.575397	−	0.996618i	−0.420601	−	0.907246i	$-0.638181\pi$
$101$	584.050	−	1011.60i	0.575397	−	0.996618i	0.995998	−	0.0893719i	$-0.0284860\pi$
$102$		0			0
$103$	−587.649	−	1017.84i	−0.562163	−	0.973695i	−0.997307	−	0.0733346i	$-0.976636\pi$
$103$	−587.649	−	1017.84i	−0.562163	−	0.973695i	0.435144	−	0.900361i	$-0.356697\pi$
$104$		0			0
$105$	93.3669	−	510.535i	0.0867779	−	0.474506i
$106$		0			0
$107$	−59.0400			−0.0533422			−0.0266711	−	0.999644i	$-0.508491\pi$
$107$	−59.0400			−0.0533422			−0.0266711	+	0.999644i	$0.508491\pi$
$108$		0			0
$109$	−890.020			−0.782096			−0.391048	−	0.920370i	$-0.627887\pi$
$109$	−890.020			−0.782096			−0.391048	+	0.920370i	$0.627887\pi$
$110$		0			0
$111$	45.4630	−	248.594i	0.0388753	−	0.212572i
$112$		0			0
$113$	260.404	+	451.033i	0.216785	+	0.375483i	0.953823	−	0.300368i	$-0.0971095\pi$
$113$	260.404	+	451.033i	0.216785	+	0.375483i	−0.737038	+	0.675851i	$0.763776\pi$
$114$		0			0
$115$	1050.67	−	1819.81i	0.851958	−	1.47563i
$116$		0			0
$117$	174.885	+	1071.19i	0.138189	+	0.846421i
$118$		0			0
$119$	−116.525	+	201.827i	−0.0897630	+	0.155474i
$120$		0			0
$121$	−866.513	−	1500.84i	−0.651024	−	1.12761i
$122$		0			0
$123$	−516.245	+	184.195i	−0.378441	+	0.135027i
$124$		0			0
$125$	−662.070			−0.473738
$126$		0			0
$127$	2825.59			1.97426			0.987129	−	0.159925i	$-0.0511251\pi$
$127$	2825.59			1.97426			0.987129	+	0.159925i	$0.0511251\pi$
$128$		0			0
$129$	380.510	+	323.424i	0.259705	+	0.220744i
$130$		0			0
$131$	174.654	+	302.510i	0.116486	+	0.201759i	0.918373	−	0.395717i	$-0.129504\pi$
$131$	174.654	+	302.510i	0.116486	+	0.201759i	−0.801887	+	0.597476i	$0.796170\pi$
$132$		0			0
$133$	−109.211	+	189.159i	−0.0712013	+	0.123324i
$134$		0			0
$135$	2001.50	+	38.1258i	1.27601	+	0.0243063i
$136$		0			0
$137$	−766.072	+	1326.87i	−0.477737	+	0.827464i	−0.999674	−	0.0255195i	$-0.991876\pi$
$137$	−766.072	+	1326.87i	−0.477737	+	0.827464i	0.521938	+	0.852984i	$0.325209\pi$
$138$		0			0
$139$	968.500	+	1677.49i	0.590986	+	1.02362i	0.994100	+	0.108468i	$0.0345946\pi$
$139$	968.500	+	1677.49i	0.590986	+	1.02362i	−0.403114	+	0.915150i	$0.632072\pi$
$140$		0			0
$141$	555.195	+	471.903i	0.331602	+	0.281854i
$142$		0			0
$143$	2225.15			1.30123
$144$		0			0
$145$	2494.94			1.42892
$146$		0			0
$147$	−239.805	+	85.5615i	−0.134549	+	0.0480068i
$148$		0			0
$149$	−1046.11	−	1811.91i	−0.575172	−	0.996227i	−0.996023	−	0.0890973i	$-0.971602\pi$
$149$	−1046.11	−	1811.91i	−0.575172	−	0.996227i	0.420851	−	0.907130i	$-0.361732\pi$
$150$		0			0
$151$	952.094	−	1649.07i	0.513114	−	0.888740i	−0.486770	−	0.873530i	$-0.661825\pi$
$151$	952.094	−	1649.07i	0.513114	−	0.888740i	0.999884	−	0.0152101i	$-0.00484170\pi$
$152$		0			0
$153$	−840.722	−	318.144i	−0.444238	−	0.168107i
$154$		0			0
$155$	−1743.24	+	3019.38i	−0.903356	+	1.56466i
$156$		0			0
$157$	−1712.42	−	2966.00i	−0.870485	−	1.50772i	−0.861496	−	0.507765i	$-0.830472\pi$
$157$	−1712.42	−	2966.00i	−0.870485	−	1.50772i	−0.00898981	−	0.999960i	$-0.502862\pi$
$158$		0			0
$159$	−691.729	+	3782.41i	−0.345017	+	1.88657i
$160$		0			0
$161$	−1030.87			−0.504621
$162$		0			0
$163$	−1660.66			−0.797994			−0.398997	−	0.916952i	$-0.630642\pi$
$163$	−1660.66			−0.797994			−0.398997	+	0.916952i	$0.630642\pi$
$164$		0			0
$165$	738.314	−	4037.14i	0.348350	−	1.90479i
$166$		0			0
$167$	−384.497	−	665.969i	−0.178163	−	0.308588i	0.763088	−	0.646294i	$-0.223682\pi$
$167$	−384.497	−	665.969i	−0.178163	−	0.308588i	−0.941251	+	0.337706i	$0.890349\pi$
$168$		0			0
$169$	290.527	−	503.207i	0.132238	−	0.229043i
$170$		0			0
$171$	−787.952	−	298.175i	−0.352376	−	0.133345i
$172$		0			0
$173$	−1120.25	+	1940.34i	−0.492320	+	0.852724i	−0.999961	−	0.00884532i	$-0.997184\pi$
$173$	−1120.25	+	1940.34i	−0.492320	+	0.852724i	0.507641	+	0.861569i	$0.330518\pi$
$174$		0			0
$175$	−275.101	−	476.490i	−0.118833	−	0.205824i
$176$		0			0
$177$	−1668.88	+	595.451i	−0.708704	+	0.252863i
$178$		0			0
$179$	−3062.23			−1.27867			−0.639335	−	0.768928i	$-0.720790\pi$
$179$	−3062.23			−1.27867			−0.639335	+	0.768928i	$0.720790\pi$
$180$		0			0
$181$	−4550.35			−1.86865			−0.934323	−	0.356429i	$-0.883994\pi$
$181$	−4550.35			−1.86865			−0.934323	+	0.356429i	$0.883994\pi$
$182$		0			0
$183$	2513.25	+	2136.21i	1.01522	+	0.862912i
$184$		0			0
$185$	−346.986	−	600.998i	−0.137897	−	0.238844i
$186$		0			0
$187$	−921.438	+	1595.98i	−0.360333	+	0.624114i
$188$		0			0
$189$	−474.749	−	859.698i	−0.182714	−	0.330867i
$190$		0			0
$191$	2140.18	−	3706.89i	0.810773	−	1.40430i	−0.101550	−	0.994830i	$-0.532380\pi$
$191$	2140.18	−	3706.89i	0.810773	−	1.40430i	0.912324	−	0.409470i	$-0.134286\pi$
$192$		0			0
$193$	566.185	+	980.662i	0.211165	+	0.365749i	0.952080	−	0.305851i	$-0.0989408\pi$
$193$	566.185	+	980.662i	0.211165	+	0.365749i	−0.740914	+	0.671600i	$0.765607\pi$
$194$		0			0
$195$	2270.96	+	1930.27i	0.833985	+	0.708868i
$196$		0			0
$197$	2041.65			0.738385			0.369192	−	0.929353i	$-0.379634\pi$
$197$	2041.65			0.738385			0.369192	+	0.929353i	$0.379634\pi$
$198$		0			0
$199$	−2442.55			−0.870090			−0.435045	−	0.900409i	$-0.643268\pi$
$199$	−2442.55			−0.870090			−0.435045	+	0.900409i	$0.643268\pi$
$200$		0			0
$201$	−410.614	+	146.506i	−0.144092	+	0.0514116i
$202$		0			0
$203$	−611.982	−	1059.98i	−0.211590	−	0.366484i
$204$		0			0
$205$	−752.582	+	1303.51i	−0.256403	+	0.444103i
$206$		0			0
$207$	−640.687	−	3924.26i	−0.215125	−	1.31766i
$208$		0			0
$209$	−863.602	+	1495.80i	−0.285821	+	0.495056i
$210$		0			0
$211$	2074.61	+	3593.33i	0.676881	+	1.17239i	0.975915	+	0.218150i	$0.0700023\pi$
$211$	2074.61	+	3593.33i	0.676881	+	1.17239i	−0.299034	+	0.954242i	$0.596664\pi$
$212$		0			0
$213$	−591.213	+	3232.78i	−0.190184	+	1.03994i
$214$		0			0
$215$	1371.35			0.435001
$216$		0			0
$217$	1710.39			0.535064
$218$		0			0
$219$	−820.357	+	4485.75i	−0.253126	+	1.38411i
$220$		0			0
$221$	−669.165	−	1159.03i	−0.203678	−	0.352781i
$222$		0			0
$223$	−420.852	+	728.938i	−0.126378	+	0.218894i	−0.922271	−	0.386544i	$-0.873669\pi$
$223$	−420.852	+	728.938i	−0.126378	+	0.218894i	0.795893	+	0.605438i	$0.207002\pi$
$224$		0			0
$225$	1642.90	−	1343.38i	0.486784	−	0.398038i
$226$		0			0
$227$	−2764.16	+	4787.66i	−0.808210	+	1.39986i	0.105892	+	0.994378i	$0.466230\pi$
$227$	−2764.16	+	4787.66i	−0.808210	+	1.39986i	−0.914102	+	0.405483i	$0.867103\pi$
$228$		0			0
$229$	2807.92	+	4863.46i	0.810274	+	1.40343i	0.912673	+	0.408691i	$0.134015\pi$
$229$	2807.92	+	4863.46i	0.810274	+	1.40343i	−0.102399	+	0.994743i	$0.532652\pi$
$230$		0			0
$231$	−1896.29	+	676.592i	−0.540117	+	0.192712i
$232$		0			0
$233$	−680.141			−0.191234			−0.0956170	−	0.995418i	$-0.530482\pi$
$233$	−680.141			−0.191234			−0.0956170	+	0.995418i	$0.530482\pi$
$234$		0			0
$235$	2000.91			0.555426
$236$		0			0
$237$	−3752.69	−	3189.70i	−1.02854	−	0.874233i
$238$		0			0
$239$	−968.159	−	1676.90i	−0.262029	−	0.453848i	0.704752	−	0.709454i	$-0.251058\pi$
$239$	−968.159	−	1676.90i	−0.262029	−	0.453848i	−0.966781	+	0.255606i	$0.917725\pi$
$240$		0			0
$241$	−1398.89	+	2422.95i	−0.373903	+	0.647619i	−0.990162	−	0.139925i	$-0.955314\pi$
$241$	−1398.89	+	2422.95i	−0.373903	+	0.647619i	0.616259	+	0.787543i	$0.288647\pi$
$242$		0			0
$243$	2977.59	−	2341.55i	0.786060	−	0.618151i
$244$		0			0
$245$	−349.587	+	605.503i	−0.0911604	+	0.157894i
$246$		0			0
$247$	−627.163	−	1086.28i	−0.161561	−	0.279831i
$248$		0			0
$249$	2575.35	+	2188.99i	0.655447	+	0.557115i
$250$		0			0
$251$	4591.67			1.15468			0.577338	−	0.816505i	$-0.304092\pi$
$251$	4591.67			1.15468			0.577338	+	0.816505i	$0.304092\pi$
$252$		0			0
$253$	−8151.77			−2.02568
$254$		0			0
$255$	−2324.88	+	829.510i	−0.570939	+	0.203709i
$256$		0			0
$257$	3362.86	+	5824.65i	0.816224	+	1.41374i	0.908446	+	0.418003i	$0.137270\pi$
$257$	3362.86	+	5824.65i	0.816224	+	1.41374i	−0.0922221	+	0.995738i	$0.529397\pi$
$258$		0			0
$259$	−170.224	+	294.837i	−0.0408386	+	0.0707346i
$260$		0			0
$261$	3654.74	−	2988.44i	0.866754	−	0.708735i
$262$		0			0
$263$	1440.03	−	2494.21i	0.337628	−	0.584788i	−0.646358	−	0.763034i	$-0.723709\pi$
$263$	1440.03	−	2494.21i	0.337628	−	0.584788i	0.983986	+	0.178246i	$0.0570422\pi$
$264$		0			0
$265$	5279.46	+	9144.29i	1.22383	+	2.11973i
$266$		0			0
$267$	373.753	−	2043.70i	0.0856678	−	0.468436i
$268$		0			0
$269$	3221.70			0.730226			0.365113	−	0.930963i	$-0.381030\pi$
$269$	3221.70			0.730226			0.365113	+	0.930963i	$0.381030\pi$
$270$		0			0
$271$	5847.48			1.31074			0.655368	−	0.755310i	$-0.272514\pi$
$271$	5847.48			1.31074			0.655368	+	0.755310i	$0.272514\pi$
$272$		0			0
$273$	263.037	−	1438.30i	0.0583140	−	0.318864i
$274$		0			0
$275$	−2175.41	−	3767.92i	−0.477026	−	0.826233i
$276$		0			0
$277$	1273.93	−	2206.52i	0.276329	−	0.478616i	−0.694140	−	0.719840i	$-0.744215\pi$
$277$	1273.93	−	2206.52i	0.276329	−	0.478616i	0.970470	+	0.241223i	$0.0775486\pi$
$278$		0			0
$279$	1063.01	+	6511.02i	0.228103	+	1.39715i
$280$		0			0
$281$	−3928.66	+	6804.63i	−0.834035	+	1.44459i	0.0607780	+	0.998151i	$0.480642\pi$
$281$	−3928.66	+	6804.63i	−0.834035	+	1.44459i	−0.894813	+	0.446440i	$0.852692\pi$
$282$		0			0
$283$	−2454.99	−	4252.16i	−0.515667	−	0.893161i	−0.999835	−	0.0181861i	$-0.994211\pi$
$283$	−2454.99	−	4252.16i	−0.515667	−	0.893161i	0.484168	−	0.874975i	$-0.339122\pi$
$284$		0			0
$285$	−2178.95	+	777.444i	−0.452877	+	0.161585i
$286$		0			0
$287$	738.401			0.151869
$288$		0			0
$289$	−3804.59			−0.774393
$290$		0			0
$291$	−5727.88	−	4868.56i	−1.15386	−	0.980757i
$292$		0			0
$293$	−1947.06	−	3372.41i	−0.388220	−	0.672417i	0.603990	−	0.796992i	$-0.293577\pi$
$293$	−1947.06	−	3372.41i	−0.388220	−	0.672417i	−0.992210	+	0.124575i	$0.960243\pi$
$294$		0			0
$295$	−2432.89	+	4213.89i	−0.480164	+	0.831669i
$296$		0			0
$297$	−3754.16	−	6798.20i	−0.733463	−	1.32819i
$298$		0			0
$299$	2959.98	−	5126.84i	0.572509	−	0.991615i
$300$		0			0
$301$	−336.377	−	582.622i	−0.0644134	−	0.111567i
$302$		0			0
$303$	−4624.74	−	3930.92i	−0.876846	−	0.745299i
$304$		0			0
$305$	9057.71			1.70047
$306$		0			0
$307$	2274.38			0.422821			0.211410	−	0.977397i	$-0.432194\pi$
$307$	2274.38			0.422821			0.211410	+	0.977397i	$0.432194\pi$
$308$		0			0
$309$	−5751.88	+	2052.25i	−1.05894	+	0.377827i
$310$		0			0
$311$	−1474.02	−	2553.07i	−0.268758	−	0.465503i	0.699783	−	0.714355i	$-0.253280\pi$
$311$	−1474.02	−	2553.07i	−0.268758	−	0.465503i	−0.968541	+	0.248853i	$0.919947\pi$
$312$		0			0
$313$	−1533.68	+	2656.42i	−0.276962	+	0.479712i	−0.970628	−	0.240585i	$-0.922661\pi$
$313$	−1533.68	+	2656.42i	−0.276962	+	0.479712i	0.693666	+	0.720296i	$0.255994\pi$
$314$		0			0
$315$	−2522.26	−	954.467i	−0.451153	−	0.170724i
$316$		0			0
$317$	1201.48	−	2081.02i	0.212876	−	0.368712i	−0.739737	−	0.672896i	$-0.765050\pi$
$317$	1201.48	−	2081.02i	0.212876	−	0.368712i	0.952613	+	0.304183i	$0.0983836\pi$
$318$		0			0
$319$	−4839.35	−	8382.00i	−0.849378	−	1.47117i
$320$		0			0
$321$	−55.1890	+	301.776i	−0.00959610	+	0.0524720i
$322$		0			0
$323$	1038.84			0.178955
$324$		0			0
$325$	3159.64			0.539278
$326$		0			0
$327$	−831.966	+	4549.23i	−0.140697	+	0.769336i
$328$		0			0
$329$	−490.802	−	850.094i	−0.0822456	−	0.142454i
$330$		0			0
$331$	3784.57	−	6555.07i	0.628456	−	1.08852i	−0.359406	−	0.933181i	$-0.617021\pi$
$331$	3784.57	−	6555.07i	0.628456	−	1.08852i	0.987862	−	0.155336i	$-0.0496460\pi$
$332$		0			0
$333$	−1228.16	−	464.758i	−0.202111	−	0.0764822i
$334$		0			0
$335$	−598.594	+	1036.79i	−0.0976259	+	0.169093i
$336$		0			0
$337$	−3615.52	−	6262.27i	−0.584422	−	1.01225i	−0.994947	−	0.100399i	$-0.967988\pi$
$337$	−3615.52	−	6262.27i	−0.584422	−	1.01225i	0.410525	−	0.911849i	$-0.365345\pi$
$338$		0			0
$339$	2548.82	−	909.411i	0.408357	−	0.145700i
$340$		0			0
$341$	13525.2			2.14789
$342$		0			0
$343$	343.000			0.0539949
$344$		0			0
$345$	−8319.60	−	7071.46i	−1.29830	−	1.10352i
$346$		0			0
$347$	−3473.62	−	6016.49i	−0.537389	−	0.930785i	−0.999044	−	0.0437252i	$-0.986077\pi$
$347$	−3473.62	−	6016.49i	−0.537389	−	0.930785i	0.461655	−	0.887060i	$-0.347256\pi$
$348$		0			0
$349$	3079.18	−	5333.29i	0.472277	−	0.818008i	−0.527220	−	0.849729i	$-0.676766\pi$
$349$	3079.18	−	5333.29i	0.472277	−	0.818008i	0.999497	+	0.0317213i	$0.0100989\pi$
$350$		0			0
$351$	5638.72	+	107.410i	0.857471	+	0.0163336i
$352$		0			0
$353$	1896.15	−	3284.22i	0.285897	−	0.495188i	−0.686929	−	0.726724i	$-0.741042\pi$
$353$	1896.15	−	3284.22i	0.285897	−	0.495188i	0.972826	+	0.231536i	$0.0743751\pi$
$354$		0			0
$355$	4512.30	+	7815.53i	0.674614	+	1.16847i
$356$		0			0
$357$	922.688	+	784.263i	0.136789	+	0.116268i
$358$		0			0
$359$	12472.6			1.83364			0.916822	−	0.399297i	$-0.130746\pi$
$359$	12472.6			1.83364			0.916822	+	0.399297i	$0.130746\pi$
$360$		0			0
$361$	−5885.37			−0.858051
$362$		0			0
$363$	−8481.38	+	3026.13i	−1.22633	+	0.437550i
$364$		0			0
$365$	6261.18	+	10844.7i	0.897878	+	1.55517i
$366$		0			0
$367$	−3782.46	+	6551.41i	−0.537991	+	0.931828i	0.461021	+	0.887389i	$0.347483\pi$
$367$	−3782.46	+	6551.41i	−0.537991	+	0.931828i	−0.999012	+	0.0444387i	$0.985850\pi$
$368$		0			0
$369$	458.917	+	2810.90i	0.0647433	+	0.396558i
$370$		0			0
$371$	2589.99	−	4486.00i	0.362441	−	0.627766i
$372$		0			0
$373$	5334.62	+	9239.84i	0.740526	+	1.28263i	0.952256	+	0.305301i	$0.0987570\pi$
$373$	5334.62	+	9239.84i	0.740526	+	1.28263i	−0.211730	+	0.977328i	$0.567910\pi$
$374$		0			0
$375$	−618.884	+	3384.09i	−0.0852241	+	0.466010i
$376$		0			0
$377$	7028.85			0.960223
$378$		0			0
$379$	1965.49			0.266386			0.133193	−	0.991090i	$-0.457477\pi$
$379$	1965.49			0.266386			0.133193	+	0.991090i	$0.457477\pi$
$380$		0			0
$381$	2641.28	−	14442.7i	0.355163	−	1.94205i
$382$		0			0
$383$	−5991.69	−	10377.9i	−0.799376	−	1.38456i	−0.920023	−	0.391865i	$-0.871830\pi$
$383$	−5991.69	−	10377.9i	−0.799376	−	1.38456i	0.120647	−	0.992696i	$-0.461503\pi$
$384$		0			0
$385$	−2764.42	+	4788.11i	−0.365942	+	0.633830i
$386$		0			0
$387$	2008.83	−	1642.60i	0.263862	−	0.215757i
$388$		0			0
$389$	−13.6143	+	23.5807i	−0.00177448	+	0.00307349i	−0.866911	−	0.498462i	$-0.833898\pi$
$389$	−13.6143	+	23.5807i	−0.00177448	+	0.00307349i	0.865137	+	0.501536i	$0.167232\pi$
$390$		0			0
$391$	2451.46	+	4246.06i	0.317074	+	0.549188i
$392$		0			0
$393$	1709.50	−	609.946i	0.219423	−	0.0782893i
$394$		0			0
$395$	−13524.6			−1.72278
$396$		0			0
$397$	5528.80			0.698948			0.349474	−	0.936946i	$-0.386360\pi$
$397$	5528.80			0.698948			0.349474	+	0.936946i	$0.386360\pi$
$398$		0			0
$399$	864.774	+	735.038i	0.108503	+	0.0922253i
$400$		0			0
$401$	−1230.58	−	2131.43i	−0.153248	−	0.265433i	0.779172	−	0.626810i	$-0.215640\pi$
$401$	−1230.58	−	2131.43i	−0.153248	−	0.265433i	−0.932420	+	0.361378i	$0.882307\pi$
$402$		0			0
$403$	−4911.12	+	8506.31i	−0.607048	+	1.05144i
$404$		0			0
$405$	2065.82	−	10194.8i	0.253461	−	1.25082i
$406$		0			0
$407$	−1346.07	+	2331.47i	−0.163937	+	0.283947i
$408$		0			0
$409$	−122.745	−	212.601i	−0.0148395	−	0.0257028i	0.858510	−	0.512796i	$-0.171390\pi$
$409$	−122.745	−	212.601i	−0.0148395	−	0.0257028i	−0.873350	+	0.487094i	$0.838057\pi$
$410$		0			0
$411$	6066.06	+	5156.01i	0.728021	+	0.618801i
$412$		0			0
$413$	2387.05			0.284405
$414$		0			0
$415$	9281.51			1.09786
$416$		0			0
$417$	9479.62	−	3382.30i	1.11324	−	0.397199i
$418$		0			0
$419$	−4185.32	−	7249.18i	−0.487986	−	0.845217i	0.511919	−	0.859034i	$-0.328935\pi$
$419$	−4185.32	−	7249.18i	−0.487986	−	0.845217i	−0.999905	+	0.0138175i	$0.995602\pi$
$420$		0			0
$421$	132.681	−	229.809i	0.0153597	−	0.0266039i	−0.858243	−	0.513243i	$-0.828444\pi$
$421$	132.681	−	229.809i	0.0153597	−	0.0266039i	0.873603	+	0.486639i	$0.161777\pi$
$422$		0			0
$423$	2931.06	−	2396.69i	0.336910	−	0.275487i
$424$		0			0
$425$	−1308.41	+	2266.24i	−0.149335	+	0.258655i
$426$		0			0
$427$	−2221.76	−	3848.20i	−0.251800	−	0.436130i
$428$		0			0
$429$	2080.01	−	11373.6i	0.234088	−	1.28001i
$430$		0			0
$431$	1925.63			0.215208			0.107604	−	0.994194i	$-0.465682\pi$
$431$	1925.63			0.215208			0.107604	+	0.994194i	$0.465682\pi$
$432$		0			0
$433$	1304.23			0.144752			0.0723758	−	0.997377i	$-0.476942\pi$
$433$	1304.23			0.144752			0.0723758	+	0.997377i	$0.476942\pi$
$434$		0			0
$435$	2332.20	−	12752.6i	0.257058	−	1.40561i
$436$		0			0
$437$	2297.59	+	3979.55i	0.251507	+	0.435624i
$438$		0			0
$439$	−8071.45	+	13980.2i	−0.877515	+	1.51990i	−0.0234565	+	0.999725i	$0.507467\pi$
$439$	−8071.45	+	13980.2i	−0.877515	+	1.51990i	−0.854059	+	0.520176i	$0.825866\pi$
$440$		0			0
$441$	213.175	+	1305.71i	0.0230186	+	0.140990i
$442$		0			0
$443$	−7465.32	+	12930.3i	−0.800650	+	1.38677i	0.118539	+	0.992949i	$0.462179\pi$
$443$	−7465.32	+	12930.3i	−0.800650	+	1.38677i	−0.919189	+	0.393817i	$0.871154\pi$
$444$		0			0
$445$	−2852.58	−	4940.82i	−0.303877	−	0.526331i
$446$		0			0
$447$	−10239.3	+	3653.34i	−1.08345	+	0.386570i
$448$		0			0
$449$	16359.4			1.71949			0.859743	−	0.510728i	$-0.170624\pi$
$449$	16359.4			1.71949			0.859743	+	0.510728i	$0.170624\pi$
$450$		0			0
$451$	5839.03			0.609643
$452$		0			0
$453$	−7539.06	−	6408.02i	−0.781933	−	0.664625i
$454$		0			0
$455$	−2007.57	−	3477.21i	−0.206849	−	0.358273i
$456$		0			0
$457$	−2895.35	+	5014.89i	−0.296365	+	0.513319i	−0.975301	−	0.220878i	$-0.929108\pi$
$457$	−2895.35	+	5014.89i	−0.296365	+	0.513319i	0.678937	+	0.734197i	$0.262441\pi$
$458$		0			0
$459$	−2412.04	+	3999.86i	−0.245282	+	0.406748i
$460$		0			0
$461$	7350.47	−	12731.4i	0.742615	−	1.28625i	−0.208686	−	0.977983i	$-0.566919\pi$
$461$	7350.47	−	12731.4i	0.742615	−	1.28625i	0.951301	−	0.308263i	$-0.0997478\pi$
$462$		0			0
$463$	−8711.68	−	15089.1i	−0.874441	−	1.51458i	−0.857357	−	0.514722i	$-0.827895\pi$
$463$	−8711.68	−	15089.1i	−0.874441	−	1.51458i	−0.0170841	−	0.999854i	$-0.505438\pi$
$464$		0			0
$465$	13803.6	+	11732.8i	1.37662	+	1.17010i
$466$		0			0
$467$	−7872.05			−0.780032			−0.390016	−	0.920808i	$-0.627531\pi$
$467$	−7872.05			−0.780032			−0.390016	+	0.920808i	$0.627531\pi$
$468$		0			0
$469$	587.315			0.0578245
$470$		0			0
$471$	−16761.1	+	5980.31i	−1.63972	+	0.585049i
$472$		0			0
$473$	−2659.96	−	4607.18i	−0.258573	−	0.447861i
$474$		0			0
$475$	−1226.29	+	2123.99i	−0.118454	+	0.205169i
$476$		0			0
$477$	18686.7	+	7071.38i	1.79372	+	0.678776i
$478$		0			0
$479$	−2334.72	+	4043.86i	−0.222706	+	0.385738i	−0.955629	−	0.294574i	$-0.904822\pi$
$479$	−2334.72	+	4043.86i	−0.222706	+	0.385738i	0.732923	+	0.680312i	$0.238156\pi$
$480$		0			0
$481$	−977.544	−	1693.16i	−0.0926656	−	0.160502i
$482$		0			0
$483$	−963.628	+	5269.17i	−0.0907797	+	0.496388i
$484$		0			0
$485$	−20643.1			−1.93269
$486$		0			0
$487$	2570.18			0.239150			0.119575	−	0.992825i	$-0.461847\pi$
$487$	2570.18			0.239150			0.119575	+	0.992825i	$0.461847\pi$
$488$		0			0
$489$	−1552.34	+	8488.27i	−0.143557	+	0.784975i
$490$		0			0
$491$	3459.20	+	5991.51i	0.317946	+	0.550699i	0.980059	−	0.198705i	$-0.0636735\pi$
$491$	3459.20	+	5991.51i	0.317946	+	0.550699i	−0.662113	+	0.749404i	$0.730340\pi$
$492$		0			0
$493$	−2910.65	+	5041.40i	−0.265901	+	0.460554i
$494$		0			0
$495$	−19945.2	−	7547.61i	−1.81105	−	0.685333i
$496$		0			0
$497$	2213.64	−	3834.13i	0.199789	−	0.346045i
$498$		0			0
$499$	10694.4	+	18523.2i	0.959412	+	1.66175i	0.723931	+	0.689872i	$0.242333\pi$
$499$	10694.4	+	18523.2i	0.959412	+	1.66175i	0.235481	+	0.971879i	$0.424333\pi$
$500$		0			0
$501$	−3763.44	+	1342.78i	−0.335605	+	0.119743i
$502$		0			0
$503$	1905.80			0.168937			0.0844687	−	0.996426i	$-0.473081\pi$
$503$	1905.80			0.168937			0.0844687	+	0.996426i	$0.473081\pi$
$504$		0			0
$505$	−16667.5			−1.46870
$506$		0			0
$507$	−2300.51	−	1955.38i	−0.201517	−	0.171285i
$508$		0			0
$509$	−628.377	−	1088.38i	−0.0547197	−	0.0947773i	0.837368	−	0.546640i	$-0.184093\pi$
$509$	−628.377	−	1088.38i	−0.0547197	−	0.0947773i	−0.892088	+	0.451862i	$0.850760\pi$
$510$		0			0
$511$	3071.60	−	5320.17i	0.265910	−	0.460569i
$512$		0			0
$513$	−2260.64	+	3748.80i	−0.194561	+	0.322638i
$514$		0			0
$515$	−8385.09	+	14523.4i	−0.717459	+	1.24267i
$516$		0			0
$517$	−3881.10	−	6722.26i	−0.330156	−	0.571846i
$518$		0			0
$519$	8870.62	+	7539.82i	0.750245	+	0.637691i
$520$		0			0
$521$	99.9041			0.00840092			0.00420046	−	0.999991i	$-0.498663\pi$
$521$	99.9041			0.00840092			0.00420046	+	0.999991i	$0.498663\pi$
$522$		0			0
$523$	1869.35			0.156292			0.0781462	−	0.996942i	$-0.475100\pi$
$523$	1869.35			0.156292			0.0781462	+	0.996942i	$0.475100\pi$
$524$		0			0
$525$	−2692.68	+	960.738i	−0.223844	+	0.0798668i
$526$		0			0
$527$	−4067.40	−	7044.94i	−0.336203	−	0.582320i
$528$		0			0
$529$	−4760.30	+	8245.08i	−0.391247	+	0.677659i
$530$		0			0
$531$	1483.55	+	9086.89i	0.121244	+	0.742631i
$532$		0			0
$533$	−2120.20	+	3672.30i	−0.172301	+	0.298433i
$534$		0			0
$535$	421.217	+	729.569i	0.0340389	+	0.0589571i
$536$		0			0
$537$	−2862.49	+	15652.2i	−0.230029	+	1.25781i
$538$		0			0
$539$	2712.33			0.216750
$540$		0			0
$541$	−14291.5			−1.13575			−0.567873	−	0.823116i	$-0.692234\pi$
$541$	−14291.5			−1.13575			−0.567873	+	0.823116i	$0.692234\pi$
$542$		0			0
$543$	−4253.54	+	23258.6i	−0.336164	+	1.83816i
$544$		0			0
$545$	6349.79	+	10998.2i	0.499073	+	0.864420i
$546$		0			0
$547$	10180.4	−	17633.0i	0.795767	−	1.37831i	−0.126584	−	0.991956i	$-0.540401\pi$
$547$	10180.4	−	17633.0i	0.795767	−	1.37831i	0.922351	−	0.386353i	$-0.126265\pi$
$548$		0			0
$549$	13268.3	−	10849.3i	1.03147	−	0.843421i
$550$		0			0
$551$	−2727.96	+	4724.97i	−0.210917	+	0.365318i
$552$		0			0
$553$	3317.44	+	5745.98i	0.255103	+	0.441852i
$554$		0			0
$555$	−3396.28	+	1211.78i	−0.259755	+	0.0926798i
$556$		0			0
$557$	−372.579			−0.0283423			−0.0141712	−	0.999900i	$-0.504511\pi$
$557$	−372.579			−0.0283423			−0.0141712	+	0.999900i	$0.504511\pi$
$558$		0			0
$559$	3863.42			0.292317
$560$		0			0
$561$	7296.31	+	6201.69i	0.549109	+	0.466730i
$562$		0			0
$563$	4272.80	+	7400.70i	0.319852	+	0.554001i	0.980457	−	0.196733i	$-0.0630333\pi$
$563$	4272.80	+	7400.70i	0.319852	+	0.554001i	−0.660605	+	0.750734i	$0.729700\pi$
$564$		0			0
$565$	3715.67	−	6435.73i	0.276672	−	0.479209i
$566$		0			0
$567$	−4838.02	+	1623.00i	−0.358338	+	0.120211i
$568$		0			0
$569$	2081.09	−	3604.56i	0.153329	−	0.265573i	−0.779121	−	0.626874i	$-0.784334\pi$
$569$	2081.09	−	3604.56i	0.153329	−	0.265573i	0.932449	+	0.361301i	$0.117667\pi$
$570$		0			0
$571$	−5177.43	−	8967.57i	−0.379455	−	0.657235i	0.611528	−	0.791223i	$-0.290555\pi$
$571$	−5177.43	−	8967.57i	−0.379455	−	0.657235i	−0.990983	+	0.133988i	$0.957222\pi$
$572$		0			0
$573$	−16946.8	−	14404.4i	−1.23553	−	1.05018i
$574$		0			0
$575$	−11575.3			−0.839515
$576$		0			0
$577$	3163.95			0.228279			0.114140	−	0.993465i	$-0.463589\pi$
$577$	3163.95			0.228279			0.114140	+	0.993465i	$0.463589\pi$
$578$		0			0
$579$	5541.79	−	1977.29i	0.397770	−	0.141923i
$580$		0			0
$581$	−2276.66	−	3943.28i	−0.162567	−	0.281575i
$582$		0			0
$583$	20480.8	−	35473.7i	1.45494	−	2.52002i
$584$		0			0
$585$	11989.2	−	9803.40i	0.847334	−	0.692856i
$586$		0			0
$587$	−1605.91	+	2781.52i	−0.112918	+	0.195580i	−0.916946	−	0.399012i	$-0.869353\pi$
$587$	−1605.91	+	2781.52i	−0.112918	+	0.195580i	0.804027	+	0.594592i	$0.202686\pi$
$588$		0			0
$589$	−3812.10	−	6602.75i	−0.266681	−	0.461905i
$590$		0			0
$591$	1908.48	−	10435.7i	0.132833	−	0.726338i
$592$		0			0
$593$	−8380.17			−0.580324			−0.290162	−	0.956978i	$-0.593709\pi$
$593$	−8380.17			−0.580324			−0.290162	+	0.956978i	$0.593709\pi$
$594$		0			0
$595$	3325.35			0.229119
$596$		0			0
$597$	−2283.23	+	12484.8i	−0.156527	+	0.855895i
$598$		0			0
$599$	13346.3	+	23116.5i	0.910379	+	1.57682i	0.813530	+	0.581523i	$0.197543\pi$
$599$	13346.3	+	23116.5i	0.910379	+	1.57682i	0.0968486	+	0.995299i	$0.469124\pi$
$600$		0			0
$601$	−1995.99	+	3457.16i	−0.135471	+	0.234643i	−0.925777	−	0.378069i	$-0.876588\pi$
$601$	−1995.99	+	3457.16i	−0.135471	+	0.234643i	0.790306	+	0.612712i	$0.209921\pi$
$602$		0			0
$603$	365.017	+	2235.76i	0.0246511	+	0.150990i
$604$		0			0
$605$	−12364.2	+	21415.3i	−0.830867	+	1.43910i
$606$		0			0
$607$	4151.27	+	7190.21i	0.277586	+	0.480793i	0.970784	−	0.239954i	$-0.0771323\pi$
$607$	4151.27	+	7190.21i	0.277586	+	0.480793i	−0.693198	+	0.720747i	$0.743799\pi$
$608$		0			0
$609$	−5990.05	+	2137.23i	−0.398570	+	0.142208i
$610$		0			0
$611$	5637.05			0.373242
$612$		0			0
$613$	−10557.7			−0.695628			−0.347814	−	0.937564i	$-0.613076\pi$
$613$	−10557.7			−0.695628			−0.347814	+	0.937564i	$0.613076\pi$
$614$		0			0
$615$	5959.24	+	5065.21i	0.390731	+	0.332112i
$616$		0			0
$617$	3494.46	+	6052.59i	0.228009	+	0.394924i	0.957218	−	0.289368i	$-0.0934450\pi$
$617$	3494.46	+	6052.59i	0.228009	+	0.394924i	−0.729209	+	0.684291i	$0.760112\pi$
$618$		0			0
$619$	13659.0	−	23658.1i	0.886919	−	1.53619i	0.0434205	−	0.999057i	$-0.486174\pi$
$619$	13659.0	−	23658.1i	0.886919	−	1.53619i	0.843498	−	0.537132i	$-0.180492\pi$
$620$		0			0
$621$	−20657.3	−	393.491i	−1.33486	−	0.0254272i
$622$		0			0
$623$	−1399.42	+	2423.86i	−0.0899942	+	0.155875i
$624$		0			0
$625$	9636.01	+	16690.1i	0.616705	+	1.06816i
$626$		0			0
$627$	6838.34	+	5812.43i	0.435561	+	0.370217i
$628$		0			0
$629$	1619.21			0.102642
$630$		0			0
$631$	−25663.2			−1.61907			−0.809536	−	0.587070i	$-0.800281\pi$
$631$	−25663.2			−1.61907			−0.809536	+	0.587070i	$0.800281\pi$
$632$		0			0
$633$	20306.1	−	7245.17i	1.27503	−	0.454928i
$634$		0			0
$635$	−20159.0	−	34916.4i	−1.25982	−	2.18207i
$636$		0			0
$637$	−984.871	+	1705.85i	−0.0612591	+	0.106104i
$638$		0			0
$639$	15971.3	+	6043.83i	0.988758	+	0.374163i
$640$		0			0
$641$	−6960.78	+	12056.4i	−0.428915	+	0.742902i	−0.996777	−	0.0802214i	$-0.974437\pi$
$641$	−6960.78	+	12056.4i	−0.428915	+	0.742902i	0.567862	+	0.823124i	$0.307771\pi$
$642$		0			0
$643$	2301.45	+	3986.23i	0.141152	+	0.244482i	0.927931	−	0.372753i	$-0.121586\pi$
$643$	2301.45	+	3986.23i	0.141152	+	0.244482i	−0.786779	+	0.617235i	$0.788253\pi$
$644$		0			0
$645$	1281.90	−	7009.48i	0.0782553	−	0.427904i
$646$		0			0
$647$	−13449.0			−0.817211			−0.408605	−	0.912711i	$-0.633985\pi$
$647$	−13449.0			−0.817211			−0.408605	+	0.912711i	$0.633985\pi$
$648$		0			0
$649$	18876.0			1.14168
$650$		0			0
$651$	1598.83	−	8742.46i	0.0962564	−	0.526335i
$652$		0			0
$653$	1136.53	+	1968.54i	0.0681103	+	0.117971i	0.898069	−	0.439854i	$-0.144970\pi$
$653$	1136.53	+	1968.54i	0.0681103	+	0.117971i	−0.829959	+	0.557824i	$0.811636\pi$
$654$		0			0
$655$	2492.12	−	4316.47i	0.148664	−	0.257494i
$656$		0			0
$657$	22161.5	+	8386.31i	1.31599	+	0.497993i
$658$		0			0
$659$	−15951.0	+	27628.0i	−0.942888	+	1.63313i	−0.182962	+	0.983120i	$0.558569\pi$
$659$	−15951.0	+	27628.0i	−0.942888	+	1.63313i	−0.759926	+	0.650010i	$0.774765\pi$
$660$		0			0
$661$	−6391.84	−	11071.0i	−0.376117	−	0.651454i	0.614376	−	0.789013i	$-0.289408\pi$
$661$	−6391.84	−	11071.0i	−0.376117	−	0.651454i	−0.990494	+	0.137559i	$0.956074\pi$
$662$		0			0
$663$	−6549.75	+	2336.93i	−0.383667	+	0.136891i
$664$		0			0
$665$	3116.63			0.181741
$666$		0			0
$667$	−25750.0			−1.49482
$668$		0			0
$669$	3332.48	+	2832.53i	0.192587	+	0.163695i
$670$		0			0
$671$	−17568.9	−	30430.3i	−1.01079	−	1.75074i
$672$		0			0
$673$	10166.6	−	17609.1i	0.582309	−	1.00859i	−0.412897	−	0.910778i	$-0.635483\pi$
$673$	10166.6	−	17609.1i	0.582309	−	1.00859i	0.995205	−	0.0978101i	$-0.0311838\pi$
$674$		0			0
$675$	−5330.78	−	9653.22i	−0.303973	−	0.550448i
$676$		0			0
$677$	12002.7	−	20789.2i	0.681388	−	1.18020i	−0.293169	−	0.956061i	$-0.594710\pi$
$677$	12002.7	−	20789.2i	0.681388	−	1.18020i	0.974557	−	0.224138i	$-0.0719567\pi$
$678$		0			0
$679$	5063.54	+	8770.31i	0.286187	+	0.495690i
$680$		0			0
$681$	21887.7	+	18604.0i	1.23163	+	1.04686i
$682$		0			0
$683$	20944.6			1.17339			0.586694	−	0.809809i	$-0.300429\pi$
$683$	20944.6			1.17339			0.586694	+	0.809809i	$0.300429\pi$
$684$		0			0
$685$	21861.9			1.21942
$686$		0			0
$687$	27483.8	−	9806.12i	1.52630	−	0.544581i
$688$		0			0
$689$	14873.5	+	25761.7i	0.822403	+	1.42444i
$690$		0			0
$691$	9976.50	−	17279.8i	0.549238	−	0.951309i	−0.449088	−	0.893487i	$-0.648251\pi$
$691$	9976.50	−	17279.8i	0.549238	−	0.951309i	0.998327	−	0.0578216i	$-0.0184155\pi$
$692$		0			0
$693$	1685.72	+	10325.1i	0.0924026	+	0.565973i
$694$		0			0
$695$	13819.4	−	23935.9i	0.754244	−	1.30639i
$696$		0			0
$697$	−1755.96	−	3041.41i	−0.0954256	−	0.165282i
$698$		0			0
$699$	−635.777	+	3476.46i	−0.0344024	+	0.188114i
$700$		0			0
$701$	−22484.4			−1.21145			−0.605723	−	0.795676i	$-0.707116\pi$
$701$	−22484.4			−1.21145			−0.605723	+	0.795676i	$0.707116\pi$
$702$		0			0
$703$	1517.57			0.0814174
$704$		0			0
$705$	1870.39	−	10227.4i	0.0999194	−	0.546364i
$706$		0			0
$707$	4088.35	+	7081.23i	0.217480	+	0.376686i
$708$		0			0
$709$	−6022.92	+	10432.0i	−0.319034	+	0.552584i	−0.980287	−	0.197580i	$-0.936692\pi$
$709$	−6022.92	+	10432.0i	−0.319034	+	0.552584i	0.661252	+	0.750164i	$0.270025\pi$
$710$		0			0
$711$	−19811.7	+	16199.8i	−1.04500	+	0.854486i
$712$		0			0
$713$	17991.7	−	31162.6i	0.945015	−	1.63681i
$714$		0			0
$715$	−15875.2	−	27496.6i	−0.830348	−	1.43820i
$716$		0			0
$717$	−9476.29	+	3381.11i	−0.493582	+	0.176109i
$718$		0			0
$719$	−6696.13			−0.347321			−0.173660	−	0.984806i	$-0.555559\pi$
$719$	−6696.13			−0.347321			−0.173660	+	0.984806i	$0.555559\pi$
$720$		0			0
$721$	8227.09			0.424956
$722$		0			0
$723$	11077.0	+	9415.18i	0.569789	+	0.484307i
$724$		0			0
$725$	−6871.72	−	11902.2i	−0.352013	−	0.609704i
$726$		0			0
$727$	−6069.27	+	10512.3i	−0.309624	+	0.536285i	−0.978280	−	0.207287i	$-0.933537\pi$
$727$	−6069.27	+	10512.3i	−0.309624	+	0.536285i	0.668656	+	0.743572i	$0.266870\pi$
$728$		0			0
$729$	−9185.19	−	17408.4i	−0.466656	−	0.884439i
$730$		0			0
$731$	−1599.85	+	2771.01i	−0.0809472	+	0.140205i
$732$		0			0
$733$	−18344.1	−	31773.0i	−0.924361	−	1.60104i	−0.792586	−	0.609760i	$-0.791266\pi$
$733$	−18344.1	−	31773.0i	−0.924361	−	1.60104i	−0.131775	−	0.991280i	$-0.542068\pi$
$734$		0			0
$735$	2768.17	+	2352.88i	0.138919	+	0.118078i
$736$		0			0
$737$	4644.29			0.232123
$738$		0			0
$739$	17644.9			0.878319			0.439160	−	0.898409i	$-0.355276\pi$
$739$	17644.9			0.878319			0.439160	+	0.898409i	$0.355276\pi$
$740$		0			0
$741$	−6138.64	+	2190.25i	−0.304330	+	0.108584i
$742$		0			0
$743$	−13958.7	−	24177.3i	−0.689228	−	1.19378i	−0.972088	−	0.234617i	$-0.924616\pi$
$743$	−13958.7	−	24177.3i	−0.689228	−	1.19378i	0.282860	−	0.959161i	$-0.408717\pi$
$744$		0			0
$745$	−14926.8	+	25854.0i	−0.734061	+	1.27143i
$746$		0			0
$747$	13596.1	−	11117.4i	0.665938	−	0.544530i
$748$		0			0
$749$	206.640	−	357.911i	0.0100807	−	0.0174603i
$750$		0			0
$751$	13973.0	+	24202.0i	0.678940	+	1.17596i	0.975301	+	0.220882i	$0.0708936\pi$
$751$	13973.0	+	24202.0i	0.678940	+	1.17596i	−0.296361	+	0.955076i	$0.595773\pi$
$752$		0			0
$753$	4292.16	−	23469.8i	0.207723	−	1.13584i
$754$		0			0
$755$	−27170.6			−1.30972
$756$		0			0
$757$	−34438.1			−1.65346			−0.826732	−	0.562596i	$-0.809803\pi$
$757$	−34438.1			−1.65346			−0.826732	+	0.562596i	$0.809803\pi$
$758$		0			0
$759$	−7620.05	+	41666.8i	−0.364414	+	1.99263i
$760$		0			0
$761$	4108.16	+	7115.55i	0.195691	+	0.338947i	0.947127	−	0.320859i	$-0.103972\pi$
$761$	4108.16	+	7115.55i	0.195691	+	0.338947i	−0.751436	+	0.659806i	$0.770638\pi$
$762$		0			0
$763$	3115.07	−	5395.46i	0.147802	−	0.256001i
$764$		0			0
$765$	2066.71	+	12658.7i	0.0976757	+	0.598272i
$766$		0			0
$767$	−6854.05	+	11871.6i	−0.322667	+	0.558875i
$768$		0			0
$769$	−5909.78	−	10236.0i	−0.277129	−	0.480001i	0.693541	−	0.720417i	$-0.256050\pi$
$769$	−5909.78	−	10236.0i	−0.277129	−	0.480001i	−0.970670	+	0.240416i	$0.922716\pi$
$770$		0			0
$771$	32915.5	−	11744.1i	1.53751	−	0.548580i
$772$		0			0
$773$	−28848.2			−1.34230			−0.671149	−	0.741322i	$-0.734199\pi$
$773$	−28848.2			−1.34230			−0.671149	+	0.741322i	$0.734199\pi$
$774$		0			0
$775$	19205.3			0.890163
$776$		0			0
$777$	1347.90	+	1145.68i	0.0622338	+	0.0528973i
$778$		0			0
$779$	−1645.74	−	2850.51i	−0.0756929	−	0.131104i
$780$		0			0
$781$	17504.7	−	30319.0i	0.802007	−	1.38912i
$782$		0			0
$783$	−11858.7	−	21474.3i	−0.541246	−	0.980112i
$784$		0			0
$785$	−24434.3	+	42321.5i	−1.11095	+	1.92423i
$786$		0			0
$787$	−16755.8	−	29022.0i	−0.758934	−	1.31451i	−0.943395	−	0.331673i	$-0.892387\pi$
$787$	−16755.8	−	29022.0i	−0.758934	−	1.31451i	0.184460	−	0.982840i	$-0.440946\pi$
$788$		0			0
$789$	−11402.7	−	9692.05i	−0.514510	−	0.437321i
$790$		0			0
$791$	−3645.66			−0.163874
$792$		0			0
$793$	25517.8			1.14270
$794$		0			0
$795$	51675.0	−	18437.5i	2.30531	−	0.822529i
$796$		0			0
$797$	−6569.60	−	11378.9i	−0.291979	−	0.505722i	0.682299	−	0.731074i	$-0.260980\pi$
$797$	−6569.60	−	11378.9i	−0.291979	−	0.505722i	−0.974278	+	0.225351i	$0.927647\pi$
$798$		0			0
$799$	−2334.31	+	4043.14i	−0.103357	+	0.179019i
$800$		0			0
$801$	−10096.7	−	3820.78i	−0.445382	−	0.168540i
$802$		0			0
$803$	24289.2	−	42070.2i	1.06743	−	1.84885i
$804$		0			0
$805$	7354.67	+	12738.7i	0.322010	+	0.557738i
$806$		0			0
$807$	3011.56	−	16467.4i	0.131365	−	0.718313i
$808$		0			0
$809$	−31104.0			−1.35174			−0.675871	−	0.737020i	$-0.736232\pi$
$809$	−31104.0			−1.35174			−0.675871	+	0.737020i	$0.736232\pi$
$810$		0			0
$811$	2003.25			0.0867368			0.0433684	−	0.999059i	$-0.486191\pi$
$811$	2003.25			0.0867368			0.0433684	+	0.999059i	$0.486191\pi$
$812$		0			0
$813$	5466.06	−	29888.7i	0.235797	−	1.28935i
$814$		0			0
$815$	11847.9	+	20521.1i	0.509218	+	0.881992i
$816$		0			0
$817$	−1499.43	+	2597.08i	−0.0642085	+	0.111212i
$818$		0			0
$819$	−7105.82	−	2688.97i	−0.303171	−	0.114725i
$820$		0			0
$821$	12368.9	−	21423.5i	0.525794	−	0.910701i	−0.473755	−	0.880657i	$-0.657102\pi$
$821$	12368.9	−	21423.5i	0.525794	−	0.910701i	0.999549	−	0.0300445i	$-0.00956490\pi$
$822$		0			0
$823$	5807.81	+	10059.4i	0.245987	+	0.426063i	0.962409	−	0.271605i	$-0.0875545\pi$
$823$	5807.81	+	10059.4i	0.245987	+	0.426063i	−0.716421	+	0.697668i	$0.754221\pi$
$824$		0			0
$825$	−21292.8	+	7597.20i	−0.898569	+	0.320607i
$826$		0			0
$827$	13542.2			0.569418			0.284709	−	0.958614i	$-0.408103\pi$
$827$	13542.2			0.569418			0.284709	+	0.958614i	$0.408103\pi$
$828$		0			0
$829$	−4556.04			−0.190878			−0.0954389	−	0.995435i	$-0.530425\pi$
$829$	−4556.04			−0.190878			−0.0954389	+	0.995435i	$0.530425\pi$
$830$		0			0
$831$	−10087.5	−	8574.14i	−0.421097	−	0.357923i
$832$		0			0
$833$	−815.672	−	1412.79i	−0.0339272	−	0.0587637i
$834$		0			0
$835$	−5486.34	+	9502.61i	−0.227380	+	0.393834i
$836$		0			0
$837$	34274.0	+	652.870i	1.41539	+	0.0269612i
$838$		0			0
$839$	−8180.96	+	14169.8i	−0.336637	+	0.583072i	−0.983798	−	0.179282i	$-0.942623\pi$
$839$	−8180.96	+	14169.8i	−0.336637	+	0.583072i	0.647161	+	0.762353i	$0.275956\pi$
$840$		0			0
$841$	−3092.13	−	5355.72i	−0.126784	−	0.219596i
$842$		0			0
$843$	31108.7	+	26441.6i	1.27098	+	1.08031i
$844$		0			0
$845$	−8290.97			−0.337536
$846$		0			0
$847$	12131.2			0.492128
$848$		0			0
$849$	−24029.3	+	8573.56i	−0.971357	+	0.346577i
$850$		0			0
$851$	3581.20	+	6202.82i	0.144256	+	0.249859i
$852$		0			0
$853$	9361.03	−	16213.8i	0.375751	−	0.650820i	−0.614688	−	0.788770i	$-0.710718\pi$
$853$	9361.03	−	16213.8i	0.375751	−	0.650820i	0.990439	+	0.137951i	$0.0440515\pi$
$854$		0			0
$855$	1936.99	+	11864.2i	0.0774778	+	0.474558i
$856$		0			0
$857$	10554.6	−	18281.1i	0.420698	−	0.728670i	−0.575310	−	0.817936i	$-0.695119\pi$
$857$	10554.6	−	18281.1i	0.420698	−	0.728670i	0.996008	+	0.0892652i	$0.0284519\pi$
$858$		0			0
$859$	17012.8	+	29467.0i	0.675748	+	1.17043i	0.976250	+	0.216649i	$0.0695127\pi$
$859$	17012.8	+	29467.0i	0.675748	+	1.17043i	−0.300501	+	0.953781i	$0.597154\pi$
$860$		0			0
$861$	690.237	−	3774.25i	0.0273208	−	0.149391i
$862$		0			0
$863$	531.752			0.0209746			0.0104873	−	0.999945i	$-0.496662\pi$
$863$	531.752			0.0209746			0.0104873	+	0.999945i	$0.496662\pi$
$864$		0			0
$865$	31969.5			1.25664
$866$		0			0
$867$	−3556.43	+	19446.7i	−0.139311	+	0.761759i
$868$		0			0
$869$	26233.2	+	45437.3i	1.02405	+	1.77371i
$870$		0			0
$871$	−1686.38	+	2920.90i	−0.0656038	+	0.113629i
$872$		0			0
$873$	−30239.3	+	24726.4i	−1.17233	+	0.958603i
$874$		0			0
$875$	2317.24	−	4013.58i	0.0895282	−	0.155067i
$876$		0			0
$877$	−14578.9	−	25251.5i	−0.561341	−	0.972271i	−0.997380	−	0.0723433i	$-0.976952\pi$
$877$	−14578.9	−	25251.5i	−0.561341	−	0.972271i	0.436039	−	0.899928i	$-0.356381\pi$
$878$		0			0
$879$	−19057.7	+	6799.73i	−0.731286	+	0.260921i
$880$		0			0
$881$	9700.33			0.370956			0.185478	−	0.982648i	$-0.440617\pi$
$881$	9700.33			0.370956			0.185478	+	0.982648i	$0.440617\pi$
$882$		0			0
$883$	−26061.2			−0.993237			−0.496618	−	0.867969i	$-0.665425\pi$
$883$	−26061.2			−0.993237			−0.496618	+	0.867969i	$0.665425\pi$
$884$		0			0
$885$	19264.6	+	16374.5i	0.731721	+	0.621945i
$886$		0			0
$887$	−112.681	−	195.169i	−0.00426544	−	0.00738796i	0.863885	−	0.503689i	$-0.168024\pi$
$887$	−112.681	−	195.169i	−0.00426544	−	0.00738796i	−0.868150	+	0.496301i	$0.834691\pi$
$888$		0			0
$889$	−9889.58	+	17129.2i	−0.373100	+	0.646228i
$890$		0			0
$891$	−38257.5	+	12834.2i	−1.43847	+	0.482560i
$892$		0			0
$893$	−2187.79	+	3789.36i	−0.0819839	+	0.142000i
$894$		0			0
$895$	21847.3	+	37840.6i	0.815949	+	1.41327i
$896$		0			0
$897$	−23438.3	−	19922.0i	−0.872445	−	0.741557i
$898$		0			0
$899$	42723.6			1.58500
$900$		0			0
$901$	−24636.5			−0.910946
$902$		0			0
$903$	−3292.44	+	1174.73i	−0.121335	+	0.0432919i
$904$		0			0
$905$	32464.1	+	56229.6i	1.19243	+	2.06534i
$906$		0			0
$907$	−20628.5	+	35729.5i	−0.755189	+	1.30803i	0.190091	+	0.981766i	$0.439122\pi$
$907$	−20628.5	+	35729.5i	−0.755189	+	1.30803i	−0.945280	+	0.326259i	$0.894212\pi$
$908$		0			0
$909$	−24415.5	+	19964.3i	−0.890881	+	0.728464i
$910$		0			0
$911$	2490.78	−	4314.17i	0.0905855	−	0.156899i	−0.817172	−	0.576394i	$-0.804459\pi$
$911$	2490.78	−	4314.17i	0.0905855	−	0.156899i	0.907758	+	0.419495i	$0.137793\pi$
$912$		0			0
$913$	−18003.0	−	31182.2i	−0.652588	−	1.13032i
$914$		0			0
$915$	8466.89	−	46297.4i	0.305909	−	1.67273i
$916$		0			0
$917$	−2445.16			−0.0880548
$918$		0			0
$919$	34708.7			1.24585			0.622923	−	0.782283i	$-0.285945\pi$
$919$	34708.7			1.24585			0.622923	+	0.782283i	$0.285945\pi$
$920$		0			0
$921$	2126.03	−	11625.2i	0.0760642	−	0.415923i
$922$		0			0
$923$	12712.2	+	22018.2i	0.453335	+	0.785200i
$924$		0			0
$925$	−1911.38	+	3310.61i	−0.0679415	+	0.117678i
$926$		0			0
$927$	5113.15	+	31318.4i	0.181163	+	1.10964i
$928$		0			0
$929$	9516.11	−	16482.4i	0.336075	−	0.582098i	−0.647616	−	0.761967i	$-0.724234\pi$
$929$	9516.11	−	16482.4i	0.336075	−	0.582098i	0.983691	+	0.179868i	$0.0575672\pi$
$930$		0			0
$931$	−764.475	−	1324.11i	−0.0269116	−	0.0466122i
$932$		0			0
$933$	−14427.6	+	5147.71i	−0.506257	+	0.180631i
$934$		0			0
$935$	26295.7			0.919746
$936$		0			0
$937$	26009.8			0.906834			0.453417	−	0.891298i	$-0.350205\pi$
$937$	26009.8			0.906834			0.453417	+	0.891298i	$0.350205\pi$
$938$		0			0
$939$	12144.3	+	10322.4i	0.422061	+	0.358742i
$940$		0			0
$941$	4154.31	+	7195.47i	0.143918	+	0.249273i	0.928969	−	0.370159i	$-0.120697\pi$
$941$	4154.31	+	7195.47i	0.143918	+	0.249273i	−0.785051	+	0.619431i	$0.787363\pi$
$942$		0			0
$943$	7767.30	−	13453.4i	0.268227	−	0.464583i
$944$		0			0
$945$	−7236.38	+	12000.0i	−0.249100	+	0.413080i
$946$		0			0
$947$	7530.53	−	13043.3i	0.258405	−	0.447570i	−0.707410	−	0.706803i	$-0.750137\pi$
$947$	7530.53	−	13043.3i	0.258405	−	0.447570i	0.965815	+	0.259233i	$0.0834699\pi$
$948$		0			0
$949$	17639.3	+	30552.1i	0.603367	+	1.04506i
$950$		0			0
$951$	−9513.78	−	8086.49i	−0.324401	−	0.275733i
$952$		0			0
$953$	−53211.6			−1.80870			−0.904351	−	0.426790i	$-0.859644\pi$
$953$	−53211.6			−1.80870			−0.904351	+	0.426790i	$0.859644\pi$
$954$		0			0
$955$	−61075.7			−2.06949
$956$		0			0
$957$	−47367.3	+	16900.5i	−1.59997	+	0.570863i
$958$		0			0
$959$	−5362.50	−	9288.12i	−0.180567	−	0.312752i
$960$		0			0
$961$	−14955.9	+	25904.4i	−0.502027	+	0.869537i
$962$		0			0
$963$	1490.90	+	564.184i	0.0498896	+	0.0188791i
$964$		0			0
$965$	8078.82	−	13992.9i	0.269499	−	0.466786i
$966$		0			0
$967$	−17366.0	−	30078.9i	−0.577512	−	1.00028i	−0.995764	−	0.0919491i	$-0.970690\pi$
$967$	−17366.0	−	30078.9i	−0.577512	−	1.00028i	0.418252	−	0.908331i	$-0.362643\pi$
$968$		0			0
$969$	971.075	−	5309.88i	0.0321934	−	0.176035i
$970$		0			0
$971$	5512.52			0.182189			0.0910943	−	0.995842i	$-0.470964\pi$
$971$	5512.52			0.182189			0.0910943	+	0.995842i	$0.470964\pi$
$972$		0			0
$973$	−13559.0			−0.446744
$974$		0			0
$975$	2953.55	−	16150.1i	0.0970145	−	0.530480i
$976$		0			0
$977$	11489.2	+	19899.9i	0.376226	+	0.651643i	0.990510	−	0.137443i	$-0.0438883\pi$
$977$	11489.2	+	19899.9i	0.376226	+	0.651643i	−0.614284	+	0.789085i	$0.710555\pi$
$978$		0			0
$979$	−11066.1	+	19167.1i	−0.361261	+	0.625722i
$980$		0			0
$981$	22475.1	+	8504.98i	0.731474	+	0.276803i
$982$		0			0
$983$	20170.2	−	34935.8i	0.654455	−	1.13355i	−0.327575	−	0.944825i	$-0.606231\pi$
$983$	20170.2	−	34935.8i	0.654455	−	1.13355i	0.982030	−	0.188724i	$-0.0604353\pi$
$984$		0			0
$985$	−14566.0	−	25229.1i	−0.471180	−	0.816108i
$986$		0			0
$987$	−4803.94	+	1714.03i	−0.154925	+	0.0552768i
$988$		0			0
$989$	−14153.5			−0.455061
$990$		0			0
$991$	−7414.17			−0.237658			−0.118829	−	0.992915i	$-0.537914\pi$
$991$	−7414.17			−0.237658			−0.118829	+	0.992915i	$0.537914\pi$
$992$		0			0
$993$	−29967.7	−	25471.9i	−0.957701	−	0.814024i
$994$		0			0
$995$	17426.2	+	30183.1i	0.555224	+	0.961677i
$996$		0			0
$997$	−3629.44	+	6286.37i	−0.115291	+	0.199690i	−0.917896	−	0.396821i	$-0.870114\pi$
$997$	−3629.44	+	6286.37i	−0.115291	+	0.199690i	0.802605	+	0.596511i	$0.203447\pi$
$998$		0			0
$999$	−3523.60	+	5843.16i	−0.111593	+	0.185054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.j.b.169.4	yes	18
3.2	odd	2		756.4.j.b.505.7		18
9.2	odd	6		2268.4.a.h.1.3		9
9.4	even	3	inner	252.4.j.b.85.4	✓	18
9.5	odd	6		756.4.j.b.253.7		18
9.7	even	3		2268.4.a.i.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.j.b.85.4	✓	18	9.4	even	3	inner
252.4.j.b.169.4	yes	18	1.1	even	1	trivial
756.4.j.b.253.7		18	9.5	odd	6
756.4.j.b.505.7		18	3.2	odd	2
2268.4.a.h.1.3		9	9.2	odd	6
2268.4.a.i.1.7		9	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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.934772 - 5.11138i) q^{3} +(-7.13443 - 12.3572i) q^{5} +(-3.50000 + 6.06218i) q^{7} +(-25.2524 - 9.55595i) q^{9} +O(q^{10})\)	\(q+(0.934772 - 5.11138i) q^{3} +(-7.13443 - 12.3572i) q^{5} +(-3.50000 + 6.06218i) q^{7} +(-25.2524 - 9.55595i) q^{9} +(-27.6768 + 47.9377i) q^{11} +(-20.0994 - 34.8132i) q^{13} +(-69.8314 + 24.9156i) q^{15} +33.2927 q^{17} +31.2031 q^{19} +(27.7144 + 23.5566i) q^{21} +(73.6336 + 127.537i) q^{23} +(-39.3002 + 68.0699i) q^{25} +(-72.4493 + 120.142i) q^{27} +(-87.4261 + 151.426i) q^{29} +(-122.171 - 211.606i) q^{31} +(219.156 + 186.278i) q^{33} +99.8820 q^{35} +48.6354 q^{37} +(-196.732 + 70.1933i) q^{39} +(-52.7429 - 91.3534i) q^{41} +(-48.0539 + 83.2317i) q^{43} +(62.0768 + 380.225i) q^{45} +(-70.1146 + 121.442i) q^{47} +(-24.5000 - 42.4352i) q^{49} +(31.1211 - 170.172i) q^{51} -739.997 q^{53} +789.833 q^{55} +(29.1677 - 159.491i) q^{57} +(-170.504 - 295.321i) q^{59} +(-317.394 + 549.743i) q^{61} +(146.313 - 119.639i) q^{63} +(-286.796 + 496.745i) q^{65} +(-41.9510 - 72.6613i) q^{67} +(720.721 - 257.151i) q^{69} -632.468 q^{71} -877.601 q^{73} +(311.195 + 264.508i) q^{75} +(-193.738 - 335.564i) q^{77} +(473.921 - 820.855i) q^{79} +(546.368 + 482.621i) q^{81} +(-325.237 + 563.326i) q^{83} +(-237.525 - 411.405i) q^{85} +(692.274 + 588.417i) q^{87} +399.833 q^{89} +281.392 q^{91} +(-1195.80 + 426.658i) q^{93} +(-222.616 - 385.582i) q^{95} +(723.363 - 1252.90i) q^{97} +(1157.00 - 946.063i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9}+O(q^{10}) \) 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9	\( 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9} - 93 q^{11} - 18 q^{13} + 162 q^{15} - 54 q^{17} - 90 q^{19} - 49 q^{21} - 246 q^{23} - 315 q^{25} - 394 q^{27} - 318 q^{29} - 18 q^{31} + 33 q^{33} + 84 q^{35} - 72 q^{37} + 268 q^{39} - 57 q^{41} - 171 q^{43} - 318 q^{45} - 1056 q^{47} - 441 q^{49} + 705 q^{51} + 1512 q^{53} - 1800 q^{55} - 1271 q^{57} - 411 q^{59} - 198 q^{61} + 308 q^{63} - 1326 q^{65} - 441 q^{67} + 642 q^{69} + 3516 q^{71} + 54 q^{73} - 2497 q^{75} - 651 q^{77} + 72 q^{79} + 1163 q^{81} - 558 q^{83} - 1008 q^{85} + 2766 q^{87} + 2784 q^{89} + 252 q^{91} - 2618 q^{93} - 156 q^{95} + 909 q^{97} + 6318 q^{99}+O(q^{100}) \) 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9 - 93 * q^11 - 18 * q^13 + 162 * q^15 - 54 * q^17 - 90 * q^19 - 49 * q^21 - 246 * q^23 - 315 * q^25 - 394 * q^27 - 318 * q^29 - 18 * q^31 + 33 * q^33 + 84 * q^35 - 72 * q^37 + 268 * q^39 - 57 * q^41 - 171 * q^43 - 318 * q^45 - 1056 * q^47 - 441 * q^49 + 705 * q^51 + 1512 * q^53 - 1800 * q^55 - 1271 * q^57 - 411 * q^59 - 198 * q^61 + 308 * q^63 - 1326 * q^65 - 441 * q^67 + 642 * q^69 + 3516 * q^71 + 54 * q^73 - 2497 * q^75 - 651 * q^77 + 72 * q^79 + 1163 * q^81 - 558 * q^83 - 1008 * q^85 + 2766 * q^87 + 2784 * q^89 + 252 * q^91 - 2618 * q^93 - 156 * q^95 + 909 * q^97 + 6318 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more